LMFDB - Embedded newform 675.2.u.e.49.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(49,675)] 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("675.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [132] 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	675.49
Dual form			675.2.u.e.124.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.42910 - 1.70314i) q^{2} +(1.70215 - 0.320463i) q^{3} +(-0.511048 + 2.89830i) q^{4} +(-2.97833 - 2.44102i) q^{6} +(-3.70709 + 0.653660i) q^{7} +(1.81569 - 1.04829i) q^{8} +(2.79461 - 1.09095i) q^{9} +(5.03989 + 1.83437i) q^{11} +(0.0589180 + 5.09710i) q^{12} +(3.93784 - 4.69294i) q^{13} +(6.41109 + 5.37954i) q^{14} +(1.15085 + 0.418876i) q^{16} +(2.43075 + 1.40339i) q^{17} +(-5.85182 - 3.20052i) q^{18} +(-1.71412 - 2.96894i) q^{19} +(-6.10054 + 2.30061i) q^{21} +(-4.07833 - 11.2051i) q^{22} +(-0.882941 - 0.155686i) q^{23} +(2.75464 - 2.36621i) q^{24} -13.6203 q^{26} +(4.40722 - 2.75252i) q^{27} -11.0783i q^{28} +(-1.61238 + 1.35294i) q^{29} +(0.576073 - 3.26707i) q^{31} +(-2.36543 - 6.49896i) q^{32} +(9.16647 + 1.50727i) q^{33} +(-1.08362 - 6.14550i) q^{34} +(1.73372 + 8.65714i) q^{36} +(-3.00072 - 1.73247i) q^{37} +(-2.60687 + 7.16230i) q^{38} +(5.19887 - 9.25000i) q^{39} +(-1.85735 - 1.55850i) q^{41} +(12.6366 + 7.10225i) q^{42} +(2.33822 - 6.42421i) q^{43} +(-7.89217 + 13.6696i) q^{44} +(0.996658 + 1.72626i) q^{46} +(3.55068 - 0.626080i) q^{47} +(2.09315 + 0.344183i) q^{48} +(6.73741 - 2.45222i) q^{49} +(4.58723 + 1.60982i) q^{51} +(11.5891 + 13.8114i) q^{52} +7.07162i q^{53} +(-10.9863 - 3.57247i) q^{54} +(-6.04572 + 5.07296i) q^{56} +(-3.86912 - 4.50426i) q^{57} +(4.60850 + 0.812603i) q^{58} +(5.74383 - 2.09058i) q^{59} +(0.0966336 + 0.548037i) q^{61} +(-6.38754 + 3.68785i) q^{62} +(-9.64675 + 5.87097i) q^{63} +(-6.46348 + 11.1951i) q^{64} +(-10.5327 - 17.7658i) q^{66} +(10.1805 - 12.1326i) q^{67} +(-5.30969 + 6.32784i) q^{68} +(-1.55279 + 0.0179489i) q^{69} +(7.71778 - 13.3676i) q^{71} +(3.93052 - 4.91040i) q^{72} +(-11.2103 + 6.47229i) q^{73} +(1.33771 + 7.58652i) q^{74} +(9.48088 - 3.45076i) q^{76} +(-19.8824 - 3.50580i) q^{77} +(-23.1837 + 4.36480i) q^{78} +(-7.60758 + 6.38352i) q^{79} +(6.61966 - 6.09755i) q^{81} +5.39058i q^{82} +(3.07222 + 3.66133i) q^{83} +(-3.55019 - 18.8569i) q^{84} +(-14.2829 + 5.19854i) q^{86} +(-2.31093 + 2.81962i) q^{87} +(11.0738 - 1.95262i) q^{88} +(1.45438 + 2.51905i) q^{89} +(-11.5304 + 19.9712i) q^{91} +(0.902451 - 2.47946i) q^{92} +(-0.0664147 - 5.74565i) q^{93} +(-6.14058 - 5.15256i) q^{94} +(-6.10898 - 10.3042i) q^{96} +(-2.18144 + 5.99345i) q^{97} +(-13.8049 - 7.97026i) q^{98} +(16.0857 - 0.371923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.42910	−	1.70314i	−1.01053	−	1.20430i	−0.978803	−	0.204803i	$-0.934344\pi$
$2$	−1.42910	−	1.70314i	−1.01053	−	1.20430i	−0.0317247	−	0.999497i	$-0.510100\pi$
$3$	1.70215	−	0.320463i	0.982735	−	0.185019i
$3$	1.70215	−	0.320463i	0.982735	−	0.185019i
$4$	−0.511048	+	2.89830i	−0.255524	+	1.44915i
$5$		0			0
$5$		0			0
$6$	−2.97833	−	2.44102i	−1.21590	−	0.996541i
$7$	−3.70709	+	0.653660i	−1.40115	+	0.247060i	−0.822615	−	0.568598i	$-0.807486\pi$
$7$	−3.70709	+	0.653660i	−1.40115	+	0.247060i	−0.578534	+	0.815659i	$0.696375\pi$
$8$	1.81569	−	1.04829i	0.641945	−	0.370627i
$9$	2.79461	−	1.09095i	0.931536	−	0.363650i
$10$		0			0
$11$	5.03989	+	1.83437i	1.51958	+	0.553083i	0.961044	−	0.276396i	$-0.0891400\pi$
$11$	5.03989	+	1.83437i	1.51958	+	0.553083i	0.558539	+	0.829478i	$0.311362\pi$
$12$	0.0589180	+	5.09710i	0.0170082	+	1.47141i
$13$	3.93784	−	4.69294i	1.09216	−	1.30159i	0.141986	−	0.989869i	$-0.454651\pi$
$13$	3.93784	−	4.69294i	1.09216	−	1.30159i	0.950175	−	0.311718i	$-0.100904\pi$
$14$	6.41109	+	5.37954i	1.71343	+	1.43774i
$15$		0			0
$16$	1.15085	+	0.418876i	0.287713	+	0.104719i
$17$	2.43075	+	1.40339i	0.589544	+	0.340373i	0.764917	−	0.644129i	$-0.222780\pi$
$17$	2.43075	+	1.40339i	0.589544	+	0.340373i	−0.175373	+	0.984502i	$0.556113\pi$
$18$	−5.85182	−	3.20052i	−1.37929	−	0.754370i
$19$	−1.71412	−	2.96894i	−0.393246	−	0.681122i	0.599630	−	0.800278i	$-0.295315\pi$
$19$	−1.71412	−	2.96894i	−0.393246	−	0.681122i	−0.992876	+	0.119156i	$0.961981\pi$
$20$		0			0
$21$	−6.10054	+	2.30061i	−1.33125	+	0.502034i
$22$	−4.07833	−	11.2051i	−0.869503	−	2.38894i
$23$	−0.882941	−	0.155686i	−0.184106	−	0.0324628i	0.0808349	−	0.996728i	$-0.474241\pi$
$23$	−0.882941	−	0.155686i	−0.184106	−	0.0324628i	−0.264941	+	0.964265i	$0.585352\pi$
$24$	2.75464	−	2.36621i	0.562289	−	0.483001i
$25$		0			0
$26$	−13.6203			−2.67116
$27$	4.40722	−	2.75252i	0.848170	−	0.529724i
$28$		−	11.0783i		−	2.09360i
$29$	−1.61238	+	1.35294i	−0.299411	+	0.251235i	−0.780099	−	0.625656i	$-0.784831\pi$
$29$	−1.61238	+	1.35294i	−0.299411	+	0.251235i	0.480688	+	0.876892i	$0.340387\pi$
$30$		0			0
$31$	0.576073	−	3.26707i	0.103466	−	0.586784i	−0.888356	−	0.459155i	$-0.848152\pi$
$31$	0.576073	−	3.26707i	0.103466	−	0.586784i	0.991822	−	0.127629i	$-0.0407366\pi$
$32$	−2.36543	−	6.49896i	−0.418153	−	1.14887i
$33$	9.16647	+	1.50727i	1.59568	+	0.262382i
$34$	−1.08362	−	6.14550i	−0.185839	−	1.05394i
$35$		0			0
$36$	1.73372	+	8.65714i	0.288953	+	1.44286i
$37$	−3.00072	−	1.73247i	−0.493316	−	0.284816i	0.232633	−	0.972565i	$-0.425266\pi$
$37$	−3.00072	−	1.73247i	−0.493316	−	0.284816i	−0.725949	+	0.687749i	$0.758599\pi$
$38$	−2.60687	+	7.16230i	−0.422889	+	1.16188i
$39$	5.19887	−	9.25000i	0.832486	−	1.48119i
$40$		0			0
$41$	−1.85735	−	1.55850i	−0.290069	−	0.243397i	0.486127	−	0.873888i	$-0.338409\pi$
$41$	−1.85735	−	1.55850i	−0.290069	−	0.243397i	−0.776196	+	0.630491i	$0.782854\pi$
$42$	12.6366	+	7.10225i	1.94986	+	1.09590i
$43$	2.33822	−	6.42421i	0.356576	−	0.979683i	−0.623633	−	0.781717i	$-0.714344\pi$
$43$	2.33822	−	6.42421i	0.356576	−	0.979683i	0.980209	−	0.197966i	$-0.0634336\pi$
$44$	−7.89217	+	13.6696i	−1.18979	+	2.06078i
$45$		0			0
$46$	0.996658	+	1.72626i	0.146949	+	0.254523i
$47$	3.55068	−	0.626080i	0.517919	−	0.0913232i	0.0914225	−	0.995812i	$-0.470859\pi$
$47$	3.55068	−	0.626080i	0.517919	−	0.0913232i	0.426497	+	0.904489i	$0.359748\pi$
$48$	2.09315	+	0.344183i	0.302120	+	0.0496785i
$49$	6.73741	−	2.45222i	0.962487	−	0.350316i
$50$		0			0
$51$	4.58723	+	1.60982i	0.642341	+	0.225420i
$52$	11.5891	+	13.8114i	1.60712	+	1.91529i
$53$			7.07162i			0.971362i	0.874136	+	0.485681i	$0.161428\pi$
$53$			7.07162i			0.971362i	−0.874136	+	0.485681i	$0.838572\pi$
$54$	−10.9863	−	3.57247i	−1.49505	−	0.486151i
$55$		0			0
$56$	−6.04572	+	5.07296i	−0.807893	+	0.677903i
$57$	−3.86912	−	4.50426i	−0.512477	−	0.596604i
$58$	4.60850	+	0.812603i	0.605126	+	0.106700i
$59$	5.74383	−	2.09058i	0.747782	−	0.272171i	0.0601101	−	0.998192i	$-0.480855\pi$
$59$	5.74383	−	2.09058i	0.747782	−	0.272171i	0.687672	+	0.726021i	$0.258633\pi$
$60$		0			0
$61$	0.0966336	+	0.548037i	0.0123727	+	0.0701689i	0.990369	−	0.138453i	$-0.0442131\pi$
$61$	0.0966336	+	0.548037i	0.0123727	+	0.0701689i	−0.977996	+	0.208622i	$0.933102\pi$
$62$	−6.38754	+	3.68785i	−0.811219	+	0.468357i
$63$	−9.64675	+	5.87097i	−1.21538	+	0.739673i
$64$	−6.46348	+	11.1951i	−0.807935	+	1.39938i
$65$		0			0
$66$	−10.5327	−	17.7658i	−1.29649	−	2.18682i
$67$	10.1805	−	12.1326i	1.24375	−	1.48224i	0.428052	−	0.903754i	$-0.359200\pi$
$67$	10.1805	−	12.1326i	1.24375	−	1.48224i	0.815694	−	0.578484i	$-0.196356\pi$
$68$	−5.30969	+	6.32784i	−0.643894	+	0.767363i
$69$	−1.55279	+	0.0179489i	−0.186934	+	0.00216079i
$70$		0			0
$71$	7.71778	−	13.3676i	0.915933	−	1.58644i	0.110402	−	0.993887i	$-0.464786\pi$
$71$	7.71778	−	13.3676i	0.915933	−	1.58644i	0.805530	−	0.592555i	$-0.201881\pi$
$72$	3.93052	−	4.91040i	0.463216	−	0.578696i
$73$	−11.2103	+	6.47229i	−1.31207	+	0.757524i	−0.982439	−	0.186585i	$-0.940258\pi$
$73$	−11.2103	+	6.47229i	−1.31207	+	0.757524i	−0.329632	+	0.944110i	$0.606925\pi$
$74$	1.33771	+	7.58652i	0.155505	+	0.881915i
$75$		0			0
$76$	9.48088	−	3.45076i	1.08753	−	0.395829i
$77$	−19.8824	−	3.50580i	−2.26581	−	0.399523i
$78$	−23.1837	+	4.36480i	−2.62504	+	0.494216i
$79$	−7.60758	+	6.38352i	−0.855920	+	0.718202i	−0.961085	−	0.276253i	$-0.910907\pi$
