LMFDB - Embedded newform 175.2.x.a.103.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			103.11
Character	$\chi$	$=$	175.103
Dual form			175.2.x.a.17.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.670945 + 0.0351627i) q^{2} +(1.37832 + 1.70208i) q^{3} +(-1.54011 - 0.161872i) q^{4} +(-0.425878 + 2.19514i) q^{5} +(0.864927 + 1.19047i) q^{6} +(2.46336 - 0.965333i) q^{7} +(-2.35483 - 0.372968i) q^{8} +(-0.373586 + 1.75758i) q^{9} +O(q^{10})$	\(q+(0.670945 + 0.0351627i) q^{2} +(1.37832 + 1.70208i) q^{3} +(-1.54011 - 0.161872i) q^{4} +(-0.425878 + 2.19514i) q^{5} +(0.864927 + 1.19047i) q^{6} +(2.46336 - 0.965333i) q^{7} +(-2.35483 - 0.372968i) q^{8} +(-0.373586 + 1.75758i) q^{9} +(-0.362928 + 1.45784i) q^{10} +(-2.32965 + 0.495182i) q^{11} +(-1.84725 - 2.84451i) q^{12} +(4.81814 + 2.45497i) q^{13} +(1.68672 - 0.561067i) q^{14} +(-4.32330 + 2.30072i) q^{15} +(1.46267 + 0.310899i) q^{16} +(-1.97071 - 5.13388i) q^{17} +(-0.312457 + 1.16611i) q^{18} +(-0.0661806 - 0.629666i) q^{19} +(1.01123 - 3.31182i) q^{20} +(5.03837 + 2.86230i) q^{21} +(-1.58048 + 0.250323i) q^{22} +(0.210437 - 4.01538i) q^{23} +(-2.61088 - 4.52218i) q^{24} +(-4.63726 - 1.86972i) q^{25} +(3.14639 + 1.81657i) q^{26} +(2.34790 - 1.19631i) q^{27} +(-3.95011 + 1.08797i) q^{28} +(3.54543 - 4.87987i) q^{29} +(-2.98160 + 1.39164i) q^{30} +(-0.355582 + 0.798651i) q^{31} +(5.57632 + 1.49417i) q^{32} +(-4.05384 - 3.28273i) q^{33} +(-1.14172 - 3.51385i) q^{34} +(1.06995 + 5.81852i) q^{35} +(0.859869 - 2.64640i) q^{36} +(-3.37339 + 2.19070i) q^{37} +(-0.0222627 - 0.424798i) q^{38} +(2.46238 + 11.5846i) q^{39} +(1.82159 - 5.01033i) q^{40} +(-4.20425 + 1.36604i) q^{41} +(3.27982 + 2.09761i) q^{42} +(4.81389 + 4.81389i) q^{43} +(3.66808 - 0.385530i) q^{44} +(-3.69904 - 1.56859i) q^{45} +(0.282384 - 2.68670i) q^{46} +(-9.20850 - 3.53481i) q^{47} +(1.48684 + 2.91810i) q^{48} +(5.13627 - 4.75592i) q^{49} +(-3.04560 - 1.41754i) q^{50} +(6.02202 - 10.4304i) q^{51} +(-7.02309 - 4.56085i) q^{52} +(-8.11171 + 6.56873i) q^{53} +(1.61738 - 0.720102i) q^{54} +(-0.0948463 - 5.32478i) q^{55} +(-6.16082 + 1.35444i) q^{56} +(0.980526 - 0.980526i) q^{57} +(2.55038 - 3.14946i) q^{58} +(2.26933 - 2.52034i) q^{59} +(7.03079 - 2.84355i) q^{60} +(1.38336 - 1.24558i) q^{61} +(-0.266659 + 0.523348i) q^{62} +(0.776377 + 4.69019i) q^{63} +(0.844556 + 0.274413i) q^{64} +(-7.44093 + 9.53097i) q^{65} +(-2.60447 - 2.34508i) q^{66} +(-8.85772 + 3.40016i) q^{67} +(2.20409 + 8.22576i) q^{68} +(7.12456 - 5.17630i) q^{69} +(0.513281 + 3.94153i) q^{70} +(-5.22766 - 3.79812i) q^{71} +(1.53525 - 3.99947i) q^{72} +(-4.92365 + 7.58176i) q^{73} +(-2.34039 + 1.35122i) q^{74} +(-3.20920 - 10.4701i) q^{75} +0.980470i q^{76} +(-5.26074 + 3.46870i) q^{77} +(1.24478 + 7.85922i) q^{78} +(4.19876 + 9.43057i) q^{79} +(-1.30538 + 3.07835i) q^{80} +(10.1969 + 4.53995i) q^{81} +(-2.86886 + 0.768708i) q^{82} +(1.39322 - 8.79644i) q^{83} +(-7.29633 - 5.22384i) q^{84} +(12.1089 - 2.13958i) q^{85} +(3.06059 + 3.39913i) q^{86} +(13.1927 - 0.691399i) q^{87} +(5.67061 - 0.297184i) q^{88} +(9.71742 + 10.7923i) q^{89} +(-2.42669 - 1.18251i) q^{90} +(14.2387 + 1.39635i) q^{91} +(-0.974077 + 6.15008i) q^{92} +(-1.84948 + 0.495566i) q^{93} +(-6.05411 - 2.69546i) q^{94} +(1.41039 + 0.122886i) q^{95} +(5.14275 + 11.5508i) q^{96} +(1.14852 + 7.25146i) q^{97} +(3.61338 - 3.01036i) q^{98} -4.27954i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	0.670945	+	0.0351627i	0.474430	+	0.0248638i	0.288053	−	0.957614i	$-0.406992\pi$
$2$	0.670945	+	0.0351627i	0.474430	+	0.0248638i	0.186377	+	0.982478i	$0.440325\pi$
$3$	1.37832	+	1.70208i	0.795773	+	0.982698i	0.999993	+	0.00377279i	$0.00120092\pi$
$3$	1.37832	+	1.70208i	0.795773	+	0.982698i	−0.204220	+	0.978925i	$0.565466\pi$
$4$	−1.54011	−	0.161872i	−0.770056	−	0.0809362i
$5$	−0.425878	+	2.19514i	−0.190458	+	0.981695i
$5$	−0.425878	+	2.19514i	−0.190458	+	0.981695i
$6$	0.864927	+	1.19047i	0.353105	+	0.486007i
$7$	2.46336	−	0.965333i	0.931062	−	0.364861i
$7$	2.46336	−	0.965333i	0.931062	−	0.364861i
$8$	−2.35483	−	0.372968i	−0.832557	−	0.131864i
$9$	−0.373586	+	1.75758i	−0.124529	+	0.585861i
$10$	−0.362928	+	1.45784i	−0.114768	+	0.461010i
$11$	−2.32965	+	0.495182i	−0.702415	+	0.149303i	−0.545255	−	0.838270i	$-0.683567\pi$
$11$	−2.32965	+	0.495182i	−0.702415	+	0.149303i	−0.157160	+	0.987573i	$0.550234\pi$
$12$	−1.84725	−	2.84451i	−0.533254	−	0.821140i
$13$	4.81814	+	2.45497i	1.33631	+	0.680885i	0.968500	−	0.249014i	$-0.0801066\pi$
$13$	4.81814	+	2.45497i	1.33631	+	0.680885i	0.367813	+	0.929900i	$0.380107\pi$
$14$	1.68672	−	0.561067i	0.450795	−	0.149951i
$15$	−4.32330	+	2.30072i	−1.11627	+	0.594043i
$16$	1.46267	+	0.310899i	0.365666	+	0.0777248i
$17$	−1.97071	−	5.13388i	−0.477968	−	1.24515i	−0.934666	−	0.355527i	$-0.884301\pi$
$17$	−1.97071	−	5.13388i	−0.477968	−	1.24515i	0.456698	−	0.889622i	$-0.349032\pi$
$18$	−0.312457	+	1.16611i	−0.0736469	+	0.274854i
$19$	−0.0661806	−	0.629666i	−0.0151829	−	0.144455i	0.984304	−	0.176480i	$-0.0564711\pi$
$19$	−0.0661806	−	0.629666i	−0.0151829	−	0.144455i	−0.999487	+	0.0320248i	$0.989804\pi$
$20$	1.01123	−	3.31182i	0.226118	−	0.740546i
$21$	5.03837	+	2.86230i	1.09946	+	0.624606i
$22$	−1.58048	+	0.250323i	−0.336959	+	0.0533691i
$23$	0.210437	−	4.01538i	0.0438792	−	0.837265i	−0.884707	−	0.466148i	$-0.845641\pi$
$23$	0.210437	−	4.01538i	0.0438792	−	0.837265i	0.928586	−	0.371117i	$-0.121025\pi$
$24$	−2.61088	−	4.52218i	−0.532944	−	0.923086i
$25$	−4.63726	−	1.86972i	−0.927451	−	0.373944i
$26$	3.14639	+	1.81657i	0.617057	+	0.356258i
$27$	2.34790	−	1.19631i	0.451853	−	0.230231i
$28$	−3.95011	+	1.08797i	−0.746501	+	0.205607i
$29$	3.54543	−	4.87987i	0.658371	−	0.906170i	−0.341055	−	0.940043i	$-0.610784\pi$
$29$	3.54543	−	4.87987i	0.658371	−	0.906170i	0.999426	+	0.0338736i	$0.0107844\pi$
$30$	−2.98160	+	1.39164i	−0.544363	+	0.254077i
$31$	−0.355582	+	0.798651i	−0.0638645	+	0.143442i	−0.942658	−	0.333760i	$-0.891682\pi$
$31$	−0.355582	+	0.798651i	−0.0638645	+	0.143442i	0.878794	+	0.477202i	$0.158349\pi$
$32$	5.57632	+	1.49417i	0.985763	+	0.264135i
$33$	−4.05384	−	3.28273i	−0.705683	−	0.571451i
$34$	−1.14172	−	3.51385i	−0.195803	−	0.602620i
$35$	1.06995	+	5.81852i	0.180854	+	0.983510i
$36$	0.859869	−	2.64640i	0.143311	−	0.441067i
$37$	−3.37339	+	2.19070i	−0.554581	+	0.360149i	−0.791299	−	0.611429i	$-0.790595\pi$
$37$	−3.37339	+	2.19070i	−0.554581	+	0.360149i	0.236718	+	0.971578i	$0.423928\pi$
$38$	−0.0222627	−	0.424798i	−0.00361149	−	0.0689114i
$39$	2.46238	+	11.5846i	0.394297	+	1.85502i
$40$	1.82159	−	5.01033i	0.288018	−	0.792203i
$41$	−4.20425	+	1.36604i	−0.656594	+	0.213340i	−0.618319	−	0.785927i	$-0.712186\pi$
$41$	−4.20425	+	1.36604i	−0.656594	+	0.213340i	−0.0382745	+	0.999267i	$0.512186\pi$
$42$	3.27982	+	2.09761i	0.506088	+	0.323668i
$43$	4.81389	+	4.81389i	0.734112	+	0.734112i	0.971432	−	0.237320i	$-0.0762690\pi$
$43$	4.81389	+	4.81389i	0.734112	+	0.734112i	−0.237320	+	0.971432i	$0.576269\pi$
$44$	3.66808	−	0.385530i	0.552983	−	0.0581209i
$45$	−3.69904	−	1.56859i	−0.551420	−	0.233831i
$46$	0.282384	−	2.68670i	0.0416352	−	0.396133i
$47$	−9.20850	−	3.53481i	−1.34320	−	0.515605i	−0.422670	−	0.906283i	$-0.638907\pi$
$47$	−9.20850	−	3.53481i	−1.34320	−	0.515605i	−0.920527	+	0.390678i	$0.872241\pi$
$48$	1.48684	+	2.91810i	0.214607	+	0.421191i
$49$	5.13627	−	4.75592i	0.733752	−	0.679417i
$50$	−3.04560	−	1.41754i	−0.430713	−	0.200470i
$51$	6.02202	−	10.4304i	0.843251	−	1.46055i
$52$	−7.02309	−	4.56085i	−0.973928	−	0.632476i
$53$	−8.11171	+	6.56873i	−1.11423	+	0.902284i	−0.995879	−	0.0906875i	$-0.971094\pi$
$53$	−8.11171	+	6.56873i	−1.11423	+	0.902284i	−0.118349	+	0.992972i	$0.537760\pi$
$54$	1.61738	−	0.720102i	0.220097	−	0.0979935i
$55$	−0.0948463	−	5.32478i	−0.0127891	−	0.717994i
$56$	−6.16082	+	1.35444i	−0.823274	+	0.180994i
$57$	0.980526	−	0.980526i	0.129874	−	0.129874i
$58$	2.55038	−	3.14946i	0.334882	−	0.413544i
$59$	2.26933	−	2.52034i	0.295441	−	0.328120i	−0.577089	−	0.816681i	$-0.695811\pi$
$59$	2.26933	−	2.52034i	0.295441	−	0.328120i	0.872530	+	0.488561i	$0.162478\pi$
$60$	7.03079	−	2.84355i	0.907672	−	0.367100i
$61$	1.38336	−	1.24558i	0.177121	−	0.159481i	−0.575802	−	0.817589i	$-0.695310\pi$
$61$	1.38336	−	1.24558i	0.177121	−	0.159481i	0.752923	+	0.658109i	$0.228643\pi$
$62$	−0.266659	+	0.523348i	−0.0338657	+	0.0664652i
$63$	0.776377	+	4.69019i	0.0978143	+	0.590909i
$64$	0.844556	+	0.274413i	0.105570	+	0.0343016i
$65$	−7.44093	+	9.53097i	−0.922934	+	1.18217i
$66$	−2.60447	−	2.34508i	−0.320589	−	0.288659i
$67$	−8.85772	+	3.40016i	−1.08214	+	0.415396i	−0.833115	−	0.553100i	$-0.813445\pi$
$67$	−8.85772	+	3.40016i	−1.08214	+	0.415396i	−0.249029	+	0.968496i	$0.580111\pi$
$68$	2.20409	+	8.22576i	0.267285	+	0.997520i
$69$	7.12456	−	5.17630i	0.857696	−	0.623153i
$70$	0.513281	+	3.94153i	0.0613488	+	0.471103i
$71$	−5.22766	−	3.79812i	−0.620410	−	0.450754i	0.232655	−	0.972559i	$-0.425259\pi$
$71$	−5.22766	−	3.79812i	−0.620410	−	0.450754i	−0.853065	+	0.521805i	$0.825259\pi$
$72$	1.53525	−	3.99947i	0.180931	−	0.471342i
$73$	−4.92365	+	7.58176i	−0.576270	+	0.887378i	−0.999829	−	0.0184903i	$-0.994114\pi$
$73$	−4.92365	+	7.58176i	−0.576270	+	0.887378i	0.423559	+	0.905869i	$0.360781\pi$
$74$	−2.34039	+	1.35122i	−0.272065	+	0.157077i
$75$	−3.20920	−	10.4701i	−0.370566	−	1.20898i
$76$			0.980470i			0.112468i
$77$	−5.26074	+	3.46870i	−0.599517	+	0.395295i
$78$	1.24478	+	7.85922i	0.140943	+	0.889882i
