LMFDB - Embedded newform 925.2.y.b.393.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] 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([9, 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("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (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			393.4
Character	$\chi$	$=$	925.393
Dual form			925.2.y.b.732.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34317 - 0.775482i) q^{2} +(-3.10523 - 0.832043i) q^{3} +(0.202746 + 0.351166i) q^{4} +(3.52563 + 3.52563i) q^{6} +(4.03042 + 1.07995i) q^{7} +2.47303i q^{8} +(6.35206 + 3.66736i) q^{9} +2.17031i q^{11} +(-0.337386 - 1.25914i) q^{12} +(-0.322197 + 0.186020i) q^{13} +(-4.57608 - 4.57608i) q^{14} +(2.32328 - 4.02404i) q^{16} +(-1.50709 + 2.61037i) q^{17} +(-5.68795 - 9.85182i) q^{18} +(-3.82515 - 1.02494i) q^{19} +(-11.6168 - 6.70696i) q^{21} +(1.68304 - 2.91511i) q^{22} -1.45449i q^{23} +(2.05766 - 7.67931i) q^{24} +0.577022 q^{26} +(-9.85364 - 9.85364i) q^{27} +(0.437909 + 1.63430i) q^{28} +(1.83172 + 1.83172i) q^{29} +(-3.31971 + 3.31971i) q^{31} +(-1.95773 + 1.13030i) q^{32} +(1.80579 - 6.73931i) q^{33} +(4.04858 - 2.33745i) q^{34} +2.97417i q^{36} +(-1.39926 - 5.91963i) q^{37} +(4.34301 + 4.34301i) q^{38} +(1.15527 - 0.309554i) q^{39} +(-6.50835 + 3.75760i) q^{41} +(10.4023 + 18.0172i) q^{42} -0.461635i 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} +(-0.130648 - 0.0754296i) q^{52} +(0.184483 - 0.0494320i) q^{53} +(5.59384 + 20.8765i) q^{54} +(-2.67074 + 9.96733i) q^{56} +(11.0251 + 6.36537i) q^{57} +(-1.03985 - 3.88079i) q^{58} +(-2.33219 - 8.70387i) q^{59} +(-0.701769 - 0.188038i) q^{61} +(7.03332 - 1.88457i) q^{62} +(21.6409 + 21.6409i) q^{63} -5.78701 q^{64} +(-7.65172 + 7.65172i) q^{66} +(2.83478 - 10.5795i) q^{67} -1.22223 q^{68} +(-1.21020 + 4.51652i) q^{69} +(0.479804 + 0.831045i) q^{71} +(-9.06949 + 15.7088i) q^{72} +(-3.33340 + 3.33340i) q^{73} +(-2.71112 + 9.03621i) q^{74} +(-0.415606 - 1.55106i) q^{76} +(-2.34382 + 8.74727i) q^{77} +(-1.79178 - 0.480107i) q^{78} +(-9.10924 - 2.44081i) q^{79} +(11.3970 + 19.7402i) q^{81} +11.6558 q^{82} +(-9.79413 + 2.62433i) q^{83} -5.43923i q^{84} +(-0.357990 + 0.620057i) q^{86} +(-4.16383 - 7.21197i) q^{87} -5.36724 q^{88} +(6.62306 - 1.77464i) q^{89} +(-1.49948 + 0.401784i) q^{91} +(0.510766 - 0.294891i) q^{92} +(13.0706 - 7.54630i) q^{93} +(19.4796 - 5.21954i) q^{94} +(7.01966 - 1.88091i) q^{96} +3.12991 q^{97} +(-8.07320 - 13.9832i) q^{98} +(-7.95933 + 13.7860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

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

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.34317	−	0.775482i	−0.949768	−	0.548349i	−0.0567591	−	0.998388i	$-0.518077\pi$
$2$	−1.34317	−	0.775482i	−0.949768	−	0.548349i	−0.893009	+	0.450039i	$0.851410\pi$
$3$	−3.10523	−	0.832043i	−1.79280	−	0.480380i	−0.799986	−	0.600019i	$-0.795160\pi$
$3$	−3.10523	−	0.832043i	−1.79280	−	0.480380i	−0.992818	+	0.119638i	$0.961826\pi$
$4$	0.202746	+	0.351166i	0.101373	+	0.175583i
$5$		0			0
$5$		0			0
$6$	3.52563	+	3.52563i	1.43933	+	1.43933i
$7$	4.03042	+	1.07995i	1.52335	+	0.408182i	0.920845	−	0.389929i	$-0.127501\pi$
$7$	4.03042	+	1.07995i	1.52335	+	0.408182i	0.602510	+	0.798111i	$0.294167\pi$
$8$			2.47303i			0.874347i
$9$	6.35206	+	3.66736i	2.11735	+	1.22245i
$10$		0			0
$11$			2.17031i			0.654374i	0.944960	+	0.327187i	$0.106101\pi$
$11$			2.17031i			0.654374i	−0.944960	+	0.327187i	$0.893899\pi$
$12$	−0.337386	−	1.25914i	−0.0973950	−	0.363483i
$13$	−0.322197	+	0.186020i	−0.0893613	+	0.0515928i	−0.544015	−	0.839076i	$-0.683096\pi$
$13$	−0.322197	+	0.186020i	−0.0893613	+	0.0515928i	0.454653	+	0.890668i	$0.349763\pi$
$14$	−4.57608	−	4.57608i	−1.22301	−	1.22301i
$15$		0			0
$16$	2.32328	−	4.02404i	0.580820	−	1.00601i
$17$	−1.50709	+	2.61037i	−0.365524	+	0.633107i	−0.988860	−	0.148848i	$-0.952444\pi$
$17$	−1.50709	+	2.61037i	−0.365524	+	0.633107i	0.623336	+	0.781954i	$0.285777\pi$
$18$	−5.68795	−	9.85182i	−1.34066	−	2.32210i
$19$	−3.82515	−	1.02494i	−0.877549	−	0.235138i	−0.208200	−	0.978086i	$-0.566760\pi$
$19$	−3.82515	−	1.02494i	−0.877549	−	0.235138i	−0.669349	+	0.742948i	$0.733427\pi$
$20$		0			0
$21$	−11.6168	−	6.70696i	−2.53499	−	1.46358i
$22$	1.68304	−	2.91511i	0.358825	−	0.621504i
$23$		−	1.45449i		−	0.303282i	−0.988436	−	0.151641i	$-0.951544\pi$
$23$		−	1.45449i		−	0.303282i	0.988436	−	0.151641i	$-0.0484557\pi$
$24$	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
$28$	0.437909	+	1.63430i	0.0827571	+	0.308854i
$29$	1.83172	+	1.83172i	0.340142	+	0.340142i	0.856421	−	0.516279i	$-0.172683\pi$
$29$	1.83172	+	1.83172i	0.340142	+	0.340142i	−0.516279	+	0.856421i	$0.672683\pi$
$30$		0			0
$31$	−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	$0.388532\pi$
$32$	−1.95773	+	1.13030i	−0.346082	+	0.199810i
$33$	1.80579	−	6.73931i	0.314348	−	1.17316i
$34$	4.04858	−	2.33745i	0.694326	−	0.400870i
$35$		0			0
$36$			2.97417i			0.495695i
$37$	−1.39926	−	5.91963i	−0.230037	−	0.973182i
$37$	−1.39926	−	5.91963i	−0.230037	−	0.973182i
$38$	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	−0.913069	−	0.407805i	$-0.866294\pi$
$41$	−6.50835	+	3.75760i	−1.01643	+	0.586838i	−0.103365	+	0.994644i	$0.532961\pi$
$42$	10.4023	+	18.0172i	1.60510	+	2.78012i
$43$		−	0.461635i		−	0.0703987i	−0.999380	−	0.0351994i	$-0.988793\pi$
$43$		−	0.461635i		−	0.0703987i	0.999380	−	0.0351994i	$-0.0112066\pi$
$44$	−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
$52$	−0.130648	−	0.0754296i	−0.0181176	−	0.0104602i
$53$	0.184483	−	0.0494320i	0.0253406	−	0.00679000i	−0.246126	−	0.969238i	$-0.579158\pi$
$53$	0.184483	−	0.0494320i	0.0253406	−	0.00679000i	0.271467	+	0.962448i	$0.412491\pi$
$54$	5.59384	+	20.8765i	0.761225	+	2.84093i
$55$		0			0
$56$	−2.67074	+	9.96733i	−0.356892	+	1.33194i
$57$	11.0251	+	6.36537i	1.46032	+	0.843114i
$58$	−1.03985	−	3.88079i	−0.136539	−	0.509572i
$59$	−2.33219	−	8.70387i	−0.303626	−	1.13315i	−0.934122	−	0.356954i	$-0.883815\pi$
$59$	−2.33219	−	8.70387i	−0.303626	−	1.13315i	0.630496	−	0.776192i	$-0.282852\pi$
$60$		0			0
$61$	−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	$0.598144\pi$
$62$	7.03332	−	1.88457i	0.893233	−	0.239341i
$63$	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
$67$	2.83478	−	10.5795i	0.346323	−	1.29250i	−0.544735	−	0.838608i	$-0.683370\pi$
$67$	2.83478	−	10.5795i	0.346323	−	1.29250i	0.891059	−	0.453888i	$-0.149963\pi$
$68$	−1.22223			−0.148217
$69$	−1.21020	+	4.51652i	−0.145691	+	0.543725i
$70$		0			0
$71$	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	$0.815198\pi$
$72$	−9.06949	+	15.7088i	−1.06885	+	1.85130i
$73$	−3.33340	+	3.33340i	−0.390145	+	0.390145i	−0.874739	−	0.484594i	$-0.838967\pi$