$79$	−7.60758	+	6.38352i	−0.855920	+	0.718202i	0.105165	+	0.994455i	$0.466463\pi$
$80$		0			0
$81$	6.61966	−	6.09755i	0.735517	−	0.677506i
$82$			5.39058i			0.595289i
$83$	3.07222	+	3.66133i	0.337220	+	0.401884i	0.907830	−	0.419338i	$-0.137738\pi$
$83$	3.07222	+	3.66133i	0.337220	+	0.401884i	−0.570610	+	0.821221i	$0.693293\pi$
$84$	−3.55019	−	18.8569i	−0.387357	−	2.05746i
$85$		0			0
$86$	−14.2829	+	5.19854i	−1.54016	+	0.560573i
$87$	−2.31093	+	2.81962i	−0.247758	+	0.302295i
$88$	11.0738	−	1.95262i	1.18048	−	0.208150i
$89$	1.45438	+	2.51905i	0.154164	+	0.267019i	0.932754	−	0.360513i	$-0.117398\pi$
$89$	1.45438	+	2.51905i	0.154164	+	0.267019i	−0.778591	+	0.627532i	$0.784065\pi$
$90$		0			0
$91$	−11.5304	+	19.9712i	−1.20871	+	2.09355i
$92$	0.902451	−	2.47946i	0.0940870	−	0.258502i
$93$	−0.0664147	−	5.74565i	−0.00688688	−	0.595796i
$94$	−6.14058	−	5.15256i	−0.633353	−	0.531446i
$95$		0			0
$96$	−6.10898	−	10.3042i	−0.623496	−	1.05166i
$97$	−2.18144	+	5.99345i	−0.221491	+	0.608543i	−0.999813	−	0.0193229i	$-0.993849\pi$
$97$	−2.18144	+	5.99345i	−0.221491	+	0.608543i	0.778322	+	0.627865i	$0.216071\pi$
$98$	−13.8049	−	7.97026i	−1.39451	−	0.805118i
$99$	16.0857	−	0.371923i	1.61667	−	0.0373797i
$100$		0			0
$101$	0.799294	+	4.53302i	0.0795328	+	0.451053i	0.998403	+	0.0564928i	$0.0179918\pi$
$101$	0.799294	+	4.53302i	0.0795328	+	0.451053i	−0.918870	+	0.394560i	$0.870897\pi$
$102$	−3.81388	−	10.1133i	−0.377630	−	1.00136i
$103$	−3.05797	−	8.40172i	−0.301311	−	0.827846i	−0.994273	−	0.106871i	$-0.965917\pi$
$103$	−3.05797	−	8.40172i	−0.301311	−	0.827846i	0.692962	−	0.720974i	$-0.256305\pi$
$104$	2.23035	−	12.6490i	0.218704	−	1.24033i
$105$		0			0
$106$	12.0439	−	10.1061i	1.16981	−	0.981589i
$107$			16.5248i			1.59751i	0.601657	+	0.798754i	$0.294507\pi$
$107$			16.5248i			1.59751i	−0.601657	+	0.798754i	$0.705493\pi$
$108$	5.72534	+	14.1801i	0.550921	+	1.36448i
$109$	6.79600			0.650939			0.325469	−	0.945553i	$-0.394478\pi$
$109$	6.79600			0.650939			0.325469	+	0.945553i	$0.394478\pi$
$110$		0			0
$111$	−5.66286	−	1.98729i	−0.537495	−	0.188626i
$112$	−4.54011	−	0.800545i	−0.429000	−	0.0756444i
$113$	5.89428	+	16.1944i	0.554487	+	1.52344i	0.827520	+	0.561436i	$0.189751\pi$
$113$	5.89428	+	16.1944i	0.554487	+	1.52344i	−0.273033	+	0.962005i	$0.588027\pi$
$114$	−2.14201	+	13.0267i	−0.200618	+	1.22006i
$115$		0			0
$116$	−3.09723	−	5.36457i	−0.287571	−	0.498088i
$117$	5.88496	−	17.4109i	0.544065	−	1.60964i
$118$	−11.7691	−	6.79487i	−1.08343	−	0.625518i
$119$	−9.92836	−	3.61363i	−0.910131	−	0.331261i
$120$		0			0
$121$	13.6090	+	11.4193i	1.23719	+	1.03812i
$122$	0.795282	−	0.947781i	0.0720015	−	0.0858080i
$123$	−3.66092	−	2.05758i	−0.330094	−	0.185526i
$124$	9.17456	+	3.33927i	0.823899	+	0.299875i
$125$		0			0
$126$	23.7853	+	8.03953i	2.11896	+	0.716218i
$127$	4.17046	−	2.40782i	0.370069	−	0.213659i	−0.303420	−	0.952857i	$-0.598128\pi$
$127$	4.17046	−	2.40782i	0.370069	−	0.213659i	0.673489	+	0.739198i	$0.264795\pi$
$128$	14.6818	−	2.58879i	1.29770	−	0.228819i
$129$	1.92128	−	11.6843i	0.169159	−	1.02874i
$130$		0			0
$131$	0.969287	−	5.49710i	0.0846870	−	0.480284i	−0.912737	−	0.408548i	$-0.866035\pi$
$131$	0.969287	−	5.49710i	0.0846870	−	0.480284i	0.997424	−	0.0717355i	$-0.0228538\pi$
$132$	−9.05302	+	25.7969i	−0.787965	+	2.24533i
$133$	8.29508	+	9.88569i	0.719274	+	0.857198i
$134$	−35.2125			−3.04190
$135$		0			0
$136$	5.88467			0.504606
$137$	2.67071	+	3.18283i	0.228174	+	0.271927i	0.867969	−	0.496618i	$-0.165425\pi$
$137$	2.67071	+	3.18283i	0.228174	+	0.271927i	−0.639795	+	0.768546i	$0.720981\pi$
$138$	2.24966	+	2.61896i	0.191504	+	0.222941i
$139$	1.48337	−	8.41259i	0.125817	−	0.713546i	−0.855002	−	0.518625i	$-0.826444\pi$
$139$	1.48337	−	8.41259i	0.125817	−	0.713546i	0.980819	−	0.194921i	$-0.0624450\pi$
$140$		0			0
$141$	5.84314	−	2.20354i	0.492081	−	0.185572i
$142$	−33.7964	+	5.95921i	−2.83613	+	0.500086i
$143$	28.4549	−	16.4284i	2.37951	−	1.37381i
$144$	3.67315	−	0.0849281i	0.306096	−	0.00707734i
$145$		0			0
$146$	27.0439	+	9.84318i	2.23817	+	0.814627i
$147$	10.6822	−	6.33312i	0.881054	−	0.522347i
$148$	6.55472	−	7.81162i	0.538795	−	0.642111i
$149$	−8.62380	−	7.23622i	−0.706489	−	0.592815i	0.217123	−	0.976144i	$-0.430333\pi$
$149$	−8.62380	−	7.23622i	−0.706489	−	0.592815i	−0.923612	+	0.383330i	$0.874777\pi$
$150$		0			0
$151$	−15.9706	−	5.81283i	−1.29967	−	0.473042i	−0.402781	−	0.915296i	$-0.631957\pi$
$151$	−15.9706	−	5.81283i	−1.29967	−	0.473042i	−0.896890	+	0.442255i	$0.854179\pi$
$152$	−6.22464	−	3.59380i	−0.504885	−	0.291495i
$153$	8.32403	+	1.27011i	0.672958	+	0.102682i
$154$	22.4431	+	38.8726i	1.80851	+	3.13244i
$155$		0			0
$156$	24.1524	+	19.7951i	1.93374	+	1.58488i
$157$	4.26867	+	11.7281i	0.340677	+	0.936002i	0.985199	+	0.171416i	$0.0548342\pi$
$157$	4.26867	+	11.7281i	0.340677	+	0.936002i	−0.644522	+	0.764586i	$0.722944\pi$
$158$	21.7440	+	3.83406i	1.72986	+	0.305021i
$159$	2.26619	+	12.0369i	0.179721	+	0.954592i
$160$		0			0
$161$	3.37491			0.265980
$162$	−19.8451	−	2.56016i	−1.55918	−	0.201145i
$163$			7.49060i			0.586709i	0.956004	+	0.293354i	$0.0947716\pi$
$163$			7.49060i			0.586709i	−0.956004	+	0.293354i	$0.905228\pi$
$164$	5.46620	−	4.58668i	0.426838	−	0.358160i
$165$		0			0
$166$	1.84523	−	10.4648i	0.143218	−	0.812229i
$167$	4.28105	+	11.7621i	0.331277	+	0.910177i	0.987780	+	0.155854i	$0.0498128\pi$
$167$	4.28105	+	11.7621i	0.331277	+	0.910177i	−0.656503	+	0.754324i	$0.727965\pi$
$168$	−8.66501	+	10.5724i	−0.668520	+	0.815675i
$169$	−4.25964	−	24.1576i	−0.327664	−	1.85828i
$170$		0			0
$171$	−8.02926	−	6.42701i	−0.614013	−	0.491486i
$172$	17.4243	+	10.0600i	1.32859	+	0.767064i
$173$	−5.18574	+	14.2477i	−0.394264	+	1.08323i	0.570771	+	0.821110i	$0.306645\pi$
$173$	−5.18574	+	14.2477i	−0.394264	+	1.08323i	−0.965035	+	0.262122i	$0.915578\pi$
$174$	8.10475	−	0.0936838i	0.614420	−	0.00710215i
$175$		0			0
$176$	5.03179	+	4.22217i	0.379285	+	0.318258i
$177$	9.10688	−	5.39916i	0.684515	−	0.405826i
$178$	2.21184	−	6.07699i	0.165785	−	0.455490i
$179$	4.06134	−	7.03445i	0.303559	−	0.525780i	−0.673380	−	0.739296i	$-0.735158\pi$
$179$	4.06134	−	7.03445i	0.303559	−	0.525780i	0.976939	+	0.213517i	$0.0684917\pi$
$180$		0			0
$181$	7.95939	+	13.7861i	0.591617	+	1.02471i	0.994015	+	0.109245i	$0.0348434\pi$
$181$	7.95939	+	13.7861i	0.591617	+	1.02471i	−0.402398	+	0.915465i	$0.631823\pi$
$182$	50.4917	−	8.90305i	3.74269	−	0.659938i
$183$	0.340110	+	0.901871i	0.0251417	+	0.0666682i
$184$	−1.76636	+	0.642901i	−0.130218	+	0.0473953i
$185$		0			0
$186$	−9.69072	+	8.32423i	−0.710558	+	0.610362i
$187$	9.67636	+	11.5318i	0.707606	+	0.843292i
$188$			10.6109i			0.773878i
$189$	−14.5388	+	13.0847i	−1.05754	+	0.951771i
$190$		0			0
$191$	−13.7721	+	11.5562i	−0.996516	+	0.836176i	−0.986498	−	0.163773i	$-0.947633\pi$
$191$	−13.7721	+	11.5562i	−0.996516	+	0.836176i	−0.0100183	+	0.999950i	$0.503189\pi$
$192$	−7.41418	+	21.1270i	−0.535073	+	1.52471i
$193$	−0.956681	−	0.168689i	−0.0688634	−	0.0121425i	0.139110	−	0.990277i	$-0.455576\pi$
$193$	−0.956681	−	0.168689i	−0.0688634	−	0.0121425i	−0.207974	+	0.978134i	$0.566687\pi$
$194$	13.3252	−	4.84996i	0.956691	−	0.348207i
$195$		0			0
$196$	3.66411	+	20.7802i	0.261722	+	1.48430i
$197$	−7.99649	+	4.61678i	−0.569727	+	0.328932i	−0.757040	−	0.653368i	$-0.773355\pi$
$197$	−7.99649	+	4.61678i	−0.569727	+	0.328932i	0.187313	+	0.982300i	$0.440022\pi$
$198$	−23.6215	−	26.8646i	−1.67871	−	1.90919i
$199$	−8.81540	+	15.2687i	−0.624907	+	1.08237i	0.363651	+	0.931535i	$0.381530\pi$
$199$	−8.81540	+	15.2687i	−0.624907	+	1.08237i	−0.988559	+	0.150836i	$0.951803\pi$
$200$		0			0
$201$	13.4406	−	23.9140i	0.948029	−	1.68676i
$202$	6.57809	−	7.83946i	0.462833	−	0.551583i
$203$	5.09286	−	6.06943i	0.357449	−	0.425991i
$204$	−7.01003	+	12.4725i	−0.490800	+	0.873248i
$205$		0			0
$206$	−9.93912	+	17.2151i	−0.692491	+	1.19943i
$207$	−2.63732	+	0.528162i	−0.183306	+	0.0367098i
$208$	6.49763	−	3.75141i	0.450530	−	0.260113i
$209$	−3.19283	−	18.1075i	−0.220853	−	1.25252i
$210$		0			0
$211$	−4.23225	+	1.54041i	−0.291360	+	0.106046i	−0.483565	−	0.875308i	$-0.660658\pi$
