LMFDB - Embedded newform 225.4.p.b.32.13

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			32.13
Character	$\chi$	$=$	225.32
Dual form			225.4.p.b.218.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.87860 + 0.771317i) q^{2} +(5.17956 + 0.414910i) q^{3} +(0.763180 + 0.440622i) q^{4} +(14.5898 + 5.18944i) q^{6} +(8.39055 - 31.3140i) q^{7} +(-15.0012 - 15.0012i) q^{8} +(26.6557 + 4.29810i) q^{9} +O(q^{10})$	\(q+(2.87860 + 0.771317i) q^{2} +(5.17956 + 0.414910i) q^{3} +(0.763180 + 0.440622i) q^{4} +(14.5898 + 5.18944i) q^{6} +(8.39055 - 31.3140i) q^{7} +(-15.0012 - 15.0012i) q^{8} +(26.6557 + 4.29810i) q^{9} +(15.0191 - 8.67129i) q^{11} +(3.77012 + 2.59888i) q^{12} +(-2.27646 - 8.49586i) q^{13} +(48.3060 - 83.6685i) q^{14} +(-35.1367 - 60.8585i) q^{16} +(23.2549 - 23.2549i) q^{17} +(73.4158 + 32.9325i) q^{18} +145.204i q^{19} +(56.4519 - 158.711i) q^{21} +(49.9223 - 13.3766i) q^{22} +(11.2331 - 3.00990i) q^{23} +(-71.4755 - 83.9238i) q^{24} -26.2120i q^{26} +(136.281 + 33.3220i) q^{27} +(20.2011 - 20.2011i) q^{28} +(110.651 + 191.653i) q^{29} +(-34.8793 + 60.4127i) q^{31} +(-10.2765 - 38.3524i) q^{32} +(81.3902 - 38.6819i) q^{33} +(84.8784 - 49.0046i) q^{34} +(18.4492 + 15.0253i) q^{36} +(-56.4980 - 56.4980i) q^{37} +(-111.998 + 417.984i) q^{38} +(-8.26604 - 44.9494i) q^{39} +(-141.694 - 81.8068i) q^{41} +(284.919 - 413.323i) q^{42} +(-107.661 - 28.8478i) q^{43} +15.2830 q^{44} +34.6571 q^{46} +(-186.165 - 49.8826i) q^{47} +(-156.742 - 329.799i) q^{48} +(-613.116 - 353.983i) q^{49} +(130.099 - 110.801i) q^{51} +(2.00612 - 7.48693i) q^{52} +(367.732 + 367.732i) q^{53} +(366.597 + 201.037i) q^{54} +(-595.615 + 343.879i) q^{56} +(-60.2466 + 752.093i) q^{57} +(170.694 + 637.039i) q^{58} +(210.017 - 363.760i) q^{59} +(226.039 + 391.511i) q^{61} +(-147.001 + 147.001i) q^{62} +(358.247 - 798.632i) q^{63} +443.859i q^{64} +(264.126 - 48.5718i) q^{66} +(225.409 - 60.3981i) q^{67} +(27.9943 - 7.50105i) q^{68} +(59.4313 - 10.9292i) q^{69} -434.936i q^{71} +(-335.391 - 464.344i) q^{72} +(-226.275 + 226.275i) q^{73} +(-119.057 - 206.213i) q^{74} +(-63.9801 + 110.817i) q^{76} +(-145.514 - 543.065i) q^{77} +(10.8756 - 135.767i) q^{78} +(-138.839 + 80.1586i) q^{79} +(692.053 + 229.138i) q^{81} +(-344.779 - 344.779i) q^{82} +(39.2062 - 146.319i) q^{83} +(113.015 - 96.2513i) q^{84} +(-287.663 - 166.082i) q^{86} +(493.605 + 1038.59i) q^{87} +(-355.384 - 95.2250i) q^{88} +125.629 q^{89} -285.140 q^{91} +(9.89909 + 2.65245i) q^{92} +(-205.725 + 298.439i) q^{93} +(-497.417 - 287.184i) q^{94} +(-37.3150 - 202.913i) q^{96} +(-263.620 + 983.843i) q^{97} +(-1491.88 - 1491.88i) q^{98} +(437.615 - 166.586i) 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 $

$2$	2.87860	+	0.771317i	1.01774	+	0.272702i	0.728859	−	0.684664i	$-0.240051\pi$
$2$	2.87860	+	0.771317i	1.01774	+	0.272702i	0.288878	+	0.957366i	$0.406718\pi$
$3$	5.17956	+	0.414910i	0.996807	+	0.0798495i
$3$	5.17956	+	0.414910i	0.996807	+	0.0798495i
$4$	0.763180	+	0.440622i	0.0953974	+	0.0550777i
$5$		0			0
$5$		0			0
$6$	14.5898	+	5.18944i	0.992712	+	0.353097i
$7$	8.39055	−	31.3140i	0.453047	−	1.69080i	−0.240719	−	0.970595i	$-0.577383\pi$
$7$	8.39055	−	31.3140i	0.453047	−	1.69080i	0.693766	−	0.720200i	$-0.255950\pi$
$8$	−15.0012	−	15.0012i	−0.662966	−	0.662966i
$9$	26.6557	+	4.29810i	0.987248	+	0.159189i
$10$		0			0
$11$	15.0191	−	8.67129i	0.411676	−	0.237681i	−0.279834	−	0.960048i	$-0.590279\pi$
$11$	15.0191	−	8.67129i	0.411676	−	0.237681i	0.691509	+	0.722367i	$0.256946\pi$
$12$	3.77012	+	2.59888i	0.0906949	+	0.0625193i
$13$	−2.27646	−	8.49586i	−0.0485674	−	0.181256i	0.937381	−	0.348305i	$-0.113243\pi$
$13$	−2.27646	−	8.49586i	−0.0485674	−	0.181256i	−0.985949	+	0.167049i	$0.946576\pi$
$14$	48.3060	−	83.6685i	0.922166	−	1.59724i
$15$		0			0
$16$	−35.1367	−	60.8585i	−0.549011	−	0.950914i
$17$	23.2549	−	23.2549i	0.331773	−	0.331773i	−0.521486	−	0.853260i	$-0.674622\pi$
$17$	23.2549	−	23.2549i	0.331773	−	0.331773i	0.853260	+	0.521486i	$0.174622\pi$
$18$	73.4158	+	32.9325i	0.961348	+	0.431237i
$19$			145.204i			1.75327i	0.481158	+	0.876634i	$0.340216\pi$
$19$			145.204i			1.75327i	−0.481158	+	0.876634i	$0.659784\pi$
$20$		0			0
$21$	56.4519	−	158.711i	0.586610	−	1.64922i
$22$	49.9223	−	13.3766i	0.483794	−	0.129632i
$23$	11.2331	−	3.00990i	0.101837	−	0.0272873i	−0.207540	−	0.978226i	$-0.566546\pi$
$23$	11.2331	−	3.00990i	0.101837	−	0.0272873i	0.309378	+	0.950939i	$0.399879\pi$
$24$	−71.4755	−	83.9238i	−0.607911	−	0.713786i
$25$		0			0
$26$		−	26.2120i		−	0.197715i
$27$	136.281	+	33.3220i	0.971385	+	0.237512i
$28$	20.2011	−	20.2011i	0.136345	−	0.136345i
$29$	110.651	+	191.653i	0.708531	+	1.22721i	0.965402	+	0.260766i	$0.0839750\pi$
$29$	110.651	+	191.653i	0.708531	+	1.22721i	−0.256872	+	0.966446i	$0.582692\pi$
$30$		0			0
$31$	−34.8793	+	60.4127i	−0.202081	+	0.350014i	−0.949199	−	0.314677i	$-0.898104\pi$
$31$	−34.8793	+	60.4127i	−0.202081	+	0.350014i	0.747118	+	0.664691i	$0.231437\pi$
$32$	−10.2765	−	38.3524i	−0.0567702	−	0.211869i
$33$	81.3902	−	38.6819i	0.429340	−	0.204050i
$34$	84.8784	−	49.0046i	0.428133	−	0.247183i
$35$		0			0
$36$	18.4492	+	15.0253i	0.0854132	+	0.0695616i
$37$	−56.4980	−	56.4980i	−0.251033	−	0.251033i	0.570361	−	0.821394i	$-0.306803\pi$
$37$	−56.4980	−	56.4980i	−0.251033	−	0.251033i	−0.821394	+	0.570361i	$0.806803\pi$
$38$	−111.998	+	417.984i	−0.478119	+	1.78437i
$39$	−8.26604	−	44.9494i	−0.0339391	−	0.184555i
$40$		0			0
$41$	−141.694	−	81.8068i	−0.539727	−	0.311612i	0.205241	−	0.978711i	$-0.434202\pi$
$41$	−141.694	−	81.8068i	−0.539727	−	0.311612i	−0.744968	+	0.667100i	$0.767535\pi$
$42$	284.919	−	413.323i	1.04676	−	1.51850i
$43$	−107.661	−	28.8478i	−0.381819	−	0.102308i	0.0628041	−	0.998026i	$-0.479996\pi$
$43$	−107.661	−	28.8478i	−0.381819	−	0.102308i	−0.444623	+	0.895718i	$0.646662\pi$
$44$	15.2830			0.0523637
$45$		0			0
$46$	34.6571			0.111085
$47$	−186.165	−	49.8826i	−0.577764	−	0.154811i	−0.0419088	−	0.999121i	$-0.513344\pi$
$47$	−186.165	−	49.8826i	−0.577764	−	0.154811i	−0.535855	+	0.844310i	$0.680011\pi$
$48$	−156.742	−	329.799i	−0.471328	−	0.991716i
$49$	−613.116	−	353.983i	−1.78751	−	1.03202i
$50$		0			0
$51$	130.099	−	110.801i	0.357206	−	0.304222i
$52$	2.00612	−	7.48693i	0.00534997	−	0.0199663i
$53$	367.732	+	367.732i	0.953054	+	0.953054i	0.998946	−	0.0458925i	$-0.0146132\pi$
$53$	367.732	+	367.732i	0.953054	+	0.953054i	−0.0458925	+	0.998946i	$0.514613\pi$
$54$	366.597	+	201.037i	0.923844	+	0.506623i
$55$		0			0
$56$	−595.615	+	343.879i	−1.42129	+	0.820584i
$57$	−60.2466	+	752.093i	−0.139997	+	1.74767i
$58$	170.694	+	637.039i	0.386435	+	1.44220i
$59$	210.017	−	363.760i	0.463422	−	0.802671i	−0.535707	−	0.844404i	$-0.679955\pi$
$59$	210.017	−	363.760i	0.463422	−	0.802671i	0.999129	+	0.0417334i	$0.0132880\pi$
$60$		0			0
$61$	226.039	+	391.511i	0.474448	+	0.821768i	0.999572	−	0.0292577i	$-0.00931436\pi$
$61$	226.039	+	391.511i	0.474448	+	0.821768i	−0.525124	+	0.851026i	$0.675981\pi$
$62$	−147.001	+	147.001i	−0.301115	+	0.301115i
$63$	358.247	−	798.632i	0.716426	−	1.59711i
$64$			443.859i			0.866913i
$65$		0			0
$66$	264.126	−	48.5718i	0.492600	−	0.0905876i
$67$	225.409	−	60.3981i	0.411016	−	0.110131i	−0.0473854	−	0.998877i	$-0.515089\pi$
$67$	225.409	−	60.3981i	0.411016	−	0.110131i	0.458401	+	0.888745i	$0.348422\pi$
$68$	27.9943	−	7.50105i	0.0499236	−	0.0133770i
$69$	59.4313	−	10.9292i	0.103691	−	0.0190685i
$70$		0			0
$71$		−	434.936i		−	0.727005i	−0.931593	−	0.363502i	$-0.881581\pi$
$71$		−	434.936i		−	0.727005i	0.931593	−	0.363502i	$-0.118419\pi$
$72$	−335.391	−	464.344i	−0.548975	−	0.760048i
$73$	−226.275	+	226.275i	−0.362788	+	0.362788i	−0.864838	−	0.502050i	$-0.832579\pi$
$73$	−226.275	+	226.275i	−0.362788	+	0.362788i	0.502050	+	0.864838i	$0.332579\pi$
$74$	−119.057	−	206.213i	−0.187028	−	0.323943i
$75$		0			0
$76$	−63.9801	+	110.817i	−0.0965660	+	0.167257i
$77$	−145.514	−	543.065i	−0.215362	−	0.803740i
$78$	10.8756	−	135.767i	0.0157875	−	0.197084i
$79$	−138.839	+	80.1586i	−0.197729	+	0.114159i	−0.595596	−	0.803284i	$-0.703084\pi$
$79$	−138.839	+	80.1586i	−0.197729	+	0.114159i	0.397867	+	0.917443i	$0.369751\pi$
