LMFDB - Embedded newform 225.4.p.b.32.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(32,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("225.32");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.p (of order $12$, degree $4$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.2
Character	$\chi$	$=$	225.32
Dual form			225.4.p.b.218.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.29910 - 1.15194i) q^{2} +(4.54171 - 2.52446i) q^{3} +(10.2271 + 5.90461i) q^{4} +(-22.4333 + 5.62113i) q^{6} +(-1.91190 + 7.13532i) q^{7} +(-11.9883 - 11.9883i) q^{8} +(14.2542 - 22.9307i) q^{9} +O(q^{10})$	\(q+(-4.29910 - 1.15194i) q^{2} +(4.54171 - 2.52446i) q^{3} +(10.2271 + 5.90461i) q^{4} +(-22.4333 + 5.62113i) q^{6} +(-1.91190 + 7.13532i) q^{7} +(-11.9883 - 11.9883i) q^{8} +(14.2542 - 22.9307i) q^{9} +(-7.55654 + 4.36277i) q^{11} +(61.3544 + 0.999152i) q^{12} +(19.7704 + 73.7842i) q^{13} +(16.4389 - 28.4731i) q^{14} +(-9.50797 - 16.4683i) q^{16} +(-5.92131 + 5.92131i) q^{17} +(-87.6951 + 82.1614i) q^{18} +106.718i q^{19} +(9.32953 + 37.2331i) q^{21} +(37.5120 - 10.0513i) q^{22} +(-102.465 + 27.4553i) q^{23} +(-84.7110 - 24.1833i) q^{24} -339.980i q^{26} +(6.85080 - 140.129i) q^{27} +(-61.6846 + 61.6846i) q^{28} +(-85.3380 - 147.810i) q^{29} +(-157.999 + 273.662i) q^{31} +(57.0093 + 212.761i) q^{32} +(-23.3059 + 38.8906i) q^{33} +(32.2773 - 18.6353i) q^{34} +(281.176 - 150.349i) q^{36} +(31.7091 + 31.7091i) q^{37} +(122.933 - 458.791i) q^{38} +(276.057 + 285.197i) q^{39} +(298.272 + 172.207i) q^{41} +(2.78172 - 170.816i) q^{42} +(431.220 + 115.545i) q^{43} -103.042 q^{44} +472.133 q^{46} +(227.629 + 60.9929i) q^{47} +(-84.7559 - 50.7917i) q^{48} +(249.789 + 144.216i) q^{49} +(-11.9448 + 41.8410i) q^{51} +(-233.473 + 871.335i) q^{52} +(-60.5508 - 60.5508i) q^{53} +(-190.872 + 594.536i) q^{54} +(108.460 - 62.6197i) q^{56} +(269.405 + 484.682i) q^{57} +(196.609 + 733.754i) q^{58} +(25.4427 - 44.0680i) q^{59} +(-36.1174 - 62.5572i) q^{61} +(994.494 - 994.494i) q^{62} +(136.365 + 145.550i) q^{63} -828.227i q^{64} +(144.994 - 140.347i) q^{66} +(17.1550 - 4.59668i) q^{67} +(-95.5208 + 25.5947i) q^{68} +(-396.055 + 383.362i) q^{69} +109.592i q^{71} +(-445.782 + 104.016i) q^{72} +(144.319 - 144.319i) q^{73} +(-99.7935 - 172.847i) q^{74} +(-630.128 + 1091.41i) q^{76} +(-16.6824 - 62.2595i) q^{77} +(-858.266 - 1544.09i) q^{78} +(140.624 - 81.1891i) q^{79} +(-322.635 - 653.718i) q^{81} +(-1083.93 - 1083.93i) q^{82} +(-74.9883 + 279.860i) q^{83} +(-124.433 + 435.873i) q^{84} +(-1720.76 - 993.479i) q^{86} +(-760.720 - 455.877i) q^{87} +(142.892 + 38.2877i) q^{88} +1107.89 q^{89} -564.273 q^{91} +(-1210.03 - 324.227i) q^{92} +(-26.7358 + 1641.75i) q^{93} +(-908.339 - 524.430i) q^{94} +(796.027 + 822.383i) q^{96} +(-52.9802 + 197.725i) q^{97} +(-907.741 - 907.741i) q^{98} +(-7.67108 + 235.465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) $ 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) $ 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7 - 36 * q^11 + 138 * q^12 + 2 * q^13 + 316 * q^16 + 480 * q^18 + 480 * q^21 + 34 * q^22 - 306 * q^23 - 180 * q^27 + 232 * q^28 - 4 * q^31 + 1770 * q^32 + 294 * q^33 - 216 * q^36 - 136 * q^37 - 114 * q^38 + 1992 * q^41 - 1698 * q^42 + 2 * q^43 - 952 * q^46 - 3462 * q^47 - 4326 * q^48 - 2496 * q^51 + 242 * q^52 - 7128 * q^56 + 2544 * q^57 - 534 * q^58 + 32 * q^61 + 4038 * q^63 + 2892 * q^66 - 610 * q^67 + 2694 * q^68 + 1854 * q^72 + 8 * q^73 + 1368 * q^76 + 6486 * q^77 - 1434 * q^78 + 3012 * q^81 + 3784 * q^82 - 2814 * q^83 + 12480 * q^86 - 4830 * q^87 + 1338 * q^88 + 992 * q^91 - 13152 * q^92 - 8310 * q^93 - 7932 * q^96 - 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−4.29910	−	1.15194i	−1.51996	−	0.407272i	−0.600232	−	0.799826i	$-0.704925\pi$
$2$	−4.29910	−	1.15194i	−1.51996	−	0.407272i	−0.919729	+	0.392553i	$0.871592\pi$
$3$	4.54171	−	2.52446i	0.874052	−	0.485832i
$3$	4.54171	−	2.52446i	0.874052	−	0.485832i
$4$	10.2271	+	5.90461i	1.27839	+	0.738077i
$5$		0			0
$5$		0			0
$6$	−22.4333	+	5.62113i	−1.52639	+	0.382469i
$7$	−1.91190	+	7.13532i	−0.103233	+	0.385271i	−0.998139	−	0.0609842i	$-0.980576\pi$
$7$	−1.91190	+	7.13532i	−0.103233	+	0.385271i	0.894906	+	0.446255i	$0.147243\pi$
$8$	−11.9883	−	11.9883i	−0.529811	−	0.529811i
$9$	14.2542	−	22.9307i	0.527934	−	0.849286i
$10$		0			0
$11$	−7.55654	+	4.36277i	−0.207126	+	0.119584i	−0.599975	−	0.800019i	$-0.704823\pi$
$11$	−7.55654	+	4.36277i	−0.207126	+	0.119584i	0.392849	+	0.919603i	$0.371489\pi$
$12$	61.3544	+	0.999152i	1.47596	+	0.0240359i
$13$	19.7704	+	73.7842i	0.421794	+	1.57416i	0.770825	+	0.637047i	$0.219844\pi$
$13$	19.7704	+	73.7842i	0.421794	+	1.57416i	−0.349030	+	0.937111i	$0.613489\pi$
$14$	16.4389	−	28.4731i	0.313821	−	0.543553i
$15$		0			0
$16$	−9.50797	−	16.4683i	−0.148562	−	0.257317i
$17$	−5.92131	+	5.92131i	−0.0844782	+	0.0844782i	−0.748083	−	0.663605i	$-0.769026\pi$
$17$	−5.92131	+	5.92131i	−0.0844782	+	0.0844782i	0.663605	+	0.748083i	$0.269026\pi$
$18$	−87.6951	+	82.1614i	−1.14833	+	1.07587i
$19$			106.718i			1.28857i	0.764787	+	0.644284i	$0.222844\pi$
$19$			106.718i			1.28857i	−0.764787	+	0.644284i	$0.777156\pi$
$20$		0			0
$21$	9.32953	+	37.2331i	0.0969462	+	0.386901i
$22$	37.5120	−	10.0513i	0.363526	−	0.0974066i
$23$	−102.465	+	27.4553i	−0.928930	+	0.248906i	−0.691398	−	0.722474i	$-0.743005\pi$
$23$	−102.465	+	27.4553i	−0.928930	+	0.248906i	−0.237531	+	0.971380i	$0.576338\pi$
$24$	−84.7110	−	24.1833i	−0.720482	−	0.205683i
$25$		0			0
$26$		−	339.980i		−	2.56445i
$27$	6.85080	−	140.129i	0.0488310	−	0.998807i
$28$	−61.6846	+	61.6846i	−0.416332	+	0.416332i
$29$	−85.3380	−	147.810i	−0.546444	−	0.946469i	−0.998515	−	0.0544866i	$-0.982648\pi$
$29$	−85.3380	−	147.810i	−0.546444	−	0.946469i	0.452070	−	0.891982i	$-0.350686\pi$
$30$		0			0
$31$	−157.999	+	273.662i	−0.915400	+	1.58552i	−0.109085	+	0.994032i	$0.534792\pi$
$31$	−157.999	+	273.662i	−0.915400	+	1.58552i	−0.806315	+	0.591487i	$0.798541\pi$
$32$	57.0093	+	212.761i	0.314935	+	1.17535i
$33$	−23.3059	+	38.8906i	−0.122941	+	0.205151i
$34$	32.2773	−	18.6353i	0.162809	−	0.0939979i
$35$		0			0
$36$	281.176	−	150.349i	1.30174	−	0.696060i
$37$	31.7091	+	31.7091i	0.140890	+	0.140890i	0.774034	−	0.633144i	$-0.218236\pi$
$37$	31.7091	+	31.7091i	0.140890	+	0.140890i	−0.633144	+	0.774034i	$0.718236\pi$
$38$	122.933	−	458.791i	0.524798	−	1.95857i
$39$	276.057	+	285.197i	1.13345	+	1.17097i
$40$		0			0
$41$	298.272	+	172.207i	1.13615	+	0.655958i	0.945475	−	0.325695i	$-0.105598\pi$
$41$	298.272	+	172.207i	1.13615	+	0.655958i	0.190677	+	0.981653i	$0.438932\pi$
$42$	2.78172	−	170.816i	0.0102197	−	0.627558i
$43$	431.220	+	115.545i	1.52931	+	0.409778i	0.922795	−	0.385292i	$-0.125899\pi$
$43$	431.220	+	115.545i	1.52931	+	0.409778i	0.606517	+	0.795070i	$0.292566\pi$
$44$	−103.042			−0.353049
$45$		0			0
$46$	472.133			1.51331
$47$	227.629	+	60.9929i	0.706448	+	0.189292i	0.594117	−	0.804379i	$-0.297502\pi$
$47$	227.629	+	60.9929i	0.706448	+	0.189292i	0.112331	+	0.993671i	$0.464168\pi$
$48$	−84.7559	−	50.7917i	−0.254864	−	0.152732i
$49$	249.789	+	144.216i	0.728249	+	0.420454i
$50$		0			0
$51$	−11.9448	+	41.8410i	−0.0327961	+	0.114881i
$52$	−233.473	+	871.335i	−0.622633	+	2.32370i
$53$	−60.5508	−	60.5508i	−0.156930	−	0.156930i	0.624275	−	0.781205i	$-0.285395\pi$
$53$	−60.5508	−	60.5508i	−0.156930	−	0.156930i	−0.781205	+	0.624275i	$0.785395\pi$
$54$	−190.872	+	594.536i	−0.481008	+	1.49826i
$55$		0			0
$56$	108.460	−	62.6197i	0.258815	−	0.149427i
$57$	269.405	+	484.682i	0.626028	+	1.12627i
$58$	196.609	+	733.754i	0.445103	+	1.66115i
$59$	25.4427	−	44.0680i	0.0561416	−	0.0972401i	−0.836589	−	0.547831i	$-0.815454\pi$
$59$	25.4427	−	44.0680i	0.0561416	−	0.0972401i	0.892730	+	0.450591i	$0.148787\pi$
$60$		0			0
$61$	−36.1174	−	62.5572i	−0.0758092	−	0.131305i	0.825629	−	0.564214i	$-0.190821\pi$
$61$	−36.1174	−	62.5572i	−0.0758092	−	0.131305i	−0.901438	+	0.432909i	$0.857487\pi$
$62$	994.494	−	994.494i	2.03711	−	2.03711i
$63$	136.365	+	145.550i	0.272705	+	0.291072i
$64$		−	828.227i		−	1.61763i
$65$		0			0
$66$	144.994	−	140.347i	0.270418	−	0.261751i
$67$	17.1550	−	4.59668i	0.0312809	−	0.00838169i	−0.243145	−	0.969990i	$-0.578179\pi$
$67$	17.1550	−	4.59668i	0.0312809	−	0.00838169i	0.274426	+	0.961608i	$0.411512\pi$
