LMFDB - Embedded newform 1050.2.s.g.101.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1050,2,Mod(101,1050)] 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("1050.101"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1050, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.s (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,2,6,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 $ x^12 - 4x^11 + 11x^10 - 32x^9 + 64x^8 - 120x^7 + 237x^6 - 360x^5 + 576x^4 - 864x^3 + 891x^2 - 972*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Root			$-0.384890 - 1.68874i$ of defining polynomial
Character	$\chi$	$=$	1050.101
Dual form			1050.2.s.g.551.3

$q$-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} +(1.68874 - 0.384890i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.27005 + 1.17770i) q^{6} +(-2.63608 - 0.226058i) q^{7} +1.00000i q^{8} +(2.70372 - 1.29996i) q^{9} +(4.29143 + 2.47766i) q^{11} +(0.511048 - 1.65494i) q^{12} +6.37523i q^{13} +(2.39594 - 1.12227i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.81377 - 3.14155i) q^{17} +(-1.69151 + 2.47766i) q^{18} +(-3.64345 + 2.10355i) q^{19} +(-4.53867 + 0.632846i) q^{21} -4.95532 q^{22} +(1.65996 - 0.958379i) q^{23} +(0.384890 + 1.68874i) q^{24} +(-3.18762 - 5.52111i) q^{26} +(4.06555 - 3.23594i) q^{27} +(-1.51381 + 2.16988i) q^{28} -0.800269i q^{29} +(4.36166 + 2.51820i) q^{31} +(0.866025 + 0.500000i) q^{32} +(8.20077 + 2.53241i) q^{33} +3.62755i q^{34} +(0.226058 - 2.99147i) q^{36} +(2.91394 + 5.04710i) q^{37} +(2.10355 - 3.64345i) q^{38} +(2.45377 + 10.7661i) q^{39} -7.45163 q^{41} +(3.61418 - 2.81739i) q^{42} +4.64827 q^{43} +(4.29143 - 2.47766i) q^{44} +(-0.958379 + 1.65996i) q^{46} +(0.303890 + 0.526352i) q^{47} +(-1.17770 - 1.27005i) q^{48} +(6.89780 + 1.19181i) q^{49} +(1.85385 - 6.00338i) q^{51} +(5.52111 + 3.18762i) q^{52} +(12.3898 + 7.15326i) q^{53} +(-1.90290 + 4.83518i) q^{54} +(0.226058 - 2.63608i) q^{56} +(-5.34323 + 4.95469i) q^{57} +(0.400134 + 0.693053i) q^{58} +(0.875658 - 1.51668i) q^{59} +(2.96447 - 1.71154i) q^{61} -5.03641 q^{62} +(-7.42108 + 2.81561i) q^{63} -1.00000 q^{64} +(-8.36827 + 1.90726i) q^{66} +(3.99147 - 6.91343i) q^{67} +(-1.81377 - 3.14155i) q^{68} +(2.43438 - 2.25736i) q^{69} +2.48759i q^{71} +(1.29996 + 2.70372i) q^{72} +(-13.0712 - 7.54666i) q^{73} +(-5.04710 - 2.91394i) q^{74} +4.20710i q^{76} +(-10.7525 - 7.50142i) q^{77} +(-7.50809 - 8.09687i) q^{78} +(-1.33404 - 2.31062i) q^{79} +(5.62019 - 7.02947i) q^{81} +(6.45330 - 3.72581i) q^{82} +7.27215 q^{83} +(-1.72127 + 4.24702i) q^{84} +(-4.02552 + 2.32413i) q^{86} +(-0.308016 - 1.35145i) q^{87} +(-2.47766 + 4.29143i) q^{88} +(-0.942474 - 1.63241i) q^{89} +(1.44117 - 16.8056i) q^{91} -1.91676i q^{92} +(8.33496 + 2.57384i) q^{93} +(-0.526352 - 0.303890i) q^{94} +(1.65494 + 0.511048i) q^{96} +17.6562i q^{97} +(-6.56957 + 2.41676i) q^{98} +(14.8237 + 1.12019i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} + 6 q^{4} - 2 q^{6} - 8 q^{7} + 6 q^{9} - 12 q^{11} - 2 q^{12} + 12 q^{14} - 6 q^{16} - 12 q^{17} + 4 q^{18} - 18 q^{21} + 24 q^{23} - 4 q^{24} - 4 q^{26} + 8 q^{27} - 4 q^{28} + 12 q^{31}+ \cdots + 48 q^{99}+O(q^{100}) $ 12 * q + 2 * q^3 + 6 * q^4 - 2 * q^6 - 8 * q^7 + 6 * q^9 - 12 * q^11 - 2 * q^12 + 12 * q^14 - 6 * q^16 - 12 * q^17 + 4 * q^18 - 18 * q^21 + 24 * q^23 - 4 * q^24 - 4 * q^26 + 8 * q^27 - 4 * q^28 + 12 * q^31 + 22 * q^33 + 6 * q^36 + 8 * q^37 - 8 * q^38 + 30 * q^39 - 4 * q^41 + 20 * q^42 - 12 * q^44 + 2 * q^46 - 16 * q^47 - 4 * q^48 - 14 * q^49 + 4 * q^51 + 12 * q^52 + 48 * q^53 - 4 * q^54 + 6 * q^56 + 36 * q^57 - 8 * q^58 + 12 * q^59 - 30 * q^61 - 8 * q^62 + 4 * q^63 - 12 * q^64 - 34 * q^66 + 4 * q^67 + 12 * q^68 + 50 * q^69 - 4 * q^72 - 20 * q^77 - 32 * q^78 - 4 * q^79 + 50 * q^81 + 40 * q^83 - 12 * q^84 - 54 * q^86 - 8 * q^87 + 26 * q^89 + 28 * q^91 + 32 * q^93 + 24 * q^94 - 2 * q^96 - 16 * q^98 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.68874	−	0.384890i	0.974997	−	0.222217i
$3$	1.68874	−	0.384890i	0.974997	−	0.222217i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.27005	+	1.17770i	−0.518496	+	0.480793i
$7$	−2.63608	−	0.226058i	−0.996343	−	0.0854419i
$7$	−2.63608	−	0.226058i	−0.996343	−	0.0854419i
$8$			1.00000i			0.353553i
$9$	2.70372	−	1.29996i	0.901240	−	0.433321i
$10$		0			0
$11$	4.29143	+	2.47766i	1.29392	+	0.747043i	0.979346	−	0.202191i	$-0.0648063\pi$
$11$	4.29143	+	2.47766i	1.29392	+	0.747043i	0.314570	+	0.949234i	$0.398140\pi$
$12$	0.511048	−	1.65494i	0.147527	−	0.477740i
$13$			6.37523i			1.76817i	0.467325	+	0.884086i	$0.345218\pi$
$13$			6.37523i			1.76817i	−0.467325	+	0.884086i	$0.654782\pi$
$14$	2.39594	−	1.12227i	0.640341	−	0.299938i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.81377	−	3.14155i	0.439905	−	0.761937i	−0.557777	−	0.829991i	$-0.688346\pi$
$17$	1.81377	−	3.14155i	0.439905	−	0.761937i	0.997682	+	0.0680536i	$0.0216789\pi$
$18$	−1.69151	+	2.47766i	−0.398692	+	0.583990i
$19$	−3.64345	+	2.10355i	−0.835865	+	0.482587i	−0.855857	−	0.517213i	$-0.826969\pi$
$19$	−3.64345	+	2.10355i	−0.835865	+	0.482587i	0.0199914	+	0.999800i	$0.493636\pi$
$20$		0			0
$21$	−4.53867	+	0.632846i	−0.990419	+	0.138098i
$22$	−4.95532			−1.05648
$23$	1.65996	−	0.958379i	0.346126	−	0.199836i	−0.316852	−	0.948475i	$-0.602626\pi$
$23$	1.65996	−	0.958379i	0.346126	−	0.199836i	0.662978	+	0.748639i	$0.269292\pi$
$24$	0.384890	+	1.68874i	0.0785654	+	0.344714i
$25$		0			0
$26$	−3.18762	−	5.52111i	−0.625143	−	1.08278i
$27$	4.06555	−	3.23594i	0.782415	−	0.622757i
$28$	−1.51381	+	2.16988i	−0.286083	+	0.410069i
$29$		−	0.800269i		−	0.148606i	−0.997236	−	0.0743031i	$-0.976327\pi$
$29$		−	0.800269i		−	0.148606i	0.997236	−	0.0743031i	$-0.0236732\pi$
$30$		0			0
$31$	4.36166	+	2.51820i	0.783377	+	0.452283i	0.837626	−	0.546245i	$-0.183943\pi$
$31$	4.36166	+	2.51820i	0.783377	+	0.452283i	−0.0542489	+	0.998527i	$0.517276\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	8.20077	+	2.53241i	1.42757	+	0.440835i
$34$			3.62755i			0.622119i
$35$		0			0
$36$	0.226058	−	2.99147i	0.0376763	−	0.498578i
$37$	2.91394	+	5.04710i	0.479050	+	0.829738i	0.999711	−	0.0240249i	$-0.00764810\pi$
$37$	2.91394	+	5.04710i	0.479050	+	0.829738i	−0.520662	+	0.853763i	$0.674315\pi$
$38$	2.10355	−	3.64345i	0.341241	−	0.591046i
$39$	2.45377	+	10.7661i	0.392917	+	1.72396i
$40$		0			0
$41$	−7.45163			−1.16375			−0.581874	−	0.813279i	$-0.697680\pi$
$41$	−7.45163			−1.16375			−0.581874	+	0.813279i	$0.697680\pi$
$42$	3.61418	−	2.81739i	0.557680	−	0.434733i
$43$	4.64827			0.708854			0.354427	−	0.935084i	$-0.384676\pi$
$43$	4.64827			0.708854			0.354427	+	0.935084i	$0.384676\pi$
$44$	4.29143	−	2.47766i	0.646958	−	0.373521i
$45$		0			0
$46$	−0.958379	+	1.65996i	−0.141305	+	0.244748i
$47$	0.303890	+	0.526352i	0.0443269	+	0.0767764i	0.887338	−	0.461120i	$-0.152552\pi$
$47$	0.303890	+	0.526352i	0.0443269	+	0.0767764i	−0.843011	+	0.537897i	$0.819219\pi$
$48$	−1.17770	−	1.27005i	−0.169986	−	0.183316i
$49$	6.89780	+	1.19181i	0.985399	+	0.170259i
$50$		0			0
$51$	1.85385	−	6.00338i	0.259591	−	0.840641i
$52$	5.52111	+	3.18762i	0.765641	+	0.442043i
$53$	12.3898	+	7.15326i	1.70187	+	0.982576i	0.943866	+	0.330329i	$0.107160\pi$
$53$	12.3898	+	7.15326i	1.70187	+	0.982576i	0.758006	+	0.652247i	$0.226174\pi$
$54$	−1.90290	+	4.83518i	−0.258951	+	0.657985i
$55$		0			0
$56$	0.226058	−	2.63608i	0.0302083	−	0.352260i
$57$	−5.34323	+	4.95469i	−0.707727	+	0.656264i
$58$	0.400134	+	0.693053i	0.0525402	+	0.0910023i
$59$	0.875658	−	1.51668i	0.114001	−	0.197456i	−0.803379	−	0.595468i	$-0.796967\pi$
$59$	0.875658	−	1.51668i	0.114001	−	0.197456i	0.917380	+	0.398013i	$0.130300\pi$
$60$		0			0
$61$	2.96447	−	1.71154i	0.379561	−	0.219140i	−0.298066	−	0.954545i	$-0.596342\pi$
$61$	2.96447	−	1.71154i	0.379561	−	0.219140i	0.677627	+	0.735405i	$0.263008\pi$
$62$	−5.03641			−0.639624
$63$	−7.42108	+	2.81561i	−0.934968	+	0.354733i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−8.36827	+	1.90726i	−1.03006	+	0.234767i
$67$	3.99147	−	6.91343i	0.487636	−	0.844610i	−0.512263	−	0.858829i	$-0.671193\pi$
$67$	3.99147	−	6.91343i	0.487636	−	0.844610i	0.999899	+	0.0142186i	$0.00452608\pi$
$68$	−1.81377	−	3.14155i	−0.219952	−	0.380969i
