LMFDB - Embedded newform 325.3.w.e.249.10

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 = [40,0,-12] 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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			249.10
Character	$\chi$	$=$	325.249
Dual form			325.3.w.e.124.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.01171 - 3.77575i) q^{2} +(-0.585883 + 0.338260i) q^{3} +(-9.76865 - 5.63993i) q^{4} +(0.684442 + 2.55437i) q^{6} +(1.21531 + 4.53560i) q^{7} +(-20.1218 + 20.1218i) q^{8} +(-4.27116 + 7.39787i) q^{9} +(1.84474 - 6.88467i) q^{11} +7.63105 q^{12} +(-12.9877 + 0.564752i) q^{13} +18.3548 q^{14} +(33.0579 + 57.2580i) q^{16} +(-9.76038 + 16.9055i) q^{17} +(23.6113 + 23.6113i) q^{18} +(2.43845 + 9.10040i) q^{19} +(-2.24624 - 2.24624i) q^{21} +(-24.1285 - 13.9306i) q^{22} +(-12.1731 - 21.0844i) q^{23} +(4.98264 - 18.5955i) q^{24} +(-11.0074 + 49.6098i) q^{26} -11.8677i q^{27} +(13.7085 - 51.1609i) q^{28} +(0.898827 + 1.55681i) q^{29} +(14.7383 - 14.7383i) q^{31} +(139.689 - 37.4296i) q^{32} +(1.24800 + 4.65762i) q^{33} +(53.9562 + 53.9562i) q^{34} +(83.4469 - 48.1781i) q^{36} +(-57.0299 - 15.2811i) q^{37} +36.8279 q^{38} +(7.41826 - 4.72411i) q^{39} +(-31.5224 - 8.44640i) q^{41} +(-10.7538 + 6.20870i) q^{42} +(-1.78308 + 3.08838i) q^{43} +(-56.8497 + 56.8497i) q^{44} +(-91.9252 + 24.6313i) q^{46} +(-41.9403 + 41.9403i) q^{47} +(-38.7362 - 22.3643i) q^{48} +(23.3406 - 13.4757i) q^{49} -13.2062i q^{51} +(130.058 + 67.7330i) q^{52} +79.2957i q^{53} +(-44.8096 - 12.0067i) q^{54} +(-115.719 - 66.8103i) q^{56} +(-4.50695 - 4.50695i) q^{57} +(6.78750 - 1.81870i) q^{58} +(-42.0377 + 11.2640i) q^{59} +(14.4213 - 24.9784i) q^{61} +(-40.7372 - 70.5588i) q^{62} +(-38.7445 - 10.3816i) q^{63} -300.836i q^{64} +18.8486 q^{66} +(1.43922 - 5.37123i) q^{67} +(190.691 - 110.096i) q^{68} +(14.2640 + 8.23535i) q^{69} +(31.4917 + 117.529i) q^{71} +(-62.9151 - 234.802i) q^{72} +(-22.0244 + 22.0244i) q^{73} +(-115.395 + 199.871i) q^{74} +(27.5053 - 102.651i) q^{76} +33.4680 q^{77} +(-10.3319 - 32.7889i) q^{78} +40.0190 q^{79} +(-34.4261 - 59.6277i) q^{81} +(-63.7830 + 110.475i) q^{82} +(-102.799 - 102.799i) q^{83} +(9.27409 + 34.6114i) q^{84} +(9.85701 + 9.85701i) q^{86} +(-1.05322 - 0.608075i) q^{87} +(101.413 + 175.652i) q^{88} +(16.6664 - 62.1998i) q^{89} +(-18.3456 - 58.2207i) q^{91} +274.622i q^{92} +(-3.64954 + 13.6203i) q^{93} +(115.925 + 200.788i) q^{94} +(-69.1807 + 69.1807i) q^{96} +(-33.3045 + 8.92391i) q^{97} +(-27.2670 - 101.762i) q^{98} +(43.0527 + 43.0527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{3} - 12 q^{6} - 44 q^{7} + 36 q^{8} + 72 q^{9} - 12 q^{11} + 120 q^{12} - 36 q^{13} - 48 q^{14} + 128 q^{16} - 32 q^{17} + 136 q^{18} - 68 q^{19} - 48 q^{21} - 72 q^{22} - 28 q^{23} + 56 q^{24}+ \cdots + 76 q^{99}+O(q^{100}) $ 40 * q - 12 * q^3 - 12 * q^6 - 44 * q^7 + 36 * q^8 + 72 * q^9 - 12 * q^11 + 120 * q^12 - 36 * q^13 - 48 * q^14 + 128 * q^16 - 32 * q^17 + 136 * q^18 - 68 * q^19 - 48 * q^21 - 72 * q^22 - 28 * q^23 + 56 * q^24 - 84 * q^26 + 76 * q^28 - 28 * q^29 + 128 * q^31 + 84 * q^32 - 68 * q^33 + 28 * q^34 + 300 * q^36 - 260 * q^37 + 8 * q^38 + 88 * q^39 + 68 * q^41 - 480 * q^42 + 32 * q^43 + 240 * q^44 + 260 * q^46 - 152 * q^47 - 480 * q^48 + 132 * q^49 + 488 * q^52 - 152 * q^54 - 288 * q^56 + 252 * q^57 + 468 * q^58 - 492 * q^59 - 100 * q^61 - 8 * q^62 - 356 * q^63 - 456 * q^66 - 56 * q^67 + 12 * q^68 + 576 * q^69 - 132 * q^71 + 396 * q^72 - 424 * q^73 + 160 * q^74 - 992 * q^76 + 344 * q^77 + 12 * q^78 + 248 * q^79 + 248 * q^82 - 112 * q^83 - 1100 * q^84 + 852 * q^86 - 1068 * q^87 + 8 * q^88 - 168 * q^89 - 160 * q^91 - 24 * q^93 - 328 * q^94 + 124 * q^96 + 1020 * q^97 + 1404 * q^98 + 76 * q^99

Character values

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

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

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 $

$2$	1.01171	−	3.77575i	0.505855	−	1.88788i	0.0480040	−	0.998847i	$-0.484714\pi$
$2$	1.01171	−	3.77575i	0.505855	−	1.88788i	0.457851	−	0.889029i	$-0.348619\pi$
$3$	−0.585883	+	0.338260i	−0.195294	+	0.112753i	−0.594459	−	0.804126i	$-0.702634\pi$
$3$	−0.585883	+	0.338260i	−0.195294	+	0.112753i	0.399164	+	0.916879i	$0.369300\pi$
$4$	−9.76865	−	5.63993i	−2.44216	−	1.40998i
$5$		0			0
$5$		0			0
$6$	0.684442	+	2.55437i	0.114074	+	0.425729i
$7$	1.21531	+	4.53560i	0.173616	+	0.647942i	0.996783	+	0.0801440i	$0.0255380\pi$
$7$	1.21531	+	4.53560i	0.173616	+	0.647942i	−0.823168	+	0.567798i	$0.807795\pi$
$8$	−20.1218	+	20.1218i	−2.51523	+	2.51523i
$9$	−4.27116	+	7.39787i	−0.474573	+	0.821985i
$10$		0			0
$11$	1.84474	−	6.88467i	0.167704	−	0.625879i	−0.829976	−	0.557799i	$-0.811646\pi$
$11$	1.84474	−	6.88467i	0.167704	−	0.625879i	0.997680	−	0.0680801i	$-0.0216873\pi$
$12$	7.63105			0.635921
$13$	−12.9877	+	0.564752i	−0.999056	+	0.0434425i
$13$	−12.9877	+	0.564752i	−0.999056	+	0.0434425i
$14$	18.3548			1.31106
$15$		0			0
$16$	33.0579	+	57.2580i	2.06612	+	3.57862i
$17$	−9.76038	+	16.9055i	−0.574140	+	0.994440i	0.421994	+	0.906598i	$0.361330\pi$
$17$	−9.76038	+	16.9055i	−0.574140	+	0.994440i	−0.996134	+	0.0878414i	$0.972003\pi$
$18$	23.6113	+	23.6113i	1.31174	+	1.31174i
$19$	2.43845	+	9.10040i	0.128339	+	0.478969i	0.999937	−	0.0112537i	$-0.00358225\pi$
$19$	2.43845	+	9.10040i	0.128339	+	0.478969i	−0.871597	+	0.490222i	$0.836916\pi$
$20$		0			0
$21$	−2.24624	−	2.24624i	−0.106964	−	0.106964i
$22$	−24.1285	−	13.9306i	−1.09675	−	0.633208i
$23$	−12.1731	−	21.0844i	−0.529265	−	0.916714i	−0.999417	−	0.0341290i	$-0.989134\pi$
$23$	−12.1731	−	21.0844i	−0.529265	−	0.916714i	0.470152	−	0.882585i	$-0.344199\pi$
$24$	4.98264	−	18.5955i	0.207610	−	0.774811i
$25$		0			0
$26$	−11.0074	+	49.6098i	−0.423363	+	1.90807i
$27$		−	11.8677i		−	0.439546i
$28$	13.7085	−	51.1609i	0.489590	−	1.82718i
$29$	0.898827	+	1.55681i	0.0309940	+	0.0536833i	0.881106	−	0.472918i	$-0.156799\pi$
$29$	0.898827	+	1.55681i	0.0309940	+	0.0536833i	−0.850112	+	0.526601i	$0.823466\pi$
$30$		0			0
$31$	14.7383	−	14.7383i	0.475428	−	0.475428i	−0.428238	−	0.903666i	$-0.640866\pi$
$31$	14.7383	−	14.7383i	0.475428	−	0.475428i	0.903666	+	0.428238i	$0.140866\pi$
$32$	139.689	−	37.4296i	4.36529	−	1.16968i
$33$	1.24800	+	4.65762i	0.0378183	+	0.141140i
$34$	53.9562	+	53.9562i	1.58695	+	1.58695i
$35$		0			0
$36$	83.4469	−	48.1781i	2.31797	−	1.33828i
$37$	−57.0299	−	15.2811i	−1.54135	−	0.413003i	−0.614647	−	0.788802i	$-0.710702\pi$
$37$	−57.0299	−	15.2811i	−1.54135	−	0.413003i	−0.926701	+	0.375799i	$0.877368\pi$
$38$	36.8279			0.969154
$39$	7.41826	−	4.72411i	0.190212	−	0.121131i
$40$		0			0
$41$	−31.5224	−	8.44640i	−0.768839	−	0.206010i	−0.146981	−	0.989139i	$-0.546955\pi$
$41$	−31.5224	−	8.44640i	−0.768839	−	0.206010i	−0.621859	+	0.783130i	$0.713622\pi$
$42$	−10.7538	+	6.20870i	−0.256043	+	0.147826i
$43$	−1.78308	+	3.08838i	−0.0414669	+	0.0718228i	−0.886014	−	0.463659i	$-0.846536\pi$
$43$	−1.78308	+	3.08838i	−0.0414669	+	0.0718228i	0.844547	+	0.535481i	$0.179870\pi$
$44$	−56.8497	+	56.8497i	−1.29204	+	1.29204i
$45$		0			0
$46$	−91.9252	+	24.6313i	−1.99837	+	0.535463i
$47$	−41.9403	+	41.9403i	−0.892348	+	0.892348i	−0.994744	−	0.102396i	$-0.967349\pi$
$47$	−41.9403	+	41.9403i	−0.892348	+	0.892348i	0.102396	+	0.994744i	$0.467349\pi$
$48$	−38.7362	−	22.3643i	−0.807004	−	0.465924i
$49$	23.3406	−	13.4757i	0.476338	−	0.275014i
$50$		0			0
$51$		−	13.2062i		−	0.258945i
$52$	130.058	+	67.7330i	2.50111	+	1.30256i
$53$			79.2957i			1.49615i	0.663617	+	0.748073i	$0.269021\pi$
$53$			79.2957i			1.49615i	−0.663617	+	0.748073i	$0.730979\pi$
$54$	−44.8096	−	12.0067i	−0.829808	−	0.222346i
$55$		0			0
$56$	−115.719	−	66.8103i	−2.06641	−	1.19304i
$57$	−4.50695	−	4.50695i	−0.0790693	−	0.0790693i
$58$	6.78750	−	1.81870i	0.117026	−	0.0313570i
$59$	−42.0377	+	11.2640i	−0.712504	+	0.190915i	−0.596825	−	0.802372i	$-0.703571\pi$
$59$	−42.0377	+	11.2640i	−0.712504	+	0.190915i	−0.115680	+	0.993287i	$0.536905\pi$
$60$		0			0
$61$	14.4213	−	24.9784i	0.236414	−	0.409481i	−0.723269	−	0.690567i	$-0.757361\pi$
$61$	14.4213	−	24.9784i	0.236414	−	0.409481i	0.959683	+	0.281085i	$0.0906944\pi$
$62$	−40.7372	−	70.5588i	−0.657051	−	1.13805i
$63$	−38.7445	−	10.3816i	−0.614992	−	0.164787i
