LMFDB - Embedded newform 1050.2.u.e.899.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1050,2,Mod(299,1050)] 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, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1050.299"); 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.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-6,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == 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:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			899.1
Root			$-0.384890 - 1.68874i$ of defining polynomial
Character	$\chi$	$=$	1050.899
Dual form			1050.2.u.e.299.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.65494 + 0.511048i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.27005 + 1.17770i) q^{6} +(-0.226058 + 2.63608i) q^{7} +1.00000 q^{8} +(2.47766 - 1.69151i) q^{9} +(-4.29143 - 2.47766i) q^{11} +(0.384890 - 1.68874i) q^{12} -6.37523 q^{13} +(2.39594 - 1.12227i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.14155 + 1.81377i) q^{17} +(-2.70372 - 1.29996i) q^{18} +(3.64345 - 2.10355i) q^{19} +(-0.973048 - 4.47808i) q^{21} +4.95532i q^{22} +(-0.958379 - 1.65996i) q^{23} +(-1.65494 + 0.511048i) q^{24} +(3.18762 + 5.52111i) q^{26} +(-3.23594 + 4.06555i) q^{27} +(-2.16988 - 1.51381i) q^{28} -0.800269i q^{29} +(4.36166 + 2.51820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(8.36827 + 1.90726i) q^{33} -3.62755i q^{34} +(0.226058 + 2.99147i) q^{36} +(5.04710 - 2.91394i) q^{37} +(-3.64345 - 2.10355i) q^{38} +(10.5506 - 3.25805i) q^{39} +7.45163 q^{41} +(-3.39161 + 3.08172i) q^{42} +4.64827i q^{43} +(4.29143 - 2.47766i) q^{44} +(-0.958379 + 1.65996i) q^{46} +(-0.526352 + 0.303890i) q^{47} +(1.27005 + 1.17770i) q^{48} +(-6.89780 - 1.19181i) q^{49} +(-6.12600 - 1.39621i) q^{51} +(3.18762 - 5.52111i) q^{52} +(7.15326 - 12.3898i) q^{53} +(5.13884 + 0.769634i) q^{54} +(-0.226058 + 2.63608i) q^{56} +(-4.95469 + 5.34323i) q^{57} +(-0.693053 + 0.400134i) q^{58} +(0.875658 - 1.51668i) q^{59} +(2.96447 - 1.71154i) q^{61} -5.03641i q^{62} +(3.89885 + 6.91368i) q^{63} +1.00000 q^{64} +(-2.53241 - 8.20077i) q^{66} +(-6.91343 - 3.99147i) q^{67} +(-3.14155 + 1.81377i) q^{68} +(2.43438 + 2.25736i) q^{69} -2.48759i q^{71} +(2.47766 - 1.69151i) q^{72} +(7.54666 - 13.0712i) q^{73} +(-5.04710 - 2.91394i) q^{74} +4.20710i q^{76} +(7.50142 - 10.7525i) q^{77} +(-8.09687 - 7.50809i) q^{78} +(1.33404 + 2.31062i) q^{79} +(3.27761 - 8.38196i) q^{81} +(-3.72581 - 6.45330i) q^{82} -7.27215i q^{83} +(4.36465 + 1.39635i) q^{84} +(4.02552 - 2.32413i) q^{86} +(0.408975 + 1.32440i) q^{87} +(-4.29143 - 2.47766i) q^{88} +(-0.942474 - 1.63241i) q^{89} +(1.44117 - 16.8056i) q^{91} +1.91676 q^{92} +(-8.50521 - 1.93847i) q^{93} +(0.526352 + 0.303890i) q^{94} +(0.384890 - 1.68874i) q^{96} +17.6562 q^{97} +(2.41676 + 6.56957i) q^{98} +(-14.8237 + 1.12019i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 2 q^{3} - 6 q^{4} + 2 q^{6} - 6 q^{7} + 12 q^{8} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 12 q^{14} - 6 q^{16} + 12 q^{17} - 6 q^{18} + 4 q^{21} + 2 q^{23} + 2 q^{24} + 4 q^{26} - 28 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 + 2 * q^3 - 6 * q^4 + 2 * q^6 - 6 * q^7 + 12 * q^8 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 12 * q^14 - 6 * q^16 + 12 * q^17 - 6 * q^18 + 4 * q^21 + 2 * q^23 + 2 * q^24 + 4 * q^26 - 28 * q^27 - 6 * q^28 + 12 * q^31 - 6 * q^32 + 34 * q^33 + 6 * q^36 + 42 * q^39 + 4 * q^41 + 16 * q^42 - 12 * q^44 + 2 * q^46 + 24 * q^47 + 2 * q^48 + 14 * q^49 - 8 * q^51 + 4 * q^52 + 8 * q^53 + 32 * q^54 - 6 * q^56 - 20 * q^57 + 18 * q^58 + 12 * q^59 - 30 * q^61 + 2 * q^63 + 12 * q^64 - 14 * q^66 - 6 * q^67 - 12 * q^68 + 50 * q^69 - 20 * q^77 - 12 * q^78 + 4 * q^79 - 40 * q^81 - 2 * q^82 - 20 * q^84 + 54 * q^86 - 8 * q^87 + 12 * q^88 + 26 * q^89 + 28 * q^91 - 4 * q^92 - 24 * q^93 - 24 * q^94 - 4 * q^96 + 72 * q^97 + 2 * 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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.65494	+	0.511048i	−0.955481	+	0.295053i
$3$	−1.65494	+	0.511048i	−0.955481	+	0.295053i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.27005	+	1.17770i	0.518496	+	0.480793i
$7$	−0.226058	+	2.63608i	−0.0854419	+	0.996343i
$7$	−0.226058	+	2.63608i	−0.0854419	+	0.996343i
$8$	1.00000			0.353553
$9$	2.47766	−	1.69151i	0.825887	−	0.563836i
$10$		0			0
$11$	−4.29143	−	2.47766i	−1.29392	−	0.747043i	−0.314570	−	0.949234i	$-0.601860\pi$
$11$	−4.29143	−	2.47766i	−1.29392	−	0.747043i	−0.979346	+	0.202191i	$0.935194\pi$
$12$	0.384890	−	1.68874i	0.111108	−	0.487499i
$13$	−6.37523			−1.76817			−0.884086	−	0.467325i	$-0.845218\pi$
$13$	−6.37523			−1.76817			−0.884086	+	0.467325i	$0.845218\pi$
$14$	2.39594	−	1.12227i	0.640341	−	0.299938i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.14155	+	1.81377i	0.761937	+	0.439905i	0.829991	−	0.557777i	$-0.188346\pi$
$17$	3.14155	+	1.81377i	0.761937	+	0.439905i	−0.0680536	+	0.997682i	$0.521679\pi$
$18$	−2.70372	−	1.29996i	−0.637273	−	0.306404i
$19$	3.64345	−	2.10355i	0.835865	−	0.482587i	−0.0199914	−	0.999800i	$-0.506364\pi$
$19$	3.64345	−	2.10355i	0.835865	−	0.482587i	0.855857	+	0.517213i	$0.173031\pi$
$20$		0			0
$21$	−0.973048	−	4.47808i	−0.212336	−	0.977197i
$22$			4.95532i			1.05648i
$23$	−0.958379	−	1.65996i	−0.199836	−	0.346126i	0.748639	−	0.662978i	$-0.230708\pi$
$23$	−0.958379	−	1.65996i	−0.199836	−	0.346126i	−0.948475	+	0.316852i	$0.897374\pi$
$24$	−1.65494	+	0.511048i	−0.337813	+	0.104317i
$25$		0			0
$26$	3.18762	+	5.52111i	0.625143	+	1.08278i
$27$	−3.23594	+	4.06555i	−0.622757	+	0.782415i
$28$	−2.16988	−	1.51381i	−0.410069	−	0.286083i
$29$		−	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	$0.517276\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	8.36827	+	1.90726i	1.45673	+	0.332011i
$34$		−	3.62755i		−	0.622119i
$35$		0			0
$36$	0.226058	+	2.99147i	0.0376763	+	0.498578i
$37$	5.04710	−	2.91394i	0.829738	−	0.479050i	−0.0240249	−	0.999711i	$-0.507648\pi$
$37$	5.04710	−	2.91394i	0.829738	−	0.479050i	0.853763	+	0.520662i	$0.174315\pi$
$38$	−3.64345	−	2.10355i	−0.591046	−	0.341241i
$39$	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	$0.302320\pi$
$42$	−3.39161	+	3.08172i	−0.523336	+	0.475520i
$43$			4.64827i			0.708854i	0.935084	+	0.354427i	$0.115324\pi$
$43$			4.64827i			0.708854i	−0.935084	+	0.354427i	$0.884676\pi$
$44$	4.29143	−	2.47766i	0.646958	−	0.373521i
$45$		0			0
$46$	−0.958379	+	1.65996i	−0.141305	+	0.244748i
$47$	−0.526352	+	0.303890i	−0.0767764	+	0.0443269i	−0.537897	−	0.843011i	$-0.680781\pi$
$47$	−0.526352	+	0.303890i	−0.0767764	+	0.0443269i	0.461120	+	0.887338i	$0.347448\pi$
$48$	1.27005	+	1.17770i	0.183316	+	0.169986i
$49$	−6.89780	−	1.19181i	−0.985399	−	0.170259i
$50$		0			0
$51$	−6.12600	−	1.39621i	−0.857812	−	0.195508i
$52$	3.18762	−	5.52111i	0.442043	−	0.765641i
$53$	7.15326	−	12.3898i	0.982576	−	1.70187i	0.330329	−	0.943866i	$-0.392840\pi$
$53$	7.15326	−	12.3898i	0.982576	−	1.70187i	0.652247	−	0.758006i	$-0.273826\pi$
$54$	5.13884	+	0.769634i	0.699307	+	0.104734i
$55$		0			0
$56$	−0.226058	+	2.63608i	−0.0302083	+	0.352260i
$57$	−4.95469	+	5.34323i	−0.656264	+	0.707727i
$58$	−0.693053	+	0.400134i	−0.0910023	+	0.0525402i
$59$	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	$0.263008\pi$
$62$		−	5.03641i		−	0.639624i
$63$	3.89885	+	6.91368i	0.491209	+	0.871042i
$64$	1.00000			0.125000
$65$		0			0
$66$	−2.53241	−	8.20077i	−0.311718	−	1.00944i
