LMFDB - Embedded newform 975.2.bo.h.176.6

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			176.6
Character	$\chi$	$=$	975.176
Dual form			975.2.bo.h.626.6

$q$-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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$-1$	$1$

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	−0.922936	−	0.384953i	$-0.874217\pi$
$2$	−0.447071	−	1.66849i	−0.316127	−	1.17980i	0.606809	−	0.794847i	$-0.292449\pi$
$3$	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	$-0.209241\pi$
$7$	3.09993	+	0.830623i	1.17166	+	0.313946i	0.380048	+	0.924967i	$0.375907\pi$
$8$	−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	−0.0815158	−	0.996672i	$-0.525976\pi$
$11$	1.14830	−	0.307686i	0.346225	−	0.0927708i	0.427741	+	0.903901i	$0.359309\pi$
$12$	−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	0.980549	+	0.196272i	$0.0628836\pi$
$17$	2.72229	+	4.71514i	0.660251	+	1.14359i	−0.320298	+	0.947317i	$0.603783\pi$
$18$	0.852444	−	5.11145i	0.200923	−	1.20478i
$19$	−0.476790	+	1.77941i	−0.109383	+	0.408224i	−0.998806	−	0.0488627i	$-0.984440\pi$
$19$	−0.476790	+	1.77941i	−0.109383	+	0.408224i	0.889422	+	0.457086i	$0.151107\pi$
$20$		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	$-0.968247\pi$
$23$	−1.97237	+	3.41625i	−0.411268	+	0.712337i	0.583761	+	0.811926i	$0.301581\pi$
$24$	−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	−0.326026	−	0.945361i	$-0.605710\pi$
$29$	−7.04243	−	4.06595i	−1.30775	−	0.755027i	−0.981720	+	0.190333i	$0.939043\pi$
$30$		0			0
$31$	−0.148047	−	0.148047i	−0.0265900	−	0.0265900i	0.693687	−	0.720277i	$-0.255985\pi$
$31$	−0.148047	−	0.148047i	−0.0265900	−	0.0265900i	−0.720277	+	0.693687i	$0.755985\pi$
$32$	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	0.933859	+	0.357642i	$0.116419\pi$
$37$	1.84876	+	6.89966i	0.303934	+	1.13430i	−0.629925	+	0.776656i	$0.716914\pi$
$38$	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	−0.861060	−	0.508504i	$-0.830199\pi$
$41$	−2.36667	−	8.83254i	−0.369612	−	1.37941i	0.491448	−	0.870907i	$-0.336468\pi$
$42$	2.03466	−	9.38365i	0.313955	−	1.44793i
$43$	0.678803	−	0.391907i	0.103517	−	0.0597653i	−0.447348	−	0.894360i	$-0.647631\pi$
$43$	0.678803	−	0.391907i	0.103517	−	0.0597653i	0.550864	+	0.834595i	$0.314298\pi$
$44$	−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	$-0.472154\pi$
$47$	−6.23046	−	6.23046i	−0.908806	−	0.908806i	−0.996176	+	0.0873702i	$0.972154\pi$
$48$	−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	−0.683979	−	0.729502i	$-0.739752\pi$
$59$	2.09784	−	7.82924i	0.273115	−	1.01928i	0.957094	−	0.289778i	$-0.0935814\pi$
$60$		0			0
$61$	−6.49787	−	11.2546i	−0.831967	−	1.44101i	−0.896476	−	0.443092i	$-0.853881\pi$
$61$	−6.49787	−	11.2546i	−0.831967	−	1.44101i	0.0645090	−	0.997917i	$-0.479452\pi$
$62$	−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	$-0.536973\pi$
$67$	2.29493	−	0.614925i	0.280370	−	0.0751250i	0.396264	+	0.918137i	$0.370307\pi$
$68$	−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	0.359765	−	0.933043i	$-0.382857\pi$
$71$	1.72575	+	0.462414i	0.204809	+	0.0548784i	−0.154956	+	0.987921i	$0.549524\pi$
$72$	−1.84705	−	4.93181i	−0.217677	−	0.581219i
$73$	9.70845	−	9.70845i	1.13629	−	1.13629i	0.147177	−	0.989110i	$-0.452981\pi$
$73$	9.70845	−	9.70845i	1.13629	−	1.13629i	0.989110	−	0.147177i	$-0.0470188\pi$
$74$	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	$-0.863364\pi$
$83$	−4.49219	+	4.49219i	−0.493082	+	0.493082i	0.416194	+	0.909276i	$0.363364\pi$
$84$	−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	−0.519243	−	0.854627i	$-0.673786\pi$
