LMFDB - Embedded newform 975.2.bo.h.626.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(176,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.176"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 0, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bo (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,24,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			626.19
Character	$\chi$	$=$	975.626
Dual form			975.2.bo.h.176.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.447071 - 1.66849i) q^{2} +(-1.69272 + 0.367032i) q^{3} +(-0.851938 - 0.491866i) q^{4} +(-0.144374 + 2.98837i) q^{6} +(-3.09993 + 0.830623i) q^{7} +(1.24129 - 1.24129i) q^{8} +(2.73057 - 1.24256i) q^{9} +(1.14830 + 0.307686i) q^{11} +(1.62262 + 0.519902i) q^{12} +(-3.19776 - 1.66563i) q^{13} +5.54355i q^{14} +(-2.49987 - 4.32990i) q^{16} +(-2.72229 + 4.71514i) q^{17} +(-0.852444 - 5.11145i) q^{18} +(-0.476790 - 1.77941i) q^{19} +(4.94243 - 2.54378i) q^{21} +(1.02674 - 1.77837i) q^{22} +(1.97237 + 3.41625i) q^{23} +(-1.64556 + 2.55674i) q^{24} +(-4.20871 + 4.59079i) q^{26} +(-4.16603 + 3.10551i) q^{27} +(3.04950 + 0.817112i) q^{28} +(-7.04243 + 4.06595i) q^{29} +(-0.148047 + 0.148047i) q^{31} +(-4.95075 + 1.32655i) q^{32} +(-2.05668 - 0.0993620i) q^{33} +(6.65011 + 6.65011i) q^{34} +(-2.93745 - 0.284492i) q^{36} +(-1.84876 + 6.89966i) q^{37} -3.18208 q^{38} +(6.02424 + 1.64575i) q^{39} +(-2.36667 + 8.83254i) q^{41} +(-2.03466 - 9.38365i) q^{42} +(-0.678803 - 0.391907i) q^{43} +(-0.826939 - 0.826939i) q^{44} +(6.58176 - 1.76358i) q^{46} +(6.23046 - 6.23046i) q^{47} +(5.82078 + 6.41176i) q^{48} +(2.85745 - 1.64975i) q^{49} +(2.87745 - 8.98056i) q^{51} +(1.90503 + 2.99188i) q^{52} +0.952426i q^{53} +(3.31901 + 8.33936i) q^{54} +(-2.81686 + 4.87895i) q^{56} +(1.46017 + 2.83703i) q^{57} +(3.63553 + 13.5680i) q^{58} +(2.09784 + 7.82924i) q^{59} +(-6.49787 + 11.2546i) q^{61} +(0.180828 + 0.313203i) q^{62} +(-7.43249 + 6.11993i) q^{63} -1.14613i q^{64} +(-1.08526 + 3.38712i) q^{66} +(-2.29493 - 0.614925i) q^{67} +(4.63844 - 2.67800i) q^{68} +(-4.59254 - 5.05881i) q^{69} +(1.72575 - 0.462414i) q^{71} +(1.84705 - 4.93181i) q^{72} +(-9.70845 - 9.70845i) q^{73} +(10.6855 + 6.16928i) q^{74} +(-0.469034 + 1.75046i) q^{76} -3.81522 q^{77} +(5.43918 - 9.31563i) q^{78} +0.0854873 q^{79} +(5.91208 - 6.78582i) q^{81} +(13.6789 + 7.89754i) q^{82} +(4.49219 + 4.49219i) q^{83} +(-5.46185 - 0.263872i) q^{84} +(-0.957366 + 0.957366i) q^{86} +(10.4285 - 9.46729i) q^{87} +(1.80730 - 1.04344i) q^{88} +(-5.10951 - 1.36909i) q^{89} +(11.2963 + 2.50718i) q^{91} -3.88057i q^{92} +(0.196264 - 0.304940i) q^{93} +(-7.61001 - 13.1809i) q^{94} +(7.89332 - 4.06255i) q^{96} +(0.498193 + 1.85928i) q^{97} +(-1.47511 - 5.50517i) q^{98} +(3.51784 - 0.586675i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{4} + 4 q^{9} - 16 q^{21} + 28 q^{24} - 40 q^{31} + 32 q^{34} - 60 q^{36} + 4 q^{39} - 128 q^{46} - 60 q^{54} - 48 q^{61} - 8 q^{66} - 72 q^{69} - 80 q^{76} + 80 q^{79} + 48 q^{81} + 132 q^{84}+ \cdots + 48 q^{99}+O(q^{100}) $ 96 * q + 24 * q^4 + 4 * q^9 - 16 * q^21 + 28 * q^24 - 40 * q^31 + 32 * q^34 - 60 * q^36 + 4 * q^39 - 128 * q^46 - 60 * q^54 - 48 * q^61 - 8 * q^66 - 72 * q^69 - 80 * q^76 + 80 * q^79 + 48 * q^81 + 132 * q^84 - 56 * q^91 - 72 * q^94 + 204 * q^96 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.447071	−	1.66849i	0.316127	−	1.17980i	−0.606809	−	0.794847i	$-0.707551\pi$
$2$	0.447071	−	1.66849i	0.316127	−	1.17980i	0.922936	−	0.384953i	$-0.125783\pi$
$3$	−1.69272	+	0.367032i	−0.977290	+	0.211906i
$3$	−1.69272	+	0.367032i	−0.977290	+	0.211906i
$4$	−0.851938	−	0.491866i	−0.425969	−	0.245933i
$5$		0			0
$5$		0			0
$6$	−0.144374	+	2.98837i	−0.0589404	+	1.22000i
$7$	−3.09993	+	0.830623i	−1.17166	+	0.313946i	−0.791615	−	0.611021i	$-0.790759\pi$
$7$	−3.09993	+	0.830623i	−1.17166	+	0.313946i	−0.380048	+	0.924967i	$0.624093\pi$
$8$	1.24129	−	1.24129i	0.438862	−	0.438862i
$9$	2.73057	−	1.24256i	0.910192	−	0.414188i
$10$		0			0
$11$	1.14830	+	0.307686i	0.346225	+	0.0927708i	0.427741	−	0.903901i	$-0.359309\pi$
$11$	1.14830	+	0.307686i	0.346225	+	0.0927708i	−0.0815158	+	0.996672i	$0.525976\pi$
$12$	1.62262	+	0.519902i	0.468410	+	0.150083i
$13$	−3.19776	−	1.66563i	−0.886900	−	0.461961i
$13$	−3.19776	−	1.66563i	−0.886900	−	0.461961i
$14$			5.54355i			1.48158i
$15$		0			0
$16$	−2.49987	−	4.32990i	−0.624967	−	1.08247i
$17$	−2.72229	+	4.71514i	−0.660251	+	1.14359i	0.320298	+	0.947317i	$0.396217\pi$
$17$	−2.72229	+	4.71514i	−0.660251	+	1.14359i	−0.980549	+	0.196272i	$0.937116\pi$
$18$	−0.852444	−	5.11145i	−0.200923	−	1.20478i
$19$	−0.476790	−	1.77941i	−0.109383	−	0.408224i	0.889422	−	0.457086i	$-0.151107\pi$
$19$	−0.476790	−	1.77941i	−0.109383	−	0.408224i	−0.998806	+	0.0488627i	$0.984440\pi$
$20$		0			0
$21$	4.94243	−	2.54378i	1.07853	−	0.555099i
$22$	1.02674	−	1.77837i	0.218902	−	0.379150i
$23$	1.97237	+	3.41625i	0.411268	+	0.712337i	0.995029	−	0.0995889i	$-0.0317528\pi$
$23$	1.97237	+	3.41625i	0.411268	+	0.712337i	−0.583761	+	0.811926i	$0.698419\pi$
$24$	−1.64556	+	2.55674i	−0.335898	+	0.521893i
$25$		0			0
$26$	−4.20871	+	4.59079i	−0.825395	+	0.900327i
$27$	−4.16603	+	3.10551i	−0.801752	+	0.597657i
$28$	3.04950	+	0.817112i	0.576302	+	0.154420i
$29$	−7.04243	+	4.06595i	−1.30775	+	0.755027i	−0.981720	−	0.190333i	$-0.939043\pi$
$29$	−7.04243	+	4.06595i	−1.30775	+	0.755027i	−0.326026	+	0.945361i	$0.605710\pi$
$30$		0			0
$31$	−0.148047	+	0.148047i	−0.0265900	+	0.0265900i	−0.720277	−	0.693687i	$-0.755985\pi$
$31$	−0.148047	+	0.148047i	−0.0265900	+	0.0265900i	0.693687	+	0.720277i	$0.255985\pi$
$32$	−4.95075	+	1.32655i	−0.875177	+	0.234503i
$33$	−2.05668	−	0.0993620i	−0.358021	−	0.0172967i
$34$	6.65011	+	6.65011i	1.14048	+	1.14048i
$35$		0			0
$36$	−2.93745	−	0.284492i	−0.489576	−	0.0474154i
$37$	−1.84876	+	6.89966i	−0.303934	+	1.13430i	0.629925	+	0.776656i	$0.283086\pi$
$37$	−1.84876	+	6.89966i	−0.303934	+	1.13430i	−0.933859	+	0.357642i	$0.883581\pi$
$38$	−3.18208			−0.516202
$39$	6.02424	+	1.64575i	0.964651	+	0.263531i
$40$		0			0
$41$	−2.36667	+	8.83254i	−0.369612	+	1.37941i	0.491448	+	0.870907i	$0.336468\pi$
$41$	−2.36667	+	8.83254i	−0.369612	+	1.37941i	−0.861060	+	0.508504i	$0.830199\pi$
$42$	−2.03466	−	9.38365i	−0.313955	−	1.44793i
$43$	−0.678803	−	0.391907i	−0.103517	−	0.0597653i	0.447348	−	0.894360i	$-0.352369\pi$
$43$	−0.678803	−	0.391907i	−0.103517	−	0.0597653i	−0.550864	+	0.834595i	$0.685702\pi$
$44$	−0.826939	−	0.826939i	−0.124666	−	0.124666i
$45$		0			0
$46$	6.58176	−	1.76358i	0.970428	−	0.260025i
$47$	6.23046	−	6.23046i	0.908806	−	0.908806i	−0.0873702	−	0.996176i	$-0.527846\pi$
$47$	6.23046	−	6.23046i	0.908806	−	0.908806i	0.996176	+	0.0873702i	$0.0278463\pi$
$48$	5.82078	+	6.41176i	0.840157	+	0.925457i
$49$	2.85745	−	1.64975i	0.408207	−	0.235678i
$50$		0			0
$51$	2.87745	−	8.98056i	0.402924	−	1.25753i
$52$	1.90503	+	2.99188i	0.264180	+	0.414899i
$53$			0.952426i			0.130826i	0.997858	+	0.0654129i	$0.0208365\pi$
$53$			0.952426i			0.130826i	−0.997858	+	0.0654129i	$0.979164\pi$
$54$	3.31901	+	8.33936i	0.451660	+	1.13484i
$55$		0			0
$56$	−2.81686	+	4.87895i	−0.376419	+	0.651977i
$57$	1.46017	+	2.83703i	0.193404	+	0.375774i
$58$	3.63553	+	13.5680i	0.477369	+	1.78156i
$59$	2.09784	+	7.82924i	0.273115	+	1.01928i	0.957094	+	0.289778i	$0.0935814\pi$
$59$	2.09784	+	7.82924i	0.273115	+	1.01928i	−0.683979	+	0.729502i	$0.739752\pi$
$60$		0			0
$61$	−6.49787	+	11.2546i	−0.831967	+	1.44101i	0.0645090	+	0.997917i	$0.479452\pi$
$61$	−6.49787	+	11.2546i	−0.831967	+	1.44101i	−0.896476	+	0.443092i	$0.853881\pi$
$62$	0.180828	+	0.313203i	0.0229651	+	0.0397768i
$63$	−7.43249	+	6.11993i	−0.936405	+	0.771039i
$64$		−	1.14613i		−	0.143267i
$65$		0			0
$66$	−1.08526	+	3.38712i	−0.133587	+	0.416926i
$67$	−2.29493	−	0.614925i	−0.280370	−	0.0751250i	0.115894	−	0.993262i	$-0.463027\pi$
$67$	−2.29493	−	0.614925i	−0.280370	−	0.0751250i	−0.396264	+	0.918137i	$0.629693\pi$
$68$	4.63844	−	2.67800i	0.562493	−	0.324756i
$69$	−4.59254	−	5.05881i	−0.552876	−	0.609009i
$70$		0			0
$71$	1.72575	−	0.462414i	0.204809	−	0.0548784i	−0.154956	−	0.987921i	$-0.549524\pi$
$71$	1.72575	−	0.462414i	0.204809	−	0.0548784i	0.359765	+	0.933043i	$0.382857\pi$
$72$	1.84705	−	4.93181i	0.217677	−	0.581219i
$73$	−9.70845	−	9.70845i	−1.13629	−	1.13629i	−0.989110	−	0.147177i	$-0.952981\pi$
