LMFDB - Embedded newform 875.2.bb.b.507.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] 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("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,2] 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			507.11
Character	$\chi$	$=$	875.507
Dual form			875.2.bb.b.768.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.673859 + 0.437609i) q^{2} +(-2.92974 - 1.12462i) q^{3} +(-0.550889 - 1.23732i) q^{4} +(-1.48209 - 2.03992i) q^{6} +(2.52724 - 0.782993i) q^{7} +(0.421625 - 2.66204i) q^{8} +(5.08915 + 4.58229i) q^{9} +(3.35615 + 3.72738i) q^{11} +(0.222448 + 4.24455i) q^{12} +(0.416175 - 0.816789i) q^{13} +(2.04565 + 0.578315i) q^{14} +(-0.363508 + 0.403716i) q^{16} +(-0.402827 - 0.326203i) q^{17} +(1.42412 + 5.31488i) q^{18} +(1.01710 + 0.452842i) q^{19} +(-8.28471 - 0.548217i) q^{21} +(0.630435 + 3.98041i) q^{22} +(2.81441 - 4.33381i) q^{23} +(-4.22903 + 7.32490i) q^{24} +(0.637878 - 0.368279i) q^{26} +(-5.48243 - 10.7599i) q^{27} +(-2.36104 - 2.69565i) q^{28} +(3.39698 - 4.67555i) q^{29} +(-0.340506 + 0.0357886i) q^{31} +(-5.62839 + 1.50812i) q^{32} +(-5.64074 - 14.6946i) q^{33} +(-0.128699 - 0.396095i) q^{34} +(2.86619 - 8.82122i) q^{36} +(6.37440 - 0.334068i) q^{37} +(0.487214 + 0.750244i) q^{38} +(-2.13786 + 1.92494i) q^{39} +(6.75808 - 2.19583i) q^{41} +(-5.34282 - 3.99489i) q^{42} +(-3.02167 + 3.02167i) q^{43} +(2.76308 - 6.20599i) q^{44} +(3.79303 - 1.68877i) q^{46} +(-8.03274 - 9.91961i) q^{47} +(1.51901 - 0.773974i) q^{48} +(5.77384 - 3.95762i) q^{49} +(0.813322 + 1.40871i) q^{51} +(-1.23989 - 0.0649800i) q^{52} +(-2.10095 + 5.47316i) q^{53} +(1.01424 - 9.64981i) q^{54} +(-1.01881 - 7.05773i) q^{56} +(-2.47056 - 2.47056i) q^{57} +(4.33515 - 1.66411i) q^{58} +(-8.60248 - 1.82851i) q^{59} +(0.301099 + 1.41656i) q^{61} +(-0.245114 - 0.124892i) q^{62} +(16.4494 + 7.59576i) q^{63} +(-3.41938 - 1.11102i) q^{64} +(2.62944 - 12.3706i) q^{66} +(0.885317 - 1.09328i) q^{67} +(-0.181703 + 0.678125i) q^{68} +(-13.1194 + 9.53177i) q^{69} +(-6.16371 - 4.47820i) q^{71} +(14.3439 - 11.6155i) q^{72} +(-0.0631171 + 1.20435i) q^{73} +(4.44164 + 2.56438i) q^{74} -1.50794i q^{76} +(11.4003 + 6.79213i) q^{77} +(-2.28299 + 0.361590i) q^{78} +(4.83574 + 0.508257i) q^{79} +(1.81383 + 17.2574i) q^{81} +(5.51491 + 1.47772i) q^{82} +(3.42852 + 0.543025i) q^{83} +(3.88563 + 10.5528i) q^{84} +(-3.35849 + 0.713869i) q^{86} +(-15.2105 + 9.87780i) q^{87} +(11.3375 - 7.36263i) q^{88} +(3.07374 - 0.653343i) q^{89} +(0.412231 - 2.39008i) q^{91} +(-6.91272 - 1.09487i) q^{92} +(1.03784 + 0.278088i) q^{93} +(-1.07202 - 10.1996i) q^{94} +(18.1858 + 1.91140i) q^{96} +(3.51689 - 0.557021i) q^{97} +(5.62265 - 0.140190i) q^{98} +34.3480i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) $ 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.673859	+	0.437609i	0.476491	+	0.309437i	0.760446	−	0.649401i	$-0.224980\pi$
$2$	0.673859	+	0.437609i	0.476491	+	0.309437i	−0.283956	+	0.958837i	$0.591647\pi$
$3$	−2.92974	−	1.12462i	−1.69148	−	0.649300i	−0.693986	−	0.719989i	$-0.744147\pi$
$3$	−2.92974	−	1.12462i	−1.69148	−	0.649300i	−0.997498	+	0.0706887i	$0.977480\pi$
$4$	−0.550889	−	1.23732i	−0.275444	−	0.618658i
$5$		0			0
$5$		0			0
$6$	−1.48209	−	2.03992i	−0.605059	−	0.832792i
$7$	2.52724	−	0.782993i	0.955205	−	0.295944i
$7$	2.52724	−	0.782993i	0.955205	−	0.295944i
$8$	0.421625	−	2.66204i	0.149067	−	0.941172i
$9$	5.08915	+	4.58229i	1.69638	+	1.52743i
$10$		0			0
$11$	3.35615	+	3.72738i	1.01192	+	1.12385i	0.992277	+	0.124040i	$0.0395851\pi$
$11$	3.35615	+	3.72738i	1.01192	+	1.12385i	0.0196392	+	0.999807i	$0.493748\pi$
$12$	0.222448	+	4.24455i	0.0642151	+	1.22530i
$13$	0.416175	−	0.816789i	0.115426	−	0.226536i	−0.826065	−	0.563575i	$-0.809425\pi$
$13$	0.416175	−	0.816789i	0.115426	−	0.226536i	0.941491	+	0.337039i	$0.109425\pi$
$14$	2.04565	+	0.578315i	0.546722	+	0.154561i
$15$		0			0
$16$	−0.363508	+	0.403716i	−0.0908770	+	0.100929i
$17$	−0.402827	−	0.326203i	−0.0976998	−	0.0791157i	0.579226	−	0.815167i	$-0.303355\pi$
$17$	−0.402827	−	0.326203i	−0.0976998	−	0.0791157i	−0.676926	+	0.736051i	$0.736688\pi$
$18$	1.42412	+	5.31488i	0.335668	+	1.25273i
$19$	1.01710	+	0.452842i	0.233339	+	0.103889i	0.520075	−	0.854120i	$-0.325904\pi$
$19$	1.01710	+	0.452842i	0.233339	+	0.103889i	−0.286737	+	0.958009i	$0.592571\pi$
$20$		0			0
$21$	−8.28471	−	0.548217i	−1.80787	−	0.119631i
$22$	0.630435	+	3.98041i	0.134409	+	0.848626i
$23$	2.81441	−	4.33381i	0.586844	−	0.903661i	−0.413131	−	0.910672i	$-0.635565\pi$
$23$	2.81441	−	4.33381i	0.586844	−	0.903661i	0.999975	+	0.00701045i	$0.00223151\pi$
$24$	−4.22903	+	7.32490i	−0.863248	+	1.49519i
$25$		0			0
$26$	0.637878	−	0.368279i	0.125098	−	0.0722254i
$27$	−5.48243	−	10.7599i	−1.05509	−	2.07074i
$28$	−2.36104	−	2.69565i	−0.446194	−	0.509430i
$29$	3.39698	−	4.67555i	0.630804	−	0.868227i	−0.367279	−	0.930111i	$-0.619711\pi$
$29$	3.39698	−	4.67555i	0.630804	−	0.868227i	0.998083	+	0.0618834i	$0.0197107\pi$
$30$		0			0
$31$	−0.340506	+	0.0357886i	−0.0611566	+	0.00642782i	−0.135057	−	0.990838i	$-0.543122\pi$
$31$	−0.340506	+	0.0357886i	−0.0611566	+	0.00642782i	0.0739007	+	0.997266i	$0.476455\pi$
$32$	−5.62839	+	1.50812i	−0.994968	+	0.266601i
$33$	−5.64074	−	14.6946i	−0.981927	−	2.55801i
$34$	−0.128699	−	0.396095i	−0.0220717	−	0.0679298i
$35$		0			0
$36$	2.86619	−	8.82122i	0.477698	−	1.47020i
$37$	6.37440	−	0.334068i	1.04794	−	0.0549205i	0.479419	−	0.877586i	$-0.340847\pi$
$37$	6.37440	−	0.334068i	1.04794	−	0.0549205i	0.568526	+	0.822666i	$0.307514\pi$
$38$	0.487214	+	0.750244i	0.0790365	+	0.121706i
$39$	−2.13786	+	1.92494i	−0.342332	+	0.308237i
$40$		0			0
$41$	6.75808	−	2.19583i	1.05543	−	0.342931i	0.270635	−	0.962682i	$-0.412766\pi$
$41$	6.75808	−	2.19583i	1.05543	−	0.342931i	0.784799	+	0.619750i	$0.212766\pi$
$42$	−5.34282	−	3.99489i	−0.824415	−	0.616424i
$43$	−3.02167	+	3.02167i	−0.460800	+	0.460800i	−0.898918	−	0.438118i	$-0.855645\pi$
$43$	−3.02167	+	3.02167i	−0.460800	+	0.460800i	0.438118	+	0.898918i	$0.355645\pi$
$44$	2.76308	−	6.20599i	0.416551	−	0.935588i
$45$		0			0
$46$	3.79303	−	1.68877i	0.559252	−	0.248995i
$47$	−8.03274	−	9.91961i	−1.17170	−	1.44692i	−0.869676	−	0.493622i	$-0.835673\pi$
$47$	−8.03274	−	9.91961i	−1.17170	−	1.44692i	−0.302020	−	0.953302i	$-0.597661\pi$
$48$	1.51901	−	0.773974i	0.219250	−	0.111714i
$49$	5.77384	−	3.95762i	0.824835	−	0.565374i
$50$		0			0
$51$	0.813322	+	1.40871i	0.113888	+	0.197260i
$52$	−1.23989	−	0.0649800i	−0.171942	−	0.00901111i
$53$	−2.10095	+	5.47316i	−0.288588	+	0.751796i	0.710266	+	0.703933i	$0.248575\pi$
$53$	−2.10095	+	5.47316i	−0.288588	+	0.751796i	−0.998854	+	0.0478633i	$0.984759\pi$
$54$	1.01424	−	9.64981i	0.138020	−	1.31317i
$55$		0			0
$56$	−1.01881	−	7.05773i	−0.136144	−	0.943128i
$57$	−2.47056	−	2.47056i	−0.327233	−	0.327233i
$58$	4.33515	−	1.66411i	0.569233	−	0.218508i
$59$	−8.60248	−	1.82851i	−1.11995	−	0.238052i	−0.389503	−	0.921025i	$-0.627353\pi$
$59$	−8.60248	−	1.82851i	−1.11995	−	0.238052i	−0.730444	+	0.682973i	$0.760687\pi$
$60$		0			0
$61$	0.301099	+	1.41656i	0.0385518	+	0.181372i	0.993211	−	0.116330i	$-0.0371131\pi$
$61$	0.301099	+	1.41656i	0.0385518	+	0.181372i	−0.954659	+	0.297702i	$0.903780\pi$
$62$	−0.245114	−	0.124892i	−0.0311295	−	0.0158613i
$63$	16.4494	+	7.59576i	2.07243	+	0.956976i
$64$	−3.41938	−	1.11102i	−0.427422	−	0.138878i
$65$		0			0
$66$	2.62944	−	12.3706i	0.323662	−	1.52271i
$67$	0.885317	−	1.09328i	0.108159	−	0.133565i	−0.720192	−	0.693775i	$-0.755946\pi$
$67$	0.885317	−	1.09328i	0.108159	−	0.133565i	0.828351	+	0.560210i	$0.189280\pi$
$68$	−0.181703	+	0.678125i	−0.0220347	+	0.0822348i
$69$	−13.1194	+	9.53177i	−1.57939	+	1.14749i
$70$		0			0
$71$	−6.16371	−	4.47820i	−0.731498	−	0.531465i	0.158539	−	0.987353i	$-0.449322\pi$
$71$	−6.16371	−	4.47820i	−0.731498	−	0.531465i	−0.890037	+	0.455888i	$0.849322\pi$
$72$	14.3439	−	11.6155i	1.69045	−	1.36890i
$73$	−0.0631171	+	1.20435i	−0.00738730	+	0.140958i	0.992446	+	0.122684i	$0.0391503\pi$
$73$	−0.0631171	+	1.20435i	−0.00738730	+	0.140958i	−0.999833	+	0.0182736i	$0.994183\pi$
$74$	4.44164	+	2.56438i	0.516330	+	0.298103i
$75$		0			0
$76$		−	1.50794i		−	0.172972i
$77$	11.4003	+	6.79213i	1.29918	+	0.774035i
$78$	−2.28299	+	0.361590i	−0.258497	+	0.0409420i
$79$	4.83574	+	0.508257i	0.544064	+	0.0571834i	0.372574	−	0.928003i	$-0.378475\pi$
$79$	4.83574	+	0.508257i	0.544064	+	0.0571834i	0.171490	+	0.985186i	$0.445142\pi$
