LMFDB - Embedded newform 48.5.l.a.19.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,5,Mod(19,48)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.96175822802$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.11
Character	$\chi$	$=$	48.19
Dual form			48.5.l.a.43.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.05307 - 3.43291i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(-7.56978 - 14.0960i) q^{4} +(-34.5052 + 34.5052i) q^{5} +(5.06985 + 20.1568i) q^{6} -15.7115 q^{7} +(-63.9318 - 2.95383i) q^{8} -27.0000i q^{9} +O(q^{10})$	\(q+(2.05307 - 3.43291i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(-7.56978 - 14.0960i) q^{4} +(-34.5052 + 34.5052i) q^{5} +(5.06985 + 20.1568i) q^{6} -15.7115 q^{7} +(-63.9318 - 2.95383i) q^{8} -27.0000i q^{9} +(47.6116 + 189.295i) q^{10} +(43.6544 + 43.6544i) q^{11} +(79.6053 + 23.9790i) q^{12} +(-152.012 - 152.012i) q^{13} +(-32.2568 + 53.9361i) q^{14} -253.560i q^{15} +(-141.397 + 213.408i) q^{16} +343.952 q^{17} +(-92.6886 - 55.4330i) q^{18} +(-412.525 + 412.525i) q^{19} +(747.583 + 225.190i) q^{20} +(57.7276 - 57.7276i) q^{21} +(239.487 - 60.2360i) q^{22} -317.405 q^{23} +(245.753 - 224.047i) q^{24} -1756.21i q^{25} +(-833.936 + 209.752i) q^{26} +(99.2043 + 99.2043i) q^{27} +(118.932 + 221.470i) q^{28} +(-185.679 - 185.679i) q^{29} +(-870.450 - 520.578i) q^{30} +84.5615i q^{31} +(442.312 + 923.545i) q^{32} -320.793 q^{33} +(706.158 - 1180.76i) q^{34} +(542.127 - 542.127i) q^{35} +(-380.593 + 204.384i) q^{36} +(0.769642 - 0.769642i) q^{37} +(569.218 + 2263.10i) q^{38} +1117.06 q^{39} +(2307.90 - 2104.06i) q^{40} +622.677i q^{41} +(-79.6549 - 316.693i) q^{42} +(822.991 + 822.991i) q^{43} +(284.900 - 945.808i) q^{44} +(931.640 + 931.640i) q^{45} +(-651.657 + 1089.63i) q^{46} +3361.59i q^{47} +(-264.585 - 1303.64i) q^{48} -2154.15 q^{49} +(-6028.93 - 3605.64i) q^{50} +(-1263.76 + 1263.76i) q^{51} +(-992.071 + 3293.47i) q^{52} +(-725.034 + 725.034i) q^{53} +(544.234 - 136.886i) q^{54} -3012.60 q^{55} +(1004.46 + 46.4090i) q^{56} -3031.42i q^{57} +(-1018.63 + 256.207i) q^{58} +(2834.59 + 2834.59i) q^{59} +(-3574.20 + 1919.39i) q^{60} +(-479.007 - 479.007i) q^{61} +(290.292 + 173.611i) q^{62} +424.210i q^{63} +(4078.55 + 377.687i) q^{64} +10490.4 q^{65} +(-658.611 + 1101.25i) q^{66} +(-1169.89 + 1169.89i) q^{67} +(-2603.64 - 4848.36i) q^{68} +(1166.22 - 1166.22i) q^{69} +(-748.048 - 2974.10i) q^{70} -8082.92 q^{71} +(-79.7534 + 1726.16i) q^{72} -2917.94i q^{73} +(-1.06198 - 4.22224i) q^{74} +(6452.74 + 6452.74i) q^{75} +(8937.69 + 2692.25i) q^{76} +(-685.874 - 685.874i) q^{77} +(2293.40 - 3834.76i) q^{78} -5371.72i q^{79} +(-2484.75 - 12242.6i) q^{80} -729.000 q^{81} +(2137.60 + 1278.40i) q^{82} +(4366.68 - 4366.68i) q^{83} +(-1250.72 - 376.746i) q^{84} +(-11868.1 + 11868.1i) q^{85} +(4514.92 - 1135.60i) q^{86} +1364.45 q^{87} +(-2661.95 - 2919.85i) q^{88} -1595.14i q^{89} +(5110.96 - 1285.51i) q^{90} +(2388.33 + 2388.33i) q^{91} +(2402.69 + 4474.16i) q^{92} +(-310.699 - 310.699i) q^{93} +(11540.1 + 6901.60i) q^{94} -28468.5i q^{95} +(-5018.48 - 1768.16i) q^{96} +9735.44 q^{97} +(-4422.63 + 7395.01i) q^{98} +(1178.67 - 1178.67i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} + 180 q^{8}+O(q^{10}) $ 32 * q + 12 * q^4 + 180 * q^8	$ 32 q + 12 q^{4} + 180 q^{8} + 296 q^{10} - 192 q^{11} + 360 q^{12} - 156 q^{14} + 352 q^{16} - 324 q^{18} + 704 q^{19} - 1200 q^{20} - 1568 q^{22} - 2304 q^{23} + 1188 q^{24} + 2700 q^{26} + 4680 q^{28} - 1728 q^{29} + 1512 q^{30} - 3360 q^{32} - 9312 q^{34} - 5184 q^{35} - 756 q^{36} + 3648 q^{37} - 5880 q^{38} + 5232 q^{40} + 4500 q^{42} + 1088 q^{43} + 18840 q^{44} + 680 q^{46} + 2160 q^{48} + 10976 q^{49} - 25884 q^{50} - 4032 q^{51} - 25584 q^{52} + 960 q^{53} + 972 q^{54} + 11776 q^{55} + 15456 q^{56} + 12624 q^{58} + 13056 q^{59} + 7992 q^{60} + 3776 q^{61} + 21852 q^{62} - 8664 q^{64} + 4032 q^{65} - 8856 q^{66} - 896 q^{67} - 17280 q^{68} - 9792 q^{69} - 18240 q^{70} - 39936 q^{71} + 4860 q^{72} + 24204 q^{74} - 1152 q^{75} + 16776 q^{76} + 9408 q^{77} - 3780 q^{78} - 14232 q^{80} - 23328 q^{81} - 33800 q^{82} + 24000 q^{83} - 11448 q^{84} - 11200 q^{85} - 1200 q^{86} - 11424 q^{88} + 4104 q^{90} + 30528 q^{91} - 11664 q^{92} - 8040 q^{94} + 10080 q^{96} + 52968 q^{98} - 5184 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 + 180 * q^8 + 296 * q^10 - 192 * q^11 + 360 * q^12 - 156 * q^14 + 352 * q^16 - 324 * q^18 + 704 * q^19 - 1200 * q^20 - 1568 * q^22 - 2304 * q^23 + 1188 * q^24 + 2700 * q^26 + 4680 * q^28 - 1728 * q^29 + 1512 * q^30 - 3360 * q^32 - 9312 * q^34 - 5184 * q^35 - 756 * q^36 + 3648 * q^37 - 5880 * q^38 + 5232 * q^40 + 4500 * q^42 + 1088 * q^43 + 18840 * q^44 + 680 * q^46 + 2160 * q^48 + 10976 * q^49 - 25884 * q^50 - 4032 * q^51 - 25584 * q^52 + 960 * q^53 + 972 * q^54 + 11776 * q^55 + 15456 * q^56 + 12624 * q^58 + 13056 * q^59 + 7992 * q^60 + 3776 * q^61 + 21852 * q^62 - 8664 * q^64 + 4032 * q^65 - 8856 * q^66 - 896 * q^67 - 17280 * q^68 - 9792 * q^69 - 18240 * q^70 - 39936 * q^71 + 4860 * q^72 + 24204 * q^74 - 1152 * q^75 + 16776 * q^76 + 9408 * q^77 - 3780 * q^78 - 14232 * q^80 - 23328 * q^81 - 33800 * q^82 + 24000 * q^83 - 11448 * q^84 - 11200 * q^85 - 1200 * q^86 - 11424 * q^88 + 4104 * q^90 + 30528 * q^91 - 11664 * q^92 - 8040 * q^94 + 10080 * q^96 + 52968 * q^98 - 5184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.05307	−	3.43291i	0.513268	−	0.858228i
$2$	2.05307	−	3.43291i	0.513268	−	0.858228i
$3$	−3.67423	+	3.67423i	−0.408248	+	0.408248i
$3$	−3.67423	+	3.67423i	−0.408248	+	0.408248i
$4$	−7.56978	−	14.0960i	−0.473111	−	0.881003i
$5$	−34.5052	+	34.5052i	−1.38021	+	1.38021i	−0.535969	+	0.844237i	$0.680054\pi$
$5$	−34.5052	+	34.5052i	−1.38021	+	1.38021i	−0.844237	+	0.535969i	$0.819946\pi$
$6$	5.06985	+	20.1568i	0.140829	+	0.559911i
$7$	−15.7115			−0.320642			−0.160321	−	0.987065i	$-0.551253\pi$
$7$	−15.7115			−0.320642			−0.160321	+	0.987065i	$0.551253\pi$
$8$	−63.9318	−	2.95383i	−0.998934	−	0.0461536i
$9$		−	27.0000i		−	0.333333i
$10$	47.6116	+	189.295i	0.476116	+	1.89295i
$11$	43.6544	+	43.6544i	0.360780	+	0.360780i	0.864100	−	0.503320i	$-0.167888\pi$
$11$	43.6544	+	43.6544i	0.360780	+	0.360780i	−0.503320	+	0.864100i	$0.667888\pi$
$12$	79.6053	+	23.9790i	0.552815	+	0.166521i
$13$	−152.012	−	152.012i	−0.899480	−	0.899480i	0.0959102	−	0.995390i	$-0.469424\pi$
$13$	−152.012	−	152.012i	−0.899480	−	0.899480i	−0.995390	+	0.0959102i	$0.969424\pi$
$14$	−32.2568	+	53.9361i	−0.164576	+	0.275184i
$15$		−	253.560i		−	1.12693i
$16$	−141.397	+	213.408i	−0.552332	+	0.833624i
$17$	343.952			1.19014			0.595072	−	0.803672i	$-0.297123\pi$
$17$	343.952			1.19014			0.595072	+	0.803672i	$0.297123\pi$
$18$	−92.6886	−	55.4330i	−0.286076	−	0.171089i
$19$	−412.525	+	412.525i	−1.14273	+	1.14273i	−0.154778	+	0.987949i	$0.549466\pi$
$19$	−412.525	+	412.525i	−1.14273	+	1.14273i	−0.987949	+	0.154778i	$0.950534\pi$
$20$	747.583	+	225.190i	1.86896	+	0.562975i
$21$	57.7276	−	57.7276i	0.130902	−	0.130902i
$22$	239.487	−	60.2360i	0.494808	−	0.124455i
$23$	−317.405			−0.600010			−0.300005	−	0.953938i	$-0.596988\pi$
$23$	−317.405			−0.600010			−0.300005	+	0.953938i	$0.596988\pi$
$24$	245.753	−	224.047i	0.426655	−	0.388971i
$25$		−	1756.21i		−	2.80994i
$26$	−833.936	+	209.752i	−1.23363	+	0.310284i
$27$	99.2043	+	99.2043i	0.136083	+	0.136083i
$28$	118.932	+	221.470i	0.151699	+	0.282487i
$29$	−185.679	−	185.679i	−0.220783	−	0.220783i	0.588045	−	0.808828i	$-0.299898\pi$
$29$	−185.679	−	185.679i	−0.220783	−	0.220783i	−0.808828	+	0.588045i	$0.799898\pi$
$30$	−870.450	−	520.578i	−0.967167	−	0.578420i
$31$			84.5615i			0.0879932i	0.999032	+	0.0439966i	$0.0140091\pi$
$31$			84.5615i			0.0879932i	−0.999032	+	0.0439966i	$0.985991\pi$
$32$	442.312	+	923.545i	0.431946	+	0.901900i
$33$	−320.793			−0.294576
$34$	706.158	−	1180.76i	0.610864	−	1.02142i
$35$	542.127	−	542.127i	0.442553	−	0.442553i
$36$	−380.593	+	204.384i	−0.293668	+	0.157704i
$37$	0.769642	−	0.769642i	0.000562193	−	0.000562193i	−0.706826	−	0.707388i	$-0.749873\pi$
$37$	0.769642	−	0.769642i	0.000562193	−	0.000562193i	0.707388	+	0.706826i	$0.249873\pi$
$38$	569.218	+	2263.10i	0.394195	+	1.56725i
$39$	1117.06			0.734422
$40$	2307.90	−	2104.06i	1.44244	−	1.31503i
$41$			622.677i			0.370421i	0.982699	+	0.185210i	$0.0592967\pi$
$41$			622.677i			0.370421i	−0.982699	+	0.185210i	$0.940703\pi$
$42$	−79.6549	−	316.693i	−0.0451558	−	0.179531i
$43$	822.991	+	822.991i	0.445101	+	0.445101i	0.893722	−	0.448621i	$-0.148085\pi$
$43$	822.991	+	822.991i	0.445101	+	0.445101i	−0.448621	+	0.893722i	$0.648085\pi$
$44$	284.900	−	945.808i	0.147159	−	0.488537i
$45$	931.640	+	931.640i	0.460069	+	0.460069i
$46$	−651.657	+	1089.63i	−0.307966	+	0.514946i
$47$			3361.59i			1.52177i	0.648886	+	0.760886i	$0.275235\pi$
$47$			3361.59i			1.52177i	−0.648886	+	0.760886i	$0.724765\pi$
$48$	−264.585	−	1303.64i	−0.114837	−	0.565814i
$49$	−2154.15			−0.897189
$50$	−6028.93	−	3605.64i	−2.41157	−	1.44225i
$51$	−1263.76	+	1263.76i	−0.485874	+	0.485874i
$52$	−992.071	+	3293.47i	−0.366890	+	1.21800i
$53$	−725.034	+	725.034i	−0.258111	+	0.258111i	−0.824285	−	0.566174i	$-0.808423\pi$