$79$	4.19876	+	9.43057i	0.472397	+	1.06102i	0.979921	+	0.199384i	$0.0638942\pi$
$79$	4.19876	+	9.43057i	0.472397	+	1.06102i	−0.507524	+	0.861638i	$0.669439\pi$
$80$	−1.30538	+	3.07835i	−0.145946	+	0.344170i
$81$	10.1969	+	4.53995i	1.13299	+	0.504438i
$82$	−2.86886	+	0.768708i	−0.316812	+	0.0848896i
$83$	1.39322	−	8.79644i	0.152926	−	0.965535i	−0.785201	−	0.619242i	$-0.787440\pi$
$83$	1.39322	−	8.79644i	0.152926	−	0.965535i	0.938126	−	0.346293i	$-0.112560\pi$
$84$	−7.29633	−	5.22384i	−0.796095	−	0.569968i
$85$	12.1089	−	2.13958i	1.31339	−	0.232070i
$86$	3.06059	+	3.39913i	0.330032	+	0.366537i
$87$	13.1927	−	0.691399i	1.41440	−	0.0741258i
$88$	5.67061	−	0.297184i	0.604489	−	0.0316799i
$89$	9.71742	+	10.7923i	1.03004	+	1.14398i	0.989460	+	0.144805i	$0.0462554\pi$
$89$	9.71742	+	10.7923i	1.03004	+	1.14398i	0.0405846	+	0.999176i	$0.487078\pi$
$90$	−2.42669	−	1.18251i	−0.255796	−	0.124647i
$91$	14.2387	+	1.39635i	1.49262	+	0.146377i
$92$	−0.974077	+	6.15008i	−0.101554	+	0.641190i
$93$	−1.84948	+	0.495566i	−0.191782	+	0.0513878i
$94$	−6.05411	−	2.69546i	−0.624433	−	0.278016i
$95$	1.41039	+	0.122886i	0.144703	+	0.0126078i
$96$	5.14275	+	11.5508i	0.524880	+	1.17890i
$97$	1.14852	+	7.25146i	0.116614	+	0.736275i	0.974824	+	0.222975i	$0.0715769\pi$
$97$	1.14852	+	7.25146i	0.116614	+	0.736275i	−0.858210	+	0.513299i	$0.828423\pi$
$98$	3.61338	−	3.01036i	0.365007	−	0.304092i
$99$		−	4.27954i		−	0.430110i
$100$	6.83924	+	3.63023i	0.683924	+	0.363023i
$101$	−7.48294	+	4.32028i	−0.744581	+	0.429884i	−0.823732	−	0.566979i	$-0.808112\pi$
$101$	−7.48294	+	4.32028i	−0.744581	+	0.429884i	0.0791518	+	0.996863i	$0.474779\pi$
$102$	4.40721	−	6.78650i	0.436378	−	0.671964i
$103$	7.01977	−	18.2871i	0.691679	−	1.80189i	0.101146	−	0.994872i	$-0.467749\pi$
$103$	7.01977	−	18.2871i	0.691679	−	1.80189i	0.590533	−	0.807014i	$-0.298918\pi$
$104$	−10.4303	−	7.57804i	−1.02277	−	0.743088i
$105$	−8.42888	+	9.84092i	−0.822574	+	0.960376i
$106$	−5.67348	+	4.12203i	−0.551058	+	0.400367i
$107$	1.35568	+	5.05946i	0.131058	+	0.489117i	0.999983	−	0.00582782i	$-0.00185506\pi$
$107$	1.35568	+	5.05946i	0.131058	+	0.489117i	−0.868925	+	0.494944i	$0.835188\pi$
$108$	−3.80968	+	1.46240i	−0.366586	+	0.140719i
$109$	−3.01581	−	2.71545i	−0.288862	−	0.260093i	0.511941	−	0.859021i	$-0.328927\pi$
$109$	−3.01581	−	2.71545i	−0.288862	−	0.260093i	−0.800803	+	0.598928i	$0.795593\pi$
$110$	0.123597	−	3.57597i	0.0117845	−	0.340956i
$111$	−8.37836	−	2.72230i	−0.795239	−	0.258389i
$112$	3.90319	−	0.646103i	0.368817	−	0.0610510i
$113$	−2.16130	+	4.24179i	−0.203318	+	0.399034i	−0.970040	−	0.242945i	$-0.921886\pi$
$113$	−2.16130	+	4.24179i	−0.203318	+	0.399034i	0.766722	+	0.641979i	$0.221886\pi$
$114$	0.692357	−	0.623401i	0.0648452	−	0.0583869i
$115$	8.72469	+	2.17200i	0.813582	+	0.202540i
$116$	−6.25029	+	6.94165i	−0.580325	+	0.644516i
$117$	−6.11480	+	7.55115i	−0.565314	+	0.698104i
$118$	1.61121	−	1.61121i	0.148324	−	0.148324i
$119$	−9.81047	−	10.7442i	−0.899324	−	0.984918i
$120$	11.0387	−	3.80535i	1.00769	−	0.347379i
$121$	−4.86695	+	2.16690i	−0.442450	+	0.196991i
$122$	0.971957	−	0.787075i	0.0879968	−	0.0712584i
$123$	−8.11992	−	5.27314i	−0.732149	−	0.475463i
$124$	0.676917	−	1.17245i	0.0607889	−	0.105289i
$125$	6.07920	−	9.38314i	0.543740	−	0.839253i
$126$	0.355986	+	3.17416i	0.0317138	+	0.282777i
$127$	−5.95516	−	11.6877i	−0.528435	−	1.03711i	−0.988781	−	0.149372i	$-0.952275\pi$
$127$	−5.95516	−	11.6877i	−0.528435	−	1.03711i	0.460346	−	0.887740i	$-0.347725\pi$
$128$	−10.2222	−	3.92393i	−0.903521	−	0.346829i
$129$	−1.55856	+	14.8287i	−0.137224	+	1.30560i
$130$	−5.32759	+	6.13312i	−0.467261	+	0.537910i
$131$	5.04196	−	0.529932i	0.440518	−	0.0463003i	0.118327	−	0.992975i	$-0.462247\pi$
$131$	5.04196	−	0.529932i	0.440518	−	0.0463003i	0.322192	+	0.946674i	$0.395580\pi$
$132$	5.71198	+	5.71198i	0.497164	+	0.497164i
$133$	−0.770864	−	1.48721i	−0.0668424	−	0.128957i
$134$	−6.06261	+	1.96986i	−0.523729	+	0.170170i
$135$	1.62615	+	5.66344i	0.139957	+	0.487431i
$136$	2.72591	+	12.8244i	0.233745	+	1.09968i
$137$	0.136459	+	2.60380i	0.0116585	+	0.222458i	0.998245	+	0.0592186i	$0.0188609\pi$
$137$	0.136459	+	2.60380i	0.0116585	+	0.222458i	−0.986587	+	0.163239i	$0.947806\pi$
$138$	4.96220	−	3.22249i	0.422411	−	0.274317i
$139$	−1.39562	+	4.29528i	−0.118375	+	0.364321i	−0.992636	−	0.121135i	$-0.961346\pi$
$139$	−1.39562	+	4.29528i	−0.118375	+	0.364321i	0.874261	+	0.485456i	$0.161346\pi$
$140$	−0.705982	−	9.13438i	−0.0596664	−	0.771996i
$141$	−6.67571	−	20.5457i	−0.562196	−	1.73026i
$142$	−3.37392	−	2.73215i	−0.283133	−	0.229277i
$143$	−12.4402	−	3.33335i	−1.04030	−	0.278749i
$144$	−1.09286	+	2.45461i	−0.0910719	+	0.204551i
$145$	9.20207	+	9.86095i	0.764190	+	0.818907i
$146$	−3.57010	+	4.91382i	−0.295463	+	0.406670i
$147$	15.1744	+	2.18717i	1.25156	+	0.180395i
$148$	5.55001	−	2.82787i	0.456208	−	0.232450i
$149$	3.79735	+	2.19240i	0.311091	+	0.179608i	0.647415	−	0.762138i	$-0.275850\pi$
$149$	3.79735	+	2.19240i	0.311091	+	0.179608i	−0.336324	+	0.941746i	$0.609184\pi$
$150$	−1.78504	−	7.13768i	−0.145748	−	0.582790i
$151$	−1.93684	−	3.35470i	−0.157618	−	0.273002i	0.776391	−	0.630251i	$-0.217048\pi$
$151$	−1.93684	−	3.35470i	−0.157618	−	0.273002i	−0.934009	+	0.357249i	$0.883715\pi$
$152$	−0.0790015	+	1.50744i	−0.00640787	+	0.122269i
$153$	9.75945	−	1.54575i	0.789005	−	0.124966i
$154$	−3.65164	+	2.14232i	−0.294257	+	0.172633i
$155$	−1.60171	−	1.12068i	−0.128653	−	0.0900152i
$156$	−1.91712	−	18.2402i	−0.153493	−	1.46038i
$157$	3.66515	−	13.6785i	0.292511	−	1.09166i	−0.650664	−	0.759366i	$-0.725509\pi$
$157$	3.66515	−	13.6785i	0.292511	−	1.09166i	0.943174	−	0.332299i	$-0.107824\pi$
$158$	2.48553	+	6.47503i	0.197738	+	0.515126i
$159$	−22.3610	−	4.75299i	−1.77335	−	0.376936i
$160$	−5.65474	+	11.6045i	−0.447047	+	0.917413i
$161$	−3.35780	−	10.0945i	−0.264632	−	0.795555i
$162$	6.68191	+	3.40461i	0.524981	+	0.267491i
$163$	−12.4402	−	19.1562i	−0.974389	−	1.50043i	−0.862091	−	0.506753i	$-0.830846\pi$
$163$	−12.4402	−	19.1562i	−0.974389	−	1.50043i	−0.112298	−	0.993675i	$-0.535821\pi$
$164$	6.69615	−	1.42331i	0.522881	−	0.111142i
$165$	8.93249	−	7.50069i	0.695394	−	0.583928i
$166$	1.24408	−	5.85294i	0.0965594	−	0.454276i
$167$	3.49037	+	0.552820i	0.270093	+	0.0427785i	0.290012	−	0.957023i	$-0.406341\pi$
$167$	3.49037	+	0.552820i	0.270093	+	0.0427785i	−0.0199188	+	0.999802i	$0.506341\pi$
$168$	−10.7969	−	8.61938i	−0.833002	−	0.665000i
$169$	9.54644	+	13.1396i	0.734342	+	1.01073i
$170$	8.19961	−	1.00976i	0.628881	−	0.0774449i
$171$	1.13141	+	0.118916i	0.0865215	+	0.00909377i
$172$	−6.63470	−	8.19317i	−0.505891	−	0.624724i
$173$	3.92127	+	0.205505i	0.298128	+	0.0156242i	0.200814	−	0.979629i	$-0.435641\pi$
$173$	3.92127	+	0.205505i	0.298128	+	0.0156242i	0.0973145	+	0.995254i	$0.468975\pi$
$174$	8.87588			0.672879
$175$	−13.2281	−	0.129300i	−0.999952	−	0.00977415i
$176$	−3.56145			−0.268454
$177$	7.41768	+	0.388744i	0.557547	+	0.0292198i
$178$	6.14037	+	7.58273i	0.460240	+	0.568350i
$179$	−5.11639	−	0.537754i	−0.382417	−	0.0401936i	−0.0886300	−	0.996065i	$-0.528249\pi$
$179$	−5.11639	−	0.537754i	−0.382417	−	0.0401936i	−0.293787	+	0.955871i	$0.594916\pi$
$180$	5.44302	+	3.01458i	0.405699	+	0.224693i
$181$	10.5053	+	14.4592i	0.780849	+	1.07475i	0.995188	+	0.0979875i	$0.0312405\pi$
$181$	10.5053	+	14.4592i	0.780849	+	1.07475i	−0.214338	+	0.976759i	$0.568759\pi$
$182$	9.50427	+	1.43755i	0.704503	+	0.106558i
$183$	4.02680	+	0.637782i	0.297669	+	0.0471462i
$184$	−1.99315	+	9.37705i	−0.146937	+	0.691285i
$185$	−3.37224	−	8.33802i	−0.247932	−	0.613023i
$186$	−1.25832	+	0.267465i	−0.0922647	+	0.0196115i
$187$	7.13327	+	10.9843i	0.521636	+	0.803249i
$188$	13.6099	+	6.93461i	0.992607	+	0.505758i
$189$	4.62887	−	5.21345i	0.336701	−	0.379223i
$190$	0.941972	+	0.132043i	0.0683378	+	0.00957938i
$191$	8.44595	+	1.79524i	0.611128	+	0.129899i	0.503070	−	0.864245i	$-0.332204\pi$
$191$	8.44595	+	1.79524i	0.611128	+	0.129899i	0.108057	+	0.994145i	$0.465537\pi$
$192$	0.696994	+	1.81573i	0.0503012	+	0.131039i
$193$	4.22898	−	15.7828i	0.304409	−	1.13607i	−0.629045	−	0.777369i	$-0.716554\pi$
$193$	4.22898	−	15.7828i	0.304409	−	1.13607i	0.933453	−	0.358699i	$-0.116780\pi$
$194$	0.515612	+	4.90572i	0.0370188	+	0.352210i
$195$	−26.4785	+	0.471641i	−1.89616	+	0.0337749i
$196$	−8.68028	+	6.49323i	−0.620020	+	0.463802i
$197$	−24.2100	+	3.83449i	−1.72489	+	0.273196i	−0.938687	−	0.344770i	$-0.887957\pi$
$197$	−24.2100	+	3.83449i	−1.72489	+	0.273196i	−0.786205	+	0.617966i	$0.787957\pi$
$198$	0.150481	−	2.87134i	0.0106942	−	0.204057i
$199$	−8.73867	−	15.1358i	−0.619468	−	1.07295i	−0.989583	−	0.143964i	$-0.954015\pi$
$199$	−8.73867	−	15.1358i	−0.619468	−	1.07295i	0.370115	−	0.928986i	$-0.379318\pi$
$200$	10.2226	+	6.13242i	0.722846	+	0.433628i
$201$	−17.9961	−	10.3901i	−1.26935	−	0.732859i
$202$	−5.17256	+	2.63555i	−0.363940	+	0.185437i
$203$	4.02297	−	15.4434i	0.282357	−	1.08391i
$204$	−10.9630	+	15.0893i	−0.767562	+	1.05646i
$205$	−1.20816	−	9.81068i	−0.0843813	−	0.685208i
$206$	5.35291	−	12.0228i	0.372955	−	0.837670i
$207$	6.97875	+	1.86995i	0.485057	+	0.129971i
$208$	6.28409	+	5.08875i	0.435723	+	0.352842i
$209$	0.465977	+	1.43413i	0.0322323	+	0.0992007i
$210$	−6.00135	+	6.30634i	−0.414132	+	0.435179i
$211$	1.48748	−	4.57800i	0.102403	−	0.315163i	−0.886710	−	0.462327i	$-0.847015\pi$
$211$	1.48748	−	4.57800i	0.102403	−	0.315163i	0.989112	+	0.147164i	$0.0470146\pi$
$212$	13.5562	−	8.80352i	0.931046	−	0.604629i
