LMFDB - Embedded newform 875.2.bb.c.257.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

sage:traces = [288,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

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

Embedding invariants

Embedding label			257.11
Character	$\chi$	$=$	875.257
Dual form			875.2.bb.c.143.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0484513 - 0.924506i) q^{2} +(1.02662 - 0.831339i) q^{3} +(1.13668 + 0.119470i) q^{4} +(-0.718837 - 0.989394i) q^{6} +(0.0993238 + 2.64389i) q^{7} +(0.455170 - 2.87383i) q^{8} +(-0.260915 + 1.22751i) q^{9} +(0.769743 - 0.163614i) q^{11} +(1.26626 - 0.822316i) q^{12} +(-0.371838 + 0.729773i) q^{13} +(2.44910 + 0.0362743i) q^{14} +(-0.398891 - 0.0847869i) q^{16} +(6.94132 - 2.66452i) q^{17} +(1.12220 + 0.300692i) q^{18} +(-0.192403 - 1.83059i) q^{19} +(2.29993 + 2.63169i) q^{21} +(-0.113967 - 0.719560i) q^{22} +(-4.08126 - 0.213890i) q^{23} +(-1.92184 - 3.32873i) q^{24} +(0.656664 + 0.379125i) q^{26} +(2.55179 + 5.00818i) q^{27} +(-0.202965 + 3.01712i) q^{28} +(5.50382 - 7.57536i) q^{29} +(1.92037 - 4.31323i) q^{31} +(1.40844 - 5.25635i) q^{32} +(0.654214 - 0.807887i) q^{33} +(-2.12705 - 6.54639i) q^{34} +(-0.443227 + 1.36411i) q^{36} +(3.57509 + 5.50515i) q^{37} +(-1.70171 + 0.0891829i) q^{38} +(0.224953 + 1.05832i) q^{39} +(2.40999 - 0.783055i) q^{41} +(2.54445 - 1.99879i) q^{42} +(-1.79811 + 1.79811i) q^{43} +(0.894499 - 0.0940156i) q^{44} +(-0.395485 + 3.76279i) q^{46} +(-4.12878 + 10.7558i) q^{47} +(-0.479996 + 0.244570i) q^{48} +(-6.98027 + 0.525202i) q^{49} +(4.91096 - 8.50604i) q^{51} +(-0.509847 + 0.785095i) q^{52} +(-5.66273 - 6.99289i) q^{53} +(4.75373 - 2.11650i) q^{54} +(7.64330 + 0.917979i) q^{56} +(-1.71936 - 1.71936i) q^{57} +(-6.73680 - 5.45535i) q^{58} +(-7.62729 + 8.47097i) q^{59} +(-6.28292 + 5.65717i) q^{61} +(-3.89456 - 1.98438i) q^{62} +(-3.27131 - 0.567908i) q^{63} +(-5.56698 - 1.80882i) q^{64} +(-0.715198 - 0.643968i) q^{66} +(-0.327283 - 0.852602i) q^{67} +(8.20839 - 2.19943i) q^{68} +(-4.36771 + 3.17333i) q^{69} +(0.767293 + 0.557471i) q^{71} +(3.40889 + 1.30855i) q^{72} +(3.11233 + 2.02117i) q^{73} +(5.26276 - 3.03846i) q^{74} -2.10378i q^{76} +(0.509031 + 2.01886i) q^{77} +(0.989324 - 0.156693i) q^{78} +(-1.98946 - 4.46840i) q^{79} +(3.34390 + 1.48880i) q^{81} +(-0.607171 - 2.26599i) q^{82} +(5.14074 + 0.814213i) q^{83} +(2.29988 + 3.26616i) q^{84} +(1.57524 + 1.74948i) q^{86} +(-0.647369 - 12.3525i) q^{87} +(-0.119835 - 2.28659i) q^{88} +(0.386903 + 0.429700i) q^{89} +(-1.96637 - 0.910613i) q^{91} +(-4.61354 - 0.730712i) q^{92} +(-1.61426 - 6.02451i) q^{93} +(9.74379 + 4.33822i) q^{94} +(-2.92389 - 6.56715i) q^{96} +(-10.5745 + 1.67483i) q^{97} +(0.147349 + 6.47875i) q^{98} +0.987555i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.0484513	−	0.924506i	0.0342602	−	0.653724i	−0.926492	−	0.376315i	$-0.877191\pi$
$2$	0.0484513	−	0.924506i	0.0342602	−	0.653724i	0.960752	−	0.277409i	$-0.0894757\pi$
$3$	1.02662	−	0.831339i	0.592718	−	0.479974i	−0.285406	−	0.958407i	$-0.592128\pi$
$3$	1.02662	−	0.831339i	0.592718	−	0.479974i	0.878124	+	0.478433i	$0.158795\pi$
$4$	1.13668	+	0.119470i	0.568340	+	0.0597349i
$5$		0			0
$5$		0			0
$6$	−0.718837	−	0.989394i	−0.293464	−	0.403918i
$7$	0.0993238	+	2.64389i	0.0375409	+	0.999295i
$7$	0.0993238	+	2.64389i	0.0375409	+	0.999295i
$8$	0.455170	−	2.87383i	0.160927	−	1.01605i
$9$	−0.260915	+	1.22751i	−0.0869716	+	0.409169i
$10$		0			0
$11$	0.769743	−	0.163614i	0.232086	−	0.0493315i	−0.0904002	−	0.995906i	$-0.528815\pi$
$11$	0.769743	−	0.163614i	0.232086	−	0.0493315i	0.322487	+	0.946574i	$0.395481\pi$
$12$	1.26626	−	0.822316i	0.365537	−	0.237382i
$13$	−0.371838	+	0.729773i	−0.103129	+	0.202403i	−0.936805	−	0.349851i	$-0.886232\pi$
$13$	−0.371838	+	0.729773i	−0.103129	+	0.202403i	0.833676	+	0.552254i	$0.186232\pi$
$14$	2.44910	+	0.0362743i	0.654550	+	0.00969470i
$15$		0			0
$16$	−0.398891	−	0.0847869i	−0.0997228	−	0.0211967i
$17$	6.94132	−	2.66452i	1.68352	−	0.646242i	0.686774	−	0.726871i	$-0.259026\pi$
$17$	6.94132	−	2.66452i	1.68352	−	0.646242i	0.996744	+	0.0806290i	$0.0256929\pi$
$18$	1.12220	+	0.300692i	0.264504	+	0.0708737i
$19$	−0.192403	−	1.83059i	−0.0441402	−	0.419966i	−0.994171	−	0.107811i	$-0.965616\pi$
$19$	−0.192403	−	1.83059i	−0.0441402	−	0.419966i	0.950031	−	0.312155i	$-0.101051\pi$
$20$		0			0
$21$	2.29993	+	2.63169i	0.501887	+	0.574282i
$22$	−0.113967	−	0.719560i	−0.0242979	−	0.153411i
$23$	−4.08126	−	0.213890i	−0.851002	−	0.0445991i	−0.378154	−	0.925743i	$-0.623441\pi$
$23$	−4.08126	−	0.213890i	−0.851002	−	0.0445991i	−0.472848	+	0.881144i	$0.656774\pi$
$24$	−1.92184	−	3.32873i	−0.392294	−	0.679474i
$25$		0			0
$26$	0.656664	+	0.379125i	0.128782	+	0.0743525i
$27$	2.55179	+	5.00818i	0.491093	+	0.963824i
$28$	−0.202965	+	3.01712i	−0.0383569	+	0.570182i
$29$	5.50382	−	7.57536i	1.02203	−	1.40671i	0.111266	−	0.993791i	$-0.464509\pi$
$29$	5.50382	−	7.57536i	1.02203	−	1.40671i	0.910768	−	0.412919i	$-0.135491\pi$
$30$		0			0
$31$	1.92037	−	4.31323i	0.344909	−	0.774678i	−0.654911	−	0.755706i	$-0.727294\pi$
$31$	1.92037	−	4.31323i	0.344909	−	0.774678i	0.999820	−	0.0189722i	$-0.00603941\pi$
$32$	1.40844	−	5.25635i	0.248979	−	0.929201i
$33$	0.654214	−	0.807887i	0.113884	−	0.140635i
$34$	−2.12705	−	6.54639i	−0.364786	−	1.12270i
$35$		0			0
$36$	−0.443227	+	1.36411i	−0.0738712	+	0.227352i
$37$	3.57509	+	5.50515i	0.587740	+	0.905041i	0.999982	−	0.00603374i	$-0.00192061\pi$
$37$	3.57509	+	5.50515i	0.587740	+	0.905041i	−0.412241	+	0.911075i	$0.635254\pi$
$38$	−1.70171	+	0.0891829i	−0.276054	+	0.0144674i
$39$	0.224953	+	1.05832i	0.0360213	+	0.169467i
$40$		0			0
$41$	2.40999	−	0.783055i	0.376378	−	0.122293i	−0.114718	−	0.993398i	$-0.536596\pi$
$41$	2.40999	−	0.783055i	0.376378	−	0.122293i	0.491096	+	0.871106i	$0.336596\pi$
$42$	2.54445	−	1.99879i	0.392617	−	0.308420i
$43$	−1.79811	+	1.79811i	−0.274209	+	0.274209i	−0.830792	−	0.556583i	$-0.812112\pi$
$43$	−1.79811	+	1.79811i	−0.274209	+	0.274209i	0.556583	+	0.830792i	$0.312112\pi$
$44$	0.894499	−	0.0940156i	0.134851	−	0.0141734i
$45$		0			0
$46$	−0.395485	+	3.76279i	−0.0583111	+	0.554793i
$47$	−4.12878	+	10.7558i	−0.602244	+	1.56890i	0.205050	+	0.978751i	$0.434264\pi$
$47$	−4.12878	+	10.7558i	−0.602244	+	1.56890i	−0.807294	+	0.590149i	$0.799069\pi$
$48$	−0.479996	+	0.244570i	−0.0692814	+	0.0353006i
$49$	−6.98027	+	0.525202i	−0.997181	+	0.0750288i
$50$		0			0
$51$	4.91096	−	8.50604i	0.687673	−	1.19108i
$52$	−0.509847	+	0.785095i	−0.0707030	+	0.108873i
$53$	−5.66273	−	6.99289i	−0.777836	−	0.960547i	0.222060	−	0.975033i	$-0.428722\pi$
$53$	−5.66273	−	6.99289i	−0.777836	−	0.960547i	−0.999895	+	0.0144862i	$0.995389\pi$
$54$	4.75373	−	2.11650i	0.646900	−	0.288019i
$55$		0			0
$56$	7.64330	+	0.917979i	1.02138	+	0.122670i
$57$	−1.71936	−	1.71936i	−0.227735	−	0.227735i
$58$	−6.73680	−	5.45535i	−0.884585	−	0.716323i
$59$	−7.62729	+	8.47097i	−0.992989	+	1.10283i	0.00171029	+	0.999999i	$0.499456\pi$
$59$	−7.62729	+	8.47097i	−0.992989	+	1.10283i	−0.994699	+	0.102827i	$0.967211\pi$
$60$		0			0
$61$	−6.28292	+	5.65717i	−0.804446	+	0.724326i	−0.964872	−	0.262722i	$-0.915380\pi$
$61$	−6.28292	+	5.65717i	−0.804446	+	0.724326i	0.160426	+	0.987048i	$0.448713\pi$
$62$	−3.89456	−	1.98438i	−0.494609	−	0.252016i
$63$	−3.27131	−	0.567908i	−0.412146	−	0.0715497i
$64$	−5.56698	−	1.80882i	−0.695872	−	0.226103i
$65$		0			0
$66$	−0.715198	−	0.643968i	−0.0880348	−	0.0792669i
$67$	−0.327283	−	0.852602i	−0.0399840	−	0.104162i	0.912135	−	0.409891i	$-0.134433\pi$
$67$	−0.327283	−	0.852602i	−0.0399840	−	0.104162i	−0.952119	+	0.305729i	$0.901100\pi$
$68$	8.20839	−	2.19943i	0.995414	−	0.266720i
$69$	−4.36771	+	3.17333i	−0.525811	+	0.382024i
$70$		0			0
$71$	0.767293	+	0.557471i	0.0910610	+	0.0661597i	0.632384	−	0.774655i	$-0.282076\pi$
$71$	0.767293	+	0.557471i	0.0910610	+	0.0661597i	−0.541323	+	0.840815i	$0.682076\pi$
$72$	3.40889	+	1.30855i	0.401742	+	0.154214i
$73$	3.11233	+	2.02117i	0.364270	+	0.236560i	0.713776	−	0.700374i	$-0.246984\pi$
$73$	3.11233	+	2.02117i	0.364270	+	0.236560i	−0.349505	+	0.936934i	$0.613650\pi$
$74$	5.26276	−	3.03846i	0.611783	−	0.353213i
$75$		0			0
$76$		−	2.10378i		−	0.241320i
$77$	0.509031	+	2.01886i	0.0580094	+	0.230071i
$78$	0.989324	−	0.156693i	0.112019	−	0.0177420i
$79$	−1.98946	−	4.46840i	−0.223832	−	0.502735i	0.766366	−	0.642404i	$-0.222063\pi$
$79$	−1.98946	−	4.46840i	−0.223832	−	0.502735i	−0.990198	+	0.139669i	$0.955396\pi$
