LMFDB - Embedded newform 1014.2.g.e.437.18

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			437.18
Character	$\chi$	$=$	1014.437
Dual form			1014.2.g.e.239.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.72717 - 0.129918i) q^{3} -1.00000i q^{4} +(1.54530 - 1.54530i) q^{5} +(1.12943 - 1.31316i) q^{6} +(0.651496 - 0.651496i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.96624 - 0.448782i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.72717 - 0.129918i) q^{3} -1.00000i q^{4} +(1.54530 - 1.54530i) q^{5} +(1.12943 - 1.31316i) q^{6} +(0.651496 - 0.651496i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.96624 - 0.448782i) q^{9} -2.18538i q^{10} +(-2.32321 - 2.32321i) q^{11} +(-0.129918 - 1.72717i) q^{12} -0.921354i q^{14} +(2.46823 - 2.86975i) q^{15} -1.00000 q^{16} -7.60059 q^{17} +(1.78011 - 2.41479i) q^{18} +(-2.61512 - 2.61512i) q^{19} +(-1.54530 - 1.54530i) q^{20} +(1.04060 - 1.20989i) q^{21} -3.28551 q^{22} +6.68859 q^{23} +(-1.31316 - 1.12943i) q^{24} +0.224123i q^{25} +(5.06490 - 1.16049i) q^{27} +(-0.651496 - 0.651496i) q^{28} +7.08445i q^{29} +(-0.283920 - 3.77452i) q^{30} +(6.55026 + 6.55026i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-4.31440 - 3.71075i) q^{33} +(-5.37443 + 5.37443i) q^{34} -2.01351i q^{35} +(-0.448782 - 2.96624i) q^{36} +(1.13927 - 1.13927i) q^{37} -3.69834 q^{38} -2.18538 q^{40} +(5.29792 - 5.29792i) q^{41} +(-0.119701 - 1.59134i) q^{42} +10.2062i q^{43} +(-2.32321 + 2.32321i) q^{44} +(3.89022 - 5.27722i) q^{45} +(4.72955 - 4.72955i) q^{46} +(1.78843 + 1.78843i) q^{47} +(-1.72717 + 0.129918i) q^{48} +6.15111i q^{49} +(0.158479 + 0.158479i) q^{50} +(-13.1275 + 0.987455i) q^{51} -7.08357i q^{53} +(2.76084 - 4.40202i) q^{54} -7.18008 q^{55} -0.921354 q^{56} +(-4.85651 - 4.17701i) q^{57} +(5.00946 + 5.00946i) q^{58} +(-4.95111 - 4.95111i) q^{59} +(-2.86975 - 2.46823i) q^{60} +2.47439 q^{61} +9.26346 q^{62} +(1.64011 - 2.22487i) q^{63} +1.00000i q^{64} +(-5.67464 + 0.426848i) q^{66} +(-1.79671 - 1.79671i) q^{67} +7.60059i q^{68} +(11.5523 - 0.868969i) q^{69} +(-1.42376 - 1.42376i) q^{70} +(-4.60918 + 4.60918i) q^{71} +(-2.41479 - 1.78011i) q^{72} +(7.82194 - 7.82194i) q^{73} -1.61117i q^{74} +(0.0291177 + 0.387099i) q^{75} +(-2.61512 + 2.61512i) q^{76} -3.02712 q^{77} +2.90723 q^{79} +(-1.54530 + 1.54530i) q^{80} +(8.59719 - 2.66239i) q^{81} -7.49239i q^{82} +(-4.21539 + 4.21539i) q^{83} +(-1.20989 - 1.04060i) q^{84} +(-11.7452 + 11.7452i) q^{85} +(7.21686 + 7.21686i) q^{86} +(0.920399 + 12.2361i) q^{87} +3.28551i q^{88} +(1.20906 + 1.20906i) q^{89} +(-0.980758 - 6.48236i) q^{90} -6.68859i q^{92} +(12.1644 + 10.4624i) q^{93} +2.52922 q^{94} -8.08226 q^{95} +(-1.12943 + 1.31316i) q^{96} +(1.61485 + 1.61485i) q^{97} +(4.34949 + 4.34949i) q^{98} +(-7.93381 - 5.84858i) 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
$3$	1.72717	−	0.129918i	0.997183	−	0.0750083i
$3$	1.72717	−	0.129918i	0.997183	−	0.0750083i
$4$		−	1.00000i		−	0.500000i
$5$	1.54530	−	1.54530i	0.691077	−	0.691077i	−0.271392	−	0.962469i	$-0.587484\pi$
$5$	1.54530	−	1.54530i	0.691077	−	0.691077i	0.962469	+	0.271392i	$0.0874839\pi$
$6$	1.12943	−	1.31316i	0.461087	−	0.536096i
$7$	0.651496	−	0.651496i	0.246242	−	0.246242i	−0.573184	−	0.819427i	$-0.694292\pi$
$7$	0.651496	−	0.651496i	0.246242	−	0.246242i	0.819427	+	0.573184i	$0.194292\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.96624	−	0.448782i	0.988748	−	0.149594i
$10$		−	2.18538i		−	0.691077i
$11$	−2.32321	−	2.32321i	−0.700473	−	0.700473i	0.264039	−	0.964512i	$-0.414945\pi$
$11$	−2.32321	−	2.32321i	−0.700473	−	0.700473i	−0.964512	+	0.264039i	$0.914945\pi$
$12$	−0.129918	−	1.72717i	−0.0375042	−	0.498591i
$13$		0			0
$13$		0			0
$14$		−	0.921354i		−	0.246242i
$15$	2.46823	−	2.86975i	0.637294	−	0.740967i
$16$	−1.00000			−0.250000
$17$	−7.60059			−1.84341			−0.921707	−	0.387887i	$-0.873205\pi$
$17$	−7.60059			−1.84341			−0.921707	+	0.387887i	$0.873205\pi$
$18$	1.78011	−	2.41479i	0.419577	−	0.569171i
$19$	−2.61512	−	2.61512i	−0.599949	−	0.599949i	0.340350	−	0.940299i	$-0.389455\pi$
$19$	−2.61512	−	2.61512i	−0.599949	−	0.599949i	−0.940299	+	0.340350i	$0.889455\pi$
$20$	−1.54530	−	1.54530i	−0.345539	−	0.345539i
$21$	1.04060	−	1.20989i	0.227078	−	0.264019i
$22$	−3.28551			−0.700473
$23$	6.68859			1.39467			0.697334	−	0.716747i	$-0.254370\pi$
$23$	6.68859			1.39467			0.697334	+	0.716747i	$0.254370\pi$
$24$	−1.31316	−	1.12943i	−0.268048	−	0.230544i
$25$			0.224123i			0.0448246i
$26$		0			0
$27$	5.06490	−	1.16049i	0.974741	−	0.223337i
$28$	−0.651496	−	0.651496i	−0.123121	−	0.123121i
$29$			7.08445i			1.31555i	0.753215	+	0.657775i	$0.228502\pi$
$29$			7.08445i			1.31555i	−0.753215	+	0.657775i	$0.771498\pi$
$30$	−0.283920	−	3.77452i	−0.0518365	−	0.689130i
$31$	6.55026	+	6.55026i	1.17646	+	1.17646i	0.980640	+	0.195821i	$0.0627372\pi$
$31$	6.55026	+	6.55026i	1.17646	+	1.17646i	0.195821	+	0.980640i	$0.437263\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−4.31440	−	3.71075i	−0.751041	−	0.645958i
$34$	−5.37443	+	5.37443i	−0.921707	+	0.921707i
$35$		−	2.01351i		−	0.340345i
$36$	−0.448782	−	2.96624i	−0.0747970	−	0.494374i
$37$	1.13927	−	1.13927i	0.187295	−	0.187295i	−0.607231	−	0.794526i	$-0.707720\pi$
$37$	1.13927	−	1.13927i	0.187295	−	0.187295i	0.794526	+	0.607231i	$0.207720\pi$
$38$	−3.69834			−0.599949
$39$		0			0
$40$	−2.18538			−0.345539
$41$	5.29792	−	5.29792i	0.827396	−	0.827396i	−0.159760	−	0.987156i	$-0.551072\pi$
$41$	5.29792	−	5.29792i	0.827396	−	0.827396i	0.987156	+	0.159760i	$0.0510720\pi$
$42$	−0.119701	−	1.59134i	−0.0184702	−	0.245549i
$43$			10.2062i			1.55643i	0.627999	+	0.778214i	$0.283874\pi$
$43$			10.2062i			1.55643i	−0.627999	+	0.778214i	$0.716126\pi$
$44$	−2.32321	+	2.32321i	−0.350237	+	0.350237i
$45$	3.89022	−	5.27722i	0.579920	−	0.786682i
$46$	4.72955	−	4.72955i	0.697334	−	0.697334i
$47$	1.78843	+	1.78843i	0.260869	+	0.260869i	0.825407	−	0.564538i	$-0.190946\pi$
$47$	1.78843	+	1.78843i	0.260869	+	0.260869i	−0.564538	+	0.825407i	$0.690946\pi$
$48$	−1.72717	+	0.129918i	−0.249296	+	0.0187521i
$49$			6.15111i			0.878729i
$50$	0.158479	+	0.158479i	0.0224123	+	0.0224123i
$51$	−13.1275	+	0.987455i	−1.83822	+	0.138271i
$52$		0			0
$53$		−	7.08357i		−	0.973003i	−0.873680	−	0.486501i	$-0.838273\pi$
$53$		−	7.08357i		−	0.973003i	0.873680	−	0.486501i	$-0.161727\pi$
$54$	2.76084	−	4.40202i	0.375702	−	0.599039i
$55$	−7.18008			−0.968162
$56$	−0.921354			−0.123121
$57$	−4.85651	−	4.17701i	−0.643261	−	0.553258i
$58$	5.00946	+	5.00946i	0.657775	+	0.657775i
$59$	−4.95111	−	4.95111i	−0.644580	−	0.644580i	0.307098	−	0.951678i	$-0.400642\pi$
$59$	−4.95111	−	4.95111i	−0.644580	−	0.644580i	−0.951678	+	0.307098i	$0.900642\pi$
$60$	−2.86975	−	2.46823i	−0.370483	−	0.318647i
$61$	2.47439			0.316813			0.158407	−	0.987374i	$-0.449364\pi$
$61$	2.47439			0.316813			0.158407	+	0.987374i	$0.449364\pi$
$62$	9.26346			1.17646
$63$	1.64011	−	2.22487i	0.206635	−	0.280308i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−5.67464	+	0.426848i	−0.698500	+	0.0525413i
$67$	−1.79671	−	1.79671i	−0.219503	−	0.219503i	0.588786	−	0.808289i	$-0.299606\pi$
$67$	−1.79671	−	1.79671i	−0.219503	−	0.219503i	−0.808289	+	0.588786i	$0.799606\pi$
$68$			7.60059i			0.921707i
$69$	11.5523	−	0.868969i	1.39074	−	0.104612i
$70$	−1.42376	−	1.42376i	−0.170172	−	0.170172i
$71$	−4.60918	+	4.60918i	−0.547009	+	0.547009i	−0.925574	−	0.378566i	$-0.876417\pi$
$71$	−4.60918	+	4.60918i	−0.547009	+	0.547009i	0.378566	+	0.925574i	$0.376417\pi$
$72$	−2.41479	−	1.78011i	−0.284585	−	0.209788i
$73$	7.82194	−	7.82194i	0.915489	−	0.915489i	−0.0812086	−	0.996697i	$-0.525878\pi$
$73$	7.82194	−	7.82194i	0.915489	−	0.915489i	0.996697	+	0.0812086i	$0.0258780\pi$
$74$		−	1.61117i		−	0.187295i
$75$	0.0291177	+	0.387099i	0.00336222	+	0.0446984i
$76$	−2.61512	+	2.61512i	−0.299975	+	0.299975i
$77$	−3.02712			−0.344972
$78$		0			0
$79$	2.90723			0.327089			0.163545	−	0.986536i	$-0.447707\pi$
$79$	2.90723			0.327089			0.163545	+	0.986536i	$0.447707\pi$