$213$	−0.740676	−	14.1329i	−0.0507503	−	0.968373i
$214$	0.731682	+	3.44229i	0.0500167	+	0.235310i
$215$	−12.6173	+	8.51702i	−0.860492	+	0.580856i
$216$	−5.97508	+	1.94142i	−0.406553	+	0.132097i
$217$	−0.104963	+	2.31062i	−0.00712533	+	0.156855i
$218$	−1.92796	−	1.92796i	−0.130578	−	0.130578i
$219$	−19.6912	+	2.06962i	−1.33060	+	0.139852i
$220$	−0.715861	+	8.21612i	−0.0482634	+	0.553931i
$221$	3.10833	−	29.5738i	0.209089	−	1.98935i
$222$	−5.52570	−	2.12112i	−0.370861	−	0.142360i
$223$	−2.94413	−	5.77818i	−0.197154	−	0.386936i	0.771172	−	0.636627i	$-0.219671\pi$
$223$	−2.94413	−	5.77818i	−0.197154	−	0.386936i	−0.968325	+	0.249691i	$0.919671\pi$
$224$	15.1788	−	1.70233i	1.01418	−	0.113742i
$225$	5.01861	−	7.45186i	0.334574	−	0.496791i
$226$	−1.59927	+	2.77001i	−0.106382	+	0.184258i
$227$	18.9570	+	12.3108i	1.25822	+	0.817097i	0.989276	−	0.146059i	$-0.0466590\pi$
$227$	18.9570	+	12.3108i	1.25822	+	0.817097i	0.268943	+	0.963156i	$0.413326\pi$
$228$	−1.66884	+	1.35140i	−0.110522	+	0.0894987i
$229$	−11.9800	+	5.33383i	−0.791660	+	0.352470i	−0.762403	−	0.647102i	$-0.775981\pi$
$229$	−11.9800	+	5.33383i	−0.791660	+	0.352470i	−0.0292566	+	0.999572i	$0.509314\pi$
$230$	5.77742	+	1.76408i	0.380952	+	0.116320i
$231$	−13.1550	−	4.17325i	−0.865535	−	0.274579i
$232$	−10.1689	+	10.1689i	−0.667623	+	0.667623i
$233$	−12.6777	+	15.6556i	−0.830542	+	1.02563i	0.168659	+	0.985674i	$0.446056\pi$
$233$	−12.6777	+	15.6556i	−0.830542	+	1.02563i	−0.999201	+	0.0399599i	$0.987277\pi$
$234$	−4.36822	+	4.85140i	−0.285559	+	0.317146i
$235$	11.6811	−	18.7085i	0.761991	−	1.22041i
$236$	−3.90299	+	3.51427i	−0.254063	+	0.228759i
$237$	−10.2644	+	20.1450i	−0.666743	+	1.30856i
$238$	−6.20449	−	7.55373i	−0.402178	−	0.489635i
$239$	13.8342	+	4.49501i	0.894861	+	0.290758i	0.720114	−	0.693855i	$-0.244089\pi$
$239$	13.8342	+	4.49501i	0.894861	+	0.290758i	0.174747	+	0.984613i	$0.444089\pi$
$240$	−7.03884	+	2.02107i	−0.454355	+	0.130460i
$241$	21.3511	+	19.2247i	1.37535	+	1.23837i	0.941340	+	0.337461i	$0.109568\pi$
$241$	21.3511	+	19.2247i	1.37535	+	1.23837i	0.434009	+	0.900909i	$0.357099\pi$
$242$	−3.34165	+	1.28274i	−0.214809	+	0.0824576i
$243$	4.28115	+	15.9775i	0.274636	+	1.02496i
$244$	−2.33216	+	1.69441i	−0.149301	+	0.108474i
$245$	8.25247	+	13.3003i	0.527231	+	0.849722i
$246$	−5.26260	−	3.82351i	−0.335531	−	0.243778i
$247$	1.22694	−	3.19629i	0.0780684	−	0.203375i
$248$	1.13521	−	1.74806i	0.0720857	−	0.111002i
$249$	16.8926	−	9.75293i	1.07052	−	0.618067i
$250$	4.40875	−	6.08181i	0.278834	−	0.384647i
$251$			10.7051i			0.675699i	0.941200	+	0.337850i	$0.109700\pi$
$251$			10.7051i			0.675699i	−0.941200	+	0.337850i	$0.890300\pi$
$252$	−0.436496	−	7.34910i	−0.0274966	−	0.462950i
$253$	1.49810	+	9.45863i	0.0941847	+	0.594659i
$254$	−3.58462	−	8.05118i	−0.224919	−	0.505176i
$255$	20.3316	+	17.6613i	1.27321	+	1.10599i
$256$	−8.34304	−	3.71456i	−0.521440	−	0.232160i
$257$	5.64851	−	1.51351i	0.352344	−	0.0944103i	−0.0783057	−	0.996929i	$-0.524951\pi$
$257$	5.64851	−	1.51351i	0.352344	−	0.0944103i	0.430650	+	0.902519i	$0.358284\pi$
$258$	−1.56713	+	9.89446i	−0.0975651	+	0.616002i
$259$	−6.19510	+	8.65293i	−0.384945	+	0.537667i
$260$	13.0027	−	13.4743i	0.806392	−	0.835640i
$261$	7.25226	+	8.05445i	0.448904	+	0.498558i
$262$	3.40151	−	0.178266i	0.210146	−	0.0110133i
$263$	−2.53371	+	0.132786i	−0.156235	+	0.00818794i	−0.130293	−	0.991476i	$-0.541592\pi$
$263$	−2.53371	+	0.132786i	−0.156235	+	0.00818794i	−0.0259420	+	0.999663i	$0.508259\pi$
$264$	8.32174	+	9.24223i	0.512168	+	0.568820i
$265$	−10.9647	−	20.6038i	−0.673554	−	1.26568i
$266$	−0.464913	−	1.02494i	−0.0285056	−	0.0628431i
$267$	−4.97566	+	31.4151i	−0.304505	+	1.92257i
$268$	14.1923	−	3.80281i	0.866932	−	0.232294i
$269$	21.3506	+	9.50590i	1.30177	+	0.579585i	0.936288	−	0.351234i	$-0.114238\pi$
$269$	21.3506	+	9.50590i	1.30177	+	0.579585i	0.365481	+	0.930819i	$0.380904\pi$
$270$	0.891918	+	3.85704i	0.0542804	+	0.234732i
$271$	−8.15975	−	18.3271i	−0.495670	−	1.11329i	−0.972204	−	0.234136i	$-0.924774\pi$
$271$	−8.15975	−	18.3271i	−0.495670	−	1.11329i	0.476534	−	0.879156i	$-0.341893\pi$
$272$	−1.28637	−	8.12184i	−0.0779978	−	0.492459i
$273$	17.2487	+	26.1600i	1.04394	+	1.58328i
$274$			1.75181i			0.105831i
$275$	11.7290	+	2.05951i	0.707287	+	0.124193i
$276$	−11.8105	+	6.81881i	−0.710910	+	0.410444i
$277$	−5.76296	+	8.87418i	−0.346263	+	0.533198i	−0.968300	−	0.249790i	$-0.919638\pi$
$277$	−5.76296	+	8.87418i	−0.346263	+	0.533198i	0.622038	+	0.782987i	$0.286305\pi$
$278$	−1.08742	+	2.83282i	−0.0652190	+	0.169901i
$279$	−1.27086	−	0.923331i	−0.0760841	−	0.0552784i
$280$	−0.349419	−	14.1007i	−0.0208818	−	0.842677i
$281$	−10.1750	+	7.39260i	−0.606992	+	0.441006i	−0.848354	−	0.529430i	$-0.822406\pi$
$281$	−10.1750	+	7.39260i	−0.606992	+	0.441006i	0.241362	+	0.970435i	$0.422406\pi$
$282$	−3.75659	−	14.0198i	−0.223702	−	0.834867i
$283$	22.8578	−	8.77430i	1.35876	−	0.521578i	0.433580	−	0.901115i	$-0.357250\pi$
$283$	22.8578	−	8.77430i	1.35876	−	0.521578i	0.925176	+	0.379537i	$0.123917\pi$
$284$	7.43638	+	6.69575i	0.441268	+	0.397320i
$285$	1.73480	+	2.56997i	0.102761	+	0.152232i
$286$	−8.22951	−	2.67393i	−0.486621	−	0.158113i
$287$	−9.03789	+	7.42356i	−0.533490	+	0.438199i
$288$	−4.70936	+	9.24265i	−0.277502	+	0.544628i
$289$	−9.83955	+	8.85957i	−0.578797	+	0.521151i
$290$	5.82734	+	6.93973i	0.342193	+	0.407515i
$291$	−10.7596	+	11.9497i	−0.630737	+	0.700504i
$292$	8.81026	−	10.8798i	0.515582	−	0.636690i
$293$	−2.01237	+	2.01237i	−0.117564	+	0.117564i	−0.763441	−	0.645877i	$-0.776492\pi$
$293$	−2.01237	+	2.01237i	−0.117564	+	0.117564i	0.645877	+	0.763441i	$0.276492\pi$
$294$	10.1043	+	2.00104i	0.589293	+	0.116703i
$295$	4.56604	+	6.05484i	0.265845	+	0.352526i
$296$	8.76081	−	3.90056i	0.509212	−	0.226716i
$297$	−4.87738	+	3.94962i	−0.283014	+	0.229180i
$298$	2.47072	+	1.60451i	0.143125	+	0.0929465i
$299$	10.8715	−	18.8301i	0.628718	−	1.08897i
$300$	3.24771	+	16.6446i	0.187507	+	0.960974i
$301$	16.5053	+	7.21133i	0.951352	+	0.415654i
$302$	−1.18155	−	2.31893i	−0.0679907	−	0.133439i
$303$	−17.6674	−	6.78186i	−1.01496	−	0.389608i
$304$	0.0989626	−	0.941566i	0.00567589	−	0.0540025i
$305$	2.14508	+	3.56713i	0.122827	+	0.204253i
$306$	6.60241	−	0.693941i	0.377435	−	0.0396700i
$307$	0.990654	+	0.990654i	0.0565396	+	0.0565396i	0.734811	−	0.678272i	$-0.237271\pi$
$307$	0.990654	+	0.990654i	0.0565396	+	0.0565396i	−0.678272	+	0.734811i	$0.737271\pi$
$308$	8.66362	−	4.49061i	0.493656	−	0.255876i
$309$	40.8017	−	13.2573i	2.32113	−	0.754180i
$310$	−1.03526	−	0.808236i	−0.0587986	−	0.0459047i
$311$	−3.45657	−	16.2619i	−0.196004	−	0.922126i	−0.960669	−	0.277697i	$-0.910429\pi$
$311$	−3.45657	−	16.2619i	−0.196004	−	0.922126i	0.764665	−	0.644428i	$-0.222905\pi$
$312$	−1.47780	−	28.1981i	−0.0836641	−	1.59641i
$313$	−24.5390	+	15.9358i	−1.38703	+	0.900746i	−0.999775	−	0.0212272i	$-0.993243\pi$
$313$	−24.5390	+	15.9358i	−1.38703	+	0.900746i	−0.387253	+	0.921973i	$0.626576\pi$
$314$	2.94009	−	9.04866i	0.165919	−	0.510646i
$315$	−10.6263	−	0.293196i	−0.598722	−	0.0165197i
$316$	−4.94001	−	15.2038i	−0.277898	−	0.855281i
$317$	−0.188117	−	0.152334i	−0.0105657	−	0.00855595i	0.624023	−	0.781406i	$-0.285497\pi$
$317$	−0.188117	−	0.152334i	−0.0105657	−	0.00855595i	−0.634589	+	0.772850i	$0.718830\pi$
$318$	−14.8359	−	3.97527i	−0.831956	−	0.222922i
$319$	−5.84319	+	13.1240i	−0.327156	+	0.734804i
$320$	−0.962052	+	1.73705i	−0.0537803	+	0.0971040i
$321$	−6.74306	+	9.28103i	−0.376361	+	0.518017i
$322$	−1.89795	−	6.89090i	−0.105769	−	0.384015i
$323$	−3.10221	+	1.58065i	−0.172611	+	0.0879499i
$324$	−14.9695	−	8.64262i	−0.831637	−	0.480146i
$325$	−17.7529	−	20.3929i	−0.984752	−	1.13119i
$326$	−7.67309	−	13.2902i	−0.424973	−	0.736075i
$327$	0.465167	−	8.87591i	0.0257238	−	0.490839i
$328$	10.4098	−	1.64875i	0.574784	−	0.0910368i
$329$	−26.0961	+	0.181759i	−1.43872	+	0.0100207i
$330$	6.25696	−	4.71846i	0.344434	−	0.259743i
$331$	3.57176	+	33.9831i	0.196322	+	1.86788i	0.439967	+	0.898014i	$0.354990\pi$
$331$	3.57176	+	33.9831i	0.196322	+	1.86788i	−0.243645	+	0.969864i	$0.578343\pi$
$332$	−3.56962	+	13.3220i	−0.195908	+	0.731139i
$333$	−2.59009	−	6.74743i	−0.141936	−	0.369757i
$334$	2.32241	+	0.493643i	0.127077	+	0.0270109i
$335$	−3.69151	−	20.8920i	−0.201689	−	1.14145i
$336$	6.47956	+	5.75302i	0.353489	+	0.313853i
$337$	−7.42698	−	3.78424i	−0.404574	−	0.206141i	0.239849	−	0.970810i	$-0.422902\pi$
$337$	−7.42698	−	3.78424i	−0.404574	−	0.206141i	−0.644422	+	0.764670i	$0.722902\pi$
$338$	5.94312	+	9.15160i	0.323263	+	0.497781i
$339$	−10.1988	+	2.16783i	−0.553925	+	0.117740i
$340$	−18.9953	+	1.33510i	−1.03017	+	0.0724059i
$341$	0.432904	−	2.03665i	0.0234431	−	0.110291i
$342$	0.754936	+	0.119570i	0.0408223	+	0.00646561i
$343$	8.06141	−	16.6737i	0.435275	−	0.900297i
$344$	−9.54046	−	13.1313i	−0.514387	−	0.707993i
$345$	8.32849	+	17.8439i	0.448391	+	0.960681i
$346$	2.62373	+	0.275765i	0.141052	+	0.0148252i
$347$	4.04395	+	4.99386i	0.217090	+	0.268084i	0.874044	−	0.485847i	$-0.161489\pi$
$347$	4.04395	+	4.99386i	0.217090	+	0.268084i	−0.656954	+	0.753931i	$0.728155\pi$
$348$	−20.4301	−	1.07070i	−1.09517	−	0.0573955i
$349$	−6.49322			−0.347574			−0.173787	−	0.984783i	$-0.555600\pi$
$349$	−6.49322			−0.347574			−0.173787	+	0.984783i	$0.555600\pi$
$350$	−8.87080	−	0.551890i	−0.474164	−	0.0294998i
$351$	14.2494			0.760577
$352$	−13.7307	−	0.719598i	−0.731851	−	0.0383547i
