LMFDB - Embedded newform 225.4.h.d.46.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, 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 $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			46.12
Character	$\chi$	$=$	225.46
Dual form			225.4.h.d.181.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.856692 - 2.63663i) q^{2} +(0.254251 + 0.184724i) q^{4} +(7.75979 + 8.04895i) q^{5} -7.15708 q^{7} +(18.6477 - 13.5483i) q^{8} +O(q^{10})$	\(q+(0.856692 - 2.63663i) q^{2} +(0.254251 + 0.184724i) q^{4} +(7.75979 + 8.04895i) q^{5} -7.15708 q^{7} +(18.6477 - 13.5483i) q^{8} +(27.8698 - 13.5642i) q^{10} +(-15.3917 + 47.3707i) q^{11} +(16.6242 + 51.1641i) q^{13} +(-6.13142 + 18.8706i) q^{14} +(-18.9696 - 58.3826i) q^{16} +(10.7434 - 7.80553i) q^{17} +(124.404 - 90.3850i) q^{19} +(0.486099 + 3.47988i) q^{20} +(111.713 + 81.1643i) q^{22} +(-66.4882 + 204.630i) q^{23} +(-4.57128 + 124.916i) q^{25} +149.143 q^{26} +(-1.81970 - 1.32209i) q^{28} +(56.2588 + 40.8744i) q^{29} +(122.680 - 89.1322i) q^{31} +14.2140 q^{32} +(-11.3765 - 35.0133i) q^{34} +(-55.5375 - 57.6070i) q^{35} +(-92.0967 - 283.445i) q^{37} +(-131.735 - 405.440i) q^{38} +(253.752 + 44.9620i) q^{40} +(-110.882 - 341.260i) q^{41} +451.178 q^{43} +(-12.6639 + 9.20084i) q^{44} +(482.572 + 350.609i) q^{46} +(-124.804 - 90.6754i) q^{47} -291.776 q^{49} +(325.442 + 119.068i) q^{50} +(-5.22453 + 16.0794i) q^{52} +(-39.5720 - 28.7507i) q^{53} +(-500.721 + 243.700i) q^{55} +(-133.463 + 96.9665i) q^{56} +(155.967 - 113.317i) q^{58} +(9.36171 + 28.8124i) q^{59} +(175.261 - 539.399i) q^{61} +(-129.909 - 399.820i) q^{62} +(163.934 - 504.537i) q^{64} +(-282.817 + 530.831i) q^{65} +(-557.154 + 404.796i) q^{67} +4.17339 q^{68} +(-199.467 + 97.0802i) q^{70} +(684.549 + 497.354i) q^{71} +(-110.215 + 339.207i) q^{73} -826.236 q^{74} +48.3262 q^{76} +(110.160 - 339.036i) q^{77} +(-158.437 - 115.111i) q^{79} +(322.718 - 605.722i) q^{80} -994.767 q^{82} +(-580.078 + 421.451i) q^{83} +(146.193 + 25.9038i) q^{85} +(386.521 - 1189.59i) q^{86} +(354.775 + 1091.88i) q^{88} +(-371.049 + 1141.97i) q^{89} +(-118.981 - 366.186i) q^{91} +(-54.7048 + 39.7453i) q^{92} +(-345.996 + 251.381i) q^{94} +(1692.85 + 299.955i) q^{95} +(-1001.28 - 727.475i) q^{97} +(-249.962 + 769.305i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) $ 64 * q - 72 * q^4 + 20 * q^7	$ 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) $ 64 * q - 72 * q^4 + 20 * q^7 + 50 * q^10 + 180 * q^13 - 244 * q^16 - 116 * q^19 - 210 * q^22 + 440 * q^25 + 980 * q^28 + 42 * q^31 + 40 * q^34 - 1170 * q^37 - 3040 * q^40 + 1040 * q^43 + 700 * q^46 + 4188 * q^49 + 3280 * q^52 + 2640 * q^55 - 4530 * q^58 + 88 * q^61 - 3018 * q^64 - 2860 * q^67 - 3720 * q^70 - 5280 * q^73 + 9288 * q^76 - 1144 * q^79 + 2840 * q^82 + 470 * q^85 + 7610 * q^88 - 1180 * q^91 + 2170 * q^94 + 2050 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.856692	−	2.63663i	0.302886	−	0.932189i	−0.677571	−	0.735457i	$-0.736967\pi$
$2$	0.856692	−	2.63663i	0.302886	−	0.932189i	0.980457	−	0.196731i	$-0.0630327\pi$
$3$		0			0
$3$		0			0
$4$	0.254251	+	0.184724i	0.0317814	+	0.0230905i
$5$	7.75979	+	8.04895i	0.694057	+	0.719920i
$5$	7.75979	+	8.04895i	0.694057	+	0.719920i
$6$		0			0
$7$	−7.15708			−0.386446			−0.193223	−	0.981155i	$-0.561894\pi$
$7$	−7.15708			−0.386446			−0.193223	+	0.981155i	$0.561894\pi$
$8$	18.6477	−	13.5483i	0.824118	−	0.598757i
$9$		0			0
$10$	27.8698	−	13.5642i	0.881322	−	0.428938i
$11$	−15.3917	+	47.3707i	−0.421888	+	1.29844i	0.484055	+	0.875037i	$0.339163\pi$
$11$	−15.3917	+	47.3707i	−0.421888	+	1.29844i	−0.905943	+	0.423400i	$0.860837\pi$
$12$		0			0
$13$	16.6242	+	51.1641i	0.354672	+	1.09157i	0.956200	+	0.292716i	$0.0945589\pi$
$13$	16.6242	+	51.1641i	0.354672	+	1.09157i	−0.601528	+	0.798852i	$0.705441\pi$
$14$	−6.13142	+	18.8706i	−0.117049	+	0.360241i
$15$		0			0
$16$	−18.9696	−	58.3826i	−0.296401	−	0.912228i
$17$	10.7434	−	7.80553i	0.153274	−	0.111360i	−0.508505	−	0.861059i	$-0.669802\pi$
$17$	10.7434	−	7.80553i	0.153274	−	0.111360i	0.661779	+	0.749699i	$0.269802\pi$
$18$		0			0
$19$	124.404	−	90.3850i	1.50212	−	1.09135i	0.532593	−	0.846372i	$-0.321218\pi$
$19$	124.404	−	90.3850i	1.50212	−	1.09135i	0.969527	−	0.244983i	$-0.0787822\pi$
$20$	0.486099	+	3.47988i	0.00543475	+	0.0389062i
$21$		0			0
$22$	111.713	+	81.1643i	1.08260	+	0.786558i
$23$	−66.4882	+	204.630i	−0.602772	+	1.85514i	−0.0913347	+	0.995820i	$0.529113\pi$
$23$	−66.4882	+	204.630i	−0.602772	+	1.85514i	−0.511437	+	0.859321i	$0.670887\pi$
$24$		0			0
$25$	−4.57128	+	124.916i	−0.0365702	+	0.999331i
$26$	149.143			1.12497
$27$		0			0
$28$	−1.81970	−	1.32209i	−0.0122818	−	0.00892325i
$29$	56.2588	+	40.8744i	0.360241	+	0.261730i	0.753153	−	0.657846i	$-0.228532\pi$
$29$	56.2588	+	40.8744i	0.360241	+	0.261730i	−0.392912	+	0.919576i	$0.628532\pi$
$30$		0			0
$31$	122.680	−	89.1322i	0.710773	−	0.516407i	−0.172650	−	0.984983i	$-0.555233\pi$
$31$	122.680	−	89.1322i	0.710773	−	0.516407i	0.883423	+	0.468576i	$0.155233\pi$
$32$	14.2140			0.0785218
$33$		0			0
$34$	−11.3765	−	35.0133i	−0.0573839	−	0.176610i
$35$	−55.5375	−	57.6070i	−0.268216	−	0.278210i
$36$		0			0
$37$	−92.0967	−	283.445i	−0.409206	−	1.25941i	−0.917332	−	0.398123i	$-0.869662\pi$
$37$	−92.0967	−	283.445i	−0.409206	−	1.25941i	0.508127	−	0.861282i	$-0.330338\pi$
$38$	−131.735	−	405.440i	−0.562376	−	1.73082i
$39$		0			0
$40$	253.752	+	44.9620i	1.00304	+	0.177728i
$41$	−110.882	−	341.260i	−0.422363	−	1.29990i	−0.905497	−	0.424352i	$-0.860502\pi$
$41$	−110.882	−	341.260i	−0.422363	−	1.29990i	0.483135	−	0.875546i	$-0.339498\pi$
$42$		0			0
$43$	451.178			1.60009			0.800047	−	0.599937i	$-0.204808\pi$
$43$	451.178			1.60009			0.800047	+	0.599937i	$0.204808\pi$
$44$	−12.6639	+	9.20084i	−0.0433898	+	0.0315245i
$45$		0			0
$46$	482.572	+	350.609i	1.54677	+	1.12379i
$47$	−124.804	−	90.6754i	−0.387330	−	0.281412i	0.377030	−	0.926201i	$-0.376945\pi$
$47$	−124.804	−	90.6754i	−0.387330	−	0.281412i	−0.764361	+	0.644789i	$0.776945\pi$
$48$		0			0
$49$	−291.776			−0.850659
$50$	325.442	+	119.068i	0.920489	+	0.336774i
$51$		0			0
$52$	−5.22453	+	16.0794i	−0.0139329	+	0.0428811i
$53$	−39.5720	−	28.7507i	−0.102559	−	0.0745135i	0.535324	−	0.844647i	$-0.320190\pi$
$53$	−39.5720	−	28.7507i	−0.102559	−	0.0745135i	−0.637883	+	0.770133i	$0.720190\pi$
$54$		0			0
$55$	−500.721	+	243.700i	−1.22759	+	0.597464i
$56$	−133.463	+	96.9665i	−0.318477	+	0.231387i
$57$		0			0
$58$	155.967	−	113.317i	0.353094	−	0.256538i
$59$	9.36171	+	28.8124i	0.0206575	+	0.0635772i	0.960854	−	0.277056i	$-0.0893587\pi$
$59$	9.36171	+	28.8124i	0.0206575	+	0.0635772i	−0.940196	+	0.340633i	$0.889359\pi$
$60$		0			0
$61$	175.261	−	539.399i	0.367868	−	1.13218i	−0.580298	−	0.814404i	$-0.697064\pi$
$61$	175.261	−	539.399i	0.367868	−	1.13218i	0.948166	−	0.317776i	$-0.102936\pi$
$62$	−129.909	−	399.820i	−0.266105	−	0.818987i
$63$		0			0
$64$	163.934	−	504.537i	0.320184	−	0.985425i
$65$	−282.817	+	530.831i	−0.539679	+	1.01295i
$66$		0			0
$67$	−557.154	+	404.796i	−1.01593	+	0.738115i	−0.965444	−	0.260610i	$-0.916076\pi$
$67$	−557.154	+	404.796i	−1.01593	+	0.738115i	−0.0504840	+	0.998725i	$0.516076\pi$
$68$	4.17339			0.00744262
$69$		0			0
$70$	−199.467	+	97.0802i	−0.340584	+	0.165761i
$71$	684.549	+	497.354i	1.14424	+	0.831339i	0.987704	−	0.156333i	$-0.0499674\pi$
$71$	684.549	+	497.354i	1.14424	+	0.831339i	0.156536	+	0.987672i	$0.449967\pi$
$72$		0			0
