LMFDB - Embedded newform 105.2.j.a.92.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(8,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("105.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			92.10
Character	$\chi$	$=$	105.92
Dual form			105.2.j.a.8.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24414 - 1.24414i) q^{2} +(0.474620 - 1.66575i) q^{3} -1.09578i q^{4} +(-1.67522 + 1.48109i) q^{5} +(-1.48194 - 2.66293i) q^{6} +(0.707107 + 0.707107i) q^{7} +(1.12498 + 1.12498i) q^{8} +(-2.54947 - 1.58120i) q^{9} +O(q^{10})$	\(q+(1.24414 - 1.24414i) q^{2} +(0.474620 - 1.66575i) q^{3} -1.09578i q^{4} +(-1.67522 + 1.48109i) q^{5} +(-1.48194 - 2.66293i) q^{6} +(0.707107 + 0.707107i) q^{7} +(1.12498 + 1.12498i) q^{8} +(-2.54947 - 1.58120i) q^{9} +(-0.241524 + 3.92690i) q^{10} -1.55221i q^{11} +(-1.82530 - 0.520079i) q^{12} +(-4.50889 + 4.50889i) q^{13} +1.75948 q^{14} +(1.67204 + 3.49346i) q^{15} +4.99083 q^{16} +(2.13370 - 2.13370i) q^{17} +(-5.13914 + 1.20467i) q^{18} -4.20993i q^{19} +(1.62295 + 1.83567i) q^{20} +(1.51347 - 0.842259i) q^{21} +(-1.93117 - 1.93117i) q^{22} +(3.76050 + 3.76050i) q^{23} +(2.40787 - 1.34000i) q^{24} +(0.612732 - 4.96231i) q^{25} +11.2194i q^{26} +(-3.84392 + 3.49632i) q^{27} +(0.774834 - 0.774834i) q^{28} -2.97115 q^{29} +(6.42662 + 2.26611i) q^{30} -5.79770 q^{31} +(3.95934 - 3.95934i) q^{32} +(-2.58559 - 0.736708i) q^{33} -5.30926i q^{34} +(-2.23185 - 0.137270i) q^{35} +(-1.73265 + 2.79366i) q^{36} +(-1.23123 - 1.23123i) q^{37} +(-5.23775 - 5.23775i) q^{38} +(5.37069 + 9.65070i) q^{39} +(-3.55078 - 0.218391i) q^{40} -2.68458i q^{41} +(0.835085 - 2.93087i) q^{42} +(-2.09578 + 2.09578i) q^{43} -1.70088 q^{44} +(6.61283 - 1.12714i) q^{45} +9.35721 q^{46} +(0.0358428 - 0.0358428i) q^{47} +(2.36874 - 8.31349i) q^{48} +1.00000i q^{49} +(-5.41150 - 6.93615i) q^{50} +(-2.54153 - 4.56692i) q^{51} +(4.94075 + 4.94075i) q^{52} +(-4.30833 - 4.30833i) q^{53} +(-0.432457 + 9.13231i) q^{54} +(2.29896 + 2.60029i) q^{55} +1.59096i q^{56} +(-7.01270 - 1.99811i) q^{57} +(-3.69653 + 3.69653i) q^{58} +4.93760 q^{59} +(3.82807 - 1.83219i) q^{60} +3.31687 q^{61} +(-7.21316 + 7.21316i) q^{62} +(-0.684672 - 2.92083i) q^{63} +0.129684i q^{64} +(0.875305 - 14.2315i) q^{65} +(-4.13342 + 2.30028i) q^{66} +(1.71008 + 1.71008i) q^{67} +(-2.33807 - 2.33807i) q^{68} +(8.04889 - 4.47927i) q^{69} +(-2.94752 + 2.60596i) q^{70} -5.73577i q^{71} +(-1.08929 - 4.64692i) q^{72} +(7.26776 - 7.26776i) q^{73} -3.06366 q^{74} +(-7.97518 - 3.37587i) q^{75} -4.61315 q^{76} +(1.09758 - 1.09758i) q^{77} +(18.6887 + 5.32495i) q^{78} -3.59379i q^{79} +(-8.36074 + 7.39187i) q^{80} +(3.99962 + 8.06245i) q^{81} +(-3.34000 - 3.34000i) q^{82} +(12.2139 + 12.2139i) q^{83} +(-0.922931 - 1.65843i) q^{84} +(-0.414214 + 6.73463i) q^{85} +5.21490i q^{86} +(-1.41016 + 4.94920i) q^{87} +(1.74620 - 1.74620i) q^{88} +1.35643 q^{89} +(6.82498 - 9.62963i) q^{90} -6.37653 q^{91} +(4.12069 - 4.12069i) q^{92} +(-2.75170 + 9.65754i) q^{93} -0.0891871i q^{94} +(6.23529 + 7.05256i) q^{95} +(-4.71611 - 8.47447i) q^{96} +(10.9812 + 10.9812i) q^{97} +(1.24414 + 1.24414i) q^{98} +(-2.45435 + 3.95731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3}+O(q^{10}) $ 24 * q - 4 * q^3	$ 24 q - 4 q^{3} - 16 q^{10} + 16 q^{12} - 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 4 q^{21} + 8 q^{22} - 16 q^{25} - 16 q^{27} + 20 q^{30} + 28 q^{33} + 16 q^{36} - 16 q^{37} + 64 q^{40} - 20 q^{42} - 40 q^{43} + 20 q^{45} - 64 q^{46} + 16 q^{48} - 20 q^{51} + 40 q^{55} + 4 q^{57} + 40 q^{58} + 32 q^{60} + 32 q^{61} - 8 q^{63} - 16 q^{66} + 24 q^{67} - 8 q^{70} - 8 q^{72} + 32 q^{73} - 60 q^{75} + 32 q^{76} + 60 q^{78} + 52 q^{81} - 80 q^{82} + 24 q^{85} + 4 q^{87} + 96 q^{88} - 24 q^{90} - 24 q^{91} - 76 q^{93} - 96 q^{96} + 24 q^{97}+O(q^{100}) $ 24 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 - 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 4 * q^21 + 8 * q^22 - 16 * q^25 - 16 * q^27 + 20 * q^30 + 28 * q^33 + 16 * q^36 - 16 * q^37 + 64 * q^40 - 20 * q^42 - 40 * q^43 + 20 * q^45 - 64 * q^46 + 16 * q^48 - 20 * q^51 + 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 + 32 * q^61 - 8 * q^63 - 16 * q^66 + 24 * q^67 - 8 * q^70 - 8 * q^72 + 32 * q^73 - 60 * q^75 + 32 * q^76 + 60 * q^78 + 52 * q^81 - 80 * q^82 + 24 * q^85 + 4 * q^87 + 96 * q^88 - 24 * q^90 - 24 * q^91 - 76 * q^93 - 96 * q^96 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	1.24414	−	1.24414i	0.879741	−	0.879741i	−0.113766	−	0.993508i	$-0.536291\pi$
$2$	1.24414	−	1.24414i	0.879741	−	0.879741i	0.993508	+	0.113766i	$0.0362914\pi$
$3$	0.474620	−	1.66575i	0.274022	−	0.961723i
$3$	0.474620	−	1.66575i	0.274022	−	0.961723i
$4$		−	1.09578i		−	0.547890i
$5$	−1.67522	+	1.48109i	−0.749182	+	0.662365i
$5$	−1.67522	+	1.48109i	−0.749182	+	0.662365i
$6$	−1.48194	−	2.66293i	−0.605000	−	1.08714i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	1.12498	+	1.12498i	0.397740	+	0.397740i
$9$	−2.54947	−	1.58120i	−0.849824	−	0.527067i
$10$	−0.241524	+	3.92690i	−0.0763766	+	1.24180i
$11$		−	1.55221i		−	0.468008i	−0.972236	−	0.234004i	$-0.924817\pi$
$11$		−	1.55221i		−	0.468008i	0.972236	−	0.234004i	$-0.0751828\pi$
$12$	−1.82530	−	0.520079i	−0.526919	−	0.150134i
$13$	−4.50889	+	4.50889i	−1.25054	+	1.25054i	−0.295062	+	0.955478i	$0.595340\pi$
$13$	−4.50889	+	4.50889i	−1.25054	+	1.25054i	−0.955478	+	0.295062i	$0.904660\pi$
$14$	1.75948			0.470242
$15$	1.67204	+	3.49346i	0.431719	+	0.902008i
$16$	4.99083			1.24771
$17$	2.13370	−	2.13370i	0.517499	−	0.517499i	−0.399315	−	0.916814i	$-0.630752\pi$
$17$	2.13370	−	2.13370i	0.517499	−	0.517499i	0.916814	+	0.399315i	$0.130752\pi$
$18$	−5.13914	+	1.20467i	−1.21131	+	0.283943i
$19$		−	4.20993i		−	0.965823i	−0.875669	−	0.482912i	$-0.839579\pi$
$19$		−	4.20993i		−	0.965823i	0.875669	−	0.482912i	$-0.160421\pi$
$20$	1.62295	+	1.83567i	0.362903	+	0.410469i
$21$	1.51347	−	0.842259i	0.330267	−	0.183796i
$22$	−1.93117	−	1.93117i	−0.411726	−	0.411726i
$23$	3.76050	+	3.76050i	0.784119	+	0.784119i	0.980523	−	0.196404i	$-0.0629263\pi$
$23$	3.76050	+	3.76050i	0.784119	+	0.784119i	−0.196404	+	0.980523i	$0.562926\pi$
$24$	2.40787	−	1.34000i	0.491505	−	0.273526i
$25$	0.612732	−	4.96231i	0.122546	−	0.992463i
$26$			11.2194i			2.20030i
$27$	−3.84392	+	3.49632i	−0.739763	+	0.672868i
$28$	0.774834	−	0.774834i	0.146430	−	0.146430i
$29$	−2.97115			−0.551728			−0.275864	−	0.961197i	$-0.588964\pi$
$29$	−2.97115			−0.551728			−0.275864	+	0.961197i	$0.588964\pi$
$30$	6.42662	+	2.26611i	1.17334	+	0.413732i
$31$	−5.79770			−1.04130			−0.520649	−	0.853771i	$-0.674310\pi$
$31$	−5.79770			−1.04130			−0.520649	+	0.853771i	$0.674310\pi$
$32$	3.95934	−	3.95934i	0.699919	−	0.699919i
$33$	−2.58559	−	0.736708i	−0.450094	−	0.128244i
$34$		−	5.30926i		−	0.910531i
$35$	−2.23185	−	0.137270i	−0.377252	−	0.0232029i
$36$	−1.73265	+	2.79366i	−0.288775	+	0.465610i
$37$	−1.23123	−	1.23123i	−0.202414	−	0.202414i	0.598620	−	0.801033i	$-0.295716\pi$
$37$	−1.23123	−	1.23123i	−0.202414	−	0.202414i	−0.801033	+	0.598620i	$0.795716\pi$
$38$	−5.23775	−	5.23775i	−0.849675	−	0.849675i
$39$	5.37069	+	9.65070i	0.859998	+	1.54535i
$40$	−3.55078	−	0.218391i	−0.561428	−	0.0345306i
$41$		−	2.68458i		−	0.419261i	−0.977781	−	0.209631i	$-0.932774\pi$
$41$		−	2.68458i		−	0.419261i	0.977781	−	0.209631i	$-0.0672261\pi$
$42$	0.835085	−	2.93087i	0.128856	−	0.452242i
$43$	−2.09578	+	2.09578i	−0.319603	+	0.319603i	−0.848615	−	0.529011i	$-0.822563\pi$
$43$	−2.09578	+	2.09578i	−0.319603	+	0.319603i	0.529011	+	0.848615i	$0.322563\pi$
$44$	−1.70088			−0.256417
$45$	6.61283	−	1.12714i	0.985783	−	0.168025i
$46$	9.35721			1.37964
$47$	0.0358428	−	0.0358428i	0.00522821	−	0.00522821i	−0.704488	−	0.709716i	$-0.748823\pi$
$47$	0.0358428	−	0.0358428i	0.00522821	−	0.00522821i	0.709716	+	0.704488i	$0.248823\pi$
$48$	2.36874	−	8.31349i	0.341899	−	1.19995i
$49$			1.00000i			0.142857i
$50$	−5.41150	−	6.93615i	−0.765302	−	0.980920i
$51$	−2.54153	−	4.56692i	−0.355885	−	0.639497i
$52$	4.94075	+	4.94075i	0.685158	+	0.685158i
$53$	−4.30833	−	4.30833i	−0.591794	−	0.591794i	0.346322	−	0.938116i	$-0.387431\pi$
$53$	−4.30833	−	4.30833i	−0.591794	−	0.591794i	−0.938116	+	0.346322i	$0.887431\pi$
$54$	−0.432457	+	9.13231i	−0.0588500	+	1.24275i
$55$	2.29896	+	2.60029i	0.309992	+	0.350623i
$56$			1.59096i			0.212601i
$57$	−7.01270	−	1.99811i	−0.928855	−	0.264657i
$58$	−3.69653	+	3.69653i	−0.485378	+	0.485378i
$59$	4.93760			0.642821			0.321410	−	0.946940i	$-0.395843\pi$
$59$	4.93760			0.642821			0.321410	+	0.946940i	$0.395843\pi$
$60$	3.82807	−	1.83219i	0.494201	−	0.236535i
$61$	3.31687			0.424681			0.212341	−	0.977196i	$-0.431891\pi$
$61$	3.31687			0.424681			0.212341	+	0.977196i	$0.431891\pi$
$62$	−7.21316	+	7.21316i	−0.916073	+	0.916073i
$63$	−0.684672	−	2.92083i	−0.0862606	−	0.367989i
$64$			0.129684i			0.0162105i
$65$	0.875305	−	14.2315i	0.108568	−	1.76519i
$66$	−4.13342	+	2.30028i	−0.508788	+	0.283145i
$67$	1.71008	+	1.71008i	0.208919	+	0.208919i	0.803808	−	0.594889i	$-0.202804\pi$