$67$	−6.91343	−	3.99147i	−0.844610	−	0.487636i	0.0142186	−	0.999899i	$-0.495474\pi$
$67$	−6.91343	−	3.99147i	−0.844610	−	0.487636i	−0.858829	+	0.512263i	$0.828807\pi$
$68$	−3.14155	+	1.81377i	−0.380969	+	0.219952i
$69$	2.43438	+	2.25736i	0.293065	+	0.271754i
$70$		0			0
$71$		−	2.48759i		−	0.295222i	−0.989045	−	0.147611i	$-0.952842\pi$
$71$		−	2.48759i		−	0.295222i	0.989045	−	0.147611i	$-0.0471584\pi$
$72$	2.47766	−	1.69151i	0.291995	−	0.199346i
$73$	7.54666	−	13.0712i	0.883270	−	1.52987i	0.0355852	−	0.999367i	$-0.488670\pi$
$73$	7.54666	−	13.0712i	0.883270	−	1.52987i	0.847684	−	0.530501i	$-0.177996\pi$
$74$	−5.04710	−	2.91394i	−0.586713	−	0.338739i
$75$		0			0
$76$			4.20710i			0.482587i
$77$	7.50142	−	10.7525i	0.854866	−	1.22536i
$78$	−8.09687	−	7.50809i	−0.916790	−	0.850124i
$79$	1.33404	+	2.31062i	0.150091	+	0.259965i	0.931261	−	0.364354i	$-0.118710\pi$
$79$	1.33404	+	2.31062i	0.150091	+	0.259965i	−0.781170	+	0.624319i	$0.785377\pi$
$80$		0			0
$81$	3.27761	−	8.38196i	0.364178	−	0.931329i
$82$	−3.72581	−	6.45330i	−0.411447	−	0.712648i
$83$		−	7.27215i		−	0.798222i	−0.916903	−	0.399111i	$-0.869319\pi$
$83$		−	7.27215i		−	0.798222i	0.916903	−	0.399111i	$-0.130681\pi$
$84$	4.36465	+	1.39635i	0.476223	+	0.152355i
$85$		0			0
$86$	4.02552	−	2.32413i	0.434083	−	0.250618i
$87$	0.408975	+	1.32440i	0.0438468	+	0.141990i
$88$	−4.29143	−	2.47766i	−0.457468	−	0.264120i
$89$	−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
$92$	1.91676			0.199836
$93$	−8.50521	−	1.93847i	−0.881949	−	0.201009i
$94$	0.526352	+	0.303890i	0.0542891	+	0.0313438i
$95$		0			0
$96$	0.384890	−	1.68874i	0.0392827	−	0.172357i
$97$	17.6562			1.79271			0.896356	−	0.443334i	$-0.146205\pi$
$97$	17.6562			1.79271			0.896356	+	0.443334i	$0.146205\pi$
$98$	2.41676	+	6.56957i	0.244129	+	0.663627i
$99$	−14.8237	+	1.12019i	−1.48984	+	0.112583i
$100$		0			0
$101$	0.574210	−	0.994562i	0.0571361	−	0.0989626i	−0.836043	−	0.548664i	$-0.815136\pi$
$101$	0.574210	−	0.994562i	0.0571361	−	0.0989626i	0.893179	+	0.449702i	$0.148470\pi$
$102$	1.85385	+	6.00338i	0.183558	+	0.594423i
$103$	3.64182	+	6.30781i	0.358839	+	0.621527i	0.987767	−	0.155936i	$-0.0498394\pi$
$103$	3.64182	+	6.30781i	0.358839	+	0.621527i	−0.628928	+	0.777463i	$0.716506\pi$
$104$	−6.37523			−0.625143
$105$		0			0
$106$	−14.3065			−1.38957
$107$	−1.34318	−	2.32646i	−0.129850	−	0.224908i	0.793768	−	0.608221i	$-0.208116\pi$
$107$	−1.34318	−	2.32646i	−0.129850	−	0.224908i	−0.923618	+	0.383313i	$0.874783\pi$
$108$	−1.90290	−	4.83518i	−0.183106	−	0.465266i
$109$	4.51172	−	7.81452i	0.432144	−	0.748495i	−0.564914	−	0.825150i	$-0.691091\pi$
$109$	4.51172	−	7.81452i	0.432144	−	0.748495i	0.997058	+	0.0766547i	$0.0244239\pi$
$110$		0			0
$111$	−6.86349	+	7.40171i	−0.651454	+	0.702540i
$112$	2.39594	−	1.12227i	0.226395	−	0.106044i
$113$	−12.4267			−1.16901			−0.584504	−	0.811391i	$-0.698711\pi$
$113$	−12.4267			−1.16901			−0.584504	+	0.811391i	$0.698711\pi$
$114$	7.10471	+	1.61927i	0.665417	+	0.151659i
$115$		0			0
$116$	0.693053	+	0.400134i	0.0643483	+	0.0371515i
$117$	−15.7957	+	10.7838i	−1.46031	+	0.996958i
$118$	−1.75132			−0.161222
$119$	−5.49142	+	7.87134i	−0.503397	+	0.721565i
$120$		0			0
$121$	6.77761	+	11.7392i	0.616146	+	1.06720i
$122$	−2.96447	−	1.71154i	−0.268390	−	0.154955i
$123$	−12.3320	+	3.80814i	−1.11194	+	0.343368i
$124$	−4.36166	+	2.51820i	−0.391688	+	0.226141i
$125$		0			0
$126$	4.03800	−	6.83334i	0.359734	−	0.608762i
$127$			8.06679i			0.715812i	0.933758	+	0.357906i	$0.116509\pi$
$127$			8.06679i			0.715812i	−0.933758	+	0.357906i	$0.883491\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−2.37549	−	7.69261i	−0.209150	−	0.677297i
$130$		0			0
$131$	1.69151	+	2.92978i	0.147788	+	0.255976i	0.930410	−	0.366522i	$-0.119451\pi$
$131$	1.69151	+	2.92978i	0.147788	+	0.255976i	−0.782622	+	0.622497i	$0.786118\pi$
$132$	−5.83587	+	6.29351i	−0.507947	+	0.547780i
$133$	4.72148	+	10.0799i	0.409404	+	0.874042i
$134$			7.98294i			0.689621i
$135$		0			0
$136$	3.14155	+	1.81377i	0.269386	+	0.155530i
$137$	7.41370	−	12.8409i	0.633395	−	1.09707i	−0.353458	−	0.935451i	$-0.614994\pi$
$137$	7.41370	−	12.8409i	0.633395	−	1.09707i	0.986853	−	0.161622i	$-0.0516725\pi$
$138$	0.737742	−	3.23691i	0.0628007	−	0.275544i
$139$			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
$142$	−2.15432	+	1.24379i	−0.180786	+	0.104377i
$143$	27.3589	+	15.7957i	2.28787	+	1.32090i
$144$	−2.70372	−	1.29996i	−0.225310	−	0.108330i
$145$		0			0
$146$	−15.0933			−1.24913
$147$	12.0245	−	1.55272i	0.991766	−	0.128066i
$148$			5.82789i			0.479050i
$149$	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	$0.325700\pi$
$152$	3.64345	−	2.10355i	0.295523	−	0.170620i
$153$	10.8517	−	0.820036i	0.877308	−	0.0662960i
$154$	−13.0626	−	1.12019i	−1.05261	−	0.0902675i
$155$		0			0
$156$	−2.45377	+	10.7661i	−0.196458	+	0.861981i
$157$	−0.772397	+	1.33783i	−0.0616440	+	0.106770i	−0.895200	−	0.445664i	$-0.852968\pi$
$157$	−0.772397	+	1.33783i	−0.0616440	+	0.106770i	0.833556	+	0.552434i	$0.186301\pi$
$158$	1.33404	−	2.31062i	0.106130	−	0.183823i
$159$	−5.50644	+	24.1601i	−0.436689	+	1.91602i
$160$		0			0
$161$	4.59243	−	2.15111i	0.361934	−	0.169531i
$162$	−8.89780	+	1.35249i	−0.699077	+	0.106262i
$163$	2.92508	−	1.68880i	0.229110	−	0.132277i	−0.381051	−	0.924554i	$-0.624438\pi$
$163$	2.92508	−	1.68880i	0.229110	−	0.132277i	0.610161	+	0.792277i	$0.291105\pi$
$164$	−3.72581	+	6.45330i	−0.290937	+	0.503918i
$165$		0			0
$166$	−6.29787	+	3.63608i	−0.488809	+	0.282214i
$167$		−	12.7685i		−	0.988053i	−0.869447	−	0.494027i	$-0.835525\pi$
$167$		−	12.7685i		−	0.988053i	0.869447	−	0.494027i	$-0.164475\pi$
$168$	−0.973048	−	4.47808i	−0.0750723	−	0.345491i
$169$	27.6436			2.12643
$170$		0			0
$171$	5.46907	−	11.3748i	0.418230	−	0.869853i
$172$	−4.02552	−	2.32413i	−0.306943	−	0.177214i
$173$	−0.214390	+	0.123778i	−0.0162998	+	0.00941068i	−0.508128	−	0.861282i	$-0.669662\pi$
$173$	−0.214390	+	0.123778i	−0.0162998	+	0.00941068i	0.491828	+	0.870692i	$0.336329\pi$
$174$	0.942474	−	1.01638i	0.0714488	−	0.0770517i
$175$		0			0
$176$			4.95532i			0.373521i
$177$	−0.674065	+	2.95753i	−0.0506658	+	0.222301i
$178$	−0.942474	+	1.63241i	−0.0706414	+	0.122355i
$179$	−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	$0.814467\pi$
$182$	−15.2747	+	7.15471i	−1.13223	+	0.530342i
$183$	−4.03134	+	4.34748i	−0.298005	+	0.321375i
$184$	−0.958379	−	1.65996i	−0.0706526	−	0.122374i
$185$		0			0
$186$	2.57384	+	8.33496i	0.188723	+	0.611149i
$187$	−8.98783	−	15.5674i	−0.657255	−	1.13840i
$188$		−	0.607779i		−	0.0443269i
$189$	−9.98558	−	9.44924i	−0.726344	−	0.687331i
$190$		0			0
$191$	0.463759	−	0.267752i	0.0335564	−	0.0193738i	−0.483128	−	0.875550i	$-0.660499\pi$
$191$	0.463759	−	0.267752i	0.0335564	−	0.0193738i	0.516684	+	0.856176i	$0.327166\pi$
$192$	−1.65494	+	0.511048i	−0.119435	+	0.0368817i
$193$	−4.79383	−	2.76772i	−0.345068	−	0.199225i	0.317443	−	0.948277i	$-0.397176\pi$
$193$	−4.79383	−	2.76772i	−0.345068	−	0.199225i	−0.662511	+	0.749052i	$0.730509\pi$
$194$	−8.82809	−	15.2907i	−0.633820	−	1.09781i
$195$		0			0
$196$	4.48104	−	5.37776i	0.320074	−	0.384126i
$197$	−0.666454			−0.0474829			−0.0237414	−	0.999718i	$-0.507558\pi$
$197$	−0.666454			−0.0474829			−0.0237414	+	0.999718i	$0.507558\pi$
$198$	8.38196	+	12.2776i	0.595680	+	0.872531i
$199$	7.81326	+	4.51099i	0.553867	+	0.319775i	0.750680	−	0.660666i	$-0.229726\pi$
$199$	7.81326	+	4.51099i	0.553867	+	0.319775i	−0.196813	+	0.980441i	$0.563059\pi$