$89$	−5.10951	+	1.36909i	−0.541607	+	0.145123i	−0.0223639	+	0.999750i	$0.507119\pi$
$90$		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	$-0.947822\pi$
$97$	−0.498193	+	1.85928i	−0.0505838	+	0.188781i	0.936011	+	0.351971i	$0.114488\pi$
$98$	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	0.405474	+	0.914107i	$0.367107\pi$
$101$	−5.91840	+	10.2510i	−0.588903	+	1.02001i	−0.994377	+	0.105903i	$0.966227\pi$
$102$	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	$-0.414569\pi$
$107$	−4.52298	−	2.61134i	−0.437253	−	0.252448i	−0.702432	+	0.711751i	$0.747902\pi$
$108$	−5.07669	−	0.596576i	−0.488505	−	0.0574055i
$109$	1.57960	+	1.57960i	0.151298	+	0.151298i	0.778698	−	0.627399i	$-0.215881\pi$
$109$	1.57960	+	1.57960i	0.151298	+	0.151298i	−0.627399	+	0.778698i	$0.715881\pi$
$110$		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	$-0.595906\pi$
$113$	4.05939	−	2.34369i	0.381875	−	0.220476i	0.678634	+	0.734477i	$0.262572\pi$
$114$	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	$-0.582616\pi$
$127$	−13.7710	−	7.95071i	−1.22198	−	0.705512i	−0.965340	+	0.260995i	$0.915949\pi$
$128$	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	$0.0354670\pi$
$131$			2.54531i			0.222385i	−0.993799	+	0.111192i	$0.964533\pi$
$132$	−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	$-0.864609\pi$
$137$	0.986463	−	3.68153i	0.0842792	−	0.314534i	0.995177	+	0.0980984i	$0.0312760\pi$
$138$	10.4938	+	5.40096i	0.893289	+	0.459760i
$139$	−10.0439	−	17.3966i	−0.851915	−	1.47556i	−0.879478	−	0.475939i	$-0.842108\pi$
$139$	−10.0439	−	17.3966i	−0.851915	−	1.47556i	0.0275635	−	0.999620i	$-0.491225\pi$
$140$		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	0.157892	−	0.987456i	$-0.449530\pi$
$149$	−2.43030	−	0.651196i	−0.199098	−	0.0533481i	−0.356990	+	0.934108i	$0.616197\pi$
$150$		0			0
$151$	−13.6575	+	13.6575i	−1.11143	+	1.11143i	−0.118477	+	0.992957i	$0.537801\pi$
$151$	−13.6575	+	13.6575i	−1.11143	+	1.11143i	−0.992957	+	0.118477i	$0.962199\pi$
$152$	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	$-0.568971\pi$
$157$	−5.38756			−0.429974			−0.214987	+	0.976617i	$0.568971\pi$
$158$	−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	$-0.578993\pi$
$163$	−12.0398	−	3.22604i	−0.943027	−	0.252683i	−0.697401	+	0.716681i	$0.745660\pi$
$164$	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	$-0.450190\pi$
$167$	10.1406	−	2.71716i	0.784702	−	0.210260i	0.628857	+	0.777521i	$0.283523\pi$
$168$	−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	0.985483	+	0.169772i	$0.0543030\pi$
$173$	8.41484	+	14.5749i	0.639768	+	1.10811i	−0.345715	+	0.938340i	$0.612364\pi$
$174$	−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	0.298415	+	0.954436i	$0.403542\pi$
$179$	−9.06243	+	15.6966i	−0.677358	+	1.17322i	−0.975774	+	0.218783i	$0.929791\pi$
$180$		0			0
$181$			0.330859i			0.0245925i	0.999924	+	0.0122963i	$0.00391412\pi$
$181$			0.330859i			0.0245925i	−0.999924	+	0.0122963i	$0.996086\pi$
$182$	−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	−0.0486655	−	0.998815i	$-0.515497\pi$
$191$	10.9457	−	6.31949i	0.792001	−	0.457262i	0.840667	+	0.541553i	$0.182163\pi$
$192$	−0.420668	+	1.94008i	−0.0303591	+	0.140013i
$193$	−1.74154	−	6.49950i	−0.125359	−	0.467845i	0.874494	−	0.485037i	$-0.161194\pi$
$193$	−1.74154	−	6.49950i	−0.125359	−	0.467845i	−0.999852	+	0.0171925i	$0.994527\pi$
$194$	3.32492			0.238715
$195$		0			0
$196$	−3.24582			−0.231844
$197$	4.25210	+	15.8690i	0.302949	+	1.13062i	0.934696	+	0.355447i	$0.115672\pi$