$69$	2.43438	−	2.25736i	0.293065	−	0.271754i
$70$		0			0
$71$			2.48759i			0.295222i	0.989045	+	0.147611i	$0.0471584\pi$
$71$			2.48759i			0.295222i	−0.989045	+	0.147611i	$0.952842\pi$
$72$	1.29996	+	2.70372i	0.153202	+	0.318636i
$73$	−13.0712	−	7.54666i	−1.52987	−	0.883270i	−0.999367	−	0.0355852i	$-0.988670\pi$
$73$	−13.0712	−	7.54666i	−1.52987	−	0.883270i	−0.530501	−	0.847684i	$-0.677996\pi$
$74$	−5.04710	−	2.91394i	−0.586713	−	0.338739i
$75$		0			0
$76$			4.20710i			0.482587i
$77$	−10.7525	−	7.50142i	−1.22536	−	0.854866i
$78$	−7.50809	−	8.09687i	−0.850124	−	0.916790i
$79$	−1.33404	−	2.31062i	−0.150091	−	0.259965i	0.781170	−	0.624319i	$-0.214623\pi$
$79$	−1.33404	−	2.31062i	−0.150091	−	0.259965i	−0.931261	+	0.364354i	$0.881290\pi$
$80$		0			0
$81$	5.62019	−	7.02947i	0.624466	−	0.781052i
$82$	6.45330	−	3.72581i	0.712648	−	0.411447i
$83$	7.27215			0.798222			0.399111	−	0.916903i	$-0.369319\pi$
$83$	7.27215			0.798222			0.399111	+	0.916903i	$0.369319\pi$
$84$	−1.72127	+	4.24702i	−0.187806	+	0.463388i
$85$		0			0
$86$	−4.02552	+	2.32413i	−0.434083	+	0.250618i
$87$	−0.308016	−	1.35145i	−0.0330227	−	0.144891i
$88$	−2.47766	+	4.29143i	−0.264120	+	0.457468i
$89$	−0.942474	−	1.63241i	−0.0999021	−	0.173035i	0.811742	−	0.584016i	$-0.198520\pi$
$89$	−0.942474	−	1.63241i	−0.0999021	−	0.173035i	−0.911644	+	0.410981i	$0.865186\pi$
$90$		0			0
$91$	1.44117	−	16.8056i	0.151076	−	1.76171i
$92$		−	1.91676i		−	0.199836i
$93$	8.33496	+	2.57384i	0.864295	+	0.266895i
$94$	−0.526352	−	0.303890i	−0.0542891	−	0.0313438i
$95$		0			0
$96$	1.65494	+	0.511048i	0.168907	+	0.0521586i
$97$			17.6562i			1.79271i	0.443334	+	0.896356i	$0.353795\pi$
$97$			17.6562i			1.79271i	−0.443334	+	0.896356i	$0.646205\pi$
$98$	−6.56957	+	2.41676i	−0.663627	+	0.244129i
$99$	14.8237	+	1.12019i	1.48984	+	0.112583i
$100$		0			0
$101$	−0.574210	+	0.994562i	−0.0571361	+	0.0989626i	−0.893179	−	0.449702i	$-0.851530\pi$
$101$	−0.574210	+	0.994562i	−0.0571361	+	0.0989626i	0.836043	+	0.548664i	$0.184864\pi$
$102$	1.39621	+	6.12600i	0.138245	+	0.606565i
$103$	6.30781	−	3.64182i	0.621527	−	0.358839i	−0.155936	−	0.987767i	$-0.549839\pi$
$103$	6.30781	−	3.64182i	0.621527	−	0.358839i	0.777463	+	0.628928i	$0.216506\pi$
$104$	−6.37523			−0.625143
$105$		0			0
$106$	−14.3065			−1.38957
$107$	−2.32646	+	1.34318i	−0.224908	+	0.129850i	−0.608221	−	0.793768i	$-0.708116\pi$
$107$	−2.32646	+	1.34318i	−0.224908	+	0.129850i	0.383313	+	0.923618i	$0.374783\pi$
$108$	−0.769634	−	5.13884i	−0.0740581	−	0.494485i
$109$	−4.51172	+	7.81452i	−0.432144	+	0.748495i	−0.997058	−	0.0766547i	$-0.975576\pi$
$109$	−4.51172	+	7.81452i	−0.432144	+	0.748495i	0.564914	+	0.825150i	$0.308909\pi$
$110$		0			0
$111$	6.86349	+	7.40171i	0.651454	+	0.702540i
$112$	1.12227	+	2.39594i	0.106044	+	0.226395i
$113$		−	12.4267i		−	1.16901i	−0.811391	−	0.584504i	$-0.801289\pi$
$113$		−	12.4267i		−	1.16901i	0.811391	−	0.584504i	$-0.198711\pi$
$114$	2.15003	−	6.96250i	0.201368	−	0.652098i
$115$		0			0
$116$	−0.693053	−	0.400134i	−0.0643483	−	0.0371515i
$117$	8.28757	+	17.2368i	0.766186	+	1.59355i
$118$			1.75132i			0.161222i
$119$	−5.49142	+	7.87134i	−0.503397	+	0.721565i
$120$		0			0
$121$	6.77761	+	11.7392i	0.616146	+	1.06720i
$122$	−1.71154	+	2.96447i	−0.154955	+	0.268390i
$123$	−12.5839	+	2.86806i	−1.13465	+	0.258604i
$124$	4.36166	−	2.51820i	0.391688	−	0.226141i
$125$		0			0
$126$	5.01904	−	6.14892i	0.447131	−	0.547790i
$127$	−8.06679			−0.715812			−0.357906	−	0.933758i	$-0.616509\pi$
$127$	−8.06679			−0.715812			−0.357906	+	0.933758i	$0.616509\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	7.84974	−	1.78907i	0.691131	−	0.157519i
$130$		0			0
$131$	−1.69151	−	2.92978i	−0.147788	−	0.255976i	0.782622	−	0.622497i	$-0.213882\pi$
$131$	−1.69151	−	2.92978i	−0.147788	−	0.255976i	−0.930410	+	0.366522i	$0.880549\pi$
$132$	6.29351	−	5.83587i	0.547780	−	0.507947i
$133$	10.0799	−	4.72148i	0.874042	−	0.409404i
$134$			7.98294i			0.689621i
$135$		0			0
$136$	3.14155	+	1.81377i	0.269386	+	0.155530i
$137$	−12.8409	−	7.41370i	−1.09707	−	0.633395i	−0.161622	−	0.986853i	$-0.551673\pi$
$137$	−12.8409	−	7.41370i	−1.09707	−	0.633395i	−0.935451	+	0.353458i	$0.885006\pi$
$138$	−0.979554	+	3.17212i	−0.0833852	+	0.270029i
$139$		−	7.24669i		−	0.614656i	−0.951604	−	0.307328i	$-0.900565\pi$
$139$		−	7.24669i		−	0.614656i	0.951604	−	0.307328i	$-0.0994349\pi$
$140$		0			0
$141$	0.715780	+	0.771911i	0.0602796	+	0.0650066i
$142$	−1.24379	−	2.15432i	−0.104377	−	0.180786i
$143$	−15.7957	+	27.3589i	−1.32090	+	2.28787i
$144$	−2.47766	−	1.69151i	−0.206472	−	0.140959i
$145$		0			0
$146$	15.0933			1.24913
$147$	12.1073	−	0.642228i	0.998596	−	0.0529701i
$148$	5.82789			0.479050
$149$	5.70973	−	3.29651i	0.467759	−	0.270061i	−0.247542	−	0.968877i	$-0.579623\pi$
$149$	5.70973	−	3.29651i	0.467759	−	0.270061i	0.715301	+	0.698816i	$0.246289\pi$
$150$		0			0
$151$	−5.88717	+	10.1969i	−0.479091	+	0.829811i	−0.999713	−	0.0239772i	$-0.992367\pi$
$151$	−5.88717	+	10.1969i	−0.479091	+	0.829811i	0.520621	+	0.853788i	$0.325700\pi$
$152$	−2.10355	−	3.64345i	−0.170620	−	0.295523i
$153$	0.820036	−	10.8517i	0.0662960	−	0.877308i
$154$	13.0626	+	1.12019i	1.05261	+	0.0902675i
$155$		0			0
$156$	10.5506	+	3.25805i	0.844727	+	0.260853i
$157$	−1.33783	−	0.772397i	−0.106770	−	0.0616440i	0.445664	−	0.895200i	$-0.352968\pi$
$157$	−1.33783	−	0.772397i	−0.106770	−	0.0616440i	−0.552434	+	0.833556i	$0.686301\pi$
$158$	2.31062	+	1.33404i	0.183823	+	0.106130i
$159$	23.6765	+	7.31132i	1.87767	+	0.579825i
$160$		0			0
$161$	−4.59243	+	2.15111i	−0.361934	+	0.169531i
$162$	−1.35249	+	8.89780i	−0.106262	+	0.699077i
$163$	−1.68880	−	2.92508i	−0.132277	−	0.229110i	0.792277	−	0.610161i	$-0.208895\pi$
$163$	−1.68880	−	2.92508i	−0.132277	−	0.229110i	−0.924554	+	0.381051i	$0.875562\pi$
$164$	−3.72581	+	6.45330i	−0.290937	+	0.503918i
$165$		0			0
$166$	−6.29787	+	3.63608i	−0.488809	+	0.282214i
$167$	−12.7685			−0.988053			−0.494027	−	0.869447i	$-0.664475\pi$
$167$	−12.7685			−0.988053			−0.494027	+	0.869447i	$0.664475\pi$
$168$	−0.632846	−	4.53867i	−0.0488251	−	0.350166i
$169$	−27.6436			−2.12643
$170$		0			0
$171$	−7.11633	+	10.4238i	−0.544200	+	0.797125i
$172$	2.32413	−	4.02552i	0.177214	−	0.306943i
$173$	−0.123778	−	0.214390i	−0.00941068	−	0.0162998i	0.861282	−	0.508128i	$-0.169662\pi$
$173$	−0.123778	−	0.214390i	−0.00941068	−	0.0162998i	−0.870692	+	0.491828i	$0.836329\pi$
$174$	0.942474	+	1.01638i	0.0714488	+	0.0770517i
$175$		0			0
$176$		−	4.95532i		−	0.373521i
$177$	0.895006	−	2.89833i	0.0672728	−	0.217852i
$178$	1.63241	+	0.942474i	0.122355	+	0.0706414i
$179$	−16.9709	−	9.79815i	−1.26846	−	0.732348i	−0.293767	−	0.955877i	$-0.594909\pi$
$179$	−16.9709	−	9.79815i	−1.26846	−	0.732348i	−0.974697	+	0.223528i	$0.928242\pi$
$180$		0			0
$181$			14.8103i			1.10084i	0.834887	+	0.550422i	$0.185533\pi$
$181$			14.8103i			1.10084i	−0.834887	+	0.550422i	$0.814467\pi$
$182$	7.15471	+	15.2747i	0.530342	+	1.13223i
$183$	4.34748	−	4.03134i	0.321375	−	0.298005i
$184$	0.958379	+	1.65996i	0.0706526	+	0.122374i
$185$		0			0
$186$	−8.50521	+	1.93847i	−0.623632	+	0.142135i
$187$	15.5674	−	8.98783i	1.13840	−	0.657255i
$188$	0.607779			0.0443269
$189$	−11.4486	+	7.61114i	−0.832763	+	0.553629i
$190$		0			0
$191$	−0.463759	+	0.267752i	−0.0335564	+	0.0193738i	−0.516684	−	0.856176i	$-0.672834\pi$
$191$	−0.463759	+	0.267752i	−0.0335564	+	0.0193738i	0.483128	+	0.875550i	$0.339501\pi$
$192$	−1.68874	+	0.384890i	−0.121875	+	0.0277771i
$193$	−2.76772	+	4.79383i	−0.199225	+	0.345068i	−0.948277	−	0.317443i	$-0.897176\pi$
$193$	−2.76772	+	4.79383i	−0.199225	+	0.345068i	0.749052	+	0.662511i	$0.230509\pi$
$194$	−8.82809	−	15.2907i	−0.633820	−	1.09781i
$195$		0			0
$196$	4.48104	−	5.37776i	0.320074	−	0.384126i
$197$			0.666454i			0.0474829i	0.999718	+	0.0237414i	$0.00755785\pi$
$197$			0.666454i			0.0474829i	−0.999718	+	0.0237414i	$0.992442\pi$
$198$	−13.3978	+	6.44174i	−0.952140	+	0.457794i
$199$	−7.81326	−	4.51099i	−0.553867	−	0.319775i	0.196813	−	0.980441i	$-0.436941\pi$
$199$	−7.81326	−	4.51099i	−0.553867	−	0.319775i	−0.750680	+	0.660666i	$0.770274\pi$
$200$		0			0
$201$	4.07966	−	13.2113i	0.287757	−	0.931853i
