LMFDB - Embedded newform 1014.2.g.e.437.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(239,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("1014.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.g (of order $4$, degree $2$, 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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.1
Character	$\chi$	$=$	1014.437
Dual form			1014.2.g.e.239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.68568 - 0.398108i) q^{3} -1.00000i q^{4} +(2.32916 - 2.32916i) q^{5} +(1.47346 - 0.910449i) q^{6} +(-2.38633 + 2.38633i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.68302 + 1.34216i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.68568 - 0.398108i) q^{3} -1.00000i q^{4} +(2.32916 - 2.32916i) q^{5} +(1.47346 - 0.910449i) q^{6} +(-2.38633 + 2.38633i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.68302 + 1.34216i) q^{9} +3.29393i q^{10} +(2.36913 + 2.36913i) q^{11} +(-0.398108 + 1.68568i) q^{12} -3.37478i q^{14} +(-4.85347 + 2.99896i) q^{15} -1.00000 q^{16} -0.142195 q^{17} +(-2.84623 + 0.948129i) q^{18} +(-0.900092 - 0.900092i) q^{19} +(-2.32916 - 2.32916i) q^{20} +(4.97260 - 3.07257i) q^{21} -3.35046 q^{22} -7.27175 q^{23} +(-0.910449 - 1.47346i) q^{24} -5.84998i q^{25} +(-3.98838 - 3.33059i) q^{27} +(2.38633 + 2.38633i) q^{28} +8.53511i q^{29} +(1.31134 - 5.55251i) q^{30} +(4.04437 + 4.04437i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.05042 - 4.93677i) q^{33} +(0.100547 - 0.100547i) q^{34} +11.1163i q^{35} +(1.34216 - 2.68302i) q^{36} +(8.22509 - 8.22509i) q^{37} +1.27292 q^{38} +3.29393 q^{40} +(-0.570705 + 0.570705i) q^{41} +(-1.34353 + 5.68879i) q^{42} +4.19114i q^{43} +(2.36913 - 2.36913i) q^{44} +(9.37530 - 3.12307i) q^{45} +(5.14190 - 5.14190i) q^{46} +(3.90177 + 3.90177i) q^{47} +(1.68568 + 0.398108i) q^{48} -4.38914i q^{49} +(4.13656 + 4.13656i) q^{50} +(0.239695 + 0.0566090i) q^{51} +8.81395i q^{53} +(5.17529 - 0.465131i) q^{54} +11.0362 q^{55} -3.37478 q^{56} +(1.15893 + 1.87560i) q^{57} +(-6.03524 - 6.03524i) q^{58} +(7.10744 + 7.10744i) q^{59} +(2.99896 + 4.85347i) q^{60} +0.696989 q^{61} -5.71960 q^{62} +(-9.60542 + 3.19973i) q^{63} +1.00000i q^{64} +(5.64780 + 1.33385i) q^{66} +(0.435004 + 0.435004i) q^{67} +0.142195i q^{68} +(12.2578 + 2.89494i) q^{69} +(-7.86041 - 7.86041i) q^{70} +(5.76010 - 5.76010i) q^{71} +(0.948129 + 2.84623i) q^{72} +(-1.54199 + 1.54199i) q^{73} +11.6320i q^{74} +(-2.32892 + 9.86118i) q^{75} +(-0.900092 + 0.900092i) q^{76} -11.3071 q^{77} -4.42494 q^{79} +(-2.32916 + 2.32916i) q^{80} +(5.39719 + 7.20210i) q^{81} -0.807098i q^{82} +(-1.61291 + 1.61291i) q^{83} +(-3.07257 - 4.97260i) q^{84} +(-0.331195 + 0.331195i) q^{85} +(-2.96358 - 2.96358i) q^{86} +(3.39790 - 14.3875i) q^{87} +3.35046i q^{88} +(5.45490 + 5.45490i) q^{89} +(-4.42099 + 8.83768i) q^{90} +7.27175i q^{92} +(-5.20741 - 8.42760i) q^{93} -5.51794 q^{94} -4.19292 q^{95} +(-1.47346 + 0.910449i) q^{96} +(5.33494 + 5.33494i) q^{97} +(3.10359 + 3.10359i) q^{98} +(3.17667 + 9.53620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} + 20 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 + 20 * q^9	$ 48 q - 4 q^{3} + 20 q^{9} - 48 q^{16} - 32 q^{22} + 116 q^{27} + 8 q^{40} - 40 q^{42} + 4 q^{48} - 144 q^{55} - 80 q^{61} + 96 q^{66} - 56 q^{79} + 84 q^{81} + 224 q^{87} - 16 q^{94}+O(q^{100}) $ 48 * q - 4 * q^3 + 20 * q^9 - 48 * q^16 - 32 * q^22 + 116 * q^27 + 8 * q^40 - 40 * q^42 + 4 * q^48 - 144 * q^55 - 80 * q^61 + 96 * q^66 - 56 * q^79 + 84 * q^81 + 224 * q^87 - 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.68568	−	0.398108i	−0.973227	−	0.229848i
$3$	−1.68568	−	0.398108i	−0.973227	−	0.229848i
$4$		−	1.00000i		−	0.500000i
$5$	2.32916	−	2.32916i	1.04163	−	1.04163i	0.0425375	−	0.999095i	$-0.486456\pi$
$5$	2.32916	−	2.32916i	1.04163	−	1.04163i	0.999095	−	0.0425375i	$-0.0135442\pi$
$6$	1.47346	−	0.910449i	0.601537	−	0.371689i
$7$	−2.38633	+	2.38633i	−0.901948	+	0.901948i	−0.995605	−	0.0936566i	$-0.970144\pi$
$7$	−2.38633	+	2.38633i	−0.901948	+	0.901948i	0.0936566	+	0.995605i	$0.470144\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.68302	+	1.34216i	0.894340	+	0.447388i
$10$			3.29393i			1.04163i
$11$	2.36913	+	2.36913i	0.714321	+	0.714321i	0.967436	−	0.253115i	$-0.0814553\pi$
$11$	2.36913	+	2.36913i	0.714321	+	0.714321i	−0.253115	+	0.967436i	$0.581455\pi$
$12$	−0.398108	+	1.68568i	−0.114924	+	0.486613i
$13$		0			0
$13$		0			0
$14$		−	3.37478i		−	0.901948i
$15$	−4.85347	+	2.99896i	−1.25316	+	0.774327i
$16$	−1.00000			−0.250000
$17$	−0.142195			−0.0344874			−0.0172437	−	0.999851i	$-0.505489\pi$
$17$	−0.142195			−0.0344874			−0.0172437	+	0.999851i	$0.505489\pi$
$18$	−2.84623	+	0.948129i	−0.670864	+	0.223476i
$19$	−0.900092	−	0.900092i	−0.206495	−	0.206495i	0.596281	−	0.802776i	$-0.296645\pi$
$19$	−0.900092	−	0.900092i	−0.206495	−	0.206495i	−0.802776	+	0.596281i	$0.796645\pi$
$20$	−2.32916	−	2.32916i	−0.520816	−	0.520816i
$21$	4.97260	−	3.07257i	1.08511	−	0.670489i
$22$	−3.35046			−0.714321
$23$	−7.27175			−1.51626			−0.758132	−	0.652101i	$-0.773888\pi$
$23$	−7.27175			−1.51626			−0.758132	+	0.652101i	$0.773888\pi$
$24$	−0.910449	−	1.47346i	−0.185845	−	0.300769i
$25$		−	5.84998i		−	1.17000i
$26$		0			0
$27$	−3.98838	−	3.33059i	−0.767564	−	0.640972i
$28$	2.38633	+	2.38633i	0.450974	+	0.450974i
$29$			8.53511i			1.58493i	0.609917	+	0.792466i	$0.291203\pi$
$29$			8.53511i			1.58493i	−0.609917	+	0.792466i	$0.708797\pi$
$30$	1.31134	−	5.55251i	0.239417	−	1.01374i
$31$	4.04437	+	4.04437i	0.726390	+	0.726390i	0.969899	−	0.243509i	$-0.0782984\pi$
$31$	4.04437	+	4.04437i	0.726390	+	0.726390i	−0.243509	+	0.969899i	$0.578298\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−3.05042	−	4.93677i	−0.531011	−	0.859381i
$34$	0.100547	−	0.100547i	0.0172437	−	0.0172437i
$35$			11.1163i			1.87900i
$36$	1.34216	−	2.68302i	0.223694	−	0.447170i
$37$	8.22509	−	8.22509i	1.35220	−	1.35220i	0.468997	−	0.883200i	$-0.344616\pi$
$37$	8.22509	−	8.22509i	1.35220	−	1.35220i	0.883200	−	0.468997i	$-0.155384\pi$
$38$	1.27292			0.206495
$39$		0			0
$40$	3.29393			0.520816
$41$	−0.570705	+	0.570705i	−0.0891291	+	0.0891291i	−0.750266	−	0.661137i	$-0.770074\pi$
$41$	−0.570705	+	0.570705i	−0.0891291	+	0.0891291i	0.661137	+	0.750266i	$0.270074\pi$
$42$	−1.34353	+	5.68879i	−0.207311	+	0.877800i
$43$			4.19114i			0.639143i	0.947562	+	0.319572i	$0.103539\pi$
$43$			4.19114i			0.639143i	−0.947562	+	0.319572i	$0.896461\pi$
$44$	2.36913	−	2.36913i	0.357160	−	0.357160i
$45$	9.37530	−	3.12307i	1.39759	−	0.465560i
$46$	5.14190	−	5.14190i	0.758132	−	0.758132i
$47$	3.90177	+	3.90177i	0.569132	+	0.569132i	0.931885	−	0.362753i	$-0.118163\pi$
$47$	3.90177	+	3.90177i	0.569132	+	0.569132i	−0.362753	+	0.931885i	$0.618163\pi$
$48$	1.68568	+	0.398108i	0.243307	+	0.0574619i
$49$		−	4.38914i		−	0.627020i
$50$	4.13656	+	4.13656i	0.584998	+	0.584998i
$51$	0.239695	+	0.0566090i	0.0335641	+	0.00792685i
$52$		0			0
$53$			8.81395i			1.21069i	0.795963	+	0.605345i	$0.206965\pi$
$53$			8.81395i			1.21069i	−0.795963	+	0.605345i	$0.793035\pi$
$54$	5.17529	−	0.465131i	0.704268	−	0.0632963i
$55$	11.0362			1.48812
$56$	−3.37478			−0.450974
$57$	1.15893	+	1.87560i	0.153504	+	0.248429i
$58$	−6.03524	−	6.03524i	−0.792466	−	0.792466i
$59$	7.10744	+	7.10744i	0.925309	+	0.925309i	0.997398	−	0.0720888i	$-0.0229665\pi$
$59$	7.10744	+	7.10744i	0.925309	+	0.925309i	−0.0720888	+	0.997398i	$0.522967\pi$
$60$	2.99896	+	4.85347i	0.387164	+	0.626581i
$61$	0.696989			0.0892403			0.0446201	−	0.999004i	$-0.485792\pi$
$61$	0.696989			0.0892403			0.0446201	+	0.999004i	$0.485792\pi$
$62$	−5.71960			−0.726390
$63$	−9.60542	+	3.19973i	−1.21017	+	0.403128i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	5.64780	+	1.33385i	0.695196	+	0.164185i
$67$	0.435004	+	0.435004i	0.0531442	+	0.0531442i	0.733179	−	0.680035i	$-0.238036\pi$
$67$	0.435004	+	0.435004i	0.0531442	+	0.0531442i	−0.680035	+	0.733179i	$0.738036\pi$
$68$			0.142195i			0.0172437i
$69$	12.2578	+	2.89494i	1.47567	+	0.348510i
$70$	−7.86041	−	7.86041i	−0.939498	−	0.939498i
$71$	5.76010	−	5.76010i	0.683598	−	0.683598i	−0.277211	−	0.960809i	$-0.589410\pi$
