LMFDB - Embedded newform 225.4.h.d.181.6

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			181.6
Character	$\chi$	$=$	225.181
Dual form			225.4.h.d.46.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.626289 - 1.92752i) q^{2} +(3.14904 - 2.28791i) q^{4} +(-3.12321 - 10.7352i) q^{5} -16.4425 q^{7} +(-19.4994 - 14.1671i) q^{8} +O(q^{10})$	\(q+(-0.626289 - 1.92752i) q^{2} +(3.14904 - 2.28791i) q^{4} +(-3.12321 - 10.7352i) q^{5} -16.4425 q^{7} +(-19.4994 - 14.1671i) q^{8} +(-18.7364 + 12.7434i) q^{10} +(-1.41112 - 4.34299i) q^{11} +(-17.0513 + 52.4784i) q^{13} +(10.2977 + 31.6932i) q^{14} +(-5.47256 + 16.8428i) q^{16} +(-1.72699 - 1.25473i) q^{17} +(22.2151 + 16.1402i) q^{19} +(-34.3964 - 26.6601i) q^{20} +(-7.48743 + 5.43993i) q^{22} +(-30.4050 - 93.5770i) q^{23} +(-105.491 + 67.0569i) q^{25} +111.832 q^{26} +(-51.7780 + 37.6189i) q^{28} +(2.70250 - 1.96348i) q^{29} +(54.6052 + 39.6730i) q^{31} -156.928 q^{32} +(-1.33692 + 4.11462i) q^{34} +(51.3533 + 176.514i) q^{35} +(-56.4702 + 173.797i) q^{37} +(17.1975 - 52.9285i) q^{38} +(-91.1869 + 253.578i) q^{40} +(11.7884 - 36.2811i) q^{41} -252.976 q^{43} +(-14.3801 - 10.4477i) q^{44} +(-161.329 + 117.213i) q^{46} +(-35.6846 + 25.9263i) q^{47} -72.6451 q^{49} +(195.321 + 161.339i) q^{50} +(66.3708 + 204.268i) q^{52} +(-163.853 + 119.046i) q^{53} +(-42.2158 + 28.7128i) q^{55} +(320.618 + 232.943i) q^{56} +(-5.47720 - 3.97942i) q^{58} +(36.4118 - 112.064i) q^{59} +(-248.210 - 763.911i) q^{61} +(42.2718 - 130.099i) q^{62} +(142.063 + 437.225i) q^{64} +(616.623 + 19.1484i) q^{65} +(523.504 + 380.348i) q^{67} -8.30906 q^{68} +(308.072 - 209.533i) q^{70} +(-798.476 + 580.127i) q^{71} +(-256.874 - 790.578i) q^{73} +370.365 q^{74} +106.884 q^{76} +(23.2023 + 71.4095i) q^{77} +(822.092 - 597.285i) q^{79} +(197.904 + 6.14563i) q^{80} -77.3154 q^{82} +(-926.758 - 673.329i) q^{83} +(-8.07608 + 22.4584i) q^{85} +(158.436 + 487.616i) q^{86} +(-34.0117 + 104.677i) q^{88} +(-349.060 - 1074.29i) q^{89} +(280.365 - 862.874i) q^{91} +(-309.843 - 225.114i) q^{92} +(72.3224 + 52.5453i) q^{94} +(103.887 - 288.894i) q^{95} +(457.822 - 332.627i) q^{97} +(45.4968 + 140.025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.626289	−	1.92752i	−0.221427	−	0.681481i	−0.998635	−	0.0522374i	$-0.983365\pi$
$2$	−0.626289	−	1.92752i	−0.221427	−	0.681481i	0.777208	−	0.629244i	$-0.216635\pi$
$3$		0			0
$3$		0			0
$4$	3.14904	−	2.28791i	0.393630	−	0.285989i
$5$	−3.12321	−	10.7352i	−0.279349	−	0.960190i
$5$	−3.12321	−	10.7352i	−0.279349	−	0.960190i
$6$		0			0
$7$	−16.4425			−0.887810			−0.443905	−	0.896074i	$-0.646407\pi$
$7$	−16.4425			−0.887810			−0.443905	+	0.896074i	$0.646407\pi$
$8$	−19.4994	−	14.1671i	−0.861759	−	0.626104i
$9$		0			0
$10$	−18.7364	+	12.7434i	−0.592496	+	0.402982i
$11$	−1.41112	−	4.34299i	−0.0386790	−	0.119042i	0.929853	−	0.367932i	$-0.119934\pi$
$11$	−1.41112	−	4.34299i	−0.0386790	−	0.119042i	−0.968532	+	0.248890i	$0.919934\pi$
$12$		0			0
$13$	−17.0513	+	52.4784i	−0.363782	+	1.11961i	0.586958	+	0.809617i	$0.300325\pi$
$13$	−17.0513	+	52.4784i	−0.363782	+	1.11961i	−0.950740	+	0.309989i	$0.899675\pi$
$14$	10.2977	+	31.6932i	0.196585	+	0.605026i
$15$		0			0
$16$	−5.47256	+	16.8428i	−0.0855087	+	0.263169i
$17$	−1.72699	−	1.25473i	−0.0246386	−	0.0179010i	0.575398	−	0.817874i	$-0.304847\pi$
$17$	−1.72699	−	1.25473i	−0.0246386	−	0.0179010i	−0.600036	+	0.799973i	$0.704847\pi$
$18$		0			0
$19$	22.2151	+	16.1402i	0.268237	+	0.194885i	0.713770	−	0.700380i	$-0.246986\pi$
$19$	22.2151	+	16.1402i	0.268237	+	0.194885i	−0.445534	+	0.895265i	$0.646986\pi$
$20$	−34.3964	−	26.6601i	−0.384564	−	0.298069i
$21$		0			0
$22$	−7.48743	+	5.43993i	−0.0725602	+	0.0527181i
