LMFDB - Embedded newform 925.2.y.b.393.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] 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("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			393.9
Character	$\chi$	$=$	925.393
Dual form			925.2.y.b.732.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0909942 + 0.0525355i) q^{2} +(-1.93607 - 0.518767i) q^{3} +(-0.994480 - 1.72249i) q^{4} +(-0.148917 - 0.148917i) q^{6} +(-4.36283 - 1.16902i) q^{7} -0.419124i q^{8} +(0.881153 + 0.508734i) q^{9} -2.44344i q^{11} +(1.03181 + 3.85076i) q^{12} +(-4.02259 + 2.32245i) q^{13} +(-0.335578 - 0.335578i) q^{14} +(-1.96694 + 3.40684i) q^{16} +(3.81936 - 6.61533i) q^{17} +(0.0534532 + 0.0925836i) q^{18} +(-1.19934 - 0.321362i) q^{19} +(7.84028 + 4.52659i) q^{21} +(0.128367 - 0.222339i) q^{22} +0.150193i q^{23} +(-0.217428 + 0.811452i) q^{24} -0.488044 q^{26} +(2.80984 + 2.80984i) q^{27} +(2.32513 + 8.67750i) q^{28} +(0.503427 + 0.503427i) q^{29} +(-5.31753 + 5.31753i) q^{31} +(-1.08391 + 0.625793i) q^{32} +(-1.26757 + 4.73065i) q^{33} +(0.695080 - 0.401304i) q^{34} -2.02370i q^{36} +(2.33845 - 5.61531i) q^{37} +(-0.0922501 - 0.0922501i) q^{38} +(8.99281 - 2.40962i) q^{39} +(4.77325 - 2.75584i) q^{41} +(0.475614 + 0.823787i) q^{42} -1.79435i q^{43} +(-4.20880 + 2.42995i) q^{44} +(-0.00789049 + 0.0136667i) q^{46} +(-1.65421 + 1.65421i) q^{47} +(5.57548 - 5.57548i) q^{48} +(11.6055 + 6.70046i) q^{49} +(-10.8263 + 10.8263i) q^{51} +(8.00078 + 4.61925i) q^{52} +(11.3222 - 3.03376i) q^{53} +(0.108063 + 0.403296i) q^{54} +(-0.489964 + 1.82857i) q^{56} +(2.15529 + 1.24436i) q^{57} +(0.0193611 + 0.0722567i) q^{58} +(-0.0783231 - 0.292306i) q^{59} +(-2.65533 - 0.711494i) q^{61} +(-0.763224 + 0.204505i) q^{62} +(-3.24960 - 3.24960i) q^{63} +7.73626 q^{64} +(-0.363869 + 0.363869i) q^{66} +(-3.29741 + 12.3061i) q^{67} -15.1931 q^{68} +(0.0779154 - 0.290784i) q^{69} +(5.25961 + 9.10991i) q^{71} +(0.213223 - 0.369312i) q^{72} +(-6.35187 + 6.35187i) q^{73} +(0.507788 - 0.388109i) q^{74} +(0.639177 + 2.38544i) q^{76} +(-2.85642 + 10.6603i) q^{77} +(0.944884 + 0.253181i) q^{78} +(-4.95543 - 1.32780i) q^{79} +(-5.50858 - 9.54114i) q^{81} +0.579117 q^{82} +(-0.883111 + 0.236629i) q^{83} -18.0064i q^{84} +(0.0942673 - 0.163276i) q^{86} +(-0.713506 - 1.23583i) q^{87} -1.02410 q^{88} +(-7.43872 + 1.99320i) q^{89} +(20.2649 - 5.42996i) q^{91} +(0.258707 - 0.149364i) q^{92} +(13.0536 - 7.53653i) q^{93} +(-0.237428 + 0.0636187i) q^{94} +(2.42315 - 0.649281i) q^{96} -1.75339 q^{97} +(0.704025 + 1.21941i) q^{98} +(1.24306 - 2.15304i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.0909942	+	0.0525355i	0.0643426	+	0.0371482i	0.531826	−	0.846854i	$-0.321506\pi$
$2$	0.0909942	+	0.0525355i	0.0643426	+	0.0371482i	−0.467484	+	0.884002i	$0.654839\pi$
$3$	−1.93607	−	0.518767i	−1.11779	−	0.299510i	−0.347800	−	0.937569i	$-0.613071\pi$
$3$	−1.93607	−	0.518767i	−1.11779	−	0.299510i	−0.769988	+	0.638059i	$0.779738\pi$
$4$	−0.994480	−	1.72249i	−0.497240	−	0.861245i
$5$		0			0
$5$		0			0
$6$	−0.148917	−	0.148917i	−0.0607951	−	0.0607951i
$7$	−4.36283	−	1.16902i	−1.64900	−	0.441847i	−0.689665	−	0.724129i	$-0.742242\pi$
$7$	−4.36283	−	1.16902i	−1.64900	−	0.441847i	−0.959332	+	0.282282i	$0.908909\pi$
$8$		−	0.419124i		−	0.148183i
$9$	0.881153	+	0.508734i	0.293718	+	0.169578i
$10$		0			0
$11$		−	2.44344i		−	0.736724i	−0.929682	−	0.368362i	$-0.879919\pi$
$11$		−	2.44344i		−	0.736724i	0.929682	−	0.368362i	$-0.120081\pi$
$12$	1.03181	+	3.85076i	0.297857	+	1.11162i
$13$	−4.02259	+	2.32245i	−1.11567	+	0.644131i	−0.940291	−	0.340371i	$-0.889447\pi$
$13$	−4.02259	+	2.32245i	−1.11567	+	0.644131i	−0.175376	+	0.984502i	$0.556114\pi$
$14$	−0.335578	−	0.335578i	−0.0896869	−	0.0896869i
$15$		0			0
$16$	−1.96694	+	3.40684i	−0.491735	+	0.851711i
$17$	3.81936	−	6.61533i	0.926331	−	1.60445i	0.136925	−	0.990581i	$-0.456278\pi$
$17$	3.81936	−	6.61533i	0.926331	−	1.60445i	0.789406	−	0.613871i	$-0.210389\pi$
$18$	0.0534532	+	0.0925836i	0.0125990	+	0.0218222i
$19$	−1.19934	−	0.321362i	−0.275148	−	0.0737256i	0.118607	−	0.992941i	$-0.462157\pi$
$19$	−1.19934	−	0.321362i	−0.275148	−	0.0737256i	−0.393754	+	0.919216i	$0.628824\pi$
$20$		0			0
$21$	7.84028	+	4.52659i	1.71089	+	0.987783i
$22$	0.128367	−	0.222339i	0.0273680	−	0.0474028i
$23$			0.150193i			0.0313175i	0.999877	+	0.0156587i	$0.00498454\pi$
$23$			0.150193i			0.0313175i	−0.999877	+	0.0156587i	$0.995015\pi$
$24$	−0.217428	+	0.811452i	−0.0443823	+	0.165637i
$25$		0			0
$26$	−0.488044			−0.0957132
$27$	2.80984	+	2.80984i	0.540754	+	0.540754i
$28$	2.32513	+	8.67750i	0.439408	+	1.63989i
$29$	0.503427	+	0.503427i	0.0934840	+	0.0934840i	0.752302	−	0.658818i	$-0.228943\pi$
$29$	0.503427	+	0.503427i	0.0934840	+	0.0934840i	−0.658818	+	0.752302i	$0.728943\pi$
$30$		0			0
$31$	−5.31753	+	5.31753i	−0.955057	+	0.955057i	−0.999033	−	0.0439759i	$-0.985998\pi$
$31$	−5.31753	+	5.31753i	−0.955057	+	0.955057i	0.0439759	+	0.999033i	$0.485998\pi$
$32$	−1.08391	+	0.625793i	−0.191609	+	0.110626i
$33$	−1.26757	+	4.73065i	−0.220656	+	0.823501i
$34$	0.695080	−	0.401304i	0.119205	−	0.0688231i
$35$		0			0
$36$		−	2.02370i		−	0.337284i
$37$	2.33845	−	5.61531i	0.384438	−	0.923151i
$37$	2.33845	−	5.61531i	0.384438	−	0.923151i
$38$	−0.0922501	−	0.0922501i	−0.0149649	−	0.0149649i
$39$	8.99281	−	2.40962i	1.44000	−	0.385847i
$40$		0			0
$41$	4.77325	−	2.75584i	0.745456	−	0.430389i	−0.0785937	−	0.996907i	$-0.525043\pi$
$41$	4.77325	−	2.75584i	0.745456	−	0.430389i	0.824050	+	0.566518i	$0.191710\pi$
$42$	0.475614	+	0.823787i	0.0733888	+	0.127113i
$43$		−	1.79435i		−	0.273636i	−0.990596	−	0.136818i	$-0.956312\pi$
$43$		−	1.79435i		−	0.273636i	0.990596	−	0.136818i	$-0.0436876\pi$
$44$	−4.20880	+	2.42995i	−0.634500	+	0.366329i
$45$		0			0
$46$	−0.00789049	+	0.0136667i	−0.00116339	+	0.00201505i
$47$	−1.65421	+	1.65421i	−0.241291	+	0.241291i	−0.817384	−	0.576093i	$-0.804577\pi$
$47$	−1.65421	+	1.65421i	−0.241291	+	0.241291i	0.576093	+	0.817384i	$0.304577\pi$
$48$	5.57548	−	5.57548i	0.804752	−	0.804752i
$49$	11.6055	+	6.70046i	1.65793	+	0.957209i
$50$		0			0
$51$	−10.8263	+	10.8263i	−1.51599	+	1.51599i
$52$	8.00078	+	4.61925i	1.10951	+	0.640575i
$53$	11.3222	−	3.03376i	1.55522	−	0.416720i	0.624073	−	0.781366i	$-0.285477\pi$
$53$	11.3222	−	3.03376i	1.55522	−	0.416720i	0.931146	+	0.364647i	$0.118810\pi$
$54$	0.108063	+	0.403296i	0.0147055	+	0.0548816i
$55$		0			0
$56$	−0.489964	+	1.82857i	−0.0654742	+	0.244353i
$57$	2.15529	+	1.24436i	0.285475	+	0.164819i
$58$	0.0193611	+	0.0722567i	0.00254224	+	0.00948777i
$59$	−0.0783231	−	0.292306i	−0.0101968	−	0.0380550i	0.960640	−	0.277796i	$-0.0896040\pi$
$59$	−0.0783231	−	0.292306i	−0.0101968	−	0.0380550i	−0.970837	+	0.239741i	$0.922937\pi$
$60$		0			0
$61$	−2.65533	−	0.711494i	−0.339980	−	0.0910974i	0.0847894	−	0.996399i	$-0.472978\pi$
$61$	−2.65533	−	0.711494i	−0.339980	−	0.0910974i	−0.424770	+	0.905301i	$0.639645\pi$
$62$	−0.763224	+	0.204505i	−0.0969295	+	0.0259722i
$63$	−3.24960	−	3.24960i	−0.409412	−	0.409412i
$64$	7.73626			0.967032
$65$		0			0
$66$	−0.363869	+	0.363869i	−0.0447892	+	0.0447892i
$67$	−3.29741	+	12.3061i	−0.402843	+	1.50343i	0.405156	+	0.914247i	$0.367217\pi$
$67$	−3.29741	+	12.3061i	−0.402843	+	1.50343i	−0.807999	+	0.589183i	$0.799450\pi$
$68$	−15.1931			−1.84244
$69$	0.0779154	−	0.290784i	0.00937991	−	0.0350063i
$70$		0			0
$71$	5.25961	+	9.10991i	0.624201	+	1.08115i	0.988695	+	0.149941i	$0.0479085\pi$
$71$	5.25961	+	9.10991i	0.624201	+	1.08115i	−0.364494	+	0.931206i	$0.618758\pi$
$72$	0.213223	−	0.369312i	0.0251285	−	0.0435239i
$73$	−6.35187	+	6.35187i	−0.743431	+	0.743431i	−0.973237	−	0.229806i	$-0.926191\pi$
$73$	−6.35187	+	6.35187i	−0.743431	+	0.743431i	0.229806	+	0.973237i	$0.426191\pi$
$74$	0.507788	−	0.388109i	0.0590292	−	0.0451167i
$75$		0			0
$76$	0.639177	+	2.38544i	0.0733186	+	0.273629i
$77$	−2.85642	+	10.6603i	−0.325519	+	1.21486i
$78$	0.944884	+	0.253181i	0.106987	+	0.0286671i
$79$	−4.95543	−	1.32780i	−0.557530	−	0.149390i	−0.0309586	−	0.999521i	$-0.509856\pi$