$73$	−3.33340	+	3.33340i	−0.390145	+	0.390145i	0.484594	+	0.874739i	$0.338967\pi$
$74$	−2.71112	+	9.03621i	−0.315161	+	1.05044i
$75$		0			0
$76$	−0.415606	−	1.55106i	−0.0476733	−	0.177919i
$77$	−2.34382	+	8.74727i	−0.267104	+	0.996844i
$78$	−1.79178	−	0.480107i	−0.202880	−	0.0543614i
$79$	−9.10924	−	2.44081i	−1.02487	−	0.274613i	−0.293040	−	0.956100i	$-0.594667\pi$
$79$	−9.10924	−	2.44081i	−1.02487	−	0.274613i	−0.731830	+	0.681487i	$0.761333\pi$
$80$		0			0
$81$	11.3970	+	19.7402i	1.26634	+	2.19336i
$82$	11.6558			1.28717
$83$	−9.79413	+	2.62433i	−1.07505	+	0.288058i	−0.752565	−	0.658518i	$-0.771183\pi$
$83$	−9.79413	+	2.62433i	−1.07505	+	0.288058i	−0.322481	+	0.946576i	$0.604517\pi$
$84$		−	5.43923i		−	0.593469i
$85$		0			0
$86$	−0.357990	+	0.620057i	−0.0386030	+	0.0668624i
$87$	−4.16383	−	7.21197i	−0.446410	−	0.773205i
$88$	−5.36724			−0.572150
$89$	6.62306	−	1.77464i	0.702043	−	0.188112i	0.109897	−	0.993943i	$-0.464948\pi$
$89$	6.62306	−	1.77464i	0.702043	−	0.188112i	0.592145	+	0.805831i	$0.298281\pi$
$90$		0			0
$91$	−1.49948	+	0.401784i	−0.157188	+	0.0421184i
$92$	0.510766	−	0.294891i	0.0532511	−	0.0307445i
$93$	13.0706	−	7.54630i	1.35536	−	0.782515i
$94$	19.4796	−	5.21954i	2.00917	−	0.538354i
$95$		0			0
$96$	7.01966	−	1.88091i	0.716441	−	0.191970i
$97$	3.12991			0.317794			0.158897	−	0.987295i	$-0.449206\pi$
$97$	3.12991			0.317794			0.158897	+	0.987295i	$0.449206\pi$
$98$	−8.07320	−	13.9832i	−0.815517	−	1.41252i
$99$	−7.95933	+	13.7860i	−0.799943	+	1.38554i
$100$		0			0
$101$			0.106640i			0.0106111i	0.999986	+	0.00530554i	$0.00168881\pi$
$101$			0.106640i			0.0106111i	−0.999986	+	0.00530554i	$0.998311\pi$
$102$	−14.5166	+	3.88972i	−1.43736	+	0.385140i
$103$	−10.4126			−1.02599			−0.512994	−	0.858392i	$-0.671464\pi$
$103$	−10.4126			−1.02599			−0.512994	+	0.858392i	$0.671464\pi$
$104$	−0.460033	−	0.796801i	−0.0451100	−	0.0781328i
$105$		0			0
$106$	−0.286126	−	0.0766672i	−0.0277910	−	0.00744658i
$107$	6.93007	+	1.85691i	0.669955	+	0.179514i	0.577734	−	0.816225i	$-0.303937\pi$
$107$	6.93007	+	1.85691i	0.669955	+	0.179514i	0.0922203	+	0.995739i	$0.470604\pi$
$108$	1.46248	−	5.45804i	0.140727	−	0.525200i
$109$	−3.37101	−	12.5808i	−0.322884	−	1.20502i	−0.916422	−	0.400213i	$-0.868936\pi$
$109$	−3.37101	−	12.5808i	−0.322884	−	1.20502i	0.593538	−	0.804806i	$-0.297731\pi$
$110$		0			0
$111$	−0.580363	+	19.5461i	−0.0550856	+	1.85523i
$112$	13.7095	−	13.7095i	1.29543	−	1.29543i
$113$	−4.04388	+	7.00421i	−0.380417	+	0.658901i	−0.991122	−	0.132957i	$-0.957553\pi$
$113$	−4.04388	+	7.00421i	−0.380417	+	0.658901i	0.610705	+	0.791858i	$0.290886\pi$
$114$	−9.87247	−	17.0996i	−0.924641	−	1.60153i
$115$		0			0
$116$	−0.271864	+	1.01461i	−0.0252419	+	0.0942042i
$117$	−2.72882			−0.252279
$118$	−3.61715	+	13.4994i	−0.332986	+	1.24272i
$119$	−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
$123$	23.3364	−	6.25297i	2.10417	−	0.563811i
$124$	−1.83882	−	0.492711i	−0.165131	−	0.0442468i
$125$		0			0
$126$	−12.2854	−	45.8497i	−1.09447	−	4.08461i
$127$	−2.60019	−	9.70404i	−0.230729	−	0.861094i	−0.980028	−	0.198861i	$-0.936276\pi$
$127$	−2.60019	−	9.70404i	−0.230729	−	0.861094i	0.749298	−	0.662233i	$-0.230391\pi$
$128$	11.6884	+	6.74832i	1.03312	+	0.596473i
$129$	−0.384100	+	1.43348i	−0.0338182	+	0.126211i
$130$		0			0
$131$	−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	$-0.305128\pi$
$132$	2.73273	−	0.732234i	0.237854	−	0.0637328i
$133$	−14.3101	−	8.26191i	−1.24084	−	0.716399i
$134$	−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	−0.308693	+	0.951162i	$0.599892\pi$
$139$	−11.5314	+	19.9729i	−0.978077	+	1.69408i	−0.669384	+	0.742917i	$0.733442\pi$
$140$		0			0
$141$	36.2005	−	20.9003i	3.04863	−	1.76013i
$142$		−	1.48832i		−	0.124897i
$143$	−0.403722	−	0.699268i	−0.0337610	−	0.0584757i
$144$	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
$148$	1.79508	−	1.69155i	0.147555	−	0.139045i
$149$			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	−0.593607	−	0.804755i	$-0.702297\pi$
$151$	−2.37742	+	1.37260i	−0.193472	+	0.111701i	0.400135	+	0.916456i	$0.368963\pi$
$152$	2.53472	−	9.45969i	0.205593	−	0.767282i
$153$	−19.1463	+	11.0541i	−1.54789	+	0.893674i
$154$	9.93152	−	9.93152i	0.800305	−	0.800305i
$155$		0			0
$156$	0.342931	+	0.342931i	0.0274564	+	0.0274564i
$157$	1.85912	+	6.93834i	0.148374	+	0.553740i	0.999582	+	0.0289111i	$0.00920397\pi$
$157$	1.85912	+	6.93834i	0.148374	+	0.553740i	−0.851208	+	0.524829i	$0.824129\pi$
$158$	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
$162$		−	35.3528i		−	2.77758i
$163$	−0.0811818	+	0.140611i	−0.00635865	+	0.0110135i	−0.869187	−	0.494483i	$-0.835357\pi$
$163$	−0.0811818	+	0.140611i	−0.00635865	+	0.0110135i	0.862829	+	0.505497i	$0.168691\pi$
$164$	−2.63908	−	1.52367i	−0.206077	−	0.118979i
$165$		0			0
$166$	15.1903	+	4.07024i	1.17900	+	0.315912i
$167$	6.91676	+	11.9802i	0.535235	+	0.927055i	0.999152	+	0.0411758i	$0.0131104\pi$
$167$	6.91676	+	11.9802i	0.535235	+	0.927055i	−0.463917	+	0.885879i	$0.653556\pi$
$168$	16.5865	−	28.7287i	1.27968	−	2.21646i
$169$	−6.43079	+	11.1385i	−0.494676	+	0.856805i
$170$		0			0
$171$	−20.5387	−	20.5387i	−1.57064	−	1.57064i
$172$	0.162110	−	0.0935945i	0.0123608	−	0.00713652i
$173$	4.14277	+	15.4610i	0.314969	+	1.17548i	0.924019	+	0.382347i	$0.124884\pi$
$173$	4.14277	+	15.4610i	0.314969	+	1.17548i	−0.609050	+	0.793132i	$0.708449\pi$
$174$			12.9159i			0.979153i
$175$		0			0
$176$	8.73342	+	5.04224i	0.658307	+	0.380073i
$177$			28.9680i			2.17737i
$178$	−10.2721	−	2.75241i	−0.769929	−	0.206302i
$179$	−10.4070	−	10.4070i	−0.777858	−	0.777858i	0.201608	−	0.979466i	$-0.435383\pi$
$179$	−10.4070	−	10.4070i	−0.777858	−	0.777858i	−0.979466	+	0.201608i	$0.935383\pi$
$180$		0			0
$181$	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	$0.507705\pi$
$182$	2.32564	+	0.623153i	0.172388	+	0.0461912i
$183$	2.02270	+	1.16780i	0.149522	+	0.0863265i
$184$	3.59699			0.265174
$185$		0			0
$186$	−23.4081			−1.71637
$187$	−5.66531	−	3.27087i	−0.414288	−	0.239190i
$188$	−5.09283	−	1.36462i	−0.371433	−	0.0995251i
$189$	−29.0729	−	50.3557i	−2.11474	−	3.66284i
$190$		0			0
$191$	−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	$0.860451\pi$
$192$	17.9700	+	4.81505i	1.29687	+	0.347496i
$193$		−	13.5429i		−	0.974841i	−0.873167	−	0.487420i	$-0.837938\pi$
$193$		−	13.5429i		−	0.974841i	0.873167	−	0.487420i	$-0.162062\pi$
$194$	−4.20401	−	2.42719i	−0.301830	−	0.174262i
$195$		0			0
$196$			4.22139i			0.301528i
$197$	−3.06743	−	11.4478i	−0.218546	−	0.815623i	−0.984888	−	0.173191i	$-0.944592\pi$
$197$	−3.06743	−	11.4478i	−0.218546	−	0.815623i	0.766343	−	0.642432i	$-0.222074\pi$
$198$	21.3815	−	12.3446i	1.51952	−	0.877295i
$199$	−7.49425	−	7.49425i	−0.531253	−	0.531253i	0.389692	−	0.920945i	$-0.372581\pi$
