LMFDB - Embedded newform 507.2.s.a.5.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(5,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(52))

chi = DirichletCharacter(H, H._module([26, 3]))

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

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

chi := DirichletCharacter("507.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.s (of order $52$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$1392$
Relative dimension:	$58$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			5.14
Character	$\chi$	$=$	507.5
Dual form			507.2.s.a.203.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.308001 + 1.68071i) q^{2} +(-1.68938 - 0.382115i) q^{3} +(-0.859883 - 0.326111i) q^{4} +(-0.599116 - 0.0362399i) q^{5} +(1.16255 - 2.72165i) q^{6} +(0.705424 + 0.426444i) q^{7} +(-0.955005 + 1.57977i) q^{8} +(2.70798 + 1.29107i) q^{9} +(0.245437 - 0.995778i) q^{10} +(0.995273 + 5.43103i) q^{11} +(1.32805 + 0.879497i) q^{12} +(-0.706075 - 3.53574i) q^{13} +(-0.933999 + 1.05427i) q^{14} +(0.998284 + 0.290154i) q^{15} +(-3.73772 - 3.31133i) q^{16} +(3.91275 - 0.964407i) q^{17} +(-3.00397 + 4.15367i) q^{18} +(-3.55694 + 3.55694i) q^{19} +(0.503352 + 0.226540i) q^{20} +(-1.02877 - 0.989976i) q^{21} -9.43452 q^{22} -6.31551 q^{23} +(2.21702 - 2.30390i) q^{24} +(-4.60592 - 0.559260i) q^{25} +(6.16002 - 0.0976937i) q^{26} +(-4.08145 - 3.21586i) q^{27} +(-0.467514 - 0.596738i) q^{28} +(-5.36393 + 3.70246i) q^{29} +(-0.795137 + 1.58846i) q^{30} +(0.383240 + 0.300249i) q^{31} +(3.81032 - 2.98520i) q^{32} +(0.393890 - 9.55536i) q^{33} +(0.415754 + 6.87323i) q^{34} +(-0.407177 - 0.281054i) q^{35} +(-1.90751 - 1.99327i) q^{36} +(-3.53452 + 4.51148i) q^{37} +(-4.88264 - 7.07372i) q^{38} +(-0.158235 + 6.24299i) q^{39} +(0.629410 - 0.911858i) q^{40} +(-1.41267 - 4.53340i) q^{41} +(1.98073 - 1.42416i) q^{42} +(8.01703 + 0.973444i) q^{43} +(0.915298 - 4.99462i) q^{44} +(-1.57560 - 0.871639i) q^{45} +(1.94518 - 10.6145i) q^{46} +(-1.95023 - 0.877727i) q^{47} +(5.04910 + 7.02232i) q^{48} +(-2.93729 - 5.59655i) q^{49} +(2.35858 - 7.56895i) q^{50} +(-6.97862 + 0.134123i) q^{51} +(-0.545900 + 3.27058i) q^{52} +(1.32172 + 5.36245i) q^{53} +(6.66202 - 5.86923i) q^{54} +(-0.399465 - 3.28989i) q^{55} +(-1.34737 + 0.707153i) q^{56} +(7.36817 - 4.64985i) q^{57} +(-4.57065 - 10.1556i) q^{58} +(-0.0140922 + 0.232972i) q^{59} +(-0.763785 - 0.575050i) q^{60} +(1.98737 + 0.489844i) q^{61} +(-0.622670 + 0.551638i) q^{62} +(1.35970 + 2.06555i) q^{63} +(-0.797568 - 1.51964i) q^{64} +(0.294886 + 2.14391i) q^{65} +(15.9384 + 3.60508i) q^{66} +(10.4715 + 4.71286i) q^{67} +(-3.67901 - 0.446713i) q^{68} +(10.6693 + 2.41325i) q^{69} +(0.597780 - 0.597780i) q^{70} +(4.75329 + 15.2538i) q^{71} +(-4.62573 + 3.04500i) q^{72} +(-13.7154 + 2.51343i) q^{73} +(-6.49384 - 7.33004i) q^{74} +(7.56742 + 2.70479i) q^{75} +(4.21851 - 1.89860i) q^{76} +(-1.61394 + 4.25561i) q^{77} +(-10.4439 - 2.18880i) q^{78} +(0.660455 + 1.74148i) q^{79} +(2.11933 + 2.11933i) q^{80} +(5.66627 + 6.99238i) q^{81} +(8.05443 - 0.977985i) q^{82} +(-5.66461 - 1.76516i) q^{83} +(0.561784 + 1.18676i) q^{84} +(-2.37914 + 0.435994i) q^{85} +(-4.10533 + 13.1745i) q^{86} +(10.4765 - 4.20520i) q^{87} +(-9.53028 - 3.61436i) q^{88} +(-1.11030 + 1.11030i) q^{89} +(1.95026 - 2.37966i) q^{90} +(1.00971 - 2.79530i) q^{91} +(5.43060 + 2.05955i) q^{92} +(-0.532706 - 0.653676i) q^{93} +(2.07588 - 3.00743i) q^{94} +(2.25992 - 2.00212i) q^{95} +(-7.57776 + 3.58714i) q^{96} +(16.9828 - 1.02727i) q^{97} +(10.3108 - 3.21299i) q^{98} +(-4.31667 + 15.9921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27}+ \cdots - 58 q^{99}+O(q^{100}) $ 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{52}\right)$

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 $

$2$	−0.308001	+	1.68071i	−0.217790	+	1.18844i	0.674949	+	0.737865i	$0.264166\pi$
$2$	−0.308001	+	1.68071i	−0.217790	+	1.18844i	−0.892738	+	0.450575i	$0.851219\pi$
$3$	−1.68938	−	0.382115i	−0.975361	−	0.220614i
$3$	−1.68938	−	0.382115i	−0.975361	−	0.220614i
$4$	−0.859883	−	0.326111i	−0.429941	−	0.163055i
$5$	−0.599116	−	0.0362399i	−0.267933	−	0.0162070i	−0.0741342	−	0.997248i	$-0.523619\pi$
$5$	−0.599116	−	0.0362399i	−0.267933	−	0.0162070i	−0.193799	+	0.981041i	$0.562081\pi$
$6$	1.16255	−	2.72165i	0.474611	−	1.11111i
$7$	0.705424	+	0.426444i	0.266625	+	0.161181i	0.644335	−	0.764744i	$-0.277134\pi$
$7$	0.705424	+	0.426444i	0.266625	+	0.161181i	−0.377710	+	0.925924i	$0.623288\pi$
$8$	−0.955005	+	1.57977i	−0.337645	+	0.558534i
$9$	2.70798	+	1.29107i	0.902659	+	0.430357i
$10$	0.245437	−	0.995778i	0.0776140	−	0.314893i
$11$	0.995273	+	5.43103i	0.300086	+	1.63752i	0.695151	+	0.718864i	$0.255338\pi$
$11$	0.995273	+	5.43103i	0.300086	+	1.63752i	−0.395065	+	0.918653i	$0.629278\pi$
$12$	1.32805	+	0.879497i	0.383376	+	0.253889i
$13$	−0.706075	−	3.53574i	−0.195830	−	0.980638i
$13$	−0.706075	−	3.53574i	−0.195830	−	0.980638i
$14$	−0.933999	+	1.05427i	−0.249622	+	0.281765i
$15$	0.998284	+	0.290154i	0.257756	+	0.0749175i
$16$	−3.73772	−	3.31133i	−0.934430	−	0.827833i
$17$	3.91275	−	0.964407i	0.948982	−	0.233903i	0.265698	−	0.964056i	$-0.414397\pi$
$17$	3.91275	−	0.964407i	0.948982	−	0.233903i	0.683283	+	0.730153i	$0.260551\pi$
$18$	−3.00397	+	4.15367i	−0.708044	+	0.979028i
$19$	−3.55694	+	3.55694i	−0.816018	+	0.816018i	−0.985528	−	0.169510i	$-0.945781\pi$
$19$	−3.55694	+	3.55694i	−0.816018	+	0.816018i	0.169510	+	0.985528i	$0.445781\pi$
$20$	0.503352	+	0.226540i	0.112553	+	0.0506559i
$21$	−1.02877	−	0.989976i	−0.224497	−	0.216031i
$22$	−9.43452			−2.01145
$23$	−6.31551			−1.31687			−0.658437	−	0.752636i	$-0.728782\pi$
$23$	−6.31551			−1.31687			−0.658437	+	0.752636i	$0.728782\pi$
$24$	2.21702	−	2.30390i	0.452547	−	0.470283i
$25$	−4.60592	−	0.559260i	−0.921183	−	0.111852i
$26$	6.16002	−	0.0976937i	1.20808	−	0.0191593i
$27$	−4.08145	−	3.21586i	−0.785475	−	0.618893i
$28$	−0.467514	−	0.596738i	−0.0883519	−	0.112773i
$29$	−5.36393	+	3.70246i	−0.996057	+	0.687529i	−0.950272	−	0.311422i	$-0.899195\pi$
$29$	−5.36393	+	3.70246i	−0.996057	+	0.687529i	−0.0457859	+	0.998951i	$0.514579\pi$
$30$	−0.795137	+	1.58846i	−0.145172	+	0.290011i
$31$	0.383240	+	0.300249i	0.0688319	+	0.0539264i	0.650545	−	0.759468i	$-0.274540\pi$
$31$	0.383240	+	0.300249i	0.0688319	+	0.0539264i	−0.581713	+	0.813394i	$0.697617\pi$
$32$	3.81032	−	2.98520i	0.673576	−	0.527713i
$33$	0.393890	−	9.55536i	0.0685674	−	1.66337i
$34$	0.415754	+	6.87323i	0.0713012	+	1.17875i
$35$	−0.407177	−	0.281054i	−0.0688254	−	0.0475068i
$36$	−1.90751	−	1.99327i	−0.317918	−	0.332212i
$37$	−3.53452	+	4.51148i	−0.581071	+	0.741683i	−0.984895	−	0.173154i	$-0.944604\pi$
$37$	−3.53452	+	4.51148i	−0.581071	+	0.741683i	0.403823	+	0.914837i	$0.367681\pi$
$38$	−4.88264	−	7.07372i	−0.792068	−	1.14751i
$39$	−0.158235	+	6.24299i	−0.0253379	+	0.999679i
$40$	0.629410	−	0.911858i	0.0995184	−	0.144177i
$41$	−1.41267	−	4.53340i	−0.220621	−	0.707999i	−0.996977	−	0.0777031i	$-0.975241\pi$
$41$	−1.41267	−	4.53340i	−0.220621	−	0.707999i	0.776355	−	0.630296i	$-0.217066\pi$
$42$	1.98073	−	1.42416i	0.305633	−	0.219752i
$43$	8.01703	+	0.973444i	1.22259	+	0.148449i	0.706266	−	0.707947i	$-0.250378\pi$
$43$	8.01703	+	0.973444i	1.22259	+	0.148449i	0.516320	+	0.856396i	$0.327302\pi$
$44$	0.915298	−	4.99462i	0.137986	−	0.752967i
$45$	−1.57560	−	0.871639i	−0.234877	−	0.129936i
$46$	1.94518	−	10.6145i	0.286802	−	1.56503i