$73$	−9.70845	−	9.70845i	−1.13629	−	1.13629i	−0.147177	−	0.989110i	$-0.547019\pi$
$74$	10.6855	+	6.16928i	1.24216	+	0.717164i
$75$		0			0
$76$	−0.469034	+	1.75046i	−0.0538019	+	0.200792i
$77$	−3.81522			−0.434785
$78$	5.43918	−	9.31563i	0.615866	−	1.05479i
$79$	0.0854873			0.00961807			0.00480903	−	0.999988i	$-0.498469\pi$
$79$	0.0854873			0.00961807			0.00480903	+	0.999988i	$0.498469\pi$
$80$		0			0
$81$	5.91208	−	6.78582i	0.656897	−	0.753980i
$82$	13.6789	+	7.89754i	1.51059	+	0.872137i
$83$	4.49219	+	4.49219i	0.493082	+	0.493082i	0.909276	−	0.416194i	$-0.136636\pi$
$83$	4.49219	+	4.49219i	0.493082	+	0.493082i	−0.416194	+	0.909276i	$0.636636\pi$
$84$	−5.46185	−	0.263872i	−0.595936	−	0.0287908i
$85$		0			0
$86$	−0.957366	+	0.957366i	−0.103235	+	0.103235i
$87$	10.4285	−	9.46729i	1.11805	−	1.01500i
$88$	1.80730	−	1.04344i	0.192659	−	0.111232i
$89$	−5.10951	−	1.36909i	−0.541607	−	0.145123i	−0.0223639	−	0.999750i	$-0.507119\pi$
$89$	−5.10951	−	1.36909i	−0.541607	−	0.145123i	−0.519243	+	0.854627i	$0.673786\pi$
$90$		0			0
$91$	11.2963	+	2.50718i	1.18418	+	0.262824i
$92$		−	3.88057i		−	0.404578i
$93$	0.196264	−	0.304940i	0.0203516	−	0.0316208i
$94$	−7.61001	−	13.1809i	−0.784912	−	1.35951i
$95$		0			0
$96$	7.89332	−	4.06255i	0.805609	−	0.414633i
$97$	0.498193	+	1.85928i	0.0505838	+	0.188781i	0.986595	−	0.163190i	$-0.0521782\pi$
$97$	0.498193	+	1.85928i	0.0505838	+	0.188781i	−0.936011	+	0.351971i	$0.885512\pi$
$98$	−1.47511	−	5.50517i	−0.149008	−	0.556107i
$99$	3.51784	−	0.586675i	0.353556	−	0.0589630i
$100$		0			0
$101$	−5.91840	−	10.2510i	−0.588903	−	1.02001i	−0.994377	−	0.105903i	$-0.966227\pi$
$101$	−5.91840	−	10.2510i	−0.588903	−	1.02001i	0.405474	−	0.914107i	$-0.367107\pi$
$102$	−13.6976	−	8.81594i	−1.35626	−	0.872908i
$103$			6.77628i			0.667686i	0.942629	+	0.333843i	$0.108346\pi$
$103$			6.77628i			0.667686i	−0.942629	+	0.333843i	$0.891654\pi$
$104$	−6.03687	+	1.90183i	−0.591964	+	0.186489i
$105$		0			0
$106$	1.58911	+	0.425802i	0.154348	+	0.0413575i
$107$	4.52298	−	2.61134i	0.437253	−	0.252448i	−0.265179	−	0.964199i	$-0.585431\pi$
$107$	4.52298	−	2.61134i	0.437253	−	0.252448i	0.702432	+	0.711751i	$0.252098\pi$
$108$	5.07669	−	0.596576i	0.488505	−	0.0574055i
$109$	1.57960	−	1.57960i	0.151298	−	0.151298i	−0.627399	−	0.778698i	$-0.715881\pi$
$109$	1.57960	−	1.57960i	0.151298	−	0.151298i	0.778698	+	0.627399i	$0.215881\pi$
$110$		0			0
$111$	0.597026	−	12.3577i	0.0566672	−	1.17294i
$112$	11.3459	+	11.3459i	1.07209	+	1.07209i
$113$	−4.05939	−	2.34369i	−0.381875	−	0.220476i	0.296759	−	0.954953i	$-0.404094\pi$
$113$	−4.05939	−	2.34369i	−0.381875	−	0.220476i	−0.678634	+	0.734477i	$0.737428\pi$
$114$	5.38636	−	1.16793i	0.504479	−	0.109386i
$115$		0			0
$116$	7.99961			0.742745
$117$	−10.8014	−	0.574694i	−0.998588	−	0.0531305i
$118$	14.0009			1.28889
$119$	4.52239	−	16.8778i	0.414567	−	1.54718i
$120$		0			0
$121$	−8.30236	−	4.79337i	−0.754760	−	0.435761i
$122$	15.8733	+	15.8733i	1.43710	+	1.43710i
$123$	0.764277	−	15.8196i	0.0689125	−	1.42641i
$124$	0.198946	−	0.0533075i	0.0178659	−	0.00478715i
$125$		0			0
$126$	6.88821	+	15.1371i	0.613650	+	1.34852i
$127$	13.7710	−	7.95071i	1.22198	−	0.705512i	0.256642	−	0.966507i	$-0.417384\pi$
$127$	13.7710	−	7.95071i	1.22198	−	0.705512i	0.965340	+	0.260995i	$0.0840506\pi$
$128$	−11.8138	−	3.16550i	−1.04420	−	0.279793i
$129$	1.29286	+	0.414245i	0.113830	+	0.0364722i
$130$		0			0
$131$		−	2.54531i		−	0.222385i	−0.993799	−	0.111192i	$-0.964533\pi$
$131$		−	2.54531i		−	0.222385i	0.993799	−	0.111192i	$-0.0354670\pi$
$132$	1.70329	+	1.09626i	0.148252	+	0.0954172i
$133$	2.95603	+	5.12000i	0.256321	+	0.443960i
$134$	−2.05199	+	3.55415i	−0.177265	+	0.307032i
$135$		0			0
$136$	2.47370	+	9.23199i	0.212118	+	0.791637i
$137$	−0.986463	−	3.68153i	−0.0842792	−	0.314534i	0.910898	−	0.412633i	$-0.135391\pi$
$137$	−0.986463	−	3.68153i	−0.0842792	−	0.314534i	−0.995177	+	0.0980984i	$0.968724\pi$
$138$	−10.4938	+	5.40096i	−0.893289	+	0.459760i
$139$	−10.0439	+	17.3966i	−0.851915	+	1.47556i	0.0275635	+	0.999620i	$0.491225\pi$
$139$	−10.0439	+	17.3966i	−0.851915	+	1.47556i	−0.879478	+	0.475939i	$0.842108\pi$
$140$		0			0
$141$	−8.25962	+	12.8332i	−0.695585	+	1.08075i
$142$		−	3.08613i		−	0.258982i
$143$	−3.15950	−	2.89654i	−0.264211	−	0.242221i
$144$	−12.2062	−	8.71687i	−1.01719	−	0.726406i
$145$		0			0
$146$	−20.5388	+	11.8581i	−1.69980	+	0.981382i
$147$	−4.23133	+	3.84133i	−0.348995	+	0.316827i
$148$	4.96874	−	4.96874i	0.408428	−	0.408428i
$149$	−2.43030	+	0.651196i	−0.199098	+	0.0533481i	−0.356990	−	0.934108i	$-0.616197\pi$
$149$	−2.43030	+	0.651196i	−0.199098	+	0.0533481i	0.157892	+	0.987456i	$0.449530\pi$
$150$		0			0
$151$	−13.6575	−	13.6575i	−1.11143	−	1.11143i	−0.992957	−	0.118477i	$-0.962199\pi$
$151$	−13.6575	−	13.6575i	−1.11143	−	1.11143i	−0.118477	−	0.992957i	$-0.537801\pi$
$152$	−2.80059	−	1.61692i	−0.227158	−	0.131150i
$153$	−1.57455	+	16.2576i	−0.127295	+	1.31435i
$154$	−1.70567	+	6.36566i	−0.137447	+	0.512959i
$155$		0			0
$156$	−4.32279	−	4.36520i	−0.346100	−	0.349496i
$157$	5.38756			0.429974			0.214987	−	0.976617i	$-0.431029\pi$
$157$	5.38756			0.429974			0.214987	+	0.976617i	$0.431029\pi$
$158$	0.0382189	−	0.142635i	0.00304053	−	0.0113474i
$159$	−0.349571	−	1.61219i	−0.0277228	−	0.127855i
$160$		0			0
$161$	−8.95182	−	8.95182i	−0.705503	−	0.705503i
$162$	−8.67896	−	12.8980i	−0.681883	−	1.01336i
$163$	12.0398	−	3.22604i	0.943027	−	0.252683i	0.245626	−	0.969365i	$-0.421007\pi$
$163$	12.0398	−	3.22604i	0.943027	−	0.252683i	0.697401	+	0.716681i	$0.254340\pi$
$164$	6.36068	−	6.36068i	0.496686	−	0.496686i
$165$		0			0
$166$	9.50350	−	5.48685i	0.737615	−	0.425862i
$167$	−10.1406	−	2.71716i	−0.784702	−	0.210260i	−0.155845	−	0.987781i	$-0.549810\pi$
$167$	−10.1406	−	2.71716i	−0.784702	−	0.210260i	−0.628857	+	0.777521i	$0.716477\pi$
$168$	2.97742	−	9.29256i	0.229713	−	0.716936i
$169$	7.45138	+	10.6526i	0.573183	+	0.819427i
$170$		0			0
$171$	−3.51293	−	4.26636i	−0.268641	−	0.326257i
$172$	0.385532	+	0.667761i	0.0293965	+	0.0509163i
$173$	−8.41484	+	14.5749i	−0.639768	+	1.10811i	0.345715	+	0.938340i	$0.387636\pi$
$173$	−8.41484	+	14.5749i	−0.639768	+	1.10811i	−0.985483	+	0.169772i	$0.945697\pi$
$174$	−11.1338	−	21.6324i	−0.844052	−	1.63995i
$175$		0			0
$176$	−1.53835	−	5.74120i	−0.115957	−	0.432759i
$177$	−6.42462	−	12.4827i	−0.482904	−	0.938257i
$178$	−4.56862	+	7.91308i	−0.342433	+	0.593111i
$179$	−9.06243	−	15.6966i	−0.677358	−	1.17322i	−0.975774	−	0.218783i	$-0.929791\pi$
$179$	−9.06243	−	15.6966i	−0.677358	−	1.17322i	0.298415	−	0.954436i	$-0.403542\pi$
$180$		0			0
$181$		−	0.330859i		−	0.0245925i	−0.999924	−	0.0122963i	$-0.996086\pi$
$181$		−	0.330859i		−	0.0245925i	0.999924	−	0.0122963i	$-0.00391412\pi$
$182$	9.23348	−	17.7270i	0.684431	−	1.31401i
$183$	6.86823	−	21.4358i	0.507714	−	1.58458i
$184$	6.68883	+	1.79227i	0.493107	+	0.132128i
$185$		0			0
$186$	−0.421045	−	0.463793i	−0.0308725	−	0.0340070i
$187$	−4.57678	+	4.57678i	−0.334688	+	0.334688i
$188$	−8.37252	+	2.24341i	−0.610628	+	0.163617i
$189$	10.3349	−	13.0873i	0.751751	−	0.951959i
$190$		0			0
$191$	10.9457	+	6.31949i	0.792001	+	0.457262i	0.840667	−	0.541553i	$-0.182163\pi$
$191$	10.9457	+	6.31949i	0.792001	+	0.457262i	−0.0486655	+	0.998815i	$0.515497\pi$
$192$	0.420668	+	1.94008i	0.0303591	+	0.140013i
$193$	1.74154	−	6.49950i	0.125359	−	0.467845i	−0.874494	−	0.485037i	$-0.838806\pi$
$193$	1.74154	−	6.49950i	0.125359	−	0.467845i	0.999852	+	0.0171925i	$0.00547280\pi$
$194$	3.32492			0.238715
$195$		0			0
$196$	−3.24582			−0.231844
$197$	−4.25210	+	15.8690i	−0.302949	+	1.13062i	0.631747	+	0.775175i	$0.282338\pi$
$197$	−4.25210	+	15.8690i	−0.302949	+	1.13062i	−0.934696	+	0.355447i	$0.884328\pi$
$198$	0.593861	−	6.13176i	0.0422039	−	0.435765i
$199$	−6.32168	−	3.64982i	−0.448132	−	0.258729i	0.258909	−	0.965902i	$-0.416637\pi$
$199$	−6.32168	−	3.64982i	−0.448132	−	0.258729i	−0.707041	+	0.707173i	$0.749970\pi$
$200$		0			0
$201$	4.11036	+	0.198580i	0.289923	+	0.0140067i
$202$	−19.7496	+	5.29188i	−1.38958	+	0.372336i
$203$	18.4538	−	18.4538i	1.29520	−	1.29520i
$204$	−6.86864	+	6.23555i	−0.480901	+	0.436576i
$205$		0			0
$206$	11.3062	+	3.02948i	0.787737	+	0.211074i
$207$	9.63061	+	6.87752i	0.669373	+	0.478021i
$208$	0.781997	+	18.0098i	0.0542217	+	1.24876i