$211$	−4.23225	+	1.54041i	−0.291360	+	0.106046i	0.192205	+	0.981355i	$0.438436\pi$
$212$	−20.4957	−	3.61394i	−1.40765	−	0.248207i
$213$	8.85298	−	25.2269i	0.606596	−	1.72852i
$214$	28.1439	−	23.6156i	1.92388	−	1.61433i
$215$		0			0
$216$	5.11672	−	9.61780i	0.348149	−	0.654408i
$217$			12.4879i			0.847734i
$218$	−9.71218	−	11.5745i	−0.657792	−	0.783926i
$219$	−17.0075	+	14.6093i	−1.14926	+	0.987204i
$220$		0			0
$221$	16.1580	−	5.88101i	1.08690	−	0.395600i
$222$	4.70817	+	12.4847i	0.315992	+	0.837917i
$223$	−24.1963	+	4.26645i	−1.62030	+	0.285703i	−0.908878	−	0.417061i	$-0.863060\pi$
$223$	−24.1963	+	4.26645i	−1.62030	+	0.285703i	−0.711423	+	0.702764i	$0.751949\pi$
$224$	13.0170	+	22.5461i	0.869733	+	1.50642i
$225$		0			0
$226$	19.1578	−	33.1822i	1.27435	−	2.20725i
$227$	5.81410	−	15.9741i	0.385895	−	1.06024i	−0.582936	−	0.812518i	$-0.698096\pi$
$227$	5.81410	−	15.9741i	0.385895	−	1.06024i	0.968831	−	0.247721i	$-0.0796816\pi$
$228$	15.0320	−	8.91197i	0.995519	−	0.590210i
$229$	11.2404	+	9.43183i	0.742788	+	0.623273i	0.933585	−	0.358356i	$-0.116663\pi$
$229$	11.2404	+	9.43183i	0.742788	+	0.623273i	−0.190797	+	0.981630i	$0.561107\pi$
$230$		0			0
$231$	−34.9662	+	0.404179i	−2.30061	+	0.0265930i
$232$	−1.50930	+	4.14677i	−0.0990905	+	0.272249i
$233$	−22.1275	−	12.7753i	−1.44962	−	0.836939i	−0.451162	−	0.892442i	$-0.648990\pi$
$233$	−22.1275	−	12.7753i	−1.44962	−	0.836939i	−0.998458	+	0.0555035i	$0.982324\pi$
$234$	−38.0634	+	14.8591i	−2.48828	+	0.971367i
$235$		0			0
$236$	3.12376	+	17.7157i	0.203339	+	1.15319i
$237$	−10.9035	+	13.3036i	−0.708261	+	0.864164i
$238$	8.03413	+	22.0736i	0.520776	+	1.43082i
$239$	1.11927	−	6.34771i	0.0723998	−	0.410599i	−0.926971	−	0.375133i	$-0.877597\pi$
$239$	1.11927	−	6.34771i	0.0723998	−	0.410599i	0.999371	−	0.0354667i	$-0.0112918\pi$
$240$		0			0
$241$	2.05438	−	1.72383i	0.132334	−	0.111042i	−0.574218	−	0.818702i	$-0.694694\pi$
$241$	2.05438	−	1.72383i	0.132334	−	0.111042i	0.706552	+	0.707661i	$0.250249\pi$
$242$		−	39.4975i		−	2.53900i
$243$	9.31359	−	12.5003i	0.597467	−	0.801893i
$244$	−1.63776			−0.104847
$245$		0			0
$246$	1.72748	+	9.17555i	0.110140	+	0.585012i
$247$	−20.6830	−	3.64697i	−1.31603	−	0.232051i
$248$	−2.37887	−	6.53590i	−0.151059	−	0.415030i
$249$	6.40270	+	5.24759i	0.405754	+	0.332553i
$250$		0			0
$251$	9.83460	+	17.0340i	0.620755	+	1.07518i	0.989345	+	0.145587i	$0.0465070\pi$
$251$	9.83460	+	17.0340i	0.620755	+	1.07518i	−0.368591	+	0.929592i	$0.620160\pi$
$252$	−12.0859	−	30.9595i	−0.761339	−	1.95027i
$253$	−4.16434	−	2.40428i	−0.261810	−	0.151156i
$254$	−10.0609	−	3.66186i	−0.631275	−	0.229765i
$255$		0			0
$256$	−5.58555	−	4.68683i	−0.349097	−	0.292927i
$257$	3.56777	−	4.25190i	0.222551	−	0.265226i	−0.643203	−	0.765696i	$-0.722395\pi$
$257$	3.56777	−	4.25190i	0.222551	−	0.265226i	0.865754	+	0.500469i	$0.166839\pi$
$258$	−22.6456	+	13.4258i	−1.40985	+	0.835855i
$259$	12.2564	+	4.46096i	0.761575	+	0.277191i
$260$		0			0
$261$	−3.02996	+	5.53997i	−0.187550	+	0.342915i
$262$	−10.7475	+	6.20509i	−0.663985	+	0.383352i
$263$	−13.8789	+	2.44722i	−0.855808	+	0.150902i	−0.584303	−	0.811535i	$-0.698632\pi$
$263$	−13.8789	+	2.44722i	−0.855808	+	0.150902i	−0.271504	+	0.962437i	$0.587521\pi$
$264$	18.2236	−	6.87240i	1.12158	−	0.422967i
$265$		0			0
$266$	4.98217	−	28.2553i	0.305477	−	1.73244i
$267$	3.28283	+	3.82173i	0.200906	+	0.233886i
$268$	29.9613	+	35.7065i	1.83018	+	2.18112i
$269$	−10.6489			−0.649278			−0.324639	−	0.945838i	$-0.605243\pi$
$269$	−10.6489			−0.649278			−0.324639	+	0.945838i	$0.605243\pi$
$270$		0			0
$271$	−18.7000			−1.13595			−0.567973	−	0.823047i	$-0.692272\pi$
$271$	−18.7000			−1.13595			−0.567973	+	0.823047i	$0.692272\pi$
$272$	2.20958	+	2.63328i	0.133976	+	0.159666i
$273$	−13.2263	+	37.6889i	−0.800495	+	2.28104i
$274$	1.60408	−	9.09717i	0.0969058	−	0.549580i
$275$		0			0
$276$	0.741528	−	4.50961i	0.0446347	−	0.271447i
$277$	7.24183	−	1.27693i	0.435119	−	0.0767233i	0.0482019	−	0.998838i	$-0.484651\pi$
$277$	7.24183	−	1.27693i	0.435119	−	0.0767233i	0.386918	+	0.922114i	$0.373540\pi$
$278$	−16.4477	+	9.49607i	−0.986466	+	0.569536i
$279$	−1.95431	−	9.75865i	−0.117002	−	0.584235i
$280$		0			0
$281$	−15.3253	−	5.57797i	−0.914233	−	0.332754i	−0.158291	−	0.987392i	$-0.550599\pi$
$281$	−15.3253	−	5.57797i	−0.914233	−	0.332754i	−0.755942	+	0.654639i	$0.772821\pi$
$282$	−12.1034	−	6.80258i	−0.720745	−	0.405088i
$283$	−0.347160	+	0.413729i	−0.0206365	+	0.0245936i	−0.776264	−	0.630408i	$-0.782888\pi$
$283$	−0.347160	+	0.413729i	−0.0206365	+	0.0245936i	0.755627	+	0.655002i	$0.227332\pi$
$284$	34.7991	+	29.1999i	2.06495	+	1.73270i
$285$		0			0
$286$	−68.6447	−	24.9846i	−4.05905	−	1.47737i
$287$	7.90409	+	4.56343i	0.466564	+	0.269371i
$288$	−13.7005	−	15.5815i	−0.807309	−	0.918148i
$289$	−4.56097	−	7.89983i	−0.268292	−	0.464696i
$290$		0			0
$291$	−1.79245	+	10.9008i	−0.105075	+	0.639016i
$292$	−13.0296	−	35.7986i	−0.762500	−	2.09495i
$293$	17.0904	+	3.01350i	0.998432	+	0.176051i	0.648900	−	0.760874i	$-0.275229\pi$
$293$	17.0904	+	3.01350i	0.998432	+	0.176051i	0.349532	+	0.936924i	$0.386340\pi$
$294$	−26.0521	−	9.14260i	−1.51939	−	0.533207i
$295$		0			0
$296$	−7.26453			−0.422242
$297$	27.2610	−	5.78794i	1.58185	−	0.335850i
$298$			25.0288i			1.44988i
$299$	−4.20751	+	3.53052i	−0.243327	+	0.204175i
$300$		0			0
$301$	−4.46875	+	25.3435i	−0.257575	+	1.46078i
$302$	12.9236	+	35.5073i	0.743670	+	2.04322i
$303$	2.81318	+	7.45973i	0.161613	+	0.428550i
$304$	−0.729079	−	4.13481i	−0.0418156	−	0.237148i
$305$		0			0
$306$	−9.73271	−	15.9921i	−0.556382	−	0.914206i
$307$	3.85973	+	2.22842i	0.220287	+	0.127182i	0.606083	−	0.795401i	$-0.292740\pi$
$307$	3.85973	+	2.22842i	0.220287	+	0.127182i	−0.385796	+	0.922584i	$0.626073\pi$
$308$	20.3217	−	55.8334i	1.15794	−	3.18140i
$309$	−7.89756	−	13.3210i	−0.449276	−	0.757804i
$310$		0			0
$311$	−9.04919	−	7.59317i	−0.513133	−	0.430569i	0.349097	−	0.937086i	$-0.386488\pi$
$311$	−9.04919	−	7.59317i	−0.513133	−	0.430569i	−0.862230	+	0.506517i	$0.830933\pi$
$312$	−0.257134	−	22.2451i	−0.0145574	−	1.25938i
$313$	1.21223	−	3.33057i	0.0685191	−	0.188255i	−0.900707	−	0.434427i	$-0.856951\pi$
$313$	1.21223	−	3.33057i	0.0685191	−	0.188255i	0.969226	+	0.246173i	$0.0791730\pi$
$314$	13.8741	−	24.0307i	0.782964	−	1.35613i
$315$		0			0
$316$	−14.6135	−	25.3113i	−0.822074	−	1.42387i
$317$	−3.82945	+	0.675236i	−0.215084	+	0.0379250i	−0.280151	−	0.959956i	$-0.590385\pi$
$317$	−3.82945	+	0.675236i	−0.215084	+	0.0379250i	0.0650679	+	0.997881i	$0.479274\pi$
$318$	17.2619	−	21.0617i	0.968002	−	1.18108i
$319$	−10.6080	+	3.86099i	−0.593933	+	0.216174i
$320$		0			0
$321$	5.29557	+	28.1276i	0.295570	+	1.56993i
$322$	−4.82309	−	5.74793i	−0.268780	−	0.320320i
$323$		−	9.62234i		−	0.535402i
$324$	14.2896	+	22.3019i	0.793865	+	1.23899i
$325$		0			0
$326$	12.7575	−	10.7048i	0.706573	−	0.592886i
$327$	11.5678	−	2.17787i	0.639700	−	0.120436i
$328$	−5.00614	−	0.882718i	−0.276418	−	0.0487399i
$329$	−12.7534	+	4.64187i	−0.703120	+	0.255915i
$330$		0			0
$331$	3.47191	+	19.6902i	0.190833	+	1.08227i	0.918228	+	0.396051i	$0.129620\pi$
$331$	3.47191	+	19.6902i	0.190833	+	1.08227i	−0.727395	+	0.686219i	$0.759269\pi$
$332$	−12.1817	+	7.03311i	−0.668557	+	0.385992i
$333$	−10.2759	−	1.56793i	−0.563114	−	0.0859220i
$334$	13.9144	−	24.1004i	0.761362	−	1.31872i
$335$		0			0
$336$	−7.98448	+	0.0922937i	−0.435589	+	0.00503503i
$337$	−16.7068	+	19.9104i	−0.910078	+	1.08459i	0.0860160	+	0.996294i	$0.472586\pi$
$337$	−16.7068	+	19.9104i	−0.910078	+	1.08459i	−0.996094	+	0.0882954i	$0.971858\pi$
$338$	−35.0563	+	41.7784i	−1.90681	+	2.27245i
$339$	15.2226	+	25.6763i	0.826779	+	1.39455i
$340$		0			0
$341$	8.89636	−	15.4089i	0.481765	−	0.834441i
$342$	0.528549	+	22.8598i	0.0285806	+	1.23612i
$343$	−0.553536	+	0.319584i	−0.0298881	+	0.0172559i
$344$	−2.48895	−	14.1155i	−0.134195	−	0.761059i
$345$		0			0
$346$	31.6767	−	11.5294i	1.70295	−	0.619824i
$347$	20.5622	+	3.62567i	1.10384	+	0.194636i	0.695733	−	0.718300i	$-0.255080\pi$
$347$	20.5622	+	3.62567i	1.10384	+	0.194636i	0.408102	+	0.912936i	$0.366191\pi$
