LMFDB - Embedded newform 275.2.bm.b.107.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(7,275)] 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("275.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.bm (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.4
Character	$\chi$	$=$	275.107
Dual form			275.2.bm.b.18.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.237790 - 1.50135i) q^{2} +(-0.710333 - 0.361933i) q^{3} +(-0.295389 - 0.0959778i) q^{4} +(-0.712297 + 0.980393i) q^{6} +(-0.0869260 - 0.170602i) q^{7} +(1.16585 - 2.28811i) q^{8} +(-1.38978 - 1.91287i) q^{9} +(1.77694 - 2.80044i) q^{11} +(0.175087 + 0.175087i) q^{12} +(-3.05749 - 0.484259i) q^{13} +(-0.276803 + 0.0899388i) q^{14} +(-3.66057 - 2.65956i) q^{16} +(3.66088 - 0.579827i) q^{17} +(-3.20235 + 1.63168i) q^{18} +(0.229844 + 0.707388i) q^{19} +0.152646i q^{21} +(-3.78190 - 3.33373i) q^{22} +(1.14886 - 1.14886i) q^{23} +(-1.65629 + 1.20336i) q^{24} +(-1.45408 + 4.47521i) q^{26} +(0.669017 + 4.22401i) q^{27} +(0.00930302 + 0.0587369i) q^{28} +(-2.95025 + 9.07993i) q^{29} +(-0.283900 + 0.206266i) q^{31} +(-1.23166 + 1.23166i) q^{32} +(-2.27579 + 1.34611i) q^{33} -5.63413i q^{34} +(0.226933 + 0.698428i) q^{36} +(4.81621 - 2.45398i) q^{37} +(1.11669 - 0.176866i) q^{38} +(1.99657 + 1.45059i) q^{39} +(6.36824 - 2.06917i) q^{41} +(0.229174 + 0.0362976i) q^{42} +(3.72708 + 3.72708i) q^{43} +(-0.793670 + 0.656674i) q^{44} +(-1.45165 - 1.99802i) q^{46} +(-5.61318 + 11.0165i) q^{47} +(1.63764 + 3.21405i) q^{48} +(4.09295 - 5.63346i) q^{49} +(-2.81030 - 0.913123i) q^{51} +(0.856672 + 0.436496i) q^{52} +(1.41265 - 8.91914i) q^{53} +6.50079 q^{54} -0.491699 q^{56} +(0.0927608 - 0.585669i) q^{57} +(12.9306 + 6.58847i) q^{58} +(9.15496 + 2.97463i) q^{59} +(-3.46383 + 4.76756i) q^{61} +(0.242168 + 0.475281i) q^{62} +(-0.205531 + 0.403377i) q^{63} +(-3.76284 - 5.17911i) q^{64} +(1.47982 + 3.73685i) q^{66} +(-4.13426 - 4.13426i) q^{67} +(-1.13704 - 0.180089i) q^{68} +(-1.23188 + 0.400262i) q^{69} +(9.27272 + 6.73702i) q^{71} +(-5.99713 + 0.949851i) q^{72} +(-2.14008 + 1.09042i) q^{73} +(-2.53903 - 7.81434i) q^{74} -0.231015i q^{76} +(-0.632224 - 0.0597184i) q^{77} +(2.65261 - 2.65261i) q^{78} +(0.542434 - 0.394101i) q^{79} +(-1.13837 + 3.50353i) q^{81} +(-1.59224 - 10.0530i) q^{82} +(2.60980 + 16.4776i) q^{83} +(0.0146506 - 0.0450899i) q^{84} +(6.48191 - 4.70938i) q^{86} +(5.38198 - 5.38198i) q^{87} +(-4.33608 - 7.33074i) q^{88} -7.92190i q^{89} +(0.183160 + 0.563709i) q^{91} +(-0.449625 + 0.229095i) q^{92} +(0.276318 - 0.0437645i) q^{93} +(15.2048 + 11.0469i) q^{94} +(1.32067 - 0.429111i) q^{96} +(1.36201 + 0.215721i) q^{97} +(-7.48452 - 7.48452i) q^{98} +(-7.82643 + 0.492943i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} + 4 q^{3} - 20 q^{6} + 10 q^{8} - 24 q^{11} - 12 q^{12} + 10 q^{13} - 8 q^{16} + 10 q^{18} - 10 q^{22} + 24 q^{23} + 20 q^{26} + 16 q^{27} - 50 q^{28} - 28 q^{31} - 66 q^{33} + 24 q^{36}+ \cdots + 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 + 4 * q^3 - 20 * q^6 + 10 * q^8 - 24 * q^11 - 12 * q^12 + 10 * q^13 - 8 * q^16 + 10 * q^18 - 10 * q^22 + 24 * q^23 + 20 * q^26 + 16 * q^27 - 50 * q^28 - 28 * q^31 - 66 * q^33 + 24 * q^36 + 8 * q^37 - 10 * q^38 + 40 * q^41 + 10 * q^42 + 60 * q^46 + 28 * q^47 + 54 * q^48 + 20 * q^51 + 50 * q^52 + 24 * q^53 - 80 * q^56 - 30 * q^57 + 50 * q^58 - 60 * q^61 - 100 * q^62 + 30 * q^63 - 100 * q^66 + 8 * q^67 + 30 * q^68 + 24 * q^71 - 80 * q^72 - 50 * q^73 - 70 * q^77 - 60 * q^78 - 12 * q^81 + 10 * q^82 - 90 * q^83 + 100 * q^86 - 170 * q^88 + 20 * q^91 + 68 * q^92 + 8 * q^93 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.237790	−	1.50135i	0.168143	−	1.06161i	−0.748859	−	0.662730i	$-0.769398\pi$
$2$	0.237790	−	1.50135i	0.168143	−	1.06161i	0.917002	−	0.398884i	$-0.130602\pi$
$3$	−0.710333	−	0.361933i	−0.410111	−	0.208962i	0.236749	−	0.971571i	$-0.423918\pi$
$3$	−0.710333	−	0.361933i	−0.410111	−	0.208962i	−0.646860	+	0.762609i	$0.723918\pi$
$4$	−0.295389	−	0.0959778i	−0.147695	−	0.0479889i
$5$		0			0
$5$		0			0
$6$	−0.712297	+	0.980393i	−0.290794	+	0.400244i
$7$	−0.0869260	−	0.170602i	−0.0328550	−	0.0644815i	0.873996	−	0.485934i	$-0.161520\pi$
$7$	−0.0869260	−	0.170602i	−0.0328550	−	0.0644815i	−0.906851	+	0.421452i	$0.861520\pi$
$8$	1.16585	−	2.28811i	0.412191	−	0.808970i
$9$	−1.38978	−	1.91287i	−0.463259	−	0.637622i
$10$		0			0
$11$	1.77694	−	2.80044i	0.535768	−	0.844365i
$11$	1.77694	−	2.80044i	0.535768	−	0.844365i
$12$	0.175087	+	0.175087i	0.0505433	+	0.0505433i
$13$	−3.05749	−	0.484259i	−0.847995	−	0.134309i	−0.282711	−	0.959205i	$-0.591234\pi$
$13$	−3.05749	−	0.484259i	−0.847995	−	0.134309i	−0.565285	+	0.824896i	$0.691234\pi$
$14$	−0.276803	+	0.0899388i	−0.0739787	+	0.0240372i
$15$		0			0
$16$	−3.66057	−	2.65956i	−0.915143	−	0.664890i
$17$	3.66088	−	0.579827i	0.887894	−	0.140629i	0.304206	−	0.952606i	$-0.401609\pi$
$17$	3.66088	−	0.579827i	0.887894	−	0.140629i	0.583688	+	0.811978i	$0.301609\pi$
$18$	−3.20235	+	1.63168i	−0.754802	+	0.384591i
$19$	0.229844	+	0.707388i	0.0527299	+	0.162286i	0.973954	−	0.226747i	$-0.0728091\pi$
$19$	0.229844	+	0.707388i	0.0527299	+	0.162286i	−0.921224	+	0.389033i	$0.872809\pi$
$20$		0			0
$21$			0.152646i			0.0333100i
$22$	−3.78190	−	3.33373i	−0.806304	−	0.710753i
$23$	1.14886	−	1.14886i	0.239553	−	0.239553i	−0.577112	−	0.816665i	$-0.695820\pi$
$23$	1.14886	−	1.14886i	0.239553	−	0.239553i	0.816665	+	0.577112i	$0.195820\pi$
$24$	−1.65629	+	1.20336i	−0.338088	+	0.245635i
$25$		0			0
$26$	−1.45408	+	4.47521i	−0.285169	+	0.877660i
$27$	0.669017	+	4.22401i	0.128752	+	0.812911i
$28$	0.00930302	+	0.0587369i	0.00175811	+	0.0111002i
$29$	−2.95025	+	9.07993i	−0.547847	+	1.68610i	0.166275	+	0.986079i	$0.446826\pi$
$29$	−2.95025	+	9.07993i	−0.547847	+	1.68610i	−0.714122	+	0.700021i	$0.753174\pi$
$30$		0			0
$31$	−0.283900	+	0.206266i	−0.0509900	+	0.0370464i	−0.612988	−	0.790092i	$-0.710033\pi$
$31$	−0.283900	+	0.206266i	−0.0509900	+	0.0370464i	0.561998	+	0.827138i	$0.310033\pi$
$32$	−1.23166	+	1.23166i	−0.217729	+	0.217729i
$33$	−2.27579	+	1.34611i	−0.396165	+	0.234328i
$34$		−	5.63413i		−	0.966246i
$35$		0			0
$36$	0.226933	+	0.698428i	0.0378222	+	0.116405i
$37$	4.81621	−	2.45398i	0.791780	−	0.403432i	−0.0108264	−	0.999941i	$-0.503446\pi$
$37$	4.81621	−	2.45398i	0.791780	−	0.403432i	0.802606	+	0.596510i	$0.203446\pi$
$38$	1.11669	−	0.176866i	0.181151	−	0.0286915i
$39$	1.99657	+	1.45059i	0.319707	+	0.232280i
$40$		0			0
$41$	6.36824	−	2.06917i	0.994552	−	0.323150i	0.233866	−	0.972269i	$-0.424862\pi$
$41$	6.36824	−	2.06917i	0.994552	−	0.323150i	0.760687	+	0.649119i	$0.224862\pi$
$42$	0.229174	+	0.0362976i	0.0353623	+	0.00560084i
$43$	3.72708	+	3.72708i	0.568374	+	0.568374i	0.931673	−	0.363299i	$-0.118350\pi$
$43$	3.72708	+	3.72708i	0.568374	+	0.568374i	−0.363299	+	0.931673i	$0.618350\pi$
$44$	−0.793670	+	0.656674i	−0.119650	+	0.0989973i
$45$		0			0
$46$	−1.45165	−	1.99802i	−0.214034	−	0.294592i
$47$	−5.61318	+	11.0165i	−0.818766	+	1.60692i	−0.0242272	+	0.999706i	$0.507713\pi$
$47$	−5.61318	+	11.0165i	−0.818766	+	1.60692i	−0.794539	+	0.607213i	$0.792287\pi$
$48$	1.63764	+	3.21405i	0.236373	+	0.463909i
$49$	4.09295	−	5.63346i	0.584707	−	0.804780i
$50$		0			0
$51$	−2.81030	−	0.913123i	−0.393521	−	0.127863i
$52$	0.856672	+	0.436496i	0.118799	+	0.0605311i
$53$	1.41265	−	8.91914i	0.194043	−	1.22514i	−0.677761	−	0.735282i	$-0.737050\pi$
$53$	1.41265	−	8.91914i	0.194043	−	1.22514i	0.871804	−	0.489855i	$-0.162950\pi$
$54$	6.50079			0.884646
$55$		0			0
$56$	−0.491699			−0.0657061
$57$	0.0927608	−	0.585669i	0.0122865	−	0.0775737i
$58$	12.9306	+	6.58847i	1.69787	+	0.865108i
$59$	9.15496	+	2.97463i	1.19187	+	0.387263i	0.836765	−	0.547562i	$-0.184444\pi$
$59$	9.15496	+	2.97463i	1.19187	+	0.387263i	0.355108	+	0.934825i	$0.384444\pi$
$60$		0			0
$61$	−3.46383	+	4.76756i	−0.443498	+	0.610423i	−0.970985	−	0.239140i	$-0.923134\pi$
$61$	−3.46383	+	4.76756i	−0.443498	+	0.610423i	0.527487	+	0.849563i	$0.323134\pi$
$62$	0.242168	+	0.475281i	0.0307554	+	0.0603608i
$63$	−0.205531	+	0.403377i	−0.0258944	+	0.0508207i
$64$	−3.76284	−	5.17911i	−0.470356	−	0.647389i
$65$		0			0
$66$	1.47982	+	3.73685i	0.182154	+	0.459974i
$67$	−4.13426	−	4.13426i	−0.505081	−	0.505081i	0.407932	−	0.913012i	$-0.366250\pi$
$67$	−4.13426	−	4.13426i	−0.505081	−	0.505081i	−0.913012	+	0.407932i	$0.866250\pi$
$68$	−1.13704	−	0.180089i	−0.137886	−	0.0218390i
$69$	−1.23188	+	0.400262i	−0.148301	+	0.0481859i
$70$		0			0
$71$	9.27272	+	6.73702i	1.10047	+	0.799538i	0.981136	−	0.193317i	$-0.0619245\pi$
$71$	9.27272	+	6.73702i	1.10047	+	0.799538i	0.119333	+	0.992854i	$0.461925\pi$
