LMFDB - Embedded newform 325.3.w.e.124.10

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			124.10
Character	$\chi$	$=$	325.124
Dual form			325.3.w.e.249.10

$q$-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 $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.01171	+	3.77575i	0.505855	+	1.88788i	0.457851	+	0.889029i	$0.348619\pi$
$2$	1.01171	+	3.77575i	0.505855	+	1.88788i	0.0480040	+	0.998847i	$0.484714\pi$
$3$	−0.585883	−	0.338260i	−0.195294	−	0.112753i	0.399164	−	0.916879i	$-0.369300\pi$
$3$	−0.585883	−	0.338260i	−0.195294	−	0.112753i	−0.594459	+	0.804126i	$0.702634\pi$
$4$	−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	−0.823168	−	0.567798i	$-0.807795\pi$
$7$	1.21531	−	4.53560i	0.173616	−	0.647942i	0.996783	−	0.0801440i	$-0.0255380\pi$
$8$	−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	0.997680	+	0.0680801i	$0.0216873\pi$
$11$	1.84474	+	6.88467i	0.167704	+	0.625879i	−0.829976	+	0.557799i	$0.811646\pi$
$12$	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	−0.996134	−	0.0878414i	$-0.972003\pi$
$17$	−9.76038	−	16.9055i	−0.574140	−	0.994440i	0.421994	−	0.906598i	$-0.361330\pi$
$18$	23.6113	−	23.6113i	1.31174	−	1.31174i
$19$	2.43845	−	9.10040i	0.128339	−	0.478969i	−0.871597	−	0.490222i	$-0.836916\pi$
$19$	2.43845	−	9.10040i	0.128339	−	0.478969i	0.999937	+	0.0112537i	$0.00358225\pi$
$20$		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	0.470152	+	0.882585i	$0.344199\pi$
$23$	−12.1731	+	21.0844i	−0.529265	+	0.916714i	−0.999417	+	0.0341290i	$0.989134\pi$
$24$	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	−0.850112	−	0.526601i	$-0.823466\pi$
$29$	0.898827	−	1.55681i	0.0309940	−	0.0536833i	0.881106	+	0.472918i	$0.156799\pi$
$30$		0			0
$31$	14.7383	+	14.7383i	0.475428	+	0.475428i	0.903666	−	0.428238i	$-0.140866\pi$
$31$	14.7383	+	14.7383i	0.475428	+	0.475428i	−0.428238	+	0.903666i	$0.640866\pi$
$32$	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	−0.926701	−	0.375799i	$-0.877368\pi$
$37$	−57.0299	+	15.2811i	−1.54135	+	0.413003i	−0.614647	+	0.788802i	$0.710702\pi$
$38$	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	−0.621859	−	0.783130i	$-0.713622\pi$
$41$	−31.5224	+	8.44640i	−0.768839	+	0.206010i	−0.146981	+	0.989139i	$0.546955\pi$
$42$	−10.7538	−	6.20870i	−0.256043	−	0.147826i
$43$	−1.78308	−	3.08838i	−0.0414669	−	0.0718228i	0.844547	−	0.535481i	$-0.179870\pi$
$43$	−1.78308	−	3.08838i	−0.0414669	−	0.0718228i	−0.886014	+	0.463659i	$0.846536\pi$
$44$	−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	0.102396	−	0.994744i	$-0.467349\pi$
$47$	−41.9403	−	41.9403i	−0.892348	−	0.892348i	−0.994744	+	0.102396i	$0.967349\pi$
$48$	−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	$-0.730979\pi$
$53$		−	79.2957i		−	1.49615i	0.663617	−	0.748073i	$-0.269021\pi$
$54$	−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	−0.115680	−	0.993287i	$-0.536905\pi$
$59$	−42.0377	−	11.2640i	−0.712504	−	0.190915i	−0.596825	+	0.802372i	$0.703571\pi$
$60$		0			0
$61$	14.4213	+	24.9784i	0.236414	+	0.409481i	0.959683	−	0.281085i	$-0.0906944\pi$
$61$	14.4213	+	24.9784i	0.236414	+	0.409481i	−0.723269	+	0.690567i	$0.757361\pi$
$62$	−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	0.975834	−	0.218512i	$-0.0701204\pi$
$67$	1.43922	+	5.37123i	0.0214809	+	0.0801676i	−0.954353	+	0.298680i	$0.903454\pi$
$68$	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	−0.276205	−	0.961099i	$-0.589077\pi$
$71$	31.4917	−	117.529i	0.443545	−	1.65533i	0.719750	−	0.694234i	$-0.244257\pi$
$72$	−62.9151	+	234.802i	−0.873821	+	3.26114i
$73$	−22.0244	−	22.0244i	−0.301704	−	0.301704i	0.539976	−	0.841680i	$-0.318433\pi$