$71$	5.76010	−	5.76010i	0.683598	−	0.683598i	0.960809	+	0.277211i	$0.0894100\pi$
$72$	0.948129	+	2.84623i	0.111738	+	0.335432i
$73$	−1.54199	+	1.54199i	−0.180476	+	0.180476i	−0.791563	−	0.611087i	$-0.790732\pi$
$73$	−1.54199	+	1.54199i	−0.180476	+	0.180476i	0.611087	+	0.791563i	$0.290732\pi$
$74$			11.6320i			1.35220i
$75$	−2.32892	+	9.86118i	−0.268921	+	1.13867i
$76$	−0.900092	+	0.900092i	−0.103248	+	0.103248i
$77$	−11.3071			−1.28856
$78$		0			0
$79$	−4.42494			−0.497844			−0.248922	−	0.968524i	$-0.580076\pi$
$79$	−4.42494			−0.497844			−0.248922	+	0.968524i	$0.580076\pi$
$80$	−2.32916	+	2.32916i	−0.260408	+	0.260408i
$81$	5.39719	+	7.20210i	0.599688	+	0.800234i
$82$		−	0.807098i		−	0.0891291i
$83$	−1.61291	+	1.61291i	−0.177040	+	0.177040i	−0.790064	−	0.613024i	$-0.789953\pi$
$83$	−1.61291	+	1.61291i	−0.177040	+	0.177040i	0.613024	+	0.790064i	$0.289953\pi$
$84$	−3.07257	−	4.97260i	−0.335245	−	0.542555i
$85$	−0.331195	+	0.331195i	−0.0359232	+	0.0359232i
$86$	−2.96358	−	2.96358i	−0.319572	−	0.319572i
$87$	3.39790	−	14.3875i	0.364293	−	1.54250i
$88$			3.35046i			0.357160i
$89$	5.45490	+	5.45490i	0.578219	+	0.578219i	0.934412	−	0.356194i	$-0.115926\pi$
$89$	5.45490	+	5.45490i	0.578219	+	0.578219i	−0.356194	+	0.934412i	$0.615926\pi$
$90$	−4.42099	+	8.83768i	−0.466014	+	0.931574i
$91$		0			0
$92$			7.27175i			0.758132i
$93$	−5.20741	−	8.42760i	−0.539983	−	0.873901i
$94$	−5.51794			−0.569132
$95$	−4.19292			−0.430184
$96$	−1.47346	+	0.910449i	−0.150384	+	0.0929224i
$97$	5.33494	+	5.33494i	0.541681	+	0.541681i	0.924021	−	0.382341i	$-0.124882\pi$
$97$	5.33494	+	5.33494i	0.541681	+	0.541681i	−0.382341	+	0.924021i	$0.624882\pi$
$98$	3.10359	+	3.10359i	0.313510	+	0.313510i
$99$	3.17667	+	9.53620i	0.319267	+	0.958424i
$100$	−5.84998			−0.584998
$101$	6.12302			0.609263			0.304632	−	0.952470i	$-0.401467\pi$
$101$	6.12302			0.609263			0.304632	+	0.952470i	$0.401467\pi$
$102$	−0.209519	+	0.129462i	−0.0207455	+	0.0128186i
$103$			7.85287i			0.773767i	0.922129	+	0.386883i	$0.126448\pi$
$103$			7.85287i			0.773767i	−0.922129	+	0.386883i	$0.873552\pi$
$104$		0			0
$105$	4.42549	−	18.7385i	0.431883	−	1.82869i
$106$	−6.23241	−	6.23241i	−0.605345	−	0.605345i
$107$		−	2.00398i		−	0.193732i	−0.995297	−	0.0968658i	$-0.969118\pi$
$107$		−	2.00398i		−	0.193732i	0.995297	−	0.0968658i	$-0.0308818\pi$
$108$	−3.33059	+	3.98838i	−0.320486	+	0.383782i
$109$	6.80674	+	6.80674i	0.651967	+	0.651967i	0.953466	−	0.301499i	$-0.0974871\pi$
$109$	6.80674	+	6.80674i	0.651967	+	0.651967i	−0.301499	+	0.953466i	$0.597487\pi$
$110$	−7.80376	+	7.80376i	−0.744059	+	0.744059i
$111$	−17.1393	+	10.5904i	−1.62679	+	1.00519i
$112$	2.38633	−	2.38633i	0.225487	−	0.225487i
$113$			1.66763i			0.156878i	0.996919	+	0.0784388i	$0.0249935\pi$
$113$			1.66763i			0.156878i	−0.996919	+	0.0784388i	$0.975006\pi$
$114$	−2.14574	−	0.506761i	−0.200967	−	0.0474625i
$115$	−16.9371	+	16.9371i	−1.57939	+	1.57939i
$116$	8.53511			0.792466
$117$		0			0
$118$	−10.0514			−0.925309
$119$	0.339325	−	0.339325i	0.0311058	−	0.0311058i
$120$	−5.55251	−	1.31134i	−0.506872	−	0.119708i
$121$			0.225586i			0.0205078i
$122$	−0.492846	+	0.492846i	−0.0446201	+	0.0446201i
$123$	1.18923	−	0.734822i	0.107229	−	0.0662567i
$124$	4.04437	−	4.04437i	0.363195	−	0.363195i
$125$	−1.97974	−	1.97974i	−0.177073	−	0.177073i
$126$	4.52951	−	9.05460i	0.403521	−	0.806648i
$127$		−	13.3579i		−	1.18533i	−0.805451	−	0.592663i	$-0.798077\pi$
$127$		−	13.3579i		−	1.18533i	0.805451	−	0.592663i	$-0.201923\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	1.66853	−	7.06491i	0.146906	−	0.622031i
$130$		0			0
$131$			12.3288i			1.07717i	0.842570	+	0.538586i	$0.181041\pi$
$131$			12.3288i			1.07717i	−0.842570	+	0.538586i	$0.818959\pi$
$132$	−4.93677	+	3.05042i	−0.429690	+	0.265505i
$133$	4.29583			0.372496
$134$	−0.615189			−0.0531442
$135$	−17.0471	+	1.53211i	−1.46718	+	0.131863i
$136$	−0.100547	−	0.100547i	−0.00862185	−	0.00862185i
$137$	−6.56371	−	6.56371i	−0.560775	−	0.560775i	0.368752	−	0.929528i	$-0.379785\pi$
$137$	−6.56371	−	6.56371i	−0.560775	−	0.560775i	−0.929528	+	0.368752i	$0.879785\pi$
$138$	−10.7146	+	6.62056i	−0.912090	+	0.563580i
$139$	19.3647			1.64250			0.821248	−	0.570572i	$-0.193278\pi$
$139$	19.3647			1.64250			0.821248	+	0.570572i	$0.193278\pi$
$140$	11.1163			0.939498
$141$	−5.02381	−	8.13046i	−0.423081	−	0.684708i
$142$			8.14601i			0.683598i
$143$		0			0
$144$	−2.68302	−	1.34216i	−0.223585	−	0.111847i
$145$	19.8797	+	19.8797i	1.65092	+	1.65092i
$146$		−	2.18070i		−	0.180476i
$147$	−1.74735	+	7.39868i	−0.144119	+	0.610233i
$148$	−8.22509	−	8.22509i	−0.676098	−	0.676098i
$149$	−14.5239	+	14.5239i	−1.18984	+	1.18984i	−0.212733	+	0.977110i	$0.568236\pi$
$149$	−14.5239	+	14.5239i	−1.18984	+	1.18984i	−0.977110	+	0.212733i	$0.931764\pi$
$150$	−5.32611	−	8.61971i	−0.434875	−	0.703796i
$151$	−1.14579	+	1.14579i	−0.0932434	+	0.0932434i	−0.752190	−	0.658946i	$-0.771002\pi$
$151$	−1.14579	+	1.14579i	−0.0932434	+	0.0932434i	0.658946	+	0.752190i	$0.271002\pi$
$152$		−	1.27292i		−	0.103248i
$153$	−0.381513	−	0.190849i	−0.0308435	−	0.0154292i
$154$	7.99530	−	7.99530i	0.644280	−	0.644280i
$155$	18.8400			1.51326
$156$		0			0
$157$	−2.54214			−0.202885			−0.101442	−	0.994841i	$-0.532346\pi$
$157$	−2.54214			−0.202885			−0.101442	+	0.994841i	$0.532346\pi$
$158$	3.12890	−	3.12890i	0.248922	−	0.248922i
$159$	3.50890	−	14.8575i	0.278274	−	1.17828i
$160$		−	3.29393i		−	0.260408i
$161$	17.3528	−	17.3528i	1.36759	−	1.36759i
$162$	−8.90905	−	1.27626i	−0.699961	−	0.100273i
$163$	9.56624	−	9.56624i	0.749286	−	0.749286i	−0.225059	−	0.974345i	$-0.572257\pi$
$163$	9.56624	−	9.56624i	0.749286	−	0.749286i	0.974345	+	0.225059i	$0.0722575\pi$
$164$	0.570705	+	0.570705i	0.0445646	+	0.0445646i
$165$	−18.6035	−	4.39359i	−1.44828	−	0.342041i
$166$		−	2.28100i		−	0.177040i
$167$	5.80536	+	5.80536i	0.449233	+	0.449233i	0.895099	−	0.445867i	$-0.147104\pi$
$167$	5.80536	+	5.80536i	0.449233	+	0.449233i	−0.445867	+	0.895099i	$0.647104\pi$
$168$	5.68879	+	1.34353i	0.438900	+	0.103655i
$169$		0			0
$170$		−	0.468381i		−	0.0359232i
$171$	−1.20689	−	3.62304i	−0.0922935	−	0.277060i
$172$	4.19114			0.319572
$173$	−20.5041			−1.55889			−0.779447	−	0.626468i	$-0.784500\pi$
$173$	−20.5041			−1.55889			−0.779447	+	0.626468i	$0.784500\pi$
$174$	7.77079	+	12.5761i	0.589102	+	0.953395i
$175$	13.9600	+	13.9600i	1.05528	+	1.05528i
$176$	−2.36913	−	2.36913i	−0.178580	−	0.178580i
$177$	−9.15132	−	14.8104i	−0.687855	−	1.11322i
$178$	−7.71440			−0.578219
$179$	4.89553			0.365909			0.182955	−	0.983121i	$-0.441434\pi$
$179$	4.89553			0.365909			0.182955	+	0.983121i	$0.441434\pi$
$180$	−3.12307	−	9.37530i	−0.232780	−	0.698794i
$181$		−	25.0409i		−	1.86128i	−0.365941	−	0.930638i	$-0.619253\pi$
$181$		−	25.0409i		−	1.86128i	0.365941	−	0.930638i	$-0.380747\pi$
$182$		0			0
$183$	−1.17490	−	0.277477i	−0.0868510	−	0.0205117i
$184$	−5.14190	−	5.14190i	−0.379066	−	0.379066i
$185$		−	38.3151i		−	2.81698i
$186$	9.64141	+	2.27702i	0.706942	+	0.166959i
$187$	−0.336879	−	0.336879i	−0.0246351	−	0.0246351i
$188$	3.90177	−	3.90177i	0.284566	−	0.284566i
$189$	17.4655	−	1.56971i	1.27043	−	0.114180i
$190$	2.96484	−	2.96484i	0.215092	−	0.215092i
$191$		−	0.0923705i		−	0.00668369i	−0.999994	−	0.00334185i	$-0.998936\pi$
$191$		−	0.0923705i		−	0.00668369i	0.999994	−	0.00334185i	$-0.00106374\pi$
$192$	0.398108	−	1.68568i	0.0287310	−	0.121653i
$193$	11.9481	−	11.9481i	0.860047	−	0.860047i	−0.131297	−	0.991343i	$-0.541914\pi$
$193$	11.9481	−	11.9481i	0.860047	−	0.860047i	0.991343	+	0.131297i	$0.0419140\pi$
$194$	−7.54474			−0.541681
$195$		0			0
$196$	−4.38914			−0.313510
$197$	6.29222	−	6.29222i	0.448302	−	0.448302i	−0.446488	−	0.894790i	$-0.647325\pi$
$197$	6.29222	−	6.29222i	0.448302	−	0.448302i	0.894790	+	0.446488i	$0.147325\pi$
$198$	−8.98935	−	4.49687i	−0.638845	−	0.319578i
$199$		−	1.94847i		−	0.138123i	−0.997612	−	0.0690617i	$-0.977999\pi$
$199$		−	1.94847i		−	0.138123i	0.997612	−	0.0690617i	$-0.0220005\pi$
$200$	4.13656	−	4.13656i	0.292499	−	0.292499i
$201$	−0.560099	−	0.906456i	−0.0395063	−	0.0639365i
$202$	−4.32963	+	4.32963i	−0.304632	+	0.304632i
$203$	−20.3676	−	20.3676i	−1.42953	−	1.42953i