$72$	−5.99713	+	0.949851i	−0.706768	+	0.111941i
$73$	−2.14008	+	1.09042i	−0.250477	+	0.127624i	−0.574722	−	0.818349i	$-0.694890\pi$
$73$	−2.14008	+	1.09042i	−0.250477	+	0.127624i	0.324245	+	0.945973i	$0.394890\pi$
$74$	−2.53903	−	7.81434i	−0.295156	−	0.908398i
$75$		0			0
$76$		−	0.231015i		−	0.0264992i
$77$	−0.632224	−	0.0597184i	−0.0720486	−	0.00680554i
$78$	2.65261	−	2.65261i	0.300348	−	0.300348i
$79$	0.542434	−	0.394101i	0.0610286	−	0.0443399i	−0.556853	−	0.830611i	$-0.687991\pi$
$79$	0.542434	−	0.394101i	0.0610286	−	0.0443399i	0.617881	+	0.786271i	$0.287991\pi$
$80$		0			0
$81$	−1.13837	+	3.50353i	−0.126485	+	0.389282i
$82$	−1.59224	−	10.0530i	−0.175833	−	1.11017i
$83$	2.60980	+	16.4776i	0.286463	+	1.80865i	0.540372	+	0.841426i	$0.318284\pi$
$83$	2.60980	+	16.4776i	0.286463	+	1.80865i	−0.253909	+	0.967228i	$0.581716\pi$
$84$	0.0146506	−	0.0450899i	0.00159851	−	0.00491971i
$85$		0			0
$86$	6.48191	−	4.70938i	0.698962	−	0.507826i
$87$	5.38198	−	5.38198i	0.577009	−	0.577009i
$88$	−4.33608	−	7.33074i	−0.462227	−	0.781460i
$89$		−	7.92190i		−	0.839720i	−0.907589	−	0.419860i	$-0.862079\pi$
$89$		−	7.92190i		−	0.839720i	0.907589	−	0.419860i	$-0.137921\pi$
$90$		0			0
$91$	0.183160	+	0.563709i	0.0192004	+	0.0590927i
$92$	−0.449625	+	0.229095i	−0.0468766	+	0.0238848i
$93$	0.276318	−	0.0437645i	0.0286528	−	0.00453817i
$94$	15.2048	+	11.0469i	1.56826	+	1.13941i
$95$		0			0
$96$	1.32067	−	0.429111i	0.134790	−	0.0437960i
$97$	1.36201	+	0.215721i	0.138291	+	0.0219032i	0.225196	−	0.974313i	$-0.427698\pi$
$97$	1.36201	+	0.215721i	0.138291	+	0.0219032i	−0.0869051	+	0.996217i	$0.527698\pi$
$98$	−7.48452	−	7.48452i	−0.756051	−	0.756051i
$99$	−7.82643	+	0.492943i	−0.786585	+	0.0495427i
$100$		0			0
$101$	−2.83633	−	3.90387i	−0.282225	−	0.388449i	0.644244	−	0.764820i	$-0.277172\pi$
$101$	−2.83633	−	3.90387i	−0.282225	−	0.388449i	−0.926469	+	0.376370i	$0.877172\pi$
$102$	−2.03918	+	4.00211i	−0.201909	+	0.396268i
$103$	1.46972	+	2.88449i	0.144816	+	0.284217i	0.952009	−	0.306071i	$-0.0990144\pi$
$103$	1.46972	+	2.88449i	0.144816	+	0.284217i	−0.807193	+	0.590287i	$0.799014\pi$
$104$	−4.67262	+	6.43131i	−0.458188	+	0.630641i
$105$		0			0
$106$	−13.0548	−	4.24177i	−1.26800	−	0.411997i
$107$	9.85055	+	5.01911i	0.952289	+	0.485215i	0.859875	−	0.510505i	$-0.170542\pi$
$107$	9.85055	+	5.01911i	0.952289	+	0.485215i	0.0924142	+	0.995721i	$0.470542\pi$
$108$	0.207790	−	1.31194i	0.0199946	−	0.126241i
$109$	−9.54212			−0.913969			−0.456985	−	0.889475i	$-0.651071\pi$
$109$	−9.54212			−0.913969			−0.456985	+	0.889475i	$0.651071\pi$
$110$		0			0
$111$	−4.30929			−0.409019
$112$	−0.135527	+	0.855686i	−0.0128061	+	0.0808547i
$113$	−3.69562	−	1.88301i	−0.347654	−	0.177139i	0.271440	−	0.962455i	$-0.412500\pi$
$113$	−3.69562	−	1.88301i	−0.347654	−	0.177139i	−0.619094	+	0.785317i	$0.712500\pi$
$114$	−0.857235	−	0.278533i	−0.0802874	−	0.0260870i
$115$		0			0
$116$	1.74294	−	2.39895i	0.161828	−	0.222737i
$117$	3.32291	+	6.52158i	0.307203	+	0.602920i
$118$	6.64291	−	13.0374i	0.611529	−	1.20019i
$119$	−0.417145	−	0.574151i	−0.0382397	−	0.0526324i
$120$		0			0
$121$	−4.68496	−	9.95245i	−0.425905	−	0.904768i
$122$	6.33410	+	6.33410i	0.573462	+	0.573462i
$123$	−5.27247	−	0.835077i	−0.475403	−	0.0752964i
$124$	0.103658	−	0.0336805i	0.00930877	−	0.00302460i
$125$		0			0
$126$	0.556736	+	0.404492i	0.0495980	+	0.0360350i
$127$	−14.3879	+	2.27881i	−1.27672	+	0.202212i	−0.757728	−	0.652570i	$-0.773691\pi$
$127$	−14.3879	+	2.27881i	−1.27672	+	0.202212i	−0.518987	+	0.854782i	$0.673691\pi$
$128$	−11.7744	+	5.99935i	−1.04072	+	0.530273i
$129$	−1.29851	−	3.99642i	−0.114328	−	0.351865i
$130$		0			0
$131$			9.76926i			0.853544i	0.904359	+	0.426772i	$0.140349\pi$
$131$			9.76926i			0.853544i	−0.904359	+	0.426772i	$0.859651\pi$
$132$	0.801441	−	0.179202i	0.0697565	−	0.0155975i
$133$	0.100702	−	0.100702i	0.00873200	−	0.00873200i
$134$	−7.19006	+	5.22388i	−0.621126	+	0.451275i
$135$		0			0
$136$	2.94133	−	9.05250i	0.252217	−	0.776245i
$137$	−0.677380	−	4.27681i	−0.0578725	−	0.365392i	−0.999581	−	0.0289612i	$-0.990780\pi$
$137$	−0.677380	−	4.27681i	−0.0578725	−	0.365392i	0.941708	−	0.336431i	$-0.109220\pi$
$138$	0.308004	+	1.94466i	0.0262190	+	0.165540i
$139$	−3.24794	+	9.99613i	−0.275487	+	0.847860i	0.713604	+	0.700550i	$0.247062\pi$
$139$	−3.24794	+	9.99613i	−0.275487	+	0.847860i	−0.989090	+	0.147311i	$0.952938\pi$
$140$		0			0
$141$	7.97445	−	5.79378i	0.671570	−	0.487924i
$142$	12.3196	−	12.3196i	1.03384	−	1.03384i
$143$	−6.78912	+	7.70183i	−0.567735	+	0.644059i
$144$			10.6984i			0.891532i
$145$		0			0
$146$	1.12822	+	3.47229i	0.0933719	+	0.287369i
$147$	−4.94629	+	2.52026i	−0.407963	+	0.207868i
$148$	−1.65818	+	0.262630i	−0.136302	+	0.0215881i
$149$	−4.66189	−	3.38706i	−0.381917	−	0.277479i	0.380218	−	0.924897i	$-0.375849\pi$
$149$	−4.66189	−	3.38706i	−0.381917	−	0.277479i	−0.762135	+	0.647418i	$0.775849\pi$
$150$		0			0
$151$	−14.2318	+	4.62419i	−1.15817	+	0.376311i	−0.824214	−	0.566278i	$-0.808383\pi$
$151$	−14.2318	+	4.62419i	−1.15817	+	0.376311i	−0.333953	+	0.942590i	$0.608383\pi$
$152$	1.88655	+	0.298800i	0.153019	+	0.0242358i
$153$	−6.19694	−	6.19694i	−0.500993	−	0.500993i
$154$	−0.239995	+	0.934987i	−0.0193393	+	0.0753434i
$155$		0			0
$156$	−0.450540	−	0.620115i	−0.0360721	−	0.0496489i
$157$	2.24640	−	4.40881i	0.179282	−	0.351861i	−0.783824	−	0.620983i	$-0.786733\pi$
$157$	2.24640	−	4.40881i	0.179282	−	0.351861i	0.963106	+	0.269122i	$0.0867335\pi$
$158$	−0.462698	−	0.908095i	−0.0368103	−	0.0722442i
$159$	−4.23158	+	5.82427i	−0.335586	+	0.461895i
$160$		0			0
$161$	−0.295863	−	0.0961317i	−0.0233173	−	0.00757624i
$162$	4.98933	+	2.54219i	0.391999	+	0.199733i
$163$	1.56695	−	9.89335i	0.122733	−	0.774907i	−0.847153	−	0.531349i	$-0.821685\pi$
$163$	1.56695	−	9.89335i	0.122733	−	0.774907i	0.969886	−	0.243558i	$-0.0783147\pi$
$164$	−2.07970			−0.162398
$165$		0			0
$166$	25.3592			1.96826
$167$	1.88695	−	11.9137i	0.146017	−	0.921913i	−0.800517	−	0.599310i	$-0.795442\pi$
$167$	1.88695	−	11.9137i	0.146017	−	0.921913i	0.946534	−	0.322604i	$-0.104558\pi$
$168$	0.349270	+	0.177962i	0.0269468	+	0.0137301i
$169$	−3.24999	−	1.05599i	−0.250000	−	0.0812298i
$170$		0			0
$171$	1.03371	−	1.42277i	0.0790494	−	0.108802i
$172$	−0.743222	−	1.45866i	−0.0566702	−	0.111221i
$173$	5.65903	−	11.1065i	0.430248	−	0.844410i	−0.569501	−	0.821991i	$-0.692863\pi$
$173$	5.65903	−	11.1065i	0.430248	−	0.844410i	0.999749	−	0.0224186i	$-0.00713665\pi$
$174$	−6.80045	−	9.36001i	−0.515540	−	0.709581i
$175$		0			0
$176$	−13.9526	+	5.52533i	−1.05171	+	0.416488i
$177$	−5.42645	−	5.42645i	−0.407877	−	0.407877i
$178$	−11.8935	−	1.88375i	−0.891458	−	0.141193i
$179$	19.1909	−	6.23551i	1.43440	−	0.466064i	0.514252	−	0.857639i	$-0.328070\pi$
$179$	19.1909	−	6.23551i	1.43440	−	0.466064i	0.920146	+	0.391575i	$0.128070\pi$
$180$		0			0
$181$	−3.72935	−	2.70953i	−0.277200	−	0.201398i	0.440495	−	0.897755i	$-0.354803\pi$
$181$	−3.72935	−	2.70953i	−0.277200	−	0.201398i	−0.717695	+	0.696357i	$0.754803\pi$
$182$	0.889877	−	0.140943i	0.0659620	−	0.0104474i
$183$	4.18601	−	2.13288i	0.309439	−	0.157667i
$184$	−1.28932	−	3.96811i	−0.0950497	−	0.292533i
$185$		0			0
$186$		−	0.425256i		−	0.0311813i
$187$	4.88140	−	11.2824i	0.356963	−	0.825051i
$188$	2.71541	−	2.71541i	0.198042	−	0.198042i
$189$	0.662469	−	0.481312i	0.0481875	−	0.0350103i
$190$		0			0
$191$	1.95493	−	6.01667i	0.141454	−	0.435351i	−0.855084	−	0.518490i	$-0.826495\pi$
$191$	1.95493	−	6.01667i	0.141454	−	0.435351i	0.996538	+	0.0831389i	$0.0264945\pi$
$192$	0.798383	+	5.04079i	0.0576183	+	0.363788i
$193$	0.927951	+	5.85885i	0.0667954	+	0.421729i	0.998314	+	0.0580368i	$0.0184841\pi$
$193$	0.927951	+	5.85885i	0.0667954	+	0.421729i	−0.931519	+	0.363692i	$0.881516\pi$
$194$	0.647745	−	1.99355i	0.0465054	−	0.143129i
$195$		0			0
$196$	−1.74970	+	1.27123i	−0.124979	+	0.0908022i
$197$	−9.90515	+	9.90515i	−0.705713	+	0.705713i	−0.965631	−	0.259918i	$-0.916304\pi$
$197$	−9.90515	+	9.90515i	−0.705713	+	0.705713i	0.259918	+	0.965631i	$0.416304\pi$
$198$	−1.12097	+	11.8674i	−0.0796637	+	0.843380i
$199$		−	13.3828i		−	0.948680i	−0.880342	−	0.474340i	$-0.842687\pi$
$199$		−	13.3828i		−	0.948680i	0.880342	−	0.474340i	$-0.157313\pi$
$200$		0			0
$201$	1.44038	+	4.43303i	0.101596	+	0.312682i
$202$	−6.53551	+	3.33001i	−0.459837	+	0.234299i
$203$	1.80551	−	0.285964i	0.126722	−	0.0200708i
$204$	0.742493	+	0.539453i	0.0519849	+	0.0377693i
$205$		0			0
$206$	4.68010	−	1.52066i	0.326078	−	0.105949i
$207$	−3.79427	−	0.600953i	−0.263720	−	0.0417691i
$208$	9.90424	+	9.90424i	0.686736	+	0.686736i
$209$	2.38942	+	0.613321i	0.165280	+	0.0424243i
$210$		0			0
