LMFDB - Embedded newform 675.2.u.e.124.3

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			124.3
Character	$\chi$	$=$	675.124
Dual form			675.2.u.e.49.3

$q$-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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

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	−0.0317247	+	0.999497i	$0.510100\pi$
$2$	−1.42910	+	1.70314i	−1.01053	+	1.20430i	−0.978803	+	0.204803i	$0.934344\pi$
$3$	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	−0.578534	−	0.815659i	$-0.696375\pi$
$7$	−3.70709	−	0.653660i	−1.40115	−	0.247060i	−0.822615	+	0.568598i	$0.807486\pi$
$8$	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	0.558539	−	0.829478i	$-0.311362\pi$
$11$	5.03989	−	1.83437i	1.51958	−	0.553083i	0.961044	+	0.276396i	$0.0891400\pi$
$12$	0.0589180	−	5.09710i	0.0170082	−	1.47141i
$13$	3.93784	+	4.69294i	1.09216	+	1.30159i	0.950175	+	0.311718i	$0.100904\pi$
$13$	3.93784	+	4.69294i	1.09216	+	1.30159i	0.141986	+	0.989869i	$0.454651\pi$
$14$	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	−0.175373	−	0.984502i	$-0.556113\pi$
$17$	2.43075	−	1.40339i	0.589544	−	0.340373i	0.764917	+	0.644129i	$0.222780\pi$
$18$	−5.85182	+	3.20052i	−1.37929	+	0.754370i
$19$	−1.71412	+	2.96894i	−0.393246	+	0.681122i	−0.992876	−	0.119156i	$-0.961981\pi$
$19$	−1.71412	+	2.96894i	−0.393246	+	0.681122i	0.599630	+	0.800278i	$0.295315\pi$
$20$		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	−0.264941	−	0.964265i	$-0.585352\pi$
$23$	−0.882941	+	0.155686i	−0.184106	+	0.0324628i	0.0808349	+	0.996728i	$0.474241\pi$
$24$	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	0.480688	−	0.876892i	$-0.340387\pi$
$29$	−1.61238	−	1.35294i	−0.299411	−	0.251235i	−0.780099	+	0.625656i	$0.784831\pi$
$30$		0			0
$31$	0.576073	+	3.26707i	0.103466	+	0.586784i	0.991822	+	0.127629i	$0.0407366\pi$
$31$	0.576073	+	3.26707i	0.103466	+	0.586784i	−0.888356	+	0.459155i	$0.848152\pi$
$32$	−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	−0.725949	−	0.687749i	$-0.758599\pi$
$37$	−3.00072	+	1.73247i	−0.493316	+	0.284816i	0.232633	+	0.972565i	$0.425266\pi$
$38$	−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	−0.776196	−	0.630491i	$-0.782854\pi$
$41$	−1.85735	+	1.55850i	−0.290069	+	0.243397i	0.486127	+	0.873888i	$0.338409\pi$
$42$	12.6366	−	7.10225i	1.94986	−	1.09590i
$43$	2.33822	+	6.42421i	0.356576	+	0.979683i	0.980209	+	0.197966i	$0.0634336\pi$
$43$	2.33822	+	6.42421i	0.356576	+	0.979683i	−0.623633	+	0.781717i	$0.714344\pi$
$44$	−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	0.426497	−	0.904489i	$-0.359748\pi$
$47$	3.55068	+	0.626080i	0.517919	+	0.0913232i	0.0914225	+	0.995812i	$0.470859\pi$
$48$	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	$-0.838572\pi$
$53$		−	7.07162i		−	0.971362i	0.874136	−	0.485681i	$-0.161428\pi$
$54$	−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	0.687672	−	0.726021i	$-0.258633\pi$
$59$	5.74383	+	2.09058i	0.747782	+	0.272171i	0.0601101	+	0.998192i	$0.480855\pi$
$60$		0			0
$61$	0.0966336	−	0.548037i	0.0123727	−	0.0701689i	−0.977996	−	0.208622i	$-0.933102\pi$
$61$	0.0966336	−	0.548037i	0.0123727	−	0.0701689i	0.990369	+	0.138453i	$0.0442131\pi$
$62$	−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	0.815694	+	0.578484i	$0.196356\pi$
$67$	10.1805	+	12.1326i	1.24375	+	1.48224i	0.428052	+	0.903754i	$0.359200\pi$
$68$	−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	0.805530	+	0.592555i	$0.201881\pi$
$71$	7.71778	+	13.3676i	0.915933	+	1.58644i	0.110402	+	0.993887i	$0.464786\pi$
$72$	3.93052	+	4.91040i	0.463216	+	0.578696i
$73$	−11.2103	−	6.47229i	−1.31207	−	0.757524i	−0.329632	−	0.944110i	$-0.606925\pi$
