LMFDB - Embedded newform 507.2.p.b.25.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.10
Character	$\chi$	$=$	507.25
Dual form			507.2.p.b.142.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.494430 + 0.187512i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.28772 - 1.14082i) q^{4} +(3.75871 + 0.456390i) q^{5} +(-0.126548 - 0.513427i) q^{6} +(1.26721 + 2.41446i) q^{7} +(-0.914254 - 1.74197i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})$	\(q+(0.494430 + 0.187512i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.28772 - 1.14082i) q^{4} +(3.75871 + 0.456390i) q^{5} +(-0.126548 - 0.513427i) q^{6} +(1.26721 + 2.41446i) q^{7} +(-0.914254 - 1.74197i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(1.77284 + 0.930459i) q^{10} +(0.992966 - 0.376582i) q^{11} +(-0.207369 + 1.70783i) q^{12} +(3.43620 + 1.09202i) q^{13} +(0.173803 + 1.43140i) q^{14} +(-1.75959 - 3.35262i) q^{15} +(0.289343 + 2.38296i) q^{16} +(-2.93936 + 1.54270i) q^{17} +(-0.350654 + 0.395807i) q^{18} -4.90754i q^{19} +(-4.31952 - 4.87573i) q^{20} +(1.26721 - 2.41446i) q^{21} +0.561566 q^{22} +2.19096 q^{23} +(-0.914254 + 1.74197i) q^{24} +(9.06493 + 2.23430i) q^{25} +(1.49419 + 1.18426i) q^{26} +(0.970942 - 0.239316i) q^{27} +(1.12266 - 4.55481i) q^{28} +(2.78676 - 7.34809i) q^{29} +(-0.241336 - 1.98758i) q^{30} +(-1.53933 - 6.24529i) q^{31} +(-1.24539 + 5.05274i) q^{32} +(-0.873990 - 0.603272i) q^{33} +(-1.74258 + 0.211588i) q^{34} +(3.66113 + 9.65361i) q^{35} +(1.52332 - 0.799500i) q^{36} +(1.93163 + 7.83691i) q^{37} +(0.920224 - 2.42643i) q^{38} +(-1.05327 - 3.44828i) q^{39} +(-2.64140 - 6.96481i) q^{40} +(-0.221263 + 0.152727i) q^{41} +(1.07929 - 0.956164i) q^{42} +(-7.62733 - 1.87997i) q^{43} +(-1.70828 - 0.647864i) q^{44} +(-1.75959 + 3.35262i) q^{45} +(1.08327 + 0.410832i) q^{46} +(4.35972 + 4.92110i) q^{47} +(1.79677 - 1.59180i) q^{48} +(-0.247356 + 0.358357i) q^{49} +(4.06301 + 2.80449i) q^{50} +(2.93936 + 1.54270i) q^{51} +(-3.17907 - 5.32631i) q^{52} +(1.02359 - 0.537220i) q^{53} +(0.524937 + 0.0637389i) q^{54} +(3.90414 - 0.962285i) q^{55} +(3.04736 - 4.41486i) q^{56} +(-4.03882 + 2.78780i) q^{57} +(2.75572 - 3.11056i) q^{58} +(-4.22074 - 0.512491i) q^{59} +(-1.55888 + 6.32462i) q^{60} +(2.60402 + 1.36669i) q^{61} +(0.409981 - 3.37650i) q^{62} +(-2.70692 + 0.328679i) q^{63} +(1.16402 - 1.68638i) q^{64} +(12.4173 + 5.67284i) q^{65} +(-0.319006 - 0.462159i) q^{66} +(-7.94642 - 8.96966i) q^{67} +(5.54503 + 1.36673i) q^{68} +(-1.24461 - 1.80312i) q^{69} +5.45954i q^{70} +(-8.34800 + 5.76221i) q^{71} +(1.95296 - 0.237133i) q^{72} +(-11.6774 + 4.42864i) q^{73} +(-0.514466 + 4.23700i) q^{74} +(-3.31067 - 8.72952i) q^{75} +(-5.59863 + 6.31954i) q^{76} +(2.16754 + 1.92027i) q^{77} +(0.125827 - 1.90243i) q^{78} +(-7.35264 + 6.51387i) q^{79} +9.08890i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-0.138037 + 0.0340230i) q^{82} +(8.09145 + 5.58512i) q^{83} +(-4.38628 + 1.66350i) q^{84} +(-11.7523 + 4.45706i) q^{85} +(-3.41866 - 2.35973i) q^{86} +(-7.63042 + 1.88073i) q^{87} +(-1.56382 - 1.38542i) q^{88} +16.9607i q^{89} +(-1.49865 + 1.32769i) q^{90} +(1.71774 + 9.68040i) q^{91} +(-2.82134 - 2.49949i) q^{92} +(-4.26534 + 4.81457i) q^{93} +(1.23280 + 3.25064i) q^{94} +(2.23975 - 18.4460i) q^{95} +(4.86579 - 1.84535i) q^{96} +(-15.8462 + 1.92408i) q^{97} +(-0.189497 + 0.130800i) q^{98} +1.06198i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

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 $

$2$	0.494430	+	0.187512i	0.349615	+	0.132591i	0.523160	−	0.852235i	$-0.324753\pi$
$2$	0.494430	+	0.187512i	0.349615	+	0.132591i	−0.173545	+	0.984826i	$0.555522\pi$
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$4$	−1.28772	−	1.14082i	−0.643861	−	0.570411i
$5$	3.75871	+	0.456390i	1.68095	+	0.204104i	0.904618	−	0.426223i	$-0.140156\pi$
$5$	3.75871	+	0.456390i	1.68095	+	0.204104i	0.776330	+	0.630327i	$0.217079\pi$
$6$	−0.126548	−	0.513427i	−0.0516631	−	0.209606i
$7$	1.26721	+	2.41446i	0.478959	+	0.912581i	0.998315	+	0.0580226i	$0.0184795\pi$
$7$	1.26721	+	2.41446i	0.478959	+	0.912581i	−0.519356	+	0.854558i	$0.673828\pi$
$8$	−0.914254	−	1.74197i	−0.323238	−	0.615878i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	1.77284	+	0.930459i	0.560621	+	0.294237i
$11$	0.992966	−	0.376582i	0.299390	−	0.113544i	−0.200336	−	0.979727i	$-0.564203\pi$
$11$	0.992966	−	0.376582i	0.299390	−	0.113544i	0.499726	+	0.866184i	$0.333434\pi$
$12$	−0.207369	+	1.70783i	−0.0598622	+	0.493009i
$13$	3.43620	+	1.09202i	0.953031	+	0.302872i
$13$	3.43620	+	1.09202i	0.953031	+	0.302872i
$14$	0.173803	+	1.43140i	0.0464509	+	0.382557i
$15$	−1.75959	−	3.35262i	−0.454324	−	0.865643i
$16$	0.289343	+	2.38296i	0.0723358	+	0.595739i
$17$	−2.93936	+	1.54270i	−0.712901	+	0.374159i	−0.781855	−	0.623461i	$-0.785726\pi$
$17$	−2.93936	+	1.54270i	−0.712901	+	0.374159i	0.0689541	+	0.997620i	$0.478034\pi$
$18$	−0.350654	+	0.395807i	−0.0826500	+	0.0932926i
$19$		−	4.90754i		−	1.12587i	−0.826502	−	0.562933i	$-0.809673\pi$
$19$		−	4.90754i		−	1.12587i	0.826502	−	0.562933i	$-0.190327\pi$
$20$	−4.31952	−	4.87573i	−0.965873	−	1.09025i
$21$	1.26721	−	2.41446i	0.276527	−	0.526879i
$22$	0.561566			0.119726
$23$	2.19096			0.456846			0.228423	−	0.973562i	$-0.426643\pi$
$23$	2.19096			0.456846			0.228423	+	0.973562i	$0.426643\pi$
$24$	−0.914254	+	1.74197i	−0.186621	+	0.355577i
$25$	9.06493	+	2.23430i	1.81299	+	0.446861i
$26$	1.49419	+	1.18426i	0.293035	+	0.232252i
$27$	0.970942	−	0.239316i	0.186858	−	0.0460563i
$28$	1.12266	−	4.55481i	0.212163	−	0.860778i
$29$	2.78676	−	7.34809i	0.517489	−	1.36451i	−0.380619	−	0.924732i	$-0.624289\pi$
$29$	2.78676	−	7.34809i	0.517489	−	1.36451i	0.898108	−	0.439775i	$-0.144942\pi$
$30$	−0.241336	−	1.98758i	−0.0440617	−	0.362881i
$31$	−1.53933	−	6.24529i	−0.276471	−	1.12169i	−0.930815	−	0.365490i	$-0.880901\pi$
$31$	−1.53933	−	6.24529i	−0.276471	−	1.12169i	0.654344	−	0.756197i	$-0.272945\pi$
$32$	−1.24539	+	5.05274i	−0.220156	+	0.893207i
$33$	−0.873990	−	0.603272i	−0.152142	−	0.105016i
$34$	−1.74258	+	0.211588i	−0.298851	+	0.0362870i
$35$	3.66113	+	9.65361i	0.618844	+	1.63176i
$36$	1.52332	−	0.799500i	0.253887	−	0.133250i
$37$	1.93163	+	7.83691i	0.317557	+	1.28838i	0.885241	+	0.465133i	$0.153994\pi$
$37$	1.93163	+	7.83691i	0.317557	+	1.28838i	−0.567683	+	0.823247i	$0.692160\pi$
$38$	0.920224	−	2.42643i	0.149280	−	0.393619i
$39$	−1.05327	−	3.44828i	−0.168658	−	0.552166i
$40$	−2.64140	−	6.96481i	−0.417642	−	1.10123i
$41$	−0.221263	+	0.152727i	−0.0345554	+	0.0238519i	−0.585217	−	0.810877i	$-0.698991\pi$
$41$	−0.221263	+	0.152727i	−0.0345554	+	0.0238519i	0.550662	+	0.834728i	$0.314375\pi$
$42$	1.07929	−	0.956164i	0.166537	−	0.147539i
$43$	−7.62733	−	1.87997i	−1.16316	−	0.286692i	−0.389944	−	0.920839i	$-0.627506\pi$
$43$	−7.62733	−	1.87997i	−1.16316	−	0.286692i	−0.773213	+	0.634146i	$0.781352\pi$
$44$	−1.70828	−	0.647864i	−0.257532	−	0.0976692i
$45$	−1.75959	+	3.35262i	−0.262304	+	0.499779i
$46$	1.08327	+	0.410832i	0.159720	+	0.0605738i
$47$	4.35972	+	4.92110i	0.635930	+	0.717816i	0.974816	−	0.223011i	$-0.0715886\pi$
$47$	4.35972	+	4.92110i	0.635930	+	0.717816i	−0.338886	+	0.940827i	$0.610050\pi$
$48$	1.79677	−	1.59180i	0.259341	−	0.229756i
$49$	−0.247356	+	0.358357i	−0.0353366	+	0.0511939i
$50$	4.06301	+	2.80449i	0.574596	+	0.396615i
$51$	2.93936	+	1.54270i	0.411593	+	0.216021i
$52$	−3.17907	−	5.32631i	−0.440858	−	0.738627i
$53$	1.02359	−	0.537220i	0.140600	−	0.0737928i	−0.392956	−	0.919557i	$-0.628548\pi$
$53$	1.02359	−	0.537220i	0.140600	−	0.0737928i	0.533556	+	0.845764i	$0.320855\pi$
$54$	0.524937	+	0.0637389i	0.0714349	+	0.00867377i
$55$	3.90414	−	0.962285i	0.526435	−	0.129754i
$56$	3.04736	−	4.41486i	0.407220	−	0.589961i
$57$	−4.03882	+	2.78780i	−0.534955	+	0.369253i
$58$	2.75572	−	3.11056i	0.361843	−	0.408437i
$59$	−4.22074	−	0.512491i	−0.549493	−	0.0667206i	−0.158918	−	0.987292i	$-0.550801\pi$
$59$	−4.22074	−	0.512491i	−0.549493	−	0.0667206i	−0.390575	+	0.920571i	$0.627724\pi$
$60$	−1.55888	+	6.32462i	−0.201250	+	0.816505i
$61$	2.60402	+	1.36669i	0.333411	+	0.174987i	0.623118	−	0.782128i	$-0.285866\pi$
$61$	2.60402	+	1.36669i	0.333411	+	0.174987i	−0.289707	+	0.957115i	$0.593558\pi$
$62$	0.409981	−	3.37650i	0.0520677	−	0.428816i
$63$	−2.70692	+	0.328679i	−0.341040	+	0.0414097i
$64$	1.16402	−	1.68638i	0.145503	−	0.210797i
$65$	12.4173	+	5.67284i	1.54018	+	0.703630i
$66$	−0.319006	−	0.462159i	−0.0392669	−	0.0568879i
$67$	−7.94642	−	8.96966i	−0.970810	−	1.09582i	−0.995370	−	0.0961198i	$-0.969357\pi$
$67$	−7.94642	−	8.96966i	−0.970810	−	1.09582i	0.0245596	−	0.999698i	$-0.492182\pi$
$68$	5.54503	+	1.36673i	0.672433	+	0.165740i
$69$	−1.24461	−	1.80312i	−0.149833	−	0.217070i
$70$			5.45954i			0.652540i
$71$	−8.34800	+	5.76221i	−0.990725	+	0.683848i	−0.948998	−	0.315281i	$-0.897901\pi$
$71$	−8.34800	+	5.76221i	−0.990725	+	0.683848i	−0.0417265	+	0.999129i	$0.513286\pi$
$72$	1.95296	−	0.237133i	0.230159	−	0.0279464i
$73$	−11.6774	+	4.42864i	−1.36673	+	0.518333i	−0.925394	−	0.379007i	$-0.876266\pi$
$73$	−11.6774	+	4.42864i	−1.36673	+	0.518333i	−0.441339	+	0.897340i	$0.645496\pi$
$74$	−0.514466	+	4.23700i	−0.0598054	+	0.492542i
$75$	−3.31067	−	8.72952i	−0.382283	−	1.00800i
