LMFDB - Embedded newform 507.2.p.b.25.7

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			25.7
Character	$\chi$	$=$	507.25
Dual form			507.2.p.b.142.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.468954 - 0.177851i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.30873 - 1.15944i) q^{4} +(-1.41049 - 0.171264i) q^{5} +(0.120028 + 0.486973i) q^{6} +(2.16100 + 4.11744i) q^{7} +(0.873690 + 1.66468i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})$	\(q+(-0.468954 - 0.177851i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.30873 - 1.15944i) q^{4} +(-1.41049 - 0.171264i) q^{5} +(0.120028 + 0.486973i) q^{6} +(2.16100 + 4.11744i) q^{7} +(0.873690 + 1.66468i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(0.630994 + 0.331171i) q^{10} +(5.34881 - 2.02854i) q^{11} +(-0.210752 + 1.73570i) q^{12} +(-2.95107 - 2.07152i) q^{13} +(-0.281119 - 2.31522i) q^{14} +(0.660300 + 1.25810i) q^{15} +(0.307849 + 2.53536i) q^{16} +(2.78444 - 1.46139i) q^{17} +(0.332587 - 0.375413i) q^{18} -2.31054i q^{19} +(1.64738 + 1.85951i) q^{20} +(2.16100 - 4.11744i) q^{21} -2.86912 q^{22} +4.82695 q^{23} +(0.873690 - 1.66468i) q^{24} +(-2.89457 - 0.713447i) q^{25} +(1.01550 + 1.49630i) q^{26} +(0.970942 - 0.239316i) q^{27} +(1.94574 - 7.89417i) q^{28} +(-0.989772 + 2.60982i) q^{29} +(-0.0858969 - 0.707425i) q^{30} +(-2.56217 - 10.3951i) q^{31} +(1.20639 - 4.89451i) q^{32} +(-4.70792 - 3.24964i) q^{33} +(-1.56568 + 0.190108i) q^{34} +(-2.34289 - 6.17769i) q^{35} +(1.54818 - 0.812546i) q^{36} +(-0.678374 - 2.75227i) q^{37} +(-0.410932 + 1.08354i) q^{38} +(-0.0284248 + 3.60544i) q^{39} +(-0.947229 - 2.49764i) q^{40} +(1.03921 - 0.717312i) q^{41} +(-1.74570 + 1.54655i) q^{42} +(10.7839 + 2.65798i) q^{43} +(-9.35213 - 3.54679i) q^{44} +(0.660300 - 1.25810i) q^{45} +(-2.26362 - 0.858477i) q^{46} +(2.99600 + 3.38178i) q^{47} +(1.91168 - 1.69360i) q^{48} +(-8.30692 + 12.0347i) q^{49} +(1.23053 + 0.849376i) q^{50} +(-2.78444 - 1.46139i) q^{51} +(1.46037 + 6.13265i) q^{52} +(10.9480 - 5.74593i) q^{53} +(-0.497890 - 0.0604548i) q^{54} +(-7.89184 + 1.94516i) q^{55} +(-4.96616 + 7.19473i) q^{56} +(-1.90154 + 1.31254i) q^{57} +(0.928316 - 1.04785i) q^{58} +(10.6038 + 1.28753i) q^{59} +(0.594527 - 2.41209i) q^{60} +(4.44716 + 2.33405i) q^{61} +(-0.647243 + 5.33052i) q^{62} +(-4.61617 + 0.560505i) q^{63} +(1.46542 - 2.12303i) q^{64} +(3.80767 + 3.42726i) q^{65} +(1.62985 + 2.36124i) q^{66} +(4.90055 + 5.53158i) q^{67} +(-5.33848 - 1.31582i) q^{68} +(-2.74202 - 3.97250i) q^{69} +3.31374i q^{70} +(-2.24960 + 1.55279i) q^{71} +(-1.86632 + 0.226612i) q^{72} +(3.84165 - 1.45695i) q^{73} +(-0.171367 + 1.41134i) q^{74} +(1.05715 + 2.78747i) q^{75} +(-2.67893 + 3.02388i) q^{76} +(19.9111 + 17.6397i) q^{77} +(0.654561 - 1.68573i) q^{78} +(-0.608553 + 0.539131i) q^{79} -3.62882i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-0.614915 + 0.151563i) q^{82} +(-3.64710 - 2.51741i) q^{83} +(-7.60208 + 2.88309i) q^{84} +(-4.17770 + 1.58439i) q^{85} +(-4.58441 - 3.16439i) q^{86} +(2.71009 - 0.667977i) q^{87} +(8.05006 + 7.13173i) q^{88} -9.16163i q^{89} +(-0.533404 + 0.472555i) q^{90} +(2.15208 - 16.6274i) q^{91} +(-6.31720 - 5.59655i) q^{92} +(-7.09954 + 8.01373i) q^{93} +(-0.803534 - 2.11874i) q^{94} +(-0.395713 + 3.25899i) q^{95} +(-4.71341 + 1.78756i) q^{96} +(-11.0160 + 1.33759i) q^{97} +(6.03594 - 4.16631i) q^{98} +5.72055i 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 $

$2$	−0.468954	−	0.177851i	−0.331601	−	0.125760i	0.183185	−	0.983078i	$-0.441359\pi$
$2$	−0.468954	−	0.177851i	−0.331601	−	0.125760i	−0.514786	+	0.857319i	$0.672129\pi$
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$4$	−1.30873	−	1.15944i	−0.654367	−	0.579719i
$5$	−1.41049	−	0.171264i	−0.630789	−	0.0765916i	−0.201103	−	0.979570i	$-0.564453\pi$
$5$	−1.41049	−	0.171264i	−0.630789	−	0.0765916i	−0.429686	+	0.902978i	$0.641376\pi$
$6$	0.120028	+	0.486973i	0.0490012	+	0.198806i
$7$	2.16100	+	4.11744i	0.816780	+	1.55624i	0.830951	+	0.556345i	$0.187797\pi$
$7$	2.16100	+	4.11744i	0.816780	+	1.55624i	−0.0141710	+	0.999900i	$0.504511\pi$
$8$	0.873690	+	1.66468i	0.308896	+	0.588552i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	0.630994	+	0.331171i	0.199538	+	0.104726i
$11$	5.34881	−	2.02854i	1.61273	−	0.611626i	0.626856	−	0.779135i	$-0.284342\pi$
$11$	5.34881	−	2.02854i	1.61273	−	0.611626i	0.985871	+	0.167509i	$0.0535724\pi$
$12$	−0.210752	+	1.73570i	−0.0608390	+	0.501054i
$13$	−2.95107	−	2.07152i	−0.818480	−	0.574535i
$13$	−2.95107	−	2.07152i	−0.818480	−	0.574535i
$14$	−0.281119	−	2.31522i	−0.0751323	−	0.618770i
$15$	0.660300	+	1.25810i	0.170489	+	0.324839i
$16$	0.307849	+	2.53536i	0.0769621	+	0.633840i
$17$	2.78444	−	1.46139i	0.675326	−	0.354438i	−0.0919428	−	0.995764i	$-0.529308\pi$
$17$	2.78444	−	1.46139i	0.675326	−	0.354438i	0.767269	+	0.641326i	$0.221615\pi$
$18$	0.332587	−	0.375413i	0.0783915	−	0.0884857i
$19$		−	2.31054i		−	0.530075i	−0.964238	−	0.265037i	$-0.914616\pi$
$19$		−	2.31054i		−	0.530075i	0.964238	−	0.265037i	$-0.0853843\pi$
$20$	1.64738	+	1.85951i	0.368366	+	0.415799i
$21$	2.16100	−	4.11744i	0.471568	−	0.898498i
$22$	−2.86912			−0.611699
$23$	4.82695			1.00649			0.503244	−	0.864144i	$-0.332140\pi$
$23$	4.82695			1.00649			0.503244	+	0.864144i	$0.332140\pi$
$24$	0.873690	−	1.66468i	0.178341	−	0.339801i
$25$	−2.89457	−	0.713447i	−0.578914	−	0.142689i
$26$	1.01550	+	1.49630i	0.199155	+	0.293448i
$27$	0.970942	−	0.239316i	0.186858	−	0.0460563i
$28$	1.94574	−	7.89417i	0.367710	−	1.49186i
$29$	−0.989772	+	2.60982i	−0.183796	+	0.484631i	−0.994970	−	0.100175i	$-0.968060\pi$
$29$	−0.989772	+	2.60982i	−0.183796	+	0.484631i	0.811174	+	0.584805i	$0.198829\pi$
$30$	−0.0858969	−	0.707425i	−0.0156826	−	0.129158i
$31$	−2.56217	−	10.3951i	−0.460179	−	1.86702i	−0.497087	−	0.867701i	$-0.665597\pi$
$31$	−2.56217	−	10.3951i	−0.460179	−	1.86702i	0.0369082	−	0.999319i	$-0.488249\pi$
$32$	1.20639	−	4.89451i	0.213261	−	0.865235i
$33$	−4.70792	−	3.24964i	−0.819544	−	0.565690i
$34$	−1.56568	+	0.190108i	−0.268513	+	0.0326033i
$35$	−2.34289	−	6.17769i	−0.396020	−	1.04422i
$36$	1.54818	−	0.812546i	0.258029	−	0.135424i
$37$	−0.678374	−	2.75227i	−0.111524	−	0.452470i	0.888455	−	0.458964i	$-0.151779\pi$
$37$	−0.678374	−	2.75227i	−0.111524	−	0.452470i	−0.999979	+	0.00649341i	$0.997933\pi$
$38$	−0.410932	+	1.08354i	−0.0666619	+	0.175773i
$39$	−0.0284248	+	3.60544i	−0.00455161	+	0.577332i
$40$	−0.947229	−	2.49764i	−0.149770	−	0.394911i
$41$	1.03921	−	0.717312i	0.162297	−	0.112025i	−0.484148	−	0.874986i	$-0.660870\pi$
$41$	1.03921	−	0.717312i	0.162297	−	0.112025i	0.646445	+	0.762961i	$0.276255\pi$
$42$	−1.74570	+	1.54655i	−0.269367	+	0.238639i
$43$	10.7839	+	2.65798i	1.64452	+	0.405339i	0.949530	−	0.313677i	$-0.101561\pi$
$43$	10.7839	+	2.65798i	1.64452	+	0.405339i	0.694994	+	0.719015i	$0.255407\pi$
$44$	−9.35213	−	3.54679i	−1.40989	−	0.534699i
$45$	0.660300	−	1.25810i	0.0984317	−	0.187546i
$46$	−2.26362	−	0.858477i	−0.333752	−	0.126576i
$47$	2.99600	+	3.38178i	0.437011	+	0.493284i	0.925214	−	0.379447i	$-0.123886\pi$
$47$	2.99600	+	3.38178i	0.437011	+	0.493284i	−0.488202	+	0.872731i	$0.662347\pi$
$48$	1.91168	−	1.69360i	0.275928	−	0.244451i
$49$	−8.30692	+	12.0347i	−1.18670	+	1.71924i
$50$	1.23053	+	0.849376i	0.174024	+	0.120120i
$51$	−2.78444	−	1.46139i	−0.389899	−	0.204635i
$52$	1.46037	+	6.13265i	0.202518	+	0.850445i
$53$	10.9480	−	5.74593i	1.50382	−	0.789264i	0.506484	−	0.862249i	$-0.330945\pi$
$53$	10.9480	−	5.74593i	1.50382	−	0.789264i	0.997333	+	0.0729852i	$0.0232526\pi$
$54$	−0.497890	−	0.0604548i	−0.0677542	−	0.00822685i
$55$	−7.89184	+	1.94516i	−1.06413	+	0.262286i
$56$	−4.96616	+	7.19473i	−0.663631	+	0.961436i
$57$	−1.90154	+	1.31254i	−0.251865	+	0.173850i
$58$	0.928316	−	1.04785i	0.121894	−	0.137590i
$59$	10.6038	+	1.28753i	1.38049	+	0.167622i	0.776876	−	0.629653i	$-0.216803\pi$
$59$	10.6038	+	1.28753i	1.38049	+	0.167622i	0.603616	+	0.797275i	$0.293726\pi$
$60$	0.594527	−	2.41209i	0.0767531	−	0.311400i
$61$	4.44716	+	2.33405i	0.569400	+	0.298844i	0.724746	−	0.689016i	$-0.241957\pi$
$61$	4.44716	+	2.33405i	0.569400	+	0.298844i	−0.155346	+	0.987860i	$0.549649\pi$
$62$	−0.647243	+	5.33052i	−0.0821999	+	0.676977i
$63$	−4.61617	+	0.560505i	−0.581583	+	0.0706169i
$64$	1.46542	−	2.12303i	0.183178	−	0.265379i
$65$	3.80767	+	3.42726i	0.472283	+	0.425099i
$66$	1.62985	+	2.36124i	0.200620	+	0.290649i
$67$	4.90055	+	5.53158i	0.598697	+	0.675790i	0.967252	−	0.253816i	$-0.0816859\pi$
$67$	4.90055	+	5.53158i	0.598697	+	0.675790i	−0.368555	+	0.929606i	$0.620147\pi$
$68$	−5.33848	−	1.31582i	−0.647385	−	0.159566i
$69$	−2.74202	−	3.97250i	−0.330100	−	0.478233i
$70$			3.31374i			0.396068i
$71$	−2.24960	+	1.55279i	−0.266979	+	0.184282i	−0.694032	−	0.719945i	$-0.744167\pi$
$71$	−2.24960	+	1.55279i	−0.266979	+	0.184282i	0.427053	+	0.904227i	$0.359552\pi$
$72$	−1.86632	+	0.226612i	−0.219947	+	0.0267065i
$73$	3.84165	−	1.45695i	0.449631	−	0.170523i	−0.119386	−	0.992848i	$-0.538093\pi$
$73$	3.84165	−	1.45695i	0.449631	−	0.170523i	0.569018	+	0.822325i	$0.307324\pi$
$74$	−0.171367	+	1.41134i	−0.0199211	+	0.164065i
$75$	1.05715	+	2.78747i	0.122069	+	0.321869i
$76$	−2.67893	+	3.02388i	−0.307294	+	0.346863i
