LMFDB - Embedded newform 1274.2.n.l.961.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(753,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1274.753"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-4,6,0,0,0,0,6,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			961.6
Root			$-1.56052 + 0.900969i$ of defining polynomial
Character	$\chi$	$=$	1274.961
Dual form			1274.2.n.l.753.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.400969 + 0.694498i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.480608 - 0.277479i) q^{5} +0.801938i q^{6} +1.00000i q^{8} +(1.17845 - 2.04113i) q^{9} +(-0.277479 - 0.480608i) q^{10} +(2.15983 - 1.24698i) q^{11} +(-0.400969 + 0.694498i) q^{12} +(0.890084 - 3.49396i) q^{13} -0.445042i q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.92543 + 5.06699i) q^{17} +(2.04113 - 1.17845i) q^{18} +(2.50289 + 1.44504i) q^{19} -0.554958i q^{20} +2.49396 q^{22} +(-3.04892 + 5.28088i) q^{23} +(-0.694498 + 0.400969i) q^{24} +(-2.34601 - 4.06341i) q^{25} +(2.51781 - 2.58082i) q^{26} +4.29590 q^{27} +6.27413 q^{29} +(0.222521 - 0.385418i) q^{30} +(6.91774 - 3.99396i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.73205 + 1.00000i) q^{33} +5.85086i q^{34} +2.35690 q^{36} +(-7.89781 - 4.55980i) q^{37} +(1.44504 + 2.50289i) q^{38} +(2.78345 - 0.782807i) q^{39} +(0.277479 - 0.480608i) q^{40} +4.71379i q^{41} +6.03684 q^{43} +(2.15983 + 1.24698i) q^{44} +(-1.13274 + 0.653989i) q^{45} +(-5.28088 + 3.04892i) q^{46} +(0.213891 + 0.123490i) q^{47} -0.801938 q^{48} -4.69202i q^{50} +(-2.34601 + 4.06341i) q^{51} +(3.47090 - 0.976144i) q^{52} +(1.66487 + 2.88365i) q^{53} +(3.72036 + 2.14795i) q^{54} -1.38404 q^{55} +2.31767i q^{57} +(5.43355 + 3.13706i) q^{58} +(-5.66164 + 3.26875i) q^{59} +(0.385418 - 0.222521i) q^{60} +(-7.34481 + 12.7216i) q^{61} +7.98792 q^{62} -1.00000 q^{64} +(-1.39728 + 1.43224i) q^{65} +(1.00000 + 1.73205i) q^{66} +(1.81678 - 1.04892i) q^{67} +(-2.92543 + 5.06699i) q^{68} -4.89008 q^{69} +2.46681i q^{71} +(2.04113 + 1.17845i) q^{72} +(3.03632 - 1.75302i) q^{73} +(-4.55980 - 7.89781i) q^{74} +(1.88135 - 3.25860i) q^{75} +2.89008i q^{76} +(2.80194 + 0.713792i) q^{78} +(-7.54288 + 13.0646i) q^{79} +(0.480608 - 0.277479i) q^{80} +(-1.81282 - 3.13990i) q^{81} +(-2.35690 + 4.08226i) q^{82} -11.6039i q^{83} -3.24698i q^{85} +(5.22805 + 3.01842i) q^{86} +(2.51573 + 4.35737i) q^{87} +(1.24698 + 2.15983i) q^{88} +(-7.69904 - 4.44504i) q^{89} -1.30798 q^{90} -6.09783 q^{92} +(5.54760 + 3.20291i) q^{93} +(0.123490 + 0.213891i) q^{94} +(-0.801938 - 1.38900i) q^{95} +(-0.694498 - 0.400969i) q^{96} -9.52542i q^{97} -5.87800i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} + 6 q^{4} + 6 q^{9} - 4 q^{10} + 4 q^{12} + 8 q^{13} - 6 q^{16} + 8 q^{17} - 8 q^{22} - 18 q^{25} + 2 q^{26} - 4 q^{27} + 32 q^{29} + 2 q^{30} + 12 q^{36} + 16 q^{38} - 12 q^{39} + 4 q^{40}+ \cdots + 8 q^{95}+O(q^{100}) $ 12 * q - 4 * q^3 + 6 * q^4 + 6 * q^9 - 4 * q^10 + 4 * q^12 + 8 * q^13 - 6 * q^16 + 8 * q^17 - 8 * q^22 - 18 * q^25 + 2 * q^26 - 4 * q^27 + 32 * q^29 + 2 * q^30 + 12 * q^36 + 16 * q^38 - 12 * q^39 + 4 * q^40 - 40 * q^43 + 8 * q^48 - 18 * q^51 + 4 * q^52 + 24 * q^53 + 24 * q^55 + 4 * q^61 + 20 * q^62 - 12 * q^64 + 8 * q^65 + 12 * q^66 - 8 * q^68 - 56 * q^69 - 12 * q^74 - 12 * q^75 + 16 * q^78 - 16 * q^79 + 2 * q^81 - 12 * q^82 - 20 * q^87 - 4 * q^88 - 36 * q^90 - 8 * q^94 + 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.400969	+	0.694498i	0.231499	+	0.400969i	0.958250	−	0.285933i	$-0.0923035\pi$
$3$	0.400969	+	0.694498i	0.231499	+	0.400969i	−0.726750	+	0.686902i	$0.758970\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.480608	−	0.277479i	−0.214934	−	0.124092i	0.388668	−	0.921378i	$-0.372935\pi$
$5$	−0.480608	−	0.277479i	−0.214934	−	0.124092i	−0.603603	+	0.797285i	$0.706269\pi$
$6$			0.801938i			0.327390i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	1.17845	−	2.04113i	0.392816	−	0.680377i
$10$	−0.277479	−	0.480608i	−0.0877466	−	0.151982i
$11$	2.15983	−	1.24698i	0.651214	−	0.375978i	−0.137707	−	0.990473i	$-0.543973\pi$
$11$	2.15983	−	1.24698i	0.651214	−	0.375978i	0.788921	+	0.614494i	$0.210640\pi$
$12$	−0.400969	+	0.694498i	−0.115750	+	0.200484i
$13$	0.890084	−	3.49396i	0.246865	−	0.969050i
$13$	0.890084	−	3.49396i	0.246865	−	0.969050i
$14$		0			0
$15$		−	0.445042i		−	0.114909i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.92543	+	5.06699i	0.709520	+	1.22893i	0.965035	+	0.262120i	$0.0844217\pi$
$17$	2.92543	+	5.06699i	0.709520	+	1.22893i	−0.255515	+	0.966805i	$0.582245\pi$
$18$	2.04113	−	1.17845i	0.481099	−	0.277763i
$19$	2.50289	+	1.44504i	0.574201	+	0.331515i	0.758826	−	0.651294i	$-0.225773\pi$
$19$	2.50289	+	1.44504i	0.574201	+	0.331515i	−0.184624	+	0.982809i	$0.559107\pi$
$20$		−	0.554958i		−	0.124092i
$21$		0			0
$22$	2.49396			0.531714
$23$	−3.04892	+	5.28088i	−0.635743	+	1.10114i	0.350614	+	0.936520i	$0.385973\pi$
$23$	−3.04892	+	5.28088i	−0.635743	+	1.10114i	−0.986357	+	0.164619i	$0.947360\pi$
$24$	−0.694498	+	0.400969i	−0.141764	+	0.0818474i
$25$	−2.34601	−	4.06341i	−0.469202	−	0.812682i
$26$	2.51781	−	2.58082i	0.493784	−	0.506140i
$27$	4.29590			0.826746
$28$		0			0
$29$	6.27413			1.16508			0.582538	−	0.812803i	$-0.302060\pi$
$29$	6.27413			1.16508			0.582538	+	0.812803i	$0.302060\pi$
$30$	0.222521	−	0.385418i	0.0406266	−	0.0703673i
$31$	6.91774	−	3.99396i	1.24246	−	0.717336i	0.272868	−	0.962052i	$-0.412028\pi$
$31$	6.91774	−	3.99396i	1.24246	−	0.717336i	0.969595	+	0.244715i	$0.0786945\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.73205	+	1.00000i	0.301511	+	0.174078i
$34$			5.85086i			1.00341i
$35$		0			0
$36$	2.35690			0.392816
$37$	−7.89781	−	4.55980i	−1.29839	−	0.749627i	−0.318266	−	0.948002i	$-0.603100\pi$
$37$	−7.89781	−	4.55980i	−1.29839	−	0.749627i	−0.980126	+	0.198375i	$0.936434\pi$
$38$	1.44504	+	2.50289i	0.234417	+	0.406022i
$39$	2.78345	−	0.782807i	0.445708	−	0.125349i
$40$	0.277479	−	0.480608i	0.0438733	−	0.0759908i
$41$			4.71379i			0.736171i	0.929792	+	0.368085i	$0.119987\pi$
$41$			4.71379i			0.736171i	−0.929792	+	0.368085i	$0.880013\pi$
$42$		0			0
$43$	6.03684			0.920609			0.460304	−	0.887761i	$-0.347740\pi$
$43$	6.03684			0.920609			0.460304	+	0.887761i	$0.347740\pi$
$44$	2.15983	+	1.24698i	0.325607	+	0.187989i
$45$	−1.13274	+	0.653989i	−0.168859	+	0.0974910i
$46$	−5.28088	+	3.04892i	−0.778623	+	0.449538i
$47$	0.213891	+	0.123490i	0.0311992	+	0.0180128i	0.515518	−	0.856878i	$-0.327599\pi$
$47$	0.213891	+	0.123490i	0.0311992	+	0.0180128i	−0.484319	+	0.874891i	$0.660933\pi$
$48$	−0.801938			−0.115750
$49$		0			0
$50$		−	4.69202i		−	0.663552i
$51$	−2.34601	+	4.06341i	−0.328507	+	0.568991i
$52$	3.47090	−	0.976144i	0.481327	−	0.135367i
$53$	1.66487	+	2.88365i	0.228688	+	0.396099i	0.957420	−	0.288700i	$-0.0932231\pi$
$53$	1.66487	+	2.88365i	0.228688	+	0.396099i	−0.728731	+	0.684800i	$0.759890\pi$
$54$	3.72036	+	2.14795i	0.506276	+	0.292299i
$55$	−1.38404			−0.186624
$56$		0			0
$57$			2.31767i			0.306983i
$58$	5.43355	+	3.13706i	0.713460	+	0.411917i
$59$	−5.66164	+	3.26875i	−0.737083	+	0.425555i	−0.821008	−	0.570917i	$-0.806588\pi$
$59$	−5.66164	+	3.26875i	−0.737083	+	0.425555i	0.0839249	+	0.996472i	$0.473254\pi$
$60$	0.385418	−	0.222521i	0.0497572	−	0.0287273i
$61$	−7.34481	+	12.7216i	−0.940407	+	1.62883i	−0.175711	+	0.984442i	$0.556222\pi$
$61$	−7.34481	+	12.7216i	−0.940407	+	1.62883i	−0.764696	+	0.644391i	$0.777111\pi$
$62$	7.98792			1.01447
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.39728	+	1.43224i	−0.173311	+	0.177648i
$66$	1.00000	+	1.73205i	0.123091	+	0.213201i
$67$	1.81678	−	1.04892i	0.221955	−	0.128146i	−0.384900	−	0.922958i	$-0.625764\pi$
$67$	1.81678	−	1.04892i	0.221955	−	0.128146i	0.606855	+	0.794813i	$0.292431\pi$
$68$	−2.92543	+	5.06699i	−0.354760	+	0.614463i
$69$	−4.89008			−0.588697
$70$		0			0
$71$			2.46681i			0.292757i	0.989229	+	0.146378i	$0.0467617\pi$
$71$			2.46681i			0.292757i	−0.989229	+	0.146378i	$0.953238\pi$
$72$	2.04113	+	1.17845i	0.240550	+	0.138881i
$73$	3.03632	−	1.75302i	0.355374	−	0.205176i	−0.311675	−	0.950189i	$-0.600890\pi$