$73$	−22.0244	−	22.0244i	−0.301704	−	0.301704i	−0.841680	+	0.539976i	$0.818433\pi$
$74$	−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	−0.277952	+	0.960595i	$0.589656\pi$
$83$	−102.799	+	102.799i	−1.23855	+	1.23855i	−0.960595	+	0.277952i	$0.910344\pi$
$84$	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	0.994135	+	0.108148i	$0.0344919\pi$
$89$	16.6664	+	62.1998i	0.187263	+	0.698874i	−0.806872	+	0.590726i	$0.798841\pi$
$90$		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	0.0830260	−	0.996547i	$-0.473542\pi$
$97$	−33.3045	−	8.92391i	−0.343345	−	0.0919990i	−0.426371	+	0.904548i	$0.640208\pi$
$98$	−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	0.441518	−	0.897252i	$-0.354440\pi$
$101$	−11.5913	−	6.69225i	−0.114766	−	0.0662599i	−0.556284	+	0.830992i	$0.687773\pi$
$102$	−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	0.189519	−	0.981877i	$-0.439307\pi$
$107$	−60.5676	−	34.9687i	−0.566052	−	0.326811i	−0.755571	+	0.655067i	$0.772641\pi$
$108$	−66.9332	−	115.932i	−0.619752	−	1.07344i
$109$	−8.24515	−	8.24515i	−0.0756436	−	0.0756436i	0.668273	−	0.743916i	$-0.267034\pi$
$109$	−8.24515	−	8.24515i	−0.0756436	−	0.0756436i	−0.743916	+	0.668273i	$0.767034\pi$
$110$		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	−0.267906	−	0.963445i	$-0.586332\pi$
$113$	48.8736	−	28.2172i	0.432510	−	0.249710i	0.700415	+	0.713736i	$0.252998\pi$
$114$	−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	−0.584597	−	0.811324i	$-0.698747\pi$
$127$	52.1117	−	90.2601i	0.410328	−	0.710709i	0.994926	+	0.100614i	$0.0320808\pi$
$128$	−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	0.763104	+	0.646275i	$0.223674\pi$
$137$	−30.2634	+	112.945i	−0.220901	+	0.824414i	−0.984005	+	0.178139i	$0.942992\pi$
$138$	45.5257	+	45.5257i	0.329896	+	0.329896i
$139$	23.7650	+	41.1622i	0.170971	+	0.296131i	0.938760	−	0.344573i	$-0.111976\pi$
$139$	23.7650	+	41.1622i	0.170971	+	0.296131i	−0.767788	+	0.640703i	$0.778643\pi$
$140$		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	0.272433	+	0.962175i	$0.412172\pi$
$149$	−66.2437	+	247.225i	−0.444588	+	1.65923i	−0.717021	+	0.697052i	$0.754495\pi$
$150$		0			0
$151$	107.425	−	107.425i	0.711427	−	0.711427i	−0.255407	−	0.966834i	$-0.582209\pi$
$151$	107.425	−	107.425i	0.711427	−	0.711427i	0.966834	+	0.255407i	$0.0822094\pi$
$152$	−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	$0.0606610\pi$
$157$			59.4781i			0.378841i	−0.981896	+	0.189421i	$0.939339\pi$
$158$	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	−0.891641	−	0.452744i	$-0.850445\pi$
$163$	17.4271	−	65.0388i	0.106915	−	0.399011i	0.998555	+	0.0537328i	$0.0171119\pi$
$164$	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	0.371988	−	0.928238i	$-0.378676\pi$
$167$	193.429	−	51.8291i	1.15826	−	0.310354i	0.786270	+	0.617883i	$0.212010\pi$
$168$	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	0.998916	−	0.0465536i	$-0.0148238\pi$
$173$	79.4314	+	137.579i	0.459141	+	0.795256i	−0.539775	+	0.841810i	$0.681491\pi$
$174$	−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	0.482323	−	0.875993i	$-0.339793\pi$
$179$	−6.29150	−	3.63240i	−0.0351481	−	0.0202927i	−0.517471	+	0.855701i	$0.673126\pi$
$180$		0			0
$181$		−	40.6680i		−	0.224685i	−0.993670	−	0.112343i	$-0.964165\pi$
$181$		−	40.6680i		−	0.224685i	0.993670	−	0.112343i	$-0.0358354\pi$
$182$	−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	0.967210	−	0.253980i	$-0.0817397\pi$
$191$	50.3575	+	87.2217i	0.263652	+	0.456658i	−0.703558	+	0.710638i	$0.748406\pi$
$192$	101.761	−	176.255i	0.530005	−	0.917995i
