LMFDB - Embedded newform 75.2.g.c.31.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [75,2,Mod(16,75)] 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("75.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(75, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.g (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.598878015160$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 $ x^12 + 3x^10 - 2x^9 + 34x^8 - 22x^7 + 236x^6 - 179x^5 + 877x^4 - 409x^3 + 96x^2 - 11x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.1
Root			$-2.17386 + 1.57940i$ of defining polynomial
Character	$\chi$	$=$	75.31
Dual form			75.2.g.c.46.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.830342 - 2.55553i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-4.22323 + 3.06835i) q^{4} +(-1.34843 - 1.78375i) q^{5} +(-2.17386 - 1.57940i) q^{6} +1.68704 q^{7} +(7.00026 + 5.08599i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-3.43876 + 4.92706i) q^{10} +(0.333373 + 1.02602i) q^{11} +(-1.61313 + 4.96470i) q^{12} +(0.827310 - 2.54620i) q^{13} +(-1.40082 - 4.31129i) q^{14} +(-2.13936 - 0.650495i) q^{15} +(3.95852 - 12.1831i) q^{16} +(3.18079 + 2.31098i) q^{17} -2.68704 q^{18} +(0.952655 + 0.692144i) q^{19} +(11.1679 + 3.39571i) q^{20} +(1.36485 - 0.991619i) q^{21} +(2.34520 - 1.70389i) q^{22} +(-1.25552 - 3.86409i) q^{23} +8.65280 q^{24} +(-1.36350 + 4.81050i) q^{25} -7.19384 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-7.12476 + 5.17644i) q^{28} +(-4.81846 + 3.50082i) q^{29} +(0.114039 + 6.00733i) q^{30} +(5.74653 + 4.17510i) q^{31} -17.1155 q^{32} +(0.872782 + 0.634113i) q^{33} +(3.26463 - 10.0475i) q^{34} +(-2.27485 - 3.00925i) q^{35} +(1.61313 + 4.96470i) q^{36} +(-1.41587 + 4.35761i) q^{37} +(0.977766 - 3.00925i) q^{38} +(-0.827310 - 2.54620i) q^{39} +(-0.367227 - 19.3448i) q^{40} +(-3.47998 + 10.7103i) q^{41} +(-3.66740 - 2.66452i) q^{42} +2.58587 q^{43} +(-4.55609 - 3.31019i) q^{44} +(-2.11313 + 0.731222i) q^{45} +(-8.83229 + 6.41703i) q^{46} +(1.55155 - 1.12727i) q^{47} +(-3.95852 - 12.1831i) q^{48} -4.15389 q^{49} +(13.4255 - 0.509905i) q^{50} +3.93167 q^{51} +(4.31872 + 13.2917i) q^{52} +(2.06187 - 1.49803i) q^{53} +(-2.17386 + 1.57940i) q^{54} +(1.38062 - 1.97816i) q^{55} +(11.8097 + 8.58028i) q^{56} +1.17755 q^{57} +(12.9474 + 9.40685i) q^{58} +(0.412843 - 1.27060i) q^{59} +(11.0309 - 3.81712i) q^{60} +(-2.24997 - 6.92470i) q^{61} +(5.89800 - 18.1522i) q^{62} +(0.521325 - 1.60447i) q^{63} +(6.29470 + 19.3731i) q^{64} +(-5.65734 + 1.95765i) q^{65} +(0.895787 - 2.75695i) q^{66} +(-10.0683 - 7.31502i) q^{67} -20.5241 q^{68} +(-3.28699 - 2.38814i) q^{69} +(-5.80133 + 8.31216i) q^{70} +(4.84181 - 3.51778i) q^{71} +(7.00026 - 5.08599i) q^{72} +(-1.01996 - 3.13911i) q^{73} +12.3117 q^{74} +(1.72445 + 4.69322i) q^{75} -6.14702 q^{76} +(0.562414 + 1.73093i) q^{77} +(-5.81994 + 4.22843i) q^{78} +(3.23934 - 2.35351i) q^{79} +(-27.0693 + 9.36699i) q^{80} +(-0.809017 - 0.587785i) q^{81} +30.2600 q^{82} +(-7.17988 - 5.21649i) q^{83} +(-2.72142 + 8.37566i) q^{84} +(-0.166861 - 8.78989i) q^{85} +(-2.14716 - 6.60827i) q^{86} +(-1.84049 + 5.66445i) q^{87} +(-2.88461 + 8.87792i) q^{88} +(4.77234 + 14.6877i) q^{89} +(3.62328 + 4.79300i) q^{90} +(1.39571 - 4.29555i) q^{91} +(17.1587 + 12.4666i) q^{92} +7.10310 q^{93} +(-4.16908 - 3.02901i) q^{94} +(-0.0499753 - 2.63260i) q^{95} +(-13.8468 + 10.0603i) q^{96} +(-8.71166 + 6.32939i) q^{97} +(3.44915 + 10.6154i) q^{98} +1.07882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 10 q^{4} - 6 q^{5} - 12 q^{7} + 9 q^{8} - 3 q^{9} - 9 q^{10} - 4 q^{11} - 2 q^{13} + 6 q^{14} - 9 q^{15} + 16 q^{16} - q^{17} + 7 q^{19} + 26 q^{20} - 3 q^{21} + 13 q^{22} + 19 q^{23}+ \cdots + 6 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 10 * q^4 - 6 * q^5 - 12 * q^7 + 9 * q^8 - 3 * q^9 - 9 * q^10 - 4 * q^11 - 2 * q^13 + 6 * q^14 - 9 * q^15 + 16 * q^16 - q^17 + 7 * q^19 + 26 * q^20 - 3 * q^21 + 13 * q^22 + 19 * q^23 + 6 * q^24 + 4 * q^25 - 56 * q^26 + 3 * q^27 + q^28 - q^29 + 19 * q^30 + 13 * q^31 - 32 * q^32 - q^33 - 25 * q^34 - 10 * q^35 + 8 * q^37 - 22 * q^38 + 2 * q^39 - 28 * q^40 + 8 * q^41 - 16 * q^42 - 4 * q^43 + 33 * q^44 - 6 * q^45 - 22 * q^46 - 13 * q^47 - 16 * q^48 - 28 * q^49 + 81 * q^50 + 26 * q^51 + 44 * q^52 + 44 * q^53 + 9 * q^55 + 45 * q^56 - 22 * q^57 + 41 * q^58 - 22 * q^59 + 14 * q^60 - 8 * q^61 + 41 * q^62 + 3 * q^63 + 49 * q^64 - 38 * q^65 - 3 * q^66 - 6 * q^67 - 100 * q^68 + 6 * q^69 - 45 * q^70 - 21 * q^71 + 9 * q^72 - 16 * q^73 - 44 * q^74 - 4 * q^75 - 52 * q^76 + q^77 - 19 * q^78 + 10 * q^79 - 99 * q^80 - 3 * q^81 + 26 * q^82 - 10 * q^83 - 6 * q^84 + 23 * q^85 + 56 * q^86 - 4 * q^87 - 16 * q^88 + 57 * q^89 + 16 * q^90 - 7 * q^91 + 3 * q^92 + 22 * q^93 - 23 * q^94 + 21 * q^95 - 23 * q^96 + 4 * q^97 - 18 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.830342	−	2.55553i	−0.587140	−	1.80703i	−0.590500	−	0.807038i	$-0.701069\pi$
$2$	−0.830342	−	2.55553i	−0.587140	−	1.80703i	0.00335992	−	0.999994i	$-0.498931\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−4.22323	+	3.06835i	−2.11161	+	1.53418i
$5$	−1.34843	−	1.78375i	−0.603034	−	0.797715i
$5$	−1.34843	−	1.78375i	−0.603034	−	0.797715i
$6$	−2.17386	−	1.57940i	−0.887476	−	0.644789i
$7$	1.68704			0.637642			0.318821	−	0.947815i	$-0.396713\pi$
$7$	1.68704			0.637642			0.318821	+	0.947815i	$0.396713\pi$
$8$	7.00026	+	5.08599i	2.47497	+	1.79817i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−3.43876	+	4.92706i	−1.08743	+	1.55807i
$11$	0.333373	+	1.02602i	0.100516	+	0.309356i	0.988652	−	0.150225i	$-0.0479998\pi$
$11$	0.333373	+	1.02602i	0.100516	+	0.309356i	−0.888136	+	0.459581i	$0.848000\pi$
$12$	−1.61313	+	4.96470i	−0.465670	+	1.43319i
$13$	0.827310	−	2.54620i	0.229455	−	0.706189i	−0.768354	−	0.640025i	$-0.778924\pi$
$13$	0.827310	−	2.54620i	0.229455	−	0.706189i	0.997809	−	0.0661638i	$-0.0210760\pi$
$14$	−1.40082	−	4.31129i	−0.374385	−	1.15224i
$15$	−2.13936	−	0.650495i	−0.552380	−	0.167957i
$16$	3.95852	−	12.1831i	0.989631	−	3.04577i
$17$	3.18079	+	2.31098i	0.771454	+	0.560494i	0.902402	−	0.430895i	$-0.141802\pi$
$17$	3.18079	+	2.31098i	0.771454	+	0.560494i	−0.130948	+	0.991389i	$0.541802\pi$
$18$	−2.68704			−0.633342
$19$	0.952655	+	0.692144i	0.218554	+	0.158789i	0.691676	−	0.722208i	$-0.256873\pi$
$19$	0.952655	+	0.692144i	0.218554	+	0.158789i	−0.473121	+	0.880997i	$0.656873\pi$
$20$	11.1679	+	3.39571i	2.49721	+	0.759305i
$21$	1.36485	−	0.991619i	0.297834	−	0.216389i
$22$	2.34520	−	1.70389i	0.499999	−	0.363270i
$23$	−1.25552	−	3.86409i	−0.261794	−	0.805719i	−0.992415	−	0.122935i	$-0.960769\pi$
$23$	−1.25552	−	3.86409i	−0.261794	−	0.805719i	0.730621	−	0.682783i	$-0.239231\pi$
$24$	8.65280			1.76625
$25$	−1.36350	+	4.81050i	−0.272699	+	0.962099i
$26$	−7.19384			−1.41083
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−7.12476	+	5.17644i	−1.34645	+	0.978256i
$29$	−4.81846	+	3.50082i	−0.894766	+	0.650086i	−0.937116	−	0.349017i	$-0.886516\pi$
$29$	−4.81846	+	3.50082i	−0.894766	+	0.650086i	0.0423500	+	0.999103i	$0.486516\pi$
$30$	0.114039	+	6.00733i	0.0208205	+	1.09678i
$31$	5.74653	+	4.17510i	1.03211	+	0.749870i	0.968729	−	0.248120i	$-0.0798128\pi$
$31$	5.74653	+	4.17510i	1.03211	+	0.749870i	0.0633776	+	0.997990i	$0.479813\pi$
$32$	−17.1155			−3.02563
$33$	0.872782	+	0.634113i	0.151932	+	0.110385i
$34$	3.26463	−	10.0475i	0.559879	−	1.72313i
$35$	−2.27485	−	3.00925i	−0.384520	−	0.508657i
$36$	1.61313	+	4.96470i	0.268855	+	0.827450i
$37$	−1.41587	+	4.35761i	−0.232768	+	0.716387i	0.764641	+	0.644456i	$0.222916\pi$
$37$	−1.41587	+	4.35761i	−0.232768	+	0.716387i	−0.997410	+	0.0719311i	$0.977084\pi$
$38$	0.977766	−	3.00925i	0.158615	−	0.488165i
$39$	−0.827310	−	2.54620i	−0.132476	−	0.407718i
$40$	−0.367227	−	19.3448i	−0.0580637	−	3.05868i
$41$	−3.47998	+	10.7103i	−0.543481	+	1.67266i	0.181093	+	0.983466i	$0.442037\pi$
$41$	−3.47998	+	10.7103i	−0.543481	+	1.67266i	−0.724574	+	0.689197i	$0.757963\pi$
$42$	−3.66740	−	2.66452i	−0.565892	−	0.411144i
$43$	2.58587			0.394342			0.197171	−	0.980369i	$-0.436825\pi$
$43$	2.58587			0.394342			0.197171	+	0.980369i	$0.436825\pi$
$44$	−4.55609	−	3.31019i	−0.686857	−	0.499031i
$45$	−2.11313	+	0.731222i	−0.315007	+	0.109004i
$46$	−8.83229	+	6.41703i	−1.30225	+	0.946140i
$47$	1.55155	−	1.12727i	0.226317	−	0.164429i	−0.468849	−	0.883278i	$-0.655331\pi$
$47$	1.55155	−	1.12727i	0.226317	−	0.164429i	0.695166	+	0.718850i	$0.255331\pi$
$48$	−3.95852	−	12.1831i	−0.571364	−	1.75848i
$49$	−4.15389			−0.593413
$50$	13.4255	−	0.509905i	1.89866	−	0.0721114i
$51$	3.93167			0.550544
$52$	4.31872	+	13.2917i	0.598899	+	1.84322i
$53$	2.06187	−	1.49803i	0.283219	−	0.205771i	−0.437101	−	0.899412i	$-0.643995\pi$
$53$	2.06187	−	1.49803i	0.283219	−	0.205771i	0.720320	+	0.693642i	$0.243995\pi$
$54$	−2.17386	+	1.57940i	−0.295825	+	0.214930i
$55$	1.38062	−	1.97816i	0.186163	−	0.266735i
$56$	11.8097	+	8.58028i	1.57814	+	1.14659i
$57$	1.17755			0.155970
$58$	12.9474	+	9.40685i	1.70008	+	1.23518i
$59$	0.412843	−	1.27060i	0.0537476	−	0.165418i	−0.920579	−	0.390555i	$-0.872283\pi$
$59$	0.412843	−	1.27060i	0.0537476	−	0.165418i	0.974327	+	0.225137i	$0.0722830\pi$
$60$	11.0309	−	3.81712i	1.42409	−	0.492788i
