LMFDB - Embedded newform 925.2.y.b.193.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] 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("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] 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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.16
Character	$\chi$	$=$	925.193
Dual form			925.2.y.b.532.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.10315 - 1.21425i) q^{2} +(-0.180195 - 0.672498i) q^{3} +(1.94883 - 3.37547i) q^{4} +(-1.19556 - 1.19556i) q^{6} +(1.19887 + 4.47423i) q^{7} -4.60849i q^{8} +(2.17829 - 1.25764i) q^{9} -4.52235i q^{11} +(-2.62117 - 0.702340i) q^{12} +(1.72863 + 0.998024i) q^{13} +(7.95426 + 7.95426i) q^{14} +(-1.69822 - 2.94140i) q^{16} +(-1.95835 - 3.39197i) q^{17} +(3.05419 - 5.29000i) q^{18} +(-0.380525 - 1.42014i) q^{19} +(2.79288 - 1.61247i) q^{21} +(-5.49128 - 9.51118i) q^{22} -2.17011i q^{23} +(-3.09920 + 0.830428i) q^{24} +4.84742 q^{26} +(-2.71519 - 2.71519i) q^{27} +(17.4390 + 4.67278i) q^{28} +(1.43325 + 1.43325i) q^{29} +(-5.05094 + 5.05094i) q^{31} +(0.838921 + 0.484351i) q^{32} +(-3.04127 + 0.814906i) q^{33} +(-8.23743 - 4.75588i) q^{34} -9.80369i q^{36} +(1.78340 + 5.81545i) q^{37} +(-2.52471 - 2.52471i) q^{38} +(0.359679 - 1.34234i) q^{39} +(-0.811286 - 0.468396i) q^{41} +(3.91591 - 6.78255i) q^{42} +0.784090i q^{43} +(-15.2651 - 8.81329i) q^{44} +(-2.63506 - 4.56407i) q^{46} +(-6.76780 + 6.76780i) q^{47} +(-1.67207 + 1.67207i) q^{48} +(-12.5193 + 7.22802i) q^{49} +(-1.92821 + 1.92821i) q^{51} +(6.73760 - 3.88996i) q^{52} +(3.31335 - 12.3656i) q^{53} +(-9.00738 - 2.41352i) q^{54} +(20.6194 - 5.52496i) q^{56} +(-0.886472 + 0.511805i) q^{57} +(4.75469 + 1.27401i) q^{58} +(7.44042 + 1.99365i) q^{59} +(1.29225 + 4.82274i) q^{61} +(-4.48976 + 16.7560i) q^{62} +(8.23845 + 8.23845i) q^{63} +9.14537 q^{64} +(-5.40675 + 5.40675i) q^{66} +(-6.92312 + 1.85504i) q^{67} -15.2660 q^{68} +(-1.45939 + 0.391044i) q^{69} +(-6.96450 + 12.0629i) q^{71} +(-5.79581 - 10.0386i) q^{72} +(-6.73477 + 6.73477i) q^{73} +(10.8122 + 10.0653i) q^{74} +(-5.53521 - 1.48316i) q^{76} +(20.2340 - 5.42169i) q^{77} +(-0.873483 - 3.25988i) q^{78} +(-1.39018 - 5.18821i) q^{79} +(2.43622 - 4.21965i) q^{81} -2.27501 q^{82} +(2.38257 - 8.89188i) q^{83} -12.5697i q^{84} +(0.952085 + 1.64906i) q^{86} +(0.705596 - 1.22213i) q^{87} -20.8412 q^{88} +(-0.159121 + 0.593846i) q^{89} +(-2.39300 + 8.93078i) q^{91} +(-7.32514 - 4.22917i) q^{92} +(4.30691 + 2.48659i) q^{93} +(-6.01587 + 22.4515i) q^{94} +(0.174556 - 0.651451i) q^{96} -3.08147 q^{97} +(-17.5533 + 30.4032i) q^{98} +(-5.68747 - 9.85100i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.10315	−	1.21425i	1.48715	−	0.858608i	0.487260	−	0.873257i	$-0.337996\pi$
$2$	2.10315	−	1.21425i	1.48715	−	0.858608i	0.999893	+	0.0146492i	$0.00466316\pi$
$3$	−0.180195	−	0.672498i	−0.104036	−	0.388267i	0.894198	−	0.447671i	$-0.147747\pi$
$3$	−0.180195	−	0.672498i	−0.104036	−	0.388267i	−0.998234	+	0.0594043i	$0.981080\pi$
$4$	1.94883	−	3.37547i	0.974415	−	1.68774i
$5$		0			0
$5$		0			0
$6$	−1.19556	−	1.19556i	−0.488086	−	0.488086i
$7$	1.19887	+	4.47423i	0.453129	+	1.69110i	0.693530	+	0.720428i	$0.256054\pi$
$7$	1.19887	+	4.47423i	0.453129	+	1.69110i	−0.240401	+	0.970674i	$0.577279\pi$
$8$		−	4.60849i		−	1.62935i
$9$	2.17829	−	1.25764i	0.726097	−	0.419213i
$10$		0			0
$11$		−	4.52235i		−	1.36354i	−0.731567	−	0.681770i	$-0.761211\pi$
$11$		−	4.52235i		−	1.36354i	0.731567	−	0.681770i	$-0.238789\pi$
$12$	−2.62117	−	0.702340i	−0.756667	−	0.202748i
$13$	1.72863	+	0.998024i	0.479435	+	0.276802i	0.720181	−	0.693786i	$-0.244059\pi$
$13$	1.72863	+	0.998024i	0.479435	+	0.276802i	−0.240746	+	0.970588i	$0.577392\pi$
$14$	7.95426	+	7.95426i	2.12586	+	2.12586i
$15$		0			0
$16$	−1.69822	−	2.94140i	−0.424554	−	0.735349i
$17$	−1.95835	−	3.39197i	−0.474971	−	0.822673i	0.524618	−	0.851337i	$-0.324208\pi$
$17$	−1.95835	−	3.39197i	−0.474971	−	0.822673i	−0.999589	+	0.0286642i	$0.990875\pi$
$18$	3.05419	−	5.29000i	0.719878	−	1.24687i
$19$	−0.380525	−	1.42014i	−0.0872984	−	0.325802i	0.908441	−	0.418013i	$-0.137273\pi$
$19$	−0.380525	−	1.42014i	−0.0872984	−	0.325802i	−0.995740	+	0.0922109i	$0.970607\pi$
$20$		0			0
$21$	2.79288	−	1.61247i	0.609457	−	0.351870i
$22$	−5.49128	−	9.51118i	−1.17075	−	2.02779i
$23$		−	2.17011i		−	0.452499i	−0.974069	−	0.226249i	$-0.927354\pi$
$23$		−	2.17011i		−	0.452499i	0.974069	−	0.226249i	$-0.0726464\pi$
$24$	−3.09920	+	0.830428i	−0.632621	+	0.169510i
$25$		0			0
$26$	4.84742			0.950657
$27$	−2.71519	−	2.71519i	−0.522538	−	0.522538i
$28$	17.4390	+	4.67278i	3.29567	+	0.883072i
$29$	1.43325	+	1.43325i	0.266149	+	0.266149i	0.827546	−	0.561398i	$-0.189736\pi$
$29$	1.43325	+	1.43325i	0.266149	+	0.266149i	−0.561398	+	0.827546i	$0.689736\pi$
$30$		0			0
$31$	−5.05094	+	5.05094i	−0.907176	+	0.907176i	−0.996043	−	0.0888677i	$-0.971675\pi$
$31$	−5.05094	+	5.05094i	−0.907176	+	0.907176i	0.0888677	+	0.996043i	$0.471675\pi$
$32$	0.838921	+	0.484351i	0.148302	+	0.0856220i
$33$	−3.04127	+	0.814906i	−0.529417	+	0.141857i
$34$	−8.23743	−	4.75588i	−1.41271	−	0.815627i
$35$		0			0
$36$		−	9.80369i		−	1.63395i
$37$	1.78340	+	5.81545i	0.293188	+	0.956055i
$37$	1.78340	+	5.81545i	0.293188	+	0.956055i
$38$	−2.52471	−	2.52471i	−0.409562	−	0.409562i
$39$	0.359679	−	1.34234i	0.0575947	−	0.214946i
$40$		0			0
$41$	−0.811286	−	0.468396i	−0.126702	−	0.0731512i	0.435310	−	0.900281i	$-0.356639\pi$
$41$	−0.811286	−	0.468396i	−0.126702	−	0.0731512i	−0.562011	+	0.827130i	$0.689972\pi$
$42$	3.91591	−	6.78255i	0.604237	−	1.04657i
$43$			0.784090i			0.119573i	0.998211	+	0.0597863i	$0.0190419\pi$
$43$			0.784090i			0.119573i	−0.998211	+	0.0597863i	$0.980958\pi$
$44$	−15.2651	−	8.81329i	−2.30129	−	1.32865i
$45$		0			0
$46$	−2.63506	−	4.56407i	−0.388519	−	0.672935i
$47$	−6.76780	+	6.76780i	−0.987185	+	0.987185i	−0.999919	−	0.0127338i	$-0.995947\pi$
$47$	−6.76780	+	6.76780i	−0.987185	+	0.987185i	0.0127338	+	0.999919i	$0.495947\pi$
$48$	−1.67207	+	1.67207i	−0.241343	+	0.241343i
$49$	−12.5193	+	7.22802i	−1.78847	+	1.03257i
$50$		0			0
$51$	−1.92821	+	1.92821i	−0.270003	+	0.270003i
$52$	6.73760	−	3.88996i	0.934337	−	0.539440i
$53$	3.31335	−	12.3656i	0.455124	−	1.69855i	−0.232598	−	0.972573i	$-0.574723\pi$
$53$	3.31335	−	12.3656i	0.455124	−	1.69855i	0.687722	−	0.725974i	$-0.258611\pi$
$54$	−9.00738	−	2.41352i	−1.22575	−	0.328438i
$55$		0			0
$56$	20.6194	−	5.52496i	2.75539	−	0.738304i
$57$	−0.886472	+	0.511805i	−0.117416	+	0.0677902i
$58$	4.75469	+	1.27401i	0.624321	+	0.167286i
$59$	7.44042	+	1.99365i	0.968660	+	0.259552i	0.708262	−	0.705950i	$-0.249479\pi$
$59$	7.44042	+	1.99365i	0.968660	+	0.259552i	0.260398	+	0.965501i	$0.416146\pi$
$60$		0			0
$61$	1.29225	+	4.82274i	0.165455	+	0.617488i	0.997982	+	0.0635026i	$0.0202271\pi$
$61$	1.29225	+	4.82274i	0.165455	+	0.617488i	−0.832526	+	0.553986i	$0.813106\pi$
$62$	−4.48976	+	16.7560i	−0.570200	+	2.12802i
$63$	8.23845	+	8.23845i	1.03795	+	1.03795i
$64$	9.14537			1.14317
$65$		0			0
$66$	−5.40675	+	5.40675i	−0.665525	+	0.665525i
$67$	−6.92312	+	1.85504i	−0.845794	+	0.226630i	−0.655592	−	0.755115i	$-0.727581\pi$
$67$	−6.92312	+	1.85504i	−0.845794	+	0.226630i	−0.190202	+	0.981745i	$0.560914\pi$
$68$	−15.2660			−1.85127
$69$	−1.45939	+	0.391044i	−0.175690	+	0.0470761i
$70$		0			0
$71$	−6.96450	+	12.0629i	−0.826534	+	1.43160i	0.0742071	+	0.997243i	$0.476357\pi$
$71$	−6.96450	+	12.0629i	−0.826534	+	1.43160i	−0.900741	+	0.434356i	$0.856976\pi$
$72$	−5.79581	−	10.0386i	−0.683042	−	1.18306i
$73$	−6.73477	+	6.73477i	−0.788245	+	0.788245i	−0.981206	−	0.192962i	$-0.938191\pi$
$73$	−6.73477	+	6.73477i	−0.788245	+	0.788245i	0.192962	+	0.981206i	$0.438191\pi$
$74$	10.8122	+	10.0653i	1.25689	+	1.17007i
$75$		0			0
$76$	−5.53521	−	1.48316i	−0.634933	−	0.170130i
$77$	20.2340	−	5.42169i	2.30588	−	0.617859i
$78$	−0.873483	−	3.25988i	−0.0989025	−	0.369109i