$193$	48.2157	−	12.9194i	0.249822	−	0.0669396i	−0.131735	−	0.991285i	$-0.542055\pi$
$193$	48.2157	−	12.9194i	0.249822	−	0.0669396i	0.381557	+	0.924345i	$0.375388\pi$
$194$		−	134.778i		−	0.694731i
$195$		0			0
$196$	−304.008			−1.55106
$197$	31.6818	+	118.238i	0.160821	+	0.600194i	0.998536	+	0.0540858i	$0.0172244\pi$
$197$	31.6818	+	118.238i	0.160821	+	0.600194i	−0.837715	+	0.546108i	$0.816109\pi$
$198$	206.113	+	118.999i	1.04098	+	0.601007i
$199$	−240.233	+	138.699i	−1.20720	+	0.696979i	−0.962147	−	0.272530i	$-0.912140\pi$
$199$	−240.233	+	138.699i	−1.20720	+	0.696979i	−0.245056	+	0.969509i	$0.578806\pi$
$200$		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	−0.852339	−	0.522989i	$-0.824817\pi$
$211$	5.64470	−	9.77692i	0.0267522	−	0.0463361i	0.879092	+	0.476653i	$0.158150\pi$
$212$	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	0.974240	+	0.225513i	$0.0724057\pi$
$223$	54.2514	+	202.469i	0.243280	+	0.907932i	−0.730961	+	0.682420i	$0.760928\pi$
$224$	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	0.341701	−	0.939809i	$-0.388997\pi$
$227$	38.0720	+	10.2014i	0.167718	+	0.0449399i	−0.173983	+	0.984749i	$0.555664\pi$
$228$	18.6079	−	69.4457i	0.0816136	−	0.304586i
$229$	−198.602	+	198.602i	−0.867260	+	0.867260i	−0.992168	−	0.124909i	$-0.960136\pi$
$229$	−198.602	+	198.602i	−0.867260	+	0.867260i	0.124909	+	0.992168i	$0.460136\pi$
$230$		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	0.459157	−	0.888355i	$-0.348151\pi$
$239$	−102.578	−	102.578i	−0.429198	−	0.429198i	−0.888355	+	0.459157i	$0.848151\pi$
$240$		0			0
$241$	21.0941	+	5.65216i	0.0875275	+	0.0234529i	0.302317	−	0.953207i	$-0.402240\pi$
$241$	21.0941	+	5.65216i	0.0875275	+	0.0234529i	−0.214790	+	0.976660i	$0.568907\pi$
$242$	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	−0.974014	−	0.226489i	$-0.927275\pi$
$251$	−317.484	+	183.299i	−1.26488	+	0.730276i	−0.290862	+	0.956765i	$0.593942\pi$
$252$	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	−0.416651	−	0.909067i	$-0.636796\pi$
$257$	148.790	−	257.712i	0.578949	−	1.00277i	0.995600	−	0.0937031i	$-0.0298705\pi$
$258$	−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	0.504057	−	0.863671i	$-0.331840\pi$
$263$	2.13671	+	1.23363i	0.00812437	+	0.00469061i	−0.495932	+	0.868361i	$0.665174\pi$
$264$	−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	0.848041	−	0.529931i	$-0.177782\pi$
$269$	−9.39160	−	16.2667i	−0.0349130	−	0.0604711i	−0.882954	+	0.469460i	$0.844449\pi$
$270$		0			0
$271$	−81.2004	−	303.044i	−0.299633	−	1.11824i	−0.937468	−	0.348071i	$-0.886837\pi$
$271$	−81.2004	−	303.044i	−0.299633	−	1.11824i	0.637835	−	0.770173i	$-0.279830\pi$
$272$	−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	−0.999576	−	0.0291194i	$-0.990730\pi$
$277$	−145.427	−	251.886i	−0.525006	−	0.909337i	0.474570	−	0.880218i	$-0.342604\pi$
$278$	−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	−0.606938	−	0.794749i	$-0.707602\pi$
$281$	52.7748	−	52.7748i	0.187811	−	0.187811i	0.794749	+	0.606938i	$0.207602\pi$
$282$	−135.837	+	78.4255i	−0.481691	+	0.278105i
$283$	175.204	−	303.462i	0.619095	−	1.07230i	−0.370556	−	0.928810i	$-0.620833\pi$
$283$	175.204	−	303.462i	0.619095	−	1.07230i	0.989651	−	0.143494i	$-0.0458339\pi$
$284$	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	−0.887507	−	0.460794i	$-0.847565\pi$
$293$	32.6677	−	121.918i	0.111494	−	0.416101i	0.999001	+	0.0446937i	$0.0142312\pi$
$294$	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	0.961570	+	0.274560i	$0.0885321\pi$
$307$	379.492	+	379.492i	1.23613	+	1.23613i	0.274560	+	0.961570i	$0.411468\pi$
$308$	−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	$-0.787837\pi$