$200$		0			0
$201$	13.4812	+	3.07256i	0.950887	+	0.216722i
$202$	−1.14842			−0.0808026
$203$	2.10957	+	0.180907i	0.148063	+	0.0126972i
$204$	4.27215	−	4.60717i	0.299110	−	0.322566i
$205$		0			0
$206$	3.64182	−	6.30781i	0.253737	−	0.439486i
$207$	−5.18237	−	2.49171i	−0.360200	−	0.173186i
$208$	3.18762	+	5.52111i	0.221021	+	0.382820i
$209$	−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	$0.371183\pi$
$212$	7.15326	+	12.3898i	0.491288	+	0.850936i
$213$	1.27128	+	4.11681i	0.0871064	+	0.282079i
$214$	−1.34318	+	2.32646i	−0.0918181	+	0.159034i
$215$		0			0
$216$	−3.23594	+	4.06555i	−0.220178	+	0.276625i
$217$	−7.62417	+	10.9284i	−0.517562	+	0.741868i
$218$	−9.02343			−0.611144
$219$	−5.80927	+	25.4888i	−0.392554	+	1.72237i
$220$		0			0
$221$	−20.0281	−	11.5632i	−1.34724	−	0.777827i
$222$	9.84182	+	2.24310i	0.660540	+	0.150547i
$223$	−5.23397			−0.350493			−0.175246	−	0.984525i	$-0.556072\pi$
$223$	−5.23397			−0.350493			−0.175246	+	0.984525i	$0.556072\pi$
$224$	−2.16988	−	1.51381i	−0.144981	−	0.101146i
$225$		0			0
$226$	6.21336	+	10.7619i	0.413306	+	0.715868i
$227$	11.6587	+	6.73117i	0.773817	+	0.446763i	0.834234	−	0.551410i	$-0.185910\pi$
$227$	11.6587	+	6.73117i	0.773817	+	0.446763i	−0.0604178	+	0.998173i	$0.519243\pi$
$228$	−2.15003	−	6.96250i	−0.142389	−	0.461103i
$229$	−14.3082	+	8.26082i	−0.945509	+	0.545890i	−0.891683	−	0.452660i	$-0.850475\pi$
$229$	−14.3082	+	8.26082i	−0.945509	+	0.545890i	−0.0538263	+	0.998550i	$0.517142\pi$
$230$		0			0
$231$	−6.91939	+	21.6283i	−0.455262	+	1.42303i
$232$		−	0.800269i		−	0.0525402i
$233$	−9.31796	−	16.1392i	−0.610440	−	1.05731i	−0.991166	−	0.132625i	$-0.957659\pi$
$233$	−9.31796	−	16.1392i	−0.610440	−	1.05731i	0.380727	−	0.924688i	$-0.375674\pi$
$234$	17.2368	+	8.28757i	1.12681	+	0.541775i
$235$		0			0
$236$	0.875658	+	1.51668i	0.0570005	+	0.0987278i
$237$	−3.38859	−	3.14218i	−0.220113	−	0.204107i
$238$	9.56249	+	0.820036i	0.619844	+	0.0531551i
$239$		−	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	$0.922253\pi$
$242$	6.77761	−	11.7392i	0.435681	−	0.754622i
$243$	−1.14066	+	15.5467i	−0.0731735	+	0.997319i
$244$			3.42307i			0.219140i
$245$		0			0
$246$	9.46395	+	8.77576i	0.603399	+	0.559522i
$247$	−23.2279	+	13.4106i	−1.47795	+	0.853297i
$248$	4.36166	+	2.51820i	0.276966	+	0.159906i
$249$	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	$0.527369\pi$
$252$	−7.93685	−	0.0803398i	−0.499974	−	0.00506093i
$253$			9.49815i			0.597144i
$254$	6.98605	−	4.03340i	0.438344	−	0.253078i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.96256	−	5.75189i	0.621448	−	0.358793i	−0.155985	−	0.987759i	$-0.549855\pi$
$257$	9.96256	−	5.75189i	0.621448	−	0.358793i	0.777432	+	0.628966i	$0.216522\pi$
$258$	−5.47425	+	5.90354i	−0.340812	+	0.367538i
$259$	6.54044	+	13.9633i	0.406403	+	0.867635i
$260$		0			0
$261$	−1.35366	−	1.98279i	−0.0837895	−	0.122732i
$262$	1.69151	−	2.92978i	0.104502	−	0.181002i
$263$	−6.39277	+	11.0726i	−0.394195	+	0.682766i	−0.992998	−	0.118130i	$-0.962310\pi$
$263$	−6.39277	+	11.0726i	−0.394195	+	0.682766i	0.598803	+	0.800896i	$0.295643\pi$
$264$	8.36827	+	1.90726i	0.515032	+	0.117383i
$265$		0			0
$266$	6.36874	−	9.12889i	0.390493	−	0.559728i
$267$	2.39398	+	2.21990i	0.146509	+	0.135856i
$268$	6.91343	−	3.99147i	0.422305	−	0.243818i
$269$	−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	$0.0994888\pi$
$272$		−	3.62755i		−	0.219952i
$273$	6.20340	+	28.5488i	0.375447	+	1.72785i
$274$	−14.8274			−0.895756
$275$		0			0
$276$	−3.17212	+	0.979554i	−0.190939	+	0.0589622i
$277$	6.76068	+	3.90328i	0.406210	+	0.234525i	0.689160	−	0.724609i	$-0.257980\pi$
$277$	6.76068	+	3.90328i	0.406210	+	0.234525i	−0.282950	+	0.959135i	$0.591313\pi$
$278$	6.27582	−	3.62334i	0.376398	−	0.217314i
$279$	15.0663	−	1.13852i	0.901994	−	0.0681615i
$280$		0			0
$281$			23.0892i			1.37738i	0.725054	+	0.688692i	$0.241815\pi$
$281$			23.0892i			1.37738i	−0.725054	+	0.688692i	$0.758185\pi$
$282$	−1.02638	−	0.233928i	−0.0611203	−	0.0139302i
$283$	12.3752	−	21.4345i	0.735631	−	1.27415i	−0.218815	−	0.975766i	$-0.570219\pi$
$283$	12.3752	−	21.4345i	0.735631	−	1.27415i	0.954446	−	0.298384i	$-0.0964477\pi$
$284$	2.15432	+	1.24379i	0.127835	+	0.0738056i
$285$		0			0
$286$		−	31.5913i		−	1.86803i
$287$	−1.68450	+	19.6431i	−0.0994329	+	1.15949i
$288$	0.226058	+	2.99147i	0.0133206	+	0.176274i
$289$	−1.92045	−	3.32632i	−0.112968	−	0.195666i
$290$		0			0
$291$	−29.2199	+	9.02314i	−1.71290	+	0.528946i
$292$	7.54666	+	13.0712i	0.441635	+	0.764934i
$293$			25.3384i			1.48029i	0.672449	+	0.740143i	$0.265242\pi$
$293$			25.3384i			1.48029i	−0.672449	+	0.740143i	$0.734758\pi$
$294$	−7.35696	−	9.63718i	−0.429066	−	0.562052i
$295$		0			0
$296$	5.04710	−	2.91394i	0.293357	−	0.169370i
$297$	23.9599	−	9.42947i	1.39029	−	0.547153i
$298$	−5.70973	−	3.29651i	−0.330756	−	0.190962i
$299$	6.10989	+	10.5826i	0.353344	+	0.612010i
$300$		0			0
$301$	−12.2532	−	1.05078i	−0.706262	−	0.0605659i
$302$	11.7743			0.677538
$303$	−0.442016	+	1.93939i	−0.0253932	+	0.111415i
$304$	−3.64345	−	2.10355i	−0.208966	−	0.120647i
$305$		0			0
$306$	−6.13602	−	8.98783i	−0.350773	−	0.513800i
$307$	13.1396			0.749919			0.374960	−	0.927041i	$-0.377657\pi$
$307$	13.1396			0.749919			0.374960	+	0.927041i	$0.377657\pi$
$308$	5.56119	+	11.8726i	0.316878	+	0.676507i
$309$	−9.25059	−	8.57792i	−0.526248	−	0.487981i
$310$		0			0
$311$	−3.80332	+	6.58755i	−0.215667	+	0.373545i	−0.953479	−	0.301461i	$-0.902526\pi$
$311$	−3.80332	+	6.58755i	−0.215667	+	0.373545i	0.737812	+	0.675006i	$0.235859\pi$
$312$	10.5506	−	3.25805i	0.597312	−	0.184451i
$313$	−6.21272	−	10.7608i	−0.351164	−	0.608234i	0.635290	−	0.772274i	$-0.280881\pi$
$313$	−6.21272	−	10.7608i	−0.351164	−	0.608234i	−0.986454	+	0.164040i	$0.947547\pi$
$314$	1.54479			0.0871777
$315$		0			0
$316$	−2.66807			−0.150091
$317$	−13.8679	−	24.0199i	−0.778898	−	1.34909i	−0.932577	−	0.360971i	$-0.882445\pi$
$317$	−13.8679	−	24.0199i	−0.778898	−	1.34909i	0.153679	−	0.988121i	$-0.450888\pi$
$318$	23.6765	−	7.31132i	1.32771	−	0.409998i
$319$	−1.98279	+	3.43430i	−0.111015	+	0.192284i
$320$		0			0
$321$	3.41182	+	3.16373i	0.190429	+	0.176582i
$322$	−4.15913	−	2.90161i	−0.231779	−	0.161700i
$323$	15.2614			0.849169
$324$	5.62019	+	7.02947i	0.312233	+	0.390526i
$325$		0			0
$326$	−2.92508	−	1.68880i	−0.162005	−	0.0935337i
$327$	−3.47303	+	15.2383i	−0.192059	+	0.842678i
$328$	7.45163			0.411447
$329$	−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	$0.938360\pi$
$332$	6.29787	+	3.63608i	0.345640	+	0.199556i
$333$	7.57604	−	15.7570i	0.415165	−	0.863477i
$334$	−11.0578	+	6.38423i	−0.605056	+	0.349329i
$335$		0			0
$336$	−3.39161	+	3.08172i	−0.185027	+	0.168122i
$337$		−	5.58238i		−	0.304092i	−0.988373	−	0.152046i	$-0.951414\pi$
$337$		−	5.58238i		−	0.304092i	0.988373	−	0.152046i	$-0.0485861\pi$
$338$	−13.8218	−	23.9401i	−0.751807	−	1.30217i
$339$	20.5655	−	6.35064i	1.11696	−	0.344920i
$340$		0			0
$341$	−12.4785	−	21.6134i	−0.675749	−	1.17043i
$342$	−12.5854	+	0.951048i	−0.680541	+	0.0514268i
$343$	4.70101	−	17.9137i	0.253831	−	0.967249i
$344$			4.64827i			0.250618i
$345$		0			0
$346$	0.214390	+	0.123778i	0.0115257	+	0.00665435i
$347$	−15.9546	+	27.6342i	−0.856489	+	1.48348i	0.0187674	+	0.999824i	$0.494026\pi$
$347$	−15.9546	+	27.6342i	−0.856489	+	1.48348i	−0.875257	+	0.483659i	$0.839308\pi$
$348$	−1.35145	−	0.308016i	−0.0724453	−	0.0165114i
$349$		−	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
