LMFDB - Embedded newform 375.2.l.a.107.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,2,Mod(32,375)] 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("375.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [64,0,0,20,0,-6,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.7
Character	$\chi$	$=$	375.107
Dual form			375.2.l.a.368.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.74302 + 0.888111i) q^{2} +(1.59808 - 0.667932i) q^{3} +(1.07379 + 1.47795i) q^{4} +(3.37868 + 0.255059i) q^{6} +(-0.551254 - 0.551254i) q^{7} +(-0.0529901 - 0.334566i) q^{8} +(2.10773 - 2.13482i) q^{9} +(-0.937544 + 0.304626i) q^{11} +(2.70317 + 1.64466i) q^{12} +(2.14163 + 4.20319i) q^{13} +(-0.471270 - 1.45042i) q^{14} +(1.33382 - 4.10508i) q^{16} +(-3.38054 + 0.535425i) q^{17} +(5.56977 - 1.84912i) q^{18} +(-3.79078 + 5.21756i) q^{19} +(-1.24915 - 0.512749i) q^{21} +(-1.90469 - 0.301674i) q^{22} +(0.435998 - 0.855694i) q^{23} +(-0.308150 - 0.499270i) q^{24} +9.22822i q^{26} +(1.94242 - 4.81944i) q^{27} +(0.222792 - 1.40666i) q^{28} +(-8.30669 + 6.03516i) q^{29} +(-2.73448 - 1.98672i) q^{31} +(5.49158 - 5.49158i) q^{32} +(-1.29480 + 1.11303i) q^{33} +(-6.36785 - 2.06904i) q^{34} +(5.41842 + 0.822768i) q^{36} +(3.63316 - 1.85119i) q^{37} +(-11.2411 + 5.72765i) q^{38} +(6.22994 + 5.28657i) q^{39} +(-3.89453 - 1.26541i) q^{41} +(-1.72191 - 2.00311i) q^{42} +(4.93949 - 4.93949i) q^{43} +(-1.45695 - 1.05853i) q^{44} +(1.51990 - 1.10427i) q^{46} +(0.732455 - 4.62454i) q^{47} +(-0.610356 - 7.45115i) q^{48} -6.39224i q^{49} +(-5.04475 + 3.11362i) q^{51} +(-3.91242 + 7.67856i) q^{52} +(3.42818 + 0.542970i) q^{53} +(7.66586 - 6.67528i) q^{54} +(-0.155220 + 0.213642i) q^{56} +(-2.57300 + 10.8701i) q^{57} +(-19.8386 + 3.14212i) q^{58} +(-0.172592 + 0.531183i) q^{59} +(2.95410 + 9.09178i) q^{61} +(-3.00182 - 5.89140i) q^{62} +(-2.33873 + 0.0149310i) q^{63} +(6.23890 - 2.02714i) q^{64} +(-3.24536 + 0.790106i) q^{66} +(1.08040 + 6.82141i) q^{67} +(-4.42132 - 4.42132i) q^{68} +(0.125215 - 1.65869i) q^{69} +(-5.08421 - 6.99781i) q^{71} +(-0.825927 - 0.592052i) q^{72} +(8.03649 + 4.09480i) q^{73} +7.97671 q^{74} -11.7818 q^{76} +(0.684752 + 0.348898i) q^{77} +(6.16382 + 14.7475i) q^{78} +(3.84334 + 5.28990i) q^{79} +(-0.114912 - 8.99927i) q^{81} +(-5.66440 - 5.66440i) q^{82} +(0.223482 + 1.41101i) q^{83} +(-0.583510 - 2.39676i) q^{84} +(12.9964 - 4.22279i) q^{86} +(-9.24369 + 15.1930i) q^{87} +(0.151598 + 0.297528i) q^{88} +(-3.04398 - 9.36841i) q^{89} +(1.13644 - 3.49761i) q^{91} +(1.73284 - 0.274455i) q^{92} +(-5.69692 - 1.34849i) q^{93} +(5.38378 - 7.41014i) q^{94} +(5.10800 - 12.4440i) q^{96} +(5.51558 + 0.873583i) q^{97} +(5.67701 - 11.1418i) q^{98} +(-1.32577 + 2.64356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 20 q^{4} - 6 q^{6} - 20 q^{7} + 10 q^{9} - 40 q^{12} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 30 q^{27} + 80 q^{28} - 12 q^{31} + 50 q^{33} - 20 q^{34} - 22 q^{36} + 120 q^{37} - 30 q^{39} - 60 q^{42}+ \cdots + 42 q^{96}+O(q^{100}) $ 64 * q + 20 * q^4 - 6 * q^6 - 20 * q^7 + 10 * q^9 - 40 * q^12 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 30 * q^27 + 80 * q^28 - 12 * q^31 + 50 * q^33 - 20 * q^34 - 22 * q^36 + 120 * q^37 - 30 * q^39 - 60 * q^42 - 20 * q^43 - 12 * q^46 - 100 * q^48 - 16 * q^51 - 100 * q^52 - 120 * q^54 + 70 * q^57 - 120 * q^58 - 12 * q^61 + 70 * q^63 + 100 * q^64 - 30 * q^66 + 60 * q^67 + 80 * q^69 + 40 * q^72 + 80 * q^73 - 64 * q^76 - 70 * q^78 + 60 * q^79 + 14 * q^81 - 60 * q^82 + 130 * q^84 - 100 * q^87 - 60 * q^88 - 12 * q^91 - 20 * q^93 - 260 * q^94 + 42 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.74302	+	0.888111i	1.23250	+	0.627989i	0.944143	−	0.329535i	$-0.106892\pi$
$2$	1.74302	+	0.888111i	1.23250	+	0.627989i	0.288354	+	0.957524i	$0.406892\pi$
$3$	1.59808	−	0.667932i	0.922653	−	0.385631i
$3$	1.59808	−	0.667932i	0.922653	−	0.385631i
$4$	1.07379	+	1.47795i	0.536895	+	0.738973i
$5$		0			0
$5$		0			0
$6$	3.37868	+	0.255059i	1.37934	+	0.104127i
$7$	−0.551254	−	0.551254i	−0.208355	−	0.208355i	0.595213	−	0.803568i	$-0.297068\pi$
$7$	−0.551254	−	0.551254i	−0.208355	−	0.208355i	−0.803568	+	0.595213i	$0.797068\pi$
$8$	−0.0529901	−	0.334566i	−0.0187348	−	0.118287i
$9$	2.10773	−	2.13482i	0.702578	−	0.711607i
$10$		0			0
$11$	−0.937544	+	0.304626i	−0.282680	+	0.0918483i	−0.446925	−	0.894571i	$-0.647481\pi$
$11$	−0.937544	+	0.304626i	−0.282680	+	0.0918483i	0.164245	+	0.986420i	$0.447481\pi$
$12$	2.70317	+	1.64466i	0.780339	+	0.474773i
$13$	2.14163	+	4.20319i	0.593981	+	1.16575i	0.970895	+	0.239505i	$0.0769853\pi$
$13$	2.14163	+	4.20319i	0.593981	+	1.16575i	−0.376914	+	0.926248i	$0.623015\pi$
$14$	−0.471270	−	1.45042i	−0.125952	−	0.387641i
$15$		0			0
$16$	1.33382	−	4.10508i	0.333455	−	1.02627i
$17$	−3.38054	+	0.535425i	−0.819901	+	0.129860i	−0.552274	−	0.833663i	$-0.686240\pi$
$17$	−3.38054	+	0.535425i	−0.819901	+	0.129860i	−0.267627	+	0.963522i	$0.586240\pi$
$18$	5.56977	−	1.84912i	1.31281	−	0.435842i
$19$	−3.79078	+	5.21756i	−0.869664	+	1.19699i	0.109514	+	0.993985i	$0.465070\pi$
$19$	−3.79078	+	5.21756i	−0.869664	+	1.19699i	−0.979178	+	0.203004i	$0.934930\pi$
$20$		0			0
$21$	−1.24915	−	0.512749i	−0.272587	−	0.111891i
$22$	−1.90469	−	0.301674i	−0.406082	−	0.0643171i
$23$	0.435998	−	0.855694i	0.0909118	−	0.178424i	−0.841073	−	0.540921i	$-0.818076\pi$
$23$	0.435998	−	0.855694i	0.0909118	−	0.178424i	0.931985	+	0.362497i	$0.118076\pi$
$24$	−0.308150	−	0.499270i	−0.0629008	−	0.101913i
$25$		0			0
$26$			9.22822i			1.80980i
$27$	1.94242	−	4.81944i	0.373819	−	0.927502i
$28$	0.222792	−	1.40666i	0.0421038	−	0.265833i
$29$	−8.30669	+	6.03516i	−1.54251	+	1.12070i	−0.593778	+	0.804629i	$0.702364\pi$
$29$	−8.30669	+	6.03516i	−1.54251	+	1.12070i	−0.948735	+	0.316073i	$0.897636\pi$
$30$		0			0
$31$	−2.73448	−	1.98672i	−0.491128	−	0.356825i	0.314490	−	0.949261i	$-0.398166\pi$
$31$	−2.73448	−	1.98672i	−0.491128	−	0.356825i	−0.805618	+	0.592436i	$0.798166\pi$
$32$	5.49158	−	5.49158i	0.970784	−	0.970784i
$33$	−1.29480	+	1.11303i	−0.225396	+	0.193754i
$34$	−6.36785	−	2.06904i	−1.09208	−	0.354837i
$35$		0			0
$36$	5.41842	+	0.822768i	0.903069	+	0.137128i
$37$	3.63316	−	1.85119i	0.597288	−	0.304333i	−0.129086	−	0.991633i	$-0.541204\pi$
$37$	3.63316	−	1.85119i	0.597288	−	0.304333i	0.726374	+	0.687300i	$0.241204\pi$
$38$	−11.2411	+	5.72765i	−1.82355	+	0.929148i
$39$	6.22994	+	5.28657i	0.997589	+	0.846529i
$40$		0			0
$41$	−3.89453	−	1.26541i	−0.608223	−	0.197624i	−0.0113186	−	0.999936i	$-0.503603\pi$
$41$	−3.89453	−	1.26541i	−0.608223	−	0.197624i	−0.596905	+	0.802312i	$0.703603\pi$
$42$	−1.72191	−	2.00311i	−0.265696	−	0.309087i
$43$	4.93949	−	4.93949i	0.753265	−	0.753265i	−0.221822	−	0.975087i	$-0.571201\pi$
$43$	4.93949	−	4.93949i	0.753265	−	0.753265i	0.975087	+	0.221822i	$0.0712005\pi$
$44$	−1.45695	−	1.05853i	−0.219643	−	0.159580i
$45$		0			0
$46$	1.51990	−	1.10427i	0.224097	−	0.162816i
$47$	0.732455	−	4.62454i	0.106840	−	0.674558i	−0.874897	−	0.484310i	$-0.839071\pi$
$47$	0.732455	−	4.62454i	0.106840	−	0.674558i	0.981736	−	0.190248i	$-0.0609293\pi$
$48$	−0.610356	−	7.45115i	−0.0880973	−	1.07548i
$49$		−	6.39224i		−	0.913177i
$50$		0			0
$51$	−5.04475	+	3.11362i	−0.706407	+	0.435994i
$52$	−3.91242	+	7.67856i	−0.542555	+	1.06482i
$53$	3.42818	+	0.542970i	0.470896	+	0.0745826i	0.387373	−	0.921923i	$-0.373383\pi$
$53$	3.42818	+	0.542970i	0.470896	+	0.0745826i	0.0835235	+	0.996506i	$0.473383\pi$
$54$	7.66586	−	6.67528i	1.04319	−	0.908390i
$55$		0			0
$56$	−0.155220	+	0.213642i	−0.0207421	+	0.0285491i
$57$	−2.57300	+	10.8701i	−0.340802	+	1.43978i
$58$	−19.8386	+	3.14212i	−2.60493	+	0.412581i
$59$	−0.172592	+	0.531183i	−0.0224696	+	0.0691542i	−0.961663	−	0.274236i	$-0.911575\pi$
$59$	−0.172592	+	0.531183i	−0.0224696	+	0.0691542i	0.939193	+	0.343390i	$0.111575\pi$
$60$		0			0
$61$	2.95410	+	9.09178i	0.378233	+	1.16408i	0.941271	+	0.337652i	$0.109633\pi$
$61$	2.95410	+	9.09178i	0.378233	+	1.16408i	−0.563038	+	0.826431i	$0.690367\pi$
$62$	−3.00182	−	5.89140i	−0.381231	−	0.748209i
$63$	−2.33873	+	0.0149310i	−0.294652	+	0.00188113i
$64$	6.23890	−	2.02714i	0.779862	−	0.253393i
$65$		0			0
$66$	−3.24536	+	0.790106i	−0.399476	+	0.0972553i
$67$	1.08040	+	6.82141i	0.131992	+	0.833367i	0.961487	+	0.274852i	$0.0886288\pi$
$67$	1.08040	+	6.82141i	0.131992	+	0.833367i	−0.829494	+	0.558515i	$0.811371\pi$
$68$	−4.42132	−	4.42132i	−0.536164	−	0.536164i
$69$	0.125215	−	1.65869i	0.0150741	−	0.199682i
$70$		0			0