$64$		−	300.836i		−	4.70057i
$65$		0			0
$66$	18.8486			0.285585
$67$	1.43922	−	5.37123i	0.0214809	−	0.0801676i	−0.954353	−	0.298680i	$-0.903454\pi$
$67$	1.43922	−	5.37123i	0.0214809	−	0.0801676i	0.975834	+	0.218512i	$0.0701204\pi$
$68$	190.691	−	110.096i	2.80429	−	1.61906i
$69$	14.2640	+	8.23535i	0.206725	+	0.119353i
$70$		0			0
$71$	31.4917	+	117.529i	0.443545	+	1.65533i	0.719750	+	0.694234i	$0.244257\pi$
$71$	31.4917	+	117.529i	0.443545	+	1.65533i	−0.276205	+	0.961099i	$0.589077\pi$
$72$	−62.9151	−	234.802i	−0.873821	−	3.26114i
$73$	−22.0244	+	22.0244i	−0.301704	+	0.301704i	−0.841680	−	0.539976i	$-0.818433\pi$
$73$	−22.0244	+	22.0244i	−0.301704	+	0.301704i	0.539976	+	0.841680i	$0.318433\pi$
$74$	−115.395	+	199.871i	−1.55940	+	2.70095i
$75$		0			0
$76$	27.5053	−	102.651i	0.361912	−	1.35067i
$77$	33.4680			0.434650
$78$	−10.3319	−	32.7889i	−0.132461	−	0.420371i
$79$	40.0190			0.506569			0.253285	−	0.967392i	$-0.418489\pi$
$79$	40.0190			0.506569			0.253285	+	0.967392i	$0.418489\pi$
$80$		0			0
$81$	−34.4261	−	59.6277i	−0.425013	−	0.736144i
$82$	−63.7830	+	110.475i	−0.777842	+	1.34726i
$83$	−102.799	−	102.799i	−1.23855	−	1.23855i	−0.960595	−	0.277952i	$-0.910344\pi$
$83$	−102.799	−	102.799i	−1.23855	−	1.23855i	−0.277952	−	0.960595i	$-0.589656\pi$
$84$	9.27409	+	34.6114i	0.110406	+	0.412040i
$85$		0			0
$86$	9.85701	+	9.85701i	0.114616	+	0.114616i
$87$	−1.05322	−	0.608075i	−0.0121059	−	0.00698936i
$88$	101.413	+	175.652i	1.15242	+	1.99604i
$89$	16.6664	−	62.1998i	0.187263	−	0.698874i	−0.806872	−	0.590726i	$-0.798841\pi$
$89$	16.6664	−	62.1998i	0.187263	−	0.698874i	0.994135	−	0.108148i	$-0.0344919\pi$
$90$		0			0
$91$	−18.3456	−	58.2207i	−0.201600	−	0.639788i
$92$			274.622i			2.98502i
$93$	−3.64954	+	13.6203i	−0.0392423	+	0.146454i
$94$	115.925	+	200.788i	1.23324	+	2.13604i
$95$		0			0
$96$	−69.1807	+	69.1807i	−0.720632	+	0.720632i
$97$	−33.3045	+	8.92391i	−0.343345	+	0.0919990i	−0.426371	−	0.904548i	$-0.640208\pi$
$97$	−33.3045	+	8.92391i	−0.343345	+	0.0919990i	0.0830260	+	0.996547i	$0.473542\pi$
$98$	−27.2670	−	101.762i	−0.278234	−	1.03839i
$99$	43.0527	+	43.0527i	0.434876	+	0.434876i
$100$		0			0
$101$	−11.5913	+	6.69225i	−0.114766	+	0.0662599i	−0.556284	−	0.830992i	$-0.687773\pi$
$101$	−11.5913	+	6.69225i	−0.114766	+	0.0662599i	0.441518	+	0.897252i	$0.354440\pi$
$102$	−49.8633	−	13.3608i	−0.488856	−	0.130989i
$103$	−28.4963			−0.276663			−0.138332	−	0.990386i	$-0.544174\pi$
$103$	−28.4963			−0.276663			−0.138332	+	0.990386i	$0.544174\pi$
$104$	249.973	−	272.701i	2.40359	−	2.62212i
$105$		0			0
$106$	299.401	+	80.2242i	2.82454	+	0.756832i
$107$	−60.5676	+	34.9687i	−0.566052	+	0.326811i	−0.755571	−	0.655067i	$-0.772641\pi$
$107$	−60.5676	+	34.9687i	−0.566052	+	0.326811i	0.189519	+	0.981877i	$0.439307\pi$
$108$	−66.9332	+	115.932i	−0.619752	+	1.07344i
$109$	−8.24515	+	8.24515i	−0.0756436	+	0.0756436i	−0.743916	−	0.668273i	$-0.767034\pi$
$109$	−8.24515	+	8.24515i	−0.0756436	+	0.0756436i	0.668273	+	0.743916i	$0.267034\pi$
$110$		0			0
$111$	38.5819	−	10.3380i	0.347584	−	0.0931349i
$112$	−219.524	+	219.524i	−1.96003	+	1.96003i
$113$	48.8736	+	28.2172i	0.432510	+	0.249710i	0.700415	−	0.713736i	$-0.252998\pi$
$113$	48.8736	+	28.2172i	0.432510	+	0.249710i	−0.267906	+	0.963445i	$0.586332\pi$
$114$	−21.5768	+	12.4574i	−0.189271	+	0.109275i
$115$		0			0
$116$		−	20.2773i		−	0.174804i
$117$	51.2947	−	98.4936i	0.438416	−	0.841826i
$118$			170.120i			1.44169i
$119$	−88.5383	−	23.7238i	−0.744019	−	0.199359i
$120$		0			0
$121$	60.7935	+	35.0991i	0.502425	+	0.290075i
$122$	−79.7220	−	79.7220i	−0.653459	−	0.653459i
$123$	21.3255	−	5.71416i	0.173378	−	0.0464566i
$124$	−227.096	+	60.8501i	−1.83142	+	0.490726i
$125$		0			0
$126$	−78.3964	+	135.787i	−0.622194	+	1.07767i
$127$	52.1117	+	90.2601i	0.410328	+	0.710709i	0.994926	−	0.100614i	$-0.0320808\pi$
$127$	52.1117	+	90.2601i	0.410328	+	0.710709i	−0.584597	+	0.811324i	$0.698747\pi$
$128$	−577.127	−	154.641i	−4.50880	−	1.20813i
$129$		−	2.41258i		−	0.0187021i
$130$		0			0
$131$	−171.159			−1.30656			−0.653278	−	0.757118i	$-0.726607\pi$
$131$	−171.159			−1.30656			−0.653278	+	0.757118i	$0.726607\pi$
$132$	14.0773	−	52.5373i	0.106646	−	0.398010i
$133$	−38.3123	+	22.1196i	−0.288062	+	0.166313i
$134$	−18.8244	−	10.8683i	−0.140480	−	0.0811064i
$135$		0			0
$136$	−143.773	−	536.566i	−1.05715	−	3.94534i
$137$	−30.2634	−	112.945i	−0.220901	−	0.824414i	−0.984005	−	0.178139i	$-0.942992\pi$
$137$	−30.2634	−	112.945i	−0.220901	−	0.824414i	0.763104	−	0.646275i	$-0.223674\pi$
$138$	45.5257	−	45.5257i	0.329896	−	0.329896i
$139$	23.7650	−	41.1622i	0.170971	−	0.296131i	−0.767788	−	0.640703i	$-0.778643\pi$
$139$	23.7650	−	41.1622i	0.170971	−	0.296131i	0.938760	+	0.344573i	$0.111976\pi$
$140$		0			0
$141$	10.3854	−	38.7589i	0.0736554	−	0.274886i
$142$	475.619			3.34943
$143$	−20.0709	+	90.4580i	−0.140356	+	0.632574i
$144$	−564.783			−3.92210
$145$		0			0
$146$	60.8764	+	105.441i	0.416962	+	0.722199i
$147$	−9.11657	+	15.7904i	−0.0620175	+	0.107417i
$148$	470.920	+	470.920i	3.18189	+	3.18189i
$149$	−66.2437	−	247.225i	−0.444588	−	1.65923i	−0.717021	−	0.697052i	$-0.754495\pi$
$149$	−66.2437	−	247.225i	−0.444588	−	1.65923i	0.272433	−	0.962175i	$-0.412172\pi$
$150$		0			0
$151$	107.425	+	107.425i	0.711427	+	0.711427i	0.966834	−	0.255407i	$-0.0822094\pi$
$151$	107.425	+	107.425i	0.711427	+	0.711427i	−0.255407	+	0.966834i	$0.582209\pi$
$152$	−232.183	−	134.051i	−1.52752	−	0.881914i
$153$	−83.3763	−	144.412i	−0.544943	−	0.943869i
$154$	33.8599	−	126.367i	0.219870	−	0.820565i
$155$		0			0
$156$	−99.1100	+	4.30965i	−0.635321	+	0.0276260i
$157$		−	59.4781i		−	0.378841i	−0.981896	−	0.189421i	$-0.939339\pi$
$157$		−	59.4781i		−	0.378841i	0.981896	−	0.189421i	$-0.0606610\pi$
$158$	40.4876	−	151.102i	0.256250	−	0.956340i
$159$	−26.8226	−	46.4580i	−0.168695	−	0.292189i
$160$		0			0
$161$	80.8364	−	80.8364i	0.502089	−	0.502089i
$162$	−259.969	+	69.6584i	−1.60474	+	0.429990i
$163$	17.4271	+	65.0388i	0.106915	+	0.399011i	0.998555	−	0.0537328i	$-0.0171119\pi$
$163$	17.4271	+	65.0388i	0.106915	+	0.399011i	−0.891641	+	0.452744i	$0.850445\pi$
$164$	260.294	+	260.294i	1.58716	+	1.58716i
$165$		0			0
$166$	−492.148	+	284.142i	−2.96475	+	1.71170i
$167$	193.429	+	51.8291i	1.15826	+	0.310354i	0.786270	−	0.617883i	$-0.212010\pi$
$167$	193.429	+	51.8291i	1.15826	+	0.310354i	0.371988	+	0.928238i	$0.378676\pi$
$168$	90.3970			0.538078
$169$	168.362	−	14.6697i	0.996226	−	0.0868029i
$170$		0			0
$171$	−77.7386	−	20.8300i	−0.454611	−	0.121813i
$172$	34.8365	−	20.1129i	0.202538	−	0.116935i
$173$	79.4314	−	137.579i	0.459141	−	0.795256i	−0.539775	−	0.841810i	$-0.681491\pi$
$173$	79.4314	−	137.579i	0.459141	−	0.795256i	0.998916	+	0.0465536i	$0.0148238\pi$
$174$	−3.36149	+	3.36149i	−0.0193189	+	0.0193189i
$175$		0			0
$176$	455.186	−	121.967i	2.58628	−	0.692992i
$177$	20.8191	−	20.8191i	0.117622	−	0.117622i
$178$	−217.989	−	125.856i	−1.22466	−	0.707057i
$179$	−6.29150	+	3.63240i	−0.0351481	+	0.0202927i	−0.517471	−	0.855701i	$-0.673126\pi$
$179$	−6.29150	+	3.63240i	−0.0351481	+	0.0202927i	0.482323	+	0.875993i	$0.339793\pi$
$180$		0			0
$181$			40.6680i			0.224685i	0.993670	+	0.112343i	$0.0358354\pi$
$181$			40.6680i			0.224685i	−0.993670	+	0.112343i	$0.964165\pi$
$182$	−238.388	+	10.3659i	−1.30982	+	0.0569557i
$183$			19.5126i			0.106626i
$184$	669.203	+	179.312i	3.63697	+	0.974524i
$185$		0			0
$186$	47.7345	+	27.5595i	0.256637	+	0.148169i
$187$	98.3833	+	98.3833i	0.526114	+	0.526114i
$188$	646.241	−	173.160i	3.43745	−	0.921063i
$189$	53.8272	−	14.4230i	0.284800	−	0.0763120i
$190$		0			0
$191$	50.3575	−	87.2217i	0.263652	−	0.456658i	−0.703558	−	0.710638i	$-0.748406\pi$
$191$	50.3575	−	87.2217i	0.263652	−	0.456658i	0.967210	+	0.253980i	$0.0817397\pi$
$192$	101.761	+	176.255i	0.530005	+	0.917995i
$193$	48.2157	+	12.9194i	0.249822	+	0.0669396i	0.381557	−	0.924345i	$-0.375388\pi$
$193$	48.2157	+	12.9194i	0.249822	+	0.0669396i	−0.131735	+	0.991285i	$0.542055\pi$
$194$			134.778i			0.694731i
$195$		0			0
$196$	−304.008			−1.55106
$197$	31.6818	−	118.238i	0.160821	−	0.600194i	−0.837715	−	0.546108i	$-0.816109\pi$
$197$	31.6818	−	118.238i	0.160821	−	0.600194i	0.998536	−	0.0540858i	$-0.0172244\pi$
