LMFDB - Embedded newform 925.2.t.b.843.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(82,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, 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("925.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.t (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			843.14
Character	$\chi$	$=$	925.843
Dual form			925.2.t.b.282.14

$q$-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} +(3.52563 - 3.52563i) q^{6} +(-1.07995 - 4.03042i) q^{7} +2.47303 q^{8} +(-6.35206 + 3.66736i) q^{9} -2.17031i q^{11} +(1.25914 + 0.337386i) q^{12} +(0.186020 - 0.322197i) q^{13} +(4.57608 - 4.57608i) q^{14} +(2.32328 + 4.02404i) q^{16} +(-2.61037 + 1.50709i) q^{17} +(-9.85182 - 5.68795i) q^{18} +(3.82515 - 1.02494i) q^{19} +(-11.6168 + 6.70696i) q^{21} +(2.91511 - 1.68304i) q^{22} -1.45449 q^{23} +(-2.05766 - 7.67931i) q^{24} +0.577022 q^{26} +(9.85364 + 9.85364i) q^{27} +(1.63430 + 0.437909i) q^{28} +(-1.83172 + 1.83172i) q^{29} +(-3.31971 - 3.31971i) q^{31} +(-1.13030 + 1.95773i) q^{32} +(-6.73931 + 1.80579i) q^{33} +(-4.04858 - 2.33745i) q^{34} -2.97417i q^{36} +(5.91963 + 1.39926i) q^{37} +(4.34301 + 4.34301i) q^{38} +(-1.15527 - 0.309554i) q^{39} +(-6.50835 - 3.75760i) q^{41} +(-18.0172 - 10.4023i) q^{42} -0.461635 q^{43} +(0.762140 + 0.440021i) q^{44} +(-1.12793 - 1.95363i) q^{46} +(-9.19431 + 9.19431i) q^{47} +(10.5625 - 10.5625i) q^{48} +(-9.01581 + 5.20528i) q^{49} +(6.85181 + 6.85181i) q^{51} +(0.0754296 + 0.130648i) q^{52} +(-0.0494320 + 0.184483i) q^{53} +(-5.59384 + 20.8765i) q^{54} +(-2.67074 - 9.96733i) q^{56} +(-6.36537 - 11.0251i) q^{57} +(-3.88079 - 1.03985i) q^{58} +(2.33219 - 8.70387i) q^{59} +(-0.701769 + 0.188038i) q^{61} +(1.88457 - 7.03332i) q^{62} +(21.6409 + 21.6409i) q^{63} +5.78701 q^{64} +(-7.65172 - 7.65172i) q^{66} +(10.5795 - 2.83478i) q^{67} -1.22223i q^{68} +(1.21020 + 4.51652i) q^{69} +(0.479804 - 0.831045i) q^{71} +(-15.7088 + 9.06949i) q^{72} +(3.33340 - 3.33340i) q^{73} +(2.71112 + 9.03621i) q^{74} +(-0.415606 + 1.55106i) q^{76} +(-8.74727 + 2.34382i) q^{77} +(-0.480107 - 1.79178i) q^{78} +(9.10924 - 2.44081i) q^{79} +(11.3970 - 19.7402i) q^{81} -11.6558i q^{82} +(2.62433 - 9.79413i) q^{83} -5.43923i q^{84} +(-0.357990 - 0.620057i) q^{86} +(7.21197 + 4.16383i) q^{87} -5.36724i q^{88} +(-6.62306 - 1.77464i) q^{89} +(-1.49948 - 0.401784i) q^{91} +(0.294891 - 0.510766i) q^{92} +(-7.54630 + 13.0706i) q^{93} +(-19.4796 - 5.21954i) q^{94} +(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} - 8 q^{6} + 2 q^{7} - 12 q^{8} - 14 q^{12} + 6 q^{13} - 26 q^{16} - 12 q^{17} - 18 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 24 q^{26} + 68 q^{27} + 26 q^{28}+ \cdots + 32 q^{99}+O(q^{100}) $ 68 * q + 4 * q^2 + 8 * q^3 - 30 * q^4 - 8 * q^6 + 2 * q^7 - 12 * q^8 - 14 * q^12 + 6 * q^13 - 26 * q^16 - 12 * q^17 - 18 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 24 * q^26 + 68 * q^27 + 26 * q^28 + 14 * q^29 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 16 * q^37 + 36 * q^38 + 52 * q^39 - 18 * q^41 - 132 * q^42 - 8 * q^43 - 36 * q^44 - 52 * q^46 + 24 * q^47 + 60 * q^48 - 36 * q^49 - 8 * q^51 + 26 * q^52 - 82 * q^53 + 40 * q^54 + 16 * q^56 + 6 * q^57 - 86 * q^58 - 8 * q^59 + 4 * q^61 - 10 * q^62 + 48 * q^63 - 20 * q^64 + 80 * q^66 + 40 * q^67 + 8 * q^69 + 4 * q^71 + 90 * q^72 + 60 * q^73 - 44 * q^74 + 72 * q^76 - 66 * q^77 + 24 * q^78 + 56 * q^79 - 6 * q^81 - 24 * q^83 - 4 * q^86 + 84 * q^87 - 22 * q^89 + 44 * q^91 - 44 * q^92 + 34 * q^93 - 20 * q^94 - 8 * q^96 - 42 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

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	0.998388	+	0.0567591i	$0.0180767\pi$
$2$	0.775482	+	1.34317i	0.548349	+	0.949768i	−0.450039	+	0.893009i	$0.648590\pi$
$3$	−0.832043	−	3.10523i	−0.480380	−	1.79280i	−0.600019	−	0.799986i	$-0.704840\pi$
$3$	−0.832043	−	3.10523i	−0.480380	−	1.79280i	0.119638	−	0.992818i	$-0.461826\pi$
$4$	−0.202746	+	0.351166i	−0.101373	+	0.175583i
$5$		0			0
$5$		0			0
$6$	3.52563	−	3.52563i	1.43933	−	1.43933i
$7$	−1.07995	−	4.03042i	−0.408182	−	1.52335i	−0.798111	−	0.602510i	$-0.794167\pi$
$7$	−1.07995	−	4.03042i	−0.408182	−	1.52335i	0.389929	−	0.920845i	$-0.372499\pi$
$8$	2.47303			0.874347
$9$	−6.35206	+	3.66736i	−2.11735	+	1.22245i
$10$		0			0
$11$		−	2.17031i		−	0.654374i	−0.944960	−	0.327187i	$-0.893899\pi$
$11$		−	2.17031i		−	0.654374i	0.944960	−	0.327187i	$-0.106101\pi$
$12$	1.25914	+	0.337386i	0.363483	+	0.0973950i
$13$	0.186020	−	0.322197i	0.0515928	−	0.0893613i	−0.839076	−	0.544015i	$-0.816904\pi$
$13$	0.186020	−	0.322197i	0.0515928	−	0.0893613i	0.890668	+	0.454653i	$0.150237\pi$
$14$	4.57608	−	4.57608i	1.22301	−	1.22301i
$15$		0			0
$16$	2.32328	+	4.02404i	0.580820	+	1.00601i
$17$	−2.61037	+	1.50709i	−0.633107	+	0.365524i	−0.781954	−	0.623336i	$-0.785777\pi$
$17$	−2.61037	+	1.50709i	−0.633107	+	0.365524i	0.148848	+	0.988860i	$0.452444\pi$
$18$	−9.85182	−	5.68795i	−2.32210	−	1.34066i
$19$	3.82515	−	1.02494i	0.877549	−	0.235138i	0.208200	−	0.978086i	$-0.433240\pi$
$19$	3.82515	−	1.02494i	0.877549	−	0.235138i	0.669349	+	0.742948i	$0.266573\pi$
$20$		0			0
$21$	−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	$-0.548456\pi$
$23$	−1.45449			−0.303282			−0.151641	+	0.988436i	$0.548456\pi$
$24$	−2.05766	−	7.67931i	−0.420019	−	1.56753i
$25$		0			0
$26$	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	−0.856421	−	0.516279i	$-0.827317\pi$
$29$	−1.83172	+	1.83172i	−0.340142	+	0.340142i	0.516279	+	0.856421i	$0.327317\pi$
$30$		0			0
$31$	−3.31971	−	3.31971i	−0.596237	−	0.596237i	0.343072	−	0.939309i	$-0.388532\pi$
$31$	−3.31971	−	3.31971i	−0.596237	−	0.596237i	−0.939309	+	0.343072i	$0.888532\pi$
$32$	−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
$35$		0			0
$36$		−	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
$40$		0			0
$41$	−6.50835	−	3.75760i	−1.01643	−	0.586838i	−0.103365	−	0.994644i	$-0.532961\pi$
$41$	−6.50835	−	3.75760i	−1.01643	−	0.586838i	−0.913069	+	0.407805i	$0.866294\pi$
$42$	−18.0172	−	10.4023i	−2.78012	−	1.60510i
$43$	−0.461635			−0.0703987			−0.0351994	−	0.999380i	$-0.511207\pi$
$43$	−0.461635			−0.0703987			−0.0351994	+	0.999380i	$0.511207\pi$
