LMFDB - Embedded newform 1050.2.s.f.551.5

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)

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")

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);

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			551.5
Root			$-0.384890 + 1.68874i$ of defining polynomial
Character	$\chi$	$=$	1050.551
Dual form			1050.2.s.f.101.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.511048 - 1.65494i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.27005 - 1.17770i) q^{6} +(-2.63608 + 0.226058i) q^{7} +1.00000i q^{8} +(-2.47766 - 1.69151i) q^{9} +(-4.29143 + 2.47766i) q^{11} +(1.68874 - 0.384890i) q^{12} -6.37523i q^{13} +(-2.39594 - 1.12227i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.81377 - 3.14155i) q^{17} +(-1.29996 - 2.70372i) q^{18} +(-3.64345 - 2.10355i) q^{19} +(-0.973048 + 4.47808i) q^{21} -4.95532 q^{22} +(-1.65996 - 0.958379i) q^{23} +(1.65494 + 0.511048i) 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} +(1.90726 + 8.36827i) q^{33} -3.62755i q^{34} +(0.226058 - 2.99147i) q^{36} +(2.91394 - 5.04710i) q^{37} +(-2.10355 - 3.64345i) q^{38} +(-10.5506 - 3.25805i) q^{39} +7.45163 q^{41} +(-3.08172 + 3.39161i) 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} +(-6.12600 + 1.39621i) q^{51} +(5.52111 - 3.18762i) q^{52} +(-12.3898 + 7.15326i) q^{53} +(-5.13884 + 0.769634i) 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} +(6.91368 + 3.89885i) q^{63} -1.00000 q^{64} +(-2.53241 + 8.20077i) q^{66} +(3.99147 + 6.91343i) q^{67} +(1.81377 - 3.14155i) q^{68} +(-2.43438 + 2.25736i) q^{69} +2.48759i q^{71} +(1.69151 - 2.47766i) 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} +(3.27761 + 8.38196i) q^{81} +(6.45330 + 3.72581i) q^{82} -7.27215 q^{83} +(-4.36465 + 1.39635i) q^{84} +(4.02552 + 2.32413i) q^{86} +(-1.32440 - 0.408975i) q^{87} +(-2.47766 - 4.29143i) q^{88} +(0.942474 - 1.63241i) q^{89} +(1.44117 + 16.8056i) q^{91} -1.91676i q^{92} +(-1.93847 - 8.50521i) q^{93} +(-0.526352 + 0.303890i) q^{94} +(0.384890 + 1.68874i) 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} + 12 q^{11} + 2 q^{12} - 12 q^{14} - 6 q^{16} + 12 q^{17} + 4 q^{18} + 4 q^{21} - 24 q^{23} - 2 q^{24} + 4 q^{26} - 8 q^{27} - 4 q^{28} + 12 q^{31} + 2 q^{33}+ \cdots + 48 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 + 6 * q^4 + 2 * q^6 - 8 * q^7 + 12 * q^11 + 2 * q^12 - 12 * q^14 - 6 * q^16 + 12 * q^17 + 4 * q^18 + 4 * q^21 - 24 * q^23 - 2 * q^24 + 4 * q^26 - 8 * q^27 - 4 * q^28 + 12 * q^31 + 2 * q^33 + 6 * q^36 + 8 * q^37 + 8 * q^38 - 42 * q^39 + 4 * q^41 - 24 * q^42 + 12 * q^44 + 2 * q^46 + 16 * q^47 + 4 * q^48 - 14 * q^49 - 8 * q^51 + 12 * q^52 - 48 * q^53 - 32 * q^54 - 6 * q^56 + 36 * q^57 - 8 * q^58 - 12 * q^59 - 30 * q^61 + 8 * q^62 - 20 * q^63 - 12 * q^64 - 14 * q^66 + 4 * q^67 - 12 * q^68 - 50 * q^69 - 4 * q^72 + 20 * q^77 - 32 * q^78 - 4 * q^79 - 40 * q^81 - 40 * q^83 + 20 * q^84 + 54 * q^86 - 64 * q^87 - 26 * q^89 + 28 * q^91 - 4 * q^93 + 24 * q^94 - 4 * q^96 + 16 * q^98 + 48 * q^99

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	0.511048	−	1.65494i	0.295053	−	0.955481i
$3$	0.511048	−	1.65494i	0.295053	−	0.955481i
$4$	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
$9$	−2.47766	−	1.69151i	−0.825887	−	0.563836i
$10$		0			0
$11$	−4.29143	+	2.47766i	−1.29392	+	0.747043i	−0.979346	−	0.202191i	$-0.935194\pi$
$11$	−4.29143	+	2.47766i	−1.29392	+	0.747043i	−0.314570	+	0.949234i	$0.601860\pi$
$12$	1.68874	−	0.384890i	0.487499	−	0.111108i
$13$		−	6.37523i		−	1.76817i	−0.467325	−	0.884086i	$-0.654782\pi$
$13$		−	6.37523i		−	1.76817i	0.467325	−	0.884086i	$-0.345218\pi$
$14$	−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	$-0.311654\pi$
$17$	−1.81377	−	3.14155i	−0.439905	−	0.761937i	−0.997682	+	0.0680536i	$0.978321\pi$
$18$	−1.29996	−	2.70372i	−0.306404	−	0.637273i
$19$	−3.64345	−	2.10355i	−0.835865	−	0.482587i	0.0199914	−	0.999800i	$-0.493636\pi$
$19$	−3.64345	−	2.10355i	−0.835865	−	0.482587i	−0.855857	+	0.517213i	$0.826969\pi$
$20$		0			0
$21$	−0.973048	+	4.47808i	−0.212336	+	0.977197i
$22$	−4.95532			−1.05648
$23$	−1.65996	−	0.958379i	−0.346126	−	0.199836i	0.316852	−	0.948475i	$-0.397374\pi$
$23$	−1.65996	−	0.958379i	−0.346126	−	0.199836i	−0.662978	+	0.748639i	$0.730708\pi$
$24$	1.65494	+	0.511048i	0.337813	+	0.104317i
$25$		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	−0.0542489	−	0.998527i	$-0.517276\pi$
$31$	4.36166	−	2.51820i	0.783377	−	0.452283i	0.837626	+	0.546245i	$0.183943\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.90726	+	8.36827i	0.332011	+	1.45673i
$34$		−	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	−0.520662	−	0.853763i	$-0.674315\pi$
$37$	2.91394	−	5.04710i	0.479050	−	0.829738i	0.999711	+	0.0240249i	$0.00764810\pi$
$38$	−2.10355	−	3.64345i	−0.341241	−	0.591046i
$39$	−10.5506	−	3.25805i	−1.68945	−	0.521705i
$40$		0			0
$41$	7.45163			1.16375			0.581874	−	0.813279i	$-0.302320\pi$
$41$	7.45163			1.16375			0.581874	+	0.813279i	$0.302320\pi$
$42$	−3.08172	+	3.39161i	−0.475520	+	0.523336i
$43$	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	$-0.847448\pi$
$47$	−0.303890	+	0.526352i	−0.0443269	+	0.0767764i	0.843011	+	0.537897i	$0.180781\pi$
$48$	1.17770	+	1.27005i	0.169986	+	0.183316i
$49$	6.89780	−	1.19181i	0.985399	−	0.170259i
$50$		0			0
$51$	−6.12600	+	1.39621i	−0.857812	+	0.195508i
$52$	5.52111	−	3.18762i	0.765641	−	0.442043i
$53$	−12.3898	+	7.15326i	−1.70187	+	0.982576i	−0.758006	+	0.652247i	$0.773826\pi$
$53$	−12.3898	+	7.15326i	−1.70187	+	0.982576i	−0.943866	+	0.330329i	$0.892840\pi$
$54$	−5.13884	+	0.769634i	−0.699307	+	0.104734i
$55$		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	$-0.203033\pi$
$59$	−0.875658	−	1.51668i	−0.114001	−	0.197456i	−0.917380	+	0.398013i	$0.869700\pi$
$60$		0			0
$61$	2.96447	+	1.71154i	0.379561	+	0.219140i	0.677627	−	0.735405i	$-0.263008\pi$
$61$	2.96447	+	1.71154i	0.379561	+	0.219140i	−0.298066	+	0.954545i	$0.596342\pi$
$62$	5.03641			0.639624