$53$	−725.034	+	725.034i	−0.258111	+	0.258111i	0.566174	+	0.824285i	$0.308423\pi$
$54$	544.234	−	136.886i	0.186637	−	0.0469431i
$55$	−3012.60			−0.995902
$56$	1004.46	+	46.4090i	0.320301	+	0.0147988i
$57$		−	3031.42i		−	0.933033i
$58$	−1018.63	+	256.207i	−0.302804	+	0.0761614i
$59$	2834.59	+	2834.59i	0.814304	+	0.814304i	0.985276	−	0.170972i	$-0.0546908\pi$
$59$	2834.59	+	2834.59i	0.814304	+	0.814304i	−0.170972	+	0.985276i	$0.554691\pi$
$60$	−3574.20	+	1919.39i	−0.992832	+	0.533165i
$61$	−479.007	−	479.007i	−0.128731	−	0.128731i	0.639806	−	0.768537i	$-0.279015\pi$
$61$	−479.007	−	479.007i	−0.128731	−	0.128731i	−0.768537	+	0.639806i	$0.779015\pi$
$62$	290.292	+	173.611i	0.0755182	+	0.0451641i
$63$			424.210i			0.106881i
$64$	4078.55	+	377.687i	0.995740	+	0.0922088i
$65$	10490.4			2.48294
$66$	−658.611	+	1101.25i	−0.151196	+	0.252813i
$67$	−1169.89	+	1169.89i	−0.260614	+	0.260614i	−0.825303	−	0.564690i	$-0.808996\pi$
$67$	−1169.89	+	1169.89i	−0.260614	+	0.260614i	0.564690	+	0.825303i	$0.308996\pi$
$68$	−2603.64	−	4848.36i	−0.563071	−	1.04852i
$69$	1166.22	−	1166.22i	0.244953	−	0.244953i
$70$	−748.048	−	2974.10i	−0.152663	−	0.606959i
$71$	−8082.92			−1.60344			−0.801718	−	0.597702i	$-0.796080\pi$
$71$	−8082.92			−1.60344			−0.801718	+	0.597702i	$0.796080\pi$
$72$	−79.7534	+	1726.16i	−0.0153845	+	0.332978i
$73$		−	2917.94i		−	0.547559i	−0.961793	−	0.273779i	$-0.911726\pi$
$73$		−	2917.94i		−	0.547559i	0.961793	−	0.273779i	$-0.0882738\pi$
$74$	−1.06198	−	4.22224i	−0.000193934	−	0.000771045i
$75$	6452.74	+	6452.74i	1.14715	+	1.14715i
$76$	8937.69	+	2692.25i	1.54738	+	0.466109i
$77$	−685.874	−	685.874i	−0.115681	−	0.115681i
$78$	2293.40	−	3834.76i	0.376956	−	0.630302i
$79$		−	5371.72i		−	0.860714i	−0.902659	−	0.430357i	$-0.858388\pi$
$79$		−	5371.72i		−	0.860714i	0.902659	−	0.430357i	$-0.141612\pi$
$80$	−2484.75	−	12242.6i	−0.388242	−	1.91291i
$81$	−729.000			−0.111111
$82$	2137.60	+	1278.40i	0.317906	+	0.190125i
$83$	4366.68	−	4366.68i	0.633863	−	0.633863i	−0.315172	−	0.949035i	$-0.602062\pi$
$83$	4366.68	−	4366.68i	0.633863	−	0.633863i	0.949035	+	0.315172i	$0.102062\pi$
$84$	−1250.72	−	376.746i	−0.177256	−	0.0533937i
$85$	−11868.1	+	11868.1i	−1.64265	+	1.64265i
$86$	4514.92	−	1135.60i	0.610454	−	0.153542i
$87$	1364.45			0.180269
$88$	−2661.95	−	2919.85i	−0.343744	−	0.377047i
$89$		−	1595.14i		−	0.201381i	−0.994918	−	0.100690i	$-0.967895\pi$
$89$		−	1595.14i		−	0.201381i	0.994918	−	0.100690i	$-0.0321051\pi$
$90$	5110.96	−	1285.51i	0.630983	−	0.158705i
$91$	2388.33	+	2388.33i	0.288411	+	0.288411i
$92$	2402.69	+	4474.16i	0.283872	+	0.528611i
$93$	−310.699	−	310.699i	−0.0359231	−	0.0359231i
$94$	11540.1	+	6901.60i	1.30603	+	0.781077i
$95$		−	28468.5i		−	3.15440i
$96$	−5018.48	−	1768.16i	−0.544540	−	0.191858i
$97$	9735.44			1.03469			0.517347	−	0.855775i	$-0.326920\pi$
$97$	9735.44			1.03469			0.517347	+	0.855775i	$0.326920\pi$
$98$	−4422.63	+	7395.01i	−0.460498	+	0.769992i
$99$	1178.67	−	1178.67i	0.120260	−	0.120260i
$100$	−24755.7	+	13294.1i	−2.47557	+	1.32941i
$101$	−4787.83	+	4787.83i	−0.469350	+	0.469350i	−0.901704	−	0.432354i	$-0.857683\pi$
$101$	−4787.83	+	4787.83i	−0.469350	+	0.469350i	0.432354	+	0.901704i	$0.357683\pi$
$102$	1743.78	+	6932.97i	0.167607	+	0.666375i
$103$	−3615.06			−0.340754			−0.170377	−	0.985379i	$-0.554499\pi$
$103$	−3615.06			−0.340754			−0.170377	+	0.985379i	$0.554499\pi$
$104$	9269.39	+	10167.4i	0.857007	+	0.940035i
$105$			3983.80i			0.361343i
$106$	1000.43	+	3977.52i	0.0890379	+	0.353998i
$107$	−7005.75	−	7005.75i	−0.611910	−	0.611910i	0.331534	−	0.943443i	$-0.392434\pi$
$107$	−7005.75	−	7005.75i	−0.611910	−	0.611910i	−0.943443	+	0.331534i	$0.892434\pi$
$108$	647.434	−	2149.34i	0.0555070	−	0.184272i
$109$	−11367.4	−	11367.4i	−0.956774	−	0.956774i	0.0423296	−	0.999104i	$-0.486522\pi$
$109$	−11367.4	−	11367.4i	−0.956774	−	0.956774i	−0.999104	+	0.0423296i	$0.986522\pi$
$110$	−6185.09	+	10342.0i	−0.511165	+	0.854711i
$111$			5.65569i			0.000459028i
$112$	2221.55	−	3352.95i	0.177101	−	0.267295i
$113$	−16880.3			−1.32198			−0.660988	−	0.750397i	$-0.729862\pi$
$113$	−16880.3			−1.32198			−0.660988	+	0.750397i	$0.729862\pi$
$114$	−10406.6	−	6223.74i	−0.800755	−	0.478896i
$115$	10952.1	−	10952.1i	0.828138	−	0.828138i
$116$	−1211.79	+	4022.88i	−0.0900557	+	0.298966i
$117$	−4104.33	+	4104.33i	−0.299827	+	0.299827i
$118$	15550.5	−	3911.28i	1.11681	−	0.280902i
$119$	−5403.99			−0.381611
$120$	−748.973	+	16210.6i	−0.0520120	+	1.12573i
$121$		−	10829.6i		−	0.739676i
$122$	−2627.82	+	660.952i	−0.176554	+	0.0444069i
$123$	−2287.86	−	2287.86i	−0.151224	−	0.151224i
$124$	1191.98	−	640.112i	0.0775223	−	0.0416306i
$125$	39032.7	+	39032.7i	2.49809	+	2.49809i
$126$	1456.28	+	870.934i	0.0917281	+	0.0548585i
$127$			28621.7i			1.77455i	0.461242	+	0.887274i	$0.347404\pi$
$127$			28621.7i			1.77455i	−0.461242	+	0.887274i	$0.652596\pi$
$128$	9670.13	−	13225.9i	0.590218	−	0.807244i
$129$	−6047.72			−0.363423
$130$	21537.6	−	36012.6i	1.27441	−	2.13093i
$131$	−10867.3	+	10867.3i	−0.633254	+	0.633254i	−0.948883	−	0.315629i	$-0.897785\pi$
$131$	−10867.3	+	10867.3i	−0.633254	+	0.633254i	0.315629	+	0.948883i	$0.397785\pi$
$132$	2428.33	+	4521.91i	0.139367	+	0.259522i
$133$	6481.37	−	6481.37i	0.366407	−	0.366407i
$134$	1614.27	+	6418.03i	0.0899012	+	0.357431i
$135$	−6846.12			−0.375645
$136$	−21989.5	−	1015.97i	−1.18888	−	0.0549294i
$137$			13661.6i			0.727879i	0.931423	+	0.363940i	$0.118569\pi$
$137$			13661.6i			0.727879i	−0.931423	+	0.363940i	$0.881431\pi$
$138$	−1609.20	−	6397.88i	−0.0844990	−	0.335952i
$139$	−5087.63	−	5087.63i	−0.263321	−	0.263321i	0.563081	−	0.826402i	$-0.309616\pi$
$139$	−5087.63	−	5087.63i	−0.263321	−	0.263321i	−0.826402	+	0.563081i	$0.809616\pi$
$140$	−11745.6	−	3538.07i	−0.599267	−	0.180514i
$141$	−12351.3	−	12351.3i	−0.621261	−	0.621261i
$142$	−16594.8	+	27748.0i	−0.822993	+	1.37611i
$143$		−	13272.0i		−	0.649028i
$144$	5762.01	+	3817.72i	0.277875	+	0.184111i
$145$	12813.8			0.609453
$146$	−10017.0	−	5990.75i	−0.469930	−	0.281045i
$147$	7914.85	−	7914.85i	0.366276	−	0.366276i
$148$	−16.6749	−	5.02289i	−0.000761273	−	0.000229314i
$149$	−4283.42	+	4283.42i	−0.192938	+	0.192938i	−0.796964	−	0.604026i	$-0.793562\pi$
$149$	−4283.42	+	4283.42i	−0.192938	+	0.192938i	0.604026	+	0.796964i	$0.293562\pi$
$150$	35399.6	−	8903.74i	1.57332	−	0.395722i
$151$	23645.1			1.03702			0.518509	−	0.855072i	$-0.326487\pi$
$151$	23645.1			1.03702			0.518509	+	0.855072i	$0.326487\pi$
$152$	27592.0	−	25154.9i	1.19425	−	1.08877i
$153$		−	9286.70i		−	0.396715i
$154$	−3762.70	+	946.396i	−0.158656	+	0.0399054i
$155$	−2917.81	−	2917.81i	−0.121449	−	0.121449i
$156$	−8455.87	−	15746.1i	−0.347463	−	0.647028i
$157$	1072.54	+	1072.54i	0.0435124	+	0.0435124i	0.728528	−	0.685016i	$-0.240205\pi$
$157$	1072.54	+	1072.54i	0.0435124	+	0.0435124i	−0.685016	+	0.728528i	$0.740205\pi$
$158$	−18440.6	−	11028.5i	−0.738689	−	0.441777i
$159$		−	5327.89i		−	0.210747i
$160$	−47129.1	−	16605.0i	−1.84098	−	0.648634i
$161$	4986.91			0.192389
$162$	−1496.69	+	2502.59i	−0.0570298	+	0.0953587i
$163$	10944.1	−	10944.1i	0.411911	−	0.411911i	−0.470493	−	0.882404i	$-0.655924\pi$
$163$	10944.1	−	10944.1i	0.411911	−	0.411911i	0.882404	+	0.470493i	$0.155924\pi$
$164$	8777.29	−	4713.53i	0.326342	−	0.175250i
$165$	11069.0	−	11069.0i	0.406575	−	0.406575i
$166$	−6025.32	−	23955.6i	−0.218657	−	0.869341i
$167$	20214.2			0.724808			0.362404	−	0.932021i	$-0.381956\pi$
$167$	20214.2			0.724808			0.362404	+	0.932021i	$0.381956\pi$
$168$	−3861.15	+	3520.11i	−0.136804	+	0.124721i
$169$			17654.3i			0.618128i
$170$	16376.1	+	65108.3i	0.566647	+	2.25288i
$171$	11138.2	+	11138.2i	0.380909	+	0.380909i
$172$	5371.06	−	17830.8i	0.181553	−	0.602717i
$173$	−8248.65	−	8248.65i	−0.275607	−	0.275607i	0.555745	−	0.831353i	$-0.312433\pi$
$173$	−8248.65	−	8248.65i	−0.275607	−	0.275607i	−0.831353	+	0.555745i	$0.812433\pi$
$174$	2801.33	−	4684.05i	0.0925263	−	0.154712i
$175$			27592.7i			0.900986i
$176$	−15488.8	+	3143.59i	−0.500025	+	0.101485i
$177$	−20829.9			−0.664876
$178$	−5475.97	−	3274.93i	−0.172831	−	0.103362i
$179$	−35369.3	+	35369.3i	−1.10387	+	1.10387i	−0.109936	+	0.993939i	$0.535065\pi$
$179$	−35369.3	+	35369.3i	−1.10387	+	1.10387i	−0.993939	+	0.109936i	$0.964935\pi$
$180$	6080.13	−	20184.7i	0.187658	−	0.622986i
$181$	−20858.6	+	20858.6i	−0.636689	+	0.636689i	−0.949737	−	0.313048i	$-0.898650\pi$
$181$	−20858.6	+	20858.6i	−0.636689	+	0.636689i	0.313048	+	0.949737i	$0.398650\pi$
$182$	13102.4	−	3295.52i	0.395555	−	0.0994903i
$183$	3519.97			0.105108
$184$	20292.3	+	937.561i	0.599371	+	0.0276926i
$185$			53.1132i			0.00155188i
$186$	−1704.49	+	428.714i	−0.0492684	+	0.0123920i
$187$	15015.0	+	15015.0i	0.429380	+	0.429380i
$188$	47385.2	−	25446.5i	1.34069	−	0.719967i
$189$	−1558.65	−	1558.65i	−0.0436339	−	0.0436339i
$190$	−97729.7	−	58447.9i	−2.70720	−	1.61905i
$191$		−	10542.5i		−	0.288987i	−0.989506	−	0.144494i	$-0.953845\pi$
$191$		−	10542.5i		−	0.288987i	0.989506	−	0.144494i	$-0.0461553\pi$
$192$	−16373.3	+	13597.8i	−0.444153	+	0.368865i
