LMFDB - Embedded newform 875.2.bb.a.418.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			418.18
Character	$\chi$	$=$	875.418
Dual form			875.2.bb.a.157.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.936298 - 2.43914i) q^{2} +(-0.156245 - 2.98133i) q^{3} +(-3.58646 - 3.22926i) q^{4} +(-7.41816 - 2.41031i) q^{6} +(2.37291 - 1.17017i) q^{7} +(-6.57879 + 3.35206i) q^{8} +(-5.88033 + 0.618047i) q^{9} +(0.0110705 - 0.105329i) q^{11} +(-9.06711 + 11.1969i) q^{12} +(0.247208 - 1.56081i) q^{13} +(-0.632446 - 6.88349i) q^{14} +(1.00752 + 9.58587i) q^{16} +(3.87956 + 2.51942i) q^{17} +(-3.99823 + 14.9216i) q^{18} +(-0.828774 - 0.920447i) q^{19} +(-3.85940 - 6.89159i) q^{21} +(-0.246547 - 0.125622i) q^{22} +(-0.144646 - 0.0555245i) q^{23} +(11.0215 + 19.0898i) q^{24} +(-3.57557 - 2.06436i) q^{26} +(1.36030 + 8.58862i) q^{27} +(-12.2891 - 3.46600i) q^{28} +(4.84593 - 1.57454i) q^{29} +(0.611278 + 2.87584i) q^{31} +(10.0607 + 2.69575i) q^{32} +(-0.315750 - 0.0165478i) q^{33} +(9.77764 - 7.10387i) q^{34} +(23.0854 + 16.7725i) q^{36} +(0.400833 + 0.324588i) q^{37} +(-3.02108 + 1.15968i) q^{38} +(-4.69190 - 0.493139i) q^{39} +(2.31834 + 3.19093i) q^{41} +(-20.4231 + 2.96104i) q^{42} +(-4.39882 - 4.39882i) q^{43} +(-0.379839 + 0.342008i) q^{44} +(-0.270864 + 0.300825i) q^{46} +(-2.75397 - 4.24074i) q^{47} +(28.4212 - 4.50147i) q^{48} +(4.26142 - 5.55340i) q^{49} +(6.90505 - 11.9599i) q^{51} +(-5.92685 + 4.79947i) q^{52} +(12.6632 - 0.663649i) q^{53} +(22.2225 + 4.72354i) q^{54} +(-11.6884 + 15.6524i) q^{56} +(-2.61466 + 2.61466i) q^{57} +(0.696716 - 13.2941i) q^{58} +(-11.3795 - 5.06647i) q^{59} +(-3.48040 - 7.81711i) q^{61} +(7.58691 + 1.20165i) q^{62} +(-13.2303 + 8.34753i) q^{63} +(4.66418 - 6.41969i) q^{64} +(-0.335998 + 0.754665i) q^{66} +(1.15735 - 1.78216i) q^{67} +(-5.77803 - 21.5639i) q^{68} +(-0.142937 + 0.439913i) q^{69} +(2.43082 + 7.48129i) q^{71} +(36.6137 - 23.7772i) q^{72} +(8.60076 + 10.6211i) q^{73} +(1.16701 - 0.673776i) q^{74} +5.97747i q^{76} +(-0.0969831 - 0.262891i) q^{77} +(-5.59585 + 10.9825i) q^{78} +(1.28595 - 6.04991i) q^{79} +(8.04241 - 1.70947i) q^{81} +(9.95377 - 2.66710i) q^{82} +(4.06079 + 7.96975i) q^{83} +(-8.41316 + 37.1794i) q^{84} +(-14.8479 + 6.61073i) q^{86} +(-5.45136 - 14.2013i) q^{87} +(0.280239 + 0.730047i) q^{88} +(-12.4217 + 5.53052i) q^{89} +(-1.23980 - 3.99294i) q^{91} +(0.339465 + 0.666237i) q^{92} +(8.47830 - 2.27175i) q^{93} +(-12.9223 + 2.74672i) q^{94} +(6.46499 - 30.4154i) q^{96} +(-4.91146 + 9.63928i) q^{97} +(-9.55556 - 15.5938i) q^{98} +0.626212i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.936298	−	2.43914i	0.662062	−	1.72473i	−0.0265966	−	0.999646i	$-0.508467\pi$
$2$	0.936298	−	2.43914i	0.662062	−	1.72473i	0.688659	−	0.725085i	$-0.258200\pi$
$3$	−0.156245	−	2.98133i	−0.0902079	−	1.72127i	−0.551630	−	0.834089i	$-0.685994\pi$
$3$	−0.156245	−	2.98133i	−0.0902079	−	1.72127i	0.461422	−	0.887181i	$-0.347339\pi$
$4$	−3.58646	−	3.22926i	−1.79323	−	1.61463i
$5$		0			0
$5$		0			0
$6$	−7.41816	−	2.41031i	−3.02845	−	0.984003i
$7$	2.37291	−	1.17017i	0.896876	−	0.442281i
$7$	2.37291	−	1.17017i	0.896876	−	0.442281i
$8$	−6.57879	+	3.35206i	−2.32595	+	1.18513i
$9$	−5.88033	+	0.618047i	−1.96011	+	0.206016i
$10$		0			0
$11$	0.0110705	−	0.105329i	0.00333789	−	0.0317579i	−0.992726	−	0.120394i	$-0.961584\pi$
$11$	0.0110705	−	0.105329i	0.00333789	−	0.0317579i	0.996064	+	0.0886362i	$0.0282508\pi$
$12$	−9.06711	+	11.1969i	−2.61745	+	3.23228i
$13$	0.247208	−	1.56081i	0.0685631	−	0.432890i	−0.929399	−	0.369077i	$-0.879674\pi$
$13$	0.247208	−	1.56081i	0.0685631	−	0.432890i	0.997962	−	0.0638133i	$-0.0203262\pi$
$14$	−0.632446	−	6.88349i	−0.169028	−	1.83969i
$15$		0			0
$16$	1.00752	+	9.58587i	0.251879	+	2.39647i
$17$	3.87956	+	2.51942i	0.940933	+	0.611049i	0.921339	−	0.388759i	$-0.127096\pi$
$17$	3.87956	+	2.51942i	0.940933	+	0.611049i	0.0195932	+	0.999808i	$0.493763\pi$
$18$	−3.99823	+	14.9216i	−0.942393	+	3.51706i
$19$	−0.828774	−	0.920447i	−0.190134	−	0.211165i	0.640539	−	0.767925i	$-0.278711\pi$
$19$	−0.828774	−	0.920447i	−0.190134	−	0.211165i	−0.830673	+	0.556760i	$0.812044\pi$
$20$		0			0
$21$	−3.85940	−	6.89159i	−0.842191	−	1.50387i
$22$	−0.246547	−	0.125622i	−0.0525640	−	0.0267827i
$23$	−0.144646	−	0.0555245i	−0.0301609	−	0.0115777i	0.343241	−	0.939247i	$-0.388475\pi$
$23$	−0.144646	−	0.0555245i	−0.0301609	−	0.0115777i	−0.373402	+	0.927670i	$0.621809\pi$
$24$	11.0215	+	19.0898i	2.24975	+	3.89668i
$25$		0			0
$26$	−3.57557	−	2.06436i	−0.701227	−	0.404853i
$27$	1.36030	+	8.58862i	0.261791	+	1.65288i
$28$	−12.2891	−	3.46600i	−2.32242	−	0.655012i
$29$	4.84593	−	1.57454i	0.899866	−	0.292384i	0.177684	−	0.984088i	$-0.443139\pi$
$29$	4.84593	−	1.57454i	0.899866	−	0.292384i	0.722182	+	0.691703i	$0.243139\pi$
$30$		0			0
$31$	0.611278	+	2.87584i	0.109789	+	0.516516i	0.998333	+	0.0577240i	$0.0183843\pi$
$31$	0.611278	+	2.87584i	0.109789	+	0.516516i	−0.888544	+	0.458792i	$0.848282\pi$
$32$	10.0607	+	2.69575i	1.77850	+	0.476546i
$33$	−0.315750	−	0.0165478i	−0.0549650	−	0.00288060i
$34$	9.77764	−	7.10387i	1.67685	−	1.21830i
$35$		0			0
$36$	23.0854	+	16.7725i	3.84756	+	2.79542i
$37$	0.400833	+	0.324588i	0.0658965	+	0.0533619i	0.661703	−	0.749766i	$-0.269834\pi$
$37$	0.400833	+	0.324588i	0.0658965	+	0.0533619i	−0.595806	+	0.803128i	$0.703167\pi$
$38$	−3.02108	+	1.15968i	−0.490083	+	0.188125i
$39$	−4.69190	−	0.493139i	−0.751306	−	0.0789654i
$40$		0			0
$41$	2.31834	+	3.19093i	0.362064	+	0.498339i	0.950722	−	0.310043i	$-0.100344\pi$
$41$	2.31834	+	3.19093i	0.362064	+	0.498339i	−0.588658	+	0.808382i	$0.700344\pi$
$42$	−20.4231	+	2.96104i	−3.15135	+	0.456898i
$43$	−4.39882	−	4.39882i	−0.670814	−	0.670814i	0.287090	−	0.957904i	$-0.407312\pi$
$43$	−4.39882	−	4.39882i	−0.670814	−	0.670814i	−0.957904	+	0.287090i	$0.907312\pi$
$44$	−0.379839	+	0.342008i	−0.0572629	+	0.0515597i
$45$		0			0
$46$	−0.270864	+	0.300825i	−0.0399367	+	0.0443542i
$47$	−2.75397	−	4.24074i	−0.401708	−	0.618576i	0.578703	−	0.815538i	$-0.303559\pi$
$47$	−2.75397	−	4.24074i	−0.401708	−	0.618576i	−0.980411	+	0.196962i	$0.936892\pi$
$48$	28.4212	−	4.50147i	4.10224	−	0.649732i
$49$	4.26142	−	5.55340i	0.608775	−	0.793343i
$50$		0			0
$51$	6.90505	−	11.9599i	0.966900	−	1.67472i
$52$	−5.92685	+	4.79947i	−0.821907	+	0.665567i
$53$	12.6632	−	0.663649i	1.73942	−	0.0911593i	0.843991	−	0.536358i	$-0.180200\pi$
$53$	12.6632	−	0.663649i	1.73942	−	0.0911593i	0.895432	+	0.445199i	$0.146867\pi$
$54$	22.2225	+	4.72354i	3.02410	+	0.642792i
$55$		0			0
$56$	−11.6884	+	15.6524i	−1.56193	+	2.09164i
$57$	−2.61466	+	2.61466i	−0.346320	+	0.346320i
$58$	0.696716	−	13.2941i	0.0914832	−	1.74560i
$59$	−11.3795	−	5.06647i	−1.48148	−	0.659599i	−0.502693	−	0.864465i	$-0.667657\pi$
$59$	−11.3795	−	5.06647i	−1.48148	−	0.659599i	−0.978790	+	0.204866i	$0.934324\pi$
$60$		0			0
$61$	−3.48040	−	7.81711i	−0.445620	−	1.00088i	−0.987091	−	0.160159i	$-0.948799\pi$
$61$	−3.48040	−	7.81711i	−0.445620	−	1.00088i	0.541472	−	0.840719i	$-0.317867\pi$
$62$	7.58691	+	1.20165i	0.963538	+	0.152609i
$63$	−13.2303	+	8.34753i	−1.66686	+	1.05169i
$64$	4.66418	−	6.41969i	0.583022	−	0.802461i
$65$		0			0
$66$	−0.335998	+	0.754665i	−0.0413585	+	0.0928928i
$67$	1.15735	−	1.78216i	0.141393	−	0.217726i	−0.760879	−	0.648894i	$-0.775232\pi$
$67$	1.15735	−	1.78216i	0.141393	−	0.217726i	0.902272	+	0.431168i	$0.141898\pi$
$68$	−5.77803	−	21.5639i	−0.700689	−	2.61501i
$69$	−0.142937	+	0.439913i	−0.0172075	+	0.0529594i
$70$		0			0
$71$	2.43082	+	7.48129i	0.288485	+	0.887866i	0.985332	+	0.170646i	$0.0545856\pi$
$71$	2.43082	+	7.48129i	0.288485	+	0.887866i	−0.696847	+	0.717220i	$0.745414\pi$
$72$	36.6137	−	23.7772i	4.31496	−	2.80217i
$73$	8.60076	+	10.6211i	1.00664	+	1.24310i	0.969831	+	0.243778i	$0.0783868\pi$
$73$	8.60076	+	10.6211i	1.00664	+	1.24310i	0.0368115	+	0.999322i	$0.488280\pi$
$74$	1.16701	−	0.673776i	0.135663	−	0.0783249i
$75$		0			0
$76$			5.97747i			0.685663i
$77$	−0.0969831	−	0.262891i	−0.0110523	−	0.0299592i
$78$	−5.59585	+	10.9825i	−0.633606	+	1.24352i
$79$	1.28595	−	6.04991i	0.144680	−	0.680668i	−0.844691	−	0.535255i	$-0.820216\pi$
$79$	1.28595	−	6.04991i	0.144680	−	0.680668i	0.989371	−	0.145413i	$-0.0464511\pi$
$80$		0			0
$81$	8.04241	−	1.70947i	0.893601	−	0.189941i
$82$	9.95377	−	2.66710i	1.09921	−	0.294532i