$199$	−7.49425	−	7.49425i	−0.531253	−	0.531253i	−0.920945	+	0.389692i	$0.872581\pi$
$200$		0			0
$201$	−17.6053	+	30.4932i	−1.24178	+	2.15083i
$202$	0.0826974	−	0.143236i	0.00581857	−	0.0100781i
$203$	5.40444	+	9.36076i	0.379317	+	0.656996i
$204$	3.79529	+	1.01695i	0.265724	+	0.0712005i
$205$		0			0
$206$	13.9860	+	8.07481i	0.974450	+	0.562599i
$207$	5.33414	−	9.23900i	0.370748	−	0.642155i
$208$			1.72871i			0.119864i
$209$	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
$213$	−0.798435	−	2.97980i	−0.0547079	−	0.204173i
$214$	−7.86829	−	7.86829i	−0.537865	−	0.537865i
$215$		0			0
$216$	24.3683	−	24.3683i	1.65805	−	1.65805i
$217$	−16.9649	+	9.79470i	−1.15165	+	0.664908i
$218$	−5.22831	+	19.5123i	−0.354106	+	1.32154i
$219$	13.1245	−	7.57744i	0.886872	−	0.512036i
$220$		0			0
$221$		−	1.12140i		−	0.0754336i
$222$	15.9371	−	25.8037i	1.06963	−	1.73183i
$223$	−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
$227$	−5.91849	−	10.2511i	−0.392824	−	0.680391i	0.599997	−	0.800002i	$-0.295168\pi$
$227$	−5.91849	−	10.2511i	−0.392824	−	0.680391i	−0.992821	+	0.119611i	$0.961835\pi$
$228$			5.16221i			0.341875i
$229$	10.1713	−	5.87243i	0.672141	−	0.388061i	−0.124746	−	0.992189i	$-0.539812\pi$
$229$	10.1713	−	5.87243i	0.672141	−	0.388061i	0.796887	+	0.604128i	$0.206478\pi$
$230$		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	$0.507026\pi$
$233$	−15.5975	+	15.5975i	−1.02183	+	1.02183i	−0.999756	+	0.0220706i	$0.992974\pi$
$234$	3.66528	+	2.11615i	0.239607	+	0.138337i
$235$		0			0
$236$	2.58366	−	2.58366i	0.168182	−	0.168182i
$237$	26.2554	+	15.1586i	1.70547	+	0.984654i
$238$	18.8418	−	5.04865i	1.22133	−	0.327255i
$239$	4.07548	+	15.2099i	0.263621	+	0.983846i	0.963089	+	0.269183i	$0.0867535\pi$
$239$	4.07548	+	15.2099i	0.263621	+	0.983846i	−0.699468	+	0.714663i	$0.746580\pi$
$240$		0			0
$241$	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	$-0.0180855\pi$
$242$	−8.44822	−	4.87758i	−0.543072	−	0.313543i
$243$	−8.14560	−	30.3998i	−0.522540	−	1.95015i
$244$	−0.0762479	−	0.284561i	−0.00488127	−	0.0182172i
$245$		0			0
$246$	−36.1939	−	9.69813i	−2.30764	−	0.618330i
$247$	1.42311	−	0.381321i	0.0905503	−	0.0242629i
$248$	−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	−0.455447	+	0.890263i	$0.650521\pi$
$251$	−21.3201	+	21.3201i	−1.34571	+	1.34571i	−0.890263	+	0.455447i	$0.849479\pi$
$252$	−3.21195	+	11.9871i	−0.202334	+	0.755119i
$253$	3.15670			0.198460
$254$	−4.03280	+	15.0506i	−0.253040	+	0.944360i
$255$		0			0
$256$	−4.67940	−	8.10495i	−0.292462	−	0.506559i
$257$	2.91528	−	5.04941i	0.181850	−	0.314974i	−0.760660	−	0.649150i	$-0.775125\pi$
$257$	2.91528	−	5.04941i	0.181850	−	0.314974i	0.942511	+	0.334176i	$0.108458\pi$
$258$	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
$262$	−5.89705	+	22.0081i	−0.364321	+	1.35966i
$263$	−19.4059	−	5.19979i	−1.19662	−	0.320633i	−0.395120	−	0.918630i	$-0.629297\pi$
$263$	−19.4059	−	5.19979i	−1.19662	−	0.320633i	−0.801498	+	0.597997i	$0.795964\pi$
$264$	16.6665	+	4.46578i	1.02575	+	0.274850i
$265$		0			0
$266$	12.8139	+	22.1944i	0.785673	+	1.36083i
$267$	−22.0427			−1.34899
$268$	4.28991	−	1.14948i	0.262048	−	0.0702155i
$269$			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	−0.562600	−	0.826729i	$-0.690199\pi$
$271$	7.15555	−	12.3938i	0.434669	−	0.752868i	0.997269	+	0.0738613i	$0.0235322\pi$
$272$	7.00281	+	12.1292i	0.424607	+	0.735442i
$273$	4.99053			0.302040
$274$	10.1775	−	2.72705i	0.614845	−	0.164747i
$275$		0			0
$276$	−1.83141	+	0.490724i	−0.110238	+	0.0295381i
$277$	3.28707	−	1.89779i	0.197501	−	0.114027i	−0.397988	−	0.917391i	$-0.630292\pi$
$277$	3.28707	−	1.89779i	0.197501	−	0.114027i	0.595489	+	0.803363i	$0.296958\pi$
$278$	30.9772	−	17.8847i	1.85789	−	1.07265i
$279$	−33.2616	+	8.91241i	−1.99132	+	0.533572i
$280$		0			0
$281$	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	$0.368137\pi$
$282$	−64.8314			−3.86065
$283$	7.46035	+	12.9217i	0.443472	+	0.768115i	0.997944	−	0.0640865i	$-0.0204134\pi$
$283$	7.46035	+	12.9217i	0.443472	+	0.768115i	−0.554473	+	0.832202i	$0.687080\pi$
$284$	−0.194556	+	0.336982i	−0.0115448	+	0.0199962i
$285$		0			0
$286$			1.25232i			0.0740511i
$287$	−30.2894	+	8.11601i	−1.78793	+	0.479073i
$288$	−16.5809			−0.977036
$289$	3.95733	+	6.85430i	0.232784	+	0.403194i
$290$		0			0
$291$	−9.71907	−	2.60422i	−0.569742	−	0.152662i
$292$	−1.84641	−	0.494744i	−0.108053	−	0.0289527i
$293$	−0.391817	+	1.46228i	−0.0228902	+	0.0854275i	−0.976426	−	0.215852i	$-0.930747\pi$
$293$	−0.391817	+	1.46228i	−0.0228902	+	0.0854275i	0.953536	+	0.301280i	$0.0974137\pi$
$294$	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
$298$	8.66344	−	15.0055i	0.501860	−	0.869246i
$299$	0.270564	+	0.468631i	0.0156471	+	0.0271017i
$300$		0			0
$301$	0.498542	−	1.86058i	0.0287355	−	0.107242i
$302$	4.25772			0.245004
$303$	0.0887290	−	0.331141i	0.00509735	−	0.0190236i
$304$	−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	$0.0740758\pi$
$307$	21.0899	+	21.0899i	1.20366	+	1.20366i	0.230621	+	0.973044i	$0.425924\pi$
$308$	−3.54694	+	0.950400i	−0.202106	+	0.0541541i
$309$	32.3336	+	8.66376i	1.83939	+	0.492864i
$310$		0			0
$311$	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	$0.808807\pi$
$312$	0.765535	+	2.85702i	0.0433399	+	0.161747i
$313$	5.59126	+	3.22812i	0.316037	+	0.182464i	0.649625	−	0.760255i	$-0.274926\pi$
$313$	5.59126	+	3.22812i	0.316037	+	0.182464i	−0.333588	+	0.942719i	$0.608259\pi$
$314$	2.88343	−	10.7611i	0.162722	−	0.607285i
$315$		0			0
$316$	−0.989728	−	3.69372i	−0.0556766	−	0.207788i
$317$	−21.4124	+	5.73743i	−1.20264	+	0.322246i	−0.803870	−	0.594805i	$-0.797229\pi$
$317$	−21.4124	+	5.73743i	−1.20264	+	0.322246i	−0.398769	+	0.917051i	$0.630562\pi$
$318$	0.824696	+	0.476138i	0.0462466	+	0.0267005i
$319$	−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
$327$			41.8710i			2.31547i
$328$	−9.29264	−	16.0953i	−0.513100	−	0.888716i
$329$	−46.9863	+	27.1275i	−2.59044	+	1.49559i
$330$		0			0
$331$	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
$333$	12.8213	−	42.7335i	0.702600	−	2.34178i
$334$		−	21.4553i		−	1.17398i
$335$		0			0
$336$	−53.9782	+	31.1643i	−2.94475	+	1.70015i
$337$	2.09537	−	7.82004i	0.114142	−	0.425985i	−0.885079	−	0.465441i	$-0.845896\pi$
$337$	2.09537	−	7.82004i	0.114142	−	0.425985i	0.999221	+	0.0394559i	$0.0125625\pi$
$338$	17.2754	−	9.97393i	0.939656	−	0.542510i
$339$	18.3850	−	18.3850i	0.998535	−	0.998535i
$340$		0			0
$341$	−7.20480	−	7.20480i	−0.390162	−	0.390162i
$342$	11.6597	+	43.5145i	0.630483	+	2.35299i
$343$	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
$347$		−	26.0269i		−	1.39720i	−0.715513	−	0.698599i	$-0.753807\pi$
$347$		−	26.0269i		−	1.39720i	0.715513	−	0.698599i	$-0.246193\pi$