$23$	−30.4050	−	93.5770i	−0.275647	−	0.848354i	−0.989047	−	0.147598i	$-0.952846\pi$
$23$	−30.4050	−	93.5770i	−0.275647	−	0.848354i	0.713400	−	0.700757i	$-0.247154\pi$
$24$		0			0
$25$	−105.491	+	67.0569i	−0.843929	+	0.536455i
$26$	111.832			0.843542
$27$		0			0
$28$	−51.7780	+	37.6189i	−0.349469	+	0.253904i
$29$	2.70250	−	1.96348i	0.0173049	−	0.0125728i	−0.579099	−	0.815257i	$-0.696596\pi$
$29$	2.70250	−	1.96348i	0.0173049	−	0.0125728i	0.596404	+	0.802684i	$0.296596\pi$
$30$		0			0
$31$	54.6052	+	39.6730i	0.316367	+	0.229854i	0.734624	−	0.678475i	$-0.237359\pi$
$31$	54.6052	+	39.6730i	0.316367	+	0.229854i	−0.418257	+	0.908329i	$0.637359\pi$
$32$	−156.928			−0.866914
$33$		0			0
$34$	−1.33692	+	4.11462i	−0.00674353	+	0.0207545i
$35$	51.3533	+	176.514i	0.248008	+	0.852466i
$36$		0			0
$37$	−56.4702	+	173.797i	−0.250909	+	0.772219i	0.743699	+	0.668515i	$0.233070\pi$
$37$	−56.4702	+	173.797i	−0.250909	+	0.772219i	−0.994608	+	0.103704i	$0.966930\pi$
$38$	17.1975	−	52.9285i	0.0734159	−	0.225951i
$39$		0			0
$40$	−91.1869	+	253.578i	−0.360448	+	1.00235i
$41$	11.7884	−	36.2811i	0.0449035	−	0.138199i	−0.926091	−	0.377300i	$-0.876853\pi$
$41$	11.7884	−	36.2811i	0.0449035	−	0.138199i	0.970995	+	0.239101i	$0.0768527\pi$
$42$		0			0
$43$	−252.976			−0.897173			−0.448586	−	0.893739i	$-0.648072\pi$
$43$	−252.976			−0.897173			−0.448586	+	0.893739i	$0.648072\pi$
$44$	−14.3801	−	10.4477i	−0.0492699	−	0.0357967i
$45$		0			0
$46$	−161.329	+	117.213i	−0.517102	+	0.375697i
$47$	−35.6846	+	25.9263i	−0.110747	+	0.0804627i	−0.641780	−	0.766888i	$-0.721804\pi$
$47$	−35.6846	+	25.9263i	−0.110747	+	0.0804627i	0.531033	+	0.847351i	$0.321804\pi$
$48$		0			0
$49$	−72.6451			−0.211793
$50$	195.321	+	161.339i	0.552452	+	0.456336i
$51$		0			0
$52$	66.3708	+	204.268i	0.177000	+	0.544749i
$53$	−163.853	+	119.046i	−0.424659	+	0.308533i	−0.779510	−	0.626390i	$-0.784532\pi$
$53$	−163.853	+	119.046i	−0.424659	+	0.308533i	0.354851	+	0.934923i	$0.384532\pi$
$54$		0			0
$55$	−42.2158	+	28.7128i	−0.103498	+	0.0703934i
$56$	320.618	+	232.943i	0.765078	+	0.555862i
$57$		0			0
$58$	−5.47720	−	3.97942i	−0.0123999	−	0.00900903i
$59$	36.4118	−	112.064i	0.0803460	−	0.247280i	−0.902813	−	0.430034i	$-0.858501\pi$
$59$	36.4118	−	112.064i	0.0803460	−	0.247280i	0.983159	+	0.182755i	$0.0585014\pi$
$60$		0			0
$61$	−248.210	−	763.911i	−0.520984	−	1.60342i	−0.772123	−	0.635473i	$-0.780805\pi$
$61$	−248.210	−	763.911i	−0.520984	−	1.60342i	0.251139	−	0.967951i	$-0.419195\pi$
$62$	42.2718	−	130.099i	0.0865892	−	0.266494i
$63$		0			0
$64$	142.063	+	437.225i	0.277467	+	0.853954i
$65$	616.623	+	19.1484i	1.17666	+	0.0365395i
$66$		0			0
$67$	523.504	+	380.348i	0.954571	+	0.693536i	0.951884	−	0.306460i	$-0.0991446\pi$
$67$	523.504	+	380.348i	0.954571	+	0.693536i	0.00268734	+	0.999996i	$0.499145\pi$
$68$	−8.30906			−0.0148180
$69$		0			0
$70$	308.072	−	209.533i	0.526024	−	0.357772i
$71$	−798.476	+	580.127i	−1.33467	+	0.969696i	−0.335050	+	0.942200i	$0.608753\pi$
$71$	−798.476	+	580.127i	−1.33467	+	0.969696i	−0.999622	+	0.0274953i	$0.991247\pi$
$72$		0			0
$73$	−256.874	−	790.578i	−0.411847	−	1.26754i	−0.915040	−	0.403362i	$-0.867842\pi$
$73$	−256.874	−	790.578i	−0.411847	−	1.26754i	0.503193	−	0.864174i	$-0.332158\pi$
$74$	370.365			0.581811
$75$		0			0
$76$	106.884			0.161321
$77$	23.2023	+	71.4095i	0.0343396	+	0.105687i
$78$		0			0
$79$	822.092	−	597.285i	1.17079	−	0.850630i	0.179689	−	0.983724i	$-0.442491\pi$
$79$	822.092	−	597.285i	1.17079	−	0.850630i	0.991104	+	0.133093i	$0.0424909\pi$
$80$	197.904	+	6.14563i	0.276579	+	0.00858878i
$81$		0			0
$82$	−77.3154			−0.104123
$83$	−926.758	−	673.329i	−1.22560	−	0.890452i	−0.229049	−	0.973415i	$-0.573562\pi$