$80$		0			0
$81$	3.34390	+	1.48880i	0.371544	+	0.165422i
$82$	−0.607171	−	2.26599i	−0.0670509	−	0.250237i
$83$	5.14074	+	0.814213i	0.564269	+	0.0893715i	0.432051	−	0.901849i	$-0.357790\pi$
$83$	5.14074	+	0.814213i	0.564269	+	0.0893715i	0.132218	+	0.991221i	$0.457790\pi$
$84$	2.29988	+	3.26616i	0.250938	+	0.356367i
$85$		0			0
$86$	1.57524	+	1.74948i	0.169863	+	0.188652i
$87$	−0.647369	−	12.3525i	−0.0694053	−	1.32433i
$88$	−0.119835	−	2.28659i	−0.0127744	−	0.243751i
$89$	0.386903	+	0.429700i	0.0410117	+	0.0455481i	0.763302	−	0.646042i	$-0.223577\pi$
$89$	0.386903	+	0.429700i	0.0410117	+	0.0455481i	−0.722290	+	0.691590i	$0.756910\pi$
$90$		0			0
$91$	−1.96637	−	0.910613i	−0.206132	−	0.0954582i
$92$	−4.61354	−	0.730712i	−0.480994	−	0.0761820i
$93$	−1.61426	−	6.02451i	−0.167391	−	0.624713i
$94$	9.74379	+	4.33822i	1.00500	+	0.447453i
$95$		0			0
$96$	−2.92389	−	6.56715i	−0.298418	−	0.670257i
$97$	−10.5745	+	1.67483i	−1.07368	+	0.170054i	−0.668148	−	0.744029i	$-0.732913\pi$
$97$	−10.5745	+	1.67483i	−1.07368	+	0.170054i	−0.405529	+	0.914082i	$0.632913\pi$
$98$	0.147349	+	6.47875i	0.0148845	+	0.654452i
$99$			0.987555i			0.0992530i
$100$		0			0
$101$	−5.47339	+	3.16006i	−0.544622	+	0.314438i	−0.746950	−	0.664880i	$-0.768483\pi$
$101$	−5.47339	+	3.16006i	−0.544622	+	0.314438i	0.202328	+	0.979318i	$0.435149\pi$
$102$	−7.62594	−	4.95234i	−0.755081	−	0.490355i
$103$	−9.24375	−	3.54834i	−0.910814	−	0.349629i	−0.142569	−	0.989785i	$-0.545536\pi$
$103$	−9.24375	−	3.54834i	−0.910814	−	0.349629i	−0.768245	+	0.640156i	$0.778870\pi$
$104$	1.92800	+	1.40077i	0.189056	+	0.137357i
$105$		0			0
$106$	−6.73933	+	4.89641i	−0.654582	+	0.475581i
$107$	5.25791	−	1.40885i	0.508302	−	0.136199i	0.00445150	−	0.999990i	$-0.498583\pi$
$107$	5.25791	−	1.40885i	0.508302	−	0.136199i	0.503850	+	0.863791i	$0.331916\pi$
$108$	2.30225	+	5.99756i	0.221534	+	0.577115i
$109$	−12.1845	−	10.9709i	−1.16706	−	1.05083i	−0.997869	−	0.0652420i	$-0.979218\pi$
$109$	−12.1845	−	10.9709i	−1.16706	−	1.05083i	−0.169190	−	0.985583i	$-0.554115\pi$
$110$		0			0
$111$	8.24689	+	2.67958i	0.782760	+	0.254334i
$112$	0.184548	−	1.06304i	0.0174381	−	0.100448i
$113$	−8.36368	−	4.26151i	−0.786789	−	0.400889i	0.0139501	−	0.999903i	$-0.495559\pi$
$113$	−8.36368	−	4.26151i	−0.786789	−	0.400889i	−0.800739	+	0.599014i	$0.795559\pi$
$114$	−1.67287	+	1.50626i	−0.156678	+	0.141074i
$115$		0			0
$116$	7.16111	−	7.95322i	0.664893	−	0.738438i
$117$	−0.798784	−	0.646843i	−0.0738476	−	0.0598006i
$118$	7.46191	+	7.46191i	0.686924	+	0.686924i
$119$	7.73414	+	18.0874i	0.708987	+	1.65807i
$120$		0			0
$121$	−9.48326	+	4.22222i	−0.862115	+	0.383838i
$122$	4.92567	+	6.08270i	0.445949	+	0.550701i
$123$	1.82316	−	2.80742i	0.164389	−	0.253137i
$124$	2.69815	−	4.67333i	0.242301	−	0.419678i
$125$		0			0
$126$	−0.683534	+	2.99683i	−0.0608940	+	0.266979i
$127$	−2.59888	+	1.32420i	−0.230613	+	0.117503i	−0.565480	−	0.824762i	$-0.691309\pi$
$127$	−2.59888	+	1.32420i	−0.230613	+	0.117503i	0.334866	+	0.942266i	$0.391309\pi$
$128$	1.95833	−	5.10161i	0.173093	−	0.450923i
$129$	−0.351133	+	3.34081i	−0.0309156	+	0.294142i
$130$		0			0
$131$	−6.69495	+	0.703668i	−0.584941	+	0.0614797i	−0.392377	−	0.919805i	$-0.628347\pi$
$131$	−6.69495	+	0.703668i	−0.584941	+	0.0614797i	−0.192564	+	0.981284i	$0.561680\pi$
$132$	0.840150	−	0.840150i	0.0731256	−	0.0731256i
$133$	4.82076	−	0.690511i	0.418013	−	0.0598749i
$134$	−0.804093	+	0.261266i	−0.0694631	+	0.0225699i
$135$		0			0
$136$	−4.49791	−	21.1610i	−0.385693	−	1.81454i
$137$	19.4502	−	1.01934i	1.66175	−	0.0870884i	0.801840	−	0.597539i	$-0.203855\pi$
$137$	19.4502	−	1.01934i	1.66175	−	0.0870884i	0.859907	+	0.510451i	$0.170521\pi$
$138$	2.72214	+	4.19173i	0.231724	+	0.356824i
$139$	0.317252	−	0.976401i	0.0269090	−	0.0828172i	−0.936700	−	0.350133i	$-0.886137\pi$
$139$	0.317252	−	0.976401i	0.0269090	−	0.0828172i	0.963609	+	0.267315i	$0.0861365\pi$
$140$		0			0
$141$	4.70307	+	14.4746i	0.396070	+	1.21898i
$142$	0.552562	−	0.682357i	0.0463700	−	0.0572621i
$143$	−0.166819	+	0.622576i	−0.0139501	+	0.0520624i
$144$	0.208153	−	0.467520i	0.0173461	−	0.0389600i
$145$		0			0
$146$	2.01938	−	2.77944i	0.167125	−	0.230028i
$147$	−6.72945	+	6.34215i	−0.555036	+	0.523092i
$148$	3.40603	+	6.68471i	0.279974	+	0.549480i
$149$	9.86165	+	5.69362i	0.807897	+	0.466440i	0.846225	−	0.532825i	$-0.178870\pi$
$149$	9.86165	+	5.69362i	0.807897	+	0.466440i	−0.0383277	+	0.999265i	$0.512203\pi$
$150$		0			0
$151$	−5.54607	−	9.60607i	−0.451333	−	0.781731i	0.547136	−	0.837043i	$-0.315718\pi$
$151$	−5.54607	−	9.60607i	−0.451333	−	0.781731i	−0.998469	+	0.0553124i	$0.982385\pi$
$152$	−5.34838	−	0.280297i	−0.433811	−	0.0227351i
$153$	1.45963	+	9.21574i	0.118004	+	0.745049i
$154$	1.89111	−	0.372785i	0.152390	−	0.0300399i
$155$		0			0
$156$	0.129262	+	1.22985i	0.0103493	+	0.0984667i
$157$	−16.1035	−	4.31493i	−1.28520	−	0.344369i	−0.449365	−	0.893348i	$-0.648350\pi$
$157$	−16.1035	−	4.31493i	−1.28520	−	0.344369i	−0.835836	+	0.548979i	$0.815017\pi$
$158$	−4.22746	+	1.62277i	−0.336319	+	0.129101i
$159$	−11.6269	−	2.47138i	−0.922075	−	0.195993i
$160$		0			0
$161$	0.160134	−	10.8116i	0.0126203	−	0.852076i
$162$	1.53842	−	3.01932i	0.120870	−	0.237220i
$163$	17.2516	−	11.2033i	1.35125	−	0.877510i	0.352938	−	0.935647i	$-0.385183\pi$
$163$	17.2516	−	11.2033i	1.35125	−	0.877510i	0.998309	+	0.0581372i	$0.0185161\pi$
$164$	2.83294	−	0.602161i	0.221216	−	0.0470209i
$165$		0			0
$166$	1.00182	−	4.71319i	0.0777563	−	0.365815i
$167$	−0.739956	+	4.67190i	−0.0572595	+	0.361522i	0.942377	+	0.334553i	$0.108585\pi$
$167$	−0.739956	+	4.67190i	−0.0572595	+	0.361522i	−0.999636	+	0.0269687i	$0.991415\pi$
$168$	8.60990	−	5.41176i	0.664268	−	0.417526i
$169$	7.24690	+	9.97451i	0.557454	+	0.767270i
$170$		0			0
$171$	2.29726	+	0.241452i	0.175676	+	0.0184643i
$172$	−2.25870	+	1.82906i	−0.172224	+	0.139464i
$173$	−0.264149	+	5.04027i	−0.0200829	+	0.383204i	0.970035	+	0.242966i	$0.0781203\pi$
$173$	−0.264149	+	5.04027i	−0.0200829	+	0.383204i	−0.990118	+	0.140239i	$0.955213\pi$
$174$	−11.4514			−0.868126
$175$		0			0
$176$	−0.320916			−0.0241900
$177$	−0.788072	+	15.0373i	−0.0592351	+	1.13027i
$178$	0.416006	−	0.336875i	0.0311810	−	0.0252498i
$179$	3.59011	+	0.377335i	0.268337	+	0.0282034i	0.237741	−	0.971328i	$-0.423593\pi$
$179$	3.59011	+	0.377335i	0.268337	+	0.0282034i	0.0305957	+	0.999532i	$0.490260\pi$
$180$		0			0
$181$	7.29441	+	10.0399i	0.542189	+	0.746259i	0.988927	−	0.148406i	$-0.0474142\pi$
$181$	7.29441	+	10.0399i	0.542189	+	0.746259i	−0.446737	+	0.894665i	$0.647414\pi$
$182$	−0.937141	+	1.77380i	−0.0694655	+	0.131483i
$183$	−1.74714	+	11.0310i	−0.129152	+	0.815434i
$184$	−2.47235	+	11.6315i	−0.182264	+	0.857486i
$185$		0			0
$186$	−5.64791	+	1.20050i	−0.414125	+	0.0880250i
$187$	4.90708	−	3.18670i	0.358841	−	0.233034i
$188$	−5.97810	+	11.7327i	−0.435998	+	0.855694i
$189$	−12.9876	+	7.24408i	−0.944709	+	0.526930i
$190$		0			0
$191$	−22.6901	−	4.82293i	−1.64180	−	0.348975i	−0.707845	−	0.706367i	$-0.750333\pi$
$191$	−22.6901	−	4.82293i	−1.64180	−	0.348975i	−0.933954	+	0.357392i	$0.883666\pi$
$192$	−7.21890	+	2.77108i	−0.520979	+	0.199985i
$193$	−14.4367	−	3.86831i	−1.03918	−	0.278447i	−0.301406	−	0.953496i	$-0.597456\pi$
$193$	−14.4367	−	3.86831i	−1.03918	−	0.278447i	−0.737773	+	0.675049i	$0.764123\pi$
$194$	1.03605	+	9.85732i	0.0743838	+	0.707715i
$195$		0			0
$196$	−7.99708	−	0.236946i	−0.571220	−	0.0169247i
$197$	0.235850	+	1.48910i	0.0168036	+	0.106094i	0.994665	−	0.103162i	$-0.0328960\pi$
$197$	0.235850	+	1.48910i	0.0168036	+	0.106094i	−0.977861	+	0.209256i	$0.932896\pi$
$198$	0.913001	+	0.0478483i	0.0648841	+	0.00340043i
$199$	1.75472	+	3.03927i	0.124389	+	0.215448i	0.921494	−	0.388393i	$-0.126970\pi$
$199$	1.75472	+	3.03927i	0.124389	+	0.215448i	−0.797105	+	0.603841i	$0.793636\pi$
$200$		0			0
$201$	−1.04480	−	0.603214i	−0.0736943	−	0.0425474i
$202$	2.65630	+	5.21329i	0.186897	+	0.366806i
$203$	20.5751	+	13.7991i	1.44409	+	0.968505i
$204$	6.59841	−	9.08193i	0.461981	−	0.635863i
$205$		0			0
$206$	−3.72834	+	8.37398i	−0.259766	+	0.583443i
$207$	1.32741	−	4.95398i	0.0922616	−	0.344325i
$208$	0.210198	−	0.259573i	0.0145746	−	0.0179982i
$209$	−0.447610	−	1.37760i	−0.0309619	−	0.0952908i
$210$		0			0
$211$	−6.16756	+	18.9818i	−0.424593	+	1.30676i	0.478791	+	0.877929i	$0.341075\pi$
$211$	−6.16756	+	18.9818i	−0.424593	+	1.30676i	−0.903384	+	0.428833i	$0.858925\pi$