$348$	1.68840	−	2.92439i	0.0905077	−	0.156764i
$349$	2.63616	+	1.52199i	0.141110	+	0.0814701i	0.568893	−	0.822412i	$-0.307372\pi$
$349$	2.63616	+	1.52199i	0.141110	+	0.0814701i	−0.427783	+	0.903882i	$0.640705\pi$
$350$		0			0
$351$	5.00779	+	1.34183i	0.267296	+	0.0716217i
$352$	−2.45310	−	4.24889i	−0.130751	−	0.226467i
$353$	−3.45536	+	5.98486i	−0.183910	+	0.318542i	−0.943209	−	0.332200i	$-0.892209\pi$
$353$	−3.45536	+	5.98486i	−0.183910	+	0.318542i	0.759298	+	0.650743i	$0.225542\pi$
$354$	22.4641	−	38.9090i	1.19396	−	2.06799i
$355$		0			0
$356$	1.96599	+	1.96599i	0.104197	+	0.104197i
$357$	35.0152	−	20.2161i	1.85320	−	1.06995i
$358$	5.90799	+	22.0489i	0.312247	+	1.16532i
$359$		−	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
$362$		−	35.6255i		−	1.87244i
$363$	−19.5311	−	5.23333i	−1.02512	−	0.274679i
$364$	−0.445106	−	0.445106i	−0.0233299	−	0.0233299i
$365$		0			0
$366$	−1.81122	−	3.13713i	−0.0946741	−	0.163980i
$367$	19.4287	+	5.20590i	1.01417	+	0.271746i	0.727370	−	0.686245i	$-0.240742\pi$
$367$	19.4287	+	5.20590i	1.01417	+	0.271746i	0.286799	+	0.957991i	$0.407409\pi$
$368$	−5.85292	−	3.37918i	−0.305104	−	0.176152i
$369$	−55.1219			−2.86953
$370$		0			0
$371$	0.796926			0.0413743
$372$	5.30001	+	3.05996i	0.274793	+	0.158652i
$373$	1.01275	+	0.271365i	0.0524380	+	0.0140507i	0.284943	−	0.958545i	$-0.408025\pi$
$373$	1.01275	+	0.271365i	0.0524380	+	0.0140507i	−0.232505	+	0.972595i	$0.574692\pi$
$374$	5.07300	+	8.78670i	0.262319	+	0.454349i
$375$		0			0
$376$	−22.7378	−	22.7378i	−1.17261	−	1.17261i
$377$	−0.930911	−	0.249437i	−0.0479444	−	0.0128467i
$378$			90.1820i			4.63846i
$379$	−13.4701	−	7.77696i	−0.691912	−	0.399476i	0.112416	−	0.993661i	$-0.464141\pi$
$379$	−13.4701	−	7.77696i	−0.691912	−	0.399476i	−0.804328	+	0.594186i	$0.797474\pi$
$380$		0			0
$381$			32.2967i			1.65461i
$382$	3.77323	+	14.0819i	0.193055	+	0.720492i
$383$	−3.67241	+	2.12027i	−0.187651	+	0.108341i	−0.590883	−	0.806758i	$-0.701220\pi$
$383$	−3.67241	+	2.12027i	−0.187651	+	0.108341i	0.403231	+	0.915098i	$0.367887\pi$
$384$	−30.6804	−	30.6804i	−1.56565	−	1.56565i
$385$		0			0
$386$	−10.5023	+	18.1905i	−0.534553	+	0.925872i
$387$	1.69298	−	2.93234i	0.0860593	−	0.149059i
$388$	0.634575	+	1.09912i	0.0322157	+	0.0557992i
$389$	14.7360	+	3.94851i	0.747146	+	0.200197i	0.612252	−	0.790663i	$-0.290264\pi$
$389$	14.7360	+	3.94851i	0.747146	+	0.200197i	0.134894	+	0.990860i	$0.456931\pi$
$390$		0			0
$391$	3.79675	+	2.19205i	0.192010	+	0.110857i
$392$	−12.8728	+	22.2963i	−0.650174	+	1.12613i
$393$			47.2266i			2.38226i
$394$	−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	0.538786	−	0.842443i	$-0.318883\pi$
$397$	−6.05031	−	6.05031i	−0.303657	−	0.303657i	−0.842443	+	0.538786i	$0.818883\pi$
$398$	4.25443	+	15.8777i	0.213255	+	0.795879i
$399$	37.5617	+	37.5617i	1.88044	+	1.88044i
$400$		0			0
$401$	−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	$0.348764\pi$
$402$	47.2939	−	27.3051i	2.35880	−	1.36186i
$403$	0.452066	−	1.68713i	0.0225190	−	0.0840420i
$404$	−0.0374483	+	0.0216208i	−0.00186312	+	0.00107567i
$405$		0			0
$406$		−	16.7642i		−	0.831992i
$407$	12.8475	−	3.03684i	0.636825	−	0.150530i
$408$	16.9447	+	16.9447i	0.838888	+	0.838888i
$409$	−4.20165	+	1.12583i	−0.207758	+	0.0556686i	−0.361197	−	0.932490i	$-0.617632\pi$
$409$	−4.20165	+	1.12583i	−0.207758	+	0.0556686i	0.153439	+	0.988158i	$0.450965\pi$
$410$		0			0
$411$	18.9137	−	10.9198i	0.932942	−	0.538634i
$412$	−2.11112	−	3.65656i	−0.104007	−	0.180146i
$413$		−	37.5989i		−	1.85012i
$414$	−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	$-0.352724\pi$
$419$	−2.15841	−	1.24616i	−0.105445	−	0.0608788i	−0.551795	+	0.833980i	$0.686057\pi$
$420$		0			0
$421$	−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	$0.404112\pi$
$422$	19.6909	+	11.3685i	0.958536	+	0.553411i
$423$	−92.1217	+	24.6839i	−4.47911	+	1.20017i
$424$	0.122247	+	0.456230i	0.00593682	+	0.0221565i
$425$		0			0
$426$	−1.23835	+	4.62157i	−0.0599980	+	0.223916i
$427$	−2.62535	−	1.51575i	−0.127050	−	0.0733521i
$428$	0.752959	+	2.81008i	0.0363956	+	0.135830i
$429$	0.671829	+	2.50730i	0.0324362	+	0.121054i
$430$		0			0
$431$	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	$0.359809\pi$
$432$	−62.5442	+	16.7587i	−3.00916	+	0.806301i
$433$	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
$437$	−1.49077	+	5.56363i	−0.0713132	+	0.266145i
$438$	−23.5047			−1.12310
$439$	3.38942	−	12.6495i	0.161768	−	0.603727i	−0.836662	−	0.547719i	$-0.815496\pi$
$439$	3.38942	−	12.6495i	0.161768	−	0.603727i	0.998430	−	0.0560075i	$-0.0178371\pi$
$440$		0			0
$441$	38.1793	+	66.1285i	1.81806	+	3.14898i
$442$	−0.869627	+	1.50624i	−0.0413639	+	0.0716444i
$443$	0.485132	−	0.485132i	0.0230493	−	0.0230493i	−0.695488	−	0.718538i	$-0.744812\pi$
$443$	0.485132	−	0.485132i	0.0230493	−	0.0230493i	0.718538	+	0.695488i	$0.244812\pi$
$444$	−6.98157	+	3.75907i	−0.331331	+	0.178398i
$445$		0			0
$446$	2.14359	+	7.99997i	0.101502	+	0.378810i
$447$	9.29532	−	34.6906i	0.439653	−	1.64081i
$448$	−23.3241	−	6.24967i	−1.10196	−	0.295269i
$449$	14.3950	+	3.85712i	0.679341	+	0.182029i	0.581959	−	0.813218i	$-0.302286\pi$
$449$	14.3950	+	3.85712i	0.679341	+	0.182029i	0.0973822	+	0.995247i	$0.468953\pi$
$450$		0			0
$451$	−8.15516	−	14.1252i	−0.384012	−	0.665128i
$452$	−3.27952			−0.154256
$453$	8.52449	−	2.28413i	0.400515	−	0.107318i
$454$			18.3587i			0.861618i
$455$		0			0
$456$	−15.7417	+	27.2655i	−0.737174	+	1.27682i
$457$	9.41987	+	16.3157i	0.440643	+	0.763216i	0.997737	−	0.0672332i	$-0.0214171\pi$
$457$	9.41987	+	16.3157i	0.440643	+	0.763216i	−0.557094	+	0.830449i	$0.688084\pi$
$458$	−18.2158			−0.851171
$459$	40.5720	−	10.8712i	1.89374	−	0.507425i
$460$		0			0
$461$	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	$0.319855\pi$
$462$	−39.1031	+	22.5762i	−1.81924	+	1.05034i
$463$	32.9086	−	18.9998i	1.52939	−	0.882996i	0.530007	−	0.847993i	$-0.322189\pi$
$463$	32.9086	−	18.9998i	1.52939	−	0.882996i	0.999387	−	0.0350030i	$-0.0111441\pi$
$464$	11.6265	−	3.11531i	0.539747	−	0.144625i
$465$		0			0
$466$	33.0458	−	8.85459i	1.53082	−	0.410181i
$467$	−24.7489			−1.14524			−0.572622	−	0.819820i	$-0.694074\pi$
$467$	−24.7489			−1.14524			−0.572622	+	0.819820i	$0.694074\pi$
$468$	−0.553256	−	0.958267i	−0.0255743	−	0.0442959i
$469$	22.8507	−	39.5786i	1.05515	−	1.82757i
$470$		0			0
$471$		−	23.0920i		−	1.06402i
$472$	21.5249	−	5.76758i	0.990764	−	0.265474i
$473$	1.00189			0.0460671
$474$	−23.5104	−	40.7212i	−1.07987	−	1.87039i
$475$		0			0
$476$	−4.92609	−	1.31994i	−0.225787	−	0.0604994i
$477$	1.35313	+	0.362570i	0.0619556	+	0.0166009i
$478$	6.32092	−	23.5900i	0.289112	−	1.07898i
$479$	6.64188	+	24.7878i	0.303475	+	1.13259i	0.934250	+	0.356619i	$0.116071\pi$
