LMFDB - Embedded newform 875.2.bb.a.507.15

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			507.15
Character	$\chi$	$=$	875.507
Dual form			875.2.bb.a.768.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.69351 + 1.09978i) q^{2} +(0.0509090 + 0.0195422i) q^{3} +(0.844998 + 1.89790i) q^{4} +(0.0647231 + 0.0890837i) q^{6} +(2.64536 + 0.0453616i) q^{7} +(-0.0244829 + 0.154579i) q^{8} +(-2.22722 - 2.00540i) q^{9} +(2.53998 + 2.82093i) q^{11} +(0.00592906 + 0.113133i) q^{12} +(1.38789 - 2.72389i) q^{13} +(4.43007 + 2.98614i) q^{14} +(2.56878 - 2.85292i) q^{16} +(2.63674 + 2.13519i) q^{17} +(-1.56633 - 5.84563i) q^{18} +(3.38312 + 1.50626i) q^{19} +(0.133786 + 0.0540054i) q^{21} +(1.19908 + 7.57071i) q^{22} +(-3.12944 + 4.81891i) q^{23} +(-0.00426721 + 0.00739102i) q^{24} +(5.34609 - 3.08657i) q^{26} +(-0.148466 - 0.291380i) q^{27} +(2.14923 + 5.05895i) q^{28} +(-1.14694 + 1.57863i) q^{29} +(-4.49990 + 0.472959i) q^{31} +(7.79020 - 2.08738i) q^{32} +(0.0741808 + 0.193248i) q^{33} +(2.11711 + 6.51580i) q^{34} +(1.92404 - 5.92160i) q^{36} +(-8.17923 + 0.428655i) q^{37} +(4.07280 + 6.27156i) q^{38} +(0.123887 - 0.111548i) q^{39} +(7.75457 - 2.51961i) q^{41} +(0.167175 + 0.238595i) q^{42} +(-5.09273 + 5.09273i) q^{43} +(-3.20756 + 7.20430i) q^{44} +(-10.5995 + 4.71920i) q^{46} +(-5.87669 - 7.25711i) q^{47} +(0.186526 - 0.0950399i) q^{48} +(6.99588 + 0.239996i) q^{49} +(0.0925076 + 0.160228i) q^{51} +(6.34242 + 0.332392i) q^{52} +(2.38575 - 6.21509i) q^{53} +(0.0690257 - 0.656736i) q^{54} +(-0.0717781 + 0.407807i) q^{56} +(0.142796 + 0.142796i) q^{57} +(-3.67851 + 1.41205i) q^{58} +(3.16655 + 0.673070i) q^{59} +(-2.94484 - 13.8544i) q^{61} +(-8.14080 - 4.14794i) q^{62} +(-5.80085 - 5.40605i) q^{63} +(8.18628 + 2.65988i) q^{64} +(-0.0869038 + 0.408850i) q^{66} +(-8.87250 + 10.9566i) q^{67} +(-1.82433 + 6.80848i) q^{68} +(-0.253489 + 0.184170i) q^{69} +(1.76180 + 1.28002i) q^{71} +(0.364522 - 0.295184i) q^{72} +(-0.114904 + 2.19250i) q^{73} +(-14.3231 - 8.26943i) q^{74} +7.69359i q^{76} +(6.59120 + 7.57761i) q^{77} +(0.332483 - 0.0526601i) q^{78} +(-6.51601 - 0.684861i) q^{79} +(0.937960 + 8.92409i) q^{81} +(15.9035 + 4.26133i) q^{82} +(6.83177 + 1.08205i) q^{83} +(0.0105526 + 0.299547i) q^{84} +(-14.2255 + 3.02372i) q^{86} +(-0.0892396 + 0.0579529i) q^{87} +(-0.498243 + 0.323563i) q^{88} +(3.73767 - 0.794467i) q^{89} +(3.79503 - 7.14272i) q^{91} +(-11.7902 - 1.86738i) q^{92} +(-0.238328 - 0.0638599i) q^{93} +(-1.97103 - 18.7531i) q^{94} +(0.437383 + 0.0459708i) q^{96} +(-4.26064 + 0.674820i) q^{97} +(11.5837 + 8.10037i) q^{98} -11.3765i 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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.69351	+	1.09978i	1.19749	+	0.777662i	0.980116	−	0.198425i	$-0.0635826\pi$
$2$	1.69351	+	1.09978i	1.19749	+	0.777662i	0.217379	+	0.976087i	$0.430249\pi$
$3$	0.0509090	+	0.0195422i	0.0293923	+	0.0112827i	0.373020	−	0.927823i	$-0.378322\pi$
$3$	0.0509090	+	0.0195422i	0.0293923	+	0.0112827i	−0.343627	+	0.939106i	$0.611656\pi$
$4$	0.844998	+	1.89790i	0.422499	+	0.948948i
$5$		0			0
$5$		0			0
$6$	0.0647231	+	0.0890837i	0.0264231	+	0.0363683i
$7$	2.64536	+	0.0453616i	0.999853	+	0.0171451i
$7$	2.64536	+	0.0453616i	0.999853	+	0.0171451i
$8$	−0.0244829	+	0.154579i	−0.00865601	+	0.0546519i
$9$	−2.22722	−	2.00540i	−0.742408	−	0.668467i
$10$		0			0
$11$	2.53998	+	2.82093i	0.765832	+	0.850543i	0.992349	−	0.123464i	$-0.0394004\pi$
$11$	2.53998	+	2.82093i	0.765832	+	0.850543i	−0.226517	+	0.974007i	$0.572734\pi$
$12$	0.00592906	+	0.113133i	0.00171157	+	0.0326587i
$13$	1.38789	−	2.72389i	0.384932	−	0.755471i	−0.614509	−	0.788910i	$-0.710646\pi$
$13$	1.38789	−	2.72389i	0.384932	−	0.755471i	0.999441	+	0.0334387i	$0.0106459\pi$
$14$	4.43007	+	2.98614i	1.18399	+	0.798079i
$15$		0			0
$16$	2.56878	−	2.85292i	0.642195	−	0.713230i
$17$	2.63674	+	2.13519i	0.639503	+	0.517859i	0.893336	−	0.449389i	$-0.148358\pi$
$17$	2.63674	+	2.13519i	0.639503	+	0.517859i	−0.253834	+	0.967248i	$0.581692\pi$
$18$	−1.56633	−	5.84563i	−0.369188	−	1.37783i
$19$	3.38312	+	1.50626i	0.776140	+	0.345560i	0.756284	−	0.654243i	$-0.227013\pi$
$19$	3.38312	+	1.50626i	0.776140	+	0.345560i	0.0198559	+	0.999803i	$0.493679\pi$
$20$		0			0
$21$	0.133786	+	0.0540054i	0.0291946	+	0.0117849i
$22$	1.19908	+	7.57071i	0.255645	+	1.61408i
$23$	−3.12944	+	4.81891i	−0.652533	+	1.00481i	0.345266	+	0.938505i	$0.387789\pi$
$23$	−3.12944	+	4.81891i	−0.652533	+	1.00481i	−0.997799	+	0.0663077i	$0.978878\pi$
$24$	−0.00426721	+	0.00739102i	−0.000871040	+	0.00150869i
$25$		0			0
$26$	5.34609	−	3.08657i	1.04846	−	0.605326i
$27$	−0.148466	−	0.291380i	−0.0285722	−	0.0560761i
$28$	2.14923	+	5.05895i	0.406167	+	0.956052i
$29$	−1.14694	+	1.57863i	−0.212982	+	0.293144i	−0.902120	−	0.431486i	$-0.857989\pi$
$29$	−1.14694	+	1.57863i	−0.212982	+	0.293144i	0.689138	+	0.724630i	$0.257989\pi$
$30$		0			0
$31$	−4.49990	+	0.472959i	−0.808206	+	0.0849459i	−0.499614	−	0.866248i	$-0.666525\pi$
$31$	−4.49990	+	0.472959i	−0.808206	+	0.0849459i	−0.308593	+	0.951194i	$0.599858\pi$
$32$	7.79020	−	2.08738i	1.37712	−	0.369000i
$33$	0.0741808	+	0.193248i	0.0129132	+	0.0336401i
$34$	2.11711	+	6.51580i	0.363082	+	1.11745i
$35$		0			0
$36$	1.92404	−	5.92160i	0.320674	−	0.986933i
$37$	−8.17923	+	0.428655i	−1.34466	+	0.0704705i	−0.711027	−	0.703165i	$-0.751769\pi$
$37$	−8.17923	+	0.428655i	−1.34466	+	0.0704705i	−0.633631	+	0.773636i	$0.718436\pi$
$38$	4.07280	+	6.27156i	0.660695	+	1.01738i
$39$	0.123887	−	0.111548i	0.0198378	−	0.0178620i
$40$		0			0
$41$	7.75457	−	2.51961i	1.21106	−	0.393497i	0.367242	−	0.930126i	$-0.380302\pi$
$41$	7.75457	−	2.51961i	1.21106	−	0.393497i	0.843819	+	0.536628i	$0.180302\pi$
$42$	0.167175	+	0.238595i	0.0257957	+	0.0368159i
$43$	−5.09273	+	5.09273i	−0.776634	+	0.776634i	−0.979257	−	0.202623i	$-0.935054\pi$
$43$	−5.09273	+	5.09273i	−0.776634	+	0.776634i	0.202623	+	0.979257i	$0.435054\pi$
$44$	−3.20756	+	7.20430i	−0.483558	+	1.08609i
$45$		0			0
$46$	−10.5995	+	4.71920i	−1.56281	+	0.695808i
$47$	−5.87669	−	7.25711i	−0.857204	−	1.05856i	−0.997653	−	0.0684709i	$-0.978188\pi$
$47$	−5.87669	−	7.25711i	−0.857204	−	1.05856i	0.140449	−	0.990088i	$-0.455145\pi$
$48$	0.186526	−	0.0950399i	0.0269228	−	0.0137178i
$49$	6.99588	+	0.239996i	0.999412	+	0.0342851i
$50$		0			0
$51$	0.0925076	+	0.160228i	0.0129537	+	0.0224364i
$52$	6.34242	+	0.332392i	0.879536	+	0.0460945i
$53$	2.38575	−	6.21509i	0.327708	−	0.853708i	−0.666428	−	0.745569i	$-0.732178\pi$
$53$	2.38575	−	6.21509i	0.327708	−	0.853708i	0.994136	−	0.108139i	$-0.0344890\pi$
$54$	0.0690257	−	0.656736i	0.00939321	−	0.0893704i
$55$		0			0
$56$	−0.0717781	+	0.407807i	−0.00959175	+	0.0544955i
$57$	0.142796	+	0.142796i	0.0189138	+	0.0189138i
$58$	−3.67851	+	1.41205i	−0.483012	+	0.185411i
$59$	3.16655	+	0.673070i	0.412249	+	0.0876263i	0.409368	−	0.912370i	$-0.365749\pi$
$59$	3.16655	+	0.673070i	0.412249	+	0.0876263i	0.00288177	+	0.999996i	$0.499083\pi$
$60$		0			0
$61$	−2.94484	−	13.8544i	−0.377048	−	1.77387i	−0.600979	−	0.799265i	$-0.705222\pi$
$61$	−2.94484	−	13.8544i	−0.377048	−	1.77387i	0.223931	−	0.974605i	$-0.428111\pi$
$62$	−8.14080	−	4.14794i	−1.03388	−	0.526789i
$63$	−5.80085	−	5.40605i	−0.730838	−	0.681098i
$64$	8.18628	+	2.65988i	1.02329	+	0.332485i
$65$		0			0
$66$	−0.0869038	+	0.408850i	−0.0106971	+	0.0503260i
$67$	−8.87250	+	10.9566i	−1.08395	+	1.33856i	−0.146984	+	0.989139i	$0.546957\pi$
$67$	−8.87250	+	10.9566i	−1.08395	+	1.33856i	−0.936964	+	0.349426i	$0.886377\pi$
$68$	−1.82433	+	6.80848i	−0.221232	+	0.825650i
$69$	−0.253489	+	0.184170i	−0.0305164	+	0.0221715i
$70$		0			0
$71$	1.76180	+	1.28002i	0.209087	+	0.151910i	0.687400	−	0.726279i	$-0.258752\pi$
$71$	1.76180	+	1.28002i	0.209087	+	0.151910i	−0.478314	+	0.878189i	$0.658752\pi$
$72$	0.364522	−	0.295184i	0.0429593	−	0.0347878i
$73$	−0.114904	+	2.19250i	−0.0134485	+	0.256613i	0.983628	+	0.180209i	$0.0576773\pi$
$73$	−0.114904	+	2.19250i	−0.0134485	+	0.256613i	−0.997077	+	0.0764042i	$0.975656\pi$
$74$	−14.3231	−	8.26943i	−1.66502	−	0.961301i
$75$		0			0
$76$			7.69359i			0.882515i
$77$	6.59120	+	7.57761i	0.751137	+	0.863548i
$78$	0.332483	−	0.0526601i	0.0376463	−	0.00596258i
$79$	−6.51601	−	0.684861i	−0.733109	−	0.0770529i	−0.269385	−	0.963033i	$-0.586820\pi$
$79$	−6.51601	−	0.684861i	−0.733109	−	0.0770529i	−0.463724	+	0.885980i	$0.653487\pi$
$80$		0			0
$81$	0.937960	+	8.92409i	0.104218	+	0.991566i
$82$	15.9035	+	4.26133i	1.75625	+	0.470585i