$47$	−1.95023	−	0.877727i	−0.284470	−	0.128030i	0.263154	−	0.964754i	$-0.415237\pi$
$47$	−1.95023	−	0.877727i	−0.284470	−	0.128030i	−0.547625	+	0.836724i	$0.684468\pi$
$48$	5.04910	+	7.02232i	0.728775	+	1.01358i
$49$	−2.93729	−	5.59655i	−0.419613	−	0.799506i
$50$	2.35858	−	7.56895i	0.333554	−	1.07041i
$51$	−6.97862	+	0.134123i	−0.977202	+	0.0187809i
$52$	−0.545900	+	3.27058i	−0.0757028	+	0.453548i
$53$	1.32172	+	5.36245i	0.181553	+	0.736589i	0.989157	+	0.146863i	$0.0469178\pi$
$53$	1.32172	+	5.36245i	0.181553	+	0.736589i	−0.807604	+	0.589725i	$0.799236\pi$
$54$	6.66202	−	5.86923i	0.906586	−	0.798702i
$55$	−0.399465	−	3.28989i	−0.0538638	−	0.443608i
$56$	−1.34737	+	0.707153i	−0.180050	+	0.0944973i
$57$	7.36817	−	4.64985i	0.975938	−	0.615887i
$58$	−4.57065	−	10.1556i	−0.600156	−	1.33349i
$59$	−0.0140922	+	0.232972i	−0.00183465	+	0.0303303i	−0.998978	−	0.0452064i	$-0.985605\pi$
$59$	−0.0140922	+	0.232972i	−0.00183465	+	0.0303303i	0.997143	+	0.0755367i	$0.0240670\pi$
$60$	−0.763785	−	0.575050i	−0.0986042	−	0.0742386i
$61$	1.98737	+	0.489844i	0.254457	+	0.0627181i	0.364481	−	0.931211i	$-0.381246\pi$
$61$	1.98737	+	0.489844i	0.254457	+	0.0627181i	−0.110024	+	0.993929i	$0.535093\pi$
$62$	−0.622670	+	0.551638i	−0.0790792	+	0.0700580i
$63$	1.35970	+	2.06555i	0.171306	+	0.260235i
$64$	−0.797568	−	1.51964i	−0.0996960	−	0.189955i
$65$	0.294886	+	2.14391i	0.0365761	+	0.265919i
$66$	15.9384	+	3.60508i	1.96189	+	0.443754i
$67$	10.4715	+	4.71286i	1.27930	+	0.575768i	0.932161	−	0.362045i	$-0.117921\pi$
$67$	10.4715	+	4.71286i	1.27930	+	0.575768i	0.347143	+	0.937812i	$0.387152\pi$
$68$	−3.67901	−	0.446713i	−0.446146	−	0.0541719i
$69$	10.6693	+	2.41325i	1.28443	+	0.290521i
$70$	0.597780	−	0.597780i	0.0714484	−	0.0714484i
$71$	4.75329	+	15.2538i	0.564112	+	1.81030i	0.585695	+	0.810531i	$0.300822\pi$
$71$	4.75329	+	15.2538i	0.564112	+	1.81030i	−0.0215834	+	0.999767i	$0.506871\pi$
$72$	−4.62573	+	3.04500i	−0.545148	+	0.358857i
$73$	−13.7154	+	2.51343i	−1.60526	+	0.294175i	−0.906828	−	0.421500i	$-0.861504\pi$
$73$	−13.7154	+	2.51343i	−1.60526	+	0.294175i	−0.698433	+	0.715675i	$0.746119\pi$
$74$	−6.49384	−	7.33004i	−0.754894	−	0.852099i
$75$	7.56742	+	2.70479i	0.873810	+	0.312322i
$76$	4.21851	−	1.89860i	0.483896	−	0.217784i
$77$	−1.61394	+	4.25561i	−0.183925	+	0.484971i
$78$	−10.4439	−	2.18880i	−1.18254	−	0.247832i
$79$	0.660455	+	1.74148i	0.0743070	+	0.195932i	0.967023	−	0.254687i	$-0.0819726\pi$
$79$	0.660455	+	1.74148i	0.0743070	+	0.195932i	−0.892716	+	0.450619i	$0.851203\pi$
$80$	2.11933	+	2.11933i	0.236948	+	0.236948i
$81$	5.66627	+	6.99238i	0.629585	+	0.776931i
$82$	8.05443	−	0.977985i	0.889463	−	0.108000i
$83$	−5.66461	−	1.76516i	−0.621771	−	0.193752i	−0.0295973	−	0.999562i	$-0.509422\pi$
$83$	−5.66461	−	1.76516i	−0.621771	−	0.193752i	−0.592174	+	0.805810i	$0.701730\pi$
$84$	0.561784	+	1.18676i	0.0612957	+	0.129486i
$85$	−2.37914	+	0.435994i	−0.258054	+	0.0472902i
$86$	−4.10533	+	13.1745i	−0.442689	+	1.42064i
$87$	10.4765	−	4.20520i	1.12319	−	0.450844i
$88$	−9.53028	−	3.61436i	−1.01593	−	0.385292i
$89$	−1.11030	+	1.11030i	−0.117691	+	0.117691i	−0.763500	−	0.645808i	$-0.776520\pi$
$89$	−1.11030	+	1.11030i	−0.117691	+	0.117691i	0.645808	+	0.763500i	$0.276520\pi$
$90$	1.95026	−	2.37966i	0.205575	−	0.250839i
$91$	1.00971	−	2.79530i	0.105847	−	0.293027i
$92$	5.43060	+	2.05955i	0.566179	+	0.214723i
$93$	−0.532706	−	0.653676i	−0.0552391	−	0.0677830i
$94$	2.07588	−	3.00743i	0.214110	−	0.310192i
$95$	2.25992	−	2.00212i	0.231863	−	0.205413i
$96$	−7.57776	+	3.58714i	−0.773401	+	0.366111i
$97$	16.9828	−	1.02727i	1.72434	−	0.104304i	0.831745	−	0.555157i	$-0.187342\pi$
$97$	16.9828	−	1.02727i	1.72434	−	0.104304i	0.892598	+	0.450854i	$0.148880\pi$
$98$	10.3108	−	3.21299i	1.04155	−	0.324561i
$99$	−4.31667	+	15.9921i	−0.433842	+	1.60726i
$100$	3.77817	+	1.98294i	0.377817	+	0.198294i
$101$	−0.873058	+	7.19028i	−0.0868726	+	0.715460i	0.882577	+	0.470168i	$0.155807\pi$
$101$	−0.873058	+	7.19028i	−0.0868726	+	0.715460i	−0.969449	+	0.245292i	$0.921116\pi$
$102$	1.92400	−	11.7703i	0.190505	−	1.16544i
$103$	−0.814537	+	1.55197i	−0.0802587	+	0.152920i	−0.922278	−	0.386527i	$-0.873675\pi$
$103$	−0.814537	+	1.55197i	−0.0802587	+	0.152920i	0.842019	+	0.539447i	$0.181367\pi$
$104$	6.25997	+	2.26121i	0.613840	+	0.221730i
$105$	0.580479	+	0.630394i	0.0566490	+	0.0615201i
$106$	−9.41980	+	0.569793i	−0.914932	+	0.0553432i
$107$	−7.66886	−	8.65635i	−0.741376	−	0.836841i	0.249951	−	0.968259i	$-0.419586\pi$
$107$	−7.66886	−	8.65635i	−0.741376	−	0.836841i	−0.991327	+	0.131418i	$0.958047\pi$
$108$	2.46084	+	4.09627i	0.236794	+	0.394164i
$109$	6.23174	+	7.95423i	0.596892	+	0.761877i	0.987318	−	0.158758i	$-0.0507489\pi$
$109$	6.23174	+	7.95423i	0.596892	+	0.761877i	−0.390425	+	0.920635i	$0.627672\pi$
$110$	5.65238	+	0.341906i	0.538933	+	0.0325994i
$111$	7.69503	−	6.27099i	0.730380	−	0.595216i
$112$	−1.22458	−	3.92982i	−0.115712	−	0.371333i
$113$	−5.01620	−	9.55757i	−0.471884	−	0.899100i	−0.998790	−	0.0491767i	$-0.984340\pi$
$113$	−5.01620	−	9.55757i	−0.471884	−	0.899100i	0.526906	−	0.849924i	$-0.323352\pi$
$114$	5.54563	+	13.8159i	0.519396	+	1.29398i
$115$	3.78372	+	0.228873i	0.352834	+	0.0213425i
$116$	5.81976	−	1.43444i	0.540352	−	0.133185i
$117$	2.65286	−	10.4863i	0.245257	−	0.969458i
$118$	−0.387217	−	0.0954404i	−0.0356462	−	0.00878600i
$119$	3.17141	+	0.988253i	0.290723	+	0.0905930i
$120$	−1.41174	+	1.29996i	−0.128874	+	0.118670i
$121$	−18.2203	+	6.91007i	−1.65640	+	0.628188i
$122$	−1.43540	+	3.18932i	−0.129955	+	0.288748i
$123$	0.654240	+	8.19842i	0.0589908	+	0.739227i
$124$	−0.231627	−	0.383158i	−0.0208007	−	0.0344086i
$125$	5.69111	+	1.04293i	0.509028	+	0.0932829i
$126$	−3.89038	+	1.64907i	−0.346583	+	0.146911i
$127$	16.5365	−	6.27148i	1.46738	−	0.556504i	0.513871	−	0.857867i	$-0.328211\pi$
$127$	16.5365	−	6.27148i	1.46738	−	0.556504i	0.953509	+	0.301364i	$0.0974418\pi$
$128$	12.0423	−	3.75253i	1.06440	−	0.331680i
$129$	−13.1718	−	4.70794i	−1.15971	−	0.414511i
$130$	−3.69411	−	0.164708i	−0.323995	−	0.0144459i
$131$	−10.3046	+	7.11278i	−0.900321	+	0.621447i	−0.925711	−	0.378231i	$-0.876533\pi$
$131$	−10.3046	+	7.11278i	−0.900321	+	0.621447i	0.0253901	+	0.999678i	$0.491917\pi$
$132$	−3.45480	+	8.08804i	−0.300702	+	0.703973i
$133$	−4.02599	+	0.992316i	−0.349097	+	0.0860447i
$134$	−11.1462	+	16.1481i	−0.962885	+	1.39498i
$135$	2.32872	+	2.07459i	0.200424	+	0.178552i
$136$	−2.21316	+	7.10227i	−0.189777	+	0.609015i
$137$	−7.47555	−	9.54184i	−0.638679	−	0.815214i	0.354095	−	0.935209i	$-0.384789\pi$
$137$	−7.47555	−	9.54184i	−0.638679	−	0.815214i	−0.992774	+	0.119995i	$0.961712\pi$
$138$	−7.34212	+	17.1886i	−0.625002	+	1.46319i
$139$	12.0424	+	10.6686i	1.02142	+	0.904899i	0.995500	−	0.0947651i	$-0.0302100\pi$
$139$	12.0424	+	10.6686i	1.02142	+	0.904899i	0.0259200	+	0.999664i	$0.491748\pi$
$140$	0.258470	+	0.374458i	0.0218447	+	0.0316475i
$141$	2.95928	+	2.22802i	0.249216	+	0.187633i
$142$	−27.1013	+	3.29069i	−2.27429	+	0.276149i
$143$	18.5000	−	7.35374i	1.54705	−	0.614951i
$144$	−5.84649	−	13.7927i	−0.487208	−	1.14939i
$145$	3.34780	−	2.02381i	0.278019	−	0.168069i
$146$		−	23.8257i		−	1.97183i
$147$	2.82367	+	10.5770i	0.232892	+	0.872380i
$148$	4.51051	−	2.72670i	0.370762	−	0.224133i
$149$	−6.91372	+	15.3616i	−0.566394	+	1.25848i	0.376819	+	0.926287i	$0.377018\pi$
$149$	−6.91372	+	15.3616i	−0.566394	+	1.25848i	−0.943213	+	0.332188i	$0.892213\pi$
$150$	−6.87674	+	11.8855i	−0.561483	+	0.970451i