$73$	3.03632	−	1.75302i	0.355374	−	0.205176i	0.667050	+	0.745013i	$0.267557\pi$
$74$	−4.55980	−	7.89781i	−0.530066	−	0.918102i
$75$	1.88135	−	3.25860i	0.217240	−	0.376271i
$76$			2.89008i			0.331515i
$77$		0			0
$78$	2.80194	+	0.713792i	0.317257	+	0.0808210i
$79$	−7.54288	+	13.0646i	−0.848640	+	1.46989i	0.0337823	+	0.999429i	$0.489245\pi$
$79$	−7.54288	+	13.0646i	−0.848640	+	1.46989i	−0.882422	+	0.470458i	$0.844089\pi$
$80$	0.480608	−	0.277479i	0.0537336	−	0.0310231i
$81$	−1.81282	−	3.13990i	−0.201425	−	0.348878i
$82$	−2.35690	+	4.08226i	−0.260276	+	0.450811i
$83$		−	11.6039i		−	1.27369i	−0.770992	−	0.636845i	$-0.780239\pi$
$83$		−	11.6039i		−	1.27369i	0.770992	−	0.636845i	$-0.219761\pi$
$84$		0			0
$85$		−	3.24698i		−	0.352184i
$86$	5.22805	+	3.01842i	0.563755	+	0.325484i
$87$	2.51573	+	4.35737i	0.269715	+	0.467159i
$88$	1.24698	+	2.15983i	0.132928	+	0.230239i
$89$	−7.69904	−	4.44504i	−0.816096	−	0.471173i	0.0329721	−	0.999456i	$-0.489503\pi$
$89$	−7.69904	−	4.44504i	−0.816096	−	0.471173i	−0.849068	+	0.528283i	$0.822836\pi$
$90$	−1.30798			−0.137873
$91$		0			0
$92$	−6.09783			−0.635743
$93$	5.54760	+	3.20291i	0.575259	+	0.332126i
$94$	0.123490	+	0.213891i	0.0127370	+	0.0220611i
$95$	−0.801938	−	1.38900i	−0.0822771	−	0.142508i
$96$	−0.694498	−	0.400969i	−0.0708820	−	0.0409237i
$97$		−	9.52542i		−	0.967160i	−0.875300	−	0.483580i	$-0.839336\pi$
$97$		−	9.52542i		−	0.967160i	0.875300	−	0.483580i	$-0.160664\pi$
$98$		0			0
$99$		−	5.87800i		−	0.590761i
$100$	2.34601	−	4.06341i	0.234601	−	0.406341i
$101$	−1.41789	−	2.45587i	−0.141086	−	0.244368i	0.786820	−	0.617183i	$-0.211726\pi$
$101$	−1.41789	−	2.45587i	−0.141086	−	0.244368i	−0.927906	+	0.372815i	$0.878393\pi$
$102$	−4.06341	+	2.34601i	−0.402338	+	0.232290i
$103$	2.10992	−	3.65448i	0.207896	−	0.360087i	−0.743155	−	0.669119i	$-0.766672\pi$
$103$	2.10992	−	3.65448i	0.207896	−	0.360087i	0.951052	+	0.309032i	$0.100005\pi$
$104$	3.49396	+	0.890084i	0.342611	+	0.0872799i
$105$		0			0
$106$			3.32975i			0.323414i
$107$	6.95473	−	12.0459i	0.672339	−	1.16453i	−0.304900	−	0.952384i	$-0.598623\pi$
$107$	6.95473	−	12.0459i	0.672339	−	1.16453i	0.977239	−	0.212141i	$-0.0680437\pi$
$108$	2.14795	+	3.72036i	0.206686	+	0.357991i
$109$	2.12793	−	1.22856i	0.203819	−	0.117675i	−0.394617	−	0.918846i	$-0.629123\pi$
$109$	2.12793	−	1.22856i	0.203819	−	0.117675i	0.598436	+	0.801171i	$0.295789\pi$
$110$	−1.19862	−	0.692021i	−0.114284	−	0.0659817i
$111$		−	7.31336i		−	0.694153i
$112$		0			0
$113$	11.7681			1.10705			0.553524	−	0.832833i	$-0.313283\pi$
$113$	11.7681			1.10705			0.553524	+	0.832833i	$0.313283\pi$
$114$	−1.15883	+	2.00716i	−0.108535	+	0.187988i
$115$	2.93067	−	1.69202i	0.273286	−	0.157782i
$116$	3.13706	+	5.43355i	0.291269	+	0.504493i
$117$	−6.08271	−	5.93423i	−0.562347	−	0.548619i
$118$	−6.53750			−0.601826
$119$		0			0
$120$	0.445042			0.0406266
$121$	−2.39008	+	4.13975i	−0.217280	+	0.376341i
$122$	−12.7216	+	7.34481i	−1.15176	+	0.664968i
$123$	−3.27372	+	1.89008i	−0.295181	+	0.170423i
$124$	6.91774	+	3.99396i	0.621231	+	0.358668i
$125$			5.37867i			0.481083i
$126$		0			0
$127$	−2.45042			−0.217439			−0.108720	−	0.994072i	$-0.534675\pi$
$127$	−2.45042			−0.217439			−0.108720	+	0.994072i	$0.534675\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	2.42058	+	4.19257i	0.213120	+	0.369135i
$130$	−1.92620	+	0.541719i	−0.168939	+	0.0475119i
$131$	−2.03050	+	3.51693i	−0.177406	+	0.307275i	−0.940991	−	0.338431i	$-0.890104\pi$
$131$	−2.03050	+	3.51693i	−0.177406	+	0.307275i	0.763586	+	0.645707i	$0.223437\pi$
$132$			2.00000i			0.174078i
$133$		0			0
$134$	2.09783			0.181225
$135$	−2.06464	−	1.19202i	−0.177696	−	0.102593i
$136$	−5.06699	+	2.92543i	−0.434491	+	0.250853i
$137$	8.89765	−	5.13706i	0.760178	−	0.438889i	−0.0691817	−	0.997604i	$-0.522039\pi$
$137$	8.89765	−	5.13706i	0.760178	−	0.438889i	0.829360	+	0.558715i	$0.188705\pi$
$138$	−4.23494	−	2.44504i	−0.360502	−	0.208136i
$139$	−3.19136			−0.270687			−0.135344	−	0.990799i	$-0.543214\pi$
$139$	−3.19136			−0.270687			−0.135344	+	0.990799i	$0.543214\pi$
$140$		0			0
$141$			0.198062i			0.0166799i
$142$	−1.23341	+	2.13632i	−0.103505	+	0.179276i
$143$	−2.43446	−	8.65628i	−0.203580	−	0.723875i
$144$	1.17845	+	2.04113i	0.0982040	+	0.170094i
$145$	−3.01539	−	1.74094i	−0.250415	−	0.144577i
$146$	3.50604			0.290162
$147$		0			0
$148$		−	9.11960i		−	0.749627i
$149$	−20.6853	−	11.9426i	−1.69460	−	0.978380i	−0.950710	−	0.310082i	$-0.899643\pi$
$149$	−20.6853	−	11.9426i	−1.69460	−	0.978380i	−0.743894	−	0.668298i	$-0.767023\pi$
$150$	3.25860	−	1.88135i	0.266064	−	0.153612i
$151$	−12.6981	+	7.33124i	−1.03336	+	0.596608i	−0.917944	−	0.396710i	$-0.870152\pi$
$151$	−12.6981	+	7.33124i	−1.03336	+	0.596608i	−0.115411	+	0.993318i	$0.536819\pi$
$152$	−1.44504	+	2.50289i	−0.117208	+	0.203011i
$153$	13.7899			1.11484
$154$		0			0
$155$	−4.43296			−0.356064
$156$	2.06965	+	2.01913i	0.165705	+	0.161660i
$157$	−3.20775	−	5.55599i	−0.256006	−	0.443416i	0.709162	−	0.705046i	$-0.249073\pi$
$157$	−3.20775	−	5.55599i	−0.256006	−	0.443416i	−0.965168	+	0.261630i	$0.915740\pi$
$158$	−13.0646	+	7.54288i	−1.03937	+	0.600079i
$159$	−1.33513	+	2.31251i	−0.105882	+	0.183394i
$160$	0.554958			0.0438733
$161$		0			0
$162$		−	3.62565i		−	0.284858i
$163$	8.63933	+	4.98792i	0.676684	+	0.390684i	0.798605	−	0.601856i	$-0.205572\pi$
$163$	8.63933	+	4.98792i	0.676684	+	0.390684i	−0.121920	+	0.992540i	$0.538905\pi$
$164$	−4.08226	+	2.35690i	−0.318771	+	0.184043i
$165$	−0.554958	−	0.961216i	−0.0432034	−	0.0748305i
$166$	5.80194	−	10.0493i	0.450318	−	0.779973i
$167$			6.80433i			0.526535i	0.964723	+	0.263267i	$0.0848002\pi$
$167$			6.80433i			0.526535i	−0.964723	+	0.263267i	$0.915200\pi$
$168$		0			0
$169$	−11.4155	−	6.21983i	−0.878116	−	0.478449i
$170$	1.62349	−	2.81197i	0.124516	−	0.215668i
$171$	5.89904	−	3.40581i	0.451111	−	0.260449i
$172$	3.01842	+	5.22805i	0.230152	+	0.398635i
$173$	1.64310	−	2.84594i	0.124923	−	0.216373i	−0.796780	−	0.604270i	$-0.793465\pi$
$173$	1.64310	−	2.84594i	0.124923	−	0.216373i	0.921703	+	0.387897i	$0.126798\pi$
$174$			5.03146i			0.381434i
$175$		0			0
$176$			2.49396i			0.187989i
$177$	−4.54028	−	2.62133i	−0.341269	−	0.197032i
$178$	−4.44504	−	7.69904i	−0.333170	−	0.577067i
$179$	−2.92058	−	5.05860i	−0.218295	−	0.378097i	0.735992	−	0.676990i	$-0.236716\pi$
$179$	−2.92058	−	5.05860i	−0.218295	−	0.378097i	−0.954287	+	0.298893i	$0.903383\pi$
$180$	−1.13274	−	0.653989i	−0.0844297	−	0.0487455i
$181$	−10.6703			−0.793114			−0.396557	−	0.918010i	$-0.629795\pi$
$181$	−10.6703			−0.793114			−0.396557	+	0.918010i	$0.629795\pi$
$182$		0			0
$183$	−11.7802			−0.870815
$184$	−5.28088	−	3.04892i	−0.389312	−	0.224769i
$185$	2.53050	+	4.38295i	0.186046	+	0.322241i
$186$	3.20291	+	5.54760i	0.234849	+	0.406770i
$187$	12.6369	+	7.29590i	0.924099	+	0.533529i
$188$			0.246980i			0.0180128i
$189$		0			0
$190$		−	1.60388i		−	0.116357i
$191$	11.5429	−	19.9928i	0.835213	−	1.44663i	−0.0586435	−	0.998279i	$-0.518678\pi$
$191$	11.5429	−	19.9928i	0.835213	−	1.44663i	0.893857	−	0.448353i	$-0.147989\pi$
$192$	−0.400969	−	0.694498i	−0.0289374	−	0.0501211i
$193$	−11.5062	+	6.64310i	−0.828234	+	0.478181i	−0.853248	−	0.521506i	$-0.825370\pi$
$193$	−11.5062	+	6.64310i	−0.828234	+	0.478181i	0.0250136	+	0.999687i	$0.492037\pi$
$194$	4.76271	−	8.24925i	0.341943	−	0.592262i
$195$	−1.55496	−	0.396125i	−0.111353	−	0.0283671i
$196$		0			0
$197$			14.8834i			1.06040i	0.847874	+	0.530198i	$0.177883\pi$
$197$			14.8834i			1.06040i	−0.847874	+	0.530198i	$0.822117\pi$
$198$	2.93900	−	5.09050i	0.208866	−	0.361766i
$199$	3.77479	+	6.53813i	0.267588	+	0.463476i	0.968238	−	0.250029i	$-0.0804401\pi$
$199$	3.77479	+	6.53813i	0.267588	+	0.463476i	−0.700651	+	0.713505i	$0.747107\pi$
$200$	4.06341	−	2.34601i	0.287326	−	0.165888i
$201$	1.45694	+	0.841166i	0.102765	+	0.0593313i
$202$		−	2.83579i		−	0.199525i
$203$		0			0
$204$	−4.69202			−0.328507
$205$	1.30798	−	2.26549i	0.0913532	−	0.158228i
$206$	3.65448	−	2.10992i	0.254620	−	0.147005i
$207$	7.18598	+	12.4465i	0.499460	+	0.865090i