$73$	−110.215	+	339.207i	−0.176708	+	0.543851i	−0.999707	−	0.0241912i	$-0.992299\pi$
$73$	−110.215	+	339.207i	−0.176708	+	0.543851i	0.822999	+	0.568042i	$0.192299\pi$
$74$	−826.236			−1.29795
$75$		0			0
$76$	48.3262			0.0729394
$77$	110.160	−	339.036i	0.163037	−	0.501776i
$78$		0			0
$79$	−158.437	−	115.111i	−0.225640	−	0.163937i	0.469222	−	0.883080i	$-0.344535\pi$
$79$	−158.437	−	115.111i	−0.225640	−	0.163937i	−0.694862	+	0.719143i	$0.744535\pi$
$80$	322.718	−	605.722i	0.451012	−	0.846523i
$81$		0			0
$82$	−994.767			−1.33968
$83$	−580.078	+	421.451i	−0.767130	+	0.557353i	−0.901089	−	0.433634i	$-0.857231\pi$
$83$	−580.078	+	421.451i	−0.767130	+	0.557353i	0.133959	+	0.990987i	$0.457231\pi$
$84$		0			0
$85$	146.193	+	25.9038i	0.186551	+	0.0330548i
$86$	386.521	−	1189.59i	0.484647	−	1.49159i
$87$		0			0
$88$	354.775	+	1091.88i	0.429763	+	1.32267i
$89$	−371.049	+	1141.97i	−0.441922	+	1.36010i	0.443902	+	0.896076i	$0.353594\pi$
$89$	−371.049	+	1141.97i	−0.441922	+	1.36010i	−0.885824	+	0.464022i	$0.846406\pi$
$90$		0			0
$91$	−118.981	−	366.186i	−0.137062	−	0.421832i
$92$	−54.7048	+	39.7453i	−0.0619931	+	0.0450406i
$93$		0			0
$94$	−345.996	+	251.381i	−0.379646	+	0.275829i
$95$	1692.85	+	299.955i	1.82824	+	0.323945i
$96$		0			0
$97$	−1001.28	−	727.475i	−1.04809	−	0.761483i	−0.0762433	−	0.997089i	$-0.524293\pi$
$97$	−1001.28	−	727.475i	−1.04809	−	0.761483i	−0.971849	+	0.235606i	$0.924293\pi$
$98$	−249.962	+	769.305i	−0.257653	+	0.792975i
$99$		0			0
$100$	−24.2373	+	30.9157i	−0.0242373	+	0.0309157i
$101$	365.423			0.360010			0.180005	−	0.983666i	$-0.442389\pi$
$101$	365.423			0.360010			0.180005	+	0.983666i	$0.442389\pi$
$102$		0			0
$103$	−157.043	−	114.098i	−0.150232	−	0.109150i	0.510130	−	0.860097i	$-0.329597\pi$
$103$	−157.043	−	114.098i	−0.150232	−	0.109150i	−0.660362	+	0.750947i	$0.729597\pi$
$104$	1003.19	+	728.861i	0.945875	+	0.687218i
$105$		0			0
$106$	−109.706	+	79.7060i	−0.100524	+	0.0730352i
$107$	286.289			0.258660			0.129330	−	0.991602i	$-0.458717\pi$
$107$	286.289			0.258660			0.129330	+	0.991602i	$0.458717\pi$
$108$		0			0
$109$	−437.785	−	1347.36i	−0.384699	−	1.18398i	−0.936699	−	0.350137i	$-0.886135\pi$
$109$	−437.785	−	1347.36i	−0.384699	−	1.18398i	0.552000	−	0.833844i	$-0.313865\pi$
$110$	213.582	+	1528.99i	0.185130	+	1.32530i
$111$		0			0
$112$	135.767	+	417.849i	0.114543	+	0.352527i
$113$	−348.438	−	1072.38i	−0.290074	−	0.892755i	−0.984832	−	0.173512i	$-0.944489\pi$
$113$	−348.438	−	1072.38i	−0.290074	−	0.892755i	0.694758	−	0.719244i	$-0.255511\pi$
$114$		0			0
$115$	−2162.99	+	1052.72i	−1.75391	+	0.853626i
$116$	6.75336	+	20.7847i	0.00540547	+	0.0166363i
$117$		0			0
$118$	83.9877			0.0655228
$119$	−76.8914	+	55.8648i	−0.0592321	+	0.0430346i
$120$		0			0
$121$	−930.279	−	675.887i	−0.698933	−	0.507804i
$122$	−1272.05	−	924.198i	−0.943983	−	0.685844i
$123$		0			0
$124$	47.6564			0.0345135
$125$	−1040.92	+	932.531i	−0.744820	+	0.667265i
$126$		0			0
$127$	−294.997	+	907.909i	−0.206116	+	0.634361i	0.793549	+	0.608506i	$0.208231\pi$
$127$	−294.997	+	907.909i	−0.206116	+	0.634361i	−0.999666	+	0.0258551i	$0.991769\pi$
$128$	−1097.84	−	797.629i	−0.758097	−	0.550790i
$129$		0			0
$130$	1157.32	+	1200.44i	0.780795	+	0.809890i
$131$	1193.22	−	866.926i	0.795818	−	0.578196i	−0.113866	−	0.993496i	$-0.536323\pi$
$131$	1193.22	−	866.926i	0.795818	−	0.578196i	0.909684	+	0.415300i	$0.136323\pi$
$132$		0			0
$133$	−890.371	+	646.893i	−0.580489	+	0.421750i
$134$	589.987	+	1815.79i	0.380352	+	1.17060i
$135$		0			0
$136$	94.5873	−	291.110i	0.0596382	−	0.183547i
$137$	−286.735	−	882.480i	−0.178813	−	0.550331i	0.820974	−	0.570966i	$-0.193431\pi$
$137$	−286.735	−	882.480i	−0.178813	−	0.550331i	−0.999787	+	0.0206352i	$0.993431\pi$
$138$		0			0
$139$	285.429	−	878.460i	0.174171	−	0.536043i	−0.825424	−	0.564514i	$-0.809064\pi$
$139$	285.429	−	878.460i	0.174171	−	0.536043i	0.999595	+	0.0284706i	$0.00906369\pi$
$140$	−3.47905	−	24.9058i	−0.00210024	−	0.0150352i
$141$		0			0
$142$	1897.79	−	1378.82i	1.12154	−	0.814846i
$143$	−2679.56			−1.56696
$144$		0			0
$145$	107.560	+	770.001i	0.0616027	+	0.441001i
$146$	799.941	+	581.191i	0.453449	+	0.329450i
$147$		0			0
$148$	28.9434	−	89.0786i	0.0160752	−	0.0494744i
$149$	−1993.74			−1.09620			−0.548098	−	0.836414i	$-0.684648\pi$
$149$	−1993.74			−1.09620			−0.548098	+	0.836414i	$0.684648\pi$
$150$		0			0
$151$	1706.75			0.919825			0.459913	−	0.887964i	$-0.347881\pi$
$151$	1706.75			0.919825			0.459913	+	0.887964i	$0.347881\pi$
$152$	1095.28	−	3370.94i	0.584469	−	1.79881i
$153$		0			0
$154$	−799.539	−	580.899i	−0.418368	−	0.303962i
$155$	1669.39	+	295.798i	0.865088	+	0.153284i
$156$		0			0
$157$	489.227			0.248692			0.124346	−	0.992239i	$-0.460317\pi$
$157$	489.227			0.248692			0.124346	+	0.992239i	$0.460317\pi$
$158$	−439.238	+	319.125i	−0.221164	+	0.160685i
$159$		0			0
$160$	110.297	+	114.408i	0.0544986	+	0.0565295i
$161$	475.862	−	1464.55i	0.232939	−	0.716912i
$162$		0			0
$163$	−1064.87	−	3277.32i	−0.511698	−	1.57485i	−0.789210	−	0.614123i	$-0.789510\pi$
$163$	−1064.87	−	3277.32i	−0.511698	−	1.57485i	0.277512	−	0.960722i	$-0.410490\pi$
$164$	34.8471	−	107.248i	0.0165921	−	0.0510652i
$165$		0			0
$166$	614.262	+	1890.50i	0.287205	+	0.883925i
$167$	748.980	−	544.166i	0.347053	−	0.252148i	−0.400579	−	0.916262i	$-0.631191\pi$
$167$	748.980	−	544.166i	0.347053	−	0.252148i	0.747632	+	0.664114i	$0.231191\pi$
$168$		0			0
$169$	−563.993	+	409.765i	−0.256710	+	0.186511i
$170$	193.541	−	363.265i	0.0873171	−	0.163889i
$171$		0			0
$172$	114.713	+	83.3436i	0.0508532	+	0.0369470i
$173$	−200.254	+	616.317i	−0.0880058	+	0.270854i	−0.985368	−	0.170441i	$-0.945481\pi$
$173$	−200.254	+	616.317i	−0.0880058	+	0.270854i	0.897362	+	0.441295i	$0.145481\pi$
$174$		0			0
$175$	32.7170	−	894.037i	0.0141324	−	0.386188i
$176$	3057.60			1.30952
$177$		0			0
$178$	2693.08	+	1956.64i	1.13401	+	0.823910i
$179$	−1657.52	−	1204.26i	−0.692115	−	0.502851i	0.185240	−	0.982693i	$-0.440694\pi$
$179$	−1657.52	−	1204.26i	−0.692115	−	0.502851i	−0.877355	+	0.479842i	$0.840694\pi$
$180$		0			0
$181$	729.361	−	529.912i	0.299519	−	0.217614i	−0.427867	−	0.903842i	$-0.640735\pi$
$181$	729.361	−	529.912i	0.299519	−	0.217614i	0.727386	+	0.686228i	$0.240735\pi$
$182$	−1067.43			−0.434741
$183$		0			0
$184$	1532.54	+	4716.67i	0.614023	+	1.88977i
$185$	1566.78	−	2940.75i	0.622659	−	1.16869i
$186$		0			0
$187$	204.395	+	629.062i	0.0799295	+	0.245998i
$188$	−14.9816	−	46.1086i	−0.00581195	−	0.0178873i
$189$		0			0
$190$	2241.13	−	4206.46i	0.855728	−	1.60615i
$191$	−899.058	−	2767.02i	−0.340594	−	1.04824i	−0.963900	−	0.266264i	$-0.914211\pi$
$191$	−899.058	−	2767.02i	−0.340594	−	1.04824i	0.623306	−	0.781978i	$-0.285789\pi$
$192$		0			0
$193$	184.846			0.0689406			0.0344703	−	0.999406i	$-0.489026\pi$
$193$	184.846			0.0689406			0.0344703	+	0.999406i	$0.489026\pi$
$194$	−2775.87	+	2016.79i	−1.02730	+	0.746377i
$195$		0			0
$196$	−74.1844	−	53.8981i	−0.0270351	−	0.0196422i
$197$	−2578.89	−	1873.67i	−0.932682	−	0.677633i	0.0139660	−	0.999902i	$-0.495554\pi$
$197$	−2578.89	−	1873.67i	−0.932682	−	0.677633i	−0.946648	+	0.322269i	$0.895554\pi$
$198$		0			0
$199$	2048.58			0.729749			0.364874	−	0.931057i	$-0.381112\pi$
$199$	2048.58			0.729749			0.364874	+	0.931057i	$0.381112\pi$
$200$	1607.16	+	2391.33i	0.568218	+	0.845463i
$201$		0			0
$202$	313.055	−	963.485i	0.109042	−	0.335597i
$203$	−402.649	−	292.541i	−0.139214	−	0.101145i