$348$	−6.99109	−	8.13873i	−0.374762	−	0.436282i
$349$	8.83183	−	7.41078i	0.472757	−	0.396690i	−0.375042	−	0.927008i	$-0.622372\pi$
$349$	8.83183	−	7.41078i	0.472757	−	0.396690i	0.847799	+	0.530318i	$0.177927\pi$
$350$		0			0
$351$	4.43752	−	31.5218i	0.236857	−	1.68251i
$352$		−	37.0931i		−	1.97707i
$353$	6.80132	+	8.10550i	0.361998	+	0.431412i	0.916047	−	0.401072i	$-0.131362\pi$
$353$	6.80132	+	8.10550i	0.361998	+	0.431412i	−0.554049	+	0.832484i	$0.686918\pi$
$354$	−22.2102	−	7.79432i	−1.18046	−	0.414263i
$355$		0			0
$356$	−8.04423	+	2.92786i	−0.426343	+	0.155176i
$357$	−18.0576	−	2.96925i	−0.955707	−	0.157150i
$358$	−17.7847	+	3.13592i	−0.939951	+	0.165739i
$359$	−9.71352	−	16.8243i	−0.512660	−	0.887953i	−0.999892	−	0.0146804i	$-0.995327\pi$
$359$	−9.71352	−	16.8243i	−0.512660	−	0.887953i	0.487232	−	0.873272i	$-0.338006\pi$
$360$		0			0
$361$	3.62359	−	6.27624i	0.190715	−	0.330328i
$362$	12.1048	−	33.2576i	0.636213	−	1.74798i
$363$	26.8241	+	15.0762i	1.40790	+	0.791296i
$364$	−51.9898	−	43.6247i	−2.72501	−	2.28655i
$365$		0			0
$366$	1.04996	−	1.86812i	0.0548822	−	0.0976482i
$367$	4.08698	−	11.2289i	0.213339	−	0.586143i	−0.786153	−	0.618032i	$-0.787930\pi$
$367$	4.08698	−	11.2289i	0.213339	−	0.586143i	0.999491	+	0.0318889i	$0.0101523\pi$
$368$	−0.950921	−	0.549014i	−0.0495702	−	0.0286194i
$369$	−6.89080	−	2.32912i	−0.358721	−	0.121249i
$370$		0			0
$371$	−4.62244	−	26.2152i	−0.239985	−	1.36102i
$372$	16.6865	+	2.74381i	0.865157	+	0.142260i
$373$	−9.52781	−	26.1774i	−0.493331	−	1.35542i	−0.897614	−	0.440782i	$-0.854701\pi$
$373$	−9.52781	−	26.1774i	−0.493331	−	1.35542i	0.404283	−	0.914634i	$-0.367521\pi$
$374$	5.81180	−	32.9603i	0.300521	−	1.70434i
$375$		0			0
$376$	5.79063	−	4.85892i	0.298629	−	0.250579i
$377$			12.8945i			0.664098i
$378$	43.0624	+	6.06216i	2.21489	+	0.311804i
$379$	−19.6724			−1.01050			−0.505251	−	0.862973i	$-0.668600\pi$
$379$	−19.6724			−1.01050			−0.505251	+	0.862973i	$0.668600\pi$
$380$		0			0
$381$	6.32713	−	5.43494i	0.324148	−	0.278440i
$382$	39.3636	+	6.94086i	2.01401	+	0.355125i
$383$	−1.76754	−	4.85629i	−0.0903173	−	0.248145i	0.886307	−	0.463098i	$-0.153262\pi$
$383$	−1.76754	−	4.85629i	−0.0903173	−	0.248145i	−0.976624	+	0.214953i	$0.931040\pi$
$384$	24.1609	−	9.11146i	1.23296	−	0.464967i
$385$		0			0
$386$	1.07989	+	1.87043i	0.0549652	+	0.0952025i
$387$	−0.474081	−	20.5040i	−0.0240989	−	1.04228i
$388$	−16.2560	−	9.38540i	−0.825273	−	0.476472i
$389$	8.84157	+	3.21807i	0.448285	+	0.163162i	0.556291	−	0.830988i	$-0.312224\pi$
$389$	8.84157	+	3.21807i	0.448285	+	0.163162i	−0.108005	+	0.994150i	$0.534446\pi$
$390$		0			0
$391$	−1.92772	−	1.61755i	−0.0974890	−	0.0818030i
$392$	9.66244	−	11.5152i	0.488027	−	0.581608i
$393$	−0.111748	−	9.66749i	−0.00563693	−	0.487660i
$394$	19.2908	+	7.02128i	0.971857	+	0.353727i
$395$		0			0
$396$	−7.14263	+	46.8113i	−0.358931	+	2.35235i
$397$	6.95786	−	4.01712i	0.349205	−	0.201614i	−0.315130	−	0.949048i	$-0.602048\pi$
$397$	6.95786	−	4.01712i	0.349205	−	0.201614i	0.664335	+	0.747435i	$0.268715\pi$
$398$	38.6029	−	6.80673i	1.93499	−	0.341190i
$399$	17.2874	+	14.1686i	0.865454	+	0.709319i
$400$		0			0
$401$	−1.68169	+	9.53732i	−0.0839794	+	0.476271i	0.913593	+	0.406630i	$0.133296\pi$
$401$	−1.68169	+	9.53732i	−0.0839794	+	0.476271i	−0.997572	+	0.0696405i	$0.977815\pi$
$402$	−59.9369	+	11.2843i	−2.98938	+	0.562810i
$403$	−13.0637	−	15.5687i	−0.650749	−	0.775532i
$404$	−13.5465			−0.673965
$405$		0			0
$406$	−17.6153			−0.874232
$407$	−11.9453	−	14.2359i	−0.592107	−	0.705646i
$408$	10.0166	−	1.88582i	0.495894	−	0.0933619i
$409$	−2.41577	+	13.7005i	−0.119452	+	0.677446i	0.864997	+	0.501776i	$0.167320\pi$
$409$	−2.41577	+	13.7005i	−0.119452	+	0.677446i	−0.984449	+	0.175669i	$0.943791\pi$
$410$		0			0
$411$	5.56592	+	4.56178i	0.274546	+	0.225016i
$412$	25.9135	−	4.56924i	1.27666	−	0.225110i
$413$	−19.9264	+	11.5045i	−0.980512	+	0.566099i
$414$	4.66853	+	3.73692i	0.229446	+	0.183660i
$415$		0			0
$416$	−39.8139	−	14.4911i	−1.95204	−	0.710484i
$417$	−0.171015	−	14.7948i	−0.00837465	−	0.724505i
$418$	−26.2766	+	31.3152i	−1.28523	+	1.53168i
$419$	23.8549	+	20.0166i	1.16539	+	0.977876i	0.999965	−	0.00834704i	$-0.00265698\pi$
$419$	23.8549	+	20.0166i	1.16539	+	0.977876i	0.165422	+	0.986223i	$0.447101\pi$
$420$		0			0
$421$	−14.6085	−	5.31705i	−0.711974	−	0.259137i	−0.0394593	−	0.999221i	$-0.512564\pi$
$421$	−14.6085	−	5.31705i	−0.711974	−	0.259137i	−0.672515	+	0.740084i	$0.734786\pi$
$422$	8.67186	+	5.00670i	0.422139	+	0.243722i
$423$	9.23972	−	5.62326i	0.449251	−	0.273412i
$424$	7.41313	+	12.8399i	0.360013	+	0.623561i
$425$		0			0
$426$	−55.6167	+	20.9739i	−2.69464	+	1.01619i
$427$	−0.716460	−	1.96846i	−0.0346719	−	0.0952603i
$428$	−47.8937	−	8.44495i	−2.31503	−	0.408202i
$429$	43.1696	−	37.0823i	2.08425	−	1.79035i
$430$		0			0
$431$	5.10872			0.246078			0.123039	−	0.992402i	$-0.460736\pi$
$431$	5.10872			0.246078			0.123039	+	0.992402i	$0.460736\pi$
$432$	6.22502	−	1.32167i	0.299502	−	0.0635888i
$433$			9.22565i			0.443356i	0.975120	+	0.221678i	$0.0711534\pi$
$433$			9.22565i			0.443356i	−0.975120	+	0.221678i	$0.928847\pi$
$434$	21.2686	−	17.8465i	1.02093	−	0.856658i
$435$		0			0
$436$	−3.47308	+	19.6968i	−0.166331	+	0.943308i
$437$	1.05124	+	2.88827i	0.0502878	+	0.138165i
$438$	49.1871	+	8.08797i	2.35025	+	0.386458i
$439$	2.32033	+	13.1592i	0.110743	+	0.628057i	0.988770	+	0.149445i	$0.0477487\pi$
$439$	2.32033	+	13.1592i	0.110743	+	0.628057i	−0.878027	+	0.478612i	$0.841140\pi$
$440$		0			0
$441$	16.1532	−	14.2032i	0.769198	−	0.676340i
$442$	−33.1075	−	19.1147i	−1.57477	−	0.909191i
$443$	2.63433	−	7.23777i	0.125161	−	0.343877i	−0.861248	−	0.508184i	$-0.830317\pi$
$443$	2.63433	−	7.23777i	0.125161	−	0.343877i	0.986409	+	0.164308i	$0.0525390\pi$
$444$	8.65377	−	15.3971i	0.410690	−	0.730712i
$445$		0			0
$446$	41.8453	+	35.1124i	1.98143	+	1.66262i
$447$	−16.9979	−	9.55351i	−0.803973	−	0.451865i
$448$	16.6429	−	45.7261i	0.786305	−	2.16035i
$449$	−16.9493	+	29.3570i	−0.799886	+	1.38544i	0.119805	+	0.992797i	$0.461773\pi$
$449$	−16.9493	+	29.3570i	−0.799886	+	1.38544i	−0.919690	+	0.392645i	$0.871560\pi$
$450$		0			0
$451$	−6.50196	−	11.2617i	−0.306165	−	0.530294i
$452$	−49.9485	+	8.80726i	−2.34938	+	0.414259i
$453$	−29.0471	−	4.77630i	−1.36475	−	0.224410i
$454$	−35.5151	+	12.9264i	−1.66680	+	0.606667i
$455$		0			0
$456$	−11.7469	−	4.12240i	−0.550100	−	0.193049i
$457$	16.4891	+	19.6509i	0.771325	+	0.919230i	0.998507	−	0.0546225i	$-0.0173956\pi$
$457$	16.4891	+	19.6509i	0.771325	+	0.919230i	−0.227182	+	0.973852i	$0.572951\pi$
$458$		−	32.6230i		−	1.52437i
$459$	14.5757	−	0.505628i	0.680337	−	0.0236007i
$460$		0			0
$461$	11.2323	−	9.42502i	0.523140	−	0.438967i	−0.342585	−	0.939487i	$-0.611302\pi$
$461$	11.2323	−	9.42502i	0.523140	−	0.438967i	0.865725	+	0.500520i	$0.166858\pi$
$462$	50.6586	+	58.9746i	2.35685	+	2.74375i
$463$	−0.536066	−	0.0945229i	−0.0249131	−	0.00439285i	0.161178	−	0.986925i	$-0.448471\pi$
$463$	−0.536066	−	0.0945229i	−0.0249131	−	0.00439285i	−0.186091	+	0.982533i	$0.559582\pi$
$464$	−2.42232	+	0.881652i	−0.112453	+	0.0409297i
$465$		0			0
$466$	9.86433	+	55.9434i	0.456956	+	2.59153i
$467$	−35.6559	+	20.5859i	−1.64996	+	0.952604i	−0.672872	+	0.739759i	$0.734940\pi$
$467$	−35.6559	+	20.5859i	−1.64996	+	0.952604i	−0.977086	+	0.212845i	$0.931727\pi$
$468$	47.4545	+	25.9542i	2.19359	+	1.19973i
$469$	−29.8094	+	51.6314i	−1.37647	+	2.38412i
$470$		0			0
$471$	11.0243	+	18.5949i	0.507973	+	0.856810i
$472$	8.23749	−	9.81706i	0.379161	−	0.451867i
$473$	23.5687	−	28.0881i	1.08369	−	1.29149i
$474$	38.2402	−	0.442023i	1.75643	−	0.0203028i
$475$		0			0
$476$	15.5472	−	26.9286i	0.712607	−	1.23427i
$477$	7.71479	+	19.7624i	0.353236	+	0.904859i
$478$	−12.4106	+	7.16525i	−0.567647	+	0.327731i
$479$	−1.02370	−	5.80571i	−0.0467742	−	0.265270i	0.952448	−	0.304701i	$-0.0985565\pi$
$479$	−1.02370	−	5.80571i	−0.0467742	−	0.265270i	−0.999222	+	0.0394312i	$0.987445\pi$
$480$		0			0
$481$	−19.9467	+	7.26002i	−0.909493	+	0.331028i
$482$	−5.87183	−	1.03536i	−0.267455	−	0.0471595i
$483$	5.74459	−	1.08153i	0.261388	−	0.0492115i