$83$	6.83177	+	1.08205i	0.749884	+	0.118770i	0.519667	−	0.854369i	$-0.326056\pi$
$83$	6.83177	+	1.08205i	0.749884	+	0.118770i	0.230218	+	0.973139i	$0.426056\pi$
$84$	0.0105526	+	0.299547i	0.00115138	+	0.0326833i
$85$		0			0
$86$	−14.2255	+	3.02372i	−1.53398	+	0.326056i
$87$	−0.0892396	+	0.0579529i	−0.00956749	+	0.00621320i
$88$	−0.498243	+	0.323563i	−0.0531129	+	0.0344919i
$89$	3.73767	−	0.794467i	0.396193	−	0.0842133i	−0.00550702	−	0.999985i	$-0.501753\pi$
$89$	3.73767	−	0.794467i	0.396193	−	0.0842133i	0.401700	+	0.915772i	$0.368420\pi$
$90$		0			0
$91$	3.79503	−	7.14272i	0.397828	−	0.748760i
$92$	−11.7902	−	1.86738i	−1.22921	−	0.194688i
$93$	−0.238328	−	0.0638599i	−0.0247135	−	0.00662196i
$94$	−1.97103	−	18.7531i	−0.203296	−	1.93423i
$95$		0			0
$96$	0.437383	+	0.0459708i	0.0446402	+	0.00469188i
$97$	−4.26064	+	0.674820i	−0.432603	+	0.0685176i	−0.368939	−	0.929454i	$-0.620279\pi$
$97$	−4.26064	+	0.674820i	−0.432603	+	0.0685176i	−0.0636644	+	0.997971i	$0.520279\pi$
$98$	11.5837	+	8.10037i	1.17013	+	0.818261i
$99$		−	11.3765i		−	1.14338i
$100$		0			0
$101$	−6.04964	−	3.49276i	−0.601962	−	0.347543i	0.167851	−	0.985812i	$-0.446317\pi$
$101$	−6.04964	−	3.49276i	−0.601962	−	0.347543i	−0.769813	+	0.638270i	$0.779651\pi$
$102$	−0.0195526	+	0.373086i	−0.00193600	+	0.0369410i
$103$	−7.49562	+	6.06984i	−0.738566	+	0.598079i	−0.923015	−	0.384763i	$-0.874283\pi$
$103$	−7.49562	+	6.06984i	−0.738566	+	0.598079i	0.184450	+	0.982842i	$0.440950\pi$
$104$	0.387076	+	0.281228i	0.0379560	+	0.0275766i
$105$		0			0
$106$	10.8755	−	7.90153i	1.05632	−	0.767465i
$107$	−0.858034	+	3.20223i	−0.0829493	+	0.309571i	−0.994918	−	0.100689i	$-0.967895\pi$
$107$	−0.858034	+	3.20223i	−0.0829493	+	0.309571i	0.911969	+	0.410260i	$0.134562\pi$
$108$	0.427556	−	0.527988i	0.0411416	−	0.0508057i
$109$	2.02932	−	9.54720i	0.194374	−	0.914456i	−0.767519	−	0.641027i	$-0.778509\pi$
$109$	2.02932	−	9.54720i	0.194374	−	0.914456i	0.961892	−	0.273429i	$-0.0881579\pi$
$110$		0			0
$111$	−0.424774	−	0.138017i	−0.0403177	−	0.0131000i
$112$	6.92477	−	7.43048i	0.654329	−	0.702115i
$113$	−4.16559	−	2.12247i	−0.391866	−	0.199666i	0.246945	−	0.969030i	$-0.420573\pi$
$113$	−4.16559	−	2.12247i	−0.391866	−	0.199666i	−0.638811	+	0.769364i	$0.720573\pi$
$114$	0.0847825	+	0.398870i	0.00794061	+	0.0373576i
$115$		0			0
$116$	−3.96524	−	0.842838i	−0.368163	−	0.0782556i
$117$	−8.55364	+	3.28343i	−0.790784	+	0.303554i
$118$	4.62236	+	4.62236i	0.425523	+	0.425523i
$119$	6.87827	+	5.76795i	0.630530	+	0.528747i
$120$		0			0
$121$	−0.356354	+	3.39048i	−0.0323958	+	0.308225i
$122$	10.2496	−	26.7012i	0.927959	−	2.41742i
$123$	0.444016	+	0.0232699i	0.0400356	+	0.00209818i
$124$	−4.70003	−	8.14070i	−0.422075	−	0.731056i
$125$		0			0
$126$	−3.87835	−	15.5349i	−0.345511	−	1.38396i
$127$	−10.9199	+	5.56395i	−0.968982	+	0.493721i	−0.865499	−	0.500910i	$-0.832999\pi$
$127$	−10.9199	+	5.56395i	−0.968982	+	0.493721i	−0.103483	+	0.994631i	$0.532999\pi$
$128$	0.787347	+	0.972292i	0.0695923	+	0.0859393i
$129$	−0.358789	+	0.159743i	−0.0315896	+	0.0140646i
$130$		0			0
$131$	−4.18789	+	9.40615i	−0.365898	+	0.821819i	0.632967	+	0.774179i	$0.281837\pi$
$131$	−4.18789	+	9.40615i	−0.365898	+	0.821819i	−0.998865	+	0.0476406i	$0.984830\pi$
$132$	−0.304081	+	0.304081i	−0.0264669	+	0.0264669i
$133$	8.88125	+	4.13807i	0.770102	+	0.358816i
$134$	−27.0756	+	8.79739i	−2.33897	+	0.759979i
$135$		0			0
$136$	−0.394610	+	0.355309i	−0.0338375	+	0.0304675i
$137$	−10.1362	−	15.6084i	−0.865993	−	1.33351i	−0.941725	−	0.336384i	$-0.890796\pi$
$137$	−10.1362	−	15.6084i	−0.865993	−	1.33351i	0.0757320	−	0.997128i	$-0.475871\pi$
$138$	−0.631833	+	0.0331130i	−0.0537852	+	0.00281876i
$139$	4.94661	−	15.2241i	0.419566	−	1.29129i	−0.488537	−	0.872543i	$-0.662469\pi$
$139$	4.94661	−	15.2241i	0.419566	−	1.29129i	0.908103	−	0.418747i	$-0.137531\pi$
$140$		0			0
$141$	−0.157357	−	0.484296i	−0.0132519	−	0.0407851i
$142$	1.57588	+	4.10532i	0.132245	+	0.344511i
$143$	11.2091	−	3.00348i	0.937354	−	0.251163i
$144$	−11.4425	+	1.20266i	−0.953542	+	0.100221i
$145$		0			0
$146$	−2.60586	+	3.58666i	−0.215663	+	0.296834i
$147$	0.351464	+	0.148933i	0.0289882	+	0.0122838i
$148$	−7.72497	−	15.1611i	−0.634989	−	1.24624i
$149$	−1.52167	+	0.878534i	−0.124660	+	0.0719723i	−0.561033	−	0.827793i	$-0.689596\pi$
$149$	−1.52167	+	0.878534i	−0.124660	+	0.0719723i	0.436373	+	0.899766i	$0.356263\pi$
$150$		0			0
$151$	0.749583	−	1.29832i	0.0610002	−	0.105655i	−0.833913	−	0.551897i	$-0.813904\pi$
$151$	0.749583	−	1.29832i	0.0610002	−	0.105655i	0.894913	+	0.446241i	$0.147238\pi$
$152$	−0.315665	+	0.486081i	−0.0256038	+	0.0394264i
$153$	−1.59070	−	10.0433i	−0.128600	−	0.811949i
$154$	2.82859	+	20.0817i	0.227934	+	1.61823i
$155$		0			0
$156$	0.316391	+	0.140866i	0.0253316	+	0.0112783i
$157$	−1.02623	−	3.82995i	−0.0819023	−	0.305664i	0.912807	−	0.408391i	$-0.133910\pi$
$157$	−1.02623	−	3.82995i	−0.0819023	−	0.305664i	−0.994710	+	0.102727i	$0.967243\pi$
$158$	−10.2818	−	8.32601i	−0.817973	−	0.662382i
$159$	0.242912	−	0.269781i	0.0192642	−	0.0213951i
$160$		0			0
$161$	−8.49709	+	12.6058i	−0.669665	+	0.993477i
$162$	−8.22609	+	16.1446i	−0.646303	+	1.26844i
$163$	0.567303	+	10.8248i	0.0444346	+	0.847862i	0.926398	+	0.376545i	$0.122888\pi$
$163$	0.567303	+	10.8248i	0.0444346	+	0.847862i	−0.881964	+	0.471317i	$0.843779\pi$
$164$	11.3346	+	12.5883i	0.885080	+	0.982981i
$165$		0			0
$166$	10.3797	+	9.34591i	0.805620	+	0.725383i
$167$	1.97743	−	12.4850i	0.153018	−	0.966117i	−0.784991	−	0.619507i	$-0.787333\pi$
$167$	1.97743	−	12.4850i	0.153018	−	0.966117i	0.938009	−	0.346610i	$-0.112667\pi$
$168$	−0.0116236	+	0.0193584i	−0.000896778	+	0.00149353i
$169$	2.14788	+	2.95630i	0.165221	+	0.227407i
$170$		0			0
$171$	−4.51430	−	10.1393i	−0.345217	−	0.775371i
$172$	−13.9688	−	5.36213i	−1.06511	−	0.408858i
$173$	−11.2496	−	7.30558i	−0.855292	−	0.555433i	0.0408678	−	0.999165i	$-0.486988\pi$
$173$	−11.2496	−	7.30558i	−0.855292	−	0.555433i	−0.896160	+	0.443731i	$0.853654\pi$
$174$	−0.214864			−0.0162888
$175$		0			0
$176$	14.5725			1.09845
$177$	0.148053	+	0.0961465i	0.0111283	+	0.00722681i
$178$	7.20354	+	2.76518i	0.539928	+	0.207259i
$179$	−2.19411	−	4.92806i	−0.163996	−	0.368340i	0.812791	−	0.582556i	$-0.197947\pi$
$179$	−2.19411	−	4.92806i	−0.163996	−	0.368340i	−0.976786	+	0.214215i	$0.931281\pi$
$180$		0			0
$181$	12.4457	+	17.1301i	0.925085	+	1.27327i	0.961746	+	0.273942i	$0.0883276\pi$
$181$	12.4457	+	17.1301i	0.925085	+	1.27327i	−0.0366616	+	0.999328i	$0.511672\pi$
$182$	14.2824	−	7.92258i	1.05868	−	0.587261i
$183$	0.120825	−	0.762861i	0.00893166	−	0.0563923i
$184$	−0.668285	−	0.601726i	−0.0492666	−	0.0443598i
$185$		0			0
$186$	−0.333380	−	0.370256i	−0.0244446	−	0.0271485i
$187$	0.674037	+	12.8614i	0.0492905	+	0.940518i
$188$	8.80745	−	17.2856i	0.642349	−	1.26068i
$189$	−0.379528	−	0.777541i	−0.0276066	−	0.0565578i
$190$		0			0
$191$	−10.1181	+	11.2373i	−0.732121	+	0.813103i	−0.988138	−	0.153570i	$-0.950923\pi$
$191$	−10.1181	+	11.2373i	−0.732121	+	0.813103i	0.256017	+	0.966672i	$0.417590\pi$
$192$	0.364776	+	0.295390i	0.0263254	+	0.0213179i
$193$	−3.46038	−	12.9143i	−0.249084	−	0.929593i	−0.971287	−	0.237912i	$-0.923537\pi$
$193$	−3.46038	−	12.9143i	−0.249084	−	0.929593i	0.722203	−	0.691681i	$-0.243130\pi$
$194$	−7.95761	−	3.54296i	−0.571323	−	0.254370i
$195$		0			0
$196$	5.45602	+	13.4803i	0.389716	+	0.962875i
$197$	1.47858	+	9.33538i	0.105344	+	0.665118i	0.982690	+	0.185259i	$0.0593123\pi$
$197$	1.47858	+	9.33538i	0.105344	+	0.665118i	−0.877345	+	0.479859i	$0.840688\pi$
$198$	12.5117	−	19.2663i	0.889167	−	1.36920i
$199$	6.97072	−	12.0736i	0.494141	−	0.855878i	−0.505836	−	0.862630i	$-0.668816\pi$
$199$	6.97072	−	12.0736i	0.494141	−	0.855878i	0.999977	+	0.00675174i	$0.00214916\pi$
$200$		0			0
$201$	−0.665806	+	0.384403i	−0.0469624	+	0.0271137i
$202$	−6.40388	−	12.5683i	−0.450575	−	0.884304i
$203$	−3.10569	+	4.12402i	−0.217977	+	0.289450i
$204$	−0.225927	+	0.310962i	−0.0158181	+	0.0217717i
$205$		0			0
$206$	−19.3694	+	2.03581i	−1.34953	+	0.141842i
$207$	16.6338	−	4.45702i	1.15613	−	0.309784i
$208$	−4.20585	−	10.9566i	−0.291623	−	0.759705i
$209$	4.34399	+	13.3694i	0.300480	+	0.924782i
$210$		0			0
$211$	−1.35065	+	4.15686i	−0.0929824	+	0.286170i	−0.986723	−	0.162415i	$-0.948072\pi$
$211$	−1.35065	+	4.15686i	−0.0929824	+	0.286170i	0.893740	+	0.448585i	$0.148072\pi$
$212$	13.8115	−	0.723832i	0.948580	−	0.0497130i
$213$	0.0646770	+	0.0995938i	0.00443159	+	0.00682406i
$214$	−4.97484	+	4.47937i	−0.340073	+	0.306203i