$80$		0			0
$81$	692.053	+	229.138i	0.949318	+	0.314318i
$82$	−344.779	−	344.779i	−0.464323	−	0.464323i
$83$	39.2062	−	146.319i	0.0518486	−	0.193502i	−0.935144	−	0.354268i	$-0.884730\pi$
$83$	39.2062	−	146.319i	0.0518486	−	0.193502i	0.986992	+	0.160767i	$0.0513966\pi$
$84$	113.015	−	96.2513i	0.146796	−	0.125022i
$85$		0			0
$86$	−287.663	−	166.082i	−0.360692	−	0.208245i
$87$	493.605	+	1038.59i	0.608276	+	1.27987i
$88$	−355.384	−	95.2250i	−0.430501	−	0.115352i
$89$	125.629			0.149625			0.0748124	−	0.997198i	$-0.476164\pi$
$89$	125.629			0.149625			0.0748124	+	0.997198i	$0.476164\pi$
$90$		0			0
$91$	−285.140			−0.328470
$92$	9.89909	+	2.65245i	0.0112180	+	0.00300584i
$93$	−205.725	+	298.439i	−0.229384	+	0.332760i
$94$	−497.417	−	287.184i	−0.545794	−	0.315114i
$95$		0			0
$96$	−37.3150	−	202.913i	−0.0396713	−	0.215726i
$97$	−263.620	+	983.843i	−0.275944	+	1.02984i	0.679263	+	0.733895i	$0.262300\pi$
$97$	−263.620	+	983.843i	−0.275944	+	1.02984i	−0.955206	+	0.295941i	$0.904367\pi$
$98$	−1491.88	−	1491.88i	−1.53778	−	1.53778i
$99$	437.615	−	166.586i	0.444262	−	0.169116i
$100$		0			0
$101$	−98.3353	+	56.7739i	−0.0968785	+	0.0559328i	−0.547656	−	0.836703i	$-0.684480\pi$
$101$	−98.3353	+	56.7739i	−0.0968785	+	0.0559328i	0.450778	+	0.892636i	$0.351147\pi$
$102$	459.965	−	218.605i	0.446503	−	0.212207i
$103$	−255.540	−	953.687i	−0.244457	−	0.912326i	−0.973656	−	0.228024i	$-0.926774\pi$
$103$	−255.540	−	953.687i	−0.244457	−	0.912326i	0.729199	−	0.684302i	$-0.239893\pi$
$104$	−93.2985	+	161.598i	−0.0879680	+	0.152365i
$105$		0			0
$106$	774.913	+	1342.19i	0.710059	+	1.22986i
$107$	−54.7470	+	54.7470i	−0.0494634	+	0.0494634i	−0.731406	−	0.681942i	$-0.761135\pi$
$107$	−54.7470	+	54.7470i	−0.0494634	+	0.0494634i	0.681942	+	0.731406i	$0.261135\pi$
$108$	89.3248	+	85.4793i	0.0795860	+	0.0761597i
$109$			1089.23i			0.957147i	0.878048	+	0.478573i	$0.158846\pi$
$109$			1089.23i			0.957147i	−0.878048	+	0.478573i	$0.841154\pi$
$110$		0			0
$111$	−269.193	−	316.077i	−0.230187	−	0.270276i
$112$	−2200.54	+	589.632i	−1.85653	+	0.497455i
$113$	−1253.08	+	335.761i	−1.04318	+	0.279520i	−0.739432	−	0.673232i	$-0.764906\pi$
$113$	−1253.08	+	335.761i	−1.04318	+	0.279520i	−0.303751	+	0.952751i	$0.598239\pi$
$114$	−753.528	+	2118.50i	−0.619073	+	1.74049i
$115$		0			0
$116$			195.021i			0.156097i
$117$	−24.1645	−	236.248i	−0.0190941	−	0.186676i
$118$	885.129	−	885.129i	0.690532	−	0.690532i
$119$	−533.082	−	923.325i	−0.410652	−	0.711269i
$120$		0			0
$121$	−515.117	+	892.210i	−0.387015	+	0.670330i
$122$	348.696	+	1301.35i	0.258766	+	0.965727i
$123$	−699.968	−	482.513i	−0.513122	−	0.353714i
$124$	−53.2383	+	30.7371i	−0.0385560	+	0.0222603i
$125$		0			0
$126$	1647.25	−	2022.62i	1.16467	−	1.43007i
$127$	1888.92	+	1888.92i	1.31980	+	1.31980i	0.913931	+	0.405869i	$0.133031\pi$
$127$	1888.92	+	1888.92i	1.31980	+	1.31980i	0.405869	+	0.913931i	$0.366969\pi$
$128$	−424.568	+	1584.51i	−0.293179	+	1.09416i
$129$	−545.670	−	194.089i	−0.372430	−	0.132469i
$130$		0			0
$131$	−581.255	−	335.588i	−0.387668	−	0.223820i	0.293481	−	0.955965i	$-0.405186\pi$
$131$	−581.255	−	335.588i	−0.387668	−	0.223820i	−0.681149	+	0.732145i	$0.738519\pi$
$132$	79.1594	+	6.34109i	0.0521965	+	0.00418122i
$133$	4546.91	+	1218.34i	2.96442	+	0.794313i
$134$	695.447			0.448339
$135$		0			0
$136$	−697.703			−0.439908
$137$	−1707.28	−	457.464i	−1.06469	−	0.285283i	−0.316381	−	0.948632i	$-0.602468\pi$
$137$	−1707.28	−	457.464i	−1.06469	−	0.285283i	−0.748310	+	0.663349i	$0.769134\pi$
$138$	179.509	+	14.3796i	0.110730	+	0.00887008i
$139$	−450.428	−	260.055i	−0.274855	−	0.158687i	0.356237	−	0.934396i	$-0.384060\pi$
$139$	−450.428	−	260.055i	−0.274855	−	0.158687i	−0.631092	+	0.775708i	$0.717393\pi$
$140$		0			0
$141$	−943.554	−	335.612i	−0.563557	−	0.200451i
$142$	335.473	−	1252.00i	0.198256	−	0.739900i
$143$	−107.860	−	107.860i	−0.0630752	−	0.0630752i
$144$	−675.017	−	1773.25i	−0.390635	−	1.02618i
$145$		0			0
$146$	−825.886	+	476.825i	−0.468156	+	0.270290i
$147$	−3028.80	−	2087.86i	−1.69940	−	1.17146i
$148$	−18.2239	−	68.0124i	−0.0101216	−	0.0377742i
$149$	1068.70	−	1851.04i	0.587590	−	1.01774i	−0.406957	−	0.913447i	$-0.633410\pi$
$149$	1068.70	−	1851.04i	0.587590	−	1.01774i	0.994547	−	0.104289i	$-0.0332566\pi$
$150$		0			0
$151$	1014.78	+	1757.66i	0.546900	+	0.947258i	0.998485	+	0.0550300i	$0.0175254\pi$
$151$	1014.78	+	1757.66i	0.546900	+	0.947258i	−0.451585	+	0.892228i	$0.649141\pi$
$152$	2178.23	−	2178.23i	1.16236	−	1.16236i
$153$	719.828	−	519.924i	0.380357	−	0.274728i
$154$		−	1675.50i		−	0.876726i
$155$		0			0
$156$	13.4972	−	37.9466i	0.00692719	−	0.0194754i
$157$	−235.616	+	63.1332i	−0.119772	+	0.0320929i	−0.318207	−	0.948021i	$-0.603081\pi$
$157$	−235.616	+	63.1332i	−0.119772	+	0.0320929i	0.198435	+	0.980114i	$0.436414\pi$
$158$	−461.489	+	123.655i	−0.232367	+	0.0622627i
$159$	1752.11	+	2057.27i	0.873910	+	1.02611i
$160$		0			0
$161$		−	377.007i		−	0.184549i
$162$	1815.40	+	1193.39i	0.880441	+	0.578774i
$163$	−1746.22	+	1746.22i	−0.839108	+	0.839108i	−0.988742	−	0.149633i	$-0.952191\pi$
$163$	−1746.22	+	1746.22i	−0.839108	+	0.839108i	0.149633	+	0.988742i	$0.452191\pi$
$164$	−72.0918	−	124.867i	−0.0343257	−	0.0594539i
$165$		0			0
$166$	225.717	−	390.954i	0.105537	−	0.182795i
$167$	−10.7984	−	40.3002i	−0.00500363	−	0.0186738i	0.963379	−	0.268144i	$-0.0864102\pi$
$167$	−10.7984	−	40.3002i	−0.00500363	−	0.0186738i	−0.968383	+	0.249470i	$0.919744\pi$
$168$	−3227.71	+	1534.01i	−1.48228	+	0.704475i
$169$	1835.66	−	1059.82i	0.835530	−	0.482394i
$170$		0			0
$171$	−624.102	+	3870.51i	−0.279101	+	1.73091i
$172$	−69.4540	−	69.4540i	−0.0307896	−	0.0307896i
$173$	608.606	−	2271.35i	0.267465	−	0.998193i	−0.693259	−	0.720688i	$-0.743826\pi$
$173$	608.606	−	2271.35i	0.267465	−	0.998193i	0.960724	−	0.277505i	$-0.0895073\pi$
$174$	619.807	+	3370.41i	0.270043	+	1.46845i
$175$		0			0
$176$	−1055.44	−	609.361i	−0.452029	−	0.260979i
$177$	1238.72	−	1796.98i	0.526035	−	0.763104i
$178$	361.634	+	96.8996i	0.152279	+	0.0408030i
$179$	−3861.04			−1.61222			−0.806111	−	0.591764i	$-0.798432\pi$
$179$	−3861.04			−1.61222			−0.806111	+	0.591764i	$0.798432\pi$
$180$		0			0
$181$	1336.19			0.548721			0.274360	−	0.961627i	$-0.411534\pi$
$181$	1336.19			0.548721			0.274360	+	0.961627i	$0.411534\pi$
$182$	−820.803	−	219.933i	−0.334296	−	0.0895744i
$183$	1008.34	+	2121.64i	0.407315	+	0.857028i
$184$	−213.662	−	123.358i	−0.0856053	−	0.0494242i
$185$		0			0
$186$	−822.391	+	700.407i	−0.324197	+	0.276109i
$187$	147.618	−	550.918i	0.0577267	−	0.215439i
$188$	−120.098	−	120.098i	−0.0465905	−	0.0465905i
$189$	2186.92	−	3987.92i	0.841667	−	1.53481i
$190$		0			0
$191$	1813.42	−	1046.98i	0.686986	−	0.396632i	−0.115496	−	0.993308i	$-0.536846\pi$
$191$	1813.42	−	1046.98i	0.686986	−	0.396632i	0.802482	+	0.596676i	$0.203512\pi$
$192$	−184.162	+	2299.00i	−0.0692225	+	0.864145i
$193$	635.771	+	2372.73i	0.237118	+	0.884937i	0.977183	+	0.212401i	$0.0681283\pi$
$193$	635.771	+	2372.73i	0.237118	+	0.884937i	−0.740064	+	0.672536i	$0.765205\pi$
$194$	−1517.71	+	2628.75i	−0.561676	+	0.972852i
$195$		0			0
$196$	−311.945	−	540.305i	−0.113683	−	0.196904i
$197$	1820.36	−	1820.36i	0.658351	−	0.658351i	−0.296639	−	0.954990i	$-0.595866\pi$
$197$	1820.36	−	1820.36i	0.658351	−	0.658351i	0.954990	+	0.296639i	$0.0958657\pi$
$198$	1388.21	−	141.992i	0.498261	−	0.0509645i
$199$			185.331i			0.0660189i	0.999455	+	0.0330095i	$0.0105092\pi$
$199$			185.331i			0.0660189i	−0.999455	+	0.0330095i	$0.989491\pi$
$200$		0			0
$201$	1192.58	−	219.311i	0.418498	−	0.0769603i
$202$	−326.858	+	87.5814i	−0.113850	+	0.0305060i
$203$	6929.85	−	1856.85i	2.39596	−	0.641996i
$204$	148.110	−	27.2370i	0.0508324	−	0.00934791i
$205$		0			0
$206$		−	2942.38i		−	0.995172i
$207$	312.363	−	31.9500i	0.104883	−	0.0107279i
$208$	−437.058	+	437.058i	−0.145695	+	0.145695i
$209$	1259.11	+	2180.84i	0.416719	+	0.721778i
$210$		0			0
$211$	2573.74	−	4457.84i	0.839732	−	1.45446i	−0.0503871	−	0.998730i	$-0.516046\pi$
$211$	2573.74	−	4457.84i	0.839732	−	1.45446i	0.890119	−	0.455728i	$-0.150621\pi$
$212$	118.615	+	442.676i	0.0384268	+	0.143411i