$80$	−1.54530	+	1.54530i	−0.172769	+	0.172769i
$81$	8.59719	−	2.66239i	0.955243	−	0.295821i
$82$		−	7.49239i		−	0.827396i
$83$	−4.21539	+	4.21539i	−0.462699	+	0.462699i	−0.899539	−	0.436840i	$-0.856098\pi$
$83$	−4.21539	+	4.21539i	−0.462699	+	0.462699i	0.436840	+	0.899539i	$0.356098\pi$
$84$	−1.20989	−	1.04060i	−0.132009	−	0.113539i
$85$	−11.7452	+	11.7452i	−1.27394	+	1.27394i
$86$	7.21686	+	7.21686i	0.778214	+	0.778214i
$87$	0.920399	+	12.2361i	0.0986771	+	1.31184i
$88$			3.28551i			0.350237i
$89$	1.20906	+	1.20906i	0.128160	+	0.128160i	0.768277	−	0.640117i	$-0.221114\pi$
$89$	1.20906	+	1.20906i	0.128160	+	0.128160i	−0.640117	+	0.768277i	$0.721114\pi$
$90$	−0.980758	−	6.48236i	−0.103381	−	0.683301i
$91$		0			0
$92$		−	6.68859i		−	0.697334i
$93$	12.1644	+	10.4624i	1.26139	+	1.08490i
$94$	2.52922			0.260869
$95$	−8.08226			−0.829223
$96$	−1.12943	+	1.31316i	−0.115272	+	0.134024i
$97$	1.61485	+	1.61485i	0.163964	+	0.163964i	0.784320	−	0.620356i	$-0.213012\pi$
$97$	1.61485	+	1.61485i	0.163964	+	0.163964i	−0.620356	+	0.784320i	$0.713012\pi$
$98$	4.34949	+	4.34949i	0.439365	+	0.439365i
$99$	−7.93381	−	5.84858i	−0.797378	−	0.587804i
$100$	0.224123			0.0224123
$101$	9.70536			0.965720			0.482860	−	0.875698i	$-0.339598\pi$
$101$	9.70536			0.965720			0.482860	+	0.875698i	$0.339598\pi$
$102$	−8.58432	+	9.98080i	−0.849975	+	0.988246i
$103$		−	3.74528i		−	0.369034i	−0.982829	−	0.184517i	$-0.940928\pi$
$103$		−	3.74528i		−	0.369034i	0.982829	−	0.184517i	$-0.0590720\pi$
$104$		0			0
$105$	−0.261591	−	3.47767i	−0.0255287	−	0.339386i
$106$	−5.00884	−	5.00884i	−0.486501	−	0.486501i
$107$			1.11378i			0.107673i	0.998550	+	0.0538364i	$0.0171450\pi$
$107$			1.11378i			0.107673i	−0.998550	+	0.0538364i	$0.982855\pi$
$108$	−1.16049	−	5.06490i	−0.111668	−	0.487371i
$109$	−10.9765	−	10.9765i	−1.05136	−	1.05136i	−0.998608	−	0.0527507i	$-0.983201\pi$
$109$	−10.9765	−	10.9765i	−1.05136	−	1.05136i	−0.0527507	−	0.998608i	$-0.516799\pi$
$110$	−5.07708	+	5.07708i	−0.484081	+	0.484081i
$111$	1.81970	−	2.11573i	0.172718	−	0.200816i
$112$	−0.651496	+	0.651496i	−0.0615606	+	0.0615606i
$113$		−	6.67701i		−	0.628120i	−0.949403	−	0.314060i	$-0.898311\pi$
$113$		−	6.67701i		−	0.628120i	0.949403	−	0.314060i	$-0.101689\pi$
$114$	−6.38766	+	0.480481i	−0.598259	+	0.0450012i
$115$	10.3358	−	10.3358i	0.963823	−	0.963823i
$116$	7.08445			0.657775
$117$		0			0
$118$	−7.00193			−0.644580
$119$	−4.95175	+	4.95175i	−0.453926	+	0.453926i
$120$	−3.77452	+	0.283920i	−0.344565	+	0.0259183i
$121$		−	0.205425i		−	0.0186750i
$122$	1.74966	−	1.74966i	0.158407	−	0.158407i
$123$	8.46212	−	9.83871i	0.763004	−	0.887127i
$124$	6.55026	−	6.55026i	0.588230	−	0.588230i
$125$	8.07281	+	8.07281i	0.722054	+	0.722054i
$126$	−0.413487	−	2.73296i	−0.0368364	−	0.243471i
$127$		−	2.39435i		−	0.212464i	−0.994341	−	0.106232i	$-0.966121\pi$
$127$		−	2.39435i		−	0.212464i	0.994341	−	0.106232i	$-0.0338787\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	1.32597	+	17.6278i	0.116745	+	1.55204i
$130$		0			0
$131$			13.2464i			1.15734i	0.815561	+	0.578670i	$0.196428\pi$
$131$			13.2464i			1.15734i	−0.815561	+	0.578670i	$0.803572\pi$
$132$	−3.71075	+	4.31440i	−0.322979	+	0.375521i
$133$	−3.40748			−0.295466
$134$	−2.54094			−0.219503
$135$	6.03347	−	9.62008i	0.519278	−	0.827965i
$136$	5.37443	+	5.37443i	0.460854	+	0.460854i
$137$	9.48530	+	9.48530i	0.810384	+	0.810384i	0.984691	−	0.174307i	$-0.0557687\pi$
$137$	9.48530	+	9.48530i	0.810384	+	0.810384i	−0.174307	+	0.984691i	$0.555769\pi$
$138$	7.55428	−	8.78319i	0.643063	−	0.747675i
$139$	−1.31939			−0.111909			−0.0559545	−	0.998433i	$-0.517820\pi$
$139$	−1.31939			−0.111909			−0.0559545	+	0.998433i	$0.517820\pi$
$140$	−2.01351			−0.170172
$141$	3.32127	+	2.85657i	0.279702	+	0.240567i
$142$			6.51836i			0.547009i
$143$		0			0
$144$	−2.96624	+	0.448782i	−0.247187	+	0.0373985i
$145$	10.9476	+	10.9476i	0.909146	+	0.909146i
$146$		−	11.0619i		−	0.915489i
$147$	0.799141	+	10.6240i	0.0659120	+	0.876254i
$148$	−1.13927	−	1.13927i	−0.0936474	−	0.0936474i
$149$	−6.35345	+	6.35345i	−0.520495	+	0.520495i	−0.917721	−	0.397226i	$-0.869973\pi$
$149$	−6.35345	+	6.35345i	−0.520495	+	0.520495i	0.397226	+	0.917721i	$0.369973\pi$
$150$	0.294310	+	0.253131i	0.0240303	+	0.0206681i
$151$	−5.69619	+	5.69619i	−0.463549	+	0.463549i	−0.899817	−	0.436268i	$-0.856300\pi$
$151$	−5.69619	+	5.69619i	−0.463549	+	0.463549i	0.436268	+	0.899817i	$0.356300\pi$
$152$			3.69834i			0.299975i
$153$	−22.5452	+	3.41101i	−1.82267	+	0.275764i
$154$	−2.14050	+	2.14050i	−0.172486	+	0.172486i
$155$	20.2442			1.62605
$156$		0			0
$157$	−7.01232			−0.559644			−0.279822	−	0.960052i	$-0.590275\pi$
$157$	−7.01232			−0.559644			−0.279822	+	0.960052i	$0.590275\pi$
$158$	2.05572	−	2.05572i	0.163545	−	0.163545i
$159$	−0.920284	−	12.2345i	−0.0729833	−	0.970261i
$160$			2.18538i			0.172769i
$161$	4.35759	−	4.35759i	0.343426	−	0.343426i
$162$	4.19654	−	7.96173i	0.329711	−	0.625532i
$163$	−9.96734	+	9.96734i	−0.780702	+	0.780702i	−0.979949	−	0.199247i	$-0.936150\pi$
$163$	−9.96734	+	9.96734i	−0.780702	+	0.780702i	0.199247	+	0.979949i	$0.436150\pi$
$164$	−5.29792	−	5.29792i	−0.413698	−	0.413698i
$165$	−12.4012	+	0.932823i	−0.965434	+	0.0726202i
$166$			5.96146i			0.462699i
$167$	−0.776467	−	0.776467i	−0.0600848	−	0.0600848i	0.676426	−	0.736511i	$-0.263528\pi$
$167$	−0.776467	−	0.776467i	−0.0600848	−	0.0600848i	−0.736511	+	0.676426i	$0.763528\pi$
$168$	−1.59134	+	0.119701i	−0.122774	+	0.00923511i
$169$		0			0
$170$			16.6102i			1.27394i
$171$	−8.93070	−	6.58346i	−0.682947	−	0.503450i
$172$	10.2062			0.778214
$173$	−0.547630			−0.0416355			−0.0208178	−	0.999783i	$-0.506627\pi$
$173$	−0.547630			−0.0416355			−0.0208178	+	0.999783i	$0.506627\pi$
$174$	9.30302	+	8.00138i	0.705260	+	0.606583i
$175$	0.146015	+	0.146015i	0.0110377	+	0.0110377i
$176$	2.32321	+	2.32321i	0.175118	+	0.175118i
$177$	−9.19466	−	7.90818i	−0.691113	−	0.594415i
$178$	1.70987			0.128160
$179$	−12.3694			−0.924529			−0.462265	−	0.886742i	$-0.652963\pi$
$179$	−12.3694			−0.924529			−0.462265	+	0.886742i	$0.652963\pi$
$180$	−5.27722	−	3.89022i	−0.393341	−	0.289960i
$181$		−	12.3295i		−	0.916442i	−0.888838	−	0.458221i	$-0.848487\pi$
$181$		−	12.3295i		−	0.916442i	0.888838	−	0.458221i	$-0.151513\pi$
$182$		0			0
$183$	4.27370	−	0.321468i	0.315921	−	0.0237636i
$184$	−4.72955	−	4.72955i	−0.348667	−	0.348667i
$185$		−	3.52102i		−	0.258870i
$186$	15.9996	−	1.20349i	1.17315	−	0.0882443i
$187$	17.6577	+	17.6577i	1.29126	+	1.29126i
$188$	1.78843	−	1.78843i	0.130435	−	0.130435i
$189$	2.54371	−	4.05582i	0.185028	−	0.295017i
$190$	−5.71502	+	5.71502i	−0.414611	+	0.414611i
$191$		−	15.0865i		−	1.09162i	−0.837910	−	0.545809i	$-0.816223\pi$
$191$		−	15.0865i		−	1.09162i	0.837910	−	0.545809i	$-0.183777\pi$
$192$	0.129918	+	1.72717i	0.00937604	+	0.124648i
$193$	−6.56204	+	6.56204i	−0.472346	+	0.472346i	−0.902673	−	0.430327i	$-0.858398\pi$
$193$	−6.56204	+	6.56204i	−0.472346	+	0.472346i	0.430327	+	0.902673i	$0.358398\pi$
$194$	2.28375			0.163964
$195$		0			0
$196$	6.15111			0.439365
$197$	−18.3296	+	18.3296i	−1.30593	+	1.30593i	−0.381609	+	0.924324i	$0.624630\pi$
$197$	−18.3296	+	18.3296i	−1.30593	+	1.30593i	−0.924324	+	0.381609i	$0.875370\pi$
$198$	−9.74562	+	1.47448i	−0.692591	+	0.104787i
$199$		−	0.532738i		−	0.0377648i	−0.999822	−	0.0188824i	$-0.993989\pi$
$199$		−	0.532738i		−	0.0377648i	0.999822	−	0.0188824i	$-0.00601082\pi$
$200$	0.158479	−	0.158479i	0.0112062	−	0.0112062i
$201$	−3.33666	−	2.86981i	−0.235350	−	0.202421i
$202$	6.86273	−	6.86273i	0.482860	−	0.482860i
$203$	4.61549	+	4.61549i	0.323944	+	0.323944i
$204$	0.987455	+	13.1275i	0.0691357	+	0.919111i
$205$		−	16.3737i		−	1.14359i
$206$	−2.64831	−	2.64831i	−0.184517	−	0.184517i
$207$	19.8400	−	3.00172i	1.37897	−	0.208634i
$208$		0			0
$209$			12.1509i			0.840497i
$210$	−2.64406	−	2.27411i	−0.182457	−	0.156929i
$211$	−18.0776			−1.24452			−0.622258	−	0.782812i	$-0.713785\pi$
$211$	−18.0776			−1.24452			−0.622258	+	0.782812i	$0.713785\pi$
$212$	−7.08357			−0.486501