$44$	0.762140	+	0.440021i	0.114897	+	0.0663357i
$45$		0			0
$46$	−1.12793	−	1.95363i	−0.166304	−	0.288047i
$47$	−9.19431	+	9.19431i	−1.34113	+	1.34113i	−0.446188	+	0.894939i	$0.647219\pi$
$47$	−9.19431	+	9.19431i	−1.34113	+	1.34113i	−0.894939	+	0.446188i	$0.852781\pi$
$48$	10.5625	−	10.5625i	1.52456	−	1.52456i
$49$	−9.01581	+	5.20528i	−1.28797	+	0.743611i
$50$		0			0
$51$	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	$-0.920842\pi$
$53$	−0.0494320	+	0.184483i	−0.00679000	+	0.0253406i	0.962448	+	0.271467i	$0.0875088\pi$
$54$	−5.59384	+	20.8765i	−0.761225	+	2.84093i
$55$		0			0
$56$	−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	−0.630496	−	0.776192i	$-0.717148\pi$
$59$	2.33219	−	8.70387i	0.303626	−	1.13315i	0.934122	−	0.356954i	$-0.116185\pi$
$60$		0			0
$61$	−0.701769	+	0.188038i	−0.0898523	+	0.0240758i	−0.303465	−	0.952843i	$-0.598144\pi$
$61$	−0.701769	+	0.188038i	−0.0898523	+	0.0240758i	0.213613	+	0.976918i	$0.431477\pi$
$62$	1.88457	−	7.03332i	0.239341	−	0.893233i
$63$	21.6409	+	21.6409i	2.72650	+	2.72650i
$64$	5.78701			0.723377
$65$		0			0
$66$	−7.65172	−	7.65172i	−0.941861	−	0.941861i
$67$	10.5795	−	2.83478i	1.29250	−	0.346323i	0.453888	−	0.891059i	$-0.350037\pi$
$67$	10.5795	−	2.83478i	1.29250	−	0.346323i	0.838608	+	0.544735i	$0.183370\pi$
$68$		−	1.22223i		−	0.148217i
$69$	1.21020	+	4.51652i	0.145691	+	0.543725i
$70$		0			0
$71$	0.479804	−	0.831045i	0.0569423	−	0.0986269i	−0.836149	−	0.548502i	$-0.815198\pi$
$71$	0.479804	−	0.831045i	0.0569423	−	0.0986269i	0.893091	+	0.449875i	$0.148532\pi$
$72$	−15.7088	+	9.06949i	−1.85130	+	1.06885i
$73$	3.33340	−	3.33340i	0.390145	−	0.390145i	−0.484594	−	0.874739i	$-0.661033\pi$
$73$	3.33340	−	3.33340i	0.390145	−	0.390145i	0.874739	+	0.484594i	$0.161033\pi$
$74$	2.71112	+	9.03621i	0.315161	+	1.05044i
$75$		0			0
$76$	−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	0.293040	−	0.956100i	$-0.405333\pi$
$79$	9.10924	−	2.44081i	1.02487	−	0.274613i	0.731830	+	0.681487i	$0.238667\pi$
$80$		0			0
$81$	11.3970	−	19.7402i	1.26634	−	2.19336i
$82$		−	11.6558i		−	1.28717i
$83$	2.62433	−	9.79413i	0.288058	−	1.07505i	−0.658518	−	0.752565i	$-0.728817\pi$
$83$	2.62433	−	9.79413i	0.288058	−	1.07505i	0.946576	−	0.322481i	$-0.104517\pi$
$84$		−	5.43923i		−	0.593469i
$85$		0			0
$86$	−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	−0.109897	−	0.993943i	$-0.535052\pi$
$89$	−6.62306	−	1.77464i	−0.702043	−	0.188112i	−0.592145	+	0.805831i	$0.701719\pi$
$90$		0			0
$91$	−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
$95$		0			0
$96$	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
$100$		0			0
$101$		−	0.106640i		−	0.0106111i	−0.999986	−	0.00530554i	$-0.998311\pi$
$101$		−	0.106640i		−	0.0106111i	0.999986	−	0.00530554i	$-0.00168881\pi$
$102$	−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
$105$		0			0
$106$	−0.286126	+	0.0766672i	−0.0277910	+	0.00744658i
$107$	−1.85691	−	6.93007i	−0.179514	−	0.669955i	−0.995739	−	0.0922203i	$-0.970604\pi$
$107$	−1.85691	−	6.93007i	−0.179514	−	0.669955i	0.816225	−	0.577734i	$-0.196063\pi$
$108$	−5.45804	+	1.46248i	−0.525200	+	0.140727i
$109$	3.37101	−	12.5808i	0.322884	−	1.20502i	−0.593538	−	0.804806i	$-0.702269\pi$
$109$	3.37101	−	12.5808i	0.322884	−	1.20502i	0.916422	−	0.400213i	$-0.131064\pi$
$110$		0			0
$111$	−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	$-0.542447\pi$
$113$	7.00421	−	4.04388i	0.658901	−	0.380417i	0.791858	+	0.610705i	$0.209114\pi$
$114$	9.87247	−	17.0996i	0.924641	−	1.60153i
$115$		0			0
$116$	−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
$120$		0			0
$121$	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
$125$		0			0
$126$	−12.2854	+	45.8497i	−1.09447	+	4.08461i
$127$	9.70404	+	2.60019i	0.861094	+	0.230729i	0.662233	−	0.749298i	$-0.269609\pi$
$127$	9.70404	+	2.60019i	0.861094	+	0.230729i	0.198861	+	0.980028i	$0.436276\pi$
$128$	6.74832	+	11.6884i	0.596473	+	1.03312i
$129$	0.384100	+	1.43348i	0.0338182	+	0.126211i
$130$		0			0
$131$	−3.80218	+	14.1899i	−0.332198	+	1.23978i	0.574677	+	0.818381i	$0.305128\pi$
$131$	−3.80218	+	14.1899i	−0.332198	+	1.23978i	−0.906875	+	0.421400i	$0.861539\pi$
$132$	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
$135$		0			0
$136$	−6.45550	+	3.72709i	−0.553555	+	0.319595i
$137$	−4.80375	+	4.80375i	−0.410412	+	0.410412i	−0.881882	−	0.471470i	$-0.843724\pi$
$137$	−4.80375	+	4.80375i	−0.410412	+	0.410412i	0.471470	+	0.881882i	$0.343724\pi$
$138$	−5.12799	+	5.12799i	−0.436523	+	0.436523i
$139$	11.5314	+	19.9729i	0.978077	+	1.69408i	0.669384	+	0.742917i	$0.266558\pi$
$139$	11.5314	+	19.9729i	0.978077	+	1.69408i	0.308693	+	0.951162i	$0.400108\pi$
$140$		0			0
$141$	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
$145$		0			0
$146$	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	$0.151294\pi$
$149$			11.1717i			0.915220i	−0.889153	+	0.457610i	$0.848706\pi$
$150$		0			0
$151$	−2.37742	−	1.37260i	−0.193472	−	0.111701i	0.400135	−	0.916456i	$-0.368963\pi$
$151$	−2.37742	−	1.37260i	−0.193472	−	0.111701i	−0.593607	+	0.804755i	$0.702297\pi$
$152$	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
$155$		0			0
$156$	0.342931	−	0.342931i	0.0274564	−	0.0274564i
$157$	−6.93834	−	1.85912i	−0.553740	−	0.148374i	−0.0289111	−	0.999582i	$-0.509204\pi$
$157$	−6.93834	−	1.85912i	−0.553740	−	0.148374i	−0.524829	+	0.851208i	$0.675871\pi$
$158$	10.3425	+	10.3425i	0.822804	+	0.822804i
$159$	0.613990			0.0486926
$160$		0			0
$161$	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	$-0.664643\pi$
$163$	0.140611	−	0.0811818i	0.0110135	−	0.00635865i	0.505497	+	0.862829i	$0.331309\pi$
$164$	2.63908	−	1.52367i	0.206077	−	0.118979i
$165$		0			0
$166$	15.1903	−	4.07024i	1.17900	−	0.315912i
$167$	−11.9802	−	6.91676i	−0.927055	−	0.535235i	−0.0411758	−	0.999152i	$-0.513110\pi$
$167$	−11.9802	−	6.91676i	−0.927055	−	0.535235i	−0.885879	+	0.463917i	$0.846444\pi$
$168$	−28.7287	+	16.5865i	−2.21646	+	1.27968i
$169$	6.43079	+	11.1385i	0.494676	+	0.856805i
$170$		0			0
$171$	−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	$-0.208449\pi$
$173$	15.4610	+	4.14277i	1.17548	+	0.314969i	0.382347	+	0.924019i	$0.375116\pi$
$174$			12.9159i			0.979153i
$175$		0			0