$151$	8.13180	−	3.65982i	0.661756	−	0.297832i	−0.0515649	−	0.998670i	$-0.516421\pi$
$151$	8.13180	−	3.65982i	0.661756	−	0.297832i	0.713321	+	0.700837i	$0.247190\pi$
$152$	−2.22226	−	9.01605i	−0.180249	−	0.731298i
$153$	11.8408	+	2.44005i	0.957268	+	0.197267i
$154$	−6.65534	−	4.02329i	−0.536302	−	0.324206i
$155$	−0.218724	−	0.193773i	−0.0175684	−	0.0155642i
$156$	2.17197	−	5.31664i	0.173897	−	0.425672i
$157$	14.6170	−	12.9495i	1.16656	−	1.03349i	0.167701	−	0.985838i	$-0.446366\pi$
$157$	14.6170	−	12.9495i	1.16656	−	1.03349i	0.998864	−	0.0476483i	$-0.0151727\pi$
$158$	−3.13034	+	0.573656i	−0.249036	+	0.0456376i
$159$	−0.183816	−	9.56423i	−0.0145775	−	0.758493i
$160$	−2.39101	+	1.65040i	−0.189026	+	0.130475i
$161$	−4.45511	−	2.69321i	−0.351112	−	0.212254i
$162$	−13.4974	+	7.36968i	−1.06045	+	0.579017i
$163$	1.89649	−	2.42069i	0.148544	−	0.189603i	−0.707182	−	0.707032i	$-0.750034\pi$
$163$	1.89649	−	2.42069i	0.148544	−	0.189603i	0.855726	+	0.517429i	$0.173111\pi$
$164$	−0.263664	+	4.35888i	−0.0205887	+	0.340371i
$165$	−0.582270	+	5.71049i	−0.0453297	+	0.444561i
$166$	4.71143	−	8.97688i	0.365678	−	0.696741i
$167$	1.85600	+	0.340124i	0.143621	+	0.0263196i	0.251585	−	0.967835i	$-0.419048\pi$
$167$	1.85600	+	0.340124i	0.143621	+	0.0263196i	−0.107963	+	0.994155i	$0.534433\pi$
$168$	2.54642	−	0.679797i	0.196461	−	0.0524475i
$169$	−12.0029	+	4.99299i	−0.923301	+	0.384077i
$170$		−	4.13293i		−	0.316981i
$171$	−14.2244	+	5.03984i	−1.08777	+	0.385406i
$172$	−6.57626	−	3.45149i	−0.501435	−	0.263173i
$173$	−4.19056	+	11.0496i	−0.318603	+	0.840086i	0.676054	+	0.736852i	$0.263688\pi$
$173$	−4.19056	+	11.0496i	−0.318603	+	0.840086i	−0.994657	+	0.103234i	$0.967081\pi$
$174$	3.84094	+	18.9031i	0.291181	+	1.43304i
$175$	−3.01063	−	2.35868i	−0.227582	−	0.178299i
$176$	14.2639	−	23.5954i	1.07518	−	1.77857i
$177$	0.112829	−	0.388192i	0.00848075	−	0.0291783i
$178$	−1.52411	−	2.20806i	−0.114237	−	0.165501i
$179$	15.3897	+	3.79323i	1.15028	+	0.283519i	0.767953	−	0.640507i	$-0.221276\pi$
$179$	15.3897	+	3.79323i	1.15028	+	0.283519i	0.382330	+	0.924026i	$0.375122\pi$
$180$	1.07058	+	1.26333i	0.0797966	+	0.0941629i
$181$	14.4684	+	16.3314i	1.07543	+	1.21391i	0.975750	+	0.218887i	$0.0702427\pi$
$181$	14.4684	+	16.3314i	1.07543	+	1.21391i	0.0996776	+	0.995020i	$0.468219\pi$
$182$	4.38709	+	2.55799i	0.325192	+	0.189610i
$183$	−3.17024	−	1.58694i	−0.234351	−	0.117310i
$184$	6.03134	−	9.97706i	0.444636	−	0.735519i
$185$	2.28108	−	2.57481i	0.167709	−	0.189304i
$186$	1.26271	−	0.693991i	0.0925866	−	0.0508859i
$187$	9.13198	+	20.2904i	0.667797	+	1.48378i
$188$	1.39073	+	1.39073i	0.101430	+	0.101430i
$189$	−1.50777	−	4.00905i	−0.109674	−	0.291616i
$190$	2.66892	+	4.41493i	0.193624	+	0.320292i
$191$			5.88760i			0.426012i	0.977051	+	0.213006i	$0.0683254\pi$
$191$			5.88760i			0.426012i	−0.977051	+	0.213006i	$0.931675\pi$
$192$	0.766714	+	2.87200i	0.0553328	+	0.207269i
$193$	−7.63214	−	12.6251i	−0.549374	−	0.908775i	−0.999872	−	0.0159979i	$-0.994908\pi$
$193$	−7.63214	−	12.6251i	−0.549374	−	0.908775i	0.450498	−	0.892777i	$-0.351246\pi$
$194$	−3.50418	+	28.8596i	−0.251586	+	2.07200i
$195$	0.321046	−	3.73454i	0.0229906	−	0.267436i
$196$	0.700636	+	5.77026i	0.0500454	+	0.412161i
$197$	19.6142	−	15.3667i	1.39745	−	1.09483i	0.414690	−	0.909963i	$-0.363890\pi$
$197$	19.6142	−	15.3667i	1.39745	−	1.09483i	0.982763	−	0.184872i	$-0.0591870\pi$
$198$	−25.5485	−	12.1806i	−1.81565	−	0.865641i
$199$	−3.58006	+	4.04105i	−0.253783	+	0.286462i	−0.861571	−	0.507638i	$-0.830519\pi$
$199$	−3.58006	+	4.04105i	−0.253783	+	0.286462i	0.607787	+	0.794100i	$0.292057\pi$
$200$	5.28218	−	6.74220i	0.373506	−	0.476746i
$201$	−15.8895	−	11.9631i	−1.12076	−	0.843814i
$202$	−11.8159	−	3.68197i	−0.831361	−	0.259063i
$203$	−5.36274	+	0.324386i	−0.376390	+	0.0227674i
$204$	6.04453	+	2.16047i	0.423202	+	0.151263i
$205$	0.682061	+	2.76723i	0.0476372	+	0.193272i
$206$	−2.35753	−	1.84701i	−0.164257	−	0.128687i
$207$	−17.1022	−	8.15377i	−1.18869	−	0.566726i
$208$	−9.06890	+	15.5537i	−0.628815	+	1.07845i
$209$	−22.8580	−	15.7777i	−1.58112	−	1.09137i
$210$	−1.23830	+	0.781454i	−0.0854505	+	0.0539254i
$211$	−1.28762	−	3.39517i	−0.0886433	−	0.233733i	0.883362	−	0.468691i	$-0.155274\pi$
$211$	−1.28762	−	3.39517i	−0.0886433	−	0.233733i	−0.972006	+	0.234957i	$0.924505\pi$
$212$	0.612222	−	5.04210i	0.0420476	−	0.346293i
$213$	−2.20136	−	27.5858i	−0.150835	−	1.89015i
$214$	16.9108	−	10.2229i	1.15600	−	0.698826i
$215$	−4.76785	−	0.873742i	−0.325165	−	0.0595887i
$216$	8.97814	−	3.37659i	0.610885	−	0.229748i
$217$	0.142307	+	0.375233i	0.00966044	+	0.0254725i
$218$	−15.2881	+	8.02382i	−1.03544	+	0.543442i
$219$	24.1308	+	0.994717i	1.63061	+	0.0672168i
$220$	−0.729374	+	2.95919i	−0.0491744	+	0.199508i
$221$	−6.17259	−	13.1535i	−0.415213	−	0.884802i
$222$	8.16962	+	14.8646i	0.548309	+	0.997645i
$223$	−1.56103	+	25.8069i	−0.104534	+	1.72816i	0.447455	+	0.894306i	$0.352330\pi$
$223$	−1.56103	+	25.8069i	−0.104534	+	1.72816i	−0.551989	+	0.833851i	$0.686131\pi$
$224$	3.96091	−	0.480942i	0.264650	−	0.0321343i
$225$	−11.7507	−	7.46103i	−0.783378	−	0.497402i
$226$	17.6085	−	5.48702i	1.17130	−	0.364991i
$227$	11.9876	−	5.39519i	0.795646	−	0.358091i	0.0285243	−	0.999593i	$-0.490919\pi$
$227$	11.9876	−	5.39519i	0.795646	−	0.358091i	0.767121	+	0.641502i	$0.221688\pi$
$228$	−7.85212	+	1.59548i	−0.520020	+	0.105664i
$229$	0.218224	−	0.170968i	0.0144207	−	0.0112979i	−0.609483	−	0.792799i	$-0.708623\pi$
$229$	0.218224	−	0.170968i	0.0144207	−	0.0112979i	0.623903	+	0.781502i	$0.285546\pi$
$230$	−1.55006	+	6.28884i	−0.102208	+	0.414674i
$231$	4.35268	−	6.57260i	0.286385	−	0.432446i
$232$	−0.726450	−	12.0097i	−0.0476938	−	0.788473i
$233$	−1.36679	+	0.717345i	−0.0895412	+	0.0469948i	−0.508899	−	0.860826i	$-0.669947\pi$
$233$	−1.36679	+	0.717345i	−0.0895412	+	0.0469948i	0.419358	+	0.907821i	$0.362255\pi$
$234$	16.8073	+	7.68848i	1.09873	+	0.502611i
$235$	1.13661	+	0.596537i	0.0741440	+	0.0389138i
$236$	0.0880922	−	0.195733i	0.00573431	−	0.0127411i
$237$	−0.450312	−	3.19438i	−0.0292509	−	0.207497i
$238$	−2.63776	+	5.02584i	−0.170981	+	0.325777i
$239$	3.98627	+	3.98627i	0.257850	+	0.257850i	0.824179	−	0.566329i	$-0.191637\pi$
$239$	3.98627	+	3.98627i	0.257850	+	0.257850i	−0.566329	+	0.824179i	$0.691637\pi$
$240$	−2.77051	−	4.39016i	−0.178836	−	0.283384i
$241$	−1.28044	−	21.1681i	−0.0824802	−	1.36356i	−0.770301	−	0.637680i	$-0.779894\pi$
$241$	−1.28044	−	21.1681i	−0.0824802	−	1.36356i	0.687821	−	0.725880i	$-0.258567\pi$
$242$	−6.00192	−	32.7514i	−0.385818	−	2.10534i
$243$	−6.90055	−	13.9779i	−0.442671	−	0.896684i
$244$	−1.54917	−	1.06931i	−0.0991752	−	0.0684557i
$245$	1.55696	+	3.45943i	0.0994707	+	0.221015i
$246$	−13.9807	−	1.42554i	−0.891374	−	0.0908890i
$247$	15.0879	+	10.0650i	0.960019	+	0.640418i
$248$	−0.840322	+	0.318692i	−0.0533605	+	0.0202370i
$249$	8.89515	+	5.14655i	0.563707	+	0.326150i
$250$	−3.50574	+	9.24387i	−0.221722	+	0.584634i
$251$	−0.703836	−	5.79661i	−0.0444257	−	0.365879i	−0.997920	−	0.0644672i	$-0.979465\pi$
$251$	−0.703836	−	5.79661i	−0.0444257	−	0.365879i	0.953494	−	0.301412i	$-0.0974579\pi$
$252$	−0.495586	−	2.21955i	−0.0312190	−	0.139818i
$253$	−6.28565	−	34.2997i	−0.395176	−	2.15640i
$254$	5.44726	+	29.7247i	0.341791	+	1.86509i
$255$	4.18587	+	0.172549i	0.262129	+	0.0108055i
$256$	2.18413	+	17.9879i	0.136508	+	1.12425i
$257$	3.19459	−	8.42344i	0.199273	−	0.525440i	−0.797712	−	0.603039i	$-0.793956\pi$
$257$	3.19459	−	8.42344i	0.199273	−	0.525440i	0.996985	+	0.0775992i	$0.0247255\pi$