$209$		−	2.18999i		−	0.151485i
$210$		0			0
$211$	−13.1703	−	22.8117i	−0.906684	−	1.57042i	−0.818641	−	0.574305i	$-0.805272\pi$
$211$	−13.1703	−	22.8117i	−0.906684	−	1.57042i	−0.0880423	−	0.996117i	$-0.528061\pi$
$212$	0.468467	−	0.811408i	0.0321744	−	0.0557277i
$213$	−2.75149	+	1.41614i	−0.188529	+	0.0970324i
$214$	−2.33491	−	8.71401i	−0.159611	−	0.595677i
$215$		0			0
$216$	−1.31640	+	9.02608i	−0.0895698	+	0.614147i
$217$	0.335964	−	0.581907i	0.0228067	−	0.0395024i
$218$	−1.92936	−	3.34174i	−0.130672	−	0.226331i
$219$	19.9970	+	12.8703i	1.35127	+	0.869696i
$220$		0			0
$221$	16.5589	−	10.5436i	1.11387	−	0.709238i
$222$	−20.3518	−	6.52091i	−1.36593	−	0.437655i
$223$	−3.29955	−	0.884112i	−0.220954	−	0.0592045i	0.146643	−	0.989189i	$-0.453153\pi$
$223$	−3.29955	−	0.884112i	−0.220954	−	0.0592045i	−0.367598	+	0.929985i	$0.619820\pi$
$224$	14.2451	−	8.22441i	0.951791	−	0.549517i
$225$		0			0
$226$	−5.72526	+	5.72526i	−0.380838	+	0.380838i
$227$	−11.8793	+	3.18305i	−0.788456	+	0.211266i	−0.630510	−	0.776181i	$-0.717154\pi$
$227$	−11.8793	+	3.18305i	−0.788456	+	0.211266i	−0.157947	+	0.987448i	$0.550487\pi$
$228$	0.151467	−	3.13518i	0.0100311	−	0.207633i
$229$	−4.45823	−	4.45823i	−0.294608	−	0.294608i	0.544289	−	0.838898i	$-0.316799\pi$
$229$	−4.45823	−	4.45823i	−0.294608	−	0.294608i	−0.838898	+	0.544289i	$0.816799\pi$
$230$		0			0
$231$	6.45808	−	1.40031i	0.424911	−	0.0921335i
$232$	−3.69467	+	13.7887i	−0.242567	+	0.905273i
$233$	7.44279			0.487594			0.243797	−	0.969826i	$-0.421607\pi$
$233$	7.44279			0.487594			0.243797	+	0.969826i	$0.421607\pi$
$234$	−5.78785	+	17.7651i	−0.378364	+	1.16134i
$235$		0			0
$236$	2.06371	−	7.70188i	0.134336	−	0.501349i
$237$	−0.144706	+	0.0313766i	−0.00939964	+	0.00203813i
$238$	−26.1386	−	15.0911i	−1.69431	−	0.978213i
$239$	13.3710	+	13.3710i	0.864899	+	0.864899i	0.991902	−	0.127003i	$-0.0405358\pi$
$239$	13.3710	+	13.3710i	0.864899	+	0.864899i	−0.127003	+	0.991902i	$0.540536\pi$
$240$		0			0
$241$	28.0098	−	7.50522i	1.80427	−	0.483453i	0.809640	−	0.586926i	$-0.199662\pi$
$241$	28.0098	−	7.50522i	1.80427	−	0.483453i	0.994632	+	0.103473i	$0.0329955\pi$
$242$	−11.7094	+	11.7094i	−0.752711	+	0.752711i
$243$	−7.51685	+	13.6564i	−0.482206	+	0.876058i
$244$	11.0716	−	6.39217i	0.708784	−	0.409217i
$245$		0			0
$246$	−26.0532	−	8.34768i	−1.66109	−	0.532228i
$247$	−1.43916	+	6.48427i	−0.0915716	+	0.412584i
$248$			0.367538i			0.0233387i
$249$	−9.25278	−	5.95522i	−0.586371	−	0.377397i
$250$		0			0
$251$	12.0103	−	20.8025i	0.758085	−	1.31304i	−0.185741	−	0.982599i	$-0.559468\pi$
$251$	12.0103	−	20.8025i	0.758085	−	1.31304i	0.943826	−	0.330443i	$-0.107198\pi$
$252$	9.34221	−	1.55801i	0.588504	−	0.0981456i
$253$	1.21374	+	4.52975i	0.0763073	+	0.284783i
$254$	−7.10906	−	26.5314i	−0.446062	−	1.66473i
$255$		0			0
$256$	−9.41708	+	16.3109i	−0.588568	+	1.01943i
$257$	3.23213	+	5.59821i	0.201615	+	0.349207i	0.949049	−	0.315129i	$-0.102048\pi$
$257$	3.23213	+	5.59821i	0.201615	+	0.349207i	−0.747434	+	0.664336i	$0.768714\pi$
$258$	1.26917	−	1.97193i	0.0790148	−	0.122767i
$259$		−	22.9241i		−	1.42443i
$260$		0			0
$261$	−14.1777	+	19.8530i	−0.877576	+	1.22887i
$262$	−4.24682	−	1.13793i	−0.262370	−	0.0703018i
$263$	−13.8940	+	8.02170i	−0.856740	+	0.494639i	−0.862919	−	0.505342i	$-0.831366\pi$
$263$	−13.8940	+	8.02170i	−0.856740	+	0.494639i	0.00617933	+	0.999981i	$0.498033\pi$
$264$	−2.67627	+	2.42959i	−0.164713	+	0.149531i
$265$		0			0
$266$	9.86422	−	2.64311i	0.604814	−	0.162060i
$267$	9.15144	+	0.442124i	0.560059	+	0.0270575i
$268$	1.65268	+	1.65268i	0.100953	+	0.100953i
$269$	−9.95173	−	5.74563i	−0.606767	−	0.350317i	0.164932	−	0.986305i	$-0.447260\pi$
$269$	−9.95173	−	5.74563i	−0.606767	−	0.350317i	−0.771699	+	0.635988i	$0.780593\pi$
$270$		0			0
$271$	−3.04037	+	11.3468i	−0.184690	+	0.689271i	0.810007	+	0.586420i	$0.199463\pi$
$271$	−3.04037	+	11.3468i	−0.184690	+	0.689271i	−0.994697	+	0.102851i	$0.967204\pi$
$272$	27.2214			1.65054
$273$	−20.0417	−	0.0978270i	−1.21298	−	0.00592076i
$274$	−6.58362			−0.397731
$275$		0			0
$276$	1.42430	+	6.56871i	0.0857325	+	0.395390i
$277$	−17.1100	−	9.87847i	−1.02804	−	0.593540i	−0.111618	−	0.993751i	$-0.535603\pi$
$277$	−17.1100	−	9.87847i	−1.02804	−	0.593540i	−0.916423	+	0.400211i	$0.868937\pi$
$278$	24.5357	+	24.5357i	1.47155	+	1.47155i
$279$	−0.220296	+	0.588211i	−0.0131888	+	0.0352153i
$280$		0			0
$281$	1.76652	−	1.76652i	0.105382	−	0.105382i	−0.652450	−	0.757832i	$-0.726259\pi$
$281$	1.76652	−	1.76652i	0.105382	−	0.105382i	0.757832	+	0.652450i	$0.226259\pi$
$282$	17.7194	+	19.5184i	1.05517	+	1.16231i
$283$	6.29734	−	3.63577i	0.374338	−	0.216124i	−0.301014	−	0.953620i	$-0.597325\pi$
$283$	6.29734	−	3.63577i	0.374338	−	0.216124i	0.675352	+	0.737496i	$0.263992\pi$
$284$	−1.69768	−	0.454891i	−0.100739	−	0.0269928i
$285$		0			0
$286$	−6.24538	+	3.97664i	−0.369297	+	0.235144i
$287$		−	29.3460i		−	1.73224i
$288$	−11.8701	+	9.77385i	−0.699450	+	0.575930i
$289$	−6.32169	−	10.9495i	−0.371864	−	0.644087i
$290$		0			0
$291$	−1.52571	−	2.96438i	−0.0894390	−	0.173775i
$292$	3.49573	+	13.0462i	0.204572	+	0.763474i
$293$	0.545330	+	2.03520i	0.0318585	+	0.118898i	0.980024	−	0.198880i	$-0.0637303\pi$
$293$	0.545330	+	2.03520i	0.0318585	+	0.118898i	−0.948165	+	0.317777i	$0.897064\pi$
$294$	4.51751	+	8.77729i	0.263467	+	0.511902i
$295$		0			0
$296$	6.26963	+	10.8593i	0.364415	+	0.631185i
$297$	−5.73937	+	2.28423i	−0.333032	+	0.132545i
$298$			4.34606i			0.251760i
$299$	−0.616988	−	14.2096i	−0.0356813	−	0.821761i
$300$		0			0
$301$	2.42977	+	0.651055i	0.140050	+	0.0375262i
$302$	−28.8933	+	16.6816i	−1.66262	+	0.959917i
$303$	13.7806	+	15.1797i	0.791675	+	0.872053i
$304$	−6.51273	+	6.51273i	−0.373531	+	0.373531i
$305$		0			0
$306$	26.4218	+	9.89544i	1.51043	+	0.565685i
$307$	9.18929	+	9.18929i	0.524461	+	0.524461i	0.918915	−	0.394455i	$-0.129066\pi$
$307$	9.18929	+	9.18929i	0.524461	+	0.524461i	−0.394455	+	0.918915i	$0.629066\pi$
$308$	3.25033	+	1.87658i	0.185205	+	0.106928i
$309$	−2.48711	−	11.4703i	−0.141487	−	0.652523i
$310$		0			0
$311$	−12.7422			−0.722542			−0.361271	−	0.932461i	$-0.617657\pi$
$311$	−12.7422			−0.722542			−0.361271	+	0.932461i	$0.617657\pi$
$312$	9.52068	−	5.43498i	0.539002	−	0.307695i
$313$	−25.4351			−1.43768			−0.718838	−	0.695178i	$-0.755326\pi$
$313$	−25.4351			−1.43768			−0.718838	+	0.695178i	$0.755326\pi$
$314$	2.40862	−	8.98909i	0.135926	−	0.507284i
$315$		0			0
$316$	−0.0728298	−	0.0420483i	−0.00409700	−	0.00236540i
$317$	3.36120	+	3.36120i	0.188784	+	0.188784i	0.795170	−	0.606386i	$-0.207382\pi$
$317$	3.36120	+	3.36120i	0.188784	+	0.188784i	−0.606386	+	0.795170i	$0.707382\pi$
$318$	−2.84620	−	0.137506i	−0.159607	−	0.00771093i
$319$	−9.33785	+	2.50207i	−0.522819	+	0.140089i
$320$		0			0
$321$	−6.69767	+	6.08034i	−0.373828	+	0.339372i
$322$	−18.9381	+	10.9339i	−1.05538	+	0.609324i
$323$	9.68810	+	2.59592i	0.539061	+	0.144441i
$324$	−8.37444	+	2.87314i	−0.465247	+	0.159619i
$325$		0			0
$326$		−	21.5305i		−	1.19246i
$327$	−2.09405	+	3.25358i	−0.115801	+	0.179923i
$328$	8.02601	+	13.9015i	0.443162	+	0.767579i
$329$	−14.1388	+	24.4891i	−0.779498	+	1.35013i
$330$		0			0
$331$	5.30136	+	19.7850i	0.291389	+	1.08748i	0.944043	+	0.329823i	$0.106989\pi$
$331$	5.30136	+	19.7850i	0.291389	+	1.08748i	−0.652653	+	0.757657i	$0.726344\pi$
$332$	−1.61751	−	6.03662i	−0.0887723	−	0.331303i
$333$	3.52509	+	21.1372i	0.193174	+	1.15831i
$334$	−9.06712	+	15.7047i	−0.496131	+	0.859324i
$335$		0			0
$336$	−23.3698	−	15.0411i	−1.27492	−	0.820560i
$337$		−	23.0073i		−	1.25329i	−0.779305	−	0.626644i	$-0.784428\pi$
$337$		−	23.0073i		−	1.25329i	0.779305	−	0.626644i	$-0.215572\pi$
$338$	21.1050	−	7.67012i	1.14796	−	0.417199i
$339$	7.73160	+	2.47727i	0.419923	+	0.134547i
$340$		0			0
$341$	−0.215554	+	0.124450i	−0.0116729	+	0.00673937i
$342$	−8.68891	+	3.95393i	−0.469842	+	0.213804i
$343$	8.39758	−	8.39758i	0.453427	−	0.453427i
$344$	−1.32906	+	0.356121i	−0.0716581	+	0.0192007i
$345$		0			0
$346$	20.5561	+	20.5561i	1.10510	+	1.10510i
$347$	−4.34312	−	2.50750i	−0.233151	−	0.134610i	0.378874	−	0.925448i	$-0.376311\pi$
$347$	−4.34312	−	2.50750i	−0.233151	−	0.134610i	−0.612025	+	0.790839i	$0.709645\pi$
$348$	−13.5411	+	2.93612i	−0.725878	+	0.157392i
$349$	−0.823955	+	3.07504i	−0.0441053	+	0.164603i	−0.984466	−	0.175576i	$-0.943821\pi$