$79$	−4.95543	−	1.32780i	−0.557530	−	0.149390i	−0.526571	+	0.850131i	$0.676523\pi$
$80$		0			0
$81$	−5.50858	−	9.54114i	−0.612065	−	1.06013i
$82$	0.579117			0.0639528
$83$	−0.883111	+	0.236629i	−0.0969340	+	0.0259734i	−0.306960	−	0.951722i	$-0.599312\pi$
$83$	−0.883111	+	0.236629i	−0.0969340	+	0.0259734i	0.210026	+	0.977696i	$0.432645\pi$
$84$		−	18.0064i		−	1.96466i
$85$		0			0
$86$	0.0942673	−	0.163276i	0.0101651	−	0.0176065i
$87$	−0.713506	−	1.23583i	−0.0764958	−	0.132495i
$88$	−1.02410			−0.109170
$89$	−7.43872	+	1.99320i	−0.788503	+	0.211279i	−0.630530	−	0.776165i	$-0.717162\pi$
$89$	−7.43872	+	1.99320i	−0.788503	+	0.211279i	−0.157973	+	0.987444i	$0.550496\pi$
$90$		0			0
$91$	20.2649	−	5.42996i	2.12434	−	0.569215i
$92$	0.258707	−	0.149364i	0.0269720	−	0.0155723i
$93$	13.0536	−	7.53653i	1.35360	−	0.781501i
$94$	−0.237428	+	0.0636187i	−0.0244889	+	0.00656177i
$95$		0			0
$96$	2.42315	−	0.649281i	0.247312	−	0.0662670i
$97$	−1.75339			−0.178030			−0.0890150	−	0.996030i	$-0.528372\pi$
$97$	−1.75339			−0.178030			−0.0890150	+	0.996030i	$0.528372\pi$
$98$	0.704025	+	1.21941i	0.0711172	+	0.123179i
$99$	1.24306	−	2.15304i	0.124932	−	0.216389i
$100$		0			0
$101$		−	1.85688i		−	0.184766i	−0.995724	−	0.0923831i	$-0.970552\pi$
$101$		−	1.85688i		−	0.184766i	0.995724	−	0.0923831i	$-0.0294485\pi$
$102$	−1.55390	+	0.416367i	−0.153859	+	0.0412265i
$103$	−3.56156			−0.350931			−0.175466	−	0.984486i	$-0.556143\pi$
$103$	−3.56156			−0.350931			−0.175466	+	0.984486i	$0.556143\pi$
$104$	0.973393	+	1.68597i	0.0954491	+	0.165323i
$105$		0			0
$106$	1.18963	+	0.318761i	0.115547	+	0.0309608i
$107$	−11.0067	−	2.94924i	−1.06406	−	0.285114i	−0.316010	−	0.948756i	$-0.602343\pi$
$107$	−11.0067	−	2.94924i	−1.06406	−	0.285114i	−0.748050	+	0.663642i	$0.769010\pi$
$108$	2.04559	−	7.63425i	0.196837	−	0.734606i
$109$	−1.72341	−	6.43186i	−0.165073	−	0.616061i	−0.998031	−	0.0627245i	$-0.980021\pi$
$109$	−1.72341	−	6.43186i	−0.165073	−	0.616061i	0.832958	−	0.553336i	$-0.186646\pi$
$110$		0			0
$111$	−7.44042	+	9.65849i	−0.706214	+	0.916743i
$112$	12.5641	−	12.5641i	1.18720	−	1.18720i
$113$	−4.15153	+	7.19065i	−0.390543	+	0.676440i	−0.992521	−	0.122073i	$-0.961046\pi$
$113$	−4.15153	+	7.19065i	−0.390543	+	0.676440i	0.601978	+	0.798512i	$0.294379\pi$
$114$	0.130746	+	0.226459i	0.0122455	+	0.0212098i
$115$		0			0
$116$	0.366500	−	1.36779i	0.0340286	−	0.126997i
$117$	−4.72603			−0.436921
$118$	0.00822949	−	0.0307129i	0.000757586	−	0.00282735i
$119$	−24.3967	+	24.3967i	−2.23644	+	2.23644i
$120$		0			0
$121$	5.02962			0.457238
$122$	−0.204241	−	0.204241i	−0.0184911	−	0.0184911i
$123$	−10.6710	+	2.85927i	−0.962168	+	0.257812i
$124$	14.4476	+	3.87122i	1.29743	+	0.347645i
$125$		0			0
$126$	−0.124975	−	0.466415i	−0.0111337	−	0.0415515i
$127$	−1.28331	−	4.78938i	−0.113875	−	0.424988i	0.885325	−	0.464973i	$-0.153936\pi$
$127$	−1.28331	−	4.78938i	−0.113875	−	0.424988i	−0.999200	+	0.0399843i	$0.987269\pi$
$128$	2.87176	+	1.65801i	0.253831	+	0.146549i
$129$	−0.930851	+	3.47398i	−0.0819569	+	0.305867i
$130$		0			0
$131$	−3.53198	−	13.1815i	−0.308590	−	1.15168i	−0.929810	−	0.368039i	$-0.880029\pi$
$131$	−3.53198	−	13.1815i	−0.308590	−	1.15168i	0.621220	−	0.783636i	$-0.286637\pi$
$132$	9.40908	−	2.52116i	0.818955	−	0.219438i
$133$	4.85685	+	2.80410i	0.421142	+	0.243146i
$134$	−0.946554	+	0.946554i	−0.0817698	+	0.0817698i
$135$		0			0
$136$	−2.77264	−	1.60079i	−0.237752	−	0.137266i
$137$	7.46542	−	7.46542i	0.637814	−	0.637814i	−0.312202	−	0.950016i	$-0.601067\pi$
$137$	7.46542	−	7.46542i	0.637814	−	0.637814i	0.950016	+	0.312202i	$0.101067\pi$
$138$	0.0223663	−	0.0223663i	0.00190395	−	0.00190395i
$139$	3.87366	−	6.70937i	0.328559	−	0.569081i	−0.653667	−	0.756782i	$-0.726770\pi$
$139$	3.87366	−	6.70937i	0.328559	−	0.569081i	0.982226	+	0.187701i	$0.0601036\pi$
$140$		0			0
$141$	4.06081	−	2.34451i	0.341982	−	0.197443i
$142$			1.10527i			0.0927518i
$143$	5.67475	+	9.82895i	0.474546	+	0.821938i
$144$	−3.46635	+	2.00130i	−0.288863	+	0.166775i
$145$		0			0
$146$	−0.911683	+	0.244285i	−0.0754514	+	0.0202171i
$147$	−18.9931	−	18.9931i	−1.56652	−	1.56652i
$148$	−11.9978	+	1.55636i	−0.986217	+	0.127932i
$149$		−	1.69346i		−	0.138734i	−0.997591	−	0.0693670i	$-0.977902\pi$
$149$		−	1.69346i		−	0.138734i	0.997591	−	0.0693670i	$-0.0220980\pi$
$150$		0			0
$151$	−9.78475	+	5.64923i	−0.796271	+	0.459727i	−0.842166	−	0.539219i	$-0.818720\pi$
$151$	−9.78475	+	5.64923i	−0.796271	+	0.459727i	0.0458944	+	0.998946i	$0.485386\pi$
$152$	−0.134691	+	0.502673i	−0.0109249	+	0.0407722i
$153$	6.73088	−	3.88608i	0.544159	−	0.314171i
$154$	−0.819963	+	0.819963i	−0.0660745	+	0.0660745i
$155$		0			0
$156$	−13.0937	−	13.0937i	−1.04834	−	1.04834i
$157$	2.43506	+	9.08776i	0.194339	+	0.725282i	0.992437	+	0.122755i	$0.0391729\pi$
$157$	2.43506	+	9.08776i	0.194339	+	0.725282i	−0.798098	+	0.602527i	$0.794160\pi$
$158$	−0.381159	−	0.381159i	−0.0303234	−	0.0303234i
$159$	−23.4943			−1.86322
$160$		0			0
$161$	0.175579	−	0.655269i	0.0138375	−	0.0516424i
$162$		−	1.15758i		−	0.0909485i
$163$	7.93075	−	13.7365i	0.621184	−	1.07592i	−0.368081	−	0.929794i	$-0.619985\pi$
$163$	7.93075	−	13.7365i	0.621184	−	1.07592i	0.989266	−	0.146129i	$-0.0466815\pi$
$164$	−9.49380	−	5.48125i	−0.741341	−	0.428013i
$165$		0			0
$166$	−0.0927894	−	0.0248628i	−0.00720185	−	0.00192973i
$167$	−0.265234	−	0.459399i	−0.0205244	−	0.0355494i	0.855581	−	0.517669i	$-0.173200\pi$
$167$	−0.265234	−	0.459399i	−0.0205244	−	0.0355494i	−0.876105	+	0.482120i	$0.839867\pi$
$168$	1.89720	−	3.28605i	0.146372	−	0.253524i
$169$	4.28751	−	7.42618i	0.329808	−	0.571245i
$170$		0			0
$171$	−0.893314	−	0.893314i	−0.0683135	−	0.0683135i
$172$	−3.09076	+	1.78445i	−0.235668	+	0.136063i
$173$	−0.719913	−	2.68675i	−0.0547340	−	0.204270i	0.933144	−	0.359503i	$-0.117054\pi$
$173$	−0.719913	−	2.68675i	−0.0547340	−	0.204270i	−0.987878	+	0.155233i	$0.950387\pi$
$174$		−	0.149938i		−	0.0113667i
$175$		0			0
$176$	8.32440	+	4.80610i	0.627476	+	0.362273i
$177$			0.606555i			0.0455914i
$178$	−0.781594	−	0.209427i	−0.0585829	−	0.0156973i
$179$	6.41009	+	6.41009i	0.479112	+	0.479112i	0.904848	−	0.425735i	$-0.139985\pi$
$179$	6.41009	+	6.41009i	0.479112	+	0.479112i	−0.425735	+	0.904848i	$0.639985\pi$
$180$		0			0
$181$	0.557213	+	0.965121i	0.0414173	+	0.0717369i	0.885991	−	0.463703i	$-0.153479\pi$
$181$	0.557213	+	0.965121i	0.0414173	+	0.0717369i	−0.844574	+	0.535439i	$0.820146\pi$
$182$	2.12925	+	0.570532i	0.157831	+	0.0422906i
$183$	4.77179	+	2.75500i	0.352741	+	0.203655i
$184$	0.0629497			0.00464071
$185$		0			0
$186$	1.58374			0.116126
$187$	−16.1641	−	9.33237i	−1.18204	−	0.682450i
$188$	4.49444	+	1.20428i	0.327791	+	0.0878312i
$189$	−8.97411	−	15.5436i	−0.652771	−	1.13063i
$190$		0			0
$191$	−12.9182	−	12.9182i	−0.934729	−	0.934729i	0.0632677	−	0.997997i	$-0.479848\pi$
$191$	−12.9182	−	12.9182i	−0.934729	−	0.934729i	−0.997997	+	0.0632677i	$0.979848\pi$
$192$	−14.9779	−	4.01332i	−1.08094	−	0.289636i
$193$			6.70355i			0.482532i	0.970459	+	0.241266i	$0.0775627\pi$
$193$			6.70355i			0.482532i	−0.970459	+	0.241266i	$0.922437\pi$
$194$	−0.159549	−	0.0921154i	−0.0114549	−	0.00661350i
$195$		0			0
$196$		−	26.6539i		−	1.90385i
$197$	3.73320	+	13.9325i	0.265980	+	0.992650i	0.961648	+	0.274287i	$0.0884418\pi$
$197$	3.73320	+	13.9325i	0.265980	+	0.992650i	−0.695668	+	0.718363i	$0.744892\pi$
$198$	0.226222	−	0.130609i	0.0160769	−	0.00928201i
$199$	−6.68443	−	6.68443i	−0.473847	−	0.473847i	0.429310	−	0.903157i	$-0.358757\pi$
$199$	−6.68443	−	6.68443i	−0.473847	−	0.473847i	−0.903157	+	0.429310i	$0.858757\pi$
$200$		0			0
$201$	12.7680	−	22.1148i	0.900586	−	1.55986i
$202$	0.0975521	−	0.168965i	0.00686374	−	0.0118883i
$203$	−1.60785	−	2.78488i	−0.112849	−	0.195460i
$204$	29.4149	+	7.88169i	2.05945	+	0.551829i
$205$		0			0
$206$	−0.324082	−	0.187109i	−0.0225798	−	0.0130365i
$207$	−0.0764084	+	0.132343i	−0.00531075	+	0.00919849i
$208$		−	18.2725i		−	1.26697i
$209$	−0.785229	+	2.93051i	−0.0543154	+	0.202708i
$210$		0			0
$211$	−15.4569			−1.06410			−0.532049	−	0.846713i	$-0.678578\pi$