$80$		0			0
$81$	1.81383	+	17.2574i	0.201536	+	1.91749i
$82$	5.51491	+	1.47772i	0.609020	+	0.163186i
$83$	3.42852	+	0.543025i	0.376329	+	0.0596047i	0.341734	−	0.939797i	$-0.388986\pi$
$83$	3.42852	+	0.543025i	0.376329	+	0.0596047i	0.0345952	+	0.999401i	$0.488986\pi$
$84$	3.88563	+	10.5528i	0.423957	+	1.15141i
$85$		0			0
$86$	−3.35849	+	0.713869i	−0.362155	+	0.0769784i
$87$	−15.2105	+	9.87780i	−1.63074	+	1.05901i
$88$	11.3375	−	7.36263i	1.20858	−	0.784859i
$89$	3.07374	−	0.653343i	0.325816	−	0.0692543i	−0.0421001	−	0.999113i	$-0.513405\pi$
$89$	3.07374	−	0.653343i	0.325816	−	0.0692543i	0.367916	+	0.929859i	$0.380071\pi$
$90$		0			0
$91$	0.412231	−	2.39008i	0.0432136	−	0.250549i
$92$	−6.91272	−	1.09487i	−0.720700	−	0.114148i
$93$	1.03784	+	0.278088i	0.107619	+	0.0288364i
$94$	−1.07202	−	10.1996i	−0.110571	−	1.05201i
$95$		0			0
$96$	18.1858	+	1.91140i	1.85608	+	0.195081i
$97$	3.51689	−	0.557021i	0.357086	−	0.0565569i	0.0246858	−	0.999695i	$-0.492141\pi$
$97$	3.51689	−	0.557021i	0.357086	−	0.0565569i	0.332400	+	0.943138i	$0.392141\pi$
$98$	5.62265	−	0.140190i	0.567973	−	0.0141613i
$99$			34.3480i			3.45211i
$100$		0			0
$101$	−8.57568	−	4.95117i	−0.853312	−	0.492660i	0.00845468	−	0.999964i	$-0.497309\pi$
$101$	−8.57568	−	4.95117i	−0.853312	−	0.492660i	−0.861767	+	0.507304i	$0.830642\pi$
$102$	−0.0684023	+	1.30519i	−0.00677283	+	0.129233i
$103$	−5.77149	+	4.67366i	−0.568682	+	0.460510i	−0.870026	−	0.493006i	$-0.835898\pi$
$103$	−5.77149	+	4.67366i	−0.568682	+	0.460510i	0.301344	+	0.953516i	$0.402565\pi$
$104$	−1.99885	−	1.45225i	−0.196004	−	0.142405i
$105$		0			0
$106$	−3.81085	+	2.76875i	−0.370143	+	0.268924i
$107$	0.403711	−	1.50667i	0.0390282	−	0.145655i	−0.943662	−	0.330910i	$-0.892644\pi$
$107$	0.403711	−	1.50667i	0.0390282	−	0.145655i	0.982691	+	0.185255i	$0.0593110\pi$
$108$	−10.2932	+	12.7110i	−0.990460	+	1.22312i
$109$	1.24225	−	5.84432i	0.118986	−	0.559784i	−0.877755	−	0.479110i	$-0.840959\pi$
$109$	1.24225	−	5.84432i	0.118986	−	0.559784i	0.996741	−	0.0806741i	$-0.0257073\pi$
$110$		0			0
$111$	−19.0510	−	6.19005i	−1.80824	−	0.587533i
$112$	−0.602563	+	1.30491i	−0.0569368	+	0.123302i
$113$	−2.24970	−	1.14628i	−0.211634	−	0.107833i	0.344960	−	0.938617i	$-0.387892\pi$
$113$	−2.24970	−	1.14628i	−0.211634	−	0.107833i	−0.556595	+	0.830784i	$0.687892\pi$
$114$	−0.583669	−	2.74595i	−0.0546656	−	0.257181i
$115$		0			0
$116$	−7.65649	−	1.62744i	−0.710888	−	0.151104i
$117$	5.86074	−	2.24973i	0.541826	−	0.207987i
$118$	−4.99668	−	4.99668i	−0.459982	−	0.459982i
$119$	−1.27345	−	0.508980i	−0.116737	−	0.0466581i
$120$		0			0
$121$	−1.47982	+	14.0795i	−0.134529	+	1.27996i
$122$	−0.417002	+	1.08633i	−0.0377536	+	0.0983514i
$123$	−22.2689	−	1.16706i	−2.00792	−	0.105230i
$124$	0.231863	+	0.401598i	0.0208219	+	0.0360645i
$125$		0			0
$126$	7.76060	+	12.3169i	0.691369	+	1.09728i
$127$	8.21389	−	4.18519i	0.728865	−	0.371375i	−0.0498468	−	0.998757i	$-0.515873\pi$
$127$	8.21389	−	4.18519i	0.728865	−	0.371375i	0.778712	+	0.627381i	$0.215873\pi$
$128$	5.51603	+	6.81173i	0.487553	+	0.602078i
$129$	12.2509	−	5.45446i	1.07863	−	0.480238i
$130$		0			0
$131$	2.28451	−	5.13108i	0.199598	−	0.448305i	−0.785820	−	0.618455i	$-0.787759\pi$
$131$	2.28451	−	5.13108i	0.199598	−	0.448305i	0.985418	+	0.170150i	$0.0544254\pi$
$132$	−15.0745	+	15.0745i	−1.31207	+	1.31207i
$133$	2.92502	+	0.348056i	0.253631	+	0.0301803i
$134$	1.07501	−	0.349291i	0.0928664	−	0.0301741i
$135$		0			0
$136$	−1.03821	+	0.934804i	−0.0890254	+	0.0801588i
$137$	2.35453	+	3.62566i	0.201161	+	0.309761i	0.924826	−	0.380391i	$-0.124210\pi$
$137$	2.35453	+	3.62566i	0.201161	+	0.309761i	−0.723665	+	0.690152i	$0.757544\pi$
$138$	−13.0118	+	0.681919i	−1.10764	+	0.0580488i
$139$	1.99140	−	6.12890i	0.168908	−	0.519847i	−0.830395	−	0.557176i	$-0.811885\pi$
$139$	1.99140	−	6.12890i	0.168908	−	0.519847i	0.999303	+	0.0373290i	$0.0118849\pi$
$140$		0			0
$141$	12.3780	+	38.0956i	1.04242	+	3.20823i
$142$	−2.19377	−	5.71498i	−0.184097	−	0.479590i
$143$	4.44123	−	1.19002i	0.371394	−	0.0995147i
$144$	−3.69989	+	0.388874i	−0.308324	+	0.0324062i
$145$		0			0
$146$	−0.569565	+	0.783939i	−0.0471376	+	0.0648793i
$147$	−21.3667	+	5.10140i	−1.76229	+	0.420756i
$148$	−3.92493	−	7.70311i	−0.322627	−	0.633192i
$149$	1.92554	−	1.11171i	0.157746	−	0.0910749i	−0.419049	−	0.907964i	$-0.637636\pi$
$149$	1.92554	−	1.11171i	0.157746	−	0.0910749i	0.576795	+	0.816889i	$0.304303\pi$
$150$		0			0
$151$	6.19286	−	10.7263i	0.503968	−	0.872897i	−0.496022	−	0.868310i	$-0.665206\pi$
$151$	6.19286	−	10.7263i	0.503968	−	0.872897i	0.999989	−	0.00458736i	$-0.00146021\pi$
$152$	1.63432	−	2.51663i	0.132561	−	0.204125i
$153$	−0.555290	−	3.50596i	−0.0448925	−	0.283440i
$154$	4.70989	+	9.56581i	0.379534	+	0.770835i
$155$		0			0
$156$	3.55948	+	1.58478i	0.284987	+	0.126884i
$157$	4.35511	+	16.2535i	0.347576	+	1.29717i	0.889574	+	0.456791i	$0.151001\pi$
$157$	4.35511	+	16.2535i	0.347576	+	1.29717i	−0.541998	+	0.840380i	$0.682332\pi$
$158$	3.03619	+	2.45866i	0.241547	+	0.195601i
$159$	12.3105	−	13.6721i	0.976283	−	1.08427i
$160$		0			0
$161$	3.71933	−	13.1562i	0.293124	−	1.03685i
$162$	−6.32974	+	12.4228i	−0.497312	+	0.976029i
$163$	−0.952430	−	18.1734i	−0.0746001	−	1.42345i	−0.737804	−	0.675015i	$-0.764137\pi$
$163$	−0.952430	−	18.1734i	−0.0746001	−	1.42345i	0.663204	−	0.748439i	$-0.269196\pi$
$164$	−6.43989	−	7.15222i	−0.502871	−	0.558495i
$165$		0			0
$166$	2.07271	+	1.86628i	0.160873	+	0.144851i
$167$	0.0529161	−	0.334099i	0.00409477	−	0.0258534i	−0.985556	−	0.169348i	$-0.945834\pi$
$167$	0.0529161	−	0.334099i	0.00409477	−	0.0258534i	0.989651	+	0.143494i	$0.0458339\pi$
$168$	−4.95242	+	21.8231i	−0.382087	+	1.68369i
$169$	7.14727	+	9.83737i	0.549790	+	0.756721i
$170$		0			0
$171$	3.10112	+	6.96522i	0.237148	+	0.532644i
$172$	5.40336	+	2.07416i	0.412002	+	0.158153i
$173$	14.9288	+	9.69487i	1.13501	+	0.737087i	0.968515	−	0.248955i	$-0.0800870\pi$
$173$	14.9288	+	9.69487i	1.13501	+	0.737087i	0.166499	+	0.986042i	$0.446754\pi$
$174$	−14.5723			−1.10473
$175$		0			0
$176$	−2.72479			−0.205389
$177$	23.1466	+	15.0316i	1.73981	+	1.12984i
$178$	2.35718	+	0.904835i	0.176678	+	0.0678203i
$179$	−4.01032	−	9.00732i	−0.299745	−	0.673239i	0.699393	−	0.714737i	$-0.253454\pi$
$179$	−4.01032	−	9.00732i	−0.299745	−	0.673239i	−0.999139	+	0.0414980i	$0.986787\pi$
$180$		0			0
$181$	12.6158	+	17.3642i	0.937727	+	1.29067i	0.956768	+	0.290852i	$0.0939388\pi$
$181$	12.6158	+	17.3642i	0.937727	+	1.29067i	−0.0190405	+	0.999819i	$0.506061\pi$
$182$	1.32371	−	1.43018i	0.0981197	−	0.106012i
$183$	0.710952	−	4.48877i	0.0525551	−	0.331820i
$184$	−10.3501	−	9.31930i	−0.763022	−	0.687028i
$185$		0			0
$186$	0.577664	+	0.641561i	0.0423564	+	0.0470415i
$187$	−0.136065	−	2.59627i	−0.00995004	−	0.189858i
$188$	−7.84855	+	15.4036i	−0.572414	+	1.12343i
$189$	−22.2803	−	22.9000i	−1.62065	−	1.66573i
$190$		0			0
$191$	0.485439	−	0.539134i	0.0351251	−	0.0390104i	−0.725326	−	0.688405i	$-0.758311\pi$
$191$	0.485439	−	0.539134i	0.0351251	−	0.0390104i	0.760451	+	0.649395i	$0.224978\pi$
$192$	8.76840	+	7.10051i	0.632805	+	0.512435i
$193$	−3.80877	−	14.2145i	−0.274161	−	1.02318i	−0.956401	−	0.292055i	$-0.905661\pi$
$193$	−3.80877	−	14.2145i	−0.274161	−	1.02318i	0.682240	−	0.731128i	$-0.261006\pi$
$194$	2.61365	+	1.16367i	0.187649	+	0.0835467i
$195$		0			0
$196$	−8.07757	−	4.96386i	−0.576969	−	0.354562i
$197$	3.82227	+	24.1329i	0.272326	+	1.71940i	0.622420	+	0.782683i	$0.286149\pi$
$197$	3.82227	+	24.1329i	0.272326	+	1.71940i	−0.350095	+	0.936714i	$0.613851\pi$
$198$	−15.0310	+	23.1457i	−1.06821	+	1.64490i
$199$	0.487743	−	0.844796i	0.0345752	−	0.0598860i	−0.848220	−	0.529644i	$-0.822326\pi$
$199$	0.487743	−	0.844796i	0.0345752	−	0.0598860i	0.882795	+	0.469758i	$0.155659\pi$
$200$		0			0
$201$	−3.82326	+	2.20736i	−0.269672	+	0.155695i
$202$	−3.61212	−	7.08919i	−0.254148	−	0.498794i
$203$	4.92406	−	14.4760i	0.345601	−	1.01602i
$204$	1.29498	−	1.78238i	0.0906665	−	0.124792i
$205$		0			0
$206$	−5.93441	+	0.623732i	−0.413470	+	0.0434575i
$207$	34.1817	−	9.15896i	2.37579	−	0.636592i
$208$	0.178468	+	0.464926i	0.0123745	+	0.0322368i
$209$	1.72562	+	5.31092i	0.119364	+	0.367364i
$210$		0			0
$211$	−8.83060	+	27.1778i	−0.607923	+	1.87100i	−0.132636	+	0.991165i	$0.542344\pi$
$211$	−8.83060	+	27.1778i	−0.607923	+	1.87100i	−0.475287	+	0.879831i	$0.657656\pi$