$67$	1.71008	+	1.71008i	0.208919	+	0.208919i	−0.594889	+	0.803808i	$0.702804\pi$
$68$	−2.33807	−	2.33807i	−0.283533	−	0.283533i
$69$	8.04889	−	4.47927i	0.968972	−	0.539240i
$70$	−2.94752	+	2.60596i	−0.352296	+	0.311471i
$71$		−	5.73577i		−	0.680711i	−0.940297	−	0.340356i	$-0.889453\pi$
$71$		−	5.73577i		−	0.680711i	0.940297	−	0.340356i	$-0.110547\pi$
$72$	−1.08929	−	4.64692i	−0.128374	−	0.547644i
$73$	7.26776	−	7.26776i	0.850627	−	0.850627i	−0.139583	−	0.990210i	$-0.544576\pi$
$73$	7.26776	−	7.26776i	0.850627	−	0.850627i	0.990210	+	0.139583i	$0.0445763\pi$
$74$	−3.06366			−0.356143
$75$	−7.97518	−	3.37587i	−0.920894	−	0.389812i
$76$	−4.61315			−0.529165
$77$	1.09758	−	1.09758i	0.125080	−	0.125080i
$78$	18.6887	+	5.32495i	2.11608	+	0.602931i
$79$		−	3.59379i		−	0.404333i	−0.979351	−	0.202166i	$-0.935202\pi$
$79$		−	3.59379i		−	0.404333i	0.979351	−	0.202166i	$-0.0647982\pi$
$80$	−8.36074	+	7.39187i	−0.934759	+	0.826437i
$81$	3.99962	+	8.06245i	0.444402	+	0.895828i
$82$	−3.34000	−	3.34000i	−0.368841	−	0.368841i
$83$	12.2139	+	12.2139i	1.34065	+	1.34065i	0.895417	+	0.445228i	$0.146877\pi$
$83$	12.2139	+	12.2139i	1.34065	+	1.34065i	0.445228	+	0.895417i	$0.353123\pi$
$84$	−0.922931	−	1.65843i	−0.100700	−	0.180950i
$85$	−0.414214	+	6.73463i	−0.0449278	+	0.730474i
$86$			5.21490i			0.562337i
$87$	−1.41016	+	4.94920i	−0.151185	+	0.530610i
$88$	1.74620	−	1.74620i	0.186145	−	0.186145i
$89$	1.35643			0.143782			0.0718908	−	0.997413i	$-0.477097\pi$
$89$	1.35643			0.143782			0.0718908	+	0.997413i	$0.477097\pi$
$90$	6.82498	−	9.62963i	0.719416	−	1.01505i
$91$	−6.37653			−0.668442
$92$	4.12069	−	4.12069i	0.429611	−	0.429611i
$93$	−2.75170	+	9.65754i	−0.285338	+	1.00144i
$94$		−	0.0891871i		−	0.00919895i
$95$	6.23529	+	7.05256i	0.639727	+	0.723577i
$96$	−4.71611	−	8.47447i	−0.481336	−	0.864922i
$97$	10.9812	+	10.9812i	1.11497	+	1.11497i	0.992468	+	0.122503i	$0.0390922\pi$
$97$	10.9812	+	10.9812i	1.11497	+	1.11497i	0.122503	+	0.992468i	$0.460908\pi$
$98$	1.24414	+	1.24414i	0.125677	+	0.125677i
$99$	−2.45435	+	3.95731i	−0.246671	+	0.397724i
$100$	−5.43760	−	0.671419i	−0.543760	−	0.0671419i
$101$		−	12.7033i		−	1.26402i	−0.774958	−	0.632012i	$-0.782229\pi$
$101$		−	12.7033i		−	1.26402i	0.774958	−	0.632012i	$-0.217771\pi$
$102$	−8.84392	−	2.51988i	−0.875679	−	0.249505i
$103$	−1.46798	+	1.46798i	−0.144644	+	0.144644i	−0.775721	−	0.631076i	$-0.782613\pi$
$103$	−1.46798	+	1.46798i	−0.144644	+	0.144644i	0.631076	+	0.775721i	$0.282613\pi$
$104$	−10.1448			−0.994779
$105$	−1.28794	+	3.65256i	−0.125690	+	0.356454i
$106$	−10.7203			−1.04125
$107$	−13.5523	+	13.5523i	−1.31015	+	1.31015i	−0.388849	+	0.921302i	$0.627127\pi$
$107$	−13.5523	+	13.5523i	−1.31015	+	1.31015i	−0.921302	+	0.388849i	$0.872873\pi$
$108$	3.83120	+	4.21209i	0.368658	+	0.405309i
$109$			4.84158i			0.463739i	0.972747	+	0.231869i	$0.0744842\pi$
$109$			4.84158i			0.463739i	−0.972747	+	0.231869i	$0.925516\pi$
$110$	6.09536	+	0.374895i	0.581170	+	0.0357449i
$111$	−2.63530	+	1.46656i	−0.250132	+	0.139200i
$112$	3.52905	+	3.52905i	0.333464	+	0.333464i
$113$	−10.6222	−	10.6222i	−0.999254	−	0.999254i	0.000746132	−	1.00000i	$-0.499762\pi$
$113$	−10.6222	−	10.6222i	−0.999254	−	0.999254i	−1.00000		0.000746132i	$0.999762\pi$
$114$	−11.2107	+	6.23886i	−1.04998	+	0.584323i
$115$	−11.8693	−	0.730023i	−1.10682	−	0.0680750i
$116$			3.25572i			0.302286i
$117$	18.6247	−	4.36583i	1.72186	−	0.403621i
$118$	6.14308	−	6.14308i	0.565516	−	0.565516i
$119$	3.01751			0.276615
$120$	−2.04906	+	5.81108i	−0.187053	+	0.530477i
$121$	8.59066			0.780969
$122$	4.12665	−	4.12665i	0.373610	−	0.373610i
$123$	−4.47185	−	1.27415i	−0.403213	−	0.114887i
$124$			6.35300i			0.570517i
$125$	6.32318	+	9.22049i	0.565563	+	0.824705i
$126$	−4.48575	−	2.78209i	−0.399623	−	0.247849i
$127$	10.1595	+	10.1595i	0.901511	+	0.901511i	0.995567	−	0.0940560i	$-0.0299833\pi$
$127$	10.1595	+	10.1595i	0.901511	+	0.901511i	−0.0940560	+	0.995567i	$0.529983\pi$
$128$	8.08003	+	8.08003i	0.714180	+	0.714180i
$129$	2.49636	+	4.48575i	0.219792	+	0.394948i
$130$	−16.6170	−	18.7950i	−1.45740	−	1.64843i
$131$			0.509374i			0.0445042i	0.999752	+	0.0222521i	$0.00708365\pi$
$131$			0.509374i			0.0445042i	−0.999752	+	0.0222521i	$0.992916\pi$
$132$	−0.807270	+	2.83324i	−0.0702638	+	0.246602i
$133$	2.97687	−	2.97687i	0.258127	−	0.258127i
$134$	4.25516			0.367590
$135$	1.26104	−	11.5503i	0.108533	−	0.994093i
$136$	4.80074			0.411660
$137$	−2.61947	+	2.61947i	−0.223797	+	0.223797i	−0.810095	−	0.586298i	$-0.800585\pi$
$137$	−2.61947	+	2.61947i	−0.223797	+	0.223797i	0.586298	+	0.810095i	$0.300585\pi$
$138$	4.44112	−	15.5868i	0.378053	−	1.32684i
$139$		−	6.35379i		−	0.538921i	−0.963011	−	0.269461i	$-0.913155\pi$
$139$		−	6.35379i		−	0.538921i	0.963011	−	0.269461i	$-0.0868454\pi$
$140$	−0.150418	+	2.44562i	−0.0127126	+	0.206692i
$141$	−0.0426936	−	0.0767170i	−0.00359545	−	0.00646074i
$142$	−7.13612	−	7.13612i	−0.598850	−	0.598850i
$143$	6.99872	+	6.99872i	0.585262	+	0.585262i
$144$	−12.7240	−	7.89149i	−1.06033	−	0.657624i
$145$	4.97733	−	4.40054i	0.413344	−	0.365445i
$146$		−	18.0843i		−	1.49666i
$147$	1.66575	+	0.474620i	0.137389	+	0.0391460i
$148$	−1.34916	+	1.34916i	−0.110900	+	0.110900i
$149$	−4.27965			−0.350602			−0.175301	−	0.984515i	$-0.556090\pi$
$149$	−4.27965			−0.350602			−0.175301	+	0.984515i	$0.556090\pi$
$150$	−14.1223	+	5.72219i	−1.15308	+	0.467215i
$151$	−5.21232			−0.424172			−0.212086	−	0.977251i	$-0.568026\pi$
$151$	−5.21232			−0.424172			−0.212086	+	0.977251i	$0.568026\pi$
$152$	4.73607	−	4.73607i	0.384146	−	0.384146i
$153$	−8.81363	+	2.06601i	−0.712539	+	0.167027i
$154$		−	2.73108i		−	0.220077i
$155$	9.71243	−	8.58693i	0.780121	−	0.689719i
$156$	10.5750	−	5.88509i	0.846681	−	0.471185i
$157$	−4.35999	−	4.35999i	−0.347965	−	0.347965i	0.511386	−	0.859351i	$-0.329132\pi$
$157$	−4.35999	−	4.35999i	−0.347965	−	0.347965i	−0.859351	+	0.511386i	$0.829132\pi$
$158$	−4.47119	−	4.47119i	−0.355708	−	0.355708i
$159$	−9.22143	+	5.13179i	−0.731307	+	0.406978i
$160$	−0.768623	+	12.4969i	−0.0607650	+	0.987968i
$161$			5.31816i			0.419129i
$162$	15.0069	+	5.05474i	1.17906	+	0.397138i
$163$	5.34339	−	5.34339i	0.418527	−	0.418527i	−0.466169	−	0.884696i	$-0.654366\pi$
$163$	5.34339	−	5.34339i	0.418527	−	0.418527i	0.884696	+	0.466169i	$0.154366\pi$
$164$	−2.94171			−0.229709
$165$	5.42257	−	2.59535i	0.422147	−	0.202048i
$166$	30.3916			2.35884
$167$	13.8232	−	13.8232i	1.06967	−	1.06967i	0.0722908	−	0.997384i	$-0.476969\pi$
$167$	13.8232	−	13.8232i	1.06967	−	1.06967i	0.997384	−	0.0722908i	$-0.0230310\pi$
$168$	2.65015	+	0.755101i	0.204463	+	0.0582573i
$169$		−	27.6601i		−	2.12770i
$170$	7.86350	+	8.89418i	0.603103	+	0.682153i
$171$	−6.65673	+	10.7331i	−0.509053	+	0.820780i
$172$	2.29651	+	2.29651i	0.175108	+	0.175108i
$173$	−2.06635	−	2.06635i	−0.157102	−	0.157102i	0.624179	−	0.781281i	$-0.285433\pi$
$173$	−2.06635	−	2.06635i	−0.157102	−	0.157102i	−0.781281	+	0.624179i	$0.785433\pi$
$174$	4.40306	+	7.91195i	0.333795	+	0.599803i
$175$	3.94215	−	3.07562i	0.297999	−	0.232495i
$176$		−	7.74679i		−	0.583936i
$177$	2.34348	−	8.22483i	0.176147	−	0.618216i
$178$	1.68759	−	1.68759i	0.126491	−	0.126491i
$179$	−11.9186			−0.890841			−0.445420	−	0.895322i	$-0.646946\pi$
$179$	−11.9186			−0.890841			−0.445420	+	0.895322i	$0.646946\pi$
$180$	−1.23510	−	7.24621i	−0.0920591	−	0.540101i
$181$	−17.5945			−1.30779			−0.653893	−	0.756587i	$-0.726865\pi$
$181$	−17.5945			−1.30779			−0.653893	+	0.756587i	$0.726865\pi$
$182$	−7.93331	+	7.93331i	−0.588056	+	0.588056i
$183$	1.57425	−	5.52508i	0.116372	−	0.408426i
$184$			8.46097i			0.623751i
$185$	3.88616	+	0.239018i	0.285716	+	0.0175730i
$186$	8.59184	+	15.4389i	0.629985	+	1.13203i
$187$	−3.31195	−	3.31195i	−0.242194	−	0.242194i
$188$	−0.0392758	−	0.0392758i	−0.00286449	−	0.00286449i
$189$	−5.19034	−	0.245787i	−0.377541	−	0.0178783i
$190$	16.5320	+	1.01680i	1.19936	+	0.0737663i
$191$			5.54023i			0.400877i	0.979706	+	0.200438i	$0.0642366\pi$
$191$			5.54023i			0.400877i	−0.979706	+	0.200438i	$0.935763\pi$
$192$	0.216021	+	0.0615505i	0.0155900	+	0.00444202i
$193$	−13.9027	+	13.9027i	−1.00074	+	1.00074i	−0.000740397		1.00000i	$0.500236\pi$
$193$	−13.9027	+	13.9027i	−1.00074	+	1.00074i	−1.00000		0.000740397i	$0.999764\pi$
$194$	27.3243			1.96177
$195$	−23.2907	−	8.21257i	−1.66788	−	0.588115i
$196$	1.09578			0.0782700
$197$	−12.7155	+	12.7155i	−0.905939	+	0.905939i	−0.995942	−	0.0900024i	$-0.971313\pi$
$197$	−12.7155	+	12.7155i	−0.905939	+	0.905939i	0.0900024	+	0.995942i	$0.471313\pi$
$198$	1.86989	+	7.97701i	0.132888	+	0.566901i
$199$			6.11487i			0.433472i	0.976230	+	0.216736i	$0.0695411\pi$
$199$			6.11487i			0.433472i	−0.976230	+	0.216736i	$0.930459\pi$
$200$	6.27181	−	4.89318i	0.443484	−	0.346000i
$201$	3.66021	−	2.03693i	0.258171	−	0.143674i
$202$	−15.8047	−	15.8047i	−1.11201	−	1.11201i
$203$	−2.10092	−	2.10092i	−0.147455	−	0.147455i
$204$	−5.00434	+	2.78495i	−0.350374	+	0.194986i
