LMFDB - Embedded newform 325.3.w.b.124.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(24,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.24"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$N$	$=$	$325 = 5^{2} \cdot 13$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	325.w (of order $12$ , degree $4$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,6] 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:	$8.85560859171$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{2} + 1$ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			124.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	325.124
Dual form			325.3.w.b.249.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.133975 + 0.500000i) q^{2} +(0.633975 + 0.366025i) q^{3} +(3.23205 - 1.86603i) q^{4} +(-0.0980762 + 0.366025i) q^{6} +(1.53590 - 5.73205i) q^{7} +(2.83013 + 2.83013i) q^{8} +(-4.23205 - 7.33013i) q^{9} +(-4.19615 - 15.6603i) q^{11} +2.73205 q^{12} +(-11.2583 - 6.50000i) q^{13} +3.07180 q^{14} +(6.42820 - 11.1340i) q^{16} +(9.23205 + 15.9904i) q^{17} +(3.09808 - 3.09808i) q^{18} +(-1.63397 + 6.09808i) q^{19} +(3.07180 - 3.07180i) q^{21} +(7.26795 - 4.19615i) q^{22} +(-10.0981 + 17.4904i) q^{23} +(0.758330 + 2.83013i) q^{24} +(1.74167 - 6.50000i) q^{26} -12.7846i q^{27} +(-5.73205 - 21.3923i) q^{28} +(4.69615 - 8.13397i) q^{29} +(-11.9282 - 11.9282i) q^{31} +(21.8923 + 5.86603i) q^{32} +(3.07180 - 11.4641i) q^{33} +(-6.75833 + 6.75833i) q^{34} +(-27.3564 - 15.7942i) q^{36} +(30.2846 - 8.11474i) q^{37} -3.26795 q^{38} +(-4.75833 - 8.24167i) q^{39} +(44.9186 - 12.0359i) q^{41} +(1.94744 + 1.12436i) q^{42} +(25.9808 + 45.0000i) q^{43} +(-42.7846 - 42.7846i) q^{44} +(-10.0981 - 2.70577i) q^{46} +(34.3205 + 34.3205i) q^{47} +(8.15064 - 4.70577i) q^{48} +(11.9378 + 6.89230i) q^{49} +13.5167i q^{51} -48.5167 q^{52} -14.7654i q^{53} +(6.39230 - 1.71281i) q^{54} +(20.5692 - 11.8756i) q^{56} +(-3.26795 + 3.26795i) q^{57} +(4.69615 + 1.25833i) q^{58} +(92.9615 + 24.9090i) q^{59} +(-12.8135 - 22.1936i) q^{61} +(4.36603 - 7.56218i) q^{62} +(-48.5167 + 13.0000i) q^{63} -39.6936i q^{64} +6.14359 q^{66} +(-10.4571 - 39.0263i) q^{67} +(59.6769 + 34.4545i) q^{68} +(-12.8038 + 7.39230i) q^{69} +(-11.9737 + 44.6865i) q^{71} +(8.76795 - 32.7224i) q^{72} +(-19.2750 - 19.2750i) q^{73} +(8.11474 + 14.0551i) q^{74} +(6.09808 + 22.7583i) q^{76} -96.2102 q^{77} +(3.48334 - 3.48334i) q^{78} -62.7461 q^{79} +(-33.4090 + 57.8660i) q^{81} +(12.0359 + 20.8468i) q^{82} +(24.4833 - 24.4833i) q^{83} +(4.19615 - 15.6603i) q^{84} +(-19.0192 + 19.0192i) q^{86} +(5.95448 - 3.43782i) q^{87} +(32.4449 - 56.1962i) q^{88} +(23.1699 + 86.4711i) q^{89} +(-54.5500 + 54.5500i) q^{91} +75.3731i q^{92} +(-3.19615 - 11.9282i) q^{93} +(-12.5622 + 21.7583i) q^{94} +(11.7321 + 11.7321i) q^{96} +(-52.9545 - 14.1891i) q^{97} +(-1.84679 + 6.89230i) q^{98} +(-97.0333 + 97.0333i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q + 4 q^{2} + 6 q^{3} + 6 q^{4} + 10 q^{6} + 20 q^{7} - 6 q^{8} - 10 q^{9} + 4 q^{11} + 4 q^{12} + 40 q^{14} - 2 q^{16} + 30 q^{17} + 2 q^{18} - 10 q^{19} + 40 q^{21} + 36 q^{22} - 30 q^{23} - 42 q^{24}+ \cdots - 208 q^{99}+O(q^{100})$ 4 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 + 10 * q^6 + 20 * q^7 - 6 * q^8 - 10 * q^9 + 4 * q^11 + 4 * q^12 + 40 * q^14 - 2 * q^16 + 30 * q^17 + 2 * q^18 - 10 * q^19 + 40 * q^21 + 36 * q^22 - 30 * q^23 - 42 * q^24 + 52 * q^26 - 16 * q^28 - 2 * q^29 - 20 * q^31 + 46 * q^32 + 40 * q^33 + 18 * q^34 - 54 * q^36 + 38 * q^37 - 20 * q^38 + 26 * q^39 + 100 * q^41 + 84 * q^42 - 88 * q^44 - 30 * q^46 + 68 * q^47 - 54 * q^48 + 72 * q^49 - 104 * q^52 - 16 * q^54 - 84 * q^56 - 20 * q^57 - 2 * q^58 + 164 * q^59 - 124 * q^61 + 14 * q^62 - 104 * q^63 + 80 * q^66 - 170 * q^67 + 114 * q^68 - 72 * q^69 - 86 * q^71 + 42 * q^72 + 58 * q^73 - 68 * q^74 + 14 * q^76 - 80 * q^77 + 104 * q^78 + 40 * q^79 - 2 * q^81 + 62 * q^82 + 188 * q^83 - 4 * q^84 - 180 * q^86 - 42 * q^87 + 12 * q^88 + 110 * q^89 + 52 * q^91 + 8 * q^93 - 26 * q^94 + 40 * q^96 - 146 * q^97 + 100 * q^98 - 208 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$ .

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.133975	+	0.500000i	0.0669873	+	0.250000i	0.991297	−	0.131643i	$-0.0420252\pi$
$2$	0.133975	+	0.500000i	0.0669873	+	0.250000i	−0.924310	+	0.381643i	$0.875358\pi$
$3$	0.633975	+	0.366025i	0.211325	+	0.122008i	0.601927	−	0.798551i	$-0.294400\pi$
$3$	0.633975	+	0.366025i	0.211325	+	0.122008i	−0.390602	+	0.920560i	$0.627733\pi$
$4$	3.23205	−	1.86603i	0.808013	−	0.466506i
$5$		0			0
$5$		0			0
$6$	−0.0980762	+	0.366025i	−0.0163460	+	0.0610042i
$7$	1.53590	−	5.73205i	0.219414	−	0.818864i	−0.765152	−	0.643850i	$-0.777336\pi$
$7$	1.53590	−	5.73205i	0.219414	−	0.818864i	0.984566	−	0.175014i	$-0.0559972\pi$
$8$	2.83013	+	2.83013i	0.353766	+	0.353766i
$9$	−4.23205	−	7.33013i	−0.470228	−	0.814459i
$10$		0			0
$11$	−4.19615	−	15.6603i	−0.381468	−	1.42366i	−0.843659	−	0.536879i	$-0.819603\pi$
$11$	−4.19615	−	15.6603i	−0.381468	−	1.42366i	0.462191	−	0.886780i	$-0.347063\pi$
$12$	2.73205			0.227671
$13$	−11.2583	−	6.50000i	−0.866025	−	0.500000i
$13$	−11.2583	−	6.50000i	−0.866025	−	0.500000i
$14$	3.07180			0.219414
$15$		0			0
$16$	6.42820	−	11.1340i	0.401763	−	0.695873i
$17$	9.23205	+	15.9904i	0.543062	+	0.940611i	0.998726	+	0.0504590i	$0.0160684\pi$
$17$	9.23205	+	15.9904i	0.543062	+	0.940611i	−0.455664	+	0.890152i	$0.650598\pi$
$18$	3.09808	−	3.09808i	0.172115	−	0.172115i
$19$	−1.63397	+	6.09808i	−0.0859987	+	0.320951i	−0.995501	−	0.0947465i	$-0.969796\pi$
$19$	−1.63397	+	6.09808i	−0.0859987	+	0.320951i	0.909503	+	0.415698i	$0.136463\pi$
$20$		0			0
$21$	3.07180	−	3.07180i	0.146276	−	0.146276i
$22$	7.26795	−	4.19615i	0.330361	−	0.190734i
$23$	−10.0981	+	17.4904i	−0.439047	+	0.760451i	−0.997616	−	0.0690064i	$-0.978017\pi$
$23$	−10.0981	+	17.4904i	−0.439047	+	0.760451i	0.558569	+	0.829458i	$0.311350\pi$
$24$	0.758330	+	2.83013i	0.0315971	+	0.117922i
$25$		0			0
$26$	1.74167	−	6.50000i	0.0669873	−	0.250000i
$27$		−	12.7846i		−	0.473504i
$28$	−5.73205	−	21.3923i	−0.204716	−	0.764011i
$29$	4.69615	−	8.13397i	0.161936	−	0.280482i	−0.773627	−	0.633642i	$-0.781559\pi$
$29$	4.69615	−	8.13397i	0.161936	−	0.280482i	0.935563	+	0.353160i	$0.114893\pi$
$30$		0			0
$31$	−11.9282	−	11.9282i	−0.384781	−	0.384781i	0.488040	−	0.872821i	$-0.337712\pi$
$31$	−11.9282	−	11.9282i	−0.384781	−	0.384781i	−0.872821	+	0.488040i	$0.837712\pi$
$32$	21.8923	+	5.86603i	0.684135	+	0.183313i
$33$	3.07180	−	11.4641i	0.0930848	−	0.347397i
$34$	−6.75833	+	6.75833i	−0.198774	+	0.198774i
$35$		0			0
$36$	−27.3564	−	15.7942i	−0.759900	−	0.438729i
$37$	30.2846	−	8.11474i	0.818503	−	0.219317i	0.174811	−	0.984602i	$-0.444069\pi$
$37$	30.2846	−	8.11474i	0.818503	−	0.219317i	0.643692	+	0.765285i	$0.277402\pi$
$38$	−3.26795			−0.0859987
$39$	−4.75833	−	8.24167i	−0.122008	−	0.211325i
$40$		0			0
$41$	44.9186	−	12.0359i	1.09558	−	0.293558i	0.334614	−	0.942355i	$-0.391394\pi$
$41$	44.9186	−	12.0359i	1.09558	−	0.293558i	0.760962	+	0.648797i	$0.224728\pi$
$42$	1.94744	+	1.12436i	0.0463676	+	0.0267704i
$43$	25.9808	+	45.0000i	0.604204	+	1.04651i	0.992177	+	0.124841i	$0.0398420\pi$
$43$	25.9808	+	45.0000i	0.604204	+	1.04651i	−0.387973	+	0.921671i	$0.626825\pi$
$44$	−42.7846	−	42.7846i	−0.972377	−	0.972377i
$45$		0			0
$46$	−10.0981	−	2.70577i	−0.219523	−	0.0588211i
$47$	34.3205	+	34.3205i	0.730224	+	0.730224i	0.970664	−	0.240440i	$-0.0772918\pi$
$47$	34.3205	+	34.3205i	0.730224	+	0.730224i	−0.240440	+	0.970664i	$0.577292\pi$
$48$	8.15064	−	4.70577i	0.169805	−	0.0980369i
$49$	11.9378	+	6.89230i	0.243629	+	0.140659i
$50$		0			0
$51$			13.5167i			0.265033i
$52$	−48.5167			−0.933013
$53$		−	14.7654i		−	0.278592i	−0.990251	−	0.139296i	$-0.955516\pi$
$53$		−	14.7654i		−	0.278592i	0.990251	−	0.139296i	$-0.0444839\pi$
$54$	6.39230	−	1.71281i	0.118376	−	0.0317188i
$55$		0			0
$56$	20.5692	−	11.8756i	0.367307	−	0.212065i
$57$	−3.26795	+	3.26795i	−0.0573324	+	0.0573324i
$58$	4.69615	+	1.25833i	0.0809681	+	0.0216953i