$212$	7.92942	−	0.415563i	0.544595	−	0.0285410i
$213$	13.0218	+	20.0518i	0.892238	+	1.37393i
$214$	0.931378	−	0.838617i	0.0636677	−	0.0573266i
$215$		0			0
$216$	−30.9547	+	10.0578i	−2.10620	+	0.684347i
$217$	−0.832516	+	0.357060i	−0.0565148	+	0.0242388i
$218$	3.39463	−	3.39463i	0.229913	−	0.229913i
$219$	1.53935	−	3.45743i	0.104020	−	0.233632i
$220$		0			0
$221$	−0.434085	+	0.193267i	−0.0291997	+	0.0130005i
$222$	−10.1289	−	12.5081i	−0.679806	−	0.839490i
$223$	19.9284	−	10.1540i	1.33450	−	0.679963i	0.366385	−	0.930463i	$-0.380595\pi$
$223$	19.9284	−	10.1540i	1.33450	−	0.679963i	0.968116	+	0.250501i	$0.0805952\pi$
$224$	−13.0434	+	8.21837i	−0.871500	+	0.549113i
$225$		0			0
$226$	−1.01436	−	1.75692i	−0.0674742	−	0.116869i
$227$	5.57177	+	0.292004i	0.369811	+	0.0193810i	0.236337	−	0.971671i	$-0.424053\pi$
$227$	5.57177	+	0.292004i	0.369811	+	0.0193810i	0.133475	+	0.991052i	$0.457387\pi$
$228$	−1.69586	+	4.41786i	−0.112311	+	0.292580i
$229$	−1.66622	+	15.8530i	−0.110107	+	1.04760i	0.790352	+	0.612654i	$0.209898\pi$
$229$	−1.66622	+	15.8530i	−0.110107	+	1.04760i	−0.900458	+	0.434942i	$0.856769\pi$
$230$		0			0
$231$	−25.7613	−	32.7201i	−1.69497	−	2.15283i
$232$	−11.0142	−	11.0142i	−0.723119	−	0.723119i
$233$	−11.4661	+	4.40142i	−0.751168	+	0.288346i	−0.703672	−	0.710525i	$-0.748458\pi$
$233$	−11.4661	+	4.40142i	−0.751168	+	0.288346i	−0.0474962	+	0.998871i	$0.515124\pi$
$234$	4.93382	+	1.04872i	0.322534	+	0.0685567i
$235$		0			0
$236$	2.47656	+	11.6513i	0.161210	+	0.758435i
$237$	−13.5959	−	6.92744i	−0.883146	−	0.449985i
$238$	−0.635393	−	0.900256i	−0.0411864	−	0.0583549i
$239$	−14.3549	−	4.66418i	−0.928540	−	0.301701i	−0.194574	−	0.980888i	$-0.562333\pi$
$239$	−14.3549	−	4.66418i	−0.928540	−	0.301701i	−0.733965	+	0.679187i	$0.762333\pi$
$240$		0			0
$241$	4.82571	−	22.7032i	0.310851	−	1.46244i	−0.494259	−	0.869315i	$-0.664561\pi$
$241$	4.82571	−	22.7032i	0.310851	−	1.46244i	0.805110	−	0.593125i	$-0.202106\pi$
$242$	−7.15852	+	8.84004i	−0.460167	+	0.568259i
$243$	4.71744	−	17.6057i	0.302624	−	1.12941i
$244$	1.58686	−	1.15292i	0.101588	−	0.0738083i
$245$		0			0
$246$	−14.4954	−	10.5315i	−0.924191	−	0.671464i
$247$	0.793167	−	0.642294i	0.0504680	−	0.0408682i
$248$	−0.0482952	+	0.921528i	−0.00306675	+	0.0585171i
$249$	−9.43397	−	5.44671i	−0.597854	−	0.345171i
$250$		0			0
$251$		−	22.1623i		−	1.39887i	−0.714697	−	0.699434i	$-0.753435\pi$
$251$		−	22.1623i		−	1.39887i	0.714697	−	0.699434i	$-0.246565\pi$
$252$	0.336577	−	24.5375i	0.0212024	−	1.54572i
$253$	25.5993	−	4.05453i	1.60941	−	0.254906i
$254$	7.36649	+	0.774249i	0.462215	+	0.0485807i
$255$		0			0
$256$	1.48778	+	14.1553i	0.0929865	+	0.884708i
$257$	0.227789	+	0.0610358i	0.0142091	+	0.00380731i	0.265917	−	0.963996i	$-0.414325\pi$
$257$	0.227789	+	0.0610358i	0.0142091	+	0.00380731i	−0.251708	+	0.967803i	$0.580992\pi$
$258$	10.6423	+	1.68558i	0.662562	+	0.104939i
$259$	15.8480	−	5.83538i	0.984749	−	0.362593i
$260$		0			0
$261$	38.7125	−	8.22859i	2.39624	−	0.509337i
$262$	3.78485	−	2.45791i	0.233829	−	0.151850i
$263$	−19.2075	+	12.4735i	−1.18439	+	0.769151i	−0.977854	−	0.209289i	$-0.932885\pi$
$263$	−19.2075	+	12.4735i	−1.18439	+	0.769151i	−0.206534	+	0.978439i	$0.566218\pi$
$264$	−41.4959	+	8.82023i	−2.55390	+	0.542848i
$265$		0			0
$266$	1.81874	+	1.51456i	0.111514	+	0.0928635i
$267$	−9.74001	−	1.54267i	−0.596079	−	0.0944096i
$268$	−1.84044	−	0.493144i	−0.112423	−	0.0301236i
$269$	−1.11584	−	10.6165i	−0.0680340	−	0.647301i	−0.974402	−	0.224812i	$-0.927823\pi$
$269$	−1.11584	−	10.6165i	−0.0680340	−	0.647301i	0.906368	−	0.422489i	$-0.138843\pi$
$270$		0			0
$271$	−18.3674	−	1.93050i	−1.11574	−	0.117269i	−0.471337	−	0.881953i	$-0.656228\pi$
$271$	−18.3674	−	1.93050i	−1.11574	−	0.117269i	−0.644405	+	0.764684i	$0.722895\pi$
$272$	0.278124	−	0.0440505i	0.0168637	−	0.00267095i
$273$	−3.89566	+	6.53870i	−0.235776	+	0.395740i
$274$			3.47355i			0.209845i
$275$		0			0
$276$	19.0211	+	10.9819i	1.14494	+	0.661030i
$277$	−0.546310	+	10.4242i	−0.0328246	+	0.626331i	0.931843	+	0.362861i	$0.118200\pi$
$277$	−0.546310	+	10.4242i	−0.0328246	+	0.626331i	−0.964668	+	0.263469i	$0.915133\pi$
$278$	4.02399	−	3.25856i	0.241343	−	0.195436i
$279$	−1.89688	−	1.37816i	−0.113563	−	0.0825084i
$280$		0			0
$281$	23.9465	−	17.3981i	1.42853	−	1.03789i	0.438239	−	0.898858i	$-0.355602\pi$
$281$	23.9465	−	17.3981i	1.42853	−	1.03789i	0.990288	−	0.139028i	$-0.0443978\pi$
$282$	−8.32996	+	31.0878i	−0.496042	+	1.85125i
$283$	−17.5374	+	21.6568i	−1.04249	+	1.28737i	−0.0857806	+	0.996314i	$0.527338\pi$
$283$	−17.5374	+	21.6568i	−1.04249	+	1.28737i	−0.956707	+	0.291051i	$0.905995\pi$
$284$	−2.14543	+	10.0935i	−0.127308	+	0.598936i
$285$		0			0
$286$	3.51353	+	1.14161i	0.207759	+	0.0675051i
$287$	15.3599	−	10.8409i	0.906668	−	0.639919i
$288$	−35.5544	−	18.1159i	−2.09506	−	1.06749i
$289$	−3.47864	−	16.3657i	−0.204626	−	0.962688i
$290$		0			0
$291$	−10.9300	−	2.32324i	−0.640728	−	0.136191i
$292$	1.52493	−	0.585365i	0.0892397	−	0.0342559i
$293$	−4.85076	−	4.85076i	−0.283385	−	0.283385i	0.551073	−	0.834457i	$-0.314219\pi$
$293$	−4.85076	−	4.85076i	−0.283385	−	0.283385i	−0.834457	+	0.551073i	$0.814219\pi$
$294$	−16.6305	−	5.91263i	−0.969913	−	0.344831i
$295$		0			0
$296$	1.79831	−	17.1097i	0.104524	−	0.994483i
$297$	21.7063	−	56.5468i	1.25953	−	3.28118i
$298$	1.78404	+	0.0934974i	0.103346	+	0.00541616i
$299$	−2.36852	−	4.10240i	−0.136975	−	0.237248i
$300$		0			0
$301$	−5.27052	+	10.0024i	−0.303788	+	0.576529i
$302$	8.86706	−	4.51799i	0.510242	−	0.259981i
$303$	19.5563	+	24.1500i	1.12348	+	1.38738i
$304$	−0.552543	+	0.246008i	−0.0316905	+	0.0141095i
$305$		0			0
$306$	1.16006	−	2.60553i	0.0663159	−	0.148948i
$307$	−4.10345	+	4.10345i	−0.234196	+	0.234196i	−0.814442	−	0.580245i	$-0.802957\pi$
$307$	−4.10345	+	4.10345i	−0.234196	+	0.234196i	0.580245	+	0.814442i	$0.302957\pi$
$308$	2.12372	−	17.8475i	0.121010	−	1.01695i
$309$	22.1650	−	7.20186i	1.26093	−	0.409700i
$310$		0			0
$311$	−18.4026	+	16.5698i	−1.04352	+	0.939587i	−0.998235	−	0.0593868i	$-0.981085\pi$
$311$	−18.4026	+	16.5698i	−1.04352	+	0.939587i	−0.0452825	+	0.998974i	$0.514419\pi$
$312$	4.22288	+	6.50267i	0.239074	+	0.368141i
$313$	−7.13845	+	0.374110i	−0.403489	+	0.0211460i	−0.253001	−	0.967466i	$-0.581418\pi$
$313$	−7.13845	+	0.374110i	−0.403489	+	0.0211460i	−0.150488	+	0.988612i	$0.548084\pi$
$314$	−4.17795	+	12.8584i	−0.235776	+	0.725642i
$315$		0			0
$316$	−2.03508	−	6.26334i	−0.114482	−	0.352340i
$317$	−2.46462	−	6.42055i	−0.138427	−	0.360614i	0.846790	−	0.531928i	$-0.178532\pi$
$317$	−2.46462	−	6.42055i	−0.138427	−	0.360614i	−0.985217	+	0.171314i	$0.945199\pi$
$318$	14.2786	−	3.82593i	0.800703	−	0.214548i
$319$	28.8283	−	3.02998i	1.61408	−	0.169646i
$320$		0			0
$321$	−2.87720	+	3.96013i	−0.160590	+	0.221033i
$322$	8.26359	−	7.23782i	0.460512	−	0.403348i
$323$	−0.261996	−	0.514197i	−0.0145779	−	0.0286107i
$324$	20.3537	−	11.7512i	1.13076	−	0.652844i
$325$		0			0
$326$	7.31107	−	12.6631i	0.404923	−	0.701347i
$327$	−10.2121	+	15.7253i	−0.564731	+	0.869609i
$328$	−2.99601	−	18.9161i	−0.165427	−	1.04447i
$329$	−28.0676	−	18.7796i	−1.54742	−	1.03535i
$330$		0			0
$331$	16.8201	+	7.48880i	0.924517	+	0.411622i	0.813081	−	0.582150i	$-0.197788\pi$
$331$	16.8201	+	7.48880i	0.924517	+	0.411622i	0.111436	+	0.993772i	$0.464455\pi$
$332$	−1.21684	−	4.54131i	−0.0667828	−	0.249237i
$333$	33.9711	+	27.5092i	1.86160	+	1.50750i
$334$	0.181863	−	0.201979i	0.00995110	−	0.0110518i
$335$		0			0
$336$	3.23288	−	3.14539i	0.176368	−	0.171595i
$337$	−5.72591	+	11.2377i	−0.311910	+	0.612158i	−0.992740	−	0.120284i	$-0.961620\pi$
$337$	−5.72591	+	11.2377i	−0.311910	+	0.612158i	0.680829	+	0.732442i	$0.261620\pi$
$338$	0.511328	+	9.75671i	0.0278126	+	0.530695i
$339$	5.30191	+	5.88837i	0.287960	+	0.319812i
$340$		0			0
$341$	−1.27618	−	1.14908i	−0.0691093	−	0.0622263i
$342$	−0.958330	+	6.05066i	−0.0518206	+	0.327182i
$343$	11.4931	−	14.5227i	0.620568	−	0.784153i
$344$	6.76978	+	9.31780i	0.365002	+	0.502382i
$345$		0			0
$346$	5.81734	+	13.0660i	0.312742	+	0.702430i
$347$	−9.60936	−	3.68869i	−0.515857	−	0.198019i	0.0864907	−	0.996253i	$-0.472435\pi$
$347$	−9.60936	−	3.68869i	−0.515857	−	0.198019i	−0.602348	+	0.798234i	$0.705768\pi$
$348$	20.6013	+	13.3786i	1.10434	+	0.717169i
$349$	11.2771			0.603650			0.301825	−	0.953363i	$-0.402404\pi$
$349$	11.2771			0.603650			0.301825	+	0.953363i	$0.402404\pi$
$350$		0			0
$351$	−11.0702			−0.590883