$212$	−5.60127	−	8.62520i	−0.384697	−	0.592381i
$213$	1.25116	−	0.0655708i	0.0857284	−	0.00449283i
$214$	−1.04774	−	4.92923i	−0.0716221	−	0.336955i
$215$		0			0
$216$	15.5542	−	5.05385i	1.05833	−	0.343871i
$217$	11.5944	+	4.64884i	0.787080	+	0.315584i
$218$	−10.7331	+	10.7331i	−0.726934	+	0.726934i
$219$	4.87545	−	0.512430i	0.329452	−	0.0346268i
$220$		0			0
$221$	−0.636549	+	6.05636i	−0.0428189	+	0.407395i
$222$	2.87686	−	7.49447i	0.193082	−	0.502996i
$223$	7.80285	−	3.97575i	0.522518	−	0.266236i	−0.172777	−	0.984961i	$-0.555274\pi$
$223$	7.80285	−	3.97575i	0.522518	−	0.266236i	0.695294	+	0.718725i	$0.255274\pi$
$224$	14.0371	+	3.20166i	0.937893	+	0.213920i
$225$		0			0
$226$	−4.34502	+	7.52579i	−0.289026	+	0.500608i
$227$	5.11458	−	7.87576i	0.339467	−	0.522733i	−0.627171	−	0.778882i	$-0.715787\pi$
$227$	5.11458	−	7.87576i	0.339467	−	0.522733i	0.966637	+	0.256149i	$0.0824538\pi$
$228$	−1.74895	−	2.15978i	−0.115827	−	0.143035i
$229$	7.85820	−	3.49870i	0.519285	−	0.231200i	−0.130321	−	0.991472i	$-0.541601\pi$
$229$	7.85820	−	3.49870i	0.519285	−	0.231200i	0.649606	+	0.760271i	$0.274934\pi$
$230$		0			0
$231$	2.20094	+	1.64942i	0.144811	+	0.108524i
$232$	−19.2651	−	19.2651i	−1.26482	−	1.26482i
$233$	−2.16487	−	1.75308i	−0.141825	−	0.114848i	0.555782	−	0.831328i	$-0.312419\pi$
$233$	−2.16487	−	1.75308i	−0.141825	−	0.114848i	−0.697608	+	0.716480i	$0.745752\pi$
$234$	−0.636712	+	0.707140i	−0.0416232	+	0.0462272i
$235$		0			0
$236$	−9.68182	+	8.71755i	−0.630233	+	0.567464i
$237$	−5.75718	−	2.93343i	−0.373969	−	0.190547i
$238$	17.0967	−	6.27390i	1.10821	−	0.406676i
$239$	−10.2364	−	3.32600i	−0.662136	−	0.215141i	−0.0413782	−	0.999144i	$-0.513175\pi$
$239$	−10.2364	−	3.32600i	−0.662136	−	0.215141i	−0.620757	+	0.784003i	$0.713175\pi$
$240$		0			0
$241$	7.84239	+	7.06132i	0.505173	+	0.454860i	0.881881	−	0.471472i	$-0.156277\pi$
$241$	7.84239	+	7.06132i	0.505173	+	0.454860i	−0.376708	+	0.926332i	$0.622944\pi$
$242$	3.44399	+	8.97191i	0.221388	+	0.576736i
$243$	−11.6172	+	3.11283i	−0.745247	+	0.199688i
$244$	−7.81753	+	5.67977i	−0.500466	+	0.363610i
$245$		0			0
$246$	−2.50714	−	1.82155i	−0.159850	−	0.116137i
$247$	1.40746	+	0.540272i	0.0895543	+	0.0343767i
$248$	−11.5214	−	7.48208i	−0.731609	−	0.475113i
$249$	5.95446	−	3.43781i	0.377349	−	0.217862i
$250$		0			0
$251$			29.0617i			1.83436i	0.398477	+	0.917178i	$0.369539\pi$
$251$			29.0617i			1.83436i	−0.398477	+	0.917178i	$0.630461\pi$
$252$	−3.65058	−	1.03635i	−0.229965	−	0.0652841i
$253$	−3.17652	+	0.503111i	−0.199706	+	0.0316303i
$254$	1.09831	+	2.46684i	0.0689140	+	0.154783i
$255$		0			0
$256$	−15.3164	−	6.81930i	−0.957275	−	0.426206i
$257$	−4.81832	−	17.9822i	−0.300559	−	1.12170i	−0.936701	−	0.350129i	$-0.886138\pi$
$257$	−4.81832	−	17.9822i	−0.300559	−	1.12170i	0.636143	−	0.771571i	$-0.280529\pi$
$258$	3.07159	+	0.486492i	0.191229	+	0.0302876i
$259$	−14.1999	+	9.99891i	−0.882339	+	0.621302i
$260$		0			0
$261$	7.86279	+	8.73251i	0.486694	+	0.540529i
$262$	0.326166	+	6.22362i	0.0201506	+	0.384496i
$263$	1.08421	+	20.6879i	0.0668552	+	1.27567i	0.801819	+	0.597567i	$0.203866\pi$
$263$	1.08421	+	20.6879i	0.0668552	+	1.27567i	−0.734964	+	0.678106i	$0.762801\pi$
$264$	−2.02395	−	2.24783i	−0.124566	−	0.138344i
$265$		0			0
$266$	−0.404810	−	4.49027i	−0.0248205	−	0.275316i
$267$	0.754428	+	0.119490i	0.0461702	+	0.00731265i
$268$	−0.270156	−	1.00824i	−0.0165024	−	0.0615879i
$269$	1.17313	+	0.522309i	0.0715267	+	0.0318458i	0.442188	−	0.896922i	$-0.354202\pi$
$269$	1.17313	+	0.522309i	0.0715267	+	0.0318458i	−0.370661	+	0.928768i	$0.620869\pi$
$270$		0			0
$271$	5.04698	+	11.3357i	0.306582	+	0.688594i	0.999473	−	0.0324475i	$-0.0103302\pi$
$271$	5.04698	+	11.3357i	0.306582	+	0.688594i	−0.692891	+	0.721042i	$0.743664\pi$
$272$	−2.99475	+	0.474322i	−0.181583	+	0.0287600i
$273$	−2.77574	+	0.699867i	−0.167995	+	0.0423579i
$274$		−	18.0313i		−	1.08931i
$275$		0			0
$276$	−5.34381	+	3.08525i	−0.321660	+	0.185710i
$277$	−1.03160	−	0.669930i	−0.0619830	−	0.0402522i	0.513276	−	0.858224i	$-0.328432\pi$
$277$	−1.03160	−	0.669930i	−0.0619830	−	0.0402522i	−0.575259	+	0.817972i	$0.695099\pi$
$278$	−0.887317	−	0.340609i	−0.0532177	−	0.0204284i
$279$	4.79347	+	3.48266i	0.286977	+	0.208501i
$280$		0			0
$281$	1.42595	−	1.03602i	0.0850652	−	0.0618035i	−0.544440	−	0.838800i	$-0.683258\pi$
$281$	1.42595	−	1.03602i	0.0850652	−	0.0618035i	0.629505	+	0.776996i	$0.283258\pi$
$282$	13.6097	−	3.64670i	0.810445	−	0.217158i
$283$	5.40338	+	14.0763i	0.321198	+	0.836748i	0.995186	+	0.0980061i	$0.0312465\pi$
$283$	5.40338	+	14.0763i	0.321198	+	0.836748i	−0.673988	+	0.738742i	$0.735420\pi$
$284$	0.805566	+	0.725335i	0.0478016	+	0.0430407i
$285$		0			0
$286$	0.567492	+	0.184389i	0.0335565	+	0.0109032i
$287$	2.30968	+	6.29398i	0.136336	+	0.371522i
$288$	6.08473	+	3.10033i	0.358546	+	0.182689i
$289$	28.4488	−	25.6154i	1.67346	−	1.50679i
$290$		0			0
$291$	−9.46360	+	10.5104i	−0.554766	+	0.616130i
$292$	3.29625	+	2.66925i	0.192899	+	0.156206i
$293$	−2.74224	−	2.74224i	−0.160203	−	0.160203i	0.622454	−	0.782657i	$-0.286136\pi$
$293$	−2.74224	−	2.74224i	−0.160203	−	0.160203i	−0.782657	+	0.622454i	$0.786136\pi$
$294$	5.53731	+	6.52870i	0.322942	+	0.380762i
$295$		0			0
$296$	17.4482	−	7.76842i	1.01415	−	0.451530i
$297$	2.78363	+	3.43750i	0.161523	+	0.199464i
$298$	5.74160	−	8.84129i	0.332602	−	0.512162i
$299$	1.67366	−	2.89886i	0.0967902	−	0.167646i
$300$		0			0
$301$	−4.93259	−	4.57540i	−0.284310	−	0.263722i
$302$	−9.14958	+	4.66195i	−0.526499	+	0.268265i
$303$	−2.99200	+	7.79441i	−0.171886	+	0.447777i
$304$	−0.0784623	+	0.746519i	−0.00450012	+	0.0428158i
$305$		0			0
$306$	8.59073	−	0.902922i	0.491099	−	0.0516166i
$307$	−19.7851	+	19.7851i	−1.12920	+	1.12920i	−0.138889	+	0.990308i	$0.544353\pi$
$307$	−19.7851	+	19.7851i	−1.12920	+	1.12920i	−0.990308	+	0.138889i	$0.955647\pi$
$308$	0.337412	+	2.35562i	0.0192258	+	0.134224i
$309$	−12.4397	+	4.04190i	−0.707669	+	0.229935i
$310$		0			0
$311$	−4.40295	−	20.7142i	−0.249668	−	1.17460i	−0.907045	−	0.421034i	$-0.861667\pi$
$311$	−4.40295	−	20.7142i	−0.249668	−	1.17460i	0.657377	−	0.753562i	$-0.271666\pi$
$312$	3.14383	−	0.164761i	0.177984	−	0.00932777i
$313$	−2.61727	−	4.03024i	−0.147937	−	0.227802i	0.756932	−	0.653494i	$-0.226698\pi$
$313$	−2.61727	−	4.03024i	−0.147937	−	0.227802i	−0.904868	+	0.425692i	$0.860031\pi$
$314$	−4.76941	+	14.6787i	−0.269153	+	0.828369i
$315$		0			0
$316$	−1.72754	−	5.31683i	−0.0971818	−	0.299095i
$317$	18.7005	−	23.0932i	1.05033	−	1.29704i	0.0969400	−	0.995290i	$-0.469095\pi$
$317$	18.7005	−	23.0932i	1.05033	−	1.29704i	0.953386	−	0.301754i	$-0.0975722\pi$
$318$	−2.84814	+	10.6294i	−0.159716	+	0.596068i
$319$	2.99710	−	6.73159i	0.167805	−	0.376896i
$320$		0			0
$321$	4.22663	−	5.81746i	0.235908	−	0.324699i
$322$	−9.98766	−	0.671883i	−0.556591	−	0.0374426i
$323$	−6.21317	−	12.1940i	−0.345710	−	0.678495i
$324$	3.62308	+	2.09178i	0.201282	+	0.116210i
$325$		0			0
$326$	−9.52165	−	16.4920i	−0.527355	−	0.913406i
$327$	−21.6294	−	1.13355i	−1.19611	−	0.0626853i
$328$	−1.15341	−	7.28234i	−0.0636864	−	0.402100i
$329$	−28.8473	−	9.84771i	−1.59040	−	0.542922i
$330$		0			0
$331$	−2.40459	−	22.8781i	−0.132168	−	1.25749i	−0.836636	−	0.547759i	$-0.815481\pi$
$331$	−2.40459	−	22.8781i	−0.132168	−	1.25749i	0.704468	−	0.709735i	$-0.251185\pi$
$332$	5.74610	+	1.53966i	0.315358	+	0.0845000i
$333$	−7.69041	+	2.95207i	−0.421432	+	0.161772i
$334$	4.28334	+	0.910453i	0.234374	+	0.0498178i
$335$		0			0
$336$	−0.694290	−	1.24476i	−0.0378766	−	0.0679073i
$337$	−2.42351	+	4.75641i	−0.132017	+	0.259098i	−0.947547	−	0.319617i	$-0.896446\pi$
$337$	−2.42351	+	4.75641i	−0.132017	+	0.259098i	0.815530	+	0.578715i	$0.196446\pi$
$338$	9.57261	−	6.21653i	0.520681	−	0.338134i
$339$	−12.1291	+	2.57811i	−0.658760	+	0.140024i
$340$		0			0
$341$	0.772489	−	3.63428i	0.0418326	−	0.196807i
$342$	0.334529	−	2.11213i	0.0180893	−	0.114211i
$343$	−2.08188	−	18.4029i	−0.112411	−	0.993662i
$344$	4.34902	+	5.98591i	0.234484	+	0.322739i
$345$		0			0
$346$	4.64696	+	0.488415i	0.249822	+	0.0262573i
$347$	13.3772	−	10.8326i	0.718124	−	0.581525i	−0.199061	−	0.979987i	$-0.563789\pi$
$347$	13.3772	−	10.8326i	0.718124	−	0.581525i	0.917185	+	0.398462i	$0.130456\pi$
$348$	0.739905	−	14.1182i	0.0396631	−	0.756817i
$349$	−20.0775			−1.07472			−0.537362	−	0.843351i	$-0.680579\pi$
$349$	−20.0775			−1.07472			−0.537362	+	0.843351i	$0.680579\pi$
$350$		0			0
$351$	−4.60369			−0.245727
