LMFDB - Embedded newform 1274.2.n.l.753.6

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			753.6
Root			$-1.56052 - 0.900969i$ of defining polynomial
Character	$\chi$	$=$	1274.753
Dual form			1274.2.n.l.961.6

$q$-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 $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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	−0.726750	−	0.686902i	$-0.758970\pi$
$3$	0.400969	−	0.694498i	0.231499	−	0.400969i	0.958250	+	0.285933i	$0.0923035\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.480608	+	0.277479i	−0.214934	+	0.124092i	−0.603603	−	0.797285i	$-0.706269\pi$
$5$	−0.480608	+	0.277479i	−0.214934	+	0.124092i	0.388668	+	0.921378i	$0.372935\pi$
$6$		−	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	0.788921	−	0.614494i	$-0.210640\pi$
$11$	2.15983	+	1.24698i	0.651214	+	0.375978i	−0.137707	+	0.990473i	$0.543973\pi$
$12$	−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	−0.255515	−	0.966805i	$-0.582245\pi$
$17$	2.92543	−	5.06699i	0.709520	−	1.22893i	0.965035	−	0.262120i	$-0.0844217\pi$
$18$	2.04113	+	1.17845i	0.481099	+	0.277763i
$19$	2.50289	−	1.44504i	0.574201	−	0.331515i	−0.184624	−	0.982809i	$-0.559107\pi$
$19$	2.50289	−	1.44504i	0.574201	−	0.331515i	0.758826	+	0.651294i	$0.225773\pi$
$20$			0.554958i			0.124092i
$21$		0			0
$22$	2.49396			0.531714
$23$	−3.04892	−	5.28088i	−0.635743	−	1.10114i	−0.986357	−	0.164619i	$-0.947360\pi$
$23$	−3.04892	−	5.28088i	−0.635743	−	1.10114i	0.350614	−	0.936520i	$-0.385973\pi$
$24$	−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	0.969595	−	0.244715i	$-0.0786945\pi$
$31$	6.91774	+	3.99396i	1.24246	+	0.717336i	0.272868	+	0.962052i	$0.412028\pi$
$32$	−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	−0.980126	−	0.198375i	$-0.936434\pi$
$37$	−7.89781	+	4.55980i	−1.29839	+	0.749627i	−0.318266	+	0.948002i	$0.603100\pi$
$38$	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	$-0.880013\pi$
$41$		−	4.71379i		−	0.736171i	0.929792	−	0.368085i	$-0.119987\pi$
$42$		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	−0.484319	−	0.874891i	$-0.660933\pi$
$47$	0.213891	−	0.123490i	0.0311992	−	0.0180128i	0.515518	+	0.856878i	$0.327599\pi$
$48$	−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	−0.728731	−	0.684800i	$-0.759890\pi$
$53$	1.66487	−	2.88365i	0.228688	−	0.396099i	0.957420	+	0.288700i	$0.0932231\pi$
$54$	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	0.0839249	−	0.996472i	$-0.473254\pi$
$59$	−5.66164	−	3.26875i	−0.737083	−	0.425555i	−0.821008	+	0.570917i	$0.806588\pi$
$60$	0.385418	+	0.222521i	0.0497572	+	0.0287273i
$61$	−7.34481	−	12.7216i	−0.940407	−	1.62883i	−0.764696	−	0.644391i	$-0.777111\pi$
$61$	−7.34481	−	12.7216i	−0.940407	−	1.62883i	−0.175711	−	0.984442i	$-0.556222\pi$
$62$	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	0.606855	−	0.794813i	$-0.292431\pi$
$67$	1.81678	+	1.04892i	0.221955	+	0.128146i	−0.384900	+	0.922958i	$0.625764\pi$
$68$	−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	$-0.953238\pi$
$71$		−	2.46681i		−	0.292757i	0.989229	−	0.146378i	$-0.0467617\pi$
$72$	2.04113	−	1.17845i	0.240550	−	0.138881i
$73$	3.03632	+	1.75302i	0.355374	+	0.205176i	0.667050	−	0.745013i	$-0.267557\pi$
$73$	3.03632	+	1.75302i	0.355374	+	0.205176i	−0.311675	+	0.950189i	$0.600890\pi$
$74$	−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	−0.882422	−	0.470458i	$-0.844089\pi$