$63$	6.91368	+	3.89885i	0.871042	+	0.491209i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−2.53241	+	8.20077i	−0.311718	+	1.00944i
$67$	3.99147	+	6.91343i	0.487636	+	0.844610i	0.999899	−	0.0142186i	$-0.00452608\pi$
$67$	3.99147	+	6.91343i	0.487636	+	0.844610i	−0.512263	+	0.858829i	$0.671193\pi$
$68$	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	$0.952842\pi$
$72$	1.69151	−	2.47766i	0.199346	−	0.291995i
$73$	−13.0712	+	7.54666i	−1.52987	+	0.883270i	−0.530501	+	0.847684i	$0.677996\pi$
$73$	−13.0712	+	7.54666i	−1.52987	+	0.883270i	−0.999367	+	0.0355852i	$0.988670\pi$
$74$	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	−0.931261	−	0.364354i	$-0.881290\pi$
$79$	−1.33404	+	2.31062i	−0.150091	+	0.259965i	0.781170	+	0.624319i	$0.214623\pi$
$80$		0			0
$81$	3.27761	+	8.38196i	0.364178	+	0.931329i
$82$	6.45330	+	3.72581i	0.712648	+	0.411447i
$83$	−7.27215			−0.798222			−0.399111	−	0.916903i	$-0.630681\pi$
$83$	−7.27215			−0.798222			−0.399111	+	0.916903i	$0.630681\pi$
$84$	−4.36465	+	1.39635i	−0.476223	+	0.152355i
$85$		0			0
$86$	4.02552	+	2.32413i	0.434083	+	0.250618i
$87$	−1.32440	−	0.408975i	−0.141990	−	0.0438468i
$88$	−2.47766	−	4.29143i	−0.264120	−	0.457468i
$89$	0.942474	−	1.63241i	0.0999021	−	0.173035i	−0.811742	−	0.584016i	$-0.801480\pi$
$89$	0.942474	−	1.63241i	0.0999021	−	0.173035i	0.911644	+	0.410981i	$0.134814\pi$
$90$		0			0
$91$	1.44117	+	16.8056i	0.151076	+	1.76171i
$92$		−	1.91676i		−	0.199836i
$93$	−1.93847	−	8.50521i	−0.201009	−	0.881949i
$94$	−0.526352	+	0.303890i	−0.0542891	+	0.0313438i
$95$		0			0
$96$	0.384890	+	1.68874i	0.0392827	+	0.172357i
$97$		−	17.6562i		−	1.79271i	−0.443334	−	0.896356i	$-0.646205\pi$
$97$		−	17.6562i		−	1.79271i	0.443334	−	0.896356i	$-0.353795\pi$
$98$	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	$-0.148470\pi$
$101$	0.574210	+	0.994562i	0.0571361	+	0.0989626i	−0.836043	+	0.548664i	$0.815136\pi$
$102$	−6.00338	−	1.85385i	−0.594423	−	0.183558i
$103$	6.30781	+	3.64182i	0.621527	+	0.358839i	0.777463	−	0.628928i	$-0.216506\pi$
$103$	6.30781	+	3.64182i	0.621527	+	0.358839i	−0.155936	+	0.987767i	$0.549839\pi$
$104$	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	$-0.291884\pi$
$107$	2.32646	+	1.34318i	0.224908	+	0.129850i	−0.383313	+	0.923618i	$0.625217\pi$
$108$	−4.83518	−	1.90290i	−0.465266	−	0.183106i
$109$	−4.51172	−	7.81452i	−0.432144	−	0.748495i	0.564914	−	0.825150i	$-0.308909\pi$
$109$	−4.51172	−	7.81452i	−0.432144	−	0.748495i	−0.997058	+	0.0766547i	$0.975576\pi$
$110$		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	$-0.198711\pi$
$114$	−7.10471	+	1.61927i	−0.665417	+	0.151659i
$115$		0			0
$116$	0.693053	−	0.400134i	0.0643483	−	0.0371515i
$117$	−10.7838	+	15.7957i	−0.996958	+	1.46031i
$118$		−	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
$123$	3.80814	−	12.3320i	0.343368	−	1.11194i
$124$	4.36166	+	2.51820i	0.391688	+	0.226141i
$125$		0			0
$126$	4.03800	+	6.83334i	0.359734	+	0.608762i
$127$	−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
$129$	2.37549	−	7.69261i	0.209150	−	0.677297i
$130$		0			0
$131$	1.69151	−	2.92978i	0.147788	−	0.255976i	−0.782622	−	0.622497i	$-0.786118\pi$
$131$	1.69151	−	2.92978i	0.147788	−	0.255976i	0.930410	+	0.366522i	$0.119451\pi$
$132$	−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	$-0.448327\pi$
$137$	12.8409	−	7.41370i	1.09707	−	0.633395i	0.935451	+	0.353458i	$0.114994\pi$
$138$	−3.23691	+	0.737742i	−0.275544	+	0.0628007i
$139$			7.24669i			0.614656i	0.951604	+	0.307328i	$0.0994349\pi$
$139$			7.24669i			0.614656i	−0.951604	+	0.307328i	$0.900565\pi$
$140$		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
$144$	2.70372	−	1.29996i	0.225310	−	0.108330i
$145$		0			0
$146$	−15.0933			−1.24913
$147$	1.55272	−	12.0245i	0.128066	−	0.991766i
$148$	5.82789			0.479050
$149$	−5.70973	−	3.29651i	−0.467759	−	0.270061i	0.247542	−	0.968877i	$-0.420377\pi$
$149$	−5.70973	−	3.29651i	−0.467759	−	0.270061i	−0.715301	+	0.698816i	$0.753711\pi$
$150$		0			0
$151$	−5.88717	−	10.1969i	−0.479091	−	0.829811i	0.520621	−	0.853788i	$-0.325700\pi$
$151$	−5.88717	−	10.1969i	−0.479091	−	0.829811i	−0.999713	+	0.0239772i	$0.992367\pi$
$152$	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
$156$	−2.45377	−	10.7661i	−0.196458	−	0.861981i
$157$	−1.33783	+	0.772397i	−0.106770	+	0.0616440i	−0.552434	−	0.833556i	$-0.686301\pi$
$157$	−1.33783	+	0.772397i	−0.106770	+	0.0616440i	0.445664	+	0.895200i	$0.352968\pi$
$158$	−2.31062	+	1.33404i	−0.183823	+	0.106130i
$159$	5.50644	+	24.1601i	0.436689	+	1.91602i
$160$		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	−0.924554	−	0.381051i	$-0.875562\pi$
$163$	−1.68880	+	2.92508i	−0.132277	+	0.229110i	0.792277	+	0.610161i	$0.208895\pi$
$164$	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	$-0.335525\pi$
$167$	12.7685			0.988053			0.494027	+	0.869447i	$0.335525\pi$
$168$	−4.47808	−	0.973048i	−0.345491	−	0.0750723i
$169$	−27.6436			−2.12643
$170$		0			0
$171$	5.46907	+	11.3748i	0.418230	+	0.869853i
$172$	2.32413	+	4.02552i	0.177214	+	0.306943i
$173$	0.123778	−	0.214390i	0.00941068	−	0.0162998i	−0.861282	−	0.508128i	$-0.830338\pi$
$173$	0.123778	−	0.214390i	0.00941068	−	0.0162998i	0.870692	+	0.491828i	$0.163671\pi$
$174$	−0.942474	−	1.01638i	−0.0714488	−	0.0770517i
$175$		0			0
$176$		−	4.95532i		−	0.373521i
$177$	−2.95753	+	0.674065i	−0.222301	+	0.0506658i
$178$	1.63241	−	0.942474i	0.122355	−	0.0706414i
$179$	16.9709	−	9.79815i	1.26846	−	0.732348i	0.293767	−	0.955877i	$-0.405091\pi$
$179$	16.9709	−	9.79815i	1.26846	−	0.732348i	0.974697	+	0.223528i	$0.0717576\pi$
$180$		0			0
$181$		−	14.8103i		−	1.10084i	−0.834887	−	0.550422i	$-0.814467\pi$
$181$		−	14.8103i		−	1.10084i	0.834887	−	0.550422i	$-0.185533\pi$
$182$	−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
$186$	2.57384	−	8.33496i	0.188723	−	0.611149i
$187$	15.5674	+	8.98783i	1.13840	+	0.657255i
$188$	−0.607779			−0.0443269
$189$	9.98558	−	9.44924i	0.726344	−	0.687331i
$190$		0			0