$198$	206.113	−	118.999i	1.04098	−	0.601007i
$199$	−240.233	−	138.699i	−1.20720	−	0.696979i	−0.245056	−	0.969509i	$-0.578806\pi$
$199$	−240.233	−	138.699i	−1.20720	−	0.696979i	−0.962147	+	0.272530i	$0.912140\pi$
$200$		0			0
$201$	0.973659	+	3.63375i	0.00484408	+	0.0180783i
$202$	13.5412	+	50.5366i	0.0670358	+	0.250181i
$203$	−5.96873	+	5.96873i	−0.0294026	+	0.0294026i
$204$	−74.4820	+	129.007i	−0.365108	+	0.632385i
$205$		0			0
$206$	−28.8300	+	107.595i	−0.139951	+	0.522306i
$207$	207.973			1.00470
$208$	−461.684	−	724.982i	−2.21963	−	3.48549i
$209$	67.1516			0.321299
$210$		0			0
$211$	5.64470	+	9.77692i	0.0267522	+	0.0463361i	0.879092	−	0.476653i	$-0.158150\pi$
$211$	5.64470	+	9.77692i	0.0267522	+	0.0463361i	−0.852339	+	0.522989i	$0.824817\pi$
$212$	447.222	−	774.612i	2.10954	−	3.65383i
$213$	−58.2057	−	58.2057i	−0.273266	−	0.273266i
$214$	70.7564	+	264.067i	0.330637	+	1.23396i
$215$		0			0
$216$	238.801	+	238.801i	1.10556	+	1.10556i
$217$	84.7583	+	48.9352i	0.390591	+	0.225508i
$218$	22.7900	+	39.4734i	0.104541	+	0.181070i
$219$	5.45376	−	20.3537i	0.0249030	−	0.0929394i
$220$		0			0
$221$	117.218	−	225.076i	0.530397	−	1.01844i
$222$		−	156.135i		−	0.703309i
$223$	54.2514	−	202.469i	0.243280	−	0.907932i	−0.730961	−	0.682420i	$-0.760928\pi$
$223$	54.2514	−	202.469i	0.243280	−	0.907932i	0.974240	−	0.225513i	$-0.0724057\pi$
$224$	339.531	+	588.085i	1.51576	+	2.62538i
$225$		0			0
$226$	155.987	−	155.987i	0.690208	−	0.690208i
$227$	38.0720	−	10.2014i	0.167718	−	0.0449399i	−0.173983	−	0.984749i	$-0.555664\pi$
$227$	38.0720	−	10.2014i	0.167718	−	0.0449399i	0.341701	+	0.939809i	$0.388997\pi$
$228$	18.6079	+	69.4457i	0.0816136	+	0.304586i
$229$	−198.602	−	198.602i	−0.867260	−	0.867260i	0.124909	−	0.992168i	$-0.460136\pi$
$229$	−198.602	−	198.602i	−0.867260	−	0.867260i	−0.992168	+	0.124909i	$0.960136\pi$
$230$		0			0
$231$	−19.6084	+	11.3209i	−0.0848847	+	0.0490082i
$232$	−49.4121	−	13.2399i	−0.212983	−	0.0570686i
$233$	20.5995			0.0884099			0.0442049	−	0.999022i	$-0.485925\pi$
$233$	20.5995			0.0884099			0.0442049	+	0.999022i	$0.485925\pi$
$234$	−319.992	−	293.323i	−1.36749	−	1.25352i
$235$		0			0
$236$	474.180	+	127.056i	2.00924	+	0.538374i
$237$	−23.4464	+	13.5368i	−0.0989302	+	0.0571174i
$238$	−179.150	+	310.297i	−0.752732	+	1.30377i
$239$	−102.578	+	102.578i	−0.429198	+	0.429198i	−0.888355	−	0.459157i	$-0.848151\pi$
$239$	−102.578	+	102.578i	−0.429198	+	0.429198i	0.459157	+	0.888355i	$0.348151\pi$
$240$		0			0
$241$	21.0941	−	5.65216i	0.0875275	−	0.0234529i	−0.214790	−	0.976660i	$-0.568907\pi$
$241$	21.0941	−	5.65216i	0.0875275	−	0.0234529i	0.302317	+	0.953207i	$0.402240\pi$
$242$	194.031	−	194.031i	0.801781	−	0.801781i
$243$	132.839	+	76.6947i	0.546663	+	0.315616i
$244$	−281.753	+	162.670i	−1.15472	+	0.666680i
$245$		0			0
$246$		−	86.3010i		−	0.350817i
$247$	−36.8093	−	116.816i	−0.149026	−	0.472941i
$248$			593.122i			2.39162i
$249$	95.0014	+	25.4556i	0.381532	+	0.102231i
$250$		0			0
$251$	−317.484	−	183.299i	−1.26488	−	0.730276i	−0.290862	−	0.956765i	$-0.593942\pi$
$251$	−317.484	−	183.299i	−1.26488	−	0.730276i	−0.974014	+	0.226489i	$0.927275\pi$
$252$	319.930	+	319.930i	1.26956	+	1.26956i
$253$	−167.616	+	44.9125i	−0.662512	+	0.177520i
$254$	393.522	−	105.444i	1.54930	−	0.415133i
$255$		0			0
$256$	−566.097	+	980.509i	−2.21132	+	3.83011i
$257$	148.790	+	257.712i	0.578949	+	1.00277i	0.995600	+	0.0937031i	$0.0298705\pi$
$257$	148.790	+	257.712i	0.578949	+	1.00277i	−0.416651	+	0.909067i	$0.636796\pi$
$258$	−9.10929	−	2.44083i	−0.0353073	−	0.00946057i
$259$		−	277.236i		−	1.07041i
$260$		0			0
$261$	−15.3561			−0.0588358
$262$	−173.163	+	646.253i	−0.660927	+	2.46661i
$263$	2.13671	−	1.23363i	0.00812437	−	0.00469061i	−0.495932	−	0.868361i	$-0.665174\pi$
$263$	2.13671	−	1.23363i	0.00812437	−	0.00469061i	0.504057	+	0.863671i	$0.331840\pi$
$264$	−118.832	−	68.6077i	−0.450121	−	0.259878i
$265$		0			0
$266$	44.7573	+	167.036i	0.168260	+	0.627956i
$267$	11.2751	+	42.0794i	0.0422290	+	0.157601i
$268$	−44.3526	+	44.3526i	−0.165495	+	0.165495i
$269$	−9.39160	+	16.2667i	−0.0349130	+	0.0604711i	−0.882954	−	0.469460i	$-0.844449\pi$
$269$	−9.39160	+	16.2667i	−0.0349130	+	0.0604711i	0.848041	+	0.529931i	$0.177782\pi$
$270$		0			0
$271$	−81.2004	+	303.044i	−0.299633	+	1.11824i	0.637835	+	0.770173i	$0.279830\pi$
$271$	−81.2004	+	303.044i	−0.299633	+	1.11824i	−0.937468	+	0.348071i	$0.886837\pi$
$272$	−1290.63			−4.74497
$273$	30.4421	+	27.9050i	0.111510	+	0.102216i
$274$	−457.069			−1.66814
$275$		0			0
$276$	−92.8936	−	160.896i	−0.336571	−	0.582958i
$277$	−145.427	+	251.886i	−0.525006	+	0.909337i	0.474570	+	0.880218i	$0.342604\pi$
$277$	−145.427	+	251.886i	−0.525006	+	0.909337i	−0.999576	+	0.0291194i	$0.990730\pi$
$278$	−131.375	−	131.375i	−0.472572	−	0.472572i
$279$	46.0822	+	171.981i	0.165169	+	0.616420i
$280$		0			0
$281$	52.7748	+	52.7748i	0.187811	+	0.187811i	0.794749	−	0.606938i	$-0.207602\pi$
$281$	52.7748	+	52.7748i	0.187811	+	0.187811i	−0.606938	+	0.794749i	$0.707602\pi$
$282$	−135.837	−	78.4255i	−0.481691	−	0.278105i
$283$	175.204	+	303.462i	0.619095	+	1.07230i	0.989651	+	0.143494i	$0.0458339\pi$
$283$	175.204	+	303.462i	0.619095	+	1.07230i	−0.370556	+	0.928810i	$0.620833\pi$
$284$	355.222	−	1325.71i	1.25078	−	4.66798i
$285$		0			0
$286$	321.241	+	167.300i	1.12322	+	0.584965i
$287$		−	153.238i		−	0.533930i
$288$	−319.736	+	1193.27i	−1.11019	+	4.14330i
$289$	−46.0301	−	79.7265i	−0.159274	−	0.275870i
$290$		0			0
$291$	16.4939	−	16.4939i	0.0566802	−	0.0566802i
$292$	339.365	−	90.9326i	1.16221	−	0.311413i
$293$	32.6677	+	121.918i	0.111494	+	0.416101i	0.999001	−	0.0446937i	$-0.0142312\pi$
$293$	32.6677	+	121.918i	0.111494	+	0.416101i	−0.887507	+	0.460794i	$0.847565\pi$
$294$	50.3972	+	50.3972i	0.171419	+	0.171419i
$295$		0			0
$296$	1455.03	−	840.062i	4.91564	−	2.83805i
$297$	−81.7054	−	21.8929i	−0.275102	−	0.0737135i
$298$	−1000.48			−3.35731
$299$	170.008	+	266.964i	0.568590	+	0.892856i
$300$		0			0
$301$	−16.1746	−	4.33398i	−0.0537364	−	0.0143986i
$302$	514.295	−	296.929i	1.70296	−	0.983207i
$303$	4.52744	−	7.84176i	0.0149421	−	0.0258804i
$304$	−440.461	+	440.461i	−1.44888	+	1.44888i
$305$		0			0
$306$	−629.617	+	168.705i	−2.05757	+	0.551324i
$307$	379.492	−	379.492i	1.23613	−	1.23613i	0.274560	−	0.961570i	$-0.411468\pi$
$307$	379.492	−	379.492i	1.23613	−	1.23613i	0.961570	−	0.274560i	$-0.0885321\pi$
$308$	−326.937	−	188.757i	−1.06148	−	0.612848i
$309$	16.6955	−	9.63916i	0.0540308	−	0.0311947i
$310$		0			0
$311$			384.559i			1.23652i	0.785972	+	0.618262i	$0.212163\pi$
$311$			384.559i			1.23652i	−0.785972	+	0.618262i	$0.787837\pi$
$312$	−54.2114	+	244.327i	−0.173754	+	0.783099i
$313$			50.9420i			0.162754i	0.996683	+	0.0813770i	$0.0259318\pi$
$313$			50.9420i			0.162754i	−0.996683	+	0.0813770i	$0.974068\pi$
$314$	−224.574	−	60.1746i	−0.715205	−	0.191639i
$315$		0			0
$316$	−390.931	−	225.704i	−1.23712	−	0.714254i
$317$	−401.507	−	401.507i	−1.26658	−	1.26658i	−0.947842	−	0.318740i	$-0.896740\pi$
$317$	−401.507	−	401.507i	−1.26658	−	1.26658i	−0.318740	−	0.947842i	$-0.603260\pi$
$318$	−202.551	+	54.2733i	−0.636952	+	0.170671i
$319$	12.3763	−	3.31621i	0.0387971	−	0.0103956i
$320$		0			0
$321$	23.6570	−	40.9752i	0.0736980	−	0.127649i
$322$	−223.435	−	387.001i	−0.693898	−	1.20187i
$323$	−177.647	−	47.6003i	−0.549990	−	0.147369i
$324$			776.643i			2.39704i
$325$		0			0
$326$	263.201			0.807366
$327$	2.04169	−	7.61971i	0.00624371	−	0.0233019i
$328$	804.246	−	464.332i	2.45197	−	1.41565i
$329$	−241.195	−	139.254i	−0.733115	−	0.423264i
$330$		0			0
$331$	127.416	+	475.521i	0.384941	+	1.43662i	0.838260	+	0.545271i	$0.183573\pi$
$331$	127.416	+	475.521i	0.384941	+	1.43662i	−0.453318	+	0.891349i	$0.649760\pi$
$332$	424.430	+	1583.99i	1.27840	+	4.77106i
$333$	356.631	−	356.631i	1.07097	−	1.07097i
$334$	391.388	−	677.904i	1.17182	−	2.02965i
$335$		0			0
$336$	54.3592	−	202.871i	0.161783	−	0.603784i
$337$	−440.453			−1.30698			−0.653492	−	0.756934i	$-0.726697\pi$
$337$	−440.453			−1.30698			−0.653492	+	0.756934i	$0.726697\pi$
$338$	114.944	−	650.535i	0.340072	−	1.92466i
$339$	−38.1790			−0.112622
$340$		0			0
$341$	−74.2798	−	128.656i	−0.217829	−	0.377291i
$342$	−157.298	+	272.448i	−0.459935	+	0.796631i