$213$	180.459	−	2252.77i	0.0580510	−	0.724684i
$214$	−199.822	+	115.367i	−0.0638296	+	0.0368520i
$215$		0			0
$216$	−1544.52	−	2544.26i	−0.486532	−	0.801457i
$217$	1599.10	+	1599.10i	0.500250	+	0.500250i
$218$	−840.139	+	3135.44i	−0.261016	+	0.974124i
$219$	−1265.89	+	1078.12i	−0.390598	+	0.332661i
$220$		0			0
$221$	−250.509	−	144.632i	−0.0762492	−	0.0440225i
$222$	−531.104	−	1117.49i	−0.160565	−	0.337843i
$223$	−4345.30	−	1164.32i	−1.30485	−	0.349635i	−0.461571	−	0.887103i	$-0.652714\pi$
$223$	−4345.30	−	1164.32i	−1.30485	−	0.349635i	−0.843284	+	0.537469i	$0.819381\pi$
$224$	−1287.19			−0.383947
$225$		0			0
$226$	−3866.08			−1.13791
$227$	4498.66	+	1205.41i	1.31536	+	0.352450i	0.847238	−	0.531214i	$-0.178264\pi$
$227$	4498.66	+	1205.41i	1.31536	+	0.352450i	0.468123	+	0.883663i	$0.344931\pi$
$228$	−377.368	+	547.436i	−0.109613	+	0.159012i
$229$	3532.61	+	2039.55i	1.01939	+	0.588547i	0.913928	−	0.405875i	$-0.133033\pi$
$229$	3532.61	+	2039.55i	1.01939	+	0.588547i	0.105466	+	0.994423i	$0.466367\pi$
$230$		0			0
$231$	−528.375	−	2873.21i	−0.150496	−	0.818370i
$232$	1215.13	−	4534.93i	0.343867	−	1.28333i
$233$	−2530.52	−	2530.52i	−0.711500	−	0.711500i	0.255349	−	0.966849i	$-0.417810\pi$
$233$	−2530.52	−	2530.52i	−0.711500	−	0.711500i	−0.966849	+	0.255349i	$0.917810\pi$
$234$	112.662	−	698.700i	0.0314741	−	0.195194i
$235$		0			0
$236$	320.562	−	185.076i	0.0884186	−	0.0510485i
$237$	−752.383	+	357.581i	−0.206213	+	0.0980058i
$238$	−822.351	−	3069.05i	−0.223971	−	0.835871i
$239$	3482.36	−	6031.62i	0.942490	−	1.63244i	0.181790	−	0.983337i	$-0.441811\pi$
$239$	3482.36	−	6031.62i	0.942490	−	1.63244i	0.760700	−	0.649103i	$-0.224856\pi$
$240$		0			0
$241$	−2601.64	−	4506.16i	−0.695378	−	1.20443i	−0.970053	−	0.242893i	$-0.921904\pi$
$241$	−2601.64	−	4506.16i	−0.695378	−	1.20443i	0.274675	−	0.961537i	$-0.411430\pi$
$242$	−2170.99	+	2170.99i	−0.576680	+	0.576680i
$243$	3489.46	+	1473.97i	0.921188	+	0.389117i
$244$			398.391i			0.104526i
$245$		0			0
$246$	−1642.75	−	1928.86i	−0.425765	−	0.499917i
$247$	1233.63	−	330.551i	0.317790	−	0.0851517i
$248$	1429.49	−	383.032i	0.366020	−	0.0980747i
$249$	263.780	−	741.603i	0.0671341	−	0.188744i
$250$		0			0
$251$			653.428i			0.164319i	0.996619	+	0.0821593i	$0.0261816\pi$
$251$			653.428i			0.164319i	−0.996619	+	0.0821593i	$0.973818\pi$
$252$	625.301	−	451.648i	0.156311	−	0.112901i
$253$	142.611	−	142.611i	0.0354383	−	0.0354383i
$254$	3980.48	+	6894.40i	0.983298	+	1.70312i
$255$		0			0
$256$	−668.884	+	1158.54i	−0.163302	+	0.282847i
$257$	−8.22348	−	30.6904i	−0.00199598	−	0.00744909i	0.964921	−	0.262542i	$-0.0845607\pi$
$257$	−8.22348	−	30.6904i	−0.00199598	−	0.00744909i	−0.966917	+	0.255093i	$0.917894\pi$
$258$	−1421.06	−	979.587i	−0.342912	−	0.236382i
$259$	−2243.23	+	1295.13i	−0.538175	+	0.310716i
$260$		0			0
$261$	2125.74	+	5584.24i	0.504137	+	1.32435i
$262$	−1414.35	−	1414.35i	−0.333508	−	0.333508i
$263$	−1815.55	+	6775.73i	−0.425672	+	1.58863i	0.336780	+	0.941583i	$0.390662\pi$
$263$	−1815.55	+	6775.73i	−0.425672	+	1.58863i	−0.762452	+	0.647045i	$0.776005\pi$
$264$	−1801.23	−	640.676i	−0.419916	−	0.149359i
$265$		0			0
$266$	12149.0	+	7014.23i	2.80039	+	1.61680i
$267$	650.701	+	52.1246i	0.149147	+	0.0119475i
$268$	198.640	+	53.2255i	0.0452757	+	0.0121316i
$269$	1104.05			0.250241			0.125121	−	0.992142i	$-0.460068\pi$
$269$	1104.05			0.250241			0.125121	+	0.992142i	$0.460068\pi$
$270$		0			0
$271$	3956.84			0.886940			0.443470	−	0.896289i	$-0.353747\pi$
$271$	3956.84			0.886940			0.443470	+	0.896289i	$0.353747\pi$
$272$	−2232.36	−	598.159i	−0.497635	−	0.133341i
$273$	−1476.90	−	118.307i	−0.327421	−	0.0262282i
$274$	−4561.71	−	2633.71i	−1.00578	−	0.580686i
$275$		0			0
$276$	50.1724	+	17.8458i	0.0109421	+	0.00389199i
$277$	−291.971	+	1089.65i	−0.0633315	+	0.236357i	−0.990335	−	0.138696i	$-0.955709\pi$
$277$	−291.971	+	1089.65i	−0.0633315	+	0.236357i	0.927003	+	0.375053i	$0.122375\pi$
$278$	−1096.02	−	1096.02i	−0.236455	−	0.236455i
$279$	−1189.39	+	1460.43i	−0.255222	+	0.313382i
$280$		0			0
$281$	−4252.77	+	2455.34i	−0.902844	+	0.521257i	−0.878122	−	0.478437i	$-0.841203\pi$
$281$	−4252.77	+	2455.34i	−0.902844	+	0.521257i	−0.0247222	+	0.999694i	$0.507870\pi$
$282$	−2457.25	−	1693.87i	−0.518890	−	0.357690i
$283$	−1756.71	−	6556.15i	−0.368996	−	1.37711i	−0.861922	−	0.507040i	$-0.830740\pi$
$283$	−1756.71	−	6556.15i	−0.368996	−	1.37711i	0.492926	−	0.870071i	$-0.335927\pi$
$284$	191.642	−	331.934i	0.0400418	−	0.0693544i
$285$		0			0
$286$	−227.292	−	393.681i	−0.0469932	−	0.0813947i
$287$	−3750.58	+	3750.58i	−0.771394	+	0.771394i
$288$	−109.085	−	1066.48i	−0.0223190	−	0.218205i
$289$			3831.42i			0.779853i
$290$		0			0
$291$	−1773.64	+	4986.49i	−0.357294	+	1.00451i
$292$	−272.391	+	72.9869i	−0.0545906	+	0.0146275i
$293$	539.160	−	144.468i	0.107502	−	0.0288051i	−0.204667	−	0.978832i	$-0.565611\pi$
$293$	539.160	−	144.468i	0.107502	−	0.0288051i	0.312169	+	0.950027i	$0.398944\pi$
$294$	−7108.29	−	8346.29i	−1.41008	−	1.65566i
$295$		0			0
$296$			1695.08i			0.332852i
$297$	2335.77	−	681.269i	0.456348	−	0.133102i
$298$	4504.08	−	4504.08i	0.875551	−	0.875551i
$299$	−51.1434	−	88.5829i	−0.00989196	−	0.0171334i
$300$		0			0
$301$	−1806.68	+	3129.26i	−0.345964	+	0.599227i
$302$	1565.44	+	5842.30i	0.298281	+	1.11320i
$303$	−532.889	+	253.264i	−0.101035	+	0.0480185i
$304$	8836.90	−	5101.99i	1.66721	−	0.962563i
$305$		0			0
$306$	2473.12	−	941.435i	0.462022	−	0.175877i
$307$	−1975.51	−	1975.51i	−0.367257	−	0.367257i	0.499219	−	0.866476i	$-0.333620\pi$
$307$	−1975.51	−	1975.51i	−0.367257	−	0.367257i	−0.866476	+	0.499219i	$0.833620\pi$
$308$	128.233	−	478.573i	0.0237233	−	0.0885364i
$309$	−927.889	−	5045.71i	−0.170828	−	0.928933i
$310$		0			0
$311$	2070.74	+	1195.54i	0.377558	+	0.217983i	0.676755	−	0.736208i	$-0.263385\pi$
$311$	2070.74	+	1195.54i	0.377558	+	0.217983i	−0.299197	+	0.954191i	$0.596719\pi$
$312$	−550.294	+	798.295i	−0.0998534	+	0.144854i
$313$	−5014.78	−	1343.71i	−0.905597	−	0.242654i	−0.224179	−	0.974548i	$-0.571970\pi$
$313$	−5014.78	−	1343.71i	−0.905597	−	0.242654i	−0.681418	+	0.731894i	$0.738637\pi$
$314$	−726.940			−0.130648
$315$		0			0
$316$	−141.279			−0.0251504
$317$	−7999.38	−	2143.43i	−1.41732	−	0.379769i	−0.532786	−	0.846250i	$-0.678855\pi$
$317$	−7999.38	−	2143.43i	−1.41732	−	0.379769i	−0.884531	+	0.466481i	$0.845522\pi$
$318$	3456.82	+	7273.47i	0.609588	+	1.28263i
$319$	3323.76	+	1918.97i	0.583370	+	0.336809i
$320$		0			0
$321$	−306.280	+	260.850i	−0.0532551	+	0.0453559i
$322$	290.792	−	1085.25i	0.0503268	−	0.187822i
$323$	3376.71	+	3376.71i	0.581687	+	0.581687i
$324$	427.197	+	479.807i	0.0732506	+	0.0822714i
$325$		0			0
$326$	−6373.56	+	3679.78i	−1.08282	+	0.625165i
$327$	−451.931	+	5641.72i	−0.0764277	+	0.954091i
$328$	898.373	+	3352.77i	0.151233	+	0.564409i
$329$	−3124.05	+	5411.01i	−0.523508	+	0.906743i
$330$		0			0
$331$	−3824.32	−	6623.91i	−0.635056	−	1.09995i	−0.986503	−	0.163741i	$-0.947644\pi$
$331$	−3824.32	−	6623.91i	−0.635056	−	1.09995i	0.351447	−	0.936208i	$-0.385690\pi$
$332$	94.3929	−	94.3929i	0.0156039	−	0.0156039i
$333$	−1263.16	−	1748.83i	−0.207870	−	0.287794i
$334$		−	124.337i		−	0.0203695i
$335$		0			0
$336$	−11642.5	+	2141.01i	−1.89032	+	0.347624i
$337$	1468.20	−	393.402i	0.237323	−	0.0635904i	−0.138197	−	0.990405i	$-0.544131\pi$
$337$	1468.20	−	393.402i	0.237323	−	0.0635904i	0.375520	+	0.926814i	$0.377464\pi$
$338$	6101.58	−	1634.91i	0.981900	−	0.263099i
$339$	−6629.70	+	1219.18i	−1.06217	+	0.195330i
$340$		0			0
$341$			1209.79i			0.192123i
$342$	−4781.93	+	10660.3i	−0.756074	+	1.68550i
$343$	−8366.26	+	8366.26i	−1.31701	+	1.31701i
$344$	1182.30	+	2047.80i	0.185306	+	0.320960i
$345$		0			0
$346$	3503.86	−	6068.86i	0.544418	−	0.942960i
$347$	−808.147	−	3016.05i	−0.125025	−	0.466599i	0.874816	−	0.484456i	$-0.160982\pi$
$347$	−808.147	−	3016.05i	−0.125025	−	0.466599i	−0.999841	+	0.0178568i	$0.994316\pi$
$348$	−80.9162	+	1010.12i	−0.0124643	+	0.155599i
$349$	−10814.9	+	6243.98i	−1.65876	+	0.957687i	−0.685476	+	0.728096i	$0.740406\pi$
$349$	−10814.9	+	6243.98i	−1.65876	+	0.957687i	−0.973287	+	0.229591i	$0.926261\pi$