$77$	19.9111	+	17.6397i	2.26908	+	2.01023i
$78$	0.654561	−	1.68573i	0.0741144	−	0.190871i
$79$	−0.608553	+	0.539131i	−0.0684676	+	0.0606570i	−0.696663	−	0.717399i	$-0.745332\pi$
$79$	−0.608553	+	0.539131i	−0.0684676	+	0.0606570i	0.628195	+	0.778056i	$0.283794\pi$
$80$		−	3.62882i		−	0.405714i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	−0.614915	+	0.151563i	−0.0679060	+	0.0167373i
$83$	−3.64710	−	2.51741i	−0.400321	−	0.276322i	0.350847	−	0.936433i	$-0.385894\pi$
$83$	−3.64710	−	2.51741i	−0.400321	−	0.276322i	−0.751168	+	0.660111i	$0.770509\pi$
$84$	−7.60208	+	2.88309i	−0.829455	+	0.314571i
$85$	−4.17770	+	1.58439i	−0.453135	+	0.171851i
$86$	−4.58441	−	3.16439i	−0.494350	−	0.341225i
$87$	2.71009	−	0.667977i	0.290552	−	0.0716147i
$88$	8.05006	+	7.13173i	0.858139	+	0.760245i
$89$		−	9.16163i		−	0.971131i	−0.874200	−	0.485566i	$-0.838614\pi$
$89$		−	9.16163i		−	0.971131i	0.874200	−	0.485566i	$-0.161386\pi$
$90$	−0.533404	+	0.472555i	−0.0562257	+	0.0498117i
$91$	2.15208	−	16.6274i	0.225599	−	1.74302i
$92$	−6.31720	−	5.59655i	−0.658613	−	0.583480i
$93$	−7.09954	+	8.01373i	−0.736188	+	0.830985i
$94$	−0.803534	−	2.11874i	−0.0828782	−	0.218532i
$95$	−0.395713	+	3.25899i	−0.0405993	+	0.334365i
$96$	−4.71341	+	1.78756i	−0.481060	+	0.182442i
$97$	−11.0160	+	1.33759i	−1.11851	+	0.135812i	−0.658843	−	0.752280i	$-0.728954\pi$
$97$	−11.0160	+	1.33759i	−1.11851	+	0.135812i	−0.459666	+	0.888092i	$0.652031\pi$
$98$	6.03594	−	4.16631i	0.609722	−	0.420861i
$99$			5.72055i			0.574937i
$100$	2.96102	+	4.28978i	0.296102	+	0.428978i
$101$	−6.50192	−	1.60258i	−0.646965	−	0.159463i	−0.0978393	−	0.995202i	$-0.531193\pi$
$101$	−6.50192	−	1.60258i	−0.646965	−	0.159463i	−0.549126	+	0.835740i	$0.685039\pi$
$102$	1.04587	+	1.18054i	0.103556	+	0.116891i
$103$	−8.05285	−	11.6666i	−0.793471	−	1.14954i	−0.985753	−	0.168201i	$-0.946204\pi$
$103$	−8.05285	−	11.6666i	−0.793471	−	1.14954i	0.192282	−	0.981340i	$-0.438411\pi$
$104$	0.870084	−	6.72245i	0.0853188	−	0.659190i
$105$	−3.75323	+	5.43749i	−0.366277	+	0.530644i
$106$	−6.15601	+	0.747475i	−0.597924	+	0.0726012i
$107$	−1.00728	+	8.29570i	−0.0973775	+	0.801976i	0.859430	+	0.511254i	$0.170819\pi$
$107$	−1.00728	+	8.29570i	−0.0973775	+	0.801976i	−0.956807	+	0.290722i	$0.906104\pi$
$108$	−1.54818	−	0.812546i	−0.148973	−	0.0781872i
$109$	−3.42431	+	13.8930i	−0.327989	+	1.33070i	0.543137	+	0.839644i	$0.317236\pi$
$109$	−3.42431	+	13.8930i	−0.327989	+	1.33070i	−0.871126	+	0.491060i	$0.836610\pi$
$110$	4.04686	+	0.491378i	0.385853	+	0.0468510i
$111$	−1.87971	+	2.12176i	−0.178415	+	0.201388i
$112$	−9.77393	+	6.74646i	−0.923549	+	0.637480i
$113$	6.43660	−	9.32502i	0.605504	−	0.877224i	−0.393611	−	0.919277i	$-0.628774\pi$
$113$	6.43660	−	9.32502i	0.605504	−	0.877224i	0.999115	+	0.0420530i	$0.0133898\pi$
$114$	1.12517	−	0.277330i	0.105382	−	0.0259743i
$115$	−6.80835	−	0.826683i	−0.634882	−	0.0770886i
$116$	4.32127	−	2.26798i	0.401220	−	0.210576i
$117$	2.98337	−	2.02473i	0.275812	−	0.187186i
$118$	−4.74369	−	2.48968i	−0.436692	−	0.229194i
$119$	12.0343	+	8.30670i	1.10319	+	0.761474i
$120$	−1.51743	+	2.19837i	−0.138522	+	0.200683i
$121$	16.2612	−	14.4061i	1.47829	−	1.30965i
$122$	−1.67040	−	1.88549i	−0.151231	−	0.170705i
$123$	−1.18067	−	0.447770i	−0.106458	−	0.0403741i
$124$	−8.69930	+	16.5751i	−0.781220	+	1.48849i
$125$	10.6031	+	4.02124i	0.948373	+	0.359670i
$126$	2.26446	+	0.558139i	0.201734	+	0.0497230i
$127$	−8.53571	+	7.56198i	−0.757421	+	0.671017i	−0.950695	−	0.310128i	$-0.899628\pi$
$127$	−8.53571	+	7.56198i	−0.757421	+	0.671017i	0.193273	+	0.981145i	$0.438090\pi$
$128$	−9.36210	+	6.46219i	−0.827501	+	0.571183i
$129$	−3.93846	−	10.3849i	−0.346762	−	0.914335i
$130$	−1.17608	−	2.28442i	−0.103149	−	0.200357i
$131$	−0.367040	+	0.967804i	−0.0320684	+	0.0845574i	−0.950094	−	0.311963i	$-0.899013\pi$
$131$	−0.367040	+	0.967804i	−0.0320684	+	0.0845574i	0.918026	+	0.396521i	$0.129783\pi$
$132$	2.39366	+	9.71146i	0.208341	+	0.845274i
$133$	9.51351	−	4.99307i	0.824926	−	0.432954i
$134$	−1.31434	−	3.46562i	−0.113541	−	0.299384i
$135$	−1.41049	+	0.171264i	−0.121395	+	0.0147401i
$136$	4.86548	+	3.35840i	0.417211	+	0.287980i
$137$	4.70751	−	19.0991i	0.402190	−	1.63175i	−0.325287	−	0.945615i	$-0.605461\pi$
$137$	4.70751	−	19.0991i	0.402190	−	1.63175i	0.727477	−	0.686132i	$-0.240693\pi$
$138$	0.579369	+	2.35059i	0.0493192	+	0.200096i
$139$	0.0669578	+	0.551447i	0.00567929	+	0.0467732i	0.995273	−	0.0971166i	$-0.0309620\pi$
$139$	0.0669578	+	0.551447i	0.00567929	+	0.0467732i	−0.989594	+	0.143890i	$0.954039\pi$
$140$	−4.09643	+	10.8014i	−0.346211	+	0.912884i
$141$	1.08123	−	4.38673i	0.0910562	−	0.369430i
$142$	1.33113	−	0.328093i	0.111706	−	0.0275329i
$143$	−19.9869	−	5.09379i	−1.67138	−	0.425964i
$144$	−2.47977	−	0.611208i	−0.206647	−	0.0509340i
$145$	1.84303	−	3.51160i	0.153055	−	0.291622i
$146$	−2.06068			−0.170543
$147$	14.6232			1.20610
$148$	−2.30327	+	4.38852i	−0.189328	+	0.360734i
$149$	0.0603872	+	0.0681631i	0.00494712	+	0.00558414i	0.750979	−	0.660326i	$-0.229582\pi$
$149$	0.0603872	+	0.0681631i	0.00494712	+	0.00558414i	−0.746032	+	0.665910i	$0.768043\pi$
$150$		−	1.49521i		−	0.122083i
$151$	−1.92905	+	2.17744i	−0.156984	+	0.177198i	−0.821740	−	0.569862i	$-0.806997\pi$
$151$	−1.92905	+	2.17744i	−0.156984	+	0.177198i	0.664757	+	0.747060i	$0.268535\pi$
$152$	3.84631	−	2.01870i	0.311977	−	0.163738i
$153$	0.379044	+	3.12171i	0.0306439	+	0.252375i
$154$	−6.20017	−	11.8134i	−0.499624	−	0.951954i
$155$	1.83359	+	15.1010i	0.147278	+	1.21294i
$156$	4.21748	−	4.68561i	0.337669	−	0.375149i
$157$	−1.10919	+	9.13501i	−0.0885231	+	0.729053i	0.879097	+	0.476643i	$0.158146\pi$
$157$	−1.10919	+	9.13501i	−0.0885231	+	0.729053i	−0.967620	+	0.252411i	$0.918777\pi$
$158$	0.381268	−	0.144596i	0.0303321	−	0.0115034i
$159$	−10.9480	−	5.74593i	−0.868229	−	0.455682i
$160$	−2.53985	+	6.69702i	−0.200792	+	0.529446i
$161$	10.4310	+	19.8747i	0.822080	+	1.56634i
$162$	0.233080	+	0.444098i	0.0183125	+	0.0348916i
$163$	1.62574	+	6.59589i	0.127338	+	0.516630i	0.999618	+	0.0276243i	$0.00879420\pi$
$163$	1.62574	+	6.59589i	0.127338	+	0.516630i	−0.872280	+	0.489006i	$0.837360\pi$
$164$	−2.19172	−	0.266123i	−0.171145	−	0.0207807i
$165$	6.08391	+	5.38988i	0.473632	+	0.419601i
$166$	1.26260	+	1.82919i	0.0979967	+	0.141973i
$167$	−16.5511	−	6.27701i	−1.28076	−	0.485729i	−0.381999	−	0.924163i	$-0.624764\pi$
$167$	−16.5511	−	6.27701i	−1.28076	−	0.485729i	−0.898764	+	0.438433i	$0.855534\pi$
$168$	8.74225			0.674479
$169$	4.41764	+	12.2264i	0.339819	+	0.940491i
$170$	2.24093			0.171872
$171$	2.16039	+	0.819329i	0.165209	+	0.0626557i
$172$	−11.0314	−	15.9818i	−0.841140	−	1.21860i
$173$	12.8703	+	11.4021i	0.978511	+	0.866885i	0.991111	−	0.133035i	$-0.0424723\pi$
$173$	12.8703	+	11.4021i	0.978511	+	0.866885i	−0.0126000	+	0.999921i	$0.504011\pi$
$174$	−1.38971	−	0.168741i	−0.105354	−	0.0127922i
$175$	−3.31758	−	13.4600i	−0.250786	−	1.01748i
$176$	6.78969	+	12.9367i	0.511792	+	0.975139i
$177$	−4.96401	−	9.45813i	−0.373118	−	0.710916i
$178$	−1.62941	+	4.29639i	−0.122129	+	0.322028i
$179$	−19.0320	−	9.98878i	−1.42252	−	0.746596i	−0.434464	−	0.900689i	$-0.643062\pi$
$179$	−19.0320	−	9.98878i	−1.42252	−	0.746596i	−0.988056	+	0.154093i	$0.950754\pi$
$180$	−2.32284	+	0.880938i	−0.173134	+	0.0656612i
$181$	−0.106636	+	0.878223i	−0.00792616	+	0.0652778i	−0.996135	−	0.0878326i	$-0.972006\pi$
$181$	−0.106636	+	0.878223i	−0.00792616	+	0.0652778i	0.988209	+	0.153110i	$0.0489290\pi$
$182$	−3.96642	+	7.41474i	−0.294011	+	0.549617i
$183$	−0.605390	−	4.98583i	−0.0447517	−	0.368563i
$184$	4.21726	+	8.03532i	0.310900	+	0.592371i
$185$	0.485472	+	3.99822i	0.0356926	+	0.293955i
$186$	4.75461	−	2.49541i	0.348625	−	0.182972i
$187$	11.9290	−	13.4650i	0.872332	−	0.984659i
$188$		−	7.89953i		−	0.576133i
$189$	3.08357	+	3.48063i	0.224297	+	0.253179i
$190$	0.765185	−	1.45794i	0.0555124	−	0.105770i
$191$	−21.4778			−1.55408			−0.777039	−	0.629452i	$-0.783279\pi$
$191$	−21.4778			−1.55408			−0.777039	+	0.629452i	$0.783279\pi$
$192$	−2.57967			−0.186172
$193$	−5.77943	+	11.0118i	−0.416013	+	0.792646i	−0.999815	−	0.0192499i	$-0.993872\pi$
$193$	−5.77943	+	11.0118i	−0.416013	+	0.792646i	0.583802	+	0.811896i	$0.301564\pi$
$194$	5.40391	+	1.33194i	0.387978	+	0.0956280i
$195$	0.657575	−	5.08056i	0.0470899	−	0.363826i
$196$	24.8250	−	6.11881i	1.77321	−	0.437058i
$197$	−3.49961	+	14.1985i	−0.249337	+	1.01160i	0.704123	+	0.710078i	$0.251340\pi$
$197$	−3.49961	+	14.1985i	−0.249337	+	1.01160i	−0.953460	+	0.301521i	$0.902506\pi$
$198$	1.01741	−	2.68268i	0.0723038	−	0.190650i
$199$	0.606171	+	4.99227i	0.0429703	+	0.353892i	0.998297	+	0.0583398i	$0.0185807\pi$
$199$	0.606171	+	4.99227i	0.0429703	+	0.353892i	−0.955326	+	0.295553i	$0.904496\pi$
$200$	−1.34130	−	5.44186i	−0.0948440	−	0.384797i
$201$	1.76857	−	7.17537i	0.124745	−	0.506111i
$202$	2.76408	+	1.90791i	0.194480	+	0.134240i
$203$	−12.8846	+	1.56448i	−0.904325	+	0.109805i
$204$	1.94971	+	5.14095i	0.136507	+	0.359938i
$205$	−1.58864	+	0.833781i	−0.110955	+	0.0582338i
$206$	1.70151	+	6.90329i	0.118550	+	0.480975i
$207$	−1.71166	+	4.51328i	−0.118969	+	0.313694i
$208$	4.34356	−	8.11974i	0.301172	−	0.563003i
$209$	−4.68701	−	12.3586i	−0.324208	−	0.854865i
$210$	2.72715	−	1.88242i	0.188191	−	0.129899i