$79$	−1.39018	−	5.18821i	−0.156407	−	0.583719i	−0.998981	−	0.0451380i	$-0.985627\pi$
$79$	−1.39018	−	5.18821i	−0.156407	−	0.583719i	0.842574	−	0.538581i	$-0.181039\pi$
$80$		0			0
$81$	2.43622	−	4.21965i	0.270691	−	0.468851i
$82$	−2.27501			−0.251233
$83$	2.38257	−	8.89188i	0.261521	−	0.976010i	−0.702824	−	0.711363i	$-0.748078\pi$
$83$	2.38257	−	8.89188i	0.261521	−	0.976010i	0.964345	−	0.264647i	$-0.0852553\pi$
$84$		−	12.5697i		−	1.37147i
$85$		0			0
$86$	0.952085	+	1.64906i	0.102666	+	0.177823i
$87$	0.705596	−	1.22213i	0.0756478	−	0.131026i
$88$	−20.8412			−2.22168
$89$	−0.159121	+	0.593846i	−0.0168668	+	0.0629476i	−0.973846	−	0.227208i	$-0.927040\pi$
$89$	−0.159121	+	0.593846i	−0.0168668	+	0.0629476i	0.956980	+	0.290155i	$0.0937070\pi$
$90$		0			0
$91$	−2.39300	+	8.93078i	−0.250854	+	0.936200i
$92$	−7.32514	−	4.22917i	−0.763699	−	0.440922i
$93$	4.30691	+	2.48659i	0.446605	+	0.257848i
$94$	−6.01587	+	22.4515i	−0.620490	+	2.31570i
$95$		0			0
$96$	0.174556	−	0.651451i	0.0178155	−	0.0664884i
$97$	−3.08147			−0.312876			−0.156438	−	0.987688i	$-0.550001\pi$
$97$	−3.08147			−0.312876			−0.156438	+	0.987688i	$0.550001\pi$
$98$	−17.5533	+	30.4032i	−1.77315	+	3.07119i
$99$	−5.68747	−	9.85100i	−0.571613	−	0.990062i
$100$		0			0
$101$			4.04535i			0.402527i	0.979537	+	0.201263i	$0.0645047\pi$
$101$			4.04535i			0.402527i	−0.979537	+	0.201263i	$0.935495\pi$
$102$	−1.71398	+	6.39665i	−0.169709	+	0.633362i
$103$	−9.37287			−0.923537			−0.461768	−	0.887001i	$-0.652785\pi$
$103$	−9.37287			−0.923537			−0.461768	+	0.887001i	$0.652785\pi$
$104$	4.59938	−	7.96636i	0.451006	−	0.781165i
$105$		0			0
$106$	−8.04651	−	30.0300i	−0.781546	−	2.91677i
$107$	−0.534381	−	1.99434i	−0.0516605	−	0.192800i	0.935273	−	0.353927i	$-0.115154\pi$
$107$	−0.534381	−	1.99434i	−0.0516605	−	0.192800i	−0.986934	+	0.161127i	$0.948487\pi$
$108$	−14.4565	+	3.87360i	−1.39107	+	0.372737i
$109$	0.683860	+	0.183240i	0.0655019	+	0.0175512i	0.291421	−	0.956595i	$-0.405872\pi$
$109$	0.683860	+	0.183240i	0.0655019	+	0.0175512i	−0.225919	+	0.974146i	$0.572539\pi$
$110$		0			0
$111$	3.58952	−	2.24725i	0.340702	−	0.213299i
$112$	11.1246	−	11.1246i	1.05117	−	1.05117i
$113$	9.09219	+	15.7481i	0.855322	+	1.48146i	0.876346	+	0.481682i	$0.159974\pi$
$113$	9.09219	+	15.7481i	0.855322	+	1.48146i	−0.0210245	+	0.999779i	$0.506693\pi$
$114$	−1.24292	+	2.15280i	−0.116410	+	0.201629i
$115$		0			0
$116$	7.63108	−	2.04474i	0.708528	−	0.189850i
$117$	5.02061			0.464155
$118$	18.0691	−	4.84161i	1.66340	−	0.445706i
$119$	12.8287	−	12.8287i	1.17600	−	1.17600i
$120$		0			0
$121$	−9.45163			−0.859239
$122$	8.57383	+	8.57383i	0.776238	+	0.776238i
$123$	−0.168806	+	0.629992i	−0.0152207	+	0.0568044i
$124$	7.20589	+	26.8927i	0.647108	+	2.41504i
$125$		0			0
$126$	27.3303	+	7.32313i	2.43477	+	0.652396i
$127$	9.28942	+	2.48909i	0.824303	+	0.220871i	0.646227	−	0.763146i	$-0.276346\pi$
$127$	9.28942	+	2.48909i	0.824303	+	0.220871i	0.178076	+	0.984017i	$0.443013\pi$
$128$	17.5562	−	10.1361i	1.55177	−	0.895913i
$129$	0.527299	−	0.141289i	0.0464261	−	0.0124398i
$130$		0			0
$131$	−5.99780	−	1.60711i	−0.524031	−	0.140414i	−0.0129002	−	0.999917i	$-0.504106\pi$
$131$	−5.99780	−	1.60711i	−0.524031	−	0.140414i	−0.511130	+	0.859503i	$0.670773\pi$
$132$	−3.17623	+	11.8538i	−0.276455	+	1.03174i
$133$	5.89783	−	3.40511i	0.511407	−	0.295261i
$134$	−12.3079	+	12.3079i	−1.06324	+	1.06324i
$135$		0			0
$136$	−15.6318	+	9.02505i	−1.34042	+	0.773891i
$137$	6.43284	−	6.43284i	0.549594	−	0.549594i	−0.376729	−	0.926323i	$-0.622951\pi$
$137$	6.43284	−	6.43284i	0.549594	−	0.549594i	0.926323	+	0.376729i	$0.122951\pi$
$138$	−2.59450	+	2.59450i	−0.220859	+	0.220859i
$139$	−2.64940	−	4.58889i	−0.224719	−	0.389225i	0.731516	−	0.681824i	$-0.238813\pi$
$139$	−2.64940	−	4.58889i	−0.224719	−	0.389225i	−0.956235	+	0.292599i	$0.905480\pi$
$140$		0			0
$141$	5.77086	+	3.33181i	0.485994	+	0.280589i
$142$			33.8267i			2.83867i
$143$	4.51341	−	7.81746i	0.377430	−	0.653728i
$144$	−7.39842	−	4.27148i	−0.616535	−	0.355957i
$145$		0			0
$146$	−5.98651	+	22.3420i	−0.495447	+	1.84903i
$147$	7.11675	+	7.11675i	0.586980	+	0.586980i
$148$	23.1054	+	5.31353i	1.89926	+	0.436769i
$149$			15.7541i			1.29062i	0.763919	+	0.645312i	$0.223273\pi$
$149$			15.7541i			1.29062i	−0.763919	+	0.645312i	$0.776727\pi$
$150$		0			0
$151$	7.53981	+	4.35311i	0.613581	+	0.354251i	0.774366	−	0.632738i	$-0.218069\pi$
$151$	7.53981	+	4.35311i	0.613581	+	0.354251i	−0.160784	+	0.986990i	$0.551402\pi$
$152$	−6.54468	+	1.75364i	−0.530844	+	0.142239i
$153$	−8.53174	−	4.92580i	−0.689750	−	0.398227i
$154$	35.9719	−	35.9719i	2.89870	−	2.89870i
$155$		0			0
$156$	−3.83007	−	3.83007i	−0.306651	−	0.306651i
$157$	7.67073	+	2.05537i	0.612191	+	0.164036i	0.551575	−	0.834125i	$-0.314027\pi$
$157$	7.67073	+	2.05537i	0.612191	+	0.164036i	0.0606157	+	0.998161i	$0.480694\pi$
$158$	−9.22356	−	9.22356i	−0.733787	−	0.733787i
$159$	−8.91290			−0.706839
$160$		0			0
$161$	9.70957	−	2.60167i	0.765221	−	0.205040i
$162$		−	11.8328i		−	0.929670i
$163$	−3.54511	−	6.14031i	−0.277674	−	0.480946i	0.693132	−	0.720811i	$-0.256230\pi$
$163$	−3.54511	−	6.14031i	−0.277674	−	0.480946i	−0.970806	+	0.239865i	$0.922897\pi$
$164$	−3.16212	+	1.82565i	−0.246920	+	0.142559i
$165$		0			0
$166$	−5.78610	−	21.5940i	−0.449088	−	1.67602i
$167$	9.20413	−	15.9420i	0.712237	−	1.23363i	−0.251778	−	0.967785i	$-0.581015\pi$
$167$	9.20413	−	15.9420i	0.712237	−	1.23363i	0.964015	−	0.265846i	$-0.0856513\pi$
$168$	−7.43106	−	12.8710i	−0.573318	−	0.993017i
$169$	−4.50790	−	7.80791i	−0.346761	−	0.600608i
$170$		0			0
$171$	−2.61491	−	2.61491i	−0.199967	−	0.199967i
$172$	2.64667	+	1.52806i	0.201807	+	0.116513i
$173$	−17.0711	−	4.57418i	−1.29789	−	0.347768i	−0.457237	−	0.889345i	$-0.651161\pi$
$173$	−17.0711	−	4.57418i	−1.29789	−	0.347768i	−0.840652	+	0.541576i	$0.817828\pi$
$174$		−	3.42709i		−	0.259807i
$175$		0			0
$176$	−13.3020	+	7.67992i	−1.00268	+	0.578896i
$177$		−	5.36292i		−	0.403102i
$178$	0.386426	+	1.44216i	0.0289639	+	0.108095i
$179$	4.89803	+	4.89803i	0.366096	+	0.366096i	0.866051	−	0.499955i	$-0.166650\pi$
$179$	4.89803	+	4.89803i	0.366096	+	0.366096i	−0.499955	+	0.866051i	$0.666650\pi$
$180$		0			0
$181$	−4.02887	+	6.97821i	−0.299463	+	0.518686i	−0.976013	−	0.217711i	$-0.930141\pi$
$181$	−4.02887	+	6.97821i	−0.299463	+	0.518686i	0.676550	+	0.736397i	$0.263474\pi$
$182$	5.81141	+	21.6885i	0.430771	+	1.60766i
$183$	3.01043	−	1.73807i	0.222537	−	0.128482i
$184$	−10.0009			−0.737277
$185$		0			0
$186$	12.0774			0.885560
$187$	−15.3397	+	8.85636i	−1.12175	+	0.647641i
$188$	9.65523	+	36.0338i	0.704180	+	2.62804i
$189$	8.89323	−	15.4035i	0.646887	−	1.12044i
$190$		0			0
$191$	−10.8190	−	10.8190i	−0.782839	−	0.782839i	0.197470	−	0.980309i	$-0.436727\pi$
$191$	−10.8190	−	10.8190i	−0.782839	−	0.782839i	−0.980309	+	0.197470i	$0.936727\pi$
$192$	−1.64795	−	6.15024i	−0.118931	−	0.443856i
$193$		−	15.5270i		−	1.11766i	−0.829284	−	0.558828i	$-0.811251\pi$
$193$		−	15.5270i		−	1.11766i	0.829284	−	0.558828i	$-0.188749\pi$
$194$	−6.48079	+	3.74169i	−0.465294	+	0.268638i
$195$		0			0
$196$			56.3447i			4.02462i
$197$	−4.72326	−	1.26560i	−0.336519	−	0.0901699i	0.0866027	−	0.996243i	$-0.472399\pi$
$197$	−4.72326	−	1.26560i	−0.336519	−	0.0901699i	−0.423121	+	0.906073i	$0.639066\pi$
$198$	−23.9232	−	13.8121i	−1.70015	−	0.981582i
$199$	7.16620	+	7.16620i	0.507999	+	0.507999i	0.913912	−	0.405913i	$-0.133046\pi$
$199$	7.16620	+	7.16620i	0.507999	+	0.507999i	−0.405913	+	0.913912i	$0.633046\pi$
$200$		0			0
$201$	2.49503	+	4.32152i	0.175986	+	0.304816i
$202$	4.91208	+	8.50797i	0.345613	+	0.598619i
$203$	−4.69443	+	8.13100i	−0.329485	+	0.570684i
$204$	2.75086	+	10.2664i	0.192599	+	0.718789i
$205$		0			0
$206$	−19.7126	+	11.3811i	−1.37344	+	0.792956i
$207$	−2.72921	−	4.72713i	−0.189693	−	0.328558i
$208$		−	6.77944i		−	0.470070i
$209$	−6.42236	+	1.72087i	−0.444244	+	0.119035i
$210$		0			0
$211$	−8.64469			−0.595125			−0.297562	−	0.954702i	$-0.596174\pi$