$352$	−24.5110	−	15.9177i	−1.30644	−	0.848414i
$353$	−15.5330	−	5.96258i	−0.826740	−	0.317356i	−0.0920465	−	0.995755i	$-0.529341\pi$
$353$	−15.5330	−	5.96258i	−0.826740	−	0.317356i	−0.734694	+	0.678399i	$0.762674\pi$
$354$	9.01960	+	20.2583i	0.479386	+	1.07672i
$355$		0			0
$356$	−2.50168	−	3.44327i	−0.132589	−	0.182493i
$357$	3.15847	+	2.92333i	0.167164	+	0.154719i
$358$	1.23930	−	7.82462i	0.0654990	−	0.413544i
$359$	12.9020	+	11.6170i	0.680942	+	0.613123i	0.935245	−	0.354001i	$-0.115179\pi$
$359$	12.9020	+	11.6170i	0.680942	+	0.613123i	−0.254302	+	0.967125i	$0.581846\pi$
$360$		0			0
$361$	−11.8841	−	13.1986i	−0.625477	−	0.694662i
$362$	0.902558	+	17.2218i	0.0474374	+	0.905160i
$363$	20.1696	−	39.5851i	1.05863	−	2.07768i
$364$	−3.18438	+	0.806608i	−0.166907	+	0.0422777i
$365$		0			0
$366$	2.44341	−	2.71368i	0.127719	−	0.141847i
$367$	−5.79997	−	4.69672i	−0.302756	−	0.245167i	0.465888	−	0.884844i	$-0.345735\pi$
$367$	−5.79997	−	4.69672i	−0.302756	−	0.245167i	−0.768644	+	0.639677i	$0.779068\pi$
$368$	0.726570	+	2.71160i	0.0378751	+	0.141352i
$369$	44.4548	+	19.7926i	2.31423	+	1.03036i
$370$		0			0
$371$	−1.02415	+	15.4770i	−0.0531710	+	0.803526i
$372$	−0.227651	−	1.43733i	−0.0118032	−	0.0745222i
$373$	−16.0748	+	24.7530i	−0.832322	+	1.28166i	0.124860	+	0.992174i	$0.460152\pi$
$373$	−16.0748	+	24.7530i	−0.832322	+	1.28166i	−0.957181	+	0.289489i	$0.906515\pi$
$374$	1.04446	−	1.80906i	0.0540080	−	0.0935445i
$375$		0			0
$376$	−29.7932	+	17.2011i	−1.53647	+	0.887079i
$377$	−2.40520	−	4.72046i	−0.123874	−	0.243116i
$378$	−4.99252	−	25.1815i	−0.256788	−	1.29520i
$379$	0.558890	−	0.769246i	0.0287082	−	0.0395135i	−0.794422	−	0.607367i	$-0.792226\pi$
$379$	0.558890	−	0.769246i	0.0287082	−	0.0395135i	0.823130	+	0.567853i	$0.192226\pi$
$380$		0			0
$381$	−28.7713	+	3.02399i	−1.47400	+	0.154923i
$382$	0.563048	−	0.150868i	0.0288080	−	0.00771909i
$383$	3.63311	+	9.46458i	0.185643	+	0.483618i	0.994543	−	0.104329i	$-0.0332696\pi$
$383$	3.63311	+	9.46458i	0.185643	+	0.483618i	−0.808899	+	0.587947i	$0.799936\pi$
$384$	−8.49991	−	26.1600i	−0.433759	−	1.33497i
$385$		0			0
$386$	3.65383	−	11.2453i	0.185975	−	0.572373i
$387$	−29.2239	+	1.53156i	−1.48553	+	0.0778535i
$388$	−2.62663	−	4.04465i	−0.133347	−	0.205336i
$389$	−9.99997	+	9.00401i	−0.507018	+	0.456521i	−0.882503	−	0.470307i	$-0.844143\pi$
$389$	−9.99997	+	9.00401i	−0.507018	+	0.456521i	0.375484	+	0.926829i	$0.377476\pi$
$390$		0			0
$391$	−2.54742	+	0.827706i	−0.128828	+	0.0418589i
$392$	−8.10093	−	17.0388i	−0.409159	−	0.860590i
$393$	−12.4635	+	12.4635i	−0.628702	+	0.628702i
$394$	−7.98510	+	17.9348i	−0.402284	+	0.903544i
$395$		0			0
$396$	42.4994	−	18.9220i	2.13568	−	0.950864i
$397$	16.9763	+	20.9639i	0.852014	+	1.05215i	0.998022	+	0.0628659i	$0.0200241\pi$
$397$	16.9763	+	20.9639i	0.852014	+	1.05215i	−0.146008	+	0.989283i	$0.546643\pi$
$398$	0.698361	−	0.355833i	0.0350057	−	0.0178363i
$399$	−8.17811	−	4.30925i	−0.409418	−	0.215732i
$400$		0			0
$401$	−7.65133	−	13.2525i	−0.382089	−	0.661798i	0.609271	−	0.792962i	$-0.291462\pi$
$401$	−7.65133	−	13.2525i	−0.382089	−	0.661798i	−0.991361	+	0.131164i	$0.958129\pi$
$402$	−3.54231	−	0.185644i	−0.176674	−	0.00925910i
$403$	−0.112478	+	0.293015i	−0.00560293	+	0.0145961i
$404$	−1.40192	+	13.3384i	−0.0697481	+	0.663609i
$405$		0			0
$406$	9.65297	−	7.59999i	0.479069	−	0.377181i
$407$	22.6386	+	22.6386i	1.12215	+	1.12215i
$408$	4.09297	−	1.57114i	0.202632	−	0.0777832i
$409$	12.6937	+	2.69813i	0.627664	+	0.133414i	0.510752	−	0.859728i	$-0.329367\pi$
$409$	12.6937	+	2.69813i	0.627664	+	0.133414i	0.116912	+	0.993142i	$0.462700\pi$
$410$		0			0
$411$	−2.82066	−	13.2702i	−0.139133	−	0.654570i
$412$	8.96225	+	4.56649i	0.441538	+	0.224975i
$413$	−23.1722	+	2.11460i	−1.14023	+	0.104053i
$414$	27.0417	+	8.78639i	1.32903	+	0.431827i
$415$		0			0
$416$	−1.11058	+	5.22485i	−0.0544505	+	0.256169i
$417$	−12.7270	+	15.7165i	−0.623243	+	0.769640i
$418$	−1.16128	+	4.33396i	−0.0568001	+	0.211981i
$419$	−14.8800	+	10.8109i	−0.726935	+	0.528149i	−0.888592	−	0.458698i	$-0.848316\pi$
$419$	−14.8800	+	10.8109i	−0.726935	+	0.528149i	0.161658	+	0.986847i	$0.448316\pi$
$420$		0			0
$421$	19.9632	+	14.5041i	0.972947	+	0.706887i	0.956121	−	0.292971i	$-0.0946441\pi$
$421$	19.9632	+	14.5041i	0.972947	+	0.706887i	0.0168253	+	0.999858i	$0.494644\pi$
$422$	−17.8438	+	14.4496i	−0.868624	+	0.703398i
$423$	4.57472	−	87.2908i	0.222430	−	4.24422i
$424$	13.6839	+	7.90043i	0.664551	+	0.383679i
$425$		0			0
$426$			19.2105i			0.930754i
$427$	1.87011	+	3.34423i	0.0905008	+	0.161838i
$428$	−2.08663	+	0.330490i	−0.100861	+	0.0159748i
$429$	−14.3499	−	1.50824i	−0.692822	−	0.0728185i
$430$		0			0
$431$	3.20202	+	30.4652i	0.154236	+	1.46746i	0.748473	+	0.663165i	$0.230787\pi$
$431$	3.20202	+	30.4652i	0.154236	+	1.46746i	−0.594237	+	0.804290i	$0.702546\pi$
$432$	6.33685	+	1.69795i	0.304882	+	0.0816928i
$433$	25.6195	+	4.05772i	1.23119	+	0.195002i	0.737929	−	0.674878i	$-0.235804\pi$
$433$	25.6195	+	4.05772i	1.23119	+	0.195002i	0.493263	+	0.869880i	$0.335804\pi$
$434$	−0.717251	−	0.123709i	−0.0344292	−	0.00593820i
$435$		0			0
$436$	−7.91562	+	1.68252i	−0.379089	+	0.0805779i
$437$	4.82506	−	3.13343i	0.230814	−	0.149892i
$438$	2.55031	−	1.65619i	0.121859	−	0.0791359i
$439$	13.0257	−	2.76869i	0.621681	−	0.132142i	0.113706	−	0.993514i	$-0.463728\pi$
$439$	13.0257	−	2.76869i	0.621681	−	0.132142i	0.507974	+	0.861372i	$0.330394\pi$
$440$		0			0
$441$	47.5189	+	6.31652i	2.26281	+	0.300787i
$442$	−0.377088	−	0.0597248i	−0.0179362	−	0.00284082i
$443$	14.5088	+	3.88763i	0.689335	+	0.184707i	0.586449	−	0.809986i	$-0.300526\pi$
$443$	14.5088	+	3.88763i	0.689335	+	0.184707i	0.102886	+	0.994693i	$0.467192\pi$
$444$	2.83594	+	26.9822i	0.134588	+	1.28052i
$445$		0			0
$446$	17.8724	+	1.87846i	0.846283	+	0.0889479i
$447$	−6.89157	+	1.09152i	−0.325960	+	0.0516270i
$448$	−9.51150	−	0.130468i	−0.449376	−	0.00616402i
$449$			3.87012i			0.182642i	0.995822	+	0.0913211i	$0.0291090\pi$
$449$			3.87012i			0.182642i	−0.995822	+	0.0913211i	$0.970891\pi$
$450$		0			0
$451$	30.8658	+	17.8204i	1.45341	+	0.839129i
$452$	−0.178976	+	3.41507i	−0.00841833	+	0.160631i
$453$	−30.2065	+	24.4607i	−1.41923	+	1.14927i
$454$	3.62680	+	2.63503i	0.170214	+	0.123668i
$455$		0			0
$456$	−7.61836	+	5.53507i	−0.356763	+	0.259203i
$457$	10.9654	−	40.9235i	0.512941	−	1.91432i	0.126636	−	0.991949i	$-0.459582\pi$
$457$	10.9654	−	40.9235i	0.512941	−	1.91432i	0.386304	−	0.922371i	$-0.373751\pi$
$458$	−8.06022	+	9.95354i	−0.376629	+	0.465098i
$459$	−1.30143	+	6.12275i	−0.0607456	+	0.285785i
$460$		0			0
$461$	21.8890	+	7.11217i	1.01947	+	0.331247i	0.770620	−	0.637295i	$-0.219947\pi$
$461$	21.8890	+	7.11217i	1.01947	+	0.331247i	0.248852	+	0.968541i	$0.419947\pi$
$462$	−3.04084	−	33.3221i	−0.141473	−	1.55029i
$463$	−16.0881	−	8.19728i	−0.747676	−	0.380960i	0.0382600	−	0.999268i	$-0.487818\pi$
$463$	−16.0881	−	8.19728i	−0.747676	−	0.380960i	−0.785936	+	0.618308i	$0.787818\pi$
$464$	0.652765	+	3.07102i	0.0303038	+	0.142568i
$465$		0			0
$466$	−9.65263	−	2.05173i	−0.447149	−	0.0950445i
$467$	−25.5999	+	9.82687i	−1.18462	+	0.454733i	−0.869316	−	0.494257i	$-0.835440\pi$
$467$	−25.5999	+	9.82687i	−1.18462	+	0.454733i	−0.315305	+	0.948990i	$0.602107\pi$
$468$	−6.01224	−	6.01224i	−0.277916	−	0.277916i
$469$	1.38138	−	3.45616i	0.0637861	−	0.159591i
$470$		0			0
$471$	5.51969	−	52.5163i	0.254334	−	2.41983i
$472$	−8.49459	+	22.1292i	−0.390995	+	1.01858i
$473$	−21.4041	−	1.12174i	−0.984160	−	0.0515776i
$474$	−6.13019	−	10.6178i	−0.281569	−	0.487691i
$475$		0			0
$476$	0.0717609	+	1.85606i	0.00328916	+	0.0850721i
$477$	−35.7717	+	18.2266i	−1.63787	+	0.834538i
$478$	−7.63208	−	9.42483i	−0.349083	−	0.431082i
$479$	33.3579	−	14.8519i	1.52416	−	0.678600i	0.537781	−	0.843084i	$-0.319263\pi$
$479$	33.3579	−	14.8519i	1.52416	−	0.678600i	0.986380	+	0.164484i	$0.0525959\pi$
$480$		0			0
$481$	2.38000	−	5.34557i	0.108519	−	0.243737i
$482$	13.1870	−	13.1870i	0.600650	−	0.600650i
$483$	−25.6924	+	34.3614i	−1.16904	+	1.56350i
$484$	18.2360	−	5.92525i	0.828911	−	0.269330i
$485$		0			0
$486$	10.8833	−	9.79939i	0.493678	−	0.444509i
$487$	−19.6435	−	30.2483i	−0.890130	−	1.37068i	−0.928467	−	0.371415i	$-0.878873\pi$
$487$	−19.6435	−	30.2483i	−0.890130	−	1.37068i	0.0383371	−	0.999265i	$-0.487794\pi$
$488$	3.89789	−	0.204280i	0.176449	−	0.00924731i
$489$	−17.6479	+	54.3145i	−0.798064	+	2.45619i