$211$	−15.4569			−1.06410			−0.532049	+	0.846713i	$0.678578\pi$
$212$	−16.4853	−	16.4853i	−1.13221	−	1.13221i
$213$	−5.45702	−	20.3659i	−0.373909	−	1.39545i
$214$	−0.846608	−	0.846608i	−0.0578729	−	0.0578729i
$215$		0			0
$216$	1.17767	−	1.17767i	0.0801304	−	0.0801304i
$217$	29.4158	−	16.9832i	1.99687	−	1.15290i
$218$	0.181081	−	0.675803i	0.0122643	−	0.0457711i
$219$	15.5928	−	9.00250i	1.05366	−	0.608333i
$220$		0			0
$221$			35.4810i			2.38671i
$222$	−1.18445	+	0.487980i	−0.0794950	+	0.0327511i
$223$	7.27052	+	7.27052i	0.486870	+	0.486870i	0.907317	−	0.420447i	$-0.138127\pi$
$223$	7.27052	+	7.27052i	0.486870	+	0.486870i	−0.420447	+	0.907317i	$0.638127\pi$
$224$	5.46046	−	1.46313i	0.364842	−	0.0977592i
$225$		0			0
$226$	−0.755530	+	0.436205i	−0.0502571	+	0.0290159i
$227$	3.45410	+	5.98267i	0.229256	+	0.397084i	0.957588	−	0.288141i	$-0.0930373\pi$
$227$	3.45410	+	5.98267i	0.229256	+	0.397084i	−0.728332	+	0.685225i	$0.759704\pi$
$228$		−	4.94995i		−	0.327819i
$229$	−20.4243	+	11.7920i	−1.34967	+	0.779235i	−0.988203	−	0.153148i	$-0.951059\pi$
$229$	−20.4243	+	11.7920i	−1.34967	+	0.779235i	−0.361472	+	0.932383i	$0.617726\pi$
$230$		0			0
$231$	11.0604	−	19.1572i	0.727723	−	1.26045i
$232$	0.210998	−	0.210998i	0.0138527	−	0.0138527i
$233$	10.7828	−	10.7828i	0.706402	−	0.706402i	−0.259375	−	0.965777i	$-0.583516\pi$
$233$	10.7828	−	10.7828i	0.706402	−	0.706402i	0.965777	+	0.259375i	$0.0835165\pi$
$234$	−0.430041	−	0.248284i	−0.0281127	−	0.0162308i
$235$		0			0
$236$	−0.425603	+	0.425603i	−0.0277044	+	0.0277044i
$237$	8.90522	+	5.14143i	0.578456	+	0.333972i
$238$	−3.50165	+	0.938264i	−0.226978	+	0.0608186i
$239$	4.28082	+	15.9763i	0.276903	+	1.03342i	0.954555	+	0.298035i	$0.0963311\pi$
$239$	4.28082	+	15.9763i	0.276903	+	1.03342i	−0.677652	+	0.735383i	$0.737002\pi$
$240$		0			0
$241$	−0.943969	+	3.52294i	−0.0608064	+	0.226933i	−0.989641	−	0.143561i	$-0.954145\pi$
$241$	−0.943969	+	3.52294i	−0.0608064	+	0.226933i	0.928835	+	0.370493i	$0.120811\pi$
$242$	0.457666	+	0.264234i	0.0294199	+	0.0169856i
$243$	2.62992	+	9.81501i	0.168710	+	0.629633i
$244$	1.41513	+	5.28135i	0.0905946	+	0.338104i
$245$		0			0
$246$	−1.12121	−	0.300427i	−0.0714856	−	0.0191545i
$247$	5.57081	−	1.49269i	0.354462	−	0.0949778i
$248$	2.22871	+	2.22871i	0.141523	+	0.141523i
$249$	1.83251			0.116131
$250$		0			0
$251$	5.49768	−	5.49768i	0.347010	−	0.347010i	−0.511984	−	0.858995i	$-0.671089\pi$
$251$	5.49768	−	5.49768i	0.347010	−	0.347010i	0.858995	+	0.511984i	$0.171089\pi$
$252$	−2.36574	+	8.82908i	−0.149028	+	0.556180i
$253$	0.366988			0.0230723
$254$	0.134839	−	0.503225i	0.00846053	−	0.0315751i
$255$		0			0
$256$	−7.56205	−	13.0979i	−0.472628	−	0.818616i
$257$	−13.4897	+	23.3649i	−0.841467	+	1.45746i	0.0471867	+	0.998886i	$0.484974\pi$
$257$	−13.4897	+	23.3649i	−0.841467	+	1.45746i	−0.888654	+	0.458578i	$0.848359\pi$
$258$	−0.267210	+	0.267210i	−0.0166358	+	0.0166358i
$259$	−16.7667	+	21.7650i	−1.04183	+	1.35241i
$260$		0			0
$261$	0.187486	+	0.699706i	0.0116051	+	0.0433107i
$262$	0.371109	−	1.38500i	0.0229272	−	0.0855654i
$263$	5.22951	+	1.40124i	0.322465	+	0.0864043i	0.416421	−	0.909172i	$-0.363284\pi$
$263$	5.22951	+	1.40124i	0.322465	+	0.0864043i	−0.0939553	+	0.995576i	$0.529951\pi$
$264$	1.98273	+	0.531271i	0.122029	+	0.0326975i
$265$		0			0
$266$	0.294630	+	0.510314i	0.0180649	+	0.0312894i
$267$	15.4358			0.944659
$268$	24.4764	−	6.55842i	1.49513	−	0.400619i
$269$			18.2733i			1.11414i	0.830465	+	0.557071i	$0.188075\pi$
$269$			18.2733i			1.11414i	−0.830465	+	0.557071i	$0.811925\pi$
$270$		0			0
$271$	−8.01505	+	13.8825i	−0.486879	+	0.843300i	−0.999886	−	0.0150847i	$-0.995198\pi$
$271$	−8.01505	+	13.8825i	−0.486879	+	0.843300i	0.513007	+	0.858385i	$0.328532\pi$
$272$	15.0249	+	26.0239i	0.911019	+	1.57793i
$273$	−42.0510			−2.54504
$274$	1.07151	−	0.287110i	0.0647323	−	0.0173450i
$275$		0			0
$276$	−0.578358	+	0.154971i	−0.0348131	+	0.00932813i
$277$	−19.9375	+	11.5109i	−1.19793	+	0.691626i	−0.960093	−	0.279679i	$-0.909772\pi$
$277$	−19.9375	+	11.5109i	−1.19793	+	0.691626i	−0.237837	+	0.971305i	$0.576439\pi$
$278$	0.704961	−	0.407009i	0.0422807	−	0.0244108i
$279$	−7.39076	+	1.98035i	−0.442473	+	0.118560i
$280$		0			0
$281$	26.6973	−	7.15352i	1.59263	−	0.426743i	0.649822	−	0.760087i	$-0.274844\pi$
$281$	26.6973	−	7.15352i	1.59263	−	0.426743i	0.942805	+	0.333343i	$0.108177\pi$
$282$	0.492680			0.0293387
$283$	2.83629	+	4.91260i	0.168600	+	0.292024i	0.937928	−	0.346830i	$-0.112742\pi$
$283$	2.83629	+	4.91260i	0.168600	+	0.292024i	−0.769328	+	0.638854i	$0.779409\pi$
$284$	10.4611	−	18.1192i	0.620755	−	1.07518i
$285$		0			0
$286$			1.19250i			0.0705142i
$287$	−24.0465	+	6.44324i	−1.41942	+	0.380333i
$288$	−1.27345			−0.0750386
$289$	−20.6750	−	35.8102i	−1.21618	−	2.10648i
$290$		0			0
$291$	3.39468	+	0.909603i	0.199000	+	0.0533218i
$292$	17.2579	+	4.62423i	1.00994	+	0.270612i
$293$	−3.60695	+	13.4613i	−0.210720	+	0.786418i	0.776909	+	0.629612i	$0.216786\pi$
$293$	−3.60695	+	13.4613i	−0.210720	+	0.786418i	−0.987629	+	0.156806i	$0.949880\pi$
$294$	−0.730450	−	2.72608i	−0.0426007	−	0.158988i
$295$		0			0
$296$	−2.35351	−	0.980100i	−0.136795	−	0.0569671i
$297$	6.86567	−	6.86567i	0.398386	−	0.398386i
$298$	0.0889671	−	0.154095i	0.00515372	−	0.00892651i
$299$	−0.348816	−	0.604167i	−0.0201725	−	0.0349399i
$300$		0			0
$301$	−2.09763	+	7.82847i	−0.120905	+	0.451225i
$302$	−1.18714			−0.0683122
$303$	−0.963287	+	3.59504i	−0.0553394	+	0.206529i
$304$	3.45386	−	3.45386i	0.198093	−	0.198093i
$305$		0			0
$306$	0.816628			0.0466835
$307$	−7.33300	−	7.33300i	−0.418516	−	0.418516i	0.466176	−	0.884692i	$-0.345631\pi$
$307$	−7.33300	−	7.33300i	−0.418516	−	0.418516i	−0.884692	+	0.466176i	$0.845631\pi$
$308$	21.2029	−	5.68131i	1.20815	−	0.323723i
$309$	6.89542	+	1.84762i	0.392267	+	0.105108i
$310$		0			0
$311$	−0.463544	−	1.72997i	−0.0262852	−	0.0980975i	0.951537	−	0.307534i	$-0.0995038\pi$
$311$	−0.463544	−	1.72997i	−0.0262852	−	0.0980975i	−0.977822	+	0.209436i	$0.932837\pi$
$312$	−1.00993	−	3.76911i	−0.0571760	−	0.213384i
$313$	23.5224	+	13.5807i	1.32957	+	0.767625i	0.985232	−	0.171223i	$-0.0547718\pi$
$313$	23.5224	+	13.5807i	1.32957	+	0.767625i	0.344333	+	0.938848i	$0.388105\pi$
$314$	−0.255854	+	0.954861i	−0.0144387	+	0.0538859i
$315$		0			0
$316$	2.64095	+	9.85616i	0.148565	+	0.554452i
$317$	−6.32825	+	1.69565i	−0.355430	+	0.0952372i	−0.432116	−	0.901818i	$-0.642233\pi$
$317$	−6.32825	+	1.69565i	−0.355430	+	0.0952372i	0.0766857	+	0.997055i	$0.475566\pi$
$318$	−2.13784	−	1.23428i	−0.119884	−	0.0692152i
$319$	1.23009	−	1.23009i	0.0688719	−	0.0688719i
$320$		0			0
$321$	19.7798	+	11.4198i	1.10400	+	0.637394i
$322$	0.0504015	−	0.0504015i	0.00280877	−	0.00280877i
$323$	−6.70663	+	6.70663i	−0.373167	+	0.373167i
$324$	−10.9563	+	18.9770i	−0.608686	+	1.05428i
$325$		0			0
$326$	1.44330	−	0.833292i	0.0799373	−	0.0461518i
$327$			13.3466i			0.738066i
$328$	−1.15504	−	2.00058i	−0.0637763	−	0.110464i
$329$	9.15085	−	5.28324i	0.504502	−	0.291275i
$330$		0			0
$331$	27.9515	−	7.48959i	1.53635	−	0.411665i	0.611268	−	0.791423i	$-0.290660\pi$
$331$	27.9515	−	7.48959i	1.53635	−	0.411665i	0.925086	+	0.379758i	$0.123993\pi$
$332$	1.28583	+	1.28583i	0.0705689	+	0.0705689i
$333$	4.91722	−	3.75829i	0.269462	−	0.205953i
$334$		−	0.0557369i		−	0.00304979i
$335$		0			0
$336$	−30.8428	+	17.8071i	−1.68261	+	0.971455i
$337$	−2.11178	+	7.88127i	−0.115036	+	0.429320i	−0.999290	−	0.0376867i	$-0.988001\pi$
$337$	−2.11178	+	7.88127i	−0.115036	+	0.429320i	0.884254	+	0.467007i	$0.154668\pi$
$338$	0.780277	−	0.450493i	0.0424415	−	0.0245036i
$339$	11.7679	−	11.7679i	0.639145	−	0.639145i
$340$		0			0
$341$	12.9931	+	12.9931i	0.703613	+	0.703613i
$342$	−0.0343557	−	0.128217i	−0.00185774	−	0.00693319i
$343$	−20.4434	−	20.4434i	−1.10384	−	1.10384i
$344$	−0.752057			−0.0405482
$345$		0			0
$346$	0.0756421	−	0.282300i	0.00406654	−	0.0151765i
$347$		−	24.8690i		−	1.33504i	−0.744592	−	0.667519i	$-0.767356\pi$
$347$		−	24.8690i		−	1.33504i	0.744592	−	0.667519i	$-0.232644\pi$
$348$	−1.41913	+	2.45801i	−0.0760736	+	0.131763i