$197$	4.25210	+	15.8690i	0.302949	+	1.13062i	−0.631747	+	0.775175i	$0.717662\pi$
$198$	−0.593861	−	6.13176i	−0.0422039	−	0.435765i
$199$	−6.32168	+	3.64982i	−0.448132	+	0.258729i	−0.707041	−	0.707173i	$-0.749970\pi$
$199$	−6.32168	+	3.64982i	−0.448132	+	0.258729i	0.258909	+	0.965902i	$0.416637\pi$
$200$		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	−0.0880423	+	0.996117i	$0.528061\pi$
$211$	−13.1703	+	22.8117i	−0.906684	+	1.57042i	−0.818641	+	0.574305i	$0.805272\pi$
$212$	−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	$-0.546847\pi$
$223$	3.29955	−	0.884112i	0.220954	−	0.0592045i	0.367598	+	0.929985i	$0.380180\pi$
$224$	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	$-0.282846\pi$
$227$	11.8793	+	3.18305i	0.788456	+	0.211266i	0.157947	+	0.987448i	$0.449513\pi$
$228$	−0.151467	−	3.13518i	−0.0100311	−	0.207633i
$229$	−4.45823	+	4.45823i	−0.294608	+	0.294608i	−0.838898	−	0.544289i	$-0.816799\pi$
$229$	−4.45823	+	4.45823i	−0.294608	+	0.294608i	0.544289	+	0.838898i	$0.316799\pi$
$230$		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	$-0.578393\pi$
$233$	−7.44279			−0.487594			−0.243797	+	0.969826i	$0.578393\pi$
$234$	−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	−0.127003	−	0.991902i	$-0.540536\pi$
$239$	13.3710	−	13.3710i	0.864899	−	0.864899i	0.991902	+	0.127003i	$0.0405358\pi$
$240$		0			0
$241$	28.0098	+	7.50522i	1.80427	+	0.483453i	0.994632	−	0.103473i	$-0.0329955\pi$
$241$	28.0098	+	7.50522i	1.80427	+	0.483453i	0.809640	+	0.586926i	$0.199662\pi$
$242$	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	0.943826	+	0.330443i	$0.107198\pi$
$251$	12.0103	+	20.8025i	0.758085	+	1.31304i	−0.185741	+	0.982599i	$0.559468\pi$
$252$	−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	$-0.897952\pi$
$257$	−3.23213	+	5.59821i	−0.201615	+	0.349207i	0.747434	+	0.664336i	$0.231286\pi$
$258$	−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	$-0.168634\pi$
$263$	13.8940	+	8.02170i	0.856740	+	0.494639i	−0.00617933	+	0.999981i	$0.501967\pi$
$264$	−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	−0.771699	−	0.635988i	$-0.780593\pi$
$269$	−9.95173	+	5.74563i	−0.606767	+	0.350317i	0.164932	+	0.986305i	$0.447260\pi$
$270$		0			0
$271$	−3.04037	−	11.3468i	−0.184690	−	0.689271i	−0.994697	−	0.102851i	$-0.967204\pi$
$271$	−3.04037	−	11.3468i	−0.184690	−	0.689271i	0.810007	−	0.586420i	$-0.199463\pi$
$272$	−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	$-0.464397\pi$
$277$	17.1100	−	9.87847i	1.02804	−	0.593540i	0.916423	+	0.400211i	$0.131063\pi$
$278$	−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	0.757832	−	0.652450i	$-0.226259\pi$
$281$	1.76652	+	1.76652i	0.105382	+	0.105382i	−0.652450	+	0.757832i	$0.726259\pi$
$282$	−17.7194	+	19.5184i	−1.05517	+	1.16231i
$283$	−6.29734	−	3.63577i	−0.374338	−	0.216124i	0.301014	−	0.953620i	$-0.402675\pi$
$283$	−6.29734	−	3.63577i	−0.374338	−	0.216124i	−0.675352	+	0.737496i	$0.736008\pi$
$284$	−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	$-0.936270\pi$
$293$	−0.545330	+	2.03520i	−0.0318585	+	0.118898i	0.948165	+	0.317777i	$0.102936\pi$
$294$	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	$-0.870934\pi$
$307$	−9.18929	+	9.18929i	−0.524461	+	0.524461i	0.394455	+	0.918915i	$0.370934\pi$
$308$	−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	$-0.244674\pi$
$313$	25.4351			1.43768			0.718838	+	0.695178i	$0.244674\pi$
$314$	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	$-0.792618\pi$
$317$	−3.36120	+	3.36120i	−0.188784	+	0.188784i	0.606386	+	0.795170i	$0.292618\pi$
$318$	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	−0.652653	−	0.757657i	$-0.726344\pi$