$61$	−2.24997	−	6.92470i	−0.288079	−	0.886617i	−0.985459	−	0.169915i	$-0.945651\pi$
$61$	−2.24997	−	6.92470i	−0.288079	−	0.886617i	0.697379	−	0.716702i	$-0.254349\pi$
$62$	5.89800	−	18.1522i	0.749047	−	2.30533i
$63$	0.521325	−	1.60447i	0.0656807	−	0.202145i
$64$	6.29470	+	19.3731i	0.786838	+	2.42164i
$65$	−5.65734	+	1.95765i	−0.701706	+	0.242817i
$66$	0.895787	−	2.75695i	0.110264	−	0.339357i
$67$	−10.0683	−	7.31502i	−1.23003	−	0.893672i	−0.233141	−	0.972443i	$-0.574900\pi$
$67$	−10.0683	−	7.31502i	−1.23003	−	0.893672i	−0.996893	+	0.0787711i	$0.974900\pi$
$68$	−20.5241			−2.48891
$69$	−3.28699	−	2.38814i	−0.395707	−	0.287498i
$70$	−5.80133	+	8.31216i	−0.693392	+	0.993493i
$71$	4.84181	−	3.51778i	0.574617	−	0.417484i	−0.262162	−	0.965024i	$-0.584436\pi$
$71$	4.84181	−	3.51778i	0.574617	−	0.417484i	0.836779	+	0.547540i	$0.184436\pi$
$72$	7.00026	−	5.08599i	0.824989	−	0.599390i
$73$	−1.01996	−	3.13911i	−0.119377	−	0.367405i	0.873458	−	0.486900i	$-0.161872\pi$
$73$	−1.01996	−	3.13911i	−0.119377	−	0.367405i	−0.992835	+	0.119495i	$0.961872\pi$
$74$	12.3117			1.43120
$75$	1.72445	+	4.69322i	0.199122	+	0.541926i
$76$	−6.14702			−0.705112
$77$	0.562414	+	1.73093i	0.0640931	+	0.197258i
$78$	−5.81994	+	4.22843i	−0.658978	+	0.478776i
$79$	3.23934	−	2.35351i	0.364454	−	0.264791i	−0.390454	−	0.920623i	$-0.627682\pi$
$79$	3.23934	−	2.35351i	0.364454	−	0.264791i	0.754907	+	0.655831i	$0.227682\pi$
$80$	−27.0693	+	9.36699i	−3.02644	+	1.04726i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	30.2600			3.34166
$83$	−7.17988	−	5.21649i	−0.788094	−	0.572584i	0.119303	−	0.992858i	$-0.461934\pi$
$83$	−7.17988	−	5.21649i	−0.788094	−	0.572584i	−0.907397	+	0.420274i	$0.861934\pi$
$84$	−2.72142	+	8.37566i	−0.296931	+	0.913859i
$85$	−0.166861	−	8.78989i	−0.0180986	−	0.953398i
$86$	−2.14716	−	6.60827i	−0.231534	−	0.712588i
$87$	−1.84049	+	5.66445i	−0.197321	+	0.607292i
$88$	−2.88461	+	8.87792i	−0.307501	+	0.946389i
$89$	4.77234	+	14.6877i	0.505867	+	1.55690i	0.799309	+	0.600920i	$0.205199\pi$
$89$	4.77234	+	14.6877i	0.505867	+	1.55690i	−0.293442	+	0.955977i	$0.594801\pi$
$90$	3.62328	+	4.79300i	0.381927	+	0.505226i
$91$	1.39571	−	4.29555i	0.146310	−	0.450296i
$92$	17.1587	+	12.4666i	1.78892	+	1.29973i
$93$	7.10310			0.736557
$94$	−4.16908	−	3.02901i	−0.430008	−	0.312419i
$95$	−0.0499753	−	2.63260i	−0.00512736	−	0.270099i
$96$	−13.8468	+	10.0603i	−1.41323	+	1.02677i
$97$	−8.71166	+	6.32939i	−0.884535	+	0.642652i	−0.934447	−	0.356101i	$-0.884106\pi$
$97$	−8.71166	+	6.32939i	−0.884535	+	0.642652i	0.0499122	+	0.998754i	$0.484106\pi$
$98$	3.44915	+	10.6154i	0.348416	+	1.07232i
$99$	1.07882			0.108425
$100$	−9.00196	−	24.4995i	−0.900196	−	2.44995i
$101$	−13.5654			−1.34981			−0.674905	−	0.737905i	$-0.735815\pi$
$101$	−13.5654			−1.34981			−0.674905	+	0.737905i	$0.735815\pi$
$102$	−3.26463	−	10.0475i	−0.323246	−	0.994850i
$103$	−1.10757	+	0.804700i	−0.109133	+	0.0792894i	−0.641013	−	0.767530i	$-0.721486\pi$
$103$	−1.10757	+	0.804700i	−0.109133	+	0.0792894i	0.531880	+	0.846819i	$0.321486\pi$
$104$	18.7413	−	13.6164i	1.83774	−	1.33520i
$105$	−3.60919	−	1.09741i	−0.352221	−	0.107097i
$106$	−5.54032	−	4.02528i	−0.538124	−	0.390970i
$107$	11.0115			1.06452			0.532262	−	0.846579i	$-0.321342\pi$
$107$	11.0115			1.06452			0.532262	+	0.846579i	$0.321342\pi$
$108$	4.22323	+	3.06835i	0.406380	+	0.295253i
$109$	1.06577	−	3.28010i	0.102082	−	0.314176i	−0.886952	−	0.461861i	$-0.847182\pi$
$109$	1.06577	−	3.28010i	0.102082	−	0.314176i	0.989035	+	0.147684i	$0.0471820\pi$
$110$	−6.20163	−	1.88568i	−0.591303	−	0.179792i
$111$	1.41587	+	4.35761i	0.134389	+	0.413606i
$112$	6.67820	−	20.5534i	0.631030	−	1.94211i
$113$	1.87015	−	5.75574i	0.175929	−	0.541455i	−0.823745	−	0.566960i	$-0.808119\pi$
$113$	1.87015	−	5.75574i	0.175929	−	0.541455i	0.999675	+	0.0255053i	$0.00811946\pi$
$114$	−0.977766	−	3.00925i	−0.0915762	−	0.281842i
$115$	−5.19958	+	7.44997i	−0.484863	+	0.694713i
$116$	9.60772	−	29.5695i	0.892054	−	2.74546i
$117$	−2.16593	−	1.57364i	−0.200240	−	0.145483i
$118$	−3.58986			−0.330473
$119$	5.36612	+	3.89872i	0.491912	+	0.357395i
$120$	−11.6677	−	15.4344i	−1.06511	−	1.40896i
$121$	7.95761	−	5.78155i	0.723419	−	0.525595i
$122$	−15.8280	+	11.4997i	−1.43300	+	1.04114i
$123$	3.47998	+	10.7103i	0.313779	+	0.965713i
$124$	−37.0796			−3.32984
$125$	10.4193	−	4.05447i	0.931928	−	0.362643i
$126$	−4.53315			−0.403845
$127$	−6.25332	−	19.2457i	−0.554893	−	1.70778i	−0.696227	−	0.717822i	$-0.745139\pi$
$127$	−6.25332	−	19.2457i	−0.554893	−	1.70778i	0.141334	−	0.989962i	$-0.454861\pi$
$128$	16.5882	−	12.0521i	1.46621	−	1.06526i
$129$	2.09201	−	1.51994i	0.184192	−	0.133823i
$130$	9.70036	+	12.8320i	0.850778	+	1.12544i
$131$	2.46759	+	1.79281i	0.215595	+	0.156639i	0.690341	−	0.723484i	$-0.257460\pi$
$131$	2.46759	+	1.79281i	0.215595	+	0.156639i	−0.474747	+	0.880122i	$0.657460\pi$
$132$	−5.63164			−0.490171
$133$	1.60717	+	1.16768i	0.139359	+	0.101250i
$134$	−10.3336	+	31.8037i	−0.892691	+	2.74742i
$135$	−1.27976	+	1.83364i	−0.110144	+	0.157814i
$136$	10.5127	+	32.3549i	0.901460	+	2.77441i
$137$	−6.33795	+	19.5062i	−0.541487	+	1.66653i	0.187711	+	0.982224i	$0.439893\pi$
$137$	−6.33795	+	19.5062i	−0.541487	+	1.66653i	−0.729199	+	0.684302i	$0.760107\pi$
$138$	−3.37363	+	10.3830i	−0.287183	+	0.883858i
$139$	5.66068	+	17.4218i	0.480133	+	1.47770i	0.838908	+	0.544273i	$0.183194\pi$
$139$	5.66068	+	17.4218i	0.480133	+	1.47770i	−0.358775	+	0.933424i	$0.616806\pi$
$140$	18.8407	+	5.72871i	1.59233	+	0.484165i
$141$	0.592639	−	1.82396i	0.0499092	−	0.153605i
$142$	−13.0101	−	9.45242i	−1.09179	−	0.793230i
$143$	2.88825			0.241527
$144$	−10.3635	−	7.52956i	−0.863629	−	0.627463i
$145$	12.7419	+	3.87432i	1.05816	+	0.321745i
$146$	−7.17517	+	5.21306i	−0.593821	+	0.431436i
$147$	−3.36057	+	2.44159i	−0.277175	+	0.201379i
$148$	−7.39114	−	22.7476i	−0.607548	−	1.86984i
$149$	0.705938			0.0578327			0.0289163	−	0.999582i	$-0.490794\pi$
$149$	0.705938			0.0578327			0.0289163	+	0.999582i	$0.490794\pi$
$150$	10.5618	−	8.30385i	0.862365	−	0.678007i
$151$	7.04538			0.573345			0.286673	−	0.958029i	$-0.407451\pi$
$151$	7.04538			0.573345			0.286673	+	0.958029i	$0.407451\pi$
$152$	3.14860	+	9.69039i	0.255385	+	0.785994i
$153$	3.18079	−	2.31098i	0.257151	−	0.186831i
$154$	3.95645	−	2.87453i	0.318820	−	0.231636i
$155$	−0.301457	−	15.8802i	−0.0242136	−	1.27552i
$156$	11.3066	+	8.21470i	0.905249	+	0.657702i
$157$	−5.12880			−0.409323			−0.204662	−	0.978833i	$-0.565609\pi$
$157$	−5.12880			−0.409323			−0.204662	+	0.978833i	$0.565609\pi$
$158$	−8.70423	−	6.32399i	−0.692471	−	0.503110i
$159$	0.787563	−	2.42387i	0.0624578	−	0.192225i
$160$	23.0790	+	30.5298i	1.82456	+	2.41359i
$161$	−2.11811	−	6.51888i	−0.166931	−	0.513760i
$162$	−0.830342	+	2.55553i	−0.0652378	+	0.200781i
$163$	−7.49715	+	23.0739i	−0.587222	+	1.80728i	0.00293441	+	0.999996i	$0.499066\pi$
$163$	−7.49715	+	23.0739i	−0.587222	+	1.80728i	−0.590157	+	0.807289i	$0.700934\pi$
$164$	−18.1662	−	55.9097i	−1.41854	−	4.36581i
$165$	−0.0457853	−	2.41188i	−0.00356438	−	0.187764i
$166$	−7.36913	+	22.6799i	−0.571955	+	1.76030i
$167$	−3.68013	−	2.67377i	−0.284777	−	0.206903i	0.436221	−	0.899840i	$-0.356317\pi$
$167$	−3.68013	−	2.67377i	−0.284777	−	0.206903i	−0.720998	+	0.692937i	$0.756317\pi$
$168$	14.5976			1.12623
$169$	4.71853	+	3.42821i	0.362964	+	0.263709i
$170$	−22.3243	+	7.72503i	−1.71219	+	0.592483i
$171$	0.952655	−	0.692144i	0.0728513	−	0.0529296i
$172$	−10.9207	+	7.93437i	−0.832697	+	0.604990i
$173$	−0.827327	−	2.54625i	−0.0629005	−	0.193588i	0.914668	−	0.404206i	$-0.132452\pi$
$173$	−0.827327	−	2.54625i	−0.0629005	−	0.193588i	−0.977568	+	0.210618i	$0.932452\pi$
$174$	16.0039			1.21325
$175$	−2.30027	+	8.11551i	−0.173884	+	0.613475i
$176$	13.8197			1.04170
$177$	−0.412843	−	1.27060i	−0.0310312	−	0.0955042i
$178$	33.5723	−	24.3917i	2.51635	−	1.82823i
$179$	12.6422	−	9.18511i	0.944924	−	0.686528i	−0.00467674	−	0.999989i	$-0.501489\pi$
$179$	12.6422	−	9.18511i	0.944924	−	0.686528i	0.949601	+	0.313461i	$0.101489\pi$
$180$	6.68058	−	9.57194i	0.497941	−	0.713451i
$181$	−0.164103	−	0.119228i	−0.0121977	−	0.00886215i	0.581670	−	0.813425i	$-0.302400\pi$
$181$	−0.164103	−	0.119228i	−0.0121977	−	0.00886215i	−0.593867	+	0.804563i	$0.702400\pi$
$182$	−12.1363			−0.899603
$183$	−5.89050	−	4.27970i	−0.435439	−	0.316365i
$184$	10.8638	−	33.4352i	0.800887	−	2.46488i
$185$	9.68207	−	3.35036i	0.711840	−	0.246323i
$186$	−5.89800	−	18.1522i	−0.432462	−	1.33098i
$187$	−1.31071	+	4.03396i	−0.0958488	+	0.294992i
$188$	−3.09369	+	9.52141i	−0.225631	+	0.694420i
$189$	−0.521325	−	1.60447i	−0.0379208	−	0.116708i
$190$	−6.68619	+	2.31367i	−0.485067	+	0.167851i
$191$	−2.44734	+	7.53213i	−0.177083	+	0.545006i	−0.999722	−	0.0235578i	$-0.992501\pi$
$191$	−2.44734	+	7.53213i	−0.177083	+	0.545006i	0.822639	+	0.568563i	$0.192501\pi$
$192$	16.4798	+	11.9732i	1.18932	+	0.864094i
$193$	−16.4269			−1.18243			−0.591216	−	0.806513i	$-0.701352\pi$
$193$	−16.4269			−1.18243			−0.591216	+	0.806513i	$0.701352\pi$
$194$	23.4086	+	17.0073i	1.68064	+	1.22106i
$195$	−3.42620	+	4.90907i	−0.245356	+	0.351546i
$196$	17.5428	−	12.7456i	1.25306	−	0.910400i
$197$	13.8640	−	10.0728i	0.987770	−	0.717657i	0.0283382	−	0.999598i	$-0.490978\pi$
