LMFDB - Embedded newform 490.3.f.e.197.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [490,3,Mod(197,490)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(490, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("490.197"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	490.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-4,-4,0,12,8,0,8,0,-28,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$13.3515329537$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{30})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 225 $ x^4 + 225
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.1
Root			$-2.73861 + 2.73861i$ of defining polynomial
Character	$\chi$	$=$	490.197
Dual form			490.3.f.e.393.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{2} +(-3.73861 + 3.73861i) q^{3} +2.00000i q^{4} +(3.00000 - 4.00000i) q^{5} +7.47723 q^{6} +(2.00000 - 2.00000i) q^{8} -18.9545i q^{9} +(-7.00000 + 1.00000i) q^{10} +3.47723 q^{11} +(-7.47723 - 7.47723i) q^{12} +(-10.9545 + 10.9545i) q^{13} +(3.73861 + 26.1703i) q^{15} -4.00000 q^{16} +(6.95445 + 6.95445i) q^{17} +(-18.9545 + 18.9545i) q^{18} +18.4317i q^{19} +(8.00000 + 6.00000i) q^{20} +(-3.47723 - 3.47723i) q^{22} +(-12.6931 + 12.6931i) q^{23} +14.9545i q^{24} +(-7.00000 - 24.0000i) q^{25} +21.9089 q^{26} +(37.2158 + 37.2158i) q^{27} -49.8634i q^{29} +(22.4317 - 29.9089i) q^{30} -16.0000 q^{31} +(4.00000 + 4.00000i) q^{32} +(-13.0000 + 13.0000i) q^{33} -13.9089i q^{34} +37.9089 q^{36} +(-25.0455 - 25.0455i) q^{37} +(18.4317 - 18.4317i) q^{38} -81.9089i q^{39} +(-2.00000 - 14.0000i) q^{40} +6.04555 q^{41} +(-9.64752 + 9.64752i) q^{43} +6.95445i q^{44} +(-75.8178 - 56.8634i) q^{45} +25.3861 q^{46} +(-14.8634 - 14.8634i) q^{47} +(14.9545 - 14.9545i) q^{48} +(-17.0000 + 31.0000i) q^{50} -52.0000 q^{51} +(-21.9089 - 21.9089i) q^{52} +(-8.04555 + 8.04555i) q^{53} -74.4317i q^{54} +(10.4317 - 13.9089i) q^{55} +(-68.9089 - 68.9089i) q^{57} +(-49.8634 + 49.8634i) q^{58} -75.4772i q^{59} +(-52.3406 + 7.47723i) q^{60} -102.909 q^{61} +(16.0000 + 16.0000i) q^{62} -8.00000i q^{64} +(10.9545 + 76.6812i) q^{65} +26.0000 q^{66} +(-22.7842 - 22.7842i) q^{67} +(-13.9089 + 13.9089i) q^{68} -94.9089i q^{69} +40.3406 q^{71} +(-37.9089 - 37.9089i) q^{72} +(62.7723 - 62.7723i) q^{73} +50.0911i q^{74} +(115.897 + 63.5564i) q^{75} -36.8634 q^{76} +(-81.9089 + 81.9089i) q^{78} -101.204i q^{79} +(-12.0000 + 16.0000i) q^{80} -107.681 q^{81} +(-6.04555 - 6.04555i) q^{82} +(-51.1247 + 51.1247i) q^{83} +(48.6812 - 6.95445i) q^{85} +19.2950 q^{86} +(186.420 + 186.420i) q^{87} +(6.95445 - 6.95445i) q^{88} -82.7267i q^{89} +(18.9545 + 132.681i) q^{90} +(-25.3861 - 25.3861i) q^{92} +(59.8178 - 59.8178i) q^{93} +29.7267i q^{94} +(73.7267 + 55.2950i) q^{95} -29.9089 q^{96} +(-45.7723 - 45.7723i) q^{97} -65.9089i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 12 q^{5} + 8 q^{6} + 8 q^{8} - 28 q^{10} - 8 q^{11} - 8 q^{12} + 4 q^{15} - 16 q^{16} - 16 q^{17} - 32 q^{18} + 32 q^{20} + 8 q^{22} + 4 q^{23} - 28 q^{25} + 116 q^{27} + 24 q^{30}+ \cdots + 36 q^{97}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 12 * q^5 + 8 * q^6 + 8 * q^8 - 28 * q^10 - 8 * q^11 - 8 * q^12 + 4 * q^15 - 16 * q^16 - 16 * q^17 - 32 * q^18 + 32 * q^20 + 8 * q^22 + 4 * q^23 - 28 * q^25 + 116 * q^27 + 24 * q^30 - 64 * q^31 + 16 * q^32 - 52 * q^33 + 64 * q^36 - 144 * q^37 + 8 * q^38 - 8 * q^40 + 68 * q^41 + 60 * q^43 - 128 * q^45 - 8 * q^46 + 72 * q^47 + 16 * q^48 - 68 * q^50 - 208 * q^51 - 76 * q^53 - 24 * q^55 - 188 * q^57 - 68 * q^58 - 56 * q^60 - 324 * q^61 + 64 * q^62 + 104 * q^66 - 124 * q^67 + 32 * q^68 + 8 * q^71 - 64 * q^72 + 32 * q^73 + 124 * q^75 - 16 * q^76 - 240 * q^78 - 48 * q^80 - 124 * q^81 - 68 * q^82 - 84 * q^83 - 112 * q^85 - 120 * q^86 + 428 * q^87 - 16 * q^88 + 32 * q^90 + 8 * q^92 + 64 * q^93 + 32 * q^95 - 32 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−3.73861	+	3.73861i	−1.24620	+	1.24620i	−0.288821	+	0.957383i	$0.593263\pi$
$3$	−3.73861	+	3.73861i	−1.24620	+	1.24620i	−0.957383	+	0.288821i	$0.906737\pi$
$4$			2.00000i			0.500000i
$5$	3.00000	−	4.00000i	0.600000	−	0.800000i
$5$	3.00000	−	4.00000i	0.600000	−	0.800000i
$6$	7.47723			1.24620
$7$		0			0
$7$		0			0
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	18.9545i		−	2.10605i
$10$	−7.00000	+	1.00000i	−0.700000	+	0.100000i
$11$	3.47723			0.316111			0.158056	−	0.987430i	$-0.449477\pi$
$11$	3.47723			0.316111			0.158056	+	0.987430i	$0.449477\pi$
$12$	−7.47723	−	7.47723i	−0.623102	−	0.623102i
$13$	−10.9545	+	10.9545i	−0.842650	+	0.842650i	−0.989203	−	0.146553i	$-0.953182\pi$
$13$	−10.9545	+	10.9545i	−0.842650	+	0.842650i	0.146553	+	0.989203i	$0.453182\pi$
$14$		0			0
$15$	3.73861	+	26.1703i	0.249241	+	1.74469i
$16$	−4.00000			−0.250000
$17$	6.95445	+	6.95445i	0.409085	+	0.409085i	0.881420	−	0.472334i	$-0.156588\pi$
$17$	6.95445	+	6.95445i	0.409085	+	0.409085i	−0.472334	+	0.881420i	$0.656588\pi$
$18$	−18.9545	+	18.9545i	−1.05303	+	1.05303i
$19$			18.4317i			0.970088i	0.874490	+	0.485044i	$0.161196\pi$
$19$			18.4317i			0.970088i	−0.874490	+	0.485044i	$0.838804\pi$
$20$	8.00000	+	6.00000i	0.400000	+	0.300000i
$21$		0			0
$22$	−3.47723	−	3.47723i	−0.158056	−	0.158056i
$23$	−12.6931	+	12.6931i	−0.551872	+	0.551872i	−0.926981	−	0.375109i	$-0.877605\pi$
$23$	−12.6931	+	12.6931i	−0.551872	+	0.551872i	0.375109	+	0.926981i	$0.377605\pi$
$24$			14.9545i			0.623102i
$25$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$26$	21.9089			0.842650
$27$	37.2158	+	37.2158i	1.37836	+	1.37836i
$28$		0			0
$29$		−	49.8634i		−	1.71943i	−0.510777	−	0.859713i	$-0.670642\pi$
$29$		−	49.8634i		−	1.71943i	0.510777	−	0.859713i	$-0.329358\pi$
$30$	22.4317	−	29.9089i	0.747723	−	0.996963i
$31$	−16.0000			−0.516129			−0.258065	−	0.966128i	$-0.583085\pi$
$31$	−16.0000			−0.516129			−0.258065	+	0.966128i	$0.583085\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−13.0000	+	13.0000i	−0.393939	+	0.393939i
$34$		−	13.9089i		−	0.409085i
$35$		0			0
$36$	37.9089			1.05303
$37$	−25.0455	−	25.0455i	−0.676907	−	0.676907i	0.282392	−	0.959299i	$-0.408872\pi$
$37$	−25.0455	−	25.0455i	−0.676907	−	0.676907i	−0.959299	+	0.282392i	$0.908872\pi$
$38$	18.4317	−	18.4317i	0.485044	−	0.485044i
$39$		−	81.9089i		−	2.10023i
$40$	−2.00000	−	14.0000i	−0.0500000	−	0.350000i
$41$	6.04555			0.147452			0.0737262	−	0.997279i	$-0.476511\pi$
$41$	6.04555			0.147452			0.0737262	+	0.997279i	$0.476511\pi$
$42$		0			0
$43$	−9.64752	+	9.64752i	−0.224361	+	0.224361i	−0.810332	−	0.585971i	$-0.800713\pi$
$43$	−9.64752	+	9.64752i	−0.224361	+	0.224361i	0.585971	+	0.810332i	$0.300713\pi$
$44$			6.95445i			0.158056i
$45$	−75.8178	−	56.8634i	−1.68484	−	1.26363i
$46$	25.3861			0.551872
$47$	−14.8634	−	14.8634i	−0.316242	−	0.316242i	0.531080	−	0.847322i	$-0.321786\pi$
$47$	−14.8634	−	14.8634i	−0.316242	−	0.316242i	−0.847322	+	0.531080i	$0.821786\pi$
$48$	14.9545	−	14.9545i	0.311551	−	0.311551i
$49$		0			0
$50$	−17.0000	+	31.0000i	−0.340000	+	0.620000i
$51$	−52.0000			−1.01961
$52$	−21.9089	−	21.9089i	−0.421325	−	0.421325i
$53$	−8.04555	+	8.04555i	−0.151803	+	0.151803i	−0.778923	−	0.627120i	$-0.784234\pi$
$53$	−8.04555	+	8.04555i	−0.151803	+	0.151803i	0.627120	+	0.778923i	$0.284234\pi$
$54$		−	74.4317i		−	1.37836i
$55$	10.4317	−	13.9089i	0.189667	−	0.252889i
$56$		0			0
$57$	−68.9089	−	68.9089i	−1.20893	−	1.20893i
$58$	−49.8634	+	49.8634i	−0.859713	+	0.859713i
$59$		−	75.4772i		−	1.27928i	−0.768677	−	0.639638i	$-0.779084\pi$
$59$		−	75.4772i		−	1.27928i	0.768677	−	0.639638i	$-0.220916\pi$
$60$	−52.3406	+	7.47723i	−0.872343	+	0.124620i
$61$	−102.909			−1.68703			−0.843516	−	0.537105i	$-0.819518\pi$
$61$	−102.909			−1.68703			−0.843516	+	0.537105i	$0.819518\pi$
$62$	16.0000	+	16.0000i	0.258065	+	0.258065i
$63$		0			0
$64$		−	8.00000i		−	0.125000i