$71$	−5.08421	−	6.99781i	−0.603385	−	0.830488i	0.392628	−	0.919697i	$-0.371566\pi$
$71$	−5.08421	−	6.99781i	−0.603385	−	0.830488i	−0.996013	+	0.0892096i	$0.971566\pi$
$72$	−0.825927	−	0.592052i	−0.0973365	−	0.0697740i
$73$	8.03649	+	4.09480i	0.940600	+	0.479260i	0.855897	−	0.517147i	$-0.173006\pi$
$73$	8.03649	+	4.09480i	0.940600	+	0.479260i	0.0847030	+	0.996406i	$0.473006\pi$
$74$	7.97671			0.927274
$75$		0			0
$76$	−11.7818			−1.35146
$77$	0.684752	+	0.348898i	0.0780347	+	0.0397607i
$78$	6.16382	+	14.7475i	0.697915	+	1.66982i
$79$	3.84334	+	5.28990i	0.432410	+	0.595161i	0.968504	−	0.248997i	$-0.0801010\pi$
$79$	3.84334	+	5.28990i	0.432410	+	0.595161i	−0.536095	+	0.844158i	$0.680101\pi$
$80$		0			0
$81$	−0.114912	−	8.99927i	−0.0127680	−	0.999918i
$82$	−5.66440	−	5.66440i	−0.625528	−	0.625528i
$83$	0.223482	+	1.41101i	0.0245303	+	0.154878i	0.996913	−	0.0785138i	$-0.0250175\pi$
$83$	0.223482	+	1.41101i	0.0245303	+	0.154878i	−0.972383	+	0.233392i	$0.925017\pi$
$84$	−0.583510	−	2.39676i	−0.0636661	−	0.261508i
$85$		0			0
$86$	12.9964	−	4.22279i	1.40144	−	0.455355i
$87$	−9.24369	+	15.1930i	−0.991028	+	1.62886i
$88$	0.151598	+	0.297528i	0.0161604	+	0.0317166i
$89$	−3.04398	−	9.36841i	−0.322661	−	0.993049i	−0.972485	−	0.232964i	$-0.925157\pi$
$89$	−3.04398	−	9.36841i	−0.322661	−	0.993049i	0.649824	−	0.760085i	$-0.274843\pi$
$90$		0			0
$91$	1.13644	−	3.49761i	0.119131	−	0.366649i
$92$	1.73284	−	0.274455i	0.180661	−	0.0286139i
$93$	−5.69692	−	1.34849i	−0.590743	−	0.139832i
$94$	5.38378	−	7.41014i	0.555295	−	0.764297i
$95$		0			0
$96$	5.10800	−	12.4440i	0.521333	−	1.27006i
$97$	5.51558	+	0.873583i	0.560023	+	0.0886989i	0.430028	−	0.902816i	$-0.358504\pi$
$97$	5.51558	+	0.873583i	0.560023	+	0.0886989i	0.129995	+	0.991515i	$0.458504\pi$
$98$	5.67701	−	11.1418i	0.573465	−	1.12549i
$99$	−1.32577	+	2.64356i	−0.133245	+	0.265688i
$100$		0			0
$101$			3.43356i			0.341652i	0.985301	+	0.170826i	$0.0546437\pi$
$101$			3.43356i			0.341652i	−0.985301	+	0.170826i	$0.945356\pi$
$102$	−11.5583	+	0.946793i	−1.14444	+	0.0937464i
$103$	0.772999	−	4.88052i	0.0761658	−	0.480892i	−0.919891	−	0.392174i	$-0.871723\pi$
$103$	0.772999	−	4.88052i	0.0761658	−	0.480892i	0.996057	−	0.0887178i	$-0.0282769\pi$
$104$	1.29276	−	0.939244i	0.126765	−	0.0921004i
$105$		0			0
$106$	5.49315	+	3.99100i	0.533542	+	0.387641i
$107$	−2.44736	+	2.44736i	−0.236595	+	0.236595i	−0.815439	−	0.578844i	$-0.803504\pi$
$107$	−2.44736	+	2.44736i	−0.236595	+	0.236595i	0.578844	+	0.815439i	$0.303504\pi$
$108$	9.20863	−	2.30428i	0.886101	−	0.221730i
$109$	2.20399	+	0.716119i	0.211104	+	0.0685918i	0.412660	−	0.910885i	$-0.364600\pi$
$109$	2.20399	+	0.716119i	0.211104	+	0.0685918i	−0.201556	+	0.979477i	$0.564600\pi$
$110$		0			0
$111$	4.56962	−	5.38505i	0.433729	−	0.511127i
$112$	−2.99821	+	1.52767i	−0.283305	+	0.144351i
$113$	2.90689	−	1.48114i	0.273457	−	0.139334i	−0.311885	−	0.950120i	$-0.600960\pi$
$113$	2.90689	−	1.48114i	0.273457	−	0.139334i	0.585342	+	0.810786i	$0.300960\pi$
$114$	−14.1386	+	16.6616i	−1.32420	+	1.56050i
$115$		0			0
$116$	−17.8393	−	5.79634i	−1.65634	−	0.538176i
$117$	13.4870	+	4.28720i	1.24688	+	0.396352i
$118$	−0.772580	+	0.772580i	−0.0711217	+	0.0711217i
$119$	2.15869	+	1.56838i	0.197887	+	0.143773i
$120$		0			0
$121$	−8.11300	+	5.89444i	−0.737545	+	0.535858i
$122$	−2.92547	+	18.4707i	−0.264859	+	1.67226i
$123$	−7.06898	+	0.579051i	−0.637389	+	0.0522113i
$124$		−	6.17474i		−	0.554508i
$125$		0			0
$126$	−4.08970	−	2.05102i	−0.364339	−	0.182720i
$127$	6.90244	−	13.5468i	0.612493	−	1.20208i	−0.351508	−	0.936185i	$-0.614331\pi$
$127$	6.90244	−	13.5468i	0.612493	−	1.20208i	0.964001	−	0.265900i	$-0.0856691\pi$
$128$	−2.66650	−	0.422332i	−0.235687	−	0.0373292i
$129$	4.59447	−	11.1929i	0.404520	−	0.985484i
$130$		0			0
$131$	−0.850285	+	1.17032i	−0.0742897	+	0.102251i	−0.844545	−	0.535485i	$-0.820129\pi$
$131$	−0.850285	+	1.17032i	−0.0742897	+	0.102251i	0.770255	+	0.637736i	$0.220129\pi$
$132$	−3.03535	−	0.718483i	−0.264193	−	0.0625360i
$133$	4.96588	−	0.786518i	0.430597	−	0.0681998i
$134$	−4.17500	+	12.8493i	−0.360665	+	1.11001i
$135$		0			0
$136$	0.358270	+	1.10264i	0.0307214	+	0.0945507i
$137$	−4.30255	−	8.44422i	−0.367591	−	0.721438i	0.630928	−	0.775842i	$-0.282674\pi$
$137$	−4.30255	−	8.44422i	−0.367591	−	0.721438i	−0.998519	+	0.0544031i	$0.982674\pi$
$138$	1.69135	−	2.77991i	0.143977	−	0.236642i
$139$	6.29917	−	2.04672i	0.534288	−	0.173601i	−0.0294316	−	0.999567i	$-0.509370\pi$
$139$	6.29917	−	2.04672i	0.534288	−	0.173601i	0.563720	+	0.825966i	$0.309370\pi$
$140$		0			0
$141$	−1.91835	−	7.87962i	−0.161554	−	0.663584i
$142$	−2.64702	−	16.7126i	−0.222133	−	1.40249i
$143$	−3.28827	−	3.28827i	−0.274979	−	0.274979i
$144$	−5.95226	−	11.4999i	−0.496022	−	0.958323i
$145$		0			0
$146$	10.3711	+	14.2746i	0.858318	+	1.18137i
$147$	−4.26958	−	10.2153i	−0.352149	−	0.842546i
$148$	6.63721	+	3.38183i	0.545575	+	0.277985i
$149$	10.3466			0.847626			0.423813	−	0.905750i	$-0.360691\pi$
$149$	10.3466			0.847626			0.423813	+	0.905750i	$0.360691\pi$
$150$		0			0
$151$	5.60298			0.455964			0.227982	−	0.973665i	$-0.426787\pi$
$151$	5.60298			0.455964			0.227982	+	0.973665i	$0.426787\pi$
$152$	1.94649	+	0.991787i	0.157881	+	0.0804445i
$153$	−5.98224	+	8.34537i	−0.483636	+	0.674683i
$154$	0.883672	+	1.21627i	0.0712083	+	0.0980098i
$155$		0			0
$156$	−1.12362	+	14.8842i	−0.0899614	+	1.19169i
$157$	7.18526	+	7.18526i	0.573446	+	0.573446i	0.933090	−	0.359644i	$-0.117102\pi$
$157$	7.18526	+	7.18526i	0.573446	+	0.573446i	−0.359644	+	0.933090i	$0.617102\pi$
$158$	2.00098	+	12.6337i	0.159189	+	1.00508i
$159$	5.84118	−	1.42208i	0.463235	−	0.112778i
$160$		0			0
$161$	−0.712050	+	0.231359i	−0.0561174	+	0.0182337i
$162$	7.79205	−	15.7879i	0.612201	−	1.24042i
$163$	−8.85172	−	17.3725i	−0.693320	−	1.36072i	−0.921990	−	0.387214i	$-0.873438\pi$
$163$	−8.85172	−	17.3725i	−0.693320	−	1.36072i	0.228670	−	0.973504i	$-0.426562\pi$
$164$	−2.31170	−	7.11469i	−0.180514	−	0.555564i
$165$		0			0
$166$	−0.863599	+	2.65788i	−0.0670283	+	0.206292i
$167$	0.529779	−	0.0839087i	0.0409955	−	0.00649305i	−0.135903	−	0.990722i	$-0.543394\pi$
$167$	0.529779	−	0.0839087i	0.0409955	−	0.00649305i	0.176899	+	0.984229i	$0.443394\pi$
$168$	−0.105356	+	0.445094i	−0.00812840	+	0.0343397i
$169$	−5.43898	+	7.48611i	−0.418383	+	0.575855i
$170$		0			0
$171$	3.14859	+	19.0898i	0.240779	+	1.45984i
$172$	12.6043	+	1.99632i	0.961067	+	0.152218i
$173$	−7.23210	+	14.1938i	−0.549846	+	1.07913i	0.434132	+	0.900849i	$0.357055\pi$
$173$	−7.23210	+	14.1938i	−0.549846	+	1.07913i	−0.983979	+	0.178285i	$0.942945\pi$
$174$	−29.6050	+	18.2722i	−2.24435	+	1.38521i
$175$		0			0
$176$			4.25500i			0.320733i
$177$	0.0789781	+	0.964154i	0.00593636	+	0.0724703i
$178$	3.01448	−	19.0327i	0.225945	−	1.42656i
$179$	−14.7628	+	10.7258i	−1.10342	+	0.801684i	−0.981615	−	0.190870i	$-0.938869\pi$
$179$	−14.7628	+	10.7258i	−1.10342	+	0.801684i	−0.121808	+	0.992554i	$0.538869\pi$
$180$		0			0
$181$	8.42806	+	6.12334i	0.626453	+	0.455145i	0.855170	−	0.518348i	$-0.173453\pi$
$181$	8.42806	+	6.12334i	0.626453	+	0.455145i	−0.228717	+	0.973493i	$0.573453\pi$
$182$	5.08710	−	5.08710i	0.377081	−	0.377081i
$183$	10.7936	+	12.5563i	0.797884	+	0.928186i
$184$	−0.309390	−	0.100527i	−0.0228085	−	0.00741093i
$185$		0			0
$186$	−8.73221	−	7.40994i	−0.640277	−	0.543323i
$187$	3.00630	−	1.53179i	0.219842	−	0.112015i
$188$	7.62132	−	3.88326i	0.555842	−	0.283216i
$189$	−3.72750	+	1.58597i	−0.271136	+	0.115362i
$190$		0			0
$191$	16.3919	+	5.32604i	1.18607	+	0.385379i	0.834620	−	0.550826i	$-0.185687\pi$
$191$	16.3919	+	5.32604i	1.18607	+	0.385379i	0.351454	+	0.936205i	$0.385687\pi$
$192$	8.61628	−	7.40669i	0.621826	−	0.534532i
$193$	−13.5906	+	13.5906i	−0.978276	+	0.978276i	−0.999769	−	0.0214931i	$-0.993158\pi$
$193$	−13.5906	+	13.5906i	−0.978276	+	0.978276i	0.0214931	+	0.999769i	$0.493158\pi$
$194$	8.83791	+	6.42112i	0.634525	+	0.461009i
$195$		0			0
$196$	9.44738	−	6.86393i	0.674813	−	0.490280i
$197$	−0.334594	+	2.11254i	−0.0238388	+	0.150512i	−0.996737	−	0.0807236i	$-0.974277\pi$
$197$	−0.334594	+	2.11254i	−0.0238388	+	0.150512i	0.972898	+	0.231236i	$0.0742769\pi$
$198$	−4.65861	+	3.43033i	−0.331073	+	0.243783i
$199$			18.8648i			1.33729i	0.743582	+	0.668644i	$0.233125\pi$
$199$			18.8648i			1.33729i	−0.743582	+	0.668644i	$0.766875\pi$
$200$		0			0
$201$	6.28281	+	10.1795i	0.443155	+	0.718009i
$202$	−3.04939	+	5.98476i	−0.214554	+	0.421086i
$203$	7.90601	+	1.25219i	0.554893	+	0.0878864i