$83$	4.06079	+	7.96975i	0.445730	+	0.874794i	0.999123	+	0.0418738i	$0.0133327\pi$
$83$	4.06079	+	7.96975i	0.445730	+	0.874794i	−0.553393	+	0.832920i	$0.686667\pi$
$84$	−8.41316	+	37.1794i	−0.917951	+	4.05660i
$85$		0			0
$86$	−14.8479	+	6.61073i	−1.60109	+	0.712853i
$87$	−5.45136	−	14.2013i	−0.584447	−	1.52254i
$88$	0.280239	+	0.730047i	0.0298735	+	0.0778232i
$89$	−12.4217	+	5.53052i	−1.31670	+	0.586234i	−0.940339	−	0.340239i	$-0.889492\pi$
$89$	−12.4217	+	5.53052i	−1.31670	+	0.586234i	−0.376363	+	0.926472i	$0.622825\pi$
$90$		0			0
$91$	−1.23980	−	3.99294i	−0.129967	−	0.418573i
$92$	0.339465	+	0.666237i	0.0353916	+	0.0694600i
$93$	8.47830	−	2.27175i	0.879159	−	0.235570i
$94$	−12.9223	+	2.74672i	−1.33283	+	0.283303i
$95$		0			0
$96$	6.46499	−	30.4154i	0.659830	−	3.10426i
$97$	−4.91146	+	9.63928i	−0.498683	+	0.978721i	0.495252	+	0.868750i	$0.335076\pi$
$97$	−4.91146	+	9.63928i	−0.498683	+	0.978721i	−0.993935	+	0.109971i	$0.964924\pi$
$98$	−9.55556	−	15.5938i	−0.965257	−	1.57522i
$99$			0.626212i			0.0629366i
$100$		0			0
$101$	8.01192	−	4.62568i	0.797216	−	0.460273i	−0.0452808	−	0.998974i	$-0.514418\pi$
$101$	8.01192	−	4.62568i	0.797216	−	0.460273i	0.842497	+	0.538701i	$0.181085\pi$
$102$	−22.7067	−	28.0404i	−2.24829	−	2.77641i
$103$	−5.60006	+	3.63672i	−0.551790	+	0.358337i	−0.790220	−	0.612823i	$-0.790034\pi$
$103$	−5.60006	+	3.63672i	−0.551790	+	0.358337i	0.238430	+	0.971160i	$0.423367\pi$
$104$	3.60560	+	11.0969i	0.353558	+	1.08814i
$105$		0			0
$106$	10.2378	−	31.5086i	0.994381	−	3.06039i
$107$	−3.32004	−	12.3906i	−0.320960	−	1.19784i	−0.918311	−	0.395860i	$-0.870447\pi$
$107$	−3.32004	−	12.3906i	−0.320960	−	1.19784i	0.597350	−	0.801980i	$-0.296220\pi$
$108$	22.8562	−	35.1955i	2.19934	−	3.38669i
$109$	−4.57476	+	10.2751i	−0.438183	+	0.984175i	0.550594	+	0.834773i	$0.314401\pi$
$109$	−4.57476	+	10.2751i	−0.438183	+	0.984175i	−0.988777	+	0.149401i	$0.952265\pi$
$110$		0			0
$111$	0.905075	−	1.24573i	0.0859059	−	0.118239i
$112$	13.6078	+	21.5675i	1.28582	+	2.03793i
$113$	3.85282	+	0.610226i	0.362443	+	0.0574053i	0.335000	−	0.942218i	$-0.391264\pi$
$113$	3.85282	+	0.610226i	0.362443	+	0.0574053i	0.0274425	+	0.999623i	$0.491264\pi$
$114$	3.92942	+	8.82562i	0.368024	+	0.826595i
$115$		0			0
$116$	−22.4643	−	10.0017i	−2.08576	−	0.928639i
$117$	−0.489009	+	9.33085i	−0.0452089	+	0.862638i
$118$	−23.0124	+	23.0124i	−2.11846	+	2.11846i
$119$	12.1540	+	1.43862i	1.11416	+	0.131878i
$120$		0			0
$121$	10.7487	+	2.28470i	0.977150	+	0.207700i
$122$	−22.3257	+	1.17004i	−2.02127	+	0.105930i
$123$	9.15096	−	7.41030i	0.825114	−	0.668164i
$124$	7.09450	−	12.2880i	0.637105	−	1.10350i
$125$		0			0
$126$	7.97331	+	40.0863i	0.710319	+	3.57117i
$127$	9.62146	−	1.52389i	0.853767	−	0.135223i	0.285815	−	0.958285i	$-0.407736\pi$
$127$	9.62146	−	1.52389i	0.853767	−	0.135223i	0.567952	+	0.823062i	$0.307736\pi$
$128$	0.0540161	+	0.0831775i	0.00477439	+	0.00735192i
$129$	−12.4270	+	13.8016i	−1.09414	+	1.21516i
$130$		0			0
$131$	−6.11663	+	5.50744i	−0.534413	+	0.481187i	−0.891586	−	0.452851i	$-0.850407\pi$
$131$	−6.11663	+	5.50744i	−0.534413	+	0.481187i	0.357174	+	0.934038i	$0.383740\pi$
$132$	1.07899	+	1.07899i	0.0939137	+	0.0939137i
$133$	−3.04368	−	1.21434i	−0.263921	−	0.105296i
$134$	−3.26332	−	4.49158i	−0.281908	−	0.388013i
$135$		0			0
$136$	−33.9681	−	3.57019i	−2.91274	−	0.306141i
$137$	12.3025	−	4.72248i	1.05107	−	0.403468i	0.229341	−	0.973346i	$-0.426343\pi$
$137$	12.3025	−	4.72248i	1.05107	−	0.403468i	0.821729	+	0.569878i	$0.193009\pi$
$138$	0.939179	+	0.760532i	0.0799482	+	0.0647408i
$139$	−3.54704	−	2.57708i	−0.300856	−	0.218585i	0.427107	−	0.904201i	$-0.359533\pi$
$139$	−3.54704	−	2.57708i	−0.300856	−	0.218585i	−0.727963	+	0.685616i	$0.759533\pi$
$140$		0			0
$141$	−12.2128	+	8.87308i	−1.02850	+	0.747248i
$142$	20.5239	+	1.07561i	1.72233	+	0.0902633i
$143$	−0.161662	−	0.0433172i	−0.0135188	−	0.00362236i
$144$	−11.8490	−	55.7454i	−0.987420	−	4.64545i
$145$		0			0
$146$	33.9591	−	11.0340i	2.81047	−	0.913178i
$147$	−17.2223	−	11.8370i	−1.42047	−	0.976299i
$148$	−0.389390	−	2.45851i	−0.0320077	−	0.202089i
$149$	1.49934	+	0.865642i	0.122830	+	0.0709162i	0.560156	−	0.828387i	$-0.310741\pi$
$149$	1.49934	+	0.865642i	0.122830	+	0.0709162i	−0.437326	+	0.899303i	$0.644074\pi$
$150$		0			0
$151$	−2.72492	−	4.71971i	−0.221751	−	0.384084i	0.733589	−	0.679594i	$-0.237844\pi$
$151$	−2.72492	−	4.71971i	−0.221751	−	0.384084i	−0.955340	+	0.295510i	$0.904511\pi$
$152$	8.53772	+	3.27732i	0.692500	+	0.265826i
$153$	−24.3702	−	12.4173i	−1.97022	−	1.00388i
$154$	−0.732033	−	0.00958890i	−0.0589889	−	0.000772696i
$155$		0			0
$156$	15.2348	+	16.9200i	1.21976	+	1.35468i
$157$	−1.97748	+	7.38005i	−0.157820	+	0.588992i	0.841027	+	0.540993i	$0.181951\pi$
$157$	−1.97748	+	7.38005i	−0.157820	+	0.588992i	−0.998847	+	0.0479996i	$0.984715\pi$
$158$	−13.5525	−	8.80112i	−1.07818	−	0.700180i
$159$	−3.95711	−	37.6494i	−0.313819	−	2.98579i
$160$		0			0
$161$	−0.408206	+	0.0375055i	−0.0321711	+	0.00295584i
$162$	3.36046	−	21.2171i	0.264023	−	1.66698i
$163$	−12.9550	+	15.9981i	−1.01471	+	1.25307i	−0.0475606	+	0.998868i	$0.515145\pi$
$163$	−12.9550	+	15.9981i	−1.01471	+	1.25307i	−0.967152	+	0.254198i	$0.918189\pi$
$164$	1.98969	−	18.9306i	0.155369	−	1.47823i
$165$		0			0
$166$	23.2414	−	2.44277i	1.80389	−	0.189596i
$167$	−7.24584	+	3.69194i	−0.560700	+	0.285691i	−0.711282	−	0.702907i	$-0.751885\pi$
$167$	−7.24584	+	3.69194i	−0.560700	+	0.285691i	0.150582	+	0.988597i	$0.451885\pi$
$168$	48.4912	+	32.4014i	3.74118	+	2.49982i
$169$	9.98872	+	3.24553i	0.768363	+	0.249656i
$170$		0			0
$171$	5.44234	+	4.90031i	0.416186	+	0.374736i
$172$	1.57124	+	29.9811i	0.119806	+	2.28604i
$173$	4.31105	−	11.2307i	0.327763	−	0.853852i	−0.666363	−	0.745627i	$-0.732150\pi$
$173$	4.31105	−	11.2307i	0.327763	−	0.853852i	0.994126	−	0.108225i	$-0.0345167\pi$
$174$	−39.7430			−3.01291
$175$		0			0
$176$	1.02082			0.0769475
$177$	−13.3268	+	34.7176i	−1.00171	+	2.60953i
$178$	1.85925	+	35.4766i	0.139357	+	2.65908i
$179$	12.2574	+	11.0366i	0.916161	+	0.824915i	0.984972	−	0.172715i	$-0.0552539\pi$
$179$	12.2574	+	11.0366i	0.916161	+	0.824915i	−0.0688110	+	0.997630i	$0.521921\pi$
$180$		0			0
$181$	−17.4861	−	5.68158i	−1.29973	−	0.422308i	−0.424244	−	0.905548i	$-0.639460\pi$
$181$	−17.4861	−	5.68158i	−1.29973	−	0.422308i	−0.875488	+	0.483240i	$0.839460\pi$
$182$	−10.9001	−	0.714524i	−0.807973	−	0.0529641i
$183$	−22.7616	+	11.5976i	−1.68258	+	0.857319i
$184$	1.13772	−	0.119579i	0.0838738	−	0.00881549i
$185$		0			0
$186$	2.39709	−	22.8068i	0.175763	−	1.67228i
$187$	0.308317	−	0.380740i	0.0225464	−	0.0278424i
$188$	−3.81747	+	24.1025i	−0.278417	+	1.75786i
$189$	13.2780	+	18.7883i	0.965832	+	1.36665i
$190$		0			0
$191$	−2.67834	−	25.4827i	−0.193798	−	1.84386i	−0.469884	−	0.882728i	$-0.655704\pi$
$191$	−2.67834	−	25.4827i	−0.193798	−	1.84386i	0.276086	−	0.961133i	$-0.410962\pi$
$192$	−19.8679	−	12.9024i	−1.43385	−	0.931150i
$193$	0.143491	−	0.535514i	0.0103287	−	0.0385472i	−0.960569	−	0.278041i	$-0.910315\pi$
$193$	0.143491	−	0.535514i	0.0103287	−	0.0385472i	0.970898	+	0.239494i	$0.0769815\pi$
$194$	18.9130	+	21.0050i	1.35787	+	1.50807i
$195$		0			0
$196$	−33.2168	+	6.15580i	−2.37263	+	0.439700i
$197$	3.16908	+	1.61473i	0.225788	+	0.115045i	0.563226	−	0.826303i	$-0.309560\pi$
$197$	3.16908	+	1.61473i	0.225788	+	0.115045i	−0.337438	+	0.941348i	$0.609560\pi$
$198$	1.52742	+	0.586321i	0.108549	+	0.0416680i
$199$	1.30189	+	2.25493i	0.0922882	+	0.159848i	0.908474	−	0.417942i	$-0.137249\pi$
$199$	1.30189	+	2.25493i	0.0922882	+	0.159848i	−0.816185	+	0.577790i	$0.803915\pi$
$200$		0			0
$201$	−5.49404	−	3.17199i	−0.387520	−	0.223735i
$202$	−3.78114	−	23.8732i	−0.266040	−	1.67971i
$203$	9.65649	−	9.40678i	0.677753	−	0.660226i
$204$	−63.3862	+	20.5954i	−4.43792	+	1.44197i
$205$		0			0
$206$	3.62714	+	17.0644i	0.252715	+	1.18893i
$207$	0.884885	+	0.237104i	0.0615038	+	0.0164799i
$208$	15.2108	+	0.797163i	1.05468	+	0.0552733i
$209$	−0.106125	+	0.0771042i	−0.00734081	+	0.00533341i
$210$		0			0
$211$	2.95158	+	2.14445i	0.203195	+	0.147630i	0.684729	−	0.728797i	$-0.259920\pi$
$211$	2.95158	+	2.14445i	0.203195	+	0.147630i	−0.481534	+	0.876427i	$0.659920\pi$
$212$	−47.5590	−	38.5126i	−3.26637	−	2.64505i
$213$	21.9244	−	8.41598i	1.50223	−	0.576653i
$214$	−33.3308	−	3.50321i	−2.27845	−	0.239475i
$215$		0			0