$349$	−0.823955	+	3.07504i	−0.0441053	+	0.164603i	0.940361	+	0.340179i	$0.110488\pi$
$350$		0			0
$351$	18.4946	−	2.99166i	0.987168	−	0.159683i
$352$	−6.09310			−0.324763
$353$	1.36681	−	5.10099i	0.0727477	−	0.271498i	−0.919965	−	0.391999i	$-0.871784\pi$
$353$	1.36681	−	5.10099i	0.0727477	−	0.271498i	0.992713	+	0.120501i	$0.0384502\pi$
$354$	−23.6995	+	5.13878i	−1.25962	+	0.273123i
$355$		0			0
$356$	3.67957	+	3.67957i	0.195017	+	0.195017i
$357$	−1.46043	+	30.2292i	−0.0772941	+	1.59990i
$358$	−30.2412	+	8.10310i	−1.59830	+	0.428262i
$359$	14.4070	−	14.4070i	0.760371	−	0.760371i	−0.216018	−	0.976389i	$-0.569307\pi$
$359$	14.4070	−	14.4070i	0.760371	−	0.760371i	0.976389	+	0.216018i	$0.0693070\pi$
$360$		0			0
$361$	13.5155	−	7.80319i	0.711344	−	0.410694i
$362$	−0.552035	−	0.147917i	−0.0290143	−	0.00777436i
$363$	15.8129	+	5.06658i	0.829960	+	0.265926i
$364$	−8.39058	−	7.69226i	−0.439786	−	0.403184i
$365$		0			0
$366$	−32.6949	−	21.0429i	−1.70899	−	1.09993i
$367$	6.81696	+	11.8073i	0.355842	+	0.616337i	0.987262	−	0.159105i	$-0.0508607\pi$
$367$	6.81696	+	11.8073i	0.355842	+	0.616337i	−0.631420	+	0.775441i	$0.717527\pi$
$368$	9.86133	−	17.0803i	0.514058	−	0.890374i
$369$	4.51261	+	27.0586i	0.234917	+	1.40862i
$370$		0			0
$371$	−0.791108	−	2.95245i	−0.0410723	−	0.153284i
$372$	−0.317194	+	0.163254i	−0.0164457	+	0.00846433i
$373$	12.6759	−	21.9554i	0.656335	−	1.13681i	−0.325222	−	0.945638i	$-0.605439\pi$
$373$	12.6759	−	21.9554i	0.656335	−	1.13681i	0.981557	−	0.191169i	$-0.0612277\pi$
$374$	5.59017	+	9.68247i	0.289061	+	0.500668i
$375$		0			0
$376$		−	15.4676i		−	0.797680i
$377$	29.2924	−	1.27189i	1.50863	−	0.0655057i
$378$	−17.2156	−	23.0946i	−0.885473	−	1.18786i
$379$	25.2089	+	6.75470i	1.29489	+	0.346966i	0.839517	−	0.543333i	$-0.182838\pi$
$379$	25.2089	+	6.75470i	1.29489	+	0.346966i	0.455376	+	0.890299i	$0.349505\pi$
$380$		0			0
$381$	−20.3923	+	18.5127i	−1.04473	+	0.948435i
$382$	15.4375	−	15.4375i	0.789851	−	0.789851i
$383$	−12.5724	+	3.36875i	−0.642417	+	0.172135i	−0.565298	−	0.824887i	$-0.691239\pi$
$383$	−12.5724	+	3.36875i	−0.642417	+	0.172135i	−0.0771191	+	0.997022i	$0.524572\pi$
$384$	21.1593	+	1.02225i	1.07978	+	0.0521662i
$385$		0			0
$386$	−10.0658	−	5.81148i	−0.512334	−	0.295796i
$387$	−2.34049	−	0.226676i	−0.118974	−	0.0115226i
$388$	0.490089	−	1.82904i	0.0248805	−	0.0928552i
$389$	−18.8047			−0.953438			−0.476719	−	0.879056i	$-0.658174\pi$
$389$	−18.8047			−0.953438			−0.476719	+	0.879056i	$0.658174\pi$
$390$		0			0
$391$	−21.4774			−1.08616
$392$	1.49910	−	5.59473i	0.0757161	−	0.282576i
$393$	0.934211	+	4.30849i	0.0471247	+	0.217334i
$394$	24.5764	+	14.1892i	1.23814	+	0.714840i
$395$		0			0
$396$	−3.28554	−	1.23050i	−0.165105	−	0.0618348i
$397$	8.97652	−	2.40525i	0.450519	−	0.120716i	−0.0264234	−	0.999651i	$-0.508412\pi$
$397$	8.97652	−	2.40525i	0.450519	−	0.120716i	0.476942	+	0.878935i	$0.341745\pi$
$398$	−8.91594	+	8.91594i	−0.446916	+	0.446916i
$399$	−6.88293	−	7.58174i	−0.344577	−	0.379562i
$400$		0			0
$401$	24.4394	+	6.54850i	1.22044	+	0.327017i	0.810851	−	0.585252i	$-0.199005\pi$
$401$	24.4394	+	6.54850i	1.22044	+	0.327017i	0.409592	+	0.912269i	$0.365671\pi$
$402$	2.16895	−	6.76932i	0.108177	−	0.337623i
$403$	0.720010	−	0.226828i	0.0358663	−	0.0112991i
$404$			11.6442i			0.579323i
$405$		0			0
$406$	−22.5398	−	39.0400i	−1.11863	−	1.93752i
$407$	−4.24586	+	7.35405i	−0.210459	+	0.364527i
$408$	−7.57572	−	14.7192i	−0.375054	−	0.728710i
$409$	2.15574	+	8.04533i	0.106595	+	0.397816i	0.998521	−	0.0543639i	$-0.0173131\pi$
$409$	2.15574	+	8.04533i	0.106595	+	0.397816i	−0.891927	+	0.452180i	$0.850646\pi$
$410$		0			0
$411$	3.02104	+	5.86972i	0.149017	+	0.289532i
$412$	3.33302	−	5.77297i	0.164206	−	0.284414i
$413$	−13.0063	−	22.5276i	−0.639998	−	1.10851i
$414$	15.7806	−	12.9938i	0.775576	−	0.638612i
$415$		0			0
$416$	18.0409	+	4.00410i	0.884526	+	0.196317i
$417$	10.6164	−	33.1339i	0.519888	−	1.62258i
$418$	−3.65398	−	0.979082i	−0.178722	−	0.0478885i
$419$	−1.31380	+	0.758522i	−0.0641833	+	0.0370562i	−0.531748	−	0.846902i	$-0.678465\pi$
$419$	−1.31380	+	0.758522i	−0.0641833	+	0.0370562i	0.467565	+	0.883959i	$0.345131\pi$
$420$		0			0
$421$	−12.6589	+	12.6589i	−0.616955	+	0.616955i	−0.944749	−	0.327794i	$-0.893695\pi$
$421$	−12.6589	+	12.6589i	−0.616955	+	0.616955i	0.327794	+	0.944749i	$0.393695\pi$
$422$	−43.9492	+	11.7761i	−2.13941	+	0.573254i
$423$	9.27100	−	24.7545i	0.450771	−	1.20360i
$424$	1.18224	+	1.18224i	0.0574145	+	0.0574145i
$425$		0			0
$426$	1.13271	+	5.22394i	0.0548799	+	0.253101i
$427$	10.7946	−	40.2859i	0.522386	−	1.94957i
$428$	−5.13773			−0.248342
$429$	6.41126	+	3.74339i	0.309539	+	0.180733i
$430$		0			0
$431$	2.61881	−	9.77353i	0.126144	−	0.470775i	−0.873734	−	0.486404i	$-0.838308\pi$
$431$	2.61881	−	9.77353i	0.126144	−	0.470775i	0.999878	+	0.0156291i	$0.00497511\pi$
$432$	23.8611	+	10.2751i	1.14802	+	0.494361i
$433$	31.8042	+	18.3621i	1.52841	+	0.882428i	0.999429	+	0.0337954i	$0.0107595\pi$
$433$	31.8042	+	18.3621i	1.52841	+	0.882428i	0.528982	+	0.848633i	$0.322574\pi$
$434$	−0.820706	−	0.820706i	−0.0393952	−	0.0393952i
$435$		0			0
$436$	−2.12267	+	0.568769i	−0.101658	+	0.0272391i
$437$	5.13848	−	5.13848i	0.245807	−	0.245807i
$438$	30.4141	−	27.6108i	1.45324	−	1.31929i
$439$	−5.63717	+	3.25462i	−0.269048	+	0.155335i	−0.628455	−	0.777846i	$-0.716312\pi$
$439$	−5.63717	+	3.25462i	−0.269048	+	0.155335i	0.359407	+	0.933181i	$0.382979\pi$
$440$		0			0
$441$	5.75256	−	8.05531i	0.273931	−	0.383586i
$442$	−10.1889	−	32.3421i	−0.484636	−	1.53836i
$443$			17.2761i			0.820814i	0.911902	+	0.410407i	$0.134613\pi$
$443$			17.2761i			0.820814i	−0.911902	+	0.410407i	$0.865387\pi$
$444$	−6.58698	+	10.2344i	−0.312604	+	0.485701i
$445$		0			0
$446$	−2.95026	+	5.11001i	−0.139699	+	0.241966i
$447$	3.87479	−	1.99429i	0.183271	−	0.0943266i
$448$	0.952006	+	3.55294i	0.0449781	+	0.167860i
$449$	4.49179	+	16.7636i	0.211980	+	0.791122i	0.987208	+	0.159439i	$0.0509687\pi$
$449$	4.49179	+	16.7636i	0.211980	+	0.791122i	−0.775227	+	0.631682i	$0.782365\pi$
$450$		0			0
$451$	−5.43530	+	9.41421i	−0.255938	+	0.443298i
$452$	2.30556	+	3.99335i	0.108445	+	0.187832i
$453$	28.1311	+	18.1056i	1.32171	+	0.850673i
$454$			21.2435i			0.997008i
$455$		0			0
$456$	5.33407	+	1.70908i	0.249791	+	0.0800351i
$457$	21.1527	+	5.66785i	0.989481	+	0.265131i	0.717033	−	0.697040i	$-0.245500\pi$
$457$	21.1527	+	5.66785i	0.989481	+	0.265131i	0.272449	+	0.962170i	$0.412167\pi$
$458$	−9.43166	+	5.44537i	−0.440713	+	0.254446i
$459$	−3.30181	−	28.0975i	−0.154115	−	1.31148i
$460$		0			0
$461$	−31.4414	+	8.42468i	−1.46437	+	0.392377i	−0.900997	−	0.433826i	$-0.857163\pi$
$461$	−31.4414	+	8.42468i	−1.46437	+	0.392377i	−0.563373	+	0.826203i	$0.690497\pi$
$462$	0.550818	−	11.4013i	0.0256264	−	0.530436i
$463$	3.35500	+	3.35500i	0.155920	+	0.155920i	0.780756	−	0.624836i	$-0.214834\pi$
$463$	3.35500	+	3.35500i	0.155920	+	0.155920i	−0.624836	+	0.780756i	$0.714834\pi$
$464$	35.2103	+	20.3287i	1.63460	+	0.943734i
$465$		0			0
$466$	3.32745	−	12.4182i	0.154141	−	0.575263i
$467$	16.4147			0.759584			0.379792	−	0.925072i	$-0.375996\pi$
$467$	16.4147			0.759584			0.379792	+	0.925072i	$0.375996\pi$
$468$	8.91943	+	5.80244i	0.412301	+	0.268218i
$469$	7.62489			0.352085
$470$		0			0
$471$	−9.11961	+	1.97741i	−0.420209	+	0.0911142i
$472$	12.3224	+	7.11432i	0.567183	+	0.327463i
$473$	−0.658885	−	0.658885i	−0.0302956	−	0.0302956i
$474$	−0.0123421	+	0.255468i	−0.000566893	+	0.0117340i
$475$		0			0
$476$	−12.1544	+	12.1544i	−0.557097	+	0.557097i
$477$	1.18345	+	2.60067i	0.0541864	+	0.119077i
$478$	28.2872	−	16.3316i	1.29383	−	0.746991i
$479$	2.62410	+	0.703124i	0.119898	+	0.0321266i	0.318269	−	0.948000i	$-0.396898\pi$
$479$	2.62410	+	0.703124i	0.119898	+	0.0321266i	−0.198371	+	0.980127i	$0.563565\pi$
$480$		0			0
$481$	17.4042	−	18.9842i	0.793561	−	0.865603i
$482$		−	50.0895i		−	2.28152i
$483$	18.4385	+	11.8673i	0.838981	+	0.539980i
$484$	4.71539	+	8.16730i	0.214336	+	0.371241i
$485$		0			0
$486$	19.4250	+	18.6472i	0.881135	+	0.845853i
$487$	3.56046	+	13.2878i	0.161340	+	0.602129i	0.998479	+	0.0551382i	$0.0175599\pi$
$487$	3.56046	+	13.2878i	0.161340	+	0.602129i	−0.837139	+	0.546990i	$0.815773\pi$
$488$	5.90453	+	22.0360i	0.267285	+	0.997523i
$489$	−19.1958	+	9.87975i	−0.868065	+	0.446778i
