LMFDB - Embedded newform 225.4.h.d.46.5

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			46.5
Character	$\chi$	$=$	225.46
Dual form			225.4.h.d.181.5

$q$-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	$0.263033\pi$
$2$	−0.856692	+	2.63663i	−0.302886	+	0.932189i	−0.980457	+	0.196731i	$0.936967\pi$
$3$		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	$-0.660837\pi$
$11$	15.3917	−	47.3707i	0.421888	−	1.29844i	0.905943	−	0.423400i	$-0.139163\pi$
$12$		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	−0.661779	−	0.749699i	$-0.730198\pi$
$17$	−10.7434	+	7.80553i	−0.153274	+	0.111360i	0.508505	+	0.861059i	$0.330198\pi$
$18$		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	$-0.470887\pi$
$23$	66.4882	−	204.630i	0.602772	−	1.85514i	0.511437	−	0.859321i	$-0.329113\pi$
$24$		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	0.392912	−	0.919576i	$-0.371468\pi$
$29$	−56.2588	−	40.8744i	−0.360241	−	0.261730i	−0.753153	+	0.657846i	$0.771468\pi$
$30$		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	$0.139498\pi$
$41$	110.882	+	341.260i	0.422363	+	1.29990i	−0.483135	+	0.875546i	$0.660502\pi$
$42$		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	0.764361	−	0.644789i	$-0.223055\pi$
$47$	124.804	+	90.6754i	0.387330	+	0.281412i	−0.377030	+	0.926201i	$0.623055\pi$
$48$		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	0.637883	−	0.770133i	$-0.279810\pi$
$53$	39.5720	+	28.7507i	0.102559	+	0.0745135i	−0.535324	+	0.844647i	$0.679810\pi$
$54$		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	0.940196	−	0.340633i	$-0.110641\pi$
$59$	−9.36171	−	28.8124i	−0.0206575	−	0.0635772i	−0.960854	+	0.277056i	$0.910641\pi$
$60$		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	−0.156536	−	0.987672i	$-0.550033\pi$
$71$	−684.549	−	497.354i	−1.14424	−	0.831339i	−0.987704	+	0.156333i	$0.950033\pi$
$72$		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	−0.133959	−	0.990987i	$-0.542769\pi$
$83$	580.078	−	421.451i	0.767130	−	0.557353i	0.901089	+	0.433634i	$0.142769\pi$
$84$		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	$-0.646406\pi$
$89$	371.049	−	1141.97i	0.441922	−	1.36010i	0.885824	−	0.464022i	$-0.153594\pi$
$90$		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	$-0.557611\pi$
$101$	−365.423			−0.360010			−0.180005	+	0.983666i	$0.557611\pi$
$102$		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	$-0.541283\pi$
$107$	−286.289			−0.258660			−0.129330	+	0.991602i	$0.541283\pi$
$108$		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	$0.0555114\pi$
$113$	348.438	+	1072.38i	0.290074	+	0.892755i	−0.694758	+	0.719244i	$0.744489\pi$
$114$		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	−0.909684	−	0.415300i	$-0.863677\pi$
$131$	−1193.22	+	866.926i	−0.795818	+	0.578196i	0.113866	+	0.993496i	$0.463677\pi$
$132$		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	0.999787	−	0.0206352i	$-0.00656884\pi$
$137$	286.735	+	882.480i	0.178813	+	0.550331i	−0.820974	+	0.570966i	$0.806569\pi$
$138$		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	$-0.315352\pi$
$149$	1993.74			1.09620			0.548098	+	0.836414i	$0.315352\pi$
$150$		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	−0.747632	−	0.664114i	$-0.768809\pi$
$167$	−748.980	+	544.166i	−0.347053	+	0.252148i	0.400579	+	0.916262i	$0.368809\pi$
$168$		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	−0.897362	−	0.441295i	$-0.854519\pi$
$173$	200.254	−	616.317i	0.0880058	−	0.270854i	0.985368	+	0.170441i	$0.0545193\pi$
$174$		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	0.877355	−	0.479842i	$-0.159306\pi$
$179$	1657.52	+	1204.26i	0.692115	+	0.502851i	−0.185240	+	0.982693i	$0.559306\pi$
