LMFDB - Embedded newform 185.2.p.a.97.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(82,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.p (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:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	185.97
Dual form			185.2.p.a.103.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.775482 + 1.34317i) q^{2} +(0.832043 - 3.10523i) q^{3} +(-0.202746 - 0.351166i) q^{4} +(1.84991 + 1.25612i) q^{5} +(3.52563 + 3.52563i) q^{6} +(1.07995 - 4.03042i) q^{7} -2.47303 q^{8} +(-6.35206 - 3.66736i) q^{9} +(-3.12176 + 1.51064i) q^{10} +2.17031i q^{11} +(-1.25914 + 0.337386i) q^{12} +(-0.186020 - 0.322197i) q^{13} +(4.57608 + 4.57608i) q^{14} +(5.43975 - 4.69923i) q^{15} +(2.32328 - 4.02404i) q^{16} +(2.61037 + 1.50709i) q^{17} +(9.85182 - 5.68795i) q^{18} +(3.82515 + 1.02494i) q^{19} +(0.0660477 - 0.904297i) q^{20} +(-11.6168 - 6.70696i) q^{21} +(-2.91511 - 1.68304i) q^{22} +1.45449 q^{23} +(-2.05766 + 7.67931i) q^{24} +(1.84430 + 4.64742i) q^{25} +0.577022 q^{26} +(-9.85364 + 9.85364i) q^{27} +(-1.63430 + 0.437909i) q^{28} +(-1.83172 - 1.83172i) q^{29} +(2.09345 + 10.9507i) q^{30} +(-3.31971 + 3.31971i) q^{31} +(1.13030 + 1.95773i) q^{32} +(6.73931 + 1.80579i) q^{33} +(-4.04858 + 2.33745i) q^{34} +(7.06051 - 6.09934i) q^{35} +2.97417i q^{36} +(-5.91963 + 1.39926i) q^{37} +(-4.34301 + 4.34301i) q^{38} +(-1.15527 + 0.309554i) q^{39} +(-4.57487 - 3.10643i) q^{40} +(-6.50835 + 3.75760i) q^{41} +(18.0172 - 10.4023i) q^{42} +0.461635 q^{43} +(0.762140 - 0.440021i) q^{44} +(-7.14405 - 14.7633i) q^{45} +(-1.12793 + 1.95363i) q^{46} +(9.19431 + 9.19431i) q^{47} +(-10.5625 - 10.5625i) q^{48} +(-9.01581 - 5.20528i) q^{49} +(-7.67253 - 1.12678i) q^{50} +(6.85181 - 6.85181i) q^{51} +(-0.0754296 + 0.130648i) q^{52} +(0.0494320 + 0.184483i) q^{53} +(-5.59384 - 20.8765i) q^{54} +(-2.72618 + 4.01487i) q^{55} +(-2.67074 + 9.96733i) q^{56} +(6.36537 - 11.0251i) q^{57} +(3.88079 - 1.03985i) q^{58} +(2.33219 + 8.70387i) q^{59} +(-2.75309 - 0.957507i) q^{60} +(-0.701769 - 0.188038i) q^{61} +(-1.88457 - 7.03332i) q^{62} +(-21.6409 + 21.6409i) q^{63} +5.78701 q^{64} +(0.0605992 - 0.829698i) q^{65} +(-7.65172 + 7.65172i) q^{66} +(-10.5795 - 2.83478i) q^{67} -1.22223i q^{68} +(1.21020 - 4.51652i) q^{69} +(2.71719 + 14.2134i) q^{70} +(0.479804 + 0.831045i) q^{71} +(15.7088 + 9.06949i) q^{72} +(-3.33340 - 3.33340i) q^{73} +(2.71112 - 9.03621i) q^{74} +(15.9658 - 1.86012i) q^{75} +(-0.415606 - 1.55106i) q^{76} +(8.74727 + 2.34382i) q^{77} +(0.480107 - 1.79178i) q^{78} +(9.10924 + 2.44081i) q^{79} +(9.35254 - 4.52576i) q^{80} +(11.3970 + 19.7402i) q^{81} -11.6558i q^{82} +(-2.62433 - 9.79413i) q^{83} +5.43923i q^{84} +(2.93583 + 6.06693i) q^{85} +(-0.357990 + 0.620057i) q^{86} +(-7.21197 + 4.16383i) q^{87} -5.36724i q^{88} +(-6.62306 + 1.77464i) q^{89} +(25.3697 + 1.85294i) q^{90} +(-1.49948 + 0.401784i) q^{91} +(-0.294891 - 0.510766i) q^{92} +(7.54630 + 13.0706i) q^{93} +(-19.4796 + 5.21954i) q^{94} +(5.78870 + 6.70091i) q^{95} +(7.01966 - 1.88091i) q^{96} -3.12991i q^{97} +(13.9832 - 8.07320i) q^{98} +(7.95933 - 13.7860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22}+ \cdots + 32 q^{99}+O(q^{100}) $ 68 * q - 4 * q^2 - 8 * q^3 - 30 * q^4 - 10 * q^5 - 8 * q^6 - 2 * q^7 + 12 * q^8 - 6 * q^10 + 14 * q^12 - 6 * q^13 - 8 * q^15 - 26 * q^16 + 12 * q^17 + 18 * q^18 + 4 * q^19 + 48 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 68 * q^27 - 26 * q^28 + 14 * q^29 + 10 * q^30 - 24 * q^31 - 16 * q^32 - 2 * q^33 - 10 * q^35 - 16 * q^37 - 36 * q^38 + 52 * q^39 + 42 * q^40 - 18 * q^41 + 132 * q^42 + 8 * q^43 - 36 * q^44 - 32 * q^45 - 52 * q^46 - 24 * q^47 - 60 * q^48 - 36 * q^49 - 8 * q^50 - 8 * q^51 - 26 * q^52 + 82 * q^53 + 40 * q^54 + 18 * q^55 + 16 * q^56 - 6 * q^57 + 86 * q^58 - 8 * q^59 + 36 * q^60 + 4 * q^61 + 10 * q^62 - 48 * q^63 - 20 * q^64 + 8 * q^65 + 80 * q^66 - 40 * q^67 + 8 * q^69 - 82 * q^70 + 4 * q^71 - 90 * q^72 - 60 * q^73 - 44 * q^74 + 64 * q^75 + 72 * q^76 + 66 * q^77 - 24 * q^78 + 56 * q^79 + 34 * q^80 - 6 * q^81 + 24 * q^83 - 20 * q^85 - 4 * q^86 - 84 * q^87 - 22 * q^89 - 50 * q^90 + 44 * q^91 + 44 * q^92 - 34 * q^93 - 20 * q^94 - 28 * q^95 - 8 * q^96 + 42 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.775482	+	1.34317i	−0.548349	+	0.949768i	0.450039	+	0.893009i	$0.351410\pi$
$2$	−0.775482	+	1.34317i	−0.548349	+	0.949768i	−0.998388	+	0.0567591i	$0.981923\pi$
$3$	0.832043	−	3.10523i	0.480380	−	1.79280i	−0.119638	−	0.992818i	$-0.538174\pi$
$3$	0.832043	−	3.10523i	0.480380	−	1.79280i	0.600019	−	0.799986i	$-0.295160\pi$
$4$	−0.202746	−	0.351166i	−0.101373	−	0.175583i
$5$	1.84991	+	1.25612i	0.827303	+	0.561756i
$5$	1.84991	+	1.25612i	0.827303	+	0.561756i
$6$	3.52563	+	3.52563i	1.43933	+	1.43933i
$7$	1.07995	−	4.03042i	0.408182	−	1.52335i	−0.389929	−	0.920845i	$-0.627501\pi$
$7$	1.07995	−	4.03042i	0.408182	−	1.52335i	0.798111	−	0.602510i	$-0.205833\pi$
$8$	−2.47303			−0.874347
$9$	−6.35206	−	3.66736i	−2.11735	−	1.22245i
$10$	−3.12176	+	1.51064i	−0.987188	+	0.477708i
$11$			2.17031i			0.654374i	0.944960	+	0.327187i	$0.106101\pi$
$11$			2.17031i			0.654374i	−0.944960	+	0.327187i	$0.893899\pi$
$12$	−1.25914	+	0.337386i	−0.363483	+	0.0973950i
$13$	−0.186020	−	0.322197i	−0.0515928	−	0.0893613i	0.839076	−	0.544015i	$-0.183096\pi$
$13$	−0.186020	−	0.322197i	−0.0515928	−	0.0893613i	−0.890668	+	0.454653i	$0.849763\pi$
$14$	4.57608	+	4.57608i	1.22301	+	1.22301i
$15$	5.43975	−	4.69923i	1.40454	−	1.21334i
$16$	2.32328	−	4.02404i	0.580820	−	1.00601i
$17$	2.61037	+	1.50709i	0.633107	+	0.365524i	0.781954	−	0.623336i	$-0.214223\pi$
$17$	2.61037	+	1.50709i	0.633107	+	0.365524i	−0.148848	+	0.988860i	$0.547556\pi$
$18$	9.85182	−	5.68795i	2.32210	−	1.34066i
$19$	3.82515	+	1.02494i	0.877549	+	0.235138i	0.669349	−	0.742948i	$-0.266573\pi$
$19$	3.82515	+	1.02494i	0.877549	+	0.235138i	0.208200	+	0.978086i	$0.433240\pi$
$20$	0.0660477	−	0.904297i	0.0147687	−	0.202207i
$21$	−11.6168	−	6.70696i	−2.53499	−	1.46358i
$22$	−2.91511	−	1.68304i	−0.621504	−	0.358825i
$23$	1.45449			0.303282			0.151641	−	0.988436i	$-0.451544\pi$
$23$	1.45449			0.303282			0.151641	+	0.988436i	$0.451544\pi$
$24$	−2.05766	+	7.67931i	−0.420019	+	1.56753i
$25$	1.84430	+	4.64742i	0.368860	+	0.929485i
$26$	0.577022			0.113163
$27$	−9.85364	+	9.85364i	−1.89633	+	1.89633i
$28$	−1.63430	+	0.437909i	−0.308854	+	0.0827571i
$29$	−1.83172	−	1.83172i	−0.340142	−	0.340142i	0.516279	−	0.856421i	$-0.327317\pi$
$29$	−1.83172	−	1.83172i	−0.340142	−	0.340142i	−0.856421	+	0.516279i	$0.827317\pi$
$30$	2.09345	+	10.9507i	0.382210	+	1.99932i
$31$	−3.31971	+	3.31971i	−0.596237	+	0.596237i	−0.939309	−	0.343072i	$-0.888532\pi$
$31$	−3.31971	+	3.31971i	−0.596237	+	0.596237i	0.343072	+	0.939309i	$0.388532\pi$
$32$	1.13030	+	1.95773i	0.199810	+	0.346082i
$33$	6.73931	+	1.80579i	1.17316	+	0.314348i
$34$	−4.04858	+	2.33745i	−0.694326	+	0.400870i
$35$	7.06051	−	6.09934i	1.19344	−	1.03098i
$36$			2.97417i			0.495695i
$37$	−5.91963	+	1.39926i	−0.973182	+	0.230037i
$37$	−5.91963	+	1.39926i	−0.973182	+	0.230037i
$38$	−4.34301	+	4.34301i	−0.704530	+	0.704530i
$39$	−1.15527	+	0.309554i	−0.184991	+	0.0495683i
$40$	−4.57487	−	3.10643i	−0.723350	−	0.491170i
$41$	−6.50835	+	3.75760i	−1.01643	+	0.586838i	−0.913069	−	0.407805i	$-0.866294\pi$
$41$	−6.50835	+	3.75760i	−1.01643	+	0.586838i	−0.103365	+	0.994644i	$0.532961\pi$
$42$	18.0172	−	10.4023i	2.78012	−	1.60510i
$43$	0.461635			0.0703987			0.0351994	−	0.999380i	$-0.488793\pi$
$43$	0.461635			0.0703987			0.0351994	+	0.999380i	$0.488793\pi$
$44$	0.762140	−	0.440021i	0.114897	−	0.0663357i
$45$	−7.14405	−	14.7633i	−1.06497	−	2.20078i
$46$	−1.12793	+	1.95363i	−0.166304	+	0.288047i
$47$	9.19431	+	9.19431i	1.34113	+	1.34113i	0.894939	+	0.446188i	$0.147219\pi$
$47$	9.19431	+	9.19431i	1.34113	+	1.34113i	0.446188	+	0.894939i	$0.352781\pi$
$48$	−10.5625	−	10.5625i	−1.52456	−	1.52456i
$49$	−9.01581	−	5.20528i	−1.28797	−	0.743611i
$50$	−7.67253	−	1.12678i	−1.08506	−	0.159350i
$51$	6.85181	−	6.85181i	0.959445	−	0.959445i
$52$	−0.0754296	+	0.130648i	−0.0104602	+	0.0181176i
$53$	0.0494320	+	0.184483i	0.00679000	+	0.0253406i	0.969238	−	0.246126i	$-0.0791579\pi$
$53$	0.0494320	+	0.184483i	0.00679000	+	0.0253406i	−0.962448	+	0.271467i	$0.912491\pi$
$54$	−5.59384	−	20.8765i	−0.761225	−	2.84093i
$55$	−2.72618	+	4.01487i	−0.367599	+	0.541366i
$56$	−2.67074	+	9.96733i	−0.356892	+	1.33194i
$57$	6.36537	−	11.0251i	0.843114	−	1.46032i
$58$	3.88079	−	1.03985i	0.509572	−	0.136539i
$59$	2.33219	+	8.70387i	0.303626	+	1.13315i	0.934122	+	0.356954i	$0.116185\pi$
$59$	2.33219	+	8.70387i	0.303626	+	1.13315i	−0.630496	+	0.776192i	$0.717148\pi$
$60$	−2.75309	−	0.957507i	−0.355423	−	0.123614i
$61$	−0.701769	−	0.188038i	−0.0898523	−	0.0240758i	0.213613	−	0.976918i	$-0.431477\pi$
$61$	−0.701769	−	0.188038i	−0.0898523	−	0.0240758i	−0.303465	+	0.952843i	$0.598144\pi$
$62$	−1.88457	−	7.03332i	−0.239341	−	0.893233i
$63$	−21.6409	+	21.6409i	−2.72650	+	2.72650i
$64$	5.78701			0.723377
$65$	0.0605992	−	0.829698i	0.00751640	−	0.102911i
$66$	−7.65172	+	7.65172i	−0.941861	+	0.941861i
$67$	−10.5795	−	2.83478i	−1.29250	−	0.346323i	−0.453888	−	0.891059i	$-0.649963\pi$
