LMFDB - Embedded newform 936.2.em.a.5.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(5,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 6, 10, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.em (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$656$
Relative dimension:	$164$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.17
Character	$\chi$	$=$	936.5
Dual form			936.2.em.a.749.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32146 + 0.503724i) q^{2} +(-0.935678 - 1.45757i) q^{3} +(1.49252 - 1.33130i) q^{4} +(1.08622 + 4.05383i) q^{5} +(1.97068 + 1.45480i) q^{6} +(-0.190925 + 0.712543i) q^{7} +(-1.30170 + 2.51109i) q^{8} +(-1.24901 + 2.72763i) q^{9} +(-3.47741 - 4.80982i) q^{10} +(1.47123 - 5.49069i) q^{11} +(-3.33699 - 0.929784i) q^{12} +(2.39597 - 2.69432i) q^{13} +(-0.106624 - 1.03777i) q^{14} +(4.89238 - 5.37632i) q^{15} +(0.455258 - 3.97401i) q^{16} +4.30194 q^{17} +(0.276549 - 4.23362i) q^{18} +(-3.53386 - 3.53386i) q^{19} +(7.01808 + 4.60434i) q^{20} +(1.21722 - 0.388424i) q^{21} +(0.821623 + 7.99684i) q^{22} +(-0.804032 + 1.39263i) q^{23} +(4.87806 - 0.452248i) q^{24} +(-10.9235 + 6.30669i) q^{25} +(-1.80899 + 4.76734i) q^{26} +(5.14438 - 0.731664i) q^{27} +(0.663650 + 1.31767i) q^{28} +(3.54488 + 6.13991i) q^{29} +(-3.75691 + 9.56900i) q^{30} +(0.0838387 + 0.312890i) q^{31} +(1.40020 + 5.48083i) q^{32} +(-9.37966 + 2.99311i) q^{33} +(-5.68485 + 2.16699i) q^{34} -3.09591 q^{35} +(1.76713 + 5.73387i) q^{36} +(3.65677 - 3.65677i) q^{37} +(6.44995 + 2.88977i) q^{38} +(-6.16901 - 0.971273i) q^{39} +(-11.5935 - 2.54929i) q^{40} +(2.88951 - 0.774241i) q^{41} +(-1.41286 + 1.12643i) q^{42} +(2.07466 + 3.59342i) q^{43} +(-5.11394 - 10.1536i) q^{44} +(-12.4140 - 2.10047i) q^{45} +(0.361000 - 2.24531i) q^{46} +(8.13702 + 2.18031i) q^{47} +(-6.21836 + 3.05482i) q^{48} +(5.59091 + 3.22792i) q^{49} +(11.2582 - 13.8365i) q^{50} +(-4.02523 - 6.27038i) q^{51} +(-0.0109158 - 7.21109i) q^{52} +6.60428 q^{53} +(-6.42955 + 3.55822i) q^{54} +23.8564 q^{55} +(-1.54073 - 1.40695i) q^{56} +(-1.84429 + 8.45739i) q^{57} +(-7.77724 - 6.32802i) q^{58} +(-6.87623 + 1.84248i) q^{59} +(0.144479 - 14.5375i) q^{60} +(0.116504 - 0.0672635i) q^{61} +(-0.268400 - 0.371241i) q^{62} +(-1.70508 - 1.41075i) q^{63} +(-4.61113 - 6.53739i) q^{64} +(13.5248 + 6.78621i) q^{65} +(10.8872 - 8.68004i) q^{66} +(0.311683 - 0.0835153i) q^{67} +(6.42075 - 5.72719i) q^{68} +(2.78216 - 0.131117i) q^{69} +(4.09113 - 1.55948i) q^{70} +(2.08333 + 2.08333i) q^{71} +(-5.22348 - 6.68695i) q^{72} +(-4.47664 - 4.47664i) q^{73} +(-2.99028 + 6.67428i) q^{74} +(19.4133 + 10.0207i) q^{75} +(-9.97901 - 0.569728i) q^{76} +(3.63146 + 2.09662i) q^{77} +(8.64136 - 1.82398i) q^{78} +(6.06124 + 10.4984i) q^{79} +(16.6044 - 2.47111i) q^{80} +(-5.87994 - 6.81369i) q^{81} +(-3.42837 + 2.47864i) q^{82} +(-3.78603 - 1.01446i) q^{83} +(1.29963 - 2.20023i) q^{84} +(4.67285 + 17.4393i) q^{85} +(-4.55168 - 3.70351i) q^{86} +(5.63247 - 10.9119i) q^{87} +(11.8725 + 10.8416i) q^{88} +(6.44179 - 6.44179i) q^{89} +(17.4627 - 3.47756i) q^{90} +(1.46236 + 2.22164i) q^{91} +(0.653970 + 3.14894i) q^{92} +(0.377613 - 0.414966i) q^{93} +(-11.8510 + 1.21762i) q^{94} +(10.4871 - 18.1642i) q^{95} +(6.67854 - 7.16917i) q^{96} +(5.72493 + 1.53399i) q^{97} +(-9.01416 - 1.44929i) q^{98} +(13.1390 + 10.8709i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 656 q - 6 q^{2} + 6 q^{6} - 4 q^{7} - 16 q^{9} - 12 q^{14} + 4 q^{15} - 4 q^{16} - 2 q^{18} - 6 q^{20} - 4 q^{22} - 32 q^{24} - 24 q^{28} - 4 q^{31} - 6 q^{32} + 4 q^{33} - 6 q^{34} - 20 q^{39} - 4 q^{40}+ \cdots - 4 q^{97}+O(q^{100}) $ 656 * q - 6 * q^2 + 6 * q^6 - 4 * q^7 - 16 * q^9 - 12 * q^14 + 4 * q^15 - 4 * q^16 - 2 * q^18 - 6 * q^20 - 4 * q^22 - 32 * q^24 - 24 * q^28 - 4 * q^31 - 6 * q^32 + 4 * q^33 - 6 * q^34 - 20 * q^39 - 4 * q^40 - 12 * q^41 - 16 * q^42 - 12 * q^47 - 40 * q^48 + 42 * q^50 - 4 * q^52 - 42 * q^54 - 32 * q^55 + 16 * q^57 - 12 * q^58 + 36 * q^60 + 20 * q^63 - 12 * q^65 + 52 * q^66 - 60 * q^68 + 28 * q^70 - 54 * q^72 - 16 * q^73 + 156 * q^74 - 10 * q^76 + 28 * q^78 - 8 * q^79 - 16 * q^81 + 14 * q^84 + 102 * q^86 - 88 * q^87 - 72 * q^92 - 28 * q^94 + 32 * q^96 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	−1.32146	+	0.503724i	−0.934415	+	0.356187i
$2$	−1.32146	+	0.503724i	−0.934415	+	0.356187i
$3$	−0.935678	−	1.45757i	−0.540214	−	0.841528i
$3$	−0.935678	−	1.45757i	−0.540214	−	0.841528i
$4$	1.49252	−	1.33130i	0.746262	−	0.665652i
$5$	1.08622	+	4.05383i	0.485772	+	1.81293i	0.576559	+	0.817055i	$0.304395\pi$
$5$	1.08622	+	4.05383i	0.485772	+	1.81293i	−0.0907870	+	0.995870i	$0.528938\pi$
$6$	1.97068	+	1.45480i	0.804525	+	0.593919i
$7$	−0.190925	+	0.712543i	−0.0721629	+	0.269316i	−0.992575	−	0.121634i	$-0.961187\pi$
$7$	−0.190925	+	0.712543i	−0.0721629	+	0.269316i	0.920412	+	0.390950i	$0.127853\pi$
$8$	−1.30170	+	2.51109i	−0.460222	+	0.887804i
$9$	−1.24901	+	2.72763i	−0.416337	+	0.909210i
$10$	−3.47741	−	4.80982i	−1.09965	−	1.52100i
$11$	1.47123	−	5.49069i	0.443592	−	1.65551i	−0.276037	−	0.961147i	$-0.589021\pi$
$11$	1.47123	−	5.49069i	0.443592	−	1.65551i	0.719629	−	0.694359i	$-0.244312\pi$
$12$	−3.33699	−	0.929784i	−0.963306	−	0.268405i
$13$	2.39597	−	2.69432i	0.664522	−	0.747269i
$13$	2.39597	−	2.69432i	0.664522	−	0.747269i
$14$	−0.106624	−	1.03777i	−0.0284966	−	0.277356i
$15$	4.89238	−	5.37632i	1.26321	−	1.38816i
$16$	0.455258	−	3.97401i	0.113814	−	0.993502i
$17$	4.30194			1.04337			0.521687	−	0.853137i	$-0.325303\pi$
$17$	4.30194			1.04337			0.521687	+	0.853137i	$0.325303\pi$
$18$	0.276549	−	4.23362i	0.0651833	−	0.997873i
$19$	−3.53386	−	3.53386i	−0.810723	−	0.810723i	0.174020	−	0.984742i	$-0.444324\pi$
$19$	−3.53386	−	3.53386i	−0.810723	−	0.810723i	−0.984742	+	0.174020i	$0.944324\pi$
$20$	7.01808	+	4.60434i	1.56929	+	1.02956i
$21$	1.21722	−	0.388424i	0.265620	−	0.0847611i
$22$	0.821623	+	7.99684i	0.175171	+	1.70493i
$23$	−0.804032	+	1.39263i	−0.167652	+	0.290382i	−0.937594	−	0.347732i	$-0.886952\pi$
$23$	−0.804032	+	1.39263i	−0.167652	+	0.290382i	0.769942	+	0.638114i	$0.220285\pi$
$24$	4.87806	−	0.452248i	0.995730	−	0.0923147i
$25$	−10.9235	+	6.30669i	−2.18470	+	1.26134i
$26$	−1.80899	+	4.76734i	−0.354772	+	0.934953i
$27$	5.14438	−	0.731664i	0.990037	−	0.140809i
$28$	0.663650	+	1.31767i	0.125418	+	0.249016i
$29$	3.54488	+	6.13991i	0.658268	+	1.14015i	0.981064	+	0.193684i	$0.0620438\pi$
$29$	3.54488	+	6.13991i	0.658268	+	1.14015i	−0.322796	+	0.946468i	$0.604623\pi$
$30$	−3.75691	+	9.56900i	−0.685915	+	1.74705i
$31$	0.0838387	+	0.312890i	0.0150579	+	0.0561968i	0.973046	−	0.230611i	$-0.0740725\pi$
$31$	0.0838387	+	0.312890i	0.0150579	+	0.0561968i	−0.957988	+	0.286808i	$0.907406\pi$
$32$	1.40020	+	5.48083i	0.247522	+	0.968882i
$33$	−9.37966	+	2.99311i	−1.63279	+	0.521033i
$34$	−5.68485	+	2.16699i	−0.974944	+	0.371636i
$35$	−3.09591			−0.523304
$36$	1.76713	+	5.73387i	0.294521	+	0.955645i
$37$	3.65677	−	3.65677i	0.601169	−	0.601169i	−0.339454	−	0.940623i	$-0.610242\pi$
$37$	3.65677	−	3.65677i	0.601169	−	0.601169i	0.940623	+	0.339454i	$0.110242\pi$
$38$	6.44995	+	2.88977i	1.04632	+	0.468783i
$39$	−6.16901	−	0.971273i	−0.987831	−	0.155528i
$40$	−11.5935	−	2.54929i	−1.83309	−	0.403078i
$41$	2.88951	−	0.774241i	0.451265	−	0.120916i	−0.0260261	−	0.999661i	$-0.508285\pi$
$41$	2.88951	−	0.774241i	0.451265	−	0.120916i	0.477291	+	0.878745i	$0.341619\pi$
$42$	−1.41286	+	1.12643i	−0.218009	+	0.173812i
$43$	2.07466	+	3.59342i	0.316383	+	0.547991i	0.979730	−	0.200320i	$-0.0641983\pi$
$43$	2.07466	+	3.59342i	0.316383	+	0.547991i	−0.663348	+	0.748311i	$0.730865\pi$
$44$	−5.11394	−	10.1536i	−0.770956	−	1.53072i
$45$	−12.4140	−	2.10047i	−1.85058	−	0.313120i
$46$	0.361000	−	2.24531i	0.0532265	−	0.331053i
$47$	8.13702	+	2.18031i	1.18691	+	0.318030i	0.797662	−	0.603104i	$-0.206070\pi$
$47$	8.13702	+	2.18031i	1.18691	+	0.318030i	0.389244	+	0.921135i	$0.372736\pi$
$48$	−6.21836	+	3.05482i	−0.897544	+	0.440926i
$49$	5.59091	+	3.22792i	0.798702	+	0.461131i
$50$	11.2582	−	13.8365i	1.59214	−	1.95677i
$51$	−4.02523	−	6.27038i	−0.563645	−	0.878028i
$52$	−0.0109158	−	7.21109i	−0.00151375	−	0.999999i
$53$	6.60428			0.907168			0.453584	−	0.891214i	$-0.350145\pi$
$53$	6.60428			0.907168			0.453584	+	0.891214i	$0.350145\pi$
$54$	−6.42955	+	3.55822i	−0.874951	+	0.484212i
$55$	23.8564			3.21679
$56$	−1.54073	−	1.40695i	−0.205889	−	0.188012i
$57$	−1.84429	+	8.45739i	−0.244282	+	1.12021i
$58$	−7.77724	−	6.32802i	−1.02120	−	0.830910i
$59$	−6.87623	+	1.84248i	−0.895209	+	0.239871i	−0.676958	−	0.736022i	$-0.736702\pi$
$59$	−6.87623	+	1.84248i	−0.895209	+	0.239871i	−0.218252	+	0.975893i	$0.570035\pi$
$60$	0.144479	−	14.5375i	0.0186521	−	1.87679i
$61$	0.116504	−	0.0672635i	0.0149168	−	0.00861221i	−0.492523	−	0.870299i	$-0.663925\pi$
$61$	0.116504	−	0.0672635i	0.0149168	−	0.00861221i	0.507440	+	0.861687i	$0.330592\pi$
$62$	−0.268400	−	0.371241i	−0.0340869	−	0.0471477i
$63$	−1.70508	−	1.41075i	−0.214821	−	0.177737i
$64$	−4.61113	−	6.53739i	−0.576391	−	0.817174i
$65$	13.5248	+	6.78621i	1.67755	+	0.841726i
$66$	10.8872	−	8.68004i	1.34012	−	1.06844i
$67$	0.311683	−	0.0835153i	0.0380782	−	0.0102030i	−0.239730	−	0.970840i	$-0.577059\pi$
$67$	0.311683	−	0.0835153i	0.0380782	−	0.0102030i	0.277808	+	0.960637i	$0.410392\pi$
$68$	6.42075	−	5.72719i	0.778631	−	0.694524i
$69$	2.78216	−	0.131117i	0.334933	−	0.0157846i