$65$	10.9545	+	76.6812i	0.168530	+	1.17971i
$66$	26.0000			0.393939
$67$	−22.7842	−	22.7842i	−0.340062	−	0.340062i	0.516328	−	0.856391i	$-0.327298\pi$
$67$	−22.7842	−	22.7842i	−0.340062	−	0.340062i	−0.856391	+	0.516328i	$0.827298\pi$
$68$	−13.9089	+	13.9089i	−0.204543	+	0.204543i
$69$		−	94.9089i		−	1.37549i
$70$		0			0
$71$	40.3406			0.568177			0.284089	−	0.958798i	$-0.408309\pi$
$71$	40.3406			0.568177			0.284089	+	0.958798i	$0.408309\pi$
$72$	−37.9089	−	37.9089i	−0.526513	−	0.526513i
$73$	62.7723	−	62.7723i	0.859894	−	0.859894i	−0.131431	−	0.991325i	$-0.541957\pi$
$73$	62.7723	−	62.7723i	0.859894	−	0.859894i	0.991325	+	0.131431i	$0.0419573\pi$
$74$			50.0911i			0.676907i
$75$	115.897	+	63.5564i	1.54529	+	0.847419i
$76$	−36.8634			−0.485044
$77$		0			0
$78$	−81.9089	+	81.9089i	−1.05011	+	1.05011i
$79$		−	101.204i		−	1.28106i	−0.767932	−	0.640531i	$-0.778714\pi$
$79$		−	101.204i		−	1.28106i	0.767932	−	0.640531i	$-0.221286\pi$
$80$	−12.0000	+	16.0000i	−0.150000	+	0.200000i
$81$	−107.681			−1.32940
$82$	−6.04555	−	6.04555i	−0.0737262	−	0.0737262i
$83$	−51.1247	+	51.1247i	−0.615961	+	0.615961i	−0.944493	−	0.328532i	$-0.893446\pi$
$83$	−51.1247	+	51.1247i	−0.615961	+	0.615961i	0.328532	+	0.944493i	$0.393446\pi$
$84$		0			0
$85$	48.6812	−	6.95445i	0.572720	−	0.0818171i
$86$	19.2950			0.224361
$87$	186.420	+	186.420i	2.14276	+	2.14276i
$88$	6.95445	−	6.95445i	0.0790279	−	0.0790279i
$89$		−	82.7267i		−	0.929514i	−0.885438	−	0.464757i	$-0.846142\pi$
$89$		−	82.7267i		−	0.929514i	0.885438	−	0.464757i	$-0.153858\pi$
$90$	18.9545	+	132.681i	0.210605	+	1.47424i
$91$		0			0
$92$	−25.3861	−	25.3861i	−0.275936	−	0.275936i
$93$	59.8178	−	59.8178i	0.643202	−	0.643202i
$94$			29.7267i			0.316242i
$95$	73.7267	+	55.2950i	0.776071	+	0.582053i
$96$	−29.9089			−0.311551
$97$	−45.7723	−	45.7723i	−0.471879	−	0.471879i	0.430643	−	0.902522i	$-0.358287\pi$
$97$	−45.7723	−	45.7723i	−0.471879	−	0.471879i	−0.902522	+	0.430643i	$0.858287\pi$
$98$		0			0
$99$		−	65.9089i		−	0.665746i
$100$	48.0000	−	14.0000i	0.480000	−	0.140000i
$101$	−143.499			−1.42078			−0.710391	−	0.703807i	$-0.751482\pi$
$101$	−143.499			−1.42078			−0.710391	+	0.703807i	$0.751482\pi$
$102$	52.0000	+	52.0000i	0.509804	+	0.509804i
$103$	−39.7386	+	39.7386i	−0.385812	+	0.385812i	−0.873191	−	0.487379i	$-0.837953\pi$
$103$	−39.7386	+	39.7386i	−0.385812	+	0.385812i	0.487379	+	0.873191i	$0.337953\pi$
$104$			43.8178i			0.421325i
$105$		0			0
$106$	16.0911			0.151803
$107$	−42.4198	−	42.4198i	−0.396446	−	0.396446i	0.480531	−	0.876978i	$-0.340444\pi$
$107$	−42.4198	−	42.4198i	−0.396446	−	0.396446i	−0.876978	+	0.480531i	$0.840444\pi$
$108$	−74.4317	+	74.4317i	−0.689182	+	0.689182i
$109$		−	37.2733i		−	0.341957i	−0.985275	−	0.170978i	$-0.945307\pi$
$109$		−	37.2733i		−	0.341957i	0.985275	−	0.170978i	$-0.0546928\pi$
$110$	−24.3406	+	3.47723i	−0.221278	+	0.0316111i
$111$	187.271			1.68713
$112$		0			0
$113$	−118.636	+	118.636i	−1.04987	+	1.04987i	−0.0511834	+	0.998689i	$0.516299\pi$
$113$	−118.636	+	118.636i	−1.04987	+	1.04987i	−0.998689	+	0.0511834i	$0.983701\pi$
$114$			137.818i			1.20893i
$115$	12.6931	+	88.8514i	0.110374	+	0.772621i
$116$	99.7267			0.859713
$117$	207.636	+	207.636i	1.77466	+	1.77466i
$118$	−75.4772	+	75.4772i	−0.639638	+	0.639638i
$119$		0			0
$120$	59.8178	+	44.8634i	0.498482	+	0.373861i
$121$	−108.909			−0.900074
$122$	102.909	+	102.909i	0.843516	+	0.843516i
$123$	−22.6020	+	22.6020i	−0.183756	+	0.183756i
$124$		−	32.0000i		−	0.258065i
$125$	−117.000	−	44.0000i	−0.936000	−	0.352000i
$126$		0			0
$127$	24.9545	+	24.9545i	0.196492	+	0.196492i	0.798494	−	0.602002i	$-0.205630\pi$
$127$	24.9545	+	24.9545i	0.196492	+	0.196492i	−0.602002	+	0.798494i	$0.705630\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	72.1366i		−	0.559199i
$130$	65.7267	−	87.6356i	0.505590	−	0.674120i
$131$	70.0911			0.535047			0.267523	−	0.963551i	$-0.413795\pi$
$131$	70.0911			0.535047			0.267523	+	0.963551i	$0.413795\pi$
$132$	−26.0000	−	26.0000i	−0.196970	−	0.196970i
$133$		0			0
$134$			45.5683i			0.340062i
$135$	260.511	−	37.2158i	1.92971	−	0.275673i
$136$	27.8178			0.204543
$137$	−6.77226	−	6.77226i	−0.0494325	−	0.0494325i	0.681958	−	0.731391i	$-0.261128\pi$
$137$	−6.77226	−	6.77226i	−0.0494325	−	0.0494325i	−0.731391	+	0.681958i	$0.761128\pi$
$138$	−94.9089	+	94.9089i	−0.687746	+	0.687746i
$139$			53.0217i			0.381451i	0.981643	+	0.190726i	$0.0610841\pi$
$139$			53.0217i			0.381451i	−0.981643	+	0.190726i	$0.938916\pi$
$140$		0			0
$141$	111.137			0.788203
$142$	−40.3406	−	40.3406i	−0.284089	−	0.284089i
$143$	−38.0911	+	38.0911i	−0.266371	+	0.266371i
$144$			75.8178i			0.526513i
$145$	−199.453	−	149.590i	−1.37554	−	1.03166i
$146$	−125.545			−0.859894
$147$		0			0
$148$	50.0911	−	50.0911i	0.338453	−	0.338453i
$149$			209.091i			1.40330i	0.712524	+	0.701648i	$0.247552\pi$
$149$			209.091i			1.40330i	−0.712524	+	0.701648i	$0.752448\pi$
$150$	−52.3406	−	179.453i	−0.348937	−	1.19636i
$151$	162.091			1.07345			0.536725	−	0.843757i	$-0.319661\pi$
$151$	162.091			1.07345			0.536725	+	0.843757i	$0.319661\pi$
$152$	36.8634	+	36.8634i	0.242522	+	0.242522i
$153$	131.818	−	131.818i	0.861554	−	0.861554i
$154$		0			0
$155$	−48.0000	+	64.0000i	−0.309677	+	0.412903i
$156$	163.818			1.05011
$157$	−97.4079	−	97.4079i	−0.620432	−	0.620432i	0.325210	−	0.945642i	$-0.394565\pi$
$157$	−97.4079	−	97.4079i	−0.620432	−	0.620432i	−0.945642	+	0.325210i	$0.894565\pi$
$158$	−101.204	+	101.204i	−0.640531	+	0.640531i
$159$		−	60.1584i		−	0.378355i
$160$	28.0000	−	4.00000i	0.175000	−	0.0250000i
$161$		0			0
$162$	107.681	+	107.681i	0.664699	+	0.664699i
$163$	67.2277	−	67.2277i	0.412440	−	0.412440i	−0.470148	−	0.882588i	$-0.655799\pi$
$163$	67.2277	−	67.2277i	0.412440	−	0.412440i	0.882588	+	0.470148i	$0.155799\pi$
$164$			12.0911i			0.0737262i
$165$	13.0000	+	91.0000i	0.0787879	+	0.551515i
$166$	102.249			0.615961
$167$	−133.988	−	133.988i	−0.802324	−	0.802324i	0.181134	−	0.983458i	$-0.442023\pi$
$167$	−133.988	−	133.988i	−0.802324	−	0.802324i	−0.983458	+	0.181134i	$0.942023\pi$
$168$		0			0
$169$		−	71.0000i		−	0.420118i
$170$	−55.6356	−	41.7267i	−0.327268	−	0.245451i
$171$	349.362			2.04305
$172$	−19.2950	−	19.2950i	−0.112180	−	0.112180i
$173$	0.182195	−	0.182195i	0.00105315	−	0.00105315i	−0.706580	−	0.707633i	$-0.749763\pi$
$173$	0.182195	−	0.182195i	0.00105315	−	0.00105315i	0.707633	+	0.706580i	$0.249763\pi$
$174$		−	372.840i		−	2.14276i
$175$		0			0
$176$	−13.9089			−0.0790279
$177$	282.180	+	282.180i	1.59424	+	1.59424i
$178$	−82.7267	+	82.7267i	−0.464757	+	0.464757i
$179$		−	43.6356i		−	0.243774i	−0.992544	−	0.121887i	$-0.961105\pi$
$179$		−	43.6356i		−	0.243774i	0.992544	−	0.121887i	$-0.0388946\pi$
$180$	113.727	−	151.636i	0.631815	−	0.842420i
$181$	−3.68116			−0.0203379			−0.0101689	−	0.999948i	$-0.503237\pi$
$181$	−3.68116			−0.0203379			−0.0101689	+	0.999948i	$0.503237\pi$
$182$		0			0
$183$	384.737	−	384.737i	2.10239	−	2.10239i
$184$			50.7723i			0.275936i
$185$	−175.319	+	25.0455i	−0.947669	+	0.135381i
$186$	−119.636			−0.643202
$187$	24.1822	+	24.1822i	0.129317	+	0.129317i
$188$	29.7267	−	29.7267i	0.158121	−	0.158121i
$189$		0			0
$190$	−18.4317	−	129.022i	−0.0970088	−	0.679062i
$191$	17.9327			0.0938886			0.0469443	−	0.998898i	$-0.485052\pi$
$191$	17.9327			0.0938886			0.0469443	+	0.998898i	$0.485052\pi$
$192$	29.9089	+	29.9089i	0.155776	+	0.155776i
$193$	150.362	−	150.362i	0.779079	−	0.779079i	−0.200595	−	0.979674i	$-0.564288\pi$
$193$	150.362	−	150.362i	0.779079	−	0.779079i	0.979674	+	0.200595i	$0.0642875\pi$
$194$			91.5445i			0.471879i
$195$	−327.636	−	245.727i	−1.68018	−	1.26014i
$196$		0			0
$197$	41.0911	+	41.0911i	0.208584	+	0.208584i	0.803666	−	0.595081i	$-0.202880\pi$
$197$	41.0911	+	41.0911i	0.208584	+	0.208584i	−0.595081	+	0.803666i	$0.702880\pi$