$197$	13.8640	−	10.0728i	0.987770	−	0.717657i	0.959432	+	0.281942i	$0.0909785\pi$
$198$	−0.895787	−	2.75695i	−0.0636608	−	0.195928i
$199$	−2.01848			−0.143086			−0.0715430	−	0.997438i	$-0.522792\pi$
$199$	−2.01848			−0.143086			−0.0715430	+	0.997438i	$0.522792\pi$
$200$	−34.0110	+	26.7400i	−2.40494	+	1.89081i
$201$	−12.4451			−0.877806
$202$	11.2639	+	34.6668i	0.792528	+	2.43915i
$203$	−8.12895	+	5.90603i	−0.570541	+	0.414522i
$204$	−16.6043	+	12.0638i	−1.16254	+	0.844632i
$205$	23.7969	−	8.23461i	1.66205	−	0.575130i
$206$	2.97610	+	2.16226i	0.207355	+	0.150652i
$207$	−4.06295			−0.282394
$208$	−27.7456	−	20.1584i	−1.92381	−	1.39773i
$209$	−0.392562	+	1.20818i	−0.0271541	+	0.0835717i
$210$	0.192388	+	10.1346i	0.0132760	+	0.699355i
$211$	−7.36119	−	22.6554i	−0.506765	−	1.55966i	−0.797783	−	0.602945i	$-0.793994\pi$
$211$	−7.36119	−	22.6554i	−0.506765	−	1.55966i	0.291018	−	0.956718i	$-0.406006\pi$
$212$	−4.11123	+	12.6531i	−0.282361	+	0.869017i
$213$	1.84941	−	5.69189i	0.126719	−	0.390002i
$214$	−9.14333	−	28.1403i	−0.625025	−	1.92363i
$215$	−3.48686	−	4.61254i	−0.237802	−	0.314572i
$216$	2.67386	−	8.22930i	0.181933	−	0.559933i
$217$	9.69463	+	7.04356i	0.658115	+	0.478148i
$218$	−9.26733			−0.627663
$219$	−2.67028	−	1.94007i	−0.180441	−	0.131098i
$220$	0.239008	+	12.5905i	0.0161139	+	0.848849i
$221$	8.51571	−	6.18702i	0.572828	−	0.416184i
$222$	9.96035	−	7.23662i	0.668495	−	0.485690i
$223$	4.05158	+	12.4695i	0.271314	+	0.835017i	0.990171	+	0.139860i	$0.0446653\pi$
$223$	4.05158	+	12.4695i	0.271314	+	0.835017i	−0.718858	+	0.695157i	$0.755335\pi$
$224$	−28.8746			−1.92927
$225$	4.15371	+	2.78329i	0.276914	+	0.185552i
$226$	−16.2618			−1.08172
$227$	−8.12118	−	24.9944i	−0.539022	−	1.65894i	−0.734795	−	0.678289i	$-0.762722\pi$
$227$	−8.12118	−	24.9944i	−0.539022	−	1.65894i	0.195774	−	0.980649i	$-0.437278\pi$
$228$	−4.97305	+	3.61313i	−0.329348	+	0.239285i
$229$	−1.61484	+	1.17325i	−0.106711	+	0.0775304i	−0.639861	−	0.768490i	$-0.721008\pi$
$229$	−1.61484	+	1.17325i	−0.106711	+	0.0775304i	0.533150	+	0.846021i	$0.321008\pi$
$230$	23.3560	+	7.10166i	1.54005	+	0.468269i
$231$	1.47242	+	1.06978i	0.0968781	+	0.0703861i
$232$	−51.5357			−3.38348
$233$	0.425178	+	0.308910i	0.0278543	+	0.0202373i	0.601625	−	0.798778i	$-0.294520\pi$
$233$	0.425178	+	0.308910i	0.0278543	+	0.0202373i	−0.573771	+	0.819016i	$0.694520\pi$
$234$	−2.22302	+	6.84175i	−0.145323	+	0.447259i
$235$	−4.10291	−	1.24753i	−0.267644	−	0.0813801i
$236$	2.15512	+	6.63278i	0.140286	+	0.431757i
$237$	1.23732	−	3.80807i	0.0803723	−	0.247361i
$238$	5.50757	−	16.9505i	0.357002	−	1.09874i
$239$	−2.16612	−	6.66663i	−0.140115	−	0.431229i	0.856236	−	0.516585i	$-0.172797\pi$
$239$	−2.16612	−	6.66663i	−0.140115	−	0.431229i	−0.996350	+	0.0853565i	$0.972797\pi$
$240$	−16.3937	+	23.4890i	−1.05821	+	1.51621i
$241$	0.715542	−	2.20221i	0.0460921	−	0.141857i	−0.925362	−	0.379085i	$-0.876239\pi$
$241$	0.715542	−	2.20221i	0.0460921	−	0.141857i	0.971454	+	0.237228i	$0.0762388\pi$
$242$	−21.3824	−	15.5353i	−1.37452	−	0.998644i
$243$	−1.00000			−0.0641500
$244$	30.7496	+	22.3409i	1.96854	+	1.43023i
$245$	5.60121	+	7.40948i	0.357848	+	0.473374i
$246$	24.4808	−	17.7864i	1.56084	−	1.13402i
$247$	2.55048	−	1.85303i	0.162283	−	0.117906i
$248$	18.9927	+	58.4536i	1.20604	+	3.71180i
$249$	−8.87482			−0.562419
$250$	−19.0129	−	23.2602i	−1.20248	−	1.47110i
$251$	−6.17885			−0.390005			−0.195003	−	0.980803i	$-0.562472\pi$
$251$	−6.17885			−0.390005			−0.195003	+	0.980803i	$0.562472\pi$
$252$	2.72142	+	8.37566i	0.171433	+	0.527617i
$253$	3.54607	−	2.57637i	0.222939	−	0.161975i
$254$	−43.9907	+	31.9611i	−2.76022	+	2.00542i
$255$	−5.30156	−	7.01310i	−0.331997	−	0.439177i
$256$	−11.6138	−	8.43794i	−0.725864	−	0.527371i
$257$	13.2239			0.824882			0.412441	−	0.910984i	$-0.364676\pi$
$257$	13.2239			0.824882			0.412441	+	0.910984i	$0.364676\pi$
$258$	−5.62133	−	4.08413i	−0.349969	−	0.254267i
$259$	−2.38864	+	7.35148i	−0.148423	+	0.456799i
$260$	17.8855	−	25.6263i	1.10921	−	1.58928i
$261$	1.84049	+	5.66445i	0.113923	+	0.350620i
$262$	2.53264	−	7.79465i	0.156467	−	0.481555i
$263$	−2.15583	+	6.63498i	−0.132934	+	0.409130i	−0.995263	−	0.0972190i	$-0.969005\pi$
$263$	−2.15583	+	6.63498i	−0.132934	+	0.409130i	0.862329	+	0.506349i	$0.169005\pi$
$264$	2.88461	+	8.87792i	0.177536	+	0.546398i
$265$	−5.45239	−	1.65786i	−0.334937	−	0.101841i
$266$	1.64953	−	5.07674i	0.101139	−	0.311275i
$267$	12.4941	+	9.07752i	0.764629	+	0.555535i
$268$	64.9656			3.96841
$269$	−19.1898	−	13.9422i	−1.17002	−	0.850070i	−0.179010	−	0.983847i	$-0.557289\pi$
$269$	−19.1898	−	13.9422i	−1.17002	−	0.850070i	−0.991011	+	0.133777i	$0.957289\pi$
$270$	5.74855	+	1.74791i	0.349845	+	0.106374i
$271$	−23.4542	+	17.0405i	−1.42474	+	1.03514i	−0.433775	+	0.901021i	$0.642819\pi$
$271$	−23.4542	+	17.0405i	−1.42474	+	1.03514i	−0.990966	+	0.134114i	$0.957181\pi$
$272$	40.7460	−	29.6037i	2.47059	−	1.79499i
$273$	−1.39571	−	4.29555i	−0.0844721	−	0.259978i
$274$	55.1113			3.32940
$275$	−5.39020	+	0.204721i	−0.325041	+	0.0123451i
$276$	21.2094			1.27665
$277$	−2.65343	−	8.16641i	−0.159429	−	0.490672i	0.839154	−	0.543894i	$-0.183051\pi$
$277$	−2.65343	−	8.16641i	−0.159429	−	0.490672i	−0.998583	+	0.0532223i	$0.983051\pi$
$278$	39.8216	−	28.9321i	2.38834	−	1.73523i
$279$	5.74653	−	4.17510i	0.344036	−	0.249957i
$280$	−0.619527	−	32.6354i	−0.0370238	−	1.95034i
$281$	−13.8877	−	10.0900i	−0.828471	−	0.601919i	0.0906557	−	0.995882i	$-0.471104\pi$
$281$	−13.8877	−	10.0900i	−0.828471	−	0.601919i	−0.919126	+	0.393963i	$0.871104\pi$
$282$	−5.15327			−0.306872
$283$	7.78278	+	5.65452i	0.462638	+	0.336126i	0.794565	−	0.607179i	$-0.207699\pi$
$283$	7.78278	+	5.65452i	0.462638	+	0.336126i	−0.331927	+	0.943305i	$0.607699\pi$
$284$	−9.65426	+	29.7128i	−0.572875	+	1.76313i
$285$	−1.58783	−	2.10044i	−0.0940552	−	0.124419i
$286$	−2.39823	−	7.38100i	−0.141810	−	0.436447i
$287$	−5.87087	+	18.0687i	−0.346546	+	1.06656i
$288$	−5.28899	+	16.2779i	−0.311657	+	0.959182i
$289$	−0.476498	−	1.46651i	−0.0280293	−	0.0862654i
$290$	−0.679209	−	35.7793i	−0.0398845	−	2.10104i
$291$	−3.32756	+	10.2412i	−0.195065	+	0.600348i
$292$	13.9394	+	10.1276i	0.815742	+	0.592671i
$293$	16.8202			0.982649			0.491324	−	0.870977i	$-0.336513\pi$
$293$	16.8202			0.982649			0.491324	+	0.870977i	$0.336513\pi$
$294$	9.02998	+	6.56067i	0.526639	+	0.382626i
$295$	−2.82312	+	0.976903i	−0.164368	+	0.0568775i
$296$	−32.0743	+	23.3033i	−1.86428	+	1.35448i
$297$	0.872782	−	0.634113i	0.0506439	−	0.0367950i
$298$	−0.586170	−	1.80404i	−0.0339559	−	0.104505i
$299$	−10.8775			−0.629059
$300$	−21.6832	−	14.5293i	−1.25188	−	0.838849i
$301$	4.36247			0.251449
$302$	−5.85008	−	18.0047i	−0.336634	−	1.03605i
$303$	−10.9747	+	7.97356i	−0.630478	+	0.458069i
$304$	12.2036	−	8.86641i	0.699922	−	0.508523i
$305$	−9.31799	+	13.3508i	−0.533546	+	0.764466i
$306$	−8.54691	−	6.20969i	−0.488594	−	0.354984i
$307$	11.3212			0.646134			0.323067	−	0.946376i	$-0.395286\pi$
$307$	11.3212			0.646134			0.323067	+	0.946376i	$0.395286\pi$
$308$	−7.68632	−	5.58444i	−0.437969	−	0.318203i
$309$	−0.423056	+	1.30203i	−0.0240668	+	0.0740700i
$310$	−40.3319	+	13.9563i	−2.29070	+	0.792667i
$311$	5.73642	+	17.6549i	0.325283	+	1.00112i	0.971313	+	0.237805i	$0.0764280\pi$
$311$	5.73642	+	17.6549i	0.325283	+	1.00112i	−0.646030	+	0.763312i	$0.723572\pi$
$312$	7.15855	−	22.0318i	0.405273	−	1.24730i
$313$	−2.99731	+	9.22478i	−0.169418	+	0.521416i	−0.999335	−	0.0364720i	$-0.988388\pi$
$313$	−2.99731	+	9.22478i	−0.169418	+	0.521416i	0.829916	+	0.557888i	$0.188388\pi$
$314$	4.25866	+	13.1068i	0.240330	+	0.739660i
$315$	−3.56494	+	1.23360i	−0.200862	+	0.0695056i
$316$	−6.45903	+	19.8789i	−0.363349	+	1.11827i
$317$	−6.04859	−	4.39456i	−0.339723	−	0.246823i	0.404822	−	0.914395i	$-0.367333\pi$
$317$	−6.04859	−	4.39456i	−0.339723	−	0.246823i	−0.744545	+	0.667573i	$0.767333\pi$
$318$	−6.84822			−0.384029
$319$	−5.19825	−	3.77675i	−0.291046	−	0.211457i
$320$	26.0688	−	37.3514i	1.45729	−	2.08800i
$321$	8.90851	−	6.47241i	0.497225	−	0.361255i
$322$	−14.9004	+	10.8258i	−0.830369	+	0.603298i
$323$	1.43066	+	4.40313i	0.0796042	+	0.244997i
$324$	5.22020			0.290011
$325$	11.1205	+	7.45150i	0.616852	+	0.413335i
$326$	65.1911			3.61060
$327$	−1.06577	−	3.28010i	−0.0589371	−	0.181390i
$328$	−78.8331	+	57.2756i	−4.35283	+	3.16252i
$329$	2.61753	−	1.90175i	0.144309	−	0.104847i
$330$	−6.12560	+	2.11969i	−0.337203	+	0.116685i
$331$	20.4333	+	14.8457i	1.12312	+	0.815993i	0.984679	−	0.174378i	$-0.0557914\pi$
$331$	20.4333	+	14.8457i	1.12312	+	0.815993i	0.138439	+	0.990371i	$0.455791\pi$
$332$	46.3283			2.54259
$333$	3.70681	+	2.69315i	0.203132	+	0.147584i
$334$	−3.77714	+	11.6248i	−0.206676	+	0.636083i
$335$	0.528171	+	27.8230i	0.0288571	+	1.52013i
$336$	−6.67820	−	20.5534i	−0.364325	−	1.12128i
$337$	−4.02464	+	12.3866i	−0.219236	+	0.674739i	0.779590	+	0.626291i	$0.215428\pi$
$337$	−4.02464	+	12.3866i	−0.219236	+	0.674739i	−0.998826	+	0.0484485i	$0.984572\pi$
$338$	4.84291	−	14.9049i	0.263419	−	0.810721i
$339$	−1.87015	−	5.75574i	−0.101573	−	0.312609i
$340$	27.6752	+	36.6097i	1.50090	+	1.98544i
$341$	−2.36798	+	7.28790i	−0.128233	+	0.394662i
$342$	−2.55982	−	1.85982i	−0.138419	−	0.100568i
$343$	−18.8171			−1.01603