$204$	0.0566090	−	0.239695i	0.00396343	−	0.0167820i
$205$			2.65853i			0.185680i
$206$	−5.55282	−	5.55282i	−0.386883	−	0.386883i
$207$	−19.5103	−	9.75988i	−1.35606	−	0.678359i
$208$		0			0
$209$		−	4.26488i		−	0.295008i
$210$	10.1208	+	16.3794i	0.698403	+	1.13029i
$211$	−23.0588			−1.58743			−0.793715	−	0.608290i	$-0.791856\pi$
$211$	−23.0588			−1.58743			−0.793715	+	0.608290i	$0.791856\pi$
$212$	8.81395			0.605345
$213$	−12.0028	+	7.41653i	−0.822420	+	0.508173i
$214$	1.41703	+	1.41703i	0.0968658	+	0.0968658i
$215$	9.76184	+	9.76184i	0.665752	+	0.665752i
$216$	−0.465131	−	5.17529i	−0.0316481	−	0.352134i
$217$	−19.3024			−1.31033
$218$	−9.62618			−0.651967
$219$	3.21317	−	1.98542i	0.217126	−	0.134162i
$220$		−	11.0362i		−	0.744059i
$221$		0			0
$222$	4.63081	−	19.6079i	0.310799	−	1.31599i
$223$	−12.5380	−	12.5380i	−0.839607	−	0.839607i	0.149200	−	0.988807i	$-0.452330\pi$
$223$	−12.5380	−	12.5380i	−0.839607	−	0.839607i	−0.988807	+	0.149200i	$0.952330\pi$
$224$			3.37478i			0.225487i
$225$	7.85163	−	15.6956i	0.523442	−	1.04637i
$226$	−1.17919	−	1.17919i	−0.0784388	−	0.0784388i
$227$	−12.7737	+	12.7737i	−0.847822	+	0.847822i	−0.989861	−	0.142039i	$-0.954634\pi$
$227$	−12.7737	+	12.7737i	−0.847822	+	0.847822i	0.142039	+	0.989861i	$0.454634\pi$
$228$	1.87560	−	1.15893i	0.124215	−	0.0767521i
$229$	−5.38756	+	5.38756i	−0.356020	+	0.356020i	−0.862344	−	0.506324i	$-0.831004\pi$
$229$	−5.38756	+	5.38756i	−0.356020	+	0.356020i	0.506324	+	0.862344i	$0.331004\pi$
$230$		−	23.9526i		−	1.57939i
$231$	19.0601	+	4.50143i	1.25406	+	0.296173i
$232$	−6.03524	+	6.03524i	−0.396233	+	0.396233i
$233$	11.0397			0.723237			0.361618	−	0.932326i	$-0.382224\pi$
$233$	11.0397			0.723237			0.361618	+	0.932326i	$0.382224\pi$
$234$		0			0
$235$	18.1757			1.18565
$236$	7.10744	−	7.10744i	0.462655	−	0.462655i
$237$	7.45902	+	1.76160i	0.484515	+	0.114428i
$238$			0.479878i			0.0311058i
$239$	9.10773	−	9.10773i	0.589130	−	0.589130i	−0.348266	−	0.937396i	$-0.613229\pi$
$239$	9.10773	−	9.10773i	0.589130	−	0.589130i	0.937396	+	0.348266i	$0.113229\pi$
$240$	4.85347	−	2.99896i	0.313290	−	0.193582i
$241$	−10.8677	+	10.8677i	−0.700048	+	0.700048i	−0.964421	−	0.264373i	$-0.914835\pi$
$241$	−10.8677	+	10.8677i	−0.700048	+	0.700048i	0.264373	+	0.964421i	$0.414835\pi$
$242$	−0.159513	−	0.159513i	−0.0102539	−	0.0102539i
$243$	−6.23071	−	14.2891i	−0.399700	−	0.916646i
$244$		−	0.696989i		−	0.0446201i
$245$	−10.2230	−	10.2230i	−0.653125	−	0.653125i
$246$	−0.321312	+	1.36051i	−0.0204861	+	0.0867428i
$247$		0			0
$248$			5.71960i			0.363195i
$249$	3.36096	−	2.07674i	0.212992	−	0.131608i
$250$	2.79978			0.177073
$251$	12.5084			0.789523			0.394761	−	0.918784i	$-0.370827\pi$
$251$	12.5084			0.789523			0.394761	+	0.918784i	$0.370827\pi$
$252$	3.19973	+	9.60542i	0.201564	+	0.605084i
$253$	−17.2277	−	17.2277i	−1.08310	−	1.08310i
$254$	9.44549	+	9.44549i	0.592663	+	0.592663i
$255$	0.690140	−	0.426437i	0.0432183	−	0.0267045i
$256$	1.00000			0.0625000
$257$	3.71684			0.231850			0.115925	−	0.993258i	$-0.463017\pi$
$257$	3.71684			0.231850			0.115925	+	0.993258i	$0.463017\pi$
$258$	3.81582	+	6.17548i	0.237563	+	0.384468i
$259$			39.2556i			2.43922i
$260$		0			0
$261$	−11.4555	+	22.8999i	−0.709079	+	1.41747i
$262$	−8.71778	−	8.71778i	−0.538586	−	0.538586i
$263$			2.11876i			0.130648i	0.997864	+	0.0653242i	$0.0208082\pi$
$263$			2.11876i			0.130648i	−0.997864	+	0.0653242i	$0.979192\pi$
$264$	1.33385	−	5.64780i	0.0820925	−	0.347598i
$265$	20.5291	+	20.5291i	1.26109	+	1.26109i
$266$	−3.03761	+	3.03761i	−0.186248	+	0.186248i
$267$	−7.02357	−	11.3668i	−0.429835	−	0.695640i
$268$	0.435004	−	0.435004i	0.0265721	−	0.0265721i
$269$			2.62976i			0.160339i	0.996781	+	0.0801696i	$0.0255462\pi$
$269$			2.62976i			0.160339i	−0.996781	+	0.0801696i	$0.974454\pi$
$270$	10.9707	−	13.1375i	0.667657	−	0.799520i
$271$	0.100023	−	0.100023i	0.00607594	−	0.00607594i	−0.704062	−	0.710138i	$-0.748632\pi$
$271$	0.100023	−	0.100023i	0.00607594	−	0.00607594i	0.710138	+	0.704062i	$0.248632\pi$
$272$	0.142195			0.00862185
$273$		0			0
$274$	9.28248			0.560775
$275$	13.8594	−	13.8594i	0.835752	−	0.835752i
$276$	2.89494	−	12.2578i	0.174255	−	0.737835i
$277$			5.21523i			0.313353i	0.987650	+	0.156676i	$0.0500780\pi$
$277$			5.21523i			0.313353i	−0.987650	+	0.156676i	$0.949922\pi$
$278$	−13.6929	+	13.6929i	−0.821248	+	0.821248i
$279$	5.42292	+	16.2793i	0.324662	+	0.974618i
$280$	−7.86041	+	7.86041i	−0.469749	+	0.469749i
$281$	4.46823	+	4.46823i	0.266552	+	0.266552i	0.827709	−	0.561157i	$-0.189644\pi$
$281$	4.46823	+	4.46823i	0.266552	+	0.266552i	−0.561157	+	0.827709i	$0.689644\pi$
$282$	9.30147	+	2.19674i	0.553894	+	0.130814i
$283$			18.1017i			1.07603i	0.842935	+	0.538016i	$0.180826\pi$
$283$			18.1017i			1.07603i	−0.842935	+	0.538016i	$0.819174\pi$
$284$	−5.76010	−	5.76010i	−0.341799	−	0.341799i
$285$	7.06791	+	1.66923i	0.418667	+	0.0988769i
$286$		0			0
$287$		−	2.72378i		−	0.160780i
$288$	2.84623	−	0.948129i	0.167716	−	0.0558690i
$289$	−16.9798			−0.998811
$290$	−28.1141			−1.65092
$291$	−6.86911	−	11.1169i	−0.402674	−	0.651682i
$292$	1.54199	+	1.54199i	0.0902380	+	0.0902380i
$293$	11.8824	+	11.8824i	0.694179	+	0.694179i	0.963149	−	0.268970i	$-0.0866832\pi$
$293$	11.8824	+	11.8824i	0.694179	+	0.694179i	−0.268970	+	0.963149i	$0.586683\pi$
$294$	−3.99609	−	6.46722i	−0.233057	−	0.377176i
$295$	33.1087			1.92766
$296$	11.6320			0.676098
$297$	−1.55840	−	17.3396i	−0.0904277	−	1.00615i
$298$		−	20.5399i		−	1.18984i
$299$		0			0
$300$	9.86118	+	2.32892i	0.569336	+	0.134460i
$301$	−10.0014	−	10.0014i	−0.576474	−	0.576474i
$302$		−	1.62040i		−	0.0932434i
$303$	−10.3214	−	2.43762i	−0.592951	−	0.140038i
$304$	0.900092	+	0.900092i	0.0516238	+	0.0516238i
$305$	1.62340	−	1.62340i	0.0929556	−	0.0929556i
$306$	0.404721	−	0.134819i	0.0231364	−	0.00770711i
$307$	2.83160	−	2.83160i	0.161608	−	0.161608i	−0.621671	−	0.783279i	$-0.713546\pi$
$307$	2.83160	−	2.83160i	0.161608	−	0.161608i	0.783279	+	0.621671i	$0.213546\pi$
$308$			11.3071i			0.644280i
$309$	3.12629	−	13.2374i	0.177848	−	0.753050i
$310$	−13.3219	+	13.3219i	−0.756631	+	0.756631i
$311$	7.64225			0.433352			0.216676	−	0.976244i	$-0.430478\pi$
$311$	7.64225			0.433352			0.216676	+	0.976244i	$0.430478\pi$
$312$		0			0
$313$	13.1133			0.741206			0.370603	−	0.928791i	$-0.379151\pi$
$313$	13.1133			0.741206			0.370603	+	0.928791i	$0.379151\pi$
$314$	1.79756	−	1.79756i	0.101442	−	0.101442i
$315$	−14.9199	+	29.8252i	−0.840640	+	1.68046i
$316$			4.42494i			0.248922i
$317$	−19.7079	+	19.7079i	−1.10691	+	1.10691i	−0.113354	+	0.993555i	$0.536159\pi$
$317$	−19.7079	+	19.7079i	−1.10691	+	1.10691i	−0.993555	+	0.113354i	$0.963841\pi$
$318$	8.02466	+	12.9870i	0.450000	+	0.728275i
$319$	−20.2208	+	20.2208i	−1.13215	+	1.13215i
$320$	2.32916	+	2.32916i	0.130204	+	0.130204i
$321$	−0.797799	+	3.37806i	−0.0445288	+	0.188545i
$322$			24.5406i			1.36759i
$323$	0.127989	+	0.127989i	0.00712148	+	0.00712148i
$324$	7.20210	−	5.39719i	0.400117	−	0.299844i
$325$		0			0
$326$			13.5287i			0.749286i
$327$	−8.76415	−	14.1838i	−0.484659	−	0.784365i
$328$	−0.807098			−0.0445646
$329$	−18.6218			−1.02666
$330$	16.2614	−	10.0479i	0.895159	−	0.553118i
$331$	−10.9344	−	10.9344i	−0.601011	−	0.601011i	0.339570	−	0.940581i	$-0.389719\pi$
$331$	−10.9344	−	10.9344i	−0.601011	−	0.601011i	−0.940581	+	0.339570i	$0.889719\pi$
$332$	1.61291	+	1.61291i	0.0885201	+	0.0885201i
$333$	33.1075	−	11.0287i	1.81428	−	0.604367i
$334$	−8.21003			−0.449233
$335$	2.02639			0.110714
$336$	−4.97260	+	3.07257i	−0.271278	+	0.167622i
$337$			16.9941i			0.925729i	0.886429	+	0.462865i	$0.153178\pi$
$337$			16.9941i			0.925729i	−0.886429	+	0.462865i	$0.846822\pi$
$338$		0			0
$339$	0.663898	−	2.81109i	0.0360580	−	0.152677i
$340$	0.331195	+	0.331195i	0.0179616	+	0.0179616i
$341$			19.1633i			1.03775i
$342$	3.41528	+	1.70847i	0.184677	+	0.0923835i
$343$	−6.23037	−	6.23037i	−0.336408	−	0.336408i
$344$	−2.96358	+	2.96358i	−0.159786	+	0.159786i
$345$	35.2932	−	21.8077i	1.90012	−	1.17409i
$346$	14.4986	−	14.4986i	0.779447	−	0.779447i
$347$		−	21.5712i		−	1.15800i	−0.815326	−	0.579002i	$-0.803442\pi$
$347$		−	21.5712i		−	1.15800i	0.815326	−	0.579002i	$-0.196558\pi$