$176$	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	−0.201608	−	0.979466i	$-0.564617\pi$
$179$	10.4070	−	10.4070i	0.777858	−	0.777858i	0.979466	+	0.201608i	$0.0646168\pi$
$180$		0			0
$181$	11.4850	−	19.8925i	0.853670	−	1.47860i	−0.0242033	−	0.999707i	$-0.507705\pi$
$181$	11.4850	−	19.8925i	0.853670	−	1.47860i	0.877873	−	0.478893i	$-0.158962\pi$
$182$	−0.623153	−	2.32564i	−0.0461912	−	0.172388i
$183$	1.16780	+	2.02270i	0.0863265	+	0.149522i
$184$	−3.59699			−0.265174
$185$		0			0
$186$	−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
$190$		0			0
$191$	−6.64661	+	6.64661i	−0.480931	+	0.480931i	−0.905429	−	0.424498i	$-0.860451\pi$
$191$	−6.64661	+	6.64661i	−0.480931	+	0.480931i	0.424498	+	0.905429i	$0.360451\pi$
$192$	−4.81505	−	17.9700i	−0.347496	−	1.29687i
$193$	−13.5429			−0.974841			−0.487420	−	0.873167i	$-0.662062\pi$
$193$	−13.5429			−0.974841			−0.487420	+	0.873167i	$0.662062\pi$
$194$	4.20401	−	2.42719i	0.301830	−	0.174262i
$195$		0			0
$196$		−	4.22139i		−	0.301528i
$197$	11.4478	+	3.06743i	0.815623	+	0.218546i	0.642432	−	0.766343i	$-0.277926\pi$
$197$	11.4478	+	3.06743i	0.815623	+	0.218546i	0.173191	+	0.984888i	$0.444592\pi$
$198$	−12.3446	+	21.3815i	−0.877295	+	1.51952i
$199$	7.49425	−	7.49425i	0.531253	−	0.531253i	−0.389692	−	0.920945i	$-0.627419\pi$
$199$	7.49425	−	7.49425i	0.531253	−	0.531253i	0.920945	+	0.389692i	$0.127419\pi$
$200$		0			0
$201$	−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
$205$		0			0
$206$	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
$210$		0			0
$211$	−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			0
$216$	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
$220$		0			0
$221$			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	$-0.307221\pi$
$223$	−3.77596	−	3.77596i	−0.252857	−	0.252857i	−0.822141	+	0.569284i	$0.807221\pi$
$224$	9.11115	+	2.44132i	0.608764	+	0.163118i
$225$		0			0
$226$	10.8633	+	6.27192i	0.722615	+	0.417202i
$227$	10.2511	+	5.91849i	0.680391	+	0.392824i	0.800002	−	0.599997i	$-0.204832\pi$
$227$	10.2511	+	5.91849i	0.680391	+	0.392824i	−0.119611	+	0.992821i	$0.538165\pi$
$228$	5.16221			0.341875
$229$	−10.1713	−	5.87243i	−0.672141	−	0.388061i	0.124746	−	0.992189i	$-0.460188\pi$
$229$	−10.1713	−	5.87243i	−0.672141	−	0.388061i	−0.796887	+	0.604128i	$0.793522\pi$
$230$		0			0
$231$	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	0.0220706	−	0.999756i	$-0.492974\pi$
$233$	15.5975	−	15.5975i	1.02183	−	1.02183i	0.999756	−	0.0220706i	$-0.00702585\pi$
$234$	−3.66528	+	2.11615i	−0.239607	+	0.138337i
$235$		0			0
$236$	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	0.699468	+	0.714663i	$0.253420\pi$
$239$	−4.07548	+	15.2099i	−0.263621	+	0.983846i	−0.963089	+	0.269183i	$0.913247\pi$
$240$		0			0
$241$	2.51727	+	9.39459i	0.162152	+	0.605159i	0.998386	+	0.0567867i	$0.0180855\pi$
$241$	2.51727	+	9.39459i	0.162152	+	0.605159i	−0.836235	+	0.548372i	$0.815248\pi$
$242$	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
$245$		0			0
$246$	−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
$250$		0			0
$251$	−21.3201	−	21.3201i	−1.34571	−	1.34571i	−0.890263	−	0.455447i	$-0.849479\pi$
$251$	−21.3201	−	21.3201i	−1.34571	−	1.34571i	−0.455447	−	0.890263i	$-0.650521\pi$
$252$	−11.9871	+	3.21195i	−0.755119	+	0.202334i
$253$			3.15670i			0.198460i
$254$	4.03280	+	15.0506i	0.253040	+	0.944360i
$255$		0			0
$256$	−4.67940	+	8.10495i	−0.292462	+	0.506559i
$257$	5.04941	−	2.91528i	0.314974	−	0.181850i	−0.334176	−	0.942511i	$-0.608458\pi$
$257$	5.04941	−	2.91528i	0.314974	−	0.181850i	0.649150	+	0.760660i	$0.275125\pi$
$258$	−1.62755	+	1.62755i	−0.101327	+	0.101327i
$259$	−0.753280	−	25.3697i	−0.0468066	−	1.57640i
$260$		0			0
$261$	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	−0.918630	−	0.395120i	$-0.870703\pi$
$263$	−5.19979	−	19.4059i	−0.320633	−	1.19662i	0.597997	−	0.801498i	$-0.295964\pi$
$264$	−16.6665	+	4.46578i	−1.02575	+	0.274850i
$265$		0			0
$266$	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	$0.00903246\pi$
$269$			0.930688i			0.0567450i	−0.999597	+	0.0283725i	$0.990968\pi$
$270$		0			0
$271$	7.15555	+	12.3938i	0.434669	+	0.752868i	0.997269	−	0.0738613i	$-0.0235322\pi$
$271$	7.15555	+	12.3938i	0.434669	+	0.752868i	−0.562600	+	0.826729i	$0.690199\pi$
$272$	−12.1292	−	7.00281i	−0.735442	−	0.424607i
$273$			4.99053i			0.302040i
$274$	−10.1775	−	2.72705i	−0.614845	−	0.164747i
$275$		0			0
$276$	−1.83141	−	0.490724i	−0.110238	−	0.0295381i
$277$	1.89779	−	3.28707i	0.114027	−	0.197501i	−0.803363	−	0.595489i	$-0.796958\pi$
$277$	1.89779	−	3.28707i	0.114027	−	0.197501i	0.917391	+	0.397988i	$0.130292\pi$
$278$	−17.8847	+	30.9772i	−1.07265	+	1.85789i
$279$	33.2616	+	8.91241i	1.99132	+	0.533572i
$280$		0			0
$281$	4.91815	+	1.31781i	0.293392	+	0.0786142i	0.402513	−	0.915414i	$-0.368137\pi$
$281$	4.91815	+	1.31781i	0.293392	+	0.0786142i	−0.109121	+	0.994029i	$0.534804\pi$
$282$			64.8314i			3.86065i
$283$	12.9217	+	7.46035i	0.768115	+	0.443472i	0.832202	−	0.554473i	$-0.187080\pi$
$283$	12.9217	+	7.46035i	0.768115	+	0.443472i	−0.0640865	+	0.997944i	$0.520413\pi$
$284$	0.194556	+	0.336982i	0.0115448	+	0.0199962i
$285$		0			0
$286$		−	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
$290$		0			0
$291$	−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	$-0.569253\pi$
$293$	1.46228	−	0.391817i	0.0854275	−	0.0228902i	0.301280	+	0.953536i	$0.402586\pi$
$294$	−13.4345	+	50.1383i	−0.783516	+	2.92412i
$295$		0			0
$296$	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
$300$		0			0
$301$	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
$305$		0			0
$306$	34.2891			1.96018
$307$	−21.0899	−	21.0899i	−1.20366	−	1.20366i	−0.973044	−	0.230621i	$-0.925924\pi$
$307$	−21.0899	−	21.0899i	−1.20366	−	1.20366i	−0.230621	−	0.973044i	$-0.574076\pi$
$308$	0.950400	−	3.54694i	0.0541541	−	0.202106i
$309$	−32.3336	+	8.66376i	−1.83939	+	0.492864i
$310$		0			0
$311$	3.03440	−	11.3245i	0.172065	−	0.642156i	−0.824968	−	0.565180i	$-0.808807\pi$
$311$	3.03440	−	11.3245i	0.172065	−	0.642156i	0.997033	−	0.0769762i	$-0.0245265\pi$
$312$	−2.85702	−	0.765535i	−0.161747	−	0.0433399i
$313$	3.22812	+	5.59126i	0.182464	+	0.316037i	0.942719	−	0.333588i	$-0.108259\pi$