$83$	−926.758	−	673.329i	−1.22560	−	0.890452i	−0.996553	+	0.0829629i	$0.973562\pi$
$84$		0			0
$85$	−8.07608	+	22.4584i	−0.0103056	+	0.0286583i
$86$	158.436	+	487.616i	0.198658	+	0.611406i
$87$		0			0
$88$	−34.0117	+	104.677i	−0.0412006	+	0.126802i
$89$	−349.060	−	1074.29i	−0.415733	−	1.27949i	−0.911594	−	0.411093i	$-0.865147\pi$
$89$	−349.060	−	1074.29i	−0.415733	−	1.27949i	0.495861	−	0.868402i	$-0.334853\pi$
$90$		0			0
$91$	280.365	−	862.874i	0.322969	−	0.993998i
$92$	−309.843	−	225.114i	−0.351123	−	0.255106i
$93$		0			0
$94$	72.3224	+	52.5453i	0.0793562	+	0.0576557i
$95$	103.887	−	288.894i	0.112195	−	0.311999i
$96$		0			0
$97$	457.822	−	332.627i	0.479224	−	0.348177i	−0.321801	−	0.946807i	$-0.604288\pi$
$97$	457.822	−	332.627i	0.479224	−	0.348177i	0.801025	+	0.598630i	$0.204288\pi$
$98$	45.4968	+	140.025i	0.0468967	+	0.144333i
$99$		0			0
$100$	−178.776	+	452.519i	−0.178776	+	0.452519i
$101$	−732.732			−0.721877			−0.360938	−	0.932590i	$-0.617544\pi$
$101$	−732.732			−0.721877			−0.360938	+	0.932590i	$0.617544\pi$
$102$		0			0
$103$	148.901	−	108.183i	0.142443	−	0.103491i	−0.514282	−	0.857621i	$-0.671941\pi$
$103$	148.901	−	108.183i	0.142443	−	0.103491i	0.656725	+	0.754130i	$0.271941\pi$
$104$	1075.96	−	781.728i	1.01448	−	0.737065i
$105$		0			0
$106$	332.083	+	241.272i	0.304290	+	0.221080i
$107$	−1461.97			−1.32088			−0.660440	−	0.750879i	$-0.729630\pi$
$107$	−1461.97			−1.32088			−0.660440	+	0.750879i	$0.729630\pi$
$108$		0			0
$109$	551.250	−	1696.57i	0.484405	−	1.49085i	−0.348435	−	0.937333i	$-0.613287\pi$
$109$	551.250	−	1696.57i	0.484405	−	1.49085i	0.832840	−	0.553514i	$-0.186713\pi$
$110$	81.7838	+	63.3893i	0.0708889	+	0.0549448i
$111$		0			0
$112$	89.9823	−	276.937i	0.0759155	−	0.233644i
$113$	602.823	−	1855.30i	0.501848	−	1.54453i	−0.304158	−	0.952622i	$-0.598375\pi$
$113$	602.823	−	1855.30i	0.501848	−	1.54453i	0.806006	−	0.591907i	$-0.201625\pi$
$114$		0			0
$115$	−909.611	+	618.666i	−0.737580	+	0.501660i
$116$	4.01802	−	12.3662i	0.00321606	−	0.00989803i
$117$		0			0
$118$	−238.810			−0.186307
$119$	28.3959	+	20.6308i	0.0218744	+	0.0158926i
$120$		0			0
$121$	1059.93	−	770.085i	0.796342	−	0.578576i
$122$	−1317.00	+	956.859i	−0.977343	+	0.710081i
$123$		0			0
$124$	262.722			0.190267
$125$	1049.34	+	923.040i	0.750849	+	0.660474i
$126$		0			0
$127$	−286.464	−	881.645i	−0.200154	−	0.616011i	−0.999878	−	0.0156424i	$-0.995021\pi$
$127$	−286.464	−	881.645i	−0.200154	−	0.616011i	0.799724	−	0.600368i	$-0.204979\pi$
$128$	−261.874	+	190.263i	−0.180833	+	0.131383i
$129$		0			0
$130$	−349.275	−	1200.55i	−0.235642	−	0.809960i
$131$	2108.91	+	1532.21i	1.40654	+	1.02191i	0.993815	+	0.111050i	$0.0354213\pi$
$131$	2108.91	+	1532.21i	1.40654	+	1.02191i	0.412720	+	0.910858i	$0.364579\pi$
$132$		0			0
$133$	−365.271	−	265.385i	−0.238143	−	0.173021i
$134$	405.264	−	1247.27i	0.261265	−	0.804090i
$135$		0			0
$136$	15.8992	+	48.9328i	0.0100246	+	0.0308526i
$137$	−902.756	+	2778.40i	−0.562976	+	1.73266i	0.110915	+	0.993830i	$0.464622\pi$
$137$	−902.756	+	2778.40i	−0.562976	+	1.73266i	−0.673890	+	0.738831i	$0.735378\pi$
$138$		0			0
$139$	308.366	+	949.054i	0.188167	+	0.579120i	0.999989	−	0.00478634i	$-0.00152355\pi$
$139$	308.366	+	949.054i	0.188167	+	0.579120i	−0.811821	+	0.583906i	$0.801524\pi$
$140$	565.562	+	438.358i	0.341420	+	0.264629i
$141$		0			0
$142$	1618.28	+	1175.75i	0.956361	+	0.694837i
$143$	251.974			0.147351
$144$		0			0
$145$	−29.5190	−	22.8797i	−0.0169063	−	0.0131038i
$146$	−1362.98	+	990.261i	−0.772608	+	0.561333i
$147$		0			0
$148$	219.806	+	676.494i	0.122081	+	0.375726i
$149$	2608.22			1.43405			0.717026	−	0.697046i	$-0.245503\pi$
$149$	2608.22			1.43405			0.717026	+	0.697046i	$0.245503\pi$
$150$		0			0