$70$	4.09113	−	1.55948i	0.488983	−	0.186394i
$71$	2.08333	+	2.08333i	0.247245	+	0.247245i	0.819839	−	0.572594i	$-0.194063\pi$
$71$	2.08333	+	2.08333i	0.247245	+	0.247245i	−0.572594	+	0.819839i	$0.694063\pi$
$72$	−5.22348	−	6.68695i	−0.615593	−	0.788064i
$73$	−4.47664	−	4.47664i	−0.523951	−	0.523951i	0.394811	−	0.918762i	$-0.370810\pi$
$73$	−4.47664	−	4.47664i	−0.523951	−	0.523951i	−0.918762	+	0.394811i	$0.870810\pi$
$74$	−2.99028	+	6.67428i	−0.347613	+	0.775870i
$75$	19.4133	+	10.0207i	2.24166	+	1.15709i
$76$	−9.97901	−	0.569728i	−1.14467	−	0.0653523i
$77$	3.63146	+	2.09662i	0.413843	+	0.238932i
$78$	8.64136	−	1.82398i	0.978441	−	0.206525i
$79$	6.06124	+	10.4984i	0.681943	+	1.18116i	0.974387	+	0.224877i	$0.0721981\pi$
$79$	6.06124	+	10.4984i	0.681943	+	1.18116i	−0.292444	+	0.956283i	$0.594469\pi$
$80$	16.6044	−	2.47111i	1.85643	−	0.276278i
$81$	−5.87994	−	6.81369i	−0.653326	−	0.757076i
$82$	−3.42837	+	2.47864i	−0.378600	+	0.273720i
$83$	−3.78603	−	1.01446i	−0.415571	−	0.111352i	0.0449742	−	0.998988i	$-0.485679\pi$
$83$	−3.78603	−	1.01446i	−0.415571	−	0.111352i	−0.460545	+	0.887636i	$0.652346\pi$
$84$	1.29963	−	2.20023i	0.141801	−	0.240065i
$85$	4.67285	+	17.4393i	0.506842	+	1.89156i
$86$	−4.55168	−	3.70351i	−0.490820	−	0.399360i
$87$	5.63247	−	10.9119i	0.603865	−	1.16988i
$88$	11.8725	+	10.8416i	1.26561	+	1.15572i
$89$	6.44179	−	6.44179i	0.682828	−	0.682828i	−0.277808	−	0.960637i	$-0.589608\pi$
$89$	6.44179	−	6.44179i	0.682828	−	0.682828i	0.960637	+	0.277808i	$0.0896080\pi$
$90$	17.4627	−	3.47756i	1.84073	−	0.366566i
$91$	1.46236	+	2.22164i	0.153297	+	0.232891i
$92$	0.653970	+	3.14894i	0.0681811	+	0.328300i
$93$	0.377613	−	0.414966i	0.0391567	−	0.0430299i
$94$	−11.8510	+	1.21762i	−1.22234	+	0.125588i
$95$	10.4871	−	18.1642i	1.07595	−	1.86361i
$96$	6.67854	−	7.16917i	0.681626	−	0.731701i
$97$	5.72493	+	1.53399i	0.581279	+	0.155753i	0.537464	−	0.843286i	$-0.319382\pi$
$97$	5.72493	+	1.53399i	0.581279	+	0.155753i	0.0438146	+	0.999040i	$0.486049\pi$
$98$	−9.01416	−	1.44929i	−0.910568	−	0.146400i
$99$	13.1390	+	10.8709i	1.32052	+	1.09257i
$100$	−7.90747	+	23.9554i	−0.790747	+	2.39554i
$101$	−9.91385	+	5.72377i	−0.986465	+	0.569536i	−0.904216	−	0.427076i	$-0.859544\pi$
$101$	−9.91385	+	5.72377i	−0.986465	+	0.569536i	−0.0822495	+	0.996612i	$0.526210\pi$
$102$	8.47773	+	6.25846i	0.839421	+	0.619680i
$103$	2.43021	+	1.40308i	0.239455	+	0.138250i	0.614926	−	0.788584i	$-0.289186\pi$
$103$	2.43021	+	1.40308i	0.239455	+	0.138250i	−0.375471	+	0.926834i	$0.622519\pi$
$104$	3.64683	+	9.52369i	0.357601	+	0.933875i
$105$	2.89678	+	4.51250i	0.282696	+	0.440375i
$106$	−8.72731	+	3.32674i	−0.847671	+	0.323121i
$107$	3.10146			0.299830			0.149915	−	0.988699i	$-0.452100\pi$
$107$	3.10146			0.299830			0.149915	+	0.988699i	$0.452100\pi$
$108$	6.70405	−	7.94076i	0.645097	−	0.764100i
$109$	−9.74481	−	9.74481i	−0.933383	−	0.933383i	0.0645322	−	0.997916i	$-0.479444\pi$
$109$	−9.74481	−	9.74481i	−0.933383	−	0.933383i	−0.997916	+	0.0645322i	$0.979444\pi$
$110$	−31.5253	+	12.0170i	−3.00582	+	1.14578i
$111$	−8.75155	−	1.90843i	−0.830660	−	0.181140i
$112$	2.74473	+	1.08313i	0.259353	+	0.102346i
$113$	11.0510	+	6.38031i	1.03959	+	0.600209i	0.919718	−	0.392580i	$-0.128417\pi$
$113$	11.0510	+	6.38031i	1.03959	+	0.600209i	0.119875	+	0.992789i	$0.461751\pi$
$114$	−1.82304	−	12.1051i	−0.170743	−	1.13375i
$115$	−6.51881	−	1.74671i	−0.607883	−	0.162882i
$116$	13.4649	+	4.44465i	1.25019	+	0.412676i
$117$	4.35651	+	9.90055i	0.402759	+	0.915306i
$118$	8.15858	−	5.89849i	0.751058	−	0.543000i
$119$	−0.821349	+	3.06532i	−0.0752929	+	0.280997i
$120$	7.13198	+	19.2836i	0.651057	+	1.76034i
$121$	−18.4569	−	10.6561i	−1.67790	−	0.968737i
$122$	−0.120073	+	0.147572i	−0.0108709	+	0.0133605i
$123$	−3.83216	−	3.48721i	−0.345534	−	0.314432i
$124$	0.541684	+	0.355382i	0.0486446	+	0.0319142i
$125$	−22.5935	−	22.5935i	−2.02082	−	2.02082i
$126$	2.96383	+	1.00536i	0.264039	+	0.0895644i
$127$		−	14.1384i		−	1.25458i	−0.778787	−	0.627289i	$-0.784165\pi$
$127$		−	14.1384i		−	1.25458i	0.778787	−	0.627289i	$-0.215835\pi$
$128$	9.38648	+	6.31618i	0.829655	+	0.558276i
$129$	3.29644	−	6.38624i	0.290235	−	0.562277i
$130$	−21.2909	−	2.15494i	−1.86734	−	0.189001i
$131$	−3.09637	+	5.36307i	−0.270531	+	0.468574i	−0.968998	−	0.247069i	$-0.920533\pi$
$131$	−3.09637	+	5.36307i	−0.270531	+	0.468574i	0.698467	+	0.715642i	$0.253866\pi$
$132$	−10.0146	+	16.9545i	−0.871661	+	1.47570i
$133$	3.19273	−	1.84332i	0.276844	−	0.159836i
$134$	−0.369809	+	0.267365i	−0.0319466	+	0.0230968i
$135$	8.55397	+	20.0597i	0.736208	+	1.72646i
$136$	−5.59986	+	10.8026i	−0.480184	+	0.926312i
$137$	9.09521	+	2.43705i	0.777056	+	0.208212i	0.625486	−	0.780235i	$-0.284901\pi$
$137$	9.09521	+	2.43705i	0.777056	+	0.208212i	0.151570	+	0.988447i	$0.451567\pi$
$138$	−3.61048	+	1.57471i	−0.307344	+	0.134048i
$139$	19.3829	+	11.1907i	1.64404	+	0.949184i	0.979378	+	0.202036i	$0.0647558\pi$
$139$	19.3829	+	11.1907i	1.64404	+	0.949184i	0.664657	+	0.747148i	$0.268578\pi$
$140$	−4.62072	+	4.12160i	−0.390522	+	0.348339i
$141$	−4.43568	−	13.9003i	−0.373552	−	1.17062i
$142$	−3.80246	−	1.70361i	−0.319095	−	0.142964i
$143$	−11.2687	−	17.1195i	−0.942332	−	1.43160i
$144$	10.2710	+	6.20536i	0.855917	+	0.517113i
$145$	−21.0396	+	21.0396i	−1.74724	+	1.74724i
$146$	8.17070	+	3.66072i	0.676212	+	0.302963i
$147$	−0.526389	−	11.1694i	−0.0434158	−	0.921239i
$148$	0.589544	−	10.3261i	0.0484602	−	0.848799i
$149$	−2.60928	−	9.73798i	−0.213761	−	0.797766i	−0.986599	−	0.163163i	$-0.947830\pi$
$149$	−2.60928	−	9.73798i	−0.213761	−	0.797766i	0.772838	−	0.634603i	$-0.218836\pi$
$150$	−30.7016	−	3.46305i	−2.50678	−	0.282757i
$151$	−5.69147	+	21.2409i	−0.463166	+	1.72856i	0.199735	+	0.979850i	$0.435992\pi$
$151$	−5.69147	+	21.2409i	−0.463166	+	1.72856i	−0.662900	+	0.748708i	$0.730675\pi$
$152$	13.4739	−	4.27379i	1.09287	−	0.346650i
$153$	−5.37318	+	11.7341i	−0.434396	+	0.948646i
$154$	−5.85495	−	0.941356i	−0.471806	−	0.0758566i
$155$	−1.17734	+	0.679735i	−0.0945659	+	0.0545976i
$156$	−10.5005	+	6.76318i	−0.840709	+	0.541487i
$157$	9.46818	+	5.46645i	0.755643	+	0.436271i	0.827729	−	0.561128i	$-0.189632\pi$
$157$	9.46818	+	5.46645i	0.755643	+	0.436271i	−0.0720864	+	0.997398i	$0.522966\pi$
$158$	−13.2980	−	10.8200i	−1.05793	−	0.860794i
$159$	−6.17948	−	9.62619i	−0.490065	−	0.763407i
$160$	−20.6974	+	11.6295i	−1.63627	+	0.919395i
$161$	−0.838795	−	0.838795i	−0.0661063	−	0.0661063i
$162$	11.2023	+	6.04216i	0.880138	+	0.474717i
$163$	1.42636	−	1.42636i	0.111721	−	0.111721i	−0.649036	−	0.760758i	$-0.724828\pi$
$163$	1.42636	−	1.42636i	0.111721	−	0.111721i	0.760758	+	0.649036i	$0.224828\pi$
$164$	3.28191	−	5.00239i	0.256274	−	0.390621i
$165$	−22.3219	−	34.7723i	−1.73776	−	2.70702i
$166$	5.51411	−	0.566539i	0.427978	−	0.0439720i
$167$	3.36559	+	12.5605i	0.260437	+	0.971963i	0.964985	+	0.262307i	$0.0844832\pi$
$167$	3.36559	+	12.5605i	0.260437	+	0.971963i	−0.704548	+	0.709657i	$0.748850\pi$
$168$	−0.609099	+	3.56217i	−0.0469930	+	0.274827i
$169$	−1.51868	−	12.9110i	−0.116822	−	0.993153i
$170$	−14.9596	−	20.6916i	−1.14735	−	1.58697i
$171$	14.0529	−	5.22523i	1.07465	−	0.399583i
$172$	7.88041	+	2.60126i	0.600876	+	0.198344i
$173$	−4.59549	+	2.65321i	−0.349389	+	0.201720i	−0.664416	−	0.747363i	$-0.731320\pi$
$173$	−4.59549	+	2.65321i	−0.349389	+	0.201720i	0.315027	+	0.949083i	$0.397986\pi$
$174$	−1.94652	+	17.2569i	−0.147566	+	1.30824i
$175$	−2.40821	−	8.98756i	−0.182044	−	0.679396i
$176$	−21.1503	−	8.34635i	−1.59426	−	0.629130i
$177$	9.11948	+	8.29861i	0.685462	+	0.623762i
$178$	−5.26770	+	11.7575i	−0.394831	+	0.881259i
$179$			14.5873i			1.09031i	0.838337	+	0.545153i	$0.183528\pi$
$179$			14.5873i			1.09031i	−0.838337	+	0.545153i	$0.816472\pi$
$180$	−21.3246	+	13.3919i	−1.58944	+	0.998170i
$181$	11.0282			0.819717			0.409858	−	0.912149i	$-0.365578\pi$
$181$	11.0282			0.819717			0.409858	+	0.912149i	$0.365578\pi$
$182$	−3.05155	−	2.19919i	−0.226196	−	0.163015i
$183$	−0.207051	−	0.106875i	−0.0153057	−	0.00790045i
$184$	−2.45039	−	3.83178i	−0.180645	−	0.282483i
$185$	18.7960	+	10.8518i	1.38191	+	0.797844i
$186$	−0.289973	+	0.738574i	−0.0212619	+	0.0541549i
$187$	6.32913	−	23.6206i	0.462832	−	1.72731i
$188$	15.0473	−	7.57868i	1.09744	−	0.552732i
$189$	−0.460850	+	3.80528i	−0.0335219	+	0.276794i
$190$	−4.70857	+	29.2859i	−0.341595	+	2.12462i
$191$	−9.48885	+	5.47839i	−0.686589	+	0.396402i	−0.802333	−	0.596877i	$-0.796408\pi$
$191$	−9.48885	+	5.47839i	−0.686589	+	0.396402i	0.115744	+	0.993279i	$0.463075\pi$
$192$	−5.21416	+	12.8379i	−0.376299	+	0.926498i
$193$	23.7242	−	6.35688i	1.70770	−	0.457578i	0.732844	−	0.680396i	$-0.238192\pi$
$193$	23.7242	−	6.35688i	1.70770	−	0.457578i	0.974860	+	0.222819i	$0.0715257\pi$
$194$	−8.33799	+	0.856675i	−0.598633	+	0.0615057i
$195$	−2.76352	−	26.0631i	−0.197900	−	1.86642i
$196$	12.6419	−	2.62547i	0.902994	−	0.187533i
$197$	3.46721	−	3.46721i	0.247029	−	0.247029i	−0.572721	−	0.819750i	$-0.694112\pi$
$197$	3.46721	−	3.46721i	0.247029	−	0.247029i	0.819750	+	0.572721i	$0.194112\pi$
$198$	−22.8386	−	7.74706i	−1.62307	−	0.550560i
$199$		−	6.74097i		−	0.477854i	−0.971037	−	0.238927i	$-0.923204\pi$
$199$		−	6.74097i		−	0.477854i	0.971037	−	0.238927i	$-0.0767957\pi$
$200$	−1.61748	−	35.6393i	−0.114373	−	2.52008i
$201$	−0.413364	−	0.376156i	−0.0291565	−	0.0265320i
$202$	10.2176	−	12.5576i	0.718907	−	0.883549i
$203$	−5.05175	+	1.35361i	−0.354564	+	0.0950050i
