LMFDB - Embedded newform 925.2.t.b.643.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			643.9
Character	$\chi$	$=$	925.643
Dual form			925.2.t.b.82.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.122725 - 0.212566i) q^{2} +(1.83492 + 0.491666i) q^{3} +(0.969877 + 1.67988i) q^{4} +(0.329702 - 0.329702i) q^{6} +(3.76446 + 1.00868i) q^{7} +0.967013 q^{8} +(0.527123 + 0.304334i) q^{9} +4.37395i q^{11} +(0.953710 + 3.55930i) q^{12} +(-2.55980 - 4.43371i) q^{13} +(0.676405 - 0.676405i) q^{14} +(-1.82108 + 3.15420i) q^{16} +(2.15121 + 1.24200i) q^{17} +(0.129382 - 0.0746989i) q^{18} +(0.196130 - 0.731966i) q^{19} +(6.41155 + 3.70171i) q^{21} +(0.929753 + 0.536793i) q^{22} -3.38111 q^{23} +(1.77439 + 0.475447i) q^{24} -1.25661 q^{26} +(-3.21217 - 3.21217i) q^{27} +(1.95660 + 7.30213i) q^{28} +(4.99116 - 4.99116i) q^{29} +(-5.96470 - 5.96470i) q^{31} +(1.41400 + 2.44911i) q^{32} +(-2.15052 + 8.02585i) q^{33} +(0.528015 - 0.304850i) q^{34} +1.18067i q^{36} +(-5.22373 - 3.11652i) q^{37} +(-0.131521 - 0.131521i) q^{38} +(-2.51713 - 9.39407i) q^{39} +(4.18352 - 2.41536i) q^{41} +(1.57371 - 0.908585i) q^{42} +3.40053 q^{43} +(-7.34770 + 4.24219i) q^{44} +(-0.414947 + 0.718709i) q^{46} +(-5.91409 + 5.91409i) q^{47} +(-4.89234 + 4.89234i) q^{48} +(7.09153 + 4.09430i) q^{49} +(3.33665 + 3.33665i) q^{51} +(4.96539 - 8.60030i) q^{52} +(-0.590502 + 0.158224i) q^{53} +(-1.07701 + 0.288584i) q^{54} +(3.64028 + 0.975410i) q^{56} +(0.719765 - 1.24667i) q^{57} +(-0.448410 - 1.67349i) q^{58} +(9.92739 - 2.66004i) q^{59} +(-2.63598 + 9.83759i) q^{61} +(-1.99991 + 0.535874i) q^{62} +(1.67735 + 1.67735i) q^{63} -6.59018 q^{64} +(1.44210 + 1.44210i) q^{66} +(3.32297 - 12.4015i) q^{67} +4.81836i q^{68} +(-6.20407 - 1.66238i) q^{69} +(5.23213 + 9.06231i) q^{71} +(0.509734 + 0.294295i) q^{72} +(-3.10809 + 3.10809i) q^{73} +(-1.30355 + 0.727912i) q^{74} +(1.41983 - 0.380443i) q^{76} +(-4.41193 + 16.4656i) q^{77} +(-2.30577 - 0.617830i) q^{78} +(0.743780 - 2.77583i) q^{79} +(-5.22776 - 9.05475i) q^{81} -1.18570i q^{82} +(5.80029 - 1.55418i) q^{83} +14.3608i q^{84} +(0.417330 - 0.722837i) q^{86} +(11.6124 - 6.70440i) q^{87} +4.22967i q^{88} +(0.387792 + 1.44726i) q^{89} +(-5.16406 - 19.2725i) q^{91} +(-3.27926 - 5.67985i) q^{92} +(-8.01211 - 13.8774i) q^{93} +(0.531327 + 1.98294i) q^{94} +(1.39043 + 5.18914i) q^{96} +6.03559i q^{97} +(1.74062 - 1.00495i) q^{98} +(-1.33114 + 2.30561i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{2} + 8 q^{3} - 30 q^{4} - 8 q^{6} + 2 q^{7} - 12 q^{8} - 14 q^{12} + 6 q^{13} - 26 q^{16} - 12 q^{17} - 18 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 24 q^{26} + 68 q^{27} + 26 q^{28}+ \cdots + 32 q^{99}+O(q^{100}) $ 68 * q + 4 * q^2 + 8 * q^3 - 30 * q^4 - 8 * q^6 + 2 * q^7 - 12 * q^8 - 14 * q^12 + 6 * q^13 - 26 * q^16 - 12 * q^17 - 18 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 24 * q^26 + 68 * q^27 + 26 * q^28 + 14 * q^29 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 16 * q^37 + 36 * q^38 + 52 * q^39 - 18 * q^41 - 132 * q^42 - 8 * q^43 - 36 * q^44 - 52 * q^46 + 24 * q^47 + 60 * q^48 - 36 * q^49 - 8 * q^51 + 26 * q^52 - 82 * q^53 + 40 * q^54 + 16 * q^56 + 6 * q^57 - 86 * q^58 - 8 * q^59 + 4 * q^61 - 10 * q^62 + 48 * q^63 - 20 * q^64 + 80 * q^66 + 40 * q^67 + 8 * q^69 + 4 * q^71 + 90 * q^72 + 60 * q^73 - 44 * q^74 + 72 * q^76 - 66 * q^77 + 24 * q^78 + 56 * q^79 - 6 * q^81 - 24 * q^83 - 4 * q^86 + 84 * q^87 - 22 * q^89 + 44 * q^91 - 44 * q^92 + 34 * q^93 - 20 * q^94 - 8 * q^96 - 42 * q^98 + 32 * q^99

Character values

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

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.122725	−	0.212566i	0.0867797	−	0.150307i	−0.819369	−	0.573267i	$-0.805676\pi$
$2$	0.122725	−	0.212566i	0.0867797	−	0.150307i	0.906148	+	0.422960i	$0.139009\pi$
$3$	1.83492	+	0.491666i	1.05939	+	0.283863i	0.746128	−	0.665803i	$-0.231911\pi$
$3$	1.83492	+	0.491666i	1.05939	+	0.283863i	0.313264	+	0.949666i	$0.398577\pi$
$4$	0.969877	+	1.67988i	0.484939	+	0.839938i
$5$		0			0
$5$		0			0
$6$	0.329702	−	0.329702i	0.134600	−	0.134600i
$7$	3.76446	+	1.00868i	1.42283	+	0.381247i	0.886487	−	0.462753i	$-0.153138\pi$
$7$	3.76446	+	1.00868i	1.42283	+	0.381247i	0.536344	+	0.843999i	$0.319805\pi$
$8$	0.967013			0.341891
$9$	0.527123	+	0.304334i	0.175708	+	0.101445i
$10$		0			0
$11$			4.37395i			1.31880i	0.751794	+	0.659398i	$0.229189\pi$
$11$			4.37395i			1.31880i	−0.751794	+	0.659398i	$0.770811\pi$
$12$	0.953710	+	3.55930i	0.275312	+	1.02748i
$13$	−2.55980	−	4.43371i	−0.709961	−	1.22969i	−0.964871	−	0.262724i	$-0.915379\pi$
$13$	−2.55980	−	4.43371i	−0.709961	−	1.22969i	0.254909	−	0.966965i	$-0.417954\pi$
$14$	0.676405	−	0.676405i	0.180777	−	0.180777i
$15$		0			0
$16$	−1.82108	+	3.15420i	−0.455269	+	0.788550i
$17$	2.15121	+	1.24200i	0.521746	+	0.301230i	0.737649	−	0.675185i	$-0.235936\pi$
$17$	2.15121	+	1.24200i	0.521746	+	0.301230i	−0.215903	+	0.976415i	$0.569269\pi$
$18$	0.129382	−	0.0746989i	0.0304957	−	0.0176067i
$19$	0.196130	−	0.731966i	0.0449952	−	0.167924i	−0.939772	−	0.341802i	$-0.888963\pi$
$19$	0.196130	−	0.731966i	0.0449952	−	0.167924i	0.984767	+	0.173877i	$0.0556296\pi$
$20$		0			0
$21$	6.41155	+	3.70171i	1.39911	+	0.807779i
$22$	0.929753	+	0.536793i	0.198224	+	0.114445i
$23$	−3.38111			−0.705010			−0.352505	−	0.935810i	$-0.614670\pi$
$23$	−3.38111			−0.705010			−0.352505	+	0.935810i	$0.614670\pi$
$24$	1.77439	+	0.475447i	0.362196	+	0.0970502i
$25$		0			0
$26$	−1.25661			−0.246441
$27$	−3.21217	−	3.21217i	−0.618182	−	0.618182i
$28$	1.95660	+	7.30213i	0.369762	+	1.37997i
$29$	4.99116	−	4.99116i	0.926835	−	0.926835i	−0.0706651	−	0.997500i	$-0.522512\pi$
$29$	4.99116	−	4.99116i	0.926835	−	0.926835i	0.997500	+	0.0706651i	$0.0225122\pi$
$30$		0			0
$31$	−5.96470	−	5.96470i	−1.07129	−	1.07129i	−0.997256	−	0.0740358i	$-0.976412\pi$
$31$	−5.96470	−	5.96470i	−1.07129	−	1.07129i	−0.0740358	−	0.997256i	$-0.523588\pi$
$32$	1.41400	+	2.44911i	0.249962	+	0.432946i
$33$	−2.15052	+	8.02585i	−0.374358	+	1.39712i
$34$	0.528015	−	0.304850i	0.0905538	−	0.0522813i
$35$		0			0
$36$			1.18067i			0.196778i
$37$	−5.22373	−	3.11652i	−0.858775	−	0.512352i
$37$	−5.22373	−	3.11652i	−0.858775	−	0.512352i
$38$	−0.131521	−	0.131521i	−0.0213355	−	0.0213355i
$39$	−2.51713	−	9.39407i	−0.403064	−	1.50425i
$40$		0			0
$41$	4.18352	−	2.41536i	0.653357	−	0.377216i	−0.136384	−	0.990656i	$-0.543548\pi$
$41$	4.18352	−	2.41536i	0.653357	−	0.377216i	0.789741	+	0.613440i	$0.210215\pi$
$42$	1.57371	−	0.908585i	0.242829	−	0.140198i
$43$	3.40053			0.518576			0.259288	−	0.965800i	$-0.416512\pi$
$43$	3.40053			0.518576			0.259288	+	0.965800i	$0.416512\pi$
$44$	−7.34770	+	4.24219i	−1.10771	+	0.639535i
$45$		0			0
$46$	−0.414947	+	0.718709i	−0.0611806	+	0.105968i
$47$	−5.91409	+	5.91409i	−0.862659	+	0.862659i	−0.991646	−	0.128987i	$-0.958827\pi$
$47$	−5.91409	+	5.91409i	−0.862659	+	0.862659i	0.128987	+	0.991646i	$0.458827\pi$
$48$	−4.89234	+	4.89234i	−0.706149	+	0.706149i
$49$	7.09153	+	4.09430i	1.01308	+	0.584900i
$50$		0			0
$51$	3.33665	+	3.33665i	0.467225	+	0.467225i
$52$	4.96539	−	8.60030i	0.688575	−	1.19265i
$53$	−0.590502	+	0.158224i	−0.0811116	+	0.0217338i	−0.299147	−	0.954207i	$-0.596702\pi$
$53$	−0.590502	+	0.158224i	−0.0811116	+	0.0217338i	0.218035	+	0.975941i	$0.430035\pi$
$54$	−1.07701	+	0.288584i	−0.146563	+	0.0392713i
$55$		0			0
$56$	3.64028	+	0.975410i	0.486453	+	0.130345i
$57$	0.719765	−	1.24667i	0.0953352	−	0.165125i
$58$	−0.448410	−	1.67349i	−0.0588792	−	0.219740i
$59$	9.92739	−	2.66004i	1.29244	−	0.346307i	0.453851	−	0.891078i	$-0.350050\pi$
$59$	9.92739	−	2.66004i	1.29244	−	0.346307i	0.838585	+	0.544771i	$0.183383\pi$
$60$		0			0
$61$	−2.63598	+	9.83759i	−0.337502	+	1.25957i	0.563629	+	0.826028i	$0.309405\pi$
$61$	−2.63598	+	9.83759i	−0.337502	+	1.25957i	−0.901131	+	0.433547i	$0.857262\pi$
$62$	−1.99991	+	0.535874i	−0.253989	+	0.0680561i
$63$	1.67735	+	1.67735i	0.211327	+	0.211327i
$64$	−6.59018			−0.823773
$65$		0			0
$66$	1.44210	+	1.44210i	0.177510	+	0.177510i
$67$	3.32297	−	12.4015i	0.405966	−	1.51508i	−0.396302	−	0.918120i	$-0.629707\pi$
$67$	3.32297	−	12.4015i	0.405966	−	1.51508i	0.802268	−	0.596964i	$-0.203627\pi$
$68$			4.81836i			0.584312i