$353$	12.5999	+	15.5596i	0.670624	+	0.828151i	0.992957	−	0.118475i	$-0.0378005\pi$
$353$	12.5999	+	15.5596i	0.670624	+	0.828151i	−0.322333	+	0.946626i	$0.604467\pi$
$354$	4.96319	+	0.521652i	0.263791	+	0.0277255i
$355$	10.5637	−	9.85790i	0.560665	−	0.523203i
$356$	−13.2190	−	18.1943i	−0.700603	−	0.964298i
$357$	4.76554	−	31.5072i	0.252219	−	1.66754i
$358$	−3.41391	−	0.540710i	−0.180431	−	0.0285774i
$359$	−2.01213	+	9.46632i	−0.106196	+	0.499613i	0.892613	+	0.450824i	$0.148870\pi$
$359$	−2.01213	+	9.46632i	−0.106196	+	0.499613i	−0.998809	+	0.0487896i	$0.984464\pi$
$360$	8.12556	+	5.07338i	0.428255	+	0.267391i
$361$	18.1927	−	3.86698i	0.957511	−	0.203525i
$362$	6.54002	+	10.0708i	0.343736	+	0.529307i
$363$	−10.3965	−	5.29726i	−0.545672	−	0.278034i
$364$	−21.7031	−	4.45539i	−1.13755	−	0.233526i
$365$	−14.5461	−	14.0370i	−0.761379	−	0.734730i
$366$	2.67933	+	0.569510i	0.140051	+	0.0297688i
$367$	−7.06326	−	18.4004i	−0.368699	−	0.960494i	−0.984934	−	0.172932i	$-0.944676\pi$
$367$	−7.06326	−	18.4004i	−0.368699	−	0.960494i	0.616235	−	0.787563i	$-0.288657\pi$
$368$	1.55618	−	5.80774i	0.0811214	−	0.302749i
$369$	−0.830288	−	7.89966i	−0.0432231	−	0.411240i
$370$	−1.96940	−	5.71293i	−0.102384	−	0.297001i
$371$	−13.6410	+	24.0116i	−0.708207	+	1.24662i
$372$	2.92862	−	0.463848i	0.151842	−	0.0240494i
$373$	−0.806160	+	15.3825i	−0.0417414	+	0.796473i	0.894918	+	0.446231i	$0.147234\pi$
$373$	−0.806160	+	15.3825i	−0.0417414	+	0.796473i	−0.936659	+	0.350242i	$0.886099\pi$
$374$	4.39979	+	7.62067i	0.227508	+	0.394055i
$375$	24.3500	−	2.58566i	1.25743	−	0.133523i
$376$	20.3661	+	11.7584i	1.05030	+	0.606391i
$377$	29.0623	−	14.8080i	1.49679	−	0.762651i
$378$	3.28904	−	3.33517i	0.169170	−	0.171543i
$379$	2.05068	−	2.82252i	0.105336	−	0.144983i	−0.753095	−	0.657912i	$-0.771440\pi$
$379$	2.05068	−	2.82252i	0.105336	−	0.144983i	0.858431	+	0.512929i	$0.171440\pi$
$380$	−2.15227	−	0.417561i	−0.110409	−	0.0214204i
$381$	11.6852	−	26.2455i	0.598653	−	1.34460i
$382$	5.60364	+	1.50149i	0.286707	+	0.0768230i
$383$	9.11023	+	7.37732i	0.465511	+	0.376964i	0.833188	−	0.552990i	$-0.186513\pi$
$383$	9.11023	+	7.37732i	0.465511	+	0.376964i	−0.367677	+	0.929954i	$0.619847\pi$
$384$	−7.41058	−	22.8074i	−0.378169	−	1.16389i
$385$	−5.37383	−	13.0253i	−0.273876	−	0.663830i
$386$	3.39238	−	10.4407i	0.172668	−	0.531416i
$387$	−10.2592	+	6.66242i	−0.521505	+	0.338670i
$388$	−0.595037	−	11.3540i	−0.0302084	−	0.576411i
$389$	−1.71583	−	8.07236i	−0.0869962	−	0.409285i	−0.999999	−	0.00133179i	$-0.999576\pi$
$389$	−1.71583	−	8.07236i	−0.0869962	−	0.409285i	0.913003	−	0.407953i	$-0.133757\pi$
$390$	−17.7822	−	0.614611i	−0.900436	−	0.0311220i
$391$	−21.0292	+	6.83280i	−1.06349	+	0.345550i
$392$	−13.8688	+	9.28371i	−0.700482	+	0.468898i
$393$	7.85142	+	7.85142i	0.396052	+	0.396052i
$394$	−16.3784	+	1.72144i	−0.825133	+	0.0867250i
$395$	−22.4895	+	5.20058i	−1.13157	+	0.261670i
$396$	−0.692740	+	6.59098i	−0.0348115	+	0.331209i
$397$	6.86596	+	2.63560i	0.344593	+	0.132277i	0.524508	−	0.851405i	$-0.324249\pi$
$397$	6.86596	+	2.63560i	0.344593	+	0.132277i	−0.179916	+	0.983682i	$0.557582\pi$
$398$	−5.33095	−	10.4626i	−0.267216	−	0.524442i
$399$	1.46885	−	3.36192i	0.0735346	−	0.168306i
$400$	−6.20146	−	4.17650i	−0.310073	−	0.208825i
$401$	2.56742	−	4.44689i	0.128211	−	0.222067i	−0.794773	−	0.606907i	$-0.792410\pi$
$401$	2.56742	−	4.44689i	0.128211	−	0.222067i	0.922983	+	0.384840i	$0.125743\pi$
$402$	−11.7091	−	7.60396i	−0.583995	−	0.379251i
$403$	−3.67391	+	2.97507i	−0.183010	+	0.148199i
$404$	12.2239	−	5.44243i	0.608162	−	0.270771i
$405$	−14.3084	+	20.4501i	−0.710992	+	1.01617i
$406$	3.24223	−	10.2202i	0.160909	−	0.507221i
$407$	6.77401	−	6.77401i	0.335775	−	0.335775i
$408$	−18.0710	+	22.3159i	−0.894649	+	1.10480i
$409$	−7.00471	+	7.77952i	−0.346361	+	0.384672i	−0.891004	−	0.453995i	$-0.849998\pi$
$409$	−7.00471	+	7.77952i	−0.346361	+	0.384672i	0.544644	+	0.838668i	$0.316665\pi$
$410$	−0.465636	−	6.62491i	−0.0229961	−	0.327181i
$411$	−4.24380	+	3.82114i	−0.209331	+	0.188483i
$412$	−13.7714	+	27.0279i	−0.678470	+	1.33157i
$413$	3.15719	−	8.39916i	0.155355	−	0.413295i
$414$	4.61661	+	1.50003i	0.226894	+	0.0737223i
$415$	18.7161	+	6.80452i	0.918735	+	0.334021i
$416$	23.1994	+	20.8888i	1.13744	+	1.02416i
$417$	−9.23453	+	3.54480i	−0.452217	+	0.173590i
$418$	0.262217	+	0.978607i	0.0128254	+	0.0478652i
$419$	21.3548	−	15.5152i	1.04325	−	0.757966i	0.0723335	−	0.997381i	$-0.476955\pi$
$419$	21.3548	−	15.5152i	1.04325	−	0.757966i	0.970917	+	0.239414i	$0.0769554\pi$
$420$	14.5744	−	13.7917i	0.711158	−	0.672967i
$421$	27.2318	+	19.7850i	1.32719	+	0.964263i	0.999812	+	0.0193712i	$0.00616644\pi$
$421$	27.2318	+	19.7850i	1.32719	+	0.964263i	0.327382	+	0.944892i	$0.393834\pi$
$422$	1.15899	−	3.01928i	0.0564190	−	0.146976i
$423$	9.65289	−	14.8642i	0.469340	−	0.722720i
$424$	21.5516	−	12.4428i	1.04664	−	0.604277i
$425$	−0.460233	+	27.4918i	−0.0223246	+	1.33355i
$426$		−	9.50847i		−	0.460687i
$427$	2.20531	−	4.40372i	0.106722	−	0.213111i
$428$	−1.26891	−	8.01159i	−0.0613351	−	0.387255i
$429$	−11.4730	−	25.7687i	−0.553921	−	1.24413i
$430$	−8.76499	+	5.27080i	−0.422685	+	0.254180i
$431$	27.3413	+	12.1731i	1.31699	+	0.586360i	0.940415	−	0.340028i	$-0.110437\pi$
$431$	27.3413	+	12.1731i	1.31699	+	0.586360i	0.376570	+	0.926388i	$0.377103\pi$
$432$	3.80612	−	1.01985i	0.183122	−	0.0490674i
$433$	−1.02047	+	6.44298i	−0.0490405	+	0.309630i	0.950959	+	0.309316i	$0.100100\pi$
$433$	−1.02047	+	6.44298i	−0.0490405	+	0.309630i	−1.00000		0.000314104i	$0.999900\pi$
$434$	−0.151672	+	1.54661i	−0.00728048	+	0.0742396i
$435$	−4.10076	+	29.2542i	−0.196616	+	1.40263i
$436$	4.20513	+	4.67027i	0.201389	+	0.223665i
$437$	−2.54228	+	0.133235i	−0.121614	+	0.00637350i
$438$	−13.2845	+	0.696209i	−0.634756	+	0.0332662i
$439$	13.7868	+	15.3117i	0.658006	+	0.730790i	0.976113	−	0.217265i	$-0.0697136\pi$
$439$	13.7868	+	15.3117i	0.658006	+	0.730790i	−0.318106	+	0.948055i	$0.603047\pi$
$440$	−1.76263	+	12.5743i	−0.0840300	+	0.599457i
$441$	6.44009	+	10.8042i	0.306671	+	0.514484i
$442$	3.12542	−	19.7331i	0.148661	−	0.938608i
$443$	18.2485	−	4.88967i	0.867013	−	0.232315i	0.202217	−	0.979341i	$-0.435185\pi$
$443$	18.2485	−	4.88967i	0.867013	−	0.232315i	0.664796	+	0.747025i	$0.268519\pi$
$444$	12.4630	+	5.54887i	0.591466	+	0.263338i
$445$	−27.8290	+	16.7349i	−1.31922	+	0.793309i
$446$	−1.77217	−	3.98037i	−0.0839148	−	0.188476i
$447$	1.50231	+	9.48523i	0.0710570	+	0.448636i
$448$	2.34534	−	0.139300i	0.110807	−	0.00658133i
$449$		−	11.0725i		−	0.522542i	−0.965265	−	0.261271i	$-0.915858\pi$
$449$		−	11.0725i		−	0.522542i	0.965265	−	0.261271i	$-0.0841416\pi$
$450$	3.62924	−	4.82332i	0.171084	−	0.227374i
$451$	9.11799	−	5.26427i	0.429349	−	0.247885i
$452$	4.01527	−	6.18298i	0.188863	−	0.290823i
$453$	3.04040	−	7.92051i	0.142850	−	0.372138i
$454$	12.2862	+	8.92645i	0.576620	+	0.418939i
$455$	−9.12912	+	30.6612i	−0.427980	+	1.43742i
$456$	−2.67467	+	1.94326i	−0.125253	+	0.0910017i
$457$	−5.85690	−	21.8583i	−0.273974	−	1.02249i	−0.956526	−	0.291648i	$-0.905796\pi$
$457$	−5.85690	−	21.8583i	−0.273974	−	1.02249i	0.682551	−	0.730838i	$-0.260870\pi$
$458$	−8.22547	+	3.15746i	−0.384351	+	0.147538i
$459$	−10.7688	−	9.69623i	−0.502642	−	0.452581i
$460$	−13.0854	−	4.75742i	−0.610111	−	0.221816i
$461$	−6.07862	−	1.97506i	−0.283110	−	0.0919879i	0.164020	−	0.986457i	$-0.447554\pi$
$461$	−6.07862	−	1.97506i	−0.283110	−	0.0919879i	−0.447130	+	0.894469i	$0.647554\pi$
$462$	−8.67953	−	3.26258i	−0.403808	−	0.151789i
$463$	−15.7094	+	30.8314i	−0.730078	+	1.43286i	0.164699	+	0.986344i	$0.447335\pi$
$463$	−15.7094	+	30.8314i	−0.730078	+	1.43286i	−0.894776	+	0.446514i	$0.852665\pi$
$464$	6.70293	−	6.03535i	0.311176	−	0.280184i
$465$	−0.300183	−	4.27090i	−0.0139207	−	0.198058i
$466$	−9.05652	+	10.0583i	−0.419535	+	0.465941i
$467$	11.8051	−	14.5780i	0.546273	−	0.674591i	−0.426998	−	0.904253i	$-0.640429\pi$
$467$	11.8051	−	14.5780i	0.546273	−	0.674591i	0.973270	+	0.229662i	$0.0737620\pi$
$468$	10.6398	−	10.6398i	0.491825	−	0.491825i
$469$	−18.5375	+	16.9265i	−0.855980	+	0.781592i
$470$	8.49522	−	12.1417i	0.391855	−	0.560053i
$471$	28.3337	−	12.6150i	1.30555	−	0.581268i
$472$	−6.28388	+	5.08858i	−0.289239	+	0.234221i
$473$	−13.5984	−	8.83092i	−0.625256	−	0.406046i
$474$	−7.59518	+	13.1552i	−0.348858	+	0.604240i
$475$	−0.870404	+	3.04366i	−0.0399369	+	0.139653i
$476$	13.3700	+	18.1353i	0.612815	+	0.831231i
$477$	−8.51467	−	16.7110i	−0.389860	−	0.765144i
$478$	9.12395	+	3.50236i	0.417320	+	0.160194i
$479$	0.786564	−	7.48366i	0.0359390	−	0.341937i	−0.961747	−	0.273941i	$-0.911673\pi$
$479$	0.786564	−	7.48366i	0.0359390	−	0.341937i	0.997686	−	0.0679962i	$-0.0216606\pi$
$480$	−27.5458	+	6.36980i	−1.25729	+	0.290740i
$481$	−21.6316	+	2.27357i	−0.986315	+	0.103666i
$482$	13.6495	+	13.6495i	0.621716	+	0.621716i
$483$	12.5535	−	19.6286i	0.571204	−	0.893134i
$484$	7.84641	−	2.54945i	0.356655	−	0.115884i
$485$	−16.4071	−	0.567083i	−0.745007	−	0.0257499i
$486$	2.31061	+	10.8706i	0.104811	+	0.493098i
$487$	−0.426630	−	8.14058i	−0.0193324	−	0.368885i	−0.991115	−	0.133007i	$-0.957537\pi$
$487$	−0.426630	−	8.14058i	−0.0193324	−	0.368885i	0.971783	−	0.235878i	$-0.0757966\pi$
$488$	−3.72214	+	2.41718i	−0.168493	+	0.109421i
$489$	15.4589	−	47.5775i	0.699074	−	2.15153i
$490$	5.06929	+	9.21392i	0.229007	+	0.416242i
$491$	−2.32350	−	7.15101i	−0.104858	−	0.322721i	0.884839	−	0.465897i	$-0.154268\pi$
$491$	−2.32350	−	7.15101i	−0.104858	−	0.322721i	−0.989697	+	0.143177i	$0.954268\pi$