$484$	−40.0516	+	33.6073i	−1.82053	+	1.52760i
$485$		0			0
$486$	−34.5998	+	2.00186i	−1.56948	+	0.0908060i
$487$			11.9102i			0.539704i	0.962902	+	0.269852i	$0.0869748\pi$
$487$			11.9102i			0.539704i	−0.962902	+	0.269852i	$0.913025\pi$
$488$	0.749960	+	0.893767i	0.0339491	+	0.0404589i
$489$	2.40046	+	12.7501i	0.108552	+	0.576579i
$490$		0			0
$491$	−35.0462	+	12.7558i	−1.58161	+	0.575661i	−0.975554	−	0.219758i	$-0.929473\pi$
$491$	−35.0462	+	12.7558i	−1.58161	+	0.575661i	−0.606060	+	0.795419i	$0.707251\pi$
$492$	7.83440	−	9.55892i	0.353202	−	0.430949i
$493$	−5.81800	+	1.02587i	−0.262029	+	0.0462029i
$494$	23.3468	+	40.4379i	1.05042	+	1.81939i
$495$		0			0
$496$	2.03147	−	3.51861i	0.0912158	−	0.157990i
$497$	−19.8727	+	54.5997i	−0.891411	+	2.44913i
$498$	−0.212734	−	18.4040i	−0.00953286	−	0.824704i
$499$	14.2032	+	11.9179i	0.635821	+	0.533517i	0.902732	−	0.430204i	$-0.141558\pi$
$499$	14.2032	+	11.9179i	0.635821	+	0.533517i	−0.266911	+	0.963721i	$0.586003\pi$
$500$		0			0
$501$	11.0563	+	18.6489i	0.493958	+	0.833170i
$502$	14.9566	−	41.0930i	0.667548	−	1.83407i
$503$	−29.8502	−	17.2340i	−1.33096	−	0.768428i	−0.345510	−	0.938415i	$-0.612294\pi$
$503$	−29.8502	−	17.2340i	−1.33096	−	0.768428i	−0.985446	+	0.169987i	$0.945627\pi$
$504$	−11.3611	+	20.7725i	−0.506062	+	0.925281i
$505$		0			0
$506$	1.85644	+	10.5284i	0.0825289	+	0.468044i
$507$	−14.9921	−	39.7547i	−0.665824	−	1.76557i
$508$	4.84727	+	13.3178i	0.215063	+	0.590880i
$509$	−4.38600	+	24.8743i	−0.194406	+	1.10253i	0.718856	+	0.695159i	$0.244666\pi$
$509$	−4.38600	+	24.8743i	−0.194406	+	1.10253i	−0.913262	+	0.407373i	$0.866445\pi$
$510$		0			0
$511$	37.3271	−	31.3211i	1.65125	−	1.38556i
$512$		−	13.6056i		−	0.601287i
$513$	−15.7266	−	8.36663i	−0.694346	−	0.369396i
$514$	−12.3403			−0.544307
$515$		0			0
$516$	32.8826	+	11.5397i	1.44758	+	0.508005i
$517$	19.0435	+	3.35788i	0.837531	+	0.147679i
$518$	−9.91801	−	27.2495i	−0.435772	−	1.19727i
$519$	−4.26103	+	25.9135i	−0.187038	+	1.13748i
$520$		0			0
$521$	5.72752	+	9.92036i	0.250927	+	0.434619i	0.963781	−	0.266693i	$-0.0859311\pi$
$521$	5.72752	+	9.92036i	0.250927	+	0.434619i	−0.712854	+	0.701312i	$0.752598\pi$
$522$	13.7655	−	2.75674i	0.602497	−	0.120659i
$523$	25.0507	+	14.4630i	1.09539	+	0.632424i	0.935006	−	0.354631i	$-0.115393\pi$
$523$	25.0507	+	14.4630i	1.09539	+	0.632424i	0.160384	+	0.987055i	$0.448727\pi$
$524$	15.4369	+	5.61857i	0.674364	+	0.245448i
$525$		0			0
$526$	24.0023	+	20.1403i	1.04655	+	0.878158i
$527$	5.98528	−	7.13298i	0.260723	−	0.310718i
$528$	9.91789	+	5.57425i	0.431621	+	0.242588i
$529$	−20.8576	−	7.59154i	−0.906851	−	0.330067i
$530$		0			0
$531$	13.7710	−	12.1086i	0.597611	−	0.525468i
$532$	−32.8909	+	18.9896i	−1.42600	+	0.823302i
$533$	−14.6279	+	2.57929i	−0.633604	+	0.111722i
$534$	1.81743	−	11.0527i	0.0786480	−	0.478299i
$535$		0			0
$536$	5.76612	−	32.7013i	0.249059	−	1.41248i
$537$	4.65872	−	13.2752i	0.201039	−	0.572866i
$538$	15.2184	+	18.1366i	0.656113	+	0.781925i
$539$	38.4540			1.65633
$540$		0			0
$541$	13.9635			0.600338			0.300169	−	0.953886i	$-0.402957\pi$
$541$	13.9635			0.600338			0.300169	+	0.953886i	$0.402957\pi$
$542$	26.7242	+	31.8487i	1.14790	+	1.36802i
$543$	17.9660	+	20.9152i	0.770994	+	0.897558i
$544$	3.37084	−	19.1170i	0.144524	−	0.819634i
$545$		0			0
$546$	83.0912	−	31.3350i	3.55597	−	1.34101i
$547$	18.7679	−	3.30929i	0.802457	−	0.141495i	0.242646	−	0.970115i	$-0.421985\pi$
$547$	18.7679	−	3.30929i	0.802457	−	0.141495i	0.559811	+	0.828620i	$0.310874\pi$
$548$	−10.5897	+	6.11394i	−0.452367	+	0.261174i
$549$	0.867933	+	1.42612i	0.0370425	+	0.0608655i
$550$		0			0
$551$	6.78062	+	2.46794i	0.288864	+	0.105138i
$552$	−2.80057	+	1.66036i	−0.119200	+	0.0706698i
$553$	24.0294	−	28.6371i	1.02183	−	1.21777i
$554$	−12.5241	−	10.5090i	−0.532098	−	0.446483i
$555$		0			0
$556$	23.6241	+	8.59848i	1.00189	+	0.364657i
$557$	−25.4546	−	14.6962i	−1.07855	−	0.622700i	−0.148044	−	0.988981i	$-0.547298\pi$
$557$	−25.4546	−	14.6962i	−1.07855	−	0.622700i	−0.930504	+	0.366281i	$0.880631\pi$
$558$	−13.8274	+	17.2746i	−0.585361	+	0.731291i
$559$	−20.9409	−	36.2707i	−0.885705	−	1.53409i
$560$		0			0
$561$	20.1661	+	16.5280i	0.851414	+	0.697811i
$562$	12.4014	+	34.0727i	0.523123	+	1.43727i
$563$	25.1141	+	4.42830i	1.05844	+	0.186631i	0.675662	−	0.737212i	$-0.263858\pi$
$563$	25.1141	+	4.42830i	1.05844	+	0.186631i	0.382773	+	0.923842i	$0.374969\pi$
$564$	3.40039	+	18.0613i	0.143182	+	0.760517i
$565$		0			0
$566$	1.20076			0.0504719
$567$	−20.5539	+	26.9312i	−0.863185	+	1.13100i
$568$		−	32.3620i		−	1.35788i
$569$	7.32350	−	6.14515i	0.307017	−	0.257618i	−0.476241	−	0.879315i	$-0.658001\pi$
$569$	7.32350	−	6.14515i	0.307017	−	0.257618i	0.783258	+	0.621697i	$0.213556\pi$
$570$		0			0
$571$	5.37062	−	30.4583i	0.224754	−	1.27464i	−0.638402	−	0.769703i	$-0.720404\pi$
$571$	5.37062	−	30.4583i	0.224754	−	1.27464i	0.863156	−	0.504938i	$-0.168485\pi$
$572$	33.0727	+	90.8664i	1.38284	+	3.79931i
$573$	−19.7389	+	24.0838i	−0.824603	+	1.00611i
$574$	−3.52360	−	19.9834i	−0.147072	−	0.834089i
$575$		0			0
$576$	−5.84962	+	38.3372i	−0.243734	+	1.59738i
$577$	−31.5221	−	18.1993i	−1.31228	−	0.757647i	−0.329810	−	0.944047i	$-0.606985\pi$
$577$	−31.5221	−	18.1993i	−1.31228	−	0.757647i	−0.982474	+	0.186400i	$0.940318\pi$
$578$	−6.93641	+	19.0576i	−0.288516	+	0.792692i
$579$	−1.68247	+	0.0194479i	−0.0699211	+	0.000808226i
$580$		0			0
$581$	−13.7823	−	11.5647i	−0.571785	−	0.479785i
$582$	21.1272	−	12.5256i	0.875749	−	0.519202i
$583$	−12.9720	+	35.6402i	−0.537244	+	1.47607i
$584$	−13.5697	+	23.5034i	−0.561518	+	0.972578i
$585$		0			0
$586$	−19.2915	−	33.4139i	−0.796926	−	1.38032i
$587$	−39.7946	+	7.01686i	−1.64250	+	0.289617i	−0.917083	−	0.398696i	$-0.869463\pi$
$587$	−39.7946	+	7.01686i	−1.64250	+	0.289617i	−0.725415	+	0.688312i	$0.758352\pi$
$588$	12.8961	+	34.1968i	0.531828	+	1.41025i
$589$	−10.6872	+	3.88983i	−0.440359	+	0.160278i
$590$		0			0
$591$	−12.1317	+	10.4210i	−0.499032	+	0.428663i
$592$	−2.72770	−	3.25074i	−0.112108	−	0.133605i
$593$			11.8336i			0.485946i	0.970033	+	0.242973i	$0.0781226\pi$
$593$			11.8336i			0.485946i	−0.970033	+	0.242973i	$0.921877\pi$
$594$	−48.8165	−	38.1577i	−2.00296	−	1.56563i
$595$		0			0
$596$	25.3799	−	21.2963i	1.03960	−	0.872330i
$597$	−10.1121	+	28.8146i	−0.413859	+	1.17930i
$598$	12.0259	+	2.12049i	0.491776	+	0.0867135i
$599$	−8.76898	+	3.19165i	−0.358291	+	0.130407i	−0.514893	−	0.857255i	$-0.672168\pi$
$599$	−8.76898	+	3.19165i	−0.358291	+	0.130407i	0.156602	+	0.987662i	$0.449946\pi$
$600$		0			0
$601$	3.42397	+	19.4183i	0.139667	+	0.792088i	0.971496	+	0.237057i	$0.0761827\pi$
$601$	3.42397	+	19.4183i	0.139667	+	0.792088i	−0.831829	+	0.555032i	$0.812706\pi$
$602$	49.5498	−	28.6076i	2.01950	−	1.16596i
$603$	15.2144	−	45.0124i	0.619578	−	1.83305i
$604$	25.0091	−	43.3170i	1.01761	−	1.76254i
$605$		0			0
$606$	8.68462	−	15.4519i	0.352788	−	0.627692i
$607$	23.2154	−	27.6671i	0.942285	−	1.12297i	−0.0499698	−	0.998751i	$-0.515913\pi$
$607$	23.2154	−	27.6671i	0.942285	−	1.12297i	0.992255	−	0.124221i	$-0.0396430\pi$
$608$	−15.2404	+	18.1628i	−0.618081	+	0.736600i
$609$	6.72376	−	11.9631i	0.272461	−	0.484771i
$610$		0			0
$611$	11.0439	−	19.1285i	0.446786	−	0.773857i
$612$	−7.93514	+	23.4764i	−0.320759	+	0.948978i
$613$	3.39263	−	1.95873i	0.137027	−	0.0791125i	−0.429919	−	0.902867i	$-0.641458\pi$
$613$	3.39263	−	1.95873i	0.137027	−	0.0791125i	0.566946	+	0.823755i	$0.308125\pi$
$614$	−1.72065	−	9.75829i	−0.0694398	−	0.393813i
$615$		0			0
$616$	−39.7754	+	14.4771i	−1.60260	+	0.583298i
$617$	−36.1192	−	6.36880i	−1.45411	−	0.256398i	−0.609926	−	0.792458i	$-0.708801\pi$
$617$	−36.1192	−	6.36880i	−1.45411	−	0.256398i	−0.844180	+	0.536060i	$0.819912\pi$
$618$	−11.4011	+	32.4877i	−0.458618	+	1.30685i
$619$	−8.22380	+	6.90059i	−0.330543	+	0.277358i	−0.792921	−	0.609325i	$-0.791441\pi$
$619$	−8.22380	+	6.90059i	−0.330543	+	0.277358i	0.462378	+	0.886683i	$0.346996\pi$
$620$		0			0
$621$	−4.31985	+	1.74417i	−0.173350	+	0.0699912i
$622$			26.2634i			1.05307i
$623$	−7.03811	−	8.38770i	−0.281976	−	0.336046i
$624$	9.85773	−	8.46770i	0.394625	−	0.338979i