$198$	−65.9089	+	65.9089i	−0.332873	+	0.332873i
$199$		−	301.545i		−	1.51530i	−0.652662	−	0.757650i	$-0.726348\pi$
$199$		−	301.545i		−	1.51530i	0.652662	−	0.757650i	$-0.273652\pi$
$200$	−62.0000	−	34.0000i	−0.310000	−	0.170000i
$201$	170.362			0.847574
$202$	143.499	+	143.499i	0.710391	+	0.710391i
$203$		0			0
$204$		−	104.000i		−	0.509804i
$205$	18.1366	−	24.1822i	0.0884714	−	0.117962i
$206$	79.4772			0.385812
$207$	240.590	+	240.590i	1.16227	+	1.16227i
$208$	43.8178	−	43.8178i	0.210663	−	0.210663i
$209$			64.0911i			0.306656i
$210$		0			0
$211$	−177.703			−0.842194			−0.421097	−	0.907016i	$-0.638355\pi$
$211$	−177.703			−0.842194			−0.421097	+	0.907016i	$0.638355\pi$
$212$	−16.0911	−	16.0911i	−0.0759014	−	0.0759014i
$213$	−150.818	+	150.818i	−0.708065	+	0.708065i
$214$			84.8395i			0.396446i
$215$	9.64752	+	67.5326i	0.0448722	+	0.314105i
$216$	148.863			0.689182
$217$		0			0
$218$	−37.2733	+	37.2733i	−0.170978	+	0.170978i
$219$			469.362i			2.14321i
$220$	27.8178	+	20.8634i	0.126445	+	0.0948334i
$221$	−152.364			−0.689432
$222$	−187.271	−	187.271i	−0.843564	−	0.843564i
$223$	−249.113	+	249.113i	−1.11710	+	1.11710i	−0.124933	+	0.992165i	$0.539871\pi$
$223$	−249.113	+	249.113i	−1.11710	+	1.11710i	−0.992165	+	0.124933i	$0.960129\pi$
$224$		0			0
$225$	−454.907	+	132.681i	−2.02181	+	0.589694i
$226$	237.271			1.04987
$227$	29.3188	+	29.3188i	0.129158	+	0.129158i	0.768731	−	0.639573i	$-0.220889\pi$
$227$	29.3188	+	29.3188i	0.129158	+	0.129158i	−0.639573	+	0.768731i	$0.720889\pi$
$228$	137.818	−	137.818i	0.604464	−	0.604464i
$229$			315.089i			1.37593i	0.725742	+	0.687967i	$0.241497\pi$
$229$			315.089i			1.37593i	−0.725742	+	0.687967i	$0.758503\pi$
$230$	76.1584	−	101.545i	0.331123	−	0.441498i
$231$		0			0
$232$	−99.7267	−	99.7267i	−0.429856	−	0.429856i
$233$	81.3623	−	81.3623i	0.349194	−	0.349194i	−0.510615	−	0.859809i	$-0.670582\pi$
$233$	81.3623	−	81.3623i	0.349194	−	0.349194i	0.859809	+	0.510615i	$0.170582\pi$
$234$		−	415.271i		−	1.77466i
$235$	−104.043	+	14.8634i	−0.442738	+	0.0632483i
$236$	150.954			0.639638
$237$	378.362	+	378.362i	1.59647	+	1.59647i
$238$		0			0
$239$			438.725i			1.83567i	0.396965	+	0.917834i	$0.370064\pi$
$239$			438.725i			1.83567i	−0.396965	+	0.917834i	$0.629936\pi$
$240$	−14.9545	−	104.681i	−0.0623102	−	0.436171i
$241$	156.182			0.648059			0.324029	−	0.946047i	$-0.394962\pi$
$241$	156.182			0.648059			0.324029	+	0.946047i	$0.394962\pi$
$242$	108.909	+	108.909i	0.450037	+	0.450037i
$243$	67.6356	−	67.6356i	0.278336	−	0.278336i
$244$		−	205.818i		−	0.843516i
$245$		0			0
$246$	45.2039			0.183756
$247$	−201.909	−	201.909i	−0.817445	−	0.817445i
$248$	−32.0000	+	32.0000i	−0.129032	+	0.129032i
$249$		−	382.271i		−	1.53523i
$250$	73.0000	+	161.000i	0.292000	+	0.644000i
$251$	−185.727			−0.739947			−0.369974	−	0.929042i	$-0.620633\pi$
$251$	−185.727			−0.739947			−0.369974	+	0.929042i	$0.620633\pi$
$252$		0			0
$253$	−44.1366	+	44.1366i	−0.174453	+	0.174453i
$254$		−	49.9089i		−	0.196492i
$255$	−156.000	+	208.000i	−0.611765	+	0.815686i
$256$	16.0000			0.0625000
$257$	−168.681	−	168.681i	−0.656347	−	0.656347i	0.298167	−	0.954514i	$-0.403625\pi$
$257$	−168.681	−	168.681i	−0.656347	−	0.656347i	−0.954514	+	0.298167i	$0.903625\pi$
$258$	−72.1366	+	72.1366i	−0.279599	+	0.279599i
$259$		0			0
$260$	−153.362	+	21.9089i	−0.589855	+	0.0842650i
$261$	−945.132			−3.62120
$262$	−70.0911	−	70.0911i	−0.267523	−	0.267523i
$263$	−232.261	+	232.261i	−0.883123	+	0.883123i	−0.993851	−	0.110728i	$-0.964682\pi$
$263$	−232.261	+	232.261i	−0.883123	+	0.883123i	0.110728	+	0.993851i	$0.464682\pi$
$264$			52.0000i			0.196970i
$265$	8.04555	+	56.3188i	0.0303606	+	0.212524i
$266$		0			0
$267$	309.283	+	309.283i	1.15836	+	1.15836i
$268$	45.5683	−	45.5683i	0.170031	−	0.170031i
$269$			286.180i			1.06387i	0.846786	+	0.531933i	$0.178534\pi$
$269$			286.180i			1.06387i	−0.846786	+	0.531933i	$0.821466\pi$
$270$	−297.727	−	223.295i	−1.10269	−	0.827019i
$271$	−409.521			−1.51115			−0.755573	−	0.655064i	$-0.772642\pi$
$271$	−409.521			−1.51115			−0.755573	+	0.655064i	$0.772642\pi$
$272$	−27.8178	−	27.8178i	−0.102271	−	0.102271i
$273$		0			0
$274$			13.5445i			0.0494325i
$275$	−24.3406	−	83.4534i	−0.0885112	−	0.303467i
$276$	189.818			0.687746
$277$	−11.5010	−	11.5010i	−0.0415200	−	0.0415200i	0.686042	−	0.727562i	$-0.259347\pi$
$277$	−11.5010	−	11.5010i	−0.0415200	−	0.0415200i	−0.727562	+	0.686042i	$0.759347\pi$
$278$	53.0217	−	53.0217i	0.190726	−	0.190726i
$279$			303.271i			1.08699i
$280$		0			0
$281$	302.542			1.07666			0.538332	−	0.842733i	$-0.319055\pi$
$281$	302.542			1.07666			0.538332	+	0.842733i	$0.319055\pi$
$282$	−111.137	−	111.137i	−0.394102	−	0.394102i
$283$	−112.043	+	112.043i	−0.395913	+	0.395913i	−0.876789	−	0.480876i	$-0.840319\pi$
$283$	−112.043	+	112.043i	−0.395913	+	0.395913i	0.480876	+	0.876789i	$0.340319\pi$
$284$			80.6812i			0.284089i
$285$	−482.362	+	68.9089i	−1.69250	+	0.241786i
$286$	76.1822			0.266371
$287$		0			0
$288$	75.8178	−	75.8178i	0.263256	−	0.263256i
$289$		−	192.271i		−	0.665298i
$290$	49.8634	+	349.043i	0.171943	+	1.20360i
$291$	342.249			1.17612
$292$	125.545	+	125.545i	0.429947	+	0.429947i
$293$	100.182	−	100.182i	0.341919	−	0.341919i	−0.515170	−	0.857088i	$-0.672271\pi$
$293$	100.182	−	100.182i	0.341919	−	0.341919i	0.857088	+	0.515170i	$0.172271\pi$
$294$		0			0
$295$	−301.909	−	226.432i	−1.02342	−	0.767565i
$296$	−100.182			−0.338453
$297$	129.408	+	129.408i	0.435717	+	0.435717i
$298$	209.091	−	209.091i	0.701648	−	0.701648i
$299$		−	278.091i		−	0.930071i
$300$	−127.113	+	231.794i	−0.423709	+	0.772647i
$301$		0			0
$302$	−162.091	−	162.091i	−0.536725	−	0.536725i
$303$	536.487	−	536.487i	1.77058	−	1.77058i
$304$		−	73.7267i		−	0.242522i
$305$	−308.727	+	411.636i	−1.01222	+	1.34962i
$306$	−263.636			−0.861554
$307$	242.602	+	242.602i	0.790234	+	0.790234i	0.981532	−	0.191298i	$-0.0612696\pi$
$307$	242.602	+	242.602i	0.790234	+	0.790234i	−0.191298	+	0.981532i	$0.561270\pi$
$308$		0			0
$309$		−	297.135i		−	0.961601i
$310$	112.000	−	16.0000i	0.361290	−	0.0516129i
$311$	−7.47723			−0.0240425			−0.0120213	−	0.999928i	$-0.503827\pi$
$311$	−7.47723			−0.0240425			−0.0120213	+	0.999928i	$0.503827\pi$
$312$	−163.818	−	163.818i	−0.525057	−	0.525057i
$313$	423.089	−	423.089i	1.35172	−	1.35172i	0.467987	−	0.883736i	$-0.344980\pi$
$313$	423.089	−	423.089i	1.35172	−	1.35172i	0.883736	−	0.467987i	$-0.155020\pi$
$314$			194.816i			0.620432i
$315$		0			0
$316$	202.408			0.640531
$317$	−288.000	−	288.000i	−0.908517	−	0.908517i	0.0876353	−	0.996153i	$-0.472069\pi$
$317$	−288.000	−	288.000i	−0.908517	−	0.908517i	−0.996153	+	0.0876353i	$0.972069\pi$
$318$	−60.1584	+	60.1584i	−0.189177	+	0.189177i
$319$		−	173.386i		−	0.543530i
$320$	−32.0000	−	24.0000i	−0.100000	−	0.0750000i
$321$	317.182			0.988107
$322$		0			0
$323$	−128.182	+	128.182i	−0.396849	+	0.396849i
$324$		−	215.362i		−	0.664699i
$325$	339.588	+	186.226i	1.04489	+	0.573002i
$326$	−134.455			−0.412440
$327$	139.350	+	139.350i	0.426148	+	0.426148i
$328$	12.0911	−	12.0911i	0.0368631	−	0.0368631i
$329$		0			0
$330$	78.0000	−	104.000i	0.236364	−	0.315152i
$331$	236.634			0.714905			0.357452	−	0.933931i	$-0.383645\pi$
$331$	236.634			0.714905			0.357452	+	0.933931i	$0.383645\pi$
$332$	−102.249	−	102.249i	−0.307980	−	0.307980i
$333$	−474.725	+	474.725i	−1.42560	+	1.42560i
$334$			267.976i			0.802324i
$335$	−159.489	+	22.7842i	−0.476087	+	0.0680124i
$336$		0			0
$337$	316.271	+	316.271i	0.938490	+	0.938490i	0.998215	−	0.0597246i	$-0.0190223\pi$
$337$	316.271	+	316.271i	0.938490	+	0.938490i	−0.0597246	+	0.998215i	$0.519022\pi$
$338$	−71.0000	+	71.0000i	−0.210059	+	0.210059i
$339$		−	887.065i		−	2.61671i
$340$	13.9089	+	97.3623i	0.0409085	+	0.286360i
$341$	−55.6356			−0.163154