$151$	−434.771			−0.234312			−0.117156	−	0.993114i	$-0.537378\pi$
$151$	−434.771			−0.234312			−0.117156	+	0.993114i	$0.537378\pi$
$152$	−204.520	−	629.448i	−0.109137	−	0.335888i
$153$		0			0
$154$	123.112	−	89.4459i	0.0644197	−	0.0468036i
$155$	255.356	−	710.107i	0.132327	−	0.367982i
$156$		0			0
$157$	−2183.01			−1.10970			−0.554851	−	0.831949i	$-0.687225\pi$
$157$	−2183.01			−1.10970			−0.554851	+	0.831949i	$0.687225\pi$
$158$	−1666.15	−	1210.53i	−0.838933	−	0.609521i
$159$		0			0
$160$	490.120	+	1684.66i	0.242171	+	0.832402i
$161$	499.933	+	1538.64i	0.244722	+	0.753178i
$162$		0			0
$163$	1.56141	−	4.80554i	0.000750303	−	0.00230920i	−0.950681	−	0.310171i	$-0.899614\pi$
$163$	1.56141	−	4.80554i	0.000750303	−	0.00230920i	0.951431	+	0.307862i	$0.0996136\pi$
$164$	−45.8856	−	141.221i	−0.0218480	−	0.0672411i
$165$		0			0
$166$	−717.437	+	2208.04i	−0.335445	+	1.03239i
$167$	−182.453	−	132.560i	−0.0845428	−	0.0614239i	0.544711	−	0.838624i	$-0.316639\pi$
$167$	−182.453	−	132.560i	−0.0845428	−	0.0614239i	−0.629254	+	0.777200i	$0.716639\pi$
$168$		0			0
$169$	−685.824	−	498.280i	−0.312164	−	0.226800i
$170$	48.3470	+	1.50135i	0.0218120	+	0.000677343i
$171$		0			0
$172$	−796.631	+	578.786i	−0.353154	+	0.256582i
$173$	−1021.65	−	3144.32i	−0.448986	−	1.38184i	−0.878052	−	0.478565i	$-0.841157\pi$
$173$	−1021.65	−	3144.32i	−0.448986	−	1.38184i	0.429066	−	0.903273i	$-0.358843\pi$
$174$		0			0
$175$	1734.53	−	1102.58i	0.749248	−	0.476270i
$176$	80.8705			0.0346355
$177$		0			0
$178$	−1852.11	+	1345.64i	−0.779897	+	0.566629i
$179$	1464.76	−	1064.21i	0.611627	−	0.444373i	−0.238360	−	0.971177i	$-0.576610\pi$
$179$	1464.76	−	1064.21i	0.611627	−	0.444373i	0.849987	+	0.526804i	$0.176610\pi$
$180$		0			0
$181$	−1447.42	−	1051.61i	−0.594395	−	0.431854i	0.249490	−	0.968377i	$-0.419737\pi$
$181$	−1447.42	−	1051.61i	−0.594395	−	0.431854i	−0.843885	+	0.536524i	$0.819737\pi$
$182$	−1838.80			−0.748905
$183$		0			0
$184$	−732.838	+	2255.44i	−0.293617	+	0.903661i
$185$	2042.13	+	63.4155i	0.811568	+	0.0252022i
$186$		0			0
$187$	−3.01228	+	9.27085i	−0.00117797	+	0.00362541i
$188$	−53.0549	+	163.286i	−0.0205821	+	0.0633451i
$189$		0			0
$190$	−621.912	−	19.3126i	−0.237464	−	0.00737414i
$191$	−1406.35	+	4328.29i	−0.532774	+	1.63971i	0.215637	+	0.976474i	$0.430817\pi$
$191$	−1406.35	+	4328.29i	−0.532774	+	1.63971i	−0.748411	+	0.663235i	$0.769183\pi$
$192$		0			0
$193$	3534.94			1.31840			0.659199	−	0.751969i	$-0.270895\pi$
$193$	3534.94			1.31840			0.659199	+	0.751969i	$0.270895\pi$
$194$	−927.874	−	674.140i	−0.343389	−	0.249487i
$195$		0			0
$196$	−228.762	+	166.206i	−0.0833682	+	0.0605706i
$197$	−135.139	+	98.1842i	−0.0488744	+	0.0355093i	−0.611954	−	0.790893i	$-0.709616\pi$
$197$	−135.139	+	98.1842i	−0.0488744	+	0.0355093i	0.563080	+	0.826402i	$0.309616\pi$
$198$		0			0
$199$	−3173.44			−1.13045			−0.565224	−	0.824937i	$-0.691210\pi$
$199$	−3173.44			−1.13045			−0.565224	+	0.824937i	$0.691210\pi$
$200$	3007.01	+	186.938i	1.06314	+	0.0660925i
$201$		0			0
$202$	458.902	+	1412.36i	0.159843	+	0.491946i
$203$	−44.4358	+	32.2845i	−0.0153635	+	0.0111622i
$204$		0			0
$205$	−426.304	−	13.2383i	−0.145241	−	0.00451026i
$206$	−301.779	−	219.256i	−0.102068	−	0.0741566i
$207$		0			0
$208$	−790.569	−	574.382i	−0.263539	−	0.191472i
$209$	38.7485	−	119.256i	0.0128244	−	0.0394693i
$210$		0			0
$211$	842.745	+	2593.70i	0.274962	+	0.846245i	0.989229	+	0.146373i	$0.0467599\pi$
$211$	842.745	+	2593.70i	0.274962	+	0.846245i	−0.714268	+	0.699873i	$0.753240\pi$
$212$	−243.612	+	749.762i	−0.0789215	+	0.242895i
$213$		0			0
$214$	915.617	+	2817.98i	0.292478	+	0.900154i
$215$	790.097	+	2715.76i	0.250624	+	0.861456i
$216$		0			0
$217$	−897.844	−	652.322i	−0.280874	−	0.204067i