$348$	−14.3875	−	3.39790i	−0.771249	−	0.182146i
$349$	−4.90049	+	4.90049i	−0.262317	+	0.262317i	−0.825995	−	0.563678i	$-0.809386\pi$
$349$	−4.90049	+	4.90049i	−0.262317	+	0.262317i	0.563678	+	0.825995i	$0.309386\pi$
$350$	−19.7424			−1.05528
$351$		0			0
$352$	3.35046			0.178580
$353$	−19.7435	+	19.7435i	−1.05084	+	1.05084i	−0.0522029	+	0.998636i	$0.516624\pi$
$353$	−19.7435	+	19.7435i	−1.05084	+	1.05084i	−0.998636	+	0.0522029i	$0.983376\pi$
$354$	16.9435	+	4.00156i	0.900536	+	0.212680i
$355$		−	26.8324i		−	1.42412i
$356$	5.45490	−	5.45490i	0.289109	−	0.289109i
$357$	−0.707080	+	0.436904i	−0.0374226	+	0.0231234i
$358$	−3.46167	+	3.46167i	−0.182955	+	0.182955i
$359$	−1.69459	−	1.69459i	−0.0894372	−	0.0894372i	0.660973	−	0.750410i	$-0.270144\pi$
$359$	−1.69459	−	1.69459i	−0.0894372	−	0.0894372i	−0.750410	+	0.660973i	$0.770144\pi$
$360$	8.83768	+	4.42099i	0.465787	+	0.233007i
$361$		−	17.3797i		−	0.914719i
$362$	17.7066	+	17.7066i	0.930638	+	0.930638i
$363$	0.0898076	−	0.380266i	0.00471368	−	0.0199588i
$364$		0			0
$365$			7.18308i			0.375979i
$366$	1.02698	−	0.634573i	0.0536813	−	0.0331697i
$367$	−6.78544			−0.354197			−0.177099	−	0.984193i	$-0.556671\pi$
$367$	−6.78544			−0.354197			−0.177099	+	0.984193i	$0.556671\pi$
$368$	7.27175			0.379066
$369$	−2.29719	+	0.765233i	−0.119587	+	0.0398364i
$370$	27.0929	+	27.0929i	1.40849	+	1.40849i
$371$	−21.0330	−	21.0330i	−1.09198	−	1.09198i
$372$	−8.42760	+	5.20741i	−0.436951	+	0.269992i
$373$	−23.8514			−1.23498			−0.617490	−	0.786578i	$-0.711851\pi$
$373$	−23.8514			−1.23498			−0.617490	+	0.786578i	$0.711851\pi$
$374$	0.476419			0.0246351
$375$	2.54905	+	4.12535i	0.131633	+	0.213032i
$376$			5.51794i			0.284566i
$377$		0			0
$378$	−11.2400	+	13.4599i	−0.578123	+	0.692303i
$379$	1.83606	+	1.83606i	0.0943123	+	0.0943123i	0.752689	−	0.658377i	$-0.228757\pi$
$379$	1.83606	+	1.83606i	0.0943123	+	0.0943123i	−0.658377	+	0.752689i	$0.728757\pi$
$380$			4.19292i			0.215092i
$381$	−5.31790	+	22.5172i	−0.272444	+	1.15359i
$382$	0.0653158	+	0.0653158i	0.00334185	+	0.00334185i
$383$	1.38551	−	1.38551i	0.0707960	−	0.0707960i	−0.670822	−	0.741618i	$-0.734059\pi$
$383$	1.38551	−	1.38551i	0.0707960	−	0.0707960i	0.741618	+	0.670822i	$0.234059\pi$
$384$	0.910449	+	1.47346i	0.0464612	+	0.0751921i
$385$	−26.3360	+	26.3360i	−1.34221	+	1.34221i
$386$			16.8972i			0.860047i
$387$	−5.62520	+	11.2449i	−0.285945	+	0.571611i
$388$	5.33494	−	5.33494i	0.270840	−	0.270840i
$389$	−35.7464			−1.81241			−0.906207	−	0.422835i	$-0.861035\pi$
$389$	−35.7464			−1.81241			−0.906207	+	0.422835i	$0.861035\pi$
$390$		0			0
$391$	1.03401			0.0522920
$392$	3.10359	−	3.10359i	0.156755	−	0.156755i
$393$	4.90820	−	20.7824i	0.247586	−	1.04833i
$394$			8.89855i			0.448302i
$395$	−10.3064	+	10.3064i	−0.518571	+	0.518571i
$396$	9.53620	−	3.17667i	0.479212	−	0.159634i
$397$	20.8130	−	20.8130i	1.04457	−	1.04457i	0.0456141	−	0.998959i	$-0.485476\pi$
$397$	20.8130	−	20.8130i	1.04457	−	1.04457i	0.998959	−	0.0456141i	$-0.0145245\pi$
$398$	1.37778	+	1.37778i	0.0690617	+	0.0690617i
$399$	−7.24139	−	1.71021i	−0.362523	−	0.0856174i
$400$			5.84998i			0.292499i
$401$	−4.32964	−	4.32964i	−0.216212	−	0.216212i	0.590688	−	0.806900i	$-0.298856\pi$
$401$	−4.32964	−	4.32964i	−0.216212	−	0.216212i	−0.806900	+	0.590688i	$0.798856\pi$
$402$	1.03701	+	0.244912i	0.0517214	+	0.0122151i
$403$		0			0
$404$		−	6.12302i		−	0.304632i
$405$	29.3458	+	4.20393i	1.45820	+	0.208895i
$406$	28.8041			1.42953
$407$	38.9727			1.93180
$408$	0.129462	+	0.209519i	0.00640930	+	0.0103727i
$409$	−17.3448	−	17.3448i	−0.857646	−	0.857646i	0.133414	−	0.991060i	$-0.457406\pi$
$409$	−17.3448	−	17.3448i	−0.857646	−	0.857646i	−0.991060	+	0.133414i	$0.957406\pi$
$410$	−1.87986	−	1.87986i	−0.0928398	−	0.0928398i
$411$	8.45123	+	13.6774i	0.416869	+	0.674655i
$412$	7.85287			0.386883
$413$	−33.9214			−1.66916
$414$	20.6971	−	6.89456i	1.01721	−	0.338849i
$415$			7.51346i			0.368821i
$416$		0			0
$417$	−32.6427	−	7.70926i	−1.59852	−	0.377524i
$418$	3.01572	+	3.01572i	0.147504	+	0.147504i
$419$		−	0.205185i		−	0.0100240i	−0.999987	−	0.00501198i	$-0.998405\pi$
$419$		−	0.205185i		−	0.0100240i	0.999987	−	0.00501198i	$-0.00159537\pi$
$420$	−18.7385	−	4.42549i	−0.914345	−	0.215942i
$421$	−26.1575	−	26.1575i	−1.27484	−	1.27484i	−0.943517	−	0.331323i	$-0.892505\pi$
$421$	−26.1575	−	26.1575i	−1.27484	−	1.27484i	−0.331323	−	0.943517i	$-0.607495\pi$
$422$	16.3050	−	16.3050i	0.793715	−	0.793715i
$423$	5.23172	+	15.7054i	0.254375	+	0.763620i
$424$	−6.23241	+	6.23241i	−0.302672	+	0.302672i
$425$			0.831839i			0.0403501i
$426$	3.24299	−	13.7316i	0.157124	−	0.665296i
$427$	−1.66325	+	1.66325i	−0.0804901	+	0.0804901i
$428$	−2.00398			−0.0968658
$429$		0			0
$430$	−13.8053			−0.665752
$431$	−15.3329	+	15.3329i	−0.738560	+	0.738560i	−0.972299	−	0.233740i	$-0.924904\pi$
$431$	−15.3329	+	15.3329i	−0.738560	+	0.738560i	0.233740	+	0.972299i	$0.424904\pi$
$432$	3.98838	+	3.33059i	0.191891	+	0.160243i
$433$			9.40744i			0.452093i	0.974117	+	0.226046i	$0.0725801\pi$
$433$			9.40744i			0.452093i	−0.974117	+	0.226046i	$0.927420\pi$
$434$	13.6489	−	13.6489i	0.655166	−	0.655166i
$435$	−25.5964	−	41.4249i	−1.22726	−	1.98617i
$436$	6.80674	−	6.80674i	0.325984	−	0.325984i
$437$	6.54524	+	6.54524i	0.313102	+	0.313102i
$438$	−0.868154	+	3.67596i	−0.0414820	+	0.175644i
$439$		−	22.3316i		−	1.06583i	−0.846168	−	0.532916i	$-0.821096\pi$
$439$		−	22.3316i		−	1.06583i	0.846168	−	0.532916i	$-0.178904\pi$
$440$	7.80376	+	7.80376i	0.372030	+	0.372030i
$441$	5.89095	−	11.7762i	0.280521	−	0.560769i
$442$		0			0
$443$		−	33.7413i		−	1.60310i	−0.597930	−	0.801548i	$-0.704010\pi$
$443$		−	33.7413i		−	1.60310i	0.597930	−	0.801548i	$-0.295990\pi$
$444$	10.5904	+	17.1393i	0.502597	+	0.813397i
$445$	25.4107			1.20458
$446$	17.7314			0.839607
$447$	30.2647	−	18.7005i	1.43147	−	0.884504i
$448$	−2.38633	−	2.38633i	−0.112743	−	0.112743i
$449$	−20.3950	−	20.3950i	−0.962498	−	0.962498i	0.0368237	−	0.999322i	$-0.488276\pi$
$449$	−20.3950	−	20.3950i	−0.962498	−	0.962498i	−0.999322	+	0.0368237i	$0.988276\pi$
$450$	5.54653	+	16.6504i	0.261466	+	0.784908i
$451$	−2.70415			−0.127334
$452$	1.66763			0.0784388
$453$	2.38759	−	1.47529i	0.112179	−	0.0693152i
$454$		−	18.0648i		−	0.847822i
$455$		0			0
$456$	−0.506761	+	2.14574i	−0.0237312	+	0.100483i
$457$	27.9442	+	27.9442i	1.30717	+	1.30717i	0.923446	+	0.383728i	$0.125360\pi$
$457$	27.9442	+	27.9442i	1.30717	+	1.30717i	0.383728	+	0.923446i	$0.374640\pi$
$458$		−	7.61916i		−	0.356020i
$459$	0.567129	+	0.473594i	0.0264713	+	0.0221055i
$460$	16.9371	+	16.9371i	0.789695	+	0.789695i
$461$	23.2053	−	23.2053i	1.08078	−	1.08078i	0.0843424	−	0.996437i	$-0.473121\pi$
$461$	23.2053	−	23.2053i	1.08078	−	1.08078i	0.996437	−	0.0843424i	$-0.0268790\pi$
$462$	−16.6605	+	10.2945i	−0.775117	+	0.478944i
$463$	16.0398	−	16.0398i	0.745433	−	0.745433i	−0.228185	−	0.973618i	$-0.573279\pi$
$463$	16.0398	−	16.0398i	0.745433	−	0.745433i	0.973618	+	0.228185i	$0.0732791\pi$
$464$		−	8.53511i		−	0.396233i
$465$	−31.7581	−	7.50034i	−1.47275	−	0.347820i
$466$	−7.80627	+	7.80627i	−0.361618	+	0.361618i
$467$	−7.27148			−0.336484			−0.168242	−	0.985746i	$-0.553809\pi$
$467$	−7.27148			−0.336484			−0.168242	+	0.985746i	$0.553809\pi$
$468$		0			0
$469$	−2.07613			−0.0958667
$470$	−12.8522	+	12.8522i	−0.592826	+	0.592826i
$471$	4.28523	+	1.01205i	0.197453	+	0.0466326i
$472$			10.0514i			0.462655i
$473$	−9.92937	+	9.92937i	−0.456553	+	0.456553i
$474$	−6.51996	+	4.02868i	−0.299472	+	0.185043i
$475$	−5.26552	+	5.26552i	−0.241599	+	0.241599i
$476$	−0.339325	−	0.339325i	−0.0155529	−	0.0155529i
$477$	−11.8298	+	23.6480i	−0.541648	+	1.08277i
$478$			12.8803i			0.589130i
$479$	7.02586	+	7.02586i	0.321020	+	0.321020i	0.849158	−	0.528138i	$-0.177110\pi$
$479$	7.02586	+	7.02586i	0.321020	+	0.321020i	−0.528138	+	0.849158i	$0.677110\pi$
$480$	−1.31134	+	5.55251i	−0.0598542	+	0.253436i
$481$		0			0
$482$		−	15.3692i		−	0.700048i
$483$	−36.1595	+	22.3429i	−1.64532	+	1.01664i
$484$	0.225586			0.0102539
$485$	24.8519			1.12846
$486$	14.5097	+	5.69813i	0.658173	+	0.258473i
$487$	2.42866	+	2.42866i	0.110053	+	0.110053i	0.759989	−	0.649936i	$-0.225204\pi$