$352$	0.224121	−	4.27648i	0.0119457	−	0.227937i
$353$	10.0129	−	8.10825i	0.532931	−	0.431559i	−0.324706	−	0.945815i	$-0.605265\pi$
$353$	10.0129	−	8.10825i	0.532931	−	0.431559i	0.857637	+	0.514256i	$0.171932\pi$
$354$	13.8639	+	1.45715i	0.736858	+	0.0774469i
$355$		0			0
$356$	0.388449	+	0.534654i	0.0205878	+	0.0283366i
$357$	22.9768	+	12.1392i	1.21606	+	0.642473i
$358$	0.522794	−	3.30079i	0.0276305	−	0.174452i
$359$	−1.60689	+	7.55982i	−0.0848084	+	0.398992i	−0.999992	−	0.00404548i	$-0.998712\pi$
$359$	−1.60689	+	7.55982i	−0.0848084	+	0.398992i	0.915183	+	0.403038i	$0.132046\pi$
$360$		0			0
$361$	15.2708	−	3.24590i	0.803725	−	0.170837i
$362$	9.63536	−	6.25728i	0.506423	−	0.328875i
$363$	−6.22559	+	12.2184i	−0.326759	+	0.641300i
$364$	−2.12634	−	1.27000i	−0.111451	−	0.0665660i
$365$		0			0
$366$	10.1136	+	2.14970i	0.528644	+	0.112367i
$367$	3.08870	−	1.18564i	0.161229	−	0.0618899i	−0.276415	−	0.961038i	$-0.589146\pi$
$367$	3.08870	−	1.18564i	0.161229	−	0.0618899i	0.437644	+	0.899148i	$0.355813\pi$
$368$	1.60984	+	0.431357i	0.0839189	+	0.0224860i
$369$	0.332402	+	3.16260i	0.0173042	+	0.164638i
$370$		0			0
$371$	17.9260	−	15.6662i	0.930669	−	0.813347i
$372$	−1.11515	−	7.04080i	−0.0578180	−	0.365049i
$373$	3.79343	+	0.198805i	0.196416	+	0.0102937i	0.150290	−	0.988642i	$-0.451979\pi$
$373$	3.79343	+	0.198805i	0.196416	+	0.0102937i	0.0461259	+	0.998936i	$0.485312\pi$
$374$	−2.70837	−	4.69103i	−0.140046	−	0.242567i
$375$		0			0
$376$	29.0312	+	16.7612i	1.49717	+	0.864391i
$377$	3.48176	+	6.83335i	0.179320	+	0.351935i
$378$	6.06793	+	12.3581i	0.312101	+	0.635632i
$379$	17.8775	−	24.6063i	0.918306	−	1.26394i	−0.0459436	−	0.998944i	$-0.514629\pi$
$379$	17.8775	−	24.6063i	0.918306	−	1.26394i	0.964250	−	0.264996i	$-0.0853705\pi$
$380$		0			0
$381$	−1.56720	+	3.51999i	−0.0802902	+	0.180335i
$382$	−5.55820	+	20.7435i	−0.284382	+	1.06133i
$383$	12.7938	−	15.7990i	0.653732	−	0.807291i	−0.337232	−	0.941422i	$-0.609491\pi$
$383$	12.7938	−	15.7990i	0.653732	−	0.807291i	0.990964	+	0.134130i	$0.0428240\pi$
$384$	−2.23072	−	6.86544i	−0.113836	−	0.350350i
$385$		0			0
$386$	−4.27576	+	13.1594i	−0.217630	+	0.669797i
$387$	−1.73804	−	2.67635i	−0.0883496	−	0.136046i
$388$	−12.2199	+	0.640418i	−0.620372	+	0.0325123i
$389$	−2.32066	−	10.9179i	−0.117662	−	0.553558i	−0.997003	−	0.0773644i	$-0.975350\pi$
$389$	−2.32066	−	10.9179i	−0.117662	−	0.553558i	0.879341	−	0.476194i	$-0.157984\pi$
$390$		0			0
$391$	−28.8993	+	9.38994i	−1.46150	+	0.474870i
$392$	−1.66787	+	20.2992i	−0.0842401	+	1.02526i
$393$	−6.28817	+	6.28817i	−0.317196	+	0.317196i
$394$	1.38811	−	0.145896i	0.0699317	−	0.00735012i
$395$		0			0
$396$	−0.117983	+	1.12253i	−0.00592888	+	0.0564095i
$397$	−4.09363	+	10.6643i	−0.205453	+	0.535224i	−0.997129	−	0.0757170i	$-0.975875\pi$
$397$	−4.09363	+	10.6643i	−0.205453	+	0.535224i	0.791676	+	0.610941i	$0.209209\pi$
$398$	2.89484	−	1.47500i	0.145105	−	0.0739348i
$399$	4.37503	−	4.71657i	0.219025	−	0.236124i
$400$		0			0
$401$	14.5815	−	25.2559i	0.728165	−	1.26122i	−0.229493	−	0.973310i	$-0.573707\pi$
$401$	14.5815	−	25.2559i	0.728165	−	1.26122i	0.957658	−	0.287908i	$-0.0929597\pi$
$402$	−0.608296	+	0.936694i	−0.0303391	+	0.0467181i
$403$	2.43361	+	3.00526i	0.121227	+	0.149703i
$404$	−6.59902	+	2.93807i	−0.328314	+	0.146175i
$405$		0			0
$406$	13.7542	−	18.3532i	0.682610	−	0.910853i
$407$	3.65262	+	3.65262i	0.181054	+	0.181054i
$408$	−22.2096	−	17.9850i	−1.09954	−	0.890390i
$409$	21.5981	−	23.9872i	1.06796	−	1.18609i	0.0861370	−	0.996283i	$-0.472548\pi$
$409$	21.5981	−	23.9872i	1.06796	−	1.18609i	0.981822	−	0.189805i	$-0.0607856\pi$
$410$		0			0
$411$	19.1206	−	17.2162i	0.943147	−	0.849214i
$412$	−10.0833	−	5.13768i	−0.496767	−	0.253115i
$413$	−23.1538	−	19.3243i	−1.13933	−	0.950888i
$414$	−4.51566	−	1.46723i	−0.221933	−	0.0721103i
$415$		0			0
$416$	3.31224	+	2.98235i	0.162396	+	0.146222i
$417$	−0.486023	−	1.26613i	−0.0238007	−	0.0620029i
$418$	−1.29529	+	0.347072i	−0.0633547	+	0.0169758i
$419$	−22.7957	+	16.5620i	−1.11364	+	0.809109i	−0.983233	−	0.182351i	$-0.941629\pi$
$419$	−22.7957	+	16.5620i	−1.11364	+	0.809109i	−0.130410	+	0.991460i	$0.541629\pi$
$420$		0			0
$421$	−16.8306	−	12.2282i	−0.820274	−	0.595964i	0.0965173	−	0.995331i	$-0.469230\pi$
$421$	−16.8306	−	12.2282i	−0.820274	−	0.595964i	−0.916791	+	0.399368i	$0.869230\pi$
$422$	17.2500	+	6.62164i	0.839715	+	0.322337i
$423$	−12.1256	−	7.87447i	−0.589568	−	0.382870i
$424$	−22.6739	+	13.0908i	−1.10114	+	0.635744i
$425$		0			0
$426$		−	1.15989i		−	0.0561967i
$427$	−15.5810	−	16.0494i	−0.754015	−	0.776687i
$428$	6.14488	−	0.973254i	0.297024	−	0.0470440i
$429$	0.346312	+	0.777830i	0.0167201	+	0.0375540i
$430$		0			0
$431$	2.27190	+	1.01151i	0.109434	+	0.0487229i	0.460723	−	0.887544i	$-0.347590\pi$
$431$	2.27190	+	1.01151i	0.109434	+	0.0487229i	−0.351290	+	0.936267i	$0.614257\pi$
$432$	−0.593260	−	2.21408i	−0.0285432	−	0.106525i
$433$	9.13869	+	1.44743i	0.439178	+	0.0695589i	0.372108	−	0.928189i	$-0.378635\pi$
$433$	9.13869	+	1.44743i	0.439178	+	0.0695589i	0.0670695	+	0.997748i	$0.478635\pi$
$434$	4.85964	−	10.4939i	0.233270	−	0.503722i
$435$		0			0
$436$	−12.5391	−	13.9261i	−0.600516	−	0.666940i
$437$	0.393701	+	7.51226i	0.0188333	+	0.359360i
$438$	−0.237523	−	4.53221i	−0.0113493	−	0.216557i
$439$	14.2078	+	15.7793i	0.678099	+	0.753105i	0.979731	−	0.200319i	$-0.0641980\pi$
$439$	14.2078	+	15.7793i	0.678099	+	0.753105i	−0.301632	+	0.953425i	$0.597531\pi$
$440$		0			0
$441$	1.17657	−	8.70537i	0.0560270	−	0.414541i
$442$	5.56830	+	0.881932i	0.264857	+	0.0419492i
$443$	5.90047	+	22.0209i	0.280340	+	1.04624i	0.952178	+	0.305545i	$0.0988386\pi$
$443$	5.90047	+	22.0209i	0.280340	+	1.04624i	−0.671838	+	0.740698i	$0.734495\pi$
$444$	9.05395	+	4.03108i	0.429681	+	0.191306i
$445$		0			0
$446$	−3.29755	−	7.40641i	−0.156143	−	0.350704i
$447$	14.8575	−	2.35319i	0.702734	−	0.111302i
$448$	4.22938	−	14.8981i	0.199819	−	0.703870i
$449$		−	32.5816i		−	1.53762i	−0.639478	−	0.768809i	$-0.720850\pi$
$449$		−	32.5816i		−	1.53762i	0.639478	−	0.768809i	$-0.279150\pi$
$450$		0			0
$451$	1.72696	−	0.997060i	0.0813193	−	0.0469497i
$452$	−8.99770	−	5.84318i	−0.423216	−	0.274840i
$453$	−13.6796	−	5.25110i	−0.642723	−	0.246718i
$454$	−7.03338	−	5.11005i	−0.330093	−	0.239827i
$455$		0			0
$456$	−5.72376	+	4.15856i	−0.268040	+	0.194742i
$457$	−7.80380	+	2.09102i	−0.365046	+	0.0978138i	−0.436679	−	0.899617i	$-0.643846\pi$
$457$	−7.80380	+	2.09102i	−0.365046	+	0.0978138i	0.0716332	+	0.997431i	$0.477179\pi$
$458$	−2.85383	−	7.43447i	−0.133351	−	0.347390i
$459$	31.0572	+	27.9641i	1.44963	+	1.30525i
$460$		0			0
$461$	36.2181	+	11.7680i	1.68684	+	0.548089i	0.986220	−	0.165441i	$-0.0529046\pi$
$461$	36.2181	+	11.7680i	1.68684	+	0.548089i	0.700625	+	0.713530i	$0.252905\pi$
$462$	1.63154	−	1.95486i	0.0759061	−	0.0909485i
$463$	−32.7647	−	16.6944i	−1.52270	−	0.775856i	−0.525514	−	0.850785i	$-0.676127\pi$
$463$	−32.7647	−	16.6944i	−1.52270	−	0.775856i	−0.997189	+	0.0749286i	$0.976127\pi$
$464$	−2.83772	+	2.55509i	−0.131738	+	0.118617i
$465$		0			0
$466$	−1.72562	+	1.91650i	−0.0799378	+	0.0887799i
$467$	16.1817	+	13.1037i	0.748800	+	0.606366i	0.925874	−	0.377831i	$-0.123330\pi$
$467$	16.1817	+	13.1037i	0.748800	+	0.606366i	−0.177075	+	0.984197i	$0.556663\pi$
$468$	−0.830684	−	0.830684i	−0.0383984	−	0.0383984i
$469$	2.22168	−	0.949984i	0.102587	−	0.0438662i
$470$		0			0
$471$	−20.1193	+	8.95770i	−0.927050	+	0.412749i
$472$	20.8724	+	25.7753i	0.960731	+	1.18640i
$473$	−1.08989	+	1.67828i	−0.0501131	+	0.0771674i
$474$	−2.99091	+	5.18041i	−0.137377	+	0.237944i
$475$		0			0
$476$	6.63034	+	21.4836i	0.303901	+	0.984699i
$477$	10.0613	−	5.12650i	0.460676	−	0.234726i
$478$	−3.57087	+	9.30243i	−0.163328	+	0.425483i
$479$	−0.146303	+	1.39198i	−0.00668475	+	0.0636011i	−0.997356	−	0.0726744i	$-0.976847\pi$
$479$	−0.146303	+	1.39198i	−0.00668475	+	0.0636011i	0.990671	+	0.136276i	$0.0435133\pi$
$480$		0			0
$481$	−5.34686	+	0.561978i	−0.243796	+	0.0256240i
$482$	6.90821	−	6.90821i	0.314660	−	0.314660i
$483$	−8.82374	−	11.2325i	−0.401494	−	0.511099i
$484$	−11.2839	+	3.66635i	−0.512903	+	0.166652i
$485$		0			0
$486$	2.31496	+	10.8910i	0.105009	+	0.494027i
$487$	−26.5638	+	1.39215i	−1.20372	+	0.0630844i	−0.643624	−	0.765342i	$-0.722570\pi$
$487$	−26.5638	+	1.39215i	−1.20372	+	0.0630844i	−0.560098	+	0.828426i	$0.689237\pi$
$488$	13.3980	+	20.6310i	0.606497	+	0.933923i
$489$	8.39703	−	25.8434i	0.379727	−	1.16868i