$204$	−14.3555	−	3.99988i	−1.00509	−	0.280047i
$205$	6.27728	+	10.8726i	0.438424	+	0.759373i
$206$	−3.91819	−	0.629965i	−0.272993	−	0.0438917i
$207$	−2.79432	−	3.93251i	−0.194219	−	0.273328i
$208$	−9.61645	−	10.7482i	−0.666781	−	0.745254i
$209$	−24.6024	+	14.2042i	−1.70179	+	0.982527i
$210$	−6.10103	−	4.50392i	−0.421011	−	0.310800i
$211$	−14.9192	−	8.61359i	−1.02708	−	0.592984i	−0.110932	−	0.993828i	$-0.535384\pi$
$211$	−14.9192	−	8.61359i	−1.02708	−	0.592984i	−0.916146	+	0.400844i	$0.868717\pi$
$212$	9.85705	−	8.79231i	0.676985	−	0.603858i
$213$	1.08727	−	4.98591i	0.0744983	−	0.341629i
$214$	−4.09847	+	1.56228i	−0.280166	+	0.106795i
$215$	−12.3135	+	12.3135i	−0.839777	+	0.839777i
$216$	−4.85919	+	13.8704i	−0.330626	+	0.943762i
$217$	−0.238955			−0.0162213
$218$	17.7861	+	7.96870i	1.20463	+	0.539709i
$219$	−2.33631	+	10.7137i	−0.157874	+	0.723965i
$220$	35.6062	−	31.7601i	2.40057	−	2.14127i
$221$	10.3073	−	11.5908i	0.693345	−	0.779681i
$222$	12.5262	−	1.88645i	0.840701	−	0.126610i
$223$	−1.45171	−	0.388983i	−0.0972134	−	0.0260482i	0.209884	−	0.977726i	$-0.432691\pi$
$223$	−1.45171	−	0.388983i	−0.0972134	−	0.0260482i	−0.307098	+	0.951678i	$0.599358\pi$
$224$	−4.17265	−	0.0487274i	−0.278797	−	0.00325573i
$225$	−3.55873	−	37.6724i	−0.237248	−	2.51149i
$226$	−17.8174	−	2.86467i	−1.18520	−	0.190555i
$227$	3.26705	+	0.875402i	0.216841	+	0.0581025i	0.365604	−	0.930770i	$-0.380862\pi$
$227$	3.26705	+	0.875402i	0.216841	+	0.0581025i	−0.148763	+	0.988873i	$0.547529\pi$
$228$	8.50672	+	15.0782i	0.563372	+	0.998576i
$229$	−5.75667	−	21.4842i	−0.380412	−	1.41972i	−0.845274	−	0.534333i	$-0.820563\pi$
$229$	−5.75667	−	21.4842i	−0.380412	−	1.41972i	0.464863	−	0.885383i	$-0.346104\pi$
$230$	9.49423	−	0.975471i	0.626031	−	0.0643206i
$231$	−0.341905	−	7.25486i	−0.0224957	−	0.477335i
$232$	−20.0322	+	0.909156i	−1.31518	+	0.0596890i
$233$	−13.8103			−0.904740			−0.452370	−	0.891830i	$-0.649421\pi$
$233$	−13.8103			−0.904740			−0.452370	+	0.891830i	$0.649421\pi$
$234$	−10.7441	−	10.8887i	−0.702364	−	0.711818i
$235$			35.3543i			2.30626i
$236$	−7.81004	+	11.9043i	−0.508390	+	0.774904i
$237$	9.63073	−	18.6578i	0.625583	−	1.21195i
$238$	−0.458692	−	4.46443i	−0.0297326	−	0.289386i
$239$	−5.62723	+	1.50781i	−0.363996	+	0.0975323i	−0.436181	−	0.899859i	$-0.643669\pi$
$239$	−5.62723	+	1.50781i	−0.363996	+	0.0975323i	0.0721856	+	0.997391i	$0.477003\pi$
$240$	−19.1382	−	21.8900i	−1.23537	−	1.41299i
$241$	4.06877	−	15.1849i	0.262093	−	0.978143i	−0.701913	−	0.712263i	$-0.747671\pi$
$241$	4.06877	−	15.1849i	0.262093	−	0.978143i	0.964006	−	0.265881i	$-0.0856628\pi$
$242$	29.7579	+	4.78445i	1.91291	+	0.307556i
$243$	−4.42969	+	14.9458i	−0.284164	+	0.958776i
$244$	0.0843366	−	0.255495i	0.00539910	−	0.0163564i
$245$	−7.01245	+	26.1708i	−0.448009	+	1.67199i
$246$	6.82065	+	2.67787i	0.434869	+	0.170735i
$247$	−17.9883	+	1.05432i	−1.14457	+	0.0670850i
$248$	−0.894829	−	0.196764i	−0.0568217	−	0.0124946i
$249$	2.06386	+	6.46761i	0.130792	+	0.409868i
$250$	41.2373	+	18.4756i	2.60808	+	1.16850i
$251$			1.03989i			0.0656376i	0.999461	+	0.0328188i	$0.0104484\pi$
$251$			1.03989i			0.0656376i	−0.999461	+	0.0328188i	$0.989552\pi$
$252$	−4.42302	+	0.164412i	−0.278624	+	0.0103570i
$253$	6.46356	+	6.46356i	0.406361	+	0.406361i
$254$	7.12183	+	18.6833i	0.446864	+	1.17230i
$255$	21.0467	−	23.1286i	1.31800	−	1.44837i
$256$	−15.5855	−	3.61839i	−0.974093	−	0.226150i
$257$	−8.98110	+	15.5557i	−0.560226	+	0.970339i	0.437251	+	0.899340i	$0.355952\pi$
$257$	−8.98110	+	15.5557i	−0.560226	+	0.970339i	−0.997476	+	0.0709996i	$0.977381\pi$
$258$	−1.13921	+	10.0997i	−0.0709243	+	0.628778i
$259$	1.90743	+	3.30377i	0.118522	+	0.205286i
$260$	29.2207	−	7.87708i	1.81219	−	0.488516i
$261$	−21.1750	+	2.00030i	−1.31070	+	0.123815i
$262$	1.39023	−	8.64681i	0.0858886	−	0.534202i
$263$	22.2971	−	12.8732i	1.37490	−	0.793798i	0.383358	−	0.923600i	$-0.374768\pi$
$263$	22.2971	−	12.8732i	1.37490	−	0.793798i	0.991540	+	0.129802i	$0.0414343\pi$
$264$	4.69358	−	27.4493i	0.288870	−	1.68939i
$265$	7.17370	+	26.7726i	0.440677	+	1.64463i
$266$	−3.29054	+	4.04413i	−0.201756	+	0.247962i
$267$	−15.4168	−	3.36191i	−0.943493	−	0.205745i
$268$	0.354010	−	0.539594i	0.0216246	−	0.0329609i
$269$	−11.0793			−0.675517			−0.337758	−	0.941233i	$-0.609669\pi$
$269$	−11.0793			−0.675517			−0.337758	+	0.941233i	$0.609669\pi$
$270$	−21.4083	−	22.1993i	−1.30287	−	1.35100i
$271$	−14.3103	−	14.3103i	−0.869289	−	0.869289i	0.123104	−	0.992394i	$-0.460715\pi$
$271$	−14.3103	−	14.3103i	−0.869289	−	0.869289i	−0.992394	+	0.123104i	$0.960715\pi$
$272$	1.95849	−	17.0960i	0.118751	−	1.03659i
$273$	1.86989	−	4.21024i	0.113171	−	0.254815i
$274$	−13.2466	+	1.36100i	−0.800255	+	0.0822210i
$275$	18.5571	+	69.2562i	1.11904	+	4.17630i
$276$	3.97789	−	3.89960i	0.239441	−	0.234728i
$277$	−10.8884	−	18.8592i	−0.654219	−	1.13314i	−0.982089	−	0.188418i	$-0.939664\pi$
$277$	−10.8884	−	18.8592i	−0.654219	−	1.13314i	0.327870	−	0.944723i	$-0.393669\pi$
$278$	−31.2508	−	5.02448i	−1.87430	−	0.301348i
$279$	−0.958165	−	0.162123i	−0.0573638	−	0.00970604i
$280$	4.02996	−	7.77410i	0.240836	−	0.464592i
$281$	−25.8766	−	6.93362i	−1.54367	−	0.413625i	−0.616220	−	0.787574i	$-0.711337\pi$
$281$	−25.8766	−	6.93362i	−1.54367	−	0.413625i	−0.927449	+	0.373949i	$0.878003\pi$
$282$	12.8635	+	16.1344i	0.766011	+	0.960789i
$283$	3.07409	−	5.32447i	0.182735	−	0.316507i	−0.760076	−	0.649835i	$-0.774838\pi$
$283$	3.07409	−	5.32447i	0.182735	−	0.316507i	0.942811	+	0.333328i	$0.108172\pi$
$284$	5.88295	+	0.335874i	0.349089	+	0.0199304i
$285$	−36.2881	+	1.71017i	−2.14952	+	0.101302i
$286$	23.5146	+	16.9464i	1.39045	+	1.00206i
$287$			2.20672i			0.130258i
$288$	−16.6985	−	3.02640i	−0.983970	−	0.178332i
$289$	1.50670			0.0886297
$290$	17.2049	−	38.4012i	1.01031	−	2.25500i
$291$	−3.12080	−	9.77981i	−0.182944	−	0.573302i
$292$	−12.6413	−	0.721724i	−0.739774	−	0.0422357i
$293$	−18.3498	+	4.91683i	−1.07201	+	0.287244i	−0.751319	−	0.659940i	$-0.770582\pi$
$293$	−18.3498	+	4.91683i	−1.07201	+	0.287244i	−0.320691	+	0.947184i	$0.603915\pi$
$294$	6.32191	+	14.4948i	0.368701	+	0.845355i
$295$	−14.9382	−	25.8737i	−0.869735	−	1.50643i
$296$	4.42244	+	13.9425i	0.257049	+	0.810391i
$297$	3.55121	−	29.3227i	0.206062	−	1.70147i
$298$	8.35332	+	11.5540i	0.483895	+	0.669306i
$299$	1.82574	+	5.50300i	0.105585	+	0.318247i
$300$	42.3155	−	10.8889i	2.44308	−	0.628668i
$301$	−2.95657	+	0.792210i	−0.170414	+	0.0456622i
$302$	−3.17847	−	30.9359i	−0.182900	−	1.78016i
$303$	17.6190	+	9.09452i	1.01218	+	0.522466i
$304$	−15.6524	+	12.4348i	−0.897726	+	0.713183i
$305$	0.399223	+	0.399223i	0.0228595	+	0.0228595i
$306$	1.18970	−	18.2128i	0.0680105	−	1.04116i
$307$	7.56033	−	7.56033i	0.431491	−	0.431491i	−0.457644	−	0.889135i	$-0.651307\pi$
$307$	7.56033	−	7.56033i	0.431491	−	0.431491i	0.889135	+	0.457644i	$0.151307\pi$
$308$	8.21128	−	1.70531i	0.467881	−	0.0971693i
$309$	−0.228806	−	4.85503i	−0.0130163	−	0.276193i
$310$	1.21341	−	1.49130i	0.0689168	−	0.0847000i
$311$	−4.42184	+	7.65885i	−0.250740	+	0.434294i	−0.963730	−	0.266880i	$-0.914007\pi$
$311$	−4.42184	+	7.65885i	−0.250740	+	0.434294i	0.712990	+	0.701174i	$0.247340\pi$
$312$	10.4692	−	14.2266i	0.592700	−	0.805423i
$313$	1.14564	+	1.98430i	0.0647553	+	0.112159i	0.896585	−	0.442871i	$-0.146040\pi$
$313$	1.14564	+	1.98430i	0.0647553	+	0.112159i	−0.831830	+	0.555030i	$0.812707\pi$
$314$	−15.2654	−	2.45436i	−0.861477	−	0.138508i
$315$	3.86683	−	8.44450i	0.217871	−	0.475794i
$316$	23.0231	+	7.59973i	1.29515	+	0.427518i
$317$	20.0974	+	5.38508i	1.12878	+	0.302456i	0.774433	−	0.632656i	$-0.218035\pi$
$317$	20.0974	+	5.38508i	1.12878	+	0.302456i	0.354350	+	0.935113i	$0.384702\pi$
$318$	13.0149	+	9.60790i	0.729839	+	0.538784i
$319$	38.9277	−	10.4306i	2.17953	−	0.584004i
$320$	21.4927	−	25.7938i	1.20148	−	1.44191i
$321$	−2.90197	−	4.52060i	−0.161972	−	0.252315i
$322$	1.53096	+	0.685914i	0.0853168	+	0.0382245i
$323$	−15.2025	−	15.2025i	−0.845887	−	0.845887i
$324$	−17.8470	−	2.34161i	−0.991502	−	0.130089i
$325$	−9.18014	+	44.5420i	−0.509223	+	2.47074i
$326$	−1.16639	+	2.60338i	−0.0646004	+	0.144188i
$327$	−5.08572	+	23.3217i	−0.281241	+	1.28969i
$328$	−1.81710	+	8.26364i	−0.100332	+	0.456283i
$329$	−3.10712	+	5.38170i	−0.171301	+	0.296702i
$330$	47.0132	+	34.7062i	2.58799	+	1.91051i
$331$	6.57774	−	24.5485i	0.361545	−	1.34931i	−0.510499	−	0.859878i	$-0.670539\pi$
$331$	6.57774	−	24.5485i	0.361545	−	1.34931i	0.872044	−	0.489427i	$-0.162794\pi$
$332$	−7.00131	+	3.52625i	−0.384247	+	0.193528i
$333$	5.40697	+	14.5417i	0.296300	+	0.796878i
$334$	−10.7745	−	14.9029i	−0.589556	−	0.815453i
$335$	0.677113	+	1.17279i	0.0369946	+	0.0640765i
$336$	−0.989450	−	5.01409i	−0.0539789	−	0.273541i
$337$	−25.6455	−	14.8064i	−1.39700	−	0.806558i	−0.402923	−	0.915234i	$-0.632006\pi$
$337$	−25.6455	−	14.8064i	−1.39700	−	0.806558i	−0.994077	+	0.108675i	$0.965339\pi$
$338$	8.51045	+	16.2964i	0.462908	+	0.886406i
$339$	−1.04046	−	22.0775i	−0.0565101	−	1.19909i
$340$	30.1914	+	19.8076i	1.63736	+	1.07422i
$341$	1.84133			0.0997137
$342$	−15.9383	+	13.9837i	−0.861844	+	0.756153i
$343$	−7.01879	+	7.01879i	−0.378979	+	0.378979i
$344$	−11.7240	+	0.532089i	−0.632115	+	0.0286883i
$345$	3.55356	+	11.1360i	0.191317	+	0.599541i
$346$	4.73629	−	5.82098i	0.254624	−	0.312938i
$347$	1.43096	−	2.47849i	0.0768177	−	0.133052i	−0.825058	−	0.565049i	$-0.808857\pi$