$59$	92.9615	+	24.9090i	1.57562	+	0.422186i	0.937566	−	0.347807i	$-0.113073\pi$
$59$	92.9615	+	24.9090i	1.57562	+	0.422186i	0.638053	+	0.769993i	$0.279740\pi$
$60$		0			0
$61$	−12.8135	−	22.1936i	−0.210057	−	0.363829i	0.741675	−	0.670759i	$-0.234032\pi$
$61$	−12.8135	−	22.1936i	−0.210057	−	0.363829i	−0.951732	+	0.306930i	$0.900698\pi$
$62$	4.36603	−	7.56218i	0.0704198	−	0.121971i
$63$	−48.5167	+	13.0000i	−0.770106	+	0.206349i
$64$		−	39.6936i		−	0.620212i
$65$		0			0
$66$	6.14359			0.0930848
$67$	−10.4571	−	39.0263i	−0.156076	−	0.582482i	−0.999011	−	0.0444669i	$-0.985841\pi$
$67$	−10.4571	−	39.0263i	−0.156076	−	0.582482i	0.842935	−	0.538015i	$-0.180826\pi$
$68$	59.6769	+	34.4545i	0.877602	+	0.506684i
$69$	−12.8038	+	7.39230i	−0.185563	+	0.107135i
$70$		0			0
$71$	−11.9737	+	44.6865i	−0.168644	+	0.629388i	0.828903	+	0.559392i	$0.188965\pi$
$71$	−11.9737	+	44.6865i	−0.168644	+	0.629388i	−0.997547	+	0.0699959i	$0.977701\pi$
$72$	8.76795	−	32.7224i	0.121777	−	0.454478i
$73$	−19.2750	−	19.2750i	−0.264041	−	0.264041i	0.562653	−	0.826693i	$-0.309781\pi$
$73$	−19.2750	−	19.2750i	−0.264041	−	0.264041i	−0.826693	+	0.562653i	$0.809781\pi$
$74$	8.11474	+	14.0551i	0.109659	+	0.189934i
$75$		0			0
$76$	6.09808	+	22.7583i	0.0802378	+	0.299452i
$77$	−96.2102			−1.24948
$78$	3.48334	−	3.48334i	0.0446582	−	0.0446582i
$79$	−62.7461			−0.794255			−0.397127	−	0.917763i	$-0.629993\pi$
$79$	−62.7461			−0.794255			−0.397127	+	0.917763i	$0.629993\pi$
$80$		0			0
$81$	−33.4090	+	57.8660i	−0.412456	+	0.714395i
$82$	12.0359	+	20.8468i	0.146779	+	0.254229i
$83$	24.4833	−	24.4833i	0.294980	−	0.294980i	−0.544064	−	0.839044i	$-0.683115\pi$
$83$	24.4833	−	24.4833i	0.294980	−	0.294980i	0.839044	+	0.544064i	$0.183115\pi$
$84$	4.19615	−	15.6603i	0.0499542	−	0.186432i
$85$		0			0
$86$	−19.0192	+	19.0192i	−0.221154	+	0.221154i
$87$	5.95448	−	3.43782i	0.0684423	−	0.0395152i
$88$	32.4449	−	56.1962i	0.368692	−	0.638593i
$89$	23.1699	+	86.4711i	0.260336	+	0.971586i	0.965044	+	0.262089i	$0.0844113\pi$
$89$	23.1699	+	86.4711i	0.260336	+	0.971586i	−0.704708	+	0.709497i	$0.748922\pi$
$90$		0			0
$91$	−54.5500	+	54.5500i	−0.599450	+	0.599450i
$92$			75.3731i			0.819272i
$93$	−3.19615	−	11.9282i	−0.0343672	−	0.128260i
$94$	−12.5622	+	21.7583i	−0.133640	+	0.231472i
$95$		0			0
$96$	11.7321	+	11.7321i	0.122209	+	0.122209i
$97$	−52.9545	−	14.1891i	−0.545923	−	0.146279i	−0.0246915	−	0.999695i	$-0.507860\pi$
$97$	−52.9545	−	14.1891i	−0.545923	−	0.146279i	−0.521231	+	0.853416i	$0.674527\pi$
$98$	−1.84679	+	6.89230i	−0.0188448	+	0.0703296i
$99$	−97.0333	+	97.0333i	−0.980135	+	0.980135i
$100$		0			0
$101$	138.560	+	79.9974i	1.37188	+	0.792054i	0.991164	−	0.132640i	$-0.0423453\pi$
$101$	138.560	+	79.9974i	1.37188	+	0.792054i	0.380713	+	0.924693i	$0.375679\pi$
$102$	−6.75833	+	1.81089i	−0.0662581	+	0.0177538i
$103$	−78.7705			−0.764762			−0.382381	−	0.924005i	$-0.624896\pi$
$103$	−78.7705			−0.764762			−0.382381	+	0.924005i	$0.624896\pi$
$104$	−13.4667	−	50.2583i	−0.129487	−	0.483253i
$105$		0			0
$106$	7.38269	−	1.97818i	0.0696480	−	0.0186621i
$107$	−82.5622	−	47.6673i	−0.771609	−	0.445489i	0.0618392	−	0.998086i	$-0.480303\pi$
$107$	−82.5622	−	47.6673i	−0.771609	−	0.445489i	−0.833448	+	0.552597i	$0.813637\pi$
$108$	−23.8564	−	41.3205i	−0.220893	−	0.382597i
$109$	51.9808	+	51.9808i	0.476888	+	0.476888i	0.904135	−	0.427247i	$-0.140517\pi$
$109$	51.9808	+	51.9808i	0.476888	+	0.476888i	−0.427247	+	0.904135i	$0.640517\pi$
$110$		0			0
$111$	22.1699	+	5.94040i	0.199729	+	0.0535171i
$112$	−53.9474	−	53.9474i	−0.481674	−	0.481674i
$113$	−124.691	+	71.9904i	−1.10346	+	0.637083i	−0.937128	−	0.348987i	$-0.886526\pi$
$113$	−124.691	+	71.9904i	−1.10346	+	0.637083i	−0.166332	+	0.986070i	$0.553192\pi$
$114$	−2.07180	−	1.19615i	−0.0181737	−	0.0104926i
$115$		0			0
$116$		−	35.0526i		−	0.302177i
$117$			110.033i			0.940456i
$118$			49.8179i			0.422186i
$119$	105.837	−	28.3590i	0.889388	−	0.238311i
$120$		0			0
$121$	−122.847	+	70.9256i	−1.01526	+	0.586162i
$122$	9.38011	−	9.38011i	0.0768861	−	0.0768861i
$123$	32.8827	+	8.81089i	0.267339	+	0.0716332i
$124$	−60.8109	−	16.2942i	−0.490410	−	0.131405i
$125$		0			0
$126$	−13.0000	−	22.5167i	−0.103175	−	0.178704i
$127$	−14.2417	+	24.6673i	−0.112139	+	0.194231i	−0.916633	−	0.399731i	$-0.869104\pi$
$127$	−14.2417	+	24.6673i	−0.112139	+	0.194231i	0.804493	+	0.593962i	$0.202437\pi$
$128$	107.416	−	28.7820i	0.839188	−	0.224860i
$129$			38.0385i			0.294872i
$130$		0			0
$131$	−2.98076			−0.0227539			−0.0113770	−	0.999935i	$-0.503621\pi$
$131$	−2.98076			−0.0227539			−0.0113770	+	0.999935i	$0.503621\pi$
$132$	−11.4641	−	42.7846i	−0.0868493	−	0.324126i
$133$	32.4449	+	18.7321i	0.243946	+	0.140842i
$134$	18.1122	−	10.4571i	0.135165	−	0.0780378i
$135$		0			0
$136$	−19.1269	+	71.3827i	−0.140639	+	0.524873i
$137$	25.3494	−	94.6051i	0.185032	−	0.690548i	−0.809592	−	0.586993i	$-0.800312\pi$
$137$	25.3494	−	94.6051i	0.185032	−	0.690548i	0.994624	−	0.103555i	$-0.0330218\pi$
$138$	−5.41154	−	5.41154i	−0.0392141	−	0.0392141i
$139$	16.2154	+	28.0859i	0.116657	+	0.202057i	0.918441	−	0.395558i	$-0.129449\pi$
$139$	16.2154	+	28.0859i	0.116657	+	0.202057i	−0.801784	+	0.597614i	$0.796115\pi$
$140$		0			0
$141$	9.19615	+	34.3205i	0.0652209	+	0.243408i
$142$	−23.9474			−0.168644
$143$	−54.5500	+	203.583i	−0.381468	+	1.42366i
$144$	−108.818			−0.755680
$145$		0			0
$146$	7.05514	−	12.2199i	0.0483229	−	0.0836976i
$147$	5.04552	+	8.73909i	0.0343232	+	0.0594496i
$148$	82.7391	−	82.7391i	0.559048	−	0.559048i
$149$	33.0903	−	123.495i	0.222083	−	0.828824i	−0.761469	−	0.648201i	$-0.775522\pi$
$149$	33.0903	−	123.495i	0.222083	−	0.828824i	0.983552	−	0.180624i	$-0.0578116\pi$
$150$		0			0
$151$	127.995	−	127.995i	0.847648	−	0.847648i	−0.142191	−	0.989839i	$-0.545415\pi$
$151$	127.995	−	127.995i	0.847648	−	0.847648i	0.989839	+	0.142191i	$0.0454148\pi$
$152$	−21.8827	+	12.6340i	−0.143965	+	0.0831183i
$153$	78.1410	−	135.344i	0.510726	−	0.884603i
$154$	−12.8897	−	48.1051i	−0.0836995	−	0.312371i
$155$		0			0
$156$	−30.7583	−	17.7583i	−0.197169	−	0.113835i
$157$			97.7461i			0.622587i	0.950314	+	0.311293i	$0.100762\pi$
$157$			97.7461i			0.622587i	−0.950314	+	0.311293i	$0.899238\pi$
$158$	−8.40639	−	31.3731i	−0.0532050	−	0.198564i
$159$	5.40450	−	9.36087i	0.0339906	−	0.0588734i
$160$		0			0
$161$	84.7461	+	84.7461i	0.526374	+	0.526374i
$162$	−33.4090	−	8.95191i	−0.206228	−	0.0552587i
$163$	32.7654	−	122.282i	0.201015	−	0.750197i	−0.789613	−	0.613605i	$-0.789719\pi$
$163$	32.7654	−	122.282i	0.201015	−	0.750197i	0.990627	−	0.136591i	$-0.0436147\pi$
$164$	122.720	−	122.720i	0.748292	−	0.748292i
$165$		0			0
$166$	15.5218	+	8.96152i	0.0935049	+	0.0539851i
$167$	−50.7321	+	13.5936i	−0.303785	+	0.0813989i	−0.407491	−	0.913209i	$-0.633596\pi$
$167$	−50.7321	+	13.5936i	−0.303785	+	0.0813989i	0.103707	+	0.994608i	$0.466930\pi$
$168$	17.3872			0.103495
$169$	84.5000	+	146.358i	0.500000	+	0.866025i
$170$		0			0
$171$	51.6147	−	13.8301i	0.301841	−	0.0808779i
$172$	167.942	+	96.9615i	0.976409	+	0.563730i
$173$	68.6269	+	118.865i	0.396687	+	0.687083i	0.993315	−	0.115435i	$-0.0368263\pi$
$173$	68.6269	+	118.865i	0.396687	+	0.687083i	−0.596628	+	0.802518i	$0.703493\pi$
$174$	2.51666	+	2.51666i	0.0144636	+	0.0144636i
$175$		0			0
$176$	−201.335	−	53.9474i	−1.14395	−	0.306520i
$177$	49.8179	+	49.8179i	0.281457	+	0.281457i
$178$	−40.1314	+	23.1699i	−0.225457	+	0.130168i
$179$	−0.903811	−	0.521815i	−0.00504922	−	0.00291517i	0.497473	−	0.867479i	$-0.334261\pi$
$179$	−0.903811	−	0.521815i	−0.00504922	−	0.00291517i	−0.502522	+	0.864564i	$0.667595\pi$
$180$		0			0
$181$			23.0807i			0.127518i	0.997965	+	0.0637589i	$0.0203089\pi$
$181$			23.0807i			0.127518i	−0.997965	+	0.0637589i	$0.979691\pi$
$182$	−34.5833	−	19.9667i	−0.190018	−	0.109707i
$183$		−	18.7602i		−	0.102515i
$184$	−78.0788	+	20.9212i	−0.424342	+	0.113702i
$185$		0			0
$186$	5.53590	−	3.19615i	0.0297629	−	0.0171836i
$187$	211.674	−	211.674i	1.13195	−	1.13195i
$188$	174.969	+	46.8827i	0.930684	+	0.249376i