$213$	−7.36202	+	8.55966i	−0.504438	+	0.586498i
$214$	0.787559	+	0.787559i	0.0538364	+	0.0538364i
$215$	15.7716	+	15.7716i	1.07561	+	1.07561i
$216$	−4.40202	−	2.76084i	−0.299520	−	0.187851i
$217$	8.53493			0.579389
$218$	−15.5231			−1.05136
$219$	12.4936	−	14.5260i	0.844240	−	0.981579i
$220$			7.18008i			0.484081i
$221$		0			0
$222$	−0.209320	−	2.78277i	−0.0140487	−	0.186767i
$223$	−15.3864	−	15.3864i	−1.03035	−	1.03035i	−0.999525	−	0.0308244i	$-0.990187\pi$
$223$	−15.3864	−	15.3864i	−1.03035	−	1.03035i	−0.0308244	−	0.999525i	$-0.509813\pi$
$224$			0.921354i			0.0615606i
$225$	0.100582	+	0.664804i	0.00670550	+	0.0443203i
$226$	−4.72136	−	4.72136i	−0.314060	−	0.314060i
$227$	−16.6116	+	16.6116i	−1.10255	+	1.10255i	−0.108449	+	0.994102i	$0.534588\pi$
$227$	−16.6116	+	16.6116i	−1.10255	+	1.10255i	−0.994102	+	0.108449i	$0.965412\pi$
$228$	−4.17701	+	4.85651i	−0.276629	+	0.321630i
$229$	12.3044	−	12.3044i	0.813097	−	0.813097i	−0.172000	−	0.985097i	$-0.555023\pi$
$229$	12.3044	−	12.3044i	0.813097	−	0.813097i	0.985097	+	0.172000i	$0.0550228\pi$
$230$		−	14.6171i		−	0.963823i
$231$	−5.22835	+	0.393278i	−0.344000	+	0.0258758i
$232$	5.00946	−	5.00946i	0.328887	−	0.328887i
$233$	19.6727			1.28880			0.644399	−	0.764689i	$-0.277107\pi$
$233$	19.6727			1.28880			0.644399	+	0.764689i	$0.277107\pi$
$234$		0			0
$235$	5.52730			0.360562
$236$	−4.95111	+	4.95111i	−0.322290	+	0.322290i
$237$	5.02129	−	0.377702i	0.326168	−	0.0245344i
$238$			7.00284i			0.453926i
$239$	−9.83565	+	9.83565i	−0.636216	+	0.636216i	−0.949620	−	0.313404i	$-0.898531\pi$
$239$	−9.83565	+	9.83565i	−0.636216	+	0.636216i	0.313404	+	0.949620i	$0.398531\pi$
$240$	−2.46823	+	2.86975i	−0.159323	+	0.185242i
$241$	6.16211	−	6.16211i	0.396937	−	0.396937i	−0.480214	−	0.877151i	$-0.659441\pi$
$241$	6.16211	−	6.16211i	0.396937	−	0.396937i	0.877151	+	0.480214i	$0.159441\pi$
$242$	−0.145258	−	0.145258i	−0.00933752	−	0.00933752i
$243$	14.5029	−	5.71534i	0.930363	−	0.366639i
$244$		−	2.47439i		−	0.158407i
$245$	9.50528	+	9.50528i	0.607270	+	0.607270i
$246$	−0.973398	−	12.9406i	−0.0620616	−	0.825065i
$247$		0			0
$248$		−	9.26346i		−	0.588230i
$249$	−6.73304	+	7.82835i	−0.426689	+	0.496102i
$250$	11.4167			0.722054
$251$	14.2845			0.901630			0.450815	−	0.892617i	$-0.351133\pi$
$251$	14.2845			0.901630			0.450815	+	0.892617i	$0.351133\pi$
$252$	−2.22487	−	1.64011i	−0.140154	−	0.103318i
$253$	−15.5390	−	15.5390i	−0.976927	−	0.976927i
$254$	−1.69306	−	1.69306i	−0.106232	−	0.106232i
$255$	−18.7600	+	21.8118i	−1.17480	+	1.36591i
$256$	1.00000			0.0625000
$257$	8.02622			0.500662			0.250331	−	0.968160i	$-0.419461\pi$
$257$	8.02622			0.500662			0.250331	+	0.968160i	$0.419461\pi$
$258$	13.4024	+	11.5272i	0.834394	+	0.717649i
$259$		−	1.48446i		−	0.0922398i
$260$		0			0
$261$	3.17937	+	21.0142i	0.196798	+	1.30075i
$262$	9.36660	+	9.36660i	0.578670	+	0.578670i
$263$			9.53354i			0.587864i	0.955826	+	0.293932i	$0.0949638\pi$
$263$			9.53354i			0.587864i	−0.955826	+	0.293932i	$0.905036\pi$
$264$	0.426848	+	5.67464i	0.0262706	+	0.349250i
$265$	−10.9462	−	10.9462i	−0.672420	−	0.672420i
$266$	−2.40945	+	2.40945i	−0.147733	+	0.147733i
$267$	2.24533	+	1.93117i	0.137412	+	0.118186i
$268$	−1.79671	+	1.79671i	−0.109752	+	0.109752i
$269$			18.4999i			1.12796i	0.825790	+	0.563978i	$0.190730\pi$
$269$			18.4999i			1.12796i	−0.825790	+	0.563978i	$0.809270\pi$
$270$	−2.53611	−	11.0687i	−0.154343	−	0.673621i
$271$	−16.2890	+	16.2890i	−0.989488	+	0.989488i	−0.999945	−	0.0104572i	$-0.996671\pi$
$271$	−16.2890	+	16.2890i	−0.989488	+	0.989488i	0.0104572	+	0.999945i	$0.496671\pi$
$272$	7.60059			0.460854
$273$		0			0
$274$	13.4142			0.810384
$275$	0.520685	−	0.520685i	0.0313985	−	0.0313985i
$276$	−0.868969	−	11.5523i	−0.0523058	−	0.695369i
$277$		−	26.0384i		−	1.56450i	−0.622967	−	0.782248i	$-0.714073\pi$
$277$		−	26.0384i		−	1.56450i	0.622967	−	0.782248i	$-0.285927\pi$
$278$	−0.932948	+	0.932948i	−0.0559545	+	0.0559545i
$279$	22.3693	+	16.4900i	1.33921	+	0.987231i
$280$	−1.42376	+	1.42376i	−0.0850862	+	0.0850862i
$281$	5.80190	+	5.80190i	0.346112	+	0.346112i	0.858659	−	0.512547i	$-0.171298\pi$
$281$	5.80190	+	5.80190i	0.346112	+	0.346112i	−0.512547	+	0.858659i	$0.671298\pi$
$282$	4.36840	−	0.328592i	0.260134	−	0.0195674i
$283$			2.65033i			0.157546i	0.996893	+	0.0787730i	$0.0251002\pi$
$283$			2.65033i			0.157546i	−0.996893	+	0.0787730i	$0.974900\pi$
$284$	4.60918	+	4.60918i	0.273504	+	0.273504i
$285$	−13.9595	+	1.05003i	−0.826887	+	0.0621986i
$286$		0			0
$287$		−	6.90314i		−	0.407480i
$288$	−1.78011	+	2.41479i	−0.104894	+	0.142293i
$289$	40.7690			2.39818
$290$	15.4822			0.909146
$291$	2.99893	+	2.57933i	0.175800	+	0.151203i
$292$	−7.82194	−	7.82194i	−0.457744	−	0.457744i
$293$	−1.61094	−	1.61094i	−0.0941124	−	0.0941124i	0.658483	−	0.752595i	$-0.271198\pi$
$293$	−1.61094	−	1.61094i	−0.0941124	−	0.0941124i	−0.752595	+	0.658483i	$0.771198\pi$
$294$	8.07739	+	6.94724i	0.471083	+	0.405171i
$295$	−15.3019			−0.890909
$296$	−1.61117			−0.0936474
$297$	−14.4629	−	9.07075i	−0.839221	−	0.526339i
$298$			8.98514i			0.520495i
$299$		0			0
$300$	0.387099	−	0.0291177i	0.0223492	−	0.00168111i
$301$	6.64928	+	6.64928i	0.383258	+	0.383258i
$302$			8.05563i			0.463549i
$303$	16.7628	−	1.26090i	0.962999	−	0.0724370i
$304$	2.61512	+	2.61512i	0.149987	+	0.149987i
$305$	3.82366	−	3.82366i	0.218942	−	0.218942i
$306$	−13.5299	+	18.3538i	−0.773454	+	1.04922i
$307$	5.78243	−	5.78243i	0.330021	−	0.330021i	−0.522573	−	0.852594i	$-0.675028\pi$
$307$	5.78243	−	5.78243i	0.330021	−	0.330021i	0.852594	+	0.522573i	$0.175028\pi$
$308$			3.02712i			0.172486i
$309$	−0.486580	−	6.46875i	−0.0276806	−	0.367994i
$310$	14.3148	−	14.3148i	0.813025	−	0.813025i
$311$	−29.0322			−1.64627			−0.823133	−	0.567849i	$-0.807776\pi$
$311$	−29.0322			−1.64627			−0.823133	+	0.567849i	$0.807776\pi$
$312$		0			0
$313$	12.1203			0.685081			0.342540	−	0.939503i	$-0.388713\pi$
$313$	12.1203			0.685081			0.342540	+	0.939503i	$0.388713\pi$
$314$	−4.95846	+	4.95846i	−0.279822	+	0.279822i
$315$	−0.903626	−	5.97255i	−0.0509135	−	0.336515i
$316$		−	2.90723i		−	0.163545i
$317$	−13.3301	+	13.3301i	−0.748695	+	0.748695i	−0.974234	−	0.225539i	$-0.927586\pi$
$317$	−13.3301	+	13.3301i	−0.748695	+	0.748695i	0.225539	+	0.974234i	$0.427586\pi$
$318$	−9.30186	−	8.00038i	−0.521622	−	0.448639i
$319$	16.4586	−	16.4586i	0.921507	−	0.921507i
$320$	1.54530	+	1.54530i	0.0863846	+	0.0863846i
$321$	0.144700	+	1.92368i	0.00807636	+	0.107369i
$322$		−	6.16256i		−	0.343426i
$323$	19.8765	+	19.8765i	1.10596	+	1.10596i
$324$	−2.66239	−	8.59719i	−0.147911	−	0.477622i
$325$		0			0
$326$			14.0959i			0.780702i
$327$	−20.3844	−	17.5323i	−1.12726	−	0.969536i
$328$	−7.49239			−0.413698
$329$	2.33031			0.128474
$330$	−8.10939	+	9.42860i	−0.446407	+	0.519027i
$331$	−12.5801	−	12.5801i	−0.691467	−	0.691467i	0.271088	−	0.962555i	$-0.412617\pi$
$331$	−12.5801	−	12.5801i	−0.691467	−	0.691467i	−0.962555	+	0.271088i	$0.912617\pi$
$332$	4.21539	+	4.21539i	0.231349	+	0.231349i
$333$	2.86807	−	3.89063i	0.157169	−	0.213205i
$334$	−1.09809			−0.0600848
$335$	−5.55291			−0.303388
$336$	−1.04060	+	1.20989i	−0.0567696	+	0.0660047i
$337$		−	4.93138i		−	0.268630i	−0.990939	−	0.134315i	$-0.957117\pi$
$337$		−	4.93138i		−	0.268630i	0.990939	−	0.134315i	$-0.0428833\pi$
$338$		0			0
$339$	−0.867465	−	11.5323i	−0.0471142	−	0.626351i
$340$	11.7452	+	11.7452i	0.636971	+	0.636971i
$341$		−	30.4352i		−	1.64816i
$342$	−10.9702	+	1.65975i	−0.593199	+	0.0897488i
$343$	8.56789	+	8.56789i	0.462623	+	0.462623i
$344$	7.21686	−	7.21686i	0.389107	−	0.389107i
$345$	16.5090	−	19.1946i	0.888813	−	1.03340i
$346$	−0.387233	+	0.387233i	−0.0208178	+	0.0208178i
$347$			14.1112i			0.757528i	0.925493	+	0.378764i	$0.123651\pi$
$347$			14.1112i			0.757528i	−0.925493	+	0.378764i	$0.876349\pi$
$348$	12.2361	−	0.920399i	0.655922	−	0.0493386i
$349$	−22.4196	+	22.4196i	−1.20010	+	1.20010i	−0.225959	+	0.974137i	$0.572551\pi$
$349$	−22.4196	+	22.4196i	−1.20010	+	1.20010i	−0.974137	+	0.225959i	$0.927449\pi$
$350$	0.206497			0.0110377