$191$	0.463759	+	0.267752i	0.0335564	+	0.0193738i	0.516684	−	0.856176i	$-0.327166\pi$
$191$	0.463759	+	0.267752i	0.0335564	+	0.0193738i	−0.483128	+	0.875550i	$0.660499\pi$
$192$	−0.511048	+	1.65494i	−0.0368817	+	0.119435i
$193$	−2.76772	−	4.79383i	−0.199225	−	0.345068i	0.749052	−	0.662511i	$-0.230509\pi$
$193$	−2.76772	−	4.79383i	−0.199225	−	0.345068i	−0.948277	+	0.317443i	$0.897176\pi$
$194$	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	$0.992442\pi$
$198$	12.2776	+	8.38196i	0.872531	+	0.595680i
$199$	−7.81326	+	4.51099i	−0.553867	+	0.319775i	−0.750680	−	0.660666i	$-0.770274\pi$
$199$	−7.81326	+	4.51099i	−0.553867	+	0.319775i	0.196813	+	0.980441i	$0.436941\pi$
$200$		0			0
$201$	13.4812	−	3.07256i	0.950887	−	0.216722i
$202$			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
$207$	2.49171	+	5.18237i	0.173186	+	0.360200i
$208$	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
$213$	4.11681	+	1.27128i	0.282079	+	0.0871064i
$214$	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
$219$	5.80927	+	25.4888i	0.392554	+	1.72237i
$220$		0			0
$221$	−20.0281	+	11.5632i	−1.34724	+	0.777827i
$222$	−2.24310	−	9.84182i	−0.150547	−	0.660540i
$223$		−	5.23397i		−	0.350493i	−0.984525	−	0.175246i	$-0.943928\pi$
$223$		−	5.23397i		−	0.350493i	0.984525	−	0.175246i	$-0.0560722\pi$
$224$	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	$-0.314090\pi$
$227$	−6.73117	−	11.6587i	−0.446763	−	0.773817i	−0.998173	+	0.0604178i	$0.980757\pi$
$228$	−6.96250	−	2.15003i	−0.461103	−	0.142389i
$229$	14.3082	+	8.26082i	0.945509	+	0.545890i	0.891683	−	0.452660i	$-0.149525\pi$
$229$	14.3082	+	8.26082i	0.945509	+	0.545890i	0.0538263	+	0.998550i	$0.482858\pi$
$230$		0			0
$231$	−6.91939	−	21.6283i	−0.455262	−	1.42303i
$232$	0.800269			0.0525402
$233$	−16.1392	−	9.31796i	−1.05731	−	0.610440i	−0.132625	−	0.991166i	$-0.542341\pi$
$233$	−16.1392	−	9.31796i	−1.05731	−	0.610440i	−0.924688	+	0.380727i	$0.875674\pi$
$234$	−17.2368	+	8.28757i	−1.12681	+	0.541775i
$235$		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	−0.970319	−	0.241827i	$-0.922253\pi$
$241$	−19.3439	+	11.1682i	−1.24605	+	0.719408i	−0.275731	+	0.961235i	$0.588920\pi$
$242$	11.7392	−	6.77761i	0.754622	−	0.435681i
$243$	15.5467	−	1.14066i	0.997319	−	0.0731735i
$244$			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
$249$	−3.71642	+	12.0350i	−0.235518	+	0.762686i
$250$		0			0
$251$	−2.72107			−0.171752			−0.0858762	−	0.996306i	$-0.527369\pi$
$251$	−2.72107			−0.171752			−0.0858762	+	0.996306i	$0.527369\pi$
$252$	0.0803398	+	7.93685i	0.00506093	+	0.499974i
$253$	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	$-0.716522\pi$
$257$	5.75189	−	9.96256i	0.358793	−	0.621448i	0.987759	+	0.155985i	$0.0498551\pi$
$258$	5.90354	−	5.47425i	0.367538	−	0.340812i
$259$	−6.54044	+	13.9633i	−0.406403	+	0.867635i
$260$		0			0
$261$	−1.35366	+	1.98279i	−0.0837895	+	0.122732i
$262$	2.92978	−	1.69151i	0.181002	−	0.104502i
$263$	11.0726	−	6.39277i	0.682766	−	0.394195i	−0.118130	−	0.992998i	$-0.537690\pi$
$263$	11.0726	−	6.39277i	0.682766	−	0.394195i	0.800896	+	0.598803i	$0.204357\pi$
$264$	−8.36827	+	1.90726i	−0.515032	+	0.117383i
$265$		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	$-0.0506633\pi$
$269$	5.84575	+	10.1251i	0.356422	+	0.617341i	−0.630938	+	0.775833i	$0.717330\pi$
$270$		0			0
$271$	19.1130	+	11.0349i	1.16103	+	0.670323i	0.951552	−	0.307489i	$-0.0994888\pi$
$271$	19.1130	+	11.0349i	1.16103	+	0.670323i	0.209482	+	0.977812i	$0.432822\pi$
$272$	3.62755			0.219952
$273$	28.5488	+	6.20340i	1.72785	+	0.375447i
$274$	14.8274			0.895756
$275$		0			0
$276$	−3.17212	−	0.979554i	−0.190939	−	0.0589622i
$277$	−3.90328	−	6.76068i	−0.234525	−	0.406210i	0.724609	−	0.689160i	$-0.242020\pi$
$277$	−3.90328	−	6.76068i	−0.234525	−	0.406210i	−0.959135	+	0.282950i	$0.908687\pi$
$278$	−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	$-0.241815\pi$
$282$	0.233928	+	1.02638i	0.0139302	+	0.0611203i
$283$	−21.4345	+	12.3752i	−1.27415	+	0.735631i	−0.975766	−	0.218815i	$-0.929781\pi$
$283$	−21.4345	+	12.3752i	−1.27415	+	0.735631i	−0.298384	+	0.954446i	$0.596448\pi$
$284$	−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
$291$	−29.2199	−	9.02314i	−1.71290	−	0.528946i
$292$	−13.0712	−	7.54666i	−0.764934	−	0.441635i
$293$	25.3384			1.48029			0.740143	−	0.672449i	$-0.234758\pi$
$293$	25.3384			1.48029			0.740143	+	0.672449i	$0.234758\pi$
$294$	7.35696	−	9.63718i	0.429066	−	0.562052i
$295$		0			0
$296$	5.04710	+	2.91394i	0.293357	+	0.169370i
$297$	9.42947	−	23.9599i	0.547153	−	1.39029i
$298$	−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
$303$	1.93939	−	0.442016i	0.111415	−	0.0253932i
$304$	3.64345	−	2.10355i	0.208966	−	0.120647i
$305$		0			0
$306$	−6.13602	+	8.98783i	−0.350773	+	0.513800i
$307$		−	13.1396i		−	0.749919i	−0.927041	−	0.374960i	$-0.877657\pi$
$307$		−	13.1396i		−	0.749919i	0.927041	−	0.374960i	$-0.122343\pi$
$308$	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	$-0.235859\pi$
$311$	−3.80332	−	6.58755i	−0.215667	−	0.373545i	−0.953479	+	0.301461i	$0.902526\pi$
$312$	3.25805	−	10.5506i	0.184451	−	0.597312i
$313$	−10.7608	−	6.21272i	−0.608234	−	0.351164i	0.164040	−	0.986454i	$-0.447547\pi$
$313$	−10.7608	−	6.21272i	−0.608234	−	0.351164i	−0.772274	+	0.635290i	$0.780881\pi$
$314$	−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	$-0.0491121\pi$
$317$	24.0199	+	13.8679i	1.34909	+	0.778898i	0.360971	+	0.932577i	$0.382445\pi$
$318$	−7.31132	+	23.6765i	−0.409998	+	1.32771i
$319$	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
$324$	−5.62019	+	7.02947i	−0.312233	+	0.390526i
$325$		0			0
$326$	−2.92508	+	1.68880i	−0.162005	+	0.0935337i
$327$	−15.2383	+	3.47303i	−0.842678	+	0.192059i
$328$			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	−0.981309	−	0.192439i	$-0.938360\pi$
$331$	−5.89462	+	10.2098i	−0.323997	+	0.561180i	0.657312	+	0.753619i	$0.271694\pi$
$332$	−3.63608	−	6.29787i	−0.199556	−	0.345640i
$333$	−15.7570	+	7.57604i	−0.863477	+	0.415165i
$334$	11.0578	+	6.38423i	0.605056	+	0.349329i