$76$	−5.59863	+	6.31954i	−0.642206	+	0.724901i
$77$	2.16754	+	1.92027i	0.247014	+	0.218835i
$78$	0.125827	−	1.90243i	0.0142471	−	0.215408i
$79$	−7.35264	+	6.51387i	−0.827236	+	0.732867i	−0.966301	−	0.257416i	$-0.917129\pi$
$79$	−7.35264	+	6.51387i	−0.827236	+	0.732867i	0.139065	+	0.990283i	$0.455590\pi$
$80$			9.08890i			1.01617i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	−0.138037	+	0.0340230i	−0.0152436	+	0.00375722i
$83$	8.09145	+	5.58512i	0.888152	+	0.613047i	0.922345	−	0.386368i	$-0.126271\pi$
$83$	8.09145	+	5.58512i	0.888152	+	0.613047i	−0.0341928	+	0.999415i	$0.510886\pi$
$84$	−4.38628	+	1.66350i	−0.478582	+	0.181502i
$85$	−11.7523	+	4.45706i	−1.27472	+	0.483436i
$86$	−3.41866	−	2.35973i	−0.368644	−	0.254456i
$87$	−7.63042	+	1.88073i	−0.818067	+	0.201635i
$88$	−1.56382	−	1.38542i	−0.166703	−	0.147686i
$89$			16.9607i			1.79783i	0.438120	+	0.898917i	$0.355644\pi$
$89$			16.9607i			1.79783i	−0.438120	+	0.898917i	$0.644356\pi$
$90$	−1.49865	+	1.32769i	−0.157972	+	0.139951i
$91$	1.71774	+	9.68040i	0.180068	+	1.01478i
$92$	−2.82134	−	2.49949i	−0.294145	−	0.260590i
$93$	−4.26534	+	4.81457i	−0.442295	+	0.499248i
$94$	1.23280	+	3.25064i	0.127154	+	0.335278i
$95$	2.23975	−	18.4460i	0.229794	−	1.89252i
$96$	4.86579	−	1.84535i	0.496612	−	0.188340i
$97$	−15.8462	+	1.92408i	−1.60894	+	0.195361i	−0.875094	−	0.483953i	$-0.839200\pi$
$97$	−15.8462	+	1.92408i	−1.60894	+	0.195361i	−0.733847	+	0.679314i	$0.762277\pi$
$98$	−0.189497	+	0.130800i	−0.0191421	+	0.0132128i
$99$			1.06198i			0.106733i
$100$	−9.12416	−	13.2186i	−0.912416	−	1.32186i
$101$	4.82376	+	1.18895i	0.479982	+	0.118305i	0.471881	−	0.881662i	$-0.343575\pi$
$101$	4.82376	+	1.18895i	0.479982	+	0.118305i	0.00810082	+	0.999967i	$0.497421\pi$
$102$	1.16403	+	1.31392i	0.115257	+	0.130098i
$103$	0.155484	+	0.225258i	0.0153203	+	0.0221953i	0.830569	−	0.556915i	$-0.188015\pi$
$103$	0.155484	+	0.225258i	0.0153203	+	0.0221953i	−0.815249	+	0.579111i	$0.803400\pi$
$104$	−1.23930	−	6.98413i	−0.121523	−	0.684850i
$105$	5.86501	−	8.49693i	0.572366	−	0.829215i
$106$	0.606827	−	0.0736822i	0.0589403	−	0.00715664i
$107$	0.601834	−	4.95655i	0.0581815	−	0.479167i	−0.934273	−	0.356557i	$-0.883950\pi$
$107$	0.601834	−	4.95655i	0.0581815	−	0.479167i	0.992455	−	0.122610i	$-0.0391265\pi$
$108$	−1.52332	−	0.799500i	−0.146581	−	0.0769319i
$109$	3.76264	−	15.2656i	0.360396	−	1.46218i	−0.458733	−	0.888574i	$-0.651697\pi$
$109$	3.76264	−	15.2656i	0.360396	−	1.46218i	0.819129	−	0.573609i	$-0.194457\pi$
$110$	2.11076	+	0.256293i	0.201253	+	0.0244366i
$111$	5.35236	−	6.04157i	0.508024	−	0.573440i
$112$	−5.38690	+	3.71831i	−0.509014	+	0.351347i
$113$	0.626780	−	0.908048i	0.0589625	−	0.0854219i	−0.792394	−	0.610010i	$-0.791165\pi$
$113$	0.626780	−	0.908048i	0.0589625	−	0.0854219i	0.851356	+	0.524588i	$0.175781\pi$
$114$	−2.51966	+	0.621041i	−0.235988	+	0.0581658i
$115$	8.23518	+	0.999932i	0.767934	+	0.0932441i
$116$	−11.9714	+	6.28310i	−1.11152	+	0.583371i
$117$	−2.23955	+	2.82567i	−0.207047	+	0.261233i
$118$	−1.99076	−	1.04483i	−0.183264	−	0.0961845i
$119$	−7.44957	−	5.14206i	−0.682901	−	0.471372i
$120$	−4.23143	+	6.13029i	−0.386275	+	0.559617i
$121$	−7.38945	+	6.54648i	−0.671768	+	0.595135i
$122$	1.03123	+	1.16402i	0.0933634	+	0.105385i
$123$	0.251383	+	0.0953370i	0.0226664	+	0.00859625i
$124$	−5.14254	+	9.79829i	−0.461814	+	0.879912i
$125$	15.3514	+	5.82202i	1.37307	+	0.520737i
$126$	−1.40001	−	0.345072i	−0.124723	−	0.0307415i
$127$	0.157187	−	0.139256i	0.0139481	−	0.0123570i	−0.656120	−	0.754657i	$-0.727803\pi$
$127$	0.157187	−	0.139256i	0.0139481	−	0.0123570i	0.670068	+	0.742300i	$0.266265\pi$
$128$	9.45730	−	6.52790i	0.835915	−	0.576990i
$129$	2.78563	+	7.34511i	0.245261	+	0.646701i
$130$	5.07576	+	5.13322i	0.445174	+	0.450213i
$131$	−1.79285	+	4.72737i	−0.156642	+	0.413032i	−0.990246	−	0.139331i	$-0.955505\pi$
$131$	−1.79285	+	4.72737i	−0.156642	+	0.413032i	0.833603	+	0.552363i	$0.186274\pi$
$132$	0.437230	+	1.77391i	0.0380560	+	0.154399i
$133$	11.8491	−	6.21887i	1.02744	−	0.539244i
$134$	−2.24703	−	5.92492i	−0.194113	−	0.511835i
$135$	3.75871	−	0.456390i	0.323499	−	0.0392798i
$136$	5.37465	+	3.70985i	0.460872	+	0.318117i
$137$	−4.77706	+	19.3813i	−0.408132	+	1.65586i	0.303145	+	0.952944i	$0.401963\pi$
$137$	−4.77706	+	19.3813i	−0.408132	+	1.65586i	−0.711277	+	0.702912i	$0.751883\pi$
$138$	−0.277262	−	1.12490i	−0.0236021	−	0.0957575i
$139$	−0.432463	−	3.56165i	−0.0366810	−	0.302096i	−0.999491	−	0.0319146i	$-0.989840\pi$
$139$	−0.432463	−	3.56165i	−0.0366810	−	0.302096i	0.962810	−	0.270181i	$-0.0870835\pi$
$140$	6.29853	−	16.6079i	0.532323	−	1.40362i
$141$	1.57339	−	6.38348i	0.132503	−	0.537586i
$142$	−5.20798	+	1.28365i	−0.437044	+	0.107722i
$143$	3.82327	−	0.209674i	0.319718	−	0.0175338i
$144$	−2.33071	−	0.574467i	−0.194225	−	0.0478723i
$145$	13.8282	−	26.3475i	1.14837	−	2.18804i
$146$	−6.60406			−0.546556
$147$	0.435437			0.0359142
$148$	6.45312	−	12.2954i	0.530444	−	1.01068i
$149$	−7.49198	−	8.45669i	−0.613767	−	0.692799i	0.356649	−	0.934238i	$-0.383919\pi$
$149$	−7.49198	−	8.45669i	−0.613767	−	0.692799i	−0.970416	+	0.241439i	$0.922381\pi$
$150$		−	4.93692i		−	0.403098i
$151$	12.9881	−	14.6606i	1.05696	−	1.19306i	0.0763493	−	0.997081i	$-0.475674\pi$
$151$	12.9881	−	14.6606i	1.05696	−	1.19306i	0.980608	−	0.195978i	$-0.0627880\pi$
$152$	−8.54876	+	4.48674i	−0.693396	+	0.363922i
$153$	−0.400134	−	3.29540i	−0.0323489	−	0.266417i
$154$	0.711620	+	1.35588i	0.0573440	+	0.109260i
$155$	−2.93559	−	24.1768i	−0.235793	−	1.94193i
$156$	−2.57755	+	5.64202i	−0.206369	+	0.451723i
$157$	−1.18979	+	9.79877i	−0.0949553	+	0.782027i	0.864980	+	0.501806i	$0.167331\pi$
$157$	−1.18979	+	9.79877i	−0.0949553	+	0.782027i	−0.959936	+	0.280221i	$0.909592\pi$
$158$	−4.85679	+	1.84194i	−0.386386	+	0.146537i
$159$	−1.02359	−	0.537220i	−0.0811757	−	0.0426043i
$160$	−6.98709	+	18.4234i	−0.552378	+	1.45650i
$161$	2.77640	+	5.28998i	0.218811	+	0.416909i
$162$	−0.245742	−	0.468223i	−0.0193073	−	0.0367870i
$163$	−2.38065	−	9.65866i	−0.186467	−	0.756524i	−0.987462	−	0.157855i	$-0.949542\pi$
$163$	−2.38065	−	9.65866i	−0.186467	−	0.756524i	0.800996	−	0.598670i	$-0.204304\pi$
$164$	0.459158	+	0.0557519i	0.0358542	+	0.00435349i
$165$	−3.00975	−	2.66641i	−0.234309	−	0.207579i
$166$	2.95337	+	4.27870i	0.229226	+	0.332091i
$167$	−16.5171	−	6.26409i	−1.27813	−	0.484730i	−0.380213	−	0.924899i	$-0.624149\pi$
$167$	−16.5171	−	6.26409i	−1.27813	−	0.484730i	−0.897915	+	0.440169i	$0.854919\pi$
$168$	−5.36446			−0.413877
$169$	10.6150	+	7.50481i	0.816537	+	0.577293i
$170$	−6.64644			−0.509759
$171$	4.58863	+	1.74024i	0.350901	+	0.133079i
$172$	7.67717	+	11.1223i	0.585379	+	0.848068i
$173$	19.1472	+	16.9629i	1.45573	+	1.28967i	0.882533	+	0.470251i	$0.155837\pi$
$173$	19.1472	+	16.9629i	1.45573	+	1.28967i	0.573200	+	0.819416i	$0.305702\pi$
$174$	−4.12537	−	0.500910i	−0.312743	−	0.0379739i
$175$	6.09250	+	24.7182i	0.460550	+	1.86852i
$176$	1.18469	+	2.25723i	0.0892992	+	0.170145i
$177$	1.97588	+	3.76473i	0.148516	+	0.282974i
$178$	−3.18035	+	8.38588i	−0.238377	+	0.628549i
$179$	5.56555	+	2.92103i	0.415989	+	0.218328i	0.659714	−	0.751517i	$-0.270677\pi$
$179$	5.56555	+	2.92103i	0.415989	+	0.218328i	−0.243726	+	0.969844i	$0.578370\pi$
$180$	6.09061	−	2.30986i	0.453967	−	0.172167i
$181$	2.53355	−	20.8657i	0.188317	−	1.55093i	−0.525617	−	0.850721i	$-0.676166\pi$
$181$	2.53355	−	20.8657i	0.188317	−	1.55093i	0.713935	−	0.700212i	$-0.246911\pi$
$182$	−0.965893	+	5.10837i	−0.0715968	+	0.378658i
$183$	−0.354484	−	2.91944i	−0.0262042	−	0.215811i
$184$	−2.00309	−	3.81657i	−0.147670	−	0.281361i
$185$	3.68373	+	30.3383i	0.270834	+	2.23051i
$186$	−3.01170	+	1.58066i	−0.220829	+	0.115900i
$187$	−2.33774	+	2.63876i	−0.170952	+	0.192965i
$188$		−	11.3107i		−	0.824915i
$189$	1.80820	+	2.04104i	0.131527	+	0.148464i
$190$	4.56626	−	8.70028i	0.331271	−	0.631185i
$191$	−16.7501			−1.21199			−0.605997	−	0.795467i	$-0.707226\pi$
$191$	−16.7501			−1.21199			−0.605997	+	0.795467i	$0.707226\pi$
$192$	−2.04910			−0.147881
$193$	−3.51979	+	6.70640i	−0.253360	+	0.482737i	−0.978603	−	0.205755i	$-0.934035\pi$
$193$	−3.51979	+	6.70640i	−0.253360	+	0.482737i	0.725244	+	0.688492i	$0.241727\pi$
$194$	−8.19564	−	2.02004i	−0.588412	−	0.145031i
$195$	−2.38518	−	13.4418i	−0.170806	−	0.962587i
$196$	0.727348	−	0.179275i	0.0519534	−	0.0128054i
$197$	0.0337290	−	0.136844i	0.00240309	−	0.00974972i	−0.969728	−	0.244188i	$-0.921479\pi$
$197$	0.0337290	−	0.136844i	0.00240309	−	0.00974972i	0.972131	+	0.234438i	$0.0753249\pi$
$198$	−0.199134	+	0.525073i	−0.0141518	+	0.0373153i
$199$	−0.231618	−	1.90755i	−0.0164190	−	0.135223i	0.982194	−	0.187868i	$-0.0601577\pi$
$199$	−0.231618	−	1.90755i	−0.0164190	−	0.135223i	−0.998613	+	0.0526455i	$0.983235\pi$
$200$	−4.39557	−	17.8335i	−0.310813	−	1.26102i
$201$	−2.86780	+	11.6351i	−0.202279	+	0.820678i
$202$	2.16207	+	1.49237i	0.152122	+	0.105003i
$203$	21.2731	−	2.58302i	1.49308	−	0.181293i
$204$	−2.02514	−	5.33986i	−0.141788	−	0.373865i
$205$	−0.901366	+	0.473073i	−0.0629541	+	0.0330409i
$206$	0.0346374	+	0.140530i	0.00241330	+	0.00979116i
$207$	−0.776924	+	2.04858i	−0.0539999	+	0.142386i
$208$	−1.60800	+	8.50429i	−0.111494	+	0.589666i