$202$		−	1.14842i		−	0.0808026i
$203$	−0.180907	+	2.10957i	−0.0126972	+	0.148063i
$204$	−4.27215	−	4.60717i	−0.299110	−	0.322566i
$205$		0			0
$206$	−3.64182	+	6.30781i	−0.253737	+	0.439486i
$207$	3.24221	−	4.74908i	0.225349	−	0.330084i
$208$	5.52111	−	3.18762i	0.382820	−	0.221021i
$209$	−20.8475			−1.44205
$210$		0			0
$211$	11.4386			0.787467			0.393733	−	0.919225i	$-0.371183\pi$
$211$	11.4386			0.787467			0.393733	+	0.919225i	$0.371183\pi$
$212$	12.3898	−	7.15326i	0.850936	−	0.491288i
$213$	0.957449	+	4.20090i	0.0656033	+	0.287841i
$214$	1.34318	−	2.32646i	0.0918181	−	0.159034i
$215$		0			0
$216$	3.23594	+	4.06555i	0.220178	+	0.276625i
$217$	−10.9284	−	7.62417i	−0.741868	−	0.517562i
$218$		−	9.02343i		−	0.611144i
$219$	−24.9786	−	7.71340i	−1.68789	−	0.521223i
$220$		0			0
$221$	20.0281	+	11.5632i	1.34724	+	0.777827i
$222$	−9.64481	−	2.97833i	−0.647317	−	0.199892i
$223$			5.23397i			0.350493i	0.984525	+	0.175246i	$0.0560722\pi$
$223$			5.23397i			0.350493i	−0.984525	+	0.175246i	$0.943928\pi$
$224$	−2.16988	−	1.51381i	−0.144981	−	0.101146i
$225$		0			0
$226$	6.21336	+	10.7619i	0.413306	+	0.715868i
$227$	6.73117	−	11.6587i	0.446763	−	0.773817i	−0.551410	−	0.834234i	$-0.685910\pi$
$227$	6.73117	−	11.6587i	0.446763	−	0.773817i	0.998173	+	0.0604178i	$0.0192433\pi$
$228$	1.61927	+	7.10471i	0.107239	+	0.470521i
$229$	14.3082	−	8.26082i	0.945509	−	0.545890i	0.0538263	−	0.998550i	$-0.482858\pi$
$229$	14.3082	−	8.26082i	0.945509	−	0.545890i	0.891683	+	0.452660i	$0.149525\pi$
$230$		0			0
$231$	−21.0454	−	8.52946i	−1.38468	−	0.561197i
$232$	0.800269			0.0525402
$233$	16.1392	−	9.31796i	1.05731	−	0.610440i	0.132625	−	0.991166i	$-0.457659\pi$
$233$	16.1392	−	9.31796i	1.05731	−	0.610440i	0.924688	+	0.380727i	$0.124326\pi$
$234$	−15.7957	−	10.7838i	−1.03259	−	0.704956i
$235$		0			0
$236$	−0.875658	−	1.51668i	−0.0570005	−	0.0987278i
$237$	−3.14218	−	3.38859i	−0.204107	−	0.220113i
$238$	0.820036	−	9.56249i	0.0531551	−	0.619844i
$239$		−	24.8065i		−	1.60460i	−0.596922	−	0.802299i	$-0.703610\pi$
$239$		−	24.8065i		−	1.60460i	0.596922	−	0.802299i	$-0.296390\pi$
$240$		0			0
$241$	−19.3439	−	11.1682i	−1.24605	−	0.719408i	−0.275731	−	0.961235i	$-0.588920\pi$
$241$	−19.3439	−	11.1682i	−1.24605	−	0.719408i	−0.970319	+	0.241827i	$0.922253\pi$
$242$	−11.7392	−	6.77761i	−0.754622	−	0.435681i
$243$	6.78549	−	14.0341i	0.435290	−	0.900291i
$244$		−	3.42307i		−	0.219140i
$245$		0			0
$246$	9.46395	−	8.77576i	0.603399	−	0.559522i
$247$	−13.4106	−	23.2279i	−0.853297	−	1.47795i
$248$	−2.51820	+	4.36166i	−0.159906	+	0.276966i
$249$	12.2808	−	2.79898i	0.778265	−	0.177378i
$250$		0			0
$251$	2.72107			0.171752			0.0858762	−	0.996306i	$-0.472631\pi$
$251$	2.72107			0.171752			0.0858762	+	0.996306i	$0.472631\pi$
$252$	−1.27215	+	7.83464i	−0.0801381	+	0.493536i
$253$	9.49815			0.597144
$254$	6.98605	−	4.03340i	0.438344	−	0.253078i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.75189	−	9.96256i	−0.358793	−	0.621448i	0.628966	−	0.777432i	$-0.283478\pi$
$257$	−5.75189	−	9.96256i	−0.358793	−	0.621448i	−0.987759	+	0.155985i	$0.950145\pi$
$258$	−5.90354	+	5.47425i	−0.367538	+	0.340812i
$259$	−6.54044	−	13.9633i	−0.406403	−	0.867635i
$260$		0			0
$261$	−1.04032	−	2.16370i	−0.0643942	−	0.133930i
$262$	2.92978	+	1.69151i	0.181002	+	0.104502i
$263$	−11.0726	−	6.39277i	−0.682766	−	0.394195i	0.118130	−	0.992998i	$-0.462310\pi$
$263$	−11.0726	−	6.39277i	−0.682766	−	0.394195i	−0.800896	+	0.598803i	$0.795643\pi$
$264$	−2.53241	+	8.20077i	−0.155859	+	0.504722i
$265$		0			0
$266$	−6.36874	+	9.12889i	−0.390493	+	0.559728i
$267$	−2.21990	−	2.39398i	−0.135856	−	0.146509i
$268$	−3.99147	−	6.91343i	−0.243818	−	0.422305i
$269$	−5.84575	+	10.1251i	−0.356422	+	0.617341i	−0.987360	−	0.158492i	$-0.949337\pi$
$269$	−5.84575	+	10.1251i	−0.356422	+	0.617341i	0.630938	+	0.775833i	$0.282670\pi$
$270$		0			0
$271$	19.1130	−	11.0349i	1.16103	−	0.670323i	0.209482	−	0.977812i	$-0.432822\pi$
$271$	19.1130	−	11.0349i	1.16103	−	0.670323i	0.951552	+	0.307489i	$0.0994888\pi$
$272$	−3.62755			−0.219952
$273$	−4.03454	−	28.9351i	−0.244181	−	1.75123i
$274$	14.8274			0.895756
$275$		0			0
$276$	−0.737742	−	3.23691i	−0.0444068	−	0.194839i
$277$	−3.90328	+	6.76068i	−0.234525	+	0.406210i	−0.959135	−	0.282950i	$-0.908687\pi$
$277$	−3.90328	+	6.76068i	−0.234525	+	0.406210i	0.724609	+	0.689160i	$0.242020\pi$
$278$	3.62334	+	6.27582i	0.217314	+	0.376398i
$279$	15.0663	+	1.13852i	0.901994	+	0.0681615i
$280$		0			0
$281$		−	23.0892i		−	1.37738i	−0.725054	−	0.688692i	$-0.758185\pi$
$281$		−	23.0892i		−	1.37738i	0.725054	−	0.688692i	$-0.241815\pi$
$282$	−1.00584	−	0.310604i	−0.0598968	−	0.0184962i
$283$	−21.4345	−	12.3752i	−1.27415	−	0.735631i	−0.298384	−	0.954446i	$-0.596448\pi$
$283$	−21.4345	−	12.3752i	−1.27415	−	0.735631i	−0.975766	+	0.218815i	$0.929781\pi$
$284$	2.15432	+	1.24379i	0.127835	+	0.0738056i
$285$		0			0
$286$		−	31.5913i		−	1.86803i
$287$	19.6431	+	1.68450i	1.15949	+	0.0994329i
$288$	2.99147	+	0.226058i	0.176274	+	0.0133206i
$289$	1.92045	+	3.32632i	0.112968	+	0.195666i
$290$		0			0
$291$	6.79569	+	29.8168i	0.398370	+	1.74789i
$292$	−13.0712	+	7.54666i	−0.764934	+	0.441635i
$293$	−25.3384			−1.48029			−0.740143	−	0.672449i	$-0.765242\pi$
$293$	−25.3384			−1.48029			−0.740143	+	0.672449i	$0.765242\pi$
$294$	−10.1641	+	6.60985i	−0.592785	+	0.385494i
$295$		0			0
$296$	−5.04710	+	2.91394i	−0.293357	+	0.169370i
$297$	25.4646	−	3.81378i	1.47761	−	0.221298i
$298$	−3.29651	+	5.70973i	−0.190962	+	0.330756i
$299$	6.10989	+	10.5826i	0.353344	+	0.612010i
$300$		0			0
$301$	−12.2532	−	1.05078i	−0.706262	−	0.0605659i
$302$		−	11.7743i		−	0.677538i
$303$	−0.586898	+	1.90057i	−0.0337164	+	0.109185i
$304$	3.64345	+	2.10355i	0.208966	+	0.120647i
$305$		0			0
$306$	4.71568	+	9.80787i	0.269577	+	0.560678i
$307$			13.1396i			0.749919i	0.927041	+	0.374960i	$0.122343\pi$
$307$			13.1396i			0.749919i	−0.927041	+	0.374960i	$0.877657\pi$
$308$	−11.8726	+	5.56119i	−0.676507	+	0.316878i
$309$	9.25059	−	8.57792i	0.526248	−	0.487981i
$310$		0			0
$311$	3.80332	−	6.58755i	0.215667	−	0.373545i	−0.737812	−	0.675006i	$-0.764141\pi$
$311$	3.80332	−	6.58755i	0.215667	−	0.373545i	0.953479	+	0.301461i	$0.0974742\pi$
$312$	−10.7661	+	2.45377i	−0.609513	+	0.138917i
$313$	−10.7608	+	6.21272i	−0.608234	+	0.351164i	−0.772274	−	0.635290i	$-0.780881\pi$
$313$	−10.7608	+	6.21272i	−0.608234	+	0.351164i	0.164040	+	0.986454i	$0.447547\pi$
$314$	1.54479			0.0871777
$315$		0			0
$316$	−2.66807			−0.150091
$317$	−24.0199	+	13.8679i	−1.34909	+	0.778898i	−0.988121	−	0.153679i	$-0.950888\pi$
$317$	−24.0199	+	13.8679i	−1.34909	+	0.778898i	−0.360971	+	0.932577i	$0.617555\pi$
$318$	−24.1601	+	5.50644i	−1.35483	+	0.308786i
$319$	1.98279	−	3.43430i	0.111015	−	0.192284i
$320$		0			0
$321$	−3.41182	+	3.16373i	−0.190429	+	0.176582i
$322$	2.90161	−	4.15913i	0.161700	−	0.231779i
$323$			15.2614i			0.849169i
$324$	−3.27761	−	8.38196i	−0.182089	−	0.465665i
$325$		0			0
$326$	2.92508	+	1.68880i	0.162005	+	0.0935337i
$327$	−4.61140	+	14.9332i	−0.255011	+	0.825810i
$328$		−	7.45163i		−	0.411447i
$329$	−0.682090	−	1.45620i	−0.0376048	−	0.0802830i
$330$		0			0
$331$	−5.89462	−	10.2098i	−0.323997	−	0.561180i	0.657312	−	0.753619i	$-0.271694\pi$
$331$	−5.89462	−	10.2098i	−0.323997	−	0.561180i	−0.981309	+	0.192439i	$0.938360\pi$
$332$	3.63608	−	6.29787i	0.199556	−	0.345640i
$333$	14.4395	+	9.85792i	0.791281	+	0.540211i
$334$	11.0578	−	6.38423i	0.605056	−	0.349329i
$335$		0			0
$336$	2.81739	+	3.61418i	0.153701	+	0.197170i
$337$	5.58238			0.304092			0.152046	−	0.988373i	$-0.451414\pi$
$337$	5.58238			0.304092			0.152046	+	0.988373i	$0.451414\pi$
$338$	23.9401	−	13.8218i	1.30217	−	0.751807i
$339$	−4.78292	−	20.9856i	−0.259773	−	1.13978i
$340$		0			0
$341$	12.4785	+	21.6134i	0.675749	+	1.17043i
$342$	0.951048	−	12.5854i	0.0514268	−	0.680541i
$343$	−17.9137	−	4.70101i	−0.967249	−	0.253831i
$344$			4.64827i			0.250618i
$345$		0			0
$346$	0.214390	+	0.123778i	0.0115257	+	0.00665435i
$347$	27.6342	+	15.9546i	1.48348	+	0.856489i	0.999824	−	0.0187674i	$-0.00597419\pi$
$347$	27.6342	+	15.9546i	1.48348	+	0.856489i	0.483659	+	0.875257i	$0.339308\pi$
$348$	−1.32440	−	0.408975i	−0.0709951	−	0.0219234i