$205$	3.97611	+	4.49727i	0.277704	+	0.314103i
$206$			3.65275i			0.254499i
$207$	−3.64119	−	15.5334i	−0.253080	−	1.07965i
$208$	−22.5031	+	22.5031i	−1.56031	+	1.56031i
$209$	−6.53467			−0.452013
$210$	2.94193	+	6.14669i	0.203012	+	0.424162i
$211$	12.4900			0.859849			0.429924	−	0.902865i	$-0.358540\pi$
$211$	12.4900			0.859849			0.429924	+	0.902865i	$0.358540\pi$
$212$	−4.72098	+	4.72098i	−0.324238	+	0.324238i
$213$	−9.55439	−	2.72231i	−0.654656	−	0.186530i
$214$			33.7220i			2.30519i
$215$	0.406852	−	6.61494i	0.0277471	−	0.451135i
$216$	−8.25761	−	0.391036i	−0.561859	−	0.0266067i
$217$	−4.09959	−	4.09959i	−0.278298	−	0.278298i
$218$	6.02361	+	6.02361i	0.407970	+	0.407970i
$219$	−8.65688	−	15.5557i	−0.584978	−	1.05116i
$220$	2.84934	−	2.51916i	0.192103	−	0.169841i
$221$			19.2412i			1.29431i
$222$	−1.45407	+	5.10330i	−0.0975910	+	0.342511i
$223$	8.80424	−	8.80424i	0.589576	−	0.589576i	−0.347941	−	0.937516i	$-0.613119\pi$
$223$	8.80424	−	8.80424i	0.589576	−	0.589576i	0.937516	+	0.347941i	$0.113119\pi$
$224$	5.59935			0.374123
$225$	−9.40855	+	11.6824i	−0.627237	+	0.778829i
$226$	−26.4311			−1.75817
$227$	−15.7424	+	15.7424i	−1.04486	+	1.04486i	−0.0459126	+	0.998945i	$0.514620\pi$
$227$	−15.7424	+	15.7424i	−1.04486	+	1.04486i	−0.998945	+	0.0459126i	$0.985380\pi$
$228$	−2.18949	+	7.68438i	−0.145003	+	0.508910i
$229$			8.27446i			0.546791i	0.961902	+	0.273396i	$0.0881468\pi$
$229$			8.27446i			0.546791i	−0.961902	+	0.273396i	$0.911853\pi$
$230$	−15.6754	+	13.8589i	−1.03360	+	0.913828i
$231$	−1.30736	−	2.34922i	−0.0860179	−	0.154567i
$232$	−3.34247	−	3.34247i	−0.219444	−	0.219444i
$233$	−12.6425	−	12.6425i	−0.828239	−	0.828239i	0.159034	−	0.987273i	$-0.449162\pi$
$233$	−12.6425	−	12.6425i	−0.828239	−	0.828239i	−0.987273	+	0.159034i	$0.949162\pi$
$234$	17.7401	−	28.6035i	1.15971	−	1.86987i
$235$	−0.00695813	+	0.113131i	−0.000453898	+	0.00737986i
$236$		−	5.41052i		−	0.352195i
$237$	−5.98637	−	1.70568i	−0.388856	−	0.110796i
$238$	3.75421	−	3.75421i	0.243350	−	0.243350i
$239$	25.8260			1.67054			0.835271	−	0.549838i	$-0.185311\pi$
$239$	25.8260			1.67054			0.835271	+	0.549838i	$0.185311\pi$
$240$	8.34487	+	17.4353i	0.538659	+	1.12544i
$241$	−10.5197			−0.677631			−0.338815	−	0.940853i	$-0.610026\pi$
$241$	−10.5197			−0.677631			−0.338815	+	0.940853i	$0.610026\pi$
$242$	10.6880	−	10.6880i	0.687051	−	0.687051i
$243$	15.3284	−	2.83578i	0.983314	−	0.181915i
$244$		−	3.63456i		−	0.232679i
$245$	−1.48109	−	1.67522i	−0.0946235	−	0.107026i
$246$	−7.14885	+	3.97839i	−0.455794	+	0.253653i
$247$	18.9821	+	18.9821i	1.20780	+	1.20780i
$248$	−6.52229	−	6.52229i	−0.414166	−	0.414166i
$249$	26.1422	−	14.5483i	1.65670	−	0.921964i
$250$	19.3385	+	3.60466i	1.22308	+	0.227979i
$251$			6.94563i			0.438405i	0.975679	+	0.219202i	$0.0703455\pi$
$251$			6.94563i			0.438405i	−0.975679	+	0.219202i	$0.929655\pi$
$252$	−3.20058	+	0.750250i	−0.201618	+	0.0472613i
$253$	5.83708	−	5.83708i	0.366974	−	0.366974i
$254$	25.2798			1.58619
$255$	11.0216	+	3.88637i	0.690202	+	0.243374i
$256$	19.8460			1.24038
$257$	−8.17057	+	8.17057i	−0.509666	+	0.509666i	−0.914424	−	0.404758i	$-0.867356\pi$
$257$	−8.17057	+	8.17057i	−0.509666	+	0.509666i	0.404758	+	0.914424i	$0.367356\pi$
$258$	8.68674	+	2.47509i	0.540813	+	0.154093i
$259$		−	1.74123i		−	0.108195i
$260$	−15.5945	−	0.959142i	−0.967133	−	0.0594835i
$261$	7.57485	+	4.69797i	0.468872	+	0.290797i
$262$	0.633733	+	0.633733i	0.0391522	+	0.0391522i
$263$	−0.118860	−	0.118860i	−0.00732922	−	0.00732922i	0.703433	−	0.710762i	$-0.251650\pi$
$263$	−0.118860	−	0.118860i	−0.00732922	−	0.00732922i	−0.710762	+	0.703433i	$0.751650\pi$
$264$	−2.07996	−	3.73752i	−0.128012	−	0.230028i
$265$	13.5984	+	0.836371i	0.835345	+	0.0513779i
$266$		−	7.40729i		−	0.454170i
$267$	0.643790	−	2.25948i	0.0393993	−	0.138278i
$268$	1.87387	−	1.87387i	0.114465	−	0.114465i
$269$	−6.60330			−0.402610			−0.201305	−	0.979529i	$-0.564518\pi$
$269$	−6.60330			−0.402610			−0.201305	+	0.979529i	$0.564518\pi$
$270$	−12.8013	−	15.9391i	−0.779064	−	0.970025i
$271$	−23.8292			−1.44752			−0.723759	−	0.690052i	$-0.757587\pi$
$271$	−23.8292			−1.44752			−0.723759	+	0.690052i	$0.757587\pi$
$272$	10.6489	−	10.6489i	0.645687	−	0.645687i
$273$	−3.02643	+	10.6217i	−0.183168	+	0.642856i
$274$			6.51800i			0.393767i
$275$	−7.70253	−	0.951086i	−0.464480	−	0.0573527i
$276$	−4.90829	−	8.81981i	−0.295444	−	0.530890i
$277$	−14.3921	−	14.3921i	−0.864736	−	0.864736i	0.127147	−	0.991884i	$-0.459418\pi$
$277$	−14.3921	−	14.3921i	−0.864736	−	0.864736i	−0.991884	+	0.127147i	$0.959418\pi$
$278$	−7.90501	−	7.90501i	−0.474111	−	0.474111i
$279$	14.7811	+	9.16732i	0.884920	+	0.548833i
$280$	−2.35636	−	2.66521i	−0.140819	−	0.159277i
$281$		−	1.50698i		−	0.0898991i	−0.998989	−	0.0449495i	$-0.985687\pi$
$281$		−	1.50698i		−	0.0898991i	0.998989	−	0.0449495i	$-0.0143127\pi$
$282$	−0.148564	−	0.0423300i	−0.00884685	−	0.00252071i
$283$	8.49114	−	8.49114i	0.504746	−	0.504746i	−0.408163	−	0.912909i	$-0.633830\pi$
$283$	8.49114	−	8.49114i	0.504746	−	0.504746i	0.912909	+	0.408163i	$0.133830\pi$
$284$	−6.28515			−0.372955
$285$	14.7072	−	7.03917i	0.871180	−	0.416965i
$286$	17.4148			1.02976
$287$	1.89828	−	1.89828i	0.112052	−	0.112052i
$288$	−16.3547	+	3.83372i	−0.963712	+	0.225904i
$289$			7.89463i			0.464390i
$290$	0.717603	−	11.6674i	0.0421391	−	0.685133i
$291$	23.5039	−	13.0801i	1.37782	−	0.766768i
$292$	−7.96387	−	7.96387i	−0.466050	−	0.466050i
$293$	2.35851	+	2.35851i	0.137786	+	0.137786i	0.772635	−	0.634850i	$-0.218938\pi$
$293$	2.35851	+	2.35851i	0.137786	+	0.137786i	−0.634850	+	0.772635i	$0.718938\pi$
$294$	2.66293	−	1.48194i	0.155305	−	0.0864285i
$295$	−8.27157	+	7.31304i	−0.481590	+	0.425782i
$296$		−	2.77022i		−	0.161016i
$297$	5.42702	+	5.96656i	0.314907	+	0.346215i
$298$	−5.32449	+	5.32449i	−0.308439	+	0.308439i
$299$	−33.9114			−1.96115
$300$	−3.69921	+	8.73904i	−0.213574	+	0.504549i
$301$	−2.96388			−0.170835
$302$	−6.48486	+	6.48486i	−0.373162	+	0.373162i
$303$	−21.1606	−	6.02923i	−1.21564	−	0.346370i
$304$		−	21.0110i		−	1.20506i
$305$	−5.55649	+	4.91259i	−0.318163	+	0.281294i
$306$	−8.39500	+	13.5358i	−0.479910	+	0.773791i
$307$	−0.793602	−	0.793602i	−0.0452933	−	0.0452933i	0.684097	−	0.729391i	$-0.260196\pi$
$307$	−0.793602	−	0.793602i	−0.0452933	−	0.0452933i	−0.729391	+	0.684097i	$0.760196\pi$
$308$	−1.20270	−	1.20270i	−0.0685303	−	0.0685303i
$309$	1.74856	+	3.14203i	0.0994722	+	0.178744i
$310$	1.40028	−	22.7670i	0.0795308	−	1.29308i
$311$		−	9.91521i		−	0.562240i	−0.959673	−	0.281120i	$-0.909294\pi$
$311$		−	9.91521i		−	0.562240i	0.959673	−	0.281120i	$-0.0907059\pi$
$312$	−4.81492	+	16.8987i	−0.272591	+	0.956702i
$313$	−9.95137	+	9.95137i	−0.562484	+	0.562484i	−0.930012	−	0.367528i	$-0.880204\pi$
$313$	−9.95137	+	9.95137i	−0.562484	+	0.562484i	0.367528	+	0.930012i	$0.380204\pi$
$314$	−10.8489			−0.612238
$315$	5.47299	+	3.87897i	0.308368	+	0.218555i
$316$	−3.93800			−0.221530
$317$	14.9788	−	14.9788i	0.841296	−	0.841296i	−0.147732	−	0.989027i	$-0.547197\pi$
$317$	14.9788	−	14.9788i	0.841296	−	0.841296i	0.989027	+	0.147732i	$0.0471972\pi$
$318$	−5.08809	+	17.8574i	−0.285326	+	1.00140i
$319$			4.61183i			0.258213i
$320$	−0.192074	−	0.217249i	−0.0107372	−	0.0121446i
$321$	16.1426	+	29.0070i	0.900992	+	1.61901i
$322$	6.61654	+	6.61654i	0.368726	+	0.368726i
$323$	−8.98273	−	8.98273i	−0.499812	−	0.499812i
$324$	8.83467	−	4.38270i	0.490815	−	0.243483i
$325$	19.6118	+	25.1372i	1.08787	+	1.39436i
$326$		−	13.2959i		−	0.736391i
$327$	8.06487	+	2.29791i	0.445989	+	0.127075i
$328$	3.02009	−	3.02009i	0.166757	−	0.166757i
$329$	0.0506894			0.00279460
$330$	3.51746	−	9.97544i	0.193630	−	0.549130i
$331$	−3.10247			−0.170527			−0.0852635	−	0.996358i	$-0.527173\pi$
$331$	−3.10247			−0.170527			−0.0852635	+	0.996358i	$0.527173\pi$
$332$	13.3837	−	13.3837i	0.734526	−	0.734526i
$333$	1.19217	+	5.08582i	0.0653305	+	0.278701i
$334$		−	34.3962i		−	1.88207i
$335$	−5.39754	−	0.331976i	−0.294899	−	0.0181378i
$336$	7.55348	−	4.20357i	0.412076	−	0.229323i
$337$	−23.2030	−	23.2030i	−1.26395	−	1.26395i	−0.949163	−	0.314784i	$-0.898068\pi$
$337$	−23.2030	−	23.2030i	−1.26395	−	1.26395i	−0.314784	−	0.949163i	$-0.601932\pi$
$338$	−34.4131	−	34.4131i	−1.87183	−	1.87183i
$339$	−22.7355	+	12.6525i	−1.23482	+	0.687188i
$340$	7.37968	+	0.453887i	0.400219	+	0.0246155i
$341$			8.99922i			0.487335i
$342$	5.07157	+	21.6354i	0.274239	+	1.16991i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−4.71541			−0.254238
$345$	−6.84946	+	19.4249i	−0.368762	+	1.04580i
$346$	−5.14167			−0.276418
$347$	14.1837	−	14.1837i	0.761423	−	0.761423i	−0.215157	−	0.976580i	$-0.569026\pi$
$347$	14.1837	−	14.1837i	0.761423	−	0.761423i	0.976580	+	0.215157i	$0.0690262\pi$
$348$	5.42323	+	1.54523i	0.290716	+	0.0828330i
$349$		−	9.27152i		−	0.496293i	−0.968723	−	0.248146i	$-0.920179\pi$
$349$		−	9.27152i		−	0.496293i	0.968723	−	0.248146i	$-0.0798214\pi$
$350$	1.07809	−	8.73111i	0.0576264	−	0.466697i
$351$	1.56726	−	33.0963i	0.0836544	−	1.76655i