$490$		0			0
$491$	9.72844	+	16.8501i	0.439038	+	0.760436i	0.997616	−	0.0690160i	$-0.0219860\pi$
$491$	9.72844	+	16.8501i	0.439038	+	0.760436i	−0.558577	+	0.829452i	$0.688653\pi$
$492$	−8.43226	+	13.1014i	−0.380155	+	0.590657i
$493$		−	44.2747i		−	1.99403i
$494$	10.1755	+	5.30016i	0.457819	+	0.238465i
$495$		0			0
$496$	1.01113	+	0.270931i	0.0454009	+	0.0121651i
$497$	−4.96561	+	2.86690i	−0.222738	+	0.128598i
$498$	−14.0729	+	12.7758i	−0.630621	+	0.572496i
$499$	18.7585	−	18.7585i	0.839745	−	0.839745i	−0.149080	−	0.988825i	$-0.547631\pi$
$499$	18.7585	−	18.7585i	0.839745	−	0.839745i	0.988825	+	0.149080i	$0.0476311\pi$
$500$		0			0
$501$	18.1624	+	0.877462i	0.811437	+	0.0392021i
$502$	−29.3393	−	29.3393i	−1.30948	−	1.30948i
$503$	−34.3040	−	19.8054i	−1.52954	−	0.883081i	−0.999381	−	0.0351832i	$-0.988799\pi$
$503$	−34.3040	−	19.8054i	−1.52954	−	0.883081i	−0.530160	−	0.847898i	$-0.677868\pi$
$504$	−1.62925	+	16.8225i	−0.0725728	+	0.749332i
$505$		0			0
$506$	8.10047			0.360110
$507$	−16.5229	−	15.2969i	−0.733808	−	0.679357i
$508$	−15.6428			−0.694035
$509$	−6.03174	+	22.5108i	−0.267352	+	0.997772i	0.693442	+	0.720512i	$0.256093\pi$
$509$	−6.03174	+	22.5108i	−0.267352	+	0.997772i	−0.960795	+	0.277260i	$0.910574\pi$
$510$		0			0
$511$	38.1596	+	22.0314i	1.68808	+	0.974613i
$512$	5.70780	+	5.70780i	0.252252	+	0.252252i
$513$	7.51229	+	5.93237i	0.331676	+	0.261921i
$514$	10.7856	−	2.88998i	0.475730	−	0.127472i
$515$		0			0
$516$	−0.897686	−	0.988827i	−0.0395184	−	0.0435307i
$517$	9.07146	−	5.23741i	0.398962	−	0.230341i
$518$	−38.2486	−	10.2487i	−1.68055	−	0.450302i
$519$	8.89446	−	27.7597i	0.390424	−	1.21852i
$520$		0			0
$521$			0.498625i			0.0218452i	0.999940	+	0.0109226i	$0.00347683\pi$
$521$			0.498625i			0.0218452i	−0.999940	+	0.0109226i	$0.996523\pi$
$522$	26.7862	+	32.5310i	1.17240	+	1.42384i
$523$	−10.5230	−	18.2263i	−0.460138	−	0.796983i	0.538829	−	0.842415i	$-0.318867\pi$
$523$	−10.5230	−	18.2263i	−0.460138	−	0.796983i	−0.998967	+	0.0454324i	$0.985533\pi$
$524$	−1.25195	+	2.16845i	−0.0546918	+	0.0947290i
$525$		0			0
$526$	7.17253	+	26.7682i	0.312737	+	1.16715i
$527$	−0.295036	−	1.10109i	−0.0128520	−	0.0479642i
$528$	4.71119	+	9.15359i	0.205028	+	0.398359i
$529$	3.71951	−	6.44237i	0.161718	−	0.280103i
$530$		0			0
$531$	15.4566	+	18.7716i	0.670760	+	0.814619i
$532$		−	5.81589i		−	0.252151i
$533$	22.2798	−	24.3024i	0.965043	−	1.05265i
$534$	4.82902	−	15.0714i	0.208972	−	0.652205i
$535$		0			0
$536$	−3.61197	+	2.08537i	−0.156013	+	0.0900744i
$537$	21.1013	+	23.2437i	0.910588	+	1.00304i
$538$	−14.0357	+	14.0357i	−0.605120	+	0.605120i
$539$	3.78881	−	1.01521i	0.163196	−	0.0437281i
$540$		0			0
$541$	−9.37270	−	9.37270i	−0.402964	−	0.402964i	0.476312	−	0.879276i	$-0.341973\pi$
$541$	−9.37270	−	9.37270i	−0.402964	−	0.402964i	−0.879276	+	0.476312i	$0.841973\pi$
$542$	17.5728	+	10.1457i	0.754817	+	0.435794i
$543$	0.121436	+	0.560050i	0.00521131	+	0.0240340i
$544$	7.22249	−	26.9547i	0.309662	−	1.15567i
$545$		0			0
$546$	−9.12329	+	33.3957i	−0.390441	+	1.42920i
$547$	−27.7702			−1.18737			−0.593685	−	0.804698i	$-0.702327\pi$
$547$	−27.7702			−1.18737			−0.593685	+	0.804698i	$0.702327\pi$
$548$	−0.970416	+	3.62164i	−0.0414541	+	0.154709i
$549$	−3.75832	+	38.8057i	−0.160401	+	1.65618i
$550$		0			0
$551$	10.5927	+	10.5927i	0.451266	+	0.451266i
$552$	−11.9801	−	0.578782i	−0.509907	−	0.0246346i
$553$	−0.265004	+	0.0710077i	−0.0112691	+	0.00301956i
$554$	−24.1315	+	24.1315i	−1.02525	+	1.02525i
$555$		0			0
$556$	17.1136	−	9.88054i	0.725778	−	0.419028i
$557$	20.6607	+	5.53600i	0.875420	+	0.234568i	0.668430	−	0.743775i	$-0.266967\pi$
$557$	20.6607	+	5.53600i	0.875420	+	0.234568i	0.206990	+	0.978343i	$0.433633\pi$
$558$	0.882937	+	0.630533i	0.0373777	+	0.0266926i
$559$	1.51788	+	2.38386i	0.0641995	+	0.100826i
$560$		0			0
$561$	6.06737	−	9.42702i	0.256164	−	0.398009i
$562$	−2.15766	−	3.73718i	−0.0910154	−	0.157643i
$563$	0.827364	−	1.43304i	0.0348692	−	0.0603953i	−0.848064	−	0.529894i	$-0.822232\pi$
$563$	0.827364	−	1.43304i	0.0348692	−	0.0603953i	0.882933	+	0.469498i	$0.155565\pi$
$564$	13.3489	−	6.87044i	0.562090	−	0.289298i
$565$		0			0
$566$	−3.25089	−	12.1325i	−0.136645	−	0.509967i
$567$	−12.6906	+	25.9463i	−0.532953	+	1.08964i
$568$	1.56817	−	2.71614i	0.0657988	−	0.113967i
$569$	15.9653	+	27.6527i	0.669300	+	1.15926i	0.978100	+	0.208134i	$0.0667391\pi$
$569$	15.9653	+	27.6527i	0.669300	+	1.15926i	−0.308800	+	0.951127i	$0.599928\pi$
$570$		0			0
$571$		−	2.79633i		−	0.117023i	−0.998287	−	0.0585113i	$-0.981365\pi$
$571$		−	2.79633i		−	0.117023i	0.998287	−	0.0585113i	$-0.0186354\pi$
$572$	1.26699	+	4.02173i	0.0529753	+	0.168157i
$573$	−20.8474	−	6.67968i	−0.870911	−	0.279048i
$574$	−48.9636	−	13.1198i	−2.04370	−	0.547608i
$575$		0			0
$576$	−1.42414	−	3.12961i	−0.0593393	−	0.130400i
$577$	13.0485	−	13.0485i	0.543215	−	0.543215i	−0.381255	−	0.924470i	$-0.624508\pi$
$577$	13.0485	−	13.0485i	0.543215	−	0.543215i	0.924470	+	0.381255i	$0.124508\pi$
$578$	−21.0953	+	5.65248i	−0.877451	+	0.235112i
$579$	−0.562400	+	11.6410i	−0.0233725	+	0.483784i
$580$		0			0
$581$	−17.6568	−	10.1942i	−0.732527	−	0.422925i
$582$	−5.62814	+	1.22035i	−0.233294	+	0.0505852i
$583$	−0.293048	+	1.09367i	−0.0121368	+	0.0452952i
$584$	−24.1020			−0.997347
$585$		0			0
$586$	3.63951			0.150347
$587$	−9.06530	+	33.8321i	−0.374165	+	1.39640i	0.480396	+	0.877052i	$0.340493\pi$
$587$	−9.06530	+	33.8321i	−0.374165	+	1.39640i	−0.854561	+	0.519351i	$0.826174\pi$
$588$	5.49425	−	1.19132i	0.226579	−	0.0491292i
$589$	0.334023	+	0.192848i	0.0137632	+	0.00794618i
$590$		0			0
$591$	1.37314	−	28.4224i	0.0564835	−	1.16914i
$592$	34.4965	−	9.24331i	1.41780	−	0.379898i
$593$	21.8499	−	21.8499i	0.897267	−	0.897267i	−0.0979268	−	0.995194i	$-0.531221\pi$
$593$	21.8499	−	21.8499i	0.897267	−	0.897267i	0.995194	+	0.0979268i	$0.0312211\pi$
$594$	1.24532	+	10.5973i	0.0510960	+	0.434813i
$595$		0			0
$596$	2.39076	+	0.640603i	0.0979295	+	0.0262401i
$597$	12.0404	+	3.85786i	0.492781	+	0.157892i
$598$	−23.9844	−	5.32325i	−0.980795	−	0.217684i
$599$			32.0326i			1.30882i	0.756142	+	0.654408i	$0.227082\pi$
$599$			32.0326i			1.30882i	−0.756142	+	0.654408i	$0.772918\pi$
$600$		0			0
$601$	−1.29184	−	2.23753i	−0.0526953	−	0.0912709i	0.838475	−	0.544941i	$-0.183448\pi$
$601$	−1.29184	−	2.23753i	−0.0526953	−	0.0912709i	−0.891170	+	0.453670i	$0.850115\pi$
$602$	2.17256	−	3.76298i	0.0885468	−	0.153368i
$603$	−7.03056	+	1.17250i	−0.286307	+	0.0477477i
$604$	4.91768	+	18.3530i	0.200098	+	0.746775i
$605$		0			0
$606$	31.4881	−	16.2064i	1.27912	−	0.658340i
$607$	−24.5886	+	42.5887i	−0.998020	+	1.72862i	−0.444540	+	0.895759i	$0.646633\pi$
$607$	−24.5886	+	42.5887i	−0.998020	+	1.72862i	−0.553480	+	0.832862i	$0.686701\pi$
$608$	4.72094	+	8.17690i	0.191459	+	0.331617i
$609$	−24.4638	+	38.0101i	−0.991325	+	1.54025i
$610$		0			0
$611$	−30.3011	+	9.54592i	−1.22585	+	0.386187i
$612$	9.33801	−	13.0760i	0.377467	−	0.528567i
$613$	18.1986	+	4.87630i	0.735035	+	0.196952i	0.606870	−	0.794801i	$-0.292425\pi$
$613$	18.1986	+	4.87630i	0.735035	+	0.196952i	0.128165	+	0.991753i	$0.459091\pi$
$614$	19.4405	−	11.2240i	0.784555	−	0.452963i
$615$		0			0
$616$	−4.73579	+	4.73579i	−0.190810	+	0.190810i
$617$	−15.0853	+	4.04209i	−0.607310	+	0.162728i	−0.549352	−	0.835591i	$-0.685126\pi$
$617$	−15.0853	+	4.04209i	−0.607310	+	0.162728i	−0.0579578	+	0.998319i	$0.518459\pi$
$618$	−20.2500	−	0.978318i	−0.814575	−	0.0393537i
$619$	−30.0941	−	30.0941i	−1.20958	−	1.20958i	−0.971161	−	0.238423i	$-0.923370\pi$
$619$	−30.0941	−	30.0941i	−1.20958	−	1.20958i	−0.238423	−	0.971161i	$-0.576630\pi$
$620$		0			0
$621$	−18.8262	−	8.10695i	−0.755468	−	0.325321i
$622$	−5.69665	+	21.2602i	−0.228415	+	0.852455i
$623$	16.9763			0.680141
$624$	−7.93389	−	30.1985i	−0.317610	−	1.20891i
$625$		0			0
$626$	−11.3713	+	42.4382i	−0.454488	+	1.69617i
$627$	0.803798	+	3.70704i	0.0321006	+	0.148045i
$628$	−4.58987	−	2.64996i	−0.183156	−	0.105745i
$629$	−27.5000	−	27.5000i	−1.09650	−	1.09650i
$630$		0			0
$631$	−46.4467	+	12.4453i	−1.84901	+	0.495441i	−0.999485	−	0.0321033i	$-0.989779\pi$
$631$	−46.4467	+	12.4453i	−1.84901	+	0.495441i	−0.849527	+	0.527545i	$0.823113\pi$
$632$	0.106114	−	0.106114i	0.00422100	−	0.00422100i
$633$	30.6663	+	33.7798i	1.21887	+	1.34263i
$634$	7.11082	−	4.10543i	0.282407	−	0.163048i