$331$	5.30136	−	19.7850i	0.291389	−	1.08748i	0.944043	−	0.329823i	$-0.106989\pi$
$332$	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	$-0.623689\pi$
$347$	4.34312	−	2.50750i	0.233151	−	0.134610i	0.612025	+	0.790839i	$0.290355\pi$
$348$	13.5411	+	2.93612i	0.725878	+	0.157392i
$349$	−0.823955	−	3.07504i	−0.0441053	−	0.164603i	0.940361	−	0.340179i	$-0.110488\pi$
$349$	−0.823955	−	3.07504i	−0.0441053	−	0.164603i	−0.984466	+	0.175576i	$0.943821\pi$
$350$		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	$-0.128216\pi$
$353$	−1.36681	−	5.10099i	−0.0727477	−	0.271498i	−0.992713	+	0.120501i	$0.961550\pi$
$354$	−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	0.976389	−	0.216018i	$-0.0693070\pi$
$359$	14.4070	+	14.4070i	0.760371	+	0.760371i	−0.216018	+	0.976389i	$0.569307\pi$
$360$		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	$-0.949139\pi$
$367$	−6.81696	+	11.8073i	−0.355842	+	0.616337i	0.631420	+	0.775441i	$0.282473\pi$
$368$	−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	−0.981557	−	0.191169i	$-0.938772\pi$
$373$	−12.6759	−	21.9554i	−0.656335	−	1.13681i	0.325222	−	0.945638i	$-0.394561\pi$
$374$	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	0.455376	−	0.890299i	$-0.349505\pi$
$379$	25.2089	−	6.75470i	1.29489	−	0.346966i	0.839517	+	0.543333i	$0.182838\pi$
$380$		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	$-0.308761\pi$
$383$	12.5724	+	3.36875i	0.642417	+	0.172135i	0.0771191	+	0.997022i	$0.475428\pi$
$384$	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	$-0.491588\pi$
$397$	−8.97652	−	2.40525i	−0.450519	−	0.120716i	−0.476942	+	0.878935i	$0.658255\pi$
$398$	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	0.409592	−	0.912269i	$-0.365671\pi$
$401$	24.4394	−	6.54850i	1.22044	−	0.327017i	0.810851	+	0.585252i	$0.199005\pi$
$402$	−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	−0.891927	−	0.452180i	$-0.850646\pi$
$409$	2.15574	−	8.04533i	0.106595	−	0.397816i	0.998521	+	0.0543639i	$0.0173131\pi$
$410$		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	0.467565	−	0.883959i	$-0.345131\pi$
$419$	−1.31380	−	0.758522i	−0.0641833	−	0.0370562i	−0.531748	+	0.846902i	$0.678465\pi$
$420$		0			0
$421$	−12.6589	−	12.6589i	−0.616955	−	0.616955i	0.327794	−	0.944749i	$-0.393695\pi$
$421$	−12.6589	−	12.6589i	−0.616955	−	0.616955i	−0.944749	+	0.327794i	$0.893695\pi$
$422$	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	0.999878	−	0.0156291i	$-0.00497511\pi$
$431$	2.61881	+	9.77353i	0.126144	+	0.470775i	−0.873734	+	0.486404i	$0.838308\pi$
$432$	−23.8611	+	10.2751i	−1.14802	+	0.494361i
$433$	−31.8042	+	18.3621i	−1.52841	+	0.882428i	−0.528982	+	0.848633i	$0.677426\pi$
$433$	−31.8042	+	18.3621i	−1.52841	+	0.882428i	−0.999429	+	0.0337954i	$0.989241\pi$
$434$	−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	0.359407	−	0.933181i	$-0.382979\pi$
$439$	−5.63717	−	3.25462i	−0.269048	−	0.155335i	−0.628455	+	0.777846i	$0.716312\pi$
$440$		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	−0.775227	−	0.631682i	$-0.782365\pi$
$449$	4.49179	−	16.7636i	0.211980	−	0.791122i	0.987208	−	0.159439i	$-0.0509687\pi$
$450$		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	$-0.754500\pi$
$457$	−21.1527	+	5.66785i	−0.989481	+	0.265131i	−0.272449	+	0.962170i	$0.587833\pi$
$458$	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	−0.563373	−	0.826203i	$-0.690497\pi$
$461$	−31.4414	−	8.42468i	−1.46437	−	0.392377i	−0.900997	+	0.433826i	$0.857163\pi$
$462$	−0.550818	−	11.4013i	−0.0256264	−	0.530436i