$211$	−8.64469			−0.595125			−0.297562	+	0.954702i	$0.596174\pi$
$212$	−35.2826	−	35.2826i	−2.42322	−	2.42322i
$213$	9.36723	+	2.50994i	0.641832	+	0.171978i
$214$	−3.54551	−	3.54551i	−0.242366	−	0.242366i
$215$		0			0
$216$	−12.5129	+	12.5129i	−0.851395	+	0.851395i
$217$	−28.6545	−	16.5437i	−1.94519	−	1.12306i
$218$	1.66076	−	0.444999i	0.112481	−	0.0301392i
$219$	5.74269	+	3.31555i	0.388055	+	0.224044i
$220$		0			0
$221$		−	7.81794i		−	0.525891i
$222$	4.82058	−	9.08490i	0.323536	−	0.609739i
$223$	15.4450	+	15.4450i	1.03427	+	1.03427i	0.999391	+	0.0348829i	$0.0111058\pi$
$223$	15.4450	+	15.4450i	1.03427	+	1.03427i	0.0348829	+	0.999391i	$0.488894\pi$
$224$	−1.16135	+	4.33420i	−0.0775956	+	0.289591i
$225$		0			0
$226$	38.2445	+	22.0805i	2.54399	+	1.46877i
$227$	−8.32107	+	14.4125i	−0.552289	+	0.956593i	0.445820	+	0.895123i	$0.352912\pi$
$227$	−8.32107	+	14.4125i	−0.552289	+	0.956593i	−0.998109	+	0.0614699i	$0.980421\pi$
$228$			3.98968i			0.264223i
$229$	15.9930	+	9.23358i	1.05685	+	0.610172i	0.924559	−	0.381039i	$-0.124434\pi$
$229$	15.9930	+	9.23358i	1.05685	+	0.610172i	0.132290	+	0.991211i	$0.457767\pi$
$230$		0			0
$231$	−7.29216	−	12.6304i	−0.479789	−	0.831019i
$232$	6.60513	−	6.60513i	0.433648	−	0.433648i
$233$	−13.8266	+	13.8266i	−0.905809	+	0.905809i	−0.995931	−	0.0901215i	$-0.971274\pi$
$233$	−13.8266	+	13.8266i	−0.905809	+	0.905809i	0.0901215	+	0.995931i	$0.471274\pi$
$234$	10.5591	−	6.09630i	0.690270	−	0.398528i
$235$		0			0
$236$	21.2296	−	21.2296i	1.38193	−	1.38193i
$237$	−3.23856	+	1.86978i	−0.210367	+	0.121455i
$238$	11.4033	−	42.5579i	0.739169	−	2.75862i
$239$	−23.9019	−	6.40449i	−1.54608	−	0.414272i	−0.617858	−	0.786290i	$-0.711999\pi$
$239$	−23.9019	−	6.40449i	−1.54608	−	0.414272i	−0.928226	+	0.372018i	$0.878666\pi$
$240$		0			0
$241$	5.11826	−	1.37143i	0.329696	−	0.0883419i	−0.0901738	−	0.995926i	$-0.528742\pi$
$241$	5.11826	−	1.37143i	0.329696	−	0.0883419i	0.419870	+	0.907584i	$0.362076\pi$
$242$	−19.8782	+	11.4767i	−1.27782	+	0.737749i
$243$	−14.4037	−	3.85947i	−0.924001	−	0.247585i
$244$	18.7974	+	5.03675i	1.20338	+	0.322445i
$245$		0			0
$246$	0.409946	+	1.52994i	0.0261372	+	0.0975454i
$247$	0.759546	−	2.83466i	0.0483287	−	0.180365i
$248$	23.2772	+	23.2772i	1.47810	+	1.47810i
$249$	−6.40910			−0.406160
$250$		0			0
$251$	−19.4085	+	19.4085i	−1.22506	+	1.22506i	−0.259243	+	0.965812i	$0.583473\pi$
$251$	−19.4085	+	19.4085i	−1.22506	+	1.22506i	−0.965812	+	0.259243i	$0.916527\pi$
$252$	43.8640	−	11.7533i	2.76317	−	0.740390i
$253$	−9.81398			−0.617000
$254$	22.5594	−	6.04478i	1.41551	−	0.379283i
$255$		0			0
$256$	15.4703	−	26.7953i	0.966891	−	1.67470i
$257$	−5.78096	−	10.0129i	−0.360607	−	0.624589i	0.627454	−	0.778653i	$-0.284097\pi$
$257$	−5.78096	−	10.0129i	−0.360607	−	0.624589i	−0.988061	+	0.154065i	$0.950764\pi$
$258$	0.937429	−	0.937429i	0.0583618	−	0.0583618i
$259$	−23.8816	+	14.9513i	−1.48393	+	0.929028i
$260$		0			0
$261$	4.92456	+	1.31953i	0.304823	+	0.0816770i
$262$	−14.5657	+	3.90287i	−0.899874	+	0.241120i
$263$	1.34811	+	5.03120i	0.0831277	+	0.310237i	0.994953	−	0.100341i	$-0.0319935\pi$
$263$	1.34811	+	5.03120i	0.0831277	+	0.310237i	−0.911825	+	0.410578i	$0.865327\pi$
$264$	3.75548	+	14.0157i	0.231134	+	0.862604i
$265$		0			0
$266$	8.26935	−	14.3229i	0.507026	−	0.878196i
$267$	0.428034			0.0261952
$268$	−7.23033	+	26.9840i	−0.441663	+	1.64831i
$269$		−	15.6120i		−	0.951881i	−0.879477	−	0.475941i	$-0.842108\pi$
$269$		−	15.6120i		−	0.951881i	0.879477	−	0.475941i	$-0.157892\pi$
$270$		0			0
$271$	−1.95093	−	3.37911i	−0.118510	−	0.205266i	0.800667	−	0.599109i	$-0.204479\pi$
$271$	−1.95093	−	3.37911i	−0.118510	−	0.205266i	−0.919178	+	0.393843i	$0.871145\pi$
$272$	−6.65142	+	11.5206i	−0.403301	+	0.698538i
$273$	6.43714			0.389594
$274$	5.71812	−	21.3403i	0.345444	−	1.28922i
$275$		0			0
$276$	−1.52415	+	5.68822i	−0.0917433	+	0.342391i
$277$	0.852343	+	0.492101i	0.0512123	+	0.0295675i	0.525388	−	0.850863i	$-0.323920\pi$
$277$	0.852343	+	0.492101i	0.0512123	+	0.0295675i	−0.474175	+	0.880430i	$0.657254\pi$
$278$	−11.1442	−	6.43409i	−0.668383	−	0.385891i
$279$	−4.65017	+	17.3547i	−0.278399	+	1.03900i
$280$		0			0
$281$	4.53841	−	16.9376i	0.270739	−	1.01041i	−0.687904	−	0.725801i	$-0.741469\pi$
$281$	4.53841	−	16.9376i	0.270739	−	1.01041i	0.958643	−	0.284610i	$-0.0918641\pi$
$282$	16.1827			0.963663
$283$	3.70198	−	6.41202i	0.220060	−	0.381155i	−0.734766	−	0.678321i	$-0.762708\pi$
$283$	3.70198	−	6.41202i	0.220060	−	0.381155i	0.954826	+	0.297166i	$0.0960414\pi$
$284$	27.1453	+	47.0170i	1.61077	+	2.78994i
$285$		0			0
$286$		−	21.9217i		−	1.29626i
$287$	1.12309	−	4.19143i	0.0662939	−	0.247412i
$288$	2.43655			0.143575
$289$	0.829699	−	1.43708i	0.0488058	−	0.0845341i
$290$		0			0
$291$	0.555266	+	2.07228i	0.0325503	+	0.121479i
$292$	9.60810	+	35.8579i	0.562272	+	2.09843i
$293$	8.20949	−	2.19973i	0.479603	−	0.128509i	−0.0109145	−	0.999940i	$-0.503474\pi$
$293$	8.20949	−	2.19973i	0.479603	−	0.128509i	0.490518	+	0.871431i	$0.336808\pi$
$294$	23.6092	+	6.32606i	1.37691	+	0.368943i
$295$		0			0
$296$	26.8004	−	8.21875i	1.55774	−	0.477705i
$297$	−12.2790	+	12.2790i	−0.712501	+	0.712501i
$298$	19.1295	+	33.1332i	1.10814	+	1.91936i
$299$	2.16582	−	3.75131i	0.125253	−	0.216944i
$300$		0			0
$301$	−3.50820	+	0.940020i	−0.202209	+	0.0541818i
$302$	21.1432			1.21665
$303$	2.72049	−	0.728953i	0.156288	−	0.0418772i
$304$	−3.53097	+	3.53097i	−0.202515	+	0.202515i
$305$		0			0
$306$	−23.9247			−1.36768
$307$	−6.02262	−	6.02262i	−0.343729	−	0.343729i	0.514038	−	0.857767i	$-0.328149\pi$
$307$	−6.02262	−	6.02262i	−0.343729	−	0.343729i	−0.857767	+	0.514038i	$0.828149\pi$
$308$	21.1319	−	78.8654i	1.20410	−	4.49377i
$309$	1.68895	+	6.30324i	0.0960809	+	0.358579i
$310$		0			0
$311$	−18.4702	−	4.94907i	−1.04735	−	0.280636i	−0.306192	−	0.951970i	$-0.599055\pi$
$311$	−18.4702	−	4.94907i	−1.04735	−	0.280636i	−0.741155	+	0.671334i	$0.765722\pi$
$312$	−6.18615	−	1.65757i	−0.350222	−	0.0938416i
$313$	−5.57898	+	3.22103i	−0.315343	+	0.182063i	−0.649315	−	0.760520i	$-0.724944\pi$
$313$	−5.57898	+	3.22103i	−0.315343	+	0.182063i	0.333972	+	0.942583i	$0.391611\pi$
$314$	18.6284	−	4.99148i	1.05126	−	0.281685i
$315$		0			0
$316$	−20.2219	−	5.41843i	−1.13757	−	0.304811i
$317$	5.17746	−	19.3226i	0.290795	−	1.08526i	−0.653704	−	0.756750i	$-0.726786\pi$
$317$	5.17746	−	19.3226i	0.290795	−	1.08526i	0.944499	−	0.328513i	$-0.106547\pi$
$318$	−18.7452	+	10.8225i	−1.05118	+	0.606898i
$319$	6.48168	−	6.48168i	0.362904	−	0.362904i
$320$		0			0
$321$	−1.24489	+	0.718740i	−0.0694832	+	0.0401162i
$322$	17.2616	−	17.2616i	0.961951	−	0.961951i
$323$	−4.07186	+	4.07186i	−0.226564	+	0.226564i
$324$	−9.49555	−	16.4468i	−0.527531	−	0.913710i
$325$		0			0
$326$	−14.9118	−	8.60933i	−0.825888	−	0.476827i
$327$		−	0.492914i		−	0.0272582i
$328$	−2.15860	+	3.73880i	−0.119189	+	0.206441i
$329$	−38.3944	−	22.1670i	−2.11675	−	1.22211i
$330$		0			0
$331$	−3.37049	+	12.5789i	−0.185259	+	0.691397i	0.809316	+	0.587374i	$0.199838\pi$
$331$	−3.37049	+	12.5789i	−0.185259	+	0.691397i	−0.994575	+	0.104023i	$0.966829\pi$
$332$	−25.3711	−	25.3711i	−1.39242	−	1.39242i
$333$	11.1985	+	10.4249i	0.613674	+	0.571281i
$334$		−	44.7047i		−	2.44613i
$335$		0			0
$336$	−9.48584	−	5.47665i	−0.517495	−	0.298776i
$337$	24.7331	−	6.62721i	1.34730	−	0.361007i	0.488161	−	0.872754i	$-0.337668\pi$
$337$	24.7331	−	6.62721i	1.34730	−	0.361007i	0.859137	+	0.511746i	$0.171001\pi$
$338$	−18.9616	−	10.9475i	−1.03137	−	0.595464i
$339$	8.95223	−	8.95223i	0.486218	−	0.486218i
$340$		0			0
$341$	22.8421	+	22.8421i	1.23697	+	1.23697i
$342$	−8.67473	−	2.32439i	−0.469076	−	0.125688i
$343$	−24.4213	−	24.4213i	−1.31863	−	1.31863i
$344$	3.61347			0.194825
$345$		0			0
$346$	−41.4572	+	11.1084i	−2.22876	+	0.597193i
$347$			2.09128i			0.112266i	0.998423	+	0.0561330i	$0.0178771\pi$
$347$			2.09128i			0.112266i	−0.998423	+	0.0561330i	$0.982123\pi$