$349$	16.0098	+	9.24327i	0.856985	+	0.494781i	0.863002	−	0.505201i	$-0.168582\pi$
$349$	16.0098	+	9.24327i	0.856985	+	0.494781i	−0.00601629	+	0.999982i	$0.501915\pi$
$350$		0			0
$351$	−17.8285	−	4.77714i	−0.951617	−	0.254985i
$352$	1.52909	+	2.64845i	0.0815005	+	0.141163i
$353$	−9.10206	+	15.7652i	−0.484454	+	0.839099i	−0.999841	−	0.0178589i	$-0.994315\pi$
$353$	−9.10206	+	15.7652i	−0.484454	+	0.839099i	0.515387	+	0.856958i	$0.327648\pi$
$354$	−0.0318657	+	0.0551930i	−0.00169364	+	0.00293347i
$355$		0			0
$356$	10.8309	+	10.8309i	0.574038	+	0.574038i
$357$	59.8897	−	34.5774i	3.16970	−	1.83003i
$358$	0.246524	+	0.920038i	0.0130292	+	0.0486255i
$359$			25.4475i			1.34307i	0.740974	+	0.671534i	$0.234364\pi$
$359$			25.4475i			1.34307i	−0.740974	+	0.671534i	$0.765636\pi$
$360$		0			0
$361$	−15.1193	−	8.72915i	−0.795755	−	0.459429i
$362$			0.117094i			0.00615432i
$363$	−9.73766	−	2.60920i	−0.511095	−	0.136947i
$364$	−29.5061	−	29.5061i	−1.54654	−	1.54654i
$365$		0			0
$366$	0.289470	+	0.501377i	0.0151309	+	0.0262074i
$367$	−10.9437	−	2.93236i	−0.571258	−	0.153068i	−0.0383846	−	0.999263i	$-0.512221\pi$
$367$	−10.9437	−	2.93236i	−0.571258	−	0.153068i	−0.532874	+	0.846195i	$0.678888\pi$
$368$	−0.511685	−	0.295421i	−0.0266734	−	0.0153999i
$369$	5.60795			0.291938
$370$		0			0
$371$	−52.9432			−2.74868
$372$	−25.9632	−	14.9898i	−1.34613	−	0.777187i
$373$	−29.5344	−	7.91372i	−1.52923	−	0.409757i	−0.606465	−	0.795110i	$-0.707413\pi$
$373$	−29.5344	−	7.91372i	−1.52923	−	0.409757i	−0.922769	+	0.385354i	$0.874079\pi$
$374$	−0.980562	−	1.69838i	−0.0507036	−	0.0878213i
$375$		0			0
$376$	0.693320	+	0.693320i	0.0357552	+	0.0357552i
$377$	−3.19426	−	0.855900i	−0.164513	−	0.0440811i
$378$		−	1.88584i		−	0.0969971i
$379$	6.07630	+	3.50815i	0.312119	+	0.180202i	0.647874	−	0.761747i	$-0.275658\pi$
$379$	6.07630	+	3.50815i	0.312119	+	0.180202i	−0.335756	+	0.941949i	$0.608992\pi$
$380$		0			0
$381$			9.93828i			0.509154i
$382$	−0.496817	−	1.85415i	−0.0254194	−	0.0948664i
$383$	18.2184	−	10.5184i	0.930919	−	0.537466i	0.0438170	−	0.999040i	$-0.486048\pi$
$383$	18.2184	−	10.5184i	0.930919	−	0.537466i	0.887102	+	0.461573i	$0.152715\pi$
$384$	−4.69980	−	4.69980i	−0.239836	−	0.239836i
$385$		0			0
$386$	−0.352175	+	0.609984i	−0.0179252	+	0.0310474i
$387$	0.912848	−	1.58110i	0.0464027	−	0.0803718i
$388$	1.74371	+	3.02020i	0.0885237	+	0.153328i
$389$	28.1825	+	7.55149i	1.42891	+	0.382876i	0.888636	−	0.458612i	$-0.151653\pi$
$389$	28.1825	+	7.55149i	1.42891	+	0.382876i	0.540275	+	0.841488i	$0.318320\pi$
$390$		0			0
$391$	0.993578	+	0.573643i	0.0502474	+	0.0290104i
$392$	2.80833	−	4.86416i	0.141842	−	0.245677i
$393$			27.3526i			1.37975i
$394$	−0.392252	+	1.46390i	−0.0197614	+	0.0737504i
$395$		0			0
$396$	−4.94479			−0.248485
$397$	1.11923	+	1.11923i	0.0561727	+	0.0561727i	0.734635	−	0.678462i	$-0.237353\pi$
$397$	1.11923	+	1.11923i	0.0561727	+	0.0561727i	−0.678462	+	0.734635i	$0.737353\pi$
$398$	−0.257074	−	0.959415i	−0.0128860	−	0.0480911i
$399$	−7.94850	−	7.94850i	−0.397923	−	0.397923i
$400$		0			0
$401$	2.72947	−	2.72947i	0.136303	−	0.136303i	−0.635663	−	0.771966i	$-0.719273\pi$
$401$	2.72947	−	2.72947i	0.136303	−	0.136303i	0.771966	+	0.635663i	$0.219273\pi$
$402$	2.32363	−	1.34155i	0.115892	−	0.0669104i
$403$	9.04059	−	33.7399i	0.450344	−	1.68071i
$404$	−3.19845	+	1.84663i	−0.159129	+	0.0918732i
$405$		0			0
$406$		−	0.337877i		−	0.0167686i
$407$	−13.7206	−	5.71385i	−0.680107	−	0.283225i
$408$	4.53758	+	4.53758i	0.224644	+	0.224644i
$409$	−15.9537	+	4.27479i	−0.788862	+	0.211375i	−0.630688	−	0.776037i	$-0.717227\pi$
$409$	−15.9537	+	4.27479i	−0.788862	+	0.211375i	−0.158174	+	0.987411i	$0.550561\pi$
$410$		0			0
$411$	−18.3264	+	10.5807i	−0.903973	+	0.521909i
$412$	3.54190	+	6.13476i	0.174497	+	0.302238i
$413$			1.36684i			0.0672580i
$414$	−0.0139054	+	0.00802831i	−0.000683415	+	0.000394570i
$415$		0			0
$416$	2.90674	−	5.03462i	0.142515	−	0.246843i
$417$	−10.9803	+	10.9803i	−0.537705	+	0.537705i
$418$	−0.225407	+	0.225407i	−0.0110250	+	0.0110250i
$419$	−15.1345	−	8.73792i	−0.739370	−	0.426875i	0.0824704	−	0.996594i	$-0.473719\pi$
$419$	−15.1345	−	8.73792i	−0.739370	−	0.426875i	−0.821840	+	0.569718i	$0.807052\pi$
$420$		0			0
$421$	−7.21676	+	7.21676i	−0.351723	+	0.351723i	−0.860750	−	0.509027i	$-0.830005\pi$
$421$	−7.21676	+	7.21676i	−0.351723	+	0.351723i	0.509027	+	0.860750i	$0.330005\pi$
$422$	−1.40649	−	0.812038i	−0.0684669	−	0.0395294i
$423$	−2.29916	+	0.616059i	−0.111789	+	0.0299538i
$424$	−1.27152	−	4.74539i	−0.0617507	−	0.230457i
$425$		0			0
$426$	0.573375	−	2.13987i	0.0277801	−	0.103677i
$427$	10.7530	+	6.20826i	0.520375	+	0.300439i
$428$	5.86592	+	21.8919i	0.283540	+	1.05819i
$429$	−5.88775	−	21.9734i	−0.284263	−	1.06088i
$430$		0			0
$431$	27.7849	+	7.44493i	1.33835	+	0.358610i	0.855822	−	0.517270i	$-0.173052\pi$
$431$	27.7849	+	7.44493i	1.33835	+	0.358610i	0.482528	+	0.875880i	$0.339719\pi$
$432$	−15.0995	+	4.04589i	−0.726474	+	0.194658i
$433$	12.0991	+	12.0991i	0.581444	+	0.581444i	0.935300	−	0.353856i	$-0.115130\pi$
$433$	12.0991	+	12.0991i	0.581444	+	0.581444i	−0.353856	+	0.935300i	$0.615130\pi$
$434$	3.56889			0.171312
$435$		0			0
$436$	−9.36492	+	9.36492i	−0.448498	+	0.448498i
$437$	0.0482665	−	0.180133i	0.00230890	−	0.00861693i
$438$	1.89180			0.0903939
$439$	−2.60805	+	9.73336i	−0.124475	+	0.464548i	−0.999820	−	0.0189505i	$-0.993967\pi$
$439$	−2.60805	+	9.73336i	−0.124475	+	0.464548i	0.875345	+	0.483499i	$0.160634\pi$
$440$		0			0
$441$	6.81750	+	11.8083i	0.324643	+	0.562298i
$442$	−1.86402	+	3.22857i	−0.0886622	+	0.153567i
$443$	−27.4924	+	27.4924i	−1.30620	+	1.30620i	−0.382069	+	0.924134i	$0.624788\pi$
$443$	−27.4924	+	27.4924i	−1.30620	+	1.30620i	−0.924134	+	0.382069i	$0.875212\pi$
$444$	24.0360	+	3.21088i	1.14070	+	0.152381i
$445$		0			0
$446$	0.279614	+	1.04354i	0.0132401	+	0.0494128i
$447$	−0.878514	+	3.27866i	−0.0415523	+	0.155075i
$448$	−33.7520	−	9.04383i	−1.59463	−	0.427281i
$449$	24.2566	+	6.49953i	1.14474	+	0.306732i	0.780855	−	0.624713i	$-0.214784\pi$
$449$	24.2566	+	6.49953i	1.14474	+	0.306732i	0.363883	+	0.931444i	$0.381451\pi$
$450$		0			0
$451$	−6.73371	−	11.6631i	−0.317078	−	0.549195i
$452$	16.5144			0.776774
$453$	21.8745	−	5.86126i	1.02776	−	0.275386i
$454$			0.725851i			0.0340659i
$455$		0			0
$456$	0.521540	−	0.903334i	0.0244234	−	0.0423025i
$457$	0.876059	+	1.51738i	0.0409803	+	0.0709800i	0.885788	−	0.464090i	$-0.153619\pi$
$457$	0.876059	+	1.51738i	0.0409803	+	0.0709800i	−0.844808	+	0.535070i	$0.820285\pi$
$458$	−2.47799			−0.115789
$459$	29.3198	−	7.85622i	1.36853	−	0.366697i
$460$		0			0
$461$	−17.9341	+	4.80544i	−0.835276	+	0.223812i	−0.651014	−	0.759066i	$-0.725656\pi$
$461$	−17.9341	+	4.80544i	−0.835276	+	0.223812i	−0.184262	+	0.982877i	$0.558990\pi$
$462$	2.01287	−	1.16213i	0.0936472	−	0.0540673i
$463$	−18.1497	+	10.4787i	−0.843488	+	0.486988i	−0.858448	−	0.512900i	$-0.828571\pi$
$463$	−18.1497	+	10.4787i	−0.843488	+	0.486988i	0.0149605	+	0.999888i	$0.495238\pi$
$464$	−2.70531	+	0.724884i	−0.125591	+	0.0336519i
$465$		0			0
$466$	1.54765	−	0.414691i	0.0716933	−	0.0192102i
$467$	−22.0375			−1.01977			−0.509887	−	0.860241i	$-0.670313\pi$
$467$	−22.0375			−1.01977			−0.509887	+	0.860241i	$0.670313\pi$
$468$	4.69994	+	8.14053i	0.217255	+	0.376296i
$469$	28.7721	−	49.8348i	1.32857	−	2.30116i
$470$		0			0
$471$		−	18.8577i		−	0.868918i
$472$	−0.122512	+	0.0328271i	−0.00563909	+	0.00151099i
$473$	−4.38439			−0.201594
$474$	0.540216	+	0.935681i	0.0248129	+	0.0429773i
$475$		0			0
$476$	66.2850	+	17.7610i	3.03817	+	0.814075i
$477$	11.5199	+	3.08676i	0.527461	+	0.141333i
$478$	−0.449791	+	1.67864i	−0.0205729	+	0.0767793i
$479$	7.10617	+	26.5206i	0.324689	+	1.21176i	0.914624	+	0.404305i	$0.132487\pi$
$479$	7.10617	+	26.5206i	0.324689	+	1.21176i	−0.589935	+	0.807451i	$0.700847\pi$
$480$		0			0
$481$	3.63462	+	28.0190i	0.165724	+	1.27756i
$482$	−0.270975	+	0.270975i	−0.0123426	+	0.0123426i
$483$	−0.679864	+	1.17756i	−0.0309349	+	0.0535808i
$484$	−5.00185	−	8.66346i	−0.227357	−	0.393794i
$485$		0			0