$492$	11.6520	+	9.43562i	0.525314	+	0.425391i
$493$	−32.0397	−	8.58501i	−1.44300	−	0.386650i
$494$	0.935601	−	2.10139i	0.0420947	−	0.0945462i
$495$	9.39419	+	1.82256i	0.422237	+	0.0819182i
$496$	−0.768398	+	1.05761i	−0.0345021	+	0.0474881i
$497$	−16.5441	−	4.30969i	−0.742102	−	0.193316i
$498$	11.6769	−	5.94969i	0.523256	−	0.266612i
$499$	13.1695	+	7.60340i	0.589547	+	0.340375i	0.764918	−	0.644127i	$-0.222779\pi$
$499$	13.1695	+	7.60340i	0.589547	+	0.340375i	−0.175372	+	0.984502i	$0.556113\pi$
$500$	−10.8815	+	13.4670i	−0.486637	+	0.602264i
$501$	3.86990	+	6.70286i	0.172894	+	0.299462i
$502$	−0.376420	+	7.18253i	−0.0168005	+	0.320572i
$503$	7.60536	−	1.20457i	0.339106	−	0.0537092i	0.0154410	−	0.999881i	$-0.495085\pi$
$503$	7.60536	−	1.20457i	0.339106	−	0.0537092i	0.323665	+	0.946172i	$0.395085\pi$
$504$	−0.0789423	−	11.3342i	−0.00351637	−	0.504864i
$505$	−6.29678	−	18.2660i	−0.280203	−	0.812826i
$506$	0.672551	+	6.39890i	0.0298986	+	0.284466i
$507$	−9.20656	+	34.3593i	−0.408877	+	1.52595i
$508$	7.27971	+	18.9643i	0.322985	+	0.841404i
$509$	−13.9447	−	2.96405i	−0.618090	−	0.131379i	−0.111783	−	0.993733i	$-0.535656\pi$
$509$	−13.9447	−	2.96405i	−0.618090	−	0.131379i	−0.506306	+	0.862354i	$0.668990\pi$
$510$	13.0204	+	12.5646i	0.576552	+	0.556372i
$511$	−4.80980	+	23.4296i	−0.212773	+	1.03646i
$512$	14.0449	+	7.15625i	0.620704	+	0.316264i
$513$	−0.908663	−	1.39922i	−0.0401184	−	0.0617770i
$514$	3.84306	−	0.816867i	0.169510	−	0.0360305i
$515$	37.1532	+	23.1975i	1.63717	+	1.02220i
$516$	4.80072	−	22.5856i	0.211340	−	0.994276i
$517$	23.2029	+	3.67498i	1.02046	+	0.161626i
$518$	−4.46084	+	5.58780i	−0.195998	+	0.245514i
$519$	5.05497	+	6.95757i	0.221889	+	0.305403i
$520$	21.0769	−	19.6686i	0.924282	−	0.862524i
$521$	18.9644	+	1.99324i	0.830846	+	0.0873255i	0.510396	−	0.859940i	$-0.329499\pi$
$521$	18.9644	+	1.99324i	0.830846	+	0.0873255i	0.320451	+	0.947265i	$0.396166\pi$
$522$	4.58265	+	5.65910i	0.200577	+	0.247692i
$523$	−39.4851	−	2.06933i	−1.72656	−	0.0904854i	−0.836973	−	0.547244i	$-0.815677\pi$
$523$	−39.4851	−	2.06933i	−1.72656	−	0.0904854i	−0.889591	+	0.456759i	$0.849010\pi$
$524$	−7.85097			−0.342971
$525$	−18.0125	−	22.6936i	−0.786130	−	0.990429i
$526$	−1.70465			−0.0743262
$527$	4.80093	+	0.251606i	0.209132	+	0.0109601i
$528$	−4.90881	−	6.06188i	−0.213629	−	0.263809i
$529$	6.79500	+	0.714183i	0.295435	+	0.0310514i
$530$	−6.63220	−	14.2096i	−0.288085	−	0.617224i
$531$	3.58192	+	4.93009i	0.155442	+	0.213948i
$532$	0.946479	+	2.41525i	0.0410351	+	0.104714i
$533$	−23.6103	−	3.73950i	−1.02268	−	0.161976i
$534$	−4.44304	+	20.9028i	−0.192269	+	0.904554i
$535$	−11.6836	+	0.821187i	−0.505125	+	0.0355030i
$536$	22.1266	−	4.70315i	0.955722	−	0.203145i
$537$	−6.13671	−	9.44971i	−0.264819	−	0.407785i
$538$	13.9908	+	7.12868i	0.603188	+	0.307339i
$539$	−9.61064	+	13.6230i	−0.413960	+	0.586784i
$540$	−1.58771	−	8.98556i	−0.0683240	−	0.386677i
$541$	−28.6781	−	6.09572i	−1.23297	−	0.262075i	−0.455064	−	0.890459i	$-0.650384\pi$
$541$	−28.6781	−	6.09572i	−1.23297	−	0.262075i	−0.777904	+	0.628384i	$0.783717\pi$
$542$	−4.83032	−	12.5834i	−0.207480	−	0.540503i
$543$	−10.1312	+	37.8103i	−0.434773	+	1.62259i
$544$	−3.31843	−	31.5727i	−0.142276	−	1.35367i
$545$	7.24515	−	5.46367i	0.310348	−	0.234038i
$546$	10.6531	+	18.1585i	0.455911	+	0.777110i
$547$	−24.3999	+	3.86457i	−1.04327	+	0.165237i	−0.654471	−	0.756087i	$-0.727109\pi$
$547$	−24.3999	+	3.86457i	−1.04327	+	0.165237i	−0.388795	+	0.921324i	$0.627109\pi$
$548$	0.211321	−	4.03224i	0.00902717	−	0.172249i
$549$	1.67241	+	2.89670i	0.0713768	+	0.123628i
$550$	7.79711	+	1.79424i	0.332470	+	0.0765067i
$551$	−3.30733	−	1.90949i	−0.140897	−	0.0813469i
$552$	−18.7077	+	9.53205i	−0.796253	+	0.405711i
$553$	19.4467	+	19.1777i	0.826957	+	0.815517i
$554$	−4.17867	+	5.75144i	−0.177535	+	0.244355i
$555$	9.54397	−	17.2323i	0.405119	−	0.731470i
$556$	2.84470	−	6.38930i	0.120642	−	0.270967i
$557$	−39.7652	−	10.6550i	−1.68490	−	0.451469i	−0.715837	−	0.698267i	$-0.753955\pi$
$557$	−39.7652	−	10.6550i	−1.68490	−	0.451469i	−0.969067	+	0.246799i	$0.920621\pi$
$558$	−0.820208	−	0.664191i	−0.0347222	−	0.0281174i
$559$	11.3761	+	35.0120i	0.481157	+	1.48085i
$560$	−0.243998	+	8.84320i	−0.0103108	+	0.373693i
$561$	−8.86421	+	27.2812i	−0.374247	+	1.15181i
$562$	−7.08684	+	4.60225i	−0.298940	+	0.194134i
$563$	1.47042	+	28.0572i	0.0619707	+	1.18247i	0.835785	+	0.549058i	$0.185013\pi$
$563$	1.47042	+	28.0572i	0.0619707	+	1.18247i	−0.773814	+	0.633413i	$0.781653\pi$
$564$	6.95556	+	32.7234i	0.292882	+	1.37790i
$565$	−8.39086	−	6.55083i	−0.353006	−	0.275596i
$566$	15.6449	−	5.08333i	0.657603	−	0.213668i
$567$	29.5011	+	1.34012i	1.23893	+	0.0562799i
$568$	10.8937	+	10.8937i	0.457088	+	0.457088i
$569$	0.00511578		0.000537690i	0.000214464		2.25411e-5i	−0.104421	−	0.994533i	$-0.533299\pi$
$569$	0.00511578		0.000537690i	0.000214464		2.25411e-5i	0.104636	+	0.994511i	$0.466632\pi$
$570$	1.07359	+	1.78531i	0.0449678	+	0.0747785i
$571$	1.78404	−	16.9740i	0.0746599	−	0.710342i	−0.891609	−	0.452806i	$-0.850423\pi$
$571$	1.78404	−	16.9740i	0.0746599	−	0.710342i	0.966269	−	0.257535i	$-0.0829104\pi$
$572$	18.6198	+	7.14747i	0.778532	+	0.298851i
$573$	8.58557	+	16.8501i	0.358667	+	0.703924i
$574$	−6.32496	+	4.66300i	−0.263999	+	0.194630i
$575$	−8.48350	+	18.2269i	−0.353786	+	0.760114i
$576$	−0.797818	+	1.38186i	−0.0332424	+	0.0575775i
$577$	0.0289548	+	0.0188034i	0.00120540	+	0.000782798i	0.545242	−	0.838279i	$-0.316438\pi$
$577$	0.0289548	+	0.0188034i	0.00120540	+	0.000782798i	−0.544036	+	0.839062i	$0.683105\pi$
$578$	−6.91333	+	5.59830i	−0.287557	+	0.232859i
$579$	32.6924	−	14.5556i	1.35865	−	0.604911i
$580$	−12.5760	−	16.6765i	−0.522190	−	0.692455i
$581$	−5.05949	−	23.0137i	−0.209903	−	0.954769i
$582$	−7.63926	+	7.63926i	−0.316658	+	0.316658i
$583$	15.6447	−	19.3196i	0.647937	−	0.800136i
$584$	14.4221	−	16.0174i	0.596791	−	0.662804i
$585$	−13.9717	−	16.6387i	−0.577657	−	0.687926i
$586$	−1.42095	+	1.27943i	−0.0586989	+	0.0528527i
$587$	0.603907	−	1.18523i	0.0249259	−	0.0489198i	−0.878208	−	0.478279i	$-0.841261\pi$
$587$	0.603907	−	1.18523i	0.0249259	−	0.0489198i	0.903134	+	0.429359i	$0.141261\pi$
$588$	−23.0162	−	5.82480i	−0.949173	−	0.240211i
$589$	0.526416	+	0.171043i	0.0216906	+	0.00704770i
$590$	2.85066	+	4.22302i	0.117360	+	0.173859i
$591$	−39.8957	−	35.9223i	−1.64109	−	1.47765i
$592$	−5.61522	+	2.15548i	−0.230784	+	0.0885898i
$593$	8.35074	+	31.1654i	0.342924	+	1.27981i	0.895019	+	0.446027i	$0.147162\pi$
$593$	8.35074	+	31.1654i	0.342924	+	1.27981i	−0.552096	+	0.833781i	$0.686172\pi$
$594$	−3.41133	+	2.47848i	−0.139969	+	0.101693i
$595$	27.7630	−	16.9596i	1.13817	−	0.695276i
$596$	−5.49346	−	3.99123i	−0.225021	−	0.163487i
$597$	13.7177	−	35.7359i	0.561429	−	1.46257i
$598$	7.95633	−	12.2517i	0.325359	−	0.501008i
$599$	−33.4655	+	19.3213i	−1.36736	+	0.789448i	−0.990591	−	0.136857i	$-0.956300\pi$
$599$	−33.4655	+	19.3213i	−1.36736	+	0.789448i	−0.376774	+	0.926305i	$0.622967\pi$
$600$	3.65211	+	25.8521i	0.149097	+	1.05541i
$601$		−	14.4856i		−	0.590882i	−0.955361	−	0.295441i	$-0.904533\pi$
$601$		−	14.4856i		−	0.590882i	0.955361	−	0.295441i	$-0.0954666\pi$
$602$	10.8206	+	5.41878i	0.441015	+	0.220853i
$603$	−2.66695	−	16.8384i	−0.108607	−	0.685714i
$604$	2.43992	+	5.48014i	0.0992788	+	0.222984i
$605$	−2.68393	−	11.6065i	−0.109117	−	0.471869i
$606$	−11.6154	−	5.17149i	−0.471842	−	0.210077i
$607$	−13.5829	+	3.63954i	−0.551315	+	0.147724i	−0.523713	−	0.851895i	$-0.675454\pi$
$607$	−13.5829	+	3.63954i	−0.551315	+	0.147724i	−0.0276015	+	0.999619i	$0.508787\pi$
$608$	0.571784	−	3.61010i	0.0231889	−	0.146409i
$609$	31.8309	−	14.4385i	1.28985	−	0.585077i
$610$	1.31380	+	2.46878i	0.0531943	+	0.0999579i
$611$	−35.6900	−	39.6378i	−1.44386	−	1.60357i
$612$	−15.2809	+	0.800837i	−0.617693	+	0.0323719i
$613$	42.7633	−	2.24113i	1.72719	−	0.0905184i	0.837317	−	0.546718i	$-0.184123\pi$
$613$	42.7633	−	2.24113i	1.72719	−	0.0905184i	0.889877	+	0.456200i	$0.150790\pi$
$614$	0.629840	+	0.699509i	0.0254183	+	0.0282299i
$615$	15.0334	−	15.5786i	0.606204	−	0.628191i
$616$	13.6819	−	6.20609i	0.551257	−	0.250051i
$617$	3.46495	−	21.8768i	0.139494	−	0.880729i	−0.814339	−	0.580390i	$-0.802900\pi$
$617$	3.46495	−	21.8768i	0.139494	−	0.880729i	0.953833	−	0.300339i	$-0.0970998\pi$
$618$	27.8419	−	7.46021i	1.11996	−	0.300094i
$619$	−15.9357	−	7.09505i	−0.640511	−	0.285174i	0.0606690	−	0.998158i	$-0.480677\pi$
$619$	−15.9357	−	7.09505i	−0.640511	−	0.285174i	−0.701180	+	0.712984i	$0.747343\pi$
$620$	2.28541	+	1.98525i	0.0917844	+	0.0797294i
$621$	−4.30957	−	9.67945i	−0.172937	−	0.388423i
$622$	−1.74735	−	11.0324i	−0.0700625	−	0.442357i
$623$	34.3556	+	17.2047i	1.37643	+	0.689293i
$624$			17.7100i			0.708966i
$625$	18.0083	+	17.3408i	0.720331	+	0.693630i
$626$	−17.0247	+	9.82921i	−0.680443	+	0.392854i
$627$	−1.79874	+	2.76982i	−0.0718348	+	0.110616i
$628$	−7.85892	+	20.4732i	−0.313605	+	0.816969i
$629$	17.8948	+	13.0013i	0.713512	+	0.518397i
$630$	−7.11933	−	0.570367i	−0.283641	−	0.0227240i
$631$	−15.1958	+	11.0404i	−0.604937	+	0.439513i	−0.847628	−	0.530591i	$-0.821970\pi$
$631$	−15.1958	+	11.0404i	−0.604937	+	0.439513i	0.242691	+	0.970104i	$0.421970\pi$
$632$	−6.37005	−	23.7734i	−0.253387	−	0.945654i
$633$	9.84236	−	3.77813i	0.391199	−	0.150167i
$634$	−0.120860	−	0.108823i	−0.00479996	−	0.00432190i
$635$	28.1922	−	8.09488i	1.11877	−	0.321235i
$636$	33.6692	+	10.9398i	1.33507	+	0.433790i