$79$	−7.54288	−	13.0646i	−0.848640	−	1.46989i	0.0337823	−	0.999429i	$-0.489245\pi$
$80$	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	$0.219761\pi$
$83$			11.6039i			1.27369i	−0.770992	+	0.636845i	$0.780239\pi$
$84$		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	−0.849068	−	0.528283i	$-0.822836\pi$
$89$	−7.69904	+	4.44504i	−0.816096	+	0.471173i	0.0329721	+	0.999456i	$0.489503\pi$
$90$	−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	$0.160664\pi$
$97$			9.52542i			0.967160i	−0.875300	+	0.483580i	$0.839336\pi$
$98$		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	−0.927906	−	0.372815i	$-0.878393\pi$
$101$	−1.41789	+	2.45587i	−0.141086	+	0.244368i	0.786820	+	0.617183i	$0.211726\pi$
$102$	−4.06341	−	2.34601i	−0.402338	−	0.232290i
$103$	2.10992	+	3.65448i	0.207896	+	0.360087i	0.951052	−	0.309032i	$-0.100005\pi$
$103$	2.10992	+	3.65448i	0.207896	+	0.360087i	−0.743155	+	0.669119i	$0.766672\pi$
$104$	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	0.977239	+	0.212141i	$0.0680437\pi$
$107$	6.95473	+	12.0459i	0.672339	+	1.16453i	−0.304900	+	0.952384i	$0.598623\pi$
$108$	2.14795	−	3.72036i	0.206686	−	0.357991i
$109$	2.12793	+	1.22856i	0.203819	+	0.117675i	0.598436	−	0.801171i	$-0.295789\pi$
$109$	2.12793	+	1.22856i	0.203819	+	0.117675i	−0.394617	+	0.918846i	$0.629123\pi$
$110$	−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	0.763586	−	0.645707i	$-0.223437\pi$
$131$	−2.03050	−	3.51693i	−0.177406	−	0.307275i	−0.940991	+	0.338431i	$0.890104\pi$
$132$		−	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	0.829360	−	0.558715i	$-0.188705\pi$
$137$	8.89765	+	5.13706i	0.760178	+	0.438889i	−0.0691817	+	0.997604i	$0.522039\pi$
$138$	−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	−0.743894	+	0.668298i	$0.767023\pi$
$149$	−20.6853	+	11.9426i	−1.69460	+	0.978380i	−0.950710	+	0.310082i	$0.899643\pi$
$150$	3.25860	+	1.88135i	0.266064	+	0.153612i
$151$	−12.6981	−	7.33124i	−1.03336	−	0.596608i	−0.115411	−	0.993318i	$-0.536819\pi$
$151$	−12.6981	−	7.33124i	−1.03336	−	0.596608i	−0.917944	+	0.396710i	$0.870152\pi$
$152$	−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	−0.965168	−	0.261630i	$-0.915740\pi$
$157$	−3.20775	+	5.55599i	−0.256006	+	0.443416i	0.709162	+	0.705046i	$0.249073\pi$
$158$	−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	−0.121920	−	0.992540i	$-0.538905\pi$
$163$	8.63933	−	4.98792i	0.676684	−	0.390684i	0.798605	+	0.601856i	$0.205572\pi$
$164$	−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	$-0.915200\pi$
$167$		−	6.80433i		−	0.526535i	0.964723	−	0.263267i	$-0.0848002\pi$
$168$		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	0.921703	−	0.387897i	$-0.126798\pi$
$173$	1.64310	+	2.84594i	0.124923	+	0.216373i	−0.796780	+	0.604270i	$0.793465\pi$
$174$		−	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	−0.954287	−	0.298893i	$-0.903383\pi$
$179$	−2.92058	+	5.05860i	−0.218295	+	0.378097i	0.735992	+	0.676990i	$0.236716\pi$
$180$	−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	0.893857	+	0.448353i	$0.147989\pi$
$191$	11.5429	+	19.9928i	0.835213	+	1.44663i	−0.0586435	+	0.998279i	$0.518678\pi$
$192$	−0.400969	+	0.694498i	−0.0289374	+	0.0501211i
$193$	−11.5062	−	6.64310i	−0.828234	−	0.478181i	0.0250136	−	0.999687i	$-0.492037\pi$
$193$	−11.5062	−	6.64310i	−0.828234	−	0.478181i	−0.853248	+	0.521506i	$0.825370\pi$