$486$	−0.276329	+	1.03127i	−0.0125345	+	0.0467795i
$487$	35.4750			1.60752			0.803762	−	0.594951i	$-0.202829\pi$
$487$	35.4750			1.60752			0.803762	+	0.594951i	$0.202829\pi$
$488$	−0.298204	+	1.11291i	−0.0134991	+	0.0503792i
$489$	−22.4805	+	22.4805i	−1.01660	+	1.01660i
$490$		0			0
$491$	1.48693			0.0671041			0.0335521	−	0.999437i	$-0.489318\pi$
$491$	1.48693			0.0671041			0.0335521	+	0.999437i	$0.489318\pi$
$492$	15.5371	+	15.5371i	0.700467	+	0.700467i
$493$	5.25310	−	1.40756i	0.236588	−	0.0633935i
$494$	0.585331	+	0.156839i	0.0263353	+	0.00705652i
$495$		0			0
$496$	−7.65672	−	28.5753i	−0.343797	−	1.28307i
$497$	−12.2972	−	45.8936i	−0.551603	−	2.05861i
$498$	0.166748	+	0.0962721i	0.00747217	+	0.00431406i
$499$	−5.71230	+	21.3186i	−0.255718	+	0.954352i	0.711972	+	0.702208i	$0.247802\pi$
$499$	−5.71230	+	21.3186i	−0.255718	+	0.954352i	−0.967690	+	0.252144i	$0.918864\pi$
$500$		0			0
$501$	0.275190	+	1.02702i	0.0122946	+	0.0458839i
$502$	0.789080	−	0.211433i	0.0352184	−	0.00943673i
$503$	−3.42397	−	1.97683i	−0.152667	−	0.0881424i	0.421720	−	0.906726i	$-0.361426\pi$
$503$	−3.42397	−	1.97683i	−0.152667	−	0.0881424i	−0.574388	+	0.818584i	$0.694760\pi$
$504$	−1.36199	+	1.36199i	−0.0606678	+	0.0606678i
$505$		0			0
$506$	0.0333938	+	0.0192799i	0.00148453	+	0.000857096i
$507$	−12.1534	+	12.1534i	−0.539749	+	0.539749i
$508$	−6.97343	+	6.97343i	−0.309396	+	0.309396i
$509$	−8.31123	+	14.3955i	−0.368389	+	0.638068i	−0.989314	−	0.145802i	$-0.953424\pi$
$509$	−8.31123	+	14.3955i	−0.368389	+	0.638068i	0.620925	+	0.783870i	$0.286757\pi$
$510$		0			0
$511$	35.1376	−	20.2867i	1.55440	−	0.897432i
$512$		−	8.22116i		−	0.363327i
$513$	−2.46698	−	4.27293i	−0.108920	−	0.188655i
$514$	−2.45498	+	1.41738i	−0.108284	+	0.0625180i
$515$		0			0
$516$	6.90962	−	1.85143i	0.304179	−	0.0815045i
$517$	4.04196	+	4.04196i	0.177765	+	0.177765i
$518$	−2.66910	+	1.09964i	−0.117274	+	0.0483154i
$519$			5.57520i			0.244724i
$520$		0			0
$521$	−1.01799	+	0.587738i	−0.0445990	+	0.0257493i	−0.522134	−	0.852864i	$-0.674864\pi$
$521$	−1.01799	+	0.587738i	−0.0445990	+	0.0257493i	0.477535	+	0.878613i	$0.341530\pi$
$522$	−0.0196993	+	0.0735188i	−0.000862215	+	0.00321783i
$523$	30.2054	−	17.4391i	1.32079	−	0.762560i	0.336937	−	0.941527i	$-0.390609\pi$
$523$	30.2054	−	17.4391i	1.32079	−	0.762560i	0.983855	+	0.178968i	$0.0572758\pi$
$524$	−19.1926	+	19.1926i	−0.838431	+	0.838431i
$525$		0			0
$526$	0.402240	+	0.402240i	0.0175385	+	0.0175385i
$527$	14.8676	+	55.4868i	0.647644	+	2.41704i
$528$	−13.6233	−	13.6233i	−0.592880	−	0.592880i
$529$	22.9774			0.999019
$530$		0			0
$531$	0.0796912	−	0.297412i	0.00345830	−	0.0129066i
$532$		−	11.1545i		−	0.483609i
$533$	−12.8006	+	22.1712i	−0.554454	+	0.960342i
$534$	1.40457	+	0.810931i	0.0607818	+	0.0350924i
$535$		0			0
$536$	5.15779	+	1.38203i	0.222783	+	0.0596944i
$537$	−9.08500	−	15.7357i	−0.392047	−	0.679045i
$538$	−0.959996	+	1.66276i	−0.0413884	+	0.0716868i
$539$	16.3722	−	28.3574i	0.705199	−	1.22144i
$540$		0			0
$541$	−4.65504	−	4.65504i	−0.200136	−	0.200136i	0.599922	−	0.800058i	$-0.295198\pi$
$541$	−4.65504	−	4.65504i	−0.200136	−	0.200136i	−0.800058	+	0.599922i	$0.795198\pi$
$542$	−1.45865	+	0.842149i	−0.0626542	+	0.0361734i
$543$	−0.578127	−	2.15760i	−0.0248098	−	0.0925915i
$544$			9.56052i			0.409904i
$545$		0			0
$546$	−3.82640	−	2.20917i	−0.163755	−	0.0945439i
$547$		−	15.3538i		−	0.656482i	−0.944594	−	0.328241i	$-0.893544\pi$
$547$		−	15.3538i		−	0.656482i	0.944594	−	0.328241i	$-0.106456\pi$
$548$	−20.2833	−	5.43490i	−0.866461	−	0.232167i
$549$	−1.97779	−	1.97779i	−0.0844100	−	0.0844100i
$550$		0			0
$551$	−0.441998	−	0.765562i	−0.0188297	−	0.0326141i
$552$	−0.121875	−	0.0326562i	−0.00518733	−	0.00138994i
$553$	20.0675	+	11.5860i	0.853357	+	0.492686i
$554$	−2.41893			−0.102771
$555$		0			0
$556$	−15.4091			−0.653491
$557$	−14.1931	−	8.19437i	−0.601379	−	0.347207i	0.168205	−	0.985752i	$-0.446203\pi$
$557$	−14.1931	−	8.19437i	−0.601379	−	0.347207i	−0.769584	+	0.638546i	$0.779536\pi$
$558$	−0.776555	−	0.208077i	−0.0328742	−	0.00880862i
$559$	4.16729	+	7.21795i	0.176258	+	0.305287i
$560$		0			0
$561$	26.4535	+	26.4535i	1.11687	+	1.11687i
$562$	2.80511	+	0.751628i	0.118327	+	0.0317055i
$563$			34.2468i			1.44333i	0.692242	+	0.721665i	$0.256623\pi$
$563$			34.2468i			1.44333i	−0.692242	+	0.721665i	$0.743377\pi$
$564$	−8.07679	−	4.66313i	−0.340094	−	0.196353i
$565$		0			0
$566$			0.596025i			0.0250528i
$567$	12.8793	+	48.0661i	0.540878	+	2.01858i
$568$	3.81818	−	2.20443i	0.160207	−	0.0924958i
$569$	−12.1154	−	12.1154i	−0.507904	−	0.507904i	0.405979	−	0.913882i	$-0.366931\pi$
$569$	−12.1154	−	12.1154i	−0.507904	−	0.507904i	−0.913882	+	0.405979i	$0.866931\pi$
$570$		0			0
$571$	−4.07340	+	7.05533i	−0.170466	+	0.295257i	−0.938583	−	0.345053i	$-0.887861\pi$
$571$	−4.07340	+	7.05533i	−0.170466	+	0.295257i	0.768117	+	0.640310i	$0.221194\pi$
$572$	11.2869	−	19.5494i	0.471927	−	0.817401i
$573$	18.3090	+	31.7120i	0.764868	+	1.32479i
$574$	−2.52659	−	0.676998i	−0.105458	−	0.0282574i
$575$		0			0
$576$	6.81682	+	3.93570i	0.284034	+	0.163987i
$577$	−6.24278	+	10.8128i	−0.259890	+	0.450143i	−0.966212	−	0.257748i	$-0.917020\pi$
$577$	−6.24278	+	10.8128i	−0.259890	+	0.450143i	0.706322	+	0.707891i	$0.250353\pi$
$578$		−	4.34470i		−	0.180716i
$579$	3.47758	−	12.9785i	0.144523	−	0.539369i
$580$		0			0
$581$	4.12949			0.171320
$582$	0.261110	+	0.261110i	0.0108234	+	0.0108234i
$583$	−7.41281	−	27.6650i	−0.307007	−	1.14577i
$584$	2.66222	+	2.66222i	0.110164	+	0.110164i
$585$		0			0
$586$	−1.03541	+	1.03541i	−0.0427723	+	0.0427723i
$587$	5.54747	−	3.20283i	0.228969	−	0.132195i	−0.381128	−	0.924522i	$-0.624464\pi$
$587$	5.54747	−	3.20283i	0.228969	−	0.132195i	0.610096	+	0.792327i	$0.291131\pi$
$588$	−13.8272	+	51.6037i	−0.570223	+	2.12810i
$589$	8.08639	−	4.66868i	0.333194	−	0.192370i
$590$		0			0
$591$		−	28.9109i		−	1.18924i
$592$	14.5309	+	19.0117i	0.597215	+	0.781376i
$593$	−29.3715	−	29.3715i	−1.20614	−	1.20614i	−0.972267	−	0.233875i	$-0.924859\pi$
$593$	−29.3715	−	29.3715i	−1.20614	−	1.20614i	−0.233875	−	0.972267i	$-0.575141\pi$
$594$	0.985427	−	0.264044i	0.0404326	−	0.0108339i
$595$		0			0
$596$	−2.91698	+	1.68412i	−0.119484	+	0.0689841i
$597$	9.47384	+	16.4092i	0.387738	+	0.671582i
$598$		−	0.0733009i		−	0.00299750i
$599$	25.2199	−	14.5607i	1.03046	−	0.594934i	0.113341	−	0.993556i	$-0.463845\pi$
$599$	25.2199	−	14.5607i	1.03046	−	0.594934i	0.917115	+	0.398622i	$0.130511\pi$
$600$		0			0
$601$	−8.70660	+	15.0803i	−0.355150	+	0.615137i	−0.987144	−	0.159836i	$-0.948903\pi$
$601$	−8.70660	+	15.0803i	−0.355150	+	0.615137i	0.631994	+	0.774973i	$0.282237\pi$
$602$	−0.602145	+	0.602145i	−0.0245416	+	0.0245416i
$603$	−9.16606	+	9.16606i	−0.373271	+	0.373271i
$604$	19.4615	+	11.2361i	0.791876	+	0.457190i
$605$		0			0
$606$	−0.276521	+	0.276521i	−0.0112329	+	0.0112329i
$607$	18.9011	+	10.9126i	0.767172	+	0.442927i	0.831865	−	0.554978i	$-0.187273\pi$
$607$	18.9011	+	10.9126i	0.767172	+	0.442927i	−0.0646926	+	0.997905i	$0.520607\pi$
$608$	1.50108	−	0.402213i	0.0608767	−	0.0163119i
$609$	1.66820	+	6.22581i	0.0675989	+	0.252283i
$610$		0			0
$611$	2.81240	−	10.4960i	0.113778	−	0.424624i
$612$	−13.3875	−	7.72925i	−0.541156	−	0.312436i
$613$	−10.6075	−	39.5877i	−0.428432	−	1.59893i	−0.756312	−	0.654212i	$-0.773001\pi$
$613$	−10.6075	−	39.5877i	−0.428432	−	1.59893i	0.327879	−	0.944720i	$-0.393666\pi$
$614$	−0.282017	−	1.05250i	−0.0113813	−	0.0424756i
$615$		0			0
$616$	4.46799	+	1.19720i	0.180021	+	0.0482364i
$617$	1.76552	−	0.473071i	0.0710773	−	0.0190451i	−0.223105	−	0.974794i	$-0.571619\pi$
$617$	1.76552	−	0.473071i	0.0710773	−	0.0190451i	0.294182	+	0.955749i	$0.404953\pi$
$618$	0.530377	+	0.530377i	0.0213349	+	0.0213349i
$619$	28.5279			1.14663			0.573317	−	0.819334i	$-0.305657\pi$
$619$	28.5279			1.14663			0.573317	+	0.819334i	$0.305657\pi$
$620$		0			0
$621$	−0.422019	+	0.422019i	−0.0169350	+	0.0169350i
$622$	0.0487050	−	0.181770i	0.00195289	−	0.00728830i
$623$	34.7840			1.39359
$624$	−9.47915	+	35.3767i	−0.379470	+	1.41620i
$625$		0			0
