LMFDB - Embedded newform 225.4.p.b.218.4

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			218.4
Character	$\chi$	$=$	225.218
Dual form			225.4.p.b.32.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.56967 + 0.956489i) q^{2} +(-4.00002 - 3.31660i) q^{3} +(4.89944 - 2.82870i) q^{4} +(17.4510 + 8.01320i) q^{6} +(-1.11867 - 4.17492i) q^{7} +(6.12165 - 6.12165i) q^{8} +(5.00028 + 26.5329i) q^{9} +O(q^{10})$	\(q+(-3.56967 + 0.956489i) q^{2} +(-4.00002 - 3.31660i) q^{3} +(4.89944 - 2.82870i) q^{4} +(17.4510 + 8.01320i) q^{6} +(-1.11867 - 4.17492i) q^{7} +(6.12165 - 6.12165i) q^{8} +(5.00028 + 26.5329i) q^{9} +(-19.8083 - 11.4363i) q^{11} +(-28.9795 - 4.93468i) q^{12} +(-10.6888 + 39.8912i) q^{13} +(7.98654 + 13.8331i) q^{14} +(-38.6265 + 66.9031i) q^{16} +(53.3704 + 53.3704i) q^{17} +(-43.2278 - 89.9311i) q^{18} +63.9989i q^{19} +(-9.37188 + 20.4099i) q^{21} +(81.6476 + 21.8774i) q^{22} +(-141.799 - 37.9948i) q^{23} +(-44.7898 + 4.18362i) q^{24} -152.622i q^{26} +(67.9981 - 122.716i) q^{27} +(-17.2904 - 17.2904i) q^{28} +(145.682 - 252.328i) q^{29} +(60.4920 + 104.775i) q^{31} +(55.9663 - 208.869i) q^{32} +(41.3037 + 111.442i) q^{33} +(-241.563 - 139.466i) q^{34} +(99.5522 + 115.852i) q^{36} +(132.295 - 132.295i) q^{37} +(-61.2142 - 228.455i) q^{38} +(175.059 - 124.115i) q^{39} +(169.696 - 97.9741i) q^{41} +(13.9326 - 81.8208i) q^{42} +(-183.258 + 49.1037i) q^{43} -129.399 q^{44} +542.516 q^{46} +(-277.799 + 74.4360i) q^{47} +(376.398 - 139.505i) q^{48} +(280.868 - 162.159i) q^{49} +(-36.4741 - 390.491i) q^{51} +(60.4708 + 225.680i) q^{52} +(508.904 - 508.904i) q^{53} +(-125.354 + 503.095i) q^{54} +(-32.4055 - 18.7093i) q^{56} +(212.259 - 255.997i) q^{57} +(-278.686 + 1040.07i) q^{58} +(-344.876 - 597.343i) q^{59} +(-98.3560 + 170.358i) q^{61} +(-316.153 - 316.153i) q^{62} +(105.179 - 50.5573i) q^{63} +181.099i q^{64} +(-254.033 - 358.303i) q^{66} +(684.688 + 183.462i) q^{67} +(412.454 + 110.517i) q^{68} +(441.183 + 622.270i) q^{69} +192.329i q^{71} +(193.036 + 131.816i) q^{72} +(-257.846 - 257.846i) q^{73} +(-345.710 + 598.788i) q^{74} +(181.033 + 313.559i) q^{76} +(-25.5868 + 95.4913i) q^{77} +(-506.187 + 610.491i) q^{78} +(-543.771 - 313.946i) q^{79} +(-678.994 + 265.344i) q^{81} +(-512.047 + 512.047i) q^{82} +(-105.991 - 395.562i) q^{83} +(11.8165 + 126.508i) q^{84} +(607.201 - 350.568i) q^{86} +(-1419.60 + 526.149i) q^{87} +(-191.268 + 51.2502i) q^{88} +231.829 q^{89} +178.500 q^{91} +(-802.211 + 214.952i) q^{92} +(105.529 - 619.731i) q^{93} +(920.452 - 531.423i) q^{94} +(-916.602 + 649.862i) q^{96} +(-139.239 - 519.648i) q^{97} +(-847.502 + 847.502i) q^{98} +(204.392 - 582.756i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−3.56967	+	0.956489i	−1.26207	+	0.338170i	−0.826987	−	0.562221i	$-0.809947\pi$
$2$	−3.56967	+	0.956489i	−1.26207	+	0.338170i	−0.435081	+	0.900391i	$0.643280\pi$
$3$	−4.00002	−	3.31660i	−0.769804	−	0.638281i
$3$	−4.00002	−	3.31660i	−0.769804	−	0.638281i
$4$	4.89944	−	2.82870i	0.612430	−	0.353587i
$5$		0			0
$5$		0			0
$6$	17.4510	+	8.01320i	1.18739	+	0.545229i
$7$	−1.11867	−	4.17492i	−0.0604023	−	0.225425i	0.929126	−	0.369763i	$-0.120561\pi$
$7$	−1.11867	−	4.17492i	−0.0604023	−	0.225425i	−0.989528	+	0.144339i	$0.953895\pi$
$8$	6.12165	−	6.12165i	0.270541	−	0.270541i
$9$	5.00028	+	26.5329i	0.185195	+	0.982702i
$10$		0			0
$11$	−19.8083	−	11.4363i	−0.542947	−	0.313470i	0.203326	−	0.979111i	$-0.434825\pi$
$11$	−19.8083	−	11.4363i	−0.542947	−	0.313470i	−0.746272	+	0.665641i	$0.768158\pi$
$12$	−28.9795	−	4.93468i	−0.697139	−	0.118710i
$13$	−10.6888	+	39.8912i	−0.228042	+	0.851064i	0.753121	+	0.657882i	$0.228547\pi$
$13$	−10.6888	+	39.8912i	−0.228042	+	0.851064i	−0.981163	+	0.193182i	$0.938119\pi$
$14$	7.98654	+	13.8331i	0.152464	+	0.264075i
$15$		0			0
$16$	−38.6265	+	66.9031i	−0.603540	+	1.04536i
$17$	53.3704	+	53.3704i	0.761425	+	0.761425i	0.976580	−	0.215155i	$-0.0690256\pi$
$17$	53.3704	+	53.3704i	0.761425	+	0.761425i	−0.215155	+	0.976580i	$0.569026\pi$
$18$	−43.2278	−	89.9311i	−0.566049	−	1.17761i
$19$			63.9989i			0.772755i	0.922341	+	0.386378i	$0.126274\pi$
$19$			63.9989i			0.772755i	−0.922341	+	0.386378i	$0.873726\pi$
$20$		0			0
$21$	−9.37188	+	20.4099i	−0.0973862	+	0.212086i
$22$	81.6476	+	21.8774i	0.791242	+	0.212013i
$23$	−141.799	−	37.9948i	−1.28552	−	0.344455i	−0.449566	−	0.893247i	$-0.648421\pi$
$23$	−141.799	−	37.9948i	−1.28552	−	0.344455i	−0.835959	+	0.548792i	$0.815088\pi$
$24$	−44.7898	+	4.18362i	−0.380945	+	0.0355824i
$25$		0			0
$26$		−	152.622i		−	1.15122i
$27$	67.9981	−	122.716i	0.484675	−	0.874694i
$28$	−17.2904	−	17.2904i	−0.116699	−	0.116699i
$29$	145.682	−	252.328i	0.932843	−	1.61573i	0.154408	−	0.988007i	$-0.450653\pi$
$29$	145.682	−	252.328i	0.932843	−	1.61573i	0.778435	−	0.627725i	$-0.216014\pi$
$30$		0			0
$31$	60.4920	+	104.775i	0.350474	+	0.607038i	0.986333	−	0.164767i	$-0.0526872\pi$
$31$	60.4920	+	104.775i	0.350474	+	0.607038i	−0.635859	+	0.771805i	$0.719354\pi$
$32$	55.9663	−	208.869i	0.309173	−	1.15385i
$33$	41.3037	+	111.442i	0.217880	+	0.587863i
$34$	−241.563	−	139.466i	−1.21846	−	0.703479i
$35$		0			0
$36$	99.5522	+	115.852i	0.460890	+	0.536354i
$37$	132.295	−	132.295i	0.587816	−	0.587816i	−0.349224	−	0.937039i	$-0.613555\pi$
$37$	132.295	−	132.295i	0.587816	−	0.587816i	0.937039	+	0.349224i	$0.113555\pi$
$38$	−61.2142	−	228.455i	−0.261323	−	0.975269i
$39$	175.059	−	124.115i	0.718765	−	0.509598i
$40$		0			0
$41$	169.696	−	97.9741i	0.646392	−	0.373195i	−0.140680	−	0.990055i	$-0.544929\pi$
$41$	169.696	−	97.9741i	0.646392	−	0.373195i	0.787073	+	0.616860i	$0.211596\pi$
$42$	13.9326	−	81.8208i	0.0511868	−	0.300600i
$43$	−183.258	+	49.1037i	−0.649919	+	0.174145i	−0.568692	−	0.822550i	$-0.692550\pi$
$43$	−183.258	+	49.1037i	−0.649919	+	0.174145i	−0.0812268	+	0.996696i	$0.525884\pi$
$44$	−129.399			−0.443356
$45$		0			0
$46$	542.516			1.73890
$47$	−277.799	+	74.4360i	−0.862152	+	0.231013i	−0.662691	−	0.748893i	$-0.730586\pi$
$47$	−277.799	+	74.4360i	−0.862152	+	0.231013i	−0.199461	+	0.979906i	$0.563919\pi$
$48$	376.398	−	139.505i	1.13184	−	0.419495i
$49$	280.868	−	162.159i	0.818858	−	0.472768i
$50$		0			0
$51$	−36.4741	−	390.491i	−0.100145	−	1.07215i
$52$	60.4708	+	225.680i	0.161265	+	0.601850i
$53$	508.904	−	508.904i	1.31893	−	1.31893i	0.404308	−	0.914623i	$-0.367513\pi$
$53$	508.904	−	508.904i	1.31893	−	1.31893i	0.914623	−	0.404308i	$-0.132487\pi$
$54$	−125.354	+	503.095i	−0.315898	+	1.26783i
$55$		0			0
$56$	−32.4055	−	18.7093i	−0.0773280	−	0.0446454i
$57$	212.259	−	255.997i	0.493235	−	0.594870i
$58$	−278.686	+	1040.07i	−0.630919	+	2.35462i
$59$	−344.876	−	597.343i	−0.761001	−	1.31809i	−0.942335	−	0.334671i	$-0.891375\pi$
$59$	−344.876	−	597.343i	−0.761001	−	1.31809i	0.181334	−	0.983422i	$-0.441958\pi$
$60$		0			0
$61$	−98.3560	+	170.358i	−0.206446	+	0.357575i	−0.950592	−	0.310442i	$-0.899523\pi$
$61$	−98.3560	+	170.358i	−0.206446	+	0.357575i	0.744147	+	0.668016i	$0.232856\pi$
$62$	−316.153	−	316.153i	−0.647604	−	0.647604i
$63$	105.179	−	50.5573i	0.210339	−	0.101105i
$64$			181.099i			0.353709i
$65$		0			0
$66$	−254.033	−	358.303i	−0.473777	−	0.668242i
$67$	684.688	+	183.462i	1.24848	+	0.334528i	0.821748	−	0.569851i	$-0.192999\pi$
$67$	684.688	+	183.462i	1.24848	+	0.334528i	0.426729	+	0.904380i	$0.359666\pi$
$68$	412.454	+	110.517i	0.735550	+	0.197090i
$69$	441.183	+	622.270i	0.769743	+	1.08569i
$70$		0			0
$71$			192.329i			0.321482i	0.986997	+	0.160741i	$0.0513884\pi$
$71$			192.329i			0.321482i	−0.986997	+	0.160741i	$0.948612\pi$
$72$	193.036	+	131.816i	0.315965	+	0.215759i
$73$	−257.846	−	257.846i	−0.413405	−	0.413405i	0.469518	−	0.882923i	$-0.344428\pi$
$73$	−257.846	−	257.846i	−0.413405	−	0.413405i	−0.882923	+	0.469518i	$0.844428\pi$
$74$	−345.710	+	598.788i	−0.543081	+	0.940645i
$75$		0			0
$76$	181.033	+	313.559i	0.273236	+	0.473259i
$77$	−25.5868	+	95.4913i	−0.0378687	+	0.141328i
$78$	−506.187	+	610.491i	−0.734800	+	0.886211i
$79$	−543.771	−	313.946i	−0.774418	−	0.447111i	0.0600303	−	0.998197i	$-0.480880\pi$
$79$	−543.771	−	313.946i	−0.774418	−	0.447111i	−0.834448	+	0.551086i	$0.814214\pi$