$69$	−6.20407	−	1.66238i	−0.746882	−	0.200126i
$70$		0			0
$71$	5.23213	+	9.06231i	0.620940	+	1.07550i	0.989311	+	0.145820i	$0.0465821\pi$
$71$	5.23213	+	9.06231i	0.620940	+	1.07550i	−0.368372	+	0.929679i	$0.620085\pi$
$72$	0.509734	+	0.294295i	0.0600727	+	0.0346830i
$73$	−3.10809	+	3.10809i	−0.363775	+	0.363775i	−0.865201	−	0.501426i	$-0.832809\pi$
$73$	−3.10809	+	3.10809i	−0.363775	+	0.363775i	0.501426	+	0.865201i	$0.332809\pi$
$74$	−1.30355	+	0.727912i	−0.151534	+	0.0846180i
$75$		0			0
$76$	1.41983	−	0.380443i	0.162866	−	0.0436398i
$77$	−4.41193	+	16.4656i	−0.502786	+	1.87642i
$78$	−2.30577	−	0.617830i	−0.261077	−	0.0699555i
$79$	0.743780	−	2.77583i	0.0836818	−	0.312305i	−0.911379	−	0.411567i	$-0.864982\pi$
$79$	0.743780	−	2.77583i	0.0836818	−	0.312305i	0.995061	+	0.0992622i	$0.0316483\pi$
$80$		0			0
$81$	−5.22776	−	9.05475i	−0.580863	−	1.00608i
$82$		−	1.18570i		−	0.130939i
$83$	5.80029	−	1.55418i	0.636664	−	0.170594i	0.0739721	−	0.997260i	$-0.476432\pi$
$83$	5.80029	−	1.55418i	0.636664	−	0.170594i	0.562692	+	0.826667i	$0.309766\pi$
$84$			14.3608i			1.56689i
$85$		0			0
$86$	0.417330	−	0.722837i	0.0450019	−	0.0779456i
$87$	11.6124	−	6.70440i	1.24498	−	0.718787i
$88$			4.22967i			0.450884i
$89$	0.387792	+	1.44726i	0.0411059	+	0.153409i	0.983428	−	0.181297i	$-0.0580295\pi$
$89$	0.387792	+	1.44726i	0.0411059	+	0.153409i	−0.942322	+	0.334706i	$0.891363\pi$
$90$		0			0
$91$	−5.16406	−	19.2725i	−0.541341	−	2.02031i
$92$	−3.27926	−	5.67985i	−0.341887	−	0.592165i
$93$	−8.01211	−	13.8774i	−0.830817	−	1.43902i
$94$	0.531327	+	1.98294i	0.0548022	+	0.204525i
$95$		0			0
$96$	1.39043	+	5.18914i	0.141910	+	0.529614i
$97$			6.03559i			0.612821i	0.951899	+	0.306411i	$0.0991281\pi$
$97$			6.03559i			0.612821i	−0.951899	+	0.306411i	$0.900872\pi$
$98$	1.74062	−	1.00495i	0.175829	−	0.101515i
$99$	−1.33114	+	2.30561i	−0.133785	+	0.231722i
$100$		0			0
$101$			1.89841i			0.188899i	0.995530	+	0.0944493i	$0.0301090\pi$
$101$			1.89841i			0.188899i	−0.995530	+	0.0944493i	$0.969891\pi$
$102$	1.11875	−	0.299768i	0.110773	−	0.0296815i
$103$		−	4.74353i		−	0.467394i	−0.972309	−	0.233697i	$-0.924918\pi$
$103$		−	4.74353i		−	0.467394i	0.972309	−	0.233697i	$-0.0750824\pi$
$104$	−2.47536	−	4.28745i	−0.242729	−	0.420419i
$105$		0			0
$106$	−0.0388362	+	0.144939i	−0.00377210	+	0.0140777i
$107$	0.586853	+	0.157247i	0.0567332	+	0.0152016i	0.287074	−	0.957908i	$-0.407317\pi$
$107$	0.586853	+	0.157247i	0.0567332	+	0.0152016i	−0.230341	+	0.973110i	$0.573984\pi$
$108$	2.28064	−	8.51145i	0.219454	−	0.819015i
$109$	−6.60438	+	1.76964i	−0.632585	+	0.169501i	−0.560842	−	0.827923i	$-0.689523\pi$
$109$	−6.60438	+	1.76964i	−0.632585	+	0.169501i	−0.0717424	+	0.997423i	$0.522856\pi$
$110$		0			0
$111$	−8.05284	−	8.28689i	−0.764342	−	0.786556i
$112$	−10.0370	+	10.0370i	−0.948404	+	0.948404i
$113$	−1.54325	−	0.890996i	−0.145177	−	0.0838178i	0.425652	−	0.904887i	$-0.360045\pi$
$113$	−1.54325	−	0.890996i	−0.145177	−	0.0838178i	−0.570829	+	0.821069i	$0.693378\pi$
$114$	−0.176666	−	0.305995i	−0.0165463	−	0.0286590i
$115$		0			0
$116$	13.2253	+	3.54372i	1.22794	+	0.329026i
$117$		−	3.11614i		−	0.288088i
$118$	0.652906	−	2.43668i	0.0601048	−	0.224314i
$119$	6.84536	+	6.84536i	0.627513	+	0.627513i
$120$		0			0
$121$	−8.13144			−0.739222
$122$	1.76764	+	1.76764i	0.160034	+	0.160034i
$123$	8.86398	−	2.37510i	0.799238	−	0.214155i
$124$	4.23493	−	15.8050i	0.380308	−	1.41933i
$125$		0			0
$126$	0.562402	−	0.150695i	0.0501027	−	0.0134250i
$127$	−0.982278	−	3.66591i	−0.0871631	−	0.325297i	0.908552	−	0.417772i	$-0.137189\pi$
$127$	−0.982278	−	3.66591i	−0.0871631	−	0.325297i	−0.995715	+	0.0924749i	$0.970522\pi$
$128$	−3.63677	+	6.29907i	−0.321448	+	0.556765i
$129$	6.23971	+	1.67192i	0.549376	+	0.147205i
$130$		0			0
$131$	15.2542	−	4.08734i	1.33276	−	0.357113i	0.479019	−	0.877805i	$-0.340993\pi$
$131$	15.2542	−	4.08734i	1.33276	−	0.357113i	0.853745	+	0.520692i	$0.174326\pi$
$132$	−15.5682	+	4.17148i	−1.35504	+	0.363081i
$133$	1.47664	−	2.55762i	0.128041	−	0.221774i
$134$	−2.22832	−	2.22832i	−0.192498	−	0.192498i
$135$		0			0
$136$	2.08025	+	1.20103i	0.178380	+	0.102988i
$137$	9.67862	−	9.67862i	0.826900	−	0.826900i	−0.160186	−	0.987087i	$-0.551210\pi$
$137$	9.67862	−	9.67862i	0.826900	−	0.826900i	0.987087	+	0.160186i	$0.0512095\pi$
$138$	−1.11476	+	1.11476i	−0.0948946	+	0.0948946i
$139$	8.37582	−	14.5073i	0.710427	−	1.23050i	−0.254269	−	0.967133i	$-0.581835\pi$
$139$	8.37582	−	14.5073i	0.710427	−	1.23050i	0.964697	−	0.263363i	$-0.0848317\pi$
$140$		0			0
$141$	−13.7596	+	7.94413i	−1.15877	+	0.669017i
$142$	2.56845			0.215540
$143$	19.3928	−	11.1964i	1.62171	−	0.936294i
$144$	−1.91986	+	1.10843i	−0.159989	+	0.0923694i
$145$		0			0
$146$	0.279234	+	1.04211i	0.0231096	+	0.0862460i
$147$	10.9994	+	10.9994i	0.907213	+	0.907213i
$148$	0.168989	−	11.7979i	0.0138908	−	0.969778i
$149$			2.73367i			0.223951i	0.993711	+	0.111976i	$0.0357179\pi$
$149$			2.73367i			0.223951i	−0.993711	+	0.111976i	$0.964282\pi$
$150$		0			0
$151$	−13.6955	+	7.90713i	−1.11453	+	0.643473i	−0.939998	−	0.341179i	$-0.889174\pi$
$151$	−13.6955	+	7.90713i	−1.11453	+	0.643473i	−0.174530	+	0.984652i	$0.555840\pi$
$152$	0.189660	−	0.707820i	0.0153834	−	0.0574118i
$153$	0.755968	+	1.30938i	0.0611164	+	0.105857i
$154$	2.95856	+	2.95856i	0.238408	+	0.238408i
$155$		0			0
$156$	13.3396	−	13.3396i	1.06802	−	1.06802i
$157$	1.28083	+	4.78011i	0.102221	+	0.381494i	0.998015	−	0.0629751i	$-0.0200589\pi$
$157$	1.28083	+	4.78011i	0.102221	+	0.381494i	−0.895794	+	0.444469i	$0.853392\pi$
$158$	−0.498766	−	0.498766i	−0.0396797	−	0.0396797i
$159$	−1.16132			−0.0920984
$160$		0			0
$161$	−12.7281	−	3.41047i	−1.00311	−	0.268783i
$162$	−2.56631			−0.201628
$163$	−14.1711	−	8.18168i	−1.10996	−	0.640839i	−0.171145	−	0.985246i	$-0.554747\pi$
$163$	−14.1711	−	8.18168i	−1.10996	−	0.640839i	−0.938820	+	0.344407i	$0.888080\pi$
$164$	8.11501	+	4.68520i	0.633676	+	0.365853i
$165$		0			0
$166$	0.381474	−	1.42368i	0.0296081	−	0.110499i
$167$	−6.76558	+	3.90611i	−0.523537	+	0.302264i	−0.738380	−	0.674384i	$-0.764409\pi$
$167$	−6.76558	+	3.90611i	−0.523537	+	0.302264i	0.214844	+	0.976648i	$0.431076\pi$
$168$	6.20005	+	3.57960i	0.478344	+	0.276172i
$169$	−6.60518	+	11.4405i	−0.508091	+	0.880039i
$170$		0			0
$171$	0.326147	−	0.326147i	0.0249411	−	0.0249411i
$172$	3.29810	+	5.71248i	0.251478	+	0.435572i
$173$	5.38695	+	20.1044i	0.409562	+	1.52851i	0.795483	+	0.605976i	$0.207217\pi$
$173$	5.38695	+	20.1044i	0.409562	+	1.52851i	−0.385921	+	0.922532i	$0.626116\pi$
$174$		−	3.29119i		−	0.249504i
$175$		0			0
$176$	−13.7963	−	7.96530i	−1.03994	−	0.600407i
$177$	19.5238			1.46750
$178$	0.355230	+	0.0951836i	0.0266256	+	0.00713431i
$179$	−8.72104	+	8.72104i	−0.651841	+	0.651841i	−0.953436	−	0.301595i	$-0.902481\pi$
$179$	−8.72104	+	8.72104i	−0.651841	+	0.651841i	0.301595	+	0.953436i	$0.402481\pi$
$180$		0			0
$181$	−1.85478	−	3.21258i	−0.137865	−	0.238789i	0.788823	−	0.614620i	$-0.210691\pi$
$181$	−1.85478	−	3.21258i	−0.137865	−	0.238789i	−0.926688	+	0.375831i	$0.877357\pi$
$182$	−4.73045	−	1.26752i	−0.350644	−	0.0939548i
$183$	−9.67361	+	16.7552i	−0.715094	+	1.23858i
$184$	−3.26958			−0.241036
$185$		0			0
$186$	−3.93314			−0.288392
$187$	−5.43246	+	9.40930i	−0.397261	+	0.688076i
$188$	−15.6709	−	4.19900i	−1.14292	−	0.306244i
$189$	−8.85201	−	15.3321i	−0.643889	−	1.11525i
$190$		0			0
$191$	7.04757	−	7.04757i	0.509945	−	0.509945i	−0.404565	−	0.914509i	$-0.632577\pi$
$191$	7.04757	−	7.04757i	0.509945	−	0.509945i	0.914509	+	0.404565i	$0.132577\pi$
$192$	−12.0925	−	3.24016i	−0.872698	−	0.233839i
$193$	−4.50078			−0.323974			−0.161987	−	0.986793i	$-0.551790\pi$
$193$	−4.50078			−0.323974			−0.161987	+	0.986793i	$0.551790\pi$
$194$	1.28296	+	0.740718i	0.0921112	+	0.0531804i
$195$		0			0
$196$			15.8839i			1.13456i
$197$	−1.24175	−	4.63427i	−0.0884710	−	0.330178i	0.907478	−	0.420100i	$-0.138005\pi$
$197$	−1.24175	−	4.63427i	−0.0884710	−	0.330178i	−0.995949	+	0.0899217i	$0.971338\pi$
$198$	0.326729	+	0.565911i	0.0232196	+	0.0402176i
$199$	2.93495	−	2.93495i	0.208053	−	0.208053i	−0.595386	−	0.803440i	$-0.703001\pi$
$199$	2.93495	−	2.93495i	0.208053	−	0.208053i	0.803440	+	0.595386i	$0.203001\pi$
$200$		0			0
$201$	12.1948	−	21.1220i	0.860153	−	1.48983i
