LMFDB - Embedded newform 700.2.p.e.551.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(451,700)] 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("700.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0] 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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.4
Character	$\chi$	$=$	700.551
Dual form			700.2.p.e.451.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00031 + 0.999687i) q^{2} +(0.739583 + 1.28100i) q^{3} +(0.00125109 - 2.00000i) q^{4} +(-2.02041 - 0.542044i) q^{6} +(-2.56107 + 0.664037i) q^{7} +(1.99812 + 2.00188i) q^{8} +(0.406034 - 0.703271i) q^{9} +(5.32875 - 3.07655i) q^{11} +(2.56292 - 1.47756i) q^{12} -3.33366i q^{13} +(1.89804 - 3.22451i) q^{14} +(-4.00000 - 0.00500436i) q^{16} +(2.21000 - 1.27594i) q^{17} +(0.296890 + 1.10940i) q^{18} +(0.352781 - 0.611035i) q^{19} +(-2.74475 - 2.78960i) q^{21} +(-2.25482 + 8.40459i) q^{22} +(1.70332 + 0.983411i) q^{23} +(-1.08662 + 4.04014i) q^{24} +(3.33262 + 3.33470i) q^{26} +5.63868 q^{27} +(1.32487 + 5.12296i) q^{28} -5.17926 q^{29} +(3.40156 + 5.89167i) q^{31} +(4.00625 - 3.99374i) q^{32} +(7.88210 + 4.55073i) q^{33} +(-0.935146 + 3.48565i) q^{34} +(-1.40603 - 0.812947i) q^{36} +(3.40886 - 5.90431i) q^{37} +(0.257952 + 0.963897i) q^{38} +(4.27040 - 2.46552i) q^{39} -2.53373i q^{41} +(5.53434 + 0.0465848i) q^{42} +4.59892i q^{43} +(-6.14644 - 10.6613i) q^{44} +(-2.68695 + 0.719067i) q^{46} +(-2.18463 + 3.78388i) q^{47} +(-2.95192 - 5.12768i) q^{48} +(6.11811 - 3.40128i) q^{49} +(3.26896 + 1.88733i) q^{51} +(-6.66732 - 0.00417071i) q^{52} +(-2.77664 - 4.80929i) q^{53} +(-5.64044 + 5.63692i) q^{54} +(-6.44664 - 3.80011i) q^{56} +1.04364 q^{57} +(5.18088 - 5.17764i) q^{58} +(3.40156 + 5.89167i) q^{59} +(3.07800 + 1.77708i) q^{61} +(-9.29244 - 2.49302i) q^{62} +(-0.572881 + 2.07074i) q^{63} +(-0.0150131 + 7.99999i) q^{64} +(-12.4339 + 3.32748i) q^{66} +(2.51253 - 1.45061i) q^{67} +(-2.54912 - 4.42159i) q^{68} +2.90926i q^{69} -3.37084i q^{71} +(2.21917 - 0.592393i) q^{72} +(2.21000 - 1.27594i) q^{73} +(2.49254 + 9.31395i) q^{74} +(-1.22163 - 0.706327i) q^{76} +(-11.6043 + 11.4177i) q^{77} +(-1.80699 + 6.73536i) q^{78} +(5.38564 + 3.10940i) q^{79} +(2.95217 + 5.11331i) q^{81} +(2.53294 + 2.53452i) q^{82} -4.70266 q^{83} +(-5.58264 + 5.48601i) q^{84} +(-4.59748 - 4.60036i) q^{86} +(-3.83049 - 6.63461i) q^{87} +(16.8064 + 4.52016i) q^{88} +(5.19692 + 3.00044i) q^{89} +(2.21367 + 8.53772i) q^{91} +(1.96895 - 3.40541i) q^{92} +(-5.03147 + 8.71475i) q^{93} +(-1.59739 - 5.96901i) q^{94} +(8.07892 + 2.17829i) q^{96} +9.46331i q^{97} +(-2.71980 + 9.51854i) q^{98} -4.99674i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 6 q^{4} - 4 q^{9} - 22 q^{14} + 18 q^{16} - 52 q^{21} + 48 q^{24} - 18 q^{26} - 28 q^{36} + 26 q^{44} - 22 q^{46} - 48 q^{54} - 16 q^{56} + 36 q^{61} - 36 q^{64} - 24 q^{66} - 14 q^{74} + 72 q^{81}+ \cdots + 60 q^{96}+O(q^{100}) $ 32 * q - 6 * q^4 - 4 * q^9 - 22 * q^14 + 18 * q^16 - 52 * q^21 + 48 * q^24 - 18 * q^26 - 28 * q^36 + 26 * q^44 - 22 * q^46 - 48 * q^54 - 16 * q^56 + 36 * q^61 - 36 * q^64 - 24 * q^66 - 14 * q^74 + 72 * q^81 - 56 * q^84 + 8 * q^86 + 108 * q^89 - 30 * q^94 + 60 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.00031	+	0.999687i	−0.707328	+	0.706886i
$2$	−1.00031	+	0.999687i	−0.707328	+	0.706886i
$3$	0.739583	+	1.28100i	0.426999	+	0.739583i	0.996605	−	0.0823346i	$-0.0262376\pi$
$3$	0.739583	+	1.28100i	0.426999	+	0.739583i	−0.569606	+	0.821918i	$0.692904\pi$
$4$	0.00125109	−	2.00000i	0.000625545	−	1.00000i
$5$		0			0
$5$		0			0
$6$	−2.02041	−	0.542044i	−0.824829	−	0.221289i
$7$	−2.56107	+	0.664037i	−0.967992	+	0.250982i
$7$	−2.56107	+	0.664037i	−0.967992	+	0.250982i
$8$	1.99812	+	2.00188i	0.706443	+	0.707770i
$9$	0.406034	−	0.703271i	0.135345	−	0.234424i
$10$		0			0
$11$	5.32875	−	3.07655i	1.60668	−	0.927616i	0.616570	−	0.787300i	$-0.288522\pi$
$11$	5.32875	−	3.07655i	1.60668	−	0.927616i	0.990107	−	0.140316i	$-0.0448118\pi$
$12$	2.56292	−	1.47756i	0.739850	−	0.426536i
$13$		−	3.33366i		−	0.924591i	−0.886726	−	0.462295i	$-0.847026\pi$
$13$		−	3.33366i		−	0.924591i	0.886726	−	0.462295i	$-0.152974\pi$
$14$	1.89804	−	3.22451i	0.507272	−	0.861786i
$15$		0			0
$16$	−4.00000	−	0.00500436i	−0.999999	−	0.00125109i
$17$	2.21000	−	1.27594i	0.536004	−	0.309462i	−0.207454	−	0.978245i	$-0.566518\pi$
$17$	2.21000	−	1.27594i	0.536004	−	0.309462i	0.743458	+	0.668783i	$0.233184\pi$
$18$	0.296890	+	1.10940i	0.0699777	+	0.261488i
$19$	0.352781	−	0.611035i	0.0809335	−	0.140181i	−0.822718	−	0.568450i	$-0.807543\pi$
$19$	0.352781	−	0.611035i	0.0809335	−	0.140181i	0.903651	+	0.428269i	$0.140877\pi$
$20$		0			0
$21$	−2.74475	−	2.78960i	−0.598953	−	0.608741i
$22$	−2.25482	+	8.40459i	−0.480730	+	1.79187i
$23$	1.70332	+	0.983411i	0.355166	+	0.205055i	0.666958	−	0.745095i	$-0.267596\pi$
$23$	1.70332	+	0.983411i	0.355166	+	0.205055i	−0.311792	+	0.950150i	$0.600929\pi$
$24$	−1.08662	+	4.04014i	−0.221805	+	0.824690i
$25$		0			0
$26$	3.33262	+	3.33470i	0.653580	+	0.653989i
$27$	5.63868			1.08516
$28$	1.32487	+	5.12296i	0.250377	+	0.968148i
$29$	−5.17926			−0.961765			−0.480882	−	0.876785i	$-0.659684\pi$
$29$	−5.17926			−0.961765			−0.480882	+	0.876785i	$0.659684\pi$
$30$		0			0
$31$	3.40156	+	5.89167i	0.610937	+	1.05817i	0.991083	+	0.133248i	$0.0425406\pi$
$31$	3.40156	+	5.89167i	0.610937	+	1.05817i	−0.380145	+	0.924927i	$0.624126\pi$
$32$	4.00625	−	3.99374i	0.708212	−	0.706000i
$33$	7.88210	+	4.55073i	1.37210	+	0.792181i
$34$	−0.935146	+	3.48565i	−0.160376	+	0.597784i
$35$		0			0
$36$	−1.40603	−	0.812947i	−0.234339	−	0.135491i
$37$	3.40886	−	5.90431i	0.560412	−	0.970663i	−0.437048	−	0.899438i	$-0.643976\pi$
$37$	3.40886	−	5.90431i	0.560412	−	0.970663i	0.997460	−	0.0712245i	$-0.0226907\pi$
$38$	0.257952	+	0.963897i	0.0418454	+	0.156365i
$39$	4.27040	−	2.46552i	0.683812	−	0.394799i
$40$		0			0
$41$		−	2.53373i		−	0.395702i	−0.980232	−	0.197851i	$-0.936604\pi$
$41$		−	2.53373i		−	0.395702i	0.980232	−	0.197851i	$-0.0633962\pi$
$42$	5.53434	+	0.0465848i	0.853967	+	0.00718819i
$43$			4.59892i			0.701329i	0.936501	+	0.350664i	$0.114044\pi$
$43$			4.59892i			0.701329i	−0.936501	+	0.350664i	$0.885956\pi$
$44$	−6.14644	−	10.6613i	−0.926610	−	1.60726i
$45$		0			0
$46$	−2.68695	+	0.719067i	−0.396170	+	0.106021i
$47$	−2.18463	+	3.78388i	−0.318660	+	0.551936i	−0.980209	−	0.197966i	$-0.936566\pi$
$47$	−2.18463	+	3.78388i	−0.318660	+	0.551936i	0.661548	+	0.749903i	$0.269900\pi$
$48$	−2.95192	−	5.12768i	−0.426073	−	0.740117i
$49$	6.11811	−	3.40128i	0.874016	−	0.485898i
$50$		0			0
$51$	3.26896	+	1.88733i	0.457746	+	0.264280i
$52$	−6.66732	−	0.00417071i	−0.924590	−	0.000578373i
$53$	−2.77664	−	4.80929i	−0.381401	−	0.660606i	0.609861	−	0.792508i	$-0.291225\pi$
$53$	−2.77664	−	4.80929i	−0.381401	−	0.660606i	−0.991263	+	0.131902i	$0.957892\pi$
$54$	−5.64044	+	5.63692i	−0.767567	+	0.767087i
$55$		0			0
$56$	−6.44664	−	3.80011i	−0.861469	−	0.507811i
$57$	1.04364			0.138234
$58$	5.18088	−	5.17764i	0.680283	−	0.679858i
$59$	3.40156	+	5.89167i	0.442845	+	0.767030i	0.997899	−	0.0647843i	$-0.0206359\pi$
$59$	3.40156	+	5.89167i	0.442845	+	0.767030i	−0.555055	+	0.831814i	$0.687303\pi$
$60$		0			0
$61$	3.07800	+	1.77708i	0.394097	+	0.227532i	0.683934	−	0.729544i	$-0.260268\pi$
$61$	3.07800	+	1.77708i	0.394097	+	0.227532i	−0.289837	+	0.957076i	$0.593601\pi$
$62$	−9.29244	−	2.49302i	−1.18014	−	0.316614i
$63$	−0.572881	+	2.07074i	−0.0721762	+	0.260889i
$64$	−0.0150131	+	7.99999i	−0.00187664	+	0.999998i
$65$		0			0
$66$	−12.4339	+	3.32748i	−1.53050	+	0.409584i
$67$	2.51253	−	1.45061i	0.306954	−	0.177220i	−0.338609	−	0.940927i	$-0.609956\pi$
$67$	2.51253	−	1.45061i	0.306954	−	0.177220i	0.645563	+	0.763707i	$0.276623\pi$
$68$	−2.54912	−	4.42159i	−0.309127	−	0.536197i
$69$			2.90926i			0.350233i
$70$		0			0
$71$		−	3.37084i		−	0.400045i	−0.979791	−	0.200023i	$-0.935898\pi$
$71$		−	3.37084i		−	0.400045i	0.979791	−	0.200023i	$-0.0641016\pi$
$72$	2.21917	−	0.592393i	0.261531	−	0.0698141i
$73$	2.21000	−	1.27594i	0.258661	−	0.149338i	−0.365063	−	0.930983i	$-0.618952\pi$
$73$	2.21000	−	1.27594i	0.258661	−	0.149338i	0.623724	+	0.781645i	$0.285619\pi$
$74$	2.49254	+	9.31395i	0.289752	+	1.08272i
$75$		0			0
$76$	−1.22163	−	0.706327i	−0.140130	−	0.0810212i