$490$		0			0
$491$	0.0638187	+	0.196414i	0.00288010	+	0.00886403i	0.952486	−	0.304582i	$-0.0985166\pi$
$491$	0.0638187	+	0.196414i	0.00288010	+	0.00886403i	−0.949606	+	0.313446i	$0.898517\pi$
$492$	2.40775	−	2.97333i	0.108550	−	0.134048i
$493$	18.0191	−	67.2481i	0.811538	−	3.02870i
$494$	0.567678	−	1.27502i	0.0255410	−	0.0573661i
$495$		0			0
$496$	−1.13172	+	1.55769i	−0.0508159	+	0.0699421i
$497$	−1.39768	+	2.08401i	−0.0626945	+	0.0934805i
$498$	−2.88977	−	5.67150i	−0.129494	−	0.254146i
$499$	20.4454	+	11.8042i	0.915262	+	0.528427i	0.882120	−	0.471024i	$-0.156116\pi$
$499$	20.4454	+	11.8042i	0.915262	+	0.528427i	0.0331413	+	0.999451i	$0.489449\pi$
$500$		0			0
$501$	3.12428	+	5.41141i	0.139582	+	0.241764i
$502$	26.8677	+	1.40808i	1.19916	+	0.0628455i
$503$	−0.515396	−	3.25409i	−0.0229804	−	0.145092i	0.973530	−	0.228558i	$-0.0734011\pi$
$503$	−0.515396	−	3.25409i	−0.0229804	−	0.145092i	−0.996511	+	0.0834657i	$0.973401\pi$
$504$	−3.12108	+	9.14269i	−0.139024	+	0.407248i
$505$		0			0
$506$	0.311223	+	2.96109i	0.0138355	+	0.131636i
$507$	15.7320	+	4.21538i	0.698682	+	0.187211i
$508$	−3.11230	+	1.19470i	−0.138086	+	0.0530062i
$509$	−13.6817	−	2.90814i	−0.606431	−	0.128901i	−0.105545	−	0.994414i	$-0.533659\pi$
$509$	−13.6817	−	2.90814i	−0.606431	−	0.128901i	−0.500885	+	0.865514i	$0.666992\pi$
$510$		0			0
$511$	−5.03461	+	8.42939i	−0.222718	+	0.372894i
$512$	−2.08486	+	4.09177i	−0.0921387	+	0.180832i
$513$	8.67694	−	5.63487i	0.383096	−	0.248786i
$514$	−16.8581	+	3.58331i	−0.743580	+	0.158053i
$515$		0			0
$516$	−0.798253	+	3.75548i	−0.0351411	+	0.165326i
$517$	−1.41829	+	8.95476i	−0.0623765	+	0.393830i
$518$	8.55605	+	13.6123i	0.375931	+	0.598092i
$519$	3.91899	+	5.39402i	0.172024	+	0.236771i
$520$		0			0
$521$	28.2500	+	2.96919i	1.23765	+	0.130083i	0.700655	−	0.713500i	$-0.252891\pi$
$521$	28.2500	+	2.96919i	1.23765	+	0.130083i	0.536999	+	0.843583i	$0.319558\pi$
$522$	8.45422	−	6.84609i	0.370031	−	0.299645i
$523$	−2.07809	+	39.6524i	−0.0908687	+	1.73388i	0.450225	+	0.892915i	$0.351344\pi$
$523$	−2.07809	+	39.6524i	−0.0908687	+	1.73388i	−0.541094	+	0.840962i	$0.681990\pi$
$524$	−7.69409			−0.336118
$525$		0			0
$526$	19.1787			0.836229
$527$	1.83723	−	35.0564i	0.0800308	−	1.52708i
$528$	−0.329458	+	0.266790i	−0.0143378	+	0.0116105i
$529$	−6.26305	−	0.658273i	−0.272307	−	0.0286206i
$530$		0			0
$531$	−8.40811	−	11.5728i	−0.364881	−	0.502215i
$532$	5.56215	−	0.208955i	0.241150	−	0.00905937i
$533$	−0.324675	+	2.04992i	−0.0140632	+	0.0887918i
$534$	0.147022	−	0.691684i	0.00636226	−	0.0299321i
$535$		0			0
$536$	−2.59921	+	0.552478i	−0.112269	+	0.0238634i
$537$	3.99936	−	2.59722i	0.172585	−	0.112078i
$538$	0.539718	−	1.05926i	0.0232689	−	0.0456677i
$539$	−5.28709	+	1.54634i	−0.227731	+	0.0666056i
$540$		0			0
$541$	1.28954	+	0.274100i	0.0554417	+	0.0117845i	0.235549	−	0.971862i	$-0.424311\pi$
$541$	1.28954	+	0.274100i	0.0554417	+	0.0117845i	−0.180107	+	0.983647i	$0.557645\pi$
$542$	10.7244	−	4.11673i	0.460654	−	0.176829i
$543$	15.8351	+	4.24301i	0.679550	+	0.182085i
$544$	−4.22927	−	40.2389i	−0.181329	−	1.72523i
$545$		0			0
$546$	0.512543	+	2.60010i	0.0219348	+	0.111274i
$547$	−3.39018	−	21.4047i	−0.144953	−	0.915200i	−0.947766	−	0.318968i	$-0.896664\pi$
$547$	−3.39018	−	21.4047i	−0.144953	−	0.915200i	0.802812	−	0.596232i	$-0.203336\pi$
$548$	22.2305	+	1.16505i	0.949639	+	0.0497685i
$549$	−5.30491	−	9.18838i	−0.226408	−	0.392150i
$550$		0			0
$551$	−14.9263	−	8.61771i	−0.635882	−	0.367127i
$552$	7.13156	+	13.9965i	0.303539	+	0.595730i
$553$	11.6164	−	5.70373i	0.493978	−	0.242547i
$554$	−0.669337	+	0.921263i	−0.0284374	+	0.0391407i
$555$		0			0
$556$	0.477264	−	1.07195i	0.0202405	−	0.0454609i
$557$	2.91942	−	10.8954i	0.123700	−	0.461654i	−0.876090	−	0.482147i	$-0.839857\pi$
$557$	2.91942	−	10.8954i	0.123700	−	0.461654i	0.999790	+	0.0204931i	$0.00652362\pi$
$558$	3.45199	−	4.26285i	0.146134	−	0.180461i
$559$	−0.643607	−	1.98082i	−0.0272217	−	0.0837797i
$560$		0			0
$561$	2.38847	−	7.35097i	0.100841	−	0.310358i
$562$	−0.888713	−	1.36850i	−0.0374881	−	0.0577266i
$563$	4.94286	−	0.259044i	0.208317	−	0.0109174i	0.0521079	−	0.998641i	$-0.483406\pi$
$563$	4.94286	−	0.259044i	0.208317	−	0.0109174i	0.156209	+	0.987724i	$0.450073\pi$
$564$	3.61661	+	17.0148i	0.152287	+	0.716453i
$565$		0			0
$566$	13.2754	−	4.31344i	0.558007	−	0.181307i
$567$	−3.60409	+	8.98876i	−0.151358	+	0.377493i
$568$	1.95133	−	1.95133i	0.0818759	−	0.0818759i
$569$	−16.8195	+	1.76780i	−0.705109	+	0.0741099i	−0.450295	−	0.892880i	$-0.648681\pi$
$569$	−16.8195	+	1.76780i	−0.705109	+	0.0741099i	−0.254814	+	0.966990i	$0.582014\pi$
$570$		0			0
$571$	−3.00592	+	28.5994i	−0.125794	+	1.19685i	0.731434	+	0.681912i	$0.238851\pi$
$571$	−3.00592	+	28.5994i	−0.125794	+	1.19685i	−0.857228	+	0.514937i	$0.827815\pi$
$572$	−0.263999	+	0.687740i	−0.0110383	+	0.0287558i
$573$	−27.3036	+	13.9119i	−1.14062	+	0.581177i
$574$	5.93072	−	1.83036i	0.247544	−	0.0763977i
$575$		0			0
$576$	3.67285	−	6.36156i	0.153035	−	0.265065i
$577$	−5.65186	+	8.70310i	−0.235290	+	0.362315i	−0.936516	−	0.350624i	$-0.885970\pi$
$577$	−5.65186	+	8.70310i	−0.235290	+	0.362315i	0.701226	+	0.712939i	$0.252636\pi$
$578$	−22.3032	−	27.5422i	−0.927692	−	1.14560i
$579$	−18.0369	+	8.03054i	−0.749588	+	0.333738i
$580$		0			0
$581$	−1.64209	+	13.6724i	−0.0681253	+	0.567227i
$582$	9.25840	+	9.25840i	0.383773	+	0.383773i
$583$	−5.50298	−	4.45623i	−0.227910	−	0.184558i
$584$	7.22514	−	8.02433i	0.298978	−	0.332049i
$585$		0			0
$586$	−2.66808	+	2.40235i	−0.110217	+	0.0992401i
$587$	4.08885	+	2.08337i	0.168765	+	0.0859899i	0.536332	−	0.844007i	$-0.319809\pi$
$587$	4.08885	+	2.08337i	0.168765	+	0.0859899i	−0.367568	+	0.929997i	$0.619809\pi$
$588$	−8.40693	+	6.40503i	−0.346696	+	0.264139i
$589$	−8.26522	−	2.68553i	−0.340563	−	0.110655i
$590$		0			0
$591$	1.48007	+	1.33266i	0.0608820	+	0.0548184i
$592$	−0.959305	−	2.49908i	−0.0394272	−	0.102711i
$593$	−14.8803	+	3.98715i	−0.611059	+	0.163733i	−0.551060	−	0.834466i	$-0.685776\pi$
$593$	−14.8803	+	3.98715i	−0.611059	+	0.163733i	−0.0599990	+	0.998198i	$0.519110\pi$
$594$	3.31286	−	2.40693i	0.135928	−	0.0987577i
$595$		0			0
$596$	10.5293	+	7.65000i	0.431298	+	0.313356i
$597$	4.32809	+	1.66140i	0.177137	+	0.0679965i
$598$	−2.59893	−	1.68776i	−0.106278	−	0.0690177i
$599$	13.4466	−	7.76339i	0.549413	−	0.317204i	−0.199472	−	0.979903i	$-0.563923\pi$
$599$	13.4466	−	7.76339i	0.549413	−	0.317204i	0.748885	+	0.662700i	$0.230589\pi$
$600$		0			0
$601$		−	41.2449i		−	1.68241i	−0.540714	−	0.841207i	$-0.681846\pi$
$601$		−	41.2449i		−	1.68241i	0.540714	−	0.841207i	$-0.318154\pi$
$602$	−4.46898	+	4.33853i	−0.182142	+	0.176825i
$603$	1.13197	−	0.179286i	0.0460974	−	0.00730110i
$604$	−5.15647	−	11.5816i	−0.209814	−	0.471249i
$605$		0			0
$606$	7.06102	+	3.14377i	0.286834	+	0.127707i
$607$	−2.89077	−	10.7885i	−0.117333	−	0.437891i	0.882118	−	0.471028i	$-0.156117\pi$
$607$	−2.89077	−	10.7885i	−0.117333	−	0.437891i	−0.999451	+	0.0331368i	$0.989450\pi$
$608$	−9.89320	−	1.56693i	−0.401222	−	0.0635474i
$609$	32.5944	−	2.93847i	1.32079	−	0.119073i
$610$		0			0
$611$	−6.31408	−	7.01250i	−0.255441	−	0.283695i
$612$	0.558129	+	10.6497i	0.0225610	+	0.430490i
$613$	0.162396	+	3.09870i	0.00655911	+	0.125155i	0.999946	+	0.0103446i	$0.00329284\pi$
$613$	0.162396	+	3.09870i	0.00655911	+	0.125155i	−0.993387	+	0.114811i	$0.963374\pi$
$614$	17.3329	+	19.2501i	0.699497	+	0.776870i
$615$		0			0
$616$	6.03357	−	0.543942i	0.243099	−	0.0219161i
$617$	−45.2349	−	7.16450i	−1.82109	−	0.288432i	−0.849935	−	0.526888i	$-0.823359\pi$
$617$	−45.2349	−	7.16450i	−1.82109	−	0.288432i	−0.971153	+	0.238456i	$0.923359\pi$
$618$	3.13404	+	11.6964i	0.126070	+	0.470498i
$619$	−16.3273	−	7.26936i	−0.656248	−	0.292180i	0.0514712	−	0.998674i	$-0.483609\pi$
$619$	−16.3273	−	7.26936i	−0.656248	−	0.292180i	−0.707719	+	0.706494i	$0.750276\pi$
$620$		0			0
$621$	−9.34334	−	20.9855i	−0.374935	−	0.842119i
$622$	−19.3638	+	3.06692i	−0.776416	+	0.122972i
$623$	−1.09765	+	1.06561i	−0.0439764	+	0.0426927i
$624$		−	0.441228i		−	0.0176633i
$625$		0			0
$626$	−3.85279	+	2.22441i	−0.153988	+	0.0889052i
$627$	−1.60478	−	1.04216i	−0.0640887	−	0.0416197i
$628$	−17.7891	−	6.82858i	−0.709861	−	0.272490i
$629$	39.4844	+	28.6871i	1.57435	+	1.14383i
$630$		0			0
$631$	0.0581461	−	0.0422456i	0.00231476	−	0.00168177i	−0.586627	−	0.809857i	$-0.699545\pi$
$631$	0.0581461	−	0.0422456i	0.00231476	−	0.00168177i	0.588942	+	0.808175i	$0.299545\pi$