$73$	−11.2103	−	6.47229i	−1.31207	−	0.757524i	−0.982439	+	0.186585i	$0.940258\pi$
$74$	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	0.105165	−	0.994455i	$-0.466463\pi$
$79$	−7.60758	−	6.38352i	−0.855920	−	0.718202i	−0.961085	+	0.276253i	$0.910907\pi$
$80$		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	−0.570610	−	0.821221i	$-0.693293\pi$
$83$	3.07222	−	3.66133i	0.337220	−	0.401884i	0.907830	+	0.419338i	$0.137738\pi$
$84$	−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	−0.778591	−	0.627532i	$-0.784065\pi$
$89$	1.45438	−	2.51905i	0.154164	−	0.267019i	0.932754	+	0.360513i	$0.117398\pi$
$90$		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	0.778322	−	0.627865i	$-0.216071\pi$
$97$	−2.18144	−	5.99345i	−0.221491	−	0.608543i	−0.999813	+	0.0193229i	$0.993849\pi$
$98$	−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	−0.918870	−	0.394560i	$-0.870897\pi$
$101$	0.799294	−	4.53302i	0.0795328	−	0.451053i	0.998403	−	0.0564928i	$-0.0179918\pi$
$102$	−3.81388	+	10.1133i	−0.377630	+	1.00136i
$103$	−3.05797	+	8.40172i	−0.301311	+	0.827846i	0.692962	+	0.720974i	$0.256305\pi$
$103$	−3.05797	+	8.40172i	−0.301311	+	0.827846i	−0.994273	+	0.106871i	$0.965917\pi$
$104$	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	$-0.705493\pi$
$107$		−	16.5248i		−	1.59751i	0.601657	−	0.798754i	$-0.294507\pi$
$108$	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	−0.273033	−	0.962005i	$-0.588027\pi$
$113$	5.89428	−	16.1944i	0.554487	−	1.52344i	0.827520	−	0.561436i	$-0.189751\pi$
$114$	−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	0.673489	−	0.739198i	$-0.264795\pi$
$127$	4.17046	+	2.40782i	0.370069	+	0.213659i	−0.303420	+	0.952857i	$0.598128\pi$
$128$	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	0.997424	+	0.0717355i	$0.0228538\pi$
$131$	0.969287	+	5.49710i	0.0846870	+	0.480284i	−0.912737	+	0.408548i	$0.866035\pi$
$132$	−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	−0.639795	−	0.768546i	$-0.720981\pi$
$137$	2.67071	−	3.18283i	0.228174	−	0.271927i	0.867969	+	0.496618i	$0.165425\pi$
$138$	2.24966	−	2.61896i	0.191504	−	0.222941i
$139$	1.48337	+	8.41259i	0.125817	+	0.713546i	0.980819	+	0.194921i	$0.0624450\pi$
$139$	1.48337	+	8.41259i	0.125817	+	0.713546i	−0.855002	+	0.518625i	$0.826444\pi$
$140$		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	−0.923612	−	0.383330i	$-0.874777\pi$
$149$	−8.62380	+	7.23622i	−0.706489	+	0.592815i	0.217123	+	0.976144i	$0.430333\pi$
$150$		0			0
$151$	−15.9706	+	5.81283i	−1.29967	+	0.473042i	−0.896890	−	0.442255i	$-0.854179\pi$
$151$	−15.9706	+	5.81283i	−1.29967	+	0.473042i	−0.402781	+	0.915296i	$0.631957\pi$
$152$	−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	−0.644522	−	0.764586i	$-0.722944\pi$
$157$	4.26867	−	11.7281i	0.340677	−	0.936002i	0.985199	−	0.171416i	$-0.0548342\pi$
$158$	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	$-0.905228\pi$
$163$		−	7.49060i		−	0.586709i	0.956004	−	0.293354i	$-0.0947716\pi$
$164$	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	−0.656503	−	0.754324i	$-0.727965\pi$
$167$	4.28105	−	11.7621i	0.331277	−	0.910177i	0.987780	−	0.155854i	$-0.0498128\pi$
$168$	−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	−0.965035	−	0.262122i	$-0.915578\pi$
$173$	−5.18574	−	14.2477i	−0.394264	−	1.08323i	0.570771	−	0.821110i	$-0.306645\pi$
$174$	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	0.976939	−	0.213517i	$-0.0684917\pi$
$179$	4.06134	+	7.03445i	0.303559	+	0.525780i	−0.673380	+	0.739296i	$0.735158\pi$
$180$		0			0
$181$	7.95939	−	13.7861i	0.591617	−	1.02471i	−0.402398	−	0.915465i	$-0.631823\pi$
$181$	7.95939	−	13.7861i	0.591617	−	1.02471i	0.994015	−	0.109245i	$-0.0348434\pi$