$204$	−10.0188	−	4.11249i	−0.701455	−	0.287932i
$205$		0			0
$206$	5.68179	−	7.82031i	0.395869	−	0.544867i
$207$	−0.907785	−	2.73435i	−0.0630954	−	0.190051i
$208$	20.1109	−	3.18526i	1.39444	−	0.220858i
$209$	1.96461	−	6.04646i	0.135895	−	0.418242i
$210$		0			0
$211$	−1.54603	−	4.75818i	−0.106433	−	0.327567i	0.883631	−	0.468184i	$-0.155091\pi$
$211$	−1.54603	−	4.75818i	−0.106433	−	0.327567i	−0.990064	+	0.140617i	$0.955091\pi$
$212$	2.87866	+	5.64970i	0.197708	+	0.388023i
$213$	−12.7990	−	7.78718i	−0.876976	−	0.533569i
$214$	−6.43931	+	2.09226i	−0.440182	+	0.143024i
$215$		0			0
$216$	−1.71535	−	0.394485i	−0.116715	−	0.0268413i
$217$	0.412209	+	2.60258i	0.0279825	+	0.176675i
$218$	3.20559	+	3.20559i	0.217110	+	0.217110i
$219$	15.5780	+	1.17599i	1.05266	+	0.0794663i
$220$		0			0
$221$	−9.49035	−	13.0623i	−0.638390	−	0.878669i
$222$	12.7474	−	5.32790i	0.855552	−	0.357585i
$223$	10.8469	+	5.52678i	0.726363	+	0.370101i	0.777746	−	0.628578i	$-0.216363\pi$
$223$	10.8469	+	5.52678i	0.726363	+	0.370101i	−0.0513829	+	0.998679i	$0.516363\pi$
$224$	−6.05452			−0.404534
$225$		0			0
$226$	6.38217			0.424536
$227$	13.3560	+	6.80520i	0.886466	+	0.451677i	0.837066	−	0.547102i	$-0.184269\pi$
$227$	13.3560	+	6.80520i	0.886466	+	0.451677i	0.0494003	+	0.998779i	$0.484269\pi$
$228$	−18.8282	+	7.86942i	−1.24693	+	0.521165i
$229$	−9.00455	−	12.3937i	−0.595037	−	0.818999i	0.400205	−	0.916426i	$-0.368939\pi$
$229$	−9.00455	−	12.3937i	−0.595037	−	0.818999i	−0.995243	+	0.0974268i	$0.968939\pi$
$230$		0			0
$231$	1.32733	+	0.100201i	0.0873319	+	0.00659274i
$232$	2.45933	+	2.45933i	0.161463	+	0.161463i
$233$	−0.338659	−	2.13821i	−0.0221863	−	0.140079i	0.974109	−	0.226080i	$-0.0725911\pi$
$233$	−0.338659	−	2.13821i	−0.0221863	−	0.140079i	−0.996295	+	0.0860013i	$0.972591\pi$
$234$	19.7006	+	19.4506i	1.28787	+	1.27153i
$235$		0			0
$236$	−0.970388	+	0.315298i	−0.0631669	+	0.0205242i
$237$	9.67527	+	5.88661i	0.628476	+	0.382377i
$238$	2.36974	+	4.65087i	0.153607	+	0.301471i
$239$	−7.04340	−	21.6774i	−0.455600	−	1.40219i	−0.870430	−	0.492293i	$-0.836159\pi$
$239$	−7.04340	−	21.6774i	−0.455600	−	1.40219i	0.414830	−	0.909899i	$-0.363841\pi$
$240$		0			0
$241$	−0.706155	+	2.17332i	−0.0454874	+	0.139996i	−0.971221	−	0.238181i	$-0.923449\pi$
$241$	−0.706155	+	2.17332i	−0.0454874	+	0.139996i	0.925733	+	0.378177i	$0.123449\pi$
$242$	−19.3760	+	3.06885i	−1.24554	+	0.197273i
$243$	−6.19453	−	14.3048i	−0.397380	−	0.917654i
$244$	−10.2651	+	14.1287i	−0.657154	+	0.904495i
$245$		0			0
$246$	−12.8356	−	5.26874i	−0.818368	−	0.335923i
$247$	−30.0488	−	4.75926i	−1.91196	−	0.302825i
$248$	−0.519788	+	1.02014i	−0.0330066	+	0.0647791i
$249$	1.29960	+	2.10564i	0.0823587	+	0.133439i
$250$		0			0
$251$		−	14.3226i		−	0.904036i	−0.892009	−	0.452018i	$-0.850704\pi$
$251$		−	14.3226i		−	0.904036i	0.892009	−	0.452018i	$-0.149296\pi$
$252$	−2.53337	−	3.44048i	−0.159587	−	0.216730i
$253$	−0.148100	+	0.935067i	−0.00931097	+	0.0587871i
$254$	24.0621	−	17.4822i	1.50979	−	1.09693i
$255$		0			0
$256$	−14.8869	−	10.8160i	−0.930432	−	0.675998i
$257$	−4.31188	+	4.31188i	−0.268968	+	0.268968i	−0.828684	−	0.559716i	$-0.810910\pi$
$257$	−4.31188	+	4.31188i	−0.268968	+	0.268968i	0.559716	+	0.828684i	$0.310910\pi$
$258$	17.9488	−	15.4291i	1.11744	−	0.960573i
$259$	−3.02327	−	0.982320i	−0.187857	−	0.0610384i
$260$		0			0
$261$	−4.62431	+	30.4538i	−0.286237	+	1.88504i
$262$	−2.52143	+	1.28473i	−0.155774	+	0.0793711i
$263$	27.7729	−	14.1510i	1.71255	−	0.872587i	0.730753	−	0.682642i	$-0.239169\pi$
$263$	27.7729	−	14.1510i	1.71255	−	0.872587i	0.981795	−	0.189945i	$-0.0608310\pi$
$264$	0.440995	+	0.374217i	0.0271414	+	0.0230315i
$265$		0			0
$266$	9.35412	+	3.03934i	0.573538	+	0.186354i
$267$	−11.1220	−	12.9383i	−0.680655	−	0.791812i
$268$	−8.92154	+	8.92154i	−0.544970	+	0.544970i
$269$	11.9339	+	8.67050i	0.727624	+	0.528649i	0.888811	−	0.458274i	$-0.151532\pi$
$269$	11.9339	+	8.67050i	0.727624	+	0.528649i	−0.161187	+	0.986924i	$0.551532\pi$
$270$		0			0
$271$	19.8939	−	14.4538i	1.20847	−	0.878004i	0.213378	−	0.976970i	$-0.431553\pi$
$271$	19.8939	−	14.4538i	1.20847	−	0.878004i	0.995091	+	0.0989656i	$0.0315534\pi$
$272$	−2.31107	+	14.5915i	−0.140129	+	0.884741i
$273$	−0.520036	−	6.34853i	−0.0314740	−	0.384230i
$274$		−	18.5395i		−	1.12001i
$275$		0			0
$276$	2.58590	−	1.59602i	0.155653	−	0.0960691i
$277$	1.52140	−	2.98592i	0.0914121	−	0.179406i	−0.840773	−	0.541387i	$-0.817899\pi$
$277$	1.52140	−	2.98592i	0.0914121	−	0.179406i	0.932186	+	0.361981i	$0.117899\pi$
$278$	12.7973	+	2.02689i	0.767529	+	0.121565i
$279$	−10.0048	+	1.65015i	−0.598975	+	0.0987922i
$280$		0			0
$281$	−0.291342	+	0.400997i	−0.0173800	+	0.0239215i	−0.817619	−	0.575760i	$-0.804706\pi$
$281$	−0.291342	+	0.400997i	−0.0173800	+	0.0239215i	0.800239	+	0.599682i	$0.204706\pi$
$282$	3.65426	−	15.4380i	0.217608	−	0.919320i
$283$	−22.6222	+	3.58300i	−1.34475	+	0.212987i	−0.786964	−	0.616999i	$-0.788348\pi$
$283$	−22.6222	+	3.58300i	−1.34475	+	0.212987i	−0.557784	+	0.829986i	$0.688348\pi$
$284$	4.88302	−	15.0284i	0.289754	−	0.891770i
$285$		0			0
$286$	−2.81116	−	8.65186i	−0.166227	−	0.511595i
$287$	1.44931	+	2.84444i	0.0855502	+	0.167902i
$288$	−0.148743	−	23.2983i	−0.00876474	−	1.37287i
$289$	−5.02660	+	1.63324i	−0.295682	+	0.0960730i
$290$		0			0
$291$	9.39785	−	2.28798i	0.550912	−	0.134124i
$292$	2.57762	+	16.2745i	0.150844	+	0.952390i
$293$	7.39973	+	7.39973i	0.432297	+	0.432297i	0.889409	−	0.457112i	$-0.151116\pi$
$293$	7.39973	+	7.39973i	0.432297	+	0.432297i	−0.457112	+	0.889409i	$0.651116\pi$
$294$	1.63040	−	21.5973i	0.0950866	−	1.25958i
$295$		0			0
$296$	−0.811866	−	1.11744i	−0.0471888	−	0.0649498i
$297$	−0.352974	+	5.11015i	−0.0204816	+	0.296521i
$298$	18.0343	+	9.18892i	1.04470	+	0.532300i
$299$	4.53039			0.261999
$300$		0			0
$301$	−5.44583			−0.313892
$302$	9.76609	+	4.97607i	0.561975	+	0.286341i
$303$	2.29339	+	5.48712i	0.131752	+	0.315227i
$304$	16.3622	+	22.5207i	0.938439	+	1.29165i
$305$		0			0
$306$	−17.8388	+	9.23322i	−1.01977	+	0.527828i
$307$	−6.95771	−	6.95771i	−0.397097	−	0.397097i	0.480111	−	0.877208i	$-0.340596\pi$
$307$	−6.95771	−	6.95771i	−0.397097	−	0.397097i	−0.877208	+	0.480111i	$0.840596\pi$
$308$	0.219627	+	1.38667i	0.0125144	+	0.0790129i
$309$	−2.02454	−	8.31578i	−0.115172	−	0.473068i
$310$		0			0
$311$	2.10692	−	0.684580i	0.119473	−	0.0388190i	−0.248671	−	0.968588i	$-0.579994\pi$
$311$	2.10692	−	0.684580i	0.119473	−	0.0388190i	0.368143	+	0.929769i	$0.379994\pi$
$312$	1.43858	−	2.36446i	0.0814437	−	0.133861i
$313$	10.9036	+	21.3996i	0.616309	+	1.20958i	0.962467	+	0.271399i	$0.0874863\pi$
$313$	10.9036	+	21.3996i	0.616309	+	1.20958i	−0.346158	+	0.938176i	$0.612514\pi$
$314$	6.14271	+	18.9053i	0.346653	+	1.06689i
$315$		0			0
$316$	−3.69125	+	11.3605i	−0.207649	+	0.639078i
$317$	−0.769521	+	0.121880i	−0.0432206	+	0.00684547i	−0.178007	−	0.984029i	$-0.556965\pi$
$317$	−0.769521	+	0.121880i	−0.0432206	+	0.00684547i	0.134787	+	0.990875i	$0.456965\pi$
$318$	11.4442	+	2.70891i	0.641760	+	0.151908i
$319$	5.94941	−	8.18866i	0.333103	−	0.458477i
$320$		0			0
$321$	−2.27641	+	5.54575i	−0.127057	+	0.309534i
$322$	−1.44659	−	0.229117i	−0.0806152	−	0.0127682i
$323$	10.0213	−	19.6678i	0.557598	−	1.09435i
$324$	13.1770	−	9.83316i	0.732058	−	0.546287i
$325$		0			0
$326$		−	38.1418i		−	2.11248i
$327$	4.00047	−	0.327696i	0.221227	−	0.0181216i
$328$	−0.216992	+	1.37003i	−0.0119814	+	0.0756473i
$329$	−2.95306	+	2.14553i	−0.162808	+	0.118287i
$330$		0			0
$331$	−12.1264	−	8.81032i	−0.666525	−	0.484259i	0.202335	−	0.979316i	$-0.435147\pi$
$331$	−12.1264	−	8.81032i	−0.666525	−	0.484259i	−0.868860	+	0.495057i	$0.835147\pi$
$332$	−1.84542	+	1.84542i	−0.101281	+	0.101281i
$333$	3.70578	−	11.6580i	0.203076	−	0.638852i
$334$	0.997933	+	0.324248i	0.0546044	+	0.0177421i
$335$		0			0
$336$	−3.77102	+	4.44394i	−0.205726	+	0.242437i
$337$	−21.4776	+	10.9434i	−1.16996	+	0.596124i	−0.927421	−	0.374019i	$-0.877980\pi$
$337$	−21.4776	+	10.9434i	−1.16996	+	0.596124i	−0.242537	+	0.970142i	$0.577980\pi$
$338$	−16.1287	+	8.21799i	−0.877287	+	0.447000i
$339$	3.65616	−	4.30858i	0.198575	−	0.234010i
$340$		0			0
$341$	3.16890	+	1.02964i	0.171606	+	0.0557581i
$342$	−11.4658	+	36.0702i	−0.620002	+	1.95045i
$343$	−7.38253	+	7.38253i	−0.398619	+	0.398619i
$344$	−1.91433	−	1.39084i	−0.103214	−	0.0749891i
$345$		0			0
$346$	−25.2113	+	18.3171i	−1.35537	+	0.984733i
$347$	5.05725	−	31.9302i	0.271487	−	1.71410i	−0.355164	−	0.934804i	$-0.615575\pi$