$202$	0.403537	+	0.232982i	0.0283927	+	0.0163926i
$203$	23.8235	−	13.7545i	1.67208	−	0.965378i
$204$	−2.36902	+	8.84131i	−0.165865	+	0.619015i
$205$		0			0
$206$	−1.00831	−	0.582150i	−0.0702525	−	0.0405603i
$207$	−1.78226	−	1.02899i	−0.123876	−	0.0715196i
$208$	18.6464			1.29290
$209$	3.20158	+	0.857861i	0.221458	+	0.0593395i
$210$		0			0
$211$	−16.2172			−1.11644			−0.558221	−	0.829692i	$-0.688516\pi$
$211$	−16.2172			−1.11644			−0.558221	+	0.829692i	$0.688516\pi$
$212$	−0.838512	−	0.838512i	−0.0575892	−	0.0575892i
$213$	5.14492	+	19.2011i	0.352524	+	1.31564i
$214$	0.105447	−	0.105447i	0.00720819	−	0.00720819i
$215$		0			0
$216$	−3.10621	−	3.10621i	−0.211351	−	0.211351i
$217$	−16.4374	−	28.4704i	−1.11584	−	1.93269i
$218$	−0.434358	+	1.62104i	−0.0294184	+	0.109791i
$219$	−7.23124	+	4.17496i	−0.488642	+	0.282118i
$220$		0			0
$221$		−	12.7171i		−	0.855447i
$222$	−2.74979	+	0.694751i	−0.184554	+	0.0466287i
$223$	−12.0819	−	12.0819i	−0.809065	−	0.809065i	0.175427	−	0.984492i	$-0.443869\pi$
$223$	−12.0819	−	12.0819i	−0.809065	−	0.809065i	−0.984492	+	0.175427i	$0.943869\pi$
$224$	2.85255	+	10.6459i	0.190594	+	0.711307i
$225$		0			0
$226$	−0.378791	+	0.218695i	−0.0251968	+	0.0145474i
$227$	3.85285	−	2.22445i	0.255723	−	0.147642i	−0.366659	−	0.930355i	$-0.619498\pi$
$227$	3.85285	−	2.22445i	0.255723	−	0.147642i	0.622382	+	0.782714i	$0.286165\pi$
$228$	2.79233			0.184927
$229$	−7.06526	+	4.07913i	−0.466886	+	0.269556i	−0.714935	−	0.699191i	$-0.753544\pi$
$229$	−7.06526	+	4.07913i	−0.466886	+	0.269556i	0.248050	+	0.968747i	$0.420210\pi$
$230$		0			0
$231$	−16.1911	+	28.0438i	−1.06530	+	1.84515i
$232$	4.82651	−	4.82651i	0.316876	−	0.316876i
$233$	−9.86567	+	9.86567i	−0.646322	+	0.646322i	−0.952102	−	0.305780i	$-0.901083\pi$
$233$	−9.86567	+	9.86567i	−0.646322	+	0.646322i	0.305780	+	0.952102i	$0.401083\pi$
$234$	−0.662386	−	0.382429i	−0.0433015	−	0.0250001i
$235$		0			0
$236$	14.0969	+	14.0969i	0.917629	+	0.917629i
$237$	2.72956	−	4.72773i	0.177304	−	0.307099i
$238$	2.29519	−	0.614994i	0.148775	−	0.0398641i
$239$	−15.3216	+	4.10540i	−0.991069	+	0.265556i	−0.717699	−	0.696353i	$-0.754805\pi$
$239$	−15.3216	+	4.10540i	−0.991069	+	0.265556i	−0.273369	+	0.961909i	$0.588138\pi$
$240$		0			0
$241$	15.9979	+	4.28663i	1.03052	+	0.276126i	0.734178	−	0.678957i	$-0.237568\pi$
$241$	15.9979	+	4.28663i	1.03052	+	0.276126i	0.296338	+	0.955083i	$0.404235\pi$
$242$	−0.997931	+	1.72847i	−0.0641495	+	0.111110i
$243$	−1.61342	−	6.02136i	−0.103501	−	0.386270i
$244$	−19.0825	+	5.11314i	−1.22163	+	0.327336i
$245$		0			0
$246$	0.582967	−	2.17566i	0.0371686	−	0.138715i
$247$	−3.74738	+	1.00411i	−0.238440	+	0.0638898i
$248$	−5.76794	−	5.76794i	−0.366264	−	0.366264i
$249$	11.4072			0.722902
$250$		0			0
$251$	3.53612	+	3.53612i	0.223198	+	0.223198i	0.809844	−	0.586646i	$-0.199552\pi$
$251$	3.53612	+	3.53612i	0.223198	+	0.223198i	−0.586646	+	0.809844i	$0.699552\pi$
$252$	−1.19092	+	4.44458i	−0.0750209	+	0.279982i
$253$		−	14.7888i		−	0.929765i
$254$	−0.899798	−	0.241100i	−0.0564583	−	0.0151280i
$255$		0			0
$256$	−5.69753	−	9.86842i	−0.356096	−	0.616776i
$257$	−18.1616	−	10.4856i	−1.13289	−	0.654073i	−0.188229	−	0.982125i	$-0.560275\pi$
$257$	−18.1616	−	10.4856i	−1.13289	−	0.654073i	−0.944660	+	0.328052i	$0.893608\pi$
$258$	1.12116	−	1.12116i	0.0698005	−	0.0698005i
$259$	−16.5209	−	17.0011i	−1.02656	−	1.05640i
$260$		0			0
$261$	4.14993	−	1.11197i	0.256874	−	0.0688293i
$262$	1.00324	−	3.74414i	0.0619803	−	0.231314i
$263$	−11.2253	−	3.00781i	−0.692182	−	0.185470i	−0.104456	−	0.994530i	$-0.533310\pi$
$263$	−11.2253	−	3.00781i	−0.692182	−	0.185470i	−0.587726	+	0.809060i	$0.699977\pi$
$264$	−2.07958	+	7.76110i	−0.127989	+	0.477663i
$265$		0			0
$266$	−0.362442	−	0.627768i	−0.0222228	−	0.0384910i
$267$			2.84627i			0.174189i
$268$	24.0559	−	6.44575i	1.46945	−	0.393737i
$269$		−	20.4566i		−	1.24726i	−0.781719	−	0.623631i	$-0.785657\pi$
$269$		−	20.4566i		−	1.24726i	0.781719	−	0.623631i	$-0.214343\pi$
$270$		0			0
$271$	11.4239	−	19.7867i	0.693951	−	1.20196i	−0.276582	−	0.960990i	$-0.589202\pi$
$271$	11.4239	−	19.7867i	0.693951	−	1.20196i	0.970533	−	0.240968i	$-0.0774650\pi$
$272$	−7.83505	+	4.52357i	−0.475070	+	0.274282i
$273$		−	37.9026i		−	2.29397i
$274$	−0.869536	−	3.24515i	−0.0525306	−	0.196047i
$275$		0			0
$276$	−3.22460	−	12.0344i	−0.194098	−	0.724384i
$277$	6.88756	+	11.9296i	0.413833	+	0.716780i	0.995305	−	0.0967861i	$-0.0308563\pi$
$277$	6.88756	+	11.9296i	0.413833	+	0.716780i	−0.581472	+	0.813567i	$0.697523\pi$
$278$	−2.05584	−	3.56083i	−0.123301	−	0.213564i
$279$	−1.32886	−	4.95939i	−0.0795570	−	0.296911i
$280$		0			0
$281$	−6.14362	−	22.9283i	−0.366498	−	1.36779i	−0.865379	−	0.501118i	$-0.832922\pi$
$281$	−6.14362	−	22.9283i	−0.366498	−	1.36779i	0.498881	−	0.866670i	$-0.333744\pi$
$282$			3.89978i			0.232228i
$283$	−18.3014	+	10.5663i	−1.08790	+	0.628102i	−0.933018	−	0.359830i	$-0.882835\pi$
$283$	−18.3014	+	10.5663i	−1.08790	+	0.628102i	−0.154887	+	0.987932i	$0.549501\pi$
$284$	−10.1490	+	17.5787i	−0.602235	+	1.04310i
$285$		0			0
$286$		−	5.49634i		−	0.325005i
$287$	18.1850	−	4.87267i	1.07343	−	0.287624i
$288$			1.72131i			0.101429i
$289$	−5.41486	−	9.37881i	−0.318521	−	0.551695i
$290$		0			0
$291$	−2.96749	+	11.0748i	−0.173957	+	0.649218i
$292$	−8.23568	−	2.20674i	−0.481957	−	0.129140i
$293$	−0.127980	+	0.477628i	−0.00747667	+	0.0279033i	−0.969563	−	0.244840i	$-0.921264\pi$
$293$	−0.127980	+	0.477628i	−0.00747667	+	0.0279033i	0.962087	+	0.272744i	$0.0879311\pi$
$294$	3.68799	−	0.988194i	0.215088	−	0.0576326i
$295$		0			0
$296$	−5.05141	−	3.01371i	−0.293607	−	0.175168i
$297$	14.0499	−	14.0499i	0.815256	−	0.815256i
$298$	0.581086	+	0.335490i	0.0336614	+	0.0194344i
$299$	8.65498	+	14.9909i	0.500530	+	0.866944i
$300$		0			0
$301$	12.8012	+	3.43006i	0.737847	+	0.197706i
$302$			3.88161i			0.223362i
$303$	−0.933381	+	3.48343i	−0.0536214	+	0.200118i
$304$	1.95160	+	1.95160i	0.111932	+	0.111932i
$305$		0			0
$306$	0.371105			0.0212146
$307$	13.0911	+	13.0911i	0.747149	+	0.747149i	0.973943	−	0.226794i	$-0.0728243\pi$
$307$	13.0911	+	13.0911i	0.747149	+	0.747149i	−0.226794	+	0.973943i	$0.572824\pi$
$308$	−31.9391	+	8.55807i	−1.81990	+	0.487641i
$309$	2.33223	−	8.70400i	0.132676	−	0.495153i
$310$		0			0
$311$	−25.2278	+	6.75978i	−1.43054	+	0.383312i	−0.889210	−	0.457499i	$-0.848745\pi$
$311$	−25.2278	+	6.75978i	−1.43054	+	0.383312i	−0.541329	+	0.840811i	$0.682079\pi$
$312$	−2.43410	−	9.08418i	−0.137804	−	0.514291i
$313$	−8.41349	+	14.5726i	−0.475558	+	0.823691i	−0.999608	−	0.0279965i	$-0.991087\pi$
$313$	−8.41349	+	14.5726i	−0.475558	+	0.823691i	0.524050	+	0.851688i	$0.324421\pi$
$314$	1.17328	+	0.314379i	0.0662119	+	0.0177414i
$315$		0			0
$316$	5.38442	−	1.44275i	0.302897	−	0.0811611i
$317$	−17.3678	+	4.65369i	−0.975472	+	0.261377i	−0.711137	−	0.703054i	$-0.751819\pi$
$317$	−17.3678	+	4.65369i	−0.975472	+	0.261377i	−0.264336	+	0.964431i	$0.585153\pi$
$318$	−0.142523	+	0.246856i	−0.00799227	+	0.0138430i
$319$	21.8311	+	21.8311i	1.22231	+	1.22231i
$320$		0			0
$321$	0.999515	+	0.577070i	0.0557875	+	0.0322089i
$322$	−2.28700	+	2.28700i	−0.127450	+	0.127450i
$323$	1.33102	−	1.33102i	0.0740599	−	0.0740599i
$324$	10.1406	−	17.5640i	0.563365	−	0.975778i
$325$		0			0
$326$	−3.47829	+	2.00819i	−0.192645	+	0.111224i
$327$	−12.9886			−0.718270
$328$	4.04552	−	2.33568i	0.223376	−	0.128966i
$329$	−28.2288	+	16.2979i	−1.55630	+	0.898533i
$330$		0			0
$331$	−1.17108	−	4.37053i	−0.0643683	−	0.240226i	0.926245	−	0.376923i	$-0.123018\pi$
$331$	−1.17108	−	4.37053i	−0.0643683	−	0.240226i	−0.990613	+	0.136697i	$0.956351\pi$
$332$	8.23640	+	8.23640i	0.452031	+	0.452031i
$333$	−1.80508	−	3.23255i	−0.0989178	−	0.177142i
$334$			1.91751i			0.104921i
$335$		0			0
$336$	−23.3519	+	13.4822i	−1.27395	+	0.735514i
$337$	−0.129673	+	0.483946i	−0.00706374	+	0.0263622i	−0.969368	−	0.245614i	$-0.921010\pi$
$337$	−0.129673	+	0.483946i	−0.00706374	+	0.0263622i	0.962304	+	0.271976i	$0.0876772\pi$
$338$	1.62124	+	2.80807i	0.0881839	+	0.152739i
$339$	−2.39367	−	2.39367i	−0.130006	−	0.130006i
$340$		0			0
$341$	26.0893	−	26.0893i	1.41281	−	1.41281i
$342$	−0.0293013	−	0.109354i	−0.00158443	−	0.00591319i
$343$	3.27551	+	3.27551i	0.176861	+	0.176861i