$208$	2.58082	+	2.51781i	0.178947	+	0.174579i
$209$	7.20775			0.498571
$210$		0			0
$211$	−2.69740			−0.185697			−0.0928483	−	0.995680i	$-0.529597\pi$
$211$	−2.69740			−0.185697			−0.0928483	+	0.995680i	$0.529597\pi$
$212$	−1.66487	+	2.88365i	−0.114344	+	0.198050i
$213$	−1.71320	+	0.989115i	−0.117386	+	0.0677730i
$214$	12.0459	−	6.95473i	0.823444	−	0.475416i
$215$	−2.90135	−	1.67510i	−0.197870	−	0.114241i
$216$			4.29590i			0.292299i
$217$		0			0
$218$	2.45712			0.166417
$219$	2.43494	+	1.40581i	0.164538	+	0.0949961i
$220$	−0.692021	−	1.19862i	−0.0466561	−	0.0808107i
$221$	20.3077	−	5.71128i	1.36605	−	0.384182i
$222$	3.65668	−	6.33355i	0.245420	−	0.425080i
$223$		−	2.62565i		−	0.175826i	−0.996128	−	0.0879131i	$-0.971980\pi$
$223$		−	2.62565i		−	0.175826i	0.996128	−	0.0879131i	$-0.0280198\pi$
$224$		0			0
$225$	−11.0586			−0.737240
$226$	10.1915	+	5.88404i	0.677926	+	0.391401i
$227$	7.90620	−	4.56465i	0.524753	−	0.302966i	−0.214124	−	0.976806i	$-0.568690\pi$
$227$	7.90620	−	4.56465i	0.524753	−	0.302966i	0.738877	+	0.673840i	$0.235356\pi$
$228$	−2.00716	+	1.15883i	−0.132927	+	0.0767456i
$229$	−9.27003	−	5.35205i	−0.612581	−	0.353674i	0.161394	−	0.986890i	$-0.448401\pi$
$229$	−9.27003	−	5.35205i	−0.612581	−	0.353674i	−0.773975	+	0.633216i	$0.781734\pi$
$230$	3.38404			0.223137
$231$		0			0
$232$			6.27413i			0.411917i
$233$	−3.55011	+	6.14898i	−0.232576	+	0.402833i	−0.958565	−	0.284873i	$-0.908049\pi$
$233$	−3.55011	+	6.14898i	−0.232576	+	0.402833i	0.725990	+	0.687706i	$0.241382\pi$
$234$	−2.30067	−	8.18055i	−0.150400	−	0.534779i
$235$	−0.0685317	−	0.118700i	−0.00447051	−	0.00774316i
$236$	−5.66164	−	3.26875i	−0.368541	−	0.212777i
$237$	−12.0978			−0.785839
$238$		0			0
$239$		−	15.6136i		−	1.00996i	−0.863132	−	0.504979i	$-0.831500\pi$
$239$		−	15.6136i		−	1.00996i	0.863132	−	0.504979i	$-0.168500\pi$
$240$	0.385418	+	0.222521i	0.0248786	+	0.0143637i
$241$	−14.4159	+	8.32304i	−0.928612	+	0.536134i	−0.886372	−	0.462973i	$-0.846783\pi$
$241$	−14.4159	+	8.32304i	−0.928612	+	0.536134i	−0.0422397	+	0.999108i	$0.513449\pi$
$242$	−4.13975	+	2.39008i	−0.266113	+	0.153640i
$243$	7.89762	−	13.6791i	0.506632	−	0.877513i
$244$	−14.6896			−0.940407
$245$		0			0
$246$	−3.78017			−0.241015
$247$	7.27670	−	7.45877i	0.463005	−	0.474590i
$248$	3.99396	+	6.91774i	0.253617	+	0.439277i
$249$	8.05887	−	4.65279i	0.510710	−	0.294859i
$250$	−2.68933	+	4.65806i	−0.170088	+	0.294602i
$251$	−11.9336			−0.753244			−0.376622	−	0.926367i	$-0.622914\pi$
$251$	−11.9336			−0.753244			−0.376622	+	0.926367i	$0.622914\pi$
$252$		0			0
$253$			15.2078i			0.956103i
$254$	−2.12212	−	1.22521i	−0.133154	−	0.0768765i
$255$	2.25502	−	1.30194i	0.141215	−	0.0815305i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.634375	−	1.09877i	0.0395712	−	0.0685394i	−0.845561	−	0.533878i	$-0.820734\pi$
$257$	0.634375	−	1.09877i	0.0395712	−	0.0685394i	0.885133	+	0.465339i	$0.154067\pi$
$258$			4.84117i			0.301398i
$259$		0			0
$260$	−1.93900	−	0.493959i	−0.120252	−	0.0306340i
$261$	7.39373	−	12.8063i	0.457660	−	0.792691i
$262$	−3.51693	+	2.03050i	−0.217277	+	0.125445i
$263$	−2.65279	−	4.59477i	−0.163578	−	0.283326i	0.772571	−	0.634928i	$-0.218970\pi$
$263$	−2.65279	−	4.59477i	−0.163578	−	0.283326i	−0.936149	+	0.351602i	$0.885637\pi$
$264$	−1.00000	+	1.73205i	−0.0615457	+	0.106600i
$265$		−	1.84787i		−	0.113514i
$266$		0			0
$267$		−	7.12929i		−	0.436306i
$268$	1.81678	+	1.04892i	0.110977	+	0.0640728i
$269$	−13.0097	−	22.5334i	−0.793215	−	1.37389i	−0.923967	−	0.382473i	$-0.875072\pi$
$269$	−13.0097	−	22.5334i	−0.793215	−	1.37389i	0.130752	−	0.991415i	$-0.458261\pi$
$270$	−1.19202	−	2.06464i	−0.0725441	−	0.125650i
$271$	−21.0446	−	12.1501i	−1.27837	−	0.738066i	−0.301820	−	0.953365i	$-0.597594\pi$
$271$	−21.0446	−	12.1501i	−1.27837	−	0.738066i	−0.976548	+	0.215299i	$0.930928\pi$
$272$	−5.85086			−0.354760
$273$		0			0
$274$	10.2741			0.620683
$275$	−10.1340	−	5.85086i	−0.611102	−	0.352820i
$276$	−2.44504	−	4.23494i	−0.147174	−	0.254913i
$277$	−0.939001	−	1.62640i	−0.0564191	−	0.0977208i	0.836436	−	0.548064i	$-0.184635\pi$
$277$	−0.939001	−	1.62640i	−0.0564191	−	0.0977208i	−0.892856	+	0.450343i	$0.851302\pi$
$278$	−2.76380	−	1.59568i	−0.165762	−	0.0957025i
$279$		−	18.8267i		−	1.12712i
$280$		0			0
$281$			31.9081i			1.90348i	0.306906	+	0.951740i	$0.400706\pi$
$281$			31.9081i			1.90348i	−0.306906	+	0.951740i	$0.599294\pi$
$282$	−0.0990311	+	0.171527i	−0.00589722	+	0.0102143i
$283$	−14.7681	−	25.5791i	−0.877872	−	1.52052i	−0.853672	−	0.520811i	$-0.825630\pi$
$283$	−14.7681	−	25.5791i	−0.877872	−	1.52052i	−0.0241996	−	0.999707i	$-0.507704\pi$
$284$	−2.13632	+	1.23341i	−0.126767	+	0.0731892i
$285$	0.643104	−	1.11389i	0.0380942	−	0.0659811i
$286$	2.21983	−	8.71379i	0.131261	−	0.515257i
$287$		0			0
$288$			2.35690i			0.138881i
$289$	−8.61625	+	14.9238i	−0.506838	+	0.877870i
$290$	−1.74094	−	3.01539i	−0.102231	−	0.177070i
$291$	6.61539	−	3.81940i	0.387801	−	0.223897i
$292$	3.03632	+	1.75302i	0.177687	+	0.102588i
$293$			8.69932i			0.508220i	0.967175	+	0.254110i	$0.0817825\pi$
$293$			8.69932i			0.508220i	−0.967175	+	0.254110i	$0.918218\pi$
$294$		0			0
$295$	3.62804			0.211233
$296$	4.55980	−	7.89781i	0.265033	−	0.459051i
$297$	9.27842	−	5.35690i	0.538388	−	0.310839i
$298$	−11.9426	−	20.6853i	−0.691819	−	1.19827i
$299$	15.7374	+	15.3532i	0.910117	+	0.887900i
$300$	3.76271			0.217240
$301$		0			0
$302$	−14.6625			−0.843731
$303$	1.13706	−	1.96945i	0.0653226	−	0.113142i
$304$	−2.50289	+	1.44504i	−0.143550	+	0.0828788i
$305$	7.05995	−	4.07606i	0.404252	−	0.233395i
$306$	11.9424	+	6.89493i	0.682700	+	0.394157i
$307$			26.1521i			1.49258i	0.665620	+	0.746290i	$0.268167\pi$
$307$			26.1521i			1.49258i	−0.665620	+	0.746290i	$0.731833\pi$
$308$		0			0
$309$	3.38404			0.192511
$310$	−3.83906	−	2.21648i	−0.218044	−	0.125888i
$311$	5.55496	+	9.62147i	0.314993	+	0.545583i	0.979436	−	0.201755i	$-0.0646646\pi$
$311$	5.55496	+	9.62147i	0.314993	+	0.545583i	−0.664443	+	0.747339i	$0.731331\pi$
$312$	0.782807	+	2.78345i	0.0443177	+	0.157582i
$313$	3.91335	−	6.77811i	0.221195	−	0.383122i	−0.733976	−	0.679176i	$-0.762337\pi$
$313$	3.91335	−	6.77811i	0.221195	−	0.383122i	0.955171	+	0.296054i	$0.0956708\pi$
$314$		−	6.41550i		−	0.362048i
$315$		0			0
$316$	−15.0858			−0.848640
$317$	9.83909	+	5.68060i	0.552619	+	0.319054i	0.750177	−	0.661237i	$-0.229968\pi$
$317$	9.83909	+	5.68060i	0.552619	+	0.319054i	−0.197559	+	0.980291i	$0.563301\pi$
$318$	−2.31251	+	1.33513i	−0.129679	+	0.0748701i
$319$	13.5511	−	7.82371i	0.758714	−	0.438044i
$320$	0.480608	+	0.277479i	0.0268668	+	0.0155116i
$321$	11.1545			0.622585
$322$		0			0
$323$			16.9095i			0.940868i
$324$	1.81282	−	3.13990i	0.100712	−	0.174439i
$325$	−16.2855	+	4.58009i	−0.903359	+	0.254058i
$326$	4.98792	+	8.63933i	0.276255	+	0.478488i
$327$	1.70647	+	0.985230i	0.0943679	+	0.0544833i
$328$	−4.71379			−0.260276
$329$		0			0
$330$		−	1.10992i		−	0.0610989i
$331$	17.5579	+	10.1371i	0.965070	+	0.557183i	0.897730	−	0.440547i	$-0.145215\pi$
$331$	17.5579	+	10.1371i	0.965070	+	0.557183i	0.0673402	+	0.997730i	$0.478549\pi$
$332$	10.0493	−	5.80194i	0.551524	−	0.318423i
$333$	−18.6143	+	10.7470i	−1.02006	+	0.588931i
$334$	−3.40217	+	5.89272i	−0.186158	+	0.322435i
$335$	−1.16421			−0.0636076
$336$		0			0
$337$	−18.6963			−1.01845			−0.509227	−	0.860632i	$-0.670069\pi$
$337$	−18.6963			−1.01845			−0.509227	+	0.860632i	$0.670069\pi$
$338$	−6.77620	−	11.0943i	−0.368577	−	0.603449i
$339$	4.71864	+	8.17292i	0.256281	+	0.443892i
$340$	2.81197	−	1.62349i	0.152500	−	0.0880461i
$341$	9.96077	−	17.2526i	0.539406	−	0.934279i
$342$	6.81163			0.368331
$343$		0			0
$344$			6.03684i			0.325484i
$345$	2.35021	+	1.35690i	0.126531	+	0.0730528i
$346$	2.84594	−	1.64310i	0.152999	−	0.0883338i
$347$	6.59999	+	11.4315i	0.354306	+	0.613676i	0.986999	−	0.160727i	$-0.0513838\pi$
$347$	6.59999	+	11.4315i	0.354306	+	0.613676i	−0.632693	+	0.774403i	$0.718050\pi$
$348$	−2.51573	+	4.35737i	−0.134857	+	0.233580i
$349$			33.2349i			1.77902i	0.456912	+	0.889512i	$0.348955\pi$