$635$		0			0
$636$	−0.495168	+	1.54543i	−0.0196347	+	0.0612801i
$637$	−11.8853	+	0.516066i	−0.470913	+	0.0204473i
$638$			16.6987i			0.661109i
$639$	4.13771	−	3.40701i	0.163685	−	0.134779i
$640$		0			0
$641$	−5.90025	+	10.2195i	−0.233046	+	0.403647i	−0.958703	−	0.284409i	$-0.908203\pi$
$641$	−5.90025	+	10.2195i	−0.233046	+	0.403647i	0.725657	+	0.688057i	$0.241536\pi$
$642$	7.15066	+	13.8933i	0.282214	+	0.548327i
$643$	−6.11802	−	22.8328i	−0.241271	−	0.900436i	−0.975221	−	0.221232i	$-0.928992\pi$
$643$	−6.11802	−	22.8328i	−0.241271	−	0.900436i	0.733950	−	0.679203i	$-0.237675\pi$
$644$	3.22329	+	12.0295i	0.127016	+	0.474029i
$645$		0			0
$646$	8.66254	−	15.0040i	0.340823	−	0.590323i
$647$	−13.0793	−	22.6540i	−0.514200	−	0.890620i	−0.999864	−	0.0164751i	$-0.994756\pi$
$647$	−13.0793	−	22.6540i	−0.514200	−	0.890620i	0.485664	−	0.874145i	$-0.338578\pi$
$648$	−1.08457	−	15.7618i	−0.0426058	−	0.619180i
$649$			9.63578i			0.378238i
$650$		0			0
$651$	−0.355113	+	1.10831i	−0.0139180	+	0.0434382i
$652$	−11.8439	−	3.17356i	−0.463843	−	0.124286i
$653$	6.39610	−	3.69279i	0.250299	−	0.144510i	−0.369602	−	0.929190i	$-0.620506\pi$
$653$	6.39610	−	3.69279i	0.250299	−	0.144510i	0.619901	+	0.784680i	$0.287173\pi$
$654$	4.49238	+	4.94848i	0.175666	+	0.193501i
$655$		0			0
$656$	44.1603	−	11.8327i	1.72417	−	0.461990i
$657$	−38.5730	−	14.4463i	−1.50488	−	0.563603i
$658$	34.5389	+	34.5389i	1.34646	+	1.34646i
$659$	1.23199	+	0.711291i	0.0479916	+	0.0277079i	0.523804	−	0.851839i	$-0.324512\pi$
$659$	1.23199	+	0.711291i	0.0479916	+	0.0277079i	−0.475812	+	0.879547i	$0.657846\pi$
$660$		0			0
$661$	−6.72014	+	25.0799i	−0.261383	+	0.975496i	0.703044	+	0.711147i	$0.251824\pi$
$661$	−6.72014	+	25.0799i	−0.261383	+	0.975496i	−0.964427	+	0.264349i	$0.914843\pi$
$662$	35.3811			1.37513
$663$	−24.1597	+	23.9249i	−0.938283	+	0.929168i
$664$	11.1522			0.432790
$665$		0			0
$666$	36.8433	+	3.56827i	1.42765	+	0.138268i
$667$	−27.7806	−	16.0391i	−1.07567	−	0.621037i
$668$	7.30267	+	7.30267i	0.282549	+	0.282549i
$669$	5.90970	+	0.285509i	0.228482	+	0.0110384i
$670$		0			0
$671$	−10.9244	+	10.9244i	−0.421732	+	0.421732i
$672$	−21.0943	+	19.1500i	−0.813730	+	0.738728i
$673$	−29.0538	+	16.7742i	−1.11994	+	0.646599i	−0.941386	−	0.337331i	$-0.890476\pi$
$673$	−29.0538	+	16.7742i	−1.11994	+	0.646599i	−0.178556	+	0.983930i	$0.557143\pi$
$674$	−38.3875	−	10.2859i	−1.47863	−	0.396198i
$675$		0			0
$676$	−1.10848	−	12.7404i	−0.0426338	−	0.490015i
$677$			7.62559i			0.293075i	0.989205	+	0.146538i	$0.0468130\pi$
$677$			7.62559i			0.293075i	−0.989205	+	0.146538i	$0.953187\pi$
$678$	7.58988	−	11.7926i	0.291488	−	0.452892i
$679$	−3.08872	−	5.34983i	−0.118534	−	0.205307i
$680$		0			0
$681$	18.9400	−	9.74807i	0.725782	−	0.373547i
$682$	0.111276	+	0.415289i	0.00426099	+	0.0159022i
$683$	5.30911	+	19.8139i	0.203147	+	0.758157i	0.990006	+	0.141024i	$0.0450393\pi$
$683$	5.30911	+	19.8139i	0.203147	+	0.758157i	−0.786859	+	0.617133i	$0.788294\pi$
$684$	0.894323	+	5.36257i	0.0341953	+	0.205043i
$685$		0			0
$686$	−10.2570	−	17.7656i	−0.391613	−	0.678293i
$687$	9.18283	+	5.91020i	0.350347	+	0.225488i
$688$			3.91886i			0.149405i
$689$	1.58639	−	3.04563i	0.0604365	−	0.116029i
$690$		0			0
$691$	9.87914	+	2.64711i	0.375820	+	0.100701i	0.441784	−	0.897121i	$-0.354346\pi$
$691$	9.87914	+	2.64711i	0.375820	+	0.100701i	−0.0659642	+	0.997822i	$0.521012\pi$
$692$	14.3378	−	8.27795i	0.545043	−	0.314681i
$693$	−10.4177	+	4.74065i	−0.395737	+	0.180082i
$694$	−6.12543	+	6.12543i	−0.232518	+	0.232518i
$695$		0			0
$696$	1.19313	−	24.6964i	0.0452255	−	0.936115i
$697$	−35.2039	−	35.2039i	−1.33344	−	1.33344i
$698$	4.76231	+	2.74952i	0.180256	+	0.104071i
$699$	−12.5985	+	2.73174i	−0.476520	+	0.103324i
$700$		0			0
$701$	−38.7093			−1.46203			−0.731016	−	0.682360i	$-0.760954\pi$
$701$	−38.7093			−1.46203			−0.731016	+	0.682360i	$0.760954\pi$
$702$	3.27684	−	32.1955i	0.123676	−	1.21514i
$703$	13.1588			0.496293
$704$	0.352650	−	1.31611i	0.0132910	−	0.0496026i
$705$		0			0
$706$	−7.89989	−	4.56100i	−0.297316	−	0.171656i
$707$	26.8613	+	26.8613i	1.01022	+	1.01022i
$708$	−0.666441	+	13.7945i	−0.0250464	+	0.518430i
$709$	−0.577806	+	0.154823i	−0.0216999	+	0.00581448i	−0.269653	−	0.962958i	$-0.586909\pi$
$709$	−0.577806	+	0.154823i	−0.0216999	+	0.00581448i	0.247953	+	0.968772i	$0.420242\pi$
$710$		0			0
$711$	0.233429	−	0.106223i	0.00875428	−	0.00398368i
$712$	−8.04181	+	4.64294i	−0.301379	+	0.174001i
$713$	−0.797769	−	0.213762i	−0.0298767	−	0.00800543i
$714$	49.7842	+	15.9513i	1.86313	+	0.596962i
$715$		0			0
$716$			17.8300i			0.666340i
$717$	−27.5409	−	17.7257i	−1.02853	−	0.661980i
$718$	−17.5970	−	30.4788i	−0.656713	−	1.13746i
$719$	19.5460	−	33.8547i	0.728944	−	1.26257i	−0.228385	−	0.973571i	$-0.573345\pi$
$719$	19.5460	−	33.8547i	0.728944	−	1.26257i	0.957330	−	0.288998i	$-0.0933221\pi$
$720$		0			0
$721$	−5.62853	−	21.0060i	−0.209618	−	0.782304i
$722$	−6.97716	−	26.0391i	−0.259663	−	0.969075i
$723$	−44.6581	+	22.9847i	−1.66085	+	0.854811i
$724$	−0.162738	+	0.281871i	−0.00604812	+	0.0104757i
$725$		0			0
$726$	15.5230	−	24.1185i	0.576113	−	0.895121i
$727$		−	0.507235i		−	0.0188123i	−0.999956	−	0.00940616i	$-0.997006\pi$
$727$		−	0.507235i		−	0.0188123i	0.999956	−	0.00940616i	$-0.00299412\pi$
$728$	17.1342	−	10.9099i	0.635035	−	0.404347i
$729$	7.71156	−	25.8753i	0.285613	−	0.958345i
$730$		0			0
$731$	3.69579	−	2.13377i	0.136694	−	0.0789202i
$732$	−16.3949	+	14.8837i	−0.605972	+	0.550119i
$733$	−34.1906	+	34.1906i	−1.26286	+	1.26286i	−0.313158	+	0.949701i	$0.601387\pi$
$733$	−34.1906	+	34.1906i	−1.26286	+	1.26286i	−0.949701	+	0.313158i	$0.898613\pi$
$734$	22.7481	−	6.09532i	0.839646	−	0.224982i
$735$		0			0
$736$	−14.2965	−	14.2965i	−0.526977	−	0.526977i
$737$	−2.44606	−	1.41224i	−0.0901019	−	0.0520204i
$738$	47.1645	+	4.56788i	1.73615	+	0.168146i
$739$	−3.71733	+	13.8733i	−0.136744	+	0.510337i	0.863240	+	0.504793i	$0.168431\pi$
$739$	−3.71733	+	13.8733i	−0.136744	+	0.510337i	−0.999985	+	0.00554351i	$0.998235\pi$
$740$		0			0
$741$	0.0561542	−	11.5043i	0.00206288	−	0.422619i
$742$	−5.27982			−0.193828
$743$	−10.4502	+	39.0006i	−0.383380	+	1.43079i	0.457326	+	0.889299i	$0.348807\pi$
$743$	−10.4502	+	39.0006i	−0.383380	+	1.43079i	−0.840705	+	0.541493i	$0.817859\pi$
$744$	−0.134898	−	0.622138i	−0.00494561	−	0.0228087i
$745$		0			0
$746$	−30.9653	−	30.9653i	−1.13372	−	1.13372i
$747$	17.8481	+	6.68443i	0.653027	+	0.244571i
$748$	6.15030	−	1.64797i	0.224877	−	0.0602557i
$749$	−11.8519	+	11.8519i	−0.433058	+	0.433058i
$750$		0			0
$751$	11.0569	−	6.38370i	0.403472	−	0.232945i	−0.284509	−	0.958673i	$-0.591831\pi$
$751$	11.0569	−	6.38370i	0.403472	−	0.232945i	0.687981	+	0.725729i	$0.258497\pi$
$752$	−42.5526	−	11.4019i	−1.55173	−	0.415785i
$753$	−12.6949	+	39.6209i	−0.462627	+	1.44387i
$754$	10.9736	−	49.4427i	0.399636	−	1.80060i
$755$		0			0
$756$	−15.2419	+	6.06616i	−0.554341	+	0.220624i
$757$	−4.53645	−	7.85737i	−0.164880	−	0.285581i	0.771733	−	0.635947i	$-0.219390\pi$
$757$	−4.53645	−	7.85737i	−0.164880	−	0.285581i	−0.936613	+	0.350366i	$0.886057\pi$
$758$	22.5403	−	39.0410i	0.818701	−	1.41803i
$759$	−3.71708	−	7.22209i	−0.134922	−	0.262145i
$760$		0			0
$761$	3.24132	+	12.0968i	0.117498	+	0.438507i	0.999462	−	0.0328095i	$-0.0104455\pi$
$761$	3.24132	+	12.0968i	0.117498	+	0.438507i	−0.881964	+	0.471317i	$0.843779\pi$
$762$	21.7715	+	42.3008i	0.788698	+	1.53240i
$763$	−3.58460	+	6.20870i	−0.129771	+	0.224770i
$764$	−6.21669	−	10.7676i	−0.224912	−	0.389559i
$765$		0			0
$766$			22.4829i			0.812341i
$767$	6.33219	−	28.5303i	0.228642	−	1.03017i
$768$	9.95383	−	31.0660i	0.359178	−	1.12100i
$769$	44.6938	+	11.9757i	1.61170	+	0.431854i	0.948548	−	0.316632i	$-0.102552\pi$
$769$	44.6938	+	11.9757i	1.61170	+	0.431854i	0.663151	+	0.748486i	$0.269219\pi$
$770$		0			0
$771$	−7.52580	−	8.28989i	−0.271035	−	0.298553i
$772$	−4.68057	+	4.68057i	−0.168457	+	0.168457i
$773$	−43.5070	+	11.6577i	−1.56484	+	0.419297i	−0.934191	−	0.356772i	$-0.883877\pi$
$773$	−43.5070	+	11.6577i	−1.56484	+	0.419297i	−0.630647	+	0.776069i	$0.717211\pi$
$774$	−1.42457	+	3.80375i	−0.0512052	+	0.136723i
$775$		0			0
$776$	2.92630	+	1.68950i	0.105048	+	0.0606496i
$777$	8.41388	+	38.8040i	0.301846	+	1.39208i
$778$	−8.40705	+	31.3755i	−0.301407	+	1.12487i
$779$	16.8451			0.603537