$344$	18.1018	+	13.1517i	0.975983	+	0.709093i
$345$	0.172432	+	9.08339i	0.00928344	+	0.489033i
$346$	−5.82005	+	4.22852i	−0.312888	+	0.227326i
$347$	4.85531	−	3.52759i	0.260647	−	0.189371i	−0.449785	−	0.893137i	$-0.648500\pi$
$347$	4.85531	−	3.52759i	0.260647	−	0.189371i	0.710432	+	0.703766i	$0.248500\pi$
$348$	−9.60772	−	29.5695i	−0.515028	−	1.58509i
$349$	−22.7183			−1.21608			−0.608042	−	0.793905i	$-0.708045\pi$
$349$	−22.7183			−1.21608			−0.608042	+	0.793905i	$0.708045\pi$
$350$	22.6494	−	0.860231i	1.21066	−	0.0459813i
$351$	−2.67723			−0.142900
$352$	−5.70586	−	17.5608i	−0.304123	−	0.935996i
$353$	3.92772	−	2.85366i	0.209052	−	0.151885i	−0.478333	−	0.878179i	$-0.658759\pi$
$353$	3.92772	−	2.85366i	0.209052	−	0.151885i	0.687385	+	0.726294i	$0.258759\pi$
$354$	−2.90425	+	2.11006i	−0.154359	+	0.112149i
$355$	−12.8036	−	3.89309i	−0.679547	−	0.206624i
$356$	−65.2218	−	47.3864i	−3.45675	−	2.51148i
$357$	6.63289			0.351050
$358$	−33.9702	−	24.6808i	−1.79538	−	1.30442i
$359$	8.92780	−	27.4769i	0.471191	−	1.45018i	−0.379835	−	0.925054i	$-0.624019\pi$
$359$	8.92780	−	27.4769i	0.471191	−	1.45018i	0.851026	−	0.525123i	$-0.175981\pi$
$360$	−18.5114	−	5.62861i	−0.975639	−	0.296654i
$361$	−5.44284	−	16.7513i	−0.286465	−	0.881649i
$362$	−0.168429	+	0.518371i	−0.00885242	+	0.0272450i
$363$	3.03954	−	9.35474i	0.159534	−	0.490996i
$364$	7.28587	+	22.4236i	0.381883	+	1.17532i
$365$	−4.22403	+	6.05220i	−0.221096	+	0.316787i
$366$	−6.04577	+	18.6070i	−0.316018	+	0.972602i
$367$	11.8998	+	8.64570i	0.621163	+	0.451302i	0.853328	−	0.521375i	$-0.174581\pi$
$367$	11.8998	+	8.64570i	0.621163	+	0.451302i	−0.232164	+	0.972677i	$0.574581\pi$
$368$	−52.0465			−2.71311
$369$	9.11070	+	6.61931i	0.474284	+	0.344588i
$370$	−16.6014	−	21.9609i	−0.863064	−	1.14169i
$371$	3.47846	−	2.52725i	0.180592	−	0.131208i
$372$	−29.9980	+	21.7948i	−1.55532	+	1.13001i
$373$	−10.2096	−	31.4220i	−0.528635	−	1.62697i	−0.757013	−	0.653399i	$-0.773342\pi$
$373$	−10.2096	−	31.4220i	−0.528635	−	1.62697i	0.228378	−	0.973572i	$-0.426658\pi$
$374$	11.3972			0.589337
$375$	6.04621	−	9.40443i	0.312225	−	0.485643i
$376$	16.5945			0.855797
$377$	4.92742	+	15.1650i	0.253775	+	0.781039i
$378$	−3.66740	+	2.66452i	−0.188631	+	0.137048i
$379$	12.2612	−	8.90826i	0.629814	−	0.457587i	−0.226522	−	0.974006i	$-0.572735\pi$
$379$	12.2612	−	8.90826i	0.629814	−	0.457587i	0.856336	+	0.516419i	$0.172735\pi$
$380$	8.28880	+	10.9647i	0.425207	+	0.562478i
$381$	−16.3714	−	11.8945i	−0.838733	−	0.609375i
$382$	21.2807			1.08882
$383$	6.47870	+	4.70705i	0.331046	+	0.240519i	0.740874	−	0.671644i	$-0.234411\pi$
$383$	6.47870	+	4.70705i	0.331046	+	0.240519i	−0.409828	+	0.912163i	$0.634411\pi$
$384$	6.33615	−	19.5007i	0.323340	−	0.995139i
$385$	2.32917	−	3.33724i	0.118706	−	0.170081i
$386$	13.6399	+	41.9793i	0.694253	+	2.13669i
$387$	0.799078	−	2.45931i	0.0406194	−	0.125014i
$388$	17.3705	−	53.4609i	0.881854	−	2.71407i
$389$	0.332078	+	1.02203i	0.0168370	+	0.0518191i	0.959122	−	0.282993i	$-0.0913272\pi$
$389$	0.332078	+	1.02203i	0.0168370	+	0.0518191i	−0.942285	+	0.334812i	$0.891327\pi$
$390$	15.3902	+	4.67956i	0.779313	+	0.236959i
$391$	4.93629	−	15.1923i	0.249639	−	0.768309i
$392$	−29.0783	−	21.1266i	−1.46868	−	1.06706i
$393$	3.05011			0.153858
$394$	−37.2532	−	27.0660i	−1.87679	−	1.36357i
$395$	−8.56607	−	2.60461i	−0.431006	−	0.131052i
$396$	−4.55609	+	3.31019i	−0.228952	+	0.166344i
$397$	19.5894	−	14.2326i	0.983166	−	0.714312i	0.0247517	−	0.999694i	$-0.492120\pi$
$397$	19.5894	−	14.2326i	0.983166	−	0.714312i	0.958414	+	0.285382i	$0.0921205\pi$
$398$	1.67603	+	5.15828i	0.0840116	+	0.258561i
$399$	1.98657			0.0994529
$400$	53.2093	+	35.6540i	2.66046	+	1.78270i
$401$	−1.99317			−0.0995340			−0.0497670	−	0.998761i	$-0.515848\pi$
$401$	−1.99317			−0.0995340			−0.0497670	+	0.998761i	$0.515848\pi$
$402$	10.3336	+	31.8037i	0.515395	+	1.58622i
$403$	15.3848	−	11.1777i	0.766371	−	0.556801i
$404$	57.2899	−	41.6235i	2.85028	−	2.07085i
$405$	0.0424402	+	2.23567i	0.00210887	+	0.111091i
$406$	21.8428	+	15.8698i	1.08404	+	0.787603i
$407$	−4.94300			−0.245015
$408$	27.5227	+	19.9964i	1.36258	+	0.989971i
$409$	2.05953	−	6.33858i	0.101837	−	0.313423i	−0.887138	−	0.461504i	$-0.847310\pi$
$409$	2.05953	−	6.33858i	0.101837	−	0.313423i	0.988975	+	0.148082i	$0.0473098\pi$
$410$	−40.8033	−	53.9761i	−2.01513	−	2.66569i
$411$	6.33795	+	19.5062i	0.312628	+	0.962169i
$412$	2.20843	−	6.79686i	0.108802	−	0.334857i
$413$	0.696484	−	2.14356i	0.0342717	−	0.105477i
$414$	3.37363	+	10.3830i	0.165805	+	0.510295i
$415$	0.376649	+	19.8411i	0.0184890	+	0.973962i
$416$	−14.1599	+	43.5796i	−0.694245	+	2.13667i
$417$	14.8199	+	10.7673i	0.725732	+	0.527275i
$418$	3.41351			0.166960
$419$	−17.2758	−	12.5516i	−0.843977	−	0.613185i	0.0795021	−	0.996835i	$-0.474667\pi$
$419$	−17.2758	−	12.5516i	−0.843977	−	0.613185i	−0.923479	+	0.383650i	$0.874667\pi$
$420$	18.6097	−	6.43964i	0.908059	−	0.314222i
$421$	−18.0708	+	13.1292i	−0.880717	+	0.639878i	−0.933441	−	0.358731i	$-0.883210\pi$
$421$	−18.0708	+	13.1292i	−0.880717	+	0.639878i	0.0527243	+	0.998609i	$0.483210\pi$
$422$	−51.7842	+	37.6235i	−2.52082	+	1.83148i
$423$	−0.592639	−	1.82396i	−0.0288151	−	0.0886838i
$424$	22.0526			1.07097
$425$	−15.4539	+	12.1502i	−0.749626	+	0.589369i
$426$	−16.0814			−0.779147
$427$	−3.79580	−	11.6823i	−0.183692	−	0.565344i
$428$	−46.5042	+	33.7873i	−2.24786	+	1.63317i
$429$	2.33664	−	1.69767i	0.112814	−	0.0819642i
$430$	−8.89219	+	12.7407i	−0.428819	+	0.614413i
$431$	24.6046	+	17.8763i	1.18516	+	0.861070i	0.992744	−	0.120244i	$-0.0383677\pi$
$431$	24.6046	+	17.8763i	1.18516	+	0.861070i	0.192416	+	0.981313i	$0.438368\pi$
$432$	−12.8101			−0.616324
$433$	−0.466511	−	0.338940i	−0.0224191	−	0.0162884i	0.576519	−	0.817084i	$-0.304411\pi$
$433$	−0.466511	−	0.338940i	−0.0224191	−	0.0162884i	−0.598938	+	0.800795i	$0.704411\pi$
$434$	9.95017	−	30.6235i	0.477624	−	1.46997i
$435$	12.5857	−	4.35512i	0.603438	−	0.208812i
$436$	5.56352	+	17.1227i	0.266444	+	0.820031i
$437$	1.47843	−	4.55015i	0.0707230	−	0.217663i
$438$	−2.74067	+	8.43491i	−0.130954	+	0.403036i
$439$	3.95681	+	12.1778i	0.188848	+	0.581215i	0.999993	−	0.00363006i	$-0.00115549\pi$
$439$	3.95681	+	12.1778i	0.188848	+	0.581215i	−0.811145	+	0.584845i	$0.801155\pi$
$440$	19.7256	−	6.82580i	0.940383	−	0.325407i
$441$	−1.28362	+	3.95058i	−0.0611249	+	0.188123i
$442$	−22.8821	−	16.6248i	−1.08839	−	0.790761i
$443$	14.3147			0.680110			0.340055	−	0.940405i	$-0.389554\pi$
$443$	14.3147			0.680110			0.340055	+	0.940405i	$0.389554\pi$
$444$	−19.3503	−	14.0588i	−0.918323	−	0.667200i
$445$	19.7640	−	28.3180i	0.936906	−	1.34240i
$446$	28.5019	−	20.7078i	1.34960	−	0.980545i
$447$	0.571116	−	0.414940i	0.0270128	−	0.0196260i
$448$	10.6194	+	32.6833i	0.501721	+	1.54414i
$449$	−11.9663			−0.564724			−0.282362	−	0.959308i	$-0.591118\pi$
$449$	−11.9663			−0.564724			−0.282362	+	0.959308i	$0.591118\pi$
$450$	3.66377	−	12.9260i	0.172712	−	0.609338i
$451$	−12.1490			−0.572076
$452$	9.76257	+	30.0461i	0.459193	+	1.41325i
$453$	5.69983	−	4.14117i	0.267802	−	0.194569i
$454$	−57.1306	+	41.5078i	−2.68127	+	1.94806i
$455$	−9.54417	+	3.30264i	−0.447438	+	0.154830i
$456$	8.24313	+	5.98899i	0.386020	+	0.280460i
$457$	−8.22154			−0.384587			−0.192294	−	0.981337i	$-0.561593\pi$
$457$	−8.22154			−0.384587			−0.192294	+	0.981337i	$0.561593\pi$
$458$	4.33913	+	3.15257i	0.202754	+	0.147310i
$459$	1.21495	−	3.73924i	0.0567091	−	0.174533i
$460$	−0.900131	−	47.4171i	−0.0419688	−	2.21083i
$461$	0.393120	+	1.20990i	0.0183094	+	0.0563506i	0.959794	−	0.280706i	$-0.0905686\pi$
$461$	0.393120	+	1.20990i	0.0183094	+	0.0563506i	−0.941484	+	0.337057i	$0.890569\pi$
$462$	1.51123	−	4.65109i	0.0703088	−	0.216388i
$463$	10.0976	−	31.0771i	0.469273	−	1.44428i	−0.384254	−	0.923227i	$-0.625541\pi$
$463$	10.0976	−	31.0771i	0.469273	−	1.44428i	0.853527	−	0.521048i	$-0.174459\pi$
$464$	23.5768	+	72.5618i	1.09452	+	3.36860i
$465$	−9.57800	−	12.6701i	−0.444169	−	0.587563i
$466$	0.436385	−	1.34305i	0.0202151	−	0.0622158i
$467$	−11.6779	−	8.48450i	−0.540389	−	0.392616i	0.283840	−	0.958872i	$-0.408391\pi$
$467$	−11.6779	−	8.48450i	−0.540389	−	0.392616i	−0.824230	+	0.566256i	$0.808391\pi$
$468$	13.9757			0.646026
$469$	−16.9856	−	12.3407i	−0.784321	−	0.569843i
$470$	0.218706	+	11.5210i	0.0100881	+	0.531423i
$471$	−4.14929	+	3.01464i	−0.191189	+	0.138907i
$472$	9.35227	−	6.79482i	0.430473	−	0.312757i
$473$	0.862060	+	2.65315i	0.0396375	+	0.121992i
$474$	−10.7590			−0.494178
$475$	−4.62850	+	3.63901i	−0.212370	+	0.166969i
$476$	−34.6250			−1.58703
$477$	−0.787563	−	2.42387i	−0.0360600	−	0.110981i
$478$	−15.2382	+	11.0712i	−0.696977	+	0.506383i
$479$	13.6415	−	9.91113i	0.623296	−	0.452851i	−0.230775	−	0.973007i	$-0.574126\pi$
$479$	13.6415	−	9.91113i	0.623296	−	0.452851i	0.854071	+	0.520156i	$0.174126\pi$
$480$	36.6163	+	11.1336i	1.67130	+	0.508176i
$481$	9.92398	+	7.21020i	0.452495	+	0.328757i
$482$	−6.22196			−0.283403
$483$	−5.54529	−	4.02889i	−0.252320	−	0.183321i
$484$	−15.8670	+	48.8336i	−0.721227	+	2.21971i
$485$	23.0371	+	7.00467i	1.04606	+	0.318066i
$486$	0.830342	+	2.55553i	0.0376651	+	0.115921i
$487$	12.3061	−	37.8744i	0.557644	−	1.71625i	−0.131212	−	0.991354i	$-0.541887\pi$