$211$	10.7959	−	9.56435i	0.743222	−	0.658437i	−0.204017	−	0.978967i	$-0.565400\pi$
$211$	10.7959	−	9.56435i	0.743222	−	0.658437i	0.947238	+	0.320531i	$0.103861\pi$
$212$	−20.9900	−	5.17357i	−1.44160	−	0.355322i
$213$	2.55584	+	0.969302i	0.175123	+	0.0664155i
$214$	1.94777	−	3.71116i	0.133147	−	0.253690i
$215$	−14.7553	−	5.59594i	−1.00630	−	0.381640i
$216$	1.24669	+	1.40722i	0.0848262	+	0.0957490i
$217$	37.2644	−	33.0134i	2.52967	−	2.24110i
$218$	4.07672	−	5.90615i	0.276110	−	0.400015i
$219$	−3.38135	−	2.33398i	−0.228491	−	0.157716i
$220$	12.5836	+	6.60439i	0.848387	+	0.445268i
$221$	−11.2444	−	1.45536i	−0.756378	−	0.0978978i
$222$	1.25886	−	0.660699i	0.0844889	−	0.0443432i
$223$	−2.29801	−	0.279029i	−0.153886	−	0.0186852i	0.0432309	−	0.999065i	$-0.486235\pi$
$223$	−2.29801	−	0.279029i	−0.153886	−	0.0186852i	−0.197117	+	0.980380i	$0.563158\pi$
$224$	22.7598	−	5.60979i	1.52070	−	0.374820i
$225$	1.69351	−	2.45348i	0.112901	−	0.163565i
$226$	−4.67693	+	3.22825i	−0.311105	+	0.214740i
$227$	13.5698	−	15.3172i	0.900662	−	1.01664i	−0.0991052	−	0.995077i	$-0.531598\pi$
$227$	13.5698	−	15.3172i	0.900662	−	1.01664i	0.999768	−	0.0215606i	$-0.00686350\pi$
$228$	4.01041	+	0.486952i	0.265596	+	0.0322492i
$229$	−0.0815131	+	0.330712i	−0.00538654	+	0.0218541i	−0.973574	−	0.228373i	$-0.926659\pi$
$229$	−0.0815131	+	0.330712i	−0.00538654	+	0.0218541i	0.968187	+	0.250228i	$0.0805054\pi$
$230$	3.04578	+	1.59855i	0.200833	+	0.105405i
$231$	3.20639	−	26.4070i	0.210965	−	1.73746i
$232$	−5.20926	+	0.632518i	−0.342004	+	0.0415269i
$233$	−1.05663	+	1.53080i	−0.0692223	+	0.100286i	−0.856066	−	0.516866i	$-0.827098\pi$
$233$	−1.05663	+	1.53080i	−0.0692223	+	0.100286i	0.786844	+	0.617152i	$0.211714\pi$
$234$	−1.75916	+	0.418911i	−0.115000	+	0.0273851i
$235$	−3.64664	−	5.28307i	−0.237881	−	0.344629i
$236$	−12.3847	−	13.9794i	−0.806175	−	0.909984i
$237$	0.789394	+	0.194568i	0.0512766	+	0.0126386i
$238$	−4.16620	−	6.03578i	−0.270054	−	0.391241i
$239$			28.2500i			1.82734i	0.406459	+	0.913669i	$0.366764\pi$
$239$			28.2500i			1.82734i	−0.406459	+	0.913669i	$0.633236\pi$
$240$	−2.98646	+	2.06140i	−0.192775	+	0.133063i
$241$	1.13944	−	0.138353i	0.0733975	−	0.00891207i	−0.0837555	−	0.996486i	$-0.526691\pi$
$241$	1.13944	−	0.138353i	0.0733975	−	0.00891207i	0.157153	+	0.987574i	$0.449768\pi$
$242$	−10.1879	+	3.86376i	−0.654902	+	0.248372i
$243$	−0.120537	+	0.992709i	−0.00773243	+	0.0636823i
$244$	−3.11397	−	8.21085i	−0.199351	−	0.525646i
$245$	13.7779	−	15.5520i	0.880238	−	0.993583i
$246$	0.474045	+	0.419967i	0.0302240	+	0.0267761i
$247$	−4.78632	+	6.81857i	−0.304546	+	0.433855i
$248$	15.0660	−	13.3473i	0.956691	−	0.847555i
$249$			4.43156i			0.280839i
$250$	−4.25720	−	3.77155i	−0.269249	−	0.238534i
$251$	1.68201	−	0.414578i	0.106168	−	0.0261679i	−0.185874	−	0.982574i	$-0.559512\pi$
$251$	1.68201	−	0.414578i	0.106168	−	0.0261679i	0.292042	+	0.956406i	$0.405665\pi$
$252$	6.69121	+	4.61861i	0.421507	+	0.290945i
$253$	25.8184	−	9.79164i	1.62319	−	0.615595i
$254$	5.34776	−	2.02814i	0.335548	−	0.127257i
$255$	3.67713	+	2.53814i	0.230271	+	0.158945i
$256$	0.530277	−	0.130702i	0.0331423	−	0.00816885i
$257$	4.29223	+	3.80258i	0.267742	+	0.237199i	0.786302	−	0.617843i	$-0.211993\pi$
$257$	4.29223	+	3.80258i	0.267742	+	0.237199i	−0.518560	+	0.855041i	$0.673532\pi$
$258$			5.57048i			0.346803i
$259$	9.86633	−	8.74081i	0.613064	−	0.543127i
$260$	−1.00954	−	8.90012i	−0.0626088	−	0.551962i
$261$	−2.08924	−	1.85091i	−0.129321	−	0.114568i
$262$	0.344250	−	0.388577i	0.0212678	−	0.0240064i
$263$	5.32100	+	14.0303i	0.328107	+	0.865147i	0.992990	+	0.118199i	$0.0377122\pi$
$263$	5.32100	+	14.0303i	0.328107	+	0.865147i	−0.664883	+	0.746948i	$0.731519\pi$
$264$	1.29634	−	10.6764i	0.0797844	−	0.657084i
$265$	−16.4260	+	6.22956i	−1.00904	+	0.382679i
$266$	−5.34942	+	0.649538i	−0.327994	+	0.0398257i
$267$	−7.53988	+	5.20440i	−0.461433	+	0.318504i
$268$		−	12.9212i		−	0.789291i
$269$	12.7877	+	18.5261i	0.779678	+	1.12956i	0.988443	+	0.151593i	$0.0484403\pi$
$269$	12.7877	+	18.5261i	0.779678	+	1.12956i	−0.208765	+	0.977966i	$0.566944\pi$
$270$	0.691913	+	0.170541i	0.0421085	+	0.0103788i
$271$	0.190069	+	0.214543i	0.0115459	+	0.0130326i	0.754255	−	0.656581i	$-0.227998\pi$
$271$	0.190069	+	0.214543i	0.0115459	+	0.0130326i	−0.742709	+	0.669614i	$0.766460\pi$
$272$	4.56233	+	6.60967i	0.276632	+	0.400770i
$273$	−14.9066	+	7.67431i	−0.902188	+	0.464470i
$274$	−5.60440	+	8.11938i	−0.338574	+	0.490510i
$275$	−16.9297	+	2.05564i	−1.02090	+	0.123960i
$276$	−1.01729	+	8.37815i	−0.0612338	+	0.504305i
$277$	2.23739	+	1.17427i	0.134432	+	0.0705551i	0.530598	−	0.847624i	$-0.321967\pi$
$277$	2.23739	+	1.17427i	0.134432	+	0.0705551i	−0.396167	+	0.918179i	$0.629660\pi$
$278$	0.0666753	−	0.270512i	0.00399892	−	0.0162242i
$279$	10.6282	+	1.29049i	0.636292	+	0.0772598i
$280$	8.23690	−	9.29754i	0.492249	−	0.555634i
$281$	−17.4445	+	12.0410i	−1.04065	+	0.718308i	−0.960445	−	0.278470i	$-0.910173\pi$
$281$	−17.4445	+	12.0410i	−1.04065	+	0.718308i	−0.0802042	+	0.996778i	$0.525557\pi$
$282$	−1.28723	+	1.86488i	−0.0766536	+	0.111052i
$283$	2.45913	−	0.606120i	0.146180	−	0.0360301i	−0.165547	−	0.986202i	$-0.552939\pi$
$283$	2.45913	−	0.606120i	0.146180	−	0.0360301i	0.311727	+	0.950172i	$0.399093\pi$
$284$	4.74449	+	0.576086i	0.281534	+	0.0341844i
$285$	2.90688	−	1.52565i	0.172189	−	0.0903717i
$286$	8.46699	+	5.94343i	0.500663	+	0.351443i
$287$	5.19921	+	2.72876i	0.306900	+	0.161073i
$288$	4.14865	+	2.86361i	0.244462	+	0.168740i
$289$	−4.03965	+	5.85244i	−0.237626	+	0.344261i
$290$	−1.48884	+	1.31899i	−0.0874275	+	0.0774540i
$291$	7.35864	+	8.30619i	0.431371	+	0.486917i
$292$	−6.71694	−	2.54740i	−0.393079	−	0.149075i
$293$	7.81458	−	14.8894i	0.456532	−	0.869850i	−0.543014	−	0.839724i	$-0.682717\pi$
$293$	7.81458	−	14.8894i	0.456532	−	0.869850i	0.999546	−	0.0301260i	$-0.00959085\pi$
$294$	−6.85761	−	2.60075i	−0.399944	−	0.151679i
$295$	−14.7360	−	3.63209i	−0.857960	−	0.211468i
$296$	3.98895	−	3.53390i	0.231853	−	0.205404i
$297$	4.70792	−	3.24964i	0.273181	−	0.188563i
$298$	−0.0161960	−	0.0427053i	−0.000938208	−	0.00247385i
$299$	−14.2447	−	9.99910i	−0.823791	−	0.578263i
$300$	1.84837	−	4.87375i	0.106716	−	0.281386i
$301$	12.3598	+	50.1458i	0.712408	+	2.89035i
$302$	1.29189	−	0.678039i	0.0743402	−	0.0390167i
$303$	2.37461	+	6.26134i	0.136418	+	0.359705i
$304$	5.85806	−	0.711297i	0.335983	−	0.0407957i
$305$	−5.87292	−	4.05378i	−0.336282	−	0.232119i
$306$	0.377445	−	1.53135i	0.0215771	−	0.0875416i
$307$	0.536715	+	2.17754i	0.0306320	+	0.124279i	0.984267	−	0.176686i	$-0.0565376\pi$
$307$	0.536715	+	2.17754i	0.0306320	+	0.124279i	−0.953635	+	0.300964i	$0.902691\pi$
$308$	−5.60622	−	46.1714i	−0.319444	−	2.63086i
$309$	−5.02686	+	13.2547i	−0.285968	+	0.754035i
$310$	1.82585	−	7.40778i	0.103702	−	0.420734i
$311$	−5.85839	+	1.44396i	−0.332199	+	0.0818797i	−0.401887	−	0.915689i	$-0.631646\pi$
$311$	−5.85839	+	1.44396i	−0.332199	+	0.0818797i	0.0696883	+	0.997569i	$0.477800\pi$
$312$	−6.02673	+	3.10272i	−0.341196	+	0.175657i
$313$	−15.8377	−	3.90365i	−0.895201	−	0.220647i	−0.235231	−	0.971939i	$-0.575585\pi$
$313$	−15.8377	−	3.90365i	−0.895201	−	0.220647i	−0.659970	+	0.751292i	$0.729431\pi$
$314$	2.14483	−	4.08663i	0.121040	−	0.230622i
$315$	6.60704			0.372265
$316$	1.42152			0.0799669
$317$	16.4428	−	31.3291i	0.923519	−	1.75962i	0.361920	−	0.932209i	$-0.382121\pi$
$317$	16.4428	−	31.3291i	0.923519	−	1.75962i	0.561599	−	0.827410i	$-0.310186\pi$
$318$	4.11217	+	4.64168i	0.230599	+	0.260293i
$319$			15.9672i			0.893991i
$320$	−2.43056	+	2.74353i	−0.135872	+	0.153368i
$321$	7.39943	−	3.88352i	0.412996	−	0.216757i
$322$	−1.35695	−	11.1755i	−0.0756198	−	0.622785i
$323$	−3.37659	−	6.43356i	−0.187879	−	0.357973i
$324$	0.210752	+	1.73570i	0.0117085	+	0.0964279i
$325$	7.06416	+	8.10158i	0.391849	+	0.449395i
$326$	0.410687	−	3.38231i	0.0227458	−	0.187329i
$327$	13.3789	−	5.07395i	0.739855	−	0.280590i
$328$	2.10204	+	1.10323i	0.116066	+	0.0609160i
$329$	−7.44994	+	19.6439i	−0.410728	+	1.08300i
$330$	−1.89448	−	3.60963i	−0.104288	−	0.198704i
$331$	−12.9475	−	24.6695i	−0.711662	−	1.35596i	−0.925372	−	0.379061i	$-0.876247\pi$
$331$	−12.9475	−	24.6695i	−0.711662	−	1.35596i	0.213710	−	0.976897i	$-0.431445\pi$
$332$	1.85430	+	7.52321i	0.101768	+	0.412890i
$333$	2.81397	+	0.341678i	0.154205	+	0.0187238i
$334$	6.64534	+	5.88726i	0.363617	+	0.322136i
$335$	−5.96480	−	8.64150i	−0.325892	−	0.472136i
$336$	11.1044	+	4.21136i	0.605797	+	0.229749i
$337$	30.4045			1.65624			0.828120	−	0.560551i	$-0.189411\pi$
$337$	30.4045			1.65624			0.828120	+	0.560551i	$0.189411\pi$
$338$	0.102801	−	6.51930i	0.00559163	−	0.354603i
$339$	−11.3307			−0.615401
$340$	7.30450	+	2.77023i	0.396142	+	0.150237i
$341$	−34.7914	−	50.4041i	−1.88406	−	2.72953i
$342$	−0.867407	−	0.768456i	−0.0469040	−	0.0415533i
$343$	−35.1900	−	4.27284i	−1.90008	−	0.230711i
$344$	4.99707	+	20.2739i	0.269424	+	1.09310i
$345$	3.18724	+	6.07277i	0.171595	+	0.326947i
$346$	−4.00771	−	7.63606i	−0.215456	−	0.410517i
$347$	4.17082	−	10.9976i	0.223902	−	0.590380i	−0.775246	−	0.631659i	$-0.782374\pi$
$347$	4.17082	−	10.9976i	0.223902	−	0.590380i	0.999148	+	0.0412795i	$0.0131434\pi$
$348$	−4.32127	−	2.26798i	−0.231644	−	0.121576i