$311$		−	384.559i		−	1.23652i	0.785972	−	0.618262i	$-0.212163\pi$
$312$	−54.2114	−	244.327i	−0.173754	−	0.783099i
$313$		−	50.9420i		−	0.162754i	−0.996683	−	0.0813770i	$-0.974068\pi$
$313$		−	50.9420i		−	0.162754i	0.996683	−	0.0813770i	$-0.0259318\pi$
$314$	−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	−0.318740	+	0.947842i	$0.603260\pi$
$317$	−401.507	+	401.507i	−1.26658	+	1.26658i	−0.947842	+	0.318740i	$0.896740\pi$
$318$	−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	−0.453318	−	0.891349i	$-0.649760\pi$
$331$	127.416	−	475.521i	0.384941	−	1.43662i	0.838260	−	0.545271i	$-0.183573\pi$
$332$	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	−0.364865	−	0.931061i	$-0.618885\pi$
$347$	89.8817	−	51.8932i	0.259025	−	0.149548i	0.623890	+	0.781512i	$0.285551\pi$
$348$	6.85900	−	11.8801i	0.0197098	−	0.0341383i
$349$	−107.471	−	401.086i	−0.307939	−	1.14924i	−0.930386	−	0.366581i	$-0.880528\pi$
$349$	−107.471	−	401.086i	−0.307939	−	1.14924i	0.622447	−	0.782662i	$-0.286138\pi$
$350$		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	0.942695	−	0.333655i	$-0.108282\pi$
$353$	−14.3072	−	53.3953i	−0.0405304	−	0.151261i	−0.983226	+	0.182394i	$0.941615\pi$
$354$	−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	−0.329519	−	0.944149i	$-0.606886\pi$
$359$	220.652	−	220.652i	0.614630	−	0.614630i	0.944149	+	0.329519i	$0.106886\pi$
$360$		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	−0.368365	−	0.929681i	$-0.620082\pi$
$367$	−498.267	−	287.675i	−1.35768	−	0.783854i	−0.989310	+	0.145827i	$0.953416\pi$
$368$	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	−0.266985	−	0.963701i	$-0.586028\pi$
$373$	161.923	−	93.4865i	0.434111	−	0.250634i	0.701097	+	0.713066i	$0.252694\pi$
$374$	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	0.624358	−	0.781139i	$-0.285361\pi$
$379$	589.586	−	157.979i	1.55564	−	0.416832i	0.931279	+	0.364307i	$0.118694\pi$
$380$		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	0.232226	−	0.972662i	$-0.425399\pi$
$383$	−20.2953	−	5.43811i	−0.0529904	−	0.0141987i	−0.285217	+	0.958463i	$0.592066\pi$
$384$	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	$-0.815196\pi$
$389$		−	426.740i		−	1.09702i	0.836145	−	0.548509i	$-0.184804\pi$
$390$		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	−0.880397	−	0.474237i	$-0.842724\pi$
$397$	47.3096	−	176.562i	0.119168	−	0.444740i	0.999565	+	0.0294969i	$0.00939053\pi$
$398$	−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	0.993777	+	0.111384i	$0.0355283\pi$
$401$	75.7220	+	282.598i	0.188833	+	0.704734i	−0.804945	+	0.593350i	$0.797805\pi$
$402$	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	−0.437955	−	0.898997i	$-0.644297\pi$
$409$	159.847	−	596.557i	0.390824	−	1.45857i	0.828779	−	0.559577i	$-0.189036\pi$
$410$		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	−0.637960	−	0.770070i	$-0.720221\pi$
$419$	145.778	−	252.496i	0.347920	−	0.602615i	0.985880	+	0.167455i	$0.0535548\pi$
$420$		0			0
$421$	541.067	+	541.067i	1.28519	+	1.28519i	0.937672	+	0.347523i	$0.112977\pi$
$421$	541.067	+	541.067i	1.28519	+	1.28519i	0.347523	+	0.937672i	$0.387023\pi$
$422$	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	−0.883314	−	0.468782i	$-0.844693\pi$
$431$	−609.389	+	163.285i	−1.41390	+	0.378852i	−0.530581	+	0.847634i	$0.678026\pi$
$432$	679.522	+	392.322i	1.57297	+	0.908154i
$433$	−190.701	−	330.304i	−0.440419	−	0.762828i	0.557302	−	0.830310i	$-0.311837\pi$
$433$	−190.701	−	330.304i	−0.440419	−	0.762828i	−0.997720	+	0.0674824i	$0.978503\pi$
$434$	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	−0.417598	−	0.908632i	$-0.637128\pi$