$335$		0			0
$336$	−3.39161	−	3.08172i	−0.185027	−	0.168122i
$337$	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
$339$	−20.5655	−	6.35064i	−1.11696	−	0.344920i
$340$		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	$-0.994026\pi$
$347$	−27.6342	+	15.9546i	−1.48348	+	0.856489i	−0.483659	+	0.875257i	$0.660692\pi$
$348$	−0.308016	−	1.35145i	−0.0165114	−	0.0724453i
$349$		−	1.64353i		−	0.0879759i	−0.999032	−	0.0439879i	$-0.985994\pi$
$349$		−	1.64353i		−	0.0879759i	0.999032	−	0.0439879i	$-0.0140063\pi$
$350$		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	$-0.0396392\pi$
$353$	7.30038	+	12.6446i	0.388560	+	0.673006i	−0.603696	+	0.797215i	$0.706306\pi$
$354$	−2.89833	−	0.895006i	−0.154044	−	0.0475690i
$355$		0			0
$356$	1.88495			0.0999021
$357$	15.8330	−	5.06534i	0.837970	−	0.268086i
$358$	19.5963			1.03570
$359$	−0.438209	−	0.253000i	−0.0231278	−	0.0133528i	0.488392	−	0.872625i	$-0.337584\pi$
$359$	−0.438209	−	0.253000i	−0.0231278	−	0.0133528i	−0.511519	+	0.859272i	$0.670917\pi$
$360$		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
$366$	5.78070	−	1.31751i	0.302162	−	0.0688672i
$367$	1.17547	−	0.678660i	0.0613592	−	0.0354258i	−0.469007	−	0.883195i	$-0.655388\pi$
$367$	1.17547	−	0.678660i	0.0613592	−	0.0354258i	0.530366	+	0.847769i	$0.322055\pi$
$368$	1.65996	−	0.958379i	0.0865314	−	0.0499590i
$369$	−18.4626	−	12.6045i	−0.961125	−	0.656163i
$370$		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	−0.0351422	+	0.999382i	$0.511188\pi$
$373$	−17.0548	+	29.5397i	−0.883062	+	1.52951i	−0.847919	+	0.530125i	$0.822145\pi$
$374$	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
$378$	13.3724	−	3.19049i	0.687801	−	0.164101i
$379$	−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
$381$	−4.12252	+	13.3501i	−0.211203	+	0.683945i
$382$	0.267752	+	0.463759i	0.0136994	+	0.0237280i
$383$	16.2631	−	28.1685i	0.831004	−	1.43934i	−0.0662394	−	0.997804i	$-0.521100\pi$
$383$	16.2631	−	28.1685i	0.831004	−	1.43934i	0.897243	−	0.441537i	$-0.145567\pi$
$384$	−1.27005	+	1.17770i	−0.0648120	+	0.0600991i
$385$		0			0
$386$		−	5.53544i		−	0.281747i
$387$	−11.5168	−	7.86258i	−0.585433	−	0.399677i
$388$	15.2907	−	8.82809i	0.776267	−	0.448178i
$389$	6.15025	−	3.55085i	0.311830	−	0.180035i	−0.335915	−	0.941892i	$-0.609046\pi$
$389$	6.15025	−	3.55085i	0.311830	−	0.180035i	0.647745	+	0.761857i	$0.275712\pi$
$390$		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
$396$	6.44174	+	13.3978i	0.323709	+	0.673265i
$397$	−11.2790	−	6.51194i	−0.566077	−	0.326825i	0.189504	−	0.981880i	$-0.439312\pi$
$397$	−11.2790	−	6.51194i	−0.566077	−	0.326825i	−0.755581	+	0.655055i	$0.772645\pi$
$398$	−9.02198			−0.452231
$399$	12.9651	−	14.2688i	0.649067	−	0.714334i
$400$		0			0
$401$	−20.2676	−	11.7015i	−1.01211	−	0.584345i	−0.100305	−	0.994957i	$-0.531982\pi$
$401$	−20.2676	−	11.7015i	−1.01211	−	0.584345i	−0.911810	+	0.410612i	$0.865315\pi$
$402$	13.2113	+	4.07966i	0.658920	+	0.203475i
$403$	−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
$408$	−1.39621	−	6.12600i	−0.0691226	−	0.303282i
$409$	11.4311	−	6.59972i	0.565229	−	0.326335i	−0.190013	−	0.981782i	$-0.560853\pi$
$409$	11.4311	−	6.59972i	0.565229	−	0.326335i	0.755242	+	0.655447i	$0.227520\pi$
$410$		0			0
$411$	−5.70692	−	25.0397i	−0.281502	−	1.23512i
$412$			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
$417$	11.9928	+	3.70340i	0.587292	+	0.181356i
$418$	18.0545	+	10.4238i	0.883073	+	0.509843i
$419$	−27.9492			−1.36541			−0.682704	−	0.730695i	$-0.739196\pi$
$419$	−27.9492			−1.36541			−0.682704	+	0.730695i	$0.739196\pi$
$420$		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
$423$	1.64326	−	0.790091i	0.0798982	−	0.0384155i
$424$	−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
$429$	53.3497	−	12.1592i	2.57575	−	0.587052i
$430$		0			0
$431$	−2.89638	+	1.67223i	−0.139514	+	0.0805483i	−0.568132	−	0.822937i	$-0.692334\pi$
$431$	−2.89638	+	1.67223i	−0.139514	+	0.0805483i	0.428619	+	0.903486i	$0.359000\pi$
$432$	−0.769634	−	5.13884i	−0.0370290	−	0.247242i
$433$		−	14.6756i		−	0.705264i	−0.935762	−	0.352632i	$-0.885287\pi$
$433$		−	14.6756i		−	0.705264i	0.935762	−	0.352632i	$-0.114713\pi$
$434$	−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
$438$	−7.71340	+	24.9786i	−0.368561	+	1.19352i
$439$	−5.70453	−	3.29351i	−0.272262	−	0.157191i	0.357653	−	0.933855i	$-0.383577\pi$
$439$	−5.70453	−	3.29351i	−0.272262	−	0.157191i	−0.629915	+	0.776664i	$0.716910\pi$
$440$		0			0
$441$	−19.1064	−	8.71477i	−0.909827	−	0.414989i
$442$	−23.1265			−1.10001
$443$	−35.2654	−	20.3605i	−1.67551	−	0.967357i	−0.964464	−	0.264213i	$-0.914888\pi$
$443$	−35.2654	−	20.3605i	−1.67551	−	0.967357i	−0.711047	−	0.703144i	$-0.751779\pi$
$444$	2.97833	−	9.64481i	0.141345	−	0.457723i
$445$		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
$453$	−19.8839	+	4.53183i	−0.934226	+	0.212924i
$454$		−	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	−0.949224	−	0.314602i	$-0.898129\pi$
$457$	−4.32166	+	7.48533i	−0.202159	+	0.350149i	0.747065	+	0.664751i	$0.231462\pi$
$458$	8.26082	+	14.3082i	0.386003	+	0.668576i
$459$	17.5398	+	6.90285i	0.818690	+	0.322197i
$460$		0			0
$461$	24.7864			1.15442			0.577210	−	0.816596i	$-0.304141\pi$
$461$	24.7864			1.15442			0.577210	+	0.816596i	$0.304141\pi$
$462$	4.82176	−	22.1903i	0.224329	−	1.03239i
$463$	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	$-0.842713\pi$
$467$	−0.636712	+	1.10282i	−0.0294635	+	0.0510323i	0.850918	+	0.525299i	$0.176047\pi$
$468$	−19.0713	−	1.44117i	−0.881572	−	0.0666182i
$469$	−12.0847	−	17.3220i	−0.558018	−	0.799857i
$470$		0			0
$471$	0.594576	+	2.60876i	0.0273966	+	0.120205i
$472$	1.51668	−	0.875658i	0.0698111	−	0.0403054i
$473$	−19.9477	+	11.5168i	−0.917198	+	0.529545i
$474$	1.02692	+	4.50570i	0.0471678	+	0.206954i
$475$		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	$-0.272037\pi$
$479$	−7.11334	−	12.3207i	−0.325017	−	0.562945i	−0.981516	+	0.191381i	$0.938703\pi$
$480$		0			0