$313$	3.22812	+	5.59126i	0.182464	+	0.316037i	−0.760255	+	0.649625i	$0.774926\pi$
$314$	−2.88343	−	10.7611i	−0.162722	−	0.607285i
$315$		0			0
$316$	−0.989728	+	3.69372i	−0.0556766	+	0.207788i
$317$	−5.73743	+	21.4124i	−0.322246	+	1.20264i	0.594805	+	0.803870i	$0.297229\pi$
$317$	−5.73743	+	21.4124i	−0.322246	+	1.20264i	−0.917051	+	0.398769i	$0.869438\pi$
$318$	0.476138	+	0.824696i	0.0267005	+	0.0462466i
$319$	3.97540	+	3.97540i	0.222580	+	0.222580i
$320$		0			0
$321$	−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
$325$		0			0
$326$	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
$330$		0			0
$331$	8.07555	+	2.16384i	0.443873	+	0.118935i	0.473831	−	0.880616i	$-0.342871\pi$
$331$	8.07555	+	2.16384i	0.443873	+	0.118935i	−0.0299583	+	0.999551i	$0.509537\pi$
$332$	2.90729	+	2.90729i	0.159558	+	0.159558i
$333$	−42.7335	+	12.8213i	−2.34178	+	0.702600i
$334$		−	21.4553i		−	1.17398i
$335$		0			0
$336$	−53.9782	−	31.1643i	−2.94475	−	1.70015i
$337$	7.82004	−	2.09537i	0.425985	−	0.114142i	−0.0394559	−	0.999221i	$-0.512562\pi$
$337$	7.82004	−	2.09537i	0.425985	−	0.114142i	0.465441	+	0.885079i	$0.345896\pi$
$338$	−9.97393	+	17.2754i	−0.542510	+	0.939656i
$339$	−18.3850	−	18.3850i	−0.998535	−	0.998535i
$340$		0			0
$341$	−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
$345$		0			0
$346$	6.42528	+	23.9795i	0.345425	+	1.28915i
$347$	26.0269			1.39720			0.698599	−	0.715513i	$-0.253807\pi$
$347$	26.0269			1.39720			0.698599	+	0.715513i	$0.253807\pi$
$348$	−2.92439	+	1.68840i	−0.156764	+	0.0905077i
$349$	−2.63616	+	1.52199i	−0.141110	+	0.0814701i	−0.568893	−	0.822412i	$-0.692628\pi$
$349$	−2.63616	+	1.52199i	−0.141110	+	0.0814701i	0.427783	+	0.903882i	$0.359295\pi$
$350$		0			0
$351$	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	$-0.607791\pi$
$353$	5.98486	−	3.45536i	0.318542	−	0.183910i	0.650743	+	0.759298i	$0.274458\pi$
$354$	−22.4641	−	38.9090i	−1.19396	−	2.06799i
$355$		0			0
$356$	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	$-0.886010\pi$
$359$		−	13.2822i		−	0.701008i	0.936561	−	0.350504i	$-0.113990\pi$
$360$		0			0
$361$	−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
$365$		0			0
$366$	−1.81122	+	3.13713i	−0.0946741	+	0.163980i
$367$	−5.20590	−	19.4287i	−0.271746	−	1.01417i	−0.957991	−	0.286799i	$-0.907409\pi$
$367$	−5.20590	−	19.4287i	−0.271746	−	1.01417i	0.686245	−	0.727370i	$-0.259258\pi$
$368$	−3.37918	−	5.85292i	−0.176152	−	0.305104i
$369$	55.1219			2.86953
$370$		0			0
$371$	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	$-0.0746921\pi$
$373$	0.271365	+	1.01275i	0.0140507	+	0.0524380i	−0.958545	+	0.284943i	$0.908025\pi$
$374$	−5.07300	+	8.78670i	−0.262319	+	0.454349i
$375$		0			0
$376$	−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	−0.112416	−	0.993661i	$-0.535859\pi$
$379$	13.4701	−	7.77696i	0.691912	−	0.399476i	0.804328	+	0.594186i	$0.202526\pi$
$380$		0			0
$381$		−	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	$-0.798780\pi$
$383$	2.12027	−	3.67241i	0.108341	−	0.187651i	0.915098	+	0.403231i	$0.132113\pi$
$384$	30.6804	−	30.6804i	1.56565	−	1.56565i
$385$		0			0
$386$	−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	−0.612252	−	0.790663i	$-0.709736\pi$
$389$	−14.7360	+	3.94851i	−0.747146	+	0.200197i	−0.134894	+	0.990860i	$0.543069\pi$
$390$		0			0
$391$	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
$395$		0			0
$396$	−6.45488			−0.324370
$397$	6.05031	+	6.05031i	0.303657	+	0.303657i	0.842443	−	0.538786i	$-0.181117\pi$
$397$	6.05031	+	6.05031i	0.303657	+	0.303657i	−0.538786	+	0.842443i	$0.681117\pi$
$398$	15.8777	+	4.25443i	0.795879	+	0.213255i
$399$	−37.5617	+	37.5617i	−1.88044	+	1.88044i
$400$		0			0
$401$	−8.64655	−	8.64655i	−0.431788	−	0.431788i	0.457448	−	0.889236i	$-0.348764\pi$
$401$	−8.64655	−	8.64655i	−0.431788	−	0.431788i	−0.889236	+	0.457448i	$0.848764\pi$
$402$	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
$405$		0			0
$406$			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	0.361197	−	0.932490i	$-0.382368\pi$
$409$	4.20165	+	1.12583i	0.207758	+	0.0556686i	−0.153439	+	0.988158i	$0.549035\pi$
$410$		0			0
$411$	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
$415$		0			0
$416$	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	−0.446350	−	0.894858i	$-0.647276\pi$
$419$	2.15841	−	1.24616i	0.105445	−	0.0608788i	0.551795	+	0.833980i	$0.313943\pi$
$420$		0			0
$421$	−13.5065	−	13.5065i	−0.658265	−	0.658265i	0.296704	−	0.954969i	$-0.404112\pi$
$421$	−13.5065	−	13.5065i	−0.658265	−	0.658265i	−0.954969	+	0.296704i	$0.904112\pi$
$422$	−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
$425$		0			0
$426$	−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
$430$		0			0
$431$	25.9052	−	6.94129i	1.24781	−	0.334350i	0.426321	−	0.904572i	$-0.359809\pi$
$431$	25.9052	−	6.94129i	1.24781	−	0.334350i	0.821491	+	0.570222i	$0.193143\pi$
$432$	−16.7587	+	62.5442i	−0.806301	+	3.00916i
$433$	12.4207	+	12.4207i	0.596902	+	0.596902i	0.939487	−	0.342585i	$-0.111302\pi$
$433$	12.4207	+	12.4207i	0.596902	+	0.596902i	−0.342585	+	0.939487i	$0.611302\pi$
$434$	−30.3825			−1.45841
$435$		0			0
$436$	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	−0.998430	−	0.0560075i	$-0.982163\pi$
$439$	−3.38942	−	12.6495i	−0.161768	−	0.603727i	0.836662	−	0.547719i	$-0.184504\pi$
$440$		0			0
$441$	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	$-0.755188\pi$
$443$	−0.485132	+	0.485132i	−0.0230493	+	0.0230493i	0.695488	+	0.718538i	$0.255188\pi$
$444$	6.98157	+	3.75907i	0.331331	+	0.178398i
$445$		0			0
$446$	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	−0.581959	−	0.813218i	$-0.697714\pi$
$449$	−14.3950	+	3.85712i	−0.679341	+	0.182029i	−0.0973822	+	0.995247i	$0.531047\pi$
$450$		0			0
$451$	−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
$455$		0			0
$456$	−15.7417	−	27.2655i	−0.737174	−	1.27682i
$457$	−16.3157	−	9.41987i	−0.763216	−	0.440643i	0.0672332	−	0.997737i	$-0.478583\pi$
$457$	−16.3157	−	9.41987i	−0.763216	−	0.440643i	−0.830449	+	0.557094i	$0.811916\pi$
$458$		−	18.2158i		−	0.851171i
$459$	−40.5720	−	10.8712i	−1.89374	−	0.507425i
$460$		0			0
$461$	12.4218	+	3.32842i	0.578542	+	0.155020i	0.536211	−	0.844084i	$-0.319855\pi$