$182$	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	−0.0100183	−	0.999950i	$-0.503189\pi$
$191$	−13.7721	−	11.5562i	−0.996516	−	0.836176i	−0.986498	+	0.163773i	$0.947633\pi$
$192$	−7.41418	−	21.1270i	−0.535073	−	1.52471i
$193$	−0.956681	+	0.168689i	−0.0688634	+	0.0121425i	−0.207974	−	0.978134i	$-0.566687\pi$
$193$	−0.956681	+	0.168689i	−0.0688634	+	0.0121425i	0.139110	+	0.990277i	$0.455576\pi$
$194$	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	0.187313	−	0.982300i	$-0.440022\pi$
$197$	−7.99649	−	4.61678i	−0.569727	−	0.328932i	−0.757040	+	0.653368i	$0.773355\pi$
$198$	−23.6215	+	26.8646i	−1.67871	+	1.90919i
$199$	−8.81540	−	15.2687i	−0.624907	−	1.08237i	−0.988559	−	0.150836i	$-0.951803\pi$
$199$	−8.81540	−	15.2687i	−0.624907	−	1.08237i	0.363651	−	0.931535i	$-0.381530\pi$
$200$		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	0.192205	−	0.981355i	$-0.438436\pi$
$211$	−4.23225	−	1.54041i	−0.291360	−	0.106046i	−0.483565	+	0.875308i	$0.660658\pi$
$212$	−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	−0.711423	−	0.702764i	$-0.751949\pi$
$223$	−24.1963	−	4.26645i	−1.62030	−	0.285703i	−0.908878	+	0.417061i	$0.863060\pi$
$224$	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	0.968831	+	0.247721i	$0.0796816\pi$
$227$	5.81410	+	15.9741i	0.385895	+	1.06024i	−0.582936	+	0.812518i	$0.698096\pi$
$228$	15.0320	+	8.91197i	0.995519	+	0.590210i
$229$	11.2404	−	9.43183i	0.742788	−	0.623273i	−0.190797	−	0.981630i	$-0.561107\pi$
$229$	11.2404	−	9.43183i	0.742788	−	0.623273i	0.933585	+	0.358356i	$0.116663\pi$
$230$		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	−0.998458	−	0.0555035i	$-0.982324\pi$
$233$	−22.1275	+	12.7753i	−1.44962	+	0.836939i	−0.451162	+	0.892442i	$0.648990\pi$
$234$	−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	0.999371	+	0.0354667i	$0.0112918\pi$
$239$	1.11927	+	6.34771i	0.0723998	+	0.410599i	−0.926971	+	0.375133i	$0.877597\pi$
$240$		0			0
$241$	2.05438	+	1.72383i	0.132334	+	0.111042i	0.706552	−	0.707661i	$-0.250249\pi$
$241$	2.05438	+	1.72383i	0.132334	+	0.111042i	−0.574218	+	0.818702i	$0.694694\pi$
$242$			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	−0.368591	−	0.929592i	$-0.620160\pi$
$251$	9.83460	−	17.0340i	0.620755	−	1.07518i	0.989345	−	0.145587i	$-0.0465070\pi$
$252$	−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	0.865754	−	0.500469i	$-0.166839\pi$
$257$	3.56777	+	4.25190i	0.222551	+	0.265226i	−0.643203	+	0.765696i	$0.722395\pi$
$258$	−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	−0.271504	−	0.962437i	$-0.587521\pi$
$263$	−13.8789	−	2.44722i	−0.855808	−	0.150902i	−0.584303	+	0.811535i	$0.698632\pi$
$264$	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	0.386918	−	0.922114i	$-0.373540\pi$
$277$	7.24183	+	1.27693i	0.435119	+	0.0767233i	0.0482019	+	0.998838i	$0.484651\pi$
$278$	−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	−0.755942	−	0.654639i	$-0.772821\pi$
$281$	−15.3253	+	5.57797i	−0.914233	+	0.332754i	−0.158291	+	0.987392i	$0.550599\pi$
$282$	−12.1034	+	6.80258i	−0.720745	+	0.405088i
$283$	−0.347160	−	0.413729i	−0.0206365	−	0.0245936i	0.755627	−	0.655002i	$-0.227332\pi$
$283$	−0.347160	−	0.413729i	−0.0206365	−	0.0245936i	−0.776264	+	0.630408i	$0.782888\pi$
$284$	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	0.349532	−	0.936924i	$-0.386340\pi$
$293$	17.0904	−	3.01350i	0.998432	−	0.176051i	0.648900	+	0.760874i	$0.275229\pi$
$294$	−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	−0.385796	−	0.922584i	$-0.626073\pi$
$307$	3.85973	−	2.22842i	0.220287	−	0.127182i	0.606083	+	0.795401i	$0.292740\pi$
$308$	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	−0.862230	−	0.506517i	$-0.830933\pi$