$216$	−37.7387	−	51.9429i	−2.56779	−	3.53427i
$217$	4.81572	+	6.10881i	0.326912	+	0.414693i
$218$	20.7790	+	20.7790i	1.40733	+	1.40733i
$219$	30.3210	−	27.3011i	2.04890	−	1.84484i
$220$		0			0
$221$	4.89139	−	5.43244i	0.329030	−	0.365425i
$222$	−2.19109	−	3.37398i	−0.147056	−	0.226446i
$223$	−0.783365	+	0.124073i	−0.0524580	+	0.00830853i	−0.182608	−	0.983186i	$-0.558454\pi$
$223$	−0.783365	+	0.124073i	−0.0524580	+	0.00830853i	0.130150	+	0.991494i	$0.458454\pi$
$224$	27.0276	−	5.37589i	1.80586	−	0.359192i
$225$		0			0
$226$	5.09581	−	8.82620i	0.338968	−	0.587110i
$227$	6.14551	−	4.97653i	0.407892	−	0.330304i	−0.403318	−	0.915060i	$-0.632143\pi$
$227$	6.14551	−	4.97653i	0.407892	−	0.330304i	0.811209	+	0.584756i	$0.198810\pi$
$228$	17.8208	−	0.933948i	1.18021	−	0.0618522i
$229$	−20.5352	−	4.36489i	−1.35700	−	0.288440i	−0.528743	−	0.848782i	$-0.677336\pi$
$229$	−20.5352	−	4.36489i	−1.35700	−	0.288440i	−0.828261	+	0.560342i	$0.810670\pi$
$230$		0			0
$231$	−0.768611	+	0.330214i	−0.0505709	+	0.0217265i
$232$	−26.6024	+	26.6024i	−1.74653	+	1.74653i
$233$	0.907297	−	17.3123i	0.0594390	−	1.13416i	−0.792277	−	0.610161i	$-0.791105\pi$
$233$	0.907297	−	17.3123i	0.0594390	−	1.13416i	0.851717	−	0.524003i	$-0.175562\pi$
$234$	22.3014	+	9.92922i	1.45789	+	0.649093i
$235$		0			0
$236$	24.4511	+	54.9180i	1.59163	+	3.57486i
$237$	−18.2377	−	2.88856i	−1.18466	−	0.187632i
$238$	14.8888	−	28.2983i	0.965095	−	1.83431i
$239$	6.02822	−	8.29714i	0.389933	−	0.536697i	−0.568249	−	0.822857i	$-0.692379\pi$
$239$	6.02822	−	8.29714i	0.389933	−	0.536697i	0.958182	+	0.286160i	$0.0923788\pi$
$240$		0			0
$241$	−11.2231	+	25.2076i	−0.722947	+	1.62376i	0.0573496	+	0.998354i	$0.481735\pi$
$241$	−11.2231	+	25.2076i	−0.722947	+	1.62376i	−0.780296	+	0.625410i	$0.784932\pi$
$242$	15.6366	−	24.0783i	1.00516	−	1.54781i
$243$	0.398760	+	1.48819i	0.0255804	+	0.0954675i
$244$	−12.7612	+	39.2748i	−0.816950	+	2.51431i
$245$		0			0
$246$	−9.50673	−	29.2587i	−0.606127	−	1.86547i
$247$	−1.64152	+	1.06602i	−0.104447	+	0.0678290i
$248$	−13.6614	−	16.8705i	−0.867503	−	1.07128i
$249$	23.1260	−	13.3518i	1.46555	−	0.846134i
$250$		0			0
$251$			0.542621i			0.0342499i	0.999853	+	0.0171250i	$0.00545131\pi$
$251$			0.542621i			0.0342499i	−0.999853	+	0.0171250i	$0.994549\pi$
$252$	74.4062	+	12.7860i	4.68715	+	0.805439i
$253$	−0.00744966	+	0.0146208i	−0.000468356	+	0.000919201i
$254$	5.29157	−	24.8949i	0.332023	−	1.56205i
$255$		0			0
$256$	15.7770	−	3.35351i	0.986063	−	0.209594i
$257$	16.6152	−	4.45204i	1.03643	−	0.277711i	0.299797	−	0.954003i	$-0.403081\pi$
$257$	16.6152	−	4.45204i	1.03643	−	0.277711i	0.736633	+	0.676293i	$0.236414\pi$
$258$	22.0286	+	43.2337i	1.37144	+	2.69161i
$259$	1.33096	+	0.301178i	0.0827020	+	0.0187143i
$260$		0			0
$261$	−27.5225	+	12.2538i	−1.70360	+	0.758492i
$262$	7.70642	+	20.0759i	0.476104	+	1.24029i
$263$	7.21872	+	18.8054i	0.445126	+	1.15959i	0.954279	+	0.298916i	$0.0966251\pi$
$263$	7.21872	+	18.8054i	0.445126	+	1.15959i	−0.509154	+	0.860676i	$0.670042\pi$
$264$	2.13272	−	0.949549i	0.131260	−	0.0584407i
$265$		0			0
$266$	−5.81173	+	6.28699i	−0.356340	+	0.385480i
$267$	18.4291	+	36.1692i	1.12784	+	2.21352i
$268$	−9.90586	+	2.65427i	−0.605097	+	0.162135i
$269$	2.42544	−	0.515544i	0.147882	−	0.0314332i	−0.133376	−	0.991066i	$-0.542582\pi$
$269$	2.42544	−	0.515544i	0.147882	−	0.0314332i	0.281258	+	0.959632i	$0.409248\pi$
$270$		0			0
$271$	−1.71463	+	8.06671i	−0.104157	+	0.490018i	0.894887	+	0.446293i	$0.147256\pi$
$271$	−1.71463	+	8.06671i	−0.104157	+	0.490018i	−0.999044	+	0.0437253i	$0.986077\pi$
$272$	−20.2421	+	39.7274i	−1.22736	+	2.40882i
$273$	−11.7105	+	4.32013i	−0.708754	+	0.261466i
$274$		−	34.4291i		−	2.07994i
$275$		0			0
$276$	1.93323	−	1.11615i	0.116367	−	0.0671844i
$277$	−8.07986	−	9.97780i	−0.485472	−	0.599508i	0.474274	−	0.880377i	$-0.342711\pi$
$277$	−8.07986	−	9.97780i	−0.485472	−	0.599508i	−0.959746	+	0.280869i	$0.909377\pi$
$278$	−9.60693	+	6.23881i	−0.576185	+	0.374179i
$279$	−5.37192	−	16.5331i	−0.321609	−	0.989809i
$280$		0			0
$281$	8.46995	−	26.0678i	0.505275	−	1.55508i	−0.295033	−	0.955487i	$-0.595331\pi$
$281$	8.46995	−	26.0678i	0.505275	−	1.55508i	0.800308	−	0.599589i	$-0.204669\pi$
$282$	10.2079	+	38.0964i	0.607872	+	2.26861i
$283$	8.66959	−	13.3500i	0.515353	−	0.793575i	−0.481193	−	0.876615i	$-0.659796\pi$
$283$	8.66959	−	13.3500i	0.515353	−	0.793575i	0.996546	+	0.0830401i	$0.0264630\pi$
$284$	15.4410	−	34.6811i	0.916255	−	2.05794i
$285$		0			0
$286$	−0.257020	+	0.353758i	−0.0151979	+	0.0209181i
$287$	9.23514	+	4.85894i	0.545133	+	0.286814i
$288$	−60.8263	−	9.63393i	−3.58422	−	0.567685i
$289$	1.78903	+	4.01822i	0.105237	+	0.236366i
$290$		0			0
$291$	29.5052	+	13.1366i	1.72963	+	0.770080i
$292$	3.45189	−	65.8660i	0.202007	−	3.85452i
$293$	16.2607	−	16.2607i	0.949961	−	0.949961i	−0.0488456	−	0.998806i	$-0.515554\pi$
$293$	16.2607	−	16.2607i	0.949961	−	0.949961i	0.998806	+	0.0488456i	$0.0155542\pi$
$294$	−44.9973	+	30.9247i	−2.62430	+	1.80357i
$295$		0			0
$296$	−3.72503	−	0.791780i	−0.216513	−	0.0460213i
$297$	0.919691	−	0.0481990i	0.0533659	−	0.00279679i
$298$	3.51525	−	2.84659i	0.203633	−	0.164899i
$299$	−0.122421	+	0.212039i	−0.00707978	+	0.0122625i
$300$		0			0
$301$	−15.5854	−	5.29066i	−0.898325	−	0.304949i
$302$	−14.0634	+	2.22742i	−0.809255	+	0.128173i
$303$	−15.0425	−	23.1634i	−0.864169	−	1.33070i
$304$	7.98828	−	8.87188i	0.458159	−	0.508837i
$305$		0			0
$306$	−53.1052	+	47.8161i	−3.03582	+	2.73347i
$307$	−7.08123	−	7.08123i	−0.404147	−	0.404147i	0.475544	−	0.879692i	$-0.342251\pi$
$307$	−7.08123	−	7.08123i	−0.404147	−	0.404147i	−0.879692	+	0.475544i	$0.842251\pi$
$308$	−0.501117	+	1.25603i	−0.0285538	+	0.0715690i
$309$	11.7172	+	16.1274i	0.666570	+	0.917455i
$310$		0			0
$311$	6.77650	+	0.712239i	0.384260	+	0.0403874i	0.294689	−	0.955593i	$-0.404784\pi$
$311$	6.77650	+	0.712239i	0.384260	+	0.0403874i	0.0895708	+	0.995980i	$0.471450\pi$
$312$	32.5201	−	12.4833i	1.84109	−	0.706727i
$313$	−7.20477	−	5.83431i	−0.407238	−	0.329775i	0.403717	−	0.914884i	$-0.367718\pi$
$313$	−7.20477	−	5.83431i	−0.407238	−	0.329775i	−0.810954	+	0.585109i	$0.801052\pi$
$314$	16.1495	+	11.7333i	0.911367	+	0.662147i
$315$		0			0
$316$	−24.1487	+	17.5451i	−1.35847	+	0.986987i
$317$	17.9147	+	0.938869i	1.00619	+	0.0527321i	0.548304	−	0.836279i	$-0.315274\pi$
$317$	17.9147	+	0.938869i	1.00619	+	0.0527321i	0.457885	+	0.889011i	$0.348607\pi$
$318$	−95.5371	−	25.5991i	−5.35746	−	1.43553i
$319$	−0.112198	−	0.527848i	−0.00628186	−	0.0295538i
$320$		0			0
$321$	−36.4216	+	11.8341i	−2.03285	+	0.660514i
$322$	−0.290721	+	1.03079i	−0.0162013	+	0.0574435i
$323$	−0.896291	−	5.65896i	−0.0498710	−	0.314873i
$324$	−34.3641	−	19.8401i	−1.90911	−	1.10223i
$325$		0			0
$326$	26.8918	+	46.5780i	1.48940	+	2.57972i
$327$	31.3482	+	12.0334i	1.73356	+	0.665450i
$328$	−25.9481	−	13.2212i	−1.43274	−	0.730018i
$329$	−11.4973	−	6.84031i	−0.633867	−	0.377118i
$330$		0			0
$331$	−14.2559	−	15.8328i	−0.783577	−	0.870250i	0.210648	−	0.977562i	$-0.432442\pi$
$331$	−14.2559	−	15.8328i	−0.783577	−	0.870250i	−0.994225	+	0.107311i	$0.965776\pi$
$332$	11.1725	−	41.6965i	0.613173	−	2.28839i
$333$	−2.55764	−	1.66095i	−0.140158	−	0.0910195i
$334$	2.22089	+	21.1304i	0.121522	+	1.15620i
$335$		0			0
$336$	62.1735	−	43.9391i	3.39184	−	2.39707i
$337$	0.304839	−	1.92468i	0.0166057	−	0.104844i	−0.977993	−	0.208636i	$-0.933098\pi$
$337$	0.304839	−	1.92468i	0.0166057	−	0.104844i	0.994599	+	0.103792i	$0.0330976\pi$
$338$	17.2687	−	21.3251i	0.939295	−	1.15993i
$339$	1.21730	−	11.5818i	0.0661147	−	0.629040i
$340$		0			0
$341$	0.309677	−	0.0325483i	0.0167699	−	0.00176259i
$342$	17.0482	−	8.68648i	0.921860	−	0.469711i
$343$	3.61357	−	18.1643i	0.195115	−	0.980780i
$344$	43.6840	+	14.1938i	2.35528	+	0.765278i
$345$		0			0
$346$	−23.3567	−	21.0305i	−1.25567	−	1.13061i
$347$	−1.52700	−	29.1369i	−0.0819737	−	1.56415i	−0.661969	−	0.749531i	$-0.730279\pi$
$347$	−1.52700	−	29.1369i	−0.0819737	−	1.56415i	0.579996	−	0.814620i	$-0.303054\pi$
$348$	−26.3085	+	68.5361i	−1.41029	+	3.67392i
$349$	−6.38042			−0.341536			−0.170768	−	0.985311i	$-0.554625\pi$
$349$	−6.38042			−0.341536			−0.170768	+	0.985311i	$0.554625\pi$
$350$		0			0
$351$	13.7415			0.733466
$352$	0.395318	−	1.02984i	0.0210705	−	0.0548906i
$353$	−0.331785	−	6.33084i	−0.0176591	−	0.336957i	−0.993145	−	0.116893i	$-0.962707\pi$