$349$			33.2349i			1.77902i	−0.456912	+	0.889512i	$0.651045\pi$
$350$		0			0
$351$	3.82371	−	15.0097i	0.204094	−	0.801158i
$352$	−1.24698	+	2.15983i	−0.0664642	+	0.115119i
$353$	−16.8886	+	9.75063i	−0.898889	+	0.518974i	−0.876839	−	0.480783i	$-0.840352\pi$
$353$	−16.8886	+	9.75063i	−0.898889	+	0.518974i	−0.0220491	+	0.999757i	$0.507019\pi$
$354$	−2.62133	−	4.54028i	−0.139322	−	0.241313i
$355$	0.684489	−	1.18557i	0.0363289	−	0.0629235i
$356$		−	8.89008i		−	0.471173i
$357$		0			0
$358$		−	5.84117i		−	0.308715i
$359$	−3.77991	−	2.18233i	−0.199496	−	0.115179i	0.396924	−	0.917851i	$-0.370078\pi$
$359$	−3.77991	−	2.18233i	−0.199496	−	0.115179i	−0.596420	+	0.802672i	$0.703411\pi$
$360$	−0.653989	−	1.13274i	−0.0344683	−	0.0597008i
$361$	−5.32371	−	9.22093i	−0.280195	−	0.485312i
$362$	−9.24071	−	5.33513i	−0.485681	−	0.280408i
$363$	−3.83340			−0.201201
$364$		0			0
$365$	−1.94571			−0.101843
$366$	−10.2019	−	5.89008i	−0.533263	−	0.307880i
$367$	−14.7506	−	25.5488i	−0.769976	−	1.33364i	−0.937575	−	0.347783i	$-0.886935\pi$
$367$	−14.7506	−	25.5488i	−0.769976	−	1.33364i	0.167599	−	0.985855i	$-0.446399\pi$
$368$	−3.04892	−	5.28088i	−0.158936	−	0.275285i
$369$	9.62147	+	5.55496i	0.500874	+	0.289180i
$370$			5.06100i			0.263109i
$371$		0			0
$372$			6.40581i			0.332126i
$373$	−4.94869	+	8.57138i	−0.256233	+	0.443809i	−0.965230	−	0.261403i	$-0.915815\pi$
$373$	−4.94869	+	8.57138i	−0.256233	+	0.443809i	0.708996	+	0.705212i	$0.249148\pi$
$374$	7.29590	+	12.6369i	0.377262	+	0.653437i
$375$	−3.73548	+	2.15668i	−0.192899	+	0.111370i
$376$	−0.123490	+	0.213891i	−0.00636850	+	0.0110306i
$377$	5.58450	−	21.9215i	0.287616	−	1.12902i
$378$		0			0
$379$		−	20.2935i		−	1.04241i	−0.853432	−	0.521204i	$-0.825483\pi$
$379$		−	20.2935i		−	1.04241i	0.853432	−	0.521204i	$-0.174517\pi$
$380$	0.801938	−	1.38900i	0.0411385	−	0.0712540i
$381$	−0.982542	−	1.70181i	−0.0503371	−	0.0871865i
$382$	19.9928	−	11.5429i	1.02292	−	0.590585i
$383$	14.3773	+	8.30074i	0.734646	+	0.424148i	0.820119	−	0.572192i	$-0.193907\pi$
$383$	14.3773	+	8.30074i	0.734646	+	0.424148i	−0.0854734	+	0.996340i	$0.527240\pi$
$384$		−	0.801938i		−	0.0409237i
$385$		0			0
$386$	−13.2862			−0.676250
$387$	7.11410	−	12.3220i	0.361630	−	0.626361i
$388$	8.24925	−	4.76271i	0.418792	−	0.241790i
$389$	11.2174	+	19.4292i	0.568747	+	0.985098i	0.996690	+	0.0812928i	$0.0259049\pi$
$389$	11.2174	+	19.4292i	0.568747	+	0.985098i	−0.427943	+	0.903805i	$0.640762\pi$
$390$	−1.14857	−	1.12053i	−0.0581602	−	0.0567404i
$391$	−35.6775			−1.80429
$392$		0			0
$393$	−3.25667			−0.164277
$394$	−7.44169	+	12.8894i	−0.374907	+	0.649358i
$395$	7.25033	−	4.18598i	0.364804	−	0.210620i
$396$	5.09050	−	2.93900i	0.255807	−	0.147690i
$397$	17.9073	+	10.3388i	0.898741	+	0.518888i	0.876791	−	0.480871i	$-0.159679\pi$
$397$	17.9073	+	10.3388i	0.898741	+	0.518888i	0.0219493	+	0.999759i	$0.493013\pi$
$398$			7.54958i			0.378426i
$399$		0			0
$400$	4.69202			0.234601
$401$	−27.4336	−	15.8388i	−1.36997	−	0.790951i	−0.379043	−	0.925379i	$-0.623747\pi$
$401$	−27.4336	−	15.8388i	−1.36997	−	0.790951i	−0.990923	+	0.134428i	$0.957080\pi$
$402$	0.841166	+	1.45694i	0.0419536	+	0.0726657i
$403$	−7.79736	−	27.7253i	−0.388414	−	1.38109i
$404$	1.41789	−	2.45587i	0.0705429	−	0.122184i
$405$			2.01208i			0.0999811i
$406$		0			0
$407$	−22.7439			−1.12737
$408$	−4.06341	−	2.34601i	−0.201169	−	0.116145i
$409$	6.32682	−	3.65279i	0.312841	−	0.180619i	−0.335356	−	0.942091i	$-0.608857\pi$
$409$	6.32682	−	3.65279i	0.312841	−	0.180619i	0.648197	+	0.761473i	$0.275523\pi$
$410$	2.26549	−	1.30798i	0.111884	−	0.0645965i
$411$	7.13537	+	4.11960i	0.351962	+	0.203205i
$412$	4.21983			0.207896
$413$		0			0
$414$			14.3720i			0.706343i
$415$	−3.21983	+	5.57691i	−0.158055	+	0.273760i
$416$	0.976144	+	3.47090i	0.0478594	+	0.170175i
$417$	−1.27963	−	2.21639i	−0.0626640	−	0.108537i
$418$	6.24210	+	3.60388i	0.305311	+	0.176271i
$419$	31.5381			1.54074			0.770368	−	0.637599i	$-0.220072\pi$
$419$	31.5381			1.54074			0.770368	+	0.637599i	$0.220072\pi$
$420$		0			0
$421$		−	0.359289i		−	0.0175107i	−0.999962	−	0.00875533i	$-0.997213\pi$
$421$		−	0.359289i		−	0.0175107i	0.999962	−	0.00875533i	$-0.00278694\pi$
$422$	−2.33602	−	1.34870i	−0.113715	−	0.0656536i
$423$	0.504118	−	0.291053i	0.0245111	−	0.0141515i
$424$	−2.88365	+	1.66487i	−0.140042	+	0.0808534i
$425$	13.7262	−	23.7744i	0.665817	−	1.15323i
$426$	−1.97823			−0.0958455
$427$		0			0
$428$	13.9095			0.672339
$429$	5.03563	−	5.16163i	0.243122	−	0.249206i
$430$	−1.67510	−	2.90135i	−0.0807803	−	0.139916i
$431$	−31.0259	+	17.9128i	−1.49447	+	0.862830i	−0.999980	−	0.00635609i	$-0.997977\pi$
$431$	−31.0259	+	17.9128i	−1.49447	+	0.862830i	−0.494485	+	0.869186i	$0.664643\pi$
$432$	−2.14795	+	3.72036i	−0.103343	+	0.178996i
$433$	−4.89977			−0.235468			−0.117734	−	0.993045i	$-0.537563\pi$
$433$	−4.89977			−0.235468			−0.117734	+	0.993045i	$0.537563\pi$
$434$		0			0
$435$		−	2.79225i		−	0.133878i
$436$	2.12793	+	1.22856i	0.101909	+	0.0588374i
$437$	−15.2622	+	8.81163i	−0.730089	+	0.421517i
$438$	1.40581	+	2.43494i	0.0671724	+	0.116346i
$439$	−19.5646	+	33.8870i	−0.933770	+	1.61734i	−0.156956	+	0.987606i	$0.550168\pi$
$439$	−19.5646	+	33.8870i	−0.933770	+	1.61734i	−0.776813	+	0.629731i	$0.783165\pi$
$440$		−	1.38404i		−	0.0659817i
$441$		0			0
$442$	20.4426	+	5.20775i	0.972358	+	0.247707i
$443$	0.269282	−	0.466411i	0.0127940	−	0.0221598i	−0.859558	−	0.511039i	$-0.829261\pi$
$443$	0.269282	−	0.466411i	0.0127940	−	0.0221598i	0.872352	+	0.488879i	$0.162594\pi$
$444$	6.33355	−	3.65668i	0.300577	−	0.173538i
$445$	2.46681	+	4.27264i	0.116938	+	0.202543i
$446$	1.31282	−	2.27388i	0.0621640	−	0.107671i
$447$		−	19.1545i		−	0.905978i
$448$		0			0
$449$			14.0194i			0.661615i	0.943698	+	0.330808i	$0.107321\pi$
$449$			14.0194i			0.661615i	−0.943698	+	0.330808i	$0.892679\pi$
$450$	−9.57703	−	5.52930i	−0.451466	−	0.260654i
$451$	5.87800	+	10.1810i	0.276784	+	0.479404i
$452$	5.88404	+	10.1915i	0.276762	+	0.479366i
$453$	−10.1831	−	5.87920i	−0.478442	−	0.276229i
$454$	9.12929			0.428459
$455$		0			0
$456$	−2.31767			−0.108535
$457$	1.67342	+	0.966148i	0.0782792	+	0.0451945i	0.538629	−	0.842543i	$-0.318943\pi$
$457$	1.67342	+	0.966148i	0.0782792	+	0.0451945i	−0.460350	+	0.887738i	$0.652276\pi$
$458$	−5.35205	−	9.27003i	−0.250085	−	0.433160i
$459$	12.5673	+	21.7673i	0.586593	+	1.01601i
$460$	2.93067	+	1.69202i	0.136643	+	0.0788909i
$461$			28.6926i			1.33635i	0.744005	+	0.668174i	$0.232924\pi$
$461$			28.6926i			1.33635i	−0.744005	+	0.668174i	$0.767076\pi$
$462$		0			0
$463$		−	27.7198i		−	1.28825i	−0.764922	−	0.644123i	$-0.777222\pi$
$463$		−	27.7198i		−	1.28825i	0.764922	−	0.644123i	$-0.222778\pi$
$464$	−3.13706	+	5.43355i	−0.145635	+	0.252246i
$465$	−1.77748	−	3.07868i	−0.0824286	−	0.142771i
$466$	−6.14898	+	3.55011i	−0.284846	+	0.164456i
$467$	−11.2513	+	19.4878i	−0.520648	+	0.901788i	0.479064	+	0.877780i	$0.340976\pi$
$467$	−11.2513	+	19.4878i	−0.520648	+	0.901788i	−0.999712	+	0.0240083i	$0.992357\pi$
$468$	2.09783	−	8.23490i	0.0969724	−	0.380658i
$469$		0			0
$470$		−	0.137063i		−	0.00632226i
$471$	2.57242	−	4.45556i	0.118531	−	0.205301i
$472$	−3.26875	−	5.66164i	−0.150456	−	0.260598i
$473$	13.0386	−	7.52781i	0.599513	−	0.346129i
$474$	−10.4770	−	6.04892i	−0.481226	−	0.277836i
$475$		−	13.5603i		−	0.622191i
$476$		0			0
$477$	7.84787			0.359329
$478$	7.80678	−	13.5217i	0.357074	−	0.618470i
$479$	7.43232	−	4.29105i	0.339591	−	0.196063i	−0.320500	−	0.947249i	$-0.603851\pi$
$479$	7.43232	−	4.29105i	0.339591	−	0.196063i	0.660091	+	0.751185i	$0.270518\pi$
$480$	0.222521	+	0.385418i	0.0101566	+	0.0175918i
$481$	−22.9615	+	23.5360i	−1.04695	+	1.07315i
$482$	−16.6461			−0.758209
$483$		0			0
$484$	−4.78017			−0.217280
$485$	−2.64310	+	4.57799i	−0.120017	+	0.207876i
$486$	13.6791	−	7.89762i	0.620495	−	0.358243i
$487$	−13.9400	+	8.04825i	−0.631681	+	0.364701i	−0.781403	−	0.624027i	$-0.785496\pi$
$487$	−13.9400	+	8.04825i	−0.631681	+	0.364701i	0.149722	+	0.988728i	$0.452162\pi$
$488$	−12.7216	−	7.34481i	−0.575879	−	0.332484i
$489$			8.00000i			0.361773i
$490$		0			0