$215$		0			0
$216$	0.0486761	−	0.0158158i	0.00331199	−	0.00107613i
$217$	−11.9253	+	1.04702i	−0.809544	+	0.0710767i
$218$	13.9365	−	13.9365i	0.943899	−	0.943899i
$219$	−0.0486958	+	0.109373i	−0.00329056	+	0.00739072i
$220$		0			0
$221$	9.47552	−	4.21877i	0.637392	−	0.283785i
$222$	−0.567571	−	0.700892i	−0.0380929	−	0.0470408i
$223$	−5.03366	+	2.56478i	−0.337079	+	0.171750i	−0.614334	−	0.789046i	$-0.710575\pi$
$223$	−5.03366	+	2.56478i	−0.337079	+	0.171750i	0.277255	+	0.960796i	$0.410575\pi$
$224$	20.7026	−	5.16849i	1.38325	−	0.345334i
$225$		0			0
$226$	−4.72023	−	8.17568i	−0.313985	−	0.543838i
$227$	16.5074	+	0.865117i	1.09564	+	0.0574198i	0.591576	−	0.806249i	$-0.298506\pi$
$227$	16.5074	+	0.865117i	1.09564	+	0.0574198i	0.504060	+	0.863669i	$0.331839\pi$
$228$	−0.150349	+	0.391673i	−0.00995713	+	0.0259392i
$229$	−2.91929	+	27.7751i	−0.192912	+	1.83543i	0.286780	+	0.957996i	$0.407415\pi$
$229$	−2.91929	+	27.7751i	−0.192912	+	1.83543i	−0.479692	+	0.877437i	$0.659252\pi$
$230$		0			0
$231$	0.187469	+	0.514575i	0.0123346	+	0.0338565i
$232$	−0.215943	−	0.215943i	−0.0141773	−	0.0141773i
$233$	−15.0402	+	5.77338i	−0.985314	+	0.378227i	−0.797064	−	0.603894i	$-0.793615\pi$
$233$	−15.0402	+	5.77338i	−0.985314	+	0.378227i	−0.188250	+	0.982121i	$0.560282\pi$
$234$	−18.0968	−	3.84659i	−1.18302	−	0.251459i
$235$		0			0
$236$	1.39831	+	6.57852i	0.0910221	+	0.428225i
$237$	−0.318340	−	0.162203i	−0.0206784	−	0.0105362i
$238$	5.30496	+	17.3327i	0.343870	+	1.12351i
$239$	14.3559	+	4.66452i	0.928606	+	0.301722i	0.733993	−	0.679157i	$-0.237655\pi$
$239$	14.3559	+	4.66452i	0.928606	+	0.301722i	0.194614	+	0.980880i	$0.437655\pi$
$240$		0			0
$241$	−5.19859	+	24.4574i	−0.334871	+	1.57544i	0.412451	+	0.910980i	$0.364673\pi$
$241$	−5.19859	+	24.4574i	−0.334871	+	1.57544i	−0.747322	+	0.664462i	$0.768661\pi$
$242$	−4.33227	+	5.34991i	−0.278489	+	0.343905i
$243$	−0.380565	+	1.42029i	−0.0244133	+	0.0911115i
$244$	23.8058	−	17.2959i	1.52401	−	1.10726i
$245$		0			0
$246$	0.726356	+	0.527729i	0.0463108	+	0.0336467i
$247$	8.79829	−	7.12471i	0.559822	−	0.453335i
$248$	0.0370612	−	0.707170i	0.00235339	−	0.0449053i
$249$	0.326653	+	0.188593i	0.0207008	+	0.0119516i
$250$		0			0
$251$		−	12.4908i		−	0.788410i	−0.919023	−	0.394205i	$-0.871020\pi$
$251$		−	12.4908i		−	0.788410i	0.919023	−	0.394205i	$-0.128980\pi$
$252$	5.35841	−	15.5775i	0.337548	−	0.981290i
$253$	−21.5425	+	3.41200i	−1.35437	+	0.214511i
$254$	−24.6121	−	2.58683i	−1.54430	−	0.162312i
$255$		0			0
$256$	−1.53540	−	14.6083i	−0.0959623	−	0.913020i
$257$	−5.56457	−	1.49102i	−0.347109	−	0.0930075i	0.0810527	−	0.996710i	$-0.474172\pi$
$257$	−5.56457	−	1.49102i	−0.347109	−	0.0930075i	−0.428161	+	0.903702i	$0.640838\pi$
$258$	−0.783297	−	0.124062i	−0.0487659	−	0.00772376i
$259$	−21.6565	+	0.762926i	−1.34567	+	0.0474059i
$260$		0			0
$261$	5.72029	−	1.21589i	0.354077	−	0.0752614i
$262$	−17.4370	+	11.3237i	−1.07726	+	0.699580i
$263$	−5.42424	+	3.52255i	−0.334473	+	0.217209i	−0.700938	−	0.713223i	$-0.747235\pi$
$263$	−5.42424	+	3.52255i	−0.334473	+	0.217209i	0.366464	+	0.930432i	$0.380568\pi$
$264$	−0.0316882	+	0.00673553i	−0.00195027	+	0.000414543i
$265$		0			0
$266$	10.4895	+	16.7753i	0.643155	+	1.02856i
$267$	0.205807	+	0.0325966i	0.0125952	+	0.00199488i
$268$	−28.2918	−	7.58076i	−1.72819	−	0.463068i
$269$	1.59755	+	15.1996i	0.0974041	+	0.926738i	0.928681	+	0.370880i	$0.120944\pi$
$269$	1.59755	+	15.1996i	0.0974041	+	0.926738i	−0.831277	+	0.555859i	$0.812390\pi$
$270$		0			0
$271$	−4.48618	−	0.471517i	−0.272516	−	0.0286426i	−0.0327154	−	0.999465i	$-0.510415\pi$
$271$	−4.48618	−	0.471517i	−0.272516	−	0.0286426i	−0.239801	+	0.970822i	$0.577082\pi$
$272$	12.8647	−	2.03757i	0.780038	−	0.123546i
$273$	0.332786	−	0.289466i	0.0201411	−	0.0175193i
$274$		−	37.5806i		−	2.27032i
$275$		0			0
$276$	−0.563733	−	0.325471i	−0.0339327	−	0.0195911i
$277$	0.296475	−	5.65708i	0.0178134	−	0.339901i	−0.975155	−	0.221523i	$-0.928897\pi$
$277$	0.296475	−	5.65708i	0.0178134	−	0.339901i	0.992969	−	0.118378i	$-0.0377694\pi$
$278$	25.1203	−	20.3420i	1.50662	−	1.22003i
$279$	10.9708	+	7.97073i	0.656803	+	0.477195i
$280$		0			0
$281$	8.30707	−	6.03544i	0.495558	−	0.360044i	−0.311760	−	0.950161i	$-0.600918\pi$
$281$	8.30707	−	6.03544i	0.495558	−	0.360044i	0.807318	+	0.590117i	$0.200918\pi$
$282$	0.266133	−	0.993220i	0.0158480	−	0.0591454i
$283$	17.8045	−	21.9867i	1.05837	−	1.30697i	0.108575	−	0.994088i	$-0.465371\pi$
$283$	17.8045	−	21.9867i	1.05837	−	1.30697i	0.949791	−	0.312885i	$-0.101296\pi$
$284$	−0.940630	+	4.42532i	−0.0558161	+	0.262594i
$285$		0			0
$286$	22.2860	+	7.24115i	1.31780	+	0.428178i
$287$	20.6279	−	6.31353i	1.21763	−	0.372676i
$288$	−21.5365	−	10.9734i	−1.26905	−	0.646615i
$289$	−1.14114	−	5.36865i	−0.0671260	−	0.315803i
$290$		0			0
$291$	−0.230093	−	0.0489077i	−0.0134883	−	0.00286702i
$292$	−4.25823	+	1.63458i	−0.249194	+	0.0956567i
$293$	13.4826	+	13.4826i	0.787661	+	0.787661i	0.981110	−	0.193449i	$-0.0619675\pi$
$293$	13.4826	+	13.4826i	0.787661	+	0.787661i	−0.193449	+	0.981110i	$0.561968\pi$
$294$	0.431415	+	0.638752i	0.0251607	+	0.0372528i
$295$		0			0
$296$	0.133990	−	1.27483i	0.00778802	−	0.0740981i
$297$	0.444864	−	1.15891i	0.0258136	−	0.0672468i
$298$	−3.54315	−	0.185689i	−0.205249	−	0.0107567i
$299$	8.78286	+	15.2124i	0.507926	+	0.879754i
$300$		0			0
$301$	−13.7031	+	13.2411i	−0.789836	+	0.763205i
$302$	2.69729	−	1.37434i	0.155212	−	0.0790843i
$303$	−0.239725	−	0.296036i	−0.0137719	−	0.0170068i
$304$	12.9877	−	5.78251i	0.744897	−	0.331650i
$305$		0			0
$306$	8.35152	−	18.7578i	0.477424	−	1.07231i
$307$	−13.9902	+	13.9902i	−0.798461	+	0.798461i	−0.982853	−	0.184392i	$-0.940968\pi$
$307$	−13.9902	+	13.9902i	−0.798461	+	0.798461i	0.184392	+	0.982853i	$0.440968\pi$
$308$	−8.81196	+	18.9125i	−0.502108	+	1.07764i
$309$	−0.500213	+	0.162529i	−0.0284561	+	0.00924595i
$310$		0			0
$311$	−0.132551	+	0.119349i	−0.00751626	+	0.00676767i	−0.672880	−	0.739751i	$-0.734943\pi$
$311$	−0.132551	+	0.119349i	−0.00751626	+	0.00676767i	0.665364	+	0.746519i	$0.268276\pi$
$312$	0.0142099	+	0.0218813i	0.000804477	+	0.00123879i
$313$	13.7239	−	0.719241i	0.775723	−	0.0406539i	0.339634	−	0.940558i	$-0.389697\pi$
$313$	13.7239	−	0.719241i	0.775723	−	0.0406539i	0.436089	+	0.899904i	$0.356363\pi$
$314$	2.47417	−	7.61471i	0.139625	−	0.429723i
$315$		0			0
$316$	−4.20622	−	12.9454i	−0.236619	−	0.728237i
$317$	−4.37431	−	11.3955i	−0.245686	−	0.640034i	0.754176	−	0.656673i	$-0.228037\pi$
$317$	−4.37431	−	11.3955i	−0.245686	−	0.640034i	−0.999862	+	0.0166391i	$0.994703\pi$
$318$	0.708076	−	0.189728i	0.0397069	−	0.0106394i
$319$	−7.36642	+	0.774242i	−0.412440	+	0.0433492i
$320$		0			0
$321$	−0.106260	+	0.146254i	−0.00593086	+	0.00816313i
$322$	−28.2536	+	12.0032i	−1.57451	+	0.668911i
$323$	5.70424	+	11.1952i	0.317392	+	0.622918i
$324$	−16.1444	+	9.32098i	−0.896912	+	0.517832i
$325$		0			0
$326$	−10.9441	+	18.9558i	−0.606140	+	1.04987i
$327$	0.289883	−	0.446381i	0.0160306	−	0.0246849i
$328$	0.199625	+	1.26038i	0.0110224	+	0.0695929i
$329$	−15.2168	−	19.4643i	−0.838929	−	1.07310i
$330$		0			0
$331$	7.85181	+	3.49585i	0.431574	+	0.192149i	0.611014	−	0.791620i	$-0.290762\pi$
$331$	7.85181	+	3.49585i	0.431574	+	0.192149i	−0.179440	+	0.983769i	$0.557429\pi$
$332$	3.71922	+	13.8803i	0.204119	+	0.761781i
$333$	19.0766	+	15.4479i	1.04539	+	0.846542i
$334$	17.0795	−	18.9688i	0.934551	−	1.03792i
$335$		0			0
$336$	0.497741	−	0.242954i	0.0271540	−	0.0132542i
$337$	−3.14995	+	6.18213i	−0.171589	+	0.336762i	−0.960746	−	0.277429i	$-0.910518\pi$
$337$	−3.14995	+	6.18213i	−0.171589	+	0.336762i	0.789157	+	0.614191i	$0.210518\pi$
$338$	0.386178	+	7.36872i	0.0210053	+	0.400806i
$339$	−0.170589	−	0.189458i	−0.00926510	−	0.0102899i
$340$		0			0
$341$	−12.7638	−	11.4926i	−0.691201	−	0.622360i
$342$	3.50596	−	22.1358i	0.189581	−	1.19697i
$343$	18.4958	+	0.952220i	0.998677	+	0.0514151i
$344$	−0.662544	−	0.911914i	−0.0357220	−	0.0491671i
$345$		0			0
$346$	−11.0168	−	24.7442i	−0.592268	−	1.33026i
$347$	14.2593	+	5.47365i	0.765481	+	0.293841i	0.709608	−	0.704597i	$-0.248872\pi$
$347$	14.2593	+	5.47365i	0.765481	+	0.293841i	0.0558738	+	0.998438i	$0.482206\pi$
$348$	−0.185396	−	0.120397i	−0.00993826	−	0.00645398i
$349$	−27.7967			−1.48792			−0.743961	−	0.668224i	$-0.767055\pi$
$349$	−27.7967			−1.48792			−0.743961	+	0.668224i	$0.767055\pi$
$350$		0			0
$351$	−0.999742			−0.0533623
$352$	25.6753	+	16.6737i	1.36850	+	0.888712i
$353$	−11.6058	−	4.45506i	−0.617716	−	0.237119i	0.0293301	−	0.999570i	$-0.490663\pi$