$461$	12.4218	+	3.32842i	0.578542	+	0.155020i	0.0423309	+	0.999104i	$0.486522\pi$
$462$	−22.5762	+	39.1031i	−1.05034	+	1.81924i
$463$	−18.9998	+	32.9086i	−0.882996	+	1.52939i	−0.0350030	+	0.999387i	$0.511144\pi$
$463$	−18.9998	+	32.9086i	−0.882996	+	1.52939i	−0.847993	+	0.530007i	$0.822189\pi$
$464$	−11.6265	−	3.11531i	−0.539747	−	0.144625i
$465$		0			0
$466$	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
$470$		0			0
$471$			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
$475$		0			0
$476$	−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	0.630775	+	0.775966i	$0.282737\pi$
$479$	−6.64188	+	24.7878i	−0.303475	+	1.13259i	−0.934250	+	0.356619i	$0.883929\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	−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
$490$		0			0
$491$	−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
$495$		0			0
$496$	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	0.787888	+	0.615818i	$0.211174\pi$
$499$	9.23613	+	34.4697i	0.413466	+	1.54308i	−0.374422	+	0.927258i	$0.622159\pi$
$500$		0			0
$501$	−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	0.992744	+	0.120246i	$0.0383682\pi$
$503$	13.4680	+	23.3272i	0.600508	+	1.04011i	−0.392236	+	0.919865i	$0.628298\pi$
$504$	53.5185	+	53.5185i	2.38391	+	2.38391i
$505$		0			0
$506$	−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	0.939731	−	0.341914i	$-0.111075\pi$
$509$	3.92018	+	6.78995i	0.173759	+	0.300959i	−0.765972	+	0.642874i	$0.777742\pi$
$510$		0			0
$511$	−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
$515$		0			0
$516$	−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			0
$521$	8.21305	+	4.74181i	0.359820	+	0.207742i	0.669002	−	0.743261i	$-0.266722\pi$
$521$	8.21305	+	4.74181i	0.359820	+	0.207742i	−0.309182	+	0.951003i	$0.600055\pi$
$522$	28.4645	−	7.62704i	1.24586	−	0.333827i
$523$	9.49329	−	16.4429i	0.415113	−	0.718996i	−0.580328	−	0.814383i	$-0.697076\pi$
$523$	9.49329	−	16.4429i	0.415113	−	0.718996i	0.995440	+	0.0953869i	$0.0304088\pi$
$524$	−4.21214	−	4.21214i	−0.184008	−	0.184008i
$525$		0			0
$526$	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			0
$531$	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
$535$		0			0
$536$	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
$540$		0			0
$541$	27.2508	−	27.2508i	1.17160	−	1.17160i	0.189775	−	0.981828i	$-0.439224\pi$
$541$	27.2508	−	27.2508i	1.17160	−	1.17160i	0.981828	−	0.189775i	$-0.0607760\pi$
$542$	−11.0980	+	19.2223i	−0.476700	+	0.825668i
$543$	−71.3268	−	19.1120i	−3.06093	−	0.820173i
$544$		−	6.81386i		−	0.292142i
$545$		0			0
$546$	−6.70315	+	3.87006i	−0.286868	+	0.165623i
$547$	−35.5804			−1.52131			−0.760653	−	0.649158i	$-0.775121\pi$
$547$	−35.5804			−1.52131			−0.760653	+	0.649158i	$0.775121\pi$
$548$	−0.712973	−	2.66085i	−0.0304567	−	0.113666i
$549$	3.76807	−	3.76807i	0.160817	−	0.160817i
$550$		0			0
$551$	−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
$555$		0			0
$556$	−9.35173			−0.396602
$557$	22.1651	+	38.3911i	0.939165	+	1.62668i	0.767033	+	0.641608i	$0.221732\pi$
$557$	22.1651	+	38.3911i	0.939165	+	1.62668i	0.172132	+	0.985074i	$0.444934\pi$
$558$	13.8228	+	51.5875i	0.585167	+	2.18387i
$559$	−0.0858735	+	0.148737i	−0.00363206	+	0.00629092i
$560$		0			0
$561$	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	$-0.698008\pi$
$563$	−27.6526			−1.16542			−0.582710	+	0.812680i	$0.698008\pi$
$564$	−14.6790	+	8.47491i	−0.618096	+	0.356858i
$565$		0			0
$566$			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	−0.511064	−	0.859543i	$-0.670748\pi$
$569$	8.31252	−	8.31252i	0.348479	−	0.348479i	0.859543	+	0.511064i	$0.170748\pi$
$570$		0			0
$571$	−3.99555	−	6.92050i	−0.167209	−	0.289614i	0.770229	−	0.637768i	$-0.220142\pi$
$571$	−3.99555	−	6.92050i	−0.167209	−	0.289614i	−0.937437	+	0.348154i	$0.886809\pi$
$572$	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
$575$		0			0
$576$	−36.7595	+	21.2231i	−1.53164	+	0.884296i
$577$	15.1952	−	8.77295i	0.632584	−	0.365223i	−0.149168	−	0.988812i	$-0.547660\pi$
$577$	15.1952	−	8.77295i	0.632584	−	0.365223i	0.781752	+	0.623589i	$0.214326\pi$
$578$	−12.2754			−0.510588
$579$	11.2683	+	42.0538i	0.468294	+	1.74770i
$580$		0			0
$581$	−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
$585$		0			0
$586$	1.66025	+	1.66025i	0.0685844	+	0.0685844i
$587$	−1.89900	+	3.28916i	−0.0783800	+	0.135758i	−0.902551	−	0.430583i	$-0.858308\pi$
$587$	−1.89900	+	3.28916i	−0.0783800	+	0.135758i	0.824171	+	0.566341i	$0.191641\pi$
$588$	−13.1084	+	3.51238i	−0.540580	+	0.144848i
$589$	−16.1009	−	9.29585i	−0.663425	−	0.383029i
$590$		0			0
$591$		−	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	$-0.118784\pi$
$593$	13.7978	+	13.7978i	0.566606	+	0.566606i	−0.364570	+	0.931176i	$0.618784\pi$
$594$	45.3085	+	12.1404i	1.85903	+	0.498126i
$595$		0			0
$596$	−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	0.981092	−	0.193543i	$-0.0619978\pi$
$599$	31.9153	+	18.4263i	1.30403	+	0.752879i	0.322933	+	0.946422i	$0.395331\pi$
$600$		0			0
$601$	−4.55733	−	7.89352i	−0.185897	−	0.321983i	0.757981	−	0.652276i	$-0.226186\pi$
$601$	−4.55733	−	7.89352i	−0.185897	−	0.321983i	−0.943878	+	0.330293i	$0.892852\pi$
$602$	−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
$605$		0			0
$606$	−0.375973	−	0.375973i	−0.0152728	−	0.0152728i
$607$	7.51612	+	13.0183i	0.305070	+	0.528396i	0.977277	−	0.211967i	$-0.0679869\pi$
$607$	7.51612	+	13.0183i	0.305070	+	0.528396i	−0.672207	+	0.740363i	$0.734654\pi$
$608$	−2.31699	+	8.64711i	−0.0939662	+	0.350687i
$609$	8.99344	−	33.5640i	0.364433	−	1.36008i
$610$		0			0
$611$	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	$-0.476754\pi$
$613$	−8.97541	−	2.40495i	−0.362513	−	0.0971352i	−0.435478	+	0.900199i	$0.643421\pi$
$614$	11.9726	−	44.6823i	0.483174	−	1.80323i
$615$		0			0
$616$	−21.6322	+	5.79634i	−0.871588	+	0.233541i
$617$	−3.77320	+	14.0818i	−0.151903	+	0.566911i	0.847447	+	0.530880i	$0.178138\pi$
$617$	−3.77320	+	14.0818i	−0.151903	+	0.566911i	−0.999351	+	0.0360316i	$0.988528\pi$
$618$	−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	$0.323003\pi$
$620$		0			0
$621$	−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
$625$		0			0
$626$	−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