$487$	12.3061	−	37.8744i	0.557644	−	1.71625i	0.688856	−	0.724898i	$-0.258113\pi$
$488$	19.4686	−	59.9181i	0.881301	−	2.71236i
$489$	7.49715	+	23.0739i	0.339033	+	1.04344i
$490$	14.2842	−	20.4665i	0.645295	−	0.924580i
$491$	4.33411	−	13.3390i	0.195596	−	0.601981i	−0.804374	−	0.594124i	$-0.797499\pi$
$491$	4.33411	−	13.3390i	0.195596	−	0.601981i	0.999969	−	0.00785739i	$-0.00250111\pi$
$492$	−47.5596	−	34.5541i	−2.14415	−	1.55782i
$493$	−23.4168			−1.05464
$494$	−6.85324	−	4.97917i	−0.308342	−	0.224024i
$495$	−1.45471	−	1.92434i	−0.0653842	−	0.0864925i
$496$	73.6133	−	53.4832i	3.30534	−	2.40147i
$497$	8.16834	−	5.93464i	0.366400	−	0.266205i
$498$	7.36913	+	22.6799i	0.330219	+	1.01631i
$499$	15.2315			0.681857			0.340929	−	0.940089i	$-0.389259\pi$
$499$	15.2315			0.681857			0.340929	+	0.940089i	$0.389259\pi$
$500$	−31.5624	+	49.0930i	−1.41151	+	2.19550i
$501$	−4.54890			−0.203230
$502$	5.13055	+	15.7902i	0.228988	+	0.704752i
$503$	−19.2004	+	13.9499i	−0.856104	+	0.621996i	−0.926822	−	0.375501i	$-0.877471\pi$
$503$	−19.2004	+	13.9499i	−0.856104	+	0.621996i	0.0707185	+	0.997496i	$0.477471\pi$
$504$	11.8097	−	8.58028i	0.526048	−	0.382196i
$505$	18.2920	+	24.1973i	0.813982	+	1.07676i
$506$	−9.52843	−	6.92281i	−0.423590	−	0.307756i
$507$	5.83243			0.259027
$508$	85.4620	+	62.0918i	3.79176	+	2.75488i
$509$	−3.86570	+	11.8974i	−0.171344	+	0.527343i	−0.999448	−	0.0332320i	$-0.989420\pi$
$509$	−3.86570	+	11.8974i	−0.171344	+	0.527343i	0.828103	+	0.560575i	$0.189420\pi$
$510$	−13.5201	+	19.3716i	−0.598678	+	0.857787i
$511$	−1.72071	−	5.29581i	−0.0761198	−	0.234273i
$512$	0.752345	−	2.31548i	0.0332493	−	0.102331i
$513$	0.363882	−	1.11991i	0.0160658	−	0.0494454i
$514$	−10.9803	−	33.7940i	−0.484321	−	1.49059i
$515$	2.92886	+	0.890552i	0.129061	+	0.0392424i
$516$	−4.17134	+	12.8381i	−0.183633	+	0.565165i
$517$	1.67384	+	1.21612i	0.0736154	+	0.0534847i
$518$	20.7703			0.912595
$519$	−2.16597	−	1.57367i	−0.0950755	−	0.0690764i
$520$	−49.5594	−	15.0691i	−2.17333	−	0.660823i
$521$	22.6232	−	16.4367i	0.991141	−	0.720106i	0.0309702	−	0.999520i	$-0.490140\pi$
$521$	22.6232	−	16.4367i	0.991141	−	0.720106i	0.960171	+	0.279414i	$0.0901403\pi$
$522$	12.9474	−	9.40685i	0.566693	−	0.411727i
$523$	4.85196	+	14.9328i	0.212162	+	0.652966i	0.999343	+	0.0362446i	$0.0115395\pi$
$523$	4.85196	+	14.9328i	0.212162	+	0.652966i	−0.787181	+	0.616722i	$0.788460\pi$
$524$	−15.9222			−0.695564
$525$	2.90922	+	7.91765i	0.126969	+	0.345555i
$526$	18.7460			0.817362
$527$	8.62993	+	26.5602i	0.375926	+	1.15698i
$528$	11.1804	−	8.12302i	0.486564	−	0.353509i
$529$	5.25252	−	3.81618i	0.228370	−	0.165921i
$530$	0.290640	+	15.3103i	0.0126246	+	0.665038i
$531$	−1.08084	−	0.785274i	−0.0469043	−	0.0340780i
$532$	−10.3703			−0.449609
$533$	24.3915	+	17.7214i	1.05651	+	0.767601i
$534$	12.8235	−	39.4666i	0.554926	−	1.70789i
$535$	−14.8482	−	19.6418i	−0.641945	−	0.849187i
$536$	−33.2764	−	102.414i	−1.43732	−	4.42362i
$537$	4.82890	−	14.8618i	0.208382	−	0.641335i
$538$	−19.6956	+	60.6168i	−0.849137	+	2.61338i
$539$	−1.38479	−	4.26196i	−0.0596473	−	0.183576i
$540$	−0.221546	−	11.6706i	−0.00953383	−	0.502223i
$541$	−7.40971	+	22.8048i	−0.318569	+	0.980453i	0.655692	+	0.755028i	$0.272377\pi$
$541$	−7.40971	+	22.8048i	−0.318569	+	0.980453i	−0.974261	+	0.225425i	$0.927623\pi$
$542$	63.0224	+	45.7885i	2.70705	+	1.96678i
$543$	−0.202843			−0.00870482
$544$	−54.4409	−	39.5536i	−2.33413	−	1.69585i
$545$	−7.28796	+	2.52191i	−0.312182	+	0.108027i
$546$	−9.81848	+	7.13354i	−0.420192	+	0.305287i
$547$	4.55219	−	3.30736i	0.194637	−	0.141412i	−0.486198	−	0.873848i	$-0.661617\pi$
$547$	4.55219	−	3.30736i	0.194637	−	0.141412i	0.680836	+	0.732436i	$0.261617\pi$
$548$	−33.0853	−	101.826i	−1.41333	−	4.34980i
$549$	−7.28106			−0.310748
$550$	4.99888	+	13.6048i	0.213153	+	0.580112i
$551$	−7.01341			−0.298781
$552$	−10.8638	−	33.4352i	−0.462392	−	1.42310i
$553$	5.46490	−	3.97048i	0.232391	−	0.168842i
$554$	−18.6663	+	13.5618i	−0.793053	+	0.576187i
$555$	5.86367	−	8.40148i	0.248899	−	0.356623i
$556$	−77.3626	−	56.2072i	−3.28090	−	2.38372i
$557$	−42.4247			−1.79759			−0.898796	−	0.438366i	$-0.855557\pi$
$557$	−42.4247			−1.79759			−0.898796	+	0.438366i	$0.855557\pi$
$558$	−15.4412	−	11.2187i	−0.653677	−	0.474924i
$559$	2.13932	−	6.58414i	0.0904835	−	0.278480i
$560$	−45.6670	+	15.8025i	−1.92978	+	0.667778i
$561$	1.31071	+	4.03396i	0.0553383	+	0.170314i
$562$	−14.2538	+	43.8686i	−0.601259	+	1.85048i
$563$	1.78796	−	5.50279i	0.0753537	−	0.231915i	−0.906284	−	0.422669i	$-0.861093\pi$
$563$	1.78796	−	5.50279i	0.0753537	−	0.231915i	0.981638	+	0.190754i	$0.0610933\pi$
$564$	3.09369	+	9.52141i	0.130268	+	0.400924i
$565$	−12.7885	+	4.42531i	−0.538018	+	0.186174i
$566$	7.98793	−	24.5843i	0.335758	−	1.03336i
$567$	−1.36485	−	0.991619i	−0.0573181	−	0.0416441i
$568$	51.7853			2.17286
$569$	17.8029	+	12.9346i	0.746336	+	0.542245i	0.894689	−	0.446690i	$-0.147397\pi$
$569$	17.8029	+	12.9346i	0.746336	+	0.542245i	−0.148353	+	0.988934i	$0.547397\pi$
$570$	−4.04930	+	5.80184i	−0.169606	+	0.243012i
$571$	−27.1946	+	19.7580i	−1.13806	+	0.826847i	−0.986847	−	0.161654i	$-0.948317\pi$
$571$	−27.1946	+	19.7580i	−1.13806	+	0.826847i	−0.151210	+	0.988502i	$0.548317\pi$
$572$	−12.1977	+	8.86216i	−0.510012	+	0.370546i
$573$	2.44734	+	7.53213i	0.102239	+	0.314659i
$574$	51.0499			2.13078
$575$	20.3001	−	0.771002i	0.846572	−	0.0321530i
$576$	20.3701			0.848754
$577$	12.4333	+	38.2658i	0.517605	+	1.59303i	0.778491	+	0.627656i	$0.215985\pi$
$577$	12.4333	+	38.2658i	0.517605	+	1.59303i	−0.260886	+	0.965370i	$0.584015\pi$
$578$	−3.35205	+	2.43541i	−0.139427	+	0.101300i
$579$	−13.2896	+	9.65547i	−0.552297	+	0.401268i
$580$	−65.6998	+	22.7346i	−2.72803	+	0.944002i
$581$	−12.1128	−	8.80043i	−0.502522	−	0.365103i
$582$	28.9346			1.19938
$583$	2.22438	+	1.61611i	0.0921243	+	0.0669323i
$584$	8.82549	−	27.1621i	0.365201	−	1.12397i
$585$	0.113622	+	5.98540i	0.00469771	+	0.247466i
$586$	−13.9665	−	42.9846i	−0.576952	−	1.77568i
$587$	−0.872353	+	2.68483i	−0.0360059	+	0.110815i	−0.967444	−	0.253085i	$-0.918555\pi$
$587$	−0.872353	+	2.68483i	−0.0360059	+	0.110815i	0.931438	+	0.363899i	$0.118555\pi$
$588$	6.70076	−	20.6228i	0.276335	−	0.850471i
$589$	2.58469	+	7.95485i	0.106500	+	0.327774i
$590$	4.84066	+	6.40339i	0.199287	+	0.263623i
$591$	5.29558	−	16.2981i	0.217831	−	0.670415i
$592$	47.4844	+	34.4994i	1.95160	+	1.41792i
$593$	−24.6805			−1.01351			−0.506754	−	0.862091i	$-0.669155\pi$
$593$	−24.6805			−1.01351			−0.506754	+	0.862091i	$0.669155\pi$
$594$	−2.34520	−	1.70389i	−0.0962248	−	0.0699114i
$595$	−0.281501	−	14.8289i	−0.0115404	−	0.607927i
$596$	−2.98134	+	2.16607i	−0.122120	+	0.0887256i
$597$	−1.63298	+	1.18643i	−0.0668335	+	0.0485574i
$598$	9.03200	+	27.7976i	0.369346	+	1.13673i
$599$	−7.71547			−0.315245			−0.157623	−	0.987499i	$-0.550383\pi$
$599$	−7.71547			−0.315245			−0.157623	+	0.987499i	$0.550383\pi$
$600$	−11.7981	+	41.6243i	−0.481654	+	1.69930i
$601$	22.6506			0.923938			0.461969	−	0.886896i	$-0.347143\pi$
$601$	22.6506			0.923938			0.461969	+	0.886896i	$0.347143\pi$
$602$	−3.62234	−	11.1484i	−0.147636	−	0.454376i
$603$	−10.0683	+	7.31502i	−0.410011	+	0.297891i
$604$	−29.7543	+	21.6177i	−1.21068	+	0.879613i
$605$	−21.0431	−	6.39837i	−0.855522	−	0.260131i
$606$	29.4894	+	21.4253i	1.19792	+	0.870343i
$607$	−24.6423			−1.00020			−0.500099	−	0.865968i	$-0.666703\pi$
$607$	−24.6423			−1.00020			−0.500099	+	0.865968i	$0.666703\pi$
$608$	−16.3052	−	11.8464i	−0.661264	−	0.480436i
$609$	−3.10498	+	9.55616i	−0.125820	+	0.387235i
$610$	41.8555	+	12.7266i	1.69468	+	0.515286i
$611$	−1.58663	−	4.88315i	−0.0641883	−	0.197551i
$612$	−6.34229	+	19.5196i	−0.256372	+	0.789031i
$613$	−12.9180	+	39.7574i	−0.521751	+	1.60579i	0.248901	+	0.968529i	$0.419931\pi$
$613$	−12.9180	+	39.7574i	−0.521751	+	1.60579i	−0.770652	+	0.637256i	$0.780069\pi$
$614$	−9.40045	−	28.9316i	−0.379371	−	1.16758i
$615$	14.4119	−	20.6494i	0.581144	−	0.832664i
$616$	−4.86646	+	14.9774i	−0.196075	+	0.603458i
$617$	−12.8949	−	9.36871i	−0.519130	−	0.377170i	0.297146	−	0.954832i	$-0.403965\pi$
$617$	−12.8949	−	9.36871i	−0.519130	−	0.377170i	−0.816276	+	0.577662i	$0.803965\pi$
$618$	3.67866			0.147977
$619$	38.1613	+	27.7258i	1.53383	+	1.11440i	0.954059	+	0.299619i	$0.0968595\pi$
$619$	38.1613	+	27.7258i	1.53383	+	1.11440i	0.579775	+	0.814777i	$0.303141\pi$
$620$	49.9990	+	66.1405i	2.00801	+	2.65627i
$621$	−3.28699	+	2.38814i	−0.131902	+	0.0958327i
$622$	40.3544	−	29.3192i	1.61806	−	1.17559i
$623$	8.05113	+	24.7788i	0.322562	+	0.992743i
$624$	−34.2955			−1.37292
$625$	−21.2818	−	13.1182i	−0.851270	−	0.524727i
$626$	26.0630			1.04169
$627$	0.392562	+	1.20818i	0.0156774	+	0.0482501i
$628$	21.6601	−	15.7370i	0.864332	−	0.627974i
$629$	−14.5739	+	10.5886i	−0.581101	+	0.422195i
$630$	6.11262	+	8.08599i	0.243533	+	0.322154i
$631$	−26.1825	−	19.0227i	−1.04231	−	0.757282i	−0.0715741	−	0.997435i	$-0.522802\pi$
$631$	−26.1825	−	19.0227i	−1.04231	−	0.757282i	−0.970735	+	0.240153i	$0.922802\pi$
$632$	34.6462			1.37815
$633$	−19.2718	−	14.0018i	−0.765987	−	0.556522i
$634$	−6.20802	+	19.1063i	−0.246552	+	0.758809i
$635$	−25.8974	+	37.1058i	−1.02771	+	1.47250i
$636$	4.11123	+	12.6531i	0.163021	+	0.501727i
$637$	−3.43656	+	10.5766i	−0.136161	+	0.419061i