$349$	6.60607	−	2.50535i	0.353615	−	0.134108i	−0.171400	−	0.985202i	$-0.554829\pi$
$349$	6.60607	−	2.50535i	0.353615	−	0.134108i	0.525015	+	0.851093i	$0.324060\pi$
$350$	−0.838072	+	6.90214i	−0.0447968	+	0.368935i
$351$	−3.36106	−	1.30508i	−0.179400	−	0.0696602i
$352$	−3.47594	−	28.6270i	−0.185268	−	1.52582i
$353$	5.50642	+	10.4916i	0.293077	+	0.558412i	0.986822	−	0.161809i	$-0.0517327\pi$
$353$	5.50642	+	10.4916i	0.293077	+	0.558412i	−0.693745	+	0.720221i	$0.744040\pi$
$354$	0.645756	+	5.31828i	0.0343216	+	0.282663i
$355$	3.43897	−	1.80491i	0.182522	−	0.0957947i
$356$	−10.6223	+	11.9901i	−0.562983	+	0.635476i
$357$		−	14.6228i		−	0.773921i
$358$	7.14864	+	8.06914i	0.377817	+	0.426467i
$359$	2.48279	−	4.73056i	0.131037	−	0.249669i	−0.811094	−	0.584916i	$-0.801127\pi$
$359$	2.48279	−	4.73056i	0.131037	−	0.249669i	0.942130	+	0.335247i	$0.108820\pi$
$360$	2.67122			0.140786
$361$	13.6614			0.719021
$362$	0.206200	−	0.392881i	0.0108376	−	0.0206494i
$363$	−21.0934	−	5.19906i	−1.10712	−	0.272880i
$364$	−22.0949	+	19.2656i	−1.15809	+	1.00979i
$365$	−5.66812	+	1.39707i	−0.296683	+	0.0731258i
$366$	−0.602835	+	2.44580i	−0.0315107	+	0.127844i
$367$	−7.67497	+	20.2372i	−0.400630	+	1.05637i	0.571225	+	0.820794i	$0.306468\pi$
$367$	−7.67497	+	20.2372i	−0.400630	+	1.05637i	−0.971855	+	0.235581i	$0.924301\pi$
$368$	1.48597	+	12.2381i	0.0774615	+	0.637953i
$369$	0.302191	+	1.22604i	0.0157314	+	0.0638249i
$370$	0.483423	−	1.96132i	0.0251320	−	0.101964i
$371$	47.3170	+	32.6606i	2.45658	+	1.69565i
$372$	18.5828	−	2.25636i	0.963475	−	0.116987i
$373$	1.66554	+	4.39167i	0.0862384	+	0.227392i	0.971197	−	0.238278i	$-0.0765828\pi$
$373$	1.66554	+	4.39167i	0.0862384	+	0.227392i	−0.884959	+	0.465669i	$0.845814\pi$
$374$	−7.98890	+	4.19290i	−0.413096	+	0.216810i
$375$	−2.71385	−	11.0105i	−0.140143	−	0.568581i
$376$	−3.01201	+	7.94201i	−0.155332	+	0.409578i
$377$	8.32716	−	5.65142i	0.428871	−	0.291063i
$378$	−0.827020	−	2.18067i	−0.0425373	−	0.112162i
$379$	1.34492	−	0.928333i	0.0690841	−	0.0476853i	−0.533022	−	0.846101i	$-0.678944\pi$
$379$	1.34492	−	0.928333i	0.0690841	−	0.0476853i	0.602106	+	0.798416i	$0.294328\pi$
$380$	4.29647	−	3.80634i	0.220404	−	0.195261i
$381$	11.0722	+	2.72906i	0.567247	+	0.139814i
$382$	10.0721	+	3.81984i	0.515334	+	0.195440i
$383$	−5.76875	+	10.9914i	−0.294770	+	0.561636i	−0.987131	−	0.159915i	$-0.948878\pi$
$383$	−5.76875	+	10.9914i	−0.294770	+	0.561636i	0.692361	+	0.721551i	$0.256570\pi$
$384$	10.6366	+	4.03392i	0.542795	+	0.205855i
$385$	−25.0633	−	28.2906i	−1.27735	−	1.44182i
$386$	4.66875	−	4.13615i	0.237633	−	0.210524i
$387$	−6.30927	+	9.14055i	−0.320718	+	0.464640i
$388$	15.9679	+	11.0219i	0.810648	+	0.559550i
$389$	−5.81773	−	3.05338i	−0.294971	−	0.154813i	0.310746	−	0.950493i	$-0.399421\pi$
$389$	−5.81773	−	3.05338i	−0.294971	−	0.154813i	−0.605717	+	0.795680i	$0.707114\pi$
$390$	−1.21195	+	2.26560i	−0.0613697	+	0.114723i
$391$	13.4403	−	7.05404i	0.679708	−	0.356738i
$392$	−27.2915	−	3.31379i	−1.37843	−	0.167372i
$393$	1.00499	−	0.247708i	0.0506950	−	0.0124952i
$394$	4.16637	−	6.03603i	0.209899	−	0.304091i
$395$	0.950690	−	0.656214i	0.0478344	−	0.0330177i
$396$	6.63262	−	7.48668i	0.333302	−	0.376220i
$397$	−23.6587	−	2.87268i	−1.18739	−	0.144176i	−0.497092	−	0.867698i	$-0.665599\pi$
$397$	−23.6587	−	2.87268i	−1.18739	−	0.144176i	−0.690301	+	0.723522i	$0.742522\pi$
$398$	0.603613	−	2.44895i	0.0302564	−	0.122755i
$399$	−9.51351	−	4.99307i	−0.476271	−	0.249966i
$400$	0.917757	−	7.55841i	0.0458879	−	0.377920i
$401$	−16.2940	+	1.97845i	−0.813682	+	0.0987989i	−0.516790	−	0.856112i	$-0.672873\pi$
$401$	−16.2940	+	1.97845i	−0.813682	+	0.0987989i	−0.296892	+	0.954911i	$0.595950\pi$
$402$	−2.10552	+	3.05038i	−0.105014	+	0.152139i
$403$	−13.9725	+	35.9843i	−0.696021	+	1.79251i
$404$	6.65120	+	9.63592i	0.330909	+	0.479405i
$405$	0.942195	+	1.06352i	0.0468181	+	0.0528467i
$406$	6.32055	+	1.55788i	0.313684	+	0.0773161i
$407$	−9.21156	−	13.3453i	−0.456600	−	0.661500i
$408$		−	5.91199i		−	0.292687i
$409$	−18.4189	+	12.7137i	−0.910757	+	0.628650i	−0.928556	−	0.371192i	$-0.878949\pi$
$409$	−18.4189	+	12.7137i	−0.910757	+	0.628650i	0.0177996	+	0.999842i	$0.494334\pi$
$410$	0.893286	−	0.108465i	0.0441163	−	0.00535669i
$411$	−18.3924	+	6.97533i	−0.907232	+	0.344068i
$412$	−2.98761	+	24.6052i	−0.147189	+	1.21221i
$413$	17.6134	+	46.4427i	0.866698	+	2.28529i
$414$	1.60538	−	1.81210i	0.0789002	−	0.0890599i
$415$	4.71304	+	4.17539i	0.231354	+	0.204962i
$416$	−13.6992	+	11.9450i	−0.671658	+	0.585651i
$417$	0.415796	−	0.368363i	0.0203616	−	0.0180388i
$418$			6.62923i			0.324246i
$419$	4.71387	+	4.17613i	0.230288	+	0.204017i	0.770374	−	0.637593i	$-0.220070\pi$
$419$	4.71387	+	4.17613i	0.230288	+	0.204017i	−0.540086	+	0.841610i	$0.681608\pi$
$420$	11.2164	−	2.76460i	0.547304	−	0.134898i
$421$	−19.0472	−	13.1474i	−0.928306	−	0.640763i	0.00494547	−	0.999988i	$-0.498426\pi$
$421$	−19.0472	−	13.1474i	−0.928306	−	0.640763i	−0.933251	+	0.359225i	$0.883041\pi$
$422$	−6.76382	+	2.56518i	−0.329258	+	0.124871i
$423$	−4.22442	+	1.60211i	−0.205398	+	0.0778973i
$424$	19.1302	+	13.2047i	0.929047	+	0.641275i
$425$	−9.10237	+	2.24353i	−0.441530	+	0.108827i
$426$	−1.02618	−	0.909117i	−0.0497186	−	0.0440468i
$427$			23.3548i			1.13022i
$428$	10.9366	−	9.68899i	0.528641	−	0.468335i
$429$	7.16172	+	19.3425i	0.345771	+	0.933863i
$430$	5.92431	+	5.24848i	0.285696	+	0.253104i
$431$	−0.732931	+	0.827308i	−0.0353040	+	0.0398500i	−0.765898	−	0.642963i	$-0.777705\pi$
$431$	−0.732931	+	0.827308i	−0.0353040	+	0.0398500i	0.730593	+	0.682813i	$0.239243\pi$
$432$	0.905655	+	2.38802i	0.0435733	+	0.114893i
$433$	4.16153	−	34.2733i	0.199990	−	1.64707i	−0.454316	−	0.890840i	$-0.650116\pi$
$433$	4.16153	−	34.2733i	0.199990	−	1.64707i	0.654307	−	0.756229i	$-0.272961\pi$
$434$	−23.3468	+	8.85426i	−1.12068	+	0.425018i
$435$	−3.93695	+	0.478032i	−0.188762	+	0.0229199i
$436$	20.5895	−	14.2119i	0.986059	−	0.680628i
$437$		−	11.1529i		−	0.533514i
$438$	1.17060	+	1.69591i	0.0559334	+	0.0810335i
$439$	5.00100	+	1.23264i	0.238685	+	0.0588305i	0.356843	−	0.934164i	$-0.383853\pi$
$439$	5.00100	+	1.23264i	0.238685	+	0.0588305i	−0.118159	+	0.992995i	$0.537699\pi$
$440$	−10.1331	−	11.4379i	−0.483076	−	0.545280i
$441$	−8.30692	−	12.0347i	−0.395568	−	0.573079i
$442$	5.01426	+	2.68232i	0.238504	+	0.127585i
$443$	11.2146	−	16.2472i	0.532823	−	0.771927i	−0.460455	−	0.887683i	$-0.652314\pi$
$443$	11.2146	−	16.2472i	0.532823	−	0.771927i	0.993278	+	0.115756i	$0.0369291\pi$
$444$	4.92009	−	0.597407i	0.233497	−	0.0283517i
$445$	−1.56906	+	12.9224i	−0.0743805	+	0.612579i
$446$	1.02804	+	0.539556i	0.0486790	+	0.0255487i
$447$	0.0217933	−	0.0884188i	0.00103079	−	0.00418207i
$448$	11.9082	+	1.44592i	0.562610	+	0.0683133i
$449$	−6.95198	+	7.84716i	−0.328084	+	0.370331i	−0.889288	−	0.457347i	$-0.848800\pi$
$449$	−6.95198	+	7.84716i	−0.328084	+	0.370331i	0.561204	+	0.827677i	$0.310338\pi$
$450$	−1.23053	+	0.849376i	−0.0580079	+	0.0400400i
$451$	4.10342	−	5.94483i	0.193223	−	0.279931i
$452$	−19.2356	+	4.74114i	−0.904765	+	0.223005i
$453$	2.88782	+	0.350645i	0.135682	+	0.0164748i
$454$	−9.08781	+	4.76965i	−0.426512	+	0.223851i
$455$	−5.88315	+	23.0841i	−0.275806	+	1.08220i
$456$	−3.84631	−	2.01870i	−0.180120	−	0.0945342i
$457$	−21.9200	−	15.1303i	−1.02538	−	0.707766i	−0.0683180	−	0.997664i	$-0.521763\pi$
$457$	−21.9200	−	15.1303i	−1.02538	−	0.707766i	−0.957058	+	0.289898i	$0.906379\pi$
$458$	0.0970433	−	0.140592i	0.00453454	−	0.00656941i
$459$	2.35380	−	2.08528i	0.109866	−	0.0973326i
$460$	7.95183	+	8.97576i	0.370756	+	0.418497i
$461$	−19.4044	−	7.35914i	−0.903755	−	0.342749i	−0.141434	−	0.989948i	$-0.545171\pi$
$461$	−19.4044	−	7.35914i	−0.903755	−	0.342749i	−0.762321	+	0.647199i	$0.775940\pi$
$462$	−6.20017	+	11.8134i	−0.288458	+	0.549611i
$463$	−21.4089	−	8.11931i	−0.994954	−	0.377336i	−0.197229	−	0.980357i	$-0.563194\pi$
$463$	−21.4089	−	8.11931i	−0.994954	−	0.377336i	−0.797725	+	0.603021i	$0.793963\pi$
$464$	−6.92152	−	1.70600i	−0.321324	−	0.0791992i
$465$	11.3863	−	10.0874i	0.528026	−	0.467790i
$466$	0.767765	−	0.529950i	0.0355660	−	0.0245495i
$467$	0.150308	+	0.396329i	0.00695542	+	0.0183399i	0.938449	−	0.345418i	$-0.112263\pi$
$467$	0.150308	+	0.396329i	0.00695542	+	0.0183399i	−0.931494	+	0.363758i	$0.881494\pi$
$468$	−6.25198	−	0.809192i	−0.288998	−	0.0374049i
$469$	−12.1858	+	32.1314i	−0.562690	+	1.48369i
$470$	0.770509	+	3.12608i	0.0355409	+	0.144195i
$471$	8.14806	−	4.27643i	0.375443	−	0.197048i
$472$	7.12108	+	18.7767i	0.327774	+	0.864270i
$473$	63.0726	−	7.65840i	2.90008	−	0.352134i
$474$	−0.335585	−	0.231638i	−0.0154139	−	0.0106395i
$475$	−1.64845	+	6.68802i	−0.0756360	+	0.306867i
$476$	−6.11865	−	24.8243i	−0.280448	−	1.13782i
$477$	1.49034	+	12.2740i	0.0682380	+	0.561990i
$478$	5.02428	−	13.2479i	0.229805	−	0.605947i
$479$	0.346261	−	1.40484i	0.0158211	−	0.0641886i	−0.962501	−	0.271279i	$-0.912553\pi$
$479$	0.346261	−	1.40484i	0.0158211	−	0.0641886i	0.978322	+	0.207091i	$0.0663995\pi$
$480$	6.95434	−	1.71409i	0.317421	−	0.0782372i
$481$	−3.69944	+	9.52741i	−0.168680	+	0.434412i
$482$	−0.558949	−	0.137769i	−0.0254594	−	0.00627519i
$483$	10.4310	−	19.8747i	0.474628	−	0.904328i
$484$	−37.9846			−1.72657