$344$	3.28836			0.177296
$345$		0			0
$346$	4.93462	+	1.32223i	0.265287	+	0.0710834i
$347$	−5.86619			−0.314914			−0.157457	−	0.987526i	$-0.550330\pi$
$347$	−5.86619			−0.314914			−0.157457	+	0.987526i	$0.550330\pi$
$348$	22.5251	+	13.0049i	1.20747	+	0.697135i
$349$	18.2252	+	10.5223i	0.975571	+	0.563246i	0.900930	−	0.433964i	$-0.142886\pi$
$349$	18.2252	+	10.5223i	0.975571	+	0.563246i	0.0746410	+	0.997210i	$0.476219\pi$
$350$		0			0
$351$	−6.01930	+	22.4643i	−0.321286	+	1.19906i
$352$	−10.7123	+	6.18475i	−0.570967	+	0.329648i
$353$	13.3327	+	7.69762i	0.709627	+	0.409703i	0.810923	−	0.585153i	$-0.198966\pi$
$353$	13.3327	+	7.69762i	0.709627	+	0.409703i	−0.101296	+	0.994856i	$0.532299\pi$
$354$	2.39606	−	4.15010i	0.127349	−	0.220575i
$355$		0			0
$356$	−2.05511	+	2.05511i	−0.108920	+	0.108920i
$357$	9.19507	+	15.9263i	0.486655	+	0.842910i
$358$	0.783507	+	2.92409i	0.0414096	+	0.154543i
$359$		−	28.7191i		−	1.51574i	−0.652407	−	0.757869i	$-0.726241\pi$
$359$		−	28.7191i		−	1.51574i	0.652407	−	0.757869i	$-0.273759\pi$
$360$		0			0
$361$	15.9572	+	9.21288i	0.839851	+	0.484888i
$362$	−0.910513			−0.0478555
$363$	−14.9206	−	3.99795i	−0.783126	−	0.209838i
$364$	27.3670	−	27.3670i	1.43442	−	1.43442i
$365$		0			0
$366$	2.37439	+	4.11256i	0.124111	+	0.214967i
$367$	11.0742	+	2.96732i	0.578068	+	0.154893i	0.535994	−	0.844222i	$-0.319937\pi$
$367$	11.0742	+	2.96732i	0.578068	+	0.154893i	0.0420738	+	0.999115i	$0.486604\pi$
$368$	6.15727	−	10.6647i	0.320970	−	0.555936i
$369$	2.94031			0.153066
$370$		0			0
$371$	−2.38252			−0.123694
$372$	15.5415	−	26.9187i	0.805791	−	1.39567i
$373$	10.6519	+	2.85417i	0.551535	+	0.147783i	0.523815	−	0.851832i	$-0.324508\pi$
$373$	10.6519	+	2.85417i	0.551535	+	0.147783i	0.0277207	+	0.999616i	$0.491175\pi$
$374$	1.33340	+	2.30951i	0.0689483	+	0.119422i
$375$		0			0
$376$	−5.71900	+	5.71900i	−0.294935	+	0.294935i
$377$	−34.9057	−	9.35296i	−1.79774	−	0.481702i
$378$	−4.34545			−0.223506
$379$	24.3009	+	14.0302i	1.24826	+	0.720681i	0.970761	−	0.240046i	$-0.0771627\pi$
$379$	24.3009	+	14.0302i	1.24826	+	0.720681i	0.277494	+	0.960727i	$0.410496\pi$
$380$		0			0
$381$		−	7.20961i		−	0.369359i
$382$	−0.633161	−	2.36299i	−0.0323953	−	0.120901i
$383$	−4.08788	−	7.08041i	−0.208881	−	0.361792i	0.742481	−	0.669867i	$-0.233649\pi$
$383$	−4.08788	−	7.08041i	−0.208881	−	0.361792i	−0.951362	+	0.308075i	$0.900315\pi$
$384$	−9.77022	+	9.77022i	−0.498585	+	0.498585i
$385$		0			0
$386$	−0.552359	+	0.956713i	−0.0281143	+	0.0486954i
$387$	1.79250	+	1.03490i	0.0911178	+	0.0526069i
$388$	−10.1390	+	5.85378i	−0.514732	+	0.297181i
$389$	−6.73768	+	25.1454i	−0.341614	+	1.27492i	0.554904	+	0.831914i	$0.312755\pi$
$389$	−6.73768	+	25.1454i	−0.341614	+	1.27492i	−0.896518	+	0.443007i	$0.853912\pi$
$390$		0			0
$391$	−7.27349	−	4.19935i	−0.367836	−	0.212370i
$392$	6.85760	+	3.95924i	0.346361	+	0.199972i
$393$	29.9998			1.51329
$394$	−1.13748	−	0.304787i	−0.0573055	−	0.0153550i
$395$		0			0
$396$	−5.16418			−0.259510
$397$	24.8666	+	24.8666i	1.24802	+	1.24802i	0.956594	+	0.291423i	$0.0941287\pi$
$397$	24.8666	+	24.8666i	1.24802	+	1.24802i	0.291423	+	0.956594i	$0.405871\pi$
$398$	−0.263679	−	0.984063i	−0.0132170	−	0.0493266i
$399$	3.96702	−	3.96702i	0.198599	−	0.198599i
$400$		0			0
$401$	21.5174	+	21.5174i	1.07453	+	1.07453i	0.996990	+	0.0775363i	$0.0247054\pi$
$401$	21.5174	+	21.5174i	1.07453	+	1.07453i	0.0775363	+	0.996990i	$0.475295\pi$
$402$	−2.99321	−	5.18439i	−0.149288	−	0.258574i
$403$	−11.1773	+	41.7142i	−0.556780	+	2.07793i
$404$	−3.18909	+	1.84122i	−0.158663	+	0.0916042i
$405$		0			0
$406$		−	6.75209i		−	0.335101i
$407$	13.6315	−	22.8483i	0.675688	−	1.13255i
$408$	3.22659	+	3.22659i	0.159740	+	0.159740i
$409$	−4.96725	−	18.5380i	−0.245615	−	0.916647i	−0.973073	−	0.230495i	$-0.925965\pi$
$409$	−4.96725	−	18.5380i	−0.245615	−	0.916647i	0.727459	−	0.686151i	$-0.240701\pi$
$410$		0			0
$411$	22.5181	−	13.0009i	1.11074	−	0.641285i
$412$	7.96855	−	4.60064i	0.392582	−	0.226657i
$413$	40.0544			1.97095
$414$	−0.437456	+	0.252565i	−0.0214998	+	0.0124129i
$415$		0			0
$416$	7.23910	−	12.5385i	0.354926	−	0.614750i
$417$	22.5017	−	22.5017i	1.10191	−	1.10191i
$418$	0.575266	−	0.575266i	0.0281372	−	0.0281372i
$419$	14.4238	+	8.32758i	0.704649	+	0.406829i	0.809076	−	0.587703i	$-0.199968\pi$
$419$	14.4238	+	8.32758i	0.704649	+	0.406829i	−0.104428	+	0.994532i	$0.533301\pi$
$420$		0			0
$421$	−1.63243	−	1.63243i	−0.0795600	−	0.0795600i	0.666207	−	0.745767i	$-0.267917\pi$
$421$	−1.63243	−	1.63243i	−0.0795600	−	0.0795600i	−0.745767	+	0.666207i	$0.767917\pi$
$422$	−1.99026	+	3.44723i	−0.0968844	+	0.167809i
$423$	−4.91731	+	1.31759i	−0.239088	+	0.0640634i
$424$	−0.571022	+	0.153005i	−0.0277313	+	0.00743058i
$425$		0			0
$426$	4.71291	+	1.26282i	0.228341	+	0.0611838i
$427$	−19.8460	+	34.3744i	−0.960417	+	1.66349i
$428$	0.305020	+	1.13835i	0.0147437	+	0.0550242i
$429$	41.0892	−	11.0098i	1.98380	−	0.531559i
$430$		0			0
$431$	−4.00348	+	14.9412i	−0.192841	+	0.719692i	0.799974	+	0.600034i	$0.204846\pi$
$431$	−4.00348	+	14.9412i	−0.192841	+	0.719692i	−0.992815	+	0.119658i	$0.961820\pi$
$432$	15.9814	−	4.28221i	0.768907	−	0.206028i
$433$	25.3131	+	25.3131i	1.21647	+	1.21647i	0.968860	+	0.247609i	$0.0796449\pi$
$433$	25.3131	+	25.3131i	1.21647	+	1.21647i	0.247609	+	0.968860i	$0.420355\pi$
$434$	−8.06910			−0.387329
$435$		0			0
$436$	−9.37821	−	9.37821i	−0.449135	−	0.449135i
$437$	−0.663136	+	2.47486i	−0.0317221	+	0.118388i
$438$			2.04949i			0.0979283i
$439$	−19.5391	−	5.23549i	−0.932551	−	0.249876i	−0.239609	−	0.970870i	$-0.577019\pi$
$439$	−19.5391	−	5.23549i	−0.932551	−	0.249876i	−0.692942	+	0.720993i	$0.743686\pi$
$440$		0			0
$441$	2.49207	+	4.31639i	0.118670	+	0.205543i
$442$	−2.70323	−	1.56071i	−0.128579	−	0.0742354i
$443$	−14.1936	+	14.1936i	−0.674357	+	0.674357i	−0.958717	−	0.284360i	$-0.908219\pi$
$443$	−14.1936	+	14.1936i	−0.674357	+	0.674357i	0.284360	+	0.958717i	$0.408219\pi$
$444$	6.11068	−	21.5650i	0.290000	−	1.02343i
$445$		0			0
$446$	−4.05096	+	1.08545i	−0.191818	+	0.0513976i
$447$	−1.34405	+	5.01607i	−0.0635715	+	0.237252i
$448$	−24.8085	−	6.64741i	−1.17209	−	0.314061i
$449$	−0.795805	+	2.96998i	−0.0375563	+	0.140162i	−0.982158	−	0.188056i	$-0.939781\pi$
$449$	−0.795805	+	2.96998i	−0.0375563	+	0.140162i	0.944602	+	0.328218i	$0.106448\pi$
$450$		0			0
$451$	10.5647	+	18.2985i	0.497470	+	0.861644i
$452$		−	3.45663i		−	0.162586i
$453$	−29.0179	+	7.77533i	−1.36338	+	0.365317i
$454$		−	1.09198i		−	0.0512492i
$455$		0			0
$456$	0.696022	−	1.20554i	0.0325942	−	0.0564548i
$457$	3.30575	−	1.90857i	0.154636	−	0.0892793i	−0.420685	−	0.907207i	$-0.638210\pi$
$457$	3.30575	−	1.90857i	0.154636	−	0.0892793i	0.575321	+	0.817927i	$0.304877\pi$
$458$			2.00244i			0.0935681i
$459$	−2.92053	−	10.8996i	−0.136319	−	0.508749i
$460$		0			0
$461$	9.05566	+	33.7962i	0.421764	+	1.57404i	0.770890	+	0.636969i	$0.219812\pi$
$461$	9.05566	+	33.7962i	0.421764	+	1.57404i	−0.349126	+	0.937076i	$0.613521\pi$
$462$	3.97410	+	6.88335i	0.184892	+	0.320242i
$463$	−14.1107	−	24.4405i	−0.655782	−	1.13585i	−0.981697	−	0.190449i	$-0.939006\pi$
$463$	−14.1107	−	24.4405i	−0.655782	−	1.13585i	0.325915	−	0.945399i	$-0.394328\pi$
$464$	6.65382	+	24.8324i	0.308896	+	1.15282i
$465$		0			0
$466$	0.886341	+	3.30787i	0.0410590	+	0.153234i
$467$			15.9774i			0.739345i	0.929162	+	0.369672i	$0.120530\pi$
$467$			15.9774i			0.739345i	−0.929162	+	0.369672i	$0.879470\pi$
$468$	5.23474	−	3.02228i	0.241976	−	0.139705i
$469$	25.0184	−	43.3331i	1.15524	−	2.00094i
$470$		0			0
$471$			9.40086i			0.433169i
$472$	9.59991	−	2.57229i	0.441872	−	0.118399i
$473$			14.8738i			0.683896i
$474$	−0.669969	−	1.16042i	−0.0307727	−	0.0532999i
$475$		0			0
$476$	−4.86020	+	18.1385i	−0.222767	+	0.831378i
$477$	−0.359420	−	0.0963063i	−0.0164567	−	0.00440956i
$478$	−1.00767	+	3.76067i	−0.0460897	+	0.172009i
$479$	19.8825	−	5.32750i	0.908454	−	0.243420i	0.225811	−	0.974171i	$-0.427497\pi$
$479$	19.8825	−	5.32750i	0.908454	−	0.243420i	0.682643	+	0.730752i	$0.260830\pi$
$480$		0			0
$481$	−0.446015	+	31.1381i	−0.0203365	+	1.41978i
$482$	2.87453	−	2.87453i	0.130931	−	0.130931i
$483$	−21.6782	−	12.5159i	−0.986390	−	0.569493i
$484$	−7.88650	−	13.6598i	−0.358477	−	0.620901i
$485$		0			0
