LMFDB - Embedded newform 275.2.bm.b.7.1

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)

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")

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);

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			7.1
Character	$\chi$	$=$	275.7
Dual form			275.2.bm.b.118.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50135 + 0.237790i) q^{2} +(0.361933 + 0.710333i) q^{3} +(0.295389 - 0.0959778i) q^{4} +(-0.712297 - 0.980393i) q^{6} +(-0.170602 - 0.0869260i) q^{7} +(2.28811 - 1.16585i) q^{8} +(1.38978 - 1.91287i) q^{9} +(1.77694 + 2.80044i) q^{11} +(0.175087 + 0.175087i) q^{12} +(0.484259 + 3.05749i) q^{13} +(0.276803 + 0.0899388i) q^{14} +(-3.66057 + 2.65956i) q^{16} +(-0.579827 + 3.66088i) q^{17} +(-1.63168 + 3.20235i) q^{18} +(-0.229844 + 0.707388i) q^{19} -0.152646i q^{21} +(-3.33373 - 3.78190i) q^{22} +(1.14886 - 1.14886i) q^{23} +(1.65629 + 1.20336i) q^{24} +(-1.45408 - 4.47521i) q^{26} +(4.22401 + 0.669017i) q^{27} +(-0.0587369 - 0.00930302i) q^{28} +(2.95025 + 9.07993i) q^{29} +(-0.283900 - 0.206266i) q^{31} +(1.23166 - 1.23166i) q^{32} +(-1.34611 + 2.27579i) q^{33} -5.63413i q^{34} +(0.226933 - 0.698428i) q^{36} +(-2.45398 + 4.81621i) q^{37} +(0.176866 - 1.11669i) q^{38} +(-1.99657 + 1.45059i) q^{39} +(6.36824 + 2.06917i) q^{41} +(0.0362976 + 0.229174i) q^{42} +(-3.72708 - 3.72708i) q^{43} +(0.793670 + 0.656674i) q^{44} +(-1.45165 + 1.99802i) q^{46} +(11.0165 - 5.61318i) q^{47} +(-3.21405 - 1.63764i) q^{48} +(-4.09295 - 5.63346i) q^{49} +(-2.81030 + 0.913123i) q^{51} +(0.436496 + 0.856672i) q^{52} +(8.91914 - 1.41265i) q^{53} -6.50079 q^{54} -0.491699 q^{56} +(-0.585669 + 0.0927608i) q^{57} +(-6.58847 - 12.9306i) q^{58} +(-9.15496 + 2.97463i) q^{59} +(-3.46383 - 4.76756i) q^{61} +(0.475281 + 0.242168i) q^{62} +(-0.403377 + 0.205531i) q^{63} +(3.76284 - 5.17911i) q^{64} +(1.47982 - 3.73685i) q^{66} +(-4.13426 - 4.13426i) q^{67} +(0.180089 + 1.13704i) q^{68} +(1.23188 + 0.400262i) q^{69} +(9.27272 - 6.73702i) q^{71} +(0.949851 - 5.99713i) q^{72} +(-1.09042 + 2.14008i) q^{73} +(2.53903 - 7.81434i) q^{74} +0.231015i q^{76} +(-0.0597184 - 0.632224i) q^{77} +(2.65261 - 2.65261i) q^{78} +(-0.542434 - 0.394101i) q^{79} +(-1.13837 - 3.50353i) q^{81} +(-10.0530 - 1.59224i) q^{82} +(-16.4776 - 2.60980i) q^{83} +(-0.0146506 - 0.0450899i) q^{84} +(6.48191 + 4.70938i) q^{86} +(-5.38198 + 5.38198i) q^{87} +(7.33074 + 4.33608i) q^{88} -7.92190i q^{89} +(0.183160 - 0.563709i) q^{91} +(0.229095 - 0.449625i) q^{92} +(0.0437645 - 0.276318i) q^{93} +(-15.2048 + 11.0469i) q^{94} +(1.32067 + 0.429111i) q^{96} +(0.215721 + 1.36201i) 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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.50135	+	0.237790i	−1.06161	+	0.168143i	−0.662730	−	0.748859i	$-0.730602\pi$
$2$	−1.50135	+	0.237790i	−1.06161	+	0.168143i	−0.398884	+	0.917002i	$0.630602\pi$
$3$	0.361933	+	0.710333i	0.208962	+	0.410111i	0.971571	−	0.236749i	$-0.0760819\pi$
$3$	0.361933	+	0.710333i	0.208962	+	0.410111i	−0.762609	+	0.646860i	$0.776082\pi$
$4$	0.295389	−	0.0959778i	0.147695	−	0.0479889i
$5$		0			0
$5$		0			0
$6$	−0.712297	−	0.980393i	−0.290794	−	0.400244i
$7$	−0.170602	−	0.0869260i	−0.0644815	−	0.0328550i	0.421452	−	0.906851i	$-0.361520\pi$
$7$	−0.170602	−	0.0869260i	−0.0644815	−	0.0328550i	−0.485934	+	0.873996i	$0.661520\pi$
$8$	2.28811	−	1.16585i	0.808970	−	0.412191i
$9$	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
$13$	0.484259	+	3.05749i	0.134309	+	0.847995i	0.959205	+	0.282711i	$0.0912336\pi$
$13$	0.484259	+	3.05749i	0.134309	+	0.847995i	−0.824896	+	0.565285i	$0.808766\pi$
$14$	0.276803	+	0.0899388i	0.0739787	+	0.0240372i
$15$		0			0
$16$	−3.66057	+	2.65956i	−0.915143	+	0.664890i
$17$	−0.579827	+	3.66088i	−0.140629	+	0.887894i	0.811978	+	0.583688i	$0.198391\pi$
$17$	−0.579827	+	3.66088i	−0.140629	+	0.887894i	−0.952606	+	0.304206i	$0.901609\pi$
$18$	−1.63168	+	3.20235i	−0.384591	+	0.754802i
$19$	−0.229844	+	0.707388i	−0.0527299	+	0.162286i	−0.973954	−	0.226747i	$-0.927191\pi$
$19$	−0.229844	+	0.707388i	−0.0527299	+	0.162286i	0.921224	+	0.389033i	$0.127191\pi$
$20$		0			0
$21$		−	0.152646i		−	0.0333100i
$22$	−3.33373	−	3.78190i	−0.710753	−	0.806304i
$23$	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
$27$	4.22401	+	0.669017i	0.812911	+	0.128752i
$28$	−0.0587369	−	0.00930302i	−0.0111002	−	0.00175811i
$29$	2.95025	+	9.07993i	0.547847	+	1.68610i	0.714122	+	0.700021i	$0.246826\pi$
$29$	2.95025	+	9.07993i	0.547847	+	1.68610i	−0.166275	+	0.986079i	$0.553174\pi$
$30$		0			0
$31$	−0.283900	−	0.206266i	−0.0509900	−	0.0370464i	0.561998	−	0.827138i	$-0.310033\pi$
$31$	−0.283900	−	0.206266i	−0.0509900	−	0.0370464i	−0.612988	+	0.790092i	$0.710033\pi$
$32$	1.23166	−	1.23166i	0.217729	−	0.217729i
$33$	−1.34611	+	2.27579i	−0.234328	+	0.396165i
$34$		−	5.63413i		−	0.966246i
$35$		0			0
$36$	0.226933	−	0.698428i	0.0378222	−	0.116405i
$37$	−2.45398	+	4.81621i	−0.403432	+	0.791780i	−0.999941	−	0.0108264i	$-0.996554\pi$
$37$	−2.45398	+	4.81621i	−0.403432	+	0.791780i	0.596510	+	0.802606i	$0.296554\pi$
$38$	0.176866	−	1.11669i	0.0286915	−	0.181151i
$39$	−1.99657	+	1.45059i	−0.319707	+	0.232280i
$40$		0			0
$41$	6.36824	+	2.06917i	0.994552	+	0.323150i	0.760687	−	0.649119i	$-0.224862\pi$
$41$	6.36824	+	2.06917i	0.994552	+	0.323150i	0.233866	+	0.972269i	$0.424862\pi$
$42$	0.0362976	+	0.229174i	0.00560084	+	0.0353623i
$43$	−3.72708	−	3.72708i	−0.568374	−	0.568374i	0.363299	−	0.931673i	$-0.381650\pi$
$43$	−3.72708	−	3.72708i	−0.568374	−	0.568374i	−0.931673	+	0.363299i	$0.881650\pi$
$44$	0.793670	+	0.656674i	0.119650	+	0.0989973i
$45$		0			0
$46$	−1.45165	+	1.99802i	−0.214034	+	0.294592i
$47$	11.0165	−	5.61318i	1.60692	−	0.818766i	0.607213	−	0.794539i	$-0.292287\pi$
$47$	11.0165	−	5.61318i	1.60692	−	0.818766i	0.999706	−	0.0242272i	$-0.00771250\pi$
$48$	−3.21405	−	1.63764i	−0.463909	−	0.236373i
$49$	−4.09295	−	5.63346i	−0.584707	−	0.804780i
$50$		0			0
$51$	−2.81030	+	0.913123i	−0.393521	+	0.127863i
$52$	0.436496	+	0.856672i	0.0605311	+	0.118799i
$53$	8.91914	−	1.41265i	1.22514	−	0.194043i	0.489855	−	0.871804i	$-0.337050\pi$
$53$	8.91914	−	1.41265i	1.22514	−	0.194043i	0.735282	+	0.677761i	$0.237050\pi$
$54$	−6.50079			−0.884646
$55$		0			0
$56$	−0.491699			−0.0657061
$57$	−0.585669	+	0.0927608i	−0.0775737	+	0.0122865i
$58$	−6.58847	−	12.9306i	−0.865108	−	1.69787i
$59$	−9.15496	+	2.97463i	−1.19187	+	0.387263i	−0.836765	−	0.547562i	$-0.815556\pi$
$59$	−9.15496	+	2.97463i	−1.19187	+	0.387263i	−0.355108	+	0.934825i	$0.615556\pi$
$60$		0			0
$61$	−3.46383	−	4.76756i	−0.443498	−	0.610423i	0.527487	−	0.849563i	$-0.323134\pi$
$61$	−3.46383	−	4.76756i	−0.443498	−	0.610423i	−0.970985	+	0.239140i	$0.923134\pi$
$62$	0.475281	+	0.242168i	0.0603608	+	0.0307554i
$63$	−0.403377	+	0.205531i	−0.0508207	+	0.0258944i
$64$	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	$0.866250\pi$
$68$	0.180089	+	1.13704i	0.0218390	+	0.137886i
$69$	1.23188	+	0.400262i	0.148301	+	0.0481859i
$70$		0			0
$71$	9.27272	−	6.73702i	1.10047	−	0.799538i	0.119333	−	0.992854i	$-0.461925\pi$
$71$	9.27272	−	6.73702i	1.10047	−	0.799538i	0.981136	+	0.193317i	$0.0619245\pi$