$343$	252.180	+	252.180i	0.735220	+	0.735220i
$344$	−26.2651	−	98.0228i	−0.0763521	−	0.284950i
$345$		0			0
$346$	−439.104	−	439.104i	−1.26909	−	1.26909i
$347$	89.8817	+	51.8932i	0.259025	+	0.149548i	0.623890	−	0.781512i	$-0.285551\pi$
$347$	89.8817	+	51.8932i	0.259025	+	0.149548i	−0.364865	+	0.931061i	$0.618885\pi$
$348$	6.85900	+	11.8801i	0.0197098	+	0.0341383i
$349$	−107.471	+	401.086i	−0.307939	+	1.14924i	0.622447	+	0.782662i	$0.286138\pi$
$349$	−107.471	+	401.086i	−0.307939	+	1.14924i	−0.930386	+	0.366581i	$0.880528\pi$
$350$		0			0
$351$	6.70233	+	154.135i	0.0190949	+	0.439131i
$352$		−	1030.76i		−	2.92830i
$353$	−14.3072	+	53.3953i	−0.0405304	+	0.151261i	−0.983226	−	0.182394i	$-0.941615\pi$
$353$	−14.3072	+	53.3953i	−0.0405304	+	0.151261i	0.942695	+	0.333655i	$0.108282\pi$
$354$	−57.5448	−	99.6705i	−0.162556	−	0.281555i
$355$		0			0
$356$	−513.610	+	513.610i	−1.44273	+	1.44273i
$357$	59.8979	−	16.0496i	0.167781	−	0.0449569i
$358$	7.34987	+	27.4301i	0.0205304	+	0.0766204i
$359$	220.652	+	220.652i	0.614630	+	0.614630i	0.944149	−	0.329519i	$-0.106886\pi$
$359$	220.652	+	220.652i	0.614630	+	0.614630i	−0.329519	+	0.944149i	$0.606886\pi$
$360$		0			0
$361$	235.764	−	136.118i	0.653085	−	0.377059i
$362$	153.552	+	41.1442i	0.424178	+	0.113658i
$363$	−47.4905			−0.130828
$364$	−149.149	+	672.206i	−0.409751	+	1.84672i
$365$		0			0
$366$	73.6746	+	19.7410i	0.201297	+	0.0539373i
$367$	−498.267	+	287.675i	−1.35768	+	0.783854i	−0.989310	−	0.145827i	$-0.953416\pi$
$367$	−498.267	+	287.675i	−1.35768	+	0.783854i	−0.368365	+	0.929681i	$0.620082\pi$
$368$	804.835	−	1394.01i	2.18705	−	3.78808i
$369$	197.123	−	197.123i	0.534208	−	0.534208i
$370$		0			0
$371$	−359.653	+	96.3688i	−0.969416	+	0.259754i
$372$	112.468	−	112.468i	0.302334	−	0.302334i
$373$	161.923	+	93.4865i	0.434111	+	0.250634i	0.701097	−	0.713066i	$-0.252694\pi$
$373$	161.923	+	93.4865i	0.434111	+	0.250634i	−0.266985	+	0.963701i	$0.586028\pi$
$374$	471.006	−	271.936i	1.25937	−	0.727100i
$375$		0			0
$376$		−	1687.83i		−	4.48892i
$377$	−12.5529	−	19.7119i	−0.0332969	−	0.0522861i
$378$		−	217.830i		−	0.576270i
$379$	589.586	+	157.979i	1.55564	+	0.416832i	0.931279	−	0.364307i	$-0.118694\pi$
$379$	589.586	+	157.979i	1.55564	+	0.416832i	0.624358	+	0.781139i	$0.285361\pi$
$380$		0			0
$381$	−61.0628	−	35.2546i	−0.160270	−	0.0925318i
$382$	−278.381	−	278.381i	−0.728745	−	0.728745i
$383$	−20.2953	+	5.43811i	−0.0529904	+	0.0141987i	−0.285217	−	0.958463i	$-0.592066\pi$
$383$	−20.2953	+	5.43811i	−0.0529904	+	0.0141987i	0.232226	+	0.972662i	$0.425399\pi$
$384$	390.438	−	104.618i	1.01677	−	0.272441i
$385$		0			0
$386$	97.5605	−	168.980i	0.252748	−	0.437772i
$387$	−15.2316	−	26.3820i	−0.0393582	−	0.0681704i
$388$	375.670	+	100.660i	0.968221	+	0.259434i
$389$			426.740i			1.09702i	0.836145	+	0.548509i	$0.184804\pi$
$389$			426.740i			1.09702i	−0.836145	+	0.548509i	$0.815196\pi$
$390$		0			0
$391$	475.256			1.21549
$392$	−198.500	+	740.812i	−0.506377	+	1.88983i
$393$	100.279	−	57.8962i	0.255163	−	0.147318i
$394$	−414.385	−	239.245i	−1.05174	−	0.607222i
$395$		0			0
$396$	−177.752	−	663.381i	−0.448869	−	1.67520i
$397$	47.3096	+	176.562i	0.119168	+	0.444740i	0.999565	−	0.0294969i	$-0.00939053\pi$
$397$	47.3096	+	176.562i	0.119168	+	0.444740i	−0.880397	+	0.474237i	$0.842724\pi$
$398$	−766.739	+	766.739i	−1.92648	+	1.92648i
$399$	14.9644	−	25.9190i	0.0375047	−	0.0649600i
$400$		0			0
$401$	75.7220	−	282.598i	0.188833	−	0.704734i	−0.804945	−	0.593350i	$-0.797805\pi$
$401$	75.7220	−	282.598i	0.188833	−	0.704734i	0.993777	−	0.111384i	$-0.0355283\pi$
$402$	14.7052			0.0365801
$403$	−183.093	+	199.740i	−0.454325	+	0.495632i
$404$	150.975			0.373701
$405$		0			0
$406$	16.4978	+	28.5751i	0.0406350	+	0.0703819i
$407$	−210.411	+	364.442i	−0.516980	+	0.895435i
$408$	265.733	+	265.733i	0.651306	+	0.651306i
$409$	159.847	+	596.557i	0.390824	+	1.45857i	0.828779	+	0.559577i	$0.189036\pi$
$409$	159.847	+	596.557i	0.390824	+	1.45857i	−0.437955	+	0.898997i	$0.644297\pi$
$410$		0			0
$411$	55.9355	+	55.9355i	0.136096	+	0.136096i
$412$	278.370	+	160.717i	0.675656	+	0.390090i
$413$	−102.178	−	176.977i	−0.247404	−	0.428516i
$414$	210.408	−	785.255i	0.508233	−	1.89675i
$415$		0			0
$416$	−1793.11	+	565.015i	−4.31035	+	1.35821i
$417$			32.1550i			0.0771103i
$418$	67.9379	−	253.548i	0.162531	−	0.606574i
$419$	145.778	+	252.496i	0.347920	+	0.602615i	0.985880	−	0.167455i	$-0.0535548\pi$
$419$	145.778	+	252.496i	0.347920	+	0.602615i	−0.637960	+	0.770070i	$0.720221\pi$
$420$		0			0
$421$	541.067	−	541.067i	1.28519	−	1.28519i	0.347523	−	0.937672i	$-0.387023\pi$
$421$	541.067	−	541.067i	1.28519	−	1.28519i	0.937672	−	0.347523i	$-0.112977\pi$
$422$	42.6260	−	11.4216i	0.101010	−	0.0270654i
$423$	−131.135	−	489.403i	−0.310012	−	1.15698i
$424$	−1595.58	−	1595.58i	−3.76315	−	3.76315i
$425$		0			0
$426$	−278.658	+	160.883i	−0.654126	+	0.377660i
$427$	130.818	+	35.0526i	0.306366	+	0.0820904i
$428$	788.885			1.84319
$429$	−18.8391	−	59.7870i	−0.0439141	−	0.139364i
$430$		0			0
$431$	−609.389	−	163.285i	−1.41390	−	0.378852i	−0.530581	−	0.847634i	$-0.678026\pi$
$431$	−609.389	−	163.285i	−1.41390	−	0.378852i	−0.883314	+	0.468782i	$0.844693\pi$
$432$	679.522	−	392.322i	1.57297	−	0.908154i
$433$	−190.701	+	330.304i	−0.440419	+	0.762828i	−0.997720	−	0.0674824i	$-0.978503\pi$
$433$	−190.701	+	330.304i	−0.440419	+	0.762828i	0.557302	+	0.830310i	$0.311837\pi$
$434$	270.518	−	270.518i	0.623314	−	0.623314i
$435$		0			0
$436$	127.046	−	34.0419i	0.291390	−	0.0780778i
$437$	162.193	−	162.193i	0.371152	−	0.371152i
$438$	−71.3330	−	41.1841i	−0.162861	−	0.0940277i
$439$	−620.437	+	358.209i	−1.41330	+	0.815966i	−0.995697	−	0.0926655i	$-0.970461\pi$
$439$	−620.437	+	358.209i	−1.41330	+	0.815966i	−0.417598	+	0.908632i	$0.637128\pi$
$440$		0			0
$441$			230.227i			0.522058i
$442$	−731.241	−	670.297i	−1.65439	−	1.51651i
$443$		−	463.386i		−	1.04602i	−0.852327	−	0.523010i	$-0.824809\pi$
$443$		−	463.386i		−	1.04602i	0.852327	−	0.523010i	$-0.175191\pi$
$444$	−435.198	−	116.611i	−0.980176	−	0.262637i
$445$		0			0
$446$	−709.586	−	409.680i	−1.59100	−	0.918564i
$447$	122.437	+	122.437i	0.273909	+	0.273909i
$448$	1364.47	−	365.609i	3.04570	−	0.816092i
$449$	−672.899	+	180.303i	−1.49866	+	0.401565i	−0.912651	−	0.408739i	$-0.865969\pi$
$449$	−672.899	+	180.303i	−1.49866	+	0.401565i	−0.586010	+	0.810304i	$0.699302\pi$
$450$		0			0
$451$	−116.301	+	201.440i	−0.257874	+	0.446652i
$452$	−318.286	−	551.287i	−0.704172	−	1.21966i
$453$	−99.2765	−	26.6011i	−0.219154	−	0.0587220i
$454$		−	154.071i		−	0.339364i
$455$		0			0
$456$	181.376			0.397755
$457$	16.1775	−	60.3753i	0.0353994	−	0.132112i	−0.945965	−	0.324269i	$-0.894882\pi$
$457$	16.1775	−	60.3753i	0.0353994	−	0.132112i	0.981364	+	0.192157i	$0.0615483\pi$
$458$	−950.802	+	548.946i	−2.07599	+	1.19857i
$459$	200.630	+	115.834i	0.437102	+	0.252361i
$460$		0			0
$461$	−87.7005	−	327.303i	−0.190240	−	0.709985i	−0.993448	−	0.114286i	$-0.963542\pi$
$461$	−87.7005	−	327.303i	−0.190240	−	0.709985i	0.803208	−	0.595699i	$-0.203125\pi$
$462$	22.9069	+	85.4898i	0.0495821	+	0.185043i
$463$	108.625	−	108.625i	0.234612	−	0.234612i	−0.580003	−	0.814615i	$-0.696948\pi$
$463$	108.625	−	108.625i	0.234612	−	0.234612i	0.814615	+	0.580003i	$0.196948\pi$
$464$	−59.4267	+	102.930i	−0.128075	+	0.221832i
$465$		0			0
$466$	20.8407	−	77.7786i	0.0447226	−	0.166907i
$467$	20.6180			0.0441499			0.0220749	−	0.999756i	$-0.492973\pi$
$467$	20.6180			0.0441499			0.0220749	+	0.999756i	$0.492973\pi$
$468$	−1056.58	+	672.851i	−2.25764	+	1.43772i
$469$	26.1108			0.0556734
$470$		0			0
$471$	20.1191	+	34.8472i	0.0427156	+	0.0739856i
$472$	619.225	−	1072.53i	1.31192	−	2.27231i
$473$	17.9732	+	17.9732i	0.0379983	+	0.0379983i
$474$	27.3907	+	102.223i	0.0577862	+	0.215661i
$475$		0			0
$476$	731.099	+	731.099i	1.53592	+	1.53592i
$477$	−586.619	−	338.685i	−1.22981	−	0.710031i
$478$	283.531	+	491.090i	0.593161	+	1.02738i
$479$	−172.750	+	644.710i	−0.360646	+	1.34595i	0.512581	+	0.858639i	$0.328689\pi$
$479$	−172.750	+	644.710i	−0.360646	+	1.34595i	−0.873228	+	0.487312i	$0.837977\pi$
$480$		0			0
$481$	749.319	+	166.259i	1.55783	+	0.345653i
$482$		−	85.3646i		−	0.177105i
$483$	−20.0170	+	74.7044i	−0.0414430	+	0.154668i