$193$	58923.2			1.58187			0.790936	−	0.611898i	$-0.209594\pi$
$193$	58923.2			1.58187			0.790936	+	0.611898i	$0.209594\pi$
$194$	19987.6	−	33420.9i	0.531076	−	0.888004i
$195$	−38544.2	+	38544.2i	−1.01365	+	1.01365i
$196$	16306.4	+	30365.0i	0.424470	+	0.790426i
$197$	42937.8	−	42937.8i	1.10639	−	1.10639i	0.112767	−	0.993621i	$-0.464029\pi$
$197$	42937.8	−	42937.8i	1.10639	−	1.10639i	0.993621	−	0.112767i	$-0.0359714\pi$
$198$	−1626.37	−	6466.16i	−0.0414848	−	0.164936i
$199$	1840.22			0.0464691			0.0232346	−	0.999730i	$-0.492604\pi$
$199$	1840.22			0.0464691			0.0232346	+	0.999730i	$0.492604\pi$
$200$	−5187.55	+	112278.i	−0.129689	+	2.80695i
$201$		−	8596.94i		−	0.212790i
$202$	6606.44	+	26266.0i	0.161907	+	0.643711i
$203$	2917.29	+	2917.29i	0.0707925	+	0.0707925i
$204$	27380.4	+	8247.63i	0.657929	+	0.198184i
$205$	−21485.6	−	21485.6i	−0.511257	−	0.511257i
$206$	−7421.99	+	12410.2i	−0.174898	+	0.292445i
$207$			8569.95i			0.200003i
$208$	53934.6	−	10946.5i	1.24664	−	0.253017i
$209$	−36017.0			−0.824546
$210$	13676.1	+	8179.04i	0.310115	+	0.185466i
$211$	10976.7	−	10976.7i	0.246551	−	0.246551i	−0.573003	−	0.819553i	$-0.694222\pi$
$211$	10976.7	−	10976.7i	0.246551	−	0.246551i	0.819553	+	0.573003i	$0.194222\pi$
$212$	15708.5	+	4731.76i	0.349512	+	0.105281i
$213$	29698.5	−	29698.5i	0.654600	−	0.654600i
$214$	−38433.5	+	9666.81i	−0.839232	+	0.211084i
$215$	−56794.9			−1.22866
$216$	−6049.28	−	6635.34i	−0.129657	−	0.142218i
$217$		−	1328.59i		−	0.0282143i
$218$	−62361.6	+	15685.2i	−1.31221	+	0.330049i
$219$	10721.2	+	10721.2i	0.223540	+	0.223540i
$220$	22804.7	+	42465.8i	0.471172	+	0.877392i
$221$	−52284.8	−	52284.8i	−1.07051	−	1.07051i
$222$	19.4155	+	11.6115i	0.000393951	+	0.000235605i
$223$			70392.8i			1.41553i	0.706448	+	0.707765i	$0.250296\pi$
$223$			70392.8i			1.41553i	−0.706448	+	0.707765i	$0.749704\pi$
$224$	−6949.38	−	14510.3i	−0.138500	−	0.289187i
$225$	−47417.8			−0.936647
$226$	−34656.5	+	57948.6i	−0.678528	+	1.13456i
$227$	34485.5	−	34485.5i	0.669245	−	0.669245i	−0.288296	−	0.957541i	$-0.593089\pi$
$227$	34485.5	−	34485.5i	0.669245	−	0.669245i	0.957541	+	0.288296i	$0.0930889\pi$
$228$	−42731.1	+	22947.2i	−0.822005	+	0.441428i
$229$	8730.13	−	8730.13i	0.166475	−	0.166475i	−0.618953	−	0.785428i	$-0.712443\pi$
$229$	8730.13	−	8730.13i	0.166475	−	0.166475i	0.785428	+	0.618953i	$0.212443\pi$
$230$	−15112.2	−	60083.2i	−0.285674	−	1.13579i
$231$	5040.13			0.0944534
$232$	11322.3	+	12419.2i	0.210358	+	0.230738i
$233$			38780.0i			0.714325i	0.934042	+	0.357162i	$0.116256\pi$
$233$			38780.0i			0.714325i	−0.934042	+	0.357162i	$0.883744\pi$
$234$	5663.31	+	22516.3i	0.103428	+	0.411211i
$235$	−115992.	−	115992.i	−2.10036	−	2.10036i
$236$	18499.3	−	61413.8i	0.332148	−	1.10266i
$237$	19737.0	+	19737.0i	0.351385	+	0.351385i
$238$	−11094.8	+	18551.4i	−0.195869	+	0.327509i
$239$			79247.0i			1.38735i	0.720286	+	0.693677i	$0.244010\pi$
$239$			79247.0i			1.38735i	−0.720286	+	0.693677i	$0.755990\pi$
$240$	54111.7	+	35852.6i	0.939440	+	0.622441i
$241$	−48185.2			−0.829621			−0.414810	−	0.909908i	$-0.636152\pi$
$241$	−48185.2			−0.829621			−0.414810	+	0.909908i	$0.636152\pi$
$242$	−37177.0	−	22234.0i	−0.634811	−	0.379652i
$243$	2678.52	−	2678.52i	0.0453609	−	0.0453609i
$244$	−3126.12	+	10378.1i	−0.0525081	+	0.174316i
$245$	74329.3	−	74329.3i	1.23831	−	1.23831i
$246$	−12551.2	+	3156.88i	−0.207403	+	0.0521661i
$247$	125417.			2.05572
$248$	249.780	−	5406.17i	0.00406120	−	0.0878994i
$249$			32088.4i			0.517547i
$250$	214133.	−	53858.9i	3.42613	−	0.861742i
$251$	−29523.0	−	29523.0i	−0.468611	−	0.468611i	0.432853	−	0.901464i	$-0.357507\pi$
$251$	−29523.0	−	29523.0i	−0.468611	−	0.468611i	−0.901464	+	0.432853i	$0.857507\pi$
$252$	5979.68	−	3211.17i	0.0941623	−	0.0505665i
$253$	−13856.1	−	13856.1i	−0.216472	−	0.216472i
$254$	98255.8	+	58762.4i	1.52297	+	0.910820i
$255$		−	87212.5i		−	1.34121i
$256$	−25549.8	−	60350.4i	−0.389859	−	0.920874i
$257$	−39080.4			−0.591688			−0.295844	−	0.955236i	$-0.595601\pi$
$257$	−39080.4			−0.591688			−0.295844	+	0.955236i	$0.595601\pi$
$258$	−12416.4	+	20761.3i	−0.186534	+	0.311900i
$259$	−12.0922	+	12.0922i	−0.000180263	+	0.000180263i
$260$	−79410.0	−	147873.i	−1.17470	−	2.18747i
$261$	−5013.33	+	5013.33i	−0.0735944	+	0.0735944i
$262$	14995.1	+	59617.7i	0.218447	+	0.868506i
$263$	45953.7			0.664368			0.332184	−	0.943215i	$-0.392214\pi$
$263$	45953.7			0.664368			0.332184	+	0.943215i	$0.392214\pi$
$264$	20508.9	+	947.567i	0.294262	+	0.0135957i
$265$		−	50034.8i		−	0.712493i
$266$	−8943.25	−	35556.7i	−0.126396	−	0.502526i
$267$	5860.91	+	5860.91i	0.0822133	+	0.0822133i
$268$	25346.7	+	7635.04i	0.352901	+	0.106302i
$269$	2533.97	+	2533.97i	0.0350184	+	0.0350184i	0.724399	−	0.689381i	$-0.242117\pi$
$269$	2533.97	+	2533.97i	0.0350184	+	0.0350184i	−0.689381	+	0.724399i	$0.742117\pi$
$270$	−14055.6	+	23502.1i	−0.192807	+	0.322389i
$271$			49077.7i			0.668260i	0.942527	+	0.334130i	$0.108442\pi$
$271$			49077.7i			0.668260i	−0.942527	+	0.334130i	$0.891558\pi$
$272$	−48633.7	+	73402.0i	−0.657355	+	0.992134i
$273$	−17550.6			−0.235487
$274$	46899.0	+	28048.2i	0.624686	+	0.373597i
$275$	76666.4	−	76666.4i	1.01377	−	1.01377i
$276$	−25267.2	−	7611.08i	−0.331694	−	0.0999144i
$277$	70048.1	−	70048.1i	0.912929	−	0.912929i	−0.0835730	−	0.996502i	$-0.526633\pi$
$277$	70048.1	−	70048.1i	0.912929	−	0.912929i	0.996502	+	0.0835730i	$0.0266332\pi$
$278$	−27910.7	+	7020.11i	−0.361144	+	0.0908352i
$279$	2283.16			0.0293311
$280$	−36260.5	+	33057.8i	−0.462506	+	0.421656i
$281$			11528.5i			0.146003i	0.997332	+	0.0730014i	$0.0232577\pi$
$281$			11528.5i			0.146003i	−0.997332	+	0.0730014i	$0.976742\pi$
$282$	−67759.0	+	17042.8i	−0.852057	+	0.214310i
$283$	−1792.16	−	1792.16i	−0.0223771	−	0.0223771i	0.695830	−	0.718207i	$-0.255037\pi$
$283$	−1792.16	−	1792.16i	−0.0223771	−	0.0223771i	−0.718207	+	0.695830i	$0.755037\pi$
$284$	61185.9	+	113937.i	0.758603	+	1.41263i
$285$	104600.	+	104600.i	1.28778	+	1.28778i
$286$	−45561.6	−	27248.4i	−0.557014	−	0.333126i
$287$		−	9783.18i		−	0.118773i
$288$	24935.7	−	11942.4i	0.300633	−	0.143982i
$289$	34781.8			0.416444
$290$	26307.6	−	43988.5i	0.312813	−	0.523050i
$291$	−35770.3	+	35770.3i	−0.422412	+	0.422412i
$292$	−41131.4	+	22088.2i	−0.482401	+	0.259056i
$293$	−79514.9	+	79514.9i	−0.926218	+	0.926218i	−0.997459	−	0.0712415i	$-0.977304\pi$
$293$	−79514.9	+	79514.9i	−0.926218	+	0.926218i	0.0712415	+	0.997459i	$0.477304\pi$
$294$	−10921.2	−	43420.8i	−0.126350	−	0.502346i
$295$	−195616.			−2.24782
$296$	−51.4780	+	46.9312i	−0.000587541	+	0.000535646i
$297$			8661.40i			0.0981918i
$298$	5910.44	+	23498.8i	0.0665560	+	0.264614i
$299$	48249.5	+	48249.5i	0.539697	+	0.539697i
$300$	42112.3	−	139804.i	0.467914	−	1.55338i
$301$	−12930.4	−	12930.4i	−0.142718	−	0.142718i
$302$	48545.0	−	81171.4i	0.532269	−	0.889998i
$303$		−	35183.3i		−	0.383222i
$304$	−29706.3	−	146366.i	−0.321441	−	1.58377i
$305$	33056.4			0.355350
$306$	−31880.4	−	19066.3i	−0.340472	−	0.203621i
$307$	−95746.9	+	95746.9i	−1.01589	+	1.01589i	−0.0160211	+	0.999872i	$0.505100\pi$
$307$	−95746.9	+	95746.9i	−1.01589	+	1.01589i	−0.999872	+	0.0160211i	$0.994900\pi$
$308$	−4476.20	+	14860.0i	−0.0471854	+	0.156646i
$309$	13282.6	−	13282.6i	0.139112	−	0.139112i
$310$	−16007.1	+	4026.11i	−0.166567	+	0.0418950i
$311$	113649.			1.17502			0.587510	−	0.809217i	$-0.300108\pi$
$311$	113649.			1.17502			0.587510	+	0.809217i	$0.300108\pi$
$312$	−71415.4	−	3299.59i	−0.733640	−	0.0338962i
$313$			173781.i			1.77383i	0.461929	+	0.886917i	$0.347158\pi$
$313$			173781.i			1.77383i	−0.461929	+	0.886917i	$0.652842\pi$
$314$	5883.92	−	1479.93i	0.0596771	−	0.0150100i
$315$	−14637.4	−	14637.4i	−0.147518	−	0.147518i
$316$	−75720.0	+	40662.7i	−0.758292	+	0.407214i
$317$	16567.5	+	16567.5i	0.164869	+	0.164869i	0.784720	−	0.619851i	$-0.212807\pi$
$317$	16567.5	+	16567.5i	0.164869	+	0.164869i	−0.619851	+	0.784720i	$0.712807\pi$
$318$	−18290.2	−	10938.5i	−0.180869	−	0.108170i
$319$		−	16211.4i		−	0.159308i
$320$	−153763.	+	127699.i	−1.50159	+	1.24706i
$321$	51481.6			0.499622
$322$	10238.5	−	17119.6i	0.0987470	−	0.165113i
$323$	−141889.	+	141889.i	−1.36001	+	1.36001i
$324$	5518.37	+	10276.0i	0.0525679	+	0.0978892i
$325$	−266966.	+	266966.i	−2.52749	+	2.52749i
$326$	−15101.1	−	60039.0i	−0.142093	−	0.564935i
$327$	83533.2			0.781203
$328$	1839.28	−	39808.9i	0.0170962	−	0.370026i
$329$		−	52815.6i		−	0.487944i
$330$	−15273.4	−	60724.4i	−0.140252	−	0.557616i
$331$	−56796.6	−	56796.6i	−0.518401	−	0.518401i	0.398686	−	0.917087i	$-0.369466\pi$
$331$	−56796.6	−	56796.6i	−0.518401	−	0.518401i	−0.917087	+	0.398686i	$0.869466\pi$
$332$	−94607.8	−	28498.1i	−0.858323	−	0.258547i
$333$	−20.7803	−	20.7803i	−0.000187398	−	0.000187398i
$334$	41501.2	−	69393.5i	0.372021	−	0.622051i
$335$		−	80734.8i		−	0.719401i
$336$	4157.02	+	20482.0i	0.0368217	+	0.181424i
$337$	143537.			1.26388			0.631938	−	0.775019i	$-0.282260\pi$
$337$	143537.			1.26388			0.631938	+	0.775019i	$0.282260\pi$
$338$	60605.8	+	36245.7i	0.530495	+	0.317265i
$339$	62022.2	−	62022.2i	0.539694	−	0.539694i
$340$	257132.	+	77454.5i	2.22433	+	0.670021i
$341$	−3691.48	+	3691.48i	−0.0317462	+	0.0317462i