$353$	−0.331785	−	6.33084i	−0.0176591	−	0.336957i	0.975485	−	0.220064i	$-0.0706266\pi$
$354$	72.2031	+	65.0120i	3.83755	+	3.45535i
$355$		0			0
$356$	62.4095	+	20.2781i	3.30770	+	1.07474i
$357$	2.39001	−	36.4598i	0.126493	−	1.92966i
$358$	38.3964	−	19.5639i	2.02931	−	1.03399i
$359$	−13.0750	+	1.37424i	−0.690073	+	0.0725296i	−0.443073	−	0.896486i	$-0.646112\pi$
$359$	−13.0750	+	1.37424i	−0.690073	+	0.0725296i	−0.247001	+	0.969015i	$0.579445\pi$
$360$		0			0
$361$	1.82568	−	17.3702i	0.0960887	−	0.914223i
$362$	−30.2304	+	37.3314i	−1.58887	+	1.96209i
$363$	5.13201	−	32.4022i	0.269360	−	1.70067i
$364$	−8.44772	+	18.3241i	−0.442781	+	0.960445i
$365$		0			0
$366$	6.97654	+	66.3774i	0.364670	+	3.46960i
$367$	6.77091	+	4.39708i	0.353439	+	0.229526i	0.709130	−	0.705078i	$-0.249088\pi$
$367$	6.77091	+	4.39708i	0.353439	+	0.229526i	−0.355691	+	0.934603i	$0.615755\pi$
$368$	0.386518	−	1.44250i	0.0201486	−	0.0751957i
$369$	−15.6048	−	17.3308i	−0.812351	−	0.902208i
$370$		0			0
$371$	29.2720	−	16.3928i	1.51973	−	0.851073i
$372$	−37.7431	−	19.2311i	−1.95689	−	0.997086i
$373$	9.84679	+	3.77983i	0.509847	+	0.195712i	0.599672	−	0.800246i	$-0.295298\pi$
$373$	9.84679	+	3.77983i	0.509847	+	0.195712i	−0.0898253	+	0.995958i	$0.528631\pi$
$374$	−0.640001	−	1.10851i	−0.0330936	−	0.0573199i
$375$		0			0
$376$	32.3330	+	18.6675i	1.66745	+	0.962702i
$377$	−1.25960	−	7.95280i	−0.0648727	−	0.409590i
$378$	58.2593	−	14.7955i	2.99654	−	0.760997i
$379$	29.5616	−	9.60515i	1.51848	−	0.493384i	0.573135	−	0.819461i	$-0.305727\pi$
$379$	29.5616	−	9.60515i	1.51848	−	0.493384i	0.945343	+	0.326077i	$0.105727\pi$
$380$		0			0
$381$	−6.04652	−	28.4466i	−0.309772	−	1.45736i
$382$	−64.6635	−	17.3265i	−3.30847	−	0.886502i
$383$	12.9898	+	0.680767i	0.663748	+	0.0347856i	0.381235	−	0.924478i	$-0.375499\pi$
$383$	12.9898	+	0.680767i	0.663748	+	0.0347856i	0.282513	+	0.959264i	$0.408832\pi$
$384$	0.239540	−	0.174036i	0.0122240	−	0.00888122i
$385$		0			0
$386$	−1.17184	−	0.851394i	−0.0596453	−	0.0433348i
$387$	28.5852	+	23.1478i	1.45307	+	1.17667i
$388$	48.7425	−	18.7105i	2.47452	−	0.949881i
$389$	−8.02779	−	0.843755i	−0.407025	−	0.0427801i	−0.101196	−	0.994867i	$-0.532267\pi$
$389$	−8.02779	−	0.843755i	−0.407025	−	0.0427801i	−0.305829	+	0.952086i	$0.598934\pi$
$390$		0			0
$391$	−0.421275	−	0.579836i	−0.0213048	−	0.0293236i
$392$	−9.41965	+	50.8192i	−0.475764	+	2.56676i
$393$	17.3752	+	17.3752i	0.876461	+	0.876461i
$394$	6.90575	−	6.21797i	0.347907	−	0.313257i
$395$		0			0
$396$	2.02220	−	2.24588i	0.101619	−	0.112860i
$397$	11.0775	+	17.0578i	0.555963	+	0.856108i	0.999188	−	0.0403030i	$-0.0128323\pi$
$397$	11.0775	+	17.0578i	0.555963	+	0.856108i	−0.443225	+	0.896411i	$0.646166\pi$
$398$	6.71904	−	1.06419i	0.336795	−	0.0533431i
$399$	−3.14477	+	9.26395i	−0.157436	+	0.463777i
$400$		0			0
$401$	−14.0818	+	24.3904i	−0.703213	+	1.21800i	0.264119	+	0.964490i	$0.414919\pi$
$401$	−14.0818	+	24.3904i	−0.703213	+	1.21800i	−0.967333	+	0.253511i	$0.918415\pi$
$402$	−12.8810	+	10.4308i	−0.642445	+	0.520242i
$403$	4.63975	−	0.243159i	0.231122	−	0.0121126i
$404$	−43.6719	−	9.28275i	−2.17276	−	0.461834i
$405$		0			0
$406$	−13.9031	−	32.3611i	−0.689999	−	1.60605i
$407$	0.0386260	−	0.0386260i	0.00191462	−	0.00191462i
$408$	−5.33656	+	101.828i	−0.264199	+	5.04122i
$409$	3.53088	+	1.57205i	0.174591	+	0.0777328i	0.492171	−	0.870499i	$-0.336204\pi$
$409$	3.53088	+	1.57205i	0.174591	+	0.0777328i	−0.317580	+	0.948231i	$0.602870\pi$
$410$		0			0
$411$	−16.0014	−	35.9398i	−0.789293	−	1.77278i
$412$	31.8283	+	5.04110i	1.56807	+	0.248357i
$413$	−32.9311	+	1.29359i	−1.62044	+	0.0636536i
$414$	1.40685	−	1.93636i	0.0691427	−	0.0951668i
$415$		0			0
$416$	6.69464	−	15.0364i	0.328232	−	0.737220i
$417$	−7.12890	+	10.9775i	−0.349104	+	0.537572i
$418$	0.0887034	+	0.331046i	0.00433862	+	0.0161920i
$419$	−2.14134	+	6.59038i	−0.104612	+	0.321961i	−0.989639	−	0.143577i	$-0.954139\pi$
$419$	−2.14134	+	6.59038i	−0.104612	+	0.321961i	0.885028	+	0.465539i	$0.154139\pi$
$420$		0			0
$421$	7.05679	+	21.7186i	0.343927	+	1.05850i	0.962156	+	0.272500i	$0.0878504\pi$
$421$	7.05679	+	21.7186i	0.343927	+	1.05850i	−0.618229	+	0.785998i	$0.712150\pi$
$422$	7.99416	−	5.19147i	0.389149	−	0.252717i
$423$	18.8152	+	23.2349i	0.914828	+	1.12972i
$424$	−81.0838	+	46.8138i	−3.93778	+	2.27348i
$425$		0			0
$426$		−	61.3564i		−	2.97273i
$427$	−17.4060	−	14.4767i	−0.842335	−	0.700575i
$428$	−28.1051	+	55.1595i	−1.35851	+	2.66623i
$429$	−0.103884	+	0.488735i	−0.00501556	+	0.0235963i
$430$		0			0
$431$	−5.41482	+	1.15095i	−0.260823	+	0.0554395i	−0.336467	−	0.941695i	$-0.609232\pi$
$431$	−5.41482	+	1.15095i	−0.260823	+	0.0554395i	0.0756443	+	0.997135i	$0.475899\pi$
$432$	−80.9589	+	21.6929i	−3.89514	+	1.04370i
$433$	13.5702	+	26.6331i	0.652143	+	1.27990i	0.946035	+	0.324064i	$0.105049\pi$
$433$	13.5702	+	26.6331i	0.652143	+	1.27990i	−0.293892	+	0.955839i	$0.594951\pi$
$434$	19.4092	−	6.02654i	0.931671	−	0.289283i
$435$		0			0
$436$	49.5881	−	22.0780i	2.37484	−	1.05735i
$437$	0.0687718	+	0.179157i	0.00328980	+	0.00857022i
$438$	−38.2018	−	99.5191i	−1.82535	−	4.75521i
$439$	6.73922	−	3.00050i	0.321646	−	0.143206i	−0.239562	−	0.970881i	$-0.577004\pi$
$439$	6.73922	−	3.00050i	0.321646	−	0.143206i	0.561207	+	0.827675i	$0.310337\pi$
$440$		0			0
$441$	−21.6263	+	35.2896i	−1.02982	+	1.68046i
$442$	−8.67067	−	17.0172i	−0.412422	−	0.809424i
$443$	8.73088	−	2.33943i	0.414817	−	0.111150i	−0.0453736	−	0.998970i	$-0.514448\pi$
$443$	8.73088	−	2.33943i	0.414817	−	0.111150i	0.460190	+	0.887820i	$0.347781\pi$
$444$	−7.26879	+	1.54503i	−0.344961	+	0.0733238i
$445$		0			0
$446$	−0.430832	+	2.02690i	−0.0204005	+	0.0959767i
$447$	2.34650	−	4.60526i	0.110986	−	0.217821i
$448$	3.55558	−	20.6912i	0.167985	−	0.977569i
$449$			1.97023i			0.0929809i	0.998919	+	0.0464905i	$0.0148037\pi$
$449$			1.97023i			0.0929809i	−0.998919	+	0.0464905i	$0.985196\pi$
$450$		0			0
$451$	0.361763	−	0.208864i	0.0170347	−	0.00983501i
$452$	−11.8474	−	14.6303i	−0.557254	−	0.688151i
$453$	−13.6452	+	8.86132i	−0.641109	+	0.416341i
$454$	−6.38443	−	19.6493i	−0.299636	−	0.922186i
$455$		0			0
$456$	8.43680	−	25.9658i	0.395089	−	1.21596i
$457$	0.527159	+	1.96739i	0.0246595	+	0.0920304i	0.977159	−	0.212510i	$-0.0681638\pi$
$457$	0.527159	+	1.96739i	0.0246595	+	0.0920304i	−0.952499	+	0.304540i	$0.901497\pi$
$458$	−29.8736	+	46.0014i	−1.39590	+	2.14950i
$459$	−16.3609	+	36.7473i	−0.763664	+	1.71522i
$460$		0			0
$461$	−15.8458	+	21.8099i	−0.738014	+	1.01579i	0.260716	+	0.965415i	$0.416041\pi$
$461$	−15.8458	+	21.8099i	−0.738014	+	1.01579i	−0.998730	+	0.0503737i	$0.983959\pi$
$462$	0.0857886	+	2.18393i	0.00399125	+	0.101605i
$463$	−6.28827	−	0.995965i	−0.292241	−	0.0462864i	0.00859262	−	0.999963i	$-0.497265\pi$
$463$	−6.28827	−	0.995965i	−0.292241	−	0.0462864i	−0.300834	+	0.953677i	$0.597265\pi$
$464$	19.9757	+	44.8661i	0.927347	+	2.08285i
$465$		0			0
$466$	−41.3775	−	18.4225i	−1.91678	−	0.853404i
$467$	1.25472	−	23.9414i	0.0580613	−	1.10788i	−0.801881	−	0.597484i	$-0.796167\pi$
$467$	1.25472	−	23.9414i	0.0580613	−	1.10788i	0.859942	−	0.510392i	$-0.170500\pi$
$468$	31.8855	−	31.8855i	1.47391	−	1.47391i
$469$	0.660864	−	5.58321i	0.0305159	−	0.257809i
$470$		0			0
$471$	22.3113	+	4.74241i	1.02805	+	0.218519i
$472$	91.8463	−	4.81346i	4.22757	−	0.221558i
$473$	−0.512021	+	0.414626i	−0.0235427	+	0.0190645i
$474$	−24.1215	+	41.7797i	−1.10794	+	1.91900i
$475$		0			0
$476$	−38.9441	−	44.4080i	−1.78500	−	2.03544i
$477$	−74.0535	+	11.7289i	−3.39068	+	0.537031i
$478$	−14.5937	−	22.4723i	−0.667499	−	1.02786i
$479$	−1.12148	+	1.24553i	−0.0512418	+	0.0569098i	−0.768221	−	0.640185i	$-0.778858\pi$
$479$	−1.12148	+	1.24553i	−0.0512418	+	0.0569098i	0.716979	+	0.697095i	$0.245524\pi$
$480$		0			0
$481$	0.605709	−	0.545383i	0.0276179	−	0.0248673i
$482$	50.9766	+	50.9766i	2.32192	+	2.32192i
$483$	0.175596	+	1.21114i	0.00798990	+	0.0551086i
$484$	−31.1717	−	42.9041i	−1.41689	−	1.95019i
$485$		0			0
$486$	4.00326	+	0.420760i	0.181592	+	0.0190861i
$487$	−28.7873	+	11.0504i	−1.30448	+	0.500743i	−0.908641	−	0.417578i	$-0.862879\pi$
$487$	−28.7873	+	11.0504i	−1.30448	+	0.500743i	−0.395838	+	0.918320i	$0.629546\pi$
$488$	49.1002	+	39.7606i	2.22266	+	1.79988i
$489$	49.7196	+	36.1234i	2.24840	+	1.63356i
$490$		0			0
$491$	−5.12812	+	3.72580i	−0.231429	+	0.168143i	−0.697456	−	0.716627i	$-0.745685\pi$
