LMFDB - Embedded newform 1274.2.g.p.393.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(295,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1274.295"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,-5,-1,-5,4,-1,0,10,-4,-2,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.23207289578928.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 3x^{8} + 13x^{7} + x^{6} - 39x^{5} + 3x^{4} + 117x^{3} - 81x^{2} - 162x + 243 $ x^10 - 2x^9 - 3x^8 + 13x^7 + x^6 - 39x^5 + 3x^4 + 117x^3 - 81x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			393.2
Root			$1.16412 + 1.28251i$ of defining polynomial
Character	$\chi$	$=$	1274.393
Dual form			1274.2.g.p.295.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.02863 - 1.78164i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.38549 q^{5} +(-1.02863 + 1.78164i) q^{6} +1.00000 q^{8} +(-0.616155 + 1.06721i) q^{9} +(1.69274 + 2.93192i) q^{10} +(-1.90582 - 3.30098i) q^{11} +2.05726 q^{12} +(-3.24071 - 1.58045i) q^{13} +(3.48241 + 6.03172i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.02198 + 3.50217i) q^{17} +1.23231 q^{18} +(-3.07934 + 5.33357i) q^{19} +(1.69274 - 2.93192i) q^{20} +(-1.90582 + 3.30098i) q^{22} +(-0.528629 - 0.915612i) q^{23} +(-1.02863 - 1.78164i) q^{24} +6.46154 q^{25} +(0.251642 + 3.59676i) q^{26} -3.63659 q^{27} +(-1.15418 - 1.99910i) q^{29} +(3.48241 - 6.03172i) q^{30} +3.98121 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.92077 + 6.79097i) q^{33} +4.04396 q^{34} +(-0.616155 - 1.06721i) q^{36} +(2.71208 + 4.69745i) q^{37} +6.15867 q^{38} +(0.517693 + 7.39946i) q^{39} -3.38549 q^{40} +(-2.26094 - 3.91606i) q^{41} +(3.46973 - 6.00975i) q^{43} +3.81165 q^{44} +(2.08599 - 3.61304i) q^{45} +(-0.528629 + 0.915612i) q^{46} +5.54067 q^{47} +(-1.02863 + 1.78164i) q^{48} +(-3.23077 - 5.59586i) q^{50} +8.31946 q^{51} +(2.98906 - 2.01631i) q^{52} -7.63439 q^{53} +(1.81830 + 3.14938i) q^{54} +(6.45214 + 11.1754i) q^{55} +12.6700 q^{57} +(-1.15418 + 1.99910i) q^{58} +(3.74061 - 6.47892i) q^{59} -6.96483 q^{60} +(6.39653 - 11.0791i) q^{61} +(-1.99060 - 3.44783i) q^{62} +1.00000 q^{64} +(10.9714 + 5.35060i) q^{65} +7.84154 q^{66} +(4.42405 + 7.66269i) q^{67} +(-2.02198 - 3.50217i) q^{68} +(-1.08753 + 1.88365i) q^{69} +(-7.21308 + 12.4934i) q^{71} +(-0.616155 + 1.06721i) q^{72} +7.23580 q^{73} +(2.71208 - 4.69745i) q^{74} +(-6.64653 - 11.5121i) q^{75} +(-3.07934 - 5.33357i) q^{76} +(6.14928 - 4.14807i) q^{78} -0.445826 q^{79} +(1.69274 + 2.93192i) q^{80} +(5.58917 + 9.68073i) q^{81} +(-2.26094 + 3.91606i) q^{82} +15.1718 q^{83} +(6.84539 - 11.8566i) q^{85} -6.93946 q^{86} +(-2.37445 + 4.11266i) q^{87} +(-1.90582 - 3.30098i) q^{88} +(-4.11790 - 7.13241i) q^{89} -4.17197 q^{90} +1.05726 q^{92} +(-4.09518 - 7.09307i) q^{93} +(-2.77034 - 4.79836i) q^{94} +(10.4251 - 18.0567i) q^{95} +2.05726 q^{96} +(-6.18181 + 10.7072i) q^{97} +4.69713 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - q^{3} - 5 q^{4} + 4 q^{5} - q^{6} + 10 q^{8} - 4 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 6 q^{13} + 3 q^{15} - 5 q^{16} - 3 q^{17} + 8 q^{18} - 5 q^{19} - 2 q^{20} - 4 q^{22} + 4 q^{23}+ \cdots + 54 q^{99}+O(q^{100}) $ 10 * q - 5 * q^2 - q^3 - 5 * q^4 + 4 * q^5 - q^6 + 10 * q^8 - 4 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 6 * q^13 + 3 * q^15 - 5 * q^16 - 3 * q^17 + 8 * q^18 - 5 * q^19 - 2 * q^20 - 4 * q^22 + 4 * q^23 - q^24 + 6 * q^25 + 8 * q^27 + q^29 + 3 * q^30 + 42 * q^31 - 5 * q^32 + 6 * q^34 - 4 * q^36 + 10 * q^37 + 10 * q^38 - 28 * q^39 + 4 * q^40 - 9 * q^41 + 9 * q^43 + 8 * q^44 + 3 * q^45 + 4 * q^46 + 26 * q^47 - q^48 - 3 * q^50 + 12 * q^51 + 6 * q^52 + 30 * q^53 - 4 * q^54 + 7 * q^55 - 26 * q^57 + q^58 + q^59 - 6 * q^60 - 15 * q^61 - 21 * q^62 + 10 * q^64 + 44 * q^65 - 3 * q^68 - 18 * q^69 - q^71 - 4 * q^72 + 8 * q^73 + 10 * q^74 - 25 * q^75 - 5 * q^76 + 11 * q^78 + 2 * q^79 - 2 * q^80 + 23 * q^81 - 9 * q^82 + 96 * q^83 + 12 * q^85 - 18 * q^86 - 27 * q^87 - 4 * q^88 - 9 * q^89 - 6 * q^90 - 8 * q^92 - 2 * q^93 - 13 * q^94 + 6 * q^95 + 2 * q^96 - 19 * q^97 + 54 * q^99

Character values

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

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

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.02863	−	1.78164i	−0.593879	−	1.02863i	−0.993704	−	0.112037i	$-0.964262\pi$
$3$	−1.02863	−	1.78164i	−0.593879	−	1.02863i	0.399825	−	0.916592i	$-0.369071\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−3.38549			−1.51404			−0.757019	−	0.653393i	$-0.773345\pi$
$5$	−3.38549			−1.51404			−0.757019	+	0.653393i	$0.773345\pi$
$6$	−1.02863	+	1.78164i	−0.419936	+	0.727351i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−0.616155	+	1.06721i	−0.205385	+	0.355737i
$10$	1.69274	+	2.93192i	0.535293	+	0.927155i
$11$	−1.90582	−	3.30098i	−0.574627	−	0.995284i	−0.996082	−	0.0884342i	$-0.971814\pi$
$11$	−1.90582	−	3.30098i	−0.574627	−	0.995284i	0.421455	−	0.906849i	$-0.361520\pi$
$12$	2.05726			0.593879
$13$	−3.24071	−	1.58045i	−0.898810	−	0.438338i
$13$	−3.24071	−	1.58045i	−0.898810	−	0.438338i
$14$		0			0
$15$	3.48241	+	6.03172i	0.899155	+	1.55738i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.02198	+	3.50217i	−0.490402	+	0.849401i	−0.999939	−	0.0110479i	$-0.996483\pi$
$17$	−2.02198	+	3.50217i	−0.490402	+	0.849401i	0.509537	+	0.860449i	$0.329817\pi$
$18$	1.23231			0.290458
$19$	−3.07934	+	5.33357i	−0.706448	+	1.22360i	0.259718	+	0.965684i	$0.416370\pi$
$19$	−3.07934	+	5.33357i	−0.706448	+	1.22360i	−0.966166	+	0.257920i	$0.916963\pi$
$20$	1.69274	−	2.93192i	0.378509	−	0.655597i
$21$		0			0
$22$	−1.90582	+	3.30098i	−0.406323	+	0.703772i
$23$	−0.528629	−	0.915612i	−0.110227	−	0.190918i	0.805635	−	0.592412i	$-0.201824\pi$
$23$	−0.528629	−	0.915612i	−0.110227	−	0.190918i	−0.915862	+	0.401494i	$0.868491\pi$
$24$	−1.02863	−	1.78164i	−0.209968	−	0.363675i
$25$	6.46154			1.29231
$26$	0.251642	+	3.59676i	0.0493511	+	0.705383i
$27$	−3.63659			−0.699863
$28$		0			0
$29$	−1.15418	−	1.99910i	−0.214326	−	0.371224i	0.738738	−	0.673993i	$-0.235422\pi$
$29$	−1.15418	−	1.99910i	−0.214326	−	0.371224i	−0.953064	+	0.302769i	$0.902089\pi$
$30$	3.48241	−	6.03172i	0.635799	−	1.10124i
$31$	3.98121			0.715046			0.357523	−	0.933904i	$-0.383621\pi$
$31$	3.98121			0.715046			0.357523	+	0.933904i	$0.383621\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−3.92077	+	6.79097i	−0.682518	+	1.18216i
$34$	4.04396			0.693533
$35$		0			0
$36$	−0.616155	−	1.06721i	−0.102693	−	0.177869i
$37$	2.71208	+	4.69745i	0.445863	+	0.772257i	0.998112	−	0.0614223i	$-0.0195636\pi$
$37$	2.71208	+	4.69745i	0.445863	+	0.772257i	−0.552249	+	0.833679i	$0.686230\pi$
$38$	6.15867			0.999069
$39$	0.517693	+	7.39946i	0.0828972	+	1.18486i
$40$	−3.38549			−0.535293
$41$	−2.26094	−	3.91606i	−0.353099	−	0.611586i	0.633691	−	0.773586i	$-0.281539\pi$
$41$	−2.26094	−	3.91606i	−0.353099	−	0.611586i	−0.986791	+	0.162000i	$0.948206\pi$
$42$		0			0
$43$	3.46973	−	6.00975i	0.529129	−	0.916479i	−0.470294	−	0.882510i	$-0.655852\pi$
$43$	3.46973	−	6.00975i	0.529129	−	0.916479i	0.999423	−	0.0339686i	$-0.0108146\pi$
$44$	3.81165			0.574627
$45$	2.08599	−	3.61304i	0.310961	−	0.538599i
$46$	−0.528629	+	0.915612i	−0.0779421	+	0.135000i
$47$	5.54067			0.808190			0.404095	−	0.914717i	$-0.367586\pi$
$47$	5.54067			0.808190			0.404095	+	0.914717i	$0.367586\pi$
$48$	−1.02863	+	1.78164i	−0.148470	+	0.257157i
$49$		0			0
$50$	−3.23077	−	5.59586i	−0.456900	−	0.791374i
$51$	8.31946			1.16496
$52$	2.98906	−	2.01631i	0.414509	−	0.279612i
$53$	−7.63439			−1.04866			−0.524332	−	0.851514i	$-0.675685\pi$
$53$	−7.63439			−1.04866			−0.524332	+	0.851514i	$0.675685\pi$
$54$	1.81830	+	3.14938i	0.247439	+	0.428577i
$55$	6.45214	+	11.1754i	0.870007	+	1.50690i
$56$		0			0
$57$	12.6700			1.67818
$58$	−1.15418	+	1.99910i	−0.151551	+	0.262495i
$59$	3.74061	−	6.47892i	0.486985	−	0.843483i	−0.512903	−	0.858447i	$-0.671430\pi$
$59$	3.74061	−	6.47892i	0.486985	−	0.843483i	0.999888	+	0.0149633i	$0.00476315\pi$
$60$	−6.96483			−0.899155
$61$	6.39653	−	11.0791i	0.818992	−	1.41854i	−0.0874337	−	0.996170i	$-0.527867\pi$