$487$	2.42866	+	2.42866i	0.110053	+	0.110053i	−0.649936	+	0.759989i	$0.725204\pi$
$488$	0.492846	+	0.492846i	0.0223101	+	0.0223101i
$489$	−19.9340	+	12.3172i	−0.901447	+	0.557003i
$490$	14.4575			0.653125
$491$	37.9730			1.71370			0.856848	−	0.515570i	$-0.172420\pi$
$491$	37.9730			1.71370			0.856848	+	0.515570i	$0.172420\pi$
$492$	−0.734822	−	1.18923i	−0.0331283	−	0.0536145i
$493$		−	1.21365i		−	0.0546602i
$494$		0			0
$495$	29.6103	+	14.8124i	1.33088	+	0.665766i
$496$	−4.04437	−	4.04437i	−0.181598	−	0.181598i
$497$			27.4910i			1.23314i
$498$	−0.908085	+	3.84504i	−0.0406923	+	0.172300i
$499$	−10.8427	−	10.8427i	−0.485385	−	0.485385i	0.421462	−	0.906846i	$-0.361517\pi$
$499$	−10.8427	−	10.8427i	−0.485385	−	0.485385i	−0.906846	+	0.421462i	$0.861517\pi$
$500$	−1.97974	+	1.97974i	−0.0885367	+	0.0885367i
$501$	−7.47481	−	12.0971i	−0.333950	−	0.540460i
$502$	−8.84477	+	8.84477i	−0.394761	+	0.394761i
$503$			42.2308i			1.88298i	0.337044	+	0.941489i	$0.390573\pi$
$503$			42.2308i			1.88298i	−0.337044	+	0.941489i	$0.609427\pi$
$504$	−9.05460	−	4.52951i	−0.403324	−	0.201760i
$505$	14.2615	−	14.2615i	0.634628	−	0.634628i
$506$	24.3637			1.08310
$507$		0			0
$508$	−13.3579			−0.592663
$509$	−3.21023	+	3.21023i	−0.142291	+	0.142291i	−0.774664	−	0.632373i	$-0.782081\pi$
$509$	−3.21023	+	3.21023i	−0.142291	+	0.142291i	0.632373	+	0.774664i	$0.282081\pi$
$510$	−0.186466	+	0.789540i	−0.00825687	+	0.0349614i
$511$		−	7.35938i		−	0.325560i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	0.592075	+	6.58775i	0.0261408	+	0.290856i
$514$	−2.62820	+	2.62820i	−0.115925	+	0.115925i
$515$	18.2906	+	18.2906i	0.805980	+	0.805980i
$516$	−7.06491	−	1.66853i	−0.311016	−	0.0734528i
$517$			18.4876i			0.813086i
$518$	−27.7579	−	27.7579i	−1.21961	−	1.21961i
$519$	34.5632	+	8.16283i	1.51716	+	0.358308i
$520$		0			0
$521$		−	18.0741i		−	0.791840i	−0.918285	−	0.395920i	$-0.870426\pi$
$521$		−	18.0741i		−	0.791840i	0.918285	−	0.395920i	$-0.129574\pi$
$522$	−8.09239	−	24.2929i	−0.354194	−	1.06327i
$523$	−33.5994			−1.46920			−0.734599	−	0.678502i	$-0.762630\pi$
$523$	−33.5994			−1.46920			−0.734599	+	0.678502i	$0.762630\pi$
$524$	12.3288			0.538586
$525$	−17.9745	−	29.0896i	−0.784470	−	1.26957i
$526$	−1.49819	−	1.49819i	−0.0653242	−	0.0653242i
$527$	−0.575090	−	0.575090i	−0.0250513	−	0.0250513i
$528$	3.05042	+	4.93677i	0.132753	+	0.214845i
$529$	29.8784			1.29906
$530$	−29.0325			−1.26109
$531$	9.53005	+	28.6087i	0.413569	+	1.24151i
$532$		−	4.29583i		−	0.186248i
$533$		0			0
$534$	13.0040	+	3.07116i	0.562738	+	0.132902i
$535$	−4.66758	−	4.66758i	−0.201797	−	0.201797i
$536$			0.615189i			0.0265721i
$537$	−8.25229	−	1.94895i	−0.356113	−	0.0841035i
$538$	−1.85952	−	1.85952i	−0.0801696	−	0.0801696i
$539$	10.3985	−	10.3985i	0.447894	−	0.447894i
$540$	1.53211	+	17.0471i	0.0659314	+	0.733588i
$541$	−5.65934	+	5.65934i	−0.243314	+	0.243314i	−0.818220	−	0.574906i	$-0.805039\pi$
$541$	−5.65934	+	5.65934i	−0.243314	+	0.243314i	0.574906	+	0.818220i	$0.305039\pi$
$542$			0.141453i			0.00607594i
$543$	−9.96899	+	42.2109i	−0.427810	+	1.81144i
$544$	−0.100547	+	0.100547i	−0.00431093	+	0.00431093i
$545$	31.7080			1.35822
$546$		0			0
$547$	−30.0294			−1.28396			−0.641982	−	0.766720i	$-0.721888\pi$
$547$	−30.0294			−1.28396			−0.641982	+	0.766720i	$0.721888\pi$
$548$	−6.56371	+	6.56371i	−0.280388	+	0.280388i
$549$	1.87004	+	0.935473i	0.0798112	+	0.0399250i
$550$			19.6001i			0.835752i
$551$	7.68239	−	7.68239i	0.327281	−	0.327281i
$552$	6.62056	+	10.7146i	0.281790	+	0.456045i
$553$	10.5594	−	10.5594i	0.449030	−	0.449030i
$554$	−3.68772	−	3.68772i	−0.156676	−	0.156676i
$555$	−15.2536	+	64.5870i	−0.647477	+	2.74156i
$556$		−	19.3647i		−	0.821248i
$557$	20.7242	+	20.7242i	0.878112	+	0.878112i	0.993339	−	0.115227i	$-0.0367595\pi$
$557$	20.7242	+	20.7242i	0.878112	+	0.878112i	−0.115227	+	0.993339i	$0.536760\pi$
$558$	−15.3458	−	7.67664i	−0.649640	−	0.324978i
$559$		0			0
$560$		−	11.1163i		−	0.469749i
$561$	0.433756	+	0.701985i	0.0183132	+	0.0296378i
$562$	−6.31903			−0.266552
$563$	−41.6799			−1.75660			−0.878299	−	0.478112i	$-0.841321\pi$
$563$	−41.6799			−1.75660			−0.878299	+	0.478112i	$0.841321\pi$
$564$	−8.13046	+	5.02381i	−0.342354	+	0.211540i
$565$	3.88418	+	3.88418i	0.163409	+	0.163409i
$566$	−12.7998	−	12.7998i	−0.538016	−	0.538016i
$567$	−30.0661	−	4.30711i	−1.26266	−	0.180882i
$568$	8.14601			0.341799
$569$	−27.4610			−1.15122			−0.575612	−	0.817723i	$-0.695236\pi$
$569$	−27.4610			−1.15122			−0.575612	+	0.817723i	$0.695236\pi$
$570$	−6.17809	+	3.81744i	−0.258772	+	0.159895i
$571$			10.7688i			0.450660i	0.974283	+	0.225330i	$0.0723460\pi$
$571$			10.7688i			0.450660i	−0.974283	+	0.225330i	$0.927654\pi$
$572$		0			0
$573$	−0.0367734	+	0.155707i	−0.00153623	+	0.00650475i
$574$	1.92600	+	1.92600i	0.0803898	+	0.0803898i
$575$			42.5396i			1.77402i
$576$	−1.34216	+	2.68302i	−0.0559235	+	0.111793i
$577$	−7.41899	−	7.41899i	−0.308857	−	0.308857i	0.535609	−	0.844466i	$-0.320082\pi$
$577$	−7.41899	−	7.41899i	−0.308857	−	0.308857i	−0.844466	+	0.535609i	$0.820082\pi$
$578$	12.0065	−	12.0065i	0.499405	−	0.499405i
$579$	−24.8974	+	15.3841i	−1.03470	+	0.639340i
$580$	19.8797	−	19.8797i	0.825458	−	0.825458i
$581$		−	7.69788i		−	0.319362i
$582$	12.7180	+	3.00362i	0.527178	+	0.124504i
$583$	−20.8814	+	20.8814i	−0.864820	+	0.864820i
$584$	−2.18070			−0.0902380
$585$		0			0
$586$	−16.8043			−0.694179
$587$	4.76148	−	4.76148i	0.196527	−	0.196527i	−0.601982	−	0.798509i	$-0.705622\pi$
$587$	4.76148	−	4.76148i	0.196527	−	0.196527i	0.798509	+	0.601982i	$0.205622\pi$
$588$	7.39868	+	1.74735i	0.305116	+	0.0720596i
$589$		−	7.28061i		−	0.299992i
$590$	−23.4114	+	23.4114i	−0.963832	+	0.963832i
$591$	−13.1116	+	8.10168i	−0.539341	+	0.333258i
$592$	−8.22509	+	8.22509i	−0.338049	+	0.338049i
$593$	27.7862	+	27.7862i	1.14104	+	1.14104i	0.988260	+	0.152785i	$0.0488241\pi$
$593$	27.7862	+	27.7862i	1.14104	+	1.14104i	0.152785	+	0.988260i	$0.451176\pi$
$594$	13.3629	+	11.1590i	0.548287	+	0.457859i
$595$		−	1.58068i		−	0.0648017i
$596$	14.5239	+	14.5239i	0.594922	+	0.594922i
$597$	−0.775702	+	3.28449i	−0.0317474	+	0.134425i
$598$		0			0
$599$			7.95696i			0.325113i	0.986699	+	0.162556i	$0.0519739\pi$
$599$			7.95696i			0.325113i	−0.986699	+	0.162556i	$0.948026\pi$
$600$	−8.61971	+	5.32611i	−0.351898	+	0.217438i
$601$	38.0035			1.55019			0.775097	−	0.631842i	$-0.217701\pi$
$601$	38.0035			1.55019			0.775097	+	0.631842i	$0.217701\pi$
$602$	14.1442			0.576474
$603$	0.583278	+	1.75097i	0.0237529	+	0.0713051i
$604$	1.14579	+	1.14579i	0.0466217	+	0.0466217i
$605$	0.525426	+	0.525426i	0.0213616	+	0.0213616i
$606$	9.02202	−	5.57470i	0.366494	−	0.226457i
$607$	17.6620			0.716878			0.358439	−	0.933553i	$-0.383309\pi$
$607$	17.6620			0.716878			0.358439	+	0.933553i	$0.383309\pi$
$608$	−1.27292			−0.0516238
$609$	26.2247	+	42.4417i	1.06268	+	1.71983i
$610$			2.29583i			0.0929556i
$611$		0			0
$612$	−0.190849	+	0.381513i	−0.00771462	+	0.0154217i
$613$	−13.0941	−	13.0941i	−0.528866	−	0.528866i	0.391368	−	0.920234i	$-0.372002\pi$
$613$	−13.0941	−	13.0941i	−0.528866	−	0.528866i	−0.920234	+	0.391368i	$0.872002\pi$
$614$			4.00449i			0.161608i
$615$	1.05838	−	4.48142i	0.0426780	−	0.180708i
$616$	−7.99530	−	7.99530i	−0.322140	−	0.322140i
$617$	−7.95747	+	7.95747i	−0.320356	+	0.320356i	−0.848904	−	0.528548i	$-0.822737\pi$
$617$	−7.95747	+	7.95747i	−0.320356	+	0.320356i	0.528548	+	0.848904i	$0.322737\pi$
$618$	7.14964	+	11.5709i	0.287601	+	0.465449i
$619$	11.3554	−	11.3554i	0.456411	−	0.456411i	−0.441064	−	0.897475i	$-0.645399\pi$
$619$	11.3554	−	11.3554i	0.456411	−	0.456411i	0.897475	+	0.441064i	$0.145399\pi$
$620$		−	18.8400i		−	0.756631i
$621$	29.0025	+	24.2192i	1.16383	+	0.971883i
$622$	−5.40389	+	5.40389i	−0.216676	+	0.216676i
$623$	−26.0344			−1.04305
$624$		0			0
$625$	20.0276			0.801105
$626$	−9.27248	+	9.27248i	−0.370603	+	0.370603i
$627$	−1.69788	+	7.18921i	−0.0678068	+	0.287109i
$628$			2.54214i			0.101442i
$629$	−1.16957	+	1.16957i	−0.0466338	+	0.0466338i
$630$	−10.5397	−	31.6396i	−0.419911	−	1.26055i
$631$	7.28724	−	7.28724i	0.290101	−	0.290101i	−0.547019	−	0.837120i	$-0.684238\pi$