$491$	−11.0382			−0.498145			−0.249073	−	0.968485i	$-0.580126\pi$
$491$	−11.0382			−0.498145			−0.249073	+	0.968485i	$0.580126\pi$
$492$	−3.27372	−	1.89008i	−0.147591	−	0.0852116i
$493$	18.3545	+	31.7909i	0.826645	+	1.43179i
$494$	10.0312	−	2.82114i	0.451325	−	0.126929i
$495$	−1.63102	+	2.82501i	−0.0733090	+	0.126975i
$496$			7.98792i			0.358668i
$497$		0			0
$498$	9.30559			0.416993
$499$	11.9340	+	6.89008i	0.534238	+	0.308443i	0.742741	−	0.669579i	$-0.233526\pi$
$499$	11.9340	+	6.89008i	0.534238	+	0.308443i	−0.208502	+	0.978022i	$0.566859\pi$
$500$	−4.65806	+	2.68933i	−0.208315	+	0.120271i
$501$	−4.72560	+	2.72832i	−0.211124	+	0.121893i
$502$	−10.3348	−	5.96681i	−0.461266	−	0.266312i
$503$	28.1823			1.25658			0.628292	−	0.777977i	$-0.283754\pi$
$503$	28.1823			1.25658			0.628292	+	0.777977i	$0.283754\pi$
$504$		0			0
$505$			1.57374i			0.0700307i
$506$	−7.60388	+	13.1703i	−0.338033	+	0.585491i
$507$	−0.257597	−	10.4220i	−0.0114403	−	0.462858i
$508$	−1.22521	−	2.12212i	−0.0543599	−	0.0941541i
$509$	−20.0776	−	11.5918i	−0.889923	−	0.513797i	−0.0160056	−	0.999872i	$-0.505095\pi$
$509$	−20.0776	−	11.5918i	−0.889923	−	0.513797i	−0.873917	+	0.486075i	$0.838428\pi$
$510$	2.60388			0.115302
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	10.7521	+	6.20775i	0.474719	+	0.274079i
$514$	1.09877	−	0.634375i	0.0484647	−	0.0279811i
$515$	−2.02808	+	1.17092i	−0.0893681	+	0.0515967i
$516$	−2.42058	+	4.19257i	−0.106560	+	0.184568i
$517$	0.615957			0.0270898
$518$		0			0
$519$	2.63533			0.115678
$520$	−1.43224	−	1.39728i	−0.0628081	−	0.0612749i
$521$	7.74578	+	13.4161i	0.339349	+	0.587770i	0.984310	−	0.176445i	$-0.0564599\pi$
$521$	7.74578	+	13.4161i	0.339349	+	0.587770i	−0.644961	+	0.764215i	$0.723127\pi$
$522$	12.8063	−	7.39373i	0.560517	−	0.323615i
$523$	20.6129	−	35.7026i	0.901339	−	1.56117i	0.0755819	−	0.997140i	$-0.475919\pi$
$523$	20.6129	−	35.7026i	0.901339	−	1.56117i	0.825757	−	0.564026i	$-0.190748\pi$
$524$	−4.06100			−0.177406
$525$		0			0
$526$		−	5.30559i		−	0.231335i
$527$	40.4747	+	23.3681i	1.76311	+	1.01793i
$528$	−1.73205	+	1.00000i	−0.0753778	+	0.0435194i
$529$	−7.09179	−	12.2833i	−0.308339	−	0.534059i
$530$	0.923936	−	1.60030i	0.0401332	−	0.0695127i
$531$			15.4082i			0.668659i
$532$		0			0
$533$	16.4698	+	4.19567i	0.713386	+	0.181735i
$534$	3.56465	−	6.17415i	0.154257	−	0.267182i
$535$	−6.68500	+	3.85958i	−0.289018	+	0.166864i
$536$	1.04892	+	1.81678i	0.0453063	+	0.0784729i
$537$	2.34213	−	4.05668i	0.101070	−	0.175059i
$538$		−	26.0194i		−	1.12178i
$539$		0			0
$540$		−	2.38404i		−	0.102593i
$541$	7.66392	+	4.42476i	0.329497	+	0.190235i	0.655618	−	0.755093i	$-0.272408\pi$
$541$	7.66392	+	4.42476i	0.329497	+	0.190235i	−0.326121	+	0.945328i	$0.605742\pi$
$542$	−12.1501	−	21.0446i	−0.521892	−	0.903943i
$543$	−4.27844	−	7.41047i	−0.183605	−	0.318014i
$544$	−5.06699	−	2.92543i	−0.217245	−	0.125427i
$545$	−1.36360			−0.0584102
$546$		0			0
$547$	21.6329			0.924958			0.462479	−	0.886630i	$-0.346960\pi$
$547$	21.6329			0.924958			0.462479	+	0.886630i	$0.346960\pi$
$548$	8.89765	+	5.13706i	0.380089	+	0.219444i
$549$	17.3110	+	29.9835i	0.738814	+	1.27966i
$550$	−5.85086	−	10.1340i	−0.249481	−	0.432114i
$551$	15.7034	+	9.06638i	0.668988	+	0.386241i
$552$		−	4.89008i		−	0.208136i
$553$		0			0
$554$		−	1.87800i		−	0.0797887i
$555$	−2.02930	+	3.51486i	−0.0861391	+	0.149197i
$556$	−1.59568	−	2.76380i	−0.0676719	−	0.117211i
$557$	−21.5848	+	12.4620i	−0.914576	+	0.528031i	−0.881901	−	0.471436i	$-0.843736\pi$
$557$	−21.5848	+	12.4620i	−0.914576	+	0.528031i	−0.0326751	+	0.999466i	$0.510403\pi$
$558$	9.41335	−	16.3044i	0.398499	−	0.690220i
$559$	5.37329	−	21.0925i	0.227266	−	0.892116i
$560$		0			0
$561$			11.7017i			0.494047i
$562$	−15.9541	+	27.6333i	−0.672982	+	1.16564i
$563$	12.0305	+	20.8374i	0.507025	+	0.878193i	0.999967	+	0.00813097i	$0.00258820\pi$
$563$	12.0305	+	20.8374i	0.507025	+	0.878193i	−0.492942	+	0.870062i	$0.664078\pi$
$564$	−0.171527	+	0.0990311i	−0.00722259	+	0.00416996i
$565$	−5.65583	−	3.26540i	−0.237943	−	0.137376i
$566$		−	29.5362i		−	1.24150i
$567$		0			0
$568$	−2.46681			−0.103505
$569$	16.8470	−	29.1798i	0.706262	−	1.22328i	−0.259973	−	0.965616i	$-0.583714\pi$
$569$	16.8470	−	29.1798i	0.706262	−	1.22328i	0.966234	−	0.257665i	$-0.0829532\pi$
$570$	1.11389	−	0.643104i	0.0466557	−	0.0269367i
$571$	−2.19083	−	3.79462i	−0.0916832	−	0.158800i	0.816536	−	0.577294i	$-0.195891\pi$
$571$	−2.19083	−	3.79462i	−0.0916832	−	0.158800i	−0.908219	+	0.418494i	$0.862558\pi$
$572$	6.27933	−	6.43645i	0.262552	−	0.269121i
$573$	18.5133			0.773406
$574$		0			0
$575$	28.6112			1.19317
$576$	−1.17845	+	2.04113i	−0.0491020	+	0.0850472i
$577$	−31.3254	+	18.0858i	−1.30410	+	0.752920i	−0.981104	−	0.193482i	$-0.938022\pi$
$577$	−31.3254	+	18.0858i	−1.30410	+	0.752920i	−0.322991	+	0.946402i	$0.604689\pi$
$578$	−14.9238	+	8.61625i	−0.620748	+	0.358389i
$579$	−9.22725	−	5.32736i	−0.383471	−	0.221397i
$580$		−	3.48188i		−	0.144577i
$581$		0			0
$582$	7.63879			0.316638
$583$	7.19170	+	4.15213i	0.297850	+	0.171964i
$584$	1.75302	+	3.03632i	0.0725405	+	0.125644i
$585$	1.27678	+	4.53986i	0.0527882	+	0.187700i
$586$	−4.34966	+	7.53383i	−0.179683	+	0.311220i
$587$			35.0616i			1.44715i	0.690248	+	0.723573i	$0.257502\pi$
$587$			35.0616i			1.44715i	−0.690248	+	0.723573i	$0.742498\pi$
$588$		0			0
$589$	23.0858			0.951232
$590$	3.14197	+	1.81402i	0.129353	+	0.0746820i
$591$	−10.3365	+	5.96777i	−0.425186	+	0.245481i
$592$	7.89781	−	4.55980i	0.324598	−	0.187407i
$593$	−21.1444	−	12.2078i	−0.868298	−	0.501312i	−0.00151591	−	0.999999i	$-0.500483\pi$
$593$	−21.1444	−	12.2078i	−0.868298	−	0.501312i	−0.866782	+	0.498687i	$0.833816\pi$
$594$	10.7138			0.439592
$595$		0			0
$596$		−	23.8853i		−	0.978380i
$597$	−3.02715	+	5.24317i	−0.123893	+	0.214589i
$598$	5.95237	+	21.1650i	0.243410	+	0.865500i
$599$	−16.3002	−	28.2328i	−0.666008	−	1.15356i	−0.979011	−	0.203808i	$-0.934668\pi$
$599$	−16.3002	−	28.2328i	−0.666008	−	1.15356i	0.313002	−	0.949752i	$-0.398665\pi$
$600$	3.25860	+	1.88135i	0.133032	+	0.0768060i
$601$	−15.9989			−0.652610			−0.326305	−	0.945265i	$-0.605804\pi$
$601$	−15.9989			−0.652610			−0.326305	+	0.945265i	$0.605804\pi$
$602$		0			0
$603$		−	4.94438i		−	0.201351i
$604$	−12.6981	−	7.33124i	−0.516678	−	0.298304i
$605$	2.29739	−	1.32640i	0.0934020	−	0.0539257i
$606$	1.96945	−	1.13706i	0.0800035	−	0.0461900i
$607$	8.79656	−	15.2361i	0.357041	−	0.618414i	−0.630424	−	0.776251i	$-0.717119\pi$
$607$	8.79656	−	15.2361i	0.357041	−	0.618414i	0.987465	+	0.157837i	$0.0504522\pi$
$608$	−2.89008			−0.117208
$609$		0			0
$610$	8.15213			0.330070
$611$	0.621849	−	0.637409i	0.0251573	−	0.0257868i
$612$	6.89493	+	11.9424i	0.278711	+	0.482742i
$613$	−14.8635	+	8.58144i	−0.600331	+	0.346601i	−0.769172	−	0.639042i	$-0.779331\pi$
$613$	−14.8635	+	8.58144i	−0.600331	+	0.346601i	0.168841	+	0.985643i	$0.445998\pi$
$614$	−13.0761	+	22.6484i	−0.527707	+	0.914015i
$615$	2.09783			0.0845929
$616$		0			0
$617$		−	29.5797i		−	1.19083i	−0.803417	−	0.595417i	$-0.796987\pi$
$617$		−	29.5797i		−	1.19083i	0.803417	−	0.595417i	$-0.203013\pi$
$618$	2.93067	+	1.69202i	0.117889	+	0.0680631i
$619$	30.5076	−	17.6136i	1.22620	−	0.707949i	0.259970	−	0.965617i	$-0.416287\pi$
$619$	30.5076	−	17.6136i	1.22620	−	0.707949i	0.966234	+	0.257668i	$0.0829540\pi$
$620$	−2.21648	−	3.83906i	−0.0890160	−	0.154180i
$621$	−13.0978	+	22.6861i	−0.525598	+	0.910362i
$622$			11.1099i			0.445467i
$623$		0			0
$624$	−0.713792	+	2.80194i	−0.0285745	+	0.112167i
$625$	−10.2376	+	17.7320i	−0.409503	+	0.709281i
$626$	6.77811	−	3.91335i	0.270908	−	0.156409i
$627$	2.89008	+	5.00577i	0.115419	+	0.199911i
$628$	3.20775	−	5.55599i	0.128003	−	0.221708i
$629$		−	53.3575i		−	2.12750i
$630$		0			0
$631$		−	9.55065i		−	0.380205i	−0.981764	−	0.190103i	$-0.939118\pi$
$631$		−	9.55065i		−	0.380205i	0.981764	−	0.190103i	$-0.0608821\pi$
$632$	−13.0646	−	7.54288i	−0.519684	−	0.300040i
$633$	−1.08157	−	1.87334i	−0.0429887	−	0.0744585i
$634$	5.68060	+	9.83909i	0.225606	+	0.390760i
$635$	1.17769	+	0.679940i	0.0467352	+	0.0269826i