$61$	6.39653	−	11.0791i	0.818992	−	1.41854i	0.906426	−	0.422365i	$-0.138800\pi$
$62$	−1.99060	−	3.44783i	−0.252807	−	0.437874i
$63$		0			0
$64$	1.00000			0.125000
$65$	10.9714	+	5.35060i	1.36083	+	0.663660i
$66$	7.84154			0.965227
$67$	4.42405	+	7.66269i	0.540484	+	0.936146i	0.998876	+	0.0473960i	$0.0150923\pi$
$67$	4.42405	+	7.66269i	0.540484	+	0.936146i	−0.458392	+	0.888750i	$0.651574\pi$
$68$	−2.02198	−	3.50217i	−0.245201	−	0.424700i
$69$	−1.08753	+	1.88365i	−0.130923	+	0.226765i
$70$		0			0
$71$	−7.21308	+	12.4934i	−0.856036	+	1.48270i	0.0196454	+	0.999807i	$0.493746\pi$
$71$	−7.21308	+	12.4934i	−0.856036	+	1.48270i	−0.875681	+	0.482890i	$0.839587\pi$
$72$	−0.616155	+	1.06721i	−0.0726146	+	0.125772i
$73$	7.23580			0.846886			0.423443	−	0.905923i	$-0.360821\pi$
$73$	7.23580			0.846886			0.423443	+	0.905923i	$0.360821\pi$
$74$	2.71208	−	4.69745i	0.315273	−	0.546068i
$75$	−6.64653	−	11.5121i	−0.767475	−	1.32931i
$76$	−3.07934	−	5.33357i	−0.353224	−	0.611802i
$77$		0			0
$78$	6.14928	−	4.14807i	0.696268	−	0.469676i
$79$	−0.445826			−0.0501594			−0.0250797	−	0.999685i	$-0.507984\pi$
$79$	−0.445826			−0.0501594			−0.0250797	+	0.999685i	$0.507984\pi$
$80$	1.69274	+	2.93192i	0.189255	+	0.327799i
$81$	5.58917	+	9.68073i	0.621019	+	1.07564i
$82$	−2.26094	+	3.91606i	−0.249679	+	0.432457i
$83$	15.1718			1.66532			0.832659	−	0.553786i	$-0.186817\pi$
$83$	15.1718			1.66532			0.832659	+	0.553786i	$0.186817\pi$
$84$		0			0
$85$	6.84539	−	11.8566i	0.742486	−	1.28602i
$86$	−6.93946			−0.748302
$87$	−2.37445	+	4.11266i	−0.254568	+	0.440924i
$88$	−1.90582	−	3.30098i	−0.203161	−	0.351886i
$89$	−4.11790	−	7.13241i	−0.436497	−	0.756034i	0.560920	−	0.827870i	$-0.310448\pi$
$89$	−4.11790	−	7.13241i	−0.436497	−	0.756034i	−0.997416	+	0.0718359i	$0.977114\pi$
$90$	−4.17197			−0.439765
$91$		0			0
$92$	1.05726			0.110227
$93$	−4.09518	−	7.09307i	−0.424651	−	0.735517i
$94$	−2.77034	−	4.79836i	−0.285738	−	0.494913i
$95$	10.4251	−	18.0567i	1.06959	−	1.85258i
$96$	2.05726			0.209968
$97$	−6.18181	+	10.7072i	−0.627668	+	1.08715i	0.360351	+	0.932817i	$0.382657\pi$
$97$	−6.18181	+	10.7072i	−0.627668	+	1.08715i	−0.988019	+	0.154335i	$0.950676\pi$
$98$		0			0
$99$	4.69713			0.472079
$100$	−3.23077	+	5.59586i	−0.323077	+	0.559586i
$101$	−6.11736	−	10.5956i	−0.608700	−	1.05430i	−0.991455	−	0.130450i	$-0.958358\pi$
$101$	−6.11736	−	10.5956i	−0.608700	−	1.05430i	0.382755	−	0.923850i	$-0.374975\pi$
$102$	−4.15973	−	7.20486i	−0.411875	−	0.713388i
$103$	−11.1906			−1.10264			−0.551320	−	0.834294i	$-0.685876\pi$
$103$	−11.1906			−1.10264			−0.551320	+	0.834294i	$0.685876\pi$
$104$	−3.24071	−	1.58045i	−0.317777	−	0.154976i
$105$		0			0
$106$	3.81720	+	6.61158i	0.370759	+	0.642173i
$107$	−0.681703	−	1.18074i	−0.0659027	−	0.114147i	0.831191	−	0.555986i	$-0.187659\pi$
$107$	−0.681703	−	1.18074i	−0.0659027	−	0.114147i	−0.897094	+	0.441840i	$0.854326\pi$
$108$	1.81830	−	3.14938i	0.174966	−	0.303049i
$109$	3.12889			0.299694			0.149847	−	0.988709i	$-0.452122\pi$
$109$	3.12889			0.299694			0.149847	+	0.988709i	$0.452122\pi$
$110$	6.45214	−	11.1754i	0.615188	−	1.06554i
$111$	5.57944	−	9.66388i	0.529577	−	0.917255i
$112$		0			0
$113$	6.53202	−	11.3138i	0.614481	−	1.06431i	−0.375995	−	0.926622i	$-0.622699\pi$
$113$	6.53202	−	11.3138i	0.614481	−	1.06431i	0.990475	−	0.137690i	$-0.0439677\pi$
$114$	−6.33499	−	10.9725i	−0.593326	−	1.02767i
$115$	1.78967	+	3.09980i	0.166887	+	0.289057i
$116$	2.30836			0.214326
$117$	3.68345	−	2.48472i	0.340535	−	0.229712i
$118$	−7.48121			−0.688701
$119$		0			0
$120$	3.48241	+	6.03172i	0.317899	+	0.550618i
$121$	−1.76432	+	3.05590i	−0.160393	+	0.277809i
$122$	−12.7931			−1.15823
$123$	−4.65133	+	8.05635i	−0.419397	+	0.726416i
$124$	−1.99060	+	3.44783i	−0.178761	+	0.309624i
$125$	−4.94803			−0.442566
$126$		0			0
$127$	1.67077	+	2.89385i	0.148257	+	0.256788i	0.930583	−	0.366081i	$-0.119301\pi$
$127$	1.67077	+	2.89385i	0.148257	+	0.256788i	−0.782327	+	0.622868i	$0.785967\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−14.2763			−1.25696
$130$	−0.851932	−	12.1768i	−0.0747194	−	1.06798i
$131$	2.53538			0.221517			0.110759	−	0.993847i	$-0.464672\pi$
$131$	2.53538			0.221517			0.110759	+	0.993847i	$0.464672\pi$
$132$	−3.92077	−	6.79097i	−0.341259	−	0.591078i
$133$		0			0
$134$	4.42405	−	7.66269i	0.382180	−	0.661955i
$135$	12.3117			1.05962
$136$	−2.02198	+	3.50217i	−0.173383	+	0.300309i
$137$	−6.30346	+	10.9179i	−0.538541	+	0.932780i	0.460442	+	0.887690i	$0.347691\pi$
$137$	−6.30346	+	10.9179i	−0.538541	+	0.932780i	−0.998983	+	0.0450901i	$0.985643\pi$
$138$	2.17505			0.185153
$139$	−9.41422	+	16.3059i	−0.798504	+	1.38305i	0.122086	+	0.992520i	$0.461042\pi$
$139$	−9.41422	+	16.3059i	−0.798504	+	1.38305i	−0.920590	+	0.390530i	$0.872292\pi$
$140$		0			0
$141$	−5.69930	−	9.87147i	−0.479967	−	0.831328i
$142$	14.4262			1.21062
$143$	0.959171	+	13.7096i	0.0802099	+	1.14645i
$144$	1.23231			0.102693
$145$	3.90747	+	6.76793i	0.324498	+	0.562046i
$146$	−3.61790	−	6.26639i	−0.299420	−	0.518610i
$147$		0			0
$148$	−5.42415			−0.445863
$149$	−0.450300	+	0.779942i	−0.0368900	+	0.0638954i	−0.883881	−	0.467712i	$-0.845078\pi$
$149$	−0.450300	+	0.779942i	−0.0368900	+	0.0638954i	0.846991	+	0.531607i	$0.178412\pi$
$150$	−6.64653	+	11.5121i	−0.542687	+	0.939961i
$151$	−8.51968			−0.693321			−0.346661	−	0.937991i	$-0.612684\pi$
$151$	−8.51968			−0.693321			−0.346661	+	0.937991i	$0.612684\pi$
$152$	−3.07934	+	5.33357i	−0.249767	+	0.432609i
$153$	−2.49170	−	4.31576i	−0.201442	−	0.348908i
$154$		0			0
$155$	−13.4783			−1.08261
$156$	−6.66697	−	3.25140i	−0.533785	−	0.260320i
$157$	17.1609			1.36959			0.684794	−	0.728737i	$-0.259892\pi$
$157$	17.1609			1.36959			0.684794	+	0.728737i	$0.259892\pi$
$158$	0.222913	+	0.386097i	0.0177340	+	0.0307162i
$159$	7.85296	+	13.6017i	0.622780	+	1.07869i
$160$	1.69274	−	2.93192i	0.133823	−	0.231789i
$161$		0			0
$162$	5.58917	−	9.68073i	0.439127	−	0.760590i
$163$	−7.66813	+	13.2816i	−0.600614	+	1.04029i	0.392114	+	0.919917i	$0.371744\pi$
$163$	−7.66813	+	13.2816i	−0.600614	+	1.04029i	−0.992728	+	0.120377i	$0.961590\pi$
$164$	4.52188			0.353099
$165$	13.2737	−	22.9908i	1.03336	−	1.78983i
$166$	−7.58589	−	13.1391i	−0.588779	−	1.01980i
$167$	8.86135	+	15.3483i	0.685712	+	1.18769i	0.973212	+	0.229908i	$0.0738424\pi$
$167$	8.86135	+	15.3483i	0.685712	+	1.18769i	−0.287500	+	0.957780i	$0.592824\pi$
$168$		0			0
$169$	8.00435	+	10.2436i	0.615719	+	0.787966i
$170$	−13.6908			−1.05003
$171$	−3.79470	−	6.57261i	−0.290188	−	0.502620i
$172$	3.46973	+	6.00975i	0.264565	+	0.458239i
$173$	−0.566755	+	0.981648i	−0.0430896	+	0.0746333i	−0.886766	−	0.462219i	$-0.847053\pi$
$173$	−0.566755	+	0.981648i	−0.0430896	+	0.0746333i	0.843676	+	0.536852i	$0.180387\pi$
$174$	4.74890			0.360013
$175$		0			0
$176$	−1.90582	+	3.30098i	−0.143657	+	0.248821i
$177$	−15.3908			−1.15684
$178$	−4.11790	+	7.13241i	−0.308650	+	0.534597i
$179$	−6.33334	−	10.9697i	−0.473376	−	0.819912i	0.526159	−	0.850386i	$-0.323632\pi$
$179$	−6.33334	−	10.9697i	−0.473376	−	0.819912i	−0.999536	+	0.0304742i	$0.990298\pi$
$180$	2.08599	+	3.61304i	0.155480	+	0.269300i
$181$	0.919394			0.0683380			0.0341690	−	0.999416i	$-0.489122\pi$
$181$	0.919394			0.0683380			0.0341690	+	0.999416i	$0.489122\pi$
$182$		0			0
$183$	−26.3186			−1.94553
$184$	−0.528629	−	0.915612i	−0.0389710	−	0.0674998i
$185$	−9.18171	−	15.9032i	−0.675053	−	1.16923i
$186$	−4.09518	+	7.09307i	−0.300273	+	0.520089i
$187$	15.4141			1.12719
$188$	−2.77034	+	4.79836i	−0.202048	+	0.349957i
$189$		0			0
$190$	−20.8501			−1.51263
$191$	−1.54293	+	2.67244i	−0.111643	+	0.193371i	−0.916433	−	0.400189i	$-0.868945\pi$
$191$	−1.54293	+	2.67244i	−0.111643	+	0.193371i	0.804790	+	0.593560i	$0.202278\pi$
$192$	−1.02863	−	1.78164i	−0.0742349	−	0.128579i
$193$	10.4549	+	18.1084i	0.752560	+	1.30347i	0.946578	+	0.322474i	$0.104514\pi$
$193$	10.4549	+	18.1084i	0.752560	+	1.30347i	−0.194019	+	0.980998i	$0.562152\pi$
$194$	12.3636			0.887656
$195$	−1.75264	−	25.0508i	−0.125509	−	1.79393i
$196$		0			0
$197$	1.71308	+	2.96714i	0.122052	+	0.211400i	0.920577	−	0.390562i	$-0.127719\pi$
$197$	1.71308	+	2.96714i	0.122052	+	0.211400i	−0.798525	+	0.601962i	$0.794386\pi$