$631$	7.28724	−	7.28724i	0.290101	−	0.290101i	0.837120	+	0.547019i	$0.184238\pi$
$632$	−3.12890	−	3.12890i	−0.124461	−	0.124461i
$633$	38.8696	+	9.17988i	1.54493	+	0.364867i
$634$		−	27.8712i		−	1.10691i
$635$	−31.1128	−	31.1128i	−1.23467	−	1.23467i
$636$	−14.8575	−	3.50890i	−0.589138	−	0.139137i
$637$		0			0
$638$		−	28.5966i		−	1.13215i
$639$	23.1855	−	7.72347i	0.917203	−	0.305536i
$640$	−3.29393			−0.130204
$641$	37.0693			1.46415			0.732075	−	0.681224i	$-0.238552\pi$
$641$	37.0693			1.46415			0.732075	+	0.681224i	$0.238552\pi$
$642$	−1.82452	−	2.95278i	−0.0720080	−	0.116537i
$643$	25.9375	+	25.9375i	1.02288	+	1.02288i	0.999732	+	0.0231431i	$0.00736732\pi$
$643$	25.9375	+	25.9375i	1.02288	+	1.02288i	0.0231431	+	0.999732i	$0.492633\pi$
$644$	−17.3528	−	17.3528i	−0.683796	−	0.683796i
$645$	−12.5691	−	20.3416i	−0.494906	−	0.800949i
$646$	−0.181003			−0.00712148
$647$	−34.7092			−1.36456			−0.682280	−	0.731091i	$-0.739012\pi$
$647$	−34.7092			−1.36456			−0.682280	+	0.731091i	$0.739012\pi$
$648$	−1.27626	+	8.90905i	−0.0501364	+	0.349980i
$649$			33.6769i			1.32194i
$650$		0			0
$651$	32.5376	+	7.68444i	1.27525	+	0.301177i
$652$	−9.56624	−	9.56624i	−0.374643	−	0.374643i
$653$		−	21.1748i		−	0.828635i	−0.910132	−	0.414318i	$-0.864020\pi$
$653$		−	21.1748i		−	0.828635i	0.910132	−	0.414318i	$-0.135980\pi$
$654$	16.2266	+	3.83226i	0.634512	+	0.149853i
$655$	28.7158	+	28.7158i	1.12202	+	1.12202i
$656$	0.570705	−	0.570705i	0.0222823	−	0.0222823i
$657$	−6.20678	+	2.06758i	−0.242150	+	0.0806641i
$658$	13.1676	−	13.1676i	0.513328	−	0.513328i
$659$		−	49.9732i		−	1.94668i	−0.229368	−	0.973340i	$-0.573666\pi$
$659$		−	49.9732i		−	1.94668i	0.229368	−	0.973340i	$-0.426334\pi$
$660$	−4.39359	+	18.6035i	−0.171020	+	0.724138i
$661$	14.0852	−	14.0852i	0.547849	−	0.547849i	−0.377969	−	0.925818i	$-0.623377\pi$
$661$	14.0852	−	14.0852i	0.547849	−	0.547849i	0.925818	+	0.377969i	$0.123377\pi$
$662$	15.4636			0.601011
$663$		0			0
$664$	−2.28100			−0.0885201
$665$	10.0057	−	10.0057i	0.388004	−	0.388004i
$666$	−15.6121	+	31.2090i	−0.604956	+	1.20932i
$667$		−	62.0652i		−	2.40318i
$668$	5.80536	−	5.80536i	0.224616	−	0.224616i
$669$	16.1436	+	26.1265i	0.624146	+	1.01011i
$670$	−1.43287	+	1.43287i	−0.0553568	+	0.0553568i
$671$	1.65126	+	1.65126i	0.0637462	+	0.0637462i
$672$	1.34353	−	5.68879i	0.0518277	−	0.219450i
$673$		−	18.5527i		−	0.715152i	−0.933884	−	0.357576i	$-0.883603\pi$
$673$		−	18.5527i		−	0.715152i	0.933884	−	0.357576i	$-0.116397\pi$
$674$	−12.0167	−	12.0167i	−0.462865	−	0.462865i
$675$	−19.4839	+	23.3320i	−0.749935	+	0.898047i
$676$		0			0
$677$			0.482183i			0.0185318i	0.999957	+	0.00926589i	$0.00294947\pi$
$677$			0.482183i			0.0185318i	−0.999957	+	0.00926589i	$0.997051\pi$
$678$	1.51829	+	2.45719i	0.0583098	+	0.0943677i
$679$	−25.4618			−0.977136
$680$	−0.468381			−0.0179616
$681$	26.6177	−	16.4471i	1.01999	−	0.630253i
$682$	−13.5505	−	13.5505i	−0.518875	−	0.518875i
$683$	26.4767	+	26.4767i	1.01310	+	1.01310i	0.999913	+	0.0131901i	$0.00419867\pi$
$683$	26.4767	+	26.4767i	1.01310	+	1.01310i	0.0131901	+	0.999913i	$0.495801\pi$
$684$	−3.62304	+	1.20689i	−0.138530	+	0.0461467i
$685$	−30.5759			−1.16824
$686$	8.81107			0.336408
$687$	11.2265	−	6.93686i	0.428319	−	0.264658i
$688$		−	4.19114i		−	0.159786i
$689$		0			0
$690$	−9.53574	+	40.3764i	−0.363019	+	1.53710i
$691$	20.4205	+	20.4205i	0.776834	+	0.776834i	0.979291	−	0.202457i	$-0.0648927\pi$
$691$	20.4205	+	20.4205i	0.776834	+	0.776834i	−0.202457	+	0.979291i	$0.564893\pi$
$692$			20.5041i			0.779447i
$693$	−30.3371	−	15.1759i	−1.15241	−	0.576486i
$694$	15.2531	+	15.2531i	0.579002	+	0.579002i
$695$	45.1036	−	45.1036i	1.71088	−	1.71088i
$696$	12.5761	−	7.77079i	0.476697	−	0.294551i
$697$	0.0811515	−	0.0811515i	0.00307383	−	0.00307383i
$698$		−	6.93033i		−	0.262317i
$699$	−18.6094	−	4.39501i	−0.703873	−	0.166234i
$700$	13.9600	−	13.9600i	0.527638	−	0.527638i
$701$	−4.85063			−0.183206			−0.0916029	−	0.995796i	$-0.529199\pi$
$701$	−4.85063			−0.183206			−0.0916029	+	0.995796i	$0.529199\pi$
$702$		0			0
$703$	−14.8067			−0.558444
$704$	−2.36913	+	2.36913i	−0.0892901	+	0.0892901i
$705$	−30.6384	−	7.23590i	−1.15391	−	0.272520i
$706$		−	27.9215i		−	1.05084i
$707$	−14.6115	+	14.6115i	−0.549524	+	0.549524i
$708$	−14.8104	+	9.15132i	−0.556608	+	0.343928i
$709$	15.6072	−	15.6072i	0.586140	−	0.586140i	−0.350444	−	0.936584i	$-0.613969\pi$
$709$	15.6072	−	15.6072i	0.586140	−	0.586140i	0.936584	+	0.350444i	$0.113969\pi$
$710$	18.9734	+	18.9734i	0.712058	+	0.712058i
$711$	−11.8722	−	5.93899i	−0.445242	−	0.222729i
$712$			7.71440i			0.289109i
$713$	−29.4096	−	29.4096i	−1.10140	−	1.10140i
$714$	0.191043	−	0.808919i	0.00714961	−	0.0302730i
$715$		0			0
$716$		−	4.89553i		−	0.182955i
$717$	−18.9786	+	11.7268i	−0.708767	+	0.437947i
$718$	2.39652			0.0894372
$719$	−39.8320			−1.48548			−0.742742	−	0.669578i	$-0.766475\pi$
$719$	−39.8320			−1.48548			−0.742742	+	0.669578i	$0.766475\pi$
$720$	−9.37530	+	3.12307i	−0.349397	+	0.116390i
$721$	−18.7395	−	18.7395i	−0.697897	−	0.697897i
$722$	12.2893	+	12.2893i	0.457360	+	0.457360i
$723$	22.6459	−	13.9929i	0.842209	−	0.520401i
$724$	−25.0409			−0.930638
$725$	49.9303			1.85436
$726$	0.205385	+	0.332392i	0.00762254	+	0.0123362i
$727$		−	39.3672i		−	1.46005i	−0.683422	−	0.730024i	$-0.739509\pi$
$727$		−	39.3672i		−	1.46005i	0.683422	−	0.730024i	$-0.260491\pi$
$728$		0			0
$729$	4.81437	+	26.5673i	0.178310	+	0.983974i
$730$	−5.07920	−	5.07920i	−0.187990	−	0.187990i
$731$		−	0.595960i		−	0.0220424i
$732$	−0.277477	+	1.17490i	−0.0102558	+	0.0434255i
$733$	8.27459	+	8.27459i	0.305629	+	0.305629i	0.843211	−	0.537582i	$-0.180662\pi$
$733$	8.27459	+	8.27459i	0.305629	+	0.305629i	−0.537582	+	0.843211i	$0.680662\pi$
$734$	4.79803	−	4.79803i	0.177099	−	0.177099i
$735$	13.1629	+	21.3026i	0.485519	+	0.785758i
$736$	−5.14190	+	5.14190i	−0.189533	+	0.189533i
$737$			2.06117i			0.0759241i
$738$	1.08326	−	2.16546i	0.0398753	−	0.0797117i
$739$	15.1517	−	15.1517i	0.557363	−	0.557363i	−0.371193	−	0.928556i	$-0.621051\pi$
$739$	15.1517	−	15.1517i	0.557363	−	0.557363i	0.928556	+	0.371193i	$0.121051\pi$
$740$	−38.3151			−1.40849
$741$		0			0
$742$	29.7452			1.09198
$743$	11.2633	−	11.2633i	0.413211	−	0.413211i	−0.469644	−	0.882856i	$-0.655618\pi$
$743$	11.2633	−	11.2633i	0.413211	−	0.413211i	0.882856	+	0.469644i	$0.155618\pi$
$744$	2.27702	−	9.64141i	0.0834796	−	0.353471i
$745$			67.6569i			2.47876i
$746$	16.8655	−	16.8655i	0.617490	−	0.617490i
$747$	−6.49227	+	2.16268i	−0.237540	+	0.0791285i
$748$	−0.336879	+	0.336879i	−0.0123175	+	0.0123175i
$749$	4.78215	+	4.78215i	0.174736	+	0.174736i
$750$	−4.71952	−	1.11461i	−0.172332	−	0.0406999i
$751$			16.4580i			0.600560i	0.953851	+	0.300280i	$0.0970801\pi$
$751$			16.4580i			0.600560i	−0.953851	+	0.300280i	$0.902920\pi$
$752$	−3.90177	−	3.90177i	−0.142283	−	0.142283i
$753$	−21.0851	−	4.97969i	−0.768384	−	0.181470i
$754$		0			0
$755$			5.33748i			0.194251i
$756$	−1.56971	−	17.4655i	−0.0570899	−	0.635213i
$757$	14.1884			0.515686			0.257843	−	0.966187i	$-0.416988\pi$
$757$	14.1884			0.515686			0.257843	+	0.966187i	$0.416988\pi$
$758$	−2.59659			−0.0943123
$759$	22.1819	+	35.8989i	0.805153	+	1.30305i
$760$	−2.96484	−	2.96484i	−0.107546	−	0.107546i
$761$	−6.25317	−	6.25317i	−0.226677	−	0.226677i	0.584626	−	0.811303i	$-0.301241\pi$
$761$	−6.25317	−	6.25317i	−0.226677	−	0.226677i	−0.811303	+	0.584626i	$0.801241\pi$
$762$	−12.1617	−	19.6824i	−0.440573	−	0.713017i
$763$	−32.4862			−1.17608
$764$	−0.0923705			−0.00334185
$765$	−1.33312	+	0.444086i	−0.0481992	+	0.0160559i
$766$			1.95940i			0.0707960i
$767$		0			0
$768$	−1.68568	−	0.398108i	−0.0608267	−	0.0143655i
$769$	15.6603	+	15.6603i	0.564723	+	0.564723i	0.930645	−	0.365922i	$-0.119246\pi$
$769$	15.6603	+	15.6603i	0.564723	+	0.564723i	−0.365922	+	0.930645i	$0.619246\pi$
$770$		−	37.2447i		−	1.34221i
$771$	−6.26539	−	1.47970i	−0.225643	−	0.0532902i
$772$	−11.9481	−	11.9481i	−0.430023	−	0.430023i
$773$	13.4649	−	13.4649i	0.484300	−	0.484300i	−0.422202	−	0.906502i	$-0.638743\pi$
$773$	13.4649	−	13.4649i	0.484300	−	0.484300i	0.906502	+	0.422202i	$0.138743\pi$
$774$	−3.97374	−	11.9290i	−0.142833	−	0.428778i