$218$	−3615.42			−1.12324
$219$		0			0
$220$	−67.2469	+	187.004i	−0.0206081	+	0.0573082i
$221$	95.2934	−	69.2347i	0.0290051	−	0.0210734i
$222$		0			0
$223$	−11.6372	−	35.8157i	−0.00349456	−	0.0107551i	0.949294	−	0.314390i	$-0.101800\pi$
$223$	−11.6372	−	35.8157i	−0.00349456	−	0.0107551i	−0.952789	+	0.303634i	$0.901800\pi$
$224$	2580.29			0.769655
$225$		0			0
$226$	−3953.67			−1.16369
$227$	−1025.04	−	3154.75i	−0.299710	−	0.922413i	−0.981598	−	0.190957i	$-0.938841\pi$
$227$	−1025.04	−	3154.75i	−0.299710	−	0.922413i	0.681888	−	0.731456i	$-0.261159\pi$
$228$		0			0
$229$	−3988.04	+	2897.48i	−1.15082	+	0.836118i	−0.988589	−	0.150635i	$-0.951868\pi$
$229$	−3988.04	+	2897.48i	−1.15082	+	0.836118i	−0.162228	+	0.986753i	$0.551868\pi$
$230$	1762.17	+	1365.83i	0.505192	+	0.391566i
$231$		0			0
$232$	−80.5141			−0.0227845
$233$	−5.77631	−	4.19673i	−0.00162411	−	0.00117999i	0.586973	−	0.809607i	$-0.300320\pi$
$233$	−5.77631	−	4.19673i	−0.00162411	−	0.00117999i	−0.588597	+	0.808427i	$0.700320\pi$
$234$		0			0
$235$	389.776	+	302.109i	0.108197	+	0.0838614i
$236$	−141.730	−	436.201i	−0.0390926	−	0.120315i
$237$		0			0
$238$	21.9823	−	67.6545i	0.00598698	−	0.0184260i
$239$	−2227.98	−	6857.03i	−0.602997	−	1.85583i	−0.510015	−	0.860165i	$-0.670360\pi$
$239$	−2227.98	−	6857.03i	−0.602997	−	1.85583i	−0.0929815	−	0.995668i	$-0.529640\pi$
$240$		0			0
$241$	−1061.81	+	3267.92i	−0.283806	+	0.873465i	0.702948	+	0.711241i	$0.251867\pi$
$241$	−1061.81	+	3267.92i	−0.283806	+	0.873465i	−0.986754	+	0.162224i	$0.948133\pi$
$242$	−2148.18	−	1560.74i	−0.570620	−	0.414580i
$243$		0			0
$244$	−2529.39	−	1837.71i	−0.663637	−	0.482160i
$245$	226.886	+	779.863i	0.0591642	+	0.203362i
$246$		0			0
$247$	−1225.81	+	890.601i	−0.315774	+	0.229424i
$248$	−502.715	−	1547.20i	−0.128719	−	0.396158i
$249$		0			0
$250$	1121.99	−	2600.72i	0.283842	−	0.657936i
$251$	1687.00			0.424233			0.212117	−	0.977244i	$-0.431964\pi$
$251$	1687.00			0.424233			0.212117	+	0.977244i	$0.431964\pi$
$252$		0			0
$253$	−363.499	+	264.097i	−0.0903279	+	0.0656271i
$254$	−1519.98	+	1104.33i	−0.375480	+	0.272802i
$255$		0			0
$256$	3506.15	+	2547.37i	0.855993	+	0.621915i
$257$	−2098.27			−0.509286			−0.254643	−	0.967035i	$-0.581958\pi$
$257$	−2098.27			−0.509286			−0.254643	+	0.967035i	$0.581958\pi$
$258$		0			0
$259$	928.509	−	2857.66i	0.222760	−	0.685584i
$260$	1985.58	−	1350.48i	0.473617	−	0.322128i
$261$		0			0
$262$	1632.58	−	5024.57i	0.384966	−	1.18480i
$263$	43.9940	−	135.400i	0.0103148	−	0.0317456i	−0.945767	−	0.324847i	$-0.894687\pi$
$263$	43.9940	−	135.400i	0.0103148	−	0.0317456i	0.956081	+	0.293101i	$0.0946873\pi$
$264$		0			0
$265$	1789.74	+	1387.19i	0.414878	+	0.321565i
$266$	−282.770	+	870.275i	−0.0651794	+	0.200601i
$267$		0			0
$268$	2518.74			0.574092
$269$	−2534.35	−	1841.31i	−0.574432	−	0.417349i	0.262281	−	0.964992i	$-0.415525\pi$
$269$	−2534.35	−	1841.31i	−0.574432	−	0.417349i	−0.836712	+	0.547643i	$0.815525\pi$
$270$		0			0
$271$	2812.49	−	2043.40i	0.630431	−	0.458035i	−0.226118	−	0.974100i	$-0.572604\pi$
$271$	2812.49	−	2043.40i	0.630431	−	0.458035i	0.856550	+	0.516065i	$0.172604\pi$
$272$	30.5841	−	22.2207i	0.00681778	−	0.00495341i
$273$		0			0
$274$	5920.80			1.30543
$275$	440.088	+	363.521i	0.0965030	+	0.0797133i
$276$		0			0
$277$	−1027.03	−	3160.87i	−0.222774	−	0.685626i	−0.998510	−	0.0545694i	$-0.982621\pi$
$277$	−1027.03	−	3160.87i	−0.222774	−	0.685626i	0.775736	−	0.631057i	$-0.217379\pi$
$278$	1636.19	−	1188.76i	0.352994	−	0.256465i
$279$		0			0
$280$	1499.34	−	4169.44i	0.320009	−	0.889899i
$281$	−2319.48	−	1685.20i	−0.492415	−	0.357760i	0.313698	−	0.949523i	$-0.398432\pi$
$281$	−2319.48	−	1685.20i	−0.492415	−	0.357760i	−0.806112	+	0.591763i	$0.798432\pi$