$67$	−10.5795	−	2.83478i	−1.29250	−	0.346323i	−0.838608	+	0.544735i	$0.816630\pi$
$68$		−	1.22223i		−	0.148217i
$69$	1.21020	−	4.51652i	0.145691	−	0.543725i
$70$	2.71719	+	14.2134i	0.324766	+	1.69883i
$71$	0.479804	+	0.831045i	0.0569423	+	0.0986269i	0.893091	−	0.449875i	$-0.148532\pi$
$71$	0.479804	+	0.831045i	0.0569423	+	0.0986269i	−0.836149	+	0.548502i	$0.815198\pi$
$72$	15.7088	+	9.06949i	1.85130	+	1.06885i
$73$	−3.33340	−	3.33340i	−0.390145	−	0.390145i	0.484594	−	0.874739i	$-0.338967\pi$
$73$	−3.33340	−	3.33340i	−0.390145	−	0.390145i	−0.874739	+	0.484594i	$0.838967\pi$
$74$	2.71112	−	9.03621i	0.315161	−	1.05044i
$75$	15.9658	−	1.86012i	1.84358	−	0.214788i
$76$	−0.415606	−	1.55106i	−0.0476733	−	0.177919i
$77$	8.74727	+	2.34382i	0.996844	+	0.267104i
$78$	0.480107	−	1.79178i	0.0543614	−	0.202880i
$79$	9.10924	+	2.44081i	1.02487	+	0.274613i	0.731830	−	0.681487i	$-0.238667\pi$
$79$	9.10924	+	2.44081i	1.02487	+	0.274613i	0.293040	+	0.956100i	$0.405333\pi$
$80$	9.35254	−	4.52576i	1.04565	−	0.505996i
$81$	11.3970	+	19.7402i	1.26634	+	2.19336i
$82$		−	11.6558i		−	1.28717i
$83$	−2.62433	−	9.79413i	−0.288058	−	1.07505i	−0.946576	−	0.322481i	$-0.895483\pi$
$83$	−2.62433	−	9.79413i	−0.288058	−	1.07505i	0.658518	−	0.752565i	$-0.271183\pi$
$84$			5.43923i			0.593469i
$85$	2.93583	+	6.06693i	0.318435	+	0.658051i
$86$	−0.357990	+	0.620057i	−0.0386030	+	0.0668624i
$87$	−7.21197	+	4.16383i	−0.773205	+	0.446410i
$88$		−	5.36724i		−	0.572150i
$89$	−6.62306	+	1.77464i	−0.702043	+	0.188112i	−0.592145	−	0.805831i	$-0.701719\pi$
$89$	−6.62306	+	1.77464i	−0.702043	+	0.188112i	−0.109897	+	0.993943i	$0.535052\pi$
$90$	25.3697	+	1.85294i	2.67420	+	0.195317i
$91$	−1.49948	+	0.401784i	−0.157188	+	0.0421184i
$92$	−0.294891	−	0.510766i	−0.0307445	−	0.0532511i
$93$	7.54630	+	13.0706i	0.782515	+	1.35536i
$94$	−19.4796	+	5.21954i	−2.00917	+	0.538354i
$95$	5.78870	+	6.70091i	0.593908	+	0.687499i
$96$	7.01966	−	1.88091i	0.716441	−	0.191970i
$97$		−	3.12991i		−	0.317794i	−0.987295	−	0.158897i	$-0.949206\pi$
$97$		−	3.12991i		−	0.317794i	0.987295	−	0.158897i	$-0.0507938\pi$
$98$	13.9832	−	8.07320i	1.41252	−	0.815517i
$99$	7.95933	−	13.7860i	0.799943	−	1.38554i
$100$	1.25809	−	1.58990i	0.125809	−	0.158990i
$101$			0.106640i			0.0106111i	0.999986	+	0.00530554i	$0.00168881\pi$
$101$			0.106640i			0.0106111i	−0.999986	+	0.00530554i	$0.998311\pi$
$102$	3.88972	+	14.5166i	0.385140	+	1.43736i
$103$		−	10.4126i		−	1.02599i	−0.858392	−	0.512994i	$-0.828536\pi$
$103$		−	10.4126i		−	1.02599i	0.858392	−	0.512994i	$-0.171464\pi$
$104$	0.460033	+	0.796801i	0.0451100	+	0.0781328i
$105$	−13.0652	−	26.9994i	−1.27503	−	2.63487i
$106$	−0.286126	−	0.0766672i	−0.0277910	−	0.00744658i
$107$	1.85691	−	6.93007i	0.179514	−	0.669955i	−0.816225	−	0.577734i	$-0.803937\pi$
$107$	1.85691	−	6.93007i	0.179514	−	0.669955i	0.995739	−	0.0922203i	$-0.0293964\pi$
$108$	5.45804	+	1.46248i	0.525200	+	0.140727i
$109$	3.37101	+	12.5808i	0.322884	+	1.20502i	0.916422	+	0.400213i	$0.131064\pi$
$109$	3.37101	+	12.5808i	0.322884	+	1.20502i	−0.593538	+	0.804806i	$0.702269\pi$
$110$	−3.27857	−	6.77521i	−0.312599	−	0.645991i
$111$	−0.580363	+	19.5461i	−0.0550856	+	1.85523i
$112$	−13.7095	−	13.7095i	−1.29543	−	1.29543i
$113$	−7.00421	−	4.04388i	−0.658901	−	0.380417i	0.132957	−	0.991122i	$-0.457553\pi$
$113$	−7.00421	−	4.04388i	−0.658901	−	0.380417i	−0.791858	+	0.610705i	$0.790886\pi$
$114$	9.87247	+	17.0996i	0.924641	+	1.60153i
$115$	2.69067	+	1.82702i	0.250906	+	0.170370i
$116$	−0.271864	+	1.01461i	−0.0252419	+	0.0942042i
$117$			2.72882i			0.252279i
$118$	−13.4994	−	3.61715i	−1.24272	−	0.332986i
$119$	8.89328	−	8.89328i	0.815246	−	0.815246i
$120$	−13.4527	+	11.6213i	−1.22805	+	1.06088i
$121$	6.28974			0.571795
$122$	0.796778	−	0.796778i	0.0721369	−	0.0721369i
$123$	6.25297	+	23.3364i	0.563811	+	2.10417i
$124$	1.83882	+	0.492711i	0.165131	+	0.0442468i
$125$	−2.42596	+	10.9140i	−0.216985	+	0.976175i
$126$	−12.2854	−	45.8497i	−1.09447	−	4.08461i
$127$	−9.70404	+	2.60019i	−0.861094	+	0.230729i	−0.662233	−	0.749298i	$-0.730391\pi$
$127$	−9.70404	+	2.60019i	−0.861094	+	0.230729i	−0.198861	+	0.980028i	$0.563724\pi$
$128$	−6.74832	+	11.6884i	−0.596473	+	1.03312i
$129$	0.384100	−	1.43348i	0.0338182	−	0.126211i
$130$	1.06744	+	0.724812i	0.0936203	+	0.0635702i
$131$	−3.80218	−	14.1899i	−0.332198	−	1.23978i	−0.906875	−	0.421400i	$-0.861539\pi$
$131$	−3.80218	−	14.1899i	−0.332198	−	1.23978i	0.574677	−	0.818381i	$-0.305128\pi$
$132$	−0.732234	−	2.73273i	−0.0637328	−	0.237854i
$133$	8.26191	−	14.3101i	0.716399	−	1.24084i
$134$	12.0118	−	12.0118i	1.03767	−	1.03767i
$135$	−30.6057	+	5.85090i	−2.63412	+	0.503565i
$136$	−6.45550	−	3.72709i	−0.553555	−	0.319595i
$137$	4.80375	+	4.80375i	0.410412	+	0.410412i	0.881882	−	0.471470i	$-0.156276\pi$
$137$	4.80375	+	4.80375i	0.410412	+	0.410412i	−0.471470	+	0.881882i	$0.656276\pi$
$138$	5.12799	+	5.12799i	0.436523	+	0.436523i
$139$	11.5314	−	19.9729i	0.978077	−	1.69408i	0.308693	−	0.951162i	$-0.400108\pi$
$139$	11.5314	−	19.9729i	0.978077	−	1.69408i	0.669384	−	0.742917i	$-0.266558\pi$
$140$	−3.57337	−	1.24279i	−0.302005	−	0.105035i
$141$	36.2005	−	20.9003i	3.04863	−	1.76013i
$142$	−1.48832			−0.124897
$143$	0.699268	−	0.403722i	0.0584757	−	0.0337610i
$144$	−29.5152	+	17.0406i	−2.45960	+	1.42005i
$145$	−1.08764	−	5.68938i	−0.0903236	−	0.472477i
$146$	7.06234	−	1.89235i	0.584483	−	0.156612i
$147$	−23.6651	+	23.6651i	−1.95187	+	1.95187i
$148$	1.69155	+	1.79508i	0.139045	+	0.147555i
$149$		−	11.1717i		−	0.915220i	−0.889153	−	0.457610i	$-0.848706\pi$
$149$		−	11.1717i		−	0.915220i	0.889153	−	0.457610i	$-0.151294\pi$
$150$	−9.88277	+	22.8874i	−0.806925	+	1.86875i
$151$	−2.37742	+	1.37260i	−0.193472	+	0.111701i	−0.593607	−	0.804755i	$-0.702297\pi$
$151$	−2.37742	+	1.37260i	−0.193472	+	0.111701i	0.400135	+	0.916456i	$0.368963\pi$
$152$	−9.45969	−	2.53472i	−0.767282	−	0.205593i
$153$	−11.0541	−	19.1463i	−0.893674	−	1.54789i
$154$	−9.93152	+	9.93152i	−0.800305	+	0.800305i
$155$	−10.3111	+	1.97118i	−0.828208	+	0.158329i
$156$	0.342931	+	0.342931i	0.0274564	+	0.0274564i
$157$	6.93834	−	1.85912i	0.553740	−	0.148374i	0.0289111	−	0.999582i	$-0.490796\pi$
$157$	6.93834	−	1.85912i	0.553740	−	0.148374i	0.524829	+	0.851208i	$0.324129\pi$
$158$	−10.3425	+	10.3425i	−0.822804	+	0.822804i
$159$	0.613990			0.0486926
$160$	−0.368213	+	5.04142i	−0.0291098	+	0.398559i
$161$	1.57077	−	5.86220i	0.123794	−	0.462006i
$162$	−35.3528			−2.77758
$163$	−0.140611	−	0.0811818i	−0.0110135	−	0.00635865i	0.494483	−	0.869187i	$-0.335357\pi$
$163$	−0.140611	−	0.0811818i	−0.0110135	−	0.00635865i	−0.505497	+	0.862829i	$0.668691\pi$
$164$	2.63908	+	1.52367i	0.206077	+	0.118979i
$165$	10.1988	+	11.8060i	0.793975	+	0.919093i
$166$	15.1903	+	4.07024i	1.17900	+	0.315912i
$167$	11.9802	−	6.91676i	0.927055	−	0.535235i	0.0411758	−	0.999152i	$-0.486890\pi$
$167$	11.9802	−	6.91676i	0.927055	−	0.535235i	0.885879	+	0.463917i	$0.153556\pi$
$168$	28.7287	+	16.5865i	2.21646	+	1.27968i
$169$	6.43079	−	11.1385i	0.494676	−	0.856805i
$170$	−10.4256	−	0.761463i	−0.799609	−	0.0584015i
$171$	−20.5387	−	20.5387i	−1.57064	−	1.57064i
$172$	−0.0935945	−	0.162110i	−0.00713652	−	0.0123608i
$173$	−15.4610	+	4.14277i	−1.17548	+	0.314969i	−0.793132	−	0.609050i	$-0.791551\pi$
$173$	−15.4610	+	4.14277i	−1.17548	+	0.314969i	−0.382347	+	0.924019i	$0.624884\pi$
$174$		−	12.9159i		−	0.979153i
$175$	20.7228	−	2.41433i	1.56650	−	0.182506i
$176$	8.73342	+	5.04224i	0.658307	+	0.380073i
$177$	28.9680			2.17737
$178$	2.75241	−	10.2721i	0.206302	−	0.769929i
$179$	10.4070	+	10.4070i	0.777858	+	0.777858i	0.979466	−	0.201608i	$-0.0646168\pi$
$179$	10.4070	+	10.4070i	0.777858	+	0.777858i	−0.201608	+	0.979466i	$0.564617\pi$
$180$	−3.73593	+	5.50193i	−0.278460	+	0.410090i
$181$	11.4850	+	19.8925i	0.853670	+	1.47860i	0.877873	+	0.478893i	$0.158962\pi$
$181$	11.4850	+	19.8925i	0.853670	+	1.47860i	−0.0242033	+	0.999707i	$0.507705\pi$
$182$	0.623153	−	2.32564i	0.0461912	−	0.172388i
$183$	−1.16780	+	2.02270i	−0.0863265	+	0.149522i
$184$	−3.59699			−0.265174
$185$	−12.7084	−	4.84730i	−0.934341	−	0.356380i
$186$	−23.4081			−1.71637
$187$	−3.27087	+	5.66531i	−0.239190	+	0.414288i
$188$	1.36462	−	5.09283i	0.0995251	−	0.371433i
$189$	29.0729	+	50.3557i	2.11474	+	3.66284i
$190$	−13.4895	+	2.57880i	−0.978634	+	0.187086i
$191$	−6.64661	−	6.64661i	−0.480931	−	0.480931i	0.424498	−	0.905429i	$-0.360451\pi$
$191$	−6.64661	−	6.64661i	−0.480931	−	0.480931i	−0.905429	+	0.424498i	$0.860451\pi$
$192$	4.81505	−	17.9700i	0.347496	−	1.29687i
$193$	13.5429			0.974841			0.487420	−	0.873167i	$-0.337938\pi$
$193$	13.5429			0.974841			0.487420	+	0.873167i	$0.337938\pi$
$194$	4.20401	+	2.42719i	0.301830	+	0.174262i
$195$	−2.52598	−	0.878519i	−0.180889	−	0.0629120i
$196$			4.22139i			0.301528i
$197$	−11.4478	+	3.06743i	−0.815623	+	0.218546i	−0.642432	−	0.766343i	$-0.722074\pi$
$197$	−11.4478	+	3.06743i	−0.815623	+	0.218546i	−0.173191	+	0.984888i	$0.555408\pi$
$198$	12.3446	+	21.3815i	0.877295	+	1.51952i
$199$	7.49425	+	7.49425i	0.531253	+	0.531253i	0.920945	−	0.389692i	$-0.127419\pi$
$199$	7.49425	+	7.49425i	0.531253	+	0.531253i	−0.389692	+	0.920945i	$0.627419\pi$
$200$	−4.56101	−	11.4932i	−0.322512	−	0.812692i
$201$	−17.6053	+	30.4932i	−1.24178	+	2.15083i