$258$	11.9696	−	20.6879i	0.745195	−	1.28797i
$259$	−4.41723	+	1.67523i	−0.274473	+	0.104094i
$260$	0.445583	−	1.93967i	0.0276339	−	0.120294i
$261$	−19.3055	+	3.10094i	−1.19498	+	0.191943i
$262$	−8.78067	−	19.5099i	−0.542472	−	1.20532i
$263$	−13.7648	−	9.50119i	−0.848777	−	0.585868i	0.0623222	−	0.998056i	$-0.480149\pi$
$263$	−13.7648	−	9.50119i	−0.848777	−	0.585868i	−0.911099	+	0.412188i	$0.864765\pi$
$264$	14.7191	+	9.74767i	0.905899	+	0.599928i
$265$	−0.597532	−	3.26063i	−0.0367061	−	0.200299i
$266$	−0.427786	−	7.07214i	−0.0262292	−	0.433621i
$267$	2.29997	−	1.45144i	0.140756	−	0.0888270i
$268$	−7.46739	−	7.46739i	−0.456143	−	0.456143i
$269$	5.67124	−	10.8057i	0.345782	−	0.658832i	−0.649008	−	0.760782i	$-0.724816\pi$
$269$	5.67124	−	10.8057i	0.345782	−	0.658832i	0.994790	+	0.101950i	$0.0325081\pi$
$270$	−4.20402	+	3.27492i	−0.255849	+	0.199305i
$271$	−3.77694	+	8.39203i	−0.229433	+	0.509779i	−0.990269	−	0.139165i	$-0.955558\pi$
$271$	−3.77694	+	8.39203i	−0.229433	+	0.509779i	0.760836	+	0.648944i	$0.224789\pi$
$272$	−17.8182	−	9.35174i	−1.08039	−	0.567032i
$273$	−2.77391	+	4.33648i	−0.167884	+	0.262456i
$274$	18.3395	−	9.62532i	1.10793	−	0.581487i
$275$	−1.54679	−	25.5715i	−0.0932750	−	1.54202i
$276$	−8.38733	−	5.55447i	−0.504858	−	0.334340i
$277$	−3.11255	+	12.6281i	−0.187015	+	0.758750i	0.800250	+	0.599667i	$0.204700\pi$
$277$	−3.11255	+	12.6281i	−0.187015	+	0.758750i	−0.987265	+	0.159084i	$0.949146\pi$
$278$	−21.6399	+	16.9538i	−1.29787	+	1.01682i
$279$	0.650161	+	1.30786i	0.0389241	+	0.0782994i
$280$	0.832857	−	0.374838i	0.0497727	−	0.0224009i
$281$	20.5566	−	6.40569i	1.22630	−	0.382131i	0.385112	−	0.922870i	$-0.374163\pi$
$281$	20.5566	−	6.40569i	1.22630	−	0.382131i	0.841191	+	0.540739i	$0.181855\pi$
$282$	−4.65612	+	4.28745i	−0.277268	+	0.255314i
$283$	−13.7915	+	1.67460i	−0.819822	+	0.0995444i	−0.519692	−	0.854354i	$-0.673953\pi$
$283$	−13.7915	+	1.67460i	−0.819822	+	0.0995444i	−0.300130	+	0.953898i	$0.597030\pi$
$284$	0.887167	−	14.6666i	0.0526437	−	0.870304i
$285$	−4.58290	+	2.51878i	−0.271467	+	0.149199i
$286$	6.66148	+	33.3580i	0.393902	+	1.97250i
$287$	0.936713	−	3.80039i	0.0552924	−	0.224330i
$288$	14.1724	−	3.16444i	0.835115	−	0.186467i
$289$	−0.673203	+	0.353324i	−0.0396002	+	0.0207838i
$290$	2.37031	+	6.25001i	0.139190	+	0.367013i
$291$	−29.0829	−	4.75395i	−1.70487	−	0.278681i
$292$	12.6133	+	2.31147i	0.738135	+	0.135268i
$293$	17.5286	−	10.5964i	1.02403	−	0.619048i	0.0974873	−	0.995237i	$-0.468919\pi$
$293$	17.5286	−	10.5964i	1.02403	−	0.619048i	0.926543	+	0.376189i	$0.122766\pi$
$294$	−18.6466	+	1.48801i	−1.08749	+	0.0867827i
$295$	0.0168857	−	0.139066i	0.000983125	−	0.00809676i
$296$	−3.75162	−	9.89222i	−0.218059	−	0.574974i
$297$	13.4033	−	25.3671i	0.777738	−	1.47195i
$298$	−23.6890	−	16.3513i	−1.37227	−	0.947208i
$299$	4.45922	+	22.3300i	0.257883	+	1.29138i
$300$	−5.62503	−	4.79362i	−0.324761	−	0.276760i
$301$	5.24028	+	4.10550i	0.302045	+	0.236637i
$302$	3.64649	+	14.7944i	0.209832	+	0.851323i
$303$	4.22244	−	11.8135i	0.242573	−	0.678666i
$304$	25.0731	−	1.51664i	1.43804	−	0.0869853i
$305$	−1.17292	−	0.365495i	−0.0671610	−	0.0209282i
$306$	−7.74799	+	19.1493i	−0.442923	+	1.09469i
$307$	−14.9401	+	19.0696i	−0.852676	+	1.08836i	0.142456	+	0.989801i	$0.454500\pi$
$307$	−14.9401	+	19.0696i	−0.852676	+	1.08836i	−0.995131	+	0.0985587i	$0.968577\pi$
$308$	2.77560	−	3.13300i	0.158154	−	0.178519i
$309$	1.96909	−	2.31061i	0.112018	−	0.131446i
$310$	0.393043	−	0.307930i	0.0223233	−	0.0174892i
$311$	2.27178	+	18.7098i	0.128821	+	1.06093i	0.903502	+	0.428583i	$0.140987\pi$
$311$	2.27178	+	18.7098i	0.128821	+	1.06093i	−0.774682	+	0.632351i	$0.782090\pi$
$312$	−9.71139	−	6.21207i	−0.549799	−	0.351689i
$313$	−3.87291	+	31.8963i	−0.218910	+	1.80288i	0.306325	+	0.951927i	$0.400900\pi$
$313$	−3.87291	+	31.8963i	−0.218910	+	1.80288i	−0.525235	+	0.850957i	$0.676023\pi$
$314$	17.2623	+	28.5554i	0.974171	+	1.61148i
$315$	−0.739764	−	1.28678i	−0.0416810	−	0.0725019i
$316$		−	1.71285i		−	0.0963553i
$317$	11.3084	+	18.7064i	0.635142	+	1.05065i	0.993140	+	0.116931i	$0.0373057\pi$
$317$	11.3084	+	18.7064i	0.635142	+	1.05065i	−0.357998	+	0.933722i	$0.616540\pi$
$318$	16.1313	+	2.63685i	0.904598	+	0.147867i
$319$	−25.4467	−	25.4467i	−1.42474	−	1.42474i
$320$	0.422764	+	0.939344i	0.0236332	+	0.0525109i
$321$	9.64785	+	17.5542i	0.538491	+	0.979780i
$322$	5.89867	−	6.65823i	0.328720	−	0.371048i
$323$	−10.4871	+	17.3478i	−0.583517	+	0.965255i
$324$	−2.59204	−	7.86046i	−0.144002	−	0.436692i
$325$	1.27473	+	16.6802i	0.0707091	+	0.925251i
$326$	3.48435	+	3.93302i	0.192980	+	0.217830i
$327$	−7.48831	−	15.8189i	−0.414105	−	0.874788i
$328$	8.51085	+	2.09774i	0.469933	+	0.115828i
$329$	−1.00144	−	1.45083i	−0.0552111	−	0.0799870i
$330$	−9.41833	−	2.73747i	−0.518462	−	0.150693i
$331$	6.24297	−	10.3271i	0.343145	−	0.567631i	−0.635775	−	0.771874i	$-0.719320\pi$
$331$	6.24297	−	10.3271i	0.343145	−	0.567631i	0.978920	+	0.204243i	$0.0654734\pi$
$332$	4.29526	+	3.36512i	0.235733	+	0.184685i
$333$	−15.3960	+	7.65366i	−0.843698	+	0.419418i
$334$	−1.14330	+	3.01463i	−0.0625585	+	0.164953i
$335$	−6.10288	−	3.20304i	−0.333436	−	0.175001i
$336$	0.567133	+	7.10687i	0.0309396	+	0.387712i
$337$		−	12.5752i		−	0.685013i	−0.939515	−	0.342507i	$-0.888724\pi$
$337$		−	12.5752i		−	0.685013i	0.939515	−	0.342507i	$-0.111276\pi$
$338$	−4.69485	−	21.7112i	−0.255366	−	1.18094i
$339$	4.82215	+	18.0631i	0.261903	+	0.981052i
$340$	2.18797	+	0.400960i	0.118659	+	0.0217451i
$341$	−1.24924	+	2.38022i	−0.0676499	+	0.128896i
$342$	−4.08938	−	25.4593i	−0.221128	−	1.37668i
$343$	0.662966	−	10.9601i	0.0357968	−	0.591791i
$344$	−9.19412	+	11.7354i	−0.495714	+	0.632732i
$345$	−6.30467	−	1.83247i	−0.339432	−	0.0986569i
$346$	−17.2805	−	10.4464i	−0.929004	−	0.561602i
$347$	−21.7654	+	15.0236i	−1.16843	+	0.806506i	−0.984319	−	0.176400i	$-0.943555\pi$
$347$	−21.7654	+	15.0236i	−1.16843	+	0.806506i	−0.184108	+	0.982906i	$0.558940\pi$
$348$	−10.3799	+	0.199492i	−0.556420	+	0.0106939i
$349$	−12.1806	+	2.23218i	−0.652012	+	0.119486i	−0.496073	−	0.868281i	$-0.665225\pi$
$349$	−12.1806	+	2.23218i	−0.652012	+	0.119486i	−0.155939	+	0.987767i	$0.549840\pi$
$350$	4.89153	−	4.33352i	0.261463	−	0.231636i
$351$	−8.48865	+	16.7016i	−0.453091	+	0.891464i
$352$	20.0050	+	17.7229i	1.06627	+	0.944634i
$353$	7.92873	+	4.79308i	0.422004	+	0.255110i	0.712368	−	0.701806i	$-0.247623\pi$
$353$	7.92873	+	4.79308i	0.422004	+	0.255110i	−0.290364	+	0.956916i	$0.593777\pi$
$354$	0.617686	+	0.309196i	0.0328296	+	0.0164336i
$355$	−2.29498	−	9.31108i	−0.121805	−	0.494181i
$356$	1.31680	−	0.592645i	0.0697904	−	0.0314101i
$357$	−4.98008	−	2.88137i	−0.263574	−	0.152499i
$358$	−11.1154	+	24.6973i	−0.587465	+	1.30529i
$359$	1.65152	−	0.998380i	0.0871640	−	0.0526925i	−0.473085	−	0.881017i	$-0.656859\pi$
$359$	1.65152	−	0.998380i	0.0871640	−	0.0526925i	0.560249	+	0.828325i	$0.310706\pi$
$360$	2.88170	−	1.65668i	0.151879	−	0.0873144i
$361$		−	6.30365i		−	0.331771i
$362$	−31.9047	+	19.2871i	−1.67687	+	1.01371i
$363$	33.4214	−	4.71142i	1.75417	−	0.247285i
$364$	−1.77981	+	2.07435i	−0.0932874	+	0.108725i
$365$	8.30818	−	1.00880i	0.434870	−	0.0528028i
$366$	3.64361	−	4.83948i	0.190455	−	0.252963i
$367$	5.16193	+	7.47834i	0.269450	+	0.390366i	0.934229	−	0.356674i	$-0.116089\pi$
$367$	5.16193	+	7.47834i	0.269450	+	0.390366i	−0.664778	+	0.747041i	$0.731474\pi$
$368$	23.6056	+	20.9127i	1.23053	+	1.09015i
$369$	2.02749	−	14.1002i	0.105547	−	0.734027i