$352$	4.29143	−	2.47766i	0.228734	−	0.132060i
$353$	12.6446	+	7.30038i	0.673006	+	0.388560i	0.797215	−	0.603696i	$-0.206306\pi$
$353$	12.6446	+	7.30038i	0.673006	+	0.388560i	−0.124209	+	0.992256i	$0.539639\pi$
$354$	2.89833	−	0.895006i	0.154044	−	0.0475690i
$355$		0			0
$356$	1.88495			0.0999021
$357$	5.06534	−	15.8330i	0.268086	−	0.837970i
$358$			19.5963i			1.03570i
$359$	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
$362$	12.8261	−	7.40517i	0.674127	−	0.389207i
$363$	−17.2158	−	15.9639i	−0.903595	−	0.837889i
$364$	13.8335	+	9.65089i	0.725072	+	0.505844i
$365$		0			0
$366$	5.78070	+	1.31751i	0.302162	+	0.0688672i
$367$	0.678660	−	1.17547i	0.0354258	−	0.0613592i	−0.847769	−	0.530366i	$-0.822055\pi$
$367$	0.678660	−	1.17547i	0.0354258	−	0.0613592i	0.883195	+	0.469007i	$0.155388\pi$
$368$	−0.958379	+	1.65996i	−0.0499590	+	0.0865314i
$369$	18.4626	−	12.6045i	0.961125	−	0.656163i
$370$		0			0
$371$	31.0434	+	21.6574i	1.61170	+	1.12439i
$372$	5.93136	−	6.39649i	0.307527	−	0.331643i
$373$	29.5397	−	17.0548i	1.52951	−	0.883062i	0.530125	−	0.847919i	$-0.322145\pi$
$373$	29.5397	−	17.0548i	1.52951	−	0.883062i	0.999382	−	0.0351422i	$-0.0111884\pi$
$374$	−8.98783	+	15.5674i	−0.464750	+	0.804970i
$375$		0			0
$376$	−0.526352	+	0.303890i	−0.0271445	+	0.0156719i
$377$			5.10190i			0.262761i
$378$	−3.19049	+	13.3724i	−0.164101	+	0.687801i
$379$	1.53951			0.0790795			0.0395398	−	0.999218i	$-0.487411\pi$
$379$	1.53951			0.0790795			0.0395398	+	0.999218i	$0.487411\pi$
$380$		0			0
$381$	−4.12252	−	13.3501i	−0.211203	−	0.683945i
$382$	−0.463759	−	0.267752i	−0.0237280	−	0.0136994i
$383$	−28.1685	+	16.2631i	−1.43934	+	0.831004i	−0.997804	−	0.0662394i	$-0.978900\pi$
$383$	−28.1685	+	16.2631i	−1.43934	+	0.831004i	−0.441537	+	0.897243i	$0.645567\pi$
$384$	1.27005	+	1.17770i	0.0648120	+	0.0600991i
$385$		0			0
$386$			5.53544i			0.281747i
$387$	7.86258	+	11.5168i	0.399677	+	0.585433i
$388$	−8.82809	+	15.2907i	−0.448178	+	0.776267i
$389$	−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
$392$	−6.89780	−	1.19181i	−0.348391	−	0.0601956i
$393$	−4.29660	−	3.98417i	−0.216735	−	0.200975i
$394$	0.333227	+	0.577166i	0.0167877	+	0.0290772i
$395$		0			0
$396$	6.44174	−	13.3978i	0.323709	−	0.673265i
$397$	6.51194	+	11.2790i	0.326825	+	0.566077i	0.981880	−	0.189504i	$-0.0606879\pi$
$397$	6.51194	+	11.2790i	0.326825	+	0.566077i	−0.655055	+	0.755581i	$0.727355\pi$
$398$		−	9.02198i		−	0.452231i
$399$	−12.9651	−	14.2688i	−0.649067	−	0.714334i
$400$		0			0
$401$	−20.2676	+	11.7015i	−1.01211	+	0.584345i	−0.911810	−	0.410612i	$-0.865315\pi$
$401$	−20.2676	+	11.7015i	−1.01211	+	0.584345i	−0.100305	+	0.994957i	$0.531982\pi$
$402$	−4.07966	−	13.2113i	−0.203475	−	0.658920i
$403$	−27.8066	−	16.0541i	−1.38514	−	0.799714i
$404$	0.574210	+	0.994562i	0.0285680	+	0.0494813i
$405$		0			0
$406$	−0.898114	−	1.91739i	−0.0445727	−	0.0951587i
$407$	−28.8791			−1.43148
$408$	−6.12600	−	1.39621i	−0.303282	−	0.0691226i
$409$	−11.4311	−	6.59972i	−0.565229	−	0.326335i	0.190013	−	0.981782i	$-0.439147\pi$
$409$	−11.4311	−	6.59972i	−0.565229	−	0.326335i	−0.755242	+	0.655447i	$0.772480\pi$
$410$		0			0
$411$	−5.70692	+	25.0397i	−0.281502	+	1.23512i
$412$	−7.28364			−0.358839
$413$	3.80015	+	2.65116i	0.186993	+	0.130455i
$414$	0.433299	+	5.73392i	0.0212955	+	0.281807i
$415$		0			0
$416$	3.18762	−	5.52111i	0.156286	−	0.270695i
$417$	−3.70340	−	11.9928i	−0.181356	−	0.587292i
$418$	10.4238	+	18.0545i	0.509843	+	0.883073i
$419$	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	$0.294609\pi$
$422$	−5.71931	−	9.90613i	−0.278412	−	0.482223i
$423$	−0.790091	+	1.64326i	−0.0384155	+	0.0798982i
$424$	7.15326	−	12.3898i	0.347393	−	0.601703i
$425$		0			0
$426$	2.92963	−	3.15936i	0.141941	−	0.153072i
$427$	3.84160	+	8.20147i	0.185908	+	0.396897i
$428$	2.68637			0.129850
$429$	−53.3497	−	12.1592i	−2.57575	−	0.587052i
$430$		0			0
$431$	−2.89638	−	1.67223i	−0.139514	−	0.0805483i	0.428619	−	0.903486i	$-0.359000\pi$
$431$	−2.89638	−	1.67223i	−0.139514	−	0.0805483i	−0.568132	+	0.822937i	$0.692334\pi$
$432$	5.13884	+	0.769634i	0.247242	+	0.0370290i
$433$	−14.6756			−0.705264			−0.352632	−	0.935762i	$-0.614713\pi$
$433$	−14.6756			−0.705264			−0.352632	+	0.935762i	$0.614713\pi$
$434$	13.2764	+	1.13852i	0.637285	+	0.0546507i
$435$		0			0
$436$	4.51172	+	7.81452i	0.216072	+	0.374248i
$437$	−6.98361	−	4.03199i	−0.334072	−	0.192876i
$438$	24.9786	−	7.71340i	1.19352	−	0.368561i
$439$	5.70453	−	3.29351i	0.272262	−	0.157191i	−0.357653	−	0.933855i	$-0.616423\pi$
$439$	5.70453	−	3.29351i	0.272262	−	0.157191i	0.629915	+	0.776664i	$0.283090\pi$
$440$		0			0
$441$	−19.1064	+	8.71477i	−0.909827	+	0.414989i
$442$			23.1265i			1.10001i
$443$	−20.3605	−	35.2654i	−0.967357	−	1.67551i	−0.703144	−	0.711047i	$-0.748221\pi$
$443$	−20.3605	−	35.2654i	−0.967357	−	1.67551i	−0.264213	−	0.964464i	$-0.585112\pi$
$444$	−2.97833	−	9.64481i	−0.141345	−	0.457723i
$445$		0			0
$446$	2.61699	+	4.53275i	0.123918	+	0.214632i
$447$	−7.76459	+	8.37348i	−0.367253	+	0.396052i
$448$	−0.226058	+	2.63608i	−0.0106802	+	0.124543i
$449$			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
$452$	6.21336	−	10.7619i	0.292252	−	0.506195i
$453$	4.53183	−	19.8839i	0.212924	−	0.934226i
$454$		−	13.4623i		−	0.631819i
$455$		0			0
$456$	−4.95469	+	5.34323i	−0.232024	+	0.250219i
$457$	−7.48533	+	4.32166i	−0.350149	+	0.202159i	−0.664751	−	0.747065i	$-0.731462\pi$
$457$	−7.48533	+	4.32166i	−0.350149	+	0.202159i	0.314602	+	0.949224i	$0.398129\pi$
$458$	14.3082	+	8.26082i	0.668576	+	0.386003i
$459$	−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	$0.304141\pi$
$462$	22.1903	−	4.82176i	1.03239	−	0.224329i
$463$			17.9797i			0.835589i	0.908542	+	0.417794i	$0.137197\pi$
$463$			17.9797i			0.835589i	−0.908542	+	0.417794i	$0.862803\pi$
$464$	−0.693053	+	0.400134i	−0.0321742	+	0.0185758i
$465$		0			0
$466$	−9.31796	+	16.1392i	−0.431646	+	0.747633i
$467$	−1.10282	+	0.636712i	−0.0510323	+	0.0294635i	−0.525299	−	0.850918i	$-0.676047\pi$
$467$	−1.10282	+	0.636712i	−0.0510323	+	0.0294635i	0.474267	+	0.880381i	$0.342713\pi$
$468$	−1.44117	−	19.0713i	−0.0666182	−	0.881572i
$469$	12.0847	−	17.3220i	0.558018	−	0.799857i
$470$		0			0
$471$	0.594576	−	2.60876i	0.0273966	−	0.120205i
$472$	0.875658	−	1.51668i	0.0403054	−	0.0698111i
$473$	11.5168	−	19.9477i	0.529545	−	0.917198i
$474$	−1.02692	+	4.50570i	−0.0471678	+	0.206954i
$475$		0			0
$476$	−4.07107	−	8.69138i	−0.186597	−	0.398369i
$477$	−3.23411	−	42.7976i	−0.148080	−	1.95957i
$478$	−21.4831	+	12.4032i	−0.982612	+	0.567311i
$479$	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
$482$			22.3364i			1.01740i
$483$	−6.50089	+	5.90692i	−0.295801	+	0.268774i
$484$	−13.5552			−0.616146
$485$		0			0
$486$	14.0341	−	6.78549i	0.636602	−	0.307796i
$487$	−34.5502	−	19.9476i	−1.56562	−	0.903910i	−0.996670	−	0.0815361i	$-0.974017\pi$
$487$	−34.5502	−	19.9476i	−1.56562	−	0.903910i	−0.568947	−	0.822374i	$-0.692649\pi$
$488$	2.96447	−	1.71154i	0.134195	−	0.0774776i
$489$	−3.97778	+	4.28971i	−0.179881	+	0.193988i
$490$		0			0
$491$			15.9778i			0.721069i	0.932746	+	0.360535i	$0.117406\pi$
$491$			15.9778i			0.721069i	−0.932746	+	0.360535i	$0.882594\pi$
$492$	2.86806	−	12.5839i	0.129302	−	0.567326i
$493$	1.45151	−	2.51408i	0.0653725	−	0.113229i
$494$	23.2279	+	13.4106i	1.04507	+	0.603372i
$495$		0			0
$496$		−	5.03641i		−	0.226141i
$497$	6.55747	+	0.562340i	0.294143	+	0.0252244i
$498$	8.56439	−	9.23600i	0.383780	−	0.413875i