$347$	5.05725	−	31.9302i	0.271487	−	1.71410i	0.626652	−	0.779299i	$-0.284425\pi$
$348$	−32.3802	+	2.65241i	−1.73576	+	0.142184i
$349$		−	8.46821i		−	0.453293i	−0.973977	−	0.226646i	$-0.927224\pi$
$349$		−	8.46821i		−	0.453293i	0.973977	−	0.226646i	$-0.0727762\pi$
$350$		0			0
$351$	24.4169	−	2.15711i	1.30328	−	0.115138i
$352$	−3.47572	+	6.82148i	−0.185256	+	0.363586i
$353$	−33.2366	−	5.26415i	−1.76900	−	0.280183i	−0.814887	−	0.579619i	$-0.803201\pi$
$353$	−33.2366	−	5.26415i	−1.76900	−	0.280183i	−0.954116	+	0.299437i	$0.903201\pi$
$354$	−0.718616	+	1.75068i	−0.0381940	+	0.0930474i
$355$		0			0
$356$	10.5774	−	14.5586i	0.560601	−	0.771602i
$357$	4.49734	+	1.06454i	0.238024	+	0.0563416i
$358$	−35.2575	+	5.58424i	−1.86342	+	0.295136i
$359$	−2.38803	+	7.34959i	−0.126035	+	0.387897i	−0.994088	−	0.108575i	$-0.965371\pi$
$359$	−2.38803	+	7.34959i	−0.126035	+	0.387897i	0.868053	+	0.496471i	$0.165371\pi$
$360$		0			0
$361$	−6.98158	−	21.4871i	−0.367452	−	1.13090i
$362$	9.25203	+	18.1581i	0.486276	+	0.954370i
$363$	−9.02815	+	14.8387i	−0.473855	+	0.778831i
$364$	6.38958	−	2.07610i	0.334905	−	0.108817i
$365$		0			0
$366$	7.66201	+	31.4717i	0.400500	+	1.64505i
$367$	1.86431	+	11.7708i	0.0973164	+	0.614431i	0.987352	+	0.158541i	$0.0506791\pi$
$367$	1.86431	+	11.7708i	0.0973164	+	0.614431i	−0.890036	+	0.455890i	$0.849321\pi$
$368$	−2.93115	−	2.93115i	−0.152796	−	0.152796i
$369$	−10.9100	+	5.64697i	−0.567955	+	0.293970i
$370$		0			0
$371$	−1.59048	−	2.18911i	−0.0825737	−	0.113653i
$372$	−4.12430	−	9.86774i	−0.213835	−	0.511619i
$373$	−22.5244	−	11.4767i	−1.16627	−	0.594243i	−0.239876	−	0.970804i	$-0.577107\pi$
$373$	−22.5244	−	11.4767i	−1.16627	−	0.594243i	−0.926392	+	0.376560i	$0.877107\pi$
$374$	6.60042			0.341299
$375$		0			0
$376$	−1.58603			−0.0817931
$377$	−43.1568	−	21.9895i	−2.22269	−	1.13251i
$378$	−7.90561	−	0.546065i	−0.406621	−	0.0280866i
$379$	−11.2506	−	15.4851i	−0.577904	−	0.795416i	0.415560	−	0.909566i	$-0.363586\pi$
$379$	−11.2506	−	15.4851i	−0.577904	−	0.795416i	−0.993464	+	0.114150i	$0.963586\pi$
$380$		0			0
$381$	1.98233	−	26.2593i	0.101558	−	1.34530i
$382$	23.8412	+	23.8412i	1.21982	+	1.21982i
$383$	−3.31513	−	20.9309i	−0.169395	−	1.06952i	−0.915095	−	0.403238i	$-0.867885\pi$
$383$	−3.31513	−	20.9309i	−0.169395	−	1.06952i	0.745700	−	0.666282i	$-0.232115\pi$
$384$	−4.54337	+	1.10612i	−0.231853	+	0.0564463i
$385$		0			0
$386$	−35.7587	+	11.6187i	−1.82007	+	0.591376i
$387$	−0.133789	−	20.9560i	−0.00680087	−	1.06526i
$388$	4.63148	+	9.08978i	0.235128	+	0.461464i
$389$	3.35765	+	10.3338i	0.170240	+	0.523944i	0.999384	−	0.0350902i	$-0.0111719\pi$
$389$	3.35765	+	10.3338i	0.170240	+	0.523944i	−0.829144	+	0.559035i	$0.811172\pi$
$390$		0			0
$391$	−1.01575	+	3.12615i	−0.0513686	+	0.158096i
$392$	−2.13863	+	0.338725i	−0.108017	+	0.0171082i
$393$	−0.577134	+	2.43819i	−0.0291125	+	0.122991i
$394$	−2.45937	+	3.38503i	−0.123901	+	0.170536i
$395$		0			0
$396$	−5.33064	+	0.879211i	−0.267875	+	0.0441820i
$397$	7.56976	+	1.19893i	0.379915	+	0.0601727i	0.343472	−	0.939163i	$-0.388397\pi$
$397$	7.56976	+	1.19893i	0.379915	+	0.0601727i	0.0364437	+	0.999336i	$0.488397\pi$
$398$	−16.7540	+	32.8816i	−0.839802	+	1.64821i
$399$	7.41055	−	4.57379i	0.370991	−	0.228976i
$400$		0			0
$401$			20.7216i			1.03479i	0.855747	+	0.517395i	$0.173098\pi$
$401$			20.7216i			1.03479i	−0.855747	+	0.517395i	$0.826902\pi$
$402$	1.91048	+	23.3229i	0.0952861	+	1.16324i
$403$	2.49429	−	15.7484i	0.124250	−	0.784481i
$404$	−5.07463	+	3.68693i	−0.252472	+	0.183432i
$405$		0			0
$406$	12.6682	+	9.20399i	0.628713	+	0.456786i
$407$	−2.84233	+	2.84233i	−0.140889	+	0.140889i
$408$	1.30903	+	1.52281i	0.0648068	+	0.0753904i
$409$	−30.3286	−	9.85436i	−1.49965	−	0.487267i	−0.559736	−	0.828671i	$-0.689098\pi$
$409$	−30.3286	−	9.85436i	−1.49965	−	0.487267i	−0.939917	+	0.341404i	$0.889098\pi$
$410$		0			0
$411$	−12.5160	−	10.6208i	−0.617368	−	0.523883i
$412$	8.04319	−	4.09821i	0.396259	−	0.201904i
$413$	0.387959	−	0.197675i	0.0190902	−	0.00972695i
$414$	0.846124	−	5.57223i	0.0415847	−	0.273860i
$415$		0			0
$416$	34.8431	+	11.3212i	1.70832	+	0.555068i
$417$	8.69952	−	7.47825i	0.426017	−	0.366211i
$418$	8.79427	−	8.79427i	0.430142	−	0.430142i
$419$	−10.4586	−	7.59860i	−0.510935	−	0.371216i	0.302243	−	0.953231i	$-0.402264\pi$
$419$	−10.4586	−	7.59860i	−0.510935	−	0.371216i	−0.813178	+	0.582015i	$0.802264\pi$
$420$		0			0
$421$	−9.92844	+	7.21344i	−0.483883	+	0.351561i	−0.802827	−	0.596212i	$-0.796672\pi$
$421$	−9.92844	+	7.21344i	−0.483883	+	0.351561i	0.318944	+	0.947773i	$0.396672\pi$
$422$	1.53104	−	9.66663i	0.0745300	−	0.470564i
$423$	−8.32873	−	11.3110i	−0.404957	−	0.549957i
$424$		−	1.17572i		−	0.0570982i
$425$		0			0
$426$	−15.3931	−	24.9401i	−0.745796	−	1.20835i
$427$	3.38342	−	6.64034i	0.163735	−	0.321349i
$428$	−6.24502	−	0.989114i	−0.301864	−	0.0478106i
$429$	−7.45127	−	3.05859i	−0.359751	−	0.147670i
$430$		0			0
$431$	−23.6623	+	32.5684i	−1.13977	+	1.56876i	−0.371760	+	0.928329i	$0.621246\pi$
$431$	−23.6623	+	32.5684i	−1.13977	+	1.56876i	−0.768013	+	0.640434i	$0.778754\pi$
$432$	−17.1933	−	14.4020i	−0.827215	−	0.692919i
$433$	0.688486	−	0.109046i	0.0330865	−	0.00524039i	−0.139869	−	0.990170i	$-0.544668\pi$
$433$	0.688486	−	0.109046i	0.0330865	−	0.00524039i	0.172956	+	0.984930i	$0.444668\pi$
$434$	−1.59290	+	4.90243i	−0.0764614	+	0.235324i
$435$		0			0
$436$	1.30824	+	4.02634i	0.0626532	+	0.192827i
$437$	2.81186	+	5.51859i	0.134510	+	0.263990i
$438$	26.1083	+	15.8848i	1.24750	+	0.759004i
$439$	32.6150	−	10.5973i	1.55663	−	0.505780i	0.600724	−	0.799456i	$-0.294879\pi$
$439$	32.6150	−	10.5973i	1.55663	−	0.505780i	0.955905	+	0.293677i	$0.0948789\pi$
$440$		0			0
$441$	−13.6463	−	13.4731i	−0.649823	−	0.641578i
$442$	−4.94102	−	31.1964i	−0.235020	−	1.48386i
$443$	20.2627	+	20.2627i	0.962712	+	0.962712i	0.999329	−	0.0366177i	$-0.0116584\pi$
$443$	20.2627	+	20.2627i	0.962712	+	0.962712i	−0.0366177	+	0.999329i	$0.511658\pi$
$444$	12.8656	+	0.971235i	0.610576	+	0.0460928i
$445$		0			0
$446$	13.9979	+	19.2665i	0.662822	+	0.912296i
$447$	16.5347	−	6.91082i	0.782065	−	0.326871i
$448$	−4.55669	−	2.32175i	−0.215283	−	0.109692i
$449$	−18.2524			−0.861386			−0.430693	−	0.902499i	$-0.641731\pi$
$449$	−18.2524			−0.861386			−0.430693	+	0.902499i	$0.641731\pi$
$450$		0			0
$451$	4.03677			0.190084
$452$	5.31043	+	2.70580i	0.249782	+	0.127270i
$453$	8.95403	−	3.74241i	0.420697	−	0.175834i
$454$	17.2359	+	23.7231i	0.808919	+	1.11338i
$455$		0			0
$456$	3.77310	+	0.284834i	0.176692	+	0.0133386i
$457$	−15.1979	−	15.1979i	−0.710929	−	0.710929i	0.255800	−	0.966730i	$-0.417661\pi$
$457$	−15.1979	−	15.1979i	−0.710929	−	0.710929i	−0.966730	+	0.255800i	$0.917661\pi$
$458$	−4.68809	−	29.5994i	−0.219060	−	1.38309i
$459$	−3.98597	+	17.3323i	−0.186049	+	0.809004i
$460$		0			0
$461$	−17.1732	+	5.57990i	−0.799835	+	0.259882i	−0.680286	−	0.732946i	$-0.738145\pi$
$461$	−17.1732	+	5.57990i	−0.799835	+	0.259882i	−0.119548	+	0.992828i	$0.538145\pi$
$462$	2.22457	+	1.35347i	0.103496	+	0.0629690i
$463$	4.61839	+	9.06411i	0.214635	+	0.421245i	0.973072	−	0.230502i	$-0.0740367\pi$
$463$	4.61839	+	9.06411i	0.214635	+	0.421245i	−0.758437	+	0.651746i	$0.774037\pi$
$464$	13.6952	+	42.1494i	0.635782	+	1.95674i
$465$		0			0
$466$	1.30868	−	4.02770i	0.0606233	−	0.186579i
$467$	11.1130	−	1.76013i	0.514250	−	0.0814493i	0.106085	−	0.994357i	$-0.466169\pi$
$467$	11.1130	−	1.76013i	0.514250	−	0.0814493i	0.408166	+	0.912908i	$0.366169\pi$
$468$	8.14599	+	24.5367i	0.376549	+	1.13421i
$469$	3.16475	−	4.35591i	0.146135	−	0.201137i
$470$		0			0
$471$	16.2819	+	6.68337i	0.750230	+	0.307954i
$472$	0.186862	+	0.0295960i	0.00860100	+	0.00136226i
$473$	−3.12629	+	6.13568i	−0.143747	+	0.282119i
$474$	11.6362	+	18.8532i	0.534467	+	0.865954i
$475$		0			0
$476$			4.87454i			0.223424i
$477$	8.38483	−	6.17410i	0.383915	−	0.282693i
$478$	6.97514	−	44.0393i	0.319035	−	2.01431i
$479$	14.0049	−	10.1752i	0.639901	−	0.464915i	−0.219915	−	0.975519i	$-0.570578\pi$
$479$	14.0049	−	10.1752i	0.639901	−	0.464915i	0.859816	+	0.510604i	$0.170578\pi$
$480$		0			0
$481$	15.5618	+	11.3063i	0.709556	+	0.515522i
$482$	−3.16099	+	3.16099i	−0.143979	+	0.143979i
$483$	−0.983383	+	0.845332i	−0.0447455	+	0.0384639i
$484$	−17.4233	−	5.66118i	−0.791969	−	0.257326i
$485$		0			0
$486$	1.90709	−	30.4349i	0.0865074	−	1.38056i
$487$	9.46599	−	4.82316i	0.428945	−	0.218558i	−0.226170	−	0.974088i	$-0.572620\pi$
$487$	9.46599	−	4.82316i	0.428945	−	0.218558i	0.655115	+	0.755530i	$0.272620\pi$