$439$	−620.437	−	358.209i	−1.41330	−	0.815966i	−0.995697	+	0.0926655i	$0.970461\pi$
$440$		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	$0.175191\pi$
$443$			463.386i			1.04602i	−0.852327	+	0.523010i	$0.824809\pi$
$444$	−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	−0.586010	−	0.810304i	$-0.699302\pi$
$449$	−672.899	−	180.303i	−1.49866	−	0.401565i	−0.912651	+	0.408739i	$0.865969\pi$
$450$		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	0.981364	−	0.192157i	$-0.0615483\pi$
$457$	16.1775	+	60.3753i	0.0353994	+	0.132112i	−0.945965	+	0.324269i	$0.894882\pi$
$458$	−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	0.803208	+	0.595699i	$0.203125\pi$
$461$	−87.7005	+	327.303i	−0.190240	+	0.709985i	−0.993448	+	0.114286i	$0.963542\pi$
$462$	22.9069	−	85.4898i	0.0495821	−	0.185043i
$463$	108.625	+	108.625i	0.234612	+	0.234612i	0.814615	−	0.580003i	$-0.196948\pi$
$463$	108.625	+	108.625i	0.234612	+	0.234612i	−0.580003	+	0.814615i	$0.696948\pi$
$464$	−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	−0.873228	−	0.487312i	$-0.837977\pi$
$479$	−172.750	−	644.710i	−0.360646	−	1.34595i	0.512581	−	0.858639i	$-0.328689\pi$
$480$		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	0.492322	−	0.870413i	$-0.336148\pi$
$487$	235.454	+	63.0896i	0.483478	+	0.129548i	−0.00884365	+	0.999961i	$0.502815\pi$
$488$	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	−0.444015	−	0.896019i	$-0.646446\pi$
$491$	−708.021	−	408.776i	−1.44200	−	0.832538i	−0.997983	+	0.0634815i	$0.979780\pi$
$492$	−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	0.843263	−	0.537501i	$-0.180632\pi$
$499$	152.575	+	152.575i	0.305761	+	0.305761i	−0.537501	+	0.843263i	$0.680632\pi$
$500$		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	−0.254022	−	0.967198i	$-0.581754\pi$
$503$	229.662	−	132.595i	0.456585	−	0.263609i	0.710607	+	0.703589i	$0.248420\pi$
$504$	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	−0.248045	−	0.968748i	$-0.579788\pi$
$509$	10.9516	−	2.93446i	0.0215158	−	0.00576515i	0.269561	+	0.962983i	$0.413121\pi$
$510$		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	−0.136401	−	0.990654i	$-0.543553\pi$
$523$	−555.704	−	320.836i	−1.06253	−	0.613453i	−0.926132	+	0.377200i	$0.876887\pi$
$524$	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	−0.00120694	−	0.999999i	$-0.500384\pi$
$541$	540.347	−	540.347i	0.998792	−	0.998792i	0.999999	+	0.00120694i	$0.000384180\pi$
$542$	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	$-0.826745\pi$
$547$		−	566.490i		−	1.03563i	0.855492	−	0.517816i	$-0.173255\pi$
$548$	−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	−0.592010	−	0.805931i	$-0.701665\pi$
$557$	−390.869	+	104.733i	−0.701740	+	0.188031i	−0.109730	+	0.993961i	$0.534999\pi$
$558$	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	0.991897	−	0.127045i	$-0.0405492\pi$
$563$	217.275	+	376.332i	0.385924	+	0.668441i	−0.605973	+	0.795486i	$0.707216\pi$
$564$	−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	0.999512	+	0.0312407i	$0.00994585\pi$
$569$	868.478	+	501.416i	1.52632	+	0.881223i	0.526811	+	0.849982i	$0.323387\pi$
$570$		0			0
$571$		−	900.202i		−	1.57654i	−0.615332	−	0.788268i	$-0.710978\pi$
$571$		−	900.202i		−	1.57654i	0.615332	−	0.788268i	$-0.289022\pi$
$572$	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	−0.261149	+	0.965298i	$0.584102\pi$
$577$	−707.660	+	707.660i	−1.22645	+	1.22645i	−0.965298	+	0.261149i	$0.915898\pi$
$578$	−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	0.992243	+	0.124317i	$0.0396738\pi$