$485$	15.7671			0.715945
$486$	0.233080	−	0.444098i	0.0105727	−	0.0201447i
$487$	−18.7156	−	21.1255i	−0.848084	−	0.957289i	0.151429	−	0.988468i	$-0.451612\pi$
$487$	−18.7156	−	21.1255i	−0.848084	−	0.957289i	−0.999514	+	0.0311787i	$0.990074\pi$
$488$			9.44232i			0.427434i
$489$	4.50479	−	5.08485i	0.203714	−	0.229945i
$490$	−9.22715	+	4.84278i	−0.416840	+	0.218775i
$491$	3.99564	+	32.9070i	0.180321	+	1.48507i	0.749030	+	0.662536i	$0.230520\pi$
$491$	3.99564	+	32.9070i	0.180321	+	1.48507i	−0.568710	+	0.822538i	$0.692557\pi$
$492$	1.02603	+	1.95493i	0.0462568	+	0.0881350i
$493$	1.05799	+	8.71331i	0.0476494	+	0.392428i
$494$	3.45726	−	2.34635i	0.155549	−	0.105567i
$495$	0.979725	−	8.06876i	0.0440354	−	0.362664i
$496$	25.5666	−	9.69614i	1.14798	−	0.435370i
$497$	−11.2549	−	5.90702i	−0.504851	−	0.264966i
$498$	0.788156	−	2.07820i	0.0353181	−	0.0931263i
$499$	−3.85963	−	7.35391i	−0.172781	−	0.329206i	0.783632	−	0.621226i	$-0.213365\pi$
$499$	−3.85963	−	7.35391i	−0.172781	−	0.329206i	−0.956412	+	0.292020i	$0.905673\pi$
$500$	−9.21431	−	17.5564i	−0.412076	−	0.785146i
$501$	4.23622	+	17.1870i	0.189261	+	0.767860i
$502$	−0.862519	−	0.104729i	−0.0384961	−	0.00467427i
$503$	14.2654	+	12.6380i	0.636063	+	0.563503i	0.918321	−	0.395836i	$-0.129545\pi$
$503$	14.2654	+	12.6380i	0.636063	+	0.563503i	−0.282258	+	0.959338i	$0.591084\pi$
$504$	−4.96616	−	7.19473i	−0.221210	−	0.320479i
$505$	8.89641	+	3.37396i	0.395885	+	0.150139i
$506$	−13.8491			−0.615668
$507$	7.55261	−	10.5810i	0.335423	−	0.469920i
$508$	19.9386			0.884633
$509$	−29.8394	−	11.3166i	−1.32261	−	0.501599i	−0.410617	−	0.911808i	$-0.634687\pi$
$509$	−29.8394	−	11.3166i	−1.32261	−	0.501599i	−0.911992	+	0.410208i	$0.865456\pi$
$510$	−1.27300	−	1.84425i	−0.0563692	−	0.0816649i
$511$	14.3007	+	12.6693i	0.632625	+	0.560457i
$512$	22.3138	+	2.70939i	0.986140	+	0.119739i
$513$	−0.552949	−	2.24340i	−0.0244133	−	0.0990486i
$514$	−1.33657	−	2.54661i	−0.0589534	−	0.112326i
$515$	9.36037	+	17.8347i	0.412467	+	0.785891i
$516$	−6.88620	+	18.1574i	−0.303148	+	0.799335i
$517$	22.8851	+	12.0110i	1.00649	+	0.528244i
$518$	−6.18142	+	2.34430i	−0.271596	+	0.103003i
$519$	2.07257	−	17.0692i	0.0909759	−	0.749254i
$520$	−2.37856	+	9.33291i	−0.104307	+	0.409275i
$521$	3.57395	+	29.4342i	0.156578	+	1.28953i	0.833104	+	0.553116i	$0.186561\pi$
$521$	3.57395	+	29.4342i	0.156578	+	1.28953i	−0.676527	+	0.736418i	$0.736516\pi$
$522$	0.650573	+	1.23956i	0.0284748	+	0.0542542i
$523$	−2.14513	−	17.6667i	−0.0937998	−	0.772511i	−0.961382	−	0.275217i	$-0.911250\pi$
$523$	−2.14513	−	17.6667i	−0.0937998	−	0.772511i	0.867582	−	0.497294i	$-0.165673\pi$
$524$	1.60246	−	0.841039i	0.0700040	−	0.0367409i
$525$	−9.19273	+	10.3764i	−0.401204	+	0.452865i
$526$		−	7.52593i		−	0.328146i
$527$	−22.3255	−	25.2003i	−0.972514	−	1.09774i
$528$	6.78969	−	12.9367i	0.295483	−	0.562997i
$529$	0.299446			0.0130194
$530$	8.81098			0.382725
$531$	−4.96401	+	9.45813i	−0.215420	+	0.410448i
$532$	−18.2398	−	4.49571i	−0.790796	−	0.194914i
$533$	−4.55270	−	0.0358928i	−0.197199	−	0.00155469i
$534$	4.46147	−	1.09965i	0.193066	−	0.0475866i
$535$	2.84151	−	11.5285i	0.122849	−	0.498419i
$536$	−4.92673	+	12.9907i	−0.212802	+	0.561114i
$537$	2.59082	+	21.3373i	0.111802	+	0.920773i
$538$	−2.70194	−	10.9622i	−0.116489	−	0.472615i
$539$	−20.0194	+	81.2219i	−0.862297	+	3.49848i
$540$	2.04452	+	1.41123i	0.0879822	+	0.0607297i
$541$	−23.5639	+	2.86117i	−1.01309	+	0.123011i	−0.610208	−	0.792241i	$-0.708914\pi$
$541$	−23.5639	+	2.86117i	−1.01309	+	0.123011i	−0.402881	+	0.915252i	$0.631991\pi$
$542$	−0.0509768	−	0.134415i	−0.00218964	−	0.00577361i
$543$	0.783340	−	0.411128i	0.0336163	−	0.0176432i
$544$	−3.79365	−	15.3915i	−0.162651	−	0.659903i
$545$	7.20930	−	19.0094i	0.308813	−	0.814272i
$546$	8.35539	−	0.947748i	0.357578	−	0.0405599i
$547$	−7.14640	−	18.8435i	−0.305558	−	0.805691i	−0.996563	−	0.0828403i	$-0.973601\pi$
$547$	−7.14640	−	18.8435i	−0.305558	−	0.805691i	0.691005	−	0.722850i	$-0.257168\pi$
$548$	−28.3051	+	19.5376i	−1.20913	+	0.834605i
$549$	−3.75936	+	3.33050i	−0.160446	+	0.142142i
$550$	8.30487	+	2.04697i	0.354121	+	0.0872830i
$551$	6.03009	+	2.28691i	0.256890	+	0.0974256i
$552$	4.21726	−	8.03532i	0.179498	−	0.342006i
$553$	−3.53492	−	1.34062i	−0.150320	−	0.0570089i
$554$	−0.840387	−	0.948600i	−0.0357046	−	0.0403022i
$555$	3.01469	−	2.67078i	0.127967	−	0.113368i
$556$	0.551739	−	0.799332i	0.0233989	−	0.0338992i
$557$	−31.5594	−	21.7839i	−1.33722	−	0.923014i	−0.337385	−	0.941367i	$-0.609542\pi$
$557$	−31.5594	−	21.7839i	−1.33722	−	0.923014i	−0.999832	+	0.0183528i	$0.994158\pi$
$558$	−4.75461	−	2.49541i	−0.201279	−	0.105639i
$559$	−26.3179	−	30.1828i	−1.11313	−	1.27660i
$560$	14.9414	−	7.84186i	0.631390	−	0.331379i
$561$	−17.8579	−	2.16834i	−0.753961	−	0.0915475i
$562$	10.3222	−	2.54418i	0.435414	−	0.107320i
$563$	17.6761	−	25.6083i	0.744961	−	1.07926i	−0.248890	−	0.968532i	$-0.580066\pi$
$563$	17.6761	−	25.6083i	0.744961	−	1.07926i	0.993851	−	0.110730i	$-0.0353188\pi$
$564$	−6.50119	+	4.48745i	−0.273749	+	0.188956i
$565$	−10.6758	+	12.0505i	−0.449133	+	0.506966i
$566$	−1.26102	−	0.153115i	−0.0530045	−	0.00643591i
$567$	1.11284	−	4.51495i	0.0467347	−	0.189610i
$568$	−4.55035	−	2.38821i	−0.190928	−	0.100207i
$569$	−4.54071	+	37.3961i	−0.190357	+	1.56773i	0.513943	+	0.857825i	$0.328184\pi$
$569$	−4.54071	+	37.3961i	−0.190357	+	1.56773i	−0.704299	+	0.709903i	$0.748739\pi$
$570$	−1.63453	+	0.198468i	−0.0684631	+	0.00831293i
$571$	−12.0511	+	17.4590i	−0.504323	+	0.730638i	−0.989620	−	0.143712i	$-0.954096\pi$
$571$	−12.0511	+	17.4590i	−0.504323	+	0.730638i	0.485297	+	0.874350i	$0.338712\pi$
$572$	20.2516	+	29.8399i	0.846760	+	1.24767i
$573$	12.2008	+	17.6759i	0.509695	+	0.738420i
$574$	−1.95288	−	2.20435i	−0.0815116	−	0.0920076i
$575$	−13.9719	−	3.44377i	−0.582670	−	0.143615i
$576$	1.46542	+	2.12303i	0.0610593	+	0.0884596i
$577$		−	2.39691i		−	0.0997846i	−0.998755	−	0.0498923i	$-0.984112\pi$
$577$		−	2.39691i		−	0.0997846i	0.998755	−	0.0498923i	$-0.0158878\pi$
$578$	2.93527	−	2.02607i	0.122091	−	0.0842735i
$579$	12.3456	−	1.49903i	0.513067	−	0.0622976i
$580$	−6.48351	+	2.45887i	−0.269213	+	0.102099i
$581$	2.48391	−	20.4568i	0.103050	−	0.848692i
$582$	−1.97360	−	5.20396i	−0.0818085	−	0.215711i
$583$	46.9027	−	52.9422i	1.94251	−	2.19264i
$584$	5.78176	+	5.12219i	0.239251	+	0.211958i
$585$	−4.55476	+	2.34491i	−0.188316	+	0.0969501i
$586$	−6.31278	+	5.59263i	−0.260778	+	0.231030i
$587$		−	6.23541i		−	0.257363i	−0.991686	−	0.128682i	$-0.958925\pi$
$587$		−	6.23541i		−	0.257363i	0.991686	−	0.128682i	$-0.0410745\pi$
$588$	−19.1379	−	16.9547i	−0.789233	−	0.699199i
$589$	−24.0184	+	5.91999i	−0.989659	+	0.243929i
$590$	6.26452	+	4.32409i	0.257906	+	0.178020i
$591$	13.6731	−	5.18553i	0.562437	−	0.213304i
$592$	6.76916	−	2.56720i	0.278211	−	0.105511i
$593$	−3.36951	−	2.32581i	−0.138369	−	0.0955094i	0.496869	−	0.867825i	$-0.334483\pi$
$593$	−3.36951	−	2.32581i	−0.138369	−	0.0955094i	−0.635239	+	0.772316i	$0.719098\pi$
$594$	−2.78575	+	0.686626i	−0.114301	+	0.0281726i
$595$	−15.5516	−	13.7775i	−0.637554	−	0.564824i
$596$		−	0.159223i		−	0.00652201i
$597$	3.76421	−	3.33480i	0.154059	−	0.136484i
$598$	4.90175	+	7.22255i	0.200447	+	0.295352i
$599$	19.9864	+	17.7064i	0.816624	+	0.723465i	0.964083	−	0.265603i	$-0.0855710\pi$
$599$	19.9864	+	17.7064i	0.816624	+	0.723465i	−0.147459	+	0.989068i	$0.547109\pi$
$600$	−3.71662	+	4.19519i	−0.151730	+	0.171268i
$601$	0.596916	+	1.57394i	0.0243487	+	0.0642023i	0.946639	−	0.322295i	$-0.104454\pi$
$601$	0.596916	+	1.57394i	0.0243487	+	0.0642023i	−0.922291	+	0.386497i	$0.873685\pi$
$602$	3.12228	−	25.7143i	0.127255	−	1.04804i
$603$	−6.90987	+	2.62057i	−0.281392	+	0.106718i
$604$	5.04922	−	0.613086i	0.205450	−	0.0249461i
$605$	−25.4034	+	17.5347i	−1.03280	+	0.712887i
$606$		−	3.35861i		−	0.136434i
$607$	8.64729	+	12.5278i	0.350983	+	0.508486i	0.958219	−	0.286035i	$-0.0923374\pi$
$607$	8.64729	+	12.5278i	0.350983	+	0.508486i	−0.607237	+	0.794521i	$0.707722\pi$
$608$	−11.3090	−	2.78741i	−0.458639	−	0.113044i
$609$	8.60685	+	9.71513i	0.348767	+	0.393677i
$610$	2.03316	+	2.94554i	0.0823203	+	0.119262i
$611$	−1.83599	−	16.1861i	−0.0742761	−	0.654822i
$612$	3.12336	−	4.52497i	0.126254	−	0.182911i
$613$	−8.96818	+	1.08893i	−0.362222	+	0.0439817i	−0.299624	−	0.954057i	$-0.596861\pi$
$613$	−8.96818	+	1.08893i	−0.362222	+	0.0439817i	−0.0625971	+	0.998039i	$0.519938\pi$
$614$	0.135582	−	1.11662i	0.00547166	−	0.0450632i
$615$	1.58864	+	0.833781i	0.0640600	+	0.0336213i
$616$	−11.9683	+	48.5573i	−0.482216	+	1.95643i
$617$	8.15733	+	0.990479i	0.328402	+	0.0398752i	0.283077	−	0.959097i	$-0.408645\pi$
$617$	8.15733	+	0.990479i	0.328402	+	0.0398752i	0.0453246	+	0.998972i	$0.485568\pi$
$618$	4.71473	−	5.32183i	0.189654	−	0.214076i
$619$	−10.2126	+	7.04922i	−0.410478	+	0.283332i	−0.755355	−	0.655315i	$-0.772536\pi$
$619$	−10.2126	+	7.04922i	−0.410478	+	0.283332i	0.344878	+	0.938648i	$0.387920\pi$
$620$	15.1090	−	21.8891i	0.606791	−	0.879088i
$621$	4.68669	−	1.15516i	0.188070	−	0.0463552i
$622$	3.00413	+	0.364767i	0.120455	+	0.0146258i
$623$	37.7225	−	19.7983i	1.51132	−	0.793201i
$624$	−9.14984	+	1.03786i	−0.366287	+	0.0415477i
$625$	−1.06829	−	0.560682i	−0.0427316	−	0.0224273i