$348$	−2.75017	−	4.76344i	−0.147425	−	0.255347i
$349$	5.38379	−	3.10833i	0.288187	−	0.166385i	−0.348937	−	0.937146i	$-0.613457\pi$
$349$	5.38379	−	3.10833i	0.288187	−	0.166385i	0.637124	+	0.770761i	$0.280124\pi$
$350$		0			0
$351$	−1.98373	−	7.40337i	−0.105883	−	0.395163i
$352$	2.19040	−	3.79389i	0.116749	−	0.202215i
$353$	−3.63418	−	6.29458i	−0.193428	−	0.335027i	0.752956	−	0.658071i	$-0.228627\pi$
$353$	−3.63418	−	6.29458i	−0.193428	−	0.335027i	−0.946384	+	0.323044i	$0.895294\pi$
$354$	−6.51195	−	11.2790i	−0.346106	−	0.599474i
$355$		0			0
$356$	1.69441	+	1.69441i	0.0898037	+	0.0898037i
$357$	−10.9389	−	6.31558i	−0.578949	−	0.334256i
$358$	16.2488	+	4.35384i	0.858774	+	0.230108i
$359$			11.8142i			0.623528i	0.950160	+	0.311764i	$0.100920\pi$
$359$			11.8142i			0.623528i	−0.950160	+	0.311764i	$0.899080\pi$
$360$		0			0
$361$	14.5825	−	8.41920i	0.767499	−	0.443116i
$362$			19.5683i			1.02849i
$363$	1.70314	+	6.35620i	0.0893916	+	0.333614i
$364$	25.4821	+	25.4821i	1.33562	+	1.33562i
$365$		0			0
$366$	4.22092	−	7.31085i	0.220631	−	0.382144i
$367$	0.642482	+	2.39777i	0.0335373	+	0.125163i	0.980665	−	0.195694i	$-0.0626959\pi$
$367$	0.642482	+	2.39777i	0.0335373	+	0.125163i	−0.947128	+	0.320857i	$0.896029\pi$
$368$	−6.38315	+	3.68531i	−0.332745	+	0.192110i
$369$	−2.35629			−0.122664
$370$		0			0
$371$	59.2989			3.07864
$372$	16.7869	−	9.69189i	0.870358	−	0.502501i
$373$	−2.41009	−	8.99456i	−0.124790	−	0.465721i	0.875043	−	0.484046i	$-0.160833\pi$
$373$	−2.41009	−	8.99456i	−0.124790	−	0.465721i	−0.999832	+	0.0183252i	$0.994167\pi$
$374$	−21.5078	+	37.2525i	−1.11214	+	1.92628i
$375$		0			0
$376$	31.1893	+	31.1893i	1.60847	+	1.60847i
$377$	1.04714	+	3.90799i	0.0539305	+	0.201272i
$378$		−	43.1946i		−	2.22169i
$379$	7.13805	−	4.12116i	0.366657	−	0.211690i	−0.305340	−	0.952243i	$-0.598770\pi$
$379$	7.13805	−	4.12116i	0.366657	−	0.211690i	0.671997	+	0.740554i	$0.265437\pi$
$380$		0			0
$381$		−	6.69564i		−	0.343028i
$382$	−35.8912	−	9.61701i	−1.83635	−	0.492049i
$383$	21.8189	+	12.5971i	1.11489	+	0.643684i	0.940092	−	0.340920i	$-0.110738\pi$
$383$	21.8189	+	12.5971i	1.11489	+	0.643684i	0.174801	+	0.984604i	$0.444072\pi$
$384$	−9.98007	−	9.98007i	−0.509293	−	0.509293i
$385$		0			0
$386$	−18.8537	−	32.6555i	−0.959627	−	1.66212i
$387$	0.986101	+	1.70798i	0.0501263	+	0.0868214i
$388$	−6.00526	+	10.4014i	−0.304871	+	0.528052i
$389$	0.855458	+	3.19261i	0.0433734	+	0.161872i	0.984216	−	0.176973i	$-0.0566305\pi$
$389$	0.855458	+	3.19261i	0.0433734	+	0.161872i	−0.940842	+	0.338845i	$0.889964\pi$
$390$		0			0
$391$	−7.36094	+	4.24984i	−0.372259	+	0.214924i
$392$	33.3102	+	57.6950i	1.68242	+	2.91404i
$393$			4.32311i			0.218072i
$394$	−11.4705	+	3.07351i	−0.577875	+	0.154841i
$395$		0			0
$396$	−44.3357			−2.22795
$397$	25.8402	+	25.8402i	1.29688	+	1.29688i	0.930442	+	0.366439i	$0.119423\pi$
$397$	25.8402	+	25.8402i	1.29688	+	1.29688i	0.366439	+	0.930442i	$0.380577\pi$
$398$	23.7732	+	6.37001i	1.19164	+	0.319300i
$399$	−3.35269	−	3.35269i	−0.167845	−	0.167845i
$400$		0			0
$401$	−3.57151	+	3.57151i	−0.178353	+	0.178353i	−0.790637	−	0.612285i	$-0.790251\pi$
$401$	−3.57151	+	3.57151i	−0.178353	+	0.178353i	0.612285	+	0.790637i	$0.290251\pi$
$402$	10.4948	+	6.05920i	0.523435	+	0.302206i
$403$	−13.7722	+	3.69024i	−0.686040	+	0.183824i
$404$	13.6550	+	7.88369i	0.679359	+	0.392228i
$405$		0			0
$406$			22.8010i			1.13159i
$407$	26.2995	−	8.06513i	1.30362	−	0.399774i
$408$	8.88611	+	8.88611i	0.439928	+	0.439928i
$409$	2.25114	−	8.40137i	0.111312	−	0.415421i	−0.887673	−	0.460475i	$-0.847679\pi$
$409$	2.25114	−	8.40137i	0.111312	−	0.415421i	0.998985	+	0.0450536i	$0.0143459\pi$
$410$		0			0
$411$	−5.48524	−	3.16690i	−0.270567	−	0.156212i
$412$	−18.2661	+	31.6379i	−0.899908	+	1.55869i
$413$			35.6803i			1.75571i
$414$	−11.4799	−	6.62791i	−0.564205	−	0.325744i
$415$		0			0
$416$	0.966788	+	1.67453i	0.0474007	+	0.0821004i
$417$	−2.60861	+	2.60861i	−0.127744	+	0.127744i
$418$	−11.4176	+	11.4176i	−0.558454	+	0.558454i
$419$	17.6791	−	10.2071i	0.863682	−	0.498647i	−0.00156147	−	0.999999i	$-0.500497\pi$
$419$	17.6791	−	10.2071i	0.863682	−	0.498647i	0.865244	+	0.501352i	$0.167164\pi$
$420$		0			0
$421$	25.1734	−	25.1734i	1.22688	−	1.22688i	0.261738	−	0.965139i	$-0.415704\pi$
$421$	25.1734	−	25.1734i	1.22688	−	1.22688i	0.965139	−	0.261738i	$-0.0842956\pi$
$422$	−18.1811	+	10.4969i	−0.885041	+	0.510979i
$423$	−6.23081	+	23.2537i	−0.302952	+	1.13063i
$424$	−56.9867	−	15.2695i	−2.76752	−	0.741555i
$425$		0			0
$426$	22.7484	−	6.09542i	1.10216	−	0.295324i
$427$	−20.0288	+	11.5636i	−0.969263	+	0.559604i
$428$	−7.77324	−	2.08283i	−0.375734	−	0.100678i
$429$	−6.07052	−	1.62659i	−0.293088	−	0.0785326i
$430$		0			0
$431$	−3.95349	−	14.7546i	−0.190433	−	0.710706i	−0.993402	−	0.114685i	$-0.963414\pi$
$431$	−3.95349	−	14.7546i	−0.190433	−	0.710706i	0.802969	−	0.596021i	$-0.203252\pi$
$432$	−3.37547	+	12.5974i	−0.162402	+	0.606093i
$433$	−10.0393	−	10.0393i	−0.482460	−	0.482460i	0.423457	−	0.905916i	$-0.360817\pi$
$433$	−10.0393	−	10.0393i	−0.482460	−	0.482460i	−0.905916	+	0.423457i	$0.860817\pi$
$434$	−80.3530			−3.85707
$435$		0			0
$436$	1.95125	−	1.95125i	0.0934478	−	0.0934478i
$437$	−3.08185	+	0.825780i	−0.147425	+	0.0395024i
$438$	16.1037			0.769463
$439$	−15.6819	+	4.20195i	−0.748455	+	0.200548i	−0.612833	−	0.790213i	$-0.709970\pi$
$439$	−15.6819	+	4.20195i	−0.748455	+	0.200548i	−0.135622	+	0.990761i	$0.543303\pi$
$440$		0			0
$441$	−18.1805	+	31.4895i	−0.865737	+	1.49950i
$442$	−9.49297	−	16.4423i	−0.451534	−	0.782080i
$443$	0.940024	−	0.940024i	0.0446619	−	0.0446619i	−0.684423	−	0.729085i	$-0.739946\pi$
$443$	0.940024	−	0.940024i	0.0446619	−	0.0446619i	0.729085	+	0.684423i	$0.239946\pi$
$444$	−0.590155	−	16.4958i	−0.0280075	−	0.782858i
$445$		0			0
$446$	51.2374	+	13.7290i	2.42616	+	0.650088i
$447$	10.5946	−	2.83881i	0.501107	−	0.134271i
$448$	10.9641	+	40.9185i	0.518004	+	1.93322i
$449$	−8.59716	−	32.0850i	−0.405725	−	1.51419i	−0.802715	−	0.596363i	$-0.796612\pi$
$449$	−8.59716	−	32.0850i	−0.405725	−	1.51419i	0.396990	−	0.917823i	$-0.370055\pi$
$450$		0			0
$451$	−2.11825	+	3.66892i	−0.0997445	+	0.172763i
$452$	70.8766			3.33375
$453$	1.56882	−	5.85492i	0.0737097	−	0.275088i
$454$			40.4156i			1.89680i
$455$		0			0
$456$	2.35864	+	4.08529i	0.110454	+	0.191311i
$457$	11.4236	−	19.7863i	0.534374	−	0.925562i	−0.464820	−	0.885405i	$-0.653881\pi$
$457$	11.4236	−	19.7863i	0.534374	−	0.925562i	0.999193	−	0.0401569i	$-0.0127858\pi$
$458$	44.8477			2.09560
$459$	−3.89253	+	14.5271i	−0.181688	+	0.678068i
$460$		0			0
$461$	8.04621	−	30.0289i	0.374750	−	1.39858i	−0.478961	−	0.877836i	$-0.658986\pi$
$461$	8.04621	−	30.0289i	0.374750	−	1.39858i	0.853710	−	0.520748i	$-0.174347\pi$
$462$	−30.6730	−	17.7091i	−1.42704	−	0.823901i
$463$	−21.3575	−	12.3308i	−0.992567	−	0.573059i	−0.0865265	−	0.996250i	$-0.527577\pi$
$463$	−21.3575	−	12.3308i	−0.992567	−	0.573059i	−0.906041	+	0.423191i	$0.860910\pi$
$464$	1.78179	−	6.64975i	0.0827177	−	0.308707i
$465$		0			0
$466$	−12.2904	+	45.8684i	−0.569341	+	2.12481i
$467$	−27.3481			−1.26552			−0.632761	−	0.774348i	$-0.718078\pi$
$467$	−27.3481			−1.26552			−0.632761	+	0.774348i	$0.718078\pi$
$468$	9.78431	−	16.9469i	0.452280	−	0.783372i
$469$	−16.5998	−	28.7517i	−0.766508	−	1.32763i
$470$		0			0
$471$		−	5.52892i		−	0.254759i
$472$	9.18773	−	34.2891i	0.422900	−	1.57828i
$473$	3.54593			0.163042
$474$	−4.54079	+	7.86487i	−0.208565	+	0.361245i
$475$		0			0
$476$	−18.3019	−	68.3036i	−0.838866	−	3.13069i
$477$	−8.33400	−	31.1029i	−0.381588	−	1.42410i
$478$	−58.0459	+	15.5534i	−2.65496	+	0.711394i
$479$	20.7905	+	5.57080i	0.949943	+	0.254537i	0.700338	−	0.713811i	$-0.253033\pi$
$479$	20.7905	+	5.57080i	0.949943	+	0.254537i	0.249605	+	0.968348i	$0.419699\pi$
$480$		0			0
$481$	−2.72113	+	11.8326i	−0.124073	+	0.539521i
$482$	9.09921	−	9.09921i	0.414458	−	0.414458i
$483$	−3.49924	−	6.06086i	−0.159221	−	0.275779i