$353$	−11.6058	−	4.45506i	−0.617716	−	0.237119i	−0.647046	+	0.762451i	$0.723996\pi$
$354$	0.144989	+	0.325651i	0.00770608	+	0.0173081i
$355$		0			0
$356$	4.66614	+	6.42239i	0.247305	+	0.340386i
$357$	0.237448	+	0.428057i	0.0125671	+	0.0226552i
$358$	1.70402	−	10.7588i	0.0900604	−	0.568619i
$359$	27.4274	+	24.6957i	1.44756	+	1.30339i	0.875533	+	0.483159i	$0.160511\pi$
$359$	27.4274	+	24.6957i	1.44756	+	1.30339i	0.572030	+	0.820232i	$0.306156\pi$
$360$		0			0
$361$	−3.53682	−	3.92804i	−0.186148	−	0.206739i
$362$	2.23769	+	42.6976i	0.117610	+	2.24414i
$363$	−0.0843988	+	0.165642i	−0.00442979	+	0.00869395i
$364$	16.7629	+	1.16700i	0.878616	+	0.0611675i
$365$		0			0
$366$	1.04360	−	1.15903i	0.0545498	−	0.0605837i
$367$	11.2604	+	9.11853i	0.587791	+	0.475983i	0.876479	−	0.481440i	$-0.159886\pi$
$367$	11.2604	+	9.11853i	0.587791	+	0.475983i	−0.288689	+	0.957423i	$0.593219\pi$
$368$	5.70913	+	21.3068i	0.297609	+	1.11069i
$369$	−22.3240	−	9.93929i	−1.16214	−	0.517419i
$370$		0			0
$371$	6.59309	−	16.3329i	0.342296	−	0.847964i
$372$	−0.0801875	−	0.506284i	−0.00415753	−	0.0262496i
$373$	−14.4541	+	22.2573i	−0.748404	+	1.15244i	0.235173	+	0.971953i	$0.424434\pi$
$373$	−14.4541	+	22.2573i	−0.748404	+	1.15244i	−0.983577	+	0.180488i	$0.942232\pi$
$374$	−13.0032	+	22.5222i	−0.672380	+	1.16460i
$375$		0			0
$376$	1.26568	−	0.730738i	0.0652722	−	0.0376849i
$377$	2.70819	+	5.31511i	0.139479	+	0.273742i
$378$	0.212389	−	1.73417i	0.0109241	−	0.0891963i
$379$	0.369609	−	0.508723i	0.0189855	−	0.0261314i	−0.799419	−	0.600774i	$-0.794859\pi$
$379$	0.369609	−	0.508723i	0.0189855	−	0.0261314i	0.818404	+	0.574643i	$0.194859\pi$
$380$		0			0
$381$	−0.664652	+	0.0698577i	−0.0340512	+	0.00357892i
$382$	−29.4937	+	7.90282i	−1.50903	+	0.404344i
$383$	4.21053	+	10.9688i	0.215148	+	0.560480i	0.998101	−	0.0616015i	$-0.0196208\pi$
$383$	4.21053	+	10.9688i	0.215148	+	0.560480i	−0.782953	+	0.622081i	$0.786287\pi$
$384$	0.0210824	+	0.0648849i	0.00107586	+	0.00331114i
$385$		0			0
$386$	8.34271	−	25.6762i	0.424633	−	1.30689i
$387$	21.5556	−	1.12968i	1.09573	−	0.0574250i
$388$	−4.88097	−	7.51604i	−0.247794	−	0.381569i
$389$	3.77113	−	3.39554i	0.191204	−	0.172161i	−0.567969	−	0.823050i	$-0.692270\pi$
$389$	3.77113	−	3.39554i	0.191204	−	0.172161i	0.759173	+	0.650889i	$0.225604\pi$
$390$		0			0
$391$	−18.5408	+	6.02427i	−0.937648	+	0.304660i
$392$	−0.208378	+	1.07554i	−0.0105247	+	0.0543230i
$393$	−0.397018	+	0.397018i	−0.0200269	+	0.0200269i
$394$	−7.76288	+	17.4357i	−0.391088	+	0.878398i
$395$		0			0
$396$	21.5915	−	9.61314i	1.08501	−	0.483078i
$397$	−18.7756	−	23.1860i	−0.942323	−	1.16367i	−0.986354	−	0.164641i	$-0.947353\pi$
$397$	−18.7756	−	23.1860i	−0.942323	−	1.16367i	0.0440310	−	0.999030i	$-0.485980\pi$
$398$	25.0834	−	12.7806i	1.25732	−	0.640634i
$399$	0.371269	+	0.384224i	0.0185867	+	0.0192352i
$400$		0			0
$401$	8.26123	+	14.3089i	0.412546	+	0.714551i	0.995167	−	0.0981931i	$-0.0313063\pi$
$401$	8.26123	+	14.3089i	0.412546	+	0.714551i	−0.582621	+	0.812744i	$0.697973\pi$
$402$	−1.55031	−	0.0812484i	−0.0773225	−	0.00405230i
$403$	−4.95709	+	12.9137i	−0.246930	+	0.643275i
$404$	1.51697	−	14.4330i	0.0754719	−	0.718067i
$405$		0			0
$406$	−9.79505	+	3.56852i	−0.486120	+	0.177102i
$407$	−21.9843	−	21.9843i	−1.08972	−	1.08972i
$408$	−0.0270327	+	0.0103769i	−0.00133832	+	0.000513732i
$409$	18.8781	+	4.01266i	0.933461	+	0.198413i	0.649447	−	0.760407i	$-0.275000\pi$
$409$	18.8781	+	4.01266i	0.933461	+	0.198413i	0.284014	+	0.958820i	$0.408334\pi$
$410$		0			0
$411$	−0.211003	−	0.992690i	−0.0104080	−	0.0489658i
$412$	−17.8537	−	9.09692i	−0.879589	−	0.448173i
$413$	8.34613	+	1.92415i	0.410686	+	0.0946815i
$414$	33.0713	+	10.7455i	1.62537	+	0.528114i
$415$		0			0
$416$	5.12616	−	24.1167i	0.251331	−	1.18242i
$417$	0.549338	−	0.678376i	0.0269012	−	0.0332202i
$418$	−7.34682	+	27.4187i	−0.359345	+	1.34109i
$419$	19.1402	−	13.9062i	0.935062	−	0.679362i	−0.0121653	−	0.999926i	$-0.503872\pi$
$419$	19.1402	−	13.9062i	0.935062	−	0.679362i	0.947227	+	0.320564i	$0.103872\pi$
$420$		0			0
$421$	−0.268667	−	0.195198i	−0.0130940	−	0.00951338i	0.581219	−	0.813747i	$-0.302576\pi$
$421$	−0.268667	−	0.195198i	−0.0130940	−	0.00951338i	−0.594313	+	0.804234i	$0.702576\pi$
$422$	−6.85898	+	5.55429i	−0.333890	+	0.270379i
$423$	−1.46471	+	27.9484i	−0.0712167	+	1.35890i
$424$	0.902312	+	0.520950i	0.0438201	+	0.0252996i
$425$		0			0
$426$			0.239794i			0.0116181i
$427$	−7.16170	−	36.7834i	−0.346579	−	1.78007i
$428$	−6.80253	+	1.07742i	−0.328813	+	0.0520788i
$429$	0.629340	+	0.0661463i	0.0303848	+	0.00319357i
$430$		0			0
$431$	−3.57389	−	34.0033i	−0.172148	−	1.63788i	−0.650352	−	0.759633i	$-0.725378\pi$
$431$	−3.57389	−	34.0033i	−0.172148	−	1.63788i	0.478203	−	0.878249i	$-0.341288\pi$
$432$	−1.21266	−	0.324931i	−0.0583441	−	0.0156333i
$433$	−3.60320	−	0.570691i	−0.173159	−	0.0274256i	0.0692529	−	0.997599i	$-0.477938\pi$
$433$	−3.60320	−	0.570691i	−0.173159	−	0.0274256i	−0.242412	+	0.970173i	$0.577938\pi$
$434$	−21.3472	−	11.3421i	−1.02470	−	0.544438i
$435$		0			0
$436$	19.8344	−	4.21592i	0.949893	−	0.201906i
$437$	−17.8458	+	11.5892i	−0.853680	+	0.554386i
$438$	−0.202753	+	0.131669i	−0.00968791	+	0.00629140i
$439$	−30.0361	+	6.38437i	−1.43355	+	0.304710i	−0.858248	−	0.513235i	$-0.828447\pi$
$439$	−30.0361	+	6.38437i	−1.43355	+	0.304710i	−0.575297	+	0.817944i	$0.695114\pi$
$440$		0			0
$441$	−15.1001	−	14.5641i	−0.719053	−	0.693528i
$442$	20.6866	+	3.27644i	0.983963	+	0.155844i
$443$	−6.25039	−	1.67479i	−0.296965	−	0.0795715i	0.107260	−	0.994231i	$-0.465792\pi$
$443$	−6.25039	−	1.67479i	−0.296965	−	0.0795715i	−0.404225	+	0.914659i	$0.632459\pi$
$444$	−0.0969902	−	0.922800i	−0.00460295	−	0.0437942i
$445$		0			0
$446$	−11.3453	−	1.19244i	−0.537214	−	0.0564635i
$447$	−0.0946350	+	0.0149887i	−0.00447608	+	0.000708941i
$448$	21.5350	+	7.40770i	1.01743	+	0.349981i
$449$		−	33.2556i		−	1.56943i	−0.619856	−	0.784715i	$-0.712809\pi$
$449$		−	33.2556i		−	1.56943i	0.619856	−	0.784715i	$-0.287191\pi$
$450$		0			0
$451$	26.8041	+	15.4754i	1.26216	+	0.728706i
$452$	0.508321	−	9.69935i	0.0239094	−	0.456219i
$453$	0.0635324	−	0.0514476i	0.00298501	−	0.00241722i
$454$	27.0041	+	19.6196i	1.26737	+	0.920795i
$455$		0			0
$456$	−0.0255693	+	0.0185772i	−0.00119739	+	0.000869955i
$457$	−7.18403	+	26.8112i	−0.336055	+	1.25417i	0.566666	+	0.823947i	$0.308233\pi$
$457$	−7.18403	+	26.8112i	−0.336055	+	1.25417i	−0.902721	+	0.430226i	$0.858434\pi$
$458$	−35.4904	+	43.8270i	−1.65836	+	2.04790i
$459$	0.230687	−	1.08529i	0.0107675	−	0.0506572i
$460$		0			0
$461$	−5.61141	−	1.82326i	−0.261350	−	0.0849176i	0.175411	−	0.984495i	$-0.443874\pi$
$461$	−5.61141	−	1.82326i	−0.261350	−	0.0849176i	−0.436761	+	0.899578i	$0.643874\pi$
$462$	−0.248438	+	1.07761i	−0.0115584	+	0.0501352i
$463$	19.8133	+	10.0954i	0.920804	+	0.469173i	0.849088	−	0.528252i	$-0.177152\pi$
$463$	19.8133	+	10.0954i	0.920804	+	0.469173i	0.0717166	+	0.997425i	$0.477152\pi$
$464$	1.55746	+	7.32729i	0.0723034	+	0.340161i
$465$		0			0
$466$	−31.8202	−	6.76359i	−1.47404	−	0.313317i
$467$	12.2764	−	4.71248i	0.568085	−	0.218068i	−0.0573358	−	0.998355i	$-0.518261\pi$
$467$	12.2764	−	4.71248i	0.568085	−	0.218068i	0.625421	+	0.780287i	$0.284927\pi$
$468$	−13.4594	−	13.4594i	−0.622162	−	0.622162i
$469$	−23.9680	+	28.5818i	−1.10674	+	1.31978i
$470$		0			0
$471$	0.0226010	−	0.215034i	0.00104140	−	0.00990825i
$472$	−0.181569	+	0.473003i	−0.00835738	+	0.0217717i
$473$	−27.3017	−	1.43082i	−1.25533	−	0.0657892i
$474$	−0.360727	−	0.624797i	−0.0165687	−	0.0286979i
$475$		0			0
$476$	−5.13485	+	17.9281i	−0.235355	+	0.821735i
$477$	−17.7773	+	9.05801i	−0.813969	+	0.414738i
$478$	19.1820	+	23.6878i	0.877363	+	1.08345i
$479$	−9.63545	+	4.28998i	−0.440255	+	0.196014i	−0.614880	−	0.788621i	$-0.710795\pi$
$479$	−9.63545	+	4.28998i	−0.440255	+	0.196014i	0.174625	+	0.984635i	$0.444129\pi$
$480$		0			0
$481$	−10.1843	+	22.8742i	−0.464363	+	1.04298i
$482$	−35.7017	+	35.7017i	−1.62617	+	1.62617i
$483$	−0.678923	+	0.475698i	−0.0308921	+	0.0216450i
$484$	−6.73589	+	2.18862i	−0.306177	+	0.0994829i
$485$		0			0
$486$	−2.20650	+	1.98674i	−0.100089	+	0.0901203i
$487$	20.1463	+	31.0226i	0.912916	+	1.40577i	0.913976	+	0.405768i	$0.132996\pi$
$487$	20.1463	+	31.0226i	0.912916	+	1.40577i	−0.00106056	+	0.999999i	$0.500338\pi$
$488$	2.21369	−	0.116015i	0.100209	−	0.00525174i
$489$	−0.182659	+	0.562165i	−0.00826011	+	0.0254220i
$490$		0			0