$490$		0			0
$491$	2.89375	+	8.90606i	0.130593	+	0.401925i	0.994879	−	0.101077i	$-0.0322289\pi$
$491$	2.89375	+	8.90606i	0.130593	+	0.401925i	−0.864285	+	0.503002i	$0.832229\pi$
$492$	10.8236	+	28.1966i	0.487968	+	1.27120i
$493$	−2.89357	+	0.775330i	−0.130320	+	0.0349191i
$494$	0.815557	−	0.0857185i	0.0366936	−	0.00385666i
$495$		0			0
$496$	0.109328	−	0.150477i	0.00490897	−	0.00675662i
$497$	−19.0836	−	6.49132i	−0.856015	−	0.291176i
$498$	−3.97364	−	7.79871i	−0.178063	−	0.349468i
$499$	−27.8046	+	16.0530i	−1.24470	+	0.718630i	−0.970048	−	0.242912i	$-0.921897\pi$
$499$	−27.8046	+	16.0530i	−1.24470	+	0.718630i	−0.274656	+	0.961543i	$0.588564\pi$
$500$		0			0
$501$	−0.530765	+	0.919313i	−0.0237128	+	0.0410719i
$502$	9.69841	−	14.9342i	0.432861	−	0.666548i
$503$	5.06296	+	31.9663i	0.225746	+	1.42531i	0.796725	+	0.604342i	$0.206564\pi$
$503$	5.06296	+	31.9663i	0.225746	+	1.42531i	−0.570979	+	0.820965i	$0.693436\pi$
$504$	27.1557	−	40.5863i	1.20961	−	1.80786i
$505$		0			0
$506$	19.0246	+	8.47031i	0.845748	+	0.376551i
$507$	−9.87630	−	36.8589i	−0.438622	−	1.63696i
$508$	−9.70335	−	7.85761i	−0.430516	−	0.348625i
$509$	−17.6550	+	19.6079i	−0.782546	+	0.869105i	−0.994123	−	0.108256i	$-0.965473\pi$
$509$	−17.6550	+	19.6079i	−0.782546	+	0.869105i	0.211577	+	0.977361i	$0.432140\pi$
$510$		0			0
$511$	0.783483	+	3.09309i	0.0346593	+	0.136830i
$512$	2.76657	−	5.42969i	0.122266	−	0.239961i
$513$	−0.703655	−	13.4265i	−0.0310671	−	0.592796i
$514$	0.126788	+	0.140812i	0.00559236	+	0.00621095i
$515$		0			0
$516$	−13.4978	−	12.1535i	−0.594207	−	0.535026i
$517$	10.0151	−	63.2328i	0.440463	−	2.78097i
$518$	13.2330	+	3.00302i	0.581423	+	0.131945i
$519$	−32.8344	−	45.1926i	−1.44127	−	1.98374i
$520$		0			0
$521$	3.65972	+	8.21986i	0.160335	+	0.360119i	0.975792	−	0.218699i	$-0.0701811\pi$
$521$	3.65972	+	8.21986i	0.160335	+	0.360119i	−0.815457	+	0.578817i	$0.803514\pi$
$522$	29.6877	+	11.3960i	1.29939	+	0.498791i
$523$	5.71287	+	3.70998i	0.249806	+	0.162226i	0.663468	−	0.748204i	$-0.269084\pi$
$523$	5.71287	+	3.70998i	0.249806	+	0.162226i	−0.413662	+	0.910431i	$0.635750\pi$
$524$	−7.60728			−0.332326
$525$		0			0
$526$	−18.4017			−0.802353
$527$	0.148839	+	0.0966572i	0.00648353	+	0.00421045i
$528$	7.98292	+	3.06435i	0.347412	+	0.133359i
$529$	−1.50605	−	3.38265i	−0.0654805	−	0.147072i
$530$		0			0
$531$	−35.4005	−	48.7246i	−1.53625	−	2.11447i
$532$	−1.18071	−	3.81092i	−0.0511901	−	0.165224i
$533$	1.01901	−	6.43377i	0.0441382	−	0.278678i
$534$	−5.88831	−	5.30186i	−0.254812	−	0.229434i
$535$		0			0
$536$	−2.53707	−	2.81770i	−0.109585	−	0.121706i
$537$	1.61936	+	30.8992i	0.0698804	+	1.33340i
$538$	3.89397	−	7.64234i	0.167881	−	0.329485i
$539$	34.1294	+	8.23895i	1.47006	+	0.354877i
$540$		0			0
$541$	2.34511	−	2.60451i	0.100824	−	0.111977i	−0.690621	−	0.723217i	$-0.742663\pi$
$541$	2.34511	−	2.60451i	0.100824	−	0.111977i	0.791445	+	0.611241i	$0.209329\pi$
$542$	−11.5323	−	9.33865i	−0.495353	−	0.401129i
$543$	−17.4329	−	65.0606i	−0.748118	−	2.79202i
$544$	2.75922	+	1.22848i	0.118300	+	0.0526708i
$545$		0			0
$546$	−5.48653	+	2.70139i	−0.234802	+	0.115609i
$547$	−4.73400	−	29.8893i	−0.202411	−	1.27798i	−0.854348	−	0.519702i	$-0.826043\pi$
$547$	−4.73400	−	29.8893i	−0.202411	−	1.27798i	0.651936	−	0.758274i	$-0.273957\pi$
$548$	3.18900	−	4.91064i	0.136228	−	0.209772i
$549$	−4.95876	+	8.58882i	−0.211635	+	0.366562i
$550$		0			0
$551$	5.57235	−	3.21720i	0.237390	−	0.137057i
$552$	19.8425	+	38.9431i	0.844552	+	1.65753i
$553$	12.6190	−	2.50187i	0.536616	−	0.106390i
$554$	−4.92987	+	6.78539i	−0.209450	+	0.288283i
$555$		0			0
$556$	−8.68043	+	0.912350i	−0.368132	+	0.0386923i
$557$	−14.5926	+	3.91007i	−0.618307	+	0.165675i	−0.554358	−	0.832278i	$-0.687036\pi$
$557$	−14.5926	+	3.91007i	−0.618307	+	0.165675i	−0.0639490	+	0.997953i	$0.520370\pi$
$558$	−0.675132	−	1.75878i	−0.0285806	−	0.0744551i
$559$	1.21052	+	3.72561i	0.0511997	+	0.157576i
$560$		0			0
$561$	−2.52119	+	7.75941i	−0.106445	+	0.327603i
$562$	23.7502	−	1.24469i	1.00184	−	0.0525042i
$563$	19.1136	+	29.4323i	0.805540	+	1.24042i	0.967310	+	0.253595i	$0.0816131\pi$
$563$	19.1136	+	29.4323i	0.805540	+	1.24042i	−0.161770	+	0.986828i	$0.551720\pi$
$564$	40.3174	−	36.3020i	1.69767	−	1.52859i
$565$		0			0
$566$	−21.2950	+	6.91915i	−0.895094	+	0.290834i
$567$	18.0964	+	42.1934i	0.759978	+	1.77195i
$568$	−14.5199	+	14.5199i	−0.609242	+	0.609242i
$569$	−1.04675	+	2.35103i	−0.0438819	+	0.0985603i	−0.934156	−	0.356864i	$-0.883846\pi$
$569$	−1.04675	+	2.35103i	−0.0438819	+	0.0985603i	0.890274	+	0.455425i	$0.150513\pi$
$570$		0			0
$571$	−18.5051	+	8.23900i	−0.774414	+	0.344791i	−0.755601	−	0.655032i	$-0.772655\pi$
$571$	−18.5051	+	8.23900i	−0.774414	+	0.344791i	−0.0188125	+	0.999823i	$0.505989\pi$
$572$	−3.91906	−	4.83963i	−0.163864	−	0.202355i
$573$	−2.02853	+	1.03359i	−0.0847430	+	0.0431787i
$574$	15.0945	−	0.583602i	0.630033	−	0.0243591i
$575$		0			0
$576$	−12.3107	−	21.3228i	−0.512946	−	0.888449i
$577$	40.0201	+	2.09736i	1.66606	+	0.0873144i	0.861892	−	0.507091i	$-0.169279\pi$
$577$	40.0201	+	2.09736i	1.66606	+	0.0873144i	0.804165	+	0.594406i	$0.202613\pi$
$578$	4.81767	−	12.5505i	0.200389	−	0.522031i
$579$	−4.82725	+	45.9282i	−0.200614	+	1.90871i
$580$		0			0
$581$	9.08987	−	1.31216i	0.377111	−	0.0544375i
$582$	−6.34861	−	6.34861i	−0.263158	−	0.263158i
$583$	−27.4516	+	10.5377i	−1.13693	+	0.436427i
$584$	3.17940	+	0.675803i	0.131565	+	0.0279649i
$585$		0			0
$586$	−1.14599	−	5.39147i	−0.0473405	−	0.222720i
$587$	−17.2988	−	8.81418i	−0.713998	−	0.363800i	0.0589574	−	0.998261i	$-0.481222\pi$
$587$	−17.2988	−	8.81418i	−0.713998	−	0.363800i	−0.772955	+	0.634460i	$0.781222\pi$
$588$	18.0827	+	23.6270i	0.745718	+	0.974362i
$589$	−0.362534	−	0.117795i	−0.0149380	−	0.00485364i
$590$		0			0
$591$	15.9421	−	75.0016i	0.655770	−	3.08515i
$592$	−2.18228	+	2.69489i	−0.0896910	+	0.110759i
$593$	−4.61082	+	17.2078i	−0.189344	+	0.706640i	0.804315	+	0.594203i	$0.202532\pi$
$593$	−4.61082	+	17.2078i	−0.189344	+	0.706640i	−0.993659	+	0.112437i	$0.964134\pi$
$594$	39.3724	−	28.6057i	1.61547	−	1.17371i
$595$		0			0
$596$	−2.43630	−	1.77007i	−0.0997945	−	0.0725050i
$597$	−2.37904	+	1.92650i	−0.0973674	+	0.0788466i
$598$	0.199198	−	3.80093i	0.00814581	−	0.155431i
$599$	12.9831	+	7.49578i	0.530474	+	0.306269i	0.741209	−	0.671274i	$-0.234253\pi$
$599$	12.9831	+	7.49578i	0.530474	+	0.306269i	−0.210735	+	0.977543i	$0.567586\pi$
$600$		0			0
$601$			20.7383i			0.845932i	0.906145	+	0.422966i	$0.139011\pi$
$601$			20.7383i			0.845932i	−0.906145	+	0.422966i	$0.860989\pi$
$602$	−7.92874	+	4.43379i	−0.323151	+	0.180708i
$603$	9.51522	−	1.50706i	0.387490	−	0.0613723i
$604$	−16.6835	−	1.75350i	−0.678840	−	0.0713490i
$605$		0			0
$606$	2.60992	+	24.8317i	0.106021	+	1.00872i
$607$	20.9910	+	5.62452i	0.851999	+	0.228292i	0.658288	−	0.752766i	$-0.271281\pi$
$607$	20.9910	+	5.62452i	0.851999	+	0.228292i	0.193711	+	0.981059i	$0.437948\pi$
$608$	−6.40757	−	1.01486i	−0.259861	−	0.0411580i
$609$	−30.7062	+	36.8733i	−1.24428	+	1.49418i
$610$		0			0
$611$	−11.4453	+	2.43276i	−0.463025	+	0.0984191i
$612$	−4.03208	+	2.61847i	−0.162987	+	0.105845i
$613$	5.93939	−	3.85709i	0.239890	−	0.155786i	−0.419095	−	0.907942i	$-0.637653\pi$
$613$	5.93939	−	3.85709i	0.239890	−	0.155786i	0.658985	+	0.752156i	$0.270986\pi$
$614$	−4.56086	+	0.969441i	−0.184061	+	0.0391234i
$615$		0			0
$616$	22.8875	−	27.4843i	0.922165	−	1.10737i
$617$	12.2737	+	1.94396i	0.494119	+	0.0782608i	0.398521	−	0.917159i	$-0.369524\pi$
$617$	12.2737	+	1.94396i	0.494119	+	0.0782608i	0.0955982	+	0.995420i	$0.469524\pi$
$618$	18.0877	+	4.84659i	0.727595	+	0.194959i
$619$	−2.86407	−	27.2498i	−0.115117	−	1.09526i	−0.887724	−	0.460377i	$-0.847714\pi$
$619$	−2.86407	−	27.2498i	−0.115117	−	1.09526i	0.772607	−	0.634884i	$-0.218952\pi$
$620$		0			0
$621$	−62.0610	−	6.52288i	−2.49042	−	0.261754i
$622$	−19.6519	+	3.11255i	−0.787969	+	0.124802i
$623$	7.25650	−	4.05787i	0.290726	−	0.162575i
$624$		−	1.56282i		−	0.0625628i
$625$		0			0
$626$	−4.97403	−	2.87176i	−0.198802	−	0.114778i
$627$	0.917150	−	17.5003i	0.0366274	−	0.698893i
$628$	17.7116	−	14.3425i	0.706768	−	0.572329i
$629$	−2.67675	−	1.94477i	−0.106729	−	0.0775432i
$630$		0			0
$631$	29.5709	−	21.4845i	1.17720	−	0.855286i	0.185347	−	0.982673i	$-0.440659\pi$
$631$	29.5709	−	21.4845i	1.17720	−	0.855286i	0.991853	+	0.127387i	$0.0406590\pi$
$632$	3.39187	−	12.6586i	0.134921	−	0.503534i