$350$		0			0
$351$	−27.1402	−	1233.69i	−0.00412716	−	0.187605i
$352$	−486.909	−	486.909i	−0.0737282	−	0.0737282i
$353$	1302.03	−	4859.23i	0.196317	−	0.732665i	−0.795605	−	0.605816i	$-0.792847\pi$
$353$	1302.03	−	4859.23i	0.196317	−	0.732665i	0.991922	−	0.126849i	$-0.0404864\pi$
$354$	4951.83	−	4217.33i	0.743466	−	0.633188i
$355$		0			0
$356$	95.8772	+	55.3548i	0.0142738	+	0.00824100i
$357$	−2378.03	−	5003.60i	−0.352546	−	0.741788i
$358$	−11114.4	−	2978.09i	−1.64082	−	0.439656i
$359$	−6972.21			−1.02501			−0.512506	−	0.858684i	$-0.671283\pi$
$359$	−6972.21			−1.02501			−0.512506	+	0.858684i	$0.671283\pi$
$360$		0			0
$361$	−14225.2			−2.07395
$362$	3846.36	+	1030.63i	0.558454	+	0.149637i
$363$	−3038.27	+	4407.53i	−0.439305	+	0.637287i
$364$	−217.613	−	125.639i	−0.0313352	−	0.0180914i
$365$		0			0
$366$	1266.15	+	6885.10i	0.180827	+	0.983305i
$367$	−2431.38	+	9074.03i	−0.345823	+	1.29063i	0.545825	+	0.837899i	$0.316216\pi$
$367$	−2431.38	+	9074.03i	−0.345823	+	1.29063i	−0.891648	+	0.452729i	$0.850450\pi$
$368$	−577.872	−	577.872i	−0.0818577	−	0.0818577i
$369$	−3425.33	−	2789.63i	−0.483240	−	0.393557i
$370$		0			0
$371$	14600.6	−	8429.67i	2.04320	−	1.17964i
$372$	−288.504	+	137.116i	−0.0402103	+	0.0191105i
$373$	−245.950	−	917.897i	−0.0341415	−	0.127418i	0.946752	−	0.321964i	$-0.104343\pi$
$373$	−245.950	−	917.897i	−0.0341415	−	0.127418i	−0.980893	+	0.194547i	$0.937676\pi$
$374$	849.865	−	1472.01i	0.117501	−	0.203518i
$375$		0			0
$376$	2044.39	+	3540.99i	0.280403	+	0.485672i
$377$	1376.37	−	1376.37i	0.188028	−	0.188028i
$378$	9371.22	−	9792.81i	1.27514	−	1.33251i
$379$			1292.12i			0.175123i	0.996159	+	0.0875613i	$0.0279074\pi$
$379$			1292.12i			0.175123i	−0.996159	+	0.0875613i	$0.972093\pi$
$380$		0			0
$381$	9000.05	+	10567.5i	1.21020	+	1.42097i
$382$	6027.65	−	1615.10i	0.807334	−	0.216324i
$383$	5738.62	−	1537.66i	0.765613	−	0.205145i	0.145180	−	0.989405i	$-0.453624\pi$
$383$	5738.62	−	1537.66i	0.765613	−	0.205145i	0.620432	+	0.784260i	$0.286957\pi$
$384$	−2856.51	+	8030.91i	−0.379611	+	1.06725i
$385$		0			0
$386$			7320.51i			0.965296i
$387$	−2745.80	−	1231.70i	−0.360664	−	0.161785i
$388$	−634.692	+	634.692i	−0.0830453	+	0.0830453i
$389$	−3075.20	−	5326.40i	−0.400820	−	0.694240i	0.593005	−	0.805198i	$-0.297941\pi$
$389$	−3075.20	−	5326.40i	−0.400820	−	0.694240i	−0.993825	+	0.110959i	$0.964608\pi$
$390$		0			0
$391$	191.230	−	331.219i	0.0247338	−	0.0428401i
$392$	3887.31	+	14507.7i	0.500865	+	1.86925i
$393$	−2871.41	−	1979.36i	−0.368558	−	0.254060i
$394$	6644.15	−	3836.00i	0.849562	−	0.490495i
$395$		0			0
$396$	407.380	+	65.6881i	0.0516960	+	0.00833573i
$397$	−9111.20	−	9111.20i	−1.15183	−	1.15183i	−0.986185	−	0.165649i	$-0.947028\pi$
$397$	−9111.20	−	9111.20i	−1.15183	−	1.15183i	−0.165649	−	0.986185i	$-0.552972\pi$
$398$	−142.949	+	533.493i	−0.0180035	+	0.0671899i
$399$	23045.5	+	8197.04i	2.89153	+	1.02848i
$400$		0			0
$401$	−3577.13	−	2065.26i	−0.445470	−	0.257192i	0.260445	−	0.965489i	$-0.416131\pi$
$401$	−3577.13	−	2065.26i	−0.445470	−	0.257192i	−0.705915	+	0.708297i	$0.749464\pi$
$402$	3602.11	+	288.548i	0.446908	+	0.0357997i
$403$	592.659	+	158.803i	0.0732567	+	0.0196291i
$404$	−100.063			−0.0123226
$405$		0			0
$406$	21380.5			2.61353
$407$	−1338.46	−	358.640i	−0.163010	−	0.0436784i
$408$	−3613.79	−	289.484i	−0.438504	−	0.0351264i
$409$	−4525.80	−	2612.97i	−0.547156	−	0.315900i	0.200818	−	0.979628i	$-0.435640\pi$
$409$	−4525.80	−	2612.97i	−0.547156	−	0.315900i	−0.747974	+	0.663728i	$0.768973\pi$
$410$		0			0
$411$	−8653.14	−	3077.83i	−1.03851	−	0.369387i
$412$	225.193	−	840.431i	0.0269283	−	0.100498i
$413$	−9628.62	−	9628.62i	−1.14720	−	1.14720i
$414$	923.810	+	148.960i	0.109669	+	0.0176835i
$415$		0			0
$416$	−302.443	+	174.615i	−0.0356454	+	0.0205799i
$417$	−2225.12	−	1533.86i	−0.261306	−	0.180128i
$418$	1942.34	+	7248.92i	0.227280	+	0.848220i
$419$	−4683.53	+	8112.11i	−0.546075	+	0.945829i	0.452464	+	0.891783i	$0.350545\pi$
$419$	−4683.53	+	8112.11i	−0.546075	+	0.945829i	−0.998538	+	0.0540462i	$0.982788\pi$
$420$		0			0
$421$	1386.04	+	2400.70i	0.160455	+	0.277916i	0.935032	−	0.354563i	$-0.115370\pi$
$421$	1386.04	+	2400.70i	0.160455	+	0.277916i	−0.774577	+	0.632480i	$0.782037\pi$
$422$	10847.2	−	10847.2i	1.25126	−	1.25126i
$423$	−4747.95	−	2129.81i	−0.545752	−	0.244811i
$424$		−	11032.8i		−	1.26368i
$425$		0			0
$426$	2257.07	−	6345.64i	0.256703	−	0.721707i
$427$	14156.4	−	3793.18i	1.60439	−	0.429895i
$428$	−65.9045	+	17.6590i	−0.00744302	+	0.00199435i
$429$	−513.918	−	603.422i	−0.0578372	−	0.0679103i
$430$		0			0
$431$		−	14381.5i		−	1.60727i	−0.595125	−	0.803633i	$-0.702898\pi$
$431$		−	14381.5i		−	1.60727i	0.595125	−	0.803633i	$-0.297102\pi$
$432$	−2760.55	−	9464.71i	−0.307447	−	1.05410i
$433$	7313.75	−	7313.75i	0.811724	−	0.811724i	−0.173168	−	0.984892i	$-0.555400\pi$
$433$	7313.75	−	7313.75i	0.811724	−	0.811724i	0.984892	+	0.173168i	$0.0554004\pi$
$434$	3369.76	+	5836.59i	0.372704	+	0.645542i
$435$		0			0
$436$	−479.937	+	831.275i	−0.0527175	+	0.0913093i
$437$	437.049	+	1631.09i	0.0478419	+	0.178548i
$438$	−4475.56	+	2127.08i	−0.488244	+	0.232045i
$439$	1284.46	−	741.581i	0.139644	−	0.0806235i	−0.428550	−	0.903518i	$-0.640976\pi$
$439$	1284.46	−	741.581i	0.139644	−	0.0806235i	0.568194	+	0.822894i	$0.307642\pi$
$440$		0			0
$441$	−14821.6	−	12070.9i	−1.60043	−	1.30341i
$442$	−609.558	−	609.558i	−0.0655967	−	0.0655967i
$443$	−2809.90	+	10486.7i	−0.301359	+	1.12469i	0.634675	+	0.772779i	$0.281134\pi$
$443$	−2809.90	+	10486.7i	−0.301359	+	1.12469i	−0.936034	+	0.351909i	$0.885533\pi$
$444$	−66.1726	−	359.836i	−0.00707300	−	0.0384618i
$445$		0			0
$446$	−11610.3	−	6703.21i	−1.23265	−	0.711673i
$447$	6303.39	−	9144.14i	0.666980	−	0.967568i
$448$	13899.0	+	3724.22i	1.46577	+	0.392752i
$449$	3675.43			0.386312			0.193156	−	0.981168i	$-0.438128\pi$
$449$	3675.43			0.386312			0.193156	+	0.981168i	$0.438128\pi$
$450$		0			0
$451$	−2837.48			−0.296257
$452$	−1104.27	−	295.887i	−0.114912	−	0.0307907i
$453$	4526.86	+	9524.93i	0.469515	+	0.987903i
$454$	12020.1	+	6939.80i	1.24258	+	0.717403i
$455$		0			0
$456$	12186.1	−	10378.5i	1.25146	−	1.06583i
$457$	−2293.65	+	8560.02i	−0.234776	+	0.876195i	0.743474	+	0.668765i	$0.233177\pi$
$457$	−2293.65	+	8560.02i	−0.234776	+	0.876195i	−0.978250	+	0.207430i	$0.933490\pi$
$458$	8595.81	+	8595.81i	0.876977	+	0.876977i
$459$	3944.11	−	2394.31i	0.401079	−	0.243479i
$460$		0			0
$461$	615.619	−	355.428i	0.0621958	−	0.0359087i	−0.468580	−	0.883421i	$-0.655234\pi$
$461$	615.619	−	355.428i	0.0621958	−	0.0359087i	0.530775	+	0.847513i	$0.321901\pi$
$462$	695.182	−	8678.36i	0.0700061	−	0.873926i
$463$	1116.15	+	4165.52i	0.112034	+	0.418117i	0.999048	−	0.0436261i	$-0.0138910\pi$
$463$	1116.15	+	4165.52i	0.112034	+	0.418117i	−0.887014	+	0.461743i	$0.847224\pi$
$464$	7775.82	−	13468.1i	0.777982	−	1.34750i
$465$		0			0
$466$	−5332.50	−	9236.16i	−0.530093	−	0.918148i
$467$	5693.93	−	5693.93i	0.564205	−	0.564205i	−0.366294	−	0.930499i	$-0.619374\pi$
$467$	5693.93	−	5693.93i	0.564205	−	0.564205i	0.930499	+	0.366294i	$0.119374\pi$
$468$	85.6540	−	190.947i	0.00846017	−	0.0188601i
$469$		−	7565.22i		−	0.744839i
$470$		0			0
$471$	−1246.58	+	229.243i	−0.121952	+	0.0224267i
$472$	−8607.35	+	2306.33i	−0.839376	+	0.224910i
$473$	−1867.13	+	500.295i	−0.181502	+	0.0486334i
$474$	−2441.61	+	449.005i	−0.236597	+	0.0435094i
$475$		0			0
$476$		−	939.550i		−	0.0904710i
$477$	8221.60	+	11382.7i	0.789185	+	1.09262i
$478$	14676.6	−	14676.6i	1.40438	−	1.40438i
$479$	−578.158	−	1001.40i	−0.0551497	−	0.0955222i	0.837133	−	0.547000i	$-0.184230\pi$
$479$	−578.158	−	1001.40i	−0.0551497	−	0.0955222i	−0.892282	+	0.451478i	$0.850897\pi$
$480$		0			0
$481$	−351.384	+	608.615i	−0.0333092	+	0.0576933i
$482$	−4013.37	−	14978.1i	−0.379262	−	1.41542i
$483$	156.424	−	1952.73i	0.0147361	−	0.183959i
$484$	−786.254	+	453.944i	−0.0738406	+	0.0426319i
$485$		0			0
$486$	8907.83	+	6934.45i	0.831415	+	0.647229i
$487$	11304.4	+	11304.4i	1.05185	+	1.05185i	0.998580	+	0.0532673i	$0.0169635\pi$
$487$	11304.4	+	11304.4i	1.05185	+	1.05185i	0.0532673	+	0.998580i	$0.483036\pi$