$479$	6.64188	+	24.7878i	0.303475	+	1.13259i	−0.630775	+	0.775966i	$0.717263\pi$
$480$		0			0
$481$	1.55201	+	1.64700i	0.0707656	+	0.0750965i
$482$	−10.6665	+	10.6665i	−0.485845	+	0.485845i
$483$	−9.75520	+	16.8965i	−0.443877	+	0.768818i
$484$	1.27522	+	2.20874i	0.0579644	+	0.100397i
$485$		0			0
$486$	−12.6335	+	47.1490i	−0.573069	+	2.13872i
$487$	−21.8694			−0.990998			−0.495499	−	0.868608i	$-0.665015\pi$
$487$	−21.8694			−0.990998			−0.495499	+	0.868608i	$0.665015\pi$
$488$	0.465024	−	1.73549i	0.0210506	−	0.0785621i
$489$	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
$493$	−7.54203	+	2.02088i	−0.339676	+	0.0910159i
$494$	−2.20719	−	0.591416i	−0.0993063	−	0.0266091i
$495$		0			0
$496$	5.64602	+	21.0712i	0.253514	+	0.946127i
$497$	1.03633	+	3.86762i	0.0464856	+	0.173487i
$498$	−43.7829	−	25.2780i	−1.96196	−	1.13274i
$499$	−9.23613	+	34.4697i	−0.413466	+	1.54308i	0.374422	+	0.927258i	$0.377841\pi$
$499$	−9.23613	+	34.4697i	−0.413466	+	1.54308i	−0.787888	+	0.615818i	$0.788826\pi$
$500$		0			0
$501$	−11.5101	−	42.9562i	−0.514233	−	1.91914i
$502$	45.1699	−	12.1032i	2.01603	−	0.540194i
$503$	23.3272	+	13.4680i	1.04011	+	0.600508i	0.919865	−	0.392236i	$-0.128298\pi$
$503$	23.3272	+	13.4680i	1.04011	+	0.600508i	0.120246	+	0.992744i	$0.461632\pi$
$504$	−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	$-0.888925\pi$
$509$	−3.92018	+	6.78995i	−0.173759	+	0.300959i	0.765972	+	0.642874i	$0.222258\pi$
$510$		0			0
$511$	−17.0349	+	9.83511i	−0.753580	+	0.435080i
$512$		−	12.4781i		−	0.551461i
$513$	27.5922	+	47.7910i	1.21822	+	2.11003i
$514$	−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
$518$	−20.6856	+	33.4918i	−0.908872	+	1.47155i
$519$		−	51.4569i		−	2.25871i
$520$		0			0
$521$	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	$0.266722\pi$
$522$	7.62704	−	28.4645i	0.333827	−	1.24586i
$523$	−16.4429	+	9.49329i	−0.718996	+	0.415113i	−0.814383	−	0.580328i	$-0.802924\pi$
$523$	−16.4429	+	9.49329i	−0.718996	+	0.415113i	0.0953869	+	0.995440i	$0.469591\pi$
$524$	4.21214	−	4.21214i	0.184008	−	0.184008i
$525$		0			0
$526$	22.0331	+	22.0331i	0.960691	+	0.960691i
$527$	−3.66253	−	13.6688i	−0.159542	−	0.595421i
$528$	−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
$532$		−	6.70027i		−	0.290493i
$533$	1.39798	−	2.42137i	0.0605532	−	0.104881i
$534$	29.6072	+	17.0937i	1.28123	+	0.739717i
$535$		0			0
$536$	26.1635	+	7.01048i	1.13009	+	0.302807i
$537$	23.6571	+	40.9753i	1.02088	+	1.76821i
$538$	0.721732	−	1.25008i	0.0311161	−	0.0538946i
$539$	−11.2971	+	19.5671i	−0.486600	+	0.842816i
$540$		0			0
$541$	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	$0.439224\pi$
$542$	−19.2223	+	11.0980i	−0.825668	+	0.476700i
$543$	−19.1120	−	71.3268i	−0.820173	−	3.06093i
$544$		−	6.81386i		−	0.292142i
$545$		0			0
$546$	−6.70315	−	3.87006i	−0.286868	−	0.165623i
$547$			35.5804i			1.52131i	0.649158	+	0.760653i	$0.275121\pi$
$547$			35.5804i			1.52131i	−0.649158	+	0.760653i	$0.724879\pi$
$548$	−2.66085	−	0.712973i	−0.113666	−	0.0304567i
$549$	−3.76807	−	3.76807i	−0.160817	−	0.160817i
$550$		0			0
$551$	−5.12918	−	8.88401i	−0.218511	−	0.378471i
$552$	−11.1695	−	2.99285i	−0.475404	−	0.127384i
$553$	−34.0781	−	19.6750i	−1.44915	−	0.836666i
$554$	−5.88682			−0.250107
$555$		0			0
$556$	−9.35173			−0.396602
$557$	−38.3911	−	22.1651i	−1.62668	−	0.939165i	−0.985074	−	0.172132i	$-0.944934\pi$
$557$	−38.3911	−	22.1651i	−1.62668	−	0.939165i	−0.641608	−	0.767033i	$-0.721732\pi$
$558$	51.5875	+	13.8228i	2.18387	+	0.585167i
$559$	0.0858735	+	0.148737i	0.00363206	+	0.00629092i
$560$		0			0
$561$	14.8706	+	14.8706i	0.627836	+	0.627836i
$562$	−7.62787	−	2.04388i	−0.321762	−	0.0862160i
$563$		−	27.6526i		−	1.16542i	−0.812680	−	0.582710i	$-0.801992\pi$
$563$		−	27.6526i		−	1.16542i	0.812680	−	0.582710i	$-0.198008\pi$
$564$	14.6790	+	8.47491i	0.618096	+	0.356858i
$565$		0			0
$566$		−	23.1415i		−	0.972709i
$567$	24.6164	+	91.8696i	1.03379	+	3.85816i
$568$	−2.05520	+	1.18657i	−0.0862341	+	0.0497873i
$569$	−8.31252	−	8.31252i	−0.348479	−	0.348479i	0.511064	−	0.859543i	$-0.329252\pi$
$569$	−8.31252	−	8.31252i	−0.348479	−	0.348479i	−0.859543	+	0.511064i	$0.829252\pi$
$570$		0			0
$571$	−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	$0.220142\pi$
$572$	0.163706	−	0.283547i	0.00684489	−	0.0118557i
$573$	15.1090	+	26.1695i	0.631186	+	1.09325i
$574$	46.9778	+	12.5877i	1.96081	+	0.525398i
$575$		0			0
$576$	−36.7595	−	21.2231i	−1.53164	−	0.884296i
$577$	8.77295	−	15.1952i	0.365223	−	0.632584i	−0.623589	−	0.781752i	$-0.714326\pi$
$577$	8.77295	−	15.1952i	0.365223	−	0.632584i	0.988812	+	0.149168i	$0.0476595\pi$
$578$		−	12.2754i		−	0.510588i
$579$	−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
$583$	0.107283	+	0.400385i	0.00444320	+	0.0165823i
$584$	−8.24359	−	8.24359i	−0.341122	−	0.341122i
$585$		0			0
$586$	1.66025	−	1.66025i	0.0685844	−	0.0685844i
$587$	−3.28916	+	1.89900i	−0.135758	+	0.0783800i	−0.566341	−	0.824171i	$-0.691641\pi$
$587$	−3.28916	+	1.89900i	−0.135758	+	0.0783800i	0.430583	+	0.902551i	$0.358308\pi$
$588$	3.51238	−	13.1084i	0.144848	−	0.540580i
$589$	16.1009	−	9.29585i	0.663425	−	0.383029i
$590$		0			0
$591$			38.1003i			1.56724i
$592$	−27.0717	−	8.12228i	−1.11264	−	0.333824i
$593$	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
$597$	17.0358	+	29.5069i	0.697229	+	1.20764i
$598$		−	0.839272i		−	0.0343204i
$599$	−31.9153	+	18.4263i	−1.30403	+	0.752879i	−0.981092	−	0.193543i	$-0.938002\pi$
$599$	−31.9153	+	18.4263i	−1.30403	+	0.752879i	−0.322933	+	0.946422i	$0.604669\pi$
$600$		0			0
$601$	−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
$605$		0			0
$606$	−0.375973	+	0.375973i	−0.0152728	+	0.0152728i
$607$	−13.0183	−	7.51612i	−0.528396	−	0.305070i	0.211967	−	0.977277i	$-0.432013\pi$
$607$	−13.0183	−	7.51612i	−0.528396	−	0.305070i	−0.740363	+	0.672207i	$0.765346\pi$
$608$	8.64711	−	2.31699i	0.350687	−	0.0939662i
$609$	−8.99344	−	33.5640i	−0.364433	−	1.36008i
$610$		0			0
$611$	1.25205	−	4.67270i	0.0506524	−	0.189037i
$612$	−7.76367	−	4.48235i	−0.313828	−	0.181188i
$613$	−2.40495	−	8.97541i	−0.0971352	−	0.362513i	0.900199	−	0.435478i	$-0.143421\pi$
$613$	−2.40495	−	8.97541i	−0.0971352	−	0.362513i	−0.997335	+	0.0729646i	$0.976754\pi$
$614$	−11.9726	−	44.6823i	−0.483174	−	1.80323i
$615$		0			0
$616$	−21.6322	−	5.79634i	−0.871588	−	0.233541i
$617$	−14.0818	+	3.77320i	−0.566911	+	0.151903i	−0.530880	−	0.847447i	$-0.678138\pi$
$617$	−14.0818	+	3.77320i	−0.566911	+	0.151903i	−0.0360316	+	0.999351i	$0.511472\pi$
$618$	−36.7111	−	36.7111i	−1.47674	−	1.47674i
$619$	−26.2648			−1.05567			−0.527837	−	0.849346i	$-0.676997\pi$
$619$	−26.2648			−1.05567			−0.527837	+	0.849346i	$0.676997\pi$
$620$		0			0