$211$	3.48696	+	4.79939i	0.240052	+	0.330404i	0.911996	−	0.410198i	$-0.134540\pi$
$211$	3.48696	+	4.79939i	0.240052	+	0.330404i	−0.671944	+	0.740602i	$0.734540\pi$
$212$	−1.27332	+	2.49903i	−0.0874521	+	0.171634i
$213$	−4.14837	−	8.14163i	−0.284241	−	0.557855i
$214$	9.87779	−	13.5956i	0.675232	−	0.929377i
$215$		0			0
$216$	10.4450	+	3.39378i	0.710691	+	0.230917i
$217$	0.0598677	+	0.0305041i	0.00406408	+	0.00207075i
$218$	−2.26902	+	14.3260i	−0.153678	+	0.970282i
$219$	1.91483			0.129392
$220$		0			0
$221$	−11.4739			−0.771818
$222$	−1.02471	+	6.46974i	−0.0687738	+	0.434220i
$223$	18.9389	+	9.64984i	1.26824	+	0.646201i	0.953046	−	0.302826i	$-0.0979300\pi$
$223$	18.9389	+	9.64984i	1.26824	+	0.646201i	0.315195	+	0.949027i	$0.397930\pi$
$224$	0.317188	+	0.103060i	0.0211930	+	0.00688602i
$225$		0			0
$226$	−3.70584	+	5.10065i	−0.246509	+	0.339290i
$227$	−5.93372	−	11.6456i	−0.393835	−	0.772944i	0.605910	−	0.795533i	$-0.292809\pi$
$227$	−5.93372	−	11.6456i	−0.393835	−	0.772944i	−0.999745	+	0.0225888i	$0.992809\pi$
$228$	−0.0836117	+	0.164097i	−0.00553732	+	0.0108676i
$229$	9.65796	+	13.2930i	0.638216	+	0.878429i	0.998519	−	0.0544066i	$-0.0173267\pi$
$229$	9.65796	+	13.2930i	0.638216	+	0.878429i	−0.360303	+	0.932835i	$0.617327\pi$
$230$		0			0
$231$	0.427475	+	0.271242i	0.0281258	+	0.0178464i
$232$	17.3363	+	17.3363i	1.13819	+	1.13819i
$233$	15.4510	+	2.44720i	1.01223	+	0.160321i	0.640450	−	0.768000i	$-0.278748\pi$
$233$	15.4510	+	2.44720i	1.01223	+	0.160321i	0.371779	+	0.928321i	$0.378748\pi$
$234$	10.5813	−	3.43808i	0.691722	−	0.224754i
$235$		0			0
$236$	−2.41878	−	1.75734i	−0.157449	−	0.114393i
$237$	−0.527947	+	0.0836185i	−0.0342938	+	0.00543161i
$238$	−0.961194	+	0.489753i	−0.0623050	+	0.0317460i
$239$	−1.63214	−	5.02322i	−0.105575	−	0.324925i	0.884290	−	0.466938i	$-0.154643\pi$
$239$	−1.63214	−	5.02322i	−0.105575	−	0.324925i	−0.989865	+	0.142012i	$0.954643\pi$
$240$		0			0
$241$		−	16.1676i		−	1.04144i	−0.853726	−	0.520722i	$-0.825663\pi$
$241$		−	16.1676i		−	1.04144i	0.853726	−	0.520722i	$-0.174337\pi$
$242$	−16.0561	+	4.66716i	−1.03213	+	0.300016i
$243$	11.1488	−	11.1488i	0.715198	−	0.715198i
$244$	1.48076	−	1.07583i	0.0947959	−	0.0688732i
$245$		0			0
$246$	−2.50748	+	7.71724i	−0.159871	+	0.492033i
$247$	−0.360188	−	2.27413i	−0.0229182	−	0.144700i
$248$	0.140973	+	0.890071i	0.00895182	+	0.0565196i
$249$	4.10997	−	12.6492i	0.260458	−	0.801609i
$250$		0			0
$251$	−15.6486	+	11.3694i	−0.987729	+	0.717627i	−0.959423	−	0.281972i	$-0.909011\pi$
$251$	−15.6486	+	11.3694i	−0.987729	+	0.717627i	−0.0283063	+	0.999599i	$0.509011\pi$
$252$	0.0994268	−	0.0994268i	0.00626330	−	0.00626330i
$253$	−1.17586	−	5.25876i	−0.0739254	−	0.330615i
$254$			22.1431i			1.38938i
$255$		0			0
$256$	2.25079	+	6.92722i	0.140674	+	0.432951i
$257$	4.19318	−	2.13653i	0.261563	−	0.133273i	−0.318292	−	0.947993i	$-0.603109\pi$
$257$	4.19318	−	2.13653i	0.261563	−	0.133273i	0.579855	+	0.814720i	$0.303109\pi$
$258$	−6.30879	+	0.999214i	−0.392768	+	0.0622083i
$259$	−0.837308	−	0.608340i	−0.0520278	−	0.0378004i
$260$		0			0
$261$	21.4689	−	6.97566i	1.32889	−	0.431783i
$262$	14.6671	+	2.32303i	0.906134	+	0.143517i
$263$	−11.2218	−	11.2218i	−0.691964	−	0.691964i	0.270700	−	0.962664i	$-0.412745\pi$
$263$	−11.2218	−	11.2218i	−0.691964	−	0.691964i	−0.962664	+	0.270700i	$0.912745\pi$
$264$	0.426823	+	6.77663i	0.0262691	+	0.417073i
$265$		0			0
$266$	−0.127243	−	0.175135i	−0.00780178	−	0.0107382i
$267$	−2.86720	+	5.62719i	−0.175470	+	0.344378i
$268$	0.824419	+	1.61801i	0.0503594	+	0.0988359i
$269$	−6.64926	+	9.15192i	−0.405412	+	0.558002i	−0.962092	−	0.272725i	$-0.912075\pi$
$269$	−6.64926	+	9.15192i	−0.405412	+	0.558002i	0.556680	+	0.830727i	$0.312075\pi$
$270$		0			0
$271$	16.9556	+	5.50921i	1.02998	+	0.334661i	0.774782	−	0.632228i	$-0.217859\pi$
$271$	16.9556	+	5.50921i	1.02998	+	0.334661i	0.255198	+	0.966889i	$0.417859\pi$
$272$	−14.9430	−	7.61384i	−0.906052	−	0.461657i
$273$	0.0739200	−	0.466712i	0.00447384	−	0.0282467i
$274$	−6.58205			−0.397636
$275$		0			0
$276$	0.402300			0.0242156
$277$	−0.732361	+	4.62395i	−0.0440033	+	0.277826i	−0.999873	−	0.0159666i	$-0.994917\pi$
$277$	−0.732361	+	4.62395i	−0.0440033	+	0.277826i	0.955869	+	0.293793i	$0.0949175\pi$
$278$	14.2353	+	7.25327i	0.853779	+	0.435022i
$279$	0.789117	+	0.256400i	0.0472432	+	0.0153502i
$280$		0			0
$281$	−7.75247	+	10.6704i	−0.462474	+	0.636541i	−0.975019	−	0.222119i	$-0.928703\pi$
$281$	−7.75247	+	10.6704i	−0.462474	+	0.636541i	0.512546	+	0.858660i	$0.328703\pi$
$282$	−6.80223	−	13.3501i	−0.405067	−	0.794989i
$283$	−10.3449	+	20.3029i	−0.614938	+	1.20688i	0.348084	+	0.937463i	$0.386832\pi$
$283$	−10.3449	+	20.3029i	−0.614938	+	1.20688i	−0.963022	+	0.269421i	$0.913168\pi$
$284$	−2.09246	−	2.88002i	−0.124164	−	0.170898i
$285$		0			0
$286$	9.94874	+	12.0243i	0.588281	+	0.711009i
$287$	−0.906570	−	0.906570i	−0.0535131	−	0.0535131i
$288$	4.06774	+	0.644267i	0.239694	+	0.0379638i
$289$	−3.10211	+	1.00794i	−0.182477	+	0.0592904i
$290$		0			0
$291$	−0.889404	−	0.646190i	−0.0521378	−	0.0378803i
$292$	0.736812	−	0.116700i	0.0431187	−	0.00682933i
$293$	6.43996	−	3.28132i	0.376226	−	0.191697i	−0.255644	−	0.966771i	$-0.582287\pi$
$293$	6.43996	−	3.28132i	0.376226	−	0.191697i	0.631870	+	0.775074i	$0.282287\pi$
$294$	2.60761	+	8.02539i	0.152079	+	0.468051i
$295$		0			0
$296$		−	13.8810i		−	0.806817i
$297$	13.0179	+	5.63227i	0.755375	+	0.326818i
$298$	−6.19371	+	6.19371i	−0.358792	+	0.358792i
$299$	−4.06896	+	2.95628i	−0.235314	+	0.170966i
$300$		0			0
$301$	0.311867	−	0.959827i	0.0179757	−	0.0553235i
$302$	3.55834	+	22.4665i	0.204759	+	1.29280i
$303$	0.601798	+	3.79960i	0.0345724	+	0.218282i
$304$	1.03998	−	3.20073i	0.0596469	−	0.183574i
$305$		0			0
$306$	−10.7773	+	7.83020i	−0.616100	+	0.447623i
$307$	−20.1272	+	20.1272i	−1.14872	+	1.14872i	−0.161918	+	0.986804i	$0.551768\pi$
$307$	−20.1272	+	20.1272i	−1.14872	+	1.14872i	−0.986804	+	0.161918i	$0.948232\pi$
$308$	0.181020	+	0.0783196i	0.0103146	+	0.00446267i
$309$		−	2.58088i		−	0.146821i
$310$		0			0
$311$	−2.32254	−	7.14803i	−0.131699	−	0.405328i	0.863363	−	0.504583i	$-0.168354\pi$
$311$	−2.32254	−	7.14803i	−0.131699	−	0.405328i	−0.995062	+	0.0992557i	$0.968354\pi$
$312$	5.64681	−	2.87720i	0.319688	−	0.162889i
$313$	1.32951	−	0.210574i	0.0751483	−	0.0119023i	−0.118747	−	0.992925i	$-0.537888\pi$
$313$	1.32951	−	0.210574i	0.0751483	−	0.0119023i	0.193895	+	0.981022i	$0.437888\pi$
$314$	−6.08499	−	4.42100i	−0.343396	−	0.249492i
$315$		0			0
$316$	−0.198054	+	0.0643517i	−0.0111414	+	0.00362006i
$317$	11.1924	+	1.77271i	0.628630	+	0.0995652i	0.462617	−	0.886558i	$-0.346911\pi$
$317$	11.1924	+	1.77271i	0.628630	+	0.0995652i	0.166013	+	0.986124i	$0.446911\pi$
$318$	7.73803	+	7.73803i	0.433927	+	0.433927i
$319$	20.1854	+	24.3965i	1.13017	+	1.36594i
$320$		0			0
$321$	−5.18059	−	7.13047i	−0.289152	−	0.397984i
$322$	−0.214680	+	0.421334i	−0.0119637	+	0.0234800i
$323$	1.25159	+	2.45639i	0.0696406	+	0.136677i
$324$	0.672523	−	0.925648i	0.0373624	−	0.0514249i
$325$		0			0
$326$	−14.4808	−	4.70509i	−0.802015	−	0.260591i
$327$	6.77808	+	3.45360i	0.374829	+	0.190985i
$328$	2.68994	−	16.9836i	0.148527	−	0.937762i
$329$	2.36737			0.130517
$330$		0			0
$331$	−17.7048			−0.973145			−0.486572	−	0.873640i	$-0.661753\pi$
$331$	−17.7048			−0.973145			−0.486572	+	0.873640i	$0.661753\pi$
$332$	0.810579	−	5.11780i	0.0444863	−	0.280876i
$333$	−11.3876	−	5.80227i	−0.624036	−	0.317962i
$334$	−17.4380	−	5.66594i	−0.954164	−	0.310027i
$335$		0			0
$336$	0.405970	−	0.558770i	0.0221475	−	0.0304834i
$337$	−3.45945	−	6.78954i	−0.188448	−	0.369850i	0.777381	−	0.629030i	$-0.216548\pi$
$337$	−3.45945	−	6.78954i	−0.188448	−	0.369850i	−0.965829	+	0.259180i	$0.916548\pi$
$338$	−2.35822	+	4.62827i	−0.128270	+	0.251745i
$339$	1.94359	+	2.67513i	0.105562	+	0.145293i
$340$		0			0
$341$	0.0731608	+	1.16157i	0.00396188	+	0.0629025i
$342$	−1.89027	−	1.89027i	−0.102214	−	0.102214i
$343$	−2.64066	−	0.418239i	−0.142582	−	0.0225828i
$344$	12.8732	−	4.18275i	0.694076	−	0.225519i
$345$		0			0
$346$	−15.3290	−	11.1372i	−0.824093	−	0.598739i
$347$	9.21879	−	1.46011i	0.494891	−	0.0783830i	0.0959998	−	0.995381i	$-0.469395\pi$
$347$	9.21879	−	1.46011i	0.494891	−	0.0783830i	0.398891	+	0.916998i	$0.369395\pi$
$348$	−2.10633	+	1.07323i	−0.112911	+	0.0575311i
$349$	0.464073	+	1.42827i	0.0248413	+	0.0764536i	0.962709	−	0.270540i	$-0.0872024\pi$
$349$	0.464073	+	1.42827i	0.0248413	+	0.0764536i	−0.937867	+	0.346994i	$0.887202\pi$
$350$		0			0
$351$		−	13.2388i		−	0.706637i
$352$	1.26061	+	5.63779i	0.0671906	+	0.300495i
$353$	−4.40229	+	4.40229i	−0.234310	+	0.234310i	−0.814489	−	0.580179i	$-0.802983\pi$