$349$			1.64353i			0.0879759i	0.999032	+	0.0439879i	$0.0140063\pi$
$349$			1.64353i			0.0879759i	−0.999032	+	0.0439879i	$0.985994\pi$
$350$		0			0
$351$	20.6299	+	25.9188i	1.10114	+	1.38344i
$352$	2.47766	+	4.29143i	0.132060	+	0.228734i
$353$	−7.30038	+	12.6446i	−0.388560	+	0.673006i	−0.992256	−	0.124209i	$-0.960361\pi$
$353$	−7.30038	+	12.6446i	−0.388560	+	0.673006i	0.603696	+	0.797215i	$0.293694\pi$
$354$	0.674065	+	2.95753i	0.0358261	+	0.157191i
$355$		0			0
$356$	−1.88495			−0.0999021
$357$	−6.24400	+	15.4063i	−0.330468	+	0.815387i
$358$	19.5963			1.03570
$359$	0.438209	−	0.253000i	0.0231278	−	0.0133528i	−0.488392	−	0.872625i	$-0.662416\pi$
$359$	0.438209	−	0.253000i	0.0231278	−	0.0133528i	0.511519	+	0.859272i	$0.329083\pi$
$360$		0			0
$361$	−0.650173	+	1.12613i	−0.0342196	+	0.0592701i
$362$	−7.40517	−	12.8261i	−0.389207	−	0.674127i
$363$	15.9639	+	17.2158i	0.837889	+	0.903595i
$364$	−13.8335	−	9.65089i	−0.725072	−	0.505844i
$365$		0			0
$366$	−1.74935	+	5.66498i	−0.0914401	+	0.296113i
$367$	1.17547	+	0.678660i	0.0613592	+	0.0354258i	0.530366	−	0.847769i	$-0.322055\pi$
$367$	1.17547	+	0.678660i	0.0613592	+	0.0354258i	−0.469007	+	0.883195i	$0.655388\pi$
$368$	−1.65996	−	0.958379i	−0.0865314	−	0.0499590i
$369$	−20.1471	+	9.68684i	−1.04882	+	0.504277i
$370$		0			0
$371$	−31.0434	−	21.6574i	−1.61170	−	1.12439i
$372$	6.39649	−	5.93136i	0.331643	−	0.307527i
$373$	−17.0548	−	29.5397i	−0.883062	−	1.52951i	−0.847919	−	0.530125i	$-0.822145\pi$
$373$	−17.0548	−	29.5397i	−0.883062	−	1.52951i	−0.0351422	−	0.999382i	$-0.511188\pi$
$374$	−8.98783	+	15.5674i	−0.464750	+	0.804970i
$375$		0			0
$376$	−0.526352	+	0.303890i	−0.0271445	+	0.0156719i
$377$	5.10190			0.262761
$378$	6.10921	−	12.3157i	0.314224	−	0.633453i
$379$	−1.53951			−0.0790795			−0.0395398	−	0.999218i	$-0.512589\pi$
$379$	−1.53951			−0.0790795			−0.0395398	+	0.999218i	$0.512589\pi$
$380$		0			0
$381$	−13.6228	+	3.10483i	−0.697915	+	0.159065i
$382$	0.267752	−	0.463759i	0.0136994	−	0.0237280i
$383$	−16.2631	−	28.1685i	−0.831004	−	1.43934i	−0.897243	−	0.441537i	$-0.854433\pi$
$383$	−16.2631	−	28.1685i	−0.831004	−	1.43934i	0.0662394	−	0.997804i	$-0.478900\pi$
$384$	1.27005	−	1.17770i	0.0648120	−	0.0600991i
$385$		0			0
$386$		−	5.53544i		−	0.281747i
$387$	12.5676	−	6.04258i	0.638848	−	0.307162i
$388$	15.2907	+	8.82809i	0.776267	+	0.448178i
$389$	−6.15025	−	3.55085i	−0.311830	−	0.180035i	0.335915	−	0.941892i	$-0.390954\pi$
$389$	−6.15025	−	3.55085i	−0.311830	−	0.180035i	−0.647745	+	0.761857i	$0.724288\pi$
$390$		0			0
$391$		−	6.95313i		−	0.351635i
$392$	−1.19181	+	6.89780i	−0.0601956	+	0.348391i
$393$	−3.98417	−	4.29660i	−0.200975	−	0.216735i
$394$	−0.333227	−	0.577166i	−0.0167877	−	0.0290772i
$395$		0			0
$396$	8.38196	−	12.2776i	0.421209	−	0.616973i
$397$	−11.2790	+	6.51194i	−0.566077	+	0.326825i	−0.755581	−	0.655055i	$-0.772645\pi$
$397$	−11.2790	+	6.51194i	−0.566077	+	0.326825i	0.189504	+	0.981880i	$0.439312\pi$
$398$	9.02198			0.452231
$399$	15.2052	−	11.8530i	0.761212	−	0.593395i
$400$		0			0
$401$	20.2676	−	11.7015i	1.01211	−	0.584345i	0.100305	−	0.994957i	$-0.468018\pi$
$401$	20.2676	−	11.7015i	1.01211	−	0.584345i	0.911810	+	0.410612i	$0.134685\pi$
$402$	3.07256	+	13.4812i	0.153245	+	0.672379i
$403$	−16.0541	+	27.8066i	−0.799714	+	1.38514i
$404$	0.574210	+	0.994562i	0.0285680	+	0.0494813i
$405$		0			0
$406$	−0.898114	−	1.91739i	−0.0445727	−	0.0951587i
$407$			28.8791i			1.43148i
$408$	6.00338	+	1.85385i	0.297211	+	0.0917792i
$409$	11.4311	+	6.59972i	0.565229	+	0.326335i	0.755242	−	0.655447i	$-0.227520\pi$
$409$	11.4311	+	6.59972i	0.565229	+	0.326335i	−0.190013	+	0.981782i	$0.560853\pi$
$410$		0			0
$411$	−24.5385	−	7.57751i	−1.21039	−	0.373771i
$412$		−	7.28364i		−	0.358839i
$413$	−2.65116	+	3.80015i	−0.130455	+	0.186993i
$414$	−0.433299	+	5.73392i	−0.0212955	+	0.281807i
$415$		0			0
$416$	−3.18762	+	5.52111i	−0.156286	+	0.270695i
$417$	−2.78918	−	12.2378i	−0.136587	−	0.599288i
$418$	18.0545	−	10.4238i	0.883073	−	0.509843i
$419$	27.9492			1.36541			0.682704	−	0.730695i	$-0.260804\pi$
$419$	27.9492			1.36541			0.682704	+	0.730695i	$0.260804\pi$
$420$		0			0
$421$	24.6795			1.20281			0.601403	−	0.798946i	$-0.294609\pi$
$421$	24.6795			1.20281			0.601403	+	0.798946i	$0.294609\pi$
$422$	−9.90613	+	5.71931i	−0.482223	+	0.278412i
$423$	1.50587	+	1.02806i	0.0732179	+	0.0499861i
$424$	−7.15326	+	12.3898i	−0.347393	+	0.601703i
$425$		0			0
$426$	−2.92963	−	3.15936i	−0.141941	−	0.153072i
$427$	−8.20147	+	3.84160i	−0.396897	+	0.185908i
$428$			2.68637i			0.129850i
$429$	−16.1447	+	52.2818i	−0.779472	+	2.52419i
$430$		0			0
$431$	2.89638	+	1.67223i	0.139514	+	0.0805483i	0.568132	−	0.822937i	$-0.307666\pi$
$431$	2.89638	+	1.67223i	0.139514	+	0.0805483i	−0.428619	+	0.903486i	$0.641000\pi$
$432$	−4.83518	−	1.90290i	−0.232633	−	0.0915532i
$433$			14.6756i			0.705264i	0.935762	+	0.352632i	$0.114713\pi$
$433$			14.6756i			0.705264i	−0.935762	+	0.352632i	$0.885287\pi$
$434$	13.2764	+	1.13852i	0.637285	+	0.0546507i
$435$		0			0
$436$	4.51172	+	7.81452i	0.216072	+	0.374248i
$437$	−4.03199	+	6.98361i	−0.192876	+	0.334072i
$438$	25.4888	−	5.80927i	1.21790	−	0.277578i
$439$	−5.70453	+	3.29351i	−0.272262	+	0.157191i	−0.629915	−	0.776664i	$-0.716910\pi$
$439$	−5.70453	+	3.29351i	−0.272262	+	0.157191i	0.357653	+	0.933855i	$0.383577\pi$
$440$		0			0
$441$	20.1990	−	5.74456i	0.961858	−	0.273550i
$442$	−23.1265			−1.10001
$443$	35.2654	−	20.3605i	1.67551	−	0.967357i	0.711047	−	0.703144i	$-0.248221\pi$
$443$	35.2654	−	20.3605i	1.67551	−	0.967357i	0.964464	−	0.264213i	$-0.0851121\pi$
$444$	9.84182	−	2.24310i	0.467072	−	0.106453i
$445$		0			0
$446$	−2.61699	−	4.53275i	−0.123918	−	0.214632i
$447$	8.37348	−	7.76459i	0.396052	−	0.367253i
$448$	2.63608	+	0.226058i	0.124543	+	0.0106802i
$449$			18.3485i			0.865919i	0.901413	+	0.432960i	$0.142531\pi$
$449$			18.3485i			0.865919i	−0.901413	+	0.432960i	$0.857469\pi$
$450$		0			0
$451$	−31.9782	−	18.4626i	−1.50579	−	0.869370i
$452$	−10.7619	−	6.21336i	−0.506195	−	0.292252i
$453$	−6.01725	+	19.4859i	−0.282715	+	0.915525i
$454$			13.4623i			0.631819i
$455$		0			0
$456$	−4.95469	−	5.34323i	−0.232024	−	0.250219i
$457$	−4.32166	−	7.48533i	−0.202159	−	0.350149i	0.747065	−	0.664751i	$-0.231462\pi$
$457$	−4.32166	−	7.48533i	−0.202159	−	0.350149i	−0.949224	+	0.314602i	$0.898129\pi$
$458$	−8.26082	+	14.3082i	−0.386003	+	0.668576i
$459$	−2.79188	−	18.6414i	−0.130314	−	0.870105i
$460$		0			0
$461$	−24.7864			−1.15442			−0.577210	−	0.816596i	$-0.695859\pi$
$461$	−24.7864			−1.15442			−0.577210	+	0.816596i	$0.695859\pi$
$462$	22.4906	−	3.13596i	1.04636	−	0.145898i
$463$	17.9797			0.835589			0.417794	−	0.908542i	$-0.362803\pi$
$463$	17.9797			0.835589			0.417794	+	0.908542i	$0.362803\pi$
$464$	−0.693053	+	0.400134i	−0.0321742	+	0.0185758i
$465$		0			0
$466$	−9.31796	+	16.1392i	−0.431646	+	0.747633i
$467$	0.636712	+	1.10282i	0.0294635	+	0.0510323i	0.880381	−	0.474267i	$-0.157287\pi$
$467$	0.636712	+	1.10282i	0.0294635	+	0.0510323i	−0.850918	+	0.525299i	$0.823953\pi$
$468$	19.0713	+	1.44117i	0.881572	+	0.0666182i
$469$	−12.0847	+	17.3220i	−0.558018	+	0.799857i
$470$		0			0
$471$	−2.55654	−	0.789463i	−0.117799	−	0.0363765i
$472$	1.51668	+	0.875658i	0.0698111	+	0.0403054i
$473$	19.9477	+	11.5168i	0.917198	+	0.529545i
$474$	4.41551	+	1.36351i	0.202811	+	0.0626282i
$475$		0			0
$476$	4.07107	+	8.69138i	0.186597	+	0.398369i
$477$	42.7976	+	3.23411i	1.95957	+	0.148080i
$478$	12.4032	+	21.4831i	0.567311	+	0.982612i
$479$	7.11334	−	12.3207i	0.325017	−	0.562945i	−0.656499	−	0.754327i	$-0.727963\pi$
$479$	7.11334	−	12.3207i	0.325017	−	0.562945i	0.981516	+	0.191381i	$0.0612967\pi$
$480$		0			0
$481$	−32.1764	+	18.5771i	−1.46712	+	0.847042i
$482$	22.3364			1.01740
$483$	−6.92751	+	5.40026i	−0.315212	+	0.245720i
$484$	13.5552			0.616146
$485$		0			0
$486$	1.14066	+	15.5467i	0.0517415	+	0.705211i
$487$	19.9476	−	34.5502i	0.903910	−	1.56562i	0.0815361	−	0.996670i	$-0.474017\pi$
$487$	19.9476	−	34.5502i	0.903910	−	1.56562i	0.822374	−	0.568947i	$-0.192649\pi$
$488$	1.71154	+	2.96447i	0.0774776	+	0.134195i
$489$	−3.97778	−	4.28971i	−0.179881	−	0.193988i
$490$		0			0