$80$		0			0
$81$	−678.994	+	265.344i	−0.931405	+	0.363984i
$82$	−512.047	+	512.047i	−0.689588	+	0.689588i
$83$	−105.991	−	395.562i	−0.140168	−	0.523116i	−0.999923	−	0.0124083i	$-0.996050\pi$
$83$	−105.991	−	395.562i	−0.140168	−	0.523116i	0.859755	−	0.510707i	$-0.170616\pi$
$84$	11.8165	+	126.508i	0.0153487	+	0.164323i
$85$		0			0
$86$	607.201	−	350.568i	0.761351	−	0.439566i
$87$	−1419.60	+	526.149i	−1.74940	+	0.648381i
$88$	−191.268	+	51.2502i	−0.231696	+	0.0620828i
$89$	231.829			0.276110			0.138055	−	0.990425i	$-0.455915\pi$
$89$	231.829			0.276110			0.138055	+	0.990425i	$0.455915\pi$
$90$		0			0
$91$	178.500			0.205625
$92$	−802.211	+	214.952i	−0.909089	+	0.243590i
$93$	105.529	−	619.731i	0.117665	−	0.691001i
$94$	920.452	−	531.423i	1.00997	−	0.583108i
$95$		0			0
$96$	−916.602	+	649.862i	−0.974482	+	0.690898i
$97$	−139.239	−	519.648i	−0.145749	−	0.543941i	−0.999721	−	0.0236228i	$-0.992480\pi$
$97$	−139.239	−	519.648i	−0.145749	−	0.543941i	0.853972	−	0.520318i	$-0.174187\pi$
$98$	−847.502	+	847.502i	−0.873578	+	0.873578i
$99$	204.392	−	582.756i	0.207497	−	0.591608i
$100$		0			0
$101$	−1250.68	−	722.083i	−1.23216	−	0.711385i	−0.264677	−	0.964337i	$-0.585265\pi$
$101$	−1250.68	−	722.083i	−1.23216	−	0.711385i	−0.967479	+	0.252952i	$0.918599\pi$
$102$	503.701	+	1359.04i	0.488959	+	1.31926i
$103$	135.250	−	504.760i	0.129384	−	0.482869i	−0.870574	−	0.492038i	$-0.836252\pi$
$103$	135.250	−	504.760i	0.129384	−	0.482869i	0.999958	+	0.00916944i	$0.00291876\pi$
$104$	178.767	+	309.634i	0.168553	+	0.291943i
$105$		0			0
$106$	−1329.86	+	2303.38i	−1.21856	+	2.11060i
$107$	424.345	+	424.345i	0.383393	+	0.383393i	0.872323	−	0.488930i	$-0.162613\pi$
$107$	424.345	+	424.345i	0.383393	+	0.383393i	−0.488930	+	0.872323i	$0.662613\pi$
$108$	−13.9739	−	793.587i	−0.0124504	−	0.707064i
$109$			868.306i			0.763015i	0.924366	+	0.381507i	$0.124595\pi$
$109$			868.306i			0.763015i	−0.924366	+	0.381507i	$0.875405\pi$
$110$		0			0
$111$	−967.953	+	90.4122i	−0.827694	+	0.0773113i
$112$	322.526	+	86.4205i	0.272105	+	0.0729104i
$113$	1212.10	+	324.781i	1.00907	+	0.270379i	0.725240	−	0.688496i	$-0.241729\pi$
$113$	1212.10	+	324.781i	1.00907	+	0.270379i	0.283828	+	0.958875i	$0.408395\pi$
$114$	−512.835	+	1116.85i	−0.421328	+	0.917563i
$115$		0			0
$116$		−	1648.36i		−	1.31936i
$117$	−1111.88	−	84.1387i	−0.878574	−	0.0664840i
$118$	1802.45	+	1802.45i	1.40617	+	1.40617i
$119$	163.114	−	282.521i	0.125652	−	0.217636i
$120$		0			0
$121$	−403.922	−	699.614i	−0.303473	−	0.525630i
$122$	188.153	−	702.196i	0.139628	−	0.521097i
$123$	−1003.73	−	170.917i	−0.735798	−	0.125293i
$124$	592.754	+	342.227i	0.429282	+	0.247846i
$125$		0			0
$126$	−327.098	+	281.076i	−0.231271	+	0.198732i
$127$	37.3046	−	37.3046i	0.0260649	−	0.0260649i	−0.693954	−	0.720019i	$-0.744133\pi$
$127$	37.3046	−	37.3046i	0.0260649	−	0.0260649i	0.720019	+	0.693954i	$0.244133\pi$
$128$	274.511	+	1024.49i	0.189559	+	0.707444i
$129$	895.891	+	411.377i	0.611464	+	0.280773i
$130$		0			0
$131$	856.776	−	494.660i	0.571427	−	0.329913i	−0.186292	−	0.982494i	$-0.559647\pi$
$131$	856.776	−	494.660i	0.571427	−	0.329913i	0.757719	+	0.652581i	$0.226314\pi$
$132$	517.599	+	429.166i	0.341297	+	0.282986i
$133$	267.190	−	71.5934i	0.174198	−	0.0466762i
$134$	−2619.59			−1.68879
$135$		0			0
$136$	653.431			0.411994
$137$	1597.06	−	427.931i	0.995958	−	0.266866i	0.276207	−	0.961098i	$-0.410923\pi$
$137$	1597.06	−	427.931i	0.995958	−	0.266866i	0.719751	+	0.694232i	$0.244256\pi$
$138$	−2170.07	−	1799.31i	−1.33861	−	1.10991i
$139$	1994.00	−	1151.24i	1.21675	−	0.702494i	0.252532	−	0.967589i	$-0.418737\pi$
$139$	1994.00	−	1151.24i	1.21675	−	0.702494i	0.964222	+	0.265095i	$0.0854033\pi$
$140$		0			0
$141$	1358.07	+	623.603i	0.811138	+	0.372460i
$142$	−183.960	−	686.550i	−0.108716	−	0.405732i
$143$	667.935	−	667.935i	0.390598	−	0.390598i
$144$	−1968.28	−	690.341i	−1.13905	−	0.399503i
$145$		0			0
$146$	1167.05	+	673.796i	0.661546	+	0.381944i
$147$	−1661.30	−	282.888i	−0.932118	−	0.158723i
$148$	273.950	−	1022.39i	0.152152	−	0.567840i
$149$	457.702	+	792.762i	0.251653	+	0.435877i	0.963981	−	0.265970i	$-0.0856923\pi$
$149$	457.702	+	792.762i	0.251653	+	0.435877i	−0.712328	+	0.701847i	$0.752359\pi$
$150$		0			0
$151$	1380.40	−	2390.93i	0.743944	−	1.28855i	−0.206742	−	0.978395i	$-0.566286\pi$
$151$	1380.40	−	2390.93i	0.743944	−	1.28855i	0.950686	−	0.310154i	$-0.100381\pi$
$152$	391.779	+	391.779i	0.209062	+	0.209062i
$153$	−1149.21	+	1682.94i	−0.607241	+	0.889266i
$154$		−	365.346i		−	0.191171i
$155$		0			0
$156$	506.607	−	1103.28i	0.260007	−	0.566239i
$157$	−1304.88	−	349.641i	−0.663316	−	0.177735i	−0.0885741	−	0.996070i	$-0.528231\pi$
$157$	−1304.88	−	349.641i	−0.663316	−	0.177735i	−0.574742	+	0.818335i	$0.694898\pi$
$158$	2241.37	+	600.573i	1.12857	+	0.302399i
$159$	−3723.46	+	347.792i	−1.85717	+	0.173470i
$160$		0			0
$161$			634.502i			0.310595i
$162$	2169.98	−	1596.64i	1.05241	−	0.774346i
$163$	645.582	+	645.582i	0.310220	+	0.310220i	0.844995	−	0.534775i	$-0.179603\pi$
$163$	645.582	+	645.582i	0.310220	+	0.310220i	−0.534775	+	0.844995i	$0.679603\pi$
$164$	554.278	−	960.037i	0.263914	−	0.457112i
$165$		0			0
$166$	756.702	+	1310.65i	0.353804	+	0.612807i
$167$	358.032	−	1336.19i	0.165900	−	0.619148i	−0.832023	−	0.554740i	$-0.812818\pi$
$167$	358.032	−	1336.19i	0.165900	−	0.619148i	0.997924	−	0.0644076i	$-0.0205158\pi$
$168$	67.5712	+	182.314i	0.0310311	+	0.0837252i
$169$	425.599	+	245.720i	0.193718	+	0.111843i
$170$		0			0
$171$	−1698.08	+	320.012i	−0.759388	+	0.143111i
$172$	−758.961	+	758.961i	−0.336455	+	0.336455i
$173$	−16.5380	−	61.7205i	−0.00726797	−	0.0271244i	0.962197	−	0.272356i	$-0.0878028\pi$
$173$	−16.5380	−	61.7205i	−0.00726797	−	0.0271244i	−0.969465	+	0.245231i	$0.921136\pi$
$174$	4564.26	−	3236.01i	1.98859	−	1.40989i
$175$		0			0
$176$	1530.25	−	883.489i	0.655379	−	0.378384i
$177$	−601.640	+	3533.20i	−0.255492	+	1.50040i
$178$	−827.551	+	221.742i	−0.348469	+	0.0933721i
$179$	−588.585			−0.245770			−0.122885	−	0.992421i	$-0.539215\pi$
$179$	−588.585			−0.245770			−0.122885	+	0.992421i	$0.539215\pi$
$180$		0			0
$181$	3146.98			1.29234			0.646169	−	0.763194i	$-0.276370\pi$
$181$	3146.98			1.29234			0.646169	+	0.763194i	$0.276370\pi$
$182$	−637.185	+	170.733i	−0.259513	+	0.0695362i
$183$	958.434	−	355.225i	0.387156	−	0.143492i
$184$	−1100.63	+	635.451i	−0.440977	+	0.254598i
$185$		0			0
$186$	216.063	+	2313.17i	0.0851748	+	0.911881i
$187$	−446.815	−	1667.54i	−0.174729	−	0.652098i
$188$	−1150.50	+	1150.50i	−0.446325	+	0.446325i
$189$	−588.398	−	146.608i	−0.226453	−	0.0564242i
$190$		0			0
$191$	2107.32	+	1216.66i	0.798326	+	0.460914i	0.842886	−	0.538093i	$-0.180855\pi$
$191$	2107.32	+	1216.66i	0.798326	+	0.460914i	−0.0445592	+	0.999007i	$0.514188\pi$
$192$	600.634	−	724.400i	0.225766	−	0.272287i
$193$	1297.37	−	4841.83i	0.483867	−	1.80582i	−0.101240	−	0.994862i	$-0.532281\pi$
$193$	1297.37	−	4841.83i	0.483867	−	1.80582i	0.585107	−	0.810956i	$-0.301052\pi$
$194$	994.076	+	1721.79i	0.367889	+	0.637203i
$195$		0			0
$196$	917.398	−	1588.98i	0.334329	−	0.579075i
$197$	−53.9821	−	53.9821i	−0.0195232	−	0.0195232i	0.697278	−	0.716801i	$-0.254394\pi$
$197$	−53.9821	−	53.9821i	−0.0195232	−	0.0195232i	−0.716801	+	0.697278i	$0.754394\pi$
$198$	−172.211	+	2275.74i	−0.0618107	+	0.816818i
$199$			84.8752i			0.0302344i	0.999886	+	0.0151172i	$0.00481213\pi$
$199$			84.8752i			0.0302344i	−0.999886	+	0.0151172i	$0.995188\pi$
$200$		0			0
$201$	−2130.29	−	3004.69i	−0.747559	−	1.05440i
$202$	5155.19	+	1381.33i	1.79563	+	0.481138i
$203$	−1216.42	−	325.939i	−0.420572	−	0.112692i
$204$	−1283.28	−	1810.02i	−0.440430	−	0.621208i
$205$		0			0
$206$			1931.19i			0.653167i
$207$	299.082	−	3952.32i	0.100423	−	1.32708i
$208$	−2255.97	−	2255.97i	−0.752037	−	0.752037i
$209$	731.910	−	1267.71i	0.242236	−	0.419565i
$210$		0			0
$211$	−375.407	−	650.225i	−0.122484	−	0.212148i	0.798263	−	0.602309i	$-0.205753\pi$
$211$	−375.407	−	650.225i	−0.122484	−	0.212148i	−0.920747	+	0.390161i	$0.872419\pi$
$212$	1053.81	−	3932.88i	0.341397	−	1.27411i