$194$	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	$-0.822117\pi$
$197$		−	14.8834i		−	1.06040i	0.847874	−	0.530198i	$-0.177883\pi$
$198$	2.93900	+	5.09050i	0.208866	+	0.361766i
$199$	3.77479	−	6.53813i	0.267588	−	0.463476i	−0.700651	−	0.713505i	$-0.747107\pi$
$199$	3.77479	−	6.53813i	0.267588	−	0.463476i	0.968238	+	0.250029i	$0.0804401\pi$
$200$	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	$0.0280198\pi$
$223$			2.62565i			0.175826i	−0.996128	+	0.0879131i	$0.971980\pi$
$224$		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	0.738877	−	0.673840i	$-0.235356\pi$
$227$	7.90620	+	4.56465i	0.524753	+	0.302966i	−0.214124	+	0.976806i	$0.568690\pi$
$228$	−2.00716	−	1.15883i	−0.132927	−	0.0767456i
$229$	−9.27003	+	5.35205i	−0.612581	+	0.353674i	−0.773975	−	0.633216i	$-0.781734\pi$
$229$	−9.27003	+	5.35205i	−0.612581	+	0.353674i	0.161394	+	0.986890i	$0.448401\pi$
$230$	3.38404			0.223137
$231$		0			0
$232$		−	6.27413i		−	0.411917i
$233$	−3.55011	−	6.14898i	−0.232576	−	0.402833i	0.725990	−	0.687706i	$-0.241382\pi$
$233$	−3.55011	−	6.14898i	−0.232576	−	0.402833i	−0.958565	+	0.284873i	$0.908049\pi$
$234$	−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	$0.168500\pi$
$239$			15.6136i			1.00996i	−0.863132	+	0.504979i	$0.831500\pi$
$240$	0.385418	−	0.222521i	0.0248786	−	0.0143637i
$241$	−14.4159	−	8.32304i	−0.928612	−	0.536134i	−0.0422397	−	0.999108i	$-0.513449\pi$
$241$	−14.4159	−	8.32304i	−0.928612	−	0.536134i	−0.886372	+	0.462973i	$0.846783\pi$
$242$	−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	0.885133	−	0.465339i	$-0.154067\pi$
$257$	0.634375	+	1.09877i	0.0395712	+	0.0685394i	−0.845561	+	0.533878i	$0.820734\pi$
$258$		−	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	−0.936149	−	0.351602i	$-0.885637\pi$
$263$	−2.65279	+	4.59477i	−0.163578	+	0.283326i	0.772571	+	0.634928i	$0.218970\pi$
$264$	−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	0.130752	+	0.991415i	$0.458261\pi$
$269$	−13.0097	+	22.5334i	−0.793215	+	1.37389i	−0.923967	+	0.382473i	$0.875072\pi$
$270$	−1.19202	+	2.06464i	−0.0725441	+	0.125650i
$271$	−21.0446	+	12.1501i	−1.27837	+	0.738066i	−0.976548	−	0.215299i	$-0.930928\pi$
$271$	−21.0446	+	12.1501i	−1.27837	+	0.738066i	−0.301820	+	0.953365i	$0.597594\pi$
$272$	−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	−0.892856	−	0.450343i	$-0.851302\pi$
$277$	−0.939001	+	1.62640i	−0.0564191	+	0.0977208i	0.836436	+	0.548064i	$0.184635\pi$
$278$	−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	$-0.599294\pi$
$281$		−	31.9081i		−	1.90348i	0.306906	−	0.951740i	$-0.400706\pi$
$282$	−0.0990311	−	0.171527i	−0.00589722	−	0.0102143i
$283$	−14.7681	+	25.5791i	−0.877872	+	1.52052i	−0.0241996	+	0.999707i	$0.507704\pi$
$283$	−14.7681	+	25.5791i	−0.877872	+	1.52052i	−0.853672	+	0.520811i	$0.825630\pi$
$284$	−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	$-0.918218\pi$
$293$		−	8.69932i		−	0.508220i	0.967175	−	0.254110i	$-0.0817825\pi$
$294$		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	$-0.731833\pi$
$307$		−	26.1521i		−	1.49258i	0.665620	−	0.746290i	$-0.268167\pi$
$308$		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	−0.664443	−	0.747339i	$-0.731331\pi$
$311$	5.55496	−	9.62147i	0.314993	−	0.545583i	0.979436	+	0.201755i	$0.0646646\pi$
$312$	0.782807	−	2.78345i	0.0443177	−	0.157582i