$481$	−32.1764	−	18.5771i	−1.46712	−	0.847042i
$482$	−22.3364			−1.01740
$483$	5.90692	−	6.50089i	0.268774	−	0.295801i
$484$	13.5552			0.616146
$485$		0			0
$486$	14.0341	+	6.78549i	0.636602	+	0.307796i
$487$	19.9476	+	34.5502i	0.903910	+	1.56562i	0.822374	+	0.568947i	$0.192649\pi$
$487$	19.9476	+	34.5502i	0.903910	+	1.56562i	0.0815361	+	0.996670i	$0.474017\pi$
$488$	−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	$-0.117406\pi$
$492$	12.5839	−	2.86806i	0.567326	−	0.129302i
$493$	−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	−0.669123	−	0.743152i	$-0.733330\pi$
$499$	6.90313	−	11.9566i	0.309027	−	0.535250i	0.978150	+	0.207902i	$0.0666634\pi$
$500$		0			0
$501$	6.52529	−	21.1310i	0.291528	−	0.944066i
$502$	−2.35652	−	1.36054i	−0.105176	−	0.0607237i
$503$	2.11183			0.0941620			0.0470810	−	0.998891i	$-0.485008\pi$
$503$	2.11183			0.0941620			0.0470810	+	0.998891i	$0.485008\pi$
$504$	−3.89885	+	6.91368i	−0.173668	+	0.307960i
$505$		0			0
$506$	8.22564	+	4.74908i	0.365674	+	0.211122i
$507$	−14.1272	+	45.7485i	−0.627411	+	2.03176i
$508$	−4.03340	−	6.98605i	−0.178953	−	0.309956i
$509$	8.09556	−	14.0219i	0.358830	−	0.621511i	−0.628936	−	0.777457i	$-0.716509\pi$
$509$	8.09556	−	14.0219i	0.358830	−	0.621511i	0.987766	+	0.155946i	$0.0498426\pi$
$510$		0			0
$511$	32.7507	−	22.8484i	1.44880	−	1.01075i
$512$		−	1.00000i		−	0.0441942i
$513$	21.6196	−	3.23792i	0.954528	−	0.142958i
$514$	9.96256	−	5.75189i	0.439430	−	0.253705i
$515$		0			0
$516$	7.84974	−	1.78907i	0.345566	−	0.0787596i
$517$		−	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	0.998529	+	0.0542143i	$0.0172654\pi$
$521$	12.4676	+	21.5945i	0.546216	+	0.946073i	−0.452314	+	0.891859i	$0.649401\pi$
$522$	−2.16370	+	1.04032i	−0.0947026	+	0.0455336i
$523$	−17.0768	−	9.85929i	−0.746716	−	0.431116i	0.0777903	−	0.996970i	$-0.475214\pi$
$523$	−17.0768	−	9.85929i	−0.746716	−	0.431116i	−0.824506	+	0.565853i	$0.808547\pi$
$524$	3.38301			0.147788
$525$		0			0
$526$	12.7855			0.557476
$527$	−15.8221	−	9.13490i	−0.689222	−	0.397923i
$528$	−8.20077	−	2.53241i	−0.356893	−	0.110209i
$529$	−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
$534$	−0.725498	−	3.18320i	−0.0313954	−	0.137750i
$535$		0			0
$536$	−6.91343	+	3.99147i	−0.298615	+	0.172405i
$537$	−7.54243	−	33.0932i	−0.325480	−	1.42808i
$538$			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	−0.759253	−	0.650795i	$-0.774436\pi$
$541$	4.27923	−	7.41184i	0.183978	−	0.318660i	0.943232	+	0.332135i	$0.107769\pi$
$542$	11.0349	+	19.1130i	0.473990	+	0.820975i
$543$	−24.5102	−	7.56879i	−1.05184	−	0.324808i
$544$	3.14155	+	1.81377i	0.134693	+	0.0777649i
$545$		0			0
$546$	21.6223	+	19.6467i	0.925348	+	0.840801i
$547$	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
$549$	−4.44987	−	9.25502i	−0.189916	−	0.394995i
$550$		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	$-0.630509\pi$
$557$	4.63348	−	2.67514i	0.196327	−	0.113349i	0.594941	+	0.803769i	$0.297175\pi$
$558$	−12.4785	−	8.51912i	−0.528257	−	0.360643i
$559$		−	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	−0.989813	−	0.142372i	$-0.954527\pi$
$563$	−14.6685	−	25.4066i	−0.618205	−	1.07076i	0.371609	−	0.928390i	$-0.378806\pi$
$564$	−0.310604	+	1.00584i	−0.0130788	+	0.0423535i
$565$		0			0
$566$	−24.7505			−1.04034
$567$	−10.5348	−	21.3546i	−0.442421	−	0.896807i
$568$	−2.48759			−0.104377
$569$	−36.5568	−	21.1061i	−1.53254	−	0.884812i	−0.999244	−	0.0388825i	$-0.987620\pi$
$569$	−36.5568	−	21.1061i	−1.53254	−	0.884812i	−0.533295	−	0.845929i	$-0.679046\pi$
$570$		0			0
$571$	15.6790	+	27.1568i	0.656145	+	1.13648i	0.981605	+	0.190921i	$0.0611473\pi$
$571$	15.6790	+	27.1568i	0.656145	+	1.13648i	−0.325461	+	0.945556i	$0.605519\pi$
$572$	−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
$576$	2.47766	+	1.69151i	0.103236	+	0.0704795i
$577$	27.7794	−	16.0385i	1.15647	−	0.667689i	0.206016	−	0.978549i	$-0.433950\pi$
$577$	27.7794	−	16.0385i	1.15647	−	0.667689i	0.950456	+	0.310859i	$0.100617\pi$
$578$	3.32632	−	1.92045i	0.138357	−	0.0798802i
$579$	−9.34795	+	2.13054i	−0.388488	+	0.0885422i
$580$		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	$-0.512730\pi$
$587$	−1.93731			−0.0799612			−0.0399806	+	0.999200i	$0.512730\pi$
$588$	11.1899	−	4.66756i	0.461464	−	0.192487i
$589$	−21.1887			−0.873063
$590$		0			0
$591$	1.10294	+	0.340590i	0.0453690	+	0.0140100i
$592$	2.91394	+	5.04710i	0.119762	+	0.207435i
$593$	5.63074	−	9.75274i	0.231227	−	0.400497i	−0.726942	−	0.686698i	$-0.759059\pi$
$593$	5.63074	−	9.75274i	0.231227	−	0.400497i	0.958169	+	0.286201i	$0.0923927\pi$
$594$	20.1461	−	16.0351i	0.826604	−	0.657929i
$595$		0			0
$596$		−	6.59303i		−	0.270061i
$597$	3.47247	+	15.2358i	0.142119	+	0.623560i
$598$	−10.5826	+	6.10989i	−0.432756	+	0.249852i
$599$	−38.4047	+	22.1730i	−1.56917	+	0.905963i	−0.572909	+	0.819619i	$0.694185\pi$
$599$	−38.4047	+	22.1730i	−1.56917	+	0.905963i	−0.996265	+	0.0863446i	$0.972481\pi$
$600$		0			0
$601$		−	17.7126i		−	0.722514i	−0.932466	−	0.361257i	$-0.882348\pi$
$601$		−	17.7126i		−	0.722514i	0.932466	−	0.361257i	$-0.117652\pi$
$602$	−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
$606$	1.90057	+	0.586898i	0.0772053	+	0.0238411i
$607$	15.8915	+	9.17497i	0.645016	+	0.372400i	0.786544	−	0.617534i	$-0.211868\pi$
$607$	15.8915	+	9.17497i	0.645016	+	0.372400i	−0.141528	+	0.989934i	$0.545201\pi$
$608$	4.20710			0.170620
$609$	3.58366	+	0.778699i	0.145217	+	0.0315545i
$610$		0			0
$611$	3.35562	+	1.93737i	0.135754	+	0.0783775i
$612$	−9.80787	+	4.71568i	−0.396460	+	0.190620i
$613$	0.315836	+	0.547045i	0.0127565	+	0.0220949i	0.872333	−	0.488912i	$-0.162606\pi$
$613$	0.315836	+	0.547045i	0.0127565	+	0.0220949i	−0.859577	+	0.511007i	$0.829273\pi$
$614$	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	$0.898392\pi$
$618$	12.3002	−	2.80340i	0.494787	−	0.112769i
$619$	10.9863	−	6.34296i	0.441578	−	0.254945i	−0.262689	−	0.964881i	$-0.584609\pi$
$619$	10.9863	−	6.34296i	0.441578	−	0.254945i	0.704267	+	0.709936i	$0.251276\pi$
$620$		0			0