$626$	1.42694	+	2.47152i	0.0570318	+	0.0987820i
$627$	3.04051	−	5.26631i	0.121426	−	0.210316i
$628$	13.2320	−	13.2320i	0.528013	−	0.528013i
$629$	−28.2157	−	36.9165i	−1.12503	−	1.47196i
$630$		0			0
$631$	4.80204	+	17.9215i	0.191166	+	0.713442i	0.993226	+	0.116199i	$0.0370709\pi$
$631$	4.80204	+	17.9215i	0.191166	+	0.713442i	−0.802060	+	0.597244i	$0.796262\pi$
$632$	−0.556515	+	2.07694i	−0.0221370	+	0.0826163i
$633$	29.9256	+	8.01854i	1.18944	+	0.318709i
$634$	−0.664916	−	0.178164i	−0.0264072	−	0.00707579i
$635$		0			0
$636$	23.3646	+	40.4686i	0.926466	+	1.60469i
$637$	−62.2458			−2.46627
$638$	0.176555	−	0.0473077i	0.00698987	−	0.00187293i
$639$			10.7030i			0.423402i
$640$		0			0
$641$	5.12828	−	8.88244i	0.202555	−	0.350835i	−0.746796	−	0.665053i	$-0.768409\pi$
$641$	5.12828	−	8.88244i	0.202555	−	0.350835i	0.949351	+	0.314218i	$0.101742\pi$
$642$	1.19990	+	2.07828i	0.0473561	+	0.0820232i
$643$	12.2193			0.481883			0.240942	−	0.970540i	$-0.422544\pi$
$643$	12.2193			0.481883			0.240942	+	0.970540i	$0.422544\pi$
$644$	−1.30330	+	0.349219i	−0.0513573	+	0.0137612i
$645$		0			0
$646$	−0.962601	+	0.257928i	−0.0378730	+	0.0101481i
$647$	−13.2479	+	7.64866i	−0.520828	+	0.300700i	−0.737273	−	0.675595i	$-0.763887\pi$
$647$	−13.2479	+	7.64866i	−0.520828	+	0.300700i	0.216446	+	0.976295i	$0.430554\pi$
$648$	−3.99892	+	2.30878i	−0.157093	+	0.0906974i
$649$	−0.714231	+	0.191378i	−0.0280360	+	0.00751223i
$650$		0			0
$651$	−65.7612	+	17.6207i	−2.57739	+	0.690608i
$652$	−31.5479			−1.23551
$653$	−22.6381	−	39.2103i	−0.885897	−	1.53442i	−0.844682	−	0.535268i	$-0.820211\pi$
$653$	−22.6381	−	39.2103i	−0.885897	−	1.53442i	−0.0412146	−	0.999150i	$-0.513123\pi$
$654$	−0.701169	+	1.21446i	−0.0274179	+	0.0474891i
$655$		0			0
$656$			21.6823i			0.846550i
$657$	−8.82838	+	2.36556i	−0.344428	+	0.0922892i
$658$	1.11023			0.0432813
$659$	−20.6457	−	35.7594i	−0.804243	−	1.39299i	−0.916801	−	0.399344i	$-0.869238\pi$
$659$	−20.6457	−	35.7594i	−0.804243	−	1.39299i	0.112559	−	0.993645i	$-0.464095\pi$
$660$		0			0
$661$	−22.9847	−	6.15874i	−0.894003	−	0.239547i	−0.217564	−	0.976046i	$-0.569811\pi$
$661$	−22.9847	−	6.15874i	−0.894003	−	0.239547i	−0.676439	+	0.736499i	$0.736478\pi$
$662$	2.93690	+	0.786939i	0.114146	+	0.0305852i
$663$	18.4064	−	68.6936i	0.714845	−	2.66784i
$664$	0.0991769	+	0.370133i	0.00384881	+	0.0143640i
$665$		0			0
$666$	0.644883	−	0.0836541i	0.0249887	−	0.00324153i
$667$	−0.0756113	+	0.0756113i	−0.00292768	+	0.00292768i
$668$	−0.527540	+	0.913727i	−0.0204111	+	0.0353531i
$669$	−10.3045	−	17.8479i	−0.398395	−	0.690040i
$670$		0			0
$671$	−1.73849	+	6.48813i	−0.0671137	+	0.250472i
$672$	−11.3308			−0.437096
$673$	−5.77687	+	21.5596i	−0.222682	+	0.831060i	0.760638	+	0.649176i	$0.224886\pi$
$673$	−5.77687	+	21.5596i	−0.222682	+	0.831060i	−0.983320	+	0.181884i	$0.941780\pi$
$674$	−0.606207	+	0.606207i	−0.0233502	+	0.0233502i
$675$		0			0
$676$	−17.0554			−0.655976
$677$	19.1688	+	19.1688i	0.736715	+	0.736715i	0.971941	−	0.235225i	$-0.0755828\pi$
$677$	19.1688	+	19.1688i	0.736715	+	0.736715i	−0.235225	+	0.971941i	$0.575583\pi$
$678$	1.68904	−	0.452578i	0.0648673	−	0.0173811i
$679$	7.64976	+	2.04975i	0.293571	+	0.0786621i
$680$		0			0
$681$	−3.58374	−	13.3747i	−0.137329	−	0.512520i
$682$	0.499696	+	1.86489i	0.0191343	+	0.0714103i
$683$	−19.2407	−	11.1086i	−0.736224	−	0.425059i	0.0844709	−	0.996426i	$-0.473080\pi$
$683$	−19.2407	−	11.1086i	−0.736224	−	0.425059i	−0.820695	+	0.571367i	$0.806413\pi$
$684$	−0.650342	+	2.42711i	−0.0248664	+	0.0928028i
$685$		0			0
$686$	−0.786225	−	2.93423i	−0.0300182	−	0.112030i
$687$	45.6600	−	12.2346i	1.74204	−	0.466778i
$688$	6.11308	+	3.52939i	0.233059	+	0.134557i
$689$	−38.4987	+	38.4987i	−1.46668	+	1.46668i
$690$		0			0
$691$	−36.9526	−	21.3346i	−1.40574	−	0.811606i	−0.410769	−	0.911740i	$-0.634740\pi$
$691$	−36.9526	−	21.3346i	−1.40574	−	0.811606i	−0.994974	+	0.100134i	$0.968073\pi$
$692$	−3.91197	+	3.91197i	−0.148711	+	0.148711i
$693$	−7.94020	+	7.94020i	−0.301623	+	0.301623i
$694$	1.30651	−	2.26294i	0.0495943	−	0.0858999i
$695$		0			0
$696$	−0.517965	+	0.299047i	−0.0196334	+	0.0113354i
$697$		−	42.1021i		−	1.59473i
$698$	0.971200	+	1.68217i	0.0367605	+	0.0636710i
$699$	−26.4699	+	15.2824i	−1.00118	+	0.578033i
$700$		0			0
$701$	−12.0518	+	3.22926i	−0.455189	+	0.121967i	−0.479126	−	0.877746i	$-0.659046\pi$
$701$	−12.0518	+	3.22926i	−0.455189	+	0.121967i	0.0239375	+	0.999713i	$0.492380\pi$
$702$	−1.37132	−	1.37132i	−0.0517573	−	0.0517573i
$703$	−4.60914	+	5.98318i	−0.173837	+	0.225660i
$704$		−	18.9031i		−	0.712436i
$705$		0			0
$706$	−1.65647	+	0.956364i	−0.0623421	+	0.0359932i
$707$	−2.17072	+	8.10125i	−0.0816385	+	0.304679i
$708$	1.04478	−	0.603206i	0.0392654	−	0.0226699i
$709$	36.3631	−	36.3631i	1.36565	−	1.36565i	0.499104	−	0.866542i	$-0.333663\pi$
$709$	36.3631	−	36.3631i	1.36565	−	1.36565i	0.866542	−	0.499104i	$-0.166337\pi$
$710$		0			0
$711$	−3.69099	−	3.69099i	−0.138423	−	0.138423i
$712$	0.835398	+	3.11775i	0.0313079	+	0.116843i
$713$	−0.798658	−	0.798658i	−0.0299100	−	0.0299100i
$714$	7.26616			0.271929
$715$		0			0
$716$	4.66661	−	17.4160i	0.174399	−	0.650867i
$717$		−	33.1518i		−	1.23808i
$718$	−1.33690	+	2.31557i	−0.0498926	+	0.0864165i
$719$	−14.6985	−	8.48621i	−0.548163	−	0.316482i	0.200218	−	0.979751i	$-0.435835\pi$
$719$	−14.6985	−	8.48621i	−0.548163	−	0.316482i	−0.748381	+	0.663269i	$0.769168\pi$
$720$		0			0
$721$	15.5385	+	4.16353i	0.578684	+	0.155058i
$722$	−0.917181	−	1.58860i	−0.0341340	−	0.0591218i
$723$	3.65517	−	6.33094i	0.135937	−	0.235450i
$724$	1.10827	−	1.91959i	0.0411887	−	0.0713409i
$725$		0			0
$726$	−0.748995	−	0.748995i	−0.0277978	−	0.0277978i
$727$	12.6935	−	7.32860i	0.470776	−	0.271803i	−0.245788	−	0.969323i	$-0.579047\pi$
$727$	12.6935	−	7.32860i	0.470776	−	0.271803i	0.716565	+	0.697521i	$0.245714\pi$
$728$	−2.27583	−	8.49351i	−0.0843478	−	0.314790i
$729$			12.6847i			0.469803i
$730$		0			0
$731$	−11.8702	−	6.85328i	−0.439037	−	0.253478i
$732$		−	10.9592i		−	0.405062i
$733$	18.8454	+	5.04961i	0.696071	+	0.186512i	0.589470	−	0.807790i	$-0.299337\pi$
$733$	18.8454	+	5.04961i	0.696071	+	0.186512i	0.106601	+	0.994302i	$0.466003\pi$
$734$	−0.841763	−	0.841763i	−0.0310700	−	0.0310700i
$735$		0			0
$736$	−0.0939899	−	0.162795i	−0.00346451	−	0.00600072i
$737$	30.0692	+	8.05702i	1.10761	+	0.296784i
$738$	0.510291	+	0.294616i	0.0187841	+	0.0108450i
$739$	−0.970989			−0.0357184			−0.0178592	−	0.999841i	$-0.505685\pi$
$739$	−0.970989			−0.0357184			−0.0178592	+	0.999841i	$0.505685\pi$
$740$		0			0
$741$	−11.5598			−0.424660
$742$	−4.81753	−	2.78140i	−0.176857	−	0.102108i
$743$	22.0611	+	5.91126i	0.809344	+	0.216863i	0.639683	−	0.768639i	$-0.279066\pi$
$743$	22.0611	+	5.91126i	0.809344	+	0.216863i	0.169662	+	0.985502i	$0.445732\pi$
$744$	−3.15874	−	5.47110i	−0.115805	−	0.200580i
$745$		0			0
$746$	−2.27171	−	2.27171i	−0.0831732	−	0.0831732i
$747$	−0.898536	−	0.240762i	−0.0328757	−	0.00880902i
$748$			37.1234i			1.35737i
$749$	44.5728	+	25.7341i	1.62865	+	0.940304i
$750$		0			0
$751$			39.2344i			1.43168i	0.698262	+	0.715842i	$0.253957\pi$
$751$			39.2344i			1.43168i	−0.698262	+	0.715842i	$0.746043\pi$
$752$	−2.38190	−	8.88937i	−0.0868589	−	0.324162i
$753$	−13.4959	+	7.79185i	−0.491817	+	0.283951i
$754$	−0.245694	−	0.245694i	−0.00894765	−	0.00894765i
$755$		0			0
$756$	−17.8491	+	30.9156i	−0.649167	+	1.12439i
$757$	−17.2169	+	29.8205i	−0.625757	+	1.08384i	0.362637	+	0.931931i	$0.381877\pi$
$757$	−17.2169	+	29.8205i	−0.625757	+	1.08384i	−0.988394	+	0.151913i	$0.951457\pi$
$758$	0.368605	+	0.638443i	0.0133884	+	0.0231893i
$759$	−0.710513	−	0.190381i	−0.0257900	−	0.00691040i
$760$		0			0
$761$	13.3522	+	7.70889i	0.484016	+	0.279447i	0.722089	−	0.691800i	$-0.243182\pi$
$761$	13.3522	+	7.70889i	0.484016	+	0.279447i	−0.238072	+	0.971247i	$0.576516\pi$
$762$	−0.522113	+	0.904326i	−0.0189142	+	0.0327603i
$763$			30.0759i			1.08882i
$764$	−9.40459	+	35.0984i	−0.340246	+	1.26982i
$765$		0			0
$766$	2.21036			0.0798637
$767$	0.993927	+	0.993927i	0.0358886	+	0.0358886i
$768$	7.84589	+	29.2812i	0.283114	+	1.05660i