$491$		−	15.9778i		−	0.721069i	−0.932746	−	0.360535i	$-0.882594\pi$
$491$		−	15.9778i		−	0.721069i	0.932746	−	0.360535i	$-0.117406\pi$
$492$	−3.80814	+	12.3320i	−0.171684	+	0.555970i
$493$	−2.51408	−	1.45151i	−0.113229	−	0.0653725i
$494$	23.2279	+	13.4106i	1.04507	+	0.603372i
$495$		0			0
$496$		−	5.03641i		−	0.226141i
$497$	0.562340	−	6.55747i	0.0252244	−	0.294143i
$498$	−9.23600	+	8.56439i	−0.413875	+	0.383780i
$499$	6.90313	+	11.9566i	0.309027	+	0.535250i	0.978150	−	0.207902i	$-0.0666634\pi$
$499$	6.90313	+	11.9566i	0.309027	+	0.535250i	−0.669123	+	0.743152i	$0.733330\pi$
$500$		0			0
$501$	−21.5627	+	4.91446i	−0.963349	+	0.219562i
$502$	−2.35652	+	1.36054i	−0.105176	+	0.0607237i
$503$	−2.11183			−0.0941620			−0.0470810	−	0.998891i	$-0.514992\pi$
$503$	−2.11183			−0.0941620			−0.0470810	+	0.998891i	$0.514992\pi$
$504$	−2.81561	−	7.42108i	−0.125417	−	0.330561i
$505$		0			0
$506$	−8.22564	+	4.74908i	−0.365674	+	0.211122i
$507$	−46.6830	+	10.6398i	−2.07326	+	0.472528i
$508$	−4.03340	+	6.98605i	−0.178953	+	0.309956i
$509$	−8.09556	−	14.0219i	−0.358830	−	0.621511i	0.628936	−	0.777457i	$-0.283491\pi$
$509$	−8.09556	−	14.0219i	−0.358830	−	0.621511i	−0.987766	+	0.155946i	$0.950157\pi$
$510$		0			0
$511$	32.7507	+	22.8484i	1.44880	+	1.01075i
$512$		−	1.00000i		−	0.0441942i
$513$	−8.00567	+	20.3421i	−0.353459	+	0.898124i
$514$	9.96256	+	5.75189i	0.439430	+	0.253705i
$515$		0			0
$516$	2.37549	−	7.69261i	0.104575	−	0.338648i
$517$			3.01174i			0.132456i
$518$	12.6458	+	8.82232i	0.555625	+	0.387630i
$519$	−0.291546	−	0.314409i	−0.0127975	−	0.0138010i
$520$		0			0
$521$	−12.4676	+	21.5945i	−0.546216	+	0.946073i	0.452314	+	0.891859i	$0.350599\pi$
$521$	−12.4676	+	21.5945i	−0.546216	+	0.946073i	−0.998529	+	0.0542143i	$0.982735\pi$
$522$	1.98279	+	1.35366i	0.0867845	+	0.0592481i
$523$	−17.0768	+	9.85929i	−0.746716	+	0.431116i	−0.824506	−	0.565853i	$-0.808547\pi$
$523$	−17.0768	+	9.85929i	−0.746716	+	0.431116i	0.0777903	+	0.996970i	$0.475214\pi$
$524$	−3.38301			−0.147788
$525$		0			0
$526$	12.7855			0.557476
$527$	15.8221	−	9.13490i	0.689222	−	0.397923i
$528$	−1.90726	−	8.36827i	−0.0830026	−	0.364182i
$529$	−9.66302	+	16.7368i	−0.420131	+	0.727689i
$530$		0			0
$531$	0.395899	−	5.23901i	0.0171806	−	0.227354i
$532$	0.951048	−	11.0902i	0.0412332	−	0.480822i
$533$		−	47.5059i		−	2.05771i
$534$	3.11948	+	0.963298i	0.134993	+	0.0416860i
$535$		0			0
$536$	6.91343	+	3.99147i	0.298615	+	0.172405i
$537$	−32.4307	−	10.0146i	−1.39949	−	0.432164i
$538$		−	11.6915i		−	0.504057i
$539$	26.6485	+	22.2050i	1.14783	+	0.956436i
$540$		0			0
$541$	4.27923	+	7.41184i	0.183978	+	0.318660i	0.943232	−	0.332135i	$-0.107769\pi$
$541$	4.27923	+	7.41184i	0.183978	+	0.318660i	−0.759253	+	0.650795i	$0.774436\pi$
$542$	−11.0349	+	19.1130i	−0.473990	+	0.820975i
$543$	5.70036	+	25.0109i	0.244626	+	1.07332i
$544$	3.14155	−	1.81377i	0.134693	−	0.0777649i
$545$		0			0
$546$	17.9615	+	23.0412i	0.768683	+	0.986074i
$547$	33.5472			1.43437			0.717187	−	0.696881i	$-0.245430\pi$
$547$	33.5472			1.43437			0.717187	+	0.696881i	$0.245430\pi$
$548$	−12.8409	+	7.41370i	−0.548536	+	0.316698i
$549$	5.79015	−	8.48121i	0.247118	−	0.361969i
$550$		0			0
$551$	1.68340	+	2.91574i	0.0717154	+	0.124215i
$552$	2.25736	+	2.43438i	0.0960796	+	0.103614i
$553$	2.99429	+	6.39254i	0.127330	+	0.271838i
$554$		−	7.80656i		−	0.331669i
$555$		0			0
$556$	−6.27582	−	3.62334i	−0.266154	−	0.153664i
$557$	−4.63348	−	2.67514i	−0.196327	−	0.113349i	0.398614	−	0.917119i	$-0.369491\pi$
$557$	−4.63348	−	2.67514i	−0.196327	−	0.113349i	−0.594941	+	0.803769i	$0.702825\pi$
$558$	−13.6170	+	6.54715i	−0.576455	+	0.277163i
$559$			29.6338i			1.25338i
$560$		0			0
$561$	22.8300	−	21.1699i	0.963883	−	0.893793i
$562$	11.5446	+	19.9958i	0.486979	+	0.843472i
$563$	14.6685	−	25.4066i	0.618205	−	1.07076i	−0.371609	−	0.928390i	$-0.621194\pi$
$563$	14.6685	−	25.4066i	0.618205	−	1.07076i	0.989813	−	0.142372i	$-0.0454730\pi$
$564$	1.02638	−	0.233928i	0.0432186	−	0.00985016i
$565$		0			0
$566$	24.7505			1.04034
$567$	−16.4043	+	17.2597i	−0.688917	+	0.724841i
$568$	−2.48759			−0.104377
$569$	36.5568	−	21.1061i	1.53254	−	0.884812i	0.533295	−	0.845929i	$-0.320954\pi$
$569$	36.5568	−	21.1061i	1.53254	−	0.884812i	0.999244	−	0.0388825i	$-0.0123798\pi$
$570$		0			0
$571$	15.6790	−	27.1568i	0.656145	−	1.13648i	−0.325461	−	0.945556i	$-0.605519\pi$
$571$	15.6790	−	27.1568i	0.656145	−	1.13648i	0.981605	−	0.190921i	$-0.0611473\pi$
$572$	15.7957	+	27.3589i	0.660450	+	1.14393i
$573$	−0.680116	+	0.630661i	−0.0284123	+	0.0263462i
$574$	−17.8536	+	8.36271i	−0.745196	+	0.349053i
$575$		0			0
$576$	−2.70372	+	1.29996i	−0.112655	+	0.0541651i
$577$	27.7794	+	16.0385i	1.15647	+	0.667689i	0.950456	−	0.310859i	$-0.100617\pi$
$577$	27.7794	+	16.0385i	1.15647	+	0.667689i	0.206016	+	0.978549i	$0.433950\pi$
$578$	−3.32632	−	1.92045i	−0.138357	−	0.0798802i
$579$	−2.82887	+	9.16083i	−0.117564	+	0.380711i
$580$		0			0
$581$	−19.1699	−	1.64393i	−0.795303	−	0.0682017i
$582$	−20.7936	−	22.4242i	−0.861924	−	0.929515i
$583$	35.4467	+	61.3955i	1.46805	+	2.54274i
$584$	7.54666	−	13.0712i	0.312283	−	0.540890i
$585$		0			0
$586$	21.9437	−	12.6692i	0.906487	−	0.523360i
$587$	1.93731			0.0799612			0.0399806	−	0.999200i	$-0.487270\pi$
$587$	1.93731			0.0799612			0.0399806	+	0.999200i	$0.487270\pi$
$588$	5.49748	−	10.8064i	0.226712	−	0.445647i
$589$	−21.1887			−0.873063
$590$		0			0
$591$	0.256512	+	1.12547i	0.0105515	+	0.0462957i
$592$	2.91394	−	5.04710i	0.119762	−	0.207435i
$593$	−5.63074	−	9.75274i	−0.231227	−	0.400497i	0.726942	−	0.686698i	$-0.240941\pi$
$593$	−5.63074	−	9.75274i	−0.231227	−	0.400497i	−0.958169	+	0.286201i	$0.907607\pi$
$594$	−20.1461	+	16.0351i	−0.826604	+	0.657929i
$595$		0			0
$596$		−	6.59303i		−	0.270061i
$597$	−14.9308	−	4.61066i	−0.611079	−	0.188702i
$598$	−10.5826	−	6.10989i	−0.432756	−	0.249852i
$599$	38.4047	+	22.1730i	1.56917	+	0.905963i	0.996265	+	0.0863446i	$0.0275186\pi$
$599$	38.4047	+	22.1730i	1.56917	+	0.905963i	0.572909	+	0.819619i	$0.305815\pi$
$600$		0			0
$601$			17.7126i			0.722514i	0.932466	+	0.361257i	$0.117652\pi$
$601$			17.7126i			0.722514i	−0.932466	+	0.361257i	$0.882348\pi$
$602$	11.1370	−	5.21659i	0.453909	−	0.212613i
$603$	1.80461	−	23.8807i	0.0734893	−	0.972499i
$604$	5.88717	+	10.1969i	0.239546	+	0.414905i
$605$		0			0
$606$	−0.442016	−	1.93939i	−0.0179557	−	0.0787823i
$607$	15.8915	−	9.17497i	0.645016	−	0.372400i	−0.141528	−	0.989934i	$-0.545201\pi$
$607$	15.8915	−	9.17497i	0.645016	−	0.372400i	0.786544	+	0.617534i	$0.211868\pi$
$608$	−4.20710			−0.170620
$609$	0.506447	+	3.63215i	0.0205223	+	0.147182i
$610$		0			0
$611$	−3.35562	+	1.93737i	−0.135754	+	0.0783775i
$612$	−8.98783	−	6.13602i	−0.363312	−	0.248034i
$613$	0.315836	−	0.547045i	0.0127565	−	0.0220949i	−0.859577	−	0.511007i	$-0.829273\pi$
$613$	0.315836	−	0.547045i	0.0127565	−	0.0220949i	0.872333	+	0.488912i	$0.162606\pi$
$614$	−6.56982	−	11.3793i	−0.265136	−	0.459230i
$615$		0			0
$616$	7.50142	−	10.7525i	0.302241	−	0.433229i
$617$			15.5902i			0.627638i	0.949483	+	0.313819i	$0.101608\pi$
$617$			15.5902i			0.627638i	−0.949483	+	0.313819i	$0.898392\pi$
$618$	−3.72228	+	12.0540i	−0.149732	+	0.484883i
$619$	10.9863	+	6.34296i	0.441578	+	0.254945i	0.704267	−	0.709936i	$-0.251276\pi$
$619$	10.9863	+	6.34296i	0.441578	+	0.254945i	−0.262689	+	0.964881i	$0.584609\pi$
$620$		0			0
$621$	3.64739	−	9.26787i	0.146365	−	0.371907i
$622$			7.60664i			0.304999i
$623$	2.11541	+	4.51622i	0.0847522	+	0.180938i
$624$	8.09687	−	7.50809i	0.324134	−	0.300564i
$625$		0			0
$626$	6.21272	−	10.7608i	0.248310	−	0.430086i
$627$	−35.2061	+	8.02401i	−1.40600	+	0.320448i
$628$	−1.33783	+	0.772397i	−0.0533852	+	0.0308220i
$629$	21.1409			0.842945
$630$		0			0
$631$	−5.96052			−0.237284			−0.118642	−	0.992937i	$-0.537854\pi$
$631$	−5.96052			−0.237284			−0.118642	+	0.992937i	$0.537854\pi$
$632$	2.31062	−	1.33404i	0.0919115	−	0.0530651i
$633$	19.3169	−	4.40261i	0.767778	−	0.174988i
$634$	13.8679	−	24.0199i	0.550764	−	0.953952i
$635$		0			0
$636$	18.1700	−	16.8488i	0.720488	−	0.668097i
$637$	−7.59808	+	43.9751i	−0.301047	+	1.74235i
$638$			3.96559i			0.156999i
$639$	3.23377	+	6.72574i	0.127926	+	0.266066i
$640$		0			0