$484$	−395.913	−	685.742i	−0.818003	−	1.41682i
$485$		0			0
$486$	423.975	−	423.975i	0.872376	−	0.872376i
$487$	235.454	−	63.0896i	0.483478	−	0.129548i	−0.00884365	−	0.999961i	$-0.502815\pi$
$487$	235.454	−	63.0896i	0.483478	−	0.129548i	0.492322	+	0.870413i	$0.336148\pi$
$488$	212.428	+	792.793i	0.435304	+	1.62458i
$489$	−32.2103	−	32.2103i	−0.0658696	−	0.0658696i
$490$		0			0
$491$	−708.021	+	408.776i	−1.44200	+	0.832538i	−0.997983	−	0.0634815i	$-0.979780\pi$
$491$	−708.021	+	408.776i	−1.44200	+	0.832538i	−0.444015	+	0.896019i	$0.646446\pi$
$492$	−240.549	−	64.4549i	−0.488921	−	0.131006i
$493$	−35.0916			−0.0711797
$494$	−478.310	+	20.7986i	−0.968239	+	0.0421025i
$495$		0			0
$496$	1331.10	+	356.667i	2.68367	+	0.719086i
$497$	−494.790	+	285.667i	−0.995554	+	0.574783i
$498$	192.228	−	332.948i	0.385999	−	0.668571i
$499$	152.575	−	152.575i	0.305761	−	0.305761i	−0.537501	−	0.843263i	$-0.680632\pi$
$499$	152.575	−	152.575i	0.305761	−	0.305761i	0.843263	+	0.537501i	$0.180632\pi$
$500$		0			0
$501$	−130.859	+	35.0634i	−0.261195	+	0.0699869i
$502$	−1013.29	+	1013.29i	−2.01851	+	2.01851i
$503$	229.662	+	132.595i	0.456585	+	0.263609i	0.710607	−	0.703589i	$-0.248420\pi$
$503$	229.662	+	132.595i	0.456585	+	0.263609i	−0.254022	+	0.967198i	$0.581754\pi$
$504$	988.508	−	570.715i	1.96132	−	1.13237i
$505$		0			0
$506$			678.313i			1.34054i
$507$	−93.6784	+	65.5449i	−0.184770	+	0.129280i
$508$		−	1175.63i		−	2.31422i
$509$	10.9516	+	2.93446i	0.0215158	+	0.00576515i	0.269561	−	0.962983i	$-0.413121\pi$
$509$	10.9516	+	2.93446i	0.0215158	+	0.00576515i	−0.248045	+	0.968748i	$0.579788\pi$
$510$		0			0
$511$	−126.660	−	73.1274i	−0.247868	−	0.143106i
$512$	1439.49	+	1439.49i	2.81150	+	2.81150i
$513$	108.001	−	28.9388i	0.210529	−	0.0564109i
$514$	1123.59	−	301.065i	2.18597	−	0.585729i
$515$		0			0
$516$	−13.6068	+	23.5676i	−0.0263697	+	0.0456737i
$517$	211.376	+	366.115i	0.408852	+	0.708152i
$518$	−1046.77	−	280.482i	−2.02080	−	0.541471i
$519$			107.474i			0.207079i
$520$		0			0
$521$	−578.575			−1.11051			−0.555255	−	0.831680i	$-0.687379\pi$
$521$	−578.575			−1.11051			−0.555255	+	0.831680i	$0.687379\pi$
$522$	−15.5360	+	57.9810i	−0.0297624	+	0.111075i
$523$	−555.704	+	320.836i	−1.06253	+	0.613453i	−0.926132	−	0.377200i	$-0.876887\pi$
$523$	−555.704	+	320.836i	−1.06253	+	0.613453i	−0.136401	+	0.990654i	$0.543553\pi$
$524$	1671.99	+	965.324i	3.19082	+	1.84222i
$525$		0			0
$526$	−2.49615	−	9.31576i	−0.00474553	−	0.0177106i
$527$	105.306	+	393.008i	0.199822	+	0.745746i
$528$	−225.429	+	225.429i	−0.426950	+	0.426950i
$529$	−31.8688	+	55.1984i	−0.0602435	+	0.104345i
$530$		0			0
$531$	96.2205	−	359.100i	0.181206	−	0.676271i
$532$	499.012			0.937993
$533$	414.174	+	91.8972i	0.777063	+	0.172415i
$534$	170.288			0.318892
$535$		0			0
$536$	79.1194	+	137.039i	0.147611	+	0.255669i
$537$	2.45739	−	4.25633i	0.00457615	−	0.00792612i
$538$	51.9175	+	51.9175i	0.0965010	+	0.0965010i
$539$	−49.7183	−	185.551i	−0.0922418	−	0.344251i
$540$		0			0
$541$	540.347	+	540.347i	0.998792	+	0.998792i	0.999999	−	0.00120694i	$-0.000384180\pi$
$541$	540.347	+	540.347i	0.998792	+	0.998792i	−0.00120694	+	0.999999i	$0.500384\pi$
$542$	1062.07	+	613.186i	1.95954	+	1.13134i
$543$	−13.7564	−	23.8267i	−0.0253340	−	0.0438798i
$544$	−730.655	+	2726.84i	−1.34312	+	5.01257i
$545$		0			0
$546$	136.161	−	86.7102i	0.249379	−	0.158810i
$547$			566.490i			1.03563i	0.855492	+	0.517816i	$0.173255\pi$
$547$			566.490i			1.03563i	−0.855492	+	0.517816i	$0.826745\pi$
$548$	−341.368	+	1274.00i	−0.622933	+	2.32482i
$549$	123.191	+	213.373i	0.224392	+	0.388658i
$550$		0			0
$551$	−11.9759	+	11.9759i	−0.0217348	+	0.0217348i
$552$	−452.729	+	121.308i	−0.820162	+	0.219762i
$553$	48.6354	+	181.510i	0.0879483	+	0.328228i
$554$	803.931	+	803.931i	1.45114	+	1.45114i
$555$		0			0
$556$	−464.304	+	268.066i	−0.835079	+	0.482133i
$557$	−390.869	−	104.733i	−0.701740	−	0.188031i	−0.109730	−	0.993961i	$-0.534999\pi$
$557$	−390.869	−	104.733i	−0.701740	−	0.188031i	−0.592010	+	0.805931i	$0.701665\pi$
$558$	695.980			1.24728
$559$	21.4140	−	41.1181i	0.0383076	−	0.0735565i
$560$		0			0
$561$	−90.9202	−	24.3620i	−0.162068	−	0.0434260i
$562$	252.658	−	145.872i	0.449569	−	0.259559i
$563$	217.275	−	376.332i	0.385924	−	0.668441i	−0.605973	−	0.795486i	$-0.707216\pi$
$563$	217.275	−	376.332i	0.385924	−	0.668441i	0.991897	+	0.127045i	$0.0405492\pi$
$564$	−320.049	+	320.049i	−0.567463	+	0.567463i
$565$		0			0
$566$	1323.05	−	354.511i	2.33755	−	0.626345i
$567$	228.609	−	228.609i	0.403190	−	0.403190i
$568$	−2998.56	−	1731.22i	−5.27916	−	3.04793i
$569$	868.478	−	501.416i	1.52632	−	0.881223i	0.526811	−	0.849982i	$-0.323387\pi$
$569$	868.478	−	501.416i	1.52632	−	0.881223i	0.999512	−	0.0312407i	$-0.00994585\pi$
$570$		0			0
$571$			900.202i			1.57654i	0.615332	+	0.788268i	$0.289022\pi$
$571$			900.202i			1.57654i	−0.615332	+	0.788268i	$0.710978\pi$
$572$	706.242	−	770.454i	1.23469	−	1.34695i
$573$			68.1357i			0.118910i
$574$	−578.588	−	155.032i	−1.00799	−	0.270091i
$575$		0			0
$576$	2225.55	+	1284.92i	3.86380	+	2.23076i
$577$	−707.660	−	707.660i	−1.22645	−	1.22645i	−0.965298	−	0.261149i	$-0.915898\pi$
$577$	−707.660	−	707.660i	−1.22645	−	1.22645i	−0.261149	−	0.965298i	$-0.584102\pi$
$578$	−347.597	+	93.1383i	−0.601378	+	0.161139i
$579$	−32.6189	+	8.74020i	−0.0563366	+	0.0150953i
$580$		0			0
$581$	341.324	−	591.190i	0.587476	−	1.01754i
$582$	−45.5899	−	78.9641i	−0.0783332	−	0.135677i
$583$	545.925	+	146.280i	0.936406	+	0.250909i
$584$		−	886.344i		−	1.51771i
$585$		0			0
$586$	493.381			0.841946
$587$	114.520	−	427.394i	0.195094	−	0.728099i	−0.797149	−	0.603783i	$-0.793659\pi$
$587$	114.520	−	427.394i	0.195094	−	0.728099i	0.992243	−	0.124317i	$-0.0396738\pi$
$588$	178.113	−	102.834i	0.302914	−	0.174887i
$589$	170.063	+	98.1856i	0.288731	+	0.166699i
$590$		0			0
$591$	21.4334	+	79.9905i	0.0362663	+	0.135348i
$592$	−1010.32	−	3770.58i	−1.70663	−	6.36922i
$593$	69.9257	−	69.9257i	0.117919	−	0.117919i	−0.645685	−	0.763604i	$-0.723428\pi$
$593$	69.9257	−	69.9257i	0.117919	−	0.117919i	0.763604	+	0.645685i	$0.223428\pi$
$594$	−165.324	+	286.350i	−0.278324	+	0.482071i
$595$		0			0
$596$	−747.219	+	2788.66i	−1.25372	+	4.67896i
$597$	187.665			0.314347
$598$	1179.99	−	371.819i	1.97323	−	0.621772i
$599$	−817.519			−1.36481			−0.682403	−	0.730976i	$-0.739065\pi$
$599$	−817.519			−1.36481			−0.682403	+	0.730976i	$0.739065\pi$
$600$		0			0
$601$	−454.343	−	786.945i	−0.755978	−	1.30939i	−0.944887	−	0.327398i	$-0.893828\pi$
$601$	−454.343	−	786.945i	−0.755978	−	1.30939i	0.188909	−	0.981995i	$-0.439505\pi$
$602$	−32.7281	+	56.6867i	−0.0543656	+	0.0941640i
$603$	33.5885	+	33.5885i	0.0557024	+	0.0557024i
$604$	−443.529	−	1655.27i	−0.734320	−	2.74052i
$605$		0			0
$606$	−25.0281	−	25.0281i	−0.0413005	−	0.0413005i
$607$	−695.997	−	401.834i	−1.14662	−	0.662000i	−0.198557	−	0.980089i	$-0.563625\pi$
$607$	−695.997	−	401.834i	−1.14662	−	0.662000i	−0.948061	+	0.318089i	$0.896959\pi$
$608$	681.249	+	1179.96i	1.12048	+	1.94072i
$609$	1.47800	−	5.51596i	0.00242693	−	0.00905741i
$610$		0			0
$611$	521.024	−	568.396i	0.852740	−	0.930271i
$612$			1880.95i			3.07344i
$613$	−198.988	+	742.633i	−0.324613	+	1.21147i	0.590087	+	0.807340i	$0.299094\pi$
$613$	−198.988	+	742.633i	−0.324613	+	1.21147i	−0.914700	+	0.404134i	$0.867573\pi$
$614$	−1048.93	−	1816.80i	−1.70836	−	2.95896i
$615$		0			0
$616$	−673.438	+	673.438i	−1.09324	+	1.09324i
$617$	210.145	−	56.3082i	0.340592	−	0.0912613i	−0.0844690	−	0.996426i	$-0.526919\pi$
$617$	210.145	−	56.3082i	0.340592	−	0.0912613i	0.425061	+	0.905165i	$0.360253\pi$
$618$	−19.5041	−	72.7902i	−0.0315600	−	0.117783i
$619$	86.7747	+	86.7747i	0.140185	+	0.140185i	0.773717	−	0.633532i	$-0.218395\pi$
$619$	86.7747	+	86.7747i	0.140185	+	0.140185i	−0.633532	+	0.773717i	$0.718395\pi$
$620$		0			0
$621$	−250.224	+	144.467i	−0.402938	+	0.232636i
$622$	1452.00	+	389.062i	2.33441	+	0.625502i
$623$	302.368			0.485342
$624$	515.725	+	268.586i	0.826483	+	0.430426i
$625$		0			0
$626$	192.344	+	51.5385i	0.307259	+	0.0823299i
$627$	−39.3430	+	22.7147i	−0.0627480	+	0.0362276i
$628$	−335.452	+	581.020i	−0.534160	+	0.925192i
$629$	814.968	−	814.968i	1.29566	−	1.29566i
$630$		0			0