$488$	2.88526	−	1.47011i	0.130610	−	0.0665490i
$489$	−25.7494	−	21.8503i	−1.16443	−	0.988105i
$490$		0			0
$491$	−7.07290	−	2.29812i	−0.319195	−	0.103713i	0.145037	−	0.989426i	$-0.453670\pi$
$491$	−7.07290	−	2.29812i	−0.319195	−	0.103713i	−0.464233	+	0.885713i	$0.653670\pi$
$492$	−8.44642	−	9.82580i	−0.380794	−	0.442981i
$493$	24.8497	−	24.8497i	1.11917	−	1.11917i
$494$	−48.1487	−	34.9821i	−2.16631	−	1.57392i
$495$		0			0
$496$	−11.8029	+	8.57533i	−0.529967	+	0.385044i
$497$	−1.05488	+	6.66027i	−0.0473179	+	0.298754i
$498$	0.395183	+	4.82434i	0.0177086	+	0.216184i
$499$		−	22.9184i		−	1.02597i	−0.858398	−	0.512985i	$-0.828540\pi$
$499$		−	22.9184i		−	1.02597i	0.858398	−	0.512985i	$-0.171460\pi$
$500$		0			0
$501$	0.790585	−	0.487949i	0.0353207	−	0.0218000i
$502$	12.7201	−	24.9646i	0.567725	−	1.11422i
$503$	8.38878	+	1.32865i	0.374037	+	0.0592416i	0.340623	−	0.940200i	$-0.389362\pi$
$503$	8.38878	+	1.32865i	0.374037	+	0.0592416i	0.0334140	+	0.999442i	$0.489362\pi$
$504$	0.128925	+	0.781667i	0.00574276	+	0.0348182i
$505$		0			0
$506$	−1.08858	+	1.49831i	−0.0483934	+	0.0666078i
$507$	−3.69172	+	15.5963i	−0.163955	+	0.692655i
$508$	27.4332	−	4.34500i	1.21715	−	0.192778i
$509$	0.901786	−	2.77541i	0.0399710	−	0.123018i	−0.929080	−	0.369879i	$-0.879399\pi$
$509$	0.901786	−	2.77541i	0.0399710	−	0.123018i	0.969051	+	0.246861i	$0.0793991\pi$
$510$		0			0
$511$	−2.17288	−	6.68742i	−0.0961223	−	0.295834i
$512$	−13.8910	−	27.2627i	−0.613902	−	1.20485i
$513$	17.7824	+	28.4041i	0.785113	+	1.25407i
$514$	−11.3451	+	3.68625i	−0.500411	+	0.162594i
$515$		0			0
$516$	21.4761	−	5.22851i	0.945431	−	0.230172i
$517$	0.722048	+	4.55883i	0.0317556	+	0.200497i
$518$	−4.39720	−	4.39720i	−0.193202	−	0.193202i
$519$	−2.07700	+	27.5134i	−0.0911704	+	1.20770i
$520$		0			0
$521$	4.48976	+	6.17962i	0.196700	+	0.270734i	0.895962	−	0.444132i	$-0.146488\pi$
$521$	4.48976	+	6.17962i	0.196700	+	0.270734i	−0.699262	+	0.714866i	$0.746488\pi$
$522$	−35.1066	+	48.9745i	−1.53657	+	2.14356i
$523$	−5.98876	−	3.05143i	−0.261870	−	0.133430i	0.318127	−	0.948048i	$-0.396946\pi$
$523$	−5.98876	−	3.05143i	−0.261870	−	0.133430i	−0.579997	+	0.814619i	$0.696946\pi$
$524$	−2.64269			−0.115447
$525$		0			0
$526$	60.9762			2.65869
$527$	10.3078	+	5.25207i	0.449013	+	0.228784i
$528$	2.84205	+	6.79985i	0.123684	+	0.295925i
$529$	12.9769	+	17.8612i	0.564215	+	0.776575i
$530$		0			0
$531$	0.770203	+	1.48805i	0.0334240	+	0.0645757i
$532$	6.49475	+	6.49475i	0.281583	+	0.281583i
$533$	−3.02189	−	19.0795i	−0.130893	−	0.826423i
$534$	−7.89514	−	32.4292i	−0.341656	−	1.40335i
$535$		0			0
$536$	2.22496	−	0.722933i	0.0961037	−	0.0312260i
$537$	−16.4281	+	27.0013i	−0.708923	+	1.16519i
$538$	13.1006	+	25.7114i	0.564808	+	1.10850i
$539$	1.94724	+	5.99300i	0.0838737	+	0.258137i
$540$		0			0
$541$	−4.34775	+	13.3810i	−0.186924	+	0.575294i	−0.999976	−	0.00689744i	$-0.997804\pi$
$541$	−4.34775	+	13.3810i	−0.186924	+	0.575294i	0.813052	+	0.582191i	$0.197804\pi$
$542$	47.5119	−	7.52515i	2.04081	−	0.323233i
$543$	17.5587	+	4.15624i	0.753516	+	0.178361i
$544$	−15.6242	+	21.5048i	−0.669881	+	0.922012i
$545$		0			0
$546$	4.73176	−	11.5274i	0.202501	−	0.493328i
$547$	18.5296	+	2.93480i	0.792269	+	0.125483i	0.539436	−	0.842027i	$-0.318638\pi$
$547$	18.5296	+	2.93480i	0.792269	+	0.125483i	0.252833	+	0.967510i	$0.418638\pi$
$548$	7.86007	−	15.4263i	0.335766	−	0.658977i
$549$	25.6358	+	12.8566i	1.09411	+	0.548706i
$550$		0			0
$551$		−	66.2186i		−	2.82101i
$552$	−0.561575	+	0.0460011i	−0.0239022	+	0.00195794i
$553$	0.797424	−	5.03474i	0.0339099	−	0.214099i
$554$	5.30365	−	3.85333i	0.225331	−	0.163712i
$555$		0			0
$556$	9.78894	+	7.11208i	0.415143	+	0.301619i
$557$	−4.41902	+	4.41902i	−0.187240	+	0.187240i	−0.794502	−	0.607262i	$-0.792268\pi$
$557$	−4.41902	+	4.41902i	−0.187240	+	0.187240i	0.607262	+	0.794502i	$0.292268\pi$
$558$	−18.9041	−	6.00917i	−0.800275	−	0.254388i
$559$	31.3401	+	10.1830i	1.32555	+	0.430696i
$560$		0			0
$561$	3.78118	−	4.45592i	0.159642	−	0.188129i
$562$	−0.863943	+	0.440201i	−0.0364432	+	0.0185688i
$563$	−39.3209	+	20.0350i	−1.65718	+	0.844375i	−0.661662	+	0.749802i	$0.730149\pi$
$563$	−39.3209	+	20.0350i	−1.65718	+	0.844375i	−0.995518	+	0.0945733i	$0.969851\pi$
$564$	9.58575	−	11.2963i	0.403633	−	0.475660i
$565$		0			0
$566$	−42.6129	−	13.8458i	−1.79115	−	0.581981i
$567$	−4.89754	+	5.02423i	−0.205677	+	0.210998i
$568$	−2.07182	+	2.07182i	−0.0869316	+	0.0869316i
$569$	7.36407	+	5.35031i	0.308718	+	0.224297i	0.731346	−	0.682006i	$-0.238892\pi$
$569$	7.36407	+	5.35031i	0.308718	+	0.224297i	−0.422628	+	0.906303i	$0.638892\pi$
$570$		0			0
$571$	14.7509	−	10.7172i	0.617307	−	0.448500i	−0.234673	−	0.972074i	$-0.575402\pi$
$571$	14.7509	−	10.7172i	0.617307	−	0.448500i	0.851980	+	0.523575i	$0.175402\pi$
$572$	1.32897	−	8.39081i	0.0555672	−	0.350837i
$573$	29.7530	−	2.43720i	1.24295	−	0.101815i
$574$			6.24505i			0.260663i
$575$		0			0
$576$	8.82236	−	17.5916i	0.367598	−	0.732983i
$577$	−15.0501	+	29.5375i	−0.626544	+	1.22966i	0.331613	+	0.943416i	$0.392407\pi$
$577$	−15.0501	+	29.5375i	−0.626544	+	1.22966i	−0.958156	+	0.286245i	$0.907593\pi$
$578$	−10.2119	−	1.61741i	−0.424761	−	0.0672755i
$579$	−12.6413	+	30.7966i	−0.525356	+	1.27986i
$580$		0			0
$581$	0.654629	−	0.901019i	0.0271586	−	0.0373806i
$582$	18.4126	+	4.35835i	0.763226	+	0.180660i
$583$	−3.37947	+	0.535255i	−0.139963	+	0.0221680i
$584$	0.944126	−	2.90572i	0.0390682	−	0.120240i
$585$		0			0
$586$	6.32606	+	19.4696i	0.261327	+	0.804282i
$587$	13.4842	+	26.4642i	0.556551	+	1.09229i	0.982276	+	0.187440i	$0.0600190\pi$
$587$	13.4842	+	26.4642i	0.556551	+	1.09229i	−0.425725	+	0.904853i	$0.639981\pi$
$588$	10.5131	−	17.2793i	0.433551	−	0.712588i
$589$	20.7316	−	6.73611i	0.854232	−	0.277557i
$590$		0			0
$591$	0.876325	+	3.59950i	0.0360472	+	0.148064i
$592$	−2.75328	−	17.3835i	−0.113159	−	0.714459i
$593$	15.2390	+	15.2390i	0.625792	+	0.625792i	0.947006	−	0.321215i	$-0.104091\pi$
$593$	15.2390	+	15.2390i	0.625792	+	0.625792i	−0.321215	+	0.947006i	$0.604091\pi$
$594$	−5.15361	+	8.59359i	−0.211455	+	0.352599i
$595$		0			0
$596$	11.1101	+	15.2917i	0.455087	+	0.626373i
$597$	12.6004	+	30.1475i	0.515699	+	1.23385i
$598$	7.89653	+	4.02348i	0.322913	+	0.164532i
$599$	−29.5824			−1.20870			−0.604351	−	0.796718i	$-0.706568\pi$
$599$	−29.5824			−1.20870			−0.604351	+	0.796718i	$0.706568\pi$
$600$		0			0
$601$	−27.6332			−1.12718			−0.563591	−	0.826054i	$-0.690581\pi$
$601$	−27.6332			−1.12718			−0.563591	+	0.826054i	$0.690581\pi$
$602$	−9.49216	−	4.83650i	−0.386871	−	0.197121i
$603$	16.8397	+	12.0712i	0.685765	+	0.491579i
$604$	6.01643	+	8.28091i	0.244805	+	0.336945i
$605$		0			0
$606$	−0.875760	+	11.6009i	−0.0355753	+	0.471255i
$607$	−20.2336	−	20.2336i	−0.821256	−	0.821256i	0.165032	−	0.986288i	$-0.447227\pi$
$607$	−20.2336	−	20.2336i	−0.821256	−	0.821256i	−0.986288	+	0.165032i	$0.947227\pi$
$608$	7.83528	+	49.4700i	0.317763	+	2.00627i
$609$	13.4708	−	3.27957i	0.545865	−	0.132895i
$610$		0			0
$611$	21.0064	−	6.82540i	0.849829	−	0.276126i
$612$	−18.7577	+	0.119754i	−0.758235	+	0.00484077i
$613$	−6.16521	−	12.0999i	−0.249011	−	0.488711i	0.732340	−	0.680940i	$-0.238428\pi$
$613$	−6.16521	−	12.0999i	−0.249011	−	0.488711i	−0.981350	+	0.192229i	$0.938428\pi$
$614$	−5.94817	−	18.3066i	−0.240049	−	0.738794i
$615$		0			0
$616$	0.0804445	−	0.247583i	0.00324120	−	0.00997540i
$617$	33.3556	−	5.28301i	1.34285	−	0.212686i	0.556694	−	0.830718i	$-0.312070\pi$
$617$	33.3556	−	5.28301i	1.34285	−	0.212686i	0.786153	+	0.618032i	$0.212070\pi$
$618$	3.85653	−	16.2926i	0.155133	−	0.655383i
$619$	−12.4660	+	17.1580i	−0.501052	+	0.689638i	−0.982378	−	0.186903i	$-0.940155\pi$
$619$	−12.4660	+	17.1580i	−0.501052	+	0.689638i	0.481327	+	0.876541i	$0.340155\pi$
$620$		0			0
$621$	−3.27708	−	3.76338i	−0.131504	−	0.151019i
$622$	4.28038	+	0.677945i	0.171628	+	0.0271831i
$623$	−3.48637	+	6.84238i	−0.139678	+	0.274134i
$624$	30.0114	−	18.5230i	1.20142	−	0.741515i
$625$		0			0
$626$			46.9834i			1.87783i
$627$	−0.899007	−	10.9750i	−0.0359029	−	0.438298i
$628$	−2.90396	+	18.3349i	−0.115881	+	0.731642i
$629$	−11.2909	+	8.20329i	−0.450196	+	0.327087i
$630$		0			0
$631$	−6.46706	−	4.69860i	−0.257450	−	0.187048i	0.451572	−	0.892235i	$-0.350863\pi$
$631$	−6.46706	−	4.69860i	−0.257450	−	0.187048i	−0.709022	+	0.705186i	$0.750863\pi$
$632$	1.56616	−	1.56616i	0.0622986	−	0.0622986i
$633$	−5.64882	−	6.57133i	−0.224520	−	0.261187i
$634$	−1.44953	−	0.470981i	−0.0575682	−	0.0187050i
$635$		0			0