$488$	2482.28	−	9263.99i	0.230261	−	0.859347i
$489$	−9769.19	+	8320.14i	−0.903431	+	0.769427i
$490$		0			0
$491$	11832.0	+	6831.20i	1.08752	+	0.627878i	0.932914	−	0.360099i	$-0.117257\pi$
$491$	11832.0	+	6831.20i	1.08752	+	0.627878i	0.154602	+	0.987977i	$0.450591\pi$
$492$	−321.595	−	676.666i	−0.0294688	−	0.0620050i
$493$	7030.06	+	1883.70i	0.642227	+	0.172084i
$494$	3806.09			0.346648
$495$		0			0
$496$	4902.17			0.443778
$497$	−13619.6	−	3649.35i	−1.22922	−	0.329368i
$498$	1331.33	−	1931.32i	0.119796	−	0.173784i
$499$	10650.2	+	6148.91i	0.955450	+	0.551629i	0.894770	−	0.446528i	$-0.147340\pi$
$499$	10650.2	+	6148.91i	0.955450	+	0.551629i	0.0606800	+	0.998157i	$0.480673\pi$
$500$		0			0
$501$	−39.2100	−	213.218i	−0.00349656	−	0.0190137i
$502$	−504.000	+	1880.95i	−0.0448100	+	0.167233i
$503$	−10869.2	−	10869.2i	−0.963483	−	0.963483i	0.0358736	−	0.999356i	$-0.488579\pi$
$503$	−10869.2	−	10869.2i	−0.963483	−	0.963483i	−0.999356	+	0.0358736i	$0.988579\pi$
$504$	−17354.6	+	6606.31i	−1.53380	+	0.583866i
$505$		0			0
$506$	520.519	−	300.522i	0.0457310	−	0.0264028i
$507$	9947.64	−	4727.76i	0.871381	−	0.414137i
$508$	609.286	+	2273.89i	0.0532140	+	0.198597i
$509$	3933.77	−	6813.50i	0.342557	−	0.593326i	−0.642350	−	0.766412i	$-0.722040\pi$
$509$	3933.77	−	6813.50i	0.342557	−	0.593326i	0.984907	+	0.173086i	$0.0553737\pi$
$510$		0			0
$511$	5187.01	+	8984.16i	0.449040	+	0.777761i
$512$	6460.49	−	6460.49i	0.557648	−	0.557648i
$513$	−4838.49	+	19788.6i	−0.416422	+	1.70310i
$514$		−	94.6883i		−	0.00812553i
$515$		0			0
$516$	−330.924	−	388.558i	−0.0282328	−	0.0331499i
$517$	−3228.57	+	865.094i	−0.274647	+	0.0735914i
$518$	−7456.30	+	1997.91i	−0.632454	+	0.169465i
$519$	4094.71	−	11512.1i	0.346316	−	0.973648i
$520$		0			0
$521$			5611.99i			0.471911i	0.971764	+	0.235956i	$0.0758220\pi$
$521$			5611.99i			0.471911i	−0.971764	+	0.235956i	$0.924178\pi$
$522$	1811.91	+	17714.4i	0.151926	+	1.48532i
$523$	−4528.31	+	4528.31i	−0.378603	+	0.378603i	−0.870598	−	0.491995i	$-0.836268\pi$
$523$	−4528.31	+	4528.31i	−0.378603	+	0.378603i	0.491995	+	0.870598i	$0.336268\pi$
$524$	−295.734	−	512.227i	−0.0246550	−	0.0427037i
$525$		0			0
$526$	−10452.5	+	18104.2i	−0.866444	+	1.50072i
$527$	593.777	+	2216.00i	0.0490803	+	0.183170i
$528$	−5213.90	−	3594.13i	−0.429746	−	0.296240i
$529$	−10419.8	+	6015.88i	−0.856399	+	0.494442i
$530$		0			0
$531$	7161.64	−	8793.61i	0.585289	−	0.718664i
$532$	2933.28	+	2933.28i	0.239049	+	0.239049i
$533$	−372.460	+	1390.04i	−0.0302683	+	0.112963i
$534$	1832.90	+	651.943i	0.148534	+	0.0528321i
$535$		0			0
$536$	−4287.45	−	2475.36i	−0.345503	−	0.199476i
$537$	−19998.5	−	1601.98i	−1.60707	−	0.128735i
$538$	3178.10	+	851.570i	0.254680	+	0.0682412i
$539$	−12278.0			−0.981167
$540$		0			0
$541$	−1601.81			−0.127296			−0.0636481	−	0.997972i	$-0.520274\pi$
$541$	−1601.81			−0.127296			−0.0636481	+	0.997972i	$0.520274\pi$
$542$	11390.1	+	3051.98i	0.902672	+	0.241870i
$543$	6920.89	+	554.400i	0.546969	+	0.0438151i
$544$	−1130.86	−	652.903i	−0.0891273	−	0.0514577i
$545$		0			0
$546$	−4160.14	−	1479.72i	−0.326076	−	0.115982i
$547$	4361.65	−	16277.9i	0.340934	−	1.27238i	−0.556357	−	0.830943i	$-0.687801\pi$
$547$	4361.65	−	16277.9i	0.340934	−	1.27238i	0.897291	−	0.441440i	$-0.145532\pi$
$548$	−1101.39	−	1101.39i	−0.0858560	−	0.0858560i
$549$	4342.47	+	11407.5i	0.337581	+	0.886816i
$550$		0			0
$551$	−27828.8	+	16067.0i	−2.15163	+	1.24224i
$552$	−1055.49	−	727.590i	−0.0813854	−	0.0561019i
$553$	1345.15	+	5020.17i	0.103439	+	0.386039i
$554$	−1680.93	+	2911.46i	−0.128910	+	0.223278i
$555$		0			0
$556$	−229.172	−	396.937i	−0.0174803	−	0.0302767i
$557$	−12036.2	+	12036.2i	−0.915600	+	0.915600i	−0.996706	−	0.0811057i	$-0.974155\pi$
$557$	−12036.2	+	12036.2i	−0.915600	+	0.915600i	0.0811057	+	0.996706i	$0.474155\pi$
$558$	−4550.23	+	3286.58i	−0.345209	+	0.249341i
$559$			980.348i			0.0741758i
$560$		0			0
$561$	993.178	−	2792.27i	0.0747451	−	0.210142i
$562$	−14135.9	+	3787.69i	−1.06101	+	0.284296i
$563$	−18547.8	+	4969.86i	−1.38845	+	0.372033i	−0.874182	−	0.485598i	$-0.838602\pi$
$563$	−18547.8	+	4969.86i	−1.38845	+	0.372033i	−0.514265	+	0.857631i	$0.671935\pi$
$564$	−572.223	−	671.882i	−0.0427215	−	0.0501620i
$565$		0			0
$566$		−	20227.5i		−	1.50216i
$567$	12981.9	−	19748.3i	0.961533	−	1.46270i
$568$	−6524.55	+	6524.55i	−0.481979	+	0.481979i
$569$	−9856.25	−	17071.5i	−0.726178	−	1.25778i	−0.958487	−	0.285136i	$-0.907961\pi$
$569$	−9856.25	−	17071.5i	−0.726178	−	1.25778i	0.232309	−	0.972642i	$-0.425372\pi$
$570$		0			0
$571$	−4422.13	+	7659.35i	−0.324099	+	0.561355i	−0.981330	−	0.192334i	$-0.938394\pi$
$571$	−4422.13	+	7659.35i	−0.324099	+	0.561355i	0.657231	+	0.753689i	$0.271728\pi$
$572$	−34.7912	−	129.843i	−0.00254317	−	0.00949125i
$573$	9827.11	−	4670.48i	0.716463	−	0.340510i
$574$	−13689.3	+	7903.52i	−0.995436	+	0.574715i
$575$		0			0
$576$	−1907.75	+	11831.4i	−0.138003	+	0.855858i
$577$	−5344.50	−	5344.50i	−0.385605	−	0.385605i	0.487511	−	0.873117i	$-0.337905\pi$
$577$	−5344.50	−	5344.50i	−0.385605	−	0.385605i	−0.873117	+	0.487511i	$0.837905\pi$
$578$	−2955.24	+	11029.1i	−0.212667	+	0.793686i
$579$	2308.55	+	12553.5i	0.165699	+	0.901045i
$580$		0			0
$581$	−4252.88	−	2455.40i	−0.303682	−	0.175331i
$582$	−8951.76	+	12986.1i	−0.637565	+	0.924896i
$583$	8711.72	+	2334.30i	0.618872	+	0.165826i
$584$	6788.81			0.481032
$585$		0			0
$586$	1663.46			0.117264
$587$	14988.2	+	4016.09i	1.05389	+	0.282388i	0.743856	−	0.668339i	$-0.232995\pi$
$587$	14988.2	+	4016.09i	1.05389	+	0.282388i	0.310029	+	0.950727i	$0.399661\pi$
$588$	−1391.56	−	2927.97i	−0.0975970	−	0.205353i
$589$	−8772.16	−	5064.61i	−0.613668	−	0.354302i
$590$		0			0
$591$	10183.9	−	8673.37i	0.708818	−	0.603680i
$592$	−1453.23	+	5423.54i	−0.100891	+	0.376531i
$593$	−7756.63	−	7756.63i	−0.537145	−	0.537145i	0.385545	−	0.922689i	$-0.374014\pi$
$593$	−7756.63	−	7756.63i	−0.537145	−	0.537145i	−0.922689	+	0.385545i	$0.874014\pi$
$594$	7249.22	−	159.477i	0.500739	−	0.0110159i
$595$		0			0
$596$	1631.21	−	941.781i	0.112109	−	0.0647263i
$597$	−76.8957	+	959.933i	−0.00527158	+	0.0658081i
$598$	−78.8955	−	294.442i	−0.00539511	−	0.0201348i
$599$	3436.79	−	5952.70i	0.234430	−	0.406045i	−0.724677	−	0.689089i	$-0.758011\pi$
$599$	3436.79	−	5952.70i	0.234430	−	0.406045i	0.959107	+	0.283044i	$0.0913443\pi$
$600$		0			0
$601$	1499.90	+	2597.90i	0.101800	+	0.176323i	0.912426	−	0.409241i	$-0.134206\pi$
$601$	1499.90	+	2597.90i	0.101800	+	0.176323i	−0.810626	+	0.585564i	$0.800873\pi$
$602$	−7614.34	+	7614.34i	−0.515511	+	0.515511i
$603$	6268.03	−	641.124i	0.423306	−	0.0432978i
$604$			1788.54i			0.120488i
$605$		0			0
$606$	−1729.32	+	318.016i	−0.115922	+	0.0213177i
$607$	−9440.13	+	2529.48i	−0.631241	+	0.169141i	−0.560233	−	0.828335i	$-0.689288\pi$
$607$	−9440.13	+	2529.48i	−0.631241	+	0.169141i	−0.0710082	+	0.997476i	$0.522622\pi$
$608$	5568.93	−	1492.19i	0.371463	−	0.0995333i
$609$	36664.0	−	6742.39i	2.43957	−	0.448630i
$610$		0			0
$611$			1695.18i			0.112242i
$612$	778.448	−	79.6233i	0.0514165	−	0.00525912i
$613$	−3413.76	+	3413.76i	−0.224927	+	0.224927i	−0.810570	−	0.585642i	$-0.800842\pi$
$613$	−3413.76	+	3413.76i	−0.224927	+	0.224927i	0.585642	+	0.810570i	$0.300842\pi$
$614$	−4162.94	−	7210.42i	−0.273620	−	0.473923i
$615$		0			0
$616$	−5963.74	+	10329.5i	−0.390075	+	0.675629i
$617$	−3554.83	−	13266.8i	−0.231948	−	0.865642i	−0.979501	−	0.201440i	$-0.935438\pi$
$617$	−3554.83	−	13266.8i	−0.231948	−	0.865642i	0.747553	−	0.664202i	$-0.231229\pi$
$618$	1220.82	−	15240.2i	0.0794639	−	0.991994i
$619$	−10576.7	+	6106.47i	−0.686776	+	0.396510i	−0.802403	−	0.596782i	$-0.796446\pi$
$619$	−10576.7	+	6106.47i	−0.686776	+	0.396510i	0.115627	+	0.993293i	$0.463112\pi$
$620$		0			0
$621$	1631.16	−	35.8843i	0.105404	−	0.00231882i
$622$	5038.67	+	5038.67i	0.324811	+	0.324811i
$623$	1054.09	−	3933.93i	0.0677871	−	0.252985i
$624$	−2445.11	+	2082.43i	−0.156863	+	0.133596i
$625$		0			0
$626$	−13399.1	−	7735.97i	−0.855488	−	0.493916i
$627$	5616.77	+	11818.2i	0.357754	+	0.752748i
$628$	−207.636	−	55.6358i	−0.0131936	−	0.00353521i
$629$	−2627.71			−0.166572
$630$		0			0