$780$		0			0
$781$	2.12396			0.0760012
$782$	−9.60193	+	35.8349i	−0.343364	+	1.28145i
$783$	16.7121	−	38.8092i	0.597241	−	1.38693i
$784$	−14.2865	−	8.24830i	−0.510231	−	0.294582i
$785$		0			0
$786$	7.60633	+	0.367476i	0.271309	+	0.0131074i
$787$	−39.8293	+	10.6722i	−1.41976	+	0.380424i	−0.885399	−	0.464831i	$-0.846115\pi$
$787$	−39.8293	+	10.6722i	−1.41976	+	0.380424i	−0.534362	+	0.845255i	$0.679448\pi$
$788$	11.4280	−	11.4280i	0.407105	−	0.407105i
$789$	20.5744	−	18.6780i	0.732466	−	0.664954i
$790$		0			0
$791$	14.5305	+	3.89345i	0.516646	+	0.138435i
$792$	3.63842	−	5.09489i	0.129286	−	0.181039i
$793$	39.5247	−	25.1667i	1.40356	−	0.893694i
$794$		−	16.0526i		−	0.569684i
$795$		0			0
$796$	3.59045	+	6.21885i	0.127260	+	0.220421i
$797$	−10.1010	+	17.4955i	−0.357796	+	0.619721i	−0.987592	−	0.157039i	$-0.949805\pi$
$797$	−10.1010	+	17.4955i	−0.357796	+	0.619721i	0.629796	+	0.776761i	$0.283138\pi$
$798$	−15.7272	+	8.09452i	−0.556738	+	0.286543i
$799$	12.4164	+	46.3386i	0.439260	+	1.63934i
$800$		0			0
$801$	−15.6531	+	2.61048i	−0.553074	+	0.0922369i
$802$	21.8522	−	37.8492i	0.771629	−	1.33650i
$803$	−8.16105	−	14.1354i	−0.287997	−	0.498826i
$804$	−3.40410	−	2.19093i	−0.120053	−	0.0772680i
$805$		0			0
$806$	−0.0565656	−	1.30274i	−0.00199244	−	0.0458870i
$807$	18.9543	+	6.07312i	0.667222	+	0.213784i
$808$	−20.0708	−	5.37797i	−0.706090	−	0.189196i
$809$	16.6563	−	9.61653i	0.585605	−	0.338099i	−0.177753	−	0.984075i	$-0.556883\pi$
$809$	16.6563	−	9.61653i	0.585605	−	0.338099i	0.763358	+	0.645976i	$0.223549\pi$
$810$		0			0
$811$	6.34354	−	6.34354i	0.222752	−	0.222752i	−0.586904	−	0.809656i	$-0.699654\pi$
$811$	6.34354	−	6.34354i	0.222752	−	0.222752i	0.809656	+	0.586904i	$0.199654\pi$
$812$	−24.7982	+	6.64467i	−0.870247	+	0.233182i
$813$	0.981838	−	20.3229i	0.0344346	−	0.712755i
$814$	10.3720	+	10.3720i	0.363537	+	0.363537i
$815$		0			0
$816$	−46.0781	+	9.99114i	−1.61306	+	0.349760i
$817$	−0.373715	+	1.39472i	−0.0130746	+	0.0487952i
$818$	14.3873			0.503041
$819$	33.9609	−	7.19036i	1.18669	−	0.251252i
$820$		0			0
$821$	−9.41992	+	35.1556i	−0.328757	+	1.22694i	0.581723	+	0.813387i	$0.302379\pi$
$821$	−9.41992	+	35.1556i	−0.328757	+	1.22694i	−0.910480	+	0.413553i	$0.864288\pi$
$822$	11.1442	−	2.41640i	0.388698	−	0.0842816i
$823$	−4.56162	−	2.63365i	−0.159008	−	0.0918034i	0.418385	−	0.908270i	$-0.362596\pi$
$823$	−4.56162	−	2.63365i	−0.159008	−	0.0918034i	−0.577393	+	0.816467i	$0.695930\pi$
$824$	8.41132	+	8.41132i	0.293022	+	0.293022i
$825$		0			0
$826$	−43.4018	+	11.6295i	−1.51014	+	0.404641i
$827$	−7.14407	+	7.14407i	−0.248424	+	0.248424i	−0.820323	−	0.571900i	$-0.806207\pi$
$827$	−7.14407	+	7.14407i	−0.248424	+	0.248424i	0.571900	+	0.820323i	$0.306207\pi$
$828$	−4.82185	−	10.5962i	−0.167571	−	0.368243i
$829$	−19.7203	+	11.3855i	−0.684915	+	0.395436i	−0.801704	−	0.597721i	$-0.796073\pi$
$829$	−19.7203	+	11.3855i	−0.684915	+	0.395436i	0.116789	+	0.993157i	$0.462740\pi$
$830$		0			0
$831$	32.5881	+	10.4415i	1.13047	+	0.362212i
$832$	−1.90903	+	3.66507i	−0.0661838	+	0.127063i
$833$			17.9643i			0.622427i
$834$	−50.5374	−	32.5266i	−1.74997	−	1.12630i
$835$		0			0
$836$	−1.07718	+	1.86574i	−0.0372552	+	0.0645279i
$837$	0.157006	−	1.07653i	0.00542691	−	0.0372103i
$838$	0.678226	+	2.53118i	0.0234289	+	0.0874380i
$839$	−3.27587	−	12.2257i	−0.113096	−	0.422079i	0.886042	−	0.463606i	$-0.153445\pi$
$839$	−3.27587	−	12.2257i	−0.113096	−	0.422079i	−0.999137	+	0.0415267i	$0.986778\pi$
$840$		0			0
$841$	18.5639	−	32.1535i	0.640133	−	1.10874i
$842$	15.4618	+	26.7806i	0.532848	+	0.922920i
$843$	−2.34184	+	3.63858i	−0.0806574	+	0.125319i
$844$			25.9122i			0.891934i
$845$		0			0
$846$	−37.1578	−	26.5356i	−1.27751	−	0.912312i
$847$	29.7182	+	7.96297i	1.02113	+	0.273611i
$848$	4.12391	−	2.38094i	0.141616	−	0.0817618i
$849$	−9.32516	+	8.46565i	−0.320039	+	0.290540i
$850$		0			0
$851$	−27.2174	+	7.29288i	−0.933000	+	0.249997i
$852$	3.04065	+	0.146900i	0.104171	+	0.00503269i
$853$	−7.79992	−	7.79992i	−0.267064	−	0.267064i	0.560852	−	0.827916i	$-0.310474\pi$
$853$	−7.79992	−	7.79992i	−0.267064	−	0.267064i	−0.827916	+	0.560852i	$0.810474\pi$
$854$	−62.3907	−	36.0213i	−2.13496	−	1.23262i
$855$		0			0
$856$	2.37289	−	8.85576i	0.0811038	−	0.302684i
$857$	−20.1264			−0.687503			−0.343752	−	0.939061i	$-0.611698\pi$
$857$	−20.1264			−0.687503			−0.343752	+	0.939061i	$0.611698\pi$
$858$	9.11210	−	9.02357i	0.311082	−	0.308060i
$859$	−21.9355			−0.748428			−0.374214	−	0.927342i	$-0.622087\pi$
$859$	−21.9355			−0.748428			−0.374214	+	0.927342i	$0.622087\pi$
$860$		0			0
$861$	10.7709	+	49.6745i	0.367073	+	1.69290i
$862$	−15.1363	−	8.73892i	−0.515543	−	0.297649i
$863$	25.0532	+	25.0532i	0.852822	+	0.852822i	0.990480	−	0.137658i	$-0.0439573\pi$
$863$	25.0532	+	25.0532i	0.852822	+	0.852822i	−0.137658	+	0.990480i	$0.543957\pi$
$864$	16.5053	−	20.9011i	0.561523	−	0.711068i
$865$		0			0
$866$	44.8558	−	44.8558i	1.52426	−	1.52426i
$867$	14.7196	+	16.2141i	0.499905	+	0.550660i
$868$	−0.572441	+	0.330499i	−0.0194299	+	0.0112179i
$869$	0.0981650	+	0.0263032i	0.00333002	+	0.000892276i
$870$		0			0
$871$	6.31441	+	5.78888i	0.213956	+	0.196149i
$872$		−	3.92148i		−	0.132798i
$873$	3.67062	+	4.45787i	0.124232	+	0.150876i
$874$	−6.27624	−	10.8708i	−0.212297	−	0.367709i
$875$		0			0
$876$	−10.7057	−	20.8005i	−0.361711	−	0.702785i
$877$	−4.34785	−	16.2264i	−0.146816	−	0.547926i	−0.999668	−	0.0257727i	$-0.991795\pi$
$877$	−4.34785	−	16.2264i	−0.146816	−	0.547926i	0.852851	−	0.522154i	$-0.174871\pi$
$878$	2.91009	+	10.8606i	0.0982109	+	0.366528i
$879$	−1.67007	−	3.24486i	−0.0563301	−	0.109446i
$880$		0			0
$881$	−16.3359	−	28.2946i	−0.550370	−	0.953269i	−0.998248	−	0.0591738i	$-0.981153\pi$
$881$	−16.3359	−	28.2946i	−0.550370	−	0.953269i	0.447878	−	0.894095i	$-0.352180\pi$
$882$	−10.8684	−	13.1994i	−0.365959	−	0.444446i
$883$			15.0338i			0.505929i	0.967476	+	0.252964i	$0.0814056\pi$
$883$			15.0338i			0.505929i	−0.967476	+	0.252964i	$0.918594\pi$
$884$	−19.2932	+	0.837720i	−0.648900	+	0.0281756i
$885$		0			0
$886$	28.8251	+	7.72365i	0.968397	+	0.259481i
$887$	13.1511	−	7.59276i	0.441569	−	0.254940i	−0.262694	−	0.964879i	$-0.584611\pi$
$887$	13.1511	−	7.59276i	0.441569	−	0.254940i	0.704263	+	0.709939i	$0.251278\pi$
$888$	−14.5984	−	16.0806i	−0.489891	−	0.539629i
$889$	−36.0852	+	36.0852i	−1.21026	+	1.21026i
$890$		0			0
$891$	8.87674	−	5.97309i	0.297382	−	0.200106i
$892$	2.37615	+	2.37615i	0.0795593	+	0.0795593i
$893$	−14.0571	−	8.11589i	−0.470404	−	0.271588i
$894$	−1.59514	−	7.35664i	−0.0533496	−	0.246043i
$895$		0			0
$896$	39.2513			1.31129
$897$	6.25976	+	23.8263i	0.209007	+	0.795538i
$898$	29.9780			1.00038
$899$	0.440659	−	1.64456i	0.0146968	−	0.0548492i
$900$		0			0
$901$	−4.49082	−	2.59278i	−0.149611	−	0.0863779i
$902$	13.2776	+	13.2776i	0.442094	+	0.442094i
$903$	−4.35187	−	0.210247i	−0.144821	−	0.00699658i
$904$	−7.94807	+	2.12968i	−0.264349	+	0.0708321i
$905$		0			0
$906$	42.7855	−	38.8419i	1.42145	−	1.29044i
$907$	−13.0097	+	7.51117i	−0.431981	+	0.249404i	−0.700190	−	0.713956i	$-0.746901\pi$
$907$	−13.0097	+	7.51117i	−0.431981	+	0.249404i	0.268209	+	0.963361i	$0.413568\pi$
$908$	11.6860	+	3.13127i	0.387815	+	0.103915i
$909$	−28.8981	−	20.6370i	−0.958489	−	0.684488i
$910$		0			0
$911$			20.7385i			0.687097i	0.939135	+	0.343548i	$0.111629\pi$
$911$			20.7385i			0.687097i	−0.939135	+	0.343548i	$0.888371\pi$
$912$	8.63382	−	13.4146i	0.285894	−	0.444201i
$913$	3.77620	+	6.54057i	0.124974	+	0.216461i
$914$	18.9135	−	32.7591i	0.625603	−	1.08358i
$915$		0			0
$916$	1.60528	+	5.99099i	0.0530400	+	0.197948i
$917$	2.11419	+	7.89028i	0.0698168	+	0.260560i
$918$	−48.3565	−	7.05253i	−1.59600	−	0.232768i
$919$	27.2006	−	47.1128i	0.897264	−	1.55411i	0.0662866	−	0.997801i	$-0.478885\pi$
$919$	27.2006	−	47.1128i	0.897264	−	1.55411i	0.830977	−	0.556306i	$-0.187782\pi$
$920$		0			0
$921$	−18.9276	−	12.1821i	−0.623687	−	0.401414i
$922$			56.2260i			1.85171i
$923$	−6.28875	−	1.39577i	−0.206997	−	0.0459422i
$924$	−6.19065	−	1.98354i	−0.203657	−	0.0652536i
$925$		0			0
$926$	7.09771	−	4.09787i	0.233245	−	0.134664i
$927$	8.41995	+	18.5031i	0.276547	+	0.607723i
$928$	29.4716	−	29.4716i	0.967453	−	0.967453i
$929$	−25.6186	+	6.86447i	−0.840518	+	0.225216i	−0.653297	−	0.757102i	$-0.726615\pi$