$352$	−6.14571	−	6.14571i	−0.327568	−	0.327568i
$353$	20.2421	+	20.2421i	1.07738	+	1.07738i	0.996744	+	0.0806368i	$0.0256954\pi$
$353$	20.2421	+	20.2421i	1.07738	+	1.07738i	0.0806368	+	0.996744i	$0.474305\pi$
$354$	−7.31723	−	13.1485i	−0.388906	−	0.698834i
$355$	8.49521	+	9.60869i	0.450879	+	0.509976i
$356$		−	1.48635i		−	0.0787765i
$357$	1.43217	−	5.02643i	0.0757985	−	0.266027i
$358$	−14.8285	+	14.8285i	−0.783710	+	0.783710i
$359$	18.8289			0.993751			0.496876	−	0.867822i	$-0.334481\pi$
$359$	18.8289			0.993751			0.496876	+	0.867822i	$0.334481\pi$
$360$	8.70730	+	6.17128i	0.458915	+	0.325255i
$361$	1.27653			0.0671857
$362$	−21.8900	+	21.8900i	−1.15051	+	1.15051i
$363$	4.07730	−	14.3099i	0.214003	−	0.751076i
$364$			6.98727i			0.366233i
$365$	−1.41088	+	22.9393i	−0.0738490	+	1.20070i
$366$	−4.91540	−	8.83258i	−0.256932	−	0.461686i
$367$	0.942012	+	0.942012i	0.0491726	+	0.0491726i	0.731266	−	0.682093i	$-0.238930\pi$
$367$	0.942012	+	0.942012i	0.0491726	+	0.0491726i	−0.682093	+	0.731266i	$0.738930\pi$
$368$	18.7680	+	18.7680i	0.978351	+	0.978351i
$369$	−4.24486	+	6.84426i	−0.220978	+	0.356298i
$370$	5.13231	−	4.53756i	0.266816	−	0.235897i
$371$		−	6.09289i		−	0.316327i
$372$	10.5825	+	3.01526i	0.548679	+	0.156334i
$373$	7.39940	−	7.39940i	0.383127	−	0.383127i	−0.489101	−	0.872227i	$-0.662675\pi$
$373$	7.39940	−	7.39940i	0.383127	−	0.383127i	0.872227	+	0.489101i	$0.162675\pi$
$374$	−8.24107			−0.426135
$375$	18.3602	−	6.15664i	0.948115	−	0.317928i
$376$	0.0806448			0.00415894
$377$	13.3966	−	13.3966i	0.689958	−	0.689958i
$378$	−6.76331	+	6.15172i	−0.347867	+	0.316411i
$379$			21.9486i			1.12743i	0.825971	+	0.563713i	$0.190627\pi$
$379$			21.9486i			1.12743i	−0.825971	+	0.563713i	$0.809373\pi$
$380$	7.72805	−	6.83250i	0.396441	−	0.350500i
$381$	21.7452	−	12.1013i	1.11404	−	0.619970i
$382$	6.89283	+	6.89283i	0.352668	+	0.352668i
$383$	19.3310	+	19.3310i	0.987768	+	0.987768i	0.999926	−	0.0121580i	$-0.00387012\pi$
$383$	19.3310	+	19.3310i	0.987768	+	0.987768i	−0.0121580	+	0.999926i	$0.503870\pi$
$384$	17.2943	−	9.62440i	0.882545	−	0.491143i
$385$	−0.213071	+	3.46429i	−0.0108591	+	0.176557i
$386$			34.5939i			1.76079i
$387$	8.65698	−	2.02929i	0.440059	−	0.103154i
$388$	12.0330	−	12.0330i	0.610882	−	0.610882i
$389$	−30.7961			−1.56142			−0.780712	−	0.624891i	$-0.785144\pi$
$389$	−30.7961			−1.56142			−0.780712	+	0.624891i	$0.785144\pi$
$390$	−39.1945	+	18.7593i	−1.98469	+	0.949914i
$391$	16.0476			0.811562
$392$	−1.12498	+	1.12498i	−0.0568200	+	0.0568200i
$393$	0.848491	+	0.241759i	0.0428007	+	0.0121951i
$394$			31.6397i			1.59398i
$395$	5.32273	+	6.02039i	0.267816	+	0.302919i
$396$	4.33634	+	2.68943i	0.217909	+	0.135149i
$397$	−20.8254	−	20.8254i	−1.04520	−	1.04520i	−0.998929	−	0.0462702i	$-0.985266\pi$
$397$	−20.8254	−	20.8254i	−1.04520	−	1.04520i	−0.0462702	−	0.998929i	$-0.514734\pi$
$398$	7.60777	+	7.60777i	0.381343	+	0.381343i
$399$	−3.54585	−	6.37161i	−0.177514	−	0.318979i
$400$	3.05804	−	24.7660i	0.152902	−	1.23830i
$401$			20.9084i			1.04412i	0.852910	+	0.522058i	$0.174835\pi$
$401$			20.9084i			1.04412i	−0.852910	+	0.522058i	$0.825165\pi$
$402$	2.01958	−	7.08805i	0.100728	−	0.353520i
$403$	26.1412	−	26.1412i	1.30218	−	1.30218i
$404$	−13.9200			−0.692547
$405$	−18.6415	−	7.58258i	−0.926302	−	0.376782i
$406$	−5.22768			−0.259445
$407$	−1.91113	+	1.91113i	−0.0947311	+	0.0947311i
$408$	2.27853	−	7.99685i	0.112804	−	0.395903i
$409$			11.5773i			0.572460i	0.958161	+	0.286230i	$0.0924022\pi$
$409$			11.5773i			0.572460i	−0.958161	+	0.286230i	$0.907598\pi$
$410$	10.5421	+	0.648391i	0.520637	+	0.0320217i
$411$	3.12014	+	5.60665i	0.153905	+	0.276556i
$412$	1.60858	+	1.60858i	0.0792493	+	0.0792493i
$413$	3.49141	+	3.49141i	0.171801	+	0.171801i
$414$	−23.8559	−	14.7956i	−1.17246	−	0.727165i
$415$	−38.5508	−	2.37106i	−1.89238	−	0.116391i
$416$			35.7044i			1.75055i
$417$	−10.5838	−	3.01563i	−0.518293	−	0.147676i
$418$	−8.13006	+	8.13006i	−0.397654	+	0.397654i
$419$	0.525515			0.0256731			0.0128365	−	0.999918i	$-0.495914\pi$
$419$	0.525515			0.0256731			0.0128365	+	0.999918i	$0.495914\pi$
$420$	4.00241	+	1.41130i	0.195297	+	0.0688643i
$421$	−15.5297			−0.756871			−0.378435	−	0.925628i	$-0.623538\pi$
$421$	−15.5297			−0.756871			−0.378435	+	0.925628i	$0.623538\pi$
$422$	15.5394	−	15.5394i	0.756445	−	0.756445i
$423$	−0.148055	+	0.0347056i	−0.00719868	+	0.00168744i
$424$		−	9.69354i		−	0.470760i
$425$	−9.28071	−	11.8955i	−0.450181	−	0.577016i
$426$	−15.2740	+	8.50008i	−0.740026	+	0.411830i
$427$	2.34538	+	2.34538i	0.113501	+	0.113501i
$428$	14.8503	+	14.8503i	0.717818	+	0.717818i
$429$	14.9799	−	8.33641i	0.723235	−	0.402486i
$430$	−7.72374	−	8.73611i	−0.372472	−	0.421292i
$431$		−	23.0144i		−	1.10856i	−0.832329	−	0.554282i	$-0.812993\pi$
$431$		−	23.0144i		−	1.10856i	0.832329	−	0.554282i	$-0.187007\pi$
$432$	−19.1843	+	17.4495i	−0.923007	+	0.839542i
$433$	−15.4001	+	15.4001i	−0.740081	+	0.740081i	−0.972593	−	0.232513i	$-0.925305\pi$
$433$	−15.4001	+	15.4001i	−0.740081	+	0.740081i	0.232513	+	0.972593i	$0.425305\pi$
$434$	−10.2010			−0.489661
$435$	−4.96788	−	10.3796i	−0.238192	−	0.497663i
$436$	5.30530			0.254078
$437$	15.8314	−	15.8314i	0.757321	−	0.757321i
$438$	−30.1239	−	8.58315i	−1.43938	−	0.410119i
$439$		−	6.04288i		−	0.288411i	−0.989548	−	0.144205i	$-0.953937\pi$
$439$		−	6.04288i		−	0.288411i	0.989548	−	0.144205i	$-0.0460626\pi$
$440$	−0.338988	+	5.51155i	−0.0161606	+	0.262753i
$441$	1.58120	−	2.54947i	0.0752952	−	0.121403i
$442$	23.9388	+	23.9388i	1.13865	+	1.13865i
$443$	8.64725	+	8.64725i	0.410843	+	0.410843i	0.882032	−	0.471189i	$-0.156175\pi$
$443$	8.64725	+	8.64725i	0.410843	+	0.410843i	−0.471189	+	0.882032i	$0.656175\pi$
$444$	1.60703	+	2.88771i	0.0762664	+	0.137045i
$445$	−2.27232	+	2.00900i	−0.107718	+	0.0952358i
$446$		−	21.9075i		−	1.03735i
$447$	−2.03121	+	7.12884i	−0.0960727	+	0.337183i
$448$	−0.0917003	+	0.0917003i	−0.00433243	+	0.00433243i
$449$	20.7599			0.979723			0.489861	−	0.871800i	$-0.337047\pi$
$449$	20.7599			0.979723			0.489861	+	0.871800i	$0.337047\pi$
$450$	2.82903	+	26.2402i	0.133362	+	1.23697i
$451$	−4.16702			−0.196217
$452$	−11.6396	+	11.6396i	−0.547481	+	0.547481i
$453$	−2.47387	+	8.68243i	−0.116232	+	0.407936i
$454$			39.1715i			1.83841i
$455$	10.6821	−	9.44422i	0.500784	−	0.442752i
$456$	−5.64130	−	10.1370i	−0.264178	−	0.474707i
$457$	17.3075	+	17.3075i	0.809612	+	0.809612i	0.984575	−	0.174963i	$-0.0559805\pi$
$457$	17.3075	+	17.3075i	0.809612	+	0.809612i	−0.174963	+	0.984575i	$0.555980\pi$
$458$	10.2946	+	10.2946i	0.481035	+	0.481035i
$459$	−0.741664	+	15.6619i	−0.0346179	+	0.731035i
$460$	−0.799945	+	13.0062i	−0.0372976	+	0.606416i
$461$		−	4.36421i		−	0.203262i	−0.994822	−	0.101631i	$-0.967594\pi$
$461$		−	4.36421i		−	0.203262i	0.994822	−	0.101631i	$-0.0324061\pi$
$462$	−4.54931	−	1.29622i	−0.211653	−	0.0603058i
$463$	2.04147	−	2.04147i	0.0948752	−	0.0948752i	−0.658076	−	0.752951i	$-0.728630\pi$
$463$	2.04147	−	2.04147i	0.0948752	−	0.0948752i	0.752951	+	0.658076i	$0.228630\pi$
$464$	−14.8285			−0.688394
$465$	−9.69400	−	20.2540i	−0.449548	−	0.939259i
$466$	−31.4582			−1.45727
$467$	13.9629	−	13.9629i	0.646128	−	0.646128i	−0.305927	−	0.952055i	$-0.598966\pi$
$467$	13.9629	−	13.9629i	0.646128	−	0.646128i	0.952055	+	0.305927i	$0.0989663\pi$
$468$	−4.78399	−	20.4086i	−0.221140	−	0.943388i
$469$			2.41842i			0.111672i
$470$	0.132094	+	0.149408i	0.00609306	+	0.00689169i
$471$	−9.33200	+	5.19333i	−0.429996	+	0.239296i
$472$	5.55469	+	5.55469i	0.255675	+	0.255675i
$473$	3.25308	+	3.25308i	0.149577	+	0.149577i
$474$	−9.57001	+	5.32578i	−0.439565	+	0.244621i
$475$	−20.8910	−	2.57956i	−0.958544	−	0.118358i
$476$		−	3.30653i		−	0.151555i
$477$	4.17163	+	17.7963i	0.191006	+	0.814836i
$478$	32.1312	−	32.1312i	1.46965	−	1.46965i
$479$	−16.0067			−0.731367			−0.365683	−	0.930739i	$-0.619165\pi$
$479$	−16.0067			−0.731367			−0.365683	+	0.930739i	$0.619165\pi$
$480$	20.4520	+	7.21162i	0.933502	+	0.329164i
$481$	11.1030			0.506252
$482$	−13.0880	+	13.0880i	−0.596140	+	0.596140i
$483$	8.85874	+	2.52410i	0.403087	+	0.114851i
$484$		−	9.41347i		−	0.427885i
$485$	−34.6601	−	2.13177i	−1.57383	−	0.0967986i
$486$	15.5425	−	22.5988i	0.705024	−	1.02510i
$487$	20.6096	+	20.6096i	0.933908	+	0.933908i	0.997947	−	0.0640391i	$-0.0203982\pi$
$487$	20.6096	+	20.6096i	0.933908	+	0.933908i	−0.0640391	+	0.997947i	$0.520398\pi$
$488$	3.73140	+	3.73140i	0.168913	+	0.168913i
$489$	−6.36470	−	11.4369i	−0.287822	−	0.517192i
$490$	−3.92690	−	0.241524i	−0.177399	−	0.0109109i
$491$			29.8846i			1.34867i	0.738423	+	0.674337i	$0.235571\pi$
$491$			29.8846i			1.34867i	−0.738423	+	0.674337i	$0.764429\pi$
$492$	−1.39619	+	4.90016i	−0.0629453	+	0.220916i
$493$	−6.33954	+	6.33954i	−0.285519	+	0.285519i
$494$	47.2328			2.12510
$495$	−1.74956	−	10.2645i	−0.0786369	−	0.461354i
$496$	−28.9353			−1.29923
$497$	4.05581	−	4.05581i	0.181928	−	0.181928i
$498$	14.4244	−	50.6249i	0.646374	−	2.26855i
$499$		−	0.940603i		−	0.0421072i	−0.999778	−	0.0210536i	$-0.993298\pi$