$370$	3.62493	+	4.62688i	0.188451	+	0.240540i
$371$	−1.35440	+	4.34644i	−0.0703172	+	0.225656i
$372$	0.244894	+	0.735806i	0.0126972	+	0.0381497i
$373$	8.07134	−	11.6934i	0.417918	−	0.605459i	−0.556323	−	0.830966i	$-0.687788\pi$
$373$	8.07134	−	11.6934i	0.417918	−	0.605459i	0.974242	+	0.225507i	$0.0724038\pi$
$374$	−36.9150	+	9.09872i	−1.90883	+	0.470484i
$375$	−9.21590	−	3.93657i	−0.475907	−	0.203284i
$376$	3.24909	−	2.24268i	0.167559	−	0.115658i
$377$	16.8783	+	16.3513i	0.869275	+	0.842133i
$378$	7.20244	−	1.29932i	0.370454	−	0.0668299i
$379$	0.0174864	−	0.00544898i	0.000898215	−	0.000279895i	−0.297054	−	0.954861i	$-0.596004\pi$
$379$	0.0174864	−	0.00544898i	0.000898215	−	0.000279895i	0.297952	+	0.954581i	$0.403696\pi$
$380$	−2.59618	+	0.984602i	−0.133181	+	0.0505090i
$381$	−30.3328	+	4.27602i	−1.55400	+	0.219067i
$382$	−9.89534	−	1.81339i	−0.506290	−	0.0927810i
$383$	8.08164	+	13.3687i	0.412952	+	0.683107i	0.991144	−	0.132795i	$-0.0423951\pi$
$383$	8.08164	+	13.3687i	0.412952	+	0.683107i	−0.578191	+	0.815901i	$0.696241\pi$
$384$	−21.7778	+	1.73789i	−1.11135	+	0.0886861i
$385$	1.12116	−	2.49111i	0.0571396	−	0.126959i
$386$	23.5698	−	8.93886i	1.19967	−	0.454976i
$387$	20.4531	+	12.9866i	1.03969	+	0.660147i
$388$	−14.9382	−	4.65494i	−0.758374	−	0.236319i
$389$	−15.7829	−	3.89013i	−0.800223	−	0.197237i	−0.182060	−	0.983287i	$-0.558277\pi$
$389$	−15.7829	−	3.89013i	−0.800223	−	0.197237i	−0.618163	+	0.786050i	$0.712123\pi$
$390$	6.17780	+	1.68983i	0.312825	+	0.0855678i
$391$	−24.7110	+	6.09072i	−1.24969	+	0.308021i
$392$	11.6464	+	0.704477i	0.588232	+	0.0355815i
$393$	20.1263	−	8.07860i	1.01524	−	0.407511i
$394$	19.7858	+	37.6987i	0.996794	+	1.89923i
$395$	−0.332579	−	1.06728i	−0.0167338	−	0.0537008i
$396$	8.92702	−	12.3436i	0.448599	−	0.620289i
$397$	−0.0516445	−	0.00312392i	−0.00259196	−	0.000156785i	0.0590825	−	0.998253i	$-0.481183\pi$
$397$	−0.0516445	−	0.00312392i	−0.00259196	−	0.000156785i	−0.0616744	+	0.998096i	$0.519644\pi$
$398$	−5.68916	−	7.26168i	−0.285172	−	0.363995i
$399$	7.18058	−	0.138004i	0.359479	−	0.00690884i
$400$	15.3637	+	17.3421i	0.768187	+	0.867104i
$401$	−6.75784	+	0.408774i	−0.337471	+	0.0204132i	−0.228245	−	0.973604i	$-0.573299\pi$
$401$	−6.75784	+	0.408774i	−0.337471	+	0.0204132i	−0.109226	+	0.994017i	$0.534837\pi$
$402$	25.0005	−	23.0210i	1.24691	−	1.14818i
$403$	0.791008	−	1.56704i	0.0394029	−	0.0780596i
$404$	3.09555	−	5.89809i	0.154010	−	0.293441i
$405$	−3.14135	−	4.39459i	−0.156095	−	0.218369i
$406$	1.10653	−	9.11310i	0.0549162	−	0.452276i
$407$	−28.0198	−	14.7059i	−1.38889	−	0.728946i
$408$	6.45274	−	11.1527i	0.319458	−	0.552142i
$409$	8.06946	−	2.51455i	0.399009	−	0.124336i	−0.0914304	−	0.995811i	$-0.529144\pi$
$409$	8.06946	−	2.51455i	0.399009	−	0.124336i	0.490440	+	0.871475i	$0.336836\pi$
$410$	−4.86098	+	0.294035i	−0.240067	+	0.0145214i
$411$	8.98293	+	18.9763i	0.443095	+	0.936030i
$412$	1.20652	−	1.06888i	0.0594410	−	0.0526601i
$413$	−0.109290	+	0.158334i	−0.00537782	+	0.00779112i
$414$	18.9716	−	26.2325i	0.932404	−	1.28926i
$415$	3.32979	+	1.26282i	0.163453	+	0.0619895i
$416$	−13.2453	−	11.3645i	−0.649402	−	0.557192i
$417$	−16.2674	−	22.6248i	−0.796619	−	1.10794i
$418$	33.5580	−	33.5580i	1.64138	−	1.64138i
$419$	−4.09090	−	1.55147i	−0.199853	−	0.0757944i	0.252647	−	0.967558i	$-0.418699\pi$
$419$	−4.09090	−	1.55147i	−0.199853	−	0.0757944i	−0.452501	+	0.891764i	$0.649468\pi$
$420$	−0.293566	−	0.731365i	−0.0143246	−	0.0356870i
$421$	−6.36320	+	20.4202i	−0.310124	+	0.995221i	0.659724	+	0.751508i	$0.270673\pi$
$421$	−6.36320	+	20.4202i	−0.310124	+	0.995221i	−0.969847	+	0.243713i	$0.921634\pi$
$422$	6.10288	−	1.11839i	0.297084	−	0.0544426i
$423$	−4.14797	−	4.89475i	−0.201681	−	0.237991i
$424$	−9.73369	−	3.03314i	−0.472710	−	0.147302i
$425$	−18.5612	+	2.25373i	−0.900349	+	0.109322i
$426$	47.0417	+	4.79660i	2.27918	+	0.232396i
$427$	1.19305	+	1.19305i	0.0577358	+	0.0577358i
$428$	3.77139	+	9.94434i	0.182297	+	0.480678i
$429$	−34.0634	+	5.35411i	−1.64460	+	0.258499i
$430$	2.93701	−	7.74426i	0.141635	−	0.373461i
$431$	−21.0125	+	9.45696i	−1.01214	+	0.455526i	−0.847481	−	0.530825i	$-0.821882\pi$
$431$	−21.0125	+	9.45696i	−1.01214	+	0.455526i	−0.164656	+	0.986351i	$0.552651\pi$
$432$	4.60652	+	25.5350i	0.221632	+	1.22855i
$433$	−3.69231	−	4.16776i	−0.177441	−	0.200290i	0.653061	−	0.757306i	$-0.273485\pi$
$433$	−3.69231	−	4.16776i	−0.177441	−	0.200290i	−0.830502	+	0.557016i	$0.811946\pi$
$434$	−0.674489	+	0.123605i	−0.0323765	+	0.00593321i
$435$	−6.42901	+	2.13974i	−0.308248	+	0.102592i
$436$	−2.76461	−	8.87194i	−0.132401	−	0.424889i
$437$	22.4639	−	22.4639i	1.07459	−	1.07459i
$438$	−9.10415	+	40.2505i	−0.435013	+	1.92324i
$439$	26.8569	+	3.26102i	1.28181	+	0.155640i	0.732956	−	0.680276i	$-0.238140\pi$
$439$	26.8569	+	3.26102i	1.28181	+	0.155640i	0.548856	+	0.835917i	$0.315063\pi$
$440$	5.57876	+	2.51080i	0.265957	+	0.119698i
$441$	−0.728578	−	18.9476i	−0.0346942	−	0.902265i
$442$	24.0084	−	6.32302i	1.14196	−	0.300755i
$443$	0.790420	+	1.50602i	0.0375540	+	0.0715531i	0.903510	−	0.428567i	$-0.140981\pi$
$443$	0.790420	+	1.50602i	0.0375540	+	0.0715531i	−0.865956	+	0.500120i	$0.833289\pi$
$444$	−8.66186	+	2.88288i	−0.411074	+	0.136816i
$445$	0.705433	−	0.624959i	0.0334407	−	0.0296259i
$446$	−42.8931	−	10.5722i	−2.03105	−	0.500608i
$447$	17.5498	−	23.3097i	0.830076	−	1.10251i
$448$	0.0854167	−	1.41211i	0.00403556	−	0.0667158i
$449$	−7.39541	−	16.4319i	−0.349011	−	0.775470i	−0.999868	−	0.0162698i	$-0.994821\pi$
$449$	−7.39541	−	16.4319i	−0.349011	−	0.775470i	0.650857	−	0.759201i	$-0.274410\pi$
$450$	16.1590	−	17.4514i	0.761744	−	0.822669i
$451$	23.2151	−	12.1842i	1.09315	−	0.573732i
$452$	1.19652	+	9.85422i	0.0562795	+	0.463504i
$453$	−15.1361	+	3.07553i	−0.711157	+	0.144501i
$454$	5.37553	+	21.8094i	0.252286	+	1.02357i
$455$	−0.706236	+	1.63812i	−0.0331088	+	0.0767960i
$456$	0.309055	+	16.0807i	0.0144728	+	0.753045i
$457$	−2.53337	+	8.12986i	−0.118506	+	0.380299i	−0.994846	−	0.101393i	$-0.967670\pi$
$457$	−2.53337	+	8.12986i	−0.118506	+	0.380299i	0.876341	+	0.481692i	$0.159978\pi$
$458$	0.220134	+	0.419430i	0.0102862	+	0.0195987i
$459$	−19.0711	−	8.64670i	−0.890163	−	0.403593i
$460$	−3.17892	−	1.43072i	−0.148218	−	0.0667075i
$461$	−1.36590	+	7.45349i	−0.0636165	+	0.347144i	−0.999993	−	0.00385444i	$-0.998773\pi$
$461$	−1.36590	+	7.45349i	−0.0636165	+	0.347144i	0.936376	+	0.350998i	$0.114158\pi$
$462$	9.70600	+	9.33995i	0.451564	+	0.434534i
$463$	−3.44877	+	18.8193i	−0.160278	+	0.874607i	0.800925	+	0.598765i	$0.204341\pi$
$463$	−3.44877	+	18.8193i	−0.160278	+	0.874607i	−0.961203	+	0.275843i	$0.911043\pi$
$464$	32.3089	+	3.92302i	1.49991	+	0.182121i
$465$	0.295464	+	0.410933i	0.0137018	+	0.0190566i
$466$	−0.784676	−	2.51811i	−0.0363494	−	0.116649i
$467$	−8.42211	+	12.2015i	−0.389729	+	0.564620i	−0.967913	−	0.251287i	$-0.919146\pi$
$467$	−8.42211	+	12.2015i	−0.389729	+	0.564620i	0.578184	+	0.815907i	$0.303762\pi$
$468$	−5.70084	+	8.15186i	−0.263521	+	0.376820i
$469$	5.37711	+	7.79009i	0.248292	+	0.359713i
$470$	−1.35268	+	1.72657i	−0.0623945	+	0.0796407i
$471$	−29.6418	+	16.2913i	−1.36582	+	0.750661i
$472$	−0.354584	−	0.244752i	−0.0163211	−	0.0112656i
$473$	2.69233	+	44.5096i	0.123794	+	2.04655i
$474$	5.50752	+	0.227030i	0.252969	+	0.0104278i
$475$	18.3722	−	14.3937i	0.842976	−	0.660429i
$476$	−2.40476	−	1.88401i	−0.110222	−	0.0863536i
$477$	−3.34411	+	16.2278i	−0.153116	+	0.743021i
$478$	−7.92753	+	5.47198i	−0.362597	+	0.250282i