$209$	−1.84809	−	4.87302i	−0.127835	−	0.337074i
$210$	4.49311	−	3.10137i	0.310054	−	0.214015i
$211$	−3.78448	+	3.35276i	−0.260534	+	0.230813i	−0.783270	−	0.621681i	$-0.786450\pi$
$211$	−3.78448	+	3.35276i	−0.260534	+	0.230813i	0.522736	+	0.852495i	$0.324911\pi$
$212$	−1.93097	−	0.475941i	−0.132619	−	0.0326877i
$213$	9.48440	+	3.59696i	0.649861	+	0.246460i
$214$	1.22698	−	2.33781i	0.0838745	−	0.159810i
$215$	−27.8110	−	10.5473i	−1.89669	−	0.719320i
$216$	−1.30457	−	1.47255i	−0.0887645	−	0.100194i
$217$	13.1284	−	11.6307i	0.891211	−	0.789544i
$218$	4.72286	−	6.84224i	0.319872	−	0.463415i
$219$	10.2782	+	7.09453i	0.694537	+	0.479404i
$220$	−6.12525	−	3.21478i	−0.412964	−	0.216740i
$221$	−11.7849	+	2.09117i	−0.792739	+	0.140668i
$222$	3.77924	−	1.98350i	0.253646	−	0.133124i
$223$	−9.03501	−	1.09705i	−0.605029	−	0.0734638i	−0.187711	−	0.982224i	$-0.560107\pi$
$223$	−9.03501	−	1.09705i	−0.605029	−	0.0734638i	−0.417318	+	0.908760i	$0.637030\pi$
$224$	−13.7778	+	3.39593i	−0.920569	+	0.226900i
$225$	−5.30358	+	7.68356i	−0.353572	+	0.512237i
$226$	0.480169	−	0.331437i	0.0319404	−	0.0220468i
$227$	−13.5064	+	15.2456i	−0.896451	+	1.01188i	0.103400	+	0.994640i	$0.467028\pi$
$227$	−13.5064	+	15.2456i	−0.896451	+	1.01188i	−0.999851	+	0.0172445i	$0.994511\pi$
$228$	8.38126	+	1.01767i	0.555063	+	0.0673968i
$229$	2.68796	−	10.9055i	0.177626	−	0.720656i	−0.812792	−	0.582554i	$-0.802054\pi$
$229$	2.68796	−	10.9055i	0.177626	−	0.720656i	0.990418	−	0.138102i	$-0.0441003\pi$
$230$	3.88422	+	2.03859i	0.256118	+	0.134421i
$231$	0.349050	−	2.87469i	0.0229658	−	0.189140i
$232$	−15.3479	+	1.86358i	−1.00764	+	0.122350i
$233$	8.33304	−	12.0725i	0.545916	−	0.790895i	−0.448793	−	0.893636i	$-0.648146\pi$
$233$	8.33304	−	12.0725i	0.545916	−	0.790895i	0.994708	+	0.102741i	$0.0327612\pi$
$234$	−1.63715	+	0.977151i	−0.107024	+	0.0638784i
$235$	14.1410	+	20.4867i	0.922456	+	1.33641i
$236$	4.85048	+	5.47506i	0.315739	+	0.356396i
$237$	9.53758	+	2.35080i	0.619532	+	0.152701i
$238$	−2.71909	−	3.93928i	−0.176252	−	0.255345i
$239$			14.8571i			0.961025i	0.876988	+	0.480512i	$0.159549\pi$
$239$			14.8571i			0.961025i	−0.876988	+	0.480512i	$0.840451\pi$
$240$	7.48002	−	5.16309i	0.482833	−	0.333276i
$241$	14.0921	−	1.71109i	0.907753	−	0.110221i	0.346676	−	0.937985i	$-0.387310\pi$
$241$	14.0921	−	1.71109i	0.907753	−	0.110221i	0.561077	+	0.827764i	$0.310387\pi$
$242$	−4.88111	+	1.85116i	−0.313770	+	0.118997i
$243$	−0.120537	+	0.992709i	−0.00773243	+	0.0636823i
$244$	−1.79410	−	4.73065i	−0.114855	−	0.302849i
$245$	−1.09329	+	1.23407i	−0.0698479	+	0.0788420i
$246$	0.106414	+	0.0942749i	0.00678473	+	0.00601075i
$247$	5.35913	−	16.8633i	0.340993	−	1.07299i
$248$	−9.47174	+	8.39123i	−0.601456	+	0.532844i
$249$		−	9.83184i		−	0.623068i
$250$	6.49849	+	5.75716i	0.411000	+	0.364115i
$251$	18.8633	−	4.64939i	1.19064	−	0.293467i	0.406267	−	0.913754i	$-0.366830\pi$
$251$	18.8633	−	4.64939i	1.19064	−	0.293467i	0.784375	+	0.620287i	$0.212984\pi$
$252$	3.86072	+	2.66486i	0.243203	+	0.167871i
$253$	2.17555	−	0.825075i	0.136775	−	0.0518721i
$254$	0.103830	−	0.0393777i	0.00651490	−	0.00247077i
$255$	10.3442	+	7.14006i	0.647776	+	0.447128i
$256$	1.92092	−	0.473463i	0.120057	−	0.0295914i
$257$	−3.04603	−	2.69855i	−0.190006	−	0.168331i	0.562757	−	0.826623i	$-0.309741\pi$
$257$	−3.04603	−	2.69855i	−0.190006	−	0.168331i	−0.752763	+	0.658292i	$0.771279\pi$
$258$			4.15398i			0.258616i
$259$	−16.4741	+	14.5948i	−1.02365	+	0.906878i
$260$	−9.51834	−	21.4710i	−0.590303	−	1.33157i
$261$	5.88239	+	5.21134i	0.364111	+	0.322574i
$262$	−1.77288	+	2.00117i	−0.109529	+	0.123633i
$263$	3.39986	+	8.96470i	0.209644	+	0.552787i	0.998053	−	0.0623645i	$-0.0198641\pi$
$263$	3.39986	+	8.96470i	0.209644	+	0.552787i	−0.788409	+	0.615151i	$0.789095\pi$
$264$	−0.251830	+	2.07400i	−0.0154990	+	0.127646i
$265$	4.09255	−	1.55210i	0.251404	−	0.0953448i
$266$	7.02464	−	0.852946i	0.430708	−	0.0522975i
$267$	13.9584	−	9.63479i	0.854240	−	0.589639i
$268$			20.6159i			1.25932i
$269$	3.63757	+	5.26994i	0.221787	+	0.321314i	0.918044	−	0.396479i	$-0.129768\pi$
$269$	3.63757	+	5.26994i	0.221787	+	0.321314i	−0.696257	+	0.717793i	$0.745153\pi$
$270$	1.94400	+	0.479153i	0.118308	+	0.0291603i
$271$	−15.2410	−	17.2035i	−0.925824	−	1.04504i	−0.998861	−	0.0477099i	$-0.984808\pi$
$271$	−15.2410	−	17.2035i	−0.925824	−	1.04504i	0.0730374	−	0.997329i	$-0.476731\pi$
$272$	−4.52667	−	6.55801i	−0.274469	−	0.397638i
$273$	6.99102	−	6.91276i	0.423116	−	0.418379i
$274$	−5.99616	+	8.68693i	−0.362241	+	0.524797i
$275$	9.84256	−	1.19510i	0.593529	−	0.0720675i
$276$	−0.454336	+	3.74179i	−0.0273478	+	0.225229i
$277$	−1.41234	−	0.741251i	−0.0848591	−	0.0445375i	0.421760	−	0.906708i	$-0.361413\pi$
$277$	−1.41234	−	0.741251i	−0.0848591	−	0.0445375i	−0.506619	+	0.862170i	$0.669105\pi$
$278$	0.454032	−	1.84208i	0.0272310	−	0.110481i
$279$	6.38530	+	0.775316i	0.382278	+	0.0464169i
$280$	13.4690	−	15.2034i	0.804930	−	0.908578i
$281$	6.76124	−	4.66695i	0.403342	−	0.278407i	−0.349074	−	0.937095i	$-0.613504\pi$
$281$	6.76124	−	4.66695i	0.403342	−	0.278407i	0.752416	+	0.658689i	$0.228888\pi$
$282$	1.97491	−	2.86115i	0.117604	−	0.170379i
$283$	−4.96960	+	1.22490i	−0.295412	+	0.0728126i	−0.384236	−	0.923235i	$-0.625535\pi$
$283$	−4.96960	+	1.22490i	−0.295412	+	0.0728126i	0.0888241	+	0.996047i	$0.471689\pi$
$284$	17.3235	+	2.10346i	1.02796	+	0.124817i
$285$	−16.4531	+	8.63526i	−0.974598	+	0.511509i
$286$	1.92965	+	0.613241i	0.114103	+	0.0362617i
$287$	−0.649138	−	0.340694i	−0.0383174	−	0.0201105i
$288$	−4.28278	−	2.95619i	−0.252365	−	0.174195i
$289$	−3.39715	+	4.92163i	−0.199833	+	0.289507i
$290$	11.7776	−	10.4340i	0.691604	−	0.612707i
$291$	10.5852	+	11.9482i	0.620514	+	0.700415i
$292$	20.0895	+	7.61894i	1.17565	+	0.445865i
$293$	12.6176	−	24.0408i	0.737127	−	1.40448i	−0.170781	−	0.985309i	$-0.554629\pi$
$293$	12.6176	−	24.0408i	0.737127	−	1.40448i	0.907908	−	0.419170i	$-0.137679\pi$
$294$	0.215293	+	0.0816498i	0.0125561	+	0.00476191i
$295$	−15.6307	−	3.85261i	−0.910052	−	0.224308i
$296$	11.8856	−	10.5297i	0.690838	−	0.612029i
$297$	0.873990	−	0.603272i	0.0507140	−	0.0350054i
$298$	−2.11852	−	5.58608i	−0.122723	−	0.323593i
$299$	7.52857	+	2.39257i	0.435389	+	0.138366i
$300$	−5.69560	+	15.0181i	−0.328836	+	0.867069i
$301$	−5.12630	−	20.7982i	−0.295475	−	1.19879i
$302$	9.17074	−	4.81318i	0.527717	−	0.276967i
$303$	−1.76172	−	4.64527i	−0.101208	−	0.266864i
$304$	11.6944	−	1.41996i	0.670723	−	0.0814405i
$305$	9.16402	+	6.32546i	0.524730	+	0.362195i
$306$	0.420091	−	1.70437i	0.0240150	−	0.0974326i
$307$	1.71918	+	6.97498i	0.0981187	+	0.398083i	0.999381	−	0.0351915i	$-0.0112041\pi$
$307$	1.71918	+	6.97498i	0.0981187	+	0.398083i	−0.901262	+	0.433275i	$0.857358\pi$
$308$	−0.600498	−	4.94555i	−0.0342166	−	0.281799i
$309$	0.0970586	−	0.255922i	0.00552147	−	0.0145589i
$310$	3.08200	−	12.5042i	0.175046	−	0.710190i
$311$	−20.6294	+	5.08469i	−1.16979	+	0.288326i	−0.775914	−	0.630839i	$-0.782711\pi$
$311$	−20.6294	+	5.08469i	−1.16979	+	0.288326i	−0.393872	+	0.919165i	$0.628865\pi$
$312$	−5.04382	+	4.98736i	−0.285550	+	0.282354i
$313$	−12.9862	−	3.20081i	−0.734024	−	0.180921i	−0.145452	−	0.989365i	$-0.546464\pi$
$313$	−12.9862	−	3.20081i	−0.734024	−	0.180921i	−0.588572	+	0.808445i	$0.700310\pi$
$314$	−2.42566	+	4.62170i	−0.136888	+	0.260818i
$315$	−10.3245			−0.581722
$316$	16.8993			0.950660
$317$	8.14780	−	15.5243i	0.457626	−	0.871933i	−0.541879	−	0.840457i	$-0.682287\pi$
$317$	8.14780	−	15.5243i	0.457626	−	0.871933i	0.999504	−	0.0314765i	$-0.0100209\pi$
$318$	−0.405356	−	0.457553i	−0.0227313	−	0.0256583i
$319$		−	8.34585i		−	0.467278i
$320$	5.14487	−	5.80736i	0.287607	−	0.324641i
$321$	−4.42104	+	2.32034i	−0.246758	+	0.129509i
$322$	0.380795	+	3.13613i	0.0212209	+	0.174770i
$323$	7.57084	+	14.4250i	0.421253	+	0.802631i
$324$	0.207369	+	1.70783i	0.0115205	+	0.0948797i
$325$	28.7090	+	17.5766i	1.59249	+	0.974975i
$326$	0.634057	−	5.22193i	0.0351172	−	0.289216i
$327$	−14.7008	+	5.57528i	−0.812956	+	0.308314i
$328$	0.468334	+	0.245801i	0.0258594	+	0.0135721i
$329$	−6.35715	+	16.7624i	−0.350481	+	0.924142i
$330$	−0.988126	−	1.88272i	−0.0543945	−	0.103640i
$331$	−8.99361	−	17.1359i	−0.494333	−	0.941874i	−0.997001	−	0.0773936i	$-0.975340\pi$
$331$	−8.99361	−	17.1359i	−0.494333	−	0.941874i	0.502667	−	0.864480i	$-0.332352\pi$
$332$	−4.04790	−	16.4230i	−0.222157	−	0.901328i
$333$	−8.01260	−	0.972906i	−0.439088	−	0.0533149i
$334$	−6.99193	−	6.19431i	−0.382581	−	0.338937i
$335$	−25.7747	−	37.3410i	−1.40822	−	2.04016i
$336$	6.12021	+	2.32109i	0.333885	+	0.126626i
$337$	5.12681			0.279275			0.139638	−	0.990203i	$-0.455406\pi$
$337$	5.12681			0.279275			0.139638	+	0.990203i	$0.455406\pi$
$338$	3.84112	+	5.70104i	0.208929	+	0.310096i
$339$	−1.10336			−0.0599263
$340$	20.2184	+	7.66783i	1.09650	+	0.415846i
$341$	−3.88036	−	5.62168i	−0.210133	−	0.304431i
$342$	1.94244	+	1.72085i	0.105035	+	0.0930529i
$343$	17.7697	+	2.15764i	0.959476	+	0.116501i
$344$	3.69848	+	15.0053i	0.199409	+	0.809032i
$345$	−3.85519	−	7.34545i	−0.207556	−	0.395466i
$346$	6.28617	+	11.9773i	0.337947	+	0.643904i
$347$	3.71783	−	9.80312i	0.199584	−	0.526259i	−0.797436	−	0.603403i	$-0.793811\pi$
$347$	3.71783	−	9.80312i	0.199584	−	0.526259i	0.997020	+	0.0771442i	$0.0245802\pi$