$491$	−5.12812	+	3.72580i	−0.231429	+	0.168143i	0.466027	+	0.884770i	$0.345685\pi$
$492$	−56.7493	−	2.97410i	−2.55846	−	0.134083i
$493$	22.7670	+	6.10040i	1.02537	+	0.274748i
$494$	1.06321	+	5.00201i	0.0478360	+	0.225051i
$495$		0			0
$496$	−26.9515	+	8.75709i	−1.21016	+	0.393205i
$497$	14.5225	+	14.9080i	0.651422	+	0.668715i
$498$	−10.9141	−	68.9087i	−0.489071	−	3.08787i
$499$	36.2714	+	20.9413i	1.62373	+	0.937462i	0.985910	+	0.167277i	$0.0534975\pi$
$499$	36.2714	+	20.9413i	1.62373	+	0.937462i	0.637821	+	0.770184i	$0.279836\pi$
$500$		0			0
$501$	12.1390	+	21.0254i	0.542331	+	0.939344i
$502$	1.32353	+	0.508055i	0.0590719	+	0.0226756i
$503$	32.8287	+	16.7270i	1.46376	+	0.745822i	0.990809	−	0.135268i	$-0.0431895\pi$
$503$	32.8287	+	16.7270i	1.46376	+	0.745822i	0.472949	+	0.881090i	$0.343189\pi$
$504$	59.0578	−	99.2653i	2.63064	−	4.42163i
$505$		0			0
$506$	0.0286870	+	0.0318602i	0.00127529	+	0.00141636i
$507$	8.11531	−	30.2867i	0.360413	−	1.34508i
$508$	−39.4280	−	25.6048i	−1.74933	−	1.13603i
$509$	4.22239	+	40.1734i	0.187154	+	1.78065i	0.536739	+	0.843748i	$0.319656\pi$
$509$	4.22239	+	40.1734i	0.187154	+	1.78065i	−0.349585	+	0.936905i	$0.613677\pi$
$510$		0			0
$511$	32.8372	+	15.1385i	1.45263	+	0.669688i
$512$	6.56128	−	41.4263i	0.289970	−	1.83080i
$513$	6.77799	−	8.37012i	0.299255	−	0.369550i
$514$	4.69767	−	44.6953i	0.207205	−	1.97143i
$515$		0			0
$516$	89.1379	−	9.36877i	3.92408	−	0.412437i
$517$	−0.477162	+	0.243126i	−0.0209855	+	0.0106927i
$518$	1.98079	−	2.96441i	0.0870310	−	0.130249i
$519$	−34.1559	−	11.0979i	−1.49928	−	0.487145i
$520$		0			0
$521$	11.8397	+	10.6605i	0.518707	+	0.467046i	0.886412	−	0.462896i	$-0.153190\pi$
$521$	11.8397	+	10.6605i	0.518707	+	0.467046i	−0.367705	+	0.929942i	$0.619856\pi$
$522$	4.11948	+	78.6044i	0.180305	+	3.44042i
$523$	4.75426	−	12.3853i	0.207889	−	0.541570i	−0.789503	−	0.613747i	$-0.789661\pi$
$523$	4.75426	−	12.3853i	0.207889	−	0.541570i	0.997392	+	0.0721772i	$0.0229947\pi$
$524$	39.7220			1.73526
$525$		0			0
$526$	52.6279			2.29469
$527$	−4.87395	+	12.6971i	−0.212312	+	0.553093i
$528$	−0.159498	−	3.04341i	−0.00694128	−	0.132447i
$529$	−17.0745	−	15.3739i	−0.742369	−	0.668432i
$530$		0			0
$531$	70.0464	+	22.7595i	3.03976	+	0.987677i
$532$	6.99463	+	14.1840i	0.303256	+	0.614955i
$533$	5.55354	−	2.82967i	0.240550	−	0.122567i
$534$	105.477	−	11.0861i	4.56442	−	0.479740i
$535$		0			0
$536$	−1.64005	+	15.6040i	−0.0708392	+	0.673990i
$537$	30.9886	−	38.2677i	1.33726	−	1.65137i
$538$	1.01345	−	6.39869i	0.0436931	−	0.275867i
$539$	−0.537759	−	0.510331i	−0.0231629	−	0.0219815i
$540$		0			0
$541$	−3.36061	−	31.9740i	−0.144484	−	1.37467i	−0.791021	−	0.611789i	$-0.790450\pi$
$541$	−3.36061	−	31.9740i	−0.144484	−	1.37467i	0.646537	−	0.762882i	$-0.276216\pi$
$542$	18.0704	+	11.7351i	0.776191	+	0.504065i
$543$	−14.2065	+	53.0195i	−0.609661	+	2.27528i
$544$	32.2394	+	35.8054i	1.38225	+	1.53515i
$545$		0			0
$546$	−0.427139	+	32.6085i	−0.0182799	+	1.39552i
$547$	0.773188	+	0.393959i	0.0330591	+	0.0168445i	0.470442	−	0.882431i	$-0.344095\pi$
$547$	0.773188	+	0.393959i	0.0330591	+	0.0168445i	−0.437383	+	0.899275i	$0.644095\pi$
$548$	−59.3723	−	22.7909i	−2.53626	−	0.973579i
$549$	25.2972	+	43.8161i	1.07966	+	1.87003i
$550$		0			0
$551$	−5.46546	−	3.15548i	−0.232836	−	0.134428i
$552$	−0.534267	−	3.37323i	−0.0227399	−	0.143574i
$553$	−4.02796	−	15.8607i	−0.171286	−	0.674465i
$554$	−31.9024	+	10.3657i	−1.35540	+	0.440397i
$555$		0			0
$556$	4.39926	+	20.6969i	0.186570	+	0.877743i
$557$	31.3762	+	8.40723i	1.32945	+	0.356226i	0.852511	−	0.522709i	$-0.175079\pi$
$557$	31.3762	+	8.40723i	1.32945	+	0.356226i	0.476941	+	0.878935i	$0.341745\pi$
$558$	−45.3562	−	2.37702i	−1.92008	−	0.100627i
$559$	−7.95314	+	5.77829i	−0.336382	+	0.244396i
$560$		0			0
$561$	−1.18328	−	0.859705i	−0.0499582	−	0.0362968i
$562$	−55.6527	−	45.0666i	−2.34757	−	1.90102i
$563$	−13.7174	+	5.26563i	−0.578121	+	0.221920i	−0.629818	−	0.776743i	$-0.716870\pi$
$563$	−13.7174	+	5.26563i	−0.578121	+	0.221920i	0.0516965	+	0.998663i	$0.483537\pi$
$564$	72.4540	+	7.61522i	3.05086	+	0.320659i
$565$		0			0
$566$	−24.4452	−	33.6459i	−1.02751	−	1.41424i
$567$	17.0836	−	13.4674i	0.717443	−	0.565577i
$568$	−41.0696	−	41.0696i	−1.72324	−	1.72324i
$569$	−31.3512	+	28.2287i	−1.31431	+	1.18341i	−0.344712	+	0.938708i	$0.612023\pi$
$569$	−31.3512	+	28.2287i	−1.31431	+	1.18341i	−0.969598	+	0.244702i	$0.921310\pi$
$570$		0			0
$571$	−15.1300	+	16.8035i	−0.633169	+	0.703206i	−0.971290	−	0.237897i	$-0.923542\pi$
$571$	−15.1300	+	16.8035i	−0.633169	+	0.703206i	0.338121	+	0.941103i	$0.390209\pi$
$572$	0.439911	+	0.677403i	0.0183936	+	0.0283236i
$573$	−75.5537	+	11.9665i	−3.15630	+	0.499909i
$574$	20.4985	−	17.9764i	0.855589	−	0.750319i
$575$		0			0
$576$	−23.4592	+	40.6326i	−0.977468	+	1.69302i
$577$	−19.9590	+	16.1625i	−0.830906	+	0.672854i	−0.947300	−	0.320349i	$-0.896200\pi$
$577$	−19.9590	+	16.1625i	−0.830906	+	0.672854i	0.116394	+	0.993203i	$0.462867\pi$
$578$	11.4761	−	0.601435i	0.477341	−	0.0250164i
$579$	−1.61896	−	0.344121i	−0.0672818	−	0.0143012i
$580$		0			0
$581$	18.9618	+	14.1597i	0.786670	+	0.587444i
$582$	59.6676	−	59.6676i	2.47330	−	2.47330i
$583$	0.0702866	−	1.34115i	0.00291097	−	0.0555447i
$584$	−92.1849	−	41.0434i	−3.81464	−	1.69839i
$585$		0			0
$586$	−24.4373	−	54.8870i	−1.00949	−	2.26736i
$587$	36.1811	+	5.73052i	1.49335	+	0.236524i	0.849077	−	0.528269i	$-0.177159\pi$
$587$	36.1811	+	5.73052i	1.49335	+	0.236524i	0.644276	+	0.764793i	$0.277159\pi$
$588$	23.5424	+	98.0682i	0.970871	+	4.04427i
$589$	2.14044	−	2.94607i	0.0881955	−	0.121391i
$590$		0			0
$591$	4.31888	−	9.70036i	0.177655	−	0.399020i
$592$	−2.70761	+	4.16936i	−0.111282	+	0.171360i
$593$	−4.31960	−	16.1210i	−0.177385	−	0.662009i	−0.996133	−	0.0878564i	$-0.971998\pi$
$593$	−4.31960	−	16.1210i	−0.177385	−	0.662009i	0.818748	−	0.574152i	$-0.194668\pi$
$594$	0.743541	−	2.28838i	0.0305078	−	0.0938935i
$595$		0			0
$596$	−2.58192	−	7.94633i	−0.105760	−	0.325494i
$597$	6.51927	−	4.23367i	0.266816	−	0.173272i
$598$	0.402571	+	0.497133i	0.0164623	+	0.0203293i
$599$	−17.1188	+	9.88355i	−0.699455	+	0.403831i	−0.807145	−	0.590354i	$-0.798988\pi$
$599$	−17.1188	+	9.88355i	−0.699455	+	0.403831i	0.107689	+	0.994185i	$0.465655\pi$
$600$		0			0
$601$			23.8371i			0.972336i	0.873865	+	0.486168i	$0.161606\pi$
$601$			23.8371i			0.972336i	−0.873865	+	0.486168i	$0.838394\pi$
$602$	−27.4972	+	33.0612i	−1.12070	+	1.34748i
$603$	−5.70414	+	11.1950i	−0.232291	+	0.455896i
$604$	−5.46834	+	25.7265i	−0.222503	+	1.04680i
$605$		0			0
$606$	−70.5830	+	15.0029i	−2.86724	+	0.609451i
$607$	−4.47778	+	1.19982i	−0.181747	+	0.0486991i	−0.348545	−	0.937292i	$-0.613324\pi$
$607$	−4.47778	+	1.19982i	−0.181747	+	0.0486991i	0.166797	+	0.985991i	$0.446657\pi$
$608$	−5.85674	−	11.4945i	−0.237522	−	0.466164i
$609$	−29.5535	−	27.3194i	−1.19757	−	1.10704i
$610$		0			0
$611$	−7.29979	+	3.25008i	−0.295318	+	0.131484i
$612$	47.3042	+	123.232i	1.91216	+	4.98135i
$613$	10.4595	+	27.2478i	0.422454	+	1.10053i	0.965403	+	0.260764i	$0.0839745\pi$
$613$	10.4595	+	27.2478i	0.422454	+	1.10053i	−0.542949	+	0.839766i	$0.682692\pi$
$614$	−23.9022	+	10.6420i	−0.964616	+	0.429475i
$615$		0			0
$616$	1.51926	+	1.40441i	0.0612126	+	0.0565853i
$617$	−7.69612	−	15.1045i	−0.309834	−	0.608084i	0.682610	−	0.730783i	$-0.260845\pi$
$617$	−7.69612	−	15.1045i	−0.309834	−	0.608084i	−0.992444	+	0.122699i	$0.960845\pi$
$618$	50.3077	−	13.4799i	2.02367	−	0.542242i
$619$	1.80856	−	0.384422i	0.0726924	−	0.0154512i	−0.171422	−	0.985198i	$-0.554836\pi$
$619$	1.80856	−	0.384422i	0.0726924	−	0.0154512i	0.244114	+	0.969746i	$0.421503\pi$
$620$		0			0
$621$	0.280116	−	1.31784i	0.0112407	−	0.0528832i
$622$	8.08208	−	15.8620i	0.324062	−	0.636007i
$623$	−23.0041	+	27.6589i	−0.921639	+	1.10813i
$624$		−	45.4728i		−	1.82037i
$625$		0			0
$626$	−20.9765	+	12.1108i	−0.838390	+	0.484044i
$627$	0.246454	+	0.304346i	0.00984243	+	0.0121544i
$628$	30.9242	−	20.0824i	1.23401	−	0.801376i
$629$	0.737284	+	2.26913i	0.0293974	+	0.0904760i
$630$		0			0
$631$	−14.8852	+	45.8121i	−0.592572	+	1.82375i	−0.0261130	+	0.999659i	$0.508313\pi$
$631$	−14.8852	+	45.8121i	−0.592572	+	1.82375i	−0.566459	+	0.824090i	$0.691687\pi$
$632$	11.8197	+	44.1116i	0.470161	+	1.75467i
$633$	5.93213	−	9.13467i	0.235781	−	0.363071i