$202$	−0.143236	−	0.0826974i	−0.0100781	−	0.00581857i
$203$	−9.36076	+	5.40444i	−0.656996	+	0.379317i
$204$	−3.79529	−	1.01695i	−0.265724	−	0.0712005i
$205$	−16.7598	−	1.22410i	−1.17056	−	0.0854948i
$206$	13.9860	+	8.07481i	0.974450	+	0.562599i
$207$	−9.23900	−	5.33414i	−0.642155	−	0.370748i
$208$	−1.72871			−0.119864
$209$	−2.22445	+	8.30177i	−0.153869	+	0.574245i
$210$	46.3967	+	3.38871i	3.20168	+	0.233843i
$211$	−14.6599			−1.00923			−0.504616	−	0.863344i	$-0.668366\pi$
$211$	−14.6599			−1.00923			−0.504616	+	0.863344i	$0.668366\pi$
$212$	0.0547618	−	0.0547618i	0.00376106	−	0.00376106i
$213$	2.97980	−	0.798435i	0.204173	−	0.0547079i
$214$	7.86829	+	7.86829i	0.537865	+	0.537865i
$215$	0.853982	+	0.579871i	0.0582411	+	0.0395469i
$216$	24.3683	−	24.3683i	1.65805	−	1.65805i
$217$	9.79470	+	16.9649i	0.664908	+	1.15165i
$218$	−19.5123	−	5.22831i	−1.32154	−	0.354106i
$219$	−13.1245	+	7.57744i	−0.886872	+	0.512036i
$220$	1.96261	+	0.143344i	0.132319	+	0.00966427i
$221$		−	1.12140i		−	0.0754336i
$222$	−25.8037	−	15.9371i	−1.73183	−	1.06963i
$223$	3.77596	−	3.77596i	0.252857	−	0.252857i	−0.569284	−	0.822141i	$-0.692779\pi$
$223$	3.77596	−	3.77596i	0.252857	−	0.252857i	0.822141	+	0.569284i	$0.192779\pi$
$224$	9.11115	−	2.44132i	0.608764	−	0.163118i
$225$	5.32869	−	36.2845i	0.355246	−	2.41896i
$226$	10.8633	−	6.27192i	0.722615	−	0.417202i
$227$	−10.2511	+	5.91849i	−0.680391	+	0.392824i	−0.800002	−	0.599997i	$-0.795168\pi$
$227$	−10.2511	+	5.91849i	−0.680391	+	0.392824i	0.119611	+	0.992821i	$0.461835\pi$
$228$	−5.16221			−0.341875
$229$	−10.1713	+	5.87243i	−0.672141	+	0.388061i	−0.796887	−	0.604128i	$-0.793522\pi$
$229$	−10.1713	+	5.87243i	−0.672141	+	0.388061i	0.124746	+	0.992189i	$0.460188\pi$
$230$	−4.54057	+	2.19721i	−0.299396	+	0.144880i
$231$	14.5562	−	25.2121i	0.957728	−	1.65883i
$232$	4.52989	+	4.52989i	0.297402	+	0.297402i
$233$	−15.5975	−	15.5975i	−1.02183	−	1.02183i	−0.999756	−	0.0220706i	$-0.992974\pi$
$233$	−15.5975	−	15.5975i	−1.02183	−	1.02183i	−0.0220706	−	0.999756i	$-0.507026\pi$
$234$	−3.66528	−	2.11615i	−0.239607	−	0.138337i
$235$	5.45940	+	28.5578i	0.356132	+	1.86290i
$236$	2.58366	−	2.58366i	0.168182	−	0.168182i
$237$	15.1586	−	26.2554i	0.984654	−	1.70547i
$238$	5.04865	+	18.8418i	0.327255	+	1.22133i
$239$	−4.07548	−	15.2099i	−0.263621	−	0.983846i	−0.963089	−	0.269183i	$-0.913247\pi$
$239$	−4.07548	−	15.2099i	−0.263621	−	0.983846i	0.699468	−	0.714663i	$-0.253420\pi$
$240$	−6.27180	−	32.8074i	−0.404843	−	2.11771i
$241$	2.51727	−	9.39459i	0.162152	−	0.605159i	−0.836235	−	0.548372i	$-0.815248\pi$
$241$	2.51727	−	9.39459i	0.162152	−	0.605159i	0.998386	−	0.0567867i	$-0.0180855\pi$
$242$	−4.87758	+	8.44822i	−0.313543	+	0.543072i
$243$	30.3998	−	8.14560i	1.95015	−	0.522540i
$244$	0.0762479	+	0.284561i	0.00488127	+	0.0182172i
$245$	−10.1399	−	20.9543i	−0.647815	−	1.33872i
$246$	−36.1939	−	9.69813i	−2.30764	−	0.618330i
$247$	−0.381321	−	1.42311i	−0.0242629	−	0.0905503i
$248$	8.20972	−	8.20972i	0.521318	−	0.521318i
$249$	−32.5966			−2.06572
$250$	−12.7781	−	11.7221i	−0.808156	−	0.741369i
$251$	−21.3201	+	21.3201i	−1.34571	+	1.34571i	−0.455447	+	0.890263i	$0.650521\pi$
$251$	−21.3201	+	21.3201i	−1.34571	+	1.34571i	−0.890263	+	0.455447i	$0.849479\pi$
$252$	11.9871	+	3.21195i	0.755119	+	0.202334i
$253$			3.15670i			0.198460i
$254$	4.03280	−	15.0506i	0.253040	−	0.944360i
$255$	21.2819	−	4.06847i	1.33273	−	0.254778i
$256$	−4.67940	−	8.10495i	−0.292462	−	0.506559i
$257$	−5.04941	−	2.91528i	−0.314974	−	0.181850i	0.334176	−	0.942511i	$-0.391542\pi$
$257$	−5.04941	−	2.91528i	−0.314974	−	0.181850i	−0.649150	+	0.760660i	$0.724875\pi$
$258$	1.62755	+	1.62755i	0.101327	+	0.101327i
$259$	−0.753280	+	25.3697i	−0.0468066	+	1.57640i
$260$	−0.303648	+	0.146937i	−0.0188314	+	0.00911267i
$261$	4.91761	+	18.3528i	0.304393	+	1.13601i
$262$	22.0081	+	5.89705i	1.35966	+	0.364321i
$263$	5.19979	−	19.4059i	0.320633	−	1.19662i	−0.597997	−	0.801498i	$-0.704036\pi$
$263$	5.19979	−	19.4059i	0.320633	−	1.19662i	0.918630	−	0.395120i	$-0.129297\pi$
$264$	−16.6665	−	4.46578i	−1.02575	−	0.274850i
$265$	−0.140289	+	0.403368i	−0.00861787	+	0.0247787i
$266$	12.8139	+	22.1944i	0.785673	+	1.36083i
$267$			22.0427i			1.34899i
$268$	1.14948	+	4.28991i	0.0702155	+	0.262048i
$269$		−	0.930688i		−	0.0567450i	−0.999597	−	0.0283725i	$-0.990968\pi$
$269$		−	0.930688i		−	0.0567450i	0.999597	−	0.0283725i	$-0.00903246\pi$
$270$	15.8754	−	45.6461i	0.966146	−	2.77793i
$271$	7.15555	−	12.3938i	0.434669	−	0.752868i	−0.562600	−	0.826729i	$-0.690199\pi$
$271$	7.15555	−	12.3938i	0.434669	−	0.752868i	0.997269	+	0.0738613i	$0.0235322\pi$
$272$	12.1292	−	7.00281i	0.735442	−	0.424607i
$273$			4.99053i			0.302040i
$274$	−10.1775	+	2.72705i	−0.614845	+	0.164747i
$275$	−10.0864	+	4.00271i	−0.608231	+	0.241373i
$276$	−1.83141	+	0.490724i	−0.110238	+	0.0295381i
$277$	−1.89779	−	3.28707i	−0.114027	−	0.197501i	0.803363	−	0.595489i	$-0.203042\pi$
$277$	−1.89779	−	3.28707i	−0.114027	−	0.197501i	−0.917391	+	0.397988i	$0.869708\pi$
$278$	17.8847	+	30.9772i	1.07265	+	1.85789i
$279$	33.2616	−	8.91241i	1.99132	−	0.533572i
$280$	−17.4608	+	15.0838i	−1.04348	+	0.901432i
$281$	4.91815	−	1.31781i	0.293392	−	0.0786142i	−0.109121	−	0.994029i	$-0.534804\pi$
$281$	4.91815	−	1.31781i	0.293392	−	0.0786142i	0.402513	+	0.915414i	$0.368137\pi$
$282$			64.8314i			3.86065i
$283$	−12.9217	+	7.46035i	−0.768115	+	0.443472i	−0.832202	−	0.554473i	$-0.812920\pi$
$283$	−12.9217	+	7.46035i	−0.768115	+	0.443472i	0.0640865	+	0.997944i	$0.479587\pi$
$284$	0.194556	−	0.336982i	0.0115448	−	0.0199962i
$285$	25.6243	−	12.3998i	1.51785	−	0.734500i
$286$			1.25232i			0.0740511i
$287$	8.11601	+	30.2894i	0.479073	+	1.78793i
$288$		−	16.5809i		−	0.977036i
$289$	−3.95733	−	6.85430i	−0.232784	−	0.403194i
$290$	8.48527	+	2.95112i	0.498272	+	0.173296i
$291$	−9.71907	−	2.60422i	−0.569742	−	0.152662i
$292$	−0.494744	+	1.84641i	−0.0289527	+	0.108053i
$293$	−1.46228	−	0.391817i	−0.0854275	−	0.0228902i	0.215852	−	0.976426i	$-0.430747\pi$
$293$	−1.46228	−	0.391817i	−0.0854275	−	0.0228902i	−0.301280	+	0.953536i	$0.597414\pi$
$294$	−13.4345	−	50.1383i	−0.783516	−	2.92412i
$295$	−6.61880	+	19.0309i	−0.385362	+	1.10802i
$296$	14.6394	−	3.46041i	0.850899	−	0.201132i
$297$	−21.3855	−	21.3855i	−1.24091	−	1.24091i
$298$	15.0055	+	8.66344i	0.869246	+	0.501860i
$299$	−0.270564	−	0.468631i	−0.0156471	−	0.0271017i
$300$	−3.89021	−	5.22953i	−0.224602	−	0.301927i
$301$	0.498542	−	1.86058i	0.0287355	−	0.107242i
$302$		−	4.25772i		−	0.245004i
$303$	0.331141	+	0.0887290i	0.0190236	+	0.00509735i
$304$	13.0113	−	13.0113i	0.746249	−	0.746249i
$305$	−1.06201	−	1.22936i	−0.0608103	−	0.0703931i
$306$	34.2891			1.96018
$307$	21.0899	−	21.0899i	1.20366	−	1.20366i	0.230621	−	0.973044i	$-0.425924\pi$
$307$	21.0899	−	21.0899i	1.20366	−	1.20366i	0.973044	−	0.230621i	$-0.0740758\pi$
$308$	−0.950400	−	3.54694i	−0.0541541	−	0.202106i
$309$	−32.3336	−	8.66376i	−1.83939	−	0.492864i
$310$	5.34845	−	15.3782i	0.303771	−	0.873425i
$311$	3.03440	+	11.3245i	0.172065	+	0.642156i	0.997033	+	0.0769762i	$0.0245265\pi$
$311$	3.03440	+	11.3245i	0.172065	+	0.642156i	−0.824968	+	0.565180i	$0.808807\pi$
$312$	2.85702	−	0.765535i	0.161747	−	0.0433399i
$313$	−3.22812	+	5.59126i	−0.182464	+	0.316037i	−0.942719	−	0.333588i	$-0.891741\pi$
$313$	−3.22812	+	5.59126i	−0.182464	+	0.316037i	0.760255	+	0.649625i	$0.225074\pi$
$314$	−2.88343	+	10.7611i	−0.162722	+	0.607285i
$315$	−67.2173	+	12.8500i	−3.78727	+	0.724013i
$316$	−0.989728	−	3.69372i	−0.0556766	−	0.207788i
$317$	5.73743	+	21.4124i	0.322246	+	1.20264i	0.917051	+	0.398769i	$0.130562\pi$
$317$	5.73743	+	21.4124i	0.322246	+	1.20264i	−0.594805	+	0.803870i	$0.702771\pi$
$318$	−0.476138	+	0.824696i	−0.0267005	+	0.0462466i
$319$	3.97540	−	3.97540i	0.222580	−	0.222580i
$320$	10.7054	+	7.26921i	0.598452	+	0.406361i
$321$	−19.9744	−	11.5322i	−1.11486	−	0.643666i
$322$	6.65585	+	6.65585i	0.370916	+	0.370916i
$323$	8.44034	+	8.44034i	0.469633	+	0.469633i
$324$	4.62140	−	8.00449i	0.256744	−	0.444694i
$325$	1.15431	−	1.45874i	0.0640294	−	0.0809165i
$326$	0.218083	−	0.125910i	0.0120785	−	0.00697352i
$327$	41.8710			2.31547
$328$	16.0953	−	9.29264i	0.888716	−	0.513100i
$329$	46.9863	−	27.1275i	2.59044	−	1.49559i
$330$	−23.7665	+	4.54344i	−1.30830	+	0.250108i
$331$	8.07555	−	2.16384i	0.443873	−	0.118935i	−0.0299583	−	0.999551i	$-0.509537\pi$
$331$	8.07555	−	2.16384i	0.443873	−	0.118935i	0.473831	+	0.880616i	$0.342871\pi$
$332$	−2.90729	+	2.90729i	−0.159558	+	0.159558i
$333$	42.7335	+	12.8213i	2.34178	+	0.702600i
$334$			21.4553i			1.17398i
$335$	−16.0103	−	18.5333i	−0.874737	−	1.01258i
$336$	−53.9782	+	31.1643i	−2.94475	+	1.70015i
$337$	−7.82004	−	2.09537i	−0.425985	−	0.114142i	0.0394559	−	0.999221i	$-0.487438\pi$
$337$	−7.82004	−	2.09537i	−0.425985	−	0.114142i	−0.465441	+	0.885079i	$0.654104\pi$
$338$	9.97393	+	17.2754i	0.542510	+	0.939656i
$339$	−18.3850	+	18.3850i	−0.998535	+	0.998535i
$340$	1.53527	−	2.26101i	0.0832617	−	0.122620i
$341$	−7.20480	−	7.20480i	−0.390162	−	0.390162i
$342$	43.5145	−	11.6597i	2.35299	−	0.630483i
$343$	−10.0628	+	10.0628i	−0.543338	+	0.543338i
$344$	−1.14164			−0.0615529
$345$	7.91206	−	6.83497i	0.425971	−	0.367982i
$346$	6.42528	−	23.9795i	0.345425	−	1.28915i