$282$		0			0
$283$	6659.26	+	4838.24i	1.39877	+	1.01627i	0.994838	+	0.101478i	$0.0323571\pi$
$283$	6659.26	+	4838.24i	1.39877	+	1.01627i	0.403933	+	0.914789i	$0.367643\pi$
$284$	−1187.15	+	3653.69i	−0.248045	+	0.763403i
$285$		0			0
$286$	−157.809	−	485.686i	−0.0326274	−	0.100417i
$287$	−193.831	+	596.550i	−0.0398658	+	0.122694i
$288$		0			0
$289$	−1516.79	−	4668.21i	−0.308730	−	0.950174i
$290$	−25.6136	+	71.2277i	−0.00518649	+	0.0144229i
$291$		0			0
$292$	−2617.68	−	1901.86i	−0.524617	−	0.381157i
$293$	−2288.26			−0.456251			−0.228125	−	0.973632i	$-0.573260\pi$
$293$	−2288.26			−0.456251			−0.228125	+	0.973632i	$0.573260\pi$
$294$		0			0
$295$	−1316.76	−	40.8901i	−0.259880	−	0.00807022i
$296$	3563.34	−	2588.92i	0.699713	−	0.508371i
$297$		0			0
$298$	−1633.50	−	5027.40i	−0.317538	−	0.977280i
$299$	5429.21			1.05010
$300$		0			0
$301$	4159.55			0.796519
$302$	272.292	+	838.029i	0.0518830	+	0.159679i
$303$		0			0
$304$	−393.420	+	285.836i	−0.0742242	+	0.0539271i
$305$	−7425.57	+	5050.45i	−1.39405	+	0.948157i
$306$		0			0
$307$	−2783.54			−0.517475			−0.258737	−	0.965948i	$-0.583306\pi$
$307$	−2783.54			−0.517475			−0.258737	+	0.965948i	$0.583306\pi$
$308$	236.444	+	171.786i	0.0437423	+	0.0317806i
$309$		0			0
$310$	−1528.67	−	47.4709i	−0.280073	−	0.00869731i
$311$	2462.79	+	7579.70i	0.449043	+	1.38201i	0.877989	+	0.478681i	$0.158885\pi$
$311$	2462.79	+	7579.70i	0.449043	+	1.38201i	−0.428946	+	0.903330i	$0.641115\pi$
$312$		0			0
$313$	−1489.79	+	4585.11i	−0.269035	+	0.828005i	0.721701	+	0.692205i	$0.243360\pi$
$313$	−1489.79	+	4585.11i	−0.269035	+	0.828005i	−0.990736	+	0.135800i	$0.956640\pi$
$314$	1367.20	+	4207.80i	0.245718	+	0.756242i
$315$		0			0
$316$	1222.27	−	3761.75i	0.217588	−	0.669668i
$317$	6986.98	+	5076.34i	1.23794	+	0.899418i	0.997460	−	0.0712347i	$-0.0226939\pi$
$317$	6986.98	+	5076.34i	1.23794	+	0.899418i	0.240484	+	0.970653i	$0.422694\pi$
$318$		0			0
$319$	−12.3409	−	8.96622i	−0.00216602	−	0.00157371i
$320$	4250.02	−	2890.63i	0.742448	−	0.504971i
$321$		0			0
$322$	2652.65	−	1927.26i	0.459088	−	0.333547i
$323$	−18.1136	−	55.7478i	−0.00312033	−	0.00960338i
$324$		0			0
$325$	−1720.28	−	6679.41i	−0.293612	−	1.14002i
$326$	−10.2407			−0.00173981
$327$		0			0
$328$	−743.866	+	540.450i	−0.125223	+	0.0909797i
$329$	586.742	−	426.293i	0.0983226	−	0.0714356i
$330$		0			0
$331$	1556.01	+	1130.51i	0.258388	+	0.187730i	0.709436	−	0.704770i	$-0.248950\pi$
$331$	1556.01	+	1130.51i	0.258388	+	0.187730i	−0.451048	+	0.892500i	$0.648950\pi$
$332$	−4458.92			−0.737093
$333$		0			0
$334$	−141.244	+	434.703i	−0.0231392	+	0.0712152i
$335$	2448.12	−	6807.86i	0.399269	−	1.11031i
$336$		0			0
$337$	721.800	−	2221.47i	0.116673	−	0.359084i	−0.875619	−	0.483003i	$-0.839546\pi$
$337$	721.800	−	2221.47i	0.116673	−	0.359084i	0.992292	+	0.123919i	$0.0395462\pi$
$338$	−530.921	+	1634.01i	−0.0854388	+	0.262953i
$339$		0			0
$340$	25.9509	+	89.1998i	0.00413937	+	0.0142280i
$341$	95.2447	−	293.133i	0.0151255	−	0.0465515i
$342$		0			0
$343$	6834.23			1.07584
$344$	4932.87	+	3583.94i	0.773147	+	0.561724i
$345$		0			0
$346$	−5420.88	+	3938.50i	−0.842279	+	0.611952i
$347$	5254.02	−	3817.27i	0.812826	−	0.590553i	−0.101822	−	0.994803i	$-0.532467\pi$
$347$	5254.02	−	3817.27i	0.812826	−	0.590553i	0.914649	+	0.404250i	$0.132467\pi$
$348$		0			0
$349$	4713.73			0.722980			0.361490	−	0.932376i	$-0.382268\pi$
$349$	4713.73			0.722980			0.361490	+	0.932376i	$0.382268\pi$
$350$	−3211.57	−	2652.81i	−0.490473	−	0.405140i
$351$		0			0
$352$	221.445	+	681.537i	0.0335314	+	0.103199i
$353$	3185.69	−	2314.54i	0.480331	−	0.348981i	−0.321123	−	0.947038i	$-0.604060\pi$
$353$	3185.69	−	2314.54i	0.480331	−	0.348981i	0.801454	+	0.598056i	$0.204060\pi$