$621$	9.84991	−	1.47520i	0.395263	−	0.0591978i
$622$		−	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
$627$	10.6541	−	34.5014i	0.425483	−	1.37785i
$628$	−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
$633$	5.84568	−	18.9302i	0.232345	−	0.752409i
$634$	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
$639$	4.20778	−	6.16340i	0.166457	−	0.243820i
$640$		0			0
$641$	11.2070	−	6.47036i	0.442649	−	0.255564i	−0.262071	−	0.965048i	$-0.584406\pi$
$641$	11.2070	−	6.47036i	0.442649	−	0.255564i	0.704721	+	0.709485i	$0.251072\pi$
$642$	4.53659	−	1.03396i	0.179045	−	0.0408070i
$643$			27.7420i			1.09404i	0.837120	+	0.547019i	$0.184237\pi$
$643$			27.7420i			1.09404i	−0.837120	+	0.547019i	$0.815763\pi$
$644$	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	−0.800356	−	0.599526i	$-0.795356\pi$
$647$	−23.3856	−	40.5050i	−0.919382	−	1.59242i	−0.119027	−	0.992891i	$-0.537977\pi$
$648$	−8.38196	+	3.27761i	−0.329275	+	0.128756i
$649$	7.51566	+	4.33917i	0.295015	+	0.170327i
$650$		0			0
$651$	7.03261	+	21.9822i	0.275630	+	0.861549i
$652$	−3.37759			−0.132277
$653$	27.3651	+	15.7992i	1.07088	+	0.618271i	0.928421	−	0.371530i	$-0.121167\pi$
$653$	27.3651	+	15.7992i	1.07088	+	0.618271i	0.142456	+	0.989801i	$0.454500\pi$
$654$	−14.9332	−	4.61140i	−0.583936	−	0.180320i
$655$		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	−0.714888	−	0.699239i	$-0.753522\pi$
$661$	−12.0007	+	6.92861i	−0.466773	+	0.269492i	0.248115	+	0.968731i	$0.420189\pi$
$662$	−10.2098	+	5.89462i	−0.396814	+	0.229101i
$663$	8.90115	+	39.0547i	0.345692	+	1.51676i
$664$		−	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
$669$	−8.66191	−	2.67481i	−0.334889	−	0.103414i
$670$		0			0
$671$	−16.9624			−0.654827
$672$	−1.39635	−	4.36465i	−0.0538656	−	0.168370i
$673$	−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	−0.143628	+	0.989632i	$0.545877\pi$
$677$	−24.1682	+	41.8606i	−0.928860	+	1.60883i	−0.785232	+	0.619202i	$0.787456\pi$
$678$	−14.6349	−	15.7826i	−0.562050	−	0.606126i
$679$	3.99132	+	46.5430i	0.153173	+	1.78616i
$680$		0			0
$681$	−22.7344	+	5.18152i	−0.871186	+	0.198556i
$682$	−21.6134	+	12.4785i	−0.827620	+	0.477827i
$683$	−22.8004	+	13.1638i	−0.872433	+	0.503699i	−0.868156	−	0.496291i	$-0.834695\pi$
$683$	−22.8004	+	13.1638i	−0.872433	+	0.503699i	−0.00427708	+	0.999991i	$0.501361\pi$
$684$	−7.11633	+	10.4238i	−0.272100	+	0.398562i
$685$		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	0.150911	−	0.988547i	$-0.451779\pi$
$691$	−16.5539	−	9.55742i	−0.629741	−	0.363581i	−0.780652	+	0.624966i	$0.785113\pi$
$692$	0.247556			0.00941068
$693$	−39.3296	+	0.398110i	−1.49401	+	0.0151229i
$694$	−31.9093			−1.21126
$695$		0			0
$696$	0.408975	−	1.32440i	0.0155022	−	0.0502012i
$697$	−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	$0.759134\pi$
$702$	4.90660	+	32.7613i	0.185188	+	1.23650i
$703$	−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	−0.909867	−	0.414900i	$-0.863816\pi$
$709$	−2.54606	+	4.40991i	−0.0956193	+	0.165618i	0.814248	+	0.580518i	$0.197150\pi$
$710$		0			0
$711$	7.21372	−	3.46840i	0.270536	−	0.130075i
$712$	1.63241	+	0.942474i	0.0611773	+	0.0353207i
$713$	−9.65357			−0.361529
$714$	16.2444	+	3.52978i	0.607933	+	0.132099i
$715$		0			0
$716$	16.9709	+	9.79815i	0.634232	+	0.366174i
$717$	−41.0533	−	12.6773i	−1.53316	−	0.473442i
$718$	−0.253000	−	0.438209i	−0.00944189	−	0.0163538i
$719$	20.5822	−	35.6494i	0.767587	−	1.32950i	−0.171281	−	0.985222i	$-0.554791\pi$
$719$	20.5822	−	35.6494i	0.767587	−	1.32950i	0.938868	−	0.344278i	$-0.111876\pi$
$720$		0			0
$721$	−17.4511	−	8.17418i	−0.649914	−	0.304422i
$722$		−	1.30035i		−	0.0483938i
$723$	8.59708	+	37.7205i	0.319729	+	1.40284i
$724$	12.8261	−	7.40517i	0.476679	−	0.275211i
$725$		0			0
$726$	−5.21727	−	22.8913i	−0.193631	−	0.849576i
$727$			46.1288i			1.71082i	0.517948	+	0.855412i	$0.326696\pi$
$727$			46.1288i			1.71082i	−0.517948	+	0.855412i	$0.673304\pi$
$728$	−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
$732$	5.66498	+	1.74935i	0.209384	+	0.0646579i
$733$	8.65789	+	4.99864i	0.319787	+	0.184629i	0.651297	−	0.758823i	$-0.274225\pi$
$733$	8.65789	+	4.99864i	0.319787	+	0.184629i	−0.331511	+	0.943451i	$0.607558\pi$
$734$	1.35732			0.0500996
$735$		0			0
$736$	1.91676			0.0706526
$737$	−34.2583	−	19.7790i	−1.26192	−	0.728570i
$738$	−9.68684	−	20.1471i	−0.356578	−	0.741625i
$739$	−0.418026	−	0.724042i	−0.0153773	−	0.0266343i	0.858234	−	0.513258i	$-0.171562\pi$
$739$	−0.418026	−	0.724042i	−0.0153773	−	0.0266343i	−0.873612	+	0.486624i	$0.838228\pi$
$740$		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	$0.566418\pi$
$744$	8.50521	−	1.93847i	0.311816	−	0.0710676i
$745$		0			0
$746$	−29.5397	+	17.0548i	−1.08153	+	0.624419i
$747$	18.0179	+	12.3009i	0.659241	+	0.450066i
$748$			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	0.374858	+	0.927082i	$0.377691\pi$
$751$	−16.8660	+	29.2127i	−0.615448	+	1.06599i	−0.990306	+	0.138905i	$0.955642\pi$
$752$	−0.303890	−	0.526352i	−0.0110817	−	0.0191941i
$753$	−1.39060	+	4.50321i	−0.0506762	+	0.164106i
$754$	−4.41837	−	2.55095i	−0.160908	−	0.0929001i
$755$		0			0
$756$	13.1761	+	3.92315i	0.479209	+	0.142684i
$757$	−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
$759$	4.85401	−	15.7189i	0.176189	−	0.570559i
$760$		0			0
$761$	8.95519	−	15.5108i	0.324625	−	0.562268i	−0.656811	−	0.754055i	$-0.728095\pi$
$761$	8.95519	−	15.5108i	0.324625	−	0.562268i	0.981436	+	0.191787i	$0.0614284\pi$
$762$	−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
$768$	−1.68874	+	0.384890i	−0.0609373	+	0.0138885i
$769$		−	0.619084i		−	0.0223247i	−0.999938	−	0.0111624i	$-0.996447\pi$
$769$		−	0.619084i		−	0.0223247i	0.999938	−	0.0111624i	$-0.00355317\pi$
$770$		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	0.851271	+	0.524727i	$0.175833\pi$
$773$	24.4683	+	42.3803i	0.880062	+	1.52431i	0.0287914	+	0.999585i	$0.490834\pi$
$774$	−6.04258	−	12.5676i	−0.217196	−	0.451733i
$775$		0			0
$776$	17.6562			0.633820