$347$	1.43096	−	2.47849i	0.0768177	−	0.133052i	0.901875	+	0.431996i	$0.142191\pi$
$348$	−6.12044	−	23.7848i	−0.328090	−	1.27500i
$349$	17.2696	+	4.62738i	0.924422	+	0.247698i	0.689475	−	0.724310i	$-0.257842\pi$
$349$	17.2696	+	4.62738i	0.924422	+	0.247698i	0.234947	+	0.972008i	$0.424508\pi$
$350$	7.70961	+	10.6637i	0.412096	+	0.569996i
$351$	10.3544	−	15.6136i	0.552679	−	0.833394i
$352$	32.1535	+	0.375482i	1.71379	+	0.0200133i
$353$	2.52321	−	9.41673i	0.134297	−	0.501202i	−0.865703	−	0.500558i	$-0.833128\pi$
$353$	2.52321	−	9.41673i	0.134297	−	0.501202i	1.00000		0.000644317i	$-0.000205093\pi$
$354$	−16.2313	−	6.37260i	−0.862682	−	0.338700i
$355$	−6.18249	+	10.7084i	−0.328132	+	0.568342i
$356$	1.03855	−	18.1905i	0.0550428	−	0.964095i
$357$	5.23643	−	1.67098i	0.277141	−	0.0884375i
$358$	−7.34797	−	19.2765i	−0.388352	−	1.01880i
$359$	3.05172	−	3.05172i	0.161063	−	0.161063i	−0.621974	−	0.783038i	$-0.713669\pi$
$359$	3.05172	−	3.05172i	0.161063	−	0.161063i	0.783038	+	0.621974i	$0.213669\pi$
$360$	21.4339	−	28.4386i	1.12966	−	1.49884i
$361$			5.97630i			0.314542i
$362$	−14.5733	+	5.55515i	−0.765955	+	0.291972i
$363$	1.73773	+	36.8729i	0.0912074	+	1.93533i
$364$	5.14030	+	1.36900i	0.269425	+	0.0717552i
$365$	13.2849	−	23.0101i	0.695364	−	1.20441i
$366$	0.327446	+	0.0369350i	0.0171159	+	0.00193062i
$367$	−3.53274	−	6.11889i	−0.184408	−	0.319403i	0.758969	−	0.651127i	$-0.225703\pi$
$367$	−3.53274	−	6.11889i	−0.184408	−	0.319403i	−0.943377	+	0.331723i	$0.892370\pi$
$368$	5.16826	+	3.82923i	0.269414	+	0.199613i
$369$	−1.49719	+	8.84855i	−0.0779404	+	0.460637i
$370$	−30.3045	−	4.87233i	−1.57545	−	0.253301i
$371$	−1.26092	+	4.70583i	−0.0654639	+	0.244315i
$372$	0.0111514	−	1.12206i	0.000578175	−	0.0581763i
$373$	0.857429	+	0.495037i	0.0443960	+	0.0256320i	0.522034	−	0.852925i	$-0.325174\pi$
$373$	0.857429	+	0.495037i	0.0443960	+	0.0256320i	−0.477638	+	0.878557i	$0.658507\pi$
$374$	3.53458	+	34.4019i	0.182769	+	1.77888i
$375$	−11.7913	+	54.0718i	−0.608901	+	2.79226i
$376$	−16.0669	+	17.5947i	−0.828589	+	0.907375i
$377$	25.0363	+	5.16000i	1.28943	+	0.265753i
$378$	−1.30782	−	5.26068i	−0.0672668	−	0.270580i
$379$	−16.9118	−	16.9118i	−0.868700	−	0.868700i	0.123629	−	0.992329i	$-0.460547\pi$
$379$	−16.9118	−	16.9118i	−0.868700	−	0.868700i	−0.992329	+	0.123629i	$0.960547\pi$
$380$	−8.52981	−	41.0720i	−0.437570	−	2.10695i
$381$	−20.6076	+	13.2290i	−1.05576	+	0.677740i
$382$	9.77956	−	12.0192i	0.500366	−	0.614958i
$383$	−13.3378	+	3.57385i	−0.681529	+	0.182615i	−0.582943	−	0.812513i	$-0.698099\pi$
$383$	−13.3378	+	3.57385i	−0.681529	+	0.182615i	−0.0985865	+	0.995128i	$0.531432\pi$
$384$	0.423538	−	19.5913i	0.0216136	−	0.999766i
$385$	−4.55479	+	16.9987i	−0.232133	+	0.866333i
$386$	−28.1485	+	20.3508i	−1.43272	+	1.03583i
$387$	−12.3928	+	1.17069i	−0.629961	+	0.0595093i
$388$	10.5868	−	5.33211i	0.537464	−	0.270697i
$389$	−7.30771	+	4.21911i	−0.370516	+	0.213917i	−0.673684	−	0.739020i	$-0.735289\pi$
$389$	−7.30771	+	4.21911i	−0.370516	+	0.213917i	0.303168	+	0.952937i	$0.401956\pi$
$390$	16.7805	+	33.0493i	0.849713	+	1.67352i
$391$	−3.45890	+	5.99099i	−0.174924	+	0.302977i
$392$	−15.3833	+	9.83749i	−0.776974	+	0.496868i
$393$	10.7142	−	0.504937i	0.540462	−	0.0254707i
$394$	−2.83527	+	6.32831i	−0.142839	+	0.318816i
$395$	−35.9748	+	35.9748i	−1.81009	+	1.81009i
$396$	34.0828	−	1.26692i	1.71272	−	0.0636652i
$397$	−12.3498	+	12.3498i	−0.619818	+	0.619818i	−0.945485	−	0.325666i	$-0.894411\pi$
$397$	−12.3498	+	12.3498i	−0.619818	+	0.619818i	0.325666	+	0.945485i	$0.394411\pi$
$398$	3.39559	+	8.90793i	0.170205	+	0.446514i
$399$	−5.67413	−	2.92886i	−0.284062	−	0.146626i
$400$	20.0898	+	46.2812i	1.00449	+	2.31406i
$401$	0.390527	+	1.45747i	0.0195020	+	0.0727824i	0.974991	−	0.222244i	$-0.0713382\pi$
$401$	0.390527	+	1.45747i	0.0195020	+	0.0727824i	−0.955489	+	0.295027i	$0.904672\pi$
$402$	0.735724	+	0.288855i	0.0366946	+	0.0144068i
$403$	1.04390	+	0.523787i	0.0520004	+	0.0260917i
$404$	−7.17659	+	21.7412i	−0.357049	+	1.08167i
$405$	21.2346	−	31.2374i	1.05516	−	1.55220i
$406$	5.99385	−	4.33344i	0.297470	−	0.215065i
$407$	−14.6983	−	25.4581i	−0.728566	−	1.26191i
$408$	20.9851	−	1.94554i	1.03892	−	0.0963188i
$409$	7.20624	+	26.8940i	0.356326	+	1.32983i	0.878808	+	0.477175i	$0.158339\pi$
$409$	7.20624	+	26.8940i	0.356326	+	1.32983i	−0.522483	+	0.852650i	$0.674994\pi$
$410$	−13.7720	−	11.2057i	−0.680148	−	0.553408i
$411$	−4.95802	−	15.5372i	−0.244561	−	0.766393i
$412$	5.49507	−	1.14121i	0.270723	−	0.0562236i
$413$		−	5.25138i		−	0.258404i
$414$	5.67349	+	3.78910i	0.278837	+	0.186224i
$415$		−	16.4498i		−	0.807491i
$416$	18.1219	+	9.35930i	0.888500	+	0.458878i
$417$	−1.82491	−	38.7228i	−0.0893664	−	1.89626i
$418$	25.3562	−	31.1632i	1.24021	−	1.52424i
$419$	−12.7235	+	22.0378i	−0.621585	+	1.07662i	0.367605	+	0.929982i	$0.380178\pi$
$419$	−12.7235	+	22.0378i	−0.621585	+	1.07662i	−0.989191	+	0.146635i	$0.953156\pi$
$420$	10.3310	+	2.87853i	0.504102	+	0.140458i
$421$	−6.01551	+	22.4502i	−0.293178	+	1.09415i	0.649476	+	0.760382i	$0.274988\pi$
$421$	−6.01551	+	22.4502i	−0.293178	+	1.09415i	−0.942654	+	0.333772i	$0.891678\pi$
$422$	24.0540	+	3.86739i	1.17093	+	0.188261i
$423$	−16.1103	+	19.4715i	−0.783310	+	0.946739i
$424$	−8.59682	+	16.5839i	−0.417499	+	0.805387i
$425$	−46.9923	+	27.1310i	−2.27946	+	1.31605i
$426$	1.07474	+	7.13638i	0.0520714	+	0.345759i
$427$	0.0256846	+	0.0958563i	0.00124297	+	0.00463881i
$428$	4.62901	−	4.12899i	0.223752	−	0.199582i
$429$	−14.4090	+	32.4432i	−0.695672	+	1.56637i
$430$	10.0693	−	22.4745i	0.485583	−	1.08382i
$431$	2.97453	+	2.97453i	0.143278	+	0.143278i	0.775107	−	0.631829i	$-0.217696\pi$
$431$	2.97453	+	2.97453i	0.143278	+	0.143278i	−0.631829	+	0.775107i	$0.717696\pi$
$432$	−0.565621	−	20.7769i	−0.0272134	−	0.999630i
$433$			31.7311i			1.52490i	0.647047	+	0.762450i	$0.276004\pi$
$433$			31.7311i			1.52490i	−0.647047	+	0.762450i	$0.723996\pi$
$434$	0.315770	−	0.120367i	0.0151574	−	0.00577781i
$435$	50.3530	+	10.9804i	2.41424	+	0.526468i
$436$	−27.5177	−	1.57106i	−1.31786	−	0.0752400i
$437$	7.76267	−	2.08000i	0.371339	−	0.0995000i
$438$	−2.30940	−	15.3346i	−0.110347	−	0.732716i
$439$	12.7475	−	7.35980i	0.608407	−	0.351264i	−0.163935	−	0.986471i	$-0.552419\pi$
$439$	12.7475	−	7.35980i	0.608407	−	0.351264i	0.772342	+	0.635207i	$0.219085\pi$
$440$	−31.0540	+	59.9055i	−1.48044	+	2.85588i
$441$	−15.7877	+	11.2182i	−0.751794	+	0.534202i
$442$	−7.78216	+	20.5088i	−0.370160	+	0.975506i
$443$	−8.47363	−	14.6768i	−0.402594	−	0.697314i	0.591444	−	0.806346i	$-0.298558\pi$
$443$	−8.47363	−	14.6768i	−0.402594	−	0.697314i	−0.994038	+	0.109032i	$0.965225\pi$
$444$	−15.6026	+	8.80259i	−0.740467	+	0.417753i
$445$	33.1111	+	19.1167i	1.56962	+	0.906218i
$446$	2.11431	−	0.217232i	0.100116	−	0.0102862i
$447$	−11.7523	+	12.9148i	−0.555866	+	0.610850i
$448$	5.53855	−	2.03747i	0.261672	−	0.0962616i
$449$	7.28981	−	7.28981i	0.344027	−	0.344027i	−0.513852	−	0.857879i	$-0.671782\pi$
$449$	7.28981	−	7.28981i	0.344027	−	0.344027i	0.857879	+	0.513852i	$0.171782\pi$
$450$	23.6792	+	47.9900i	1.11625	+	2.26227i
$451$		−	17.0045i		−	0.800710i
$452$	24.9881	−	5.18950i	1.17534	−	0.244094i
$453$	36.2854	−	11.5789i	1.70484	−	0.544025i
$454$	−4.75824	+	0.488878i	−0.223315	+	0.0229442i
$455$	−7.41770	+	8.34136i	−0.347747	+	0.391049i
$456$	−18.8365	−	15.6402i	−0.882102	−	0.732419i
$457$	−10.5122	−	2.81673i	−0.491739	−	0.131761i	0.00442448	−	0.999990i	$-0.498592\pi$
$457$	−10.5122	−	2.81673i	−0.491739	−	0.131761i	−0.496163	+	0.868229i	$0.665258\pi$
$458$	18.4293	+	25.4908i	0.861146	+	1.19111i
$459$	22.1308	−	3.14758i	1.03298	−	0.146916i
$460$	−12.0549	+	6.07152i	−0.562062	+	0.283086i
$461$	17.1723	+	4.60130i	0.799793	+	0.214304i	0.635493	−	0.772107i	$-0.280797\pi$
$461$	17.1723	+	4.60130i	0.799793	+	0.214304i	0.164300	+	0.986410i	$0.447464\pi$
$462$	4.10626	+	9.41480i	0.191041	+	0.438016i
$463$	20.7975	−	5.57268i	0.966543	−	0.258984i	0.259175	−	0.965830i	$-0.416549\pi$
$463$	20.7975	−	5.57268i	0.966543	−	0.258984i	0.707368	+	0.706846i	$0.249883\pi$
$464$	26.0139	−	11.2921i	1.20766	−	0.524224i
$465$	2.09237	+	1.08003i	0.0970313	+	0.0500854i
$466$	18.2497	−	6.95656i	0.845403	−	0.322256i
$467$		−	3.65966i		−	0.169349i	−0.996409	−	0.0846745i	$-0.973015\pi$
$467$		−	3.65966i		−	0.169349i	0.996409	−	0.0846745i	$-0.0269850\pi$
$468$	19.6828	+	8.97697i	0.909839	+	0.414961i
$469$			0.238033i			0.0109913i
$470$	−17.8088	−	46.7194i	−0.821460	−	2.15501i
$471$	−0.891436	−	18.9154i	−0.0410752	−	0.871574i
$472$	4.32419	−	19.6652i	0.199037	−	0.905164i
$473$	22.7826	−	6.10459i	1.04755	−	0.280689i
$474$	−3.32828	+	29.5068i	−0.152873	+	1.35529i
$475$	60.8890	+	16.3152i	2.79378	+	0.748591i
$476$	2.85499	+	5.66853i	0.130858	+	0.259816i
$477$	−8.24883	+	18.0140i	−0.377688	+	0.824806i
$478$	6.67666	−	4.82709i	0.305383	−	0.220786i
$479$	−6.63931	−	1.77900i	−0.303358	−	0.0812844i	0.103929	−	0.994585i	$-0.466858\pi$
$479$	−6.63931	−	1.77900i	−0.303358	−	0.0812844i	−0.407287	+	0.913300i	$0.633525\pi$
$480$	36.3169	+	19.2864i	1.65763	+	0.880298i
$481$	−1.09099	−	18.6140i	−0.0497450	−	0.848725i
$482$	2.27225	+	22.1158i	0.103498	+	1.00735i
$483$	−0.437759	+	2.00744i	−0.0199187	+	0.0913418i
$484$	−41.7339	+	8.66728i	−1.89700	+	0.393967i
$485$			24.8741i			1.12948i
$486$	−1.67491	−	21.9817i	−0.0759756	−	0.997110i
$487$	6.86719	−	6.86719i	0.311182	−	0.311182i	−0.534185	−	0.845367i	$-0.679382\pi$