$499$	−6.90313	−	11.9566i	−0.309027	−	0.535250i	0.669123	−	0.743152i	$-0.266670\pi$
$499$	−6.90313	−	11.9566i	−0.309027	−	0.535250i	−0.978150	+	0.207902i	$0.933337\pi$
$500$		0			0
$501$	6.52529	+	21.1310i	0.291528	+	0.944066i
$502$	1.36054	+	2.35652i	0.0607237	+	0.105176i
$503$			2.11183i			0.0941620i	0.998891	+	0.0470810i	$0.0149919\pi$
$503$			2.11183i			0.0941620i	−0.998891	+	0.0470810i	$0.985008\pi$
$504$	3.89885	+	6.91368i	0.173668	+	0.307960i
$505$		0			0
$506$	8.22564	−	4.74908i	0.365674	−	0.211122i
$507$	−45.7485	+	14.1272i	−2.03176	+	0.627411i
$508$	−6.98605	−	4.03340i	−0.309956	−	0.178953i
$509$	−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
$512$	1.00000			0.0441942
$513$	−3.23792	+	21.6196i	−0.142958	+	0.954528i
$514$	−9.96256	−	5.75189i	−0.439430	−	0.253705i
$515$		0			0
$516$	7.84974	+	1.78907i	0.345566	+	0.0787596i
$517$	3.01174			0.132456
$518$	8.82232	−	12.6458i	0.387630	−	0.555625i
$519$	0.291546	−	0.314409i	0.0127975	−	0.0138010i
$520$		0			0
$521$	12.4676	−	21.5945i	0.546216	−	0.946073i	−0.452314	−	0.891859i	$-0.649401\pi$
$521$	12.4676	−	21.5945i	0.546216	−	0.946073i	0.998529	−	0.0542143i	$-0.0172654\pi$
$522$	−1.04032	+	2.16370i	−0.0455336	+	0.0947026i
$523$	−9.85929	−	17.0768i	−0.431116	−	0.746716i	0.565853	−	0.824506i	$-0.308547\pi$
$523$	−9.85929	−	17.0768i	−0.431116	−	0.746716i	−0.996970	+	0.0777903i	$0.975214\pi$
$524$	−3.38301			−0.147788
$525$		0			0
$526$	12.7855			0.557476
$527$	9.13490	+	15.8221i	0.397923	+	0.689222i
$528$	−2.53241	−	8.20077i	−0.110209	−	0.356893i
$529$	9.66302	−	16.7368i	0.420131	−	0.727689i
$530$		0			0
$531$	−0.395899	−	5.23901i	−0.0171806	−	0.227354i
$532$	−11.0902	−	0.951048i	−0.480822	−	0.0412332i
$533$	−47.5059			−2.05771
$534$	0.725498	−	3.18320i	0.0313954	−	0.137750i
$535$		0			0
$536$	−6.91343	−	3.99147i	−0.298615	−	0.172405i
$537$	33.0932	+	7.54243i	1.42808	+	0.325480i
$538$	11.6915			0.504057
$539$	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	$0.774436\pi$
$542$	−19.1130	−	11.0349i	−0.820975	−	0.473990i
$543$	−7.56879	−	24.5102i	−0.324808	−	1.05184i
$544$	−3.14155	+	1.81377i	−0.134693	+	0.0777649i
$545$		0			0
$546$	21.6223	−	19.6467i	0.925348	−	0.840801i
$547$		−	33.5472i		−	1.43437i	−0.696881	−	0.717187i	$-0.745430\pi$
$547$		−	33.5472i		−	1.43437i	0.696881	−	0.717187i	$-0.254570\pi$
$548$	7.41370	+	12.8409i	0.316698	+	0.548536i
$549$	4.44987	−	9.25502i	0.189916	−	0.394995i
$550$		0			0
$551$	−1.68340	−	2.91574i	−0.0717154	−	0.124215i
$552$	2.43438	+	2.25736i	0.103614	+	0.0960796i
$553$	−6.39254	+	2.99429i	−0.271838	+	0.127330i
$554$		−	7.80656i		−	0.331669i
$555$		0			0
$556$	−6.27582	−	3.62334i	−0.266154	−	0.153664i
$557$	2.67514	−	4.63348i	0.113349	−	0.196327i	−0.803769	−	0.594941i	$-0.797175\pi$
$557$	2.67514	−	4.63348i	0.113349	−	0.196327i	0.917119	+	0.398614i	$0.130509\pi$
$558$	−8.51912	−	12.4785i	−0.360643	−	0.528257i
$559$		−	29.6338i		−	1.25338i
$560$		0			0
$561$	22.8300	+	21.1699i	0.963883	+	0.893793i
$562$	19.9958	−	11.5446i	0.843472	−	0.486979i
$563$	−25.4066	−	14.6685i	−1.07076	−	0.618205i	−0.142372	−	0.989813i	$-0.545473\pi$
$563$	−25.4066	−	14.6685i	−1.07076	−	0.618205i	−0.928390	+	0.371609i	$0.878806\pi$
$564$	0.310604	+	1.00584i	0.0130788	+	0.0423535i
$565$		0			0
$566$	−24.7505			−1.04034
$567$	21.3546	+	10.5348i	0.896807	+	0.442421i
$568$		−	2.48759i		−	0.104377i
$569$	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	$-0.0611473\pi$
$572$	−27.3589	+	15.7957i	−1.14393	+	0.660450i
$573$	−0.630661	+	0.680116i	−0.0263462	+	0.0284123i
$574$	17.8536	−	8.36271i	0.745196	−	0.349053i
$575$		0			0
$576$	2.47766	−	1.69151i	0.103236	−	0.0704795i
$577$	16.0385	−	27.7794i	0.667689	−	1.15647i	−0.310859	−	0.950456i	$-0.600617\pi$
$577$	16.0385	−	27.7794i	0.667689	−	1.15647i	0.978549	−	0.206016i	$-0.0660499\pi$
$578$	−1.92045	+	3.32632i	−0.0798802	+	0.138357i
$579$	9.34795	+	2.13054i	0.388488	+	0.0885422i
$580$		0			0
$581$	19.1699	+	1.64393i	0.795303	+	0.0682017i
$582$	22.4242	+	20.7936i	0.929515	+	0.861924i
$583$	−61.3955	+	35.4467i	−2.54274	+	1.46805i
$584$	7.54666	−	13.0712i	0.312283	−	0.540890i
$585$		0			0
$586$	21.9437	−	12.6692i	0.906487	−	0.523360i
$587$			1.93731i			0.0799612i	0.999200	+	0.0399806i	$0.0127296\pi$
$587$			1.93731i			0.0799612i	−0.999200	+	0.0399806i	$0.987270\pi$
$588$	−4.66756	+	11.1899i	−0.192487	+	0.461464i
$589$	21.1887			0.873063
$590$		0			0
$591$	1.10294	−	0.340590i	0.0453690	−	0.0140100i
$592$	−5.04710	−	2.91394i	−0.207435	−	0.119762i
$593$	−9.75274	+	5.63074i	−0.400497	+	0.231227i	−0.686698	−	0.726942i	$-0.740941\pi$
$593$	−9.75274	+	5.63074i	−0.400497	+	0.231227i	0.286201	+	0.958169i	$0.407607\pi$
$594$	−20.1461	−	16.0351i	−0.826604	−	0.657929i
$595$		0			0
$596$			6.59303i			0.270061i
$597$	−15.2358	−	3.47247i	−0.623560	−	0.142119i
$598$	6.10989	−	10.5826i	0.249852	−	0.432756i
$599$	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	$0.882348\pi$
$602$	5.21659	+	11.1370i	0.212613	+	0.453909i
$603$	−23.8807	+	1.80461i	−0.972499	+	0.0734893i
$604$	−5.88717	−	10.1969i	−0.239546	−	0.414905i
$605$		0			0
$606$	1.90057	−	0.586898i	0.0772053	−	0.0238411i
$607$	−9.17497	−	15.8915i	−0.372400	−	0.645016i	0.617534	−	0.786544i	$-0.288132\pi$
$607$	−9.17497	−	15.8915i	−0.372400	−	0.645016i	−0.989934	+	0.141528i	$0.954799\pi$
$608$			4.20710i			0.170620i
$609$	−3.58366	+	0.778699i	−0.145217	+	0.0315545i
$610$		0			0
$611$	3.35562	−	1.93737i	0.135754	−	0.0783775i
$612$	−4.71568	+	9.80787i	−0.190620	+	0.396460i
$613$	0.547045	+	0.315836i	0.0220949	+	0.0127565i	0.511007	−	0.859577i	$-0.329273\pi$
$613$	0.547045	+	0.315836i	0.0220949	+	0.0127565i	−0.488912	+	0.872333i	$0.662606\pi$
$614$	−6.56982	−	11.3793i	−0.265136	−	0.459230i
$615$		0			0
$616$	7.50142	−	10.7525i	0.302241	−	0.433229i
$617$	−15.5902			−0.627638			−0.313819	−	0.949483i	$-0.601608\pi$
$617$	−15.5902			−0.627638			−0.313819	+	0.949483i	$0.601608\pi$
$618$	−2.80340	+	12.3002i	−0.112769	+	0.494787i
$619$	−10.9863	−	6.34296i	−0.441578	−	0.254945i	0.262689	−	0.964881i	$-0.415391\pi$
$619$	−10.9863	−	6.34296i	−0.441578	−	0.254945i	−0.704267	+	0.709936i	$0.748724\pi$
$620$		0			0
$621$	9.84991	+	1.47520i	0.395263	+	0.0591978i
$622$	7.60664			0.304999
$623$	4.51622	−	2.11541i	0.180938	−	0.0847522i
$624$	−8.09687	−	7.50809i	−0.324134	−	0.300564i
$625$		0			0
$626$	−6.21272	+	10.7608i	−0.248310	+	0.430086i
$627$	34.5014	−	10.6541i	1.37785	−	0.425483i
$628$	−0.772397	−	1.33783i	−0.0308220	−	0.0533852i
$629$	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	$0.537854\pi$
$632$	1.33404	+	2.31062i	0.0530651	+	0.0919115i
$633$	−18.9302	+	5.84568i	−0.752409	+	0.232345i
$634$	−13.8679	+	24.0199i	−0.550764	+	0.953952i
$635$		0			0
$636$	−18.1700	−	16.8488i	−0.720488	−	0.668097i
$637$	43.9751	+	7.59808i	1.74235	+	0.301047i
$638$	3.96559			0.156999
$639$	−4.20778	−	6.16340i	−0.166457	−	0.243820i
$640$		0			0
$641$	11.2070	+	6.47036i	0.442649	+	0.255564i	0.704721	−	0.709485i	$-0.251072\pi$
$641$	11.2070	+	6.47036i	0.442649	+	0.255564i	−0.262071	+	0.965048i	$0.584406\pi$
$642$	1.03396	−	4.53659i	0.0408070	−	0.179045i
$643$	27.7420			1.09404			0.547019	−	0.837120i	$-0.315763\pi$
$643$	27.7420			1.09404			0.547019	+	0.837120i	$0.315763\pi$
$644$	−0.433299	+	5.05272i	−0.0170744	+	0.199105i
$645$		0			0
$646$	−7.63072	−	13.2168i	−0.300227	−	0.520008i
$647$	40.5050	+	23.3856i	1.59242	+	0.919382i	0.992891	+	0.119027i	$0.0379774\pi$