$342$	61103.8	−	15368.9i	0.522416	−	0.131398i
$343$	71568.1			0.608319
$344$	−50184.3	−	55046.3i	−0.424083	−	0.465169i
$345$			80481.4i			0.676172i
$346$	−45252.0	+	11381.8i	−0.377994	+	0.0950734i
$347$	159730.	+	159730.i	1.32656	+	1.32656i	0.908352	+	0.418207i	$0.137341\pi$
$347$	159730.	+	159730.i	1.32656	+	1.32656i	0.418207	+	0.908352i	$0.362659\pi$
$348$	−10328.6	−	19233.4i	−0.0852872	−	0.158817i
$349$	−11297.7	−	11297.7i	−0.0927555	−	0.0927555i	0.659206	−	0.751962i	$-0.270892\pi$
$349$	−11297.7	−	11297.7i	−0.0927555	−	0.0927555i	−0.751962	+	0.659206i	$0.770892\pi$
$350$	94723.3	+	56649.8i	0.773252	+	0.462448i
$351$		−	30160.5i		−	0.244807i
$352$	−21007.9	+	59625.6i	−0.169550	+	0.481224i
$353$	−88880.4			−0.713274			−0.356637	−	0.934243i	$-0.616077\pi$
$353$	−88880.4			−0.713274			−0.356637	+	0.934243i	$0.616077\pi$
$354$	−42765.3	+	71507.3i	−0.341260	+	0.570616i
$355$	278903.	−	278903.i	2.21307	−	2.21307i
$356$	−22485.1	+	12074.8i	−0.177417	+	0.0952755i
$357$	19855.5	−	19855.5i	0.155792	−	0.155792i
$358$	48803.9	+	194035.i	0.380792	+	1.51396i
$359$	−5197.66			−0.0403291			−0.0201646	−	0.999797i	$-0.506419\pi$
$359$	−5197.66			−0.0403291			−0.0201646	+	0.999797i	$0.506419\pi$
$360$	−56809.5	−	62313.3i	−0.438345	−	0.480812i
$361$		−	210032.i		−	1.61165i
$362$	28781.5	+	114430.i	0.219632	+	0.873217i
$363$	39790.5	+	39790.5i	0.301971	+	0.301971i
$364$	15586.9	−	51745.2i	0.117641	−	0.390542i
$365$	100684.	+	100684.i	0.755744	+	0.755744i
$366$	7226.75	−	12083.7i	0.0539487	−	0.0902067i
$367$		−	228861.i		−	1.69918i	−0.527445	−	0.849589i	$-0.676850\pi$
$367$		−	228861.i		−	1.69918i	0.527445	−	0.849589i	$-0.323150\pi$
$368$	44880.2	−	67736.8i	0.331405	−	0.500183i
$369$	16812.3			0.123474
$370$	182.333	+	109.045i	0.00133187	+	0.000796533i
$371$	11391.3	−	11391.3i	0.0827613	−	0.0827613i
$372$	−2027.70	+	6731.54i	−0.0146527	+	0.0486439i
$373$	−59501.4	+	59501.4i	−0.427671	+	0.427671i	−0.887834	−	0.460163i	$-0.847791\pi$
$373$	−59501.4	+	59501.4i	−0.427671	+	0.427671i	0.460163	+	0.887834i	$0.347791\pi$
$374$	82372.1	−	20718.3i	0.588893	−	0.148119i
$375$	−286831.			−2.03968
$376$	9929.57	−	214913.i	0.0702352	−	1.52015i
$377$			56450.8i			0.397180i
$378$	−8550.71	+	2150.68i	−0.0598437	+	0.0150519i
$379$	−134649.	−	134649.i	−0.937401	−	0.937401i	0.0607521	−	0.998153i	$-0.480650\pi$
$379$	−134649.	−	134649.i	−0.937401	−	0.937401i	−0.998153	+	0.0607521i	$0.980650\pi$
$380$	−401293.	+	215500.i	−2.77904	+	1.49238i
$381$	−105163.	−	105163.i	−0.724456	−	0.724456i
$382$	−36191.6	−	21644.6i	−0.248017	−	0.148328i
$383$		−	111285.i		−	0.758642i	−0.925265	−	0.379321i	$-0.876158\pi$
$383$		−	111285.i		−	0.758642i	0.925265	−	0.379321i	$-0.123842\pi$
$384$	13064.7	+	84125.3i	0.0886005	+	0.570511i
$385$	47332.4			0.319328
$386$	120974.	−	202278.i	0.811925	−	1.35761i
$387$	22220.8	−	22220.8i	0.148367	−	0.148367i
$388$	−73695.1	−	137231.i	−0.489526	−	0.911569i
$389$	6847.33	−	6847.33i	0.0452504	−	0.0452504i	−0.684120	−	0.729370i	$-0.739813\pi$
$389$	6847.33	−	6847.33i	0.0452504	−	0.0452504i	0.729370	+	0.684120i	$0.239813\pi$
$390$	53184.8	+	211453.i	0.349670	+	1.39022i
$391$	−109172.			−0.714099
$392$	137719.	+	6362.99i	0.896232	+	0.0414085i
$393$		−	79857.8i		−	0.517050i
$394$	−59247.3	−	235556.i	−0.381660	−	1.51741i
$395$	185352.	+	185352.i	1.18796	+	1.18796i
$396$	−25536.8	−	7692.30i	−0.162846	−	0.0490530i
$397$	−18193.4	−	18193.4i	−0.115434	−	0.115434i	0.647030	−	0.762464i	$-0.276011\pi$
$397$	−18193.4	−	18193.4i	−0.115434	−	0.115434i	−0.762464	+	0.647030i	$0.776011\pi$
$398$	3778.12	−	6317.33i	0.0238511	−	0.0398811i
$399$			47628.1i			0.299170i
$400$	374790.	+	248323.i	2.34244	+	1.55202i
$401$	−192529.			−1.19731			−0.598655	−	0.801007i	$-0.704298\pi$
$401$	−192529.			−1.19731			−0.598655	+	0.801007i	$0.704298\pi$
$402$	−29512.5	−	17650.1i	−0.182623	−	0.109218i
$403$	12854.4	−	12854.4i	0.0791481	−	0.0791481i
$404$	103732.	+	31246.7i	0.635553	+	0.191444i
$405$	25154.3	−	25154.3i	0.153356	−	0.153356i
$406$	16004.2	−	4025.39i	0.0970916	−	0.0244206i
$407$	67.1964			0.000405656
$408$	84527.3	−	77061.5i	0.507782	−	0.462932i
$409$			139859.i			0.836071i	0.908431	+	0.418035i	$0.137281\pi$
$409$			139859.i			0.836071i	−0.908431	+	0.418035i	$0.862719\pi$
$410$	−117870.	+	29646.7i	−0.701188	+	0.176363i
$411$	−50195.8	−	50195.8i	−0.297155	−	0.297155i
$412$	27365.2	+	50958.1i	0.161215	+	0.300205i
$413$	−44535.6	−	44535.6i	−0.261100	−	0.261100i
$414$	29419.9	+	17594.7i	0.171649	+	0.102655i
$415$			301346.i			1.74972i
$416$	73153.2	−	207627.i	0.422714	−	1.19977i
$417$	37386.3			0.215001
$418$	−73945.5	+	123643.i	−0.423213	+	0.707649i
$419$	−168719.	+	168719.i	−0.961025	+	0.961025i	−0.999268	−	0.0382431i	$-0.987824\pi$
$419$	−168719.	+	168719.i	−0.961025	+	0.961025i	0.0382431	+	0.999268i	$0.487824\pi$
$420$	56155.9	−	30156.5i	0.318344	−	0.170955i
$421$	146291.	−	146291.i	0.825380	−	0.825380i	−0.161494	−	0.986874i	$-0.551631\pi$
$421$	146291.	−	146291.i	0.825380	−	0.825380i	0.986874	+	0.161494i	$0.0516311\pi$
$422$	−15146.1	−	60217.9i	−0.0850500	−	0.338143i
$423$	90763.0			0.507257
$424$	48494.3	−	44211.1i	0.269749	−	0.245923i
$425$		−	604053.i		−	3.34424i
$426$	−40979.2	−	162926.i	−0.225811	−	0.897782i
$427$	7525.90	+	7525.90i	0.0412765	+	0.0412765i
$428$	−45721.4	+	151785.i	−0.249593	+	0.828595i
$429$	48764.4	+	48764.4i	0.264965	+	0.264965i
$430$	−116604.	+	194972.i	−0.630633	+	1.05447i
$431$			191126.i			1.02888i	0.857527	+	0.514440i	$0.172000\pi$
$431$			191126.i			1.02888i	−0.857527	+	0.514440i	$0.828000\pi$
$432$	−35198.2	+	7143.80i	−0.188605	+	0.0382791i
$433$	164289.			0.876259			0.438130	−	0.898912i	$-0.355641\pi$
$433$	164289.			0.876259			0.438130	+	0.898912i	$0.355641\pi$
$434$	−4560.92	−	2727.68i	−0.0242143	−	0.0144815i
$435$	−47080.7	+	47080.7i	−0.248808	+	0.248808i
$436$	−74186.9	+	246285.i	−0.390260	+	1.29558i
$437$	130938.	−	130938.i	0.685648	−	0.685648i
$438$	58816.3	−	14793.5i	0.306584	−	0.0771123i
$439$	−288987.			−1.49951			−0.749754	−	0.661717i	$-0.769828\pi$
$439$	−288987.			−1.49951			−0.749754	+	0.661717i	$0.769828\pi$
$440$	192601.	+	8898.71i	0.994840	+	0.0459644i
$441$			58162.0i			0.299063i
$442$	−286834.	+	72144.6i	−1.46820	+	0.369283i
$443$	−206491.	−	206491.i	−1.05219	−	1.05219i	−0.998561	−	0.0536283i	$-0.982921\pi$
$443$	−206491.	−	206491.i	−1.05219	−	1.05219i	−0.0536283	−	0.998561i	$-0.517079\pi$
$444$	79.7228	−	42.8123i	0.000404405	−	0.000217171i
$445$	55040.5	+	55040.5i	0.277947	+	0.277947i
$446$	241652.	+	144522.i	1.21485	+	0.726546i
$447$		−	31476.6i		−	0.157533i
$448$	−64080.0	−	5934.02i	−0.319276	−	0.0295660i
$449$	46251.1			0.229419			0.114710	−	0.993399i	$-0.463406\pi$
$449$	46251.1			0.229419			0.114710	+	0.993399i	$0.463406\pi$
$450$	−97352.2	+	162781.i	−0.480751	+	0.803857i
$451$	−27182.6	+	27182.6i	−0.133640	+	0.133640i
$452$	127780.	+	237945.i	0.625441	+	1.16466i
$453$	−86877.5	+	86877.5i	−0.423361	+	0.423361i
$454$	−47584.5	−	189187.i	−0.230862	−	0.917867i
$455$	−164820.			−0.796134
$456$	−8954.31	+	193804.i	−0.0430628	+	0.932039i
$457$		−	53103.3i		−	0.254267i	−0.991886	−	0.127133i	$-0.959422\pi$
$457$		−	53103.3i		−	0.254267i	0.991886	−	0.127133i	$-0.0405776\pi$
$458$	−12046.2	−	47893.3i	−0.0574272	−	0.228320i
$459$	34121.5	+	34121.5i	0.161958	+	0.161958i
$460$	−237287.	−	71476.5i	−1.12139	−	0.337791i
$461$	−194088.	−	194088.i	−0.913267	−	0.913267i	0.0832610	−	0.996528i	$-0.473466\pi$
$461$	−194088.	−	194088.i	−0.913267	−	0.913267i	−0.996528	+	0.0832610i	$0.973466\pi$
$462$	10347.8	−	17302.3i	0.0484799	−	0.0810625i
$463$		−	51900.1i		−	0.242107i	−0.992646	−	0.121053i	$-0.961373\pi$
$463$		−	51900.1i		−	0.242107i	0.992646	−	0.121053i	$-0.0386272\pi$
$464$	65879.7	−	13370.9i	0.305996	−	0.0621047i
$465$	21441.4			0.0991625
$466$	133128.	+	79618.1i	0.613053	+	0.366640i
$467$	182584.	−	182584.i	0.837200	−	0.837200i	−0.151290	−	0.988489i	$-0.548343\pi$
$467$	182584.	−	182584.i	0.837200	−	0.837200i	0.988489	+	0.151290i	$0.0483426\pi$
$468$	88923.6	+	26785.9i	0.405999	+	0.122297i
$469$	18380.8	−	18380.8i	0.0835638	−	0.0835638i
$470$	−636332.	+	160051.i	−2.88064	+	0.724540i
$471$	−7881.50			−0.0355277
$472$	−172848.	−	189593.i	−0.775853	−	0.851019i
$473$			71854.3i			0.321167i
$474$	108277.	−	27233.8i	0.481924	−	0.121214i
$475$	724481.	+	724481.i	3.21100	+	3.21100i
$476$	40907.0	+	76174.9i	0.180544	+	0.336200i
$477$	19575.9	+	19575.9i	0.0860370	+	0.0860370i
$478$	272048.	+	162700.i	1.19067	+	0.712085i
$479$		−	258608.i		−	1.12712i	−0.826074	−	0.563561i	$-0.809431\pi$
$479$		−	258608.i		−	1.12712i	0.826074	−	0.563561i	$-0.190569\pi$
$480$	234174.	−	112153.i	1.01638	−	0.486774i
$481$	−233.990			−0.00101136
$482$	−98927.8	+	165416.i	−0.425818	+	0.712004i
$483$	−18323.1	+	18323.1i	−0.0785424	+	0.0785424i
$484$	−152654.	+	81977.6i	−0.651656	+	0.349949i
$485$	−335923.	+	335923.i	−1.42809	+	1.42809i
$486$	−3695.92	−	14694.3i	−0.0156477	−	0.0622123i
$487$	230546.			0.972074			0.486037	−	0.873938i	$-0.338442\pi$
$487$	230546.			0.972074			0.486037	+	0.873938i	$0.338442\pi$
$488$	29208.9	+	32038.7i	0.122652	+	0.134535i