$487$	6.86719	−	6.86719i	0.311182	−	0.311182i	0.845367	+	0.534185i	$0.179382\pi$
$488$	0.0172511	+	0.380109i	0.000780921	+	0.0172067i
$489$	−3.41364	−	0.744405i	−0.154370	−	0.0336631i
$490$	−3.91618	−	38.1161i	−0.176915	−	1.72191i
$491$	−37.6140	−	21.7165i	−1.69750	−	0.980051i	−0.948123	−	0.317904i	$-0.897021\pi$
$491$	−37.6140	−	21.7165i	−1.69750	−	0.980051i	−0.749374	−	0.662146i	$-0.769646\pi$
$492$	−10.3621	−	0.102982i	−0.467161	−	0.00464280i
$493$	15.2499	+	26.4135i	0.686819	+	1.18961i
$494$	23.2398	−	10.4544i	1.04561	−	0.470366i
$495$	−29.7969	+	65.0714i	−1.33927	+	2.92474i
$496$	1.28160	−	0.190730i	0.0575454	−	0.00856403i
$497$	−1.88222	+	1.08670i	−0.0844290	+	0.0487451i
$498$	−5.98520	−	7.50709i	−0.268203	−	0.336401i
$499$	−18.7169	+	5.01518i	−0.837884	+	0.224510i	−0.652150	−	0.758090i	$-0.726133\pi$
$499$	−18.7169	+	5.01518i	−0.837884	+	0.224510i	−0.185734	+	0.982600i	$0.559466\pi$
$500$	−63.8001	−	3.64252i	−2.85323	−	0.162899i
$501$	15.1587	−	16.6582i	0.677242	−	0.744233i
$502$	−0.523820	−	1.37418i	−0.0233792	−	0.0613327i
$503$		−	31.4108i		−	1.40054i	−0.713878	−	0.700270i	$-0.753063\pi$
$503$		−	31.4108i		−	1.40054i	0.713878	−	0.700270i	$-0.246937\pi$
$504$	5.76203	−	2.44524i	0.256661	−	0.108920i
$505$	−33.9718	−	33.9718i	−1.51172	−	1.51172i
$506$	−11.7972	−	5.28550i	−0.524450	−	0.234969i
$507$	−17.3977	+	14.2941i	−0.772657	+	0.634824i
$508$	−18.8225	−	21.1019i	−0.835112	−	0.936243i
$509$	−0.455375	−	1.69948i	−0.0201841	−	0.0753282i	0.955099	−	0.296286i	$-0.0957483\pi$
$509$	−0.455375	−	1.69948i	−0.0201841	−	0.0753282i	−0.975283	+	0.220958i	$0.929082\pi$
$510$	−16.1620	+	41.1653i	−0.715666	+	1.82283i
$511$	4.04450	−	2.33509i	0.178918	−	0.103298i
$512$	22.4183	−	3.06921i	0.990758	−	0.135641i
$513$	−20.7651	−	15.5939i	−0.916802	−	0.688488i
$514$	4.03239	−	25.0803i	0.177861	−	1.10624i
$515$	−3.04811	+	11.3757i	−0.134316	+	0.501273i
$516$	−3.58202	−	13.9202i	−0.157690	−	0.612802i
$517$	23.9428	−	41.4701i	1.05300	−	1.82385i
$518$	−4.18479	−	3.40499i	−0.183869	−	0.149607i
$519$	8.16714	+	4.21570i	0.358498	+	0.185049i
$520$	−34.6461	+	25.1284i	−1.51933	+	1.10195i
$521$		−	15.5035i		−	0.679219i	−0.940567	−	0.339609i	$-0.889705\pi$
$521$		−	15.5035i		−	0.679219i	0.940567	−	0.339609i	$-0.110295\pi$
$522$	26.9744	−	13.3097i	1.18064	−	0.582549i
$523$		−	19.8249i		−	0.866884i	−0.901181	−	0.433442i	$-0.857299\pi$
$523$		−	19.8249i		−	0.866884i	0.901181	−	0.433442i	$-0.142701\pi$
$524$	2.51847	+	12.1267i	0.110020	+	0.529758i
$525$	−10.8467	+	11.9196i	−0.473388	+	0.520214i
$526$	−22.9802	+	28.2431i	−1.00198	+	1.23146i
$527$	0.360669	+	1.34604i	0.0157110	+	0.0586343i
$528$	7.62448	+	38.6375i	0.331813	+	1.68148i
$529$	10.2071	+	17.6792i	0.443785	+	0.768659i
$530$	−22.9658	−	31.7654i	−0.997570	−	1.37980i
$531$	3.56289	−	21.0571i	0.154616	−	0.913801i
$532$	2.31120	−	7.00169i	0.100203	−	0.303562i
$533$	4.83711	−	9.64030i	0.209519	−	0.417568i
$534$	22.0662	−	3.32318i	0.954897	−	0.143808i
$535$	3.36887	+	12.5728i	0.145649	+	0.543569i
$536$	−0.196005	+	0.891376i	−0.00846613	+	0.0385016i
$537$	21.2620	−	13.6490i	0.917522	−	0.588998i
$538$	14.6409	−	5.58091i	0.631213	−	0.240610i
$539$	25.9490	−	25.9490i	1.11770	−	1.11770i
$540$	39.4725	+	18.5516i	1.69863	+	0.798335i
$541$	18.0156	−	18.0156i	0.774549	−	0.774549i	−0.204349	−	0.978898i	$-0.565508\pi$
$541$	18.0156	−	18.0156i	0.774549	−	0.774549i	0.978898	+	0.204349i	$0.0655077\pi$
$542$	26.1190	+	11.7021i	1.12191	+	0.502648i
$543$	−10.3188	−	16.0743i	−0.442823	−	0.689814i
$544$	6.02357	+	23.5782i	0.258258	+	1.01091i
$545$	28.9188	−	50.0888i	1.23874	−	2.14557i
$546$	−0.350193	+	6.50558i	−0.0149869	+	0.278413i
$547$	22.9572	−	13.2543i	0.981579	−	0.566715i	0.0788326	−	0.996888i	$-0.474881\pi$
$547$	22.9572	−	13.2543i	0.981579	−	0.566715i	0.902747	+	0.430173i	$0.141547\pi$
$548$	16.8193	−	8.47113i	0.718484	−	0.361869i
$549$	0.0379554	+	0.401792i	0.00161990	+	0.0171481i
$550$	−59.4085	−	82.1717i	−2.53319	−	3.50381i
$551$	9.17047	−	34.2247i	0.390675	−	1.45802i
$552$	−3.29231	+	7.15693i	−0.140130	+	0.304619i
$553$	−8.63778	+	2.31449i	−0.367316	+	0.0984220i
$554$	23.8884	+	19.4370i	1.01492	+	0.825799i
$555$	−1.76965	−	37.5502i	−0.0751176	−	1.59392i
$556$	43.8277	−	9.10211i	1.85871	−	0.386015i
$557$	−2.81094	−	2.81094i	−0.119103	−	0.119103i	0.645043	−	0.764146i	$-0.276839\pi$
$557$	−2.81094	−	2.81094i	−0.119103	−	0.119103i	−0.764146	+	0.645043i	$0.776839\pi$
$558$	1.34784	−	0.268412i	0.0570588	−	0.0113628i
$559$	14.6526	+	3.01992i	0.619740	+	0.127729i
$560$	−1.40944	+	12.3032i	−0.0595596	+	0.519904i
$561$	−40.3507	+	12.8762i	−1.70361	+	0.543633i
$562$	37.6876	−	3.87216i	1.58976	−	0.163337i
$563$	−10.1422	−	5.85558i	−0.427441	−	0.246783i	0.270815	−	0.962632i	$-0.412707\pi$
$563$	−10.1422	−	5.85558i	−0.427441	−	0.246783i	−0.698256	+	0.715848i	$0.746040\pi$
$564$	−25.1259	−	14.8413i	−1.05799	−	0.624933i
$565$	−13.8608	+	51.7293i	−0.583130	+	2.17627i
$566$	−1.38022	+	8.58458i	−0.0580151	+	0.360837i
$567$	5.97767	−	2.88880i	0.251039	−	0.121318i
$568$	−7.94329	+	2.51954i	−0.333293	+	0.105718i
$569$	3.27428	+	5.67122i	0.137265	+	0.237750i	0.926460	−	0.376392i	$-0.122836\pi$
$569$	3.27428	+	5.67122i	0.137265	+	0.237750i	−0.789195	+	0.614142i	$0.789502\pi$
$570$	47.0919	−	20.5391i	1.97246	−	0.860289i
$571$	−8.71554	+	15.0958i	−0.364734	+	0.631738i	−0.988733	−	0.149687i	$-0.952173\pi$
$571$	−8.71554	+	15.0958i	−0.364734	+	0.631738i	0.623999	+	0.781425i	$0.285507\pi$
$572$	−39.6100	−	10.5492i	−1.65618	−	0.441085i
$573$	16.8636	+	8.70463i	0.704488	+	0.363641i
$574$	−1.11158	−	2.91610i	−0.0463963	−	0.121715i
$575$		−	20.2831i		−	0.845865i
$576$	23.5909	−	4.41218i	0.982956	−	0.183841i
$577$	9.53923	−	9.53923i	0.397123	−	0.397123i	−0.480094	−	0.877217i	$-0.659397\pi$
$577$	9.53923	−	9.53923i	0.397123	−	0.397123i	0.877217	+	0.480094i	$0.159397\pi$
$578$	−1.99105	+	0.758963i	−0.0828169	+	0.0315687i
$579$	−31.4638	−	28.6316i	−1.30759	−	1.18989i
$580$	−3.39201	+	59.4123i	−0.140845	+	2.46696i
$581$	1.44570	−	2.50402i	0.0599777	−	0.103884i
$582$	9.05034	+	11.3516i	0.375149	+	0.470540i
$583$	9.71640	−	36.2621i	0.402412	−	1.50182i
$584$	17.0685	−	5.41398i	0.706300	−	0.224032i
$585$	−35.4030	+	28.4147i	−1.46373	+	1.17480i
$586$	21.7719	−	15.7407i	0.899389	−	0.650241i
$587$	3.41113	+	0.914011i	0.140793	+	0.0377253i	0.328527	−	0.944495i	$-0.393448\pi$
$587$	3.41113	+	0.914011i	0.140793	+	0.0377253i	−0.187734	+	0.982220i	$0.560114\pi$
$588$	−15.6556	−	15.9699i	−0.645624	−	0.658586i
$589$	0.809436	−	1.40198i	0.0333522	−	0.0577678i
$590$	32.7735	+	26.6664i	1.34926	+	1.09784i
$591$	−8.29789	−	1.80950i	−0.341330	−	0.0744330i
$592$	−12.8673	−	16.1968i	−0.528841	−	0.665684i
$593$	−3.05929	+	3.05929i	−0.125630	+	0.125630i	−0.767126	−	0.641496i	$-0.778314\pi$
$593$	−3.05929	+	3.05929i	−0.125630	+	0.125630i	0.641496	+	0.767126i	$0.278314\pi$
$594$	10.0777	+	40.5376i	0.413495	+	1.66328i
$595$	−13.3184			−0.546002
$596$	−16.8586	−	11.0604i	−0.690556	−	0.453052i
$597$	−9.82542	+	6.30738i	−0.402128	+	0.258144i
$598$	−5.18464	−	6.35234i	−0.212016	−	0.259767i
$599$	−5.73425	−	3.31067i	−0.234295	−	0.135270i	0.378257	−	0.925701i	$-0.376524\pi$
$599$	−5.73425	−	3.31067i	−0.234295	−	0.135270i	−0.612552	+	0.790430i	$0.709857\pi$
$600$	−50.4333	+	35.7045i	−2.05893	+	1.45763i
$601$	12.6088	+	21.8391i	0.514323	+	0.890834i	0.999862	+	0.0166187i	$0.00529013\pi$
$601$	12.6088	+	21.8391i	0.514323	+	0.890834i	−0.485539	+	0.874215i	$0.661377\pi$
$602$	3.50794	−	2.53617i	0.142973	−	0.103367i
$603$	−0.161497	+	0.954468i	−0.00657668	+	0.0388689i
$604$	19.7834	+	39.2796i	0.804975	+	1.59826i
$605$	23.1497	−	86.3960i	0.941171	−	3.51250i
$606$	−27.8639	−	3.14297i	−1.13189	−	0.127674i
$607$	−13.2651	+	22.9758i	−0.538413	+	0.932559i	0.460577	+	0.887620i	$0.347643\pi$
$607$	−13.2651	+	22.9758i	−0.538413	+	0.932559i	−0.998990	+	0.0449390i	$0.985691\pi$
$608$	14.4204	−	24.3166i	0.584823	−	0.986167i
$609$	6.69980	+	6.09673i	0.271490	+	0.247052i
$610$	−0.728657	−	0.326460i	−0.0295025	−	0.0132180i
$611$	25.3705	−	16.6998i	1.02638	−	0.675600i
$612$	7.60207	+	24.6668i	0.307296	+	0.997095i
$613$	−13.1150	−	13.1150i	−0.529712	−	0.529712i	0.390775	−	0.920486i	$-0.372207\pi$
$613$	−13.1150	−	13.1150i	−0.529712	−	0.529712i	−0.920486	+	0.390775i	$0.872207\pi$
$614$	−6.18237	+	13.7990i	−0.249500	+	0.556883i
$615$	9.97399	−	19.3228i	0.402190	−	0.779170i
$616$	−9.99189	+	6.38973i	−0.402585	+	0.257450i
$617$	−20.9738	+	5.61991i	−0.844374	+	0.226249i	−0.654974	−	0.755651i	$-0.727321\pi$
$617$	−20.9738	+	5.61991i	−0.844374	+	0.226249i	−0.189399	+	0.981900i	$0.560654\pi$
$618$	2.74795	+	6.30048i	0.110539	+	0.253442i
$619$	−0.313186	−	0.0839180i	−0.0125880	−	0.00337295i	0.252520	−	0.967592i	$-0.418741\pi$
$619$	−0.313186	−	0.0839180i	−0.0125880	−	0.00337295i	−0.265108	+	0.964219i	$0.585407\pi$
$620$	−0.852268	+	2.58191i	−0.0342279	+	0.103692i
$621$	−3.11732	+	7.75248i	−0.125094	+	0.311096i
$622$	1.98535	−	12.3483i	0.0796052	−	0.495121i
$623$	3.36015	+	5.81995i	0.134622	+	0.233171i
$624$	−6.66833	+	24.0735i	−0.266947	+	0.963711i
$625$	35.5151	−	61.5140i	1.42061	−	2.46056i
$626$	−2.51346	−	2.04510i	−0.100458	−	0.0817384i
$627$	43.7236	+	22.5692i	1.74615	+	0.901325i
$628$	21.4090	−	4.44621i	0.854312	−	0.177423i
$629$	15.7312	−	15.7312i	0.627244	−	0.627244i
$630$	−0.856171	+	13.1069i	−0.0341107	+	0.522191i
$631$	27.7709	+	27.7709i	1.10554	+	1.10554i	0.993729	+	0.111814i	$0.0356662\pi$