$491$	−8.54554	−	26.3005i	−0.385655	−	1.18692i	−0.936004	−	0.351989i	$-0.885506\pi$
$491$	−8.54554	−	26.3005i	−0.385655	−	1.18692i	0.550350	−	0.834934i	$-0.314494\pi$
$492$	0.331029	+	0.862360i	0.0149239	+	0.0388782i
$493$	−6.39486	+	1.71350i	−0.288010	+	0.0771720i
$494$	22.7356	−	2.38961i	1.02292	−	0.107514i
$495$		0			0
$496$	−10.2099	+	14.0528i	−0.458440	+	0.630989i
$497$	4.60252	+	3.46603i	0.206451	+	0.155473i
$498$	0.345781	+	0.678633i	0.0154948	+	0.0304103i
$499$	29.8613	−	17.2404i	1.33678	−	0.771788i	0.350448	−	0.936582i	$-0.386029\pi$
$499$	29.8613	−	17.2404i	1.33678	−	0.771788i	0.986328	+	0.164794i	$0.0526959\pi$
$500$		0			0
$501$	0.344652	−	0.596956i	0.0153979	−	0.0266700i
$502$	13.7371	−	21.1533i	0.613117	−	0.944117i
$503$	0.765036	+	4.83025i	0.0341113	+	0.215370i	0.998856	−	0.0478169i	$-0.0152264\pi$
$503$	0.765036	+	4.83025i	0.0341113	+	0.215370i	−0.964745	+	0.263187i	$0.915226\pi$
$504$	0.977683	−	0.764333i	0.0435494	−	0.0340461i
$505$		0			0
$506$	−40.2350	−	17.9138i	−1.78866	−	0.796365i
$507$	0.0515739	+	0.192476i	0.00229048	+	0.00854817i
$508$	−19.7871	−	16.0233i	−0.877909	−	0.710917i
$509$	19.6524	−	21.8262i	0.871079	−	0.967431i	−0.128627	−	0.991693i	$-0.541057\pi$
$509$	19.6524	−	21.8262i	0.871079	−	0.967431i	0.999706	+	0.0242622i	$0.00772365\pi$
$510$		0			0
$511$	−0.403418	+	5.79475i	−0.0178462	+	0.256344i
$512$	14.6017	−	28.6575i	0.645311	−	1.26649i
$513$	−0.0633820	−	1.20940i	−0.00279839	−	0.0533964i
$514$	−7.78388	−	8.64488i	−0.343332	−	0.381309i
$515$		0			0
$516$	−0.606352	−	0.545962i	−0.0266932	−	0.0240346i
$517$	5.54515	−	35.0107i	0.243875	−	1.53977i
$518$	−37.5146	−	22.5253i	−1.64830	−	0.989707i
$519$	−0.429940	−	0.591762i	−0.0188723	−	0.0259755i
$520$		0			0
$521$	16.7254	+	37.5659i	0.732753	+	1.64579i	0.763124	+	0.646252i	$0.223664\pi$
$521$	16.7254	+	37.5659i	0.732753	+	1.64579i	−0.0303715	+	0.999539i	$0.509669\pi$
$522$	11.0246	+	4.23195i	0.482533	+	0.185227i
$523$	−13.9351	−	9.04956i	−0.609339	−	0.395710i	0.202760	−	0.979228i	$-0.435009\pi$
$523$	−13.9351	−	9.04956i	−0.609339	−	0.395710i	−0.812100	+	0.583519i	$0.801675\pi$
$524$	−21.3907			−0.934455
$525$		0			0
$526$	−13.0601			−0.569446
$527$	−12.8749	−	8.36107i	−0.560840	−	0.364214i
$528$	0.741874	+	0.284779i	0.0322859	+	0.0123934i
$529$	−4.07358	−	9.14942i	−0.177112	−	0.397801i
$530$		0			0
$531$	−5.70284	−	7.84928i	−0.247482	−	0.340630i
$532$	−0.348994	+	20.3523i	−0.0151308	+	0.882386i
$533$	3.89935	−	24.6195i	0.168900	−	1.06639i
$534$	0.312688	+	0.281545i	0.0135313	+	0.0121837i
$535$		0			0
$536$	−1.47644	−	1.63975i	−0.0637724	−	0.0708265i
$537$	−0.0153953	−	0.293760i	−0.000664358	−	0.0126767i
$538$	−14.0108	+	27.4977i	−0.604048	+	1.18551i
$539$	17.0924	+	20.3445i	0.736221	+	0.876300i
$540$		0			0
$541$	4.47384	−	4.96870i	0.192345	−	0.213621i	−0.639256	−	0.768994i	$-0.720758\pi$
$541$	4.47384	−	4.96870i	0.192345	−	0.213621i	0.831602	+	0.555373i	$0.187424\pi$
$542$	−7.07885	−	5.73234i	−0.304063	−	0.246225i
$543$	0.298842	+	1.11529i	0.0128245	+	0.0478618i
$544$	24.9976	+	11.1297i	1.07176	+	0.477180i
$545$		0			0
$546$	0.881926	−	0.124223i	0.0377429	−	0.00531626i
$547$	1.45799	+	9.20536i	0.0623389	+	0.393593i	0.999053	+	0.0434985i	$0.0138504\pi$
$547$	1.45799	+	9.20536i	0.0623389	+	0.393593i	−0.936715	+	0.350094i	$0.886150\pi$
$548$	21.0580	−	32.4265i	0.899553	−	1.38519i
$549$	−21.2248	+	36.7624i	−0.905851	+	1.56898i
$550$		0			0
$551$	−6.25807	+	3.61310i	−0.266603	+	0.153923i
$552$	−0.0222627	−	0.0436930i	−0.000947564	−	0.00185970i
$553$	−17.2062	−	2.10728i	−0.731680	−	0.0896107i
$554$	6.72363	−	9.25428i	0.285660	−	0.393177i
$555$		0			0
$556$	33.0736	−	3.47618i	1.40263	−	0.147423i
$557$	26.5262	−	7.10767i	1.12395	−	0.301162i	0.351469	−	0.936199i	$-0.385682\pi$
$557$	26.5262	−	7.10767i	1.12395	−	0.301162i	0.772481	+	0.635038i	$0.219015\pi$
$558$	9.81309	+	25.5640i	0.415421	+	1.08221i
$559$	6.80388	+	20.9402i	0.287774	+	0.885676i
$560$		0			0
$561$	−0.217025	+	0.667933i	−0.00916279	+	0.0282002i
$562$	20.7058	−	1.08514i	0.873421	−	0.0457741i
$563$	−16.6016	−	25.5643i	−0.699676	−	1.07741i	−0.992619	−	0.121276i	$-0.961301\pi$
$563$	−16.6016	−	25.5643i	−0.699676	−	1.07741i	0.292943	−	0.956130i	$-0.405365\pi$
$564$	0.786177	−	0.707877i	0.0331040	−	0.0298070i
$565$		0			0
$566$	54.3327	−	17.6538i	2.28377	−	0.742043i
$567$	2.07643	+	23.6500i	0.0872020	+	0.993207i
$568$	−0.240998	+	0.240998i	−0.0101120	+	0.0101120i
$569$	3.62068	−	8.13218i	0.151787	−	0.340919i	−0.821608	−	0.570053i	$-0.806923\pi$
$569$	3.62068	−	8.13218i	0.151787	−	0.340919i	0.973395	+	0.229134i	$0.0735894\pi$
$570$		0			0
$571$	39.4472	−	17.5630i	1.65081	−	0.734989i	0.651100	−	0.758992i	$-0.274308\pi$
$571$	39.4472	−	17.5630i	1.65081	−	0.734989i	0.999712	+	0.0240028i	$0.00764107\pi$
$572$	15.1720	+	18.7358i	0.634372	+	0.783384i
$573$	−0.734705	+	0.374351i	−0.0306927	+	0.0156387i
$574$	41.8772	+	11.9942i	1.74792	+	0.500627i
$575$		0			0
$576$	−12.8985	−	22.3409i	−0.537440	−	0.930873i
$577$	−2.78350	−	0.145877i	−0.115879	−	0.00607295i	−0.00569159	−	0.999984i	$-0.501812\pi$
$577$	−2.78350	−	0.145877i	−0.115879	−	0.00607295i	−0.110187	+	0.993911i	$0.535145\pi$
$578$	3.97180	−	10.3469i	0.165205	−	0.430374i
$579$	0.0762088	−	0.725079i	0.00316713	−	0.0301332i
$580$		0			0
$581$	18.0234	+	3.17230i	0.747738	+	0.131609i
$582$	−0.335877	−	0.335877i	−0.0139226	−	0.0139226i
$583$	23.5921	−	9.05615i	0.977085	−	0.375068i
$584$	−0.336101	−	0.0714405i	−0.0139080	−	0.00295623i
$585$		0			0
$586$	8.00505	+	37.6608i	0.330686	+	1.55575i
$587$	28.5627	+	14.5534i	1.17891	+	0.600684i	0.929898	−	0.367817i	$-0.119895\pi$
$587$	28.5627	+	14.5534i	1.17891	+	0.600684i	0.249011	+	0.968501i	$0.419895\pi$
$588$	0.0143275	+	0.792889i	0.000590857	+	0.0326982i
$589$	−15.9361	−	5.17795i	−0.656635	−	0.213354i
$590$		0			0
$591$	−0.107160	+	0.504150i	−0.00440799	+	0.0207380i
$592$	−19.7877	+	24.4358i	−0.813271	+	1.00431i
$593$	3.56036	−	13.2874i	0.146206	−	0.545650i	−0.853492	−	0.521105i	$-0.825520\pi$
$593$	3.56036	−	13.2874i	0.146206	−	0.545650i	0.999699	−	0.0245444i	$-0.00781352\pi$
$594$	2.02793	−	1.47338i	0.0832070	−	0.0604535i
$595$		0			0
$596$	−2.95317	−	2.14560i	−0.120967	−	0.0878873i
$597$	0.590818	−	0.478435i	0.0241806	−	0.0195810i
$598$	−1.85637	+	35.4216i	−0.0759125	+	1.44850i
$599$	27.9160	+	16.1173i	1.14062	+	0.658535i	0.946583	−	0.322460i	$-0.104510\pi$
$599$	27.9160	+	16.1173i	1.14062	+	0.658535i	0.194033	+	0.980995i	$0.437843\pi$
$600$		0			0
$601$			12.7293i			0.519238i	0.965711	+	0.259619i	$0.0835970\pi$
$601$			12.7293i			0.519238i	−0.965711	+	0.259619i	$0.916403\pi$
$602$	−37.7688	+	7.35355i	−1.53934	+	0.299708i
$603$	41.7335	−	6.60993i	1.69952	−	0.269177i
$604$	3.09746	+	0.325557i	0.126034	+	0.0132467i
$605$		0			0
$606$	−0.0804033	−	0.764987i	−0.00326616	−	0.0310755i
$607$	11.2348	+	3.01036i	0.456007	+	0.122187i	0.479509	−	0.877537i	$-0.340815\pi$
$607$	11.2348	+	3.01036i	0.456007	+	0.122187i	−0.0235020	+	0.999724i	$0.507482\pi$
$608$	29.4993	+	4.67223i	1.19635	+	0.189484i
$609$	−0.238700	+	0.149258i	−0.00967261	+	0.00604825i
$610$		0			0
$611$	−27.9238	+	5.93538i	−1.12968	+	0.240120i
$612$	17.7169	−	11.5055i	0.716164	−	0.465083i
$613$	20.1061	−	13.0570i	0.812077	−	0.527369i	−0.0705139	−	0.997511i	$-0.522464\pi$
$613$	20.1061	−	13.0570i	0.812077	−	0.527369i	0.882591	+	0.470142i	$0.155797\pi$
$614$	−39.0786	+	8.30642i	−1.57709	+	0.335220i
$615$		0			0
$616$	−1.33271	+	0.833340i	−0.0536964	+	0.0335762i
$617$	46.3033	+	7.33373i	1.86410	+	0.295245i	0.983814	−	0.179194i	$-0.0573491\pi$
$617$	46.3033	+	7.33373i	1.86410	+	0.295245i	0.880288	+	0.474439i	$0.157349\pi$
$618$	−1.02586	−	0.274879i	−0.0412663	−	0.0110573i
$619$	0.396520	+	3.77263i	0.0159375	+	0.151635i	0.999596	−	0.0284068i	$-0.00904339\pi$
$619$	0.396520	+	3.77263i	0.0159375	+	0.151635i	−0.983659	+	0.180042i	$0.942377\pi$
$620$		0			0
$621$	1.86875	+	0.196413i	0.0749903	+	0.00788180i
$622$	−0.355734	+	0.0563428i	−0.0142637	+	0.00225914i
$623$	9.92354	−	1.93211i	0.397578	−	0.0774082i
$624$		−	0.639982i		−	0.0256198i
$625$		0			0
$626$	24.0327	+	13.8753i	0.960539	+	0.554568i
$627$	−0.0401189	+	0.765515i	−0.00160220	+	0.0305717i
$628$	6.40169	−	5.18399i	0.255455	−	0.206864i
$629$	−22.4817	−	16.3339i	−0.896406	−	0.651277i
$630$		0			0
$631$	−16.4374	+	11.9425i	−0.654362	+	0.475422i	−0.864754	−	0.502195i	$-0.832526\pi$
$631$	−16.4374	+	11.9425i	−0.654362	+	0.475422i	0.210392	+	0.977617i	$0.432526\pi$
$632$	0.265396	−	0.990471i	0.0105569	−	0.0393988i
$633$	−0.149994	+	0.185227i	−0.00596174	+	0.00736213i