$353$	−4.40229	+	4.40229i	−0.234310	+	0.234310i	0.580179	+	0.814489i	$0.302983\pi$
$354$	−9.43735	+	6.85664i	−0.501589	+	0.364426i
$355$		0			0
$356$	−0.760327	+	2.34004i	−0.0402972	+	0.124022i
$357$	0.0885080	+	0.558817i	0.00468434	+	0.0295757i
$358$	−4.79826	−	30.2950i	−0.253596	−	1.60114i
$359$	8.12845	−	25.0168i	0.429003	−	1.32034i	−0.470105	−	0.882611i	$-0.655784\pi$
$359$	8.12845	−	25.0168i	0.429003	−	1.32034i	0.899108	−	0.437726i	$-0.144216\pi$
$360$		0			0
$361$	14.9238	−	10.8427i	0.785461	−	0.570671i
$362$	−4.95475	+	4.95475i	−0.260416	+	0.260416i
$363$	−0.274237	+	8.76519i	−0.0143937	+	0.460053i
$364$		−	0.184093i		−	0.00964908i
$365$		0			0
$366$	−2.20680	−	6.79184i	−0.115351	−	0.355015i
$367$	−7.27872	+	3.70869i	−0.379946	+	0.193592i	−0.633524	−	0.773723i	$-0.718392\pi$
$367$	−7.27872	+	3.70869i	−0.379946	+	0.193592i	0.253579	+	0.967315i	$0.418392\pi$
$368$	−7.26093	+	1.15002i	−0.378502	+	0.0599488i
$369$	−12.8085	−	9.30591i	−0.666783	−	0.484446i
$370$		0			0
$371$	−1.64442	+	0.534304i	−0.0853740	+	0.0277397i
$372$	−0.0858218	−	0.0135928i	−0.00444965	−	0.000704756i
$373$	−6.12473	−	6.12473i	−0.317126	−	0.317126i	0.530536	−	0.847662i	$-0.321991\pi$
$373$	−6.12473	−	6.12473i	−0.317126	−	0.317126i	−0.847662	+	0.530536i	$0.821991\pi$
$374$	−15.7781	−	10.0115i	−0.815864	−	0.517684i
$375$		0			0
$376$	18.6628	+	25.6872i	0.962461	+	1.32471i
$377$	13.4174	−	26.3331i	0.691031	−	1.35622i
$378$	−0.565088	−	1.10905i	−0.0290650	−	0.0570433i
$379$	−0.363481	+	0.500288i	−0.0186708	+	0.0256981i	−0.818250	−	0.574862i	$-0.805056\pi$
$379$	−0.363481	+	0.500288i	−0.0186708	+	0.0256981i	0.799580	+	0.600560i	$0.205056\pi$
$380$		0			0
$381$	11.0449	+	3.58872i	0.565849	+	0.183856i
$382$	−8.56825	−	4.36574i	−0.438390	−	0.223371i
$383$	−1.62362	+	10.2511i	−0.0829629	+	0.523807i	0.910850	+	0.412738i	$0.135428\pi$
$383$	−1.62362	+	10.2511i	−0.0829629	+	0.523807i	−0.993813	+	0.111069i	$0.964572\pi$
$384$	10.5351			0.537617
$385$		0			0
$386$	9.01683			0.458945
$387$	1.94959	−	12.3092i	0.0991031	−	0.625712i
$388$	−0.381619	−	0.194444i	−0.0193737	−	0.00987142i
$389$	−21.0630	−	6.84378i	−1.06794	−	0.346993i	−0.278252	−	0.960508i	$-0.589755\pi$
$389$	−21.0630	−	6.84378i	−1.06794	−	0.346993i	−0.789683	+	0.613515i	$0.789755\pi$
$390$		0			0
$391$	3.53969	−	4.87197i	0.179010	−	0.246386i
$392$	−8.11822	−	15.9329i	−0.410032	−	0.804733i
$393$	3.53581	−	6.93942i	0.178358	−	0.350048i
$394$	12.5157	+	17.2264i	0.630534	+	0.867855i
$395$		0			0
$396$	2.35915	+	0.605553i	0.118552	+	0.0304302i
$397$	−10.7769	−	10.7769i	−0.540876	−	0.540876i	0.382910	−	0.923786i	$-0.374922\pi$
$397$	−10.7769	−	10.7769i	−0.540876	−	0.540876i	−0.923786	+	0.382910i	$0.874922\pi$
$398$	−20.0922	−	3.18229i	−1.00713	−	0.159514i
$399$	−0.107980	+	0.0350847i	−0.00540574	+	0.00175643i
$400$		0			0
$401$	3.46399	+	2.51673i	0.172983	+	0.125680i	0.670908	−	0.741540i	$-0.265904\pi$
$401$	3.46399	+	2.51673i	0.172983	+	0.125680i	−0.497925	+	0.867220i	$0.665904\pi$
$402$	6.99803	−	1.10838i	0.349030	−	0.0552809i
$403$	0.967909	−	0.493174i	0.0482150	−	0.0245668i
$404$	0.463135	+	1.42538i	0.0230418	+	0.0709155i
$405$		0			0
$406$		−	2.77869i		−	0.137904i
$407$	1.68589	−	17.8481i	0.0835664	−	0.884697i
$408$	−5.36572	+	5.36572i	−0.265643	+	0.265643i
$409$	3.47523	−	2.52490i	0.171839	−	0.124848i	−0.498541	−	0.866866i	$-0.666131\pi$
$409$	3.47523	−	2.52490i	0.171839	−	0.124848i	0.670381	+	0.742017i	$0.266131\pi$
$410$		0			0
$411$	−1.06675	+	3.28312i	−0.0526190	+	0.161945i
$412$	−0.157293	−	0.993106i	−0.00774925	−	0.0489268i
$413$	−0.288327	−	1.82043i	−0.0141877	−	0.0895773i
$414$	−1.80448	+	5.55361i	−0.0886853	+	0.272945i
$415$		0			0
$416$	4.36224	−	3.16935i	0.213876	−	0.155390i
$417$	5.92504	−	5.92504i	0.290151	−	0.290151i
$418$	1.48899	−	3.44151i	0.0728288	−	0.168330i
$419$			1.20241i			0.0587414i	0.999569	+	0.0293707i	$0.00935032\pi$
$419$			1.20241i			0.0587414i	−0.999569	+	0.0293707i	$0.990650\pi$
$420$		0			0
$421$	9.67493	+	29.7764i	0.471527	+	1.45121i	0.850584	+	0.525839i	$0.176248\pi$
$421$	9.67493	+	29.7764i	0.471527	+	1.45121i	−0.379057	+	0.925373i	$0.623752\pi$
$422$	8.03473	−	4.09390i	0.391124	−	0.199288i
$423$	28.8741	−	4.57321i	1.40391	−	0.222357i
$424$	−18.7610	−	13.6307i	−0.911117	−	0.661965i
$425$		0			0
$426$	−13.2099	+	4.29214i	−0.640020	+	0.207955i
$427$	1.11445	+	0.176512i	0.0539321	+	0.00854201i
$428$	−2.42802	−	2.42802i	−0.117363	−	0.117363i
$429$	7.61008	−	3.01366i	0.367418	−	0.145501i
$430$		0			0
$431$	−5.81395	−	8.00222i	−0.280048	−	0.385453i	0.645702	−	0.763590i	$-0.276565\pi$
$431$	−5.81395	−	8.00222i	−0.280048	−	0.385453i	−0.925750	+	0.378137i	$0.876565\pi$
$432$	8.78502	−	17.2416i	0.422669	−	0.829536i
$433$	−12.2497	−	24.0414i	−0.588683	−	1.15536i	−0.972708	−	0.232033i	$-0.925462\pi$
$433$	−12.2497	−	24.0414i	−0.588683	−	1.15536i	0.384025	−	0.923323i	$-0.374538\pi$
$434$	0.0600332	−	0.0826286i	0.00288169	−	0.00396630i
$435$		0			0
$436$	2.81864	+	0.915831i	0.134988	+	0.0438604i
$437$	1.07675	+	0.548629i	0.0515077	+	0.0262445i
$438$	0.455327	−	2.87482i	0.0217564	−	0.137364i
$439$	−24.5862			−1.17344			−0.586718	−	0.809791i	$-0.699580\pi$
$439$	−24.5862			−1.17344			−0.586718	+	0.809791i	$0.699580\pi$
$440$		0			0
$441$	−16.4643			−0.784016
$442$	−2.72838	+	17.2263i	−0.129776	+	0.819372i
$443$	−27.4404	−	13.9816i	−1.30373	−	0.664286i	−0.342370	−	0.939565i	$-0.611230\pi$
$443$	−27.4404	−	13.9816i	−1.30373	−	0.664286i	−0.961364	+	0.275279i	$0.911230\pi$
$444$	1.27292	+	0.413596i	0.0604099	+	0.0196284i
$445$		0			0
$446$	18.9912	−	26.1392i	0.899262	−	1.23773i
$447$	2.08561	+	4.09323i	0.0986458	+	0.193603i
$448$	−0.556477	+	1.09215i	−0.0262911	+	0.0515992i
$449$	−4.30536	−	5.92582i	−0.203182	−	0.279657i	0.695250	−	0.718768i	$-0.255293\pi$
$449$	−4.30536	−	5.92582i	−0.203182	−	0.279657i	−0.898433	+	0.439111i	$0.855293\pi$
$450$		0			0
$451$	5.52141	−	21.5107i	0.259993	−	1.01290i
$452$	0.910918	+	0.910918i	0.0428460	+	0.0428460i
$453$	11.7830	+	1.86624i	0.553612	+	0.0876835i
$454$	−18.8951	+	6.13938i	−0.886789	+	0.288135i
$455$		0			0
$456$	−1.23193	−	0.895050i	−0.0576904	−	0.0419146i
$457$	6.65265	−	1.05368i	0.311198	−	0.0492889i	0.00111791	−	0.999999i	$-0.499644\pi$
$457$	6.65265	−	1.05368i	0.311198	−	0.0492889i	0.310080	+	0.950710i	$0.399644\pi$
$458$	22.2540	−	11.3390i	1.03986	−	0.529837i
$459$	4.89838	+	15.0757i	0.228637	+	0.703672i
$460$		0			0
$461$			29.0801i			1.35440i	0.735801	+	0.677198i	$0.236806\pi$
$461$			29.0801i			1.35440i	−0.735801	+	0.677198i	$0.763194\pi$
$462$	0.508879	−	0.577290i	0.0236752	−	0.0268580i
$463$	−17.5146	+	17.5146i	−0.813970	+	0.813970i	−0.985227	−	0.171256i	$-0.945217\pi$
$463$	−17.5146	+	17.5146i	−0.813970	+	0.813970i	0.171256	+	0.985227i	$0.445217\pi$
$464$	34.9482	−	25.3914i	1.62243	−	1.17876i
$465$		0			0
$466$	7.34819	−	22.6154i	0.340398	−	1.04764i
$467$	4.13890	+	26.1320i	0.191525	+	1.20924i	0.876763	+	0.480923i	$0.159698\pi$
$467$	4.13890	+	26.1320i	0.191525	+	1.20924i	−0.685237	+	0.728320i	$0.740302\pi$
$468$	−0.355625	−	2.24533i	−0.0164388	−	0.103790i
$469$	−0.345938	+	1.06469i	−0.0159739	+	0.0491627i
$470$		0			0
$471$	−3.19138	+	2.31868i	−0.147051	+	0.106839i
$472$	17.4796	−	17.4796i	0.804563	−	0.804563i
$473$	17.0603	−	3.81467i	0.784432	−	0.175399i
$474$			0.812515i			0.0373201i
$475$		0			0
$476$	0.0681145	+	0.209635i	0.00312202	+	0.00960860i
$477$	−19.0244	+	9.69341i	−0.871067	+	0.443831i
$478$	−7.92972	+	1.25594i	−0.362697	+	0.0574455i
$479$	21.2408	+	15.4324i	0.970519	+	0.705123i	0.955570	−	0.294765i	$-0.0952413\pi$
$479$	21.2408	+	15.4324i	0.970519	+	0.705123i	0.0149492	+	0.999888i	$0.495241\pi$
$480$		0			0
$481$	−15.9139	+	5.17073i	−0.725610	+	0.235765i
$482$	−24.2731	−	3.84449i	−1.10561	−	0.175112i
$483$	0.175368	+	0.175368i	0.00797952	+	0.00797952i
$484$	0.428672	+	3.38950i	0.0194851	+	0.154068i
$485$		0			0
$486$	−14.0872	−	19.3894i	−0.639008	−	0.879519i
$487$	−10.5939	+	20.7917i	−0.480056	+	0.942163i	0.516262	+	0.856431i	$0.327323\pi$
$487$	−10.5939	+	20.7917i	−0.480056	+	0.942163i	−0.996318	+	0.0857326i	$0.972677\pi$
$488$	6.87039	+	13.4839i	0.311008	+	0.610388i
$489$	−4.69379	+	6.46044i	−0.212260	+	0.292151i
$490$		0			0
$491$	17.4497	+	5.66974i	0.787493	+	0.255872i	0.675036	−	0.737785i	$-0.264128\pi$
$491$	17.4497	+	5.66974i	0.787493	+	0.255872i	0.112457	+	0.993657i	$0.464128\pi$
$492$	1.47728	+	0.752713i	0.0666010	+	0.0339349i
$493$	−5.53572	+	34.9512i	−0.249316	+	1.57412i
$494$	−3.49992			−0.157469
$495$		0			0
$496$	1.58781			0.0712949
$497$	0.343309	−	2.16757i	0.0153995	−	0.0972286i
$498$	−18.0135	−	9.17834i	−0.807204	−	0.411291i
$499$	11.1824	+	3.63339i	0.500595	+	0.162653i	0.548421	−	0.836203i	$-0.315229\pi$