$631$	−425.593	+	114.037i	−0.674473	+	0.180725i	−0.579769	−	0.814781i	$-0.696857\pi$
$631$	−425.593	+	114.037i	−0.674473	+	0.180725i	−0.0947043	+	0.995505i	$0.530191\pi$
$632$	−805.255	+	805.255i	−1.27414	+	1.27414i
$633$	−6.61428	−	3.81876i	−0.0104491	−	0.00603279i
$634$	−1922.20	+	1109.78i	−3.03186	+	1.75044i
$635$		0			0
$636$			605.110i			0.951430i
$637$	−295.531	+	188.200i	−0.463941	+	0.295448i
$638$		−	50.0847i		−	0.0785027i
$639$	−1003.97	−	269.012i	−1.57115	−	0.420989i
$640$		0			0
$641$	−221.018	−	127.605i	−0.344801	−	0.199071i	0.317592	−	0.948227i	$-0.397126\pi$
$641$	−221.018	−	127.605i	−0.344801	−	0.199071i	−0.662393	+	0.749156i	$0.730459\pi$
$642$	−130.778	−	130.778i	−0.203704	−	0.203704i
$643$	−714.403	+	191.424i	−1.11105	+	0.297704i	−0.767255	−	0.641342i	$-0.778378\pi$
$643$	−714.403	+	191.424i	−1.11105	+	0.297704i	−0.343792	+	0.939046i	$0.611711\pi$
$644$	−1245.57	+	333.750i	−1.93412	+	0.518246i
$645$		0			0
$646$	−359.454	+	622.593i	−0.556430	+	0.963766i
$647$	454.333	+	786.928i	0.702215	+	1.21627i	0.967687	+	0.252154i	$0.0811389\pi$
$647$	454.333	+	786.928i	0.702215	+	1.21627i	−0.265472	+	0.964119i	$0.585528\pi$
$648$	1892.54	+	507.103i	2.92058	+	0.782567i
$649$			310.195i			0.477959i
$650$		0			0
$651$	−66.2113			−0.101707
$652$	196.575	−	733.628i	0.301496	−	1.12520i
$653$	569.971	−	329.073i	0.872850	−	0.503940i	0.00455590	−	0.999990i	$-0.498550\pi$
$653$	569.971	−	329.073i	0.872850	−	0.503940i	0.868294	+	0.496049i	$0.165216\pi$
$654$	−26.7045	−	15.4179i	−0.0408326	−	0.0235747i
$655$		0			0
$656$	−558.441	−	2084.13i	−0.851282	−	3.17703i
$657$	−68.8639	−	257.003i	−0.104816	−	0.391177i
$658$	−769.808	+	769.808i	−1.16992	+	1.16992i
$659$	102.040	−	176.739i	0.154841	−	0.268193i	−0.778160	−	0.628066i	$-0.783847\pi$
$659$	102.040	−	176.739i	0.154841	−	0.268193i	0.933001	+	0.359873i	$0.117180\pi$
$660$		0			0
$661$	96.1350	−	358.781i	0.145439	−	0.542785i	−0.854297	−	0.519786i	$-0.826012\pi$
$661$	96.1350	−	358.781i	0.145439	−	0.542785i	0.999735	−	0.0229993i	$-0.00732154\pi$
$662$	1924.36			2.90689
$663$	7.45822	+	171.518i	0.0112492	+	0.258700i
$664$	4137.03			6.23046
$665$		0			0
$666$	−985.744	−	1707.36i	−1.48010	−	2.56360i
$667$	21.8830	−	37.9025i	0.0328081	−	0.0568254i
$668$	−1597.23	−	1597.23i	−2.39106	−	2.39106i
$669$	36.7021	+	136.974i	0.0548612	+	0.204745i
$670$		0			0
$671$	−145.364	−	145.364i	−0.216638	−	0.216638i
$672$	−397.851	−	229.700i	−0.592041	−	0.341815i
$673$	−280.318	−	485.525i	−0.416520	−	0.721434i	0.579067	−	0.815280i	$-0.303417\pi$
$673$	−280.318	−	485.525i	−0.416520	−	0.721434i	−0.995587	+	0.0938462i	$0.970084\pi$
$674$	−445.611	+	1663.04i	−0.661144	+	2.46742i
$675$		0			0
$676$	−1727.41	−	806.248i	−2.55533	−	1.19267i
$677$		−	255.729i		−	0.377739i	−0.982002	−	0.188869i	$-0.939518\pi$
$677$		−	255.729i		−	0.377739i	0.982002	−	0.188869i	$-0.0604823\pi$
$678$	−38.6260	+	144.154i	−0.0569705	+	0.212617i
$679$	−80.9505	−	140.210i	−0.119220	−	0.206495i
$680$		0			0
$681$	−18.8550	+	18.8550i	−0.0276873	+	0.0276873i
$682$	−560.924	+	150.299i	−0.822469	+	0.220380i
$683$	−135.545	−	505.862i	−0.198456	−	0.740648i	−0.991345	−	0.131282i	$-0.958091\pi$
$683$	−135.545	−	505.862i	−0.198456	−	0.740648i	0.792889	−	0.609366i	$-0.208576\pi$
$684$	641.921	+	641.921i	0.938481	+	0.938481i
$685$		0			0
$686$	1207.30	−	697.037i	1.75992	−	1.01609i
$687$	183.537	+	49.1786i	0.267157	+	0.0715846i
$688$	−235.779			−0.342703
$689$	−44.7824	−	1029.87i	−0.0649963	−	1.49473i
$690$		0			0
$691$	949.409	+	254.393i	1.37396	+	0.368152i	0.868925	−	0.494944i	$-0.164812\pi$
$691$	949.409	+	254.393i	1.37396	+	0.368152i	0.505039	+	0.863097i	$0.331478\pi$
$692$	−1551.88	+	895.976i	−2.24259	+	1.29476i
$693$	−142.947	+	247.592i	−0.206273	+	0.357276i
$694$	286.870	−	286.870i	0.413358	−	0.413358i
$695$		0			0
$696$	33.4282	−	8.95707i	0.0480291	−	0.0128694i
$697$	450.461	−	450.461i	0.646286	−	0.646286i
$698$	1405.67	+	811.565i	2.01386	+	1.16270i
$699$	−12.0689	+	6.96799i	−0.0172660	+	0.00996851i
$700$		0			0
$701$			741.124i			1.05724i	0.848859	+	0.528619i	$0.177290\pi$
$701$			741.124i			1.05724i	−0.848859	+	0.528619i	$0.822710\pi$
$702$	588.756	+	130.633i	0.838683	+	0.186087i
$703$		−	556.257i		−	0.791262i
$704$	−2071.16	−	554.965i	−2.94199	−	0.788303i
$705$		0			0
$706$	187.133	+	108.041i	0.265060	+	0.153033i
$707$	−44.4404	−	44.4404i	−0.0628577	−	0.0628577i
$708$	−320.792	+	85.9560i	−0.453096	+	0.121407i
$709$	−84.1747	+	22.5545i	−0.118723	+	0.0318118i	−0.317691	−	0.948194i	$-0.602908\pi$
$709$	−84.1747	+	22.5545i	−0.118723	+	0.0318118i	0.198968	+	0.980006i	$0.436241\pi$
$710$		0			0
$711$	−170.927	+	296.055i	−0.240404	+	0.416392i
$712$	916.216	+	1586.93i	1.28682	+	2.22884i
$713$	−490.158	−	131.337i	−0.687459	−	0.184204i
$714$		−	242.397i		−	0.339492i
$715$		0			0
$716$	81.9460			0.114450
$717$	25.4008	−	94.7971i	0.0354265	−	0.132213i
$718$	1056.36	−	609.892i	1.47126	−	0.849432i
$719$	−49.3722	−	28.5050i	−0.0686678	−	0.0396454i	0.465273	−	0.885167i	$-0.345956\pi$
$719$	−49.3722	−	28.5050i	−0.0686678	−	0.0396454i	−0.533941	+	0.845522i	$0.679289\pi$
$720$		0			0
$721$	−34.6318	−	129.248i	−0.0480331	−	0.179262i
$722$	−275.424	−	1027.90i	−0.381474	−	1.42368i
$723$	−10.4468	+	10.4468i	−0.0144492	+	0.0144492i
$724$	229.365	−	397.272i	0.316802	−	0.548718i
$725$		0			0
$726$	−48.0466	+	179.312i	−0.0661799	+	0.246987i
$727$	1250.81			1.72051			0.860255	−	0.509864i	$-0.170304\pi$
$727$	1250.81			1.72051			0.860255	+	0.509864i	$0.170304\pi$
$728$	1540.66	+	802.362i	2.11629	+	1.10215i
$729$	515.898			0.707679
$730$		0			0
$731$	−34.8071	−	60.2876i	−0.0476157	−	0.0824728i
$732$	110.049	−	190.611i	0.150341	−	0.260398i
$733$	146.502	+	146.502i	0.199866	+	0.199866i	0.799942	−	0.600077i	$-0.204863\pi$
$733$	146.502	+	146.502i	0.199866	+	0.199866i	−0.600077	+	0.799942i	$0.704863\pi$
$734$	582.086	+	2172.38i	0.793033	+	2.95964i
$735$		0			0
$736$	−2489.63	−	2489.63i	−3.38265	−	3.38265i
$737$	−34.3242	−	19.8171i	−0.0465728	−	0.0268888i
$738$	−544.855	−	943.717i	−0.738286	−	1.27875i
$739$	49.5739	−	185.012i	0.0670825	−	0.250355i	−0.924239	−	0.381814i	$-0.875299\pi$
$739$	49.5739	−	185.012i	0.0670825	−	0.250355i	0.991322	+	0.131459i	$0.0419661\pi$
$740$		0			0
$741$	61.0803	+	55.9897i	0.0824296	+	0.0755596i
$742$			1455.46i			1.96154i
$743$	99.4369	−	371.104i	0.133832	−	0.499466i	−0.866168	−	0.499752i	$-0.833424\pi$
$743$	99.4369	−	371.104i	0.133832	−	0.499466i	1.00000		0.000285925i	$9.10129e-5\pi$
$744$	−200.629	−	347.500i	−0.269663	−	0.467070i
$745$		0			0
$746$	516.802	−	516.802i	0.692764	−	0.692764i
$747$	1199.57	−	321.424i	1.60585	−	0.430286i
$748$	−406.197	−	1515.95i	−0.543043	−	2.02667i
$749$	−232.212	−	232.212i	−0.310030	−	0.310030i
$750$		0			0
$751$	−745.376	+	430.343i	−0.992511	+	0.573027i	−0.906024	−	0.423226i	$-0.860898\pi$
$751$	−745.376	+	430.343i	−0.992511	+	0.573027i	−0.0864874	+	0.996253i	$0.527564\pi$
$752$	−3787.88	−	1014.96i	−5.03708	−	1.34968i
$753$	248.011			0.329364
$754$	−87.1271	+	27.4541i	−0.115553	+	0.0364113i
$755$		0			0
$756$	−607.164	−	162.689i	−0.803127	−	0.215197i
$757$	841.775	−	485.999i	1.11199	−	0.642007i	0.172645	−	0.984984i	$-0.444769\pi$
$757$	841.775	−	485.999i	1.11199	−	0.642007i	0.939344	+	0.342977i	$0.111435\pi$
$758$	1192.98	−	2066.30i	1.57385	−	2.72599i
$759$	83.0111	−	83.0111i	0.109369	−	0.109369i
$760$		0			0
$761$	−8.15865	+	2.18610i	−0.0107210	+	0.00287267i	−0.264176	−	0.964475i	$-0.585100\pi$
$761$	−8.15865	+	2.18610i	−0.0107210	+	0.00287267i	0.253455	+	0.967347i	$0.418433\pi$
$762$	−194.890	+	194.890i	−0.255762	+	0.255762i
$763$	−47.4171	−	27.3763i	−0.0621456	−	0.0358798i
$764$	−983.849	+	568.026i	−1.28776	+	0.743489i
$765$		0			0
$766$			82.1319i			0.107222i
$767$	539.613	−	170.034i	0.703538	−	0.221688i
$768$		−	765.952i		−	0.997333i
$769$	−114.329	−	30.6343i	−0.148672	−	0.0398366i	0.183715	−	0.982979i	$-0.441188\pi$
$769$	−114.329	−	30.6343i	−0.148672	−	0.0398366i	−0.332388	+	0.943143i	$0.607854\pi$
$770$		0			0
$771$	−174.347	−	100.659i	−0.226131	−	0.130557i
$772$	−398.138	−	398.138i	−0.515722	−	0.515722i
$773$	423.077	−	113.363i	0.547319	−	0.146654i	0.0254447	−	0.999676i	$-0.491900\pi$
$773$	423.077	−	113.363i	0.547319	−	0.146654i	0.521874	+	0.853023i	$0.325233\pi$