$499$		−	0.940603i		−	0.0421072i	0.999778	−	0.0210536i	$-0.00670206\pi$
$500$	10.1036	−	6.92882i	0.451848	−	0.309866i
$501$	−16.4653	−	29.5869i	−0.735617	−	1.32185i
$502$	8.64136	+	8.64136i	0.385683	+	0.385683i
$503$	−23.0051	−	23.0051i	−1.02575	−	1.02575i	−0.999660	−	0.0260875i	$-0.991695\pi$
$503$	−23.0051	−	23.0051i	−1.02575	−	1.02575i	−0.0260875	−	0.999660i	$-0.508305\pi$
$504$	2.51562	−	4.05611i	0.112055	−	0.180673i
$505$	18.8147	+	21.2808i	0.837245	+	0.946984i
$506$		−	14.5243i		−	0.645685i
$507$	−46.0749	−	13.1280i	−2.04626	−	0.583036i
$508$	11.1326	−	11.1326i	0.493929	−	0.493929i
$509$	25.8128			1.14413			0.572066	−	0.820208i	$-0.306142\pi$
$509$	25.8128			1.14413			0.572066	+	0.820208i	$0.306142\pi$
$510$	18.5477	−	8.87730i	0.821306	−	0.393094i
$511$	10.2782			0.454679
$512$	8.53124	−	8.53124i	0.377031	−	0.377031i
$513$	14.7193	+	16.1826i	0.649871	+	0.714480i
$514$			20.3307i			0.896749i
$515$	0.284978	−	4.63341i	0.0125576	−	0.204172i
$516$	4.91540	−	2.73546i	0.216388	−	0.120422i
$517$	−0.0556354	−	0.0556354i	−0.00244684	−	0.00244684i
$518$	−2.16633	−	2.16633i	−0.0951833	−	0.0951833i
$519$	−4.42276	+	2.46130i	−0.194138	+	0.108039i
$520$	16.9948	−	15.0254i	0.745270	−	0.658906i
$521$		−	44.1826i		−	1.93568i	−0.251572	−	0.967838i	$-0.580948\pi$
$521$		−	44.1826i		−	1.93568i	0.251572	−	0.967838i	$-0.419052\pi$
$522$	15.2691	−	3.57925i	0.668312	−	0.156659i
$523$	13.0685	−	13.0685i	0.571447	−	0.571447i	−0.361086	−	0.932533i	$-0.617594\pi$
$523$	13.0685	−	13.0685i	0.571447	−	0.571447i	0.932533	+	0.361086i	$0.117594\pi$
$524$	0.558162			0.0243834
$525$	−3.25220	−	8.02641i	−0.141938	−	0.350301i
$526$	−0.295757			−0.0128956
$527$	−12.3706	+	12.3706i	−0.538870	+	0.538870i
$528$	−12.9042	−	3.67678i	−0.561585	−	0.160011i
$529$			5.28280i			0.229687i
$530$	17.9589	−	15.8778i	0.780087	−	0.689688i
$531$	−12.5883	−	7.80733i	−0.546285	−	0.338809i
$532$	−3.26199	−	3.26199i	−0.141425	−	0.141425i
$533$	12.1045	+	12.1045i	0.524303	+	0.524303i
$534$	−2.01015	−	3.61208i	−0.0869878	−	0.156310i
$535$	2.63089	−	42.7753i	0.113743	−	1.84934i
$536$			3.84760i			0.166191i
$537$	−5.65682	+	19.8535i	−0.244110	+	0.856743i
$538$	−8.21544	+	8.21544i	−0.354193	+	0.354193i
$539$	1.55221			0.0668583
$540$	−12.6566	−	1.38182i	−0.544654	−	0.0594640i
$541$	21.5590			0.926893			0.463446	−	0.886125i	$-0.346613\pi$
$541$	21.5590			0.926893			0.463446	+	0.886125i	$0.346613\pi$
$542$	−29.6469	+	29.6469i	−1.27344	+	1.27344i
$543$	−8.35068	+	29.3080i	−0.358362	+	1.25773i
$544$		−	16.8961i		−	0.724415i
$545$	−7.17082	−	8.11071i	−0.307164	−	0.347425i
$546$	9.44963	+	16.9802i	0.404407	+	0.726687i
$547$	−29.6665	−	29.6665i	−1.26845	−	1.26845i	−0.946891	−	0.321555i	$-0.895795\pi$
$547$	−29.6665	−	29.6665i	−1.26845	−	1.26845i	−0.321555	−	0.946891i	$-0.604205\pi$
$548$	2.87037	+	2.87037i	0.122616	+	0.122616i
$549$	−8.45626	−	5.24463i	−0.360904	−	0.223835i
$550$	−10.7663	+	8.39976i	−0.459078	+	0.358167i
$551$			12.5083i			0.532872i
$552$	14.0939	+	4.01574i	0.599876	+	0.170921i
$553$	2.54119	−	2.54119i	0.108063	−	0.108063i
$554$	−35.8116			−1.52149
$555$	2.24259	−	6.35994i	0.0951928	−	0.269965i
$556$	−6.96235			−0.295269
$557$	−19.2396	+	19.2396i	−0.815208	+	0.815208i	−0.985409	−	0.170201i	$-0.945558\pi$
$557$	−19.2396	+	19.2396i	−0.815208	+	0.815208i	0.170201	+	0.985409i	$0.445558\pi$
$558$	29.7952	−	6.98431i	1.26133	−	0.295669i
$559$		−	18.8993i		−	0.799354i
$560$	−11.1388	−	0.685090i	−0.470699	−	0.0289504i
$561$	−7.08880	+	3.94497i	−0.299290	+	0.166557i
$562$	−1.87490	−	1.87490i	−0.0790880	−	0.0790880i
$563$	2.03574	+	2.03574i	0.0857962	+	0.0857962i	0.748702	−	0.662906i	$-0.230677\pi$
$563$	2.03574	+	2.03574i	0.0857962	+	0.0857962i	−0.662906	+	0.748702i	$0.730677\pi$
$564$	−0.0840650	+	0.0467828i	−0.00353977	+	0.00196991i
$565$	33.5270	+	2.06208i	1.41049	+	0.0867523i
$566$		−	21.1284i		−	0.888092i
$567$	−2.87286	+	8.52917i	−0.120649	+	0.358191i
$568$	6.45262	−	6.45262i	0.270746	−	0.270746i
$569$	36.6125			1.53487			0.767437	−	0.641124i	$-0.221532\pi$
$569$	36.6125			1.53487			0.767437	+	0.641124i	$0.221532\pi$
$570$	9.54014	−	27.0556i	0.399592	−	1.13323i
$571$	−9.88863			−0.413826			−0.206913	−	0.978359i	$-0.566342\pi$
$571$	−9.88863			−0.413826			−0.206913	+	0.978359i	$0.566342\pi$
$572$	7.66906	−	7.66906i	0.320659	−	0.320659i
$573$	9.22865	+	2.62950i	0.385533	+	0.109849i
$574$		−	4.72347i		−	0.197154i
$575$	20.9650	−	16.3566i	0.874300	−	0.682118i
$576$	0.205056	−	0.330625i	0.00854400	−	0.0137760i
$577$	3.44953	+	3.44953i	0.143606	+	0.143606i	0.775255	−	0.631649i	$-0.217622\pi$
$577$	3.44953	+	3.44953i	0.143606	+	0.143606i	−0.631649	+	0.775255i	$0.717622\pi$
$578$	9.82204	+	9.82204i	0.408543	+	0.408543i
$579$	16.5600	+	29.7570i	0.688211	+	1.23666i
$580$	−4.82202	−	5.45405i	−0.200224	−	0.226467i
$581$			17.2730i			0.716605i
$582$	12.9687	−	45.5156i	0.537569	−	1.88668i
$583$	−6.68741	+	6.68741i	−0.276964	+	0.276964i
$584$	16.3521			0.676657
$585$	−24.7343	+	34.8987i	−1.02264	+	1.44288i
$586$	5.86864			0.242431
$587$	4.70846	−	4.70846i	0.194339	−	0.194339i	−0.603229	−	0.797568i	$-0.706120\pi$
$587$	4.70846	−	4.70846i	0.194339	−	0.194339i	0.797568	+	0.603229i	$0.206120\pi$
$588$	0.520079	−	1.82530i	0.0214477	−	0.0752741i
$589$			24.4079i			1.00571i
$590$	−1.19255	+	19.3895i	−0.0490965	+	0.798252i
$591$	15.1458	+	27.2158i	0.623016	+	1.11951i
$592$	−6.14487	−	6.14487i	−0.252553	−	0.252553i
$593$	−15.2900	−	15.2900i	−0.627884	−	0.627884i	0.319651	−	0.947535i	$-0.396434\pi$
$593$	−15.2900	−	15.2900i	−0.627884	−	0.627884i	−0.947535	+	0.319651i	$0.896434\pi$
$594$	14.1752	+	0.671263i	0.581617	+	0.0275422i
$595$	−5.05500	+	4.46921i	−0.207235	+	0.183220i
$596$			4.68955i			0.192092i
$597$	10.1859	+	2.90224i	0.416880	+	0.118781i
$598$	−42.1906	+	42.1906i	−1.72530	+	1.72530i
$599$	−9.38844			−0.383601			−0.191801	−	0.981434i	$-0.561433\pi$
$599$	−9.38844			−0.383601			−0.191801	+	0.981434i	$0.561433\pi$
$600$	−5.17412	−	12.7697i	−0.211233	−	0.521320i
$601$	−4.87361			−0.198799			−0.0993993	−	0.995048i	$-0.531692\pi$
$601$	−4.87361			−0.198799			−0.0993993	+	0.995048i	$0.531692\pi$
$602$	−3.68749	+	3.68749i	−0.150291	+	0.150291i
$603$	−1.65582	−	7.06377i	−0.0674303	−	0.287659i
$604$			5.71155i			0.232400i
$605$	−14.3912	+	12.7236i	−0.585087	+	0.517286i
$606$	−33.8280	+	18.8255i	−1.37417	+	0.764734i
$607$	−2.56287	−	2.56287i	−0.104024	−	0.104024i	0.653180	−	0.757203i	$-0.273435\pi$
$607$	−2.56287	−	2.56287i	−0.104024	−	0.104024i	−0.757203	+	0.653180i	$0.773435\pi$
$608$	−16.6685	−	16.6685i	−0.675998	−	0.675998i
$609$	−4.49675	+	2.50247i	−0.182217	+	0.101405i
$610$	−0.801103	+	13.0250i	−0.0324357	+	0.527367i
$611$			0.323222i			0.0130762i
$612$	2.26389	+	9.65780i	0.0915123	+	0.390393i
$613$	33.5166	−	33.5166i	1.35372	−	1.35372i	0.472264	−	0.881457i	$-0.343437\pi$
$613$	33.5166	−	33.5166i	1.35372	−	1.35372i	0.881457	−	0.472264i	$-0.156563\pi$
$614$	−1.97471			−0.0796927
$615$	9.37848	−	4.48873i	0.378177	−	0.181003i
$616$	2.46950			0.0994989
$617$	−2.15297	+	2.15297i	−0.0866754	+	0.0866754i	−0.749115	−	0.662440i	$-0.769521\pi$
$617$	−2.15297	+	2.15297i	−0.0866754	+	0.0866754i	0.662440	+	0.749115i	$0.269521\pi$
$618$	6.08459	+	1.73367i	0.244758	+	0.0697384i
$619$			10.1941i			0.409737i	0.978789	+	0.204869i	$0.0656767\pi$
$619$			10.1941i			0.409737i	−0.978789	+	0.204869i	$0.934323\pi$
$620$	−9.40938	−	10.6427i	−0.377890	−	0.427421i
$621$	−27.6030	−	1.30713i	−1.10767	−	0.0524534i
$622$	−12.3359	−	12.3359i	−0.494626	−	0.494626i
$623$	0.959142	+	0.959142i	0.0384272	+	0.0384272i
$624$	26.8042	+	48.1650i	1.07303	+	1.92814i
$625$	−24.2491	−	6.08114i	−0.969965	−	0.243245i
$626$			24.7618i			0.989682i
$627$	−3.10148	+	10.8852i	−0.123861	+	0.434711i
$628$	−4.77759	+	4.77759i	−0.190646	+	0.190646i
$629$	−5.25417			−0.209498
$630$	11.6352	−	1.98319i	0.463556	−	0.0790122i
$631$	44.6402			1.77710			0.888550	−	0.458781i	$-0.151714\pi$
$631$	44.6402			1.77710			0.888550	+	0.458781i	$0.151714\pi$
$632$	4.04293	−	4.04293i	0.160819	−	0.160819i
$633$	5.92801	−	20.8053i	0.235617	−	0.826937i
$634$		−	37.2716i		−	1.48025i
$635$	−32.0666	−	1.97226i	−1.27252	−	0.0782666i
$636$	5.62332	+	10.1047i	0.222979	+	0.400676i
$637$	−4.50889	−	4.50889i	−0.178649	−	0.178649i
$638$	5.73777	+	5.73777i	0.227161	+	0.227161i
$639$	−9.06940	+	14.6232i	−0.358780	+	0.578485i
$640$	−25.5031	−	1.56857i	−1.00810	−	0.0620031i
$641$			15.7329i			0.621414i	0.950506	+	0.310707i	$0.100566\pi$
$641$			15.7329i			0.621414i	−0.950506	+	0.310707i	$0.899434\pi$
$642$	56.1725	+	16.0051i	2.21695	+	0.631672i
$643$	−11.7811	+	11.7811i	−0.464600	+	0.464600i	−0.900160	−	0.435560i	$-0.856551\pi$
$643$	−11.7811	+	11.7811i	−0.464600	+	0.464600i	0.435560	+	0.900160i	$0.356551\pi$
$644$	5.82753			0.229637
$645$	−10.8258	−	3.81730i	−0.426264	−	0.150306i
$646$	−22.3516			−0.879411
$647$	−10.8002	+	10.8002i	−0.424600	+	0.424600i	−0.886784	−	0.462184i	$-0.847066\pi$
$647$	−10.8002	+	10.8002i	−0.424600	+	0.424600i	0.462184	+	0.886784i	$0.347066\pi$