$486$	−1.47794	−	0.396013i	−0.0670408	−	0.0179635i
$487$		−	6.61449i		−	0.299731i	−0.988706	−	0.149866i	$-0.952116\pi$
$487$		−	6.61449i		−	0.299731i	0.988706	−	0.149866i	$-0.0478841\pi$
$488$	−2.54902	+	9.51308i	−0.115389	+	0.430637i
$489$	−21.9802	−	21.9802i	−0.993977	−	0.993977i
$490$		0			0
$491$	−5.57169			−0.251447			−0.125723	−	0.992065i	$-0.540125\pi$
$491$	−5.57169			−0.251447			−0.125723	+	0.992065i	$0.540125\pi$
$492$	12.5868	+	12.5868i	0.567459	+	0.567459i
$493$	16.9361	−	4.53801i	0.762762	−	0.204382i
$494$	−0.246458	+	0.919793i	−0.0110887	+	0.0413835i
$495$		0			0
$496$	29.6760	−	7.95167i	1.33249	−	0.357040i
$497$	10.5551	+	39.3923i	0.473462	+	1.76699i
$498$	1.39995	−	2.42478i	0.0627332	−	0.108657i
$499$	−5.11780	−	1.37131i	−0.229104	−	0.0613883i	0.142440	−	0.989803i	$-0.454505\pi$
$499$	−5.11780	−	1.37131i	−0.229104	−	0.0613883i	−0.371545	+	0.928415i	$0.621172\pi$
$500$		0			0
$501$	−14.3348	+	3.84100i	−0.640432	+	0.171603i
$502$	1.18563	−	0.317689i	0.0529172	−	0.0141791i
$503$	2.89715	−	5.01801i	0.129178	−	0.223742i	−0.794181	−	0.607682i	$-0.792100\pi$
$503$	2.89715	−	5.01801i	0.129178	−	0.223742i	0.923358	+	0.383940i	$0.125433\pi$
$504$	1.62202	+	1.62202i	0.0722506	+	0.0722506i
$505$		0			0
$506$	−3.14360	−	1.81496i	−0.139750	−	0.0806847i
$507$	−17.7449	+	17.7449i	−0.788078	+	0.788078i
$508$	5.20559	−	5.20559i	0.230961	−	0.230961i
$509$	−18.5930	+	32.2040i	−0.824118	+	1.42742i	0.0784727	+	0.996916i	$0.474996\pi$
$509$	−18.5930	+	32.2040i	−0.824118	+	1.42742i	−0.902591	+	0.430499i	$0.858338\pi$
$510$		0			0
$511$	−14.8354	+	8.56520i	−0.656278	+	0.378902i
$512$	−17.3440			−0.766504
$513$	−2.98120	+	1.72120i	−0.131623	+	0.0759927i
$514$	−4.45776	+	2.57369i	−0.196623	+	0.113521i
$515$		0			0
$516$	3.24312	+	12.1035i	0.142771	+	0.532827i
$517$	−25.8679	−	25.8679i	−1.13767	−	1.13767i
$518$	−5.64138	+	1.42533i	−0.247868	+	0.0626253i
$519$			39.5385i			1.73555i
$520$		0			0
$521$	−29.0910	+	16.7957i	−1.27450	+	0.735832i	−0.975831	−	0.218525i	$-0.929876\pi$
$521$	−29.0910	+	16.7957i	−1.27450	+	0.735832i	−0.298668	+	0.954357i	$0.596542\pi$
$522$	0.272933	−	1.01860i	0.0119460	−	0.0445830i
$523$	−15.4267	−	26.7199i	−0.674564	−	1.16838i	−0.976596	−	0.215082i	$-0.930998\pi$
$523$	−15.4267	−	26.7199i	−0.674564	−	1.16838i	0.302031	−	0.953298i	$-0.402335\pi$
$524$	21.6609	+	21.6609i	0.946261	+	0.946261i
$525$		0			0
$526$	−2.01698	+	2.01698i	−0.0879447	+	0.0879447i
$527$	−5.42316	−	20.2395i	−0.236236	−	0.881647i
$528$	−21.3989	−	21.3989i	−0.931266	−	0.931266i
$529$	−11.5681			−0.502960
$530$		0			0
$531$	6.04249	+	1.61908i	0.262222	+	0.0702621i
$532$	5.72865			0.248369
$533$	−21.4180	−	12.3657i	−0.927716	−	0.535617i
$534$	0.605020	+	0.349309i	0.0261818	+	0.0151161i
$535$		0			0
$536$	3.21336	−	11.9924i	0.138796	−	0.517993i
$537$	−20.2903	+	11.7146i	−0.875589	+	0.505522i
$538$	−4.34838	−	2.51054i	−0.187472	−	0.108237i
$539$	−17.9083	+	31.0180i	−0.771363	+	1.33604i
$540$		0			0
$541$	−11.6465	+	11.6465i	−0.500724	+	0.500724i	−0.911663	−	0.410939i	$-0.865201\pi$
$541$	−11.6465	+	11.6465i	−0.500724	+	0.500724i	0.410939	+	0.911663i	$0.365201\pi$
$542$	−2.80399	−	4.85665i	−0.120442	−	0.208611i
$543$	−1.82387	−	6.80676i	−0.0782696	−	0.292106i
$544$			7.02475i			0.301184i
$545$		0			0
$546$	−8.05680	−	4.65159i	−0.344799	−	0.199070i
$547$	18.6903			0.799142			0.399571	−	0.916702i	$-0.369159\pi$
$547$	18.6903			0.799142			0.399571	+	0.916702i	$0.369159\pi$
$548$	25.6460	+	6.87182i	1.09554	+	0.293549i
$549$	−4.38340	+	4.38340i	−0.187079	+	0.187079i
$550$		0			0
$551$	−2.67444	−	4.63227i	−0.113935	−	0.197341i
$552$	−5.99941	−	1.60754i	−0.255352	−	0.0684214i
$553$	5.59986	−	9.69925i	0.238130	−	0.412454i
$554$	3.38110			0.143649
$555$		0			0
$556$	32.4941			1.37805
$557$	−3.08244	+	5.33894i	−0.130607	+	0.226218i	−0.923911	−	0.382608i	$-0.875026\pi$
$557$	−3.08244	+	5.33894i	−0.130607	+	0.226218i	0.793304	+	0.608826i	$0.208359\pi$
$558$	−1.21728	−	0.326170i	−0.0515317	−	0.0138079i
$559$	−8.70469	−	15.0770i	−0.368169	−	0.637688i
$560$		0			0
$561$	−14.5944	+	14.5944i	−0.616174	+	0.616174i
$562$	−5.62775	−	1.50795i	−0.237392	−	0.0636091i
$563$	24.5838			1.03609			0.518043	−	0.855355i	$-0.326661\pi$
$563$	24.5838			1.03609			0.518043	+	0.855355i	$0.326661\pi$
$564$	−26.6903	−	15.4097i	−1.12387	−	0.648864i
$565$		0			0
$566$			5.18700i			0.218026i
$567$	−10.5463	−	39.3594i	−0.442904	−	1.65294i
$568$	5.05954	+	8.76337i	0.212293	+	0.367703i
$569$	24.7919	−	24.7919i	1.03933	−	1.03933i	0.0401367	−	0.999194i	$-0.487221\pi$
$569$	24.7919	−	24.7919i	1.03933	−	1.03933i	0.999194	−	0.0401367i	$-0.0127793\pi$
$570$		0			0
$571$	10.8132	−	18.7289i	0.452516	−	0.783781i	−0.546025	−	0.837769i	$-0.683860\pi$
$571$	10.8132	−	18.7289i	0.452516	−	0.783781i	0.998542	+	0.0539873i	$0.0171930\pi$
$572$	37.6173	+	21.7184i	1.57286	+	0.908090i
$573$	16.3968	−	9.46669i	0.684986	−	0.395477i
$574$	1.19600	−	4.46352i	0.0499199	−	0.186304i
$575$		0			0
$576$	−3.47383	−	2.00562i	−0.144743	−	0.0835674i
$577$	3.05528	+	1.76397i	0.127193	+	0.0734348i	0.562246	−	0.826970i	$-0.309937\pi$
$577$	3.05528	+	1.76397i	0.127193	+	0.0734348i	−0.435054	+	0.900405i	$0.643271\pi$
$578$	−2.65815			−0.110565
$579$	−8.25858	−	2.21288i	−0.343215	−	0.0919642i
$580$		0			0
$581$	23.4026			0.970904
$582$	1.98995	+	1.98995i	0.0824859	+	0.0824859i
$583$	−0.692066	−	2.58282i	−0.0286624	−	0.106970i
$584$	−3.00556	+	3.00556i	−0.124371	+	0.124371i
$585$		0			0
$586$	0.0858211	+	0.0858211i	0.00354524	+	0.00354524i
$587$	17.6768	+	30.6172i	0.729601	+	1.26371i	0.957052	+	0.289917i	$0.0936276\pi$
$587$	17.6768	+	30.6172i	0.729601	+	1.26371i	−0.227451	+	0.973790i	$0.573039\pi$
$588$	−7.80955	+	29.1456i	−0.322060	+	1.20195i
$589$	−5.53581	+	3.19610i	−0.228099	+	0.131693i
$590$		0			0
$591$		−	9.11405i		−	0.374902i
$592$	19.3429	−	10.8013i	0.794989	−	0.443929i
$593$	25.5343	+	25.5343i	1.04857	+	1.04857i	0.998759	+	0.0498107i	$0.0158618\pi$
$593$	25.5343	+	25.5343i	1.04857	+	1.04857i	0.0498107	+	0.998759i	$0.484138\pi$
$594$	−1.26225	−	4.71079i	−0.0517909	−	0.193286i
$595$		0			0
$596$	−4.59223	+	2.65133i	−0.188105	+	0.108603i
$597$	6.82842	−	3.94239i	0.279469	−	0.161351i
$598$	4.24873			0.173743
$599$	−8.97611	+	5.18236i	−0.366754	+	0.211745i	−0.672039	−	0.740515i	$-0.734581\pi$
$599$	−8.97611	+	5.18236i	−0.366754	+	0.211745i	0.305286	+	0.952261i	$0.401248\pi$
$600$		0			0
$601$	18.8695	−	32.6829i	0.769702	−	1.33316i	−0.168023	−	0.985783i	$-0.553738\pi$
$601$	18.8695	−	32.6829i	0.769702	−	1.33316i	0.937725	−	0.347379i	$-0.112928\pi$
$602$	2.30014	−	2.30014i	0.0937466	−	0.0937466i
$603$	5.52582	−	5.52582i	0.225029	−	0.225029i
$604$	−26.5660	−	15.3379i	−1.08096	−	0.624090i
$605$		0			0
$606$	0.625909	+	0.625909i	0.0254258	+	0.0254258i
$607$	16.4454	−	28.4843i	0.667500	−	1.15614i	−0.311101	−	0.950377i	$-0.600698\pi$
$607$	16.4454	−	28.4843i	0.667500	−	1.15614i	0.978601	−	0.205767i	$-0.0659689\pi$
$608$	2.06999	−	0.554653i	0.0839493	−	0.0224942i
$609$	50.4769	−	13.5252i	2.04543	−	0.548070i
$610$		0			0
$611$	41.3603	+	11.0824i	1.67326	+	0.448348i
$612$	−1.46639	+	2.53987i	−0.0592754	+	0.102668i
$613$	6.43944	+	24.0323i	0.260087	+	0.970657i	0.965190	+	0.261552i	$0.0842341\pi$
$613$	6.43944	+	24.0323i	0.260087	+	0.970657i	−0.705103	+	0.709105i	$0.749099\pi$
$614$	4.38933	−	1.17612i	0.177139	−	0.0474642i
$615$		0			0
$616$	−4.26639	+	15.9224i	−0.171898	+	0.641532i
$617$	−14.8844	+	3.98826i	−0.599223	+	0.160561i	−0.545665	−	0.838003i	$-0.683723\pi$
$617$	−14.8844	+	3.98826i	−0.599223	+	0.160561i	−0.0535581	+	0.998565i	$0.517056\pi$
$618$	−1.56395	−	1.56395i	−0.0629113	−	0.0629113i
$619$	−9.03986			−0.363343			−0.181671	−	0.983359i	$-0.558151\pi$
$619$	−9.03986			−0.363343			−0.181671	+	0.983359i	$0.558151\pi$
$620$		0			0
$621$	10.8607	+	10.8607i	0.435825	+	0.435825i
$622$	−1.65919	+	6.19217i	−0.0665274	+	0.248283i
$623$			5.83931i			0.233947i
$624$	34.2147	+	9.16779i	1.36968	+	0.367005i
$625$		0			0
$626$	2.06509	+	3.57684i	0.0825376	+	0.142959i
$627$	5.45287	+	3.14822i	0.217767	+	0.125728i
$628$	−6.78775	+	6.78775i	−0.270861	+	0.270861i
$629$	−7.36662	−	13.1922i	−0.293726	−	0.526006i
$630$		0			0
$631$	0.852346	−	0.228386i	0.0339314	−	0.00909188i	−0.241813	−	0.970323i	$-0.577742\pi$