$632$	−13.7470	+	3.68350i	−0.546826	+	0.146522i
$633$	9.44859	+	24.6144i	0.375548	+	0.978335i
$634$	−20.4438	−	18.4076i	−0.811925	−	0.731061i
$635$		0			0
$636$	−12.9208	−	4.19823i	−0.512344	−	0.166471i
$637$	2.21225	−	5.28930i	0.0876526	−	0.209570i
$638$	−6.07818	−	3.09699i	−0.240637	−	0.122611i
$639$	−0.884499	+	0.796406i	−0.0349902	+	0.0315053i
$640$		0			0
$641$	−15.6503	+	17.3814i	−0.618149	+	0.686524i	−0.968192	−	0.250209i	$-0.919501\pi$
$641$	−15.6503	+	17.3814i	−0.618149	+	0.686524i	0.350042	+	0.936734i	$0.386167\pi$
$642$	−5.17349	−	4.18941i	−0.204181	−	0.165343i
$643$	20.9354	+	20.9354i	0.825611	+	0.825611i	0.986906	−	0.161295i	$-0.0515672\pi$
$643$	20.9354	+	20.9354i	0.825611	+	0.825611i	−0.161295	+	0.986906i	$0.551567\pi$
$644$	1.47369	−	12.2702i	0.0580714	−	0.483515i
$645$		0			0
$646$	−11.5745	+	5.15330i	−0.455393	+	0.202754i
$647$	−12.2729	−	15.1558i	−0.482499	−	0.595837i	0.476525	−	0.879161i	$-0.341896\pi$
$647$	−12.2729	−	15.1558i	−0.482499	−	0.595837i	−0.959024	+	0.283324i	$0.908563\pi$
$648$	5.80061	−	8.93215i	0.227869	−	0.350888i
$649$	−4.48509	+	7.76840i	−0.176055	+	0.304936i
$650$		0			0
$651$	15.7678	−	4.86631i	0.617989	−	0.190726i
$652$	20.9480	−	10.6735i	0.820385	−	0.418007i
$653$	−1.13219	+	2.94945i	−0.0443060	+	0.115421i	−0.953948	−	0.299972i	$-0.903023\pi$
$653$	−1.13219	+	2.94945i	−0.0443060	+	0.115421i	0.909642	+	0.415393i	$0.136356\pi$
$654$	−2.09594	+	19.9415i	−0.0819578	+	0.779776i
$655$		0			0
$656$	−1.02772	+	0.108018i	−0.0401257	+	0.00421738i
$657$	−3.29305	+	3.29305i	−0.128474	+	0.128474i
$658$	−10.5020	+	26.1924i	−0.409409	+	1.02108i
$659$	13.3517	−	4.33824i	0.520110	−	0.168994i	−0.0371852	−	0.999308i	$-0.511839\pi$
$659$	13.3517	−	4.33824i	0.520110	−	0.168994i	0.557295	+	0.830314i	$0.311839\pi$
$660$		0			0
$661$	2.64972	+	12.4660i	0.103062	+	0.484870i	0.999159	+	0.0410104i	$0.0130577\pi$
$661$	2.64972	+	12.4660i	0.103062	+	0.484870i	−0.896096	+	0.443859i	$0.853609\pi$
$662$	−21.2674	+	1.11458i	−0.826583	+	0.0433194i
$663$	4.38140	+	6.74676i	0.170159	+	0.262022i
$664$	4.67982	−	14.4030i	0.181612	−	0.558945i
$665$		0			0
$666$	2.35660	+	7.25286i	0.0913163	+	0.281043i
$667$	−24.0828	+	29.7398i	−0.932491	+	1.15153i
$668$	−1.39924	+	5.22205i	−0.0541384	+	0.202047i
$669$	4.70535	−	10.5684i	0.181919	−	0.408598i
$670$		0			0
$671$	−3.91065	+	5.38254i	−0.150969	+	0.207791i
$672$	17.0724	−	8.38270i	0.658582	−	0.323369i
$673$	14.9409	+	29.3231i	0.575928	+	1.13032i	0.976793	+	0.214185i	$0.0687095\pi$
$673$	14.9409	+	29.3231i	0.575928	+	1.13032i	−0.400865	+	0.916137i	$0.631290\pi$
$674$	4.27990	+	2.47100i	0.164856	+	0.0951795i
$675$		0			0
$676$	7.04576	+	12.2036i	0.270991	+	0.469370i
$677$	5.80896	+	0.304435i	0.223256	+	0.0117004i	0.163636	−	0.986521i	$-0.447678\pi$
$677$	5.80896	+	0.304435i	0.223256	+	0.0117004i	0.0596203	+	0.998221i	$0.481011\pi$
$678$	1.79581	+	11.3383i	0.0689677	+	0.435445i
$679$	−5.47837	−	27.7914i	−0.210241	−	1.06654i
$680$		0			0
$681$	−1.29671	−	12.3373i	−0.0496899	−	0.472768i
$682$	−3.32248	−	0.890256i	−0.127224	−	0.0340897i
$683$	16.4820	−	6.32684i	0.630666	−	0.242090i	−0.0219738	−	0.999759i	$-0.506995\pi$
$683$	16.4820	−	6.32684i	0.630666	−	0.242090i	0.652639	+	0.757669i	$0.273662\pi$
$684$	2.58241	+	0.548907i	0.0987408	+	0.0209880i
$685$		0			0
$686$	−17.1144	+	1.03307i	−0.653432	+	0.0394427i
$687$	5.15877	−	10.1247i	0.196819	−	0.386280i
$688$	0.869707	−	0.564794i	0.0331572	−	0.0215326i
$689$	7.20884	−	1.53229i	0.274635	−	0.0583754i
$690$		0			0
$691$	−7.24591	+	34.0893i	−0.275647	+	1.29682i	0.594527	+	0.804075i	$0.297339\pi$
$691$	−7.24591	+	34.0893i	−0.275647	+	1.29682i	−0.870175	+	0.492743i	$0.835994\pi$
$692$	−0.902413	+	5.69761i	−0.0343046	+	0.216591i
$693$	−2.61098	+	0.0980878i	−0.0991831	+	0.00372605i
$694$	−9.36667	−	12.8921i	−0.355554	−	0.489378i
$695$		0			0
$696$	−35.7938	−	3.76208i	−1.35676	−	0.142601i
$697$	14.6421	−	11.8569i	0.554608	−	0.449113i
$698$	−0.972782	+	18.5618i	−0.0368203	+	0.702574i
$699$	−3.67989			−0.139186
$700$		0			0
$701$	−5.86630			−0.221567			−0.110783	−	0.993845i	$-0.535336\pi$
$701$	−5.86630			−0.221567			−0.110783	+	0.993845i	$0.535336\pi$
$702$	−0.223055	+	4.25614i	−0.00841865	+	0.160637i
$703$	9.38980	−	7.60371i	0.354143	−	0.286779i
$704$	−4.58109	−	0.481492i	−0.172656	−	0.0181469i
$705$		0			0
$706$	−7.01099	−	9.64980i	−0.263862	−	0.363175i
$707$	−8.89848	−	14.1571i	−0.334662	−	0.532434i
$708$	−2.69229	+	16.9985i	−0.101183	+	0.638841i
$709$	−1.95872	+	9.21505i	−0.0735612	+	0.346078i	−0.999501	−	0.0315933i	$-0.989942\pi$
$709$	−1.95872	+	9.21505i	−0.0735612	+	0.346078i	0.925940	+	0.377672i	$0.123275\pi$
$710$		0			0
$711$	6.00408	−	1.27621i	0.225171	−	0.0478615i
$712$	1.41099	−	0.916309i	0.0528792	−	0.0343401i
$713$	−8.76010	+	17.1927i	−0.328068	+	0.643870i
$714$	12.3360	−	20.6540i	0.461663	−	0.772957i
$715$		0			0
$716$	4.03572	+	0.857819i	0.150822	+	0.0320582i
$717$	−13.2739	+	5.09536i	−0.495722	+	0.190290i
$718$	6.91124	+	1.85186i	0.257925	+	0.0691109i
$719$	−4.40181	−	41.8805i	−0.164160	−	1.56188i	−0.697879	−	0.716216i	$-0.745873\pi$
$719$	−4.40181	−	41.8805i	−0.164160	−	1.56188i	0.533719	−	0.845662i	$-0.320794\pi$
$720$		0			0
$721$	8.46329	−	24.7919i	0.315190	−	0.923297i
$722$	−2.26097	−	14.2752i	−0.0841445	−	0.531267i
$723$	13.9215	+	0.729594i	0.517746	+	0.0271339i
$724$	7.09194	+	12.2836i	0.263570	+	0.456517i
$725$		0			0
$726$	10.9944	+	6.34760i	0.408039	+	0.235581i
$727$	−5.76081	−	11.3062i	−0.213657	−	0.419325i	0.759159	−	0.650905i	$-0.225610\pi$
$727$	−5.76081	−	11.3062i	−0.213657	−	0.419325i	−0.972816	+	0.231580i	$0.925610\pi$
$728$	−3.51198	+	5.23653i	−0.130163	+	0.194079i
$729$	−15.7932	+	21.7374i	−0.584932	+	0.805090i
$730$		0			0
$731$	−7.69016	+	17.2724i	−0.284431	+	0.638842i
$732$	−3.30381	+	12.3300i	−0.122112	+	0.455729i
$733$	29.6824	−	36.6547i	1.09634	−	1.35387i	0.166449	−	0.986050i	$-0.446770\pi$
$733$	29.6824	−	36.6547i	1.09634	−	1.35387i	0.929896	−	0.367823i	$-0.119897\pi$
$734$	−0.946479	−	2.91296i	−0.0349352	−	0.107519i
$735$		0			0
$736$	−6.87248	+	21.1513i	−0.253323	+	0.779648i
$737$	−0.391422	−	0.602737i	−0.0144182	−	0.0222021i
$738$	2.93995	−	0.154076i	0.108221	−	0.00567162i
$739$	9.32981	+	43.8933i	0.343203	+	1.61464i	0.723875	+	0.689931i	$0.242359\pi$
$739$	9.32981	+	43.8933i	0.343203	+	1.61464i	−0.380673	+	0.924710i	$0.624308\pi$
$740$		0			0
$741$	1.89407	−	0.615420i	0.0695804	−	0.0226080i
$742$	−13.6149	−	17.3317i	−0.499820	−	0.636267i
$743$	−11.1530	+	11.1530i	−0.409164	+	0.409164i	−0.881447	−	0.472283i	$-0.843430\pi$
$743$	−11.1530	+	11.1530i	−0.409164	+	0.409164i	0.472283	+	0.881447i	$0.343430\pi$
$744$	−18.0482	+	1.89694i	−0.661680	+	0.0695453i
$745$		0			0
$746$	0.367593	−	3.49741i	0.0134585	−	0.128049i
$747$	−2.34075	+	6.09786i	−0.0856435	+	0.223109i
$748$	5.95850	−	3.03601i	0.217864	−	0.111007i
$749$	4.24708	+	13.7614i	0.155185	+	0.502830i
$750$		0			0
$751$	−21.6997	+	37.5850i	−0.791834	+	1.37150i	0.132996	+	0.991117i	$0.457540\pi$
$751$	−21.6997	+	37.5850i	−0.791834	+	1.37150i	−0.924830	+	0.380380i	$0.875793\pi$
$752$	2.55889	−	3.94034i	0.0933131	−	0.143689i
$753$	24.1601	+	29.8352i	0.880443	+	1.08726i
$754$	6.48617	−	2.88783i	0.236212	−	0.105168i
$755$		0			0
$756$	−15.6282	+	6.68258i	−0.568392	+	0.243043i
$757$	35.7542	+	35.7542i	1.29951	+	1.29951i	0.928716	+	0.370793i	$0.120914\pi$
$757$	35.7542	+	35.7542i	1.29951	+	1.29951i	0.370793	+	0.928716i	$0.379086\pi$
$758$	−21.8825	−	17.7201i	−0.794807	−	0.643622i
$759$	−2.84282	+	3.15727i	−0.103188	+	0.114602i
$760$		0			0
$761$	3.28308	−	2.95609i	0.119011	−	0.107158i	−0.607476	−	0.794338i	$-0.707818\pi$
$761$	3.28308	−	2.95609i	0.119011	−	0.107158i	0.726488	+	0.687179i	$0.241151\pi$
$762$	3.17832	+	1.61944i	0.115138	+	0.0586660i
$763$	27.7957	−	33.3040i	1.00627	−	1.20569i
$764$	−25.2152	−	8.19292i	−0.912255	−	0.296409i
$765$		0			0
$766$	−13.9864	−	12.5934i	−0.505349	−	0.455018i
$767$	−3.34577	−	8.71602i	−0.120809	−	0.314717i
$768$	−21.3932	+	5.73230i	−0.771962	+	0.206847i
$769$	29.9959	−	21.7933i	1.08168	−	0.785888i	0.103706	−	0.994608i	$-0.466930\pi$
$769$	29.9959	−	21.7933i	1.08168	−	0.785888i	0.977975	+	0.208720i	$0.0669299\pi$
$770$		0			0
$771$	−19.8959	−	14.4552i	−0.716533	−	0.520592i
$772$	−15.9478	−	6.12179i	−0.573974	−	0.220328i
$773$	5.44891	+	3.53856i	0.195984	+	0.127273i	0.638900	−	0.769290i	$-0.279390\pi$
$773$	5.44891	+	3.53856i	0.195984	+	0.127273i	−0.442917	+	0.896563i	$0.646056\pi$