$189$	−73.2820	−	19.6359i	−0.387736	−	0.103893i
$190$		0			0
$191$	−147.002	−	254.615i	−0.769643	−	1.33306i	−0.937756	−	0.347294i	$-0.887101\pi$
$191$	−147.002	−	254.615i	−0.769643	−	1.33306i	0.168113	−	0.985768i	$-0.446233\pi$
$192$	14.5289	−	25.1647i	0.0756711	−	0.131066i
$193$	−319.279	+	85.5507i	−1.65430	+	0.443268i	−0.960812	−	0.277202i	$-0.910593\pi$
$193$	−319.279	+	85.5507i	−1.65430	+	0.443268i	−0.693486	+	0.720470i	$0.743926\pi$
$194$		−	28.3782i		−	0.146279i
$195$		0			0
$196$	51.4449			0.262474
$197$	−22.8057	−	85.1122i	−0.115765	−	0.432041i	0.883578	−	0.468284i	$-0.155128\pi$
$197$	−22.8057	−	85.1122i	−0.115765	−	0.432041i	−0.999343	+	0.0362429i	$0.988461\pi$
$198$	−61.5167	−	35.5167i	−0.310690	−	0.179377i
$199$	−174.452	+	100.720i	−0.876643	+	0.506130i	−0.869550	−	0.493845i	$-0.835591\pi$
$199$	−174.452	+	100.720i	−0.876643	+	0.506130i	−0.00709275	+	0.999975i	$0.502258\pi$
$200$		0			0
$201$	7.65510	−	28.5692i	0.0380851	−	0.142135i
$202$	−21.4352	+	79.9974i	−0.106115	+	0.396027i
$203$	−39.4115	−	39.4115i	−0.194146	−	0.194146i
$204$	25.2224	+	43.6865i	0.123639	+	0.214150i
$205$		0			0
$206$	−10.5532	−	39.3853i	−0.0512294	−	0.191191i
$207$	170.942			0.825808
$208$	−144.742	+	83.5666i	−0.695873	+	0.401763i
$209$	102.354			0.489731
$210$		0			0
$211$	−36.6481	+	63.4763i	−0.173687	+	0.300836i	−0.939706	−	0.341983i	$-0.888902\pi$
$211$	−36.6481	+	63.4763i	−0.173687	+	0.300836i	0.766019	+	0.642818i	$0.222235\pi$
$212$	−27.5526	−	47.7224i	−0.129965	−	0.225106i
$213$	−23.9474	+	23.9474i	−0.112429	+	0.112429i
$214$	12.7724	−	47.6673i	0.0596842	−	0.222744i
$215$		0			0
$216$	36.1821	−	36.1821i	0.167510	−	0.167510i
$217$	−86.6936	+	50.0526i	−0.399510	+	0.230657i
$218$	−19.0263	+	32.9545i	−0.0872765	+	0.151167i
$219$	−5.16472	−	19.2750i	−0.0235832	−	0.0880137i
$220$		0			0
$221$		−	240.033i		−	1.08612i
$222$			11.8808i			0.0535171i
$223$	−98.4801	−	367.533i	−0.441615	−	1.64813i	−0.724723	−	0.689040i	$-0.758032\pi$
$223$	−98.4801	−	367.533i	−0.441615	−	1.64813i	0.283108	−	0.959088i	$-0.408634\pi$
$224$	67.2487	−	116.478i	0.300217	−	0.519992i
$225$		0			0
$226$	−52.7006	−	52.7006i	−0.233189	−	0.233189i
$227$	404.107	+	108.280i	1.78021	+	0.477005i	0.990621	−	0.136635i	$-0.0436289\pi$
$227$	404.107	+	108.280i	1.78021	+	0.477005i	0.789586	+	0.613640i	$0.210296\pi$
$228$	−4.46410	+	16.6603i	−0.0195794	+	0.0730713i
$229$	72.2679	−	72.2679i	0.315581	−	0.315581i	−0.531486	−	0.847067i	$-0.678366\pi$
$229$	72.2679	−	72.2679i	0.315581	−	0.315581i	0.847067	+	0.531486i	$0.178366\pi$
$230$		0			0
$231$	−60.9948	−	35.2154i	−0.264047	−	0.152448i
$232$	36.3109	−	9.72947i	0.156512	−	0.0419374i
$233$	256.592			1.10125			0.550627	−	0.834751i	$-0.314389\pi$
$233$	256.592			1.10125			0.550627	+	0.834751i	$0.314389\pi$
$234$	−55.0167	+	14.7417i	−0.235114	+	0.0629986i
$235$		0			0
$236$	346.937	−	92.9615i	1.47007	−	0.393905i
$237$	−39.7795	−	22.9667i	−0.167846	−	0.0969058i
$238$	28.3590	+	49.1192i	0.119155	+	0.206383i
$239$	−39.3449	−	39.3449i	−0.164623	−	0.164623i	0.619988	−	0.784611i	$-0.287137\pi$
$239$	−39.3449	−	39.3449i	−0.164623	−	0.164623i	−0.784611	+	0.619988i	$0.787137\pi$
$240$		0			0
$241$	233.351	+	62.5263i	0.968262	+	0.259445i	0.708094	−	0.706118i	$-0.249555\pi$
$241$	233.351	+	62.5263i	0.968262	+	0.259445i	0.260168	+	0.965563i	$0.416222\pi$
$242$	−51.9212	−	51.9212i	−0.214550	−	0.214550i
$243$	−142.007	+	81.9878i	−0.584391	+	0.337398i
$244$	−82.8275	−	47.8205i	−0.339457	−	0.195986i
$245$		0			0
$246$			17.6218i			0.0716332i
$247$	58.0333	−	58.0333i	0.234953	−	0.234953i
$248$		−	67.5167i		−	0.272245i
$249$	24.4833	−	6.56029i	0.0983267	−	0.0263466i
$250$		0			0
$251$	−221.375	+	127.811i	−0.881972	+	0.509207i	−0.871308	−	0.490736i	$-0.836728\pi$
$251$	−221.375	+	127.811i	−0.881972	+	0.509207i	−0.0106638	+	0.999943i	$0.503394\pi$
$252$	−132.550	+	132.550i	−0.525992	+	0.525992i
$253$	316.277	+	84.7461i	1.25011	+	0.334965i
$254$	−14.2417	−	3.81604i	−0.0560696	−	0.0150238i
$255$		0			0
$256$	−50.6051	−	87.6506i	−0.197676	−	0.342385i
$257$	49.5211	−	85.7731i	0.192689	−	0.333747i	−0.753451	−	0.657504i	$-0.771612\pi$
$257$	49.5211	−	85.7731i	0.192689	−	0.333747i	0.946141	+	0.323756i	$0.104946\pi$
$258$	−19.0192	+	5.09619i	−0.0737180	+	0.0197527i
$259$		−	186.056i		−	0.718364i
$260$		0			0
$261$	−79.4974			−0.304588
$262$	−0.399346	−	1.49038i	−0.00152422	−	0.00568848i
$263$	221.130	+	127.669i	0.840797	+	0.485434i	0.857535	−	0.514426i	$-0.171995\pi$
$263$	221.130	+	127.669i	0.840797	+	0.485434i	−0.0167383	+	0.999860i	$0.505328\pi$
$264$	41.1384	−	23.7513i	0.155827	−	0.0899670i
$265$		0			0
$266$	−5.01924	+	18.7321i	−0.0188693	+	0.0704212i
$267$	−16.9615	+	63.3013i	−0.0635263	+	0.237083i
$268$	−106.622	−	106.622i	−0.397842	−	0.397842i
$269$	−46.3538	−	80.2872i	−0.172319	−	0.298465i	0.766911	−	0.641753i	$-0.221793\pi$
$269$	−46.3538	−	80.2872i	−0.172319	−	0.298465i	−0.939230	+	0.343288i	$0.888459\pi$
$270$		0			0
$271$	−113.133	−	422.219i	−0.417466	−	1.55800i	−0.779845	−	0.625973i	$-0.784702\pi$
$271$	−113.133	−	422.219i	−0.417466	−	1.55800i	0.362379	−	0.932031i	$-0.381965\pi$
$272$	237.382			0.872728
$273$	−54.5500	+	14.6166i	−0.199817	+	0.0535407i
$274$	50.6987			0.185032
$275$		0			0
$276$	−27.5885	+	47.7846i	−0.0999582	+	0.173133i
$277$	174.423	+	302.110i	0.629686	+	1.09065i	0.987615	+	0.156899i	$0.0501498\pi$
$277$	174.423	+	302.110i	0.629686	+	1.09065i	−0.357929	+	0.933749i	$0.616517\pi$
$278$	−11.8705	+	11.8705i	−0.0426996	+	0.0426996i
$279$	−36.9545	+	137.916i	−0.132453	+	0.494323i
$280$		0			0
$281$	91.9737	−	91.9737i	0.327309	−	0.327309i	−0.524254	−	0.851562i	$-0.675656\pi$
$281$	91.9737	−	91.9737i	0.327309	−	0.327309i	0.851562	+	0.524254i	$0.175656\pi$
$282$	−15.9282	+	9.19615i	−0.0564830	+	0.0326105i
$283$	17.7846	−	30.8038i	0.0628431	−	0.108848i	−0.832892	−	0.553435i	$-0.813317\pi$
$283$	17.7846	−	30.8038i	0.0628431	−	0.108848i	0.895735	+	0.444588i	$0.146650\pi$
$284$	44.6865	+	166.772i	0.157347	+	0.587227i
$285$		0			0
$286$	−109.100			−0.381468
$287$		−	275.962i		−	0.961538i
$288$	−49.6506	−	185.299i	−0.172398	−	0.643398i
$289$	−25.9615	+	44.9667i	−0.0898323	+	0.155594i
$290$		0			0
$291$	−28.3782	−	28.3782i	−0.0975197	−	0.0975197i
$292$	−98.2654	−	26.3301i	−0.336525	−	0.0901717i
$293$	−103.631	+	386.758i	−0.353691	+	1.31999i	0.528433	+	0.848975i	$0.322780\pi$
$293$	−103.631	+	386.758i	−0.353691	+	1.31999i	−0.882124	+	0.471017i	$0.843887\pi$
$294$	−3.69358	+	3.69358i	−0.0125632	+	0.0125632i
$295$		0			0
$296$	108.675	+	62.7436i	0.367145	+	0.211971i
$297$	−200.210	+	53.6462i	−0.674109	+	0.180627i
$298$	66.1807			0.222083
$299$	227.375	−	131.275i	0.760451	−	0.439047i
$300$		0			0
$301$	297.846	−	79.8076i	0.989522	−	0.265142i
$302$	81.1455	+	46.8494i	0.268694	+	0.155130i
$303$	58.5622	+	101.433i	0.193275	+	0.334761i
$304$	57.3923	+	57.3923i	0.188790	+	0.188790i
$305$		0			0
$306$	78.1410	+	20.9378i	0.255363	+	0.0684243i
$307$	−260.219	−	260.219i	−0.847619	−	0.847619i	0.142216	−	0.989836i	$-0.454577\pi$
$307$	−260.219	−	260.219i	−0.847619	−	0.847619i	−0.989836	+	0.142216i	$0.954577\pi$
$308$	−310.956	+	179.531i	−1.00960	+	0.582892i
$309$	−49.9385	−	28.8320i	−0.161613	−	0.0933075i
$310$		0			0
$311$			71.4782i			0.229833i	0.993375	+	0.114917i	$0.0366601\pi$
$311$			71.4782i			0.229833i	−0.993375	+	0.114917i	$0.963340\pi$
$312$	9.85829	−	36.7917i	0.0315971	−	0.117922i
$313$		−	394.315i		−	1.25979i	−0.776679	−	0.629897i	$-0.783097\pi$
$313$		−	394.315i		−	1.25979i	0.776679	−	0.629897i	$-0.216903\pi$
$314$	−48.8731	+	13.0955i	−0.155647	+	0.0417054i
$315$		0			0
$316$	−202.799	+	117.086i	−0.641768	+	0.370525i
$317$	−206.054	+	206.054i	−0.650014	+	0.650014i	−0.952996	−	0.302982i	$-0.902018\pi$
$317$	−206.054	+	206.054i	−0.650014	+	0.650014i	0.302982	+	0.952996i	$0.402018\pi$
$318$	5.40450	+	1.44813i	0.0169953	+	0.00455387i
$319$	−147.086	−	39.4115i	−0.461084	−	0.123547i
$320$		0			0
$321$	−34.8949	−	60.4397i	−0.108707	−	0.188286i
$322$	−31.0192	+	53.7269i	−0.0963330	+	0.166854i
$323$	−112.595	+	30.1699i	−0.348593	+	0.0934052i