$636$	−2.67025			−0.105882
$637$		0			0
$638$	15.6474			0.619487
$639$	5.03509	+	2.90701i	0.199185	+	0.115000i
$640$	0.277479	+	0.480608i	0.0109683	+	0.0189977i
$641$	10.6957	+	18.5254i	0.422454	+	0.731711i	0.996179	−	0.0873368i	$-0.0278356\pi$
$641$	10.6957	+	18.5254i	0.422454	+	0.731711i	−0.573725	+	0.819048i	$0.694502\pi$
$642$	9.66010	+	5.57726i	0.381254	+	0.220117i
$643$		−	4.05429i		−	0.159886i	−0.996799	−	0.0799429i	$-0.974526\pi$
$643$		−	4.05429i		−	0.159886i	0.996799	−	0.0799429i	$-0.0254738\pi$
$644$		0			0
$645$		−	2.68664i		−	0.105787i
$646$	−8.45473	+	14.6440i	−0.332647	+	0.576161i
$647$	13.9366	+	24.1389i	0.547905	+	0.948999i	0.998418	+	0.0562289i	$0.0179077\pi$
$647$	13.9366	+	24.1389i	0.547905	+	0.948999i	−0.450513	+	0.892770i	$0.648759\pi$
$648$	3.13990	−	1.81282i	0.123347	−	0.0712144i
$649$	−8.15213	+	14.1199i	−0.319999	+	0.554255i
$650$	−16.3937	−	4.17629i	−0.643015	−	0.163808i
$651$		0			0
$652$			9.97584i			0.390684i
$653$	−4.73556	+	8.20223i	−0.185317	+	0.320978i	−0.943683	−	0.330850i	$-0.892664\pi$
$653$	−4.73556	+	8.20223i	−0.185317	+	0.320978i	0.758366	+	0.651829i	$0.225998\pi$
$654$	0.985230	+	1.70647i	0.0385255	+	0.0667282i
$655$	1.95175	−	1.12684i	0.0762611	−	0.0440294i
$656$	−4.08226	−	2.35690i	−0.159386	−	0.0920213i
$657$		−	8.26337i		−	0.322385i
$658$		0			0
$659$	1.29829			0.0505742			0.0252871	−	0.999680i	$-0.491950\pi$
$659$	1.29829			0.0505742			0.0252871	+	0.999680i	$0.491950\pi$
$660$	0.554958	−	0.961216i	0.0216017	−	0.0374153i
$661$	−9.38292	+	5.41723i	−0.364953	+	0.210706i	−0.671251	−	0.741230i	$-0.734243\pi$
$661$	−9.38292	+	5.41723i	−0.364953	+	0.210706i	0.306298	+	0.951936i	$0.400910\pi$
$662$	10.1371	+	17.5579i	0.393988	+	0.682408i
$663$	12.1092	+	11.8136i	0.470284	+	0.458804i
$664$	11.6039			0.450318
$665$		0			0
$666$	−21.4940			−0.832874
$667$	−19.1293	+	33.1329i	−0.740689	+	1.28291i
$668$	−5.89272	+	3.40217i	−0.227996	+	0.131634i
$669$	1.82351	−	1.05280i	0.0705008	−	0.0407037i
$670$	−1.00824	−	0.582105i	−0.0389515	−	0.0224887i
$671$			36.6353i			1.41429i
$672$		0			0
$673$	17.8025			0.686237			0.343119	−	0.939292i	$-0.388517\pi$
$673$	17.8025			0.686237			0.343119	+	0.939292i	$0.388517\pi$
$674$	−16.1915	−	9.34817i	−0.623673	−	0.360078i
$675$	−10.0782	−	17.4560i	−0.387911	−	0.671881i
$676$	−0.321218	−	12.9960i	−0.0123545	−	0.499847i
$677$	−17.0640	+	29.5557i	−0.655822	+	1.13592i	0.325865	+	0.945416i	$0.394345\pi$
$677$	−17.0640	+	29.5557i	−0.655822	+	1.13592i	−0.981687	+	0.190501i	$0.938989\pi$
$678$			9.43727i			0.362436i
$679$		0			0
$680$	3.24698			0.124516
$681$	6.34028	+	3.66056i	0.242960	+	0.140273i
$682$	17.2526	−	9.96077i	0.660635	−	0.381418i
$683$	20.3434	−	11.7453i	0.778417	−	0.449420i	−0.0574517	−	0.998348i	$-0.518298\pi$
$683$	20.3434	−	11.7453i	0.778417	−	0.449420i	0.835869	+	0.548929i	$0.184964\pi$
$684$	5.89904	+	3.40581i	0.225555	+	0.130225i
$685$	−5.70171			−0.217851
$686$		0			0
$687$		−	8.58402i		−	0.327501i
$688$	−3.01842	+	5.22805i	−0.115076	+	0.199318i
$689$	11.5572	−	3.25032i	0.440295	−	0.123827i
$690$	1.35690	+	2.35021i	0.0516561	+	0.0894711i
$691$	20.7898	+	12.0030i	0.790880	+	0.456615i	0.840272	−	0.542164i	$-0.182395\pi$
$691$	20.7898	+	12.0030i	0.790880	+	0.456615i	−0.0493920	+	0.998779i	$0.515728\pi$
$692$	3.28621			0.124923
$693$		0			0
$694$			13.2000i			0.501064i
$695$	1.53379	+	0.885535i	0.0581800	+	0.0335903i
$696$	−4.35737	+	2.51573i	−0.165166	+	0.0953585i
$697$	−23.8847	+	13.7899i	−0.904699	+	0.522328i
$698$	−16.6174	+	28.7823i	−0.628980	+	1.08942i
$699$	−5.69394			−0.215365
$700$		0			0
$701$	3.28621			0.124118			0.0620592	−	0.998072i	$-0.480233\pi$
$701$	3.28621			0.124118			0.0620592	+	0.998072i	$0.480233\pi$
$702$	10.8163	−	11.0869i	0.408234	−	0.418449i
$703$	−13.1782	−	22.8253i	−0.497026	−	0.860874i
$704$	−2.15983	+	1.24698i	−0.0814017	+	0.0469973i
$705$	0.0549581	−	0.0951903i	0.00206984	−	0.00358507i
$706$	−19.5013			−0.733939
$707$		0			0
$708$		−	5.24267i		−	0.197032i
$709$	−20.6278	−	11.9095i	−0.774693	−	0.447269i	0.0598532	−	0.998207i	$-0.480937\pi$
$709$	−20.6278	−	11.9095i	−0.774693	−	0.447269i	−0.834546	+	0.550938i	$0.814270\pi$
$710$	1.18557	−	0.684489i	0.0444936	−	0.0256884i
$711$	17.7778	+	30.7920i	0.666719	+	1.15479i
$712$	4.44504	−	7.69904i	0.166585	−	0.288534i
$713$			48.7090i			1.82417i
$714$		0			0
$715$	−1.23191	+	4.83579i	−0.0460710	+	0.180848i
$716$	2.92058	−	5.05860i	0.109147	−	0.189049i
$717$	10.8436	−	6.26055i	0.404962	−	0.233805i
$718$	−2.18233	−	3.77991i	−0.0814439	−	0.141065i
$719$	16.9172	−	29.3015i	0.630906	−	1.09276i	−0.356461	−	0.934310i	$-0.616017\pi$
$719$	16.9172	−	29.3015i	0.630906	−	1.09276i	0.987367	−	0.158451i	$-0.0506501\pi$
$720$		−	1.30798i		−	0.0487455i
$721$		0			0
$722$		−	10.6474i		−	0.396256i
$723$	−11.5607	−	6.67456i	−0.429946	−	0.248230i
$724$	−5.33513	−	9.24071i	−0.198278	−	0.343428i
$725$	−14.7192	−	25.4943i	−0.546656	−	0.946836i
$726$	−3.31982	−	1.91670i	−0.123210	−	0.0711353i
$727$	−19.3163			−0.716403			−0.358202	−	0.933644i	$-0.616610\pi$
$727$	−19.3163			−0.716403			−0.358202	+	0.933644i	$0.616610\pi$
$728$		0			0
$729$	1.78986			0.0662910
$730$	−1.68503	−	0.972853i	−0.0623658	−	0.0360069i
$731$	17.6603	+	30.5886i	0.653191	+	1.13136i
$732$	−5.89008	−	10.2019i	−0.217704	−	0.377074i
$733$	14.0233	+	8.09634i	0.517962	+	0.299045i	0.736100	−	0.676873i	$-0.236665\pi$
$733$	14.0233	+	8.09634i	0.517962	+	0.299045i	−0.218139	+	0.975918i	$0.569999\pi$
$734$		−	29.5013i		−	1.08891i
$735$		0			0
$736$		−	6.09783i		−	0.224769i
$737$	2.61596	−	4.53097i	0.0963600	−	0.166900i
$738$	5.55496	+	9.62147i	0.204481	+	0.354171i
$739$	−29.2075	+	16.8629i	−1.07441	+	0.620313i	−0.929384	−	0.369114i	$-0.879661\pi$
$739$	−29.2075	+	16.8629i	−1.07441	+	0.620313i	−0.145030	+	0.989427i	$0.546328\pi$
$740$	−2.53050	+	4.38295i	−0.0930230	+	0.161121i
$741$	8.09783	+	2.06292i	0.297481	+	0.0757832i
$742$		0			0
$743$		−	32.5512i		−	1.19419i	−0.802171	−	0.597095i	$-0.796322\pi$
$743$		−	32.5512i		−	1.19419i	0.802171	−	0.597095i	$-0.203678\pi$
$744$	−3.20291	+	5.54760i	−0.117424	+	0.203385i
$745$	6.62767	+	11.4795i	0.242819	+	0.420575i
$746$	−8.57138	+	4.94869i	−0.313821	+	0.181184i
$747$	−23.6850	−	13.6746i	−0.866590	−	0.500326i
$748$			14.5918i			0.533529i
$749$		0			0
$750$	−4.31336			−0.157501
$751$	−20.8780	+	36.1618i	−0.761849	+	1.31956i	0.180047	+	0.983658i	$0.442375\pi$
$751$	−20.8780	+	36.1618i	−0.761849	+	1.31956i	−0.941896	+	0.335903i	$0.890958\pi$
$752$	−0.213891	+	0.123490i	−0.00779979	+	0.00450321i
$753$	−4.78501	−	8.28788i	−0.174376	−	0.302027i
$754$	15.7971	−	16.1924i	0.575296	−	0.589691i
$755$	8.13706			0.296138
$756$		0			0
$757$	29.9603			1.08893			0.544463	−	0.838785i	$-0.316734\pi$
$757$	29.9603			1.08893			0.544463	+	0.838785i	$0.316734\pi$
$758$	10.1468	−	17.5747i	0.368547	−	0.638341i
$759$	−10.5618	+	6.09783i	−0.383368	+	0.221337i
$760$	1.38900	−	0.801938i	0.0503842	−	0.0290893i
$761$	45.5040	+	26.2717i	1.64952	+	0.952350i	0.977263	+	0.212030i	$0.0680073\pi$
$761$	45.5040	+	26.2717i	1.64952	+	0.952350i	0.672255	+	0.740320i	$0.265326\pi$
$762$		−	1.96508i		−	0.0711875i
$763$		0			0
$764$	23.0858			0.835213
$765$	−6.62751	−	3.82640i	−0.239618	−	0.138344i
$766$	8.30074	+	14.3773i	0.299918	+	0.519473i
$767$	6.38154	+	22.6910i	0.230424	+	0.819325i
$768$	0.400969	−	0.694498i	0.0144687	−	0.0250606i
$769$		−	2.92021i		−	0.105306i	−0.998613	−	0.0526528i	$-0.983232\pi$
$769$		−	2.92021i		−	0.105306i	0.998613	−	0.0526528i	$-0.0167677\pi$
$770$		0			0
$771$	1.01746			0.0366429
$772$	−11.5062	−	6.64310i	−0.414117	−	0.239091i
$773$	−5.06118	+	2.92208i	−0.182038	+	0.105100i	−0.588250	−	0.808679i	$-0.700183\pi$
$773$	−5.06118	+	2.92208i	−0.182038	+	0.105100i	0.406212	+	0.913779i	$0.366850\pi$
$774$	12.3220	−	7.11410i	0.442904	−	0.255711i
$775$	−32.4582	−	18.7397i	−1.16593	−	0.673151i
$776$	9.52542			0.341943
$777$		0			0
$778$			22.4349i			0.804329i
$779$	−6.81163	+	11.7981i	−0.244052	+	0.422710i
$780$	−0.434425	−	1.54470i	−0.0155549	−	0.0553090i
$781$	3.07606	+	5.32790i	0.110070	+	0.190647i