$351$		0			0
$352$	3.28551			0.175118
$353$	−0.286857	+	0.286857i	−0.0152679	+	0.0152679i	−0.714700	−	0.699432i	$-0.753437\pi$
$353$	−0.286857	+	0.286857i	−0.0152679	+	0.0152679i	0.699432	+	0.714700i	$0.253437\pi$
$354$	−12.0935	+	0.909679i	−0.642764	+	0.0483489i
$355$			14.2451i			0.756050i
$356$	1.20906	−	1.20906i	0.0640800	−	0.0640800i
$357$	−7.90920	+	9.19585i	−0.418599	+	0.486696i
$358$	−8.74646	+	8.74646i	−0.462265	+	0.462265i
$359$	−9.14289	−	9.14289i	−0.482543	−	0.482543i	0.423400	−	0.905943i	$-0.360837\pi$
$359$	−9.14289	−	9.14289i	−0.482543	−	0.482543i	−0.905943	+	0.423400i	$0.860837\pi$
$360$	−6.48236	+	0.980758i	−0.341650	+	0.0516905i
$361$		−	5.32230i		−	0.280121i
$362$	−8.71825	−	8.71825i	−0.458221	−	0.458221i
$363$	−0.0266885	−	0.354805i	−0.00140078	−	0.0186224i
$364$		0			0
$365$		−	24.1744i		−	1.26535i
$366$	2.79465	−	3.24927i	0.146079	−	0.169842i
$367$	−23.2679			−1.21457			−0.607286	−	0.794483i	$-0.707742\pi$
$367$	−23.2679			−1.21457			−0.607286	+	0.794483i	$0.707742\pi$
$368$	−6.68859			−0.348667
$369$	13.3373	−	18.0925i	0.694312	−	0.941859i
$370$	−2.48973	−	2.48973i	−0.129435	−	0.129435i
$371$	−4.61491	−	4.61491i	−0.239594	−	0.239594i
$372$	10.4624	−	12.1644i	0.542451	−	0.630695i
$373$	12.4437			0.644310			0.322155	−	0.946687i	$-0.395593\pi$
$373$	12.4437			0.644310			0.322155	+	0.946687i	$0.395593\pi$
$374$	24.9718			1.29126
$375$	14.9919	+	12.8943i	0.774180	+	0.665860i
$376$		−	2.52922i		−	0.130435i
$377$		0			0
$378$	−1.06922	−	4.66657i	−0.0549950	−	0.240023i
$379$	11.6490	+	11.6490i	0.598371	+	0.598371i	0.939879	−	0.341508i	$-0.110938\pi$
$379$	11.6490	+	11.6490i	0.598371	+	0.598371i	−0.341508	+	0.939879i	$0.610938\pi$
$380$			8.08226i			0.414611i
$381$	−0.311070	−	4.13545i	−0.0159366	−	0.211866i
$382$	−10.6677	−	10.6677i	−0.545809	−	0.545809i
$383$	21.6814	−	21.6814i	1.10787	−	1.10787i	0.114436	−	0.993431i	$-0.463494\pi$
$383$	21.6814	−	21.6814i	1.10787	−	1.10787i	0.993431	−	0.114436i	$-0.0365060\pi$
$384$	1.31316	+	1.12943i	0.0670120	+	0.0576359i
$385$	−4.67779	+	4.67779i	−0.238402	+	0.238402i
$386$			9.28012i			0.472346i
$387$	4.58035	+	30.2740i	0.232832	+	1.53891i
$388$	1.61485	−	1.61485i	0.0819818	−	0.0819818i
$389$	−2.75740			−0.139806			−0.0699030	−	0.997554i	$-0.522269\pi$
$389$	−2.75740			−0.139806			−0.0699030	+	0.997554i	$0.522269\pi$
$390$		0			0
$391$	−50.8372			−2.57095
$392$	4.34949	−	4.34949i	0.219682	−	0.219682i
$393$	1.72094	+	22.8788i	0.0868102	+	1.15408i
$394$			25.9220i			1.30593i
$395$	4.49253	−	4.49253i	0.226044	−	0.226044i
$396$	−5.84858	+	7.93381i	−0.293902	+	0.398689i
$397$	−8.65789	+	8.65789i	−0.434527	+	0.434527i	−0.890165	−	0.455638i	$-0.849411\pi$
$397$	−8.65789	+	8.65789i	−0.434527	+	0.434527i	0.455638	+	0.890165i	$0.349411\pi$
$398$	−0.376703	−	0.376703i	−0.0188824	−	0.0188824i
$399$	−5.88530	+	0.442693i	−0.294633	+	0.0221624i
$400$		−	0.224123i		−	0.0112062i
$401$	−26.5704	−	26.5704i	−1.32686	−	1.32686i	−0.908092	−	0.418771i	$-0.862461\pi$
$401$	−26.5704	−	26.5704i	−1.32686	−	1.32686i	−0.418771	−	0.908092i	$-0.637539\pi$
$402$	−4.38863	+	0.330114i	−0.218885	+	0.0164646i
$403$		0			0
$404$		−	9.70536i		−	0.482860i
$405$	9.17102	−	17.3994i	0.455711	−	0.864582i
$406$	6.52729			0.323944
$407$	−5.29352			−0.262390
$408$	9.98080	+	8.58432i	0.494123	+	0.424987i
$409$	16.0601	+	16.0601i	0.794120	+	0.794120i	0.982161	−	0.188041i	$-0.0602139\pi$
$409$	16.0601	+	16.0601i	0.794120	+	0.794120i	−0.188041	+	0.982161i	$0.560214\pi$
$410$	−11.5780	−	11.5780i	−0.571795	−	0.571795i
$411$	17.6151	+	15.1504i	0.868886	+	0.747315i
$412$	−3.74528			−0.184517
$413$	−6.45126			−0.317446
$414$	11.9064	−	16.1515i	0.585170	−	0.793804i
$415$			13.0280i			0.639521i
$416$		0			0
$417$	−2.27881	+	0.171413i	−0.111594	+	0.00839411i
$418$	8.59200	+	8.59200i	0.420248	+	0.420248i
$419$			20.0256i			0.978314i	0.872196	+	0.489157i	$0.162696\pi$
$419$			20.0256i			0.978314i	−0.872196	+	0.489157i	$0.837304\pi$
$420$	−3.47767	+	0.261591i	−0.169693	+	0.0127643i
$421$	3.14980	+	3.14980i	0.153512	+	0.153512i	0.779684	−	0.626173i	$-0.215379\pi$
$421$	3.14980	+	3.14980i	0.153512	+	0.153512i	−0.626173	+	0.779684i	$0.715379\pi$
$422$	−12.7828	+	12.7828i	−0.622258	+	0.622258i
$423$	6.10753	+	4.50230i	0.296958	+	0.218909i
$424$	−5.00884	+	5.00884i	−0.243251	+	0.243251i
$425$		−	1.70347i		−	0.0826304i
$426$	0.846854	+	11.2583i	0.0410302	+	0.545468i
$427$	1.61205	−	1.61205i	0.0780128	−	0.0780128i
$428$	1.11378			0.0538364
$429$		0			0
$430$	22.3044			1.07561
$431$	13.0972	−	13.0972i	0.630868	−	0.630868i	−0.317418	−	0.948286i	$-0.602816\pi$
$431$	13.0972	−	13.0972i	0.630868	−	0.630868i	0.948286	+	0.317418i	$0.102816\pi$
$432$	−5.06490	+	1.16049i	−0.243685	+	0.0558342i
$433$		−	33.4936i		−	1.60960i	−0.593547	−	0.804799i	$-0.702273\pi$
$433$		−	33.4936i		−	1.60960i	0.593547	−	0.804799i	$-0.297727\pi$
$434$	6.03511	−	6.03511i	0.289694	−	0.289694i
$435$	20.3306	+	17.4860i	0.974778	+	0.838391i
$436$	−10.9765	+	10.9765i	−0.525679	+	0.525679i
$437$	−17.4915	−	17.4915i	−0.836730	−	0.836730i
$438$	−1.43714	−	19.1058i	−0.0686692	−	0.912910i
$439$			11.0751i			0.528583i	0.964443	+	0.264292i	$0.0851382\pi$
$439$			11.0751i			0.528583i	−0.964443	+	0.264292i	$0.914862\pi$
$440$	5.07708	+	5.07708i	0.242040	+	0.242040i
$441$	2.76051	+	18.2457i	0.131453	+	0.868842i
$442$		0			0
$443$		−	11.4275i		−	0.542935i	−0.962448	−	0.271468i	$-0.912491\pi$
$443$		−	11.4275i		−	0.542935i	0.962448	−	0.271468i	$-0.0875090\pi$
$444$	−2.11573	−	1.81970i	−0.100408	−	0.0863592i
$445$	3.73671			0.177137
$446$	−21.7596			−1.03035
$447$	−10.1481	+	11.7989i	−0.479987	+	0.558070i
$448$	0.651496	+	0.651496i	0.0307803	+	0.0307803i
$449$	−6.40153	−	6.40153i	−0.302107	−	0.302107i	0.539731	−	0.841838i	$-0.318526\pi$
$449$	−6.40153	−	6.40153i	−0.302107	−	0.302107i	−0.841838	+	0.539731i	$0.818526\pi$
$450$	0.541210	+	0.398965i	0.0255129	+	0.0188074i
$451$	−24.6163			−1.15914
$452$	−6.67701			−0.314060
$453$	−9.09826	+	10.5783i	−0.427473	+	0.497013i
$454$			23.4924i			1.10255i
$455$		0			0
$456$	0.480481	+	6.38766i	0.0225006	+	0.299130i
$457$	−15.9390	−	15.9390i	−0.745596	−	0.745596i	0.228053	−	0.973649i	$-0.426764\pi$
$457$	−15.9390	−	15.9390i	−0.745596	−	0.745596i	−0.973649	+	0.228053i	$0.926764\pi$
$458$		−	17.4010i		−	0.813097i
$459$	−38.4963	+	8.82043i	−1.79685	+	0.411702i
$460$	−10.3358	−	10.3358i	−0.481911	−	0.481911i
$461$	1.02031	−	1.02031i	0.0475204	−	0.0475204i	−0.682947	−	0.730468i	$-0.739302\pi$
$461$	1.02031	−	1.02031i	0.0475204	−	0.0475204i	0.730468	+	0.682947i	$0.239302\pi$
$462$	−3.41891	+	3.97509i	−0.159062	+	0.184938i
$463$	−1.78731	+	1.78731i	−0.0830633	+	0.0830633i	−0.747418	−	0.664354i	$-0.768707\pi$
$463$	−1.78731	+	1.78731i	−0.0830633	+	0.0830633i	0.664354	+	0.747418i	$0.268707\pi$
$464$		−	7.08445i		−	0.328887i
$465$	34.9651	−	2.63009i	1.62147	−	0.121967i
$466$	13.9107	−	13.9107i	0.644399	−	0.644399i
$467$	−2.75233			−0.127363			−0.0636813	−	0.997970i	$-0.520284\pi$
$467$	−2.75233			−0.127363			−0.0636813	+	0.997970i	$0.520284\pi$
$468$		0			0
$469$	−2.34110			−0.108102
$470$	3.90839	−	3.90839i	0.180281	−	0.180281i
$471$	−12.1115	+	0.911028i	−0.558068	+	0.0419780i
$472$			7.00193i			0.322290i
$473$	23.7111	−	23.7111i	1.09024	−	1.09024i
$474$	3.28351	−	3.81766i	0.150817	−	0.175351i
$475$	0.586109	−	0.586109i	0.0268925	−	0.0268925i
$476$	4.95175	+	4.95175i	0.226963	+	0.226963i
$477$	−3.17898	−	21.0116i	−0.145555	−	0.962054i
$478$			13.9097i			0.636216i
$479$	−19.9749	−	19.9749i	−0.912674	−	0.912674i	0.0838076	−	0.996482i	$-0.473292\pi$
$479$	−19.9749	−	19.9749i	−0.912674	−	0.912674i	−0.996482	+	0.0838076i	$0.973292\pi$
$480$	0.283920	+	3.77452i	0.0129591	+	0.172283i
$481$		0			0
$482$		−	8.71454i		−	0.396937i
$483$	6.96017	−	8.09243i	0.316699	−	0.368218i
$484$	−0.205425			−0.00933752
$485$	4.99085			0.226623
$486$	6.21376	−	14.2965i	0.281862	−	0.648501i
$487$	22.2883	+	22.2883i	1.00998	+	1.00998i	0.999950	+	0.0100276i	$0.00319194\pi$
$487$	22.2883	+	22.2883i	1.00998	+	1.00998i	0.0100276	+	0.999950i	$0.496808\pi$