$637$	36.4229	−	10.3053i	1.44313	−	0.408313i
$638$	−4.38194	+	8.60003i	−0.173483	+	0.340479i
$639$	8.62850	−	7.76913i	0.341338	−	0.307342i
$640$	12.9670	−	20.7680i	0.512564	−	0.820926i
$641$	−14.1031	+	15.6631i	−0.557040	+	0.618656i	−0.954227	−	0.299082i	$-0.903320\pi$
$641$	−14.1031	+	15.6631i	−0.557040	+	0.618656i	0.397187	+	0.917738i	$0.369986\pi$
$642$	−4.85057	+	5.98996i	−0.191437	+	0.236405i
$643$	−3.39326	+	3.39326i	−0.133817	+	0.133817i	−0.770843	−	0.637026i	$-0.780165\pi$
$643$	−3.39326	+	3.39326i	−0.133817	+	0.133817i	0.637026	+	0.770843i	$0.280165\pi$
$644$	3.53737	+	16.0901i	0.139392	+	0.634041i
$645$	−31.8873	−	9.73648i	−1.25556	−	0.383374i
$646$	−2.13699	+	0.951450i	−0.0840788	+	0.0374343i
$647$	4.20643	−	3.40630i	0.165372	−	0.133916i	−0.543062	−	0.839692i	$-0.682735\pi$
$647$	4.20643	−	3.40630i	0.165372	−	0.133916i	0.708434	+	0.705777i	$0.249402\pi$
$648$	−22.3187	−	14.4939i	−0.876760	−	0.569374i
$649$	−4.03870	+	6.99524i	−0.158533	+	0.274587i
$650$	−11.1941	−	14.3068i	−0.439070	−	0.561157i
$651$	−4.07754	+	3.00612i	−0.159811	+	0.117819i
$652$	16.0584	+	31.5164i	0.628896	+	1.23428i
$653$	−30.5385	−	11.7226i	−1.19506	−	0.458742i	−0.322184	−	0.946677i	$-0.604417\pi$
$653$	−30.5385	−	11.7226i	−1.19506	−	0.458742i	−0.872880	+	0.487935i	$0.837750\pi$
$654$	0.624203	−	5.93889i	0.0244083	−	0.232229i
$655$	−0.983989	+	11.2935i	−0.0384476	+	0.441273i
$656$	−6.57412	+	0.690967i	−0.256676	+	0.0269777i
$657$	−11.4862	−	11.4862i	−0.448118	−	0.448118i
$658$	−17.5154	−	0.795660i	−0.682823	−	0.0310181i
$659$	−7.46494	+	2.42551i	−0.290793	+	0.0944843i	−0.450781	−	0.892635i	$-0.648854\pi$
$659$	−7.46494	+	2.42551i	−0.290793	+	0.0944843i	0.159988	+	0.987119i	$0.448854\pi$
$660$	−14.9712	+	10.1060i	−0.582753	+	0.393375i
$661$	1.03661	+	4.87685i	0.0403193	+	0.189688i	0.993698	−	0.112088i	$-0.0357539\pi$
$661$	1.03661	+	4.87685i	0.0403193	+	0.189688i	−0.953379	+	0.301776i	$0.902421\pi$
$662$	1.20152	+	22.9264i	0.0466984	+	0.891059i
$663$	54.6213	−	35.4715i	2.12132	−	1.37760i
$664$	−6.56158	+	20.1945i	−0.254639	+	0.783698i
$665$	3.59292	−	1.05878i	0.139327	−	0.0410578i
$666$	−1.50055	−	4.61823i	−0.0581453	−	0.178953i
$667$	−18.8485	−	15.2632i	−0.729815	−	0.590993i
$668$	−5.28608	−	1.41640i	−0.204524	−	0.0548022i
$669$	5.77699	−	12.9753i	0.223351	−	0.501655i
$670$	−1.74218	−	14.1472i	−0.0673064	−	0.546553i
$671$	−2.60595	+	3.58678i	−0.100602	+	0.138466i
$672$	23.8188	+	23.4893i	0.918830	+	0.906119i
$673$	34.8935	−	17.7791i	1.34505	−	0.685335i	0.374720	−	0.927138i	$-0.377739\pi$
$673$	34.8935	−	17.7791i	1.34505	−	0.685335i	0.970325	+	0.241803i	$0.0777387\pi$
$674$	−4.85004	−	2.80017i	−0.186816	−	0.107858i
$675$	−13.1246	+	1.15770i	−0.505165	+	0.0445597i
$676$	−12.5757	−	21.7817i	−0.483680	−	0.837758i
$677$	0.601307	−	11.4736i	0.0231101	−	0.440967i	−0.962431	−	0.271528i	$-0.912471\pi$
$677$	0.601307	−	11.4736i	0.0231101	−	0.440967i	0.985541	−	0.169439i	$-0.0541956\pi$
$678$	−6.91908	+	1.09588i	−0.265726	+	0.0420868i
$679$	9.82929	+	16.7542i	0.377213	+	0.642969i
$680$	−29.3123	+	0.522117i	−1.12407	+	0.0200223i
$681$	5.17476	+	49.2346i	0.198297	+	1.88667i
$682$	0.362069	−	1.35126i	0.0138643	−	0.0517425i
$683$	0.343449	+	0.894716i	0.0131417	+	0.0342354i	0.939994	−	0.341190i	$-0.110830\pi$
$683$	0.343449	+	0.894716i	0.0131417	+	0.0342354i	−0.926853	+	0.375425i	$0.877497\pi$
$684$	−1.72326	−	0.366290i	−0.0658904	−	0.0140054i
$685$	−5.77382	−	0.809355i	−0.220606	−	0.0309239i
$686$	5.99506	−	10.9037i	0.228893	−	0.416305i
$687$	−25.5909	−	13.0392i	−0.976353	−	0.497476i
$688$	5.54448	+	8.53775i	0.211381	+	0.325499i
$689$	−55.2094	+	11.7351i	−2.10331	+	0.447072i
$690$	4.96052	+	12.2651i	0.188844	+	0.466925i
$691$	−0.923146	+	4.34306i	−0.0351181	+	0.165218i	−0.992212	−	0.124560i	$-0.960248\pi$
$691$	−0.923146	+	4.34306i	−0.0351181	+	0.165218i	0.957094	+	0.289778i	$0.0935814\pi$
$692$	−6.00593	−	0.951245i	−0.228311	−	0.0361609i
$693$	−4.13118	−	10.5420i	−0.156931	−	0.400459i
$694$	2.53767	+	3.49280i	0.0963286	+	0.132585i
$695$	−8.83436	−	4.89284i	−0.335106	−	0.185596i
$696$	−31.3244	−	3.29232i	−1.18735	−	0.124795i
$697$	15.2985	+	18.8920i	0.579471	+	0.715587i
$698$	−4.35659	−	0.228319i	−0.164899	−	0.00864202i
$699$	−44.1211			−1.66881
$700$	20.3519	+	2.34040i	0.769229	+	0.0884590i
$701$	−14.7676			−0.557765			−0.278882	−	0.960325i	$-0.589964\pi$
$701$	−14.7676			−0.557765			−0.278882	+	0.960325i	$0.589964\pi$
$702$	9.56058	+	0.501049i	0.360841	+	0.0189109i
$703$	1.60266	+	1.97913i	0.0604456	+	0.0746441i
$704$	−2.10340	−	0.221076i	−0.0792750	−	0.00833213i
$705$	47.9437	−	5.90413i	1.80567	−	0.222362i
$706$	7.90671	+	10.8827i	0.297573	+	0.409574i
$707$	−14.2627	+	17.8659i	−0.536402	+	0.671917i
$708$	−11.3611	−	1.79943i	−0.426978	−	0.0676266i
$709$	8.56011	−	40.2722i	0.321482	−	1.51245i	−0.459658	−	0.888096i	$-0.652028\pi$
$709$	8.56011	−	40.2722i	0.321482	−	1.51245i	0.781139	−	0.624357i	$-0.214639\pi$
$710$	7.43432	−	6.24266i	0.279005	−	0.234283i
$711$	−18.1436	+	3.85654i	−0.680439	+	0.144632i
$712$	−18.8577	−	29.0383i	−0.706721	−	1.08826i
$713$	3.13206	+	1.59586i	0.117297	+	0.0597656i
$714$	4.30529	−	20.9720i	0.161122	−	0.784858i
$715$	12.6152	−	25.8884i	0.471781	−	0.968172i
$716$	7.79276	+	1.65640i	0.291229	+	0.0619027i
$717$	11.4171	+	29.7425i	0.426379	+	1.11076i
$718$	−1.68289	+	6.28063i	−0.0628049	+	0.234391i
$719$	0.0391298	+	0.372295i	0.00145930	+	0.0138843i	0.995227	−	0.0975838i	$-0.0311114\pi$
$719$	0.0391298	+	0.372295i	0.00145930	+	0.0138843i	−0.993768	+	0.111468i	$0.964445\pi$
$720$	−4.92278	−	3.44435i	−0.183461	−	0.128363i
$721$	−0.360955	−	51.8242i	−0.0134427	−	1.93003i
$722$	12.3423	−	1.95483i	0.459332	−	0.0727511i
$723$	−3.29326	+	62.8391i	−0.122478	+	2.33701i
$724$	−13.8387	−	23.9694i	−0.514312	−	0.890815i
$725$	−25.5651	+	16.0002i	−0.949464	+	0.594234i
$726$	−6.78919	−	3.91974i	−0.251970	−	0.145475i
$727$	−4.38289	+	2.23320i	−0.162552	+	0.0828246i	−0.533374	−	0.845880i	$-0.679076\pi$
$727$	−4.38289	+	2.23320i	−0.162552	+	0.0828246i	0.370822	+	0.928704i	$0.379076\pi$
$728$	−33.0088	−	8.59874i	−1.22339	−	0.318690i
$729$	−1.61184	+	2.21850i	−0.0596976	+	0.0821667i
$730$	−9.26608	−	9.92954i	−0.342953	−	0.367509i
$731$	15.2271	−	34.2007i	0.563196	−	1.26496i
$732$	−6.09848	−	1.63408i	−0.225406	−	0.0603975i
$733$	−17.1328	−	13.8739i	−0.632815	−	0.512444i	0.258392	−	0.966040i	$-0.416807\pi$
$733$	−17.1328	−	13.8739i	−0.632815	−	0.512444i	−0.891207	+	0.453596i	$0.850141\pi$
$734$	−4.09205	−	12.5940i	−0.151040	−	0.464854i
$735$	−11.2636	+	32.3784i	−0.415463	+	1.19429i
$736$	7.17313	−	22.0766i	0.264405	−	0.813755i
$737$	18.9517	−	12.3074i	0.698094	−	0.453348i
$738$	−0.279304	−	5.32943i	−0.0102813	−	0.196179i
$739$	−7.96350	−	37.4653i	−0.292942	−	1.37818i	−0.840679	−	0.541534i	$-0.817844\pi$
$739$	−7.96350	−	37.4653i	−0.292942	−	1.37818i	0.547737	−	0.836651i	$-0.315489\pi$
$740$	3.84394	+	13.3874i	0.141306	+	0.492129i
$741$	7.13147	−	2.31716i	0.261981	−	0.0851228i
$742$	−9.99670	+	15.6308i	−0.366990	+	0.573826i
$743$	−5.35160	−	5.35160i	−0.196331	−	0.196331i	0.602094	−	0.798425i	$-0.294333\pi$
$743$	−5.35160	−	5.35160i	−0.196331	−	0.196331i	−0.798425	+	0.602094i	$0.794333\pi$
$744$	4.54003	−	0.477176i	0.166445	−	0.0174941i
$745$	−6.42983	+	7.40201i	−0.235571	+	0.271189i
$746$	−1.08178	+	10.2924i	−0.0396067	+	0.376833i
$747$	14.9400	+	5.73493i	0.546626	+	0.209830i
$748$	−9.20799	−	18.0717i	−0.336677	−	0.660767i
$749$	8.22359	+	11.1546i	0.300483	+	0.407580i
$750$	16.4284	−	0.878623i	0.599881	−	0.0320828i
$751$	0.941197	−	1.63020i	0.0343448	−	0.0594869i	−0.848342	−	0.529448i	$-0.822399\pi$
$751$	0.941197	−	1.63020i	0.0343448	−	0.0594869i	0.882687	+	0.469962i	$0.155732\pi$
$752$	−12.3700	−	8.03316i	−0.451087	−	0.292939i
$753$	−18.2209	+	14.7550i	−0.664008	+	0.537703i
$754$	20.0199	−	8.91345i	0.729083	−	0.324609i
$755$	8.18889	−	2.82293i	0.298024	−	0.102737i
$756$	−7.97289	+	7.28001i	−0.289971	+	0.264772i
$757$	11.5638	−	11.5638i	0.420295	−	0.420295i	−0.465010	−	0.885305i	$-0.653949\pi$
$757$	11.5638	−	11.5638i	0.420295	−	0.420295i	0.885305	+	0.465010i	$0.153949\pi$
$758$	1.47514	−	1.82165i	0.0535795	−	0.0661652i
$759$	−14.0345	+	15.5869i	−0.509420	+	0.565769i
$760$	−3.27539	−	0.815404i	−0.118811	−	0.0295778i
$761$	−8.01622	+	7.21784i	−0.290588	+	0.261646i	−0.801511	−	0.597980i	$-0.795970\pi$
$761$	−8.01622	+	7.21784i	−0.290588	+	0.261646i	0.510923	+	0.859626i	$0.329304\pi$
$762$	8.76303	−	17.1984i	0.317451	−	0.623033i
$763$	−10.0503	−	3.77786i	−0.363846	−	0.136768i
$764$	−12.7171	−	4.13204i	−0.460089	−	0.149492i
$765$	−0.763214	+	22.0816i	−0.0275941	+	0.798363i
$766$	5.85306	+	5.27012i	0.211480	+	0.190417i
$767$	17.1213	−	6.57225i	0.618214	−	0.237310i
$768$	−5.17688	−	19.3204i	−0.186805	−	0.697164i
$769$	17.9924	−	13.0722i	0.648821	−	0.471396i	−0.214049	−	0.976823i	$-0.568665\pi$
$769$	17.9924	−	13.0722i	0.648821	−	0.471396i	0.862869	+	0.505427i	$0.168665\pi$
$770$	−3.14754	−	8.92821i	−0.113429	−	0.321751i
$771$	10.3616	+	7.52812i	0.373163	+	0.271119i
$772$	−9.06790	+	23.6227i	−0.326361	+	0.850199i
$773$	10.2745	−	15.8214i	0.369548	−	0.569055i	−0.604157	−	0.796865i	$-0.706490\pi$
$773$	10.2745	−	15.8214i	0.369548	−	0.569055i	0.973705	+	0.227811i	$0.0731567\pi$
$774$	−7.11764	+	4.10937i	−0.255838	+	0.147708i
$775$	3.14218	−	3.03871i	0.112871	−	0.109154i
$776$		−	17.5043i		−	0.628368i
$777$	−23.2668	+	1.38192i	−0.834693	+	0.0495761i
$778$	−0.867383	−	5.47644i	−0.0310972	−	0.196340i