$634$	5.12456	−	24.1092i	0.203522	−	0.957498i
$635$		0			0
$636$	0.717277	+	0.233058i	0.0284419	+	0.00924133i
$637$	10.3632	−	18.7229i	0.410607	−	0.741829i
$638$	−13.3266	−	6.79026i	−0.527606	−	0.268829i
$639$	−1.35696	−	6.38400i	−0.0536805	−	0.252547i
$640$		0			0
$641$	10.7436	+	2.28363i	0.424348	+	0.0901981i	0.415136	−	0.909760i	$-0.363734\pi$
$641$	10.7436	+	2.28363i	0.424348	+	0.0901981i	0.00921279	+	0.999958i	$0.497067\pi$
$642$	−0.340801	+	0.130821i	−0.0134503	+	0.00516310i
$643$	−1.99706	−	1.99706i	−0.0787564	−	0.0787564i	0.666631	−	0.745388i	$-0.267736\pi$
$643$	−1.99706	−	1.99706i	−0.0787564	−	0.0787564i	−0.745388	+	0.666631i	$0.767736\pi$
$644$	−31.1045	−	5.47471i	−1.22569	−	0.215734i
$645$		0			0
$646$	−2.65206	+	25.2326i	−0.104344	+	0.992765i
$647$	−8.05429	+	20.9821i	−0.316647	+	0.824893i	0.679209	+	0.733945i	$0.262323\pi$
$647$	−8.05429	+	20.9821i	−0.316647	+	0.824893i	−0.995856	+	0.0909482i	$0.971010\pi$
$648$	−1.40244	−	0.0734988i	−0.0550931	−	0.00288731i
$649$	6.14428	+	10.6422i	0.241184	+	0.417743i
$650$		0			0
$651$	−0.627568	−	0.179743i	−0.0245963	−	0.00704470i
$652$	−20.0649	+	10.2236i	−0.785803	+	0.400387i
$653$	4.78157	+	5.90474i	0.187117	+	0.231070i	0.862068	−	0.506792i	$-0.169169\pi$
$653$	4.78157	+	5.90474i	0.187117	+	0.231070i	−0.674951	+	0.737862i	$0.735835\pi$
$654$	0.981843	−	0.437145i	0.0383931	−	0.0170937i
$655$		0			0
$656$	12.7315	−	28.5955i	0.497083	−	1.11647i
$657$	4.65276	−	4.65276i	0.181522	−	0.181522i
$658$	−4.36342	−	49.6981i	−0.170104	−	1.93744i
$659$	−39.6715	+	12.8900i	−1.54538	+	0.502125i	−0.952855	−	0.303426i	$-0.901869\pi$
$659$	−39.6715	+	12.8900i	−1.54538	+	0.502125i	−0.592526	+	0.805551i	$0.701869\pi$
$660$		0			0
$661$	32.5603	−	29.3174i	1.26645	−	1.14031i	0.283001	−	0.959120i	$-0.408670\pi$
$661$	32.5603	−	29.3174i	1.26645	−	1.14031i	0.983447	−	0.181195i	$-0.0579965\pi$
$662$	9.45247	+	14.5555i	0.367381	+	0.565717i
$663$	0.564834	−	0.0296017i	0.0219363	−	0.00114963i
$664$	−0.334523	+	1.02956i	−0.0129820	+	0.0399545i
$665$		0			0
$666$	15.3172	+	47.1414i	0.593528	+	1.82669i
$667$	−4.01800	−	10.4672i	−0.155578	−	0.405293i
$668$	25.3661	−	6.79683i	0.981445	−	0.262977i
$669$	−0.306380	+	0.0322019i	−0.0118453	+	0.00124500i
$670$		0			0
$671$	31.6024	−	43.4970i	1.22000	−	1.67918i
$672$	1.15495	+	0.141450i	0.0445532	+	0.00545655i
$673$	13.0594	+	25.6305i	0.503402	+	0.987982i	0.993230	+	0.116163i	$0.0370596\pi$
$673$	13.0594	+	25.6305i	0.503402	+	0.987982i	−0.489828	+	0.871819i	$0.662940\pi$
$674$	−12.1335	+	7.00526i	−0.467364	+	0.269833i
$675$		0			0
$676$	−3.79579	+	6.57451i	−0.145992	+	0.252866i
$677$	22.6171	−	34.8273i	0.869245	−	1.33852i	−0.0708068	−	0.997490i	$-0.522557\pi$
$677$	22.6171	−	34.8273i	0.869245	−	1.33852i	0.940052	−	0.341030i	$-0.110776\pi$
$678$	−0.0805320	−	0.508459i	−0.00309281	−	0.0195273i
$679$	−11.3016	+	1.59187i	−0.433714	+	0.0610905i
$680$		0			0
$681$	0.823471	+	0.366633i	0.0315555	+	0.0140494i
$682$	−8.97638	−	33.5003i	−0.343724	−	1.28279i
$683$	3.59070	+	2.90769i	0.137394	+	0.111260i	0.695554	−	0.718474i	$-0.255159\pi$
$683$	3.59070	+	2.90769i	0.137394	+	0.111260i	−0.558160	+	0.829734i	$0.688492\pi$
$684$	15.4287	−	17.1354i	0.589933	−	0.655187i
$685$		0			0
$686$	30.2756	+	21.9539i	1.15593	+	0.838203i
$687$	−0.691404	+	1.35696i	−0.0263787	+	0.0517711i
$688$	1.44705	+	27.6113i	0.0551681	+	1.05267i
$689$	−13.6181	−	15.1244i	−0.518806	−	0.576193i
$690$		0			0
$691$	−0.175360	−	0.157895i	−0.00667101	−	0.00600660i	0.665788	−	0.746141i	$-0.268095\pi$
$691$	−0.175360	−	0.157895i	−0.00667101	−	0.00600660i	−0.672459	+	0.740134i	$0.734762\pi$
$692$	4.35934	−	27.5238i	0.165717	−	1.04630i
$693$	0.516058	−	30.0950i	0.0196034	−	1.14322i
$694$	18.1286	+	24.9518i	0.688151	+	0.947159i
$695$		0			0
$696$	−0.00677345	−	0.0152134i	−0.000256747	−	0.000576663i
$697$	25.8266	+	9.91391i	0.978252	+	0.375516i
$698$	−47.0740	−	30.5702i	−1.78178	−	1.15710i
$699$	−0.878505			−0.0332281
$700$		0			0
$701$	−8.97311			−0.338910			−0.169455	−	0.985538i	$-0.554201\pi$
$701$	−8.97311			−0.338910			−0.169455	+	0.985538i	$0.554201\pi$
$702$	−1.69308	−	1.09950i	−0.0639010	−	0.0414978i
$703$	−28.3170	−	10.8699i	−1.06799	−	0.409965i
$704$	13.2896	+	29.8490i	0.500872	+	1.12498i
$705$		0			0
$706$	−14.7550	−	20.3086i	−0.555313	−	0.764323i
$707$	−15.8451	−	9.51404i	−0.595915	−	0.357812i
$708$	−0.0573719	+	0.362232i	−0.00215617	+	0.0136135i
$709$	−13.1569	−	11.8465i	−0.494119	−	0.444906i	0.384011	−	0.923328i	$-0.374542\pi$
$709$	−13.1569	−	11.8465i	−0.494119	−	0.444906i	−0.878130	+	0.478422i	$0.841209\pi$
$710$		0			0
$711$	13.1392	+	14.5926i	0.492759	+	0.547264i
$712$	0.0312988	+	0.597217i	0.00117297	+	0.0223816i
$713$	11.8030	−	23.1647i	0.442026	−	0.867526i
$714$	−0.0686475	+	0.986061i	−0.00256907	+	0.0369024i
$715$		0			0
$716$	7.49892	−	8.32840i	0.280248	−	0.311247i
$717$	0.639691	+	0.518011i	0.0238897	+	0.0193455i
$718$	19.2888	+	71.9867i	0.719851	+	2.68652i
$719$	0.351469	+	0.156484i	0.0131076	+	0.00583587i	0.413280	−	0.910604i	$-0.364383\pi$
$719$	0.351469	+	0.156484i	0.0131076	+	0.00583587i	−0.400172	+	0.916440i	$0.631050\pi$
$720$		0			0
$721$	−20.1040	+	15.7169i	−0.748711	+	0.585328i
$722$	−1.66967	−	10.5419i	−0.0621388	−	0.392329i
$723$	−0.742606	+	1.14351i	−0.0276178	+	0.0425277i
$724$	−21.9945	+	38.0956i	−0.817419	+	1.41581i
$725$		0			0
$726$	−0.325100	+	0.187697i	−0.0120656	+	0.00696608i
$727$	15.1495	+	29.7326i	0.561864	+	1.10272i	0.980857	+	0.194731i	$0.0623835\pi$
$727$	15.1495	+	29.7326i	0.561864	+	1.10272i	−0.418992	+	0.907990i	$0.637617\pi$
$728$	1.01120	+	0.761507i	0.0374776	+	0.0282233i
$729$	15.7759	−	21.7137i	0.584292	−	0.804210i
$730$		0			0
$731$	−24.3021	+	2.55426i	−0.898847	+	0.0944726i
$732$	1.54993	−	0.415302i	0.0572870	−	0.0153500i
$733$	−17.5710	−	45.7741i	−0.649001	−	1.69070i	−0.720672	−	0.693276i	$-0.756167\pi$
$733$	−17.5710	−	45.7741i	−0.649001	−	1.69070i	0.0716715	−	0.997428i	$-0.477167\pi$
$734$	9.04134	+	27.8264i	0.333722	+	1.02709i
$735$		0			0
$736$	−14.3200	+	44.0726i	−0.527844	+	1.62454i
$737$	−53.4438	+	2.80087i	−1.96863	+	0.103172i
$738$	−26.8750	−	41.3838i	−0.989281	−	1.52336i
$739$	−1.05689	+	0.951626i	−0.0388782	+	0.0350061i	−0.688341	−	0.725387i	$-0.741661\pi$
$739$	−1.05689	+	0.951626i	−0.0388782	+	0.0350061i	0.649463	+	0.760394i	$0.274994\pi$
$740$		0			0
$741$	0.587145	−	0.190775i	0.0215693	−	0.00700829i
$742$	29.1281	−	20.4091i	1.06933	−	0.749241i
$743$	28.2843	−	28.2843i	1.03765	−	1.03765i	0.0383888	−	0.999263i	$-0.487777\pi$
$743$	28.2843	−	28.2843i	1.03765	−	1.03765i	0.999263	−	0.0383888i	$-0.0122225\pi$
$744$	0.0157064	−	0.0352771i	0.000575823	−	0.00129332i
$745$		0			0
$746$	−48.9564	+	21.7968i	−1.79242	+	0.798037i
$747$	−13.0460	−	16.1104i	−0.477326	−	0.589449i
$748$	−23.8400	+	12.1471i	−0.871677	+	0.444142i
$749$	−2.41507	+	8.43213i	−0.0882447	+	0.308103i
$750$		0			0
$751$	−14.2895	−	24.7501i	−0.521430	−	0.903143i	−0.999689	−	0.0249242i	$-0.992066\pi$
$751$	−14.2895	−	24.7501i	−0.521430	−	0.903143i	0.478260	−	0.878218i	$-0.341268\pi$
$752$	−35.7999	−	1.87619i	−1.30549	−	0.0684177i
$753$	0.244096	−	0.635893i	0.00889537	−	0.0231732i
$754$	−1.25911	+	11.9796i	−0.0458541	+	0.436272i
$755$		0			0
$756$	1.15499	−	1.37732i	0.0420066	−	0.0500928i
$757$	−9.94771	−	9.94771i	−0.361556	−	0.361556i	0.502830	−	0.864385i	$-0.332292\pi$
$757$	−9.94771	−	9.94771i	−0.361556	−	0.361556i	−0.864385	+	0.502830i	$0.832292\pi$
$758$	1.18542	−	0.455041i	0.0430565	−	0.0165278i
$759$	−1.16339	−	0.247286i	−0.0422283	−	0.00897590i
$760$		0			0
$761$	−4.97651	−	23.4126i	−0.180398	−	0.848708i	−0.971503	−	0.237027i	$-0.923827\pi$
$761$	−4.97651	−	23.4126i	−0.180398	−	0.848708i	0.791105	−	0.611681i	$-0.209506\pi$
$762$	−1.20243	−	0.612666i	−0.0435593	−	0.0221946i
$763$	5.80136	−	25.1637i	0.210023	−	0.910989i
$764$	−29.8770	−	9.70763i	−1.08091	−	0.351210i
$765$		0			0
$766$	−4.93269	+	23.2065i	−0.178225	+	0.838484i
$767$	6.22819	−	7.69118i	0.224887	−	0.277712i
$768$	0.207313	−	0.773701i	0.00748075	−	0.0279185i
$769$	18.1484	−	13.1856i	0.654450	−	0.475486i	−0.210334	−	0.977630i	$-0.567455\pi$
$769$	18.1484	−	13.1856i	0.654450	−	0.475486i	0.864784	+	0.502144i	$0.167455\pi$
$770$		0			0
$771$	−0.254149	−	0.184650i	−0.00915296	−	0.00665002i
$772$	21.5860	−	17.4800i	0.776897	−	0.629119i
$773$	−0.0465468	+	0.888166i	−0.00167417	+	0.0319451i	−0.999339	−	0.0363567i	$-0.988425\pi$
$773$	−0.0465468	+	0.888166i	−0.00167417	+	0.0319451i	0.997665	+	0.0683018i	$0.0217581\pi$