$769$	−8.34198	−	8.34198i	−0.300819	−	0.300819i	0.540515	−	0.841334i	$-0.318229\pi$
$769$	−8.34198	−	8.34198i	−0.300819	−	0.300819i	−0.841334	+	0.540515i	$0.818229\pi$
$770$		0			0
$771$	38.2380	−	38.2380i	1.37711	−	1.37711i
$772$	11.5468	−	6.66655i	0.415578	−	0.239934i
$773$	7.88226	−	29.4170i	0.283505	−	1.05806i	−0.666420	−	0.745577i	$-0.732174\pi$
$773$	7.88226	−	29.4170i	0.283505	−	1.05806i	0.949925	−	0.312479i	$-0.101159\pi$
$774$	0.166128	−	0.0959139i	0.00597134	−	0.00344755i
$775$		0			0
$776$			0.734890i			0.0263810i
$777$	43.7523	−	33.4404i	1.56960	−	1.19967i
$778$	2.16773	+	2.16773i	0.0777168	+	0.0777168i
$779$	−6.61037	+	1.77124i	−0.236841	+	0.0634614i
$780$		0			0
$781$	22.2595	−	12.8515i	0.796507	−	0.459864i
$782$	0.0602732	+	0.104396i	0.00215537	+	0.00373320i
$783$			2.82910i			0.101104i
$784$	−45.6548	+	26.3588i	−1.63053	+	0.941387i
$785$		0			0
$786$	−1.43698	+	2.48893i	−0.0512554	+	0.0887770i
$787$	12.7741	−	12.7741i	0.455348	−	0.455348i	−0.441777	−	0.897125i	$-0.645652\pi$
$787$	12.7741	−	12.7741i	0.455348	−	0.455348i	0.897125	+	0.441777i	$0.145652\pi$
$788$	20.2860	−	20.2860i	0.722659	−	0.722659i
$789$	−9.39775	−	5.42579i	−0.334569	−	0.193163i
$790$		0			0
$791$	26.5184	−	26.5184i	0.942886	−	0.942886i
$792$	−0.902392	−	0.520996i	−0.0320651	−	0.0185128i
$793$	12.3337	−	3.30481i	0.437983	−	0.117357i
$794$	0.0430442	+	0.160643i	0.00152758	+	0.00570101i
$795$		0			0
$796$	−4.86633	+	18.1614i	−0.172483	+	0.643714i
$797$	−11.4897	−	6.63356i	−0.406985	−	0.234973i	0.282509	−	0.959265i	$-0.408833\pi$
$797$	−11.4897	−	6.63356i	−0.406985	−	0.234973i	−0.689493	+	0.724292i	$0.742167\pi$
$798$	−0.305689	−	1.14085i	−0.0108213	−	0.0403855i
$799$	4.62512	+	17.2612i	0.163625	+	0.610656i
$800$		0			0
$801$	−7.56865	−	2.02801i	−0.267425	−	0.0716564i
$802$	0.391760	−	0.104972i	0.0138335	−	0.00370668i
$803$	15.5204	+	15.5204i	0.547703	+	0.547703i
$804$	−50.7901			−1.79123
$805$		0			0
$806$	2.59519	−	2.59519i	0.0914116	−	0.0914116i
$807$	9.47957	−	35.3782i	0.333697	−	1.24537i
$808$	−0.778263			−0.0273792
$809$	7.16080	−	26.7245i	0.251760	−	0.939582i	−0.718104	−	0.695936i	$-0.754990\pi$
$809$	7.16080	−	26.7245i	0.251760	−	0.939582i	0.969864	−	0.243646i	$-0.0783435\pi$
$810$		0			0
$811$	1.13841	+	1.97178i	0.0399749	+	0.0692385i	0.885321	−	0.464981i	$-0.153939\pi$
$811$	1.13841	+	1.97178i	0.0399749	+	0.0692385i	−0.845346	+	0.534220i	$0.820606\pi$
$812$	−3.19795	+	5.53902i	−0.112226	+	0.194381i
$813$	22.7194	−	22.7194i	0.796805	−	0.796805i
$814$	−0.948319	−	1.24075i	−0.0332386	−	0.0434882i
$815$		0			0
$816$	−15.5889	−	58.1784i	−0.545719	−	2.03665i
$817$	−0.576638	+	2.15204i	−0.0201740	+	0.0752904i
$818$	−1.67628	−	0.449157i	−0.0586096	−	0.0157044i
$819$	20.6189	+	5.52481i	0.720481	+	0.193052i
$820$		0			0
$821$	−13.8253	−	23.9461i	−0.482507	−	0.835726i	0.517292	−	0.855809i	$-0.326940\pi$
$821$	−13.8253	−	23.9461i	−0.482507	−	0.835726i	−0.999798	+	0.0200830i	$0.993607\pi$
$822$	−2.22346			−0.0775520
$823$	−3.44580	+	0.923299i	−0.120113	+	0.0321842i	−0.318375	−	0.947965i	$-0.603137\pi$
$823$	−3.44580	+	0.923299i	−0.120113	+	0.0321842i	0.198262	+	0.980149i	$0.436470\pi$
$824$			1.49274i			0.0520020i
$825$		0			0
$826$	−0.0718078	+	0.124375i	−0.00249851	+	0.00432755i
$827$	−17.2563	−	29.8888i	−0.600060	−	1.03934i	−0.992811	−	0.119690i	$-0.961810\pi$
$827$	−17.2563	−	29.8888i	−0.600060	−	1.03934i	0.392751	−	0.919645i	$-0.371523\pi$
$828$	0.303947			0.0105629
$829$	12.0971	−	3.24141i	0.420150	−	0.112579i	−0.0425488	−	0.999094i	$-0.513548\pi$
$829$	12.0971	−	3.24141i	0.420150	−	0.112579i	0.462699	+	0.886516i	$0.346881\pi$
$830$		0			0
$831$	44.5719	−	11.9430i	1.54618	−	0.414298i
$832$	−31.1198	+	17.9670i	−1.07889	+	0.622895i
$833$	88.6515	−	51.1830i	3.07159	−	1.77338i
$834$	−1.57599	+	0.422286i	−0.0545722	+	0.0146226i
$835$		0			0
$836$	5.82868	−	1.56179i	0.201589	−	0.0540156i
$837$	−29.8828			−1.03290
$838$	−0.918102	−	1.59020i	−0.0317153	−	0.0549326i
$839$	−15.9229	+	27.5792i	−0.549719	+	0.952141i	0.448575	+	0.893745i	$0.351932\pi$
$839$	−15.9229	+	27.5792i	−0.549719	+	0.952141i	−0.998294	+	0.0583957i	$0.981401\pi$
$840$		0			0
$841$		−	28.4931i		−	0.982521i
$842$	−1.03582	+	0.277547i	−0.0356967	+	0.00956490i
$843$	−55.3987			−1.90803
$844$	15.3716	+	26.6244i	0.529112	+	0.916450i
$845$		0			0
$846$	−0.241576	−	0.0647300i	−0.00830554	−	0.00222546i
$847$	−21.9434	−	5.87971i	−0.753983	−	0.202029i
$848$	−11.9345	+	44.5401i	−0.409831	+	1.52951i
$849$	−2.94275	−	10.9825i	−0.100995	−	0.376918i
$850$		0			0
$851$	0.843382	+	0.351219i	0.0289108	+	0.0120396i
$852$	−29.6531	+	29.6531i	−1.01590	+	1.01590i
$853$	−8.54847	+	14.8064i	−0.292694	+	0.506961i	−0.974446	−	0.224623i	$-0.927885\pi$
$853$	−8.54847	+	14.8064i	−0.292694	+	0.506961i	0.681752	+	0.731583i	$0.261218\pi$
$854$	0.652308	+	1.12983i	0.0223215	+	0.0386620i
$855$		0			0
$856$	−1.23610	+	4.61318i	−0.0422490	+	0.157675i
$857$	13.4046			0.457892			0.228946	−	0.973439i	$-0.426472\pi$
$857$	13.4046			0.457892			0.228946	+	0.973439i	$0.426472\pi$
$858$	0.618632	−	2.30877i	0.0211197	−	0.0788199i
$859$	−7.23511	+	7.23511i	−0.246859	+	0.246859i	−0.819680	−	0.572821i	$-0.805849\pi$
$859$	−7.23511	+	7.23511i	−0.246859	+	0.246859i	0.572821	+	0.819680i	$0.305849\pi$
$860$		0			0
$861$	49.8981			1.70052
$862$	2.13714	+	2.13714i	0.0727912	+	0.0727912i
$863$	2.40453	−	0.644292i	0.0818512	−	0.0219320i	−0.217661	−	0.976024i	$-0.569843\pi$
$863$	2.40453	−	0.644292i	0.0818512	−	0.0219320i	0.299512	+	0.954092i	$0.403176\pi$
$864$	−4.80398	−	1.28722i	−0.163435	−	0.0437922i
$865$		0			0
$866$	0.465314	+	1.73658i	0.0158120	+	0.0590113i
$867$	21.4511	+	80.0565i	0.728516	+	2.71886i
$868$	−58.5068	−	33.7789i	−1.98585	−	1.14653i
$869$	−3.24441	+	12.1083i	−0.110059	+	0.410746i
$870$		0			0
$871$	−15.3161	−	57.1606i	−0.518967	−	1.93681i
$872$	−2.69575	+	0.722324i	−0.0912896	+	0.0244610i
$873$	−1.54501	−	0.892010i	−0.0522906	−	0.0301900i
$874$	0.0138554	−	0.0138554i	0.000468664	−	0.000468664i
$875$		0			0
$876$	−31.0134	−	17.9056i	−1.04785	−	0.604975i
$877$	−11.4866	+	11.4866i	−0.387875	+	0.387875i	−0.873929	−	0.486054i	$-0.838436\pi$
$877$	−11.4866	+	11.4866i	−0.387875	+	0.387875i	0.486054	+	0.873929i	$0.338436\pi$
$878$	−0.748664	+	0.748664i	−0.0252662	+	0.0252662i
$879$	13.9666	−	24.1908i	0.471081	−	0.815935i
$880$		0			0
$881$	−46.0684	+	26.5976i	−1.55208	+	0.896096i	−0.554112	+	0.832442i	$0.686942\pi$
$881$	−46.0684	+	26.5976i	−1.55208	+	0.896096i	−0.997972	+	0.0636536i	$0.979725\pi$
$882$			1.43264i			0.0482396i
$883$	−13.3117	−	23.0566i	−0.447975	−	0.775916i	0.550279	−	0.834981i	$-0.314521\pi$
$883$	−13.3117	−	23.0566i	−0.447975	−	0.775916i	−0.998254	+	0.0590650i	$0.981188\pi$
$884$	61.1157	−	35.2852i	2.05554	−	1.18677i
$885$		0			0
$886$	−3.94598	+	1.05732i	−0.132568	+	0.0355214i
$887$	−21.7089	−	21.7089i	−0.728912	−	0.728912i	0.241491	−	0.970403i	$-0.422364\pi$
$887$	−21.7089	−	21.7089i	−0.728912	−	0.728912i	−0.970403	+	0.241491i	$0.922364\pi$
$888$	4.04811	+	3.11846i	0.135846	+	0.104649i
$889$			22.3955i			0.751120i
$890$		0			0
$891$	−23.3132	+	13.4599i	−0.781021	+	0.450923i
$892$	5.29301	−	19.7538i	0.177223	−	0.661405i
$893$	2.51556	−	1.45236i	0.0841801	−	0.0486014i
$894$	−0.252186	+	0.252186i	−0.00843435	+	0.00843435i
$895$		0			0
$896$	−10.5908	−	10.5908i	−0.353813	−	0.353813i
$897$	0.361908	+	1.35066i	0.0120838	+	0.0450972i
$898$	1.86575	+	1.86575i	0.0622609	+	0.0622609i
$899$	−5.35397			−0.178565
$900$		0			0
$901$	23.1741	−	86.4869i	0.772041	−	2.88130i
$902$		−	1.41504i		−	0.0471156i
$903$	8.12230	−	14.0682i	0.270293	−	0.468162i
$904$	3.01378	+	1.74001i	0.100237	+	0.0578717i
$905$		0			0
$906$	2.29838	+	0.615849i	0.0763586	+	0.0204602i
$907$	−5.33028	−	9.23231i	−0.176989	−	0.306554i	0.763859	−	0.645383i	$-0.223302\pi$
$907$	−5.33028	−	9.23231i	−0.176989	−	0.306554i	−0.940848	+	0.338830i	$0.889969\pi$
$908$	6.87006	−	11.8993i	0.227991	−	0.394892i
$909$	0.944656	−	1.63619i	0.0313323	−	0.0542691i
$910$		0			0
$911$	10.7665	+	10.7665i	0.356708	+	0.356708i	0.862598	−	0.505890i	$-0.168836\pi$