$633$	56.4360	−	69.6927i	2.24313	−	2.77003i
$634$	1.14889	−	5.40509i	0.0456281	−	0.214663i
$635$		0			0
$636$	−23.6985	−	7.70010i	−0.939705	−	0.305329i
$637$	−0.829611	−	6.36307i	−0.0328704	−	0.252114i
$638$	20.7522	+	10.5738i	0.821587	+	0.418619i
$639$	−10.8476	−	51.0342i	−0.429126	−	2.01888i
$640$		0			0
$641$	−43.4516	−	9.23593i	−1.71624	−	0.364797i	−0.758328	−	0.651873i	$-0.773984\pi$
$641$	−43.4516	−	9.23593i	−1.71624	−	0.364797i	−0.957908	+	0.287076i	$0.907317\pi$
$642$	−3.67182	+	1.40948i	−0.144915	+	0.0556277i
$643$	9.86123	+	9.86123i	0.388889	+	0.388889i	0.874291	−	0.485402i	$-0.161327\pi$
$643$	9.86123	+	9.86123i	0.388889	+	0.388889i	−0.485402	+	0.874291i	$0.661327\pi$
$644$	−18.3273	+	2.64562i	−0.722198	+	0.104252i
$645$		0			0
$646$	0.0484687	−	0.461149i	0.00190697	−	0.0181436i
$647$	−17.3847	+	45.2888i	−0.683464	+	1.78049i	−0.0605906	+	0.998163i	$0.519298\pi$
$647$	−17.3847	+	45.2888i	−0.683464	+	1.78049i	−0.622874	+	0.782322i	$0.714035\pi$
$648$	46.7046	+	2.44769i	1.83473	+	0.0961542i
$649$	−22.0556	−	38.2014i	−0.865759	−	1.49954i
$650$		0			0
$651$	2.84061	−	0.109827i	0.111332	−	0.00430445i
$652$	−21.9616	+	11.1900i	−0.860084	+	0.438235i
$653$	−28.5594	−	35.2679i	−1.11761	−	1.38014i	−0.916243	−	0.400624i	$-0.868793\pi$
$653$	−28.5594	−	35.2679i	−1.11761	−	1.38014i	−0.201372	−	0.979515i	$-0.564540\pi$
$654$	−13.7630	+	6.12770i	−0.538178	+	0.239612i
$655$		0			0
$656$	−1.57012	+	3.52655i	−0.0613029	+	0.137689i
$657$	−5.83988	+	5.83988i	−0.227835	+	0.227835i
$658$	−10.6955	−	24.9375i	−0.416954	−	0.972164i
$659$	−22.0985	+	7.18025i	−0.860837	+	0.279703i	−0.705978	−	0.708234i	$-0.749492\pi$
$659$	−22.0985	+	7.18025i	−0.860837	+	0.279703i	−0.154859	+	0.987937i	$0.549492\pi$
$660$		0			0
$661$	8.89784	−	8.01165i	0.346086	−	0.311617i	−0.477695	−	0.878526i	$-0.658528\pi$
$661$	8.89784	−	8.01165i	0.346086	−	0.311617i	0.823781	+	0.566909i	$0.191861\pi$
$662$	8.05723	+	12.4070i	0.313153	+	0.482213i
$663$	1.48911	−	0.0780408i	0.0578321	−	0.00303085i
$664$	2.89110	−	8.89790i	0.112197	−	0.345306i
$665$		0			0
$666$	10.8534	+	33.4034i	0.420562	+	1.29436i
$667$	−10.7024	−	27.8808i	−0.414399	−	1.07955i
$668$	−0.442538	+	0.118578i	−0.0171223	+	0.00458790i
$669$	−69.8042	+	7.33672i	−2.69879	+	0.283654i
$670$		0			0
$671$	−4.26953	+	5.87650i	−0.164823	+	0.226860i
$672$	47.4563	−	9.40877i	1.83067	−	0.362951i
$673$	10.4791	+	20.5664i	0.403939	+	0.792775i	0.999948	−	0.0102030i	$-0.00324777\pi$
$673$	10.4791	+	20.5664i	0.403939	+	0.792775i	−0.596009	+	0.802978i	$0.703248\pi$
$674$	−8.77620	+	5.06694i	−0.338046	+	0.195171i
$675$		0			0
$676$	8.23459	−	14.2627i	0.316715	−	0.548566i
$677$	6.28872	−	9.68378i	0.241695	−	0.372178i	−0.696917	−	0.717152i	$-0.745446\pi$
$677$	6.28872	−	9.68378i	0.241695	−	0.372178i	0.938612	+	0.344974i	$0.112112\pi$
$678$	0.995936	+	6.28809i	0.0382487	+	0.241493i
$679$	8.45187	−	4.16142i	0.324353	−	0.159701i
$680$		0			0
$681$	−15.9954	−	7.12162i	−0.612946	−	0.272901i
$682$	−0.357120	−	1.33279i	−0.0136748	−	0.0510352i
$683$	−11.2514	−	9.11124i	−0.430524	−	0.348632i	0.389435	−	0.921054i	$-0.372670\pi$
$683$	−11.2514	−	9.11124i	−0.430524	−	0.348632i	−0.819959	+	0.572422i	$0.806004\pi$
$684$	6.90982	−	7.67413i	0.264203	−	0.293428i
$685$		0			0
$686$	14.1000	−	4.75679i	0.538340	−	0.181615i
$687$	22.7102	−	44.5713i	0.866448	−	1.70050i
$688$	−0.121497	−	2.31830i	−0.00463202	−	0.0883842i
$689$	3.59605	+	3.99382i	0.136999	+	0.152153i
$690$		0			0
$691$	32.5795	+	29.3347i	1.23938	+	1.11594i	0.989019	+	0.147792i	$0.0472165\pi$
$691$	32.5795	+	29.3347i	1.23938	+	1.11594i	0.250362	+	0.968152i	$0.419450\pi$
$692$	3.77152	−	23.8124i	0.143372	−	0.905213i
$693$	26.8943	+	86.8056i	1.02163	+	3.29747i
$694$	−4.86115	−	6.69080i	−0.184527	−	0.253979i
$695$		0			0
$696$	19.8820	+	44.6556i	0.753624	+	1.69267i
$697$	−3.43862	−	1.31996i	−0.130247	−	0.0499971i
$698$	7.59919	+	4.93497i	0.287633	+	0.186791i
$699$	38.5425			1.45781
$700$		0			0
$701$	−30.4358			−1.14955			−0.574773	−	0.818313i	$-0.694910\pi$
$701$	−30.4358			−1.14955			−0.574773	+	0.818313i	$0.694910\pi$
$702$	−7.45976	−	4.84442i	−0.281550	−	0.182841i
$703$	6.63467	+	2.54681i	0.250231	+	0.0960549i
$704$	−7.33474	−	16.4741i	−0.276438	−	0.620890i
$705$		0			0
$706$	−7.85780	−	10.8153i	−0.295732	−	0.407041i
$707$	−25.5495	−	5.79808i	−0.960888	−	0.218059i
$708$	5.84762	−	36.9204i	0.219767	−	1.38755i
$709$	3.18109	+	2.86427i	0.119468	+	0.107570i	0.726700	−	0.686955i	$-0.241053\pi$
$709$	3.18109	+	2.86427i	0.119468	+	0.107570i	−0.607231	+	0.794525i	$0.707720\pi$
$710$		0			0
$711$	22.2808	+	24.7454i	0.835597	+	0.928025i
$712$	−0.443258	−	8.45787i	−0.0166118	−	0.316972i
$713$	−0.803220	+	1.57641i	−0.0300808	+	0.0590370i
$714$	0.849089	+	3.35209i	0.0317763	+	0.125449i
$715$		0			0
$716$	−8.93567	+	9.92407i	−0.333942	+	0.370880i
$717$	36.8106	+	29.8086i	1.37472	+	1.11322i
$718$	3.61042	+	13.4743i	0.134740	+	0.502856i
$719$	−16.8483	−	7.50137i	−0.628337	−	0.279754i	0.0677597	−	0.997702i	$-0.478415\pi$
$719$	−16.8483	−	7.50137i	−0.628337	−	0.279754i	−0.696097	+	0.717948i	$0.745082\pi$
$720$		0			0
$721$	−10.9265	+	16.3305i	−0.406923	+	0.608179i
$722$	−2.23236	−	14.0946i	−0.0830798	−	0.524545i
$723$	−39.6705	+	61.0872i	−1.47536	+	2.27186i
$724$	14.5351	−	25.1755i	0.540193	−	0.935641i
$725$		0			0
$726$	30.9143	−	17.8484i	1.14734	−	0.662415i
$727$	15.6762	+	30.7663i	0.581398	+	1.14106i	0.975089	+	0.221816i	$0.0711983\pi$
$727$	15.6762	+	30.7663i	0.581398	+	1.14106i	−0.393690	+	0.919243i	$0.628802\pi$
$728$	−6.18868	−	2.10509i	−0.229368	−	0.0780200i
$729$	−3.02204	+	4.15948i	−0.111927	+	0.154055i
$730$		0			0
$731$	2.20288	−	0.231532i	0.0814766	−	0.00856353i
$732$	−5.94569	+	1.59314i	−0.219759	+	0.0588843i
$733$	−10.0283	−	26.1246i	−0.370404	−	0.964935i	−0.984450	−	0.175665i	$-0.943792\pi$
$733$	−10.0283	−	26.1246i	−0.370404	−	0.964935i	0.614046	−	0.789270i	$-0.289541\pi$
$734$	−1.85303	−	5.70305i	−0.0683967	−	0.210504i
$735$		0			0
$736$	−9.30467	+	28.6368i	−0.342975	+	1.05557i
$737$	7.04630	−	0.369281i	0.259554	−	0.0136026i
$738$	21.2949	+	32.7913i	0.783876	+	1.20706i
$739$	−6.19977	+	5.58230i	−0.228062	+	0.205348i	−0.775237	−	0.631670i	$-0.782370\pi$
$739$	−6.19977	+	5.58230i	−0.228062	+	0.205348i	0.547175	+	0.837018i	$0.315703\pi$
$740$		0			0
$741$	−3.04611	+	0.989740i	−0.111902	+	0.0363590i
$742$	−7.46301	+	9.98114i	−0.273976	+	0.366419i
$743$	−31.5650	+	31.5650i	−1.15801	+	1.15801i	−0.173106	+	0.984903i	$0.555380\pi$
$743$	−31.5650	+	31.5650i	−1.15801	+	1.15801i	−0.984903	+	0.173106i	$0.944620\pi$
$744$	1.17786	−	2.64552i	0.0431825	−	0.0969895i
$745$		0			0
$746$	−21.6643	+	9.64557i	−0.793187	+	0.353150i
$747$	14.9600	+	18.4740i	0.547357	+	0.675929i
$748$	−3.13745	+	1.59861i	−0.114717	+	0.0584510i
$749$	−0.159440	−	4.12382i	−0.00582580	−	0.150681i
$750$		0			0
$751$	22.8072	+	39.5032i	0.832247	+	1.44149i	0.896252	+	0.443544i	$0.146279\pi$
$751$	22.8072	+	39.5032i	0.832247	+	1.44149i	−0.0640055	+	0.997950i	$0.520388\pi$
$752$	6.92468	+	0.362907i	0.252517	+	0.0132339i
$753$	−24.9241	+	64.9296i	−0.908285	+	2.36616i
$754$	0.444955	−	4.23347i	0.0162043	−	0.154174i
$755$		0			0
$756$	−16.0606	+	40.1832i	−0.584119	+	1.46145i
$757$	11.9819	+	11.9819i	0.435488	+	0.435488i	0.890490	−	0.455002i	$-0.150362\pi$
$757$	11.9819	+	11.9819i	0.435488	+	0.435488i	−0.455002	+	0.890490i	$0.650362\pi$
$758$	0.713242	−	0.273788i	0.0259061	−	0.00994443i
$759$	−79.5590	−	16.9108i	−2.88781	−	0.613823i
$760$		0			0
$761$	4.79969	+	22.5808i	0.173989	+	0.818552i	0.975401	+	0.220439i	$0.0707491\pi$
$761$	4.79969	+	22.5808i	0.173989	+	0.818552i	−0.801412	+	0.598112i	$0.795918\pi$
$762$	−20.7111	−	10.5528i	−0.750285	−	0.382289i
$763$	−1.43661	−	15.7427i	−0.0520087	−	0.569922i
$764$	−0.934503	−	0.303638i	−0.0338091	−	0.0109852i
$765$		0			0
$766$	−1.69358	+	7.96768i	−0.0611917	+	0.287884i
$767$	−5.07364	+	6.26543i	−0.183199	+	0.226231i
$768$	11.5606	−	43.1446i	0.417155	−	1.55685i
$769$	−33.2899	+	24.1865i	−1.20046	+	0.872188i	−0.994330	−	0.106336i	$-0.966088\pi$
$769$	−33.2899	+	24.1865i	−1.20046	+	0.872188i	−0.206133	+	0.978524i	$0.566088\pi$
$770$		0			0
$771$	−0.598719	−	0.434994i	−0.0215623	−	0.0156659i
$772$	−15.4897	+	12.5433i	−0.557485	+	0.451442i
$773$	0.947395	−	18.0774i	0.0340754	−	0.650198i	−0.927193	−	0.374584i	$-0.877785\pi$
$773$	0.947395	−	18.0774i	0.0340754	−	0.650198i	0.961268	−	0.275614i	$-0.0888812\pi$