$638$	−5.33526	+	16.4203i	−0.211225	+	0.650084i
$639$	−1.84941	−	5.69189i	−0.0731614	−	0.225168i
$640$	−43.8658	−	13.3379i	−1.73395	−	0.527226i
$641$	5.56360	−	17.1230i	0.219749	−	0.676317i	−0.779033	−	0.626982i	$-0.784290\pi$
$641$	5.56360	−	17.1230i	0.219749	−	0.676317i	0.998782	−	0.0493350i	$-0.0157102\pi$
$642$	−23.9376	−	17.3916i	−0.944740	−	0.686394i
$643$	21.8891			0.863224			0.431612	−	0.902059i	$-0.357945\pi$
$643$	21.8891			0.863224			0.431612	+	0.902059i	$0.357945\pi$
$644$	28.9475	+	21.0316i	1.14069	+	0.828761i
$645$	−5.53211	−	1.68210i	−0.217826	−	0.0662325i
$646$	10.0644	−	7.31220i	0.395978	−	0.287695i
$647$	−15.3926	+	11.1834i	−0.605147	+	0.439665i	−0.847702	−	0.530473i	$-0.822015\pi$
$647$	−15.3926	+	11.1834i	−0.605147	+	0.439665i	0.242555	+	0.970138i	$0.422015\pi$
$648$	−2.67386	−	8.22930i	−0.105039	−	0.323278i
$649$	1.44129			0.0565755
$650$	9.80876	−	34.6059i	0.384731	−	1.35736i
$651$	11.9832			0.469660
$652$	−39.1366	−	120.450i	−1.53271	−	4.71719i
$653$	1.87669	−	1.36349i	0.0734405	−	0.0533576i	−0.550459	−	0.834862i	$-0.685547\pi$
$653$	1.87669	−	1.36349i	0.0734405	−	0.0533576i	0.623900	+	0.781504i	$0.285547\pi$
$654$	−7.49743	+	5.44720i	−0.293173	+	0.213002i
$655$	−0.129447	−	6.81903i	−0.00505793	−	0.266442i
$656$	116.709	+	84.7937i	4.55670	+	3.31064i
$657$	−3.30065			−0.128771
$658$	−7.03341	−	5.11007i	−0.274191	−	0.199211i
$659$	2.22239	−	6.83980i	0.0865719	−	0.266441i	−0.898394	−	0.439191i	$-0.855265\pi$
$659$	2.22239	−	6.83980i	0.0865719	−	0.266441i	0.984966	+	0.172750i	$0.0552652\pi$
$660$	7.59385	+	10.0454i	0.295590	+	0.391017i
$661$	13.2943	+	40.9158i	0.517090	+	1.59144i	0.779447	+	0.626468i	$0.215500\pi$
$661$	13.2943	+	40.9158i	0.517090	+	1.59144i	−0.262358	+	0.964971i	$0.584500\pi$
$662$	20.9719	−	64.5450i	0.815098	−	2.50861i
$663$	3.25271	−	10.0108i	0.126325	−	0.388788i
$664$	−23.7300	−	73.0336i	−0.920904	−	2.83425i
$665$	−0.0843105	−	4.44131i	−0.00326942	−	0.172226i
$666$	3.80451	−	11.7091i	0.147422	−	0.453718i
$667$	19.5772	+	14.2236i	0.758031	+	0.550742i
$668$	23.7461			0.918765
$669$	10.6072	+	7.70656i	0.410097	+	0.297953i
$670$	70.6639	−	24.4523i	2.72998	−	0.944676i
$671$	6.35478	−	4.61702i	0.245324	−	0.178238i
$672$	−23.3601	+	16.9721i	−0.901135	+	0.654713i
$673$	−9.20966	−	28.3444i	−0.355006	−	1.09260i	−0.956006	−	0.293348i	$-0.905231\pi$
$673$	−9.20966	−	28.3444i	−0.355006	−	1.09260i	0.600999	−	0.799250i	$-0.294769\pi$
$674$	34.9961			1.34800
$675$	4.99640	−	0.189764i	0.192311	−	0.00730403i
$676$	−30.4464			−1.17102
$677$	−8.26144	−	25.4261i	−0.317513	−	0.977204i	−0.974708	−	0.223483i	$-0.928257\pi$
$677$	−8.26144	−	25.4261i	−0.317513	−	0.977204i	0.657195	−	0.753721i	$-0.271743\pi$
$678$	−13.1561	+	9.55846i	−0.505257	+	0.367091i
$679$	−14.6969	+	10.6780i	−0.564017	+	0.409782i
$680$	43.5372	−	62.3802i	1.66958	−	2.39217i
$681$	−21.2615	−	15.4474i	−0.814743	−	0.591946i
$682$	20.5907			0.788457
$683$	−23.0529	−	16.7489i	−0.882096	−	0.640880i	0.0517093	−	0.998662i	$-0.483533\pi$
$683$	−23.0529	−	16.7489i	−0.882096	−	0.640880i	−0.933805	+	0.357782i	$0.883533\pi$
$684$	−1.89953	+	5.84617i	−0.0726305	+	0.223534i
$685$	43.3403	−	14.9974i	1.65595	−	0.573020i
$686$	15.6246	+	48.0876i	0.596550	+	1.83599i
$687$	−0.616813	+	1.89835i	−0.0235329	+	0.0724267i
$688$	10.2362	−	31.5039i	0.390253	−	1.20107i
$689$	−2.10849	−	6.48926i	−0.0803270	−	0.247221i
$690$	23.0697	−	7.98297i	0.878248	−	0.303906i
$691$	10.7065	−	32.9512i	0.407294	−	1.25352i	−0.511671	−	0.859182i	$-0.670973\pi$
$691$	10.7065	−	32.9512i	0.407294	−	1.25352i	0.918965	−	0.394340i	$-0.129027\pi$
$692$	11.3068	+	8.21486i	0.429820	+	0.312282i
$693$	1.82001			0.0691365
$694$	−13.0464	−	9.47878i	−0.495235	−	0.359810i
$695$	23.4430	−	33.5892i	0.889245	−	1.27411i
$696$	−41.6932	+	30.2919i	−1.58038	+	1.14821i
$697$	−35.8203	+	26.0249i	−1.35679	+	0.985765i
$698$	18.8640	+	58.0574i	0.714012	+	2.19750i
$699$	0.525548			0.0198781
$700$	−15.1867	−	41.3317i	−0.574003	−	1.56219i
$701$	0.973305			0.0367612			0.0183806	−	0.999831i	$-0.494149\pi$
$701$	0.973305			0.0367612			0.0183806	+	0.999831i	$0.494149\pi$
$702$	2.22302	+	6.84175i	0.0839024	+	0.258225i
$703$	−4.36494	+	3.17131i	−0.164627	+	0.119608i
$704$	−17.7786	+	12.9169i	−0.670058	+	0.486826i
$705$	−4.05260	+	1.40235i	−0.152630	+	0.0528156i
$706$	−10.5540	−	7.66790i	−0.397204	−	0.288585i
$707$	−22.8854			−0.860696
$708$	5.64218	+	4.09928i	0.212046	+	0.154061i
$709$	−3.49938	+	10.7700i	−0.131422	+	0.404475i	−0.995016	−	0.0997119i	$-0.968208\pi$
$709$	−3.49938	+	10.7700i	−0.131422	+	0.404475i	0.863594	+	0.504187i	$0.168208\pi$
$710$	0.682499	+	35.9527i	0.0256137	+	1.34928i
$711$	−1.23732	−	3.80807i	−0.0464030	−	0.142814i
$712$	−41.2941	+	127.090i	−1.54756	+	4.76290i
$713$	8.91808	−	27.4470i	0.333985	−	1.02790i
$714$	−5.50757	−	16.9505i	−0.206115	−	0.634358i
$715$	−3.89459	−	5.15190i	−0.145649	−	0.192670i
$716$	−25.2078	+	77.5816i	−0.942060	+	2.89936i
$717$	−5.67098	−	4.12021i	−0.211787	−	0.153872i
$718$	−77.6312			−2.89717
$719$	24.8627	+	18.0638i	0.927224	+	0.673667i	0.945311	−	0.326169i	$-0.105758\pi$
$719$	24.8627	+	18.0638i	0.927224	+	0.673667i	−0.0180878	+	0.999836i	$0.505758\pi$
$720$	0.543662	+	28.6390i	0.0202611	+	1.06731i
$721$	−1.86852	+	1.35756i	−0.0695875	+	0.0505583i
$722$	−38.2891	+	27.8186i	−1.42497	+	1.03530i
$723$	−0.715542	−	2.20221i	−0.0266113	−	0.0819011i
$724$	1.05888			0.0393529
$725$	−10.2707	−	27.9526i	−0.381445	−	1.03813i
$726$	−26.4302			−0.980915
$727$	−2.02973	−	6.24688i	−0.0752787	−	0.231684i	0.906336	−	0.422558i	$-0.138868\pi$
$727$	−2.02973	−	6.24688i	−0.0752787	−	0.231684i	−0.981615	+	0.190874i	$0.938868\pi$
$728$	31.6174	−	22.9714i	1.17182	−	0.851377i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	18.9740	+	5.76924i	0.702258	+	0.213529i
$731$	8.22510	+	5.97589i	0.304216	+	0.221026i
$732$	38.0086			1.40484
$733$	25.8300	+	18.7666i	0.954051	+	0.693159i	0.951762	−	0.306838i	$-0.0992711\pi$
$733$	25.8300	+	18.7666i	0.954051	+	0.693159i	0.00228977	+	0.999997i	$0.499271\pi$
$734$	12.2134	−	37.5891i	0.450806	−	1.38744i
$735$	8.88666	+	2.70209i	0.327789	+	0.0996679i
$736$	21.4889	+	66.1360i	0.792091	+	2.43781i
$737$	4.14885	−	12.7688i	0.152825	−	0.470346i
$738$	9.35085	−	28.7789i	0.344209	−	1.05937i
$739$	−4.73017	−	14.5580i	−0.174002	−	0.535524i	0.825584	−	0.564279i	$-0.190846\pi$
$739$	−4.73017	−	14.5580i	−0.174002	−	0.535524i	−0.999586	+	0.0287550i	$0.990846\pi$
$740$	−30.6095	+	43.8574i	−1.12523	+	1.61223i
$741$	0.974196	−	2.99827i	0.0357880	−	0.110144i
$742$	−9.34676	−	6.79082i	−0.343130	−	0.249299i
$743$	16.5455			0.606995			0.303498	−	0.952832i	$-0.401846\pi$
$743$	16.5455			0.606995			0.303498	+	0.952832i	$0.401846\pi$
$744$	49.7236	+	36.1263i	1.82295	+	1.32445i
$745$	−0.951905	−	1.25921i	−0.0348751	−	0.0461340i
$746$	−71.8225	+	52.1821i	−2.62961	+	1.91052i
$747$	−7.17988	+	5.21649i	−0.262698	+	0.190861i
$748$	−6.84217	−	21.0580i	−0.250175	−	0.769959i
$749$	18.5769			0.678786
$750$	−29.0537	−	7.64238i	−1.06089	−	0.279060i
$751$	46.0279			1.67958			0.839791	−	0.542911i	$-0.182678\pi$
$751$	46.0279			1.67958			0.839791	+	0.542911i	$0.182678\pi$
$752$	−7.59174	−	23.3650i	−0.276842	−	0.852033i
$753$	−4.99879	+	3.63184i	−0.182166	+	0.132351i
$754$	34.6632	−	25.1843i	1.26236	−	0.917159i
$755$	−9.50018	−	12.5672i	−0.345747	−	0.457366i
$756$	7.12476	+	5.17644i	0.259125	+	0.188265i
$757$	−26.5282			−0.964184			−0.482092	−	0.876121i	$-0.660123\pi$
$757$	−26.5282			−0.964184			−0.482092	+	0.876121i	$0.660123\pi$
$758$	−32.9463	−	23.9369i	−1.19666	−	0.869427i
$759$	1.35448	−	4.16865i	0.0491644	−	0.151312i
$760$	13.0395	−	18.6831i	0.472994	−	0.677706i
$761$	−8.78353	−	27.0329i	−0.318403	−	0.979943i	−0.974331	−	0.225120i	$-0.927723\pi$
$761$	−8.78353	−	27.0329i	−0.318403	−	0.979943i	0.655928	−	0.754823i	$-0.272277\pi$
$762$	−16.8029	+	51.7141i	−0.608706	+	1.87341i
$763$	1.79800	−	5.53366i	0.0650918	−	0.200332i
$764$	−12.7756	−	39.3192i	−0.462204	−	1.42252i
$765$	−8.41125	−	2.55753i	−0.304109	−	0.0924678i
$766$	6.64947	−	20.4650i	0.240255	−	0.739429i
$767$	−2.89365	−	2.10236i	−0.104484	−	0.0759119i
$768$	−14.3555			−0.518009
$769$	7.24841	+	5.26628i	0.261384	+	0.189907i	0.710757	−	0.703438i	$-0.248353\pi$
$769$	7.24841	+	5.26628i	0.261384	+	0.189907i	−0.449373	+	0.893344i	$0.648353\pi$
$770$	−10.4624	−	3.18121i	−0.377039	−	0.114643i
$771$	10.6983	−	7.77279i	0.385291	−	0.279930i
$772$	69.3744	−	50.4034i	2.49684	−	1.81406i
$773$	7.13959	+	21.9734i	0.256793	+	0.790329i	0.993471	+	0.114085i	$0.0363935\pi$
$773$	7.13959	+	21.9734i	0.256793	+	0.790329i	−0.736678	+	0.676244i	$0.763607\pi$
$774$	−6.94834			−0.249753
$775$	−27.9197	+	21.9509i	−1.00290	+	0.788501i
$776$	−93.1752			−3.34479
$777$	2.38864	+	7.35148i	0.0856920	+	0.263733i
$778$	2.33609	−	1.69727i	0.0837530	−	0.0608501i
$779$	−10.7283	+	7.79455i	−0.384380	+	0.279269i
$780$	−0.593131	−	31.2449i	−0.0212375	−	1.11875i
$781$	5.22343	+	3.79504i	0.186909	+	0.135797i
$782$	−42.9232			−1.53493
$783$	4.81846	+	3.50082i	0.172198	+	0.125109i
$784$	−16.4433	+	50.6072i	−0.587260	+	1.80740i
$785$	6.91581	+	9.14848i	0.246836	+	0.326523i
$786$	−2.53264	−	7.79465i	−0.0903361	−	0.278026i