$72$	0.949851	−	5.99713i	0.111941	−	0.706768i
$73$	−1.09042	+	2.14008i	−0.127624	+	0.250477i	−0.945973	−	0.324245i	$-0.894890\pi$
$73$	−1.09042	+	2.14008i	−0.127624	+	0.250477i	0.818349	+	0.574722i	$0.194890\pi$
$74$	2.53903	−	7.81434i	0.295156	−	0.908398i
$75$		0			0
$76$			0.231015i			0.0264992i
$77$	−0.0597184	−	0.632224i	−0.00680554	−	0.0720486i
$78$	2.65261	−	2.65261i	0.300348	−	0.300348i
$79$	−0.542434	−	0.394101i	−0.0610286	−	0.0443399i	0.556853	−	0.830611i	$-0.312009\pi$
$79$	−0.542434	−	0.394101i	−0.0610286	−	0.0443399i	−0.617881	+	0.786271i	$0.712009\pi$
$80$		0			0
$81$	−1.13837	−	3.50353i	−0.126485	−	0.389282i
$82$	−10.0530	−	1.59224i	−1.11017	−	0.175833i
$83$	−16.4776	−	2.60980i	−1.80865	−	0.286463i	−0.841426	−	0.540372i	$-0.818284\pi$
$83$	−16.4776	−	2.60980i	−1.80865	−	0.286463i	−0.967228	+	0.253909i	$0.918284\pi$
$84$	−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
$88$	7.33074	+	4.33608i	0.781460	+	0.462227i
$89$		−	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
$92$	0.229095	−	0.449625i	0.0238848	−	0.0468766i
$93$	0.0437645	−	0.276318i	0.00453817	−	0.0286528i
$94$	−15.2048	+	11.0469i	−1.56826	+	1.13941i
$95$		0			0
$96$	1.32067	+	0.429111i	0.134790	+	0.0437960i
$97$	0.215721	+	1.36201i	0.0219032	+	0.138291i	0.996217	−	0.0869051i	$-0.0276977\pi$
$97$	0.215721	+	1.36201i	0.0219032	+	0.138291i	−0.974313	+	0.225196i	$0.927698\pi$
$98$	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	−0.926469	−	0.376370i	$-0.877172\pi$
$101$	−2.83633	+	3.90387i	−0.282225	+	0.388449i	0.644244	+	0.764820i	$0.277172\pi$
$102$	4.00211	−	2.03918i	0.396268	−	0.201909i
$103$	−2.88449	−	1.46972i	−0.284217	−	0.144816i	0.306071	−	0.952009i	$-0.400986\pi$
$103$	−2.88449	−	1.46972i	−0.284217	−	0.144816i	−0.590287	+	0.807193i	$0.700986\pi$
$104$	4.67262	+	6.43131i	0.458188	+	0.630641i
$105$		0			0
$106$	−13.0548	+	4.24177i	−1.26800	+	0.411997i
$107$	5.01911	+	9.85055i	0.485215	+	0.952289i	0.995721	+	0.0924142i	$0.0294584\pi$
$107$	5.01911	+	9.85055i	0.485215	+	0.952289i	−0.510505	+	0.859875i	$0.670542\pi$
$108$	1.31194	−	0.207790i	0.126241	−	0.0199946i
$109$	9.54212			0.913969			0.456985	−	0.889475i	$-0.348929\pi$
$109$	9.54212			0.913969			0.456985	+	0.889475i	$0.348929\pi$
$110$		0			0
$111$	−4.30929			−0.409019
$112$	0.855686	−	0.135527i	0.0808547	−	0.0128061i
$113$	1.88301	+	3.69562i	0.177139	+	0.347654i	0.962455	−	0.271440i	$-0.0874999\pi$
$113$	1.88301	+	3.69562i	0.177139	+	0.347654i	−0.785317	+	0.619094i	$0.787500\pi$
$114$	0.857235	−	0.278533i	0.0802874	−	0.0260870i
$115$		0			0
$116$	1.74294	+	2.39895i	0.161828	+	0.222737i
$117$	6.52158	+	3.32291i	0.602920	+	0.307203i
$118$	13.0374	−	6.64291i	1.20019	−	0.611529i
$119$	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
$123$	0.835077	+	5.27247i	0.0752964	+	0.475403i
$124$	−0.103658	−	0.0336805i	−0.00930877	−	0.00302460i
$125$		0			0
$126$	0.556736	−	0.404492i	0.0495980	−	0.0360350i
$127$	2.27881	−	14.3879i	0.202212	−	1.27672i	−0.652570	−	0.757728i	$-0.726309\pi$
$127$	2.27881	−	14.3879i	0.202212	−	1.27672i	0.854782	−	0.518987i	$-0.173691\pi$
$128$	−5.99935	+	11.7744i	−0.530273	+	1.04072i
$129$	1.29851	−	3.99642i	0.114328	−	0.351865i
$130$		0			0
$131$		−	9.76926i		−	0.853544i	−0.904359	−	0.426772i	$-0.859651\pi$
$131$		−	9.76926i		−	0.853544i	0.904359	−	0.426772i	$-0.140349\pi$
$132$	−0.179202	+	0.801441i	−0.0155975	+	0.0697565i
$133$	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
$137$	−4.27681	−	0.677380i	−0.365392	−	0.0578725i	−0.0289612	−	0.999581i	$-0.509220\pi$
$137$	−4.27681	−	0.677380i	−0.365392	−	0.0578725i	−0.336431	+	0.941708i	$0.609220\pi$
$138$	−1.94466	−	0.308004i	−0.165540	−	0.0262190i
$139$	3.24794	+	9.99613i	0.275487	+	0.847860i	0.989090	+	0.147311i	$0.0470618\pi$
$139$	3.24794	+	9.99613i	0.275487	+	0.847860i	−0.713604	+	0.700550i	$0.752938\pi$
$140$		0			0
$141$	7.97445	+	5.79378i	0.671570	+	0.487924i
$142$	−12.3196	+	12.3196i	−1.03384	+	1.03384i
$143$	−7.70183	+	6.78912i	−0.644059	+	0.567735i
$144$			10.6984i			0.891532i
$145$		0			0
$146$	1.12822	−	3.47229i	0.0933719	−	0.287369i
$147$	2.52026	−	4.94629i	0.207868	−	0.407963i
$148$	−0.262630	+	1.65818i	−0.0215881	+	0.136302i
$149$	4.66189	−	3.38706i	0.381917	−	0.277479i	−0.380218	−	0.924897i	$-0.624151\pi$
$149$	4.66189	−	3.38706i	0.381917	−	0.277479i	0.762135	+	0.647418i	$0.224151\pi$
$150$		0			0
$151$	−14.2318	−	4.62419i	−1.15817	−	0.376311i	−0.333953	−	0.942590i	$-0.608383\pi$
$151$	−14.2318	−	4.62419i	−1.15817	−	0.376311i	−0.824214	+	0.566278i	$0.808383\pi$
$152$	0.298800	+	1.88655i	0.0242358	+	0.153019i
$153$	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
$157$	−4.40881	+	2.24640i	−0.351861	+	0.179282i	−0.620983	−	0.783824i	$-0.713267\pi$
$157$	−4.40881	+	2.24640i	−0.351861	+	0.179282i	0.269122	+	0.963106i	$0.413267\pi$
$158$	0.908095	+	0.462698i	0.0722442	+	0.0368103i
$159$	4.23158	+	5.82427i	0.335586	+	0.461895i
$160$		0			0
$161$	−0.295863	+	0.0961317i	−0.0233173	+	0.00757624i
$162$	2.54219	+	4.98933i	0.199733	+	0.391999i
$163$	9.89335	−	1.56695i	0.774907	−	0.122733i	0.243558	−	0.969886i	$-0.421685\pi$
$163$	9.89335	−	1.56695i	0.774907	−	0.122733i	0.531349	+	0.847153i	$0.321685\pi$
$164$	2.07970			0.162398
$165$		0			0
$166$	25.3592			1.96826
$167$	−11.9137	+	1.88695i	−0.921913	+	0.146017i	−0.599310	−	0.800517i	$-0.704558\pi$
$167$	−11.9137	+	1.88695i	−0.921913	+	0.146017i	−0.322604	+	0.946534i	$0.604558\pi$
$168$	−0.177962	−	0.349270i	−0.0137301	−	0.0269468i
$169$	3.24999	−	1.05599i	0.250000	−	0.0812298i
$170$		0			0
$171$	1.03371	+	1.42277i	0.0790494	+	0.108802i
$172$	−1.45866	−	0.743222i	−0.111221	−	0.0566702i
$173$	11.1065	−	5.65903i	0.844410	−	0.430248i	0.0224186	−	0.999749i	$-0.492863\pi$
$173$	11.1065	−	5.65903i	0.844410	−	0.430248i	0.821991	+	0.569501i	$0.192863\pi$
$174$	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
$178$	1.88375	+	11.8935i	0.141193	+	0.891458i
$179$	−19.1909	−	6.23551i	−1.43440	−	0.466064i	−0.514252	−	0.857639i	$-0.671930\pi$
$179$	−19.1909	−	6.23551i	−1.43440	−	0.466064i	−0.920146	+	0.391575i	$0.871930\pi$
$180$		0			0
$181$	−3.72935	+	2.70953i	−0.277200	+	0.201398i	−0.717695	−	0.696357i	$-0.754803\pi$
$181$	−3.72935	+	2.70953i	−0.277200	+	0.201398i	0.440495	+	0.897755i	$0.354803\pi$
$182$	−0.140943	+	0.889877i	−0.0104474	+	0.0659620i
$183$	2.13288	−	4.18601i	0.157667	−	0.309439i
$184$	1.28932	−	3.96811i	0.0950497	−	0.292533i
$185$		0			0
$186$			0.425256i			0.0311813i
$187$	−11.2824	+	4.88140i	−0.825051	+	0.356963i
$188$	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	0.996538	−	0.0831389i	$-0.0264945\pi$
$191$	1.95493	+	6.01667i	0.141454	+	0.435351i	−0.855084	+	0.518490i	$0.826495\pi$
$192$	5.04079	+	0.798383i	0.363788	+	0.0576183i
$193$	−5.85885	−	0.927951i	−0.421729	−	0.0667954i	−0.0580368	−	0.998314i	$-0.518484\pi$
$193$	−5.85885	−	0.927951i	−0.421729	−	0.0667954i	−0.363692	+	0.931519i	$0.618484\pi$
$194$	−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	−0.259918	−	0.965631i	$-0.583696\pi$
$197$	9.90515	−	9.90515i	0.705713	−	0.705713i	0.965631	+	0.259918i	$0.0836955\pi$
$198$	−11.8674	+	1.12097i	−0.843380	+	0.0796637i
$199$		−	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