$774$	−20.3630	−	11.7566i	−0.731933	−	0.422582i
$775$		0			0
$776$		−	9.59695i		−	0.344510i
$777$	−52.9932	−	0.726899i	−1.90112	−	0.0260773i
$778$	−10.6788	+	1.69136i	−0.382854	+	0.0606381i
$779$	7.86800	+	0.826960i	0.281900	+	0.0296289i
$780$		0			0
$781$	−3.99438	−	38.0040i	−0.142930	−	1.35989i
$782$	−2.07881	−	0.557016i	−0.0743382	−	0.0199189i
$783$	−68.9320	−	10.9178i	−2.46343	−	0.390169i
$784$	−0.501082	+	3.76962i	−0.0178958	+	0.134629i
$785$		0			0
$786$	−13.8528	+	2.94451i	−0.494114	+	0.105027i
$787$	12.8762	−	8.36192i	0.458988	−	0.298070i	−0.294357	−	0.955695i	$-0.595106\pi$
$787$	12.8762	−	8.36192i	0.458988	−	0.298070i	0.753345	+	0.657625i	$0.228439\pi$
$788$	27.7544	−	18.0239i	0.988709	−	0.642075i
$789$	70.3010	−	14.9429i	2.50278	−	0.531983i
$790$		0			0
$791$	−6.58306	−	1.13542i	−0.234067	−	0.0403709i
$792$	91.4358	+	14.4820i	3.24903	+	0.514596i
$793$	1.28234	+	0.343602i	0.0455373	+	0.0122017i
$794$	2.26560	+	21.5557i	0.0804030	+	0.764983i
$795$		0			0
$796$	−1.31397	−	0.138104i	−0.0465725	−	0.00489497i
$797$	15.1507	−	2.39964i	0.536667	−	0.0849997i	0.117783	−	0.993039i	$-0.462421\pi$
$797$	15.1507	−	2.39964i	0.536667	−	0.0849997i	0.418884	+	0.908040i	$0.362421\pi$
$798$	−3.62513	−	6.48265i	−0.128328	−	0.229483i
$799$			6.61618i			0.234064i
$800$		0			0
$801$	18.6365	+	10.7598i	0.658489	+	0.380179i
$802$	0.643495	−	12.2786i	0.0227226	−	0.433573i
$803$	−4.70088	+	3.80670i	−0.165891	+	0.134336i
$804$	4.83740	+	3.51458i	0.170602	+	0.123950i
$805$		0			0
$806$	−0.204021	+	0.148230i	−0.00718632	+	0.00522117i
$807$	−8.67043	+	32.3585i	−0.305214	+	1.13907i
$808$	−16.7959	+	20.7413i	−0.590879	+	0.729675i
$809$	4.30722	−	20.2639i	0.151434	−	0.712441i	−0.835260	−	0.549855i	$-0.814683\pi$
$809$	4.30722	−	20.2639i	0.151434	−	0.712441i	0.986694	−	0.162586i	$-0.0519835\pi$
$810$		0			0
$811$	27.8184	+	9.03875i	0.976837	+	0.317394i	0.753573	−	0.657364i	$-0.228329\pi$
$811$	27.8184	+	9.03875i	0.976837	+	0.317394i	0.223264	+	0.974758i	$0.428329\pi$
$812$	−20.6240	+	1.88206i	−0.723762	+	0.0660475i
$813$	51.6407	+	26.3122i	1.81112	+	0.922811i
$814$	5.34837	+	25.1621i	0.187460	+	0.881932i
$815$		0			0
$816$	−0.864370	−	0.183728i	−0.0302590	−	0.00643175i
$817$	−4.44167	+	1.70500i	−0.155394	+	0.0596503i
$818$	7.37305	+	7.37305i	0.257793	+	0.257793i
$819$	13.0500	−	10.2745i	0.456002	−	0.359021i
$820$		0			0
$821$	−3.10205	+	29.5141i	−0.108262	+	1.03005i	0.796647	+	0.604444i	$0.206605\pi$
$821$	−3.10205	+	29.5141i	−0.108262	+	1.03005i	−0.904910	+	0.425603i	$0.860062\pi$
$822$	3.90643	−	10.1766i	0.136252	−	0.354949i
$823$	−14.8590	−	0.778726i	−0.517951	−	0.0271447i	−0.208430	−	0.978037i	$-0.566835\pi$
$823$	−14.8590	−	0.778726i	−0.517951	−	0.0271447i	−0.309521	+	0.950893i	$0.600169\pi$
$824$	10.0081	+	17.3345i	0.348647	+	0.603875i
$825$		0			0
$826$	−16.5402	−	8.71543i	−0.575506	−	0.303249i
$827$	−32.9522	+	16.7900i	−1.14586	+	0.583844i	−0.920620	−	0.390459i	$-0.872316\pi$
$827$	−32.9522	+	16.7900i	−1.14586	+	0.583844i	−0.225239	+	0.974304i	$0.572316\pi$
$828$	−30.1629	−	37.2480i	−1.04823	−	1.29446i
$829$	−37.4078	+	16.6550i	−1.29923	+	0.578453i	−0.935590	−	0.353088i	$-0.885131\pi$
$829$	−37.4078	+	16.6550i	−1.29923	+	0.578453i	−0.363636	+	0.931541i	$0.618465\pi$
$830$		0			0
$831$	13.3238	−	29.9258i	0.462199	−	1.03812i
$832$	−2.33053	+	2.33053i	−0.0807967	+	0.0807967i
$833$	−3.61684	−	0.289209i	−0.125316	−	0.0100205i
$834$	−15.4539	+	5.02127i	−0.535124	+	0.173872i
$835$		0			0
$836$	5.62066	−	5.06086i	0.194395	−	0.175034i
$837$	2.25188	+	3.46759i	0.0778363	+	0.119857i
$838$	−14.7580	+	0.773433i	−0.509806	+	0.0267178i
$839$	−6.83090	+	21.0234i	−0.235829	+	0.725807i	0.761181	+	0.648539i	$0.224620\pi$
$839$	−6.83090	+	21.0234i	−0.235829	+	0.725807i	−0.997010	+	0.0772679i	$0.975380\pi$
$840$		0			0
$841$	−1.35975	−	4.18488i	−0.0468879	−	0.144306i
$842$	7.10525	+	18.5098i	0.244863	+	0.637890i
$843$	−89.7232	+	24.0413i	−3.09023	+	0.828025i
$844$	38.4922	−	4.04569i	1.32496	−	0.139258i
$845$		0			0
$846$	41.2820	−	56.8198i	1.41930	−	1.95350i
$847$	7.28433	+	36.7410i	0.250292	+	1.26243i
$848$	−1.44589	−	2.83772i	−0.0496522	−	0.0974479i
$849$	75.7356	−	43.7260i	2.59924	−	1.50067i
$850$		0			0
$851$	16.4924	−	28.5656i	0.565351	−	0.979217i
$852$	17.6369	−	27.1584i	0.604229	−	0.930430i
$853$	2.30932	+	14.5805i	0.0790697	+	0.499226i	0.995161	+	0.0982567i	$0.0313266\pi$
$853$	2.30932	+	14.5805i	0.0790697	+	0.499226i	−0.916091	+	0.400969i	$0.868673\pi$
$854$	−0.203275	+	3.07191i	−0.00695594	+	0.105119i
$855$		0			0
$856$	−3.84060	−	1.70995i	−0.131269	−	0.0584447i
$857$	4.99249	+	18.6322i	0.170540	+	0.636465i	0.997268	+	0.0738633i	$0.0235328\pi$
$857$	4.99249	+	18.6322i	0.170540	+	0.636465i	−0.826728	+	0.562602i	$0.809800\pi$
$858$	−9.00983	−	7.29601i	−0.307590	−	0.249082i
$859$	−20.0572	+	22.2758i	−0.684344	+	0.760040i	−0.980802	−	0.195005i	$-0.937528\pi$
$859$	−20.0572	+	22.2758i	−0.684344	+	0.760040i	0.296459	+	0.955046i	$0.404194\pi$
$860$		0			0
$861$	−57.1925	+	14.4869i	−1.94911	+	0.493713i
$862$	−11.1741	+	21.9305i	−0.380592	+	0.746955i
$863$	−1.34889	−	25.7384i	−0.0459169	−	0.876147i	−0.920373	−	0.391042i	$-0.872115\pi$
$863$	−1.34889	−	25.7384i	−0.0459169	−	0.876147i	0.874456	−	0.485105i	$-0.161219\pi$
$864$	47.0845	+	52.2926i	1.60185	+	1.77903i
$865$		0			0
$866$	15.4882	+	13.9456i	0.526311	+	0.473892i
$867$	−8.21371	+	51.8593i	−0.278952	+	1.76124i
$868$	0.900420	+	0.833385i	0.0305622	+	0.0282869i
$869$	14.3350	+	19.7304i	0.486282	+	0.669309i
$870$		0			0
$871$	−0.524529	−	1.17811i	−0.0177730	−	0.0399188i
$872$	−15.0340	−	5.77103i	−0.509117	−	0.195432i
$873$	20.4504	+	13.2807i	0.692142	+	0.449482i
$874$	4.62263			0.156363
$875$		0			0
$876$	−5.12595			−0.173190
$877$	18.1027	+	11.7560i	0.611286	+	0.396973i	0.812826	−	0.582507i	$-0.197928\pi$
$877$	18.1027	+	11.7560i	0.611286	+	0.396973i	−0.201540	+	0.979480i	$0.564595\pi$
$878$	9.98906	+	3.83444i	0.337115	+	0.129406i
$879$	8.75619	+	19.6667i	0.295339	+	0.663342i
$880$		0			0
$881$	18.9856	+	26.1314i	0.639640	+	0.880388i	0.998596	−	0.0529657i	$-0.0168674\pi$
$881$	18.9856	+	26.1314i	0.639640	+	0.880388i	−0.358957	+	0.933354i	$0.616867\pi$
$882$	29.2569	+	25.0512i	0.985131	+	0.843517i
$883$	−2.76060	+	17.4297i	−0.0929015	+	0.586557i	0.896691	+	0.442657i	$0.145964\pi$
$883$	−2.76060	+	17.4297i	−0.0929015	+	0.586557i	−0.989592	+	0.143899i	$0.954036\pi$
$884$	0.478265	+	0.430632i	0.0160858	+	0.0144837i
$885$		0			0
$886$	8.07564	+	8.96891i	0.271306	+	0.301316i
$887$	−1.20691	−	23.0292i	−0.0405240	−	0.773244i	−0.941014	−	0.338368i	$-0.890125\pi$
$887$	−1.20691	−	23.0292i	−0.0405240	−	0.773244i	0.900490	−	0.434877i	$-0.143208\pi$
$888$	−24.5105	+	48.1046i	−0.822519	+	1.61429i
$889$	17.4815	−	17.0084i	0.586310	−	0.570443i
$890$		0			0
$891$	−58.2375	+	64.6793i	−1.95103	+	2.16684i
$892$	−23.5420	−	19.0640i	−0.788245	−	0.638309i
$893$	−3.67808	−	13.7268i	−0.123082	−	0.459349i
$894$	−5.12161	−	2.28029i	−0.171292	−	0.0762642i
$895$		0			0
$896$	19.2739	+	12.8958i	0.643894	+	0.430820i
$897$	2.32550	+	14.6826i	0.0776462	+	0.490239i
$898$	−1.69360	+	2.60791i	−0.0565162	+	0.0870273i
$899$	−0.989361	+	1.71362i	−0.0329970	+	0.0571525i
$900$		0			0
$901$	2.63168	−	1.51940i	0.0876739	−	0.0506185i
$902$	13.0008	+	25.5156i	0.432881	+	0.849576i
$903$	26.6902	−	23.3771i	0.888193	−	0.777941i
$904$	−3.99998	+	5.50549i	−0.133037	+	0.183110i
$905$		0			0
$906$	−31.0592	+	3.26445i	−1.03187	+	0.108454i
$907$	−39.8182	+	10.6692i	−1.32214	+	0.354266i	−0.849779	−	0.527139i	$-0.823265\pi$
$907$	−39.8182	+	10.6692i	−1.32214	+	0.354266i	−0.472361	+	0.881405i	$0.656598\pi$
$908$	−2.70812	−	7.05490i	−0.0898722	−	0.234125i
$909$	−20.9552	−	64.4936i	−0.695041	−	2.13912i
$910$		0			0
$911$	0.709840	−	2.18466i	0.0235181	−	0.0723812i	−0.938609	−	0.344984i	$-0.887884\pi$
$911$	0.709840	−	2.18466i	0.0235181	−	0.0723812i	0.962127	+	0.272603i	$0.0878844\pi$
$912$	1.89547	−	0.0993374i	0.0627653	−	0.00328939i
$913$	9.48257	+	14.6019i	0.313827	+	0.483251i
$914$	25.2977	−	22.7781i	0.836772	−	0.753433i
$915$		0			0
$916$	20.5331	−	6.67160i	0.678432	−	0.220436i
$917$	1.75588	−	14.7562i	0.0579843	−	0.487293i
$918$	−3.55635	+	3.55635i	−0.117377	+	0.117377i
$919$	−10.3836	+	23.3219i	−0.342523	+	0.769318i	0.657354	+	0.753582i	$0.271676\pi$
$919$	−10.3836	+	23.3219i	−0.342523	+	0.769318i	−0.999876	+	0.0157361i	$0.994991\pi$
$920$		0			0
$921$	16.6369	−	7.40721i	0.548203	−	0.244076i