$68$	−95.5208	+	25.5947i	−0.170347	+	0.0456444i
$69$	−396.055	+	383.362i	−0.691006	+	0.668861i
$70$		0			0
$71$			109.592i			0.183185i	0.995797	+	0.0915927i	$0.0291958\pi$
$71$			109.592i			0.183185i	−0.995797	+	0.0915927i	$0.970804\pi$
$72$	−445.782	+	104.016i	−0.729666	+	0.170256i
$73$	144.319	−	144.319i	0.231387	−	0.231387i	−0.581885	−	0.813271i	$-0.697685\pi$
$73$	144.319	−	144.319i	0.231387	−	0.231387i	0.813271	+	0.581885i	$0.197685\pi$
$74$	−99.7935	−	172.847i	−0.156767	−	0.271529i
$75$		0			0
$76$	−630.128	+	1091.41i	−0.951062	+	1.64729i
$77$	−16.6824	−	62.2595i	−0.0246901	−	0.0921446i
$78$	−858.266	−	1544.09i	−1.24589	−	2.24146i
$79$	140.624	−	81.1891i	0.200271	−	0.115626i	−0.396511	−	0.918030i	$-0.629779\pi$
$79$	140.624	−	81.1891i	0.200271	−	0.115626i	0.596782	+	0.802404i	$0.296446\pi$
$80$		0			0
$81$	−322.635	−	653.718i	−0.442572	−	0.896733i
$82$	−1083.93	−	1083.93i	−1.45975	−	1.45975i
$83$	−74.9883	+	279.860i	−0.0991691	+	0.370104i	−0.997619	−	0.0689728i	$-0.978028\pi$
$83$	−74.9883	+	279.860i	−0.0991691	+	0.370104i	0.898449	+	0.439077i	$0.144694\pi$
$84$	−124.433	+	435.873i	−0.161628	+	0.566163i
$85$		0			0
$86$	−1720.76	−	993.479i	−2.15760	−	1.24569i
$87$	−760.720	−	455.877i	−0.937446	−	0.561783i
$88$	142.892	+	38.2877i	0.173094	+	0.0463805i
$89$	1107.89			1.31950			0.659751	−	0.751484i	$-0.270662\pi$
$89$	1107.89			1.31950			0.659751	+	0.751484i	$0.270662\pi$
$90$		0			0
$91$	−564.273			−0.650021
$92$	−1210.03	−	324.227i	−1.37124	−	0.367423i
$93$	−26.7358	+	1641.75i	−0.0298105	+	1.83056i
$94$	−908.339	−	524.430i	−0.996681	−	0.575434i
$95$		0			0
$96$	796.027	+	822.383i	0.846294	+	0.874314i
$97$	−52.9802	+	197.725i	−0.0554569	+	0.206968i	−0.988095	−	0.153845i	$-0.950834\pi$
$97$	−52.9802	+	197.725i	−0.0554569	+	0.206968i	0.932638	+	0.360813i	$0.117501\pi$
$98$	−907.741	−	907.741i	−0.935670	−	0.935670i
$99$	−7.67108	+	235.465i	−0.00778760	+	0.239041i
$100$		0			0
$101$	−960.085	+	554.305i	−0.945862	+	0.546093i	−0.891793	−	0.452444i	$-0.850552\pi$
$101$	−960.085	+	554.305i	−0.945862	+	0.546093i	−0.0540686	+	0.998537i	$0.517219\pi$
$102$	99.5500	−	166.119i	0.0966364	−	0.161257i
$103$	−74.0766	−	276.457i	−0.0708639	−	0.264468i	0.921400	−	0.388616i	$-0.127047\pi$
$103$	−74.0766	−	276.457i	−0.0708639	−	0.264468i	−0.992264	+	0.124148i	$0.960380\pi$
$104$	647.531	−	1121.56i	0.610535	−	1.05748i
$105$		0			0
$106$	190.563	+	330.065i	0.174614	+	0.302441i
$107$	−864.028	+	864.028i	−0.780643	+	0.780643i	−0.979939	−	0.199296i	$-0.936134\pi$
$107$	−864.028	+	864.028i	−0.780643	+	0.780643i	0.199296	+	0.979939i	$0.436134\pi$
$108$	897.470	−	1392.66i	0.799621	−	1.24082i
$109$		−	990.712i		−	0.870578i	−0.900291	−	0.435289i	$-0.856646\pi$
$109$		−	990.712i		−	0.870578i	0.900291	−	0.435289i	$-0.143354\pi$
$110$		0			0
$111$	224.062	+	63.9651i	0.191595	+	0.0546964i
$112$	135.685	−	36.3567i	0.114473	−	0.0306730i
$113$	−73.1927	+	19.6119i	−0.0609327	+	0.0163269i	−0.289157	−	0.957282i	$-0.593375\pi$
$113$	−73.1927	+	19.6119i	−0.0609327	+	0.0163269i	0.228224	+	0.973609i	$0.426708\pi$
$114$	−599.875	−	2394.03i	−0.492837	−	1.96686i
$115$		0			0
$116$		−	2015.55i		−	1.61327i
$117$	1973.74	+	598.386i	1.55959	+	0.472827i
$118$	−160.144	+	160.144i	−0.124936	+	0.124936i
$119$	−30.9295	−	53.5714i	−0.0238261	−	0.0412679i
$120$		0			0
$121$	−627.432	+	1086.74i	−0.471399	+	0.816488i
$122$	83.2102	+	310.545i	0.0617500	+	0.230454i
$123$	1789.39	+	29.1401i	1.31174	+	0.0213616i
$124$	−3231.73	+	1865.84i	−2.34047	+	1.35127i
$125$		0			0
$126$	−418.584	−	782.818i	−0.295956	−	0.553484i
$127$	−1084.18	−	1084.18i	−0.757521	−	0.757521i	0.218350	−	0.975871i	$-0.429933\pi$
$127$	−1084.18	−	1084.18i	−0.757521	−	0.757521i	−0.975871	+	0.218350i	$0.929933\pi$
$128$	−497.994	+	1858.54i	−0.343882	+	1.28338i
$129$	2250.16	−	563.825i	1.53578	−	0.384822i
$130$		0			0
$131$	1415.36	+	817.157i	0.943972	+	0.545003i	0.891203	−	0.453604i	$-0.149862\pi$
$131$	1415.36	+	817.157i	0.943972	+	0.545003i	0.0527689	+	0.998607i	$0.483195\pi$
$132$	−467.986	+	260.125i	−0.308583	+	0.171523i
$133$	−761.467	−	204.035i	−0.496448	−	0.133023i
$134$	−79.0463			−0.0509594
$135$		0			0
$136$	141.972			0.0895149
$137$	−2209.33	−	591.988i	−1.37778	−	0.369175i	−0.507465	−	0.861672i	$-0.669417\pi$
$137$	−2209.33	−	591.988i	−1.37778	−	0.369175i	−0.870314	+	0.492497i	$0.836084\pi$
$138$	2144.29	−	1191.88i	1.32271	−	0.735215i
$139$	1895.18	+	1094.18i	1.15645	+	0.667678i	0.950451	−	0.310874i	$-0.100622\pi$
$139$	1895.18	+	1094.18i	1.15645	+	0.667678i	0.206001	+	0.978552i	$0.433955\pi$
$140$		0			0
$141$	1187.80	−	297.627i	0.709437	−	0.177764i
$142$	126.243	−	471.146i	0.0746063	−	0.278435i
$143$	−471.299	−	471.299i	−0.275609	−	0.275609i
$144$	−513.158	−	16.7179i	−0.296967	−	0.00967471i
$145$		0			0
$146$	−786.687	+	454.194i	−0.445936	+	0.257461i
$147$	1498.54	+	24.4035i	0.840797	+	0.0136923i
$148$	137.062	+	511.522i	0.0761244	+	0.284100i
$149$	−311.430	+	539.412i	−0.171230	+	0.296580i	−0.938850	−	0.344326i	$-0.888108\pi$
$149$	−311.430	+	539.412i	−0.171230	+	0.296580i	0.767620	+	0.640905i	$0.221441\pi$
$150$		0			0
$151$	−1009.02	−	1747.68i	−0.543795	−	0.941881i	−0.998682	−	0.0513314i	$-0.983654\pi$
$151$	−1009.02	−	1747.68i	−0.543795	−	0.941881i	0.454887	−	0.890549i	$-0.349680\pi$
$152$	1279.36	−	1279.36i	0.682697	−	0.682697i
$153$	51.3763	+	220.183i	0.0271472	+	0.116345i
$154$			286.877i			0.150112i
$155$		0			0
$156$	1139.28	+	4546.74i	0.584715	+	2.33353i
$157$	680.891	−	182.444i	0.346121	−	0.0927428i	−0.0815706	−	0.996668i	$-0.525994\pi$
$157$	680.891	−	182.444i	0.346121	−	0.0927428i	0.427692	+	0.903925i	$0.359327\pi$
$158$	−698.080	+	187.050i	−0.351495	+	0.0941829i
$159$	−427.862	−	122.146i	−0.213407	−	0.0609233i
$160$		0			0
$161$		−	783.611i		−	0.383585i
$162$	633.996	+	3182.06i	0.307478	+	1.54325i
$163$	426.426	−	426.426i	0.204909	−	0.204909i	−0.597190	−	0.802100i	$-0.703716\pi$
$163$	426.426	−	426.426i	0.204909	−	0.204909i	0.802100	+	0.597190i	$0.203716\pi$
$164$	2033.64	+	3522.36i	0.968294	+	1.67714i
$165$		0			0
$166$	644.765	−	1116.77i	0.301467	−	0.522155i
$167$	−164.381	−	613.477i	−0.0761686	−	0.284265i	0.917327	−	0.398134i	$-0.130342\pi$
$167$	−164.381	−	613.477i	−0.0761686	−	0.284265i	−0.993496	+	0.113869i	$0.963676\pi$
$168$	334.515	−	558.204i	0.153621	−	0.256348i
$169$	−3150.58	+	1818.99i	−1.43404	+	0.827943i
$170$		0			0
$171$	2447.12	+	1521.18i	1.09436	+	0.680278i
$172$	3727.88	+	3727.88i	1.65260	+	1.65260i
$173$	−184.004	+	686.713i	−0.0808646	+	0.301791i	−0.994499	−	0.104746i	$-0.966597\pi$
$173$	−184.004	+	686.713i	−0.0808646	+	0.301791i	0.913634	+	0.406537i	$0.133264\pi$
$174$	2745.27	+	2836.16i	1.19608	+	1.23568i
$175$		0			0
$176$	143.695	+	82.9622i	0.0615420	+	0.0355313i
$177$	4.30529	−	264.373i	0.00182828	−	0.112268i
$178$	−4762.91	−	1276.22i	−2.00559	−	0.537397i
$179$	−2690.52			−1.12346			−0.561730	−	0.827321i	$-0.689864\pi$
$179$	−2690.52			−1.12346			−0.561730	+	0.827321i	$0.689864\pi$
$180$		0			0
$181$	197.441			0.0810810			0.0405405	−	0.999178i	$-0.487092\pi$
$181$	197.441			0.0810810			0.0405405	+	0.999178i	$0.487092\pi$
$182$	2425.87	+	650.009i	0.988007	+	0.264736i
$183$	−321.958	−	192.939i	−0.130054	−	0.0779371i
$184$	1557.52	+	899.232i	0.624030	+	0.360284i
$185$		0			0
$186$	2006.14	−	7027.26i	0.790846	−	2.77023i
$187$	18.9113	−	70.5779i	0.00739535	−	0.0275998i
$188$	1967.84	+	1967.84i	0.763402	+	0.763402i
$189$	986.766	+	316.795i	0.379771	+	0.121923i
$190$		0			0
$191$	306.085	−	176.718i	0.115956	−	0.0669470i	−0.440900	−	0.897556i	$-0.645341\pi$
$191$	306.085	−	176.718i	0.115956	−	0.0669470i	0.556856	+	0.830609i	$0.312007\pi$
$192$	−2090.82	−	3761.56i	−0.785897	−	1.41389i
$193$	371.803	+	1387.59i	0.138668	+	0.517517i	0.999956	+	0.00939936i	$0.00299195\pi$
$193$	371.803	+	1387.59i	0.138668	+	0.517517i	−0.861287	+	0.508118i	$0.830341\pi$
$194$	455.534	−	789.008i	0.168585	−	0.291997i
$195$		0			0
$196$	1703.08	+	2949.82i	0.620655	+	1.07501i
$197$	−2647.40	+	2647.40i	−0.957458	+	0.957458i	−0.999131	−	0.0416736i	$-0.986731\pi$
$197$	−2647.40	+	2647.40i	−0.957458	+	0.957458i	0.0416736	+	0.999131i	$0.486731\pi$
$198$	304.220	−	1003.45i	0.109192	−	0.360162i
$199$		−	3785.65i		−	1.34853i	−0.738488	−	0.674266i	$-0.764460\pi$
$199$		−	3785.65i		−	1.34853i	0.738488	−	0.674266i	$-0.235540\pi$
$200$		0			0