$77$	−11.6043	+	11.4177i	−1.32244	+	1.30117i
$78$	−1.80699	+	6.73536i	−0.204601	+	0.762629i
$79$	5.38564	+	3.10940i	0.605932	+	0.349835i	0.771372	−	0.636385i	$-0.219571\pi$
$79$	5.38564	+	3.10940i	0.605932	+	0.349835i	−0.165440	+	0.986220i	$0.552904\pi$
$80$		0			0
$81$	2.95217	+	5.11331i	0.328019	+	0.568146i
$82$	2.53294	+	2.53452i	0.279716	+	0.279891i
$83$	−4.70266			−0.516184			−0.258092	−	0.966120i	$-0.583094\pi$
$83$	−4.70266			−0.516184			−0.258092	+	0.966120i	$0.583094\pi$
$84$	−5.58264	+	5.48601i	−0.609116	+	0.598572i
$85$		0			0
$86$	−4.59748	−	4.60036i	−0.495759	−	0.496069i
$87$	−3.83049	−	6.63461i	−0.410672	−	0.711305i
$88$	16.8064	+	4.52016i	1.79156	+	0.481850i
$89$	5.19692	+	3.00044i	0.550873	+	0.318046i	0.749474	−	0.662034i	$-0.230307\pi$
$89$	5.19692	+	3.00044i	0.550873	+	0.318046i	−0.198601	+	0.980080i	$0.563640\pi$
$90$		0			0
$91$	2.21367	+	8.53772i	0.232056	+	0.894996i
$92$	1.96895	−	3.40541i	0.205278	−	0.355038i
$93$	−5.03147	+	8.71475i	−0.521739	+	0.903678i
$94$	−1.59739	−	5.96901i	−0.164758	−	0.615656i
$95$		0			0
$96$	8.07892	+	2.17829i	0.824551	+	0.222320i
$97$			9.46331i			0.960853i	0.877035	+	0.480427i	$0.159518\pi$
$97$			9.46331i			0.960853i	−0.877035	+	0.480427i	$0.840482\pi$
$98$	−2.71980	+	9.51854i	−0.274742	+	0.961518i
$99$		−	4.99674i		−	0.502191i
$100$		0			0
$101$	−7.67045	+	4.42854i	−0.763238	+	0.440656i	−0.830457	−	0.557082i	$-0.811921\pi$
$101$	−7.67045	+	4.42854i	−0.763238	+	0.440656i	0.0672190	+	0.997738i	$0.478587\pi$
$102$	−5.15672	+	1.38001i	−0.510592	+	0.136641i
$103$	4.24106	−	7.34573i	0.417884	−	0.723796i	−0.577843	−	0.816148i	$-0.696105\pi$
$103$	4.24106	−	7.34573i	0.417884	−	0.723796i	0.995726	+	0.0923523i	$0.0294386\pi$
$104$	6.67357	−	6.66106i	0.654397	−	0.653171i
$105$		0			0
$106$	7.58530	+	2.03502i	0.736749	+	0.197658i
$107$	0.613887	+	0.354428i	0.0593467	+	0.0342638i	0.529380	−	0.848385i	$-0.322425\pi$
$107$	0.613887	+	0.354428i	0.0593467	+	0.0342638i	−0.470033	+	0.882649i	$0.655758\pi$
$108$	0.00705450	−	11.2774i	0.000678820	−	1.08516i
$109$	−1.54614	−	2.67799i	−0.148093	−	0.256505i	0.782429	−	0.622739i	$-0.213980\pi$
$109$	−1.54614	−	2.67799i	−0.148093	−	0.256505i	−0.930523	+	0.366234i	$0.880647\pi$
$110$		0			0
$111$	10.0845			0.957181
$112$	10.2476	−	2.64333i	0.968305	−	0.249771i
$113$	−14.7206			−1.38479			−0.692397	−	0.721517i	$-0.743445\pi$
$113$	−14.7206			−1.38479			−0.692397	+	0.721517i	$0.743445\pi$
$114$	−1.04397	+	1.04332i	−0.0977768	+	0.0977156i
$115$		0			0
$116$	−0.00647973	+	10.3585i	−0.000601627	+	0.961765i
$117$	−2.34447	−	1.35358i	−0.216746	−	0.125138i
$118$	−9.29244	−	2.49302i	−0.855439	−	0.229501i
$119$	−4.81268	+	4.73530i	−0.441178	+	0.434084i
$120$		0			0
$121$	13.4304	−	23.2621i	1.22094	−	2.11473i
$122$	−4.85548	+	1.29940i	−0.439595	+	0.117642i
$123$	3.24570	−	1.87390i	0.292655	−	0.168964i
$124$	11.7876	−	6.79574i	1.05856	−	0.610275i
$125$		0			0
$126$	−1.49704	−	2.64409i	−0.133367	−	0.235555i
$127$			4.48071i			0.397599i	0.980040	+	0.198800i	$0.0637043\pi$
$127$			4.48071i			0.397599i	−0.980040	+	0.198800i	$0.936296\pi$
$128$	−7.98247	−	8.01750i	−0.705557	−	0.708653i
$129$	−5.89120	+	3.40128i	−0.518691	+	0.299466i
$130$		0			0
$131$	8.09104	−	14.0141i	0.706917	−	1.22442i	−0.259078	−	0.965856i	$-0.583419\pi$
$131$	8.09104	−	14.0141i	0.706917	−	1.22442i	0.965995	−	0.258560i	$-0.0832480\pi$
$132$	9.11132	−	15.7585i	0.793039	−	1.37160i
$133$	−0.497746	+	1.79916i	−0.0431600	+	0.156007i
$134$	−1.06316	+	3.96280i	−0.0918429	+	0.342334i
$135$		0			0
$136$	6.97013	+	1.87465i	0.597684	+	0.160750i
$137$	−5.35325	−	9.27211i	−0.457359	−	0.792170i	0.541461	−	0.840726i	$-0.317871\pi$
$137$	−5.35325	−	9.27211i	−0.457359	−	0.792170i	−0.998820	+	0.0485562i	$0.984538\pi$
$138$	−2.90835	−	2.91017i	−0.247575	−	0.247730i
$139$	−16.1633			−1.37095			−0.685475	−	0.728096i	$-0.740406\pi$
$139$	−16.1633			−1.37095			−0.685475	+	0.728096i	$0.740406\pi$
$140$		0			0
$141$	−6.46285			−0.544270
$142$	3.36979	+	3.37190i	0.282786	+	0.282963i
$143$	−10.2562	−	17.7642i	−0.857665	−	1.48552i
$144$	−1.62765	+	2.81105i	−0.135638	+	0.234254i
$145$		0			0
$146$	−0.935146	+	3.48565i	−0.0773932	+	0.288475i
$147$	8.88188	+	5.32174i	0.732565	+	0.438930i
$148$	−11.8044	−	6.82510i	−0.970312	−	0.561019i
$149$	3.79441	−	6.57211i	0.310850	−	0.538408i	−0.667697	−	0.744434i	$-0.732720\pi$
$149$	3.79441	−	6.57211i	0.310850	−	0.538408i	0.978547	+	0.206025i	$0.0660530\pi$
$150$		0			0
$151$	−1.80399	+	1.04154i	−0.146807	+	0.0847590i	−0.571604	−	0.820530i	$-0.693679\pi$
$151$	−1.80399	+	1.04154i	−0.146807	+	0.0847590i	0.424797	+	0.905288i	$0.360345\pi$
$152$	1.92812	−	0.514698i	0.156391	−	0.0417476i
$153$		−	2.07230i		−	0.167536i
$154$	0.193786	−	23.0220i	0.0156157	−	1.85517i
$155$		0			0
$156$	−4.92569	−	8.54389i	−0.394371	−	0.684058i
$157$	11.2939	−	6.52053i	0.901351	−	0.520395i	0.0237128	−	0.999719i	$-0.492451\pi$
$157$	11.2939	−	6.52053i	0.901351	−	0.520395i	0.877638	+	0.479324i	$0.159118\pi$
$158$	−8.49576	+	2.27358i	−0.675886	+	0.180877i
$159$	4.10712	−	7.11374i	0.325716	−	0.564156i
$160$		0			0
$161$	−5.01533	−	1.38751i	−0.395263	−	0.109351i
$162$	−8.06481	−	2.16366i	−0.633631	−	0.169993i
$163$	−1.30717	−	0.754695i	−0.102386	−	0.0591123i	0.447933	−	0.894067i	$-0.352160\pi$
$163$	−1.30717	−	0.754695i	−0.102386	−	0.0591123i	−0.550318	+	0.834955i	$0.685494\pi$
$164$	−5.06746	−	0.00316993i	−0.395702	−	0.000247530i
$165$		0			0
$166$	4.70413	−	4.70119i	0.365111	−	0.364883i
$167$	−20.2522			−1.56716			−0.783581	−	0.621290i	$-0.786609\pi$
$167$	−20.2522			−1.56716			−0.783581	+	0.621290i	$0.786609\pi$
$168$	0.100093	−	11.0686i	0.00772238	−	0.853962i
$169$	1.88672			0.145132
$170$		0			0
$171$	−0.286482	−	0.496201i	−0.0219078	−	0.0379455i
$172$	9.19784	+	0.00575367i	0.701329	+	0.000438713i
$173$	8.43190	+	4.86816i	0.641065	+	0.370119i	0.785025	−	0.619464i	$-0.212650\pi$
$173$	8.43190	+	4.86816i	0.641065	+	0.370119i	−0.143960	+	0.989584i	$0.545984\pi$
$174$	10.4642	+	2.80739i	0.793291	+	0.212828i
$175$		0			0
$176$	−21.3304	+	12.2795i	−1.60784	+	0.925605i
$177$	−5.03147	+	8.71475i	−0.378188	+	0.655041i
$178$	−8.19805	+	2.19391i	−0.614470	+	0.164441i
$179$	5.99116	−	3.45900i	0.447800	−	0.258538i	−0.259100	−	0.965850i	$-0.583426\pi$
$179$	5.99116	−	3.45900i	0.447800	−	0.258538i	0.706901	+	0.707313i	$0.250093\pi$
$180$		0			0
$181$			23.5933i			1.75367i	0.480789	+	0.876836i	$0.340350\pi$
$181$			23.5933i			1.75367i	−0.480789	+	0.876836i	$0.659650\pi$
$182$	−10.7494	−	6.32741i	−0.796799	−	0.469019i
$183$			5.25720i			0.388623i
$184$	1.43477	+	5.37481i	0.105773	+	0.396236i
$185$		0			0
$186$	−3.67899	−	13.7474i	−0.269757	−	1.00801i
$187$	7.85102	−	13.5984i	0.574123	−	0.994411i
$188$	7.56503	+	4.37399i	0.551737	+	0.319006i
$189$	−14.4410	+	3.74429i	−1.05043	+	0.272357i
$190$		0			0
$191$	−9.40212	−	5.42832i	−0.680313	−	0.392779i	0.119660	−	0.992815i	$-0.461820\pi$
$191$	−9.40212	−	5.42832i	−0.680313	−	0.392779i	−0.799973	+	0.600036i	$0.795153\pi$
$192$	−10.2590	+	5.89742i	−0.740383	+	0.425610i
$193$	−3.79621	−	6.57523i	−0.273257	−	0.473295i	0.696437	−	0.717618i	$-0.254768\pi$
$193$	−3.79621	−	6.57523i	−0.273257	−	0.473295i	−0.969694	+	0.244323i	$0.921434\pi$
$194$	−9.46035	−	9.46627i	−0.679213	−	0.679638i
$195$		0			0
$196$	−6.79491	−	12.2405i	−0.485351	−	0.874320i
$197$	13.5289			0.963896			0.481948	−	0.876200i	$-0.339929\pi$
$197$	13.5289			0.963896			0.481948	+	0.876200i	$0.339929\pi$
$198$	4.99517	+	4.99830i	0.354991	+	0.355214i
$199$	2.27997	+	3.94903i	0.161623	+	0.279939i	0.935451	−	0.353457i	$-0.114994\pi$
$199$	2.27997	+	3.94903i	0.161623	+	0.279939i	−0.773828	+	0.633396i	$0.781661\pi$
$200$		0			0
$201$	3.71644	+	2.14569i	0.262138	+	0.151345i
$202$	3.24570	−	12.0980i	0.228366	−	0.851210i
$203$	13.2644	−	3.43922i	0.930980	−	0.241386i
$204$	3.77876	−	6.53555i	0.264566	−	0.457580i
$205$		0			0
$206$	3.10104	+	11.5878i	0.216060	+	0.807357i
$207$	1.38321	−	0.798596i	0.0961397	−	0.0555063i
$208$	−0.0166828	+	13.3346i	−0.00115675	+	0.924590i
$209$		−	4.34140i		−	0.300301i
$210$		0			0
$211$			10.6803i			0.735263i	0.929971	+	0.367632i	$0.119831\pi$
$211$			10.6803i			0.735263i	−0.929971	+	0.367632i	$0.880169\pi$
$212$	−9.62205	+	5.54727i	−0.660845	+	0.380988i
$213$	4.31803	−	2.49302i	0.295867	−	0.170819i