$484$	−18.4196	+	31.9037i	−0.837255	+	1.45017i
$485$		0			0
$486$	−34.9796	+	9.37277i	−1.58671	+	0.425157i
$487$	−16.0414			−0.726904			−0.363452	−	0.931613i	$-0.618402\pi$
$487$	−16.0414			−0.726904			−0.363452	+	0.931613i	$0.618402\pi$
$488$	22.2255	−	5.95531i	1.00610	−	0.269584i
$489$	−3.49054	+	3.49054i	−0.157847	+	0.157847i
$490$		0			0
$491$	29.9068			1.34967			0.674837	−	0.737967i	$-0.264214\pi$
$491$	29.9068			1.34967			0.674837	+	0.737967i	$0.264214\pi$
$492$	1.79755	+	1.79755i	0.0810396	+	0.0810396i
$493$	2.05473	−	7.66837i	0.0925406	−	0.345366i
$494$	−1.84456	−	6.88401i	−0.0829908	−	0.309726i
$495$		0			0
$496$	23.4344	+	6.27923i	1.05224	+	0.281946i
$497$	−62.3216	−	16.6990i	−2.79551	−	0.749053i
$498$	−13.4793	+	7.78228i	−0.604022	+	0.348732i
$499$	−28.8212	+	7.72260i	−1.29021	+	0.345711i	−0.837741	−	0.546068i	$-0.816124\pi$
$499$	−28.8212	+	7.72260i	−1.29021	+	0.345711i	−0.452471	+	0.891779i	$0.649457\pi$
$500$		0			0
$501$	−12.3795	−	3.31709i	−0.553077	−	0.148196i
$502$	−17.2522	+	64.3860i	−0.770002	+	2.87369i
$503$	3.06178	−	1.76772i	0.136518	−	0.0788188i	−0.430185	−	0.902741i	$-0.641552\pi$
$503$	3.06178	−	1.76772i	0.136518	−	0.0788188i	0.566704	+	0.823922i	$0.308218\pi$
$504$	37.9668	−	37.9668i	1.69117	−	1.69117i
$505$		0			0
$506$	−20.6403	+	11.9167i	−0.917573	+	0.529761i
$507$	−4.43850	+	4.43850i	−0.197121	+	0.197121i
$508$	26.5054	−	26.5054i	1.17598	−	1.17598i
$509$	−2.44230	−	4.23019i	−0.108253	−	0.187500i	0.806810	−	0.590812i	$-0.201192\pi$
$509$	−2.44230	−	4.23019i	−0.108253	−	0.187500i	−0.915063	+	0.403312i	$0.867859\pi$
$510$		0			0
$511$	−38.2070	−	22.0588i	−1.69018	−	0.975825i
$512$		−	34.5949i		−	1.52890i
$513$	−2.82274	+	4.88913i	−0.124627	+	0.215861i
$514$	−24.3165	−	14.0391i	−1.07255	−	0.619239i
$515$		0			0
$516$	0.550698	−	2.05523i	0.0242431	−	0.0904766i
$517$	30.6063	+	30.6063i	1.34607	+	1.34607i
$518$	−32.0720	+	60.4432i	−1.40916	+	2.65572i
$519$			12.3045i			0.540108i
$520$		0			0
$521$	14.3610	+	8.29133i	0.629167	+	0.363250i	0.780430	−	0.625244i	$-0.215000\pi$
$521$	14.3610	+	8.29133i	0.629167	+	0.363250i	−0.151262	+	0.988494i	$0.548334\pi$
$522$	11.9593	−	3.20450i	0.523446	−	0.140257i
$523$	−36.8876	−	21.2971i	−1.61298	−	0.931255i	−0.988675	−	0.150076i	$-0.952048\pi$
$523$	−36.8876	−	21.2971i	−1.61298	−	0.931255i	−0.624306	−	0.781180i	$-0.714618\pi$
$524$	−17.1134	+	17.1134i	−0.747604	+	0.747604i
$525$		0			0
$526$	8.94443	+	8.94443i	0.389996	+	0.389996i
$527$	27.0242	+	7.24110i	1.17719	+	0.315427i
$528$	7.56170	+	7.56170i	0.329081	+	0.329081i
$529$	18.2906			0.795245
$530$		0			0
$531$	18.7147	−	5.01459i	0.812149	−	0.217615i
$532$		−	26.5439i		−	1.15083i
$533$	−0.934941	−	1.61937i	−0.0404968	−	0.0701425i
$534$	0.900219	−	0.519742i	0.0389563	−	0.0224914i
$535$		0			0
$536$	8.54895	+	31.9051i	0.369258	+	1.37809i
$537$	2.41132	−	4.17652i	0.104056	−	0.180230i
$538$	−18.9570	−	32.8344i	−0.817293	−	1.41559i
$539$	32.6876	+	56.6166i	1.40796	+	2.43865i
$540$		0			0
$541$	−23.0072	−	23.0072i	−0.989156	−	0.989156i	0.0107855	−	0.999942i	$-0.496567\pi$
$541$	−23.0072	−	23.0072i	−0.989156	−	0.989156i	−0.999942	+	0.0107855i	$0.996567\pi$
$542$	−8.20619	−	4.73785i	−0.352486	−	0.203508i
$543$	5.41882	+	1.45197i	0.232544	+	0.0623099i
$544$		−	3.79412i		−	0.162672i
$545$		0			0
$546$	13.5383	−	7.81633i	0.579385	−	0.334508i
$547$		−	4.03346i		−	0.172458i	−0.996275	−	0.0862292i	$-0.972518\pi$
$547$		−	4.03346i		−	0.172458i	0.996275	−	0.0862292i	$-0.0274817\pi$
$548$	−9.17736	−	34.2504i	−0.392037	−	1.46310i
$549$	8.88015	+	8.88015i	0.378996	+	0.378996i
$550$		0			0
$551$	1.49003	−	2.58081i	0.0634774	−	0.109946i
$552$	1.80212	+	6.72560i	0.0767032	+	0.286260i
$553$	21.5466	−	12.4399i	0.916255	−	0.529000i
$554$	2.39014			0.101547
$555$		0			0
$556$	−20.6529			−0.875878
$557$	6.64973	−	3.83923i	0.281758	−	0.162673i	−0.352461	−	0.935827i	$-0.614655\pi$
$557$	6.64973	−	3.83923i	0.281758	−	0.162673i	0.634219	+	0.773153i	$0.281322\pi$
$558$	11.2930	+	42.1460i	0.478070	+	1.78418i
$559$	−0.782540	+	1.35540i	−0.0330979	+	0.0573273i
$560$		0			0
$561$	8.72002	+	8.72002i	0.368160	+	0.368160i
$562$	−11.0216	−	41.1331i	−0.464917	−	1.73509i
$563$		−	9.23724i		−	0.389303i	−0.980872	−	0.194652i	$-0.937642\pi$
$563$		−	9.23724i		−	0.389303i	0.980872	−	0.194652i	$-0.0623576\pi$
$564$	22.4929	−	12.9863i	0.947120	−	0.546820i
$565$		0			0
$566$		−	17.9806i		−	0.755780i
$567$	21.8004	+	5.84141i	0.915532	+	0.245316i
$568$	55.5915	+	32.0958i	2.33257	+	1.34671i
$569$	10.2931	+	10.2931i	0.431510	+	0.431510i	0.889142	−	0.457632i	$-0.151302\pi$
$569$	10.2931	+	10.2931i	0.431510	+	0.431510i	−0.457632	+	0.889142i	$0.651302\pi$
$570$		0			0
$571$	17.8689	+	30.9499i	0.747792	+	1.29521i	0.948879	+	0.315640i	$0.102219\pi$
$571$	17.8689	+	30.9499i	0.747792	+	1.29521i	−0.201087	+	0.979573i	$0.564447\pi$
$572$	−17.5917	−	30.4698i	−0.735547	−	1.27401i
$573$	−5.32625	+	9.22533i	−0.222507	+	0.385394i
$574$	−2.72743	−	10.1789i	−0.113841	−	0.424860i
$575$		0			0
$576$	19.9213	−	11.5016i	0.830053	−	0.479232i
$577$	−1.69903	−	2.94280i	−0.0707315	−	0.122510i	0.828491	−	0.560003i	$-0.189200\pi$
$577$	−1.69903	−	2.94280i	−0.0707315	−	0.122510i	−0.899222	+	0.437492i	$0.855867\pi$
$578$		−	4.02986i		−	0.167620i
$579$	−10.4419	+	2.79789i	−0.433949	+	0.116276i
$580$		0			0
$581$	42.6407			1.76903
$582$	3.68409	+	3.68409i	0.152710	+	0.152710i
$583$	−55.9216	−	14.9841i	−2.31603	−	0.620580i
$584$	31.0371	+	31.0371i	1.28432	+	1.28432i
$585$		0			0
$586$	14.5948	−	14.5948i	0.602904	−	0.602904i
$587$	2.31742	+	1.33796i	0.0956502	+	0.0552237i	0.547062	−	0.837092i	$-0.315746\pi$
$587$	2.31742	+	1.33796i	0.0956502	+	0.0552237i	−0.451412	+	0.892316i	$0.649079\pi$
$588$	37.8918	−	10.1531i	1.56263	−	0.418705i
$589$	9.09504	+	5.25102i	0.374755	+	0.216365i
$590$		0			0
$591$			3.40444i			0.140040i
$592$	14.0770	−	15.1216i	0.578560	−	0.621493i
$593$	7.88127	+	7.88127i	0.323645	+	0.323645i	0.850164	−	0.526519i	$-0.176503\pi$
$593$	7.88127	+	7.88127i	0.323645	+	0.323645i	−0.526519	+	0.850164i	$0.676503\pi$
$594$	−10.9148	+	40.7345i	−0.447839	+	1.67136i
$595$		0			0
$596$	53.1775	+	30.7020i	2.17823	+	1.25760i
$597$	3.52794	−	6.11058i	0.144389	−	0.250089i
$598$		−	10.5194i		−	0.430171i
$599$	−6.25134	−	3.60922i	−0.255423	−	0.147469i	0.366822	−	0.930291i	$-0.380446\pi$
$599$	−6.25134	−	3.60922i	−0.255423	−	0.147469i	−0.622245	+	0.782823i	$0.713779\pi$
$600$		0			0
$601$	−18.5443	−	32.1197i	−0.756438	−	1.31019i	−0.944656	−	0.328061i	$-0.893605\pi$
$601$	−18.5443	−	32.1197i	−0.756438	−	1.31019i	0.188219	−	0.982127i	$-0.439729\pi$
$602$	−6.23685	+	6.23685i	−0.254195	+	0.254195i
$603$	−12.7476	+	12.7476i	−0.519123	+	0.519123i
$604$	29.3876	−	16.9670i	1.19577	−	0.690376i
$605$		0			0
$606$	4.83646	−	4.83646i	0.196468	−	0.196468i
$607$	25.3980	−	14.6635i	1.03087	−	0.595174i	0.113637	−	0.993522i	$-0.463750\pi$
$607$	25.3980	−	14.6635i	1.03087	−	0.595174i	0.917234	+	0.398348i	$0.130417\pi$
$608$	0.368615	−	1.37569i	0.0149493	−	0.0557916i
$609$	6.31400	+	1.69183i	0.255856	+	0.0685564i
$610$		0			0
$611$	−18.4534	+	4.94458i	−0.746546	+	0.200036i
$612$	−33.2538	+	19.1991i	−1.34421	+	0.776077i
$613$	40.7596	+	10.9215i	1.64627	+	0.441116i	0.958564	−	0.284878i	$-0.0919530\pi$
$613$	40.7596	+	10.9215i	1.64627	+	0.441116i	0.687702	+	0.725993i	$0.258620\pi$
$614$	−19.9795	−	5.35348i	−0.806306	−	0.216049i
$615$		0			0
$616$	−24.9858	−	93.2483i	−1.00671	−	3.75708i
$617$	2.50108	−	9.33416i	0.100690	−	0.375779i	−0.897131	−	0.441765i	$-0.854353\pi$
$617$	2.50108	−	9.33416i	0.100690	−	0.375779i	0.997821	+	0.0659858i	$0.0210192\pi$
$618$	11.2059	+	11.2059i	0.450766	+	0.450766i
$619$	36.1951			1.45480			0.727402	−	0.686212i	$-0.240728\pi$
$619$	36.1951			1.45480			0.727402	+	0.686212i	$0.240728\pi$
$620$		0			0
$621$	−5.89225	+	5.89225i	−0.236448	+	0.236448i
$622$	−44.8550	+	12.0189i	−1.79852	+	0.481912i
$623$	−2.84777			−0.114094