$213$	637.879	−	769.319i	0.205196	−	0.247478i
$214$	−1920.65	−	1108.89i	−0.613519	−	0.354216i
$215$		0			0
$216$	−334.965	−	1167.49i	−0.105516	−	0.367766i
$217$	369.758	−	369.758i	0.115672	−	0.115672i
$218$	−830.525	−	3099.56i	−0.258029	−	0.962976i
$219$	176.215	+	1886.56i	0.0543722	+	0.582109i
$220$		0			0
$221$	−2699.48	+	1558.54i	−0.821659	+	0.474385i
$222$	3368.79	−	1248.58i	1.01846	−	0.377473i
$223$	−5010.57	+	1342.58i	−1.50463	+	0.403164i	−0.914647	−	0.404252i	$-0.867532\pi$
$223$	−5010.57	+	1342.58i	−1.50463	+	0.403164i	−0.589982	+	0.807417i	$0.700865\pi$
$224$	−934.619			−0.278781
$225$		0			0
$226$	−4637.44			−1.36495
$227$	−401.515	+	107.586i	−0.117399	+	0.0314569i	−0.317040	−	0.948412i	$-0.602689\pi$
$227$	−401.515	+	107.586i	−0.117399	+	0.0314569i	0.199641	+	0.979869i	$0.436022\pi$
$228$	315.814	−	1854.66i	0.0917338	−	0.538718i
$229$	2238.73	−	1292.53i	0.646022	−	0.372981i	−0.140908	−	0.990023i	$-0.545002\pi$
$229$	2238.73	−	1292.53i	0.646022	−	0.372981i	0.786931	+	0.617041i	$0.211669\pi$
$230$		0			0
$231$	419.055	−	297.106i	0.119358	−	0.0846239i
$232$	−652.853	−	2436.48i	−0.184750	−	0.689495i
$233$	−1910.60	+	1910.60i	−0.537199	+	0.537199i	−0.922705	−	0.385506i	$-0.874027\pi$
$233$	−1910.60	+	1910.60i	−0.537199	+	0.537199i	0.385506	+	0.922705i	$0.374027\pi$
$234$	4049.51	−	763.153i	1.13130	−	0.213200i
$235$		0			0
$236$	−3379.40	−	1951.10i	−0.932120	−	0.538160i
$237$	1133.86	+	3059.26i	0.310768	+	0.838483i
$238$	−312.033	+	1164.52i	−0.0849836	+	0.317163i
$239$	562.224	+	973.800i	0.152164	+	0.263556i	0.932023	−	0.362400i	$-0.118042\pi$
$239$	562.224	+	973.800i	0.152164	+	0.263556i	−0.779859	+	0.625956i	$0.784709\pi$
$240$		0			0
$241$	−1712.49	+	2966.12i	−0.457722	+	0.792798i	−0.998840	−	0.0481486i	$-0.984668\pi$
$241$	−1712.49	+	2966.12i	−0.457722	+	0.792798i	0.541118	+	0.840947i	$0.318001\pi$
$242$	2111.04	+	2111.04i	0.560755	+	0.560755i
$243$	3596.03	+	1190.57i	0.949323	+	0.314302i
$244$			1112.88i			0.291986i
$245$		0			0
$246$	3746.46	−	349.940i	0.970998	−	0.0906966i
$247$	−2552.99	−	684.072i	−0.657664	−	0.176221i
$248$	1011.71	+	271.087i	0.259047	+	0.0694114i
$249$	−887.959	+	1933.78i	−0.225992	+	0.492163i
$250$		0			0
$251$			4383.71i			1.10238i	0.834380	+	0.551190i	$0.185826\pi$
$251$			4383.71i			1.10238i	−0.834380	+	0.551190i	$0.814174\pi$
$252$	372.309	−	545.223i	0.0930685	−	0.136293i
$253$	2374.26	+	2374.26i	0.589995	+	0.589995i
$254$	−97.4835	+	168.846i	−0.0240813	+	0.0417101i
$255$		0			0
$256$	−2684.22	−	4649.21i	−0.655327	−	1.13506i
$257$	−1279.00	+	4773.30i	−0.310435	+	1.15856i	0.617729	+	0.786391i	$0.288053\pi$
$257$	−1279.00	+	4773.30i	−0.310435	+	1.15856i	−0.928165	+	0.372170i	$0.878614\pi$
$258$	−3591.51	−	611.569i	−0.866658	−	0.147576i
$259$	−700.316	−	404.328i	−0.168014	−	0.0970027i
$260$		0			0
$261$	7423.47	+	2603.66i	1.76054	+	0.617480i
$262$	−2585.27	+	2585.27i	−0.609612	+	0.609612i
$263$	−2036.84	−	7601.60i	−0.477555	−	1.78226i	−0.611469	−	0.791268i	$-0.709421\pi$
$263$	−2036.84	−	7601.60i	−0.477555	−	1.78226i	0.133914	−	0.990993i	$-0.457245\pi$
$264$	935.053	+	429.360i	0.217987	+	0.100096i
$265$		0			0
$266$	−885.302	+	511.129i	−0.204065	+	0.117817i
$267$	−927.319	−	768.884i	−0.212550	−	0.176236i
$268$	3873.55	−	1037.91i	0.882890	−	0.236570i
$269$	913.858			0.207134			0.103567	−	0.994623i	$-0.466974\pi$
$269$	913.858			0.207134			0.103567	+	0.994623i	$0.466974\pi$
$270$		0			0
$271$	−1450.44			−0.325121			−0.162560	−	0.986699i	$-0.551975\pi$
$271$	−1450.44			−0.325121			−0.162560	+	0.986699i	$0.551975\pi$
$272$	−5632.16	+	1509.13i	−1.25551	+	0.336414i
$273$	−714.003	−	592.014i	−0.158291	−	0.131247i
$274$	−5291.67	+	3055.14i	−1.16672	+	0.673606i
$275$		0			0
$276$	3921.77	+	1800.80i	0.855299	+	0.392738i
$277$	1291.72	+	4820.77i	0.280188	+	1.04567i	0.952285	+	0.305212i	$0.0987272\pi$
$277$	1291.72	+	4820.77i	0.280188	+	1.04567i	−0.672097	+	0.740463i	$0.734606\pi$
$278$	−6016.77	+	6016.77i	−1.29806	+	1.29806i
$279$	−2477.52	+	2128.94i	−0.531631	+	0.456832i
$280$		0			0
$281$	−1199.86	−	692.738i	−0.254724	−	0.147065i	0.367201	−	0.930142i	$-0.380316\pi$
$281$	−1199.86	−	692.738i	−0.254724	−	0.147065i	−0.621926	+	0.783076i	$0.713649\pi$
$282$	−5444.34	−	927.073i	−1.14967	−	0.195767i
$283$	−1473.71	+	5499.95i	−0.309550	+	1.15526i	0.619407	+	0.785070i	$0.287373\pi$
$283$	−1473.71	+	5499.95i	−0.309550	+	1.15526i	−0.928957	+	0.370187i	$0.879294\pi$
$284$	544.040	+	942.304i	0.113672	+	0.196885i
$285$		0			0
$286$	−1745.43	+	3023.18i	−0.360873	+	0.625050i
$287$	−598.868	−	598.868i	−0.123171	−	0.123171i
$288$	5821.76	+	440.547i	1.19115	+	0.0901371i
$289$			783.804i			0.159537i
$290$		0			0
$291$	−1166.51	+	2540.40i	−0.234989	+	0.511756i
$292$	−1992.67	−	533.933i	−0.399356	−	0.107007i
$293$	2556.96	+	685.136i	0.509827	+	0.136608i	0.504557	−	0.863378i	$-0.331656\pi$
$293$	2556.96	+	685.136i	0.509827	+	0.136608i	0.00527019	+	0.999986i	$0.498322\pi$
$294$	6200.85	−	579.194i	1.23007	−	0.114896i
$295$		0			0
$296$		−	1619.73i		−	0.318057i
$297$	−2750.34	+	1653.15i	−0.537344	+	0.322981i
$298$	−2392.11	−	2392.11i	−0.465004	−	0.465004i
$299$	3031.32	−	5250.40i	0.586307	−	1.01551i
$300$		0			0
$301$	410.009	+	710.156i	0.0785133	+	0.135989i
$302$	−2640.68	+	9855.15i	−0.503159	+	1.87782i
$303$	2607.90	+	7036.37i	0.494454	+	1.33409i
$304$	−4281.72	−	2472.05i	−0.807808	−	0.466388i
$305$		0			0
$306$	2492.57	−	7106.74i	0.465656	−	1.32767i
$307$	3877.16	−	3877.16i	0.720787	−	0.720787i	−0.247979	−	0.968765i	$-0.579766\pi$
$307$	3877.16	−	3877.16i	0.720787	−	0.720787i	0.968765	+	0.247979i	$0.0797664\pi$
$308$	144.755	+	540.232i	0.0267797	+	0.0999434i
$309$	−2215.09	+	1570.48i	−0.407806	+	0.289131i
$310$		0			0
$311$	−2126.90	+	1227.96i	−0.387798	+	0.223895i	−0.681206	−	0.732092i	$-0.738544\pi$
$311$	−2126.90	+	1227.96i	−0.387798	+	0.223895i	0.293408	+	0.955987i	$0.405211\pi$
$312$	311.861	−	1831.44i	0.0565886	−	0.332323i
$313$	5279.09	−	1414.53i	0.953328	−	0.255443i	0.251554	−	0.967843i	$-0.419058\pi$
$313$	5279.09	−	1414.53i	0.953328	−	0.255443i	0.701774	+	0.712400i	$0.252392\pi$
$314$	4992.41			0.897255
$315$		0			0
$316$	−3552.23			−0.632370
$317$	6275.06	−	1681.40i	1.11181	−	0.297907i	0.344242	−	0.938881i	$-0.388136\pi$
$317$	6275.06	−	1681.40i	1.11181	−	0.297907i	0.767563	+	0.640974i	$0.221469\pi$
$318$	12958.8	−	4802.95i	2.28521	−	0.846968i
$319$	−5771.41	+	3332.12i	−1.01297	+	0.584837i
$320$		0			0
$321$	−290.003	−	3104.77i	−0.0504249	−	0.539849i
$322$	−606.894	−	2264.96i	−0.105034	−	0.391992i
$323$	−3415.65	+	3415.65i	−0.588395	+	0.588395i
$324$	−2576.12	+	3220.71i	−0.441721	+	0.552247i
$325$		0			0
$326$	−2922.01	−	1687.02i	−0.496426	−	0.286612i
$327$	2879.83	−	3473.24i	0.487018	−	0.587372i
$328$	439.057	−	1638.58i	0.0739113	−	0.275841i
$329$	621.529	+	1076.52i	0.104152	+	0.180396i
$330$		0			0
$331$	4312.10	−	7468.78i	0.716056	−	1.24025i	−0.246495	−	0.969144i	$-0.579279\pi$
$331$	4312.10	−	7468.78i	0.716056	−	1.24025i	0.962551	−	0.271101i	$-0.0873877\pi$
$332$	−1638.22	−	1638.22i	−0.270810	−	0.270810i
$333$	4171.69	+	2848.67i	0.686508	+	0.468787i
$334$			5112.22i			0.837509i
$335$		0			0
$336$	−1003.49	−	1415.37i	−0.162930	−	0.229806i
$337$	−67.6282	−	18.1209i	−0.0109316	−	0.00292911i	0.253349	−	0.967375i	$-0.418468\pi$
$337$	−67.6282	−	18.1209i	−0.0109316	−	0.00292911i	−0.264281	+	0.964446i	$0.585135\pi$
$338$	−1754.28	−	470.057i	−0.282308	−	0.0756442i
$339$	−3771.25	−	5319.18i	−0.604207	−	0.852207i
$340$		0			0
$341$		−	2767.22i		−	0.439453i
$342$	5755.48	−	2766.53i	0.910003	−	0.437418i
$343$	−2039.50	−	2039.50i	−0.321057	−	0.321057i
$344$	−821.244	+	1422.44i	−0.128717	+	0.222944i
$345$		0			0
$346$	118.070	+	204.503i	0.0183453	+	0.0317750i
$347$	2421.66	−	9037.76i	0.374644	−	1.39819i	−0.479220	−	0.877695i	$-0.659080\pi$
$347$	2421.66	−	9037.76i	0.374644	−	1.39819i	0.853864	−	0.520496i	$-0.174253\pi$
$348$	−5466.95	+	6593.46i	−0.842125	+	1.01565i
$349$	1120.32	+	646.818i	0.171832	+	0.0992074i	0.583449	−	0.812149i	$-0.301703\pi$
$349$	1120.32	+	646.818i	0.171832	+	0.0992074i	−0.411617	+	0.911357i	$0.635036\pi$