$463$	−3.35500	+	3.35500i	−0.155920	+	0.155920i	−0.780756	−	0.624836i	$-0.785166\pi$
$463$	−3.35500	+	3.35500i	−0.155920	+	0.155920i	0.624836	+	0.780756i	$0.285166\pi$
$464$	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	$-0.624004\pi$
$467$	−16.4147			−0.759584			−0.379792	+	0.925072i	$0.624004\pi$
$468$	−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	−0.198371	−	0.980127i	$-0.563565\pi$
$479$	2.62410	−	0.703124i	0.119898	−	0.0321266i	0.318269	+	0.948000i	$0.396898\pi$
$480$		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	0.837139	+	0.546990i	$0.184227\pi$
$487$	−3.56046	+	13.2878i	−0.161340	+	0.602129i	−0.998479	+	0.0551382i	$0.982440\pi$
$488$	−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	−0.558577	−	0.829452i	$-0.688653\pi$
$491$	9.72844	−	16.8501i	0.439038	−	0.760436i	0.997616	+	0.0690160i	$0.0219860\pi$
$492$	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	0.988825	−	0.149080i	$-0.0476311\pi$
$499$	18.7585	+	18.7585i	0.839745	+	0.839745i	−0.149080	+	0.988825i	$0.547631\pi$
$500$		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	0.530160	−	0.847898i	$-0.322132\pi$
$503$	34.3040	−	19.8054i	1.52954	−	0.883081i	0.999381	−	0.0351832i	$-0.0112015\pi$
$504$	−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	−0.960795	−	0.277260i	$-0.910574\pi$
$509$	−6.03174	−	22.5108i	−0.267352	−	0.997772i	0.693442	−	0.720512i	$-0.256093\pi$
$510$		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	$-0.996523\pi$
$521$		−	0.498625i		−	0.0218452i	0.999940	−	0.0109226i	$-0.00347683\pi$
$522$	−26.7862	+	32.5310i	−1.17240	+	1.42384i
$523$	10.5230	−	18.2263i	0.460138	−	0.796983i	−0.538829	−	0.842415i	$-0.681133\pi$
$523$	10.5230	−	18.2263i	0.460138	−	0.796983i	0.998967	+	0.0454324i	$0.0144666\pi$
$524$	−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	−0.879276	−	0.476312i	$-0.841973\pi$
$541$	−9.37270	+	9.37270i	−0.402964	+	0.402964i	0.476312	+	0.879276i	$0.341973\pi$
$542$	−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	$-0.297673\pi$
$547$	27.7702			1.18737			0.593685	+	0.804698i	$0.297673\pi$
$548$	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	$-0.733033\pi$
$557$	−20.6607	+	5.53600i	−0.875420	+	0.234568i	−0.206990	+	0.978343i	$0.566367\pi$
$558$	−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	$-0.177768\pi$
$563$	−0.827364	−	1.43304i	−0.0348692	−	0.0603953i	−0.882933	+	0.469498i	$0.844435\pi$
$564$	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	−0.308800	−	0.951127i	$-0.599928\pi$
$569$	15.9653	−	27.6527i	0.669300	−	1.15926i	0.978100	−	0.208134i	$-0.0667391\pi$
$570$		0			0
$571$			2.79633i			0.117023i	0.998287	+	0.0585113i	$0.0186354\pi$
$571$			2.79633i			0.117023i	−0.998287	+	0.0585113i	$0.981365\pi$
$572$	−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	$-0.375492\pi$
$577$	−13.0485	−	13.0485i	−0.543215	−	0.543215i	−0.924470	+	0.381255i	$0.875492\pi$
$578$	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	0.854561	+	0.519351i	$0.173826\pi$
$587$	9.06530	+	33.8321i	0.374165	+	1.39640i	−0.480396	+	0.877052i	$0.659507\pi$
$588$	−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	$-0.468779\pi$
$593$	−21.8499	−	21.8499i	−0.897267	−	0.897267i	−0.995194	+	0.0979268i	$0.968779\pi$
$594$	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	$-0.772918\pi$
$599$		−	32.0326i		−	1.30882i	0.756142	−	0.654408i	$-0.227082\pi$
$600$		0			0
$601$	−1.29184	+	2.23753i	−0.0526953	+	0.0912709i	−0.891170	−	0.453670i	$-0.850115\pi$
$601$	−1.29184	+	2.23753i	−0.0526953	+	0.0912709i	0.838475	+	0.544941i	$0.183448\pi$