$198$	−2.34857	−	4.06783i	−0.166905	−	0.289088i
$199$	−6.44121	+	11.1565i	−0.456605	+	0.790863i	−0.998779	−	0.0494031i	$-0.984268\pi$
$199$	−6.44121	+	11.1565i	−0.456605	+	0.790863i	0.542174	+	0.840266i	$0.317601\pi$
$200$	6.46154			0.456900
$201$	9.10142	−	15.7641i	0.641965	−	1.11192i
$202$	−6.11736	+	10.5956i	−0.430416	+	0.745503i
$203$		0			0
$204$	−4.15973	+	7.20486i	−0.291239	+	0.504441i
$205$	7.65439	+	13.2578i	0.534606	+	0.925964i
$206$	5.59528	+	9.69132i	0.389842	+	0.675226i
$207$	1.30287			0.0905557
$208$	0.251642	+	3.59676i	0.0174482	+	0.249390i
$209$	23.4747			1.62378
$210$		0			0
$211$	2.06776	+	3.58146i	0.142350	+	0.246558i	0.928381	−	0.371629i	$-0.121201\pi$
$211$	2.06776	+	3.58146i	0.142350	+	0.246558i	−0.786031	+	0.618187i	$0.787867\pi$
$212$	3.81720	−	6.61158i	0.262166	−	0.454085i
$213$	29.6783			2.03353
$214$	−0.681703	+	1.18074i	−0.0466003	+	0.0807140i
$215$	−11.7467	+	20.3460i	−0.801121	+	1.38758i
$216$	−3.63659			−0.247439
$217$		0			0
$218$	−1.56445	−	2.70970i	−0.105958	−	0.183524i
$219$	−7.44295	−	12.8916i	−0.502948	−	0.871132i
$220$	−12.9043			−0.870007
$221$	12.0876	−	8.15386i	0.813103	−	0.548488i
$222$	−11.1589			−0.748935
$223$	−1.07475	−	1.86151i	−0.0719703	−	0.124656i	0.827794	−	0.561031i	$-0.189595\pi$
$223$	−1.07475	−	1.86151i	−0.0719703	−	0.124656i	−0.899765	+	0.436375i	$0.856262\pi$
$224$		0			0
$225$	−3.98131	+	6.89583i	−0.265421	+	0.459722i
$226$	−13.0640			−0.869007
$227$	−3.91933	+	6.78848i	−0.260135	+	0.450567i	−0.966278	−	0.257503i	$-0.917100\pi$
$227$	−3.91933	+	6.78848i	−0.260135	+	0.450567i	0.706143	+	0.708070i	$0.250434\pi$
$228$	−6.33499	+	10.9725i	−0.419545	+	0.726673i
$229$	−11.9548			−0.789996			−0.394998	−	0.918682i	$-0.629255\pi$
$229$	−11.9548			−0.789996			−0.394998	+	0.918682i	$0.629255\pi$
$230$	1.78967	−	3.09980i	0.118007	−	0.204394i
$231$		0			0
$232$	−1.15418	−	1.99910i	−0.0757757	−	0.131247i
$233$	28.0681			1.83880			0.919400	−	0.393325i	$-0.128675\pi$
$233$	28.0681			1.83880			0.919400	+	0.393325i	$0.128675\pi$
$234$	−3.99355	−	1.94761i	−0.261067	−	0.127319i
$235$	−18.7579			−1.22363
$236$	3.74061	+	6.47892i	0.243493	+	0.421742i
$237$	0.458590	+	0.794301i	0.0297886	+	0.0515954i
$238$		0			0
$239$	−14.8144			−0.958262			−0.479131	−	0.877743i	$-0.659048\pi$
$239$	−14.8144			−0.958262			−0.479131	+	0.877743i	$0.659048\pi$
$240$	3.48241	−	6.03172i	0.224789	−	0.389346i
$241$	0.473016	−	0.819288i	0.0304696	−	0.0527750i	−0.850388	−	0.526155i	$-0.823633\pi$
$241$	0.473016	−	0.819288i	0.0304696	−	0.0527750i	0.880858	+	0.473380i	$0.156966\pi$
$242$	3.52865			0.226830
$243$	6.04348	−	10.4676i	0.387689	−	0.671497i
$244$	6.39653	+	11.0791i	0.409496	+	0.709268i
$245$		0			0
$246$	9.30267			0.593117
$247$	18.4087	−	12.4178i	1.17132	−	0.790124i
$248$	3.98121			0.252807
$249$	−15.6061	−	27.0306i	−0.988998	−	1.71299i
$250$	2.47402	+	4.28512i	0.156471	+	0.271015i
$251$	6.43291	−	11.1421i	0.406042	−	0.703285i	−0.588400	−	0.808570i	$-0.700242\pi$
$251$	6.43291	−	11.1421i	0.406042	−	0.703285i	0.994442	+	0.105285i	$0.0335754\pi$
$252$		0			0
$253$	−2.01495	+	3.48999i	−0.126679	+	0.219414i
$254$	1.67077	−	2.89385i	0.104833	−	0.181576i
$255$	−28.1655			−1.76379
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.70763	+	2.95771i	0.106519	+	0.184497i	0.914358	−	0.404907i	$-0.132696\pi$
$257$	1.70763	+	2.95771i	0.106519	+	0.184497i	−0.807839	+	0.589404i	$0.799363\pi$
$258$	7.13813	+	12.3636i	0.444401	+	0.769725i
$259$		0			0
$260$	−10.1194	+	6.82619i	−0.627581	+	0.423342i
$261$	2.84462			0.176077
$262$	−1.26769	−	2.19570i	−0.0783181	−	0.135651i
$263$	0.223096	+	0.386413i	0.0137567	+	0.0238272i	0.872822	−	0.488039i	$-0.162288\pi$
$263$	0.223096	+	0.386413i	0.0137567	+	0.0238272i	−0.859065	+	0.511866i	$0.828954\pi$
$264$	−3.92077	+	6.79097i	−0.241307	+	0.417955i
$265$	25.8462			1.58772
$266$		0			0
$267$	−8.47158	+	14.6732i	−0.518452	+	0.897986i
$268$	−8.84811			−0.540484
$269$	−2.05561	+	3.56043i	−0.125333	+	0.217083i	−0.921863	−	0.387516i	$-0.873333\pi$
$269$	−2.05561	+	3.56043i	−0.125333	+	0.217083i	0.796530	+	0.604599i	$0.206667\pi$
$270$	−6.15583	−	10.6622i	−0.374632	−	0.648881i
$271$	6.67506	+	11.5615i	0.405481	+	0.702314i	0.994377	−	0.105895i	$-0.0337707\pi$
$271$	6.67506	+	11.5615i	0.405481	+	0.702314i	−0.588896	+	0.808209i	$0.700437\pi$
$272$	4.04396			0.245201
$273$		0			0
$274$	12.6069			0.761611
$275$	−12.3146	−	21.3294i	−0.742596	−	1.28621i
$276$	−1.08753	−	1.88365i	−0.0654614	−	0.113382i
$277$	−9.47805	+	16.4165i	−0.569481	+	0.986369i	0.427137	+	0.904187i	$0.359522\pi$
$277$	−9.47805	+	16.4165i	−0.569481	+	0.986369i	−0.996617	+	0.0821822i	$0.973811\pi$
$278$	18.8284			1.12926
$279$	−2.45304	+	4.24879i	−0.146860	+	0.254368i
$280$		0			0
$281$	−0.101414			−0.00604986			−0.00302493	−	0.999995i	$-0.500963\pi$
$281$	−0.101414			−0.00604986			−0.00302493	+	0.999995i	$0.500963\pi$
$282$	−5.69930	+	9.87147i	−0.339388	+	0.587837i
$283$	−2.43889	−	4.22429i	−0.144977	−	0.251108i	0.784387	−	0.620271i	$-0.212978\pi$
$283$	−2.43889	−	4.22429i	−0.144977	−	0.251108i	−0.929364	+	0.369164i	$0.879644\pi$
$284$	−7.21308	−	12.4934i	−0.428018	−	0.741349i
$285$	−42.8941			−2.54083
$286$	11.3933	−	7.68545i	0.673697	−	0.454450i
$287$		0			0
$288$	−0.616155	−	1.06721i	−0.0363073	−	0.0628861i
$289$	0.323209	+	0.559814i	0.0190123	+	0.0329302i
$290$	3.90747	−	6.76793i	0.229454	−	0.397427i
$291$	25.4351			1.49103
$292$	−3.61790	+	6.26639i	−0.211722	+	0.366713i
$293$	−12.4185	+	21.5095i	−0.725497	+	1.25660i	0.233272	+	0.972412i	$0.425057\pi$
$293$	−12.4185	+	21.5095i	−0.725497	+	1.25660i	−0.958769	+	0.284186i	$0.908277\pi$
$294$		0			0
$295$	−12.6638	+	21.9343i	−0.737314	+	1.27707i
$296$	2.71208	+	4.69745i	0.157636	+	0.273034i
$297$	6.93070	+	12.0043i	0.402160	+	0.696562i
$298$	0.900600			0.0521704
$299$	0.266051	+	3.80270i	0.0153861	+	0.219916i
$300$	13.2931			0.767475
$301$		0			0
$302$	4.25984	+	7.37826i	0.245126	+	0.424571i
$303$	−12.5850	+	21.7978i	−0.722989	+	1.25225i
$304$	6.15867			0.353224
$305$	−21.6554	+	37.5082i	−1.23998	+	2.14772i
$306$	−2.49170	+	4.31576i	−0.142441	+	0.246715i
$307$	−11.9098			−0.679727			−0.339864	−	0.940475i	$-0.610381\pi$
$307$	−11.9098			−0.679727			−0.339864	+	0.940475i	$0.610381\pi$
$308$		0			0
$309$	11.5109	+	19.9375i	0.654835	+	1.13421i
$310$	6.73917	+	11.6726i	0.382759	+	0.662958i
$311$	−3.96385			−0.224769			−0.112385	−	0.993665i	$-0.535849\pi$
$311$	−3.96385			−0.224769			−0.112385	+	0.993665i	$0.535849\pi$
$312$	0.517693	+	7.39946i	0.0293086	+	0.418912i
$313$	27.4483			1.55147			0.775733	−	0.631061i	$-0.217380\pi$
$313$	27.4483			1.55147			0.775733	+	0.631061i	$0.217380\pi$
$314$	−8.58044	−	14.8618i	−0.484222	−	0.838698i
$315$		0			0
$316$	0.222913	−	0.386097i	0.0125398	−	0.0217197i
$317$	−24.5715			−1.38008			−0.690038	−	0.723774i	$-0.742406\pi$
$317$	−24.5715			−1.38008			−0.690038	+	0.723774i	$0.742406\pi$
$318$	7.85296	−	13.6017i	0.440372	−	0.762747i
$319$	−4.39933	+	7.61986i	−0.246315	+	0.426630i
$320$	−3.38549			−0.189255
$321$	−1.40244	+	2.42910i	−0.0782765	+	0.135579i
$322$		0			0
$323$	−12.4527	−	21.5687i	−0.692887	−	1.20012i
$324$	−11.1783			−0.621019
$325$	−20.9400	−	10.2122i	−1.16154	−	0.566468i
$326$	15.3363			0.849396
$327$	−3.21847	−	5.57455i	−0.177982	−	0.308274i
$328$	−2.26094	−	3.91606i	−0.124839	−	0.216228i
$329$		0			0
$330$	−26.5475			−1.46139
$331$	−14.3268	+	24.8148i	−0.787472	+	1.36394i	0.140039	+	0.990146i	$0.455277\pi$
$331$	−14.3268	+	24.8148i	−0.787472	+	1.36394i	−0.927511	+	0.373796i	$0.878056\pi$
$332$	−7.58589	+	13.1391i	−0.416330	+	0.721104i
$333$	−6.68424			−0.366294
$334$	8.86135	−	15.3483i	0.484872	−	0.839822i
$335$	−14.9776	−	25.9419i	−0.818313	−	1.41736i
$336$		0			0
$337$	8.86295			0.482795			0.241398	−	0.970426i	$-0.422394\pi$
$337$	8.86295			0.482795			0.241398	+	0.970426i	$0.422394\pi$
$338$	4.86900	−	12.0537i	0.264839	−	0.655637i
$339$	−26.8761			−1.45971
$340$	6.84539	+	11.8566i	0.371243	+	0.643012i
$341$	−7.58747	−	13.1419i	−0.410885	−	0.711673i
$342$	−3.79470	+	6.57261i	−0.205194	+	0.355406i
$343$		0			0
$344$	3.46973	−	6.00975i	0.187075	−	0.324024i