$354$		0			0
$355$	8721.62	+	6759.98i	1.30393	+	1.01066i
$356$	−3557.10	−	2584.38i	−0.529567	−	0.384753i
$357$		0			0
$358$	−2968.65	−	2156.85i	−0.438262	−	0.318416i
$359$	−2913.64	+	8967.26i	−0.428345	+	1.31831i	0.471409	+	0.881915i	$0.343746\pi$
$359$	−2913.64	+	8967.26i	−0.428345	+	1.31831i	−0.899754	+	0.436397i	$0.856254\pi$
$360$		0			0
$361$	−1886.54	−	5806.18i	−0.275046	−	0.846506i
$362$	−1120.50	+	3448.53i	−0.162685	+	0.500693i
$363$		0			0
$364$	−1091.30	−	3358.68i	−0.157142	−	0.483633i
$365$	−7684.78	+	5226.75i	−1.10203	+	0.749536i
$366$		0			0
$367$	2067.94	+	1502.45i	0.294130	+	0.213698i	0.725057	−	0.688689i	$-0.241813\pi$
$367$	2067.94	+	1502.45i	0.294130	+	0.213698i	−0.430927	+	0.902387i	$0.641813\pi$
$368$	1742.49			0.246831
$369$		0			0
$370$	−1156.73	−	3975.96i	−0.162528	−	0.558649i
$371$	2694.14	−	1957.41i	0.377016	−	0.273918i
$372$		0			0
$373$	−3360.65	−	10343.0i	−0.466509	−	1.43577i	−0.857074	−	0.515193i	$-0.827720\pi$
$373$	−3360.65	−	10343.0i	−0.466509	−	1.43577i	0.390565	−	0.920575i	$-0.372280\pi$
$374$	19.7563			0.00273148
$375$		0			0
$376$	1063.13			0.145816
$377$	56.9593	+	175.303i	0.00778131	+	0.0239484i
$378$		0			0
$379$	−5989.27	+	4351.46i	−0.811737	+	0.589761i	−0.914334	−	0.404962i	$-0.867285\pi$
$379$	−5989.27	+	4351.46i	−0.811737	+	0.589761i	0.102597	+	0.994723i	$0.467285\pi$
$380$	−333.820	−	1147.42i	−0.0450648	−	0.154899i
$381$		0			0
$382$	9223.65			1.23540
$383$	5046.70	+	3666.64i	0.673301	+	0.489182i	0.871128	−	0.491055i	$-0.163389\pi$
$383$	5046.70	+	3666.64i	0.673301	+	0.489182i	−0.197828	+	0.980237i	$0.563389\pi$
$384$		0			0
$385$	694.132	−	472.110i	0.0918864	−	0.0624959i
$386$	−2213.90	−	6813.67i	−0.291928	−	0.898463i
$387$		0			0
$388$	680.678	−	2094.91i	0.0890624	−	0.274106i
$389$	−2416.91	−	7438.49i	−0.315019	−	0.969528i	−0.975747	−	0.218903i	$-0.929752\pi$
$389$	−2416.91	−	7438.49i	−0.315019	−	0.969528i	0.660728	−	0.750625i	$-0.270248\pi$
$390$		0			0
$391$	−64.9047	+	199.756i	−0.00839481	+	0.0258366i
$392$	1416.53	+	1029.17i	0.182515	+	0.132605i
$393$		0			0
$394$	273.888	+	198.991i	0.0350210	+	0.0254443i
$395$	−8979.57	−	6959.92i	−1.14383	−	0.886560i
$396$		0			0
$397$	−6541.82	+	4752.91i	−0.827013	+	0.600860i	−0.918713	−	0.394926i	$-0.870770\pi$
$397$	−6541.82	+	4752.91i	−0.827013	+	0.600860i	0.0916994	+	0.995787i	$0.470770\pi$
$398$	1987.49	+	6116.87i	0.250311	+	0.770379i
$399$		0			0
$400$	−552.120	−	2143.74i	−0.0690150	−	0.267967i
$401$	−1345.64			−0.167576			−0.0837882	−	0.996484i	$-0.526702\pi$
$401$	−1345.64			−0.167576			−0.0837882	+	0.996484i	$0.526702\pi$
$402$		0			0
$403$	−3013.06	+	2189.12i	−0.372435	+	0.270590i
$404$	−2307.40	+	1676.43i	−0.284153	+	0.206449i
$405$		0			0
$406$	90.0587	+	65.4315i	0.0110087	+	0.00799830i
$407$	834.486			0.101631
$408$		0			0
$409$	917.900	−	2825.00i	0.110971	−	0.341534i	−0.880114	−	0.474762i	$-0.842534\pi$
$409$	917.900	−	2825.00i	0.110971	−	0.341534i	0.991085	+	0.133228i	$0.0425342\pi$
$410$	241.472	+	830.000i	0.0290865	+	0.0999776i
$411$		0			0
$412$	221.382	−	681.344i	0.0264726	−	0.0814743i
$413$	−598.700	+	1842.61i	−0.0713320	+	0.219537i
$414$		0			0
$415$	−4333.90	+	12051.9i	−0.512633	+	1.42556i
$416$	2675.82	−	8235.34i	0.315368	−	0.970603i
$417$		0			0
$418$	−254.136			−0.0297373
$419$	−12542.9	−	9112.94i	−1.46243	−	1.06252i	−0.982721	−	0.185095i	$-0.940741\pi$
$419$	−12542.9	−	9112.94i	−1.46243	−	1.06252i	−0.479713	−	0.877425i	$-0.659259\pi$
$420$		0			0
$421$	−1956.11	+	1421.19i	−0.226448	+	0.164524i	−0.695225	−	0.718793i	$-0.744695\pi$
$421$	−1956.11	+	1421.19i	−0.226448	+	0.164524i	0.468776	+	0.883317i	$0.344695\pi$
$422$	4471.61	−	3248.81i	0.515816	−	0.374763i
$423$		0			0
$424$	4881.57			0.559127