$647$	40.5050	+	23.3856i	1.59242	+	0.919382i	0.599526	+	0.800356i	$0.295356\pi$
$648$	3.27761	−	8.38196i	0.128756	−	0.329275i
$649$	−7.51566	+	4.33917i	−0.295015	+	0.170327i
$650$		0			0
$651$	7.03261	−	21.9822i	0.275630	−	0.861549i
$652$			3.37759i			0.132277i
$653$	15.7992	+	27.3651i	0.618271	+	1.07088i	0.989801	+	0.142456i	$0.0455001\pi$
$653$	15.7992	+	27.3651i	0.618271	+	1.07088i	−0.371530	+	0.928421i	$0.621167\pi$
$654$	14.9332	−	4.61140i	0.583936	−	0.180320i
$655$		0			0
$656$	−3.72581	−	6.45330i	−0.145469	−	0.251959i
$657$	−3.41197	−	45.1512i	−0.133113	−	1.76152i
$658$	−0.920062	+	1.31881i	−0.0358678	+	0.0514125i
$659$			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	$0.753522\pi$
$662$	−5.89462	+	10.2098i	−0.229101	+	0.396814i
$663$	39.0547	+	8.90115i	1.51676	+	0.345692i
$664$		−	7.27215i		−	0.282214i
$665$		0			0
$666$	−17.4340	+	1.31744i	−0.675552	+	0.0510498i
$667$	−1.32841	+	0.766960i	−0.0514364	+	0.0296968i
$668$	11.0578	+	6.38423i	0.427840	+	0.247013i
$669$	8.66191	−	2.67481i	0.334889	−	0.103414i
$670$		0			0
$671$	−16.9624			−0.654827
$672$	4.36465	+	1.39635i	0.168370	+	0.0538656i
$673$		−	21.1836i		−	0.816568i	−0.912855	−	0.408284i	$-0.866127\pi$
$673$		−	21.1836i		−	0.816568i	0.912855	−	0.408284i	$-0.133873\pi$
$674$	−4.83448	+	2.79119i	−0.186217	+	0.107513i
$675$		0			0
$676$	−13.8218	+	23.9401i	−0.531608	+	0.920771i
$677$	−41.8606	+	24.1682i	−1.60883	+	0.928860i	−0.619202	+	0.785232i	$0.712544\pi$
$677$	−41.8606	+	24.1682i	−1.60883	+	0.928860i	−0.989632	+	0.143628i	$0.954123\pi$
$678$	−15.7826	−	14.6349i	−0.606126	−	0.562050i
$679$	−3.99132	+	46.5430i	−0.153173	+	1.78616i
$680$		0			0
$681$	−22.7344	−	5.18152i	−0.871186	−	0.198556i
$682$	−12.4785	+	21.6134i	−0.477827	+	0.827620i
$683$	13.1638	−	22.8004i	0.503699	−	0.872433i	−0.496291	−	0.868156i	$-0.665305\pi$
$683$	13.1638	−	22.8004i	0.503699	−	0.872433i	0.999991	−	0.00427708i	$-0.00136144\pi$
$684$	7.11633	+	10.4238i	0.272100	+	0.398562i
$685$		0			0
$686$	−17.8642	+	4.88565i	−0.682059	+	0.186535i
$687$	19.4575	−	20.9833i	0.742349	−	0.800563i
$688$	4.02552	−	2.32413i	0.153471	−	0.0886068i
$689$	−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	$0.451779\pi$
$692$		−	0.247556i		−	0.00941068i
$693$	0.398110	−	39.3296i	0.0151229	−	1.49401i
$694$	31.9093			1.21126
$695$		0			0
$696$	0.408975	+	1.32440i	0.0155022	+	0.0502012i
$697$	23.4096	+	13.5156i	0.886704	+	0.511939i
$698$	−1.42333	+	0.821763i	−0.0538740	+	0.0311042i
$699$	23.6686	+	21.9475i	0.895227	+	0.830130i
$700$		0			0
$701$		−	36.3536i		−	1.37306i	−0.727103	−	0.686528i	$-0.759134\pi$
$701$		−	36.3536i		−	1.37306i	0.727103	−	0.686528i	$-0.240866\pi$
$702$	−32.7613	−	4.90660i	−1.23650	−	0.185188i
$703$	12.2592	−	21.2336i	0.462366	−	0.800842i
$704$	−4.29143	−	2.47766i	−0.161740	−	0.0933804i
$705$		0			0
$706$		−	14.6008i		−	0.549507i
$707$	2.49194	+	1.73849i	0.0937189	+	0.0653827i
$708$	−2.22426	−	2.06252i	−0.0835928	−	0.0775143i
$709$	2.54606	+	4.40991i	0.0956193	+	0.165618i	0.909867	−	0.414900i	$-0.136184\pi$
$709$	2.54606	+	4.40991i	0.0956193	+	0.165618i	−0.814248	+	0.580518i	$0.802850\pi$
$710$		0			0
$711$	7.21372	+	3.46840i	0.270536	+	0.130075i
$712$	−0.942474	−	1.63241i	−0.0353207	−	0.0611773i
$713$		−	9.65357i		−	0.361529i
$714$	−16.2444	+	3.52978i	−0.607933	+	0.132099i
$715$		0			0
$716$	16.9709	−	9.79815i	0.634232	−	0.366174i
$717$	12.6773	+	41.0533i	0.473442	+	1.53316i
$718$	−0.438209	−	0.253000i	−0.0163538	−	0.00944189i
$719$	−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
$722$	1.30035			0.0483938
$723$	37.7205	+	8.59708i	1.40284	+	0.319729i
$724$	−12.8261	−	7.40517i	−0.476679	−	0.275211i
$725$		0			0
$726$	−5.21727	+	22.8913i	−0.193631	+	0.849576i
$727$	−46.1288			−1.71082			−0.855412	−	0.517948i	$-0.826696\pi$
$727$	−46.1288			−1.71082			−0.855412	+	0.517948i	$0.826696\pi$
$728$	1.44117	−	16.8056i	0.0534134	−	0.622857i
$729$	−6.05736	−	26.3118i	−0.224347	−	0.974509i
$730$		0			0
$731$	−8.43091	+	14.6028i	−0.311828	+	0.540103i
$732$	−1.74935	−	5.66498i	−0.0646579	−	0.209384i
$733$	4.99864	+	8.65789i	0.184629	+	0.319787i	0.943451	−	0.331511i	$-0.107558\pi$
$733$	4.99864	+	8.65789i	0.184629	+	0.319787i	−0.758823	+	0.651297i	$0.774225\pi$
$734$	−1.35732			−0.0500996
$735$		0			0
$736$	1.91676			0.0706526
$737$	19.7790	+	34.2583i	0.728570	+	1.26192i
$738$	−20.1471	−	9.68684i	−0.741625	−	0.356578i
$739$	0.418026	−	0.724042i	0.0153773	−	0.0266343i	−0.858234	−	0.513258i	$-0.828438\pi$
$739$	0.418026	−	0.724042i	0.0153773	−	0.0266343i	0.873612	+	0.486624i	$0.161772\pi$
$740$		0			0
$741$	31.5873	−	34.0643i	1.16039	−	1.25138i
$742$	3.23411	−	37.7131i	0.118728	−	1.38449i
$743$	53.3336			1.95662			0.978310	−	0.207146i	$-0.0664175\pi$
$743$	53.3336			1.95662			0.978310	+	0.207146i	$0.0664175\pi$
$744$	−8.50521	−	1.93847i	−0.311816	−	0.0710676i
$745$		0			0
$746$	−29.5397	−	17.0548i	−1.08153	−	0.624419i
$747$	−12.3009	−	18.0179i	−0.450066	−	0.659241i
$748$	17.9757			0.657255
$749$	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	$-0.377691\pi$
$752$	0.526352	+	0.303890i	0.0191941	+	0.0110817i
$753$	4.50321	−	1.39060i	0.164106	−	0.0506762i
$754$	4.41837	−	2.55095i	0.160908	−	0.0929001i
$755$		0			0
$756$	13.1761	−	3.92315i	0.479209	−	0.142684i
$757$			37.1033i			1.34854i	0.738483	+	0.674272i	$0.235542\pi$
$757$			37.1033i			1.34854i	−0.738483	+	0.674272i	$0.764458\pi$
$758$	−0.769757	−	1.33326i	−0.0279588	−	0.0484261i
$759$	−4.85401	−	15.7189i	−0.176189	−	0.570559i
$760$		0			0
$761$	8.95519	+	15.5108i	0.324625	+	0.562268i	0.981436	−	0.191787i	$-0.0614284\pi$
$761$	8.95519	+	15.5108i	0.324625	+	0.562268i	−0.656811	+	0.754055i	$0.728095\pi$
$762$	−9.50024	+	10.2452i	−0.344157	+	0.371146i
$763$	19.5798	+	13.6598i	0.708835	+	0.494517i
$764$			0.535503i			0.0193738i
$765$		0			0
$766$	28.1685	+	16.2631i	1.01777	+	0.587608i
$767$	−5.58252	+	9.66922i	−0.201573	+	0.349135i
$768$	0.384890	−	1.68874i	0.0138885	−	0.0609373i
$769$		−	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
$772$	4.79383	−	2.76772i	0.172534	−	0.0996125i
$773$	42.3803	+	24.4683i	1.52431	+	0.880062i	0.999585	+	0.0287914i	$0.00916585\pi$
$773$	42.3803	+	24.4683i	1.52431	+	0.880062i	0.524727	+	0.851271i	$0.324167\pi$
$774$	6.04258	−	12.5676i	0.217196	−	0.451733i
$775$		0			0
$776$	17.6562			0.633820
$777$	−17.9599	−	19.7659i	−0.644309	−	0.709098i
$778$			7.10169i			0.254608i
$779$	27.1496	−	15.6749i	0.972737	−	0.561610i
$780$		0			0
$781$	−6.16340	+	10.6753i	−0.220544	+	0.381993i
$782$	−6.02159	+	3.47656i	−0.215331	+	0.124322i
$783$	3.25353	+	2.58962i	0.116272	+	0.0925456i
$784$	2.41676	+	6.56957i	0.0863128	+	0.234628i
$785$		0			0
$786$	−1.30209	+	5.71305i	−0.0464440	+	0.203778i
$787$	0.0336053	−	0.0582062i	0.00119790	−	0.00207483i	−0.865426	−	0.501037i	$-0.832952\pi$
$787$	0.0336053	−	0.0582062i	0.00119790	−	0.00207483i	0.866624	+	0.498962i	$0.166285\pi$
$788$	0.333227	−	0.577166i	0.0118707	−	0.0205607i
$789$	4.92103	−	21.5915i	0.175193	−	0.768678i
$790$		0			0
$791$	2.80916	−	32.7578i	0.0998822	−	1.16473i
$792$	−14.8237	+	1.12019i	−0.526737	+	0.0398042i
$793$	−18.8992	+	10.9114i	−0.671129	+	0.387477i
$794$	6.51194	−	11.2790i	0.231100	−	0.400277i
$795$		0			0
$796$	−7.81326	+	4.51099i	−0.276934	+	0.159888i
$797$		−	7.61311i		−	0.269670i	−0.990868	−	0.134835i	$-0.956950\pi$
$797$		−	7.61311i		−	0.269670i	0.990868	−	0.134835i	$-0.0430505\pi$
$798$	−5.87460	+	18.3625i	−0.207959	+	0.650026i
$799$	−2.20475			−0.0779984
$800$		0			0