$630$		0			0
$631$	−5.87855	+	21.9390i	−0.234021	+	0.873379i	0.744566	+	0.667549i	$0.232656\pi$
$631$	−5.87855	+	21.9390i	−0.234021	+	0.873379i	−0.978588	+	0.205831i	$0.934010\pi$
$632$	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
$635$		0			0
$636$	−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
$640$		0			0
$641$	14.2444	+	24.6721i	0.562622	+	0.974490i	0.997267	+	0.0738875i	$0.0235406\pi$
$641$	14.2444	+	24.6721i	0.562622	+	0.974490i	−0.434645	+	0.900602i	$0.643126\pi$
$642$	−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
$645$		0			0
$646$	−17.8822	−	4.79152i	−0.703565	−	0.188520i
$647$	11.7748	−	20.3945i	0.462915	−	0.801792i	−0.536190	−	0.844097i	$-0.680137\pi$
$647$	11.7748	−	20.3945i	0.462915	−	0.801792i	0.999105	+	0.0423052i	$0.0134702\pi$
$648$	28.1852	−	48.8181i	1.10722	−	1.91776i
$649$	−18.8901	−	5.06159i	−0.741502	−	0.198685i
$650$		0			0
$651$	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	$-0.581631\pi$
$653$	−31.1291	−	17.9724i	−1.21818	−	0.703315i	−0.964528	+	0.263982i	$0.914964\pi$
$654$	−32.4702	−	56.2400i	−1.26969	−	2.19916i
$655$		0			0
$656$		−	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	0.375992	+	0.926623i	$0.377302\pi$
$659$	−15.7744	+	27.3220i	−0.614483	+	1.06432i	−0.990475	+	0.137692i	$0.956031\pi$
$660$		0			0
$661$	−25.7696	+	6.90493i	−1.00232	+	0.268571i	−0.722417	−	0.691458i	$-0.756969\pi$
$661$	−25.7696	+	6.90493i	−1.00232	+	0.268571i	−0.279903	+	0.960028i	$0.590302\pi$
$662$	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
$665$		0			0
$666$	−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
$670$		0			0
$671$	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	$-0.468828\pi$
$673$	17.6421	−	4.72719i	0.680054	−	0.182220i	0.582279	+	0.812989i	$0.302161\pi$
$674$	8.87876	+	8.87876i	0.341997	+	0.341997i
$675$		0			0
$676$	−5.21526			−0.200587
$677$	4.45728	+	4.45728i	0.171307	+	0.171307i	0.787554	−	0.616246i	$-0.211347\pi$
$677$	4.45728	+	4.45728i	0.171307	+	0.171307i	−0.616246	+	0.787554i	$0.711347\pi$
$678$	10.4370	−	38.9515i	0.400831	−	1.49592i
$679$	−12.6148	+	3.38013i	−0.484113	+	0.129718i
$680$		0			0
$681$	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	$-0.165653\pi$
$683$	0.0832112	+	0.144126i	0.00318399	+	0.00551483i	−0.864429	+	0.502755i	$0.832320\pi$
$684$	−3.04836	−	11.3766i	−0.116557	−	0.434996i
$685$		0			0
$686$	−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
$690$		0			0
$691$	4.32835	−	2.49897i	0.164658	−	0.0950654i	−0.415407	−	0.909636i	$-0.636361\pi$
$691$	4.32835	−	2.49897i	0.164658	−	0.0950654i	0.580065	+	0.814571i	$0.303027\pi$
$692$	−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
$695$		0			0
$696$	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
$700$		0			0
$701$	16.1194	+	4.31919i	0.608822	+	0.163133i	0.550041	−	0.835137i	$-0.314612\pi$
$701$	16.1194	+	4.31919i	0.608822	+	0.163133i	0.0587810	+	0.998271i	$0.481279\pi$
$702$	5.68576	+	5.68576i	0.214595	+	0.214595i
$703$	24.0776	−	0.714915i	0.908105	−	0.0269635i
$704$		−	12.5596i		−	0.473359i
$705$		0			0
$706$	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	0.739888	−	0.672730i	$-0.234878\pi$
$709$	1.78823	+	1.78823i	0.0671583	+	0.0671583i	−0.672730	+	0.739888i	$0.734878\pi$
$710$		0			0
$711$	−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
$715$		0			0
$716$	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	0.388546	−	0.921429i	$-0.372978\pi$
$719$	37.0250	−	21.3764i	1.38080	−	0.797205i	0.992254	+	0.124224i	$0.0396442\pi$
$720$		0			0
$721$	−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
$725$		0			0
$726$	22.1753	−	22.1753i	0.823002	−	0.823002i
$727$	20.6361	−	35.7427i	0.765349	−	1.32562i	−0.174713	−	0.984619i	$-0.555900\pi$
$727$	20.6361	−	35.7427i	0.765349	−	1.32562i	0.940062	−	0.341004i	$-0.110767\pi$
$728$	−3.70825	−	0.993623i	−0.137437	−	0.0368261i
$729$			32.7935i			1.21458i
$730$		0			0
$731$	1.20504	−	0.695728i	0.0445699	−	0.0257324i
$732$	−0.947068			−0.0350046
$733$	11.5672	+	43.1692i	0.427243	+	1.59449i	0.758976	+	0.651118i	$0.225700\pi$
$733$	11.5672	+	43.1692i	0.427243	+	1.59449i	−0.331734	+	0.943373i	$0.607634\pi$
$734$	22.0590	−	22.0590i	0.814214	−	0.814214i
$735$		0			0
$736$	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			0
$741$	−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	$-0.0800671\pi$
$743$	0.144780	+	0.540326i	0.00531146	+	0.0198226i	−0.963219	+	0.268717i	$0.913400\pi$
$744$	−18.6622	+	32.3239i	−0.684190	+	1.18505i
$745$		0			0
$746$	−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
$750$		0			0
$751$			13.6763i			0.499056i	0.968368	+	0.249528i	$0.0802755\pi$
$751$			13.6763i			0.499056i	−0.968368	+	0.249528i	$0.919725\pi$
$752$	−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
$755$		0			0
$756$	11.7888	+	20.4188i	0.428754	+	0.742624i
$757$	−26.0809	+	15.0578i	−0.947926	+	0.547285i	−0.892436	−	0.451174i	$-0.851005\pi$
$757$	−26.0809	+	15.0578i	−0.947926	+	0.547285i	−0.0554901	+	0.998459i	$0.517672\pi$
$758$	20.8916	+	12.0618i	0.758818	+	0.438104i
$759$	9.80226	−	2.62651i	0.355799	−	0.0953362i
$760$		0			0
$761$	−25.1569	+	14.5244i	−0.911938	+	0.526507i	−0.881054	−	0.473015i	$-0.843165\pi$
$761$	−25.1569	+	14.5244i	−0.911938	+	0.526507i	−0.0308836	+	0.999523i	$0.509832\pi$
$762$	43.3801	−	25.0455i	1.57150	−	0.907304i
$763$	−54.3463			−1.96747
$764$	−0.986490	−	3.68163i	−0.0356899	−	0.133197i
$765$		0			0
$766$	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	−0.841716	−	0.539920i	$-0.818454\pi$
$769$	−8.36905	+	8.36905i	−0.301796	+	0.301796i	0.539920	+	0.841716i	$0.318454\pi$
$770$		0			0
$771$	−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	$-0.652923\pi$
$773$	−11.6490	+	3.12135i	−0.418987	+	0.112267i	0.0431651	+	0.999068i	$0.486256\pi$
$774$	4.54795	+	2.62576i	0.163473	+	0.0943810i
$775$		0			0
$776$		−	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			0
$781$	−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
$785$		0			0
$786$	36.6234	+	63.4335i	1.30631	+	2.26260i
$787$	−25.9763	+	25.9763i	−0.925955	+	0.925955i	−0.997442	−	0.0714865i	$-0.977226\pi$
$787$	−25.9763	+	25.9763i	−0.925955	+	0.925955i	0.0714865	+	0.997442i	$0.477226\pi$