$345$	3.68181	−	6.37708i	0.198222	−	0.343330i
$346$	1.13351			0.0609379
$347$	−0.628304	+	1.08825i	−0.0337291	+	0.0584205i	−0.882397	−	0.470505i	$-0.844072\pi$
$347$	−0.628304	+	1.08825i	−0.0337291	+	0.0584205i	0.848668	+	0.528926i	$0.177405\pi$
$348$	−2.37445	−	4.11266i	−0.127284	−	0.220462i
$349$	−11.8310	−	20.4919i	−0.633298	−	1.09690i	−0.986873	−	0.161499i	$-0.948367\pi$
$349$	−11.8310	−	20.4919i	−0.633298	−	1.09690i	0.353575	−	0.935406i	$-0.384966\pi$
$350$		0			0
$351$	11.7851	+	5.74746i	0.629044	+	0.306777i
$352$	3.81165			0.203161
$353$	5.96308	+	10.3284i	0.317383	+	0.549723i	0.979941	−	0.199287i	$-0.0638627\pi$
$353$	5.96308	+	10.3284i	0.317383	+	0.549723i	−0.662558	+	0.749010i	$0.730529\pi$
$354$	7.69539	+	13.3288i	0.409005	+	0.708418i
$355$	24.4198	−	42.2964i	1.29607	−	2.24486i
$356$	8.23580			0.436497
$357$		0			0
$358$	−6.33334	+	10.9697i	−0.334728	+	0.579765i
$359$	−2.96827			−0.156659			−0.0783296	−	0.996928i	$-0.524959\pi$
$359$	−2.96827			−0.156659			−0.0783296	+	0.996928i	$0.524959\pi$
$360$	2.08599	−	3.61304i	0.109941	−	0.190424i
$361$	−9.46462	−	16.3932i	−0.498138	−	0.862800i
$362$	−0.459697	−	0.796218i	−0.0241611	−	0.0418483i
$363$	7.25934			0.381016
$364$		0			0
$365$	−24.4967			−1.28222
$366$	13.1593	+	22.7926i	0.687848	+	1.19139i
$367$	−6.64234	−	11.5049i	−0.346728	−	0.600550i	0.638939	−	0.769258i	$-0.279374\pi$
$367$	−6.64234	−	11.5049i	−0.346728	−	0.600550i	−0.985666	+	0.168708i	$0.946040\pi$
$368$	−0.528629	+	0.915612i	−0.0275567	+	0.0477296i
$369$	5.57236			0.290085
$370$	−9.18171	+	15.9032i	−0.477334	+	0.826767i
$371$		0			0
$372$	8.19037			0.424651
$373$	−9.83098	+	17.0278i	−0.509029	+	0.881664i	0.490917	+	0.871207i	$0.336662\pi$
$373$	−9.83098	+	17.0278i	−0.509029	+	0.881664i	−0.999945	+	0.0104571i	$0.996671\pi$
$374$	−7.70707	−	13.3490i	−0.398523	−	0.690262i
$375$	5.08969	+	8.81560i	0.262831	+	0.455236i
$376$	5.54067			0.285738
$377$	0.580881	+	8.30262i	0.0299169	+	0.427607i
$378$		0			0
$379$	−17.0038	−	29.4514i	−0.873425	−	1.51282i	−0.858431	−	0.512929i	$-0.828560\pi$
$379$	−17.0038	−	29.4514i	−0.873425	−	1.51282i	−0.0149946	−	0.999888i	$-0.504773\pi$
$380$	10.4251	+	18.0567i	0.534794	+	0.926291i
$381$	3.43720	−	5.95340i	0.176093	−	0.305002i
$382$	3.08586			0.157887
$383$	−17.9032	+	31.0092i	−0.914810	+	1.58450i	−0.107631	+	0.994191i	$0.534326\pi$
$383$	−17.9032	+	31.0092i	−0.914810	+	1.58450i	−0.807179	+	0.590306i	$0.799007\pi$
$384$	−1.02863	+	1.78164i	−0.0524920	+	0.0909188i
$385$		0			0
$386$	10.4549	−	18.1084i	0.532140	−	0.921693i
$387$	4.27579	+	7.40588i	0.217350	+	0.376462i
$388$	−6.18181	−	10.7072i	−0.313834	−	0.543576i
$389$	−14.7591			−0.748318			−0.374159	−	0.927365i	$-0.622069\pi$
$389$	−14.7591			−0.748318			−0.374159	+	0.927365i	$0.622069\pi$
$390$	−20.8183	+	14.0432i	−1.05418	+	0.711107i
$391$	4.27550			0.216222
$392$		0			0
$393$	−2.60796	−	4.51713i	−0.131554	−	0.227859i
$394$	1.71308	−	2.96714i	0.0863036	−	0.149482i
$395$	1.50934			0.0759432
$396$	−2.34857	+	4.06783i	−0.118020	+	0.204416i
$397$	14.2043	−	24.6026i	0.712895	−	1.23477i	−0.250871	−	0.968021i	$-0.580717\pi$
$397$	14.2043	−	24.6026i	0.712895	−	1.23477i	0.963766	−	0.266750i	$-0.0859497\pi$
$398$	12.8824			0.645737
$399$		0			0
$400$	−3.23077	−	5.59586i	−0.161539	−	0.279793i
$401$	−10.3718	−	17.9645i	−0.517944	−	0.897105i	−0.999783	−	0.0208450i	$-0.993364\pi$
$401$	−10.3718	−	17.9645i	−0.517944	−	0.897105i	0.481839	−	0.876260i	$-0.339969\pi$
$402$	−18.2028			−0.907875
$403$	−12.9019	−	6.29210i	−0.642690	−	0.313432i
$404$	12.2347			0.608700
$405$	−18.9221	−	32.7740i	−0.940246	−	1.62855i
$406$		0			0
$407$	10.3375	−	17.9050i	0.512410	−	0.887520i
$408$	8.31946			0.411875
$409$	7.88886	−	13.6639i	0.390079	−	0.675637i	−0.602380	−	0.798209i	$-0.705781\pi$
$409$	7.88886	−	13.6639i	0.390079	−	0.675637i	0.992460	+	0.122572i	$0.0391143\pi$
$410$	7.65439	−	13.2578i	0.378023	−	0.654755i
$411$	25.9357			1.27931
$412$	5.59528	−	9.69132i	0.275660	−	0.477457i
$413$		0			0
$414$	−0.651435	−	1.12832i	−0.0320163	−	0.0554538i
$415$	−51.3639			−2.52135
$416$	2.98906	−	2.01631i	0.146551	−	0.0988576i
$417$	38.7350			1.89686
$418$	−11.7373	−	20.3297i	−0.574092	−	0.994357i
$419$	2.80653	+	4.86106i	0.137108	+	0.237478i	0.926401	−	0.376539i	$-0.122886\pi$
$419$	2.80653	+	4.86106i	0.137108	+	0.237478i	−0.789293	+	0.614017i	$0.789553\pi$
$420$		0			0
$421$	15.1986			0.740736			0.370368	−	0.928885i	$-0.379232\pi$
$421$	15.1986			0.740736			0.370368	+	0.928885i	$0.379232\pi$
$422$	2.06776	−	3.58146i	0.100657	−	0.174343i
$423$	−3.41391	+	5.91307i	−0.165990	+	0.287503i
$424$	−7.63439			−0.370759
$425$	−13.0651	+	22.6294i	−0.633750	+	1.09769i
$426$	−14.8392	−	25.7022i	−0.718960	−	1.24528i
$427$		0			0
$428$	1.36341			0.0659027
$429$	23.4389	−	15.8110i	1.13164	−	0.763360i
$430$	23.4935			1.13296
$431$	−1.68571	−	2.91974i	−0.0811980	−	0.140639i	0.822567	−	0.568668i	$-0.192541\pi$
$431$	−1.68571	−	2.91974i	−0.0811980	−	0.140639i	−0.903765	+	0.428030i	$0.859208\pi$
$432$	1.81830	+	3.14938i	0.0874829	+	0.151525i
$433$	−8.11993	+	14.0641i	−0.390219	+	0.675879i	−0.992478	−	0.122421i	$-0.960934\pi$
$433$	−8.11993	+	14.0641i	−0.390219	+	0.675879i	0.602259	+	0.798301i	$0.294267\pi$
$434$		0			0
$435$	8.03867	−	13.9234i	0.385425	−	0.667575i
$436$	−1.56445	+	2.70970i	−0.0749234	+	0.129771i
$437$	6.51130			0.311478
$438$	−7.44295	+	12.8916i	−0.355638	+	0.615983i
$439$	12.0552	+	20.8802i	0.575361	+	0.996555i	0.996002	+	0.0893280i	$0.0284719\pi$
$439$	12.0552	+	20.8802i	0.575361	+	0.996555i	−0.420641	+	0.907227i	$0.638195\pi$
$440$	6.45214	+	11.1754i	0.307594	+	0.532768i
$441$		0			0
$442$	−13.1053	−	6.39128i	−0.623354	−	0.304002i
$443$	−24.9857			−1.18711			−0.593554	−	0.804794i	$-0.702276\pi$
$443$	−24.9857			−1.18711			−0.593554	+	0.804794i	$0.702276\pi$
$444$	5.57944	+	9.66388i	0.264789	+	0.458627i
$445$	13.9411	+	24.1467i	0.660872	+	1.14466i
$446$	−1.07475	+	1.86151i	−0.0508907	+	0.0881452i
$447$	1.85277			0.0876328
$448$		0			0
$449$	18.3685	−	31.8153i	0.866865	−	1.50145i	0.00168225	−	0.999999i	$-0.499465\pi$
$449$	18.3685	−	31.8153i	0.866865	−	1.50145i	0.865183	−	0.501456i	$-0.167202\pi$
$450$	7.96262			0.375362
$451$	−8.61790	+	14.9266i	−0.405801	+	0.702868i
$452$	6.53202	+	11.3138i	0.307240	+	0.532156i
$453$	8.76359	+	15.1790i	0.411749	+	0.713170i
$454$	7.83866			0.367887
$455$		0			0
$456$	12.6700			0.593326
$457$	−0.583289	−	1.01029i	−0.0272851	−	0.0472592i	0.852060	−	0.523443i	$-0.175353\pi$
$457$	−0.583289	−	1.01029i	−0.0272851	−	0.0472592i	−0.879346	+	0.476184i	$0.842020\pi$
$458$	5.97741	+	10.3532i	0.279306	+	0.483772i
$459$	7.35311	−	12.7360i	0.343214	−	0.594464i
$460$	−3.57934			−0.166887
$461$	−6.97353	+	12.0785i	−0.324790	+	0.562552i	−0.981470	−	0.191617i	$-0.938627\pi$
$461$	−6.97353	+	12.0785i	−0.324790	+	0.562552i	0.656680	+	0.754169i	$0.271960\pi$
$462$		0			0
$463$	−14.0476			−0.652849			−0.326425	−	0.945223i	$-0.605844\pi$
$463$	−14.0476			−0.652849			−0.326425	+	0.945223i	$0.605844\pi$
$464$	−1.15418	+	1.99910i	−0.0535815	+	0.0928059i
$465$	13.8642	+	24.0135i	0.642937	+	1.11360i
$466$	−14.0340	−	24.3076i	−0.650114	−	1.12603i
$467$	−8.46057			−0.391508			−0.195754	−	0.980653i	$-0.562715\pi$
$467$	−8.46057			−0.391508			−0.195754	+	0.980653i	$0.562715\pi$
$468$	0.310101	+	4.43232i	0.0143344	+	0.204884i
$469$		0			0
$470$	9.37894	+	16.2448i	0.432618	+	0.749317i
$471$	−17.6522	−	30.5745i	−0.813370	−	1.40880i
$472$	3.74061	−	6.47892i	0.172175	−	0.298216i
$473$	−26.4508			−1.21621
$474$	0.458590	−	0.794301i	0.0210637	−	0.0364835i
$475$	−19.8973	+	34.4631i	−0.912949	+	1.58127i
$476$		0			0
$477$	4.70397	−	8.14751i	0.215380	−	0.373049i
$478$	7.40719	+	12.8296i	0.338797	+	0.586813i
$479$	0.909522	+	1.57534i	0.0415571	+	0.0719791i	0.886056	−	0.463579i	$-0.153435\pi$
$479$	0.909522	+	1.57534i	0.0415571	+	0.0719791i	−0.844499	+	0.535558i	$0.820101\pi$
$480$	−6.96483			−0.317899
$481$	−1.36495	−	19.5094i	−0.0622362	−	0.889551i
$482$	−0.946032			−0.0430906
$483$		0			0
$484$	−1.76432	−	3.05590i	−0.0801965	−	0.138904i
$485$	20.9285	−	36.2491i	0.950312	−	1.64599i
$486$	−12.0870			−0.548275
$487$	−11.0288	+	19.1025i	−0.499764	+	0.865617i	−1.00000		0.000272262i	$-0.999913\pi$