$922$	11.6378	+	14.3714i	0.383269	+	0.473298i
$923$	−6.22293	+	3.17074i	−0.204830	+	0.104366i
$924$	−26.2936	+	49.9000i	−0.864995	+	1.64159i
$925$		0			0
$926$	−7.25389	−	12.5641i	−0.238378	−	0.412882i
$927$	−50.7881	−	2.66169i	−1.66810	−	0.0874214i
$928$	−12.0682	+	31.4389i	−0.396160	+	1.03203i
$929$	4.69716	−	44.6905i	0.154109	−	1.46625i	−0.594960	−	0.803755i	$-0.702832\pi$
$929$	4.69716	−	44.6905i	0.154109	−	1.46625i	0.749069	−	0.662492i	$-0.230501\pi$
$930$		0			0
$931$	7.66474	−	1.41065i	0.251202	−	0.0462323i
$932$	11.7625	+	11.7625i	0.385293	+	0.385293i
$933$	72.5496	−	27.8492i	2.37517	−	0.911741i
$934$	−21.5510	−	4.58082i	−0.705172	−	0.149889i
$935$		0			0
$936$	−3.51782	−	16.5501i	−0.114984	−	0.540956i
$937$	50.8942	+	25.9319i	1.66264	+	0.847158i	0.994686	+	0.102956i	$0.0328301\pi$
$937$	50.8942	+	25.9319i	1.66264	+	0.847158i	0.667955	+	0.744202i	$0.267170\pi$
$938$	2.44330	−	1.72446i	0.0797767	−	0.0563057i
$939$	21.3345	+	6.93200i	0.696226	+	0.226217i
$940$		0			0
$941$	−6.78377	+	31.9151i	−0.221145	+	1.04040i	0.717777	+	0.696273i	$0.245160\pi$
$941$	−6.78377	+	31.9151i	−0.221145	+	1.04040i	−0.938922	+	0.344131i	$0.888174\pi$
$942$	26.7011	−	32.9732i	0.869970	−	1.07432i
$943$	9.50367	−	35.4682i	0.309482	−	1.15500i
$944$	3.86527	−	2.80828i	0.125804	−	0.0914018i
$945$		0			0
$946$	−13.9324	−	10.1225i	−0.452983	−	0.329111i
$947$	28.4911	−	23.0717i	0.925837	−	0.749728i	−0.0425722	−	0.999093i	$-0.513555\pi$
$947$	28.4911	−	23.0717i	0.925837	−	0.749728i	0.968410	+	0.249365i	$0.0802219\pi$
$948$	−1.08162	+	20.6386i	−0.0351295	+	0.670312i
$949$	0.957429	+	0.552772i	0.0310795	+	0.0179437i
$950$		0			0
$951$			21.5823i			0.699854i
$952$	−1.89184	+	3.17538i	−0.0613150	+	0.102915i
$953$	−46.1551	+	7.31025i	−1.49511	+	0.236802i	−0.849795	−	0.527113i	$-0.823274\pi$
$953$	−46.1551	+	7.31025i	−1.49511	+	0.236802i	−0.645316	+	0.763916i	$0.723274\pi$
$954$	−32.0812	−	3.37187i	−1.03867	−	0.109168i
$955$		0			0
$956$	2.13687	+	20.3310i	0.0691114	+	0.657551i
$957$	−87.8669	−	23.5439i	−2.84034	−	0.761065i
$958$	28.9779	+	4.58964i	0.936232	+	0.148285i
$959$	8.78932	+	7.31932i	0.283822	+	0.236353i
$960$		0			0
$961$	−30.2079	+	6.42089i	−0.974449	+	0.207125i
$962$	3.94306	−	2.56065i	0.127129	−	0.0825587i
$963$	8.95855	−	5.81775i	0.288685	−	0.187474i
$964$	−30.7494	+	6.53599i	−0.990373	+	0.210510i
$965$		0			0
$966$	−32.3499	+	11.9115i	−1.04084	+	0.383247i
$967$	−7.10565	−	1.12542i	−0.228502	−	0.0361912i	0.0411332	−	0.999154i	$-0.486903\pi$
$967$	−7.10565	−	1.12542i	−0.228502	−	0.0361912i	−0.269635	+	0.962962i	$0.586903\pi$
$968$	36.8563	+	9.87561i	1.18461	+	0.317414i
$969$	0.189304	+	1.80111i	0.00608132	+	0.0578599i
$970$		0			0
$971$	22.1815	+	2.33137i	0.711839	+	0.0748173i	0.453525	−	0.891244i	$-0.350166\pi$
$971$	22.1815	+	2.33137i	0.711839	+	0.0748173i	0.258314	+	0.966061i	$0.416833\pi$
$972$	−24.3826	+	3.86183i	−0.782074	+	0.123868i
$973$	0.233851	−	17.0484i	0.00749691	−	0.546548i
$974$		−	28.9792i		−	0.928555i
$975$		0			0
$976$	−0.681341	−	0.393372i	−0.0218092	−	0.0125915i
$977$	3.00231	−	57.2875i	0.0960525	−	1.83279i	−0.348812	−	0.937193i	$-0.613415\pi$
$977$	3.00231	−	57.2875i	0.0960525	−	1.83279i	0.444865	−	0.895598i	$-0.353252\pi$
$978$	−35.6607	+	28.8775i	−1.14030	+	0.923400i
$979$	12.7512	+	9.26427i	0.407529	+	0.296087i
$980$		0			0
$981$	33.1024	−	24.0503i	1.05688	−	0.767867i
$982$	−1.94739	+	7.26776i	−0.0621438	+	0.231924i
$983$	−11.7205	+	14.4736i	−0.373825	+	0.461635i	−0.928990	−	0.370105i	$-0.879322\pi$
$983$	−11.7205	+	14.4736i	−0.373825	+	0.461635i	0.555165	+	0.831740i	$0.312655\pi$
$984$	−12.4959	+	58.7885i	−0.398354	+	1.87411i
$985$		0			0
$986$	−2.28915	−	0.743790i	−0.0729014	−	0.0236871i
$987$	61.1108	+	86.5848i	1.94518	+	2.75602i
$988$	−1.23167	−	0.627566i	−0.0391846	−	0.0199655i
$989$	4.59112	+	21.5995i	0.145989	+	0.686825i
$990$		0			0
$991$	41.3573	+	8.79076i	1.31376	+	0.279248i	0.810932	−	0.585140i	$-0.198961\pi$
$991$	41.3573	+	8.79076i	1.31376	+	0.279248i	0.502825	+	0.864388i	$0.332294\pi$
$992$	1.86252	−	0.714956i	0.0591352	−	0.0226999i
$993$	−40.8565	−	40.8565i	−1.29654	−	1.29654i
$994$	−10.0190	−	12.7254i	−0.317782	−	0.403625i
$995$		0			0
$996$	−1.54223	+	14.6733i	−0.0488674	+	0.464942i
$997$	−6.11742	+	15.9364i	−0.193741	+	0.504712i	−0.995697	−	0.0926712i	$-0.970459\pi$
$997$	−6.11742	+	15.9364i	−0.193741	+	0.504712i	0.801956	+	0.597383i	$0.203793\pi$
$998$	−25.7613	−	1.35009i	−0.815460	−	0.0427365i
$999$	−38.5417	−	66.7562i	−1.21941	−	2.11207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.b.507.11		288
5.2	odd	4		875.2.bb.c.493.8		288
5.3	odd	4		175.2.x.a.3.11	✓	288
5.4	even	2		875.2.bb.a.507.8		288
7.5	odd	6	inner	875.2.bb.b.257.11		288
25.6	even	5		175.2.x.a.17.8	yes	288
25.8	odd	20	inner	875.2.bb.b.143.11		288
25.17	odd	20		875.2.bb.a.143.8		288
25.19	even	10		875.2.bb.c.857.11		288
35.12	even	12		875.2.bb.c.243.11		288
35.19	odd	6		875.2.bb.a.257.8		288
35.33	even	12		175.2.x.a.103.8	yes	288
175.19	odd	30		875.2.bb.c.607.8		288
175.33	even	60	inner	875.2.bb.b.768.11		288
175.117	even	60		875.2.bb.a.768.8		288
175.131	odd	30		175.2.x.a.117.11	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.11	✓	288	5.3	odd	4
175.2.x.a.17.8	yes	288	25.6	even	5
175.2.x.a.103.8	yes	288	35.33	even	12
175.2.x.a.117.11	yes	288	175.131	odd	30
875.2.bb.a.143.8		288	25.17	odd	20
875.2.bb.a.257.8		288	35.19	odd	6
875.2.bb.a.507.8		288	5.4	even	2
875.2.bb.a.768.8		288	175.117	even	60
875.2.bb.b.143.11		288	25.8	odd	20	inner
875.2.bb.b.257.11		288	7.5	odd	6	inner
875.2.bb.b.507.11		288	1.1	even	1	trivial
875.2.bb.b.768.11		288	175.33	even	60	inner
875.2.bb.c.243.11		288	35.12	even	12
875.2.bb.c.493.8		288	5.2	odd	4
875.2.bb.c.607.8		288	175.19	odd	30
875.2.bb.c.857.11		288	25.19	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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.673859 + 0.437609i) q^{2} +(-2.92974 - 1.12462i) q^{3} +(-0.550889 - 1.23732i) q^{4} +(-1.48209 - 2.03992i) q^{6} +(2.52724 - 0.782993i) q^{7} +(0.421625 - 2.66204i) q^{8} +(5.08915 + 4.58229i) q^{9} +(3.35615 + 3.72738i) q^{11} +(0.222448 + 4.24455i) q^{12} +(0.416175 - 0.816789i) q^{13} +(2.04565 + 0.578315i) q^{14} +(-0.363508 + 0.403716i) q^{16} +(-0.402827 - 0.326203i) q^{17} +(1.42412 + 5.31488i) q^{18} +(1.01710 + 0.452842i) q^{19} +(-8.28471 - 0.548217i) q^{21} +(0.630435 + 3.98041i) q^{22} +(2.81441 - 4.33381i) q^{23} +(-4.22903 + 7.32490i) q^{24} +(0.637878 - 0.368279i) q^{26} +(-5.48243 - 10.7599i) q^{27} +(-2.36104 - 2.69565i) q^{28} +(3.39698 - 4.67555i) q^{29} +(-0.340506 + 0.0357886i) q^{31} +(-5.62839 + 1.50812i) q^{32} +(-5.64074 - 14.6946i) q^{33} +(-0.128699 - 0.396095i) q^{34} +(2.86619 - 8.82122i) q^{36} +(6.37440 - 0.334068i) q^{37} +(0.487214 + 0.750244i) q^{38} +(-2.13786 + 1.92494i) q^{39} +(6.75808 - 2.19583i) q^{41} +(-5.34282 - 3.99489i) q^{42} +(-3.02167 + 3.02167i) q^{43} +(2.76308 - 6.20599i) q^{44} +(3.79303 - 1.68877i) q^{46} +(-8.03274 - 9.91961i) q^{47} +(1.51901 - 0.773974i) q^{48} +(5.77384 - 3.95762i) q^{49} +(0.813322 + 1.40871i) q^{51} +(-1.23989 - 0.0649800i) q^{52} +(-2.10095 + 5.47316i) q^{53} +(1.01424 - 9.64981i) q^{54} +(-1.01881 - 7.05773i) q^{56} +(-2.47056 - 2.47056i) q^{57} +(4.33515 - 1.66411i) q^{58} +(-8.60248 - 1.82851i) q^{59} +(0.301099 + 1.41656i) q^{61} +(-0.245114 - 0.124892i) q^{62} +(16.4494 + 7.59576i) q^{63} +(-3.41938 - 1.11102i) q^{64} +(2.62944 - 12.3706i) q^{66} +(0.885317 - 1.09328i) q^{67} +(-0.181703 + 0.678125i) q^{68} +(-13.1194 + 9.53177i) q^{69} +(-6.16371 - 4.47820i) q^{71} +(14.3439 - 11.6155i) q^{72} +(-0.0631171 + 1.20435i) q^{73} +(4.44164 + 2.56438i) q^{74} -1.50794i q^{76} +(11.4003 + 6.79213i) q^{77} +(-2.28299 + 0.361590i) q^{78} +(4.83574 + 0.508257i) q^{79} +(1.81383 + 17.2574i) q^{81} +(5.51491 + 1.47772i) q^{82} +(3.42852 + 0.543025i) q^{83} +(3.88563 + 10.5528i) q^{84} +(-3.35849 + 0.713869i) q^{86} +(-15.2105 + 9.87780i) q^{87} +(11.3375 - 7.36263i) q^{88} +(3.07374 - 0.653343i) q^{89} +(0.412231 - 2.39008i) q^{91} +(-6.91272 - 1.09487i) q^{92} +(1.03784 + 0.278088i) q^{93} +(-1.07202 - 10.1996i) q^{94} +(18.1858 + 1.91140i) q^{96} +(3.51689 - 0.557021i) q^{97} +(5.62265 - 0.140190i) q^{98} +34.3480i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) \) 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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