$201$	66.3090	−	64.1839i	0.0232690	−	0.0225233i
$202$	4766.03	−	1277.05i	1.66008	−	0.444818i
$203$	1217.83	−	326.316i	0.421058	−	0.112822i
$204$	−369.215	+	357.382i	−0.126717	+	0.122656i
$205$		0			0
$206$			1273.85i			0.430842i
$207$	−830.983	+	2740.94i	−0.279021	+	0.920332i
$208$	1027.12	−	1027.12i	0.342395	−	0.342395i
$209$	−465.586	−	806.418i	−0.154092	−	0.266895i
$210$		0			0
$211$	676.890	−	1172.41i	0.220849	−	0.382521i	−0.734217	−	0.678915i	$-0.762451\pi$
$211$	676.890	−	1172.41i	0.220849	−	0.382521i	0.955066	+	0.296394i	$0.0957840\pi$
$212$	−261.730	−	976.788i	−0.0847908	−	0.316444i
$213$	276.660	+	497.734i	0.0889974	+	0.160114i
$214$	4709.85	−	2719.24i	1.50448	−	0.868613i
$215$		0			0
$216$	−1762.03	+	1597.77i	−0.555050	+	0.503308i
$217$	−1650.59	−	1650.59i	−0.516355	−	0.516355i
$218$	−1141.24	+	4259.17i	−0.354563	+	1.32325i
$219$	291.126	−	1019.78i	0.0898288	−	0.314659i
$220$		0			0
$221$	−553.966	−	319.832i	−0.168614	−	0.0973496i
$222$	−889.579	−	533.098i	−0.268940	−	0.161168i
$223$	1896.57	+	508.185i	0.569525	+	0.152604i	0.532079	−	0.846695i	$-0.321411\pi$
$223$	1896.57	+	508.185i	0.569525	+	0.152604i	0.0374461	+	0.999299i	$0.488078\pi$
$224$	−1627.12			−0.485341
$225$		0			0
$226$	337.255			0.0992648
$227$	3048.34	+	816.800i	0.891301	+	0.238823i	0.675277	−	0.737564i	$-0.264024\pi$
$227$	3048.34	+	816.800i	0.891301	+	0.238823i	0.216025	+	0.976388i	$0.430691\pi$
$228$	−106.627	+	6547.62i	−0.0309718	+	1.90187i
$229$	−3455.23	−	1994.88i	−0.997066	−	0.575656i	−0.0896872	−	0.995970i	$-0.528587\pi$
$229$	−3455.23	−	1994.88i	−0.997066	−	0.575656i	−0.907379	+	0.420314i	$0.861920\pi$
$230$		0			0
$231$	−232.938	−	240.651i	−0.0663472	−	0.0685439i
$232$	−748.928	+	2795.04i	−0.211937	+	0.790962i
$233$	−2166.38	−	2166.38i	−0.609118	−	0.609118i	0.333598	−	0.942715i	$-0.391737\pi$
$233$	−2166.38	−	2166.38i	−0.609118	−	0.609118i	−0.942715	+	0.333598i	$0.891737\pi$
$234$	−7795.98	−	4846.15i	−2.17795	−	1.35386i
$235$		0			0
$236$	520.409	−	300.458i	0.143541	−	0.0828736i
$237$	433.713	−	723.736i	0.118872	−	0.198362i
$238$	71.2579	+	265.938i	0.0194074	+	0.0724294i
$239$	1946.01	−	3370.59i	0.526682	−	0.912239i	−0.472835	−	0.881151i	$-0.656769\pi$
$239$	1946.01	−	3370.59i	0.526682	−	0.912239i	0.999517	−	0.0310884i	$-0.00989735\pi$
$240$		0			0
$241$	−3291.66	−	5701.33i	−0.879812	−	1.52388i	−0.851547	−	0.524278i	$-0.824335\pi$
$241$	−3291.66	−	5701.33i	−0.879812	−	1.52388i	−0.0282647	−	0.999600i	$-0.508998\pi$
$242$	3949.26	−	3949.26i	1.04904	−	1.04904i
$243$	−3115.60	−	2154.52i	−0.822493	−	0.568775i
$244$		−	853.037i		−	0.223812i
$245$		0			0
$246$	−7659.22	−	2186.55i	−1.98510	−	0.566705i
$247$	−7874.10	+	2109.86i	−2.02841	+	0.543511i
$248$	5174.85	−	1386.60i	1.32501	−	0.355036i
$249$	365.921	+	1460.35i	0.0931297	+	0.371670i
$250$		0			0
$251$			6323.18i			1.59010i	0.606543	+	0.795051i	$0.292556\pi$
$251$			6323.18i			1.59010i	−0.606543	+	0.795051i	$0.707444\pi$
$252$	535.206	+	2293.74i	0.133789	+	0.573380i
$253$	654.497	−	654.497i	0.162640	−	0.162640i
$254$	3412.08	+	5909.89i	0.842885	+	1.45992i
$255$		0			0
$256$	968.943	−	1678.26i	0.236558	−	0.409731i
$257$	365.257	+	1363.16i	0.0886541	+	0.330861i	0.995981	−	0.0895642i	$-0.0285474\pi$
$257$	365.257	+	1363.16i	0.0886541	+	0.330861i	−0.907327	+	0.420426i	$0.861881\pi$
$258$	−10323.2	−	168.112i	−2.49106	−	0.0405666i
$259$	−286.879	+	165.630i	−0.0688255	+	0.0397364i
$260$		0			0
$261$	−4605.81	−	150.050i	−1.09231	−	0.0355857i
$262$	−5143.45	−	5143.45i	−1.21284	−	1.21284i
$263$	−85.0248	+	317.317i	−0.0199348	+	0.0743977i	−0.975177	−	0.221428i	$-0.928928\pi$
$263$	−85.0248	+	317.317i	−0.0199348	+	0.0743977i	0.955242	+	0.295826i	$0.0955948\pi$
$264$	745.628	−	186.833i	0.173827	−	0.0435559i
$265$		0			0
$266$	3038.59	+	1754.33i	0.700405	+	0.404379i
$267$	5031.70	−	2796.81i	1.15331	−	0.641057i
$268$	202.588	+	54.2832i	0.0461754	+	0.0123727i
$269$	−764.226			−0.173218			−0.0866091	−	0.996242i	$-0.527603\pi$
$269$	−764.226			−0.173218			−0.0866091	+	0.996242i	$0.527603\pi$
$270$		0			0
$271$	4645.09			1.04121			0.520607	−	0.853797i	$-0.325706\pi$
$271$	4645.09			1.04121			0.520607	+	0.853797i	$0.325706\pi$
$272$	153.813	+	41.2142i	0.0342879	+	0.00918742i
$273$	−2562.76	+	1424.49i	−0.568152	+	0.315801i
$274$	8816.19	+	5090.03i	1.94382	+	1.12226i
$275$		0			0
$276$	−6314.10	+	1582.13i	−1.37704	+	0.345047i
$277$	1549.76	−	5783.77i	0.336158	−	1.25456i	−0.566450	−	0.824096i	$-0.691684\pi$
$277$	1549.76	−	5783.77i	0.336158	−	1.25456i	0.902608	−	0.430463i	$-0.141650\pi$
$278$	−6887.13	−	6887.13i	−1.48584	−	1.48584i
$279$	4023.11	+	7523.85i	0.863288	+	1.61448i
$280$		0			0
$281$	4201.11	−	2425.51i	0.891877	−	0.514925i	0.0173209	−	0.999850i	$-0.494486\pi$
$281$	4201.11	−	2425.51i	0.891877	−	0.514925i	0.874556	+	0.484925i	$0.161153\pi$
$282$	−5449.31	−	88.7415i	−1.15071	−	0.0187393i
$283$	−92.5845	−	345.530i	−0.0194473	−	0.0725782i	0.955520	−	0.294925i	$-0.0952948\pi$
$283$	−92.5845	−	345.530i	−0.0194473	−	0.0725782i	−0.974968	+	0.222347i	$0.928628\pi$
$284$	−647.098	+	1120.81i	−0.135205	+	0.234182i
$285$		0			0
$286$	1483.25	+	2569.07i	0.306667	+	0.531162i
$287$	−1799.02	+	1799.02i	−0.370010	+	0.370010i
$288$	5691.39	+	1725.48i	1.16447	+	0.353039i
$289$			4842.88i			0.985727i
$290$		0			0
$291$	258.528	+	1031.75i	0.0520796	+	0.207844i
$292$	2328.11	−	623.814i	0.466582	−	0.125020i
$293$	8233.45	−	2206.15i	1.64165	−	0.439879i	0.684392	−	0.729114i	$-0.260068\pi$
$293$	8233.45	−	2206.15i	1.64165	−	0.439879i	0.957258	+	0.289236i	$0.0934011\pi$
$294$	−6414.25	−	1831.14i	−1.27240	−	0.363245i
$295$		0			0
$296$		−	760.273i		−	0.149290i
$297$	559.581	+	1088.78i	0.109327	+	0.212718i
$298$	1960.24	−	1960.24i	0.381052	−	0.381052i
$299$	−4051.54	−	7017.48i	−0.783635	−	1.35730i
$300$		0			0
$301$	−1648.90	+	2855.98i	−0.315751	+	0.546897i
$302$	2324.67	+	8675.77i	0.442946	+	1.65310i
$303$	−2961.10	+	4941.19i	−0.561422	+	0.936844i
$304$	1757.46	−	1014.67i	0.331570	−	0.191432i
$305$		0			0
$306$	32.7665	−	1005.77i	0.00612137	−	0.187896i
$307$	6239.03	+	6239.03i	1.15987	+	1.15987i	0.984503	+	0.175367i	$0.0561111\pi$
$307$	6239.03	+	6239.03i	1.15987	+	1.15987i	0.175367	+	0.984503i	$0.443889\pi$
$308$	197.006	−	735.237i	0.0364463	−	0.136020i
$309$	−1034.34	−	1068.59i	−0.190426	−	0.196730i
$310$		0			0
$311$	−1983.11	−	1144.95i	−0.361582	−	0.208760i	0.308192	−	0.951324i	$-0.400276\pi$
$311$	−1983.11	−	1144.95i	−0.361582	−	0.208760i	−0.669775	+	0.742565i	$0.733609\pi$
$312$	109.572	−	6728.45i	0.0198824	−	1.22091i
$313$	5911.34	+	1583.94i	1.06750	+	0.286037i	0.749467	−	0.662042i	$-0.230310\pi$
$313$	5911.34	+	1583.94i	1.06750	+	0.286037i	0.318036	+	0.948079i	$0.396977\pi$
$314$	−3137.38			−0.563862
$315$		0			0
$316$	1917.56			0.341365
$317$	−8685.87	−	2327.37i	−1.53895	−	0.412361i	−0.613024	−	0.790064i	$-0.710047\pi$
$317$	−8685.87	−	2327.37i	−1.53895	−	0.412361i	−0.925927	+	0.377704i	$0.876714\pi$
$318$	1698.72	+	1017.99i	0.299558	+	0.179516i
$319$	1289.72	+	744.620i	0.226365	+	0.130692i
$320$		0			0
$321$	−1742.96	+	6105.37i	−0.303061	+	1.06158i
$322$	−902.673	+	3368.82i	−0.156224	+	0.583035i
$323$	−631.910	−	631.910i	−0.108856	−	0.108856i
$324$	560.337	−	8590.67i	0.0960797	−	1.47302i
$325$		0			0
$326$	−2324.46	+	1342.03i	−0.394909	+	0.228001i
$327$	−2501.01	−	4499.53i	−0.422955	−	0.760931i
$328$	−1511.29	−	5640.22i	−0.254412	−	0.949479i
$329$	−870.409	+	1507.59i	−0.145858	+	0.252633i
$330$		0			0
$331$	368.018	+	637.425i	0.0611120	+	0.105849i	0.894963	−	0.446141i	$-0.147202\pi$
$331$	368.018	+	637.425i	0.0611120	+	0.105849i	−0.833851	+	0.551990i	$0.813869\pi$
$332$	−2419.38	+	2419.38i	−0.399942	+	0.399942i
$333$	1179.10	−	275.124i	0.194037	−	0.0452754i
$334$			2826.75i			0.463093i
$335$		0			0
$336$	524.460	−	507.652i	0.0851537	−	0.0824247i
$337$	4360.75	−	1168.46i	0.704883	−	0.188873i	0.111466	−	0.993768i	$-0.464445\pi$
$337$	4360.75	−	1168.46i	0.704883	−	0.188873i	0.593417	+	0.804896i	$0.297779\pi$
$338$	15640.0	−	4190.74i	2.51688	−	0.674396i
$339$	−282.910	+	273.844i	−0.0453262	+	0.0438736i
$340$		0			0
$341$		−	2757.25i		−	0.437869i
$342$	−8768.10	−	9358.64i	−1.38633	−	1.47970i
$343$	−3298.23	+	3298.23i	−0.519207	+	0.519207i
$344$	−3784.39	−	6554.76i	−0.593141	−	1.02735i
$345$		0			0
$346$	1582.11	−	2740.29i	0.245822	−	0.425777i