$621$	−14.3320	+	14.3320i	−0.575123	+	0.575123i
$622$	4.70625	−	17.5640i	0.188703	−	0.704251i
$623$	28.6102			1.14624
$624$	1.43836	−	5.36803i	0.0575805	−	0.214893i
$625$		0			0
$626$	−5.00669	−	8.67185i	−0.200108	−	0.346597i
$627$	−13.8149	+	23.9280i	−0.551712	+	0.955593i
$628$	−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	−0.978588	−	0.205831i	$-0.934010\pi$
$631$	−5.87855	−	21.9390i	−0.234021	−	0.873379i	0.744566	−	0.667549i	$-0.232656\pi$
$632$	6.03620	−	22.5274i	0.240107	−	0.896091i
$633$	45.5224	+	12.1977i	1.80935	+	0.484815i
$634$	33.2098	+	8.89855i	1.31893	+	0.353406i
$635$		0			0
$636$	−0.124484	−	0.215612i	−0.00493610	−	0.00854958i
$637$	−3.87315			−0.153460
$638$	8.42252	−	2.25681i	0.333451	−	0.0893479i
$639$			7.03847i			0.278437i
$640$		0			0
$641$	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	$-0.0235406\pi$
$642$	17.8861	+	30.9796i	0.705907	+	1.22267i
$643$	−31.7473			−1.25199			−0.625996	−	0.779826i	$-0.715307\pi$
$643$	−31.7473			−1.25199			−0.625996	+	0.779826i	$0.715307\pi$
$644$	2.37707	−	0.636934i	0.0936697	−	0.0250987i
$645$		0			0
$646$	−17.8822	+	4.79152i	−0.703565	+	0.188520i
$647$	20.3945	−	11.7748i	0.801792	−	0.462915i	−0.0423052	−	0.999105i	$-0.513470\pi$
$647$	20.3945	−	11.7748i	0.801792	−	0.462915i	0.844097	+	0.536190i	$0.180137\pi$
$648$	−48.8181	+	28.1852i	−1.91776	+	1.10722i
$649$	18.8901	−	5.06159i	0.741502	−	0.198685i
$650$		0			0
$651$	60.8295	−	16.2992i	2.38410	−	0.638817i
$652$	−0.0658370			−0.00257838
$653$	−17.9724	−	31.1291i	−0.703315	−	1.21818i	−0.967296	−	0.253649i	$-0.918369\pi$
$653$	−17.9724	−	31.1291i	−0.703315	−	1.21818i	0.263982	−	0.964528i	$-0.414964\pi$
$654$	32.4702	−	56.2400i	1.26969	−	2.19916i
$655$		0			0
$656$			34.9198i			1.36339i
$657$	−33.3988	+	8.94918i	−1.30301	+	0.349141i
$658$	84.1477			3.28042
$659$	15.7744	+	27.3220i	0.614483	+	1.06432i	0.990475	+	0.137692i	$0.0439685\pi$
$659$	15.7744	+	27.3220i	0.614483	+	1.06432i	−0.375992	+	0.926623i	$0.622698\pi$
$660$		0			0
$661$	−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	$0.756969\pi$
$662$	−12.5249	−	3.35604i	−0.486794	−	0.130436i
$663$	−0.933054	+	3.48221i	−0.0362368	+	0.135238i
$664$	−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
$668$	−2.80469	+	4.85786i	−0.108517	+	0.187956i
$669$	8.58346	+	14.8670i	0.331856	+	0.574791i
$670$		0			0
$671$	0.408102	−	1.52306i	0.0157546	−	0.0587970i
$672$	30.3235			1.16975
$673$	−4.72719	+	17.6421i	−0.182220	+	0.680054i	0.812989	+	0.582279i	$0.197839\pi$
$673$	−4.72719	+	17.6421i	−0.182220	+	0.680054i	−0.995209	+	0.0977743i	$0.968828\pi$
$674$	−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	0.616246	−	0.787554i	$-0.288653\pi$
$677$	−4.45728	−	4.45728i	−0.171307	−	0.171307i	−0.787554	+	0.616246i	$0.788653\pi$
$678$	−38.9515	+	10.4370i	−1.49592	+	0.400831i
$679$	12.6148	+	3.38013i	0.484113	+	0.129718i
$680$		0			0
$681$	9.84887	+	36.7565i	0.377410	+	1.40851i
$682$	4.09011	+	15.2645i	0.156619	+	0.584508i
$683$	0.144126	+	0.0832112i	0.00551483	+	0.00318399i	0.502755	−	0.864429i	$-0.332320\pi$
$683$	0.144126	+	0.0832112i	0.00551483	+	0.00318399i	−0.497240	+	0.867613i	$0.665653\pi$
$684$	3.04836	−	11.3766i	0.116557	−	0.434996i
$685$		0			0
$686$	−5.71255	−	21.3195i	−0.218106	−	0.813983i
$687$	−36.4704	+	9.77222i	−1.39143	+	0.372834i
$688$	−1.85764	−	1.07251i	−0.0708218	−	0.0408890i
$689$	−0.0502443	+	0.0502443i	−0.00191416	+	0.00191416i
$690$		0			0
$691$	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
$695$		0			0
$696$	17.8354	−	10.2973i	0.676049	−	0.390317i
$697$		−	22.6522i		−	0.858014i
$698$	−2.36055	−	4.08859i	−0.0893481	−	0.154755i
$699$	61.4116	−	35.4560i	2.32280	−	1.34107i
$700$		0			0
$701$	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
$703$	−0.714915	+	24.0776i	−0.0269635	+	0.908105i
$704$		−	12.5596i		−	0.473359i
$705$		0			0
$706$	9.28231	−	5.35914i	0.349344	−	0.201694i
$707$	−0.115166	+	0.429804i	−0.00433125	+	0.0161644i
$708$	−10.1726	+	5.87313i	−0.382308	+	0.220726i
$709$	−1.78823	+	1.78823i	−0.0671583	+	0.0671583i	−0.739888	−	0.672730i	$-0.765122\pi$
$709$	−1.78823	+	1.78823i	−0.0671583	+	0.0671583i	0.672730	+	0.739888i	$0.265122\pi$
$710$		0			0
$711$	−48.9111	−	48.9111i	−1.83431	−	1.83431i
$712$	4.38874	+	16.3790i	0.164475	+	0.613829i
$713$	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
$717$		−	50.6211i		−	1.89048i
$718$	−10.3001	+	17.8403i	−0.384397	+	0.665795i
$719$	−37.0250	−	21.3764i	−1.38080	−	0.797205i	−0.388546	−	0.921429i	$-0.627022\pi$
$719$	−37.0250	−	21.3764i	−1.38080	−	0.797205i	−0.992254	+	0.124224i	$0.960356\pi$
$720$		0			0
$721$	−41.9673	−	11.2451i	−1.56294	−	0.418789i
$722$	2.57285	+	4.45631i	0.0957516	+	0.165847i
$723$	−15.6334	+	27.0778i	−0.581412	+	1.00704i
$724$	−4.65705	+	8.06625i	−0.173078	+	0.299780i
$725$		0			0
$726$	22.1753	+	22.1753i	0.823002	+	0.823002i
$727$	35.7427	−	20.6361i	1.32562	−	0.765349i	0.341004	−	0.940062i	$-0.389233\pi$
$727$	35.7427	−	20.6361i	1.32562	−	0.765349i	0.984619	+	0.174713i	$0.0558998\pi$
$728$	−0.993623	−	3.70825i	−0.0368261	−	0.137437i
$729$			32.7935i			1.21458i
$730$		0			0
$731$	1.20504	+	0.695728i	0.0445699	+	0.0257324i
$732$			0.947068i			0.0350046i
$733$	43.1692	+	11.5672i	1.59449	+	0.427243i	0.943373	−	0.331734i	$-0.107634\pi$
$733$	43.1692	+	11.5672i	1.59449	+	0.427243i	0.651118	+	0.758976i	$0.274300\pi$
$734$	−22.0590	−	22.0590i	−0.814214	−	0.814214i
$735$		0			0
$736$	1.64401	+	2.84750i	0.0605988	+	0.104960i
$737$	22.9609	+	6.15236i	0.845776	+	0.226625i
$738$	74.0384	+	42.7461i	2.72539	+	1.57350i
$739$	19.7035			0.724803			0.362402	−	0.932022i	$-0.381957\pi$
$739$	19.7035			0.724803			0.362402	+	0.932022i	$0.381957\pi$
$740$		0			0
$741$	−4.73636			−0.173994
$742$	−1.07041	−	0.618002i	−0.0392960	−	0.0226876i
$743$	0.540326	+	0.144780i	0.0198226	+	0.00531146i	0.268717	−	0.963219i	$-0.413400\pi$
$743$	0.540326	+	0.144780i	0.0198226	+	0.00531146i	−0.248894	+	0.968531i	$0.580067\pi$
$744$	18.6622	+	32.3239i	0.684190	+	1.18505i
$745$		0			0
$746$	−1.14986	−	1.14986i	−0.0420993	−	0.0420993i
$747$	−71.8373	−	19.2487i	−2.62839	−	0.704275i
$748$		−	2.65262i		−	0.0969893i
$749$	25.9257	+	14.9682i	0.947305	+	0.546927i
$750$		0			0
$751$		−	13.6763i		−	0.499056i	−0.968368	−	0.249528i	$-0.919725\pi$
$751$		−	13.6763i		−	0.499056i	0.968368	−	0.249528i	$-0.0802755\pi$
$752$	15.6373	+	58.3592i	0.570233	+	2.12814i
$753$	83.9428	−	48.4644i	3.05905	−	1.76614i
$754$	1.05694	+	1.05694i	0.0384916	+	0.0384916i
$755$		0			0
$756$	11.7888	−	20.4188i	0.428754	−	0.742624i
$757$	−15.0578	+	26.0809i	−0.547285	+	0.947926i	0.451174	+	0.892436i	$0.351005\pi$
$757$	−15.0578	+	26.0809i	−0.547285	+	0.947926i	−0.998459	+	0.0554901i	$0.982328\pi$
$758$	12.0618	+	20.8916i	0.438104	+	0.758818i