$774$	−2.55851	+	1.47716i	−0.0919638	+	0.0530953i
$775$		0			0
$776$			31.1516i			1.11828i
$777$	−6.26539	+	22.0700i	−0.224769	+	0.791756i
$778$	−10.2061	+	1.61648i	−0.365905	+	0.0579537i
$779$	−1.89714	−	4.26104i	−0.0679721	−	0.152668i
$780$		0			0
$781$	0.681829	+	0.303570i	0.0243978	+	0.0108626i
$782$	7.28085	+	27.1725i	0.260363	+	0.971687i
$783$	51.9834	+	8.23336i	1.85773	+	0.294236i
$784$	2.82890	+	0.382337i	0.101032	+	0.0136549i
$785$		0			0
$786$	5.50878	+	6.11812i	0.196492	+	0.218226i
$787$	0.373328	+	7.12353i	0.0133077	+	0.253926i	0.997180	+	0.0750519i	$0.0239123\pi$
$787$	0.373328	+	7.12353i	0.0133077	+	0.253926i	−0.983872	+	0.178874i	$0.942754\pi$
$788$	0.0901835	+	1.72080i	0.00321265	+	0.0613011i
$789$	18.3118	+	20.3373i	0.651916	+	0.724026i
$790$		0			0
$791$	10.4362	−	22.5359i	0.371069	−	0.801284i
$792$	2.83807	+	0.449506i	0.100846	+	0.0159725i
$793$	−1.79222	−	6.68866i	−0.0636436	−	0.237521i
$794$	9.66083	+	4.30128i	0.342850	+	0.152647i
$795$		0			0
$796$	1.63146	+	3.66431i	0.0578255	+	0.129878i
$797$	29.5739	−	4.68404i	1.04756	−	0.165917i	0.391154	−	0.920325i	$-0.372076\pi$
$797$	29.5739	−	4.68404i	1.04756	−	0.165917i	0.656406	+	0.754408i	$0.272076\pi$
$798$	−4.14852	−	4.27326i	−0.146856	−	0.151272i
$799$			85.6610i			3.03047i
$800$		0			0
$801$	−0.628409	+	0.362812i	−0.0222037	+	0.0128193i
$802$	−22.6427	−	14.7044i	−0.799542	−	0.519229i
$803$	2.72638	+	1.04656i	0.0962120	+	0.0369323i
$804$	−1.11553	−	0.810483i	−0.0393418	−	0.0285835i
$805$		0			0
$806$	2.89629	−	2.10428i	0.102017	−	0.0741200i
$807$	1.63857	−	0.439053i	0.0576803	−	0.0154554i
$808$	6.59016	+	17.1680i	0.231841	+	0.603967i
$809$	−1.59024	−	1.43186i	−0.0559098	−	0.0503414i	0.640702	−	0.767790i	$-0.278643\pi$
$809$	−1.59024	−	1.43186i	−0.0559098	−	0.0503414i	−0.696612	+	0.717448i	$0.745310\pi$
$810$		0			0
$811$	11.1135	+	3.61100i	0.390248	+	0.126799i	0.497567	−	0.867425i	$-0.334227\pi$
$811$	11.1135	+	3.61100i	0.390248	+	0.126799i	−0.107319	+	0.994225i	$0.534227\pi$
$812$	21.7387	+	18.1432i	0.762878	+	0.636702i
$813$	14.6051	+	7.44168i	0.512224	+	0.260991i
$814$	3.55384	−	3.19989i	0.124562	−	0.112156i
$815$		0			0
$816$	−2.68014	+	2.97660i	−0.0938237	+	0.104202i
$817$	3.63756	+	2.94564i	0.127262	+	0.103055i
$818$	−21.1298	−	21.1298i	−0.738786	−	0.738786i
$819$	1.63084	−	2.17614i	0.0569862	−	0.0760405i
$820$		0			0
$821$	24.0040	−	10.6873i	0.837744	−	0.372988i	0.0574100	−	0.998351i	$-0.481716\pi$
$821$	24.0040	−	10.6873i	0.837744	−	0.372988i	0.780334	+	0.625363i	$0.215049\pi$
$822$	−14.9901	−	18.5112i	−0.522839	−	0.645653i
$823$	−10.6054	+	16.3309i	−0.369682	+	0.569261i	−0.973735	−	0.227683i	$-0.926885\pi$
$823$	−10.6054	+	16.3309i	−0.369682	+	0.569261i	0.604053	+	0.796944i	$0.293552\pi$
$824$	−14.4048	+	24.9499i	−0.501816	+	0.869171i
$825$		0			0
$826$	−18.9873	+	20.4696i	−0.660652	+	0.712228i
$827$	15.3550	−	7.82374i	0.533944	−	0.272058i	−0.166160	−	0.986099i	$-0.553137\pi$
$827$	15.3550	−	7.82374i	0.533944	−	0.272058i	0.700104	+	0.714041i	$0.253137\pi$
$828$	2.10070	−	5.47250i	0.0730042	−	0.190182i
$829$	−4.34045	+	41.2966i	−0.150750	+	1.43429i	0.613665	+	0.789567i	$0.289695\pi$
$829$	−4.34045	+	41.2966i	−0.150750	+	1.43429i	−0.764415	+	0.644725i	$0.776972\pi$
$830$		0			0
$831$	−1.61600	+	0.169848i	−0.0560584	+	0.00589198i
$832$	3.39004	−	3.39004i	0.117529	−	0.117529i
$833$	−47.0529	+	22.2447i	−1.63029	+	0.770733i
$834$	−1.19410	+	0.387986i	−0.0413482	+	0.0134348i
$835$		0			0
$836$	−0.344208	−	1.61937i	−0.0119047	−	0.0560071i
$837$	26.5018	−	1.38890i	0.916036	−	0.0480074i
$838$	14.2072	+	21.8772i	0.490781	+	0.755736i
$839$	−11.9529	+	36.7873i	−0.412660	+	1.27004i	0.501666	+	0.865061i	$0.332720\pi$
$839$	−11.9529	+	36.7873i	−0.412660	+	1.27004i	−0.914327	+	0.404977i	$0.867280\pi$
$840$		0			0
$841$	−18.1325	−	55.8062i	−0.625260	−	1.92435i
$842$	−12.1205	+	14.9675i	−0.417699	+	0.515815i
$843$	0.602629	−	2.24904i	0.0207557	−	0.0774612i
$844$	−9.27830	+	20.8394i	−0.319372	+	0.717322i
$845$		0			0
$846$	−7.86749	+	10.8287i	−0.270490	+	0.372298i
$847$	−12.1050	−	24.6533i	−0.415932	−	0.847098i
$848$	1.66591	+	3.26953i	0.0572075	+	0.112276i
$849$	17.2494	+	9.95893i	0.591997	+	0.341789i
$850$		0			0
$851$	−13.4134	−	23.2326i	−0.459804	−	0.796404i
$852$	1.43001	+	0.0749435i	0.0489913	+	0.00256752i
$853$	−4.26100	−	26.9029i	−0.145894	−	0.921138i	−0.946677	−	0.322184i	$-0.895583\pi$
$853$	−4.26100	−	26.9029i	−0.145894	−	0.921138i	0.800783	−	0.598954i	$-0.204417\pi$
$854$	−15.5927	+	13.6271i	−0.533572	+	0.466309i
$855$		0			0
$856$	−1.65556	−	15.7516i	−0.0565860	−	0.538380i
$857$	−37.0493	−	9.92732i	−1.26558	−	0.339111i	−0.437244	−	0.899343i	$-0.644045\pi$
$857$	−37.0493	−	9.92732i	−1.26558	−	0.339111i	−0.828336	+	0.560232i	$0.810712\pi$
$858$	0.735888	−	0.282481i	0.0251228	−	0.00964374i
$859$	0.881487	+	0.187366i	0.0300759	+	0.00639284i	0.222925	−	0.974836i	$-0.428439\pi$
$859$	0.881487	+	0.187366i	0.0300759	+	0.00639284i	−0.192849	+	0.981228i	$0.561773\pi$
$860$		0			0
$861$	7.60358	+	4.54138i	0.259129	+	0.154770i
$862$	1.04523	−	2.05137i	0.0356006	−	0.0698701i
$863$	−0.986845	+	0.640865i	−0.0335926	+	0.0218153i	−0.561326	−	0.827595i	$-0.689709\pi$
$863$	−0.986845	+	0.640865i	−0.0335926	+	0.0218153i	0.527733	+	0.849410i	$0.323042\pi$
$864$	29.9188	−	6.35943i	1.01786	−	0.216352i
$865$		0			0
$866$	1.78094	−	8.37865i	0.0605187	−	0.284718i
$867$	7.91096	−	49.9479i	0.268670	−	1.69632i
$868$	12.6237	+	6.66943i	0.428478	+	0.226375i
$869$	−2.26247	−	3.11402i	−0.0767490	−	0.105636i
$870$		0			0
$871$	0.743903	+	0.0781873i	0.0252062	+	0.00264928i
$872$	−37.0746	+	30.0225i	−1.25551	+	1.01669i
$873$	0.703169	−	13.4173i	0.0237987	−	0.454105i
$874$	6.96421			0.235568
$875$		0			0
$876$	5.60304			0.189309
$877$	−2.16993	+	41.4047i	−0.0732732	+	1.39814i	0.676501	+	0.736442i	$0.263496\pi$
$877$	−2.16993	+	41.4047i	−0.0732732	+	1.39814i	−0.749774	+	0.661694i	$0.769838\pi$
$878$	15.2764	−	12.3706i	0.515555	−	0.417488i
$879$	−5.09495	−	0.535501i	−0.171849	−	0.0180620i
$880$		0			0
$881$	20.7423	+	28.5494i	0.698827	+	0.961852i	0.999966	+	0.00827221i	$0.00263316\pi$
$881$	20.7423	+	28.5494i	0.698827	+	0.961852i	−0.301139	+	0.953580i	$0.597367\pi$
$882$	−7.99116	−	1.50953i	−0.269076	−	0.0508285i
$883$	2.01591	−	12.7280i	0.0678407	−	0.428330i	−0.930269	−	0.366877i	$-0.880427\pi$
$883$	2.01591	−	12.7280i	0.0678407	−	0.428330i	0.998110	−	0.0614522i	$-0.0195732\pi$
$884$	−1.44711	+	6.80810i	−0.0486714	+	0.228981i
$885$		0			0
$886$	20.6443	−	4.38808i	0.693559	−	0.147421i
$887$	−38.4301	+	24.9568i	−1.29036	+	0.837968i	−0.993150	−	0.116845i	$-0.962722\pi$
$887$	−38.4301	+	24.9568i	−1.29036	+	0.837968i	−0.297207	+	0.954813i	$0.596055\pi$
$888$	11.4544	−	22.4805i	0.384384	−	0.754397i
$889$	−3.75915	−	6.73962i	−0.126078	−	0.226040i
$890$		0			0
$891$	2.81753	+	0.598885i	0.0943909	+	0.0200634i
$892$	9.34433	−	3.58695i	0.312871	−	0.120100i
$893$	20.4839	+	5.48864i	0.685467	+	0.183670i
$894$	−1.45568	−	13.8498i	−0.0486851	−	0.463208i
$895$		0			0
$896$	13.6826	+	4.67088i	0.457103	+	0.156043i
$897$	−0.691729	−	4.36740i	−0.0230961	−	0.145823i
$898$	−30.1218	−	1.57862i	−1.00518	−	0.0526792i
$899$	−22.1049	−	38.2867i	−0.737238	−	1.27693i
$900$		0			0
$901$	−57.9395	−	33.4514i	−1.93025	−	1.11443i
$902$	−0.838114	−	1.64489i	−0.0279062	−	0.0547689i
$903$	−8.86760	−	0.596535i	−0.295095	−	0.0198514i
$904$	−16.0538	+	22.0961i	−0.533940	+	0.734905i
$905$		0			0
$906$	−5.51747	+	12.3924i	−0.183306	+	0.411711i
$907$	5.09475	−	19.0139i	0.169168	−	0.631345i	−0.828303	−	0.560280i	$-0.810693\pi$
$907$	5.09475	−	19.0139i	0.169168	−	0.631345i	0.997472	−	0.0710652i	$-0.0226398\pi$
$908$	6.75456	−	8.34119i	0.224158	−	0.276812i
$909$	−2.45091	−	7.54313i	−0.0812916	−	0.250190i
$910$		0			0
$911$	10.8138	−	33.2815i	0.358278	−	1.10267i	−0.595807	−	0.803128i	$-0.703168\pi$
$911$	10.8138	−	33.2815i	0.358278	−	1.10267i	0.954085	−	0.299537i	$-0.0968323\pi$
$912$	0.540059	+	0.831618i	0.0178831	+	0.0275376i
$913$	4.09027	−	0.214362i	0.135368	−	0.00709434i
$914$	1.55506	+	7.31597i	0.0514367	+	0.241991i
$915$		0			0
$916$	9.35025	−	3.03808i	0.308941	−	0.100381i
$917$	−2.52539	−	17.6308i	−0.0833956	−	0.582220i
$918$	27.3577	−	27.3577i	0.902939	−	0.902939i
$919$	−36.1268	+	3.79708i	−1.19171	+	0.125254i	−0.679547	−	0.733632i	$-0.737824\pi$
$919$	−36.1268	+	3.79708i	−1.19171	+	0.125254i	−0.512167	+	0.858886i	$0.671157\pi$
$920$		0			0