$631$	0.852346	−	0.228386i	0.0339314	−	0.00909188i	0.275745	+	0.961231i	$0.411076\pi$
$632$	0.719245	−	2.68426i	0.0286100	−	0.106774i
$633$	−29.7574	−	7.97346i	−1.18275	−	0.316917i
$634$	−1.14225	+	4.26292i	−0.0453644	+	0.169302i
$635$		0			0
$636$	−1.12633	−	1.95087i	−0.0446621	−	0.0773570i
$637$		−	41.9224i		−	1.66103i
$638$	7.31976	−	1.96132i	0.289792	−	0.0776496i
$639$			6.36927i			0.251964i
$640$		0			0
$641$	23.9371	−	41.4602i	0.945458	−	1.63758i	0.190626	−	0.981663i	$-0.438948\pi$
$641$	23.9371	−	41.4602i	0.945458	−	1.63758i	0.754832	−	0.655918i	$-0.227718\pi$
$642$	0.245331	−	0.141642i	0.00968244	−	0.00559016i
$643$		−	2.96948i		−	0.117105i	−0.998284	−	0.0585523i	$-0.981352\pi$
$643$		−	2.96948i		−	0.117105i	0.998284	−	0.0585523i	$-0.0186485\pi$
$644$	−6.61548	−	24.6893i	−0.260686	−	0.972895i
$645$		0			0
$646$	−0.119580	−	0.446279i	−0.00470482	−	0.0175586i
$647$	−1.83889	−	3.18505i	−0.0722941	−	0.125217i	0.827612	−	0.561300i	$-0.189699\pi$
$647$	−1.83889	−	3.18505i	−0.0722941	−	0.125217i	−0.899906	+	0.436083i	$0.856365\pi$
$648$	−5.05531	−	8.75606i	−0.198591	−	0.343971i
$649$	11.6349	+	43.4219i	0.456708	+	1.70446i
$650$		0			0
$651$	−16.1634	−	60.3225i	−0.633493	−	2.36423i
$652$		−	31.7409i		−	1.24307i
$653$	−5.95590	+	3.43864i	−0.233072	+	0.134564i	−0.611989	−	0.790867i	$-0.709630\pi$
$653$	−5.95590	+	3.43864i	−0.233072	+	0.134564i	0.378916	+	0.925431i	$0.376297\pi$
$654$	−1.59402	+	2.76093i	−0.0623312	+	0.107961i
$655$		0			0
$656$			17.5942i			0.686939i
$657$	−2.58424	+	0.692446i	−0.100821	+	0.0270149i
$658$			8.00064i			0.311898i
$659$	9.37543	+	16.2387i	0.365215	+	0.632571i	0.988811	−	0.149176i	$-0.0476622\pi$
$659$	9.37543	+	16.2387i	0.365215	+	0.632571i	−0.623596	+	0.781747i	$0.714329\pi$
$660$		0			0
$661$	−7.54321	+	28.1516i	−0.293397	+	1.09497i	0.649086	+	0.760715i	$0.275152\pi$
$661$	−7.54321	+	28.1516i	−0.293397	+	1.09497i	−0.942482	+	0.334256i	$0.891515\pi$
$662$	−1.07275	−	0.287441i	−0.0416934	−	0.0111717i
$663$	6.25257	−	23.3349i	0.242830	−	0.906253i
$664$	5.60895	−	1.50291i	0.217669	−	0.0583243i
$665$		0			0
$666$	−0.908658	−	0.0130154i	−0.0352098	−	0.000504336i
$667$	−16.8757	+	16.8757i	−0.653428	+	0.653428i
$668$	−13.1236	−	7.57690i	−0.507766	−	0.293159i
$669$	−16.2291	−	28.1096i	−0.627453	−	1.08678i
$670$		0			0
$671$	−43.0292	−	11.5296i	−1.66112	−	0.445096i
$672$			20.9368i			0.807655i
$673$	−7.31994	+	27.3184i	−0.282163	+	1.05305i	0.668725	+	0.743510i	$0.266840\pi$
$673$	−7.31994	+	27.3184i	−0.282163	+	1.05305i	−0.950888	+	0.309536i	$0.899826\pi$
$674$	0.0869564	+	0.0869564i	0.00334943	+	0.00334943i
$675$		0			0
$676$	−25.6248			−0.985571
$677$	−11.9853	−	11.9853i	−0.460633	−	0.460633i	0.438230	−	0.898863i	$-0.355605\pi$
$677$	−11.9853	−	11.9853i	−0.460633	−	0.460633i	−0.898863	+	0.438230i	$0.855605\pi$
$678$	−0.802575	+	0.215049i	−0.0308227	+	0.00825892i
$679$	−6.08800	+	22.7207i	−0.233636	+	0.871942i
$680$		0			0
$681$	8.16336	−	2.18737i	0.312821	−	0.0838201i
$682$	−2.34389	−	8.74750i	−0.0897520	−	0.334959i
$683$	−6.84107	+	11.8491i	−0.261766	+	0.453393i	−0.966711	−	0.255869i	$-0.917638\pi$
$683$	−6.84107	+	11.8491i	−0.261766	+	0.453393i	0.704945	+	0.709262i	$0.250972\pi$
$684$	0.864208	+	0.231564i	0.0330438	+	0.00885407i
$685$		0			0
$686$	1.09825	−	0.294275i	0.0419313	−	0.0112355i
$687$	−14.9698	+	4.01113i	−0.571132	+	0.153034i
$688$	−6.19263	+	10.7260i	−0.236092	+	0.408923i
$689$	2.21309	+	2.21309i	0.0843120	+	0.0843120i
$690$		0			0
$691$	−12.5733	−	7.25918i	−0.478310	−	0.276152i	0.241402	−	0.970425i	$-0.422393\pi$
$691$	−12.5733	−	7.25918i	−0.478310	−	0.276152i	−0.719712	+	0.694273i	$0.755726\pi$
$692$	−28.5482	+	28.5482i	−1.08524	+	1.08524i
$693$	−7.33666	+	7.33666i	−0.278697	+	0.278697i
$694$	−0.719928	+	1.24695i	−0.0273281	+	0.0473337i
$695$		0			0
$696$	11.2293	−	6.48324i	0.425646	−	0.245747i
$697$	11.9995			0.454515
$698$	4.47337	−	2.58270i	0.169319	−	0.0977566i
$699$	−22.9533	+	13.2521i	−0.868175	+	0.501241i
$700$		0			0
$701$	−6.61099	−	24.6725i	−0.249693	−	0.931869i	−0.970966	−	0.239217i	$-0.923109\pi$
$701$	−6.61099	−	24.6725i	−0.249693	−	0.931869i	0.721273	−	0.692651i	$-0.243558\pi$
$702$	4.03643	+	4.03643i	0.152345	+	0.152345i
$703$	−3.30571	+	3.21235i	−0.124677	+	0.121156i
$704$		−	28.8251i		−	1.08639i
$705$		0			0
$706$	3.27251	−	1.88938i	0.123162	−	0.0711078i
$707$	−1.91489	+	7.14648i	−0.0720170	+	0.268771i
$708$	18.9357	+	32.7976i	0.711647	+	1.23261i
$709$	0.827189	+	0.827189i	0.0310657	+	0.0310657i	0.722469	−	0.691403i	$-0.243007\pi$
$709$	0.827189	+	0.827189i	0.0310657	+	0.0310657i	−0.691403	+	0.722469i	$0.743007\pi$
$710$		0			0
$711$	1.23684	−	1.23684i	0.0463852	−	0.0463852i
$712$	0.375000	+	1.39952i	0.0140537	+	0.0524492i
$713$	20.1673	+	20.1673i	0.755271	+	0.755271i
$714$	4.51386			0.168927
$715$		0			0
$716$	−23.1086	−	6.19193i	−0.863610	−	0.231403i
$717$	−30.1323			−1.12531
$718$	−6.10471	−	3.52456i	−0.227826	−	0.131535i
$719$	5.80482	+	3.35141i	0.216483	+	0.124987i	0.604321	−	0.796741i	$-0.293445\pi$
$719$	5.80482	+	3.35141i	0.216483	+	0.124987i	−0.387838	+	0.921728i	$0.626778\pi$
$720$		0			0
$721$	4.78472	−	17.8568i	0.178192	−	0.665023i
$722$	3.91669	−	2.26130i	0.145764	−	0.0841569i
$723$	27.2473	+	15.7312i	1.01334	+	0.585051i
$724$	3.59782	−	6.23161i	0.133712	−	0.231596i
$725$		0			0
$726$	−2.68095	+	2.68095i	−0.0994995	+	0.0994995i
$727$	10.5202	+	18.2215i	0.390171	+	0.675797i	0.992472	−	0.122473i	$-0.0390824\pi$
$727$	10.5202	+	18.2215i	0.390171	+	0.675797i	−0.602300	+	0.798270i	$0.705749\pi$
$728$	−4.99371	−	18.6368i	−0.185079	−	0.690726i
$729$			19.5246i			0.723134i
$730$		0			0
$731$	7.31527	+	4.22347i	0.270565	+	0.156211i
$732$	−37.5289			−1.38711
$733$	−25.3437	−	6.79083i	−0.936092	−	0.250825i	−0.241641	−	0.970366i	$-0.577686\pi$
$733$	−25.3437	−	6.79083i	−0.936092	−	0.250825i	−0.694450	+	0.719541i	$0.744352\pi$
$734$	1.98983	−	1.98983i	0.0734460	−	0.0734460i
$735$		0			0
$736$	−4.78088	−	8.28072i	−0.176225	−	0.305231i
$737$	54.2435	+	14.5345i	1.99809	+	0.535386i
$738$	0.360849	−	0.625009i	0.0132830	−	0.0230069i
$739$	33.7980			1.24328			0.621640	−	0.783303i	$-0.286467\pi$
$739$	33.7980			1.24328			0.621640	+	0.783303i	$0.286467\pi$
$740$		0			0
$741$	−7.36982			−0.270737
$742$	−0.292394	+	0.506442i	−0.0107341	+	0.0185921i
$743$	0.485894	+	0.130195i	0.0178257	+	0.00477639i	0.267721	−	0.963497i	$-0.413729\pi$
$743$	0.485894	+	0.130195i	0.0178257	+	0.00477639i	−0.249895	+	0.968273i	$0.580396\pi$
$744$	−7.74781	−	13.4196i	−0.284049	−	0.491987i
$745$		0			0
$746$	1.91396	−	1.91396i	0.0700749	−	0.0700749i
$747$	3.53045	+	0.945982i	0.129172	+	0.0346117i
$748$	−21.0753			−0.770588
$749$	2.05057	+	1.18390i	0.0749262	+	0.0432587i
$750$		0			0
$751$			16.9759i			0.619459i	0.950825	+	0.309730i	$0.100239\pi$
$751$			16.9759i			0.619459i	−0.950825	+	0.309730i	$0.899761\pi$
$752$	−7.88420	−	29.4242i	−0.287507	−	1.07299i
$753$	4.74991	+	8.22709i	0.173097	+	0.299812i
$754$	−6.27192	+	6.27192i	−0.228410	+	0.228410i
$755$		0			0
$756$	17.1707	−	29.7406i	0.624494	−	1.08165i
$757$	18.6230	+	10.7520i	0.676866	+	0.390789i	0.798673	−	0.601765i	$-0.205536\pi$
$757$	18.6230	+	10.7520i	0.676866	+	0.390789i	−0.121807	+	0.992554i	$0.538869\pi$
$758$	5.96467	−	3.44370i	0.216646	−	0.125081i
$759$	7.27115	−	27.1363i	0.263926	−	0.984985i
$760$		0			0
$761$	5.87890	+	3.39418i	0.213110	+	0.123039i	0.602756	−	0.797926i	$-0.294069\pi$
$761$	5.87890	+	3.39418i	0.213110	+	0.123039i	−0.389646	+	0.920965i	$0.627403\pi$
$762$	−1.53252	−	0.884799i	−0.0555172	−	0.0320529i
$763$	−26.6469			−0.964683
$764$	18.6743	+	5.00377i	0.675614	+	0.181030i
$765$		0			0
$766$	−2.00674			−0.0725064
$767$	−37.2060	−	37.2060i	−1.34343	−	1.34343i
$768$	−5.60256	−	20.9090i	−0.202165	−	0.754490i
$769$	−7.17556	+	7.17556i	−0.258757	+	0.258757i	−0.824549	−	0.565791i	$-0.808571\pi$
$769$	−7.17556	+	7.17556i	−0.258757	+	0.258757i	0.565791	+	0.824549i	$0.308571\pi$
$770$		0			0
$771$	−28.1697	−	28.1697i	−1.01451	−	1.01451i
$772$	−4.36521	−	7.56076i	−0.157107	−	0.272118i
$773$	7.27088	−	27.1353i	0.261515	−	0.975988i	−0.702834	−	0.711354i	$-0.748082\pi$
$773$	7.27088	−	27.1353i	0.261515	−	0.975988i	0.964349	−	0.264634i	$-0.0852512\pi$
$774$	0.439968	−	0.254016i	0.0158143	−	0.00913041i