$214$	−0.968395	+	0.259156i	−0.0661981	+	0.0177155i
$215$		0			0
$216$	11.2668	+	11.2879i	0.766607	+	0.768047i
$217$	−12.6239	−	12.8302i	−0.856965	−	0.870970i
$218$	4.22377	+	1.13317i	0.286070	+	0.0767482i
$219$	3.26896	+	1.88733i	0.220896	+	0.127534i
$220$		0			0
$221$	−4.25356	−	7.36739i	−0.286126	−	0.495584i
$222$	−10.0877	+	10.0814i	−0.677041	+	0.676617i
$223$	−10.9683			−0.734492			−0.367246	−	0.930124i	$-0.619699\pi$
$223$	−10.9683			−0.734492			−0.367246	+	0.930124i	$0.619699\pi$
$224$	−7.60828	+	12.8885i	−0.508349	+	0.861151i
$225$		0			0
$226$	14.7252	−	14.7160i	0.979503	−	0.978891i
$227$	−5.62977	−	9.75105i	−0.373661	−	0.647200i	0.616465	−	0.787383i	$-0.288564\pi$
$227$	−5.62977	−	9.75105i	−0.373661	−	0.647200i	−0.990126	+	0.140183i	$0.955231\pi$
$228$	0.00130569	−	2.08729i	8.64716e−5	−	0.138234i
$229$	6.16780	+	3.56098i	0.407580	+	0.235316i	0.689749	−	0.724048i	$-0.257721\pi$
$229$	6.16780	+	3.56098i	0.407580	+	0.235316i	−0.282169	+	0.959365i	$0.591054\pi$
$230$		0			0
$231$	−23.2084	−	6.42072i	−1.52700	−	0.422452i
$232$	−10.3488	−	10.3682i	−0.679432	−	0.680708i
$233$	2.81304	−	4.87233i	0.184289	−	0.319197i	−0.759048	−	0.651035i	$-0.774335\pi$
$233$	2.81304	−	4.87233i	0.184289	−	0.319197i	0.943337	+	0.331838i	$0.107669\pi$
$234$	3.69835	−	0.989731i	0.241769	−	0.0647007i
$235$		0			0
$236$	11.7876	−	6.79574i	0.767306	−	0.442365i
$237$			9.19865i			0.597516i
$238$	0.0803690	−	9.54795i	0.00520955	−	0.618902i
$239$		−	18.9288i		−	1.22440i	−0.790701	−	0.612202i	$-0.790284\pi$
$239$		−	18.9288i		−	1.22440i	0.790701	−	0.612202i	$-0.209716\pi$
$240$		0			0
$241$	−4.08233	+	2.35694i	−0.262966	+	0.151824i	−0.625687	−	0.780074i	$-0.715181\pi$
$241$	−4.08233	+	2.35694i	−0.262966	+	0.151824i	0.362721	+	0.931898i	$0.381848\pi$
$242$	9.82022	+	36.6955i	0.631268	+	2.35887i
$243$	4.09127	−	7.08628i	0.262455	−	0.454585i
$244$	3.55801	−	6.15377i	0.227779	−	0.393955i
$245$		0			0
$246$	−1.37339	+	5.11917i	−0.0875644	+	0.326386i
$247$	−2.03698	−	1.17605i	−0.129610	−	0.0748304i
$248$	−4.99766	+	18.5818i	−0.317352	+	1.17994i
$249$	−3.47801	−	6.02408i	−0.220410	−	0.381761i
$250$		0			0
$251$	−23.7582			−1.49961			−0.749803	−	0.661661i	$-0.769852\pi$
$251$	−23.7582			−1.49961			−0.749803	+	0.661661i	$0.769852\pi$
$252$	4.14077	+	1.14835i	0.260844	+	0.0723394i
$253$	12.1021			0.760850
$254$	−4.47931	−	4.48211i	−0.281057	−	0.281233i
$255$		0			0
$256$	15.9999	+	0.0400349i	0.999997	+	0.00250218i
$257$	13.1978	+	7.61973i	0.823254	+	0.475306i	0.851537	−	0.524294i	$-0.175671\pi$
$257$	13.1978	+	7.61973i	0.823254	+	0.475306i	−0.0282835	+	0.999600i	$0.509004\pi$
$258$	2.49282	−	9.29170i	0.155196	−	0.578476i
$259$	−4.80962	+	17.3849i	−0.298855	+	1.08025i
$260$		0			0
$261$	−2.10295	+	3.64242i	−0.130170	+	0.225460i
$262$	5.91614	+	22.1070i	0.365500	+	1.36577i
$263$	−14.6556	+	8.46144i	−0.903705	+	0.521755i	−0.878401	−	0.477925i	$-0.841389\pi$
$263$	−14.6556	+	8.46144i	−0.903705	+	0.521755i	−0.0253049	+	0.999680i	$0.508056\pi$
$264$	6.63940	+	24.8719i	0.408627	+	1.53076i
$265$		0			0
$266$	−1.30070	−	2.29731i	−0.0797508	−	0.140857i
$267$			8.87631i			0.543221i
$268$	−2.89807	−	5.02687i	−0.177028	−	0.307065i
$269$	0.516112	−	0.297978i	0.0314679	−	0.0181680i	−0.484184	−	0.874966i	$-0.660883\pi$
$269$	0.516112	−	0.297978i	0.0314679	−	0.0181680i	0.515651	+	0.856798i	$0.327550\pi$
$270$		0			0
$271$	−7.12334	+	12.3380i	−0.432712	+	0.749479i	−0.997106	−	0.0760266i	$-0.975777\pi$
$271$	−7.12334	+	12.3380i	−0.432712	+	0.749479i	0.564394	+	0.825506i	$0.309110\pi$
$272$	−8.84638	+	5.09271i	−0.536390	+	0.308791i
$273$	−9.29958	+	9.15006i	−0.562836	+	0.553787i
$274$	14.6241	+	3.92343i	0.883476	+	0.237023i
$275$		0			0
$276$	5.81851	+	0.00363974i	0.350233	+	0.000219087i
$277$	−11.5802	−	20.0576i	−0.695789	−	1.20514i	−0.969914	−	0.243448i	$-0.921721\pi$
$277$	−11.5802	−	20.0576i	−0.695789	−	1.20514i	0.274124	−	0.961694i	$-0.411612\pi$
$278$	16.1683	−	16.1582i	0.969712	−	0.969105i
$279$	5.52458			0.330748
$280$		0			0
$281$	−6.58882			−0.393056			−0.196528	−	0.980498i	$-0.562967\pi$
$281$	−6.58882			−0.393056			−0.196528	+	0.980498i	$0.562967\pi$
$282$	6.46487	−	6.46083i	0.384977	−	0.384737i
$283$	13.4034	+	23.2154i	0.796751	+	1.38001i	0.921722	+	0.387852i	$0.126783\pi$
$283$	13.4034	+	23.2154i	0.796751	+	1.38001i	−0.124971	+	0.992160i	$0.539884\pi$
$284$	−6.74168	−	0.00421723i	−0.400045	−	0.000250246i
$285$		0			0
$286$	28.0180	+	7.51681i	1.65674	+	0.444478i
$287$	1.68249	+	6.48905i	0.0993143	+	0.383036i
$288$	−1.18201	−	4.43907i	−0.0696505	−	0.261575i
$289$	−5.24393	+	9.08276i	−0.308467	+	0.534280i
$290$		0			0
$291$	−12.1225	+	6.99890i	−0.710631	+	0.410283i
$292$	−2.54912	−	4.42159i	−0.149176	−	0.258754i
$293$			14.2428i			0.832071i	0.909348	+	0.416036i	$0.136581\pi$
$293$			14.2428i			0.832071i	−0.909348	+	0.416036i	$0.863419\pi$
$294$	−14.2047	+	3.55570i	−0.828437	+	0.207372i
$295$		0			0
$296$	18.6310	−	4.97343i	1.08291	−	0.289075i
$297$	30.0471	−	17.3477i	1.74351	−	1.00662i
$298$	2.77446	+	10.3674i	0.160720	+	0.600566i
$299$	3.27836	−	5.67828i	0.189592	−	0.328384i
$300$		0			0
$301$	−3.05385	−	11.7781i	−0.176021	−	0.678880i
$302$	0.763347	−	2.84529i	0.0439257	−	0.163728i
$303$	−11.3459	−	6.55054i	−0.651803	−	0.376319i
$304$	−1.41418	+	2.44237i	−0.0811089	+	0.140080i
$305$		0			0
$306$	2.07166	+	2.07295i	0.118429	+	0.118503i
$307$	26.0778			1.48834			0.744169	−	0.667991i	$-0.232846\pi$
$307$	26.0778			1.48834			0.744169	+	0.667991i	$0.232846\pi$
$308$	22.8209	+	23.2229i	1.30034	+	1.32325i
$309$	12.5465			0.713743
$310$		0			0
$311$	1.47742	+	2.55897i	0.0837770	+	0.145106i	0.904869	−	0.425689i	$-0.139968\pi$
$311$	1.47742	+	2.55897i	0.0837770	+	0.145106i	−0.821092	+	0.570795i	$0.806635\pi$
$312$	13.4684	+	3.62241i	0.762501	+	0.205078i
$313$	−20.3259	−	11.7352i	−1.14889	−	0.663311i	−0.200272	−	0.979740i	$-0.564182\pi$
$313$	−20.3259	−	11.7352i	−1.14889	−	0.663311i	−0.948616	+	0.316430i	$0.897516\pi$
$314$	−4.77893	+	17.8129i	−0.269691	+	1.00524i
$315$		0			0
$316$	6.22554	−	10.7674i	0.350214	−	0.605713i
$317$	−6.64685	+	11.5127i	−0.373324	+	0.646616i	−0.990075	−	0.140542i	$-0.955115\pi$
$317$	−6.64685	+	11.5127i	−0.373324	+	0.646616i	0.616751	+	0.787159i	$0.288449\pi$
$318$	3.00311	+	11.2218i	0.168406	+	0.629287i
$319$	−27.5990	+	15.9343i	−1.54525	+	0.892148i
$320$		0			0
$321$			1.04851i			0.0585224i
$322$	6.40398	−	3.62581i	0.356880	−	0.202059i
$323$		−	1.80052i		−	0.100183i
$324$	10.2303	−	5.89795i	0.568351	−	0.327664i
$325$		0			0
$326$	2.06204	−	0.551830i	0.114206	−	0.0305631i
$327$	2.28700	−	3.96119i	0.126471	−	0.219054i
$328$	5.07221	−	5.06270i	0.280066	−	0.279541i
$329$	3.08233	−	11.1414i	0.169934	−	0.614248i
$330$		0			0
$331$	−26.5406	−	15.3232i	−1.45880	−	0.842241i	−0.459852	−	0.887996i	$-0.652098\pi$
$331$	−26.5406	−	15.3232i	−1.45880	−	0.842241i	−0.998953	+	0.0457544i	$0.985431\pi$
$332$	−0.00588345	+	9.40531i	−0.000322896	+	0.516184i
$333$	−2.76822	−	4.79470i	−0.151698	−	0.262748i
$334$	20.2585	−	20.2459i	1.10850	−	1.10780i
$335$		0			0
$336$	10.9650	+	11.1721i	0.598191	+	0.609490i
$337$	−16.1059			−0.877346			−0.438673	−	0.898647i	$-0.644551\pi$
$337$	−16.1059			−0.877346			−0.438673	+	0.898647i	$0.644551\pi$
$338$	−1.88731	+	1.88613i	−0.102656	+	0.102592i
$339$	−10.8871	−	18.8570i	−0.591305	−	1.02417i
$340$		0			0
$341$	36.2520	+	20.9301i	1.96316	+	1.13343i
$342$	0.782618	+	0.209964i	0.0423191	+	0.0113536i
$343$	−13.4103	+	12.7736i	−0.724088	+	0.689707i
$344$	−9.20647	+	9.18921i	−0.496379	+	0.495449i
$345$		0			0
$346$	−13.3012	+	3.55958i	−0.715075	+	0.191364i
$347$	−30.3763	+	17.5378i	−1.63069	+	0.941477i	−0.646803	+	0.762657i	$0.723895\pi$
$347$	−30.3763	+	17.5378i	−1.63069	+	0.941477i	−0.983882	+	0.178820i	$0.942772\pi$
$348$	−13.2740	+	7.65269i	−0.711562	+	0.410227i
$349$			20.3154i			1.08746i	0.839261	+	0.543729i	$0.182988\pi$
$349$			20.3154i			1.08746i	−0.839261	+	0.543729i	$0.817012\pi$
$350$		0			0
$351$		−	18.7974i		−	1.00333i
$352$	9.06134	−	33.6071i	0.482971	−	1.79126i
$353$	25.0845	−	14.4826i	1.33511	−	0.770829i	0.349036	−	0.937109i	$-0.386509\pi$
$353$	25.0845	−	14.4826i	1.33511	−	0.770829i	0.986079	+	0.166280i	$0.0531757\pi$
$354$	−3.67899	−	13.7474i	−0.195536	−	0.730664i
$355$		0			0
$356$	6.00739	−	10.3901i	0.318391	−	0.550673i