$324$			249.368i			0.769654i
$325$		0			0
$326$	65.5307			0.201015
$327$	13.9282	+	51.9808i	0.0425939	+	0.158963i
$328$	161.188	+	93.0622i	0.491428	+	0.283726i
$329$	249.440	−	144.014i	0.758175	−	0.437733i
$330$		0			0
$331$	−119.397	+	445.597i	−0.360717	+	1.34622i	0.512417	+	0.858737i	$0.328750\pi$
$331$	−119.397	+	445.597i	−0.360717	+	1.34622i	−0.873135	+	0.487479i	$0.837917\pi$
$332$	33.4449	−	124.818i	0.100738	−	0.375958i
$333$	−187.648	−	187.648i	−0.563508	−	0.563508i
$334$	−13.5936	−	23.5448i	−0.0406994	−	0.0704935i
$335$		0			0
$336$	−14.4552	−	53.9474i	−0.0430213	−	0.160558i
$337$	−144.779			−0.429613			−0.214806	−	0.976657i	$-0.568912\pi$
$337$	−144.779			−0.429613			−0.214806	+	0.976657i	$0.568912\pi$
$338$	−61.8583	+	61.8583i	−0.183013	+	0.183013i
$339$	−105.401			−0.310918
$340$		0			0
$341$	−136.746	+	236.851i	−0.401015	+	0.694578i
$342$	13.8301	+	23.9545i	0.0404390	+	0.0700423i
$343$	263.454	−	263.454i	0.768087	−	0.768087i
$344$	−53.8269	+	200.885i	−0.156473	+	0.583967i
$345$		0			0
$346$	−50.2384	+	50.2384i	−0.145198	+	0.145198i
$347$	−421.911	+	243.590i	−1.21588	+	0.701989i	−0.964034	−	0.265778i	$-0.914371\pi$
$347$	−421.911	+	243.590i	−1.21588	+	0.701989i	−0.251847	+	0.967767i	$0.581038\pi$
$348$	12.8301	−	22.2224i	0.0368682	−	0.0638576i
$349$	3.04036	+	11.3468i	0.00871164	+	0.0325123i	0.970145	−	0.242526i	$-0.0779761\pi$
$349$	3.04036	+	11.3468i	0.00871164	+	0.0325123i	−0.961433	+	0.275039i	$0.911309\pi$
$350$		0			0
$351$	−83.1000	+	143.933i	−0.236752	+	0.410067i
$352$		−	367.454i		−	1.04390i
$353$	−73.9993	−	276.169i	−0.209630	−	0.782349i	−0.987988	−	0.154529i	$-0.950614\pi$
$353$	−73.9993	−	276.169i	−0.209630	−	0.782349i	0.778358	−	0.627820i	$-0.216053\pi$
$354$	−18.2346	+	31.5833i	−0.0515102	+	0.0892184i
$355$		0			0
$356$	236.244	+	236.244i	0.663605	+	0.663605i
$357$	77.4782	+	20.7602i	0.217026	+	0.0581519i
$358$	0.139820	−	0.521815i	0.000390559	−	0.00145758i
$359$	−92.0770	+	92.0770i	−0.256482	+	0.256482i	−0.823622	−	0.567140i	$-0.808050\pi$
$359$	−92.0770	+	92.0770i	−0.256482	+	0.256482i	0.567140	+	0.823622i	$0.308050\pi$
$360$		0			0
$361$	278.119	+	160.572i	0.770411	+	0.444797i
$362$	−11.5404	+	3.09223i	−0.0318795	+	0.00854207i
$363$	−103.842			−0.286067
$364$	−74.5167	+	278.100i	−0.204716	+	0.764011i
$365$		0			0
$366$	9.38011	−	2.51339i	0.0256287	−	0.00686719i
$367$	10.8686	+	6.27499i	0.0296147	+	0.0170981i	0.514734	−	0.857350i	$-0.327891\pi$
$367$	10.8686	+	6.27499i	0.0296147	+	0.0170981i	−0.485120	+	0.874448i	$0.661224\pi$
$368$	129.825	+	224.863i	0.352785	+	0.611042i
$369$	−278.322	−	278.322i	−0.754261	−	0.754261i
$370$		0			0
$371$	−84.6359	−	22.6781i	−0.228129	−	0.0611270i
$372$	−32.5885	−	32.5885i	−0.0876034	−	0.0876034i
$373$	−269.574	+	155.638i	−0.722718	+	0.417261i	−0.815752	−	0.578402i	$-0.803677\pi$
$373$	−269.574	+	155.638i	−0.722718	+	0.417261i	0.0930345	+	0.995663i	$0.470343\pi$
$374$	134.196	+	77.4782i	0.358813	+	0.207161i
$375$		0			0
$376$			194.263i			0.516656i
$377$	−105.742	+	61.0500i	−0.280482	+	0.161936i
$378$		−	39.2717i		−	0.103893i
$379$	−379.858	+	101.783i	−1.00226	+	0.268556i	−0.722394	−	0.691482i	$-0.756958\pi$
$379$	−379.858	+	101.783i	−1.00226	+	0.268556i	−0.279871	+	0.960038i	$0.590292\pi$
$380$		0			0
$381$	−18.0577	+	10.4256i	−0.0473956	+	0.0273638i
$382$	107.613	−	107.613i	0.281709	−	0.281709i
$383$	713.051	+	191.061i	1.86175	+	0.498855i	0.999965	−	0.00841386i	$-0.00267825\pi$
$383$	713.051	+	191.061i	1.86175	+	0.498855i	0.861788	+	0.507269i	$0.169345\pi$
$384$	78.6340	+	21.0699i	0.204776	+	0.0548696i
$385$		0			0
$386$	−85.5507	−	148.178i	−0.221634	−	0.383881i
$387$	219.904	−	380.885i	0.568227	−	0.984198i
$388$	−197.629	+	52.9545i	−0.509353	+	0.136481i
$389$			344.478i			0.885548i	0.896633	+	0.442774i	$0.146006\pi$
$389$			344.478i			0.885548i	−0.896633	+	0.442774i	$0.853994\pi$
$390$		0			0
$391$	−372.904			−0.953718
$392$	14.2795	+	53.2917i	0.0364272	+	0.135948i
$393$	−1.88973	−	1.09103i	−0.00480847	−	0.00277617i
$394$	39.5007	−	22.8057i	0.100256	−	0.0578826i
$395$		0			0
$396$	−132.550	+	494.683i	−0.334722	+	1.24920i
$397$	−181.783	+	678.422i	−0.457891	+	1.70887i	0.221556	+	0.975148i	$0.428886\pi$
$397$	−181.783	+	678.422i	−0.457891	+	1.70887i	−0.679447	+	0.733725i	$0.737780\pi$
$398$	−73.7321	−	73.7321i	−0.185256	−	0.185256i
$399$	13.7128	+	23.7513i	0.0343680	+	0.0595270i
$400$		0			0
$401$	146.833	+	547.989i	0.366168	+	1.36656i	0.865831	+	0.500336i	$0.166790\pi$
$401$	146.833	+	547.989i	0.366168	+	1.36656i	−0.499663	+	0.866220i	$0.666543\pi$
$402$	15.3102			0.0380851
$403$	56.7583	+	211.825i	0.140840	+	0.525620i
$404$	597.109			1.47799
$405$		0			0
$406$	14.4256	−	24.9859i	0.0355311	−	0.0615417i
$407$	−254.158	−	440.214i	−0.624466	−	1.08161i
$408$	−38.2539	+	38.2539i	−0.0937595	+	0.0937595i
$409$	−26.3212	+	98.2321i	−0.0643550	+	0.240176i	−0.990609	−	0.136723i	$-0.956343\pi$
$409$	−26.3212	+	98.2321i	−0.0643550	+	0.240176i	0.926254	+	0.376899i	$0.123010\pi$
$410$		0			0
$411$	50.6987	−	50.6987i	0.123355	−	0.123355i
$412$	−254.590	+	146.988i	−0.617938	+	0.356767i
$413$	285.559	−	494.603i	0.691426	−	1.19758i
$414$	22.9019	+	85.4711i	0.0553187	+	0.206452i
$415$		0			0
$416$	−208.342	−	208.342i	−0.500821	−	0.500821i
$417$			23.7410i			0.0569328i
$418$	13.7128	+	51.1769i	0.0328058	+	0.122433i
$419$	322.279	−	558.203i	0.769162	−	1.33223i	−0.168856	−	0.985641i	$-0.554007\pi$
$419$	322.279	−	558.203i	0.769162	−	1.33223i	0.938018	−	0.346587i	$-0.112659\pi$
$420$		0			0
$421$	346.619	+	346.619i	0.823322	+	0.823322i	0.986583	−	0.163261i	$-0.0522013\pi$
$421$	346.619	+	346.619i	0.823322	+	0.823322i	−0.163261	+	0.986583i	$0.552201\pi$
$422$	−36.6481	−	9.81982i	−0.0868437	−	0.0232697i
$423$	106.328	−	396.820i	0.251365	−	0.938108i
$424$	41.7879	−	41.7879i	0.0985563	−	0.0985563i
$425$		0			0
$426$	−15.1821	−	8.76537i	−0.0356387	−	0.0205760i
$427$	−146.895	+	39.3604i	−0.344016	+	0.0921788i
$428$	−355.794			−0.831293
$429$	−109.100	+	109.100i	−0.254312	+	0.254312i
$430$		0			0
$431$	101.699	−	27.2501i	0.235960	−	0.0632253i	−0.138901	−	0.990306i	$-0.544357\pi$
$431$	101.699	−	27.2501i	0.235960	−	0.0632253i	0.374861	+	0.927081i	$0.377690\pi$
$432$	−142.344	−	82.1821i	−0.329499	−	0.190236i
$433$	344.616	+	596.892i	0.795880	+	1.37850i	0.922279	+	0.386525i	$0.126325\pi$
$433$	344.616	+	596.892i	0.795880	+	1.37850i	−0.126399	+	0.991979i	$0.540342\pi$
$434$	−36.6410	−	36.6410i	−0.0844263	−	0.0844263i
$435$		0			0
$436$	265.002	+	71.0070i	0.607802	+	0.162860i
$437$	−90.1577	−	90.1577i	−0.206310	−	0.206310i
$438$	8.94555	−	5.16472i	0.0204236	−	0.0117916i
$439$	−78.0577	−	45.0666i	−0.177808	−	0.102657i	0.408454	−	0.912779i	$-0.366068\pi$
$439$	−78.0577	−	45.0666i	−0.177808	−	0.102657i	−0.586262	+	0.810121i	$0.699401\pi$
$440$		0			0
$441$		−	116.674i		−	0.264568i
$442$	120.017	−	32.1584i	0.271531	−	0.0727565i
$443$			642.277i			1.44983i	0.688836	+	0.724917i	$0.258122\pi$
$443$			642.277i			1.44983i	−0.688836	+	0.724917i	$0.741878\pi$
$444$	82.7391	−	22.1699i	0.186349	−	0.0499321i
$445$		0			0
$446$	170.572	−	98.4801i	0.382450	−	0.220807i
$447$	66.1807	−	66.1807i	0.148055	−	0.148055i
$448$	−227.526	−	60.9653i	−0.507870	−	0.136083i
$449$	−22.6007	−	6.05583i	−0.0503355	−	0.0134874i	0.233563	−	0.972342i	$-0.424961\pi$
$449$	−22.6007	−	6.05583i	−0.0503355	−	0.0134874i	−0.283899	+	0.958854i	$0.591628\pi$
$450$		0			0
$451$	−376.970	−	652.932i	−0.835855	−	1.44774i
$452$	−268.672	+	465.353i	−0.594407	+	1.02954i
$453$	127.995	−	34.2961i	0.282549	−	0.0757089i
$454$			216.560i			0.477005i
$455$		0			0
$456$	−18.4974			−0.0405645
$457$	−61.2795	−	228.698i	−0.134091	−	0.500433i	−1.00000		0.000232237i	$-0.999926\pi$
$457$	−61.2795	−	228.698i	−0.134091	−	0.500433i	0.865909	−	0.500201i	$-0.166741\pi$
$458$	45.8160	+	26.4519i	0.100035	+	0.0577553i
$459$	204.431	−	118.028i	0.445383	−	0.257142i
$460$		0			0
$461$	−12.6032	+	47.0359i	−0.0273389	+	0.102030i	−0.978247	−	0.207443i	$-0.933486\pi$
$461$	−12.6032	+	47.0359i	−0.0273389	+	0.102030i	0.950908	+	0.309473i	$0.100153\pi$