$202$	3.33001	−	6.53551i	0.234299	−	0.459837i
$203$	0.285964	−	1.80551i	0.0200708	−	0.126722i
$204$	−0.742493	+	0.539453i	−0.0519849	+	0.0377693i
$205$		0			0
$206$	4.68010	+	1.52066i	0.326078	+	0.105949i
$207$	−0.600953	−	3.79427i	−0.0417691	−	0.263720i
$208$	−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	−0.671944	−	0.740602i	$-0.734540\pi$
$211$	3.48696	−	4.79939i	0.240052	−	0.330404i	0.911996	+	0.410198i	$0.134540\pi$
$212$	2.49903	−	1.27332i	0.171634	−	0.0874521i
$213$	8.14163	+	4.14837i	0.557855	+	0.284241i
$214$	−9.87779	−	13.5956i	−0.675232	−	0.929377i
$215$		0			0
$216$	10.4450	−	3.39378i	0.710691	−	0.230917i
$217$	0.0305041	+	0.0598677i	0.00207075	+	0.00406408i
$218$	−14.3260	+	2.26902i	−0.970282	+	0.153678i
$219$	−1.91483			−0.129392
$220$		0			0
$221$	−11.4739			−0.771818
$222$	6.46974	−	1.02471i	0.434220	−	0.0687738i
$223$	−9.64984	−	18.9389i	−0.646201	−	1.26824i	−0.949027	−	0.315195i	$-0.897930\pi$
$223$	−9.64984	−	18.9389i	−0.646201	−	1.26824i	0.302826	−	0.953046i	$-0.402070\pi$
$224$	−0.317188	+	0.103060i	−0.0211930	+	0.00688602i
$225$		0			0
$226$	−3.70584	−	5.10065i	−0.246509	−	0.339290i
$227$	−11.6456	−	5.93372i	−0.772944	−	0.393835i	0.0225888	−	0.999745i	$-0.492809\pi$
$227$	−11.6456	−	5.93372i	−0.772944	−	0.393835i	−0.795533	+	0.605910i	$0.792809\pi$
$228$	−0.164097	+	0.0836117i	−0.0108676	+	0.00553732i
$229$	−9.65796	+	13.2930i	−0.638216	+	0.878429i	−0.998519	−	0.0544066i	$-0.982673\pi$
$229$	−9.65796	+	13.2930i	−0.638216	+	0.878429i	0.360303	+	0.932835i	$0.382673\pi$
$230$		0			0
$231$	0.427475	−	0.271242i	0.0281258	−	0.0178464i
$232$	17.3363	+	17.3363i	1.13819	+	1.13819i
$233$	−2.44720	−	15.4510i	−0.160321	−	1.01223i	−0.928321	−	0.371779i	$-0.878748\pi$
$233$	−2.44720	−	15.4510i	−0.160321	−	1.01223i	0.768000	−	0.640450i	$-0.221252\pi$
$234$	−10.5813	−	3.43808i	−0.691722	−	0.224754i
$235$		0			0
$236$	−2.41878	+	1.75734i	−0.157449	+	0.114393i
$237$	0.0836185	−	0.527947i	0.00543161	−	0.0342938i
$238$	−0.489753	+	0.961194i	−0.0317460	+	0.0623050i
$239$	1.63214	−	5.02322i	0.105575	−	0.324925i	−0.884290	−	0.466938i	$-0.845357\pi$
$239$	1.63214	−	5.02322i	0.105575	−	0.324925i	0.989865	+	0.142012i	$0.0453572\pi$
$240$		0			0
$241$			16.1676i			1.04144i	0.853726	+	0.520722i	$0.174337\pi$
$241$			16.1676i			1.04144i	−0.853726	+	0.520722i	$0.825663\pi$
$242$	4.66716	−	16.0561i	0.300016	−	1.03213i
$243$	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
$247$	−2.27413	−	0.360188i	−0.144700	−	0.0229182i
$248$	−0.890071	−	0.140973i	−0.0565196	−	0.00895182i
$249$	−4.10997	−	12.6492i	−0.260458	−	0.801609i
$250$		0			0
$251$	−15.6486	−	11.3694i	−0.987729	−	0.717627i	−0.0283063	−	0.999599i	$-0.509011\pi$
$251$	−15.6486	−	11.3694i	−0.987729	−	0.717627i	−0.959423	+	0.281972i	$0.909011\pi$
$252$	−0.0994268	+	0.0994268i	−0.00626330	+	0.00626330i
$253$	5.25876	+	1.17586i	0.330615	+	0.0739254i
$254$			22.1431i			1.38938i
$255$		0			0
$256$	2.25079	−	6.92722i	0.140674	−	0.432951i
$257$	−2.13653	+	4.19318i	−0.133273	+	0.261563i	−0.947993	−	0.318292i	$-0.896891\pi$
$257$	−2.13653	+	4.19318i	−0.133273	+	0.261563i	0.814720	+	0.579855i	$0.196891\pi$
$258$	−0.999214	+	6.30879i	−0.0622083	+	0.392768i
$259$	0.837308	−	0.608340i	0.0520278	−	0.0378004i
$260$		0			0
$261$	21.4689	+	6.97566i	1.32889	+	0.431783i
$262$	2.32303	+	14.6671i	0.143517	+	0.906134i
$263$	11.2218	+	11.2218i	0.691964	+	0.691964i	0.962664	−	0.270700i	$-0.0872550\pi$
$263$	11.2218	+	11.2218i	0.691964	+	0.691964i	−0.270700	+	0.962664i	$0.587255\pi$
$264$	−0.426823	+	6.77663i	−0.0262691	+	0.417073i
$265$		0			0
$266$	−0.127243	+	0.175135i	−0.00780178	+	0.0107382i
$267$	5.62719	−	2.86720i	0.344378	−	0.175470i
$268$	−1.61801	−	0.824419i	−0.0988359	−	0.0503594i
$269$	6.64926	+	9.15192i	0.405412	+	0.558002i	0.962092	−	0.272725i	$-0.0879249\pi$
$269$	6.64926	+	9.15192i	0.405412	+	0.558002i	−0.556680	+	0.830727i	$0.687925\pi$
$270$		0			0
$271$	16.9556	−	5.50921i	1.02998	−	0.334661i	0.255198	−	0.966889i	$-0.417859\pi$
$271$	16.9556	−	5.50921i	1.02998	−	0.334661i	0.774782	+	0.632228i	$0.217859\pi$
$272$	−7.61384	−	14.9430i	−0.461657	−	0.906052i
$273$	0.466712	−	0.0739200i	0.0282467	−	0.00447384i
$274$	6.58205			0.397636
$275$		0			0
$276$	0.402300			0.0242156
$277$	4.62395	−	0.732361i	0.277826	−	0.0440033i	−0.0159666	−	0.999873i	$-0.505083\pi$
$277$	4.62395	−	0.732361i	0.277826	−	0.0440033i	0.293793	+	0.955869i	$0.405083\pi$
$278$	−7.25327	−	14.2353i	−0.435022	−	0.853779i
$279$	−0.789117	+	0.256400i	−0.0472432	+	0.0153502i
$280$		0			0
$281$	−7.75247	−	10.6704i	−0.462474	−	0.636541i	0.512546	−	0.858660i	$-0.328703\pi$
$281$	−7.75247	−	10.6704i	−0.462474	−	0.636541i	−0.975019	+	0.222119i	$0.928703\pi$
$282$	−13.3501	−	6.80223i	−0.794989	−	0.405067i
$283$	−20.3029	+	10.3449i	−1.20688	+	0.614938i	−0.937463	−	0.348084i	$-0.886832\pi$
$283$	−20.3029	+	10.3449i	−1.20688	+	0.614938i	−0.269421	+	0.963022i	$0.586832\pi$
$284$	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
$288$	−0.644267	−	4.06774i	−0.0379638	−	0.239694i
$289$	3.10211	+	1.00794i	0.182477	+	0.0592904i
$290$		0			0
$291$	−0.889404	+	0.646190i	−0.0521378	+	0.0378803i
$292$	−0.116700	+	0.736812i	−0.00682933	+	0.0431187i
$293$	3.28132	−	6.43996i	0.191697	−	0.376226i	−0.775074	−	0.631870i	$-0.782287\pi$
$293$	3.28132	−	6.43996i	0.191697	−	0.376226i	0.966771	+	0.255644i	$0.0822875\pi$
$294$	−2.60761	+	8.02539i	−0.152079	+	0.468051i
$295$		0			0
$296$			13.8810i			0.806817i
$297$	5.63227	+	13.0179i	0.326818	+	0.755375i
$298$	−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
$302$	22.4665	+	3.55834i	1.29280	+	0.204759i
$303$	−3.79960	−	0.601798i	−0.218282	−	0.0345724i
$304$	−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	$-0.448232\pi$
$307$	20.1272	−	20.1272i	1.14872	−	1.14872i	0.986804	−	0.161918i	$-0.0517681\pi$
$308$	−0.0783196	−	0.181020i	−0.00446267	−	0.0103146i
$309$		−	2.58088i		−	0.146821i
$310$		0			0
$311$	−2.32254	+	7.14803i	−0.131699	+	0.405328i	−0.995062	−	0.0992557i	$-0.968354\pi$
$311$	−2.32254	+	7.14803i	−0.131699	+	0.405328i	0.863363	+	0.504583i	$0.168354\pi$
$312$	−2.87720	+	5.64681i	−0.162889	+	0.319688i
$313$	0.210574	−	1.32951i	0.0119023	−	0.0751483i	−0.981022	−	0.193895i	$-0.937888\pi$
$313$	0.210574	−	1.32951i	0.0119023	−	0.0751483i	0.992925	+	0.118747i	$0.0378878\pi$
$314$	6.08499	−	4.42100i	0.343396	−	0.249492i
$315$		0			0
$316$	−0.198054	−	0.0643517i	−0.0111414	−	0.00362006i
$317$	1.77271	+	11.1924i	0.0995652	+	0.628630i	0.986124	+	0.166013i	$0.0530894\pi$
$317$	1.77271	+	11.1924i	0.0995652	+	0.628630i	−0.886558	+	0.462617i	$0.846911\pi$
$318$	−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
$322$	0.421334	−	0.214680i	0.0234800	−	0.0119637i
$323$	−2.45639	−	1.25159i	−0.136677	−	0.0696406i
$324$	−0.672523	−	0.925648i	−0.0373624	−	0.0514249i
$325$		0			0
$326$	−14.4808	+	4.70509i	−0.802015	+	0.260591i
$327$	3.45360	+	6.77808i	0.190985	+	0.374829i
$328$	16.9836	−	2.68994i	0.937762	−	0.148527i
$329$	−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	$0.661753\pi$
$332$	−5.11780	+	0.810579i	−0.280876	+	0.0444863i
$333$	5.80227	+	11.3876i	0.317962	+	0.624036i
$334$	17.4380	−	5.66594i	0.954164	−	0.310027i