$624$	−4.55916	+	1.22162i	−0.182513	+	0.0489041i
$625$		0			0
$626$	−7.82230	+	13.5486i	−0.312642	+	0.541512i
$627$	2.31456	+	4.00893i	0.0924346	+	0.160101i
$628$	21.8868	−	21.8868i	0.873378	−	0.873378i
$629$	16.2333	−	17.4379i	0.647265	−	0.695296i
$630$		0			0
$631$	−24.9812	−	6.69368i	−0.994484	−	0.266471i	−0.275351	−	0.961344i	$-0.588794\pi$
$631$	−24.9812	−	6.69368i	−0.994484	−	0.266471i	−0.719133	+	0.694872i	$0.755461\pi$
$632$	−23.9098	+	6.40661i	−0.951080	+	0.254841i
$633$	1.55773	+	5.81354i	0.0619143	+	0.231067i
$634$	−12.5735	−	46.9250i	−0.499358	−	1.86363i
$635$		0			0
$636$	−17.3697	+	30.0853i	−0.688755	+	1.19296i
$637$	−28.8550			−1.14327
$638$	5.76154	−	21.5023i	0.228101	−	0.851286i
$639$			35.0353i			1.38597i
$640$		0			0
$641$	−23.6056	−	40.8862i	−0.932367	−	1.61491i	−0.779263	−	0.626697i	$-0.784406\pi$
$641$	−23.6056	−	40.8862i	−0.932367	−	1.61491i	−0.153104	−	0.988210i	$-0.548927\pi$
$642$	−1.74547	+	3.02324i	−0.0688881	+	0.119318i
$643$	46.2642			1.82448			0.912240	−	0.409655i	$-0.134351\pi$
$643$	46.2642			1.82448			0.912240	+	0.409655i	$0.134351\pi$
$644$	10.1404	−	37.8446i	0.399589	−	1.49129i
$645$		0			0
$646$	−3.61946	+	13.5080i	−0.142406	+	0.531466i
$647$	24.4072	+	14.0915i	0.959548	+	0.553995i	0.896034	−	0.443986i	$-0.146436\pi$
$647$	24.4072	+	14.0915i	0.959548	+	0.553995i	0.0635140	+	0.997981i	$0.479769\pi$
$648$	−19.4462	−	11.2273i	−0.763920	−	0.441049i
$649$	9.01600	−	33.6482i	0.353909	−	1.32081i
$650$		0			0
$651$	−5.96219	+	22.2512i	−0.233677	+	0.872093i
$652$	−27.6353			−1.08228
$653$	9.63180	−	16.6828i	0.376921	−	0.652847i	−0.613691	−	0.789546i	$-0.710316\pi$
$653$	9.63180	−	16.6828i	0.376921	−	0.652847i	0.990613	+	0.136699i	$0.0436493\pi$
$654$	−0.598523	−	1.03667i	−0.0234041	−	0.0405371i
$655$		0			0
$656$			3.18175i			0.124227i
$657$	−6.20039	+	23.1402i	−0.241900	+	0.902785i
$658$	−107.666			−4.19724
$659$	−14.5221	+	25.1530i	−0.565699	+	0.979820i	0.431285	+	0.902216i	$0.358060\pi$
$659$	−14.5221	+	25.1530i	−0.565699	+	0.979820i	−0.996984	+	0.0776043i	$0.975273\pi$
$660$		0			0
$661$	−1.49896	−	5.59420i	−0.0583028	−	0.217589i	0.930628	−	0.365967i	$-0.119262\pi$
$661$	−1.49896	−	5.59420i	−0.0583028	−	0.217589i	−0.988931	+	0.148378i	$0.952595\pi$
$662$	8.18528	+	30.5479i	0.318130	+	1.18728i
$663$	−5.25755	+	1.40876i	−0.204186	+	0.0547116i
$664$	−40.9781	−	10.9800i	−1.59026	−	0.426108i
$665$		0			0
$666$	36.2106	+	8.32730i	1.40313	+	0.322676i
$667$	3.11032	−	3.11032i	0.120432	−	0.120432i
$668$	−35.8746	−	62.1366i	−1.38803	−	2.40414i
$669$	7.60362	−	13.1699i	0.293973	−	0.509176i
$670$		0			0
$671$	21.8101	−	5.84400i	0.841969	−	0.225605i
$672$	3.12401			0.120511
$673$	7.42208	−	1.98874i	0.286100	−	0.0766603i	−0.112915	−	0.993605i	$-0.536019\pi$
$673$	7.42208	−	1.98874i	0.286100	−	0.0766603i	0.399015	+	0.916944i	$0.369352\pi$
$674$	43.9703	−	43.9703i	1.69367	−	1.69367i
$675$		0			0
$676$	−35.1405			−1.35156
$677$	−5.23876	−	5.23876i	−0.201342	−	0.201342i	0.599233	−	0.800575i	$-0.295472\pi$
$677$	−5.23876	−	5.23876i	−0.201342	−	0.201342i	−0.800575	+	0.599233i	$0.795472\pi$
$678$	7.95760	−	29.6982i	0.305610	−	1.14055i
$679$	−3.69427	−	13.7872i	−0.141773	−	0.529105i
$680$		0			0
$681$	11.1918	+	2.99884i	0.428871	+	0.114916i
$682$	75.7765	+	20.3043i	2.90163	+	0.777490i
$683$	21.3135	−	12.3053i	0.815537	−	0.470851i	−0.0333377	−	0.999444i	$-0.510614\pi$
$683$	21.3135	−	12.3053i	0.815537	−	0.470851i	0.848875	+	0.528593i	$0.177280\pi$
$684$	−13.9226	+	3.73055i	−0.532343	+	0.142641i
$685$		0			0
$686$	−81.0153	−	21.7080i	−3.09318	−	0.828815i
$687$	3.32770	−	12.4191i	0.126960	−	0.473820i
$688$	2.30632	−	1.33155i	0.0879276	−	0.0507650i
$689$	18.0687	−	18.0687i	0.688364	−	0.688364i
$690$		0			0
$691$	18.7787	−	10.8419i	0.714376	−	0.412445i	−0.0983035	−	0.995156i	$-0.531342\pi$
$691$	18.7787	−	10.8419i	0.714376	−	0.412445i	0.812679	+	0.582712i	$0.198008\pi$
$692$	−48.7086	+	48.7086i	−1.85162	+	1.85162i
$693$	37.2571	−	37.2571i	1.41528	−	1.41528i
$694$	2.53935	+	4.39829i	0.0963925	+	0.166957i
$695$		0			0
$696$	−5.63216	−	3.25173i	−0.213486	−	0.123256i
$697$			3.66914i			0.138979i
$698$	7.54861	−	13.0746i	0.285719	−	0.494880i
$699$	11.7898	+	6.80687i	0.445933	+	0.257459i
$700$		0			0
$701$	−7.42616	+	27.7148i	−0.280482	+	1.04677i	0.671595	+	0.740918i	$0.265609\pi$
$701$	−7.42616	+	27.7148i	−0.280482	+	1.04677i	−0.952078	+	0.305856i	$0.901057\pi$
$702$	−13.1617	−	13.1617i	−0.496755	−	0.496755i
$703$	7.58012	−	4.74559i	0.285890	−	0.178983i
$704$		−	41.3585i		−	1.55876i
$705$		0			0
$706$	−15.2865	−	8.82564i	−0.575313	−	0.332157i
$707$	−18.0998	+	4.84983i	−0.680714	+	0.182397i
$708$	−18.1024	−	10.4514i	−0.680329	−	0.392788i
$709$	−32.1630	+	32.1630i	−1.20791	+	1.20791i	−0.236205	+	0.971703i	$0.575904\pi$
$709$	−32.1630	+	32.1630i	−1.20791	+	1.20791i	−0.971703	+	0.236205i	$0.924096\pi$
$710$		0			0
$711$	−9.55310	−	9.55310i	−0.358269	−	0.358269i
$712$	2.73673	+	0.733305i	0.102563	+	0.0274818i
$713$	10.9611	+	10.9611i	0.410496	+	0.410496i
$714$	−30.6749			−1.14798
$715$		0			0
$716$	26.0786	−	6.98774i	0.974604	−	0.261144i
$717$			17.2280i			0.643393i
$718$	14.3454	+	24.8470i	0.535366	+	0.927281i
$719$	8.70722	−	5.02711i	0.324724	−	0.187480i	−0.328772	−	0.944409i	$-0.606635\pi$
$719$	8.70722	−	5.02711i	0.324724	−	0.187480i	0.653496	+	0.756930i	$0.273301\pi$
$720$		0			0
$721$	−11.2368	−	41.9364i	−0.418481	−	1.56179i
$722$	20.4461	−	35.4137i	0.760926	−	1.31796i
$723$	−1.84458	−	3.19490i	−0.0686005	−	0.118820i
$724$	15.7032	+	27.1987i	0.583603	+	1.01083i
$725$		0			0
$726$	11.3000	+	11.3000i	0.419383	+	0.419383i
$727$	−22.2087	−	12.8222i	−0.823676	−	0.475549i	0.0280066	−	0.999608i	$-0.491084\pi$
$727$	−22.2087	−	12.8222i	−0.823676	−	0.475549i	−0.851682	+	0.524058i	$0.824417\pi$
$728$	41.1574	+	11.0281i	1.52539	+	0.408728i
$729$		−	4.23536i		−	0.156865i
$730$		0			0
$731$	2.65961	−	1.53553i	0.0983692	−	0.0567935i
$732$		−	13.5488i		−	0.500779i
$733$	−0.868126	−	3.23989i	−0.0320650	−	0.119668i	0.948038	−	0.318156i	$-0.103064\pi$
$733$	−0.868126	−	3.23989i	−0.0320650	−	0.119668i	−0.980103	+	0.198488i	$0.936397\pi$
$734$	4.26274	+	4.26274i	0.157341	+	0.157341i
$735$		0			0
$736$	1.05109	−	1.82055i	0.0387438	−	0.0671063i
$737$	8.38916	+	31.3088i	0.309019	+	1.15327i
$738$	−4.95564	+	2.86114i	−0.182420	+	0.105320i
$739$	−16.3666			−0.602055			−0.301028	−	0.953615i	$-0.597330\pi$
$739$	−16.3666			−0.602055			−0.301028	+	0.953615i	$0.597330\pi$
$740$		0			0
$741$	−2.04317			−0.0750578
$742$	124.715	−	72.0040i	4.57841	−	2.64335i
$743$	3.47128	+	12.9550i	0.127349	+	0.475273i	0.999913	−	0.0132280i	$-0.00421071\pi$
$743$	3.47128	+	12.9550i	0.127349	+	0.475273i	−0.872564	+	0.488501i	$0.837544\pi$
$744$	11.4594	−	19.8483i	0.420123	−	0.727674i
$745$		0			0
$746$	−15.9905	−	15.9905i	−0.585453	−	0.585453i
$747$	−5.99282	−	22.3655i	−0.219266	−	0.818312i
$748$			69.0381i			2.52428i
$749$	8.28247	−	4.78189i	0.302635	−	0.174726i
$750$		0			0
$751$			10.8836i			0.397150i	0.980086	+	0.198575i	$0.0636313\pi$
$751$			10.8836i			0.397150i	−0.980086	+	0.198575i	$0.936369\pi$
$752$	31.4000	+	8.41360i	1.14504	+	0.306812i
$753$	16.5495	+	9.55488i	0.603098	+	0.348199i
$754$	6.94759	+	6.94759i	0.253016	+	0.253016i
$755$		0			0
$756$	−34.6628	−	60.0377i	−1.26067	−	2.18355i
$757$	−3.24560	−	5.62155i	−0.117963	−	0.204319i	0.800997	−	0.598668i	$-0.204303\pi$
$757$	−3.24560	−	5.62155i	−0.117963	−	0.204319i	−0.918960	+	0.394350i	$0.870970\pi$
$758$	10.0083	−	17.3348i	0.363517	−	0.629630i
$759$	1.76843	+	6.59989i	0.0641901	+	0.239561i
$760$		0			0
$761$	8.40713	−	4.85386i	0.304758	−	0.175952i	−0.339820	−	0.940490i	$-0.610366\pi$
$761$	8.40713	−	4.85386i	0.304758	−	0.175952i	0.644578	+	0.764538i	$0.277033\pi$
$762$	−8.13022	−	14.0819i	−0.294527	−	0.510135i
$763$			3.27943i			0.118723i
$764$	−57.6039	+	15.4349i	−2.08403	+	0.558415i
$765$		0			0
$766$	61.1846			2.21069
$767$	10.8720	+	10.8720i	0.392565	+	0.392565i