$759$	−9.80226	−	2.62651i	−0.355799	−	0.0953362i
$760$		0			0
$761$	−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	$0.843165\pi$
$762$	25.0455	−	43.3801i	0.907304	−	1.57150i
$763$		−	54.3463i		−	1.96747i
$764$	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
$768$	7.78692	+	29.0612i	0.280986	+	1.04865i
$769$	8.36905	+	8.36905i	0.301796	+	0.301796i	0.841716	−	0.539920i	$-0.181546\pi$
$769$	8.36905	+	8.36905i	0.301796	+	0.301796i	−0.539920	+	0.841716i	$0.681546\pi$
$770$		0			0
$771$	−13.2539	+	13.2539i	−0.477329	+	0.477329i
$772$	4.75581	−	2.74577i	0.171165	−	0.0988223i
$773$	3.12135	−	11.6490i	0.112267	−	0.418987i	−0.886801	−	0.462152i	$-0.847077\pi$
$773$	3.12135	−	11.6490i	0.112267	−	0.418987i	0.999068	+	0.0431651i	$0.0137442\pi$
$774$	−4.54795	+	2.62576i	−0.163473	+	0.0943810i
$775$		0			0
$776$			7.74034i			0.277862i
$777$	−23.4478	+	78.1520i	−0.841186	+	2.80369i
$778$	−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
$782$	−3.39980	−	5.88862i	−0.121576	−	0.210577i
$783$		−	36.0982i		−	1.29004i
$784$	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
$792$	−34.0931	−	19.6836i	−1.21144	−	0.699428i
$793$	0.261087	−	0.0699579i	0.00927145	−	0.00248428i
$794$	3.43472	+	12.8185i	0.121894	+	0.454913i
$795$		0			0
$796$	1.11230	−	4.15115i	0.0394243	−	0.147134i
$797$	−23.6455	−	13.6517i	−0.837566	−	0.483569i	0.0188700	−	0.999822i	$-0.493993\pi$
$797$	−23.6455	−	13.6517i	−0.837566	−	0.483569i	−0.856436	+	0.516253i	$0.827326\pi$
$798$	−21.3235	−	79.5804i	−0.754843	−	2.81711i
$799$	−10.1438	−	37.8572i	−0.358862	−	1.33929i
$800$		0			0
$801$	48.5783	+	13.0165i	1.71643	+	0.459916i
$802$	18.3191	−	4.90858i	0.646869	−	0.173328i
$803$	−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
$807$	0.774372	−	2.89000i	0.0272592	−	0.101733i
$808$	−0.263723			−0.00927776
$809$	−2.23198	+	8.32987i	−0.0784723	+	0.292863i	−0.993998	−	0.109396i	$-0.965108\pi$
$809$	−2.23198	+	8.32987i	−0.0784723	+	0.292863i	0.915526	+	0.402259i	$0.131775\pi$
$810$		0			0
$811$	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	$0.774356\pi$
$812$	−2.19145	+	3.79570i	−0.0769049	+	0.133203i
$813$	−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
$817$	−0.473151	+	1.76582i	−0.0165534	+	0.0617783i
$818$	6.51661	+	1.74612i	0.227848	+	0.0610516i
$819$	−10.9983	−	2.94698i	−0.384311	−	0.102976i
$820$		0			0
$821$	−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	$0.964610\pi$
$822$	−33.8725			−1.18144
$823$	52.8840	−	14.1702i	1.84342	−	0.493943i	0.844299	−	0.535873i	$-0.180017\pi$
$823$	52.8840	−	14.1702i	1.84342	−	0.493943i	0.999121	+	0.0419300i	$0.0133506\pi$
$824$		−	25.7507i		−	0.897069i
$825$		0			0
$826$	−29.1573	+	50.5019i	−1.01451	+	1.75718i
$827$	7.34082	+	12.7147i	0.255265	+	0.442133i	0.964968	−	0.262369i	$-0.0845038\pi$
$827$	7.34082	+	12.7147i	0.255265	+	0.442133i	−0.709702	+	0.704502i	$0.751170\pi$
$828$	4.32589			0.150335
$829$	−20.7635	+	5.56356i	−0.721146	+	0.193231i	−0.600683	−	0.799487i	$-0.705105\pi$
$829$	−20.7635	+	5.56356i	−0.721146	+	0.193231i	−0.120463	+	0.992718i	$0.538438\pi$
$830$		0			0
$831$	−11.7862	+	3.15809i	−0.408857	+	0.109553i
$832$	1.86456	−	1.07650i	0.0646419	−	0.0373210i
$833$	−27.1754	+	15.6897i	−0.941570	+	0.543616i
$834$	−111.072	+	29.7617i	−3.84612	+	1.03056i
$835$		0			0
$836$	3.36629	−	0.901996i	0.116426	−	0.0311962i
$837$	65.4224			2.26133
$838$	1.93275	+	3.34762i	0.0667656	+	0.115641i
$839$	10.8636	−	18.8162i	0.375052	−	0.649609i	−0.615283	−	0.788306i	$-0.710958\pi$
$839$	10.8636	−	18.8162i	0.375052	−	0.649609i	0.990335	+	0.138697i	$0.0442916\pi$
$840$		0			0
$841$		−	22.2896i		−	0.768607i
$842$	28.6156	−	7.66752i	0.986158	−	0.264240i
$843$	−16.3684			−0.563759
$844$	−2.97224	−	5.14807i	−0.102309	−	0.177204i
$845$		0			0
$846$	142.877	+	38.2839i	4.91223	+	1.31623i
$847$	25.3503	+	6.79259i	0.871046	+	0.233396i
$848$	0.229689	−	0.857209i	0.00788754	−	0.0294367i
$849$	−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
$853$	22.5236	−	39.0120i	0.771194	−	1.33575i	−0.165715	−	0.986174i	$-0.552993\pi$
$853$	22.5236	−	39.0120i	0.771194	−	1.33575i	0.936909	−	0.349573i	$-0.113673\pi$
$854$	2.35087	+	4.07182i	0.0804451	+	0.139335i
$855$		0			0
$856$	−4.59218	+	17.1382i	−0.156957	+	0.585773i
$857$	30.2373			1.03289			0.516444	−	0.856321i	$-0.327256\pi$
$857$	30.2373			1.03289			0.516444	+	0.856321i	$0.327256\pi$
$858$	1.04198	−	3.88873i	0.0355727	−	0.132759i
$859$	−4.95333	+	4.95333i	−0.169005	+	0.169005i	−0.786542	−	0.617537i	$-0.788131\pi$
$859$	−4.95333	+	4.95333i	−0.169005	+	0.169005i	0.617537	+	0.786542i	$0.288131\pi$
$860$		0			0
$861$	100.808			3.43554
$862$	−29.4124	−	29.4124i	−1.00179	−	1.00179i
$863$	−7.55800	+	2.02516i	−0.257277	+	0.0689372i	−0.385152	−	0.922853i	$-0.625851\pi$
$863$	−7.55800	+	2.02516i	−0.257277	+	0.0689372i	0.127875	+	0.991790i	$0.459184\pi$
$864$	30.4283	+	8.15325i	1.03519	+	0.277379i
$865$		0			0
$866$	−7.05116	−	26.3153i	−0.239608	−	0.894229i
$867$	−6.58534	−	24.5768i	−0.223650	−	0.834672i
$868$	−6.87913	−	3.97166i	−0.233493	−	0.134807i
$869$	5.29733	−	19.7699i	0.179700	−	0.670648i
$870$		0			0
$871$	1.05465	+	3.93602i	0.0357356	+	0.133367i
$872$	31.1126	−	8.33659i	1.05360	−	0.282313i
$873$	19.8814	+	11.4785i	0.672882	+	0.388489i
$874$	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	0.607211	−	0.794540i	$-0.292288\pi$
$881$	47.4583	−	27.4000i	1.59891	−	0.923131i	0.991698	−	0.128590i	$-0.0410452\pi$
$882$		−	118.430i		−	3.98773i
$883$	6.73321	+	11.6623i	0.226591	+	0.392467i	0.956795	−	0.290762i	$-0.0939087\pi$
$883$	6.73321	+	11.6623i	0.226591	+	0.392467i	−0.730205	+	0.683228i	$0.760575\pi$
$884$	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	0.969119	−	0.246594i	$-0.0793115\pi$
$887$	21.5186	+	21.5186i	0.722524	+	0.722524i	−0.246594	+	0.969119i	$0.579312\pi$
$888$	−48.3379	−	1.43525i	−1.62211	−	0.0481640i
$889$		−	41.9194i		−	1.40593i
$890$		0			0
$891$	−42.8425	+	24.7351i	−1.43528	+	0.828658i
$892$	0.560429	−	2.09155i	0.0187645	−	0.0700302i
$893$	44.5932	−	25.7459i	1.49226	−	0.861554i
$894$	−39.3872	+	39.3872i	−1.31730	+	1.31730i
$895$		0			0
$896$	39.8215	+	39.8215i	1.33034	+	1.33034i
$897$	−0.450243	−	1.68033i	−0.0150332	−	0.0561045i
$898$	−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
$902$			25.2967i			0.842289i
$903$	−3.09617	+	5.36272i	−0.103034	+	0.178460i
$904$	−17.3216	−	10.0006i	−0.576108	−	0.332616i
$905$		0			0
$906$	−13.2212	−	3.54260i	−0.439244	−	0.117695i
$907$	−25.7359	−	44.5758i	−0.854545	−	1.48012i	−0.877067	−	0.480369i	$-0.840503\pi$
$907$	−25.7359	−	44.5758i	−0.854545	−	1.48012i	0.0225216	−	0.999746i	$-0.492831\pi$
$908$	2.39989	−	4.15674i	0.0796433	−	0.137946i
$909$	−0.391088	+	0.677384i	−0.0129716	+	0.0224674i
$910$		0			0