$347$	1052.99	+	3929.82i	0.162904	+	0.607964i	0.998298	+	0.0583140i	$0.0185724\pi$
$347$	1052.99	+	3929.82i	0.162904	+	0.607964i	−0.835395	+	0.549651i	$0.814761\pi$
$348$	−5088.18	−	9154.05i	−0.783779	−	1.41008i
$349$	2120.49	−	1224.26i	0.325235	−	0.187775i	−0.328489	−	0.944508i	$-0.606539\pi$
$349$	2120.49	−	1224.26i	0.325235	−	0.187775i	0.653724	+	0.756733i	$0.273206\pi$
$350$		0			0
$351$	10474.7	−	2264.92i	1.59288	−	0.344424i
$352$	−1359.02	−	1359.02i	−0.205784	−	0.205784i
$353$	2812.90	−	10497.9i	0.424123	−	1.58285i	−0.341707	−	0.939807i	$-0.611005\pi$
$353$	2812.90	−	10497.9i	0.424123	−	1.58285i	0.765830	−	0.643043i	$-0.222328\pi$
$354$	−323.051	+	1131.61i	−0.0485027	+	0.169899i
$355$		0			0
$356$	11330.5	+	6541.64i	1.68683	+	0.973894i
$357$	−275.712	−	165.226i	−0.0408745	−	0.0244949i
$358$	11566.8	+	3099.32i	1.70762	+	0.457554i
$359$	−6928.63			−1.01861			−0.509303	−	0.860587i	$-0.670097\pi$
$359$	−6928.63			−1.01861			−0.509303	+	0.860587i	$0.670097\pi$
$360$		0			0
$361$	−4529.72			−0.660406
$362$	−848.818	−	227.440i	−0.123240	−	0.0330221i
$363$	−106.171	+	6519.61i	−0.0153514	+	0.942674i
$364$	−5770.88	−	3331.82i	−0.830978	−	0.479766i
$365$		0			0
$366$	1161.87	+	1200.34i	0.165935	+	0.171429i
$367$	−2434.22	+	9084.65i	−0.346227	+	1.29214i	0.544944	+	0.838472i	$0.316551\pi$
$367$	−2434.22	+	9084.65i	−0.346227	+	1.29214i	−0.891172	+	0.453666i	$0.850116\pi$
$368$	1426.37	+	1426.37i	0.202051	+	0.202051i
$369$	8200.47	−	4384.91i	1.15691	−	0.618615i
$370$		0			0
$371$	547.817	−	316.282i	0.0766610	−	0.0442603i
$372$	−9967.34	+	16632.5i	−1.38920	+	2.31816i
$373$	−1500.97	−	5601.71i	−0.208358	−	0.777602i	−0.988400	−	0.151875i	$-0.951469\pi$
$373$	−1500.97	−	5601.71i	−0.208358	−	0.777602i	0.780042	−	0.625727i	$-0.215198\pi$
$374$	−162.603	+	281.637i	−0.0224813	+	0.0389388i
$375$		0			0
$376$	−1997.67	−	3460.07i	−0.273995	−	0.474573i
$377$	9218.86	−	9218.86i	1.25940	−	1.25940i
$378$	−3877.28	−	2498.63i	−0.527581	−	0.339989i
$379$			6617.31i			0.896856i	0.893819	+	0.448428i	$0.148016\pi$
$379$			6617.31i			0.896856i	−0.893819	+	0.448428i	$0.851984\pi$
$380$		0			0
$381$	−7660.97	−	2187.05i	−1.03014	−	0.294084i
$382$	−1519.46	+	407.137i	−0.203514	+	0.0545313i
$383$	−12012.4	+	3218.73i	−1.60263	+	0.429423i	−0.945836	−	0.324646i	$-0.894755\pi$
$383$	−12012.4	+	3218.73i	−1.60263	+	0.429423i	−0.656795	+	0.754070i	$0.728088\pi$
$384$	2430.06	+	9698.10i	0.322939	+	1.28881i
$385$		0			0
$386$		−	6393.68i		−	0.843082i
$387$	8796.23	−	8241.18i	1.15539	−	1.08249i
$388$	−1709.32	+	1709.32i	−0.223654	+	0.223654i
$389$	4995.39	+	8652.28i	0.651096	+	1.12773i	0.982857	+	0.184369i	$0.0590240\pi$
$389$	4995.39	+	8652.28i	0.651096	+	1.12773i	−0.331761	+	0.943364i	$0.607643\pi$
$390$		0			0
$391$	444.154	−	769.297i	0.0574471	−	0.0995014i
$392$	−1265.64	−	4723.43i	−0.163073	−	0.608595i
$393$	8491.02	+	138.276i	1.08986	+	0.0177483i
$394$	14431.1	−	8331.78i	1.84524	−	1.06535i
$395$		0			0
$396$	−1468.78	+	2362.82i	−0.186386	+	0.299839i
$397$	−1248.70	−	1248.70i	−0.157860	−	0.157860i	0.623758	−	0.781618i	$-0.285605\pi$
$397$	−1248.70	−	1248.70i	−0.157860	−	0.157860i	−0.781618	+	0.623758i	$0.785605\pi$
$398$	−4360.85	+	16274.9i	−0.549220	+	2.04972i
$399$	−3973.44	+	995.628i	−0.498548	+	0.124922i
$400$		0			0
$401$	7999.65	+	4618.60i	0.996218	+	0.575166i	0.907127	−	0.420857i	$-0.138271\pi$
$401$	7999.65	+	4618.60i	0.996218	+	0.575166i	0.0890905	+	0.996024i	$0.471604\pi$
$402$	−359.005	+	199.549i	−0.0445412	+	0.0247577i
$403$	−23315.6	−	6247.40i	−2.88197	−	0.772221i
$404$	−13091.8			−1.61224
$405$		0			0
$406$	−5611.47			−0.685942
$407$	−377.950	−	101.271i	−0.0460302	−	0.0123338i
$408$	644.797	−	358.403i	0.0782407	−	0.0434892i
$409$	−2817.50	−	1626.68i	−0.340626	−	0.196661i	0.319923	−	0.947444i	$-0.396343\pi$
$409$	−2817.50	−	1626.68i	−0.340626	−	0.196661i	−0.660549	+	0.750783i	$0.729676\pi$
$410$		0			0
$411$	−11528.6	+	2888.73i	−1.38361	+	0.346692i
$412$	874.787	−	3264.75i	0.104606	−	0.390395i
$413$	265.796	+	265.796i	0.0316681	+	0.0316681i
$414$	6729.89	−	10826.3i	0.798927	−	1.28523i
$415$		0			0
$416$	−14571.3	+	8412.77i	−1.71735	+	0.991514i
$417$	11369.6	+	185.152i	1.33518	+	0.0217433i
$418$	1072.65	+	4003.20i	0.125515	+	0.468428i
$419$	1840.03	−	3187.02i	0.214537	−	0.371590i	−0.738592	−	0.674153i	$-0.764509\pi$
$419$	1840.03	−	3187.02i	0.214537	−	0.371590i	0.953129	+	0.302563i	$0.0978423\pi$
$420$		0			0
$421$	−3430.26	−	5941.39i	−0.397104	−	0.687804i	0.596263	−	0.802789i	$-0.296651\pi$
$421$	−3430.26	−	5941.39i	−0.397104	−	0.687804i	−0.993367	+	0.114985i	$0.963318\pi$
$422$	−4260.56	+	4260.56i	−0.491472	+	0.491472i
$423$	4643.28	−	4350.28i	0.533721	−	0.500043i
$424$			1451.80i			0.166287i
$425$		0			0
$426$	−616.030	−	2458.50i	−0.0700628	−	0.279613i
$427$	515.419	−	138.106i	0.0584142	−	0.0156520i
$428$	−13938.3	+	3734.74i	−1.57414	+	0.421789i
$429$	−3330.28	−	950.728i	−0.374796	−	0.106997i
$430$		0			0
$431$			3116.28i			0.348273i	0.984722	+	0.174137i	$0.0557134\pi$
$431$			3116.28i			0.348273i	−0.984722	+	0.174137i	$0.944287\pi$
$432$	−2372.82	+	1219.52i	−0.264264	+	0.135820i
$433$	−526.507	+	526.507i	−0.0584349	+	0.0584349i	−0.735720	−	0.677285i	$-0.763156\pi$
$433$	−526.507	+	526.507i	−0.0584349	+	0.0584349i	0.677285	+	0.735720i	$0.263156\pi$
$434$	5194.66	+	8997.41i	0.574543	+	0.995137i
$435$		0			0
$436$	5849.77	−	10132.1i	0.642554	−	1.11294i
$437$	−2929.98	−	10934.8i	−0.320732	−	1.19699i
$438$	−2426.31	+	4048.77i	−0.264688	+	0.441685i
$439$	−3213.40	+	1855.26i	−0.349356	+	0.201701i	−0.664401	−	0.747376i	$-0.731313\pi$
$439$	−3213.40	+	1855.26i	−0.349356	+	0.201701i	0.315046	+	0.949076i	$0.397980\pi$
$440$		0			0
$441$	6867.52	−	3672.16i	0.741553	−	0.396519i
$442$	2013.13	+	2013.13i	0.216640	+	0.216640i
$443$	508.773	−	1898.77i	0.0545655	−	0.203641i	−0.933261	−	0.359198i	$-0.883050\pi$
$443$	508.773	−	1898.77i	0.0545655	−	0.203641i	0.987827	+	0.155556i	$0.0497170\pi$
$444$	1913.81	+	1977.17i	0.204562	+	0.211335i
$445$		0			0
$446$	−7568.16	−	4369.48i	−0.803504	−	0.463903i
$447$	−52.6987	+	3236.05i	−0.00557621	+	0.342415i
$448$	5909.67	+	1583.49i	0.623226	+	0.166993i
$449$	6556.48			0.689131			0.344565	−	0.938762i	$-0.388026\pi$
$449$	6556.48			0.689131			0.344565	+	0.938762i	$0.388026\pi$
$450$		0			0
$451$	−3005.20			−0.313768
$452$	−864.350	−	231.602i	−0.0899460	−	0.0241010i
$453$	−8994.62	−	5390.20i	−0.932901	−	0.559059i
$454$	−12164.2	−	7023.01i	−1.25748	−	0.726005i
$455$		0			0
$456$	2580.79	−	9040.18i	0.265036	−	0.928389i
$457$	3310.69	−	12355.7i	0.338879	−	1.26471i	−0.560724	−	0.828003i	$-0.689477\pi$
$457$	3310.69	−	12355.7i	0.338879	−	1.26471i	0.899603	−	0.436710i	$-0.143856\pi$
$458$	12556.4	+	12556.4i	1.28105	+	1.28105i
$459$	789.180	+	870.311i	0.0802522	+	0.0885025i
$460$		0			0
$461$	−1996.02	+	1152.40i	−0.201657	+	0.116427i	−0.597428	−	0.801922i	$-0.703811\pi$
$461$	−1996.02	+	1152.40i	−0.201657	+	0.116427i	0.395771	+	0.918349i	$0.370477\pi$
$462$	724.210	+	1302.91i	0.0729292	+	0.131206i
$463$	−320.306	−	1195.40i	−0.0321509	−	0.119989i	0.947985	−	0.318314i	$-0.103117\pi$
$463$	−320.306	−	1195.40i	−0.0321509	−	0.119989i	−0.980136	+	0.198325i	$0.936450\pi$
$464$	−1622.78	+	2810.74i	−0.162362	+	0.281219i
$465$		0			0
$466$	6817.95	+	11809.0i	0.677759	+	1.17391i
$467$	3769.54	−	3769.54i	0.373519	−	0.373519i	−0.495238	−	0.868757i	$-0.664919\pi$
$467$	3769.54	−	3769.54i	0.373519	−	0.373519i	0.868757	+	0.495238i	$0.164919\pi$
$468$	16652.3	+	17773.9i	1.64478	+	1.75555i
$469$			131.195i			0.0129169i
$470$		0			0
$471$	2631.83	−	2547.49i	0.257470	−	0.249219i
$472$	−833.312	+	223.285i	−0.0812633	+	0.0217744i
$473$	−3762.63	+	1008.19i	−0.365763	+	0.0980058i
$474$	−2698.28	+	2611.80i	−0.261468	+	0.253089i
$475$		0			0
$476$		−	730.507i		−	0.0703419i
$477$	−2251.58	+	525.369i	−0.216127	+	0.0504298i
$478$	−12248.8	+	12248.8i	−1.17207	+	1.17207i
$479$	1205.53	+	2088.04i	0.114994	+	0.199175i	0.917777	−	0.397096i	$-0.129982\pi$
$479$	1205.53	+	2088.04i	0.114994	+	0.199175i	−0.802783	+	0.596271i	$0.796648\pi$
$480$		0			0
$481$	−1712.73	+	2966.53i	−0.162357	+	0.281210i
$482$	7583.60	+	28302.4i	0.716646	+	2.67456i
$483$	−1978.19	−	3558.93i	−0.186358	−	0.335273i
$484$	−12833.6	+	7409.49i	−1.20526	+	0.695858i
$485$		0			0
$486$	10912.4	+	12851.5i	1.01851	+	1.19950i
$487$	13278.0	+	13278.0i	1.23549	+	1.23549i	0.961825	+	0.273666i	$0.0882362\pi$