$489$			80422.2i			0.336324i
$490$	−102562.	−	407769.i	−0.427166	−	1.69833i
$491$	43455.9	+	43455.9i	0.180254	+	0.180254i	0.791467	−	0.611212i	$-0.209318\pi$
$491$	43455.9	+	43455.9i	0.180254	+	0.180254i	−0.611212	+	0.791467i	$0.709318\pi$
$492$	−14931.2	+	49568.4i	−0.0616829	+	0.204774i
$493$	−63864.5	−	63864.5i	−0.262764	−	0.262764i
$494$	257491.	−	430547.i	1.05514	−	1.76428i
$495$			81340.3i			0.331967i
$496$	−18046.1	−	11956.7i	−0.0733533	−	0.0486014i
$497$	126995.			0.514129
$498$	110157.	+	65879.9i	0.444173	+	0.265641i
$499$	−333596.	+	333596.i	−1.33974	+	1.33974i	−0.443431	+	0.896308i	$0.646239\pi$
$499$	−333596.	+	333596.i	−1.33974	+	1.33974i	−0.896308	+	0.443431i	$0.853761\pi$
$500$	254738.	−	845676.i	1.01895	−	3.38270i
$501$	−74271.6	+	74271.6i	−0.295902	+	0.295902i
$502$	−161963.	+	40736.9i	−0.642698	+	0.161652i
$503$	−168598.			−0.666373			−0.333186	−	0.942861i	$-0.608124\pi$
$503$	−168598.			−0.666373			−0.333186	+	0.942861i	$0.608124\pi$
$504$	1253.04	−	27120.5i	0.00493293	−	0.106767i
$505$		−	330410.i		−	1.29560i
$506$	−76014.5	+	19119.2i	−0.296890	+	0.0746740i
$507$	−64866.2	−	64866.2i	−0.252350	−	0.252350i
$508$	403453.	−	216660.i	1.56338	−	0.839559i
$509$	119567.	+	119567.i	0.461506	+	0.461506i	0.899149	−	0.437643i	$-0.144187\pi$
$509$	119567.	+	119567.i	0.461506	+	0.461506i	−0.437643	+	0.899149i	$0.644187\pi$
$510$	−299393.	−	179054.i	−1.15107	−	0.688403i
$511$			45845.1i			0.175571i
$512$	−259633.	−	36193.6i	−0.990423	−	0.138067i
$513$	−81848.5			−0.311011
$514$	−80234.9	+	134159.i	−0.303695	+	0.507803i
$515$	124738.	−	124738.i	0.470311	−	0.470311i
$516$	45779.9	+	85249.0i	0.171940	+	0.320177i
$517$	−146748.	+	146748.i	−0.549025	+	0.549025i
$518$	16.6853	+	66.3377i	6.21834e−5	+	0.000247230i
$519$	60614.9			0.225032
$520$	−670670.	−	30986.9i	−2.48029	−	0.114596i
$521$			329505.i			1.21391i	0.794736	+	0.606955i	$0.207609\pi$
$521$			329505.i			1.21391i	−0.794736	+	0.606955i	$0.792391\pi$
$522$	6917.58	+	27503.0i	0.0253871	+	0.100935i
$523$	−73393.6	−	73393.6i	−0.268321	−	0.268321i	0.560102	−	0.828423i	$-0.310762\pi$
$523$	−73393.6	−	73393.6i	−0.268321	−	0.268321i	−0.828423	+	0.560102i	$0.810762\pi$
$524$	235448.	+	70922.7i	0.857498	+	0.258299i
$525$	−101382.	−	101382.i	−0.367826	−	0.367826i
$526$	94346.3	−	157755.i	0.340999	−	0.570179i
$527$			29085.1i			0.104725i
$528$	45359.1	−	68459.7i	0.162703	−	0.245565i
$529$	−179095.			−0.639988
$530$	−171765.	−	102725.i	−0.611482	−	0.365700i
$531$	76534.0	−	76534.0i	0.271435	−	0.271435i
$532$	−140424.	−	42299.1i	−0.496157	−	0.149454i
$533$	94654.5	−	94654.5i	0.333186	−	0.333186i
$534$	32152.9	−	8087.11i	0.112755	−	0.0283603i
$535$	483469.			1.68912
$536$	78249.1	−	71337.8i	0.272364	−	0.248308i
$537$		−	259910.i		−	0.901310i
$538$	13901.3	−	3496.47i	0.0480277	−	0.0120800i
$539$	−94038.0	−	94038.0i	−0.323688	−	0.323688i
$540$	51823.6	+	96503.3i	0.177722	+	0.330944i
$541$	287914.	+	287914.i	0.983714	+	0.983714i	0.999869	−	0.0161559i	$-0.00514281\pi$
$541$	287914.	+	287914.i	0.983714	+	0.983714i	−0.0161559	+	0.999869i	$0.505143\pi$
$542$	168479.	+	100760.i	0.573520	+	0.342997i
$543$		−	153279.i		−	0.519854i
$544$	152134.	+	317655.i	0.514078	+	1.07339i
$545$	784470.			2.64109
$546$	−36032.7	+	60249.7i	−0.120868	+	0.202101i
$547$	−92320.4	+	92320.4i	−0.308548	+	0.308548i	−0.844346	−	0.535798i	$-0.820011\pi$
$547$	−92320.4	+	92320.4i	−0.308548	+	0.308548i	0.535798	+	0.844346i	$0.320011\pi$
$548$	192574.	−	103415.i	0.641264	−	0.344368i
$549$	−12933.2	+	12933.2i	−0.0429102	+	0.0429102i
$550$	−105787.	−	420591.i	−0.349710	−	1.39038i
$551$	153194.			0.504590
$552$	−78003.5	+	71113.9i	−0.255998	+	0.233387i
$553$			84397.6i			0.275981i
$554$	−96655.1	−	384283.i	−0.314924	−	1.25208i
$555$	−195.150	−	195.150i	−0.000633554	−	0.000633554i
$556$	−33203.2	+	110228.i	−0.107407	+	0.356567i
$557$	−232942.	−	232942.i	−0.750821	−	0.750821i	0.223811	−	0.974633i	$-0.428150\pi$
$557$	−232942.	−	232942.i	−0.750821	−	0.750821i	−0.974633	+	0.223811i	$0.928150\pi$
$558$	4687.49	−	7837.89i	0.0150547	−	0.0251727i
$559$		−	250209.i		−	0.800718i
$560$	39039.1	+	192349.i	0.124487	+	0.613359i
$561$	−110337.			−0.350587
$562$	39576.4	+	23668.9i	0.125304	+	0.0749386i
$563$	−198765.	+	198765.i	−0.627081	+	0.627081i	−0.947333	−	0.320251i	$-0.896233\pi$
$563$	−198765.	+	198765.i	−0.627081	+	0.627081i	0.320251	+	0.947333i	$0.396233\pi$
$564$	−80607.8	+	267601.i	−0.253407	+	0.841258i
$565$	582458.	−	582458.i	1.82460	−	1.82460i
$566$	−9831.78	+	2472.90i	−0.0306902	+	0.00771921i
$567$	11453.7			0.0356269
$568$	516756.	+	23875.6i	1.60173	+	0.0740043i
$569$			398647.i			1.23130i	0.788020	+	0.615650i	$0.211106\pi$
$569$			398647.i			1.23130i	−0.788020	+	0.615650i	$0.788894\pi$
$570$	573833.	−	144331.i	1.76618	−	0.444232i
$571$	−260127.	−	260127.i	−0.797837	−	0.797837i	0.184917	−	0.982754i	$-0.440798\pi$
$571$	−260127.	−	260127.i	−0.797837	−	0.797837i	−0.982754	+	0.184917i	$0.940798\pi$
$572$	−187082.	+	100466.i	−0.571796	+	0.307063i
$573$	38735.8	+	38735.8i	0.117979	+	0.117979i
$574$	−33584.8	−	20085.6i	−0.101934	−	0.0609622i
$575$			557432.i			1.68599i
$576$	10197.6	−	110121.i	0.0307363	−	0.331913i
$577$	21582.1			0.0648250			0.0324125	−	0.999475i	$-0.489681\pi$
$577$	21582.1			0.0648250			0.0324125	+	0.999475i	$0.489681\pi$
$578$	71409.6	−	119403.i	0.213748	−	0.357404i
$579$	−216498.	+	216498.i	−0.645797	+	0.645797i
$580$	−96997.3	−	180623.i	−0.288339	−	0.536930i
$581$	−68607.0	+	68607.0i	−0.203243	+	0.203243i
$582$	49357.3	+	196235.i	0.145715	+	0.579337i
$583$	−63301.8			−0.186242
$584$	−8619.10	+	186549.i	−0.0252718	+	0.546975i
$585$		−	283241.i		−	0.827645i
$586$	109718.	+	436217.i	0.319508	+	1.27030i
$587$	−144875.	−	144875.i	−0.420453	−	0.420453i	0.464907	−	0.885360i	$-0.346088\pi$
$587$	−144875.	−	144875.i	−0.420453	−	0.420453i	−0.885360	+	0.464907i	$0.846088\pi$
$588$	−171482.	−	51654.4i	−0.495979	−	0.149401i
$589$	−34883.7	−	34883.7i	−0.100552	−	0.100552i
$590$	−401614.	+	671533.i	−1.15373	+	1.92914i
$591$			315527.i			0.903362i
$592$	55.4226	+	273.073i	0.000158141	+	0.000779174i
$593$	−646586.			−1.83873			−0.919363	−	0.393411i	$-0.871295\pi$
$593$	−646586.			−1.83873			−0.919363	+	0.393411i	$0.871295\pi$
$594$	29733.8	+	17782.5i	0.0842710	+	0.0503988i
$595$	186466.	−	186466.i	0.526702	−	0.526702i
$596$	92803.9	+	27954.8i	0.261260	+	0.0786979i
$597$	−6761.42	+	6761.42i	−0.0189709	+	0.0189709i
$598$	264696.	−	66576.5i	0.740193	−	0.186174i
$599$	−352563.			−0.982615			−0.491308	−	0.870986i	$-0.663481\pi$
$599$	−352563.			−0.982615			−0.491308	+	0.870986i	$0.663481\pi$
$600$	−393475.	−	431596.i	−1.09299	−	1.19888i
$601$			316097.i			0.875129i	0.899187	+	0.437564i	$0.144159\pi$
$601$			316097.i			0.875129i	−0.899187	+	0.437564i	$0.855841\pi$
$602$	−70936.0	+	17841.9i	−0.195737	+	0.0492320i
$603$	31587.2	+	31587.2i	0.0868712	+	0.0868712i
$604$	−178988.	−	333302.i	−0.490625	−	0.913616i
$605$	373677.	+	373677.i	1.02091	+	1.02091i
$606$	−120781.	−	72233.8i	−0.328892	−	0.196696i
$607$		−	147576.i		−	0.400532i	−0.979742	−	0.200266i	$-0.935819\pi$
$607$		−	147576.i		−	0.400532i	0.979742	−	0.200266i	$-0.0641807\pi$
$608$	−563450.	−	198520.i	−1.52422	−	0.537030i
$609$	−21437.6			−0.0578018
$610$	67867.2	−	113480.i	0.182390	−	0.304971i
$611$	511003.	−	511003.i	1.36880	−	1.36880i
$612$	−130906.	+	70298.2i	−0.349507	+	0.187690i
$613$	26844.4	−	26844.4i	0.0714385	−	0.0714385i	−0.670485	−	0.741923i	$-0.733914\pi$
$613$	26844.4	−	26844.4i	0.0714385	−	0.0714385i	0.741923	+	0.670485i	$0.233914\pi$
$614$	132115.	+	525266.i	0.350442	+	1.39329i
$615$	157886.			0.417440
$616$	41823.2	+	45875.1i	0.110219	+	0.120897i
$617$			243032.i			0.638402i	0.947687	+	0.319201i	$0.103414\pi$
$617$			243032.i			0.638402i	−0.947687	+	0.319201i	$0.896586\pi$
$618$	−18327.8	−	72868.1i	−0.0479881	−	0.190792i
$619$	−254198.	−	254198.i	−0.663423	−	0.663423i	0.292762	−	0.956185i	$-0.405425\pi$
$619$	−254198.	−	254198.i	−0.663423	−	0.663423i	−0.956185	+	0.292762i	$0.905425\pi$
$620$	−19042.4	+	63216.7i	−0.0495380	+	0.164456i
$621$	−31488.0	−	31488.0i	−0.0816511	−	0.0816511i
$622$	233330.	−	390148.i	0.603101	−	1.00844i
$623$			25061.9i			0.0645712i
$624$	−157948.	+	238389.i	−0.405645	+	0.612232i
$625$	−1.59603e6			−4.08583
$626$	596574.	+	356785.i	1.52235	+	0.910453i
$627$	132335.	−	132335.i	0.336620	−	0.336620i
$628$	6999.66	−	23237.4i	0.0177483	−	0.0589207i
$629$	264.720	−	264.720i	0.000669091	−	0.000669091i
$630$	−80300.7	+	20197.3i	−0.202320	+	0.0508876i
$631$	217913.			0.547299			0.273650	−	0.961829i	$-0.411769\pi$
$631$	217913.			0.547299			0.273650	+	0.961829i	$0.411769\pi$
$632$	−15867.1	+	343424.i	−0.0397251	+	0.859797i
$633$			80661.8i			0.201308i
$634$	90889.2	−	22860.5i	0.226117	−	0.0568732i
$635$	−987596.	−	987596.i	−2.44924	−	2.44924i
$636$	−75102.1	+	40330.9i	−0.185668	+	0.0997066i
$637$	327457.	+	327457.i	0.807003	+	0.807003i
$638$	−55652.2	−	33283.1i	−0.136723	−	0.0817679i
$639$			218239.i			0.534479i
$640$	122692.	+	790031.i	0.299541	+	1.92879i
$641$	492918.			1.19966			0.599831	−	0.800127i	$-0.295235\pi$
$641$	492918.			1.19966			0.599831	+	0.800127i	$0.295235\pi$