$641$	−11.2070	−	6.47036i	−0.442649	−	0.255564i	0.262071	−	0.965048i	$-0.415594\pi$
$641$	−11.2070	−	6.47036i	−0.442649	−	0.255564i	−0.704721	+	0.709485i	$0.748928\pi$
$642$	1.37286	−	4.44578i	0.0541825	−	0.175461i
$643$		−	27.7420i		−	1.09404i	−0.837120	−	0.547019i	$-0.815763\pi$
$643$		−	27.7420i		−	1.09404i	0.837120	−	0.547019i	$-0.184237\pi$
$644$	−0.433299	+	5.05272i	−0.0170744	+	0.199105i
$645$		0			0
$646$	−7.63072	−	13.2168i	−0.300227	−	0.520008i
$647$	23.3856	−	40.5050i	0.919382	−	1.59242i	0.119027	−	0.992891i	$-0.462023\pi$
$647$	23.3856	−	40.5050i	0.919382	−	1.59242i	0.800356	−	0.599526i	$-0.204644\pi$
$648$	7.02947	+	5.62019i	0.276144	+	0.220782i
$649$	7.51566	−	4.33917i	0.295015	−	0.170327i
$650$		0			0
$651$	−21.3897	−	8.66903i	−0.838330	−	0.339766i
$652$	−3.37759			−0.132277
$653$	−27.3651	+	15.7992i	−1.07088	+	0.618271i	−0.928421	−	0.371530i	$-0.878833\pi$
$653$	−27.3651	+	15.7992i	−1.07088	+	0.618271i	−0.142456	+	0.989801i	$0.545500\pi$
$654$	−3.47303	−	15.2383i	−0.135806	−	0.595864i
$655$		0			0
$656$	3.72581	+	6.45330i	0.145469	+	0.251959i
$657$	−45.1512	−	3.41197i	−1.76152	−	0.133113i
$658$	1.31881	+	0.920062i	0.0514125	+	0.0358678i
$659$			29.8627i			1.16329i	0.813444	+	0.581643i	$0.197590\pi$
$659$			29.8627i			1.16329i	−0.813444	+	0.581643i	$0.802410\pi$
$660$		0			0
$661$	−12.0007	−	6.92861i	−0.466773	−	0.269492i	0.248115	−	0.968731i	$-0.420189\pi$
$661$	−12.0007	−	6.92861i	−0.466773	−	0.269492i	−0.714888	+	0.699239i	$0.753522\pi$
$662$	10.2098	+	5.89462i	0.396814	+	0.229101i
$663$	38.2729	+	11.8187i	1.48640	+	0.459001i
$664$			7.27215i			0.282214i
$665$		0			0
$666$	−17.4340	−	1.31744i	−0.675552	−	0.0510498i
$667$	−0.766960	−	1.32841i	−0.0296968	−	0.0514364i
$668$	−6.38423	+	11.0578i	−0.247013	+	0.427840i
$669$	2.01450	+	8.83884i	0.0778853	+	0.341729i
$670$		0			0
$671$	16.9624			0.654827
$672$	−4.24702	−	1.72127i	−0.163833	−	0.0663996i
$673$	−21.1836			−0.816568			−0.408284	−	0.912855i	$-0.633873\pi$
$673$	−21.1836			−0.816568			−0.408284	+	0.912855i	$0.633873\pi$
$674$	−4.83448	+	2.79119i	−0.186217	+	0.107513i
$675$		0			0
$676$	−13.8218	+	23.9401i	−0.531608	+	0.920771i
$677$	24.1682	+	41.8606i	0.928860	+	1.60883i	0.785232	+	0.619202i	$0.212544\pi$
$677$	24.1682	+	41.8606i	0.928860	+	1.60883i	0.143628	+	0.989632i	$0.454123\pi$
$678$	14.6349	+	15.7826i	0.562050	+	0.606126i
$679$	3.99132	−	46.5430i	0.153173	−	1.78616i
$680$		0			0
$681$	6.87989	−	22.2794i	0.263638	−	0.853747i
$682$	−21.6134	−	12.4785i	−0.827620	−	0.477827i
$683$	22.8004	+	13.1638i	0.872433	+	0.503699i	0.868156	−	0.496291i	$-0.165305\pi$
$683$	22.8004	+	13.1638i	0.872433	+	0.503699i	0.00427708	+	0.999991i	$0.498639\pi$
$684$	5.46907	+	11.3748i	0.209115	+	0.434926i
$685$		0			0
$686$	17.8642	−	4.88565i	0.682059	−	0.186535i
$687$	20.9833	−	19.4575i	0.800563	−	0.742349i
$688$	−2.32413	−	4.02552i	−0.0886068	−	0.153471i
$689$	−45.6037	+	78.9880i	−1.73736	+	3.00920i
$690$		0			0
$691$	−16.5539	+	9.55742i	−0.629741	+	0.363581i	−0.780652	−	0.624966i	$-0.785113\pi$
$691$	−16.5539	+	9.55742i	−0.629741	+	0.363581i	0.150911	+	0.988547i	$0.451779\pi$
$692$	−0.247556			−0.00941068
$693$	−38.8232	−	6.30392i	−1.47477	−	0.239466i
$694$	−31.9093			−1.21126
$695$		0			0
$696$	1.35145	−	0.308016i	0.0512266	−	0.0116753i
$697$	−13.5156	+	23.4096i	−0.511939	+	0.886704i
$698$	−0.821763	−	1.42333i	−0.0311042	−	0.0538740i
$699$	23.6686	−	21.9475i	0.895227	−	0.830130i
$700$		0			0
$701$			36.3536i			1.37306i	0.727103	+	0.686528i	$0.240866\pi$
$701$			36.3536i			1.37306i	−0.727103	+	0.686528i	$0.759134\pi$
$702$	−30.8254	−	12.1314i	−1.16343	−	0.457871i
$703$	−21.2336	−	12.2592i	−0.800842	−	0.462366i
$704$	−4.29143	−	2.47766i	−0.161740	−	0.0933804i
$705$		0			0
$706$		−	14.6008i		−	0.549507i
$707$	1.73849	−	2.49194i	0.0653827	−	0.0937189i
$708$	−2.06252	−	2.22426i	−0.0775143	−	0.0835928i
$709$	−2.54606	−	4.40991i	−0.0956193	−	0.165618i	0.814248	−	0.580518i	$-0.197150\pi$
$709$	−2.54606	−	4.40991i	−0.0956193	−	0.165618i	−0.909867	+	0.414900i	$0.863816\pi$
$710$		0			0
$711$	−6.61058	−	4.51307i	−0.247916	−	0.169253i
$712$	1.63241	−	0.942474i	0.0611773	−	0.0353207i
$713$	9.65357			0.361529
$714$	−2.29568	−	16.4642i	−0.0859136	−	0.616158i
$715$		0			0
$716$	−16.9709	+	9.79815i	−0.634232	+	0.366174i
$717$	−9.54778	−	41.8918i	−0.356568	−	1.56448i
$718$	−0.253000	+	0.438209i	−0.00944189	+	0.0163538i
$719$	−20.5822	−	35.6494i	−0.767587	−	1.32950i	−0.938868	−	0.344278i	$-0.888124\pi$
$719$	−20.5822	−	35.6494i	−0.767587	−	1.32950i	0.171281	−	0.985222i	$-0.445209\pi$
$720$		0			0
$721$	−17.4511	+	8.17418i	−0.649914	+	0.304422i
$722$		−	1.30035i		−	0.0483938i
$723$	−36.9655	−	11.4150i	−1.37476	−	0.424528i
$724$	12.8261	+	7.40517i	0.476679	+	0.275211i
$725$		0			0
$726$	−22.4331	−	6.92736i	−0.832570	−	0.257098i
$727$		−	46.1288i		−	1.71082i	−0.517948	−	0.855412i	$-0.673304\pi$
$727$		−	46.1288i		−	1.71082i	0.517948	−	0.855412i	$-0.326696\pi$
$728$	16.8056	+	1.44117i	0.622857	+	0.0534134i
$729$	6.05736	−	26.3118i	0.224347	−	0.974509i
$730$		0			0
$731$	8.43091	−	14.6028i	0.311828	−	0.540103i
$732$	−1.31751	−	5.78070i	−0.0486965	−	0.213661i
$733$	8.65789	−	4.99864i	0.319787	−	0.184629i	−0.331511	−	0.943451i	$-0.607558\pi$
$733$	8.65789	−	4.99864i	0.319787	−	0.184629i	0.651297	+	0.758823i	$0.274225\pi$
$734$	−1.35732			−0.0500996
$735$		0			0
$736$	1.91676			0.0706526
$737$	34.2583	−	19.7790i	1.26192	−	0.728570i
$738$	12.6045	−	18.4626i	0.463977	−	0.679618i
$739$	−0.418026	+	0.724042i	−0.0153773	+	0.0266343i	−0.873612	−	0.486624i	$-0.838228\pi$
$739$	−0.418026	+	0.724042i	−0.0153773	+	0.0266343i	0.858234	+	0.513258i	$0.171562\pi$
$740$		0			0
$741$	−31.5873	−	34.0643i	−1.16039	−	1.25138i
$742$	37.7131	+	3.23411i	1.38449	+	0.118728i
$743$			53.3336i			1.95662i	0.207146	+	0.978310i	$0.433582\pi$
$743$			53.3336i			1.95662i	−0.207146	+	0.978310i	$0.566418\pi$
$744$	−2.57384	+	8.33496i	−0.0943617	+	0.305574i
$745$		0			0
$746$	29.5397	+	17.0548i	1.08153	+	0.624419i
$747$	19.6619	−	9.45353i	0.719390	−	0.345887i
$748$		−	17.9757i		−	0.657255i
$749$	6.43637	−	3.01482i	0.235180	−	0.110159i
$750$		0			0
$751$	−16.8660	−	29.2127i	−0.615448	−	1.06599i	−0.990306	−	0.138905i	$-0.955642\pi$
$751$	−16.8660	−	29.2127i	−0.615448	−	1.06599i	0.374858	−	0.927082i	$-0.377691\pi$
$752$	0.303890	−	0.526352i	0.0110817	−	0.0191941i
$753$	4.59519	−	1.04731i	0.167458	−	0.0381662i
$754$	−4.41837	+	2.55095i	−0.160908	+	0.0929001i
$755$		0			0
$756$	0.867138	+	13.7204i	0.0315375	+	0.499004i
$757$	−37.1033			−1.34854			−0.674272	−	0.738483i	$-0.735542\pi$
$757$	−37.1033			−1.34854			−0.674272	+	0.738483i	$0.735542\pi$
$758$	1.33326	−	0.769757i	0.0484261	−	0.0279588i
$759$	16.0400	−	3.65575i	0.582213	−	0.132695i
$760$		0			0
$761$	−8.95519	−	15.5108i	−0.324625	−	0.562268i	0.656811	−	0.754055i	$-0.271905\pi$
$761$	−8.95519	−	15.5108i	−0.324625	−	0.562268i	−0.981436	+	0.191787i	$0.938572\pi$
$762$	10.2452	−	9.50024i	0.371146	−	0.344157i
$763$	13.6598	−	19.5798i	0.494517	−	0.708835i
$764$			0.535503i			0.0193738i
$765$		0			0
$766$	28.1685	+	16.2631i	1.01777	+	0.587608i
$767$	9.66922	+	5.58252i	0.349135	+	0.201573i
$768$	−0.511048	+	1.65494i	−0.0184408	+	0.0597175i
$769$			0.619084i			0.0223247i	0.999938	+	0.0111624i	$0.00355317\pi$
$769$			0.619084i			0.0223247i	−0.999938	+	0.0111624i	$0.996447\pi$
$770$		0			0
$771$	−13.5480	−	14.6104i	−0.487918	−	0.526180i
$772$	2.76772	+	4.79383i	0.0996125	+	0.172534i
$773$	−24.4683	+	42.3803i	−0.880062	+	1.52431i	−0.0287914	+	0.999585i	$0.509166\pi$
$773$	−24.4683	+	42.3803i	−0.880062	+	1.52431i	−0.851271	+	0.524727i	$0.824167\pi$
$774$	−7.86258	+	11.5168i	−0.282615	+	0.413964i
$775$		0			0
$776$	−17.6562			−0.633820
$777$	−16.4195	−	21.0630i	−0.589045	−	0.755632i
$778$	7.10169			0.254608
$779$	27.1496	−	15.6749i	0.972737	−	0.561610i
$780$		0			0
$781$	−6.16340	+	10.6753i	−0.220544	+	0.381993i
$782$	3.47656	+	6.02159i	0.124322	+	0.215331i
$783$	−2.58962	−	3.25353i	−0.0925456	−	0.116272i
$784$	−2.41676	−	6.56957i	−0.0863128	−	0.234628i
$785$		0			0
$786$	5.59869	+	1.72888i	0.199699	+	0.0616672i
$787$	0.0582062	+	0.0336053i	0.00207483	+	0.00119790i	0.501037	−	0.865426i	$-0.332952\pi$