$487$	13278.0	+	13278.0i	1.23549	+	1.23549i	0.273666	+	0.961825i	$0.411764\pi$
$488$	−316.967	+	1182.94i	−0.0294025	+	0.109732i
$489$	860.207	−	3013.20i	0.0795499	−	0.278653i
$490$		0			0
$491$	−4882.30	−	2818.80i	−0.448748	−	0.259085i	0.258553	−	0.965997i	$-0.416754\pi$
$491$	−4882.30	−	2818.80i	−0.448748	−	0.259085i	−0.707301	+	0.706912i	$0.750088\pi$
$492$	18128.2	+	10863.7i	1.66115	+	0.995474i
$493$	1380.54	+	369.915i	0.126119	+	0.0337934i
$494$	36282.0			3.30446
$495$		0			0
$496$	6008.99			0.543975
$497$	−781.973	−	209.529i	−0.0705760	−	0.0189108i
$498$	109.104	−	6699.70i	0.00981741	−	0.602853i
$499$	−5518.24	−	3185.96i	−0.495051	−	0.285818i	0.231617	−	0.972807i	$-0.425598\pi$
$499$	−5518.24	−	3185.96i	−0.495051	−	0.285818i	−0.726667	+	0.686990i	$0.758932\pi$
$500$		0			0
$501$	−2295.27	−	2371.26i	−0.204680	−	0.211457i
$502$	7283.92	−	27184.0i	0.647604	−	2.41689i
$503$	5861.56	+	5861.56i	0.519591	+	0.519591i	0.917448	−	0.397857i	$-0.130246\pi$
$503$	5861.56	+	5861.56i	0.519591	+	0.519591i	−0.397857	+	0.917448i	$0.630246\pi$
$504$	110.104	−	3379.67i	0.00973104	−	0.298695i
$505$		0			0
$506$	−3567.69	+	2059.81i	−0.313445	+	0.180968i
$507$	−9717.06	+	16214.8i	−0.851183	+	1.42037i
$508$	−4686.33	−	17489.6i	−0.409296	−	1.52751i
$509$	10716.8	−	18562.0i	0.933228	−	1.61640i	0.155465	−	0.987841i	$-0.450312\pi$
$509$	10716.8	−	18562.0i	0.933228	−	1.61640i	0.777763	−	0.628557i	$-0.216354\pi$
$510$		0			0
$511$	753.837	+	1305.68i	0.0652598	+	0.113033i
$512$	4785.52	−	4785.52i	0.413070	−	0.413070i
$513$	14954.3	+	731.103i	1.28703	+	0.0629220i
$514$		−	6281.10i		−	0.539003i
$515$		0			0
$516$	26341.8	+	7520.05i	2.24735	+	0.641573i
$517$	−1986.18	+	532.196i	−0.168960	+	0.0452727i
$518$	1424.12	−	381.591i	0.120796	−	0.0323671i
$519$	897.886	+	3583.36i	0.0759399	+	0.303068i
$520$		0			0
$521$		−	18398.8i		−	1.54715i	−0.633703	−	0.773577i	$-0.718466\pi$
$521$		−	18398.8i		−	1.54715i	0.633703	−	0.773577i	$-0.281534\pi$
$522$	19628.0	+	5950.70i	1.64577	+	0.498956i
$523$	12039.3	−	12039.3i	1.00658	−	1.00658i	0.00659910	−	0.999978i	$-0.497899\pi$
$523$	12039.3	−	12039.3i	1.00658	−	1.00658i	0.999978	−	0.00659910i	$-0.00210057\pi$
$524$	9649.99	+	16714.3i	0.804508	+	1.39345i
$525$		0			0
$526$	731.060	−	1266.23i	0.0606003	−	0.104963i
$527$	−684.877	−	2555.99i	−0.0566104	−	0.211273i
$528$	862.054	+	14.0385i	0.0710532	+	0.00115709i
$529$	−791.700	+	457.088i	−0.0650695	+	0.0375679i
$530$		0			0
$531$	−647.846	−	1211.57i	−0.0529456	−	0.0990166i
$532$	−6582.85	−	6582.85i	−0.536471	−	0.536471i
$533$	−6809.22	+	25412.4i	−0.553359	+	2.06516i
$534$	−24853.5	+	6227.57i	−2.01408	+	0.504669i
$535$		0			0
$536$	−260.765	−	150.553i	−0.0210137	−	0.0121322i
$537$	−12219.6	+	6792.12i	−0.981962	+	0.545813i
$538$	3285.49	+	880.343i	0.263285	+	0.0705470i
$539$	−2516.72			−0.201119
$540$		0			0
$541$	11737.9			0.932811			0.466405	−	0.884571i	$-0.345549\pi$
$541$	11737.9			0.932811			0.466405	+	0.884571i	$0.345549\pi$
$542$	−19969.7	−	5350.86i	−1.58260	−	0.424058i
$543$	896.719	−	498.431i	0.0708690	−	0.0393918i
$544$	−1597.40	−	922.257i	−0.125897	−	0.0726865i
$545$		0			0
$546$	12658.5	−	3171.85i	0.992187	−	0.248613i
$547$	−2248.74	+	8392.40i	−0.175775	+	0.656002i	0.820643	+	0.571441i	$0.193615\pi$
$547$	−2248.74	+	8392.40i	−0.175775	+	0.656002i	−0.996418	+	0.0845610i	$0.973051\pi$
$548$	−19099.6	−	19099.6i	−1.48886	−	1.48886i
$549$	−1949.31	−	63.5054i	−0.151538	−	0.00493687i
$550$		0			0
$551$	15774.0	−	9107.10i	1.21959	−	0.704130i
$552$	9343.85	+	152.164i	0.720472	+	0.0117328i
$553$	310.452	+	1158.62i	0.0238730	+	0.0890951i
$554$	−13325.1	+	23079.8i	−1.02189	+	1.76997i
$555$		0			0
$556$	12921.4	+	22380.6i	0.985595	+	1.70710i
$557$	−3736.22	+	3736.22i	−0.284217	+	0.284217i	−0.834788	−	0.550571i	$-0.814410\pi$
$557$	−3736.22	+	3736.22i	−0.284217	+	0.284217i	0.550571	+	0.834788i	$0.314410\pi$
$558$	−8628.73	−	36980.2i	−0.654629	−	2.80555i
$559$			34101.6i			2.58022i
$560$		0			0
$561$	−92.2815	−	368.285i	−0.00694497	−	0.0277166i
$562$	−20855.1	+	5588.10i	−1.56533	+	0.419430i
$563$	9471.07	−	2537.76i	0.708984	−	0.189972i	0.113733	−	0.993511i	$-0.463719\pi$
$563$	9471.07	−	2537.76i	0.708984	−	0.189972i	0.595251	+	0.803540i	$0.297053\pi$
$564$	13905.1	+	3969.62i	1.03814	+	0.296367i
$565$		0			0
$566$			1592.12i			0.118236i
$567$	5281.34	−	1052.26i	0.391174	−	0.0779377i
$568$	1313.81	−	1313.81i	0.0970536	−	0.0970536i
$569$	−5188.49	−	8986.72i	−0.382272	−	0.662114i	0.609115	−	0.793082i	$-0.291525\pi$
$569$	−5188.49	−	8986.72i	−0.382272	−	0.662114i	−0.991387	+	0.130968i	$0.958192\pi$
$570$		0			0
$571$	2372.48	−	4109.26i	0.173880	−	0.301168i	−0.765893	−	0.642968i	$-0.777703\pi$
$571$	2372.48	−	4109.26i	0.173880	−	0.301168i	0.939773	+	0.341799i	$0.111036\pi$
$572$	−2037.18	−	7602.86i	−0.148914	−	0.555755i
$573$	944.030	−	1575.30i	0.0688262	−	0.114850i
$574$	9806.54	−	5661.81i	0.713096	−	0.411706i
$575$		0			0
$576$	−18991.8	−	11805.7i	−1.37383	−	0.854002i
$577$	−2575.02	−	2575.02i	−0.185788	−	0.185788i	0.608085	−	0.793872i	$-0.291938\pi$
$577$	−2575.02	−	2575.02i	−0.185788	−	0.185788i	−0.793872	+	0.608085i	$0.791938\pi$
$578$	5578.70	−	20820.0i	0.401459	−	1.49827i
$579$	5191.53	+	5363.42i	0.372630	+	0.384967i
$580$		0			0
$581$	−1853.52	−	1070.13i	−0.132353	−	0.0764140i
$582$	77.0834	−	4733.42i	0.00549005	−	0.337125i
$583$	721.724	+	193.385i	0.0512706	+	0.0137379i
$584$	−3460.26			−0.245182
$585$		0			0
$586$	−37937.8			−2.67439
$587$	8790.07	+	2355.29i	0.618067	+	0.165610i	0.554249	−	0.832351i	$-0.313006\pi$
$587$	8790.07	+	2355.29i	0.618067	+	0.165610i	0.0638179	+	0.997962i	$0.479672\pi$
$588$	15181.6	+	9097.86i	1.06476	+	0.638077i
$589$	−29204.6	−	16861.3i	−2.04305	−	1.17955i
$590$		0			0
$591$	−5340.45	+	18706.9i	−0.371704	+	1.30203i
$592$	220.705	−	823.683i	0.0153225	−	0.0571844i
$593$	−9619.29	−	9619.29i	−0.666133	−	0.666133i	0.290686	−	0.956819i	$-0.406117\pi$
$593$	−9619.29	−	9619.29i	−0.666133	−	0.666133i	−0.956819	+	0.290686i	$0.906117\pi$
$594$	−1151.49	−	5325.36i	−0.0795390	−	0.367849i
$595$		0			0
$596$	−6370.05	+	3677.75i	−0.437797	+	0.252762i
$597$	−9556.73	−	17193.3i	−0.655161	−	1.17869i
$598$	9334.27	+	34836.0i	0.638306	+	2.38219i
$599$	−339.119	+	587.372i	−0.0231320	+	0.0400657i	−0.877360	−	0.479833i	$-0.840697\pi$
$599$	−339.119	+	587.372i	−0.0231320	+	0.0400657i	0.854228	+	0.519899i	$0.174030\pi$
$600$		0			0
$601$	−4560.19	−	7898.48i	−0.309508	−	0.536083i	0.668747	−	0.743490i	$-0.266831\pi$
$601$	−4560.19	−	7898.48i	−0.309508	−	0.536083i	−0.978255	+	0.207407i	$0.933498\pi$
$602$	10378.7	−	10378.7i	0.702666	−	0.702666i
$603$	139.126	−	458.899i	0.00939579	−	0.0309914i
$604$		−	23831.5i		−	1.60545i
$605$		0			0
$606$	18422.0	−	17831.6i	1.23489	−	1.19532i
$607$	−13311.1	+	3566.69i	−0.890082	+	0.238497i	−0.674752	−	0.738045i	$-0.735749\pi$
$607$	−13311.1	+	3566.69i	−0.890082	+	0.238497i	−0.215330	+	0.976541i	$0.569083\pi$
$608$	−22705.5	+	6083.91i	−1.51452	+	0.405815i
$609$	4707.25	−	4556.39i	0.313214	−	0.303176i
$610$		0			0
$611$			18001.3i			1.19190i
$612$	−774.669	+	2555.19i	−0.0511669	+	0.168771i
$613$	−7501.39	+	7501.39i	−0.494255	+	0.494255i	−0.909644	−	0.415389i	$-0.863645\pi$
$613$	−7501.39	+	7501.39i	−0.494255	+	0.494255i	0.415389	+	0.909644i	$0.363645\pi$
$614$	−19635.2	−	34009.2i	−1.29057	−	2.23534i
$615$		0			0
$616$	−546.390	+	946.376i	−0.0357381	+	0.0619003i
$617$	−5746.81	−	21447.4i	−0.374972	−	1.39942i	−0.853385	−	0.521281i	$-0.825454\pi$
$617$	−5746.81	−	21447.4i	−0.374972	−	1.39942i	0.478413	−	0.878135i	$-0.341212\pi$
$618$	3215.78	+	5785.46i	0.209317	+	0.376578i
$619$	−6003.77	+	3466.28i	−0.389841	+	0.225075i	−0.682091	−	0.731267i	$-0.738929\pi$
$619$	−6003.77	+	3466.28i	−0.389841	+	0.225075i	0.292250	+	0.956342i	$0.405596\pi$
$620$		0			0
$621$	3145.32	+	14546.3i	0.203248	+	0.939976i
$622$	7206.69	+	7206.69i	0.464569	+	0.464569i
$623$	−2118.17	+	7905.13i	−0.136216	+	0.508366i
$624$	2071.96	−	7257.82i	0.132924	−	0.465618i
$625$		0			0
$626$	−23588.8	−	13619.0i	−1.50607	−	0.869529i
$627$	−4150.33	−	2487.16i	−0.264351	−	0.158417i
$628$	8040.79	+	2154.52i	0.510928	+	0.136903i
$629$	−375.519			−0.0238043
$630$		0			0
$631$	5174.87			0.326479			0.163239	−	0.986586i	$-0.447806\pi$
$631$	5174.87			0.326479			0.163239	+	0.986586i	$0.447806\pi$