$634$	19.0635	−	42.8173i	0.757109	−	1.70049i
$635$		0			0
$636$	−107.388	+	147.806i	−4.25820	+	5.86091i
$637$	−7.61434	−	8.02411i	−0.301691	−	0.317927i
$638$	−1.39255	−	0.220557i	−0.0551314	−	0.00873195i
$639$	−18.9178	−	42.4901i	−0.748377	−	1.68088i
$640$		0			0
$641$	27.7155	+	12.3398i	1.09470	+	0.487391i	0.872998	−	0.487724i	$-0.162173\pi$
$641$	27.7155	+	12.3398i	1.09470	+	0.487391i	0.221700	+	0.975115i	$0.428839\pi$
$642$	−5.23645	+	99.9175i	−0.206666	+	3.94343i
$643$	15.1791	−	15.1791i	0.598605	−	0.598605i	−0.341336	−	0.939941i	$-0.610879\pi$
$643$	15.1791	−	15.1791i	0.598605	−	0.598605i	0.939941	+	0.341336i	$0.110879\pi$
$644$	1.58513	+	1.18369i	0.0624628	+	0.0466440i
$645$		0			0
$646$	−14.6422	−	3.11229i	−0.576089	−	0.122452i
$647$	19.9489	−	1.04548i	0.784271	−	0.0411019i	0.344003	−	0.938968i	$-0.388217\pi$
$647$	19.9489	−	1.04548i	0.784271	−	0.0411019i	0.440268	+	0.897866i	$0.354883\pi$
$648$	−47.1791	+	38.2049i	−1.85337	+	1.50083i
$649$	−0.659624	+	1.14250i	−0.0258925	+	0.0448471i
$650$		0			0
$651$	17.4599	−	15.3117i	0.684309	−	0.600113i
$652$	98.1244	−	15.5414i	3.84285	−	0.608647i
$653$	24.0672	+	37.0603i	0.941824	+	1.45028i	0.892266	+	0.451511i	$0.149115\pi$
$653$	24.0672	+	37.0603i	0.941824	+	1.45028i	0.0495582	+	0.998771i	$0.484219\pi$
$654$	58.7024	−	65.1956i	2.29545	−	2.54935i
$655$		0			0
$656$	−28.2520	+	25.4382i	−1.10306	+	0.993196i
$657$	−57.1396	−	57.1396i	−2.22923	−	2.22923i
$658$	−27.4494	+	21.6390i	−1.07009	+	0.843575i
$659$	20.2475	+	27.8683i	0.788730	+	1.08559i	0.994265	+	0.106944i	$0.0341066\pi$
$659$	20.2475	+	27.8683i	0.788730	+	1.08559i	−0.205535	+	0.978650i	$0.565893\pi$
$660$		0			0
$661$	−25.7734	−	2.70889i	−1.00247	−	0.105364i	−0.410952	−	0.911657i	$-0.634804\pi$
$661$	−25.7734	−	2.70889i	−1.00247	−	0.105364i	−0.591516	+	0.806293i	$0.701470\pi$
$662$	−51.9662	+	19.9480i	−2.01973	+	0.775300i
$663$	−16.9601	−	13.7340i	−0.658677	−	0.533386i
$664$	−53.4302	−	38.8193i	−2.07349	−	1.50648i
$665$		0			0
$666$	−6.44600	+	4.68329i	−0.249777	+	0.181474i
$667$	−0.788371	−	0.0413168i	−0.0305259	−	0.00159979i
$668$	37.9091	+	10.1577i	1.46675	+	0.393014i
$669$	0.492298	+	2.31608i	0.0190333	+	0.0895449i
$670$		0			0
$671$	−0.861899	+	0.280048i	−0.0332732	+	0.0108111i
$672$	−20.2502	−	79.7382i	−0.781169	−	3.07597i
$673$	−7.73152	−	48.8149i	−0.298028	−	1.88168i	−0.449600	−	0.893230i	$-0.648434\pi$
$673$	−7.73152	−	48.8149i	−0.298028	−	1.88168i	0.151572	−	0.988446i	$-0.451566\pi$
$674$	−4.40914	−	2.54562i	−0.169834	−	0.0980536i
$675$		0			0
$676$	−25.3434	−	43.8961i	−0.974748	−	1.68831i
$677$	−25.3946	−	9.74806i	−0.975992	−	0.374648i	−0.182485	−	0.983209i	$-0.558414\pi$
$677$	−25.3946	−	9.74806i	−0.975992	−	0.374648i	−0.793508	+	0.608560i	$0.791747\pi$
$678$	−27.1100	−	13.8132i	−1.04115	−	0.530494i
$679$	−0.374899	+	28.6204i	−0.0143873	+	1.09835i
$680$		0			0
$681$	−15.7969	−	17.5442i	−0.605338	−	0.672295i
$682$	0.210560	−	0.785819i	0.00806274	−	0.0300906i
$683$	−15.4137	−	10.0098i	−0.589789	−	0.383013i	0.214965	−	0.976622i	$-0.431036\pi$
$683$	−15.4137	−	10.0098i	−0.589789	−	0.383013i	−0.804754	+	0.593608i	$0.797703\pi$
$684$	−3.69436	−	35.1495i	−0.141257	−	1.34397i
$685$		0			0
$686$	−40.9219	−	25.8212i	−1.56240	−	0.985858i
$687$	−9.80465	+	61.9041i	−0.374071	+	2.36179i
$688$	37.7346	−	46.5984i	1.43862	−	1.77655i
$689$	2.09461	−	19.9289i	0.0797982	−	0.759230i
$690$		0			0
$691$	−24.2574	+	2.54955i	−0.922793	+	0.0969895i	−0.553995	−	0.832520i	$-0.686897\pi$
$691$	−24.2574	+	2.54955i	−0.922793	+	0.0969895i	−0.368798	+	0.929509i	$0.620231\pi$
$692$	−51.7281	+	26.3568i	−1.96641	+	1.00194i
$693$	0.732772	+	1.48595i	0.0278357	+	0.0564464i
$694$	−72.4987	−	23.5562i	−2.75201	−	0.894183i
$695$		0			0
$696$	83.4668	+	75.1539i	3.16380	+	2.84870i
$697$	0.954884	+	18.2203i	0.0361688	+	0.690142i
$698$	−5.97397	+	15.5627i	−0.226118	+	0.589058i
$699$	−51.7553			−1.95756
$700$		0			0
$701$	−8.02401			−0.303063			−0.151531	−	0.988452i	$-0.548420\pi$
$701$	−8.02401			−0.303063			−0.151531	+	0.988452i	$0.548420\pi$
$702$	12.8661	−	33.5174i	0.485600	−	1.26503i
$703$	−0.0334338	−	0.637955i	−0.00126098	−	0.0240609i
$704$	−0.624545	−	0.562343i	−0.0235384	−	0.0211941i
$705$		0			0
$706$	−15.7524	−	5.11828i	−0.592851	−	0.192629i
$707$	13.5988	−	20.3516i	0.511434	−	0.765401i
$708$	159.908	−	81.4772i	6.00971	−	3.06210i
$709$	−2.50116	+	0.262883i	−0.0939331	+	0.00987276i	−0.151378	−	0.988476i	$-0.548371\pi$
$709$	−2.50116	+	0.262883i	−0.0939331	+	0.00987276i	0.0574453	+	0.998349i	$0.481705\pi$
$710$		0			0
$711$	−3.82267	+	36.3702i	−0.143361	+	1.36399i
$712$	63.1814	−	78.0225i	2.36782	−	2.92402i
$713$	0.0712604	−	0.449921i	0.00266872	−	0.0168497i
$714$	−86.6928	−	39.9668i	−3.24440	−	1.49572i
$715$		0			0
$716$	−8.32054	−	79.1646i	−0.310953	−	2.95852i
$717$	−25.6784	−	16.6757i	−0.958976	−	0.622766i
$718$	−8.89015	+	33.1785i	−0.331777	+	1.23821i
$719$	−26.3473	−	29.2617i	−0.982589	−	1.09128i	−0.995818	−	0.0913630i	$-0.970878\pi$
$719$	−26.3473	−	29.2617i	−0.982589	−	1.09128i	0.0132288	−	0.999912i	$-0.495789\pi$
$720$		0			0
$721$	−9.03288	+	15.1826i	−0.336402	+	0.565430i
$722$	−40.6590	−	20.7168i	−1.51317	−	0.771000i
$723$	76.9056	+	29.5213i	2.86015	+	1.09791i
$724$	44.3658	+	76.8439i	1.64884	+	2.85588i
$725$		0			0
$726$	−74.2284	−	42.8558i	−2.75487	−	1.59053i
$727$	4.51898	+	28.5317i	0.167600	+	1.05818i	0.917821	+	0.396995i	$0.129947\pi$
$727$	4.51898	+	28.5317i	0.167600	+	1.05818i	−0.750221	+	0.661187i	$0.770053\pi$
$728$	21.5410	+	22.1128i	0.798361	+	0.819554i
$729$	27.8335	−	9.04365i	1.03087	−	0.334950i
$730$		0			0
$731$	−5.98304	−	28.1480i	−0.221291	−	1.04109i
$732$	119.085	+	31.9087i	4.40151	+	1.17938i
$733$	−9.36598	−	0.490850i	−0.345940	−	0.0181300i	−0.121425	−	0.992601i	$-0.538746\pi$
$733$	−9.36598	−	0.490850i	−0.345940	−	0.0181300i	−0.224515	+	0.974471i	$0.572080\pi$
$734$	17.0647	−	12.3982i	0.629869	−	0.457626i
$735$		0			0
$736$	−1.30556	−	0.948546i	−0.0481236	−	0.0349639i
$737$	−0.174901	−	0.141632i	−0.00644257	−	0.00521709i
$738$	−56.8830	+	21.8353i	−2.09389	+	0.803770i
$739$	7.21113	+	0.757921i	0.265266	+	0.0278806i	0.236228	−	0.971698i	$-0.424089\pi$
$739$	7.21113	+	0.757921i	0.265266	+	0.0278806i	0.0290382	+	0.999578i	$0.490756\pi$
$740$		0			0
$741$	3.43462	+	4.72735i	0.126174	+	0.173664i
$742$	−12.5770	−	86.7471i	−0.461716	−	3.18459i
$743$	−3.41793	−	3.41793i	−0.125392	−	0.125392i	0.641626	−	0.767018i	$-0.278260\pi$
$743$	−3.41793	−	3.41793i	−0.125392	−	0.125392i	−0.767018	+	0.641626i	$0.778260\pi$
$744$	−48.1619	+	43.3652i	−1.76570	+	1.58984i
$745$		0			0
$746$	18.4390	−	20.4786i	0.675101	−	0.749776i
$747$	−28.8045	−	44.3550i	−1.05390	−	1.62286i
$748$	−2.33527	+	0.369871i	−0.0853860	+	0.0135238i
$749$	−22.3772	−	25.5167i	−0.817644	−	0.932360i
$750$		0			0
$751$	−5.61814	+	9.73090i	−0.205009	+	0.355086i	−0.950136	−	0.311837i	$-0.899056\pi$
$751$	−5.61814	+	9.73090i	−0.205009	+	0.355086i	0.745127	+	0.666923i	$0.232389\pi$
$752$	37.8766	−	30.6718i	1.38122	−	1.11849i
$753$	1.61773	−	0.0847816i	0.0589534	−	0.00308961i
$754$	−20.5774	−	4.37385i	−0.749383	−	0.159286i
$755$		0			0
$756$	13.0512	−	110.261i	0.474668	−	4.01017i
$757$	−4.30306	+	4.30306i	−0.156397	+	0.156397i	−0.780968	−	0.624571i	$-0.785274\pi$
$757$	−4.30306	+	4.30306i	−0.156397	+	0.156397i	0.624571	+	0.780968i	$0.285274\pi$
$758$	4.25018	−	81.0982i	0.154373	−	2.94562i
$759$	0.0447533	+	0.0199255i	0.00162444	+	0.000723248i
$760$		0			0
$761$	−2.87986	−	6.46828i	−0.104395	−	0.234475i	0.853794	−	0.520611i	$-0.174296\pi$
$761$	−2.87986	−	6.46828i	−0.104395	−	0.234475i	−0.958189	+	0.286136i	$0.907629\pi$
$762$	−75.0466	−	11.8862i	−2.71865	−	0.430592i
$763$	1.16805	+	29.7351i	0.0422862	+	1.07648i
$764$	−72.6844	+	100.041i	−2.62963	+	3.61937i
$765$		0			0
$766$	13.8228	−	31.0465i	0.499439	−	1.12176i
$767$	−10.7209	+	16.5087i	−0.387109	+	0.596096i
$768$	−12.4630	−	46.5124i	−0.449719	−	1.67837i
$769$	−5.23318	+	16.1061i	−0.188713	+	0.580800i	−0.999993	−	0.00385911i	$-0.998772\pi$
$769$	−5.23318	+	16.1061i	−0.188713	+	0.580800i	0.811279	+	0.584659i	$0.198772\pi$
$770$		0			0
$771$	−15.8690	−	48.8398i	−0.571509	−	1.75892i
$772$	−2.24394	+	1.45723i	−0.0807611	+	0.0524468i
$773$	−7.10023	−	8.76806i	−0.255378	−	0.315365i	0.633292	−	0.773913i	$-0.281703\pi$
$773$	−7.10023	−	8.76806i	−0.255378	−	0.315365i	−0.888670	+	0.458548i	$0.848370\pi$