$342$	−349.362	−	349.362i	−1.02153	−	1.02153i
$343$		0			0
$344$			38.5901i			0.112180i
$345$	−379.636	−	284.727i	−1.10039	−	0.825295i
$346$	−0.364391			−0.00105315
$347$	−100.329	−	100.329i	−0.289132	−	0.289132i	0.547605	−	0.836737i	$-0.315540\pi$
$347$	−100.329	−	100.329i	−0.289132	−	0.289132i	−0.836737	+	0.547605i	$0.815540\pi$
$348$	−372.840	+	372.840i	−1.07138	+	1.07138i
$349$		−	298.861i		−	0.856336i	−0.903699	−	0.428168i	$-0.859159\pi$
$349$		−	298.861i		−	0.856336i	0.903699	−	0.428168i	$-0.140841\pi$
$350$		0			0
$351$	−815.358			−2.32296
$352$	13.9089	+	13.9089i	0.0395139	+	0.0395139i
$353$	24.3623	−	24.3623i	0.0690151	−	0.0690151i	−0.671757	−	0.740772i	$-0.734460\pi$
$353$	24.3623	−	24.3623i	0.0690151	−	0.0690151i	0.740772	+	0.671757i	$0.234460\pi$
$354$		−	564.360i		−	1.59424i
$355$	121.022	−	161.362i	0.340906	−	0.454542i
$356$	165.453			0.464757
$357$		0			0
$358$	−43.6356	+	43.6356i	−0.121887	+	0.121887i
$359$			492.087i			1.37072i	0.728206	+	0.685358i	$0.240354\pi$
$359$			492.087i			1.37072i	−0.728206	+	0.685358i	$0.759646\pi$
$360$	−265.362	+	37.9089i	−0.737118	+	0.105303i
$361$	21.2733			0.0589288
$362$	3.68116	+	3.68116i	0.0101689	+	0.0101689i
$363$	407.168	−	407.168i	1.12168	−	1.12168i
$364$		0			0
$365$	−62.7723	−	439.406i	−0.171979	−	1.20385i
$366$	−769.473			−2.10239
$367$	51.4891	+	51.4891i	0.140297	+	0.140297i	0.773767	−	0.633470i	$-0.218370\pi$
$367$	51.4891	+	51.4891i	0.140297	+	0.140297i	−0.633470	+	0.773767i	$0.718370\pi$
$368$	50.7723	−	50.7723i	0.137968	−	0.137968i
$369$		−	114.590i		−	0.310542i
$370$	200.364	+	150.273i	0.541525	+	0.406144i
$371$		0			0
$372$	119.636	+	119.636i	0.321601	+	0.321601i
$373$	−243.271	+	243.271i	−0.652202	+	0.652202i	−0.953523	−	0.301321i	$-0.902572\pi$
$373$	−243.271	+	243.271i	−0.652202	+	0.652202i	0.301321	+	0.953523i	$0.402572\pi$
$374$		−	48.3644i		−	0.129317i
$375$	601.917	−	272.919i	1.60511	−	0.727783i
$376$	−59.4534			−0.158121
$377$	546.226	+	546.226i	1.44887	+	1.44887i
$378$		0			0
$379$		−	33.5683i		−	0.0885708i	−0.999019	−	0.0442854i	$-0.985899\pi$
$379$		−	33.5683i		−	0.0885708i	0.999019	−	0.0442854i	$-0.0141011\pi$
$380$	−110.590	+	147.453i	−0.291026	+	0.388035i
$381$	−186.590			−0.489738
$382$	−17.9327	−	17.9327i	−0.0469443	−	0.0469443i
$383$	508.693	−	508.693i	1.32818	−	1.32818i	0.421223	−	0.906957i	$-0.361601\pi$
$383$	508.693	−	508.693i	1.32818	−	1.32818i	0.906957	−	0.421223i	$-0.138399\pi$
$384$		−	59.8178i		−	0.155776i
$385$		0			0
$386$	−300.725			−0.779079
$387$	182.863	+	182.863i	0.472515	+	0.472515i
$388$	91.5445	−	91.5445i	0.235939	−	0.235939i
$389$			531.089i			1.36527i	0.730761	+	0.682634i	$0.239166\pi$
$389$			531.089i			1.36527i	−0.730761	+	0.682634i	$0.760834\pi$
$390$	81.9089	+	573.362i	0.210023	+	1.47016i
$391$	−176.547			−0.451526
$392$		0			0
$393$	−262.043	+	262.043i	−0.666777	+	0.666777i
$394$		−	82.1822i		−	0.208584i
$395$	−404.816	−	303.612i	−1.02485	−	0.768637i
$396$	131.818			0.332873
$397$	−190.137	−	190.137i	−0.478934	−	0.478934i	0.425857	−	0.904791i	$-0.359973\pi$
$397$	−190.137	−	190.137i	−0.478934	−	0.478934i	−0.904791	+	0.425857i	$0.859973\pi$
$398$	−301.545	+	301.545i	−0.757650	+	0.757650i
$399$		0			0
$400$	28.0000	+	96.0000i	0.0700000	+	0.240000i
$401$	552.540			1.37791			0.688953	−	0.724806i	$-0.258071\pi$
$401$	552.540			1.37791			0.688953	+	0.724806i	$0.258071\pi$
$402$	−170.362	−	170.362i	−0.423787	−	0.423787i
$403$	175.271	−	175.271i	0.434916	−	0.434916i
$404$		−	286.998i		−	0.710391i
$405$	−323.043	+	430.725i	−0.797638	+	1.06352i
$406$		0			0
$407$	−87.0890	−	87.0890i	−0.213978	−	0.213978i
$408$	−104.000	+	104.000i	−0.254902	+	0.254902i
$409$		−	125.317i		−	0.306398i	−0.988195	−	0.153199i	$-0.951042\pi$
$409$		−	125.317i		−	0.306398i	0.988195	−	0.153199i	$-0.0489575\pi$
$410$	−42.3188	+	6.04555i	−0.103217	+	0.0147452i
$411$	50.6377			0.123206
$412$	−79.4772	−	79.4772i	−0.192906	−	0.192906i
$413$		0			0
$414$		−	481.180i		−	1.16227i
$415$	51.1247	+	357.873i	0.123192	+	0.862345i
$416$	−87.6356			−0.210663
$417$	−198.228	−	198.228i	−0.475366	−	0.475366i
$418$	64.0911	−	64.0911i	0.153328	−	0.153328i
$419$		−	116.269i		−	0.277492i	−0.990328	−	0.138746i	$-0.955693\pi$
$419$		−	116.269i		−	0.277492i	0.990328	−	0.138746i	$-0.0443072\pi$
$420$		0			0
$421$	534.449			1.26948			0.634738	−	0.772728i	$-0.281108\pi$
$421$	534.449			1.26948			0.634738	+	0.772728i	$0.281108\pi$
$422$	177.703	+	177.703i	0.421097	+	0.421097i
$423$	−281.727	+	281.727i	−0.666021	+	0.666021i
$424$			32.1822i			0.0759014i
$425$	118.226	−	215.588i	0.278178	−	0.507266i
$426$	301.636			0.708065
$427$		0			0
$428$	84.8395	−	84.8395i	0.198223	−	0.198223i
$429$		−	284.816i		−	0.663906i
$430$	57.8851	−	77.1801i	0.134616	−	0.179489i
$431$	−477.473			−1.10783			−0.553913	−	0.832575i	$-0.686866\pi$
$431$	−477.473			−1.10783			−0.553913	+	0.832575i	$0.686866\pi$
$432$	−148.863	−	148.863i	−0.344591	−	0.344591i
$433$	542.271	−	542.271i	1.25236	−	1.25236i	0.297699	−	0.954660i	$-0.403781\pi$
$433$	542.271	−	542.271i	1.25236	−	1.25236i	0.954660	−	0.297699i	$-0.0962190\pi$
$434$		0			0
$435$	1304.94	−	186.420i	2.99986	−	0.428551i
$436$	74.5466			0.170978
$437$	−233.954	−	233.954i	−0.535365	−	0.535365i
$438$	469.362	−	469.362i	1.07160	−	1.07160i
$439$			268.547i			0.611723i	0.952076	+	0.305862i	$0.0989445\pi$
$439$			268.547i			0.611723i	−0.952076	+	0.305862i	$0.901055\pi$
$440$	−6.95445	−	48.6812i	−0.0158056	−	0.110639i
$441$		0			0
$442$	152.364	+	152.364i	0.344716	+	0.344716i
$443$	62.3525	−	62.3525i	0.140751	−	0.140751i	−0.633221	−	0.773971i	$-0.718267\pi$
$443$	62.3525	−	62.3525i	0.140751	−	0.140751i	0.773971	+	0.633221i	$0.218267\pi$
$444$			374.542i			0.843564i
$445$	−330.907	−	248.180i	−0.743611	−	0.557708i
$446$	498.226			1.11710
$447$	−781.711	−	781.711i	−1.74879	−	1.74879i
$448$		0			0
$449$			100.410i			0.223630i	0.993729	+	0.111815i	$0.0356664\pi$
$449$			100.410i			0.223630i	−0.993729	+	0.111815i	$0.964334\pi$
$450$	587.588	+	322.226i	1.30575	+	0.716057i
$451$	21.0217			0.0466114
$452$	−237.271	−	237.271i	−0.524936	−	0.524936i
$453$	−605.996	+	605.996i	−1.33774	+	1.33774i
$454$		−	58.6377i		−	0.129158i
$455$		0			0
$456$	−275.636			−0.604464
$457$	−491.905	−	491.905i	−1.07638	−	1.07638i	−0.996831	−	0.0795469i	$-0.974653\pi$
$457$	−491.905	−	491.905i	−1.07638	−	1.07638i	−0.0795469	−	0.996831i	$-0.525347\pi$
$458$	315.089	−	315.089i	0.687967	−	0.687967i
$459$			517.631i			1.12774i
$460$	−177.703	+	25.3861i	−0.386311	+	0.0551872i
$461$	191.636			0.415695			0.207848	−	0.978161i	$-0.433354\pi$
$461$	191.636			0.415695			0.207848	+	0.978161i	$0.433354\pi$
$462$		0			0
$463$	268.079	−	268.079i	0.579005	−	0.579005i	−0.355624	−	0.934629i	$-0.615732\pi$
$463$	268.079	−	268.079i	0.579005	−	0.579005i	0.934629	+	0.355624i	$0.115732\pi$
$464$			199.453i			0.429856i
$465$	−59.8178	−	418.725i	−0.128640	−	0.900483i
$466$	−162.725			−0.349194
$467$	−136.487	−	136.487i	−0.292264	−	0.292264i	0.545710	−	0.837974i	$-0.316260\pi$
$467$	−136.487	−	136.487i	−0.292264	−	0.292264i	−0.837974	+	0.545710i	$0.816260\pi$
$468$	−415.271	+	415.271i	−0.887332	+	0.887332i
$469$		0			0
$470$	118.907	+	89.1801i	0.252993	+	0.189745i
$471$	728.341			1.54637
$472$	−150.954	−	150.954i	−0.319819	−	0.319819i
$473$	−33.5466	+	33.5466i	−0.0709230	+	0.0709230i
$474$		−	756.725i		−	1.59647i
$475$	442.360	−	129.022i	0.931285	−	0.271625i
$476$		0			0
$477$	152.499	+	152.499i	0.319704	+	0.319704i
$478$	438.725	−	438.725i	0.917834	−	0.917834i
$479$			741.545i			1.54811i	0.633119	+	0.774055i	$0.281775\pi$
$479$			741.545i			1.54811i	−0.633119	+	0.774055i	$0.718225\pi$
$480$	−89.7267	+	119.636i	−0.186931	+	0.249241i
$481$	548.720			1.14079
$482$	−156.182	−	156.182i	−0.324029	−	0.324029i
$483$		0			0
$484$		−	217.818i		−	0.450037i
$485$	−320.406	+	45.7723i	−0.660630	+	0.0943758i