$499$	11.1824	+	3.63339i	0.500595	+	0.162653i	−0.0478260	+	0.998856i	$0.515229\pi$
$500$		0			0
$501$	−5.65234	+	7.77978i	−0.252528	+	0.347575i
$502$	13.3483	+	26.1975i	0.595763	+	1.16925i
$503$	2.42460	−	4.75855i	0.108108	−	0.212173i	−0.830615	−	0.556848i	$-0.812011\pi$
$503$	2.42460	−	4.75855i	0.108108	−	0.212173i	0.938722	+	0.344674i	$0.112011\pi$
$504$	0.683353	+	0.940555i	0.0304390	+	0.0418956i
$505$		0			0
$506$	−8.17484	+	0.514888i	−0.363416	+	0.0228896i
$507$	1.92638	+	1.92638i	0.0855536	+	0.0855536i
$508$	4.46873	+	0.707777i	0.198268	+	0.0314025i
$509$	−18.6283	+	6.05272i	−0.825687	+	0.268282i	−0.691228	−	0.722637i	$-0.742930\pi$
$509$	−18.6283	+	6.05272i	−0.825687	+	0.268282i	−0.134459	+	0.990919i	$0.542930\pi$
$510$		0			0
$511$	0.372057	+	0.270315i	0.0164588	+	0.0119580i
$512$	−15.1686	+	2.40248i	−0.670365	+	0.106175i
$513$	−2.83424	+	1.44412i	−0.125135	+	0.0637594i
$514$	−2.21058	−	6.80347i	−0.0975046	−	0.300088i
$515$		0			0
$516$			1.30513i			0.0574550i
$517$	20.8767	+	35.2950i	0.918158	+	1.55227i
$518$	−1.11243	+	1.11243i	−0.0488775	+	0.0488775i
$519$	−8.03959	+	5.84110i	−0.352899	+	0.256396i
$520$		0			0
$521$	5.78913	−	17.8171i	0.253626	−	0.780582i	−0.740471	−	0.672089i	$-0.765397\pi$
$521$	5.78913	−	17.8171i	0.253626	−	0.780582i	0.994097	−	0.108493i	$-0.0346026\pi$
$522$	−5.36781	−	33.8910i	−0.234943	−	1.48337i
$523$	−0.403961	−	2.55051i	−0.0176640	−	0.111526i	0.977281	−	0.211948i	$-0.0679807\pi$
$523$	−0.403961	−	2.55051i	−0.0176640	−	0.111526i	−0.994945	+	0.100422i	$0.967981\pi$
$524$	0.937631	−	2.88573i	0.0409606	−	0.126064i
$525$		0			0
$526$	−19.5162	+	14.1794i	−0.850948	+	0.618250i
$527$	−0.919727	+	0.919727i	−0.0400639	+	0.0400639i
$528$	11.9108	+	1.12506i	0.518350	+	0.0489621i
$529$			20.3603i			0.885228i
$530$		0			0
$531$	−7.03330	−	21.6463i	−0.305219	−	0.939368i
$532$	−0.0394115	+	0.0200812i	−0.00170871	+	0.000870630i
$533$	−20.4729	+	3.24258i	−0.886778	+	0.140452i
$534$	7.76658	+	5.64275i	0.336093	+	0.244186i
$535$		0			0
$536$	−14.2796	+	4.63972i	−0.616784	+	0.200405i
$537$	−15.8888	−	2.51654i	−0.685652	−	0.108597i
$538$	12.1591	+	12.1591i	0.524216	+	0.524216i
$539$	−8.50325	−	21.4724i	−0.366261	−	0.924881i
$540$		0			0
$541$	5.42829	+	7.47139i	0.233380	+	0.321220i	0.909604	−	0.415476i	$-0.136385\pi$
$541$	5.42829	+	7.47139i	0.233380	+	0.321220i	−0.676224	+	0.736696i	$0.736385\pi$
$542$	12.3031	−	24.1462i	0.528464	−	1.03717i
$543$	1.66841	+	3.27444i	0.0715983	+	0.140520i
$544$	−3.79482	+	5.22312i	−0.162701	+	0.223939i
$545$		0			0
$546$	−0.683120	−	0.221959i	−0.0292348	−	0.00949898i
$547$	−0.954295	−	0.486237i	−0.0408027	−	0.0207900i	0.433470	−	0.901168i	$-0.357289\pi$
$547$	−0.954295	−	0.486237i	−0.0408027	−	0.0207900i	−0.474273	+	0.880378i	$0.657289\pi$
$548$	−0.210388	+	1.32834i	−0.00898732	+	0.0567437i
$549$	13.9337			0.594674
$550$		0			0
$551$	−7.10113			−0.302518
$552$	−0.520344	+	3.28533i	−0.0221473	+	0.139833i
$553$	−0.114386	−	0.0582826i	−0.00486419	−	0.00247843i
$554$	6.76800	+	2.19906i	0.287545	+	0.0934290i
$555$		0			0
$556$	1.91881	−	2.64102i	0.0813758	−	0.112004i
$557$	19.5384	+	38.3462i	0.827868	+	1.62478i	0.779876	+	0.625934i	$0.215282\pi$
$557$	19.5384	+	38.3462i	0.827868	+	1.62478i	0.0479915	+	0.998848i	$0.484718\pi$
$558$	0.572590	−	1.12377i	0.0242396	−	0.0475730i
$559$	−9.59064	−	13.2004i	−0.405641	−	0.558316i
$560$		0			0
$561$	−7.55089	+	6.24752i	−0.318799	+	0.263771i
$562$	14.1765	+	14.1765i	0.597998	+	0.597998i
$563$	25.5439	+	4.04575i	1.07655	+	0.170508i	0.669435	−	0.742871i	$-0.266536\pi$
$563$	25.5439	+	4.04575i	1.07655	+	0.170508i	0.407111	+	0.913379i	$0.366536\pi$
$564$	−2.91164	+	0.946049i	−0.122602	+	0.0398359i
$565$		0			0
$566$	28.0219	+	20.3591i	1.17785	+	0.855756i
$567$	0.696664	−	0.110341i	0.0292571	−	0.00463387i
$568$	26.2257	−	13.3626i	1.10040	−	0.560684i
$569$	8.39651	+	25.8418i	0.352000	+	1.08334i	0.957729	+	0.287673i	$0.0928816\pi$
$569$	8.39651	+	25.8418i	0.352000	+	1.08334i	−0.605729	+	0.795671i	$0.707118\pi$
$570$		0			0
$571$			40.5475i			1.69686i	0.529308	+	0.848430i	$0.322451\pi$
$571$			40.5475i			1.69686i	−0.529308	+	0.848430i	$0.677549\pi$
$572$	2.74464	−	1.62343i	0.114759	−	0.0678791i
$573$	−3.56628	+	3.56628i	−0.148984	+	0.148984i
$574$	−1.57665	+	1.14550i	−0.0658081	+	0.0478124i
$575$		0			0
$576$	−4.67742	+	14.3956i	−0.194893	+	0.599818i
$577$	−5.28872	−	33.3917i	−0.220172	−	1.39011i	−0.811815	−	0.583914i	$-0.801521\pi$
$577$	−5.28872	−	33.3917i	−0.220172	−	1.39011i	0.591643	−	0.806200i	$-0.298479\pi$
$578$	0.775613	+	4.89703i	0.0322612	+	0.203689i
$579$	1.46136	−	4.49759i	0.0607319	−	0.186913i
$580$		0			0
$581$	2.58426	−	1.87757i	0.107213	−	0.0778948i
$582$	−1.18165	+	1.18165i	−0.0489808	+	0.0489808i
$583$	−22.4673	−	19.8048i	−0.930502	−	0.820233i
$584$			6.16801i			0.255234i
$585$		0			0
$586$	−3.39505	−	10.4489i	−0.140248	−	0.431640i
$587$	−8.62859	+	4.39649i	−0.356140	+	0.181462i	−0.622902	−	0.782300i	$-0.714046\pi$
$587$	−8.62859	+	4.39649i	−0.356140	+	0.181462i	0.266762	+	0.963763i	$0.414046\pi$
$588$	1.70297	−	0.269724i	0.0702293	−	0.0111232i
$589$	−0.211163	−	0.153419i	−0.00870081	−	0.00632151i
$590$		0			0
$591$	10.6210	−	3.45096i	0.436888	−	0.141953i
$592$	−24.1566	−	3.82603i	−0.992829	−	0.157249i
$593$	14.0452	+	14.0452i	0.576769	+	0.576769i	0.934012	−	0.357243i	$-0.116283\pi$
$593$	14.0452	+	14.0452i	0.576769	+	0.576769i	−0.357243	+	0.934012i	$0.616283\pi$
$594$	11.5515	−	18.2051i	0.473965	−	0.746964i
$595$		0			0
$596$	1.05199	+	1.44794i	0.0430912	+	0.0593099i
$597$	−4.84367	+	9.50623i	−0.198238	+	0.389064i
$598$	3.47084	+	6.81191i	0.141933	+	0.278560i
$599$	2.65433	−	3.65338i	0.108453	−	0.149273i	−0.751340	−	0.659915i	$-0.770592\pi$
$599$	2.65433	−	3.65338i	0.108453	−	0.149273i	0.859793	+	0.510642i	$0.170592\pi$
$600$		0			0
$601$	−7.96746	−	2.58878i	−0.324999	−	0.105599i	0.141973	−	0.989871i	$-0.454655\pi$
$601$	−7.96746	−	2.58878i	−0.324999	−	0.105599i	−0.466973	+	0.884272i	$0.654655\pi$
$602$	−1.36688	−	0.696458i	−0.0557097	−	0.0283855i
$603$	−2.16258	+	13.6540i	−0.0880671	+	0.556034i
$604$	4.64774			0.189114
$605$		0			0
$606$	5.84763			0.237544
$607$	−1.20123	+	7.58425i	−0.0487563	+	0.307835i	−1.00000		0.000605683i	$-0.999807\pi$
$607$	−1.20123	+	7.58425i	−0.0487563	+	0.307835i	0.951244	+	0.308441i	$0.0998072\pi$
$608$	−1.15435	−	0.588172i	−0.0468152	−	0.0238535i
$609$	−1.38601	−	0.450342i	−0.0561640	−	0.0182488i
$610$		0			0
$611$	22.4971	−	30.9646i	0.910134	−	1.25269i
$612$	1.23574	+	2.42528i	0.0499519	+	0.0980361i
$613$	−19.4882	+	38.2477i	−0.787120	+	1.54481i	0.0506058	+	0.998719i	$0.483885\pi$
$613$	−19.4882	+	38.2477i	−0.787120	+	1.54481i	−0.837726	+	0.546091i	$0.816115\pi$
$614$	25.4319	+	35.0041i	1.02635	+	1.41265i
$615$		0			0
$616$	−0.873721	+	1.37698i	−0.0352032	+	0.0554799i
$617$	−33.4407	−	33.4407i	−1.34627	−	1.34627i	−0.889671	−	0.456601i	$-0.849067\pi$
$617$	−33.4407	−	33.4407i	−1.34627	−	1.34627i	−0.456601	−	0.889671i	$-0.650933\pi$
$618$	−3.87481	−	0.613709i	−0.155868	−	0.0246870i
$619$	−20.0674	+	6.52029i	−0.806576	+	0.262073i	−0.683147	−	0.730281i	$-0.739389\pi$
$619$	−20.0674	+	6.52029i	−0.806576	+	0.262073i	−0.123429	+	0.992353i	$0.539389\pi$
$620$		0			0
$621$	5.62139	+	4.08418i	0.225578	+	0.163892i
$622$	−11.2840	+	1.78720i	−0.452445	+	0.0716603i
$623$	−1.35149	+	0.688620i	−0.0541464	+	0.0275890i
$624$	−3.45064	−	10.6200i	−0.138136	−	0.425139i
$625$		0			0
$626$		−	2.04613i		−	0.0817798i
$627$	−1.47530	−	1.30047i	−0.0589179	−	0.0519358i
$628$	−1.08671	+	1.08671i	−0.0433645	+	0.0433645i
$629$	16.2087	−	11.7763i	0.646282	−	0.469552i
$630$		0			0
$631$	−8.72043	+	26.8387i	−0.347155	+	1.06843i	0.613265	+	0.789877i	$0.289856\pi$
$631$	−8.72043	+	26.8387i	−0.347155	+	1.06843i	−0.960420	+	0.278555i	$0.910144\pi$
$632$	−0.269351	−	1.70061i	−0.0107142	−	0.0676467i
$633$	−0.739847	−	4.67121i	−0.0294063	−	0.185664i
$634$	5.32290	−	16.3822i	0.211399	−	0.650621i
$635$		0			0
$636$	1.80896	−	1.31429i	0.0717301	−	0.0521150i
$637$	−15.2422	+	15.2422i	−0.603918	+	0.603918i
$638$	41.4275	−	24.5041i	1.64013	−	0.970125i
$639$		−	27.1004i		−	1.07208i
$640$		0			0
$641$	−5.23436	−	16.1097i	−0.206745	−	0.636295i	−0.999637	−	0.0269333i	$-0.991426\pi$
$641$	−5.23436	−	16.1097i	−0.206745	−	0.636295i	0.792893	−	0.609362i	$-0.208574\pi$
$642$	−11.9372	+	6.08232i	−0.471124	+	0.240050i
$643$	−6.19838	+	0.981726i	−0.244440	+	0.0387155i	−0.277452	−	0.960739i	$-0.589490\pi$
$643$	−6.19838	+	0.981726i	−0.244440	+	0.0387155i	0.0330121	+	0.999455i	$0.489490\pi$
$644$	0.0781682	+	0.0567925i	0.00308026	+	0.00223794i
$645$		0			0
$646$	3.98552	−	1.29497i	0.156808	−	0.0509500i