$774$	83.2250	−	48.0500i	2.99146	−	1.72712i
$775$		0			0
$776$		−	79.8783i		−	2.86746i
$777$	0.689953	−	4.01509i	0.0247519	−	0.144041i
$778$	−9.57443	+	18.7909i	−0.343260	+	0.673686i
$779$	1.01569	−	4.77847i	0.0363910	−	0.171206i
$780$		0			0
$781$	0.814908	−	0.173214i	0.0291597	−	0.00619809i
$782$	−1.80874	+	0.484650i	−0.0646804	+	0.0173311i
$783$	20.1150	+	39.4780i	0.718853	+	1.41083i
$784$	57.5276	+	35.2543i	2.05456	+	1.25908i
$785$		0			0
$786$	58.6488	−	26.1121i	2.09193	−	0.931388i
$787$	−2.39900	−	6.24961i	−0.0855151	−	0.222775i	0.884154	−	0.467195i	$-0.154736\pi$
$787$	−2.39900	−	6.24961i	−0.0855151	−	0.222775i	−0.969669	+	0.244421i	$0.921402\pi$
$788$	−6.15140	−	16.0249i	−0.219134	−	0.570865i
$789$	54.9372	−	24.4596i	1.95582	−	0.870785i
$790$		0			0
$791$	9.85646	−	3.06042i	0.350455	−	0.108816i
$792$	−2.09910	−	4.11971i	−0.0745882	−	0.146388i
$793$	−13.0614	+	3.49979i	−0.463824	+	0.124281i
$794$	51.9782	−	11.0483i	1.84464	−	0.392090i
$795$		0			0
$796$	2.61260	−	12.2913i	0.0926013	−	0.435655i
$797$	3.92708	−	7.70734i	0.139104	−	0.273008i	−0.810936	−	0.585135i	$-0.801042\pi$
$797$	3.92708	−	7.70734i	0.139104	−	0.273008i	0.950040	+	0.312127i	$0.101042\pi$
$798$	19.6516	+	16.3443i	0.695659	+	0.578584i
$799$		−	23.3907i		−	0.827502i
$800$		0			0
$801$	69.6258	−	40.1985i	2.46011	−	1.42034i
$802$	46.3069	+	57.1843i	1.63515	+	2.01925i
$803$	1.21392	−	0.788329i	0.0428383	−	0.0278195i
$804$	9.46097	+	29.1179i	0.333663	+	1.02691i
$805$		0			0
$806$	3.75109	−	11.5447i	0.132126	−	0.406643i
$807$	−1.91597	−	7.15048i	−0.0674452	−	0.251709i
$808$	−37.2031	+	57.2878i	−1.30880	+	2.01538i
$809$	−4.03448	+	9.06159i	−0.141845	+	0.318588i	−0.970473	−	0.241211i	$-0.922455\pi$
$809$	−4.03448	+	9.06159i	−0.141845	+	0.318588i	0.828628	+	0.559800i	$0.189122\pi$
$810$		0			0
$811$	−6.48171	+	8.92131i	−0.227604	+	0.313270i	−0.907511	−	0.420029i	$-0.862020\pi$
$811$	−6.48171	+	8.92131i	−0.227604	+	0.313270i	0.679907	+	0.733298i	$0.262020\pi$
$812$	−65.0095	+	2.55369i	−2.28139	+	0.0896170i
$813$	24.3174	+	3.85150i	0.852849	+	0.135078i
$814$	−0.0580487	−	0.130380i	−0.00203461	−	0.00456980i
$815$		0			0
$816$	121.603	+	54.1411i	4.25695	+	1.89532i
$817$	−0.403252	+	7.69451i	−0.0141080	+	0.269197i
$818$	7.14040	−	7.14040i	0.249658	−	0.249658i
$819$	9.75827	+	22.7135i	0.340982	+	0.793674i
$820$		0			0
$821$	5.85056	+	1.24357i	0.204186	+	0.0434011i	0.308869	−	0.951105i	$-0.400050\pi$
$821$	5.85056	+	1.24357i	0.204186	+	0.0434011i	−0.104683	+	0.994506i	$0.533383\pi$
$822$	−102.644	+	5.37936i	−3.58013	+	0.187627i
$823$	−31.4147	+	25.4391i	−1.09505	+	0.886752i	−0.994135	−	0.108144i	$-0.965509\pi$
$823$	−31.4147	+	25.4391i	−1.09505	+	0.886752i	−0.100912	+	0.994895i	$0.532176\pi$
$824$	24.6511	−	42.6969i	0.858761	−	1.48742i
$825$		0			0
$826$	−27.6781	+	81.5348i	−0.963044	+	2.83696i
$827$	14.7814	−	2.34114i	0.513999	−	0.0814094i	0.105954	−	0.994371i	$-0.466211\pi$
$827$	14.7814	−	2.34114i	0.513999	−	0.0814094i	0.408045	+	0.912962i	$0.366211\pi$
$828$	−2.40793	−	3.70789i	−0.0836813	−	0.128858i
$829$	8.38379	−	9.31115i	0.291181	−	0.323389i	−0.579750	−	0.814794i	$-0.696850\pi$
$829$	8.38379	−	9.31115i	0.291181	−	0.323389i	0.870931	+	0.491405i	$0.163516\pi$
$830$		0			0
$831$	−28.4846	+	25.6477i	−0.988121	+	0.889708i
$832$	−8.86689	−	8.86689i	−0.307404	−	0.307404i
$833$	30.5238	−	10.8085i	1.05759	−	0.374492i
$834$	20.1010	+	27.6666i	0.696040	+	0.958016i
$835$		0			0
$836$	0.629601	+	0.0661737i	0.0217752	+	0.00228867i
$837$	−23.8680	+	9.16205i	−0.824998	+	0.316687i
$838$	14.0699	+	11.3936i	0.486037	+	0.393585i
$839$	28.6107	+	20.7869i	0.987750	+	0.717643i	0.959427	−	0.281956i	$-0.0909833\pi$
$839$	28.6107	+	20.7869i	0.987750	+	0.717643i	0.0283231	+	0.999599i	$0.490983\pi$
$840$		0			0
$841$	−2.45765	+	1.78558i	−0.0847464	+	0.0615719i
$842$	59.5818	+	3.12255i	2.05333	+	0.107610i
$843$	−79.0401	−	21.1787i	−2.72228	−	0.729434i
$844$	−3.66073	−	17.2224i	−0.126007	−	0.592818i
$845$		0			0
$846$	74.2898	−	24.1382i	2.55414	−	0.829889i
$847$	28.1791	−	7.15633i	0.968245	−	0.245894i
$848$	19.1200	+	120.719i	0.656584	+	4.14551i
$849$	−41.1553	−	23.7610i	−1.41244	−	0.815475i
$850$		0			0
$851$	−0.0399564	−	0.0692065i	−0.00136969	−	0.00237237i
$852$	−105.808	−	40.6159i	−3.62493	−	1.39148i
$853$	−24.9715	−	12.7236i	−0.855007	−	0.435648i	−0.0291816	−	0.999574i	$-0.509290\pi$
$853$	−24.9715	−	12.7236i	−0.855007	−	0.435648i	−0.825825	+	0.563927i	$0.809290\pi$
$854$	−51.6078	+	28.9012i	−1.76598	+	0.988978i
$855$		0			0
$856$	63.3757	+	70.3859i	2.16614	+	2.40574i
$857$	−6.76369	+	25.2424i	−0.231043	+	0.862265i	0.748850	+	0.662740i	$0.230606\pi$
$857$	−6.76369	+	25.2424i	−0.231043	+	0.862265i	−0.979893	+	0.199525i	$0.936060\pi$
$858$	1.09483	+	0.710988i	0.0373767	+	0.0242727i
$859$	2.62848	+	25.0083i	0.0896824	+	0.853271i	0.943204	+	0.332214i	$0.107796\pi$
$859$	2.62848	+	25.0083i	0.0896824	+	0.853271i	−0.853522	+	0.521057i	$0.825538\pi$
$860$		0			0
$861$	13.0431	−	28.2921i	0.444509	−	0.964193i
$862$	−2.26254	+	14.2851i	−0.0770625	+	0.486553i
$863$	19.6913	−	24.3167i	0.670300	−	0.827751i	−0.322621	−	0.946528i	$-0.604564\pi$
$863$	19.6913	−	24.3167i	0.670300	−	0.827751i	0.992921	+	0.118777i	$0.0378973\pi$
$864$	−9.46721	+	90.0745i	−0.322081	+	3.06440i
$865$		0			0
$866$	77.6675	−	8.16318i	2.63925	−	0.277396i
$867$	11.7001	−	5.96150i	0.397356	−	0.202463i
$868$	2.45558	−	37.4602i	0.0833479	−	1.27148i
$869$	−0.622995	−	0.202423i	−0.0211337	−	0.00686674i
$870$		0			0
$871$	−2.49551	−	2.24697i	−0.0845572	−	0.0761356i
$872$	−4.34631	−	82.9325i	−0.147184	−	2.80845i
$873$	22.9235	−	59.7176i	0.775841	−	2.02114i
$874$	0.501379			0.0169594
$875$		0			0
$876$	−196.907			−6.65288
$877$	4.94227	−	12.8751i	0.166889	−	0.434760i	−0.824476	−	0.565898i	$-0.808530\pi$
$877$	4.94227	−	12.8751i	0.166889	−	0.434760i	0.991364	+	0.131138i	$0.0418631\pi$
$878$	−1.00871	−	19.2473i	−0.0340422	−	0.649564i
$879$	−51.0191	−	45.9378i	−1.72083	−	1.54944i
$880$		0			0
$881$	−3.33473	−	1.08352i	−0.112350	−	0.0365047i	0.252302	−	0.967648i	$-0.418812\pi$
$881$	−3.33473	−	1.08352i	−0.112350	−	0.0365047i	−0.364652	+	0.931144i	$0.618812\pi$
$882$	65.8276	+	85.7911i	2.21653	+	2.88874i
$883$	−31.5512	+	16.0761i	−1.06178	+	0.541005i	−0.895495	−	0.445072i	$-0.853178\pi$
$883$	−31.5512	+	16.0761i	−1.06178	+	0.541005i	−0.166288	+	0.986077i	$0.553178\pi$
$884$	−35.0855	+	3.68763i	−1.18005	+	0.124029i
$885$		0			0
$886$	2.46850	−	23.4862i	0.0829310	−	0.789036i
$887$	0.270776	−	0.334381i	0.00909178	−	0.0112274i	−0.772580	−	0.634918i	$-0.781034\pi$
$887$	0.270776	−	0.334381i	0.00909178	−	0.0112274i	0.781672	+	0.623690i	$0.214367\pi$
$888$	−1.77854	+	11.2292i	−0.0596838	+	0.376829i
$889$	21.0477	−	14.8748i	0.705917	−	0.498884i
$890$		0			0
$891$	−0.0910228	−	0.866025i	−0.00304938	−	0.0290129i
$892$	3.21017	+	2.08471i	0.107484	+	0.0698011i
$893$	−1.62096	+	6.04950i	−0.0542433	+	0.202439i
$894$	−9.03585	−	10.0353i	−0.302204	−	0.335632i
$895$		0			0
$896$	0.225507	+	0.134165i	0.00753366	+	0.00448214i
$897$	0.651286	+	0.331847i	0.0217458	+	0.0110800i
$898$	4.80567	+	1.84472i	0.160367	+	0.0615592i
$899$	7.49033	+	12.9736i	0.249816	+	0.432695i
$900$		0			0
$901$	50.7997	+	29.3292i	1.69238	+	0.977097i
$902$	−0.170730	−	1.07795i	−0.00568469	−	0.0358917i
$903$	−13.3381	+	47.2917i	−0.443863	+	1.57377i
$904$	−27.3924	+	8.90032i	−0.911057	+	0.296020i
$905$		0			0
$906$	8.83798	+	41.5794i	0.293622	+	1.38138i
$907$	12.2853	+	3.29185i	0.407928	+	0.109304i	0.456947	−	0.889494i	$-0.348943\pi$
$907$	12.2853	+	3.29185i	0.407928	+	0.109304i	−0.0490192	+	0.998798i	$0.515610\pi$
$908$	−38.1111	−	1.99732i	−1.26476	−	0.0662833i
$909$	−44.2538	+	32.1523i	−1.46781	+	1.06642i
$910$		0			0
$911$	5.78586	+	4.20367i	0.191694	+	0.139274i	0.679493	−	0.733682i	$-0.262200\pi$
$911$	5.78586	+	4.20367i	0.191694	+	0.139274i	−0.487799	+	0.872956i	$0.662200\pi$
$912$	−27.6981	−	22.4295i	−0.917176	−	0.742714i
$913$	0.884402	−	0.339490i	0.0292694	−	0.0112355i
$914$	5.29230	+	0.556244i	0.175054	+	0.0183989i
$915$		0			0
$916$	59.5532	+	81.9680i	1.96769	+	2.70830i
$917$	−8.06961	+	20.2261i	−0.266482	+	0.667926i
$918$	74.3130	+	74.3130i	2.45270	+	2.45270i
$919$	38.5665	−	34.7254i	1.27219	−	1.14549i	0.290117	−	0.956991i	$-0.406306\pi$
$919$	38.5665	−	34.7254i	1.27219	−	1.14549i	0.982074	−	0.188495i	$-0.0603611\pi$