$357$	−9.62527	−	2.66288i	−0.509423	−	0.140934i
$358$	−2.53512	+	9.44937i	−0.133985	+	0.499415i
$359$	−8.85350	−	5.11157i	−0.467270	−	0.269778i	0.247826	−	0.968804i	$-0.420284\pi$
$359$	−8.85350	−	5.11157i	−0.467270	−	0.269778i	−0.715096	+	0.699026i	$0.753617\pi$
$360$		0			0
$361$	9.25109	+	16.0234i	0.486900	+	0.843335i
$362$	−23.5859	−	23.6006i	−1.23965	−	1.24042i
$363$	39.7314			2.08536
$364$	17.0782	−	4.41666i	0.895141	−	0.231496i
$365$		0			0
$366$	−5.25555	−	5.25884i	−0.274712	−	0.274884i
$367$	14.1114	+	24.4416i	0.736608	+	1.27584i	0.954014	+	0.299761i	$0.0969070\pi$
$367$	14.1114	+	24.4416i	0.736608	+	1.27584i	−0.217406	+	0.976081i	$0.569760\pi$
$368$	−6.80835	−	3.94217i	−0.354910	−	0.205500i
$369$	−1.78190	−	1.02878i	−0.0927620	−	0.0535561i
$370$		0			0
$371$	10.3047	+	10.4731i	0.534994	+	0.543737i
$372$	17.4232	+	10.0738i	0.903351	+	0.522304i
$373$	6.41470	−	11.1106i	0.332141	−	0.575285i	−0.650791	−	0.759257i	$-0.725562\pi$
$373$	6.41470	−	11.1106i	0.332141	−	0.575285i	0.982931	+	0.183973i	$0.0588958\pi$
$374$	5.74063	+	21.4512i	0.296841	+	1.10921i
$375$		0			0
$376$	−11.9400	+	3.18731i	−0.615759	+	0.164373i
$377$			17.2659i			0.889239i
$378$	10.7024	−	18.1820i	0.550473	−	0.935180i
$379$			18.2296i			0.936394i	0.883624	+	0.468197i	$0.155096\pi$
$379$			18.2296i			0.936394i	−0.883624	+	0.468197i	$0.844904\pi$
$380$		0			0
$381$	−5.73977	+	3.31386i	−0.294058	+	0.169774i
$382$	14.8317	−	3.96916i	0.758854	−	0.203080i
$383$	−16.8600	+	29.2023i	−0.861504	+	1.49217i	0.00897238	+	0.999960i	$0.497144\pi$
$383$	−16.8600	+	29.2023i	−0.861504	+	1.49217i	−0.870477	+	0.492210i	$0.836189\pi$
$384$	4.36668	−	16.1551i	0.222836	−	0.824412i
$385$		0			0
$386$	10.3706	+	2.78226i	0.527848	+	0.141613i
$387$	3.23429	+	1.86732i	0.164408	+	0.0949210i
$388$	18.9266	+	0.0118395i	0.960853	+	0.000601057i
$389$	17.3437	+	30.0401i	0.879360	+	1.52310i	0.852045	+	0.523469i	$0.175362\pi$
$389$	17.3437	+	30.0401i	0.879360	+	1.52310i	0.0273150	+	0.999627i	$0.491304\pi$
$390$		0			0
$391$	5.01911			0.253827
$392$	19.0337	+	5.45152i	0.961346	+	0.275343i
$393$	23.9360			1.20741
$394$	−13.5332	+	13.5247i	−0.681791	+	0.681364i
$395$		0			0
$396$	−9.99347	−	0.00625137i	−0.502191	−	0.000314143i
$397$	24.7314	+	14.2787i	1.24124	+	0.716627i	0.969346	−	0.245701i	$-0.0790181\pi$
$397$	24.7314	+	14.2787i	1.24124	+	0.716627i	0.271890	+	0.962328i	$0.412351\pi$
$398$	−6.22848	−	1.67100i	−0.312205	−	0.0837598i
$399$	−2.67284	+	0.693018i	−0.133809	+	0.0346943i
$400$		0			0
$401$	−1.67926	+	2.90857i	−0.0838583	+	0.145247i	−0.904904	−	0.425615i	$-0.860058\pi$
$401$	−1.67926	+	2.90857i	−0.0838583	+	0.145247i	0.821046	+	0.570862i	$0.193391\pi$
$402$	−5.86263	+	1.56892i	−0.292401	+	0.0782507i
$403$	19.6408	−	11.3396i	0.978378	−	0.564867i
$404$	8.84747	+	15.3464i	0.440178	+	0.763514i
$405$		0			0
$406$	−9.83043	+	16.7006i	−0.487876	+	0.828836i
$407$		−	41.9501i		−	2.07939i
$408$	2.75357	+	10.3152i	0.136322	+	0.510677i
$409$	6.05900	−	3.49816i	0.299598	−	0.172973i	−0.342664	−	0.939458i	$-0.611329\pi$
$409$	6.05900	−	3.49816i	0.299598	−	0.172973i	0.642262	+	0.766485i	$0.277996\pi$
$410$		0			0
$411$	7.91835	−	13.7150i	0.390583	−	0.676510i
$412$	−14.6861	−	8.49130i	−0.723534	−	0.418336i
$413$	−12.6239	−	12.8302i	−0.621181	−	0.631332i
$414$	−0.585295	+	2.18162i	−0.0287657	+	0.107221i
$415$		0			0
$416$	−13.3138	−	13.3555i	−0.652761	−	0.654806i
$417$	−11.9541	−	20.7051i	−0.585394	−	1.01393i
$418$	4.34004	+	4.34276i	0.212278	+	0.212411i
$419$	10.0657			0.491743			0.245871	−	0.969302i	$-0.420926\pi$
$419$	10.0657			0.491743			0.245871	+	0.969302i	$0.420926\pi$
$420$		0			0
$421$	−8.08361			−0.393971			−0.196985	−	0.980406i	$-0.563115\pi$
$421$	−8.08361			−0.393971			−0.196985	+	0.980406i	$0.563115\pi$
$422$	−10.6770	−	10.6837i	−0.519747	−	0.520072i
$423$	1.77406	+	3.07277i	0.0862579	+	0.149403i
$424$	4.07952	−	15.1680i	0.198119	−	0.736625i
$425$		0			0
$426$	−1.82715	+	6.81048i	−0.0885255	+	0.329969i
$427$	−9.06300	−	2.50732i	−0.438589	−	0.121338i
$428$	0.709623	−	1.22733i	0.0343009	−	0.0593252i
$429$	15.1706	−	26.2762i	0.732443	−	1.26863i
$430$		0			0
$431$	1.70089	−	0.982009i	0.0819290	−	0.0473017i	−0.458476	−	0.888707i	$-0.651604\pi$
$431$	1.70089	−	0.982009i	0.0819290	−	0.0473017i	0.540405	+	0.841405i	$0.318271\pi$
$432$	−22.5547	−	0.0282180i	−1.08516	−	0.00135764i
$433$			32.6523i			1.56917i	0.620022	+	0.784584i	$0.287123\pi$
$433$			32.6523i			1.56917i	−0.620022	+	0.784584i	$0.712877\pi$
$434$	25.4540	+	0.214257i	1.22183	+	0.0102847i
$435$		0			0
$436$	−5.35791	+	3.08893i	−0.256598	+	0.147933i
$437$	1.20180	−	0.693858i	0.0574898	−	0.0331917i
$438$	−5.15672	+	1.38001i	−0.246398	+	0.0659395i
$439$	−12.2319	+	21.1863i	−0.583797	+	1.01117i	0.411228	+	0.911533i	$0.365100\pi$
$439$	−12.2319	+	21.1863i	−0.583797	+	1.01117i	−0.995024	+	0.0996329i	$0.968233\pi$
$440$		0			0
$441$	0.0921348	−	5.68372i	0.00438737	−	0.270654i
$442$	11.6200	+	3.11746i	0.552706	+	0.148282i
$443$	32.5609	+	18.7990i	1.54701	+	0.893169i	0.998368	+	0.0571150i	$0.0181902\pi$
$443$	32.5609	+	18.7990i	1.54701	+	0.893169i	0.548647	+	0.836054i	$0.315143\pi$
$444$	0.0126167	−	20.1690i	0.000598760	−	0.957181i
$445$		0			0
$446$	10.9717	−	10.9649i	0.519527	−	0.519202i
$447$	11.2251			0.530930
$448$	−5.27384	−	20.4985i	−0.249165	−	0.968461i
$449$	−30.2759			−1.42881			−0.714404	−	0.699733i	$-0.753302\pi$
$449$	−30.2759			−1.42881			−0.714404	+	0.699733i	$0.753302\pi$
$450$		0			0
$451$	−7.79515	−	13.5016i	−0.367059	−	0.635766i
$452$	−0.0184168	+	29.4411i	−0.000866251	+	1.38479i
$453$	−2.66841	−	1.54060i	−0.125373	−	0.0723839i
$454$	15.3795	+	4.12609i	0.721797	+	0.193647i
$455$		0			0
$456$	2.08533	+	2.08925i	0.0976544	+	0.0978379i
$457$	−13.2874	+	23.0145i	−0.621559	+	1.07657i	0.367637	+	0.929969i	$0.380167\pi$
$457$	−13.2874	+	23.0145i	−0.621559	+	1.07657i	−0.989196	+	0.146602i	$0.953166\pi$
$458$	−9.72960	+	2.60378i	−0.454634	+	0.121667i
$459$	12.4615	−	7.19464i	0.581652	−	0.335817i
$460$		0			0
$461$		−	26.3218i		−	1.22593i	−0.790110	−	0.612965i	$-0.789977\pi$
$461$		−	26.3218i		−	1.22593i	0.790110	−	0.612965i	$-0.210023\pi$
$462$	29.6344	−	16.7784i	1.37872	−	0.780604i
$463$		−	33.8611i		−	1.57366i	−0.617169	−	0.786830i	$-0.711721\pi$
$463$		−	33.8611i		−	1.57366i	0.617169	−	0.786830i	$-0.288279\pi$
$464$	20.7170	+	0.0259189i	0.961764	+	0.00120325i
$465$		0			0
$466$	2.05689	+	7.68602i	0.0952834	+	0.356048i
$467$	−10.4121	+	18.0343i	−0.481814	+	0.834526i	−0.999782	−	0.0208739i	$-0.993355\pi$
$467$	−10.4121	+	18.0343i	−0.481814	+	0.834526i	0.517968	+	0.855400i	$0.326688\pi$
$468$	−2.71009	+	4.68724i	−0.125274	+	0.216668i
$469$	−5.47149	+	5.38351i	−0.252650	+	0.248588i
$470$		0			0
$471$	16.7056	+	9.64495i	0.769751	+	0.444416i
$472$	−4.99766	+	18.5818i	−0.230036	+	0.855295i
$473$	14.1488	+	24.5065i	0.650563	+	1.12681i
$474$	−9.19577	−	9.20152i	−0.422376	−	0.422640i
$475$		0			0
$476$	9.46457	+	9.63128i	0.433808	+	0.441449i
$477$	−4.50964			−0.206482
$478$	18.9229	+	18.9348i	0.865514	+	0.866056i
$479$	−2.62335	−	4.54378i	−0.119864	−	0.207611i	0.799850	−	0.600200i	$-0.204913\pi$
$479$	−2.62335	−	4.54378i	−0.119864	−	0.207611i	−0.919714	+	0.392590i	$0.871579\pi$
$480$		0			0
$481$	−19.6830	−	11.3640i	−0.897466	−	0.518152i
$482$	1.72741	−	6.43873i	0.0786814	−	0.293276i
$483$	−1.93185	−	7.45080i	−0.0879024	−	0.339023i
$484$	−46.5073	−	26.8898i	−2.11397	−	1.22226i
$485$		0			0
$486$	2.99152	+	11.1785i	0.135698	+	0.507067i
$487$	−10.3791	+	5.99236i	−0.470321	+	0.271540i	−0.716374	−	0.697716i	$-0.754200\pi$
$487$	−10.3791	+	5.99236i	−0.470321	+	0.271540i	0.246053	+	0.969256i	$0.420866\pi$
$488$	2.59272	+	9.71259i	0.117367	+	0.439668i
$489$		−	2.23264i		−	0.100963i
$490$		0			0
$491$			22.8018i			1.02903i	0.857481	+	0.514515i	$0.172028\pi$
$491$			22.8018i			1.02903i	−0.857481	+	0.514515i	$0.827972\pi$
$492$	−3.74375	−	6.49374i	−0.168781	−	0.292760i
$493$	−11.4462	+	6.60845i	−0.515509	+	0.297630i
$494$	3.21330	−	0.859925i	0.144573	−	0.0386898i
$495$		0			0
$496$	−13.5767	−	23.5837i	−0.609613	−	1.05894i
$497$	2.23836	+	8.63295i	0.100404	+	0.387241i
$498$	9.50129	+	2.54905i	0.425763	+	0.114226i
$499$	−18.0567	−	10.4251i	−0.808330	−	0.466689i	0.0380458	−	0.999276i	$-0.487887\pi$
$499$	−18.0567	−	10.4251i	−0.808330	−	0.466689i	−0.846376	+	0.532587i	$0.821220\pi$