$486$	−135.271			−0.278336
$487$	−557.406	−	557.406i	−1.14457	−	1.14457i	−0.987604	−	0.156966i	$-0.949829\pi$
$487$	−557.406	−	557.406i	−1.14457	−	1.14457i	−0.156966	−	0.987604i	$-0.550171\pi$
$488$	−205.818	+	205.818i	−0.421758	+	0.421758i
$489$			502.677i			1.02797i
$490$		0			0
$491$	−232.000			−0.472505			−0.236253	−	0.971692i	$-0.575919\pi$
$491$	−232.000			−0.472505			−0.236253	+	0.971692i	$0.575919\pi$
$492$	−45.2039	−	45.2039i	−0.0918779	−	0.0918779i
$493$	346.772	−	346.772i	0.703392	−	0.703392i
$494$			403.818i			0.817445i
$495$	−263.636	−	197.727i	−0.532597	−	0.399448i
$496$	64.0000			0.129032
$497$		0			0
$498$	−382.271	+	382.271i	−0.767613	+	0.767613i
$499$			658.566i			1.31977i	0.751366	+	0.659886i	$0.229395\pi$
$499$			658.566i			1.31977i	−0.751366	+	0.659886i	$0.770605\pi$
$500$	88.0000	−	234.000i	0.176000	−	0.468000i
$501$	1001.86			1.99972
$502$	185.727	+	185.727i	0.369974	+	0.369974i
$503$	−230.055	+	230.055i	−0.457367	+	0.457367i	−0.897790	−	0.440424i	$-0.854828\pi$
$503$	−230.055	+	230.055i	−0.457367	+	0.457367i	0.440424	+	0.897790i	$0.354828\pi$
$504$		0			0
$505$	−430.497	+	573.996i	−0.852469	+	1.13663i
$506$	88.2733			0.174453
$507$	265.442	+	265.442i	0.523553	+	0.523553i
$508$	−49.9089	+	49.9089i	−0.0982459	+	0.0982459i
$509$			121.590i			0.238880i	0.992841	+	0.119440i	$0.0381100\pi$
$509$			121.590i			0.238880i	−0.992841	+	0.119440i	$0.961890\pi$
$510$	364.000	−	52.0000i	0.713725	−	0.101961i
$511$		0			0
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−685.950	+	685.950i	−1.33714	+	1.33714i
$514$			337.362i			0.656347i
$515$	39.7386	+	278.170i	0.0771624	+	0.540136i
$516$	144.273			0.279599
$517$	−51.6832	−	51.6832i	−0.0999676	−	0.0999676i
$518$		0			0
$519$			1.36232i			0.00262489i
$520$	175.271	+	131.453i	0.337060	+	0.252795i
$521$	488.269			0.937177			0.468588	−	0.883417i	$-0.344763\pi$
$521$	488.269			0.937177			0.468588	+	0.883417i	$0.344763\pi$
$522$	945.132	+	945.132i	1.81060	+	1.81060i
$523$	−461.952	+	461.952i	−0.883274	+	0.883274i	−0.993866	−	0.110592i	$-0.964725\pi$
$523$	−461.952	+	461.952i	−0.883274	+	0.883274i	0.110592	+	0.993866i	$0.464725\pi$
$524$			140.182i			0.267523i
$525$		0			0
$526$	464.523			0.883123
$527$	−111.271	−	111.271i	−0.211141	−	0.211141i
$528$	52.0000	−	52.0000i	0.0984848	−	0.0984848i
$529$			206.772i			0.390874i
$530$	48.2733	−	64.3644i	0.0910817	−	0.121442i
$531$	−1430.63			−2.69422
$532$		0			0
$533$	−66.2257	+	66.2257i	−0.124251	+	0.124251i
$534$		−	618.566i		−	1.15836i
$535$	−296.938	+	42.4198i	−0.555025	+	0.0792893i
$536$	−91.1366			−0.170031
$537$	163.137	+	163.137i	0.303793	+	0.303793i
$538$	286.180	−	286.180i	0.531933	−	0.531933i
$539$		0			0
$540$	74.4317	+	521.022i	0.137836	+	0.964855i
$541$	443.586			0.819937			0.409968	−	0.912100i	$-0.365540\pi$
$541$	443.586			0.819937			0.409968	+	0.912100i	$0.365540\pi$
$542$	409.521	+	409.521i	0.755573	+	0.755573i
$543$	13.7624	−	13.7624i	0.0253452	−	0.0253452i
$544$			55.6356i			0.102271i
$545$	−149.093	−	111.820i	−0.273565	−	0.205174i
$546$		0			0
$547$	−686.507	−	686.507i	−1.25504	−	1.25504i	−0.953432	−	0.301608i	$-0.902477\pi$
$547$	−686.507	−	686.507i	−1.25504	−	1.25504i	−0.301608	−	0.953432i	$-0.597523\pi$
$548$	13.5445	−	13.5445i	0.0247163	−	0.0247163i
$549$			1950.58i			3.55297i
$550$	−59.1128	+	107.794i	−0.107478	+	0.195989i
$551$	919.065			1.66799
$552$	−189.818	−	189.818i	−0.343873	−	0.343873i
$553$		0			0
$554$			23.0021i			0.0415200i
$555$	561.814	−	749.085i	1.01228	−	1.34970i
$556$	−106.043			−0.190726
$557$	32.2277	+	32.2277i	0.0578595	+	0.0578595i	0.735444	−	0.677585i	$-0.236973\pi$
$557$	32.2277	+	32.2277i	0.0578595	+	0.0578595i	−0.677585	+	0.735444i	$0.736973\pi$
$558$	303.271	−	303.271i	0.543497	−	0.543497i
$559$		−	211.366i		−	0.378115i
$560$		0			0
$561$	−180.816			−0.322310
$562$	−302.542	−	302.542i	−0.538332	−	0.538332i
$563$	506.602	−	506.602i	0.899826	−	0.899826i	−0.0955945	−	0.995420i	$-0.530475\pi$
$563$	506.602	−	506.602i	0.899826	−	0.899826i	0.995420	+	0.0955945i	$0.0304752\pi$
$564$			222.273i			0.394102i
$565$	118.636	+	830.449i	0.209975	+	1.46982i
$566$	224.087			0.395913
$567$		0			0
$568$	80.6812	−	80.6812i	0.142044	−	0.142044i
$569$		−	836.087i		−	1.46940i	−0.678394	−	0.734699i	$-0.737324\pi$
$569$		−	836.087i		−	1.46940i	0.678394	−	0.734699i	$-0.262676\pi$
$570$	551.271	+	413.453i	0.967142	+	0.725357i
$571$	1034.65			1.81200			0.906001	−	0.423275i	$-0.139120\pi$
$571$	1034.65			1.81200			0.906001	+	0.423275i	$0.139120\pi$
$572$	−76.1822	−	76.1822i	−0.133186	−	0.133186i
$573$	−67.0435	+	67.0435i	−0.117004	+	0.117004i
$574$		0			0
$575$	393.485	+	215.782i	0.684322	+	0.375273i
$576$	−151.636			−0.263256
$577$	−84.5010	−	84.5010i	−0.146449	−	0.146449i	0.630081	−	0.776530i	$-0.283022\pi$
$577$	−84.5010	−	84.5010i	−0.146449	−	0.146449i	−0.776530	+	0.630081i	$0.783022\pi$
$578$	−192.271	+	192.271i	−0.332649	+	0.332649i
$579$			1124.29i			1.94178i
$580$	299.180	−	398.907i	0.515828	−	0.687770i
$581$		0			0
$582$	−342.249	−	342.249i	−0.588058	−	0.588058i
$583$	−27.9762	+	27.9762i	−0.0479866	+	0.0479866i
$584$		−	251.089i		−	0.429947i
$585$	1453.45	−	207.636i	2.48453	−	0.354933i
$586$	−200.364			−0.341919
$587$	808.313	+	808.313i	1.37702	+	1.37702i	0.849607	+	0.527416i	$0.176839\pi$
$587$	808.313	+	808.313i	1.37702	+	1.37702i	0.527416	+	0.849607i	$0.323161\pi$
$588$		0			0
$589$		−	294.907i		−	0.500691i
$590$	75.4772	+	528.341i	0.127928	+	0.895493i
$591$	−307.247			−0.519877
$592$	100.182	+	100.182i	0.169227	+	0.169227i
$593$	63.1822	−	63.1822i	0.106547	−	0.106547i	−0.651824	−	0.758370i	$-0.725996\pi$
$593$	63.1822	−	63.1822i	0.106547	−	0.106547i	0.758370	+	0.651824i	$0.225996\pi$
$594$		−	258.816i		−	0.435717i
$595$		0			0
$596$	−418.182			−0.701648
$597$	1127.36	+	1127.36i	1.88837	+	1.88837i
$598$	−278.091	+	278.091i	−0.465035	+	0.465035i
$599$		−	389.362i		−	0.650021i	−0.945710	−	0.325010i	$-0.894632\pi$
$599$		−	389.362i		−	0.650021i	0.945710	−	0.325010i	$-0.105368\pi$
$600$	358.907	−	104.681i	0.598178	−	0.174469i
$601$	−478.638			−0.796402			−0.398201	−	0.917298i	$-0.630365\pi$
$601$	−478.638			−0.796402			−0.398201	+	0.917298i	$0.630365\pi$
$602$		0			0
$603$	−431.861	+	431.861i	−0.716188	+	0.716188i
$604$			324.182i			0.536725i
$605$	−326.727	+	435.636i	−0.540044	+	0.720059i
$606$	−1072.97			−1.77058
$607$	−452.780	−	452.780i	−0.745931	−	0.745931i	0.227781	−	0.973712i	$-0.426853\pi$
$607$	−452.780	−	452.780i	−0.745931	−	0.745931i	−0.973712	+	0.227781i	$0.926853\pi$
$608$	−73.7267	+	73.7267i	−0.121261	+	0.121261i
$609$		0			0
$610$	720.362	−	102.909i	1.18092	−	0.168703i
$611$	325.640			0.532962
$612$	263.636	+	263.636i	0.430777	+	0.430777i
$613$	−807.041	+	807.041i	−1.31654	+	1.31654i	−0.400051	+	0.916493i	$0.631008\pi$
$613$	−807.041	+	807.041i	−1.31654	+	1.31654i	−0.916493	+	0.400051i	$0.868992\pi$
$614$		−	485.204i		−	0.790234i
$615$	22.6020	+	158.214i	0.0367512	+	0.257258i
$616$		0			0
$617$	15.0890	+	15.0890i	0.0244555	+	0.0244555i	0.719229	−	0.694773i	$-0.244495\pi$
$617$	15.0890	+	15.0890i	0.0244555	+	0.0244555i	−0.694773	+	0.719229i	$0.744495\pi$
$618$	−297.135	+	297.135i	−0.480800	+	0.480800i
$619$		−	143.976i		−	0.232595i	−0.993214	−	0.116297i	$-0.962897\pi$
$619$		−	143.976i		−	0.232595i	0.993214	−	0.116297i	$-0.0371026\pi$
$620$	−128.000	−	96.0000i	−0.206452	−	0.154839i
$621$	−944.766			−1.52136
$622$	7.47723	+	7.47723i	0.0120213	+	0.0120213i
$623$		0			0
$624$			327.636i			0.525057i
$625$	−527.000	+	336.000i	−0.843200	+	0.537600i
$626$	−846.178			−1.35172
$627$	−239.612	−	239.612i	−0.382156	−	0.382156i
$628$	194.816	−	194.816i	0.310216	−	0.310216i
$629$		−	348.356i		−	0.553825i
$630$		0			0
$631$	395.200			0.626307			0.313154	−	0.949703i	$-0.398615\pi$
$631$	395.200			0.626307			0.313154	+	0.949703i	$0.398615\pi$