$350$		0			0
$351$	4168.48	+	4024.22i	0.633894	+	0.611957i
$352$	−3497.28	+	3497.28i	−0.529562	+	0.529562i
$353$	−877.966	−	3276.61i	−0.132378	−	0.494041i	0.867617	−	0.497233i	$-0.165651\pi$
$353$	−877.966	−	3276.61i	−0.132378	−	0.494041i	−0.999995	+	0.00319198i	$0.998984\pi$
$354$	−1231.82	−	13187.8i	−0.184944	−	1.98001i
$355$		0			0
$356$	1135.83	−	655.773i	0.169098	−	0.0976289i
$357$	−1589.47	+	589.106i	−0.235640	+	0.0873356i
$358$	2101.05	−	562.975i	0.310179	−	0.0831122i
$359$	1562.38			0.229692			0.114846	−	0.993383i	$-0.463363\pi$
$359$	1562.38			0.229692			0.114846	+	0.993383i	$0.463363\pi$
$360$		0			0
$361$	2763.15			0.402850
$362$	−11233.7	+	3010.05i	−1.63102	+	0.437030i
$363$	−704.646	+	4138.12i	−0.101885	+	0.598333i
$364$	874.551	−	504.922i	0.125931	−	0.0727063i
$365$		0			0
$366$	−3081.52	+	2184.77i	−0.440092	+	0.312021i
$367$	2940.65	+	10974.6i	0.418258	+	1.56096i	0.778220	+	0.627992i	$0.216123\pi$
$367$	2940.65	+	10974.6i	0.418258	+	1.56096i	−0.359963	+	0.932967i	$0.617211\pi$
$368$	8019.16	−	8019.16i	1.13595	−	1.13595i
$369$	3448.07	+	4012.64i	0.486448	+	0.566097i
$370$		0			0
$371$	−2693.93	−	1555.34i	−0.376986	−	0.217653i
$372$	−1236.00	−	3334.85i	−0.172267	−	0.464795i
$373$	−896.797	+	3346.89i	−0.124489	+	0.464599i	−0.999821	−	0.0189232i	$-0.993976\pi$
$373$	−896.797	+	3346.89i	−0.124489	+	0.464599i	0.875332	+	0.483523i	$0.160643\pi$
$374$	3189.96	+	5525.17i	0.441040	+	0.763903i
$375$		0			0
$376$	−1244.92	+	2156.26i	−0.170749	+	0.295746i
$377$	8508.52	+	8508.52i	1.16236	+	1.16236i
$378$	2240.61	−	39.4540i	0.304880	−	0.00536850i
$379$		−	832.823i		−	0.112874i	−0.998406	−	0.0564370i	$-0.982026\pi$
$379$		−	832.823i		−	0.112874i	0.998406	−	0.0564370i	$-0.0179740\pi$
$380$		0			0
$381$	−272.943	+	25.4944i	−0.0367016	+	0.00342814i
$382$	−8686.16	−	2327.45i	−1.16341	−	0.311735i
$383$	−922.702	−	247.237i	−0.123101	−	0.0329849i	0.196742	−	0.980455i	$-0.436964\pi$
$383$	−922.702	−	247.237i	−0.123101	−	0.0329849i	−0.319844	+	0.947470i	$0.603630\pi$
$384$	2299.77	−	5008.41i	0.305624	−	0.665585i
$385$		0			0
$386$			18524.7i			2.44269i
$387$	−2219.21	−	4616.83i	−0.291495	−	0.606426i
$388$	−2152.12	−	2152.12i	−0.281591	−	0.281591i
$389$	4171.75	−	7225.69i	0.543743	−	0.941791i	−0.454941	−	0.890521i	$-0.650340\pi$
$389$	4171.75	−	7225.69i	0.543743	−	0.941791i	0.998685	−	0.0512699i	$-0.0163269\pi$
$390$		0			0
$391$	−5540.06	−	9595.66i	−0.716554	−	1.24111i
$392$	726.695	−	2712.06i	0.0936317	−	0.349438i
$393$	−5067.71	−	862.939i	−0.650464	−	0.110762i
$394$	244.332	+	141.065i	0.0312417	+	0.0180374i
$395$		0			0
$396$	−647.032	−	3433.34i	−0.0821075	−	0.435687i
$397$	−1932.08	+	1932.08i	−0.244252	+	0.244252i	−0.818607	−	0.574354i	$-0.805253\pi$
$397$	−1932.08	+	1932.08i	−0.244252	+	0.244252i	0.574354	+	0.818607i	$0.305253\pi$
$398$	−81.1822	−	302.976i	−0.0102244	−	0.0381578i
$399$	−1306.21	−	599.789i	−0.163891	−	0.0752557i
$400$		0			0
$401$	−10785.5	+	6227.03i	−1.34315	+	0.775469i	−0.987269	−	0.159061i	$-0.949153\pi$
$401$	−10785.5	+	6227.03i	−1.34315	+	0.775469i	−0.355884	+	0.934530i	$0.615820\pi$
$402$	10478.4	+	8688.13i	1.30004	+	1.07792i
$403$	−4826.20	+	1293.18i	−0.596551	+	0.159845i
$404$	−8170.21			−1.00615
$405$		0			0
$406$	4653.98			0.568899
$407$	−4133.50	+	1107.57i	−0.503415	+	0.134890i
$408$	−2613.73	−	2167.17i	−0.317155	−	0.262968i
$409$	1331.65	−	768.829i	0.160992	−	0.0929490i	−0.417339	−	0.908751i	$-0.637037\pi$
$409$	1331.65	−	768.829i	0.160992	−	0.0929490i	0.578332	+	0.815802i	$0.303704\pi$
$410$		0			0
$411$	−7807.55	−	3585.09i	−0.937027	−	0.430266i
$412$	−765.162	−	2855.62i	−0.0914971	−	0.341472i
$413$	−2108.06	+	2108.06i	−0.251164	+	0.251164i
$414$	2712.73	+	14394.5i	0.322037	+	1.70882i
$415$		0			0
$416$	7733.82	+	4465.13i	0.911495	+	0.526252i
$417$	−11794.2	−	2008.34i	−1.38505	−	0.235849i
$418$	−1400.13	+	5225.35i	−0.163834	+	0.611436i
$419$	−2700.92	−	4678.13i	−0.314913	−	0.545445i	0.664506	−	0.747283i	$-0.268642\pi$
$419$	−2700.92	−	4678.13i	−0.314913	−	0.545445i	−0.979419	+	0.201838i	$0.935309\pi$
$420$		0			0
$421$	−445.843	+	772.222i	−0.0516129	+	0.0893962i	−0.890678	−	0.454635i	$-0.849770\pi$
$421$	−445.843	+	772.222i	−0.0516129	+	0.0893962i	0.839065	+	0.544032i	$0.183103\pi$
$422$	1962.01	+	1962.01i	0.226325	+	0.226325i
$423$	−3364.08	−	6998.62i	−0.386683	−	0.804455i
$424$		−	6230.67i		−	0.713651i
$425$		0			0
$426$	−1541.17	+	3356.34i	−0.175281	+	0.381725i
$427$	821.257	+	220.055i	0.0930759	+	0.0249396i
$428$	3279.40	+	878.713i	0.370364	+	0.0992387i
$429$	−4887.03	+	456.476i	−0.549995	+	0.0513726i
$430$		0			0
$431$		−	1615.29i		−	0.180523i	−0.995918	−	0.0902617i	$-0.971230\pi$
$431$		−	1615.29i		−	0.180523i	0.995918	−	0.0902617i	$-0.0287703\pi$
$432$	5583.56	+	9289.38i	0.621850	+	1.03457i
$433$	−4832.08	−	4832.08i	−0.536293	−	0.536293i	0.386145	−	0.922438i	$-0.373807\pi$
$433$	−4832.08	−	4832.08i	−0.536293	−	0.536293i	−0.922438	+	0.386145i	$0.873807\pi$
$434$	−966.243	+	1673.58i	−0.106869	+	0.185103i
$435$		0			0
$436$	2456.17	+	4254.22i	0.269792	+	0.467294i
$437$	2431.63	−	9074.95i	0.266180	−	0.993396i
$438$	−2433.50	−	6565.84i	−0.265473	−	0.716274i
$439$	15456.2	+	8923.63i	1.68037	+	0.970164i	0.961412	+	0.275113i	$0.0887152\pi$
$439$	15456.2	+	8923.63i	1.68037	+	0.970164i	0.718961	+	0.695051i	$0.244618\pi$
$440$		0			0
$441$	5706.98	+	6641.42i	0.616238	+	0.717138i
$442$	8145.50	−	8145.50i	0.876566	−	0.876566i
$443$	1257.84	+	4694.34i	0.134903	+	0.503464i	0.999998	+	0.00185701i	$0.000591106\pi$
$443$	1257.84	+	4694.34i	0.134903	+	0.503464i	−0.865095	+	0.501607i	$0.832742\pi$
$444$	−4486.68	+	3181.01i	−0.479569	+	0.340009i
$445$		0			0
$446$	16601.9	−	9585.11i	1.76261	−	1.01764i
$447$	798.464	−	4689.08i	0.0844879	−	0.496165i
$448$	756.075	−	202.590i	0.0797348	−	0.0213649i
$449$	−14045.3			−1.47626			−0.738128	−	0.674661i	$-0.764290\pi$
$449$	−14045.3			−1.47626			−0.738128	+	0.674661i	$0.764290\pi$
$450$		0			0
$451$	−4481.85			−0.467942
$452$	6857.32	−	1837.41i	0.713587	−	0.191205i
$453$	−13451.4	+	4985.50i	−1.39515	+	0.517085i
$454$	1330.37	−	768.089i	0.137527	−	0.0794014i
$455$		0			0
$456$	−267.747	−	2866.50i	−0.0274965	−	0.294377i
$457$	572.375	+	2136.13i	0.0585877	+	0.218652i	0.989013	−	0.147830i	$-0.0472288\pi$
$457$	572.375	+	2136.13i	0.0585877	+	0.218652i	−0.930425	+	0.366482i	$0.880562\pi$
$458$	−6755.21	+	6755.21i	−0.689193	+	0.689193i
$459$	10178.5	−	2920.33i	1.03506	−	0.296970i
$460$		0			0
$461$	−2227.80	−	1286.22i	−0.225073	−	0.129946i	0.383224	−	0.923656i	$-0.374814\pi$
$461$	−2227.80	−	1286.22i	−0.225073	−	0.129946i	−0.608297	+	0.793709i	$0.708147\pi$
$462$	−1211.71	+	1461.39i	−0.122021	+	0.147164i
$463$	4445.19	−	16589.7i	0.446189	−	1.66520i	−0.266589	−	0.963810i	$-0.585897\pi$
$463$	4445.19	−	16589.7i	0.446189	−	1.66520i	0.712778	−	0.701390i	$-0.247437\pi$
$464$	11254.4	+	19493.1i	1.12602	+	1.95032i
$465$		0			0
$466$	4992.73	−	8647.66i	0.496317	−	0.859646i
$467$	−1263.48	−	1263.48i	−0.125197	−	0.125197i	0.641732	−	0.766929i	$-0.278216\pi$
$467$	−1263.48	−	1263.48i	−0.125197	−	0.125197i	−0.766929	+	0.641732i	$0.778216\pi$
$468$	−5685.59	+	2732.93i	−0.561574	+	0.269936i
$469$		−	3063.75i		−	0.301644i
$470$		0			0
$471$	4059.92	+	5726.34i	0.397179	+	0.560203i
$472$	−5767.94	−	1545.52i	−0.562481	−	0.150716i
$473$	4191.58	+	1123.13i	0.407461	+	0.109179i
$474$	−6973.65	−	9836.03i	−0.675760	−	0.953131i
$475$		0			0
$476$		−	1845.60i		−	0.177716i
$477$	16047.4	+	10958.1i	1.54038	+	1.05186i
$478$	−2938.38	−	2938.38i	−0.281168	−	0.281168i
$479$	−5777.16	+	10006.3i	−0.551075	+	0.954491i	0.447122	+	0.894473i	$0.352449\pi$
$479$	−5777.16	+	10006.3i	−0.551075	+	0.954491i	−0.998197	+	0.0600176i	$0.980884\pi$
$480$		0			0
$481$	3863.33	+	6691.49i	0.366222	+	0.634315i
$482$	3275.95	−	12226.0i	0.309576	−	1.15535i
$483$	2104.39	−	2538.02i	0.198247	−	0.239097i
$484$	−3957.99	−	2285.14i	−0.371712	−	0.214608i
$485$		0			0
$486$	−13975.4	−	810.388i	−1.30440	−	0.0756377i
$487$	9096.73	−	9096.73i	0.846431	−	0.846431i	−0.143254	−	0.989686i	$-0.545757\pi$
$487$	9096.73	−	9096.73i	0.846431	−	0.846431i	0.989686	+	0.143254i	$0.0457567\pi$