$768$	−20.8075	−	5.57534i	−0.750824	−	0.201183i
$769$	36.7369	+	36.7369i	1.32477	+	1.32477i	0.909867	+	0.414900i	$0.136184\pi$
$769$	36.7369	+	36.7369i	1.32477	+	1.32477i	0.414900	+	0.909867i	$0.363816\pi$
$770$		0			0
$771$	−5.69197	+	5.69197i	−0.204991	+	0.204991i
$772$	−52.4108	−	30.2594i	−1.88631	−	1.08906i
$773$	8.20308	−	2.19801i	0.295044	−	0.0790568i	−0.108261	−	0.994123i	$-0.534528\pi$
$773$	8.20308	−	2.19801i	0.295044	−	0.0790568i	0.403305	+	0.915066i	$0.367861\pi$
$774$	4.14784	+	2.39476i	0.149091	+	0.0860777i
$775$		0			0
$776$			14.2009i			0.509783i
$777$	14.3581	+	13.3662i	0.515093	+	0.479510i
$778$	5.67580	+	5.67580i	0.203487	+	0.203487i
$779$	−0.356473	+	1.33037i	−0.0127720	+	0.0476656i
$780$		0			0
$781$	54.5525	+	31.4959i	1.95204	+	1.12701i
$782$	−10.3208	+	17.8761i	−0.369070	+	0.639248i
$783$		−	7.78311i		−	0.278146i
$784$	42.5210	+	24.5495i	1.51861	+	0.876767i
$785$		0			0
$786$	5.24935	+	9.09215i	0.187238	+	0.324306i
$787$	−23.7345	+	23.7345i	−0.846042	+	0.846042i	−0.989637	−	0.143595i	$-0.954134\pi$
$787$	−23.7345	+	23.7345i	−0.846042	+	0.846042i	0.143595	+	0.989637i	$0.454134\pi$
$788$	−13.4768	+	13.4768i	−0.480092	+	0.480092i
$789$	3.14055	−	1.81320i	0.111807	−	0.0645515i
$790$		0			0
$791$	−59.5605	+	59.5605i	−2.11773	+	2.11773i
$792$	−45.3982	+	26.2106i	−1.61315	+	0.931355i
$793$	−2.57939	+	9.62641i	−0.0915968	+	0.341844i
$794$	85.7223	+	22.9692i	3.04217	+	0.815147i
$795$		0			0
$796$	38.1550	−	10.2236i	1.35237	−	0.362366i
$797$	−28.3561	+	16.3714i	−1.00442	+	0.579904i	−0.909554	−	0.415586i	$-0.863577\pi$
$797$	−28.3561	+	16.3714i	−1.00442	+	0.579904i	−0.0948693	+	0.995490i	$0.530243\pi$
$798$	−11.1223	−	2.98020i	−0.393723	−	0.105498i
$799$	36.2099	+	9.70242i	1.28101	+	0.343247i
$800$		0			0
$801$	0.400232	+	1.49369i	0.0141415	+	0.0527768i
$802$	−3.17470	+	11.8481i	−0.112103	+	0.418372i
$803$	30.4570	+	30.4570i	1.07480	+	1.07480i
$804$	19.4496			0.685933
$805$		0			0
$806$	−24.4840	+	24.4840i	−0.862413	+	0.862413i
$807$	−10.4991	+	2.81321i	−0.369584	+	0.0990298i
$808$	18.6429			0.655855
$809$	−18.8260	+	5.04441i	−0.661887	+	0.177352i	−0.574097	−	0.818787i	$-0.694647\pi$
$809$	−18.8260	+	5.04441i	−0.661887	+	0.177352i	−0.0877894	+	0.996139i	$0.527980\pi$
$810$		0			0
$811$	−11.6244	+	20.1341i	−0.408190	+	0.707005i	−0.994687	−	0.102946i	$-0.967173\pi$
$811$	−11.6244	+	20.1341i	−0.408190	+	0.707005i	0.586497	+	0.809951i	$0.300506\pi$
$812$	18.2973	+	31.6919i	0.642109	+	1.11217i
$813$	−1.92089	+	1.92089i	−0.0673687	+	0.0673687i
$814$	45.5187	−	48.8965i	1.59543	−	1.71382i
$815$		0			0
$816$	8.94613	+	2.39711i	0.313177	+	0.0839156i
$817$	1.11352	−	0.298366i	0.0389570	−	0.0104385i
$818$	−5.46692	−	20.4028i	−0.191146	−	0.713368i
$819$	6.01904	+	22.4634i	0.210322	+	0.784934i
$820$		0			0
$821$	−12.4512	+	21.5661i	−0.434550	+	0.752662i	−0.997259	−	0.0739930i	$-0.976426\pi$
$821$	−12.4512	+	21.5661i	−0.434550	+	0.752662i	0.562709	+	0.826655i	$0.309759\pi$
$822$	−15.3817			−0.536499
$823$	3.58759	−	13.3891i	0.125056	−	0.466714i	−0.874786	−	0.484509i	$-0.838998\pi$
$823$	3.58759	−	13.3891i	0.125056	−	0.466714i	0.999842	+	0.0177955i	$0.00566479\pi$
$824$			43.1947i			1.50476i
$825$		0			0
$826$	43.3250	+	75.0411i	1.50747	+	2.61101i
$827$	−1.78380	+	3.08963i	−0.0620287	+	0.107437i	−0.895372	−	0.445319i	$-0.853090\pi$
$827$	−1.78380	+	3.08963i	−0.0620287	+	0.107437i	0.833343	+	0.552756i	$0.186424\pi$
$828$	−21.2751			−0.739360
$829$	12.6086	−	47.0558i	0.437914	−	1.63432i	−0.296082	−	0.955163i	$-0.595680\pi$
$829$	12.6086	−	47.0558i	0.437914	−	1.63432i	0.733996	−	0.679154i	$-0.237653\pi$
$830$		0			0
$831$	0.177349	−	0.661874i	0.00615215	−	0.0229601i
$832$	15.8089	+	9.12729i	0.548076	+	0.316432i
$833$	49.0345	+	28.3101i	1.69894	+	0.980885i
$834$	−2.31879	+	8.65383i	−0.0802930	+	0.299658i
$835$		0			0
$836$	−6.70735	+	25.0322i	−0.231978	+	0.865755i
$837$	27.4285			0.948067
$838$	24.7879	−	42.9339i	0.856285	−	1.48313i
$839$	−18.9565	−	32.8336i	−0.654451	−	1.13354i	−0.982031	−	0.188719i	$-0.939566\pi$
$839$	−18.9565	−	32.8336i	−0.654451	−	1.13354i	0.327580	−	0.944824i	$-0.393767\pi$
$840$		0			0
$841$		−	24.8916i		−	0.858330i
$842$	22.3766	−	83.5104i	0.771147	−	2.87796i
$843$	−12.2083			−0.420476
$844$	−16.8470	+	29.1799i	−0.579899	+	1.00441i
$845$		0			0
$846$	15.1316	+	56.4718i	0.520234	+	1.94154i
$847$	−11.3312	−	42.2888i	−0.389346	−	1.45306i
$848$	−41.9989	+	11.2536i	−1.44225	+	0.386450i
$849$	−4.97915	−	1.33416i	−0.170884	−	0.0457882i
$850$		0			0
$851$	12.6202	−	3.87016i	0.432614	−	0.132667i
$852$	26.7274	−	26.7274i	0.915665	−	0.915665i
$853$	4.00565	+	6.93798i	0.137151	+	0.237552i	0.926417	−	0.376499i	$-0.122872\pi$
$853$	4.00565	+	6.93798i	0.137151	+	0.237552i	−0.789266	+	0.614051i	$0.789539\pi$
$854$	−28.0824	+	48.6402i	−0.960961	+	1.66443i
$855$		0			0
$856$	−9.19086	+	2.46268i	−0.314137	+	0.0841728i
$857$	−30.5365			−1.04311			−0.521554	−	0.853219i	$-0.674647\pi$
$857$	−30.5365			−1.04311			−0.521554	+	0.853219i	$0.674647\pi$
$858$	−14.7423	+	3.95019i	−0.503295	+	0.134857i
$859$	−6.75070	+	6.75070i	−0.230331	+	0.230331i	−0.812831	−	0.582500i	$-0.802075\pi$
$859$	−6.75070	+	6.75070i	−0.230331	+	0.230331i	0.582500	+	0.812831i	$0.302075\pi$
$860$		0			0
$861$	−3.02110			−0.102959
$862$	−26.2307	−	26.2307i	−0.893420	−	0.893420i
$863$	0.412406	−	1.53912i	0.0140385	−	0.0523923i	−0.958551	−	0.284920i	$-0.908033\pi$
$863$	0.412406	−	1.53912i	0.0140385	−	0.0523923i	0.972590	+	0.232528i	$0.0746996\pi$
$864$	−0.962723	−	3.59293i	−0.0327525	−	0.122234i
$865$		0			0
$866$	−33.3045	−	8.92393i	−1.13173	−	0.303247i
$867$	−1.11594	−	0.299016i	−0.0378994	−	0.0101551i
$868$	−111.685	+	64.4816i	−3.79085	+	2.18865i
$869$	−23.4629	+	6.28686i	−0.795924	+	0.213267i
$870$		0			0
$871$	−13.8189	−	3.70276i	−0.468235	−	0.125463i
$872$	0.844457	−	3.15156i	0.0285969	−	0.106725i
$873$	−6.71234	+	3.87537i	−0.227178	+	0.131161i
$874$	−5.47889	+	5.47889i	−0.185326	+	0.185326i
$875$		0			0
$876$	22.3831	−	12.9229i	0.756254	−	0.436623i
$877$	−3.33771	+	3.33771i	−0.112707	+	0.112707i	−0.761211	−	0.648504i	$-0.775395\pi$
$877$	−3.33771	+	3.33771i	−0.112707	+	0.112707i	0.648504	+	0.761211i	$0.275395\pi$
$878$	−27.8791	+	27.8791i	−0.940875	+	0.940875i
$879$	−2.95862	−	5.12449i	−0.0997919	−	0.172845i
$880$		0			0
$881$	26.9466	+	15.5576i	0.907854	+	0.524150i	0.879740	−	0.475455i	$-0.157717\pi$
$881$	26.9466	+	15.5576i	0.907854	+	0.524150i	0.0281138	+	0.999605i	$0.491050\pi$
$882$			88.3029i			2.97331i
$883$	4.05330	−	7.02051i	0.136404	−	0.236259i	−0.789729	−	0.613456i	$-0.789779\pi$
$883$	4.05330	−	7.02051i	0.136404	−	0.236259i	0.926133	+	0.377197i	$0.123112\pi$
$884$	−26.3892	−	15.2358i	−0.887566	−	0.512436i
$885$		0			0
$886$	0.835584	−	3.11844i	0.0280720	−	0.104766i
$887$	24.9312	+	24.9312i	0.837107	+	0.837107i	0.988477	−	0.151370i	$-0.0483686\pi$
$887$	24.9312	+	24.9312i	0.837107	+	0.837107i	−0.151370	+	0.988477i	$0.548369\pi$
$888$	−10.3564	−	16.5423i	−0.347538	−	0.555122i
$889$			44.5471i			1.49406i
$890$		0			0
$891$	−19.0827	−	11.0174i	−0.639296	−	0.369098i
$892$	82.2339	−	22.0345i	2.75339	−	0.737770i
$893$	12.1865	+	7.03589i	0.407806	+	0.235447i
$894$	18.8350	−	18.8350i	0.629937	−	0.629937i
$895$		0			0
$896$	66.3989	+	66.3989i	2.21823	+	2.21823i
$897$	−2.91302	−	0.780541i	−0.0972629	−	0.0260615i
$898$	−57.0405	−	57.0405i	−1.90347	−	1.90347i
$899$	−14.4786			−0.482887
$900$		0			0
$901$	−48.4325	+	12.9774i	−1.61352	+	0.432341i
$902$			10.2884i			0.342566i
$903$	1.26432	+	2.18987i	0.0420740	+	0.0728744i
$904$	72.5751	−	41.9012i	2.41381	−	1.39361i
$905$		0			0
$906$	−3.80990	−	14.2187i	−0.126575	−	0.472386i
$907$	−4.95785	+	8.58725i	−0.164623	+	0.285135i	−0.936521	−	0.350611i	$-0.885974\pi$
$907$	−4.95785	+	8.58725i	−0.164623	+	0.285135i	0.771899	+	0.635746i	$0.219307\pi$
$908$	32.4327	+	56.1751i	1.07632	+	1.86424i
$909$	5.08758	+	8.81194i	0.168744	+	0.292274i
$910$		0			0