$774$	37.7472	+	21.7933i	1.35679	+	0.783345i
$775$		0			0
$776$		−	0.675128i		−	0.0242357i
$777$	−1.11742	−	0.384374i	−0.0400872	−	0.0137893i
$778$	10.1208	−	1.60298i	0.362849	−	0.0574696i
$779$	30.0298	+	3.15626i	1.07593	+	0.113085i
$780$		0			0
$781$	0.864075	+	8.22113i	0.0309190	+	0.294175i
$782$	−38.0244	−	10.1886i	−1.35975	−	0.364344i
$783$	0.630263	+	0.0998239i	0.0225238	+	0.00356742i
$784$	18.6556	−	19.3422i	0.666271	−	0.690793i
$785$		0			0
$786$	−1.10899	+	0.235723i	−0.0395563	+	0.00840795i
$787$	−9.61316	+	6.24286i	−0.342672	+	0.222534i	−0.704488	−	0.709716i	$-0.748823\pi$
$787$	−9.61316	+	6.24286i	−0.342672	+	0.222534i	0.361816	+	0.932249i	$0.382157\pi$
$788$	−16.4682	+	10.6946i	−0.586655	+	0.380978i
$789$	−0.344981	+	0.0733280i	−0.0122817	+	0.00261055i
$790$		0			0
$791$	−10.9232	−	5.80367i	−0.388385	−	0.206355i
$792$	1.75857	+	0.278530i	0.0624881	+	0.00989715i
$793$	−41.8249	−	11.2069i	−1.48524	−	0.397970i
$794$	−6.29731	−	59.9149i	−0.223483	−	2.12630i
$795$		0			0
$796$	28.8048	+	3.02750i	1.02096	+	0.107307i
$797$	−6.72244	+	1.06473i	−0.238121	+	0.0377146i	−0.274354	−	0.961629i	$-0.588464\pi$
$797$	−6.72244	+	1.06473i	−0.238121	+	0.0377146i	0.0362333	+	0.999343i	$0.488464\pi$
$798$	0.206187	+	1.05900i	0.00729894	+	0.0374883i
$799$		−	31.6829i		−	1.12086i
$800$		0			0
$801$	−9.91786	−	5.72608i	−0.350430	−	0.202321i
$802$	−1.74611	+	33.3178i	−0.0616573	+	1.17649i
$803$	−6.47675	+	5.24477i	−0.228560	+	0.185084i
$804$	−1.29216	−	0.938811i	−0.0455711	−	0.0331093i
$805$		0			0
$806$	−22.5971	+	16.4177i	−0.795948	+	0.578290i
$807$	−0.215704	+	0.805018i	−0.00759314	+	0.0283380i
$808$	0.688020	−	0.849634i	0.0242045	−	0.0298900i
$809$	−4.20054	+	19.7620i	−0.147683	+	0.694794i	0.840537	+	0.541754i	$0.182240\pi$
$809$	−4.20054	+	19.7620i	−0.147683	+	0.694794i	−0.988220	+	0.153040i	$0.951094\pi$
$810$		0			0
$811$	−44.8838	−	14.5836i	−1.57608	−	0.512101i	−0.615041	−	0.788495i	$-0.710860\pi$
$811$	−44.8838	−	14.5836i	−1.57608	−	0.512101i	−0.961044	+	0.276394i	$0.910860\pi$
$812$	−10.4513	−	2.40948i	−0.366768	−	0.0845562i
$813$	−0.219173	−	0.111674i	−0.00768673	−	0.00391658i
$814$	−13.0528	−	61.4086i	−0.457500	−	2.15237i
$815$		0			0
$816$	0.694749	+	0.147673i	0.0243211	+	0.00516960i
$817$	−24.9003	+	9.55833i	−0.871151	+	0.334404i
$818$	27.5572	+	27.5572i	0.963517	+	0.963517i
$819$	−22.7764	+	8.29787i	−0.795872	+	0.289951i
$820$		0			0
$821$	4.44023	−	42.2460i	0.154965	−	1.47439i	−0.590061	−	0.807359i	$-0.700896\pi$
$821$	4.44023	−	42.2460i	0.154965	−	1.47439i	0.745026	−	0.667036i	$-0.232437\pi$
$822$	0.734405	−	1.91319i	0.0256153	−	0.0667302i
$823$	−10.9948	−	0.576213i	−0.383255	−	0.0200855i	−0.140264	−	0.990114i	$-0.544795\pi$
$823$	−10.9948	−	0.576213i	−0.383255	−	0.0200855i	−0.242991	+	0.970029i	$0.578128\pi$
$824$	−0.754754	−	1.30727i	−0.0262931	−	0.0455410i
$825$		0			0
$826$	12.0181	+	12.4375i	0.418165	+	0.432756i
$827$	−13.5701	+	6.91433i	−0.471880	+	0.240435i	−0.673724	−	0.738983i	$-0.735307\pi$
$827$	−13.5701	+	6.91433i	−0.471880	+	0.240435i	0.201844	+	0.979418i	$0.435307\pi$
$828$	22.5145	+	27.8031i	0.782433	+	0.966224i
$829$	−22.8989	+	10.1953i	−0.795312	+	0.354096i	−0.763837	−	0.645409i	$-0.776687\pi$
$829$	−22.8989	+	10.1953i	−0.795312	+	0.354096i	−0.0314750	+	0.999505i	$0.510020\pi$
$830$		0			0
$831$	0.125645	−	0.282203i	0.00435857	−	0.00978950i
$832$	18.6069	−	18.6069i	0.645078	−	0.645078i
$833$	17.9339	+	15.5703i	0.621372	+	0.539480i
$834$	1.67638	−	0.544688i	0.0580482	−	0.0188610i
$835$		0			0
$836$	−21.7031	+	19.5416i	−0.750617	+	0.675859i
$837$	0.805892	+	1.24096i	0.0278557	+	0.0428940i
$838$	47.7080	−	2.50027i	1.64805	−	0.0863704i
$839$	5.42302	−	16.6903i	0.187223	−	0.576214i	−0.812756	−	0.582604i	$-0.802034\pi$
$839$	5.42302	−	16.6903i	0.187223	−	0.576214i	0.999980	+	0.00638981i	$0.00203395\pi$
$840$		0			0
$841$	7.78489	+	23.9594i	0.268445	+	0.826188i
$842$	−0.240316	−	0.626046i	−0.00828185	−	0.0215750i
$843$	0.540850	−	0.144920i	0.0186279	−	0.00499132i
$844$	−9.03059	+	0.949153i	−0.310846	+	0.0326712i
$845$		0			0
$846$	−33.2176	+	45.7201i	−1.14204	+	1.57189i
$847$	−1.09648	+	8.95288i	−0.0376756	+	0.307624i
$848$	−11.6027	−	22.7715i	−0.398438	−	0.781978i
$849$	1.33608	−	0.771384i	0.0458540	−	0.0264738i
$850$		0			0
$851$	23.5307	−	40.7564i	0.806623	−	1.39711i
$852$	−0.134367	+	0.206907i	−0.00460333	+	0.00708851i
$853$	−2.70636	−	17.0873i	−0.0926639	−	0.585057i	−0.989706	−	0.143113i	$-0.954289\pi$
$853$	−2.70636	−	17.0873i	−0.0926639	−	0.585057i	0.897043	−	0.441944i	$-0.145711\pi$
$854$	28.3252	−	70.1695i	0.969269	−	2.40115i
$855$		0			0
$856$	−0.473990	−	0.211034i	−0.0162006	−	0.00721299i
$857$	7.83496	+	29.2405i	0.267637	+	0.998836i	0.960616	+	0.277878i	$0.0896311\pi$
$857$	7.83496	+	29.2405i	0.267637	+	0.998836i	−0.692979	+	0.720958i	$0.743702\pi$
$858$	0.993050	+	0.804156i	0.0339022	+	0.0274534i
$859$	16.3706	−	18.1814i	0.558558	−	0.620342i	−0.396042	−	0.918233i	$-0.629616\pi$
$859$	16.3706	−	18.1814i	0.558558	−	0.620342i	0.954600	+	0.297891i	$0.0962831\pi$
$860$		0			0
$861$	1.17353	+	0.0816986i	0.0399938	+	0.00278428i
$862$	31.3438	−	61.5156i	1.06757	−	2.09523i
$863$	1.71198	+	32.6665i	0.0582764	+	1.11198i	0.858678	+	0.512515i	$0.171286\pi$
$863$	1.71198	+	32.6665i	0.0582764	+	1.11198i	−0.800402	+	0.599464i	$0.795380\pi$
$864$	−1.76480	−	1.96001i	−0.0600396	−	0.0666807i
$865$		0			0
$866$	−5.47443	−	4.92920i	−0.186029	−	0.167501i
$867$	0.0468206	−	0.295613i	0.00159011	−	0.0100396i
$868$	−12.0640	−	21.7483i	−0.409479	−	0.738185i
$869$	−14.6186	−	20.1208i	−0.495902	−	0.682550i
$870$		0			0
$871$	17.5306	+	39.3743i	0.594001	+	1.33415i
$872$	1.42611	+	0.547433i	0.0482943	+	0.0185384i
$873$	10.8427	+	7.04133i	0.366970	+	0.238313i
$874$	−42.9677			−1.45340
$875$		0			0
$876$	−0.248726			−0.00840366
$877$	−3.10180	−	2.01433i	−0.104740	−	0.0680191i	0.491206	−	0.871043i	$-0.336556\pi$
$877$	−3.10180	−	2.01433i	−0.104740	−	0.0680191i	−0.595946	+	0.803024i	$0.703223\pi$
$878$	−57.8880	−	22.2211i	−1.95362	−	0.749926i
$879$	0.422907	+	0.949864i	0.0142643	+	0.0320381i
$880$		0			0
$881$	13.7300	+	18.8977i	0.462575	+	0.636680i	0.975040	−	0.222028i	$-0.0712676\pi$
$881$	13.7300	+	18.8977i	0.462575	+	0.636680i	−0.512465	+	0.858708i	$0.671268\pi$
$882$	−9.55496	−	41.2713i	−0.321732	−	1.38968i
$883$	−7.03524	+	44.4188i	−0.236755	+	1.49481i	0.527311	+	0.849672i	$0.323200\pi$
$883$	−7.03524	+	44.4188i	−0.236755	+	1.49481i	−0.764066	+	0.645139i	$0.776800\pi$
$884$	16.0136	+	14.4187i	0.538595	+	0.484953i
$885$		0			0
$886$	−8.74322	−	9.71033i	−0.293734	−	0.326225i
$887$	−2.70240	−	51.5648i	−0.0907376	−	1.73138i	−0.543208	−	0.839598i	$-0.682791\pi$
$887$	−2.70240	−	51.5648i	−0.0907376	−	1.73138i	0.452471	−	0.891779i	$-0.350543\pi$
$888$	0.0317343	−	0.0622820i	0.00106493	−	0.00209005i
$889$	−29.1394	+	14.2233i	−0.977305	+	0.477035i
$890$		0			0
$891$	−22.7919	+	25.3129i	−0.763556	+	0.848015i
$892$	−9.12112	−	7.38613i	−0.305398	−	0.247306i
$893$	−8.95044	−	33.4035i	−0.299515	−	1.11781i
$894$	−0.176750	−	0.0786941i	−0.00591140	−	0.00263192i
$895$		0			0
$896$	2.03871	+	2.60778i	0.0681086	+	0.0871198i
$897$	0.149845	+	0.946083i	0.00500317	+	0.0315888i
$898$	36.5739	−	56.3189i	1.22049	−	1.87938i
$899$	4.41450	−	7.64614i	0.147232	−	0.255013i
$900$		0			0
$901$	19.5610	−	11.2935i	0.651670	−	0.376242i
$902$	28.3736	+	55.6864i	0.944738	+	1.85415i
$903$	−0.956373	+	0.406303i	−0.0318261	+	0.0135209i
$904$	0.430076	−	0.591949i	0.0143041	−	0.0196879i
$905$		0			0
$906$	0.164174	−	0.0172554i	0.00545432	−	0.000573272i
$907$	−1.89080	+	0.506638i	−0.0627830	+	0.0168226i	−0.290074	−	0.957004i	$-0.593680\pi$
$907$	−1.89080	+	0.506638i	−0.0627830	+	0.0168226i	0.227291	+	0.973827i	$0.427013\pi$
$908$	12.3068	+	32.0604i	0.408416	+	1.06396i
$909$	6.46952	+	19.9111i	0.214580	+	0.660410i
$910$		0			0
$911$	12.2158	−	37.5963i	0.404726	−	1.24562i	−0.516397	−	0.856349i	$-0.672727\pi$
$911$	12.2158	−	37.5963i	0.404726	−	1.24562i	0.921124	−	0.389270i	$-0.127273\pi$
$912$	0.774195	−	0.0405739i	0.0256362	−	0.00134353i
$913$	14.3002	+	22.0203i	0.473267	+	0.728767i
$914$	−41.6527	+	37.5042i	−1.37775	+	1.24053i
$915$		0			0
$916$	−55.1811	+	17.9294i	−1.82324	+	0.592405i
$917$	−11.5052	+	24.6927i	−0.379934	+	0.815425i
$918$	1.58426	−	1.58426i	0.0522883	−	0.0522883i
$919$	−1.55562	+	3.49397i	−0.0513151	+	0.115256i	−0.937384	−	0.348299i	$-0.886759\pi$
$919$	−1.55562	+	3.49397i	−0.0513151	+	0.115256i	0.886068	+	0.463554i	$0.153426\pi$
$920$		0			0