$348$	11.9714	+	6.28310i	0.641737	+	0.336809i
$349$	−32.3055	+	12.2519i	−1.72928	+	0.655828i	−0.999609	−	0.0279756i	$-0.991094\pi$
$349$	−32.3055	+	12.2519i	−1.72928	+	0.655828i	−0.729667	+	0.683803i	$0.760325\pi$
$350$	−1.62267	+	13.3639i	−0.0867351	+	0.714328i
$351$	3.59769	+	0.237951i	0.192031	+	0.0127009i
$352$	0.666145	+	5.48619i	0.0355056	+	0.292415i
$353$	10.8495	+	20.6720i	0.577461	+	1.10026i	0.982553	+	0.185984i	$0.0595471\pi$
$353$	10.8495	+	20.6720i	0.577461	+	1.10026i	−0.405092	+	0.914276i	$0.632761\pi$
$354$	0.271001	+	2.23190i	0.0144036	+	0.118624i
$355$	−34.0075	+	17.8485i	−1.80493	+	0.947302i
$356$	19.3492	−	21.8407i	1.02550	−	1.15755i
$357$			9.05190i			0.479077i
$358$	2.20404	+	2.48785i	0.116487	+	0.131487i
$359$	−1.14494	+	2.18151i	−0.0604278	+	0.115136i	−0.913797	−	0.406172i	$-0.866863\pi$
$359$	−1.14494	+	2.18151i	−0.0604278	+	0.115136i	0.853369	+	0.521308i	$0.174556\pi$
$360$	7.44886			0.392589
$361$	−5.08392			−0.267575
$362$	5.16524	−	9.84154i	0.271479	−	0.517260i
$363$	9.58534	+	2.36257i	0.503100	+	0.124003i
$364$	8.83164	−	14.4253i	0.462904	−	0.756091i
$365$	−45.9131	+	11.3166i	−2.40320	+	0.592336i
$366$	0.372163	−	1.50993i	0.0194533	−	0.0789251i
$367$	12.3302	−	32.5120i	0.643630	−	1.69711i	−0.0708763	−	0.997485i	$-0.522580\pi$
$367$	12.3302	−	32.5120i	0.643630	−	1.69711i	0.714507	−	0.699629i	$-0.246651\pi$
$368$	0.633939	+	5.22095i	0.0330463	+	0.272161i
$369$	−0.0643410	−	0.261042i	−0.00334946	−	0.0135893i
$370$	−3.86746	+	15.6909i	−0.201060	+	0.815731i
$371$	2.59419	+	1.79064i	0.134684	+	0.0929655i
$372$	10.9851	−	1.33384i	0.569552	−	0.0691562i
$373$	−3.00012	−	7.91066i	−0.155340	−	0.409598i	0.834642	−	0.550793i	$-0.185675\pi$
$373$	−3.00012	−	7.91066i	−0.155340	−	0.409598i	−0.989982	+	0.141195i	$0.954906\pi$
$374$	−1.65065	+	0.866326i	−0.0853529	+	0.0447966i
$375$	−3.92916	−	15.9412i	−0.202901	−	0.823202i
$376$	4.58650	−	12.0936i	0.236531	−	0.623680i
$377$	17.6002	−	22.2063i	0.906454	−	1.14368i
$378$	0.511309	+	1.34821i	0.0262989	+	0.0693445i
$379$	−26.0276	+	17.9656i	−1.33695	+	0.922829i	−0.999826	−	0.0186323i	$-0.994069\pi$
$379$	−26.0276	+	17.9656i	−1.33695	+	0.922829i	−0.337122	+	0.941461i	$0.609453\pi$
$380$	−23.9278	+	21.1982i	−1.22747	+	1.08744i
$381$	−0.203898	−	0.0502564i	−0.0104460	−	0.00257471i
$382$	−8.28175	−	3.14085i	−0.423731	−	0.160700i
$383$	9.98330	−	19.0216i	0.510123	−	0.971958i	−0.485112	−	0.874452i	$-0.661221\pi$
$383$	9.98330	−	19.0216i	0.510123	−	0.971958i	0.995235	−	0.0975058i	$-0.0310864\pi$
$384$	−10.7447	−	4.07493i	−0.548314	−	0.207948i
$385$	7.27076	+	8.20699i	0.370552	+	0.418267i
$386$	−2.99782	+	2.65584i	−0.152585	+	0.135179i
$387$	4.46249	−	6.46503i	0.226841	−	0.328636i
$388$	22.6006	+	15.6000i	1.14737	+	0.791972i
$389$	−22.1468	−	11.6235i	−1.12289	−	0.589336i	−0.202084	−	0.979368i	$-0.564772\pi$
$389$	−22.1468	−	11.6235i	−1.12289	−	0.589336i	−0.920801	+	0.390032i	$0.872464\pi$
$390$	1.34120	−	7.09327i	0.0679143	−	0.359182i
$391$	−6.44002	+	3.37998i	−0.325686	+	0.170933i
$392$	0.850392	+	0.103256i	0.0429513	+	0.00521523i
$393$	4.90900	−	1.20996i	0.247626	−	0.0610344i
$394$	0.0423365	−	0.0613351i	0.00213288	−	0.00309002i
$395$	−30.6093	+	21.1281i	−1.54012	+	1.06307i
$396$	1.21153	−	1.36753i	0.0608815	−	0.0687210i
$397$	5.62178	+	0.682608i	0.282149	+	0.0342591i	0.260388	−	0.965504i	$-0.416150\pi$
$397$	5.62178	+	0.682608i	0.282149	+	0.0342591i	0.0217613	+	0.999763i	$0.493073\pi$
$398$	0.243170	−	0.986580i	0.0121890	−	0.0494528i
$399$	−11.8491	−	6.21887i	−0.593195	−	0.311333i
$400$	−2.70137	+	22.2478i	−0.135069	+	1.11239i
$401$	−12.5385	+	1.52245i	−0.626144	+	0.0760276i	−0.427457	−	0.904035i	$-0.640591\pi$
$401$	−12.5385	+	1.52245i	−0.626144	+	0.0760276i	−0.198686	+	0.980063i	$0.563668\pi$
$402$	−3.59966	+	5.21500i	−0.179535	+	0.260101i
$403$	1.53055	−	23.1411i	0.0762421	−	1.15274i
$404$	−4.85528	−	7.03408i	−0.241559	−	0.349959i
$405$	−2.51079	−	2.83410i	−0.124762	−	0.140828i
$406$	11.0024	+	2.71185i	0.546040	+	0.134587i
$407$	4.86928	+	7.05437i	0.241361	+	0.349672i
$408$		−	6.53069i		−	0.323317i
$409$	−2.09544	+	1.44638i	−0.103613	+	0.0715187i	−0.618744	−	0.785592i	$-0.712358\pi$
$409$	−2.09544	+	1.44638i	−0.103613	+	0.0715187i	0.515132	+	0.857111i	$0.327743\pi$
$410$	−0.534369	+	0.0648841i	−0.0263906	+	0.00320440i
$411$	18.6642	−	7.07839i	0.920636	−	0.349151i
$412$	0.0567587	−	0.467450i	0.00279630	−	0.0230296i
$413$	−4.11116	−	10.8402i	−0.202297	−	0.533413i
$414$	−0.768269	+	0.867196i	−0.0377583	+	0.0426204i
$415$	27.8644	+	24.6857i	1.36781	+	1.21178i
$416$	−9.79711	+	16.0023i	−0.480343	+	0.784576i
$417$	−2.68552	+	2.37916i	−0.131510	+	0.116508i
$418$		−	2.75590i		−	0.134796i
$419$	−15.1096	−	13.3859i	−0.738153	−	0.653946i	0.207830	−	0.978165i	$-0.433360\pi$
$419$	−15.1096	−	13.3859i	−0.738153	−	0.653946i	−0.945982	+	0.324219i	$0.894899\pi$
$420$	−17.2460	+	4.25075i	−0.841517	+	0.207415i
$421$	−10.4854	−	7.23752i	−0.511025	−	0.352735i	0.284480	−	0.958682i	$-0.408179\pi$
$421$	−10.4854	−	7.23752i	−0.511025	−	0.352735i	−0.795505	+	0.605947i	$0.792794\pi$
$422$	−2.49984	+	0.948065i	−0.121690	+	0.0461511i
$423$	−6.14729	+	2.33136i	−0.298891	+	0.113355i
$424$	−1.87164	−	1.29190i	−0.0908947	−	0.0627401i
$425$	−30.0920	+	7.41701i	−1.45968	+	0.359778i
$426$	4.01490	+	3.55689i	0.194522	+	0.172332i
$427$			8.01919i			0.388076i
$428$	−6.42953	+	5.69607i	−0.310783	+	0.275330i
$429$	−2.34442	−	3.02738i	−0.113190	−	0.146163i
$430$	−11.7728	−	10.4298i	−0.567735	−	0.502970i
$431$	17.1051	−	19.3076i	0.823922	−	0.930016i	−0.174585	−	0.984642i	$-0.555858\pi$
$431$	17.1051	−	19.3076i	0.823922	−	0.930016i	0.998507	+	0.0546262i	$0.0173967\pi$
$432$	0.851214	+	2.24447i	0.0409541	+	0.107987i
$433$	4.58216	−	37.7374i	0.220204	−	1.81355i	−0.293920	−	0.955830i	$-0.594960\pi$
$433$	4.58216	−	37.7374i	0.220204	−	1.81355i	0.514124	−	0.857716i	$-0.328117\pi$
$434$	8.67196	−	3.28884i	0.416267	−	0.157869i
$435$	−29.5389	+	3.58668i	−1.41628	+	0.171968i
$436$	−22.2606	+	15.3654i	−1.06609	+	0.735869i
$437$		−	10.7522i		−	0.514348i
$438$	3.75154	+	5.43504i	0.179255	+	0.259696i
$439$	37.2170	+	9.17316i	1.77627	+	0.437811i	0.984842	−	0.173453i	$-0.0554926\pi$
$439$	37.2170	+	9.17316i	1.77627	+	0.437811i	0.791427	+	0.611264i	$0.209339\pi$
$440$	−5.24564	−	5.92111i	−0.250076	−	0.282278i
$441$	−0.247356	−	0.358357i	−0.0117789	−	0.0170646i
$442$	−6.21893	−	1.17588i	−0.295804	−	0.0559308i
$443$	−12.0339	+	17.4341i	−0.571747	+	0.828319i	−0.997052	−	0.0767316i	$-0.975552\pi$
$443$	−12.0339	+	17.4341i	−0.571747	+	0.828319i	0.425305	+	0.905050i	$0.360167\pi$
$444$	−13.7847	+	1.67377i	−0.654193	+	0.0794334i
$445$	−7.74071	+	63.7505i	−0.366945	+	3.02206i
$446$	−4.26147	−	2.23659i	−0.201786	−	0.105906i
$447$	−2.70379	+	10.9697i	−0.127885	+	0.518850i
$448$	5.54675	+	0.673497i	0.262059	+	0.0318197i
$449$	0.491619	−	0.554923i	0.0232009	−	0.0261885i	−0.736796	−	0.676115i	$-0.763662\pi$
$449$	0.491619	−	0.554923i	0.0232009	−	0.0261885i	0.759997	+	0.649927i	$0.225201\pi$
$450$	−4.06301	+	2.80449i	−0.191532	+	0.132205i
$451$	−0.162192	+	0.234976i	−0.00763733	+	0.0110646i
$452$	−1.84304	+	0.454268i	−0.0866893	+	0.0213670i
$453$	−19.4435	−	2.36087i	−0.913535	−	0.110923i
$454$	−9.53670	+	5.00525i	−0.447580	+	0.234908i
$455$	2.03845	+	37.1698i	0.0955640	+	1.74255i
$456$	8.54876	+	4.48674i	0.400332	+	0.210111i
$457$	10.6987	+	7.38475i	0.500462	+	0.345444i	0.791401	−	0.611298i	$-0.209352\pi$
$457$	10.6987	+	7.38475i	0.500462	+	0.345444i	−0.290939	+	0.956742i	$0.593968\pi$
$458$	3.37393	−	4.88798i	0.157653	−	0.228400i
$459$	−2.48476	+	2.20131i	−0.115979	+	0.102748i
$460$	−9.46388	−	10.6825i	−0.441255	−	0.498074i
$461$	25.3342	+	9.60800i	1.17993	+	0.447489i	0.865071	−	0.501649i	$-0.167273\pi$
$461$	25.3342	+	9.60800i	1.17993	+	0.447489i	0.314861	+	0.949138i	$0.398042\pi$
$462$	0.711620	−	1.35588i	0.0331076	−	0.0630812i
$463$	5.71297	+	2.16664i	0.265504	+	0.100692i	0.483765	−	0.875198i	$-0.339269\pi$
$463$	5.71297	+	2.16664i	0.265504	+	0.100692i	−0.218261	+	0.975891i	$0.570038\pi$
$464$	18.3165	+	4.51462i	0.850323	+	0.209586i
$465$	−18.2295	+	16.1499i	−0.845373	+	0.748935i
$466$	6.38385	−	4.40645i	0.295726	−	0.204125i
$467$	−10.7755	−	28.4127i	−0.498632	−	1.31478i	−0.914215	−	0.405229i	$-0.867192\pi$
$467$	−10.7755	−	28.4127i	−0.498632	−	1.31478i	0.415584	−	0.909555i	$-0.363577\pi$
$468$	6.10750	−	1.08375i	0.282320	−	0.0500962i
$469$	11.5871	−	30.5527i	0.535044	−	1.41079i
$470$	3.15020	+	12.7809i	0.145308	+	0.589537i
$471$	8.74010	−	4.58716i	0.402723	−	0.211365i
$472$	2.96609	+	7.82093i	0.136525	+	0.359987i
$473$	−8.28164	+	1.00557i	−0.380790	+	0.0462363i
$474$	4.27486	+	2.95072i	0.196351	+	0.135531i
$475$	10.9649	−	44.4865i	0.503106	−	2.04118i
$476$	3.72679	+	15.1202i	0.170817	+	0.693032i
$477$	0.139340	+	1.14757i	0.00637996	+	0.0525437i
$478$	−2.78589	+	7.34578i	−0.127424	+	0.335988i
$479$	−5.62612	+	22.8261i	−0.257064	+	1.04295i	0.690487	+	0.723345i	$0.257396\pi$
$479$	−5.62612	+	22.8261i	−0.257064	+	1.04295i	−0.947551	+	0.319605i	$0.896450\pi$
$480$	19.1313	−	4.71544i	0.873221	−	0.215230i
$481$	−1.92061	+	29.0386i	−0.0875724	+	1.32405i
$482$	7.28841	+	1.79643i	0.331978	+	0.0818252i