$311$	−9.04919	+	7.59317i	−0.513133	+	0.430569i	0.349097	+	0.937086i	$0.386488\pi$
$312$	−0.257134	+	22.2451i	−0.0145574	+	1.25938i
$313$	1.21223	+	3.33057i	0.0685191	+	0.188255i	0.969226	−	0.246173i	$-0.0791730\pi$
$313$	1.21223	+	3.33057i	0.0685191	+	0.188255i	−0.900707	+	0.434427i	$0.856951\pi$
$314$	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	0.0650679	−	0.997881i	$-0.479274\pi$
$317$	−3.82945	−	0.675236i	−0.215084	−	0.0379250i	−0.280151	+	0.959956i	$0.590385\pi$
$318$	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	−0.727395	−	0.686219i	$-0.759269\pi$
$331$	3.47191	−	19.6902i	0.190833	−	1.08227i	0.918228	−	0.396051i	$-0.129620\pi$
$332$	−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	−0.996094	−	0.0882954i	$-0.971858\pi$
$337$	−16.7068	−	19.9104i	−0.910078	−	1.08459i	0.0860160	−	0.996294i	$-0.472586\pi$
$338$	−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	0.408102	−	0.912936i	$-0.366191\pi$
$347$	20.5622	−	3.62567i	1.10384	−	0.194636i	0.695733	+	0.718300i	$0.255080\pi$
$348$	−6.99109	+	8.13873i	−0.374762	+	0.436282i
$349$	8.83183	+	7.41078i	0.472757	+	0.396690i	0.847799	−	0.530318i	$-0.177927\pi$
$349$	8.83183	+	7.41078i	0.472757	+	0.396690i	−0.375042	+	0.927008i	$0.622372\pi$
$350$		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	−0.554049	−	0.832484i	$-0.686918\pi$
$353$	6.80132	−	8.10550i	0.361998	−	0.431412i	0.916047	+	0.401072i	$0.131362\pi$
$354$	−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	0.487232	+	0.873272i	$0.338006\pi$
$359$	−9.71352	+	16.8243i	−0.512660	+	0.887953i	−0.999892	+	0.0146804i	$0.995327\pi$
$360$		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	0.999491	−	0.0318889i	$-0.0101523\pi$
$367$	4.08698	+	11.2289i	0.213339	+	0.586143i	−0.786153	+	0.618032i	$0.787930\pi$
$368$	−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	0.404283	+	0.914634i	$0.367521\pi$
$373$	−9.52781	+	26.1774i	−0.493331	+	1.35542i	−0.897614	+	0.440782i	$0.854701\pi$
$374$	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	−0.976624	−	0.214953i	$-0.931040\pi$
$383$	−1.76754	+	4.85629i	−0.0903173	+	0.248145i	0.886307	+	0.463098i	$0.153262\pi$
$384$	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	−0.108005	−	0.994150i	$-0.534446\pi$
$389$	8.84157	−	3.21807i	0.448285	−	0.163162i	0.556291	+	0.830988i	$0.312224\pi$
$390$		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	0.664335	−	0.747435i	$-0.268715\pi$
$397$	6.95786	+	4.01712i	0.349205	+	0.201614i	−0.315130	+	0.949048i	$0.602048\pi$
$398$	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	−0.997572	−	0.0696405i	$-0.977815\pi$
$401$	−1.68169	−	9.53732i	−0.0839794	−	0.476271i	0.913593	−	0.406630i	$-0.133296\pi$
$402$	−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	−0.984449	−	0.175669i	$-0.943791\pi$
$409$	−2.41577	−	13.7005i	−0.119452	−	0.677446i	0.864997	−	0.501776i	$-0.167320\pi$
$410$		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	0.165422	−	0.986223i	$-0.447101\pi$
$419$	23.8549	−	20.0166i	1.16539	−	0.977876i	0.999965	+	0.00834704i	$0.00265698\pi$
$420$		0			0
$421$	−14.6085	+	5.31705i	−0.711974	+	0.259137i	−0.672515	−	0.740084i	$-0.734786\pi$
$421$	−14.6085	+	5.31705i	−0.711974	+	0.259137i	−0.0394593	+	0.999221i	$0.512564\pi$
$422$	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	$-0.928847\pi$
$433$		−	9.22565i		−	0.443356i	0.975120	−	0.221678i	$-0.0711534\pi$
$434$	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	−0.878027	−	0.478612i	$-0.841140\pi$
$439$	2.32033	−	13.1592i	0.110743	−	0.628057i	0.988770	−	0.149445i	$-0.0477487\pi$
$440$		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	0.986409	−	0.164308i	$-0.0525390\pi$