$487$	−11.0288	+	19.1025i	−0.499764	+	0.865617i	0.500236	+	0.865889i	$0.333247\pi$
$488$	6.39653	−	11.0791i	0.289557	−	0.501528i
$489$	31.5506			1.42677
$490$		0			0
$491$	9.99653	+	17.3145i	0.451137	+	0.781393i	0.998457	−	0.0555310i	$-0.0176852\pi$
$491$	9.99653	+	17.3145i	0.451137	+	0.781393i	−0.547320	+	0.836924i	$0.684352\pi$
$492$	−4.65133	−	8.05635i	−0.209698	−	0.363208i
$493$	9.33491			0.420423
$494$	−19.9584	−	9.73348i	−0.897973	−	0.437930i
$495$	−15.9021			−0.714746
$496$	−1.99060	−	3.44783i	−0.0893807	−	0.154812i
$497$		0			0
$498$	−15.6061	+	27.0306i	−0.699327	+	1.21127i
$499$	36.7577			1.64550			0.822750	−	0.568403i	$-0.192439\pi$
$499$	36.7577			1.64550			0.822750	+	0.568403i	$0.192439\pi$
$500$	2.47402	−	4.28512i	0.110641	−	0.191637i
$501$	18.2301	−	31.5754i	0.814460	−	1.41069i
$502$	−12.8658			−0.574230
$503$	16.7668	−	29.0409i	0.747594	−	1.29487i	−0.201378	−	0.979514i	$-0.564542\pi$
$503$	16.7668	−	29.0409i	0.747594	−	1.29487i	0.948973	−	0.315358i	$-0.102125\pi$
$504$		0			0
$505$	20.7103	+	35.8712i	0.921595	+	1.59625i
$506$	4.02989			0.179151
$507$	10.0168	−	24.7977i	0.444862	−	1.10130i
$508$	−3.34153			−0.148257
$509$	10.6267	+	18.4059i	0.471018	+	0.815828i	0.999450	−	0.0331478i	$-0.0105532\pi$
$509$	10.6267	+	18.4059i	0.471018	+	0.815828i	−0.528432	+	0.848976i	$0.677220\pi$
$510$	14.0827	+	24.3920i	0.623594	+	1.08010i
$511$		0			0
$512$	1.00000			0.0441942
$513$	11.1983	−	19.3960i	0.494417	−	0.856355i
$514$	1.70763	−	2.95771i	0.0753205	−	0.130459i
$515$	37.8856			1.66944
$516$	7.13813	−	12.3636i	0.314239	−	0.544278i
$517$	−10.5595	−	18.2897i	−0.464408	−	0.804378i
$518$		0			0
$519$	2.33192			0.102360
$520$	10.9714	+	5.35060i	0.481127	+	0.234639i
$521$	−5.70736			−0.250044			−0.125022	−	0.992154i	$-0.539900\pi$
$521$	−5.70736			−0.250044			−0.125022	+	0.992154i	$0.539900\pi$
$522$	−1.42231	−	2.46351i	−0.0622528	−	0.107825i
$523$	−8.77764	−	15.2033i	−0.383819	−	0.664794i	0.607785	−	0.794101i	$-0.292058\pi$
$523$	−8.77764	−	15.2033i	−0.383819	−	0.664794i	−0.991605	+	0.129307i	$0.958725\pi$
$524$	−1.26769	+	2.19570i	−0.0553793	+	0.0959197i
$525$		0			0
$526$	0.223096	−	0.386413i	0.00972743	−	0.0168484i
$527$	−8.04991	+	13.9429i	−0.350660	+	0.607360i
$528$	7.84154			0.341259
$529$	10.9411	−	18.9505i	0.475700	−	0.823937i
$530$	−12.9231	−	22.3834i	−0.561343	−	0.972274i
$531$	4.60959	+	7.98404i	0.200039	+	0.346478i
$532$		0			0
$533$	1.13789	+	16.2641i	0.0492877	+	0.704477i
$534$	16.9432			0.733202
$535$	2.30790	+	3.99740i	0.0997792	+	0.172823i
$536$	4.42405	+	7.66269i	0.191090	+	0.330978i
$537$	−13.0293	+	22.5674i	−0.562257	+	0.973857i
$538$	4.11123			0.177248
$539$		0			0
$540$	−6.15583	+	10.6622i	−0.264905	+	0.458828i
$541$	20.6797			0.889089			0.444545	−	0.895757i	$-0.353366\pi$
$541$	20.6797			0.889089			0.444545	+	0.895757i	$0.353366\pi$
$542$	6.67506	−	11.5615i	0.286718	−	0.496611i
$543$	−0.945715	−	1.63803i	−0.0405845	−	0.0702945i
$544$	−2.02198	−	3.50217i	−0.0866916	−	0.150154i
$545$	−10.5928			−0.453747
$546$		0			0
$547$	18.2669			0.781035			0.390517	−	0.920596i	$-0.372296\pi$
$547$	18.2669			0.781035			0.390517	+	0.920596i	$0.372296\pi$
$548$	−6.30346	−	10.9179i	−0.269270	−	0.466390i
$549$	7.88251	+	13.6529i	0.336417	+	0.582692i
$550$	−12.3146	+	21.3294i	−0.525094	+	0.909490i
$551$	14.2164			0.605641
$552$	−1.08753	+	1.88365i	−0.0462882	+	0.0801735i
$553$		0			0
$554$	18.9561			0.805367
$555$	−18.8891	+	32.7170i	−0.801799	+	1.38876i
$556$	−9.41422	−	16.3059i	−0.399252	−	0.691525i
$557$	−5.91543	−	10.2458i	−0.250645	−	0.434129i	0.713059	−	0.701104i	$-0.247309\pi$
$557$	−5.91543	−	10.2458i	−0.250645	−	0.434129i	−0.963703	+	0.266975i	$0.913976\pi$
$558$	4.90608			0.207691
$559$	−20.7425	+	13.9921i	−0.877314	+	0.591803i
$560$		0			0
$561$	−15.8554	−	27.4624i	−0.669416	−	1.15946i
$562$	0.0507070	+	0.0878272i	0.00213895	+	0.00370476i
$563$	−6.48506	+	11.2325i	−0.273313	+	0.473391i	−0.969708	−	0.244267i	$-0.921453\pi$
$563$	−6.48506	+	11.2325i	−0.273313	+	0.473391i	0.696395	+	0.717658i	$0.254786\pi$
$564$	11.3986			0.479967
$565$	−22.1141	+	38.3027i	−0.930346	+	1.61141i
$566$	−2.43889	+	4.22429i	−0.102514	+	0.177560i
$567$		0			0
$568$	−7.21308	+	12.4934i	−0.302654	+	0.524213i
$569$	−10.6978	−	18.5291i	−0.448475	−	0.776782i	0.549812	−	0.835289i	$-0.314699\pi$
$569$	−10.6978	−	18.5291i	−0.448475	−	0.776782i	−0.998287	+	0.0585066i	$0.981366\pi$
$570$	21.4470	+	37.1474i	0.898318	+	1.55593i
$571$	4.87707			0.204099			0.102050	−	0.994779i	$-0.467460\pi$
$571$	4.87707			0.204099			0.102050	+	0.994779i	$0.467460\pi$
$572$	−12.3524	−	6.02412i	−0.516481	−	0.251881i
$573$	6.34842			0.265209
$574$		0			0
$575$	−3.41576	−	5.91627i	−0.142447	−	0.246725i
$576$	−0.616155	+	1.06721i	−0.0256731	+	0.0444672i
$577$	42.7062			1.77788			0.888942	−	0.458020i	$-0.151441\pi$
$577$	42.7062			1.77788			0.888942	+	0.458020i	$0.151441\pi$
$578$	0.323209	−	0.559814i	0.0134437	−	0.0232852i
$579$	21.5084	−	37.2537i	0.893859	−	1.54821i
$580$	−7.81494			−0.324498
$581$		0			0
$582$	−12.7176	−	22.0275i	−0.527160	−	0.913069i
$583$	14.5498	+	25.2010i	0.602591	+	1.04372i
$584$	7.23580			0.299420
$585$	−12.4703	+	8.41198i	−0.515583	+	0.347793i
$586$	24.8370			1.02601
$587$	10.9345	+	18.9390i	0.451313	+	0.781698i	0.998468	−	0.0553339i	$-0.0176223\pi$
$587$	10.9345	+	18.9390i	0.451313	+	0.781698i	−0.547155	+	0.837032i	$0.684289\pi$
$588$		0			0
$589$	−12.2595	+	21.2340i	−0.505143	+	0.874933i
$590$	25.3276			1.04272
$591$	3.52424	−	6.10417i	0.144968	−	0.251092i
$592$	2.71208	−	4.69745i	0.111466	−	0.193064i
$593$	−16.2927			−0.669061			−0.334531	−	0.942385i	$-0.608578\pi$
$593$	−16.2927			−0.669061			−0.334531	+	0.942385i	$0.608578\pi$
$594$	6.93070	−	12.0043i	0.284370	−	0.492544i
$595$		0			0
$596$	−0.450300	−	0.779942i	−0.0184450	−	0.0319477i
$597$	26.5025			1.08467
$598$	3.16021	−	2.13176i	0.129231	−	0.0871741i
$599$	−7.21526			−0.294808			−0.147404	−	0.989076i	$-0.547092\pi$
$599$	−7.21526			−0.294808			−0.147404	+	0.989076i	$0.547092\pi$
$600$	−6.64653	−	11.5121i	−0.271343	−	0.469981i
$601$	8.29314	+	14.3641i	0.338284	+	0.585926i	0.984110	−	0.177559i	$-0.0568201\pi$
$601$	8.29314	+	14.3641i	0.338284	+	0.585926i	−0.645826	+	0.763485i	$0.723487\pi$
$602$		0			0
$603$	−10.9036			−0.444029
$604$	4.25984	−	7.37826i	0.173330	−	0.300217i
$605$	5.97310	−	10.3457i	0.242841	−	0.420613i
$606$	25.1700			1.02246
$607$	2.00072	−	3.46535i	0.0812067	−	0.140654i	−0.822562	−	0.568676i	$-0.807456\pi$
$607$	2.00072	−	3.46535i	0.0812067	−	0.140654i	0.903769	+	0.428022i	$0.140789\pi$
$608$	−3.07934	−	5.33357i	−0.124884	−	0.216305i
$609$		0			0
$610$	43.3108			1.75360
$611$	−17.9557	−	8.75676i	−0.726409	−	0.354261i
$612$	4.98341			0.201442
$613$	−17.0864	−	29.5946i	−0.690115	−	1.19531i	−0.971800	−	0.235807i	$-0.924227\pi$
$613$	−17.0864	−	29.5946i	−0.690115	−	1.19531i	0.281685	−	0.959507i	$-0.409107\pi$
$614$	5.95489	+	10.3142i	0.240320	+	0.416246i
$615$	15.7470	−	27.2747i	0.634982	−	1.09982i
$616$		0			0
$617$	15.0353	−	26.0419i	0.605298	−	1.04841i	−0.386707	−	0.922203i	$-0.626387\pi$
$617$	15.0353	−	26.0419i	0.605298	−	1.04841i	0.992004	−	0.126204i	$-0.0402793\pi$
$618$	11.5109	−	19.9375i	0.463038	−	0.802005i
$619$	22.5602			0.906773			0.453386	−	0.891314i	$-0.350216\pi$
$619$	22.5602			0.906773			0.453386	+	0.891314i	$0.350216\pi$
$620$	6.73917	−	11.6726i	0.270651	−	0.468782i
$621$	1.92241	+	3.32971i	0.0771436	+	0.133617i
$622$	1.98193	+	3.43280i	0.0794680	+	0.137643i
$623$		0			0
$624$	6.14928	−	4.14807i	0.246168	−	0.166056i
$625$	−15.5562			−0.622248
$626$	−13.7241	−	23.7709i	−0.548526	−	0.950076i
$627$	−24.1467	−	41.8234i	−0.964328	−	1.67026i
$628$	−8.58044	+	14.8618i	−0.342397	+	0.593049i
$629$	−21.9350			−0.874607
$630$		0			0
$631$	−2.69111	+	4.66114i	−0.107131	+	0.185557i	−0.914607	−	0.404344i	$-0.867500\pi$
$631$	−2.69111	+	4.66114i	−0.107131	+	0.185557i	0.807476	+	0.589901i	$0.200833\pi$
$632$	−0.445826			−0.0177340
$633$	4.25391	−	7.36798i	0.169078	−	0.292851i
$634$	12.2858	+	21.2796i	0.487930	+	0.845120i
$635$	−5.65636	−	9.79711i	−0.224466	−	0.388786i
$636$	−15.7059			−0.622780