$602$	−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	0.553480	+	0.832862i	$0.313299\pi$
$607$	24.5886	+	42.5887i	0.998020	+	1.72862i	0.444540	+	0.895759i	$0.353367\pi$
$608$	−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	$-0.707575\pi$
$613$	−18.1986	+	4.87630i	−0.735035	+	0.196952i	−0.128165	+	0.991753i	$0.540909\pi$
$614$	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	$-0.314874\pi$
$617$	15.0853	+	4.04209i	0.607310	+	0.162728i	0.0579578	+	0.998319i	$0.481541\pi$
$618$	20.2500	−	0.978318i	0.814575	−	0.0393537i
$619$	−30.0941	+	30.0941i	−1.20958	+	1.20958i	−0.238423	+	0.971161i	$0.576630\pi$
$619$	−30.0941	+	30.0941i	−1.20958	+	1.20958i	−0.971161	+	0.238423i	$0.923370\pi$
$620$		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	−0.849527	−	0.527545i	$-0.823113\pi$
$631$	−46.4467	−	12.4453i	−1.84901	−	0.495441i	−0.999485	+	0.0321033i	$0.989779\pi$
$632$	−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	0.725657	−	0.688057i	$-0.241536\pi$
$641$	−5.90025	−	10.2195i	−0.233046	−	0.403647i	−0.958703	+	0.284409i	$0.908203\pi$
$642$	−7.15066	+	13.8933i	−0.282214	+	0.548327i
$643$	6.11802	−	22.8328i	0.241271	−	0.900436i	−0.733950	−	0.679203i	$-0.762325\pi$
$643$	6.11802	−	22.8328i	0.241271	−	0.900436i	0.975221	−	0.221232i	$-0.0710079\pi$
$644$	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	−0.485664	−	0.874145i	$-0.661422\pi$
$647$	13.0793	−	22.6540i	0.514200	−	0.890620i	0.999864	−	0.0164751i	$-0.00524441\pi$
$648$	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	$-0.379494\pi$
$653$	−6.39610	−	3.69279i	−0.250299	−	0.144510i	−0.619901	+	0.784680i	$0.712827\pi$
$654$	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	−0.475812	−	0.879547i	$-0.657846\pi$
$659$	1.23199	−	0.711291i	0.0479916	−	0.0277079i	0.523804	+	0.851839i	$0.324512\pi$
$660$		0			0
$661$	−6.72014	−	25.0799i	−0.261383	−	0.975496i	−0.964427	−	0.264349i	$-0.914843\pi$
$661$	−6.72014	−	25.0799i	−0.261383	−	0.975496i	0.703044	−	0.711147i	$-0.251824\pi$
$662$	−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	$-0.109524\pi$
$673$	29.0538	+	16.7742i	1.11994	+	0.646599i	0.178556	+	0.983930i	$0.442857\pi$
$674$	−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	0.786859	+	0.617133i	$0.211706\pi$
$683$	−5.30911	+	19.8139i	−0.203147	+	0.758157i	−0.990006	+	0.141024i	$0.954961\pi$
$684$	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	−0.0659642	−	0.997822i	$-0.521012\pi$
$691$	9.87914	−	2.64711i	0.375820	−	0.100701i	0.441784	+	0.897121i	$0.354346\pi$
$692$	−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	0.247953	−	0.968772i	$-0.420242\pi$
$709$	−0.577806	−	0.154823i	−0.0216999	−	0.00581448i	−0.269653	+	0.962958i	$0.586909\pi$
$710$		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	0.957330	+	0.288998i	$0.0933221\pi$
$719$	19.5460	+	33.8547i	0.728944	+	1.26257i	−0.228385	+	0.973571i	$0.573345\pi$
$720$		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	0.949701	+	0.313158i	$0.101387\pi$
$733$	34.1906	+	34.1906i	1.26286	+	1.26286i	0.313158	+	0.949701i	$0.398613\pi$
$734$	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	−0.999985	−	0.00554351i	$-0.998235\pi$
$739$	−3.71733	−	13.8733i	−0.136744	−	0.510337i	0.863240	−	0.504793i	$-0.168431\pi$
$740$		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	0.840705	+	0.541493i	$0.182141\pi$
$743$	10.4502	+	39.0006i	0.383380	+	1.43079i	−0.457326	+	0.889299i	$0.651193\pi$
$744$	−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	0.687981	−	0.725729i	$-0.258497\pi$
$751$	11.0569	+	6.38370i	0.403472	+	0.232945i	−0.284509	+	0.958673i	$0.591831\pi$