$500$		0			0
$501$	−14.9782	−	25.9430i	−0.669176	−	1.15905i
$502$	23.7657	−	23.7508i	1.06071	−	1.06005i
$503$	−18.5545			−0.827305			−0.413653	−	0.910435i	$-0.635747\pi$
$503$	−18.5545			−0.827305			−0.413653	+	0.910435i	$0.635747\pi$
$504$	−5.29006	+	2.99076i	−0.235638	+	0.133219i
$505$		0			0
$506$	−12.1059	+	12.0983i	−0.538171	+	0.537834i
$507$	1.39538	+	2.41688i	0.0619712	+	0.107337i
$508$	8.96143	+	0.00560578i	0.397599	+	0.000248716i
$509$	−29.7157	−	17.1564i	−1.31713	−	0.760443i	−0.333860	−	0.942623i	$-0.608351\pi$
$509$	−29.7157	−	17.1564i	−1.31713	−	0.760443i	−0.983265	+	0.182180i	$0.941685\pi$
$510$		0			0
$511$	−4.81268	+	4.73530i	−0.212900	+	0.209477i
$512$	−16.0450	+	15.9549i	−0.709094	+	0.705114i
$513$	1.98922	−	3.44543i	0.0878262	−	0.152119i
$514$	−20.8192	+	5.57152i	−0.918297	+	0.245749i
$515$		0			0
$516$	6.79520	+	11.7866i	0.299142	+	0.518878i
$517$			26.8845i			1.18238i
$518$	−12.5684	−	22.1985i	−0.552222	−	0.975345i
$519$			14.4016i			0.632161i
$520$		0			0
$521$	−18.3115	+	10.5722i	−0.802242	+	0.463175i	−0.844254	−	0.535943i	$-0.819956\pi$
$521$	−18.3115	+	10.5722i	−0.802242	+	0.463175i	0.0420126	+	0.999117i	$0.486623\pi$
$522$	−1.53767	−	5.74586i	−0.0673021	−	0.251489i
$523$	−1.98681	+	3.44125i	−0.0868769	+	0.150475i	−0.906189	−	0.422872i	$-0.861022\pi$
$523$	−1.98681	+	3.44125i	−0.0868769	+	0.150475i	0.819313	+	0.573347i	$0.194355\pi$
$524$	−28.0180	−	16.1996i	−1.22397	−	0.707683i
$525$		0			0
$526$	6.20143	−	23.1151i	0.270395	−	1.00787i
$527$	15.0349	+	8.68039i	0.654929	+	0.378124i
$528$	−31.5056	−	18.2424i	−1.37111	−	0.793897i
$529$	−9.56580	−	16.5685i	−0.415905	−	0.720368i
$530$		0			0
$531$	5.52458			0.239747
$532$	3.59770	+	0.997742i	0.155980	+	0.0432576i
$533$	−8.44659			−0.365863
$534$	−8.87353	−	8.87909i	−0.383995	−	0.384236i
$535$		0			0
$536$	7.92427	+	2.13127i	0.342276	+	0.0920570i
$537$	8.86192	+	5.11643i	0.382420	+	0.220790i
$538$	−0.218389	+	0.814022i	−0.00941543	+	0.0350950i
$539$	22.1376	−	36.9473i	0.953535	−	1.59143i
$540$		0			0
$541$	−14.6794	+	25.4255i	−0.631117	+	1.09313i	0.356207	+	0.934407i	$0.384070\pi$
$541$	−14.6794	+	25.4255i	−0.631117	+	1.09313i	−0.987324	+	0.158719i	$0.949263\pi$
$542$	−5.20856	−	19.4630i	−0.223727	−	0.836005i
$543$	−30.2229	+	17.4492i	−1.29699	+	0.748816i
$544$	3.75802	−	13.9379i	0.161124	−	0.597583i
$545$		0			0
$546$	0.155298	−	18.4496i	0.00664613	−	0.789570i
$547$		−	1.50735i		−	0.0644495i	−0.999481	−	0.0322248i	$-0.989741\pi$
$547$		−	1.50735i		−	0.0644495i	0.999481	−	0.0322248i	$-0.0102592\pi$
$548$	−18.5509	+	10.6949i	−0.792456	+	0.456864i
$549$	2.49954	−	1.44311i	0.106678	−	0.0615904i
$550$		0			0
$551$	−1.82715	+	3.16471i	−0.0778390	+	0.134821i
$552$	−5.82397	+	5.81305i	−0.247885	+	0.247420i
$553$	−15.8577	−	4.38712i	−0.674340	−	0.186559i
$554$	31.6352	+	8.48722i	1.34405	+	0.360588i
$555$		0			0
$556$	−0.0202217	+	32.3265i	−0.000857592	+	1.37095i
$557$	−22.8589	−	39.5927i	−0.968562	−	1.67760i	−0.699725	−	0.714412i	$-0.746694\pi$
$557$	−22.8589	−	39.5927i	−0.968562	−	1.67760i	−0.268837	−	0.963186i	$-0.586639\pi$
$558$	−5.52631	+	5.52286i	−0.233947	+	0.233801i
$559$	15.3312			0.648442
$560$		0			0
$561$	23.2259			0.980599
$562$	6.59088	−	6.58675i	0.278019	−	0.277845i
$563$	−9.18431	−	15.9077i	−0.387072	−	0.670429i	0.604982	−	0.796239i	$-0.293180\pi$
$563$	−9.18431	−	15.9077i	−0.387072	−	0.670429i	−0.992054	+	0.125810i	$0.959847\pi$
$564$	−0.00808561	+	12.9257i	−0.000340466	+	0.544270i
$565$		0			0
$566$	−36.6158	−	9.82344i	−1.53907	−	0.412910i
$567$	−10.9561	−	11.1352i	−0.460114	−	0.467633i
$568$	6.74801	−	6.73536i	0.283140	−	0.282609i
$569$	−4.58078	+	7.93415i	−0.192036	+	0.332617i	−0.945925	−	0.324385i	$-0.894843\pi$
$569$	−4.58078	+	7.93415i	−0.192036	+	0.332617i	0.753889	+	0.657002i	$0.228176\pi$
$570$		0			0
$571$	12.5753	−	7.26034i	0.526259	−	0.303836i	−0.213233	−	0.977001i	$-0.568399\pi$
$571$	12.5753	−	7.26034i	0.526259	−	0.303836i	0.739492	+	0.673166i	$0.235066\pi$
$572$	−35.5413	+	20.4901i	−1.48605	+	0.856735i
$573$		−	16.0588i		−	0.670864i
$574$	−8.17003	−	4.80911i	−0.341011	−	0.200729i
$575$		0			0
$576$	5.62006	+	3.25882i	0.234169	+	0.135784i
$577$	13.6384	−	7.87411i	0.567772	−	0.327804i	−0.188487	−	0.982076i	$-0.560358\pi$
$577$	13.6384	−	7.87411i	0.567772	−	0.327804i	0.756259	+	0.654272i	$0.227025\pi$
$578$	−3.83434	−	14.3279i	−0.159488	−	0.595962i
$579$	5.61523	−	9.72586i	0.233361	−	0.404193i
$580$		0			0
$581$	12.0438	−	3.12274i	0.499661	−	0.129553i
$582$	5.12953	−	19.1198i	0.212626	−	0.792539i
$583$	−29.5921	−	17.0850i	−1.22558	−	0.707588i
$584$	6.97013	+	1.87465i	0.288426	+	0.0775737i
$585$		0			0
$586$	−14.2383	−	14.2472i	−0.588179	−	0.588547i
$587$	21.3535			0.881355			0.440678	−	0.897665i	$-0.354738\pi$
$587$	21.3535			0.881355			0.440678	+	0.897665i	$0.354738\pi$
$588$	10.6546	−	17.7571i	0.439388	−	0.732290i
$589$	4.80002			0.197781
$590$		0			0
$591$	10.0058	+	17.3305i	0.411582	+	0.712881i
$592$	−13.6650	+	23.6002i	−0.561626	+	0.969961i
$593$	−15.8039	−	9.12440i	−0.648990	−	0.374694i	0.139079	−	0.990281i	$-0.455586\pi$
$593$	−15.8039	−	9.12440i	−0.648990	−	0.374694i	−0.788069	+	0.615587i	$0.788919\pi$
$594$	−12.7142	+	47.3908i	−0.521671	+	1.94447i
$595$		0			0
$596$	−13.1395	−	7.59704i	−0.538213	−	0.311187i
$597$	−3.37246	+	5.84127i	−0.138025	+	0.239067i
$598$	2.39712	+	8.95739i	0.0980256	+	0.366295i
$599$	37.6528	−	21.7389i	1.53845	−	0.888226i	0.539522	−	0.841971i	$-0.318605\pi$
$599$	37.6528	−	21.7389i	1.53845	−	0.888226i	0.998930	−	0.0462544i	$-0.0147285\pi$
$600$		0			0
$601$			0.772217i			0.0314994i	0.999876	+	0.0157497i	$0.00501349\pi$
$601$			0.772217i			0.0314994i	−0.999876	+	0.0157497i	$0.994987\pi$
$602$	14.8293	+	8.72892i	0.604395	+	0.355764i
$603$		−	2.35598i		−	0.0959430i
$604$	2.08081	+	3.60929i	0.0846671	+	0.146860i
$605$		0			0
$606$	17.8979	−	4.78973i	0.727053	−	0.194569i
$607$	2.76301	−	4.78567i	0.112147	−	0.194245i	−0.804489	−	0.593968i	$-0.797561\pi$
$607$	2.76301	−	4.78567i	0.112147	−	0.194245i	0.916636	+	0.399724i	$0.130894\pi$
$608$	−1.02698	−	3.85687i	−0.0416497	−	0.156417i
$609$	14.2158	+	14.4481i	0.576052	+	0.585466i
$610$		0			0
$611$	12.6142	+	7.28280i	0.510315	+	0.294630i
$612$	−4.14461	−	0.00259264i	−0.167536	−	0.000104801i
$613$	−13.7936	−	23.8912i	−0.557117	−	0.964955i	−0.997735	−	0.0672607i	$-0.978574\pi$
$613$	−13.7936	−	23.8912i	−0.557117	−	0.964955i	0.440618	−	0.897695i	$-0.354759\pi$
$614$	−26.0859	+	26.0696i	−1.05274	+	1.05208i
$615$		0			0
$616$	−46.0437	−	0.416374i	−1.85516	−	0.0167762i
$617$	13.6354			0.548941			0.274471	−	0.961595i	$-0.411497\pi$
$617$	13.6354			0.548941			0.274471	+	0.961595i	$0.411497\pi$
$618$	−12.5504	+	12.5425i	−0.504850	+	0.504535i
$619$	18.4295	+	31.9208i	0.740744	+	1.28301i	0.952157	+	0.305609i	$0.0988601\pi$
$619$	18.4295	+	31.9208i	0.740744	+	1.28301i	−0.211413	+	0.977397i	$0.567807\pi$
$620$		0			0
$621$	9.60447	+	5.54514i	0.385414	+	0.222519i
$622$	−4.03606	−	1.08281i	−0.161831	−	0.0434168i
$623$	−15.3021	−	4.23338i	−0.613064	−	0.169607i
$624$	−17.0939	+	9.84069i	−0.684305	+	0.393943i
$625$		0			0
$626$	32.0637	−	8.58071i	1.28152	−	0.342954i
$627$	5.56131	−	3.21083i	0.222097	−	0.128228i
$628$	−13.0269	−	22.5959i	−0.519831	−	0.901676i
$629$		−	17.3980i		−	0.693705i
$630$		0			0
$631$		−	16.3105i		−	0.649312i	−0.945832	−	0.324656i	$-0.894751\pi$
$631$		−	16.3105i		−	0.649312i	0.945832	−	0.324656i	$-0.105249\pi$
$632$	4.53654	+	16.9944i	0.180454	+	0.675999i
$633$	−13.6814	+	7.89898i	−0.543788	+	0.313956i
$634$	−4.86015	−	18.1610i	−0.193021	−	0.721267i
$635$		0			0
$636$	−14.2223	−	8.22313i	−0.563952	−	0.326068i
$637$	−11.3387	−	20.3957i	−0.449256	−	0.808107i
$638$	11.6783	−	43.5296i	0.462349	−	1.72335i
$639$	−2.37062	−	1.36868i	−0.0937801	−	0.0541440i
$640$		0			0
$641$	10.7109	+	18.5519i	0.423057	+	0.732756i	0.996237	−	0.0866736i	$-0.0276237\pi$
$641$	10.7109	+	18.5519i	0.423057	+	0.732756i	−0.573180	+	0.819430i	$0.694290\pi$
$642$	−1.04819	−	1.04884i	−0.0413686	−	0.0413945i
$643$	38.3710			1.51320			0.756601	−	0.653876i	$-0.226858\pi$
$643$	38.3710			1.51320			0.756601	+	0.653876i	$0.226858\pi$
$644$	−2.78130	+	10.0289i	−0.109599	+	0.395195i
$645$		0			0
$646$	1.79995	+	1.80108i	0.0708182	+	0.0708625i