$632$	−202.408	−	202.408i	−0.320266	−	0.320266i
$633$	664.362	−	664.362i	1.04955	−	1.04955i
$634$			576.000i			0.908517i
$635$	174.681	−	24.9545i	0.275088	−	0.0392983i
$636$	120.317			0.189177
$637$		0			0
$638$	−173.386	+	173.386i	−0.271765	+	0.271765i
$639$		−	764.634i		−	1.19661i
$640$	8.00000	+	56.0000i	0.0125000	+	0.0875000i
$641$	−100.683			−0.157072			−0.0785361	−	0.996911i	$-0.525025\pi$
$641$	−100.683			−0.157072			−0.0785361	+	0.996911i	$0.525025\pi$
$642$	−317.182	−	317.182i	−0.494053	−	0.494053i
$643$	−301.770	+	301.770i	−0.469316	+	0.469316i	−0.901693	−	0.432377i	$-0.857675\pi$
$643$	−301.770	+	301.770i	−0.469316	+	0.469316i	0.432377	+	0.901693i	$0.357675\pi$
$644$		0			0
$645$	−288.547	−	216.410i	−0.447359	−	0.335519i
$646$	256.364			0.396849
$647$	379.125	+	379.125i	0.585973	+	0.585973i	0.936538	−	0.350565i	$-0.114010\pi$
$647$	379.125	+	379.125i	0.585973	+	0.585973i	−0.350565	+	0.936538i	$0.614010\pi$
$648$	−215.362	+	215.362i	−0.332349	+	0.332349i
$649$		−	262.451i		−	0.404393i
$650$	−153.362	−	525.814i	−0.235942	−	0.808944i
$651$		0			0
$652$	134.455	+	134.455i	0.206220	+	0.206220i
$653$	−687.089	+	687.089i	−1.05220	+	1.05220i	−0.0536436	+	0.998560i	$0.517083\pi$
$653$	−687.089	+	687.089i	−1.05220	+	1.05220i	−0.998560	+	0.0536436i	$0.982917\pi$
$654$		−	278.701i		−	0.426148i
$655$	210.273	−	280.364i	0.321028	−	0.428037i
$656$	−24.1822			−0.0368631
$657$	−1189.81	−	1189.81i	−1.81098	−	1.81098i
$658$		0			0
$659$			735.842i			1.11660i	0.829638	+	0.558302i	$0.188547\pi$
$659$			735.842i			1.11660i	−0.829638	+	0.558302i	$0.811453\pi$
$660$	−182.000	+	26.0000i	−0.275758	+	0.0393939i
$661$	−46.1801			−0.0698640			−0.0349320	−	0.999390i	$-0.511121\pi$
$661$	−46.1801			−0.0698640			−0.0349320	+	0.999390i	$0.511121\pi$
$662$	−236.634	−	236.634i	−0.357452	−	0.357452i
$663$	569.631	−	569.631i	0.859173	−	0.859173i
$664$			204.499i			0.307980i
$665$		0			0
$666$	949.449			1.42560
$667$	632.919	+	632.919i	0.948904	+	0.948904i
$668$	267.976	−	267.976i	0.401162	−	0.401162i
$669$		−	1862.67i		−	2.78426i
$670$	182.273	+	136.705i	0.272050	+	0.204037i
$671$	−357.837			−0.533290
$672$		0			0
$673$	−122.772	+	122.772i	−0.182425	+	0.182425i	−0.792412	−	0.609986i	$-0.791175\pi$
$673$	−122.772	+	122.772i	−0.182425	+	0.182425i	0.609986	+	0.792412i	$0.291175\pi$
$674$		−	632.542i		−	0.938490i
$675$	632.669	−	1153.69i	0.937288	−	1.70917i
$676$	142.000			0.210059
$677$	244.364	+	244.364i	0.360952	+	0.360952i	0.864163	−	0.503211i	$-0.167848\pi$
$677$	244.364	+	244.364i	0.360952	+	0.360952i	−0.503211	+	0.864163i	$0.667848\pi$
$678$	−887.065	+	887.065i	−1.30836	+	1.30836i
$679$		0			0
$680$	83.4534	−	111.271i	0.122726	−	0.163634i
$681$	−219.224			−0.321914
$682$	55.6356	+	55.6356i	0.0815771	+	0.0815771i
$683$	501.624	−	501.624i	0.734442	−	0.734442i	−0.237055	−	0.971496i	$-0.576182\pi$
$683$	501.624	−	501.624i	0.734442	−	0.734442i	0.971496	+	0.237055i	$0.0761820\pi$
$684$			698.725i			1.02153i
$685$	−47.4058	+	6.77226i	−0.0692055	+	0.00988650i
$686$		0			0
$687$	−1178.00	−	1178.00i	−1.71470	−	1.71470i
$688$	38.5901	−	38.5901i	0.0560902	−	0.0560902i
$689$		−	176.269i		−	0.255833i
$690$	94.9089	+	664.362i	0.137549	+	0.962844i
$691$	−1144.66			−1.65652			−0.828261	−	0.560342i	$-0.810670\pi$
$691$	−1144.66			−1.65652			−0.828261	+	0.560342i	$0.810670\pi$
$692$	0.364391	+	0.364391i	0.000526576	+	0.000526576i
$693$		0			0
$694$			200.657i			0.289132i
$695$	212.087	+	159.065i	0.305161	+	0.228871i
$696$	745.679			1.07138
$697$	42.0435	+	42.0435i	0.0603206	+	0.0603206i
$698$	−298.861	+	298.861i	−0.428168	+	0.428168i
$699$			608.364i			0.870335i
$700$		0			0
$701$	496.362			0.708077			0.354039	−	0.935231i	$-0.384808\pi$
$701$	496.362			0.708077			0.354039	+	0.935231i	$0.384808\pi$
$702$	815.358	+	815.358i	1.16148	+	1.16148i
$703$	461.631	−	461.631i	0.656659	−	0.656659i
$704$		−	27.8178i		−	0.0395139i
$705$	333.410	−	444.547i	0.472922	−	0.630563i
$706$	−48.7246			−0.0690151
$707$		0			0
$708$	−564.360	+	564.360i	−0.797119	+	0.797119i
$709$			325.950i			0.459732i	0.973222	+	0.229866i	$0.0738289\pi$
$709$			325.950i			0.459732i	−0.973222	+	0.229866i	$0.926171\pi$
$710$	−282.384	+	40.3406i	−0.397724	+	0.0568177i
$711$	−1918.26			−2.69798
$712$	−165.453	−	165.453i	−0.232378	−	0.232378i
$713$	203.089	−	203.089i	0.284837	−	0.284837i
$714$		0			0
$715$	38.0911	+	266.638i	0.0532743	+	0.372920i
$716$	87.2712			0.121887
$717$	−1640.22	−	1640.22i	−2.28762	−	2.28762i
$718$	492.087	−	492.087i	0.685358	−	0.685358i
$719$			627.152i			0.872256i	0.899885	+	0.436128i	$0.143651\pi$
$719$			627.152i			0.872256i	−0.899885	+	0.436128i	$0.856349\pi$
$720$	303.271	+	227.453i	0.421210	+	0.315908i
$721$		0			0
$722$	−21.2733	−	21.2733i	−0.0294644	−	0.0294644i
$723$	−583.905	+	583.905i	−0.807614	+	0.807614i
$724$		−	7.36232i		−	0.0101689i
$725$	−1196.72	+	349.043i	−1.65065	+	0.481439i
$726$	−814.336			−1.12168
$727$	9.62370	+	9.62370i	0.0132376	+	0.0132376i	0.713695	−	0.700457i	$-0.247020\pi$
$727$	9.62370	+	9.62370i	0.0132376	+	0.0132376i	−0.700457	+	0.713695i	$0.747020\pi$
$728$		0			0
$729$		−	463.404i		−	0.635670i
$730$	−376.634	+	502.178i	−0.515936	+	0.687915i
$731$	−134.186			−0.183565
$732$	769.473	+	769.473i	1.05119	+	1.05119i
$733$	−154.683	+	154.683i	−0.211028	+	0.211028i	−0.804704	−	0.593676i	$-0.797676\pi$
$733$	−154.683	+	154.683i	−0.211028	+	0.211028i	0.593676	+	0.804704i	$0.297676\pi$
$734$		−	102.978i		−	0.140297i
$735$		0			0
$736$	−101.545			−0.137968
$737$	−79.2257	−	79.2257i	−0.107498	−	0.107498i
$738$	−114.590	+	114.590i	−0.155271	+	0.155271i
$739$			540.111i			0.730867i	0.930837	+	0.365434i	$0.119079\pi$
$739$			540.111i			0.730867i	−0.930837	+	0.365434i	$0.880921\pi$
$740$	−50.0911	−	350.638i	−0.0676907	−	0.473835i
$741$	1509.72			2.03741
$742$		0			0
$743$	142.376	−	142.376i	0.191624	−	0.191624i	−0.604774	−	0.796397i	$-0.706736\pi$
$743$	142.376	−	142.376i	0.191624	−	0.191624i	0.796397	+	0.604774i	$0.206736\pi$
$744$		−	239.271i		−	0.321601i
$745$	836.364	+	627.273i	1.12264	+	0.841978i
$746$	486.542			0.652202
$747$	969.041	+	969.041i	1.29724	+	1.29724i
$748$	−48.3644	+	48.3644i	−0.0646583	+	0.0646583i
$749$		0			0
$750$	−874.835	−	328.998i	−1.16645	−	0.438664i
$751$	−1204.09			−1.60331			−0.801656	−	0.597786i	$-0.796047\pi$
$751$	−1204.09			−1.60331			−0.801656	+	0.597786i	$0.796047\pi$
$752$	59.4534	+	59.4534i	0.0790604	+	0.0790604i
$753$	694.360	−	694.360i	0.922125	−	0.922125i
$754$		−	1092.45i		−	1.44887i
$755$	486.273	−	648.364i	0.644071	−	0.858761i
$756$		0			0
$757$	−297.410	−	297.410i	−0.392880	−	0.392880i	0.482833	−	0.875713i	$-0.339608\pi$
$757$	−297.410	−	297.410i	−0.392880	−	0.392880i	−0.875713	+	0.482833i	$0.839608\pi$
$758$	−33.5683	+	33.5683i	−0.0442854	+	0.0442854i
$759$		−	330.020i		−	0.434809i
$760$	258.043	−	36.8634i	0.339531	−	0.0485044i
$761$	736.542			0.967861			0.483931	−	0.875106i	$-0.339209\pi$
$761$	736.542			0.967861			0.483931	+	0.875106i	$0.339209\pi$
$762$	186.590	+	186.590i	0.244869	+	0.244869i
$763$		0			0
$764$			35.8654i			0.0469443i
$765$	−131.818	−	922.725i	−0.172311	−	1.20618i
$766$	−1017.39			−1.32818
$767$	826.812	+	826.812i	1.07798	+	1.07798i
$768$	−59.8178	+	59.8178i	−0.0778878	+	0.0778878i
$769$		−	1006.45i		−	1.30877i	−0.756160	−	0.654387i	$-0.772927\pi$
$769$		−	1006.45i		−	1.30877i	0.756160	−	0.654387i	$-0.227073\pi$
$770$		0			0
$771$	1261.27			1.63588
$772$	300.725	+	300.725i	0.389540	+	0.389540i
$773$	−568.586	+	568.586i	−0.735557	+	0.735557i	−0.971715	−	0.236157i	$-0.924112\pi$
$773$	−568.586	+	568.586i	−0.735557	+	0.735557i	0.236157	+	0.971715i	$0.424112\pi$
$774$		−	365.727i		−	0.472515i
$775$	112.000	+	384.000i	0.144516	+	0.495484i
$776$	−183.089			−0.235939
$777$		0			0
$778$	531.089	−	531.089i	0.682634	−	0.682634i