$180$		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	$0.0857892\pi$
$191$	899.058	+	2767.02i	0.340594	+	1.04824i	−0.623306	+	0.781978i	$0.714211\pi$
$192$		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	0.946648	−	0.322269i	$-0.104446\pi$
$197$	2578.89	+	1873.67i	0.932682	+	0.677633i	−0.0139660	+	0.999902i	$0.504446\pi$
$198$		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	−0.992671	−	0.120848i	$-0.961439\pi$
$227$	−405.456	+	1247.86i	−0.118551	+	0.364862i	0.874120	+	0.485710i	$0.161439\pi$
$228$		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	−0.536756	−	0.843737i	$-0.680351\pi$
$233$	355.013	−	257.932i	0.0998184	−	0.0725223i	0.636575	+	0.771215i	$0.280351\pi$
$234$		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	$0.251678\pi$
$239$	−1047.42	+	3223.62i	−0.283480	+	0.872462i	−0.986850	+	0.161638i	$0.948322\pi$
$240$		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	$-0.639257\pi$
$251$	−3369.50			−0.847334			−0.423667	+	0.905818i	$0.639257\pi$
$252$		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	$-0.686515\pi$
$257$	−4556.70			−1.10599			−0.552994	+	0.833185i	$0.686515\pi$
$258$		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	$-0.935441\pi$
$263$	−1302.86	−	4009.78i	−0.305466	−	0.940129i	0.674036	−	0.738698i	$-0.264559\pi$
$264$		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	−0.645747	−	0.763551i	$-0.723454\pi$
$269$	−525.519	+	381.812i	−0.119113	+	0.0865408i	0.526634	+	0.850092i	$0.323454\pi$
$270$		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	$0.648014\pi$
$281$	−6769.19	+	4918.10i	−1.43707	+	1.04409i	−0.988645	+	0.150269i	$0.951986\pi$
$282$		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	$-0.433528\pi$
$293$	2079.50			0.414627			0.207313	+	0.978275i	$0.433528\pi$
$294$		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	−0.830396	−	0.557173i	$-0.811886\pi$
$311$	926.375	−	2851.09i	0.168906	−	0.519841i	0.999303	+	0.0373323i	$0.0118860\pi$
$312$		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	−0.483971	−	0.875084i	$-0.660806\pi$
$317$	1121.63	−	814.913i	0.198729	−	0.144385i	0.682699	+	0.730699i	$0.260806\pi$
$318$		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	0.917462	−	0.397823i	$-0.130234\pi$
$347$	5317.34	+	3863.27i	0.822621	+	0.597669i	−0.0948410	+	0.995492i	$0.530234\pi$
$348$		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	0.544021	−	0.839072i	$-0.316901\pi$
$353$	−569.531	−	413.788i	−0.0858727	−	0.0623902i	−0.629893	+	0.776682i	$0.716901\pi$
$354$		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	$-0.964782\pi$
$359$	−1732.60	−	5332.39i	−0.254716	−	0.783935i	0.739170	−	0.673519i	$-0.235218\pi$
$360$		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	0.0549545	−	0.998489i	$-0.482499\pi$
$383$	7657.03	−	5563.16i	1.02156	−	0.742204i	0.966601	+	0.256285i	$0.0824986\pi$
$384$		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	$0.472920\pi$
$389$	−4368.83	+	13445.9i	−0.569431	+	1.75253i	−0.654404	+	0.756145i	$0.727080\pi$
$390$		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	$-0.383639\pi$
$401$	5740.98			0.714940			0.357470	+	0.933925i	$0.383639\pi$
$402$		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	−0.661319	−	0.750105i	$-0.730003\pi$
$419$	−1306.11	+	948.947i	−0.152286	+	0.110642i	0.509033	+	0.860747i	$0.330003\pi$
$420$		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	−0.412824	−	0.910811i	$-0.635457\pi$
$431$	2915.55	−	2118.27i	0.325840	−	0.236736i	0.738663	+	0.674075i	$0.235457\pi$
$432$		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	$-0.854762\pi$
$443$	−16740.4			−1.79540			−0.897699	+	0.440609i	$0.854762\pi$
$444$		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	$-0.0964880\pi$