$479$	7.88556	+	10.0652i	0.360300	+	0.459889i	0.933000	−	0.359876i	$-0.117181\pi$
$479$	7.88556	+	10.0652i	0.360300	+	0.459889i	−0.572700	+	0.819765i	$0.694104\pi$
$480$	4.66995	−	1.87449i	0.213153	−	0.0855586i
$481$	18.4471	+	9.31170i	0.841113	+	0.424577i
$482$	35.9719	+	4.36777i	1.63847	+	0.198947i
$483$	6.49723	+	6.25220i	0.295634	+	0.284485i
$484$	17.9208			0.814582
$485$	−10.2119			−0.463699
$486$	25.6182	−	7.29260i	1.16206	−	0.330799i
$487$	11.0899	+	4.99115i	0.502530	+	0.226170i	0.645791	−	0.763515i	$-0.276528\pi$
$487$	11.0899	+	4.99115i	0.502530	+	0.226170i	−0.143261	+	0.989685i	$0.545759\pi$
$488$	−2.67179	+	2.67179i	−0.120946	+	0.120946i
$489$	−4.12886	+	3.36477i	−0.186714	+	0.152160i
$490$	−6.29384	+	1.55129i	−0.284326	+	0.0700802i
$491$	19.8506	+	17.5861i	0.895844	+	0.793648i	0.979205	−	0.202871i	$-0.0650272\pi$
$491$	19.8506	+	17.5861i	0.895844	+	0.793648i	−0.0833615	+	0.996519i	$0.526566\pi$
$492$	2.11102	−	7.26304i	0.0951722	−	0.327443i
$493$	−17.4171	+	19.6598i	−0.784425	+	0.885433i
$494$	−21.5633	+	22.2583i	−0.970180	+	1.00145i
$495$	3.16574	−	9.42467i	0.142289	−	0.423608i
$496$	−0.438219	−	2.39128i	−0.0196766	−	0.107372i
$497$	−3.15182	+	12.7874i	−0.141378	+	0.573595i
$498$	−11.3896	+	13.3650i	−0.510379	+	0.598900i
$499$	4.03127	−	6.66853i	0.180464	−	0.298524i	−0.752432	−	0.658670i	$-0.771119\pi$
$499$	4.03127	−	6.66853i	0.180464	−	0.298524i	0.932896	+	0.360146i	$0.117273\pi$
$500$	−4.55358	−	2.75273i	−0.203642	−	0.123106i
$501$	−3.00551	−	1.28380i	−0.134276	−	0.0573561i
$502$	9.95920	+	0.602420i	0.444501	+	0.0268873i
$503$	−1.25117	−	0.474507i	−0.0557870	−	0.0211572i	0.326554	−	0.945179i	$-0.394113\pi$
$503$	−1.25117	−	0.474507i	−0.0557870	−	0.0211572i	−0.382341	+	0.924021i	$0.624882\pi$
$504$	−4.56162	+	0.175405i	−0.203191	+	0.00781316i
$505$	0.783638	−	4.27618i	0.0348714	−	0.190287i
$506$	59.5838			2.64882
$507$	22.1853	−	3.84854i	0.985285	−	0.170920i
$508$	−16.2647			−0.721628
$509$	4.17085	−	22.7596i	0.184870	−	1.00880i	−0.752011	−	0.659151i	$-0.770916\pi$
$509$	4.17085	−	22.7596i	0.184870	−	1.00880i	0.936880	−	0.349650i	$-0.113700\pi$
$510$	−1.57926	+	6.98207i	−0.0699307	+	0.309171i
$511$	−10.7470	−	4.07579i	−0.475418	−	0.180302i
$512$	−5.72439	−	0.346262i	−0.252985	−	0.0153027i
$513$	25.9561	−	3.07883i	1.14599	−	0.135934i
$514$	13.1734	+	7.96361i	0.581054	+	0.351260i
$515$	0.544245	−	0.900291i	0.0239823	−	0.0396716i
$516$	9.79090	+	8.34374i	0.431020	+	0.367313i
$517$	2.82595	−	11.4653i	0.124285	−	0.504245i
$518$	−1.45507	−	7.94004i	−0.0639319	−	0.348865i
$519$	11.3017	−	17.0657i	0.496088	−	0.749099i
$520$	−3.66850	−	1.58159i	−0.160874	−	0.0693573i
$521$	29.2436	−	33.0092i	1.28118	−	1.44616i	0.447136	−	0.894466i	$-0.352444\pi$
$521$	29.2436	−	33.0092i	1.28118	−	1.44616i	0.834048	−	0.551692i	$-0.186018\pi$
$522$	0.734358	−	33.4021i	0.0321420	−	1.46197i
$523$	−18.2412	−	16.1603i	−0.797631	−	0.706639i	0.162341	−	0.986735i	$-0.448095\pi$
$523$	−18.2412	−	16.1603i	−0.797631	−	0.706639i	−0.959972	+	0.280095i	$0.909634\pi$
$524$	11.1803	−	2.75571i	0.488416	−	0.120384i
$525$	4.18480	+	5.13510i	0.182640	+	0.224114i
$526$	20.2083	−	20.2083i	0.881124	−	0.881124i
$527$	1.78909	+	0.805202i	0.0779338	+	0.0350752i
$528$	−33.1132	+	34.4110i	−1.44107	+	1.49754i
$529$	16.8856			0.734157
$530$	5.66420			0.246037
$531$	−0.338945	+	0.612688i	−0.0147089	+	0.0265884i
$532$	3.78548	+	0.459641i	0.164121	+	0.0199279i
$533$	−15.0315	+	8.19574i	−0.651086	+	0.354997i
$534$	1.73106	+	4.31262i	0.0749104	+	0.186625i
$535$	4.28083	+	5.46408i	0.185076	+	0.236233i
$536$	−17.4456	+	12.0418i	−0.753536	+	0.520129i
$537$	−24.5496	−	12.2888i	−1.05939	−	0.530302i
$538$	16.4144	+	12.8599i	0.707675	+	0.554428i
$539$	27.4716	−	21.5226i	1.18329	−	0.927045i
$540$	−1.32588	−	2.54332i	−0.0570568	−	0.109447i
$541$	−1.74906	−	28.9154i	−0.0751979	−	1.24317i	−0.818616	−	0.574342i	$-0.805258\pi$
$541$	−1.74906	−	28.9154i	−0.0751979	−	1.24317i	0.743418	−	0.668827i	$-0.233203\pi$
$542$	−12.9412	−	8.93270i	−0.555874	−	0.383692i
$543$	−18.2021	−	33.1185i	−0.781125	−	1.42125i
$544$	12.0299	−	15.3550i	0.515778	−	0.658342i
$545$	−3.44528	−	4.99134i	−0.147579	−	0.213806i
$546$	−6.43399	−	5.99777i	−0.275349	−	0.256681i
$547$	−10.0394	+	14.5445i	−0.429252	+	0.621879i	−0.976610	−	0.215020i	$-0.931018\pi$
$547$	−10.0394	+	14.5445i	−0.429252	+	0.621879i	0.547358	+	0.836899i	$0.315634\pi$
$548$	3.31640	+	10.6427i	0.141670	+	0.454634i
$549$	4.74934	+	3.89233i	0.202697	+	0.166120i
$550$	43.4546	+	5.27635i	1.85291	+	0.224984i
$551$	5.90978	−	32.2486i	0.251765	−	1.37384i
$552$	−14.0016	+	14.5503i	−0.595947	+	0.619303i
$553$	−0.276741	+	1.51013i	−0.0117682	+	0.0642171i
$554$	−20.2655	−	9.12077i	−0.860999	−	0.387504i
$555$	−4.83748	+	3.47818i	−0.205340	+	0.147641i
$556$	−6.87588	−	13.1009i	−0.291602	−	0.555601i
$557$	−6.83689	+	21.9403i	−0.289688	+	0.929642i	0.689082	+	0.724683i	$0.258014\pi$
$557$	−6.83689	+	21.9403i	−0.289688	+	0.929642i	−0.978771	+	0.204959i	$0.934294\pi$
$558$	−2.39838	+	0.689909i	−0.101531	+	0.0292062i
$559$	−2.21878	−	29.0335i	−0.0938444	−	1.22798i
$560$	0.591250	+	2.39880i	0.0249849	+	0.101368i
$561$	−7.67406	−	37.7676i	−0.323999	−	1.59455i
$562$	4.43464	+	36.5226i	0.187064	+	1.54061i
$563$	10.1908	−	5.34852i	0.429489	−	0.225413i	−0.236105	−	0.971728i	$-0.575871\pi$
$563$	10.1908	−	5.34852i	0.429489	−	0.225413i	0.665594	+	0.746314i	$0.268178\pi$
$564$	−1.81805	−	2.88089i	−0.0765537	−	0.121307i
$565$	2.65892	+	5.90788i	0.111862	+	0.248546i
$566$	1.43330	−	23.6953i	0.0602463	−	0.995989i
$567$	1.01526	+	7.34894i	0.0426370	+	0.308626i
$568$	−28.6370	−	7.05839i	−1.20158	−	0.296163i
$569$	−6.80592	+	6.02952i	−0.285319	+	0.252770i	−0.793627	−	0.608405i	$-0.791810\pi$
$569$	−6.80592	+	6.02952i	−0.285319	+	0.252770i	0.508308	+	0.861175i	$0.330271\pi$
$570$	−2.82179	−	8.47830i	−0.118192	−	0.355117i
$571$	9.58956	+	18.2714i	0.401311	+	0.764634i	0.999321	−	0.0368550i	$-0.0117340\pi$
$571$	9.58956	+	18.2714i	0.401311	+	0.764634i	−0.598010	+	0.801489i	$0.704042\pi$
$572$	−18.3059	+	0.290320i	−0.765410	+	0.0121389i
$573$	2.24974	−	9.94637i	0.0939843	−	0.415515i
$574$	6.09884	+	2.74487i	0.254561	+	0.114569i
$575$	29.0887	+	3.53201i	1.21308	+	0.147295i
$576$	−0.197832	−	5.14486i	−0.00824299	−	0.214369i
$577$	10.5468	−	10.5468i	0.439071	−	0.439071i	−0.452629	−	0.891699i	$-0.649514\pi$
$577$	10.5468	−	10.5468i	0.439071	−	0.439071i	0.891699	+	0.452629i	$0.149514\pi$
$578$	−0.386487	−	1.24028i	−0.0160758	−	0.0515889i
$579$	8.06931	+	24.2449i	0.335349	+	1.00758i
$580$	−3.53870	+	0.648491i	−0.146936	+	0.0269271i
$581$	−3.24321	−	3.66082i	−0.134551	−	0.151877i
$582$	16.9476	−	47.4156i	0.702499	−	1.96544i
$583$	−27.8081	+	12.5154i	−1.15169	+	0.518336i
$584$	9.12759	−	24.0675i	0.377702	−	0.995919i
$585$	−1.96939	+	6.18637i	−0.0814244	+	0.255775i
$586$	12.4106	+	32.7241i	0.512678	+	1.35182i
$587$	−32.6000	−	32.6000i	−1.34554	−	1.34554i	−0.890435	−	0.455109i	$-0.849600\pi$
$587$	−32.6000	−	32.6000i	−1.34554	−	1.34554i	−0.455109	−	0.890435i	$-0.650400\pi$
$588$	1.02127	−	10.0158i	0.0421163	−	0.413047i
$589$	−2.43113	+	0.295193i	−0.100173	+	0.0121632i
$590$	0.228529	+	0.0712126i	0.00940840	+	0.00293178i
$591$	−39.0076	+	18.4653i	−1.60456	+	0.759561i
$592$	28.1500	−	5.15869i	1.15696	−	0.212021i
$593$	7.23198	−	23.2082i	0.296982	−	0.953048i	−0.678804	−	0.734319i	$-0.737501\pi$
$593$	7.23198	−	23.2082i	0.296982	−	0.953048i	0.975786	−	0.218728i	$-0.0701908\pi$
$594$	38.5065	+	30.3401i	1.57994	+	1.24487i