$313$	3.91335	+	6.77811i	0.221195	+	0.383122i	0.955171	−	0.296054i	$-0.0956708\pi$
$313$	3.91335	+	6.77811i	0.221195	+	0.383122i	−0.733976	+	0.679176i	$0.762337\pi$
$314$			6.41550i			0.362048i
$315$		0			0
$316$	−15.0858			−0.848640
$317$	9.83909	−	5.68060i	0.552619	−	0.319054i	−0.197559	−	0.980291i	$-0.563301\pi$
$317$	9.83909	−	5.68060i	0.552619	−	0.319054i	0.750177	+	0.661237i	$0.229968\pi$
$318$	−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	0.0673402	−	0.997730i	$-0.478549\pi$
$331$	17.5579	−	10.1371i	0.965070	−	0.557183i	0.897730	+	0.440547i	$0.145215\pi$
$332$	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	−0.632693	−	0.774403i	$-0.718050\pi$
$347$	6.59999	−	11.4315i	0.354306	−	0.613676i	0.986999	+	0.160727i	$0.0513838\pi$
$348$	−2.51573	−	4.35737i	−0.134857	−	0.233580i
$349$		−	33.2349i		−	1.77902i	−0.456912	−	0.889512i	$-0.651045\pi$
$349$		−	33.2349i		−	1.77902i	0.456912	−	0.889512i	$-0.348955\pi$
$350$		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	−0.0220491	−	0.999757i	$-0.507019\pi$
$353$	−16.8886	−	9.75063i	−0.898889	−	0.518974i	−0.876839	+	0.480783i	$0.840352\pi$
$354$	−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	−0.596420	−	0.802672i	$-0.703411\pi$
$359$	−3.77991	+	2.18233i	−0.199496	+	0.115179i	0.396924	+	0.917851i	$0.370078\pi$
$360$	−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	0.167599	+	0.985855i	$0.446399\pi$
$367$	−14.7506	+	25.5488i	−0.769976	+	1.33364i	−0.937575	+	0.347783i	$0.886935\pi$
$368$	−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	0.708996	−	0.705212i	$-0.249148\pi$
$373$	−4.94869	−	8.57138i	−0.256233	−	0.443809i	−0.965230	+	0.261403i	$0.915815\pi$
$374$	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	$0.174517\pi$
$379$			20.2935i			1.04241i	−0.853432	+	0.521204i	$0.825483\pi$
$380$	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	−0.0854734	−	0.996340i	$-0.527240\pi$
$383$	14.3773	−	8.30074i	0.734646	−	0.424148i	0.820119	+	0.572192i	$0.193907\pi$
$384$			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	−0.427943	−	0.903805i	$-0.640762\pi$
$389$	11.2174	−	19.4292i	0.568747	−	0.985098i	0.996690	−	0.0812928i	$-0.0259049\pi$
$390$	−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	0.0219493	−	0.999759i	$-0.493013\pi$
$397$	17.9073	−	10.3388i	0.898741	−	0.518888i	0.876791	+	0.480871i	$0.159679\pi$
$398$		−	7.54958i		−	0.378426i
$399$		0			0
$400$	4.69202			0.234601
$401$	−27.4336	+	15.8388i	−1.36997	+	0.790951i	−0.990923	−	0.134428i	$-0.957080\pi$
$401$	−27.4336	+	15.8388i	−1.36997	+	0.790951i	−0.379043	+	0.925379i	$0.623747\pi$
$402$	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	0.648197	−	0.761473i	$-0.275523\pi$
$409$	6.32682	+	3.65279i	0.312841	+	0.180619i	−0.335356	+	0.942091i	$0.608857\pi$
$410$	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	$0.00278694\pi$
$421$			0.359289i			0.0175107i	−0.999962	+	0.00875533i	$0.997213\pi$
$422$	−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	−0.494485	−	0.869186i	$-0.664643\pi$
$431$	−31.0259	−	17.9128i	−1.49447	−	0.862830i	−0.999980	+	0.00635609i	$0.997977\pi$
$432$	−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	−0.776813	−	0.629731i	$-0.783165\pi$
$439$	−19.5646	−	33.8870i	−0.933770	−	1.61734i	−0.156956	−	0.987606i	$-0.550168\pi$
$440$			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	0.872352	−	0.488879i	$-0.162594\pi$