$637$		0			0
$638$	8.79866			0.348342
$639$	−8.88876	−	15.3958i	−0.351634	−	0.609048i
$640$	1.69274	+	2.93192i	0.0669116	+	0.115894i
$641$	21.4269	−	37.1125i	0.846313	−	1.46586i	−0.0381629	−	0.999272i	$-0.512151\pi$
$641$	21.4269	−	37.1125i	0.846313	−	1.46586i	0.884476	−	0.466586i	$-0.154516\pi$
$642$	2.80488			0.110700
$643$	−11.5199	+	19.9530i	−0.454299	+	0.786870i	−0.998648	−	0.0519898i	$-0.983444\pi$
$643$	−11.5199	+	19.9530i	−0.454299	+	0.786870i	0.544348	+	0.838859i	$0.316777\pi$
$644$		0			0
$645$	48.3322			1.90308
$646$	−12.4527	+	21.5687i	−0.489945	+	0.848610i
$647$	3.97548	+	6.88574i	0.156292	+	0.270706i	0.933529	−	0.358502i	$-0.116712\pi$
$647$	3.97548	+	6.88574i	0.156292	+	0.270706i	−0.777237	+	0.629209i	$0.783379\pi$
$648$	5.58917	+	9.68073i	0.219563	+	0.380295i
$649$	−28.5157			−1.11934
$650$	1.62600	+	23.2406i	0.0637768	+	0.911572i
$651$		0			0
$652$	−7.66813	−	13.2816i	−0.300307	−	0.520147i
$653$	11.7941	+	20.4280i	0.461540	+	0.799410i	0.999038	−	0.0438547i	$-0.0139639\pi$
$653$	11.7941	+	20.4280i	0.461540	+	0.799410i	−0.537498	+	0.843265i	$0.680631\pi$
$654$	−3.21847	+	5.57455i	−0.125852	+	0.217982i
$655$	−8.58350			−0.335385
$656$	−2.26094	+	3.91606i	−0.0882748	+	0.152897i
$657$	−4.45837	+	7.72213i	−0.173938	+	0.301269i
$658$		0			0
$659$	−4.71901	+	8.17356i	−0.183826	+	0.318397i	−0.943180	−	0.332281i	$-0.892182\pi$
$659$	−4.71901	+	8.17356i	−0.183826	+	0.318397i	0.759354	+	0.650678i	$0.225515\pi$
$660$	13.2737	+	22.9908i	0.516679	+	0.894914i
$661$	−6.13000	−	10.6175i	−0.238429	−	0.412972i	0.721834	−	0.692066i	$-0.243299\pi$
$661$	−6.13000	−	10.6175i	−0.238429	−	0.412972i	−0.960264	+	0.279094i	$0.909966\pi$
$662$	28.6536			1.11365
$663$	−26.9609	−	13.1485i	−1.04708	−	0.510645i
$664$	15.1718			0.588779
$665$		0			0
$666$	3.34212	+	5.78872i	0.129505	+	0.224308i
$667$	−1.22027	+	2.11356i	−0.0472489	+	0.0818375i
$668$	−17.7227			−0.685712
$669$	−2.21103	+	3.82961i	−0.0854833	+	0.148061i
$670$	−14.9776	+	25.9419i	−0.578635	+	1.00222i
$671$	−48.7626			−1.88246
$672$		0			0
$673$	−4.64315	−	8.04217i	−0.178980	−	0.310003i	0.762551	−	0.646928i	$-0.223947\pi$
$673$	−4.64315	−	8.04217i	−0.178980	−	0.310003i	−0.941532	+	0.336925i	$0.890613\pi$
$674$	−4.43147	−	7.67554i	−0.170694	−	0.295651i
$675$	−23.4980			−0.904439
$676$	−12.8734	+	1.81019i	−0.495129	+	0.0696228i
$677$	37.3645			1.43603			0.718017	−	0.696025i	$-0.245050\pi$
$677$	37.3645			1.43603			0.718017	+	0.696025i	$0.245050\pi$
$678$	13.4380	+	23.2754i	0.516085	+	0.893886i
$679$		0			0
$680$	6.84539	−	11.8566i	0.262509	−	0.454678i
$681$	16.1261			0.617955
$682$	−7.58747	+	13.1419i	−0.290539	+	0.503229i
$683$	−13.5875	+	23.5343i	−0.519912	+	0.900514i	0.479820	+	0.877367i	$0.340702\pi$
$683$	−13.5875	+	23.5343i	−0.519912	+	0.900514i	−0.999732	+	0.0231468i	$0.992631\pi$
$684$	7.58939			0.290188
$685$	21.3403	−	36.9625i	0.815370	−	1.41226i
$686$		0			0
$687$	12.2971	+	21.2991i	0.469162	+	0.812613i
$688$	−6.93946			−0.264565
$689$	24.7408	+	12.0658i	0.942550	+	0.459670i
$690$	−7.36362			−0.280328
$691$	−4.83835	−	8.38028i	−0.184060	−	0.318801i	0.759200	−	0.650858i	$-0.225591\pi$
$691$	−4.83835	−	8.38028i	−0.184060	−	0.318801i	−0.943259	+	0.332057i	$0.892257\pi$
$692$	−0.566755	−	0.981648i	−0.0215448	−	0.0373167i
$693$		0			0
$694$	1.25661			0.0477002
$695$	31.8718	−	55.2035i	1.20896	−	2.09399i
$696$	−2.37445	+	4.11266i	−0.0900032	+	0.155890i
$697$	18.2863			0.692642
$698$	−11.8310	+	20.4919i	−0.447810	+	0.775629i
$699$	−28.8716	−	50.0071i	−1.09202	−	1.89144i
$700$		0			0
$701$	1.68502			0.0636423			0.0318212	−	0.999494i	$-0.489869\pi$
$701$	1.68502			0.0636423			0.0318212	+	0.999494i	$0.489869\pi$
$702$	−0.915120	−	13.0800i	−0.0345390	−	0.493671i
$703$	−33.4056			−1.25992
$704$	−1.90582	−	3.30098i	−0.0718284	−	0.124410i
$705$	19.2949	+	33.4198i	0.726688	+	1.25866i
$706$	5.96308	−	10.3284i	0.224424	−	0.388713i
$707$		0			0
$708$	7.69539	−	13.3288i	0.289211	−	0.500927i
$709$	0.359126	−	0.622025i	0.0134873	−	0.0233606i	−0.859203	−	0.511635i	$-0.829040\pi$
$709$	0.359126	−	0.622025i	0.0134873	−	0.0233606i	0.872690	+	0.488274i	$0.162373\pi$
$710$	−48.8396			−1.83292
$711$	0.274698	−	0.475791i	0.0103020	−	0.0178436i
$712$	−4.11790	−	7.13241i	−0.154325	−	0.267298i
$713$	−2.10458	−	3.64524i	−0.0788172	−	0.136515i
$714$		0			0
$715$	−3.24726	−	46.4136i	−0.121441	−	1.73577i
$716$	12.6667			0.473376
$717$	15.2385	+	26.3938i	0.569092	+	0.985696i
$718$	1.48413	+	2.57060i	0.0553874	+	0.0959338i
$719$	−3.00913	+	5.21197i	−0.112222	+	0.194374i	−0.916666	−	0.399655i	$-0.869130\pi$
$719$	−3.00913	+	5.21197i	−0.112222	+	0.194374i	0.804444	+	0.594028i	$0.202463\pi$
$720$	−4.17197			−0.155480
$721$		0			0
$722$	−9.46462	+	16.3932i	−0.352237	+	0.610092i
$723$	−1.94623			−0.0723811
$724$	−0.459697	+	0.796218i	−0.0170845	+	0.0295912i
$725$	−7.45779	−	12.9173i	−0.276975	−	0.479735i
$726$	−3.62967	−	6.28677i	−0.134710	−	0.233324i
$727$	−14.2302			−0.527770			−0.263885	−	0.964554i	$-0.585004\pi$
$727$	−14.2302			−0.527770			−0.263885	+	0.964554i	$0.585004\pi$
$728$		0			0
$729$	8.66905			0.321076
$730$	12.2484	+	21.2148i	0.453332	+	0.785195i
$731$	14.0314	+	24.3032i	0.518972	+	0.898885i
$732$	13.1593	−	22.7926i	0.486382	−	0.842439i
$733$	−47.2371			−1.74474			−0.872371	−	0.488844i	$-0.837419\pi$
$733$	−47.2371			−1.74474			−0.872371	+	0.488844i	$0.837419\pi$
$734$	−6.64234	+	11.5049i	−0.245173	+	0.424653i
$735$		0			0
$736$	1.05726			0.0389710
$737$	16.8629	−	29.2074i	0.621154	−	1.07587i
$738$	−2.78618	−	4.82580i	−0.102561	−	0.177640i
$739$	22.9268	+	39.7103i	0.843374	+	1.46077i	0.887026	+	0.461720i	$0.152768\pi$
$739$	22.9268	+	39.7103i	0.843374	+	1.46077i	−0.0436513	+	0.999047i	$0.513899\pi$
$740$	18.3634			0.675053
$741$	−41.0597	−	20.0243i	−1.50836	−	0.735610i
$742$		0			0
$743$	18.5214	+	32.0801i	0.679486	+	1.17690i	0.975136	+	0.221608i	$0.0711305\pi$
$743$	18.5214	+	32.0801i	0.679486	+	1.17690i	−0.295650	+	0.955296i	$0.595536\pi$
$744$	−4.09518	−	7.09307i	−0.150137	−	0.260044i
$745$	1.52449	−	2.64049i	0.0558528	−	0.0967400i
$746$	19.6620			0.719875
$747$	−9.34817	+	16.1915i	−0.342031	+	0.592416i
$748$	−7.70707	+	13.3490i	−0.281798	+	0.488089i
$749$		0			0
$750$	5.08969	−	8.81560i	0.185849	−	0.321900i
$751$	11.5864	+	20.0682i	0.422793	+	0.732298i	0.996211	−	0.0869641i	$-0.0277166\pi$
$751$	11.5864	+	20.0682i	0.422793	+	0.732298i	−0.573419	+	0.819262i	$0.694383\pi$
$752$	−2.77034	−	4.79836i	−0.101024	−	0.174978i
$753$	−26.4683			−0.964559
$754$	6.89984	−	4.65437i	0.251277	−	0.169502i
$755$	28.8433			1.04971
$756$		0			0
$757$	6.69747	+	11.6004i	0.243424	+	0.421622i	0.961687	−	0.274149i	$-0.0883961\pi$
$757$	6.69747	+	11.6004i	0.243424	+	0.421622i	−0.718264	+	0.695771i	$0.755063\pi$
$758$	−17.0038	+	29.4514i	−0.617605	+	1.06972i
$759$	8.29053			0.300927
$760$	10.4251	−	18.0567i	0.378157	−	0.654987i
$761$	7.03201	−	12.1798i	0.254910	−	0.441518i	−0.709961	−	0.704241i	$-0.751287\pi$
$761$	7.03201	−	12.1798i	0.254910	−	0.441518i	0.964871	+	0.262724i	$0.0846207\pi$
$762$	−6.87440			−0.249033
$763$		0			0
$764$	−1.54293	−	2.67244i	−0.0558213	−	0.0966854i
$765$	8.43564	+	14.6110i	0.304991	+	0.528260i
$766$	35.8064			1.29374
$767$	−22.3618	+	15.0844i	−0.807438	+	0.544667i
$768$	2.05726			0.0742349
$769$	−0.0250756	−	0.0434323i	−0.000904251	−	0.00156621i	0.865573	−	0.500783i	$-0.166954\pi$
$769$	−0.0250756	−	0.0434323i	−0.000904251	−	0.00156621i	−0.866477	+	0.499217i	$0.833621\pi$
$770$		0			0
$771$	3.51304	−	6.08477i	0.126519	−	0.219138i
$772$	−20.9098			−0.752560
$773$	−9.09389	+	15.7511i	−0.327085	+	0.566527i	−0.981932	−	0.189234i	$-0.939400\pi$
$773$	−9.09389	+	15.7511i	−0.327085	+	0.566527i	0.654847	+	0.755761i	$0.272733\pi$
$774$	4.27579	−	7.40588i	0.153690	−	0.266199i
$775$	25.7247			0.924060
$776$	−6.18181	+	10.7072i	−0.221914	+	0.384366i
$777$		0			0
$778$	7.37957	+	12.7818i	0.264570	+	0.458249i
$779$	27.8488			0.997786
$780$	22.5710	+	11.0076i	0.808170	+	0.394134i
$781$	54.9874			1.96761
$782$	−2.13775	−	3.70270i	−0.0764459	−	0.132408i
$783$	4.19729	+	7.26992i	0.149999	+	0.259806i
$784$		0			0
$785$	−58.0980			−2.07361