$595$	−1.86423	−	0.707010i	−0.0764260	−	0.0289846i
$596$	10.9546	−	10.9546i	0.448717	−	0.448717i
$597$	7.59220	−	5.45885i	0.310728	−	0.223416i
$598$	−38.9036	+	0.616985i	−1.59089	+	0.0252304i
$599$	0.873902	+	0.331427i	0.0357067	+	0.0135417i	0.372394	−	0.928075i	$-0.378537\pi$
$599$	0.873902	+	0.331427i	0.0357067	+	0.0135417i	−0.336687	+	0.941617i	$0.609306\pi$
$600$	−11.4999	+	9.37171i	−0.469481	+	0.382598i
$601$	4.75925	−	6.89497i	0.194134	−	0.281252i	−0.713813	−	0.700336i	$-0.753034\pi$
$601$	4.75925	−	6.89497i	0.194134	−	0.281252i	0.907947	+	0.419084i	$0.137649\pi$
$602$	−8.51416	+	7.54289i	−0.347011	+	0.307425i
$603$	22.2721	+	26.2818i	0.906988	+	1.07028i
$604$	−8.18590	+	0.495156i	−0.333080	+	0.0201476i
$605$	11.1665	−	3.47963i	0.453984	−	0.141467i
$606$	18.5545	+	10.7353i	0.753725	+	0.436090i
$607$	−11.0078	−	5.77735i	−0.446794	−	0.234495i	0.226293	−	0.974059i	$-0.427339\pi$
$607$	−11.0078	−	5.77735i	−0.446794	−	0.234495i	−0.673086	+	0.739564i	$0.735032\pi$
$608$	−2.93492	+	24.1713i	−0.119027	+	0.980274i
$609$	9.18362	+	1.50117i	0.372139	+	0.0608306i
$610$	0.975551	−	1.85876i	0.0394989	−	0.0752589i
$611$	−1.72641	+	7.51525i	−0.0698430	+	0.304034i
$612$	−9.38594	−	5.95956i	−0.379404	−	0.240901i
$613$	−5.27484	+	0.319069i	−0.213049	+	0.0128871i	−0.166558	−	0.986032i	$-0.553265\pi$
$613$	−5.27484	+	0.319069i	−0.213049	+	0.0128871i	−0.0464908	+	0.998919i	$0.514804\pi$
$614$	−27.4489	−	30.9834i	−1.10775	−	1.25039i
$615$	−0.0948560	−	4.93552i	−0.00382496	−	0.199019i
$616$	−5.18157	−	6.61378i	−0.208771	−	0.266477i
$617$	1.04292	+	0.0630849i	0.0419863	+	0.00253970i	0.0813583	−	0.996685i	$-0.474074\pi$
$617$	1.04292	+	0.0630849i	0.0419863	+	0.00253970i	−0.0393720	+	0.999225i	$0.512536\pi$
$618$	3.27698	+	4.02114i	0.131820	+	0.161754i
$619$	−7.69724	−	24.7013i	−0.309378	−	0.992829i	−0.970204	−	0.242290i	$-0.922102\pi$
$619$	−7.69724	−	24.7013i	−0.309378	−	0.992829i	0.660826	−	0.750539i	$-0.270206\pi$
$620$	0.124886	+	0.237950i	0.00501554	+	0.00955631i
$621$	25.7764	+	20.3098i	1.03437	+	0.815004i
$622$	−32.1454	−	1.94444i	−1.28891	−	0.0779649i
$623$	−1.25671	+	0.309751i	−0.0503489	+	0.0124099i
$624$	21.2641	−	22.8106i	0.851244	−	0.913155i
$625$	19.1528	+	4.72074i	0.766111	+	0.188829i
$626$	−52.4155	−	16.3333i	−2.09494	−	0.652811i
$627$	32.5868	+	35.3889i	1.30139	+	1.41330i
$628$	−16.7919	+	6.36833i	−0.670070	+	0.254124i
$629$	−9.47879	+	21.0610i	−0.377944	+	0.839758i
$630$	2.39055	−	0.846997i	0.0952419	−	0.0337452i
$631$	−5.71202	−	9.44884i	−0.227392	−	0.376152i	0.721163	−	0.692766i	$-0.243608\pi$
$631$	−5.71202	−	9.44884i	−0.227392	−	0.376152i	−0.948555	+	0.316613i	$0.897454\pi$
$632$	−3.38188	−	0.619752i	−0.134524	−	0.0246524i
$633$	0.877924	+	6.22774i	0.0348944	+	0.247530i
$634$	−34.9229	+	13.2445i	−1.38697	+	0.526007i
$635$	−10.1346	+	3.15806i	−0.402179	+	0.125324i
$636$	−2.96094	+	8.28406i	−0.117409	+	0.328484i
$637$	−17.7140	+	14.3371i	−0.701853	+	0.568056i
$638$	50.6062	−	34.9309i	2.00352	−	1.38293i
$639$	−6.82202	+	47.4439i	−0.269875	+	1.87685i
$640$	−7.35072	+	1.81179i	−0.290563	+	0.0716173i
$641$	3.79001	−	5.49077i	0.149696	−	0.216872i	−0.740961	−	0.671548i	$-0.765630\pi$
$641$	3.79001	−	5.49077i	0.149696	−	0.216872i	0.890657	+	0.454676i	$0.150245\pi$
$642$	−32.4751	+	10.8085i	−1.28169	+	0.426578i
$643$	−2.60712	+	8.36654i	−0.102815	+	0.329944i	−0.991767	−	0.128056i	$-0.959126\pi$
$643$	−2.60712	+	8.36654i	−0.102815	+	0.329944i	0.888952	+	0.458000i	$0.151434\pi$
$644$	2.95259	+	3.76870i	0.116348	+	0.148508i
$645$	7.72082	+	3.29795i	0.304007	+	0.129857i
$646$	−25.9265	−	22.9689i	−1.02006	−	0.903698i
$647$	−18.3450	−	26.5773i	−0.721216	−	1.04486i	−0.996508	−	0.0835005i	$-0.973390\pi$
$647$	−18.3450	−	26.5773i	−0.721216	−	1.04486i	0.275292	−	0.961361i	$-0.411225\pi$
$648$	−16.4577	+	2.27365i	−0.646519	+	0.0893172i
$649$	−1.27930	+	0.155335i	−0.0502170	+	0.00609745i
$650$	−28.4272	−	2.99508i	−1.11501	−	0.117477i
$651$	−0.0970279	−	0.688288i	−0.00380282	−	0.0269761i
$652$	−2.42017	+	1.46304i	−0.0947812	+	0.0572972i
$653$			23.7268i			0.928501i	0.885704	+	0.464251i	$0.153676\pi$
$653$			23.7268i			0.928501i	−0.885704	+	0.464251i	$0.846324\pi$
$654$	28.8934	−	7.71342i	1.12982	−	0.301619i
$655$	6.43145	−	3.88795i	0.251297	−	0.151915i
$656$	−9.73145	+	21.6224i	−0.379949	+	0.844213i
$657$	−40.3859	−	10.9012i	−1.57560	−	0.425296i
$658$	2.74687	−	1.23627i	0.107084	−	0.0481947i
$659$	−4.74548	−	19.2532i	−0.184858	−	0.749998i	−0.988031	−	0.154253i	$-0.950703\pi$
$659$	−4.74548	−	19.2532i	−0.184858	−	0.749998i	0.803174	−	0.595745i	$-0.203143\pi$
$660$	2.36294	−	4.72047i	0.0919772	−	0.183744i
$661$	−0.659481	−	0.398670i	−0.0256508	−	0.0155065i	0.504454	−	0.863438i	$-0.331694\pi$
$661$	−0.659481	−	0.398670i	−0.0256508	−	0.0155065i	−0.530105	+	0.847932i	$0.677848\pi$
$662$	15.4341	+	13.6734i	0.599862	+	0.531431i
$663$	5.40165	+	24.5799i	0.209783	+	0.954604i
$664$	8.19828	−	7.26304i	0.318155	−	0.281861i
$665$	2.44799	−	0.448612i	0.0949292	−	0.0173964i
$666$	−8.12157	−	28.2336i	−0.314705	−	1.09403i
$667$	33.8760	−	23.3829i	1.31168	−	0.905389i
$668$	−1.48502	−	0.897727i	−0.0574572	−	0.0347341i
$669$	12.4984	−	43.0010i	0.483215	−	1.66252i
$670$	7.26307	−	9.27062i	0.280597	−	0.358155i
$671$	−0.682376	+	11.2810i	−0.0263428	+	0.435499i
$672$	−6.87524	−	0.701034i	−0.265218	−	0.0270430i
$673$	−19.7653	+	37.6596i	−0.761895	+	1.45167i	0.126198	+	0.992005i	$0.459723\pi$
$673$	−19.7653	+	37.6596i	−0.761895	+	1.45167i	−0.888093	+	0.459664i	$0.847970\pi$
$674$	21.1352	+	3.87317i	0.814097	+	0.149189i
$675$	17.0003	+	17.0946i	0.654342	+	0.657971i
$676$	11.9494	−	0.379113i	0.459591	−	0.0145813i
$677$			47.1417i			1.81180i	0.423490	+	0.905901i	$0.360805\pi$
$677$			47.1417i			1.81180i	−0.423490	+	0.905901i	$0.639195\pi$
$678$	−31.8440	+	2.54117i	−1.22296	+	0.0975932i
$679$	12.4182	+	6.51755i	0.476565	+	0.250121i
$680$	1.58332	−	4.17488i	0.0607177	−	0.160099i
$681$	−22.3132	+	4.53384i	−0.855042	+	0.173737i
$682$	−3.61569	−	2.83271i	−0.138452	−	0.108470i
$683$	−3.36958	+	5.57396i	−0.128933	+	0.213282i	−0.913578	−	0.406665i	$-0.866692\pi$
$683$	−3.36958	+	5.57396i	−0.128933	+	0.213282i	0.784644	+	0.619946i	$0.212846\pi$
$684$	13.8748	+	0.305044i	0.530518	+	0.0116636i
$685$	4.13293	+	5.98758i	0.157911	+	0.228774i
$686$	18.2166	+	4.48998i	0.695512	+	0.171428i
$687$	−0.433992	+	0.205442i	−0.0165578	+	0.00783810i
$688$	−26.7420	−	30.1855i	−1.01953	−	1.15081i
$689$	18.0270	−	8.45956i	0.686773	−	0.322284i
$690$	5.02169	−	10.0319i	0.191173	−	0.381908i
$691$	−4.58195	+	7.57946i	−0.174305	+	0.288336i	−0.930703	−	0.365776i	$-0.880804\pi$
$691$	−4.58195	+	7.57946i	−0.174305	+	0.288336i	0.756398	+	0.654112i	$0.226958\pi$
$692$	7.20679	−	8.13478i	0.273961	−	0.309238i
$693$	−9.86480	+	9.44037i	−0.374733	+	0.358610i
$694$	−18.5464	−	41.2085i	−0.704013	−	1.56425i
$695$	−6.82814	−	6.82814i	−0.259006	−	0.259006i
$696$	−3.36183	+	20.5664i	−0.127430	+	0.779567i
$697$	−9.89946	−	16.3757i	−0.374969	−	0.620274i
$698$		−	21.1595i		−	0.800900i
$699$	2.58312	−	0.689595i	0.0977027	−	0.0260829i
$700$	1.81960	+	3.00999i	0.0687744	+	0.113767i
$701$	4.83155	−	39.7914i	0.182485	−	1.50290i	−0.557443	−	0.830215i	$-0.688218\pi$
$701$	4.83155	−	39.7914i	0.182485	−	1.50290i	0.739928	−	0.672686i	$-0.234859\pi$
$702$	−25.4560	−	19.4110i	−0.960774	−	0.732623i
$703$	−3.47499	−	28.6191i	−0.131062	−	1.07939i
$704$	7.45940	−	5.84407i	0.281137	−	0.220257i
$705$	−1.69221	−	1.44209i	−0.0637322	−	0.0543122i
$706$	−10.4978	+	11.8496i	−0.395091	+	0.445966i