$443$	0.269282	+	0.466411i	0.0127940	+	0.0221598i	−0.859558	+	0.511039i	$0.829261\pi$
$444$	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	$-0.892679\pi$
$449$		−	14.0194i		−	0.661615i	0.943698	−	0.330808i	$-0.107321\pi$
$450$	−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	−0.460350	−	0.887738i	$-0.652276\pi$
$457$	1.67342	−	0.966148i	0.0782792	−	0.0451945i	0.538629	+	0.842543i	$0.318943\pi$
$458$	−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	$-0.767076\pi$
$461$		−	28.6926i		−	1.33635i	0.744005	−	0.668174i	$-0.232924\pi$
$462$		0			0
$463$			27.7198i			1.28825i	0.764922	+	0.644123i	$0.222778\pi$
$463$			27.7198i			1.28825i	−0.764922	+	0.644123i	$0.777222\pi$
$464$	−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	−0.999712	−	0.0240083i	$-0.992357\pi$
$467$	−11.2513	−	19.4878i	−0.520648	−	0.901788i	0.479064	−	0.877780i	$-0.340976\pi$
$468$	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	0.660091	−	0.751185i	$-0.270518\pi$
$479$	7.43232	+	4.29105i	0.339591	+	0.196063i	−0.320500	+	0.947249i	$0.603851\pi$
$480$	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	0.149722	−	0.988728i	$-0.452162\pi$
$487$	−13.9400	−	8.04825i	−0.631681	−	0.364701i	−0.781403	+	0.624027i	$0.785496\pi$
$488$	−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	−0.208502	−	0.978022i	$-0.566859\pi$
$499$	11.9340	−	6.89008i	0.534238	−	0.308443i	0.742741	+	0.669579i	$0.233526\pi$
$500$	−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	−0.873917	−	0.486075i	$-0.838428\pi$
$509$	−20.0776	+	11.5918i	−0.889923	+	0.513797i	−0.0160056	+	0.999872i	$0.505095\pi$
$510$	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	−0.644961	−	0.764215i	$-0.723127\pi$
$521$	7.74578	−	13.4161i	0.339349	−	0.587770i	0.984310	+	0.176445i	$0.0564599\pi$
$522$	12.8063	+	7.39373i	0.560517	+	0.323615i
$523$	20.6129	+	35.7026i	0.901339	+	1.56117i	0.825757	+	0.564026i	$0.190748\pi$
$523$	20.6129	+	35.7026i	0.901339	+	1.56117i	0.0755819	+	0.997140i	$0.475919\pi$
$524$	−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	−0.326121	−	0.945328i	$-0.605742\pi$
$541$	7.66392	−	4.42476i	0.329497	−	0.190235i	0.655618	+	0.755093i	$0.272408\pi$
$542$	−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	−0.0326751	−	0.999466i	$-0.510403\pi$
$557$	−21.5848	−	12.4620i	−0.914576	−	0.528031i	−0.881901	+	0.471436i	$0.843736\pi$
$558$	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	−0.492942	−	0.870062i	$-0.664078\pi$
$563$	12.0305	−	20.8374i	0.507025	−	0.878193i	0.999967	−	0.00813097i	$-0.00258820\pi$
$564$	−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	0.966234	+	0.257665i	$0.0829532\pi$
$569$	16.8470	+	29.1798i	0.706262	+	1.22328i	−0.259973	+	0.965616i	$0.583714\pi$
$570$	1.11389	+	0.643104i	0.0466557	+	0.0269367i
$571$	−2.19083	+	3.79462i	−0.0916832	+	0.158800i	−0.908219	−	0.418494i	$-0.862558\pi$
$571$	−2.19083	+	3.79462i	−0.0916832	+	0.158800i	0.816536	+	0.577294i	$0.195891\pi$
$572$	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	−0.322991	−	0.946402i	$-0.604689\pi$
$577$	−31.3254	−	18.0858i	−1.30410	−	0.752920i	−0.981104	+	0.193482i	$0.938022\pi$
$578$	−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	$-0.742498\pi$
$587$		−	35.0616i		−	1.44715i	0.690248	−	0.723573i	$-0.257502\pi$
$588$		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	−0.866782	−	0.498687i	$-0.833816\pi$