$647$	−17.9463	−	31.0838i	−0.705540	−	1.22203i	−0.966496	−	0.256681i	$-0.917371\pi$
$647$	−17.9463	−	31.0838i	−0.705540	−	1.22203i	0.260956	−	0.965351i	$-0.415962\pi$
$648$	−4.33741	+	16.1269i	−0.170390	+	0.633525i
$649$	36.2520	+	20.9301i	1.42302	+	0.821579i
$650$		0			0
$651$	7.09899	−	25.6601i	0.278231	−	1.00570i
$652$	−1.51103	+	2.61340i	−0.0591763	+	0.102349i
$653$	−13.6634	+	23.6657i	−0.534690	+	0.926110i	0.464488	+	0.885579i	$0.346238\pi$
$653$	−13.6634	+	23.6657i	−0.534690	+	0.926110i	−0.999178	+	0.0405310i	$0.987095\pi$
$654$	1.67224	+	6.24871i	0.0653899	+	0.244344i
$655$		0			0
$656$	−0.0126797	+	10.1349i	−0.000495059	+	0.395702i
$657$		−	2.07230i		−	0.0808483i
$658$	8.05466	+	14.2263i	0.314003	+	0.554599i
$659$			22.7714i			0.887046i	0.896263	+	0.443523i	$0.146272\pi$
$659$			22.7714i			0.887046i	−0.896263	+	0.443523i	$0.853728\pi$
$660$		0			0
$661$	35.2100	−	20.3285i	1.36951	−	0.790686i	0.378643	−	0.925543i	$-0.376391\pi$
$661$	35.2100	−	20.3285i	1.36951	−	0.790686i	0.990865	+	0.134857i	$0.0430573\pi$
$662$	41.8674	−	11.2043i	1.62722	−	0.435467i
$663$	6.29173	−	10.8976i	0.244350	−	0.423227i
$664$	−9.39648	−	9.41413i	−0.364654	−	0.365339i
$665$		0			0
$666$	7.56228	+	2.02884i	0.293033	+	0.0786161i
$667$	−8.82193	−	5.09334i	−0.341587	−	0.197215i
$668$	−0.0253373	+	40.5044i	−0.000980331	+	1.56716i
$669$	−8.11198	−	14.0504i	−0.313627	−	0.543218i
$670$		0			0
$671$	21.8691			0.844249
$672$	−22.1371	−	0.214035i	−0.853957	−	0.00825657i
$673$	37.5436			1.44720			0.723599	−	0.690220i	$-0.242486\pi$
$673$	37.5436			1.44720			0.723599	+	0.690220i	$0.242486\pi$
$674$	16.1110	−	16.1009i	0.620571	−	0.620183i
$675$		0			0
$676$	0.00236046	−	3.77344i	9.07867e−5	−	0.145132i
$677$	−9.24340	−	5.33668i	−0.355253	−	0.205105i	0.311744	−	0.950166i	$-0.399087\pi$
$677$	−9.24340	−	5.33668i	−0.355253	−	0.205105i	−0.666996	+	0.745061i	$0.732420\pi$
$678$	29.7415	+	7.97919i	1.14222	+	0.306439i
$679$	−6.28399	−	24.2361i	−0.241157	−	0.930098i
$680$		0			0
$681$	8.32736	−	14.4234i	0.319105	−	0.552707i
$682$	−57.1870	+	15.3040i	−2.18980	+	0.586022i
$683$	13.9738	−	8.06776i	0.534691	−	0.308704i	−0.208233	−	0.978079i	$-0.566771\pi$
$683$	13.9738	−	8.06776i	0.534691	−	0.308704i	0.742925	+	0.669375i	$0.233438\pi$
$684$	−0.992761	+	0.572343i	−0.0379592	+	0.0218841i
$685$		0			0
$686$	0.644931	−	26.1837i	0.0246236	−	0.999697i
$687$			10.5346i			0.401919i
$688$	0.0230147	−	18.3957i	0.000877426	−	0.701328i
$689$	−16.0325	+	9.25638i	−0.610791	+	0.352640i
$690$		0			0
$691$	−10.1615	+	17.6003i	−0.386562	+	0.669546i	−0.991985	−	0.126359i	$-0.959671\pi$
$691$	−10.1615	+	17.6003i	−0.386562	+	0.669546i	0.605422	+	0.795904i	$0.293004\pi$
$692$	9.74686	−	16.8577i	0.370520	−	0.640834i
$693$	3.31802	+	12.7970i	0.126041	+	0.486117i
$694$	12.8535	−	47.9100i	0.487913	−	1.81864i
$695$		0			0
$696$	5.62787	−	20.9249i	0.213324	−	0.793158i
$697$	−3.23290	−	5.59954i	−0.122455	−	0.212098i
$698$	−20.3090	−	20.3217i	−0.768708	−	0.769189i
$699$	8.32191			0.314764
$700$		0			0
$701$	5.55111			0.209663			0.104831	−	0.994490i	$-0.466570\pi$
$701$	5.55111			0.209663			0.104831	+	0.994490i	$0.466570\pi$
$702$	18.7916	+	18.8033i	0.709242	+	0.709686i
$703$	−2.40516	−	4.16586i	−0.0907123	−	0.157118i
$704$	24.5324	+	42.6761i	0.924599	+	1.60842i
$705$		0			0
$706$	−10.6143	+	39.5638i	−0.399476	+	1.48900i
$707$	16.7038	−	16.4352i	0.628211	−	0.618110i
$708$	17.4232	+	10.0738i	0.654804	+	0.378598i
$709$	1.13330	−	1.96293i	0.0425619	−	0.0737194i	−0.843960	−	0.536407i	$-0.819781\pi$
$709$	1.13330	−	1.96293i	0.0425619	−	0.0737194i	0.886522	+	0.462687i	$0.153115\pi$
$710$		0			0
$711$	4.37351	−	2.52504i	0.164019	−	0.0946966i
$712$	4.37757	+	16.3988i	0.164056	+	0.614573i
$713$			13.3805i			0.501104i
$714$	12.2903	−	6.95855i	0.459954	−	0.260417i
$715$		0			0
$716$	−6.91050	−	11.9866i	−0.258258	−	0.447962i
$717$	24.2478	−	13.9995i	0.905549	−	0.522819i
$718$	13.9662	−	3.73756i	0.521215	−	0.139485i
$719$	−2.78544	+	4.82453i	−0.103880	+	0.179925i	−0.913280	−	0.407333i	$-0.866459\pi$
$719$	−2.78544	+	4.82453i	−0.103880	+	0.179925i	0.809400	+	0.587257i	$0.199792\pi$
$720$		0			0
$721$	−5.98379	+	21.6291i	−0.222848	+	0.805510i
$722$	−25.2723	−	6.78017i	−0.940539	−	0.252332i
$723$	−6.03845	−	3.48630i	−0.224572	−	0.129657i
$724$	47.1865	+	0.0295173i	1.75367	+	0.00109700i
$725$		0			0
$726$	−39.7439	+	39.7190i	−1.47503	+	1.47411i
$727$	−31.2822			−1.16019			−0.580097	−	0.814548i	$-0.696985\pi$
$727$	−31.2822			−1.16019			−0.580097	+	0.814548i	$0.696985\pi$
$728$	−12.6683	+	21.4909i	−0.469517	+	0.796506i
$729$	29.8164			1.10431
$730$		0			0
$731$	5.86796	+	10.1636i	0.217034	+	0.375915i
$732$	10.5144	+	0.00657723i	0.388623	+	0.000243102i
$733$	18.2504	+	10.5369i	0.674092	+	0.389187i	0.797626	−	0.603153i	$-0.206089\pi$
$733$	18.2504	+	10.5369i	0.674092	+	0.389187i	−0.123533	+	0.992340i	$0.539422\pi$
$734$	−38.5498	−	10.3423i	−1.42290	−	0.381741i
$735$		0			0
$736$	10.7514	−	2.86282i	0.396302	−	0.105525i
$737$	8.92574	−	15.4598i	0.328784	−	0.569471i
$738$	2.81091	−	0.752240i	0.103471	−	0.0276903i
$739$	−33.6932	+	19.4528i	−1.23943	+	0.715583i	−0.968977	−	0.247152i	$-0.920505\pi$
$739$	−33.6932	+	19.4528i	−1.23943	+	0.715583i	−0.270449	+	0.962734i	$0.587172\pi$
$740$		0			0
$741$		−	3.47915i		−	0.127810i
$742$	−20.7778	−	0.174895i	−0.762776	−	0.00642059i
$743$		−	15.9696i		−	0.585867i	−0.956133	−	0.292934i	$-0.905368\pi$
$743$		−	15.9696i		−	0.585867i	0.956133	−	0.292934i	$-0.0946315\pi$
$744$	−27.4993	+	7.34078i	−1.00817	+	0.269126i
$745$		0			0
$746$	4.69041	+	17.5268i	0.171728	+	0.641700i
$747$	−1.90944	+	3.30724i	−0.0698626	+	0.121006i
$748$	−27.1869	−	15.7190i	−0.994051	−	0.574745i
$749$	−1.80756	−	0.500069i	−0.0660467	−	0.0182721i
$750$		0			0
$751$	16.3642	+	9.44785i	0.597137	+	0.344757i	0.767914	−	0.640553i	$-0.221295\pi$
$751$	16.3642	+	9.44785i	0.597137	+	0.344757i	−0.170778	+	0.985310i	$0.554628\pi$
$752$	8.75743	−	15.1246i	0.319351	−	0.551537i
$753$	−17.5712	−	30.4342i	−0.640330	−	1.10908i
$754$	−17.2605	−	17.2713i	−0.628590	−	0.628983i
$755$		0			0
$756$	7.47052	+	28.8867i	0.271700	+	1.05060i
$757$	21.9755			0.798714			0.399357	−	0.916796i	$-0.369233\pi$
$757$	21.9755			0.798714			0.399357	+	0.916796i	$0.369233\pi$
$758$	−18.2239	−	18.2354i	−0.661924	−	0.662338i
$759$	8.95048	+	15.5027i	0.324882	+	0.562712i
$760$		0			0
$761$	−44.7044	−	25.8101i	−1.62053	−	0.935616i	−0.986777	−	0.162084i	$-0.948179\pi$
$761$	−44.7044	−	25.8101i	−1.62053	−	0.935616i	−0.633757	−	0.773532i	$-0.718488\pi$
$762$	2.42875	−	9.05287i	0.0879842	−	0.327951i
$763$	5.73805	+	5.83182i	0.207731	+	0.211126i
$764$	−10.8684	+	18.7974i	−0.393205	+	0.680068i
$765$		0			0
$766$	−12.3279	−	46.0662i	−0.445427	−	1.66444i
$767$	19.6408	−	11.3396i	0.709188	−	0.409450i
$768$	11.7820	+	20.5255i	0.425147	+	0.740649i
$769$		−	16.7704i		−	0.604756i	−0.953188	−	0.302378i	$-0.902220\pi$
$769$		−	16.7704i		−	0.604756i	0.953188	−	0.302378i	$-0.0977805\pi$
$770$		0			0
$771$			22.5417i			0.811819i
$772$	−13.1552	+	7.58420i	−0.473466	+	0.272961i
$773$	22.7401	−	13.1290i	0.817903	−	0.472217i	−0.0317896	−	0.999495i	$-0.510121\pi$
$773$	22.7401	−	13.1290i	0.817903	−	0.472217i	0.849693	+	0.527278i	$0.176787\pi$
$774$	−5.10203	+	1.36537i	−0.183389	+	0.0490774i
$775$		0			0
$776$	−18.9444	+	18.9088i	−0.680063	+	0.678788i
$777$	−25.8271	+	6.69650i	−0.926543	+	0.240236i
$778$	−47.3799	−	12.7113i	−1.69865	−	0.455721i
$779$	−1.54820	−	0.893852i	−0.0554699	−	0.0320256i
$780$		0			0
$781$	−10.3706	−	17.9624i	−0.371088	−	0.642744i
$782$	−5.02068	+	5.01754i	−0.179539	+	0.179427i
$783$	−29.2042			−1.04367
$784$	−24.4894	+	13.5745i	−0.874623	+	0.484804i
$785$		0			0
$786$	−23.9435	+	23.9285i	−0.854035	+	0.853501i
$787$	−14.9357	−	25.8693i	−0.532398	−	0.922141i	−0.999284	−	0.0378237i	$-0.987957\pi$
$787$	−14.9357	−	25.8693i	−0.532398	−	0.922141i	0.466886	−	0.884318i	$-0.345376\pi$
$788$	0.0169259	−	27.0579i	0.000602961	−	0.963896i
$789$	−21.6781	−	12.5159i	−0.771762	−	0.445577i
$790$		0			0
$791$	37.7003	−	9.77499i	1.34047	−	0.347559i
$792$	10.0028	−	9.98409i	0.355436	−	0.354769i
$793$	5.92419	−	10.2610i	0.210374	−	0.364378i
$794$	−39.0134	+	10.4405i	−1.38453	+	0.370521i
$795$		0			0
$796$	7.90090	−	4.55500i	0.280040	−	0.161448i
$797$			17.1648i			0.608010i	0.952670	+	0.304005i	$0.0983240\pi$