$625$		0			0
$626$	−7.40481	+	2.69513i	−0.295956	+	0.107719i
$627$	−11.2374	−	29.7984i	−0.448780	−	1.19003i
$628$	−36.1729	+	6.37827i	−1.44346	+	0.254521i
$629$	−4.86267	−	8.42239i	−0.193887	−	0.335823i
$630$		0			0
$631$	−1.62045	+	2.80670i	−0.0645090	+	0.111733i	−0.896476	−	0.443092i	$-0.853881\pi$
$631$	−1.62045	+	2.80670i	−0.0645090	+	0.111733i	0.831967	+	0.554825i	$0.187215\pi$
$632$	−7.12126	+	19.5655i	−0.283268	+	0.778273i
$633$	−6.71027	+	3.97829i	−0.266709	+	0.158123i
$634$	6.62270	+	5.55711i	0.263021	+	0.220701i
$635$		0			0
$636$	−36.0448	+	0.416646i	−1.42927	+	0.0165211i
$637$	15.0228	−	41.2747i	0.595223	−	1.63536i
$638$	21.7357	+	12.5491i	0.860524	+	0.496824i
$639$	6.98480	−	45.7769i	0.276314	−	1.81091i
$640$		0			0
$641$	0.522380	+	2.96256i	0.0206328	+	0.117014i	0.993385	−	0.114834i	$-0.0366337\pi$
$641$	0.522380	+	2.96256i	0.0206328	+	0.117014i	−0.972752	+	0.231849i	$0.925523\pi$
$642$	40.3372	−	49.2162i	1.59198	−	1.94241i
$643$	−12.9452	−	35.5666i	−0.510509	−	1.40261i	−0.880708	−	0.473659i	$-0.842933\pi$
$643$	−12.9452	−	35.5666i	−0.510509	−	1.40261i	0.370200	−	0.928952i	$-0.379289\pi$
$644$	−1.72474	+	9.78150i	−0.0679644	+	0.385445i
$645$		0			0
$646$	−16.3882	+	13.7513i	−0.644784	+	0.541038i
$647$		−	13.1670i		−	0.517650i	−0.965924	−	0.258825i	$-0.916665\pi$
$647$		−	13.1670i		−	0.517650i	0.965924	−	0.258825i	$-0.0833353\pi$
$648$	5.62726	−	18.0106i	0.221060	−	0.707524i
$649$	32.7831			1.28685
$650$		0			0
$651$	4.00191	+	21.2562i	0.156847	+	0.833097i
$652$	−21.7100	−	3.82806i	−0.850229	−	0.149918i
$653$	6.72520	+	18.4773i	0.263177	+	0.723074i	0.998949	+	0.0458437i	$0.0145976\pi$
$653$	6.72520	+	18.4773i	0.263177	+	0.723074i	−0.735771	+	0.677230i	$0.763180\pi$
$654$	−20.2408	−	16.5891i	−0.791476	−	0.648687i
$655$		0			0
$656$	−1.48471	−	2.57160i	−0.0579683	−	0.100404i
$657$	−24.2675	+	30.3174i	−0.946767	+	1.18280i
$658$	26.1317	+	15.0872i	1.01872	+	0.588158i
$659$	−17.4856	−	6.36425i	−0.681143	−	0.247916i	−0.0218050	−	0.999762i	$-0.506941\pi$
$659$	−17.4856	−	6.36425i	−0.681143	−	0.247916i	−0.659338	+	0.751846i	$0.729164\pi$
$660$		0			0
$661$	−26.9451	−	22.6096i	−1.04804	−	0.879412i	−0.0551562	−	0.998478i	$-0.517566\pi$
$661$	−26.9451	−	22.6096i	−1.04804	−	0.879412i	−0.992886	+	0.119066i	$0.962010\pi$
$662$	28.5734	−	34.0524i	1.11054	−	1.32348i
$663$	25.6186	−	15.1884i	0.994943	−	0.589868i
$664$	9.41637	+	3.42728i	0.365426	+	0.133004i
$665$		0			0
$666$	12.0149	+	19.7420i	0.465567	+	0.764985i
$667$	1.63427	−	0.943545i	0.0632791	−	0.0365342i
$668$	−36.2779	+	6.39677i	−1.40363	+	0.247498i
$669$	−39.8183	+	15.0161i	−1.53947	+	0.580557i
$670$		0			0
$671$	−0.518279	+	2.93930i	−0.0200079	+	0.113471i
$672$	29.3820	+	34.2053i	1.13343	+	1.31950i
$673$	14.8063	+	17.6455i	0.570741	+	0.680183i	0.971783	−	0.235877i	$-0.0757962\pi$
$673$	14.8063	+	17.6455i	0.570741	+	0.680183i	−0.401042	+	0.916060i	$0.631352\pi$
$674$	57.7859			2.22583
$675$		0			0
$676$	72.1928			2.77665
$677$	−7.97061	−	9.49900i	−0.306335	−	0.365076i	0.590811	−	0.806810i	$-0.298808\pi$
$677$	−7.97061	−	9.49900i	−0.306335	−	0.365076i	−0.897146	+	0.441734i	$0.854364\pi$
$678$	21.9756	−	62.6203i	0.843970	−	2.40492i
$679$	4.16911	−	23.6442i	0.159996	−	0.907380i
$680$		0			0
$681$	4.77734	−	29.0535i	0.183068	−	1.11333i
$682$	−38.9574	+	6.86923i	−1.49175	+	0.263037i
$683$	5.03898	−	2.90926i	0.192811	−	0.111320i	−0.400487	−	0.916303i	$-0.631159\pi$
$683$	5.03898	−	2.90926i	0.192811	−	0.111320i	0.593298	+	0.804983i	$0.297826\pi$
$684$	22.7307	−	19.9867i	0.869131	−	0.764210i
$685$		0			0
$686$	1.33535	+	0.486029i	0.0509841	+	0.0185567i
$687$	22.1554	+	12.4522i	0.845281	+	0.475082i
$688$	5.38189	−	6.41389i	0.205183	−	0.244527i
$689$	33.1867	+	27.8469i	1.26431	+	1.06088i
$690$		0			0
$691$	−4.15074	−	1.51075i	−0.157902	−	0.0574715i	0.261860	−	0.965106i	$-0.415664\pi$
$691$	−4.15074	−	1.51075i	−0.157902	−	0.0574715i	−0.419762	+	0.907634i	$0.637886\pi$
$692$	−38.6439	−	22.3111i	−1.46902	−	0.848140i
$693$	−59.3881	+	11.8933i	−2.25597	+	0.451790i
$694$	−23.2104	−	40.2017i	−0.881057	−	1.52603i
$695$		0			0
$696$	−1.24017	+	7.54209i	−0.0470084	+	0.285882i
$697$	−2.32756	−	6.39492i	−0.0881626	−	0.242225i
$698$	−25.2432	−	4.45105i	−0.955468	−	0.168475i
$699$	−41.7583	−	14.6544i	−1.57944	−	0.554281i
$700$		0			0
$701$	45.9990			1.73736			0.868678	−	0.495376i	$-0.164970\pi$
$701$	45.9990			1.73736			0.868678	+	0.495376i	$0.164970\pi$
$702$	−60.0277	+	37.4902i	−2.26560	+	1.41498i
$703$			11.8786i			0.448011i
$704$	−53.1111	+	44.5655i	−2.00170	+	1.67962i
$705$		0			0
$706$	4.08500	−	23.1672i	0.153741	−	0.871908i
$707$	−5.92611	−	16.2819i	−0.222874	−	0.612343i
$708$	10.9943	+	29.1537i	0.413192	+	1.09566i
$709$	1.65171	+	9.36728i	0.0620311	+	0.351796i	0.999987	+	0.00504202i	$0.00160493\pi$
$709$	1.65171	+	9.36728i	0.0620311	+	0.351796i	−0.937956	+	0.346754i	$0.887284\pi$
$710$		0			0
$711$	−14.2961	+	26.1389i	−0.536146	+	0.980286i
$712$	5.28141	+	3.04922i	0.197929	+	0.114274i
$713$	−1.01728	+	2.79495i	−0.0380973	+	0.104672i
$714$	20.7490	+	34.9979i	0.776513	+	1.30976i
$715$		0			0
$716$	18.3124	+	15.3659i	0.684367	+	0.574252i
$717$	−0.129039	−	11.1634i	−0.00481907	−	0.416906i
$718$	−14.7725	+	40.5871i	−0.551305	+	1.51470i
$719$	9.60533	−	16.6369i	0.358218	−	0.620452i	−0.629445	−	0.777045i	$-0.716718\pi$
$719$	9.60533	−	16.6369i	0.358218	−	0.620452i	0.987663	+	0.156593i	$0.0500510\pi$
$720$		0			0
$721$	16.8281	+	29.1471i	0.626710	+	1.08549i
$722$	−15.8678	+	2.79792i	−0.590537	+	0.104128i
$723$	2.94443	−	3.59256i	0.109505	−	0.133609i
$724$	−44.0238	+	16.0233i	−1.63613	+	0.595503i
$725$		0			0
$726$	−12.6575	−	67.2305i	−0.469763	−	2.49516i
$727$	22.6474	+	26.9901i	0.839944	+	1.00101i	0.999904	+	0.0138826i	$0.00441911\pi$
$727$	22.6474	+	26.9901i	0.839944	+	1.00101i	−0.159960	+	0.987124i	$0.551136\pi$
$728$			48.3487i			1.79192i
$729$	11.8472	−	24.2620i	0.438786	−	0.898592i
$730$		0			0
$731$	14.6993	−	12.3342i	0.543675	−	0.456197i
$732$	−2.78771	+	0.524841i	−0.103037	+	0.0193987i
$733$	15.2083	+	2.68164i	0.561732	+	0.0990485i	0.447302	−	0.894383i	$-0.352385\pi$
$733$	15.2083	+	2.68164i	0.561732	+	0.0990485i	0.114430	+	0.993431i	$0.463496\pi$
$734$	−24.9651	+	9.08654i	−0.921477	+	0.335390i
$735$		0			0
$736$	1.07673	+	6.10647i	0.0396890	+	0.225087i
$737$	73.5643	−	42.4724i	2.70977	−	1.56449i
$738$	5.88085	+	15.0645i	0.216477	+	0.554533i
$739$	6.55875	−	11.3601i	0.241268	−	0.417888i	−0.719808	−	0.694173i	$-0.755770\pi$
$739$	6.55875	−	11.3601i	0.241268	−	0.417888i	0.961076	+	0.276285i	$0.0891035\pi$
$740$		0			0
$741$	−36.3742	+	0.420454i	−1.33624	+	0.0154458i
$742$	−38.0421	+	45.3368i	−1.39657	+	1.66437i
$743$	−9.43078	+	11.2392i	−0.345982	+	0.412325i	−0.910772	−	0.412909i	$-0.864513\pi$
$743$	−9.43078	+	11.2392i	−0.345982	+	0.412325i	0.564790	+	0.825234i	$0.308957\pi$
$744$	−6.14371	−	10.3627i	−0.225239	−	0.379916i
$745$		0			0
$746$	−30.9676	+	53.6374i	−1.13380	+	1.96380i
$747$	12.5800	+	6.88035i	0.460278	+	0.251739i
$748$	−38.3678	+	22.1517i	−1.40287	+	0.809945i
$749$	−10.8016	−	61.2588i	−0.394681	−	2.23835i
$750$		0			0
$751$	−13.7050	+	4.98820i	−0.500101	+	0.182022i	−0.579739	−	0.814802i	$-0.696846\pi$
$751$	−13.7050	+	4.98820i	−0.500101	+	0.182022i	0.0796384	+	0.996824i	$0.474623\pi$
$752$	4.34855	+	0.766767i	0.158575	+	0.0279611i
$753$	22.1987	+	25.8428i	0.808966	+	0.941764i
$754$	21.9610	−	18.4275i	0.799774	−	0.671090i
$755$		0			0
$756$	−30.4933	−	48.8246i	−1.10903	−	1.77573i
$757$		−	13.5259i		−	0.491607i	−0.969320	−	0.245803i	$-0.920948\pi$
$757$		−	13.5259i		−	0.491607i	0.969320	−	0.245803i	$-0.0790518\pi$
$758$	28.1138	+	33.5047i	1.02114	+	1.21695i
$759$	−7.85879	−	2.75792i	−0.285256	−	0.100106i
$760$		0			0
$761$	−31.9148	+	11.6160i	−1.15691	+	0.421081i	−0.847993	−	0.530008i	$-0.822189\pi$
$761$	−31.9148	+	11.6160i	−1.15691	+	0.421081i	−0.308918	+	0.951089i	$0.599967\pi$
$762$	−18.2986	−	3.00888i	−0.662887	−	0.109000i
$763$	−25.1934	+	4.44227i	−0.912062	+	0.160821i
$764$	−26.4551	−	45.8215i	−0.957111	−	1.65776i
$765$		0			0
$766$	−5.74493	+	9.95050i	−0.207573	+	0.359526i
$767$	12.8073	−	35.1878i	0.462445	−	1.27056i