$632$	−2659.15	−	712.516i	−0.167366	−	0.0448455i
$633$	114.540	−	7033.52i	0.00719205	−	0.441639i
$634$	34660.5	+	20011.2i	2.17120	+	1.25354i
$635$		0			0
$636$	−3654.56	−	3775.56i	−0.227850	−	0.235394i
$637$	−5702.42	+	21281.7i	−0.354691	+	1.32372i
$638$	−4686.88	−	4686.88i	−0.290839	−	0.290839i
$639$	2513.02	+	1562.15i	0.155577	+	0.0967097i
$640$		0			0
$641$	1800.01	−	1039.24i	0.110914	−	0.0640365i	−0.443517	−	0.896266i	$-0.646269\pi$
$641$	1800.01	−	1039.24i	0.110914	−	0.0640365i	0.554431	+	0.832230i	$0.312936\pi$
$642$	14526.2	−	24239.8i	0.892995	−	1.49014i
$643$	2406.80	+	8982.29i	0.147613	+	0.550898i	0.999625	+	0.0273763i	$0.00871525\pi$
$643$	2406.80	+	8982.29i	0.147613	+	0.550898i	−0.852013	+	0.523521i	$0.824618\pi$
$644$	4626.92	−	8014.06i	0.283115	−	0.490370i
$645$		0			0
$646$	1988.72	+	3444.57i	0.121123	+	0.209791i
$647$	−12361.4	+	12361.4i	−0.751125	+	0.751125i	−0.974689	−	0.223564i	$-0.928231\pi$
$647$	−12361.4	+	12361.4i	−0.751125	+	0.751125i	0.223564	+	0.974689i	$0.428231\pi$
$648$	−3969.11	+	11704.8i	−0.240619	+	0.709578i
$649$			444.002i			0.0268546i
$650$		0			0
$651$	−11663.3	−	3329.64i	−0.702184	−	0.200459i
$652$	6878.98	−	1843.22i	0.413192	−	0.110715i
$653$	27553.8	−	7383.03i	1.65125	−	0.442450i	0.691286	−	0.722581i	$-0.257045\pi$
$653$	27553.8	−	7383.03i	1.65125	−	0.442450i	0.959962	+	0.280131i	$0.0903779\pi$
$654$	5568.92	+	22224.9i	0.332969	+	1.32884i
$655$		0			0
$656$		−	6549.37i		−	0.389802i
$657$	−1252.18	−	5366.48i	−0.0743565	−	0.318670i
$658$	5478.63	−	5478.63i	0.324589	−	0.324589i
$659$	−5594.17	−	9689.39i	−0.330680	−	0.572754i	0.651966	−	0.758249i	$-0.273945\pi$
$659$	−5594.17	−	9689.39i	−0.330680	−	0.572754i	−0.982645	+	0.185494i	$0.940611\pi$
$660$		0			0
$661$	−12520.6	+	21686.4i	−0.736757	+	1.27610i	0.217190	+	0.976129i	$0.430311\pi$
$661$	−12520.6	+	21686.4i	−0.736757	+	1.27610i	−0.953948	+	0.299972i	$0.903023\pi$
$662$	−847.869	−	3164.29i	−0.0497785	−	0.185776i
$663$	−3323.36	−	54.1206i	−0.194673	−	0.00317024i
$664$	4254.01	−	2456.06i	0.248626	−	0.143544i
$665$		0			0
$666$	−5385.99	−	175.467i	−0.313368	−	0.0102090i
$667$	12802.3	+	12802.3i	0.743190	+	0.743190i
$668$	1941.21	−	7244.69i	0.112437	−	0.419619i
$669$	9896.58	−	2479.79i	0.571934	−	0.143310i
$670$		0			0
$671$	545.845	+	315.144i	0.0314040	+	0.0181311i
$672$	−7389.90	+	4107.59i	−0.424213	+	0.235794i
$673$	−17393.8	−	4660.65i	−0.996257	−	0.266946i	−0.276381	−	0.961048i	$-0.589135\pi$
$673$	−17393.8	−	4660.65i	−0.996257	−	0.266946i	−0.719877	+	0.694102i	$0.755802\pi$
$674$	−20093.3			−1.14832
$675$		0			0
$676$	−42961.7			−2.44434
$677$	20774.0	+	5566.38i	1.17934	+	0.316002i	0.794663	−	0.607051i	$-0.207648\pi$
$677$	20774.0	+	5566.38i	1.17934	+	0.316002i	0.384673	+	0.923053i	$0.374314\pi$
$678$	1531.71	−	851.386i	0.0867626	−	0.0482261i
$679$	−1309.54	−	756.062i	−0.0740139	−	0.0427319i
$680$		0			0
$681$	15906.6	−	3985.74i	0.895072	−	0.224279i
$682$	−3176.18	+	11853.7i	−0.178332	+	0.665544i
$683$	−4348.95	−	4348.95i	−0.243643	−	0.243643i	0.574713	−	0.818355i	$-0.305114\pi$
$683$	−4348.95	−	4348.95i	−0.243643	−	0.243643i	−0.818355	+	0.574713i	$0.805114\pi$
$684$	16044.9	+	30006.5i	0.896920	+	1.67738i
$685$		0			0
$686$	17978.8	−	10380.1i	1.00063	−	0.577715i
$687$	−20728.6	−	337.564i	−1.15116	−	0.0187465i
$688$	−2197.20	−	8200.05i	−0.121755	−	0.454395i
$689$	3270.58	−	5664.81i	0.180841	−	0.313225i
$690$		0			0
$691$	7927.92	+	13731.6i	0.436458	+	0.755967i	0.997413	−	0.0718787i	$-0.0228994\pi$
$691$	7927.92	+	13731.6i	0.436458	+	0.755967i	−0.560955	+	0.827846i	$0.689566\pi$
$692$	−5936.61	+	5936.61i	−0.326121	+	0.326121i
$693$	−1665.45	−	504.921i	−0.0912918	−	0.0276773i
$694$		−	18107.7i		−	0.990429i
$695$		0			0
$696$	3654.54	+	14584.9i	0.199030	+	0.794308i
$697$	−2785.85	+	746.467i	−0.151394	+	0.0405659i
$698$	−10526.5	+	2820.56i	−0.570820	+	0.152951i
$699$	−15308.0	−	4370.13i	−0.828330	−	0.236471i
$700$		0			0
$701$		−	21918.5i		−	1.18096i	−0.807054	−	0.590478i	$-0.798939\pi$
$701$		−	21918.5i		−	1.18096i	0.807054	−	0.590478i	$-0.201061\pi$
$702$	−47641.0	−	2329.14i	−2.56139	−	0.125224i
$703$	−3383.93	+	3383.93i	−0.181547	+	0.181547i
$704$	3613.36	+	6258.53i	0.193443	+	0.335053i
$705$		0			0
$706$	−24185.9	+	41891.2i	−1.28930	+	2.23314i
$707$	−2119.56	−	7910.29i	−0.112750	−	0.420788i
$708$	1605.05	−	2678.35i	0.0851999	−	0.142173i
$709$	25661.5	−	14815.7i	1.35929	−	0.784787i	0.369763	−	0.929126i	$-0.379439\pi$
$709$	25661.5	−	14815.7i	1.35929	−	0.784787i	0.989528	+	0.144338i	$0.0461054\pi$
$710$		0			0
$711$	142.755	−	4381.89i	0.00752987	−	0.231130i
$712$	−13281.6	−	13281.6i	−0.699087	−	0.699087i
$713$	8675.82	−	32378.6i	0.455697	−	1.70068i
$714$	994.982	+	1027.92i	0.0521516	+	0.0538783i
$715$		0			0
$716$	−27516.2	−	15886.5i	−1.43622	−	0.829199i
$717$	329.295	−	20220.8i	0.0171517	−	1.05322i
$718$	29786.9	+	7981.37i	1.54824	+	0.414850i
$719$	−5855.14			−0.303700			−0.151850	−	0.988404i	$-0.548523\pi$
$719$	−5855.14			−0.303700			−0.151850	+	0.988404i	$0.548523\pi$
$720$		0			0
$721$	2114.24			0.109207
$722$	19473.7	+	5217.97i	1.00379	+	0.268965i
$723$	−29342.5	−	17584.1i	−1.50935	−	0.904508i
$724$	2019.25	+	1165.81i	0.103653	+	0.0598440i
$725$		0			0
$726$	7966.64	−	27906.1i	0.407258	−	1.42658i
$727$	4677.55	−	17456.9i	0.238626	−	0.890563i	−0.737855	−	0.674959i	$-0.764161\pi$
$727$	4677.55	−	17456.9i	0.238626	−	0.890563i	0.976481	−	0.215604i	$-0.0691720\pi$
$728$	6764.65	+	6764.65i	0.344388	+	0.344388i
$729$	−19589.1	−	1919.99i	−0.995231	−	0.0975455i
$730$		0			0
$731$	−3237.56	+	1869.21i	−0.163811	+	0.0945762i
$732$	−2153.46	−	3874.25i	−0.108735	−	0.195623i
$733$	9615.09	+	35884.0i	0.484504	+	1.80819i	0.582284	+	0.812986i	$0.302159\pi$
$733$	9615.09	+	35884.0i	0.484504	+	1.80819i	−0.0977795	+	0.995208i	$0.531174\pi$
$734$	20929.9	−	36251.7i	1.05250	−	1.82299i
$735$		0			0
$736$	−11682.9	−	20235.3i	−0.585104	−	1.01343i
$737$	−109.578	+	109.578i	−0.00547676	+	0.00547676i
$738$	−40305.8	+	9404.70i	−2.01040	+	0.469095i
$739$		−	16862.4i		−	0.839371i	−0.907670	−	0.419686i	$-0.862140\pi$
$739$		−	16862.4i		−	0.839371i	0.907670	−	0.419686i	$-0.137860\pi$
$740$		0			0
$741$	−30435.6	+	29460.2i	−1.50888	+	1.46052i
$742$	−2719.46	+	728.677i	−0.134548	+	0.0360520i
$743$	7561.26	−	2026.03i	0.373345	−	0.100038i	−0.0672671	−	0.997735i	$-0.521428\pi$
$743$	7561.26	−	2026.03i	0.373345	−	0.100038i	0.440613	+	0.897697i	$0.354761\pi$
$744$	20002.3	−	19361.2i	0.985643	−	0.954055i
$745$		0			0
$746$			25811.4i			1.26678i
$747$	5348.49	+	5708.72i	0.261969	+	0.279613i
$748$	610.143	−	610.143i	0.0298249	−	0.0298249i
$749$	−4513.18	−	7817.06i	−0.220171	−	0.381347i
$750$		0			0
$751$	9768.62	−	16919.7i	0.474650	−	0.822117i	−0.524929	−	0.851146i	$-0.675908\pi$
$751$	9768.62	−	16919.7i	0.474650	−	0.822117i	0.999579	+	0.0290288i	$0.00924145\pi$
$752$	−1159.84	−	4328.57i	−0.0562433	−	0.209903i
$753$	15962.6	+	28718.0i	0.772523	+	1.38983i
$754$	−50252.4	+	29013.2i	−2.42717	+	1.40133i
$755$		0			0
$756$	8221.19	+	9066.37i	0.395505	+	0.436165i
$757$	−10039.5	−	10039.5i	−0.482024	−	0.482024i	0.423754	−	0.905777i	$-0.360712\pi$
$757$	−10039.5	−	10039.5i	−0.482024	−	0.482024i	−0.905777	+	0.423754i	$0.860712\pi$
$758$	7622.74	−	28448.5i	0.365265	−	1.36319i
$759$	1320.28	−	4624.79i	0.0631400	−	0.221172i
$760$		0			0
$761$	−20084.8	−	11595.9i	−0.956731	−	0.552369i	−0.0615654	−	0.998103i	$-0.519609\pi$
$761$	−20084.8	−	11595.9i	−0.956731	−	0.552369i	−0.895165	+	0.445734i	$0.852943\pi$
$762$	30415.9	+	18227.3i	1.44600	+	0.866545i
$763$	7069.05	+	1894.15i	0.335409	+	0.0898725i
$764$	4173.81			0.197648
$765$		0			0
$766$	55350.5			2.61083
$767$	3754.54	+	1006.02i	0.176752	+	0.0473604i
$768$	163.960	−	10068.2i	0.00770364	−	0.473054i
$769$	30950.8	+	17869.4i	1.45138	+	0.837956i	0.998560	−	0.0536450i	$-0.0170839\pi$
$769$	30950.8	+	17869.4i	1.45138	+	0.837956i	0.452822	+	0.891601i	$0.350417\pi$
$770$		0			0
$771$	5100.12	+	5268.98i	0.238231	+	0.246119i
$772$	−4390.71	+	16386.4i	−0.204696	+	0.763935i
$773$	7858.61	+	7858.61i	0.365659	+	0.365659i	0.865891	−	0.500232i	$-0.166752\pi$
$773$	7858.61	+	7858.61i	0.365659	+	0.365659i	−0.500232	+	0.865891i	$0.666752\pi$
$774$	−47309.2	+	25296.9i	−2.19702	+	1.17478i
$775$		0			0
$776$	3005.51	−	1735.23i	0.139036	−	0.0802723i
$777$	−884.796	+	1476.46i	−0.0408518	+	0.0681694i