$929$	−25.6186	+	6.86447i	−0.840518	+	0.225216i	−0.187221	+	0.982318i	$0.559948\pi$
$930$		0			0
$931$	−4.29797	−	4.29797i	−0.140860	−	0.140860i
$932$	−6.34080	−	3.66086i	−0.207700	−	0.119915i
$933$	21.5689	−	4.67678i	0.706133	−	0.153111i
$934$	7.33855	−	27.3879i	0.240125	−	0.896158i
$935$		0			0
$936$	−14.1210	+	12.6943i	−0.461559	+	0.414925i
$937$	12.6619			0.413645			0.206822	−	0.978378i	$-0.433688\pi$
$937$	12.6619			0.413645			0.206822	+	0.978378i	$0.433688\pi$
$938$	3.40887	−	12.7221i	0.111303	−	0.415390i
$939$	43.0544	−	9.33549i	1.40503	−	0.304652i
$940$		0			0
$941$	35.2291	+	35.2291i	1.14844	+	1.14844i	0.986860	+	0.161576i	$0.0516576\pi$
$941$	35.2291	+	35.2291i	1.14844	+	1.14844i	0.161576	+	0.986860i	$0.448342\pi$
$942$	−0.777823	+	16.1000i	−0.0253429	+	0.524567i
$943$	−34.8421	+	9.33591i	−1.13461	+	0.304019i
$944$	28.6555	−	28.6555i	0.932656	−	0.932656i
$945$		0			0
$946$	−1.39391	+	0.804775i	−0.0453200	+	0.0261655i
$947$	−30.1697	−	8.08395i	−0.980384	−	0.262693i	−0.267178	−	0.963647i	$-0.586091\pi$
$947$	−30.1697	−	8.08395i	−0.980384	−	0.262693i	−0.713206	+	0.700954i	$0.752758\pi$
$948$	0.138713	+	0.0444450i	0.00450520	+	0.00144351i
$949$	14.8747	+	47.2159i	0.482852	+	1.53269i
$950$		0			0
$951$	−6.92322	−	4.45588i	−0.224501	−	0.144492i
$952$	−15.3366	−	26.5638i	−0.497063	−	0.860938i
$953$	−24.6186	+	42.6407i	−0.797475	+	1.38127i	0.123781	+	0.992310i	$0.460498\pi$
$953$	−24.6186	+	42.6407i	−0.797475	+	1.38127i	−0.921256	+	0.388957i	$0.872835\pi$
$954$	4.86828	−	0.811890i	0.157616	−	0.0262859i
$955$		0			0
$956$	−4.81452	−	17.9680i	−0.155713	−	0.581128i
$957$	14.8880	−	7.66259i	0.481260	−	0.247696i
$958$	2.34631	−	4.06393i	0.0758059	−	0.131300i
$959$	6.11593	+	10.5931i	0.197494	+	0.342069i
$960$		0			0
$961$			30.9562i			0.998586i
$962$	−23.8940	−	37.5259i	−0.770373	−	1.20988i
$963$	9.10558	−	12.7506i	0.293423	−	0.410881i
$964$	−27.5542	−	7.38313i	−0.887461	−	0.237795i
$965$		0			0
$966$	28.0438	−	25.4590i	0.902294	−	0.819128i
$967$	21.5311	−	21.5311i	0.692393	−	0.692393i	−0.270365	−	0.962758i	$-0.587144\pi$
$967$	21.5311	−	21.5311i	0.692393	−	0.692393i	0.962758	+	0.270365i	$0.0871444\pi$
$968$	−16.2556	+	4.35567i	−0.522474	+	0.139997i
$969$	−17.3520	−	0.838309i	−0.557426	−	0.0269304i
$970$		0			0
$971$	5.70966	+	3.29647i	0.183232	+	0.105789i	0.588810	−	0.808271i	$-0.299597\pi$
$971$	5.70966	+	3.29647i	0.183232	+	0.105789i	−0.405578	+	0.914060i	$0.632930\pi$
$972$	13.1210	−	7.93710i	0.420857	−	0.254583i
$973$	16.6854	−	62.2709i	0.534911	−	1.99631i
$974$	23.7624			0.761396
$975$		0			0
$976$	64.9753			2.07981
$977$	2.75795	−	10.2928i	0.0882347	−	0.329297i	−0.907672	−	0.419680i	$-0.862142\pi$
$977$	2.75795	−	10.2928i	0.0882347	−	0.329297i	0.995907	+	0.0903830i	$0.0288091\pi$
$978$	7.90238	+	36.4450i	0.252690	+	1.16538i
$979$	−5.44600	−	3.14425i	−0.174055	−	0.100491i
$980$		0			0
$981$	2.35047	−	6.27597i	0.0750446	−	0.200376i
$982$	32.4636	−	8.69860i	1.03596	−	0.277583i
$983$	22.6666	−	22.6666i	0.722952	−	0.722952i	−0.246254	−	0.969205i	$-0.579200\pi$
$983$	22.6666	−	22.6666i	0.722952	−	0.722952i	0.969205	+	0.246254i	$0.0791996\pi$
$984$	−18.6880	−	20.5854i	−0.595753	−	0.656239i
$985$		0			0
$986$	−73.8719	−	19.7939i	−2.35256	−	0.630367i
$987$	14.9447	−	46.6426i	0.475695	−	1.48465i
$988$	4.41547	−	4.81632i	0.140475	−	0.153228i
$989$		−	3.09195i		−	0.0983181i
$990$		0			0
$991$	10.6554	+	18.4558i	0.338481	+	0.586266i	0.984147	−	0.177353i	$-0.0567536\pi$
$991$	10.6554	+	18.4558i	0.338481	+	0.586266i	−0.645666	+	0.763620i	$0.723420\pi$
$992$	0.536552	−	0.929335i	0.0170355	−	0.0295064i
$993$	−16.2354	−	31.5446i	−0.515216	−	1.00104i
$994$	2.56341	+	9.56678i	0.0813065	+	0.303440i
$995$		0			0
$996$	4.95362	+	9.62461i	0.156961	+	0.304967i
$997$	29.3615	−	50.8556i	0.929888	−	1.61061i	0.146383	−	0.989228i	$-0.453237\pi$
$997$	29.3615	−	50.8556i	0.929888	−	1.61061i	0.783505	−	0.621386i	$-0.213430\pi$
$998$	−22.9120	−	39.6847i	−0.725266	−	1.25620i
$999$	−13.7250	−	34.4855i	−0.434241	−	1.09107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bo.h.626.19		96
3.2	odd	2	inner	975.2.bo.h.626.5		96
5.2	odd	4		195.2.bh.a.119.19	yes	96
5.3	odd	4		195.2.bh.a.119.6	yes	96
5.4	even	2	inner	975.2.bo.h.626.6		96
13.7	odd	12	inner	975.2.bo.h.176.5		96
15.2	even	4		195.2.bh.a.119.5	yes	96
15.8	even	4		195.2.bh.a.119.20	yes	96
15.14	odd	2	inner	975.2.bo.h.626.20		96
39.20	even	12	inner	975.2.bo.h.176.19		96
65.7	even	12		195.2.bh.a.59.20	yes	96
65.33	even	12		195.2.bh.a.59.5	✓	96
65.59	odd	12	inner	975.2.bo.h.176.20		96
195.59	even	12	inner	975.2.bo.h.176.6		96
195.98	odd	12		195.2.bh.a.59.19	yes	96
195.137	odd	12		195.2.bh.a.59.6	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bh.a.59.5	✓	96	65.33	even	12
195.2.bh.a.59.6	yes	96	195.137	odd	12
195.2.bh.a.59.19	yes	96	195.98	odd	12
195.2.bh.a.59.20	yes	96	65.7	even	12
195.2.bh.a.119.5	yes	96	15.2	even	4
195.2.bh.a.119.6	yes	96	5.3	odd	4
195.2.bh.a.119.19	yes	96	5.2	odd	4
195.2.bh.a.119.20	yes	96	15.8	even	4
975.2.bo.h.176.5		96	13.7	odd	12	inner
975.2.bo.h.176.6		96	195.59	even	12	inner
975.2.bo.h.176.19		96	39.20	even	12	inner
975.2.bo.h.176.20		96	65.59	odd	12	inner
975.2.bo.h.626.5		96	3.2	odd	2	inner
975.2.bo.h.626.6		96	5.4	even	2	inner
975.2.bo.h.626.19		96	1.1	even	1	trivial
975.2.bo.h.626.20		96	15.14	odd	2	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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.447071 - 1.66849i) q^{2} +(-1.69272 + 0.367032i) q^{3} +(-0.851938 - 0.491866i) q^{4} +(-0.144374 + 2.98837i) q^{6} +(-3.09993 + 0.830623i) q^{7} +(1.24129 - 1.24129i) q^{8} +(2.73057 - 1.24256i) q^{9} +(1.14830 + 0.307686i) q^{11} +(1.62262 + 0.519902i) q^{12} +(-3.19776 - 1.66563i) q^{13} +5.54355i q^{14} +(-2.49987 - 4.32990i) q^{16} +(-2.72229 + 4.71514i) q^{17} +(-0.852444 - 5.11145i) q^{18} +(-0.476790 - 1.77941i) q^{19} +(4.94243 - 2.54378i) q^{21} +(1.02674 - 1.77837i) q^{22} +(1.97237 + 3.41625i) q^{23} +(-1.64556 + 2.55674i) q^{24} +(-4.20871 + 4.59079i) q^{26} +(-4.16603 + 3.10551i) q^{27} +(3.04950 + 0.817112i) q^{28} +(-7.04243 + 4.06595i) q^{29} +(-0.148047 + 0.148047i) q^{31} +(-4.95075 + 1.32655i) q^{32} +(-2.05668 - 0.0993620i) q^{33} +(6.65011 + 6.65011i) q^{34} +(-2.93745 - 0.284492i) q^{36} +(-1.84876 + 6.89966i) q^{37} -3.18208 q^{38} +(6.02424 + 1.64575i) q^{39} +(-2.36667 + 8.83254i) q^{41} +(-2.03466 - 9.38365i) q^{42} +(-0.678803 - 0.391907i) q^{43} +(-0.826939 - 0.826939i) q^{44} +(6.58176 - 1.76358i) q^{46} +(6.23046 - 6.23046i) q^{47} +(5.82078 + 6.41176i) q^{48} +(2.85745 - 1.64975i) q^{49} +(2.87745 - 8.98056i) q^{51} +(1.90503 + 2.99188i) q^{52} +0.952426i q^{53} +(3.31901 + 8.33936i) q^{54} +(-2.81686 + 4.87895i) q^{56} +(1.46017 + 2.83703i) q^{57} +(3.63553 + 13.5680i) q^{58} +(2.09784 + 7.82924i) q^{59} +(-6.49787 + 11.2546i) q^{61} +(0.180828 + 0.313203i) q^{62} +(-7.43249 + 6.11993i) q^{63} -1.14613i q^{64} +(-1.08526 + 3.38712i) q^{66} +(-2.29493 - 0.614925i) q^{67} +(4.63844 - 2.67800i) q^{68} +(-4.59254 - 5.05881i) q^{69} +(1.72575 - 0.462414i) q^{71} +(1.84705 - 4.93181i) q^{72} +(-9.70845 - 9.70845i) q^{73} +(10.6855 + 6.16928i) q^{74} +(-0.469034 + 1.75046i) q^{76} -3.81522 q^{77} +(5.43918 - 9.31563i) q^{78} +0.0854873 q^{79} +(5.91208 - 6.78582i) q^{81} +(13.6789 + 7.89754i) q^{82} +(4.49219 + 4.49219i) q^{83} +(-5.46185 - 0.263872i) q^{84} +(-0.957366 + 0.957366i) q^{86} +(10.4285 - 9.46729i) q^{87} +(1.80730 - 1.04344i) q^{88} +(-5.10951 - 1.36909i) q^{89} +(11.2963 + 2.50718i) q^{91} -3.88057i q^{92} +(0.196264 - 0.304940i) q^{93} +(-7.61001 - 13.1809i) q^{94} +(7.89332 - 4.06255i) q^{96} +(0.498193 + 1.85928i) q^{97} +(-1.47511 - 5.50517i) q^{98} +(3.51784 - 0.586675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{4} + 4 q^{9} - 16 q^{21} + 28 q^{24} - 40 q^{31} + 32 q^{34} - 60 q^{36} + 4 q^{39} - 128 q^{46} - 60 q^{54} - 48 q^{61} - 8 q^{66} - 72 q^{69} - 80 q^{76} + 80 q^{79} + 48 q^{81} + 132 q^{84}+ \cdots + 48 q^{99}+O(q^{100}) \) 96 * q + 24 * q^4 + 4 * q^9 - 16 * q^21 + 28 * q^24 - 40 * q^31 + 32 * q^34 - 60 * q^36 + 4 * q^39 - 128 * q^46 - 60 * q^54 - 48 * q^61 - 8 * q^66 - 72 * q^69 - 80 * q^76 + 80 * q^79 + 48 * q^81 + 132 * q^84 - 56 * q^91 - 72 * q^94 + 204 * q^96 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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