$204$		0			0
$205$	1886.36	−	3540.59i	0.642679	−	1.20627i
$206$	−435.373	+	316.317i	−0.147252	+	0.106985i
$207$		0			0
$208$	2671.74	−	1941.13i	0.890633	−	0.647083i
$209$	2366.81	+	7284.29i	0.783329	+	2.41084i
$210$		0			0
$211$	−921.101	+	2834.86i	−0.300527	+	0.924927i	0.680782	+	0.732487i	$0.261640\pi$
$211$	−921.101	+	2834.86i	−0.300527	+	0.924927i	−0.981309	+	0.192441i	$0.938360\pi$
$212$	−4.75026	−	14.6198i	−0.00153891	−	0.00473628i
$213$		0			0
$214$	245.261	−	754.837i	0.0783445	−	0.241120i
$215$	3501.05	+	3631.51i	1.11056	+	1.15194i
$216$		0			0
$217$	−878.030	+	637.926i	−0.274676	+	0.199563i
$218$	−3927.54			−1.22021
$219$		0			0
$220$	−172.326	−	30.5343i	−0.0528101	−	0.00935737i
$221$	577.964	+	419.915i	0.175919	+	0.127812i
$222$		0			0
$223$	−575.194	+	1770.27i	−0.172726	+	0.531595i	−0.999522	−	0.0309059i	$-0.990161\pi$
$223$	−575.194	+	1770.27i	−0.172726	+	0.531595i	0.826797	+	0.562501i	$0.190161\pi$
$224$	−101.731			−0.0303445
$225$		0			0
$226$	−3125.98			−0.920076
$227$	405.456	−	1247.86i	0.118551	−	0.364862i	−0.874120	−	0.485710i	$-0.838561\pi$
$227$	405.456	−	1247.86i	0.118551	−	0.364862i	0.992671	+	0.120848i	$0.0385612\pi$
$228$		0			0
$229$	3473.56	+	2523.69i	1.00236	+	0.728255i	0.962592	−	0.270955i	$-0.0873393\pi$
$229$	3473.56	+	2523.69i	1.00236	+	0.728255i	0.0397643	+	0.999209i	$0.487339\pi$
$230$	922.623	+	6604.86i	0.264504	+	1.89353i
$231$		0			0
$232$	1602.87			0.453594
$233$	−355.013	+	257.932i	−0.0998184	+	0.0725223i	−0.636575	−	0.771215i	$-0.719649\pi$
$233$	−355.013	+	257.932i	−0.0998184	+	0.0725223i	0.536756	+	0.843737i	$0.319649\pi$
$234$		0			0
$235$	−238.611	−	1708.16i	−0.0662351	−	0.474163i
$236$	−2.94212	+	9.05492i	−0.000811508	+	0.00249756i
$237$		0			0
$238$	81.4226	+	250.593i	0.0221758	+	0.0682501i
$239$	1047.42	−	3223.62i	0.283480	−	0.872462i	−0.703370	−	0.710824i	$-0.748322\pi$
$239$	1047.42	−	3223.62i	0.283480	−	0.872462i	0.986850	−	0.161638i	$-0.0516777\pi$
$240$		0			0
$241$	−850.354	−	2617.12i	−0.227287	−	0.699517i	−0.998051	−	0.0623969i	$-0.980126\pi$
$241$	−850.354	−	2617.12i	−0.227287	−	0.699517i	0.770765	−	0.637120i	$-0.219874\pi$
$242$	−2579.03	+	1873.77i	−0.685067	+	0.497730i
$243$		0			0
$244$	144.201	−	104.768i	0.0378340	−	0.0274880i
$245$	−2264.12	−	2348.49i	−0.590406	−	0.612407i
$246$		0			0
$247$	6692.59	+	4862.45i	1.72405	+	1.25259i
$248$	1080.10	−	3324.21i	0.276559	−	0.851160i
$249$		0			0
$250$	1566.99	+	3543.41i	0.396421	+	0.896419i
$251$	3369.50			0.847334			0.423667	−	0.905818i	$-0.360743\pi$
$251$	3369.50			0.847334			0.423667	+	0.905818i	$0.360743\pi$
$252$		0			0
$253$	−8670.09	−	6299.19i	−2.15448	−	1.56532i
$254$	2141.10	+	1555.60i	0.528914	+	0.384279i
$255$		0			0
$256$	389.919	−	283.293i	0.0951951	−	0.0691633i
$257$	4556.70			1.10599			0.552994	−	0.833185i	$-0.313485\pi$
$257$	4556.70			1.10599			0.552994	+	0.833185i	$0.313485\pi$
$258$		0			0
$259$	659.144	+	2028.64i	0.158136	+	0.486692i
$260$	−169.964	+	82.7211i	−0.0405412	+	0.0197313i
$261$		0			0
$262$	−1263.54	−	3888.77i	−0.297945	−	0.916981i
$263$	1302.86	+	4009.78i	0.305466	+	0.940129i	0.979503	+	0.201431i	$0.0645590\pi$
$263$	1302.86	+	4009.78i	0.305466	+	0.940129i	−0.674036	+	0.738698i	$0.735441\pi$
$264$		0			0
$265$	−75.6570	−	541.612i	−0.0175380	−	0.125551i
$266$	942.841	+	2901.77i	0.217328	+	0.668867i
$267$		0			0
$268$	−216.433			−0.0493311
$269$	525.519	−	381.812i	0.119113	−	0.0865408i	−0.526634	−	0.850092i	$-0.676546\pi$
$269$	525.519	−	381.812i	0.119113	−	0.0865408i	0.645747	+	0.763551i	$0.276546\pi$
$270$		0			0
$271$	−1185.38	−	861.228i	−0.265707	−	0.193047i	0.446952	−	0.894558i	$-0.352509\pi$
$271$	−1185.38	−	861.228i	−0.265707	−	0.193047i	−0.712659	+	0.701510i	$0.752509\pi$
$272$	−659.505	−	479.159i	−0.147016	−	0.106813i
$273$		0			0
$274$	−2572.41			−0.567172
$275$	−5847.02	−	2139.22i	−1.28214	−	0.469090i
$276$		0			0
$277$	711.145	−	2188.68i	0.154255	−	0.474747i	−0.843830	−	0.536611i	$-0.819704\pi$
$277$	711.145	−	2188.68i	0.154255	−	0.474747i	0.998085	+	0.0618637i	$0.0197044\pi$
$278$	−2071.65	−	1505.14i	−0.446939	−	0.324721i
$279$		0			0
$280$	−1816.12	−	321.797i	−0.387622	−	0.0686823i
$281$	6769.19	−	4918.10i	1.43707	−	1.04409i	0.448423	−	0.893822i	$-0.351986\pi$
$281$	6769.19	−	4918.10i	1.43707	−	1.04409i	0.988645	−	0.150269i	$-0.0480140\pi$
$282$		0			0
$283$	−470.418	+	341.779i	−0.0988108	+	0.0717903i	−0.636094	−	0.771612i	$-0.719451\pi$
$283$	−470.418	+	341.779i	−0.0988108	+	0.0717903i	0.537283	+	0.843402i	$0.319451\pi$
$284$	82.1740	+	252.906i	0.0171695	+	0.0528422i
$285$		0			0
$286$	−2295.56	+	7064.99i	−0.474612	+	1.46071i
$287$	793.592	+	2442.43i	0.163220	+	0.502341i
$288$		0			0
$289$	−1463.71	+	4504.82i	−0.297925	+	0.916919i
$290$	2122.35	+	376.057i	0.429754	+	0.0761478i
$291$		0			0
$292$	−90.6819	+	65.8843i	−0.0181738	+	0.0132041i
$293$	−2079.50			−0.414627			−0.207313	−	0.978275i	$-0.566472\pi$
$293$	−2079.50			−0.414627			−0.207313	+	0.978275i	$0.566472\pi$
$294$		0			0
$295$	−159.265	+	298.930i	−0.0314330	+	0.0589979i
$296$	−5557.58	−	4037.82i	−1.09131	−	0.792884i
$297$		0			0
$298$	−1708.02	+	5256.74i	−0.332023	+	1.02186i
$299$	−11575.0			−2.23880
$300$		0			0
$301$	−3229.12			−0.618350
$302$	1462.16	−	4500.07i	0.278603	−	0.857451i
$303$		0			0
$304$	−7636.81	−	5548.47i	−1.44079	−	1.04680i
$305$	5701.59	−	2774.95i	1.07040	−	0.520962i
$306$		0			0
$307$	5017.05			0.932698			0.466349	−	0.884601i	$-0.345569\pi$
$307$	5017.05			0.932698			0.466349	+	0.884601i	$0.345569\pi$
$308$	90.6364	−	65.8512i	0.0167678	−	0.0121825i
$309$		0			0
$310$	2210.06	−	4148.16i	0.404913	−	0.759998i
$311$	−926.375	+	2851.09i	−0.168906	+	0.519841i	−0.999303	−	0.0373323i	$-0.988114\pi$
$311$	−926.375	+	2851.09i	−0.168906	+	0.519841i	0.830396	+	0.557173i	$0.188114\pi$
$312$		0			0
$313$	−1432.91	−	4410.05i	−0.258763	−	0.796392i	−0.993065	−	0.117568i	$-0.962490\pi$
$313$	−1432.91	−	4410.05i	−0.258763	−	0.796392i	0.734302	−	0.678823i	$-0.237510\pi$
$314$	419.117	−	1289.91i	0.0753253	−	0.231827i
$315$		0			0
$316$	−19.0190	−	58.5344i	−0.00338576	−	0.0104203i
$317$	−1121.63	+	814.913i	−0.198729	+	0.144385i	−0.682699	−	0.730699i	$-0.739194\pi$
$317$	−1121.63	+	814.913i	−0.198729	+	0.144385i	0.483971	+	0.875084i	$0.339194\pi$
$318$		0			0
$319$	−2802.17	+	2035.89i	−0.491822	+	0.357329i
$320$	5333.09	−	2595.61i	0.931653	−	0.453434i
$321$		0			0
$322$	−3453.81	−	2509.34i	−0.597743	−	0.434286i
$323$	631.021	−	1942.08i	0.108703	−	0.334552i
$324$		0			0
$325$	−6467.23	+	1842.75i	−1.10381	+	0.314516i
$326$	−9553.34			−1.62304
$327$		0			0
$328$	−6691.19	−	4861.43i	−1.12640	−	0.818377i
$329$	893.232	+	648.971i	0.149682	+	0.108751i
$330$		0			0
$331$	−6494.76	+	4718.72i	−1.07850	+	0.783578i	−0.977421	−	0.211300i	$-0.932230\pi$
$331$	−6494.76	+	4718.72i	−1.07850	+	0.783578i	−0.101081	+	0.994878i	$0.532230\pi$
$332$	−225.338			−0.0372500
$333$		0			0
$334$	−793.117	−	2440.96i	−0.129932	−	0.399891i
$335$	−7581.58	−	1343.37i	−1.23650	−	0.219093i
$336$		0			0
$337$	2266.96	+	6976.97i	0.366436	+	1.12777i	0.949077	+	0.315045i	$0.102019\pi$
$337$	2266.96	+	6976.97i	0.366436	+	1.12777i	−0.582641	+	0.812730i	$0.697981\pi$
$338$	597.229	+	1838.08i	0.0961094	+	0.295794i
$339$		0			0
$340$	32.3846	+	33.5914i	0.00516560	+	0.00535809i
$341$	2334.00	+	7183.33i	0.370655	+	1.14076i
$342$		0			0
$343$	4543.15			0.715180
$344$	8413.42	−	6112.71i	1.31867	−	0.958067i
$345$		0			0