$642$	105695.	−	176732.i	0.256440	−	0.428790i
$643$	26994.7	−	26994.7i	0.0652915	−	0.0652915i	−0.673707	−	0.738999i	$-0.735299\pi$
$643$	26994.7	−	26994.7i	0.0652915	−	0.0652915i	0.738999	+	0.673707i	$0.235299\pi$
$644$	−37749.8	−	70295.7i	−0.0910212	−	0.169495i
$645$	208678.	−	208678.i	0.501599	−	0.501599i
$646$	195783.	+	778399.i	0.469149	+	1.86525i
$647$	221137.			0.528266			0.264133	−	0.964486i	$-0.414914\pi$
$647$	221137.			0.528266			0.264133	+	0.964486i	$0.414914\pi$
$648$	46606.3	+	2153.34i	0.110993	+	0.00512818i
$649$			247485.i			0.587569i
$650$	368370.	+	1.46457e6i	0.871881	+	3.46644i
$651$	4881.53	+	4881.53i	0.0115185	+	0.0115185i
$652$	−237112.	−	71423.9i	−0.557775	−	0.168015i
$653$	−236639.	−	236639.i	−0.554958	−	0.554958i	0.372910	−	0.927868i	$-0.378360\pi$
$653$	−236639.	−	236639.i	−0.554958	−	0.554958i	−0.927868	+	0.372910i	$0.878360\pi$
$654$	171500.	−	286762.i	0.400967	−	0.670450i
$655$		−	749954.i		−	1.74804i
$656$	−132884.	−	88044.7i	−0.308792	−	0.204595i
$657$	−78784.4			−0.182520
$658$	−181311.	−	108434.i	−0.418768	−	0.250446i
$659$	42027.1	−	42027.1i	0.0967739	−	0.0967739i	−0.657062	−	0.753836i	$-0.728201\pi$
$659$	42027.1	−	42027.1i	0.0967739	−	0.0967739i	0.753836	+	0.657062i	$0.228201\pi$
$660$	−239819.	−	72239.3i	−0.550549	−	0.165839i
$661$	−229009.	+	229009.i	−0.524142	+	0.524142i	−0.918820	−	0.394677i	$-0.870856\pi$
$661$	−229009.	+	229009.i	−0.524142	+	0.524142i	0.394677	+	0.918820i	$0.370856\pi$
$662$	−311585.	+	78370.1i	−0.710986	+	0.178828i
$663$	384213.			0.874069
$664$	−292068.	+	266271.i	−0.662443	+	0.603933i
$665$			447282.i			1.01143i
$666$	−114.001	+	28.6735i	−0.000257015	+	6.46446e-5i
$667$	58935.5	+	58935.5i	0.132472	+	0.132472i
$668$	−153017.	−	284940.i	−0.342915	−	0.638558i
$669$	−258640.	−	258640.i	−0.577887	−	0.577887i
$670$	−277156.	−	165755.i	−0.617411	−	0.369246i
$671$		−	41821.5i		−	0.0928868i
$672$	78847.7	+	27780.5i	0.174603	+	0.0615178i
$673$	−10148.5			−0.0224064			−0.0112032	−	0.999937i	$-0.503566\pi$
$673$	−10148.5			−0.0224064			−0.0112032	+	0.999937i	$0.503566\pi$
$674$	294692.	−	492750.i	0.648707	−	1.08469i
$675$	174224.	−	174224.i	0.382385	−	0.382385i
$676$	248856.	−	133639.i	0.544572	−	0.292443i
$677$	402798.	−	402798.i	0.878840	−	0.878840i	−0.114575	−	0.993415i	$-0.536551\pi$
$677$	402798.	−	402798.i	0.878840	−	0.878840i	0.993415	+	0.114575i	$0.0365506\pi$
$678$	−85580.6	−	340253.i	−0.186173	−	0.740189i
$679$	−152958.			−0.331767
$680$	793806.	−	723694.i	1.71671	−	1.56508i
$681$			253416.i			0.546436i
$682$	5093.64	+	20251.4i	0.0109512	+	0.0435398i
$683$	201244.	+	201244.i	0.431402	+	0.431402i	0.889105	−	0.457703i	$-0.151328\pi$
$683$	201244.	+	201244.i	0.431402	+	0.431402i	−0.457703	+	0.889105i	$0.651328\pi$
$684$	72690.6	−	241317.i	0.155370	−	0.515794i
$685$	−471395.	−	471395.i	−1.00462	−	1.00462i
$686$	146935.	−	245687.i	0.312231	−	0.522076i
$687$			64153.1i			0.135926i
$688$	−292001.	+	59264.4i	−0.616890	+	0.125204i
$689$	220428.			0.464331
$690$	276286.	+	165234.i	0.580310	+	0.347058i
$691$	−253602.	+	253602.i	−0.531125	+	0.531125i	−0.920907	−	0.389782i	$-0.872550\pi$
$691$	−253602.	+	253602.i	−0.531125	+	0.531125i	0.389782	+	0.920907i	$0.372550\pi$
$692$	−53832.9	+	178714.i	−0.112418	+	0.373204i
$693$	−18518.6	+	18518.6i	−0.0385604	+	0.0385604i
$694$	876274.	−	220401.i	1.81937	−	0.457609i
$695$	351099.			0.726876
$696$	−87232.0	−	4030.37i	−0.180077	−	0.00832005i
$697$			214171.i			0.440854i
$698$	−61979.1	+	15589.0i	−0.127214	+	0.0319969i
$699$	−142487.	−	142487.i	−0.291622	−	0.291622i
$700$	388948.	−	208871.i	0.793771	−	0.426267i
$701$	387207.	+	387207.i	0.787965	+	0.787965i	0.981160	−	0.193195i	$-0.0618851\pi$
$701$	387207.	+	387207.i	0.787965	+	0.787965i	−0.193195	+	0.981160i	$0.561885\pi$
$702$	−103538.	−	61921.8i	−0.210101	−	0.125652i
$703$			634.992i			0.00128487i
$704$	161559.	+	194534.i	0.325976	+	0.392510i
$705$	852366.			1.71494
$706$	−182478.	+	305119.i	−0.366101	+	0.612152i
$707$	75223.9	−	75223.9i	0.150493	−	0.150493i
$708$	157678.	+	293619.i	0.314560	+	0.585758i
$709$	394716.	−	394716.i	0.785222	−	0.785222i	−0.195484	−	0.980707i	$-0.562628\pi$
$709$	394716.	−	394716.i	0.785222	−	0.785222i	0.980707	+	0.195484i	$0.0626279\pi$
$710$	−384841.	−	1.53006e6i	−0.763421	−	3.03522i
$711$	−145036.			−0.286905
$712$	−4711.76	+	101980.i	−0.00929444	+	0.201166i
$713$		−	26840.3i		−	0.0527968i
$714$	−27397.4	−	108927.i	−0.0537419	−	0.213668i
$715$	457952.	+	457952.i	0.895793	+	0.895793i
$716$	766304.	+	230829.i	1.49477	+	0.450261i
$717$	−291172.	−	291172.i	−0.566385	−	0.566385i
$718$	−10671.2	+	17843.1i	−0.0206997	+	0.0346116i
$719$		−	138708.i		−	0.268314i	−0.990960	−	0.134157i	$-0.957167\pi$
$719$		−	138708.i		−	0.268314i	0.990960	−	0.134157i	$-0.0428326\pi$
$720$	−330550.	+	67088.2i	−0.637635	+	0.129414i
$721$	56797.9			0.109260
$722$	−721022.	−	431211.i	−1.38317	−	0.827210i
$723$	177044.	−	177044.i	0.338691	−	0.338691i
$724$	451918.	+	136129.i	0.862149	+	0.259700i
$725$	−326092.	+	326092.i	−0.620388	+	0.620388i
$726$	218290.	−	54904.4i	0.414153	−	0.104168i
$727$	−937838.			−1.77443			−0.887216	−	0.461355i	$-0.847364\pi$
$727$	−937838.			−1.77443			−0.887216	+	0.461355i	$0.847364\pi$
$728$	−145636.	−	159745.i	−0.274793	−	0.301415i
$729$			19683.0i			0.0370370i
$730$	552351.	−	138928.i	1.03650	−	0.260701i
$731$	283069.	+	283069.i	0.529734	+	0.529734i
$732$	−26645.4	−	49617.6i	−0.0497278	−	0.0926005i
$733$	−267776.	−	267776.i	−0.498384	−	0.498384i	0.412550	−	0.910935i	$-0.364638\pi$
$733$	−267776.	−	267776.i	−0.498384	−	0.498384i	−0.910935	+	0.412550i	$0.864638\pi$
$734$	−785658.	−	469868.i	−1.45828	−	0.872134i
$735$			546207.i			1.01107i
$736$	−140392.	−	293138.i	−0.259172	−	0.541149i
$737$	−102142.			−0.188048
$738$	34516.9	−	57715.1i	0.0633751	−	0.105969i
$739$	−297244.	+	297244.i	−0.544283	+	0.544283i	−0.924781	−	0.380499i	$-0.875752\pi$
$739$	−297244.	+	297244.i	−0.544283	+	0.544283i	0.380499	+	0.924781i	$0.375752\pi$
$740$	748.687	−	402.055i	0.00136721	−	0.000734214i
$741$	−460813.	+	460813.i	−0.839244	+	0.839244i
$742$	−15718.2	−	62492.8i	−0.0285493	−	0.113507i
$743$	445982.			0.807867			0.403933	−	0.914788i	$-0.367643\pi$
$743$	445982.			0.807867			0.403933	+	0.914788i	$0.367643\pi$
$744$	18945.8	+	20781.3i	0.0342268	+	0.0375428i
$745$		−	295601.i		−	0.532590i
$746$	82102.4	+	326424.i	0.147529	+	0.586549i
$747$	−117900.	−	117900.i	−0.211288	−	0.211288i
$748$	97991.9	−	325312.i	0.175141	−	0.581430i
$749$	110071.	+	110071.i	0.196204	+	0.196204i
$750$	−588884.	+	984665.i	−1.04691	+	1.75051i
$751$			207177.i			0.367335i	0.982988	+	0.183668i	$0.0587970\pi$
$751$			207177.i			0.367335i	−0.982988	+	0.183668i	$0.941203\pi$
$752$	−717390.	−	475319.i	−1.26859	−	0.840523i
$753$	216949.			0.382619
$754$	193791.	+	115898.i	0.340871	+	0.203860i
$755$	−815877.	+	815877.i	−1.43130	+	1.43130i
$756$	−10172.1	+	33769.4i	−0.0177979	+	0.0590853i
$757$	589789.	−	589789.i	1.02921	−	1.02921i	0.0296522	−	0.999560i	$-0.490560\pi$
$757$	589789.	−	589789.i	1.02921	−	1.02921i	0.999560	−	0.0296522i	$-0.00943997\pi$
$758$	−738684.	+	185794.i	−1.28564	+	0.323366i
$759$	101821.			0.176748
$760$	−84091.0	+	1.82004e6i	−0.145587	+	3.15104i
$761$		−	307955.i		−	0.531763i	−0.964006	−	0.265882i	$-0.914337\pi$
$761$		−	307955.i		−	0.531763i	0.964006	−	0.265882i	$-0.0856630\pi$
$762$	−576922.	+	145108.i	−0.993589	+	0.249908i
$763$	178599.	+	178599.i	0.306782	+	0.306782i
$764$	−148608.	+	79804.7i	−0.254599	+	0.136723i
$765$	320439.	+	320439.i	0.547549	+	0.547549i
$766$	−382030.	−	228475.i	−0.651088	−	0.389387i
$767$		−	861784.i		−	1.46490i
$768$	315618.	+	127866.i	0.535105	+	0.216786i
$769$	202037.			0.341647			0.170824	−	0.985302i	$-0.445357\pi$
$769$	202037.			0.341647			0.170824	+	0.985302i	$0.445357\pi$
$770$	97176.9	−	162488.i	0.163901	−	0.274056i
$771$	143590.	−	143590.i	0.241555	−	0.241555i
$772$	−446035.	−	830584.i	−0.748402	−	1.39363i
$773$	−210523.	+	210523.i	−0.352323	+	0.352323i	−0.860973	−	0.508650i	$-0.830145\pi$
$773$	−210523.	+	210523.i	−0.352323	+	0.352323i	0.508650	+	0.860973i	$0.330145\pi$
$774$	−30661.1	−	121903.i	−0.0511806	−	0.203485i
$775$	148508.			0.247256
$776$	−622404.	−	28756.8i	−1.03359	−	0.0477549i
$777$		−	88.8592i		−	0.000147184i
$778$	−9448.21	−	37564.4i	−0.0156096	−	0.0620607i
$779$	−256870.	−	256870.i	−0.423290	−	0.423290i
$780$	835092.	+	251550.i	1.37260	+	0.413461i
$781$	−352855.	−	352855.i	−0.578487	−	0.578487i
$782$	−224138.	+	374779.i	−0.366524	+	0.612860i
$783$		−	36840.3i		−	0.0600896i
$784$	304590.	−	459712.i	0.495546	−	0.747918i
$785$	−74016.1			−0.120112
$786$	−274145.	−	163954.i	−0.443747	−	0.265385i
$787$	192330.	−	192330.i	0.310526	−	0.310526i	−0.534587	−	0.845113i	$-0.679533\pi$
$787$	192330.	−	192330.i	0.310526	−	0.310526i	0.845113	+	0.534587i	$0.179533\pi$
$788$	−930283.	−	280224.i	−1.49818	−	0.451287i
$789$	−168845.	+	168845.i	−0.271227	+	0.271227i
$790$	1.01684e6	−	255756.i	1.62929	−	0.409800i
$791$	265214.			0.423881
$792$	−78835.9	+	71872.8i	−0.125682	+	0.114581i
$793$			145630.i			0.231581i
$794$	−99808.8	+	25104.0i	−0.158317	+	0.0398200i