$347$	−26.0269			−1.39720			−0.698599	−	0.715513i	$-0.746193\pi$
$347$	−26.0269			−1.39720			−0.698599	+	0.715513i	$0.746193\pi$
$348$	2.92439	+	1.68840i	0.156764	+	0.0905077i
$349$	−2.63616	−	1.52199i	−0.141110	−	0.0814701i	0.427783	−	0.903882i	$-0.359295\pi$
$349$	−2.63616	−	1.52199i	−0.141110	−	0.0814701i	−0.568893	+	0.822412i	$0.692628\pi$
$350$	−12.8273	+	29.7066i	−0.685648	+	1.58789i
$351$	5.00779	+	1.34183i	0.267296	+	0.0716217i
$352$	−4.24889	+	2.45310i	−0.226467	+	0.130751i
$353$	−5.98486	−	3.45536i	−0.318542	−	0.183910i	0.332200	−	0.943209i	$-0.392209\pi$
$353$	−5.98486	−	3.45536i	−0.318542	−	0.183910i	−0.650743	+	0.759298i	$0.725542\pi$
$354$	−22.4641	+	38.9090i	−1.19396	+	2.06799i
$355$	−0.156304	+	2.14005i	−0.00829576	+	0.113582i
$356$	1.96599	+	1.96599i	0.104197	+	0.104197i
$357$	−20.2161	−	35.0152i	−1.06995	−	1.85320i
$358$	−22.0489	+	5.90799i	−1.16532	+	0.312247i
$359$			13.2822i			0.701008i	0.936561	+	0.350504i	$0.113990\pi$
$359$			13.2822i			0.701008i	−0.936561	+	0.350504i	$0.886010\pi$
$360$	17.6674	+	36.5099i	0.931155	+	1.92424i
$361$	−2.87325	−	1.65887i	−0.151224	−	0.0873090i
$362$	−35.6255			−1.87244
$363$	5.23333	−	19.5311i	0.274679	−	1.02512i
$364$	0.445106	+	0.445106i	0.0233299	+	0.0233299i
$365$	−1.97931	−	10.3536i	−0.103602	−	0.541935i
$366$	−1.81122	−	3.13713i	−0.0946741	−	0.163980i
$367$	5.20590	−	19.4287i	0.271746	−	1.01417i	−0.686245	−	0.727370i	$-0.740742\pi$
$367$	5.20590	−	19.4287i	0.271746	−	1.01417i	0.957991	−	0.286799i	$-0.0925911\pi$
$368$	3.37918	−	5.85292i	0.176152	−	0.305104i
$369$	55.1219			2.86953
$370$	16.3659	−	13.3106i	0.850823	−	0.691986i
$371$	0.796926			0.0413743
$372$	3.05996	−	5.30001i	0.158652	−	0.274793i
$373$	−0.271365	+	1.01275i	−0.0140507	+	0.0524380i	−0.972595	−	0.232505i	$-0.925308\pi$
$373$	−0.271365	+	1.01275i	−0.0140507	+	0.0524380i	0.958545	+	0.284943i	$0.0919746\pi$
$374$	−5.07300	−	8.78670i	−0.262319	−	0.454349i
$375$	31.8718	+	16.6141i	1.64585	+	0.857946i
$376$	−22.7378	−	22.7378i	−1.17261	−	1.17261i
$377$	−0.249437	+	0.930911i	−0.0128467	+	0.0479444i
$378$	−90.1820			−4.63846
$379$	13.4701	+	7.77696i	0.691912	+	0.399476i	0.804328	−	0.594186i	$-0.202526\pi$
$379$	13.4701	+	7.77696i	0.691912	+	0.399476i	−0.112416	+	0.993661i	$0.535859\pi$
$380$	1.17950	−	3.39137i	0.0605069	−	0.173974i
$381$			32.2967i			1.65461i
$382$	14.0819	−	3.77323i	0.720492	−	0.193055i
$383$	−2.12027	−	3.67241i	−0.108341	−	0.187651i	0.806758	−	0.590883i	$-0.201220\pi$
$383$	−2.12027	−	3.67241i	−0.108341	−	0.187651i	−0.915098	+	0.403231i	$0.867887\pi$
$384$	30.6804	+	30.6804i	1.56565	+	1.56565i
$385$	13.2375	+	15.3235i	0.674645	+	0.780959i
$386$	−10.5023	+	18.1905i	−0.534553	+	0.925872i
$387$	−2.93234	−	1.69298i	−0.149059	−	0.0860593i
$388$	−1.09912	+	0.634575i	−0.0557992	+	0.0322157i
$389$	−14.7360	−	3.94851i	−0.747146	−	0.200197i	−0.134894	−	0.990860i	$-0.543069\pi$
$389$	−14.7360	−	3.94851i	−0.747146	−	0.200197i	−0.612252	+	0.790663i	$0.709736\pi$
$390$	3.13886	−	2.71156i	0.158942	−	0.137305i
$391$	3.79675	+	2.19205i	0.192010	+	0.110857i
$392$	22.2963	+	12.8728i	1.12613	+	0.650174i
$393$	−47.2266			−2.38226
$394$	4.75748	−	17.7552i	0.239678	−	0.894492i
$395$	13.7853	+	15.9576i	0.693612	+	0.802915i
$396$	−6.45488			−0.324370
$397$	−6.05031	+	6.05031i	−0.303657	+	0.303657i	−0.842443	−	0.538786i	$-0.818883\pi$
$397$	−6.05031	+	6.05031i	−0.303657	+	0.303657i	0.538786	+	0.842443i	$0.318883\pi$
$398$	−15.8777	+	4.25443i	−0.795879	+	0.213255i
$399$	−37.5617	−	37.5617i	−1.88044	−	1.88044i
$400$	22.9862	+	3.37573i	1.14931	+	0.168786i
$401$	−8.64655	+	8.64655i	−0.431788	+	0.431788i	−0.889236	−	0.457448i	$-0.848764\pi$
$401$	−8.64655	+	8.64655i	−0.431788	+	0.431788i	0.457448	+	0.889236i	$0.348764\pi$
$402$	−27.3051	−	47.2939i	−1.36186	−	2.35880i
$403$	1.68713	+	0.452066i	0.0840420	+	0.0225190i
$404$	0.0374483	−	0.0216208i	0.00186312	−	0.00107567i
$405$	−3.71277	+	50.8337i	−0.184489	+	2.52595i
$406$		−	16.7642i		−	0.831992i
$407$	−3.03684	−	12.8475i	−0.150530	−	0.636825i
$408$	−16.9447	+	16.9447i	−0.838888	+	0.838888i
$409$	4.20165	−	1.12583i	0.207758	−	0.0556686i	−0.153439	−	0.988158i	$-0.549035\pi$
$409$	4.20165	−	1.12583i	0.207758	−	0.0556686i	0.361197	+	0.932490i	$0.382368\pi$
$410$	14.6411	−	21.5621i	0.723074	−	1.06488i
$411$	18.9137	−	10.9198i	0.932942	−	0.538634i
$412$	−3.65656	+	2.11112i	−0.180146	+	0.104007i
$413$	37.5989			1.85012
$414$	14.3294	−	8.27306i	0.704250	−	0.406599i
$415$	7.44789	−	21.4147i	0.365602	−	1.05121i
$416$	0.420517	−	0.728356i	0.0206175	−	0.0357106i
$417$	−52.4258	−	52.4258i	−2.56730	−	2.56730i
$418$	−9.42570	−	9.42570i	−0.461026	−	0.461026i
$419$	2.15841	+	1.24616i	0.105445	+	0.0608788i	0.551795	−	0.833980i	$-0.313943\pi$
$419$	2.15841	+	1.24616i	0.105445	+	0.0608788i	−0.446350	+	0.894858i	$0.647276\pi$
$420$	−6.83235	+	10.0621i	−0.333385	+	0.490978i
$421$	−13.5065	+	13.5065i	−0.658265	+	0.658265i	−0.954969	−	0.296704i	$-0.904112\pi$
$421$	−13.5065	+	13.5065i	−0.658265	+	0.658265i	0.296704	+	0.954969i	$0.404112\pi$
$422$	11.3685	−	19.6909i	0.553411	−	0.958536i
$423$	−24.6839	−	92.1217i	−1.20017	−	4.47911i
$424$	−0.122247	−	0.456230i	−0.00593682	−	0.0221565i
$425$	−2.18981	+	14.9110i	−0.106221	+	0.723290i
$426$	−1.23835	+	4.62157i	−0.0599980	+	0.223916i
$427$	−1.51575	+	2.62535i	−0.0733521	+	0.127050i
$428$	−2.81008	+	0.752959i	−0.135830	+	0.0363956i
$429$	−0.671829	−	2.50730i	−0.0324362	−	0.121054i
$430$	−1.44112	+	0.697366i	−0.0694968	+	0.0336300i
$431$	25.9052	+	6.94129i	1.24781	+	0.334350i	0.821491	−	0.570222i	$-0.193143\pi$
$431$	25.9052	+	6.94129i	1.24781	+	0.334350i	0.426321	+	0.904572i	$0.359809\pi$
$432$	16.7587	+	62.5442i	0.806301	+	3.00916i
$433$	−12.4207	+	12.4207i	−0.596902	+	0.596902i	−0.939487	−	0.342585i	$-0.888698\pi$
$433$	−12.4207	+	12.4207i	−0.596902	+	0.596902i	0.342585	+	0.939487i	$0.388698\pi$
$434$	−30.3825			−1.45841
$435$	−18.5718	−	1.35644i	−0.890448	−	0.0650362i
$436$	3.73448	−	3.73448i	0.178849	−	0.178849i
$437$	5.56363	+	1.49077i	0.266145	+	0.0713132i
$438$		−	23.5047i		−	1.12310i
$439$	−3.38942	+	12.6495i	−0.161768	+	0.603727i	0.836662	+	0.547719i	$0.184504\pi$
$439$	−3.38942	+	12.6495i	−0.161768	+	0.603727i	−0.998430	+	0.0560075i	$0.982163\pi$
$440$	6.74193	−	9.92889i	0.321409	−	0.473341i
$441$	38.1793	+	66.1285i	1.81806	+	3.14898i
$442$	1.50624	+	0.869627i	0.0716444	+	0.0413639i
$443$	0.485132	+	0.485132i	0.0230493	+	0.0230493i	0.718538	−	0.695488i	$-0.244812\pi$
$443$	0.485132	+	0.485132i	0.0230493	+	0.0230493i	−0.695488	+	0.718538i	$0.744812\pi$
$444$	6.98157	−	3.75907i	0.331331	−	0.178398i
$445$	−14.4812	−	5.03647i	−0.686475	−	0.238751i
$446$	2.14359	+	7.99997i	0.101502	+	0.378810i
$447$	−34.6906	−	9.29532i	−1.64081	−	0.439653i
$448$	6.24967	−	23.3241i	0.295269	−	1.10196i
$449$	−14.3950	−	3.85712i	−0.679341	−	0.182029i	−0.0973822	−	0.995247i	$-0.531047\pi$
$449$	−14.3950	−	3.85712i	−0.679341	−	0.182029i	−0.581959	+	0.813218i	$0.697714\pi$
$450$	44.6041	+	35.2953i	2.10266	+	1.66384i
$451$	−8.15516	−	14.1252i	−0.384012	−	0.665128i
$452$			3.27952i			0.154256i
$453$	2.28413	+	8.52449i	0.107318	+	0.400515i
$454$		−	18.3587i		−	0.861618i
$455$	−3.27859	−	1.14027i	−0.153703	−	0.0534567i
$456$	−15.7417	+	27.2655i	−0.737174	+	1.27682i
$457$	16.3157	−	9.41987i	0.763216	−	0.440643i	−0.0672332	−	0.997737i	$-0.521417\pi$
$457$	16.3157	−	9.41987i	0.763216	−	0.440643i	0.830449	+	0.557094i	$0.188084\pi$
$458$		−	18.2158i		−	0.851171i
$459$	−40.5720	+	10.8712i	−1.89374	+	0.507425i
$460$	0.0960656	−	1.31529i	0.00447908	−	0.0613257i
$461$	12.4218	−	3.32842i	0.578542	−	0.155020i	0.0423309	−	0.999104i	$-0.486522\pi$
$461$	12.4218	−	3.32842i	0.578542	−	0.155020i	0.536211	+	0.844084i	$0.319855\pi$
$462$	22.5762	+	39.1031i	1.05034	+	1.81924i
$463$	18.9998	+	32.9086i	0.882996	+	1.52939i	0.847993	+	0.530007i	$0.177811\pi$
$463$	18.9998	+	32.9086i	0.882996	+	1.52939i	0.0350030	+	0.999387i	$0.488856\pi$
$464$	−11.6265	+	3.11531i	−0.539747	+	0.144625i
$465$	−2.45833	+	33.6584i	−0.114002	+	1.56087i
$466$	33.0458	−	8.85459i	1.53082	−	0.410181i
$467$			24.7489i			1.14524i	0.819820	+	0.572622i	$0.194074\pi$
$467$			24.7489i			1.14524i	−0.819820	+	0.572622i	$0.805926\pi$
$468$	0.958267	−	0.553256i	0.0442959	−	0.0255743i
$469$	−22.8507	+	39.5786i	−1.05515	+	1.82757i
$470$	−42.5918	−	14.8131i	−1.96461	−	0.683279i
$471$		−	23.0920i		−	1.06402i
$472$	−5.76758	−	21.5249i	−0.265474	−	0.990764i
$473$			1.00189i			0.0460671i
$474$	23.5104	+	40.7212i	1.07987	+	1.87039i
$475$	2.29137	+	19.6674i	0.105135	+	0.902402i
$476$	−4.92609	−	1.31994i	−0.225787	−	0.0604994i
$477$	0.362570	−	1.35313i	0.0166009	−	0.0619556i
$478$	23.5900	+	6.32092i	1.07898	+	0.289112i
$479$	−6.64188	−	24.7878i	−0.303475	−	1.13259i	−0.934250	−	0.356619i	$-0.883929\pi$
$479$	−6.64188	−	24.7878i	−0.303475	−	1.13259i	0.630775	−	0.775966i	$-0.282737\pi$
$480$	15.3484	+	5.33806i	0.700554	+	0.243648i
$481$	1.55201	+	1.64700i	0.0707656	+	0.0750965i
$482$	10.6665	+	10.6665i	0.485845	+	0.485845i
$483$	−16.8965	−	9.75520i	−0.768818	−	0.443877i
$484$	−1.27522	−	2.20874i	−0.0579644	−	0.100397i
$485$	3.93155	−	5.79003i	0.178523	−	0.262912i
$486$	−12.6335	+	47.1490i	−0.573069	+	2.13872i
$487$			21.8694i			0.990998i	0.868608	+	0.495499i	$0.165015\pi$