$488$	−1.74966	−	1.74966i	−0.0792033	−	0.0792033i
$489$	−15.9204	+	18.5102i	−0.719944	+	0.837062i
$490$	13.4425			0.607270
$491$	17.0519			0.769540			0.384770	−	0.923013i	$-0.374281\pi$
$491$	17.0519			0.769540			0.384770	+	0.923013i	$0.374281\pi$
$492$	−9.83871	−	8.46212i	−0.443563	−	0.381502i
$493$		−	53.8460i		−	2.42510i
$494$		0			0
$495$	−21.2979	+	3.22229i	−0.957268	+	0.144831i
$496$	−6.55026	−	6.55026i	−0.294115	−	0.294115i
$497$			6.00572i			0.269393i
$498$	0.774502	+	10.2965i	0.0347063	+	0.461396i
$499$	−11.7658	−	11.7658i	−0.526711	−	0.526711i	0.392879	−	0.919590i	$-0.371479\pi$
$499$	−11.7658	−	11.7658i	−0.526711	−	0.526711i	−0.919590	+	0.392879i	$0.871479\pi$
$500$	8.07281	−	8.07281i	0.361027	−	0.361027i
$501$	−1.44197	−	1.24021i	−0.0644224	−	0.0554087i
$502$	10.1007	−	10.1007i	0.450815	−	0.450815i
$503$		−	11.5609i		−	0.515475i	−0.966215	−	0.257738i	$-0.917023\pi$
$503$		−	11.5609i		−	0.515475i	0.966215	−	0.257738i	$-0.0829770\pi$
$504$	−2.73296	+	0.413487i	−0.121736	+	0.0184182i
$505$	14.9977	−	14.9977i	0.667387	−	0.667387i
$506$	−21.9754			−0.976927
$507$		0			0
$508$	−2.39435			−0.106232
$509$	31.2213	−	31.2213i	1.38386	−	1.38386i	0.546219	−	0.837642i	$-0.316067\pi$
$509$	31.2213	−	31.2213i	1.38386	−	1.38386i	0.837642	−	0.546219i	$-0.183933\pi$
$510$	2.15796	+	28.6886i	0.0955562	+	1.27035i
$511$		−	10.1919i		−	0.450864i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−16.2802	−	10.2105i	−0.718786	−	0.450805i
$514$	5.67539	−	5.67539i	0.250331	−	0.250331i
$515$	−5.78757	−	5.78757i	−0.255031	−	0.255031i
$516$	17.6278	−	1.32597i	0.776022	−	0.0583725i
$517$		−	8.30978i		−	0.365464i
$518$	−1.04967	−	1.04967i	−0.0461199	−	0.0461199i
$519$	−0.945851	+	0.0711471i	−0.0415182	+	0.00312301i
$520$		0			0
$521$			32.3028i			1.41521i	0.706608	+	0.707605i	$0.250224\pi$
$521$			32.3028i			1.41521i	−0.706608	+	0.707605i	$0.749776\pi$
$522$	17.1074	+	12.6111i	0.748772	+	0.551974i
$523$	−24.2952			−1.06235			−0.531177	−	0.847261i	$-0.678250\pi$
$523$	−24.2952			−1.06235			−0.531177	+	0.847261i	$0.678250\pi$
$524$	13.2464			0.578670
$525$	0.271164	+	0.233223i	0.0118345	+	0.0101787i
$526$	6.74123	+	6.74123i	0.293932	+	0.293932i
$527$	−49.7858	−	49.7858i	−2.16870	−	2.16870i
$528$	4.31440	+	3.71075i	0.187760	+	0.161490i
$529$	21.7372			0.945096
$530$	−15.4803			−0.672420
$531$	−16.9082	−	12.4642i	−0.733752	−	0.540902i
$532$			3.40748i			0.147733i
$533$		0			0
$534$	2.95323	−	0.222143i	0.127799	−	0.00961306i
$535$	1.72111	+	1.72111i	0.0744102	+	0.0744102i
$536$			2.54094i			0.109752i
$537$	−21.3640	+	1.60700i	−0.921925	+	0.0693474i
$538$	13.0814	+	13.0814i	0.563978	+	0.563978i
$539$	14.2903	−	14.2903i	0.615526	−	0.615526i
$540$	−9.62008	−	6.03347i	−0.413982	−	0.259639i
$541$	20.6701	−	20.6701i	0.888677	−	0.888677i	−0.105719	−	0.994396i	$-0.533714\pi$
$541$	20.6701	−	20.6701i	0.888677	−	0.888677i	0.994396	+	0.105719i	$0.0337145\pi$
$542$			23.0362i			0.989488i
$543$	−1.60182	−	21.2951i	−0.0687408	−	0.913860i
$544$	5.37443	−	5.37443i	0.230427	−	0.230427i
$545$	−33.9239			−1.45314
$546$		0			0
$547$	−10.9561			−0.468447			−0.234224	−	0.972183i	$-0.575255\pi$
$547$	−10.9561			−0.468447			−0.234224	+	0.972183i	$0.575255\pi$
$548$	9.48530	−	9.48530i	0.405192	−	0.405192i
$549$	7.33964	−	1.11046i	0.313248	−	0.0473934i
$550$		−	0.736359i		−	0.0313985i
$551$	18.5267	−	18.5267i	0.789263	−	0.789263i
$552$	−8.78319	−	7.55428i	−0.373837	−	0.321532i
$553$	1.89405	−	1.89405i	0.0805432	−	0.0805432i
$554$	−18.4119	−	18.4119i	−0.782248	−	0.782248i
$555$	−0.457444	−	6.08140i	−0.0194174	−	0.258141i
$556$			1.31939i			0.0559545i
$557$	−6.71013	−	6.71013i	−0.284318	−	0.284318i	0.550511	−	0.834828i	$-0.314433\pi$
$557$	−6.71013	−	6.71013i	−0.284318	−	0.284318i	−0.834828	+	0.550511i	$0.814433\pi$
$558$	27.4777	−	4.15727i	1.16322	−	0.175991i
$559$		0			0
$560$			2.01351i			0.0850862i
$561$	32.7920	+	28.2039i	1.38448	+	1.19077i
$562$	8.20513			0.346112
$563$	−16.2857			−0.686359			−0.343180	−	0.939270i	$-0.611504\pi$
$563$	−16.2857			−0.686359			−0.343180	+	0.939270i	$0.611504\pi$
$564$	2.85657	−	3.32127i	0.120283	−	0.139851i
$565$	−10.3180	−	10.3180i	−0.434080	−	0.434080i
$566$	1.87407	+	1.87407i	0.0787730	+	0.0787730i
$567$	3.86650	−	7.33557i	0.162378	−	0.308065i
$568$	6.51836			0.273504
$569$	−15.5325			−0.651158			−0.325579	−	0.945515i	$-0.605559\pi$
$569$	−15.5325			−0.651158			−0.325579	+	0.945515i	$0.605559\pi$
$570$	−9.12834	+	10.6133i	−0.382344	+	0.444543i
$571$			12.3752i			0.517885i	0.965893	+	0.258942i	$0.0833740\pi$
$571$			12.3752i			0.517885i	−0.965893	+	0.258942i	$0.916626\pi$
$572$		0			0
$573$	−1.96000	−	26.0569i	−0.0818804	−	1.08854i
$574$	−4.88126	−	4.88126i	−0.203740	−	0.203740i
$575$			1.49907i			0.0625155i
$576$	0.448782	+	2.96624i	0.0186993	+	0.123593i
$577$	−22.5770	−	22.5770i	−0.939891	−	0.939891i	0.0584021	−	0.998293i	$-0.481399\pi$
$577$	−22.5770	−	22.5770i	−0.939891	−	0.939891i	−0.998293	+	0.0584021i	$0.981399\pi$
$578$	28.8280	−	28.8280i	1.19909	−	1.19909i
$579$	−10.4812	+	12.1863i	−0.435585	+	0.506445i
$580$	10.9476	−	10.9476i	0.454573	−	0.454573i
$581$			5.49262i			0.227872i
$582$	3.94442	−	0.296700i	0.163502	−	0.0122986i
$583$	−16.4566	+	16.4566i	−0.681562	+	0.681562i
$584$	−11.0619			−0.457744
$585$		0			0
$586$	−2.27822			−0.0941124
$587$	0.805817	−	0.805817i	0.0332596	−	0.0332596i	−0.690281	−	0.723541i	$-0.742513\pi$
$587$	0.805817	−	0.805817i	0.0332596	−	0.0332596i	0.723541	+	0.690281i	$0.242513\pi$
$588$	10.6240	−	0.799141i	0.438127	−	0.0329560i
$589$		−	34.2594i		−	1.41163i
$590$	−10.8201	+	10.8201i	−0.445455	+	0.445455i
$591$	−29.2771	+	34.0398i	−1.20430	+	1.40021i
$592$	−1.13927	+	1.13927i	−0.0468237	+	0.0468237i
$593$	−2.85356	−	2.85356i	−0.117182	−	0.117182i	0.646084	−	0.763266i	$-0.276405\pi$
$593$	−2.85356	−	2.85356i	−0.117182	−	0.117182i	−0.763266	+	0.646084i	$0.776405\pi$
$594$	−16.6408	+	3.81281i	−0.682780	+	0.156441i
$595$			15.3038i			0.627396i
$596$	6.35345	+	6.35345i	0.260248	+	0.260248i
$597$	−0.0692124	−	0.920131i	−0.00283268	−	0.0376584i
$598$		0			0
$599$		−	25.8274i		−	1.05528i	−0.849468	−	0.527640i	$-0.823077\pi$
$599$		−	25.8274i		−	1.05528i	0.849468	−	0.527640i	$-0.176923\pi$
$600$	0.253131	−	0.294310i	0.0103340	−	0.0120151i
$601$	23.5281			0.959731			0.479865	−	0.877342i	$-0.340685\pi$
$601$	23.5281			0.959731			0.479865	+	0.877342i	$0.340685\pi$
$602$	9.40351			0.383258
$603$	−6.13582	−	4.52316i	−0.249870	−	0.184197i
$604$	5.69619	+	5.69619i	0.231775	+	0.231775i
$605$	−0.317443	−	0.317443i	−0.0129059	−	0.0129059i
$606$	10.9615	−	12.7447i	0.445281	−	0.517718i
$607$	−28.1300			−1.14176			−0.570880	−	0.821034i	$-0.693398\pi$
$607$	−28.1300			−1.14176			−0.570880	+	0.821034i	$0.693398\pi$
$608$	3.69834			0.149987
$609$	8.57138	+	7.37210i	0.347330	+	0.298733i
$610$		−	5.40748i		−	0.218942i
$611$		0			0
$612$	3.41101	+	22.5452i	0.137882	+	0.911336i
$613$	−11.3583	−	11.3583i	−0.458758	−	0.458758i	0.439489	−	0.898248i	$-0.355159\pi$
$613$	−11.3583	−	11.3583i	−0.458758	−	0.458758i	−0.898248	+	0.439489i	$0.855159\pi$
$614$		−	8.17759i		−	0.330021i
$615$	−2.12724	−	28.2802i	−0.0857787	−	1.14037i
$616$	2.14050	+	2.14050i	0.0862430	+	0.0862430i
$617$	14.3013	−	14.3013i	0.575749	−	0.575749i	−0.357980	−	0.933729i	$-0.616535\pi$
$617$	14.3013	−	14.3013i	0.575749	−	0.575749i	0.933729	+	0.357980i	$0.116535\pi$
$618$	−4.91816	−	4.23003i	−0.197837	−	0.170157i
$619$	−18.7314	+	18.7314i	−0.752880	+	0.752880i	−0.975016	−	0.222136i	$-0.928697\pi$
$619$	−18.7314	+	18.7314i	−0.752880	+	0.752880i	0.222136	+	0.975016i	$0.428697\pi$
$620$		−	20.2442i		−	0.813025i
$621$	33.8771	−	7.76206i	1.35944	−	0.311481i
$622$	−20.5289	+	20.5289i	−0.823133	+	0.823133i
$623$	1.57539			0.0631168
$624$		0			0
$625$	23.8292			0.953166
$626$	8.57036	−	8.57036i	0.342540	−	0.342540i
$627$	1.57863	+	20.9867i	0.0630442	+	0.838129i
$628$			7.01232i			0.279822i
$629$	−8.65912	+	8.65912i	−0.345262	+	0.345262i
$630$	−4.86219	−	3.58427i	−0.193714	−	0.142801i