$911$	−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	$-0.500401\pi$
$912$	51.2290	−	29.5771i	1.69636	−	0.979395i
$913$	−5.69562	−	21.2563i	−0.188497	−	0.703482i
$914$		−	29.2198i		−	0.966504i
$915$		0			0
$916$	4.12439	+	2.38122i	0.136274	+	0.0786776i
$917$		−	61.2975i		−	2.02422i
$918$	−62.9257	−	16.8609i	−2.07686	−	0.556492i
$919$	−22.2439	−	22.2439i	−0.733760	−	0.733760i	0.237603	−	0.971362i	$-0.423638\pi$
$919$	−22.2439	−	22.2439i	−0.733760	−	0.733760i	−0.971362	+	0.237603i	$0.923638\pi$
$920$		0			0
$921$	−47.9412	−	83.0367i	−1.57972	−	2.73615i
$922$	−19.2658	−	5.16226i	−0.634486	−	0.170010i
$923$	−0.309183	−	0.178507i	−0.0101769	−	0.00587562i
$924$	11.8048			0.388350
$925$		0			0
$926$	−58.9361			−1.93676
$927$	−66.1417	−	38.1869i	−2.17238	−	1.25422i
$928$	−5.65641	−	1.51563i	−0.185681	−	0.0497530i
$929$	−17.4258	−	30.1824i	−0.571723	−	0.990253i	−0.996389	−	0.0849029i	$-0.972942\pi$
$929$	−17.4258	−	30.1824i	−0.571723	−	0.990253i	0.424667	−	0.905350i	$-0.360391\pi$
$930$		0			0
$931$	−29.1517	−	29.1517i	−0.955407	−	0.955407i
$932$	−8.63964	−	2.31498i	−0.283001	−	0.0758298i
$933$		−	37.6900i		−	1.23392i
$934$	33.2421	+	19.1924i	1.08772	+	0.627993i
$935$		0			0
$936$		−	6.74844i		−	0.220580i
$937$	−11.4806	−	42.8463i	−0.375056	−	1.39973i	−0.853263	−	0.521481i	$-0.825380\pi$
$937$	−11.4806	−	42.8463i	−0.375056	−	1.39973i	0.478207	−	0.878247i	$-0.341287\pi$
$938$	−61.3849	+	35.4406i	−2.00429	+	1.15718i
$939$	−14.6762	−	14.6762i	−0.478940	−	0.478940i
$940$		0			0
$941$	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	$0.0447392\pi$
$942$	−17.9074	+	31.0166i	−0.583456	+	1.01057i
$943$	5.46538	+	9.46632i	0.177977	+	0.308266i
$944$	−40.4430	−	10.8367i	−1.31631	−	0.352704i
$945$		0			0
$946$	−1.34572	−	0.776950i	−0.0437530	−	0.0252608i
$947$	11.0634	−	19.1624i	0.359512	−	0.622693i	−0.628367	−	0.777917i	$-0.716276\pi$
$947$	11.0634	−	19.1624i	0.359512	−	0.622693i	0.987879	+	0.155224i	$0.0496098\pi$
$948$			12.2933i			0.399269i
$949$	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
$953$	2.76692	+	10.3263i	0.0896293	+	0.334501i	0.996151	−	0.0876591i	$-0.0279386\pi$
$953$	2.76692	+	10.3263i	0.0896293	+	0.334501i	−0.906521	+	0.422160i	$0.861272\pi$
$954$	−1.53632	−	1.53632i	−0.0497403	−	0.0497403i
$955$		0			0
$956$	−4.51491	+	4.51491i	−0.146023	+	0.146023i
$957$	15.6522	−	9.03683i	0.505965	−	0.292119i
$958$	10.3013	−	38.4451i	0.332821	−	1.24210i
$959$	−24.5489	+	14.1733i	−0.792726	+	0.457680i
$960$		0			0
$961$			8.95909i			0.289003i
$962$	−0.807405	−	3.41576i	−0.0260318	−	0.110128i
$963$	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
$967$	12.0951	+	20.9493i	0.388951	+	0.673684i	0.992309	−	0.123787i	$-0.0395041\pi$
$967$	12.0951	+	20.9493i	0.388951	+	0.673684i	−0.603357	+	0.797471i	$0.706171\pi$
$968$			15.5547i			0.499947i
$969$	−33.2319	+	19.1864i	−1.06756	+	0.616357i
$970$		0			0
$971$	−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
$975$		0			0
$976$	−2.38708	+	2.38708i	−0.0764085	+	0.0764085i
$977$	42.1852	+	24.3556i	1.34962	+	0.779205i	0.988196	−	0.153195i	$-0.0489562\pi$
$977$	42.1852	+	24.3556i	1.34962	+	0.779205i	0.361427	+	0.932400i	$0.382290\pi$
$978$	−0.781959	+	0.209525i	−0.0250043	+	0.00669988i
$979$	3.85153	+	14.3741i	0.123096	+	0.459399i
$980$		0			0
$981$	24.7254	−	92.2765i	0.789422	−	2.94616i
$982$	17.8125	+	10.2841i	0.568420	+	0.328178i
$983$	2.11914	+	7.90875i	0.0675902	+	0.252250i	0.991451	−	0.130478i	$-0.0416512\pi$
$983$	2.11914	+	7.90875i	0.0675902	+	0.252250i	−0.923861	+	0.382728i	$0.874985\pi$
$984$	15.4638	+	57.7115i	0.492966	+	1.83978i
$985$		0			0
$986$	11.6974	+	3.13432i	0.372522	+	0.0998169i
$987$	168.474	−	45.1425i	5.36260	−	1.43690i
$988$	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	0.189834	−	0.981816i	$-0.439205\pi$
$991$	36.8837	−	36.8837i	1.17165	−	1.17165i	0.981816	−	0.189834i	$-0.0607948\pi$
$992$	2.74684	−	10.2514i	0.0872124	−	0.325481i
$993$	−26.8768			−0.852910
$994$	1.60731	−	5.99855i	0.0509806	−	0.190262i
$995$		0			0
$996$	6.60881	+	11.4468i	0.209408	+	0.362705i
$997$	−17.4612	+	30.2437i	−0.553002	+	0.957828i	0.445054	+	0.895504i	$0.353184\pi$
$997$	−17.4612	+	30.2437i	−0.553002	+	0.957828i	−0.998056	+	0.0623238i	$0.980149\pi$
$998$	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.y.b.393.4		68
5.2	odd	4		925.2.t.b.282.14		68
5.3	odd	4		185.2.p.a.97.4	✓	68
5.4	even	2		185.2.u.a.23.14	yes	68
37.29	odd	12		925.2.t.b.843.14		68
185.29	odd	12		185.2.p.a.103.4	yes	68
185.103	even	12		185.2.u.a.177.14	yes	68
185.177	even	12	inner	925.2.y.b.732.4		68

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.34317 - 0.775482i) q^{2} +(-3.10523 - 0.832043i) q^{3} +(0.202746 + 0.351166i) q^{4} +(3.52563 + 3.52563i) q^{6} +(4.03042 + 1.07995i) q^{7} +2.47303i q^{8} +(6.35206 + 3.66736i) q^{9} +2.17031i q^{11} +(-0.337386 - 1.25914i) q^{12} +(-0.322197 + 0.186020i) q^{13} +(-4.57608 - 4.57608i) q^{14} +(2.32328 - 4.02404i) q^{16} +(-1.50709 + 2.61037i) q^{17} +(-5.68795 - 9.85182i) q^{18} +(-3.82515 - 1.02494i) q^{19} +(-11.6168 - 6.70696i) q^{21} +(1.68304 - 2.91511i) q^{22} -1.45449i q^{23} +(2.05766 - 7.67931i) q^{24} +0.577022 q^{26} +(-9.85364 - 9.85364i) q^{27} +(0.437909 + 1.63430i) q^{28} +(1.83172 + 1.83172i) q^{29} +(-3.31971 + 3.31971i) q^{31} +(-1.95773 + 1.13030i) q^{32} +(1.80579 - 6.73931i) q^{33} +(4.04858 - 2.33745i) q^{34} +2.97417i q^{36} +(-1.39926 - 5.91963i) q^{37} +(4.34301 + 4.34301i) q^{38} +(1.15527 - 0.309554i) q^{39} +(-6.50835 + 3.75760i) q^{41} +(10.4023 + 18.0172i) q^{42} -0.461635i 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} +(-0.130648 - 0.0754296i) q^{52} +(0.184483 - 0.0494320i) q^{53} +(5.59384 + 20.8765i) q^{54} +(-2.67074 + 9.96733i) q^{56} +(11.0251 + 6.36537i) q^{57} +(-1.03985 - 3.88079i) q^{58} +(-2.33219 - 8.70387i) q^{59} +(-0.701769 - 0.188038i) q^{61} +(7.03332 - 1.88457i) q^{62} +(21.6409 + 21.6409i) q^{63} -5.78701 q^{64} +(-7.65172 + 7.65172i) q^{66} +(2.83478 - 10.5795i) q^{67} -1.22223 q^{68} +(-1.21020 + 4.51652i) q^{69} +(0.479804 + 0.831045i) q^{71} +(-9.06949 + 15.7088i) q^{72} +(-3.33340 + 3.33340i) q^{73} +(-2.71112 + 9.03621i) q^{74} +(-0.415606 - 1.55106i) q^{76} +(-2.34382 + 8.74727i) q^{77} +(-1.79178 - 0.480107i) q^{78} +(-9.10924 - 2.44081i) q^{79} +(11.3970 + 19.7402i) q^{81} +11.6558 q^{82} +(-9.79413 + 2.62433i) q^{83} -5.43923i q^{84} +(-0.357990 + 0.620057i) q^{86} +(-4.16383 - 7.21197i) q^{87} -5.36724 q^{88} +(6.62306 - 1.77464i) q^{89} +(-1.49948 + 0.401784i) q^{91} +(0.510766 - 0.294891i) q^{92} +(13.0706 - 7.54630i) q^{93} +(19.4796 - 5.21954i) q^{94} +(7.01966 - 1.88091i) q^{96} +3.12991 q^{97} +(-8.07320 - 13.9832i) q^{98} +(-7.95933 + 13.7860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more