$768$	−11.0094	−	6.18771i	−0.397267	−	0.223280i
$769$	1.51739	+	1.27324i	0.0547184	+	0.0459142i	0.669737	−	0.742599i	$-0.266407\pi$
$769$	1.51739	+	1.27324i	0.0547184	+	0.0459142i	−0.615018	+	0.788513i	$0.710851\pi$
$770$		0			0
$771$	4.71029	−	8.38070i	0.169637	−	0.301824i
$772$	0.977821	−	2.68654i	0.0351925	−	0.0966907i
$773$	46.5224	+	26.8597i	1.67329	+	0.966077i	0.965775	+	0.259382i	$0.0835190\pi$
$773$	46.5224	+	26.8597i	1.67329	+	0.966077i	0.707519	+	0.706694i	$0.249814\pi$
$774$	−34.2437	+	30.1098i	−1.23086	+	1.08227i
$775$		0			0
$776$	2.32206	+	13.1691i	0.0833571	+	0.472742i
$777$	22.2918	+	3.66549i	0.799712	+	0.131499i
$778$	−7.15469	−	19.6574i	−0.256508	−	0.704750i
$779$	−1.44338	+	8.18582i	−0.0517145	+	0.293287i
$780$		0			0
$781$	63.4178	−	53.2139i	2.26927	−	1.90414i
$782$			5.59482i			0.200070i
$783$	−3.38209	+	10.4008i	−0.120866	+	0.371695i
$784$	8.78093			0.313605
$785$		0			0
$786$	−16.3054	+	14.0062i	−0.581593	+	0.499583i
$787$	16.6884	+	2.94262i	0.594877	+	0.104893i	0.462977	−	0.886370i	$-0.346781\pi$
$787$	16.6884	+	2.94262i	0.594877	+	0.104893i	0.131900	+	0.991263i	$0.457892\pi$
$788$	−9.29421	−	25.5356i	−0.331093	−	0.909669i
$789$	−22.8396	+	8.61319i	−0.813112	+	0.306638i
$790$		0			0
$791$	−32.4363	−	56.1812i	−1.15330	−	1.99757i
$792$	28.8168	−	17.5378i	1.02396	−	0.623179i
$793$	2.95243	+	1.70459i	0.104844	+	0.0605316i
$794$	−16.7852	−	6.10931i	−0.595684	−	0.216811i
$795$		0			0
$796$	−39.7482	−	33.3527i	−1.40884	−	1.18216i
$797$	0.104393	−	0.124410i	0.00369778	−	0.00440684i	−0.764192	−	0.644988i	$-0.776862\pi$
$797$	0.104393	−	0.124410i	0.00369778	−	0.00440684i	0.767890	+	0.640582i	$0.221307\pi$
$798$	−0.574388	−	49.6913i	−0.0203331	−	1.75905i
$799$	9.50945	+	3.46116i	0.336420	+	0.122447i
$800$		0			0
$801$	6.81257	+	5.45312i	0.240710	+	0.192676i
$802$	18.6467	−	10.7657i	0.658437	−	0.380149i
$803$	−68.3714	+	12.0557i	−2.41277	+	0.425437i
$804$	62.4411	+	51.1762i	2.20213	+	1.80485i
$805$		0			0
$806$	−7.84629	+	44.4985i	−0.276374	+	1.56739i
$807$	−18.1261	+	3.41259i	−0.638068	+	0.120129i
$808$	6.20321	+	7.39269i	0.218228	+	0.260074i
$809$	24.6513			0.866695			0.433347	−	0.901227i	$-0.357332\pi$
$809$	24.6513			0.866695			0.433347	+	0.901227i	$0.357332\pi$
$810$		0			0
$811$	−9.59786			−0.337026			−0.168513	−	0.985699i	$-0.553897\pi$
$811$	−9.59786			−0.337026			−0.168513	+	0.985699i	$0.553897\pi$
$812$	14.9883	+	17.8624i	0.525987	+	0.626847i
$813$	−31.8302	+	5.99266i	−1.11633	+	0.210172i
$814$	−7.17457	+	40.6890i	−0.251469	+	1.42615i
$815$		0			0
$816$	4.60491	+	3.77414i	0.161204	+	0.132121i
$817$	−23.0811	+	4.06982i	−0.807506	+	0.142385i
$818$	26.7862	−	15.4650i	0.936557	−	0.540722i
$819$	−10.4353	+	68.3906i	−0.364638	+	2.38976i
$820$		0			0
$821$	−7.75048	−	2.82094i	−0.270493	−	0.0984516i	0.203212	−	0.979135i	$-0.434862\pi$
$821$	−7.75048	−	2.82094i	−0.270493	−	0.0984516i	−0.473706	+	0.880683i	$0.657084\pi$
$822$	−0.184932	−	15.9988i	−0.00645024	−	0.558021i
$823$	−2.77633	+	3.30870i	−0.0967768	+	0.115334i	−0.812259	−	0.583297i	$-0.801763\pi$
$823$	−2.77633	+	3.30870i	−0.0967768	+	0.115334i	0.715482	+	0.698631i	$0.246207\pi$
$824$	−14.3598	−	12.0493i	−0.500247	−	0.419757i
$825$		0			0
$826$	48.0705	+	17.4962i	1.67259	+	0.608772i
$827$	−9.89730	−	5.71421i	−0.344163	−	0.198703i	0.317948	−	0.948108i	$-0.397006\pi$
$827$	−9.89730	−	5.71421i	−0.344163	−	0.198703i	−0.662111	+	0.749405i	$0.730339\pi$
$828$	−0.182974	−	7.91366i	−0.00635880	−	0.275019i
$829$	14.4282	+	24.9904i	0.501113	+	0.867954i	0.999999	+	0.00128593i	$0.000409323\pi$
$829$	14.4282	+	24.9904i	0.501113	+	0.867954i	−0.498886	+	0.866668i	$0.666257\pi$
$830$		0			0
$831$	11.9175	−	4.49426i	0.413412	−	0.155904i
$832$	27.0856	+	74.4171i	0.939025	+	2.57995i
$833$	19.8184	+	3.49452i	0.686666	+	0.121078i
$834$	−24.9532	+	21.4346i	−0.864059	+	0.742219i
$835$		0			0
$836$	54.1125			1.87152
$837$	−6.45382	−	15.9844i	−0.223077	−	0.552501i
$838$		−	69.2339i		−	2.39165i
$839$	14.9031	−	12.5052i	0.514513	−	0.431728i	−0.348201	−	0.937420i	$-0.613207\pi$
$839$	14.9031	−	12.5052i	0.514513	−	0.431728i	0.862714	+	0.505692i	$0.168763\pi$
$840$		0			0
$841$	−4.26650	+	24.1965i	−0.147121	+	0.834363i
$842$	11.8213	+	32.4789i	0.407390	+	1.11930i
$843$	−27.8735	−	4.58332i	−0.960015	−	0.157858i
$844$	−2.30169	−	13.0536i	−0.0792276	−	0.449322i
$845$		0			0
$846$	−22.7817	−	7.70031i	−0.783251	−	0.264742i
$847$	−57.9144	−	33.4369i	−1.98996	−	1.14890i
$848$	−2.96213	+	8.13839i	−0.101720	+	0.279473i
$849$	−0.458332	+	0.815479i	−0.0157299	+	0.0279872i
$850$		0			0
$851$	2.37974	+	1.99684i	0.0815764	+	0.0684507i
$852$	68.5907	+	38.5508i	2.34988	+	1.32073i
$853$	0.256981	−	0.706049i	0.00879885	−	0.0241746i	−0.935215	−	0.354079i	$-0.884794\pi$
$853$	0.256981	−	0.706049i	0.00879885	−	0.0241746i	0.944014	+	0.329905i	$0.107017\pi$
$854$	−2.32866	+	4.03335i	−0.0796850	+	0.138019i
$855$		0			0
$856$	17.3228	+	30.0039i	0.592080	+	1.02551i
$857$	35.8762	−	6.32595i	1.22551	−	0.216090i	0.476813	−	0.879005i	$-0.341792\pi$
$857$	35.8762	−	6.32595i	1.22551	−	0.216090i	0.748695	+	0.662914i	$0.230681\pi$
$858$	−124.850	−	20.5294i	−4.26231	−	0.700863i
$859$	27.3052	−	9.93826i	0.931640	−	0.339089i	0.168781	−	0.985654i	$-0.446017\pi$
$859$	27.3052	−	9.93826i	0.931640	−	0.339089i	0.762859	+	0.646564i	$0.223795\pi$
$860$		0			0
$861$	14.9163	+	5.23466i	0.508347	+	0.178397i
$862$	−7.30088	−	8.70085i	−0.248669	−	0.296352i
$863$		−	2.49689i		−	0.0849951i	−0.999097	−	0.0424975i	$-0.986469\pi$
$863$		−	2.49689i		−	0.0849951i	0.999097	−	0.0424975i	$-0.0135315\pi$
$864$	−28.3135	−	22.1315i	−0.963246	−	0.752928i
$865$		0			0
$866$	15.7125	−	13.1844i	0.533934	−	0.448024i
$867$	−10.2950	−	11.9850i	−0.349638	−	0.407034i
$868$	−36.1937	−	6.38192i	−1.22849	−	0.216616i
$869$	−50.0511	+	18.2171i	−1.69787	+	0.617973i
$870$		0			0
$871$	−16.8486	−	95.5529i	−0.570891	−	3.23769i
$872$	12.3395	−	7.12419i	0.417867	−	0.241256i
$873$	0.442292	+	19.1292i	0.0149693	+	0.647424i
$874$	3.41678	−	5.91804i	0.115574	−	0.200181i
$875$		0			0
$876$	−33.6504	−	56.7589i	−1.13694	−	1.91771i
$877$	−23.2839	+	27.7487i	−0.786241	+	0.937006i	−0.999197	−	0.0400561i	$-0.987246\pi$
$877$	−23.2839	+	27.7487i	−0.786241	+	0.937006i	0.212956	+	0.977062i	$0.431691\pi$
$878$	19.0960	−	22.7577i	0.644459	−	0.768037i
$879$	30.0561	−	0.347422i	1.01377	−	0.0117183i
$880$		0			0
$881$	−5.21700	+	9.03610i	−0.175765	+	0.304434i	−0.940426	−	0.339999i	$-0.889573\pi$
$881$	−5.21700	+	9.03610i	−0.175765	+	0.304434i	0.764661	+	0.644433i	$0.222907\pi$
$882$	−47.2744	−	7.21330i	−1.59181	−	0.242885i
$883$	23.3890	−	13.5036i	0.787102	−	0.454434i	−0.0518393	−	0.998655i	$-0.516508\pi$
$883$	23.3890	−	13.5036i	0.787102	−	0.454434i	0.838941	+	0.544222i	$0.183175\pi$
$884$	8.78745	+	49.8361i	0.295554	+	1.67617i
$885$		0			0
$886$	−16.0916	+	5.85688i	−0.540609	+	0.196766i
$887$	12.0663	+	2.12762i	0.405148	+	0.0714384i	0.372509	−	0.928029i	$-0.378498\pi$
$887$	12.0663	+	2.12762i	0.405148	+	0.0714384i	0.0326390	+	0.999467i	$0.489609\pi$
$888$	−12.3653	+	2.32801i	−0.414952	+	0.0781229i
$889$	−13.8864	+	11.6521i	−0.465735	+	0.390798i
$890$		0			0
$891$	44.5475	−	18.5881i	1.49240	−	0.622724i
$892$		−	72.3084i		−	2.42106i
$893$	−7.94508	−	9.46858i	−0.265872	−	0.316854i
$894$	8.02081	+	42.6027i	0.268256	+	1.42485i
$895$		0			0
$896$	−52.7344	+	19.1938i	−1.76173	+	0.641218i
$897$	−6.03040	+	7.35781i	−0.201349	+	0.245670i
$898$	74.2212	−	13.0872i	2.47679	−	0.436726i
$899$	3.49132	+	6.04714i	0.116442	+	0.201684i
$900$		0			0
$901$	−9.92428	+	17.1894i	−0.330626	+	0.572660i
$902$	−9.88830	+	27.1679i	−0.329244	+	0.904592i
$903$	0.515196	+	44.5705i	0.0171446	+	1.48321i
$904$	27.6787	+	23.2252i	0.920578	+	0.772457i
$905$		0			0
$906$	33.3766	+	56.2971i	1.10886	+	1.87035i
$907$	1.54965	−	4.25762i	0.0514552	−	0.141372i	−0.911303	−	0.411737i	$-0.864922\pi$
$907$	1.54965	−	4.25762i	0.0514552	−	0.141372i	0.962758	+	0.270365i	$0.0871444\pi$
$908$	43.3265	+	25.0146i	1.43784	+	0.830137i
$909$	7.17901	+	11.7960i	0.238113	+	0.391250i
$910$		0			0
$911$	2.98118	+	16.9071i	0.0987710	+	0.560158i	0.993526	+	0.113601i	$0.0362387\pi$