$631$	0.750726	−	0.750726i	0.0298859	−	0.0298859i	−0.692006	−	0.721892i	$-0.743273\pi$
$631$	0.750726	−	0.750726i	0.0298859	−	0.0298859i	0.721892	+	0.692006i	$0.243273\pi$
$632$	−2.05572	−	2.05572i	−0.0817723	−	0.0817723i
$633$	−31.2232	+	2.34861i	−1.24101	+	0.0933490i
$634$			18.8517i			0.748695i
$635$	−3.69998	−	3.69998i	−0.146829	−	0.146829i
$636$	−12.2345	+	0.920284i	−0.485131	+	0.0364916i
$637$		0			0
$638$		−	23.2760i		−	0.921507i
$639$	−11.6034	+	15.7405i	−0.459024	+	0.622683i
$640$	2.18538			0.0863846
$641$	7.42813			0.293394			0.146697	−	0.989182i	$-0.453136\pi$
$641$	7.42813			0.293394			0.146697	+	0.989182i	$0.453136\pi$
$642$	1.46257	+	1.25793i	0.0577229	+	0.0496466i
$643$	9.59682	+	9.59682i	0.378462	+	0.378462i	0.870547	−	0.492085i	$-0.163765\pi$
$643$	9.59682	+	9.59682i	0.378462	+	0.378462i	−0.492085	+	0.870547i	$0.663765\pi$
$644$	−4.35759	−	4.35759i	−0.171713	−	0.171713i
$645$	29.2892	+	25.1912i	1.15326	+	0.991902i
$646$	28.1095			1.10596
$647$	1.57540			0.0619354			0.0309677	−	0.999520i	$-0.490141\pi$
$647$	1.57540			0.0619354			0.0309677	+	0.999520i	$0.490141\pi$
$648$	−7.96173	−	4.19654i	−0.312766	−	0.164855i
$649$			23.0049i			0.903022i
$650$		0			0
$651$	14.7413	−	1.10884i	0.577757	−	0.0434590i
$652$	9.96734	+	9.96734i	0.390351	+	0.390351i
$653$			40.1725i			1.57207i	0.618180	+	0.786037i	$0.287870\pi$
$653$			40.1725i			1.57207i	−0.618180	+	0.786037i	$0.712130\pi$
$654$	−26.8111	+	2.01674i	−1.04840	+	0.0788606i
$655$	20.4696	+	20.4696i	0.799812	+	0.799812i
$656$	−5.29792	+	5.29792i	−0.206849	+	0.206849i
$657$	19.6914	−	26.7121i	0.768235	−	1.04214i
$658$	1.64778	−	1.64778i	0.0642370	−	0.0642370i
$659$		−	4.06465i		−	0.158336i	−0.996861	−	0.0791681i	$-0.974774\pi$
$659$		−	4.06465i		−	0.158336i	0.996861	−	0.0791681i	$-0.0252264\pi$
$660$	0.932823	+	12.4012i	0.0363101	+	0.482717i
$661$	1.29912	−	1.29912i	0.0505301	−	0.0505301i	−0.681390	−	0.731920i	$-0.738624\pi$
$661$	1.29912	−	1.29912i	0.0505301	−	0.0505301i	0.731920	+	0.681390i	$0.238624\pi$
$662$	−17.7910			−0.691467
$663$		0			0
$664$	5.96146			0.231349
$665$	−5.26556	+	5.26556i	−0.204190	+	0.204190i
$666$	−0.723064	−	4.77912i	−0.0280182	−	0.185187i
$667$			47.3850i			1.83475i
$668$	−0.776467	+	0.776467i	−0.0300424	+	0.0300424i
$669$	−28.5739	−	24.5760i	−1.10473	−	0.950162i
$670$	−3.92650	+	3.92650i	−0.151694	+	0.151694i
$671$	−5.74852	−	5.74852i	−0.221919	−	0.221919i
$672$	0.119701	+	1.59134i	0.00461755	+	0.0613871i
$673$		−	41.9536i		−	1.61719i	−0.588364	−	0.808596i	$-0.700228\pi$
$673$		−	41.9536i		−	1.61719i	0.588364	−	0.808596i	$-0.299772\pi$
$674$	−3.48701	−	3.48701i	−0.134315	−	0.134315i
$675$	0.260093	+	1.13516i	0.0100110	+	0.0436924i
$676$		0			0
$677$			3.81278i			0.146537i	0.997312	+	0.0732685i	$0.0233430\pi$
$677$			3.81278i			0.146537i	−0.997312	+	0.0732685i	$0.976657\pi$
$678$	−8.76799	−	7.54120i	−0.336732	−	0.289618i
$679$	2.10414			0.0807495
$680$	16.6102			0.636971
$681$	−26.5329	+	30.8492i	−1.01674	+	1.18215i
$682$	−21.5209	−	21.5209i	−0.824079	−	0.824079i
$683$	32.7277	+	32.7277i	1.25229	+	1.25229i	0.954690	+	0.297601i	$0.0961864\pi$
$683$	32.7277	+	32.7277i	1.25229	+	1.25229i	0.297601	+	0.954690i	$0.403814\pi$
$684$	−6.58346	+	8.93070i	−0.251725	+	0.341474i
$685$	29.3152			1.12008
$686$	12.1168			0.462623
$687$	19.6532	−	22.8504i	0.749818	−	0.871796i
$688$		−	10.2062i		−	0.389107i
$689$		0			0
$690$	−1.89903	−	25.2462i	−0.0722947	−	0.961107i
$691$	2.41360	+	2.41360i	0.0918178	+	0.0918178i	0.751524	−	0.659706i	$-0.229319\pi$
$691$	2.41360	+	2.41360i	0.0918178	+	0.0918178i	−0.659706	+	0.751524i	$0.729319\pi$
$692$			0.547630i			0.0208178i
$693$	−8.97917	+	1.35852i	−0.341090	+	0.0516058i
$694$	9.97811	+	9.97811i	0.378764	+	0.378764i
$695$	−2.03884	+	2.03884i	−0.0773378	+	0.0773378i
$696$	8.00138	−	9.30302i	0.303292	−	0.352630i
$697$	−40.2673	+	40.2673i	−1.52523	+	1.52523i
$698$			31.7062i			1.20010i
$699$	33.9781	−	2.55584i	1.28517	−	0.0966706i
$700$	0.146015	−	0.146015i	0.00551886	−	0.00551886i
$701$	−3.17954			−0.120090			−0.0600448	−	0.998196i	$-0.519124\pi$
$701$	−3.17954			−0.120090			−0.0600448	+	0.998196i	$0.519124\pi$
$702$		0			0
$703$	−5.95865			−0.224735
$704$	2.32321	−	2.32321i	0.0875591	−	0.0875591i
$705$	9.54660	−	0.718097i	0.359546	−	0.0270451i
$706$			0.405678i			0.0152679i
$707$	6.32300	−	6.32300i	0.237801	−	0.237801i
$708$	−7.90818	+	9.19466i	−0.297208	+	0.345557i
$709$	9.68360	−	9.68360i	0.363675	−	0.363675i	−0.501489	−	0.865164i	$-0.667214\pi$
$709$	9.68360	−	9.68360i	0.363675	−	0.363675i	0.865164	+	0.501489i	$0.167214\pi$
$710$	10.0728	+	10.0728i	0.378025	+	0.378025i
$711$	8.62355	−	1.30471i	0.323409	−	0.0489306i
$712$		−	1.70987i		−	0.0640800i
$713$	43.8120	+	43.8120i	1.64077	+	1.64077i
$714$	0.909796	+	12.0951i	0.0340483	+	0.452648i
$715$		0			0
$716$			12.3694i			0.462265i
$717$	−15.7100	+	18.2657i	−0.586702	+	0.682145i
$718$	−12.9300			−0.482543
$719$	34.8980			1.30148			0.650738	−	0.759302i	$-0.274460\pi$
$719$	34.8980			1.30148			0.650738	+	0.759302i	$0.274460\pi$
$720$	−3.89022	+	5.27722i	−0.144980	+	0.196670i
$721$	−2.44004	−	2.44004i	−0.0908717	−	0.0908717i
$722$	−3.76344	−	3.76344i	−0.140061	−	0.140061i
$723$	9.84246	−	11.4436i	0.366045	−	0.425592i
$724$	−12.3295			−0.458221
$725$	−1.58779			−0.0589690
$726$	−0.269757	−	0.232013i	−0.0100116	−	0.00861082i
$727$		−	12.2780i		−	0.455366i	−0.973735	−	0.227683i	$-0.926885\pi$
$727$		−	12.2780i		−	0.455366i	0.973735	−	0.227683i	$-0.0731149\pi$
$728$		0			0
$729$	24.3065	−	11.7556i	0.900241	−	0.435391i
$730$	−17.0939	−	17.0939i	−0.632673	−	0.632673i
$731$		−	77.5730i		−	2.86914i
$732$	−0.321468	−	4.27370i	−0.0118818	−	0.157960i
$733$	16.2820	+	16.2820i	0.601390	+	0.601390i	0.940681	−	0.339292i	$-0.110187\pi$
$733$	16.2820	+	16.2820i	0.601390	+	0.601390i	−0.339292	+	0.940681i	$0.610187\pi$
$734$	−16.4529	+	16.4529i	−0.607286	+	0.607286i
$735$	17.6522	+	15.1823i	0.651109	+	0.560009i
$736$	−4.72955	+	4.72955i	−0.174333	+	0.174333i
$737$			8.34827i			0.307513i
$738$	−3.36245	−	22.2242i	−0.123773	−	0.818086i
$739$	29.5957	−	29.5957i	1.08869	−	1.08869i	0.0930315	−	0.995663i	$-0.470344\pi$
$739$	29.5957	−	29.5957i	1.08869	−	1.08869i	0.995663	−	0.0930315i	$-0.0296557\pi$
$740$	−3.52102			−0.129435
$741$		0			0
$742$	−6.52647			−0.239594
$743$	32.4529	−	32.4529i	1.19058	−	1.19058i	0.213677	−	0.976904i	$-0.431456\pi$
$743$	32.4529	−	32.4529i	1.19058	−	1.19058i	0.976904	−	0.213677i	$-0.0685441\pi$
$744$	−1.20349	−	15.9996i	−0.0441222	−	0.586573i
$745$			19.6359i			0.719405i
$746$	8.79902	−	8.79902i	0.322155	−	0.322155i
$747$	−10.6121	+	14.3957i	−0.388275	+	0.526709i
$748$	17.6577	−	17.6577i	0.645631	−	0.645631i
$749$	0.725621	+	0.725621i	0.0265136	+	0.0265136i
$750$	19.7186	−	1.48324i	0.720020	−	0.0541601i
$751$			14.0347i			0.512135i	0.966659	+	0.256068i	$0.0824269\pi$
$751$			14.0347i			0.512135i	−0.966659	+	0.256068i	$0.917573\pi$
$752$	−1.78843	−	1.78843i	−0.0652173	−	0.0652173i
$753$	24.6718	−	1.85582i	0.899090	−	0.0676297i
$754$		0			0
$755$			17.6046i			0.640697i
$756$	−4.05582	−	2.54371i	−0.147509	−	0.0925138i
$757$	−42.8599			−1.55777			−0.778884	−	0.627168i	$-0.784214\pi$
$757$	−42.8599			−1.55777			−0.778884	+	0.627168i	$0.784214\pi$
$758$	16.4742			0.598371
$759$	−28.8573	−	24.8197i	−1.04745	−	0.900897i
$760$	5.71502	+	5.71502i	0.207306	+	0.207306i
$761$	−5.41086	−	5.41086i	−0.196143	−	0.196143i	0.602201	−	0.798344i	$-0.294291\pi$
$761$	−5.41086	−	5.41086i	−0.196143	−	0.196143i	−0.798344	+	0.602201i	$0.794291\pi$
$762$	−3.14417	−	2.70425i	−0.113901	−	0.0979646i
$763$	−14.3023			−0.517778
$764$	−15.0865			−0.545809
$765$	−29.5680	+	40.1100i	−1.06903	+	1.45018i
$766$		−	30.6621i		−	1.10787i
$767$		0			0
$768$	1.72717	−	0.129918i	0.0623239	−	0.00468802i
$769$	−10.5271	−	10.5271i	−0.379618	−	0.379618i	0.491346	−	0.870964i	$-0.336505\pi$
$769$	−10.5271	−	10.5271i	−0.379618	−	0.379618i	−0.870964	+	0.491346i	$0.836505\pi$
$770$			6.61540i			0.238402i
$771$	13.8627	−	1.04275i	0.499251	−	0.0375538i
$772$	6.56204	+	6.56204i	0.236173	+	0.236173i