$483$	2.77640	−	5.28998i	0.126330	−	0.240702i
$484$	16.9839			0.771997
$485$	−60.4396			−2.74442
$486$	−0.245742	+	0.468223i	−0.0111471	+	0.0212390i
$487$	1.48417	+	1.67529i	0.0672544	+	0.0759145i	0.781175	−	0.624312i	$-0.214621\pi$
$487$	1.48417	+	1.67529i	0.0672544	+	0.0759145i	−0.713921	+	0.700227i	$0.753082\pi$
$488$		−	5.78562i		−	0.261903i
$489$	−6.59656	+	7.44598i	−0.298307	+	0.336719i
$490$	−0.771960	+	0.405156i	−0.0348736	+	0.0183031i
$491$	−0.424022	−	3.49213i	−0.0191358	−	0.157598i	0.980009	−	0.198955i	$-0.0637548\pi$
$491$	−0.424022	−	3.49213i	−0.0191358	−	0.157598i	−0.999144	+	0.0413574i	$0.986832\pi$
$492$	−0.214949	−	0.409551i	−0.00969064	−	0.0184640i
$493$	3.14457	+	25.8979i	0.141624	+	1.16638i
$494$	5.81179	−	7.33281i	0.261485	−	0.329919i
$495$	−0.484676	+	3.99167i	−0.0217846	+	0.179412i
$496$	14.4369	−	5.47518i	0.648234	−	0.245843i
$497$	−24.4913	−	12.8540i	−1.09858	−	0.576581i
$498$	1.84359	−	4.86115i	0.0826134	−	0.217834i
$499$	10.7881	+	20.5549i	0.482940	+	0.920166i	0.998012	+	0.0630189i	$0.0200728\pi$
$499$	10.7881	+	20.5549i	0.482940	+	0.920166i	−0.515072	+	0.857147i	$0.672235\pi$
$500$	−13.1264	−	25.0103i	−0.587032	−	1.11850i
$501$	4.22751	+	17.1517i	0.188871	+	0.766280i
$502$	10.1984	+	1.23831i	0.455177	+	0.0552685i
$503$	25.6854	+	22.7552i	1.14525	+	1.01461i	0.999681	+	0.0252584i	$0.00804084\pi$
$503$	25.6854	+	22.7552i	1.14525	+	1.01461i	0.145572	+	0.989348i	$0.453498\pi$
$504$	3.04736	+	4.41486i	0.135740	+	0.196654i
$505$	17.5885	+	6.67044i	0.782678	+	0.296830i
$506$	1.23037			0.0546964
$507$	0.146340	−	12.9992i	0.00649919	−	0.577314i
$508$	−0.361280			−0.0160292
$509$	−11.4399	−	4.33859i	−0.507066	−	0.192305i	0.0877872	−	0.996139i	$-0.472020\pi$
$509$	−11.4399	−	4.33859i	−0.507066	−	0.192305i	−0.594853	+	0.803835i	$0.702790\pi$
$510$	3.77561	+	5.46991i	0.167187	+	0.242212i
$511$	−25.4904	−	22.5825i	−1.12763	−	0.998993i
$512$	−21.7768	−	2.64419i	−0.962409	−	0.116858i
$513$	−1.17445	−	4.76493i	−0.0518533	−	0.210377i
$514$	−1.00004	−	1.90541i	−0.0441098	−	0.0840441i
$515$	0.481616	+	0.917643i	0.0212225	+	0.0404362i
$516$	4.79234	−	12.6364i	0.210971	−	0.556285i
$517$	6.18225	+	3.24469i	0.271895	+	0.142701i
$518$	−10.8820	+	4.12701i	−0.478128	+	0.181330i
$519$	3.08337	−	25.3938i	0.135345	−	1.11467i
$520$	−1.47068	−	26.8170i	−0.0644937	−	1.17600i
$521$	−3.27149	−	26.9431i	−0.143327	−	1.18040i	−0.869871	−	0.493280i	$-0.835798\pi$
$521$	−3.27149	−	26.9431i	−0.143327	−	1.18040i	0.726544	−	0.687120i	$-0.241125\pi$
$522$	1.93124	+	3.67966i	0.0845279	+	0.161054i
$523$	−0.214136	−	1.76357i	−0.00936353	−	0.0771156i	0.987278	−	0.159004i	$-0.0508281\pi$
$523$	−0.214136	−	1.76357i	−0.00936353	−	0.0771156i	−0.996642	+	0.0818879i	$0.973905\pi$
$524$	7.70178	−	4.04221i	0.336454	−	0.176585i
$525$	16.8818	−	19.0556i	0.736781	−	0.831654i
$526$			5.06993i			0.221059i
$527$	14.1592	+	15.9825i	0.616786	+	0.696207i
$528$	1.18469	−	2.25723i	0.0515569	−	0.0982335i
$529$	−18.1997			−0.791292
$530$	2.31452			0.100536
$531$	1.97588	−	3.76473i	0.0857460	−	0.163375i
$532$	−22.3529	−	5.50950i	−0.969121	−	0.238867i
$533$	−0.927084	+	0.283176i	−0.0401565	+	0.0122657i
$534$	8.70809	−	2.14635i	0.376836	−	0.0928817i
$535$	4.52424	−	18.3556i	0.195600	−	0.793580i
$536$	−8.35978	+	22.0429i	−0.361088	+	0.952110i
$537$	−0.757635	−	6.23969i	−0.0326944	−	0.269262i
$538$	0.810346	+	3.28770i	0.0349365	+	0.141743i
$539$	−0.110665	+	0.448987i	−0.00476669	+	0.0193392i
$540$	−5.36084	−	3.70032i	−0.230694	−	0.159236i
$541$	3.74774	−	0.455059i	0.161128	−	0.0195645i	−0.0395750	−	0.999217i	$-0.512600\pi$
$541$	3.74774	−	0.455059i	0.161128	−	0.0195645i	0.200703	+	0.979652i	$0.435677\pi$
$542$	−4.30972	−	11.3638i	−0.185118	−	0.488117i
$543$	−18.6113	+	9.76798i	−0.798689	+	0.419184i
$544$	−4.13420	−	16.7731i	−0.177252	−	0.719141i
$545$	21.1098	−	55.6619i	0.904244	−	2.38430i
$546$	4.75280	−	2.10697i	0.203401	−	0.0901700i
$547$	13.6256	+	35.9276i	0.582587	+	1.53615i	0.824503	+	0.565857i	$0.191455\pi$
$547$	13.6256	+	35.9276i	0.582587	+	1.53615i	−0.241917	+	0.970297i	$0.577776\pi$
$548$	28.2621	−	19.5079i	1.20730	−	0.833338i
$549$	−2.20128	+	1.95016i	−0.0939483	+	0.0832310i
$550$	5.09055	+	1.25471i	0.217062	+	0.0535009i
$551$	−36.0610	−	13.6761i	−1.53625	−	0.582624i
$552$	−2.00309	+	3.81657i	−0.0852572	+	0.162444i
$553$	−25.0448	−	9.49824i	−1.06501	−	0.403906i
$554$	−0.559307	−	0.631327i	−0.0237627	−	0.0268225i
$555$	22.8753	−	20.2658i	0.971003	−	0.860234i
$556$	−3.50632	+	5.07978i	−0.148701	+	0.215431i
$557$	36.6830	+	25.3204i	1.55431	+	1.07286i	0.964076	+	0.265628i	$0.0855793\pi$
$557$	36.6830	+	25.3204i	1.55431	+	1.07286i	0.590233	+	0.807233i	$0.299036\pi$
$558$	3.01170	+	1.58066i	0.127495	+	0.0669148i
$559$	−24.1561	−	14.7892i	−1.02169	−	0.625515i
$560$	−21.9448	+	11.5175i	−0.927337	+	0.486704i
$561$	3.49964	+	0.424933i	0.147755	+	0.0179407i
$562$	4.21807	−	1.03966i	0.177928	−	0.0438554i
$563$	2.96702	−	4.29847i	0.125045	−	0.181159i	−0.755461	−	0.655193i	$-0.772587\pi$
$563$	2.96702	−	4.29847i	0.125045	−	0.181159i	0.880507	+	0.474034i	$0.157203\pi$
$564$	−9.30850	+	6.42519i	−0.391958	+	0.270549i
$565$	2.77031	−	3.12703i	0.116548	−	0.131555i
$566$	−2.68680	−	0.326237i	−0.112935	−	0.0137128i
$567$	0.652566	−	2.64756i	0.0274052	−	0.111187i
$568$	17.6697	+	9.27380i	0.741406	+	0.389120i
$569$	−4.32830	+	35.6467i	−0.181452	+	1.49439i	0.562858	+	0.826554i	$0.309702\pi$
$569$	−4.32830	+	35.6467i	−0.181452	+	1.49439i	−0.744310	+	0.667835i	$0.767221\pi$
$570$	−9.75412	+	1.18436i	−0.408555	+	0.0496076i
$571$	−11.3456	+	16.4370i	−0.474800	+	0.687866i	−0.985071	−	0.172147i	$-0.944930\pi$
$571$	−11.3456	+	16.4370i	−0.474800	+	0.687866i	0.510272	+	0.860013i	$0.329545\pi$
$572$	−5.16251	−	4.09167i	−0.215855	−	0.171081i
$573$	9.51514	+	13.7851i	0.397501	+	0.575879i
$574$	−0.257069	−	0.290171i	−0.0107298	−	0.0121115i
$575$	19.8609	+	4.89526i	0.828255	+	0.204147i
$576$	1.16402	+	1.68638i	0.0485009	+	0.0702657i
$577$		−	1.79919i		−	0.0749012i	−0.999298	−	0.0374506i	$-0.988076\pi$
$577$		−	1.79919i		−	0.0749012i	0.999298	−	0.0374506i	$-0.0119237\pi$
$578$	−2.60252	+	1.79639i	−0.108251	+	0.0747200i
$579$	7.51872	−	0.912938i	0.312467	−	0.0379404i
$580$	−47.8648	+	18.1527i	−1.98748	+	0.753750i
$581$	−3.23152	+	26.6140i	−0.134066	+	1.10413i
$582$	2.99319	+	7.89239i	0.124072	+	0.327150i
$583$	0.814079	−	0.918906i	0.0337157	−	0.0380572i
$584$	18.3906	+	16.2927i	0.761009	+	0.674195i
$585$	−9.70744	+	9.59877i	−0.401353	+	0.396860i
$586$	10.7465	−	9.52053i	0.443932	−	0.393290i
$587$		−	19.6810i		−	0.812321i	−0.913802	−	0.406160i	$-0.866867\pi$
$587$		−	19.6810i		−	0.812321i	0.913802	−	0.406160i	$-0.133133\pi$
$588$	−0.560721	−	0.496756i	−0.0231238	−	0.0204859i
$589$	−30.6490	+	7.55430i	−1.26287	+	0.311269i
$590$	−7.00585	−	4.83579i	−0.288426	−	0.199086i
$591$	−0.131781	+	0.0499778i	−0.00542073	+	0.00205581i
$592$	−18.1161	+	6.87054i	−0.744568	+	0.282377i
$593$	−6.89083	−	4.75640i	−0.282972	−	0.195322i	0.418121	−	0.908391i	$-0.362689\pi$
$593$	−6.89083	−	4.75640i	−0.282972	−	0.195322i	−0.701093	+	0.713070i	$0.747304\pi$
$594$	0.545248	−	0.134391i	0.0223718	−	0.00551415i
$595$	−25.6540	−	22.7275i	−1.05171	−	0.931735i
$596$			19.4369i			0.796166i
$597$	−1.43831	+	1.27423i	−0.0588660	+	0.0521508i
$598$	3.27371	+	2.59466i	0.133872	+	0.106103i
$599$	18.3140	+	16.2248i	0.748290	+	0.662927i	0.948483	−	0.316829i	$-0.102618\pi$
$599$	18.3140	+	16.2248i	0.748290	+	0.662927i	−0.200192	+	0.979757i	$0.564157\pi$
$600$	−12.1797	+	13.7481i	−0.497235	+	0.561262i
$601$	−4.32675	−	11.4087i	−0.176492	−	0.465371i	0.817355	−	0.576135i	$-0.195440\pi$
$601$	−4.32675	−	11.4087i	−0.176492	−	0.465371i	−0.993847	+	0.110764i	$0.964670\pi$
$602$	1.36533	−	11.2445i	0.0556466	−	0.458291i
$603$	11.2046	−	4.24935i	0.456287	−	0.173047i
$604$	−33.4502	+	4.06158i	−1.36107	+	0.165264i
$605$	−30.7626	+	21.2339i	−1.25068	+	0.863280i
$606$		−	2.62711i		−	0.106719i
$607$	7.09052	+	10.2724i	0.287795	+	0.416943i	0.940040	−	0.341065i	$-0.110788\pi$
$607$	7.09052	+	10.2724i	0.287795	+	0.416943i	−0.652244	+	0.758009i	$0.726172\pi$
$608$	24.7965	+	6.11180i	1.00563	+	0.247866i
$609$	−14.2103	−	16.0401i	−0.575830	−	0.649977i
$610$	3.34486	+	4.84586i	0.135429	+	0.196203i
$611$	9.60692	+	21.6708i	0.388654	+	0.876707i
$612$	−3.24420	+	4.70004i	−0.131139	+	0.189988i
$613$	−11.2604	+	1.36726i	−0.454804	+	0.0552232i	−0.344734	−	0.938701i	$-0.612031\pi$
$613$	−11.2604	+	1.36726i	−0.454804	+	0.0552232i	−0.110070	+	0.993924i	$0.535108\pi$
$614$	−0.457883	+	3.77101i	−0.0184787	+	0.152185i
$615$	0.901366	+	0.473073i	0.0363466	+	0.0190762i
$616$	1.36336	−	5.53139i	0.0549315	−	0.222866i
$617$	41.8443	+	5.08082i	1.68459	+	0.204546i	0.906085	−	0.423095i	$-0.139056\pi$
$617$	41.8443	+	5.08082i	1.68459	+	0.204546i	0.778503	+	0.627641i	$0.215980\pi$
$618$	0.0959773	−	0.108336i	0.00386077	−	0.00435791i
$619$	−14.1633	+	9.77625i	−0.569273	+	0.392941i	−0.817644	−	0.575724i	$-0.804720\pi$
$619$	−14.1633	+	9.77625i	−0.569273	+	0.392941i	0.248371	+	0.968665i	$0.420105\pi$
$620$	−23.8012	+	34.4820i	−0.955878	+	1.38483i
$621$	2.12729	−	0.524330i	0.0853653	−	0.0210406i
$622$	−11.1532	−	1.35425i	−0.447204	−	0.0543004i
$623$	−40.9510	+	21.4927i	−1.64067	+	0.861089i