$707$	−3.68213	+	4.69989i	−0.138481	+	0.176757i
$708$	−0.223613	+	0.297005i	−0.00840390	+	0.0111621i
$709$	−17.2237	−	5.36713i	−0.646851	−	0.201567i	−0.0435134	−	0.999053i	$-0.513855\pi$
$709$	−17.2237	−	5.36713i	−0.646851	−	0.201567i	−0.603338	+	0.797486i	$0.706163\pi$
$710$	16.3561	−	0.989360i	0.613832	−	0.0371300i
$711$	−0.459876	+	5.56858i	−0.0172467	+	0.208838i
$712$	−0.693675	−	2.81435i	−0.0259966	−	0.105472i
$713$	−2.42035	−	1.89623i	−0.0906430	−	0.0710143i
$714$	6.37662	−	7.48260i	0.238639	−	0.280029i
$715$	−11.3501	+	3.73531i	−0.424471	+	0.139693i
$716$	−11.9964	−	8.28049i	−0.448325	−	0.309456i
$717$	−5.21109	−	8.25751i	−0.194612	−	0.308383i
$718$	1.16931	+	3.08323i	0.0436384	+	0.115065i
$719$	−0.139976	+	1.15281i	−0.00522023	+	0.0429925i	−0.995086	−	0.0990122i	$-0.968432\pi$
$719$	−0.139976	+	1.15281i	−0.00522023	+	0.0429925i	0.989866	+	0.142005i	$0.0453548\pi$
$720$	3.00288	+	8.47529i	0.111911	+	0.315855i
$721$	−1.23642	+	0.747443i	−0.0460467	+	0.0278362i
$722$	10.5946	+	1.94153i	0.394290	+	0.0722564i
$723$	−5.92553	+	36.2502i	−0.220373	+	1.34816i
$724$	−7.11527	−	18.7614i	−0.264437	−	0.697263i
$725$	26.7765	−	14.0534i	0.994453	−	0.521929i
$726$	−2.37532	+	57.6228i	−0.0881564	+	2.13858i
$727$	−1.74328	+	7.07275i	−0.0646545	+	0.262314i	−0.994370	−	0.105965i	$-0.966207\pi$
$727$	−1.74328	+	7.07275i	−0.0646545	+	0.262314i	0.929715	+	0.368279i	$0.120053\pi$
$728$	3.45165	+	4.26464i	0.127927	+	0.158058i
$729$	6.31644	+	26.2508i	0.233942	+	0.972250i
$730$	−0.863438	+	14.2743i	−0.0319573	+	0.528317i
$731$	32.3074	−	3.92283i	1.19493	−	0.145091i
$732$	2.20852	+	2.39843i	0.0816293	+	0.0886485i
$733$	24.0725	−	7.50131i	0.889140	−	0.277067i	0.181289	−	0.983430i	$-0.441973\pi$
$733$	24.0725	−	7.50131i	0.889140	−	0.277067i	0.707850	+	0.706363i	$0.249665\pi$
$734$	−14.1588	+	6.37236i	−0.522611	+	0.235208i
$735$	−1.30839	−	6.43921i	−0.0482608	−	0.237514i
$736$	−24.0641	+	18.8530i	−0.887015	+	0.694932i
$737$	−15.1736	+	61.5619i	−0.558928	+	2.26766i
$738$	23.0739	+	7.75049i	0.849360	+	0.285300i
$739$	−0.593608	−	9.81351i	−0.0218362	−	0.360996i	−0.992639	−	0.121115i	$-0.961353\pi$
$739$	−0.593608	−	9.81351i	−0.0218362	−	0.360996i	0.970802	−	0.239881i	$-0.0771085\pi$
$740$	−2.80114	+	1.47015i	−0.102972	+	0.0540438i
$741$	−21.6431	−	22.7688i	−0.795080	−	0.836432i
$742$	−6.88793	−	3.61507i	−0.252864	−	0.132713i
$743$	3.90053	−	8.66663i	0.143097	−	0.317948i	−0.826387	−	0.563102i	$-0.809608\pi$
$743$	3.90053	−	8.66663i	0.143097	−	0.317948i	0.969484	+	0.245154i	$0.0788386\pi$
$744$	1.54140	−	0.217291i	0.0565103	−	0.00796626i
$745$	4.69882	−	8.95286i	0.172152	−	0.328007i
$746$	17.1671	+	17.1671i	0.628534	+	0.628534i
$747$	−13.0607	−	12.0934i	−0.477865	−	0.442476i
$748$	−1.23551	−	20.4254i	−0.0451747	−	0.746828i
$749$	−1.71835	−	9.37673i	−0.0627871	−	0.342618i
$750$	9.45473	−	14.2768i	0.345238	−	0.521314i
$751$	−21.6754	−	14.9615i	−0.790948	−	0.545952i	0.102704	−	0.994712i	$-0.467251\pi$
$751$	−21.6754	−	14.9615i	−0.790948	−	0.545952i	−0.893652	+	0.448760i	$0.851866\pi$
$752$	4.38297	+	9.73856i	0.159830	+	0.355129i
$753$	−1.02593	+	10.0616i	−0.0373870	+	0.366665i
$754$	−32.6802	+	23.3312i	−1.19014	+	0.849673i
$755$	−5.00452	+	1.89797i	−0.182133	+	0.0690740i
$756$	−0.0108921	+	3.93902i	−0.000396141	+	0.143261i
$757$	−11.1066	+	29.2857i	−0.403676	+	1.06441i	0.566937	+	0.823761i	$0.308128\pi$
$757$	−11.1066	+	29.2857i	−0.403676	+	1.06441i	−0.970613	+	0.240646i	$0.922641\pi$
$758$	0.00377231	+	0.0310678i	0.000137017	+	0.00112843i
$759$	−2.48761	+	60.3469i	−0.0902946	+	2.19045i
$760$	1.00465	+	5.48220i	0.0364425	+	0.198860i
$761$	7.07225	+	38.5920i	0.256369	+	1.39896i	0.819731	+	0.572749i	$0.194123\pi$
$761$	7.07225	+	38.5920i	0.256369	+	1.39896i	−0.563362	+	0.826210i	$0.690492\pi$
$762$	2.15581	−	52.2977i	0.0780967	−	1.89454i
$763$	1.00399	+	8.26859i	0.0363468	+	0.299343i
$764$	1.92001	−	5.06265i	0.0694635	−	0.183160i
$765$	−7.00556	−	1.89098i	−0.253287	−	0.0683686i
$766$	−24.9580	+	9.46531i	−0.901768	+	0.341996i
$767$	0.833678	−	0.114669i	0.0301024	−	0.00414046i
$768$	3.18365	−	31.2229i	0.114880	−	1.12666i
$769$	−1.92021	−	4.26653i	−0.0692446	−	0.153855i	0.874027

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.s (of order \(52\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.308001 + 1.68071i) q^{2} +(-1.68938 - 0.382115i) q^{3} +(-0.859883 - 0.326111i) q^{4} +(-0.599116 - 0.0362399i) q^{5} +(1.16255 - 2.72165i) q^{6} +(0.705424 + 0.426444i) q^{7} +(-0.955005 + 1.57977i) q^{8} +(2.70798 + 1.29107i) q^{9} +(0.245437 - 0.995778i) q^{10} +(0.995273 + 5.43103i) q^{11} +(1.32805 + 0.879497i) q^{12} +(-0.706075 - 3.53574i) q^{13} +(-0.933999 + 1.05427i) q^{14} +(0.998284 + 0.290154i) q^{15} +(-3.73772 - 3.31133i) q^{16} +(3.91275 - 0.964407i) q^{17} +(-3.00397 + 4.15367i) q^{18} +(-3.55694 + 3.55694i) q^{19} +(0.503352 + 0.226540i) q^{20} +(-1.02877 - 0.989976i) q^{21} -9.43452 q^{22} -6.31551 q^{23} +(2.21702 - 2.30390i) q^{24} +(-4.60592 - 0.559260i) q^{25} +(6.16002 - 0.0976937i) q^{26} +(-4.08145 - 3.21586i) q^{27} +(-0.467514 - 0.596738i) q^{28} +(-5.36393 + 3.70246i) q^{29} +(-0.795137 + 1.58846i) q^{30} +(0.383240 + 0.300249i) q^{31} +(3.81032 - 2.98520i) q^{32} +(0.393890 - 9.55536i) q^{33} +(0.415754 + 6.87323i) q^{34} +(-0.407177 - 0.281054i) q^{35} +(-1.90751 - 1.99327i) q^{36} +(-3.53452 + 4.51148i) q^{37} +(-4.88264 - 7.07372i) q^{38} +(-0.158235 + 6.24299i) q^{39} +(0.629410 - 0.911858i) q^{40} +(-1.41267 - 4.53340i) q^{41} +(1.98073 - 1.42416i) q^{42} +(8.01703 + 0.973444i) q^{43} +(0.915298 - 4.99462i) q^{44} +(-1.57560 - 0.871639i) q^{45} +(1.94518 - 10.6145i) q^{46} +(-1.95023 - 0.877727i) q^{47} +(5.04910 + 7.02232i) q^{48} +(-2.93729 - 5.59655i) q^{49} +(2.35858 - 7.56895i) q^{50} +(-6.97862 + 0.134123i) q^{51} +(-0.545900 + 3.27058i) q^{52} +(1.32172 + 5.36245i) q^{53} +(6.66202 - 5.86923i) q^{54} +(-0.399465 - 3.28989i) q^{55} +(-1.34737 + 0.707153i) q^{56} +(7.36817 - 4.64985i) q^{57} +(-4.57065 - 10.1556i) q^{58} +(-0.0140922 + 0.232972i) q^{59} +(-0.763785 - 0.575050i) q^{60} +(1.98737 + 0.489844i) q^{61} +(-0.622670 + 0.551638i) q^{62} +(1.35970 + 2.06555i) q^{63} +(-0.797568 - 1.51964i) q^{64} +(0.294886 + 2.14391i) q^{65} +(15.9384 + 3.60508i) q^{66} +(10.4715 + 4.71286i) q^{67} +(-3.67901 - 0.446713i) q^{68} +(10.6693 + 2.41325i) q^{69} +(0.597780 - 0.597780i) q^{70} +(4.75329 + 15.2538i) q^{71} +(-4.62573 + 3.04500i) q^{72} +(-13.7154 + 2.51343i) q^{73} +(-6.49384 - 7.33004i) q^{74} +(7.56742 + 2.70479i) q^{75} +(4.21851 - 1.89860i) q^{76} +(-1.61394 + 4.25561i) q^{77} +(-10.4439 - 2.18880i) q^{78} +(0.660455 + 1.74148i) q^{79} +(2.11933 + 2.11933i) q^{80} +(5.66627 + 6.99238i) q^{81} +(8.05443 - 0.977985i) q^{82} +(-5.66461 - 1.76516i) q^{83} +(0.561784 + 1.18676i) q^{84} +(-2.37914 + 0.435994i) q^{85} +(-4.10533 + 13.1745i) q^{86} +(10.4765 - 4.20520i) q^{87} +(-9.53028 - 3.61436i) q^{88} +(-1.11030 + 1.11030i) q^{89} +(1.95026 - 2.37966i) q^{90} +(1.00971 - 2.79530i) q^{91} +(5.43060 + 2.05955i) q^{92} +(-0.532706 - 0.653676i) q^{93} +(2.07588 - 3.00743i) q^{94} +(2.25992 - 2.00212i) q^{95} +(-7.57776 + 3.58714i) q^{96} +(16.9828 - 1.02727i) q^{97} +(10.3108 - 3.21299i) q^{98} +(-4.31667 + 15.9921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27}+ \cdots - 58 q^{99}+O(q^{100}) \) 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Introduction

L-functions

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