$488$	440.769	+	1644.97i	0.0408866	+	0.152591i
$489$	−441.200	−	4723.48i	−0.0408011	−	0.436816i
$490$		0			0
$491$	13521.1	−	7806.44i	1.24277	−	0.717514i	0.273114	−	0.961982i	$-0.411946\pi$
$491$	13521.1	−	7806.44i	1.24277	−	0.717514i	0.969658	+	0.244467i	$0.0786131\pi$
$492$	−5401.18	+	2001.85i	−0.494927	+	0.183435i
$493$	21242.0	−	5691.77i	1.94055	−	0.519969i
$494$	9767.64			0.889609
$495$		0			0
$496$	−9346.39			−0.846099
$497$	802.958	−	215.152i	0.0724700	−	0.0194183i
$498$	1320.07	−	7752.29i	0.118783	−	0.697567i
$499$	−5598.88	+	3232.52i	−0.502285	+	0.289995i	−0.729657	−	0.683813i	$-0.760320\pi$
$499$	−5598.88	+	3232.52i	−0.502285	+	0.289995i	0.227371	+	0.973808i	$0.426987\pi$
$500$		0			0
$501$	−5863.76	+	4157.35i	−0.522901	+	0.370732i
$502$	−4192.97	−	15648.4i	−0.372792	−	1.39128i
$503$	−6632.99	+	6632.99i	−0.587973	+	0.587973i	−0.937082	−	0.349109i	$-0.886484\pi$
$503$	−6632.99	+	6632.99i	−0.587973	+	0.587973i	0.349109	+	0.937082i	$0.386484\pi$
$504$	334.377	−	953.366i	0.0295523	−	0.0842585i
$505$		0			0
$506$	−10746.3	−	6204.37i	−0.944132	−	0.545095i
$507$	−887.449	−	2394.43i	−0.0777377	−	0.209744i
$508$	77.2484	−	288.295i	0.00674674	−	0.0251792i
$509$	−6199.50	−	10737.8i	−0.539858	−	0.935062i	−0.998911	−	0.0466529i	$-0.985145\pi$
$509$	−6199.50	−	10737.8i	−0.539858	−	0.935062i	0.459053	−	0.888409i	$-0.348189\pi$
$510$		0			0
$511$	−788.042	+	1364.93i	−0.0682210	+	0.118162i
$512$	8028.87	+	8028.87i	0.693026	+	0.693026i
$513$	7853.70	+	4351.80i	0.675924	+	0.374535i
$514$		−	18262.4i		−	1.56716i
$515$		0			0
$516$	5553.03	−	518.684i	0.473757	−	0.0442515i
$517$	6353.98	+	1702.54i	0.540518	+	0.144831i
$518$	2886.63	+	773.470i	0.244848	+	0.0656068i
$519$	−138.550	+	301.733i	−0.0117181	+	0.0255195i
$520$		0			0
$521$		−	5292.07i		−	0.445009i	−0.974932	−	0.222505i	$-0.928577\pi$
$521$		−	5292.07i		−	0.445009i	0.974932	−	0.222505i	$-0.0714233\pi$
$522$	−28989.7	−	2193.72i	−2.43073	−	0.183940i
$523$	10307.9	+	10307.9i	0.861818	+	0.861818i	0.991549	−	0.129731i	$-0.0414114\pi$
$523$	10307.9	+	10307.9i	0.861818	+	0.861818i	−0.129731	+	0.991549i	$0.541411\pi$
$524$	2798.48	−	4847.12i	0.233306	−	0.404098i
$525$		0			0
$526$	14541.7	+	25187.0i	1.20541	+	2.08784i
$527$	−2363.41	+	8820.38i	−0.195355	+	0.729074i
$528$	−9051.20	−	1541.25i	−0.746028	−	0.127035i
$529$	8126.33	+	4691.74i	0.667899	+	0.385612i
$530$		0			0
$531$	14124.8	−	12137.5i	1.15436	−	0.991942i
$532$	1106.57	−	1106.57i	0.0901801	−	0.0901801i
$533$	2094.46	+	7816.61i	0.170208	+	0.635225i
$534$	4045.65	+	1857.69i	0.327851	+	0.150543i
$535$		0			0
$536$	5314.51	−	3068.34i	0.428269	−	0.247261i
$537$	2354.35	+	1952.10i	0.189195	+	0.156871i
$538$	−3262.17	+	874.095i	−0.261416	+	0.0700463i
$539$	−7418.01			−0.592795
$540$		0			0
$541$	2250.01			0.178808			0.0894042	−	0.995995i	$-0.471504\pi$
$541$	2250.01			0.178808			0.0894042	+	0.995995i	$0.471504\pi$
$542$	5177.57	−	1387.33i	0.410324	−	0.109946i
$543$	−12588.0	−	10437.3i	−0.994847	−	0.824875i
$544$	14134.4	−	8160.48i	1.11398	−	0.643158i
$545$		0			0
$546$	3115.01	+	1430.36i	0.244158	+	0.112113i
$547$	156.037	+	582.339i	0.0121968	+	0.0455192i	0.971756	−	0.235988i	$-0.0758325\pi$
$547$	156.037	+	582.339i	0.0121968	+	0.0455192i	−0.959559	+	0.281507i	$0.909166\pi$
$548$	6614.23	−	6614.23i	0.515594	−	0.515594i
$549$	−5011.90	−	1757.84i	−0.389622	−	0.136653i
$550$		0			0
$551$	16148.7	+	9323.48i	1.24856	+	0.720859i
$552$	6510.10	+	1108.55i	0.501971	+	0.0854765i
$553$	−702.403	+	2621.40i	−0.0540130	+	0.201579i
$554$	−9222.03	−	15973.0i	−0.707232	−	1.22496i
$555$		0			0
$556$	6512.99	−	11280.8i	0.496785	−	0.860457i
$557$	−12393.2	−	12393.2i	−0.942763	−	0.942763i	0.0556858	−	0.998448i	$-0.482265\pi$
$557$	−12393.2	−	12393.2i	−0.942763	−	0.942763i	−0.998448	+	0.0556858i	$0.982265\pi$
$558$	6807.61	−	9969.31i	0.516468	−	0.756335i
$559$		−	7835.23i		−	0.592835i
$560$		0			0
$561$	−3743.29	+	8152.08i	−0.281714	+	0.613513i
$562$	4945.69	+	1325.19i	0.371212	+	0.0994660i
$563$	7231.44	+	1937.66i	0.541330	+	0.145049i	0.519115	−	0.854704i	$-0.326262\pi$
$563$	7231.44	+	1937.66i	0.541330	+	0.145049i	0.0222149	+	0.999753i	$0.492928\pi$
$564$	8417.79	−	786.269i	0.628463	−	0.0587020i
$565$		0			0
$566$		−	21042.6i		−	1.56269i
$567$	1867.36	+	2537.92i	0.138310	+	0.187976i
$568$	1177.37	+	1177.37i	0.0869743	+	0.0869743i
$569$	−2313.39	+	4006.90i	−0.170443	+	0.295216i	−0.938575	−	0.345076i	$-0.887853\pi$
$569$	−2313.39	+	4006.90i	−0.170443	+	0.295216i	0.768132	+	0.640292i	$0.221187\pi$
$570$		0			0
$571$	−2881.89	−	4991.59i	−0.211215	−	0.365834i	0.740880	−	0.671637i	$-0.234409\pi$
$571$	−2881.89	−	4991.59i	−0.211215	−	0.365834i	−0.952095	+	0.305803i	$0.901075\pi$
$572$	1383.12	−	5161.89i	0.101104	−	0.377324i
$573$	−4394.13	−	11855.8i	−0.320362	−	0.864370i
$574$	2710.57	+	1564.95i	0.197103	+	0.113797i
$575$		0			0
$576$	−4805.10	+	905.546i	−0.347591	+	0.0655054i
$577$	−2612.53	+	2612.53i	−0.188494	+	0.188494i	−0.795045	−	0.606551i	$-0.792553\pi$
$577$	−2612.53	+	2612.53i	−0.188494	+	0.188494i	0.606551	+	0.795045i	$0.292553\pi$
$578$	−749.700	−	2797.92i	−0.0539505	−	0.201346i
$579$	−21247.9	+	15064.6i	−1.52510	+	1.08128i
$580$		0			0
$581$	−1532.87	+	885.005i	−0.109457	+	0.0631948i
$582$	1734.17	−	10184.1i	0.123512	−	0.725338i
$583$	−15900.5	+	4260.52i	−1.12955	+	0.302663i
$584$	−3156.88			−0.223686
$585$		0			0
$586$	−9782.83			−0.689633
$587$	10572.5	−	2832.89i	0.743397	−	0.199193i	0.132809	−	0.991142i	$-0.457600\pi$
$587$	10572.5	−	2832.89i	0.743397	−	0.199193i	0.610587	+	0.791949i	$0.290933\pi$
$588$	−8939.63	+	3313.30i	−0.626980	+	0.232378i
$589$	−6705.50	+	3871.42i	−0.469092	+	0.270830i
$590$		0			0
$591$	36.8921	+	394.967i	0.00256775	+	0.0274903i
$592$	3740.85	+	13961.1i	0.259710	+	0.969249i
$593$	9032.02	−	9032.02i	0.625465	−	0.625465i	−0.321459	−	0.946924i	$-0.604173\pi$
$593$	9032.02	−	9032.02i	0.625465	−	0.625465i	0.946924	+	0.321459i	$0.104173\pi$
$594$	8236.59	−	8531.86i	0.568942	−	0.589337i
$595$		0			0
$596$	4484.97	+	2589.40i	0.308241	+	0.177963i
$597$	281.497	−	339.502i	0.0192980	−	0.0232745i
$598$	−5798.85	+	21641.6i	−0.396543	+	1.47992i
$599$	−8108.91	−	14045.0i	−0.553123	−	0.958038i	−0.998047	−	0.0624693i	$-0.980102\pi$
$599$	−8108.91	−	14045.0i	−0.553123	−	0.958038i	0.444923	−	0.895569i	$-0.353231\pi$
$600$		0			0
$601$	−10083.1	+	17464.4i	−0.684354	+	1.18534i	0.289285	+	0.957243i	$0.406582\pi$
$601$	−10083.1	+	17464.4i	−0.684354	+	1.18534i	−0.973639	+	0.228093i	$0.926751\pi$
$602$	−2142.85	−	2142.85i	−0.145076	−	0.145076i
$603$	−1444.15	+	19084.2i	−0.0975294	+	1.28883i
$604$		−	15619.0i		−	1.05220i
$605$		0			0
$606$	−16039.5	−	22623.1i	−1.07518	−	1.51650i
$607$	−10316.3	−	2764.25i	−0.689831	−	0.184840i	−0.103159	−	0.994665i	$-0.532895\pi$
$607$	−10316.3	−	2764.25i	−0.689831	−	0.184840i	−0.586671	+	0.809825i	$0.699562\pi$
$608$	13367.4	+	3581.78i	0.891643	+	0.238915i
$609$	3784.70	+	5338.15i	0.251829	+	0.355193i
$610$		0			0
$611$		−	11877.4i		−	0.786427i
$612$	−869.950	+	11496.2i	−0.0574602	+	0.759326i
$613$	11953.6	+	11953.6i	0.787604	+	0.787604i	0.981101	−	0.193497i	$-0.0619829\pi$
$613$	11953.6	+	11953.6i	0.787604	+	0.787604i	−0.193497	+	0.981101i	$0.561983\pi$
$614$	−10131.7	+	17548.6i	−0.665933	+	1.15343i
$615$		0			0
$616$	427.931	+	741.199i	0.0279900	+	0.0484801i
$617$	−828.238	+	3091.02i	−0.0540415	+	0.201686i	−0.987668	−	0.156562i	$-0.949959\pi$
$617$	−828.238	+	3091.02i	−0.0540415	+	0.201686i	0.933627	+	0.358247i	$0.116626\pi$
$618$	6404.99	−	7724.79i	0.416904	−	0.502810i
$619$	19520.5	+	11270.2i	1.26752	+	0.731805i	0.974519	−	0.224306i	$-0.0720116\pi$
$619$	19520.5	+	11270.2i	1.26752	+	0.731805i	0.293004	+	0.956111i	$0.405345\pi$
$620$		0			0
$621$	−14304.6	+	14817.4i	−0.924355	+	0.957492i
$622$	6417.77	−	6417.77i	0.413713	−	0.413713i
$623$	−259.339	−	967.867i	−0.0166777	−	0.0622420i
$624$	1541.76	+	16506.1i	0.0989101	+	1.05893i
$625$		0			0
$626$	−17491.6	+	10098.8i	−1.11678	+	0.644774i
$627$	−7132.13	+	2643.39i	−0.454274	+	0.168368i
$628$	−7382.21	+	1978.06i	−0.469080	+	0.125690i
$629$	14121.3			0.895155