$648$	−4.57060	+	13.5696i	−0.179550	+	0.533063i
$649$		−	7.66417i		−	0.300845i
$650$	55.6741	+	6.87448i	2.18372	+	0.269639i
$651$	−8.77466	+	4.88316i	−0.343906	+	0.191386i
$652$	−5.85518	−	5.85518i	−0.229307	−	0.229307i
$653$	−7.88328	−	7.88328i	−0.308497	−	0.308497i	0.535830	−	0.844326i	$-0.319999\pi$
$653$	−7.88328	−	7.88328i	−0.308497	−	0.308497i	−0.844326	+	0.535830i	$0.819999\pi$
$654$	12.8928	−	7.17493i	0.504147	−	0.280562i
$655$	−0.754429	−	0.853314i	−0.0294780	−	0.0333417i
$656$		−	13.3983i		−	0.523115i
$657$	−30.0207	+	7.03717i	−1.17122	+	0.274546i
$658$	0.0630648	−	0.0630648i	0.00245852	−	0.00245852i
$659$	−6.73141			−0.262219			−0.131109	−	0.991368i	$-0.541854\pi$
$659$	−6.73141			−0.262219			−0.131109	+	0.991368i	$0.541854\pi$
$660$	−2.84394	−	5.94195i	−0.110700	−	0.231290i
$661$	4.43191			0.172381			0.0861906	−	0.996279i	$-0.472531\pi$
$661$	4.43191			0.172381			0.0861906	+	0.996279i	$0.472531\pi$
$662$	−3.85991	+	3.85991i	−0.150020	+	0.150020i
$663$	32.0512	+	9.13228i	1.24476	+	0.354668i
$664$			27.4807i			1.06646i
$665$	−0.577896	+	9.39592i	−0.0224099	+	0.364358i
$666$	7.81072	+	4.84426i	0.302659	+	0.187711i
$667$	−11.1730	−	11.1730i	−0.432621	−	0.432621i
$668$	−15.1472	−	15.1472i	−0.586064	−	0.586064i
$669$	−10.4870	−	18.8444i	−0.405452	−	0.728565i
$670$	−7.12834	+	6.30229i	−0.275392	+	0.243479i
$671$		−	5.14846i		−	0.198754i
$672$	2.65756	−	9.32715i	0.102518	−	0.359802i
$673$	−3.35642	+	3.35642i	−0.129381	+	0.129381i	−0.768832	−	0.639451i	$-0.779162\pi$
$673$	−3.35642	+	3.35642i	−0.129381	+	0.129381i	0.639451	+	0.768832i	$0.279162\pi$
$674$	−57.7356			−2.22389
$675$	14.9946	+	21.2170i	0.577141	+	0.816644i
$676$	−30.3094			−1.16575
$677$	6.31136	−	6.31136i	0.242565	−	0.242565i	−0.575345	−	0.817911i	$-0.695132\pi$
$677$	6.31136	−	6.31136i	0.242565	−	0.242565i	0.817911	+	0.575345i	$0.195132\pi$
$678$	−12.5447	+	44.0277i	−0.481777	+	1.69087i
$679$			15.5298i			0.595977i
$680$	−8.04230	+	7.11034i	−0.308408	+	0.272669i
$681$	18.7513	+	33.6946i	0.718551	+	1.29118i
$682$	11.1963	+	11.1963i	0.428729	+	0.428729i
$683$	−21.4480	−	21.4480i	−0.820686	−	0.820686i	0.165520	−	0.986206i	$-0.447070\pi$
$683$	−21.4480	−	21.4480i	−0.820686	−	0.820686i	−0.986206	+	0.165520i	$0.947070\pi$
$684$	11.7611	+	7.29431i	0.449697	+	0.278905i
$685$	0.508516	−	8.26788i	0.0194294	−	0.315899i
$686$			1.75948i			0.0671774i
$687$	13.7832	+	3.92722i	0.525862	+	0.149833i
$688$	−10.4597	+	10.4597i	−0.398771	+	0.398771i
$689$	38.8515			1.48012
$690$	15.6456	+	32.6890i	0.595619	+	1.24445i
$691$	18.7943			0.714968			0.357484	−	0.933919i	$-0.383635\pi$
$691$	18.7943			0.714968			0.357484	+	0.933919i	$0.383635\pi$
$692$	−2.26427	+	2.26427i	−0.0860745	+	0.0860745i
$693$	−4.53372	+	1.06275i	−0.172222	+	0.0403706i
$694$		−	35.2932i		−	1.33971i
$695$	9.41054	+	10.6440i	0.356962	+	0.403750i
$696$	−7.15414	+	3.98133i	−0.271177	+	0.150912i
$697$	−5.72810	−	5.72810i	−0.216967	−	0.216967i
$698$	−11.5351	−	11.5351i	−0.436610	−	0.436610i
$699$	−27.0597	+	15.0589i	−1.02349	+	0.569581i
$700$	−3.37020	−	4.31973i	−0.127382	−	0.163271i
$701$		−	10.0310i		−	0.378867i	−0.981894	−	0.189434i	$-0.939335\pi$
$701$		−	10.0310i		−	0.378867i	0.981894	−	0.189434i	$-0.0606652\pi$
$702$	−39.2266	−	43.1264i	−1.48051	−	1.62770i
$703$	−5.18340	+	5.18340i	−0.195496	+	0.195496i
$704$	0.201296			0.00758663
$705$	0.185146	+	0.0652848i	0.00697301	+	0.00245877i
$706$	50.3682			1.89563
$707$	8.98258	−	8.98258i	0.337825	−	0.337825i
$708$	−9.01260	−	2.56794i	−0.338714	−	0.0965092i
$709$		−	48.4192i		−	1.81842i	−0.416335	−	0.909211i	$-0.636686\pi$
$709$		−	48.4192i		−	1.81842i	0.416335	−	0.909211i	$-0.363314\pi$
$710$	22.5238	+	1.38533i	0.845304	+	0.0519904i
$711$	−5.68250	+	9.16227i	−0.213110	+	0.343612i
$712$	1.52596	+	1.52596i	0.0571876	+	0.0571876i
$713$	−21.8023	−	21.8023i	−0.816502	−	0.816502i
$714$	−4.47177	−	8.03542i	−0.167352	−	0.300718i
$715$	−22.0902	−	1.35865i	−0.826125	−	0.0508108i
$716$			13.0602i			0.488083i
$717$	12.2575	−	43.0197i	0.457765	−	1.60660i
$718$	23.4258	−	23.4258i	0.874244	−	0.874244i
$719$	10.6931			0.398786			0.199393	−	0.979920i	$-0.436103\pi$
$719$	10.6931			0.398786			0.199393	+	0.979920i	$0.436103\pi$
$720$	33.0035	−	5.62538i	1.22997	−	0.209646i
$721$	−2.07604			−0.0773157
$722$	1.58818	−	1.58818i	0.0591060	−	0.0591060i
$723$	−4.99284	+	17.5232i	−0.185686	+	0.651693i
$724$			19.2797i			0.716523i
$725$	−1.82052	+	14.7438i	−0.0676123	+	0.547569i
$726$	−12.7308	−	22.8763i	−0.472486	−	0.849020i
$727$	30.9245	+	30.9245i	1.14693	+	1.14693i	0.987154	+	0.159773i	$0.0510764\pi$
$727$	30.9245	+	30.9245i	1.14693	+	1.14693i	0.159773	+	0.987154i	$0.448924\pi$
$728$	−7.17345	−	7.17345i	−0.265866	−	0.265866i
$729$	2.55143	−	26.8792i	0.0944974	−	0.995525i
$730$	26.7845	+	30.2951i	0.991337	+	1.12127i
$731$			8.94354i			0.330789i
$732$	−6.05428	−	1.72503i	−0.223773	−	0.0637590i
$733$	−23.0095	+	23.0095i	−0.849876	+	0.849876i	−0.990117	−	0.140241i	$-0.955212\pi$
$733$	−23.0095	+	23.0095i	−0.849876	+	0.849876i	0.140241	+	0.990117i	$0.455212\pi$
$734$	2.34399			0.0865184
$735$	−3.49346	+	1.67204i	−0.128858	+	0.0616742i
$736$	29.7782			1.09764
$737$	2.65439	−	2.65439i	0.0977759	−	0.0977759i
$738$	3.23403	+	13.7964i	0.119046	+	0.507854i
$739$		−	31.0959i		−	1.14388i	−0.820295	−	0.571941i	$-0.806191\pi$
$739$		−	31.0959i		−	1.14388i	0.820295	−	0.571941i	$-0.193809\pi$
$740$	0.261911	−	4.25838i	0.00962805	−	0.156541i
$741$	40.6287	−	22.6102i	1.49253	−	0.830606i
$742$	−7.58042	−	7.58042i	−0.278286	−	0.278286i
$743$	−4.41646	−	4.41646i	−0.162024	−	0.162024i	0.621439	−	0.783463i	$-0.286549\pi$
$743$	−4.41646	−	4.41646i	−0.162024	−	0.162024i	−0.783463	+	0.621439i	$0.786549\pi$
$744$	−13.9601	+	7.76892i	−0.511803	+	0.284822i
$745$	7.16936	−	6.33855i	0.262665	−	0.232227i
$746$		−	18.4118i		−	0.674105i
$747$	−11.8263	−	50.4514i	−0.432703	−	1.84592i
$748$	−3.62917	+	3.62917i	−0.132695	+	0.132695i
$749$	−19.1658			−0.700305
$750$	15.1829	−	30.5024i	0.554402	−	1.11379i
$751$	−20.7634			−0.757668			−0.378834	−	0.925465i	$-0.623675\pi$
$751$	−20.7634			−0.757668			−0.378834	+	0.925465i	$0.623675\pi$
$752$	0.178885	−	0.178885i	0.00652327	−	0.00652327i
$753$	11.5697	+	3.29654i	0.421624	+	0.120132i
$754$		−	33.3344i		−	1.21397i
$755$	8.73178	−	7.71992i	0.317782	−	0.280957i
$756$	−0.269328	+	5.68747i	−0.00979536	+	0.206851i
$757$	27.7515	+	27.7515i	1.00865	+	1.00865i	0.999962	+	0.00868333i	$0.00276403\pi$
$757$	27.7515	+	27.7515i	1.00865	+	1.00865i	0.00868333	+	0.999962i	$0.497236\pi$
$758$	27.3072	+	27.3072i	0.991843	+	0.991843i
$759$	−6.95274	−	12.4935i	−0.252369	−	0.453486i
$760$	−0.919409	+	14.9485i	−0.0333505	+	0.542240i
$761$		−	51.6155i		−	1.87106i	−0.353246	−	0.935531i	$-0.614922\pi$
$761$		−	51.6155i		−	1.87106i	0.353246	−	0.935531i	$-0.385078\pi$
$762$	11.9983	−	42.1099i	0.434652	−	1.52548i
$763$	−3.42351	+	3.42351i	−0.123939	+	0.123939i
$764$	6.07087			0.219636
$765$	11.7048	−	16.5148i	0.423189	−	0.597094i
$766$	48.1010			1.73796
$767$	−22.2631	+	22.2631i	−0.803873	+	0.803873i
$768$	9.41932	−	33.0586i	0.339891	−	1.19290i
$769$		−	15.3442i		−	0.553327i	−0.960967	−	0.276663i	$-0.910771\pi$
$769$		−	15.3442i		−	0.553327i	0.960967	−	0.276663i	$-0.0892287\pi$
$770$	4.04498	+	4.57516i	0.145771	+	0.164877i
$771$	9.73225	+	17.4881i	0.350498	+	0.629818i
$772$	15.2343	+	15.2343i	0.548296	+	0.548296i
$773$	−16.1229	−	16.1229i	−0.579900	−	0.579900i	0.354976	−	0.934876i	$-0.384489\pi$
$773$	−16.1229	−	16.1229i	−0.579900	−	0.579900i	−0.934876	+	0.354976i	$0.884489\pi$
$774$	8.24579	−	13.2952i	0.296389	−	0.477887i
$775$	−3.55244	+	28.7700i	−0.127607	+	1.03345i
$776$			24.7072i			0.886937i
$777$	−2.90046	−	0.826421i	−0.104053	−	0.0296477i
$778$	−38.3147	+	38.3147i	−1.37365	+	1.37365i
$779$	−11.3019			−0.404932
$780$	−8.99918	+	25.5214i	−0.322222	+	0.913814i
$781$	−8.90311			−0.318578
$782$	19.9655	−	19.9655i	0.713965	−	0.713965i
$783$	11.4208	−	10.3881i	0.408148	−	0.371240i
$784$			4.99083i			0.178244i
$785$	13.7615	+	0.846400i	0.491168	+	0.0302093i
$786$	1.35643	−	0.754861i	0.0483821	−	0.0269250i
$787$	−6.19650	−	6.19650i	−0.220881	−	0.220881i	0.587988	−	0.808870i	$-0.299920\pi$
$787$	−6.19650	−	6.19650i	−0.220881	−	0.220881i	−0.808870	+	0.587988i	$0.799920\pi$
$788$	13.9334	+	13.9334i	0.496355	+	0.496355i
$789$	−0.254405	+	0.141578i	−0.00905705	+	0.00504032i
$790$	14.1125	+	0.867987i	0.502099	+	0.0308816i
$791$		−	15.0221i		−	0.534124i
$792$	−7.21297	+	1.69080i	−0.256302	+	0.0600798i
$793$	−14.9554	+	14.9554i	−0.531081	+	0.531081i
$794$	−51.8196			−1.83901
$795$	7.84727	−	22.2547i	0.278314	−	0.789292i
$796$	6.70056			0.237495
$797$	−24.6954	+	24.6954i	−0.874755	+	0.874755i	−0.992986	−	0.118231i	$-0.962278\pi$
$797$	−24.6954	+	24.6954i	−0.874755	+	0.874755i	0.118231	+	0.992986i	$0.462278\pi$
$798$	−12.3387	−	3.51565i	−0.436786	−	0.124453i
$799$		−	0.152956i		−	0.00541119i
$800$	−17.2215	−	22.0735i	−0.608871	−	0.780416i
$801$	−3.45819	−	2.14479i	−0.122189	−	0.0757824i