$788$	−3.39817	+	3.39817i	−0.121055	+	0.121055i
$789$	−55.9332	+	32.2931i	−1.99128	+	1.14966i
$790$		0			0
$791$	−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
$795$		0			0
$796$	1.11230	+	4.15115i	0.0394243	+	0.147134i
$797$	13.6517	+	23.6455i	0.483569	+	0.837566i	0.999822	−	0.0188700i	$-0.00600687\pi$
$797$	13.6517	+	23.6455i	0.483569	+	0.837566i	−0.516253	+	0.856436i	$0.672674\pi$
$798$	−79.5804	−	21.3235i	−2.81711	−	0.754843i
$799$	10.1438	−	37.8572i	0.358862	−	1.33929i
$800$		0			0
$801$	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
$805$		0			0
$806$	−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	0.993998	−	0.109396i	$-0.0348918\pi$
$809$	2.23198	+	8.32987i	0.0784723	+	0.292863i	−0.915526	+	0.402259i	$0.868225\pi$
$810$		0			0
$811$	5.24640	−	9.08703i	0.184226	−	0.319089i	−0.759089	−	0.650986i	$-0.774356\pi$
$811$	5.24640	−	9.08703i	0.184226	−	0.319089i	0.943315	+	0.331898i	$0.107689\pi$
$812$	−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			0
$816$	−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
$820$		0			0
$821$	−11.4849	+	19.8924i	−0.400824	+	0.694248i	−0.993826	−	0.110953i	$-0.964610\pi$
$821$	−11.4849	+	19.8924i	−0.400824	+	0.694248i	0.593001	+	0.805202i	$0.297943\pi$
$822$			33.8725i			1.18144i
$823$	−14.1702	+	52.8840i	−0.493943	+	1.84342i	0.0419300	+	0.999121i	$0.486649\pi$
$823$	−14.1702	+	52.8840i	−0.493943	+	1.84342i	−0.535873	+	0.844299i	$0.680017\pi$
$824$		−	25.7507i		−	0.897069i
$825$		0			0
$826$	−29.1573	−	50.5019i	−1.01451	−	1.75718i
$827$	−12.7147	−	7.34082i	−0.442133	−	0.255265i	0.262369	−	0.964968i	$-0.415496\pi$
$827$	−12.7147	−	7.34082i	−0.442133	−	0.255265i	−0.704502	+	0.709702i	$0.748830\pi$
$828$			4.32589i			0.150335i
$829$	20.7635	+	5.56356i	0.721146	+	0.193231i	0.600683	−	0.799487i	$-0.294895\pi$
$829$	20.7635	+	5.56356i	0.721146	+	0.193231i	0.120463	+	0.992718i	$0.461562\pi$
$830$		0			0
$831$	−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
$835$		0			0
$836$	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	0.615283	−	0.788306i	$-0.289042\pi$
$839$	−10.8636	−	18.8162i	−0.375052	−	0.649609i	−0.990335	+	0.138697i	$0.955708\pi$
$840$		0			0
$841$			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
$845$		0			0
$846$	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
$850$		0			0
$851$	−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	$-0.947007\pi$
$853$	−39.0120	+	22.5236i	−1.33575	+	0.771194i	−0.349573	+	0.936909i	$0.613673\pi$
$854$	−2.35087	+	4.07182i	−0.0804451	+	0.139335i
$855$		0			0
$856$	−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	0.786542	−	0.617537i	$-0.211869\pi$
$859$	4.95333	+	4.95333i	0.169005	+	0.169005i	−0.617537	+	0.786542i	$0.711869\pi$
$860$		0			0
$861$	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	$-0.874149\pi$
$863$	2.02516	−	7.55800i	0.0689372	−	0.257277i	0.991790	+	0.127875i	$0.0408156\pi$
$864$	−30.4283	+	8.15325i	−1.03519	+	0.277379i
$865$		0			0
$866$	−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
$870$		0			0
$871$	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
$875$		0			0
$876$	5.32187	−	3.07258i	0.179809	−	0.103813i
$877$	−28.3951	+	28.3951i	−0.958835	+	0.958835i	−0.999186	−	0.0403503i	$-0.987153\pi$
$877$	−28.3951	+	28.3951i	−0.958835	+	0.958835i	0.0403503	+	0.999186i	$0.487153\pi$
$878$	14.3620	−	14.3620i	0.484695	−	0.484695i
$879$	−2.43336	−	4.21471i	−0.0820753	−	0.142159i
$880$		0			0
$881$	47.4583	+	27.4000i	1.59891	+	0.923131i	0.991698	+	0.128590i	$0.0410452\pi$
$881$	47.4583	+	27.4000i	1.59891	+	0.923131i	0.607211	+	0.794540i	$0.292288\pi$
$882$	118.430			3.98773
$883$	11.6623	+	6.73321i	0.392467	+	0.226591i	0.683228	−	0.730205i	$-0.260575\pi$
$883$	11.6623	+	6.73321i	0.392467	+	0.226591i	−0.290762	+	0.956795i	$0.593909\pi$
$884$	−0.393798	−	0.227359i	−0.0132448	−	0.00764692i
$885$		0			0
$886$	−1.02783	−	0.275406i	−0.0345306	−	0.00925245i
$887$	−21.5186	−	21.5186i	−0.722524	−	0.722524i	0.246594	−	0.969119i	$-0.420688\pi$
$887$	−21.5186	−	21.5186i	−0.722524	−	0.722524i	−0.969119	+	0.246594i	$0.920688\pi$
$888$	−1.43525	−	48.3379i	−0.0481640	−	1.62211i
$889$		−	41.9194i		−	1.40593i
$890$		0			0
$891$	−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
$895$		0			0
$896$	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
$900$		0			0
$901$	−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
$905$		0			0
$906$	−13.2212	+	3.54260i	−0.439244	+	0.117695i
$907$	44.5758	+	25.7359i	1.48012	+	0.854545i	0.999746	−	0.0225216i	$-0.00716946\pi$
$907$	44.5758	+	25.7359i	1.48012	+	0.854545i	0.480369	+	0.877067i	$0.340503\pi$
$908$	−4.15674	+	2.39989i	−0.137946	+	0.0796433i
$909$	0.391088	+	0.677384i	0.0129716	+	0.0224674i
$910$		0			0
$911$	−30.2208	+	30.2208i	−1.00126	+	1.00126i	−0.00125893	+	0.999999i	$0.500401\pi$
$911$	−30.2208	+	30.2208i	−1.00126	+	1.00126i	−0.999999	+	0.00125893i	$0.999599\pi$
$912$	29.5771	−	51.2290i	0.979395	−	1.69636i
$913$	−21.2563	−	5.69562i	−0.703482	−	0.188497i
$914$		−	29.2198i		−	0.966504i
$915$		0			0
$916$	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	−0.237603	−	0.971362i	$-0.576362\pi$
$919$	22.2439	−	22.2439i	0.733760	−	0.733760i	0.971362	+	0.237603i	$0.0763616\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$	−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	−0.424667	−	0.905350i	$-0.639609\pi$
$929$	17.4258	−	30.1824i	0.571723	−	0.990253i	0.996389	−	0.0849029i	$-0.0270580\pi$
$930$		0			0
$931$	−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
$935$		0			0
$936$			6.74844i			0.220580i
$937$	42.8463	+	11.4806i	1.39973	+	0.375056i	0.878247	−	0.478207i	$-0.158713\pi$
$937$	42.8463	+	11.4806i	1.39973	+	0.375056i	0.521481	+	0.853263i	$0.325380\pi$
$938$	35.4406	−	61.3849i	1.15718	−	2.00429i
$939$	14.6762	−	14.6762i	0.478940	−	0.478940i
$940$		0			0
$941$	11.4650	+	19.8579i	0.373748	+	0.647350i	0.990139	−	0.140090i	$-0.0447392\pi$
$941$	11.4650	+	19.8579i	0.373748	+	0.647350i	−0.616391	+	0.787440i	$0.711406\pi$
$942$	−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
$945$		0			0
$946$	−1.34572	+	0.776950i	−0.0437530	+	0.0252608i
$947$	19.1624	−	11.0634i	0.622693	−	0.359512i	−0.155224	−	0.987879i	$-0.549610\pi$