$593$	−21.1444	+	12.2078i	−0.868298	+	0.501312i	−0.00151591	+	0.999999i	$0.500483\pi$
$594$	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	0.313002	+	0.949752i	$0.398665\pi$
$599$	−16.3002	+	28.2328i	−0.666008	+	1.15356i	−0.979011	+	0.203808i	$0.934668\pi$
$600$	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	0.987465	−	0.157837i	$-0.0504522\pi$
$607$	8.79656	+	15.2361i	0.357041	+	0.618414i	−0.630424	+	0.776251i	$0.717119\pi$
$608$	−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	0.168841	−	0.985643i	$-0.445998\pi$
$613$	−14.8635	−	8.58144i	−0.600331	−	0.346601i	−0.769172	+	0.639042i	$0.779331\pi$
$614$	−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	$0.203013\pi$
$617$			29.5797i			1.19083i	−0.803417	+	0.595417i	$0.796987\pi$
$618$	2.93067	−	1.69202i	0.117889	−	0.0680631i
$619$	30.5076	+	17.6136i	1.22620	+	0.707949i	0.966234	−	0.257668i	$-0.0829540\pi$
$619$	30.5076	+	17.6136i	1.22620	+	0.707949i	0.259970	+	0.965617i	$0.416287\pi$
$620$	−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	$0.0608821\pi$
$631$			9.55065i			0.380205i	−0.981764	+	0.190103i	$0.939118\pi$
$632$	−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	−0.573725	−	0.819048i	$-0.694502\pi$
$641$	10.6957	−	18.5254i	0.422454	−	0.731711i	0.996179	+	0.0873368i	$0.0278356\pi$
$642$	9.66010	−	5.57726i	0.381254	−	0.220117i
$643$			4.05429i			0.159886i	0.996799	+	0.0799429i	$0.0254738\pi$
$643$			4.05429i			0.159886i	−0.996799	+	0.0799429i	$0.974526\pi$
$644$		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	−0.450513	−	0.892770i	$-0.648759\pi$
$647$	13.9366	−	24.1389i	0.547905	−	0.948999i	0.998418	−	0.0562289i	$-0.0179077\pi$
$648$	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	0.758366	−	0.651829i	$-0.225998\pi$
$653$	−4.73556	−	8.20223i	−0.185317	−	0.320978i	−0.943683	+	0.330850i	$0.892664\pi$
$654$	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	0.306298	−	0.951936i	$-0.400910\pi$
$661$	−9.38292	−	5.41723i	−0.364953	−	0.210706i	−0.671251	+	0.741230i	$0.734243\pi$
$662$	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	−0.981687	−	0.190501i	$-0.938989\pi$
$677$	−17.0640	−	29.5557i	−0.655822	−	1.13592i	0.325865	−	0.945416i	$-0.394345\pi$
$678$		−	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	0.835869	−	0.548929i	$-0.184964\pi$
$683$	20.3434	+	11.7453i	0.778417	+	0.449420i	−0.0574517	+	0.998348i	$0.518298\pi$
$684$	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	−0.0493920	−	0.998779i	$-0.515728\pi$
$691$	20.7898	−	12.0030i	0.790880	−	0.456615i	0.840272	+	0.542164i	$0.182395\pi$
$692$	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	−0.834546	−	0.550938i	$-0.814270\pi$
$709$	−20.6278	+	11.9095i	−0.774693	+	0.447269i	0.0598532	+	0.998207i	$0.480937\pi$
$710$	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	0.987367	+	0.158451i	$0.0506501\pi$
$719$	16.9172	+	29.3015i	0.630906	+	1.09276i	−0.356461	+	0.934310i	$0.616017\pi$
$720$			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	−0.218139	−	0.975918i	$-0.569999\pi$
$733$	14.0233	−	8.09634i	0.517962	−	0.299045i	0.736100	+	0.676873i	$0.236665\pi$
$734$			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	−0.145030	−	0.989427i	$-0.546328\pi$
$739$	−29.2075	−	16.8629i	−1.07441	−	0.620313i	−0.929384	+	0.369114i	$0.879661\pi$