$779$	1.13839	+	2.55687i	0.0407871	+	0.0916093i
$780$	40.8562	+	3.55975i	1.46289	+	0.127460i
$781$	14.0594	+	6.25964i	0.503084	+	0.223987i
$782$	−14.3497	+	3.84499i	−0.513144	+	0.137497i
$783$	2.48646	−	15.6989i	0.0888588	−	0.561032i
$784$	8.99125	−	5.35946i	0.321116	−	0.191409i
$785$	28.4653	+	13.8709i	1.01597	+	0.495073i
$786$	4.99180	+	5.54395i	0.178051	+	0.197746i
$787$	21.2387	−	1.11308i	0.757080	−	0.0396769i	0.330110	−	0.943943i	$-0.392914\pi$
$787$	21.2387	−	1.11308i	0.757080	−	0.0396769i	0.426970	+	0.904266i	$0.359581\pi$
$788$	37.9068	−	1.98661i	1.35038	−	0.0707702i
$789$	−3.71827	−	4.12956i	−0.132374	−	0.147016i
$790$	−15.2721	+	2.69851i	−0.543358	+	0.0960087i
$791$	−1.22932	+	12.5354i	−0.0437094	+	0.445708i
$792$	−1.59613	+	10.0776i	−0.0567161	+	0.358092i
$793$	9.72309	−	2.60530i	0.345277	−	0.0925167i
$794$	4.51401	+	2.00977i	0.160196	+	0.0713240i
$795$	19.9565	−	47.0614i	0.707785	−	1.66909i
$796$	11.0085	+	24.7254i	0.390185	+	0.876369i
$797$	−2.99428	−	18.9052i	−0.106063	−	0.669655i	−0.982235	−	0.187656i	$-0.939911\pi$
$797$	−2.99428	−	18.9052i	−0.106063	−	0.669655i	0.876172	−	0.481999i	$-0.160089\pi$
$798$	1.10373	−	2.20401i	0.0390717	−	0.0780213i
$799$			54.2414i			1.91892i
$800$	−23.0651	−	17.3550i	−0.815476	−	0.613593i
$801$	−22.5987	+	13.0473i	−0.798484	+	0.461005i
$802$	1.87896	−	2.89334i	0.0663484	−	0.102168i
$803$	7.71603	−	20.1009i	0.272293	−	0.709347i
$804$	26.0342	+	18.9150i	0.918155	+	0.667079i
$805$	23.5887	−	3.07181i	0.831394	−	0.108267i
$806$	−2.56960	+	1.86693i	−0.0905104	+	0.0657597i
$807$	13.2481	+	49.4427i	0.466356	+	1.74046i
$808$	19.2324	−	7.38261i	0.676592	−	0.259719i
$809$	−9.99313	−	8.99785i	−0.351340	−	0.316348i	0.474497	−	0.880257i	$-0.342630\pi$
$809$	−9.99313	−	8.99785i	−0.351340	−	0.316348i	−0.825837	+	0.563910i	$0.809297\pi$
$810$	−10.3193	+	13.2178i	−0.362582	+	0.464425i
$811$	−11.0873	−	3.60249i	−0.389328	−	0.126500i	0.107811	−	0.994171i	$-0.465616\pi$
$811$	−11.0873	−	3.60249i	−0.389328	−	0.126500i	−0.497139	+	0.867671i	$0.665616\pi$
$812$	−8.69569	+	23.1334i	−0.305159	+	0.811822i
$813$	19.9475	−	39.1492i	0.699589	−	1.37302i
$814$	4.78318	−	4.30679i	0.167650	−	0.150953i
$815$	47.3484	−	19.1497i	1.65854	−	0.670784i
$816$	12.0510	−	13.3840i	0.421870	−	0.468534i
$817$	2.71256	−	3.34973i	0.0949004	−	0.117192i
$818$	−4.97332	+	4.97332i	−0.173888	+	0.173888i
$819$	−7.77357	+	24.5040i	−0.271631	+	0.856239i
$820$	0.272618	+	15.3051i	0.00952024	+	0.534478i
$821$	9.65900	−	4.30046i	0.337101	−	0.150087i	−0.231203	−	0.972905i	$-0.574266\pi$
$821$	9.65900	−	4.30046i	0.337101	−	0.150087i	0.568305	+	0.822818i	$0.307600\pi$
$822$	−2.98172	+	2.41455i	−0.103999	+	0.0842171i
$823$	17.0777	+	11.0904i	0.595290	+	0.386586i	0.806830	−	0.590784i	$-0.201181\pi$
$823$	17.0777	+	11.0904i	0.595290	+	0.386586i	−0.211540	+	0.977369i	$0.567848\pi$
$824$	−23.3509	+	40.4449i	−0.813466	+	1.40897i
$825$	12.6609	+	22.8024i	0.440796	+	0.793879i
$826$	2.41364	−	5.52436i	0.0839813	−	0.192217i
$827$	10.1913	+	20.0015i	0.354385	+	0.695519i	0.997531	−	0.0702240i	$-0.0223714\pi$
$827$	10.1913	+	20.0015i	0.354385	+	0.695519i	−0.643147	+	0.765743i	$0.722371\pi$
$828$	−10.4454	−	4.00960i	−0.363002	−	0.139343i
$829$	−4.94891	+	47.0857i	−0.171883	+	1.63535i	0.480166	+	0.877178i	$0.340576\pi$
$829$	−4.94891	+	47.0857i	−0.171883	+	1.63535i	−0.652049	+	0.758177i	$0.726090\pi$
$830$	12.3182	+	5.22357i	0.427570	+	0.181313i
$831$	−23.0478	+	2.42242i	−0.799518	+	0.0840328i
$832$	3.39552	+	3.39552i	0.117718	+	0.117718i
$833$	−34.5384	−	16.9964i	−1.19669	−	0.588891i
$834$	−6.32051	+	2.05366i	−0.218861	+	0.0711123i
$835$	−2.69999	+	7.42641i	−0.0934369	+	0.257001i
$836$	−0.485511	−	2.28415i	−0.0167917	−	0.0789989i
$837$	0.120566	+	2.30054i	0.00416737	+	0.0795182i
$838$	14.8735	−	9.65894i	0.513795	−	0.333663i
$839$	−6.43734	+	19.8121i	−0.222242	+	0.683989i	0.776318	+	0.630341i	$0.217085\pi$
$839$	−6.43734	+	19.8121i	−0.222242	+	0.683989i	−0.998560	+	0.0536483i	$0.982915\pi$
$840$	23.5189	−	20.0300i	0.811479	−	0.691100i
$841$	−2.28155	−	7.02190i	−0.0786743	−	0.242135i
$842$	17.5753	+	14.2322i	0.605685	+	0.490474i
$843$	−26.6073	−	7.12940i	−0.916403	−	0.245550i
$844$	−3.03194	+	6.80986i	−0.104364	+	0.234405i
$845$	−32.9087	+	15.3599i	−1.13210	+	0.528397i
$846$	6.99923	−	9.63361i	0.240638	−	0.331210i
$847$	−9.89725	+	10.0361i	−0.340073	+	0.344844i
$848$	−13.9069	+	7.08593i	−0.477566	+	0.243332i
$849$	46.4400	+	26.8121i	1.59382	+	0.920190i
$850$	−1.27548	+	18.4293i	−0.0437485	+	0.632120i
$851$	8.08662	+	14.0064i	0.277206	+	0.480135i
$852$	−1.14701	+	21.8862i	−0.0392958	+	0.749809i
$853$	−6.88501	+	1.09048i	−0.235738	+	0.0373373i	−0.273186	−	0.961961i	$-0.588077\pi$
$853$	−6.88501	+	1.09048i	−0.235738	+	0.0373373i	0.0374474	+	0.999299i	$0.488077\pi$
$854$	1.63449	−	2.87711i	0.0559310	−	0.0984527i
$855$	−0.742883	+	2.43297i	−0.0254061	+	0.0832057i
$856$	−1.30537	−	12.4198i	−0.0446167	−	0.424500i
$857$	3.63237	−	13.5562i	0.124079	−	0.463071i	−0.875726	−	0.482809i	$-0.839617\pi$
$857$	3.63237	−	13.5562i	0.124079	−	0.463071i	0.999805	+	0.0197380i	$0.00628321\pi$
$858$	−6.79164	−	17.6928i	−0.231863	−	0.604023i
$859$	−24.5629	−	5.22100i	−0.838074	−	0.178138i	−0.231170	−	0.972913i	$-0.574255\pi$
$859$	−24.5629	−	5.22100i	−0.838074	−	0.178138i	−0.606904	+	0.794775i	$0.707589\pi$
$860$	20.8107	−	11.0748i	0.709639	−	0.377647i
$861$	−25.0926	−	5.15120i	−0.855154	−	0.175553i
$862$	17.9165	+	9.12891i	0.610238	+	0.310932i
$863$	−22.7336	−	35.0067i	−0.773861	−	1.19164i	−0.977156	−	0.212524i	$-0.931831\pi$
$863$	−22.7336	−	35.0067i	−0.773861	−	1.19164i	0.203294	−	0.979118i	$-0.434835\pi$
$864$	14.8801	−	3.16287i	0.506232	−	0.107603i
$865$	−2.12109	+	8.52020i	−0.0721193	+	0.289695i
$866$	−0.911231	+	4.28700i	−0.0309649	+	0.145678i
$867$	−28.6418	−	4.53641i	−0.972726	−	0.154065i
$868$	0.535680	−	3.54162i	0.0181822	−	0.120211i
$869$	−14.4515	−	19.8907i	−0.490233	−	0.674747i
$870$	−3.78004	+	19.4838i	−0.128155	+	0.660562i
$871$	−51.0251	−	5.36295i	−1.72892	−	0.181717i
$872$	6.08894	+	7.51921i	0.206197	+	0.254633i
$873$	−13.1741	−	0.690427i	−0.445877	−	0.0233674i
$874$	−1.71041			−0.0578556
$875$	5.91740	−	28.9825i	0.200045	−	0.979787i
$876$	30.6616			1.03596
$877$	−2.12049	−	0.111130i	−0.0716038	−	0.00375260i	0.0165004	−	0.999864i	$-0.494748\pi$
$877$	−2.12049	−	0.111130i	−0.0716038	−	0.00375260i	−0.0881042	+	0.996111i	$0.528081\pi$
$878$	8.71176	+	10.7581i	0.294008	+	0.363069i
$879$	−6.19890	−	0.651531i	−0.209084	−	0.0219756i
$880$	1.51674	−	7.81786i	0.0511294	−	0.263540i
$881$	19.7829	+	27.2288i	0.666502	+	0.917361i	0.999675	−	0.0255045i	$-0.00811923\pi$
$881$	19.7829	+	27.2288i	0.666502	+	0.917361i	−0.333173	+	0.942866i	$0.608119\pi$
$882$	3.94104	+	7.47545i	0.132702	+	0.251712i
$883$	8.94861	+	1.41732i	0.301145	+	0.0476967i	0.305178	−	0.952295i	$-0.401284\pi$
$883$	8.94861	+	1.41732i	0.301145	+	0.0476967i	−0.00403352	+	0.999992i	$0.501284\pi$
$884$	−9.57436	+	45.0438i	−0.322021	+	1.51499i
$885$	−4.01238	+	16.1173i	−0.134875	+	0.541776i
$886$	12.4157	−	2.63903i	0.417113	−	0.0886601i
$887$	1.78573	+	2.74978i	0.0599589	+	0.0923287i	0.867379	−	0.497649i	$-0.165803\pi$
$887$	1.78573	+	2.74978i	0.0599589	+	0.0923287i	−0.807420	+	0.589978i	$0.799137\pi$
$888$	18.7143	+	9.53540i	0.628010	+	0.319987i
$889$	−25.9522	−	23.0422i	−0.870408	−	0.772810i
$890$	−19.2602	+	10.2496i	−0.645603	+	0.343569i
$891$	−26.0032	−	5.52716i	−0.871142	−	0.185167i
$892$	3.59896	+	9.37562i	0.120502	+	0.313919i
$893$	−1.61633	+	6.03222i	−0.0540883	+	0.201860i
$894$	0.674443	+	6.41689i	0.0225567	+	0.214613i
$895$	3.35940	−	11.0022i	0.112292	−	0.367761i
$896$	−28.9688	+	0.201767i	−0.967779	+	0.00674057i
$897$	47.0348	−	7.44958i	1.57045	−	0.248734i
$898$	0.389338	−	7.42902i	0.0129924	−	0.247910i
$899$	2.63662	+	4.56676i	0.0879362	+	0.152310i
$900$	−8.93547	+	10.6643i	−0.297849	+	0.355478i
$901$	49.7089	+	28.6994i	1.65604	+	0.956117i
$902$	6.30277	−	3.21142i	0.209859	−	0.106929i
$903$	10.4754	+	38.0330i	0.348598	+	1.26566i
$904$	6.67154	−	9.18258i	0.221892	−	0.305408i
$905$	−36.2140	+	16.9026i	−1.20379	+	0.561861i
$906$	2.31845	−	5.20732i	0.0770253	−	0.173002i
$907$	22.6742	+	6.07553i	0.752884	+	0.201735i	0.614797	−	0.788686i	$-0.289238\pi$
$907$	22.6742	+	6.07553i	0.752884	+	0.201735i	0.138087	+	0.990420i	$0.455905\pi$
$908$	−27.2031	−	22.0286i	−0.902767	−	0.731046i
$909$	−4.79773	−	14.7659i	−0.159131	−	0.489754i
$910$	−7.20327	+	20.2510i	−0.238786	+	0.671313i
$911$	−1.84178	+	5.66842i	−0.0610209	+	0.187803i	−0.976920	−	0.213606i	$-0.931479\pi$
$911$	−1.84178	+	5.66842i	−0.0610209	+	0.187803i	0.915899	+	0.401409i	$0.131479\pi$
$912$	1.73903	−	1.12934i	0.0575849	−	0.0373961i
$913$	1.11013	+	21.1825i	0.0367399	+	0.701039i
$914$	−3.16106	−	14.8716i	−0.104559	−	0.491910i
$915$	−3.11494	+	8.56775i	−0.102977	+	0.283241i
$916$	19.3139	−	6.27548i	0.638150	−	0.207348i
$917$	11.9086	−	6.17258i	0.393257	−	0.203837i
$918$	−6.88430	−	6.88430i	−0.227216	−	0.227216i
$919$	26.2261	−	2.75648i	0.865120	−	0.0909278i	0.338437	−	0.940989i	$-0.390102\pi$
$919$	26.2261	−	2.75648i	0.865120	−	0.0909278i	0.526684	+	0.850061i	$0.323435\pi$
$920$	−19.7351	−	8.36872i	−0.650646	−	0.275909i
$921$	−0.320737	+	3.05161i	−0.0105687	+	0.100554i
$922$	−4.00897	−	1.53890i	−0.132029	−	0.0506810i
$923$	−15.8634	−	31.1336i	−0.522149	−	1.02478i
$924$	19.5846	+	8.55670i	0.644287	+	0.281495i
$925$	19.7393	−	3.85155i	0.649023	−	0.126638i