$782$	−30.8977	−	17.8388i	−1.10490	−	0.637913i
$783$	26.9530			0.963222
$784$		0			0
$785$			3.56033i			0.127074i
$786$	−2.82036	−	1.62833i	−0.100599	−	0.0580808i
$787$	30.5639	−	17.6461i	1.08949	−	0.629015i	0.156047	−	0.987750i	$-0.450125\pi$
$787$	30.5639	−	17.6461i	1.08949	−	0.629015i	0.933440	+	0.358735i	$0.116792\pi$
$788$	−12.8894	+	7.44169i	−0.459165	+	0.265099i
$789$	2.12737	−	3.68472i	0.0757365	−	0.131180i
$790$	8.37196			0.297861
$791$		0			0
$792$	5.87800			0.208866
$793$	37.9112	+	36.9858i	1.34627	+	1.31340i
$794$	10.3388	+	17.9073i	0.366909	+	0.635506i
$795$	1.28334	−	0.740939i	0.0455155	−	0.0262784i
$796$	−3.77479	+	6.53813i	−0.133794	+	0.231738i
$797$	35.4228			1.25474			0.627370	−	0.778721i	$-0.284131\pi$
$797$	35.4228			1.25474			0.627370	+	0.778721i	$0.284131\pi$
$798$		0			0
$799$			1.44504i			0.0511219i
$800$	4.06341	+	2.34601i	0.143663	+	0.0829440i
$801$	−18.1458	+	10.4765i	−0.641151	+	0.370169i
$802$	−15.8388	−	27.4336i	−0.559287	−	0.968713i
$803$	4.37196	−	7.57246i	0.154283	−	0.267226i
$804$			1.68233i			0.0593313i
$805$		0			0
$806$	7.10992	−	27.9095i	0.250436	−	0.983069i
$807$	10.4330	−	18.0704i	0.367258	−	0.636109i
$808$	2.45587	−	1.41789i	0.0863971	−	0.0498814i
$809$	−0.0199098	−	0.0344848i	−0.000699992	−	0.00121242i	0.865675	−	0.500606i	$-0.166889\pi$
$809$	−0.0199098	−	0.0344848i	−0.000699992	−	0.00121242i	−0.866375	+	0.499394i	$0.833556\pi$
$810$	−1.00604	+	1.74251i	−0.0353487	+	0.0612257i
$811$		−	16.4638i		−	0.578123i	−0.957310	−	0.289062i	$-0.906657\pi$
$811$		−	16.4638i		−	0.578123i	0.957310	−	0.289062i	$-0.0933432\pi$
$812$		0			0
$813$		−	19.4873i		−	0.683448i
$814$	−19.6968	−	11.3720i	−0.690373	−	0.398587i
$815$	−2.76809	−	4.79447i	−0.0969618	−	0.167943i
$816$	−2.34601	−	4.06341i	−0.0821268	−	0.142248i
$817$	15.1095	+	8.72348i	0.528615	+	0.305196i
$818$	7.30559			0.255434
$819$		0			0
$820$	2.61596			0.0913532
$821$	−11.0584	−	6.38458i	−0.385941	−	0.222823i	0.294459	−	0.955664i	$-0.404861\pi$
$821$	−11.0584	−	6.38458i	−0.385941	−	0.222823i	−0.680400	+	0.732841i	$0.738194\pi$
$822$	4.11960	+	7.13537i	0.143688	+	0.248874i
$823$	−10.1468	−	17.5747i	−0.353694	−	0.612615i	0.633200	−	0.773988i	$-0.281741\pi$
$823$	−10.1468	−	17.5747i	−0.353694	−	0.612615i	−0.986893	+	0.161373i	$0.948408\pi$
$824$	3.65448	+	2.10992i	0.127310	+	0.0735024i
$825$		−	9.38404i		−	0.326710i
$826$		0			0
$827$			27.4711i			0.955265i	0.878560	+	0.477632i	$0.158505\pi$
$827$			27.4711i			0.955265i	−0.878560	+	0.477632i	$0.841495\pi$
$828$	−7.18598	+	12.4465i	−0.249730	+	0.432545i
$829$	−15.3545	−	26.5948i	−0.533284	−	0.923675i	−0.999244	−	0.0388693i	$-0.987624\pi$
$829$	−15.3545	−	26.5948i	−0.533284	−	0.923675i	0.465960	−	0.884806i	$-0.345709\pi$
$830$	−5.57691	+	3.21983i	−0.193577	+	0.111762i
$831$	0.753020	−	1.30427i	0.0261220	−	0.0452446i
$832$	−0.890084	+	3.49396i	−0.0308581	+	0.121131i
$833$		0			0
$834$		−	2.55927i		−	0.0886203i
$835$	1.88806	−	3.27021i	0.0653390	−	0.113170i
$836$	3.60388	+	6.24210i	0.124643	+	0.215887i
$837$	29.7179	−	17.1576i	1.02720	−	0.593055i
$838$	27.3128	+	15.7690i	0.943505	+	0.544733i
$839$		−	42.5991i		−	1.47068i	−0.677696	−	0.735342i	$-0.737022\pi$
$839$		−	42.5991i		−	1.47068i	0.677696	−	0.735342i	$-0.262978\pi$
$840$		0			0
$841$	10.3647			0.357402
$842$	0.179644	−	0.311153i	0.00619095	−	0.0107230i
$843$	−22.1601	+	12.7942i	−0.763236	+	0.440655i
$844$	−1.34870	−	2.33602i	−0.0464241	−	0.0804090i
$845$	3.76051	+	6.15686i	0.129365	+	0.211803i
$846$	0.582105			0.0200132
$847$		0			0
$848$	−3.32975			−0.114344
$849$	11.8431	−	20.5128i	0.406454	−	0.703998i
$850$	23.7744	−	13.7262i	0.815456	−	0.470804i
$851$	48.1595	−	27.8049i	1.65089	−	0.953140i
$852$	−1.71320	−	0.989115i	−0.0586932	−	0.0338865i
$853$			39.2524i			1.34398i	0.740562	+	0.671988i	$0.234559\pi$
$853$			39.2524i			1.34398i	−0.740562	+	0.671988i	$0.765441\pi$
$854$		0			0
$855$	−3.78017			−0.129279
$856$	12.0459	+	6.95473i	0.411722	+	0.237708i
$857$	−2.56033	−	4.43463i	−0.0874594	−	0.151484i	0.818977	−	0.573826i	$-0.194541\pi$
$857$	−2.56033	−	4.43463i	−0.0874594	−	0.151484i	−0.906437	+	0.422342i	$0.861208\pi$
$858$	6.94180	−	1.95229i	0.236989	−	0.0666500i
$859$	1.14310	−	1.97991i	0.0390022	−	0.0675538i	−0.845865	−	0.533396i	$-0.820915\pi$
$859$	1.14310	−	1.97991i	0.0390022	−	0.0675538i	0.884868	+	0.465843i	$0.154249\pi$
$860$		−	3.35019i		−	0.114241i
$861$		0			0
$862$	−35.8256			−1.22023
$863$	32.1726	+	18.5749i	1.09517	+	0.632296i	0.934948	−	0.354785i	$-0.115446\pi$
$863$	32.1726	+	18.5749i	1.09517	+	0.632296i	0.160221	+	0.987081i	$0.448779\pi$
$864$	−3.72036	+	2.14795i	−0.126569	+	0.0730747i
$865$	−1.57938	+	0.911854i	−0.0537004	+	0.0310040i
$866$	−4.24333	−	2.44989i	−0.144194	−	0.0832505i
$867$	−13.8194			−0.469331
$868$		0			0
$869$			37.6233i			1.27628i
$870$	1.39612	−	2.41816i	0.0473331	−	0.0819833i
$871$	−2.04779	−	7.28137i	−0.0693867	−	0.246720i
$872$	1.22856	+	2.12793i	0.0416043	+	0.0720608i
$873$	−19.4426	−	11.2252i	−0.658033	−	0.379916i
$874$	−17.6233			−0.596115
$875$		0			0
$876$			2.81163i			0.0949961i
$877$	−1.16672	−	0.673604i	−0.0393972	−	0.0227460i	0.480172	−	0.877174i	$-0.340574\pi$
$877$	−1.16672	−	0.673604i	−0.0393972	−	0.0227460i	−0.519569	+	0.854428i	$0.673908\pi$
$878$	−33.8870	+	19.5646i	−1.14363	+	0.660275i
$879$	−6.04166	+	3.48816i	−0.203780	+	0.117653i
$880$	0.692021	−	1.19862i	0.0233280	−	0.0404053i
$881$	−29.5157			−0.994410			−0.497205	−	0.867633i	$-0.665640\pi$
$881$	−29.5157			−0.994410			−0.497205	+	0.867633i	$0.665640\pi$
$882$		0			0
$883$	−16.0968			−0.541699			−0.270850	−	0.962622i	$-0.587305\pi$
$883$	−16.0968			−0.541699			−0.270850	+	0.962622i	$0.587305\pi$
$884$	15.1000	+	14.7314i	0.507867	+	0.495470i
$885$	1.45473	+	2.51967i	0.0489002	+	0.0846977i
$886$	0.466411	−	0.269282i	0.0156694	−	0.00904672i
$887$	−11.8116	+	20.4583i	−0.396596	+	0.686924i	−0.993303	−	0.115535i	$-0.963142\pi$
$887$	−11.8116	+	20.4583i	−0.396596	+	0.686924i	0.596708	+	0.802459i	$0.296475\pi$
$888$	7.31336			0.245420
$889$		0			0
$890$			4.93362i			0.165375i
$891$	−7.83079	−	4.52111i	−0.262341	−	0.151463i
$892$	2.27388	−	1.31282i	0.0761350	−	0.0439566i
$893$	0.356896	+	0.618162i	0.0119431	+	0.0206860i
$894$	9.57726	−	16.5883i	0.320312	−	0.554796i
$895$			3.24160i			0.108355i
$896$		0			0
$897$	−4.35258	+	17.0858i	−0.145329	+	0.570477i
$898$	−7.00969	+	12.1411i	−0.233916	+	0.405155i
$899$	43.4028	−	25.0586i	1.44756	−	0.835751i
$900$	−5.52930	−	9.57703i	−0.184310	−	0.319234i
$901$	−9.74094	+	16.8718i	−0.324518	+	0.562081i
$902$			11.7560i			0.391432i
$903$		0			0
$904$			11.7681i			0.391401i
$905$	5.12821	+	2.96077i	0.170467	+	0.0984194i
$906$	−5.87920	−	10.1831i	−0.195323	−	0.338310i
$907$	12.7927	+	22.1576i	0.424774	+	0.735730i	0.996399	−	0.0847848i	$-0.0270203\pi$
$907$	12.7927	+	22.1576i	0.424774	+	0.735730i	−0.571625	+	0.820515i	$0.693687\pi$
$908$	7.90620	+	4.56465i	0.262376	+	0.151483i
$909$	−6.68366			−0.221683
$910$		0			0
$911$	−51.8732			−1.71864			−0.859318	−	0.511441i	$-0.829112\pi$
$911$	−51.8732			−1.71864			−0.859318	+	0.511441i	$0.829112\pi$
$912$	−2.00716	−	1.15883i	−0.0664637	−	0.0383728i
$913$	−14.4698	−	25.0624i	−0.478880	−	0.829445i
$914$	0.966148	+	1.67342i	0.0319573	+	0.0553517i
$915$	5.66164	+	3.26875i	0.187168	+	0.108062i
$916$		−	10.7041i		−	0.353674i
$917$		0			0
$918$			25.1347i			0.829568i
$919$	9.79954	−	16.9733i	0.323257	−	0.559898i	−0.657901	−	0.753104i	$-0.728555\pi$
$919$	9.79954	−	16.9733i	0.323257	−	0.559898i	0.981158	+	0.193207i	$0.0618888\pi$
$920$	1.69202	+	2.93067i	0.0557843	+	0.0966212i
$921$	−18.1626	+	10.4862i	−0.598478	+	0.345532i
$922$	−14.3463	+	24.8485i	−0.472470	+	0.818343i
$923$	8.61894	+	2.19567i	0.283696	+	0.0722713i
$924$		0			0
$925$			42.7894i			1.40691i
$926$	13.8599	−	24.0060i	0.455464	−	0.788887i
$927$	−4.97285	−	8.61323i	−0.163330	−	0.282896i
$928$	−5.43355	+	3.13706i	−0.178365	+	0.102979i
$929$	3.03218	+	1.75063i	0.0994825	+	0.0574362i	0.548916	−	0.835878i	$-0.315041\pi$
$929$	3.03218	+	1.75063i	0.0994825	+	0.0574362i	−0.449433	+	0.893314i	$0.648374\pi$
$930$		−	3.55496i		−	0.116572i