$787$	−0.628511	+	1.93436i	−0.0224040	+	0.0689524i	−0.961633	−	0.274338i	$-0.911541\pi$
$787$	−0.628511	+	1.93436i	−0.0224040	+	0.0689524i	0.939229	+	0.343290i	$0.111541\pi$
$788$	−27.6440	+	85.0794i	−0.984776	+	3.03083i
$789$	2.15583	+	6.63498i	0.0767497	+	0.236211i
$790$	0.456615	+	24.0536i	0.0162456	+	0.855788i
$791$	3.15503	−	9.71018i	0.112180	−	0.345254i
$792$	7.55201	+	5.48686i	0.268349	+	0.194967i
$793$	−19.4931			−0.692220
$794$	−52.6376	−	38.2435i	−1.86804	−	1.35721i
$795$	−5.38554	+	1.86360i	−0.191005	+	0.0660950i
$796$	8.52449	−	6.19340i	0.302142	−	0.219519i
$797$	9.86379	−	7.16646i	0.349393	−	0.253849i	−0.399221	−	0.916855i	$-0.630719\pi$
$797$	9.86379	−	7.16646i	0.349393	−	0.253849i	0.748614	+	0.663006i	$0.230719\pi$
$798$	−1.64953	−	5.07674i	−0.0583928	−	0.179715i
$799$	7.54024			0.266754
$800$	23.3370	−	82.3343i	0.825086	−	2.91096i
$801$	15.4436			0.545673
$802$	1.65501	+	5.09359i	0.0584404	+	0.179861i
$803$	2.88075	−	2.09299i	0.101659	−	0.0738599i
$804$	52.5583	−	38.1858i	1.85359	−	1.34671i
$805$	−8.77191	+	12.5684i	−0.309169	+	0.442978i
$806$	−41.3396	−	30.0350i	−1.45612	−	1.05794i
$807$	−23.7199			−0.834979
$808$	−94.9616	−	68.9936i	−3.34074	−	2.42719i
$809$	2.72972	−	8.40121i	0.0959718	−	0.295371i	−0.891534	−	0.452954i	$-0.850370\pi$
$809$	2.72972	−	8.40121i	0.0959718	−	0.295371i	0.987506	+	0.157583i	$0.0503702\pi$
$810$	5.67807	−	1.96482i	0.199507	−	0.0690369i
$811$	−4.30102	−	13.2372i	−0.151029	−	0.464820i	0.846708	−	0.532058i	$-0.178581\pi$
$811$	−4.30102	−	13.2372i	−0.151029	−	0.464820i	−0.997737	+	0.0672381i	$0.978581\pi$
$812$	16.2086	−	49.8850i	0.568811	−	1.75062i
$813$	−8.95871	+	27.5721i	−0.314196	+	0.966995i
$814$	4.10438	+	12.6320i	0.143858	+	0.442750i
$815$	51.2673	−	17.7404i	1.79581	−	0.621419i
$816$	15.5636	−	47.8998i	0.544835	−	1.67683i
$817$	2.46344	+	1.78980i	0.0861850	+	0.0626170i
$818$	−17.9085			−0.626158
$819$	−3.65401	−	2.65479i	−0.127681	−	0.0927660i
$820$	−75.2330	+	107.794i	−2.62725	+	3.76433i
$821$	23.8603	−	17.3355i	0.832731	−	0.605015i	−0.0875994	−	0.996156i	$-0.527920\pi$
$821$	23.8603	−	17.3355i	0.832731	−	0.605015i	0.920331	+	0.391141i	$0.127920\pi$
$822$	44.5860	−	32.3936i	1.55511	−	1.12986i
$823$	−12.9682	−	39.9121i	−0.452044	−	1.39125i	−0.874571	−	0.484898i	$-0.838857\pi$
$823$	−12.9682	−	39.9121i	−0.452044	−	1.39125i	0.422527	−	0.906350i	$-0.361143\pi$
$824$	−11.8460			−0.412675
$825$	−4.24043	+	3.33390i	−0.147633	+	0.116072i
$826$	−6.05624			−0.210724
$827$	11.5781	+	35.6336i	0.402609	+	1.23910i	0.922875	+	0.385099i	$0.125833\pi$
$827$	11.5781	+	35.6336i	0.402609	+	1.23910i	−0.520266	+	0.854004i	$0.674167\pi$
$828$	17.1587	−	12.4666i	0.596307	−	0.433243i
$829$	7.73108	−	5.61696i	0.268512	−	0.195085i	−0.445379	−	0.895342i	$-0.646931\pi$
$829$	7.73108	−	5.61696i	0.268512	−	0.195085i	0.713891	+	0.700257i	$0.246931\pi$
$830$	50.3918	−	17.4374i	1.74913	−	0.605263i
$831$	−6.94677	−	5.04712i	−0.240981	−	0.175083i
$832$	54.5355			1.89068
$833$	−13.2126	−	9.59954i	−0.457791	−	0.332604i
$834$	15.2105	−	46.8131i	0.526696	−	1.62100i
$835$	0.193056	+	10.1698i	0.00668099	+	0.351941i
$836$	−2.04925	−	6.30695i	−0.0708748	−	0.218130i
$837$	2.19498	−	6.75545i	0.0758695	−	0.233502i
$838$	−17.7311	+	54.5708i	−0.612512	+	1.88512i
$839$	16.9128	+	52.0522i	0.583895	+	1.79704i	0.603665	+	0.797238i	$0.293707\pi$
$839$	16.9128	+	52.0522i	0.583895	+	1.79704i	−0.0197702	+	0.999805i	$0.506293\pi$
$840$	−19.6838	−	26.0385i	−0.679157	−	0.898413i
$841$	2.00037	−	6.15651i	0.0689783	−	0.212294i
$842$	48.5570	+	35.2787i	1.67338	+	1.21579i
$843$	−17.1661			−0.591233
$844$	100.603	+	73.0922i	3.46289	+	2.51594i
$845$	−0.247529	−	13.0394i	−0.00851527	−	0.448567i
$846$	−4.16908	+	3.02901i	−0.143336	+	0.104140i
$847$	13.4248	−	9.75371i	0.461283	−	0.335141i
$848$	−10.0887	−	31.0499i	−0.346448	−	1.06626i
$849$	9.62005			0.330159
$850$	43.8821	+	29.4042i	1.50514	+	1.00856i
$851$	18.6159			0.638144
$852$	9.65426	+	29.7128i	0.330750	+	1.01794i
$853$	12.3834	−	8.99706i	0.423999	−	0.308053i	−0.355246	−	0.934773i	$-0.615603\pi$
$853$	12.3834	−	8.99706i	0.423999	−	0.308053i	0.779245	+	0.626720i	$0.215603\pi$
$854$	−26.7026	+	19.4005i	−0.913743	+	0.663873i
$855$	−2.51919	−	0.765989i	−0.0861546	−	0.0261963i
$856$	77.0836	+	56.0045i	2.63466	+	1.91419i
$857$	−8.66910			−0.296131			−0.148065	−	0.988978i	$-0.547305\pi$
$857$	−8.66910			−0.296131			−0.148065	+	0.988978i	$0.547305\pi$
$858$	−6.27865	−	4.56171i	−0.214350	−	0.155734i
$859$	−9.39653	+	28.9195i	−0.320605	+	0.986722i	0.652780	+	0.757547i	$0.273603\pi$
$859$	−9.39653	+	28.9195i	−0.320605	+	0.986722i	−0.973385	+	0.229174i	$0.926397\pi$
$860$	28.8787	+	8.78088i	0.984755	+	0.299425i
$861$	5.87087	+	18.0687i	0.200079	+	0.615779i
$862$	25.2531	−	77.7211i	0.860125	−	2.64719i
$863$	−5.57545	+	17.1595i	−0.189791	+	0.584115i	−0.999998	−	0.00202803i	$-0.999354\pi$
$863$	−5.57545	+	17.1595i	−0.189791	+	0.584115i	0.810207	+	0.586143i	$0.199354\pi$
$864$	5.28899	+	16.2779i	0.179935	+	0.553784i
$865$	−3.42627	+	4.90917i	−0.116497	+	0.166917i
$866$	−0.478808	+	1.47362i	−0.0162706	+	0.0500756i
$867$	−1.24749	−	0.906354i	−0.0423669	−	0.0307814i
$868$	−62.5548			−2.12325
$869$	3.49465	+	2.53901i	0.118548	+	0.0861301i
$870$	−21.5801	−	28.5469i	−0.731632	−	0.967829i
$871$	−26.9551	+	19.5840i	−0.913338	+	0.663579i
$872$	24.1432	−	17.5411i	0.817591	−	0.594015i
$873$	3.32756	+	10.2412i	0.112621	+	0.346611i
$874$	−12.8556			−0.434848
$875$	17.5778	−	6.84006i	0.594237	−	0.231236i
$876$	17.2301			0.582149
$877$	6.89285	+	21.2140i	0.232755	+	0.716346i	0.997411	+	0.0719076i	$0.0229087\pi$
$877$	6.89285	+	21.2140i	0.232755	+	0.716346i	−0.764656	+	0.644438i	$0.777091\pi$
$878$	27.8352	−	20.2235i	0.939393	−	0.682509i
$879$	13.6079	−	9.88669i	0.458982	−	0.333470i
$880$	−18.6349	−	24.6508i	−0.628181	−	0.830980i
$881$	−6.27761	−	4.56095i	−0.211498	−	0.153662i	0.476993	−	0.878907i	$-0.341727\pi$
$881$	−6.27761	−	4.56095i	−0.211498	−	0.153662i	−0.688491	+	0.725245i	$0.741727\pi$
$882$	11.1617			0.375833
$883$	16.1421	+	11.7279i	0.543224	+	0.394675i	0.825281	−	0.564722i	$-0.191017\pi$
$883$	16.1421	+	11.7279i	0.543224	+	0.394675i	−0.282057	+	0.959398i	$0.591017\pi$
$884$	−16.9798	+	52.2584i	−0.571092	+	1.75764i
$885$	−1.70974	+	2.44972i	−0.0574722	+	0.0823463i
$886$	−11.8861	−	36.5816i	−0.399320	−	1.22898i
$887$	2.65844	−	8.18183i	0.0892616	−	0.274719i	−0.896454	−	0.443137i	$-0.853866\pi$
$887$	2.65844	−	8.18183i	0.0892616	−	0.274719i	0.985716	+	0.168418i	$0.0538657\pi$
$888$	−12.2513	+	37.7056i	−0.411126	+	1.26532i
$889$	−10.5496	−	32.4684i	−0.353823	−	1.08895i
$890$	−88.7783	−	26.9940i	−2.97585	−	0.904841i
$891$	0.333373	−	1.02602i	0.0111684	−	0.0343729i
$892$	−55.3715	−	40.2297i	−1.85397	−	1.34699i
$893$	2.25832			0.0755719
$894$	−1.53461	−	1.11496i	−0.0513251	−	0.0372899i
$895$	−33.4310	−	10.1651i	−1.11748	−	0.339781i
$896$	27.9851	−	20.3323i	0.934916	−	0.679256i
$897$	−8.80004	+	6.39360i	−0.293825	+	0.213476i
$898$	9.93611	+	30.5802i	0.331572	+	1.02047i
$899$	−42.3057			−1.41097
$900$	−26.0822	+	0.990607i	−0.869406	+	0.0330202i
$901$	10.0203			0.333824
$902$	10.0879	+	31.0472i	0.335889	+	1.03376i
$903$	3.52932	−	2.56420i	0.117448	−	0.0853312i
$904$	42.3652	−	30.7801i	1.40905	−	1.02373i
$905$	0.00860869	+	0.453488i	0.000286163	+	0.0150745i
$906$	−15.3157	−	11.1275i	−0.508830	−	0.369687i
$907$	6.26125			0.207902			0.103951	−	0.994582i	$-0.466852\pi$
$907$	6.26125			0.207902			0.103951	+	0.994582i	$0.466852\pi$
$908$	110.989	+	80.6385i	3.68331	+	2.67608i
$909$	−4.19195	+	12.9015i	−0.139038	+	0.427915i
$910$	16.3649	+	21.6481i	0.542491	+	0.717627i
$911$	0.279838	+	0.861253i	0.00927145	+	0.0285346i	0.955585	−	0.294715i	$-0.0952247\pi$
$911$	0.279838	+	0.861253i	0.00927145	+	0.0285346i	−0.946314	+	0.323250i	$0.895225\pi$
$912$	4.66135	−	14.3461i	0.154353	−	0.475048i
$913$	2.95862	−	9.10571i	0.0979162	−	0.301355i
$914$	6.82669	+	21.0104i	0.225807	+	0.694962i
$915$	0.309010	+	16.2780i	0.0102156	+	0.538135i
$916$	3.21988	−	9.90978i	0.106388	−	0.327428i
$917$	4.16293	+	3.02455i	0.137472	+	0.0998794i
$918$	−10.5646			−0.348682
$919$	−35.5913	−	25.8586i	−1.17405	−	0.852997i	−0.182561	−	0.983194i	$-0.558439\pi$
$919$	−35.5913	−	25.8586i	−1.17405	−	0.852997i	−0.991488	+	0.130198i	$0.958439\pi$
$920$	−74.2889	+	25.7067i	−2.44923	+	0.847526i
$921$	9.15903	−	6.65443i	0.301800	−	0.219271i
$922$	2.76551	−	2.00926i	0.0910771	−	0.0661714i
$923$	−4.95129	−	15.2385i	−0.162974	−	0.501582i
$924$	−9.50081			−0.312554
$925$	−19.0317	−	12.7526i	−0.625760	−	0.419304i
$926$	−87.8029			−2.88538
$927$	0.423056	+	1.30203i	0.0138950	+	0.0427643i
$928$	82.4707	−	59.9184i	2.70723	−	1.96692i
$929$	29.7271	−	21.5980i	0.975313	−	0.708606i	0.0186568	−	0.999826i	$-0.494061\pi$
$929$	29.7271	−	21.5980i	0.975313	−	0.708606i	0.956656	+	0.291220i	$0.0940610\pi$
$930$	−24.4258	+	34.9974i	−0.800955	+	1.14761i
$931$	−3.95722	−	2.87509i	−0.129693	−	0.0942273i
$932$	−2.74347			−0.0898652
$933$	15.0181	+	10.9113i	0.491672	+	0.357221i
$934$	−11.9857	+	36.8883i	−0.392185	+	1.20702i
$935$	8.96295	−	3.10152i	0.293120	−	0.101430i
$936$	−7.15855	−	22.0318i	−0.233985	−	0.720131i
$937$	7.61696	−	23.4426i	0.248835	−	0.765836i	−0.746147	−	0.665782i	$-0.768098\pi$
$937$	7.61696	−	23.4426i	0.248835	−	0.765836i	0.994982	−	0.100055i	$-0.0319017\pi$