$740$	−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	$0.203678\pi$
$743$			32.5512i			1.19419i	−0.802171	+	0.597095i	$0.796322\pi$
$744$	−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	−0.941896	−	0.335903i	$-0.890958\pi$
$751$	−20.8780	−	36.1618i	−0.761849	−	1.31956i	0.180047	−	0.983658i	$-0.442375\pi$
$752$	−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	0.672255	−	0.740320i	$-0.265326\pi$
$761$	45.5040	−	26.2717i	1.64952	−	0.952350i	0.977263	−	0.212030i	$-0.0680073\pi$
$762$			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	$0.0167677\pi$
$769$			2.92021i			0.105306i	−0.998613	+	0.0526528i	$0.983232\pi$
$770$		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	0.406212	−	0.913779i	$-0.366850\pi$
$773$	−5.06118	−	2.92208i	−0.182038	−	0.105100i	−0.588250	+	0.808679i	$0.700183\pi$
$774$	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	0.933440	−	0.358735i	$-0.116792\pi$
$787$	30.5639	+	17.6461i	1.08949	+	0.629015i	0.156047	+	0.987750i	$0.450125\pi$
$788$	−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	−0.866375	−	0.499394i	$-0.833556\pi$
$809$	−0.0199098	+	0.0344848i	−0.000699992	+	0.00121242i	0.865675	+	0.500606i	$0.166889\pi$
$810$	−1.00604	−	1.74251i	−0.0353487	−	0.0612257i
$811$			16.4638i			0.578123i	0.957310	+	0.289062i	$0.0933432\pi$
$811$			16.4638i			0.578123i	−0.957310	+	0.289062i	$0.906657\pi$
$812$		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	−0.680400	−	0.732841i	$-0.738194\pi$
$821$	−11.0584	+	6.38458i	−0.385941	+	0.222823i	0.294459	+	0.955664i	$0.404861\pi$
$822$	4.11960	−	7.13537i	0.143688	−	0.248874i
$823$	−10.1468	+	17.5747i	−0.353694	+	0.612615i	−0.986893	−	0.161373i	$-0.948408\pi$
$823$	−10.1468	+	17.5747i	−0.353694	+	0.612615i	0.633200	+	0.773988i	$0.281741\pi$
$824$	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	$-0.841495\pi$
$827$		−	27.4711i		−	0.955265i	0.878560	−	0.477632i	$-0.158505\pi$
$828$	−7.18598	−	12.4465i	−0.249730	−	0.432545i
$829$	−15.3545	+	26.5948i	−0.533284	+	0.923675i	0.465960	+	0.884806i	$0.345709\pi$
$829$	−15.3545	+	26.5948i	−0.533284	+	0.923675i	−0.999244	+	0.0388693i	$0.987624\pi$
$830$	−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	$0.262978\pi$
$839$			42.5991i			1.47068i	−0.677696	+	0.735342i	$0.737022\pi$
$840$		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	$-0.765441\pi$
$853$		−	39.2524i		−	1.34398i	0.740562	−	0.671988i	$-0.234559\pi$
$854$		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	−0.906437	−	0.422342i	$-0.861208\pi$
$857$	−2.56033	+	4.43463i	−0.0874594	+	0.151484i	0.818977	+	0.573826i	$0.194541\pi$
$858$	6.94180	+	1.95229i	0.236989	+	0.0666500i
$859$	1.14310	+	1.97991i	0.0390022	+	0.0675538i	0.884868	−	0.465843i	$-0.154249\pi$
$859$	1.14310	+	1.97991i	0.0390022	+	0.0675538i	−0.845865	+	0.533396i	$0.820915\pi$
$860$			3.35019i			0.114241i
$861$		0			0
$862$	−35.8256			−1.22023
$863$	32.1726	−	18.5749i	1.09517	−	0.632296i	0.160221	−	0.987081i	$-0.448779\pi$
$863$	32.1726	−	18.5749i	1.09517	−	0.632296i	0.934948	+	0.354785i	$0.115446\pi$
$864$	−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	−0.519569	−	0.854428i	$-0.673908\pi$
$877$	−1.16672	+	0.673604i	−0.0393972	+	0.0227460i	0.480172	+	0.877174i	$0.340574\pi$
$878$	−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	0.596708	−	0.802459i	$-0.296475\pi$
$887$	−11.8116	−	20.4583i	−0.396596	−	0.686924i	−0.993303	+	0.115535i	$0.963142\pi$