$921$	−0.985624	+	0.438828i	−0.0324774	+	0.0144599i
$922$	−7.49782	−	9.25904i	−0.246928	−	0.304930i
$923$	5.93181	−	3.02241i	0.195248	−	0.0994838i
$924$	−0.818199	+	0.790611i	−0.0269168	+	0.0260092i
$925$		0			0
$926$	22.4514	+	38.8870i	0.737800	+	1.27791i
$927$	28.8669	+	1.51285i	0.948113	+	0.0496885i
$928$	−5.63971	+	14.6919i	−0.185133	+	0.482287i
$929$	1.91707	−	18.2397i	0.0628971	−	0.598426i	−0.916995	−	0.398899i	$-0.869393\pi$
$929$	1.91707	−	18.2397i	0.0628971	−	0.598426i	0.979892	−	0.199528i	$-0.0639408\pi$
$930$		0			0
$931$	23.3064	+	11.3496i	0.763837	+	0.371967i
$932$	−23.6662	−	23.6662i	−0.775212	−	0.775212i
$933$	−0.00908037	+	0.00348563i	−0.000297278	+	0.000114114i
$934$	25.9730	+	5.52073i	0.849862	+	0.180644i
$935$		0			0
$936$	−0.298132	−	1.40260i	−0.00974475	−	0.0458454i
$937$	−33.1453	−	16.8884i	−1.08281	−	0.551720i	−0.180838	−	0.983513i	$-0.557881\pi$
$937$	−33.1453	−	16.8884i	−1.08281	−	0.551720i	−0.901973	+	0.431793i	$0.857881\pi$
$938$	−72.0238	+	22.0441i	−2.35166	+	0.719765i
$939$	0.712728	+	0.231579i	0.0232590	+	0.00755731i
$940$		0			0
$941$	3.62373	−	17.0483i	0.118130	−	0.555758i	−0.878781	−	0.477225i	$-0.841643\pi$
$941$	3.62373	−	17.0483i	0.118130	−	0.555758i	0.996911	−	0.0785338i	$-0.0250239\pi$
$942$	0.274765	−	0.339307i	0.00895234	−	0.0110552i
$943$	−12.1257	+	45.2536i	−0.394866	+	1.47366i
$944$	10.0544	−	7.30493i	0.327242	−	0.237755i
$945$		0			0
$946$	−44.6622	−	32.4490i	−1.45209	−	1.05501i
$947$	−18.4756	+	14.9613i	−0.600377	+	0.486175i	−0.880664	−	0.473741i	$-0.842903\pi$
$947$	−18.4756	+	14.9613i	−0.600377	+	0.486175i	0.280288	+	0.959916i	$0.409570\pi$
$948$	0.0388466	−	0.741238i	0.00126168	−	0.0240743i
$949$	5.81265	+	3.35594i	0.188687	+	0.108938i
$950$		0			0
$951$		−	0.665616i		−	0.0215841i
$952$	−1.06000	+	0.922020i	−0.0343549	+	0.0298828i
$953$	−27.4941	+	4.35463i	−0.890621	+	0.141060i	−0.584943	−	0.811075i	$-0.698883\pi$
$953$	−27.4941	+	4.35463i	−0.890621	+	0.141060i	−0.305678	+	0.952135i	$0.598883\pi$
$954$	−40.0680	−	4.21132i	−1.29725	−	0.136346i
$955$		0			0
$956$	3.27794	+	31.1875i	0.106016	+	1.00868i
$957$	−0.390148	−	0.104540i	−0.0126117	−	0.00337929i
$958$	−21.0358	−	3.33174i	−0.679636	−	0.107644i
$959$	−26.1059	−	41.7496i	−0.843002	−	1.34816i
$960$		0			0
$961$	−10.2971	+	2.18873i	−0.332166	+	0.0706041i
$962$	−42.4039	+	27.5374i	−1.36716	+	0.887841i
$963$	8.33279	−	5.41138i	0.268520	−	0.174379i
$964$	−50.8105	+	10.8001i	−1.63650	+	0.347848i
$965$		0			0
$966$	−1.67293	+	0.0589348i	−0.0538256	+	0.00189620i
$967$	−17.6999	−	2.80338i	−0.569189	−	0.0901507i	−0.134795	−	0.990874i	$-0.543038\pi$
$967$	−17.6999	−	2.80338i	−0.569189	−	0.0901507i	−0.434394	+	0.900723i	$0.643038\pi$
$968$	−0.515372	−	0.138094i	−0.0165647	−	0.00443849i
$969$	0.0716191	+	0.681410i	0.00230074	+	0.0218901i
$970$		0			0
$971$	−15.8054	−	1.66122i	−0.507221	−	0.0533110i	−0.152538	−	0.988298i	$-0.548745\pi$
$971$	−15.8054	−	1.66122i	−0.507221	−	0.0533110i	−0.354683	+	0.934987i	$0.615411\pi$
$972$	−3.01714	+	0.477867i	−0.0967747	+	0.0153276i
$973$	13.7762	−	40.0488i	0.441643	−	1.28391i
$974$			74.6937i			2.39334i
$975$		0			0
$976$	−47.0900	−	27.1874i	−1.50731	−	0.870249i
$977$	−0.285577	+	5.44914i	−0.00913643	+	0.174333i	0.990250	+	0.139303i	$0.0444862\pi$
$977$	−0.285577	+	5.44914i	−0.00913643	+	0.174333i	−0.999386	+	0.0350305i	$0.988847\pi$
$978$	−0.927593	+	0.751150i	−0.0296612	+	0.0240191i
$979$	11.7347	+	8.52579i	0.375044	+	0.272486i
$980$		0			0
$981$	−23.6657	+	17.1942i	−0.755588	+	0.548967i
$982$	14.4527	−	53.9384i	0.461206	−	1.72124i
$983$	13.2762	−	16.3947i	0.423444	−	0.522910i	−0.520123	−	0.854091i	$-0.674114\pi$
$983$	13.2762	−	16.3947i	0.423444	−	0.522910i	0.943567	+	0.331182i	$0.107447\pi$
$984$	−0.0144678	+	0.0680659i	−0.000461218	+	0.00216986i
$985$		0			0
$986$	−12.7143	−	4.13111i	−0.404904	−	0.131561i
$987$	−0.394299	−	1.28828i	−0.0125507	−	0.0410063i
$988$	20.9565	+	10.6779i	0.666715	+	0.339708i
$989$	−8.60404	−	40.4788i	−0.273592	−	1.28715i
$990$		0			0
$991$	3.91217	+	0.831558i	0.124274	+	0.0264153i	0.269629	−	0.962964i	$-0.413099\pi$
$991$	3.91217	+	0.831558i	0.124274	+	0.0264153i	−0.145355	+	0.989380i	$0.546432\pi$
$992$	−34.0679	+	13.0774i	−1.08166	+	0.415209i
$993$	0.331412	+	0.331412i	0.0105170	+	0.0105170i
$994$	3.98256	+	10.9315i	0.126319	+	0.346727i
$995$		0			0
$996$	−0.0819093	+	0.779315i	−0.00259540	+	0.0246935i
$997$	1.01769	−	2.65118i	0.0322306	−	0.0839636i	−0.916521	−	0.399987i	$-0.869015\pi$
$997$	1.01769	−	2.65118i	0.0322306	−	0.0839636i	0.948751	+	0.316024i	$0.102348\pi$
$998$	69.5313	+	3.64398i	2.20097	+	0.115348i
$999$	1.33924	+	2.31963i	0.0423716	+	0.0733897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.507.15		288
5.2	odd	4		175.2.x.a.3.4	✓	288
5.3	odd	4		875.2.bb.c.493.15		288
5.4	even	2		875.2.bb.b.507.4		288
7.5	odd	6	inner	875.2.bb.a.257.15		288
25.6	even	5		875.2.bb.c.857.4		288
25.8	odd	20	inner	875.2.bb.a.143.15		288
25.17	odd	20		875.2.bb.b.143.4		288
25.19	even	10		175.2.x.a.17.15	yes	288
35.12	even	12		175.2.x.a.103.15	yes	288
35.19	odd	6		875.2.bb.b.257.4		288
35.33	even	12		875.2.bb.c.243.4		288
175.19	odd	30		175.2.x.a.117.4	yes	288
175.33	even	60	inner	875.2.bb.a.768.15		288
175.117	even	60		875.2.bb.b.768.4		288
175.131	odd	30		875.2.bb.c.607.15		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.4	✓	288	5.2	odd	4
175.2.x.a.17.15	yes	288	25.19	even	10
175.2.x.a.103.15	yes	288	35.12	even	12
175.2.x.a.117.4	yes	288	175.19	odd	30
875.2.bb.a.143.15		288	25.8	odd	20	inner
875.2.bb.a.257.15		288	7.5	odd	6	inner
875.2.bb.a.507.15		288	1.1	even	1	trivial
875.2.bb.a.768.15		288	175.33	even	60	inner
875.2.bb.b.143.4		288	25.17	odd	20
875.2.bb.b.257.4		288	35.19	odd	6
875.2.bb.b.507.4		288	5.4	even	2
875.2.bb.b.768.4		288	175.117	even	60
875.2.bb.c.243.4		288	35.33	even	12
875.2.bb.c.493.15		288	5.3	odd	4
875.2.bb.c.607.15		288	175.131	odd	30
875.2.bb.c.857.4		288	25.6	even	5

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+(1.69351 + 1.09978i) q^{2} +(0.0509090 + 0.0195422i) q^{3} +(0.844998 + 1.89790i) q^{4} +(0.0647231 + 0.0890837i) q^{6} +(2.64536 + 0.0453616i) q^{7} +(-0.0244829 + 0.154579i) q^{8} +(-2.22722 - 2.00540i) q^{9} +(2.53998 + 2.82093i) q^{11} +(0.00592906 + 0.113133i) q^{12} +(1.38789 - 2.72389i) q^{13} +(4.43007 + 2.98614i) q^{14} +(2.56878 - 2.85292i) q^{16} +(2.63674 + 2.13519i) q^{17} +(-1.56633 - 5.84563i) q^{18} +(3.38312 + 1.50626i) q^{19} +(0.133786 + 0.0540054i) q^{21} +(1.19908 + 7.57071i) q^{22} +(-3.12944 + 4.81891i) q^{23} +(-0.00426721 + 0.00739102i) q^{24} +(5.34609 - 3.08657i) q^{26} +(-0.148466 - 0.291380i) q^{27} +(2.14923 + 5.05895i) q^{28} +(-1.14694 + 1.57863i) q^{29} +(-4.49990 + 0.472959i) q^{31} +(7.79020 - 2.08738i) q^{32} +(0.0741808 + 0.193248i) q^{33} +(2.11711 + 6.51580i) q^{34} +(1.92404 - 5.92160i) q^{36} +(-8.17923 + 0.428655i) q^{37} +(4.07280 + 6.27156i) q^{38} +(0.123887 - 0.111548i) q^{39} +(7.75457 - 2.51961i) q^{41} +(0.167175 + 0.238595i) q^{42} +(-5.09273 + 5.09273i) q^{43} +(-3.20756 + 7.20430i) q^{44} +(-10.5995 + 4.71920i) q^{46} +(-5.87669 - 7.25711i) q^{47} +(0.186526 - 0.0950399i) q^{48} +(6.99588 + 0.239996i) q^{49} +(0.0925076 + 0.160228i) q^{51} +(6.34242 + 0.332392i) q^{52} +(2.38575 - 6.21509i) q^{53} +(0.0690257 - 0.656736i) q^{54} +(-0.0717781 + 0.407807i) q^{56} +(0.142796 + 0.142796i) q^{57} +(-3.67851 + 1.41205i) q^{58} +(3.16655 + 0.673070i) q^{59} +(-2.94484 - 13.8544i) q^{61} +(-8.14080 - 4.14794i) q^{62} +(-5.80085 - 5.40605i) q^{63} +(8.18628 + 2.65988i) q^{64} +(-0.0869038 + 0.408850i) q^{66} +(-8.87250 + 10.9566i) q^{67} +(-1.82433 + 6.80848i) q^{68} +(-0.253489 + 0.184170i) q^{69} +(1.76180 + 1.28002i) q^{71} +(0.364522 - 0.295184i) q^{72} +(-0.114904 + 2.19250i) q^{73} +(-14.3231 - 8.26943i) q^{74} +7.69359i q^{76} +(6.59120 + 7.57761i) q^{77} +(0.332483 - 0.0526601i) q^{78} +(-6.51601 - 0.684861i) q^{79} +(0.937960 + 8.92409i) q^{81} +(15.9035 + 4.26133i) q^{82} +(6.83177 + 1.08205i) q^{83} +(0.0105526 + 0.299547i) q^{84} +(-14.2255 + 3.02372i) q^{86} +(-0.0892396 + 0.0579529i) q^{87} +(-0.498243 + 0.323563i) q^{88} +(3.73767 - 0.794467i) q^{89} +(3.79503 - 7.14272i) q^{91} +(-11.7902 - 1.86738i) q^{92} +(-0.238328 - 0.0638599i) q^{93} +(-1.97103 - 18.7531i) q^{94} +(0.437383 + 0.0459708i) q^{96} +(-4.26064 + 0.674820i) q^{97} +(11.5837 + 8.10037i) q^{98} -11.3765i 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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