$773$	19.4099	−	19.4099i	0.698125	−	0.698125i	−0.265881	−	0.964006i	$-0.585663\pi$
$773$	19.4099	−	19.4099i	0.698125	−	0.698125i	0.964006	+	0.265881i	$0.0856628\pi$
$774$	24.6458	+	18.1682i	0.885873	+	0.653041i
$775$	−1.46806	+	1.46806i	−0.0527344	+	0.0527344i
$776$		−	2.28375i		−	0.0819818i
$777$	−0.192858	−	2.56391i	−0.00691875	−	0.0919799i
$778$	−1.94978	+	1.94978i	−0.0699030	+	0.0699030i
$779$	−27.7094			−0.992792
$780$		0			0
$781$	21.4161			0.766330
$782$	−35.9473	+	35.9473i	−1.28547	+	1.28547i
$783$	8.22145	+	35.8821i	0.293811	+	1.28232i
$784$		−	6.15111i		−	0.219682i
$785$	−10.8361	+	10.8361i	−0.386757	+	0.386757i
$786$	17.3946	+	14.9608i	0.620445	+	0.533635i
$787$	−23.7619	+	23.7619i	−0.847021	+	0.847021i	−0.989760	−	0.142740i	$-0.954409\pi$
$787$	−23.7619	+	23.7619i	−0.847021	+	0.847021i	0.142740	+	0.989760i	$0.454409\pi$
$788$	18.3296	+	18.3296i	0.652967	+	0.652967i
$789$	1.23858	+	16.4661i	0.0440947	+	0.586207i
$790$		−	6.35340i		−	0.226044i
$791$	−4.35004	−	4.35004i	−0.154670	−	0.154670i
$792$	1.47448	+	9.74562i	0.0523933	+	0.346295i
$793$		0			0
$794$			12.2441i			0.434527i
$795$	−20.3281	−	17.4839i	−0.720963	−	0.620089i
$796$	−0.532738			−0.0188824
$797$	16.8310			0.596186			0.298093	−	0.954537i	$-0.403649\pi$
$797$	16.8310			0.596186			0.298093	+	0.954537i	$0.403649\pi$
$798$	−3.84850	+	4.47457i	−0.136236	+	0.158398i
$799$	−13.5931	−	13.5931i	−0.480890	−	0.480890i
$800$	−0.158479	−	0.158479i	−0.00560308	−	0.00560308i
$801$	4.12897	+	3.04376i	0.145890	+	0.107546i
$802$	−37.5762			−1.32686
$803$	−36.3439			−1.28255
$804$	−2.86981	+	3.33666i	−0.101210	+	0.117675i
$805$		−	13.4675i		−	0.474668i
$806$		0			0
$807$	2.40347	+	31.9524i	0.0846061	+	1.12478i
$808$	−6.86273	−	6.86273i	−0.241430	−	0.241430i
$809$		−	26.6363i		−	0.936482i	−0.883601	−	0.468241i	$-0.844888\pi$
$809$		−	26.6363i		−	0.936482i	0.883601	−	0.468241i	$-0.155112\pi$
$810$	−5.81833	−	18.7881i	−0.204435	−	0.660147i
$811$	16.0384	+	16.0384i	0.563184	+	0.563184i	0.930211	−	0.367026i	$-0.119624\pi$
$811$	16.0384	+	16.0384i	0.563184	+	0.563184i	−0.367026	+	0.930211i	$0.619624\pi$
$812$	4.61549	−	4.61549i	0.161972	−	0.161972i
$813$	−26.0177	+	30.2502i	−0.912481	+	1.06092i
$814$	−3.74308	+	3.74308i	−0.131195	+	0.131195i
$815$			30.8050i			1.07905i
$816$	13.1275	−	0.987455i	0.459555	−	0.0345678i
$817$	26.6904	−	26.6904i	0.933778	−	0.933778i
$818$	22.7124			0.794120
$819$		0			0
$820$	−16.3737			−0.571795
$821$	−28.8103	+	28.8103i	−1.00549	+	1.00549i	−0.00550257	+	0.999985i	$0.501752\pi$
$821$	−28.8103	+	28.8103i	−1.00549	+	1.00549i	−0.999985	+	0.00550257i	$0.998248\pi$
$822$	23.1687	−	1.74275i	0.808101	−	0.0607855i
$823$			6.11615i			0.213196i	0.994302	+	0.106598i	$0.0339957\pi$
$823$			6.11615i			0.213196i	−0.994302	+	0.106598i	$0.966004\pi$
$824$	−2.64831	+	2.64831i	−0.0922584	+	0.0922584i
$825$	0.831665	−	0.966958i	0.0289549	−	0.0336652i
$826$	−4.56173	+	4.56173i	−0.158723	+	0.158723i
$827$	−5.91290	−	5.91290i	−0.205612	−	0.205612i	0.596788	−	0.802399i	$-0.296443\pi$
$827$	−5.91290	−	5.91290i	−0.205612	−	0.205612i	−0.802399	+	0.596788i	$0.796443\pi$
$828$	−3.00172	−	19.8400i	−0.104317	−	0.689487i
$829$			9.99203i			0.347038i	0.984831	+	0.173519i	$0.0555137\pi$
$829$			9.99203i			0.347038i	−0.984831	+	0.173519i	$0.944486\pi$
$830$	9.21222	+	9.21222i	0.319761	+	0.319761i
$831$	−3.38286	−	44.9728i	−0.117350	−	1.56009i
$832$		0			0
$833$		−	46.7520i		−	1.61986i
$834$	−1.49015	+	1.73257i	−0.0515998	+	0.0599939i
$835$	−2.39974			−0.0830465
$836$	12.1509			0.420248
$837$	40.7779	+	25.5749i	1.40949	+	0.883998i
$838$	14.1602	+	14.1602i	0.489157	+	0.489157i
$839$	4.46518	+	4.46518i	0.154155	+	0.154155i	0.779971	−	0.625816i	$-0.215234\pi$
$839$	4.46518	+	4.46518i	0.154155	+	0.154155i	−0.625816	+	0.779971i	$0.715234\pi$
$840$	−2.27411	+	2.64406i	−0.0784643	+	0.0912287i
$841$	−21.1894			−0.730670
$842$	4.45449			0.153512
$843$	10.7747	+	9.26711i	0.371099	+	0.319176i
$844$			18.0776i			0.622258i
$845$		0			0
$846$	7.50228	−	1.13507i	0.257934	−	0.0390245i
$847$	−0.133834	−	0.133834i	−0.00459858	−	0.00459858i
$848$			7.08357i			0.243251i
$849$	0.344327	+	4.57758i	0.0118173	+	0.157102i
$850$	−1.20453	−	1.20453i	−0.0413152	−	0.0413152i
$851$	7.62011	−	7.62011i	0.261214	−	0.261214i
$852$	8.55966	+	7.36202i	0.293249	+	0.252219i
$853$	19.0738	−	19.0738i	0.653073	−	0.653073i	−0.300659	−	0.953732i	$-0.597207\pi$
$853$	19.0738	−	19.0738i	0.653073	−	0.653073i	0.953732	+	0.300659i	$0.0972066\pi$
$854$		−	2.27979i		−	0.0780128i
$855$	−23.9740	+	3.62717i	−0.819892	+	0.124047i
$856$	0.787559	−	0.787559i	0.0269182	−	0.0269182i
$857$	3.83142			0.130879			0.0654394	−	0.997857i	$-0.479155\pi$
$857$	3.83142			0.130879			0.0654394	+	0.997857i	$0.479155\pi$
$858$		0			0
$859$	14.2959			0.487771			0.243886	−	0.969804i	$-0.421578\pi$
$859$	14.2959			0.487771			0.243886	+	0.969804i	$0.421578\pi$
$860$	15.7716	−	15.7716i	0.537806	−	0.537806i
$861$	−0.896844	−	11.9229i	−0.0305644	−	0.406332i
$862$		−	18.5222i		−	0.630868i
$863$	−9.37420	+	9.37420i	−0.319102	+	0.319102i	−0.848422	−	0.529320i	$-0.822447\pi$
$863$	−9.37420	+	9.37420i	−0.319102	+	0.319102i	0.529320	+	0.848422i	$0.322447\pi$
$864$	−2.76084	+	4.40202i	−0.0939256	+	0.149760i
$865$	−0.846250	+	0.846250i	−0.0287734	+	0.0287734i
$866$	−23.6835	−	23.6835i	−0.804799	−	0.804799i
$867$	70.4150	−	5.29663i	2.39142	−	0.179883i
$868$		−	8.53493i		−	0.289694i
$869$	−6.75410	−	6.75410i	−0.229117	−	0.229117i
$870$	26.7404	−	2.01142i	0.906585	−	0.0681935i
$871$		0			0
$872$			15.5231i			0.525679i
$873$	5.51476	+	4.06533i	0.186646	+	0.137591i
$874$	−24.7367			−0.836730
$875$	10.5188			0.355601
$876$	−14.5260	−	12.4936i	−0.490789	−	0.422120i
$877$	6.92967	+	6.92967i	0.233998	+	0.233998i	0.814359	−	0.580361i	$-0.197089\pi$
$877$	6.92967	+	6.92967i	0.233998	+	0.233998i	−0.580361	+	0.814359i	$0.697089\pi$
$878$	7.83125	+	7.83125i	0.264292	+	0.264292i
$879$	−2.99167	−	2.57309i	−0.100906	−	0.0867880i
$880$	7.18008			0.242040
$881$	−47.9400			−1.61514			−0.807569	−	0.589773i	$-0.799217\pi$
$881$	−47.9400			−1.61514			−0.807569	+	0.589773i	$0.799217\pi$
$882$	14.8536	+	10.9497i	0.500147	+	0.368694i
$883$			27.9325i			0.940003i	0.882666	+	0.470002i	$0.155747\pi$
$883$			27.9325i			0.940003i	−0.882666	+	0.470002i	$0.844253\pi$
$884$		0			0
$885$	−26.4290	+	1.98799i	−0.888400	+	0.0668256i
$886$	−8.08044	−	8.08044i	−0.271468	−	0.271468i
$887$		−	34.2162i		−	1.14887i	−0.818551	−	0.574434i	$-0.805222\pi$
$887$		−	34.2162i		−	1.14887i	0.818551	−	0.574434i	$-0.194778\pi$
$888$	−2.78277	+	0.209320i	−0.0933836	+	0.00702433i
$889$	−1.55991	−	1.55991i	−0.0523177	−	0.0523177i
$890$	2.64225	−	2.64225i	0.0885684	−	0.0885684i
$891$	−26.1583	−	13.7878i	−0.876337	−	0.461907i
$892$	−15.3864	+	15.3864i	−0.515175	+	0.515175i
$893$		−	9.35391i		−	0.313017i
$894$	1.16733	+	15.5189i	0.0390415	+	0.519029i
$895$	−19.1143	+	19.1143i	−0.638921	+	0.638921i
$896$	0.921354			0.0307803
$897$		0			0
$898$	−9.05313			−0.302107
$899$	−46.4050	+	46.4050i	−1.54769	+	1.54769i
$900$	0.664804	−	0.100582i	0.0221601	−	0.00335275i
$901$			53.8393i			1.79365i
$902$	−17.4064	+	17.4064i	−0.579569	+	0.579569i
$903$	12.3483	+	10.6206i	0.410926	+	0.353431i
$904$	−4.72136	+	4.72136i	−0.157030	+	0.157030i
$905$	−19.0527	−	19.0527i	−0.633332	−	0.633332i
$906$	1.04657	+	13.9134i	0.0347700	+	0.462243i
$907$		−	20.1854i		−	0.670245i	−0.942175	−	0.335123i	$-0.891222\pi$
$907$		−	20.1854i		−	0.670245i	0.942175	−	0.335123i	$-0.108778\pi$
$908$	16.6116	+	16.6116i	0.551275	+	0.551275i
$909$	28.7885	−	4.35559i	0.954853	−	0.144466i
$910$		0			0
$911$			48.5102i			1.60721i	0.595160	+	0.803607i	$0.297089\pi$
$911$			48.5102i			1.60721i	−0.595160	+	0.803607i	$0.702911\pi$
$912$	4.85651	+	4.17701i	0.160815	+	0.138315i
$913$	19.5864			0.648216
$914$	−22.5412			−0.745596
$915$	6.10736	−	7.10089i	0.201903	−	0.234748i
$916$	−12.3044	−	12.3044i	−0.406549	−	0.406549i
$917$	8.62996	+	8.62996i	0.284986	+	0.284986i
$918$	−20.9840	+	33.4580i	−0.692575	+	1.10428i