$462$	9.43594	−	35.2154i	0.0204241	−	0.0762238i
$463$	−521.191	−	521.191i	−1.12568	−	1.12568i	−0.990871	−	0.134811i	$-0.956957\pi$
$463$	−521.191	−	521.191i	−1.12568	−	1.12568i	−0.134811	−	0.990871i	$-0.543043\pi$
$464$	−60.3756	−	104.574i	−0.130120	−	0.225374i
$465$		0			0
$466$	34.3768	+	128.296i	0.0737700	+	0.275314i
$467$	141.415			0.302817			0.151408	−	0.988471i	$-0.451619\pi$
$467$	141.415			0.302817			0.151408	+	0.988471i	$0.451619\pi$
$468$	205.325	+	355.633i	0.438729	+	0.759900i
$469$	−239.762			−0.511219
$470$		0			0
$471$	−35.7776	+	61.9686i	−0.0759609	+	0.131568i
$472$	192.597	+	333.588i	0.408045	+	0.706755i
$473$	595.692	−	595.692i	1.25939	−	1.25939i
$474$	6.15390	−	22.9667i	0.0129829	−	0.0484529i
$475$		0			0
$476$	289.153	−	289.153i	0.607463	−	0.607463i
$477$	−108.232	+	62.4878i	−0.226902	+	0.131002i
$478$	14.4012	−	24.9437i	0.0301281	−	0.0521834i
$479$	−193.783	−	723.207i	−0.404557	−	1.50983i	−0.804872	−	0.593449i	$-0.797766\pi$
$479$	−193.783	−	723.207i	−0.404557	−	1.50983i	0.400315	−	0.916378i	$-0.368901\pi$
$480$		0			0
$481$	−393.700	−	105.492i	−0.818503	−	0.219317i
$482$			125.053i			0.259445i
$483$	22.7077	+	84.7461i	0.0470138	+	0.175458i
$484$	−264.698	+	458.470i	−0.546897	+	0.947253i
$485$		0			0
$486$	−60.0192	−	60.0192i	−0.123496	−	0.123496i
$487$	234.885	+	62.9371i	0.482309	+	0.129234i	0.491778	−	0.870721i	$-0.336347\pi$
$487$	234.885	+	62.9371i	0.482309	+	0.129234i	−0.00946847	+	0.999955i	$0.503014\pi$
$488$	26.5469	−	99.0744i	0.0543994	−	0.203021i
$489$	65.5307	−	65.5307i	0.134010	−	0.134010i
$490$		0			0
$491$	−73.3191	−	42.3308i	−0.149326	−	0.0862135i	0.423475	−	0.905908i	$-0.360810\pi$
$491$	−73.3191	−	42.3308i	−0.149326	−	0.0862135i	−0.572801	+	0.819694i	$0.694143\pi$
$492$	122.720	−	32.8827i	0.249431	−	0.0668347i
$493$	173.420			0.351766
$494$	36.7917	+	21.2417i	0.0744770	+	0.0429993i
$495$		0			0
$496$	−209.485	+	56.1314i	−0.422349	+	0.113168i
$497$	237.755	+	137.268i	0.478380	+	0.276193i
$498$	6.56029	+	11.3628i	0.0131733	+	0.0228168i
$499$	134.397	+	134.397i	0.269334	+	0.269334i	0.828832	−	0.559498i	$-0.189006\pi$
$499$	134.397	+	134.397i	0.269334	+	0.269334i	−0.559498	+	0.828832i	$0.689006\pi$
$500$		0			0
$501$	−37.1384	−	9.95121i	−0.0741286	−	0.0198627i
$502$	−93.5641	−	93.5641i	−0.186383	−	0.186383i
$503$	−689.703	+	398.200i	−1.37118	+	0.791650i	−0.991076	−	0.133295i	$-0.957444\pi$
$503$	−689.703	+	398.200i	−1.37118	+	0.791650i	−0.380102	+	0.924945i	$0.624111\pi$
$504$	−174.100	−	100.517i	−0.345436	−	0.199438i
$505$		0			0
$506$			169.492i			0.334965i
$507$			123.717i			0.244017i
$508$			106.301i			0.209254i
$509$	−79.6051	+	21.3301i	−0.156395	+	0.0419059i	−0.336167	−	0.941802i	$-0.609131\pi$
$509$	−79.6051	+	21.3301i	−0.156395	+	0.0419059i	0.179772	+	0.983708i	$0.442464\pi$
$510$		0			0
$511$	−140.090	+	80.8808i	−0.274148	+	0.158279i
$512$	351.581	−	351.581i	0.686682	−	0.686682i
$513$	77.9615	+	20.8897i	0.151972	+	0.0407207i
$514$	49.5211	+	13.2691i	0.0963446	+	0.0258155i
$515$		0			0
$516$	70.9808	+	122.942i	0.137560	+	0.238260i
$517$	393.454	−	681.482i	0.761032	−	1.31815i
$518$	93.0282	−	24.9268i	0.179591	−	0.0481213i
$519$			100.477i			0.193597i
$520$		0			0
$521$	677.011			1.29945			0.649723	−	0.760171i	$-0.274885\pi$
$521$	677.011			1.29945			0.649723	+	0.760171i	$0.274885\pi$
$522$	−10.6506	−	39.7487i	−0.0204035	−	0.0761470i
$523$	159.049	+	91.8269i	0.304109	+	0.175577i	0.644287	−	0.764784i	$-0.277154\pi$
$523$	159.049	+	91.8269i	0.304109	+	0.175577i	−0.340179	+	0.940361i	$0.610488\pi$
$524$	−9.63397	+	5.56218i	−0.0183854	+	0.0106148i
$525$		0			0
$526$	−34.2089	+	127.669i	−0.0650358	+	0.242717i
$527$	80.6147	−	300.858i	0.152969	−	0.570889i
$528$	−107.895	−	107.895i	−0.204346	−	0.204346i
$529$	60.5577	+	104.889i	0.114476	+	0.198278i
$530$		0			0
$531$	−210.832	−	786.836i	−0.397047	−	1.48180i
$532$	139.818			0.262816
$533$	−583.942	−	156.467i	−1.09558	−	0.293558i
$534$	−33.9230			−0.0635263
$535$		0			0
$536$	80.8545	−	140.044i	0.150848	−	0.261276i
$537$	−0.381995	−	0.661635i	−0.000711351	−	0.00123210i
$538$	33.9334	−	33.9334i	0.0630732	−	0.0630732i
$539$	57.8423	−	215.870i	0.107314	−	0.400502i
$540$		0			0
$541$	317.629	−	317.629i	0.587114	−	0.587114i	−0.349735	−	0.936849i	$-0.613728\pi$
$541$	317.629	−	317.629i	0.587114	−	0.587114i	0.936849	+	0.349735i	$0.113728\pi$
$542$	195.953	−	113.133i	0.361536	−	0.208733i
$543$	−8.44813	+	14.6326i	−0.0155583	+	0.0269477i
$544$	108.311	+	404.222i	0.199101	+	0.743055i
$545$		0			0
$546$	−14.6166	−	25.3167i	−0.0267704	−	0.0463676i
$547$			724.904i			1.32524i	0.748958	+	0.662618i	$0.230555\pi$
$547$			724.904i			1.32524i	−0.748958	+	0.662618i	$0.769445\pi$
$548$	−94.6051	−	353.071i	−0.172637	−	0.644290i
$549$	−108.454	+	187.849i	−0.197549	+	0.342165i
$550$		0			0
$551$	41.9282	+	41.9282i	0.0760947	+	0.0760947i
$552$	−57.1577	−	15.3154i	−0.103547	−	0.0277452i
$553$	−96.3717	+	359.664i	−0.174271	+	0.650387i
$554$	−127.687	+	127.687i	−0.230481	+	0.230481i
$555$		0			0
$556$	104.818	+	60.5167i	0.188521	+	0.108843i
$557$	−115.933	+	31.0641i	−0.208138	+	0.0557703i	−0.361381	−	0.932418i	$-0.617695\pi$
$557$	−115.933	+	31.0641i	−0.208138	+	0.0557703i	0.153244	+	0.988188i	$0.451028\pi$
$558$	−73.9090			−0.132453
$559$		−	675.500i		−	1.20841i
$560$		0			0
$561$	211.674	−	56.7180i	0.377316	−	0.101102i
$562$	58.3090	+	33.6647i	0.103753	+	0.0599016i
$563$	−308.818	−	534.888i	−0.548522	−	0.950068i	−0.998376	−	0.0569660i	$-0.981857\pi$
$563$	−308.818	−	534.888i	−0.548522	−	0.950068i	0.449854	−	0.893102i	$-0.351476\pi$
$564$	93.7654	+	93.7654i	0.166251	+	0.166251i
$565$		0			0
$566$	17.7846	+	4.76537i	0.0314216	+	0.00841938i
$567$	280.378	+	280.378i	0.494494	+	0.494494i
$568$	−160.356	+	92.5814i	−0.282316	+	0.162995i
$569$	381.315	+	220.153i	0.670150	+	0.386911i	0.796133	−	0.605121i	$-0.206875\pi$
$569$	381.315	+	220.153i	0.670150	+	0.386911i	−0.125983	+	0.992032i	$0.540209\pi$
$570$		0			0
$571$		−	618.249i		−	1.08275i	−0.840782	−	0.541374i	$-0.817904\pi$
$571$		−	618.249i		−	1.08275i	0.840782	−	0.541374i	$-0.182096\pi$
$572$	203.583	+	759.783i	0.355915	+	1.32829i
$573$		−	215.226i		−	0.375612i
$574$	137.981	−	36.9718i	0.240385	−	0.0644109i
$575$		0			0
$576$	−290.959	+	167.985i	−0.505137	+	0.291641i
$577$	−266.237	+	266.237i	−0.461415	+	0.461415i	−0.899119	−	0.437704i	$-0.855792\pi$
$577$	−266.237	+	266.237i	−0.461415	+	0.461415i	0.437704	+	0.899119i	$0.355792\pi$
$578$	−25.9615	−	6.95637i	−0.0449161	−	0.0120352i
$579$	−233.729	−	62.6274i	−0.403677	−	0.108165i
$580$		0			0
$581$	−102.736	−	177.944i	−0.176826	−	0.306271i
$582$	10.3872	−	17.9911i	0.0178473	−	0.0309125i
$583$	−231.229	+	61.9578i	−0.396620	+	0.106274i
$584$		−	109.101i		−	0.186817i
$585$		0			0
$586$	−207.263			−0.353691
$587$	−124.629	−	465.123i	−0.212316	−	0.792373i	−0.987094	−	0.160140i	$-0.948805\pi$
$587$	−124.629	−	465.123i	−0.212316	−	0.792373i	0.774779	−	0.632233i	$-0.217861\pi$
$588$	32.6147	+	18.8301i	0.0554672	+	0.0320240i
$589$	92.2295	−	53.2487i	0.156587	−	0.0904053i
$590$		0			0
$591$	16.6950	−	62.3064i	0.0282487	−	0.105425i
$592$	104.326	−	389.351i	0.176227	−	0.657688i
$593$	389.671	+	389.671i	0.657118	+	0.657118i	0.954697	−	0.297579i	$-0.0961792\pi$
$593$	389.671	+	389.671i	0.657118	+	0.657118i	−0.297579	+	0.954697i	$0.596179\pi$
$594$	−53.6462	−	92.9179i	−0.0903134	−	0.156427i
$595$		0			0
$596$	−123.495	−	460.889i	−0.207206	−	0.773304i
$597$	−147.464			−0.247009
$598$	96.1000	+	96.1000i	0.160702	+	0.160702i
$599$	−808.596			−1.34991			−0.674955	−	0.737859i	$-0.735837\pi$
$599$	−808.596			−1.34991			−0.674955	+	0.737859i	$0.735837\pi$
$600$		0			0
$601$	221.344	−	383.379i	0.368293	−	0.637903i	−0.621006	−	0.783806i	$-0.713276\pi$
$601$	221.344	−	383.379i	0.368293	−	0.637903i	0.989299	+	0.145904i	$0.0466089\pi$
$602$	79.8076	+	138.231i	0.132571	+	0.229619i
$603$	−241.813	+	241.813i	−0.401016	+	0.401016i
$604$	174.844	−	652.527i	0.289477	−	1.08034i
$605$		0			0
$606$	−42.8705	+	42.8705i	−0.0707434	+	0.0707434i