$449$	18160.7			1.90882			0.954408	+	0.298505i	$0.0964880\pi$
$450$		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	−0.812176	−	0.583412i	$-0.801717\pi$
$461$	1858.95	−	5721.26i	0.187809	−	0.578017i	0.999985	+	0.00539516i	$0.00171734\pi$
$462$		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	−0.165960	−	0.986133i	$-0.553072\pi$
$467$	7272.50	−	5283.78i	0.720624	−	0.523564i	0.886583	+	0.462569i	$0.153072\pi$
$468$		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	0.301099	−	0.953593i	$-0.402647\pi$
$479$	−5375.66	−	3905.65i	−0.512777	−	0.372554i	−0.813876	+	0.581039i	$0.802647\pi$
$480$		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	$0.119224\pi$
$491$	4273.47	+	13152.4i	0.392788	+	1.20888i	−0.537883	+	0.843020i	$0.680776\pi$
$492$		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	0.0303278	−	0.999540i	$-0.490345\pi$
$503$	−10276.2	−	7466.09i	−0.910919	−	0.661822i	−0.941247	+	0.337718i	$0.890345\pi$
$504$		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	$0.0287680\pi$
$509$	2793.42	+	8597.26i	0.243254	+	0.748658i	−0.752665	+	0.658404i	$0.771232\pi$
$510$		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	0.935232	−	0.354036i	$-0.115191\pi$
$521$	10554.5	+	7668.29i	0.887526	+	0.644825i	−0.0477059	+	0.998861i	$0.515191\pi$
$522$		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	$-0.708394\pi$
$557$	−16009.1			−1.21783			−0.608913	+	0.793237i	$0.708394\pi$
$558$		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	0.977829	−	0.209404i	$-0.0671525\pi$
$563$	850.464	+	2617.46i	0.0636639	+	0.195937i	−0.914165	+	0.405342i	$0.867153\pi$
$564$		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	−0.727308	−	0.686312i	$-0.759229\pi$
$569$	−4062.83	+	2951.82i	−0.299337	+	0.217481i	0.427971	+	0.903793i	$0.359229\pi$
$570$		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	$-0.885385\pi$
$587$	−5487.34	−	16888.3i	−0.385838	−	1.18749i	0.550033	−	0.835143i	$-0.314615\pi$
$588$		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	$-0.211601\pi$
$593$	22731.1			1.57413			0.787063	+	0.616873i	$0.211601\pi$
$594$		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	$-0.346767\pi$
$599$	13575.9			0.926036			0.463018	+	0.886349i	$0.346767\pi$
$600$		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	−0.483704	−	0.875231i	$-0.660709\pi$
$617$	3053.20	−	2218.28i	0.199217	−	0.144740i	0.682922	+	0.730492i	$0.260709\pi$
$618$		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	0.898119	−	0.439752i	$-0.144934\pi$
$641$	−1411.17	−	4343.13i	−0.0869544	−	0.267618i	−0.985074	+	0.172134i	$0.944934\pi$
$642$		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	−0.261913	−	0.965092i	$-0.584353\pi$
$647$	−20747.7	−	15074.1i	−1.26070	−	0.915956i	−0.998792	+	0.0491360i	$0.984353\pi$
$648$		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	0.302753	−	0.953069i	$-0.402094\pi$
$653$	−8512.09	−	6184.40i	−0.510113	−	0.370619i	−0.812866	+	0.582450i	$0.802094\pi$
$654$		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	0.865048	−	0.501688i	$-0.167288\pi$
$659$	−2193.75	−	6751.65i	−0.129676	−	0.399100i	−0.994724	+	0.102588i	$0.967288\pi$
$660$		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	$0.247596\pi$
$677$	−4869.04	+	14985.4i	−0.276414	+	0.850716i	−0.988842	+	0.148970i	$0.952404\pi$
$678$		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	−0.304044	−	0.952658i	$-0.598337\pi$
$683$	9068.24	−	6588.47i	0.508033	−	0.369108i	0.812077	+	0.583550i	$0.198337\pi$
$684$		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	$-0.430831\pi$
$701$	8002.88			0.431191			0.215595	+	0.976483i	$0.430831\pi$
$702$		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	−0.418870	−	0.908046i	$-0.637574\pi$