$631$	8057.84			0.508364			0.254182	−	0.967156i	$-0.418194\pi$
$631$	8057.84			0.508364			0.254182	+	0.967156i	$0.418194\pi$
$632$	3285.22	+	880.273i	0.206771	+	0.0554041i
$633$	15180.4	−	22021.8i	0.953188	−	1.38276i
$634$	−21373.7	−	12340.1i	−1.33889	−	0.773011i
$635$		0			0
$636$	430.701	+	2342.08i	0.0268529	+	0.146021i
$637$	−1611.66	+	6014.78i	−0.100245	+	0.374120i
$638$	8087.63	+	8087.63i	0.501869	+	0.501869i
$639$	1869.40	−	11593.5i	0.115731	−	0.717734i
$640$		0			0
$641$	21555.5	−	12445.1i	1.32823	−	0.766852i	0.343201	−	0.939262i	$-0.388489\pi$
$641$	21555.5	−	12445.1i	1.32823	−	0.766852i	0.985025	+	0.172410i	$0.0551555\pi$
$642$	−1082.86	+	514.643i	−0.0665684	+	0.0316376i
$643$	−2856.76	−	10661.6i	−0.175210	−	0.653891i	−0.996516	−	0.0834036i	$-0.973421\pi$
$643$	−2856.76	−	10661.6i	−0.175210	−	0.653891i	0.821306	−	0.570488i	$-0.193246\pi$
$644$	166.118	−	287.724i	0.0101645	−	0.0176055i
$645$		0			0
$646$	7115.66	+	12324.7i	0.433377	+	0.750632i
$647$	−17868.7	+	17868.7i	−1.08577	+	1.08577i	−0.0898058	+	0.995959i	$0.528625\pi$
$647$	−17868.7	+	17868.7i	−1.08577	+	1.08577i	−0.995959	+	0.0898058i	$0.971375\pi$
$648$	−6944.28	−	13819.0i	−0.420983	−	0.837747i
$649$		−	7284.48i		−	0.440587i
$650$		0			0
$651$	7619.17	+	8946.14i	0.458708	+	0.538597i
$652$	−2102.10	+	563.257i	−0.126265	+	0.0338326i
$653$	23200.9	−	6216.66i	1.39039	−	0.372553i	0.515503	−	0.856888i	$-0.327605\pi$
$653$	23200.9	−	6216.66i	1.39039	−	0.372553i	0.874882	+	0.484335i	$0.160939\pi$
$654$	−5652.48	+	15891.6i	−0.337966	+	0.950172i
$655$		0			0
$656$			11497.7i			0.684313i
$657$	−7004.09	+	5058.98i	−0.415914	+	0.300410i
$658$	−13166.5	+	13166.5i	−0.780065	+	0.780065i
$659$	14654.5	+	25382.4i	0.866250	+	1.50039i	0.865801	+	0.500389i	$0.166810\pi$
$659$	14654.5	+	25382.4i	0.866250	+	1.50039i	0.000449468		1.00000i	$0.499857\pi$
$660$		0			0
$661$	5726.89	−	9919.27i	0.336990	−	0.583684i	−0.646875	−	0.762596i	$-0.723924\pi$
$661$	5726.89	−	9919.27i	0.336990	−	0.583684i	0.983865	+	0.178912i	$0.0572578\pi$
$662$	−5899.53	−	22017.3i	−0.346362	−	1.29264i
$663$	−1237.52	−	853.067i	−0.0724906	−	0.0499704i
$664$	−2783.11	+	1606.83i	−0.162659	+	0.0939111i
$665$		0			0
$666$	−2287.23	−	6008.47i	−0.133075	−	0.349585i
$667$	1819.81	+	1819.81i	0.105642	+	0.105642i
$668$	9.51603	−	35.5143i	0.000551177	−	0.00205702i
$669$	−22023.6	−	7833.57i	−1.27277	−	0.452710i
$670$		0			0
$671$	6789.81	+	3920.10i	0.390637	+	0.225535i
$672$	−6667.09	−	534.069i	−0.382721	−	0.0306580i
$673$	−17479.3	−	4683.57i	−1.00116	−	0.268259i	−0.279227	−	0.960225i	$-0.590078\pi$
$673$	−17479.3	−	4683.57i	−1.00116	−	0.268259i	−0.721930	+	0.691966i	$0.756745\pi$
$674$	4529.78			0.258873
$675$		0			0
$676$	1867.92			0.106277
$677$	3702.99	+	992.214i	0.210218	+	0.0563277i	0.362391	−	0.932026i	$-0.381960\pi$
$677$	3702.99	+	992.214i	0.210218	+	0.0563277i	−0.152173	+	0.988354i	$0.548627\pi$
$678$	−20024.6	−	1604.08i	−1.13428	−	0.0908616i
$679$	28596.1	+	16510.0i	1.61623	+	0.933129i
$680$		0			0
$681$	22801.0	+	8110.05i	1.28302	+	0.456355i
$682$	−933.134	+	3482.50i	−0.0523923	+	0.195531i
$683$	15444.0	+	15444.0i	0.865222	+	0.865222i	0.991939	−	0.126717i	$-0.0404440\pi$
$683$	15444.0	+	15444.0i	0.865222	+	0.865222i	−0.126717	+	0.991939i	$0.540444\pi$
$684$	−2181.74	+	2678.90i	−0.121960	+	0.149752i
$685$		0			0
$686$	−30536.1	+	17630.0i	−1.69953	+	0.981222i
$687$	17451.1	+	12029.7i	0.969144	+	0.668066i
$688$	2027.23	+	7565.73i	0.112336	+	0.419245i
$689$	2287.07	−	3961.33i	0.126459	−	0.219034i
$690$		0			0
$691$	10639.5	+	18428.2i	0.585741	+	1.01453i	0.994783	+	0.102017i	$0.0325297\pi$
$691$	10639.5	+	18428.2i	0.585741	+	1.01453i	−0.409042	+	0.912516i	$0.634137\pi$
$692$	1465.28	−	1465.28i	0.0804937	−	0.0804937i
$693$	−1544.62	−	15101.2i	−0.0846687	−	0.827774i
$694$		−	9305.32i		−	0.508970i
$695$		0			0
$696$	8175.43	−	22984.8i	0.445243	−	1.25177i
$697$	−5197.48	+	1392.66i	−0.282451	+	0.0756826i
$698$	−35947.8	+	9632.19i	−1.94935	+	0.522326i
$699$	−12057.0	−	14156.9i	−0.652416	−	0.766042i
$700$		0			0
$701$		−	510.344i		−	0.0274970i	−0.999905	−	0.0137485i	$-0.995624\pi$
$701$		−	510.344i		−	0.0274970i	0.999905	−	0.0137485i	$-0.00437642\pi$
$702$	873.437	−	3572.21i	0.0469598	−	0.192058i
$703$	8203.74	−	8203.74i	0.440128	−	0.440128i
$704$	3848.83	+	6666.37i	0.206049	+	0.356887i
$705$		0			0
$706$	7496.01	−	12983.5i	0.399598	−	0.692124i
$707$	952.729	+	3555.63i	0.0506804	+	0.189142i
$708$	1737.16	−	825.610i	0.0922125	−	0.0438253i
$709$	8375.17	−	4835.41i	0.443634	−	0.256132i	−0.261504	−	0.965202i	$-0.584218\pi$
$709$	8375.17	−	4835.41i	0.443634	−	0.256132i	0.705138	+	0.709070i	$0.250885\pi$
$710$		0			0
$711$	−4045.38	+	1539.94i	−0.213380	+	0.0812268i
$712$	−1884.58	−	1884.58i	−0.0991962	−	0.0991962i
$713$	−209.966	+	783.604i	−0.0110285	+	0.0411588i
$714$	−2986.03	−	16237.6i	−0.156512	−	0.851086i
$715$		0			0
$716$	−2946.67	−	1701.26i	−0.153802	−	0.0887975i
$717$	20539.7	−	29796.3i	1.06983	−	1.55197i
$718$	−20070.2	−	5377.79i	−1.04319	−	0.279523i
$719$	6320.54			0.327839			0.163920	−	0.986474i	$-0.447586\pi$
$719$	6320.54			0.327839			0.163920	+	0.986474i	$0.447586\pi$
$720$		0			0
$721$	−32007.8			−1.65331
$722$	−40948.6	−	10972.2i	−2.11073	−	0.565570i
$723$	−11605.7	−	24419.4i	−0.596984	−	1.25611i
$724$	1019.76	+	588.756i	0.0523466	+	0.0302223i
$725$		0			0
$726$	−12145.6	+	10344.0i	−0.620887	+	0.528791i
$727$	−1688.83	+	6302.81i	−0.0861558	+	0.321538i	−0.995531	−	0.0944399i	$-0.969894\pi$
$727$	−1688.83	+	6302.81i	−0.0861558	+	0.321538i	0.909375	+	0.415978i	$0.136561\pi$
$728$	4277.44	+	4277.44i	0.217764	+	0.217764i
$729$	17462.3	+	9082.34i	0.887176	+	0.461431i
$730$		0			0
$731$	−3174.51	+	1832.80i	−0.160620	+	0.0927342i
$732$	−165.296	+	2063.49i	−0.00834635	+	0.104192i
$733$	−1760.23	−	6569.29i	−0.0886982	−	0.331026i	0.907291	−	0.420504i	$-0.138147\pi$
$733$	−1760.23	−	6569.29i	−0.0886982	−	0.331026i	−0.995989	+	0.0894781i	$0.971480\pi$
$734$	−13997.9	+	24245.1i	−0.703914	+	1.21921i
$735$		0			0
$736$	−230.874	−	399.885i	−0.0115627	−	0.0200271i
$737$	2861.71	−	2861.71i	0.143029	−	0.143029i
$738$	−7708.44	−	10672.2i	−0.384487	−	0.532318i
$739$		−	5975.83i		−	0.297462i	−0.988878	−	0.148731i	$-0.952481\pi$
$739$		−	5975.83i		−	0.297462i	0.988878	−	0.148731i	$-0.0475189\pi$
$740$		0			0
$741$	6526.83	−	1200.26i	0.323575	−	0.0595044i
$742$	48531.2	−	13003.9i	2.40113	−	0.643380i
$743$	699.672	−	187.477i	0.0345471	−	0.00925686i	−0.241504	−	0.970400i	$-0.577641\pi$
$743$	699.672	−	187.477i	0.0345471	−	0.00925686i	0.276051	+	0.961143i	$0.410974\pi$
$744$	7563.07	−	1390.82i	0.372682	−	0.0685351i
$745$		0			0
$746$		−	2831.96i		−	0.138988i
$747$	1673.96	−	3731.73i	0.0819908	−	0.182780i
$748$	355.406	−	355.406i	0.0173729	−	0.0173729i
$749$	1254.99	+	2173.70i	0.0612233	+	0.106042i
$750$		0			0
$751$	10732.0	−	18588.3i	0.521459	−	0.903193i	−0.478230	−	0.878235i	$-0.658721\pi$
$751$	10732.0	−	18588.3i	0.521459	−	0.903193i	0.999688	−	0.0249581i	$-0.00794524\pi$
$752$	3505.42	+	13082.4i	0.169986	+	0.634397i
$753$	−271.114	+	3384.47i	−0.0131208	+	0.163794i
$754$	5023.62	−	2900.39i	0.242639	−	0.140087i
$755$		0			0
$756$	3426.18	−	2079.90i	0.164827	−	0.100060i
$757$	−15108.9	−	15108.9i	−0.725420	−	0.725420i	0.244284	−	0.969704i	$-0.421447\pi$
$757$	−15108.9	−	15108.9i	−0.725420	−	0.725420i	−0.969704	+	0.244284i	$0.921447\pi$
$758$	−996.631	+	3719.48i	−0.0477563	+	0.178229i
$759$	797.835	−	679.494i	0.0381549	−	0.0324955i
$760$		0			0
$761$	−17720.2	−	10230.7i	−0.844094	−	0.487338i	0.0145596	−	0.999894i	$-0.495365\pi$
$761$	−17720.2	−	10230.7i	−0.844094	−	0.487338i	−0.858654	+	0.512556i	$0.828699\pi$
$762$	17756.6	+	37361.5i	0.844165	+	1.77620i
$763$	34108.0	+	9139.21i	1.61834	+	0.433633i
$764$	1845.29			0.0873823
$765$		0			0
$766$	17705.2			0.835136
$767$	−3568.55	−	956.191i	−0.167996	−	0.0450144i
$768$	−3945.22	+	5723.21i	−0.185366	+	0.268904i
$769$	−35643.4	−	20578.7i	−1.67144	−	0.965004i	−0.966835	−	0.255401i	$-0.917792\pi$
$769$	−35643.4	−	20578.7i	−1.67144	−	0.965004i	−0.704602	−	0.709603i	$-0.748874\pi$
$770$		0			0
$771$	−29.8602	−	162.375i	−0.00139480	−	0.00758468i