$335$		0			0
$336$	0.405970	+	0.558770i	0.0221475	+	0.0304834i
$337$	−6.78954	−	3.45945i	−0.369850	−	0.188448i	0.259180	−	0.965829i	$-0.416548\pi$
$337$	−6.78954	−	3.45945i	−0.369850	−	0.188448i	−0.629030	+	0.777381i	$0.716548\pi$
$338$	−4.62827	+	2.35822i	−0.251745	+	0.128270i
$339$	−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
$343$	0.418239	+	2.64066i	0.0225828	+	0.142582i
$344$	−12.8732	−	4.18275i	−0.694076	−	0.225519i
$345$		0			0
$346$	−15.3290	+	11.1372i	−0.824093	+	0.598739i
$347$	−1.46011	+	9.21879i	−0.0783830	+	0.494891i	0.916998	+	0.398891i	$0.130605\pi$
$347$	−1.46011	+	9.21879i	−0.0783830	+	0.494891i	−0.995381	+	0.0959998i	$0.969395\pi$
$348$	−1.07323	+	2.10633i	−0.0575311	+	0.112911i
$349$	−0.464073	+	1.42827i	−0.0248413	+	0.0764536i	−0.962709	−	0.270540i	$-0.912798\pi$
$349$	−0.464073	+	1.42827i	−0.0248413	+	0.0764536i	0.937867	+	0.346994i	$0.112798\pi$
$350$		0			0
$351$			13.2388i			0.706637i
$352$	5.63779	+	1.26061i	0.300495	+	0.0671906i
$353$	−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
$357$	0.558817	+	0.0885080i	0.0295757	+	0.00468434i
$358$	30.2950	+	4.79826i	1.60114	+	0.253596i
$359$	−8.12845	−	25.0168i	−0.429003	−	1.32034i	−0.899108	−	0.437726i	$-0.855784\pi$
$359$	−8.12845	−	25.0168i	−0.429003	−	1.32034i	0.470105	−	0.882611i	$-0.344216\pi$
$360$		0			0
$361$	14.9238	+	10.8427i	0.785461	+	0.570671i
$362$	4.95475	−	4.95475i	0.260416	−	0.260416i
$363$	−8.76519	+	0.274237i	−0.460053	+	0.0143937i
$364$		−	0.184093i		−	0.00964908i
$365$		0			0
$366$	−2.20680	+	6.79184i	−0.115351	+	0.355015i
$367$	3.70869	−	7.27872i	0.193592	−	0.379946i	−0.773723	−	0.633524i	$-0.781608\pi$
$367$	3.70869	−	7.27872i	0.193592	−	0.379946i	0.967315	+	0.253579i	$0.0816076\pi$
$368$	−1.15002	+	7.26093i	−0.0599488	+	0.378502i
$369$	12.8085	−	9.30591i	0.666783	−	0.484446i
$370$		0			0
$371$	−1.64442	−	0.534304i	−0.0853740	−	0.0277397i
$372$	−0.0135928	−	0.0858218i	−0.000704756	−	0.00444965i
$373$	6.12473	+	6.12473i	0.317126	+	0.317126i	0.847662	−	0.530536i	$-0.178009\pi$
$373$	6.12473	+	6.12473i	0.317126	+	0.317126i	−0.530536	+	0.847662i	$0.678009\pi$
$374$	15.7781	−	10.0115i	0.815864	−	0.517684i
$375$		0			0
$376$	18.6628	−	25.6872i	0.962461	−	1.32471i
$377$	−26.3331	+	13.4174i	−1.35622	+	0.691031i
$378$	1.10905	+	0.565088i	0.0570433	+	0.0290650i
$379$	0.363481	+	0.500288i	0.0186708	+	0.0256981i	0.818250	−	0.574862i	$-0.194944\pi$
$379$	0.363481	+	0.500288i	0.0186708	+	0.0256981i	−0.799580	+	0.600560i	$0.794944\pi$
$380$		0			0
$381$	11.0449	−	3.58872i	0.565849	−	0.183856i
$382$	−4.36574	−	8.56825i	−0.223371	−	0.438390i
$383$	−10.2511	+	1.62362i	−0.523807	+	0.0829629i	−0.412738	−	0.910850i	$-0.635428\pi$
$383$	−10.2511	+	1.62362i	−0.523807	+	0.0829629i	−0.111069	+	0.993813i	$0.535428\pi$
$384$	−10.5351			−0.537617
$385$		0			0
$386$	9.01683			0.458945
$387$	−12.3092	+	1.94959i	−0.625712	+	0.0991031i
$388$	0.194444	+	0.381619i	0.00987142	+	0.0193737i
$389$	21.0630	−	6.84378i	1.06794	−	0.346993i	0.278252	−	0.960508i	$-0.410245\pi$
$389$	21.0630	−	6.84378i	1.06794	−	0.346993i	0.789683	+	0.613515i	$0.210245\pi$
$390$		0			0
$391$	3.53969	+	4.87197i	0.179010	+	0.246386i
$392$	−15.9329	−	8.11822i	−0.804733	−	0.410032i
$393$	6.93942	−	3.53581i	0.350048	−	0.178358i
$394$	−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	$0.874922\pi$
$398$	3.18229	+	20.0922i	0.159514	+	1.00713i
$399$	0.107980	+	0.0350847i	0.00540574	+	0.00175643i
$400$		0			0
$401$	3.46399	−	2.51673i	0.172983	−	0.125680i	−0.497925	−	0.867220i	$-0.665904\pi$
$401$	3.46399	−	2.51673i	0.172983	−	0.125680i	0.670908	+	0.741540i	$0.265904\pi$
$402$	−1.10838	+	6.99803i	−0.0552809	+	0.349030i
$403$	0.493174	−	0.967909i	0.0245668	−	0.0482150i
$404$	−0.463135	+	1.42538i	−0.0230418	+	0.0709155i
$405$		0			0
$406$			2.77869i			0.137904i
$407$	−17.8481	+	1.68589i	−0.884697	+	0.0835664i
$408$	−5.36572	+	5.36572i	−0.265643	+	0.265643i
$409$	−3.47523	−	2.52490i	−0.171839	−	0.124848i	0.498541	−	0.866866i	$-0.333869\pi$
$409$	−3.47523	−	2.52490i	−0.171839	−	0.124848i	−0.670381	+	0.742017i	$0.733869\pi$
$410$		0			0
$411$	−1.06675	−	3.28312i	−0.0526190	−	0.161945i
$412$	−0.993106	−	0.157293i	−0.0489268	−	0.00774925i
$413$	1.82043	+	0.288327i	0.0895773	+	0.0141877i
$414$	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
$418$	3.44151	−	1.48899i	0.168330	−	0.0728288i
$419$			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	−0.379057	−	0.925373i	$-0.623752\pi$
$421$	9.67493	−	29.7764i	0.471527	−	1.45121i	0.850584	−	0.525839i	$-0.176248\pi$
$422$	−4.09390	+	8.03473i	−0.199288	+	0.391124i
$423$	4.57321	−	28.8741i	0.222357	−	1.40391i
$424$	18.7610	−	13.6307i	0.911117	−	0.661965i
$425$		0			0
$426$	−13.2099	−	4.29214i	−0.640020	−	0.207955i
$427$	0.176512	+	1.11445i	0.00854201	+	0.0539321i
$428$	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	−0.925750	−	0.378137i	$-0.876565\pi$
$431$	−5.81395	+	8.00222i	−0.280048	+	0.385453i	0.645702	+	0.763590i	$0.276565\pi$
$432$	−17.2416	+	8.78502i	−0.829536	+	0.422669i
$433$	24.0414	+	12.2497i	1.15536	+	0.588683i	0.923323	−	0.384025i	$-0.125462\pi$
$433$	24.0414	+	12.2497i	1.15536	+	0.588683i	0.232033	+	0.972708i	$0.425462\pi$
$434$	−0.0600332	−	0.0826286i	−0.00288169	−	0.00396630i
$435$		0			0
$436$	2.81864	−	0.915831i	0.134988	−	0.0438604i
$437$	0.548629	+	1.07675i	0.0262445	+	0.0515077i
$438$	2.87482	−	0.455327i	0.137364	−	0.0217564i
$439$	24.5862			1.17344			0.586718	−	0.809791i	$-0.300420\pi$
$439$	24.5862			1.17344			0.586718	+	0.809791i	$0.300420\pi$
$440$		0			0
$441$	−16.4643			−0.784016
$442$	17.2263	−	2.72838i	0.819372	−	0.129776i
$443$	13.9816	+	27.4404i	0.664286	+	1.30373i	0.939565	+	0.342370i	$0.111230\pi$
$443$	13.9816	+	27.4404i	0.664286	+	1.30373i	−0.275279	+	0.961364i	$0.588770\pi$
$444$	−1.27292	+	0.413596i	−0.0604099	+	0.0196284i
$445$		0			0
$446$	18.9912	+	26.1392i	0.899262	+	1.23773i
$447$	4.09323	+	2.08561i	0.193603	+	0.0986458i
$448$	−1.09215	+	0.556477i	−0.0515992	+	0.0262911i
$449$	4.30536	−	5.92582i	0.203182	−	0.279657i	−0.695250	−	0.718768i	$-0.744707\pi$
$449$	4.30536	−	5.92582i	0.203182	−	0.279657i	0.898433	+	0.439111i	$0.144707\pi$
$450$		0			0
$451$	5.52141	+	21.5107i	0.259993	+	1.01290i
$452$	0.910918	+	0.910918i	0.0428460	+	0.0428460i
$453$	−1.86624	−	11.7830i	−0.0876835	−	0.553612i
$454$	18.8951	+	6.13938i	0.886789	+	0.288135i
$455$		0			0
$456$	−1.23193	+	0.895050i	−0.0576904	+	0.0419146i
$457$	−1.05368	+	6.65265i	−0.0492889	+	0.311198i	0.950710	+	0.310080i	$0.100356\pi$
$457$	−1.05368	+	6.65265i	−0.0492889	+	0.311198i	−0.999999	+	0.00111791i	$0.999644\pi$
$458$	11.3390	−	22.2540i	0.529837	−	1.03986i
$459$	−4.89838	+	15.0757i	−0.228637	+	0.703672i
$460$		0			0
$461$		−	29.0801i		−	1.35440i	−0.735801	−	0.677198i	$-0.763194\pi$
$461$		−	29.0801i		−	1.35440i	0.735801	−	0.677198i	$-0.236806\pi$
$462$	−0.577290	+	0.508879i	−0.0268580	+	0.0236752i
$463$	−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
$467$	26.1320	+	4.13890i	1.20924	+	0.191525i	0.728320	−	0.685237i	$-0.240302\pi$
$467$	26.1320	+	4.13890i	1.20924	+	0.191525i	0.480923	+	0.876763i	$0.340302\pi$
$468$	2.24533	+	0.355625i	0.103790	+	0.0164388i