$779$			111.430i			0.143042i
$780$	491.453	−	655.271i	0.630068	−	0.840091i
$781$	140.273			0.179607
$782$	176.547	+	176.547i	0.225763	+	0.225763i
$783$	1855.71	−	1855.71i	2.37000	−	2.37000i
$784$		0			0
$785$	−681.855	+	97.4079i	−0.868605	+	0.124086i
$786$	524.087			0.666777
$787$	471.212	+	471.212i	0.598744	+	0.598744i	0.939978	−	0.341234i	$-0.110845\pi$
$787$	471.212	+	471.212i	0.598744	+	0.598744i	−0.341234	+	0.939978i	$0.610845\pi$
$788$	−82.1822	+	82.1822i	−0.104292	+	0.104292i
$789$		−	1736.67i		−	2.20110i
$790$	101.204	+	708.428i	0.128106	+	0.896744i
$791$		0			0
$792$	−131.818	−	131.818i	−0.166437	−	0.166437i
$793$	1127.31	−	1127.31i	1.42158	−	1.42158i
$794$			380.273i			0.478934i
$795$	−240.634	−	180.475i	−0.302684	−	0.227013i
$796$	603.089			0.757650
$797$	−202.408	−	202.408i	−0.253962	−	0.253962i	0.568631	−	0.822593i	$-0.307473\pi$
$797$	−202.408	−	202.408i	−0.253962	−	0.253962i	−0.822593	+	0.568631i	$0.807473\pi$
$798$		0			0
$799$		−	206.733i		−	0.258740i
$800$	68.0000	−	124.000i	0.0850000	−	0.155000i
$801$	−1568.04			−1.95760
$802$	−552.540	−	552.540i	−0.688953	−	0.688953i
$803$	218.273	−	218.273i	0.271822	−	0.271822i
$804$			340.725i			0.423787i
$805$		0			0
$806$	−350.542			−0.434916
$807$	−1069.92	−	1069.92i	−1.32580	−	1.32580i
$808$	−286.998	+	286.998i	−0.355195	+	0.355195i
$809$		−	159.364i		−	0.196989i	−0.995138	−	0.0984947i	$-0.968597\pi$
$809$		−	159.364i		−	0.196989i	0.995138	−	0.0984947i	$-0.0314027\pi$
$810$	753.768	−	107.681i	0.930578	−	0.132940i
$811$	−741.545			−0.914358			−0.457179	−	0.889375i	$-0.651140\pi$
$811$	−741.545			−0.914358			−0.457179	+	0.889375i	$0.651140\pi$
$812$		0			0
$813$	1531.04	−	1531.04i	1.88320	−	1.88320i
$814$			174.178i			0.213978i
$815$	−67.2277	−	470.594i	−0.0824880	−	0.577416i
$816$	208.000			0.254902
$817$	−177.820	−	177.820i	−0.217650	−	0.217650i
$818$	−125.317	+	125.317i	−0.153199	+	0.153199i
$819$		0			0
$820$	48.3644	+	36.2733i	0.0589810	+	0.0442357i
$821$	1577.90			1.92193			0.960963	−	0.276678i	$-0.0892336\pi$
$821$	1577.90			1.92193			0.960963	+	0.276678i	$0.0892336\pi$
$822$	−50.6377	−	50.6377i	−0.0616030	−	0.0616030i
$823$	−430.238	+	430.238i	−0.522767	+	0.522767i	−0.918406	−	0.395639i	$-0.870523\pi$
$823$	−430.238	+	430.238i	−0.522767	+	0.522767i	0.395639	+	0.918406i	$0.370523\pi$
$824$			158.954i			0.192906i
$825$	403.000	+	221.000i	0.488485	+	0.267879i
$826$		0			0
$827$	1014.44	+	1014.44i	1.22665	+	1.22665i	0.965223	+	0.261426i	$0.0841929\pi$
$827$	1014.44	+	1014.44i	1.22665	+	1.22665i	0.261426	+	0.965223i	$0.415807\pi$
$828$	−481.180	+	481.180i	−0.581135	+	0.581135i
$829$			397.814i			0.479872i	0.970789	+	0.239936i	$0.0771264\pi$
$829$			397.814i			0.479872i	−0.970789	+	0.239936i	$0.922874\pi$
$830$	306.748	−	408.998i	0.369576	−	0.492769i
$831$	85.9959			0.103485
$832$	87.6356	+	87.6356i	0.105331	+	0.105331i
$833$		0			0
$834$			396.455i			0.475366i
$835$	−937.917	+	133.988i	−1.12325	+	0.160465i
$836$	−128.182			−0.153328
$837$	−595.453	−	595.453i	−0.711414	−	0.711414i
$838$	−116.269	+	116.269i	−0.138746	+	0.138746i
$839$			1475.70i			1.75888i	0.476011	+	0.879439i	$0.342082\pi$
$839$			1475.70i			1.75888i	−0.476011	+	0.879439i	$0.657918\pi$
$840$		0			0
$841$	−1645.35			−1.95643
$842$	−534.449	−	534.449i	−0.634738	−	0.634738i
$843$	−1131.09	+	1131.09i	−1.34174	+	1.34174i
$844$		−	355.406i		−	0.421097i
$845$	−284.000	−	213.000i	−0.336095	−	0.252071i
$846$	563.453			0.666021
$847$		0			0
$848$	32.1822	−	32.1822i	0.0379507	−	0.0379507i
$849$		−	837.774i		−	0.986778i
$850$	−333.814	+	97.3623i	−0.392722	+	0.114544i
$851$	635.810			0.747132
$852$	−301.636	−	301.636i	−0.354032	−	0.354032i
$853$	−307.404	+	307.404i	−0.360380	+	0.360380i	−0.863953	−	0.503573i	$-0.832018\pi$
$853$	−307.404	+	307.404i	−0.360380	+	0.360380i	0.503573	+	0.863953i	$0.332018\pi$
$854$		0			0
$855$	1048.09	−	1397.45i	1.22583	−	1.63444i
$856$	−169.679			−0.198223
$857$	−850.723	−	850.723i	−0.992675	−	0.992675i	0.00729827	−	0.999973i	$-0.497677\pi$
$857$	−850.723	−	850.723i	−0.992675	−	0.992675i	−0.999973	+	0.00729827i	$0.997677\pi$
$858$	−284.816	+	284.816i	−0.331953	+	0.331953i
$859$			917.996i			1.06868i	0.845270	+	0.534340i	$0.179440\pi$
$859$			917.996i			1.06868i	−0.845270	+	0.534340i	$0.820560\pi$
$860$	−135.065	+	19.2950i	−0.157053	+	0.0224361i
$861$		0			0
$862$	477.473	+	477.473i	0.553913	+	0.553913i
$863$	897.821	−	897.821i	1.04035	−	1.04035i	0.0411983	−	0.999151i	$-0.486882\pi$
$863$	897.821	−	897.821i	1.04035	−	1.04035i	0.999151	−	0.0411983i	$-0.0131175\pi$
$864$			297.727i			0.344591i
$865$	−0.182195	−	1.27537i	−0.000210631	−	0.00147441i
$866$	−1084.54			−1.25236
$867$	718.828	+	718.828i	0.829098	+	0.829098i
$868$		0			0
$869$		−	351.909i		−	0.404958i
$870$	−1491.36	−	1118.52i	−1.71420	−	1.28565i
$871$	499.176			0.573107
$872$	−74.5466	−	74.5466i	−0.0854892	−	0.0854892i
$873$	−867.588	+	867.588i	−0.993801	+	0.993801i
$874$			467.909i			0.535365i
$875$		0			0
$876$	−938.725			−1.07160
$877$	285.048	+	285.048i	0.325026	+	0.325026i	0.850691	−	0.525666i	$-0.176184\pi$
$877$	285.048	+	285.048i	0.325026	+	0.325026i	−0.525666	+	0.850691i	$0.676184\pi$
$878$	268.547	−	268.547i	0.305862	−	0.305862i
$879$			749.085i			0.852201i
$880$	−41.7267	+	55.6356i	−0.0474167	+	0.0632223i
$881$	−338.402			−0.384111			−0.192055	−	0.981384i	$-0.561515\pi$
$881$	−338.402			−0.384111			−0.192055	+	0.981384i	$0.561515\pi$
$882$		0			0
$883$	−455.410	+	455.410i	−0.515753	+	0.515753i	−0.916283	−	0.400530i	$-0.868826\pi$
$883$	−455.410	+	455.410i	−0.515753	+	0.515753i	0.400530	+	0.916283i	$0.368826\pi$
$884$		−	304.729i		−	0.344716i
$885$	1975.26	−	282.180i	2.23193	−	0.318848i
$886$	−124.705			−0.140751
$887$	−285.398	−	285.398i	−0.321757	−	0.321757i	0.527684	−	0.849441i	$-0.323060\pi$
$887$	−285.398	−	285.398i	−0.321757	−	0.321757i	−0.849441	+	0.527684i	$0.823060\pi$
$888$	374.542	−	374.542i	0.421782	−	0.421782i
$889$		0			0
$890$	82.7267	+	579.087i	0.0929514	+	0.650659i
$891$	−374.432			−0.420238
$892$	−498.226	−	498.226i	−0.558549	−	0.558549i
$893$	273.957	−	273.957i	0.306782	−	0.306782i
$894$			1563.42i			1.74879i
$895$	−174.542	−	130.907i	−0.195019	−	0.146265i
$896$		0			0
$897$	1039.67	+	1039.67i	1.15906	+	1.15906i
$898$	100.410	−	100.410i	0.111815	−	0.111815i
$899$			797.814i			0.887446i
$900$	−265.362	−	909.814i	−0.294847	−	1.01090i
$901$	−111.905			−0.124201
$902$	−21.0217	−	21.0217i	−0.0233057	−	0.0233057i
$903$		0			0
$904$			474.542i			0.524936i
$905$	−11.0435	+	14.7246i	−0.0122027	+	0.0162703i
$906$	1211.99			1.33774
$907$	−431.350	−	431.350i	−0.475579	−	0.475579i	0.428135	−	0.903715i	$-0.359171\pi$
$907$	−431.350	−	431.350i	−0.475579	−	0.475579i	−0.903715	+	0.428135i	$0.859171\pi$
$908$	−58.6377	+	58.6377i	−0.0645789	+	0.0645789i
$909$			2719.94i			2.99224i
$910$		0			0
$911$	−716.063			−0.786019			−0.393009	−	0.919534i	$-0.628566\pi$
$911$	−716.063			−0.786019			−0.393009	+	0.919534i	$0.628566\pi$
$912$	275.636	+	275.636i	0.302232	+	0.302232i
$913$	−177.772	+	177.772i	−0.194712	+	0.194712i
$914$			983.810i			1.07638i
$915$	−384.737	−	2693.16i	−0.420477	−	2.94334i
$916$	−630.178			−0.687967
$917$		0			0
$918$	517.631	−	517.631i	0.563869	−	0.563869i
$919$		−	257.069i		−	0.279727i	−0.990171	−	0.139864i	$-0.955334\pi$
$919$		−	257.069i		−	0.279727i	0.990171	−	0.139864i	$-0.0446664\pi$
$920$	203.089	+	152.317i	0.220749	+	0.165562i
$921$	−1813.99			−1.96959
$922$	−191.636	−	191.636i	−0.207848	−	0.207848i
$923$	−441.909	+	441.909i	−0.478775	+	0.478775i
$924$		0			0
$925$	−425.774	+	776.412i	−0.460297	+	0.839364i
$926$	−536.158			−0.579005
$927$	753.224	+	753.224i	0.812539	+	0.812539i
$928$	199.453	−	199.453i	0.214928	−	0.214928i
$929$			1275.68i			1.37318i	0.727046	+	0.686588i	$0.240893\pi$
$929$			1275.68i			1.37318i	−0.727046	+	0.686588i	$0.759107\pi$