$607$	816.485	−	471.398i	1.34512	−	0.776603i	0.357563	−	0.933889i	$-0.383608\pi$
$607$	816.485	−	471.398i	1.34512	−	0.776603i	0.987553	+	0.157286i	$0.0502745\pi$
$608$	−71.5429	+	123.916i	−0.117669	+	0.203809i
$609$	−10.5603	−	39.4115i	−0.0173404	−	0.0647152i
$610$		0			0
$611$	−163.308	−	609.475i	−0.267280	−	0.997504i
$612$		−	583.252i		−	0.953027i
$613$	−260.758	−	973.161i	−0.425380	−	1.58754i	−0.763093	−	0.646289i	$-0.776320\pi$
$613$	−260.758	−	973.161i	−0.425380	−	1.58754i	0.337713	−	0.941249i	$-0.390347\pi$
$614$	95.2468	−	164.972i	0.155125	−	0.268685i
$615$		0			0
$616$	−272.287	−	272.287i	−0.442025	−	0.442025i
$617$	268.378	+	71.9115i	0.434972	+	0.116550i	0.469659	−	0.882848i	$-0.344377\pi$
$617$	268.378	+	71.9115i	0.434972	+	0.116550i	−0.0346873	+	0.999398i	$0.511044\pi$
$618$	7.72551	−	28.8320i	0.0125008	−	0.0466537i
$619$	−206.483	+	206.483i	−0.333576	+	0.333576i	−0.853943	−	0.520367i	$-0.825795\pi$
$619$	−206.483	+	206.483i	−0.333576	+	0.333576i	0.520367	+	0.853943i	$0.325795\pi$
$620$		0			0
$621$	223.608	+	129.100i	0.360077	+	0.207890i
$622$	−35.7391	+	9.57626i	−0.0574583	+	0.0153959i
$623$	531.244			0.852718
$624$	−122.350			−0.196074
$625$		0			0
$626$	197.158	−	52.8282i	0.314948	−	0.0843902i
$627$	64.8897	+	37.4641i	0.103492	+	0.0597514i
$628$	182.397	+	315.920i	0.290441	+	0.503058i
$629$	409.347	+	409.347i	0.650790	+	0.650790i
$630$		0			0
$631$	−428.813	−	114.900i	−0.679577	−	0.182092i	−0.0975117	−	0.995234i	$-0.531088\pi$
$631$	−428.813	−	114.900i	−0.679577	−	0.182092i	−0.582065	+	0.813142i	$0.697755\pi$
$632$	−177.580	−	177.580i	−0.280980	−	0.280980i
$633$	−46.4679	+	26.8282i	−0.0734090	+	0.0423827i
$634$	−130.633	−	75.4212i	−0.206046	−	0.118961i
$635$		0			0
$636$		−	40.3397i		−	0.0634273i
$637$	−89.6000	−	155.192i	−0.140659	−	0.243629i
$638$		−	78.8231i		−	0.123547i
$639$	378.231	−	101.347i	0.591911	−	0.158602i
$640$		0			0
$641$	−471.717	+	272.346i	−0.735908	+	0.424877i	−0.820580	−	0.571532i	$-0.806349\pi$
$641$	−471.717	+	272.346i	−0.735908	+	0.424877i	0.0846714	+	0.996409i	$0.473016\pi$
$642$	25.5448	−	25.5448i	0.0397894	−	0.0397894i
$643$	373.478	+	100.073i	0.580837	+	0.155635i	0.537262	−	0.843415i	$-0.319459\pi$
$643$	373.478	+	100.073i	0.580837	+	0.155635i	0.0435749	+	0.999050i	$0.486125\pi$
$644$	432.042	+	115.765i	0.670873	+	0.179760i
$645$		0			0
$646$	−30.1699	−	52.2558i	−0.0467026	−	0.0808913i
$647$	−251.757	+	436.056i	−0.389114	+	0.673966i	−0.992331	−	0.123612i	$-0.960552\pi$
$647$	−251.757	+	436.056i	−0.389114	+	0.673966i	0.603216	+	0.797578i	$0.293886\pi$
$648$	−258.320	+	69.2166i	−0.398642	+	0.106816i
$649$		−	1560.32i		−	2.40420i
$650$		0			0
$651$	−73.2820			−0.112568
$652$	−122.282	−	456.363i	−0.187549	−	0.699943i
$653$	−26.9667	−	15.5692i	−0.0412966	−	0.0238426i	0.479210	−	0.877701i	$-0.340923\pi$
$653$	−26.9667	−	15.5692i	−0.0412966	−	0.0238426i	−0.520506	+	0.853858i	$0.674257\pi$
$654$	−24.1244	+	13.9282i	−0.0368874	+	0.0212969i
$655$		0			0
$656$	154.738	−	577.492i	0.235882	−	0.880323i
$657$	−59.7154	+	222.861i	−0.0908910	+	0.339210i
$658$	105.426	+	105.426i	0.160221	+	0.160221i
$659$	379.488	+	657.293i	0.575855	+	0.997410i	0.995948	+	0.0899292i	$0.0286641\pi$
$659$	379.488	+	657.293i	0.575855	+	0.997410i	−0.420093	+	0.907481i	$0.638003\pi$
$660$		0			0
$661$	67.8083	+	253.064i	0.102584	+	0.382850i	0.998060	−	0.0622605i	$-0.0198310\pi$
$661$	67.8083	+	253.064i	0.102584	+	0.382850i	−0.895475	+	0.445111i	$0.853164\pi$
$662$	−238.795			−0.360717
$663$	87.8583	−	152.175i	0.132516	−	0.229525i
$664$	138.582			0.208708
$665$		0			0
$666$	68.6840	−	118.964i	0.103129	−	0.178625i
$667$	94.8442	+	164.275i	0.142195	+	0.246289i
$668$	−138.603	+	138.603i	−0.207489	+	0.207489i
$669$	72.0924	−	269.053i	0.107761	−	0.402171i
$670$		0			0
$671$	−293.790	+	293.790i	−0.437839	+	0.437839i
$672$	85.2679	−	49.2295i	0.126887	−	0.0732581i
$673$	157.160	−	272.210i	0.233522	−	0.404472i	−0.725320	−	0.688412i	$-0.758308\pi$
$673$	157.160	−	272.210i	0.233522	−	0.404472i	0.958842	+	0.283940i	$0.0916416\pi$
$674$	−19.3968	−	72.3897i	−0.0287786	−	0.107403i
$675$		0			0
$676$	546.217	+	315.358i	0.808013	+	0.466506i
$677$			547.384i			0.808544i	0.914639	+	0.404272i	$0.132475\pi$
$677$			547.384i			0.808544i	−0.914639	+	0.404272i	$0.867525\pi$
$678$	−14.1211	−	52.7006i	−0.0208276	−	0.0777295i
$679$	−162.665	+	281.745i	−0.239566	+	0.414941i
$680$		0			0
$681$	216.560	+	216.560i	0.318003	+	0.318003i
$682$	−136.746	−	36.6410i	−0.200508	−	0.0537258i
$683$	−67.7789	+	252.954i	−0.0992371	+	0.370358i	−0.997628	−	0.0688393i	$-0.978070\pi$
$683$	−67.7789	+	252.954i	−0.0992371	+	0.370358i	0.898391	+	0.439197i	$0.144737\pi$
$684$	141.014	−	141.014i	0.206161	−	0.206161i
$685$		0			0
$686$	167.023	+	96.4308i	0.243474	+	0.140570i
$687$	72.2679	−	19.3641i	0.105194	−	0.0281865i
$688$	668.038			0.970986
$689$	−95.9749	+	166.233i	−0.139296	+	0.241268i
$690$		0			0
$691$	1062.75	−	284.764i	1.53799	−	0.412104i	0.612377	−	0.790566i	$-0.290214\pi$
$691$	1062.75	−	284.764i	1.53799	−	0.412104i	0.925617	+	0.378462i	$0.123547\pi$
$692$	443.611	+	256.119i	0.641057	+	0.370114i
$693$	407.167	+	705.233i	0.587542	+	1.01765i
$694$	−178.321	−	178.321i	−0.256946	−	0.256946i
$695$		0			0
$696$	26.5814	+	7.12247i	0.0381917	+	0.0102334i
$697$	607.149	+	607.149i	0.871089	+	0.871089i
$698$	−5.26606	+	3.04036i	−0.00754450	+	0.00435582i
$699$	162.673	+	93.9193i	0.232722	+	0.134362i
$700$		0			0
$701$			638.323i			0.910589i	0.890341	+	0.455295i	$0.150466\pi$
$701$			638.323i			0.910589i	−0.890341	+	0.455295i	$0.849534\pi$
$702$	−83.1000	−	22.2666i	−0.118376	−	0.0317188i
$703$			197.937i			0.281561i
$704$	−621.611	+	166.560i	−0.882971	+	0.236591i
$705$		0			0
$706$	128.171	−	73.9993i	0.181545	−	0.104815i
$707$	671.363	−	671.363i	0.949594	−	0.949594i
$708$	253.976	+	68.0526i	0.358723	+	0.0961194i
$709$	625.185	+	167.518i	0.881784	+	0.236273i	0.671177	−	0.741297i	$-0.265789\pi$
$709$	625.185	+	167.518i	0.881784	+	0.236273i	0.210608	+	0.977571i	$0.432456\pi$
$710$		0			0
$711$	265.545	+	459.937i	0.373481	+	0.646888i
$712$	−179.151	+	310.298i	−0.251616	+	0.435812i
$713$	329.081	−	88.1769i	0.461544	−	0.123670i
$714$			41.5204i			0.0581519i
$715$		0			0
$716$	−3.89488			−0.00543978
$717$	−10.5424	−	39.3449i	−0.0147035	−	0.0548743i
$718$	−58.3744	−	33.7025i	−0.0813015	−	0.0469394i
$719$	−1058.38	+	611.056i	−1.47202	+	0.849870i	−0.999505	−	0.0314543i	$-0.989986\pi$
$719$	−1058.38	+	611.056i	−1.47202	+	0.849870i	−0.472512	+	0.881324i	$0.656653\pi$
$720$		0			0
$721$	−120.984	+	451.517i	−0.167800	+	0.626237i
$722$	−43.0251	+	160.572i	−0.0595915	+	0.222399i
$723$	125.053	+	125.053i	0.172963	+	0.172963i
$724$	43.0692	+	74.5981i	0.0594879	+	0.103036i
$725$		0			0
$726$	−13.9122	−	51.9212i	−0.0191629	−	0.0715168i
$727$	−508.974			−0.700102			−0.350051	−	0.936731i	$-0.613836\pi$
$727$	−508.974			−0.700102			−0.350051	+	0.936731i	$0.613836\pi$
$728$	−308.767			−0.424130
$729$	481.323			0.660251
$730$		0			0
$731$	−479.711	+	830.885i	−0.656240	+	1.13664i
$732$	−35.0070	−	60.6340i	−0.0478238	−	0.0828333i
$733$	−861.681	+	861.681i	−1.17555	+	1.17555i	−0.194689	+	0.980865i	$0.562370\pi$
$733$	−861.681	+	861.681i	−1.17555	+	1.17555i	−0.980865	+	0.194689i	$0.937630\pi$
$734$	−1.68138	+	6.27499i	−0.00229071	+	0.00854903i
$735$		0			0
$736$	−323.669	+	323.669i	−0.439768	+	0.439768i
$737$	−567.282	+	327.520i	−0.769718	+	0.444397i
$738$	101.873	−	176.449i	0.138039	−	0.239091i
$739$	−40.4242	−	150.865i	−0.0547013	−	0.204148i	0.933167	−	0.359444i	$-0.117034\pi$
$739$	−40.4242	−	150.865i	−0.0547013	−	0.204148i	−0.987868	+	0.155296i	$0.950367\pi$
$740$		0			0
$741$	58.0333	−	15.5500i	0.0783176	−	0.0209851i
$742$		−	45.3562i		−	0.0611270i
$743$	−98.9409	−	369.252i	−0.133164	−	0.496975i	0.866835	−	0.498596i	$-0.166151\pi$
$743$	−98.9409	−	369.252i	−0.133164	−	0.496975i	−0.999999	+	0.00162070i	$0.999484\pi$
$744$	24.7128	−	42.8038i	0.0332161	−	0.0575321i
$745$		0			0
$746$	−113.935	−	113.935i	−0.152728	−	0.152728i
$747$	−283.081	−	75.8513i	−0.378957	−	0.101541i