$795$	183840.	+	183840.i	0.290874	+	0.290874i
$796$	−13930.1	−	25939.9i	−0.0219851	−	0.0409394i
$797$	571951.	+	571951.i	0.900415	+	0.900415i	0.995472	−	0.0950572i	$-0.0303034\pi$
$797$	571951.	+	571951.i	0.900415	+	0.900415i	−0.0950572	+	0.995472i	$0.530303\pi$
$798$	163503.	+	97784.1i	0.256756	+	0.153554i
$799$			1.15623e6i			1.81113i
$800$	1.62194e6	−	776795.i	2.53429	−	1.21374i
$801$	−43068.7			−0.0671269
$802$	−395276.	+	660934.i	−0.614541	+	1.02757i
$803$	127381.	−	127381.i	0.197548	−	0.197548i
$804$	−121183.	+	65076.9i	−0.187469	+	0.100673i
$805$	−172074.	+	172074.i	−0.265536	+	0.265536i
$806$	−17737.0	−	70518.9i	−0.0273029	−	0.108551i
$807$	−18620.8			−0.0285924
$808$	320237.	−	291952.i	0.490512	−	0.447187i
$809$		−	472462.i		−	0.721888i	−0.932588	−	0.360944i	$-0.882455\pi$
$809$		−	472462.i		−	0.721888i	0.932588	−	0.360944i	$-0.117545\pi$
$810$	−34708.8	−	137996.i	−0.0529018	−	0.210328i
$811$	446564.	+	446564.i	0.678957	+	0.678957i	0.959764	−	0.280807i	$-0.0906021\pi$
$811$	446564.	+	446564.i	0.678957	+	0.678957i	−0.280807	+	0.959764i	$0.590602\pi$
$812$	19039.0	−	63205.4i	0.0288757	−	0.0958611i
$813$	−180323.	−	180323.i	−0.272816	−	0.272816i
$814$	137.959	−	230.679i	0.000208210	−	0.000348145i
$815$			755254.i			1.13705i
$816$	−91004.5	−	448388.i	−0.136673	−	0.673401i
$817$	−679008.			−1.01726
$818$	480123.	+	287140.i	0.717539	+	0.429129i
$819$	64485.0	−	64485.0i	0.0961371	−	0.0961371i
$820$	−140221.	+	465503.i	−0.208538	+	0.692301i
$821$	212424.	−	212424.i	0.315150	−	0.315150i	−0.531751	−	0.846901i	$-0.678466\pi$
$821$	212424.	−	212424.i	0.315150	−	0.315150i	0.846901	+	0.531751i	$0.178466\pi$
$822$	−275373.	+	69262.1i	−0.407548	+	0.102507i
$823$	532734.			0.786522			0.393261	−	0.919427i	$-0.371347\pi$
$823$	532734.			0.786522			0.393261	+	0.919427i	$0.371347\pi$
$824$	231117.	+	10678.3i	0.340391	+	0.0157270i
$825$			563380.i			0.827740i
$826$	−244322.	+	61452.0i	−0.358098	+	0.0900691i
$827$	499565.	+	499565.i	0.730435	+	0.730435i	0.970706	−	0.240271i	$-0.0772363\pi$
$827$	499565.	+	499565.i	0.730435	+	0.730435i	−0.240271	+	0.970706i	$0.577236\pi$
$828$	120802.	−	64872.6i	0.176204	−	0.0946238i
$829$	827901.	+	827901.i	1.20467	+	1.20467i	0.972729	+	0.231945i	$0.0745090\pi$
$829$	827901.	+	827901.i	1.20467	+	1.20467i	0.231945	+	0.972729i	$0.425491\pi$
$830$	1.03450e6	+	618686.i	1.50166	+	0.898078i
$831$			514746.i			0.745403i
$832$	−562576.	−	677402.i	−0.812708	−	0.978588i
$833$	−740924.			−1.06778
$834$	76756.8	−	128344.i	0.110353	−	0.184520i
$835$	−697494.	+	697494.i	−1.00039	+	1.00039i
$836$	272641.	+	507697.i	0.390102	+	0.726427i
$837$	−8388.86	+	8388.86i	−0.0119744	+	0.0119744i
$838$	232804.	+	925588.i	0.331515	+	1.31804i
$839$	−924441.			−1.31327			−0.656637	−	0.754207i	$-0.728022\pi$
$839$	−924441.			−1.31327			−0.656637	+	0.754207i	$0.728022\pi$
$840$	11767.5	−	254692.i	0.0166773	−	0.360958i
$841$		−	638328.i		−	0.902509i
$842$	−201858.	−	802552.i	−0.284723	−	1.13201i
$843$	−42358.5	−	42358.5i	−0.0596054	−	0.0596054i
$844$	−237819.	−	71636.7i	−0.333858	−	0.100566i
$845$	−609166.	−	609166.i	−0.853144	−	0.853144i
$846$	186343.	−	311582.i	0.260359	−	0.435342i
$847$			170149.i			0.237171i
$848$	−52210.3	−	257245.i	−0.0726047	−	0.357730i
$849$	13169.6			0.0182709
$850$	−2.07366e6	−	1.24016e6i	−2.87012	−	1.71649i
$851$	−244.288	+	244.288i	−0.000337321	+	0.000337321i
$852$	−643443.	−	193821.i	−0.886403	−	0.267006i
$853$	−65994.6	+	65994.6i	−0.0907007	+	0.0907007i	−0.751001	−	0.660301i	$-0.770429\pi$
$853$	−65994.6	+	65994.6i	−0.0907007	+	0.0907007i	0.660301	+	0.751001i	$0.270429\pi$
$854$	41287.0	−	10384.5i	0.0566106	−	0.0142387i
$855$	−768649.			−1.05147
$856$	427197.	+	468584.i	0.583016	+	0.639499i
$857$		−	969269.i		−	1.31972i	−0.751387	−	0.659861i	$-0.770615\pi$
$857$		−	969269.i		−	1.31972i	0.751387	−	0.659861i	$-0.229385\pi$
$858$	267521.	−	67287.0i	0.363398	−	0.0914022i
$859$	−427483.	−	427483.i	−0.579338	−	0.579338i	0.355383	−	0.934721i	$-0.384351\pi$
$859$	−427483.	−	427483.i	−0.579338	−	0.579338i	−0.934721	+	0.355383i	$0.884351\pi$
$860$	429925.	+	800583.i	0.581294	+	1.08245i
$861$	35945.7	+	35945.7i	0.0484887	+	0.0484887i
$862$	656118.	+	392395.i	0.883013	+	0.528091i
$863$			231279.i			0.310538i	0.987872	+	0.155269i	$0.0496244\pi$
$863$			231279.i			0.310538i	−0.987872	+	0.155269i	$0.950376\pi$
$864$	−47740.4	+	135499.i	−0.0639527	+	0.181513i
$865$	569242.			0.760790
$866$	337297.	−	563990.i	0.449756	−	0.752030i
$867$	−127797.	+	127797.i	−0.170013	+	0.170013i
$868$	−18727.8	+	10057.1i	−0.0248569	+	0.0133485i
$869$	234499.	−	234499.i	0.310528	−	0.310528i
$870$	64963.8	+	258284.i	0.0858288	+	0.341240i
$871$	355676.			0.468833
$872$	693163.	+	760318.i	0.911596	+	0.999913i
$873$		−	262857.i		−	0.344898i
$874$	−180673.	−	718322.i	−0.236521	−	0.940364i
$875$	−613261.	−	613261.i	−0.800994	−	0.800994i
$876$	69969.4	−	232284.i	0.0911801	−	0.302699i
$877$	633395.	+	633395.i	0.823522	+	0.823522i	0.986611	−	0.163089i	$-0.0521458\pi$
$877$	633395.	+	633395.i	0.823522	+	0.823522i	−0.163089	+	0.986611i	$0.552146\pi$
$878$	−593311.	+	992066.i	−0.769650	+	1.28692i
$879$		−	584312.i		−	0.756254i
$880$	425973.	−	642913.i	0.550068	−	0.830208i
$881$	566139.			0.729410			0.364705	−	0.931123i	$-0.381170\pi$
$881$	566139.			0.729410			0.364705	+	0.931123i	$0.381170\pi$
$882$	199665.	+	119411.i	0.256664	+	0.153499i
$883$	260579.	−	260579.i	0.334209	−	0.334209i	−0.519974	−	0.854182i	$-0.674058\pi$
$883$	260579.	−	260579.i	0.334209	−	0.334209i	0.854182	+	0.519974i	$0.174058\pi$
$884$	−341225.	+	1.13279e6i	−0.436652	+	1.44959i
$885$	718740.	−	718740.i	0.917667	−	0.917667i
$886$	−1.13281e6	+	284924.i	−1.44307	+	0.362963i
$887$	486021.			0.617742			0.308871	−	0.951104i	$-0.400049\pi$
$887$	486021.			0.617742			0.308871	+	0.951104i	$0.400049\pi$
$888$	16.7059	−	361.578i	2.11858e−5	−	0.000458539i
$889$		−	449689.i		−	0.568995i
$890$	301951.	−	75947.0i	0.381203	−	0.0958805i
$891$	−31824.0	−	31824.0i	−0.0400866	−	0.0400866i
$892$	992261.	−	532858.i	1.24708	−	0.669703i
$893$	−1.38674e6	−	1.38674e6i	−1.73897	−	1.73897i
$894$	−108056.	−	64623.8i	−0.135200	−	0.0808570i
$895$		−	2.44084e6i		−	3.04715i
$896$	−151932.	+	207798.i	−0.189249	+	0.258837i
$897$	−354560.			−0.440661
$898$	94956.9	−	158776.i	0.117754	−	0.196894i
$899$	15701.3	−	15701.3i	0.0194274	−	0.0194274i
$900$	358942.	+	668403.i	0.443138	+	0.825189i
$901$	−249377.	+	249377.i	−0.307189	+	0.307189i
$902$	37507.6	+	149123.i	0.0461006	+	0.183287i
$903$	95018.7			0.116529
$904$	1.07919e6	+	49861.5i	1.32057	+	0.0610139i
$905$		−	1.43946e6i		−	1.75752i
$906$	119877.	+	476609.i	0.146042	+	0.580638i
$907$	−74724.1	−	74724.1i	−0.0908335	−	0.0908335i	0.660230	−	0.751063i	$-0.270459\pi$
$907$	−74724.1	−	74724.1i	−0.0908335	−	0.0908335i	−0.751063	+	0.660230i	$0.770459\pi$
$908$	−747157.	−	225062.i	−0.906234	−	0.272979i
$909$	129272.	+	129272.i	0.156450	+	0.156450i
$910$	−338387.	+	565812.i	−0.408631	+	0.683265i
$911$			1.13845e6i			1.37176i	0.727713	+	0.685881i	$0.240583\pi$
$911$			1.13845e6i			1.37176i	−0.727713	+	0.685881i	$0.759417\pi$
$912$	646930.	+	428634.i	0.777799	+	0.515344i
$913$	381249.			0.457370
$914$	−182299.	−	109025.i	−0.218219	−	0.130507i
$915$	−121457.	+	121457.i	−0.145071	+	0.145071i
$916$	−189145.	−	56975.1i	−0.225426	−	0.0679038i
$917$	170741.	−	170741.i	0.203048	−	0.203048i
$918$	187190.	−	47082.2i	0.222125	−	0.0558690i
$919$	−1.24460e6			−1.47366			−0.736831	−	0.676077i	$-0.763679\pi$
$919$	−1.24460e6			−1.47366			−0.736831	+	0.676077i	$0.763679\pi$
$920$	−732540.	+	667839.i	−0.865477	+	0.789034i
$921$		−	703593.i		−	0.829473i
$922$	−1.06477e6	+	267811.i	−1.25254	+	0.315040i
$923$	1.22870e6	+	1.22870e6i	1.44226	+	1.44226i
$924$	−38152.6	−	71045.8i	−0.0446869	−	0.0832137i
$925$	−1351.66	−	1351.66i	−0.00157973	−	0.00157973i
$926$	−178169.	−	106555.i	−0.207783	−	0.124266i
$927$			97606.6i			0.113585i
$928$	89354.8	−	253611.i	0.103758	−	0.294491i
$929$	674064.			0.781033			0.390517	−	0.920596i	$-0.372296\pi$
$929$	674064.			0.781033			0.390517	+	0.920596i	$0.372296\pi$
$930$	44020.8	−	73606.5i	0.0508970	−	0.0851041i
$931$	888640.	−	888640.i	1.02524	−	1.02524i
$932$	546644.	−	293556.i	0.629322	−	0.337955i
$933$	−417574.	+	417574.i	−0.479700	+	0.479700i
$934$	−251937.	−	1.00165e6i	−0.288800	−	1.14822i
$935$	−1.03619e6			−1.18527
$936$	274520.	−	250273.i	0.313345	−	0.285669i
$937$		−	379981.i		−	0.432796i	−0.976305	−	0.216398i	$-0.930569\pi$
$937$		−	379981.i		−	0.432796i	0.976305	−	0.216398i	$-0.0694309\pi$
$938$	−25362.5	−	100837.i	−0.0288261	−	0.114607i
$939$	−638511.	−	638511.i	−0.724165	−	0.724165i
$940$	−756997.	+	2.51307e6i	−0.856719	+	2.84413i
$941$	149316.	+	149316.i	0.168627	+	0.168627i	0.786376	−	0.617749i	$-0.211955\pi$
$941$	149316.	+	149316.i	0.168627	+	0.168627i	−0.617749	+	0.786376i	$0.711955\pi$
$942$	−16181.3	+	27056.5i	−0.0182352	+	0.0304909i
$943$		−	197641.i		−	0.222256i
$944$	−1.00573e6	+	204122.i	−1.12859	+	0.229058i
$945$	107563.			0.120448
$946$	246670.	+	147522.i	0.275634	+	0.164845i
$947$	666541.	−	666541.i	0.743236	−	0.743236i	−0.229963	−	0.973199i	$-0.573861\pi$