$801$	−5.09637	−	2.45036i	−0.180071	−	0.0865793i
$802$	20.2676	+	11.7015i	0.715673	+	0.413194i
$803$	−64.7720	+	37.3961i	−2.28575	+	1.31968i
$804$	−9.40149	+	10.1387i	−0.331565	+	0.357566i
$805$		0			0
$806$			32.1083i			1.13097i
$807$	4.49995	−	19.7440i	0.158406	−	0.695021i
$808$	0.574210	−	0.994562i	0.0202007	−	0.0349886i
$809$	−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	$0.766676\pi$
$812$	−1.21145	+	1.73649i	−0.0425137	+	0.0609387i
$813$	−25.9916	+	28.0298i	−0.911564	+	0.983048i
$814$	14.4395	+	25.0100i	0.506105	+	0.876600i
$815$		0			0
$816$	1.85385	+	6.00338i	0.0648977	+	0.210160i
$817$	9.77786	+	16.9357i	0.342084	+	0.592507i
$818$			13.1994i			0.461508i
$819$	−24.8561	−	44.0763i	−0.868541	−	1.54015i
$820$		0			0
$821$	−32.4054	+	18.7093i	−1.13096	+	0.652958i	−0.944175	−	0.329444i	$-0.893139\pi$
$821$	−32.4054	+	18.7093i	−1.13096	+	0.652958i	−0.186781	+	0.982402i	$0.559805\pi$
$822$	24.5385	−	7.57751i	0.855878	−	0.264296i
$823$	29.7795	+	17.1932i	1.03805	+	0.599318i	0.919280	−	0.393604i	$-0.128772\pi$
$823$	29.7795	+	17.1932i	1.03805	+	0.599318i	0.118768	+	0.992922i	$0.462105\pi$
$824$	3.64182	+	6.30781i	0.126869	+	0.219743i
$825$		0			0
$826$	0.395899	−	4.61660i	0.0137751	−	0.160632i
$827$	−4.15552			−0.144502			−0.0722508	−	0.997386i	$-0.523018\pi$
$827$	−4.15552			−0.144502			−0.0722508	+	0.997386i	$0.523018\pi$
$828$	4.74908	−	3.24221i	0.165042	−	0.112675i
$829$	24.3399	+	14.0526i	0.845359	+	0.488068i	0.859082	−	0.511837i	$-0.171035\pi$
$829$	24.3399	+	14.0526i	0.845359	+	0.488068i	−0.0137231	+	0.999906i	$0.504368\pi$
$830$		0			0
$831$	−13.1833	−	3.00467i	−0.457323	−	0.104231i
$832$	−6.37523			−0.221021
$833$	−19.5081	−	16.2552i	−0.675915	−	0.563208i
$834$	−8.53440	+	9.20366i	−0.295522	+	0.318697i
$835$		0			0
$836$	10.4238	−	18.0545i	0.360513	−	0.624427i
$837$	−24.3519	+	9.58376i	−0.841727	+	0.331263i
$838$	−13.9746	−	24.2047i	−0.482745	−	0.836138i
$839$	−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
$842$	−12.3398	−	21.3731i	−0.425256	−	0.736565i
$843$	−11.7997	−	38.2112i	−0.406402	−	1.31606i
$844$	−5.71931	+	9.90613i	−0.196867	+	0.340983i
$845$		0			0
$846$	1.81815	−	0.137393i	0.0625094	−	0.00472368i
$847$	−32.4774	+	15.2126i	−1.11594	+	0.522709i
$848$	−14.3065			−0.491288
$849$	−9.52622	+	41.7972i	−0.326939	+	1.43448i
$850$		0			0
$851$	−9.67407	−	5.58533i	−0.331623	−	0.191462i
$852$	−4.20090	−	0.957449i	−0.143921	−	0.0328017i
$853$	23.7742			0.814012			0.407006	−	0.913426i	$-0.366573\pi$
$853$	23.7742			0.814012			0.407006	+	0.913426i	$0.366573\pi$
$854$	5.18188	−	7.42766i	0.177320	−	0.254169i
$855$		0			0
$856$	−1.34318	−	2.32646i	−0.0459091	−	0.0795168i
$857$	−19.3662	−	11.1811i	−0.661535	−	0.381938i	0.131326	−	0.991339i	$-0.458076\pi$
$857$	−19.3662	−	11.1811i	−0.661535	−	0.381938i	−0.792862	+	0.609402i	$0.791410\pi$
$858$	16.1447	+	52.2818i	0.551170	+	1.78487i
$859$	37.1729	−	21.4618i	1.26832	−	0.732267i	0.293653	−	0.955912i	$-0.405129\pi$
$859$	37.1729	−	21.4618i	1.26832	−	0.732267i	0.974671	+	0.223645i	$0.0717957\pi$
$860$		0			0
$861$	−7.25079	−	33.3690i	−0.247106	−	1.13721i
$862$			3.34445i			0.113912i
$863$	11.7599	+	20.3687i	0.400312	+	0.693360i	0.993763	−	0.111510i	$-0.0355686\pi$
$863$	11.7599	+	20.3687i	0.400312	+	0.693360i	−0.593452	+	0.804870i	$0.702235\pi$
$864$	−1.90290	−	4.83518i	−0.0647379	−	0.164496i
$865$		0			0
$866$	7.33780	+	12.7094i	0.249348	+	0.431884i
$867$	4.87814	+	4.52342i	0.165670	+	0.153623i
$868$	−5.65219	−	12.0669i	−0.191848	−	0.409578i
$869$		−	13.2212i		−	0.448497i
$870$		0			0
$871$	44.0747	+	25.4466i	1.49342	+	0.862224i
$872$	4.51172	−	7.81452i	0.152786	−	0.264633i
$873$	43.7460	−	29.8655i	1.48058	−	1.01080i
$874$			8.06398i			0.272768i
$875$		0			0
$876$	−19.1693	−	17.7754i	−0.647670	−	0.600574i
$877$	7.09026	−	4.09356i	0.239421	−	0.138230i	−0.375490	−	0.926827i	$-0.622525\pi$
$877$	7.09026	−	4.09356i	0.239421	−	0.138230i	0.614911	+	0.788597i	$0.289192\pi$
$878$	−5.70453	−	3.29351i	−0.192518	−	0.111151i
$879$	−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	$0.351808\pi$
$882$	17.1004	+	12.1892i	0.575800	+	0.410432i
$883$			5.41249i			0.182145i	0.995844	+	0.0910724i	$0.0290295\pi$
$883$			5.41249i			0.182145i	−0.995844	+	0.0910724i	$0.970971\pi$
$884$	20.0281	−	11.5632i	0.673618	−	0.388913i
$885$		0			0
$886$	−20.3605	+	35.2654i	−0.684025	+	1.18477i
$887$	20.8711	−	12.0499i	0.700782	−	0.404597i	−0.106856	−	0.994274i	$-0.534079\pi$
$887$	20.8711	−	12.0499i	0.700782	−	0.404597i	0.807639	+	0.589678i	$0.200745\pi$
$888$	−6.86349	+	7.40171i	−0.230324	+	0.248385i
$889$	−21.2647	−	1.82356i	−0.713195	−	0.0611604i
$890$		0			0
$891$	−34.8333	+	27.8498i	−1.16696	+	0.933005i
$892$	2.61699	−	4.53275i	0.0876231	−	0.151768i
$893$	−1.27849	+	2.21441i	−0.0427831	+	0.0741026i
$894$	11.1339	+	2.53759i	0.372375	+	0.0848698i
$895$		0			0
$896$	2.39594	−	1.12227i	0.0800427	−	0.0374923i
$897$	−15.5197	−	14.3912i	−0.518189	−	0.480508i
$898$	15.8903	−	9.17425i	0.530265	−	0.306149i
$899$	2.01524	−	3.49050i	0.0672120	−	0.116415i
$900$		0			0
$901$	44.9446	−	25.9488i	1.49732	−	0.864480i
$902$			36.9252i			1.22948i
$903$	20.8153	−	4.52299i	0.692690	−	0.150516i
$904$	−12.4267			−0.413306
$905$		0			0
$906$	−19.4859	+	6.01725i	−0.647374	+	0.199910i
$907$	18.7564	+	10.8290i	0.622797	+	0.359572i	0.777957	−	0.628317i	$-0.216256\pi$
$907$	18.7564	+	10.8290i	0.622797	+	0.359572i	−0.155160	+	0.987889i	$0.549589\pi$
$908$	−11.6587	+	6.73117i	−0.386908	+	0.223382i
$909$	−0.259610	−	3.43547i	−0.00861071	−	0.113947i
$910$		0			0
$911$		−	47.4302i		−	1.57143i	−0.618587	−	0.785716i	$-0.712295\pi$
$911$		−	47.4302i		−	1.57143i	0.618587	−	0.785716i	$-0.287705\pi$
$912$	7.10471	+	1.61927i	0.235261	+	0.0536194i
$913$	−18.0179	+	31.2080i	−0.596306	+	1.03283i
$914$	7.48533	+	4.32166i	0.247593	+	0.142948i
$915$		0			0
$916$		−	16.5216i		−	0.545890i
$917$	−8.10549	+	3.79664i	−0.267667	+	0.125376i
$918$	14.7480	+	11.7385i	0.486755	+	0.387429i
$919$	5.32208	+	9.21812i	0.175559	+	0.304078i	0.940355	−	0.340196i	$-0.110493\pi$
$919$	5.32208	+	9.21812i	0.175559	+	0.304078i	−0.764795	+	0.644273i	$0.777160\pi$
$920$		0			0
$921$	−21.7453	+	6.71499i	−0.716533	+	0.221266i
$922$	−12.3932	−	21.4657i	−0.408149	−	0.706935i
$923$			15.8590i			0.522004i
$924$	−15.2709	−	16.8065i	−0.502377	−	0.552893i
$925$		0			0
$926$	15.5709	−	8.98986i	0.511691	−	0.295425i
$927$	19.6929	+	9.46846i	0.646800	+	0.310985i
$928$	0.693053	+	0.400134i	0.0227506	+	0.0131351i
$929$	−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
$932$	18.6359			0.610440
$933$	2.92772	−	12.8457i	0.0958494	−	0.420549i
$934$	1.10282	+	0.636712i	0.0360853	+	0.0208339i
$935$		0			0
$936$	−15.7957	+	10.7838i	−0.516297	+	0.352478i
$937$	40.0917			1.30974			0.654870	−	0.755742i	$-0.272723\pi$
$937$	40.0917			1.30974			0.654870	+	0.755742i	$0.272723\pi$
$938$	−21.0436	−	1.80461i	−0.687099	−	0.0589226i
$939$	15.7809	+	14.6334i	0.514992	+	0.477543i
$940$		0			0
$941$	−13.6315	+	23.6104i	−0.444374	+	0.769678i	−0.998008	−	0.0630819i	$-0.979907\pi$
$941$	−13.6315	+	23.6104i	−0.444374	+	0.769678i	0.553635	+	0.832760i	$0.313240\pi$
$942$	−2.55654	+	0.789463i	−0.0832966	+	0.0257221i
$943$	−7.14148	−	12.3694i	−0.232559	−	0.402803i
$944$	−1.75132			−0.0570005
$945$		0			0
$946$	−23.0337			−0.748889
$947$	11.3531	+	19.6642i	0.368926	+	0.638999i	0.989398	−	0.145230i	$-0.0463921\pi$
$947$	11.3531	+	19.6642i	0.368926	+	0.638999i	−0.620472	+	0.784229i	$0.713059\pi$