$911$	−0.888702	−	0.888702i	−0.0294440	−	0.0294440i	0.692232	−	0.721676i	$-0.256628\pi$
$911$	−0.888702	−	0.888702i	−0.0294440	−	0.0294440i	−0.721676	+	0.692232i	$0.756628\pi$
$912$	3.01084	+	1.73831i	0.0996989	+	0.0575612i
$913$	−40.2122	−	10.7748i	−1.33083	−	0.356594i
$914$		−	55.4847i		−	1.83527i
$915$		0			0
$916$	62.3354	−	35.9894i	2.05962	−	1.18912i
$917$		−	28.7623i		−	0.949814i
$918$	9.45305	+	35.2793i	0.311997	+	1.16439i
$919$	−13.9691	−	13.9691i	−0.460799	−	0.460799i	0.438118	−	0.898917i	$-0.355645\pi$
$919$	−13.9691	−	13.9691i	−0.460799	−	0.460799i	−0.898917	+	0.438118i	$0.855645\pi$
$920$		0			0
$921$	−2.96495	+	5.13545i	−0.0976985	+	0.169219i
$922$	−19.5403	−	72.9254i	−0.643526	−	2.40167i
$923$	−24.0781	+	13.9015i	−0.792539	+	0.457573i
$924$	−56.8447			−1.87005
$925$		0			0
$926$	−59.8907			−1.96813
$927$	−20.4169	+	11.7877i	−0.670578	+	0.387158i
$928$	0.508188	+	1.89659i	0.0166821	+	0.0622585i
$929$	−16.4629	+	28.5147i	−0.540132	+	0.935535i	0.458764	+	0.888558i	$0.348292\pi$
$929$	−16.4629	+	28.5147i	−0.540132	+	0.935535i	−0.998896	+	0.0469774i	$0.985041\pi$
$930$		0			0
$931$	15.0287	+	15.0287i	0.492546	+	0.492546i
$932$	19.7256	+	73.6169i	0.646133	+	2.41140i
$933$			13.3130i			0.435847i
$934$	−57.5173	+	33.2076i	−1.88202	+	1.08659i
$935$		0			0
$936$		−	23.1374i		−	0.756270i
$937$	54.6618	+	14.6466i	1.78572	+	0.478483i	0.991608	−	0.129284i	$-0.0412679\pi$
$937$	54.6618	+	14.6466i	1.78572	+	0.478483i	0.794115	+	0.607767i	$0.207935\pi$
$938$	−69.8238	−	40.3128i	−2.27983	−	1.31626i
$939$	3.17144	+	3.17144i	0.103496	+	0.103496i
$940$		0			0
$941$	19.8813	+	34.4355i	0.648113	+	1.12256i	0.983573	+	0.180510i	$0.0577748\pi$
$941$	19.8813	+	34.4355i	0.648113	+	1.12256i	−0.335460	+	0.942054i	$0.608892\pi$
$942$	−6.71352	−	11.6282i	−0.218738	−	0.378866i
$943$	−1.01647	+	1.76058i	−0.0331008	+	0.0573323i
$944$	−6.77131	−	25.2709i	−0.220387	−	0.822497i
$945$		0			0
$946$	7.45762	−	4.30566i	0.242468	−	0.139989i
$947$	28.2853	+	48.9916i	0.919150	+	1.59201i	0.800710	+	0.599053i	$0.204456\pi$
$947$	28.2853	+	48.9916i	0.919150	+	1.59201i	0.118440	+	0.992961i	$0.462211\pi$
$948$			14.5756i			0.473392i
$949$	−18.3634	+	4.92045i	−0.596100	+	0.159725i
$950$		0			0
$951$	−13.9273			−0.451625
$952$	−59.1207	−	59.1207i	−1.91611	−	1.91611i
$953$	8.59989	+	2.30433i	0.278578	+	0.0746447i	0.395403	−	0.918508i	$-0.370605\pi$
$953$	8.59989	+	2.30433i	0.278578	+	0.0746447i	−0.116825	+	0.993153i	$0.537272\pi$
$954$	−55.2945	−	55.2945i	−1.79023	−	1.79023i
$955$		0			0
$956$	−68.1989	+	68.1989i	−2.20571	+	2.20571i
$957$	−5.52688	−	3.19095i	−0.178659	−	0.103149i
$958$	50.4900	−	13.5288i	1.63126	−	0.437094i
$959$	36.4941	+	21.0699i	1.17846	+	0.680382i
$960$		0			0
$961$		−	20.0240i		−	0.645935i
$962$	8.64487	+	28.1900i	0.278722	+	0.908880i
$963$	−3.67219	−	3.67219i	−0.118335	−	0.118335i
$964$	5.34539	−	19.9493i	0.172163	−	0.642522i
$965$		0			0
$966$	−14.7189	−	8.49794i	−0.473572	−	0.273417i
$967$	−14.9557	+	25.9040i	−0.480943	+	0.833018i	−0.999761	−	0.0218671i	$-0.993039\pi$
$967$	−14.9557	+	25.9040i	−0.480943	+	0.833018i	0.518818	+	0.854885i	$0.326372\pi$
$968$			43.5577i			1.40000i
$969$	3.47205	+	2.00459i	0.111538	+	0.0643967i
$970$		0			0
$971$	−13.5655	−	23.4962i	−0.435339	−	0.754029i	0.561984	−	0.827148i	$-0.310038\pi$
$971$	−13.5655	−	23.4962i	−0.435339	−	0.754029i	−0.997323	+	0.0731189i	$0.976705\pi$
$972$	−41.0980	+	41.0980i	−1.31822	+	1.31822i
$973$	17.3555	−	17.3555i	0.556392	−	0.556392i
$974$	−33.7374	+	19.4783i	−1.08102	+	0.624126i
$975$		0			0
$976$	11.9911	−	11.9911i	0.383825	−	0.383825i
$977$	14.5390	−	8.39410i	0.465144	−	0.268551i	−0.249061	−	0.968488i	$-0.580122\pi$
$977$	14.5390	−	8.39410i	0.465144	−	0.268551i	0.714205	+	0.699937i	$0.246789\pi$
$978$	−3.10272	+	11.5795i	−0.0992142	+	0.370272i
$979$	2.68558	+	0.719599i	0.0858315	+	0.0229985i
$980$		0			0
$981$	1.72010	−	0.460898i	0.0549184	−	0.0147153i
$982$	62.8984	−	36.3144i	2.00717	−	1.15884i
$983$	−1.66842	−	0.447052i	−0.0532143	−	0.0142587i	0.232114	−	0.972689i	$-0.425436\pi$
$983$	−1.66842	−	0.447052i	−0.0532143	−	0.0142587i	−0.285328	+	0.958430i	$0.592103\pi$
$984$	2.90331	+	0.777939i	0.0925540	+	0.0247998i
$985$		0			0
$986$	−4.98994	−	18.6227i	−0.158912	−	0.593068i
$987$	−7.98879	+	29.8146i	−0.254286	+	0.949008i
$988$	−8.08810	−	8.08810i	−0.257317	−	0.257317i
$989$	1.70156			0.0541065
$990$		0			0
$991$	−8.93323	+	8.93323i	−0.283773	+	0.283773i	−0.834612	−	0.550838i	$-0.814308\pi$
$991$	−8.93323	+	8.93323i	−0.283773	+	0.283773i	0.550838	+	0.834612i	$0.314308\pi$
$992$	−6.68377	+	1.79091i	−0.212210	+	0.0568614i
$993$	9.06661			0.287720
$994$	−151.349	+	40.5537i	−4.80049	+	1.28629i
$995$		0			0
$996$	−12.4902	+	21.6337i	−0.395769	+	0.685491i
$997$	13.0904	+	22.6733i	0.414577	+	0.718069i	0.995384	−	0.0959724i	$-0.0305961\pi$
$997$	13.0904	+	22.6733i	0.414577	+	0.718069i	−0.580807	+	0.814042i	$0.697263\pi$
$998$	−51.2380	+	51.2380i	−1.62191	+	1.62191i
$999$	10.9478	−	20.6323i	0.346373	−	0.652777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.b.193.16		68
5.2	odd	4		925.2.t.b.82.16		68
5.3	odd	4		185.2.p.a.82.2	✓	68
5.4	even	2		185.2.u.a.8.2	yes	68
37.14	odd	12		925.2.t.b.643.16		68
185.14	odd	12		185.2.p.a.88.2	yes	68
185.88	even	12		185.2.u.a.162.2	yes	68
185.162	even	12	inner	925.2.y.b.532.16		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.82.2	✓	68	5.3	odd	4
185.2.p.a.88.2	yes	68	185.14	odd	12
185.2.u.a.8.2	yes	68	5.4	even	2
185.2.u.a.162.2	yes	68	185.88	even	12
925.2.t.b.82.16		68	5.2	odd	4
925.2.t.b.643.16		68	37.14	odd	12
925.2.y.b.193.16		68	1.1	even	1	trivial
925.2.y.b.532.16		68	185.162	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.10315 - 1.21425i) q^{2} +(-0.180195 - 0.672498i) q^{3} +(1.94883 - 3.37547i) q^{4} +(-1.19556 - 1.19556i) q^{6} +(1.19887 + 4.47423i) q^{7} -4.60849i q^{8} +(2.17829 - 1.25764i) q^{9} -4.52235i q^{11} +(-2.62117 - 0.702340i) q^{12} +(1.72863 + 0.998024i) q^{13} +(7.95426 + 7.95426i) q^{14} +(-1.69822 - 2.94140i) q^{16} +(-1.95835 - 3.39197i) q^{17} +(3.05419 - 5.29000i) q^{18} +(-0.380525 - 1.42014i) q^{19} +(2.79288 - 1.61247i) q^{21} +(-5.49128 - 9.51118i) q^{22} -2.17011i q^{23} +(-3.09920 + 0.830428i) q^{24} +4.84742 q^{26} +(-2.71519 - 2.71519i) q^{27} +(17.4390 + 4.67278i) q^{28} +(1.43325 + 1.43325i) q^{29} +(-5.05094 + 5.05094i) q^{31} +(0.838921 + 0.484351i) q^{32} +(-3.04127 + 0.814906i) q^{33} +(-8.23743 - 4.75588i) q^{34} -9.80369i q^{36} +(1.78340 + 5.81545i) q^{37} +(-2.52471 - 2.52471i) q^{38} +(0.359679 - 1.34234i) q^{39} +(-0.811286 - 0.468396i) q^{41} +(3.91591 - 6.78255i) q^{42} +0.784090i q^{43} +(-15.2651 - 8.81329i) q^{44} +(-2.63506 - 4.56407i) q^{46} +(-6.76780 + 6.76780i) q^{47} +(-1.67207 + 1.67207i) q^{48} +(-12.5193 + 7.22802i) q^{49} +(-1.92821 + 1.92821i) q^{51} +(6.73760 - 3.88996i) q^{52} +(3.31335 - 12.3656i) q^{53} +(-9.00738 - 2.41352i) q^{54} +(20.6194 - 5.52496i) q^{56} +(-0.886472 + 0.511805i) q^{57} +(4.75469 + 1.27401i) q^{58} +(7.44042 + 1.99365i) q^{59} +(1.29225 + 4.82274i) q^{61} +(-4.48976 + 16.7560i) q^{62} +(8.23845 + 8.23845i) q^{63} +9.14537 q^{64} +(-5.40675 + 5.40675i) q^{66} +(-6.92312 + 1.85504i) q^{67} -15.2660 q^{68} +(-1.45939 + 0.391044i) q^{69} +(-6.96450 + 12.0629i) q^{71} +(-5.79581 - 10.0386i) q^{72} +(-6.73477 + 6.73477i) q^{73} +(10.8122 + 10.0653i) q^{74} +(-5.53521 - 1.48316i) q^{76} +(20.2340 - 5.42169i) q^{77} +(-0.873483 - 3.25988i) q^{78} +(-1.39018 - 5.18821i) q^{79} +(2.43622 - 4.21965i) q^{81} -2.27501 q^{82} +(2.38257 - 8.89188i) q^{83} -12.5697i q^{84} +(0.952085 + 1.64906i) q^{86} +(0.705596 - 1.22213i) q^{87} -20.8412 q^{88} +(-0.159121 + 0.593846i) q^{89} +(-2.39300 + 8.93078i) q^{91} +(-7.32514 - 4.22917i) q^{92} +(4.30691 + 2.48659i) q^{93} +(-6.01587 + 22.4515i) q^{94} +(0.174556 - 0.651451i) q^{96} -3.08147 q^{97} +(-17.5533 + 30.4032i) q^{98} +(-5.68747 - 9.85100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more