$626$	6.73290	+	4.64738i	0.269101	+	0.185747i
$627$	−7.50843	+	10.8778i	−0.299858	+	0.434419i
$628$	12.0431	−	10.6693i	0.480572	−	0.425750i
$629$	−5.91102	−	6.67216i	−0.235688	−	0.266037i
$630$	−3.09840	−	1.17507i	−0.123443	−	0.0468158i
$631$	0.677224	−	1.29034i	0.0269599	−	0.0513678i	−0.871604	−	0.490212i	$-0.836920\pi$
$631$	0.677224	−	1.29034i	0.0269599	−	0.0513678i	0.898563	+	0.438844i	$0.144612\pi$
$632$	−1.42917	−	0.542011i	−0.0568492	−	0.0215600i
$633$	−14.0041	−	3.45170i	−0.556612	−	0.137193i
$634$	−13.2828	+	11.7676i	−0.527529	+	0.467350i
$635$	13.3346	−	9.20420i	0.529167	−	0.365258i
$636$	7.66592	+	20.2134i	0.303973	+	0.801512i
$637$	49.4443	−	18.3072i	1.95905	−	0.725358i
$638$	2.83978	−	7.48788i	0.112428	−	0.296448i
$639$	−0.654162	−	2.65404i	−0.0258783	−	0.104992i
$640$	14.3119	−	7.51144i	0.565726	−	0.296916i
$641$	4.47820	+	11.8081i	0.176878	+	0.466390i	0.993909	−	0.110204i	$-0.0351505\pi$
$641$	4.47820	+	11.8081i	0.176878	+	0.466390i	−0.817031	+	0.576594i	$0.804381\pi$
$642$	−4.16068	+	0.505198i	−0.164209	+	0.0199386i
$643$	23.4787	+	16.2062i	0.925909	+	0.639109i	0.932617	−	0.360869i	$-0.117520\pi$
$643$	23.4787	+	16.2062i	0.925909	+	0.639109i	−0.00670793	+	0.999978i	$0.502135\pi$
$644$	9.39198	−	38.1048i	0.370096	−	1.50154i
$645$	3.77659	+	15.3222i	0.148703	+	0.603311i
$646$	0.439253	+	3.61758i	0.0172822	+	0.142332i
$647$	0.339986	−	0.896470i	0.0133662	−	0.0352439i	−0.928167	−	0.372164i	$-0.878616\pi$
$647$	0.339986	−	0.896470i	0.0133662	−	0.0352439i	0.941533	+	0.336920i	$0.109385\pi$
$648$	0.449919	−	1.82539i	0.0176745	−	0.0717082i
$649$	59.3293	−	14.6234i	2.32888	−	0.574017i
$650$	−1.87190	−	5.05564i	−0.0734218	−	0.198298i
$651$	−48.3381	−	11.9143i	−1.89452	−	0.466957i
$652$	5.51986	−	10.5172i	0.216174	−	0.411886i
$653$	16.2939			0.637631			0.318815	−	0.947817i	$-0.396715\pi$
$653$	16.2939			0.637631			0.318815	+	0.947817i	$0.396715\pi$
$654$	−7.17650			−0.280623
$655$	0.683454	−	1.30221i	0.0267048	−	0.0508817i
$656$	2.13856	+	2.41394i	0.0834969	+	0.0942485i
$657$			4.10865i			0.160294i
$658$	6.98736	−	7.88710i	0.272396	−	0.307471i
$659$	14.3822	−	7.54835i	0.560250	−	0.294042i	−0.160729	−	0.986999i	$-0.551385\pi$
$659$	14.3822	−	7.54835i	0.560250	−	0.294042i	0.720979	+	0.692957i	$0.243692\pi$
$660$	−1.71300	−	14.1078i	−0.0666785	−	0.549147i
$661$	17.3792	+	33.1134i	0.675974	+	1.28796i	0.945705	+	0.325025i	$0.105373\pi$
$661$	17.3792	+	33.1134i	0.675974	+	1.28796i	−0.269731	+	0.962936i	$0.586935\pi$
$662$	1.68432	+	13.8716i	0.0654628	+	0.539135i
$663$	5.18979	+	10.0807i	0.201555	+	0.391501i
$664$	1.00424	−	8.27068i	0.0389722	−	0.320965i
$665$	−14.2738	+	5.41334i	−0.553515	+	0.209920i
$666$	−1.25886	−	0.660699i	−0.0487797	−	0.0256016i
$667$	−4.77758	+	12.5974i	−0.184989	+	0.487775i
$668$	14.3832	+	27.4049i	0.556503	+	1.06033i
$669$	1.07578	+	2.04973i	0.0415922	+	0.0792473i
$670$	1.26032	+	5.11331i	0.0486904	+	0.197545i
$671$	28.5217	+	3.46316i	1.10107	+	0.133694i
$672$	−17.5458	−	15.5442i	−0.676845	−	0.599632i
$673$	11.5435	+	16.7236i	0.444969	+	0.644649i	0.979722	−	0.200359i	$-0.0642110\pi$
$673$	11.5435	+	16.7236i	0.444969	+	0.644649i	−0.534754	+	0.845008i	$0.679596\pi$
$674$	−14.2583	−	5.40747i	−0.549210	−	0.208288i
$675$	−2.98120			−0.114746
$676$	8.39421	−	21.1231i	0.322854	−	0.812426i
$677$	8.80803			0.338520			0.169260	−	0.985571i	$-0.445862\pi$
$677$	8.80803			0.338520			0.169260	+	0.985571i	$0.445862\pi$
$678$	5.31360	+	2.01518i	0.204068	+	0.0773926i
$679$	−29.3131	−	42.4673i	−1.12493	−	1.62975i
$680$	−6.28751	−	5.57025i	−0.241115	−	0.213609i
$681$	−20.3144	−	2.46661i	−0.778448	−	0.0945207i
$682$	7.35117	+	29.8249i	0.281491	+	1.14205i
$683$	−13.5848	−	25.8837i	−0.519809	−	0.990414i	−0.993936	−	0.109958i	$-0.964929\pi$
$683$	−13.5848	−	25.8837i	−0.519809	−	0.990414i	0.474127	−	0.880457i	$-0.342764\pi$
$684$	−1.87742	−	3.57713i	−0.0717850	−	0.136775i
$685$	−9.91087	+	26.1328i	−0.378675	+	0.998484i
$686$	15.7426	+	8.26233i	0.601054	+	0.315457i
$687$	0.318475	−	0.120782i	0.0121506	−	0.00460811i
$688$	−3.41915	+	28.1592i	−0.130354	+	1.07356i
$689$	−44.2110	−	5.72222i	−1.68430	−	0.217999i
$690$	−0.414620	−	3.41470i	−0.0157843	−	0.129996i
$691$	−13.7314	−	26.1629i	−0.522366	−	0.995284i	−0.993566	−	0.113258i	$-0.963871\pi$
$691$	−13.7314	−	26.1629i	−0.522366	−	0.995284i	0.471200	−	0.882026i	$-0.343821\pi$
$692$	−3.62379	−	29.8446i	−0.137756	−	1.13452i
$693$	−23.5540	+	12.3621i	−0.894743	+	0.469597i
$694$	−3.91185	+	4.41557i	−0.148492	+	0.167613i
$695$		−	0.789277i		−	0.0299390i
$696$	3.47975	+	3.92782i	0.131899	+	0.148884i
$697$	1.84534	−	3.51599i	0.0698971	−	0.133178i
$698$	−3.54352			−0.134124
$699$	1.86006			0.0703538
$700$	−11.2641	+	21.4620i	−0.425745	+	0.811189i
$701$	12.0300	+	2.96513i	0.454366	+	0.111991i	0.459856	−	0.887994i	$-0.347901\pi$
$701$	12.0300	+	2.96513i	0.454366	+	0.111991i	−0.00548932	+	0.999985i	$0.501747\pi$
$702$	1.34408	+	1.20979i	0.0507289	+	0.0456607i
$703$	−6.35923	+	1.56741i	−0.239843	+	0.0591160i
$704$	3.53162	−	14.3283i	0.133103	−	0.540020i
$705$	−2.27635	+	6.00225i	−0.0857324	+	0.226058i
$706$	−0.716318	−	5.89941i	−0.0269590	−	0.222027i
$707$	−7.45211	−	30.2344i	−0.280266	−	1.13708i
$708$	−4.46954	+	18.1336i	−0.167976	+	0.681503i
$709$	10.5541	+	7.28500i	0.396369	+	0.273594i	0.749532	−	0.661968i	$-0.230278\pi$
$709$	10.5541	+	7.28500i	0.396369	+	0.273594i	−0.353163	+	0.935562i	$0.614894\pi$
$710$	−1.93372	+	0.234797i	−0.0725714	+	0.00881176i
$711$	−0.288300	−	0.760185i	−0.0108121	−	0.0285092i
$712$	15.2512	−	8.00443i	0.571562	−	0.299979i
$713$	−12.3675	−	50.1767i	−0.463165	−	1.87913i
$714$	−2.60068	+	6.85743i	−0.0973280	+	0.256633i
$715$	27.3188	+	10.6078i	1.02167	+	0.396707i
$716$	13.3265	+	35.1391i	0.498035	+	1.31321i
$717$	23.2493	−	16.0478i	0.868260	−	0.599316i
$718$	−2.00565	+	1.77685i	−0.0748502	+	0.0663115i
$719$	−30.2976	−	7.46769i	−1.12991	−	0.278498i	−0.370323	−	0.928903i	$-0.620753\pi$
$719$	−30.2976	−	7.46769i	−1.12991	−	0.278498i	−0.759588	+	0.650405i	$0.774599\pi$
$720$	3.39300	+	1.28680i	0.126450	+	0.0479561i
$721$	30.6342	−	58.3685i	1.14088	−	2.17376i
$722$	−6.40657	−	2.42969i	−0.238428	−	0.0904238i
$723$	−0.761135	−	0.859144i	−0.0283069	−	0.0319519i
$724$	1.15780	−	1.02572i	0.0430294	−	0.0381207i
$725$	4.72693	−	6.84814i	0.175554	−	0.254333i
$726$	8.96719	+	6.18960i	0.332804	+	0.229718i
$727$	−34.6398	−	18.1803i	−1.28472	−	0.674272i	−0.322504	−	0.946568i	$-0.604525\pi$
$727$	−34.6398	−	18.1803i	−1.28472	−	0.674272i	−0.962213	+	0.272296i	$0.912217\pi$
$728$	29.5595	−	10.9447i	1.09555	−	0.405637i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	2.90656	+	0.352920i	0.107577	+	0.0130622i
$731$	33.9114	−	8.35840i	1.25426	−	0.309147i
$732$	−4.98847	+	7.22704i	−0.184379	+	0.267119i
$733$	−18.3414	+	12.6601i	−0.677454	+	0.467612i	−0.856445	−	0.516238i	$-0.827332\pi$
$733$	−18.3414	+	12.6601i	−0.677454	+	0.467612i	0.178992	+	0.983851i	$0.442717\pi$
$734$	7.19842	−	8.12533i	0.265698	−	0.299912i
$735$	−20.6258	−	2.50443i	−0.760795	−	0.0923772i
$736$	5.82317	−	23.6255i	0.214645	−	0.870849i
$737$	37.4331	+	19.6464i	1.37887	+	0.723685i
$738$	0.0763380	−	0.628700i	0.00281004	−	0.0231428i
$739$	−21.7790	+	2.64445i	−0.801153	+	0.0972776i	−0.510864	−	0.859661i	$-0.670675\pi$
$739$	−21.7790	+	2.64445i	−0.801153	+	0.0972776i	−0.290289	+	0.956939i	$0.593751\pi$
$740$	4.00033	−	5.79548i	0.147055	−	0.213046i
$741$	8.33052	+	0.0656766i	0.306029	+	0.00241269i
$742$	−16.3808	−	23.7317i	−0.601358	−	0.871218i
$743$	31.9474	+	36.0611i	1.17204	+	1.32295i	0.936326	+	0.351131i	$0.114203\pi$
$743$	31.9474	+	36.0611i	1.17204	+	1.32295i	0.235709	+	0.971824i	$0.424259\pi$
$744$	−19.5431	−	4.81693i	−0.716484	−	0.176597i
$745$	−0.0735015	−	0.106485i	−0.00269289	−	0.00390132i
$746$		−	2.35571i		−	0.0862486i
$747$	3.64710	−	2.51741i	0.133440	−	0.0921073i
$748$	−31.2237	+	3.79124i	−1.14165	+	0.138621i
$749$	−36.3338	+	13.7796i	−1.32761	+	0.503495i
$750$	−0.685560	+	5.64610i	−0.0250331	+	0.206166i
$751$	−9.02807	−	23.8051i	−0.329439	−	0.868659i	−0.992737	−	0.120304i	$-0.961613\pi$
$751$	−9.02807	−	23.8051i	−0.329439	−	0.868659i	0.663298	−	0.748355i	$-0.269156\pi$
$752$	−7.65173	+	8.63702i	−0.279030	+	0.314960i
$753$	−1.29668	−	1.14876i	−0.0472537	−	0.0418631i
$754$	−4.91017	+	1.16926i	−0.178818	+	0.0425821i
$755$	3.09381	−	2.74088i	0.112595	−	0.0997507i
$756$		−	8.13043i		−	0.295701i
$757$	21.9796	+	19.4723i	0.798864	+	0.707731i	0.960244	−	0.279161i	$-0.0900563\pi$
$757$	21.9796	+	19.4723i	0.798864	+	0.707731i	−0.161381	+	0.986892i	$0.551595\pi$
$758$	−0.795812	+	0.196150i	−0.0289052	+	0.00712449i
$759$	−22.7249	−	15.6859i	−0.824861	−	0.569361i
$760$	−5.77089	+	2.18861i	−0.209332	+	0.0793893i
$761$	8.30544	−	3.14984i	0.301072	−	0.114181i	−0.199443	−	0.979909i	$-0.563913\pi$
$761$	8.30544	−	3.14984i	0.301072	−	0.114181i	0.500515	+	0.865728i	$0.333144\pi$
$762$	−4.70700	−	3.24901i	−0.170517	−	0.117699i
$763$	−64.6033	+	15.9233i	−2.33880	+	0.576461i
$764$	28.1087	+	24.9022i	1.01694	+	0.900928i
$765$		−	4.46805i		−	0.161543i
$766$	4.66012	−	4.12851i	0.168377	−	0.149169i
$767$	−28.6253	−	25.7655i	−1.03360	−	0.930337i
$768$	−0.408797	−	0.362162i	−0.0147512	−	0.0130684i
$769$	5.84679	−	6.59967i	0.210841	−	0.237990i	−0.633571	−	0.773684i	$-0.718412\pi$