$947$	19.1624	−	11.0634i	0.622693	−	0.359512i	0.777917	+	0.628367i	$0.216276\pi$
$948$	12.2933			0.399269
$949$	−0.453931	−	1.69409i	−0.0147352	−	0.0549925i
$950$		0			0
$951$	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	$-0.361272\pi$
$953$	10.3263	+	2.76692i	0.334501	+	0.0896293i	−0.0876591	+	0.996151i	$0.527939\pi$
$954$	1.53632	−	1.53632i	0.0497403	−	0.0497403i
$955$		0			0
$956$	−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
$960$		0			0
$961$		−	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
$965$		0			0
$966$	26.2059	+	15.1300i	0.843160	+	0.486799i
$967$	−20.9493	−	12.0951i	−0.673684	−	0.388951i	0.123787	−	0.992309i	$-0.460496\pi$
$967$	−20.9493	−	12.0951i	−0.673684	−	0.388951i	−0.797471	+	0.603357i	$0.793829\pi$
$968$	15.5547			0.499947
$969$	33.2319	+	19.1864i	1.06756	+	0.616357i
$970$		0			0
$971$	−3.56909	−	6.18184i	−0.114537	−	0.198385i	0.803057	−	0.595902i	$-0.203205\pi$
$971$	−3.56909	−	6.18184i	−0.114537	−	0.198385i	−0.917595	+	0.397517i	$0.869872\pi$
$972$	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
$975$		0			0
$976$	−2.38708	−	2.38708i	−0.0764085	−	0.0764085i
$977$	−24.3556	−	42.1852i	−0.779205	−	1.34962i	−0.932400	−	0.361427i	$-0.882290\pi$
$977$	−24.3556	−	42.1852i	−0.779205	−	1.34962i	0.153195	−	0.988196i	$-0.451044\pi$
$978$	0.209525	−	0.781959i	0.00669988	−	0.0250043i
$979$	−3.85153	+	14.3741i	−0.123096	+	0.459399i
$980$		0			0
$981$	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	$-0.374985\pi$
$983$	7.90875	+	2.11914i	0.252250	+	0.0675902i	−0.130478	+	0.991451i	$0.541651\pi$
$984$	−15.4638	+	57.7115i	−0.492966	+	1.83978i
$985$		0			0
$986$	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
$990$		0			0
$991$	36.8837	+	36.8837i	1.17165	+	1.17165i	0.981816	+	0.189834i	$0.0607948\pi$
$991$	36.8837	+	36.8837i	1.17165	+	1.17165i	0.189834	+	0.981816i	$0.439205\pi$
$992$	10.2514	−	2.74684i	0.325481	−	0.0872124i
$993$		−	26.8768i		−	0.852910i
$994$	−1.60731	−	5.99855i	−0.0509806	−	0.190262i
$995$		0			0
$996$	6.60881	−	11.4468i	0.209408	−	0.362705i
$997$	−30.2437	+	17.4612i	−0.957828	+	0.553002i	−0.895504	−	0.445054i	$-0.853184\pi$
$997$	−30.2437	+	17.4612i	−0.957828	+	0.553002i	−0.0623238	+	0.998056i	$0.519851\pi$
$998$	−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	925.2.t.b.843.14		68
5.2	odd	4		925.2.y.b.732.4		68
5.3	odd	4		185.2.u.a.177.14	yes	68
5.4	even	2		185.2.p.a.103.4	yes	68
37.23	odd	12		925.2.y.b.393.4		68
185.23	even	12		185.2.p.a.97.4	✓	68
185.97	even	12	inner	925.2.t.b.282.14		68
185.134	odd	12		185.2.u.a.23.14	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.4	✓	68	185.23	even	12
185.2.p.a.103.4	yes	68	5.4	even	2
185.2.u.a.23.14	yes	68	185.134	odd	12
185.2.u.a.177.14	yes	68	5.3	odd	4
925.2.t.b.282.14		68	185.97	even	12	inner
925.2.t.b.843.14		68	1.1	even	1	trivial
925.2.y.b.393.4		68	37.23	odd	12
925.2.y.b.732.4		68	5.2	odd	4

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.t (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} +(3.52563 - 3.52563i) q^{6} +(-1.07995 - 4.03042i) q^{7} +2.47303 q^{8} +(-6.35206 + 3.66736i) q^{9} -2.17031i q^{11} +(1.25914 + 0.337386i) q^{12} +(0.186020 - 0.322197i) q^{13} +(4.57608 - 4.57608i) q^{14} +(2.32328 + 4.02404i) q^{16} +(-2.61037 + 1.50709i) q^{17} +(-9.85182 - 5.68795i) q^{18} +(3.82515 - 1.02494i) q^{19} +(-11.6168 + 6.70696i) q^{21} +(2.91511 - 1.68304i) q^{22} -1.45449 q^{23} +(-2.05766 - 7.67931i) q^{24} +0.577022 q^{26} +(9.85364 + 9.85364i) q^{27} +(1.63430 + 0.437909i) q^{28} +(-1.83172 + 1.83172i) q^{29} +(-3.31971 - 3.31971i) q^{31} +(-1.13030 + 1.95773i) q^{32} +(-6.73931 + 1.80579i) q^{33} +(-4.04858 - 2.33745i) q^{34} -2.97417i q^{36} +(5.91963 + 1.39926i) q^{37} +(4.34301 + 4.34301i) q^{38} +(-1.15527 - 0.309554i) q^{39} +(-6.50835 - 3.75760i) q^{41} +(-18.0172 - 10.4023i) q^{42} -0.461635 q^{43} +(0.762140 + 0.440021i) q^{44} +(-1.12793 - 1.95363i) q^{46} +(-9.19431 + 9.19431i) q^{47} +(10.5625 - 10.5625i) q^{48} +(-9.01581 + 5.20528i) q^{49} +(6.85181 + 6.85181i) q^{51} +(0.0754296 + 0.130648i) q^{52} +(-0.0494320 + 0.184483i) q^{53} +(-5.59384 + 20.8765i) q^{54} +(-2.67074 - 9.96733i) q^{56} +(-6.36537 - 11.0251i) q^{57} +(-3.88079 - 1.03985i) q^{58} +(2.33219 - 8.70387i) q^{59} +(-0.701769 + 0.188038i) q^{61} +(1.88457 - 7.03332i) q^{62} +(21.6409 + 21.6409i) q^{63} +5.78701 q^{64} +(-7.65172 - 7.65172i) q^{66} +(10.5795 - 2.83478i) q^{67} -1.22223i q^{68} +(1.21020 + 4.51652i) q^{69} +(0.479804 - 0.831045i) q^{71} +(-15.7088 + 9.06949i) q^{72} +(3.33340 - 3.33340i) q^{73} +(2.71112 + 9.03621i) q^{74} +(-0.415606 + 1.55106i) q^{76} +(-8.74727 + 2.34382i) q^{77} +(-0.480107 - 1.79178i) q^{78} +(9.10924 - 2.44081i) q^{79} +(11.3970 - 19.7402i) q^{81} -11.6558i q^{82} +(2.62433 - 9.79413i) q^{83} -5.43923i q^{84} +(-0.357990 - 0.620057i) q^{86} +(7.21197 + 4.16383i) q^{87} -5.36724i q^{88} +(-6.62306 - 1.77464i) q^{89} +(-1.49948 - 0.401784i) q^{91} +(0.294891 - 0.510766i) q^{92} +(-7.54630 + 13.0706i) q^{93} +(-19.4796 - 5.21954i) q^{94} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 8 q^{3} - 30 q^{4} - 8 q^{6} + 2 q^{7} - 12 q^{8} - 14 q^{12} + 6 q^{13} - 26 q^{16} - 12 q^{17} - 18 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 24 q^{26} + 68 q^{27} + 26 q^{28}+ \cdots + 32 q^{99}+O(q^{100}) \) 68 * q + 4 * q^2 + 8 * q^3 - 30 * q^4 - 8 * q^6 + 2 * q^7 - 12 * q^8 - 14 * q^12 + 6 * q^13 - 26 * q^16 - 12 * q^17 - 18 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 24 * q^26 + 68 * q^27 + 26 * q^28 + 14 * q^29 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 16 * q^37 + 36 * q^38 + 52 * q^39 - 18 * q^41 - 132 * q^42 - 8 * q^43 - 36 * q^44 - 52 * q^46 + 24 * q^47 + 60 * q^48 - 36 * q^49 - 8 * q^51 + 26 * q^52 - 82 * q^53 + 40 * q^54 + 16 * q^56 + 6 * q^57 - 86 * q^58 - 8 * q^59 + 4 * q^61 - 10 * q^62 + 48 * q^63 - 20 * q^64 + 80 * q^66 + 40 * q^67 + 8 * q^69 + 4 * q^71 + 90 * q^72 + 60 * q^73 - 44 * q^74 + 72 * q^76 - 66 * q^77 + 24 * q^78 + 56 * q^79 - 6 * q^81 - 24 * q^83 - 4 * q^86 + 84 * q^87 - 22 * q^89 + 44 * q^91 - 44 * q^92 + 34 * q^93 - 20 * q^94 - 8 * q^96 - 42 * q^98 + 32 * q^99

Introduction

L-functions

Modular forms

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