$797$			17.1648i			0.608010i	−0.952670	+	0.304005i	$0.901676\pi$
$798$	1.98087	−	3.36524i	0.0701222	−	0.119128i
$799$			11.1498i			0.394453i
$800$		0			0
$801$	4.22025	−	2.43656i	0.149115	−	0.0860917i
$802$	−1.22787	−	4.58821i	−0.0433576	−	0.162015i
$803$	7.85102	−	13.5984i	0.277056	−	0.479876i
$804$	4.29603	−	7.43020i	0.151509	−	0.262043i
$805$		0			0
$806$	−8.31087	+	30.9778i	−0.292738	+	1.09115i
$807$	0.763416	+	0.440758i	0.0268735	+	0.0155154i
$808$	−24.1919	−	6.50653i	−0.851067	−	0.228899i
$809$	13.6136	+	23.5795i	0.478630	+	0.829011i	0.999700	−	0.0245028i	$-0.00780027\pi$
$809$	13.6136	+	23.5795i	0.478630	+	0.829011i	−0.521070	+	0.853514i	$0.674467\pi$
$810$		0			0
$811$	26.6882			0.937148			0.468574	−	0.883424i	$-0.344768\pi$
$811$	26.6882			0.937148			0.468574	+	0.883424i	$0.344768\pi$
$812$	−6.86185	−	26.5332i	−0.240804	−	0.931131i
$813$	−21.0732			−0.739069
$814$	41.9370	+	41.9632i	1.46989	+	1.47081i
$815$		0			0
$816$	−13.0664	−	7.56569i	−0.457415	−	0.264852i
$817$	2.81010	+	1.62241i	0.0983130	+	0.0567610i
$818$	−2.56382	+	9.55636i	−0.0896420	+	0.334130i
$819$	6.90315	+	1.90979i	0.241216	+	0.0667334i
$820$		0			0
$821$	3.81521	−	6.60813i	0.133152	−	0.230625i	−0.791738	−	0.610861i	$-0.790824\pi$
$821$	3.81521	−	6.60813i	0.133152	−	0.230625i	0.924890	+	0.380235i	$0.124157\pi$
$822$	5.78987	+	21.6352i	0.201945	+	0.754613i
$823$	−4.69139	+	2.70858i	−0.163532	+	0.0944150i	−0.579532	−	0.814949i	$-0.696765\pi$
$823$	−4.69139	+	2.70858i	−0.163532	+	0.0944150i	0.416001	+	0.909364i	$0.363431\pi$
$824$	23.1794	−	6.18759i	0.807492	−	0.215555i
$825$		0			0
$826$	25.4540	+	0.214257i	0.885658	+	0.00745495i
$827$			54.4560i			1.89362i	0.321792	+	0.946810i	$0.395715\pi$
$827$			54.4560i			1.89362i	−0.321792	+	0.946810i	$0.604285\pi$
$828$	−1.59546	−	2.76742i	−0.0554461	−	0.0961744i
$829$	−1.41764	+	0.818472i	−0.0492365	+	0.0284267i	−0.524416	−	0.851462i	$-0.675716\pi$
$829$	−1.41764	+	0.818472i	−0.0492365	+	0.0284267i	0.475180	+	0.879889i	$0.342383\pi$
$830$		0			0
$831$	17.1291	−	29.6685i	0.594202	−	1.02919i
$832$	26.6692	+	0.0500485i	0.924589	+	0.00173512i
$833$	9.18117	−	15.3232i	0.318109	−	0.530917i
$834$	32.6564	+	8.76121i	1.13080	+	0.303376i
$835$		0			0
$836$	−8.68280	−	0.00543148i	−0.300301	−	0.000187852i
$837$	19.1803	+	33.2212i	0.662968	+	1.14829i
$838$	−10.0689	+	10.0626i	−0.347823	+	0.347606i
$839$	−13.4985			−0.466021			−0.233011	−	0.972474i	$-0.574858\pi$
$839$	−13.4985			−0.466021			−0.233011	+	0.972474i	$0.574858\pi$
$840$		0			0
$841$	−2.17525			−0.0750086
$842$	8.08613	−	8.08108i	0.278667	−	0.278492i
$843$	−4.87298	−	8.44024i	−0.167834	−	0.290697i
$844$	21.3606	+	0.0133620i	0.735263	+	0.000459941i
$845$		0			0
$846$	−4.84643	−	1.30022i	−0.166624	−	0.0447025i
$847$	−18.9491	+	68.4939i	−0.651100	+	2.35348i
$848$	11.0825	+	19.2510i	0.380575	+	0.661083i
$849$	−19.8259	+	34.3394i	−0.680423	+	1.17853i
$850$		0			0
$851$	11.6127	−	6.70461i	0.398079	−	0.229831i
$852$	−4.98063	−	8.63918i	−0.170634	−	0.295974i
$853$			37.8821i			1.29706i	0.761189	+	0.648530i	$0.224616\pi$
$853$			37.8821i			1.29706i	−0.761189	+	0.648530i	$0.775384\pi$
$854$	11.5724	−	6.55206i	0.395998	−	0.224207i
$855$		0			0
$856$	0.517101	+	1.93711i	0.0176741	+	0.0662092i
$857$	−16.1748	+	9.33854i	−0.552522	+	0.318998i	−0.750138	−	0.661281i	$-0.770013\pi$
$857$	−16.1748	+	9.33854i	−0.552522	+	0.318998i	0.197617	+	0.980279i	$0.436680\pi$
$858$	11.0927	+	41.4503i	0.378698	+	1.41509i
$859$	−13.6369	+	23.6198i	−0.465285	+	0.805898i	−0.999214	−	0.0396315i	$-0.987382\pi$
$859$	−13.6369	+	23.6198i	−0.465285	+	0.805898i	0.533929	+	0.845529i	$0.320715\pi$
$860$		0			0
$861$	−7.06810	+	6.95445i	−0.240880	+	0.237007i
$862$	−0.719720	+	2.68267i	−0.0245137	+	0.0913722i
$863$	20.9749	+	12.1098i	0.713993	+	0.412224i	0.812538	−	0.582909i	$-0.198085\pi$
$863$	20.9749	+	12.1098i	0.713993	+	0.412224i	−0.0985450	+	0.995133i	$0.531419\pi$
$864$	22.5900	−	22.5194i	0.768526	−	0.766126i
$865$		0			0
$866$	−32.6421	−	32.6625i	−1.10922	−	1.10992i
$867$	−15.5133			−0.526859
$868$	−25.6762	+	25.2317i	−0.871506	+	0.856420i
$869$	38.2650			1.29805
$870$		0			0
$871$	−4.83583	−	8.37591i	−0.163856	−	0.283807i
$872$	2.27163	−	8.44613i	0.0769271	−	0.286022i
$873$	6.65527	+	3.84242i	0.225247	+	0.130046i
$874$	−0.508532	+	1.89550i	−0.0172014	+	0.0641161i
$875$		0			0
$876$	3.77876	−	6.53555i	0.127672	−	0.220816i
$877$	14.0625	−	24.3570i	0.474857	−	0.822477i	−0.524728	−	0.851270i	$-0.675833\pi$
$877$	14.0625	−	24.3570i	0.474857	−	0.822477i	0.999585	+	0.0287932i	$0.00916642\pi$
$878$	−8.94392	−	33.4210i	−0.301843	−	1.12790i
$879$	−18.2449	+	10.5337i	−0.615386	+	0.355293i
$880$		0			0
$881$		−	12.3462i		−	0.415953i	−0.978134	−	0.207976i	$-0.933312\pi$
$881$		−	12.3462i		−	0.415953i	0.978134	−	0.207976i	$-0.0666877\pi$
$882$	5.58978	+	5.77761i	0.188218	+	0.194542i
$883$			33.0518i			1.11228i	0.831088	+	0.556140i	$0.187718\pi$
$883$			33.0518i			1.11228i	−0.831088	+	0.556140i	$0.812282\pi$
$884$	−14.7401	+	8.49791i	−0.495763	+	0.285815i
$885$		0			0
$886$	−51.3642	+	13.7458i	−1.72561	+	0.461799i
$887$	15.1276	−	26.2017i	0.507934	−	0.879767i	−0.492024	−	0.870582i	$-0.663743\pi$
$887$	15.1276	−	26.2017i	0.507934	−	0.879767i	0.999958	−	0.00918566i	$-0.00292393\pi$
$888$	20.1501	+	20.1880i	0.676194	+	0.677464i
$889$	−2.97536	−	11.4754i	−0.0997903	−	0.384873i
$890$		0			0
$891$	31.4627	+	18.1650i	1.05404	+	0.608551i
$892$	−0.0137223	+	21.9366i	−0.000459458	+	0.734492i
$893$	1.54139	+	2.66977i	0.0515806	+	0.0893403i
$894$	−11.2286	+	11.2216i	−0.375542	+	0.375307i
$895$		0			0
$896$	25.7675	+	15.2327i	0.860833	+	0.508888i
$897$	9.69847			0.323823
$898$	30.2854	−	30.2664i	1.01064	−	1.01000i
$899$	−17.6175	−	30.5145i	−0.587578	−	1.01771i
$900$		0			0
$901$	−12.2728	−	7.08568i	−0.408865	−	0.236058i
$902$	21.2950	+	5.71311i	0.709045	+	0.190226i
$903$	12.8292	−	12.6229i	0.426928	−	0.420063i
$904$	−29.4135	−	29.4687i	−0.978278	−	0.980115i
$905$		0			0
$906$	4.20936	−	1.12648i	0.139847	−	0.0374249i
$907$	32.3561	−	18.6808i	1.07437	−	0.620287i	0.144997	−	0.989432i	$-0.453683\pi$
$907$	32.3561	−	18.6808i	1.07437	−	0.620287i	0.929372	+	0.369145i	$0.120350\pi$
$908$	−19.5091	+	11.2473i	−0.647433	+	0.373256i
$909$			7.19254i			0.238561i
$910$		0			0
$911$			21.4157i			0.709535i	0.934955	+	0.354768i	$0.115440\pi$
$911$			21.4157i			0.709535i	−0.934955	+	0.354768i	$0.884560\pi$
$912$	−4.17457	−	0.00522277i	−0.138234	−	0.000172943i
$913$	−25.0593	+	14.4680i	−0.829340	+	0.478820i
$914$	−9.71570	−	36.3049i	−0.321367	−	1.20086i
$915$		0			0
$916$	7.12968	−	12.3311i	0.235571	−	0.407433i
$917$	−11.4158	+	41.2637i	−0.376983	+	1.36265i
$918$	−5.27299	+	19.6545i	−0.174035	+	0.648694i
$919$	13.1132	+	7.57091i	0.432565	+	0.249741i	0.700439	−	0.713713i	$-0.252988\pi$
$919$	13.1132	+	7.57091i	0.432565	+	0.249741i	−0.267874	+	0.963454i	$0.586321\pi$
$920$		0			0
$921$	19.2867	+	33.4055i	0.635518	+	1.10075i
$922$	26.3136	+	26.3300i	0.866592	+	0.867134i
$923$	−11.2372			−0.369878
$924$	−12.8705	+	46.4088i	−0.423407	+	1.52674i
$925$		0			0
$926$	33.8505	+	33.8717i	1.11240	+	1.11309i
$927$	−3.44402	−	5.96522i	−0.113117	−	0.195924i
$928$	−20.7494	+	20.6846i	−0.681133	+	0.679006i
$929$	−12.1825	−	7.03359i	−0.399696	−	0.230765i	0.286657	−	0.958033i	$-0.407456\pi$
$929$	−12.1825	−	7.03359i	−0.399696	−	0.230765i	−0.686353	+	0.727269i	$0.740789\pi$
$930$		0			0
$931$	0.0800511	−	4.93829i	0.00262357	−	0.161846i
$932$	−9.74114	−	5.63218i	−0.319082	−	0.184488i
$933$	−2.18536	+	3.78515i	−0.0715453	+	0.123920i
$934$	−7.61328	−	28.4487i	−0.249114	−	0.930871i
$935$		0			0
$936$	−1.97483	−	7.39794i	−0.0645495	−	0.241809i
$937$			6.12130i			0.199974i	0.994989	+	0.0999871i	$0.0318802\pi$
$937$			6.12130i			0.199974i	−0.994989	+	0.0999871i	$0.968120\pi$
$938$	0.0913707	−	10.8550i	0.00298336	−	0.354427i
$939$		−	34.7165i		−	1.13293i
$940$		0			0
$941$	24.8876	−	14.3689i	0.811312	−	0.468411i	−0.0360991	−	0.999348i	$-0.511493\pi$
$941$	24.8876	−	14.3689i	0.811312	−	0.468411i	0.847411	+	0.530937i	$0.178160\pi$
$942$	−26.3527	+	7.05235i	−0.858618	+	0.229778i
$943$	2.49170	−	4.31575i	0.0811409	−	0.140540i
$944$	−13.5767	−	23.5837i	−0.441885	−	0.767583i
$945$		0			0
$946$	−38.6521	−	10.3697i	−1.25669	−	0.337149i
$947$	−9.92118	−	5.72800i	−0.322395	−	0.186135i	0.330065	−	0.943958i	$-0.392929\pi$