$775$		0			0
$776$			5.83649i			0.209518i
$777$	−21.9557	−	39.3184i	−0.787658	−	1.41054i
$778$	4.51817	+	4.51817i	0.161984	+	0.161984i
$779$	−0.947447	−	3.53592i	−0.0339458	−	0.126687i
$780$		0			0
$781$	−39.6381	+	22.8851i	−1.41836	+	0.818892i
$782$	−1.78528	+	1.03073i	−0.0638414	+	0.0368588i
$783$	−32.0649			−1.14591
$784$	−25.8285	+	14.9121i	−0.922445	+	0.532574i
$785$		0			0
$786$	3.68173	−	6.37694i	0.131323	−	0.227458i
$787$	−9.47199	+	9.47199i	−0.337640	+	0.337640i	−0.855478	−	0.517838i	$-0.826737\pi$
$787$	−9.47199	+	9.47199i	−0.337640	+	0.337640i	0.517838	+	0.855478i	$0.326737\pi$
$788$	6.58066	−	6.58066i	0.234426	−	0.234426i
$789$	−19.1187	−	11.0382i	−0.680644	−	0.392970i
$790$		0			0
$791$	−4.91077	−	4.91077i	−0.174607	−	0.174607i
$792$	−1.28723	+	2.22955i	−0.0457398	+	0.0792237i
$793$	50.3646	−	13.4952i	1.78850	−	0.479227i
$794$	8.33753	−	2.23404i	0.295888	−	0.0792829i
$795$		0			0
$796$	7.77690	+	2.08381i	0.275645	+	0.0738588i
$797$	−17.2891	+	29.9455i	−0.612410	+	1.06072i	0.378423	+	0.925633i	$0.376466\pi$
$797$	−17.2891	+	29.9455i	−0.612410	+	1.06072i	−0.990833	+	0.135092i	$0.956867\pi$
$798$	−0.356401	−	1.33011i	−0.0126164	−	0.0470852i
$799$	−20.0678	+	5.37715i	−0.709947	+	0.190230i
$800$		0			0
$801$	−0.236037	+	0.880902i	−0.00833996	+	0.0311251i
$802$	7.21458	−	1.93314i	0.254756	−	0.0682615i
$803$	−13.5946	−	13.5946i	−0.479744	−	0.479744i
$804$	47.3097			1.66849
$805$		0			0
$806$	7.49528	+	7.49528i	0.264010	+	0.264010i
$807$	10.0578	−	37.5363i	0.354052	−	1.32134i
$808$			1.83578i			0.0645826i
$809$	−28.4366	−	7.61955i	−0.999776	−	0.267889i	−0.278424	−	0.960458i	$-0.589812\pi$
$809$	−28.4366	−	7.61955i	−0.999776	−	0.267889i	−0.721352	+	0.692569i	$0.756479\pi$
$810$		0			0
$811$	−3.59932	−	6.23420i	−0.126389	−	0.218912i	0.795886	−	0.605447i	$-0.207005\pi$
$811$	−3.59932	−	6.23420i	−0.126389	−	0.218912i	−0.922275	+	0.386534i	$0.873672\pi$
$812$	46.2118	+	26.6804i	1.62172	+	0.936298i
$813$	30.6904	−	30.6904i	1.07636	−	1.07636i
$814$	−3.18385	−	5.70165i	−0.111594	−	0.199843i
$815$		0			0
$816$	−16.6008	+	4.44816i	−0.581143	+	0.155717i
$817$	0.666945	−	2.48907i	0.0233335	−	0.0870817i
$818$	−4.55016	−	1.21921i	−0.159093	−	0.0426287i
$819$	3.14320	−	11.7306i	0.109832	−	0.409900i
$820$		0			0
$821$	−10.3931	−	18.0014i	−0.362721	−	0.628252i	0.625686	−	0.780075i	$-0.284819\pi$
$821$	−10.3931	−	18.0014i	−0.362721	−	0.628252i	−0.988408	+	0.151823i	$0.951486\pi$
$822$		−	6.38212i		−	0.222602i
$823$	19.8259	−	5.31233i	0.691087	−	0.185176i	0.103852	−	0.994593i	$-0.466883\pi$
$823$	19.8259	−	5.31233i	0.691087	−	0.185176i	0.587235	+	0.809417i	$0.300216\pi$
$824$		−	4.58705i		−	0.159798i
$825$		0			0
$826$	4.91567	−	8.51420i	0.171038	−	0.296247i
$827$	−17.8279	+	10.2930i	−0.619937	+	0.357921i	−0.776845	−	0.629692i	$-0.783181\pi$
$827$	−17.8279	+	10.2930i	−0.619937	+	0.357921i	0.156907	+	0.987613i	$0.449848\pi$
$828$		−	3.99197i		−	0.138730i
$829$	−0.0273552	−	0.102091i	−0.000950086	−	0.00354577i	0.965449	−	0.260591i	$-0.0839176\pi$
$829$	−0.0273552	−	0.102091i	−0.000950086	−	0.00354577i	−0.966399	+	0.257046i	$0.917251\pi$
$830$		0			0
$831$	6.77275	+	25.2763i	0.234944	+	0.876823i
$832$	16.8696	+	29.2189i	0.584847	+	1.01298i
$833$	10.1703	+	17.6154i	0.352379	+	0.610338i
$834$	−2.02157	−	7.54462i	−0.0700014	−	0.261249i
$835$		0			0
$836$	1.66404	+	6.21028i	0.0575520	+	0.214787i
$837$			38.3192i			1.32451i
$838$	3.54032	−	2.04400i	0.122298	−	0.0706090i
$839$	−25.4547	+	44.0888i	−0.878793	+	1.52211i	−0.0261266	+	0.999659i	$0.508317\pi$
$839$	−25.4547	+	44.0888i	−0.878793	+	1.52211i	−0.852666	+	0.522456i	$0.825016\pi$
$840$		0			0
$841$		−	20.8233i		−	0.718046i
$842$	−0.547340	+	0.146659i	−0.0188626	+	0.00505422i
$843$		−	45.0922i		−	1.55306i
$844$	−15.7287	−	27.2430i	−0.541406	−	0.937742i
$845$		0			0
$846$	−0.323402	+	1.20695i	−0.0111188	+	0.0414959i
$847$	−30.6105	−	8.20206i	−1.05179	−	0.281826i
$848$	0.576278	−	2.15070i	0.0197895	−	0.0738553i
$849$	−38.7767	+	10.3902i	−1.33081	+	0.356590i
$850$		0			0
$851$	17.6620	+	10.5373i	0.605446	+	0.361214i
$852$	−27.2655	+	27.2655i	−0.934101	+	0.934101i
$853$	−18.7508	−	10.8258i	−0.642014	−	0.370667i	0.143376	−	0.989668i	$-0.454204\pi$
$853$	−18.7508	−	10.8258i	−0.642014	−	0.370667i	−0.785390	+	0.619001i	$0.787538\pi$
$854$	4.87121	+	8.43718i	0.166689	+	0.288715i
$855$		0			0
$856$	0.567494	+	0.152059i	0.0193965	+	0.00519729i
$857$			8.91910i			0.304670i	0.988329	+	0.152335i	$0.0486793\pi$
$857$			8.91910i			0.304670i	−0.988329	+	0.152335i	$0.951321\pi$
$858$	2.70236	−	10.0853i	0.0922570	−	0.344308i
$859$	34.0010	+	34.0010i	1.16010	+	1.16010i	0.984453	+	0.175647i	$0.0562018\pi$
$859$	34.0010	+	34.0010i	1.16010	+	1.16010i	0.175647	+	0.984453i	$0.443798\pi$
$860$		0			0
$861$	35.7638			1.21883
$862$	2.68466	+	2.68466i	0.0914399	+	0.0914399i
$863$	−45.8461	+	12.2844i	−1.56062	+	0.418166i	−0.932859	−	0.360241i	$-0.882694\pi$
$863$	−45.8461	+	12.2844i	−1.56062	+	0.418166i	−0.627759	+	0.778408i	$0.716028\pi$
$864$	3.32497	−	12.4090i	0.113118	−	0.422161i
$865$		0			0
$866$	8.48725	−	2.27415i	0.288408	−	0.0772788i
$867$	−5.32460	−	19.8717i	−0.180833	−	0.674877i
$868$	31.8845	−	55.2255i	1.08223	−	1.87448i
$869$	12.1413	+	3.25326i	0.411866	+	0.110359i
$870$		0			0
$871$	−63.4908	+	17.0123i	−2.15130	+	0.576440i
$872$	−6.38652	+	1.71126i	−0.216275	+	0.0579507i
$873$	−1.83684	+	3.18150i	−0.0621675	+	0.107677i
$874$	0.444687	+	0.444687i	0.0150418	+	0.0150418i
$875$		0			0
$876$	−14.0268	−	8.09840i	−0.473923	−	0.273619i
$877$	34.2418	−	34.2418i	1.15626	−	1.15626i	0.170989	−	0.985273i	$-0.445304\pi$
$877$	34.2418	−	34.2418i	1.15626	−	1.15626i	0.985273	−	0.170989i	$-0.0546963\pi$
$878$	−3.51082	+	3.51082i	−0.118485	+	0.118485i
$879$	−0.469666	+	0.813486i	−0.0158415	+	0.0274382i
$880$		0			0
$881$	28.3215	−	16.3514i	0.954175	−	0.550893i	0.0597995	−	0.998210i	$-0.480954\pi$
$881$	28.3215	−	16.3514i	0.954175	−	0.550893i	0.894375	+	0.447317i	$0.147621\pi$
$882$	1.22336			0.0411926
$883$	−2.72693	+	1.57439i	−0.0917684	+	0.0529825i	−0.545182	−	0.838318i	$-0.683539\pi$
$883$	−2.72693	+	1.57439i	−0.0917684	+	0.0529825i	0.453414	+	0.891300i	$0.350206\pi$
$884$	21.3632	−	12.3341i	0.718522	−	0.414839i
$885$		0			0
$886$	1.27516	+	4.75898i	0.0428400	+	0.159881i
$887$	1.64239	+	1.64239i	0.0551461	+	0.0551461i	0.734142	−	0.678996i	$-0.237585\pi$
$887$	1.64239	+	1.64239i	0.0551461	+	0.0551461i	−0.678996	+	0.734142i	$0.737585\pi$
$888$	−7.78720	−	8.01352i	−0.261321	−	0.268916i
$889$		−	14.7910i		−	0.496074i
$890$		0			0
$891$	39.6050	−	22.8660i	1.32682	−	0.766039i
$892$	8.57815	−	32.0141i	0.287218	−	1.07191i
$893$	3.16898	+	5.48884i	0.106046	+	0.183677i
$894$	0.901297	+	0.901297i	0.0301439	+	0.0301439i
$895$		0			0
$896$	−20.0443	+	20.0443i	−0.669632	+	0.669632i
$897$	8.51071	+	31.7624i	0.284164	+	1.06052i
$898$	0.533652	+	0.533652i	0.0178082	+	0.0178082i
$899$	−59.5415			−1.98582
$900$		0			0
$901$	−1.46681	−	0.393030i	−0.0488665	−	0.0130937i
$902$	5.18619			0.172681
$903$	21.8027	+	12.5878i	0.725548	+	0.418895i
$904$	−1.49234	−	0.861604i	−0.0496346	−	0.0286565i
$905$		0			0
$906$	−1.90845	+	7.12244i	−0.0634041	+	0.236627i
$907$	7.21849	−	4.16760i	0.239686	−	0.138383i	−0.375346	−	0.926885i	$-0.622476\pi$
$907$	7.21849	−	4.16760i	0.239686	−	0.138383i	0.615032	+	0.788502i	$0.289143\pi$
$908$	7.47359	+	4.31488i	0.248020	+	0.143194i
$909$	−0.577751	+	1.00069i	−0.0191628	+	0.0331909i
$910$		0			0
$911$	26.7018	−	26.7018i	0.884669	−	0.884669i	−0.109336	−	0.994005i	$-0.534872\pi$
$911$	26.7018	−	26.7018i	0.884669	−	0.884669i	0.994005	+	0.109336i	$0.0348725\pi$
$912$	2.62149	+	4.54056i	0.0868064	+	0.150353i
$913$	6.79791	+	25.3702i	0.224978	+	0.839630i
$914$		−	0.936919i		−	0.0309905i
$915$		0			0
$916$	−13.7049	−	7.91251i	−0.452822	−	0.261437i
$917$	61.5466			2.03245
$918$	−2.67530	−	0.716845i	−0.0882981	−	0.0236594i
$919$	−41.4518	+	41.4518i	−1.36737	+	1.36737i	−0.503195	+	0.864173i	$0.667842\pi$
$919$	−41.4518	+	41.4518i	−1.36737	+	1.36737i	−0.864173	+	0.503195i	$0.832158\pi$
$920$		0			0
$921$	17.5847	+	30.4576i	0.579436	+	1.00361i
$922$	8.29527	+	2.22271i	0.273190	+	0.0732011i
$923$	26.7864	−	46.3955i	0.881686	−	1.52713i
$924$	−62.8135			−2.06641
$925$		0			0
$926$	−6.92697			−0.227634