$948$	4.41551	−	1.36351i	0.143409	−	0.0442848i
$949$	−48.1117	+	83.3319i	−1.56177	+	2.70507i
$950$		0			0
$951$	35.2258	+	32.6644i	1.14228	+	1.05921i
$952$	−5.49142	+	7.87134i	−0.177978	+	0.255112i
$953$	38.7288			1.25455			0.627274	−	0.778799i	$-0.284171\pi$
$953$	38.7288			1.25455			0.627274	+	0.778799i	$0.284171\pi$
$954$	−35.4467	+	24.1996i	−1.14763	+	0.783491i
$955$		0			0
$956$	21.4831	+	12.4032i	0.694812	+	0.401150i
$957$	1.52632	−	6.69687i	0.0493388	−	0.216479i
$958$	−14.2267			−0.459643
$959$	32.1737	+	22.4459i	1.03894	+	0.724815i
$960$		0			0
$961$	−2.81730	−	4.87970i	−0.0908805	−	0.157410i
$962$	32.1764	+	18.5771i	1.03741	+	0.598949i
$963$	−7.26318	−	3.49218i	−0.234053	−	0.112534i
$964$	19.3439	−	11.1682i	0.623025	−	0.359704i
$965$		0			0
$966$	8.36598	+	2.67647i	0.269171	+	0.0861141i
$967$			39.1631i			1.25940i	0.776838	+	0.629700i	$0.216822\pi$
$967$			39.1631i			1.25940i	−0.776838	+	0.629700i	$0.783178\pi$
$968$	6.77761	+	11.7392i	0.217840	+	0.377311i
$969$	−25.2568	+	7.79932i	−0.811365	+	0.250550i
$970$		0			0
$971$	−13.4005	−	23.2104i	−0.430044	−	0.744858i	0.566833	−	0.823833i	$-0.308169\pi$
$971$	−13.4005	−	23.2104i	−0.430044	−	0.744858i	−0.996877	+	0.0789753i	$0.974835\pi$
$972$	−12.8935	−	8.76118i	−0.413559	−	0.281015i
$973$	−19.1028	−	1.63817i	−0.612408	−	0.0525174i
$974$			39.8951i			1.27832i
$975$		0			0
$976$	−2.96447	−	1.71154i	−0.0948903	−	0.0547849i
$977$	−13.9386	+	24.1424i	−0.445936	+	0.772383i	−0.998117	−	0.0613410i	$-0.980462\pi$
$977$	−13.9386	+	24.1424i	−0.445936	+	0.772383i	0.552181	+	0.833724i	$0.313796\pi$
$978$	5.70389	+	1.30000i	0.182390	+	0.0415695i
$979$			9.34052i			0.298524i
$980$		0			0
$981$	−2.03982	−	26.9933i	−0.0651264	−	0.861831i
$982$	13.8372	−	7.98891i	0.441563	−	0.254936i
$983$	−18.9161	−	10.9212i	−0.603329	−	0.348332i	0.167021	−	0.985953i	$-0.446585\pi$
$983$	−18.9161	−	10.9212i	−0.603329	−	0.348332i	−0.770350	+	0.637621i	$0.779919\pi$
$984$	−12.3320	+	3.80814i	−0.393130	+	0.121399i
$985$		0			0
$986$	−2.90301			−0.0924507
$987$	1.87301	+	2.06135i	0.0596185	+	0.0656134i
$988$		−	26.8212i		−	0.853297i
$989$	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	$-0.217822\pi$
$992$	−4.36166	+	2.51820i	−0.138483	+	0.0799531i
$993$	14.9729	+	13.8841i	0.475151	+	0.440600i
$994$	−2.79174	−	5.96011i	−0.0885485	−	0.189043i
$995$		0			0
$996$	−12.2808	−	2.79898i	−0.389132	−	0.0886891i
$997$	6.02334	−	10.4327i	0.190761	−	0.330408i	−0.754742	−	0.656022i	$-0.772238\pi$
$997$	6.02334	−	10.4327i	0.190761	−	0.330408i	0.945503	+	0.325614i	$0.105571\pi$
$998$	−6.90313	+	11.9566i	−0.218515	+	0.378479i
$999$	−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.u.e.899.1		12
3.2	odd	2		1050.2.u.g.899.5		12
5.2	odd	4		1050.2.s.f.101.5		12
5.3	odd	4		210.2.r.b.101.2	yes	12
5.4	even	2		1050.2.u.h.899.6		12
7.5	odd	6		1050.2.u.f.299.2		12
15.2	even	4		1050.2.s.g.101.3		12
15.8	even	4		210.2.r.a.101.4	✓	12
15.14	odd	2		1050.2.u.f.899.2		12
21.5	even	6		1050.2.u.h.299.6		12
35.3	even	12		1470.2.b.b.881.5		12
35.12	even	12		1050.2.s.g.551.3		12
35.18	odd	12		1470.2.b.a.881.2		12
35.19	odd	6		1050.2.u.g.299.5		12
35.33	even	12		210.2.r.a.131.4	yes	12
105.38	odd	12		1470.2.b.a.881.8		12
105.47	odd	12		1050.2.s.f.551.5		12
105.53	even	12		1470.2.b.b.881.11		12
105.68	odd	12		210.2.r.b.131.2	yes	12
105.89	even	6	inner	1050.2.u.e.299.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.4	✓	12	15.8	even	4
210.2.r.a.131.4	yes	12	35.33	even	12
210.2.r.b.101.2	yes	12	5.3	odd	4
210.2.r.b.131.2	yes	12	105.68	odd	12
1050.2.s.f.101.5		12	5.2	odd	4
1050.2.s.f.551.5		12	105.47	odd	12
1050.2.s.g.101.3		12	15.2	even	4
1050.2.s.g.551.3		12	35.12	even	12
1050.2.u.e.299.1		12	105.89	even	6	inner
1050.2.u.e.899.1		12	1.1	even	1	trivial
1050.2.u.f.299.2		12	7.5	odd	6
1050.2.u.f.899.2		12	15.14	odd	2
1050.2.u.g.299.5		12	35.19	odd	6
1050.2.u.g.899.5		12	3.2	odd	2
1050.2.u.h.299.6		12	21.5	even	6
1050.2.u.h.899.6		12	5.4	even	2
1470.2.b.a.881.2		12	35.18	odd	12
1470.2.b.a.881.8		12	105.38	odd	12
1470.2.b.b.881.5		12	35.3	even	12
1470.2.b.b.881.11		12	105.53	even	12

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.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.65494 + 0.511048i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.27005 + 1.17770i) q^{6} +(-0.226058 + 2.63608i) q^{7} +1.00000 q^{8} +(2.47766 - 1.69151i) q^{9} +(-4.29143 - 2.47766i) q^{11} +(0.384890 - 1.68874i) q^{12} -6.37523 q^{13} +(2.39594 - 1.12227i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.14155 + 1.81377i) q^{17} +(-2.70372 - 1.29996i) q^{18} +(3.64345 - 2.10355i) q^{19} +(-0.973048 - 4.47808i) q^{21} +4.95532i q^{22} +(-0.958379 - 1.65996i) q^{23} +(-1.65494 + 0.511048i) q^{24} +(3.18762 + 5.52111i) q^{26} +(-3.23594 + 4.06555i) q^{27} +(-2.16988 - 1.51381i) q^{28} -0.800269i q^{29} +(4.36166 + 2.51820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(8.36827 + 1.90726i) q^{33} -3.62755i q^{34} +(0.226058 + 2.99147i) q^{36} +(5.04710 - 2.91394i) q^{37} +(-3.64345 - 2.10355i) q^{38} +(10.5506 - 3.25805i) q^{39} +7.45163 q^{41} +(-3.39161 + 3.08172i) q^{42} +4.64827i q^{43} +(4.29143 - 2.47766i) q^{44} +(-0.958379 + 1.65996i) q^{46} +(-0.526352 + 0.303890i) q^{47} +(1.27005 + 1.17770i) q^{48} +(-6.89780 - 1.19181i) q^{49} +(-6.12600 - 1.39621i) q^{51} +(3.18762 - 5.52111i) q^{52} +(7.15326 - 12.3898i) q^{53} +(5.13884 + 0.769634i) q^{54} +(-0.226058 + 2.63608i) q^{56} +(-4.95469 + 5.34323i) q^{57} +(-0.693053 + 0.400134i) q^{58} +(0.875658 - 1.51668i) q^{59} +(2.96447 - 1.71154i) q^{61} -5.03641i q^{62} +(3.89885 + 6.91368i) q^{63} +1.00000 q^{64} +(-2.53241 - 8.20077i) q^{66} +(-6.91343 - 3.99147i) q^{67} +(-3.14155 + 1.81377i) q^{68} +(2.43438 + 2.25736i) q^{69} -2.48759i q^{71} +(2.47766 - 1.69151i) q^{72} +(7.54666 - 13.0712i) q^{73} +(-5.04710 - 2.91394i) q^{74} +4.20710i q^{76} +(7.50142 - 10.7525i) q^{77} +(-8.09687 - 7.50809i) q^{78} +(1.33404 + 2.31062i) q^{79} +(3.27761 - 8.38196i) q^{81} +(-3.72581 - 6.45330i) q^{82} -7.27215i q^{83} +(4.36465 + 1.39635i) q^{84} +(4.02552 - 2.32413i) q^{86} +(0.408975 + 1.32440i) q^{87} +(-4.29143 - 2.47766i) q^{88} +(-0.942474 - 1.63241i) q^{89} +(1.44117 - 16.8056i) q^{91} +1.91676 q^{92} +(-8.50521 - 1.93847i) q^{93} +(0.526352 + 0.303890i) q^{94} +(0.384890 - 1.68874i) q^{96} +17.6562 q^{97} +(2.41676 + 6.56957i) q^{98} +(-14.8237 + 1.12019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 2 q^{3} - 6 q^{4} + 2 q^{6} - 6 q^{7} + 12 q^{8} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 12 q^{14} - 6 q^{16} + 12 q^{17} - 6 q^{18} + 4 q^{21} + 2 q^{23} + 2 q^{24} + 4 q^{26} - 28 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 2 * q^3 - 6 * q^4 + 2 * q^6 - 6 * q^7 + 12 * q^8 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 12 * q^14 - 6 * q^16 + 12 * q^17 - 6 * q^18 + 4 * q^21 + 2 * q^23 + 2 * q^24 + 4 * q^26 - 28 * q^27 - 6 * q^28 + 12 * q^31 - 6 * q^32 + 34 * q^33 + 6 * q^36 + 42 * q^39 + 4 * q^41 + 16 * q^42 - 12 * q^44 + 2 * q^46 + 24 * q^47 + 2 * q^48 + 14 * q^49 - 8 * q^51 + 4 * q^52 + 8 * q^53 + 32 * q^54 - 6 * q^56 - 20 * q^57 + 18 * q^58 + 12 * q^59 - 30 * q^61 + 2 * q^63 + 12 * q^64 - 14 * q^66 - 6 * q^67 - 12 * q^68 + 50 * q^69 - 20 * q^77 - 12 * q^78 + 4 * q^79 - 40 * q^81 - 2 * q^82 - 20 * q^84 + 54 * q^86 - 8 * q^87 + 12 * q^88 + 26 * q^89 + 28 * q^91 - 4 * q^92 - 24 * q^93 - 24 * q^94 - 4 * q^96 + 72 * q^97 + 2 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more