$930$	−358.907	+	478.542i	−0.385921	+	0.514562i
$931$		0			0
$932$	162.725	+	162.725i	0.174597	+	0.174597i
$933$	27.9545	−	27.9545i	0.0299619	−	0.0299619i
$934$			272.974i			0.292264i
$935$	169.275	−	24.1822i	0.181043	−	0.0258633i
$936$	830.542			0.887332
$937$	589.180	+	589.180i	0.628794	+	0.628794i	0.947765	−	0.318970i	$-0.103337\pi$
$937$	589.180	+	589.180i	0.628794	+	0.628794i	−0.318970	+	0.947765i	$0.603337\pi$
$938$		0			0
$939$			3163.53i			3.36904i
$940$	−29.7267	−	208.087i	−0.0316242	−	0.221369i
$941$	−197.275			−0.209644			−0.104822	−	0.994491i	$-0.533427\pi$
$941$	−197.275			−0.209644			−0.104822	+	0.994491i	$0.533427\pi$
$942$	−728.341	−	728.341i	−0.773185	−	0.773185i
$943$	−76.7365	+	76.7365i	−0.0813749	+	0.0813749i
$944$			301.909i			0.319819i
$945$		0			0
$946$	67.0932			0.0709230
$947$	−1095.42	−	1095.42i	−1.15672	−	1.15672i	−0.985176	−	0.171548i	$-0.945123\pi$
$947$	−1095.42	−	1095.42i	−1.15672	−	1.15672i	−0.171548	−	0.985176i	$-0.554877\pi$
$948$	−756.725	+	756.725i	−0.798233	+	0.798233i
$949$			1375.27i			1.44918i
$950$	−571.382	−	313.339i	−0.601455	−	0.329830i
$951$	2153.44			2.26440
$952$		0			0
$953$	1139.41	−	1139.41i	1.19560	−	1.19560i	0.220128	−	0.975471i	$-0.429353\pi$
$953$	1139.41	−	1139.41i	1.19560	−	1.19560i	0.975471	−	0.220128i	$-0.0706475\pi$
$954$		−	304.998i		−	0.319704i
$955$	53.7981	−	71.7309i	0.0563331	−	0.0751108i
$956$	−877.449			−0.917834
$957$	648.224	+	648.224i	0.677350	+	0.677350i
$958$	741.545	−	741.545i	0.774055	−	0.774055i
$959$		0			0
$960$	209.362	−	29.9089i	0.218086	−	0.0311551i
$961$	−705.000			−0.733611
$962$	−548.720	−	548.720i	−0.570396	−	0.570396i
$963$	−804.043	+	804.043i	−0.834936	+	0.834936i
$964$			312.364i			0.324029i
$965$	−150.362	−	1052.54i	−0.155816	−	1.09071i
$966$		0			0
$967$	−184.424	−	184.424i	−0.190718	−	0.190718i	0.605289	−	0.796006i	$-0.293058\pi$
$967$	−184.424	−	184.424i	−0.190718	−	0.190718i	−0.796006	+	0.605289i	$0.793058\pi$
$968$	−217.818	+	217.818i	−0.225018	+	0.225018i
$969$		−	958.447i		−	0.989110i
$970$	366.178	+	274.634i	0.377503	+	0.283127i
$971$	−1490.18			−1.53468			−0.767342	−	0.641238i	$-0.778421\pi$
$971$	−1490.18			−1.53468			−0.767342	+	0.641238i	$0.778421\pi$
$972$	135.271	+	135.271i	0.139168	+	0.139168i
$973$		0			0
$974$			1114.81i			1.14457i
$975$	−1965.81	+	573.362i	−2.01622	+	0.588064i
$976$	411.636			0.421758
$977$	−744.089	−	744.089i	−0.761606	−	0.761606i	0.215007	−	0.976613i	$-0.431023\pi$
$977$	−744.089	−	744.089i	−0.761606	−	0.761606i	−0.976613	+	0.215007i	$0.931023\pi$
$978$	502.677	−	502.677i	0.513985	−	0.513985i
$979$		−	287.659i		−	0.293830i
$980$		0			0
$981$	−706.495			−0.720178
$982$	232.000	+	232.000i	0.236253	+	0.236253i
$983$	−505.893	+	505.893i	−0.514642	+	0.514642i	−0.915945	−	0.401303i	$-0.868557\pi$
$983$	−505.893	+	505.893i	−0.514642	+	0.514642i	0.401303	+	0.915945i	$0.368557\pi$
$984$			90.4079i			0.0918779i
$985$	287.638	−	41.0911i	0.292018	−	0.0417169i
$986$	−693.545			−0.703392
$987$		0			0
$988$	403.818	−	403.818i	0.408722	−	0.408722i
$989$		−	244.913i		−	0.247637i
$990$	65.9089	+	461.362i	0.0665746	+	0.466023i
$991$	1293.54			1.30528			0.652642	−	0.757667i	$-0.273661\pi$
$991$	1293.54			1.30528			0.652642	+	0.757667i	$0.273661\pi$
$992$	−64.0000	−	64.0000i	−0.0645161	−	0.0645161i
$993$	−884.681	+	884.681i	−0.890918	+	0.890918i
$994$		0			0
$995$	−1206.18	−	904.634i	−1.21224	−	0.909179i
$996$	764.542			0.767613
$997$	−128.224	−	128.224i	−0.128609	−	0.128609i	0.639872	−	0.768481i	$-0.278987\pi$
$997$	−128.224	−	128.224i	−0.128609	−	0.128609i	−0.768481	+	0.639872i	$0.778987\pi$
$998$	658.566	−	658.566i	0.659886	−	0.659886i
$999$		−	1864.18i		−	1.86605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.3.f.e.197.1		4
5.3	odd	4	inner	490.3.f.e.393.1		4
7.3	odd	6		70.3.l.a.37.1	yes	8
7.5	odd	6		70.3.l.a.67.2	yes	8
7.6	odd	2		490.3.f.l.197.2		4
35.3	even	12		70.3.l.a.23.2	✓	8
35.12	even	12		350.3.p.c.193.2		8
35.13	even	4		490.3.f.l.393.2		4
35.17	even	12		350.3.p.c.93.1		8
35.19	odd	6		350.3.p.c.207.1		8
35.24	odd	6		350.3.p.c.107.2		8
35.33	even	12		70.3.l.a.53.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.a.23.2	✓	8	35.3	even	12
70.3.l.a.37.1	yes	8	7.3	odd	6
70.3.l.a.53.1	yes	8	35.33	even	12
70.3.l.a.67.2	yes	8	7.5	odd	6
350.3.p.c.93.1		8	35.17	even	12
350.3.p.c.107.2		8	35.24	odd	6
350.3.p.c.193.2		8	35.12	even	12
350.3.p.c.207.1		8	35.19	odd	6
490.3.f.e.197.1		4	1.1	even	1	trivial
490.3.f.e.393.1		4	5.3	odd	4	inner
490.3.f.l.197.2		4	7.6	odd	2
490.3.f.l.393.2		4	35.13	even	4

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	490.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-3.73861 + 3.73861i) q^{3} +2.00000i q^{4} +(3.00000 - 4.00000i) q^{5} +7.47723 q^{6} +(2.00000 - 2.00000i) q^{8} -18.9545i q^{9} +(-7.00000 + 1.00000i) q^{10} +3.47723 q^{11} +(-7.47723 - 7.47723i) q^{12} +(-10.9545 + 10.9545i) q^{13} +(3.73861 + 26.1703i) q^{15} -4.00000 q^{16} +(6.95445 + 6.95445i) q^{17} +(-18.9545 + 18.9545i) q^{18} +18.4317i q^{19} +(8.00000 + 6.00000i) q^{20} +(-3.47723 - 3.47723i) q^{22} +(-12.6931 + 12.6931i) q^{23} +14.9545i q^{24} +(-7.00000 - 24.0000i) q^{25} +21.9089 q^{26} +(37.2158 + 37.2158i) q^{27} -49.8634i q^{29} +(22.4317 - 29.9089i) q^{30} -16.0000 q^{31} +(4.00000 + 4.00000i) q^{32} +(-13.0000 + 13.0000i) q^{33} -13.9089i q^{34} +37.9089 q^{36} +(-25.0455 - 25.0455i) q^{37} +(18.4317 - 18.4317i) q^{38} -81.9089i q^{39} +(-2.00000 - 14.0000i) q^{40} +6.04555 q^{41} +(-9.64752 + 9.64752i) q^{43} +6.95445i q^{44} +(-75.8178 - 56.8634i) q^{45} +25.3861 q^{46} +(-14.8634 - 14.8634i) q^{47} +(14.9545 - 14.9545i) q^{48} +(-17.0000 + 31.0000i) q^{50} -52.0000 q^{51} +(-21.9089 - 21.9089i) q^{52} +(-8.04555 + 8.04555i) q^{53} -74.4317i q^{54} +(10.4317 - 13.9089i) q^{55} +(-68.9089 - 68.9089i) q^{57} +(-49.8634 + 49.8634i) q^{58} -75.4772i q^{59} +(-52.3406 + 7.47723i) q^{60} -102.909 q^{61} +(16.0000 + 16.0000i) q^{62} -8.00000i q^{64} +(10.9545 + 76.6812i) q^{65} +26.0000 q^{66} +(-22.7842 - 22.7842i) q^{67} +(-13.9089 + 13.9089i) q^{68} -94.9089i q^{69} +40.3406 q^{71} +(-37.9089 - 37.9089i) q^{72} +(62.7723 - 62.7723i) q^{73} +50.0911i q^{74} +(115.897 + 63.5564i) q^{75} -36.8634 q^{76} +(-81.9089 + 81.9089i) q^{78} -101.204i q^{79} +(-12.0000 + 16.0000i) q^{80} -107.681 q^{81} +(-6.04555 - 6.04555i) q^{82} +(-51.1247 + 51.1247i) q^{83} +(48.6812 - 6.95445i) q^{85} +19.2950 q^{86} +(186.420 + 186.420i) q^{87} +(6.95445 - 6.95445i) q^{88} -82.7267i q^{89} +(18.9545 + 132.681i) q^{90} +(-25.3861 - 25.3861i) q^{92} +(59.8178 - 59.8178i) q^{93} +29.7267i q^{94} +(73.7267 + 55.2950i) q^{95} -29.9089 q^{96} +(-45.7723 - 45.7723i) q^{97} -65.9089i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 12 q^{5} + 8 q^{6} + 8 q^{8} - 28 q^{10} - 8 q^{11} - 8 q^{12} + 4 q^{15} - 16 q^{16} - 16 q^{17} - 32 q^{18} + 32 q^{20} + 8 q^{22} + 4 q^{23} - 28 q^{25} + 116 q^{27} + 24 q^{30}+ \cdots + 36 q^{97}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 12 * q^5 + 8 * q^6 + 8 * q^8 - 28 * q^10 - 8 * q^11 - 8 * q^12 + 4 * q^15 - 16 * q^16 - 16 * q^17 - 32 * q^18 + 32 * q^20 + 8 * q^22 + 4 * q^23 - 28 * q^25 + 116 * q^27 + 24 * q^30 - 64 * q^31 + 16 * q^32 - 52 * q^33 + 64 * q^36 - 144 * q^37 + 8 * q^38 - 8 * q^40 + 68 * q^41 + 60 * q^43 - 128 * q^45 - 8 * q^46 + 72 * q^47 + 16 * q^48 - 68 * q^50 - 208 * q^51 - 76 * q^53 - 24 * q^55 - 188 * q^57 - 68 * q^58 - 56 * q^60 - 324 * q^61 + 64 * q^62 + 104 * q^66 - 124 * q^67 + 32 * q^68 + 8 * q^71 - 64 * q^72 + 32 * q^73 + 124 * q^75 - 16 * q^76 - 240 * q^78 - 48 * q^80 - 124 * q^81 - 68 * q^82 - 84 * q^83 - 112 * q^85 - 120 * q^86 + 428 * q^87 - 16 * q^88 + 32 * q^90 + 8 * q^92 + 64 * q^93 + 32 * q^95 - 32 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more