$748$	289.153	−	1079.13i	0.386568	−	1.44269i
$749$	−400.038	+	400.038i	−0.534097	+	0.534097i
$750$		0			0
$751$	−906.415	−	523.319i	−1.20694	−	0.696830i	−0.244854	−	0.969560i	$-0.578740\pi$
$751$	−906.415	−	523.319i	−1.20694	−	0.696830i	−0.962091	+	0.272730i	$0.912073\pi$
$752$	602.743	−	161.504i	0.801520	−	0.214767i
$753$	−187.128			−0.248510
$754$	−44.6917	−	44.6917i	−0.0592728	−	0.0592728i
$755$		0			0
$756$	−273.492	+	73.2820i	−0.361762	+	0.0969339i
$757$	−326.345	−	188.415i	−0.431103	−	0.248897i	0.268713	−	0.963220i	$-0.413402\pi$
$757$	−326.345	−	188.415i	−0.431103	−	0.248897i	−0.699816	+	0.714323i	$0.746735\pi$
$758$	−101.783	−	176.293i	−0.134278	−	0.232576i
$759$	169.492	+	169.492i	0.223310	+	0.223310i
$760$		0			0
$761$	−742.044	−	198.830i	−0.975091	−	0.261275i	−0.264115	−	0.964491i	$-0.585080\pi$
$761$	−742.044	−	198.830i	−0.975091	−	0.261275i	−0.710976	+	0.703216i	$0.751747\pi$
$762$	−7.63209	−	7.63209i	−0.0100159	−	0.0100159i
$763$	377.794	−	218.119i	0.495142	−	0.285871i
$764$	−950.235	−	548.619i	−1.24376	−	0.718087i
$765$		0			0
$766$			382.123i			0.498855i
$767$	−884.683	−	884.683i	−1.15343	−	1.15343i
$768$		−	74.0910i		−	0.0964727i
$769$	65.7006	−	17.6044i	0.0854364	−	0.0228926i	−0.215848	−	0.976427i	$-0.569251\pi$
$769$	65.7006	−	17.6044i	0.0854364	−	0.0228926i	0.301284	+	0.953534i	$0.402585\pi$
$770$		0			0
$771$	62.7903	−	36.2520i	0.0814400	−	0.0470194i
$772$	−872.288	+	872.288i	−1.12991	+	1.12991i
$773$	−890.771	−	238.681i	−1.15236	−	0.308773i	−0.368447	−	0.929649i	$-0.620110\pi$
$773$	−890.771	−	238.681i	−1.15236	−	0.308773i	−0.783909	+	0.620876i	$0.786777\pi$
$774$	219.904	+	58.9230i	0.284113	+	0.0761280i
$775$		0			0
$776$	−109.711	−	190.025i	−0.141380	−	0.244877i
$777$	68.1013	−	117.955i	0.0876465	−	0.151808i
$778$	−172.239	+	46.1513i	−0.221387	+	0.0593205i
$779$			293.583i			0.376872i
$780$		0			0
$781$	750.046			0.960366
$782$	−49.9596	−	186.452i	−0.0638870	−	0.238430i
$783$	−103.990	−	60.0385i	−0.132809	−	0.0766775i
$784$	153.477	−	88.6103i	0.195762	−	0.113023i
$785$		0			0
$786$	0.292342	−	1.09103i	0.000371936	−	0.00138808i
$787$	318.489	−	1188.62i	0.404687	−	1.51031i	−0.399944	−	0.916540i	$-0.630970\pi$
$787$	318.489	−	1188.62i	0.404687	−	1.51031i	0.804632	−	0.593774i	$-0.202363\pi$
$788$	−232.531	−	232.531i	−0.295090	−	0.295090i
$789$	93.4603	+	161.878i	0.118454	+	0.205169i
$790$		0			0
$791$	221.140	+	825.305i	0.279570	+	1.04337i
$792$	−549.233			−0.693476
$793$			333.150i			0.420114i
$794$	−363.565			−0.457891
$795$		0			0
$796$	−375.892	+	651.063i	−0.472226	+	0.817919i
$797$	12.7372	+	22.0615i	0.0159814	+	0.0276807i	0.873906	−	0.486096i	$-0.161579\pi$
$797$	12.7372	+	22.0615i	0.0159814	+	0.0276807i	−0.857924	+	0.513776i	$0.828246\pi$
$798$	−10.0385	+	10.0385i	−0.0125795	+	0.0125795i
$799$	−231.949	+	865.647i	−0.290300	+	1.08341i
$800$		0			0
$801$	535.788	−	535.788i	0.668899	−	0.668899i
$802$	−254.323	+	146.833i	−0.317110	+	0.183084i
$803$	−220.970	+	382.732i	−0.275181	+	0.476628i
$804$	−28.5692	−	106.622i	−0.0355339	−	0.132614i
$805$		0			0
$806$	−98.3083	+	56.7583i	−0.121971	+	0.0704198i
$807$		−	67.8667i		−	0.0840975i
$808$	165.738	+	618.544i	0.205122	+	0.765525i
$809$	−351.463	+	608.752i	−0.434442	+	0.752475i	−0.997250	−	0.0741123i	$-0.976388\pi$
$809$	−351.463	+	608.752i	−0.434442	+	0.752475i	0.562808	+	0.826588i	$0.309721\pi$
$810$		0			0
$811$	506.292	+	506.292i	0.624282	+	0.624282i	0.946623	−	0.322342i	$-0.104470\pi$
$811$	506.292	+	506.292i	0.624282	+	0.624282i	−0.322342	+	0.946623i	$0.604470\pi$
$812$	−200.923	−	53.8372i	−0.247442	−	0.0663019i
$813$	82.8193	−	309.086i	0.101869	−	0.380179i
$814$	186.056	−	186.056i	0.228570	−	0.228570i
$815$		0			0
$816$	150.494	+	86.8878i	0.184429	+	0.106480i
$817$	−316.865	+	84.9038i	−0.387840	+	0.103921i
$818$	−52.6424			−0.0643550
$819$	630.717	+	169.000i	0.770106	+	0.206349i
$820$		0			0
$821$	−1090.79	+	292.276i	−1.32861	+	0.356000i	−0.852197	−	0.523220i	$-0.824730\pi$
$821$	−1090.79	+	292.276i	−1.32861	+	0.356000i	−0.476414	+	0.879221i	$0.658064\pi$
$822$	32.1417	+	18.5570i	0.0391018	+	0.0225755i
$823$	−259.726	−	449.858i	−0.315584	−	0.546607i	0.663978	−	0.747752i	$-0.268867\pi$
$823$	−259.726	−	449.858i	−0.315584	−	0.546607i	−0.979561	+	0.201145i	$0.935534\pi$
$824$	−222.931	−	222.931i	−0.270547	−	0.270547i
$825$		0			0
$826$	285.559	+	76.5153i	0.345713	+	0.0926335i
$827$	571.769	+	571.769i	0.691377	+	0.691377i	0.962535	−	0.271158i	$-0.0874064\pi$
$827$	571.769	+	571.769i	0.691377	+	0.691377i	−0.271158	+	0.962535i	$0.587406\pi$
$828$	552.494	−	318.983i	0.667263	−	0.385245i
$829$	848.094	+	489.647i	1.02303	+	0.590648i	0.914981	−	0.403497i	$-0.132205\pi$
$829$	848.094	+	489.647i	1.02303	+	0.590648i	0.108052	+	0.994145i	$0.465539\pi$
$830$		0			0
$831$			255.373i			0.307308i
$832$	−258.008	+	446.883i	−0.310106	+	0.537119i
$833$			254.520i			0.305547i
$834$	−11.8705	+	3.18069i	−0.0142332	+	0.00381377i
$835$		0			0
$836$	330.813	−	190.995i	0.395709	−	0.228463i
$837$	−152.497	+	152.497i	−0.182195	+	0.182195i
$838$	322.279	+	86.3543i	0.384581	+	0.103048i
$839$	−513.757	−	137.661i	−0.612344	−	0.164077i	−0.0606993	−	0.998156i	$-0.519333\pi$
$839$	−513.757	−	137.661i	−0.612344	−	0.164077i	−0.551645	+	0.834079i	$0.686000\pi$
$840$		0			0
$841$	376.392	+	651.931i	0.447553	+	0.775185i
$842$	−126.871	+	219.747i	−0.150678	+	0.260983i
$843$	91.9737	−	24.6443i	0.109103	−	0.0292340i
$844$			273.545i			0.324105i
$845$		0			0
$846$	212.655			0.251365
$847$	217.869	+	813.099i	0.257224	+	0.959975i
$848$	−164.397	−	94.9148i	−0.193865	−	0.111928i
$849$	22.5500	−	13.0192i	0.0265606	−	0.0153348i
$850$		0			0
$851$	−163.886	+	611.633i	−0.192581	+	0.718722i
$852$	−32.7128	+	122.086i	−0.0383953	+	0.143293i
$853$	713.043	+	713.043i	0.835924	+	0.835924i	0.988320	−	0.152396i	$-0.0486989\pi$
$853$	713.043	+	713.043i	0.835924	+	0.835924i	−0.152396	+	0.988320i	$0.548699\pi$
$854$	−39.3604	−	68.1742i	−0.0460894	−	0.0798292i
$855$		0			0
$856$	−98.7569	−	368.566i	−0.115370	−	0.430568i
$857$	−311.663			−0.363667			−0.181834	−	0.983329i	$-0.558203\pi$
$857$	−311.663			−0.363667			−0.181834	+	0.983329i	$0.558203\pi$
$858$	−69.1666	−	39.9334i	−0.0806138	−	0.0465424i
$859$	1475.02			1.71714			0.858568	−	0.512700i	$-0.171355\pi$
$859$	1475.02			1.71714			0.858568	+	0.512700i	$0.171355\pi$
$860$		0			0
$861$	101.009	−	174.953i	0.117316	−	0.203197i
$862$	27.2501	+	47.1985i	0.0316126	+	0.0547547i
$863$	700.396	−	700.396i	0.811583	−	0.811583i	−0.173288	−	0.984871i	$-0.555439\pi$
$863$	700.396	−	700.396i	0.811583	−	0.811583i	0.984871	+	0.173288i	$0.0554392\pi$
$864$	74.9948	−	279.885i	0.0867996	−	0.323940i
$865$		0			0
$866$	−252.276	+	252.276i	−0.291312	+	0.291312i
$867$	−32.9179	+	19.0052i	−0.0379676	+	0.0219206i
$868$	−186.799	+	323.545i	−0.215206	+	0.372747i
$869$	263.292	+	982.620i	0.302983	+	1.13075i
$870$		0			0
$871$	−135.942	+	507.342i	−0.156076	+	0.582482i
$872$			294.224i			0.337413i
$873$	120.098	+	448.212i	0.137569	+	0.513416i
$874$	33.0000	−	57.1577i	0.0377574	−	0.0653978i
$875$		0			0
$876$	−52.6603	−	52.6603i	−0.0601144	−	0.0601144i
$877$	132.301	+	35.4498i	0.150856	+	0.0404217i	0.333457	−	0.942765i	$-0.391785\pi$
$877$	132.301	+	35.4498i	0.150856	+	0.0404217i	−0.182601	+	0.983187i	$0.558452\pi$
$878$	12.0756	−	45.0666i	0.0137535	−	0.0513287i
$879$	−207.263	+	207.263i	−0.235794	+	0.235794i
$880$		0			0
$881$	383.677	+	221.516i	0.435502	+	0.251437i	0.701688	−	0.712485i	$-0.252430\pi$
$881$	383.677	+	221.516i	0.435502	+	0.251437i	−0.266186	+	0.963922i	$0.585764\pi$
$882$	58.3372	−	15.6314i	0.0661419	−	0.0177227i
$883$	−1305.20			−1.47814			−0.739069	−	0.673630i	$-0.764734\pi$
$883$	−1305.20			−1.47814			−0.739069	+	0.673630i	$0.764734\pi$
$884$	−447.908	−	775.800i	−0.506684	−	0.877602i
$885$		0			0
$886$	−321.138	+	86.0488i	−0.362459	+	0.0971205i
$887$	−1491.95	−	861.377i	−1.68202	−	0.971113i	−0.960319	−	0.278904i	$-0.910029\pi$
$887$	−1491.95	−	861.377i	−1.68202	−	0.971113i	−0.721697	−	0.692209i	$-0.756638\pi$
$888$	45.9315	+	79.5556i	0.0517246	+	0.0895897i