$777$	19.7659	+	17.9599i	0.709098	+	0.644309i
$778$	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
$786$	−1.30209	−	5.71305i	−0.0464440	−	0.203778i
$787$	0.0582062	−	0.0336053i	0.00207483	−	0.00119790i	−0.498962	−	0.866624i	$-0.666285\pi$
$787$	0.0582062	−	0.0336053i	0.00207483	−	0.00119790i	0.501037	+	0.865426i	$0.332952\pi$
$788$	−0.577166	+	0.333227i	−0.0205607	+	0.0118707i
$789$	−4.92103	−	21.5915i	−0.175193	−	0.768678i
$790$		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	$-0.456950\pi$
$797$	7.61311			0.269670			0.134835	+	0.990868i	$0.456950\pi$
$798$	18.3625	−	5.87460i	0.650026	−	0.207959i
$799$	2.20475			0.0779984
$800$		0			0
$801$	−5.09637	+	2.45036i	−0.180071	+	0.0865793i
$802$	−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
$807$	19.7440	−	4.49995i	0.695021	−	0.158406i
$808$	−0.994562	+	0.574210i	−0.0349886	+	0.0202007i
$809$	16.9690	−	9.79703i	0.596597	−	0.344445i	−0.171105	−	0.985253i	$-0.554734\pi$
$809$	16.9690	−	9.79703i	0.596597	−	0.344445i	0.767702	+	0.640807i	$0.221400\pi$
$810$		0			0
$811$		−	38.1099i		−	1.33822i	−0.743164	−	0.669110i	$-0.766676\pi$
$811$		−	38.1099i		−	1.33822i	0.743164	−	0.669110i	$-0.233324\pi$
$812$	−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
$816$	1.85385	−	6.00338i	0.0648977	−	0.210160i
$817$	−16.9357	−	9.77786i	−0.592507	−	0.342084i
$818$	13.1994			0.461508
$819$	24.8561	−	44.0763i	0.868541	−	1.54015i
$820$		0			0
$821$	−32.4054	−	18.7093i	−1.13096	−	0.652958i	−0.186781	−	0.982402i	$-0.559805\pi$
$821$	−32.4054	−	18.7093i	−1.13096	−	0.652958i	−0.944175	+	0.329444i	$0.893139\pi$
$822$	7.57751	−	24.5385i	0.264296	−	0.855878i
$823$	17.1932	+	29.7795i	0.599318	+	1.03805i	0.992922	+	0.118768i	$0.0378946\pi$
$823$	17.1932	+	29.7795i	0.599318	+	1.03805i	−0.393604	+	0.919280i	$0.628772\pi$
$824$	−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	$0.976982\pi$
$828$	−3.24221	+	4.74908i	−0.112675	+	0.165042i
$829$	−24.3399	+	14.0526i	−0.845359	+	0.488068i	−0.859082	−	0.511837i	$-0.828965\pi$
$829$	−24.3399	+	14.0526i	−0.845359	+	0.488068i	0.0137231	+	0.999906i	$0.495632\pi$
$830$		0			0
$831$	−13.1833	+	3.00467i	−0.457323	+	0.104231i
$832$			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
$837$	−9.58376	+	24.3519i	−0.331263	+	0.841727i
$838$	−24.2047	−	13.9746i	−0.836138	−	0.482745i
$839$	23.6646			0.816992			0.408496	−	0.912760i	$-0.366053\pi$
$839$	23.6646			0.816992			0.408496	+	0.912760i	$0.366053\pi$
$840$		0			0
$841$	28.3596			0.977916
$842$	21.3731	+	12.3398i	0.736565	+	0.425256i
$843$	−38.2112	−	11.7997i	−1.31606	−	0.406402i
$844$	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
$849$	9.52622	+	41.7972i	0.326939	+	1.43448i
$850$		0			0
$851$	−9.67407	+	5.58533i	−0.331623	+	0.191462i
$852$	0.957449	+	4.20090i	0.0328017	+	0.143921i
$853$			23.7742i			0.814012i	0.913426	+	0.407006i	$0.133427\pi$
$853$			23.7742i			0.814012i	−0.913426	+	0.407006i	$0.866573\pi$
$854$	−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	$-0.0419236\pi$
$857$	11.1811	+	19.3662i	0.381938	+	0.661535i	−0.609402	+	0.792862i	$0.708590\pi$
$858$	52.2818	+	16.1447i	1.78487	+	0.551170i
$859$	−37.1729	−	21.4618i	−1.26832	−	0.732267i	−0.293653	−	0.955912i	$-0.594871\pi$
$859$	−37.1729	−	21.4618i	−1.26832	−	0.732267i	−0.974671	+	0.223645i	$0.928204\pi$
$860$		0			0
$861$	−7.25079	+	33.3690i	−0.247106	+	1.13721i
$862$	−3.34445			−0.113912
$863$	20.3687	+	11.7599i	0.693360	+	0.400312i	0.804870	−	0.593452i	$-0.202235\pi$
$863$	20.3687	+	11.7599i	0.693360	+	0.400312i	−0.111510	+	0.993763i	$0.535569\pi$
$864$	1.90290	−	4.83518i	0.0647379	−	0.164496i
$865$		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
$873$	−29.8655	+	43.7460i	−1.01080	+	1.48058i
$874$			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	−0.788597	−	0.614911i	$-0.789192\pi$
$877$	4.09356	−	7.09026i	0.138230	−	0.239421i	0.926827	+	0.375490i	$0.122525\pi$
$878$	−3.29351	−	5.70453i	−0.111151	−	0.192518i
$879$	12.9491	−	41.9336i	0.436764	−	1.41439i
$880$		0			0
$881$	26.6496			0.897847			0.448923	−	0.893570i	$-0.351808\pi$
$881$	26.6496			0.897847			0.448923	+	0.893570i	$0.351808\pi$
$882$	−12.1892	−	17.1004i	−0.410432	−	0.575800i
$883$	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	$-0.700745\pi$
$887$	12.0499	−	20.8711i	0.404597	−	0.700782i	0.994274	+	0.106856i	$0.0340785\pi$
$888$	7.40171	−	6.86349i	0.248385	−	0.230324i
$889$	21.2647	−	1.82356i	0.713195	−	0.0611604i
$890$		0			0
$891$	−34.8333	−	27.8498i	−1.16696	−	0.933005i
$892$	4.53275	−	2.61699i	0.151768	−	0.0876231i
$893$	2.21441	−	1.27849i	0.0741026	−	0.0427831i
$894$	−11.1339	+	2.53759i	−0.372375	+	0.0848698i
$895$		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
$903$	−4.52299	+	20.8153i	−0.150516	+	0.692690i
$904$	12.4267			0.413306
$905$		0			0
$906$	−19.4859	−	6.01725i	−0.647374	−	0.199910i
$907$	−10.8290	−	18.7564i	−0.359572	−	0.622797i	0.628317	−	0.777957i	$-0.283744\pi$
$907$	−10.8290	−	18.7564i	−0.359572	−	0.622797i	−0.987889	+	0.155160i	$0.950411\pi$
$908$	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	$0.712295\pi$
$912$	−1.61927	−	7.10471i	−0.0536194	−	0.235261i
$913$	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	−0.940355	−	0.340196i	$-0.889507\pi$
$919$	−5.32208	+	9.21812i	−0.175559	+	0.304078i	0.764795	+	0.644273i	$0.222840\pi$
$920$		0			0
$921$	−21.7453	−	6.71499i	−0.716533	−	0.221266i
$922$	21.4657	+	12.3932i	0.706935	+	0.408149i
$923$	15.8590			0.522004
$924$	15.2709	−	16.8065i	0.502377	−	0.552893i
$925$		0			0
$926$	15.5709	+	8.98986i	0.511691	+	0.295425i
$927$	−9.46846	−	19.6929i	−0.310985	−	0.646800i
$928$	0.400134	+	0.693053i	0.0131351	+	0.0227506i
$929$	17.1983	−	29.7883i	0.564257	−	0.977322i	−0.432861	−	0.901460i	$-0.642496\pi$
$929$	17.1983	−	29.7883i	0.564257	−	0.977322i	0.997118	−	0.0758612i	$-0.0241706\pi$
$930$		0			0
$931$	−27.6388	−	10.1675i	−0.905826	−	0.333227i
$932$		−	18.6359i		−	0.610440i
$933$	−12.8457	+	2.92772i	−0.420549	+	0.0958494i
$934$	−1.10282	+	0.636712i	−0.0360853	+	0.0208339i