$778$	−11508.8	−	42951.4i	−0.530347	−	1.97928i
$779$	−18377.6	+	31831.0i	−0.845246	+	1.46401i
$780$		0			0
$781$	−478.124	−	828.135i	−0.0219060	−	0.0379424i
$782$	−2795.65	+	2795.65i	−0.127842	+	0.127842i
$783$	−21297.0	+	10945.7i	−0.972023	+	0.499575i
$784$		−	5484.80i		−	0.249854i
$785$		0			0
$786$	−36344.5	−	10375.6i	−1.64932	−	0.470847i
$787$	−2599.53	+	696.542i	−0.117742	+	0.0315490i	−0.317209	−	0.948356i	$-0.602746\pi$
$787$	−2599.53	+	696.542i	−0.117742	+	0.0315490i	0.199467	+	0.979905i	$0.436079\pi$
$788$	−42707.0	+	11443.3i	−1.93068	+	0.517324i
$789$	414.896	+	1655.80i	0.0187208	+	0.0747124i
$790$		0			0
$791$		−	559.750i		−	0.0251611i
$792$	2914.77	−	2730.85i	0.130773	−	0.122521i
$793$	3901.68	−	3901.68i	0.174719	−	0.174719i
$794$	3929.85	+	6806.70i	0.175649	+	0.304233i
$795$		0			0
$796$	22352.8	−	38716.2i	0.995320	−	1.72395i
$797$	−7691.54	−	28705.2i	−0.341842	−	1.27577i	−0.896258	−	0.443533i	$-0.853725\pi$
$797$	−7691.54	−	28705.2i	−0.341842	−	1.27577i	0.554416	−	0.832240i	$-0.312942\pi$
$798$	18229.1	+	296.860i	0.808651	+	0.0131688i
$799$	−1709.02	+	986.702i	−0.0756705	+	0.0436884i
$800$		0			0
$801$	15792.0	−	25404.6i	0.696610	−	1.12063i
$802$	−29070.9	−	29070.9i	−1.27996	−	1.27996i
$803$	−460.920	+	1720.18i	−0.0202559	+	0.0755962i
$804$	1057.13	−	264.886i	0.0463707	−	0.0116192i
$805$		0			0
$806$	93039.5	+	53716.4i	4.06598	+	2.34749i
$807$	−3470.89	+	1929.26i	−0.151402	+	0.0841550i
$808$	18154.9	+	4864.59i	0.790454	+	0.211802i
$809$	13804.2			0.599913			0.299957	−	0.953953i	$-0.403028\pi$
$809$	13804.2			0.599913			0.299957	+	0.953953i	$0.403028\pi$
$810$		0			0
$811$	42231.9			1.82856			0.914280	−	0.405082i	$-0.132757\pi$
$811$	42231.9			1.82856			0.914280	+	0.405082i	$0.132757\pi$
$812$	14381.6	+	3853.54i	0.621547	+	0.166543i
$813$	21096.6	−	11726.3i	0.910075	−	0.505855i
$814$	1508.19	+	870.752i	0.0649410	+	0.0374937i
$815$		0			0
$816$	802.619	−	201.113i	0.0344330	−	0.00862790i
$817$	−12330.7	+	46018.9i	−0.528027	+	1.97062i
$818$	10238.9	+	10238.9i	0.437644	+	0.437644i
$819$	−8043.27	+	12939.2i	−0.343168	+	0.552054i
$820$		0			0
$821$	13907.5	−	8029.52i	0.591201	−	0.341330i	−0.174371	−	0.984680i	$-0.555789\pi$
$821$	13907.5	−	8029.52i	0.591201	−	0.341330i	0.765572	+	0.643350i	$0.222456\pi$
$822$	52890.1	+	861.312i	2.24423	+	0.0365471i
$823$	5838.49	+	21789.5i	0.247287	+	0.922886i	0.972220	+	0.234068i	$0.0752037\pi$
$823$	5838.49	+	21789.5i	0.247287	+	0.922886i	−0.724934	+	0.688819i	$0.758130\pi$
$824$	−2426.19	+	4202.29i	−0.102573	+	0.177662i
$825$		0			0
$826$	−836.501	−	1448.86i	−0.0352368	−	0.0610319i
$827$	−13252.9	+	13252.9i	−0.557253	+	0.557253i	−0.928524	−	0.371271i	$-0.878922\pi$
$827$	−13252.9	+	13252.9i	−0.557253	+	0.557253i	0.371271	+	0.928524i	$0.378922\pi$
$828$	−24682.8	+	23125.3i	−1.03597	+	0.970602i
$829$		−	5055.46i		−	0.211801i	−0.994377	−	0.105901i	$-0.966227\pi$
$829$		−	5055.46i		−	0.211801i	0.994377	−	0.105901i	$-0.0337726\pi$
$830$		0			0
$831$	−7562.35	−	30180.5i	−0.315686	−	1.25987i
$832$	61110.1	−	16374.4i	2.54641	−	0.682308i
$833$	−2333.03	+	625.133i	−0.0970403	+	0.0260019i
$834$	−48665.6	−	13893.0i	−2.02056	−	0.576830i
$835$		0			0
$836$		−	10996.4i		−	0.454927i
$837$	37265.5	+	24015.0i	1.53893	+	0.991730i
$838$	−11581.7	+	11581.7i	−0.477427	+	0.477427i
$839$	21738.9	+	37653.0i	0.894531	+	1.54937i	0.834384	+	0.551184i	$0.185824\pi$
$839$	21738.9	+	37653.0i	0.894531	+	1.54937i	0.0601475	+	0.998190i	$0.480843\pi$
$840$		0			0
$841$	−2370.66	+	4106.11i	−0.0972021	+	0.168359i
$842$	7902.91	+	29494.1i	0.323459	+	1.20716i
$843$	12957.1	−	21621.5i	0.529379	−	0.883374i
$844$	13845.2	−	7993.55i	0.564660	−	0.326006i
$845$		0			0
$846$	−24973.2	+	13353.5i	−1.01489	+	0.542676i
$847$	−6554.69	−	6554.69i	−0.265905	−	0.265905i
$848$	−421.453	+	1572.88i	−0.0170669	+	0.0636946i
$849$	−1292.77	−	1335.57i	−0.0522588	−	0.0539890i
$850$		0			0
$851$	−4119.65	−	2378.48i	−0.165946	−	0.0958087i
$852$	−109.499	+	6723.94i	−0.00440302	+	0.270374i
$853$	−13764.3	−	3688.14i	−0.552499	−	0.148042i	−0.0282408	−	0.999601i	$-0.508991\pi$
$853$	−13764.3	−	3688.14i	−0.552499	−	0.148042i	−0.524258	+	0.851560i	$0.675657\pi$
$854$	−2374.93			−0.0951619
$855$		0			0
$856$	20716.4			0.827186
$857$	34076.0	+	9130.63i	1.35824	+	0.363940i	0.863170	−	0.504913i	$-0.168475\pi$
$857$	34076.0	+	9130.63i	1.35824	+	0.363940i	0.495071	+	0.868853i	$0.335142\pi$
$858$	13222.0	+	7923.56i	0.526099	+	0.315275i
$859$	−4594.34	−	2652.54i	−0.182488	−	0.105359i	0.405973	−	0.913885i	$-0.366933\pi$
$859$	−4594.34	−	2652.54i	−0.182488	−	0.105359i	−0.588461	+	0.808526i	$0.700266\pi$
$860$		0			0
$861$	−3629.07	+	12712.2i	−0.143645	+	0.503171i
$862$	3589.76	−	13397.2i	0.141842	−	0.529362i
$863$	20991.2	+	20991.2i	0.827984	+	0.827984i	0.987238	−	0.159254i	$-0.0509088\pi$
$863$	20991.2	+	20991.2i	0.827984	+	0.827984i	−0.159254	+	0.987238i	$0.550909\pi$
$864$	30204.6	−	6531.05i	1.18933	−	0.257165i
$865$		0			0
$866$	2870.01	−	1657.00i	0.112618	−	0.0650199i
$867$	12225.6	+	21994.9i	0.478898	+	0.861577i
$868$	−7134.62	−	26626.8i	−0.278992	−	1.04121i
$869$	−708.419	+	1227.02i	−0.0276542	+	0.0478984i
$870$		0			0
$871$	678.324	+	1174.89i	0.0263882	+	0.0457057i
$872$	−11876.9	+	11876.9i	−0.461242	+	0.461242i
$873$	3778.78	+	4033.28i	0.146497	+	0.156364i
$874$			50385.1i			1.95000i
$875$		0			0
$876$	8998.78	−	8710.39i	0.347078	−	0.335955i
$877$	7502.01	−	2010.16i	0.288854	−	0.0773981i	−0.111483	−	0.993766i	$-0.535560\pi$
$877$	7502.01	−	2010.16i	0.288854	−	0.0773981i	0.400336	+	0.916368i	$0.368893\pi$
$878$	15951.9	−	4274.29i	0.613154	−	0.164294i
$879$	31824.6	−	30804.7i	1.22118	−	1.18204i
$880$		0			0
$881$			47965.9i			1.83429i	0.398550	+	0.917146i	$0.369513\pi$
$881$			47965.9i			1.83429i	−0.398550	+	0.917146i	$0.630487\pi$
$882$	−33754.3	+	7876.01i	−1.28862	+	0.300679i
$883$	26596.6	−	26596.6i	1.01364	−	1.01364i	0.0137372	−	0.999906i	$-0.495627\pi$
$883$	26596.6	−	26596.6i	1.01364	−	1.01364i	0.999906	−	0.0137372i	$-0.00437282\pi$
$884$	−3776.97	−	6541.91i	−0.143703	−	0.248901i
$885$		0			0
$886$	−4374.53	+	7576.91i	−0.165875	+	0.287304i
$887$	7985.39	+	29801.9i	0.302281	+	1.12813i	0.935261	+	0.353960i	$0.115165\pi$
$887$	7985.39	+	29801.9i	0.302281	+	1.12813i	−0.632980	+	0.774168i	$0.718168\pi$
$888$	−1919.28	−	3452.94i	−0.0725301	−	0.130488i
$889$	9808.79	−	5663.11i	0.370052	−	0.213650i
$890$		0			0
$891$	5290.03	+	3532.27i	0.198903	+	0.132812i
$892$	16395.8	+	16395.8i	0.615439	+	0.615439i
$893$	−6509.04	+	24292.1i	−0.243916	+	0.910306i
$894$	3954.29	−	13851.4i	0.147932	−	0.518187i
$895$		0			0
$896$	−12309.2	−	7106.69i	−0.458951	−	0.264975i
$897$	−36116.3	−	21643.4i	−1.34436	−	0.805631i
$898$	−28187.0	−	7552.68i	−1.04745	−	0.280664i
$899$	53933.2			2.00086
$900$		0			0
$901$	717.080			0.0265143
$902$	12919.7	+	3461.82i	0.476916	+	0.127789i
$903$	−279.020	+	17133.6i	−0.0102826	+	0.631419i
$904$	1112.57	+	642.340i	0.0409330	+	0.0236327i
$905$		0			0
$906$	32459.6	+	33534.3i	1.19028	+	1.22969i
$907$	4776.39	−	17825.7i	0.174859	−	0.652584i	−0.821716	−	0.569897i	$-0.806983\pi$
$907$	4776.39	−	17825.7i	0.174859	−	0.652584i	0.996576	−	0.0826873i	$-0.0263503\pi$
$908$	26352.8	+	26352.8i	0.963158	+	0.963158i
$909$	−974.637	+	29916.6i	−0.0355629	+	1.09161i
$910$		0			0
$911$	−30948.1	+	17867.9i	−1.12553	+	0.649824i	−0.942807	−	0.333340i	$-0.891824\pi$
$911$	−30948.1	+	17867.9i	−1.12553	+	0.649824i	−0.182722	+	0.983165i	$0.558491\pi$
$912$	5420.38	−	9044.98i	0.196806	−	0.328409i
$913$	−654.313	−	2441.93i	−0.0237181	−	0.0885171i
$914$	−28466.0	+	49304.5i	−1.03017	+	1.78430i
$915$		0			0
$916$	−23558.0	−	40803.6i	−0.849757	−	1.47182i
$917$	−8536.71	+	8536.71i	−0.307423	+	0.307423i
$918$	−2390.22	−	4650.64i	−0.0859356	−	0.167205i
$919$		−	4406.96i		−	0.158185i	−0.996867	−	0.0790926i	$-0.974798\pi$
$919$		−	4406.96i		−	0.158185i	0.996867	−	0.0790926i	$-0.0252023\pi$
$920$		0			0
$921$	44086.0	+	12585.7i	1.57729	+	0.450284i
$922$	9908.59	−	2655.00i	0.353929	−	0.0948349i
$923$	−8086.15	+	2166.68i	−0.288363	+	0.0772666i
$924$	−961.332	−	3836.57i	−0.0342267	−	0.136595i
$925$		0			0
$926$			5508.11i			0.195473i
$927$	−7395.27	−	2242.05i	−0.262020	−	0.0794377i
$928$	26583.2	−	26583.2i	0.940340	−	0.940340i
$929$	14845.9	+	25713.9i	0.524305	+	0.908123i	0.999600	+	0.0282963i	$0.00900820\pi$