$911$	2.98118	+	16.9071i	0.0987710	+	0.560158i	−0.894755	+	0.446557i	$0.852650\pi$
$912$	−2.56605	−	6.80442i	−0.0849706	−	0.225317i
$913$	8.76742	+	24.0883i	0.290159	+	0.797206i
$914$	9.90363	−	56.1663i	0.327583	−	1.85781i
$915$		0			0
$916$	−33.0807	+	27.7580i	−1.09302	+	0.917150i
$917$			21.0118i			0.693872i
$918$	−21.6914	−	24.1019i	−0.715922	−	0.795481i
$919$	42.1043			1.38889			0.694447	−	0.719544i	$-0.255649\pi$
$919$	42.1043			1.38889			0.694447	+	0.719544i	$0.255649\pi$
$920$		0			0
$921$	7.28395	+	2.55619i	0.240014	+	0.0842294i
$922$	−32.1042	−	5.66084i	−1.05730	−	0.186430i
$923$	−32.3419	−	88.8586i	−1.06455	−	2.92482i
$924$	16.6980	−	101.549i	0.549323	−	3.34072i
$925$		0			0
$926$	0.605108	+	1.04808i	0.0198851	+	0.0344420i
$927$	−17.7117	−	20.1434i	−0.581728	−	0.661596i
$928$	12.6067	+	7.27848i	0.413835	+	0.238928i
$929$	−24.1410	−	8.78662i	−0.792042	−	0.288280i	−0.0858572	−	0.996307i	$-0.527363\pi$
$929$	−24.1410	−	8.78662i	−0.792042	−	0.288280i	−0.706185	+	0.708028i	$0.749585\pi$
$930$		0			0
$931$	−18.8292	−	15.7996i	−0.617102	−	0.517810i
$932$	48.3349	−	57.6033i	1.58326	−	1.88686i
$933$	−17.8364	−	10.0248i	−0.583937	−	0.328196i
$934$	86.0166	+	31.3075i	2.81455	+	1.02441i
$935$		0			0
$936$	−7.56641	−	37.7821i	−0.247316	−	1.23495i
$937$	−38.5244	+	22.2421i	−1.25854	+	0.726617i	−0.972790	−	0.231688i	$-0.925575\pi$
$937$	−38.5244	+	22.2421i	−1.25854	+	0.726617i	−0.285748	+	0.958305i	$0.592242\pi$
$938$	130.536	−	23.0170i	4.26215	−	0.751533i
$939$	0.996066	−	6.05759i	0.0325054	−	0.197682i
$940$		0			0
$941$	−3.84491	+	21.8056i	−0.125341	+	0.710842i	0.855764	+	0.517366i	$0.173087\pi$
$941$	−3.84491	+	21.8056i	−0.125341	+	0.710842i	−0.981105	+	0.193476i	$0.938024\pi$
$942$	15.9149	−	45.3500i	0.518535	−	1.47758i
$943$	1.39729	+	1.66523i	0.0455021	+	0.0542273i
$944$	7.48598			0.243648
$945$		0			0
$946$	−81.5201			−2.65045
$947$	−17.6914	−	21.0838i	−0.574894	−	0.685131i	0.397734	−	0.917501i	$-0.369797\pi$
$947$	−17.6914	−	21.0838i	−0.574894	−	0.685131i	−0.972628	+	0.232369i	$0.925352\pi$
$948$	−32.9857	−	38.4005i	−1.07133	−	1.24719i
$949$	−13.7705	+	78.0963i	−0.447009	+	2.53511i
$950$		0			0
$951$	−6.30190	+	2.37655i	−0.204353	+	0.0770649i
$952$	−21.8150	+	3.84657i	−0.707028	+	0.124668i
$953$	−4.40592	+	2.54376i	−0.142722	+	0.0824005i	−0.569661	−	0.821880i	$-0.692925\pi$
$953$	−4.40592	+	2.54376i	−0.142722	+	0.0824005i	0.426939	+	0.904281i	$0.359592\pi$
$954$	22.6329	−	41.3818i	0.732767	−	1.33979i
$955$		0			0
$956$	17.8256	+	6.48798i	0.576520	+	0.209836i
$957$	−16.8190	+	9.97144i	−0.543682	+	0.322331i
$958$	−8.42495	+	10.0405i	−0.272198	+	0.324393i
$959$	−11.9811	−	10.0533i	−0.386888	−	0.324638i
$960$		0			0
$961$	18.7886	+	6.83848i	0.606083	+	0.220596i
$962$	40.8707	+	23.5967i	1.31773	+	0.760789i
$963$	18.0277	+	46.1802i	0.580934	+	1.48814i
$964$	3.94628	+	6.83516i	0.127101	+	0.220146i
$965$		0			0
$966$	−10.0516	−	8.23821i	−0.323405	−	0.265060i
$967$	4.00003	+	10.9900i	0.128632	+	0.353414i	0.987245	−	0.159211i	$-0.0508951\pi$
$967$	4.00003	+	10.9900i	0.128632	+	0.353414i	−0.858612	+	0.512626i	$0.828673\pi$
$968$	36.6807	+	6.46780i	1.17896	+	0.207883i
$969$	−3.08360	−	16.3786i	−0.0990596	−	0.526158i
$970$		0			0
$971$	9.40243			0.301738			0.150869	−	0.988554i	$-0.451793\pi$
$971$	9.40243			0.301738			0.150869	+	0.988554i	$0.451793\pi$
$972$	31.4699	+	33.3818i	1.00940	+	1.07072i
$973$			32.1558i			1.03087i
$974$	20.2848	−	17.0209i	0.649966	−	0.545386i
$975$		0			0
$976$	−0.118348	+	0.671186i	−0.00378823	+	0.0214841i
$977$	−12.9578	−	35.6014i	−0.414558	−	1.13899i	−0.954740	−	0.297441i	$-0.903867\pi$
$977$	−12.9578	−	35.6014i	−0.414558	−	1.13899i	0.540182	−	0.841548i	$-0.318355\pi$
$978$	18.2847	−	22.3095i	0.584679	−	0.713379i
$979$	2.70902	+	15.3636i	0.0865806	+	0.491023i
$980$		0			0
$981$	18.9921	−	7.41409i	0.606373	−	0.236714i
$982$	71.8095	+	41.4592i	2.29153	+	1.32302i
$983$	19.6332	−	53.9418i	0.626202	−	1.72048i	−0.0650694	−	0.997881i	$-0.520727\pi$
$983$	19.6332	−	53.9418i	0.626202	−	1.72048i	0.691271	−	0.722595i	$-0.257051\pi$
$984$	−8.80406	+	0.101767i	−0.280663	+	0.00324422i
$985$		0			0
$986$	10.0617	+	8.44278i	0.320430	+	0.268873i
$987$	−20.2207	+	11.9882i	−0.643631	+	0.381587i
$988$	21.1400	−	58.0817i	0.672554	−	1.84783i
$989$	−3.06467	+	5.30817i	−0.0974510	+	0.168790i
$990$		0			0
$991$	13.9592	+	24.1781i	0.443430	+	0.768043i	0.997941	−	0.0641332i	$-0.0204282\pi$
$991$	13.9592	+	24.1781i	0.443430	+	0.768043i	−0.554512	+	0.832176i	$0.687095\pi$
$992$	−22.5952	+	3.98415i	−0.717400	+	0.126497i
$993$	12.2197	+	32.4030i	0.387780	+	1.02828i
$994$	121.391	−	44.1827i	3.85029	−	1.40139i
$995$		0			0
$996$	−18.4812	+	15.8752i	−0.585599	+	0.503024i
$997$	12.6888	+	15.1219i	0.401858	+	0.478916i	0.928586	−	0.371118i	$-0.121026\pi$
$997$	12.6888	+	15.1219i	0.401858	+	0.478916i	−0.526727	+	0.850034i	$0.676581\pi$
$998$		−	41.2218i		−	1.30485i
$999$	−17.9935	+	0.624190i	−0.569289	+	0.0197485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.e.49.3		132
5.2	odd	4		675.2.l.f.76.10	✓	66
5.3	odd	4		675.2.l.g.76.2	yes	66
5.4	even	2	inner	675.2.u.e.49.20		132
27.16	even	9	inner	675.2.u.e.124.20		132
135.43	odd	36		675.2.l.g.151.2	yes	66
135.97	odd	36		675.2.l.f.151.10	yes	66
135.124	even	18	inner	675.2.u.e.124.3		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.10	✓	66	5.2	odd	4
675.2.l.f.151.10	yes	66	135.97	odd	36
675.2.l.g.76.2	yes	66	5.3	odd	4
675.2.l.g.151.2	yes	66	135.43	odd	36
675.2.u.e.49.3		132	1.1	even	1	trivial
675.2.u.e.49.20		132	5.4	even	2	inner
675.2.u.e.124.3		132	135.124	even	18	inner
675.2.u.e.124.20		132	27.16	even	9	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.42910 - 1.70314i) q^{2} +(1.70215 - 0.320463i) q^{3} +(-0.511048 + 2.89830i) q^{4} +(-2.97833 - 2.44102i) q^{6} +(-3.70709 + 0.653660i) q^{7} +(1.81569 - 1.04829i) q^{8} +(2.79461 - 1.09095i) q^{9} +(5.03989 + 1.83437i) q^{11} +(0.0589180 + 5.09710i) q^{12} +(3.93784 - 4.69294i) q^{13} +(6.41109 + 5.37954i) q^{14} +(1.15085 + 0.418876i) q^{16} +(2.43075 + 1.40339i) q^{17} +(-5.85182 - 3.20052i) q^{18} +(-1.71412 - 2.96894i) q^{19} +(-6.10054 + 2.30061i) q^{21} +(-4.07833 - 11.2051i) q^{22} +(-0.882941 - 0.155686i) q^{23} +(2.75464 - 2.36621i) q^{24} -13.6203 q^{26} +(4.40722 - 2.75252i) q^{27} -11.0783i q^{28} +(-1.61238 + 1.35294i) q^{29} +(0.576073 - 3.26707i) q^{31} +(-2.36543 - 6.49896i) q^{32} +(9.16647 + 1.50727i) q^{33} +(-1.08362 - 6.14550i) q^{34} +(1.73372 + 8.65714i) q^{36} +(-3.00072 - 1.73247i) q^{37} +(-2.60687 + 7.16230i) q^{38} +(5.19887 - 9.25000i) q^{39} +(-1.85735 - 1.55850i) q^{41} +(12.6366 + 7.10225i) q^{42} +(2.33822 - 6.42421i) q^{43} +(-7.89217 + 13.6696i) q^{44} +(0.996658 + 1.72626i) q^{46} +(3.55068 - 0.626080i) q^{47} +(2.09315 + 0.344183i) q^{48} +(6.73741 - 2.45222i) q^{49} +(4.58723 + 1.60982i) q^{51} +(11.5891 + 13.8114i) q^{52} +7.07162i q^{53} +(-10.9863 - 3.57247i) q^{54} +(-6.04572 + 5.07296i) q^{56} +(-3.86912 - 4.50426i) q^{57} +(4.60850 + 0.812603i) q^{58} +(5.74383 - 2.09058i) q^{59} +(0.0966336 + 0.548037i) q^{61} +(-6.38754 + 3.68785i) q^{62} +(-9.64675 + 5.87097i) q^{63} +(-6.46348 + 11.1951i) q^{64} +(-10.5327 - 17.7658i) q^{66} +(10.1805 - 12.1326i) q^{67} +(-5.30969 + 6.32784i) q^{68} +(-1.55279 + 0.0179489i) q^{69} +(7.71778 - 13.3676i) q^{71} +(3.93052 - 4.91040i) q^{72} +(-11.2103 + 6.47229i) q^{73} +(1.33771 + 7.58652i) q^{74} +(9.48088 - 3.45076i) q^{76} +(-19.8824 - 3.50580i) q^{77} +(-23.1837 + 4.36480i) q^{78} +(-7.60758 + 6.38352i) q^{79} +(6.61966 - 6.09755i) q^{81} +5.39058i q^{82} +(3.07222 + 3.66133i) q^{83} +(-3.55019 - 18.8569i) q^{84} +(-14.2829 + 5.19854i) q^{86} +(-2.31093 + 2.81962i) q^{87} +(11.0738 - 1.95262i) q^{88} +(1.45438 + 2.51905i) q^{89} +(-11.5304 + 19.9712i) q^{91} +(0.902451 - 2.47946i) q^{92} +(-0.0664147 - 5.74565i) q^{93} +(-6.14058 - 5.15256i) q^{94} +(-6.10898 - 10.3042i) q^{96} +(-2.18144 + 5.99345i) q^{97} +(-13.8049 - 7.97026i) q^{98} +(16.0857 - 0.371923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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