$346$	1453.44	+	1055.99i	0.225831	+	0.164076i
$347$	−5317.34	−	3863.27i	−0.822621	−	0.597669i	0.0948410	−	0.995492i	$-0.469766\pi$
$347$	−5317.34	−	3863.27i	−0.822621	−	0.597669i	−0.917462	+	0.397823i	$0.869766\pi$
$348$		0			0
$349$	11655.8			1.78774			0.893868	−	0.448331i	$-0.147981\pi$
$349$	11655.8			1.78774			0.893868	+	0.448331i	$0.147981\pi$
$350$	−2329.21	−	852.177i	−0.355719	−	0.130145i
$351$		0			0
$352$	−218.777	+	673.326i	−0.0331274	+	0.101956i
$353$	569.531	+	413.788i	0.0858727	+	0.0623902i	0.629893	−	0.776682i	$-0.283099\pi$
$353$	569.531	+	413.788i	0.0858727	+	0.0623902i	−0.544021	+	0.839072i	$0.683099\pi$
$354$		0			0
$355$	1308.78	+	9369.27i	0.195670	+	1.40076i
$356$	−305.289	+	221.806i	−0.0454503	+	0.0330216i
$357$		0			0
$358$	−4595.16	+	3338.58i	−0.678384	+	0.492875i
$359$	1732.60	+	5332.39i	0.254716	+	0.783935i	0.993885	+	0.110416i	$0.0352182\pi$
$359$	1732.60	+	5332.39i	0.254716	+	0.783935i	−0.739170	+	0.673519i	$0.764782\pi$
$360$		0			0
$361$	5187.42	−	15965.2i	0.756294	−	2.32763i
$362$	−772.342	−	2377.03i	−0.112137	−	0.345121i
$363$		0			0
$364$	37.3924	−	115.082i	0.00538432	−	0.0165712i
$365$	−3585.50	+	1745.06i	−0.514175	+	0.250248i
$366$		0			0
$367$	−1908.15	+	1386.35i	−0.271402	+	0.197185i	−0.715159	−	0.698962i	$-0.753646\pi$
$367$	−1908.15	+	1386.35i	−0.271402	+	0.197185i	0.443756	+	0.896147i	$0.353646\pi$
$368$	13208.1			1.87097
$369$		0			0
$370$	−6411.42	−	6650.34i	−0.900848	−	0.934418i
$371$	283.220	+	205.771i	0.0396335	+	0.0287954i
$372$		0			0
$373$	−1665.42	+	5125.62i	−0.231185	+	0.711514i	0.766420	+	0.642340i	$0.222036\pi$
$373$	−1665.42	+	5125.62i	−0.231185	+	0.711514i	−0.997605	+	0.0691739i	$0.977964\pi$
$374$	1833.71			0.253526
$375$		0			0
$376$	−3555.80			−0.487703
$377$	−1156.04	+	3557.94i	−0.157929	+	0.486056i
$378$		0			0
$379$	2275.81	+	1653.47i	0.308445	+	0.224098i	0.731229	−	0.682132i	$-0.238947\pi$
$379$	2275.81	+	1653.47i	0.308445	+	0.224098i	−0.422784	+	0.906230i	$0.638947\pi$
$380$	375.001	+	388.975i	0.0506241	+	0.0525106i
$381$		0			0
$382$	−8065.81			−1.08032
$383$	−7657.03	+	5563.16i	−1.02156	+	0.742204i	−0.966601	−	0.256285i	$-0.917501\pi$
$383$	−7657.03	+	5563.16i	−1.02156	+	0.742204i	−0.0549545	+	0.998489i	$0.517501\pi$
$384$		0			0
$385$	3583.70	−	1744.18i	0.474396	−	0.230888i
$386$	158.357	−	487.371i	0.0208812	−	0.0642657i
$387$		0			0
$388$	−120.195	−	369.923i	−0.0157268	−	0.0484020i
$389$	4368.83	−	13445.9i	0.569431	−	1.75253i	−0.0849726	−	0.996383i	$-0.527080\pi$
$389$	4368.83	−	13445.9i	0.569431	−	1.75253i	0.654404	−	0.756145i	$-0.272920\pi$
$390$		0			0
$391$	882.934	+	2717.39i	0.114199	+	0.351469i
$392$	−5440.94	+	3953.08i	−0.701044	+	0.509338i
$393$		0			0
$394$	−7149.50	+	5194.41i	−0.914179	+	0.664190i
$395$	−302.914	−	2168.49i	−0.0385854	−	0.276225i
$396$		0			0
$397$	−11467.9	−	8331.93i	−1.44977	−	1.05332i	−0.985885	−	0.167423i	$-0.946455\pi$
$397$	−11467.9	−	8331.93i	−1.44977	−	1.05332i	−0.463884	−	0.885896i	$-0.653545\pi$
$398$	1755.00	−	5401.34i	0.221031	−	0.680264i
$399$		0			0
$400$	7379.65	−	2102.74i	0.922457	−	0.262842i
$401$	−5740.98			−0.714940			−0.357470	−	0.933925i	$-0.616361\pi$
$401$	−5740.98			−0.714940			−0.357470	+	0.933925i	$0.616361\pi$
$402$		0			0
$403$	6599.83	+	4795.06i	0.815784	+	0.592702i
$404$	92.9092	+	67.5025i	0.0114416	+	0.00831281i
$405$		0			0
$406$	−1116.27	+	811.017i	−0.136452	+	0.0991382i
$407$	14844.5			1.80790
$408$		0			0
$409$	312.072	+	960.459i	0.0377285	+	0.116117i	0.968147	−	0.250382i	$-0.0805563\pi$
$409$	312.072	+	960.459i	0.0377285	+	0.116117i	−0.930418	+	0.366499i	$0.880556\pi$
$410$	−7719.18	−	8006.83i	−0.929813	−	0.964462i
$411$		0			0
$412$	−18.8516	−	58.0193i	−0.00225425	−	0.00693788i
$413$	−67.0026	−	206.213i	−0.00798300	−	0.0245692i
$414$		0			0
$415$	−7893.52	−	1398.65i	−0.933681	−	0.165438i
$416$	236.296	+	727.246i	0.0278495	+	0.0857119i
$417$		0			0
$418$	21233.6			2.48462
$419$	1306.11	−	948.947i	0.152286	−	0.110642i	−0.509033	−	0.860747i	$-0.669997\pi$
$419$	1306.11	−	948.947i	0.152286	−	0.110642i	0.661319	+	0.750105i	$0.269997\pi$
$420$		0			0
$421$	7924.08	+	5757.18i	0.917330	+	0.666480i	0.942858	−	0.333195i	$-0.108127\pi$
$421$	7924.08	+	5757.18i	0.917330	+	0.666480i	−0.0255276	+	0.999674i	$0.508127\pi$
$422$	6685.36	+	4857.20i	0.771181	+	0.560296i
$423$		0			0
$424$	−1127.45			−0.129136
$425$	925.928	+	1377.71i	0.105680	+	0.157244i
$426$		0			0
$427$	−1254.36	+	3860.53i	−0.142161	+	0.437527i
$428$	72.7893	+	52.8845i	0.00822057	+	0.00597259i
$429$		0			0
$430$	12574.3	−	6119.88i	1.41020	−	0.686341i
$431$	−2915.55	+	2118.27i	−0.325840	+	0.236736i	−0.738663	−	0.674075i	$-0.764543\pi$
$431$	−2915.55	+	2118.27i	−0.325840	+	0.236736i	0.412824	+	0.910811i	$0.364543\pi$
$432$		0			0
$433$	8305.22	−	6034.09i	0.921763	−	0.669700i	−0.0221993	−	0.999754i	$-0.507067\pi$
$433$	8305.22	−	6034.09i	0.921763	−	0.669700i	0.943962	+	0.330054i	$0.107067\pi$
$434$	929.773	+	2861.55i	0.102835	+	0.316494i
$435$		0			0
$436$	137.583	−	423.438i	0.0151125	−	0.0465115i
$437$	10224.0	+	31466.3i	1.11918	+	3.44448i
$438$		0			0
$439$	4195.10	−	12911.2i	0.456084	−	1.40368i	−0.413773	−	0.910380i	$-0.635789\pi$
$439$	4195.10	−	12911.2i	0.456084	−	1.40368i	0.869858	−	0.493303i	$-0.164211\pi$
$440$	−6035.55	+	11328.4i	−0.653940	+	1.22741i
$441$		0			0
$442$	1602.30	−	1164.14i	0.172429	−	0.125277i
$443$	16740.4			1.79540			0.897699	−	0.440609i	$-0.145238\pi$
$443$	16740.4			1.79540			0.897699	+	0.440609i	$0.145238\pi$
$444$		0			0
$445$	−12070.9	+	5874.90i	−1.28588	+	0.625836i
$446$	4174.77	+	3033.15i	0.443231	+	0.322026i
$447$		0			0
$448$	−1173.29	+	3611.02i	−0.123734	+	0.380814i
$449$	−18160.7			−1.90882			−0.954408	−	0.298505i	$-0.903512\pi$
$449$	−18160.7			−1.90882			−0.954408	+	0.298505i	$0.903512\pi$
$450$		0			0
$451$	17872.4			1.86603
$452$	109.504	−	337.020i	0.0113952	−	0.0350710i
$453$		0			0
$454$	−2942.80	−	2138.07i	−0.304213	−	0.221024i
$455$	2024.15	−	3799.20i	0.208557	−	0.391449i
$456$		0			0
$457$	2032.75			0.208070			0.104035	−	0.994574i	$-0.466825\pi$
$457$	2032.75			0.208070			0.104035	+	0.994574i	$0.466825\pi$
$458$	9629.81	−	6996.47i	0.982471	−	0.713807i
$459$		0			0
$460$	−744.406	−	131.901i	−0.0754524	−	0.0133693i
$461$	−1858.95	+	5721.26i	−0.187809	+	0.578017i	−0.999985	−	0.00539516i	$-0.998283\pi$
$461$	−1858.95	+	5721.26i	−0.187809	+	0.578017i	0.812176	+	0.583412i	$0.198283\pi$
$462$		0			0
$463$	1811.95	+	5576.62i	0.181876	+	0.559757i	0.999881	−	0.0154550i	$-0.00491968\pi$
$463$	1811.95	+	5576.62i	0.181876	+	0.559757i	−0.818005	+	0.575212i	$0.804920\pi$
$464$	1319.14	−	4059.90i	0.131982	−	0.406199i
$465$		0			0
$466$	375.934	+	1157.01i	0.0373709	+	0.115016i
$467$	−7272.50	+	5283.78i	−0.720624	+	0.523564i	−0.886583	−	0.462569i	$-0.846928\pi$
$467$	−7272.50	+	5283.78i	−0.720624	+	0.523564i	0.165960	+	0.986133i	$0.446928\pi$
$468$		0			0
$469$	3987.60	−	2897.16i	0.392602	−	0.285242i
$470$	−4708.21	−	834.242i	−0.462071	−	0.0818739i
$471$		0			0
$472$	564.933	+	410.448i	0.0550915	+	0.0400263i
$473$	−6944.39	+	21372.6i	−0.675060	+	2.07762i
$474$		0			0
$475$	10721.9	+	15953.3i	1.03569	+	1.54103i
$476$	−29.8693			−0.00287617
$477$		0			0
$478$	−7602.16	−	5523.30i	−0.727437	−	0.528514i
$479$	5375.66	+	3905.65i	0.512777	+	0.372554i	0.813876	−	0.581039i	$-0.197353\pi$
$479$	5375.66	+	3905.65i	0.512777	+	0.372554i	−0.301099	+	0.953593i	$0.597353\pi$
$480$		0			0