$647$	42.9518	+	6.80289i	1.68861	+	0.267449i	0.925479	−	0.378798i	$-0.123662\pi$
$647$	42.9518	+	6.80289i	1.68861	+	0.267449i	0.763128	+	0.646247i	$0.223662\pi$
$648$	6.68931	+	6.68931i	0.262781	+	0.262781i
$649$	24.5981	−	20.3522i	0.965559	−	0.798893i
$650$		0			0
$651$	−0.0314855	−	0.0433361i	−0.00123402	−	0.00169848i
$652$	−1.41240	+	2.77200i	−0.0553140	+	0.108560i
$653$	4.41780	+	8.67042i	0.172882	+	0.339300i	0.961147	−	0.276035i	$-0.0890207\pi$
$653$	4.41780	+	8.67042i	0.172882	+	0.339300i	−0.788266	+	0.615335i	$0.789021\pi$
$654$	6.79682	−	9.35503i	0.265777	−	0.365810i
$655$		0			0
$656$	−28.8145	−	9.36239i	−1.12502	−	0.365540i
$657$	5.06007	+	2.57823i	0.197412	+	0.100586i
$658$	0.562936	−	3.55424i	0.0219455	−	0.138559i
$659$	−3.37375			−0.131423			−0.0657113	−	0.997839i	$-0.520932\pi$
$659$	−3.37375			−0.131423			−0.0657113	+	0.997839i	$0.520932\pi$
$660$		0			0
$661$	9.93056			0.386254			0.193127	−	0.981174i	$-0.438137\pi$
$661$	9.93056			0.386254			0.193127	+	0.981174i	$0.438137\pi$
$662$	−4.21003	+	26.5811i	−0.163628	+	1.03310i
$663$	8.15028	+	4.15278i	0.316531	+	0.161280i
$664$	40.7453	+	13.2389i	1.58122	+	0.513771i
$665$		0			0
$666$	−11.4191	+	15.7170i	−0.442481	+	0.609022i
$667$	7.04213	+	13.8210i	0.272672	+	0.535150i
$668$	−1.70084	+	3.33809i	−0.0658075	+	0.129154i
$669$	−9.96031	−	13.7092i	−0.385088	−	0.530028i
$670$		0			0
$671$	7.19624	+	18.1719i	0.277808	+	0.701520i
$672$	−0.188008	−	0.188008i	−0.00725256	−	0.00725256i
$673$	37.7823	+	5.98412i	1.45640	+	0.230671i	0.833885	−	0.551938i	$-0.186111\pi$
$673$	37.7823	+	5.98412i	1.45640	+	0.230671i	0.622514	+	0.782609i	$0.286111\pi$
$674$	−11.0161	+	3.57935i	−0.424324	+	0.137871i
$675$		0			0
$676$	0.858662	+	0.623855i	0.0330255	+	0.0239944i
$677$	31.7956	−	5.03592i	1.22200	−	0.193546i	0.488092	−	0.872792i	$-0.337693\pi$
$677$	31.7956	−	5.03592i	1.22200	−	0.193546i	0.733911	+	0.679246i	$0.237693\pi$
$678$	4.47847	−	2.28189i	0.171994	−	0.0876356i
$679$	−0.0815917	−	0.251113i	−0.00313120	−	0.00963684i
$680$		0			0
$681$			10.4198i			0.399289i
$682$	1.76132	+	0.166370i	0.0674443	+	0.00637063i
$683$	28.7223	−	28.7223i	1.09903	−	1.09903i	0.104505	−	0.994524i	$-0.466674\pi$
$683$	28.7223	−	28.7223i	1.09903	−	1.09903i	0.994524	−	0.104505i	$-0.0333260\pi$
$684$	−0.441900	+	0.321059i	−0.0168965	+	0.0122760i
$685$		0			0
$686$	−1.25585	+	3.86510i	−0.0479484	+	0.147570i
$687$	−2.04918	−	12.9380i	−0.0781811	−	0.493616i
$688$	−3.73084	−	23.5556i	−0.142237	−	0.898050i
$689$	−8.63834	+	26.5861i	−0.329095	+	1.01285i
$690$		0			0
$691$	20.4397	−	14.8503i	0.777564	−	0.564933i	−0.126683	−	0.991943i	$-0.540433\pi$
$691$	20.4397	−	14.8503i	0.777564	−	0.564933i	0.904247	+	0.427010i	$0.140433\pi$
$692$	−2.73759	+	2.73759i	−0.104068	+	0.104068i
$693$	0.764417	+	1.29235i	0.0290378	+	0.0490925i
$694$		−	14.1878i		−	0.538562i
$695$		0			0
$696$	−6.03999	−	18.5892i	−0.228945	−	0.704621i
$697$	22.1136	−	11.2675i	0.837613	−	0.426785i
$698$	2.25468	−	0.357107i	0.0853410	−	0.0135167i
$699$	−10.0896	−	7.33055i	−0.381625	−	0.277267i
$700$		0			0
$701$	26.8458	−	8.72273i	1.01395	−	0.329453i	0.245525	−	0.969390i	$-0.421040\pi$
$701$	26.8458	−	8.72273i	1.01395	−	0.329453i	0.768427	+	0.639937i	$0.221040\pi$
$702$	−19.8761	−	3.14807i	−0.750175	−	0.118816i
$703$	2.84289	+	2.84289i	0.107222	+	0.107222i
$704$	−21.1902	+	1.33465i	−0.798634	+	0.0503015i
$705$		0			0
$706$	5.56255	+	7.65620i	0.209349	+	0.288145i
$707$	−0.419457	+	0.823230i	−0.0157753	+	0.0309608i
$708$	1.08210	+	2.12373i	0.0406677	+	0.0798148i
$709$	4.79615	−	6.60134i	0.180123	−	0.247918i	−0.709402	−	0.704804i	$-0.751035\pi$
$709$	4.79615	−	6.60134i	0.180123	−	0.247918i	0.889526	+	0.456885i	$0.151035\pi$
$710$		0			0
$711$	−1.50773	−	0.489890i	−0.0565441	−	0.0183723i
$712$	−18.1262	−	9.23576i	−0.679308	−	0.346125i
$713$	−0.0891912	+	0.563131i	−0.00334024	+	0.0210894i
$714$	0.860026			0.0321856
$715$		0			0
$716$	−6.26727			−0.234219
$717$	−0.658703	+	4.15889i	−0.0245997	+	0.155317i
$718$	−35.6261	−	18.1524i	−1.32955	−	0.677441i
$719$	0.986856	+	0.320649i	0.0368035	+	0.0119582i	0.327361	−	0.944899i	$-0.393841\pi$
$719$	0.986856	+	0.320649i	0.0368035	+	0.0119582i	−0.290557	+	0.956858i	$0.593841\pi$
$720$		0			0
$721$	0.364342	−	0.501474i	0.0135688	−	0.0186759i
$722$	−12.7300	−	24.9840i	−0.473762	−	0.929810i
$723$	−5.85157	+	11.4843i	−0.217622	+	0.427107i
$724$	0.841554	+	1.15830i	0.0312761	+	0.0430479i
$725$		0			0
$726$	13.0944	+	2.49600i	0.485978	+	0.0926353i
$727$	3.27903	+	3.27903i	0.121612	+	0.121612i	0.765294	−	0.643681i	$-0.222594\pi$
$727$	3.27903	+	3.27903i	0.121612	+	0.121612i	−0.643681	+	0.765294i	$0.722594\pi$
$728$	1.50337	+	0.238110i	0.0557184	+	0.00882493i
$729$	−1.44390	+	0.469153i	−0.0534779	+	0.0173760i
$730$		0			0
$731$	15.8055	+	11.4833i	0.584586	+	0.424726i
$732$	−1.44121	+	0.228265i	−0.0532687	+	0.00843693i
$733$	−40.6968	+	20.7361i	−1.50317	+	0.765904i	−0.995420	−	0.0956003i	$-0.969523\pi$
$733$	−40.6968	+	20.7361i	−1.50317	+	0.765904i	−0.507751	+	0.861504i	$0.669523\pi$
$734$	3.83723	+	11.8098i	0.141635	+	0.435907i
$735$		0			0
$736$			2.83001i			0.104315i
$737$	−18.9241	+	4.23142i	−0.697079	+	0.155866i
$738$	−17.0171	+	17.0171i	−0.626410	+	0.626410i
$739$	−3.07164	+	2.23167i	−0.112992	+	0.0820934i	−0.642846	−	0.765995i	$-0.722247\pi$
$739$	−3.07164	+	2.23167i	−0.112992	+	0.0820934i	0.529854	+	0.848089i	$0.322247\pi$
$740$		0			0
$741$	−0.567231	+	1.74576i	−0.0208377	+	0.0641320i
$742$	0.411150	+	2.59590i	0.0150938	+	0.0952984i
$743$	−6.63736	−	41.9067i	−0.243501	−	1.53741i	−0.741931	−	0.670476i	$-0.766090\pi$
$743$	−6.63736	−	41.9067i	−0.243501	−	1.53741i	0.498430	−	0.866930i	$-0.333910\pi$
$744$	0.222008	−	0.683270i	0.00813920	−	0.0250499i
$745$		0			0
$746$	−10.6517	+	7.73895i	−0.389988	+	0.283343i
$747$	27.8924	−	27.8924i	1.02053	−	1.02053i
$748$	−2.52477	+	2.86419i	−0.0923149	+	0.104725i
$749$		−	2.11681i		−	0.0773467i
$750$		0			0
$751$	−3.08775	−	9.50312i	−0.112674	−	0.346774i	0.878781	−	0.477225i	$-0.158357\pi$
$751$	−3.08775	−	9.50312i	−0.112674	−	0.346774i	−0.991455	+	0.130451i	$0.958357\pi$
$752$	49.8464	−	25.3980i	1.81771	−	0.926171i
$753$	15.2306	−	2.41230i	0.555035	−	0.0879089i
$754$	−36.3446	−	26.4059i	−1.32359	−	0.961647i
$755$		0			0
$756$	−0.241881	+	0.0785920i	−0.00879714	+	0.00285837i
$757$	−29.0217	−	4.59658i	−1.05481	−	0.167065i	−0.395140	−	0.918621i	$-0.629304\pi$
$757$	−29.0217	−	4.59658i	−1.05481	−	0.167065i	−0.659670	+	0.751555i	$0.729304\pi$
$758$	0.664675	+	0.664675i	0.0241421	+	0.0241421i
$759$	−1.06807	+	4.16105i	−0.0387684	+	0.151037i
$760$		0			0
$761$	−17.8404	−	24.5552i	−0.646713	−	0.890124i	0.352238	−	0.935910i	$-0.385421\pi$
$761$	−17.8404	−	24.5552i	−0.646713	−	0.890124i	−0.998951	+	0.0457864i	$0.985421\pi$
$762$	8.01429	−	15.7289i	0.290327	−	0.569799i
$763$	0.829459	+	1.62790i	0.0300284	+	0.0589341i
$764$	−1.15493	+	1.58963i	−0.0417840	+	0.0575107i
$765$		0			0
$766$	15.0044	+	4.87523i	0.542131	+	0.176149i
$767$	−26.5507	−	13.5283i	−0.958690	−	0.488477i
$768$	0.908377	−	5.73527i	0.0327782	−	0.206954i
$769$	37.6421			1.35741			0.678705	−	0.734411i	$-0.262542\pi$
$769$	37.6421			1.35741			0.678705	+	0.734411i	$0.262542\pi$
$770$		0			0
$771$	−3.75184			−0.135119
$772$	0.288213	−	1.81970i	0.0103730	−	0.0654926i
$773$	−22.9995	−	11.7188i	−0.827234	−	0.421497i	−0.0115072	−	0.999934i	$-0.503663\pi$
$773$	−22.9995	−	11.7188i	−0.827234	−	0.421497i	−0.815727	+	0.578437i	$0.803663\pi$
$774$	−18.0168	−	5.85402i	−0.647601	−	0.210418i
$775$		0			0
$776$	2.08149	−	2.86493i	0.0747213	−	0.102845i
$777$	0.374589	+	0.735173i	0.0134383	+	0.0263742i
$778$	−15.2835	+	29.9955i	−0.547939	+	1.07539i
$779$	2.92741	+	4.02923i	0.104885	+	0.144362i
$780$		0			0
$781$	35.3437	−	13.9964i	1.26470	−	0.500831i
$782$	−6.47282	−	6.47282i	−0.231467	−	0.231467i
$783$	−40.3275	−	6.38724i	−1.44119	−	0.228261i
$784$	−29.9651	+	9.73624i	−1.07018	+	0.347723i
$785$		0			0
$786$	−9.57771	−	6.95861i	−0.341626	−	0.248206i
$787$	17.0625	−	2.70244i	0.608213	−	0.0963315i	0.155272	−	0.987872i	$-0.450375\pi$
$787$	17.0625	−	2.70244i	0.608213	−	0.0963315i	0.452942	+	0.891540i	$0.350375\pi$
$788$	3.87655	−	1.97520i	0.138096	−	0.0703636i
$789$	3.90967	+	12.0327i	0.139188	+	0.428376i
$790$		0			0
$791$			0.794162i			0.0282372i
$792$	−7.99654	+	18.4824i	−0.284145	+	0.656745i
$793$	12.8994	−	12.8994i	0.458070	−	0.458070i
$794$	−18.7425	+	13.6172i	−0.665145	+	0.483256i
$795$		0			0
$796$	−1.28445	+	3.95313i	−0.0455261	+	0.140115i
$797$	6.97213	+	44.0203i	0.246965	+	1.55928i	0.729858	+	0.683599i	$0.239586\pi$
$797$	6.97213	+	44.0203i	0.246965	+	1.55928i	−0.482892	+	0.875680i	$0.660414\pi$