$888$	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	−0.571625	−	0.820515i	$-0.693687\pi$
$907$	12.7927	−	22.1576i	0.424774	−	0.735730i	0.996399	+	0.0847848i	$0.0270203\pi$
$908$	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	0.981158	−	0.193207i	$-0.0618888\pi$
$919$	9.79954	+	16.9733i	0.323257	+	0.559898i	−0.657901	+	0.753104i	$0.728555\pi$
$920$	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	−0.449433	−	0.893314i	$-0.648374\pi$
$929$	3.03218	−	1.75063i	0.0994825	−	0.0574362i	0.548916	+	0.835878i	$0.315041\pi$
$930$			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	0.606142	−	0.795357i	$-0.292716\pi$
$941$	6.76133	+	3.90366i	0.220413	+	0.127256i	−0.385728	+	0.922612i	$0.626050\pi$
$942$	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	−0.203701	−	0.979033i	$-0.565297\pi$
$947$	16.6889	−	9.63533i	0.542316	−	0.313106i	0.746017	+	0.665927i	$0.231964\pi$
$948$	−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	$0.292868\pi$
$967$			49.4838i			1.59129i	−0.605762	+	0.795646i	$0.707132\pi$
$968$	−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	0.843707	−	0.536804i	$-0.180369\pi$
$971$	−1.34093	−	2.32256i	−0.0430325	−	0.0745344i	−0.886739	+	0.462270i	$0.847035\pi$
$972$	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	1.00000		0.000276237i	$8.79291e-5\pi$
$977$	46.8930	+	27.0737i	1.50024	+	0.866163i	0.500239	+	0.865887i	$0.333245\pi$
$978$	−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	0.886286	−	0.463139i	$-0.153277\pi$
$983$	29.1061	+	16.8044i	0.928339	+	0.535977i	0.0420531	+	0.999115i	$0.486610\pi$
$984$	−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	−0.433100	−	0.901346i	$-0.642580\pi$
$991$	17.7560	−	30.7543i	0.564038	−	0.976943i	0.997138	−	0.0755969i	$-0.0240862\pi$
$992$	−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	0.267821	−	0.963469i	$-0.413696\pi$
$997$	30.5743	−	52.9563i	0.968299	−	1.67714i	0.700478	−	0.713674i	$-0.252970\pi$
$998$	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.753.6		12
7.2	even	3	inner	1274.2.n.l.961.3		12
7.3	odd	6		1274.2.d.k.883.6		6
7.4	even	3		1274.2.d.m.883.4		6
7.5	odd	6		182.2.n.b.51.1	yes	12
7.6	odd	2		182.2.n.b.25.4	yes	12
13.12	even	2	inner	1274.2.n.l.753.3		12
21.5	even	6		1638.2.dm.d.415.5		12
21.20	even	2		1638.2.dm.d.1117.2		12
91.12	odd	6		182.2.n.b.51.4	yes	12
91.25	even	6		1274.2.d.m.883.1		6
91.38	odd	6		1274.2.d.k.883.3		6
91.51	even	6	inner	1274.2.n.l.961.6		12
91.90	odd	2		182.2.n.b.25.1	✓	12
273.194	even	6		1638.2.dm.d.415.2		12
273.272	even	2		1638.2.dm.d.1117.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.n.b.25.1	✓	12	91.90	odd	2
182.2.n.b.25.4	yes	12	7.6	odd	2
182.2.n.b.51.1	yes	12	7.5	odd	6
182.2.n.b.51.4	yes	12	91.12	odd	6
1274.2.d.k.883.3		6	91.38	odd	6
1274.2.d.k.883.6		6	7.3	odd	6
1274.2.d.m.883.1		6	91.25	even	6
1274.2.d.m.883.4		6	7.4	even	3
1274.2.n.l.753.3		12	13.12	even	2	inner
1274.2.n.l.753.6		12	1.1	even	1	trivial
1274.2.n.l.961.3		12	7.2	even	3	inner
1274.2.n.l.961.6		12	91.51	even	6	inner
1638.2.dm.d.415.2		12	273.194	even	6
1638.2.dm.d.415.5		12	21.5	even	6
1638.2.dm.d.1117.2		12	21.20	even	2
1638.2.dm.d.1117.5		12	273.272	even	2

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

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Database

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