$443$	2.63433	+	7.23777i	0.125161	+	0.343877i	−0.861248	+	0.508184i	$0.830317\pi$
$444$	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	−0.919690	−	0.392645i	$-0.871560\pi$
$449$	−16.9493	−	29.3570i	−0.799886	−	1.38544i	0.119805	−	0.992797i	$-0.461773\pi$
$450$		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	−0.227182	−	0.973852i	$-0.572951\pi$
$457$	16.4891	−	19.6509i	0.771325	−	0.919230i	0.998507	+	0.0546225i	$0.0173956\pi$
$458$			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	0.865725	−	0.500520i	$-0.166858\pi$
$461$	11.2323	+	9.42502i	0.523140	+	0.438967i	−0.342585	+	0.939487i	$0.611302\pi$
$462$	50.6586	−	58.9746i	2.35685	−	2.74375i
$463$	−0.536066	+	0.0945229i	−0.0249131	+	0.00439285i	−0.186091	−	0.982533i	$-0.559582\pi$
$463$	−0.536066	+	0.0945229i	−0.0249131	+	0.00439285i	0.161178	+	0.986925i	$0.448471\pi$
$464$	−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	−0.977086	−	0.212845i	$-0.931727\pi$
$467$	−35.6559	−	20.5859i	−1.64996	−	0.952604i	−0.672872	−	0.739759i	$-0.734940\pi$
$468$	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	−0.999222	−	0.0394312i	$-0.987445\pi$
$479$	−1.02370	+	5.80571i	−0.0467742	+	0.265270i	0.952448	+	0.304701i	$0.0985565\pi$
$480$		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	$-0.913025\pi$
$487$		−	11.9102i		−	0.539704i	0.962902	−	0.269852i	$-0.0869748\pi$
$488$	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	−0.606060	−	0.795419i	$-0.707251\pi$
$491$	−35.0462	−	12.7558i	−1.58161	−	0.575661i	−0.975554	+	0.219758i	$0.929473\pi$
$492$	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	−0.266911	−	0.963721i	$-0.586003\pi$
$499$	14.2032	−	11.9179i	0.635821	−	0.533517i	0.902732	+	0.430204i	$0.141558\pi$
$500$		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	−0.985446	−	0.169987i	$-0.945627\pi$
$503$	−29.8502	+	17.2340i	−1.33096	+	0.768428i	−0.345510	+	0.938415i	$0.612294\pi$
$504$	−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	−0.913262	−	0.407373i	$-0.866445\pi$
$509$	−4.38600	−	24.8743i	−0.194406	−	1.10253i	0.718856	−	0.695159i	$-0.244666\pi$
$510$		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	−0.712854	−	0.701312i	$-0.752598\pi$
$521$	5.72752	−	9.92036i	0.250927	−	0.434619i	0.963781	+	0.266693i	$0.0859311\pi$
$522$	13.7655	+	2.75674i	0.602497	+	0.120659i
$523$	25.0507	−	14.4630i	1.09539	−	0.632424i	0.160384	−	0.987055i	$-0.448727\pi$
$523$	25.0507	−	14.4630i	1.09539	−	0.632424i	0.935006	+	0.354631i	$0.115393\pi$
$524$	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	0.559811	−	0.828620i	$-0.310874\pi$
$547$	18.7679	+	3.30929i	0.802457	+	0.141495i	0.242646	+	0.970115i	$0.421985\pi$
$548$	−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	−0.930504	−	0.366281i	$-0.880631\pi$
$557$	−25.4546	+	14.6962i	−1.07855	+	0.622700i	−0.148044	+	0.988981i	$0.547298\pi$
$558$	−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	0.382773	−	0.923842i	$-0.374969\pi$
$563$	25.1141	−	4.42830i	1.05844	−	0.186631i	0.675662	+	0.737212i	$0.263858\pi$
$564$	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	0.783258	−	0.621697i	$-0.213556\pi$
$569$	7.32350	+	6.14515i	0.307017	+	0.257618i	−0.476241	+	0.879315i	$0.658001\pi$
$570$		0			0
$571$	5.37062	+	30.4583i	0.224754	+	1.27464i	0.863156	+	0.504938i	$0.168485\pi$
$571$	5.37062	+	30.4583i	0.224754	+	1.27464i	−0.638402	+	0.769703i	$0.720404\pi$
$572$	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	−0.982474	−	0.186400i	$-0.940318\pi$
$577$	−31.5221	+	18.1993i	−1.31228	+	0.757647i	−0.329810	+	0.944047i	$0.606985\pi$
$578$	−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	−0.725415	−	0.688312i	$-0.758352\pi$
$587$	−39.7946	−	7.01686i	−1.64250	−	0.289617i	−0.917083	+	0.398696i	$0.869463\pi$