$630$		0			0
$631$	23109.9			1.45799			0.728995	−	0.684519i	$-0.239988\pi$
$631$	23109.9			1.45799			0.728995	+	0.684519i	$0.239988\pi$
$632$	−5250.65	+	1406.91i	−0.330474	+	0.0885503i
$633$	−654.902	+	3845.99i	−0.0411216	+	0.241492i
$634$	−20791.6	+	12004.0i	−1.30243	+	0.751958i
$635$		0			0
$636$	−17259.1	+	12236.5i	−1.07605	+	0.762908i
$637$	3466.58	+	12937.5i	0.215622	+	0.804711i
$638$	17414.9	−	17414.9i	1.08066	−	1.08066i
$639$	−5103.05	+	961.698i	−0.315921	+	0.0595370i
$640$		0			0
$641$	−19437.9	−	11222.5i	−1.19774	−	0.691514i	−0.237687	−	0.971342i	$-0.576389\pi$
$641$	−19437.9	−	11222.5i	−1.19774	−	0.691514i	−0.960050	+	0.279828i	$0.909723\pi$
$642$	4004.90	+	10805.6i	0.246201	+	0.664274i
$643$	−1118.02	+	4172.53i	−0.0685701	+	0.255907i	−0.991699	−	0.128585i	$-0.958957\pi$
$643$	−1118.02	+	4172.53i	−0.0685701	+	0.255907i	0.923128	+	0.384492i	$0.125623\pi$
$644$	1794.81	+	3108.71i	0.109822	+	0.190218i
$645$		0			0
$646$	8925.69	−	15459.7i	0.543617	−	0.941572i
$647$	−15250.5	−	15250.5i	−0.926678	−	0.926678i	0.0708115	−	0.997490i	$-0.477441\pi$
$647$	−15250.5	−	15250.5i	−0.926678	−	0.926678i	−0.997490	+	0.0708115i	$0.977441\pi$
$648$	−2532.22	+	5780.91i	−0.153511	+	0.350456i
$649$			15776.4i			0.954205i
$650$		0			0
$651$	−2705.38	+	252.698i	−0.162876	+	0.0152135i
$652$	4989.15	+	1336.84i	0.299678	+	0.0802985i
$653$	−13595.3	−	3642.84i	−0.814737	−	0.218308i	−0.172693	−	0.984976i	$-0.555247\pi$
$653$	−13595.3	−	3642.84i	−0.814737	−	0.218308i	−0.642044	+	0.766668i	$0.721913\pi$
$654$	−6957.91	+	15152.8i	−0.416018	+	0.905998i
$655$		0			0
$656$			15137.6i			0.900951i
$657$	5552.10	−	8130.70i	0.329693	−	0.482814i
$658$	−3248.33	−	3248.33i	−0.192451	−	0.192451i
$659$	10510.6	−	18204.9i	0.621298	−	1.07612i	−0.367946	−	0.929847i	$-0.619939\pi$
$659$	10510.6	−	18204.9i	0.621298	−	1.07612i	0.989244	−	0.146273i	$-0.0467277\pi$
$660$		0			0
$661$	5045.72	+	8739.44i	0.296907	+	0.514259i	0.975427	−	0.220324i	$-0.0707114\pi$
$661$	5045.72	+	8739.44i	0.296907	+	0.514259i	−0.678519	+	0.734582i	$0.737378\pi$
$662$	−8248.96	+	30785.5i	−0.484297	+	1.80742i
$663$	15967.0	+	2718.89i	0.935306	+	0.159266i
$664$	−3070.33	−	1772.66i	−0.179446	−	0.103603i
$665$		0			0
$666$	−17616.3	−	6178.61i	−1.02495	−	0.359484i
$667$	−30244.7	+	30244.7i	−1.75574	+	1.75574i
$668$	−2025.53	−	7559.36i	−0.117320	−	0.437845i
$669$	24495.1	+	11247.7i	1.41560	+	0.650019i
$670$		0			0
$671$	3896.52	−	2249.66i	0.224178	−	0.129429i
$672$	3738.49	+	3099.76i	0.214606	+	0.177940i
$673$	−20531.1	+	5501.29i	−1.17595	+	0.315095i	−0.793319	−	0.608806i	$-0.791649\pi$
$673$	−20531.1	+	5501.29i	−1.17595	+	0.315095i	−0.382632	+	0.923901i	$0.624982\pi$
$674$	258.743			0.0147869
$675$		0			0
$676$	2780.27			0.158185
$677$	−19637.6	+	5261.88i	−1.11482	+	0.298715i	−0.768786	−	0.639506i	$-0.779139\pi$
$677$	−19637.6	+	5261.88i	−1.11482	+	0.298715i	−0.346035	+	0.938222i	$0.612472\pi$
$678$	18549.8	+	15380.5i	1.05074	+	0.871219i
$679$	−2013.73	+	1162.63i	−0.113814	+	0.0657106i
$680$		0			0
$681$	1962.89	+	901.322i	0.110452	+	0.0507176i
$682$	2646.82	+	9878.05i	0.148610	+	0.554619i
$683$	−2795.61	+	2795.61i	−0.156619	+	0.156619i	−0.781067	−	0.624447i	$-0.785324\pi$
$683$	−2795.61	+	2795.61i	−0.156619	+	0.156619i	0.624447	+	0.781067i	$0.285324\pi$
$684$	−7414.42	+	6371.23i	−0.414470	+	0.356155i
$685$		0			0
$686$	9231.08	+	5329.56i	0.513767	+	0.296624i
$687$	−13241.7	−	2254.83i	−0.735377	−	0.125221i
$688$	3793.41	−	14157.2i	0.210207	−	0.784504i
$689$	14861.2	+	25740.4i	0.821723	+	1.42327i
$690$		0			0
$691$	−7633.98	+	13222.4i	−0.420276	+	0.727939i	−0.995966	−	0.0897289i	$-0.971400\pi$
$691$	−7633.98	+	13222.4i	−0.420276	+	0.727939i	0.575691	+	0.817668i	$0.304733\pi$
$692$	−255.615	−	255.615i	−0.0140420	−	0.0140420i
$693$	−2661.61	−	201.411i	−0.145896	−	0.0110403i
$694$			34578.1i			1.89130i
$695$		0			0
$696$	−5469.42	+	11911.2i	−0.297871	+	0.648698i
$697$	14285.7	+	3827.84i	0.776339	+	0.208020i
$698$	−4617.85	−	1237.35i	−0.250413	−	0.0670979i
$699$	13979.1	−	1305.73i	0.756422	−	0.0706540i
$700$		0			0
$701$		−	3591.48i		−	0.193507i	−0.995308	−	0.0967534i	$-0.969154\pi$
$701$		−	3591.48i		−	0.193507i	0.995308	−	0.0967534i	$-0.0308458\pi$
$702$	−18729.2	−	10378.0i	−1.00696	−	0.557967i
$703$	8466.73	+	8466.73i	0.454237	+	0.454237i
$704$	2071.10	−	3587.26i	0.110877	−	0.192045i
$705$		0			0
$706$	6268.09	+	10856.7i	0.334140	+	0.578747i
$707$	−1615.54	+	6029.28i	−0.0859387	+	0.320728i
$708$	7046.65	+	19012.6i	0.374053	+	1.00923i
$709$	−8700.55	−	5023.27i	−0.460869	−	0.266083i	0.251541	−	0.967847i	$-0.419063\pi$
$709$	−8700.55	−	5023.27i	−0.460869	−	0.266083i	−0.712410	+	0.701764i	$0.752396\pi$
$710$		0			0
$711$	5610.92	−	15997.7i	0.295958	−	0.843825i
$712$	1419.17	−	1419.17i	0.0746992	−	0.0746992i
$713$	−4596.77	−	17155.4i	−0.241445	−	0.901086i
$714$	5110.40	−	3623.22i	0.267860	−	0.189910i
$715$		0			0
$716$	−2883.74	+	1664.93i	−0.150517	+	0.0869012i
$717$	980.804	−	5759.89i	0.0510862	−	0.300010i
$718$	−5577.18	+	1494.40i	−0.289887	+	0.0776749i
$719$	2245.00			0.116446			0.0582229	−	0.998304i	$-0.481457\pi$
$719$	2245.00			0.116446			0.0582229	+	0.998304i	$0.481457\pi$
$720$		0			0
$721$	−2258.63			−0.116666
$722$	−9863.51	+	2642.92i	−0.508424	+	0.136232i
$723$	16687.4	−	6184.87i	0.858384	−	0.318144i
$724$	15418.5	−	8901.85i	0.791467	−	0.456954i
$725$		0			0
$726$	−1442.71	−	15445.7i	−0.0737522	−	0.789591i
$727$	819.398	+	3058.04i	0.0418017	+	0.156006i	0.983672	−	0.179971i	$-0.0576003\pi$
$727$	819.398	+	3058.04i	0.0418017	+	0.156006i	−0.941870	+	0.335977i	$0.890934\pi$
$728$	1092.72	−	1092.72i	0.0556301	−	0.0556301i
$729$	−10435.5	−	16688.9i	−0.530180	−	0.847885i
$730$		0			0
$731$	−12401.2	−	7159.85i	−0.627463	−	0.362266i
$732$	3690.97	−	4451.53i	0.186369	−	0.224772i
$733$	−3257.98	+	12159.0i	−0.164170	+	0.612690i	0.833975	+	0.551802i	$0.186060\pi$
$733$	−3257.98	+	12159.0i	−0.164170	+	0.612690i	−0.998145	+	0.0608874i	$0.980607\pi$
$734$	−20994.3	−	36363.1i	−1.05574	−	1.82859i
$735$		0			0
$736$	−15871.9	+	27490.9i	−0.794899	+	1.37681i
$737$	−11464.4	−	11464.4i	−0.572992	−	0.572992i
$738$	−16146.5	−	11025.7i	−0.805367	−	0.549950i
$739$		−	10277.3i		−	0.511578i	−0.966733	−	0.255789i	$-0.917665\pi$
$739$		−	10277.3i		−	0.511578i	0.966733	−	0.255789i	$-0.0823352\pi$
$740$		0			0
$741$	7943.22	+	11203.6i	0.393794	+	0.555429i
$742$	11104.1	+	2975.33i	0.549385	+	0.147207i
$743$	−26719.9	−	7159.58i	−1.31932	−	0.353512i	−0.470600	−	0.882347i	$-0.655963\pi$
$743$	−26719.9	−	7159.58i	−1.31932	−	0.353512i	−0.848725	+	0.528835i	$0.822629\pi$
$744$	−3147.77	−	4439.79i	−0.155111	−	0.218778i
$745$		0			0
$746$		−	12805.1i		−	0.628454i
$747$	9965.45	−	4790.16i	0.488108	−	0.234622i
$748$	−6906.09	−	6906.09i	−0.337582	−	0.337582i
$749$	1296.91	−	2246.31i	0.0632683	−	0.109584i
$750$		0			0
$751$	−6999.69	−	12123.8i	−0.340110	−	0.589088i	0.644343	−	0.764737i	$-0.277131\pi$
$751$	−6999.69	−	12123.8i	−0.340110	−	0.589088i	−0.984453	+	0.175649i	$0.943798\pi$
$752$	5750.41	−	21460.8i	0.278851	−	1.04069i
$753$	14539.0	−	17534.9i	0.703628	−	0.848616i
$754$	−38510.9	−	22234.3i	−1.86006	−	1.07391i
$755$		0			0
$756$	−3297.53	+	946.100i	−0.158638	+	0.0455150i
$757$	2542.95	−	2542.95i	0.122094	−	0.122094i	−0.643420	−	0.765514i	$-0.722485\pi$
$757$	2542.95	−	2542.95i	0.122094	−	0.122094i	0.765514	+	0.643420i	$0.222485\pi$
$758$	796.586	+	2972.90i	0.0381706	+	0.142455i
$759$	−1622.60	−	17371.6i	−0.0775979	−	0.830763i
$760$		0			0
$761$	−13170.8	+	7604.19i	−0.627389	+	0.362223i	−0.779740	−	0.626103i	$-0.784649\pi$
$761$	−13170.8	+	7604.19i	−0.627389	+	0.362223i	0.152351	+	0.988326i	$0.451315\pi$
$762$	949.932	−	352.074i	0.0451606	−	0.0167379i
$763$	3625.11	−	971.345i	0.172002	−	0.0460879i
$764$	13766.3			0.651893
$765$		0			0
$766$	3530.22			0.166517
$767$	27515.1	−	7372.64i	1.29532	−	0.347080i
$768$	−4682.65	+	27499.4i	−0.220014	+	1.29206i
$769$	23692.9	−	13679.1i	1.11104	−	0.641458i	0.171940	−	0.985107i	$-0.444996\pi$
$769$	23692.9	−	13679.1i	1.11104	−	0.641458i	0.939098	+	0.343649i	$0.111663\pi$
$770$		0			0