$752$	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	$-0.780610\pi$
$757$	4.53645	−	7.85737i	0.164880	−	0.285581i	0.936613	+	0.350366i	$0.113943\pi$
$758$	−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	−0.881964	−	0.471317i	$-0.843779\pi$
$761$	3.24132	−	12.0968i	0.117498	−	0.438507i	0.999462	+	0.0328095i	$0.0104455\pi$
$762$	−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	0.663151	−	0.748486i	$-0.269219\pi$
$769$	44.6938	−	11.9757i	1.61170	−	0.431854i	0.948548	+	0.316632i	$0.102552\pi$
$770$		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	$-0.116123\pi$
$773$	43.5070	+	11.6577i	1.56484	+	0.419297i	0.630647	+	0.776069i	$0.282789\pi$
$774$	−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	$-0.153885\pi$
$787$	39.8293	+	10.6722i	1.41976	+	0.380424i	0.534362	+	0.845255i	$0.320552\pi$
$788$	−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	$-0.0501949\pi$
$797$	10.1010	+	17.4955i	0.357796	+	0.619721i	−0.629796	+	0.776761i	$0.716862\pi$
$798$	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	0.763358	−	0.645976i	$-0.223549\pi$
$809$	16.6563	+	9.61653i	0.585605	+	0.338099i	−0.177753	+	0.984075i	$0.556883\pi$
$810$		0			0
$811$	6.34354	+	6.34354i	0.222752	+	0.222752i	0.809656	−	0.586904i	$-0.199654\pi$
$811$	6.34354	+	6.34354i	0.222752	+	0.222752i	−0.586904	+	0.809656i	$0.699654\pi$
$812$	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	−0.910480	−	0.413553i	$-0.864288\pi$
$821$	−9.41992	−	35.1556i	−0.328757	−	1.22694i	0.581723	−	0.813387i	$-0.302379\pi$
$822$	−11.1442	−	2.41640i	−0.388698	−	0.0842816i
$823$	4.56162	−	2.63365i	0.159008	−	0.0918034i	−0.418385	−	0.908270i	$-0.637404\pi$
$823$	4.56162	−	2.63365i	0.159008	−	0.0918034i	0.577393	+	0.816467i	$0.304070\pi$
$824$	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	$-0.193793\pi$
$827$	7.14407	+	7.14407i	0.248424	+	0.248424i	−0.571900	+	0.820323i	$0.693793\pi$
$828$	4.82185	−	10.5962i	0.167571	−	0.368243i
$829$	−19.7203	−	11.3855i	−0.684915	−	0.395436i	0.116789	−	0.993157i	$-0.462740\pi$
$829$	−19.7203	−	11.3855i	−0.684915	−	0.395436i	−0.801704	+	0.597721i	$0.796073\pi$
$830$		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	−0.999137	−	0.0415267i	$-0.986778\pi$
$839$	−3.27587	+	12.2257i	−0.113096	+	0.422079i	0.886042	+	0.463606i	$0.153445\pi$
$840$		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	$-0.689526\pi$
$853$	7.79992	−	7.79992i	0.267064	−	0.267064i	0.827916	+	0.560852i	$0.189526\pi$
$854$	−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	$-0.388302\pi$
$857$	20.1264			0.687503			0.343752	+	0.939061i	$0.388302\pi$
$858$	−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	$-0.956043\pi$
$863$	−25.0532	+	25.0532i	−0.852822	+	0.852822i	0.137658	+	0.990480i	$0.456043\pi$
$864$	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	−0.852851	−	0.522154i	$-0.825129\pi$
$877$	4.34785	−	16.2264i	0.146816	−	0.547926i	0.999668	−	0.0257727i	$-0.00820462\pi$
$878$	−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	0.447878	+	0.894095i	$0.352180\pi$
$881$	−16.3359	+	28.2946i	−0.550370	+	0.953269i	−0.998248	+	0.0591738i	$0.981153\pi$
$882$	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	$-0.415389\pi$
$887$	−13.1511	−	7.59276i	−0.441569	−	0.254940i	−0.704263	+	0.709939i	$0.748722\pi$
$888$	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	$-0.253099\pi$
$907$	13.0097	+	7.51117i	0.431981	+	0.249404i	−0.268209	+	0.963361i	$0.586432\pi$
$908$	−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	$-0.888371\pi$
$911$		−	20.7385i		−	0.687097i	0.939135	−	0.343548i	$-0.111629\pi$