$931$		0			0
$932$	−7.10023			−0.232576
$933$	−4.45473	+	7.71582i	−0.145841	+	0.252605i
$934$	−19.4878	+	11.2513i	−0.637661	+	0.368154i
$935$	−4.04892	−	7.01293i	−0.132414	−	0.229347i
$936$	5.93423	−	6.08271i	0.193966	−	0.198820i
$937$	12.9129			0.421847			0.210923	−	0.977503i	$-0.432353\pi$
$937$	12.9129			0.421847			0.210923	+	0.977503i	$0.432353\pi$
$938$		0			0
$939$	6.27652			0.204826
$940$	0.0685317	−	0.118700i	0.00223526	−	0.00387158i
$941$	6.76133	−	3.90366i	0.220413	−	0.127256i	−0.385728	−	0.922612i	$-0.626050\pi$
$941$	6.76133	−	3.90366i	0.220413	−	0.127256i	0.606142	+	0.795357i	$0.292716\pi$
$942$	4.45556	−	2.57242i	0.145170	−	0.0838139i
$943$	−24.8930	−	14.3720i	−0.810627	−	0.468015i
$944$		−	6.53750i		−	0.212777i
$945$		0			0
$946$	15.0556			0.489500
$947$	16.6889	+	9.63533i	0.542316	+	0.313106i	0.746017	−	0.665927i	$-0.231964\pi$
$947$	16.6889	+	9.63533i	0.542316	+	0.313106i	−0.203701	+	0.979033i	$0.565297\pi$
$948$	−6.04892	−	10.4770i	−0.196460	−	0.340278i
$949$	−3.42240	−	12.1691i	−0.111096	−	0.395026i
$950$	6.78017	−	11.7436i	0.219978	−	0.381013i
$951$			9.11098i			0.295444i
$952$		0			0
$953$	45.7482			1.48193			0.740965	−	0.671543i	$-0.234368\pi$
$953$	45.7482			1.48193			0.740965	+	0.671543i	$0.234368\pi$
$954$	6.79646	+	3.92394i	0.220043	+	0.127042i
$955$	−11.0952	+	6.40581i	−0.359032	+	0.207287i
$956$	13.5217	−	7.80678i	0.437324	−	0.252489i
$957$	10.8671	+	6.27413i	0.351284	+	0.202814i
$958$	8.58211			0.277275
$959$		0			0
$960$			0.445042i			0.0143637i
$961$	16.4034	−	28.4116i	0.529143	−	0.916502i
$962$	−31.6532	+	8.90205i	−1.02054	+	0.287014i
$963$	−16.3916	−	28.3910i	−0.528211	−	0.914889i
$964$	−14.4159	−	8.32304i	−0.464306	−	0.268067i
$965$	7.37329			0.237355
$966$		0			0
$967$		−	49.4838i		−	1.59129i	−0.605762	−	0.795646i	$-0.707132\pi$
$967$		−	49.4838i		−	1.59129i	0.605762	−	0.795646i	$-0.292868\pi$
$968$	−4.13975	−	2.39008i	−0.133056	−	0.0768202i
$969$	−11.7436	+	6.78017i	−0.377259	+	0.217810i
$970$	−4.57799	+	2.64310i	−0.146990	+	0.0848650i
$971$	−1.34093	+	2.32256i	−0.0430325	+	0.0745344i	−0.886739	−	0.462270i	$-0.847035\pi$
$971$	−1.34093	+	2.32256i	−0.0430325	+	0.0745344i	0.843707	+	0.536804i	$0.180369\pi$
$972$	15.7952			0.506632
$973$		0			0
$974$	−16.0965			−0.515765
$975$	−9.71086	−	9.47380i	−0.310996	−	0.303405i
$976$	−7.34481	−	12.7216i	−0.235102	−	0.407208i
$977$	46.8930	−	27.0737i	1.50024	−	0.866163i	0.500239	−	0.865887i	$-0.333245\pi$
$977$	46.8930	−	27.0737i	1.50024	−	0.866163i	1.00000		0.000276237i	$-8.79291e-5\pi$
$978$	−4.00000	+	6.92820i	−0.127906	+	0.221540i
$979$	−22.1715			−0.708604
$980$		0			0
$981$		−	5.79118i		−	0.184898i
$982$	−9.55933	−	5.51908i	−0.305050	−	0.176121i
$983$	29.1061	−	16.8044i	0.928339	−	0.535977i	0.0420531	−	0.999115i	$-0.486610\pi$
$983$	29.1061	−	16.8044i	0.928339	−	0.535977i	0.886286	+	0.463139i	$0.153277\pi$
$984$	−1.89008	−	3.27372i	−0.0602537	−	0.104362i
$985$	4.12983	−	7.15307i	0.131587	−	0.227916i
$986$			36.7090i			1.16905i
$987$		0			0
$988$	10.0978	+	2.57242i	0.321255	+	0.0818395i
$989$	−18.4058	+	31.8798i	−0.585271	+	1.01372i
$990$	−2.82501	+	1.63102i	−0.0897848	+	0.0518373i
$991$	17.7560	+	30.7543i	0.564038	+	0.976943i	0.997138	+	0.0755969i	$0.0240862\pi$
$991$	17.7560	+	30.7543i	0.564038	+	0.976943i	−0.433100	+	0.901346i	$0.642580\pi$
$992$	−3.99396	+	6.91774i	−0.126808	+	0.219638i
$993$			16.2586i			0.515951i
$994$		0			0
$995$		−	4.18970i		−	0.132822i
$996$	8.05887	+	4.65279i	0.255355	+	0.147429i
$997$	30.5743	+	52.9563i	0.968299	+	1.67714i	0.700478	+	0.713674i	$0.252970\pi$
$997$	30.5743	+	52.9563i	0.968299	+	1.67714i	0.267821	+	0.963469i	$0.413696\pi$
$998$	6.89008	+	11.9340i	0.218102	+	0.377763i
$999$	−33.9282	−	19.5884i	−1.07344	−	0.619751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.n.l.961.6		12
7.2	even	3		1274.2.d.m.883.1		6
7.3	odd	6		182.2.n.b.25.1	✓	12
7.4	even	3	inner	1274.2.n.l.753.3		12
7.5	odd	6		1274.2.d.k.883.3		6
7.6	odd	2		182.2.n.b.51.4	yes	12
13.12	even	2	inner	1274.2.n.l.961.3		12
21.17	even	6		1638.2.dm.d.1117.5		12
21.20	even	2		1638.2.dm.d.415.2		12
91.12	odd	6		1274.2.d.k.883.6		6
91.25	even	6	inner	1274.2.n.l.753.6		12
91.38	odd	6		182.2.n.b.25.4	yes	12
91.51	even	6		1274.2.d.m.883.4		6
91.90	odd	2		182.2.n.b.51.1	yes	12
273.38	even	6		1638.2.dm.d.1117.2		12
273.272	even	2		1638.2.dm.d.415.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.n.b.25.1	✓	12	7.3	odd	6
182.2.n.b.25.4	yes	12	91.38	odd	6
182.2.n.b.51.1	yes	12	91.90	odd	2
182.2.n.b.51.4	yes	12	7.6	odd	2
1274.2.d.k.883.3		6	7.5	odd	6
1274.2.d.k.883.6		6	91.12	odd	6
1274.2.d.m.883.1		6	7.2	even	3
1274.2.d.m.883.4		6	91.51	even	6
1274.2.n.l.753.3		12	7.4	even	3	inner
1274.2.n.l.753.6		12	91.25	even	6	inner
1274.2.n.l.961.3		12	13.12	even	2	inner
1274.2.n.l.961.6		12	1.1	even	1	trivial
1638.2.dm.d.415.2		12	21.20	even	2
1638.2.dm.d.415.5		12	273.272	even	2
1638.2.dm.d.1117.2		12	273.38	even	6
1638.2.dm.d.1117.5		12	21.17	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.400969 + 0.694498i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.480608 - 0.277479i) q^{5} +0.801938i q^{6} +1.00000i q^{8} +(1.17845 - 2.04113i) q^{9} +(-0.277479 - 0.480608i) q^{10} +(2.15983 - 1.24698i) q^{11} +(-0.400969 + 0.694498i) q^{12} +(0.890084 - 3.49396i) q^{13} -0.445042i q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.92543 + 5.06699i) q^{17} +(2.04113 - 1.17845i) q^{18} +(2.50289 + 1.44504i) q^{19} -0.554958i q^{20} +2.49396 q^{22} +(-3.04892 + 5.28088i) q^{23} +(-0.694498 + 0.400969i) q^{24} +(-2.34601 - 4.06341i) q^{25} +(2.51781 - 2.58082i) q^{26} +4.29590 q^{27} +6.27413 q^{29} +(0.222521 - 0.385418i) q^{30} +(6.91774 - 3.99396i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.73205 + 1.00000i) q^{33} +5.85086i q^{34} +2.35690 q^{36} +(-7.89781 - 4.55980i) q^{37} +(1.44504 + 2.50289i) q^{38} +(2.78345 - 0.782807i) q^{39} +(0.277479 - 0.480608i) q^{40} +4.71379i q^{41} +6.03684 q^{43} +(2.15983 + 1.24698i) q^{44} +(-1.13274 + 0.653989i) q^{45} +(-5.28088 + 3.04892i) q^{46} +(0.213891 + 0.123490i) q^{47} -0.801938 q^{48} -4.69202i q^{50} +(-2.34601 + 4.06341i) q^{51} +(3.47090 - 0.976144i) q^{52} +(1.66487 + 2.88365i) q^{53} +(3.72036 + 2.14795i) q^{54} -1.38404 q^{55} +2.31767i q^{57} +(5.43355 + 3.13706i) q^{58} +(-5.66164 + 3.26875i) q^{59} +(0.385418 - 0.222521i) q^{60} +(-7.34481 + 12.7216i) q^{61} +7.98792 q^{62} -1.00000 q^{64} +(-1.39728 + 1.43224i) q^{65} +(1.00000 + 1.73205i) q^{66} +(1.81678 - 1.04892i) q^{67} +(-2.92543 + 5.06699i) q^{68} -4.89008 q^{69} +2.46681i q^{71} +(2.04113 + 1.17845i) q^{72} +(3.03632 - 1.75302i) q^{73} +(-4.55980 - 7.89781i) q^{74} +(1.88135 - 3.25860i) q^{75} +2.89008i q^{76} +(2.80194 + 0.713792i) q^{78} +(-7.54288 + 13.0646i) q^{79} +(0.480608 - 0.277479i) q^{80} +(-1.81282 - 3.13990i) q^{81} +(-2.35690 + 4.08226i) q^{82} -11.6039i q^{83} -3.24698i q^{85} +(5.22805 + 3.01842i) q^{86} +(2.51573 + 4.35737i) q^{87} +(1.24698 + 2.15983i) q^{88} +(-7.69904 - 4.44504i) q^{89} -1.30798 q^{90} -6.09783 q^{92} +(5.54760 + 3.20291i) q^{93} +(0.123490 + 0.213891i) q^{94} +(-0.801938 - 1.38900i) q^{95} +(-0.694498 - 0.400969i) q^{96} -9.52542i q^{97} -5.87800i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} + 6 q^{4} + 6 q^{9} - 4 q^{10} + 4 q^{12} + 8 q^{13} - 6 q^{16} + 8 q^{17} - 8 q^{22} - 18 q^{25} + 2 q^{26} - 4 q^{27} + 32 q^{29} + 2 q^{30} + 12 q^{36} + 16 q^{38} - 12 q^{39} + 4 q^{40}+ \cdots + 8 q^{95}+O(q^{100}) \) 12 * q - 4 * q^3 + 6 * q^4 + 6 * q^9 - 4 * q^10 + 4 * q^12 + 8 * q^13 - 6 * q^16 + 8 * q^17 - 8 * q^22 - 18 * q^25 + 2 * q^26 - 4 * q^27 + 32 * q^29 + 2 * q^30 + 12 * q^36 + 16 * q^38 - 12 * q^39 + 4 * q^40 - 40 * q^43 + 8 * q^48 - 18 * q^51 + 4 * q^52 + 24 * q^53 + 24 * q^55 + 4 * q^61 + 20 * q^62 - 12 * q^64 + 8 * q^65 + 12 * q^66 - 8 * q^68 - 56 * q^69 - 12 * q^74 - 12 * q^75 + 16 * q^78 - 16 * q^79 + 2 * q^81 - 12 * q^82 - 20 * q^87 - 4 * q^88 - 36 * q^90 - 8 * q^94 + 8 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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