$469$	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
$473$	3.81467	−	17.0603i	0.175399	−	0.784432i
$474$			0.812515i			0.0373201i
$475$		0			0
$476$	0.0681145	−	0.209635i	0.00312202	−	0.00960860i
$477$	9.69341	−	19.0244i	0.443831	−	0.871067i
$478$	−1.25594	+	7.92972i	−0.0574455	+	0.362697i
$479$	−21.2408	+	15.4324i	−0.970519	+	0.705123i	−0.955570	−	0.294765i	$-0.904759\pi$
$479$	−21.2408	+	15.4324i	−0.970519	+	0.705123i	−0.0149492	+	0.999888i	$0.504759\pi$
$480$		0			0
$481$	−15.9139	−	5.17073i	−0.725610	−	0.235765i
$482$	−3.84449	−	24.2731i	−0.175112	−	1.10561i
$483$	−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
$487$	20.7917	−	10.5939i	0.942163	−	0.480056i	0.0857326	−	0.996318i	$-0.472677\pi$
$487$	20.7917	−	10.5939i	0.942163	−	0.480056i	0.856431	+	0.516262i	$0.172677\pi$
$488$	−13.4839	−	6.87039i	−0.610388	−	0.311008i
$489$	4.69379	+	6.46044i	0.212260	+	0.292151i
$490$		0			0
$491$	17.4497	−	5.66974i	0.787493	−	0.255872i	0.112457	−	0.993657i	$-0.464128\pi$
$491$	17.4497	−	5.66974i	0.787493	−	0.255872i	0.675036	+	0.737785i	$0.264128\pi$
$492$	0.752713	+	1.47728i	0.0339349	+	0.0666010i
$493$	−34.9512	+	5.53572i	−1.57412	+	0.249316i
$494$	3.49992			0.157469
$495$		0			0
$496$	1.58781			0.0712949
$497$	−2.16757	+	0.343309i	−0.0972286	+	0.0153995i
$498$	9.17834	+	18.0135i	0.411291	+	0.807204i
$499$	−11.1824	+	3.63339i	−0.500595	+	0.162653i	−0.548421	−	0.836203i	$-0.684771\pi$
$499$	−11.1824	+	3.63339i	−0.500595	+	0.162653i	0.0478260	+	0.998856i	$0.484771\pi$
$500$		0			0
$501$	−5.65234	−	7.77978i	−0.252528	−	0.347575i
$502$	26.1975	+	13.3483i	1.16925	+	0.595763i
$503$	4.75855	−	2.42460i	0.212173	−	0.108108i	−0.344674	−	0.938722i	$-0.612011\pi$
$503$	4.75855	−	2.42460i	0.212173	−	0.108108i	0.556848	+	0.830615i	$0.312011\pi$
$504$	−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
$508$	−0.707777	−	4.46873i	−0.0314025	−	0.198268i
$509$	18.6283	+	6.05272i	0.825687	+	0.268282i	0.691228	−	0.722637i	$-0.257070\pi$
$509$	18.6283	+	6.05272i	0.825687	+	0.268282i	0.134459	+	0.990919i	$0.457070\pi$
$510$		0			0
$511$	0.372057	−	0.270315i	0.0164588	−	0.0119580i
$512$	2.40248	−	15.1686i	0.106175	−	0.670365i
$513$	−1.44412	+	2.83424i	−0.0637594	+	0.125135i
$514$	2.21058	−	6.80347i	0.0975046	−	0.300088i
$515$		0			0
$516$		−	1.30513i		−	0.0574550i
$517$	35.2950	+	20.8767i	1.55227	+	0.918158i
$518$	−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	0.994097	+	0.108493i	$0.0346026\pi$
$521$	5.78913	+	17.8171i	0.253626	+	0.780582i	−0.740471	+	0.672089i	$0.765397\pi$
$522$	−33.8910	−	5.36781i	−1.48337	−	0.234943i
$523$	2.55051	+	0.403961i	0.111526	+	0.0176640i	0.211948	−	0.977281i	$-0.432019\pi$
$523$	2.55051	+	0.403961i	0.111526	+	0.0176640i	−0.100422	+	0.994945i	$0.532019\pi$
$524$	−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
$528$	−1.12506	−	11.9108i	−0.0489621	−	0.518350i
$529$			20.3603i			0.885228i
$530$		0			0
$531$	−7.03330	+	21.6463i	−0.305219	+	0.939368i
$532$	0.0200812	−	0.0394115i	0.000870630	−	0.00170871i
$533$	−3.24258	+	20.4729i	−0.140452	+	0.886778i
$534$	−7.76658	+	5.64275i	−0.336093	+	0.244186i
$535$		0			0
$536$	−14.2796	−	4.63972i	−0.616784	−	0.200405i
$537$	−2.51654	−	15.8888i	−0.108597	−	0.685652i
$538$	−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	−0.676224	−	0.736696i	$-0.736385\pi$
$541$	5.42829	−	7.47139i	0.233380	−	0.321220i	0.909604	+	0.415476i	$0.136385\pi$
$542$	−24.1462	+	12.3031i	−1.03717	+	0.528464i
$543$	−3.27444	−	1.66841i	−0.140520	−	0.0715983i
$544$	3.79482	+	5.22312i	0.162701	+	0.223939i
$545$		0			0
$546$	−0.683120	+	0.221959i	−0.0292348	+	0.00949898i
$547$	−0.486237	−	0.954295i	−0.0207900	−	0.0408027i	0.880378	−	0.474273i	$-0.157289\pi$
$547$	−0.486237	−	0.954295i	−0.0207900	−	0.0408027i	−0.901168	+	0.433470i	$0.857289\pi$
$548$	−1.32834	+	0.210388i	−0.0567437	+	0.00898732i
$549$	−13.9337			−0.594674
$550$		0			0
$551$	−7.10113			−0.302518
$552$	3.28533	−	0.520344i	0.139833	−	0.0221473i
$553$	0.0582826	+	0.114386i	0.00247843	+	0.00486419i
$554$	−6.76800	+	2.19906i	−0.287545	+	0.0934290i
$555$		0			0
$556$	1.91881	+	2.64102i	0.0813758	+	0.112004i
$557$	38.3462	+	19.5384i	1.62478	+	0.827868i	0.998848	+	0.0479915i	$0.0152820\pi$
$557$	38.3462	+	19.5384i	1.62478	+	0.827868i	0.625934	+	0.779876i	$0.284718\pi$
$558$	1.12377	−	0.572590i	0.0475730	−	0.0242396i
$559$	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
$563$	−4.04575	−	25.5439i	−0.170508	−	1.07655i	−0.913379	−	0.407111i	$-0.866536\pi$
$563$	−4.04575	−	25.5439i	−0.170508	−	1.07655i	0.742871	−	0.669435i	$-0.233464\pi$
$564$	2.91164	+	0.946049i	0.122602	+	0.0398359i
$565$		0			0
$566$	28.0219	−	20.3591i	1.17785	−	0.855756i
$567$	−0.110341	+	0.696664i	−0.00463387	+	0.0292571i
$568$	13.3626	−	26.2257i	0.560684	−	1.10040i
$569$	−8.39651	+	25.8418i	−0.352000	+	1.08334i	0.605729	+	0.795671i	$0.292882\pi$
$569$	−8.39651	+	25.8418i	−0.352000	+	1.08334i	−0.957729	+	0.287673i	$0.907118\pi$
$570$		0			0
$571$		−	40.5475i		−	1.69686i	−0.529308	−	0.848430i	$-0.677549\pi$
$571$		−	40.5475i		−	1.69686i	0.529308	−	0.848430i	$-0.322451\pi$
$572$	−1.62343	+	2.74464i	−0.0678791	+	0.114759i
$573$	−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
$577$	−33.3917	−	5.28872i	−1.39011	−	0.220172i	−0.583914	−	0.811815i	$-0.698479\pi$
$577$	−33.3917	−	5.28872i	−1.39011	−	0.220172i	−0.806200	+	0.591643i	$0.798479\pi$
$578$	−4.89703	−	0.775613i	−0.203689	−	0.0322612i
$579$	−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
$583$	19.8048	+	22.4673i	0.820233	+	0.930502i
$584$			6.16801i			0.255234i
$585$		0			0
$586$	−3.39505	+	10.4489i	−0.140248	+	0.431640i
$587$	4.39649	−	8.62859i	0.181462	−	0.356140i	−0.782300	−	0.622902i	$-0.785954\pi$
$587$	4.39649	−	8.62859i	0.181462	−	0.356140i	0.963763	+	0.266762i	$0.0859536\pi$
$588$	0.269724	−	1.70297i	0.0111232	−	0.0702293i
$589$	0.211163	−	0.153419i	0.00870081	−	0.00632151i
$590$		0			0
$591$	10.6210	+	3.45096i	0.436888	+	0.141953i
$592$	−3.82603	−	24.1566i	−0.157249	−	0.992829i
$593$	−14.0452	−	14.0452i	−0.576769	−	0.576769i	0.357243	−	0.934012i	$-0.383717\pi$
$593$	−14.0452	−	14.0452i	−0.576769	−	0.576769i	−0.934012	+	0.357243i	$0.883717\pi$
$594$	−11.5515	−	18.2051i	−0.473965	−	0.746964i
$595$		0			0
$596$	1.05199	−	1.44794i	0.0430912	−	0.0593099i
$597$	9.50623	−	4.84367i	0.389064	−	0.198238i
$598$	−6.81191	−	3.47084i	−0.278560	−	0.141933i
$599$	−2.65433	−	3.65338i	−0.108453	−	0.149273i	0.751340	−	0.659915i	$-0.229408\pi$
$599$	−2.65433	−	3.65338i	−0.108453	−	0.149273i	−0.859793	+	0.510642i	$0.829408\pi$
$600$		0			0
$601$	−7.96746	+	2.58878i	−0.324999	+	0.105599i	−0.466973	−	0.884272i	$-0.654655\pi$
$601$	−7.96746	+	2.58878i	−0.324999	+	0.105599i	0.141973	+	0.989871i	$0.454655\pi$
$602$	−0.696458	−	1.36688i	−0.0283855	−	0.0557097i
$603$	−13.6540	+	2.16258i	−0.556034	+	0.0880671i
$604$	−4.64774			−0.189114
$605$		0			0
$606$	5.84763			0.237544
$607$	7.58425	−	1.20123i	0.307835	−	0.0487563i	−0.000605683	−	1.00000i	$-0.500193\pi$
$607$	7.58425	−	1.20123i	0.307835	−	0.0487563i	0.308441	+	0.951244i	$0.400193\pi$
$608$	0.588172	+	1.15435i	0.0238535	+	0.0468152i
$609$	1.38601	−	0.450342i	0.0561640	−	0.0182488i
$610$		0			0