$636$	8.37396	+	7.10593i	0.332049	+	0.281768i
$637$	26.8678	−	13.6898i	1.06454	−	0.542410i
$638$	17.6424	−	8.98923i	0.698468	−	0.355887i
$639$	−25.6552	−	3.89566i	−1.01491	−	0.154110i
$640$		0			0
$641$	39.9287	+	12.9736i	1.57709	+	0.512427i	0.961304	−	0.275488i	$-0.0888395\pi$
$641$	39.9287	+	12.9736i	1.57709	+	0.512427i	0.615784	+	0.787915i	$0.288840\pi$
$642$	−8.89306	+	7.64462i	−0.350981	+	0.301709i
$643$	10.8134	−	10.8134i	0.426437	−	0.426437i	−0.460975	−	0.887413i	$-0.652500\pi$
$643$	10.8134	−	10.8134i	0.426437	−	0.426437i	0.887413	+	0.460975i	$0.152500\pi$
$644$	−1.10653	−	0.803941i	−0.0436034	−	0.0316797i
$645$		0			0
$646$	34.9344	−	25.3813i	1.37448	−	0.998615i
$647$	0.0667390	−	0.421374i	0.00262378	−	0.0165659i	−0.986342	−	0.164712i	$-0.947331\pi$
$647$	0.0667390	−	0.421374i	0.00262378	−	0.0165659i	0.988965	+	0.148146i	$0.0473306\pi$
$648$	−3.00476	+	0.515317i	−0.118038	+	0.0202436i
$649$		−	0.550584i		−	0.0216123i
$650$		0			0
$651$	2.39709	+	3.88381i	0.0939494	+	0.152219i
$652$	16.1707	−	31.7368i	0.633293	−	1.24291i
$653$	−8.39719	−	1.32998i	−0.328608	−	0.0520463i	−0.0100490	−	0.999950i	$-0.503199\pi$
$653$	−8.39719	−	1.32998i	−0.328608	−	0.0520463i	−0.318559	+	0.947903i	$0.603199\pi$
$654$	7.26391	+	2.98168i	0.284042	+	0.116593i
$655$		0			0
$656$	−10.3892	+	14.2995i	−0.405630	+	0.558302i
$657$	25.6804	−	8.52571i	1.00189	−	0.332620i
$658$	−7.05270	+	1.11704i	−0.274943	+	0.0435467i
$659$	11.7433	−	36.1421i	0.457453	−	1.40790i	−0.410778	−	0.911735i	$-0.634743\pi$
$659$	11.7433	−	36.1421i	0.457453	−	1.40790i	0.868231	−	0.496160i	$-0.165257\pi$
$660$		0			0
$661$	5.76600	+	17.7459i	0.224271	+	0.690236i	0.998365	+	0.0571648i	$0.0182061\pi$
$661$	5.76600	+	17.7459i	0.224271	+	0.690236i	−0.774093	+	0.633071i	$0.781794\pi$
$662$	−13.3119	−	26.1261i	−0.517382	−	1.01542i
$663$	−23.8911	−	14.5358i	−0.927854	−	0.564524i
$664$	0.460233	−	0.149539i	0.0178605	−	0.00580323i
$665$		0			0
$666$	16.8128	−	17.0288i	0.651482	−	0.659854i
$667$	1.54255	+	9.73930i	0.0597279	+	0.377107i
$668$	0.692884	+	0.692884i	0.0268085	+	0.0268085i
$669$	21.0258	+	1.58725i	0.812904	+	0.0613666i
$670$		0			0
$671$	−5.53919	−	7.62404i	−0.213838	−	0.294323i
$672$	−9.67562	+	4.04400i	−0.373245	+	0.156001i
$673$	−13.5503	−	6.90421i	−0.522325	−	0.266138i	0.172888	−	0.984941i	$-0.444690\pi$
$673$	−13.5503	−	6.90421i	−0.522325	−	0.266138i	−0.695213	+	0.718804i	$0.744690\pi$
$674$	−47.1547			−1.81633
$675$		0			0
$676$	−16.9044			−0.650169
$677$	−6.94944	−	3.54092i	−0.267089	−	0.136089i	0.315318	−	0.948986i	$-0.397889\pi$
$677$	−6.94944	−	3.54092i	−0.267089	−	0.136089i	−0.582407	+	0.812898i	$0.697889\pi$
$678$	10.1992	−	4.26285i	0.391699	−	0.163714i
$679$	−2.55892	−	3.52205i	−0.0982024	−	0.135164i
$680$		0			0
$681$	25.8893	+	1.95440i	0.992081	+	0.0748929i
$682$	4.60901	+	4.60901i	0.176488	+	0.176488i
$683$	2.04378	+	12.9039i	0.0782029	+	0.493754i	0.995438	+	0.0954080i	$0.0304156\pi$
$683$	2.04378	+	12.9039i	0.0782029	+	0.493754i	−0.917235	+	0.398346i	$0.869584\pi$
$684$	−24.8328	+	25.1520i	−0.949507	+	0.961709i
$685$		0			0
$686$	−19.4244	+	6.31136i	−0.741626	+	0.240969i
$687$	−22.6682	−	13.7917i	−0.864844	−	0.526187i
$688$	−13.6886	−	26.8653i	−0.521872	−	1.02423i
$689$	5.05968	+	15.5721i	0.192759	+	0.593250i
$690$		0			0
$691$	−13.0283	+	40.0970i	−0.495620	+	1.52536i	0.320368	+	0.947293i	$0.396193\pi$
$691$	−13.0283	+	40.0970i	−0.495620	+	1.52536i	−0.815988	+	0.578068i	$0.803807\pi$
$692$	−28.7434	+	4.55251i	−1.09266	+	0.173061i
$693$	2.18811	−	0.726436i	0.0831194	−	0.0275950i
$694$	37.1724	−	51.1634i	1.41105	−	1.94214i
$695$		0			0
$696$	5.57288	+	2.28755i	0.211240	+	0.0867093i
$697$	13.8431	+	2.19254i	0.524346	+	0.0830482i
$698$	7.52071	−	14.7602i	0.284663	−	0.558682i
$699$	−1.96938	−	3.19083i	−0.0744889	−	0.120688i
$700$		0			0
$701$			42.0365i			1.58770i	0.608116	+	0.793848i	$0.291925\pi$
$701$			42.0365i			1.58770i	−0.608116	+	0.793848i	$0.708075\pi$
$702$	44.4749	+	17.9251i	1.67860	+	0.676538i
$703$	−4.11382	+	25.9737i	−0.155156	+	0.979615i
$704$	−5.23172	+	3.80106i	−0.197178	+	0.143258i
$705$		0			0
$706$	−53.2567	−	38.6932i	−2.00434	−	1.45624i
$707$	1.89277	−	1.89277i	0.0711848	−	0.0711848i
$708$	−1.34016	+	1.15203i	−0.0503664	+	0.0432958i
$709$	28.0166	+	9.10314i	1.05219	+	0.341876i	0.783526	−	0.621359i	$-0.213419\pi$
$709$	28.0166	+	9.10314i	1.05219	+	0.341876i	0.268660	+	0.963235i	$0.413419\pi$
$710$		0			0
$711$	19.3937	+	2.94487i	0.727322	+	0.110441i
$712$	−2.97305	+	1.51485i	−0.111420	+	0.0567712i
$713$	−2.89225	+	1.47368i	−0.108316	+	0.0551896i
$714$	6.89350	+	5.84965i	0.257983	+	0.218918i
$715$		0			0
$716$	−31.7043	−	10.3014i	−1.18485	−	0.384980i
$717$	−25.7349	−	29.9377i	−0.961089	−	1.11804i
$718$	−10.6896	+	10.6896i	−0.398933	+	0.398933i
$719$	25.9550	+	18.8574i	0.967957	+	0.703262i	0.954985	−	0.296654i	$-0.0958708\pi$
$719$	25.9550	+	18.8574i	0.967957	+	0.703262i	0.0129720	+	0.999916i	$0.495871\pi$
$720$		0			0
$721$	−3.11653	+	2.26429i	−0.116066	+	0.0843265i
$722$	6.91392	−	43.6527i	0.257309	−	1.62459i
$723$	0.323137	+	3.94481i	0.0120176	+	0.146709i
$724$			19.0314i			0.707297i
$725$		0			0
$726$	−28.9146	+	17.8461i	−1.07312	+	0.662332i
$727$	−21.4016	+	42.0031i	−0.793742	+	1.55781i	0.0357969	+	0.999359i	$0.488603\pi$
$727$	−21.4016	+	42.0031i	−0.793742	+	1.55781i	−0.829539	+	0.558448i	$0.811397\pi$
$728$	−1.23040	−	0.194876i	−0.0456017	−	0.00722260i
$729$	−19.4540	−	18.7227i	−0.720519	−	0.693435i
$730$		0			0
$731$	−14.0534	+	19.3428i	−0.519784	+	0.715421i
$732$	−6.96745	+	29.4351i	−0.257524	+	1.08795i
$733$	3.67592	−	0.582209i	0.135773	−	0.0215044i	−0.0881779	−	0.996105i	$-0.528104\pi$
$733$	3.67592	−	0.582209i	0.135773	−	0.0215044i	0.223951	+	0.974600i	$0.428104\pi$
$734$	−7.20426	+	22.1724i	−0.265914	+	0.818399i
$735$		0			0
$736$	−2.30480	−	7.09343i	−0.0849559	−	0.261467i
$737$	−3.09091	−	6.06625i	−0.113855	−	0.223453i
$738$	−24.0315	+	0.153423i	−0.884612	+	0.00564759i
$739$	−45.0233	+	14.6289i	−1.65621	+	0.538134i	−0.980072	−	0.198643i	$-0.936347\pi$
$739$	−45.0233	+	14.6289i	−1.65621	+	0.538134i	−0.676136	+	0.736777i	$0.736347\pi$
$740$		0			0
$741$	−51.1993	+	12.4649i	−1.88085	+	0.457908i
$742$	−0.828062	−	5.22818i	−0.0303991	−	0.191932i
$743$	−37.4947	−	37.4947i	−1.37555	−	1.37555i	−0.851991	−	0.523556i	$-0.824605\pi$
$743$	−37.4947	−	37.4947i	−1.37555	−	1.37555i	−0.523556	−	0.851991i	$-0.675395\pi$
$744$	−0.149279	+	1.97745i	−0.00547284	+	0.0724970i
$745$		0			0
$746$	−29.0677	−	40.0083i	−1.06424	−	1.46481i
$747$	3.48329	+	2.49694i	0.127447	+	0.0913581i
$748$	5.49203	+	2.79833i	0.200809	+	0.102317i
$749$	2.69823			0.0985913
$750$		0			0
$751$	−21.2697			−0.776142			−0.388071	−	0.921629i	$-0.626858\pi$
$751$	−21.2697			−0.776142			−0.388071	+	0.921629i	$0.626858\pi$
$752$	−18.0071	−	9.17508i	−0.656652	−	0.334581i
$753$	−9.56654	−	22.8887i	−0.348624	−	0.834112i
$754$	−55.6938	−	76.6559i	−2.02825	−	2.79164i
$755$		0			0
$756$	−6.34654	−	3.80605i	−0.230821	−	0.138425i
$757$	−22.1455	−	22.1455i	−0.804891	−	0.804891i	0.178964	−	0.983856i	$-0.442725\pi$
$757$	−22.1455	−	22.1455i	−0.804891	−	0.804891i	−0.983856	+	0.178964i	$0.942725\pi$
$758$	−5.85746	−	36.9825i	−0.212752	−	1.34327i
$759$	0.387885	+	1.59323i	0.0140793	+	0.0578307i
$760$		0			0
$761$	33.4555	−	10.8703i	1.21276	−	0.394050i	0.368320	−	0.929699i	$-0.379933\pi$
$761$	33.4555	−	10.8703i	1.21276	−	0.394050i	0.844440	+	0.535649i	$0.179933\pi$
$762$	26.7764	−	44.0098i	0.970006	−	1.59431i
$763$	−0.820194	−	1.60972i	−0.0296930	−	0.0582758i
$764$	9.72984	+	29.9454i	0.352013	+	1.08339i
$765$		0			0
$766$	12.8106	−	39.4271i	0.462867	−	1.42456i
$767$	−2.60229	+	0.412162i	−0.0939632	+	0.0148823i
$768$	−31.0148	−	7.34138i	−1.11915	−	0.264909i
$769$	−17.0696	+	23.4943i	−0.615545	+	0.847225i	−0.997019	−	0.0771542i	$-0.975417\pi$
$769$	−17.0696	+	23.4943i	−0.615545	+	0.847225i	0.381474	+	0.924380i	$0.375417\pi$
$770$		0			0
$771$	−4.01070	+	9.77079i	−0.144442	+	0.351886i
$772$	−34.6798	−	5.49273i	−1.24815	−	0.197688i
$773$	−17.9588	+	35.2461i	−0.645933	+	1.26771i	0.303227	+	0.952918i	$0.401936\pi$
$773$	−17.9588	+	35.2461i	−0.645933	+	1.26771i	−0.949159	+	0.314796i	$0.898064\pi$
$774$	18.3781	−	36.6455i	0.660587	−	1.31720i
$775$		0			0
$776$		−	1.89162i		−	0.0679051i
$777$	−5.48756	+	0.449510i	−0.196865	+	0.0161261i
$778$	−3.32511	+	20.9939i	−0.119211	+	0.752669i
$779$	21.3656	−	15.5230i	0.765503	−	0.556170i
$780$		0			0
$781$	6.89839	+	5.01197i	0.246844	+	0.179342i