$921$	−3.86362	+	36.7599i	−0.127311	+	1.21128i
$922$	12.6344	−	32.9137i	0.416091	−	1.08395i
$923$	−0.692136	+	0.352661i	−0.0227819	+	0.0116080i
$924$	2.30471	+	2.13781i	0.0758193	+	0.0703289i
$925$		0			0
$926$	−17.0216	+	29.4823i	−0.559364	+	0.968847i
$927$	6.76745	−	10.4210i	0.222272	−	0.342269i
$928$	−32.0670	−	39.5994i	−1.05265	−	1.29992i
$929$	−3.00637	+	1.33852i	−0.0986357	+	0.0439154i	−0.455461	−	0.890256i	$-0.650526\pi$
$929$	−3.00637	+	1.33852i	−0.0986357	+	0.0439154i	0.356826	+	0.934171i	$0.383859\pi$
$930$		0			0
$931$	2.30445	+	12.6769i	0.0755253	+	0.415470i
$932$	−2.25132	−	2.25132i	−0.0737446	−	0.0737446i
$933$	−21.7407	−	17.6053i	−0.711758	−	0.576370i
$934$	12.8985	−	14.3252i	0.422050	−	0.468734i
$935$		0			0
$936$	−2.22250	+	2.00115i	−0.0726447	+	0.0654096i
$937$	−8.94070	−	4.55551i	−0.292080	−	0.148822i	0.301811	−	0.953368i	$-0.402409\pi$
$937$	−8.94070	−	4.55551i	−0.292080	−	0.148822i	−0.593891	+	0.804546i	$0.702409\pi$
$938$	−0.770623	−	2.09998i	−0.0251617	−	0.0685668i
$939$	−6.03743	−	1.96168i	−0.197024	−	0.0640170i
$940$		0			0
$941$	11.2179	+	10.1007i	0.365694	+	0.329272i	0.831407	−	0.555663i	$-0.187536\pi$
$941$	11.2179	+	10.1007i	0.365694	+	0.329272i	−0.465713	+	0.884936i	$0.654202\pi$
$942$	7.30664	+	19.0345i	0.238063	+	0.620176i
$943$	−10.0033	+	2.68038i	−0.325752	+	0.0872851i
$944$	3.76069	−	2.73230i	0.122400	−	0.0889288i
$945$		0			0
$946$	1.49877	+	1.08892i	0.0487293	+	0.0354039i
$947$	−53.2064	−	20.4240i	−1.72898	−	0.663692i	−0.729190	−	0.684312i	$-0.760103\pi$
$947$	−53.2064	−	20.4240i	−1.72898	−	0.663692i	−0.999787	+	0.0206198i	$0.993436\pi$
$948$	−6.19361	−	4.02218i	−0.201159	−	0.130634i
$949$	−2.63228	+	1.51975i	−0.0854473	+	0.0493330i
$950$		0			0
$951$		−	39.2544i		−	1.27291i
$952$	55.5006	−	13.9938i	1.79878	−	0.453540i
$953$	15.7565	−	2.49558i	0.510403	−	0.0808399i	0.104079	−	0.994569i	$-0.466810\pi$
$953$	15.7565	−	2.49558i	0.510403	−	0.0808399i	0.406324	+	0.913729i	$0.366810\pi$
$954$	−4.25199	−	9.55013i	−0.137663	−	0.309197i
$955$		0			0
$956$	−11.2381	−	5.00353i	−0.363467	−	0.161826i
$957$	−2.51936	−	9.40237i	−0.0814392	−	0.303935i
$958$	1.27980	+	0.202701i	0.0413486	+	0.00654897i
$959$	4.62690	+	51.3230i	0.149410	+	1.65731i
$960$		0			0
$961$	5.82696	+	6.47150i	0.187966	+	0.208758i
$962$	0.260489	+	4.97043i	0.00839852	+	0.160253i
$963$	0.357511	+	6.82172i	0.0115206	+	0.219827i
$964$	8.07068	+	8.96339i	0.259939	+	0.288691i
$965$		0			0
$966$	−10.8121	+	7.61337i	−0.347873	+	0.244956i
$967$	−30.4690	−	4.82581i	−0.979817	−	0.155188i	−0.354074	−	0.935217i	$-0.615204\pi$
$967$	−30.4690	−	4.82581i	−0.979817	−	0.155188i	−0.625743	+	0.780030i	$0.715204\pi$
$968$	7.81746	+	29.1751i	0.251263	+	0.937725i
$969$	−16.5159	−	7.35337i	−0.530568	−	0.236224i
$970$		0			0
$971$	−1.64054	−	3.68471i	−0.0526474	−	0.118248i	0.885307	−	0.465008i	$-0.153949\pi$
$971$	−1.64054	−	3.68471i	−0.0526474	−	0.118248i	−0.937954	+	0.346760i	$0.887282\pi$
$972$	−13.5770	+	2.15038i	−0.435482	+	0.0689736i
$973$	2.61300	+	0.741798i	0.0837690	+	0.0237810i
$974$			24.6259i			0.789064i
$975$		0			0
$976$	2.98586	−	1.72388i	0.0955749	−	0.0551802i
$977$	20.5729	+	13.3602i	0.658184	+	0.427430i	0.830049	−	0.557691i	$-0.188312\pi$
$977$	20.5729	+	13.3602i	0.658184	+	0.427430i	−0.171864	+	0.985121i	$0.554979\pi$
$978$	−23.4855	−	9.01525i	−0.750984	−	0.288276i
$979$	0.368121	+	0.267456i	0.0117652	+	0.00854792i
$980$		0			0
$981$	16.6460	−	12.0940i	0.531467	−	0.386133i
$982$	0.184678	−	0.0494843i	0.00589331	−	0.00157911i
$983$	16.3702	+	42.6458i	0.522128	+	1.36019i	0.900629	+	0.434590i	$0.143107\pi$
$983$	16.3702	+	42.6458i	0.522128	+	1.36019i	−0.378500	+	0.925601i	$0.623560\pi$
$984$	−7.23821	−	6.51731i	−0.230746	−	0.207764i
$985$		0			0
$986$	−61.2982	−	19.9170i	−1.95213	−	0.634286i
$987$	−37.8019	+	13.8720i	−1.20325	+	0.441552i
$988$	1.53528	+	0.782265i	0.0488438	+	0.0248872i
$989$	7.72316	−	6.95396i	0.245582	−	0.221123i
$990$		0			0
$991$	30.6797	−	34.0732i	0.974571	−	1.08237i	−0.0220102	−	0.999758i	$-0.507007\pi$
$991$	30.6797	−	34.0732i	0.974571	−	1.08237i	0.996582	−	0.0826135i	$-0.0263267\pi$
$992$	−19.9671	−	16.1691i	−0.633957	−	0.513368i
$993$	−21.4880	−	21.4880i	−0.681902	−	0.681902i
$994$	1.85896	+	1.39314i	0.0589625	+	0.0441876i
$995$		0			0
$996$	7.17903	−	3.19631i	0.227476	−	0.101279i
$997$	14.3515	+	17.7226i	0.454517	+	0.561281i	0.951963	−	0.306213i	$-0.0990621\pi$
$997$	14.3515	+	17.7226i	0.454517	+	0.561281i	−0.497446	+	0.867495i	$0.665729\pi$
$998$	11.9036	−	18.3300i	0.376802	−	0.580225i
$999$	−18.4479	+	31.9527i	−0.583665	+	1.01094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.c.257.11		288
5.2	odd	4		875.2.bb.b.243.11		288
5.3	odd	4		875.2.bb.a.243.8		288
5.4	even	2		175.2.x.a.47.8	yes	288
7.3	odd	6	inner	875.2.bb.c.507.11		288
25.6	even	5		875.2.bb.a.607.11		288
25.8	odd	20	inner	875.2.bb.c.768.11		288
25.17	odd	20		175.2.x.a.33.8	✓	288
25.19	even	10		875.2.bb.b.607.8		288
35.3	even	12		875.2.bb.a.493.11		288
35.17	even	12		875.2.bb.b.493.8		288
35.24	odd	6		175.2.x.a.122.8	yes	288
175.17	even	60		175.2.x.a.108.8	yes	288
175.31	odd	30		875.2.bb.a.857.8		288
175.94	odd	30		875.2.bb.b.857.11		288
175.108	even	60	inner	875.2.bb.c.143.11		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.8	✓	288	25.17	odd	20
175.2.x.a.47.8	yes	288	5.4	even	2
175.2.x.a.108.8	yes	288	175.17	even	60
175.2.x.a.122.8	yes	288	35.24	odd	6
875.2.bb.a.243.8		288	5.3	odd	4
875.2.bb.a.493.11		288	35.3	even	12
875.2.bb.a.607.11		288	25.6	even	5
875.2.bb.a.857.8		288	175.31	odd	30
875.2.bb.b.243.11		288	5.2	odd	4
875.2.bb.b.493.8		288	35.17	even	12
875.2.bb.b.607.8		288	25.19	even	10
875.2.bb.b.857.11		288	175.94	odd	30
875.2.bb.c.143.11		288	175.108	even	60	inner
875.2.bb.c.257.11		288	1.1	even	1	trivial
875.2.bb.c.507.11		288	7.3	odd	6	inner
875.2.bb.c.768.11		288	25.8	odd	20	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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0484513 - 0.924506i) q^{2} +(1.02662 - 0.831339i) q^{3} +(1.13668 + 0.119470i) q^{4} +(-0.718837 - 0.989394i) q^{6} +(0.0993238 + 2.64389i) q^{7} +(0.455170 - 2.87383i) q^{8} +(-0.260915 + 1.22751i) q^{9} +(0.769743 - 0.163614i) q^{11} +(1.26626 - 0.822316i) q^{12} +(-0.371838 + 0.729773i) q^{13} +(2.44910 + 0.0362743i) q^{14} +(-0.398891 - 0.0847869i) q^{16} +(6.94132 - 2.66452i) q^{17} +(1.12220 + 0.300692i) q^{18} +(-0.192403 - 1.83059i) q^{19} +(2.29993 + 2.63169i) q^{21} +(-0.113967 - 0.719560i) q^{22} +(-4.08126 - 0.213890i) q^{23} +(-1.92184 - 3.32873i) q^{24} +(0.656664 + 0.379125i) q^{26} +(2.55179 + 5.00818i) q^{27} +(-0.202965 + 3.01712i) q^{28} +(5.50382 - 7.57536i) q^{29} +(1.92037 - 4.31323i) q^{31} +(1.40844 - 5.25635i) q^{32} +(0.654214 - 0.807887i) q^{33} +(-2.12705 - 6.54639i) q^{34} +(-0.443227 + 1.36411i) q^{36} +(3.57509 + 5.50515i) q^{37} +(-1.70171 + 0.0891829i) q^{38} +(0.224953 + 1.05832i) q^{39} +(2.40999 - 0.783055i) q^{41} +(2.54445 - 1.99879i) q^{42} +(-1.79811 + 1.79811i) q^{43} +(0.894499 - 0.0940156i) q^{44} +(-0.395485 + 3.76279i) q^{46} +(-4.12878 + 10.7558i) q^{47} +(-0.479996 + 0.244570i) q^{48} +(-6.98027 + 0.525202i) q^{49} +(4.91096 - 8.50604i) q^{51} +(-0.509847 + 0.785095i) q^{52} +(-5.66273 - 6.99289i) q^{53} +(4.75373 - 2.11650i) q^{54} +(7.64330 + 0.917979i) q^{56} +(-1.71936 - 1.71936i) q^{57} +(-6.73680 - 5.45535i) q^{58} +(-7.62729 + 8.47097i) q^{59} +(-6.28292 + 5.65717i) q^{61} +(-3.89456 - 1.98438i) q^{62} +(-3.27131 - 0.567908i) q^{63} +(-5.56698 - 1.80882i) q^{64} +(-0.715198 - 0.643968i) q^{66} +(-0.327283 - 0.852602i) q^{67} +(8.20839 - 2.19943i) q^{68} +(-4.36771 + 3.17333i) q^{69} +(0.767293 + 0.557471i) q^{71} +(3.40889 + 1.30855i) q^{72} +(3.11233 + 2.02117i) q^{73} +(5.26276 - 3.03846i) q^{74} -2.10378i q^{76} +(0.509031 + 2.01886i) q^{77} +(0.989324 - 0.156693i) q^{78} +(-1.98946 - 4.46840i) q^{79} +(3.34390 + 1.48880i) q^{81} +(-0.607171 - 2.26599i) q^{82} +(5.14074 + 0.814213i) q^{83} +(2.29988 + 3.26616i) q^{84} +(1.57524 + 1.74948i) q^{86} +(-0.647369 - 12.3525i) q^{87} +(-0.119835 - 2.28659i) q^{88} +(0.386903 + 0.429700i) q^{89} +(-1.96637 - 0.910613i) q^{91} +(-4.61354 - 0.730712i) q^{92} +(-1.61426 - 6.02451i) q^{93} +(9.74379 + 4.33822i) q^{94} +(-2.92389 - 6.56715i) q^{96} +(-10.5745 + 1.67483i) q^{97} +(0.147349 + 6.47875i) q^{98} +0.987555i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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