$587$	114.520	+	427.394i	0.195094	+	0.728099i	−0.797149	+	0.603783i	$0.793659\pi$
$588$	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	0.763604	−	0.645685i	$-0.223428\pi$
$593$	69.9257	+	69.9257i	0.117919	+	0.117919i	−0.645685	+	0.763604i	$0.723428\pi$
$594$	−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	0.188909	+	0.981995i	$0.439505\pi$
$601$	−454.343	+	786.945i	−0.755978	+	1.30939i	−0.944887	+	0.327398i	$0.893828\pi$
$602$	−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	−0.948061	−	0.318089i	$-0.896959\pi$
$607$	−695.997	+	401.834i	−1.14662	+	0.662000i	−0.198557	+	0.980089i	$0.563625\pi$
$608$	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	−0.914700	−	0.404134i	$-0.867573\pi$
$613$	−198.988	−	742.633i	−0.324613	−	1.21147i	0.590087	−	0.807340i	$-0.299094\pi$
$614$	−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	0.425061	−	0.905165i	$-0.360253\pi$
$617$	210.145	+	56.3082i	0.340592	+	0.0912613i	−0.0844690	+	0.996426i	$0.526919\pi$
$618$	−19.5041	+	72.7902i	−0.0315600	+	0.117783i
$619$	86.7747	−	86.7747i	0.140185	−	0.140185i	−0.633532	−	0.773717i	$-0.718395\pi$
$619$	86.7747	−	86.7747i	0.140185	−	0.140185i	0.773717	+	0.633532i	$0.218395\pi$
$620$		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	−0.0947043	−	0.995505i	$-0.530191\pi$
$631$	−425.593	−	114.037i	−0.674473	−	0.180725i	−0.579769	+	0.814781i	$0.696857\pi$
$632$	−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	−0.662393	−	0.749156i	$-0.730459\pi$
$641$	−221.018	+	127.605i	−0.344801	+	0.199071i	0.317592	+	0.948227i	$0.397126\pi$
$642$	−130.778	+	130.778i	−0.203704	+	0.203704i
$643$	−714.403	−	191.424i	−1.11105	−	0.297704i	−0.343792	−	0.939046i	$-0.611711\pi$
$643$	−714.403	−	191.424i	−1.11105	−	0.297704i	−0.767255	+	0.641342i	$0.778378\pi$
$644$	−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	−0.265472	−	0.964119i	$-0.585528\pi$
$647$	454.333	−	786.928i	0.702215	−	1.21627i	0.967687	−	0.252154i	$-0.0811389\pi$
$648$	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	0.868294	−	0.496049i	$-0.165216\pi$
$653$	569.971	+	329.073i	0.872850	+	0.503940i	0.00455590	+	0.999990i	$0.498550\pi$
$654$	−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	0.933001	−	0.359873i	$-0.117180\pi$
$659$	102.040	+	176.739i	0.154841	+	0.268193i	−0.778160	+	0.628066i	$0.783847\pi$
$660$		0			0
$661$	96.1350	+	358.781i	0.145439	+	0.542785i	0.999735	+	0.0229993i	$0.00732154\pi$
$661$	96.1350	+	358.781i	0.145439	+	0.542785i	−0.854297	+	0.519786i	$0.826012\pi$
$662$	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	−0.995587	−	0.0938462i	$-0.970084\pi$
$673$	−280.318	+	485.525i	−0.416520	+	0.721434i	0.579067	+	0.815280i	$0.303417\pi$
$674$	−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	$0.0604823\pi$
$677$			255.729i			0.377739i	−0.982002	+	0.188869i	$0.939518\pi$
$678$	−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	0.792889	+	0.609366i	$0.208576\pi$
$683$	−135.545	+	505.862i	−0.198456	+	0.740648i	−0.991345	+	0.131282i	$0.958091\pi$
$684$	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	0.505039	−	0.863097i	$-0.331478\pi$
$691$	949.409	−	254.393i	1.37396	−	0.368152i	0.868925	+	0.494944i	$0.164812\pi$
$692$	−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	$-0.822710\pi$
$701$		−	741.124i		−	1.05724i	0.848859	−	0.528619i	$-0.177290\pi$
$702$	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	0.198968	−	0.980006i	$-0.436241\pi$
$709$	−84.1747	−	22.5545i	−0.118723	−	0.0318118i	−0.317691	+	0.948194i	$0.602908\pi$
$710$		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	−0.533941	−	0.845522i	$-0.679289\pi$