$926$	−11.6243	+	20.1338i	−0.381997	+	0.661638i
$927$	29.5187	+	19.1697i	0.969521	+	0.629614i
$928$	27.0618	−	21.9142i	0.888348	−	0.719370i
$929$	−16.5460	+	7.36674i	−0.542855	+	0.241695i	−0.659797	−	0.751444i	$-0.729358\pi$
$929$	−16.5460	+	7.36674i	−0.542855	+	0.241695i	0.116941	+	0.993139i	$0.462691\pi$
$930$	−0.0512297	−	2.87610i	−0.00167989	−	0.0943110i
$931$	−3.33456	−	2.91938i	−0.109286	−	0.0956789i
$932$	22.0593	−	22.0593i	0.722575	−	0.722575i
$933$	22.9148	−	28.2974i	0.750196	−	0.926415i
$934$	8.43315	−	9.36596i	0.275941	−	0.306464i
$935$	−27.1499	+	10.9805i	−0.887896	+	0.359102i
$936$	17.2156	−	15.5010i	0.562711	−	0.506667i
$937$	8.01861	−	15.7374i	0.261957	−	0.514119i	−0.722141	−	0.691746i	$-0.756842\pi$
$937$	8.01861	−	15.7374i	0.261957	−	0.514119i	0.984098	+	0.177627i	$0.0568420\pi$
$938$	−13.0328	+	10.7049i	−0.425536	+	0.349527i
$939$	−60.9467	−	19.8028i	−1.98892	−	0.646239i
$940$	−21.0186	+	26.9224i	−0.685551	+	0.878112i
$941$	42.4424	+	38.2153i	1.38358	+	1.24578i	0.936212	+	0.351435i	$0.114306\pi$
$941$	42.4424	+	38.2153i	1.38358	+	1.24578i	0.447371	+	0.894349i	$0.352360\pi$
$942$	19.4539	−	7.46767i	0.633844	−	0.243310i
$943$	4.60046	+	17.1691i	0.149812	+	0.559104i
$944$	4.10284	−	2.98088i	0.133536	−	0.0970195i
$945$	9.47290	+	12.3813i	0.308154	+	0.402764i
$946$	−8.81328	−	6.40322i	−0.286544	−	0.208187i
$947$	−8.78475	+	22.8851i	−0.285466	+	0.743665i	0.713604	+	0.700549i	$0.247062\pi$
$947$	−8.78475	+	22.8851i	−0.285466	+	0.743665i	−0.999070	+	0.0431153i	$0.986272\pi$
$948$	19.0692	−	29.3640i	0.619339	−	0.953698i
$949$	−42.3359	+	24.4426i	−1.37428	+	0.793441i
$950$	−0.691017	+	2.01152i	−0.0224196	+	0.0652625i
$951$		−	0.530156i		−	0.0171915i
$952$	19.0947	+	28.9597i	0.618864	+	0.938590i
$953$	−0.0716264	−	0.452231i	−0.00232021	−	0.0146492i	0.986501	−	0.163755i	$-0.0523606\pi$
$953$	−0.0716264	−	0.452231i	−0.00232021	−	0.0146492i	−0.988821	+	0.149106i	$0.952361\pi$
$954$	−5.12528	−	11.5116i	−0.165937	−	0.372700i
$955$	−7.53775	+	17.7755i	−0.243916	+	0.575201i
$956$	−20.5786	−	9.16220i	−0.665561	−	0.296327i
$957$	−30.3919	+	8.14350i	−0.982432	+	0.263242i
$958$	0.790887	−	4.99347i	0.0255524	−	0.161332i
$959$	2.84968	+	6.28237i	0.0920211	+	0.202868i
$960$	−4.28262	+	0.756718i	−0.138221	+	0.0244230i
$961$	20.2316	+	22.4695i	0.652634	+	0.724823i
$962$	−14.5935	+	0.764815i	−0.470515	+	0.0246586i
$963$	−9.39889	+	0.492575i	−0.302875	+	0.0158730i
$964$	−29.7712	−	33.0643i	−0.958867	−	1.06493i
$965$	32.8443	+	16.0047i	1.05730	+	0.515210i
$966$	9.11291	−	12.7283i	0.293203	−	0.409527i
$967$	5.43506	−	34.3156i	0.174780	−	1.10352i	−0.731812	−	0.681506i	$-0.761325\pi$
$967$	5.43506	−	34.3156i	0.174780	−	1.10352i	0.906592	−	0.422009i	$-0.138675\pi$
$968$	12.2690	−	3.28747i	0.394341	−	0.105663i
$969$	−6.96623	−	3.10157i	−0.223788	−	0.0996367i
$970$	−10.9883	−	0.957400i	−0.352814	−	0.0307403i
$971$	13.2470	+	29.7532i	0.425116	+	0.954826i	0.991430	+	0.130637i	$0.0417022\pi$
$971$	13.2470	+	29.7532i	0.425116	+	0.954826i	−0.566314	+	0.824189i	$0.691631\pi$
$972$	−4.00715	−	25.3001i	−0.128529	−	0.811502i
$973$	0.708460	+	11.9280i	0.0227122	+	0.382396i
$974$		−	5.47688i		−	0.175491i
$975$	10.2413	−	58.3248i	0.327984	−	1.86789i
$976$	2.41064	−	1.39179i	0.0771628	−	0.0445500i
$977$	−30.4424	+	46.8772i	−0.973939	+	1.49973i	−0.111381	+	0.993778i	$0.535527\pi$
$977$	−30.4424	+	46.8772i	−0.973939	+	1.49973i	−0.862559	+	0.505957i	$0.831139\pi$
$978$	12.0450	−	31.3783i	0.385157	−	1.00337i
$979$	−27.9823	−	20.3303i	−0.894319	−	0.649761i
$980$	−10.5568	−	21.8197i	−0.337225	−	0.697006i
$981$	5.89929	−	4.28608i	0.188350	−	0.136844i
$982$	−1.30750	−	4.87964i	−0.0417238	−	0.155716i
$983$	−26.5609	+	10.1958i	−0.847160	+	0.325194i	−0.742938	−	0.669360i	$-0.766568\pi$
$983$	−26.5609	+	10.1958i	−0.847160	+	0.325194i	−0.104222	+	0.994554i	$0.533235\pi$
$984$	17.1543	+	15.4458i	0.546859	+	0.492394i
$985$	1.89328	−	54.7773i	0.0603251	−	1.74535i
$986$	−21.1950	−	6.88668i	−0.674987	−	0.219317i
$987$	−36.2781	−	44.1672i	−1.15475	−	1.40586i
$988$	−2.40702	+	4.72404i	−0.0765775	+	0.150292i
$989$	20.3426	−	18.3166i	0.646858	−	0.582434i
$990$	6.23890	+	1.55317i	0.198285	+	0.0493629i
$991$	−1.00198	+	1.11281i	−0.0318289	+	0.0353496i	−0.758849	−	0.651267i	$-0.774238\pi$
$991$	−1.00198	+	1.11281i	−0.0318289	+	0.0353496i	0.727020	+	0.686616i	$0.240905\pi$
$992$	−3.17616	+	3.92223i	−0.100843	+	0.124531i
$993$	−52.9190	+	52.9190i	−1.67933	+	1.67933i
$994$	−10.9486	−	3.47330i	−0.347269	−	0.110166i
$995$	36.9468	−	12.7366i	1.17129	−	0.403776i
$996$	−27.5952	+	12.2862i	−0.874387	+	0.389302i
$997$	21.8781	−	17.7165i	0.692885	−	0.561087i	−0.216886	−	0.976197i	$-0.569590\pi$
$997$	21.8781	−	17.7165i	0.692885	−	0.561087i	0.909771	+	0.415110i	$0.136257\pi$
$998$	8.56864	+	5.56454i	0.271236	+	0.176142i
$999$	−5.29960	+	9.17917i	−0.167672	+	0.290416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.103.11	yes	288
5.2	odd	4		875.2.bb.b.257.8		288
5.3	odd	4		875.2.bb.a.257.11		288
5.4	even	2		875.2.bb.c.243.8		288
7.3	odd	6	inner	175.2.x.a.3.8	✓	288
25.6	even	5		875.2.bb.b.768.8		288
25.8	odd	20		875.2.bb.c.607.11		288
25.17	odd	20	inner	175.2.x.a.117.8	yes	288
25.19	even	10		875.2.bb.a.768.11		288
35.3	even	12		875.2.bb.a.507.11		288
35.17	even	12		875.2.bb.b.507.8		288
35.24	odd	6		875.2.bb.c.493.11		288
175.17	even	60	inner	175.2.x.a.17.11	yes	288
175.31	odd	30		875.2.bb.b.143.8		288
175.94	odd	30		875.2.bb.a.143.11		288
175.108	even	60		875.2.bb.c.857.8		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.8	✓	288	7.3	odd	6	inner
175.2.x.a.17.11	yes	288	175.17	even	60	inner
175.2.x.a.103.11	yes	288	1.1	even	1	trivial
175.2.x.a.117.8	yes	288	25.17	odd	20	inner
875.2.bb.a.143.11		288	175.94	odd	30
875.2.bb.a.257.11		288	5.3	odd	4
875.2.bb.a.507.11		288	35.3	even	12
875.2.bb.a.768.11		288	25.19	even	10
875.2.bb.b.143.8		288	175.31	odd	30
875.2.bb.b.257.8		288	5.2	odd	4
875.2.bb.b.507.8		288	35.17	even	12
875.2.bb.b.768.8		288	25.6	even	5
875.2.bb.c.243.8		288	5.4	even	2
875.2.bb.c.493.11		288	35.24	odd	6
875.2.bb.c.607.11		288	25.8	odd	20
875.2.bb.c.857.8		288	175.108	even	60

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.670945 + 0.0351627i) q^{2} +(1.37832 + 1.70208i) q^{3} +(-1.54011 - 0.161872i) q^{4} +(-0.425878 + 2.19514i) q^{5} +(0.864927 + 1.19047i) q^{6} +(2.46336 - 0.965333i) q^{7} +(-2.35483 - 0.372968i) q^{8} +(-0.373586 + 1.75758i) q^{9} +O(q^{10})\)	\(q+(0.670945 + 0.0351627i) q^{2} +(1.37832 + 1.70208i) q^{3} +(-1.54011 - 0.161872i) q^{4} +(-0.425878 + 2.19514i) q^{5} +(0.864927 + 1.19047i) q^{6} +(2.46336 - 0.965333i) q^{7} +(-2.35483 - 0.372968i) q^{8} +(-0.373586 + 1.75758i) q^{9} +(-0.362928 + 1.45784i) q^{10} +(-2.32965 + 0.495182i) q^{11} +(-1.84725 - 2.84451i) q^{12} +(4.81814 + 2.45497i) q^{13} +(1.68672 - 0.561067i) q^{14} +(-4.32330 + 2.30072i) q^{15} +(1.46267 + 0.310899i) q^{16} +(-1.97071 - 5.13388i) q^{17} +(-0.312457 + 1.16611i) q^{18} +(-0.0661806 - 0.629666i) q^{19} +(1.01123 - 3.31182i) q^{20} +(5.03837 + 2.86230i) q^{21} +(-1.58048 + 0.250323i) q^{22} +(0.210437 - 4.01538i) q^{23} +(-2.61088 - 4.52218i) q^{24} +(-4.63726 - 1.86972i) q^{25} +(3.14639 + 1.81657i) q^{26} +(2.34790 - 1.19631i) q^{27} +(-3.95011 + 1.08797i) q^{28} +(3.54543 - 4.87987i) q^{29} +(-2.98160 + 1.39164i) q^{30} +(-0.355582 + 0.798651i) q^{31} +(5.57632 + 1.49417i) q^{32} +(-4.05384 - 3.28273i) q^{33} +(-1.14172 - 3.51385i) q^{34} +(1.06995 + 5.81852i) q^{35} +(0.859869 - 2.64640i) q^{36} +(-3.37339 + 2.19070i) q^{37} +(-0.0222627 - 0.424798i) q^{38} +(2.46238 + 11.5846i) q^{39} +(1.82159 - 5.01033i) q^{40} +(-4.20425 + 1.36604i) q^{41} +(3.27982 + 2.09761i) q^{42} +(4.81389 + 4.81389i) q^{43} +(3.66808 - 0.385530i) q^{44} +(-3.69904 - 1.56859i) q^{45} +(0.282384 - 2.68670i) q^{46} +(-9.20850 - 3.53481i) q^{47} +(1.48684 + 2.91810i) q^{48} +(5.13627 - 4.75592i) q^{49} +(-3.04560 - 1.41754i) q^{50} +(6.02202 - 10.4304i) q^{51} +(-7.02309 - 4.56085i) q^{52} +(-8.11171 + 6.56873i) q^{53} +(1.61738 - 0.720102i) q^{54} +(-0.0948463 - 5.32478i) q^{55} +(-6.16082 + 1.35444i) q^{56} +(0.980526 - 0.980526i) q^{57} +(2.55038 - 3.14946i) q^{58} +(2.26933 - 2.52034i) q^{59} +(7.03079 - 2.84355i) q^{60} +(1.38336 - 1.24558i) q^{61} +(-0.266659 + 0.523348i) q^{62} +(0.776377 + 4.69019i) q^{63} +(0.844556 + 0.274413i) q^{64} +(-7.44093 + 9.53097i) q^{65} +(-2.60447 - 2.34508i) q^{66} +(-8.85772 + 3.40016i) q^{67} +(2.20409 + 8.22576i) q^{68} +(7.12456 - 5.17630i) q^{69} +(0.513281 + 3.94153i) q^{70} +(-5.22766 - 3.79812i) q^{71} +(1.53525 - 3.99947i) q^{72} +(-4.92365 + 7.58176i) q^{73} +(-2.34039 + 1.35122i) q^{74} +(-3.20920 - 10.4701i) q^{75} +0.980470i q^{76} +(-5.26074 + 3.46870i) q^{77} +(1.24478 + 7.85922i) q^{78} +(4.19876 + 9.43057i) q^{79} +(-1.30538 + 3.07835i) q^{80} +(10.1969 + 4.53995i) q^{81} +(-2.86886 + 0.768708i) q^{82} +(1.39322 - 8.79644i) q^{83} +(-7.29633 - 5.22384i) q^{84} +(12.1089 - 2.13958i) q^{85} +(3.06059 + 3.39913i) q^{86} +(13.1927 - 0.691399i) q^{87} +(5.67061 - 0.297184i) q^{88} +(9.71742 + 10.7923i) q^{89} +(-2.42669 - 1.18251i) q^{90} +(14.2387 + 1.39635i) q^{91} +(-0.974077 + 6.15008i) q^{92} +(-1.84948 + 0.495566i) q^{93} +(-6.05411 - 2.69546i) q^{94} +(1.41039 + 0.122886i) q^{95} +(5.14275 + 11.5508i) q^{96} +(1.14852 + 7.25146i) q^{97} +(3.61338 - 3.01036i) q^{98} -4.27954i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

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