$611$	22.4971	+	30.9646i	0.910134	+	1.25269i
$612$	2.42528	+	1.23574i	0.0980361	+	0.0499519i
$613$	−38.2477	+	19.4882i	−1.54481	+	0.787120i	−0.998719	−	0.0506058i	$-0.983885\pi$
$613$	−38.2477	+	19.4882i	−1.54481	+	0.787120i	−0.546091	+	0.837726i	$0.683885\pi$
$614$	−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	$-0.650933\pi$
$618$	0.613709	+	3.87481i	0.0246870	+	0.155868i
$619$	20.0674	+	6.52029i	0.806576	+	0.262073i	0.683147	−	0.730281i	$-0.260611\pi$
$619$	20.0674	+	6.52029i	0.806576	+	0.262073i	0.123429	+	0.992353i	$0.460611\pi$
$620$		0			0
$621$	5.62139	−	4.08418i	0.225578	−	0.163892i
$622$	1.78720	−	11.2840i	0.0716603	−	0.452445i
$623$	−0.688620	+	1.35149i	−0.0275890	+	0.0541464i
$624$	3.45064	−	10.6200i	0.138136	−	0.425139i
$625$		0			0
$626$			2.04613i			0.0817798i
$627$	−1.30047	−	1.47530i	−0.0519358	−	0.0589179i
$628$	−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	−0.960420	−	0.278555i	$-0.910144\pi$
$631$	−8.72043	−	26.8387i	−0.347155	−	1.06843i	0.613265	−	0.789877i	$-0.289856\pi$
$632$	−1.70061	−	0.269351i	−0.0676467	−	0.0107142i
$633$	4.67121	+	0.739847i	0.185664	+	0.0294063i
$634$	−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
$638$	24.5041	−	41.4275i	0.970125	−	1.64013i
$639$		−	27.1004i		−	1.07208i
$640$		0			0
$641$	−5.23436	+	16.1097i	−0.206745	+	0.636295i	0.792893	+	0.609362i	$0.208574\pi$
$641$	−5.23436	+	16.1097i	−0.206745	+	0.636295i	−0.999637	+	0.0269333i	$0.991426\pi$
$642$	6.08232	−	11.9372i	0.240050	−	0.471124i
$643$	−0.981726	+	6.19838i	−0.0387155	+	0.244440i	−0.999455	−	0.0330121i	$-0.989490\pi$
$643$	−0.981726	+	6.19838i	−0.0387155	+	0.244440i	0.960739	+	0.277452i	$0.0894900\pi$
$644$	−0.0781682	+	0.0567925i	−0.00308026	+	0.00223794i
$645$		0			0
$646$	3.98552	+	1.29497i	0.156808	+	0.0509500i
$647$	6.80289	+	42.9518i	0.267449	+	1.68861i	0.646247	+	0.763128i	$0.276338\pi$
$647$	6.80289	+	42.9518i	0.267449	+	1.68861i	−0.378798	+	0.925479i	$0.623662\pi$
$648$	−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
$652$	2.77200	−	1.41240i	0.108560	−	0.0553140i
$653$	−8.67042	−	4.41780i	−0.339300	−	0.172882i	0.276035	−	0.961147i	$-0.410979\pi$
$653$	−8.67042	−	4.41780i	−0.339300	−	0.172882i	−0.615335	+	0.788266i	$0.710979\pi$
$654$	−6.79682	−	9.35503i	−0.265777	−	0.365810i
$655$		0			0
$656$	−28.8145	+	9.36239i	−1.12502	+	0.365540i
$657$	2.57823	+	5.06007i	0.100586	+	0.197412i
$658$	3.55424	−	0.562936i	0.138559	−	0.0219455i
$659$	3.37375			0.131423			0.0657113	−	0.997839i	$-0.479068\pi$
$659$	3.37375			0.131423			0.0657113	+	0.997839i	$0.479068\pi$
$660$		0			0
$661$	9.93056			0.386254			0.193127	−	0.981174i	$-0.438137\pi$
$661$	9.93056			0.386254			0.193127	+	0.981174i	$0.438137\pi$
$662$	26.5811	−	4.21003i	1.03310	−	0.163628i
$663$	−4.15278	−	8.15028i	−0.161280	−	0.316531i
$664$	−40.7453	+	13.2389i	−1.58122	+	0.513771i
$665$		0			0
$666$	−11.4191	−	15.7170i	−0.442481	−	0.609022i
$667$	13.8210	+	7.04213i	0.535150	+	0.272672i
$668$	−3.33809	+	1.70084i	−0.129154	+	0.0658075i
$669$	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
$673$	−5.98412	−	37.7823i	−0.230671	−	1.45640i	−0.782609	−	0.622514i	$-0.786111\pi$
$673$	−5.98412	−	37.7823i	−0.230671	−	1.45640i	0.551938	−	0.833885i	$-0.313889\pi$
$674$	11.0161	+	3.57935i	0.424324	+	0.137871i
$675$		0			0
$676$	0.858662	−	0.623855i	0.0330255	−	0.0239944i
$677$	−5.03592	+	31.7956i	−0.193546	+	1.22200i	0.679246	+	0.733911i	$0.262307\pi$
$677$	−5.03592	+	31.7956i	−0.193546	+	1.22200i	−0.872792	+	0.488092i	$0.837693\pi$
$678$	2.28189	−	4.47847i	0.0876356	−	0.171994i
$679$	0.0815917	−	0.251113i	0.00313120	−	0.00963684i
$680$		0			0
$681$		−	10.4198i		−	0.399289i
$682$	0.166370	+	1.76132i	0.00637063	+	0.0674443i
$683$	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
$687$	−12.9380	−	2.04918i	−0.493616	−	0.0781811i
$688$	23.5556	+	3.73084i	0.898050	+	0.142237i
$689$	8.63834	+	26.5861i	0.329095	+	1.01285i
$690$		0			0
$691$	20.4397	+	14.8503i	0.777564	+	0.564933i	0.904247	−	0.427010i	$-0.140433\pi$
$691$	20.4397	+	14.8503i	0.777564	+	0.564933i	−0.126683	+	0.991943i	$0.540433\pi$
$692$	2.73759	−	2.73759i	0.104068	−	0.104068i
$693$	−1.29235	−	0.764417i	−0.0490925	−	0.0290378i
$694$		−	14.1878i		−	0.538562i
$695$		0			0
$696$	−6.03999	+	18.5892i	−0.228945	+	0.704621i
$697$	−11.2675	+	22.1136i	−0.426785	+	0.837613i
$698$	0.357107	−	2.25468i	0.0135167	−	0.0853410i
$699$	10.0896	−	7.33055i	0.381625	−	0.277267i
$700$		0			0
$701$	26.8458	+	8.72273i	1.01395	+	0.329453i	0.768427	−	0.639937i	$-0.221040\pi$
$701$	26.8458	+	8.72273i	1.01395	+	0.329453i	0.245525	+	0.969390i	$0.421040\pi$
$702$	−3.14807	−	19.8761i	−0.118816	−	0.750175i
$703$	−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
$707$	0.823230	−	0.419457i	0.0309608	−	0.0157753i
$708$	−2.12373	−	1.08210i	−0.0798148	−	0.0406677i
$709$	−4.79615	−	6.60134i	−0.180123	−	0.247918i	0.709402	−	0.704804i	$-0.248965\pi$
$709$	−4.79615	−	6.60134i	−0.180123	−	0.247918i	−0.889526	+	0.456885i	$0.848965\pi$
$710$		0			0
$711$	−1.50773	+	0.489890i	−0.0565441	+	0.0183723i
$712$	−9.23576	−	18.1262i	−0.346125	−	0.679308i
$713$	−0.563131	+	0.0891912i	−0.0210894	+	0.00334024i
$714$	−0.860026			−0.0321856
$715$		0			0
$716$	−6.26727			−0.234219
$717$	4.15889	−	0.658703i	0.155317	−	0.0245997i
$718$	18.1524	+	35.6261i	0.677441	+	1.32955i
$719$	−0.986856	+	0.320649i	−0.0368035	+	0.0119582i	−0.327361	−	0.944899i	$-0.606159\pi$
$719$	−0.986856	+	0.320649i	−0.0368035	+	0.0119582i	0.290557	+	0.956858i	$0.406159\pi$
$720$		0			0
$721$	0.364342	+	0.501474i	0.0135688	+	0.0186759i
$722$	−24.9840	−	12.7300i	−0.929810	−	0.473762i
$723$	−11.4843	+	5.85157i	−0.427107	+	0.217622i
$724$	−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	$0.722594\pi$
$728$	−0.238110	−	1.50337i	−0.00882493	−	0.0557184i
$729$	1.44390	+	0.469153i	0.0534779	+	0.0173760i
$730$		0			0
$731$	15.8055	−	11.4833i	0.584586	−	0.424726i
$732$	0.228265	−	1.44121i	0.00843693	−	0.0532687i
$733$	−20.7361	+	40.6968i	−0.765904	+	1.50317i	0.0956003	+	0.995420i	$0.469523\pi$
$733$	−20.7361	+	40.6968i	−0.765904	+	1.50317i	−0.861504	+	0.507751i	$0.830477\pi$
$734$	−3.83723	+	11.8098i	−0.141635	+	0.435907i
$735$		0			0
$736$		−	2.83001i		−	0.104315i
$737$	4.23142	−	18.9241i	0.155866	−	0.697079i
$738$	−17.0171	+	17.0171i	−0.626410	+	0.626410i
$739$	3.07164	+	2.23167i	0.112992	+	0.0820934i	0.642846	−	0.765995i	$-0.277753\pi$
$739$	3.07164	+	2.23167i	0.112992	+	0.0820934i	−0.529854	+	0.848089i	$0.677753\pi$
$740$		0			0
$741$	−0.567231	−	1.74576i	−0.0208377	−	0.0641320i
$742$	2.59590	+	0.411150i	0.0952984	+	0.0150938i
$743$	41.9067	+	6.63736i	1.53741	+	0.243501i	0.866930	−	0.498430i	$-0.166090\pi$
$743$	41.9067	+	6.63736i	1.53741	+	0.243501i	0.670476	+	0.741931i	$0.266090\pi$
$744$	−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
$748$	−2.86419	+	2.52477i	−0.104725	+	0.0923149i
$749$		−	2.11681i		−	0.0773467i
$750$		0			0
$751$	−3.08775	+	9.50312i	−0.112674	+	0.346774i	−0.991455	−	0.130451i	$-0.958357\pi$
$751$	−3.08775	+	9.50312i	−0.112674	+	0.346774i	0.878781	+	0.477225i	$0.158357\pi$
$752$	−25.3980	+	49.8464i	−0.926171	+	1.81771i
$753$	2.41230	−	15.2306i	0.0879089	−	0.555035i
$754$	36.3446	−	26.4059i	1.32359	−	0.961647i