$802$	26.0130	+	26.0130i	0.918552	+	0.918552i
$803$	−11.2811	−	11.2811i	−0.398100	−	0.398100i
$804$	−2.23203	−	4.01078i	−0.0787177	−	0.141449i
$805$	−7.87668	−	8.90909i	−0.277617	−	0.314004i
$806$		−	65.0467i		−	2.29117i
$807$	−3.13406	+	10.9995i	−0.110324	+	0.387200i
$808$	14.2909	−	14.2909i	0.502753	−	0.502753i
$809$	20.4064			0.717449			0.358725	−	0.933443i	$-0.383212\pi$
$809$	20.4064			0.717449			0.358725	+	0.933443i	$0.383212\pi$
$810$	−32.6265	+	13.7588i	−1.14638	+	0.483436i
$811$	10.0632			0.353368			0.176684	−	0.984268i	$-0.443463\pi$
$811$	10.0632			0.353368			0.176684	+	0.984268i	$0.443463\pi$
$812$	−2.30214	+	2.30214i	−0.0807894	+	0.0807894i
$813$	−11.3098	+	39.6935i	−0.396652	+	1.39211i
$814$			4.75543i			0.166678i
$815$	−1.03731	+	16.8654i	−0.0363353	+	0.590770i
$816$	−12.6843	−	22.7927i	−0.444040	−	0.797904i
$817$	8.82308	+	8.82308i	0.308680	+	0.308680i
$818$	14.4038	+	14.4038i	0.503617	+	0.503617i
$819$	16.2568	+	10.0826i	0.568058	+	0.352313i
$820$	4.92801	−	4.35694i	0.172094	−	0.152151i
$821$		−	55.9052i		−	1.95110i	−0.219767	−	0.975552i	$-0.570530\pi$
$821$		−	55.9052i		−	1.95110i	0.219767	−	0.975552i	$-0.429470\pi$
$822$	10.8574	+	3.09357i	0.378695	+	0.107901i
$823$	−25.7909	+	25.7909i	−0.899015	+	0.899015i	−0.995349	−	0.0963344i	$-0.969288\pi$
$823$	−25.7909	+	25.7909i	−0.899015	+	0.899015i	0.0963344	+	0.995349i	$0.469288\pi$
$824$	−3.30289			−0.115062
$825$	−5.24005	+	12.3791i	−0.182435	+	0.430986i
$826$	8.68762			0.302281
$827$	25.9659	−	25.9659i	0.902922	−	0.902922i	−0.0927663	−	0.995688i	$-0.529571\pi$
$827$	25.9659	−	25.9659i	0.902922	−	0.902922i	0.995688	+	0.0927663i	$0.0295710\pi$
$828$	−17.0212	+	3.98995i	−0.591528	+	0.138660i
$829$		−	12.6797i		−	0.440385i	−0.975456	−	0.220193i	$-0.929331\pi$
$829$		−	12.6797i		−	0.440385i	0.975456	−	0.220193i	$-0.0706686\pi$
$830$	−50.9126	+	45.0127i	−1.76720	+	1.56241i
$831$	−30.8044	+	17.1429i	−1.06859	+	0.594681i
$832$	−0.584729	−	0.584729i	−0.0202718	−	0.0202718i
$833$	2.13370	+	2.13370i	0.0739284	+	0.0739284i
$834$	−16.9197	+	9.41593i	−0.585881	+	0.326047i
$835$	−2.68349	+	43.6305i	−0.0928661	+	1.50989i
$836$			7.16056i			0.247653i
$837$	22.2859	−	20.2706i	0.770313	−	0.700656i
$838$	0.653815	−	0.653815i	0.0225857	−	0.0225857i
$839$	27.2730			0.941569			0.470785	−	0.882248i	$-0.343971\pi$
$839$	27.2730			0.941569			0.470785	+	0.882248i	$0.343971\pi$
$840$	−5.55796	+	2.66015i	−0.191768	+	0.0917839i
$841$	−20.1723			−0.695596
$842$	−19.3211	+	19.3211i	−0.665851	+	0.665851i
$843$	−2.51026	−	0.715244i	−0.0864581	−	0.0246343i
$844$		−	13.6863i		−	0.471103i
$845$	40.9672	+	46.3368i	1.40931	+	1.59403i
$846$	−0.141023	+	0.227380i	−0.00484846	+	0.00781749i
$847$	6.07451	+	6.07451i	0.208723	+	0.208723i
$848$	−21.5021	−	21.5021i	−0.738385	−	0.738385i
$849$	−10.1141	−	18.1742i	−0.347115	−	0.623738i
$850$	−26.3462	−	3.25315i	−0.903668	−	0.111582i
$851$		−	9.26012i		−	0.317433i
$852$	−2.98306	+	10.4695i	−0.102198	+	0.358679i
$853$	8.57549	−	8.57549i	0.293619	−	0.293619i	−0.544889	−	0.838508i	$-0.683428\pi$
$853$	8.57549	−	8.57549i	0.293619	−	0.293619i	0.838508	+	0.544889i	$0.183428\pi$
$854$	5.83597			0.199703
$855$	−4.74519	−	27.8395i	−0.162282	−	0.952092i
$856$	−30.4921			−1.04220
$857$	20.8458	−	20.8458i	0.712077	−	0.712077i	−0.254892	−	0.966970i	$-0.582040\pi$
$857$	20.8458	−	20.8458i	0.712077	−	0.712077i	0.966970	+	0.254892i	$0.0820399\pi$
$858$	8.26541	−	29.0088i	0.282177	−	0.990344i
$859$			9.52782i			0.325085i	0.986702	+	0.162543i	$0.0519695\pi$
$859$			9.52782i			0.325085i	−0.986702	+	0.162543i	$0.948031\pi$
$860$	−7.24852	−	0.445820i	−0.247172	−	0.0152023i
$861$	−2.26111	−	4.06304i	−0.0770585	−	0.138468i
$862$	−28.6332	−	28.6332i	−0.975249	−	0.975249i
$863$	32.3773	+	32.3773i	1.10213	+	1.10213i	0.994153	+	0.107982i	$0.0344389\pi$
$863$	32.3773	+	32.3773i	1.10213	+	1.10213i	0.107982	+	0.994153i	$0.465561\pi$
$864$	−1.37625	+	29.0625i	−0.0468208	+	0.988727i
$865$	6.52205	+	0.401139i	0.221756	+	0.0136391i
$866$			38.3198i			1.30216i
$867$	13.1505	+	3.74695i	0.446615	+	0.127253i
$868$	−4.49225	+	4.49225i	−0.152477	+	0.152477i
$869$	−5.57830			−0.189231
$870$	−19.0944	−	6.73293i	−0.647362	−	0.228268i
$871$	−15.4211			−0.522524
$872$	−5.44667	+	5.44667i	−0.184447	+	0.184447i
$873$	−10.6328	−	45.3597i	−0.359865	−	1.53519i
$874$		−	39.3931i		−	1.33249i
$875$	−2.04870	+	10.9910i	−0.0692588	+	0.371565i
$876$	−17.0457	+	9.48604i	−0.575919	+	0.320503i
$877$	−22.3025	−	22.3025i	−0.753102	−	0.753102i	0.221955	−	0.975057i	$-0.428756\pi$
$877$	−22.3025	−	22.3025i	−0.753102	−	0.753102i	−0.975057	+	0.221955i	$0.928756\pi$
$878$	−7.51820	−	7.51820i	−0.253727	−	0.253727i
$879$	5.04809	−	2.80930i	0.170268	−	0.0947553i
$880$	11.4737	+	12.9776i	0.386779	+	0.437474i
$881$			31.6927i			1.06775i	0.845562	+	0.533877i	$0.179266\pi$
$881$			31.6927i			1.06775i	−0.845562	+	0.533877i	$0.820734\pi$
$882$	−1.20467	−	5.13914i	−0.0405633	−	0.173044i
$883$	−19.2435	+	19.2435i	−0.647595	+	0.647595i	−0.952411	−	0.304816i	$-0.901405\pi$
$883$	−19.2435	+	19.2435i	−0.647595	+	0.647595i	0.304816	+	0.952411i	$0.401405\pi$
$884$	21.0842			0.709137
$885$	8.25588	+	17.2493i	0.277518	+	0.579830i
$886$	21.5168			0.722872
$887$	7.26863	−	7.26863i	0.244057	−	0.244057i	−0.574469	−	0.818526i	$-0.694792\pi$
$887$	7.26863	−	7.26863i	0.244057	−	0.244057i	0.818526	+	0.574469i	$0.194792\pi$
$888$	−4.61451	−	1.31480i	−0.154853	−	0.0441219i
$889$			14.3677i			0.481878i
$890$	−0.327611	+	5.32658i	−0.0109815	+	0.178547i
$891$	12.5146	−	6.20823i	0.419254	−	0.207983i
$892$	−9.64751	−	9.64751i	−0.323023	−	0.323023i
$893$	−0.150896	−	0.150896i	−0.00504953	−	0.00504953i
$894$	6.34218	+	11.3964i	0.212114	+	0.381153i
$895$	19.9664	−	17.6526i	0.667402	−	0.590061i
$896$			11.4269i			0.381745i
$897$	−16.0950	+	56.4880i	−0.537397	+	1.88608i
$898$	25.8283	−	25.8283i	0.861903	−	0.861903i
$899$	17.2258			0.574513
$900$	12.8014	+	10.3097i	0.426712	+	0.343657i
$901$	−18.3854			−0.612506
$902$	−5.18437	+	5.18437i	−0.172621	+	0.172621i
$903$	−1.40672	+	4.93710i	−0.0468126	+	0.164296i
$904$		−	23.8995i		−	0.794886i
$905$	29.4746	−	26.0590i	0.979769	−	0.866231i
$906$	7.72434	+	13.8800i	0.256624	+	0.461133i
$907$	20.0346	+	20.0346i	0.665238	+	0.665238i	0.956610	−	0.291372i	$-0.0941117\pi$
$907$	20.0346	+	20.0346i	0.665238	+	0.665238i	−0.291372	+	0.956610i	$0.594112\pi$
$908$	17.2502	+	17.2502i	0.572467	+	0.572467i
$909$	−20.0864	+	32.3867i	−0.666225	+	1.07420i
$910$	1.54009	−	25.0400i	0.0510533	−	0.830068i
$911$			34.2452i			1.13459i	0.823514	+	0.567296i	$0.192011\pi$
$911$			34.2452i			1.13459i	−0.823514	+	0.567296i	$0.807989\pi$
$912$	−34.9992	−	9.97224i	−1.15894	−	0.330214i
$913$	18.9584	−	18.9584i	0.627432	−	0.627432i
$914$	43.0661			1.42450
$915$	5.54594	+	11.5873i	0.183343	+	0.383066i
$916$	9.06698			0.299582
$917$	−0.360182	+	0.360182i	−0.0118942	+	0.0118942i
$918$	18.5629	+	20.4084i	0.612667	+	0.673576i
$919$		−	44.3406i		−	1.46266i	−0.682023	−	0.731331i	$-0.738900\pi$
$919$		−	44.3406i		−	1.46266i	0.682023	−	0.731331i	$-0.261100\pi$
$920$	−12.5315	−	14.1740i	−0.413151	−	0.467303i
$921$	−1.69861	+	0.945287i	−0.0559709	+	0.0311483i
$922$	−5.42970	−	5.42970i	−0.178818	−	0.178818i
$923$	25.8620	+	25.8620i	0.851257	+	0.851257i
$924$	−2.57423	+	1.43258i	−0.0846860	+	0.0471284i
$925$	−6.86418	+	5.35535i	−0.225693	+	0.176083i
$926$		−	5.07976i		−	0.166931i
$927$	6.06375	−	1.42141i	0.199160	−	0.0466851i
$928$	−11.7638	+	11.7638i	−0.386165	+	0.386165i
$929$	−9.88243			−0.324232			−0.162116	−	0.986772i	$-0.551832\pi$
$929$	−9.88243			−0.324232			−0.162116	+	0.986772i	$0.551832\pi$
$930$	−37.2596	−	13.1382i	−1.22179	−	0.430818i
$931$	4.20993			0.137975
$932$	−13.8534	+	13.8534i	−0.453784	+	0.453784i
$933$	−16.5163	−	4.70596i	−0.540720	−	0.154066i
$934$		−	34.7438i		−	1.13685i
$935$	10.4535	+	0.642945i	0.341867	+	0.0210265i
$936$	25.8639	+	16.0409i	0.845387	+	0.524315i
$937$	−22.4981	−	22.4981i	−0.734980	−	0.734980i	0.236622	−	0.971602i	$-0.423960\pi$
$937$	−22.4981	−	22.4981i	−0.734980	−	0.734980i	−0.971602	+	0.236622i	$0.923960\pi$
$938$	3.00885	+	3.00885i	0.0982426	+	0.0982426i
$939$	11.8534	+	21.2996i	0.386821	+	0.695088i
$940$	0.123967	+	0.00762458i	0.00404335	+	0.000248686i
$941$			56.4149i			1.83907i	0.393006	+	0.919536i	$0.371435\pi$
$941$			56.4149i			1.83907i	−0.393006	+	0.919536i	$0.628565\pi$
$942$	−5.14910	+	18.0716i	−0.167767	+	0.588804i
$943$	10.0954	−	10.0954i	0.328751	−	0.328751i
$944$	24.6427			0.802052
$945$	9.05899	−	7.27562i	0.294689	−	0.236676i
$946$	8.09460			0.263178
$947$	−8.25095	+	8.25095i	−0.268120	+	0.268120i	−0.828342	−	0.560222i	$-0.810716\pi$
$947$	−8.25095	+	8.25095i	−0.268120	+	0.268120i	0.560222	+	0.828342i	$0.310716\pi$
$948$	−1.86905	+	6.55974i	−0.0607041	+	0.213051i
$949$			65.5390i			2.12749i
$950$	−29.2007	+	22.7820i	−0.947395	+	0.739146i
$951$	−17.8418	−	32.0603i	−0.578560	−	1.03963i
$952$	3.39463	+	3.39463i	0.110021	+	0.110021i
$953$	−18.3169	−	18.3169i	−0.593344	−	0.593344i	0.345189	−	0.938533i	$-0.387815\pi$