$624$	7.91234	−	3.50763i	0.316747	−	0.140418i
$625$	13.7103	+	7.19574i	0.548413	+	0.287829i
$626$	−5.82058	−	4.01765i	−0.232637	−	0.160578i
$627$	−2.96058	+	4.28914i	−0.118234	+	0.171292i
$628$	12.7108	−	11.2608i	0.507215	−	0.449353i
$629$	−17.7677	−	20.0556i	−0.708446	−	0.799670i
$630$	−5.10476	−	1.93598i	−0.203378	−	0.0771313i
$631$	3.61164	−	6.88140i	0.143777	−	0.273944i	−0.802909	−	0.596101i	$-0.796716\pi$
$631$	3.61164	−	6.88140i	0.143777	−	0.273944i	0.946686	+	0.322157i	$0.104408\pi$
$632$	18.0691	+	6.85271i	0.718750	+	0.272586i
$633$	4.90909	+	1.20998i	0.195119	+	0.0480925i
$634$	6.93952	−	6.14788i	0.275603	−	0.244163i
$635$	0.654378	−	0.451684i	0.0259682	−	0.0179245i
$636$	0.705223	+	1.85952i	0.0279639	+	0.0737348i
$637$	−1.24130	+	0.961271i	−0.0491821	+	0.0380869i
$638$	1.56495	−	4.12644i	0.0619570	−	0.163367i
$639$	−2.42752	−	9.84882i	−0.0960310	−	0.389613i
$640$	38.5265	−	20.2203i	1.52290	−	0.799277i
$641$	−2.90934	−	7.67131i	−0.114912	−	0.302999i	0.865205	−	0.501418i	$-0.167188\pi$
$641$	−2.90934	−	7.67131i	−0.114912	−	0.302999i	−0.980117	+	0.198420i	$0.936419\pi$
$642$	−2.62098	+	0.318245i	−0.103442	+	0.0125601i
$643$	−12.1232	−	8.36804i	−0.478092	−	0.330003i	0.304527	−	0.952504i	$-0.401502\pi$
$643$	−12.1232	−	8.36804i	−0.478092	−	0.330003i	−0.782619	+	0.622500i	$0.786117\pi$
$644$	2.45970	−	9.97940i	0.0969258	−	0.393243i
$645$	7.11816	+	28.8795i	0.280277	+	1.13713i
$646$	1.03838	+	8.55180i	0.0408544	+	0.336466i
$647$	7.01235	−	18.4901i	0.275684	−	0.726919i	−0.723641	−	0.690177i	$-0.757533\pi$
$647$	7.01235	−	18.4901i	0.275684	−	0.726919i	0.999325	−	0.0367423i	$-0.0116981\pi$
$648$	−0.470808	+	1.91014i	−0.0184951	+	0.0750375i
$649$	−4.38404	+	1.08057i	−0.172089	+	0.0424161i
$650$	10.8988	+	14.0737i	0.427485	+	0.552016i
$651$	−17.0297	−	4.19743i	−0.667445	−	0.164510i
$652$	−7.95320	+	15.1536i	−0.311471	+	0.593459i
$653$	13.2603			0.518914			0.259457	−	0.965755i	$-0.416456\pi$
$653$	13.2603			0.518914			0.259457	+	0.965755i	$0.416456\pi$
$654$	−8.31394			−0.325101
$655$	−8.89635	+	16.9506i	−0.347609	+	0.662314i
$656$	−0.427962	−	0.483069i	−0.0167091	−	0.0188607i
$657$		−	12.4889i		−	0.487240i
$658$	−6.28632	+	7.09579i	−0.245066	+	0.276623i
$659$	−10.7548	+	5.64457i	−0.418949	+	0.219881i	−0.661006	−	0.750381i	$-0.729870\pi$
$659$	−10.7548	+	5.64457i	−0.418949	+	0.219881i	0.242057	+	0.970262i	$0.422178\pi$
$660$	0.833827	+	6.86718i	0.0324567	+	0.267305i
$661$	8.07816	+	15.3916i	0.314204	+	0.598666i	0.990428	−	0.138030i	$-0.0440772\pi$
$661$	8.07816	+	15.3916i	0.314204	+	0.598666i	−0.676224	+	0.736696i	$0.736385\pi$
$662$	−1.23351	−	10.1589i	−0.0479419	−	0.394837i
$663$	8.41559	+	8.51087i	0.326835	+	0.330535i
$664$	2.33145	−	19.2012i	0.0904779	−	0.745153i
$665$	47.3755	−	17.9671i	1.83714	−	0.696736i
$666$	−3.77924	−	1.98350i	−0.146442	−	0.0768589i
$667$	6.10568	−	16.0994i	0.236413	−	0.623369i
$668$	14.1232	+	26.9094i	0.546441	+	1.04116i
$669$	4.22962	+	8.05886i	0.163526	+	0.311574i
$670$	−5.74185	−	23.2956i	−0.221827	−	0.899987i
$671$	3.10038	+	0.376454i	0.119689	+	0.0145328i
$672$	10.6215	+	9.40982i	0.409733	+	0.362992i
$673$	−23.2965	−	33.7508i	−0.898014	−	1.30100i	−0.953144	−	0.302518i	$-0.902173\pi$
$673$	−23.2965	−	33.7508i	−0.898014	−	1.30100i	0.0551302	−	0.998479i	$-0.482443\pi$
$674$	2.53485	+	0.961341i	0.0976387	+	0.0370295i
$675$	9.33622			0.359351
$676$	−5.10749	−	21.7739i	−0.196442	−	0.837458i
$677$	21.2124			0.815258			0.407629	−	0.913148i	$-0.366356\pi$
$677$	21.2124			0.815258			0.407629	+	0.913148i	$0.366356\pi$
$678$	−0.545534	−	0.206894i	−0.0209511	−	0.00794571i
$679$	−24.7261	−	35.8219i	−0.948900	−	1.37472i
$680$	18.5086	+	16.3972i	0.709774	+	0.628805i
$681$	20.2194	+	2.45508i	0.774808	+	0.0940787i
$682$	−0.864432	−	3.50714i	−0.0331008	−	0.134295i
$683$	16.7760	+	31.9640i	0.641916	+	1.22307i	0.961316	+	0.275448i	$0.0888263\pi$
$683$	16.7760	+	31.9640i	0.641916	+	1.22307i	−0.319400	+	0.947620i	$0.603481\pi$
$684$	−3.92357	−	7.47575i	−0.150022	−	0.285842i
$685$	−26.8010	+	70.6685i	−1.02402	+	2.70011i
$686$	8.38130	+	4.39885i	0.320000	+	0.167949i
$687$	−10.5020	+	3.98288i	−0.400676	+	0.151956i
$688$	2.27297	−	18.7196i	0.0866560	−	0.713676i
$689$	4.10391	−	0.728219i	0.156346	−	0.0277429i
$690$	−0.528757	−	4.35470i	−0.0201294	−	0.165781i
$691$	18.6520	+	35.5383i	0.709554	+	1.35194i	0.926700	+	0.375802i	$0.122633\pi$
$691$	18.6520	+	35.5383i	0.709554	+	1.35194i	−0.217146	+	0.976139i	$0.569675\pi$
$692$	−5.30457	−	43.6870i	−0.201649	−	1.66073i
$693$	−2.56410	+	1.34574i	−0.0974022	+	0.0511206i
$694$	3.67641	−	4.14981i	0.139555	−	0.157525i
$695$		−	13.5846i		−	0.515294i
$696$	10.2523	+	11.5725i	0.388613	+	0.438653i
$697$	0.414760	−	0.790260i	0.0157102	−	0.0299332i
$698$	−18.2702			−0.691537
$699$	−14.6692			−0.554839
$700$	20.3537	−	38.7807i	0.769296	−	1.46577i
$701$	43.1294	+	10.6304i	1.62898	+	0.401506i	0.944757	−	0.327771i	$-0.106297\pi$
$701$	43.1294	+	10.6304i	1.62898	+	0.401506i	0.684218	+	0.729277i	$0.260144\pi$
$702$	1.73419	+	0.792262i	0.0654526	+	0.0299020i
$703$	38.4599	−	9.47952i	1.45054	−	0.357527i
$704$	0.520774	−	2.11286i	0.0196274	−	0.0796316i
$705$	8.82727	−	23.2756i	0.332454	−	0.876610i
$706$	1.48806	+	12.2553i	0.0560038	+	0.461233i
$707$	3.24203	+	13.1534i	0.121929	+	0.494685i
$708$	1.75050	−	7.10205i	0.0657878	−	0.266911i
$709$	−14.7118	−	10.1548i	−0.552512	−	0.381372i	0.258848	−	0.965918i	$-0.416657\pi$
$709$	−14.7118	−	10.1548i	−0.552512	−	0.381372i	−0.811360	+	0.584546i	$0.801272\pi$
$710$	−20.1612	+	2.44801i	−0.756635	+	0.0918721i
$711$	−3.48329	−	9.18468i	−0.130634	−	0.344453i
$712$	29.5450	−	15.5064i	1.10725	−	0.581127i
$713$	−3.37260	−	13.6832i	−0.126305	−	0.512438i
$714$	−1.69734	+	4.47553i	−0.0635215	+	0.167492i
$715$	14.4663	+	0.956799i	0.541008	+	0.0357822i
$716$	−3.83451	−	10.1108i	−0.143302	−	0.377857i
$717$	12.2271	−	8.43978i	0.456631	−	0.315189i
$718$	−0.975154	+	0.863911i	−0.0363924	+	0.0322409i
$719$	15.9552	+	3.93260i	0.595029	+	0.146661i	0.525318	−	0.850906i	$-0.323946\pi$
$719$	15.9552	+	3.93260i	0.595029	+	0.146661i	0.0697104	+	0.997567i	$0.477792\pi$
$720$	−8.49827	−	3.22297i	−0.316712	−	0.120113i
$721$	−0.346846	+	0.660860i	−0.0129172	+	0.0246117i
$722$	−2.51364	−	0.953299i	−0.0935481	−	0.0354781i
$723$	−9.41343	−	10.6256i	−0.350089	−	0.395169i
$724$	−27.0665	+	23.9789i	−1.00592	+	0.891167i
$725$	41.6797	−	60.3834i	1.54794	−	2.24259i
$726$	4.29626	+	2.96550i	0.159449	+	0.110060i
$727$	−4.08644	−	2.14473i	−0.151558	−	0.0795436i	0.387239	−	0.921979i	$-0.373429\pi$
$727$	−4.08644	−	2.14473i	−0.151558	−	0.0795436i	−0.538797	+	0.842436i	$0.681121\pi$
$728$	15.2925	−	11.8426i	0.566776	−	0.438915i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	−24.8228	−	3.01403i	−0.918732	−	0.111554i
$731$	25.3197	−	6.24075i	0.936484	−	0.230823i
$732$	−2.87408	+	4.16383i	−0.106229	+	0.153899i
$733$	7.78911	−	5.37644i	0.287697	−	0.198583i	−0.415471	−	0.909606i	$-0.636383\pi$
$733$	7.78911	−	5.37644i	0.287697	−	0.198583i	0.703169	+	0.711023i	$0.251768\pi$
$734$	12.1928	−	13.7628i	0.450045	−	0.507996i
$735$	1.63668	+	0.198729i	0.0603699	+	0.00733024i
$736$	−2.72859	+	11.0703i	−0.100577	+	0.408058i
$737$	−11.2683	−	5.91408i	−0.415075	−	0.217848i
$738$	0.0171365	−	0.141131i	0.000630802	−	0.00519512i
$739$	39.6184	−	4.81055i	1.45739	−	0.176959i	0.646837	−	0.762628i	$-0.276091\pi$
$739$	39.6184	−	4.81055i	1.45739	−	0.176959i	0.810550	+	0.585669i	$0.199168\pi$
$740$	29.8669	−	43.2697i	1.09793	−	1.59063i
$741$	−16.9226	+	5.16896i	−0.621666	+	0.189887i
$742$	0.946878	+	1.37179i	0.0347610	+	0.0503600i
$743$	18.2833	+	20.6375i	0.670748	+	0.757118i	0.981100	−	0.193504i	$-0.0619852\pi$
$743$	18.2833	+	20.6375i	0.670748	+	0.757118i	−0.310352	+	0.950622i	$0.600447\pi$
$744$	12.2864	+	3.02833i	0.450442	+	0.111024i
$745$	−24.3006	−	35.2056i	−0.890307	−	1.28983i
$746$		−	4.47382i		−	0.163798i
$747$	−8.09145	+	5.58512i	−0.296051	+	0.204349i
$748$	6.02071	−	0.731046i	0.220139	−	0.0267297i
$749$	12.7300	−	4.82787i	0.465145	−	0.176406i
$750$	1.04649	−	8.61859i	0.0382123	−	0.314706i
$751$	11.1751	+	29.4662i	0.407784	+	1.07524i	0.968889	+	0.247494i	$0.0796070\pi$
$751$	11.1751	+	29.4662i	0.407784	+	1.07524i	−0.561105	+	0.827744i	$0.689624\pi$
$752$	−10.4653	+	11.8129i	−0.381631	+	0.430772i
$753$	−14.5420	−	12.8831i	−0.529938	−	0.469484i
$754$	12.8660	−	7.67922i	0.468552	−	0.279661i
$755$	55.5095	−	49.1772i	2.02020	−	1.78974i
$756$		−	4.69113i		−	0.170615i
$757$	−3.80001	−	3.36652i	−0.138114	−	0.122358i	0.591238	−	0.806497i	$-0.298640\pi$
$757$	−3.80001	−	3.36652i	−0.138114	−	0.122358i	−0.729351	+	0.684139i	$0.760178\pi$
$758$	−16.2376	+	4.00221i	−0.589776	+	0.145367i
$759$	−1.91487	−	1.32174i	−0.0695055	−	0.0479762i
$760$	−34.1800	+	12.9628i	−1.23984	+	0.470209i
$761$	−25.6184	+	9.71576i	−0.928665	+	0.352196i	−0.772122	−	0.635475i	$-0.780804\pi$
$761$	−25.6184	+	9.71576i	−0.928665	+	0.352196i	−0.156544	+	0.987671i	$0.550035\pi$
$762$	−0.0913896	−	0.0630817i	−0.00331069	−	0.00228521i
$763$	41.6263	−	10.2600i	1.50697	−	0.371436i
$764$	21.5695	+	19.1089i	0.780356	+	0.691335i
$765$		−	12.5691i		−	0.454436i
$766$	8.50282	−	7.53284i	0.307220	−	0.272173i
$767$	−13.9437	−	6.37016i	−0.503477	−	0.230013i