$935$		0			0
$936$	−15.7957	−	10.7838i	−0.516297	−	0.352478i
$937$		−	40.0917i		−	1.30974i	−0.755742	−	0.654870i	$-0.772723\pi$
$937$		−	40.0917i		−	1.30974i	0.755742	−	0.654870i	$-0.227277\pi$
$938$	−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	$-0.313240\pi$
$941$	−13.6315	−	23.6104i	−0.444374	−	0.769678i	−0.998008	+	0.0630819i	$0.979907\pi$
$942$	−0.789463	+	2.55654i	−0.0257221	+	0.0832966i
$943$	−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	$-0.453608\pi$
$947$	−19.6642	−	11.3531i	−0.638999	−	0.368926i	−0.784229	+	0.620472i	$0.786941\pi$
$948$	−1.36351	+	4.41551i	−0.0442848	+	0.143409i
$949$	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	$0.784171\pi$
$954$	35.4467	+	24.1996i	1.14763	+	0.783491i
$955$		0			0
$956$	21.4831	−	12.4032i	0.694812	−	0.401150i
$957$	6.69687	−	1.52632i	0.216479	−	0.0493388i
$958$		−	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
$963$	−3.49218	−	7.26318i	−0.112534	−	0.234053i
$964$	−19.3439	−	11.1682i	−0.623025	−	0.359704i
$965$		0			0
$966$	8.36598	−	2.67647i	0.269171	−	0.0861141i
$967$	−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
$969$	25.2568	+	7.79932i	0.811365	+	0.250550i
$970$		0			0
$971$	−13.4005	+	23.2104i	−0.430044	+	0.744858i	−0.996877	−	0.0789753i	$-0.974835\pi$
$971$	−13.4005	+	23.2104i	−0.430044	+	0.744858i	0.566833	+	0.823833i	$0.308169\pi$
$972$	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	$-0.813796\pi$
$977$	−24.1424	+	13.9386i	−0.772383	+	0.445936i	0.0613410	+	0.998117i	$0.480462\pi$
$978$	1.30000	+	5.70389i	0.0415695	+	0.182390i
$979$			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	$-0.279919\pi$
$983$	−10.9212	−	18.9161i	−0.348332	−	0.603329i	−0.985953	+	0.167021i	$0.946585\pi$
$984$	12.3320	+	3.80814i	0.393130	+	0.121399i
$985$		0			0
$986$	−2.90301			−0.0924507
$987$	−2.06135	−	1.87301i	−0.0656134	−	0.0596185i
$988$	−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	0.774856	+	0.632137i	$0.217822\pi$
$991$	29.4300	+	50.9743i	0.934875	+	1.61925i	0.160019	+	0.987114i	$0.448845\pi$
$992$	−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
$996$	−12.2808	+	2.79898i	−0.389132	+	0.0886891i
$997$	10.4327	−	6.02334i	0.330408	−	0.190761i	−0.325614	−	0.945503i	$-0.605571\pi$
$997$	10.4327	−	6.02334i	0.330408	−	0.190761i	0.656022	+	0.754742i	$0.272238\pi$
$998$	11.9566	−	6.90313i	0.378479	−	0.218515i
$999$	4.48534	+	29.9486i	0.141910	+	0.947531i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.4	✓	12	35.24	odd	6
210.2.r.a.131.4	yes	12	15.14	odd	2
210.2.r.b.101.2	yes	12	105.59	even	6
210.2.r.b.131.2	yes	12	5.4	even	2
1050.2.s.f.101.5		12	21.17	even	6	inner
1050.2.s.f.551.5		12	1.1	even	1	trivial
1050.2.s.g.101.3		12	7.3	odd	6
1050.2.s.g.551.3		12	3.2	odd	2
1050.2.u.e.299.1		12	5.2	odd	4
1050.2.u.e.899.1		12	105.38	odd	12
1050.2.u.f.299.2		12	15.8	even	4
1050.2.u.f.899.2		12	35.17	even	12
1050.2.u.g.299.5		12	15.2	even	4
1050.2.u.g.899.5		12	35.3	even	12
1050.2.u.h.299.6		12	5.3	odd	4
1050.2.u.h.899.6		12	105.17	odd	12
1470.2.b.a.881.2		12	105.89	even	6
1470.2.b.a.881.8		12	35.9	even	6
1470.2.b.b.881.5		12	105.44	odd	6
1470.2.b.b.881.11		12	35.19	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.511048 - 1.65494i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.27005 - 1.17770i) q^{6} +(-2.63608 + 0.226058i) q^{7} +1.00000i q^{8} +(-2.47766 - 1.69151i) q^{9} +(-4.29143 + 2.47766i) q^{11} +(1.68874 - 0.384890i) q^{12} -6.37523i q^{13} +(-2.39594 - 1.12227i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.81377 - 3.14155i) q^{17} +(-1.29996 - 2.70372i) q^{18} +(-3.64345 - 2.10355i) q^{19} +(-0.973048 + 4.47808i) q^{21} -4.95532 q^{22} +(-1.65996 - 0.958379i) q^{23} +(1.65494 + 0.511048i) 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} +(1.90726 + 8.36827i) q^{33} -3.62755i q^{34} +(0.226058 - 2.99147i) q^{36} +(2.91394 - 5.04710i) q^{37} +(-2.10355 - 3.64345i) q^{38} +(-10.5506 - 3.25805i) q^{39} +7.45163 q^{41} +(-3.08172 + 3.39161i) 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} +(-6.12600 + 1.39621i) q^{51} +(5.52111 - 3.18762i) q^{52} +(-12.3898 + 7.15326i) q^{53} +(-5.13884 + 0.769634i) 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} +(6.91368 + 3.89885i) q^{63} -1.00000 q^{64} +(-2.53241 + 8.20077i) q^{66} +(3.99147 + 6.91343i) q^{67} +(1.81377 - 3.14155i) q^{68} +(-2.43438 + 2.25736i) q^{69} +2.48759i q^{71} +(1.69151 - 2.47766i) 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} +(3.27761 + 8.38196i) q^{81} +(6.45330 + 3.72581i) q^{82} -7.27215 q^{83} +(-4.36465 + 1.39635i) q^{84} +(4.02552 + 2.32413i) q^{86} +(-1.32440 - 0.408975i) q^{87} +(-2.47766 - 4.29143i) q^{88} +(0.942474 - 1.63241i) q^{89} +(1.44117 + 16.8056i) q^{91} -1.91676i q^{92} +(-1.93847 - 8.50521i) q^{93} +(-0.526352 + 0.303890i) q^{94} +(0.384890 + 1.68874i) q^{96} -17.6562i q^{97} +(6.56957 + 2.41676i) q^{98} +(14.8237 + 1.12019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 6 q^{4} + 2 q^{6} - 8 q^{7} + 12 q^{11} + 2 q^{12} - 12 q^{14} - 6 q^{16} + 12 q^{17} + 4 q^{18} + 4 q^{21} - 24 q^{23} - 2 q^{24} + 4 q^{26} - 8 q^{27} - 4 q^{28} + 12 q^{31} + 2 q^{33}+ \cdots + 48 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 + 6 * q^4 + 2 * q^6 - 8 * q^7 + 12 * q^11 + 2 * q^12 - 12 * q^14 - 6 * q^16 + 12 * q^17 + 4 * q^18 + 4 * q^21 - 24 * q^23 - 2 * q^24 + 4 * q^26 - 8 * q^27 - 4 * q^28 + 12 * q^31 + 2 * q^33 + 6 * q^36 + 8 * q^37 + 8 * q^38 - 42 * q^39 + 4 * q^41 - 24 * q^42 + 12 * q^44 + 2 * q^46 + 16 * q^47 + 4 * q^48 - 14 * q^49 - 8 * q^51 + 12 * q^52 - 48 * q^53 - 32 * q^54 - 6 * q^56 + 36 * q^57 - 8 * q^58 - 12 * q^59 - 30 * q^61 + 8 * q^62 - 20 * q^63 - 12 * q^64 - 14 * q^66 + 4 * q^67 - 12 * q^68 - 50 * q^69 - 4 * q^72 + 20 * q^77 - 32 * q^78 - 4 * q^79 - 40 * q^81 - 40 * q^83 + 20 * q^84 + 54 * q^86 - 64 * q^87 - 26 * q^89 + 28 * q^91 - 4 * q^93 + 24 * q^94 - 4 * q^96 + 16 * q^98 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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