$953$	−18.3169	−	18.3169i	−0.593344	−	0.593344i	−0.938533	+	0.345189i	$0.887815\pi$
$954$	27.3312	+	16.9510i	0.884881	+	0.548809i
$955$	−8.20559	−	9.28111i	−0.265527	−	0.300330i
$956$		−	28.2996i		−	0.915274i
$957$	7.68217	+	2.18887i	0.248329	+	0.0707560i
$958$	−19.9147	+	19.9147i	−0.643414	+	0.643414i
$959$	−3.70450			−0.119624
$960$	−0.453045	+	0.216837i	−0.0146220	+	0.00699837i
$961$	2.61332			0.0843005
$962$	13.8137	−	13.8137i	0.445371	−	0.445371i
$963$	55.9801	−	13.1223i	1.80393	−	0.422861i
$964$			11.5272i			0.371267i
$965$	2.69892	−	43.8814i	0.0868814	−	1.41259i
$966$	14.1619	−	7.88119i	0.455651	−	0.253573i
$967$	−6.55794	−	6.55794i	−0.210889	−	0.210889i	0.593756	−	0.804645i	$-0.297644\pi$
$967$	−6.55794	−	6.55794i	−0.210889	−	0.210889i	−0.804645	+	0.593756i	$0.797644\pi$
$968$	9.66430	+	9.66430i	0.310622	+	0.310622i
$969$	−19.2264	+	10.6996i	−0.617641	+	0.343722i
$970$	−45.7743	+	40.4699i	−1.46972	+	1.29941i
$971$			13.9212i			0.446753i	0.974732	+	0.223377i	$0.0717079\pi$
$971$			13.9212i			0.446753i	−0.974732	+	0.223377i	$0.928292\pi$
$972$	−3.10739	−	16.7965i	−0.0996696	−	0.538748i
$973$	4.49280	−	4.49280i	0.144033	−	0.144033i
$974$	51.2825			1.64320
$975$	51.1806	−	20.7377i	1.63909	−	0.664139i
$976$	16.5539			0.529878
$977$	27.2013	−	27.2013i	0.870248	−	0.870248i	−0.122251	−	0.992499i	$-0.539011\pi$
$977$	27.2013	−	27.2013i	0.870248	−	0.870248i	0.992499	+	0.122251i	$0.0390114\pi$
$978$	−22.1477	−	6.31049i	−0.708204	−	0.201787i
$979$		−	2.10546i		−	0.0672909i
$980$	−1.83567	+	1.62295i	−0.0586385	+	0.0518433i
$981$	7.65550	−	12.3435i	0.244421	−	0.394096i
$982$	37.1807	+	37.1807i	1.18648	+	1.18648i
$983$	−36.8517	−	36.8517i	−1.17539	−	1.17539i	−0.980907	−	0.194479i	$-0.937698\pi$
$983$	−36.8517	−	36.8517i	−1.17539	−	1.17539i	−0.194479	−	0.980907i	$-0.562302\pi$
$984$	−3.59734	−	6.46413i	−0.114679	−	0.206069i
$985$	2.46844	−	40.1340i	0.0786510	−	1.27878i
$986$			15.7746i			0.502365i
$987$	0.0240582	−	0.0844361i	0.000765781	−	0.00268763i
$988$	20.8002	−	20.8002i	0.661742	−	0.661742i
$989$	−15.7624			−0.501215
$990$	−14.9472	−	10.5938i	−0.475052	−	0.336692i
$991$	−41.8651			−1.32989			−0.664945	−	0.746893i	$-0.731545\pi$
$991$	−41.8651			−1.32989			−0.664945	+	0.746893i	$0.731545\pi$
$992$	−22.9551	+	22.9551i	−0.728824	+	0.728824i
$993$	−1.47249	+	5.16795i	−0.0467281	+	0.164000i
$994$		−	10.0920i		−	0.320099i
$995$	−9.05669	−	10.2438i	−0.287116	−	0.324749i
$996$	−15.9418	−	28.6461i	−0.505135	−	0.907687i
$997$	11.4463	+	11.4463i	0.362507	+	0.362507i	0.864735	−	0.502228i	$-0.167486\pi$
$997$	11.4463	+	11.4463i	0.362507	+	0.362507i	−0.502228	+	0.864735i	$0.667486\pi$
$998$	−1.17024	−	1.17024i	−0.0370434	−	0.0370434i
$999$	9.03756	+	0.427970i	0.285936	+	0.0135404i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.j.a.92.10	yes	24
3.2	odd	2	inner	105.2.j.a.92.3	yes	24
5.2	odd	4		525.2.j.b.218.10		24
5.3	odd	4	inner	105.2.j.a.8.3	✓	24
5.4	even	2		525.2.j.b.407.3		24
7.2	even	3		735.2.y.j.557.3		48
7.3	odd	6		735.2.y.g.422.10		48
7.4	even	3		735.2.y.j.422.10		48
7.5	odd	6		735.2.y.g.557.3		48
7.6	odd	2		735.2.j.h.197.10		24
15.2	even	4		525.2.j.b.218.3		24
15.8	even	4	inner	105.2.j.a.8.10	yes	24
15.14	odd	2		525.2.j.b.407.10		24
21.2	odd	6		735.2.y.j.557.10		48
21.5	even	6		735.2.y.g.557.10		48
21.11	odd	6		735.2.y.j.422.3		48
21.17	even	6		735.2.y.g.422.3		48
21.20	even	2		735.2.j.h.197.3		24
35.3	even	12		735.2.y.g.128.10		48
35.13	even	4		735.2.j.h.638.3		24
35.18	odd	12		735.2.y.j.128.10		48
35.23	odd	12		735.2.y.j.263.3		48
35.33	even	12		735.2.y.g.263.3		48
105.23	even	12		735.2.y.j.263.10		48
105.38	odd	12		735.2.y.g.128.3		48
105.53	even	12		735.2.y.j.128.3		48
105.68	odd	12		735.2.y.g.263.10		48
105.83	odd	4		735.2.j.h.638.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.3	✓	24	5.3	odd	4	inner
105.2.j.a.8.10	yes	24	15.8	even	4	inner
105.2.j.a.92.3	yes	24	3.2	odd	2	inner
105.2.j.a.92.10	yes	24	1.1	even	1	trivial
525.2.j.b.218.3		24	15.2	even	4
525.2.j.b.218.10		24	5.2	odd	4
525.2.j.b.407.3		24	5.4	even	2
525.2.j.b.407.10		24	15.14	odd	2
735.2.j.h.197.3		24	21.20	even	2
735.2.j.h.197.10		24	7.6	odd	2
735.2.j.h.638.3		24	35.13	even	4
735.2.j.h.638.10		24	105.83	odd	4
735.2.y.g.128.3		48	105.38	odd	12
735.2.y.g.128.10		48	35.3	even	12
735.2.y.g.263.3		48	35.33	even	12
735.2.y.g.263.10		48	105.68	odd	12
735.2.y.g.422.3		48	21.17	even	6
735.2.y.g.422.10		48	7.3	odd	6
735.2.y.g.557.3		48	7.5	odd	6
735.2.y.g.557.10		48	21.5	even	6
735.2.y.j.128.3		48	105.53	even	12
735.2.y.j.128.10		48	35.18	odd	12
735.2.y.j.263.3		48	35.23	odd	12
735.2.y.j.263.10		48	105.23	even	12
735.2.y.j.422.3		48	21.11	odd	6
735.2.y.j.422.10		48	7.4	even	3
735.2.y.j.557.3		48	7.2	even	3
735.2.y.j.557.10		48	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24414 - 1.24414i) q^{2} +(0.474620 - 1.66575i) q^{3} -1.09578i q^{4} +(-1.67522 + 1.48109i) q^{5} +(-1.48194 - 2.66293i) q^{6} +(0.707107 + 0.707107i) q^{7} +(1.12498 + 1.12498i) q^{8} +(-2.54947 - 1.58120i) q^{9} +O(q^{10})\)	\(q+(1.24414 - 1.24414i) q^{2} +(0.474620 - 1.66575i) q^{3} -1.09578i q^{4} +(-1.67522 + 1.48109i) q^{5} +(-1.48194 - 2.66293i) q^{6} +(0.707107 + 0.707107i) q^{7} +(1.12498 + 1.12498i) q^{8} +(-2.54947 - 1.58120i) q^{9} +(-0.241524 + 3.92690i) q^{10} -1.55221i q^{11} +(-1.82530 - 0.520079i) q^{12} +(-4.50889 + 4.50889i) q^{13} +1.75948 q^{14} +(1.67204 + 3.49346i) q^{15} +4.99083 q^{16} +(2.13370 - 2.13370i) q^{17} +(-5.13914 + 1.20467i) q^{18} -4.20993i q^{19} +(1.62295 + 1.83567i) q^{20} +(1.51347 - 0.842259i) q^{21} +(-1.93117 - 1.93117i) q^{22} +(3.76050 + 3.76050i) q^{23} +(2.40787 - 1.34000i) q^{24} +(0.612732 - 4.96231i) q^{25} +11.2194i q^{26} +(-3.84392 + 3.49632i) q^{27} +(0.774834 - 0.774834i) q^{28} -2.97115 q^{29} +(6.42662 + 2.26611i) q^{30} -5.79770 q^{31} +(3.95934 - 3.95934i) q^{32} +(-2.58559 - 0.736708i) q^{33} -5.30926i q^{34} +(-2.23185 - 0.137270i) q^{35} +(-1.73265 + 2.79366i) q^{36} +(-1.23123 - 1.23123i) q^{37} +(-5.23775 - 5.23775i) q^{38} +(5.37069 + 9.65070i) q^{39} +(-3.55078 - 0.218391i) q^{40} -2.68458i q^{41} +(0.835085 - 2.93087i) q^{42} +(-2.09578 + 2.09578i) q^{43} -1.70088 q^{44} +(6.61283 - 1.12714i) q^{45} +9.35721 q^{46} +(0.0358428 - 0.0358428i) q^{47} +(2.36874 - 8.31349i) q^{48} +1.00000i q^{49} +(-5.41150 - 6.93615i) q^{50} +(-2.54153 - 4.56692i) q^{51} +(4.94075 + 4.94075i) q^{52} +(-4.30833 - 4.30833i) q^{53} +(-0.432457 + 9.13231i) q^{54} +(2.29896 + 2.60029i) q^{55} +1.59096i q^{56} +(-7.01270 - 1.99811i) q^{57} +(-3.69653 + 3.69653i) q^{58} +4.93760 q^{59} +(3.82807 - 1.83219i) q^{60} +3.31687 q^{61} +(-7.21316 + 7.21316i) q^{62} +(-0.684672 - 2.92083i) q^{63} +0.129684i q^{64} +(0.875305 - 14.2315i) q^{65} +(-4.13342 + 2.30028i) q^{66} +(1.71008 + 1.71008i) q^{67} +(-2.33807 - 2.33807i) q^{68} +(8.04889 - 4.47927i) q^{69} +(-2.94752 + 2.60596i) q^{70} -5.73577i q^{71} +(-1.08929 - 4.64692i) q^{72} +(7.26776 - 7.26776i) q^{73} -3.06366 q^{74} +(-7.97518 - 3.37587i) q^{75} -4.61315 q^{76} +(1.09758 - 1.09758i) q^{77} +(18.6887 + 5.32495i) q^{78} -3.59379i q^{79} +(-8.36074 + 7.39187i) q^{80} +(3.99962 + 8.06245i) q^{81} +(-3.34000 - 3.34000i) q^{82} +(12.2139 + 12.2139i) q^{83} +(-0.922931 - 1.65843i) q^{84} +(-0.414214 + 6.73463i) q^{85} +5.21490i q^{86} +(-1.41016 + 4.94920i) q^{87} +(1.74620 - 1.74620i) q^{88} +1.35643 q^{89} +(6.82498 - 9.62963i) q^{90} -6.37653 q^{91} +(4.12069 - 4.12069i) q^{92} +(-2.75170 + 9.65754i) q^{93} -0.0891871i q^{94} +(6.23529 + 7.05256i) q^{95} +(-4.71611 - 8.47447i) q^{96} +(10.9812 + 10.9812i) q^{97} +(1.24414 + 1.24414i) q^{98} +(-2.45435 + 3.95731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3}+O(q^{10}) \) 24 * q - 4 * q^3	\( 24 q - 4 q^{3} - 16 q^{10} + 16 q^{12} - 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 4 q^{21} + 8 q^{22} - 16 q^{25} - 16 q^{27} + 20 q^{30} + 28 q^{33} + 16 q^{36} - 16 q^{37} + 64 q^{40} - 20 q^{42} - 40 q^{43} + 20 q^{45} - 64 q^{46} + 16 q^{48} - 20 q^{51} + 40 q^{55} + 4 q^{57} + 40 q^{58} + 32 q^{60} + 32 q^{61} - 8 q^{63} - 16 q^{66} + 24 q^{67} - 8 q^{70} - 8 q^{72} + 32 q^{73} - 60 q^{75} + 32 q^{76} + 60 q^{78} + 52 q^{81} - 80 q^{82} + 24 q^{85} + 4 q^{87} + 96 q^{88} - 24 q^{90} - 24 q^{91} - 76 q^{93} - 96 q^{96} + 24 q^{97}+O(q^{100}) \) 24 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 - 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 4 * q^21 + 8 * q^22 - 16 * q^25 - 16 * q^27 + 20 * q^30 + 28 * q^33 + 16 * q^36 - 16 * q^37 + 64 * q^40 - 20 * q^42 - 40 * q^43 + 20 * q^45 - 64 * q^46 + 16 * q^48 - 20 * q^51 + 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 + 32 * q^61 - 8 * q^63 - 16 * q^66 + 24 * q^67 - 8 * q^70 - 8 * q^72 + 32 * q^73 - 60 * q^75 + 32 * q^76 + 60 * q^78 + 52 * q^81 - 80 * q^82 + 24 * q^85 + 4 * q^87 + 96 * q^88 - 24 * q^90 - 24 * q^91 - 76 * q^93 - 96 * q^96 + 24 * q^97

Introduction

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