$481$	12971.2	−	9424.10i	1.22959	−	0.893351i
$482$	−7628.87			−0.720924
$483$		0			0
$484$	−111.672	−	343.690i	−0.0104876	−	0.0322774i
$485$	−1914.34	−	13704.3i	−0.179228	−	1.28306i
$486$		0			0
$487$	2239.85	+	6893.56i	0.208414	+	0.641431i	0.999556	+	0.0297992i	$0.00948677\pi$
$487$	2239.85	+	6893.56i	0.208414	+	0.641431i	−0.791142	+	0.611632i	$0.790513\pi$
$488$	−4039.74	−	12433.0i	−0.374734	−	1.15331i
$489$		0			0
$490$	−8131.76	+	3957.71i	−0.749705	+	0.364880i
$491$	−4273.47	−	13152.4i	−0.392788	−	1.20888i	−0.930671	−	0.365858i	$-0.880776\pi$
$491$	−4273.47	−	13152.4i	−0.392788	−	1.20888i	0.537883	−	0.843020i	$-0.319224\pi$
$492$		0			0
$493$	923.456			0.0843618
$494$	18554.0	−	13480.2i	1.68984	−	1.22774i
$495$		0			0
$496$	−7530.96	−	5471.56i	−0.681754	−	0.495323i
$497$	−4899.38	−	3559.61i	−0.442187	−	0.321268i
$498$		0			0
$499$	9216.11			0.826793			0.413397	−	0.910551i	$-0.364342\pi$
$499$	9216.11			0.826793			0.413397	+	0.910551i	$0.364342\pi$
$500$	−436.916	+	44.8142i	−0.0390789	+	0.00400831i
$501$		0			0
$502$	2886.62	−	8884.12i	0.256646	−	0.789876i
$503$	10276.2	+	7466.09i	0.910919	+	0.661822i	0.941247	−	0.337718i	$-0.109655\pi$
$503$	10276.2	+	7466.09i	0.910919	+	0.661822i	−0.0303278	+	0.999540i	$0.509655\pi$
$504$		0			0
$505$	2835.61	+	2941.27i	0.249867	+	0.259178i
$506$	−24036.2	+	17463.3i	−2.11174	+	1.53427i
$507$		0			0
$508$	−242.716	+	176.344i	−0.0211984	+	0.0154015i
$509$	−2793.42	−	8597.26i	−0.243254	−	0.748658i	−0.995919	−	0.0902544i	$-0.971232\pi$
$509$	−2793.42	−	8597.26i	−0.243254	−	0.748658i	0.752665	−	0.658404i	$-0.228768\pi$
$510$		0			0
$511$	788.817	−	2427.73i	0.0682881	−	0.210169i
$512$	−3767.60	−	11595.5i	−0.325207	−	1.00088i
$513$		0			0
$514$	3903.69	−	12014.3i	0.334989	−	1.03099i
$515$	−300.248	−	2149.41i	−0.0256903	−	0.183911i
$516$		0			0
$517$	6216.30	−	4516.41i	0.528806	−	0.384200i
$518$	5913.44			0.501586
$519$		0			0
$520$	1917.99	+	13730.4i	0.161749	+	1.15792i
$521$	−10554.5	−	7668.29i	−0.887526	−	0.644825i	0.0477059	−	0.998861i	$-0.484809\pi$
$521$	−10554.5	−	7668.29i	−0.887526	−	0.644825i	−0.935232	+	0.354036i	$0.884809\pi$
$522$		0			0
$523$	−3201.49	+	9853.17i	−0.267670	+	0.823803i	0.723396	+	0.690433i	$0.242580\pi$
$523$	−3201.49	+	9853.17i	−0.267670	+	0.823803i	−0.991066	+	0.133370i	$0.957420\pi$
$524$	463.520			0.0386431
$525$		0			0
$526$	11688.5			0.968899
$527$	622.274	−	1915.16i	0.0514359	−	0.158303i
$528$		0			0
$529$	−27609.3	−	20059.3i	−2.26920	−	1.64867i
$530$	−1492.84	−	264.516i	−0.122349	−	0.0216789i
$531$		0			0
$532$	−345.875			−0.0281872
$533$	15616.9	−	11346.4i	1.26913	−	0.922074i
$534$		0			0
$535$	2221.54	+	2304.33i	0.179525	+	0.186214i
$536$	−4905.31	+	15097.0i	−0.395293	+	1.21659i
$537$		0			0
$538$	−556.487	−	1712.69i	−0.0445946	−	0.137248i
$539$	4490.92	−	13821.6i	0.358883	−	1.10453i
$540$		0			0
$541$	−1162.41	−	3577.53i	−0.0923770	−	0.284307i	0.894184	−	0.447699i	$-0.147756\pi$
$541$	−1162.41	−	3577.53i	−0.0923770	−	0.284307i	−0.986561	+	0.163392i	$0.947756\pi$
$542$	−3286.24	+	2387.59i	−0.260436	+	0.189218i
$543$		0			0
$544$	152.706	−	110.948i	0.0120353	−	0.00874419i
$545$	7447.74	−	13979.0i	0.585369	−	1.09870i
$546$		0			0
$547$	7890.38	+	5732.70i	0.616761	+	0.448103i	0.851789	−	0.523886i	$-0.175518\pi$
$547$	7890.38	+	5732.70i	0.616761	+	0.448103i	−0.235028	+	0.971989i	$0.575518\pi$
$548$	90.1127	−	277.338i	0.00702449	−	0.0216192i
$549$		0			0
$550$	−10649.4	+	13583.8i	−0.825623	+	1.05312i
$551$	10693.3			0.826766
$552$		0			0
$553$	1133.95	+	823.861i	0.0871978	+	0.0633529i
$554$	−5161.50	−	3750.05i	−0.395832	−	0.287589i
$555$		0			0
$556$	234.844	−	170.624i	0.0179129	−	0.0130145i
$557$	16009.1			1.21783			0.608913	−	0.793237i	$-0.291606\pi$
$557$	16009.1			1.21783			0.608913	+	0.793237i	$0.291606\pi$
$558$		0			0
$559$	7500.49	+	23084.1i	0.567508	+	1.74661i
$560$	−2309.72	+	4335.21i	−0.174292	+	0.327135i
$561$		0			0
$562$	−7168.10	−	22061.1i	−0.538021	−	1.65586i
$563$	−850.464	−	2617.46i	−0.0636639	−	0.195937i	0.914165	−	0.405342i	$-0.132847\pi$
$563$	−850.464	−	2617.46i	−0.0636639	−	0.195937i	−0.977829	+	0.209404i	$0.932847\pi$
$564$		0			0
$565$	5927.75	−	11126.0i	0.441385	−	0.828453i
$566$	498.140	+	1533.12i	0.0369936	+	0.113855i
$567$		0			0
$568$	19503.6			1.44076
$569$	4062.83	−	2951.82i	0.299337	−	0.217481i	−0.427971	−	0.903793i	$-0.640771\pi$
$569$	4062.83	−	2951.82i	0.299337	−	0.217481i	0.727308	+	0.686312i	$0.240771\pi$
$570$		0			0
$571$	10.2190	+	7.42452i	0.000748950	+	0.000544144i	0.588160	−	0.808745i	$-0.299853\pi$
$571$	10.2190	+	7.42452i	0.000748950	+	0.000544144i	−0.587411	+	0.809289i	$0.699853\pi$
$572$	−681.280	−	494.979i	−0.0498003	−	0.0361820i
$573$		0			0
$574$	7119.63			0.517714
$575$	−25257.7	−	9240.89i	−1.83186	−	0.670212i
$576$		0			0
$577$	−5786.32	+	17808.5i	−0.417483	+	1.28488i	0.492528	+	0.870296i	$0.336073\pi$
$577$	−5786.32	+	17808.5i	−0.417483	+	1.28488i	−0.910011	+	0.414584i	$0.863927\pi$
$578$	10623.6	+	7718.50i	0.764504	+	0.555445i
$579$		0			0
$580$	−114.891	+	215.643i	−0.00822512	+	0.0154381i
$581$	4151.66	−	3016.36i	0.296455	−	0.215387i
$582$		0			0
$583$	1971.02	−	1432.03i	0.140019	−	0.101730i
$584$	2540.43	+	7818.64i	0.180006	+	0.554002i
$585$		0			0
$586$	−1781.49	+	5482.86i	−0.125585	+	0.386510i
$587$	5487.34	+	16888.3i	0.385838	+	1.18749i	0.935871	+	0.352344i	$0.114615\pi$
$587$	5487.34	+	16888.3i	0.385838	+	1.18749i	−0.550033	+	0.835143i	$0.685385\pi$
$588$		0			0
$589$	7205.69	−	22176.8i	0.504084	−	1.55141i
$590$	651.727	+	676.013i	0.0454765	+	0.0471712i
$591$		0			0
$592$	−14801.2	+	10753.7i	−1.02758	+	0.746577i
$593$	−22731.1			−1.57413			−0.787063	−	0.616873i	$-0.788399\pi$
$593$	−22731.1			−1.57413			−0.787063	+	0.616873i	$0.788399\pi$
$594$		0			0
$595$	−1046.31	−	185.395i	−0.0720919	−	0.0127739i
$596$	−506.909	−	368.291i	−0.0348386	−	0.0253117i
$597$		0			0
$598$	−9916.23	+	30519.0i	−0.678102	+	2.08698i
$599$	−13575.9			−0.926036			−0.463018	−	0.886349i	$-0.653233\pi$
$599$	−13575.9			−0.926036			−0.463018	+	0.886349i	$0.653233\pi$
$600$		0			0
$601$	−28512.0			−1.93516			−0.967578	−	0.252573i	$-0.918723\pi$
$601$	−28512.0			−1.93516			−0.967578	+	0.252573i	$0.918723\pi$
$602$	−2766.36	+	8513.99i	−0.187290	+	0.576419i
$603$		0			0
$604$	433.944	+	315.279i	0.0292333	+	0.0212393i
$605$	−1778.59	−	12732.5i	−0.119520	−	0.855621i
$606$		0			0
$607$	−23489.6			−1.57070			−0.785349	−	0.619053i	$-0.787517\pi$
$607$	−23489.6			−1.57070			−0.785349	+	0.619053i	$0.787517\pi$
$608$	1768.28	−	1284.73i	0.117949	−	0.0856951i
$609$		0			0
$610$	−2432.01	−	17410.3i	−0.161425	−	1.15561i
$611$	2564.56	−	7892.89i	0.169805	−	0.522606i
$612$		0			0
$613$	−6495.01	−	19989.6i	−0.427946	−	1.31708i	−0.900145	−	0.435590i	$-0.856540\pi$
$613$	−6495.01	−	19989.6i	−0.427946	−	1.31708i	0.472199	−	0.881492i	$-0.343460\pi$
$614$	4298.07	−	13228.1i	0.282502	−	0.869451i
$615$		0			0
$616$	−2539.15	−	7814.71i	−0.166080	−	0.511142i
$617$	−3053.20	+	2218.28i	−0.199217	+	0.144740i	−0.682922	−	0.730492i	$-0.739291\pi$
$617$	−3053.20	+	2218.28i	−0.199217	+	0.144740i	0.483704	+	0.875231i	$0.339291\pi$
$618$		0			0
$619$	−13979.6	+	10156.8i	−0.907736	+	0.659509i	−0.940441	−	0.339956i	$-0.889588\pi$
$619$	−13979.6	+	10156.8i	−0.907736	+	0.659509i	0.0327052	+	0.999465i	$0.489588\pi$
$620$	369.804	+	383.584i	0.0239543	+	0.0248469i
$621$		0			0
$622$	6723.64	+	4885.01i	0.433430	+	0.314905i
$623$	2655.63	−	8173.18i	0.170779	−	0.525604i