$487$			21.8694i			0.990998i	−0.868608	+	0.495499i	$0.834985\pi$
$488$	1.73549	+	0.465024i	0.0785621	+	0.0210506i
$489$	−0.369082	+	0.369082i	−0.0166905	+	0.0166905i
$490$	36.0085	+	2.62998i	1.62670	+	0.118810i
$491$	−13.2615			−0.598483			−0.299242	−	0.954177i	$-0.596734\pi$
$491$	−13.2615			−0.598483			−0.299242	+	0.954177i	$0.596734\pi$
$492$	6.92718	−	6.92718i	0.312301	−	0.312301i
$493$	−2.02088	−	7.54203i	−0.0910159	−	0.339676i
$494$	2.20719	+	0.591416i	0.0993063	+	0.0266091i
$495$	32.0409	−	15.5048i	1.44013	−	0.696890i
$496$	5.64602	+	21.0712i	0.253514	+	0.946127i
$497$	3.86762	−	1.03633i	0.173487	−	0.0464856i
$498$	25.2780	−	43.7829i	1.13274	−	1.96196i
$499$	9.23613	−	34.4697i	0.413466	−	1.54308i	−0.374422	−	0.927258i	$-0.622159\pi$
$499$	9.23613	−	34.4697i	0.413466	−	1.54308i	0.787888	−	0.615818i	$-0.211174\pi$
$500$	4.32446	−	1.36084i	0.193396	−	0.0608588i
$501$	−11.5101	−	42.9562i	−0.514233	−	1.91914i
$502$	−12.1032	−	45.1699i	−0.540194	−	2.01603i
$503$	−13.4680	+	23.3272i	−0.600508	+	1.04011i	0.392236	+	0.919865i	$0.371702\pi$
$503$	−13.4680	+	23.3272i	−0.600508	+	1.04011i	−0.992744	+	0.120246i	$0.961632\pi$
$504$	53.5185	−	53.5185i	2.38391	−	2.38391i
$505$	−0.133953	+	0.197274i	−0.00596083	+	0.00877857i
$506$	−4.23999	−	2.44796i	−0.188491	−	0.108825i
$507$	−29.2367	−	29.2367i	−1.29845	−	1.29845i
$508$	2.88055	+	2.88055i	0.127804	+	0.127804i
$509$	3.92018	−	6.78995i	0.173759	−	0.300959i	−0.765972	−	0.642874i	$-0.777742\pi$
$509$	3.92018	−	6.78995i	0.173759	−	0.300959i	0.939731	+	0.341914i	$0.111075\pi$
$510$	−11.0391	+	31.7404i	−0.488819	+	1.40549i
$511$	−17.0349	+	9.83511i	−0.753580	+	0.435080i
$512$	−12.4781			−0.551461
$513$	−47.7910	+	27.5922i	−2.11003	+	1.21822i
$514$	7.83146	−	4.52150i	0.345431	−	0.199435i
$515$	13.0796	−	19.2624i	0.576355	−	0.848802i
$516$	−0.581264	+	0.155749i	−0.0255887	+	0.00685648i
$517$	−19.9545	+	19.9545i	−0.877599	+	0.877599i
$518$	−33.4918	−	20.6856i	−1.47155	−	0.908872i
$519$			51.4569i			2.25871i
$520$	−0.149863	+	2.05187i	−0.00657194	+	0.0899803i
$521$	8.21305	−	4.74181i	0.359820	−	0.207742i	−0.309182	−	0.951003i	$-0.600055\pi$
$521$	8.21305	−	4.74181i	0.359820	−	0.207742i	0.669002	+	0.743261i	$0.266722\pi$
$522$	−28.4645	−	7.62704i	−1.24586	−	0.333827i
$523$	−9.49329	−	16.4429i	−0.415113	−	0.718996i	0.580328	−	0.814383i	$-0.302924\pi$
$523$	−9.49329	−	16.4429i	−0.415113	−	0.718996i	−0.995440	+	0.0953869i	$0.969591\pi$
$524$	−4.21214	+	4.21214i	−0.184008	+	0.184008i
$525$	9.74523	−	66.3579i	0.425317	−	2.89609i
$526$	22.0331	+	22.0331i	0.960691	+	0.960691i
$527$	−13.6688	+	3.66253i	−0.595421	+	0.159542i
$528$	22.9239	−	22.9239i	0.997635	−	0.997635i
$529$	−20.8845			−0.908020
$530$	−0.433002	−	0.501237i	−0.0188084	−	0.0217723i
$531$	17.1060	−	63.8405i	0.742338	−	2.77044i
$532$	−6.70027			−0.290493
$533$	2.42137	+	1.39798i	0.104881	+	0.0605532i
$534$	−29.6072	−	17.0937i	−1.28123	−	0.739717i
$535$	12.1401	−	10.4875i	0.524864	−	0.453413i
$536$	26.1635	+	7.01048i	1.13009	+	0.302807i
$537$	40.9753	−	23.6571i	1.76821	−	1.02088i
$538$	1.25008	+	0.721732i	0.0538946	+	0.0311161i
$539$	11.2971	−	19.5671i	0.486600	−	0.842816i
$540$	8.25981	+	9.56143i	0.355445	+	0.411458i
$541$	27.2508	+	27.2508i	1.17160	+	1.17160i	0.981828	+	0.189775i	$0.0607760\pi$
$541$	27.2508	+	27.2508i	1.17160	+	1.17160i	0.189775	+	0.981828i	$0.439224\pi$
$542$	11.0980	+	19.2223i	0.476700	+	0.825668i
$543$	71.3268	−	19.1120i	3.06093	−	0.820173i
$544$			6.81386i			0.292142i
$545$	−9.56697	+	27.5076i	−0.409804	+	1.17830i
$546$	−6.70315	−	3.87006i	−0.286868	−	0.165623i
$547$	35.5804			1.52131			0.760653	−	0.649158i	$-0.224879\pi$
$547$	35.5804			1.52131			0.760653	+	0.649158i	$0.224879\pi$
$548$	0.712973	−	2.66085i	0.0304567	−	0.113666i
$549$	3.76807	+	3.76807i	0.160817	+	0.160817i
$550$	2.44546	−	16.6518i	0.104275	−	0.710034i
$551$	−5.12918	−	8.88401i	−0.218511	−	0.378471i
$552$	−2.99285	+	11.1695i	−0.127384	+	0.475404i
$553$	19.6750	−	34.0781i	0.836666	−	1.44915i
$554$	5.88682			0.250107
$555$	−25.6259	+	35.4293i	−1.08776	+	1.50389i
$556$	−9.35173			−0.396602
$557$	−22.1651	+	38.3911i	−0.939165	+	1.62668i	−0.172132	+	0.985074i	$0.555066\pi$
$557$	−22.1651	+	38.3911i	−0.939165	+	1.62668i	−0.767033	+	0.641608i	$0.778268\pi$
$558$	−13.8228	+	51.5875i	−0.585167	+	2.18387i
$559$	−0.0858735	−	0.148737i	−0.00363206	−	0.00629092i
$560$	−8.14046	−	42.5822i	−0.343997	−	1.79943i
$561$	14.8706	+	14.8706i	0.627836	+	0.627836i
$562$	−2.04388	+	7.62787i	−0.0862160	+	0.321762i
$563$	27.6526			1.16542			0.582710	−	0.812680i	$-0.301992\pi$
$563$	27.6526			1.16542			0.582710	+	0.812680i	$0.301992\pi$
$564$	−14.6790	−	8.47491i	−0.618096	−	0.356858i
$565$	−7.87751	−	16.2790i	−0.331409	−	0.684861i
$566$		−	23.1415i		−	0.972709i
$567$	91.8696	−	24.6164i	3.85816	−	1.03379i
$568$	−1.18657	−	2.05520i	−0.0497873	−	0.0862341i
$569$	8.31252	+	8.31252i	0.348479	+	0.348479i	0.859543	−	0.511064i	$-0.170748\pi$
$569$	8.31252	+	8.31252i	0.348479	+	0.348479i	−0.511064	+	0.859543i	$0.670748\pi$
$570$	−3.21612	+	44.0337i	−0.134708	+	1.84437i
$571$	−3.99555	+	6.92050i	−0.167209	+	0.289614i	−0.937437	−	0.348154i	$-0.886809\pi$
$571$	−3.99555	+	6.92050i	−0.167209	+	0.289614i	0.770229	+	0.637768i	$0.220142\pi$
$572$	−0.283547	−	0.163706i	−0.0118557	−	0.00684489i
$573$	−26.1695	+	15.1090i	−1.09325	+	0.631186i
$574$	−46.9778	−	12.5877i	−1.96081	−	0.525398i
$575$	2.68251	+	6.75963i	0.111869	+	0.281896i
$576$	−36.7595	−	21.2231i	−1.53164	−	0.884296i
$577$	−15.1952	−	8.77295i	−0.632584	−	0.365223i	0.149168	−	0.988812i	$-0.452340\pi$
$577$	−15.1952	−	8.77295i	−0.632584	−	0.365223i	−0.781752	+	0.623589i	$0.785674\pi$
$578$	12.2754			0.510588
$579$	11.2683	−	42.0538i	0.468294	−	1.74770i
$580$	−1.77740	+	1.53544i	−0.0738025	+	0.0637556i
$581$	−42.3086			−1.75526
$582$	11.0349	−	11.0349i	0.457411	−	0.457411i
$583$	−0.400385	+	0.107283i	−0.0165823	+	0.00444320i
$584$	8.24359	+	8.24359i	0.341122	+	0.341122i
$585$	−3.42774	+	5.04806i	−0.141719	+	0.208711i
$586$	1.66025	−	1.66025i	0.0685844	−	0.0685844i
$587$	1.89900	+	3.28916i	0.0783800	+	0.135758i	0.902551	−	0.430583i	$-0.141692\pi$
$587$	1.89900	+	3.28916i	0.0783800	+	0.135758i	−0.824171	+	0.566341i	$0.808359\pi$
$588$	13.1084	+	3.51238i	0.540580	+	0.144848i
$589$	−16.1009	+	9.29585i	−0.663425	+	0.383029i
$590$	−20.4290	−	23.6483i	−0.841049	−	0.973585i
$591$			38.1003i			1.56724i
$592$	−8.12228	+	27.0717i	−0.333824	+	1.11264i
$593$	−13.7978	+	13.7978i	−0.566606	+	0.566606i	−0.931176	−	0.364570i	$-0.881216\pi$
$593$	−13.7978	+	13.7978i	−0.566606	+	0.566606i	0.364570	+	0.931176i	$0.381216\pi$
$594$	45.3085	−	12.1404i	1.85903	−	0.498126i
$595$	27.6228	−	5.28066i	1.13242	−	0.216486i
$596$	−3.92311	+	2.26501i	−0.160697	+	0.0927784i
$597$	29.5069	−	17.0358i	1.20764	−	0.697229i
$598$	0.839272			0.0343204
$599$	31.9153	−	18.4263i	1.30403	−	0.752879i	0.322933	−	0.946422i	$-0.395331\pi$
$599$	31.9153	−	18.4263i	1.30403	−	0.752879i	0.981092	+	0.193543i	$0.0619978\pi$
$600$	−39.4840	+	4.60012i	−1.61193	+	0.187799i
$601$	−4.55733	+	7.89352i	−0.185897	+	0.321983i	−0.943878	−	0.330293i	$-0.892852\pi$
$601$	−4.55733	+	7.89352i	−0.185897	+	0.321983i	0.757981	+	0.652276i	$0.226186\pi$
$602$	2.11248	+	2.11248i	0.0860982	+	0.0860982i
$603$	56.8057	+	56.8057i	2.31331	+	2.31331i
$604$	0.964022	+	0.556578i	0.0392255	+	0.0226469i
$605$	11.6354	+	7.90070i	0.473047	+	0.321209i
$606$	−0.375973	+	0.375973i	−0.0152728	+	0.0152728i
$607$	−7.51612	+	13.0183i	−0.305070	+	0.528396i	−0.977277	−	0.211967i	$-0.932013\pi$
$607$	−7.51612	+	13.0183i	−0.305070	+	0.528396i	0.672207	+	0.740363i	$0.265346\pi$
$608$	2.31699	+	8.64711i	0.0939662	+	0.350687i
$609$	8.99344	+	33.5640i	0.364433	+	1.36008i
$610$	2.47482	−	0.473111i	0.100202	−	0.0191557i
$611$	1.25205	−	4.67270i	0.0506524	−	0.189037i
$612$	−4.48235	+	7.76367i	−0.181188	+	0.313828i
$613$	8.97541	−	2.40495i	0.362513	−	0.0971352i	−0.0729646	−	0.997335i	$-0.523246\pi$
$613$	8.97541	−	2.40495i	0.362513	−	0.0971352i	0.435478	+	0.900199i	$0.356579\pi$
$614$	11.9726	+	44.6823i	0.483174	+	1.80323i
$615$	−17.7460	+	51.0246i	−0.715588	+	2.05751i
$616$	−21.6322	−	5.79634i	−0.871588	−	0.233541i
$617$	3.77320	+	14.0818i	0.151903	+	0.566911i	0.999351	+	0.0360316i	$0.0114717\pi$
$617$	3.77320	+	14.0818i	0.151903	+	0.566911i	−0.847447	+	0.530880i	$0.821862\pi$
$618$	36.7111	−	36.7111i	1.47674	−	1.47674i
$619$	26.2648			1.05567			0.527837	−	0.849346i	$-0.323003\pi$
$619$	26.2648			1.05567			0.527837	+	0.849346i	$0.323003\pi$
$620$	2.78274	+	3.22126i	0.111758	+	0.129369i
$621$	−14.3320	+	14.3320i	−0.575123	+	0.575123i
$622$	−17.5640	−	4.70625i	−0.704251	−	0.188703i
$623$			28.6102i			1.14624i
$624$	−1.43836	+	5.36803i	−0.0575805	+	0.214893i
$625$	−18.1971	+	17.1425i	−0.727884	+	0.685700i
$626$	−5.00669	−	8.67185i	−0.200108	−	0.346597i
$627$	23.9280	+	13.8149i	0.955593	+	0.551712i
$628$	−2.05958	−	2.05958i	−0.0821861	−	0.0821861i
$629$	−17.5612	−	5.26886i	−0.700212	−	0.210083i
$630$	34.8661	−	100.250i	1.38910	−	3.99404i
$631$	−5.87855	−	21.9390i	−0.234021	−	0.873379i	−0.978588	−	0.205831i	$-0.934010\pi$
$631$	−5.87855	−	21.9390i	−0.234021	−	0.873379i	0.744566	−	0.667549i	$-0.232656\pi$
$632$	−22.5274	−	6.03620i	−0.896091	−	0.240107i