$775$	23.6595	−	23.6595i	0.849874	−	0.849874i
$776$			7.54474i			0.270840i
$777$	15.6280	−	66.1722i	0.560650	−	2.37392i
$778$	25.2765	−	25.2765i	0.906207	−	0.906207i
$779$	1.02737			0.0368095
$780$		0			0
$781$	27.2929			0.976617
$782$	−0.731154	+	0.731154i	−0.0261460	+	0.0261460i
$783$	28.4269	−	34.0413i	1.01590	−	1.21654i
$784$			4.38914i			0.156755i
$785$	−5.92105	+	5.92105i	−0.211331	+	0.211331i
$786$	11.2248	+	18.1660i	0.400374	+	0.647960i
$787$	26.2145	−	26.2145i	0.934446	−	0.934446i	−0.0635338	−	0.997980i	$-0.520237\pi$
$787$	26.2145	−	26.2145i	0.934446	−	0.934446i	0.997980	+	0.0635338i	$0.0202371\pi$
$788$	−6.29222	−	6.29222i	−0.224151	−	0.224151i
$789$	0.843496	−	3.57155i	0.0300292	−	0.127150i
$790$		−	14.5754i		−	0.518571i
$791$	−3.97952	−	3.97952i	−0.141495	−	0.141495i
$792$	−4.49687	+	8.98935i	−0.159789	+	0.319423i
$793$		0			0
$794$			29.4340i			1.04457i
$795$	−26.4327	−	42.7783i	−0.937470	−	1.51719i
$796$	−1.94847			−0.0690617
$797$	34.4856			1.22154			0.610772	−	0.791807i	$-0.290859\pi$
$797$	34.4856			1.22154			0.610772	+	0.791807i	$0.290859\pi$
$798$	6.32973	−	3.91114i	0.224070	−	0.138453i
$799$	−0.554813	−	0.554813i	−0.0196279	−	0.0196279i
$800$	−4.13656	−	4.13656i	−0.146250	−	0.146250i
$801$	7.31424	+	21.9570i	0.258436	+	0.775812i
$802$	6.12304			0.216212
$803$	−7.30635			−0.257835
$804$	−0.906456	+	0.560099i	−0.0319682	+	0.0197532i
$805$		−	80.8349i		−	2.84906i
$806$		0			0
$807$	1.04693	−	4.43293i	0.0368536	−	0.156046i
$808$	4.32963	+	4.32963i	0.152316	+	0.152316i
$809$			34.1047i			1.19906i	0.800353	+	0.599529i	$0.204645\pi$
$809$			34.1047i			1.19906i	−0.800353	+	0.599529i	$0.795355\pi$
$810$	−23.7232	+	17.7780i	−0.833549	+	0.624655i
$811$	−16.8736	−	16.8736i	−0.592512	−	0.592512i	0.345797	−	0.938309i	$-0.387609\pi$
$811$	−16.8736	−	16.8736i	−0.592512	−	0.592512i	−0.938309	+	0.345797i	$0.887609\pi$
$812$	−20.3676	+	20.3676i	−0.714763	+	0.714763i
$813$	−0.208426	+	0.128786i	−0.00730981	+	0.00451672i
$814$	−27.5578	+	27.5578i	−0.965902	+	0.965902i
$815$		−	44.5626i		−	1.56096i
$816$	−0.239695	−	0.0566090i	−0.00839101	−	0.00198171i
$817$	3.77241	−	3.77241i	0.131980	−	0.131980i
$818$	24.5293			0.857646
$819$		0			0
$820$	2.65853			0.0928398
$821$	17.3246	−	17.3246i	0.604633	−	0.604633i	−0.336905	−	0.941539i	$-0.609380\pi$
$821$	17.3246	−	17.3246i	0.604633	−	0.604633i	0.941539	+	0.336905i	$0.109380\pi$
$822$	−15.6473	−	3.69543i	−0.545762	−	0.128893i
$823$			31.5996i			1.10149i	0.834673	+	0.550746i	$0.185657\pi$
$823$			31.5996i			1.10149i	−0.834673	+	0.550746i	$0.814343\pi$
$824$	−5.55282	+	5.55282i	−0.193442	+	0.193442i
$825$	−28.8800	+	17.8449i	−1.00547	+	0.621281i
$826$	23.9860	−	23.9860i	0.834581	−	0.834581i
$827$	−4.25498	−	4.25498i	−0.147960	−	0.147960i	0.629246	−	0.777206i	$-0.283364\pi$
$827$	−4.25498	−	4.25498i	−0.147960	−	0.147960i	−0.777206	+	0.629246i	$0.783364\pi$
$828$	−9.75988	+	19.5103i	−0.339179	+	0.678028i
$829$			50.2981i			1.74693i	0.486890	+	0.873463i	$0.338131\pi$
$829$			50.2981i			1.74693i	−0.486890	+	0.873463i	$0.661869\pi$
$830$	−5.31282	−	5.31282i	−0.184411	−	0.184411i
$831$	2.07622	−	8.79120i	0.0720234	−	0.304963i
$832$		0			0
$833$			0.624115i			0.0216243i
$834$	28.5332	−	17.6306i	0.988022	−	0.610498i
$835$	27.0433			0.935870
$836$	−4.26488			−0.147504
$837$	−2.66036	−	29.6006i	−0.0919556	−	1.02315i
$838$	0.145088	+	0.145088i	0.00501198	+	0.00501198i
$839$	−8.72909	−	8.72909i	−0.301362	−	0.301362i	0.540185	−	0.841546i	$-0.318354\pi$
$839$	−8.72909	−	8.72909i	−0.301362	−	0.301362i	−0.841546	+	0.540185i	$0.818354\pi$
$840$	16.3794	−	10.1208i	0.565143	−	0.349202i
$841$	−43.8482			−1.51201
$842$	36.9923			1.27484
$843$	−5.75315	−	9.31083i	−0.198149	−	0.320682i
$844$			23.0588i			0.793715i
$845$		0			0
$846$	−14.8047	−	7.40598i	−0.508998	−	0.254623i
$847$	−0.538323	−	0.538323i	−0.0184970	−	0.0184970i
$848$		−	8.81395i		−	0.302672i
$849$	7.20642	−	30.5136i	0.247324	−	1.04722i
$850$	−0.588199	−	0.588199i	−0.0201751	−	0.0201751i
$851$	−59.8108	+	59.8108i	−2.05029	+	2.05029i
$852$	7.41653	+	12.0028i	0.254086	+	0.411210i
$853$	−19.5003	+	19.5003i	−0.667678	+	0.667678i	−0.957178	−	0.289500i	$-0.906511\pi$
$853$	−19.5003	+	19.5003i	−0.667678	+	0.667678i	0.289500	+	0.957178i	$0.406511\pi$
$854$		−	2.35218i		−	0.0804901i
$855$	−11.2497	−	5.62758i	−0.384731	−	0.192459i
$856$	1.41703	−	1.41703i	0.0484329	−	0.0484329i
$857$	−14.8471			−0.507168			−0.253584	−	0.967313i	$-0.581609\pi$
$857$	−14.8471			−0.507168			−0.253584	+	0.967313i	$0.581609\pi$
$858$		0			0
$859$	11.2338			0.383293			0.191647	−	0.981464i	$-0.438617\pi$
$859$	11.2338			0.383293			0.191647	+	0.981464i	$0.438617\pi$
$860$	9.76184	−	9.76184i	0.332876	−	0.332876i
$861$	−1.08436	+	4.59142i	−0.0369548	+	0.156475i
$862$		−	21.6840i		−	0.738560i
$863$	−35.5847	+	35.5847i	−1.21132	+	1.21132i	−0.240721	+	0.970594i	$0.577384\pi$
$863$	−35.5847	+	35.5847i	−1.21132	+	1.21132i	−0.970594	+	0.240721i	$0.922616\pi$
$864$	−5.17529	+	0.465131i	−0.176067	+	0.0158241i
$865$	−47.7573	+	47.7573i	−1.62380	+	1.62380i
$866$	−6.65207	−	6.65207i	−0.226046	−	0.226046i
$867$	28.6224	+	6.75979i	0.972069	+	0.229574i
$868$			19.3024i			0.655166i
$869$	−10.4833	−	10.4833i	−0.355620	−	0.355620i
$870$	47.3913	+	11.1924i	1.60671	+	0.379459i
$871$		0			0
$872$			9.62618i			0.325984i
$873$	7.15339	+	21.4741i	0.242105	+	0.726788i
$874$	−9.25637			−0.313102
$875$	9.44863			0.319422
$876$	−1.98542	−	3.21317i	−0.0670810	−	0.108563i
$877$	6.09777	+	6.09777i	0.205907	+	0.205907i	0.802525	−	0.596618i	$-0.203489\pi$
$877$	6.09777	+	6.09777i	0.205907	+	0.205907i	−0.596618	+	0.802525i	$0.703489\pi$
$878$	15.7909	+	15.7909i	0.532916	+	0.532916i
$879$	−15.2995	−	24.7604i	−0.516038	−	0.835149i
$880$	−11.0362			−0.372030
$881$	54.6331			1.84064			0.920318	−	0.391170i	$-0.127930\pi$
$881$	54.6331			1.84064			0.920318	+	0.391170i	$0.127930\pi$
$882$	4.16147	+	12.4925i	0.140124	+	0.420645i
$883$		−	9.33621i		−	0.314189i	−0.987584	−	0.157094i	$-0.949787\pi$
$883$		−	9.33621i		−	0.314189i	0.987584	−	0.157094i	$-0.0502126\pi$
$884$		0			0
$885$	−55.8106	−	13.1808i	−1.87605	−	0.443069i
$886$	23.8587	+	23.8587i	0.801548	+	0.801548i
$887$		−	39.3322i		−	1.32064i	−0.750982	−	0.660322i	$-0.770420\pi$
$887$		−	39.3322i		−	1.32064i	0.750982	−	0.660322i	$-0.229580\pi$
$888$	−19.6079	−	4.63081i	−0.657997	−	0.155400i
$889$	31.8765	+	31.8765i	1.06910	+	1.06910i
$890$	−17.9681	+	17.9681i	−0.602291	+	0.602291i
$891$	−4.27608	+	29.8494i	−0.143254	+	0.999993i
$892$	−12.5380	+	12.5380i	−0.419803	+	0.419803i
$893$		−	7.02391i		−	0.235046i
$894$	−8.17709	+	34.6236i	−0.273483	+	1.15799i
$895$	11.4025	−	11.4025i	0.381143	−	0.381143i
$896$	3.37478			0.112743
$897$		0			0
$898$	28.8428			0.962498
$899$	−34.5192	+	34.5192i	−1.15128	+	1.15128i
$900$	−15.6956	−	7.85163i	−0.523187	−	0.261721i
$901$		−	1.25330i		−	0.0417535i
$902$	1.91212	−	1.91212i	0.0636668	−	0.0636668i
$903$	12.8776	+	20.8409i	0.428538	+	0.693541i
$904$	−1.17919	+	1.17919i	−0.0392194	+	0.0392194i
$905$	−58.3243	−	58.3243i	−1.93877	−	1.93877i
$906$	−0.645093	+	2.73147i	−0.0214318	+	0.0907469i
$907$		−	20.0550i		−	0.665917i	−0.942942	−	0.332958i	$-0.891953\pi$
$907$		−	20.0550i		−	0.665917i	0.942942	−	0.332958i	$-0.108047\pi$
$908$	12.7737	+	12.7737i	0.423911	+	0.423911i
$909$	16.4282	+	8.21809i	0.544888	+	0.272577i
$910$		0			0
$911$		−	28.3515i		−	0.939327i	−0.882846	−	0.469663i	$-0.844375\pi$
$911$		−	28.3515i		−	0.939327i	0.882846	−	0.469663i	$-0.155625\pi$
$912$	−1.15893	−	1.87560i	−0.0383761	−	0.0621073i
$913$	−7.64241			−0.252927
$914$	−39.5191			−1.30717
$915$	−3.38282	+	2.09024i	−0.111832	+	0.0691012i
$916$	5.38756	+	5.38756i	0.178010	+	0.178010i
$917$	−29.4206	−	29.4206i	−0.971554	−	0.971554i
$918$	−0.735902	+	0.0661393i	−0.0242884	+	0.00218292i
$919$	40.9204			1.34984			0.674920	−	0.737891i	$-0.264178\pi$
$919$	40.9204			1.34984			0.674920	+	0.737891i	$0.264178\pi$
$920$	−23.9526			−0.789695
$921$	−5.90046	+	3.64589i	−0.194427	+	0.120136i
$922$			32.8173i			1.08078i
$923$		0			0
$924$	4.50143	−	19.0601i	0.148086	−	0.627030i
$925$	−48.1166	−	48.1166i	−1.58206	−	1.58206i
$926$			22.6837i			0.745433i
$927$	−10.5398	+	21.0694i	−0.346174	+	0.692010i