$947$	666541.	−	666541.i	0.743236	−	0.743236i	0.973199	+	0.229963i	$0.0738606\pi$
$948$	128809.	−	427617.i	0.143327	−	0.475816i
$949$	−443562.	+	443562.i	−0.492518	+	0.492518i
$950$	3.97449e6	−	999668.i	4.40387	−	1.10766i
$951$	−121746.			−0.134615
$952$	345487.	+	15962.5i	0.381204	+	0.0176127i
$953$			1.39655e6i			1.53769i	0.639434	+	0.768846i	$0.279169\pi$
$953$			1.39655e6i			1.53769i	−0.639434	+	0.768846i	$0.720831\pi$
$954$	107393.	−	27011.6i	0.117999	−	0.0296793i
$955$	363772.	+	363772.i	0.398862	+	0.398862i
$956$	1.11707e6	−	599882.i	1.22226	−	0.656372i
$957$	59564.4	+	59564.4i	0.0650374	+	0.0650374i
$958$	−887779.	−	530941.i	−0.967328	−	0.578516i
$959$		−	214643.i		−	0.233389i
$960$	95766.4	−	1.03416e6i	0.103913	−	1.12213i
$961$	916370.			0.992257
$962$	−480.398	+	803.266i	−0.000519100	+	0.000867979i
$963$	−189155.	+	189155.i	−0.203970	+	0.203970i
$964$	364751.	+	679221.i	0.392503	+	0.730898i
$965$	−2.03315e6	+	2.03315e6i	−2.18331	+	2.18331i
$966$	25282.9	+	100520.i	0.0270940	+	0.107721i
$967$	46484.2			0.0497110			0.0248555	−	0.999691i	$-0.492087\pi$
$967$	46484.2			0.0497110			0.0248555	+	0.999691i	$0.492087\pi$
$968$	−31988.8	+	692355.i	−0.0341387	+	0.738888i
$969$		−	1.04266e6i		−	1.11044i
$970$	463520.	+	1.84287e6i	0.492635	+	1.95862i
$971$	761678.	+	761678.i	0.807854	+	0.807854i	0.984309	−	0.176454i	$-0.0564628\pi$
$971$	761678.	+	761678.i	0.807854	+	0.807854i	−0.176454	+	0.984309i	$0.556463\pi$
$972$	−58032.3	−	17480.7i	−0.0614239	−	0.0185023i
$973$	79934.2	+	79934.2i	0.0844319	+	0.0844319i
$974$	473327.	−	791443.i	0.498935	−	0.834261i
$975$		−	1.96179e6i		−	2.06368i
$976$	169954.	−	34493.7i	0.178415	−	0.0362110i
$977$	−807656.			−0.846131			−0.423065	−	0.906099i	$-0.639046\pi$
$977$	−807656.			−0.846131			−0.423065	+	0.906099i	$0.639046\pi$
$978$	276082.	+	165113.i	0.288643	+	0.172625i
$979$	69634.7	−	69634.7i	0.0726541	−	0.0726541i
$980$	−1.61041e6	−	485093.i	−1.67681	−	0.505095i
$981$	−306921.	+	306921.i	−0.318925	+	0.318925i
$982$	238398.	−	59962.1i	0.247218	−	0.0621805i
$983$	625523.			0.647346			0.323673	−	0.946169i	$-0.395082\pi$
$983$	625523.			0.647346			0.323673	+	0.946169i	$0.395082\pi$
$984$	139509.	+	153025.i	0.144083	+	0.158042i
$985$			2.96315e6i			3.05409i
$986$	−350360.	+	88122.8i	−0.360380	+	0.0906430i
$987$	194057.	+	194057.i	0.199202	+	0.199202i
$988$	−949382.	−	1.76789e6i	−0.972584	−	1.81110i
$989$	−261222.	−	261222.i	−0.267065	−	0.267065i
$990$	279234.	+	166998.i	0.284904	+	0.170388i
$991$		−	1.57499e6i		−	1.60373i	−0.597509	−	0.801863i	$-0.703843\pi$
$991$		−	1.57499e6i		−	1.60373i	0.597509	−	0.801863i	$-0.296157\pi$
$992$	−78096.3	+	37402.6i	−0.0793610	+	0.0380083i
$993$	417368.			0.423273
$994$	260729.	−	435961.i	0.263886	−	0.441240i
$995$	−63497.2	+	63497.2i	−0.0641370	+	0.0641370i
$996$	452320.	−	242902.i	0.455960	−	0.244857i
$997$	−961501.	+	961501.i	−0.967296	+	0.967296i	−0.999482	−	0.0321857i	$-0.989753\pi$
$997$	−961501.	+	961501.i	−0.967296	+	0.967296i	0.0321857	+	0.999482i	$0.489753\pi$
$998$	460309.	+	1.83011e6i	0.462156	+	1.83745i
$999$	152.704			0.000153009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.5.l.a.19.11	✓	32
3.2	odd	2		144.5.m.c.19.6		32
4.3	odd	2		192.5.l.a.175.16		32
8.3	odd	2		384.5.l.a.223.1		32
8.5	even	2		384.5.l.b.223.16		32
12.11	even	2		576.5.m.b.559.16		32
16.3	odd	4		384.5.l.b.31.16		32
16.5	even	4		192.5.l.a.79.16		32
16.11	odd	4	inner	48.5.l.a.43.11	yes	32
16.13	even	4		384.5.l.a.31.1		32
48.5	odd	4		576.5.m.b.271.16		32
48.11	even	4		144.5.m.c.91.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.5.l.a.19.11	✓	32	1.1	even	1	trivial
48.5.l.a.43.11	yes	32	16.11	odd	4	inner
144.5.m.c.19.6		32	3.2	odd	2
144.5.m.c.91.6		32	48.11	even	4
192.5.l.a.79.16		32	16.5	even	4
192.5.l.a.175.16		32	4.3	odd	2
384.5.l.a.31.1		32	16.13	even	4
384.5.l.a.223.1		32	8.3	odd	2
384.5.l.b.31.16		32	16.3	odd	4
384.5.l.b.223.16		32	8.5	even	2
576.5.m.b.271.16		32	48.5	odd	4
576.5.m.b.559.16		32	12.11	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.05307 - 3.43291i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(-7.56978 - 14.0960i) q^{4} +(-34.5052 + 34.5052i) q^{5} +(5.06985 + 20.1568i) q^{6} -15.7115 q^{7} +(-63.9318 - 2.95383i) q^{8} -27.0000i q^{9} +O(q^{10})\)	\(q+(2.05307 - 3.43291i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(-7.56978 - 14.0960i) q^{4} +(-34.5052 + 34.5052i) q^{5} +(5.06985 + 20.1568i) q^{6} -15.7115 q^{7} +(-63.9318 - 2.95383i) q^{8} -27.0000i q^{9} +(47.6116 + 189.295i) q^{10} +(43.6544 + 43.6544i) q^{11} +(79.6053 + 23.9790i) q^{12} +(-152.012 - 152.012i) q^{13} +(-32.2568 + 53.9361i) q^{14} -253.560i q^{15} +(-141.397 + 213.408i) q^{16} +343.952 q^{17} +(-92.6886 - 55.4330i) q^{18} +(-412.525 + 412.525i) q^{19} +(747.583 + 225.190i) q^{20} +(57.7276 - 57.7276i) q^{21} +(239.487 - 60.2360i) q^{22} -317.405 q^{23} +(245.753 - 224.047i) q^{24} -1756.21i q^{25} +(-833.936 + 209.752i) q^{26} +(99.2043 + 99.2043i) q^{27} +(118.932 + 221.470i) q^{28} +(-185.679 - 185.679i) q^{29} +(-870.450 - 520.578i) q^{30} +84.5615i q^{31} +(442.312 + 923.545i) q^{32} -320.793 q^{33} +(706.158 - 1180.76i) q^{34} +(542.127 - 542.127i) q^{35} +(-380.593 + 204.384i) q^{36} +(0.769642 - 0.769642i) q^{37} +(569.218 + 2263.10i) q^{38} +1117.06 q^{39} +(2307.90 - 2104.06i) q^{40} +622.677i q^{41} +(-79.6549 - 316.693i) q^{42} +(822.991 + 822.991i) q^{43} +(284.900 - 945.808i) q^{44} +(931.640 + 931.640i) q^{45} +(-651.657 + 1089.63i) q^{46} +3361.59i q^{47} +(-264.585 - 1303.64i) q^{48} -2154.15 q^{49} +(-6028.93 - 3605.64i) q^{50} +(-1263.76 + 1263.76i) q^{51} +(-992.071 + 3293.47i) q^{52} +(-725.034 + 725.034i) q^{53} +(544.234 - 136.886i) q^{54} -3012.60 q^{55} +(1004.46 + 46.4090i) q^{56} -3031.42i q^{57} +(-1018.63 + 256.207i) q^{58} +(2834.59 + 2834.59i) q^{59} +(-3574.20 + 1919.39i) q^{60} +(-479.007 - 479.007i) q^{61} +(290.292 + 173.611i) q^{62} +424.210i q^{63} +(4078.55 + 377.687i) q^{64} +10490.4 q^{65} +(-658.611 + 1101.25i) q^{66} +(-1169.89 + 1169.89i) q^{67} +(-2603.64 - 4848.36i) q^{68} +(1166.22 - 1166.22i) q^{69} +(-748.048 - 2974.10i) q^{70} -8082.92 q^{71} +(-79.7534 + 1726.16i) q^{72} -2917.94i q^{73} +(-1.06198 - 4.22224i) q^{74} +(6452.74 + 6452.74i) q^{75} +(8937.69 + 2692.25i) q^{76} +(-685.874 - 685.874i) q^{77} +(2293.40 - 3834.76i) q^{78} -5371.72i q^{79} +(-2484.75 - 12242.6i) q^{80} -729.000 q^{81} +(2137.60 + 1278.40i) q^{82} +(4366.68 - 4366.68i) q^{83} +(-1250.72 - 376.746i) q^{84} +(-11868.1 + 11868.1i) q^{85} +(4514.92 - 1135.60i) q^{86} +1364.45 q^{87} +(-2661.95 - 2919.85i) q^{88} -1595.14i q^{89} +(5110.96 - 1285.51i) q^{90} +(2388.33 + 2388.33i) q^{91} +(2402.69 + 4474.16i) q^{92} +(-310.699 - 310.699i) q^{93} +(11540.1 + 6901.60i) q^{94} -28468.5i q^{95} +(-5018.48 - 1768.16i) q^{96} +9735.44 q^{97} +(-4422.63 + 7395.01i) q^{98} +(1178.67 - 1178.67i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} + 180 q^{8}+O(q^{10}) \) 32 * q + 12 * q^4 + 180 * q^8	\( 32 q + 12 q^{4} + 180 q^{8} + 296 q^{10} - 192 q^{11} + 360 q^{12} - 156 q^{14} + 352 q^{16} - 324 q^{18} + 704 q^{19} - 1200 q^{20} - 1568 q^{22} - 2304 q^{23} + 1188 q^{24} + 2700 q^{26} + 4680 q^{28} - 1728 q^{29} + 1512 q^{30} - 3360 q^{32} - 9312 q^{34} - 5184 q^{35} - 756 q^{36} + 3648 q^{37} - 5880 q^{38} + 5232 q^{40} + 4500 q^{42} + 1088 q^{43} + 18840 q^{44} + 680 q^{46} + 2160 q^{48} + 10976 q^{49} - 25884 q^{50} - 4032 q^{51} - 25584 q^{52} + 960 q^{53} + 972 q^{54} + 11776 q^{55} + 15456 q^{56} + 12624 q^{58} + 13056 q^{59} + 7992 q^{60} + 3776 q^{61} + 21852 q^{62} - 8664 q^{64} + 4032 q^{65} - 8856 q^{66} - 896 q^{67} - 17280 q^{68} - 9792 q^{69} - 18240 q^{70} - 39936 q^{71} + 4860 q^{72} + 24204 q^{74} - 1152 q^{75} + 16776 q^{76} + 9408 q^{77} - 3780 q^{78} - 14232 q^{80} - 23328 q^{81} - 33800 q^{82} + 24000 q^{83} - 11448 q^{84} - 11200 q^{85} - 1200 q^{86} - 11424 q^{88} + 4104 q^{90} + 30528 q^{91} - 11664 q^{92} - 8040 q^{94} + 10080 q^{96} + 52968 q^{98} - 5184 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 + 180 * q^8 + 296 * q^10 - 192 * q^11 + 360 * q^12 - 156 * q^14 + 352 * q^16 - 324 * q^18 + 704 * q^19 - 1200 * q^20 - 1568 * q^22 - 2304 * q^23 + 1188 * q^24 + 2700 * q^26 + 4680 * q^28 - 1728 * q^29 + 1512 * q^30 - 3360 * q^32 - 9312 * q^34 - 5184 * q^35 - 756 * q^36 + 3648 * q^37 - 5880 * q^38 + 5232 * q^40 + 4500 * q^42 + 1088 * q^43 + 18840 * q^44 + 680 * q^46 + 2160 * q^48 + 10976 * q^49 - 25884 * q^50 - 4032 * q^51 - 25584 * q^52 + 960 * q^53 + 972 * q^54 + 11776 * q^55 + 15456 * q^56 + 12624 * q^58 + 13056 * q^59 + 7992 * q^60 + 3776 * q^61 + 21852 * q^62 - 8664 * q^64 + 4032 * q^65 - 8856 * q^66 - 896 * q^67 - 17280 * q^68 - 9792 * q^69 - 18240 * q^70 - 39936 * q^71 + 4860 * q^72 + 24204 * q^74 - 1152 * q^75 + 16776 * q^76 + 9408 * q^77 - 3780 * q^78 - 14232 * q^80 - 23328 * q^81 - 33800 * q^82 + 24000 * q^83 - 11448 * q^84 - 11200 * q^85 - 1200 * q^86 - 11424 * q^88 + 4104 * q^90 + 30528 * q^91 - 11664 * q^92 - 8040 * q^94 + 10080 * q^96 + 52968 * q^98 - 5184 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more