$719$	6078.70	−	4416.43i	0.315295	−	0.229075i	0.734165	+	0.678971i	$0.237574\pi$
$720$		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	$-0.424706\pi$
$743$	9492.12			0.468684			0.234342	+	0.972154i	$0.424706\pi$
$744$		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	$0.239545\pi$
$761$	−5507.46	+	16950.2i	−0.262346	+	0.807417i	−0.992293	+	0.123914i	$0.960455\pi$
$762$		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	$-0.789187\pi$
$773$	4531.20	−	13945.6i	0.210836	−	0.648886i	0.999423	−	0.0339629i	$-0.0108128\pi$
$774$		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	−0.243090	−	0.970004i	$-0.578161\pi$
$797$	−27916.9	−	20282.8i	−1.24074	−	0.901448i	−0.997647	+	0.0685556i	$0.978161\pi$
$798$		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	0.898218	−	0.439550i	$-0.144862\pi$
$809$	−1997.67	−	6148.20i	−0.0868163	−	0.267193i	−0.985035	+	0.172356i	$0.944862\pi$
$810$		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	0.998496	−	0.0548212i	$-0.0174589\pi$
$821$	29520.8	+	21448.1i	1.25491	+	0.911746i	0.256414	+	0.966567i	$0.417459\pi$
$822$		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	−0.875545	−	0.483136i	$-0.839498\pi$
$827$	2776.99	−	8546.71i	0.116766	−	0.359369i	0.992311	+	0.123767i	$0.0394976\pi$
$828$		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	$-0.722104\pi$
$839$	7963.84	−	24510.2i	0.327702	−	1.00856i	0.970206	−	0.242281i	$-0.0778957\pi$
$840$		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	$-0.388195\pi$
$857$	17264.2			0.688138			0.344069	+	0.938944i	$0.388195\pi$
$858$		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	$0.165826\pi$
$863$	11616.3	+	35751.1i	0.458194	+	1.41018i	−0.409149	+	0.912467i	$0.634174\pi$
$864$		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	−0.998971	−	0.0453430i	$-0.985562\pi$
$881$	−33067.3	+	24024.8i	−1.26455	+	0.918747i	−0.265575	+	0.964090i	$0.585562\pi$
$882$		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	$0.0481626\pi$
$887$	7328.06	+	22553.5i	0.277398	+	0.853744i	−0.711177	+	0.703013i	$0.751837\pi$
$888$		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	$-0.688736\pi$
$911$	10468.8	−	32219.8i	0.380734	−	1.17178i	0.939528	−	0.342471i	$-0.111264\pi$
$912$		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	−0.184971	−	0.982744i	$-0.559219\pi$
$929$	−33320.9	−	24209.1i	−1.17678	−	0.854977i	−0.991804	+	0.127766i	$0.959219\pi$
$930$		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	0.946247	−	0.323444i	$-0.104841\pi$
$941$	−271.295	−	834.961i	−0.00939848	−	0.0289255i	−0.955646	+	0.294518i	$0.904841\pi$
$942$		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	0.441163	−	0.897427i	$-0.354566\pi$
$947$	−8043.72	−	5844.10i	−0.276014	−	0.200536i	−0.717177	+	0.696891i	$0.754566\pi$
$948$		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	0.227919	−	0.973680i	$-0.426808\pi$
$953$	−18466.1	−	13416.4i	−0.627675	−	0.456033i	−0.855594	+	0.517648i	$0.826808\pi$
$954$		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	0.912180	−	0.409789i	$-0.134398\pi$
$971$	24336.7	+	17681.6i	0.804327	+	0.584378i	−0.107853	+	0.994167i	$0.534398\pi$
$972$		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	$-0.705374\pi$
$977$	10834.3	−	33344.5i	0.354779	−	1.09190i	0.956137	−	0.292918i	$-0.0946264\pi$
$978$		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	−0.180891	−	0.983503i	$-0.557898\pi$
$983$	21530.1	−	15642.5i	0.698578	−	0.507547i	0.879469	+	0.475956i	$0.157898\pi$
$984$		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.46.5	✓	64
3.2	odd	2	inner	225.4.h.d.46.12	yes	64
25.6	even	5	inner	225.4.h.d.181.5	yes	64
75.56	odd	10	inner	225.4.h.d.181.12	yes	64

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