$919$	17.4088			0.574263			0.287131	−	0.957891i	$-0.407298\pi$
$919$	17.4088			0.574263			0.287131	+	0.957891i	$0.407298\pi$
$920$	−14.6171			−0.481911
$921$	9.23601	−	10.7385i	0.304337	−	0.353845i
$922$		−	1.44293i		−	0.0475204i
$923$		0			0
$924$	0.393278	+	5.22835i	0.0129379	+	0.172000i
$925$	0.255337	+	0.255337i	0.00839542	+	0.00839542i
$926$			2.52764i			0.0830633i
$927$	−1.68082	−	11.1094i	−0.0552052	−	0.364881i
$928$	−5.00946	−	5.00946i	−0.164444	−	0.164444i
$929$	−11.5506	+	11.5506i	−0.378964	+	0.378964i	−0.870728	−	0.491764i	$-0.836352\pi$
$929$	−11.5506	+	11.5506i	−0.378964	+	0.378964i	0.491764	+	0.870728i	$0.336352\pi$
$930$	22.8643	−	26.5838i	0.749751	−	0.871718i
$931$	16.0859	−	16.0859i	0.527193	−	0.527193i
$932$		−	19.6727i		−	0.644399i
$933$	−50.1436	+	3.77181i	−1.64163	+	0.123484i
$934$	−1.94619	+	1.94619i	−0.0636813	+	0.0636813i
$935$	54.5729			1.78472
$936$		0			0
$937$	16.1182			0.526560			0.263280	−	0.964719i	$-0.415196\pi$
$937$	16.1182			0.526560			0.263280	+	0.964719i	$0.415196\pi$
$938$	−1.65541	+	1.65541i	−0.0540510	+	0.0540510i
$939$	20.9339	−	1.57465i	0.683151	−	0.0513867i
$940$		−	5.52730i		−	0.180281i
$941$	20.2081	−	20.2081i	0.658765	−	0.658765i	−0.296323	−	0.955088i	$-0.595760\pi$
$941$	20.2081	−	20.2081i	0.658765	−	0.658765i	0.955088	+	0.296323i	$0.0957605\pi$
$942$	−7.91992	+	9.20830i	−0.258045	+	0.300023i
$943$	35.4356	−	35.4356i	1.15394	−	1.15394i
$944$	4.95111	+	4.95111i	0.161145	+	0.161145i
$945$	−2.33666	−	10.1982i	−0.0760115	−	0.331748i
$946$		−	33.5325i		−	1.09024i
$947$	−11.8229	−	11.8229i	−0.384192	−	0.384192i	0.488418	−	0.872610i	$-0.337574\pi$
$947$	−11.8229	−	11.8229i	−0.384192	−	0.384192i	−0.872610	+	0.488418i	$0.837574\pi$
$948$	−0.377702	−	5.02129i	−0.0122672	−	0.163084i
$949$		0			0
$950$		−	0.828883i		−	0.0268925i
$951$	−21.2916	+	24.7553i	−0.690428	+	0.802744i
$952$	7.00284			0.226963
$953$	29.9481			0.970115			0.485057	−	0.874482i	$-0.338799\pi$
$953$	29.9481			0.970115			0.485057	+	0.874482i	$0.338799\pi$
$954$	−17.1053	−	12.6095i	−0.553805	−	0.408249i
$955$	−23.3130	−	23.3130i	−0.754392	−	0.754392i
$956$	9.83565	+	9.83565i	0.318108	+	0.318108i
$957$	26.2886	−	30.5652i	0.849790	−	0.988031i
$958$	−28.2487			−0.912674
$959$	12.3593			0.399101
$960$	2.86975	+	2.46823i	0.0926209	+	0.0796617i
$961$			54.8117i			1.76812i
$962$		0			0
$963$	0.499843	+	3.30373i	0.0161072	+	0.106461i
$964$	−6.16211	−	6.16211i	−0.198468	−	0.198468i
$965$			20.2806i			0.652855i
$966$	−0.800629	−	10.6438i	−0.0257598	−	0.342458i
$967$	−17.6856	−	17.6856i	−0.568731	−	0.568731i	0.363042	−	0.931773i	$-0.381738\pi$
$967$	−17.6856	−	17.6856i	−0.568731	−	0.568731i	−0.931773	+	0.363042i	$0.881738\pi$
$968$	−0.145258	+	0.145258i	−0.00466876	+	0.00466876i
$969$	36.9124	+	31.7477i	1.18580	+	1.01988i
$970$	3.52906	−	3.52906i	0.113311	−	0.113311i
$971$			32.1109i			1.03049i	0.857044	+	0.515243i	$0.172298\pi$
$971$			32.1109i			1.03049i	−0.857044	+	0.515243i	$0.827702\pi$
$972$	−5.71534	−	14.5029i	−0.183320	−	0.465182i
$973$	−0.859576	+	0.859576i	−0.0275567	+	0.0275567i
$974$	31.5204			1.00998
$975$		0			0
$976$	−2.47439			−0.0792033
$977$	17.8100	−	17.8100i	0.569791	−	0.569791i	−0.362279	−	0.932070i	$-0.618001\pi$
$977$	17.8100	−	17.8100i	0.569791	−	0.569791i	0.932070	+	0.362279i	$0.118001\pi$
$978$	1.83132	+	24.3461i	0.0585591	+	0.778503i
$979$		−	5.61779i		−	0.179545i
$980$	9.50528	−	9.50528i	0.303635	−	0.303635i
$981$	−37.4850	−	27.6329i	−1.19680	−	0.882251i
$982$	12.0575	−	12.0575i	0.384770	−	0.384770i
$983$	19.3966	+	19.3966i	0.618655	+	0.618655i	0.945186	−	0.326531i	$-0.105880\pi$
$983$	19.3966	+	19.3966i	0.618655	+	0.618655i	−0.326531	+	0.945186i	$0.605880\pi$
$984$	−12.9406	+	0.973398i	−0.412533	+	0.0310308i
$985$			56.6494i			1.80500i
$986$	−38.0749	−	38.0749i	−1.21255	−	1.21255i
$987$	4.02484	−	0.302749i	0.128112	−	0.00963662i
$988$		0			0
$989$			68.2649i			2.17070i
$990$	−12.7814	+	17.3384i	−0.406218	+	0.551049i
$991$	5.96134			0.189368			0.0946842	−	0.995507i	$-0.469816\pi$
$991$	5.96134			0.189368			0.0946842	+	0.995507i	$0.469816\pi$
$992$	−9.26346			−0.294115
$993$	−23.3624	−	20.0937i	−0.741385	−	0.637653i
$994$	4.24668	+	4.24668i	0.134697	+	0.134697i
$995$	−0.823238	−	0.823238i	−0.0260984	−	0.0260984i
$996$	7.82835	+	6.73304i	0.248051	+	0.213345i
$997$	17.7808			0.563123			0.281562	−	0.959543i	$-0.409148\pi$
$997$	17.7808			0.563123			0.281562	+	0.959543i	$0.409148\pi$
$998$	−16.6394			−0.526711
$999$	4.44818	−	7.09241i	0.140734	−	0.224394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.g.e.437.18	yes	48
3.2	odd	2	inner	1014.2.g.e.437.9	yes	48
13.5	odd	4	inner	1014.2.g.e.239.9	yes	48
13.8	odd	4	inner	1014.2.g.e.239.16	yes	48
13.12	even	2	inner	1014.2.g.e.437.7	yes	48
39.5	even	4	inner	1014.2.g.e.239.18	yes	48
39.8	even	4	inner	1014.2.g.e.239.7	✓	48
39.38	odd	2	inner	1014.2.g.e.437.16	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.g.e.239.7	✓	48	39.8	even	4	inner
1014.2.g.e.239.9	yes	48	13.5	odd	4	inner
1014.2.g.e.239.16	yes	48	13.8	odd	4	inner
1014.2.g.e.239.18	yes	48	39.5	even	4	inner
1014.2.g.e.437.7	yes	48	13.12	even	2	inner
1014.2.g.e.437.9	yes	48	3.2	odd	2	inner
1014.2.g.e.437.16	yes	48	39.38	odd	2	inner
1014.2.g.e.437.18	yes	48	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.72717 - 0.129918i) q^{3} -1.00000i q^{4} +(1.54530 - 1.54530i) q^{5} +(1.12943 - 1.31316i) q^{6} +(0.651496 - 0.651496i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.96624 - 0.448782i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.72717 - 0.129918i) q^{3} -1.00000i q^{4} +(1.54530 - 1.54530i) q^{5} +(1.12943 - 1.31316i) q^{6} +(0.651496 - 0.651496i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.96624 - 0.448782i) q^{9} -2.18538i q^{10} +(-2.32321 - 2.32321i) q^{11} +(-0.129918 - 1.72717i) q^{12} -0.921354i q^{14} +(2.46823 - 2.86975i) q^{15} -1.00000 q^{16} -7.60059 q^{17} +(1.78011 - 2.41479i) q^{18} +(-2.61512 - 2.61512i) q^{19} +(-1.54530 - 1.54530i) q^{20} +(1.04060 - 1.20989i) q^{21} -3.28551 q^{22} +6.68859 q^{23} +(-1.31316 - 1.12943i) q^{24} +0.224123i q^{25} +(5.06490 - 1.16049i) q^{27} +(-0.651496 - 0.651496i) q^{28} +7.08445i q^{29} +(-0.283920 - 3.77452i) q^{30} +(6.55026 + 6.55026i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-4.31440 - 3.71075i) q^{33} +(-5.37443 + 5.37443i) q^{34} -2.01351i q^{35} +(-0.448782 - 2.96624i) q^{36} +(1.13927 - 1.13927i) q^{37} -3.69834 q^{38} -2.18538 q^{40} +(5.29792 - 5.29792i) q^{41} +(-0.119701 - 1.59134i) q^{42} +10.2062i q^{43} +(-2.32321 + 2.32321i) q^{44} +(3.89022 - 5.27722i) q^{45} +(4.72955 - 4.72955i) q^{46} +(1.78843 + 1.78843i) q^{47} +(-1.72717 + 0.129918i) q^{48} +6.15111i q^{49} +(0.158479 + 0.158479i) q^{50} +(-13.1275 + 0.987455i) q^{51} -7.08357i q^{53} +(2.76084 - 4.40202i) q^{54} -7.18008 q^{55} -0.921354 q^{56} +(-4.85651 - 4.17701i) q^{57} +(5.00946 + 5.00946i) q^{58} +(-4.95111 - 4.95111i) q^{59} +(-2.86975 - 2.46823i) q^{60} +2.47439 q^{61} +9.26346 q^{62} +(1.64011 - 2.22487i) q^{63} +1.00000i q^{64} +(-5.67464 + 0.426848i) q^{66} +(-1.79671 - 1.79671i) q^{67} +7.60059i q^{68} +(11.5523 - 0.868969i) q^{69} +(-1.42376 - 1.42376i) q^{70} +(-4.60918 + 4.60918i) q^{71} +(-2.41479 - 1.78011i) q^{72} +(7.82194 - 7.82194i) q^{73} -1.61117i q^{74} +(0.0291177 + 0.387099i) q^{75} +(-2.61512 + 2.61512i) q^{76} -3.02712 q^{77} +2.90723 q^{79} +(-1.54530 + 1.54530i) q^{80} +(8.59719 - 2.66239i) q^{81} -7.49239i q^{82} +(-4.21539 + 4.21539i) q^{83} +(-1.20989 - 1.04060i) q^{84} +(-11.7452 + 11.7452i) q^{85} +(7.21686 + 7.21686i) q^{86} +(0.920399 + 12.2361i) q^{87} +3.28551i q^{88} +(1.20906 + 1.20906i) q^{89} +(-0.980758 - 6.48236i) q^{90} -6.68859i q^{92} +(12.1644 + 10.4624i) q^{93} +2.52922 q^{94} -8.08226 q^{95} +(-1.12943 + 1.31316i) q^{96} +(1.61485 + 1.61485i) q^{97} +(4.34949 + 4.34949i) q^{98} +(-7.93381 - 5.84858i) 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

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Database

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