$631$	27.7709	+	27.7709i	1.10554	+	1.10554i	0.111814	+	0.993729i	$0.464334\pi$
$632$	−34.2523	+	1.55453i	−1.36248	+	0.0618358i
$633$	1.40465	+	29.8053i	0.0558299	+	1.18465i
$634$	−29.2706	+	3.00736i	−1.16248	+	0.119438i
$635$	57.3145	−	15.3574i	2.27446	−	0.609438i
$636$	−22.0384	−	6.14055i	−0.873880	−	0.243489i
$637$	22.0927	−	7.32971i	0.875343	−	0.290414i
$638$	−46.1873	+	33.3925i	−1.82857	+	1.32202i
$639$	−8.28464	+	3.08044i	−0.327735	+	0.121860i
$640$	−15.4089	+	44.9119i	−0.609090	+	1.77530i
$641$	−13.4618	−	23.3166i	−0.531711	−	0.920950i	−0.999315	−	0.0370119i	$-0.988216\pi$
$641$	−13.4618	−	23.3166i	−0.531711	−	0.920950i	0.467604	−	0.883938i	$-0.345117\pi$
$642$	6.11198	+	4.51200i	0.241221	+	0.178075i
$643$	−40.2204	+	10.7770i	−1.58614	+	0.425005i	−0.940820	−	0.338908i	$-0.889942\pi$
$643$	−40.2204	+	10.7770i	−1.58614	+	0.425005i	−0.645320	+	0.763913i	$0.723276\pi$
$644$	−2.36861	−	0.135230i	−0.0933364	−	0.00532883i
$645$	29.4694	+	6.42632i	1.16036	+	0.253036i
$646$	27.7473	+	12.4316i	1.09170	+	0.489116i
$647$	−16.4282			−0.645859			−0.322930	−	0.946423i	$-0.604668\pi$
$647$	−16.4282			−0.645859			−0.322930	+	0.946423i	$0.604668\pi$
$648$	24.7637	−	5.89564i	0.972811	−	0.231603i
$649$			40.4660i			1.58843i
$650$	−10.3057	−	63.4848i	−0.404221	−	2.49008i
$651$	0.223585	+	0.348293i	0.00876298	+	0.0136507i
$652$	0.229958	−	4.02780i	0.00900586	−	0.157741i
$653$	−2.55225	+	4.42062i	−0.0998772	+	0.172992i	−0.911634	−	0.411004i	$-0.865178\pi$
$653$	−2.55225	+	4.42062i	−0.0998772	+	0.172992i	0.811756	+	0.583996i	$0.198512\pi$
$654$	−5.02713	−	33.3806i	−0.196576	−	1.30528i
$655$	−25.1043	−	6.72667i	−0.980906	−	0.262833i
$656$	−1.76137	−	11.8354i	−0.0687700	−	0.462095i
$657$	17.8020	−	6.61924i	0.694522	−	0.258241i
$658$	1.39506	−	8.67684i	0.0543850	−	0.338258i
$659$	−12.9588	−	22.4453i	−0.504802	−	0.874343i	−0.999985	−	0.00555404i	$-0.998232\pi$
$659$	−12.9588	−	22.4453i	−0.504802	−	0.874343i	0.495182	−	0.868789i	$-0.335101\pi$
$660$	−79.6085	−	22.1813i	−3.09876	−	0.863405i
$661$	−8.44547	−	31.5189i	−0.328491	−	1.22594i	−0.910756	−	0.412945i	$-0.864500\pi$
$661$	−8.44547	−	31.5189i	−0.328491	−	1.22594i	0.582265	−	0.812999i	$-0.302166\pi$
$662$	3.67341	+	35.7532i	0.142771	+	1.38959i
$663$	−26.5387	−	4.17836i	−1.03068	−	0.162274i
$664$	7.47570	−	8.18653i	0.290114	−	0.317699i
$665$	10.9405	+	10.9405i	0.424255	+	0.424255i
$666$	−14.4701	−	16.4926i	−0.560704	−	0.639077i
$667$	−11.4008			−0.441440
$668$	21.7451	+	14.2663i	0.841344	+	0.551979i
$669$	0.791359	+	2.47992i	0.0305957	+	0.0958794i
$670$	−1.48554	−	1.20872i	−0.0573915	−	0.0466971i
$671$	−0.197920	−	0.738647i	−0.00764061	−	0.0285151i
$672$	3.83324	+	6.12752i	0.147870	+	0.236374i
$673$	−17.3777	+	10.0330i	−0.669860	+	0.386744i	−0.796023	−	0.605266i	$-0.793067\pi$
$673$	−17.3777	+	10.0330i	−0.669860	+	0.386744i	0.126164	+	0.992009i	$0.459734\pi$
$674$	41.3479	+	6.64790i	1.59266	+	0.256067i
$675$	−51.5803	+	40.4363i	−1.98533	+	1.55640i
$676$	−19.4551	−	17.2481i	−0.748274	−	0.663390i
$677$	23.0498	+	39.9235i	0.885877	+	1.53438i	0.844705	+	0.535232i	$0.179776\pi$
$677$	23.0498	+	39.9235i	0.885877	+	1.53438i	0.0411723	+	0.999152i	$0.486891\pi$
$678$	12.4959	+	28.6505i	0.479903	+	1.10032i
$679$	−2.18607	+	3.78638i	−0.0838936	+	0.145308i
$680$	−49.8744	−	10.9669i	−1.91259	−	0.420561i
$681$	−1.78095	−	5.58104i	−0.0682460	−	0.213866i
$682$	−2.43325	+	0.927523i	−0.0931739	+	0.0355167i
$683$	29.3588	+	29.3588i	1.12338	+	1.12338i	0.991229	+	0.132152i	$0.0421887\pi$
$683$	29.3588	+	29.3588i	1.12338	+	1.12338i	0.132152	+	0.991229i	$0.457811\pi$
$684$	14.0179	−	26.5075i	0.535988	−	1.01354i
$685$			39.5176i			1.50989i
$686$	5.73954	−	12.8106i	0.219136	−	0.489111i
$687$	−25.9283	+	28.4930i	−0.989226	+	1.08708i
$688$	15.2248	−	6.60879i	0.580439	−	0.251958i
$689$	15.8236	−	17.7940i	0.602833	−	0.677898i
$690$	−10.3054	−	12.9258i	−0.392318	−	0.492075i
$691$	11.0889	−	41.3845i	0.421843	−	1.57434i	−0.348878	−	0.937168i	$-0.613437\pi$
$691$	11.0889	−	41.3845i	0.421843	−	1.57434i	0.770722	−	0.637172i	$-0.219896\pi$
$692$	−3.32666	+	10.0780i	−0.126461	+	0.383107i
$693$	−10.2545	+	7.28657i	−0.389538	+	0.276794i
$694$	−0.642480	+	3.99604i	−0.0243882	+	0.151687i
$695$	−24.3111	+	90.7304i	−0.922174	+	3.44160i
$696$	20.0689	+	28.3477i	0.760710	+	1.07452i
$697$	12.4305	−	3.33074i	0.470838	−	0.126161i
$698$	−25.1521	+	2.58421i	−0.952020	+	0.0978140i
$699$	12.9220	+	20.1294i	0.488753	+	0.761364i
$700$	−15.5595	−	10.2081i	−0.588094	−	0.385830i
$701$		−	23.5543i		−	0.889635i	−0.895621	−	0.444818i	$-0.853268\pi$
$701$		−	23.5543i		−	0.889635i	0.895621	−	0.444818i	$-0.146732\pi$
$702$	−5.81803	+	25.8486i	−0.219587	+	0.975593i
$703$	−25.8450			−0.974762
$704$	−42.6788	+	15.7003i	−1.60852	+	0.591728i
$705$	51.5314	−	33.0803i	1.94078	−	1.24588i
$706$	1.40911	+	13.7149i	0.0530327	+	0.516165i
$707$	−2.18562	−	8.15685i	−0.0821988	−	0.306770i
$708$	24.6590	+	0.245069i	0.926743	+	0.00921027i
$709$	−16.0362	−	4.29689i	−0.602253	−	0.161373i	−0.0552058	−	0.998475i	$-0.517581\pi$
$709$	−16.0362	−	4.29689i	−0.602253	−	0.161373i	−0.547047	+	0.837102i	$0.684248\pi$
$710$	2.77585	−	17.2650i	0.104176	−	0.647944i
$711$	−36.2063	+	3.42023i	−1.35784	+	0.128269i
$712$	7.79060	+	24.5612i	0.291965	+	0.920470i
$713$	−0.503148	−	0.134818i	−0.0188430	−	0.00504898i
$714$	−6.07803	+	4.84585i	−0.227465	+	0.181351i
$715$	57.1591	−	64.2767i	2.13763	−	2.40381i
$716$	19.4201	+	21.7719i	0.725764	+	0.813653i
$717$	7.46302	+	6.79125i	0.278712	+	0.253624i
$718$	−2.49551	+	5.56995i	−0.0931314	+	0.207869i
$719$	−4.51058			−0.168216			−0.0841080	−	0.996457i	$-0.526804\pi$
$719$	−4.51058			−0.168216			−0.0841080	+	0.996457i	$0.526804\pi$
$720$	−13.9989	+	48.3772i	−0.521707	+	1.80291i
$721$	−1.46374	+	1.46374i	−0.0545126	+	0.0545126i
$722$	−3.01041	−	7.89745i	−0.112036	−	0.293913i
$723$	−25.9400	+	8.27764i	−0.964721	+	0.307849i
$724$	16.4598	−	14.6818i	0.611724	−	0.545646i
$725$	−77.4450	−	44.7129i	−2.87623	−	1.66059i
$726$	−20.8701	−	47.8508i	−0.774563	−	1.77591i
$727$	−7.09910	+	4.09866i	−0.263291	+	0.152011i	−0.625835	−	0.779956i	$-0.715242\pi$
$727$	−7.09910	+	4.09866i	−0.263291	+	0.152011i	0.362544	+	0.931967i	$0.381908\pi$
$728$	−7.48230	+	0.780206i	−0.277313	+	0.0289164i
$729$	25.9293	−	7.52792i	0.960346	−	0.278812i
$730$	−5.96474	+	37.0989i	−0.220765	+	1.37309i
$731$	8.92507	+	15.4587i	0.330106	+	0.571760i
$732$	−0.451313	+	0.116134i	−0.0166810	+	0.00429245i
$733$	−7.41362	+	1.98647i	−0.273828	+	0.0733721i	−0.393120	−	0.919487i	$-0.628604\pi$
$733$	−7.41362	+	1.98647i	−0.273828	+	0.0733721i	0.119292	+	0.992859i	$0.461938\pi$
$734$	7.75061	+	6.30635i	0.286080	+	0.232772i
$735$	44.7071	−	14.2663i	1.64905	−	0.526222i
$736$	−8.75854	−	2.45681i	−0.322844	−	0.0905593i
$737$		−	1.83423i		−	0.0675646i
$738$	−2.47875	−	12.4472i	−0.0912441	−	0.458187i
$739$	−31.9363	+	31.9363i	−1.17480	+	1.17480i	−0.193745	+	0.981052i	$0.562063\pi$
$739$	−31.9363	+	31.9363i	−1.17480	+	1.17480i	−0.981052	+	0.193745i	$0.937937\pi$
$740$	42.5005	−	8.82649i	1.56235	−	0.324468i
$741$	18.3680	+	25.2327i	0.674767	+	0.926947i
$742$	−0.704177	−	6.85374i	−0.0258512	−	0.251609i
$743$	13.0617	−	3.49986i	0.479186	−	0.128398i	−0.0111375	−	0.999938i	$-0.503545\pi$
$743$	13.0617	−	3.49986i	0.479186	−	0.128398i	0.490324	+	0.871540i	$0.336879\pi$
$744$	0.550474	+	1.48838i	0.0201814	+	0.0545668i
$745$	36.6418	−	21.1552i	1.34245	−	0.775065i
$746$	−1.38242	−	0.222265i	−0.0506141	−	0.00813770i
$747$	7.49588	−	9.05982i	0.274260	−	0.331481i
$748$	−21.9999	−	43.6804i	−0.804395	−	1.59711i
$749$	−0.592148	+	2.20993i	−0.0216366	+	0.0807489i
$750$	−11.6555	−	77.3934i	−0.425598	−	2.82601i
$751$	18.5951	+	10.7359i	0.678546	+	0.391759i	0.799307	−	0.600923i	$-0.205200\pi$
$751$	18.5951	+	10.7359i	0.678546	+	0.391759i	−0.120761	+	0.992682i	$0.538534\pi$
$752$	12.3690	−	31.3440i	0.451051	−	1.14300i
$753$	1.51572	−	0.973007i	0.0552358	−	0.0354583i
$754$	−35.6837	+	5.79263i	−1.29952	+	0.210955i
$755$	−92.2890			−3.35874
$756$	4.37816	+	6.29301i	0.159232	+	0.228875i
$757$			33.5088i			1.21790i	0.793209	+	0.608950i	$0.208409\pi$
$757$			33.5088i			1.21790i	−0.793209	+	0.608950i	$0.791591\pi$
$758$	30.8671	+	13.8294i	1.12115	+	0.502307i
$759$	3.37327	−	15.4689i	0.122442	−	0.561486i
$760$	31.9608	+	49.9784i	1.15934	+	1.81291i
$761$	4.27232	+	15.9445i	0.154871	+	0.577988i	0.999116	+	0.0420303i	$0.0133826\pi$
$761$	4.27232	+	15.9445i	0.154871	+	0.577988i	−0.844245	+	0.535957i	$0.819951\pi$
$762$	20.5685	−	27.8621i	0.745117	−	1.00934i
$763$	8.80412	−	5.08306i	0.318731	−	0.184019i
$764$	−6.86893	+	20.8092i	−0.248509	+	0.752849i
$765$	−53.4045	−	9.03611i	−1.93084	−	0.326701i
$766$	15.8251	−	11.4413i	0.571786	−	0.413390i
$767$	−11.5110	+	22.9413i	−0.415638	+	0.828361i
$768$	9.30894	+	26.1026i	0.335907	+	0.941895i
$769$	−12.1417	−	45.3134i	−0.437841	−	1.63404i	−0.734176	−	0.678959i	$-0.762431\pi$
$769$	−12.1417	−	45.3134i	−0.437841	−	1.63404i	0.296335	−	0.955084i	$-0.404235\pi$
$770$	−2.54367	−	24.7575i	−0.0916676	−	0.892198i
$771$	31.0770	−	1.46458i	1.11921	−	0.0527457i
$772$	26.9460	−	41.0719i	0.969807	−	1.47821i
$773$	−33.9360	+	33.9360i	−1.22059	+	1.22059i	−0.253171	+	0.967422i	$0.581474\pi$
$773$	−33.9360	+	33.9360i	−1.22059	+	1.22059i	−0.967422	+	0.253171i	$0.918526\pi$
$774$	15.7869	−	7.78956i	0.567448	−	0.279990i
$775$	−2.88911	−	2.88911i	−0.103780	−	0.103780i