$769$	5.84679	−	6.59967i	0.210841	−	0.237990i	0.844412	+	0.535694i	$0.179950\pi$
$770$	6.72204	+	17.7246i	0.242245	+	0.638749i
$771$	0.691201	−	5.69255i	0.0248930	−	0.205012i
$772$	20.3312	−	7.71062i	0.731737	−	0.277511i
$773$	−14.7321	+	1.78880i	−0.529878	+	0.0643388i	−0.381104	−	0.924532i	$-0.624456\pi$
$773$	−14.7321	+	1.78880i	−0.529878	+	0.0643388i	−0.148774	+	0.988871i	$0.547533\pi$
$774$	4.58441	−	3.16439i	0.164783	−	0.113742i
$775$			31.9174i			1.14651i
$776$	−11.8513	−	17.1695i	−0.425436	−	0.616350i
$777$	−12.7983	−	3.15449i	−0.459135	−	0.113167i
$778$	2.18520	+	2.46659i	0.0783434	+	0.0884314i
$779$	−1.65738	−	2.40113i	−0.0593818	−	0.0860294i
$780$	−6.75118	+	5.88668i	−0.241731	+	0.210777i
$781$	−8.88280	+	12.8690i	−0.317852	+	0.460488i
$782$	−7.55748	+	0.917644i	−0.270255	+	0.0328149i
$783$	−0.336442	+	2.77085i	−0.0120234	+	0.0990220i
$784$	−33.0695	−	17.3562i	−1.18105	−	0.619864i
$785$	3.12900	−	12.6948i	0.111679	−	0.453099i
$786$	−0.515349	−	0.0625747i	−0.0183819	−	0.00223197i
$787$	−28.0630	+	31.6766i	−1.00034	+	1.12915i	−0.00871857	+	0.999962i	$0.502775\pi$
$787$	−28.0630	+	31.6766i	−1.00034	+	1.12915i	−0.991620	+	0.129187i	$0.958763\pi$
$788$	21.0423	−	14.5244i	0.749601	−	0.517412i
$789$	8.52406	−	12.3492i	0.303465	−	0.439644i
$790$	−0.562538	+	0.138653i	−0.0200142	+	0.00493306i
$791$	52.3046	+	6.35093i	1.85974	+	0.225813i
$792$	−9.52287	+	4.99799i	−0.338381	+	0.177596i
$793$	−8.28886	−	16.1003i	−0.294346	−	0.571739i
$794$	10.5839	+	5.55487i	0.375609	+	0.197135i
$795$	14.4579	+	9.97955i	0.512768	+	0.353938i
$796$	4.99491	−	7.23637i	0.177040	−	0.256486i
$797$	15.2339	−	13.4961i	0.539612	−	0.478055i	−0.348738	−	0.937220i	$-0.613390\pi$
$797$	15.2339	−	13.4961i	0.539612	−	0.478055i	0.888351	+	0.459165i	$0.151851\pi$
$798$	3.57338	+	4.03351i	0.126496	+	0.142785i
$799$	13.2843	+	5.03806i	0.469964	+	0.178234i
$800$	−6.98394	+	13.3068i	−0.246920	+	0.470466i
$801$	8.56628	+	3.24876i	0.302675	+	0.114789i
$802$	7.99300	+	1.97010i	0.282243	+	0.0695665i
$803$	17.5928	−	15.5859i	0.620836	−	0.550013i
$804$	−10.6340	+	7.34010i	−0.375031	+	0.258866i
$805$	−11.3090	−	29.8194i	−0.398590	−	1.05100i
$806$	12.9523	−	14.3900i	0.456226	−	0.506865i
$807$	7.98249	−	21.0481i	0.280997	−	0.740928i
$808$	−3.01289	−	12.2238i	−0.105993	−	0.430030i
$809$	45.2865	−	23.7682i	1.59219	−	0.835645i	0.592645	−	0.805464i	$-0.298084\pi$
$809$	45.2865	−	23.7682i	1.59219	−	0.835645i	0.999544	−	0.0301815i	$-0.00960854\pi$
$810$	−0.252699	−	0.666312i	−0.00887893	−	0.0234118i
$811$	22.4241	−	2.72278i	0.787418	−	0.0956099i	0.283057	−	0.959103i	$-0.408651\pi$
$811$	22.4241	−	2.72278i	0.787418	−	0.0956099i	0.504361	+	0.863493i	$0.331728\pi$
$812$	18.6765	+	12.8915i	0.655416	+	0.452401i
$813$	0.0685943	−	0.278298i	0.00240571	−	0.00976033i
$814$	1.94634	+	7.89660i	0.0682191	+	0.276776i
$815$	−1.16345	−	9.58185i	−0.0407538	−	0.335638i
$816$	2.84796	−	7.50944i	0.0996984	−	0.262883i
$817$	6.14138	−	24.9166i	0.214860	−	0.871720i
$818$	10.8988	−	2.68630i	0.381066	−	0.0939244i
$819$	14.7837	+	7.90838i	0.516586	+	0.276341i
$820$	3.04582	+	0.750727i	0.106365	+	0.0262165i
$821$	16.2786	−	31.0163i	0.568128	−	1.08248i	−0.416716	−	0.909037i	$-0.636819\pi$
$821$	16.2786	−	31.0163i	0.568128	−	1.08248i	0.984844	−	0.173441i	$-0.0554886\pi$
$822$	9.86578			0.344109
$823$	4.92080			0.171528			0.0857642	−	0.996315i	$-0.472667\pi$
$823$	4.92080			0.171528			0.0857642	+	0.996315i	$0.472667\pi$
$824$	12.3854	−	23.5984i	0.431465	−	0.822088i
$825$	11.3089	+	12.7652i	0.393727	+	0.444426i
$826$		−	24.9120i		−	0.866801i
$827$	−25.5414	+	28.8303i	−0.888163	+	1.00253i	0.111798	+	0.993731i	$0.464339\pi$
$827$	−25.5414	+	28.8303i	−0.888163	+	1.00253i	−0.999961	+	0.00879784i	$0.997200\pi$
$828$	7.47297	−	3.92212i	0.259704	−	0.136303i
$829$	0.0300703	+	0.247651i	0.00104439	+	0.00860129i	0.993222	−	0.116235i	$-0.0370825\pi$
$829$	0.0300703	+	0.247651i	0.00104439	+	0.00860129i	−0.992177	+	0.124836i	$0.960159\pi$
$830$	−1.46760	−	2.79629i	−0.0509413	−	0.0970605i
$831$	−0.304574	−	2.50839i	−0.0105656	−	0.0870152i
$832$	−8.72246	+	3.22957i	−0.302397	+	0.111965i
$833$	−5.54284	+	45.6494i	−0.192048	+	1.58166i
$834$	−0.260503	+	0.0987958i	−0.00902048	+	0.00342102i
$835$	22.2701	+	11.6882i	0.770688	+	0.404488i
$836$	−8.19501	+	21.6085i	−0.283430	+	0.747345i
$837$	−4.97543	−	9.47989i	−0.171976	−	0.327673i
$838$	−1.46786	−	2.79678i	−0.0507065	−	0.0966131i
$839$	−3.00505	−	12.1920i	−0.103746	−	0.420913i	0.895986	−	0.444083i	$-0.146470\pi$
$839$	−3.00505	−	12.1920i	−0.103746	−	0.420913i	−0.999732	+	0.0231697i	$0.992624\pi$
$840$	−12.3308	−	1.49723i	−0.425454	−	0.0516594i
$841$	15.8753	+	14.0643i	0.547425	+	0.484976i
$842$	6.59401	+	9.55308i	0.227245	+	0.329221i
$843$	19.8192	+	7.51642i	0.682608	+	0.258879i
$844$	−25.2183			−0.868048
$845$	−4.13709	−	18.0017i	−0.142320	−	0.619278i
$846$	2.26600			0.0779066
$847$	94.4567	+	35.8227i	3.24557	+	1.23088i
$848$	17.9383	+	25.9881i	0.616004	+	0.892436i
$849$	−1.89577	−	1.67951i	−0.0650627	−	0.0576405i
$850$	4.66761	+	0.566751i	0.160098	+	0.0194394i
$851$	−3.27448	−	13.2851i	−0.112248	−	0.455406i
$852$	−2.22107	−	4.23189i	−0.0760926	−	0.144982i
$853$	26.7096	+	50.8910i	0.914521	+	1.74247i	0.615308	+	0.788287i	$0.289032\pi$
$853$	26.7096	+	50.8910i	0.914521	+	1.74247i	0.299213	+	0.954186i	$0.403276\pi$
$854$	4.15367	−	10.9523i	0.142136	−	0.374781i
$855$	−2.90688	−	1.52565i	−0.0994133	−	0.0521761i
$856$	−14.6897	+	5.57108i	−0.502085	+	0.190416i
$857$	−6.51774	+	53.6784i	−0.222642	+	1.83362i	0.269376	+	0.963035i	$0.413183\pi$
$857$	−6.51774	+	53.6784i	−0.222642	+	1.83362i	−0.492018	+	0.870585i	$0.663740\pi$
$858$	0.0815542	−	10.3444i	0.00278421	−	0.353154i
$859$	−6.67345	−	54.9608i	−0.227695	−	1.87524i	−0.439946	−	0.898024i	$-0.645003\pi$
$859$	−6.67345	−	54.9608i	−0.227695	−	1.87524i	0.212251	−	0.977215i	$-0.431921\pi$
$860$	12.8226	+	24.4314i	0.437247	+	0.833104i
$861$	−0.707766	−	5.82898i	−0.0241206	−	0.198651i
$862$	0.490849	−	0.257617i	0.0167184	−	0.00877448i
$863$	2.33759	−	2.63859i	0.0795724	−	0.0898186i	−0.707376	−	0.706837i	$-0.750121\pi$
$863$	2.33759	−	2.63859i	0.0795724	−	0.0898186i	0.786948	+	0.617019i	$0.211660\pi$
$864$		−	5.04099i		−	0.171498i
$865$	−16.2006	−	18.2867i	−0.550838	−	0.621767i
$866$	−8.04711	+	15.3325i	−0.273452	+	0.521019i
$867$	7.11125			0.241511
$868$	−87.0462			−2.95454
$869$	−2.16139	+	4.11818i	−0.0733200	+	0.139700i
$870$	1.93127	+	0.476014i	0.0654761	+	0.0161384i
$871$	−3.00312	−	26.4756i	−0.101757	−	0.897093i
$872$	−26.1191	+	6.43778i	−0.884504	+	0.218011i
$873$	2.65567	−	10.7745i	0.0898809	−	0.364661i
$874$	−1.98355	+	5.23018i	−0.0670945	+	0.176914i
$875$	6.35615	+	52.3476i	0.214877	+	1.76967i
$876$	1.71919	+	6.97502i	0.0580860	+	0.235664i
$877$	4.97067	−	20.1668i	0.167848	−	0.680984i	−0.825358	−	0.564610i	$-0.809027\pi$
$877$	4.97067	−	20.1668i	0.167848	−	0.680984i	0.993205	−	0.116374i	$-0.0371272\pi$
$878$	−2.12601	−	1.46748i	−0.0717495	−	0.0495251i
$879$	−16.6929	+	2.02689i	−0.563039	+	0.0683653i
$880$	−7.36118	−	19.4098i	−0.248145	−	0.654306i
$881$	−11.8590	+	6.22409i	−0.399540	+	0.209695i	−0.652511	−	0.757779i	$-0.726285\pi$
$881$	−11.8590	+	6.22409i	−0.399540	+	0.209695i	0.252971	+	0.967474i	$0.418592\pi$
$882$	1.75519	+	7.12110i	0.0591004	+	0.239780i
$883$	−2.76604	+	7.29345i	−0.0930847	+	0.245444i	−0.973470	−	0.228815i	$-0.926515\pi$
$883$	−2.76604	+	7.29345i	−0.0930847	+	0.245444i	0.880385	+	0.474259i	$0.157284\pi$
$884$	13.0285	+	14.9418i	0.438196	+	0.502547i
$885$	5.38183	+	14.1907i	0.180908	+	0.477016i
$886$	−8.14872	+	5.62466i	−0.273762	+	0.188964i
$887$	−16.6711	+	14.7693i	−0.559762	+	0.495906i	−0.894902	−	0.446262i	$-0.852755\pi$
$887$	−16.6711	+	14.7693i	−0.559762	+	0.495906i	0.335140	+	0.942168i	$0.391216\pi$
$888$	−5.17433	−	1.27536i	−0.173639	−	0.0427982i
$889$	−49.5816	−	18.8038i	−1.66291	−	0.630660i
$890$	3.03407	−	5.78094i	0.101702	−	0.193778i
$891$	−5.34881	−	2.02854i	−0.179192	−	0.0679585i
$892$	2.68397	+	3.02958i	0.0898660	+	0.101438i
$893$	7.81375	−	6.92238i	0.261477	−	0.231649i
$894$	−0.0259454	+	0.0375884i	−0.000867744	+	0.00125714i
$895$	25.1337	+	17.3485i	0.840127	+	0.579898i
$896$	−46.8391	−	24.5831i	−1.56479	−	0.821263i
$897$	−0.137205	+	17.4033i	−0.00458114	+	0.581078i
$898$	4.65579	−	2.44354i	0.155366	−	0.0815422i
$899$	29.6653	+	3.60202i	0.989394	+	0.120134i
$900$	−5.06101	+	1.24743i	−0.168700	+	0.0415809i
$901$	22.0869	−	31.9984i	0.735821	−	1.06602i
$902$	−2.98161	+	2.05806i	−0.0992768	+	0.0685258i
$903$	34.2480	−	38.6580i	1.13970	−	1.28646i
$904$	21.1467	+	2.56768i	0.703330	+	0.0853997i
$905$	0.300816	−	1.22046i	0.00999947	−	0.0405694i
$906$	−1.29189	−	0.678039i	−0.0429203	−	0.0225263i
$907$	−1.33416	+	10.9878i	−0.0443000	+	0.364843i	0.953654	+	0.300906i	$0.0972890\pi$
$907$	−1.33416	+	10.9878i	−0.0443000	+	0.364843i	−0.997954	+	0.0639377i	$0.979634\pi$
$908$	−35.5186	+	4.31274i	−1.17873	+	0.143123i
$909$	3.80405	−	5.51112i	0.126172	−	0.182792i
$910$	6.86446	−	9.77908i	0.227555	−	0.324173i
$911$	−3.81105	−	5.52127i	−0.126266	−	0.182928i	0.754753	−	0.656009i	$-0.227757\pi$
$911$	−3.81105	−	5.52127i	−0.126266	−	0.182928i	−0.881019	+	0.473082i	$0.843141\pi$