$588$	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	$-0.921877\pi$
$593$		−	11.8336i		−	0.485946i	0.970033	−	0.242973i	$-0.0781226\pi$
$594$	−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	0.156602	−	0.987662i	$-0.449946\pi$
$599$	−8.76898	−	3.19165i	−0.358291	−	0.130407i	−0.514893	+	0.857255i	$0.672168\pi$
$600$		0			0
$601$	3.42397	−	19.4183i	0.139667	−	0.792088i	−0.831829	−	0.555032i	$-0.812706\pi$
$601$	3.42397	−	19.4183i	0.139667	−	0.792088i	0.971496	−	0.237057i	$-0.0761827\pi$
$602$	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	0.992255	+	0.124221i	$0.0396430\pi$
$607$	23.2154	+	27.6671i	0.942285	+	1.12297i	−0.0499698	+	0.998751i	$0.515913\pi$
$608$	−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	0.566946	−	0.823755i	$-0.308125\pi$
$613$	3.39263	+	1.95873i	0.137027	+	0.0791125i	−0.429919	+	0.902867i	$0.641458\pi$
$614$	−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	−0.844180	−	0.536060i	$-0.819912\pi$
$617$	−36.1192	+	6.36880i	−1.45411	+	0.256398i	−0.609926	+	0.792458i	$0.708801\pi$
$618$	−11.4011	−	32.4877i	−0.458618	−	1.30685i
$619$	−8.22380	−	6.90059i	−0.330543	−	0.277358i	0.462378	−	0.886683i	$-0.346996\pi$
$619$	−8.22380	−	6.90059i	−0.330543	−	0.277358i	−0.792921	+	0.609325i	$0.791441\pi$
$620$		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	0.831967	−	0.554825i	$-0.187215\pi$
$631$	−1.62045	−	2.80670i	−0.0645090	−	0.111733i	−0.896476	+	0.443092i	$0.853881\pi$
$632$	−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	−0.972752	−	0.231849i	$-0.925523\pi$
$641$	0.522380	−	2.96256i	0.0206328	−	0.117014i	0.993385	+	0.114834i	$0.0366337\pi$
$642$	40.3372	+	49.2162i	1.59198	+	1.94241i
$643$	−12.9452	+	35.5666i	−0.510509	+	1.40261i	0.370200	+	0.928952i	$0.379289\pi$
$643$	−12.9452	+	35.5666i	−0.510509	+	1.40261i	−0.880708	+	0.473659i	$0.842933\pi$
$644$	−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	$0.0833353\pi$
$647$			13.1670i			0.517650i	−0.965924	+	0.258825i	$0.916665\pi$
$648$	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	−0.735771	−	0.677230i	$-0.763180\pi$
$653$	6.72520	−	18.4773i	0.263177	−	0.723074i	0.998949	−	0.0458437i	$-0.0145976\pi$
$654$	−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	−0.659338	−	0.751846i	$-0.729164\pi$
$659$	−17.4856	+	6.36425i	−0.681143	+	0.247916i	−0.0218050	+	0.999762i	$0.506941\pi$
$660$		0			0
$661$	−26.9451	+	22.6096i	−1.04804	+	0.879412i	−0.992886	−	0.119066i	$-0.962010\pi$
$661$	−26.9451	+	22.6096i	−1.04804	+	0.879412i	−0.0551562	+	0.998478i	$0.517566\pi$
$662$	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	−0.401042	−	0.916060i	$-0.631352\pi$
$673$	14.8063	−	17.6455i	0.570741	−	0.680183i	0.971783	+	0.235877i	$0.0757962\pi$
$674$	57.7859			2.22583
$675$		0			0
$676$	72.1928			2.77665
$677$	−7.97061	+	9.49900i	−0.306335	+	0.365076i	−0.897146	−	0.441734i	$-0.854364\pi$
$677$	−7.97061	+	9.49900i	−0.306335	+	0.365076i	0.590811	+	0.806810i	$0.298808\pi$
$678$	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	0.593298	−	0.804983i	$-0.297826\pi$
$683$	5.03898	+	2.90926i	0.192811	+	0.111320i	−0.400487	+	0.916303i	$0.631159\pi$
$684$	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	−0.419762	−	0.907634i	$-0.637886\pi$
$691$	−4.15074	+	1.51075i	−0.157902	+	0.0574715i	0.261860	+	0.965106i	$0.415664\pi$
$692$	−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	−0.937956	−	0.346754i	$-0.887284\pi$
$709$	1.65171	−	9.36728i	0.0620311	−	0.351796i	0.999987	−	0.00504202i	$-0.00160493\pi$
$710$		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	0.987663	−	0.156593i	$-0.0500510\pi$
$719$	9.60533	+	16.6369i	0.358218	+	0.620452i	−0.629445	+	0.777045i	$0.716718\pi$