$624$		0			0
$625$	−15583.2	−	1142.05i	−0.997325	−	0.0730915i
$626$	−12855.2			−0.820763
$627$		0			0
$628$	124.387	+	90.3721i	0.00790376	+	0.00574242i
$629$	−3201.87	−	2326.29i	−0.202968	−	0.147465i
$630$		0			0
$631$	7560.47	−	5493.00i	0.476985	−	0.346550i	−0.323172	−	0.946340i	$-0.604749\pi$
$631$	7560.47	−	5493.00i	0.476985	−	0.346550i	0.800157	+	0.599790i	$0.204749\pi$
$632$	−4514.05			−0.284113
$633$		0			0
$634$	1187.73	+	3655.45i	0.0744018	+	0.228985i
$635$	−9596.83	+	4670.76i	−0.599746	+	0.291895i
$636$		0			0
$637$	−4850.55	−	14928.5i	−0.301705	−	0.928552i
$638$	2967.30	+	9132.40i	0.184132	+	0.566701i
$639$		0			0
$640$	−2098.95	−	15025.9i	−0.129638	−	0.928049i
$641$	1411.17	+	4343.13i	0.0869544	+	0.267618i	0.985074	−	0.172134i	$-0.0550663\pi$
$641$	1411.17	+	4343.13i	0.0869544	+	0.267618i	−0.898119	+	0.439752i	$0.855066\pi$
$642$		0			0
$643$	−752.275			−0.0461381			−0.0230691	−	0.999734i	$-0.507344\pi$
$643$	−752.275			−0.0461381			−0.0230691	+	0.999734i	$0.507344\pi$
$644$	391.527	−	284.461i	0.0239570	−	0.0174058i
$645$		0			0
$646$	−4579.96	−	3327.53i	−0.278941	−	0.202663i
$647$	20747.7	+	15074.1i	1.26070	+	0.915956i	0.998792	−	0.0491360i	$-0.0156468\pi$
$647$	20747.7	+	15074.1i	1.26070	+	0.915956i	0.261913	+	0.965092i	$0.415647\pi$
$648$		0			0
$649$	−1508.96			−0.0912661
$650$	−681.772	+	18630.4i	−0.0411405	+	1.12422i
$651$		0			0
$652$	334.657	−	1029.97i	0.0201015	−	0.0618661i
$653$	8512.09	+	6184.40i	0.510113	+	0.370619i	0.812866	−	0.582450i	$-0.197906\pi$
$653$	8512.09	+	6184.40i	0.510113	+	0.370619i	−0.302753	+	0.953069i	$0.597906\pi$
$654$		0			0
$655$	16237.0	+	2877.02i	0.968598	+	0.171625i
$656$	−17820.2	+	12947.2i	−1.06061	+	0.770582i
$657$		0			0
$658$	2476.32	−	1799.15i	0.146713	−	0.106593i
$659$	2193.75	+	6751.65i	0.129676	+	0.399100i	0.994724	−	0.102588i	$-0.0327124\pi$
$659$	2193.75	+	6751.65i	0.129676	+	0.399100i	−0.865048	+	0.501688i	$0.832712\pi$
$660$		0			0
$661$	−6944.82	+	21373.9i	−0.408657	+	1.25772i	0.509146	+	0.860680i	$0.329961\pi$
$661$	−6944.82	+	21373.9i	−0.408657	+	1.25772i	−0.917803	+	0.397036i	$0.870039\pi$
$662$	6877.50	+	21166.8i	0.403779	+	1.24270i
$663$		0			0
$664$	−5107.14	+	15718.2i	−0.298487	+	0.918649i
$665$	−12115.9	−	2146.81i	−0.706518	−	0.125187i
$666$		0			0
$667$	−12104.7	+	8794.55i	−0.702690	+	0.510534i
$668$	290.950			0.0168521
$669$		0			0
$670$	−10037.1	+	18839.0i	−0.578754	+	1.08629i
$671$	22854.2	+	16604.5i	1.31487	+	0.955306i
$672$		0			0
$673$	−9009.19	+	27727.4i	−0.516016	+	1.58813i	0.265409	+	0.964136i	$0.414493\pi$
$673$	−9009.19	+	27727.4i	−0.516016	+	1.58813i	−0.781426	+	0.623999i	$0.785507\pi$
$674$	20337.8			1.16229
$675$		0			0
$676$	−219.089			−0.0124653
$677$	4869.04	−	14985.4i	0.276414	−	0.850716i	−0.712428	−	0.701746i	$-0.752404\pi$
$677$	4869.04	−	14985.4i	0.276414	−	0.850716i	0.988842	−	0.148970i	$-0.0475957\pi$
$678$		0			0
$679$	7166.27	+	5206.60i	0.405031	+	0.294272i
$680$	3077.11	−	1497.62i	0.173532	−	0.0844576i
$681$		0			0
$682$	20939.3			1.17567
$683$	−9068.24	+	6588.47i	−0.508033	+	0.369108i	−0.812077	−	0.583550i	$-0.801663\pi$
$683$	−9068.24	+	6588.47i	−0.508033	+	0.369108i	0.304044	+	0.952658i	$0.401663\pi$
$684$		0			0
$685$	4878.03	−	9155.77i	0.272088	−	0.510692i
$686$	3892.08	−	11978.6i	0.216618	−	0.666683i
$687$		0			0
$688$	−8558.69	−	26340.9i	−0.474269	−	1.45965i
$689$	813.152	−	2502.62i	0.0449617	−	0.138378i
$690$		0			0
$691$	570.544	+	1755.95i	0.0314103	+	0.0966709i	0.965533	−	0.260282i	$-0.0838156\pi$
$691$	570.544	+	1755.95i	0.0314103	+	0.0966709i	−0.934122	+	0.356953i	$0.883816\pi$
$692$	−164.763	+	119.708i	−0.00905111	+	0.00657601i
$693$		0			0
$694$	−14741.3	+	10710.2i	−0.806301	+	0.585812i
$695$	9285.55	−	4519.26i	0.506793	−	0.246655i
$696$		0			0
$697$	−3854.96	−	2800.79i	−0.209494	−	0.152206i
$698$	9985.42	−	30732.0i	0.541481	−	1.66651i
$699$		0			0
$700$	173.469	−	221.266i	0.00936643	−	0.0119473i
$701$	−8002.88			−0.431191			−0.215595	−	0.976483i	$-0.569169\pi$
$701$	−8002.88			−0.431191			−0.215595	+	0.976483i	$0.569169\pi$
$702$		0			0
$703$	−37076.3	−	26937.5i	−1.98913	−	1.44519i
$704$	21377.1	+	15531.4i	1.14443	+	0.831477i
$705$		0			0
$706$	1578.92	−	1147.15i	0.0841691	−	0.0611524i
$707$	−2615.36			−0.139124
$708$		0			0
$709$	−2060.93	−	6342.89i	−0.109168	−	0.335983i	0.881518	−	0.472150i	$-0.156522\pi$
$709$	−2060.93	−	6342.89i	−0.109168	−	0.335983i	−0.990686	+	0.136166i	$0.956522\pi$
$710$	25824.5	+	4575.82i	1.36504	+	0.241869i
$711$		0			0
$712$	8552.59	+	26322.2i	0.450171	+	1.38548i
$713$	10082.3	+	31030.2i	0.529573	+	1.62986i
$714$		0			0
$715$	−20792.8	−	21567.6i	−1.08756	−	1.12809i
$716$	−198.970	−	612.367i	−0.0103853	−	0.0319626i
$717$		0			0
$718$	15543.8			0.807926
$719$	−6078.70	+	4416.43i	−0.315295	+	0.229075i	−0.734165	−	0.678971i	$-0.762426\pi$
$719$	−6078.70	+	4416.43i	−0.315295	+	0.229075i	0.418870	+	0.908046i	$0.362426\pi$
$720$		0			0
$721$	1123.97	+	816.612i	0.0580566	+	0.0421806i
$722$	−37650.4	−	27354.6i	−1.94072	−	1.41002i
$723$		0			0
$724$	283.329			0.0145440
$725$	−5363.06	+	6840.79i	−0.274729	+	0.350429i
$726$		0			0
$727$	10212.2	−	31429.8i	0.520974	−	1.60339i	−0.251169	−	0.967943i	$-0.580815\pi$
$727$	10212.2	−	31429.8i	0.520974	−	1.60339i	0.772142	−	0.635449i	$-0.219185\pi$
$728$	−7179.92	−	5216.52i	−0.365530	−	0.265573i
$729$		0			0
$730$	1529.40	+	10948.6i	0.0775417	+	0.555105i
$731$	4847.19	−	3521.69i	0.245253	−	0.178186i
$732$		0			0
$733$	12580.8	−	9140.51i	0.633948	−	0.460590i	−0.223818	−	0.974631i	$-0.571852\pi$
$733$	12580.8	−	9140.51i	0.633948	−	0.460590i	0.857766	+	0.514041i	$0.171852\pi$
$734$	2020.60	+	6218.76i	0.101610	+	0.312723i
$735$		0			0
$736$	−945.062	+	2908.60i	−0.0473308	+	0.145669i
$737$	−10599.9	−	32623.3i	−0.529788	−	1.63052i
$738$		0			0
$739$	−2576.39	+	7929.33i	−0.128247	+	0.394702i	−0.994479	−	0.104940i	$-0.966535\pi$
$739$	−2576.39	+	7929.33i	−0.128247	+	0.394702i	0.866232	+	0.499642i	$0.166535\pi$
$740$	941.584	−	458.267i	0.0467747	−	0.0227652i
$741$		0			0
$742$	785.174	−	570.463i	0.0388472	−	0.0282242i
$743$	−9492.12			−0.468684			−0.234342	−	0.972154i	$-0.575294\pi$
$743$	−9492.12			−0.468684			−0.234342	+	0.972154i	$0.575294\pi$
$744$		0			0
$745$	−15471.0	−	16047.5i	−0.760822	−	0.789173i
$746$	12087.6	+	8782.17i	0.593243	+	0.431016i
$747$		0			0
$748$	−64.2355	+	197.696i	−0.00313995	+	0.00966377i
$749$	−2048.99			−0.0999581
$750$		0			0
$751$	8136.39			0.395341			0.197671	−	0.980269i	$-0.436662\pi$
$751$	8136.39			0.395341			0.197671	+	0.980269i	$0.436662\pi$
$752$	−2926.37	+	9006.45i	−0.141907	+	0.436744i
$753$		0			0
$754$	8390.58	+	6096.11i	0.405261	+	0.294439i
$755$	13244.0	+	13737.6i	0.638411	+	0.662201i
$756$		0			0
$757$	6875.91			0.330131			0.165066	−	0.986283i	$-0.447216\pi$
$757$	6875.91			0.330131			0.165066	+	0.986283i	$0.447216\pi$
$758$	6309.27	−	4583.95i	0.302326	−	0.219653i
$759$		0			0
$760$	35631.7	−	17341.9i	1.70065	−	0.827705i
$761$	5507.46	−	16950.2i	0.262346	−	0.807417i	−0.729947	−	0.683504i	$-0.760455\pi$
$761$	5507.46	−	16950.2i	0.262346	−	0.807417i	0.992293	−	0.123914i	$-0.0395446\pi$
$762$		0			0
$763$	3133.26	+	9643.19i	0.148665	+	0.457545i
$764$	282.548	−	869.595i	0.0133799	−	0.0411791i
$765$		0			0
$766$	8108.26	+	24954.6i	0.382458	+	1.17709i
$767$	−1318.53	+	957.968i	−0.0620722	+	0.0450981i
$768$		0			0
$769$	−18966.1	+	13779.6i	−0.889380	+	0.646173i	−0.935716	−	0.352753i	$-0.885245\pi$