$928$	6.03524	+	6.03524i	0.198116	+	0.198116i
$929$	8.76253	−	8.76253i	0.287489	−	0.287489i	−0.548597	−	0.836087i	$-0.684838\pi$
$929$	8.76253	−	8.76253i	0.287489	−	0.287489i	0.836087	+	0.548597i	$0.184838\pi$
$930$	27.7599	−	17.1528i	0.910284	−	0.562464i
$931$	−3.95063	+	3.95063i	−0.129477	+	0.129477i
$932$		−	11.0397i		−	0.361618i
$933$	−12.8824	−	3.04244i	−0.421750	−	0.0996050i
$934$	5.14172	−	5.14172i	0.168242	−	0.168242i
$935$	−1.56929			−0.0513214
$936$		0			0
$937$	33.8204			1.10487			0.552433	−	0.833557i	$-0.313700\pi$
$937$	33.8204			1.10487			0.552433	+	0.833557i	$0.313700\pi$
$938$	1.46804	−	1.46804i	0.0479333	−	0.0479333i
$939$	−22.1047	−	5.22050i	−0.721361	−	0.170364i
$940$		−	18.1757i		−	0.592826i
$941$	−0.799445	+	0.799445i	−0.0260612	+	0.0260612i	−0.720017	−	0.693956i	$-0.755866\pi$
$941$	−0.799445	+	0.799445i	−0.0260612	+	0.0260612i	0.693956	+	0.720017i	$0.255866\pi$
$942$	−3.74574	+	2.31449i	−0.122043	+	0.0754101i
$943$	4.15002	−	4.15002i	0.135143	−	0.135143i
$944$	−7.10744	−	7.10744i	−0.231327	−	0.231327i
$945$	37.0238	−	44.3360i	1.20438	−	1.44225i
$946$		−	14.0423i		−	0.456553i
$947$	−0.565895	−	0.565895i	−0.0183891	−	0.0183891i	0.697852	−	0.716242i	$-0.254139\pi$
$947$	−0.565895	−	0.565895i	−0.0183891	−	0.0183891i	−0.716242	+	0.697852i	$0.754139\pi$
$948$	1.76160	−	7.45902i	0.0572142	−	0.242258i
$949$		0			0
$950$		−	7.44657i		−	0.241599i
$951$	41.0671	−	25.3754i	1.33169	−	0.822852i
$952$	0.479878			0.0155529
$953$	27.1966			0.880985			0.440492	−	0.897756i	$-0.354804\pi$
$953$	27.1966			0.880985			0.440492	+	0.897756i	$0.354804\pi$
$954$	−8.35676	−	25.0866i	−0.270560	−	0.812208i
$955$	−0.215146	−	0.215146i	−0.00696195	−	0.00696195i
$956$	−9.10773	−	9.10773i	−0.294565	−	0.294565i
$957$	42.1359	−	26.0357i	1.36206	−	0.841616i
$958$	−9.93607			−0.321020
$959$	31.3263			1.01158
$960$	−2.99896	−	4.85347i	−0.0967909	−	0.156645i
$961$			1.71384i			0.0552852i
$962$		0			0
$963$	2.68966	−	5.37671i	0.0866732	−	0.173262i
$964$	10.8677	+	10.8677i	0.350024	+	0.350024i
$965$		−	55.6583i		−	1.79170i
$966$	9.76979	−	41.3675i	0.314338	−	1.33098i
$967$	2.51021	+	2.51021i	0.0807228	+	0.0807228i	0.746315	−	0.665593i	$-0.231821\pi$
$967$	2.51021	+	2.51021i	0.0807228	+	0.0807228i	−0.665593	+	0.746315i	$0.731821\pi$
$968$	−0.159513	+	0.159513i	−0.00512696	+	0.00512696i
$969$	−0.164794	−	0.266701i	−0.00529396	−	0.00856768i
$970$	−17.5729	+	17.5729i	−0.564232	+	0.564232i
$971$		−	7.79592i		−	0.250183i	−0.992145	−	0.125091i	$-0.960078\pi$
$971$		−	7.79592i		−	0.250183i	0.992145	−	0.125091i	$-0.0399224\pi$
$972$	−14.2891	+	6.23071i	−0.458323	+	0.199850i
$973$	−46.2107	+	46.2107i	−1.48145	+	1.48145i
$974$	−3.43464			−0.110053
$975$		0			0
$976$	−0.696989			−0.0223101
$977$	39.0459	−	39.0459i	1.24919	−	1.24919i	0.293108	−	0.956079i	$-0.405310\pi$
$977$	39.0459	−	39.0459i	1.24919	−	1.24919i	0.956079	−	0.293108i	$-0.0946897\pi$
$978$	5.38589	−	22.8051i	0.172222	−	0.729225i
$979$			25.8468i			0.826067i
$980$	−10.2230	+	10.2230i	−0.326562	+	0.326562i
$981$	9.12686	+	27.3984i	0.291398	+	0.874763i
$982$	−26.8509	+	26.8509i	−0.856848	+	0.856848i
$983$	−6.16289	−	6.16289i	−0.196566	−	0.196566i	0.601960	−	0.798526i	$-0.294387\pi$
$983$	−6.16289	−	6.16289i	−0.196566	−	0.196566i	−0.798526	+	0.601960i	$0.794387\pi$
$984$	1.36051	+	0.321312i	0.0433714	+	0.0102431i
$985$		−	29.3112i		−	0.933932i
$986$	0.858182	+	0.858182i	0.0273301	+	0.0273301i
$987$	31.3904	+	7.41350i	0.999168	+	0.235974i
$988$		0			0
$989$		−	30.4769i		−	0.969110i
$990$	−31.4116	+	10.4637i	−0.998325	+	0.332559i
$991$	−39.1078			−1.24230			−0.621150	−	0.783692i	$-0.713334\pi$
$991$	−39.1078			−1.24230			−0.621150	+	0.783692i	$0.713334\pi$
$992$	5.71960			0.181598
$993$	14.0789	+	22.7850i	0.446779	+	0.723061i
$994$	−19.4391	−	19.4391i	−0.616570	−	0.616570i
$995$	−4.53830	−	4.53830i	−0.143874	−	0.143874i
$996$	−2.07674	−	3.36096i	−0.0658039	−	0.106496i
$997$	−33.5848			−1.06364			−0.531821	−	0.846857i	$-0.678492\pi$
$997$	−33.5848			−1.06364			−0.531821	+	0.846857i	$0.678492\pi$
$998$	15.3338			0.485385
$999$	−60.1992	+	5.41042i	−1.90462	+	0.171178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.g.e.437.1	yes	48
3.2	odd	2	inner	1014.2.g.e.437.19	yes	48
13.5	odd	4	inner	1014.2.g.e.239.19	yes	48
13.8	odd	4	inner	1014.2.g.e.239.6	yes	48
13.12	even	2	inner	1014.2.g.e.437.24	yes	48
39.5	even	4	inner	1014.2.g.e.239.1	✓	48
39.8	even	4	inner	1014.2.g.e.239.24	yes	48
39.38	odd	2	inner	1014.2.g.e.437.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.g.e.239.1	✓	48	39.5	even	4	inner
1014.2.g.e.239.6	yes	48	13.8	odd	4	inner
1014.2.g.e.239.19	yes	48	13.5	odd	4	inner
1014.2.g.e.239.24	yes	48	39.8	even	4	inner
1014.2.g.e.437.1	yes	48	1.1	even	1	trivial
1014.2.g.e.437.6	yes	48	39.38	odd	2	inner
1014.2.g.e.437.19	yes	48	3.2	odd	2	inner
1014.2.g.e.437.24	yes	48	13.12	even	2	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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.68568 - 0.398108i) q^{3} -1.00000i q^{4} +(2.32916 - 2.32916i) q^{5} +(1.47346 - 0.910449i) q^{6} +(-2.38633 + 2.38633i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.68302 + 1.34216i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.68568 - 0.398108i) q^{3} -1.00000i q^{4} +(2.32916 - 2.32916i) q^{5} +(1.47346 - 0.910449i) q^{6} +(-2.38633 + 2.38633i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.68302 + 1.34216i) q^{9} +3.29393i q^{10} +(2.36913 + 2.36913i) q^{11} +(-0.398108 + 1.68568i) q^{12} -3.37478i q^{14} +(-4.85347 + 2.99896i) q^{15} -1.00000 q^{16} -0.142195 q^{17} +(-2.84623 + 0.948129i) q^{18} +(-0.900092 - 0.900092i) q^{19} +(-2.32916 - 2.32916i) q^{20} +(4.97260 - 3.07257i) q^{21} -3.35046 q^{22} -7.27175 q^{23} +(-0.910449 - 1.47346i) q^{24} -5.84998i q^{25} +(-3.98838 - 3.33059i) q^{27} +(2.38633 + 2.38633i) q^{28} +8.53511i q^{29} +(1.31134 - 5.55251i) q^{30} +(4.04437 + 4.04437i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.05042 - 4.93677i) q^{33} +(0.100547 - 0.100547i) q^{34} +11.1163i q^{35} +(1.34216 - 2.68302i) q^{36} +(8.22509 - 8.22509i) q^{37} +1.27292 q^{38} +3.29393 q^{40} +(-0.570705 + 0.570705i) q^{41} +(-1.34353 + 5.68879i) q^{42} +4.19114i q^{43} +(2.36913 - 2.36913i) q^{44} +(9.37530 - 3.12307i) q^{45} +(5.14190 - 5.14190i) q^{46} +(3.90177 + 3.90177i) q^{47} +(1.68568 + 0.398108i) q^{48} -4.38914i q^{49} +(4.13656 + 4.13656i) q^{50} +(0.239695 + 0.0566090i) q^{51} +8.81395i q^{53} +(5.17529 - 0.465131i) q^{54} +11.0362 q^{55} -3.37478 q^{56} +(1.15893 + 1.87560i) q^{57} +(-6.03524 - 6.03524i) q^{58} +(7.10744 + 7.10744i) q^{59} +(2.99896 + 4.85347i) q^{60} +0.696989 q^{61} -5.71960 q^{62} +(-9.60542 + 3.19973i) q^{63} +1.00000i q^{64} +(5.64780 + 1.33385i) q^{66} +(0.435004 + 0.435004i) q^{67} +0.142195i q^{68} +(12.2578 + 2.89494i) q^{69} +(-7.86041 - 7.86041i) q^{70} +(5.76010 - 5.76010i) q^{71} +(0.948129 + 2.84623i) q^{72} +(-1.54199 + 1.54199i) q^{73} +11.6320i q^{74} +(-2.32892 + 9.86118i) q^{75} +(-0.900092 + 0.900092i) q^{76} -11.3071 q^{77} -4.42494 q^{79} +(-2.32916 + 2.32916i) q^{80} +(5.39719 + 7.20210i) q^{81} -0.807098i q^{82} +(-1.61291 + 1.61291i) q^{83} +(-3.07257 - 4.97260i) q^{84} +(-0.331195 + 0.331195i) q^{85} +(-2.96358 - 2.96358i) q^{86} +(3.39790 - 14.3875i) q^{87} +3.35046i q^{88} +(5.45490 + 5.45490i) q^{89} +(-4.42099 + 8.83768i) q^{90} +7.27175i q^{92} +(-5.20741 - 8.42760i) q^{93} -5.51794 q^{94} -4.19292 q^{95} +(-1.47346 + 0.910449i) q^{96} +(5.33494 + 5.33494i) q^{97} +(3.10359 + 3.10359i) q^{98} +(3.17667 + 9.53620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} + 20 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 + 20 * q^9	\( 48 q - 4 q^{3} + 20 q^{9} - 48 q^{16} - 32 q^{22} + 116 q^{27} + 8 q^{40} - 40 q^{42} + 4 q^{48} - 144 q^{55} - 80 q^{61} + 96 q^{66} - 56 q^{79} + 84 q^{81} + 224 q^{87} - 16 q^{94}+O(q^{100}) \) 48 * q - 4 * q^3 + 20 * q^9 - 48 * q^16 - 32 * q^22 + 116 * q^27 + 8 * q^40 - 40 * q^42 + 4 * q^48 - 144 * q^55 - 80 * q^61 + 96 * q^66 - 56 * q^79 + 84 * q^81 + 224 * q^87 - 16 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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