$768$	−1.48086	−	1.31192i	−0.0534358	−	0.0473400i
$769$	16.2677	−	18.3625i	0.586629	−	0.662168i	−0.377991	−	0.925809i	$-0.623385\pi$
$769$	16.2677	−	18.3625i	0.586629	−	0.662168i	0.964621	+	0.263641i	$0.0849235\pi$
$770$	2.05597	+	5.42114i	0.0740919	+	0.195364i
$771$	−0.490519	+	4.03979i	−0.0176656	+	0.145489i
$772$	12.1833	−	4.62052i	0.438487	−	0.166296i
$773$	47.3066	−	5.74406i	1.70150	−	0.206599i	0.788635	−	0.614862i	$-0.210788\pi$
$773$	47.3066	−	5.74406i	1.70150	−	0.206599i	0.912865	+	0.408263i	$0.133865\pi$
$774$	3.41866	−	2.35973i	0.122881	−	0.0848188i
$775$		−	60.0524i		−	2.15715i
$776$	17.8392	+	25.8445i	0.640389	+	0.927763i
$777$	21.3697	+	5.26715i	0.766633	+	0.188958i
$778$	−8.77046	−	9.89981i	−0.314436	−	0.354925i
$779$	0.749511	+	1.08585i	0.0268540	+	0.0389048i
$780$	−12.2632	+	20.0304i	−0.439095	+	0.717202i
$781$	−6.11933	+	8.86538i	−0.218967	+	0.317228i
$782$	−3.81793	+	0.463580i	−0.136529	+	0.0165776i
$783$	0.947272	−	7.80149i	0.0338527	−	0.278802i
$784$	−0.925521	−	0.485751i	−0.0330543	−	0.0173482i
$785$	−8.94413	+	36.2878i	−0.319230	+	1.29517i
$786$	2.65404	+	0.322259i	0.0946665	+	0.0114946i
$787$	34.8358	−	39.3215i	1.24176	−	1.40166i	0.358001	−	0.933721i	$-0.383459\pi$
$787$	34.8358	−	39.3215i	1.24176	−	1.40166i	0.883761	−	0.467938i	$-0.155003\pi$
$788$	−0.199548	+	0.137738i	−0.00710860	+	0.00490671i
$789$	5.44646	−	7.89056i	0.193899	−	0.280911i
$790$	−19.0959	+	4.70673i	−0.679403	+	0.167458i
$791$	2.98671	+	0.362652i	0.106195	+	0.0128944i
$792$	1.84993	−	0.970917i	0.0657343	−	0.0345000i
$793$	7.45548	+	7.53988i	0.264752	+	0.267749i
$794$	2.65158	+	1.39166i	0.0941010	+	0.0493880i
$795$	−3.60219	−	2.48641i	−0.127756	−	0.0881839i
$796$	−1.87791	+	2.72063i	−0.0665609	+	0.0964301i
$797$	−8.89072	+	7.87649i	−0.314926	+	0.279000i	−0.805746	−	0.592261i	$-0.798235\pi$
$797$	−8.89072	+	7.87649i	−0.314926	+	0.279000i	0.490821	+	0.871261i	$0.336697\pi$
$798$	−4.69241	−	5.29664i	−0.166110	−	0.187499i
$799$	−20.4066	−	7.73919i	−0.721932	−	0.273793i
$800$	−22.5787	+	43.0202i	−0.798279	+	1.52099i
$801$	−15.8586	−	6.01436i	−0.560334	−	0.212507i
$802$	−6.48490	−	1.59838i	−0.228990	−	0.0564409i
$803$	−9.92748	+	8.79498i	−0.350333	+	0.310368i
$804$	16.9665	−	11.7112i	0.598364	−	0.413021i
$805$	8.02138	+	21.1506i	0.282717	+	0.745462i
$806$	5.09599	−	11.1546i	0.179498	−	0.392905i
$807$	2.27070	−	5.98733i	0.0799323	−	0.210764i
$808$	−2.33903	−	9.48982i	−0.0822868	−	0.333851i
$809$	11.4421	−	6.00530i	0.402284	−	0.211135i	−0.251432	−	0.967875i	$-0.580901\pi$
$809$	11.4421	−	6.00530i	0.402284	−	0.211135i	0.653716	+	0.756740i	$0.273209\pi$
$810$	−0.709982	−	1.87207i	−0.0249462	−	0.0657778i
$811$	25.6463	−	3.11402i	0.900563	−	0.109348i	0.342858	−	0.939387i	$-0.388605\pi$
$811$	25.6463	−	3.11402i	0.900563	−	0.109348i	0.557705	+	0.830039i	$0.311682\pi$
$812$	−30.3406	−	20.9426i	−1.06475	−	0.734941i
$813$	−5.50035	+	22.3158i	−0.192906	+	0.782649i
$814$	1.08473	+	4.40094i	0.0380199	+	0.154253i
$815$	−4.54004	−	37.3906i	−0.159031	−	1.30974i
$816$	−2.82570	+	7.45075i	−0.0989191	+	0.260828i
$817$	−9.22601	+	37.4314i	−0.322777	+	1.30956i
$818$	−1.30726	+	0.322211i	−0.0457073	+	0.0112658i
$819$	−9.66045	−	1.82660i	−0.337563	−	0.0638266i
$820$	1.70040	+	0.419111i	0.0593806	+	0.0146360i
$821$	15.6500	−	29.8186i	0.546189	−	1.04068i	−0.443342	−	0.896353i	$-0.646207\pi$
$821$	15.6500	−	29.8186i	0.546189	−	1.04068i	0.989531	−	0.144323i	$-0.0461005\pi$
$822$	10.5554			0.368162
$823$	46.1352			1.60817			0.804086	−	0.594513i	$-0.202655\pi$
$823$	46.1352			1.60817			0.804086	+	0.594513i	$0.202655\pi$
$824$	0.250240	−	0.476792i	0.00871751	−	0.0166098i
$825$	−6.57476	−	7.42137i	−0.228904	−	0.258379i
$826$		−	6.13063i		−	0.213312i
$827$	−10.9813	+	12.3953i	−0.381857	+	0.431027i	−0.907742	−	0.419528i	$-0.862196\pi$
$827$	−10.9813	+	12.3953i	−0.381857	+	0.431027i	0.525886	+	0.850555i	$0.323734\pi$
$828$	3.33753	−	1.75167i	0.115987	−	0.0608747i
$829$	3.86842	+	31.8593i	0.134356	+	1.10652i	0.891419	+	0.453179i	$0.149710\pi$
$829$	3.86842	+	31.8593i	0.134356	+	1.10652i	−0.757063	+	0.653341i	$0.773367\pi$
$830$	9.14812	+	17.4303i	0.317536	+	0.605014i
$831$	0.192261	+	1.58341i	0.00666945	+	0.0549278i
$832$	5.84137	−	4.52360i	0.202513	−	0.156828i
$833$	0.174233	−	1.43494i	0.00603682	−	0.0497177i
$834$	−1.77392	+	0.672760i	−0.0614259	+	0.0232958i
$835$	−59.2240	−	31.0832i	−2.04953	−	1.07568i
$836$	−3.17942	+	8.38343i	−0.109962	+	0.289947i
$837$	−2.98919	−	5.69543i	−0.103322	−	0.196863i
$838$	−4.96061	−	9.45165i	−0.171361	−	0.326502i
$839$	9.66173	+	39.1992i	0.333560	+	1.35331i	0.863105	+	0.505024i	$0.168516\pi$
$839$	9.66173	+	39.1992i	0.333560	+	1.35331i	−0.529545	+	0.848282i	$0.677637\pi$
$840$	−20.1635	−	2.44829i	−0.695705	−	0.0844739i
$841$	−24.5216	−	21.7242i	−0.845572	−	0.749112i
$842$	−3.82715	−	5.54458i	−0.131892	−	0.191079i
$843$	−7.68164	−	2.91326i	−0.264570	−	0.100338i
$844$	8.69825			0.299406
$845$	36.4736	+	33.0530i	1.25473	+	1.13706i
$846$	−3.47656			−0.119527
$847$	−25.1702	−	9.54580i	−0.864858	−	0.327997i
$848$	1.57634	+	2.28372i	0.0541317	+	0.0784234i
$849$	3.83113	+	3.39408i	0.131484	+	0.116485i
$850$	−16.2691	−	1.97543i	−0.558027	−	0.0677568i
$851$	4.23211	+	17.1703i	0.145075	+	0.588591i
$852$	−8.10978	−	15.4519i	−0.277837	−	0.529373i
$853$	14.5995	+	27.8169i	0.499876	+	0.952434i	0.996430	+	0.0844278i	$0.0269062\pi$
$853$	14.5995	+	27.8169i	0.499876	+	0.952434i	−0.496554	+	0.868006i	$0.665401\pi$
$854$	−1.50370	+	3.96493i	−0.0514555	+	0.135677i
$855$	16.4531	+	8.63526i	0.562684	+	0.295320i
$856$	−9.18436	+	3.48317i	−0.313915	+	0.119052i
$857$	−1.14400	+	9.42166i	−0.0390782	+	0.321838i	0.960040	+	0.279861i	$0.0902885\pi$
$857$	−1.14400	+	9.42166i	−0.0390782	+	0.321838i	−0.999119	+	0.0419764i	$0.986635\pi$
$858$	−0.591480	−	1.93643i	−0.0201928	−	0.0661088i
$859$	−1.59170	−	13.1088i	−0.0543081	−	0.447267i	−0.994345	−	0.106195i	$-0.966133\pi$
$859$	−1.59170	−	13.1088i	−0.0543081	−	0.447267i	0.940037	−	0.341072i	$-0.110790\pi$
$860$	23.7802	+	45.3093i	0.810897	+	1.54504i
$861$	0.0883668	+	0.727766i	0.00301153	+	0.0248022i
$862$	12.0777	−	6.33885i	0.411367	−	0.215902i
$863$	−3.16510	+	3.57265i	−0.107741	+	0.121615i	−0.799907	−	0.600124i	$-0.795118\pi$
$863$	−3.16510	+	3.57265i	−0.107741	+	0.121615i	0.692166	+	0.721738i	$0.256657\pi$
$864$			5.20396i			0.177042i
$865$	64.2270	+	72.4973i	2.18378	+	2.46498i
$866$	9.34179	−	17.7993i	0.317447	−	0.604845i
$867$	5.98022			0.203099
$868$	−30.1743			−1.02418
$869$	−4.84791	+	9.23692i	−0.164454	+	0.313341i
$870$	−15.2775	−	3.76556i	−0.517955	−	0.127664i
$871$	−17.5105	−	39.4992i	−0.593320	−	1.33838i
$872$	−30.0322	+	7.40228i	−1.01702	+	0.250673i
$873$	3.82010	−	15.4988i	0.129291	−	0.524554i
$874$	2.01617	−	5.31621i	0.0681980	−	0.179823i
$875$	5.39636	+	44.4431i	0.182430	+	1.50245i
$876$	−5.14187	−	20.8614i	−0.173728	−	0.704841i
$877$	−2.43267	+	9.86972i	−0.0821453	+	0.333277i	−0.997608	−	0.0691265i	$-0.977979\pi$
$877$	−2.43267	+	9.86972i	−0.0821453	+	0.333277i	0.915463	+	0.402403i	$0.131825\pi$
$878$	16.6811	+	11.5141i	0.562959	+	0.388583i
$879$	−26.9528	+	3.27266i	−0.909095	+	0.110384i
$880$	3.42272	+	9.02497i	0.115380	+	0.304232i
$881$	−24.5007	+	12.8590i	−0.825451	+	0.433230i	−0.823877	−	0.566769i	$-0.808193\pi$
$881$	−24.5007	+	12.8590i	−0.825451	+	0.433230i	−0.00157380	+	0.999999i	$0.500501\pi$
$882$	−0.0551038	−	0.223565i	−0.00185544	−	0.00752782i
$883$	2.30780	−	6.08518i	0.0776638	−	0.204783i	−0.890561	−	0.454864i	$-0.849688\pi$
$883$	2.30780	−	6.08518i	0.0776638	−	0.204783i	0.968225	+	0.250081i	$0.0804573\pi$
$884$	17.5613	+	10.7516i	0.590652	+	0.361617i
$885$	5.70859	+	15.0523i	0.191892	+	0.505978i
$886$	−9.21902	+	6.36343i	−0.309719	+	0.213784i
$887$	−27.1129	+	24.0199i	−0.910361	+	0.806509i	−0.981600	−	0.190950i	$-0.938843\pi$
$887$	−27.1129	+	24.0199i	−0.910361	+	0.806509i	0.0712390	+	0.997459i	$0.477305\pi$
$888$	−15.4176	−	3.80010i	−0.517381	−	0.127523i
$889$	0.535417	+	0.203057i	0.0179573	+	0.00681031i
$890$	−15.7812	+	30.0687i	−0.528989	+	1.00790i
$891$	−0.992966	−	0.376582i	−0.0332656	−	0.0126160i
$892$	10.3830	+	11.7200i	0.347650	+	0.392416i
$893$	24.1505	−	21.3955i	0.808165	−	0.715972i
$894$	−3.39380	+	4.91676i	−0.113506	+	0.164441i
$895$	19.5862	+	13.5194i	0.654694	+	0.451902i
$896$	27.7457	+	14.5621i	0.926919	+	0.486485i
$897$	−2.30767	−	7.55503i	−0.0770509	−	0.252255i
$898$	0.347126	−	0.182186i	0.0115838	−	0.00607962i
$899$	−50.1807	−	6.09304i	−1.67362	−	0.203214i
$900$	15.5951	−	3.84385i	0.519837	−	0.128128i
$901$	−2.17993	+	3.15817i	−0.0726239	+	0.105214i
$902$	−0.124253	+	0.0857660i	−0.00413719	+	0.00285569i
$903$	−14.2045	+	16.0336i	−0.472697	+	0.533564i
$904$	−2.15482	−	0.261643i	−0.0716684	−	0.00870212i
$905$	19.0458	−	77.2718i	0.633104	−	2.56860i
$906$	−9.17074	−	4.81318i	−0.304678	−	0.159907i
$907$	−4.04989	+	33.3538i	−0.134474	+	1.10750i	0.756677	+	0.653789i	$0.226822\pi$
$907$	−4.04989	+	33.3538i	−0.134474	+	1.10750i	−0.891151	+	0.453707i	$0.850101\pi$
$908$	34.7850	−	4.22366i	1.15438	−	0.140167i
$909$	−2.82221	+	4.08868i	−0.0936069	+	0.135613i
$910$	−5.96193	+	18.7601i	−0.197636	+	0.621891i
$911$	−24.9466	−	36.1414i	−0.826519	−	1.19742i	−0.977927	−	0.208948i	$-0.932996\pi$