$772$	−560.269	+	2090.95i	−0.0261199	+	0.0974807i
$773$	12436.1	+	12436.1i	0.578649	+	0.578649i	0.934531	−	0.355882i	$-0.115820\pi$
$773$	12436.1	+	12436.1i	0.578649	+	0.578649i	−0.355882	+	0.934531i	$0.615820\pi$
$774$	−6954.02	−	5663.44i	−0.322942	−	0.263008i
$775$		0			0
$776$	18713.4	−	10804.2i	0.865687	−	0.499805i
$777$	−12156.3	+	5777.46i	−0.561267	+	0.266750i
$778$	−4743.91	−	17704.5i	−0.218608	−	0.815858i
$779$	11878.7	−	20574.5i	0.546339	−	0.946286i
$780$		0			0
$781$	−3771.45	−	6532.35i	−0.172795	−	0.299290i
$782$	805.948	−	805.948i	0.0368550	−	0.0368550i
$783$	8693.42	+	29805.9i	0.396779	+	1.36038i
$784$			49751.1i			2.26636i
$785$		0			0
$786$	−6738.90	−	7912.55i	−0.305812	−	0.359073i
$787$	−23471.2	+	6289.08i	−1.06310	+	0.284856i	−0.747653	−	0.664089i	$-0.768820\pi$
$787$	−23471.2	+	6289.08i	−1.06310	+	0.284856i	−0.315442	+	0.948945i	$0.602153\pi$
$788$	2191.35	−	587.170i	0.0990655	−	0.0265445i
$789$	−12215.1	+	34342.0i	−0.551164	+	1.54957i
$790$		0			0
$791$			42056.1i			1.89044i
$792$	−9063.74	−	4065.77i	−0.406649	−	0.182413i
$793$	2811.66	−	2811.66i	0.125908	−	0.125908i
$794$	−19199.8	−	33255.1i	−0.858157	−	1.48637i
$795$		0			0
$796$	−81.6609	+	141.441i	−0.00363617	+	0.00629804i
$797$	8595.91	+	32080.4i	0.382036	+	1.42578i	0.842786	+	0.538249i	$0.180914\pi$
$797$	8595.91	+	32080.4i	0.382036	+	1.42578i	−0.460750	+	0.887530i	$0.652419\pi$
$798$	60016.2	+	41371.4i	2.66234	+	1.83525i
$799$	−5489.25	+	3169.22i	−0.243049	+	0.140324i
$800$		0			0
$801$	3348.72	+	539.965i	0.147717	+	0.0238186i
$802$	−8704.14	−	8704.14i	−0.383234	−	0.383234i
$803$	−1436.36	+	5360.56i	−0.0631232	+	0.235579i
$804$	1006.78	+	358.102i	0.0441624	+	0.0157081i
$805$		0			0
$806$	1583.54	+	914.256i	0.0692032	+	0.0399545i
$807$	5718.47	+	458.080i	0.249442	+	0.0199816i
$808$	2326.82	+	623.470i	0.101309	+	0.0271456i
$809$	21561.9			0.937054			0.468527	−	0.883449i	$-0.344785\pi$
$809$	21561.9			0.937054			0.468527	+	0.883449i	$0.344785\pi$
$810$		0			0
$811$	−34494.6			−1.49355			−0.746775	−	0.665077i	$-0.768399\pi$
$811$	−34494.6			−1.49355			−0.746775	+	0.665077i	$0.768399\pi$
$812$	6106.89	+	1636.34i	0.263928	+	0.0707193i
$813$	20494.7	+	1641.73i	0.884108	+	0.0708217i
$814$	−3576.26	−	2064.76i	−0.153990	−	0.0889063i
$815$		0			0
$816$	−11314.5	−	4024.43i	−0.485399	−	0.172651i
$817$	4188.82	−	15632.9i	0.179373	−	0.669431i
$818$	−11012.5	−	11012.5i	−0.470714	−	0.470714i
$819$	−7600.60	−	1225.56i	−0.324282	−	0.0522888i
$820$		0			0
$821$	20162.0	−	11640.5i	0.857073	−	0.494831i	−0.00595789	−	0.999982i	$-0.501896\pi$
$821$	20162.0	−	11640.5i	0.857073	−	0.494831i	0.863031	+	0.505151i	$0.168563\pi$
$822$	−22534.9	−	15534.1i	−0.956199	−	0.659143i
$823$	3796.00	+	14166.9i	0.160778	+	0.600031i	0.998541	+	0.0539975i	$0.0171963\pi$
$823$	3796.00	+	14166.9i	0.160778	+	0.600031i	−0.837763	+	0.546034i	$0.816137\pi$
$824$	−10473.0	+	18139.9i	−0.442774	+	0.766907i
$825$		0			0
$826$	−20290.2	−	35143.6i	−0.854705	−	1.48039i
$827$	13463.5	−	13463.5i	0.566109	−	0.566109i	−0.364927	−	0.931036i	$-0.618906\pi$
$827$	13463.5	−	13463.5i	0.566109	−	0.566109i	0.931036	+	0.364927i	$0.118906\pi$
$828$	252.467	+	113.250i	0.0105964	+	0.00475329i
$829$			40270.0i			1.68713i	0.537024	+	0.843567i	$0.319548\pi$
$829$			40270.0i			1.68713i	−0.537024	+	0.843567i	$0.680452\pi$
$830$		0			0
$831$	−1964.39	+	5522.77i	−0.0820023	+	0.230545i
$832$	3770.97	−	1010.43i	0.157133	−	0.0421037i
$833$	−22489.8	+	6026.12i	−0.935445	+	0.250652i
$834$	−5222.13	−	6131.62i	−0.216820	−	0.254581i
$835$		0			0
$836$			2219.16i			0.0918077i
$837$	−6766.47	+	7070.88i	−0.279431	+	0.292002i
$838$	−19739.0	+	19739.0i	−0.813690	+	0.813690i
$839$	−6626.11	−	11476.8i	−0.272656	−	0.472255i	0.696885	−	0.717183i	$-0.254569\pi$
$839$	−6626.11	−	11476.8i	−0.272656	−	0.472255i	−0.969541	+	0.244928i	$0.921236\pi$
$840$		0			0
$841$	−12292.8	+	21291.8i	−0.504031	+	0.873008i
$842$	2138.16	+	7979.71i	0.0875128	+	0.326602i
$843$	−23046.2	+	10953.1i	−0.941583	+	0.447501i
$844$	3928.45	−	2268.09i	0.160217	−	0.0925011i
$845$		0			0
$846$	−12024.7	−	9793.04i	−0.488672	−	0.397981i
$847$	23616.5	+	23616.5i	0.958055	+	0.958055i
$848$	9458.74	−	35300.5i	0.383036	−	1.42951i
$849$	−6378.80	−	34686.8i	−0.257856	−	1.40218i
$850$		0			0
$851$	−804.701	−	464.594i	−0.0324146	−	0.0187146i
$852$	1130.34	−	1639.76i	0.0454518	−	0.0659356i
$853$	−30985.0	−	8302.39i	−1.24373	−	0.333257i	−0.423821	−	0.905746i	$-0.639311\pi$
$853$	−30985.0	−	8302.39i	−1.24373	−	0.333257i	−0.819913	+	0.572489i	$0.805978\pi$
$854$	43676.2			1.75008
$855$		0			0
$856$	1642.54			0.0655851
$857$	43531.9	+	11664.3i	1.73515	+	0.464931i	0.981359	−	0.192186i	$-0.0615576\pi$
$857$	43531.9	+	11664.3i	1.73515	+	0.464931i	0.753788	+	0.657117i	$0.228224\pi$
$858$	−1013.93	−	2133.40i	−0.0403439	−	0.0848871i
$859$	−14333.6	−	8275.49i	−0.569331	−	0.328703i	0.187551	−	0.982255i	$-0.439945\pi$
$859$	−14333.6	−	8275.49i	−0.569331	−	0.328703i	−0.756882	+	0.653551i	$0.773278\pi$
$860$		0			0
$861$	−20982.5	+	17870.2i	−0.830526	+	0.707335i
$862$	11092.7	−	41398.5i	0.438304	−	1.63577i
$863$	15700.9	+	15700.9i	0.619310	+	0.619310i	0.945354	−	0.326045i	$-0.105716\pi$
$863$	15700.9	+	15700.9i	0.619310	+	0.619310i	−0.326045	+	0.945354i	$0.605716\pi$
$864$	−122.517	−	5569.16i	−0.00482422	−	0.219290i
$865$		0			0
$866$	26694.6	−	15412.1i	1.04748	−	0.604763i
$867$	−1589.69	+	19845.1i	−0.0622709	+	0.777363i
$868$	515.803	+	1925.00i	0.0201699	+	0.0752752i
$869$	−1390.16	+	2407.82i	−0.0542668	+	0.0939929i
$870$		0			0
$871$	−1026.27	−	1777.55i	−0.0399240	−	0.0691503i
$872$	16339.7	−	16339.7i	0.634555	−	0.634555i
$873$	−11255.6	+	25091.9i	−0.436363	+	0.972776i
$874$			5032.35i			0.194762i
$875$		0			0
$876$	−1441.15	+	265.022i	−0.0555843	+	0.0102218i
$877$	−13598.3	+	3643.66i	−0.523583	+	0.140294i	−0.510924	−	0.859626i	$-0.670697\pi$
$877$	−13598.3	+	3643.66i	−0.523583	+	0.140294i	−0.0126598	+	0.999920i	$0.504030\pi$
$878$	4269.42	−	1143.99i	0.164107	−	0.0439724i
$879$	2852.56	−	524.576i	0.109459	−	0.0201291i
$880$		0			0
$881$		−	7520.39i		−	0.287592i	−0.989607	−	0.143796i	$-0.954069\pi$
$881$		−	7520.39i		−	0.287592i	0.989607	−	0.143796i	$-0.0459309\pi$
$882$	−33354.9	−	46179.4i	−1.27338	−	1.76297i
$883$	23246.2	−	23246.2i	0.885953	−	0.885953i	−0.108179	−	0.994131i	$-0.534502\pi$
$883$	23246.2	−	23246.2i	0.885953	−	0.885953i	0.994131	+	0.108179i	$0.0345019\pi$
$884$	−127.456	−	220.760i	−0.00484932	−	0.00839927i
$885$		0			0
$886$	−16177.1	+	28019.6i	−0.613409	+	1.06246i
$887$	−10928.9	−	40787.4i	−0.413707	−	1.54397i	−0.787412	−	0.616427i	$-0.788579\pi$
$887$	−10928.9	−	40787.4i	−0.413707	−	1.54397i	0.373705	−	0.927548i	$-0.378087\pi$
$888$	−703.304	+	8779.75i	−0.0265781	+	0.331790i
$889$	74998.7	−	43300.5i	2.82944	−	1.63358i
$890$		0			0
$891$	12380.9	−	2559.54i	0.465519	−	0.0962378i
$892$	−2803.22	−	2803.22i	−0.105223	−	0.105223i
$893$	7243.16	−	27031.8i	0.271426	−	1.01297i
$894$	25197.9	−	21460.4i	0.942668	−	0.802843i
$895$		0			0
$896$	46055.0	+	26589.8i	1.71717	+	0.991411i
$897$	−228.146	−	480.040i	−0.00849229	−	0.0178685i
$898$	10580.1	+	2834.92i	0.393165	+	0.105348i
$899$	−15437.7			−0.572721
$900$		0			0
$901$	17103.1			0.632395
$902$	−8167.96	−	2188.60i	−0.301512	−	0.0807898i
$903$	−10656.2	+	15458.6i	−0.392707	+	0.569689i
$904$	23834.5	+	13760.8i	0.876906	+	0.506282i
$905$		0			0
$906$	5684.26	+	30910.1i	0.208440	+	1.13346i
$907$	2662.48	−	9936.50i	0.0974709	−	0.363767i	−0.899912	−	0.436072i	$-0.856369\pi$
$907$	2662.48	−	9936.50i	0.0974709	−	0.363767i	0.997382	+	0.0723059i	$0.0230358\pi$
$908$	2902.16	+	2902.16i	0.106070	+	0.106070i
$909$	−2865.22	+	1090.69i	−0.104547	+	0.0397976i
$910$		0			0
$911$	12942.9	−	7472.60i	0.470711	−	0.271765i	−0.245826	−	0.969314i	$-0.579059\pi$
$911$	12942.9	−	7472.60i	0.470711	−	0.271765i	0.716537	+	0.697549i	$0.245726\pi$
$912$	47888.1	−	22759.5i	1.73874	−	0.826364i
$913$	−679.936	−	2537.56i	−0.0246469	−	0.0919834i
$914$	−13205.0	+	22871.7i	−0.477880	+	0.827712i
$915$		0			0
$916$	1797.34	+	3113.09i	0.0648317	+	0.112292i
$917$	−15385.6	+	15385.6i	−0.554065	+	0.554065i
$918$	13200.3	−	3850.10i	0.474591	−	0.138423i