$719$	−49.3722	+	28.5050i	−0.0686678	+	0.0396454i	0.465273	+	0.885167i	$0.345956\pi$
$720$		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	−0.600077	−	0.799942i	$-0.704863\pi$
$733$	146.502	−	146.502i	0.199866	−	0.199866i	0.799942	+	0.600077i	$0.204863\pi$
$734$	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	0.991322	−	0.131459i	$-0.0419661\pi$
$739$	49.5739	+	185.012i	0.0670825	+	0.250355i	−0.924239	+	0.381814i	$0.875299\pi$
$740$		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	1.00000		0.000285925i	$-9.10129e-5\pi$
$743$	99.4369	+	371.104i	0.133832	+	0.499466i	−0.866168	+	0.499752i	$0.833424\pi$
$744$	−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	−0.0864874	−	0.996253i	$-0.527564\pi$
$751$	−745.376	−	430.343i	−0.992511	−	0.573027i	−0.906024	+	0.423226i	$0.860898\pi$
$752$	−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	0.939344	−	0.342977i	$-0.111435\pi$
$757$	841.775	+	485.999i	1.11199	+	0.642007i	0.172645	+	0.984984i	$0.444769\pi$
$758$	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	0.253455	−	0.967347i	$-0.418433\pi$
$761$	−8.15865	−	2.18610i	−0.0107210	−	0.00287267i	−0.264176	+	0.964475i	$0.585100\pi$
$762$	−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	−0.332388	−	0.943143i	$-0.607854\pi$
$769$	−114.329	+	30.6343i	−0.148672	+	0.0398366i	0.183715	+	0.982979i	$0.441188\pi$
$770$		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	0.521874	−	0.853023i	$-0.325233\pi$
$773$	423.077	+	113.363i	0.547319	+	0.146654i	0.0254447	+	0.999676i	$0.491900\pi$
$774$	−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	−0.752069	−	0.659084i	$-0.770944\pi$
$787$	180.053	−	671.967i	0.228784	−	0.853833i	0.980853	−	0.194749i	$-0.0623892\pi$
$788$	−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	−0.688787	−	0.724963i	$-0.741857\pi$
$797$	−774.868	−	1342.11i	−0.972230	−	1.68395i	−0.283443	−	0.958989i	$-0.591477\pi$
$798$	−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	−0.978586	−	0.205836i	$-0.934009\pi$
$809$	−251.626	+	435.829i	−0.311034	+	0.538726i	0.667553	+	0.744562i	$0.267342\pi$
$810$		0			0
$811$	1082.95	+	1082.95i	1.33533	+	1.33533i	0.900529	+	0.434796i	$0.143180\pi$
$811$	1082.95	+	1082.95i	1.33533	+	1.33533i	0.434796	+	0.900529i	$0.356820\pi$
$812$	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	−0.846482	−	0.532417i	$-0.821284\pi$
$821$	−1078.26	+	288.919i	−1.31335	+	0.351911i	−0.466866	+	0.884328i	$0.654617\pi$
$822$	267.789	+	154.608i	0.325778	+	0.188088i
$823$	−521.053	−	902.490i	−0.633114	−	1.09659i	−0.986911	−	0.161264i	$-0.948443\pi$
$823$	−521.053	−	902.490i	−0.633114	−	1.09659i	0.353797	−	0.935322i	$-0.384890\pi$
$824$	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	0.968764	−	0.247985i	$-0.0797684\pi$
$827$	596.084	+	596.084i	0.720779	+	0.720779i	−0.247985	+	0.968764i	$0.579768\pi$
$828$	−2031.62	+	1172.95i	−2.45364	+	1.41661i
$829$	330.908	+	191.050i	0.399165	+	0.230458i	0.686124	−	0.727485i	$-0.259311\pi$
$829$	330.908	+	191.050i	0.399165	+	0.230458i	−0.286959	+	0.957943i	$0.592644\pi$
$830$		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	−0.216247	−	0.976339i	$-0.569382\pi$
$839$	−748.130	−	200.461i	−0.891692	−	0.238928i	−0.675445	+	0.737410i	$0.736048\pi$
$840$		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	0.714124	−	0.700020i	$-0.246825\pi$
$853$	12.0307	+	12.0307i	0.0141040	+	0.0141040i	−0.700020	+	0.714124i	$0.746825\pi$
$854$	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	−0.414804	−	0.909911i	$-0.636150\pi$
$863$	427.277	−	427.277i	0.495107	−	0.495107i	0.909911	+	0.414804i	$0.136150\pi$