$774$	−115.022	+	30.8200i	−0.148607	+	0.0398191i
$775$		0			0
$776$	490.582	−	849.713i	0.632193	−	1.09499i
$777$	93.7778	+	162.428i	0.120692	+	0.209045i
$778$	1611.26	+	431.737i	2.07103	+	0.554932i
$779$		−	307.463i		−	0.394689i
$780$		0			0
$781$	867.240			1.11042
$782$	480.822	−	1794.45i	0.614861	−	2.29469i
$783$	18.4759	−	10.6670i	0.0235962	−	0.0136233i
$784$	1543.18	+	890.957i	1.96834	+	1.13642i
$785$		0			0
$786$	−117.148	−	437.203i	−0.149044	−	0.556238i
$787$	180.053	+	671.967i	0.228784	+	0.853833i	0.980853	+	0.194749i	$0.0623892\pi$
$787$	180.053	+	671.967i	0.228784	+	0.853833i	−0.752069	+	0.659084i	$0.770944\pi$
$788$	−976.343	+	976.343i	−1.23901	+	1.23901i
$789$	−0.834575	+	1.44553i	−0.00105776	+	0.00183210i
$790$		0			0
$791$	−68.5852	+	255.963i	−0.0867070	+	0.323595i
$792$	−1732.60			−2.18763
$793$	−173.193	+	332.557i	−0.218402	+	0.419365i
$794$	714.518			0.899896
$795$		0			0
$796$	1564.50	+	2709.80i	1.96546	+	3.40427i
$797$	−774.868	+	1342.11i	−0.972230	+	1.68395i	−0.283443	+	0.958989i	$0.591477\pi$
$797$	−774.868	+	1342.11i	−0.972230	+	1.68395i	−0.688787	+	0.724963i	$0.741857\pi$
$798$	−82.7243	−	82.7243i	−0.103664	−	0.103664i
$799$	−299.668	−	1118.38i	−0.375054	−	1.39972i
$800$		0			0
$801$	388.961	+	388.961i	0.485594	+	0.485594i
$802$	−990.412	−	571.815i	−1.23493	−	0.712986i
$803$	111.001	+	192.260i	0.138233	+	0.239427i
$804$	10.9827	−	40.9881i	0.0136601	−	0.0509803i
$805$		0			0
$806$	568.931	+	893.393i	0.705870	+	1.10843i
$807$		−	12.7072i		−	0.0157462i
$808$	98.5783	−	367.899i	0.122003	−	0.455321i
$809$	−251.626	−	435.829i	−0.311034	−	0.538726i	0.667553	−	0.744562i	$-0.267342\pi$
$809$	−251.626	−	435.829i	−0.311034	−	0.538726i	−0.978586	+	0.205836i	$0.934009\pi$
$810$		0			0
$811$	1082.95	−	1082.95i	1.33533	−	1.33533i	0.434796	−	0.900529i	$-0.356820\pi$
$811$	1082.95	−	1082.95i	1.33533	−	1.33533i	0.900529	−	0.434796i	$-0.143180\pi$
$812$	91.9696	−	24.6432i	0.113263	−	0.0303488i
$813$	−54.9337	−	205.015i	−0.0675692	−	0.252172i
$814$	1163.17	+	1163.17i	1.42895	+	1.42895i
$815$		0			0
$816$	756.160	−	436.569i	0.926666	−	0.535011i
$817$	−32.4535	−	8.69588i	−0.0397227	−	0.0106437i
$818$	2414.17			2.95131
$819$	509.066	+	112.952i	0.621571	+	0.137914i
$820$		0			0
$821$	−1078.26	−	288.919i	−1.31335	−	0.351911i	−0.466866	−	0.884328i	$-0.654617\pi$
$821$	−1078.26	−	288.919i	−1.31335	−	0.351911i	−0.846482	+	0.532417i	$0.821284\pi$
$822$	267.789	−	154.608i	0.325778	−	0.188088i
$823$	−521.053	+	902.490i	−0.633114	+	1.09659i	0.353797	+	0.935322i	$0.384890\pi$
$823$	−521.053	+	902.490i	−0.633114	+	1.09659i	−0.986911	+	0.161264i	$0.948443\pi$
$824$	573.398	−	573.398i	0.695872	−	0.695872i
$825$		0			0
$826$	−771.596	+	206.748i	−0.934135	+	0.250301i
$827$	596.084	−	596.084i	0.720779	−	0.720779i	−0.247985	−	0.968764i	$-0.579768\pi$
$827$	596.084	−	596.084i	0.720779	−	0.720779i	0.968764	+	0.247985i	$0.0797684\pi$
$828$	−2031.62	−	1172.95i	−2.45364	−	1.41661i
$829$	330.908	−	191.050i	0.399165	−	0.230458i	−0.286959	−	0.957943i	$-0.592644\pi$
$829$	330.908	−	191.050i	0.399165	−	0.230458i	0.686124	+	0.727485i	$0.259311\pi$
$830$		0			0
$831$		−	196.768i		−	0.236785i
$832$	169.898	+	3907.18i	0.204204	+	4.69613i
$833$			526.112i			0.631587i
$834$	121.409	+	32.5315i	0.145575	+	0.0390066i
$835$		0			0
$836$	−655.980	−	378.730i	−0.784665	−	0.453027i
$837$	−174.910	−	174.910i	−0.208972	−	0.208972i
$838$	1100.85	−	294.971i	1.31366	−	0.351994i
$839$	−748.130	+	200.461i	−0.891692	+	0.238928i	−0.675445	−	0.737410i	$-0.736048\pi$
$839$	−748.130	+	200.461i	−0.891692	+	0.238928i	−0.216247	+	0.976339i	$0.569382\pi$
$840$		0			0
$841$	418.884	−	725.529i	0.498079	−	0.862698i
$842$	−1495.53	−	2590.34i	−1.77617	−	3.07641i
$843$	−48.7715	−	13.0683i	−0.0578547	−	0.0155021i
$844$		−	127.343i		−	0.150880i
$845$		0			0
$846$	−1980.54			−2.34106
$847$	−85.3126	+	318.391i	−0.100723	+	0.375904i
$848$	−4540.31	+	2621.35i	−5.35414	+	3.09122i
$849$	−205.298	−	118.529i	−0.241812	−	0.139610i
$850$		0			0
$851$	372.037	+	1388.46i	0.437176	+	1.63156i
$852$	240.315	+	896.867i	0.282060	+	1.05266i
$853$	12.0307	−	12.0307i	0.0141040	−	0.0141040i	−0.700020	−	0.714124i	$-0.746825\pi$
$853$	12.0307	−	12.0307i	0.0141040	−	0.0141040i	0.714124	+	0.700020i	$0.246825\pi$
$854$	264.700	−	458.474i	0.309953	−	0.536854i
$855$		0			0
$856$	515.097	−	1922.37i	0.601749	−	2.24576i
$857$	702.817			0.820090			0.410045	−	0.912065i	$-0.365513\pi$
$857$	702.817			0.820090			0.410045	+	0.912065i	$0.365513\pi$
$858$	−244.801	+	10.6448i	−0.285316	+	0.0124065i
$859$	−151.163			−0.175976			−0.0879879	−	0.996122i	$-0.528044\pi$
$859$	−151.163			−0.175976			−0.0879879	+	0.996122i	$0.528044\pi$
$860$		0			0
$861$	51.8342	+	89.7796i	0.0602024	+	0.104274i
$862$	−1233.05	+	2135.70i	−1.43045	+	2.47762i
$863$	427.277	+	427.277i	0.495107	+	0.495107i	0.909911	−	0.414804i	$-0.136150\pi$
$863$	427.277	+	427.277i	0.495107	+	0.495107i	−0.414804	+	0.909911i	$0.636150\pi$
$864$	−444.205	−	1657.79i	−0.514126	−	1.91874i
$865$		0			0
$866$	1054.21	+	1054.21i	1.21734	+	1.21734i
$867$	53.9366	+	31.1403i	0.0622106	+	0.0359173i
$868$	−551.983	−	956.062i	−0.635925	−	1.10145i
$869$	73.8246	−	275.517i	0.0849536	−	0.317051i
$870$		0			0
$871$	−15.6587	+	70.5729i	−0.0179779	+	0.0810251i
$872$		−	331.815i		−	0.380522i
$873$	76.2309	−	284.497i	0.0873206	−	0.325885i
$874$	−448.309	−	776.495i	−0.512940	−	0.888438i
$875$		0			0
$876$	−168.069	+	168.069i	−0.191860	+	0.191860i
$877$	1035.18	−	277.375i	1.18036	−	0.316277i	0.385291	−	0.922795i	$-0.374101\pi$
$877$	1035.18	−	277.375i	1.18036	−	0.316277i	0.795069	+	0.606519i	$0.207434\pi$
$878$	724.808	+	2705.02i	0.825521	+	3.08089i
$879$	−60.3793	−	60.3793i	−0.0686909	−	0.0686909i
$880$		0			0
$881$	−142.992	+	82.5567i	−0.162307	+	0.0937079i	−0.578953	−	0.815361i	$-0.696539\pi$
$881$	−142.992	+	82.5567i	−0.162307	+	0.0937079i	0.416646	+	0.909069i	$0.363205\pi$
$882$	869.282	+	232.923i	0.985580	+	0.264085i
$883$	−413.168			−0.467914			−0.233957	−	0.972247i	$-0.575167\pi$
$883$	−413.168			−0.467914			−0.233957	+	0.972247i	$0.575167\pi$
$884$	−2414.47	+	1537.59i	−2.73130	+	1.73935i
$885$		0			0
$886$	−1749.63	−	468.813i	−1.97475	−	0.529134i
$887$	−1107.73	+	639.547i	−1.24885	+	0.721023i	−0.970880	−	0.239567i	$-0.922994\pi$
$887$	−1107.73	+	639.547i	−1.24885	+	0.721023i	−0.277969	+	0.960590i	$0.589661\pi$
$888$	−568.319	+	984.357i	−0.639999	+	1.10851i
$889$	−346.052	+	346.052i	−0.389259	+	0.389259i
$890$		0			0
$891$	−474.024	+	127.014i	−0.532014	+	0.142553i
$892$	−1671.87	+	1671.87i	−1.87430	+	1.87430i
$893$	−483.943	−	279.405i	−0.541930	−	0.312883i
$894$	586.164	−	338.422i	0.655664	−	0.378548i
$895$		0			0
$896$		−	2805.55i		−	3.13120i
$897$	−189.908	−	98.9028i	−0.211715	−	0.110260i
$898$			2723.11i			3.03242i
$899$	36.1919	+	9.69759i	0.0402579	+	0.0107871i
$900$		0			0
$901$	−1340.53	−	773.956i	−1.48783	−	0.858997i
$902$	642.924	+	642.924i	0.712776	+	0.712776i
$903$	10.9425	−	2.93203i	0.0121179	−	0.00324698i
$904$	−1551.21	+	415.645i	−1.71594	+	0.459784i
$905$		0			0
$906$	−200.878	+	347.931i	−0.221720	+	0.384030i
$907$	−106.588	−	184.616i	−0.117517	−	0.203546i	0.801266	−	0.598308i	$-0.204160\pi$
$907$	−106.588	−	184.616i	−0.117517	−	0.203546i	−0.918783	+	0.394762i	$0.870827\pi$
$908$	−429.447	−	115.070i	−0.472959	−	0.126729i
$909$		−	114.335i		−	0.125781i
$910$		0			0
$911$	1073.07			1.17791			0.588954	−	0.808167i	$-0.299540\pi$
$911$	1073.07			1.17791			0.588954	+	0.808167i	$0.299540\pi$
$912$	109.068	−	407.049i	0.119593	−	0.446326i
$913$	−897.379	+	518.102i	−0.982890	+	0.567472i
$914$	−211.595	−	122.165i	−0.231505	−	0.133659i
$915$		0			0
$916$	819.973	+	3060.18i	0.895167	+	3.34081i
$917$	−208.011	−	776.307i	−0.226838	−	0.846573i
$918$	640.338	−	640.338i	0.697536	−	0.697536i
$919$	468.990	−	812.315i	0.510327	−	0.883912i	−0.489601	−	0.871946i	$-0.662858\pi$
$919$	468.990	−	812.315i	0.510327	−	0.883912i	0.999928	−	0.0119659i	$-0.00380894\pi$
$920$		0			0
$921$	−93.9711	+	350.705i	−0.102032	+	0.380787i
$922$	−1324.54			−1.43660
$923$	−475.380	−	1508.64i	−0.515038	−	1.63450i
$924$	255.396			0.276403
$925$		0			0
$926$	−300.245	−	520.040i	−0.324239	−	0.561598i
$927$	121.712	−	210.812i	0.131297	−	0.227413i
$928$	183.827	+	183.827i	0.198090	+	0.198090i