$786$	−2.60796	+	4.51713i	−0.0930230	+	0.161121i
$787$	−3.68104	+	6.37575i	−0.131215	+	0.227271i	−0.924145	−	0.382042i	$-0.875221\pi$
$787$	−3.68104	+	6.37575i	−0.131215	+	0.227271i	0.792930	+	0.609312i	$0.208554\pi$
$788$	−3.42616			−0.122052
$789$	0.458965	−	0.794951i	0.0163396	−	0.0283010i
$790$	−0.754670	−	1.30713i	−0.0268500	−	0.0465055i
$791$		0			0
$792$	4.69713			0.166905
$793$	−38.2393	+	25.7948i	−1.35792	+	0.915999i
$794$	−28.4087			−1.00819
$795$	−26.5861	−	46.0485i	−0.942912	−	1.63317i
$796$	−6.44121	−	11.1565i	−0.228303	−	0.395432i
$797$	−16.3412	+	28.3038i	−0.578834	+	1.00257i	0.416779	+	0.909008i	$0.363159\pi$
$797$	−16.3412	+	28.3038i	−0.578834	+	1.00257i	−0.995613	+	0.0935627i	$0.970174\pi$
$798$		0			0
$799$	−11.2031	+	19.4044i	−0.396338	+	0.686477i
$800$	−3.23077	+	5.59586i	−0.114225	+	0.197844i
$801$	10.1491			0.358599
$802$	−10.3718	+	17.9645i	−0.366241	+	0.634349i
$803$	−13.7902	−	23.8852i	−0.486644	−	0.842892i
$804$	9.10142	+	15.7641i	0.320982	+	0.555958i
$805$		0			0
$806$	1.00184	+	14.3194i	0.0352883	+	0.504381i
$807$	8.45785			0.297730
$808$	−6.11736	−	10.5956i	−0.215208	−	0.372751i
$809$	21.7436	+	37.6610i	0.764465	+	1.32409i	0.940529	+	0.339713i	$0.110330\pi$
$809$	21.7436	+	37.6610i	0.764465	+	1.32409i	−0.176064	+	0.984379i	$0.556337\pi$
$810$	−18.9221	+	32.7740i	−0.664854	+	1.15156i
$811$	52.1463			1.83110			0.915552	−	0.402199i	$-0.131754\pi$
$811$	52.1463			1.83110			0.915552	+	0.402199i	$0.131754\pi$
$812$		0			0
$813$	13.7323	−	23.7851i	0.481613	−	0.834179i
$814$	−20.6750			−0.724657
$815$	25.9604	−	44.9647i	0.909352	−	1.57504i
$816$	−4.15973	−	7.20486i	−0.145620	−	0.252221i
$817$	21.3689	+	37.0121i	0.747605	+	1.29489i
$818$	−15.7777			−0.551655
$819$		0			0
$820$	−15.3088			−0.534606
$821$	20.8070	+	36.0388i	0.726171	+	1.25776i	0.958490	+	0.285125i	$0.0920351\pi$
$821$	20.8070	+	36.0388i	0.726171	+	1.25776i	−0.232320	+	0.972639i	$0.574632\pi$
$822$	−12.9678	−	22.4609i	−0.452305	−	0.783416i
$823$	−17.7643	+	30.7686i	−0.619223	+	1.07253i	0.370405	+	0.928870i	$0.379219\pi$
$823$	−17.7643	+	30.7686i	−0.619223	+	1.07253i	−0.989628	+	0.143655i	$0.954114\pi$
$824$	−11.1906			−0.389842
$825$	−25.3342	+	43.8801i	−0.882024	+	1.52771i
$826$		0			0
$827$	28.5697			0.993467			0.496734	−	0.867903i	$-0.334533\pi$
$827$	28.5697			0.993467			0.496734	+	0.867903i	$0.334533\pi$
$828$	−0.651435	+	1.12832i	−0.0226389	+	0.0392118i
$829$	−0.762246	−	1.32025i	−0.0264739	−	0.0458541i	0.852485	−	0.522752i	$-0.175095\pi$
$829$	−0.762246	−	1.32025i	−0.0264739	−	0.0458541i	−0.878959	+	0.476898i	$0.841761\pi$
$830$	25.6819	+	44.4824i	0.891433	+	1.54401i
$831$	38.9976			1.35281
$832$	−3.24071	−	1.58045i	−0.112351	−	0.0547923i
$833$		0			0
$834$	−19.3675	−	33.5455i	−0.670641	−	1.16158i
$835$	−30.0000	−	51.9616i	−1.03819	−	1.79820i
$836$	−11.7373	+	20.3297i	−0.405944	+	0.703116i
$837$	−14.4780			−0.500434
$838$	2.80653	−	4.86106i	0.0969501	−	0.167923i
$839$	13.9446	−	24.1527i	0.481420	−	0.833844i	−0.518353	−	0.855167i	$-0.673455\pi$
$839$	13.9446	−	24.1527i	0.481420	−	0.833844i	0.999773	+	0.0213231i	$0.00678788\pi$
$840$		0			0
$841$	11.8357	−	20.5001i	0.408129	−	0.706900i
$842$	−7.59931	−	13.1624i	−0.261890	−	0.453606i
$843$	0.104317	+	0.180683i	0.00359288	+	0.00622306i
$844$	−4.13551			−0.142350
$845$	−27.0986	−	34.6794i	−0.932222	−	1.19301i
$846$	6.82783			0.234746
$847$		0			0
$848$	3.81720	+	6.61158i	0.131083	+	0.227042i
$849$	−5.01744	+	8.69045i	−0.172198	+	0.298256i
$850$	26.1302			0.896258
$851$	2.86736	−	4.96642i	0.0982920	−	0.170247i
$852$	−14.8392	+	25.7022i	−0.508382	+	0.880543i
$853$	18.2171			0.623741			0.311871	−	0.950125i	$-0.399044\pi$
$853$	18.2171			0.623741			0.311871	+	0.950125i	$0.399044\pi$
$854$		0			0
$855$	12.8469	+	22.2515i	0.439355	+	0.760985i
$856$	−0.681703	−	1.18074i	−0.0233001	−	0.0403570i
$857$	1.02430			0.0349893			0.0174947	−	0.999847i	$-0.494431\pi$
$857$	1.02430			0.0349893			0.0174947	+	0.999847i	$0.494431\pi$
$858$	−25.4121	−	12.3932i	−0.867556	−	0.423096i
$859$	−50.1695			−1.71176			−0.855880	−	0.517174i	$-0.826984\pi$
$859$	−50.1695			−1.71176			−0.855880	+	0.517174i	$0.826984\pi$
$860$	−11.7467	−	20.3460i	−0.400561	−	0.693791i
$861$		0			0
$862$	−1.68571	+	2.91974i	−0.0574156	+	0.0994468i
$863$	−34.9290			−1.18900			−0.594499	−	0.804096i	$-0.702650\pi$
$863$	−34.9290			−1.18900			−0.594499	+	0.804096i	$0.702650\pi$
$864$	1.81830	−	3.14938i	0.0618597	−	0.107144i
$865$	1.91874	−	3.32336i	0.0652392	−	0.112998i
$866$	16.2399			0.551853
$867$	0.664923	−	1.15168i	0.0225820	−	0.0391131i
$868$		0			0
$869$	0.849666	+	1.47167i	0.0288230	+	0.0499228i
$870$	−16.0773			−0.545073
$871$	−2.22656	−	31.8245i	−0.0754440	−	1.07833i
$872$	3.12889			0.105958
$873$	−7.61791	−	13.1946i	−0.257827	−	0.446570i
$874$	−3.25565	−	5.63896i	−0.110124	−	0.190741i
$875$		0			0
$876$	14.8859			0.502948
$877$	10.1631	−	17.6031i	0.343185	−	0.594414i	−0.641837	−	0.766841i	$-0.721828\pi$
$877$	10.1631	−	17.6031i	0.343185	−	0.594414i	0.985022	+	0.172427i	$0.0551609\pi$
$878$	12.0552	−	20.8802i	0.406842	−	0.704671i
$879$	51.0962			1.72343
$880$	6.45214	−	11.1754i	0.217502	−	0.376724i
$881$	0.505117	+	0.874889i	0.0170178	+	0.0294757i	0.874409	−	0.485190i	$-0.161249\pi$
$881$	0.505117	+	0.874889i	0.0170178	+	0.0294757i	−0.857391	+	0.514665i	$0.827916\pi$
$882$		0			0
$883$	18.3609			0.617894			0.308947	−	0.951079i	$-0.400024\pi$
$883$	18.3609			0.617894			0.308947	+	0.951079i	$0.400024\pi$
$884$	1.01763	+	14.5451i	0.0342266	+	0.489206i
$885$	52.1053			1.75150
$886$	12.4929	+	21.6383i	0.419706	+	0.726953i
$887$	−9.59364	−	16.6167i	−0.322123	−	0.557933i	0.658803	−	0.752315i	$-0.271063\pi$
$887$	−9.59364	−	16.6167i	−0.322123	−	0.557933i	−0.980926	+	0.194382i	$0.937730\pi$
$888$	5.57944	−	9.66388i	0.187234	−	0.324298i
$889$		0			0
$890$	13.9411	−	24.1467i	0.467307	−	0.809400i
$891$	21.3039	−	36.8995i	0.713709	−	1.23618i
$892$	2.14949			0.0719703
$893$	−17.0616	+	29.5515i	−0.570944	+	0.988905i
$894$	−0.926383	−	1.60454i	−0.0309829	−	0.0536639i
$895$	21.4415	+	37.1377i	0.716709	+	1.24138i
$896$		0			0
$897$	6.50137	−	4.38558i	0.217074	−	0.146430i
$898$	−36.7371			−1.22593
$899$	−4.59503	−	7.95883i	−0.153253	−	0.265442i
$900$	−3.98131	−	6.89583i	−0.132710	−	0.229861i
$901$	15.4366	−	26.7369i	0.514267	−	0.890736i
$902$	17.2358			0.573889
$903$		0			0
$904$	6.53202	−	11.3138i	0.217252	−	0.376291i
$905$	−3.11260			−0.103466
$906$	8.76359	−	15.1790i	0.291151	−	0.504288i
$907$	−12.1030	−	20.9631i	−0.401875	−	0.696067i	0.592077	−	0.805881i	$-0.298308\pi$
$907$	−12.1030	−	20.9631i	−0.401875	−	0.696067i	−0.993952	+	0.109814i	$0.964975\pi$
$908$	−3.91933	−	6.78848i	−0.130068	−	0.225284i
$909$	15.0770			0.500072
$910$		0			0
$911$	−7.43708			−0.246401			−0.123201	−	0.992382i	$-0.539316\pi$
$911$	−7.43708			−0.246401			−0.123201	+	0.992382i	$0.539316\pi$
$912$	−6.33499	−	10.9725i	−0.209772	−	0.363337i
$913$	−28.9147	−	50.0818i	−0.956937	−	1.65746i
$914$	−0.583289	+	1.01029i	−0.0192935	+	0.0334173i
$915$	89.1015			2.94560
$916$	5.97741	−	10.3532i	0.197499	−	0.342078i
$917$		0			0
$918$	−14.7062			−0.485378
$919$	12.1643	−	21.0692i	0.401263	−	0.695008i	−0.592615	−	0.805486i	$-0.701905\pi$
$919$	12.1643	−	21.0692i	0.401263	−	0.695008i	0.993879	+	0.110477i	$0.0352379\pi$
$920$	1.78967	+	3.09980i	0.0590036	+	0.102197i
$921$	12.2507	+	21.2189i	0.403676	+	0.699187i
$922$	13.9471			0.459322
$923$	43.1207	−	29.0876i	1.41934	−	0.957430i
$924$		0			0
$925$	17.5242	+	30.3528i	0.576192	+	0.997994i
$926$	7.02382	+	12.1656i	0.230817	+	0.399787i
$927$	6.89513	−	11.9427i	0.226466	−	0.392250i
$928$	2.30836			0.0757757
$929$	−11.3168	+	19.6012i	−0.371291	+	0.643094i	−0.989764	−	0.142711i	$-0.954418\pi$
$929$	−11.3168	+	19.6012i	−0.371291	+	0.643094i	0.618474	+	0.785805i	$0.287751\pi$
$930$	13.8642	−	24.0135i	0.454625	−	0.787434i
$931$		0			0
$932$	−14.0340	+	24.3076i	−0.459700	+	0.796223i
$933$	4.07733	+	7.06215i	0.133486	+	0.231204i
$934$	4.23028	+	7.32707i	0.138419	+	0.239749i
$935$	−52.1844			−1.70661
$936$	3.68345	−	2.48472i	0.120397	−	0.0812155i
$937$	−49.8108			−1.62725			−0.813623	−	0.581393i	$-0.802508\pi$