$947$	−9.92118	−	5.72800i	−0.322395	−	0.186135i	−0.652460	+	0.757823i	$0.726263\pi$
$948$	18.3973	+	0.0115083i	0.597516	+	0.000373774i
$949$	−4.25356	−	7.36739i	−0.138076	−	0.239155i
$950$		0			0
$951$	−19.6636			−0.637635
$952$	−19.0958	−	0.172683i	−0.618898	−	0.00559670i
$953$	−39.4042			−1.27643			−0.638214	−	0.769859i	$-0.720326\pi$
$953$	−39.4042			−1.27643			−0.638214	+	0.769859i	$0.720326\pi$
$954$	4.51105	−	4.50823i	0.146051	−	0.145959i
$955$		0			0
$956$	−37.8577	−	0.0236817i	−1.22440	−	0.000765921i
$957$	−40.8235	−	23.5694i	−1.31964	−	0.761892i
$958$	7.16653	+	1.92267i	0.231540	+	0.0621186i
$959$	19.8671	+	20.1917i	0.641541	+	0.652024i
$960$		0			0
$961$	−7.64115	+	13.2349i	−0.246489	+	0.426931i
$962$	31.0495	−	8.30929i	1.00108	−	0.267902i
$963$	0.498517	−	0.287819i	0.0160645	−	0.00927484i
$964$	4.70876	+	8.16761i	0.151659	+	0.263061i
$965$		0			0
$966$	9.38093	+	5.52188i	0.301826	+	0.177664i
$967$		−	6.27278i		−	0.201719i	−0.994901	−	0.100860i	$-0.967841\pi$
$967$		−	6.27278i		−	0.201719i	0.994901	−	0.100860i	$-0.0321593\pi$
$968$	73.4032	−	19.5945i	2.35927	−	0.629792i
$969$	2.30645	−	1.33163i	0.0740939	−	0.0427782i
$970$		0			0
$971$	−14.2485	+	24.6792i	−0.457257	+	0.791993i	−0.998815	−	0.0486706i	$-0.984502\pi$
$971$	−14.2485	+	24.6792i	−0.457257	+	0.791993i	0.541557	+	0.840664i	$0.317835\pi$
$972$	−14.1674	−	8.19140i	−0.454421	−	0.262739i
$973$	41.3952	−	10.7330i	1.32707	−	0.344084i
$974$	4.39184	−	16.3701i	0.140723	−	0.524531i
$975$		0			0
$976$	−12.3031	−	7.12373i	−0.393812	−	0.228025i
$977$	−13.7290	−	23.7793i	−0.439228	−	0.760766i	0.558402	−	0.829571i	$-0.311415\pi$
$977$	−13.7290	−	23.7793i	−0.439228	−	0.760766i	−0.997630	+	0.0688047i	$0.978081\pi$
$978$	2.23194	+	2.23334i	0.0713696	+	0.0714143i
$979$	36.9241			1.18010
$980$		0			0
$981$	−2.51114			−0.0801744
$982$	−22.7946	−	22.8089i	−0.727406	−	0.727861i
$983$	13.4398	+	23.2784i	0.428662	+	0.742465i	0.996755	−	0.0804998i	$-0.0256516\pi$
$983$	13.4398	+	23.2784i	0.428662	+	0.742465i	−0.568092	+	0.822965i	$0.692318\pi$
$984$	10.2366	+	2.75319i	0.326332	+	0.0877686i
$985$		0			0
$986$	4.84337	−	18.0531i	0.154244	−	0.574928i
$987$	16.5518	−	4.29157i	0.526849	−	0.136602i
$988$	−2.35465	+	4.07249i	−0.0749115	+	0.129563i
$989$	−4.52263	+	7.83342i	−0.143811	+	0.249088i
$990$		0			0
$991$	−21.5616	+	12.4486i	−0.684927	+	0.395443i	−0.801709	−	0.597715i	$-0.796075\pi$
$991$	−21.5616	+	12.4486i	−0.684927	+	0.395443i	0.116782	+	0.993158i	$0.462742\pi$
$992$	37.1573	+	10.0186i	1.17974	+	0.318090i
$993$		−	45.3312i		−	1.43854i
$994$	−10.8693	−	6.39798i	−0.344754	−	0.202932i
$995$		0			0
$996$	−12.0525	+	6.94847i	−0.381898	+	0.220171i
$997$	−11.7417	+	6.77909i	−0.371864	+	0.214696i	−0.674273	−	0.738483i	$-0.735543\pi$
$997$	−11.7417	+	6.77909i	−0.371864	+	0.214696i	0.302408	+	0.953178i	$0.402209\pi$
$998$	28.4842	−	7.62276i	0.901650	−	0.241294i
$999$	19.2214	−	33.2925i	0.608140	−	1.05333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.p.e.551.4		32
4.3	odd	2	inner	700.2.p.e.551.6		32
5.2	odd	4		140.2.s.b.19.5	yes	32
5.3	odd	4		140.2.s.b.19.12	yes	32
5.4	even	2	inner	700.2.p.e.551.13		32
7.3	odd	6	inner	700.2.p.e.451.6		32
20.3	even	4		140.2.s.b.19.14	yes	32
20.7	even	4		140.2.s.b.19.3	✓	32
20.19	odd	2	inner	700.2.p.e.551.11		32
28.3	even	6	inner	700.2.p.e.451.4		32
35.2	odd	12		980.2.c.d.979.16		32
35.3	even	12		140.2.s.b.59.3	yes	32
35.12	even	12		980.2.c.d.979.15		32
35.13	even	4		980.2.s.e.19.12		32
35.17	even	12		140.2.s.b.59.14	yes	32
35.18	odd	12		980.2.s.e.619.3		32
35.23	odd	12		980.2.c.d.979.17		32
35.24	odd	6	inner	700.2.p.e.451.11		32
35.27	even	4		980.2.s.e.19.5		32
35.32	odd	12		980.2.s.e.619.14		32
35.33	even	12		980.2.c.d.979.18		32
140.3	odd	12		140.2.s.b.59.5	yes	32
140.23	even	12		980.2.c.d.979.14		32
140.27	odd	4		980.2.s.e.19.3		32
140.47	odd	12		980.2.c.d.979.20		32
140.59	even	6	inner	700.2.p.e.451.13		32
140.67	even	12		980.2.s.e.619.12		32
140.83	odd	4		980.2.s.e.19.14		32
140.87	odd	12		140.2.s.b.59.12	yes	32
140.103	odd	12		980.2.c.d.979.13		32
140.107	even	12		980.2.c.d.979.19		32
140.123	even	12		980.2.s.e.619.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.3	✓	32	20.7	even	4
140.2.s.b.19.5	yes	32	5.2	odd	4
140.2.s.b.19.12	yes	32	5.3	odd	4
140.2.s.b.19.14	yes	32	20.3	even	4
140.2.s.b.59.3	yes	32	35.3	even	12
140.2.s.b.59.5	yes	32	140.3	odd	12
140.2.s.b.59.12	yes	32	140.87	odd	12
140.2.s.b.59.14	yes	32	35.17	even	12
700.2.p.e.451.4		32	28.3	even	6	inner
700.2.p.e.451.6		32	7.3	odd	6	inner
700.2.p.e.451.11		32	35.24	odd	6	inner
700.2.p.e.451.13		32	140.59	even	6	inner
700.2.p.e.551.4		32	1.1	even	1	trivial
700.2.p.e.551.6		32	4.3	odd	2	inner
700.2.p.e.551.11		32	20.19	odd	2	inner
700.2.p.e.551.13		32	5.4	even	2	inner
980.2.c.d.979.13		32	140.103	odd	12
980.2.c.d.979.14		32	140.23	even	12
980.2.c.d.979.15		32	35.12	even	12
980.2.c.d.979.16		32	35.2	odd	12
980.2.c.d.979.17		32	35.23	odd	12
980.2.c.d.979.18		32	35.33	even	12
980.2.c.d.979.19		32	140.107	even	12
980.2.c.d.979.20		32	140.47	odd	12
980.2.s.e.19.3		32	140.27	odd	4
980.2.s.e.19.5		32	35.27	even	4
980.2.s.e.19.12		32	35.13	even	4
980.2.s.e.19.14		32	140.83	odd	4
980.2.s.e.619.3		32	35.18	odd	12
980.2.s.e.619.5		32	140.123	even	12
980.2.s.e.619.12		32	140.67	even	12
980.2.s.e.619.14		32	35.32	odd	12

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00031 + 0.999687i) q^{2} +(0.739583 + 1.28100i) q^{3} +(0.00125109 - 2.00000i) q^{4} +(-2.02041 - 0.542044i) q^{6} +(-2.56107 + 0.664037i) q^{7} +(1.99812 + 2.00188i) q^{8} +(0.406034 - 0.703271i) q^{9} +(5.32875 - 3.07655i) q^{11} +(2.56292 - 1.47756i) q^{12} -3.33366i q^{13} +(1.89804 - 3.22451i) q^{14} +(-4.00000 - 0.00500436i) q^{16} +(2.21000 - 1.27594i) q^{17} +(0.296890 + 1.10940i) q^{18} +(0.352781 - 0.611035i) q^{19} +(-2.74475 - 2.78960i) q^{21} +(-2.25482 + 8.40459i) q^{22} +(1.70332 + 0.983411i) q^{23} +(-1.08662 + 4.04014i) q^{24} +(3.33262 + 3.33470i) q^{26} +5.63868 q^{27} +(1.32487 + 5.12296i) q^{28} -5.17926 q^{29} +(3.40156 + 5.89167i) q^{31} +(4.00625 - 3.99374i) q^{32} +(7.88210 + 4.55073i) q^{33} +(-0.935146 + 3.48565i) q^{34} +(-1.40603 - 0.812947i) q^{36} +(3.40886 - 5.90431i) q^{37} +(0.257952 + 0.963897i) q^{38} +(4.27040 - 2.46552i) q^{39} -2.53373i q^{41} +(5.53434 + 0.0465848i) q^{42} +4.59892i q^{43} +(-6.14644 - 10.6613i) q^{44} +(-2.68695 + 0.719067i) q^{46} +(-2.18463 + 3.78388i) q^{47} +(-2.95192 - 5.12768i) q^{48} +(6.11811 - 3.40128i) q^{49} +(3.26896 + 1.88733i) q^{51} +(-6.66732 - 0.00417071i) q^{52} +(-2.77664 - 4.80929i) q^{53} +(-5.64044 + 5.63692i) q^{54} +(-6.44664 - 3.80011i) q^{56} +1.04364 q^{57} +(5.18088 - 5.17764i) q^{58} +(3.40156 + 5.89167i) q^{59} +(3.07800 + 1.77708i) q^{61} +(-9.29244 - 2.49302i) q^{62} +(-0.572881 + 2.07074i) q^{63} +(-0.0150131 + 7.99999i) q^{64} +(-12.4339 + 3.32748i) q^{66} +(2.51253 - 1.45061i) q^{67} +(-2.54912 - 4.42159i) q^{68} +2.90926i q^{69} -3.37084i q^{71} +(2.21917 - 0.592393i) q^{72} +(2.21000 - 1.27594i) q^{73} +(2.49254 + 9.31395i) q^{74} +(-1.22163 - 0.706327i) q^{76} +(-11.6043 + 11.4177i) q^{77} +(-1.80699 + 6.73536i) q^{78} +(5.38564 + 3.10940i) q^{79} +(2.95217 + 5.11331i) q^{81} +(2.53294 + 2.53452i) q^{82} -4.70266 q^{83} +(-5.58264 + 5.48601i) q^{84} +(-4.59748 - 4.60036i) q^{86} +(-3.83049 - 6.63461i) q^{87} +(16.8064 + 4.52016i) q^{88} +(5.19692 + 3.00044i) q^{89} +(2.21367 + 8.53772i) q^{91} +(1.96895 - 3.40541i) q^{92} +(-5.03147 + 8.71475i) q^{93} +(-1.59739 - 5.96901i) q^{94} +(8.07892 + 2.17829i) q^{96} +9.46331i q^{97} +(-2.71980 + 9.51854i) q^{98} -4.99674i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 6 q^{4} - 4 q^{9} - 22 q^{14} + 18 q^{16} - 52 q^{21} + 48 q^{24} - 18 q^{26} - 28 q^{36} + 26 q^{44} - 22 q^{46} - 48 q^{54} - 16 q^{56} + 36 q^{61} - 36 q^{64} - 24 q^{66} - 14 q^{74} + 72 q^{81}+ \cdots + 60 q^{96}+O(q^{100}) \) 32 * q - 6 * q^4 - 4 * q^9 - 22 * q^14 + 18 * q^16 - 52 * q^21 + 48 * q^24 - 18 * q^26 - 28 * q^36 + 26 * q^44 - 22 * q^46 - 48 * q^54 - 16 * q^56 + 36 * q^61 - 36 * q^64 - 24 * q^66 - 14 * q^74 + 72 * q^81 - 56 * q^84 + 8 * q^86 + 108 * q^89 - 30 * q^94 + 60 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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