$720$		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	−0.159960	−	0.987124i	$-0.551136\pi$
$727$	22.6474	−	26.9901i	0.839944	−	1.00101i	0.999904	−	0.0138826i	$-0.00441911\pi$
$728$		−	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	0.114430	−	0.993431i	$-0.463496\pi$
$733$	15.2083	−	2.68164i	0.561732	−	0.0990485i	0.447302	+	0.894383i	$0.352385\pi$
$734$	−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	0.961076	−	0.276285i	$-0.0891035\pi$
$739$	6.55875	+	11.3601i	0.241268	+	0.417888i	−0.719808	+	0.694173i	$0.755770\pi$
$740$		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	0.564790	−	0.825234i	$-0.308957\pi$
$743$	−9.43078	−	11.2392i	−0.345982	−	0.412325i	−0.910772	+	0.412909i	$0.864513\pi$
$744$	−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	0.0796384	−	0.996824i	$-0.474623\pi$
$751$	−13.7050	−	4.98820i	−0.500101	−	0.182022i	−0.579739	+	0.814802i	$0.696846\pi$
$752$	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	$0.0790518\pi$
$757$			13.5259i			0.491607i	−0.969320	+	0.245803i	$0.920948\pi$
$758$	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	−0.308918	−	0.951089i	$-0.599967\pi$
$761$	−31.9148	−	11.6160i	−1.15691	−	0.421081i	−0.847993	+	0.530008i	$0.822189\pi$
$762$	−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	−0.615018	−	0.788513i	$-0.710851\pi$
$769$	1.51739	−	1.27324i	0.0547184	−	0.0459142i	0.669737	+	0.742599i	$0.266407\pi$
$770$		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	0.707519	−	0.706694i	$-0.249814\pi$
$773$	46.5224	−	26.8597i	1.67329	−	0.966077i	0.965775	−	0.259382i	$-0.0835190\pi$
$774$	−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	0.131900	−	0.991263i	$-0.457892\pi$
$787$	16.6884	−	2.94262i	0.594877	−	0.104893i	0.462977	+	0.886370i	$0.346781\pi$
$788$	−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	0.767890	−	0.640582i	$-0.221307\pi$
$797$	0.104393	+	0.124410i	0.00369778	+	0.00440684i	−0.764192	+	0.644988i	$0.776862\pi$
$798$	−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	−0.473706	−	0.880683i	$-0.657084\pi$
$821$	−7.75048	+	2.82094i	−0.270493	+	0.0984516i	0.203212	+	0.979135i	$0.434862\pi$
$822$	−0.184932	+	15.9988i	−0.00645024	+	0.558021i
$823$	−2.77633	−	3.30870i	−0.0967768	−	0.115334i	0.715482	−	0.698631i	$-0.246207\pi$
$823$	−2.77633	−	3.30870i	−0.0967768	−	0.115334i	−0.812259	+	0.583297i	$0.801763\pi$
$824$	−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	−0.662111	−	0.749405i	$-0.730339\pi$
$827$	−9.89730	+	5.71421i	−0.344163	+	0.198703i	0.317948	+	0.948108i	$0.397006\pi$
$828$	−0.182974	+	7.91366i	−0.00635880	+	0.275019i
$829$	14.4282	−	24.9904i	0.501113	−	0.867954i	−0.498886	−	0.866668i	$-0.666257\pi$
$829$	14.4282	−	24.9904i	0.501113	−	0.867954i	0.999999	−	0.00128593i	$-0.000409323\pi$
$830$		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	0.862714	−	0.505692i	$-0.168763\pi$
$839$	14.9031	+	12.5052i	0.514513	+	0.431728i	−0.348201	+	0.937420i	$0.613207\pi$
$840$		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	0.944014	−	0.329905i	$-0.107017\pi$
$853$	0.256981	+	0.706049i	0.00879885	+	0.0241746i	−0.935215	+	0.354079i	$0.884794\pi$
$854$	−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	0.748695	−	0.662914i	$-0.230681\pi$
$857$	35.8762	+	6.32595i	1.22551	+	0.216090i	0.476813	+	0.879005i	$0.341792\pi$
$858$	−124.850	+	20.5294i	−4.26231	+	0.700863i
$859$	27.3052	+	9.93826i	0.931640	+	0.339089i	0.762859	−	0.646564i	$-0.223795\pi$
$859$	27.3052	+	9.93826i	0.931640	+	0.339089i	0.168781	+	0.985654i	$0.446017\pi$
$860$		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	$0.0135315\pi$
$863$			2.49689i			0.0849951i	−0.999097	+	0.0424975i	$0.986469\pi$