$771$	20947.2	−	14851.3i	0.978461	−	0.693719i
$772$	−7339.70	−	27392.1i	−0.342178	−	1.27703i
$773$	8996.52	−	8996.52i	0.418606	−	0.418606i	−0.466117	−	0.884723i	$-0.654347\pi$
$773$	8996.52	−	8996.52i	0.418606	−	0.418606i	0.884723	+	0.466117i	$0.154347\pi$
$774$	12337.8	+	14357.9i	0.572961	+	0.666775i
$775$		0			0
$776$	−4033.48	−	2328.73i	−0.186590	−	0.107728i
$777$	1460.28	+	3939.99i	0.0674225	+	0.181913i
$778$	−7980.47	+	29783.5i	−0.367755	+	1.37248i
$779$	6270.23	+	10860.4i	0.288388	+	0.499503i
$780$		0			0
$781$	2199.53	−	3809.70i	0.100775	−	0.174548i
$782$	28954.3	+	28954.3i	1.32405	+	1.32405i
$783$	−21058.7	−	35035.4i	−0.961145	−	1.59906i
$784$			25054.6i			1.14134i
$785$		0			0
$786$	18915.4	−	1766.81i	0.858386	−	0.0801780i
$787$	9237.00	+	2475.05i	0.418378	+	0.112104i	0.461866	−	0.886950i	$-0.347180\pi$
$787$	9237.00	+	2475.05i	0.418378	+	0.112104i	−0.0434876	+	0.999054i	$0.513847\pi$
$788$	−417.181	−	111.783i	−0.0188597	−	0.00505345i
$789$	−17064.1	+	37161.9i	−0.769959	+	1.67681i
$790$		0			0
$791$		−	5423.74i		−	0.243800i
$792$	−2316.21	−	4818.65i	−0.103918	−	0.216191i
$793$	−5744.46	−	5744.46i	−0.257241	−	0.257241i
$794$	5048.86	−	8744.89i	0.225664	−	0.390862i
$795$		0			0
$796$	240.086	+	415.841i	0.0106905	+	0.0185165i
$797$	−4397.74	+	16412.6i	−0.195453	+	0.729440i	0.796696	+	0.604380i	$0.206579\pi$
$797$	−4397.74	+	16412.6i	−0.195453	+	0.729440i	−0.992149	+	0.125060i	$0.960088\pi$
$798$	5236.44	+	891.670i	0.232291	+	0.0395548i
$799$	−18798.9	−	10853.6i	−0.832363	−	0.480565i
$800$		0			0
$801$	1159.21	+	6151.10i	0.0511343	+	0.271334i
$802$	32544.7	−	32544.7i	1.43291	−	1.43291i
$803$	2158.67	+	8056.27i	0.0948666	+	0.354047i
$804$	−18936.6	−	8695.35i	−0.830650	−	0.381420i
$805$		0			0
$806$	15991.0	−	9232.42i	0.698833	−	0.403471i
$807$	−3655.45	−	3030.91i	−0.159452	−	0.132209i
$808$	−12076.6	+	3235.91i	−0.525809	+	0.140890i
$809$	−35676.8			−1.55047			−0.775234	−	0.631674i	$-0.782368\pi$
$809$	−35676.8			−1.55047			−0.775234	+	0.631674i	$0.782368\pi$
$810$		0			0
$811$	−7308.64			−0.316450			−0.158225	−	0.987403i	$-0.550577\pi$
$811$	−7308.64			−0.316450			−0.158225	+	0.987403i	$0.550577\pi$
$812$	−6881.77	+	1843.96i	−0.297417	+	0.0796927i
$813$	5801.77	+	4810.52i	0.250279	+	0.207518i
$814$	13695.8	−	7907.30i	0.589728	−	0.340480i
$815$		0			0
$816$	27533.9	+	12643.1i	1.18123	+	0.542398i
$817$	−3142.58	−	11728.3i	−0.134572	−	0.502228i
$818$	−4018.17	+	4018.17i	−0.171751	+	0.171751i
$819$	892.549	+	4736.13i	0.0380808	+	0.202068i
$820$		0			0
$821$	27154.4	+	15677.6i	1.15432	+	0.666446i	0.949936	−	0.312445i	$-0.101148\pi$
$821$	27154.4	+	15677.6i	1.15432	+	0.666446i	0.204383	+	0.978891i	$0.434481\pi$
$822$	31299.5	+	5329.73i	1.32809	+	0.226150i
$823$	9907.77	−	36976.3i	0.419639	−	1.56612i	−0.355719	−	0.934593i	$-0.615764\pi$
$823$	9907.77	−	36976.3i	0.419639	−	1.56612i	0.775358	−	0.631522i	$-0.217569\pi$
$824$	−2262.01	−	3917.92i	−0.0956322	−	0.165640i
$825$		0			0
$826$	5508.73	−	9541.41i	0.232050	−	0.401923i
$827$	−19437.5	−	19437.5i	−0.817301	−	0.817301i	0.168415	−	0.985716i	$-0.446135\pi$
$827$	−19437.5	−	19437.5i	−0.817301	−	0.817301i	−0.985716	+	0.168415i	$0.946135\pi$
$828$	−9714.58	−	20210.2i	−0.407735	−	0.848252i
$829$		−	45658.8i		−	1.91290i	−0.291892	−	0.956451i	$-0.594285\pi$
$829$		−	45658.8i		−	1.91290i	0.291892	−	0.956451i	$-0.405715\pi$
$830$		0			0
$831$	10821.7	−	23567.3i	0.451744	−	0.983803i
$832$	−7224.27	−	1935.74i	−0.301029	−	0.0806606i
$833$	23644.6	+	6335.54i	0.983476	+	0.263522i
$834$	44022.4	−	4111.94i	1.82778	−	0.170725i
$835$		0			0
$836$		−	8281.40i		−	0.342606i
$837$	16971.0	−	298.834i	0.700839	−	0.0123408i
$838$	14116.0	+	14116.0i	0.581895	+	0.581895i
$839$	1519.20	−	2631.33i	0.0625131	−	0.108276i	−0.833075	−	0.553160i	$-0.813422\pi$
$839$	1519.20	−	2631.33i	0.0625131	−	0.108276i	0.895588	+	0.444884i	$0.146755\pi$
$840$		0			0
$841$	−30251.9	−	52397.9i	−1.24039	−	2.14842i
$842$	852.887	−	3183.02i	0.0349079	−	0.130278i
$843$	2501.91	+	6750.42i	0.102219	+	0.275797i
$844$	−3678.57	−	2123.83i	−0.150026	−	0.0866174i
$845$		0			0
$846$	18702.7	+	21765.0i	0.760063	+	0.884512i
$847$	−2468.98	+	2468.98i	−0.100159	+	0.100159i
$848$	14390.1	+	53704.4i	0.582732	+	2.17479i
$849$	24136.0	−	17112.2i	0.975671	−	0.691741i
$850$		0			0
$851$	−23785.8	+	13732.7i	−0.958128	+	0.553175i
$852$	949.082	−	5573.60i	0.0381632	−	0.224118i
$853$	42662.6	−	11431.4i	1.71247	−	0.458856i	0.736445	−	0.676498i	$-0.236503\pi$
$853$	42662.6	−	11431.4i	1.71247	−	0.458856i	0.976029	+	0.217642i	$0.0698365\pi$
$854$	−3142.10			−0.125902
$855$		0			0
$856$	5195.39			0.207447
$857$	17258.5	−	4624.39i	0.687909	−	0.184325i	0.102100	−	0.994774i	$-0.467444\pi$
$857$	17258.5	−	4624.39i	0.687909	−	0.184325i	0.585808	+	0.810450i	$0.300777\pi$
$858$	17008.4	−	6303.85i	0.676758	−	0.250828i
$859$	−20839.6	+	12031.8i	−0.827751	+	0.477902i	−0.853082	−	0.521777i	$-0.825269\pi$
$859$	−20839.6	+	12031.8i	−0.827751	+	0.477902i	0.0253309	+	0.999679i	$0.491936\pi$
$860$		0			0
$861$	409.274	+	4381.69i	0.0161998	+	0.173435i
$862$	1545.00	+	5766.03i	0.0610476	+	0.227833i
$863$	−5456.05	+	5456.05i	−0.215210	+	0.215210i	−0.806476	−	0.591266i	$-0.798628\pi$
$863$	−5456.05	+	5456.05i	−0.215210	+	0.215210i	0.591266	+	0.806476i	$0.298628\pi$
$864$	−21826.0	−	21070.7i	−0.859416	−	0.829674i
$865$		0			0
$866$	21870.8	+	12627.1i	0.858197	+	0.495480i
$867$	2599.57	−	3135.23i	0.101829	−	0.122812i
$868$	765.676	−	2857.54i	0.0299409	−	0.111741i
$869$	7180.77	+	12437.5i	0.280312	+	0.485514i
$870$		0			0
$871$	−14637.0	+	25352.1i	−0.569410	+	0.986247i
$872$	5315.47	+	5315.47i	0.206427	+	0.206427i
$873$	13091.6	−	6292.82i	0.507540	−	0.243963i
$874$			34720.4i			1.34375i
$875$		0			0
$876$	6199.86	+	8744.63i	0.239125	+	0.337276i
$877$	−13168.1	−	3528.38i	−0.507018	−	0.135855i	−0.00376284	−	0.999993i	$-0.501198\pi$
$877$	−13168.1	−	3528.38i	−0.507018	−	0.135855i	−0.503255	+	0.864138i	$0.667864\pi$
$878$	−63708.8	−	17070.7i	−2.44882	−	0.656160i
$879$	−7955.57	−	11221.0i	−0.305273	−	0.430574i
$880$		0			0
$881$		−	14206.6i		−	0.543282i	−0.962399	−	0.271641i	$-0.912434\pi$
$881$		−	14206.6i		−	0.543282i	0.962399	−	0.271641i	$-0.0875664\pi$
$882$	−26724.5	−	18249.0i	−1.02025	−	0.696684i
$883$	−14209.3	−	14209.3i	−0.541541	−	0.541541i	0.382439	−	0.923981i	$-0.375084\pi$
$883$	−14209.3	−	14209.3i	−0.541541	−	0.541541i	−0.923981	+	0.382439i	$0.875084\pi$
$884$	−8817.29	+	15272.0i	−0.335472	+	0.581055i
$885$		0			0
$886$	−8980.17	−	15554.1i	−0.340513	−	0.589786i
$887$	3862.13	−	14413.7i	0.146198	−	0.545618i	−0.853501	−	0.521091i	$-0.825525\pi$
$887$	3862.13	−	14413.7i	0.146198	−	0.545618i	0.999699	−	0.0245273i	$-0.00780805\pi$
$888$	−5372.00	+	6478.95i	−0.203010	+	0.244841i
$889$	−197.475	−	114.012i	−0.00745006	−	0.00430129i
$890$		0			0
$891$	16484.2	+	2509.18i	0.619802	+	0.0943442i
$892$	−20751.2	+	20751.2i	−0.778927	+	0.778927i
$893$	−4763.82	−	17778.8i	−0.178516	−	0.666232i
$894$	1634.80	+	17502.2i	0.0611587	+	0.654765i
$895$		0			0
$896$	3970.07	−	2292.12i	0.148025	−	0.0854625i
$897$	−29538.8	+	10948.0i	−1.09952	+	0.407518i
$898$	50137.0	−	13434.2i	1.86313	−	0.499225i
$899$	35250.4			1.30775
$900$		0			0
$901$	54320.8			2.00853
$902$	15998.7	−	4286.84i	0.590575	−	0.158244i
$903$	715.264	−	4200.47i	0.0263593	−	0.154798i
$904$	9408.25	−	5431.86i	0.346143	−	0.199846i
$905$		0			0
$906$	43248.4	−	30662.7i	1.58591	−	1.12439i
$907$	−11773.8	−	43940.5i	−0.431029	−	1.60862i	−0.750395	−	0.660990i	$-0.770137\pi$
$907$	−11773.8	−	43940.5i	−0.431029	−	1.60862i	0.319366	−	0.947631i	$-0.396530\pi$
$908$	−1662.87	+	1662.87i	−0.0607757	+	0.0607757i
$909$	12905.2	−	36795.0i	0.470890	−	1.34259i
$910$		0			0
$911$	3046.77	+	1759.05i	0.110806	+	0.0639737i	0.554379	−	0.832265i	$-0.312956\pi$
$911$	3046.77	+	1759.05i	0.110806	+	0.0639737i	−0.443573	+	0.896238i	$0.646289\pi$
$912$	8928.14	+	24089.0i	0.324167	+	0.874636i
$913$	−2424.28	+	9047.54i	−0.0878773	+	0.327963i
$914$	−4086.38	−	7077.82i	−0.147883	−	0.256142i
$915$		0			0
$916$	7312.34	−	12665.3i	0.263763	−	0.456850i
$917$	−3023.61	−	3023.61i	−0.108886	−	0.108886i