$776$	−11.3042	+	12.3790i	−0.405796	+	0.444381i
$777$	3.03073	−	5.87148i	0.108727	−	0.210638i
$778$	7.53160	−	9.25647i	0.270021	−	0.331860i
$779$	−12.9472	−	7.47505i	−0.463880	−	0.267821i
$780$	−38.8225	−	35.2207i	−1.39007	−	1.26110i
$781$	14.5039	−	8.37386i	0.518992	−	0.299640i
$782$	1.55300	−	9.65920i	0.0555352	−	0.345412i
$783$	22.7286	+	28.9924i	0.812253	+	1.03610i
$784$	15.3731	−	20.7488i	0.549038	−	0.741029i
$785$	−11.8755	+	44.3201i	−0.423856	+	1.58185i
$786$	−13.9041	+	6.06428i	−0.495944	+	0.216306i
$787$	1.69698	+	6.33320i	0.0604906	+	0.225754i	0.989553	−	0.144169i	$-0.0460508\pi$
$787$	1.69698	+	6.33320i	0.0604906	+	0.225754i	−0.929062	+	0.369923i	$0.879384\pi$
$788$	0.558984	−	9.79081i	0.0199130	−	0.348783i
$789$	−39.6265	−	20.4543i	−1.41074	−	0.728194i
$790$	29.4179	−	65.6606i	1.04664	−	2.33610i
$791$	−6.65616	+	6.65616i	−0.236666	+	0.236666i
$792$	−44.4009	+	18.8425i	−1.57772	+	0.669539i
$793$	0.0979102	−	0.475060i	0.00347689	−	0.0168699i
$794$	10.0989	−	22.5407i	0.358396	−	0.799938i
$795$	32.3106	−	35.5067i	1.14594	−	1.25929i
$796$	−8.97428	−	10.0611i	−0.318085	−	0.356605i
$797$	−2.43288	−	1.40462i	−0.0861769	−	0.0497543i	0.456292	−	0.889830i	$-0.349177\pi$
$797$	−2.43288	−	1.40462i	−0.0861769	−	0.0497543i	−0.542469	+	0.840076i	$0.682510\pi$
$798$	8.97349	+	1.01218i	0.317658	+	0.0358309i
$799$	35.0050	+	9.37956i	1.23839	+	0.331825i
$800$	−49.8609	−	51.0392i	−1.76285	−	1.80451i
$801$	9.52495	+	25.6167i	0.336548	+	0.905122i
$802$	−1.25023	−	1.72927i	−0.0441471	−	0.0610626i
$803$	−31.1660	+	17.9937i	−1.09982	+	0.634984i
$804$	−1.11773	−	0.0111084i	−0.0394195	−	0.000391763i
$805$	2.48921	−	4.31144i	0.0877332	−	0.151958i
$806$	−1.64332	−	0.166327i	−0.0578835	−	0.00585862i
$807$	10.3667	+	16.1488i	0.364924	+	0.568466i
$808$	−1.46798	−	32.3452i	−0.0516432	−	1.13790i
$809$		−	34.0664i		−	1.19771i	−0.800857	−	0.598856i	$-0.795622\pi$
$809$		−	34.0664i		−	1.19771i	0.800857	−	0.598856i	$-0.204378\pi$
$810$	−12.3257	+	51.9754i	−0.433081	+	1.82623i
$811$	−3.47880	−	3.47880i	−0.122157	−	0.122157i	0.643385	−	0.765543i	$-0.277529\pi$
$811$	−3.47880	−	3.47880i	−0.122157	−	0.122157i	−0.765543	+	0.643385i	$0.777529\pi$
$812$	−5.73779	+	8.74572i	−0.201357	+	0.306915i
$813$	−7.46841	+	34.2481i	−0.261929	+	1.20113i
$814$	32.2471	+	26.2381i	1.13026	+	0.919644i
$815$	7.33157	+	4.23288i	0.256814	+	0.148271i
$816$	−26.7510	+	13.1417i	−0.936474	+	0.460051i
$817$	5.36707	−	20.0302i	0.187770	−	0.700767i
$818$	−23.0699	−	31.9095i	−0.806622	−	1.11569i
$819$	−7.88633	+	1.21393i	−0.275571	+	0.0424183i
$820$	23.8437	+	7.87060i	0.832657	+	0.274853i
$821$	−3.65531	−	0.979439i	−0.127571	−	0.0341826i	0.194468	−	0.980909i	$-0.437702\pi$
$821$	−3.65531	−	0.979439i	−0.127571	−	0.0341826i	−0.322040	+	0.946726i	$0.604368\pi$
$822$	14.3783	+	18.0343i	0.501500	+	0.629019i
$823$	−42.9361	−	24.7892i	−1.49666	−	0.864096i	−0.496665	−	0.867942i	$-0.665442\pi$
$823$	−42.9361	−	24.7892i	−1.49666	−	0.864096i	−0.999993	+	0.00384634i	$0.998776\pi$
$824$	−6.68667	+	4.27607i	−0.232941	+	0.148964i
$825$	83.5821	−	91.8498i	2.90995	−	3.19780i
$826$	2.64525	+	6.93951i	0.0920400	+	0.241456i
$827$	6.91108	+	6.91108i	0.240322	+	0.240322i	0.816983	−	0.576661i	$-0.195645\pi$
$827$	6.91108	+	6.91108i	0.240322	+	0.240322i	−0.576661	+	0.816983i	$0.695645\pi$
$828$	−9.40596	−	2.14927i	−0.326880	−	0.0746924i
$829$	−5.10376			−0.177261			−0.0886305	−	0.996065i	$-0.528249\pi$
$829$	−5.10376			−0.177261			−0.0886305	+	0.996065i	$0.528249\pi$
$830$	8.28618	+	21.7378i	0.287618	+	0.754532i
$831$	−17.3006	+	33.5167i	−0.600151	+	1.16268i
$832$	−28.6619	−	3.23953i	−0.993673	−	0.112310i
$833$	24.0518	+	13.8863i	0.833345	+	0.481132i
$834$	21.9172	+	50.2515i	0.758929	+	1.74007i
$835$	−47.2625	+	27.2870i	−1.63558	+	0.944305i
$836$	−17.8096	+	53.9535i	−0.615958	+	1.86602i
$837$	0.660229	+	1.54829i	0.0228209	+	0.0535166i
$838$	5.71270	−	35.5313i	0.197342	−	1.22741i
$839$	−27.6553	−	7.41022i	−0.954767	−	0.255829i	−0.252383	−	0.967627i	$-0.581214\pi$
$839$	−27.6553	−	7.41022i	−0.954767	−	0.255829i	−0.702384	+	0.711798i	$0.747881\pi$
$840$	−15.1020	+	1.40012i	−0.521070	+	0.0483087i
$841$	−10.6323	+	18.4157i	−0.366632	+	0.635026i
$842$	−3.35943	−	32.6972i	−0.115774	−	1.12682i
$843$	14.1060	+	44.2046i	0.485835	+	1.52249i
$844$	−33.7345	+	7.00597i	−1.16119	+	0.241155i
$845$	50.6893	−	20.1806i	1.74376	−	0.694235i
$846$	11.4809	−	33.8461i	0.394721	−	1.16365i
$847$	11.1168	−	11.1168i	0.381979	−	0.381979i
$848$	3.00665	−	26.2455i	0.103249	−	0.901273i
$849$	−10.6371	+	0.501303i	−0.365066	+	0.0172047i
$850$	48.4320	−	59.5237i	1.66120	−	2.04165i
$851$	2.15235	+	8.03267i	0.0737815	+	0.275356i
$852$	−5.01499	−	8.88908i	−0.171811	−	0.304535i
$853$	−43.3000	−	11.6022i	−1.48256	−	0.397251i	−0.575344	−	0.817912i	$-0.695132\pi$
$853$	−43.3000	−	11.6022i	−1.48256	−	0.397251i	−0.907218	+	0.420660i	$0.861798\pi$
$854$	−0.0822263	−	0.113732i	−0.00281373	−	0.00389184i
$855$	36.4467	+	51.2922i	1.24645	+	1.75416i
$856$	−4.03719	+	7.78805i	−0.137988	+	0.266190i
$857$	0.831641	+	1.44044i	0.0284083	+	0.0492046i	0.879880	−	0.475196i	$-0.157623\pi$
$857$	0.831641	+	1.44044i	0.0284083	+	0.0492046i	−0.851472	+	0.524401i	$0.824289\pi$
$858$	2.69851	−	50.1305i	0.0921256	−	1.71143i
$859$	−24.7012	−	14.2613i	−0.842796	−	0.486588i	0.0154178	−	0.999881i	$-0.495092\pi$
$859$	−24.7012	−	14.2613i	−0.842796	−	0.486588i	−0.858214	+	0.513293i	$0.828425\pi$
$860$	−1.98519	+	34.7714i	−0.0676944	+	1.18569i
$861$	3.21644	−	2.06478i	0.109616	−	0.0703675i
$862$	−5.42907	−	2.43238i	−0.184915	−	0.0828473i
$863$	−7.09241	−	7.09241i	−0.241429	−	0.241429i	0.576012	−	0.817441i	$-0.304608\pi$
$863$	−7.09241	−	7.09241i	−0.241429	−	0.241429i	−0.817441	+	0.576012i	$0.804608\pi$
$864$	11.2133	+	27.1710i	0.381483	+	0.924376i
$865$	−15.7474	−	15.7474i	−0.535426	−	0.535426i
$866$	−15.9837	−	41.9314i	−0.543149	−	1.42489i
$867$	−1.40979	−	2.19613i	−0.0478790	−	0.0745843i
$868$	−0.356646	+	0.318121i	−0.0121053	+	0.0107977i
$869$	66.5608	−	17.8349i	2.25792	−	0.605008i
$870$	−72.0706	+	10.8539i	−2.44342	+	0.367981i
$871$	0.521766	−	1.03987i	0.0176794	−	0.0352347i
$872$	37.1549	−	11.7852i	1.25822	−	0.399098i
$873$	−11.3347	+	13.6995i	−0.383621	+	0.463659i
$874$	−9.21033	+	6.65889i	−0.311544	+	0.225240i
$875$	20.4125	−	11.7852i	0.690068	−	0.398411i
$876$	10.7762	+	19.1008i	0.364094	+	0.645357i
$877$	−3.59059	+	0.962096i	−0.121246	+	0.0324877i	−0.318932	−	0.947778i	$-0.603324\pi$
$877$	−3.59059	+	0.962096i	−0.121246	+	0.0324877i	0.197686	+	0.980265i	$0.436657\pi$
$878$	−13.1381	+	16.1469i	−0.443389	+	0.544933i
$879$	24.3362	+	22.1456i	0.820839	+	0.746952i
$880$	10.8608	−	94.8055i	0.366118	−	3.19589i
$881$	7.72232			0.260172			0.130086	−	0.991503i	$-0.458475\pi$
$881$	7.72232			0.260172			0.130086	+	0.991503i	$0.458475\pi$
$882$	15.2119	−	22.7771i	0.512212	−	0.766945i
$883$	−22.8901			−0.770313			−0.385157	−	0.922851i	$-0.625853\pi$
$883$	−22.8901			−0.770313			−0.385157	+	0.922851i	$0.625853\pi$
$884$	−0.0469591	−	31.0217i	−0.00157941	−	1.04337i
$885$	−23.7354	+	45.9829i	−0.797855	+	1.54570i
$886$	18.5906	+	15.1264i	0.624564	+	0.508181i
$887$	35.3145	+	20.3888i	1.18575	+	0.684590i	0.957337	−	0.288975i	$-0.0933145\pi$
$887$	35.3145	+	20.3888i	1.18575	+	0.684590i	0.228409	+	0.973565i	$0.426648\pi$
$888$	16.1842	−	19.4917i	0.543105	−	0.654099i
$889$	10.0742	+	2.69937i	0.337877	+	0.0905340i
$890$	−53.3846	−	8.58314i	−1.78946	−	0.287708i
$891$	−46.0626	+	22.2605i	−1.54315	+	0.745753i
$892$	−2.68456	+	1.35209i	−0.0898857	+	0.0452715i
$893$	−21.0502	−	36.4600i	−0.704417	−	1.22009i
$894$	9.02474	−	22.9864i	0.301832	−	0.768779i
$895$	−59.1343	+	15.8450i	−1.97664	+	0.529640i
$896$	−6.29266	+	5.48235i	−0.210223	+	0.183152i
$897$	6.31270	−	7.81018i	0.210775	−	0.260774i
$898$	−5.96116	+	13.3053i	−0.198926	+	0.444002i
$899$	−1.62392	+	1.62392i	−0.0541608	+	0.0541608i
$900$	−55.4649	−	51.4892i	−1.84883	−	1.71631i
$901$	28.4112			0.946516
$902$	8.56557	+	22.4708i	0.285202	+	0.748195i
$903$	3.92110	+	3.56815i	0.130486	+	0.118740i
$904$	−30.4067	+	19.4448i	−1.01131	+	0.646725i
$905$	11.9790	+	44.7062i	0.398195	+	1.48609i
$906$	−42.1172	+	33.5789i	−1.39925	+	1.11559i
$907$	25.5863	+	44.3168i	0.849580	+	1.47152i	0.881583	+	0.472028i	$0.156478\pi$
$907$	25.5863	+	44.3168i	0.849580	+	1.47152i	−0.0320032	+	0.999488i	$0.510189\pi$
$908$	6.04157	−	3.04287i	0.200497	−	0.100981i
$909$	−3.22980	−	34.1904i	−0.107126	−	1.13402i
$910$	5.60046	−	14.7593i	0.185654	−	0.489265i
$911$	14.2776	−	8.24317i	0.473038	−	0.273108i	−0.244473	−	0.969656i	$-0.578615\pi$
$911$	14.2776	−	8.24317i	0.473038	−	0.273108i	0.717510	+	0.696548i	$0.245282\pi$
$912$	32.7701	+	11.1795i	1.08513	+	0.370190i
$913$	−11.1402	+	19.2954i	−0.368688	+	0.638586i
$914$	15.3103	−	1.57303i	0.506420	−	0.0520314i
$915$	0.208351	−	0.955440i	0.00688786	−	0.0315859i
$916$	−37.1940	−	24.4018i	−1.22892	−	0.806258i
$917$	−3.23024	−	3.23024i	−0.106672	−	0.106672i
$918$	−27.6595	+	15.3072i	−0.912901	+	0.505214i
$919$	54.7229			1.80514			0.902571	−	0.430541i	$-0.141677\pi$
$919$	54.7229			1.80514			0.902571	+	0.430541i	$0.141677\pi$
$920$	12.8717	−	14.0956i	0.424368	−	0.464719i
$921$	−18.0937	−	3.94566i	−0.596209	−	0.130014i
$922$	−25.0103	+	2.56965i	−0.823671	+	0.0846269i
$923$	10.6047	−	0.621558i	0.349059	−	0.0204588i
$924$	−10.1687	−	10.3729i	−0.334527	−	0.341243i
$925$	−16.8826	+	63.0068i	−0.555097	+	2.07165i
$926$	−24.6760	+	17.8403i	−0.810905	+	0.586269i