$938$	−17.4333	+	53.6542i	−0.569217	+	1.75187i
$939$	2.99731	+	9.22478i	0.0978137	+	0.301039i
$940$	21.1554	−	7.32055i	0.690012	−	0.238770i
$941$	−18.2777	+	56.2530i	−0.595836	+	1.83379i	−0.0453159	+	0.998973i	$0.514429\pi$
$941$	−18.2777	+	56.2530i	−0.595836	+	1.83379i	−0.550520	+	0.834822i	$0.685571\pi$
$942$	11.1493	+	8.10045i	0.363264	+	0.263927i
$943$	45.7546			1.48998
$944$	−13.8456	−	10.0594i	−0.450635	−	0.327406i
$945$	−2.15900	+	3.09342i	−0.0702324	+	0.100629i
$946$	6.06439	−	4.40604i	0.197170	−	0.143253i
$947$	24.3482	−	17.6900i	0.791210	−	0.574848i	−0.117112	−	0.993119i	$-0.537364\pi$
$947$	24.3482	−	17.6900i	0.791210	−	0.574848i	0.908322	+	0.418271i	$0.137364\pi$
$948$	6.45903	+	19.8789i	0.209780	+	0.645635i
$949$	−8.83661			−0.286849
$950$	13.1428	+	8.80664i	0.426410	+	0.285725i
$951$	−7.47647			−0.242441
$952$	17.7354	+	54.5841i	0.574809	+	1.76908i
$953$	16.6975	−	12.1315i	0.540886	−	0.392977i	−0.283528	−	0.958964i	$-0.591505\pi$
$953$	16.6975	−	12.1315i	0.540886	−	0.392977i	0.824414	+	0.565987i	$0.191505\pi$
$954$	−5.54032	+	4.02528i	−0.179375	+	0.130323i
$955$	16.7355	−	5.79109i	0.541547	−	0.187395i
$956$	29.6036	+	21.5083i	0.957449	+	0.695628i
$957$	−6.42538			−0.207703
$958$	−36.6553	−	26.6316i	−1.18428	−	0.860429i
$959$	−10.6924	+	32.9078i	−0.345275	+	1.06265i
$960$	−0.864511	−	45.5407i	−0.0279020	−	1.46982i
$961$	6.01162	+	18.5019i	0.193923	+	0.596834i
$962$	10.1856	−	31.3480i	0.328396	−	1.01070i
$963$	3.40275	−	10.4726i	0.109652	−	0.337474i
$964$	3.73527	+	11.4960i	0.120305	+	0.370260i
$965$	22.1504	+	29.3013i	0.713047	+	0.943244i
$966$	−5.69146	+	17.5165i	−0.183120	+	0.563585i
$967$	18.2850	+	13.2849i	0.588007	+	0.427212i	0.841602	−	0.540098i	$-0.181613\pi$
$967$	18.2850	+	13.2849i	0.588007	+	0.427212i	−0.253595	+	0.967311i	$0.581613\pi$
$968$	85.1103			2.73555
$969$	3.74552	+	2.72128i	0.120324	+	0.0874202i
$970$	−1.22799	−	64.6881i	−0.0394284	−	2.07701i
$971$	−19.5281	+	14.1880i	−0.626687	+	0.455315i	−0.855251	−	0.518214i	$-0.826597\pi$
$971$	−19.5281	+	14.1880i	−0.626687	+	0.455315i	0.228564	+	0.973529i	$0.426597\pi$
$972$	4.22323	−	3.06835i	0.135460	−	0.0984175i
$973$	9.54981	+	29.3913i	0.306153	+	0.942242i
$974$	−107.007			−3.42874
$975$	13.3765	−	0.508043i	0.428391	−	0.0162704i
$976$	−93.2708			−2.98553
$977$	7.12302	+	21.9224i	0.227886	+	0.701360i	0.997986	+	0.0634371i	$0.0202062\pi$
$977$	7.12302	+	21.9224i	0.227886	+	0.701360i	−0.770100	+	0.637923i	$0.779794\pi$
$978$	52.7407	−	38.3184i	1.68646	−	1.22529i
$979$	−13.4789	+	9.79299i	−0.430787	+	0.312985i
$980$	−46.3901	−	14.1054i	−1.48188	−	0.450581i
$981$	−2.79022	−	2.02721i	−0.0890847	−	0.0647239i
$982$	−37.6870			−1.20264
$983$	−24.1664	−	17.5579i	−0.770787	−	0.560010i	0.131413	−	0.991328i	$-0.458049\pi$
$983$	−24.1664	−	17.5579i	−0.770787	−	0.560010i	−0.902200	+	0.431318i	$0.858049\pi$
$984$	−30.1116	+	92.6738i	−0.959921	+	2.95433i
$985$	−36.6619	−	11.1474i	−1.16814	−	0.355187i
$986$	19.4440	+	59.8424i	0.619222	+	1.90577i
$987$	0.999807	−	3.07709i	0.0318242	−	0.0979449i
$988$	−5.08550	+	15.6515i	−0.161791	+	0.497942i
$989$	−3.24661	−	9.99204i	−0.103236	−	0.317728i
$990$	−3.70979	+	5.31540i	−0.117905	+	0.168934i
$991$	5.14700	−	15.8408i	0.163500	−	0.503201i	−0.835423	−	0.549608i	$-0.814777\pi$
$991$	5.14700	−	15.8408i	0.163500	−	0.503201i	0.998923	+	0.0464072i	$0.0147772\pi$
$992$	−98.3550	−	71.4591i	−3.12277	−	2.26883i
$993$	25.2570			0.801507
$994$	−21.9487	−	15.9466i	−0.696169	−	0.505797i
$995$	2.72177	+	3.60045i	0.0862858	+	0.114142i
$996$	37.4804	−	27.2311i	1.18761	−	0.862850i
$997$	−10.1074	+	7.34343i	−0.320103	+	0.232569i	−0.736220	−	0.676743i	$-0.763391\pi$
$997$	−10.1074	+	7.34343i	−0.320103	+	0.232569i	0.416116	+	0.909311i	$0.363391\pi$
$998$	−12.6474	−	38.9246i	−0.400346	−	1.23214i
$999$	4.58187			0.144964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.g.c.31.1	✓	12
3.2	odd	2		225.2.h.d.181.3		12
5.2	odd	4		375.2.i.d.349.6		24
5.3	odd	4		375.2.i.d.349.1		24
5.4	even	2		375.2.g.c.151.3		12
25.2	odd	20		1875.2.b.f.1249.1		12
25.3	odd	20		375.2.i.d.274.6		24
25.4	even	10		375.2.g.c.226.3		12
25.11	even	5		1875.2.a.j.1.1		6
25.14	even	10		1875.2.a.k.1.6		6
25.21	even	5	inner	75.2.g.c.46.1	yes	12
25.22	odd	20		375.2.i.d.274.1		24
25.23	odd	20		1875.2.b.f.1249.12		12
75.11	odd	10		5625.2.a.p.1.6		6
75.14	odd	10		5625.2.a.q.1.1		6
75.71	odd	10		225.2.h.d.46.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.1	✓	12	1.1	even	1	trivial
75.2.g.c.46.1	yes	12	25.21	even	5	inner
225.2.h.d.46.3		12	75.71	odd	10
225.2.h.d.181.3		12	3.2	odd	2
375.2.g.c.151.3		12	5.4	even	2
375.2.g.c.226.3		12	25.4	even	10
375.2.i.d.274.1		24	25.22	odd	20
375.2.i.d.274.6		24	25.3	odd	20
375.2.i.d.349.1		24	5.3	odd	4
375.2.i.d.349.6		24	5.2	odd	4
1875.2.a.j.1.1		6	25.11	even	5
1875.2.a.k.1.6		6	25.14	even	10
1875.2.b.f.1249.1		12	25.2	odd	20
1875.2.b.f.1249.12		12	25.23	odd	20
5625.2.a.p.1.6		6	75.11	odd	10
5625.2.a.q.1.1		6	75.14	odd	10

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.830342 - 2.55553i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-4.22323 + 3.06835i) q^{4} +(-1.34843 - 1.78375i) q^{5} +(-2.17386 - 1.57940i) q^{6} +1.68704 q^{7} +(7.00026 + 5.08599i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-3.43876 + 4.92706i) q^{10} +(0.333373 + 1.02602i) q^{11} +(-1.61313 + 4.96470i) q^{12} +(0.827310 - 2.54620i) q^{13} +(-1.40082 - 4.31129i) q^{14} +(-2.13936 - 0.650495i) q^{15} +(3.95852 - 12.1831i) q^{16} +(3.18079 + 2.31098i) q^{17} -2.68704 q^{18} +(0.952655 + 0.692144i) q^{19} +(11.1679 + 3.39571i) q^{20} +(1.36485 - 0.991619i) q^{21} +(2.34520 - 1.70389i) q^{22} +(-1.25552 - 3.86409i) q^{23} +8.65280 q^{24} +(-1.36350 + 4.81050i) q^{25} -7.19384 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-7.12476 + 5.17644i) q^{28} +(-4.81846 + 3.50082i) q^{29} +(0.114039 + 6.00733i) q^{30} +(5.74653 + 4.17510i) q^{31} -17.1155 q^{32} +(0.872782 + 0.634113i) q^{33} +(3.26463 - 10.0475i) q^{34} +(-2.27485 - 3.00925i) q^{35} +(1.61313 + 4.96470i) q^{36} +(-1.41587 + 4.35761i) q^{37} +(0.977766 - 3.00925i) q^{38} +(-0.827310 - 2.54620i) q^{39} +(-0.367227 - 19.3448i) q^{40} +(-3.47998 + 10.7103i) q^{41} +(-3.66740 - 2.66452i) q^{42} +2.58587 q^{43} +(-4.55609 - 3.31019i) q^{44} +(-2.11313 + 0.731222i) q^{45} +(-8.83229 + 6.41703i) q^{46} +(1.55155 - 1.12727i) q^{47} +(-3.95852 - 12.1831i) q^{48} -4.15389 q^{49} +(13.4255 - 0.509905i) q^{50} +3.93167 q^{51} +(4.31872 + 13.2917i) q^{52} +(2.06187 - 1.49803i) q^{53} +(-2.17386 + 1.57940i) q^{54} +(1.38062 - 1.97816i) q^{55} +(11.8097 + 8.58028i) q^{56} +1.17755 q^{57} +(12.9474 + 9.40685i) q^{58} +(0.412843 - 1.27060i) q^{59} +(11.0309 - 3.81712i) q^{60} +(-2.24997 - 6.92470i) q^{61} +(5.89800 - 18.1522i) q^{62} +(0.521325 - 1.60447i) q^{63} +(6.29470 + 19.3731i) q^{64} +(-5.65734 + 1.95765i) q^{65} +(0.895787 - 2.75695i) q^{66} +(-10.0683 - 7.31502i) q^{67} -20.5241 q^{68} +(-3.28699 - 2.38814i) q^{69} +(-5.80133 + 8.31216i) q^{70} +(4.84181 - 3.51778i) q^{71} +(7.00026 - 5.08599i) q^{72} +(-1.01996 - 3.13911i) q^{73} +12.3117 q^{74} +(1.72445 + 4.69322i) q^{75} -6.14702 q^{76} +(0.562414 + 1.73093i) q^{77} +(-5.81994 + 4.22843i) q^{78} +(3.23934 - 2.35351i) q^{79} +(-27.0693 + 9.36699i) q^{80} +(-0.809017 - 0.587785i) q^{81} +30.2600 q^{82} +(-7.17988 - 5.21649i) q^{83} +(-2.72142 + 8.37566i) q^{84} +(-0.166861 - 8.78989i) q^{85} +(-2.14716 - 6.60827i) q^{86} +(-1.84049 + 5.66445i) q^{87} +(-2.88461 + 8.87792i) q^{88} +(4.77234 + 14.6877i) q^{89} +(3.62328 + 4.79300i) q^{90} +(1.39571 - 4.29555i) q^{91} +(17.1587 + 12.4666i) q^{92} +7.10310 q^{93} +(-4.16908 - 3.02901i) q^{94} +(-0.0499753 - 2.63260i) q^{95} +(-13.8468 + 10.0603i) q^{96} +(-8.71166 + 6.32939i) q^{97} +(3.44915 + 10.6154i) q^{98} +1.07882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 10 q^{4} - 6 q^{5} - 12 q^{7} + 9 q^{8} - 3 q^{9} - 9 q^{10} - 4 q^{11} - 2 q^{13} + 6 q^{14} - 9 q^{15} + 16 q^{16} - q^{17} + 7 q^{19} + 26 q^{20} - 3 q^{21} + 13 q^{22} + 19 q^{23}+ \cdots + 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 10 * q^4 - 6 * q^5 - 12 * q^7 + 9 * q^8 - 3 * q^9 - 9 * q^10 - 4 * q^11 - 2 * q^13 + 6 * q^14 - 9 * q^15 + 16 * q^16 - q^17 + 7 * q^19 + 26 * q^20 - 3 * q^21 + 13 * q^22 + 19 * q^23 + 6 * q^24 + 4 * q^25 - 56 * q^26 + 3 * q^27 + q^28 - q^29 + 19 * q^30 + 13 * q^31 - 32 * q^32 - q^33 - 25 * q^34 - 10 * q^35 + 8 * q^37 - 22 * q^38 + 2 * q^39 - 28 * q^40 + 8 * q^41 - 16 * q^42 - 4 * q^43 + 33 * q^44 - 6 * q^45 - 22 * q^46 - 13 * q^47 - 16 * q^48 - 28 * q^49 + 81 * q^50 + 26 * q^51 + 44 * q^52 + 44 * q^53 + 9 * q^55 + 45 * q^56 - 22 * q^57 + 41 * q^58 - 22 * q^59 + 14 * q^60 - 8 * q^61 + 41 * q^62 + 3 * q^63 + 49 * q^64 - 38 * q^65 - 3 * q^66 - 6 * q^67 - 100 * q^68 + 6 * q^69 - 45 * q^70 - 21 * q^71 + 9 * q^72 - 16 * q^73 - 44 * q^74 - 4 * q^75 - 52 * q^76 + q^77 - 19 * q^78 + 10 * q^79 - 99 * q^80 - 3 * q^81 + 26 * q^82 - 10 * q^83 - 6 * q^84 + 23 * q^85 + 56 * q^86 - 4 * q^87 - 16 * q^88 + 57 * q^89 + 16 * q^90 - 7 * q^91 + 3 * q^92 + 22 * q^93 - 23 * q^94 + 21 * q^95 - 23 * q^96 + 4 * q^97 - 18 * q^98 + 6 * q^99

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