$633$	−12.1977	+	45.5224i	−0.484815	+	1.80935i
$634$	−33.2098	−	8.89855i	−1.31893	−	0.353406i
$635$	−21.2177	−	7.37938i	−0.841999	−	0.292842i
$636$	−0.124484	−	0.215612i	−0.00493610	−	0.00854958i
$637$			3.87315i			0.153460i
$638$	2.25681	+	8.42252i	0.0893479	+	0.333451i
$639$		−	7.03847i		−	0.278437i
$640$	−27.1659	+	13.1458i	−1.07383	+	0.519632i
$641$	14.2444	−	24.6721i	0.562622	−	0.974490i	−0.434645	−	0.900602i	$-0.643126\pi$
$641$	14.2444	−	24.6721i	0.562622	−	0.974490i	0.997267	−	0.0738875i	$-0.0235406\pi$
$642$	30.9796	−	17.8861i	1.22267	−	0.705907i
$643$		−	31.7473i		−	1.25199i	−0.779826	−	0.625996i	$-0.784693\pi$
$643$		−	31.7473i		−	1.25199i	0.779826	−	0.625996i	$-0.215307\pi$
$644$	−2.37707	+	0.636934i	−0.0936697	+	0.0250987i
$645$	2.51118	−	2.16933i	0.0988777	−	0.0854172i
$646$	−17.8822	+	4.79152i	−0.703565	+	0.188520i
$647$	−11.7748	−	20.3945i	−0.462915	−	0.801792i	0.536190	−	0.844097i	$-0.319863\pi$
$647$	−11.7748	−	20.3945i	−0.462915	−	0.801792i	−0.999105	+	0.0423052i	$0.986530\pi$
$648$	−28.1852	−	48.8181i	−1.10722	−	1.91776i
$649$	−18.8901	+	5.06159i	−0.741502	+	0.198685i
$650$	1.06420	+	2.68167i	0.0417414	+	0.105184i
$651$	60.8295	−	16.2992i	2.38410	−	0.638817i
$652$			0.0658370i			0.00257838i
$653$	31.1291	−	17.9724i	1.21818	−	0.703315i	0.253649	−	0.967296i	$-0.418369\pi$
$653$	31.1291	−	17.9724i	1.21818	−	0.703315i	0.964528	+	0.263982i	$0.0850358\pi$
$654$	−32.4702	+	56.2400i	−1.26969	+	2.19916i
$655$	10.7907	−	31.0261i	0.421626	−	1.21229i
$656$			34.9198i			1.36339i
$657$	8.94918	+	33.3988i	0.349141	+	1.30301i
$658$			84.1477i			3.28042i
$659$	−15.7744	−	27.3220i	−0.614483	−	1.06432i	−0.990475	−	0.137692i	$-0.956031\pi$
$659$	−15.7744	−	27.3220i	−0.614483	−	1.06432i	0.375992	−	0.926623i	$-0.377302\pi$
$660$	2.07809	−	5.97507i	0.0808896	−	0.232579i
$661$	−25.7696	−	6.90493i	−1.00232	−	0.268571i	−0.279903	−	0.960028i	$-0.590302\pi$
$661$	−25.7696	−	6.90493i	−1.00232	−	0.268571i	−0.722417	+	0.691458i	$0.756969\pi$
$662$	−3.35604	+	12.5249i	−0.130436	+	0.486794i
$663$	−3.48221	−	0.933054i	−0.135238	−	0.0362368i
$664$	6.49004	+	24.2211i	0.251862	+	0.939963i
$665$	33.2590	−	16.0943i	1.28973	−	0.624108i
$666$	−50.3602	+	47.4559i	−1.95142	+	1.83888i
$667$	−2.66421	−	2.66421i	−0.103159	−	0.103159i
$668$	−4.85786	−	2.80469i	−0.187956	−	0.108517i
$669$	−8.58346	−	14.8670i	−0.331856	−	0.574791i
$670$	37.3092	−	7.13240i	1.44138	−	0.275549i
$671$	0.408102	−	1.52306i	0.0157546	−	0.0587970i
$672$		−	30.3235i		−	1.16975i
$673$	−17.6421	−	4.72719i	−0.680054	−	0.182220i	−0.0977743	−	0.995209i	$-0.531172\pi$
$673$	−17.6421	−	4.72719i	−0.680054	−	0.182220i	−0.582279	+	0.812989i	$0.697839\pi$
$674$	8.87876	−	8.87876i	0.341997	−	0.341997i
$675$	−63.9671	−	27.6210i	−2.46209	−	1.06313i
$676$	−5.21526			−0.200587
$677$	−4.45728	+	4.45728i	−0.171307	+	0.171307i	−0.787554	−	0.616246i	$-0.788653\pi$
$677$	−4.45728	+	4.45728i	−0.171307	+	0.171307i	0.616246	+	0.787554i	$0.288653\pi$
$678$	−10.4370	−	38.9515i	−0.400831	−	1.49592i
$679$	−12.6148	−	3.38013i	−0.484113	−	0.129718i
$680$	−7.26038	−	15.0037i	−0.278423	−	0.575365i
$681$	9.84887	+	36.7565i	0.377410	+	1.40851i
$682$	15.2645	−	4.09011i	0.584508	−	0.156619i
$683$	−0.0832112	+	0.144126i	−0.00318399	+	0.00551483i	−0.867613	−	0.497240i	$-0.834347\pi$
$683$	−0.0832112	+	0.144126i	−0.00318399	+	0.00551483i	0.864429	+	0.502755i	$0.167680\pi$
$684$	−3.04836	+	11.3766i	−0.116557	+	0.434996i
$685$	2.85237	+	14.9206i	0.108984	+	0.570086i
$686$	−5.71255	−	21.3195i	−0.218106	−	0.813983i
$687$	9.77222	+	36.4704i	0.372834	+	1.39143i
$688$	1.07251	−	1.85764i	0.0408890	−	0.0708218i
$689$	0.0502443	−	0.0502443i	0.00191416	−	0.00191416i
$690$	3.04490	+	15.9277i	0.115917	+	0.606356i
$691$	4.32835	+	2.49897i	0.164658	+	0.0950654i	0.580065	−	0.814571i	$-0.303027\pi$
$691$	4.32835	+	2.49897i	0.164658	+	0.0950654i	−0.415407	+	0.909636i	$0.636361\pi$
$692$	4.58945	+	4.58945i	0.174465	+	0.174465i
$693$	−46.9675	−	46.9675i	−1.78415	−	1.78415i
$694$	20.1834	−	34.9587i	0.766152	−	1.32701i
$695$	46.4204	−	22.4631i	1.76082	−	0.852076i
$696$	17.8354	−	10.2973i	0.676049	−	0.390317i
$697$	−22.6522			−0.858014
$698$	4.08859	−	2.36055i	0.154755	−	0.0893481i
$699$	−61.4116	+	35.4560i	−2.32280	+	1.34107i
$700$	−5.04929	−	6.78765i	−0.190845	−	0.256549i
$701$	16.1194	−	4.31919i	0.608822	−	0.163133i	0.0587810	−	0.998271i	$-0.481279\pi$
$701$	16.1194	−	4.31919i	0.608822	−	0.163133i	0.550041	+	0.835137i	$0.314612\pi$
$702$	−5.68576	+	5.68576i	−0.214595	+	0.214595i
$703$	−24.0776	−	0.714915i	−0.908105	−	0.0269635i
$704$			12.5596i			0.473359i
$705$	93.2209	+	6.80863i	3.51090	+	0.256428i
$706$	9.28231	−	5.35914i	0.349344	−	0.201694i
$707$	0.429804	+	0.115166i	0.0161644	+	0.00433125i
$708$	−5.87313	−	10.1726i	−0.220726	−	0.382308i
$709$	1.78823	−	1.78823i	0.0671583	−	0.0671583i	−0.672730	−	0.739888i	$-0.734878\pi$
$709$	1.78823	−	1.78823i	0.0671583	−	0.0671583i	0.739888	+	0.672730i	$0.234878\pi$
$710$	−2.75325	−	1.86951i	−0.103328	−	0.0701616i
$711$	−48.9111	−	48.9111i	−1.83431	−	1.83431i
$712$	16.3790	−	4.38874i	0.613829	−	0.164475i
$713$	−4.82848	+	4.82848i	−0.180828	+	0.180828i
$714$	62.7088			2.34682
$715$	1.80070	+	0.131519i	0.0673425	+	0.00491854i
$716$	1.54461	−	5.76457i	0.0577249	−	0.215432i
$717$	−50.6211			−1.89048
$718$	−17.8403	−	10.3001i	−0.665795	−	0.384397i
$719$	37.0250	+	21.3764i	1.38080	+	0.797205i	0.992254	−	0.124224i	$-0.0396442\pi$
$719$	37.0250	+	21.3764i	1.38080	+	0.797205i	0.388546	+	0.921429i	$0.372978\pi$
$720$	−76.0055	−	5.55126i	−2.83256	−	0.206883i
$721$	−41.9673	−	11.2451i	−1.56294	−	0.418789i
$722$	4.45631	−	2.57285i	0.165847	−	0.0957516i
$723$	−27.0778	−	15.6334i	−1.00704	−	0.581412i
$724$	4.65705	−	8.06625i	0.173078	−	0.299780i
$725$	5.13454	−	11.8910i	0.190692	−	0.441621i
$726$	22.1753	+	22.1753i	0.823002	+	0.823002i
$727$	−20.6361	−	35.7427i	−0.765349	−	1.32562i	−0.940062	−	0.341004i	$-0.889233\pi$
$727$	−20.6361	−	35.7427i	−0.765349	−	1.32562i	0.174713	−	0.984619i	$-0.444100\pi$
$728$	3.70825	−	0.993623i	0.137437	−	0.0368261i
$729$		−	32.7935i		−	1.21458i
$730$	15.4417	+	5.37051i	0.571522	+	0.198772i
$731$	1.20504	+	0.695728i	0.0445699	+	0.0257324i
$732$	0.947068			0.0350046
$733$	−11.5672	+	43.1692i	−0.427243	+	1.59449i	0.331734	+	0.943373i	$0.392366\pi$
$733$	−11.5672	+	43.1692i	−0.427243	+	1.59449i	−0.758976	+	0.651118i	$0.774300\pi$
$734$	22.0590	+	22.0590i	0.814214	+	0.814214i
$735$	−73.5046	+	14.0519i	−2.71126	+	0.518312i
$736$	1.64401	+	2.84750i	0.0605988	+	0.104960i
$737$	6.15236	−	22.9609i	0.226625	−	0.845776i
$738$	−42.7461	+	74.0384i	−1.57350	+	2.72539i
$739$	−19.7035			−0.724803			−0.362402	−	0.932022i	$-0.618043\pi$
$739$	−19.7035			−0.724803			−0.362402	+	0.932022i	$0.618043\pi$
$740$	0.874371	+	5.44553i	0.0321425	+	0.200182i
$741$	−4.73636			−0.173994
$742$	−0.618002	+	1.07041i	−0.0226876	+	0.0392960i
$743$	−0.144780	+	0.540326i	−0.00531146	+	0.0198226i	−0.968531	−	0.248894i	$-0.919933\pi$
$743$	−0.144780	+	0.540326i	−0.00531146	+	0.0198226i	0.963219	+	0.268717i	$0.0865996\pi$
$744$	−18.6622	−	32.3239i	−0.684190	−	1.18505i
$745$	14.0330	−	20.6666i	0.514130	−	0.757164i
$746$	−1.14986	−	1.14986i	−0.0420993	−	0.0420993i
$747$	−19.2487	+	71.8373i	−0.704275	+	2.62839i
$748$	2.65262			0.0969893
$749$	−25.9257	−	14.9682i	−0.947305	−	0.546927i
$750$	−47.0316	+	29.9255i	−1.71735	+	1.09273i
$751$		−	13.6763i		−	0.499056i	−0.968368	−	0.249528i	$-0.919725\pi$
$751$		−	13.6763i		−	0.499056i	0.968368	−	0.249528i	$-0.0802755\pi$
$752$	58.3592	−	15.6373i	2.12814	−	0.570233i
$753$	48.4644	+	83.9428i	1.76614	+	3.05905i
$754$	−1.05694	−	1.05694i	−0.0384916	−	0.0384916i
$755$	−6.12216	−	0.447148i	−0.222808	−	0.0162734i
$756$	11.7888	−	20.4188i	0.428754	−	0.742624i
$757$	26.0809	+	15.0578i	0.947926	+	0.547285i	0.892436	−	0.451174i	$-0.148995\pi$
$757$	26.0809	+	15.0578i	0.947926	+	0.547285i	0.0554901	+	0.998459i	$0.482328\pi$
$758$	−20.8916	+	12.0618i	−0.758818	+	0.438104i
$759$	9.80226	+	2.62651i	0.355799	+	0.0953362i
$760$	−14.3156	−	16.5715i	−0.519282	−	0.601113i
$761$	−25.1569	−	14.5244i	−0.911938	−	0.526507i	−0.0308836	−	0.999523i	$-0.509832\pi$
$761$	−25.1569	−	14.5244i	−0.911938	−	0.526507i	−0.881054	+	0.473015i	$0.843165\pi$
$762$	−43.3801	−	25.0455i	−1.57150	−	0.907304i
$763$	54.3463			1.96747
$764$	−0.986490	+	3.68163i	−0.0356899	+	0.133197i
$765$	3.60107	−	49.3043i	0.130197	−	1.78260i
$766$	6.57692			0.237634
$767$	2.37052	−	2.37052i	0.0855946	−	0.0855946i
$768$	−29.0612	+	7.78692i	−1.04865	+	0.280986i
$769$	−8.36905	−	8.36905i	−0.301796	−	0.301796i	0.539920	−	0.841716i	$-0.318454\pi$
$769$	−8.36905	−	8.36905i	−0.301796	−	0.301796i	−0.841716	+	0.539920i	$0.818454\pi$
$770$	−30.8476	+	5.89714i	−1.11167	+	0.212518i
$771$	−13.2539	+	13.2539i	−0.477329	+	0.477329i
$772$	−2.74577	−	4.75581i	−0.0988223	−	0.171165i
$773$	11.6490	+	3.12135i	0.418987	+	0.112267i	0.462152	−	0.886801i	$-0.347077\pi$
$773$	11.6490	+	3.12135i	0.418987	+	0.112267i	−0.0431651	+	0.999068i	$0.513744\pi$
$774$	4.54795	−	2.62576i	0.163473	−	0.0943810i
$775$	−21.5506	−	9.30555i	−0.774121	−	0.334265i
$776$			7.74034i			0.277862i
$777$	78.1520	+	23.4478i	2.80369	+	0.841186i
$778$	16.7311	−	16.7311i	0.599838	−	0.599838i