$919$		−	26923.8i		−	0.966413i	−0.875506	−	0.483207i	$-0.839472\pi$
$919$		−	26923.8i		−	0.966413i	0.875506	−	0.483207i	$-0.160528\pi$
$920$		0			0
$921$	−9412.59	−	11051.9i	−0.336759	−	0.395410i
$922$	2046.27	−	548.296i	0.0730913	−	0.0195848i
$923$	−3695.15	+	990.113i	−0.131774	+	0.0353087i
$924$	862.756	−	2425.59i	0.0307171	−	0.0863594i
$925$		0			0
$926$			12851.7i			0.456085i
$927$	−2712.54	−	26519.5i	−0.0961075	−	0.939607i
$928$	6213.26	−	6213.26i	0.219785	−	0.219785i
$929$	−15434.9	−	26734.1i	−0.545106	−	0.944151i	−0.998600	−	0.0528918i	$-0.983156\pi$
$929$	−15434.9	−	26734.1i	−0.545106	−	0.944151i	0.453494	−	0.891259i	$-0.350177\pi$
$930$		0			0
$931$	51399.7	−	89027.0i	1.80941	−	3.13399i
$932$	−816.237	−	3046.24i	−0.0286875	−	0.107063i
$933$	10229.5	+	7051.54i	0.358947	+	0.247435i
$934$	20782.4	−	11998.7i	0.728073	−	0.420353i
$935$		0			0
$936$	−3181.50	+	3906.50i	−0.111101	+	0.136419i
$937$	−2293.85	−	2293.85i	−0.0799753	−	0.0799753i	0.665988	−	0.745963i	$-0.268010\pi$
$937$	−2293.85	−	2293.85i	−0.0799753	−	0.0799753i	−0.745963	+	0.665988i	$0.768010\pi$
$938$	5835.18	−	21777.2i	0.203119	−	0.758050i
$939$	−25416.8	−	9040.48i	−0.883330	−	0.314191i
$940$		0			0
$941$	−43555.5	−	25146.8i	−1.50889	−	0.871160i	−0.999946	−	0.0103625i	$-0.996701\pi$
$941$	−43555.5	−	25146.8i	−1.50889	−	0.871160i	−0.508947	−	0.860798i	$-0.669965\pi$
$942$	−3765.23	−	301.615i	−0.130231	−	0.0104322i
$943$	−1837.89	−	492.460i	−0.0634675	−	0.0170061i
$944$	−29517.2			−1.01769
$945$		0			0
$946$	−5760.59			−0.197984
$947$	45061.0	+	12074.1i	1.54624	+	0.414313i	0.928274	−	0.371896i	$-0.121292\pi$
$947$	45061.0	+	12074.1i	1.54624	+	0.414313i	0.617961	+	0.786209i	$0.287959\pi$
$948$	−731.761	−	58.6179i	−0.0250701	−	0.00200825i
$949$	2437.51	+	1407.30i	0.0833772	+	0.0481379i
$950$		0			0
$951$	−40543.9	−	14421.0i	−1.38247	−	0.491729i
$952$	−5854.11	+	21847.8i	−0.199299	+	0.743795i
$953$	19475.8	+	19475.8i	0.661997	+	0.661997i	0.955850	−	0.293854i	$-0.0949379\pi$
$953$	19475.8	+	19475.8i	0.661997	+	0.661997i	−0.293854	+	0.955850i	$0.594938\pi$
$954$	14887.0	+	39107.7i	0.505224	+	1.32721i
$955$		0			0
$956$	5315.33	−	3068.81i	0.179822	−	0.103820i
$957$	16419.4	+	11318.5i	0.554613	+	0.382315i
$958$	−891.887	−	3328.57i	−0.0300789	−	0.112256i
$959$	−28650.0	+	49623.3i	−0.964710	+	1.67093i
$960$		0			0
$961$	12462.4	+	21585.5i	0.418327	+	0.724563i
$962$	−1480.93	+	1480.93i	−0.0496331	+	0.0496331i
$963$	−1694.63	+	1224.01i	−0.0567067	+	0.0409586i
$964$		−	4585.35i		−	0.153199i
$965$		0			0
$966$	1956.46	−	5500.48i	0.0651636	−	0.183204i
$967$	3128.82	−	838.365i	0.104050	−	0.0278800i	−0.206418	−	0.978464i	$-0.566181\pi$
$967$	3128.82	−	838.365i	0.104050	−	0.0278800i	0.310468	+	0.950584i	$0.399514\pi$
$968$	21111.6	−	5656.84i	0.700984	−	0.187828i
$969$	16088.8	+	18890.9i	0.533382	+	0.626277i
$970$		0			0
$971$		−	2493.85i		−	0.0824218i	−0.999150	−	0.0412109i	$-0.986878\pi$
$971$		−	2493.85i		−	0.0824218i	0.999150	−	0.0412109i	$-0.0131216\pi$
$972$	2013.62	+	2662.44i	0.0664473	+	0.0878577i
$973$	−11922.7	+	11922.7i	−0.392830	+	0.392830i
$974$	23821.4	+	41260.0i	0.783664	+	1.35735i
$975$		0			0
$976$	15884.5	−	27512.8i	0.520954	−	0.902319i
$977$	−13535.1	−	50513.8i	−0.443222	−	1.65413i	−0.720590	−	0.693362i	$-0.756129\pi$
$977$	−13535.1	−	50513.8i	−0.443222	−	1.65413i	0.277368	−	0.960764i	$-0.410538\pi$
$978$	−34539.0	+	16415.2i	−1.12928	+	0.536707i
$979$	1886.83	−	1089.36i	0.0615969	−	0.0355630i
$980$		0			0
$981$	−4681.61	+	29034.1i	−0.152367	+	0.944941i
$982$	28790.5	+	28790.5i	0.935582	+	0.935582i
$983$	7471.98	−	27885.8i	0.242441	−	0.904801i	−0.732212	−	0.681077i	$-0.761512\pi$
$983$	7471.98	−	27885.8i	0.242441	−	0.904801i	0.974653	−	0.223724i	$-0.0718215\pi$
$984$	3262.08	+	17738.6i	0.105682	+	0.574682i
$985$		0			0
$986$	18783.8	+	10844.8i	0.606691	+	0.350273i
$987$	−18426.3	+	26730.4i	−0.594240	+	0.862046i
$988$	1087.13	+	291.296i	0.0350064	+	0.00937992i
$989$	−1296.20			−0.0416752
$990$		0			0
$991$	33344.3			1.06884			0.534418	−	0.845220i	$-0.320531\pi$
$991$	33344.3			1.06884			0.534418	+	0.845220i	$0.320531\pi$
$992$	2675.41	+	716.874i	0.0856294	+	0.0229443i
$993$	−17060.0	−	35895.7i	−0.545198	−	1.14715i
$994$	−36390.4	−	21010.0i	−1.16120	−	0.670419i
$995$		0			0
$996$	528.078	−	449.749i	0.0168000	−	0.0143081i
$997$	−5162.21	+	19265.6i	−0.163981	+	0.611984i	0.834187	+	0.551481i	$0.185937\pi$
$997$	−5162.21	+	19265.6i	−0.163981	+	0.611984i	−0.998168	+	0.0605030i	$0.980730\pi$
$998$	25914.9	+	25914.9i	0.821966	+	0.821966i
$999$	−5817.01	−	9582.26i	−0.184226	−	0.303473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.p.b.32.13		64
5.2	odd	4		45.4.l.a.23.4	yes	64
5.3	odd	4	inner	225.4.p.b.68.13		64
5.4	even	2		45.4.l.a.32.4	yes	64
9.2	odd	6	inner	225.4.p.b.182.13		64
15.2	even	4		135.4.m.a.98.13		64
15.14	odd	2		135.4.m.a.17.13		64
45.2	even	12		45.4.l.a.38.4	yes	64
45.7	odd	12		135.4.m.a.8.13		64
45.29	odd	6		45.4.l.a.2.4	✓	64
45.34	even	6		135.4.m.a.62.13		64
45.38	even	12	inner	225.4.p.b.218.13		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.4	✓	64	45.29	odd	6
45.4.l.a.23.4	yes	64	5.2	odd	4
45.4.l.a.32.4	yes	64	5.4	even	2
45.4.l.a.38.4	yes	64	45.2	even	12
135.4.m.a.8.13		64	45.7	odd	12
135.4.m.a.17.13		64	15.14	odd	2
135.4.m.a.62.13		64	45.34	even	6
135.4.m.a.98.13		64	15.2	even	4
225.4.p.b.32.13		64	1.1	even	1	trivial
225.4.p.b.68.13		64	5.3	odd	4	inner
225.4.p.b.182.13		64	9.2	odd	6	inner
225.4.p.b.218.13		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)

\(f(q)\)	\(=\)	\(q+(2.87860 + 0.771317i) q^{2} +(5.17956 + 0.414910i) q^{3} +(0.763180 + 0.440622i) q^{4} +(14.5898 + 5.18944i) q^{6} +(8.39055 - 31.3140i) q^{7} +(-15.0012 - 15.0012i) q^{8} +(26.6557 + 4.29810i) q^{9} +O(q^{10})\)	\(q+(2.87860 + 0.771317i) q^{2} +(5.17956 + 0.414910i) q^{3} +(0.763180 + 0.440622i) q^{4} +(14.5898 + 5.18944i) q^{6} +(8.39055 - 31.3140i) q^{7} +(-15.0012 - 15.0012i) q^{8} +(26.6557 + 4.29810i) q^{9} +(15.0191 - 8.67129i) q^{11} +(3.77012 + 2.59888i) q^{12} +(-2.27646 - 8.49586i) q^{13} +(48.3060 - 83.6685i) q^{14} +(-35.1367 - 60.8585i) q^{16} +(23.2549 - 23.2549i) q^{17} +(73.4158 + 32.9325i) q^{18} +145.204i q^{19} +(56.4519 - 158.711i) q^{21} +(49.9223 - 13.3766i) q^{22} +(11.2331 - 3.00990i) q^{23} +(-71.4755 - 83.9238i) q^{24} -26.2120i q^{26} +(136.281 + 33.3220i) q^{27} +(20.2011 - 20.2011i) q^{28} +(110.651 + 191.653i) q^{29} +(-34.8793 + 60.4127i) q^{31} +(-10.2765 - 38.3524i) q^{32} +(81.3902 - 38.6819i) q^{33} +(84.8784 - 49.0046i) q^{34} +(18.4492 + 15.0253i) q^{36} +(-56.4980 - 56.4980i) q^{37} +(-111.998 + 417.984i) q^{38} +(-8.26604 - 44.9494i) q^{39} +(-141.694 - 81.8068i) q^{41} +(284.919 - 413.323i) q^{42} +(-107.661 - 28.8478i) q^{43} +15.2830 q^{44} +34.6571 q^{46} +(-186.165 - 49.8826i) q^{47} +(-156.742 - 329.799i) q^{48} +(-613.116 - 353.983i) q^{49} +(130.099 - 110.801i) q^{51} +(2.00612 - 7.48693i) q^{52} +(367.732 + 367.732i) q^{53} +(366.597 + 201.037i) q^{54} +(-595.615 + 343.879i) q^{56} +(-60.2466 + 752.093i) q^{57} +(170.694 + 637.039i) q^{58} +(210.017 - 363.760i) q^{59} +(226.039 + 391.511i) q^{61} +(-147.001 + 147.001i) q^{62} +(358.247 - 798.632i) q^{63} +443.859i q^{64} +(264.126 - 48.5718i) q^{66} +(225.409 - 60.3981i) q^{67} +(27.9943 - 7.50105i) q^{68} +(59.4313 - 10.9292i) q^{69} -434.936i q^{71} +(-335.391 - 464.344i) q^{72} +(-226.275 + 226.275i) q^{73} +(-119.057 - 206.213i) q^{74} +(-63.9801 + 110.817i) q^{76} +(-145.514 - 543.065i) q^{77} +(10.8756 - 135.767i) q^{78} +(-138.839 + 80.1586i) q^{79} +(692.053 + 229.138i) q^{81} +(-344.779 - 344.779i) q^{82} +(39.2062 - 146.319i) q^{83} +(113.015 - 96.2513i) q^{84} +(-287.663 - 166.082i) q^{86} +(493.605 + 1038.59i) q^{87} +(-355.384 - 95.2250i) q^{88} +125.629 q^{89} -285.140 q^{91} +(9.89909 + 2.65245i) q^{92} +(-205.725 + 298.439i) q^{93} +(-497.417 - 287.184i) q^{94} +(-37.3150 - 202.913i) q^{96} +(-263.620 + 983.843i) q^{97} +(-1491.88 - 1491.88i) q^{98} +(437.615 - 166.586i) 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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