$798$	0.0269979	+	0.170458i	0.000955714	+	0.00603414i
$799$	−14.1615	+	43.5847i	−0.500999	+	1.54192i
$800$		0			0
$801$	−15.1535	+	11.0097i	−0.535424	+	0.389008i
$802$	4.60219	−	4.60219i	0.162509	−	0.162509i
$803$	−0.749124	+	7.93078i	−0.0264360	+	0.279871i
$804$		−	1.44771i		−	0.0510569i
$805$		0			0
$806$	−0.510267	−	1.57044i	−0.0179734	−	0.0553164i
$807$	8.03556	−	4.09432i	0.282865	−	0.144127i
$808$	−12.2392	+	1.93850i	−0.430574	+	0.0681962i
$809$	12.3255	+	8.95497i	0.433340	+	0.314840i	0.782983	−	0.622043i	$-0.213697\pi$
$809$	12.3255	+	8.95497i	0.433340	+	0.314840i	−0.349643	+	0.936883i	$0.613697\pi$
$810$		0			0
$811$	−43.3276	+	14.0780i	−1.52144	+	0.494345i	−0.946183	−	0.323631i	$-0.895096\pi$
$811$	−43.3276	+	14.0780i	−1.52144	+	0.494345i	−0.575253	+	0.817976i	$0.695096\pi$
$812$	−0.560774	−	0.0888178i	−0.0196793	−	0.00311689i
$813$	−10.0502	−	10.0502i	−0.352475	−	0.352475i
$814$	−26.3953	−	6.77521i	−0.925155	−	0.237471i
$815$		0			0
$816$	7.85881	+	10.8167i	0.275113	+	0.378661i
$817$	−1.77984	+	3.49314i	−0.0622688	+	0.122209i
$818$	−2.96438	−	5.81793i	−0.103647	−	0.203419i
$819$	0.823747	−	1.13379i	0.0287840	−	0.0396178i
$820$		0			0
$821$	−27.3071	−	8.87260i	−0.953023	−	0.309656i	−0.209079	−	0.977899i	$-0.567047\pi$
$821$	−27.3071	−	8.87260i	−0.953023	−	0.309656i	−0.743943	+	0.668243i	$0.767047\pi$
$822$	4.67545	+	2.38226i	0.163075	+	0.0830909i
$823$	4.21701	−	26.6252i	0.146996	−	0.928095i	−0.798390	−	0.602141i	$-0.794314\pi$
$823$	4.21701	−	26.6252i	0.146996	−	0.928095i	0.945386	−	0.325954i	$-0.105686\pi$
$824$	8.31350			0.289614
$825$		0			0
$826$	−2.80165			−0.0974820
$827$	6.20779	−	39.1944i	0.215866	−	1.36292i	−0.607006	−	0.794697i	$-0.707630\pi$
$827$	6.20779	−	39.1944i	0.215866	−	1.36292i	0.822872	−	0.568227i	$-0.192370\pi$
$828$	1.06311	+	0.541680i	0.0369455	+	0.0188247i
$829$	10.3353	+	3.35814i	0.358959	+	0.116633i	0.482944	−	0.875651i	$-0.339567\pi$
$829$	10.3353	+	3.35814i	0.358959	+	0.116633i	−0.123985	+	0.992284i	$0.539567\pi$
$830$		0			0
$831$	2.19378	−	3.01948i	0.0761013	−	0.104744i
$832$	8.99683	+	17.6573i	0.311909	+	0.612156i
$833$	11.7174	−	22.9966i	0.405983	−	0.796786i
$834$	−7.48663	−	10.3045i	−0.259241	−	0.356815i
$835$		0			0
$836$	−0.646943	−	0.410500i	−0.0223750	−	0.0141974i
$837$	−1.06120	−	1.06120i	−0.0366805	−	0.0366805i
$838$	1.80523	+	0.285920i	0.0623606	+	0.00987695i
$839$	−38.3426	+	12.4583i	−1.32373	+	0.430107i	−0.883775	−	0.467912i	$-0.845007\pi$
$839$	−38.3426	+	12.4583i	−1.32373	+	0.430107i	−0.439958	+	0.898019i	$0.645007\pi$
$840$		0			0
$841$	−50.2797	−	36.5303i	−1.73378	−	1.25967i
$842$	47.0053	−	7.44491i	1.61991	−	0.256569i
$843$	9.36879	−	4.77364i	0.322678	−	0.164413i
$844$	−0.569376	−	1.75236i	−0.0195987	−	0.0603187i
$845$		0			0
$846$		−	44.4376i		−	1.52780i
$847$	−1.29066	+	1.66439i	−0.0443477	+	0.0571891i
$848$	−28.8921	+	28.8921i	−0.992159	+	0.992159i
$849$	14.6966	−	10.6777i	0.504386	−	0.366458i
$850$		0			0
$851$	2.71386	−	8.35241i	0.0930300	−	0.286317i
$852$	0.443967	+	2.80310i	0.0152101	+	0.0960326i
$853$	2.18326	+	13.7845i	0.0747533	+	0.471974i	0.996459	+	0.0840831i	$0.0267961\pi$
$853$	2.18326	+	13.7845i	0.0747533	+	0.471974i	−0.921705	+	0.387890i	$0.873204\pi$
$854$	0.530012	−	1.63121i	0.0181366	−	0.0558188i
$855$		0			0
$856$	22.9686	−	16.6876i	0.785049	−	0.570372i
$857$	−26.9229	+	26.9229i	−0.919668	+	0.919668i	−0.997005	−	0.0773373i	$-0.975358\pi$
$857$	−26.9229	+	26.9229i	−0.919668	+	0.919668i	0.0773373	+	0.997005i	$0.475358\pi$
$858$	−2.71494	−	12.1420i	−0.0926867	−	0.414521i
$859$			18.3200i			0.625071i	0.949906	+	0.312535i	$0.101178\pi$
$859$			18.3200i			0.625071i	−0.949906	+	0.312535i	$0.898822\pi$
$860$		0			0
$861$	0.315849	+	0.972084i	0.0107641	+	0.0331285i
$862$	−13.3966	+	6.82592i	−0.456291	+	0.232492i
$863$	12.0033	−	1.90114i	0.408597	−	0.0647154i	0.0512472	−	0.998686i	$-0.483680\pi$
$863$	12.0033	−	1.90114i	0.408597	−	0.0647154i	0.357350	+	0.933971i	$0.383680\pi$
$864$	−6.02655	−	4.37855i	−0.205028	−	0.148961i
$865$		0			0
$866$	−39.0074	+	12.6743i	−1.32552	+	0.430689i
$867$	2.56834	+	0.406785i	0.0872253	+	0.0138151i
$868$	−0.0147565	−	0.0147565i	−0.000500870	−	0.000500870i
$869$	−0.139785	−	2.21935i	−0.00474187	−	0.0752863i
$870$		0			0
$871$	10.6384	+	14.6425i	0.360469	+	0.496143i
$872$	−11.1247	+	21.8334i	−0.376730	+	0.739374i
$873$	−1.48025	−	2.90515i	−0.0500987	−	0.0983243i
$874$	1.07972	−	1.48611i	0.0365222	−	0.0502685i
$875$		0			0
$876$	−0.565619	−	0.183781i	−0.0191105	−	0.00620938i
$877$	11.4361	+	5.82698i	0.386169	+	0.196763i	0.636287	−	0.771452i	$-0.280469\pi$
$877$	11.4361	+	5.82698i	0.386169	+	0.196763i	−0.250118	+	0.968215i	$0.580469\pi$
$878$	−5.84636	+	36.9125i	−0.197305	+	1.24574i
$879$	−5.76213			−0.194352
$880$		0			0
$881$	13.8380			0.466216			0.233108	−	0.972451i	$-0.425110\pi$
$881$	13.8380			0.466216			0.233108	+	0.972451i	$0.425110\pi$
$882$	−3.91506	+	24.7187i	−0.131827	+	0.832322i
$883$	−38.8377	−	19.7888i	−1.30699	−	0.665947i	−0.344893	−	0.938642i	$-0.612085\pi$
$883$	−38.8377	−	19.7888i	−1.30699	−	0.665947i	−0.962100	+	0.272695i	$0.912085\pi$
$884$	3.38926	+	1.10124i	0.113993	+	0.0370387i
$885$		0			0
$886$	−27.5163	+	37.8730i	−0.924429	+	1.27237i
$887$	4.72114	+	9.26576i	0.158520	+	0.311114i	0.956583	−	0.291461i	$-0.0941414\pi$
$887$	4.72114	+	9.26576i	0.158520	+	0.311114i	−0.798062	+	0.602575i	$0.794141\pi$
$888$	−5.02399	+	9.86013i	−0.168594	+	0.330884i
$889$	1.63945	+	2.25651i	0.0549853	+	0.0756808i
$890$		0			0
$891$	7.78863	+	9.41351i	0.260929	+	0.315364i
$892$	−4.66817	−	4.66817i	−0.156302	−	0.156302i
$893$	−9.08308	−	1.43862i	−0.303954	−	0.0481415i
$894$	6.64130	−	2.15789i	0.222118	−	0.0721706i
$895$		0			0
$896$	2.04700	+	1.48723i	0.0683855	+	0.0496850i
$897$	3.96029	−	0.627249i	0.132230	−	0.0209432i
$898$	−9.92048	+	5.05474i	−0.331051	+	0.168679i
$899$	−1.03530	−	3.18633i	−0.0345292	−	0.106270i
$900$		0			0
$901$		−	33.4710i		−	1.11508i
$902$	−30.9821	−	13.4046i	−1.03159	−	0.446324i
$903$	−0.568922	+	0.568922i	−0.0189325	+	0.0189325i
$904$	−8.61708	+	6.26067i	−0.286600	+	0.208227i
$905$		0			0
$906$	5.60375	−	17.2466i	0.186172	−	0.572979i
$907$	−2.55097	−	16.1062i	−0.0847036	−	0.534798i	−0.993155	−	0.116806i	$-0.962734\pi$
$907$	−2.55097	−	16.1062i	−0.0847036	−	0.534798i	0.908451	−	0.417991i	$-0.137266\pi$
$908$	0.635040	+	4.00948i	0.0210745	+	0.133059i
$909$	−3.52571	+	10.8510i	−0.116940	+	0.359906i
$910$		0			0
$911$	14.3281	−	10.4099i	0.474710	−	0.344897i	−0.324564	−	0.945864i	$-0.605218\pi$
$911$	14.3281	−	10.4099i	0.474710	−	0.344897i	0.799274	+	0.600967i	$0.205218\pi$
$912$	−1.89718	+	1.89718i	−0.0628219	+	0.0628219i
$913$	50.7821	+	21.9712i	1.68064	+	0.727140i
$914$		−	10.2385i		−	0.338659i
$915$		0			0
$916$	−1.57702	−	4.85357i	−0.0521062	−	0.160366i
$917$	1.66665	−	0.849203i	0.0550378	−	0.0280431i
$918$	23.7986	−	3.76933i	0.785472	−	0.124406i
$919$	−7.38632	−	5.36648i	−0.243652	−	0.177024i	0.459257	−	0.888304i	$-0.348116\pi$
$919$	−7.38632	−	5.36648i	−0.243652	−	0.177024i	−0.702909	+	0.711280i	$0.748116\pi$
$920$		0			0
$921$	21.5818	−	7.01234i	0.711143	−	0.231064i
$922$	43.6594	+	6.91497i	1.43785	+	0.227732i
$923$	−25.0888	−	25.0888i	−0.825807	−	0.825807i
$924$	−0.100238	−	0.121150i	−0.00329760	−	0.00398555i
$925$		0			0
$926$	22.1307	+	30.4602i	0.727259	+	1.00099i
$927$	3.47505	−	6.82017i	0.114136	−	0.224004i
$928$	−7.54970	−	14.8171i	−0.247831	−	0.486396i
$929$	1.06529	−	1.46625i	0.0349511	−	0.0481061i	−0.791184	−	0.611578i	$-0.790535\pi$
$929$	1.06529	−	1.46625i	0.0349511	−	0.0481061i	0.826135	+	0.563472i	$0.190535\pi$
$930$		0			0
$931$	4.92578	+	1.60048i	0.161436	+	0.0524537i
$932$	−4.32918	−	2.20583i	−0.141807	−	0.0722543i
$933$	−0.937332	+	5.91808i	−0.0306869	+	0.193749i
$934$	40.2174			1.31595
$935$		0			0
$936$	18.7961			0.614371
$937$	2.37143	−	14.9726i	0.0774711	−	0.489133i	−0.918195	−	0.396130i	$-0.870353\pi$
$937$	2.37143	−	14.9726i	0.0774711	−	0.489133i	0.995666	−	0.0930039i	$-0.0296469\pi$
$938$	1.51621	+	0.772546i	0.0495059	+	0.0252245i
$939$	−1.02061	−	0.331616i	−0.0333063	−	0.0108219i
$940$		0			0
$941$	−12.8308	+	17.6600i	−0.418271	+	0.575701i	−0.965211	−	0.261471i	$-0.915792\pi$
$941$	−12.8308	+	17.6600i	−0.418271	+	0.575701i	0.546940	+	0.837172i	$0.315792\pi$
$942$	2.72226	+	5.34274i	0.0886961	+	0.174076i
$943$	4.93902	−	9.69338i	0.160837	−	0.315660i
$944$	−25.6012	−	35.2370i	−0.833247	−	1.14687i
$945$		0			0
$946$	−1.67038	−	26.5205i	−0.0543087	−	0.862256i
$947$	−6.90662	−	6.90662i	−0.224435	−	0.224435i	0.585928	−	0.810363i	$-0.300730\pi$
$947$	−6.90662	−	6.90662i	−0.224435	−	0.224435i	−0.810363	+	0.585928i	$0.800730\pi$