$937$	−49.8108			−1.62725			−0.813623	+	0.581393i	$0.802508\pi$
$938$		0			0
$939$	−28.2341	−	48.9028i	−0.921384	−	1.59588i
$940$	9.37894	−	16.2448i	0.305907	−	0.529847i
$941$	−35.0734			−1.14336			−0.571681	−	0.820476i	$-0.693708\pi$
$941$	−35.0734			−1.14336			−0.571681	+	0.820476i	$0.693708\pi$
$942$	−17.6522	+	30.5745i	−0.575139	+	0.996170i
$943$	−2.39040	+	4.14029i	−0.0778420	+	0.134826i
$944$	−7.48121			−0.243493
$945$		0			0
$946$	13.2254	+	22.9070i	0.429995	+	0.744772i
$947$	17.4151	+	30.1638i	0.565914	+	0.980191i	0.996964	+	0.0778634i	$0.0248098\pi$
$947$	17.4151	+	30.1638i	0.565914	+	0.980191i	−0.431050	+	0.902328i	$0.641857\pi$
$948$	−0.917180			−0.0297886
$949$	−23.4491	−	11.4358i	−0.761190	−	0.371223i
$950$	39.7945			1.29110
$951$	25.2750	+	43.7776i	0.819598	+	1.41959i
$952$		0			0
$953$	−9.11097	+	15.7807i	−0.295133	+	0.511186i	−0.975016	−	0.222135i	$-0.928697\pi$
$953$	−9.11097	+	15.7807i	−0.295133	+	0.511186i	0.679883	+	0.733321i	$0.262031\pi$
$954$	−9.40794			−0.304593
$955$	5.22358	−	9.04751i	0.169031	−	0.292770i
$956$	7.40719	−	12.8296i	0.239566	−	0.414940i
$957$	18.1011			0.585126
$958$	0.909522	−	1.57534i	0.0293853	−	0.0508969i
$959$		0			0
$960$	3.48241	+	6.03172i	0.112394	+	0.194673i
$961$	−15.1500			−0.488710
$962$	−16.2131	+	10.9368i	−0.522733	+	0.352615i
$963$	1.68014			0.0541417
$964$	0.473016	+	0.819288i	0.0152348	+	0.0263875i
$965$	−35.3949	−	61.3058i	−1.13940	−	1.97350i
$966$		0			0
$967$	−16.6734			−0.536181			−0.268090	−	0.963394i	$-0.586393\pi$
$967$	−16.6734			−0.536181			−0.268090	+	0.963394i	$0.586393\pi$
$968$	−1.76432	+	3.05590i	−0.0567075	+	0.0982203i
$969$	−25.6184	+	44.3724i	−0.822982	+	1.42545i
$970$	−41.8569			−1.34394
$971$	2.89367	−	5.01199i	0.0928624	−	0.160842i	−0.815852	−	0.578261i	$-0.803732\pi$
$971$	2.89367	−	5.01199i	0.0928624	−	0.160842i	0.908714	+	0.417418i	$0.137065\pi$
$972$	6.04348	+	10.4676i	0.193845	+	0.335749i
$973$		0			0
$974$	22.0577			0.706773
$975$	3.34509	+	47.8119i	0.107129	+	1.53121i
$976$	−12.7931			−0.409496
$977$	6.57257	+	11.3840i	0.210275	+	0.364207i	0.951801	−	0.306717i	$-0.0992306\pi$
$977$	6.57257	+	11.3840i	0.210275	+	0.364207i	−0.741525	+	0.670925i	$0.765897\pi$
$978$	−15.7753	−	27.3236i	−0.504439	−	0.873714i
$979$	−15.6960	+	27.1862i	−0.501646	+	0.868876i
$980$		0			0
$981$	−1.92788	+	3.33919i	−0.0615526	+	0.106612i
$982$	9.99653	−	17.3145i	0.319002	−	0.552528i
$983$	37.1843			1.18599			0.592997	−	0.805205i	$-0.297945\pi$
$983$	37.1843			1.18599			0.592997	+	0.805205i	$0.297945\pi$
$984$	−4.65133	+	8.05635i	−0.148279	+	0.256827i
$985$	−5.79961	−	10.0452i	−0.184791	−	0.320067i
$986$	−4.66746	−	8.08427i	−0.148642	−	0.257456i
$987$		0			0
$988$	1.54978	+	22.1513i	0.0493051	+	0.704725i
$989$	−7.33680			−0.233297
$990$	7.95104	+	13.7716i	0.252701	+	0.437691i
$991$	−1.42901	−	2.47512i	−0.0453941	−	0.0786249i	0.842436	−	0.538797i	$-0.181121\pi$
$991$	−1.42901	−	2.47512i	−0.0453941	−	0.0786249i	−0.887830	+	0.460172i	$0.847788\pi$
$992$	−1.99060	+	3.44783i	−0.0632017	+	0.109469i
$993$	58.9479			1.87065
$994$		0			0
$995$	21.8066	−	37.7702i	0.691317	−	1.19740i
$996$	31.2123			0.988998
$997$	−19.0032	+	32.9145i	−0.601837	+	1.04241i	0.390706	+	0.920516i	$0.372231\pi$
$997$	−19.0032	+	32.9145i	−0.601837	+	1.04241i	−0.992543	+	0.121897i	$0.961102\pi$
$998$	−18.3789	−	31.8331i	−0.581772	−	1.00766i
$999$	−9.86272	−	17.0827i	−0.312043	−	0.540474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.g.p.393.2		10
7.2	even	3		182.2.h.d.81.4	yes	10
7.3	odd	6		1274.2.e.s.471.4		10
7.4	even	3		182.2.e.d.107.2	✓	10
7.5	odd	6		1274.2.h.s.263.2		10
7.6	odd	2		1274.2.g.q.393.4		10
13.9	even	3	inner	1274.2.g.p.295.2		10
21.2	odd	6		1638.2.p.k.991.1		10
21.11	odd	6		1638.2.m.j.289.1		10
91.9	even	3		182.2.e.d.165.2	yes	10
91.48	odd	6		1274.2.g.q.295.4		10
91.61	odd	6		1274.2.e.s.165.4		10
91.74	even	3		182.2.h.d.9.4	yes	10
91.87	odd	6		1274.2.h.s.373.2		10
273.74	odd	6		1638.2.p.k.919.1		10
273.191	odd	6		1638.2.m.j.1621.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.e.d.107.2	✓	10	7.4	even	3
182.2.e.d.165.2	yes	10	91.9	even	3
182.2.h.d.9.4	yes	10	91.74	even	3
182.2.h.d.81.4	yes	10	7.2	even	3
1274.2.e.s.165.4		10	91.61	odd	6
1274.2.e.s.471.4		10	7.3	odd	6
1274.2.g.p.295.2		10	13.9	even	3	inner
1274.2.g.p.393.2		10	1.1	even	1	trivial
1274.2.g.q.295.4		10	91.48	odd	6
1274.2.g.q.393.4		10	7.6	odd	2
1274.2.h.s.263.2		10	7.5	odd	6
1274.2.h.s.373.2		10	91.87	odd	6
1638.2.m.j.289.1		10	21.11	odd	6
1638.2.m.j.1621.1		10	273.191	odd	6
1638.2.p.k.919.1		10	273.74	odd	6
1638.2.p.k.991.1		10	21.2	odd	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.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.02863 - 1.78164i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.38549 q^{5} +(-1.02863 + 1.78164i) q^{6} +1.00000 q^{8} +(-0.616155 + 1.06721i) q^{9} +(1.69274 + 2.93192i) q^{10} +(-1.90582 - 3.30098i) q^{11} +2.05726 q^{12} +(-3.24071 - 1.58045i) q^{13} +(3.48241 + 6.03172i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.02198 + 3.50217i) q^{17} +1.23231 q^{18} +(-3.07934 + 5.33357i) q^{19} +(1.69274 - 2.93192i) q^{20} +(-1.90582 + 3.30098i) q^{22} +(-0.528629 - 0.915612i) q^{23} +(-1.02863 - 1.78164i) q^{24} +6.46154 q^{25} +(0.251642 + 3.59676i) q^{26} -3.63659 q^{27} +(-1.15418 - 1.99910i) q^{29} +(3.48241 - 6.03172i) q^{30} +3.98121 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.92077 + 6.79097i) q^{33} +4.04396 q^{34} +(-0.616155 - 1.06721i) q^{36} +(2.71208 + 4.69745i) q^{37} +6.15867 q^{38} +(0.517693 + 7.39946i) q^{39} -3.38549 q^{40} +(-2.26094 - 3.91606i) q^{41} +(3.46973 - 6.00975i) q^{43} +3.81165 q^{44} +(2.08599 - 3.61304i) q^{45} +(-0.528629 + 0.915612i) q^{46} +5.54067 q^{47} +(-1.02863 + 1.78164i) q^{48} +(-3.23077 - 5.59586i) q^{50} +8.31946 q^{51} +(2.98906 - 2.01631i) q^{52} -7.63439 q^{53} +(1.81830 + 3.14938i) q^{54} +(6.45214 + 11.1754i) q^{55} +12.6700 q^{57} +(-1.15418 + 1.99910i) q^{58} +(3.74061 - 6.47892i) q^{59} -6.96483 q^{60} +(6.39653 - 11.0791i) q^{61} +(-1.99060 - 3.44783i) q^{62} +1.00000 q^{64} +(10.9714 + 5.35060i) q^{65} +7.84154 q^{66} +(4.42405 + 7.66269i) q^{67} +(-2.02198 - 3.50217i) q^{68} +(-1.08753 + 1.88365i) q^{69} +(-7.21308 + 12.4934i) q^{71} +(-0.616155 + 1.06721i) q^{72} +7.23580 q^{73} +(2.71208 - 4.69745i) q^{74} +(-6.64653 - 11.5121i) q^{75} +(-3.07934 - 5.33357i) q^{76} +(6.14928 - 4.14807i) q^{78} -0.445826 q^{79} +(1.69274 + 2.93192i) q^{80} +(5.58917 + 9.68073i) q^{81} +(-2.26094 + 3.91606i) q^{82} +15.1718 q^{83} +(6.84539 - 11.8566i) q^{85} -6.93946 q^{86} +(-2.37445 + 4.11266i) q^{87} +(-1.90582 - 3.30098i) q^{88} +(-4.11790 - 7.13241i) q^{89} -4.17197 q^{90} +1.05726 q^{92} +(-4.09518 - 7.09307i) q^{93} +(-2.77034 - 4.79836i) q^{94} +(10.4251 - 18.0567i) q^{95} +2.05726 q^{96} +(-6.18181 + 10.7072i) q^{97} +4.69713 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - q^{3} - 5 q^{4} + 4 q^{5} - q^{6} + 10 q^{8} - 4 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 6 q^{13} + 3 q^{15} - 5 q^{16} - 3 q^{17} + 8 q^{18} - 5 q^{19} - 2 q^{20} - 4 q^{22} + 4 q^{23}+ \cdots + 54 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - q^3 - 5 * q^4 + 4 * q^5 - q^6 + 10 * q^8 - 4 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 6 * q^13 + 3 * q^15 - 5 * q^16 - 3 * q^17 + 8 * q^18 - 5 * q^19 - 2 * q^20 - 4 * q^22 + 4 * q^23 - q^24 + 6 * q^25 + 8 * q^27 + q^29 + 3 * q^30 + 42 * q^31 - 5 * q^32 + 6 * q^34 - 4 * q^36 + 10 * q^37 + 10 * q^38 - 28 * q^39 + 4 * q^40 - 9 * q^41 + 9 * q^43 + 8 * q^44 + 3 * q^45 + 4 * q^46 + 26 * q^47 - q^48 - 3 * q^50 + 12 * q^51 + 6 * q^52 + 30 * q^53 - 4 * q^54 + 7 * q^55 - 26 * q^57 + q^58 + q^59 - 6 * q^60 - 15 * q^61 - 21 * q^62 + 10 * q^64 + 44 * q^65 - 3 * q^68 - 18 * q^69 - q^71 - 4 * q^72 + 8 * q^73 + 10 * q^74 - 25 * q^75 - 5 * q^76 + 11 * q^78 + 2 * q^79 - 2 * q^80 + 23 * q^81 - 9 * q^82 + 96 * q^83 + 12 * q^85 - 18 * q^86 - 27 * q^87 - 4 * q^88 - 9 * q^89 - 6 * q^90 - 8 * q^92 - 2 * q^93 - 13 * q^94 + 6 * q^95 + 2 * q^96 - 19 * q^97 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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