$755$		0			0
$756$	−0.241881	−	0.0785920i	−0.00879714	−	0.00285837i
$757$	−4.59658	−	29.0217i	−0.167065	−	1.05481i	−0.918621	−	0.395140i	$-0.870696\pi$
$757$	−4.59658	−	29.0217i	−0.167065	−	1.05481i	0.751555	−	0.659670i	$-0.229304\pi$
$758$	−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	−0.998951	−	0.0457864i	$-0.985421\pi$
$761$	−17.8404	+	24.5552i	−0.646713	+	0.890124i	0.352238	+	0.935910i	$0.385421\pi$
$762$	−15.7289	+	8.01429i	−0.569799	+	0.290327i
$763$	−1.62790	−	0.829459i	−0.0589341	−	0.0300284i
$764$	1.15493	+	1.58963i	0.0417840	+	0.0575107i
$765$		0			0
$766$	15.0044	−	4.87523i	0.542131	−	0.176149i
$767$	−13.5283	−	26.5507i	−0.488477	−	0.958690i
$768$	5.73527	−	0.908377i	0.206954	−	0.0327782i
$769$	−37.6421			−1.35741			−0.678705	−	0.734411i	$-0.737458\pi$
$769$	−37.6421			−1.35741			−0.678705	+	0.734411i	$0.737458\pi$
$770$		0			0
$771$	−3.75184			−0.135119
$772$	−1.81970	+	0.288213i	−0.0654926	+	0.0103730i
$773$	11.7188	+	22.9995i	0.421497	+	0.827234i	0.999934	+	0.0115072i	$0.00366294\pi$
$773$	11.7188	+	22.9995i	0.421497	+	0.827234i	−0.578437	+	0.815727i	$0.696337\pi$
$774$	18.0168	−	5.85402i	0.647601	−	0.210418i
$775$		0			0
$776$	2.08149	+	2.86493i	0.0747213	+	0.102845i
$777$	0.735173	+	0.374589i	0.0263742	+	0.0134383i
$778$	−29.9955	+	15.2835i	−1.07539	+	0.547939i
$779$	−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
$783$	6.38724	+	40.3275i	0.228261	+	1.44119i
$784$	29.9651	+	9.73624i	1.07018	+	0.347723i
$785$		0			0
$786$	−9.57771	+	6.95861i	−0.341626	+	0.248206i
$787$	−2.70244	+	17.0625i	−0.0963315	+	0.608213i	0.891540	+	0.452942i	$0.149625\pi$
$787$	−2.70244	+	17.0625i	−0.0963315	+	0.608213i	−0.987872	+	0.155272i	$0.950375\pi$
$788$	1.97520	−	3.87655i	0.0703636	−	0.138096i
$789$	−3.90967	+	12.0327i	−0.139188	+	0.428376i
$790$		0			0
$791$		−	0.794162i		−	0.0282372i
$792$	18.4824	−	7.99654i	0.656745	−	0.284145i
$793$	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
$797$	44.0203	+	6.97213i	1.55928	+	0.246965i	0.875680	−	0.482892i	$-0.160414\pi$
$797$	44.0203	+	6.97213i	1.55928	+	0.246965i	0.683599	+	0.729858i	$0.260414\pi$
$798$	−0.170458	−	0.0269979i	−0.00603414	−	0.000955714i
$799$	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
$803$	−7.93078	+	0.749124i	−0.279871	+	0.0264360i
$804$		−	1.44771i		−	0.0510569i
$805$		0			0
$806$	−0.510267	+	1.57044i	−0.0179734	+	0.0553164i
$807$	−4.09432	+	8.03556i	−0.144127	+	0.282865i
$808$	−1.93850	+	12.2392i	−0.0681962	+	0.430574i
$809$	−12.3255	+	8.95497i	−0.433340	+	0.314840i	−0.782983	−	0.622043i	$-0.786303\pi$
$809$	−12.3255	+	8.95497i	−0.433340	+	0.314840i	0.349643	+	0.936883i	$0.386303\pi$
$810$		0			0
$811$	−43.3276	−	14.0780i	−1.52144	−	0.494345i	−0.575253	−	0.817976i	$-0.695096\pi$
$811$	−43.3276	−	14.0780i	−1.52144	−	0.494345i	−0.946183	+	0.323631i	$0.895096\pi$
$812$	−0.0888178	−	0.560774i	−0.00311689	−	0.0196793i
$813$	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
$817$	3.49314	−	1.77984i	0.122209	−	0.0622688i
$818$	5.81793	+	2.96438i	0.203419	+	0.103647i
$819$	−0.823747	−	1.13379i	−0.0287840	−	0.0396178i
$820$		0			0
$821$	−27.3071	+	8.87260i	−0.953023	+	0.309656i	−0.743943	−	0.668243i	$-0.767047\pi$
$821$	−27.3071	+	8.87260i	−0.953023	+	0.309656i	−0.209079	+	0.977899i	$0.567047\pi$
$822$	2.38226	+	4.67545i	0.0830909	+	0.163075i
$823$	26.6252	−	4.21701i	0.928095	−	0.146996i	0.325954	−	0.945386i	$-0.394314\pi$
$823$	26.6252	−	4.21701i	0.928095	−	0.146996i	0.602141	+	0.798390i	$0.294314\pi$
$824$	−8.31350			−0.289614
$825$		0			0
$826$	−2.80165			−0.0974820
$827$	−39.1944	+	6.20779i	−1.36292	+	0.215866i	−0.794697	−	0.607006i	$-0.792370\pi$
$827$	−39.1944	+	6.20779i	−1.36292	+	0.215866i	−0.568227	+	0.822872i	$0.692370\pi$
$828$	−0.541680	−	1.06311i	−0.0188247	−	0.0369455i
$829$	−10.3353	+	3.35814i	−0.358959	+	0.116633i	−0.482944	−	0.875651i	$-0.660433\pi$
$829$	−10.3353	+	3.35814i	−0.358959	+	0.116633i	0.123985	+	0.992284i	$0.460433\pi$
$830$		0			0
$831$	2.19378	+	3.01948i	0.0761013	+	0.104744i
$832$	17.6573	+	8.99683i	0.612156	+	0.311909i
$833$	22.9966	−	11.7174i	0.796786	−	0.405983i
$834$	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
$838$	−0.285920	−	1.80523i	−0.00987695	−	0.0623606i
$839$	38.3426	+	12.4583i	1.32373	+	0.430107i	0.883775	−	0.467912i	$-0.154993\pi$
$839$	38.3426	+	12.4583i	1.32373	+	0.430107i	0.439958	+	0.898019i	$0.354993\pi$
$840$		0			0
$841$	−50.2797	+	36.5303i	−1.73378	+	1.25967i
$842$	−7.44491	+	47.0053i	−0.256569	+	1.61991i
$843$	4.77364	−	9.36879i	0.164413	−	0.322678i
$844$	0.569376	−	1.75236i	0.0195987	−	0.0603187i
$845$		0			0
$846$			44.4376i			1.52780i
$847$	1.66439	−	1.29066i	0.0571891	−	0.0443477i
$848$	−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
$852$	2.80310	+	0.443967i	0.0960326	+	0.0152101i
$853$	−13.7845	−	2.18326i	−0.471974	−	0.0747533i	−0.0840831	−	0.996459i	$-0.526796\pi$
$853$	−13.7845	−	2.18326i	−0.471974	−	0.0747533i	−0.387890	+	0.921705i	$0.626796\pi$
$854$	−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	−0.0773373	−	0.997005i	$-0.524642\pi$
$857$	26.9229	−	26.9229i	0.919668	−	0.919668i	0.997005	+	0.0773373i	$0.0246418\pi$
$858$	12.1420	+	2.71494i	0.414521	+	0.0926867i
$859$			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
$862$	6.82592	−	13.3966i	0.232492	−	0.456291i
$863$	1.90114	−	12.0033i	0.0647154	−	0.408597i	−0.933971	−	0.357350i	$-0.883680\pi$
$863$	1.90114	−	12.0033i	0.0647154	−	0.408597i	0.998686	−	0.0512472i	$-0.0163196\pi$
$864$	6.02655	−	4.37855i	0.205028	−	0.148961i
$865$		0			0
$866$	−39.0074	−	12.6743i	−1.32552	−	0.430689i
$867$	0.406785	+	2.56834i	0.0138151	+	0.0872253i
$868$	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
$872$	21.8334	−	11.1247i	0.739374	−	0.376730i
$873$	2.90515	+	1.48025i	0.0983243	+	0.0500987i
$874$	−1.07972	−	1.48611i	−0.0365222	−	0.0502685i
$875$		0			0
$876$	−0.565619	+	0.183781i	−0.0191105	+	0.00620938i
$877$	5.82698	+	11.4361i	0.196763	+	0.386169i	0.968215	−	0.250118i	$-0.0804694\pi$
$877$	5.82698	+	11.4361i	0.196763	+	0.386169i	−0.771452	+	0.636287i	$0.780469\pi$
$878$	−36.9125	+	5.84636i	−1.24574	+	0.197305i
$879$	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	$0.425110\pi$
$882$	24.7187	−	3.91506i	0.832322	−	0.131827i
$883$	19.7888	+	38.8377i	0.665947	+	1.30699i	0.938642	+	0.344893i	$0.112085\pi$
$883$	19.7888	+	38.8377i	0.665947	+	1.30699i	−0.272695	+	0.962100i	$0.587915\pi$
$884$	−3.38926	+	1.10124i	−0.113993	+	0.0370387i
$885$		0			0
$886$	−27.5163	−	37.8730i	−0.924429	−	1.27237i
$887$	9.26576	+	4.72114i	0.311114	+	0.158520i	0.602575	−	0.798062i	$-0.294141\pi$
$887$	9.26576	+	4.72114i	0.311114	+	0.158520i	−0.291461	+	0.956583i	$0.594141\pi$
$888$	−9.86013	+	5.02399i	−0.330884	+	0.168594i
$889$	−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
$893$	1.43862	+	9.08308i	0.0481415	+	0.303954i
$894$	−6.64130	−	2.15789i	−0.222118	−	0.0721706i
$895$		0			0
$896$	2.04700	−	1.48723i	0.0683855	−	0.0496850i
$897$	−0.627249	+	3.96029i	−0.0209432	+	0.132230i
$898$	−5.05474	+	9.92048i	−0.168679	+	0.331051i
$899$	1.03530	−	3.18633i	0.0345292	−	0.106270i
$900$		0			0
$901$			33.4710i			1.11508i
$902$	−13.4046	−	30.9821i	−0.446324	−	1.03159i