$948$	0.163975	+	0.0259711i	0.00532567	+	0.000843503i
$949$	7.07131	−	2.29761i	0.229545	−	0.0745835i
$950$		0			0
$951$	−7.30875	−	5.31012i	−0.237003	−	0.172192i
$952$	−1.80005	+	0.285100i	−0.0583400	+	0.00924015i
$953$	11.6216	−	5.92153i	0.376462	−	0.191817i	−0.255513	−	0.966806i	$-0.582244\pi$
$953$	11.6216	−	5.92153i	0.376462	−	0.191817i	0.631975	+	0.774989i	$0.282244\pi$
$954$	10.0294	+	30.8672i	0.324713	+	0.999363i
$955$		0			0
$956$			1.64046i			0.0530561i
$957$	−5.50846	−	24.6354i	−0.178063	−	0.796349i
$958$	28.2202	−	28.2202i	0.911755	−	0.911755i
$959$	−0.670750	+	0.487328i	−0.0216596	+	0.0157367i
$960$		0			0
$961$	−9.54147	+	29.3656i	−0.307789	+	0.947279i
$962$	3.97890	+	25.1218i	0.128285	+	0.809960i
$963$	−4.08921	−	25.8182i	−0.131773	−	0.831981i
$964$	−1.55173	+	4.77572i	−0.0499777	+	0.153816i
$965$		0			0
$966$	0.304989	−	0.221588i	0.00981287	−	0.00712946i
$967$	13.6319	−	13.6319i	0.438372	−	0.438372i	−0.453092	−	0.891464i	$-0.649679\pi$
$967$	13.6319	−	13.6319i	0.438372	−	0.438372i	0.891464	+	0.453092i	$0.149679\pi$
$968$	−28.2343	−	0.883368i	−0.907484	−	0.0283925i
$969$		−	2.19785i		−	0.0706051i
$970$		0			0
$971$	1.26967	+	3.90765i	0.0407457	+	0.125403i	0.969360	−	0.245643i	$-0.0789992\pi$
$971$	1.26967	+	3.90765i	0.0407457	+	0.125403i	−0.928615	+	0.371046i	$0.878999\pi$
$972$	−4.36328	+	2.22320i	−0.139952	+	0.0713093i
$973$	1.98769	−	0.314819i	0.0637224	−	0.0100926i
$974$	28.6965	+	20.8492i	0.919495	+	0.668052i
$975$		0			0
$976$	25.3592	−	8.23971i	0.811729	−	0.263747i
$977$	−30.3314	−	4.80402i	−0.970386	−	0.153694i	−0.348935	−	0.937147i	$-0.613457\pi$
$977$	−30.3314	−	4.80402i	−0.970386	−	0.153694i	−0.621451	+	0.783453i	$0.713457\pi$
$978$	8.58324	+	8.58324i	0.274462	+	0.274462i
$979$	−22.1848	−	14.0768i	−0.709030	−	0.449895i
$980$		0			0
$981$	13.2614	+	18.2528i	0.423405	+	0.582767i
$982$	12.6616	−	24.8498i	0.404048	−	0.792990i
$983$	12.5871	+	24.7035i	0.401465	+	0.787919i	0.999912	−	0.0132429i	$-0.00421546\pi$
$983$	12.5871	+	24.7035i	0.401465	+	0.787919i	−0.598447	+	0.801162i	$0.704215\pi$
$984$	−8.05767	+	11.0904i	−0.256869	+	0.353550i
$985$		0			0
$986$	51.1575	+	16.6221i	1.62919	+	0.529355i
$987$	−1.68162	−	0.856827i	−0.0535265	−	0.0272731i
$988$	−0.111871	+	0.706325i	−0.00355909	+	0.0224712i
$989$	8.56376			0.272312
$990$		0			0
$991$	9.10087			0.289099			0.144549	−	0.989498i	$-0.453827\pi$
$991$	9.10087			0.289099			0.144549	+	0.989498i	$0.453827\pi$
$992$	0.0956197	−	0.603719i	0.00303593	−	0.0191681i
$993$	12.5763	+	6.40795i	0.399097	+	0.203350i
$994$	−3.17264	−	1.03085i	−0.100630	−	0.0326966i
$995$		0			0
$996$	−2.42808	+	3.34196i	−0.0769366	+	0.105894i
$997$	−13.1070	−	25.7239i	−0.415103	−	0.814685i	−0.999994	−	0.00357282i	$-0.998863\pi$
$997$	−13.1070	−	25.7239i	−0.415103	−	0.814685i	0.584891	−	0.811112i	$-0.301137\pi$
$998$	8.11406	−	15.9247i	0.256846	−	0.504089i
$999$	13.5878	+	18.7019i	0.429898	+	0.591703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.bm.b.107.4		32
5.2	odd	4		55.2.l.a.8.4	yes	32
5.3	odd	4	inner	275.2.bm.b.118.1		32
5.4	even	2		55.2.l.a.52.1	yes	32
11.7	odd	10	inner	275.2.bm.b.7.1		32
15.2	even	4		495.2.bj.a.118.1		32
15.14	odd	2		495.2.bj.a.217.4		32
20.7	even	4		880.2.cm.a.833.4		32
20.19	odd	2		880.2.cm.a.657.1		32
55.2	even	20		605.2.e.b.483.14		32
55.4	even	10		605.2.m.e.282.1		32
55.7	even	20		55.2.l.a.18.1	yes	32
55.9	even	10		605.2.e.b.362.14		32
55.14	even	10		605.2.m.c.457.4		32
55.17	even	20		605.2.m.c.233.4		32
55.18	even	20	inner	275.2.bm.b.18.4		32
55.19	odd	10		605.2.m.d.457.1		32
55.24	odd	10		605.2.e.b.362.3		32
55.27	odd	20		605.2.m.d.233.1		32
55.29	odd	10		55.2.l.a.7.4	✓	32
55.32	even	4		605.2.m.e.118.1		32
55.37	odd	20		605.2.m.e.403.4		32
55.39	odd	10		605.2.m.c.112.4		32
55.42	odd	20		605.2.e.b.483.3		32
55.47	odd	20		605.2.m.c.578.4		32
55.49	even	10		605.2.m.d.112.1		32
55.52	even	20		605.2.m.d.578.1		32
55.54	odd	2		605.2.m.e.602.4		32
165.29	even	10		495.2.bj.a.172.1		32
165.62	odd	20		495.2.bj.a.73.4		32
220.7	odd	20		880.2.cm.a.513.1		32
220.139	even	10		880.2.cm.a.337.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.4	✓	32	55.29	odd	10
55.2.l.a.8.4	yes	32	5.2	odd	4
55.2.l.a.18.1	yes	32	55.7	even	20
55.2.l.a.52.1	yes	32	5.4	even	2
275.2.bm.b.7.1		32	11.7	odd	10	inner
275.2.bm.b.18.4		32	55.18	even	20	inner
275.2.bm.b.107.4		32	1.1	even	1	trivial
275.2.bm.b.118.1		32	5.3	odd	4	inner
495.2.bj.a.73.4		32	165.62	odd	20
495.2.bj.a.118.1		32	15.2	even	4
495.2.bj.a.172.1		32	165.29	even	10
495.2.bj.a.217.4		32	15.14	odd	2
605.2.e.b.362.3		32	55.24	odd	10
605.2.e.b.362.14		32	55.9	even	10
605.2.e.b.483.3		32	55.42	odd	20
605.2.e.b.483.14		32	55.2	even	20
605.2.m.c.112.4		32	55.39	odd	10
605.2.m.c.233.4		32	55.17	even	20
605.2.m.c.457.4		32	55.14	even	10
605.2.m.c.578.4		32	55.47	odd	20
605.2.m.d.112.1		32	55.49	even	10
605.2.m.d.233.1		32	55.27	odd	20
605.2.m.d.457.1		32	55.19	odd	10
605.2.m.d.578.1		32	55.52	even	20
605.2.m.e.118.1		32	55.32	even	4
605.2.m.e.282.1		32	55.4	even	10
605.2.m.e.403.4		32	55.37	odd	20
605.2.m.e.602.4		32	55.54	odd	2
880.2.cm.a.337.4		32	220.139	even	10
880.2.cm.a.513.1		32	220.7	odd	20
880.2.cm.a.657.1		32	20.19	odd	2
880.2.cm.a.833.4		32	20.7	even	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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.bm (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.237790 - 1.50135i) q^{2} +(-0.710333 - 0.361933i) q^{3} +(-0.295389 - 0.0959778i) q^{4} +(-0.712297 + 0.980393i) q^{6} +(-0.0869260 - 0.170602i) q^{7} +(1.16585 - 2.28811i) q^{8} +(-1.38978 - 1.91287i) q^{9} +(1.77694 - 2.80044i) q^{11} +(0.175087 + 0.175087i) q^{12} +(-3.05749 - 0.484259i) q^{13} +(-0.276803 + 0.0899388i) q^{14} +(-3.66057 - 2.65956i) q^{16} +(3.66088 - 0.579827i) q^{17} +(-3.20235 + 1.63168i) q^{18} +(0.229844 + 0.707388i) q^{19} +0.152646i q^{21} +(-3.78190 - 3.33373i) q^{22} +(1.14886 - 1.14886i) q^{23} +(-1.65629 + 1.20336i) q^{24} +(-1.45408 + 4.47521i) q^{26} +(0.669017 + 4.22401i) q^{27} +(0.00930302 + 0.0587369i) q^{28} +(-2.95025 + 9.07993i) q^{29} +(-0.283900 + 0.206266i) q^{31} +(-1.23166 + 1.23166i) q^{32} +(-2.27579 + 1.34611i) q^{33} -5.63413i q^{34} +(0.226933 + 0.698428i) q^{36} +(4.81621 - 2.45398i) q^{37} +(1.11669 - 0.176866i) q^{38} +(1.99657 + 1.45059i) q^{39} +(6.36824 - 2.06917i) q^{41} +(0.229174 + 0.0362976i) q^{42} +(3.72708 + 3.72708i) q^{43} +(-0.793670 + 0.656674i) q^{44} +(-1.45165 - 1.99802i) q^{46} +(-5.61318 + 11.0165i) q^{47} +(1.63764 + 3.21405i) q^{48} +(4.09295 - 5.63346i) q^{49} +(-2.81030 - 0.913123i) q^{51} +(0.856672 + 0.436496i) q^{52} +(1.41265 - 8.91914i) q^{53} +6.50079 q^{54} -0.491699 q^{56} +(0.0927608 - 0.585669i) q^{57} +(12.9306 + 6.58847i) q^{58} +(9.15496 + 2.97463i) q^{59} +(-3.46383 + 4.76756i) q^{61} +(0.242168 + 0.475281i) q^{62} +(-0.205531 + 0.403377i) q^{63} +(-3.76284 - 5.17911i) q^{64} +(1.47982 + 3.73685i) q^{66} +(-4.13426 - 4.13426i) q^{67} +(-1.13704 - 0.180089i) q^{68} +(-1.23188 + 0.400262i) q^{69} +(9.27272 + 6.73702i) q^{71} +(-5.99713 + 0.949851i) q^{72} +(-2.14008 + 1.09042i) q^{73} +(-2.53903 - 7.81434i) q^{74} -0.231015i q^{76} +(-0.632224 - 0.0597184i) q^{77} +(2.65261 - 2.65261i) q^{78} +(0.542434 - 0.394101i) q^{79} +(-1.13837 + 3.50353i) q^{81} +(-1.59224 - 10.0530i) q^{82} +(2.60980 + 16.4776i) q^{83} +(0.0146506 - 0.0450899i) q^{84} +(6.48191 - 4.70938i) q^{86} +(5.38198 - 5.38198i) q^{87} +(-4.33608 - 7.33074i) q^{88} -7.92190i q^{89} +(0.183160 + 0.563709i) q^{91} +(-0.449625 + 0.229095i) q^{92} +(0.276318 - 0.0437645i) q^{93} +(15.2048 + 11.0469i) q^{94} +(1.32067 - 0.429111i) q^{96} +(1.36201 + 0.215721i) q^{97} +(-7.48452 - 7.48452i) q^{98} +(-7.82643 + 0.492943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 4 q^{3} - 20 q^{6} + 10 q^{8} - 24 q^{11} - 12 q^{12} + 10 q^{13} - 8 q^{16} + 10 q^{18} - 10 q^{22} + 24 q^{23} + 20 q^{26} + 16 q^{27} - 50 q^{28} - 28 q^{31} - 66 q^{33} + 24 q^{36}+ \cdots + 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 + 4 * q^3 - 20 * q^6 + 10 * q^8 - 24 * q^11 - 12 * q^12 + 10 * q^13 - 8 * q^16 + 10 * q^18 - 10 * q^22 + 24 * q^23 + 20 * q^26 + 16 * q^27 - 50 * q^28 - 28 * q^31 - 66 * q^33 + 24 * q^36 + 8 * q^37 - 10 * q^38 + 40 * q^41 + 10 * q^42 + 60 * q^46 + 28 * q^47 + 54 * q^48 + 20 * q^51 + 50 * q^52 + 24 * q^53 - 80 * q^56 - 30 * q^57 + 50 * q^58 - 60 * q^61 - 100 * q^62 + 30 * q^63 - 100 * q^66 + 8 * q^67 + 30 * q^68 + 24 * q^71 - 80 * q^72 - 50 * q^73 - 70 * q^77 - 60 * q^78 - 12 * q^81 + 10 * q^82 - 90 * q^83 + 100 * q^86 - 170 * q^88 + 20 * q^91 + 68 * q^92 + 8 * q^93 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more