$769$	−18966.1	+	13779.6i	−0.889380	+	0.646173i	0.0463361	+	0.998926i	$0.485245\pi$
$770$	−1528.63	−	10943.1i	−0.0715427	−	0.512159i
$771$		0			0
$772$	46.9974	+	34.1456i	0.00219103	+	0.00159188i
$773$	−4531.20	+	13945.6i	−0.210836	+	0.648886i	0.788587	+	0.614923i	$0.210813\pi$
$773$	−4531.20	+	13945.6i	−0.210836	+	0.648886i	−0.999423	+	0.0339629i	$0.989187\pi$
$774$		0			0
$775$	10573.3	+	15732.2i	0.490068	+	0.729183i
$776$	−28527.7			−1.31969
$777$		0			0
$778$	−31709.1	−	23038.0i	−1.46121	−	1.06163i
$779$	−44638.9	−	32432.1i	−2.05309	−	1.49166i
$780$		0			0
$781$	−34096.4	+	24772.5i	−1.56218	+	1.13499i
$782$	7921.16			0.362225
$783$		0			0
$784$	5534.89	+	17034.6i	0.252136	+	0.775995i
$785$	3796.30	+	3937.77i	0.172606	+	0.179038i
$786$		0			0
$787$	2673.75	+	8228.97i	0.121104	+	0.372720i	0.993171	−	0.116666i	$-0.0372207\pi$
$787$	2673.75	+	8228.97i	0.121104	+	0.372720i	−0.872067	+	0.489387i	$0.837221\pi$
$788$	−309.573	−	952.767i	−0.0139950	−	0.0430722i
$789$		0			0
$790$	−5977.01	−	1059.06i	−0.269180	−	0.0476958i
$791$	2493.80	+	7675.14i	0.112098	+	0.345002i
$792$		0			0
$793$	30511.5			1.36632
$794$	−31792.7	+	23098.7i	−1.42101	+	1.03242i
$795$		0			0
$796$	520.854	+	378.422i	0.0231924	+	0.0168503i
$797$	27916.9	+	20282.8i	1.24074	+	0.901448i	0.997647	−	0.0685556i	$-0.0218390\pi$
$797$	27916.9	+	20282.8i	1.24074	+	0.901448i	0.243090	+	0.970004i	$0.421839\pi$
$798$		0			0
$799$	−2048.59			−0.0907056
$800$	−64.9760	+	1775.56i	−0.00287156	+	0.0784693i
$801$		0			0
$802$	−4918.25	+	15136.8i	−0.216546	+	0.666459i
$803$	−14372.1	−	10441.9i	−0.631605	−	0.458888i
$804$		0			0
$805$	15480.7	−	7534.43i	0.677792	−	0.329880i
$806$	18296.8	−	13293.4i	0.799600	−	0.580943i
$807$		0			0
$808$	6814.29	−	4950.87i	0.296690	−	0.215558i
$809$	1997.67	+	6148.20i	0.0868163	+	0.267193i	0.985035	−	0.172356i	$-0.0551381\pi$
$809$	1997.67	+	6148.20i	0.0868163	+	0.267193i	−0.898218	+	0.439550i	$0.855138\pi$
$810$		0			0
$811$	764.897	−	2354.11i	0.0331186	−	0.101929i	−0.933131	−	0.359537i	$-0.882935\pi$
$811$	764.897	−	2354.11i	0.0331186	−	0.101929i	0.966249	+	0.257609i	$0.0829346\pi$
$812$	−48.3344	−	148.758i	−0.00208892	−	0.00642904i
$813$		0			0
$814$	12717.2	−	39139.4i	0.547588	−	1.68530i
$815$	18115.9	−	34002.4i	0.778615	−	1.46141i
$816$		0			0
$817$	56128.5	−	40779.7i	2.40353	−	1.74627i
$818$	2799.72			0.119670
$819$		0			0
$820$	1133.64	−	551.742i	0.0482787	−	0.0234972i
$821$	−29520.8	−	21448.1i	−1.25491	−	0.911746i	−0.256414	−	0.966567i	$-0.582541\pi$
$821$	−29520.8	−	21448.1i	−1.25491	−	0.911746i	−0.998496	+	0.0548212i	$0.982541\pi$
$822$		0			0
$823$	−3399.91	+	10463.8i	−0.144002	+	0.443191i	−0.996881	−	0.0789163i	$-0.974854\pi$
$823$	−3399.91	+	10463.8i	−0.144002	+	0.443191i	0.852880	+	0.522107i	$0.174854\pi$
$824$	−4474.33			−0.189163
$825$		0			0
$826$	−601.107			−0.0253210
$827$	−2776.99	+	8546.71i	−0.116766	+	0.359369i	−0.992311	−	0.123767i	$-0.960502\pi$
$827$	−2776.99	+	8546.71i	−0.116766	+	0.359369i	0.875545	+	0.483136i	$0.160502\pi$
$828$		0			0
$829$	3309.40	+	2404.42i	0.138649	+	0.100735i	0.654948	−	0.755674i	$-0.272691\pi$
$829$	3309.40	+	2404.42i	0.138649	+	0.100735i	−0.516299	+	0.856409i	$0.672691\pi$
$830$	−10450.0	+	19614.1i	−0.437019	+	0.820258i
$831$		0			0
$832$	28539.5			1.18922
$833$	−3134.67	+	2277.47i	−0.130384	+	0.0947294i
$834$		0			0
$835$	10191.9	+	1805.89i	0.422401	+	0.0748448i
$836$	−743.821	+	2289.25i	−0.0307722	+	0.0947072i
$837$		0			0
$838$	−1383.08	−	4256.69i	−0.0570141	−	0.175471i
$839$	−7963.84	+	24510.2i	−0.327702	+	1.00856i	0.642504	+	0.766283i	$0.277896\pi$
$839$	−7963.84	+	24510.2i	−0.327702	+	1.00856i	−0.970206	+	0.242281i	$0.922104\pi$
$840$		0			0
$841$	−6042.28	−	18596.2i	−0.247746	−	0.762484i
$842$	21968.0	−	15960.7i	0.899132	−	0.653257i
$843$		0			0
$844$	−757.858	+	550.616i	−0.0309082	+	0.0224561i
$845$	−7674.64	−	1359.86i	−0.312445	−	0.0553618i
$846$		0			0
$847$	6658.09	+	4837.38i	0.270100	+	0.196239i
$848$	−927.874	+	2855.70i	−0.0375747	+	0.115643i
$849$		0			0
$850$	4425.74	−	1261.06i	0.178590	−	0.0508869i
$851$	64124.5			2.58303
$852$		0			0
$853$	−20272.2	−	14728.6i	−0.813725	−	0.591205i	0.101184	−	0.994868i	$-0.467737\pi$
$853$	−20272.2	−	14728.6i	−0.813725	−	0.591205i	−0.914908	+	0.403662i	$0.867737\pi$
$854$	9104.17	+	6614.57i	0.364799	+	0.265042i
$855$		0			0
$856$	5338.62	−	3878.73i	0.213166	−	0.154874i
$857$	−17264.2			−0.688138			−0.344069	−	0.938944i	$-0.611805\pi$
$857$	−17264.2			−0.688138			−0.344069	+	0.938944i	$0.611805\pi$
$858$		0			0
$859$	12574.5	+	38700.3i	0.499460	+	1.53718i	0.809889	+	0.586583i	$0.199527\pi$
$859$	12574.5	+	38700.3i	0.499460	+	1.53718i	−0.310429	+	0.950596i	$0.600473\pi$
$860$	219.317	+	1570.05i	0.00869611	+	0.0622536i
$861$		0			0
$862$	3087.36	+	9501.91i	0.121991	+	0.375448i
$863$	−11616.3	−	35751.1i	−0.458194	−	1.41018i	−0.867344	−	0.497710i	$-0.834174\pi$
$863$	−11616.3	−	35751.1i	−0.458194	−	1.41018i	0.409149	−	0.912467i	$-0.365826\pi$
$864$		0			0
$865$	−6514.63	+	3170.66i	−0.256074	+	0.124631i
$866$	−8794.64	−	27067.1i	−0.345097	−	1.06210i
$867$		0			0
$868$	−341.081			−0.0133376
$869$	7891.52	−	5733.52i	0.308057	−	0.223816i
$870$		0			0
$871$	−29973.3	−	21776.9i	−1.16602	−	0.847166i
$872$	−26418.2	−	19193.9i	−1.02595	−	0.745399i
$873$		0			0
$874$	91723.9			3.54989
$875$	7449.94	−	6674.20i	0.287833	−	0.257862i
$876$		0			0
$877$	−7016.09	+	21593.3i	−0.270144	+	0.831418i	0.720319	+	0.693643i	$0.243995\pi$
$877$	−7016.09	+	21593.3i	−0.270144	+	0.831418i	−0.990463	+	0.137776i	$0.956005\pi$
$878$	−30448.1	−	22121.8i	−1.17036	−	0.850313i
$879$		0			0
$880$	23726.3	+	24610.5i	0.908880	+	0.942748i
$881$	33067.3	−	24024.8i	1.26455	−	0.918747i	0.265575	−	0.964090i	$-0.414438\pi$
$881$	33067.3	−	24024.8i	1.26455	−	0.918747i	0.998971	+	0.0453430i	$0.0144381\pi$
$882$		0			0
$883$	−23625.2	+	17164.7i	−0.900399	+	0.654178i	−0.938568	−	0.345093i	$-0.887847\pi$
$883$	−23625.2	+	17164.7i	−0.900399	+	0.654178i	0.0381695	+	0.999271i	$0.487847\pi$
$884$	69.3794	+	213.528i	0.00263969	+	0.00812412i
$885$		0			0
$886$	14341.4	−	44138.3i	0.543802	−	1.67365i
$887$	−7328.06	−	22553.5i	−0.277398	−	0.853744i	−0.988575	−	0.150731i	$-0.951837\pi$
$887$	−7328.06	−	22553.5i	−0.277398	−	0.853744i	0.711177	−	0.703013i	$-0.248163\pi$
$888$		0			0
$889$	2111.32	−	6497.98i	0.0796529	−	0.245146i
$890$	5148.85	+	36859.5i	0.193921	+	1.38824i
$891$		0			0
$892$	−473.255	+	343.840i	−0.0177643	+	0.0129065i
$893$	−23721.8			−0.888937
$894$		0			0
$895$	−3168.98	−	22686.0i	−0.118355	−	0.847275i
$896$	7857.35	+	5708.70i	0.292964	+	0.212851i
$897$		0			0
$898$	−15558.2	+	47883.1i	−0.578155	+	1.77938i
$899$	10545.0			0.391209
$900$		0			0
$901$	−649.552			−0.0240174
$902$	15311.1	−	47122.8i	0.565194	−	1.73949i
$903$		0			0
$904$	−21026.6	−	15276.7i	−0.773598	−	0.562052i
$905$	9924.93	+	1758.59i	0.364548	+	0.0645939i
$906$		0			0
$907$	−1482.16			−0.0542606			−0.0271303	−	0.999632i	$-0.508637\pi$
$907$	−1482.16			−0.0542606			−0.0271303	+	0.999632i	$0.508637\pi$
$908$	333.599	−	242.374i	0.0121926	−	0.00885842i
$909$		0			0
$910$	−8283.01	−	8591.66i	−0.301735	−	0.312979i
$911$	−10468.8	+	32219.8i	−0.380734	+	1.17178i	0.558795	+	0.829306i	$0.311264\pi$
$911$	−10468.8	+	32219.8i	−0.380734	+	1.17178i	−0.939528	+	0.342471i	$0.888736\pi$
$912$		0			0
$913$	−11036.1	−	33965.5i	−0.400045	−	1.23121i
$914$	1741.44	−	5359.61i	0.0630217	−	0.193961i