$911$	−24.9466	−	36.1414i	−0.826519	−	1.19742i	0.151408	−	0.988471i	$-0.451619\pi$
$912$	−7.81181	−	8.81771i	−0.258675	−	0.291984i
$913$	10.1378	+	2.49874i	0.335512	+	0.0826962i
$914$	3.90500	+	5.65737i	0.129166	+	0.187129i
$915$		−	11.1351i		−	0.368115i
$916$	−15.9026	+	10.9768i	−0.525436	+	0.362682i
$917$	−13.6860	+	1.66178i	−0.451950	+	0.0548767i
$918$	−1.64131	+	0.622467i	−0.0541713	+	0.0205445i
$919$	2.12364	−	17.4898i	0.0700525	−	0.576934i	−0.914846	−	0.403802i	$-0.867688\pi$
$919$	2.12364	−	17.4898i	0.0700525	−	0.576934i	0.984899	−	0.173132i	$-0.0553886\pi$
$920$	−5.78720	−	15.2596i	−0.190798	−	0.503094i
$921$	4.76369	−	5.37710i	0.156969	−	0.177181i
$922$	10.7244	+	9.50096i	0.353188	+	0.312897i
$923$	−34.9779	+	10.6839i	−1.15131	+	0.351666i
$924$	−3.72898	+	3.30359i	−0.122675	+	0.108680i
$925$			75.3569i			2.47772i
$926$	2.41839	+	2.14251i	0.0794732	+	0.0704071i
$927$	−0.265756	+	0.0655029i	−0.00872856	+	0.00215140i
$928$	33.6574	+	23.2320i	1.10486	+	0.762629i
$929$	18.0640	−	6.85075i	0.592659	−	0.224766i	−0.0399957	−	0.999200i	$-0.512734\pi$
$929$	18.0640	−	6.85075i	0.592659	−	0.224766i	0.632655	+	0.774434i	$0.281965\pi$
$930$	−12.0415	+	4.56675i	−0.394857	+	0.149749i
$931$	1.75865	+	1.21391i	0.0576375	+	0.0397843i
$932$	−24.5032	+	6.03950i	−0.802629	+	0.197830i
$933$	15.9035	+	14.0892i	0.520656	+	0.461261i
$934$		−	16.0686i		−	0.525782i
$935$	−9.99118	+	8.85142i	−0.326747	+	0.289472i
$936$	6.96974	+	1.31784i	0.227813	+	0.0430750i
$937$	33.6585	+	29.8189i	1.09958	+	0.974140i	0.999782	−	0.0208682i	$-0.00664303\pi$
$937$	33.6585	+	29.8189i	1.09958	+	0.974140i	0.0997944	+	0.995008i	$0.468181\pi$
$938$	11.4580	−	12.9335i	0.374118	−	0.422292i
$939$	4.74279	+	12.5057i	0.154775	+	0.408109i
$940$	5.16208	−	42.5136i	0.168369	−	1.38664i
$941$	−27.6809	+	10.4980i	−0.902373	+	0.342225i	−0.761775	−	0.647842i	$-0.775672\pi$
$941$	−27.6809	+	10.4980i	−0.902373	+	0.342225i	−0.140598	+	0.990067i	$0.544903\pi$
$942$	5.18152	−	0.629150i	0.168823	−	0.0204988i
$943$	−0.484777	+	0.334617i	−0.0157865	+	0.0108966i
$944$		−	10.2061i		−	0.332181i
$945$	5.86501	+	8.49693i	0.190789	+	0.276405i
$946$	−4.28325	−	1.05573i	−0.139260	−	0.0343246i
$947$	−3.18351	−	3.59344i	−0.103450	−	0.116771i	0.694505	−	0.719488i	$-0.255623\pi$
$947$	−3.18351	−	3.59344i	−0.103450	−	0.116771i	−0.797955	+	0.602717i	$0.794085\pi$
$948$	−9.59990	−	13.9079i	−0.311790	−	0.451706i
$949$	−44.9620	+	2.46578i	−1.45953	+	0.0800427i
$950$	13.7632	−	19.9394i	0.446536	−	0.646919i
$951$	−17.4047	+	2.11332i	−0.564388	+	0.0685291i
$952$	−2.14650	+	17.6780i	−0.0695685	+	0.572948i
$953$	−11.4163	−	5.99175i	−0.369811	−	0.194092i	0.269572	−	0.962980i	$-0.413118\pi$
$953$	−11.4163	−	5.99175i	−0.369811	−	0.194092i	−0.639383	+	0.768888i	$0.720810\pi$
$954$	−0.146290	+	0.593521i	−0.00473631	+	0.0192160i
$955$	−62.9588	−	7.64458i	−2.03730	−	0.247373i
$956$	16.9493	−	19.1318i	0.548179	−	0.618766i
$957$	−6.86850	+	4.74098i	−0.222027	+	0.153254i
$958$	−7.06190	+	10.2309i	−0.228160	+	0.330546i
$959$	−52.8489	+	13.0261i	−1.70658	+	0.420634i
$960$	−7.70198	−	0.935190i	−0.248580	−	0.0301831i
$961$	−9.18498	+	4.82065i	−0.296290	+	0.155505i
$962$	−6.39470	+	13.9974i	−0.206174	+	0.451294i
$963$	4.42104	+	2.32034i	0.142466	+	0.0747719i
$964$	−20.0988	−	13.8732i	−0.647338	−	0.446825i
$965$	−16.2906	+	23.6010i	−0.524413	+	0.759744i
$966$	2.36467	−	2.09491i	0.0760820	−	0.0674028i
$967$	−7.97376	−	9.00052i	−0.256419	−	0.289437i	0.606178	−	0.795329i	$-0.292702\pi$
$967$	−7.97376	−	9.00052i	−0.256419	−	0.289437i	−0.862597	+	0.505892i	$0.831163\pi$
$968$	18.1596	+	6.88702i	0.583671	+	0.221357i
$969$	7.57084	−	14.4250i	0.243211	−	0.463399i
$970$	−29.8831	−	11.3332i	−0.959489	−	0.363886i
$971$	−5.87757	−	1.44869i	−0.188620	−	0.0464907i	0.143874	−	0.989596i	$-0.454044\pi$
$971$	−5.87757	−	1.44869i	−0.188620	−	0.0464907i	−0.332494	+	0.943105i	$0.607890\pi$
$972$	1.28772	−	1.14082i	0.0413037	−	0.0365919i
$973$	8.05146	−	5.55752i	0.258118	−	0.178166i
$974$	0.419683	+	1.10661i	0.0134475	+	0.0354582i
$975$	−1.84332	−	33.6117i	−0.0590334	−	1.07644i
$976$	−2.50332	+	6.60071i	−0.0801293	+	0.211284i
$977$	−6.52193	−	26.4605i	−0.208655	−	0.846547i	−0.978151	−	0.207895i	$-0.933339\pi$
$977$	−6.52193	−	26.4605i	−0.208655	−	0.846547i	0.769496	−	0.638652i	$-0.220508\pi$
$978$	−4.65775	+	2.44457i	−0.148938	+	0.0781689i
$979$	6.38711	+	16.8414i	0.204133	+	0.538254i
$980$	2.81571	−	0.341889i	0.0899446	−	0.0109213i
$981$	12.9394	+	8.93140i	0.413122	+	0.285158i
$982$	0.445170	−	1.80612i	0.0142059	−	0.0576357i
$983$	−11.7163	−	47.5351i	−0.373693	−	1.51613i	−0.793528	−	0.608533i	$-0.791758\pi$
$983$	−11.7163	−	47.5351i	−0.373693	−	1.51613i	0.419835	−	0.907600i	$-0.362088\pi$
$984$	−0.0637541	−	0.525063i	−0.00203241	−	0.0167384i
$985$	0.189232	−	0.498963i	0.00602943	−	0.0158983i
$986$	−3.30140	+	13.3943i	−0.105138	+	0.426562i
$987$	17.4065	−	4.29031i	0.554054	−	0.136562i
$988$	−26.1391	+	15.6014i	−0.831595	+	0.496347i
$989$	−16.7112	−	4.11893i	−0.531384	−	0.130974i
$990$	−0.988126	+	1.88272i	−0.0314047	+	0.0598366i
$991$	−28.5372			−0.906513			−0.453257	−	0.891380i	$-0.649738\pi$
$991$	−28.5372			−0.906513			−0.453257	+	0.891380i	$0.649738\pi$
$992$	33.4729			1.06277
$993$	−8.99361	+	17.1359i	−0.285404	+	0.543791i
$994$	−9.69892	−	10.9478i	−0.307631	−	0.347244i
$995$		−	7.27564i		−	0.230653i
$996$	−11.2164	+	12.6607i	−0.355405	+	0.401169i
$997$	49.6046	−	26.0345i	1.57099	−	0.824521i	0.570999	−	0.820951i	$-0.306556\pi$
$997$	49.6046	−	26.0345i	1.57099	−	0.824521i	0.999994	−	0.00357008i	$-0.00113639\pi$
$998$	1.47963	+	12.1859i	0.0468370	+	0.385737i
$999$	3.75099	+	7.14692i	0.118676	+	0.226118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.b.25.10	✓	192
169.142	even	26	inner	507.2.p.b.142.10	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.b.25.10	✓	192	1.1	even	1	trivial
507.2.p.b.142.10	yes	192	169.142	even	26	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.494430 + 0.187512i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.28772 - 1.14082i) q^{4} +(3.75871 + 0.456390i) q^{5} +(-0.126548 - 0.513427i) q^{6} +(1.26721 + 2.41446i) q^{7} +(-0.914254 - 1.74197i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})\)	\(q+(0.494430 + 0.187512i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.28772 - 1.14082i) q^{4} +(3.75871 + 0.456390i) q^{5} +(-0.126548 - 0.513427i) q^{6} +(1.26721 + 2.41446i) q^{7} +(-0.914254 - 1.74197i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(1.77284 + 0.930459i) q^{10} +(0.992966 - 0.376582i) q^{11} +(-0.207369 + 1.70783i) q^{12} +(3.43620 + 1.09202i) q^{13} +(0.173803 + 1.43140i) q^{14} +(-1.75959 - 3.35262i) q^{15} +(0.289343 + 2.38296i) q^{16} +(-2.93936 + 1.54270i) q^{17} +(-0.350654 + 0.395807i) q^{18} -4.90754i q^{19} +(-4.31952 - 4.87573i) q^{20} +(1.26721 - 2.41446i) q^{21} +0.561566 q^{22} +2.19096 q^{23} +(-0.914254 + 1.74197i) q^{24} +(9.06493 + 2.23430i) q^{25} +(1.49419 + 1.18426i) q^{26} +(0.970942 - 0.239316i) q^{27} +(1.12266 - 4.55481i) q^{28} +(2.78676 - 7.34809i) q^{29} +(-0.241336 - 1.98758i) q^{30} +(-1.53933 - 6.24529i) q^{31} +(-1.24539 + 5.05274i) q^{32} +(-0.873990 - 0.603272i) q^{33} +(-1.74258 + 0.211588i) q^{34} +(3.66113 + 9.65361i) q^{35} +(1.52332 - 0.799500i) q^{36} +(1.93163 + 7.83691i) q^{37} +(0.920224 - 2.42643i) q^{38} +(-1.05327 - 3.44828i) q^{39} +(-2.64140 - 6.96481i) q^{40} +(-0.221263 + 0.152727i) q^{41} +(1.07929 - 0.956164i) q^{42} +(-7.62733 - 1.87997i) q^{43} +(-1.70828 - 0.647864i) q^{44} +(-1.75959 + 3.35262i) q^{45} +(1.08327 + 0.410832i) q^{46} +(4.35972 + 4.92110i) q^{47} +(1.79677 - 1.59180i) q^{48} +(-0.247356 + 0.358357i) q^{49} +(4.06301 + 2.80449i) q^{50} +(2.93936 + 1.54270i) q^{51} +(-3.17907 - 5.32631i) q^{52} +(1.02359 - 0.537220i) q^{53} +(0.524937 + 0.0637389i) q^{54} +(3.90414 - 0.962285i) q^{55} +(3.04736 - 4.41486i) q^{56} +(-4.03882 + 2.78780i) q^{57} +(2.75572 - 3.11056i) q^{58} +(-4.22074 - 0.512491i) q^{59} +(-1.55888 + 6.32462i) q^{60} +(2.60402 + 1.36669i) q^{61} +(0.409981 - 3.37650i) q^{62} +(-2.70692 + 0.328679i) q^{63} +(1.16402 - 1.68638i) q^{64} +(12.4173 + 5.67284i) q^{65} +(-0.319006 - 0.462159i) q^{66} +(-7.94642 - 8.96966i) q^{67} +(5.54503 + 1.36673i) q^{68} +(-1.24461 - 1.80312i) q^{69} +5.45954i q^{70} +(-8.34800 + 5.76221i) q^{71} +(1.95296 - 0.237133i) q^{72} +(-11.6774 + 4.42864i) q^{73} +(-0.514466 + 4.23700i) q^{74} +(-3.31067 - 8.72952i) q^{75} +(-5.59863 + 6.31954i) q^{76} +(2.16754 + 1.92027i) q^{77} +(0.125827 - 1.90243i) q^{78} +(-7.35264 + 6.51387i) q^{79} +9.08890i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-0.138037 + 0.0340230i) q^{82} +(8.09145 + 5.58512i) q^{83} +(-4.38628 + 1.66350i) q^{84} +(-11.7523 + 4.45706i) q^{85} +(-3.41866 - 2.35973i) q^{86} +(-7.63042 + 1.88073i) q^{87} +(-1.56382 - 1.38542i) q^{88} +16.9607i q^{89} +(-1.49865 + 1.32769i) q^{90} +(1.71774 + 9.68040i) q^{91} +(-2.82134 - 2.49949i) q^{92} +(-4.26534 + 4.81457i) q^{93} +(1.23280 + 3.25064i) q^{94} +(2.23975 - 18.4460i) q^{95} +(4.86579 - 1.84535i) q^{96} +(-15.8462 + 1.92408i) q^{97} +(-0.189497 + 0.130800i) q^{98} +1.06198i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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