$927$	1.44362	−	2.50042i	0.0474147	−	0.0821246i
$928$	19.2814	+	5.16643i	0.632943	+	0.169596i
$929$	−17.9777	−	31.1383i	−0.589830	−	1.02162i	−0.994254	−	0.107044i	$-0.965861\pi$
$929$	−17.9777	−	31.1383i	−0.589830	−	1.02162i	0.404424	−	0.914571i	$-0.367472\pi$
$930$		0			0
$931$	4.38775	−	4.38775i	0.143803	−	0.143803i
$932$	−26.1416	−	7.00462i	−0.856297	−	0.229444i
$933$	−49.6146			−1.62431
$934$	3.39624	+	1.96082i	0.111129	+	0.0641601i
$935$		0			0
$936$		−	3.01335i		−	0.0984944i
$937$	−7.21273	−	26.9183i	−0.235629	−	0.879381i	−0.977864	−	0.209241i	$-0.932901\pi$
$937$	−7.21273	−	26.9183i	−0.235629	−	0.879381i	0.742235	−	0.670140i	$-0.233766\pi$
$938$	−6.14076	−	10.6361i	−0.200503	−	0.347281i
$939$	−22.6029	+	22.6029i	−0.737618	+	0.737618i
$940$		0			0
$941$	−21.5873	+	37.3903i	−0.703725	+	1.21889i	0.263425	+	0.964680i	$0.415148\pi$
$941$	−21.5873	+	37.3903i	−0.703725	+	1.21889i	−0.967150	+	0.254208i	$0.918185\pi$
$942$	1.99830	+	1.15372i	0.0651082	+	0.0375902i
$943$	−14.1450	+	8.16659i	−0.460623	+	0.265941i
$944$	−9.68826	+	36.1571i	−0.315326	+	1.17681i
$945$		0			0
$946$	3.16165	+	1.82538i	0.102794	+	0.0593483i
$947$	−23.4937	−	13.5641i	−0.763442	−	0.440773i	0.0670885	−	0.997747i	$-0.478629\pi$
$947$	−23.4937	−	13.5641i	−0.763442	−	0.440773i	−0.830530	+	0.556974i	$0.811962\pi$
$948$	10.5893			0.343926
$949$	21.7365	+	5.82427i	0.705596	+	0.189064i
$950$		0			0
$951$	−34.1566			−1.10760
$952$	6.61955	+	6.61955i	0.214541	+	0.214541i
$953$	−3.43270	−	12.8110i	−0.111196	−	0.414989i	0.887778	−	0.460271i	$-0.152248\pi$
$953$	−3.43270	−	12.8110i	−0.111196	−	0.414989i	−0.998974	+	0.0452823i	$0.985581\pi$
$954$	−0.0645812	+	0.0645812i	−0.00209089	+	0.00209089i
$955$		0			0
$956$	−21.7566	−	21.7566i	−0.703658	−	0.703658i
$957$	29.3247	+	50.7919i	0.947933	+	1.64187i
$958$	1.30763	−	4.88016i	0.0422477	−	0.157671i
$959$	46.1974	−	26.6721i	1.49179	−	0.861287i
$960$		0			0
$961$			40.1552i			1.29533i
$962$	6.56417	+	3.91624i	0.211637	+	0.126265i
$963$	0.261488	+	0.261488i	0.00842632	+	0.00842632i
$964$	8.31500	+	31.0320i	0.267808	+	0.999474i
$965$		0			0
$966$	−5.32090	+	3.07202i	−0.171197	+	0.0988408i
$967$	−35.5714	+	20.5372i	−1.14390	+	0.660431i	−0.947393	−	0.320072i	$-0.896293\pi$
$967$	−35.5714	+	20.5372i	−1.14390	+	0.660431i	−0.196506	+	0.980503i	$0.562960\pi$
$968$	−7.86321			−0.252733
$969$	3.09673	−	1.78790i	0.0994814	−	0.0574356i
$970$		0			0
$971$	−10.9286	+	18.9288i	−0.350714	+	0.607455i	−0.986375	−	0.164514i	$-0.947395\pi$
$971$	−10.9286	+	18.9288i	−0.350714	+	0.607455i	0.635660	+	0.771969i	$0.280728\pi$
$972$	8.55032	−	8.55032i	0.274252	−	0.274252i
$973$	46.1637	−	46.1637i	1.47994	−	1.47994i
$974$	−1.40602	−	0.811763i	−0.0450516	−	0.0260106i
$975$		0			0
$976$	−26.2294	−	26.2294i	−0.839583	−	0.839583i
$977$	18.9875	−	32.8873i	0.607464	−	1.05216i	−0.384192	−	0.923253i	$-0.625520\pi$
$977$	18.9875	−	32.8873i	0.607464	−	1.05216i	0.991657	−	0.128906i	$-0.0411466\pi$
$978$	−7.36975	+	1.97472i	−0.235659	+	0.0631445i
$979$	−6.33024	+	1.69618i	−0.202316	+	0.0542103i
$980$		0			0
$981$	−4.01988	−	1.07712i	−0.128345	−	0.0343899i
$982$	−0.683786	+	1.18435i	−0.0218205	+	0.0377942i
$983$	10.6310	+	39.6755i	0.339077	+	1.26545i	0.899381	+	0.437166i	$0.144018\pi$
$983$	10.6310	+	39.6755i	0.339077	+	1.26545i	−0.560304	+	0.828287i	$0.689316\pi$
$984$	8.57158	−	2.29675i	0.273252	−	0.0732177i
$985$		0			0
$986$	1.11385	−	4.15696i	0.0354723	−	0.132385i
$987$	−59.8107	+	16.0262i	−1.90380	+	0.510121i
$988$	−5.32127	−	5.32127i	−0.169292	−	0.169292i
$989$	−11.4976			−0.365602
$990$		0			0
$991$	9.05454	+	9.05454i	0.287627	+	0.287627i	0.836141	−	0.548514i	$-0.184806\pi$
$991$	9.05454	+	9.05454i	0.287627	+	0.287627i	−0.548514	+	0.836141i	$0.684806\pi$
$992$	6.17416	−	23.0423i	0.196030	−	0.731593i
$993$		−	8.59535i		−	0.272765i
$994$	9.66883	+	2.59076i	0.306677	+	0.0821738i
$995$		0			0
$996$	11.0636	+	19.1627i	0.350563	+	0.607193i
$997$	−49.3216	−	28.4758i	−1.56203	−	0.901838i	−0.997052	−	0.0767317i	$-0.975551\pi$
$997$	−49.3216	−	28.4758i	−1.56203	−	0.901838i	−0.564978	−	0.825106i	$-0.691115\pi$
$998$	−0.919576	+	0.919576i	−0.0291087	+	0.0291087i
$999$	6.76871	+	26.7903i	0.214153	+	0.847606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.t.b.643.9		68
5.2	odd	4		925.2.y.b.532.9		68
5.3	odd	4		185.2.u.a.162.9	yes	68
5.4	even	2		185.2.p.a.88.9	yes	68
37.8	odd	12		925.2.y.b.193.9		68
185.8	even	12		185.2.p.a.82.9	✓	68
185.82	even	12	inner	925.2.t.b.82.9		68
185.119	odd	12		185.2.u.a.8.9	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.82.9	✓	68	185.8	even	12
185.2.p.a.88.9	yes	68	5.4	even	2
185.2.u.a.8.9	yes	68	185.119	odd	12
185.2.u.a.162.9	yes	68	5.3	odd	4
925.2.t.b.82.9		68	185.82	even	12	inner
925.2.t.b.643.9		68	1.1	even	1	trivial
925.2.y.b.193.9		68	37.8	odd	12
925.2.y.b.532.9		68	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.122725 - 0.212566i) q^{2} +(1.83492 + 0.491666i) q^{3} +(0.969877 + 1.67988i) q^{4} +(0.329702 - 0.329702i) q^{6} +(3.76446 + 1.00868i) q^{7} +0.967013 q^{8} +(0.527123 + 0.304334i) q^{9} +4.37395i q^{11} +(0.953710 + 3.55930i) q^{12} +(-2.55980 - 4.43371i) q^{13} +(0.676405 - 0.676405i) q^{14} +(-1.82108 + 3.15420i) q^{16} +(2.15121 + 1.24200i) q^{17} +(0.129382 - 0.0746989i) q^{18} +(0.196130 - 0.731966i) q^{19} +(6.41155 + 3.70171i) q^{21} +(0.929753 + 0.536793i) q^{22} -3.38111 q^{23} +(1.77439 + 0.475447i) q^{24} -1.25661 q^{26} +(-3.21217 - 3.21217i) q^{27} +(1.95660 + 7.30213i) q^{28} +(4.99116 - 4.99116i) q^{29} +(-5.96470 - 5.96470i) q^{31} +(1.41400 + 2.44911i) q^{32} +(-2.15052 + 8.02585i) q^{33} +(0.528015 - 0.304850i) q^{34} +1.18067i q^{36} +(-5.22373 - 3.11652i) q^{37} +(-0.131521 - 0.131521i) q^{38} +(-2.51713 - 9.39407i) q^{39} +(4.18352 - 2.41536i) q^{41} +(1.57371 - 0.908585i) q^{42} +3.40053 q^{43} +(-7.34770 + 4.24219i) q^{44} +(-0.414947 + 0.718709i) q^{46} +(-5.91409 + 5.91409i) q^{47} +(-4.89234 + 4.89234i) q^{48} +(7.09153 + 4.09430i) q^{49} +(3.33665 + 3.33665i) q^{51} +(4.96539 - 8.60030i) q^{52} +(-0.590502 + 0.158224i) q^{53} +(-1.07701 + 0.288584i) q^{54} +(3.64028 + 0.975410i) q^{56} +(0.719765 - 1.24667i) q^{57} +(-0.448410 - 1.67349i) q^{58} +(9.92739 - 2.66004i) q^{59} +(-2.63598 + 9.83759i) q^{61} +(-1.99991 + 0.535874i) q^{62} +(1.67735 + 1.67735i) q^{63} -6.59018 q^{64} +(1.44210 + 1.44210i) q^{66} +(3.32297 - 12.4015i) q^{67} +4.81836i q^{68} +(-6.20407 - 1.66238i) q^{69} +(5.23213 + 9.06231i) q^{71} +(0.509734 + 0.294295i) q^{72} +(-3.10809 + 3.10809i) q^{73} +(-1.30355 + 0.727912i) q^{74} +(1.41983 - 0.380443i) q^{76} +(-4.41193 + 16.4656i) q^{77} +(-2.30577 - 0.617830i) q^{78} +(0.743780 - 2.77583i) q^{79} +(-5.22776 - 9.05475i) q^{81} -1.18570i q^{82} +(5.80029 - 1.55418i) q^{83} +14.3608i q^{84} +(0.417330 - 0.722837i) q^{86} +(11.6124 - 6.70440i) q^{87} +4.22967i q^{88} +(0.387792 + 1.44726i) q^{89} +(-5.16406 - 19.2725i) q^{91} +(-3.27926 - 5.67985i) q^{92} +(-8.01211 - 13.8774i) q^{93} +(0.531327 + 1.98294i) q^{94} +(1.39043 + 5.18914i) q^{96} +6.03559i q^{97} +(1.74062 - 1.00495i) q^{98} +(-1.33114 + 2.30561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 8 q^{3} - 30 q^{4} - 8 q^{6} + 2 q^{7} - 12 q^{8} - 14 q^{12} + 6 q^{13} - 26 q^{16} - 12 q^{17} - 18 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 24 q^{26} + 68 q^{27} + 26 q^{28}+ \cdots + 32 q^{99}+O(q^{100}) \) 68 * q + 4 * q^2 + 8 * q^3 - 30 * q^4 - 8 * q^6 + 2 * q^7 - 12 * q^8 - 14 * q^12 + 6 * q^13 - 26 * q^16 - 12 * q^17 - 18 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 24 * q^26 + 68 * q^27 + 26 * q^28 + 14 * q^29 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 16 * q^37 + 36 * q^38 + 52 * q^39 - 18 * q^41 - 132 * q^42 - 8 * q^43 - 36 * q^44 - 52 * q^46 + 24 * q^47 + 60 * q^48 - 36 * q^49 - 8 * q^51 + 26 * q^52 - 82 * q^53 + 40 * q^54 + 16 * q^56 + 6 * q^57 - 86 * q^58 - 8 * q^59 + 4 * q^61 - 10 * q^62 + 48 * q^63 - 20 * q^64 + 80 * q^66 + 40 * q^67 + 8 * q^69 + 4 * q^71 + 90 * q^72 + 60 * q^73 - 44 * q^74 + 72 * q^76 - 66 * q^77 + 24 * q^78 + 56 * q^79 - 6 * q^81 - 24 * q^83 - 4 * q^86 + 84 * q^87 - 22 * q^89 + 44 * q^91 - 44 * q^92 + 34 * q^93 - 20 * q^94 - 8 * q^96 - 42 * q^98 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more