$787$	0.0582062	+	0.0336053i	0.00207483	+	0.00119790i	−0.498962	+	0.866624i	$0.666285\pi$
$788$	0.577166	+	0.333227i	0.0205607	+	0.0118707i
$789$	−21.1593	−	6.53402i	−0.753292	−	0.232617i
$790$		0			0
$791$	−2.80916	+	32.7578i	−0.0998822	+	1.16473i
$792$	−1.12019	+	14.8237i	−0.0398042	+	0.526737i
$793$	10.9114	+	18.8992i	0.387477	+	0.671129i
$794$	6.51194	−	11.2790i	0.231100	−	0.400277i
$795$		0			0
$796$	−7.81326	+	4.51099i	−0.276934	+	0.159888i
$797$	−7.61311			−0.269670			−0.134835	−	0.990868i	$-0.543050\pi$
$797$	−7.61311			−0.269670			−0.134835	+	0.990868i	$0.543050\pi$
$798$	−7.24156	+	17.8676i	−0.256348	+	0.632508i
$799$	2.20475			0.0779984
$800$		0			0
$801$	−4.67026	−	3.18840i	−0.165016	−	0.112657i
$802$	−11.7015	+	20.2676i	−0.413194	+	0.715673i
$803$	−37.3961	−	64.7720i	−1.31968	−	2.28575i
$804$	−9.40149	−	10.1387i	−0.331565	−	0.357566i
$805$		0			0
$806$		−	32.1083i		−	1.13097i
$807$	−5.97492	+	19.3488i	−0.210327	+	0.681108i
$808$	−0.994562	−	0.574210i	−0.0349886	−	0.0202007i
$809$	−16.9690	−	9.79703i	−0.596597	−	0.344445i	0.171105	−	0.985253i	$-0.445266\pi$
$809$	−16.9690	−	9.79703i	−0.596597	−	0.344445i	−0.767702	+	0.640807i	$0.778600\pi$
$810$		0			0
$811$			38.1099i			1.33822i	0.743164	+	0.669110i	$0.233324\pi$
$811$			38.1099i			1.33822i	−0.743164	+	0.669110i	$0.766676\pi$
$812$	1.73649	+	1.21145i	0.0609387	+	0.0425137i
$813$	28.0298	−	25.9916i	0.983048	−	0.911564i
$814$	−14.4395	−	25.0100i	−0.506105	−	0.876600i
$815$		0			0
$816$	−6.12600	+	1.39621i	−0.214453	+	0.0488771i
$817$	−16.9357	+	9.77786i	−0.592507	+	0.342084i
$818$	−13.1994			−0.461508
$819$	−17.9501	−	47.3111i	−0.627229	−	1.65318i
$820$		0			0
$821$	32.4054	−	18.7093i	1.13096	−	0.652958i	0.186781	−	0.982402i	$-0.440195\pi$
$821$	32.4054	−	18.7093i	1.13096	−	0.652958i	0.944175	+	0.329444i	$0.106861\pi$
$822$	25.0397	−	5.70692i	0.873360	−	0.199052i
$823$	17.1932	−	29.7795i	0.599318	−	1.03805i	−0.393604	−	0.919280i	$-0.628772\pi$
$823$	17.1932	−	29.7795i	0.599318	−	1.03805i	0.992922	−	0.118768i	$-0.0378946\pi$
$824$	3.64182	+	6.30781i	0.126869	+	0.219743i
$825$		0			0
$826$	0.395899	−	4.61660i	0.0137751	−	0.160632i
$827$			4.15552i			0.144502i	0.997386	+	0.0722508i	$0.0230182\pi$
$827$			4.15552i			0.144502i	−0.997386	+	0.0722508i	$0.976982\pi$
$828$	−2.49171	−	5.18237i	−0.0865931	−	0.180100i
$829$	−24.3399	−	14.0526i	−0.845359	−	0.488068i	0.0137231	−	0.999906i	$-0.495632\pi$
$829$	−24.3399	−	14.0526i	−0.845359	−	0.488068i	−0.859082	+	0.511837i	$0.828965\pi$
$830$		0			0
$831$	−3.98952	+	12.9194i	−0.138395	+	0.448169i
$832$		−	6.37523i		−	0.221021i
$833$	16.2552	−	19.5081i	0.563208	−	0.675915i
$834$	8.53440	+	9.20366i	0.295522	+	0.318697i
$835$		0			0
$836$	−10.4238	+	18.0545i	−0.360513	+	0.624427i
$837$	25.8813	−	3.87619i	0.894588	−	0.133981i
$838$	−24.2047	+	13.9746i	−0.836138	+	0.482745i
$839$	−23.6646			−0.816992			−0.408496	−	0.912760i	$-0.633947\pi$
$839$	−23.6646			−0.816992			−0.408496	+	0.912760i	$0.633947\pi$
$840$		0			0
$841$	28.3596			0.977916
$842$	−21.3731	+	12.3398i	−0.736565	+	0.425256i
$843$	−8.88680	−	38.9917i	−0.306078	−	1.34295i
$844$	5.71931	−	9.90613i	0.196867	−	0.340983i
$845$		0			0
$846$	−1.81815	−	0.137393i	−0.0625094	−	0.00472368i
$847$	−15.2126	−	32.4774i	−0.522709	−	1.11594i
$848$		−	14.3065i		−	0.491288i
$849$	−40.9606	−	12.6487i	−1.40576	−	0.434101i
$850$		0			0
$851$	9.67407	+	5.58533i	0.331623	+	0.191462i
$852$	4.11681	+	1.27128i	0.141040	+	0.0435532i
$853$		−	23.7742i		−	0.814012i	−0.913426	−	0.407006i	$-0.866573\pi$
$853$		−	23.7742i		−	0.814012i	0.913426	−	0.407006i	$-0.133427\pi$
$854$	5.18188	−	7.42766i	0.177320	−	0.254169i
$855$		0			0
$856$	−1.34318	−	2.32646i	−0.0459091	−	0.0795168i
$857$	−11.1811	+	19.3662i	−0.381938	+	0.661535i	−0.991339	−	0.131326i	$-0.958076\pi$
$857$	−11.1811	+	19.3662i	−0.381938	+	0.661535i	0.609402	+	0.792862i	$0.291410\pi$
$858$	−12.1592	−	53.3497i	−0.415108	−	1.82133i
$859$	−37.1729	+	21.4618i	−1.26832	+	0.732267i	−0.974671	−	0.223645i	$-0.928204\pi$
$859$	−37.1729	+	21.4618i	−1.26832	+	0.732267i	−0.293653	+	0.955912i	$0.594871\pi$
$860$		0			0
$861$	33.8205	−	4.71573i	1.15260	−	0.160712i
$862$	−3.34445			−0.113912
$863$	−20.3687	+	11.7599i	−0.693360	+	0.400312i	−0.804870	−	0.593452i	$-0.797765\pi$
$863$	−20.3687	+	11.7599i	−0.693360	+	0.400312i	0.111510	+	0.993763i	$0.464431\pi$
$864$	5.13884	−	0.769634i	0.174827	−	0.0261835i
$865$		0			0
$866$	−7.33780	−	12.7094i	−0.249348	−	0.431884i
$867$	4.52342	+	4.87814i	0.153623	+	0.165670i
$868$	−12.0669	+	5.65219i	−0.409578	+	0.191848i
$869$		−	13.2212i		−	0.448497i
$870$		0			0
$871$	44.0747	+	25.4466i	1.49342	+	0.862224i
$872$	−7.81452	−	4.51172i	−0.264633	−	0.152786i
$873$	22.9524	+	47.7373i	0.776820	+	1.61566i
$874$		−	8.06398i		−	0.272768i
$875$		0			0
$876$	−19.1693	+	17.7754i	−0.647670	+	0.600574i
$877$	4.09356	+	7.09026i	0.138230	+	0.239421i	0.926827	−	0.375490i	$-0.122525\pi$
$877$	4.09356	+	7.09026i	0.138230	+	0.239421i	−0.788597	+	0.614911i	$0.789192\pi$
$878$	3.29351	−	5.70453i	0.111151	−	0.192518i
$879$	−42.7901	+	9.75251i	−1.44328	+	0.328944i
$880$		0			0
$881$	−26.6496			−0.897847			−0.448923	−	0.893570i	$-0.648192\pi$
$881$	−26.6496			−0.897847			−0.448923	+	0.893570i	$0.648192\pi$
$882$	−14.6206	+	15.0744i	−0.492301	+	0.507583i
$883$	5.41249			0.182145			0.0910724	−	0.995844i	$-0.470971\pi$
$883$	5.41249			0.182145			0.0910724	+	0.995844i	$0.470971\pi$
$884$	20.0281	−	11.5632i	0.673618	−	0.388913i
$885$		0			0
$886$	−20.3605	+	35.2654i	−0.684025	+	1.18477i
$887$	−12.0499	−	20.8711i	−0.404597	−	0.700782i	0.589678	−	0.807639i	$-0.299255\pi$
$887$	−12.0499	−	20.8711i	−0.404597	−	0.700782i	−0.994274	+	0.106856i	$0.965921\pi$
$888$	−7.40171	+	6.86349i	−0.248385	+	0.230324i
$889$	21.2647	+	1.82356i	0.713195	+	0.0611604i
$890$		0			0
$891$	41.5353	−	16.2416i	1.39149	−	0.544114i
$892$	4.53275	+	2.61699i	0.151768	+	0.0876231i
$893$	−2.21441	−	1.27849i	−0.0741026	−	0.0427831i
$894$	−3.36935	+	10.9111i	−0.112688	+	0.364921i
$895$		0			0
$896$	−2.39594	+	1.12227i	−0.0800427	+	0.0374923i
$897$	14.3912	+	15.5197i	0.480508	+	0.518189i
$898$	−9.17425	−	15.8903i	−0.306149	−	0.530265i
$899$	2.01524	−	3.49050i	0.0672120	−	0.116415i
$900$		0			0
$901$	44.9446	−	25.9488i	1.49732	−	0.864480i
$902$	36.9252			1.22948
$903$	−21.0969	+	2.94164i	−0.702062	+	0.0978916i
$904$	12.4267			0.413306
$905$		0			0
$906$	−4.53183	−	19.8839i	−0.150560	−	0.660597i
$907$	−10.8290	+	18.7564i	−0.359572	+	0.622797i	−0.987889	−	0.155160i	$-0.950411\pi$
$907$	−10.8290	+	18.7564i	−0.359572	+	0.622797i	0.628317	+	0.777957i	$0.283744\pi$
$908$	−6.73117	−	11.6587i	−0.223382	−	0.386908i
$909$	−0.259610	+	3.43547i	−0.00861071	+	0.113947i
$910$		0			0
$911$			47.4302i			1.57143i	0.618587	+	0.785716i	$0.287705\pi$
$911$			47.4302i			1.57143i	−0.618587	+	0.785716i	$0.712295\pi$
$912$	6.96250	+	2.15003i	0.230551	+	0.0711945i
$913$	31.2080	+	18.0179i	1.03283	+	0.596306i
$914$	7.48533	+	4.32166i	0.247593	+	0.142948i
$915$		0			0
$916$		−	16.5216i		−	0.545890i
$917$	3.79664	+	8.10549i	0.125376	+	0.267667i
$918$	11.7385	+	14.7480i	0.387429	+	0.486755i
$919$	−5.32208	−	9.21812i	−0.175559	−	0.304078i	0.764795	−	0.644273i	$-0.222840\pi$
$919$	−5.32208	−	9.21812i	−0.175559	−	0.304078i	−0.940355	+	0.340196i	$0.889507\pi$
$920$		0			0
$921$	5.05732	+	22.1895i	0.166644	+	0.731169i
$922$	21.4657	−	12.3932i	0.706935	−	0.408149i
$923$	−15.8590			−0.522004
$924$	−17.9094	+	13.9611i	−0.589177	+	0.459286i
$925$		0			0
$926$	−15.5709	+	8.98986i	−0.511691	+	0.295425i
$927$	12.3203	−	18.0464i	0.404653	−	0.592721i
$928$	0.400134	−	0.693053i	0.0131351	−	0.0227506i
$929$	−17.1983	−	29.7883i	−0.564257	−	0.977322i	−0.997118	−	0.0758612i	$-0.975829\pi$
$929$	−17.1983	−	29.7883i	−0.564257	−	0.977322i	0.432861	−	0.901460i	$-0.357504\pi$
$930$		0			0
$931$	−27.6388	+	10.1675i	−0.905826	+	0.333227i
$932$		−	18.6359i		−	0.610440i
$933$	3.88736	−	12.5885i	0.127266	−	0.412131i
$934$	−1.10282	−	0.636712i	−0.0360853	−	0.0208339i
$935$		0			0
$936$	−17.2368	+	8.28757i	−0.563404	+	0.270888i
$937$			40.0917i			1.30974i	0.755742	+	0.654870i	$0.227277\pi$
$937$			40.0917i			1.30974i	−0.755742	+	0.654870i	$0.772723\pi$