$929$	14845.9	+	25713.9i	0.524305	+	0.908123i	−0.475294	+	0.879827i	$0.657658\pi$
$930$		0			0
$931$	−15390.4	+	26657.0i	−0.541784	+	0.938397i
$932$	−9364.14	−	34947.4i	−0.329112	−	1.22826i
$933$	−11897.1	−	193.743i	−0.417464	−	0.00679836i
$934$	−20547.9	+	11863.3i	−0.719858	+	0.415610i
$935$		0			0
$936$	−16488.0	−	30835.2i	−0.575779	−	1.07680i
$937$	−10550.5	−	10550.5i	−0.367844	−	0.367844i	0.498846	−	0.866691i	$-0.333757\pi$
$937$	−10550.5	−	10550.5i	−0.367844	−	0.367844i	−0.866691	+	0.498846i	$0.833757\pi$
$938$	151.129	−	564.021i	0.00526070	−	0.0196332i
$939$	30846.1	−	7729.15i	1.07202	−	0.268617i
$940$		0			0
$941$	−36526.6	−	21088.6i	−1.26539	−	0.730573i	−0.291277	−	0.956639i	$-0.594080\pi$
$941$	−36526.6	−	21088.6i	−1.26539	−	0.730573i	−0.974112	+	0.226066i	$0.927414\pi$
$942$	−14249.1	+	7920.19i	−0.492845	+	0.273942i
$943$	−35290.4	−	9456.03i	−1.21868	−	0.326544i
$944$	−967.633			−0.0333620
$945$		0			0
$946$	17337.3			0.595860
$947$	−30245.9	−	8104.37i	−1.03787	−	0.278096i	−0.300638	−	0.953738i	$-0.597200\pi$
$947$	−30245.9	−	8104.37i	−1.03787	−	0.278096i	−0.737230	+	0.675642i	$0.763866\pi$
$948$	8709.00	−	4840.81i	0.298371	−	0.165846i
$949$	13501.7	+	7795.20i	0.461837	+	0.266641i
$950$		0			0
$951$	−45324.1	+	11356.9i	−1.54546	+	0.387248i
$952$	−271.437	+	1013.02i	−0.00924090	+	0.0344875i
$953$	−11585.6	−	11585.6i	−0.393803	−	0.393803i	0.482238	−	0.876040i	$-0.339824\pi$
$953$	−11585.6	−	11585.6i	−0.393803	−	0.393803i	−0.876040	+	0.482238i	$0.839824\pi$
$954$	10285.0	+	335.068i	0.349044	+	0.0113713i
$955$		0			0
$956$	39804.0	−	22980.9i	1.34661	−	0.777463i
$957$	7737.30	+	126.001i	0.261349	+	0.00425605i
$958$	−2777.40	−	10365.4i	−0.0936676	−	0.349572i
$959$	8448.05	−	14632.5i	0.284465	−	0.492708i
$960$		0			0
$961$	−35031.6	−	60676.6i	−1.17591	−	2.03674i
$962$	10780.5	−	10780.5i	0.361305	−	0.361305i
$963$	7496.74	+	32128.8i	0.250861	+	1.07512i
$964$		−	77744.0i		−	2.59747i
$965$		0			0
$966$	4404.78	+	17579.0i	0.146710	+	0.585501i
$967$	43844.9	−	11748.2i	1.45807	−	0.390689i	0.559249	−	0.829000i	$-0.311090\pi$
$967$	43844.9	−	11748.2i	1.45807	−	0.390689i	0.898824	+	0.438310i	$0.144423\pi$
$968$	20550.0	−	5506.35i	0.682337	−	0.182832i
$969$	−4465.18	−	1274.72i	−0.148031	−	0.0422599i
$970$		0			0
$971$			3396.55i			0.112256i	0.998424	+	0.0561280i	$0.0178755\pi$
$971$			3396.55i			0.112256i	−0.998424	+	0.0561280i	$0.982125\pi$
$972$	−19141.9	−	40430.9i	−0.631664	−	1.33418i
$973$	−11430.7	+	11430.7i	−0.376621	+	0.376621i
$974$	−41788.0	−	72379.0i	−1.37472	−	2.38108i
$975$		0			0
$976$	−686.806	+	1189.58i	−0.0225247	+	0.0390140i
$977$	4240.78	+	15826.8i	0.138868	+	0.518264i	0.999952	+	0.00980049i	$0.00311964\pi$
$977$	4240.78	+	15826.8i	0.138868	+	0.518264i	−0.861084	+	0.508463i	$0.830214\pi$
$978$	−7169.14	+	11963.1i	−0.234401	+	0.391144i
$979$	−8371.78	+	4833.45i	−0.273303	+	0.157791i
$980$		0			0
$981$	−22717.7	−	14121.8i	−0.739370	−	0.459608i
$982$	17742.4	+	17742.4i	0.576562	+	0.576562i
$983$	−9263.69	+	34572.6i	−0.300576	+	1.12176i	0.636112	+	0.771597i	$0.280542\pi$
$983$	−9263.69	+	34572.6i	−0.300576	+	1.12176i	−0.936687	+	0.350166i	$0.886125\pi$
$984$	−21102.4	−	21801.0i	−0.683657	−	0.706293i
$985$		0			0
$986$	−5508.96	−	3180.60i	−0.177932	−	0.102729i
$987$	−147.287	+	9044.35i	−0.00474993	+	0.291677i
$988$	−92987.1	−	24915.8i	−2.99424	−	0.802305i
$989$	−47357.2			−1.52262
$990$		0			0
$991$	−19832.4			−0.635719			−0.317859	−	0.948138i	$-0.602964\pi$
$991$	−19832.4			−0.635719			−0.317859	+	0.948138i	$0.602964\pi$
$992$	−67232.1	−	18014.8i	−2.15183	−	0.576582i
$993$	3280.58	+	1965.95i	0.104840	+	0.0628274i
$994$	3120.42	+	1801.57i	0.0995710	+	0.0574874i
$995$		0			0
$996$	−4880.49	+	17095.7i	−0.155265	+	0.543875i
$997$	9959.18	−	37168.2i	0.316359	−	1.18067i	−0.606358	−	0.795192i	$-0.707370\pi$
$997$	9959.18	−	37168.2i	0.316359	−	1.18067i	0.922717	−	0.385478i	$-0.125963\pi$
$998$	20053.4	+	20053.4i	0.636052	+	0.636052i
$999$	4660.59	−	4226.12i	0.147602	−	0.133842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.p.b.32.2		64
5.2	odd	4		45.4.l.a.23.15	yes	64
5.3	odd	4	inner	225.4.p.b.68.2		64
5.4	even	2		45.4.l.a.32.15	yes	64
9.2	odd	6	inner	225.4.p.b.182.2		64
15.2	even	4		135.4.m.a.98.2		64
15.14	odd	2		135.4.m.a.17.2		64
45.2	even	12		45.4.l.a.38.15	yes	64
45.7	odd	12		135.4.m.a.8.2		64
45.29	odd	6		45.4.l.a.2.15	✓	64
45.34	even	6		135.4.m.a.62.2		64
45.38	even	12	inner	225.4.p.b.218.2		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.15	✓	64	45.29	odd	6
45.4.l.a.23.15	yes	64	5.2	odd	4
45.4.l.a.32.15	yes	64	5.4	even	2
45.4.l.a.38.15	yes	64	45.2	even	12
135.4.m.a.8.2		64	45.7	odd	12
135.4.m.a.17.2		64	15.14	odd	2
135.4.m.a.62.2		64	45.34	even	6
135.4.m.a.98.2		64	15.2	even	4
225.4.p.b.32.2		64	1.1	even	1	trivial
225.4.p.b.68.2		64	5.3	odd	4	inner
225.4.p.b.182.2		64	9.2	odd	6	inner
225.4.p.b.218.2		64	45.38	even	12	inner

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.29910 - 1.15194i) q^{2} +(4.54171 - 2.52446i) q^{3} +(10.2271 + 5.90461i) q^{4} +(-22.4333 + 5.62113i) q^{6} +(-1.91190 + 7.13532i) q^{7} +(-11.9883 - 11.9883i) q^{8} +(14.2542 - 22.9307i) q^{9} +O(q^{10})\)	\(q+(-4.29910 - 1.15194i) q^{2} +(4.54171 - 2.52446i) q^{3} +(10.2271 + 5.90461i) q^{4} +(-22.4333 + 5.62113i) q^{6} +(-1.91190 + 7.13532i) q^{7} +(-11.9883 - 11.9883i) q^{8} +(14.2542 - 22.9307i) q^{9} +(-7.55654 + 4.36277i) q^{11} +(61.3544 + 0.999152i) q^{12} +(19.7704 + 73.7842i) q^{13} +(16.4389 - 28.4731i) q^{14} +(-9.50797 - 16.4683i) q^{16} +(-5.92131 + 5.92131i) q^{17} +(-87.6951 + 82.1614i) q^{18} +106.718i q^{19} +(9.32953 + 37.2331i) q^{21} +(37.5120 - 10.0513i) q^{22} +(-102.465 + 27.4553i) q^{23} +(-84.7110 - 24.1833i) q^{24} -339.980i q^{26} +(6.85080 - 140.129i) q^{27} +(-61.6846 + 61.6846i) q^{28} +(-85.3380 - 147.810i) q^{29} +(-157.999 + 273.662i) q^{31} +(57.0093 + 212.761i) q^{32} +(-23.3059 + 38.8906i) q^{33} +(32.2773 - 18.6353i) q^{34} +(281.176 - 150.349i) q^{36} +(31.7091 + 31.7091i) q^{37} +(122.933 - 458.791i) q^{38} +(276.057 + 285.197i) q^{39} +(298.272 + 172.207i) q^{41} +(2.78172 - 170.816i) q^{42} +(431.220 + 115.545i) q^{43} -103.042 q^{44} +472.133 q^{46} +(227.629 + 60.9929i) q^{47} +(-84.7559 - 50.7917i) q^{48} +(249.789 + 144.216i) q^{49} +(-11.9448 + 41.8410i) q^{51} +(-233.473 + 871.335i) q^{52} +(-60.5508 - 60.5508i) q^{53} +(-190.872 + 594.536i) q^{54} +(108.460 - 62.6197i) q^{56} +(269.405 + 484.682i) q^{57} +(196.609 + 733.754i) q^{58} +(25.4427 - 44.0680i) q^{59} +(-36.1174 - 62.5572i) q^{61} +(994.494 - 994.494i) q^{62} +(136.365 + 145.550i) q^{63} -828.227i q^{64} +(144.994 - 140.347i) q^{66} +(17.1550 - 4.59668i) q^{67} +(-95.5208 + 25.5947i) q^{68} +(-396.055 + 383.362i) q^{69} +109.592i q^{71} +(-445.782 + 104.016i) q^{72} +(144.319 - 144.319i) q^{73} +(-99.7935 - 172.847i) q^{74} +(-630.128 + 1091.41i) q^{76} +(-16.6824 - 62.2595i) q^{77} +(-858.266 - 1544.09i) q^{78} +(140.624 - 81.1891i) q^{79} +(-322.635 - 653.718i) q^{81} +(-1083.93 - 1083.93i) q^{82} +(-74.9883 + 279.860i) q^{83} +(-124.433 + 435.873i) q^{84} +(-1720.76 - 993.479i) q^{86} +(-760.720 - 455.877i) q^{87} +(142.892 + 38.2877i) q^{88} +1107.89 q^{89} -564.273 q^{91} +(-1210.03 - 324.227i) q^{92} +(-26.7358 + 1641.75i) q^{93} +(-908.339 - 524.430i) q^{94} +(796.027 + 822.383i) q^{96} +(-52.9802 + 197.725i) q^{97} +(-907.741 - 907.741i) q^{98} +(-7.67108 + 235.465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) \) 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) \) 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7 - 36 * q^11 + 138 * q^12 + 2 * q^13 + 316 * q^16 + 480 * q^18 + 480 * q^21 + 34 * q^22 - 306 * q^23 - 180 * q^27 + 232 * q^28 - 4 * q^31 + 1770 * q^32 + 294 * q^33 - 216 * q^36 - 136 * q^37 - 114 * q^38 + 1992 * q^41 - 1698 * q^42 + 2 * q^43 - 952 * q^46 - 3462 * q^47 - 4326 * q^48 - 2496 * q^51 + 242 * q^52 - 7128 * q^56 + 2544 * q^57 - 534 * q^58 + 32 * q^61 + 4038 * q^63 + 2892 * q^66 - 610 * q^67 + 2694 * q^68 + 1854 * q^72 + 8 * q^73 + 1368 * q^76 + 6486 * q^77 - 1434 * q^78 + 3012 * q^81 + 3784 * q^82 - 2814 * q^83 + 12480 * q^86 - 4830 * q^87 + 1338 * q^88 + 992 * q^91 - 13152 * q^92 - 8310 * q^93 - 7932 * q^96 - 358 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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