$889$	119.520	+	119.520i	0.134444	+	0.134444i
$890$		0			0
$891$	1046.39	+	280.378i	1.17439	+	0.314678i
$892$	−1004.12	−	1004.12i	−1.12569	−	1.12569i
$893$	−265.368	+	153.210i	−0.297165	+	0.171568i
$894$	41.9569	+	24.2238i	0.0469316	+	0.0270960i
$895$		0			0
$896$		−	659.920i		−	0.736518i
$897$	192.200			0.214270
$898$		−	12.1117i		−	0.0134874i
$899$	−153.040	+	41.0070i	−0.170234	+	0.0456141i
$900$		0			0
$901$	236.104	−	136.315i	0.262047	−	0.151293i
$902$	275.962	−	275.962i	0.305944	−	0.305944i
$903$	218.038	+	58.4232i	0.241460	+	0.0646990i
$904$	−556.633	−	149.149i	−0.615745	−	0.164988i
$905$		0			0
$906$	34.2961	+	59.4026i	0.0378544	+	0.0655658i
$907$	438.093	−	758.800i	0.483014	−	0.836604i	−0.516796	−	0.856109i	$-0.672875\pi$
$907$	438.093	−	758.800i	0.483014	−	0.836604i	0.999810	+	0.0195043i	$0.00620879\pi$
$908$	1508.15	−	404.107i	1.66096	−	0.445052i
$909$		−	1354.21i		−	1.48978i
$910$		0			0
$911$	−1103.35			−1.21114			−0.605569	−	0.795793i	$-0.707054\pi$
$911$	−1103.35			−1.21114			−0.605569	+	0.795793i	$0.707054\pi$
$912$	15.3782	+	57.3923i	0.0168621	+	0.0629302i
$913$	−486.151	−	280.679i	−0.532477	−	0.307426i
$914$	106.139	−	61.2795i	0.116126	−	0.0670454i
$915$		0			0
$916$	98.7199	−	368.428i	0.107773	−	0.402213i
$917$	−4.57815	+	17.0859i	−0.00499253	+	0.0186324i
$918$	86.4026	+	86.4026i	0.0941205	+	0.0941205i
$919$	−328.160	−	568.389i	−0.357083	−	0.618486i	0.630389	−	0.776279i	$-0.282895\pi$
$919$	−328.160	−	568.389i	−0.357083	−	0.618486i	−0.987472	+	0.157793i	$0.949562\pi$
$920$		0			0
$921$	−69.7255	−	260.219i	−0.0757063	−	0.282540i
$922$	−25.2065			−0.0273389
$923$	425.267	−	425.267i	0.460744	−	0.460744i
$924$	−262.851			−0.284471
$925$		0			0
$926$	190.769	−	330.422i	0.206014	−	0.356827i
$927$	333.361	+	577.398i	0.359613	+	0.622867i
$928$	150.524	−	150.524i	0.162202	−	0.162202i
$929$	−219.574	+	819.460i	−0.236355	+	0.882088i	0.741179	+	0.671308i	$0.234267\pi$
$929$	−219.574	+	819.460i	−0.236355	+	0.882088i	−0.977533	+	0.210780i	$0.932399\pi$
$930$		0			0
$931$	−61.5359	+	61.5359i	−0.0660966	+	0.0660966i
$932$	829.319	−	478.808i	0.889827	−	0.513742i
$933$	−26.1628	+	45.3154i	−0.0280416	+	0.0485695i
$934$	18.9461	+	70.7077i	0.0202849	+	0.0757041i
$935$		0			0
$936$	−311.408	+	311.408i	−0.332701	+	0.332701i
$937$		−	842.615i		−	0.899269i	−0.893213	−	0.449635i	$-0.851554\pi$
$937$		−	842.615i		−	0.899269i	0.893213	−	0.449635i	$-0.148446\pi$
$938$	−32.1220	−	119.881i	−0.0342452	−	0.127805i
$939$	144.329	−	249.986i	0.153705	−	0.266226i
$940$		0			0
$941$	−471.659	−	471.659i	−0.501232	−	0.501232i	0.410589	−	0.911821i	$-0.365323\pi$
$941$	−471.659	−	471.659i	−0.501232	−	0.501232i	−0.911821	+	0.410589i	$0.865323\pi$
$942$	−35.7776	−	9.58657i	−0.0379804	−	0.0101768i
$943$	−243.079	+	907.183i	−0.257772	+	0.962018i
$944$	874.911	−	874.911i	0.926813	−	0.926813i
$945$		0			0
$946$	377.654	+	218.038i	0.399211	+	0.230485i
$947$	−489.308	+	131.110i	−0.516693	+	0.138447i	−0.507737	−	0.861512i	$-0.669518\pi$
$947$	−489.308	+	131.110i	−0.516693	+	0.138447i	−0.00895652	+	0.999960i	$0.502851\pi$
$948$	−171.426			−0.180829
$949$	91.7168	+	342.292i	0.0966457	+	0.360687i
$950$		0			0
$951$	−206.054	+	55.2121i	−0.216671	+	0.0580569i
$952$	379.792	+	219.273i	0.398941	+	0.230329i
$953$	−444.613	−	770.092i	−0.466540	−	0.808071i	0.532729	−	0.846286i	$-0.321166\pi$
$953$	−444.613	−	770.092i	−0.466540	−	0.808071i	−0.999270	+	0.0382143i	$0.987833\pi$
$954$	−45.7442	−	45.7442i	−0.0479499	−	0.0479499i
$955$		0			0
$956$	−200.583	−	53.7461i	−0.209815	−	0.0562198i
$957$	−78.8231	−	78.8231i	−0.0823648	−	0.0823648i
$958$	335.642	−	193.783i	0.350356	−	0.202278i
$959$	−503.347	−	290.608i	−0.524867	−	0.303032i
$960$		0			0
$961$		−	676.436i		−	0.703888i
$962$		−	210.983i		−	0.219317i
$963$			806.922i			0.837925i
$964$	870.879	−	233.351i	0.903401	−	0.242066i
$965$		0			0
$966$	−39.3308	+	22.7077i	−0.0407151	+	0.0235069i
$967$	−384.317	+	384.317i	−0.397432	+	0.397432i	−0.877326	−	0.479894i	$-0.840675\pi$
$967$	−384.317	+	384.317i	−0.397432	+	0.397432i	0.479894	+	0.877326i	$0.340675\pi$
$968$	−548.401	−	146.943i	−0.566529	−	0.151801i
$969$	−82.4256	−	22.0859i	−0.0850626	−	0.0227924i
$970$		0			0
$971$	121.863	+	211.074i	0.125503	+	0.217378i	0.921929	−	0.387358i	$-0.126612\pi$
$971$	121.863	+	211.074i	0.125503	+	0.217378i	−0.796426	+	0.604735i	$0.793279\pi$
$972$	−305.983	+	529.977i	−0.314797	+	0.545244i
$973$	185.895	−	49.8104i	0.191053	−	0.0511926i
$974$			125.874i			0.129234i
$975$		0			0
$976$	−329.470			−0.337572
$977$	297.426	+	1110.01i	0.304428	+	1.13614i	0.933437	+	0.358742i	$0.116794\pi$
$977$	297.426	+	1110.01i	0.304428	+	1.13614i	−0.629009	+	0.777398i	$0.716539\pi$
$978$	41.5448	+	23.9859i	0.0424794	+	0.0245255i
$979$	1256.94	−	725.692i	1.28390	−	0.741259i
$980$		0			0
$981$	161.040	−	601.011i	0.164159	−	0.612651i
$982$	11.3425	−	42.3308i	0.0115504	−	0.0431067i
$983$	−774.213	−	774.213i	−0.787602	−	0.787602i	0.193499	−	0.981101i	$-0.438016\pi$
$983$	−774.213	−	774.213i	−0.787602	−	0.787602i	−0.981101	+	0.193499i	$0.938016\pi$
$984$	68.1262	+	117.998i	0.0692340	+	0.119917i
$985$		0			0
$986$	23.2339	+	86.7102i	0.0235638	+	0.0879414i
$987$	210.851			0.213628
$988$	79.2750	−	295.858i	0.0802378	−	0.299452i
$989$	−1049.42			−1.06109
$990$		0			0
$991$	391.733	−	678.501i	0.395290	−	0.684663i	−0.597848	−	0.801609i	$-0.703977\pi$
$991$	391.733	−	678.501i	0.395290	−	0.684663i	0.993138	+	0.116947i	$0.0373107\pi$
$992$	−191.165	−	331.107i	−0.192706	−	0.333777i
$993$	−238.795	+	238.795i	−0.240478	+	0.240478i
$994$	−36.7808	+	137.268i	−0.0370029	+	0.138097i
$995$		0			0
$996$	66.8897	−	66.8897i	0.0671584	−	0.0671584i
$997$	−434.428	+	250.817i	−0.435735	+	0.251572i	−0.701787	−	0.712387i	$-0.747614\pi$
$997$	−434.428	+	250.817i	−0.435735	+	0.251572i	0.266052	+	0.963959i	$0.414281\pi$
$998$	−49.1929	+	85.2046i	−0.0492915	+	0.0853753i
$999$	−103.744	−	387.177i	−0.103848	−	0.387564i

Display

a_p

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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

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)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.3.w.b.124.1		4
5.2	odd	4		13.3.f.a.7.1	yes	4
5.3	odd	4		325.3.t.a.176.1		4
5.4	even	2		325.3.w.a.124.1		4
13.2	odd	12		325.3.w.a.249.1		4
15.2	even	4		117.3.bd.b.46.1		4
20.7	even	4		208.3.bd.d.33.1		4
65.2	even	12		13.3.f.a.2.1	✓	4
65.7	even	12		169.3.d.c.70.1		4
65.12	odd	4		169.3.f.b.150.1		4
65.17	odd	12		169.3.d.c.99.1		4
65.22	odd	12		169.3.d.a.99.2		4
65.28	even	12		325.3.t.a.301.1		4
65.32	even	12		169.3.d.a.70.2		4
65.37	even	12		169.3.f.b.80.1		4
65.42	odd	12		169.3.f.c.89.1		4
65.47	even	4		169.3.f.a.19.1		4
65.54	odd	12	inner	325.3.w.b.249.1		4
65.57	even	4		169.3.f.c.19.1		4
65.62	odd	12		169.3.f.a.89.1		4
195.2	odd	12		117.3.bd.b.28.1		4
260.67	odd	12		208.3.bd.d.145.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.3.f.a.2.1	✓	4	65.2	even	12
13.3.f.a.7.1	yes	4	5.2	odd	4
117.3.bd.b.28.1		4	195.2	odd	12
117.3.bd.b.46.1		4	15.2	even	4
169.3.d.a.70.2		4	65.32	even	12
169.3.d.a.99.2		4	65.22	odd	12
169.3.d.c.70.1		4	65.7	even	12
169.3.d.c.99.1		4	65.17	odd	12
169.3.f.a.19.1		4	65.47	even	4
169.3.f.a.89.1		4	65.62	odd	12
169.3.f.b.80.1		4	65.37	even	12
169.3.f.b.150.1		4	65.12	odd	4
169.3.f.c.19.1		4	65.57	even	4
169.3.f.c.89.1		4	65.42	odd	12
208.3.bd.d.33.1		4	20.7	even	4
208.3.bd.d.145.1		4	260.67	odd	12
325.3.t.a.176.1		4	5.3	odd	4
325.3.t.a.301.1		4	65.28	even	12
325.3.w.a.124.1		4	5.4	even	2
325.3.w.a.249.1		4	13.2	odd	12
325.3.w.b.124.1		4	1.1	even	1	trivial
325.3.w.b.249.1		4	65.54	odd	12	inner

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

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L-functions

Modular forms

Varieties

Fields

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Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	325.3.w.b.124.1

Level	$325$
Weight	$3$
Character	325.124
Analytic conductor	$8.856$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$