$915$		0			0
$916$	416.971	+	1283.30i	0.0150405	+	0.0462899i
$917$	−8539.98	+	6204.66i	−0.307541	+	0.223442i
$918$		0			0
$919$	5948.80	−	4322.06i	0.213529	−	0.155138i	−0.475880	−	0.879510i	$-0.657870\pi$
$919$	5948.80	−	4322.06i	0.213529	−	0.155138i	0.689409	+	0.724373i	$0.257870\pi$
$920$	−26072.1	+	48935.7i	−0.934316	+	1.75365i
$921$		0			0
$922$	13492.3	+	9802.72i	0.481936	+	0.350147i
$923$	−14066.6	+	43292.5i	−0.501633	+	1.54387i
$924$		0			0
$925$	35827.9	−	10208.7i	1.27353	−	0.362875i
$926$	16255.7			0.576887
$927$		0			0
$928$	799.661	+	580.987i	0.0282868	+	0.0205516i
$929$	33320.9	+	24209.1i	1.17678	+	0.854977i	0.991804	−	0.127766i	$-0.0407808\pi$
$929$	33320.9	+	24209.1i	1.17678	+	0.854977i	0.184971	+	0.982744i	$0.440781\pi$
$930$		0			0
$931$	−36298.2	+	26372.2i	−1.27779	+	0.928371i
$932$	−137.909			−0.00484695
$933$		0			0
$934$	7701.07	+	23701.5i	0.269793	+	0.830338i
$935$	−3477.23	+	6526.56i	−0.121623	+	0.228279i
$936$		0			0
$937$	−1425.61	−	4387.57i	−0.0497039	−	0.152973i	0.923124	−	0.384502i	$-0.125627\pi$
$937$	−1425.61	−	4387.57i	−0.0497039	−	0.152973i	−0.972828	+	0.231530i	$0.925627\pi$
$938$	−4222.59	−	12995.8i	−0.146985	−	0.452375i
$939$		0			0
$940$	254.872	−	478.380i	0.00884363	−	0.0165990i
$941$	271.295	+	834.961i	0.00939848	+	0.0289255i	0.955646	−	0.294518i	$-0.0951593\pi$
$941$	271.295	+	834.961i	0.00939848	+	0.0289255i	−0.946247	+	0.323444i	$0.895159\pi$
$942$		0			0
$943$	77204.2			2.66608
$944$	1504.55	−	1093.12i	0.0518740	−	0.0376886i
$945$		0			0
$946$	50402.5	+	36619.6i	1.73227	+	1.25857i
$947$	8043.72	+	5844.10i	0.276014	+	0.200536i	0.717177	−	0.696891i	$-0.245434\pi$
$947$	8043.72	+	5844.10i	0.276014	+	0.200536i	−0.441163	+	0.897427i	$0.645434\pi$
$948$		0			0
$949$	−19187.4			−0.656323
$950$	51248.3	−	14602.5i	1.75022	−	0.498704i
$951$		0			0
$952$	−676.969	+	2083.50i	−0.0230470	+	0.0709312i
$953$	18466.1	+	13416.4i	0.627675	+	0.456033i	0.855594	−	0.517648i	$-0.173192\pi$
$953$	18466.1	+	13416.4i	0.627675	+	0.456033i	−0.227919	+	0.973680i	$0.573192\pi$
$954$		0			0
$955$	15295.1	−	28707.9i	0.518259	−	0.972740i
$956$	861.787	−	626.125i	0.0291550	−	0.0211824i
$957$		0			0
$958$	14903.0	−	10827.7i	0.502604	−	0.365163i
$959$	2052.19	+	6315.98i	0.0691017	+	0.212673i
$960$		0			0
$961$	−2100.11	+	6463.47i	−0.0704948	+	0.216961i
$962$	−13735.5	−	42273.7i	−0.460345	−	1.41680i
$963$		0			0
$964$	267.242	−	822.487i	0.00892873	−	0.0274798i
$965$	1434.37	+	1487.82i	0.0478487	+	0.0496317i
$966$		0			0
$967$	6781.05	−	4926.72i	0.225505	−	0.163839i	−0.469296	−	0.883041i	$-0.655492\pi$
$967$	6781.05	−	4926.72i	0.225505	−	0.163839i	0.694801	+	0.719202i	$0.255492\pi$
$968$	−26504.7			−0.880054
$969$		0			0
$970$	−37773.2	−	6693.00i	−1.25034	−	0.221546i
$971$	−24336.7	−	17681.6i	−0.804327	−	0.584378i	0.107853	−	0.994167i	$-0.465602\pi$
$971$	−24336.7	−	17681.6i	−0.804327	−	0.584378i	−0.912180	+	0.409789i	$0.865602\pi$
$972$		0			0
$973$	−2042.84	+	6287.21i	−0.0673077	+	0.207152i
$974$	20094.6			0.661061
$975$		0			0
$976$	−34816.2			−1.14184
$977$	−10834.3	+	33344.5i	−0.354779	+	1.09190i	0.601358	+	0.798979i	$0.294626\pi$
$977$	−10834.3	+	33344.5i	−0.354779	+	1.09190i	−0.956137	+	0.292918i	$0.905374\pi$
$978$		0			0
$979$	−48384.9	−	35153.7i	−1.57956	−	1.14762i
$980$	−141.832	−	1015.35i	−0.00462312	−	0.0330959i
$981$		0			0
$982$	−38339.0			−1.24587
$983$	−21530.1	+	15642.5i	−0.698578	+	0.507547i	−0.879469	−	0.475956i	$-0.842102\pi$
$983$	−21530.1	+	15642.5i	−0.698578	+	0.507547i	0.180891	+	0.983503i	$0.442102\pi$
$984$		0			0
$985$	−4930.54	−	35296.7i	−0.159493	−	1.14177i
$986$	791.118	−	2434.81i	0.0255521	−	0.0786411i
$987$		0			0
$988$	803.386	+	2472.57i	0.0258696	+	0.0796183i
$989$	−29998.0	+	92324.5i	−0.964492	+	2.96840i
$990$		0			0
$991$	10794.9	+	33223.4i	0.346027	+	1.06496i	0.961032	+	0.276437i	$0.0891538\pi$
$991$	10794.9	+	33223.4i	0.346027	+	1.06496i	−0.615005	+	0.788523i	$0.710846\pi$
$992$	1743.77	−	1266.92i	0.0558112	−	0.0405492i
$993$		0			0
$994$	−13582.6	+	9868.35i	−0.433415	+	0.314894i
$995$	15896.6	+	16488.9i	0.506487	+	0.525361i
$996$		0			0
$997$	−33966.2	−	24677.9i	−1.07896	−	0.783908i	−0.101456	−	0.994840i	$-0.532350\pi$
$997$	−33966.2	−	24677.9i	−1.07896	−	0.783908i	−0.977501	+	0.210932i	$0.932350\pi$
$998$	7895.37	−	24299.5i	0.250424	−	0.770727i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.d.46.12	yes	64
3.2	odd	2	inner	225.4.h.d.46.5	✓	64
25.6	even	5	inner	225.4.h.d.181.12	yes	64
75.56	odd	10	inner	225.4.h.d.181.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.h.d.46.5	✓	64	3.2	odd	2	inner
225.4.h.d.46.12	yes	64	1.1	even	1	trivial
225.4.h.d.181.5	yes	64	75.56	odd	10	inner
225.4.h.d.181.12	yes	64	25.6	even	5	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.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.856692 - 2.63663i) q^{2} +(0.254251 + 0.184724i) q^{4} +(7.75979 + 8.04895i) q^{5} -7.15708 q^{7} +(18.6477 - 13.5483i) q^{8} +O(q^{10})\)	\(q+(0.856692 - 2.63663i) q^{2} +(0.254251 + 0.184724i) q^{4} +(7.75979 + 8.04895i) q^{5} -7.15708 q^{7} +(18.6477 - 13.5483i) q^{8} +(27.8698 - 13.5642i) q^{10} +(-15.3917 + 47.3707i) q^{11} +(16.6242 + 51.1641i) q^{13} +(-6.13142 + 18.8706i) q^{14} +(-18.9696 - 58.3826i) q^{16} +(10.7434 - 7.80553i) q^{17} +(124.404 - 90.3850i) q^{19} +(0.486099 + 3.47988i) q^{20} +(111.713 + 81.1643i) q^{22} +(-66.4882 + 204.630i) q^{23} +(-4.57128 + 124.916i) q^{25} +149.143 q^{26} +(-1.81970 - 1.32209i) q^{28} +(56.2588 + 40.8744i) q^{29} +(122.680 - 89.1322i) q^{31} +14.2140 q^{32} +(-11.3765 - 35.0133i) q^{34} +(-55.5375 - 57.6070i) q^{35} +(-92.0967 - 283.445i) q^{37} +(-131.735 - 405.440i) q^{38} +(253.752 + 44.9620i) q^{40} +(-110.882 - 341.260i) q^{41} +451.178 q^{43} +(-12.6639 + 9.20084i) q^{44} +(482.572 + 350.609i) q^{46} +(-124.804 - 90.6754i) q^{47} -291.776 q^{49} +(325.442 + 119.068i) q^{50} +(-5.22453 + 16.0794i) q^{52} +(-39.5720 - 28.7507i) q^{53} +(-500.721 + 243.700i) q^{55} +(-133.463 + 96.9665i) q^{56} +(155.967 - 113.317i) q^{58} +(9.36171 + 28.8124i) q^{59} +(175.261 - 539.399i) q^{61} +(-129.909 - 399.820i) q^{62} +(163.934 - 504.537i) q^{64} +(-282.817 + 530.831i) q^{65} +(-557.154 + 404.796i) q^{67} +4.17339 q^{68} +(-199.467 + 97.0802i) q^{70} +(684.549 + 497.354i) q^{71} +(-110.215 + 339.207i) q^{73} -826.236 q^{74} +48.3262 q^{76} +(110.160 - 339.036i) q^{77} +(-158.437 - 115.111i) q^{79} +(322.718 - 605.722i) q^{80} -994.767 q^{82} +(-580.078 + 421.451i) q^{83} +(146.193 + 25.9038i) q^{85} +(386.521 - 1189.59i) q^{86} +(354.775 + 1091.88i) q^{88} +(-371.049 + 1141.97i) q^{89} +(-118.981 - 366.186i) q^{91} +(-54.7048 + 39.7453i) q^{92} +(-345.996 + 251.381i) q^{94} +(1692.85 + 299.955i) q^{95} +(-1001.28 - 727.475i) q^{97} +(-249.962 + 769.305i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) 64 * q - 72 * q^4 + 20 * q^7	\( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) 64 * q - 72 * q^4 + 20 * q^7 + 50 * q^10 + 180 * q^13 - 244 * q^16 - 116 * q^19 - 210 * q^22 + 440 * q^25 + 980 * q^28 + 42 * q^31 + 40 * q^34 - 1170 * q^37 - 3040 * q^40 + 1040 * q^43 + 700 * q^46 + 4188 * q^49 + 3280 * q^52 + 2640 * q^55 - 4530 * q^58 + 88 * q^61 - 3018 * q^64 - 2860 * q^67 - 3720 * q^70 - 5280 * q^73 + 9288 * q^76 - 1144 * q^79 + 2840 * q^82 + 470 * q^85 + 7610 * q^88 - 1180 * q^91 + 2170 * q^94 + 2050 * q^97

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