$911$	10.7665	+	10.7665i	0.356708	+	0.356708i	−0.505890	+	0.862598i	$0.668836\pi$
$912$	−8.47866	+	4.89515i	−0.280756	+	0.162095i
$913$	0.578188	+	2.15783i	0.0191352	+	0.0714136i
$914$			0.184097i			0.00608938i
$915$		0			0
$916$	40.6231	+	23.4538i	1.34222	+	0.774934i
$917$			61.6378i			2.03546i
$918$	3.08066	+	0.825461i	0.101677	+	0.0272443i
$919$	−13.7345	−	13.7345i	−0.453059	−	0.453059i	0.443310	−	0.896368i	$-0.353804\pi$
$919$	−13.7345	−	13.7345i	−0.453059	−	0.453059i	−0.896368	+	0.443310i	$0.853804\pi$
$920$		0			0
$921$	10.3930	+	18.0013i	0.342463	+	0.593162i
$922$	−1.88436	−	0.504913i	−0.0620581	−	0.0166284i
$923$	−42.3145	−	24.4303i	−1.39280	−	0.804133i
$924$	−43.9975			−1.44741
$925$		0			0
$926$	−2.20202			−0.0723629
$927$	−3.13828	−	1.81189i	−0.103075	−	0.0595102i
$928$	−0.860707	−	0.230626i	−0.0282541	−	0.00757066i
$929$	−2.36184	−	4.09083i	−0.0774895	−	0.134216i	0.824677	−	0.565604i	$-0.191357\pi$
$929$	−2.36184	−	4.09083i	−0.0774895	−	0.134216i	−0.902166	+	0.431389i	$0.858024\pi$
$930$		0			0
$931$	−11.7657	−	11.7657i	−0.385606	−	0.385606i
$932$	−29.2964	−	7.84996i	−0.959637	−	0.257134i
$933$			3.58980i			0.117525i
$934$	−2.00529	−	1.15775i	−0.0656149	−	0.0378828i
$935$		0			0
$936$			1.98079i			0.0647442i
$937$	−10.1474	−	37.8706i	−0.331501	−	1.23718i	−0.907613	−	0.419808i	$-0.862097\pi$
$937$	−10.1474	−	37.8706i	−0.331501	−	1.23718i	0.576112	−	0.817371i	$-0.304569\pi$
$938$	5.23619	−	3.02312i	0.170968	−	0.0987083i
$939$	−38.4957	−	38.4957i	−1.25626	−	1.25626i
$940$		0			0
$941$	3.93030	−	6.80748i	0.128124	−	0.221917i	−0.794826	−	0.606838i	$-0.792438\pi$
$941$	3.93030	−	6.80748i	0.128124	−	0.221917i	0.922950	+	0.384920i	$0.125771\pi$
$942$	0.990700	−	1.71594i	0.0322788	−	0.0559085i
$943$	0.413908	+	0.716910i	0.0134787	+	0.0233458i
$944$	1.14990	+	0.308114i	0.0374260	+	0.0100283i
$945$		0			0
$946$	−0.398954	−	0.230336i	−0.0129711	−	0.00748888i
$947$	20.1394	−	34.8825i	0.654444	−	1.13353i	−0.327589	−	0.944820i	$-0.606236\pi$
$947$	20.1394	−	34.8825i	0.654444	−	1.13353i	0.982033	−	0.188710i	$-0.0604306\pi$
$948$		−	20.4522i		−	0.664257i
$949$	10.7991	−	40.3029i	0.350555	−	1.30829i
$950$		0			0
$951$	13.1316			0.425820
$952$	10.2252	+	10.2252i	0.331402	+	0.331402i
$953$	7.91365	+	29.5341i	0.256348	+	0.956705i	0.967335	+	0.253500i	$0.0815817\pi$
$953$	7.91365	+	29.5341i	0.256348	+	0.956705i	−0.710987	+	0.703205i	$0.751752\pi$
$954$	0.886083	+	0.886083i	0.0286880	+	0.0286880i
$955$		0			0
$956$	23.2617	−	23.2617i	0.752338	−	0.752338i
$957$	−3.01967	+	1.74341i	−0.0976120	+	0.0563563i
$958$	−0.746652	+	2.78654i	−0.0241232	+	0.0900292i
$959$	−41.2976	+	23.8432i	−1.33357	+	0.769937i
$960$		0			0
$961$		−	25.5523i		−	0.824267i
$962$	−1.14126	+	2.74051i	−0.0367958	+	0.0883577i
$963$	−8.19822	−	8.19822i	−0.264184	−	0.264184i
$964$	7.00699	−	1.87752i	0.225680	−	0.0604707i
$965$		0			0
$966$	−0.123727	+	0.0714340i	−0.00398086	+	0.00229835i
$967$	10.0949	+	17.4848i	0.324629	+	0.562273i	0.981437	−	0.191784i	$-0.0614274\pi$
$967$	10.0949	+	17.4848i	0.324629	+	0.562273i	−0.656809	+	0.754057i	$0.728094\pi$
$968$		−	2.10803i		−	0.0677548i
$969$	16.4637	−	9.50530i	0.528889	−	0.305354i
$970$		0			0
$971$	−13.3211	+	23.0728i	−0.427494	+	0.740441i	−0.996650	−	0.0817885i	$-0.973937\pi$
$971$	−13.3211	+	23.0728i	−0.427494	+	0.740441i	0.569156	+	0.822230i	$0.307270\pi$
$972$	14.2908	−	14.2908i	0.458379	−	0.458379i
$973$	−24.7435	+	24.7435i	−0.793240	+	0.793240i
$974$	3.22802	+	1.86370i	0.103432	+	0.0597167i
$975$		0			0
$976$	7.64683	−	7.64683i	0.244769	−	0.244769i
$977$	5.30924	+	3.06529i	0.169858	+	0.0980674i	0.582519	−	0.812817i	$-0.302067\pi$
$977$	5.30924	+	3.06529i	0.169858	+	0.0980674i	−0.412661	+	0.910885i	$0.635401\pi$
$978$	−3.22662	+	0.864569i	−0.103176	+	0.0276459i
$979$	4.87026	+	18.1760i	0.155654	+	0.580909i
$980$		0			0
$981$	1.75352	−	6.54421i	0.0559855	−	0.208941i
$982$	0.135302	+	0.0781165i	0.00431765	+	0.00249280i
$983$	−5.47856	−	20.4463i	−0.174739	−	0.652134i	−0.996596	−	0.0824406i	$-0.973729\pi$
$983$	−5.47856	−	20.4463i	−0.174739	−	0.652134i	0.821857	−	0.569694i	$-0.192938\pi$
$984$	1.19839	+	4.47246i	0.0382033	+	0.142577i
$985$		0			0
$986$	0.551949	+	0.147894i	0.0175776	+	0.00470991i
$987$	−20.4574	+	5.48155i	−0.651166	+	0.174480i
$988$	−8.11121	−	8.11121i	−0.258052	−	0.258052i
$989$	0.269500			0.00856960
$990$		0			0
$991$	−24.8692	+	24.8692i	−0.789997	+	0.789997i	−0.981493	−	0.191497i	$-0.938666\pi$
$991$	−24.8692	+	24.8692i	−0.789997	+	0.789997i	0.191497	+	0.981493i	$0.438666\pi$
$992$	2.43603	−	9.09137i	0.0773439	−	0.288651i
$993$	−58.0013			−1.84062
$994$	1.29207	−	4.82209i	0.0409821	−	0.152947i
$995$		0			0
$996$	−1.82240	−	3.15649i	−0.0577449	−	0.100017i
$997$	8.91895	−	15.4481i	0.282466	−	0.489245i	−0.689526	−	0.724261i	$-0.742181\pi$
$997$	8.91895	−	15.4481i	0.282466	−	0.489245i	0.971992	+	0.235016i	$0.0755143\pi$
$998$	−1.63977	+	1.63977i	−0.0519060	+	0.0519060i
$999$	22.3488	−	9.20745i	0.707084	−	0.291311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.b.393.9		68
5.2	odd	4		925.2.t.b.282.9		68
5.3	odd	4		185.2.p.a.97.9	✓	68
5.4	even	2		185.2.u.a.23.9	yes	68
37.29	odd	12		925.2.t.b.843.9		68
185.29	odd	12		185.2.p.a.103.9	yes	68
185.103	even	12		185.2.u.a.177.9	yes	68
185.177	even	12	inner	925.2.y.b.732.9		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.9	✓	68	5.3	odd	4
185.2.p.a.103.9	yes	68	185.29	odd	12
185.2.u.a.23.9	yes	68	5.4	even	2
185.2.u.a.177.9	yes	68	185.103	even	12
925.2.t.b.282.9		68	5.2	odd	4
925.2.t.b.843.9		68	37.29	odd	12
925.2.y.b.393.9		68	1.1	even	1	trivial
925.2.y.b.732.9		68	185.177	even	12	inner

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0909942 + 0.0525355i) q^{2} +(-1.93607 - 0.518767i) q^{3} +(-0.994480 - 1.72249i) q^{4} +(-0.148917 - 0.148917i) q^{6} +(-4.36283 - 1.16902i) q^{7} -0.419124i q^{8} +(0.881153 + 0.508734i) q^{9} -2.44344i q^{11} +(1.03181 + 3.85076i) q^{12} +(-4.02259 + 2.32245i) q^{13} +(-0.335578 - 0.335578i) q^{14} +(-1.96694 + 3.40684i) q^{16} +(3.81936 - 6.61533i) q^{17} +(0.0534532 + 0.0925836i) q^{18} +(-1.19934 - 0.321362i) q^{19} +(7.84028 + 4.52659i) q^{21} +(0.128367 - 0.222339i) q^{22} +0.150193i q^{23} +(-0.217428 + 0.811452i) q^{24} -0.488044 q^{26} +(2.80984 + 2.80984i) q^{27} +(2.32513 + 8.67750i) q^{28} +(0.503427 + 0.503427i) q^{29} +(-5.31753 + 5.31753i) q^{31} +(-1.08391 + 0.625793i) q^{32} +(-1.26757 + 4.73065i) q^{33} +(0.695080 - 0.401304i) q^{34} -2.02370i q^{36} +(2.33845 - 5.61531i) q^{37} +(-0.0922501 - 0.0922501i) q^{38} +(8.99281 - 2.40962i) q^{39} +(4.77325 - 2.75584i) q^{41} +(0.475614 + 0.823787i) q^{42} -1.79435i q^{43} +(-4.20880 + 2.42995i) q^{44} +(-0.00789049 + 0.0136667i) q^{46} +(-1.65421 + 1.65421i) q^{47} +(5.57548 - 5.57548i) q^{48} +(11.6055 + 6.70046i) q^{49} +(-10.8263 + 10.8263i) q^{51} +(8.00078 + 4.61925i) q^{52} +(11.3222 - 3.03376i) q^{53} +(0.108063 + 0.403296i) q^{54} +(-0.489964 + 1.82857i) q^{56} +(2.15529 + 1.24436i) q^{57} +(0.0193611 + 0.0722567i) q^{58} +(-0.0783231 - 0.292306i) q^{59} +(-2.65533 - 0.711494i) q^{61} +(-0.763224 + 0.204505i) q^{62} +(-3.24960 - 3.24960i) q^{63} +7.73626 q^{64} +(-0.363869 + 0.363869i) q^{66} +(-3.29741 + 12.3061i) q^{67} -15.1931 q^{68} +(0.0779154 - 0.290784i) q^{69} +(5.25961 + 9.10991i) q^{71} +(0.213223 - 0.369312i) q^{72} +(-6.35187 + 6.35187i) q^{73} +(0.507788 - 0.388109i) q^{74} +(0.639177 + 2.38544i) q^{76} +(-2.85642 + 10.6603i) q^{77} +(0.944884 + 0.253181i) q^{78} +(-4.95543 - 1.32780i) q^{79} +(-5.50858 - 9.54114i) q^{81} +0.579117 q^{82} +(-0.883111 + 0.236629i) q^{83} -18.0064i q^{84} +(0.0942673 - 0.163276i) q^{86} +(-0.713506 - 1.23583i) q^{87} -1.02410 q^{88} +(-7.43872 + 1.99320i) q^{89} +(20.2649 - 5.42996i) q^{91} +(0.258707 - 0.149364i) q^{92} +(13.0536 - 7.53653i) q^{93} +(-0.237428 + 0.0636187i) q^{94} +(2.42315 - 0.649281i) q^{96} -1.75339 q^{97} +(0.704025 + 1.21941i) q^{98} +(1.24306 - 2.15304i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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