$779$	−28.7467	+	7.70266i	−1.02996	+	0.275976i
$780$	0.203626	+	1.06515i	0.00729097	+	0.0381386i
$781$	−1.80363	+	1.04133i	−0.0645389	+	0.0372615i
$782$	−5.88862	+	3.39980i	−0.210577	+	0.121576i
$783$	36.0982			1.29004
$784$	−41.8925	+	24.1866i	−1.49616	+	0.863809i
$785$	15.1706	+	5.27622i	0.541461	+	0.188316i
$786$	36.6234	−	63.4335i	1.30631	−	2.26260i
$787$	25.9763	+	25.9763i	0.925955	+	0.925955i	0.997442	−	0.0714865i	$-0.0227743\pi$
$787$	25.9763	+	25.9763i	0.925955	+	0.925955i	−0.0714865	+	0.997442i	$0.522774\pi$
$788$	3.39817	+	3.39817i	0.121055	+	0.121055i
$789$	−55.9332	−	32.2931i	−1.99128	−	1.14966i
$790$	−32.1241	+	6.14117i	−1.14292	+	0.218493i
$791$	−23.8627	+	23.8627i	−0.848461	+	0.848461i
$792$	−19.6836	+	34.0931i	−0.699428	+	1.21144i
$793$	0.0699579	+	0.261087i	0.00248428	+	0.00927145i
$794$	−3.43472	−	12.8185i	−0.121894	−	0.454913i
$795$	1.13582	+	0.771248i	0.0402835	+	0.0273533i
$796$	1.11230	−	4.15115i	0.0394243	−	0.147134i
$797$	−13.6517	+	23.6455i	−0.483569	+	0.837566i	−0.999822	−	0.0188700i	$-0.993993\pi$
$797$	−13.6517	+	23.6455i	−0.483569	+	0.837566i	0.516253	+	0.856436i	$0.327326\pi$
$798$	79.5804	−	21.3235i	2.81711	−	0.754843i
$799$	10.1438	+	37.8572i	0.358862	+	1.33929i
$800$	−7.01381	+	8.86362i	−0.247976	+	0.313376i
$801$	48.5783	+	13.0165i	1.71643	+	0.459916i
$802$	−4.90858	−	18.3191i	−0.173328	−	0.646869i
$803$	7.23453	−	7.23453i	0.255301	−	0.255301i
$804$	14.2776			0.503531
$805$	10.2694	−	8.87143i	0.361950	−	0.312677i
$806$	−1.91554	+	1.91554i	−0.0674722	+	0.0674722i
$807$	−2.89000	−	0.774372i	−0.101733	−	0.0272592i
$808$		−	0.263723i		−	0.00927776i
$809$	2.23198	−	8.32987i	0.0784723	−	0.292863i	−0.915526	−	0.402259i	$-0.868225\pi$
$809$	2.23198	−	8.32987i	0.0784723	−	0.292863i	0.993998	+	0.109396i	$0.0348918\pi$
$810$	−65.3993	−	44.4075i	−2.29790	−	1.56032i
$811$	5.24640	+	9.08703i	0.184226	+	0.319089i	0.943315	−	0.331898i	$-0.107689\pi$
$811$	5.24640	+	9.08703i	0.184226	+	0.319089i	−0.759089	+	0.650986i	$0.774356\pi$
$812$	3.79570	+	2.19145i	0.133203	+	0.0769049i
$813$	−32.5317	−	32.5317i	−1.14094	−	1.14094i
$814$	19.6114	+	5.88397i	0.687379	+	0.206233i
$815$	−0.158143	−	0.326804i	−0.00553950	−	0.0114474i
$816$	−11.6533	−	43.4906i	−0.407946	−	1.52248i
$817$	1.76582	+	0.473151i	0.0617783	+	0.0165534i
$818$	−1.74612	+	6.51661i	−0.0610516	+	0.227848i
$819$	10.9983	+	2.94698i	0.384311	+	0.102976i
$820$	2.96812	+	6.13366i	0.103651	+	0.214197i
$821$	−11.4849	−	19.8924i	−0.400824	−	0.694248i	0.593001	−	0.805202i	$-0.297943\pi$
$821$	−11.4849	−	19.8924i	−0.400824	−	0.694248i	−0.993826	+	0.110953i	$0.964610\pi$
$822$			33.8725i			1.18144i
$823$	14.1702	+	52.8840i	0.493943	+	1.84342i	0.535873	+	0.844299i	$0.319983\pi$
$823$	14.1702	+	52.8840i	0.493943	+	1.84342i	−0.0419300	+	0.999121i	$0.513351\pi$
$824$			25.7507i			0.897069i
$825$	4.03703	+	34.6509i	0.140551	+	1.20639i
$826$	−29.1573	+	50.5019i	−1.01451	+	1.75718i
$827$	12.7147	−	7.34082i	0.442133	−	0.255265i	−0.262369	−	0.964968i	$-0.584504\pi$
$827$	12.7147	−	7.34082i	0.442133	−	0.255265i	0.704502	+	0.709702i	$0.251170\pi$
$828$			4.32589i			0.150335i
$829$	20.7635	−	5.56356i	0.721146	−	0.193231i	0.120463	−	0.992718i	$-0.461562\pi$
$829$	20.7635	−	5.56356i	0.721146	−	0.193231i	0.600683	+	0.799487i	$0.294895\pi$
$830$	22.9880	+	26.6105i	0.797924	+	0.923665i
$831$	−11.7862	+	3.15809i	−0.408857	+	0.109553i
$832$	−1.07650	−	1.86456i	−0.0373210	−	0.0646419i
$833$	−15.6897	−	27.1754i	−0.543616	−	0.941570i
$834$	111.072	−	29.7617i	3.84612	−	1.03056i
$835$	30.8505	+	2.25325i	1.06763	+	0.0779769i
$836$	3.36629	−	0.901996i	0.116426	−	0.0311962i
$837$		−	65.4224i		−	2.26133i
$838$	−3.34762	+	1.93275i	−0.115641	+	0.0667656i
$839$	−10.8636	+	18.8162i	−0.375052	+	0.649609i	−0.990335	−	0.138697i	$-0.955708\pi$
$839$	−10.8636	+	18.8162i	−0.375052	+	0.649609i	0.615283	+	0.788306i	$0.289042\pi$
$840$	32.3106	+	66.7702i	1.11482	+	2.30379i
$841$		−	22.2896i		−	0.768607i
$842$	−7.66752	−	28.6156i	−0.264240	−	0.986158i
$843$		−	16.3684i		−	0.563759i
$844$	2.97224	+	5.14807i	0.102309	+	0.177204i
$845$	25.8877	−	12.5272i	0.890562	−	0.430949i
$846$	142.877	+	38.2839i	4.91223	+	1.31623i
$847$	6.79259	−	25.3503i	0.233396	−	0.871046i
$848$	0.857209	+	0.229689i	0.0294367	+	0.00788754i
$849$	12.4147	+	46.3321i	0.426070	+	1.59012i
$850$	−18.3299	−	14.5045i	−0.628712	−	0.497501i
$851$	−8.61004	+	2.03521i	−0.295148	+	0.0697661i
$852$	−0.884525	−	0.884525i	−0.0303033	−	0.0303033i
$853$	39.0120	+	22.5236i	1.33575	+	0.771194i	0.986174	−	0.165715i	$-0.0529932\pi$
$853$	39.0120	+	22.5236i	1.33575	+	0.771194i	0.349573	+	0.936909i	$0.386327\pi$
$854$	−2.35087	−	4.07182i	−0.0804451	−	0.139335i
$855$	−12.1955	−	63.7939i	−0.417077	−	2.18170i
$856$	−4.59218	+	17.1382i	−0.156957	+	0.585773i
$857$		−	30.2373i		−	1.03289i	−0.856321	−	0.516444i	$-0.827256\pi$
$857$		−	30.2373i		−	1.03289i	0.856321	−	0.516444i	$-0.172744\pi$
$858$	3.88873	+	1.04198i	0.132759	+	0.0355727i
$859$	4.95333	−	4.95333i	0.169005	−	0.169005i	−0.617537	−	0.786542i	$-0.711869\pi$
$859$	4.95333	−	4.95333i	0.169005	−	0.169005i	0.786542	+	0.617537i	$0.211869\pi$
$860$	0.0304900	−	0.417455i	0.00103970	−	0.0142351i
$861$	100.808			3.43554
$862$	−29.4124	+	29.4124i	−1.00179	+	1.00179i
$863$	−2.02516	−	7.55800i	−0.0689372	−	0.257277i	0.922853	−	0.385152i	$-0.125851\pi$
$863$	−2.02516	−	7.55800i	−0.0689372	−	0.257277i	−0.991790	+	0.127875i	$0.959184\pi$
$864$	−30.4283	−	8.15325i	−1.03519	−	0.277379i
$865$	−33.8052	−	11.7572i	−1.14941	−	0.399758i
$866$	−7.05116	−	26.3153i	−0.239608	−	0.894229i
$867$	−24.5768	+	6.58534i	−0.834672	+	0.223650i
$868$	3.97166	−	6.87913i	0.134807	−	0.233493i
$869$	−5.29733	+	19.7699i	−0.179700	+	0.670648i
$870$	16.2240	−	23.8932i	0.550045	−	0.810057i
$871$	1.05465	+	3.93602i	0.0357356	+	0.133367i
$872$	−8.33659	−	31.1126i	−0.282313	−	1.05360i
$873$	−11.4785	+	19.8814i	−0.388489	+	0.672882i
$874$	−6.31686	+	6.31686i	−0.213671	+	0.213671i
$875$	41.3679	+	21.5642i	1.39849	+	0.729001i
$876$	5.32187	+	3.07258i	0.179809	+	0.103813i
$877$	28.3951	+	28.3951i	0.958835	+	0.958835i	0.999186	−	0.0403503i	$-0.0128474\pi$
$877$	28.3951	+	28.3951i	0.958835	+	0.958835i	−0.0403503	+	0.999186i	$0.512847\pi$
$878$	−14.3620	−	14.3620i	−0.484695	−	0.484695i
$879$	−2.43336	+	4.21471i	−0.0820753	+	0.142159i
$880$	9.82232	+	20.2979i	0.331110	+	0.684244i
$881$	47.4583	−	27.4000i	1.59891	−	0.923131i	0.607211	−	0.794540i	$-0.292288\pi$
$881$	47.4583	−	27.4000i	1.59891	−	0.923131i	0.991698	−	0.128590i	$-0.0410452\pi$
$882$	−118.430			−3.98773
$883$	−11.6623	+	6.73321i	−0.392467	+	0.226591i	−0.683228	−	0.730205i	$-0.739425\pi$
$883$	−11.6623	+	6.73321i	−0.392467	+	0.226591i	0.290762	+	0.956795i	$0.406091\pi$
$884$	−0.393798	+	0.227359i	−0.0132448	+	0.00764692i
$885$	53.5880	+	36.3874i	1.80134	+	1.22315i
$886$	−1.02783	+	0.275406i	−0.0345306	+	0.00925245i
$887$	21.5186	−	21.5186i	0.722524	−	0.722524i	−0.246594	−	0.969119i	$-0.579312\pi$
$887$	21.5186	−	21.5186i	0.722524	−	0.722524i	0.969119	+	0.246594i	$0.0793115\pi$
$888$	1.43525	−	48.3379i	0.0481640	−	1.62211i
$889$			41.9194i			1.40593i
$890$	17.9948	−	15.5451i	0.603186	−	0.521073i
$891$	−42.8425	+	24.7351i	−1.43528	+	0.828658i
$892$	−2.09155	−	0.560429i	−0.0700302	−	0.0187645i
$893$	25.7459	+	44.5932i	0.861554	+	1.49226i
$894$	39.3872	−	39.3872i	1.31730	−	1.31730i
$895$	6.17949	+	32.3245i	0.206558	+	1.08049i
$896$	39.8215	+	39.8215i	1.33034	+	1.33034i
$897$	−1.68033	+	0.450243i	−0.0561045	+	0.0150332i
$898$	16.3438	−	16.3438i	0.545401	−	0.545401i
$899$	12.1615			0.405610
$900$	−13.8222	+	5.48526i	−0.460741	+	0.182842i
$901$	−0.148997	+	0.556066i	−0.00496382	+	0.0185252i
$902$	25.2967			0.842289
$903$	−5.36272	−	3.09617i	−0.178460	−	0.103034i
$904$	17.3216	+	10.0006i	0.576108	+	0.332616i
$905$	−3.74141	+	51.2258i	−0.124369	+	1.70280i
$906$	−13.2212	−	3.54260i	−0.439244	−	0.117695i
$907$	−44.5758	+	25.7359i	−1.48012	+	0.854545i	−0.999746	−	0.0225216i	$-0.992831\pi$
$907$	−44.5758	+	25.7359i	−1.48012	+	0.854545i	−0.480369	+	0.877067i	$0.659497\pi$
$908$	4.15674	+	2.39989i	0.137946	+	0.0796433i
$909$	0.391088	−	0.677384i	0.0129716	−	0.0224674i
$910$	4.07407	−	3.51946i	0.135054	−	0.116669i
$911$	−30.2208	−	30.2208i	−1.00126	−	1.00126i	−0.999999	−	0.00125893i	$-0.999599\pi$
$911$	−30.2208	−	30.2208i	−1.00126	−	1.00126i	−0.00125893	−	0.999999i	$-0.500401\pi$
$912$	−29.5771	−	51.2290i	−0.979395	−	1.69636i
$913$	21.2563	−	5.69562i	0.703482	−	0.188497i
$914$			29.2198i			0.966504i
$915$	−4.70108	+	2.27489i	−0.155413	+	0.0752055i
$916$	4.12439	+	2.38122i	0.136274	+	0.0786776i
$917$	−61.2975			−2.02422
$918$	16.8609	−	62.9257i	0.556492	−	2.07686i
$919$	22.2439	+	22.2439i	0.733760	+	0.733760i	0.971362	−	0.237603i	$-0.0763616\pi$
$919$	22.2439	+	22.2439i	0.733760	+	0.733760i	−0.237603	+	0.971362i	$0.576362\pi$
$920$	−6.65409	−	4.51827i	−0.219379	−	0.148963i
$921$	−47.9412	−	83.0367i	−1.57972	−	2.73615i
$922$	−5.16226	+	19.2658i	−0.170010	+	0.634486i
$923$	0.178507	−	0.309183i	0.00587562	−	0.0101769i
$924$	−11.8048			−0.388350
$925$	−17.4206	−	24.9304i	−0.572784	−	0.819706i
$926$	−58.9361			−1.93676
$927$	−38.1869	+	66.1417i	−1.25422	+	2.17238i
$928$	1.51563	−	5.65641i	0.0497530	−	0.185681i
$929$	17.4258	+	30.1824i	0.571723	+	0.990253i	0.996389	+	0.0849029i	$0.0270580\pi$