$938$	1.80461	−	21.0436i	0.0589226	−	0.687099i
$939$	−15.7809	+	14.6334i	−0.514992	+	0.477543i
$940$		0			0
$941$	13.6315	−	23.6104i	0.444374	−	0.769678i	−0.553635	−	0.832760i	$-0.686760\pi$
$941$	13.6315	−	23.6104i	0.444374	−	0.769678i	0.998008	+	0.0630819i	$0.0200929\pi$
$942$	2.60876	−	0.594576i	0.0849980	−	0.0193723i
$943$	−12.3694	+	7.14148i	−0.402803	+	0.232559i
$944$	−1.75132			−0.0570005
$945$		0			0
$946$	−23.0337			−0.748889
$947$	19.6642	−	11.3531i	0.638999	−	0.368926i	−0.145230	−	0.989398i	$-0.546392\pi$
$947$	19.6642	−	11.3531i	0.638999	−	0.368926i	0.784229	+	0.620472i	$0.213059\pi$
$948$	−4.50570	+	1.02692i	−0.146338	+	0.0333527i
$949$	48.1117	−	83.3319i	1.56177	−	2.70507i
$950$		0			0
$951$	−35.2258	+	32.6644i	−1.14228	+	1.05921i
$952$	−7.87134	−	5.49142i	−0.255112	−	0.177978i
$953$			38.7288i			1.25455i	0.778799	+	0.627274i	$0.215829\pi$
$953$			38.7288i			1.25455i	−0.778799	+	0.627274i	$0.784171\pi$
$954$	−38.6808	+	18.5980i	−1.25234	+	0.602131i
$955$		0			0
$956$	−21.4831	−	12.4032i	−0.694812	−	0.401150i
$957$	2.02660	−	6.56281i	0.0655108	−	0.212146i
$958$			14.2267i			0.459643i
$959$	32.1737	+	22.4459i	1.03894	+	0.724815i
$960$		0			0
$961$	−2.81730	−	4.87970i	−0.0908805	−	0.157410i
$962$	18.5771	−	32.1764i	0.598949	−	1.03741i
$963$	−4.54401	+	6.65590i	−0.146429	+	0.214484i
$964$	−19.3439	+	11.1682i	−0.623025	+	0.359704i
$965$		0			0
$966$	3.29926	−	8.14052i	0.106152	−	0.261917i
$967$	−39.1631			−1.25940			−0.629700	−	0.776838i	$-0.716822\pi$
$967$	−39.1631			−1.25940			−0.629700	+	0.776838i	$0.716822\pi$
$968$	−11.7392	+	6.77761i	−0.377311	+	0.217840i
$969$	5.87398	+	25.7727i	0.188699	+	0.827938i
$970$		0			0
$971$	13.4005	+	23.2104i	0.430044	+	0.744858i	0.996877	−	0.0789753i	$-0.0251648\pi$
$971$	13.4005	+	23.2104i	0.430044	+	0.744858i	−0.566833	+	0.823833i	$0.691831\pi$
$972$	−8.76118	−	12.8935i	−0.281015	−	0.413559i
$973$	−1.63817	+	19.1028i	−0.0525174	+	0.612408i
$974$			39.8951i			1.27832i
$975$		0			0
$976$	−2.96447	−	1.71154i	−0.0948903	−	0.0547849i
$977$	24.1424	+	13.9386i	0.772383	+	0.445936i	0.833724	−	0.552181i	$-0.186204\pi$
$977$	24.1424	+	13.9386i	0.772383	+	0.445936i	−0.0613410	+	0.998117i	$0.519538\pi$
$978$	5.58972	+	1.72611i	0.178739	+	0.0551949i
$979$		−	9.34052i		−	0.298524i
$980$		0			0
$981$	−2.03982	+	26.9933i	−0.0651264	+	0.861831i
$982$	7.98891	+	13.8372i	0.254936	+	0.441563i
$983$	10.9212	−	18.9161i	0.348332	−	0.603329i	−0.637621	−	0.770350i	$-0.720081\pi$
$983$	10.9212	−	18.9161i	0.348332	−	0.603329i	0.985953	+	0.167021i	$0.0534147\pi$
$984$	−2.86806	−	12.5839i	−0.0914304	−	0.401160i
$985$		0			0
$986$	2.90301			0.0924507
$987$	−1.71235	−	2.19662i	−0.0545048	−	0.0699193i
$988$	−26.8212			−0.853297
$989$	7.71594	−	4.45480i	0.245353	−	0.141654i
$990$		0			0
$991$	29.4300	−	50.9743i	0.934875	−	1.61925i	0.160019	−	0.987114i	$-0.448845\pi$
$991$	29.4300	−	50.9743i	0.934875	−	1.61925i	0.774856	−	0.632137i	$-0.217822\pi$
$992$	2.51820	+	4.36166i	0.0799531	+	0.138483i
$993$	−13.8841	−	14.9729i	−0.440600	−	0.475151i
$994$	2.79174	+	5.96011i	0.0885485	+	0.189043i
$995$		0			0
$996$	3.71642	−	12.0350i	0.117759	−	0.381343i
$997$	10.4327	+	6.02334i	0.330408	+	0.190761i	0.656022	−	0.754742i	$-0.272238\pi$
$997$	10.4327	+	6.02334i	0.330408	+	0.190761i	−0.325614	+	0.945503i	$0.605571\pi$
$998$	−11.9566	−	6.90313i	−0.378479	−	0.218515i
$999$	28.1789	+	11.0899i	0.891541	+	0.350868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.s.g.101.3		12
3.2	odd	2		1050.2.s.f.101.5		12
5.2	odd	4		1050.2.u.f.899.2		12
5.3	odd	4		1050.2.u.g.899.5		12
5.4	even	2		210.2.r.a.101.4	✓	12
7.5	odd	6		1050.2.s.f.551.5		12
15.2	even	4		1050.2.u.h.899.6		12
15.8	even	4		1050.2.u.e.899.1		12
15.14	odd	2		210.2.r.b.101.2	yes	12
21.5	even	6	inner	1050.2.s.g.551.3		12
35.4	even	6		1470.2.b.b.881.11		12
35.12	even	12		1050.2.u.e.299.1		12
35.19	odd	6		210.2.r.b.131.2	yes	12
35.24	odd	6		1470.2.b.a.881.8		12
35.33	even	12		1050.2.u.h.299.6		12
105.47	odd	12		1050.2.u.g.299.5		12
105.59	even	6		1470.2.b.b.881.5		12
105.68	odd	12		1050.2.u.f.299.2		12
105.74	odd	6		1470.2.b.a.881.2		12
105.89	even	6		210.2.r.a.131.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.4	✓	12	5.4	even	2
210.2.r.a.131.4	yes	12	105.89	even	6
210.2.r.b.101.2	yes	12	15.14	odd	2
210.2.r.b.131.2	yes	12	35.19	odd	6
1050.2.s.f.101.5		12	3.2	odd	2
1050.2.s.f.551.5		12	7.5	odd	6
1050.2.s.g.101.3		12	1.1	even	1	trivial
1050.2.s.g.551.3		12	21.5	even	6	inner
1050.2.u.e.299.1		12	35.12	even	12
1050.2.u.e.899.1		12	15.8	even	4
1050.2.u.f.299.2		12	105.68	odd	12
1050.2.u.f.899.2		12	5.2	odd	4
1050.2.u.g.299.5		12	105.47	odd	12
1050.2.u.g.899.5		12	5.3	odd	4
1050.2.u.h.299.6		12	35.33	even	12
1050.2.u.h.899.6		12	15.2	even	4
1470.2.b.a.881.2		12	105.74	odd	6
1470.2.b.a.881.8		12	35.24	odd	6
1470.2.b.b.881.5		12	105.59	even	6
1470.2.b.b.881.11		12	35.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.68874 - 0.384890i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.27005 + 1.17770i) q^{6} +(-2.63608 - 0.226058i) q^{7} +1.00000i q^{8} +(2.70372 - 1.29996i) q^{9} +(4.29143 + 2.47766i) q^{11} +(0.511048 - 1.65494i) q^{12} +6.37523i q^{13} +(2.39594 - 1.12227i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.81377 - 3.14155i) q^{17} +(-1.69151 + 2.47766i) q^{18} +(-3.64345 + 2.10355i) q^{19} +(-4.53867 + 0.632846i) q^{21} -4.95532 q^{22} +(1.65996 - 0.958379i) q^{23} +(0.384890 + 1.68874i) q^{24} +(-3.18762 - 5.52111i) q^{26} +(4.06555 - 3.23594i) q^{27} +(-1.51381 + 2.16988i) q^{28} -0.800269i q^{29} +(4.36166 + 2.51820i) q^{31} +(0.866025 + 0.500000i) q^{32} +(8.20077 + 2.53241i) q^{33} +3.62755i q^{34} +(0.226058 - 2.99147i) q^{36} +(2.91394 + 5.04710i) q^{37} +(2.10355 - 3.64345i) q^{38} +(2.45377 + 10.7661i) q^{39} -7.45163 q^{41} +(3.61418 - 2.81739i) q^{42} +4.64827 q^{43} +(4.29143 - 2.47766i) q^{44} +(-0.958379 + 1.65996i) q^{46} +(0.303890 + 0.526352i) q^{47} +(-1.17770 - 1.27005i) q^{48} +(6.89780 + 1.19181i) q^{49} +(1.85385 - 6.00338i) q^{51} +(5.52111 + 3.18762i) q^{52} +(12.3898 + 7.15326i) q^{53} +(-1.90290 + 4.83518i) q^{54} +(0.226058 - 2.63608i) q^{56} +(-5.34323 + 4.95469i) q^{57} +(0.400134 + 0.693053i) q^{58} +(0.875658 - 1.51668i) q^{59} +(2.96447 - 1.71154i) q^{61} -5.03641 q^{62} +(-7.42108 + 2.81561i) q^{63} -1.00000 q^{64} +(-8.36827 + 1.90726i) q^{66} +(3.99147 - 6.91343i) q^{67} +(-1.81377 - 3.14155i) q^{68} +(2.43438 - 2.25736i) q^{69} +2.48759i q^{71} +(1.29996 + 2.70372i) q^{72} +(-13.0712 - 7.54666i) q^{73} +(-5.04710 - 2.91394i) q^{74} +4.20710i q^{76} +(-10.7525 - 7.50142i) q^{77} +(-7.50809 - 8.09687i) q^{78} +(-1.33404 - 2.31062i) q^{79} +(5.62019 - 7.02947i) q^{81} +(6.45330 - 3.72581i) q^{82} +7.27215 q^{83} +(-1.72127 + 4.24702i) q^{84} +(-4.02552 + 2.32413i) q^{86} +(-0.308016 - 1.35145i) q^{87} +(-2.47766 + 4.29143i) q^{88} +(-0.942474 - 1.63241i) q^{89} +(1.44117 - 16.8056i) q^{91} -1.91676i q^{92} +(8.33496 + 2.57384i) q^{93} +(-0.526352 - 0.303890i) q^{94} +(1.65494 + 0.511048i) q^{96} +17.6562i q^{97} +(-6.56957 + 2.41676i) q^{98} +(14.8237 + 1.12019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} + 6 q^{4} - 2 q^{6} - 8 q^{7} + 6 q^{9} - 12 q^{11} - 2 q^{12} + 12 q^{14} - 6 q^{16} - 12 q^{17} + 4 q^{18} - 18 q^{21} + 24 q^{23} - 4 q^{24} - 4 q^{26} + 8 q^{27} - 4 q^{28} + 12 q^{31}+ \cdots + 48 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 + 6 * q^4 - 2 * q^6 - 8 * q^7 + 6 * q^9 - 12 * q^11 - 2 * q^12 + 12 * q^14 - 6 * q^16 - 12 * q^17 + 4 * q^18 - 18 * q^21 + 24 * q^23 - 4 * q^24 - 4 * q^26 + 8 * q^27 - 4 * q^28 + 12 * q^31 + 22 * q^33 + 6 * q^36 + 8 * q^37 - 8 * q^38 + 30 * q^39 - 4 * q^41 + 20 * q^42 - 12 * q^44 + 2 * q^46 - 16 * q^47 - 4 * q^48 - 14 * q^49 + 4 * q^51 + 12 * q^52 + 48 * q^53 - 4 * q^54 + 6 * q^56 + 36 * q^57 - 8 * q^58 + 12 * q^59 - 30 * q^61 - 8 * q^62 + 4 * q^63 - 12 * q^64 - 34 * q^66 + 4 * q^67 + 12 * q^68 + 50 * q^69 - 4 * q^72 - 20 * q^77 - 32 * q^78 - 4 * q^79 + 50 * q^81 + 40 * q^83 - 12 * q^84 - 54 * q^86 - 8 * q^87 + 26 * q^89 + 28 * q^91 + 32 * q^93 + 24 * q^94 - 2 * q^96 - 16 * q^98 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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