$920$		0			0
$921$	−20.0051	+	22.2179i	−0.659189	+	0.732104i
$922$	38.3610	+	59.0708i	1.26335	+	1.94539i
$923$	12.2778	−	1.94461i	0.404128	−	0.0640076i
$924$	3.82293	+	1.29775i	0.125765	+	0.0426927i
$925$		0			0
$926$	−8.31699	+	14.4055i	−0.273313	+	0.473393i
$927$	30.6825	−	24.8462i	1.00775	−	0.816057i
$928$	52.9979	−	2.77750i	1.73974	−	0.0911760i
$929$	18.5149	+	3.93545i	0.607453	+	0.129118i	0.501361	−	0.865238i	$-0.332833\pi$
$929$	18.5149	+	3.93545i	0.607453	+	0.129118i	0.106092	+	0.994356i	$0.466166\pi$
$930$		0			0
$931$	−8.64337	+	0.680104i	−0.283275	+	0.0222895i
$932$	−59.1597	+	59.1597i	−1.93784	+	1.93784i
$933$	1.06462	−	20.3143i	0.0348543	−	0.665059i
$934$	−57.2216	−	25.4767i	−1.87235	−	0.833623i
$935$		0			0
$936$	−28.0605	−	63.0249i	−0.917186	−	2.06003i
$937$	24.3434	+	3.85562i	0.795266	+	0.125958i	0.540830	−	0.841132i	$-0.318110\pi$
$937$	24.3434	+	3.85562i	0.795266	+	0.125958i	0.254436	+	0.967090i	$0.418110\pi$
$938$	−12.9995	−	6.83949i	−0.424448	−	0.223317i
$939$	−16.2683	+	22.3914i	−0.530895	+	0.730714i
$940$		0			0
$941$	16.9821	−	38.1424i	0.553600	−	1.24341i	−0.392566	−	0.919724i	$-0.628413\pi$
$941$	16.9821	−	38.1424i	0.553600	−	1.24341i	0.946166	−	0.323682i	$-0.104921\pi$
$942$	32.4574	−	49.9801i	1.05752	−	1.62844i
$943$	−0.158165	−	0.590281i	−0.00515057	−	0.0192222i
$944$	37.1015	−	114.187i	1.20755	−	3.71646i
$945$		0			0
$946$	0.531927	+	1.63710i	0.0172944	+	0.0532268i
$947$	−28.5959	+	18.5704i	−0.929240	+	0.603456i	−0.918043	−	0.396482i	$-0.870231\pi$
$947$	−28.5959	+	18.5704i	−0.929240	+	0.603456i	−0.0111977	+	0.999937i	$0.503564\pi$
$948$	56.0807	+	69.2539i	1.82142	+	2.24926i
$949$	18.7036	−	10.7985i	0.607145	−	0.350535i
$950$		0			0
$951$		−	53.5562i		−	1.73668i
$952$	−84.7809	+	31.2765i	−2.74777	+	1.01368i
$953$	1.62460	−	3.18846i	0.0526261	−	0.103284i	−0.863196	−	0.504870i	$-0.831541\pi$
$953$	1.62460	−	3.18846i	0.0526261	−	0.103284i	0.915822	+	0.401585i	$0.131541\pi$
$954$	−40.7277	+	191.609i	−1.31861	+	6.20356i
$955$		0			0
$956$	−48.4136	+	10.2906i	−1.56581	+	0.332822i
$957$	−1.55616	+	0.416971i	−0.0503034	+	0.0134788i
$958$	1.98798	+	3.90164i	0.0642289	+	0.126056i
$959$	23.6666	−	25.6020i	0.764234	−	0.826730i
$960$		0			0
$961$	20.4231	−	9.09296i	0.658810	−	0.293321i
$962$	−0.763140	−	1.98805i	−0.0246046	−	0.0640972i
$963$	27.1809	+	70.8086i	0.875891	+	2.28178i
$964$	121.653	−	54.1635i	3.91819	−	1.74449i
$965$		0			0
$966$	3.11854	+	0.705680i	0.100337	+	0.0227049i
$967$	−9.77652	−	19.1875i	−0.314392	−	0.617028i	0.678694	−	0.734421i	$-0.262546\pi$
$967$	−9.77652	−	19.1875i	−0.314392	−	0.617028i	−0.993086	+	0.117393i	$0.962546\pi$
$968$	−78.3715	+	20.9996i	−2.51896	+	0.674952i
$969$	−16.7312	+	3.55632i	−0.537483	+	0.114245i
$970$		0			0
$971$	11.3496	−	53.3956i	0.364225	−	1.71355i	−0.289813	−	0.957083i	$-0.593593\pi$
$971$	11.3496	−	53.3956i	0.364225	−	1.71355i	0.654038	−	0.756462i	$-0.273074\pi$
$972$	3.37562	−	6.62503i	0.108273	−	0.212498i
$973$	−11.4324	−	1.96455i	−0.366507	−	0.0629805i
$974$			80.5628i			2.58140i
$975$		0			0
$976$	71.4272	−	41.2385i	2.28633	−	1.32001i
$977$	8.14609	+	10.0596i	0.260616	+	0.321835i	0.890612	−	0.454764i	$-0.150277\pi$
$977$	8.14609	+	10.0596i	0.260616	+	0.321835i	−0.629995	+	0.776599i	$0.716943\pi$
$978$	134.662	−	87.4508i	4.30603	−	2.79637i
$979$	0.445009	+	1.36960i	0.0142225	+	0.0437725i
$980$		0			0
$981$	20.5506	−	63.2483i	0.656131	−	2.01936i
$982$	4.28629	+	15.9967i	0.136781	+	0.510474i
$983$	4.24814	−	6.54156i	0.135495	−	0.208643i	−0.764410	−	0.644731i	$-0.776970\pi$
$983$	4.24814	−	6.54156i	0.135495	−	0.208643i	0.899904	+	0.436087i	$0.143636\pi$
$984$	−35.3624	+	79.4253i	−1.12731	+	2.53199i
$985$		0			0
$986$	36.1964	−	49.8201i	1.15273	−	1.58660i
$987$	−18.5968	+	35.3460i	−0.591943	+	1.12508i
$988$	9.32968	+	1.47768i	0.296817	+	0.0470112i
$989$	0.392031	+	0.880516i	0.0124659	+	0.0279988i
$990$		0			0
$991$	20.9600	+	9.33198i	0.665815	+	0.296440i	0.711676	−	0.702508i	$-0.247936\pi$
$991$	20.9600	+	9.33198i	0.665815	+	0.296440i	−0.0458609	+	0.998948i	$0.514603\pi$
$992$	−1.60267	+	30.5808i	−0.0508848	+	0.970940i
$993$	−44.9754	+	44.9754i	−1.42725	+	1.42725i
$994$	49.9600	−	21.4640i	1.58464	−	0.680797i
$995$		0			0
$996$	−126.057	−	26.7941i	−3.99425	−	0.849005i
$997$	−11.3264	+	0.593593i	−0.358712	+	0.0187993i	−0.230841	−	0.972992i	$-0.574148\pi$
$997$	−11.3264	+	0.593593i	−0.358712	+	0.0187993i	−0.127871	+	0.991791i	$0.540814\pi$
$998$	85.0396	−	68.8637i	2.69188	−	2.17984i
$999$	−2.24251	+	3.88414i	−0.0709499	+	0.122889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.418.18		288
5.2	odd	4		875.2.bb.c.82.18		288
5.3	odd	4		175.2.x.a.12.1	✓	288
5.4	even	2		875.2.bb.b.418.1		288
7.3	odd	6	inner	875.2.bb.a.668.18		288
25.2	odd	20	inner	875.2.bb.a.782.18		288
25.11	even	5		875.2.bb.c.593.1		288
25.14	even	10		175.2.x.a.173.18	yes	288
25.23	odd	20		875.2.bb.b.782.1		288
35.3	even	12		175.2.x.a.87.18	yes	288
35.17	even	12		875.2.bb.c.332.1		288
35.24	odd	6		875.2.bb.b.668.1		288
175.52	even	60	inner	875.2.bb.a.157.18		288
175.73	even	60		875.2.bb.b.157.1		288
175.136	odd	30		875.2.bb.c.843.18		288
175.164	odd	30		175.2.x.a.73.1	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.12.1	✓	288	5.3	odd	4
175.2.x.a.73.1	yes	288	175.164	odd	30
175.2.x.a.87.18	yes	288	35.3	even	12
175.2.x.a.173.18	yes	288	25.14	even	10
875.2.bb.a.157.18		288	175.52	even	60	inner
875.2.bb.a.418.18		288	1.1	even	1	trivial
875.2.bb.a.668.18		288	7.3	odd	6	inner
875.2.bb.a.782.18		288	25.2	odd	20	inner
875.2.bb.b.157.1		288	175.73	even	60
875.2.bb.b.418.1		288	5.4	even	2
875.2.bb.b.668.1		288	35.24	odd	6
875.2.bb.b.782.1		288	25.23	odd	20
875.2.bb.c.82.18		288	5.2	odd	4
875.2.bb.c.332.1		288	35.17	even	12
875.2.bb.c.593.1		288	25.11	even	5
875.2.bb.c.843.18		288	175.136	odd	30

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+(0.936298 - 2.43914i) q^{2} +(-0.156245 - 2.98133i) q^{3} +(-3.58646 - 3.22926i) q^{4} +(-7.41816 - 2.41031i) q^{6} +(2.37291 - 1.17017i) q^{7} +(-6.57879 + 3.35206i) q^{8} +(-5.88033 + 0.618047i) q^{9} +(0.0110705 - 0.105329i) q^{11} +(-9.06711 + 11.1969i) q^{12} +(0.247208 - 1.56081i) q^{13} +(-0.632446 - 6.88349i) q^{14} +(1.00752 + 9.58587i) q^{16} +(3.87956 + 2.51942i) q^{17} +(-3.99823 + 14.9216i) q^{18} +(-0.828774 - 0.920447i) q^{19} +(-3.85940 - 6.89159i) q^{21} +(-0.246547 - 0.125622i) q^{22} +(-0.144646 - 0.0555245i) q^{23} +(11.0215 + 19.0898i) q^{24} +(-3.57557 - 2.06436i) q^{26} +(1.36030 + 8.58862i) q^{27} +(-12.2891 - 3.46600i) q^{28} +(4.84593 - 1.57454i) q^{29} +(0.611278 + 2.87584i) q^{31} +(10.0607 + 2.69575i) q^{32} +(-0.315750 - 0.0165478i) q^{33} +(9.77764 - 7.10387i) q^{34} +(23.0854 + 16.7725i) q^{36} +(0.400833 + 0.324588i) q^{37} +(-3.02108 + 1.15968i) q^{38} +(-4.69190 - 0.493139i) q^{39} +(2.31834 + 3.19093i) q^{41} +(-20.4231 + 2.96104i) q^{42} +(-4.39882 - 4.39882i) q^{43} +(-0.379839 + 0.342008i) q^{44} +(-0.270864 + 0.300825i) q^{46} +(-2.75397 - 4.24074i) q^{47} +(28.4212 - 4.50147i) q^{48} +(4.26142 - 5.55340i) q^{49} +(6.90505 - 11.9599i) q^{51} +(-5.92685 + 4.79947i) q^{52} +(12.6632 - 0.663649i) q^{53} +(22.2225 + 4.72354i) q^{54} +(-11.6884 + 15.6524i) q^{56} +(-2.61466 + 2.61466i) q^{57} +(0.696716 - 13.2941i) q^{58} +(-11.3795 - 5.06647i) q^{59} +(-3.48040 - 7.81711i) q^{61} +(7.58691 + 1.20165i) q^{62} +(-13.2303 + 8.34753i) q^{63} +(4.66418 - 6.41969i) q^{64} +(-0.335998 + 0.754665i) q^{66} +(1.15735 - 1.78216i) q^{67} +(-5.77803 - 21.5639i) q^{68} +(-0.142937 + 0.439913i) q^{69} +(2.43082 + 7.48129i) q^{71} +(36.6137 - 23.7772i) q^{72} +(8.60076 + 10.6211i) q^{73} +(1.16701 - 0.673776i) q^{74} +5.97747i q^{76} +(-0.0969831 - 0.262891i) q^{77} +(-5.59585 + 10.9825i) q^{78} +(1.28595 - 6.04991i) q^{79} +(8.04241 - 1.70947i) q^{81} +(9.95377 - 2.66710i) q^{82} +(4.06079 + 7.96975i) q^{83} +(-8.41316 + 37.1794i) q^{84} +(-14.8479 + 6.61073i) q^{86} +(-5.45136 - 14.2013i) q^{87} +(0.280239 + 0.730047i) q^{88} +(-12.4217 + 5.53052i) q^{89} +(-1.23980 - 3.99294i) q^{91} +(0.339465 + 0.666237i) q^{92} +(8.47830 - 2.27175i) q^{93} +(-12.9223 + 2.74672i) q^{94} +(6.46499 - 30.4154i) q^{96} +(-4.91146 + 9.63928i) q^{97} +(-9.55556 - 15.5938i) q^{98} +0.626212i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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