$918$	−33540.6	+	20160.2i	−1.20589	+	0.724822i
$919$			21586.6i			0.774838i	0.921904	+	0.387419i	$0.126633\pi$
$919$			21586.6i			0.774838i	−0.921904	+	0.387419i	$0.873367\pi$
$920$		0			0
$921$	−28367.7	+	2649.71i	−1.01493	+	0.0948000i
$922$	9182.75	+	2460.51i	0.328002	+	0.0878878i
$923$	−7672.23	−	2055.77i	−0.273602	−	0.0733114i
$924$	1212.71	−	2641.03i	0.0431768	−	0.0940298i
$925$		0			0
$926$			63471.4i			2.25248i
$927$	14069.1	+	1064.64i	0.498477	+	0.0377210i
$928$	−44550.3	−	44550.3i	−1.57590	−	1.57590i
$929$	−13917.6	+	24106.1i	−0.491521	+	0.851340i	−0.999952	−	0.00976285i	$-0.996892\pi$
$929$	−13917.6	+	24106.1i	−0.491521	+	0.851340i	0.508431	+	0.861103i	$0.330226\pi$
$930$		0			0
$931$	10378.0	+	17975.2i	0.365334	+	0.632776i
$932$	−3956.37	+	14765.4i	−0.139051	+	0.518944i
$933$	12580.3	+	2142.19i	0.441436	+	0.0751686i
$934$	5718.71	+	3301.70i	0.200345	+	0.115669i
$935$		0			0
$936$	−7321.60	+	6291.47i	−0.255677	+	0.219704i
$937$	−4451.52	+	4451.52i	−0.155203	+	0.155203i	−0.780437	−	0.625234i	$-0.785003\pi$
$937$	−4451.52	+	4451.52i	−0.155203	+	0.155203i	0.625234	+	0.780437i	$0.285003\pi$
$938$	2930.45	+	10936.6i	0.102007	+	0.380695i
$939$	−25807.9	−	11850.5i	−0.896920	−	0.411849i
$940$		0			0
$941$	38494.9	−	22225.1i	1.33358	−	0.769943i	0.347734	−	0.937593i	$-0.386951\pi$
$941$	38494.9	−	22225.1i	1.33358	−	0.769943i	0.985847	+	0.167650i	$0.0536179\pi$
$942$	−19969.7	−	16557.8i	−0.690710	−	0.572700i
$943$	−27785.2	+	7445.02i	−0.959502	+	0.257098i
$944$	53285.5			1.83718
$945$		0			0
$946$	−16036.8			−0.551164
$947$	26412.3	−	7077.16i	0.906320	−	0.242848i	0.224592	−	0.974453i	$-0.427895\pi$
$947$	26412.3	−	7077.16i	0.906320	−	0.242848i	0.681729	+	0.731605i	$0.261228\pi$
$948$	14209.0	+	11781.4i	0.486801	+	0.403629i
$949$	13041.8	−	7529.71i	0.446108	−	0.257560i
$950$		0			0
$951$	−30676.9	−	14086.3i	−1.04602	−	0.480314i
$952$	−730.971	−	2728.02i	−0.0248854	−	0.0928736i
$953$	−3775.67	+	3775.67i	−0.128338	+	0.128338i	−0.768358	−	0.640020i	$-0.778926\pi$
$953$	−3775.67	+	3775.67i	−0.128338	+	0.128338i	0.640020	+	0.768358i	$0.278926\pi$
$954$	−67765.1	−	23767.5i	−2.29976	−	0.806604i
$955$		0			0
$956$	5509.17	+	3180.72i	0.186380	+	0.107606i
$957$	34137.1	+	5812.92i	1.15308	+	0.196348i
$958$	11051.6	−	41245.1i	0.372714	−	1.39099i
$959$	−3573.16	−	6188.90i	−0.120316	−	0.208394i
$960$		0			0
$961$	7576.93	−	13123.6i	0.254336	−	0.440523i
$962$	−20191.1	−	20191.1i	−0.676703	−	0.676703i
$963$	−9137.29	+	13381.0i	−0.305758	+	0.447763i
$964$			19376.4i			0.647378i
$965$		0			0
$966$	−5084.39	+	11072.7i	−0.169345	+	0.368798i
$967$	−13761.3	−	3687.34i	−0.457637	−	0.122623i	0.0226337	−	0.999744i	$-0.492795\pi$
$967$	−13761.3	−	3687.34i	−0.457637	−	0.122623i	−0.480271	+	0.877120i	$0.659462\pi$
$968$	−6755.46	−	1810.12i	−0.224307	−	0.0601028i
$969$	24991.0	−	2334.30i	0.828510	−	0.0773875i
$970$		0			0
$971$			19639.3i			0.649080i	0.945872	+	0.324540i	$0.105209\pi$
$971$			19639.3i			0.649080i	−0.945872	+	0.324540i	$0.894791\pi$
$972$	20986.3	−	4338.92i	0.692527	−	0.143180i
$973$	−7036.94	−	7036.94i	−0.231854	−	0.231854i
$974$	−23771.4	+	41173.2i	−0.782016	+	1.35449i
$975$		0			0
$976$	−7598.30	−	13160.6i	−0.249196	−	0.431621i
$977$	−11913.2	+	44460.6i	−0.390109	+	1.45591i	0.439844	+	0.898074i	$0.355034\pi$
$977$	−11913.2	+	44460.6i	−0.390109	+	1.45591i	−0.829953	+	0.557833i	$0.811633\pi$
$978$	6092.89	+	16439.2i	0.199212	+	0.537494i
$979$	−4592.12	−	2651.26i	−0.149913	−	0.0865523i
$980$		0			0
$981$	−23038.7	+	4341.77i	−0.749816	+	0.141307i
$982$	−40799.2	+	40799.2i	−1.32582	+	1.32582i
$983$	10741.5	+	40087.7i	0.348525	+	1.30071i	0.888440	+	0.458993i	$0.151790\pi$
$983$	10741.5	+	40087.7i	0.348525	+	1.30071i	−0.539915	+	0.841719i	$0.681544\pi$
$984$	−7190.77	+	5098.19i	−0.232961	+	0.165167i
$985$		0			0
$986$	−70382.7	+	40635.5i	−2.27327	+	1.31247i
$987$	1084.26	−	6367.46i	0.0349670	−	0.205348i
$988$	−14443.3	+	3870.06i	−0.465083	+	0.124619i
$989$	27851.4			0.895472
$990$		0			0
$991$	−53757.9			−1.72318			−0.861592	−	0.507602i	$-0.830532\pi$
$991$	−53757.9			−1.72318			−0.861592	+	0.507602i	$0.830532\pi$
$992$	25269.8	−	6771.02i	0.808788	−	0.216714i
$993$	−42019.5	+	15573.7i	−1.34285	+	0.497701i
$994$	−2660.50	+	1536.04i	−0.0848954	+	0.0490144i
$995$		0			0
$996$	1119.58	+	11986.2i	0.0356178	+	0.381324i
$997$	2154.83	+	8041.92i	0.0684494	+	0.255457i	0.991668	−	0.128818i	$-0.0411183\pi$
$997$	2154.83	+	8041.92i	0.0684494	+	0.255457i	−0.923219	+	0.384275i	$0.874452\pi$
$998$	16894.3	−	16894.3i	0.535851	−	0.535851i
$999$	−7238.94	−	25230.6i	−0.229259	−	0.799058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.p.b.218.4		64
5.2	odd	4	inner	225.4.p.b.182.4		64
5.3	odd	4		45.4.l.a.2.13	✓	64
5.4	even	2		45.4.l.a.38.13	yes	64
9.5	odd	6	inner	225.4.p.b.68.4		64
15.8	even	4		135.4.m.a.62.4		64
15.14	odd	2		135.4.m.a.8.4		64
45.4	even	6		135.4.m.a.98.4		64
45.13	odd	12		135.4.m.a.17.4		64
45.14	odd	6		45.4.l.a.23.13	yes	64
45.23	even	12		45.4.l.a.32.13	yes	64
45.32	even	12	inner	225.4.p.b.32.4		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.13	✓	64	5.3	odd	4
45.4.l.a.23.13	yes	64	45.14	odd	6
45.4.l.a.32.13	yes	64	45.23	even	12
45.4.l.a.38.13	yes	64	5.4	even	2
135.4.m.a.8.4		64	15.14	odd	2
135.4.m.a.17.4		64	45.13	odd	12
135.4.m.a.62.4		64	15.8	even	4
135.4.m.a.98.4		64	45.4	even	6
225.4.p.b.32.4		64	45.32	even	12	inner
225.4.p.b.68.4		64	9.5	odd	6	inner
225.4.p.b.182.4		64	5.2	odd	4	inner
225.4.p.b.218.4		64	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-3.56967 + 0.956489i) q^{2} +(-4.00002 - 3.31660i) q^{3} +(4.89944 - 2.82870i) q^{4} +(17.4510 + 8.01320i) q^{6} +(-1.11867 - 4.17492i) q^{7} +(6.12165 - 6.12165i) q^{8} +(5.00028 + 26.5329i) q^{9} +O(q^{10})\)	\(q+(-3.56967 + 0.956489i) q^{2} +(-4.00002 - 3.31660i) q^{3} +(4.89944 - 2.82870i) q^{4} +(17.4510 + 8.01320i) q^{6} +(-1.11867 - 4.17492i) q^{7} +(6.12165 - 6.12165i) q^{8} +(5.00028 + 26.5329i) q^{9} +(-19.8083 - 11.4363i) q^{11} +(-28.9795 - 4.93468i) q^{12} +(-10.6888 + 39.8912i) q^{13} +(7.98654 + 13.8331i) q^{14} +(-38.6265 + 66.9031i) q^{16} +(53.3704 + 53.3704i) q^{17} +(-43.2278 - 89.9311i) q^{18} +63.9989i q^{19} +(-9.37188 + 20.4099i) q^{21} +(81.6476 + 21.8774i) q^{22} +(-141.799 - 37.9948i) q^{23} +(-44.7898 + 4.18362i) q^{24} -152.622i q^{26} +(67.9981 - 122.716i) q^{27} +(-17.2904 - 17.2904i) q^{28} +(145.682 - 252.328i) q^{29} +(60.4920 + 104.775i) q^{31} +(55.9663 - 208.869i) q^{32} +(41.3037 + 111.442i) q^{33} +(-241.563 - 139.466i) q^{34} +(99.5522 + 115.852i) q^{36} +(132.295 - 132.295i) q^{37} +(-61.2142 - 228.455i) q^{38} +(175.059 - 124.115i) q^{39} +(169.696 - 97.9741i) q^{41} +(13.9326 - 81.8208i) q^{42} +(-183.258 + 49.1037i) q^{43} -129.399 q^{44} +542.516 q^{46} +(-277.799 + 74.4360i) q^{47} +(376.398 - 139.505i) q^{48} +(280.868 - 162.159i) q^{49} +(-36.4741 - 390.491i) q^{51} +(60.4708 + 225.680i) q^{52} +(508.904 - 508.904i) q^{53} +(-125.354 + 503.095i) q^{54} +(-32.4055 - 18.7093i) q^{56} +(212.259 - 255.997i) q^{57} +(-278.686 + 1040.07i) q^{58} +(-344.876 - 597.343i) q^{59} +(-98.3560 + 170.358i) q^{61} +(-316.153 - 316.153i) q^{62} +(105.179 - 50.5573i) q^{63} +181.099i q^{64} +(-254.033 - 358.303i) q^{66} +(684.688 + 183.462i) q^{67} +(412.454 + 110.517i) q^{68} +(441.183 + 622.270i) q^{69} +192.329i q^{71} +(193.036 + 131.816i) q^{72} +(-257.846 - 257.846i) q^{73} +(-345.710 + 598.788i) q^{74} +(181.033 + 313.559i) q^{76} +(-25.5868 + 95.4913i) q^{77} +(-506.187 + 610.491i) q^{78} +(-543.771 - 313.946i) q^{79} +(-678.994 + 265.344i) q^{81} +(-512.047 + 512.047i) q^{82} +(-105.991 - 395.562i) q^{83} +(11.8165 + 126.508i) q^{84} +(607.201 - 350.568i) q^{86} +(-1419.60 + 526.149i) q^{87} +(-191.268 + 51.2502i) q^{88} +231.829 q^{89} +178.500 q^{91} +(-802.211 + 214.952i) q^{92} +(105.529 - 619.731i) q^{93} +(920.452 - 531.423i) q^{94} +(-916.602 + 649.862i) q^{96} +(-139.239 - 519.648i) q^{97} +(-847.502 + 847.502i) q^{98} +(204.392 - 582.756i) 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

Related objects

Downloads

Learn more