$927$	−6.86245	+	4.87624i	−0.225392	+	0.160157i
$928$	−28.6882	+	28.0260i	−0.941738	+	0.919997i
$929$	8.80390	−	32.8566i	0.288846	−	1.07799i	−0.657136	−	0.753772i	$-0.728232\pi$
$929$	8.80390	−	32.8566i	0.288846	−	1.07799i	0.945982	−	0.324218i	$-0.105101\pi$
$930$	−3.30902	−	0.373248i	−0.108507	−	0.0122393i
$931$	−8.35050	−	31.1645i	−0.273677	−	1.02137i
$932$	−20.6122	+	18.3857i	−0.675173	+	0.602242i
$933$	15.3007	−	0.721087i	0.500923	−	0.0236073i
$934$	1.84346	+	4.83611i	0.0603199	+	0.158242i
$935$	102.629			3.35632
$936$	−30.5320	−	1.94801i	−0.997971	−	0.0636727i
$937$	27.0351			0.883199			0.441600	−	0.897212i	$-0.354411\pi$
$937$	27.0351			0.883199			0.441600	+	0.897212i	$0.354411\pi$
$938$	−0.119903	−	0.314551i	−0.00391496	−	0.0102705i
$939$	1.82031	−	3.52651i	0.0594035	−	0.115083i
$940$	47.0674	+	52.7672i	1.53517	+	1.72108i
$941$	3.46476	+	12.9307i	0.112948	+	0.421528i	0.999125	−	0.0418188i	$-0.0133152\pi$
$941$	3.46476	+	12.9307i	0.112948	+	0.421528i	−0.886177	+	0.463346i	$0.846649\pi$
$942$	10.7061	+	24.5469i	0.348824	+	0.799781i
$943$	−1.24503	+	4.64652i	−0.0405438	+	0.151311i
$944$	4.19158	+	28.1650i	0.136424	+	0.916693i
$945$	−15.9265	+	2.26517i	−0.518090	+	0.0736859i
$946$	−27.0314	+	19.5432i	−0.878866	+	0.635403i
$947$	−5.66472	+	21.1410i	−0.184079	+	0.686991i	0.810747	+	0.585396i	$0.199061\pi$
$947$	−5.66472	+	21.1410i	−0.184079	+	0.686991i	−0.994826	+	0.101595i	$0.967606\pi$
$948$	−10.4651	−	40.6686i	−0.339890	−	1.32086i
$949$	−22.7874	+	1.33560i	−0.739709	+	0.0433555i
$950$	−88.6809	+	9.11139i	−2.87719	+	0.295613i
$951$	−10.9556	−	34.3320i	−0.355259	−	1.11329i
$952$	−6.62813	−	6.05262i	−0.214819	−	0.196166i
$953$	−58.5514			−1.89666			−0.948332	−	0.317279i	$-0.897231\pi$
$953$	−58.5514			−1.89666			−0.948332	+	0.317279i	$0.897231\pi$
$954$	1.82641	−	27.9600i	0.0591322	−	0.905239i
$955$	−32.5154	−	32.5154i	−1.05217	−	1.05217i
$956$	−6.39143	+	9.74201i	−0.206713	+	0.315079i
$957$	−51.6272	−	46.9800i	−1.66887	−	1.51865i
$958$	9.66972	−	0.993501i	0.312414	−	0.0320986i
$959$	−3.47301	+	6.01543i	−0.112149	+	0.194248i
$960$	−57.7065	−	7.19248i	−1.86247	−	0.232136i
$961$	26.7559	−	15.4475i	0.863094	−	0.498308i
$962$	10.8180	+	24.0481i	0.348787	+	0.775342i
$963$	−3.87377	+	8.45965i	−0.124830	+	0.272608i
$964$	−14.1429	−	28.0806i	−0.455513	−	0.904414i
$965$	51.5393	+	89.2687i	1.65911	+	2.87366i
$966$	−0.432715	−	2.87327i	−0.0139224	−	0.0924459i
$967$	−2.32638	−	8.68216i	−0.0748112	−	0.279199i	0.918379	−	0.395701i	$-0.129498\pi$
$967$	−2.32638	−	8.68216i	−0.0748112	−	0.279199i	−0.993190	+	0.116502i	$0.962832\pi$
$968$	50.7839	−	32.4759i	1.63226	−	1.04381i
$969$	−7.93401	+	36.3832i	−0.254877	+	1.16880i
$970$	−12.5297	−	32.8702i	−0.402304	−	1.05540i
$971$	−25.1686			−0.807699			−0.403849	−	0.914826i	$-0.632328\pi$
$971$	−25.1686			−0.807699			−0.403849	+	0.914826i	$0.632328\pi$
$972$	13.2860	+	28.2043i	0.426150	+	0.904653i
$973$	−11.6745	+	11.6745i	−0.374269	+	0.374269i
$974$	−5.61556	+	12.5339i	−0.179934	+	0.401612i
$975$	73.5127	−	28.2963i	2.35429	−	0.906206i
$976$	−0.214267	−	0.493610i	−0.00685851	−	0.0158001i
$977$	−3.86559	+	1.03578i	−0.123671	+	0.0331376i	−0.320124	−	0.947376i	$-0.603725\pi$
$977$	−3.86559	+	1.03578i	−0.123671	+	0.0331376i	0.196453	+	0.980513i	$0.437058\pi$
$978$	4.88597	−	0.735829i	0.156236	−	0.0235292i
$979$	−25.8926	−	44.8472i	−0.827530	−	1.43332i
$980$	24.3751	+	48.3963i	0.778633	+	1.54596i
$981$	38.7516	−	14.4089i	1.23724	−	0.460039i
$982$	60.6446	+	9.75040i	1.93525	+	0.311148i
$983$	−47.7913	−	12.8056i	−1.52431	−	0.408436i	−0.603149	−	0.797629i	$-0.706087\pi$
$983$	−47.7913	−	12.8056i	−1.52431	−	0.408436i	−0.921156	+	0.389192i	$0.872754\pi$
$984$	13.7450	−	5.08357i	0.438176	−	0.162058i
$985$	17.8216	+	10.2893i	0.567844	+	0.327845i
$986$	−33.4573	−	27.2228i	−1.06550	−	0.866950i
$987$	10.7515	−	0.506691i	0.342223	−	0.0161281i
$988$	−25.4444	+	25.5216i	−0.809494	+	0.811949i
$989$	−6.67238			−0.212169
$990$	6.59746	−	100.999i	0.209681	−	3.20995i
$991$	−11.2136			−0.356211			−0.178106	−	0.984011i	$-0.556997\pi$
$991$	−11.2136			−0.356211			−0.178106	+	0.984011i	$0.556997\pi$
$992$	−1.59751	+	0.897614i	−0.0507209	+	0.0284993i
$993$	−41.9357	+	13.3820i	−1.33079	+	0.424663i
$994$	1.93988	−	2.38415i	0.0615293	−	0.0756206i
$995$	27.3267	−	7.32217i	0.866315	−	0.232128i
$996$	11.6907	+	6.90545i	0.370435	+	0.218808i
$997$	50.7728	−	29.3137i	1.60799	−	0.928375i	0.618173	−	0.786042i	$-0.287873\pi$
$997$	50.7728	−	29.3137i	1.60799	−	0.928375i	0.989819	−	0.142333i	$-0.0454604\pi$
$998$	22.2074	−	16.0555i	0.702964	−	0.508229i
$999$	16.1363	−	21.4873i	0.510529	−	0.679829i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.em.a.5.17	✓	656
8.5	even	2	inner	936.2.em.a.5.119	yes	656
9.2	odd	6	inner	936.2.em.a.317.39	yes	656
13.8	odd	4	inner	936.2.em.a.437.66	yes	656
72.29	odd	6	inner	936.2.em.a.317.66	yes	656
104.21	odd	4	inner	936.2.em.a.437.39	yes	656
117.47	even	12	inner	936.2.em.a.749.119	yes	656
936.749	even	12	inner	936.2.em.a.749.17	yes	656

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.em.a.5.17	✓	656	1.1	even	1	trivial
936.2.em.a.5.119	yes	656	8.5	even	2	inner
936.2.em.a.317.39	yes	656	9.2	odd	6	inner
936.2.em.a.317.66	yes	656	72.29	odd	6	inner
936.2.em.a.437.39	yes	656	104.21	odd	4	inner
936.2.em.a.437.66	yes	656	13.8	odd	4	inner
936.2.em.a.749.17	yes	656	936.749	even	12	inner
936.2.em.a.749.119	yes	656	117.47	even	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.em (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32146 + 0.503724i) q^{2} +(-0.935678 - 1.45757i) q^{3} +(1.49252 - 1.33130i) q^{4} +(1.08622 + 4.05383i) q^{5} +(1.97068 + 1.45480i) q^{6} +(-0.190925 + 0.712543i) q^{7} +(-1.30170 + 2.51109i) q^{8} +(-1.24901 + 2.72763i) q^{9} +(-3.47741 - 4.80982i) q^{10} +(1.47123 - 5.49069i) q^{11} +(-3.33699 - 0.929784i) q^{12} +(2.39597 - 2.69432i) q^{13} +(-0.106624 - 1.03777i) q^{14} +(4.89238 - 5.37632i) q^{15} +(0.455258 - 3.97401i) q^{16} +4.30194 q^{17} +(0.276549 - 4.23362i) q^{18} +(-3.53386 - 3.53386i) q^{19} +(7.01808 + 4.60434i) q^{20} +(1.21722 - 0.388424i) q^{21} +(0.821623 + 7.99684i) q^{22} +(-0.804032 + 1.39263i) q^{23} +(4.87806 - 0.452248i) q^{24} +(-10.9235 + 6.30669i) q^{25} +(-1.80899 + 4.76734i) q^{26} +(5.14438 - 0.731664i) q^{27} +(0.663650 + 1.31767i) q^{28} +(3.54488 + 6.13991i) q^{29} +(-3.75691 + 9.56900i) q^{30} +(0.0838387 + 0.312890i) q^{31} +(1.40020 + 5.48083i) q^{32} +(-9.37966 + 2.99311i) q^{33} +(-5.68485 + 2.16699i) q^{34} -3.09591 q^{35} +(1.76713 + 5.73387i) q^{36} +(3.65677 - 3.65677i) q^{37} +(6.44995 + 2.88977i) q^{38} +(-6.16901 - 0.971273i) q^{39} +(-11.5935 - 2.54929i) q^{40} +(2.88951 - 0.774241i) q^{41} +(-1.41286 + 1.12643i) q^{42} +(2.07466 + 3.59342i) q^{43} +(-5.11394 - 10.1536i) q^{44} +(-12.4140 - 2.10047i) q^{45} +(0.361000 - 2.24531i) q^{46} +(8.13702 + 2.18031i) q^{47} +(-6.21836 + 3.05482i) q^{48} +(5.59091 + 3.22792i) q^{49} +(11.2582 - 13.8365i) q^{50} +(-4.02523 - 6.27038i) q^{51} +(-0.0109158 - 7.21109i) q^{52} +6.60428 q^{53} +(-6.42955 + 3.55822i) q^{54} +23.8564 q^{55} +(-1.54073 - 1.40695i) q^{56} +(-1.84429 + 8.45739i) q^{57} +(-7.77724 - 6.32802i) q^{58} +(-6.87623 + 1.84248i) q^{59} +(0.144479 - 14.5375i) q^{60} +(0.116504 - 0.0672635i) q^{61} +(-0.268400 - 0.371241i) q^{62} +(-1.70508 - 1.41075i) q^{63} +(-4.61113 - 6.53739i) q^{64} +(13.5248 + 6.78621i) q^{65} +(10.8872 - 8.68004i) q^{66} +(0.311683 - 0.0835153i) q^{67} +(6.42075 - 5.72719i) q^{68} +(2.78216 - 0.131117i) q^{69} +(4.09113 - 1.55948i) q^{70} +(2.08333 + 2.08333i) q^{71} +(-5.22348 - 6.68695i) q^{72} +(-4.47664 - 4.47664i) q^{73} +(-2.99028 + 6.67428i) q^{74} +(19.4133 + 10.0207i) q^{75} +(-9.97901 - 0.569728i) q^{76} +(3.63146 + 2.09662i) q^{77} +(8.64136 - 1.82398i) q^{78} +(6.06124 + 10.4984i) q^{79} +(16.6044 - 2.47111i) q^{80} +(-5.87994 - 6.81369i) q^{81} +(-3.42837 + 2.47864i) q^{82} +(-3.78603 - 1.01446i) q^{83} +(1.29963 - 2.20023i) q^{84} +(4.67285 + 17.4393i) q^{85} +(-4.55168 - 3.70351i) q^{86} +(5.63247 - 10.9119i) q^{87} +(11.8725 + 10.8416i) q^{88} +(6.44179 - 6.44179i) q^{89} +(17.4627 - 3.47756i) q^{90} +(1.46236 + 2.22164i) q^{91} +(0.653970 + 3.14894i) q^{92} +(0.377613 - 0.414966i) q^{93} +(-11.8510 + 1.21762i) q^{94} +(10.4871 - 18.1642i) q^{95} +(6.67854 - 7.16917i) q^{96} +(5.72493 + 1.53399i) q^{97} +(-9.01416 - 1.44929i) q^{98} +(13.1390 + 10.8709i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 656 q - 6 q^{2} + 6 q^{6} - 4 q^{7} - 16 q^{9} - 12 q^{14} + 4 q^{15} - 4 q^{16} - 2 q^{18} - 6 q^{20} - 4 q^{22} - 32 q^{24} - 24 q^{28} - 4 q^{31} - 6 q^{32} + 4 q^{33} - 6 q^{34} - 20 q^{39} - 4 q^{40}+ \cdots - 4 q^{97}+O(q^{100}) \) 656 * q - 6 * q^2 + 6 * q^6 - 4 * q^7 - 16 * q^9 - 12 * q^14 + 4 * q^15 - 4 * q^16 - 2 * q^18 - 6 * q^20 - 4 * q^22 - 32 * q^24 - 24 * q^28 - 4 * q^31 - 6 * q^32 + 4 * q^33 - 6 * q^34 - 20 * q^39 - 4 * q^40 - 12 * q^41 - 16 * q^42 - 12 * q^47 - 40 * q^48 + 42 * q^50 - 4 * q^52 - 42 * q^54 - 32 * q^55 + 16 * q^57 - 12 * q^58 + 36 * q^60 + 20 * q^63 - 12 * q^65 + 52 * q^66 - 60 * q^68 + 28 * q^70 - 54 * q^72 - 16 * q^73 + 156 * q^74 - 10 * q^76 + 28 * q^78 - 8 * q^79 - 16 * q^81 + 14 * q^84 + 102 * q^86 - 88 * q^87 - 72 * q^92 - 28 * q^94 + 32 * q^96 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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