$929$	17.4258	+	30.1824i	0.571723	+	0.990253i	−0.424667	+	0.905350i	$0.639609\pi$
$930$	−43.3028	−	29.4035i	−1.41995	−	0.964179i
$931$	−29.1517	−	29.1517i	−0.955407	−	0.955407i
$932$	−2.31498	+	8.63964i	−0.0758298	+	0.283001i
$933$	37.6900			1.23392
$934$	−33.2421	−	19.1924i	−1.08772	−	0.627993i
$935$	−13.1671	+	6.37167i	−0.430611	+	0.208376i
$936$		−	6.74844i		−	0.220580i
$937$	−42.8463	+	11.4806i	−1.39973	+	0.375056i	−0.878247	−	0.478207i	$-0.841287\pi$
$937$	−42.8463	+	11.4806i	−1.39973	+	0.375056i	−0.521481	+	0.853263i	$0.674620\pi$
$938$	−35.4406	−	61.3849i	−1.15718	−	2.00429i
$939$	14.6762	+	14.6762i	0.478940	+	0.478940i
$940$	8.92165	−	7.70712i	0.290992	−	0.251379i
$941$	11.4650	−	19.8579i	0.373748	−	0.647350i	−0.616391	−	0.787440i	$-0.711406\pi$
$941$	11.4650	−	19.8579i	0.373748	−	0.647350i	0.990139	+	0.140090i	$0.0447392\pi$
$942$	31.0166	+	17.9074i	1.01057	+	0.583456i
$943$	−9.46632	+	5.46538i	−0.308266	+	0.177977i
$944$	40.4430	+	10.8367i	1.31631	+	0.352704i
$945$	−9.47096	+	129.672i	−0.308090	+	4.21824i
$946$	−1.34572	−	0.776950i	−0.0437530	−	0.0252608i
$947$	−19.1624	−	11.0634i	−0.622693	−	0.359512i	0.155224	−	0.987879i	$-0.450390\pi$
$947$	−19.1624	−	11.0634i	−0.622693	−	0.359512i	−0.777917	+	0.628367i	$0.783724\pi$
$948$	−12.2933			−0.399269
$949$	−0.453931	+	1.69409i	−0.0147352	+	0.0549925i
$950$	−28.1937	−	12.1740i	−0.914723	−	0.394977i
$951$	71.2641			2.31090
$952$	−21.9933	+	21.9933i	−0.712808	+	0.712808i
$953$	−10.3263	+	2.76692i	−0.334501	+	0.0896293i	−0.422160	−	0.906521i	$-0.638728\pi$
$953$	−10.3263	+	2.76692i	−0.334501	+	0.0896293i	0.0876591	+	0.996151i	$0.472061\pi$
$954$	1.53632	+	1.53632i	0.0497403	+	0.0497403i
$955$	−3.94663	−	20.6446i	−0.127710	−	0.668042i
$956$	−4.51491	+	4.51491i	−0.146023	+	0.146023i
$957$	−9.03683	−	15.6522i	−0.292119	−	0.505965i
$958$	38.4451	+	10.3013i	1.24210	+	0.332821i
$959$	24.5489	−	14.1733i	0.792726	−	0.457680i
$960$	31.4799	−	27.1945i	1.01601	−	0.877698i
$961$			8.95909i			0.289003i
$962$	−3.41576	+	0.807405i	−0.110128	+	0.0260318i
$963$	−37.2103	+	37.2103i	−1.19908	+	1.19908i
$964$	−3.80942	+	1.02073i	−0.122693	+	0.0328756i
$965$	25.0531	+	17.0116i	0.806488	+	0.547623i
$966$	26.2059	−	15.1300i	0.843160	−	0.486799i
$967$	20.9493	−	12.0951i	0.673684	−	0.388951i	−0.123787	−	0.992309i	$-0.539504\pi$
$967$	20.9493	−	12.0951i	0.673684	−	0.388951i	0.797471	+	0.603357i	$0.206171\pi$
$968$	−15.5547			−0.499947
$969$	33.2319	−	19.1864i	1.06756	−	0.616357i
$970$	4.72817	+	9.77083i	0.151813	+	0.313722i
$971$	−3.56909	+	6.18184i	−0.114537	+	0.198385i	−0.917595	−	0.397517i	$-0.869872\pi$
$971$	−3.56909	+	6.18184i	−0.114537	+	0.198385i	0.803057	+	0.595902i	$0.203205\pi$
$972$	−9.02388	−	9.02388i	−0.289441	−	0.289441i
$973$	−68.0459	−	68.0459i	−2.18145	−	2.18145i
$974$	−29.3745	−	16.9594i	−0.941218	−	0.543413i
$975$	−3.56930	−	4.79812i	−0.114309	−	0.153663i
$976$	−2.38708	+	2.38708i	−0.0764085	+	0.0764085i
$977$	24.3556	−	42.1852i	0.779205	−	1.34962i	−0.153195	−	0.988196i	$-0.548956\pi$
$977$	24.3556	−	42.1852i	0.779205	−	1.34962i	0.932400	−	0.361427i	$-0.117710\pi$
$978$	−0.209525	−	0.781959i	−0.00669988	−	0.0250043i
$979$	−3.85153	−	14.3741i	−0.123096	−	0.459399i
$980$	−5.30259	+	7.80917i	−0.169385	+	0.249455i
$981$	24.7254	−	92.2765i	0.789422	−	2.94616i
$982$	10.2841	−	17.8125i	0.328178	−	0.568420i
$983$	−7.90875	+	2.11914i	−0.252250	+	0.0675902i	−0.382728	−	0.923861i	$-0.625015\pi$
$983$	−7.90875	+	2.11914i	−0.252250	+	0.0675902i	0.130478	+	0.991451i	$0.458349\pi$
$984$	−15.4638	−	57.7115i	−0.492966	−	1.83978i
$985$	−25.0305	−	8.70542i	−0.797537	−	0.277378i
$986$	11.6974	+	3.13432i	0.372522	+	0.0998169i
$987$	−45.1425	−	168.474i	−1.43690	−	5.36260i
$988$	−0.422436	+	0.422436i	−0.0134395	+	0.0134395i
$989$	0.671443			0.0213507
$990$	−4.02147	+	55.0602i	−0.127811	+	1.74993i
$991$	36.8837	−	36.8837i	1.17165	−	1.17165i	0.189834	−	0.981816i	$-0.439205\pi$
$991$	36.8837	−	36.8837i	1.17165	−	1.17165i	0.981816	−	0.189834i	$-0.0607948\pi$
$992$	−10.2514	−	2.74684i	−0.325481	−	0.0872124i
$993$		−	26.8768i		−	0.852910i
$994$	−1.60731	+	5.99855i	−0.0509806	+	0.190262i
$995$	4.44994	+	23.2774i	0.141073	+	0.737942i
$996$	6.60881	+	11.4468i	0.209408	+	0.362705i
$997$	30.2437	+	17.4612i	0.957828	+	0.553002i	0.895504	−	0.445054i	$-0.146816\pi$
$997$	30.2437	+	17.4612i	0.957828	+	0.553002i	0.0623238	+	0.998056i	$0.480149\pi$
$998$	39.1364	+	39.1364i	1.23884	+	1.23884i
$999$	44.5421	−	72.1177i	1.40925	−	2.28170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.p.a.97.4	✓	68
5.2	odd	4		925.2.y.b.393.4		68
5.3	odd	4		185.2.u.a.23.14	yes	68
5.4	even	2		925.2.t.b.282.14		68
37.29	odd	12		185.2.u.a.177.14	yes	68
185.29	odd	12		925.2.y.b.732.4		68
185.103	even	12	inner	185.2.p.a.103.4	yes	68
185.177	even	12		925.2.t.b.843.14		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.4	✓	68	1.1	even	1	trivial
185.2.p.a.103.4	yes	68	185.103	even	12	inner
185.2.u.a.23.14	yes	68	5.3	odd	4
185.2.u.a.177.14	yes	68	37.29	odd	12
925.2.t.b.282.14		68	5.4	even	2
925.2.t.b.843.14		68	185.177	even	12
925.2.y.b.393.4		68	5.2	odd	4
925.2.y.b.732.4		68	185.29	odd	12

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:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.775482 + 1.34317i) q^{2} +(0.832043 - 3.10523i) q^{3} +(-0.202746 - 0.351166i) q^{4} +(1.84991 + 1.25612i) q^{5} +(3.52563 + 3.52563i) q^{6} +(1.07995 - 4.03042i) q^{7} -2.47303 q^{8} +(-6.35206 - 3.66736i) q^{9} +(-3.12176 + 1.51064i) q^{10} +2.17031i q^{11} +(-1.25914 + 0.337386i) q^{12} +(-0.186020 - 0.322197i) q^{13} +(4.57608 + 4.57608i) q^{14} +(5.43975 - 4.69923i) q^{15} +(2.32328 - 4.02404i) q^{16} +(2.61037 + 1.50709i) q^{17} +(9.85182 - 5.68795i) q^{18} +(3.82515 + 1.02494i) q^{19} +(0.0660477 - 0.904297i) q^{20} +(-11.6168 - 6.70696i) q^{21} +(-2.91511 - 1.68304i) q^{22} +1.45449 q^{23} +(-2.05766 + 7.67931i) q^{24} +(1.84430 + 4.64742i) q^{25} +0.577022 q^{26} +(-9.85364 + 9.85364i) q^{27} +(-1.63430 + 0.437909i) q^{28} +(-1.83172 - 1.83172i) q^{29} +(2.09345 + 10.9507i) q^{30} +(-3.31971 + 3.31971i) q^{31} +(1.13030 + 1.95773i) q^{32} +(6.73931 + 1.80579i) q^{33} +(-4.04858 + 2.33745i) q^{34} +(7.06051 - 6.09934i) q^{35} +2.97417i q^{36} +(-5.91963 + 1.39926i) q^{37} +(-4.34301 + 4.34301i) q^{38} +(-1.15527 + 0.309554i) q^{39} +(-4.57487 - 3.10643i) q^{40} +(-6.50835 + 3.75760i) q^{41} +(18.0172 - 10.4023i) q^{42} +0.461635 q^{43} +(0.762140 - 0.440021i) q^{44} +(-7.14405 - 14.7633i) q^{45} +(-1.12793 + 1.95363i) q^{46} +(9.19431 + 9.19431i) q^{47} +(-10.5625 - 10.5625i) q^{48} +(-9.01581 - 5.20528i) q^{49} +(-7.67253 - 1.12678i) q^{50} +(6.85181 - 6.85181i) q^{51} +(-0.0754296 + 0.130648i) q^{52} +(0.0494320 + 0.184483i) q^{53} +(-5.59384 - 20.8765i) q^{54} +(-2.72618 + 4.01487i) q^{55} +(-2.67074 + 9.96733i) q^{56} +(6.36537 - 11.0251i) q^{57} +(3.88079 - 1.03985i) q^{58} +(2.33219 + 8.70387i) q^{59} +(-2.75309 - 0.957507i) q^{60} +(-0.701769 - 0.188038i) q^{61} +(-1.88457 - 7.03332i) q^{62} +(-21.6409 + 21.6409i) q^{63} +5.78701 q^{64} +(0.0605992 - 0.829698i) q^{65} +(-7.65172 + 7.65172i) q^{66} +(-10.5795 - 2.83478i) q^{67} -1.22223i q^{68} +(1.21020 - 4.51652i) q^{69} +(2.71719 + 14.2134i) q^{70} +(0.479804 + 0.831045i) q^{71} +(15.7088 + 9.06949i) q^{72} +(-3.33340 - 3.33340i) q^{73} +(2.71112 - 9.03621i) q^{74} +(15.9658 - 1.86012i) q^{75} +(-0.415606 - 1.55106i) q^{76} +(8.74727 + 2.34382i) q^{77} +(0.480107 - 1.79178i) q^{78} +(9.10924 + 2.44081i) q^{79} +(9.35254 - 4.52576i) q^{80} +(11.3970 + 19.7402i) q^{81} -11.6558i q^{82} +(-2.62433 - 9.79413i) q^{83} +5.43923i q^{84} +(2.93583 + 6.06693i) q^{85} +(-0.357990 + 0.620057i) q^{86} +(-7.21197 + 4.16383i) q^{87} -5.36724i q^{88} +(-6.62306 + 1.77464i) q^{89} +(25.3697 + 1.85294i) q^{90} +(-1.49948 + 0.401784i) q^{91} +(-0.294891 - 0.510766i) q^{92} +(7.54630 + 13.0706i) q^{93} +(-19.4796 + 5.21954i) q^{94} +(5.78870 + 6.70091i) q^{95} +(7.01966 - 1.88091i) q^{96} -3.12991i q^{97} +(13.9832 - 8.07320i) q^{98} +(7.95933 - 13.7860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22}+ \cdots + 32 q^{99}+O(q^{100}) \) 68 * q - 4 * q^2 - 8 * q^3 - 30 * q^4 - 10 * q^5 - 8 * q^6 - 2 * q^7 + 12 * q^8 - 6 * q^10 + 14 * q^12 - 6 * q^13 - 8 * q^15 - 26 * q^16 + 12 * q^17 + 18 * q^18 + 4 * q^19 + 48 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 68 * q^27 - 26 * q^28 + 14 * q^29 + 10 * q^30 - 24 * q^31 - 16 * q^32 - 2 * q^33 - 10 * q^35 - 16 * q^37 - 36 * q^38 + 52 * q^39 + 42 * q^40 - 18 * q^41 + 132 * q^42 + 8 * q^43 - 36 * q^44 - 32 * q^45 - 52 * q^46 - 24 * q^47 - 60 * q^48 - 36 * q^49 - 8 * q^50 - 8 * q^51 - 26 * q^52 + 82 * q^53 + 40 * q^54 + 18 * q^55 + 16 * q^56 - 6 * q^57 + 86 * q^58 - 8 * q^59 + 36 * q^60 + 4 * q^61 + 10 * q^62 - 48 * q^63 - 20 * q^64 + 8 * q^65 + 80 * q^66 - 40 * q^67 + 8 * q^69 - 82 * q^70 + 4 * q^71 - 90 * q^72 - 60 * q^73 - 44 * q^74 + 64 * q^75 + 72 * q^76 + 66 * q^77 - 24 * q^78 + 56 * q^79 + 34 * q^80 - 6 * q^81 + 24 * q^83 - 20 * q^85 - 4 * q^86 - 84 * q^87 - 22 * q^89 - 50 * q^90 + 44 * q^91 + 44 * q^92 - 34 * q^93 - 20 * q^94 - 28 * q^95 - 8 * q^96 + 42 * q^98 + 32 * q^99

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