$912$	−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	0.830977	+	0.556306i	$0.187782\pi$
$919$	27.2006	+	47.1128i	0.897264	+	1.55411i	0.0662866	+	0.997801i	$0.478885\pi$
$920$		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	−0.187221	−	0.982318i	$-0.559948\pi$
$929$	−25.6186	−	6.86447i	−0.840518	−	0.225216i	−0.653297	+	0.757102i	$0.726615\pi$
$930$		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	$-0.566312\pi$
$937$	−12.6619			−0.413645			−0.206822	+	0.978378i	$0.566312\pi$
$938$	−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	0.161576	−	0.986860i	$-0.448342\pi$
$941$	35.2291	−	35.2291i	1.14844	−	1.14844i	0.986860	−	0.161576i	$-0.0516576\pi$
$942$	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	$-0.413909\pi$
$947$	30.1697	−	8.08395i	0.980384	−	0.262693i	0.713206	+	0.700954i	$0.247242\pi$
$948$	−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	0.921256	+	0.388957i	$0.127165\pi$
$953$	24.6186	+	42.6407i	0.797475	+	1.38127i	−0.123781	+	0.992310i	$0.539502\pi$
$954$	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	$-0.412856\pi$
$967$	−21.5311	−	21.5311i	−0.692393	−	0.692393i	−0.962758	+	0.270365i	$0.912856\pi$
$968$	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	−0.405578	−	0.914060i	$-0.632930\pi$
$971$	5.70966	−	3.29647i	0.183232	−	0.105789i	0.588810	+	0.808271i	$0.299597\pi$
$972$	−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	$-0.137858\pi$
$977$	−2.75795	−	10.2928i	−0.0882347	−	0.329297i	−0.995907	+	0.0903830i	$0.971191\pi$
$978$	−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	$-0.420800\pi$
$983$	−22.6666	−	22.6666i	−0.722952	−	0.722952i	−0.969205	+	0.246254i	$0.920800\pi$
$984$	−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	−0.645666	−	0.763620i	$-0.723420\pi$
$991$	10.6554	−	18.4558i	0.338481	−	0.586266i	0.984147	+	0.177353i	$0.0567536\pi$
$992$	−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	−0.783505	−	0.621386i	$-0.786570\pi$
$997$	−29.3615	−	50.8556i	−0.929888	−	1.61061i	−0.146383	−	0.989228i	$-0.546763\pi$
$998$	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.176.6		96
3.2	odd	2	inner	975.2.bo.h.176.20		96
5.2	odd	4		195.2.bh.a.59.19	yes	96
5.3	odd	4		195.2.bh.a.59.6	yes	96
5.4	even	2	inner	975.2.bo.h.176.19		96
13.2	odd	12	inner	975.2.bo.h.626.20		96
15.2	even	4		195.2.bh.a.59.5	✓	96
15.8	even	4		195.2.bh.a.59.20	yes	96
15.14	odd	2	inner	975.2.bo.h.176.5		96
39.2	even	12	inner	975.2.bo.h.626.6		96
65.2	even	12		195.2.bh.a.119.20	yes	96
65.28	even	12		195.2.bh.a.119.5	yes	96
65.54	odd	12	inner	975.2.bo.h.626.5		96
195.2	odd	12		195.2.bh.a.119.6	yes	96
195.119	even	12	inner	975.2.bo.h.626.19		96
195.158	odd	12		195.2.bh.a.119.19	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bh.a.59.5	✓	96	15.2	even	4
195.2.bh.a.59.6	yes	96	5.3	odd	4
195.2.bh.a.59.19	yes	96	5.2	odd	4
195.2.bh.a.59.20	yes	96	15.8	even	4
195.2.bh.a.119.5	yes	96	65.28	even	12
195.2.bh.a.119.6	yes	96	195.2	odd	12
195.2.bh.a.119.19	yes	96	195.158	odd	12
195.2.bh.a.119.20	yes	96	65.2	even	12
975.2.bo.h.176.5		96	15.14	odd	2	inner
975.2.bo.h.176.6		96	1.1	even	1	trivial
975.2.bo.h.176.19		96	5.4	even	2	inner
975.2.bo.h.176.20		96	3.2	odd	2	inner
975.2.bo.h.626.5		96	65.54	odd	12	inner
975.2.bo.h.626.6		96	39.2	even	12	inner
975.2.bo.h.626.19		96	195.119	even	12	inner
975.2.bo.h.626.20		96	13.2	odd	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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
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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