$864$	−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	0.795069	−	0.606519i	$-0.207434\pi$
$877$	1035.18	+	277.375i	1.18036	+	0.316277i	0.385291	+	0.922795i	$0.374101\pi$
$878$	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	0.416646	−	0.909069i	$-0.363205\pi$
$881$	−142.992	−	82.5567i	−0.162307	−	0.0937079i	−0.578953	+	0.815361i	$0.696539\pi$
$882$	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	−0.277969	−	0.960590i	$-0.589661\pi$
$887$	−1107.73	−	639.547i	−1.24885	−	0.721023i	−0.970880	+	0.239567i	$0.922994\pi$
$888$	−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	−0.918783	−	0.394762i	$-0.870827\pi$
$907$	−106.588	+	184.616i	−0.117517	+	0.203546i	0.801266	+	0.598308i	$0.204160\pi$
$908$	−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	0.999928	+	0.0119659i	$0.00380894\pi$
$919$	468.990	+	812.315i	0.510327	+	0.883912i	−0.489601	+	0.871946i	$0.662858\pi$
$920$		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	0.768161	+	0.640257i	$0.221172\pi$
$929$	−201.792	+	753.099i	−0.217215	+	0.810656i	−0.985375	+	0.170399i	$0.945494\pi$
$930$		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	$0.260954\pi$
$937$			1369.92i			1.46203i	−0.682360	+	0.731016i	$0.739046\pi$
$938$	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	0.733177	−	0.680038i	$-0.238037\pi$
$941$	50.0032	+	50.0032i	0.0531384	+	0.0531384i	−0.680038	+	0.733177i	$0.738037\pi$
$942$	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	−0.849965	−	0.526839i	$-0.823377\pi$
$947$	−1252.54	+	335.616i	−1.32264	+	0.354400i	−0.472672	+	0.881238i	$0.656710\pi$
$948$	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	0.995482	+	0.0949514i	$0.0302696\pi$
$953$	552.713	+	957.326i	0.579971	+	1.00454i	−0.415511	+	0.909588i	$0.636397\pi$
$954$	−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	−0.504393	−	0.863474i	$-0.668284\pi$
$967$	347.232	−	347.232i	0.359082	−	0.359082i	0.863474	+	0.504393i	$0.168284\pi$
$968$	−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	0.957166	+	0.289539i	$0.0935020\pi$
$971$	708.181	+	1226.60i	0.729331	+	1.26324i	−0.227835	+	0.973700i	$0.573165\pi$
$972$	−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	−0.952202	−	0.305470i	$-0.901186\pi$
$977$	−273.859	−	1022.06i	−0.280306	−	1.04612i	0.671896	−	0.740646i	$-0.265480\pi$
$978$	−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	−0.983442	−	0.181223i	$-0.941994\pi$
$983$	−1144.87	−	1144.87i	−1.16467	−	1.16467i	−0.181223	−	0.983442i	$-0.558006\pi$
$984$	−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	−0.999560	−	0.0296628i	$-0.990557\pi$
$991$	−469.824	+	813.760i	−0.474091	+	0.821150i	0.525469	+	0.850813i	$0.323890\pi$
$992$	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	0.111479	−	0.993767i	$-0.464441\pi$
$997$	1024.76	−	591.647i	1.02785	−	0.593427i	0.916367	+	0.400340i	$0.131108\pi$
$998$	−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.124.10		40
5.2	odd	4		65.3.p.a.46.1	yes	40
5.3	odd	4		325.3.t.d.176.10		40
5.4	even	2		325.3.w.f.124.1		40
13.2	odd	12		325.3.w.f.249.1		40
65.2	even	12		65.3.p.a.41.1	✓	40
65.28	even	12		325.3.t.d.301.10		40
65.54	odd	12	inner	325.3.w.e.249.10		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.3.p.a.41.1	✓	40	65.2	even	12
65.3.p.a.46.1	yes	40	5.2	odd	4
325.3.t.d.176.10		40	5.3	odd	4
325.3.t.d.301.10		40	65.28	even	12
325.3.w.e.124.10		40	1.1	even	1	trivial
325.3.w.e.249.10		40	65.54	odd	12	inner
325.3.w.f.124.1		40	5.4	even	2
325.3.w.f.249.1		40	13.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
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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