$903$	−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
$907$	−16.1062	−	2.55097i	−0.534798	−	0.0847036i	−0.116806	−	0.993155i	$-0.537266\pi$
$907$	−16.1062	−	2.55097i	−0.534798	−	0.0847036i	−0.417991	+	0.908451i	$0.637266\pi$
$908$	−4.00948	−	0.635040i	−0.133059	−	0.0210745i
$909$	3.52571	+	10.8510i	0.116940	+	0.359906i
$910$		0			0
$911$	14.3281	+	10.4099i	0.474710	+	0.344897i	0.799274	−	0.600967i	$-0.205218\pi$
$911$	14.3281	+	10.4099i	0.474710	+	0.344897i	−0.324564	+	0.945864i	$0.605218\pi$
$912$	1.89718	−	1.89718i	0.0628219	−	0.0628219i
$913$	−21.9712	−	50.7821i	−0.727140	−	1.68064i
$914$		−	10.2385i		−	0.338659i
$915$		0			0
$916$	−1.57702	+	4.85357i	−0.0521062	+	0.160366i
$917$	−0.849203	+	1.66665i	−0.0280431	+	0.0550378i
$918$	3.76933	−	23.7986i	0.124406	−	0.785472i
$919$	7.38632	−	5.36648i	0.243652	−	0.177024i	−0.459257	−	0.888304i	$-0.651884\pi$
$919$	7.38632	−	5.36648i	0.243652	−	0.177024i	0.702909	+	0.711280i	$0.251884\pi$
$920$		0			0
$921$	21.5818	+	7.01234i	0.711143	+	0.231064i
$922$	6.91497	+	43.6594i	0.227732	+	1.43785i
$923$	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
$927$	−6.82017	+	3.47505i	−0.224004	+	0.114136i
$928$	14.8171	+	7.54970i	0.486396	+	0.247831i
$929$	−1.06529	−	1.46625i	−0.0349511	−	0.0481061i	0.791184	−	0.611578i	$-0.209465\pi$
$929$	−1.06529	−	1.46625i	−0.0349511	−	0.0481061i	−0.826135	+	0.563472i	$0.809465\pi$
$930$		0			0
$931$	4.92578	−	1.60048i	0.161436	−	0.0524537i
$932$	−2.20583	−	4.32918i	−0.0722543	−	0.141807i
$933$	−5.91808	+	0.937332i	−0.193749	+	0.0306869i
$934$	−40.2174			−1.31595
$935$		0			0
$936$	18.7961			0.614371
$937$	−14.9726	+	2.37143i	−0.489133	+	0.0774711i	−0.396130	−	0.918195i	$-0.629647\pi$
$937$	−14.9726	+	2.37143i	−0.489133	+	0.0774711i	−0.0930039	+	0.995666i	$0.529647\pi$
$938$	−0.772546	−	1.51621i	−0.0252245	−	0.0495059i
$939$	1.02061	−	0.331616i	0.0333063	−	0.0108219i
$940$		0			0
$941$	−12.8308	−	17.6600i	−0.418271	−	0.575701i	0.546940	−	0.837172i	$-0.315792\pi$
$941$	−12.8308	−	17.6600i	−0.418271	−	0.575701i	−0.965211	+	0.261471i	$0.915792\pi$
$942$	5.34274	+	2.72226i	0.174076	+	0.0886961i
$943$	9.69338	−	4.93902i	0.315660	−	0.160837i
$944$	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	$0.800730\pi$
$948$	−0.0259711	−	0.163975i	−0.000843503	−	0.00532567i
$949$	−7.07131	−	2.29761i	−0.229545	−	0.0745835i
$950$		0			0
$951$	−7.30875	+	5.31012i	−0.237003	+	0.172192i
$952$	0.285100	−	1.80005i	0.00924015	−	0.0583400i
$953$	5.92153	−	11.6216i	0.191817	−	0.376462i	−0.774989	−	0.631975i	$-0.782244\pi$
$953$	5.92153	−	11.6216i	0.191817	−	0.376462i	0.966806	+	0.255513i	$0.0822444\pi$
$954$	−10.0294	+	30.8672i	−0.324713	+	0.999363i
$955$		0			0
$956$		−	1.64046i		−	0.0530561i
$957$	−24.6354	−	5.50846i	−0.796349	−	0.178063i
$958$	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
$962$	25.1218	+	3.97890i	0.809960	+	0.128285i
$963$	25.8182	+	4.08921i	0.831981	+	0.131773i
$964$	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	−0.891464	−	0.453092i	$-0.850321\pi$
$967$	−13.6319	+	13.6319i	−0.438372	+	0.438372i	0.453092	+	0.891464i	$0.350321\pi$
$968$	0.883368	+	28.2343i	0.0283925	+	0.907484i
$969$		−	2.19785i		−	0.0706051i
$970$		0			0
$971$	1.26967	−	3.90765i	0.0407457	−	0.125403i	−0.928615	−	0.371046i	$-0.878999\pi$
$971$	1.26967	−	3.90765i	0.0407457	−	0.125403i	0.969360	+	0.245643i	$0.0789992\pi$
$972$	2.22320	−	4.36328i	0.0713093	−	0.139952i
$973$	0.314819	−	1.98769i	0.0100926	−	0.0637224i
$974$	−28.6965	+	20.8492i	−0.919495	+	0.668052i
$975$		0			0
$976$	25.3592	+	8.23971i	0.811729	+	0.263747i
$977$	−4.80402	−	30.3314i	−0.153694	−	0.970386i	−0.937147	−	0.348935i	$-0.886543\pi$
$977$	−4.80402	−	30.3314i	−0.153694	−	0.970386i	0.783453	−	0.621451i	$-0.213457\pi$
$978$	−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
$982$	−24.8498	+	12.6616i	−0.792990	+	0.404048i
$983$	−24.7035	−	12.5871i	−0.787919	−	0.401465i	0.0132429	−	0.999912i	$-0.495785\pi$
$983$	−24.7035	−	12.5871i	−0.787919	−	0.401465i	−0.801162	+	0.598447i	$0.795785\pi$
$984$	8.05767	+	11.0904i	0.256869	+	0.353550i
$985$		0			0
$986$	51.1575	−	16.6221i	1.62919	−	0.529355i
$987$	−0.856827	−	1.68162i	−0.0272731	−	0.0535265i
$988$	−0.706325	+	0.111871i	−0.0224712	+	0.00355909i
$989$	−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	$0.453827\pi$
$992$	−0.603719	+	0.0956197i	−0.0191681	+	0.00303593i
$993$	−6.40795	−	12.5763i	−0.203350	−	0.399097i
$994$	3.17264	−	1.03085i	0.100630	−	0.0326966i
$995$		0			0
$996$	−2.42808	−	3.34196i	−0.0769366	−	0.105894i
$997$	−25.7239	−	13.1070i	−0.814685	−	0.415103i	−0.00357282	−	0.999994i	$-0.501137\pi$
$997$	−25.7239	−	13.1070i	−0.814685	−	0.415103i	−0.811112	+	0.584891i	$0.801137\pi$
$998$	15.9247	−	8.11406i	0.504089	−	0.256846i
$999$	−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.7.1		32
5.2	odd	4		55.2.l.a.18.1	yes	32
5.3	odd	4	inner	275.2.bm.b.18.4		32
5.4	even	2		55.2.l.a.7.4	✓	32
11.8	odd	10	inner	275.2.bm.b.107.4		32
15.2	even	4		495.2.bj.a.73.4		32
15.14	odd	2		495.2.bj.a.172.1		32
20.7	even	4		880.2.cm.a.513.1		32
20.19	odd	2		880.2.cm.a.337.4		32
55.2	even	20		605.2.m.c.578.4		32
55.4	even	10		605.2.m.c.112.4		32
55.7	even	20		605.2.m.d.233.1		32
55.8	even	20	inner	275.2.bm.b.118.1		32
55.9	even	10		605.2.m.d.457.1		32
55.14	even	10		605.2.m.e.602.4		32
55.17	even	20		605.2.e.b.483.3		32
55.19	odd	10		55.2.l.a.52.1	yes	32
55.24	odd	10		605.2.m.c.457.4		32
55.27	odd	20		605.2.e.b.483.14		32
55.29	odd	10		605.2.m.d.112.1		32
55.32	even	4		605.2.m.e.403.4		32
55.37	odd	20		605.2.m.c.233.4		32
55.39	odd	10		605.2.e.b.362.14		32
55.42	odd	20		605.2.m.d.578.1		32
55.47	odd	20		605.2.m.e.118.1		32
55.49	even	10		605.2.e.b.362.3		32
55.52	even	20		55.2.l.a.8.4	yes	32
55.54	odd	2		605.2.m.e.282.1		32
165.74	even	10		495.2.bj.a.217.4		32
165.107	odd	20		495.2.bj.a.118.1		32
220.19	even	10		880.2.cm.a.657.1		32
220.107	odd	20		880.2.cm.a.833.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.4	✓	32	5.4	even	2
55.2.l.a.8.4	yes	32	55.52	even	20
55.2.l.a.18.1	yes	32	5.2	odd	4
55.2.l.a.52.1	yes	32	55.19	odd	10
275.2.bm.b.7.1		32	1.1	even	1	trivial
275.2.bm.b.18.4		32	5.3	odd	4	inner
275.2.bm.b.107.4		32	11.8	odd	10	inner
275.2.bm.b.118.1		32	55.8	even	20	inner
495.2.bj.a.73.4		32	15.2	even	4
495.2.bj.a.118.1		32	165.107	odd	20
495.2.bj.a.172.1		32	15.14	odd	2
495.2.bj.a.217.4		32	165.74	even	10
605.2.e.b.362.3		32	55.49	even	10
605.2.e.b.362.14		32	55.39	odd	10
605.2.e.b.483.3		32	55.17	even	20
605.2.e.b.483.14		32	55.27	odd	20
605.2.m.c.112.4		32	55.4	even	10
605.2.m.c.233.4		32	55.37	odd	20
605.2.m.c.457.4		32	55.24	odd	10
605.2.m.c.578.4		32	55.2	even	20
605.2.m.d.112.1		32	55.29	odd	10
605.2.m.d.233.1		32	55.7	even	20
605.2.m.d.457.1		32	55.9	even	10
605.2.m.d.578.1		32	55.42	odd	20
605.2.m.e.118.1		32	55.47	odd	20
605.2.m.e.282.1		32	55.54	odd	2
605.2.m.e.403.4		32	55.32	even	4
605.2.m.e.602.4		32	55.14	even	10
880.2.cm.a.337.4		32	20.19	odd	2
880.2.cm.a.513.1		32	20.7	even	4
880.2.cm.a.657.1		32	220.19	even	10
880.2.cm.a.833.4		32	220.107	odd	20

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

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