$864$	−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	0.212956	−	0.977062i	$-0.431691\pi$
$877$	−23.2839	−	27.7487i	−0.786241	−	0.937006i	−0.999197	+	0.0400561i	$0.987246\pi$
$878$	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	0.764661	−	0.644433i	$-0.222907\pi$
$881$	−5.21700	−	9.03610i	−0.175765	−	0.304434i	−0.940426	+	0.339999i	$0.889573\pi$
$882$	−47.2744	+	7.21330i	−1.59181	+	0.242885i
$883$	23.3890	+	13.5036i	0.787102	+	0.454434i	0.838941	−	0.544222i	$-0.183175\pi$
$883$	23.3890	+	13.5036i	0.787102	+	0.454434i	−0.0518393	+	0.998655i	$0.516508\pi$
$884$	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	0.0326390	−	0.999467i	$-0.489609\pi$
$887$	12.0663	−	2.12762i	0.405148	−	0.0714384i	0.372509	+	0.928029i	$0.378498\pi$
$888$	−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	0.962758	−	0.270365i	$-0.0871444\pi$
$907$	1.54965	+	4.25762i	0.0514552	+	0.141372i	−0.911303	+	0.411737i	$0.864922\pi$
$908$	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	−0.894755	−	0.446557i	$-0.852650\pi$
$911$	2.98118	−	16.9071i	0.0987710	−	0.560158i	0.993526	−	0.113601i	$-0.0362387\pi$
$912$	−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	−0.706185	−	0.708028i	$-0.749585\pi$
$929$	−24.1410	+	8.78662i	−0.792042	+	0.288280i	−0.0858572	+	0.996307i	$0.527363\pi$
$930$		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	−0.285748	−	0.958305i	$-0.592242\pi$
$937$	−38.5244	−	22.2421i	−1.25854	−	0.726617i	−0.972790	+	0.231688i	$0.925575\pi$
$938$	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	−0.981105	−	0.193476i	$-0.938024\pi$
$941$	−3.84491	−	21.8056i	−0.125341	−	0.710842i	0.855764	−	0.517366i	$-0.173087\pi$
$942$	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	−0.972628	−	0.232369i	$-0.925352\pi$
$947$	−17.6914	+	21.0838i	−0.574894	+	0.685131i	0.397734	+	0.917501i	$0.369797\pi$
$948$	−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	0.426939	−	0.904281i	$-0.359592\pi$
$953$	−4.40592	−	2.54376i	−0.142722	−	0.0824005i	−0.569661	+	0.821880i	$0.692925\pi$
$954$	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	−0.858612	−	0.512626i	$-0.828673\pi$
$967$	4.00003	−	10.9900i	0.128632	−	0.353414i	0.987245	+	0.159211i	$0.0508951\pi$
$968$	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	0.540182	+	0.841548i	$0.318355\pi$
$977$	−12.9578	+	35.6014i	−0.414558	+	1.13899i	−0.954740	+	0.297441i	$0.903867\pi$
$978$	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	0.691271	+	0.722595i	$0.257051\pi$
$983$	19.6332	+	53.9418i	0.626202	+	1.72048i	−0.0650694	+	0.997881i	$0.520727\pi$
$984$	−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	−0.554512	−	0.832176i	$-0.687095\pi$
$991$	13.9592	−	24.1781i	0.443430	−	0.768043i	0.997941	+	0.0641332i	$0.0204282\pi$
$992$	−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	−0.526727	−	0.850034i	$-0.676581\pi$
$997$	12.6888	−	15.1219i	0.401858	−	0.478916i	0.928586	+	0.371118i	$0.121026\pi$
$998$			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.124.3		132
5.2	odd	4		675.2.l.g.151.2	yes	66
5.3	odd	4		675.2.l.f.151.10	yes	66
5.4	even	2	inner	675.2.u.e.124.20		132
27.22	even	9	inner	675.2.u.e.49.20		132
135.22	odd	36		675.2.l.g.76.2	yes	66
135.49	even	18	inner	675.2.u.e.49.3		132
135.103	odd	36		675.2.l.f.76.10	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.10	✓	66	135.103	odd	36
675.2.l.f.151.10	yes	66	5.3	odd	4
675.2.l.g.76.2	yes	66	135.22	odd	36
675.2.l.g.151.2	yes	66	5.2	odd	4
675.2.u.e.49.3		132	135.49	even	18	inner
675.2.u.e.49.20		132	27.22	even	9	inner
675.2.u.e.124.3		132	1.1	even	1	trivial
675.2.u.e.124.20		132	5.4	even	2	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

Properties

Related objects

Downloads

Learn more