$782$	−4.54683	+	4.54683i	−0.162594	+	0.162594i
$783$	12.9510	+	51.7564i	0.462832	+	1.84962i
$784$	−26.2406	−	8.52609i	−0.937165	−	0.304503i
$785$		0			0
$786$	−3.17134	+	3.73725i	−0.113118	+	0.133303i
$787$	11.8192	−	6.02216i	0.421307	−	0.214667i	−0.230466	−	0.973080i	$-0.574025\pi$
$787$	11.8192	−	6.02216i	0.421307	−	0.214667i	0.651774	+	0.758413i	$0.274025\pi$
$788$	−3.48151	+	1.77392i	−0.124024	+	0.0631931i
$789$	34.9314	−	41.1648i	1.24359	−	1.46551i
$790$		0			0
$791$	−2.41892	−	0.785955i	−0.0860069	−	0.0279453i
$792$	0.954698	+	0.303476i	0.0339237	+	0.0107835i
$793$	−31.8878	+	31.8878i	−1.13237	+	1.13237i
$794$	12.1294	+	8.81254i	0.430457	+	0.312745i
$795$		0			0
$796$	−27.8811	+	20.2568i	−0.988220	+	0.717984i
$797$	−3.63324	+	22.9393i	−0.128696	+	0.812553i	0.835912	+	0.548864i	$0.184939\pi$
$797$	−3.63324	+	22.9393i	−0.128696	+	0.812553i	−0.964608	+	0.263690i	$0.915061\pi$
$798$	16.9787	−	1.39080i	0.601040	−	0.0492339i
$799$			16.0256i			0.566945i
$800$		0			0
$801$	−26.4158	−	13.2478i	−0.933355	−	0.468087i
$802$	−18.4031	+	36.1181i	−0.649836	+	1.27538i
$803$	−8.78194	−	1.39092i	−0.309908	−	0.0490846i
$804$	−8.29838	+	20.2163i	−0.292661	+	0.712975i
$805$		0			0
$806$	18.3339	−	25.2344i	0.645783	−	0.888844i
$807$	24.8627	+	5.88513i	0.875208	+	0.207166i
$808$	1.14875	−	0.181945i	0.0404130	−	0.00640080i
$809$	−7.57984	+	23.3283i	−0.266493	+	0.820181i	0.724853	+	0.688904i	$0.241908\pi$
$809$	−7.57984	+	23.3283i	−0.266493	+	0.820181i	−0.991346	+	0.131277i	$0.958092\pi$
$810$		0			0
$811$	−7.17737	−	22.0897i	−0.252032	−	0.775674i	−0.994400	−	0.105682i	$-0.966298\pi$
$811$	−7.17737	−	22.0897i	−0.252032	−	0.775674i	0.742368	−	0.669992i	$-0.233702\pi$
$812$	6.63873	+	13.0292i	0.232974	+	0.457237i
$813$	22.1380	−	36.3861i	0.776413	−	1.27612i
$814$	−7.47852	+	2.42992i	−0.262122	+	0.0851686i
$815$		0			0
$816$	6.05286	+	24.8621i	0.211893	+	0.870347i
$817$	7.04756	+	44.4965i	0.246563	+	1.55674i
$818$	−44.1115	−	44.1115i	−1.54232	−	1.54232i
$819$	−5.07144	−	9.79812i	−0.177211	−	0.342374i
$820$		0			0
$821$	14.1182	+	19.4320i	0.492729	+	0.678183i	0.980888	−	0.194572i	$-0.0623317\pi$
$821$	14.1182	+	19.4320i	0.492729	+	0.678183i	−0.488160	+	0.872754i	$0.662332\pi$
$822$	−12.3831	−	29.6277i	−0.431912	−	1.03339i
$823$	26.7301	+	13.6197i	0.931752	+	0.474751i	0.852865	−	0.522132i	$-0.174863\pi$
$823$	26.7301	+	13.6197i	0.931752	+	0.474751i	0.0788873	+	0.996884i	$0.474863\pi$
$824$	−1.67382			−0.0583102
$825$		0			0
$826$	0.851776			0.0296371
$827$	−6.22861	−	3.17364i	−0.216590	−	0.110358i	0.342330	−	0.939580i	$-0.388784\pi$
$827$	−6.22861	−	3.17364i	−0.216590	−	0.110358i	−0.558920	+	0.829222i	$0.688784\pi$
$828$	3.06645	−	4.27778i	0.106567	−	0.148663i
$829$	−4.72836	−	6.50802i	−0.164223	−	0.226033i	0.718973	−	0.695038i	$-0.244613\pi$
$829$	−4.72836	−	6.50802i	−0.164223	−	0.226033i	−0.883195	+	0.469005i	$0.844613\pi$
$830$		0			0
$831$	0.436935	−	5.78793i	0.0151571	−	0.200781i
$832$	21.8818	+	21.8818i	0.758617	+	0.758617i
$833$	3.42256	+	21.6092i	0.118585	+	0.748715i
$834$	21.8049	−	5.30856i	0.755042	−	0.183821i
$835$		0			0
$836$	11.0459	−	3.58904i	0.382031	−	0.124129i
$837$	−14.8864	+	9.31964i	−0.514549	+	0.322134i
$838$	−11.4811	−	22.5328i	−0.396606	−	0.778384i
$839$	3.47947	+	10.7087i	0.120125	+	0.369706i	0.992981	−	0.118271i	$-0.0377351\pi$
$839$	3.47947	+	10.7087i	0.120125	+	0.369706i	−0.872857	+	0.487977i	$0.837735\pi$
$840$		0			0
$841$	23.6164	−	72.6838i	0.814358	−	2.50634i
$842$	−23.7118	+	3.75557i	−0.817161	+	0.129426i
$843$	−0.197749	+	0.835423i	−0.00681084	+	0.0287735i
$844$	5.37223	−	7.39424i	0.184920	−	0.254520i
$845$		0			0
$846$	−4.47173	−	27.1120i	−0.153741	−	0.932130i
$847$	7.72166	+	1.22299i	0.265319	+	0.0420224i
$848$	6.80150	−	13.3487i	0.233565	−	0.458396i
$849$	−33.7589	+	20.8360i	−1.15860	+	0.715089i
$850$		0			0
$851$		−	3.91599i		−	0.134238i
$852$	−2.23447	−	27.2781i	−0.0765517	−	0.934533i
$853$	−2.39903	+	15.1469i	−0.0821411	+	0.518619i	0.911970	+	0.410256i	$0.134561\pi$
$853$	−2.39903	+	15.1469i	−0.0821411	+	0.518619i	−0.994111	+	0.108362i	$0.965439\pi$
$854$	11.7947	−	8.56936i	0.403607	−	0.293237i
$855$		0			0
$856$	0.948489	+	0.689118i	0.0324187	+	0.0235536i
$857$	−2.97404	+	2.97404i	−0.101591	+	0.101591i	−0.756076	−	0.654484i	$-0.772886\pi$
$857$	−2.97404	+	2.97404i	−0.101591	+	0.101591i	0.654484	+	0.756076i	$0.272886\pi$
$858$	−10.2713	−	11.9487i	−0.350657	−	0.407923i
$859$	24.1552	+	7.84850i	0.824165	+	0.267787i	0.690585	−	0.723251i	$-0.257353\pi$
$859$	24.1552	+	7.84850i	0.824165	+	0.267787i	0.133579	+	0.991038i	$0.457353\pi$
$860$		0			0
$861$	4.21601	+	3.57760i	0.143681	+	0.121924i
$862$	−70.1681	+	35.7524i	−2.38993	+	1.21773i
$863$	12.0203	−	6.12466i	0.409177	−	0.208486i	−0.237272	−	0.971443i	$-0.576253\pi$
$863$	12.0203	−	6.12466i	0.409177	−	0.208486i	0.646449	+	0.762957i	$0.276253\pi$
$864$	−15.7994	−	37.1333i	−0.537507	−	1.26330i
$865$		0			0
$866$	1.29689	+	0.421384i	0.0440700	+	0.0143192i
$867$	−6.94203	+	5.96748i	−0.235764	+	0.202666i
$868$	−3.40385	+	3.40385i	−0.115534	+	0.115534i
$869$	−5.21474	−	3.78873i	−0.176898	−	0.128524i
$870$		0			0
$871$	−26.3578	+	19.1501i	−0.893100	+	0.648875i
$872$	0.122800	−	0.775327i	0.00415852	−	0.0262559i
$873$	13.4903	−	9.93350i	0.456578	−	0.336198i
$874$			12.1162i			0.409837i
$875$		0			0
$876$	14.9895	+	24.2862i	0.506447	+	0.820556i
$877$	6.83909	−	13.4225i	0.230940	−	0.453245i	−0.746235	−	0.665683i	$-0.768140\pi$
$877$	6.83909	−	13.4225i	0.230940	−	0.453245i	0.977175	+	0.212438i	$0.0681404\pi$
$878$	66.2600	+	10.4946i	2.23617	+	0.354174i
$879$	16.7679	+	6.88286i	0.565567	+	0.232153i
$880$		0			0
$881$	26.2832	−	36.1757i	0.885504	−	1.21879i	−0.0893619	−	0.995999i	$-0.528483\pi$
$881$	26.2832	−	36.1757i	0.885504	−	1.21879i	0.974866	−	0.222792i	$-0.0715172\pi$
$882$	−11.8200	−	35.6033i	−0.398001	−	1.19883i
$883$	17.2484	−	2.73187i	0.580454	−	0.0919349i	0.140699	−	0.990052i	$-0.455065\pi$
$883$	17.2484	−	2.73187i	0.580454	−	0.0919349i	0.439755	+	0.898118i	$0.355065\pi$
$884$	9.11480	−	28.0525i	0.306564	−	0.943506i
$885$		0			0
$886$	17.3227	+	53.3138i	0.581968	+	1.79111i
$887$	19.0088	+	37.3069i	0.638253	+	1.25264i	0.952857	+	0.303420i	$0.0981284\pi$
$887$	19.0088	+	37.3069i	0.638253	+	1.25264i	−0.314604	+	0.949223i	$0.601872\pi$
$888$	−2.04380	−	1.24349i	−0.0685855	−	0.0417287i
$889$	−11.2727	+	3.66273i	−0.378075	+	0.122844i
$890$		0			0
$891$	2.84915	+	8.40220i	0.0954501	+	0.281484i
$892$	3.47904	+	21.9658i	0.116487	+	0.735468i
$893$	21.3522	+	21.3522i	0.714524	+	0.714524i
$894$	34.9578	+	2.63899i	1.16916	+	0.0882610i
$895$		0			0
$896$	1.23711	+	1.70273i	0.0413288	+	0.0568842i
$897$	7.23993	−	3.02599i	0.241734	−	0.101035i
$898$	−31.8143	−	16.2102i	−1.06166	−	0.540941i
$899$	34.7047			1.15747
$900$		0			0
$901$	−11.8798			−0.395774
$902$	7.03615	+	3.58510i	0.234278	+	0.119371i
$903$	−8.70288	+	3.63744i	−0.289614	+	0.121046i
$904$	−0.649574	−	0.894062i	−0.0216045	−	0.0297361i
$905$		0			0
$906$	18.9307	+	1.42909i	0.628930	+	0.0474783i
$907$	3.29748	+	3.29748i	0.109491	+	0.109491i	0.759730	−	0.650239i	$-0.225331\pi$
$907$	3.29748	+	3.29748i	0.109491	+	0.109491i	−0.650239	+	0.759730i	$0.725331\pi$
$908$	4.28379	+	27.0468i	0.142162	+	0.897578i
$909$	7.33004	+	7.23704i	0.243122	+	0.240038i
$910$		0			0
$911$	−32.2491	+	10.4784i	−1.06846	+	0.347164i	−0.789888	−	0.613251i	$-0.789861\pi$
$911$	−32.2491	+	10.4784i	−1.06846	+	0.347164i	−0.278573	+	0.960415i	$0.589861\pi$
$912$	41.1905	+	25.0611i	1.36395	+	0.829855i
$913$	−0.639354	−	1.25480i	−0.0211595	−	0.0415279i
$914$	−12.9928	−	39.9877i	−0.429763	−	1.32267i
$915$		0			0
$916$	8.64822	−	26.6165i	0.285745	−	0.879433i
$917$	1.11387	−	0.176419i	0.0367831	−	0.00582587i
$918$	−22.3406	+	26.6705i	−0.737351	+	0.880258i
$919$	26.7422	−	36.8075i	0.882144	−	1.21417i	−0.0936779	−	0.995603i	$-0.529862\pi$
$919$	26.7422	−	36.8075i	0.882144	−	1.21417i	0.975822	−	0.218565i	$-0.0701376\pi$
$920$		0			0
$921$	−15.7663	−	6.47171i	−0.519516	−	0.213250i
$922$	−34.8887	−	5.52582i	−1.14900	−	0.181983i
$923$	18.5246	−	36.3566i	0.609745	−	1.19669i
$924$	1.27718	+	2.06932i	0.0420162	+	0.0680755i
$925$		0			0
$926$			19.9005i			0.653972i
$927$	−8.78976	−	11.9371i	−0.288693	−	0.392064i
$928$	−12.4743	+	78.7595i	−0.409488	+	2.58541i
$929$	28.1643	−	20.4626i	0.924041	−	0.671355i	−0.0204855	−	0.999790i	$-0.506521\pi$
$929$	28.1643	−	20.4626i	0.924041	−	0.671355i	0.944527	+	0.328435i	$0.106521\pi$
$930$		0			0
$931$	33.3519	+	24.2315i	1.09306	+	0.794157i