$929$	−201.792	−	753.099i	−0.217215	−	0.810656i	−0.985375	−	0.170399i	$-0.945494\pi$
$929$	−201.792	−	753.099i	−0.217215	−	0.810656i	0.768161	−	0.640257i	$-0.221172\pi$
$930$		0			0
$931$	179.549	+	179.549i	0.192856	+	0.192856i
$932$	−201.229	−	116.180i	−0.215911	−	0.124656i
$933$	−130.081	−	225.307i	−0.139422	−	0.241487i
$934$	20.8594	−	77.8485i	0.0223334	−	0.0833495i
$935$		0			0
$936$	949.729	+	3014.02i	1.01467	+	3.22010i
$937$		−	1369.92i		−	1.46203i	−0.682360	−	0.731016i	$-0.739046\pi$
$937$		−	1369.92i		−	1.46203i	0.682360	−	0.731016i	$-0.260954\pi$
$938$	26.4166	−	98.5880i	0.0281627	−	0.105105i
$939$	−17.2316	−	29.8461i	−0.0183511	−	0.0317850i
$940$		0			0
$941$	50.0032	−	50.0032i	0.0531384	−	0.0531384i	−0.680038	−	0.733177i	$-0.738037\pi$
$941$	50.0032	−	50.0032i	0.0531384	−	0.0531384i	0.733177	+	0.680038i	$0.238037\pi$
$942$	151.929	−	40.7093i	0.161284	−	0.0432158i
$943$	205.638	+	767.451i	0.218068	+	0.813840i
$944$	−2034.63	−	2034.63i	−2.15533	−	2.15533i
$945$		0			0
$946$	86.0459	−	49.6786i	0.0909576	−	0.0525144i
$947$	−1252.54	−	335.616i	−1.32264	−	0.354400i	−0.472672	−	0.881238i	$-0.656710\pi$
$947$	−1252.54	−	335.616i	−1.32264	−	0.354400i	−0.849965	+	0.526839i	$0.823377\pi$
$948$	305.387			0.322138
$949$	273.609	−	298.485i	0.288313	−	0.314526i
$950$		0			0
$951$	371.050	+	99.4224i	0.390168	+	0.104545i
$952$	2258.92	−	1304.19i	2.37282	−	1.36995i
$953$	552.713	−	957.326i	0.579971	−	1.00454i	−0.415511	−	0.909588i	$-0.636397\pi$
$953$	552.713	−	957.326i	0.579971	−	1.00454i	0.995482	−	0.0949514i	$-0.0302696\pi$
$954$	−1872.28	+	1872.28i	−1.96256	+	1.96256i
$955$		0			0
$956$	1580.59	−	423.517i	1.65333	−	0.443009i
$957$	−6.12931	+	6.12931i	−0.00640471	+	0.00640471i
$958$	2259.49	+	1304.52i	2.35855	+	1.36171i
$959$	475.492	−	274.526i	0.495821	−	0.286262i
$960$		0			0
$961$			526.568i			0.547937i
$962$	1385.85	−	2661.04i	1.44059	−	2.76615i
$963$		−	597.428i		−	0.620382i
$964$	−237.939	−	63.7555i	−0.246825	−	0.0661364i
$965$		0			0
$966$	261.814	+	151.158i	0.271029	+	0.156479i
$967$	347.232	+	347.232i	0.359082	+	0.359082i	0.863474	−	0.504393i	$-0.168284\pi$
$967$	347.232	+	347.232i	0.359082	+	0.359082i	−0.504393	+	0.863474i	$0.668284\pi$
$968$	−1929.54	+	517.018i	−1.99332	+	0.534109i
$969$	120.182	−	32.2026i	0.124026	−	0.0332328i
$970$		0			0
$971$	708.181	−	1226.60i	0.729331	−	1.26324i	−0.227835	−	0.973700i	$-0.573165\pi$
$971$	708.181	−	1226.60i	0.729331	−	1.26324i	0.957166	−	0.289539i	$-0.0935020\pi$
$972$	−865.106	−	1498.41i	−0.890026	−	1.54157i
$973$	215.577	+	57.7637i	0.221559	+	0.0593666i
$974$		−	952.844i		−	0.978279i
$975$		0			0
$976$	1906.95			1.95384
$977$	−273.859	+	1022.06i	−0.280306	+	1.04612i	0.671896	+	0.740646i	$0.265480\pi$
$977$	−273.859	+	1022.06i	−0.280306	+	1.04612i	−0.952202	+	0.305470i	$0.901186\pi$
$978$	−154.205	+	89.0305i	−0.157674	+	0.0910332i
$979$	−397.480	−	229.485i	−0.406006	−	0.234408i
$980$		0			0
$981$	−25.7802	−	96.2129i	−0.0262795	−	0.0980764i
$982$	827.126	+	3086.87i	0.842287	+	3.14346i
$983$	−1144.87	+	1144.87i	−1.16467	+	1.16467i	−0.181223	+	0.983442i	$0.558006\pi$
$983$	−1144.87	+	1144.87i	−1.16467	+	1.16467i	−0.983442	+	0.181223i	$0.941994\pi$
$984$	−314.130	+	544.089i	−0.319238	+	0.552936i
$985$		0			0
$986$	−35.5025	+	132.497i	−0.0360066	+	0.134378i
$987$	188.416			0.190898
$988$	−299.259	+	1348.74i	−0.302894	+	1.36512i
$989$	86.8224			0.0877880
$990$		0			0
$991$	−469.824	−	813.760i	−0.474091	−	0.821150i	0.525469	−	0.850813i	$-0.323890\pi$
$991$	−469.824	−	813.760i	−0.474091	−	0.821150i	−0.999560	+	0.0296628i	$0.990557\pi$
$992$	1507.13	−	2610.42i	1.51928	−	2.63147i
$993$	−235.500	−	235.500i	−0.237161	−	0.237161i
$994$	578.025	+	2157.22i	0.581514	+	2.17024i
$995$		0			0
$996$	−784.468	−	784.468i	−0.787618	−	0.787618i
$997$	1024.76	+	591.647i	1.02785	+	0.593427i	0.916367	−	0.400340i	$-0.131108\pi$
$997$	1024.76	+	591.647i	1.02785	+	0.593427i	0.111479	+	0.993767i	$0.464441\pi$
$998$	−421.724	−	730.447i	−0.422569	−	0.731911i
$999$	−181.352	+	676.815i	−0.181534	+	0.677493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.3.w.e.249.10		40
5.2	odd	4		325.3.t.d.301.10		40
5.3	odd	4		65.3.p.a.41.1	✓	40
5.4	even	2		325.3.w.f.249.1		40
13.7	odd	12		325.3.w.f.124.1		40
65.7	even	12		325.3.t.d.176.10		40
65.33	even	12		65.3.p.a.46.1	yes	40
65.59	odd	12	inner	325.3.w.e.124.10		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.3.p.a.41.1	✓	40	5.3	odd	4
65.3.p.a.46.1	yes	40	65.33	even	12
325.3.t.d.176.10		40	65.7	even	12
325.3.t.d.301.10		40	5.2	odd	4
325.3.w.e.124.10		40	65.59	odd	12	inner
325.3.w.e.249.10		40	1.1	even	1	trivial
325.3.w.f.124.1		40	13.7	odd	12
325.3.w.f.249.1		40	5.4	even	2

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

\(f(q)\)	\(=\)	\(q+(1.01171 - 3.77575i) q^{2} +(-0.585883 + 0.338260i) q^{3} +(-9.76865 - 5.63993i) q^{4} +(0.684442 + 2.55437i) q^{6} +(1.21531 + 4.53560i) q^{7} +(-20.1218 + 20.1218i) q^{8} +(-4.27116 + 7.39787i) q^{9} +(1.84474 - 6.88467i) q^{11} +7.63105 q^{12} +(-12.9877 + 0.564752i) q^{13} +18.3548 q^{14} +(33.0579 + 57.2580i) q^{16} +(-9.76038 + 16.9055i) q^{17} +(23.6113 + 23.6113i) q^{18} +(2.43845 + 9.10040i) q^{19} +(-2.24624 - 2.24624i) q^{21} +(-24.1285 - 13.9306i) q^{22} +(-12.1731 - 21.0844i) q^{23} +(4.98264 - 18.5955i) q^{24} +(-11.0074 + 49.6098i) q^{26} -11.8677i q^{27} +(13.7085 - 51.1609i) q^{28} +(0.898827 + 1.55681i) q^{29} +(14.7383 - 14.7383i) q^{31} +(139.689 - 37.4296i) q^{32} +(1.24800 + 4.65762i) q^{33} +(53.9562 + 53.9562i) q^{34} +(83.4469 - 48.1781i) q^{36} +(-57.0299 - 15.2811i) q^{37} +36.8279 q^{38} +(7.41826 - 4.72411i) q^{39} +(-31.5224 - 8.44640i) q^{41} +(-10.7538 + 6.20870i) q^{42} +(-1.78308 + 3.08838i) q^{43} +(-56.8497 + 56.8497i) q^{44} +(-91.9252 + 24.6313i) q^{46} +(-41.9403 + 41.9403i) q^{47} +(-38.7362 - 22.3643i) q^{48} +(23.3406 - 13.4757i) q^{49} -13.2062i q^{51} +(130.058 + 67.7330i) q^{52} +79.2957i q^{53} +(-44.8096 - 12.0067i) q^{54} +(-115.719 - 66.8103i) q^{56} +(-4.50695 - 4.50695i) q^{57} +(6.78750 - 1.81870i) q^{58} +(-42.0377 + 11.2640i) q^{59} +(14.4213 - 24.9784i) q^{61} +(-40.7372 - 70.5588i) q^{62} +(-38.7445 - 10.3816i) q^{63} -300.836i q^{64} +18.8486 q^{66} +(1.43922 - 5.37123i) q^{67} +(190.691 - 110.096i) q^{68} +(14.2640 + 8.23535i) q^{69} +(31.4917 + 117.529i) q^{71} +(-62.9151 - 234.802i) q^{72} +(-22.0244 + 22.0244i) q^{73} +(-115.395 + 199.871i) q^{74} +(27.5053 - 102.651i) q^{76} +33.4680 q^{77} +(-10.3319 - 32.7889i) q^{78} +40.0190 q^{79} +(-34.4261 - 59.6277i) q^{81} +(-63.7830 + 110.475i) q^{82} +(-102.799 - 102.799i) q^{83} +(9.27409 + 34.6114i) q^{84} +(9.85701 + 9.85701i) q^{86} +(-1.05322 - 0.608075i) q^{87} +(101.413 + 175.652i) q^{88} +(16.6664 - 62.1998i) q^{89} +(-18.3456 - 58.2207i) q^{91} +274.622i q^{92} +(-3.64954 + 13.6203i) q^{93} +(115.925 + 200.788i) q^{94} +(-69.1807 + 69.1807i) q^{96} +(-33.3045 + 8.92391i) q^{97} +(-27.2670 - 101.762i) q^{98} +(43.0527 + 43.0527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} - 12 q^{6} - 44 q^{7} + 36 q^{8} + 72 q^{9} - 12 q^{11} + 120 q^{12} - 36 q^{13} - 48 q^{14} + 128 q^{16} - 32 q^{17} + 136 q^{18} - 68 q^{19} - 48 q^{21} - 72 q^{22} - 28 q^{23} + 56 q^{24}+ \cdots + 76 q^{99}+O(q^{100}) \) 40 * q - 12 * q^3 - 12 * q^6 - 44 * q^7 + 36 * q^8 + 72 * q^9 - 12 * q^11 + 120 * q^12 - 36 * q^13 - 48 * q^14 + 128 * q^16 - 32 * q^17 + 136 * q^18 - 68 * q^19 - 48 * q^21 - 72 * q^22 - 28 * q^23 + 56 * q^24 - 84 * q^26 + 76 * q^28 - 28 * q^29 + 128 * q^31 + 84 * q^32 - 68 * q^33 + 28 * q^34 + 300 * q^36 - 260 * q^37 + 8 * q^38 + 88 * q^39 + 68 * q^41 - 480 * q^42 + 32 * q^43 + 240 * q^44 + 260 * q^46 - 152 * q^47 - 480 * q^48 + 132 * q^49 + 488 * q^52 - 152 * q^54 - 288 * q^56 + 252 * q^57 + 468 * q^58 - 492 * q^59 - 100 * q^61 - 8 * q^62 - 356 * q^63 - 456 * q^66 - 56 * q^67 + 12 * q^68 + 576 * q^69 - 132 * q^71 + 396 * q^72 - 424 * q^73 + 160 * q^74 - 992 * q^76 + 344 * q^77 + 12 * q^78 + 248 * q^79 + 248 * q^82 - 112 * q^83 - 1100 * q^84 + 852 * q^86 - 1068 * q^87 + 8 * q^88 - 168 * q^89 - 160 * q^91 - 24 * q^93 - 328 * q^94 + 124 * q^96 + 1020 * q^97 + 1404 * q^98 + 76 * q^99

Introduction

L-functions

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