$912$	−3.91314	−	4.41702i	−0.129577	−	0.146262i
$913$	−24.6143	−	6.06688i	−0.814614	−	0.200784i
$914$	7.58855	+	10.9939i	0.251007	+	0.363646i
$915$			7.13613i			0.235913i
$916$	0.490119	−	0.338305i	0.0161940	−	0.0111779i
$917$	−4.77804	+	0.580159i	−0.157785	+	0.0191585i
$918$	−1.47469	+	0.559277i	−0.0486721	+	0.0184589i
$919$	−2.71149	+	22.3312i	−0.0894439	+	0.736637i	0.877131	+	0.480252i	$0.159455\pi$
$919$	−2.71149	+	22.3312i	−0.0894439	+	0.736637i	−0.966575	+	0.256385i	$0.917468\pi$
$920$	−4.57223	−	12.0560i	−0.150742	−	0.397474i
$921$	1.48719	−	1.67869i	0.0490046	−	0.0553148i
$922$	7.79097	+	6.90220i	0.256582	+	0.227312i
$923$	9.85536	+	0.0776983i	0.324393	+	0.00255747i
$924$	−34.8136	+	30.8422i	−1.14528	+	1.01463i
$925$			8.45062i			0.277855i
$926$	8.59575	+	7.61517i	0.282474	+	0.250250i
$927$	13.7640	−	3.39252i	0.452069	−	0.111425i
$928$	11.5797	+	7.99289i	0.380123	+	0.262380i
$929$	−19.2706	+	7.30837i	−0.632248	+	0.239780i	−0.649847	−	0.760065i	$-0.725167\pi$
$929$	−19.2706	+	7.30837i	−0.632248	+	0.239780i	0.0175991	+	0.999845i	$0.494398\pi$
$930$	−7.13369	+	2.70545i	−0.233923	+	0.0887152i
$931$	27.8066	+	19.1935i	0.911323	+	0.629041i
$932$	3.15771	−	0.778306i	0.103434	−	0.0254943i
$933$	4.51631	+	4.00110i	0.147857	+	0.130990i
$934$		−	0.212593i		−	0.00695625i
$935$	−19.1317	+	16.9492i	−0.625674	+	0.554298i
$936$	5.97706	+	3.19736i	0.195366	+	0.104509i
$937$	−29.4487	−	26.0892i	−0.962046	−	0.852298i	0.0270406	−	0.999634i	$-0.491392\pi$
$937$	−29.4487	−	26.0892i	−0.962046	−	0.852298i	−0.989086	+	0.147336i	$0.952930\pi$
$938$	11.4292	−	12.9009i	0.373177	−	0.421230i
$939$	5.78421	+	15.2517i	0.188761	+	0.497721i
$940$	−1.35291	+	11.1422i	−0.0441269	+	0.363418i
$941$	3.88367	−	1.47288i	0.126604	−	0.0480145i	−0.290489	−	0.956878i	$-0.593818\pi$
$941$	3.88367	−	1.47288i	0.126604	−	0.0480145i	0.417093	+	0.908864i	$0.363049\pi$
$942$	−4.58164	+	0.556311i	−0.149278	+	0.0181256i
$943$	5.01620	−	3.46243i	0.163350	−	0.112752i
$944$			27.2807i			0.887912i
$945$	−3.75323	−	5.43749i	−0.122092	−	0.176881i
$946$	−30.9402	−	7.62608i	−1.00595	−	0.247945i
$947$	−9.92252	−	11.2002i	−0.322439	−	0.363958i	0.564833	−	0.825205i	$-0.308941\pi$
$947$	−9.92252	−	11.2002i	−0.322439	−	0.363958i	−0.887272	+	0.461247i	$0.847402\pi$
$948$	−0.807517	−	1.16989i	−0.0262269	−	0.0379963i
$949$	−14.3551	−	3.65849i	−0.465986	−	0.118760i
$950$	1.96252	−	2.84320i	0.0636725	−	0.0922455i
$951$	−35.1239	+	4.26482i	−1.13897	+	0.138296i
$952$	−3.31370	+	27.2908i	−0.107398	+	0.884499i
$953$	−10.7923	−	5.66423i	−0.349597	−	0.183483i	0.280779	−	0.959772i	$-0.409407\pi$
$953$	−10.7923	−	5.66423i	−0.349597	−	0.183483i	−0.630376	+	0.776290i	$0.717099\pi$
$954$	1.48405	−	6.02103i	0.0480479	−	0.194938i
$955$	30.2941	+	3.67837i	0.980295	+	0.119029i
$956$	32.7541	−	36.9717i	1.05934	−	1.19575i
$957$	13.1407	−	9.07040i	0.424780	−	0.293204i
$958$	−0.412232	+	0.597221i	−0.0133186	+	0.0192953i
$959$	88.8123	−	21.8903i	2.86790	−	0.706874i
$960$	3.63860	+	0.441806i	0.117435	+	0.0142592i
$961$	−74.0448	+	38.8617i	−2.38854	+	1.25360i
$962$	3.42933	−	3.80997i	0.110566	−	0.122838i
$963$	−7.39943	−	3.88352i	−0.238443	−	0.125145i
$964$	−1.65163	−	1.14004i	−0.0531954	−	0.0367181i
$965$	10.0377	−	14.5422i	0.323126	−	0.468129i
$966$	−8.42640	+	7.46514i	−0.271115	+	0.240187i
$967$	39.9285	+	45.0699i	1.28401	+	1.44935i	0.829392	+	0.558667i	$0.188687\pi$
$967$	39.9285	+	45.0699i	1.28401	+	1.44935i	0.454622	+	0.890685i	$0.349775\pi$
$968$	38.1888	+	14.4831i	1.22743	+	0.465505i
$969$	−3.37659	+	6.43356i	−0.108472	+	0.206676i
$970$	−7.39403	−	2.80419i	−0.237408	−	0.0900370i
$971$	15.2878	+	3.76810i	0.490609	+	0.120924i	0.476856	−	0.878981i	$-0.341776\pi$
$971$	15.2878	+	3.76810i	0.490609	+	0.120924i	0.0137524	+	0.999905i	$0.495622\pi$
$972$	1.30873	−	1.15944i	0.0419777	−	0.0371890i
$973$	−2.12585	+	1.46737i	−0.0681518	+	0.0470418i
$974$	5.01956	+	13.2355i	0.160837	+	0.424093i
$975$	2.65457	−	10.4159i	0.0850142	−	0.333576i
$976$	−4.54861	+	11.9937i	−0.145597	+	0.383909i
$977$	−12.2145	−	49.5561i	−0.390776	−	1.58544i	−0.756034	−	0.654533i	$-0.772865\pi$
$977$	−12.2145	−	49.5561i	−0.390776	−	1.58544i	0.365258	−	0.930906i	$-0.380981\pi$
$978$	−3.01688	+	1.58338i	−0.0964693	+	0.0506310i
$979$	−18.5847	−	49.0038i	−0.593970	−	1.56617i
$980$	−36.0632	+	4.37887i	−1.15200	+	0.139878i
$981$	−11.7759	−	8.12829i	−0.375974	−	0.259516i
$982$	3.97877	−	16.1425i	0.126968	−	0.515129i
$983$	10.2561	+	41.6107i	0.327120	+	1.32718i	0.872347	+	0.488888i	$0.162597\pi$
$983$	10.2561	+	41.6107i	0.327120	+	1.32718i	−0.545227	+	0.838289i	$0.683556\pi$
$984$	−0.286149	−	2.35665i	−0.00912211	−	0.0751273i
$985$	7.36784	−	19.4274i	0.234759	−	0.619008i
$986$	1.05352	−	4.27431i	0.0335510	−	0.136122i
$987$	20.3986	−	5.02781i	0.649296	−	0.160037i
$988$	14.1697	−	3.37426i	0.450799	−	0.107349i
$989$	52.0532	+	12.8300i	1.65519	+	0.407969i
$990$	−1.89448	+	3.60963i	−0.0602106	+	0.114722i
$991$	−5.73174			−0.182075			−0.0910374	−	0.995847i	$-0.529018\pi$
$991$	−5.73174			−0.182075			−0.0910374	+	0.995847i	$0.529018\pi$
$992$	−53.9700			−1.71355
$993$	−12.9475	+	24.6695i	−0.410878	+	0.782863i
$994$	4.22746	+	4.77182i	0.134087	+	0.151353i
$995$		−	7.14534i		−	0.226523i
$996$	5.13811	−	5.79973i	0.162807	−	0.183771i
$997$	7.83682	−	4.11308i	0.248195	−	0.130263i	−0.336039	−	0.941848i	$-0.609087\pi$
$997$	7.83682	−	4.11308i	0.248195	−	0.130263i	0.584234	+	0.811585i	$0.301395\pi$
$998$	0.502091	+	4.13509i	0.0158934	+	0.130894i
$999$	−1.31732	−	2.50995i	−0.0416782	−	0.0794112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.b.25.7	✓	192
169.142	even	26	inner	507.2.p.b.142.7	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.b.25.7	✓	192	1.1	even	1	trivial
507.2.p.b.142.7	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)

\(f(q)\)	\(=\)	\(q+(-0.468954 - 0.177851i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.30873 - 1.15944i) q^{4} +(-1.41049 - 0.171264i) q^{5} +(0.120028 + 0.486973i) q^{6} +(2.16100 + 4.11744i) q^{7} +(0.873690 + 1.66468i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})\)	\(q+(-0.468954 - 0.177851i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.30873 - 1.15944i) q^{4} +(-1.41049 - 0.171264i) q^{5} +(0.120028 + 0.486973i) q^{6} +(2.16100 + 4.11744i) q^{7} +(0.873690 + 1.66468i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(0.630994 + 0.331171i) q^{10} +(5.34881 - 2.02854i) q^{11} +(-0.210752 + 1.73570i) q^{12} +(-2.95107 - 2.07152i) q^{13} +(-0.281119 - 2.31522i) q^{14} +(0.660300 + 1.25810i) q^{15} +(0.307849 + 2.53536i) q^{16} +(2.78444 - 1.46139i) q^{17} +(0.332587 - 0.375413i) q^{18} -2.31054i q^{19} +(1.64738 + 1.85951i) q^{20} +(2.16100 - 4.11744i) q^{21} -2.86912 q^{22} +4.82695 q^{23} +(0.873690 - 1.66468i) q^{24} +(-2.89457 - 0.713447i) q^{25} +(1.01550 + 1.49630i) q^{26} +(0.970942 - 0.239316i) q^{27} +(1.94574 - 7.89417i) q^{28} +(-0.989772 + 2.60982i) q^{29} +(-0.0858969 - 0.707425i) q^{30} +(-2.56217 - 10.3951i) q^{31} +(1.20639 - 4.89451i) q^{32} +(-4.70792 - 3.24964i) q^{33} +(-1.56568 + 0.190108i) q^{34} +(-2.34289 - 6.17769i) q^{35} +(1.54818 - 0.812546i) q^{36} +(-0.678374 - 2.75227i) q^{37} +(-0.410932 + 1.08354i) q^{38} +(-0.0284248 + 3.60544i) q^{39} +(-0.947229 - 2.49764i) q^{40} +(1.03921 - 0.717312i) q^{41} +(-1.74570 + 1.54655i) q^{42} +(10.7839 + 2.65798i) q^{43} +(-9.35213 - 3.54679i) q^{44} +(0.660300 - 1.25810i) q^{45} +(-2.26362 - 0.858477i) q^{46} +(2.99600 + 3.38178i) q^{47} +(1.91168 - 1.69360i) q^{48} +(-8.30692 + 12.0347i) q^{49} +(1.23053 + 0.849376i) q^{50} +(-2.78444 - 1.46139i) q^{51} +(1.46037 + 6.13265i) q^{52} +(10.9480 - 5.74593i) q^{53} +(-0.497890 - 0.0604548i) q^{54} +(-7.89184 + 1.94516i) q^{55} +(-4.96616 + 7.19473i) q^{56} +(-1.90154 + 1.31254i) q^{57} +(0.928316 - 1.04785i) q^{58} +(10.6038 + 1.28753i) q^{59} +(0.594527 - 2.41209i) q^{60} +(4.44716 + 2.33405i) q^{61} +(-0.647243 + 5.33052i) q^{62} +(-4.61617 + 0.560505i) q^{63} +(1.46542 - 2.12303i) q^{64} +(3.80767 + 3.42726i) q^{65} +(1.62985 + 2.36124i) q^{66} +(4.90055 + 5.53158i) q^{67} +(-5.33848 - 1.31582i) q^{68} +(-2.74202 - 3.97250i) q^{69} +3.31374i q^{70} +(-2.24960 + 1.55279i) q^{71} +(-1.86632 + 0.226612i) q^{72} +(3.84165 - 1.45695i) q^{73} +(-0.171367 + 1.41134i) q^{74} +(1.05715 + 2.78747i) q^{75} +(-2.67893 + 3.02388i) q^{76} +(19.9111 + 17.6397i) q^{77} +(0.654561 - 1.68573i) q^{78} +(-0.608553 + 0.539131i) q^{79} -3.62882i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-0.614915 + 0.151563i) q^{82} +(-3.64710 - 2.51741i) q^{83} +(-7.60208 + 2.88309i) q^{84} +(-4.17770 + 1.58439i) q^{85} +(-4.58441 - 3.16439i) q^{86} +(2.71009 - 0.667977i) q^{87} +(8.05006 + 7.13173i) q^{88} -9.16163i q^{89} +(-0.533404 + 0.472555i) q^{90} +(2.15208 - 16.6274i) q^{91} +(-6.31720 - 5.59655i) q^{92} +(-7.09954 + 8.01373i) q^{93} +(-0.803534 - 2.11874i) q^{94} +(-0.395713 + 3.25899i) q^{95} +(-4.71341 + 1.78756i) q^{96} +(-11.0160 + 1.33759i) q^{97} +(6.03594 - 4.16631i) q^{98} +5.72055i 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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Representations

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Database

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