$932$	2.79651	−	2.79651i	0.0916027	−	0.0916027i
$933$	2.90978	−	2.50130i	0.0952619	−	0.0818887i
$934$	20.9334	+	6.80167i	0.684962	+	0.222558i
$935$		0			0
$936$	0.719674	−	4.73948i	0.0235233	−	0.154915i
$937$	25.5737	−	13.0305i	0.835458	−	0.425687i	0.0167239	−	0.999860i	$-0.494676\pi$
$937$	25.5737	−	13.0305i	0.835458	−	0.425687i	0.818734	+	0.574173i	$0.194676\pi$
$938$	9.38474	−	4.78176i	0.306422	−	0.156130i
$939$	31.7183	+	26.9154i	1.03509	+	0.878351i
$940$		0			0
$941$	−48.7206	−	15.8303i	−1.58825	−	0.516053i	−0.624083	−	0.781358i	$-0.714527\pi$
$941$	−48.7206	−	15.8303i	−1.58825	−	0.516053i	−0.964164	+	0.265305i	$0.914527\pi$
$942$	22.4440	+	26.1093i	0.731266	+	0.850688i
$943$	−2.78081	+	2.78081i	−0.0905556	+	0.0905556i
$944$	1.95034	+	1.41701i	0.0634782	+	0.0461196i
$945$		0			0
$946$	−10.8983	+	7.91810i	−0.354335	+	0.257440i
$947$	−4.38792	+	27.7042i	−0.142588	+	0.900267i	0.807858	+	0.589377i	$0.200627\pi$
$947$	−4.38792	+	27.7042i	−0.142588	+	0.900267i	−0.950446	+	0.310890i	$0.899373\pi$
$948$	1.68912	+	20.6205i	0.0548600	+	0.669723i
$949$			42.5484i			1.38118i
$950$		0			0
$951$	−1.14835	+	0.708762i	−0.0372378	+	0.0229832i
$952$	0.410338	−	0.805334i	0.0132991	−	0.0261010i
$953$	−3.32321	−	0.526345i	−0.107649	−	0.0170500i	0.102377	−	0.994746i	$-0.467355\pi$
$953$	−3.32321	−	0.526345i	−0.107649	−	0.0170500i	−0.210027	+	0.977696i	$0.567355\pi$
$954$	20.0982	−	3.31490i	0.650702	−	0.107324i
$955$		0			0
$956$	24.4748	−	33.6867i	0.791573	−	1.08951i
$957$	4.03818	−	17.0600i	0.130536	−	0.551470i
$958$	33.4475	−	5.29756i	1.08064	−	0.171156i
$959$	−2.28312	+	7.02671i	−0.0737257	+	0.226904i
$960$		0			0
$961$	−6.04918	−	18.6175i	−0.195135	−	0.600563i
$962$	17.0832	+	33.5276i	0.550783	+	1.08097i
$963$	0.0662881	+	10.3831i	0.00213610	+	0.334589i
$964$	−3.97032	+	1.29003i	−0.127875	+	0.0415492i
$965$		0			0
$966$	−2.46480	+	0.600074i	−0.0793036	+	0.0193071i
$967$	−4.46829	−	28.2117i	−0.143690	−	0.907226i	−0.949207	−	0.314653i	$-0.898112\pi$
$967$	−4.46829	−	28.2117i	−0.143690	−	0.907226i	0.805516	−	0.592573i	$-0.201888\pi$
$968$	2.40199	+	2.40199i	0.0772028	+	0.0772028i
$969$	2.87803	−	38.1243i	0.0924556	−	1.22473i
$970$		0			0
$971$	−18.4852	−	25.4427i	−0.593218	−	0.816495i	0.401848	−	0.915706i	$-0.368368\pi$
$971$	−18.4852	−	25.4427i	−0.593218	−	0.816495i	−0.995066	+	0.0992113i	$0.968368\pi$
$972$	14.4901	−	24.5156i	0.464771	−	0.786337i
$973$	−4.60071	−	2.34418i	−0.147492	−	0.0751509i
$974$	20.7829			0.665926
$975$		0			0
$976$	41.2627			1.32079
$977$	4.10325	+	2.09071i	0.131275	+	0.0668877i	0.518394	−	0.855142i	$-0.326530\pi$
$977$	4.10325	+	2.09071i	0.131275	+	0.0668877i	−0.387120	+	0.922029i	$0.626530\pi$
$978$	−25.4761	−	60.9537i	−0.814636	−	1.94909i
$979$	5.70773	+	7.85601i	0.182420	+	0.251079i
$980$		0			0
$981$	6.17421	−	3.19573i	0.197127	−	0.102032i
$982$	−10.2872	−	10.2872i	−0.328277	−	0.328277i
$983$	2.00270	+	12.6446i	0.0638763	+	0.403299i	0.998823	+	0.0485102i	$0.0154473\pi$
$983$	2.00270	+	12.6446i	0.0638763	+	0.403299i	−0.934946	+	0.354789i	$0.884553\pi$
$984$	0.568317	+	2.33436i	0.0181173	+	0.0744166i
$985$		0			0
$986$	65.3827	−	21.2441i	2.08221	−	0.676551i
$987$	−3.28617	+	5.40117i	−0.104600	+	0.171921i
$988$	−25.2322	−	49.5210i	−0.802743	−	1.57547i
$989$	−2.07308	−	6.38029i	−0.0659202	−	0.202882i
$990$		0			0
$991$	−14.7045	+	45.2557i	−0.467103	+	1.43759i	0.389216	+	0.921147i	$0.372746\pi$
$991$	−14.7045	+	45.2557i	−0.467103	+	1.43759i	−0.856319	+	0.516448i	$0.827254\pi$
$992$	−25.9269	+	4.10641i	−0.823179	+	0.130379i
$993$	−25.2636	−	5.98003i	−0.801717	−	0.189771i
$994$	−7.75373	+	10.6721i	−0.245933	+	0.338498i
$995$		0			0
$996$	−1.71652	+	4.18175i	−0.0543900	+	0.132504i
$997$	20.1708	+	3.19474i	0.638816	+	0.101179i	0.467437	−	0.884027i	$-0.345178\pi$
$997$	20.1708	+	3.19474i	0.638816	+	0.101179i	0.171379	+	0.985205i	$0.445178\pi$
$998$	20.3541	−	39.9472i	0.644297	−	1.26451i
$999$	−1.86457	−	21.1056i	−0.0589924	−	0.667751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.l.a.107.7		64
3.2	odd	2	inner	375.2.l.a.107.2		64
5.2	odd	4		375.2.l.c.143.2		64
5.3	odd	4		75.2.l.a.8.7	yes	64
5.4	even	2		375.2.l.b.107.2		64
15.2	even	4		375.2.l.c.143.7		64
15.8	even	4		75.2.l.a.8.2	✓	64
15.14	odd	2		375.2.l.b.107.7		64
25.3	odd	20	inner	375.2.l.a.368.2		64
25.4	even	10		375.2.l.c.257.7		64
25.21	even	5		75.2.l.a.47.2	yes	64
25.22	odd	20		375.2.l.b.368.7		64
75.29	odd	10		375.2.l.c.257.2		64
75.47	even	20		375.2.l.b.368.2		64
75.53	even	20	inner	375.2.l.a.368.7		64
75.71	odd	10		75.2.l.a.47.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.l.a.8.2	✓	64	15.8	even	4
75.2.l.a.8.7	yes	64	5.3	odd	4
75.2.l.a.47.2	yes	64	25.21	even	5
75.2.l.a.47.7	yes	64	75.71	odd	10
375.2.l.a.107.2		64	3.2	odd	2	inner
375.2.l.a.107.7		64	1.1	even	1	trivial
375.2.l.a.368.2		64	25.3	odd	20	inner
375.2.l.a.368.7		64	75.53	even	20	inner
375.2.l.b.107.2		64	5.4	even	2
375.2.l.b.107.7		64	15.14	odd	2
375.2.l.b.368.2		64	75.47	even	20
375.2.l.b.368.7		64	25.22	odd	20
375.2.l.c.143.2		64	5.2	odd	4
375.2.l.c.143.7		64	15.2	even	4
375.2.l.c.257.2		64	75.29	odd	10
375.2.l.c.257.7		64	25.4	even	10

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.74302 + 0.888111i) q^{2} +(1.59808 - 0.667932i) q^{3} +(1.07379 + 1.47795i) q^{4} +(3.37868 + 0.255059i) q^{6} +(-0.551254 - 0.551254i) q^{7} +(-0.0529901 - 0.334566i) q^{8} +(2.10773 - 2.13482i) q^{9} +(-0.937544 + 0.304626i) q^{11} +(2.70317 + 1.64466i) q^{12} +(2.14163 + 4.20319i) q^{13} +(-0.471270 - 1.45042i) q^{14} +(1.33382 - 4.10508i) q^{16} +(-3.38054 + 0.535425i) q^{17} +(5.56977 - 1.84912i) q^{18} +(-3.79078 + 5.21756i) q^{19} +(-1.24915 - 0.512749i) q^{21} +(-1.90469 - 0.301674i) q^{22} +(0.435998 - 0.855694i) q^{23} +(-0.308150 - 0.499270i) q^{24} +9.22822i q^{26} +(1.94242 - 4.81944i) q^{27} +(0.222792 - 1.40666i) q^{28} +(-8.30669 + 6.03516i) q^{29} +(-2.73448 - 1.98672i) q^{31} +(5.49158 - 5.49158i) q^{32} +(-1.29480 + 1.11303i) q^{33} +(-6.36785 - 2.06904i) q^{34} +(5.41842 + 0.822768i) q^{36} +(3.63316 - 1.85119i) q^{37} +(-11.2411 + 5.72765i) q^{38} +(6.22994 + 5.28657i) q^{39} +(-3.89453 - 1.26541i) q^{41} +(-1.72191 - 2.00311i) q^{42} +(4.93949 - 4.93949i) q^{43} +(-1.45695 - 1.05853i) q^{44} +(1.51990 - 1.10427i) q^{46} +(0.732455 - 4.62454i) q^{47} +(-0.610356 - 7.45115i) q^{48} -6.39224i q^{49} +(-5.04475 + 3.11362i) q^{51} +(-3.91242 + 7.67856i) q^{52} +(3.42818 + 0.542970i) q^{53} +(7.66586 - 6.67528i) q^{54} +(-0.155220 + 0.213642i) q^{56} +(-2.57300 + 10.8701i) q^{57} +(-19.8386 + 3.14212i) q^{58} +(-0.172592 + 0.531183i) q^{59} +(2.95410 + 9.09178i) q^{61} +(-3.00182 - 5.89140i) q^{62} +(-2.33873 + 0.0149310i) q^{63} +(6.23890 - 2.02714i) q^{64} +(-3.24536 + 0.790106i) q^{66} +(1.08040 + 6.82141i) q^{67} +(-4.42132 - 4.42132i) q^{68} +(0.125215 - 1.65869i) q^{69} +(-5.08421 - 6.99781i) q^{71} +(-0.825927 - 0.592052i) q^{72} +(8.03649 + 4.09480i) q^{73} +7.97671 q^{74} -11.7818 q^{76} +(0.684752 + 0.348898i) q^{77} +(6.16382 + 14.7475i) q^{78} +(3.84334 + 5.28990i) q^{79} +(-0.114912 - 8.99927i) q^{81} +(-5.66440 - 5.66440i) q^{82} +(0.223482 + 1.41101i) q^{83} +(-0.583510 - 2.39676i) q^{84} +(12.9964 - 4.22279i) q^{86} +(-9.24369 + 15.1930i) q^{87} +(0.151598 + 0.297528i) q^{88} +(-3.04398 - 9.36841i) q^{89} +(1.13644 - 3.49761i) q^{91} +(1.73284 - 0.274455i) q^{92} +(-5.69692 - 1.34849i) q^{93} +(5.38378 - 7.41014i) q^{94} +(5.10800 - 12.4440i) q^{96} +(5.51558 + 0.873583i) q^{97} +(5.67701 - 11.1418i) q^{98} +(-1.32577 + 2.64356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 20 q^{4} - 6 q^{6} - 20 q^{7} + 10 q^{9} - 40 q^{12} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 30 q^{27} + 80 q^{28} - 12 q^{31} + 50 q^{33} - 20 q^{34} - 22 q^{36} + 120 q^{37} - 30 q^{39} - 60 q^{42}+ \cdots + 42 q^{96}+O(q^{100}) \) 64 * q + 20 * q^4 - 6 * q^6 - 20 * q^7 + 10 * q^9 - 40 * q^12 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 30 * q^27 + 80 * q^28 - 12 * q^31 + 50 * q^33 - 20 * q^34 - 22 * q^36 + 120 * q^37 - 30 * q^39 - 60 * q^42 - 20 * q^43 - 12 * q^46 - 100 * q^48 - 16 * q^51 - 100 * q^52 - 120 * q^54 + 70 * q^57 - 120 * q^58 - 12 * q^61 + 70 * q^63 + 100 * q^64 - 30 * q^66 + 60 * q^67 + 80 * q^69 + 40 * q^72 + 80 * q^73 - 64 * q^76 - 70 * q^78 + 60 * q^79 + 14 * q^81 - 60 * q^82 + 130 * q^84 - 100 * q^87 - 60 * q^88 - 12 * q^91 - 20 * q^93 - 260 * q^94 + 42 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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