$425$	266.320	+	16.5564i	0.0303962	+	0.00188965i
$426$		0			0
$427$	4081.18	+	12560.6i	0.462535	+	1.42354i
$428$	−4603.81	+	3344.86i	−0.519938	+	0.377757i
$429$		0			0
$430$	4739.85	−	3223.78i	0.531571	−	0.361545i
$431$	−6422.91	−	4666.52i	−0.717821	−	0.521527i	0.167866	−	0.985810i	$-0.446312\pi$
$431$	−6422.91	−	4666.52i	−0.717821	−	0.521527i	−0.885687	+	0.464282i	$0.846312\pi$
$432$		0			0
$433$	1146.40	+	832.906i	0.127234	+	0.0924409i	0.649582	−	0.760291i	$-0.274944\pi$
$433$	1146.40	+	832.906i	0.127234	+	0.0924409i	−0.522348	+	0.852732i	$0.674944\pi$
$434$	−695.054	+	2139.15i	−0.0768747	+	0.236596i
$435$		0			0
$436$	−2145.70	−	6603.79i	−0.235689	−	0.725377i
$437$	834.902	−	2569.57i	0.0913931	−	0.281279i
$438$		0			0
$439$	4154.10	+	12785.0i	0.451628	+	1.38997i	0.875049	+	0.484034i	$0.160829\pi$
$439$	4154.10	+	12785.0i	0.451628	+	1.38997i	−0.423422	+	0.905933i	$0.639171\pi$
$440$	1229.96	+	38.1948i	0.133264	+	0.00413833i
$441$		0			0
$442$	−193.132	−	140.319i	−0.0207836	−	0.0151002i
$443$	13347.6			1.43152			0.715759	−	0.698347i	$-0.246081\pi$
$443$	13347.6			1.43152			0.715759	+	0.698347i	$0.246081\pi$
$444$		0			0
$445$	−10442.6	+	7102.49i	−1.11242	+	0.756608i
$446$	−61.7472	+	44.8619i	−0.00655564	+	0.00476295i
$447$		0			0
$448$	−2335.87	−	7189.05i	−0.246338	−	0.758149i
$449$	3063.89			0.322035			0.161017	−	0.986952i	$-0.448522\pi$
$449$	3063.89			0.322035			0.161017	+	0.986952i	$0.448522\pi$
$450$		0			0
$451$	−174.203			−0.0181883
$452$	−2346.45	−	7221.62i	−0.244176	−	0.751496i
$453$		0			0
$454$	−5438.86	+	3951.57i	−0.562243	+	0.408494i
$455$	−10138.8	−	314.847i	−1.04465	−	0.0324401i
$456$		0			0
$457$	−185.070			−0.0189435			−0.00947177	−	0.999955i	$-0.503015\pi$
$457$	−185.070			−0.0189435			−0.00947177	+	0.999955i	$0.503015\pi$
$458$	8082.62	+	5872.37i	0.824620	+	0.599122i
$459$		0			0
$460$	−1448.95	+	4029.31i	−0.146864	+	0.408408i
$461$	−2389.28	−	7353.45i	−0.241388	−	0.742916i	−0.996210	−	0.0869857i	$-0.972277\pi$
$461$	−2389.28	−	7353.45i	−0.241388	−	0.742916i	0.754822	−	0.655930i	$-0.227723\pi$
$462$		0			0
$463$	−4560.19	+	14034.8i	−0.457732	+	1.40875i	0.410165	+	0.912011i	$0.365471\pi$
$463$	−4560.19	+	14034.8i	−0.457732	+	1.40875i	−0.867897	+	0.496744i	$0.834529\pi$
$464$	18.2810	+	56.2630i	0.00182903	+	0.00562919i
$465$		0			0
$466$	−4.47165	+	13.7623i	−0.000444517	+	0.00136808i
$467$	11511.6	+	8363.69i	1.14067	+	0.828748i	0.987213	−	0.159407i	$-0.0509582\pi$
$467$	11511.6	+	8363.69i	1.14067	+	0.828748i	0.153460	+	0.988155i	$0.450958\pi$
$468$		0			0
$469$	−8607.71	−	6253.87i	−0.847478	−	0.615729i
$470$	338.209	−	940.509i	0.0331923	−	0.0923031i
$471$		0			0
$472$	−2297.63	+	1669.33i	−0.224062	+	0.162790i
$473$	356.980	+	1098.67i	0.0347018	+	0.106801i
$474$		0			0
$475$	−3425.81	−	212.973i	−0.330920	−	0.0205724i
$476$	136.621			0.0131555
$477$		0			0
$478$	−11821.7	+	8588.96i	−1.13120	+	0.821862i
$479$	−13254.4	+	9629.85i	−1.26431	+	0.918578i	−0.998961	−	0.0455728i	$-0.985489\pi$
$479$	−13254.4	+	9629.85i	−1.26431	+	0.918578i	−0.265354	+	0.964151i	$0.585489\pi$
$480$		0			0
$481$	−8157.72	−	5926.93i	−0.773305	−	0.561839i
$482$	6963.98			0.658092
$483$		0			0
$484$	1575.88	−	4850.06i	0.147998	−	0.455490i
$485$	−5000.71	−	3875.97i	−0.468186	−	0.362884i
$486$		0			0
$487$	−4049.02	+	12461.6i	−0.376752	+	1.15952i	0.565536	+	0.824723i	$0.308669\pi$
$487$	−4049.02	+	12461.6i	−0.376752	+	1.15952i	−0.942289	+	0.334801i	$0.891331\pi$
$488$	−5982.49	+	18412.2i	−0.554948	+	1.70795i
$489$		0			0
$490$	1361.11	−	925.747i	0.125487	−	0.0853490i
$491$	−570.719	+	1756.49i	−0.0524566	+	0.161445i	−0.973853	−	0.227180i	$-0.927050\pi$
$491$	−570.719	+	1756.49i	−0.0524566	+	0.161445i	0.921396	+	0.388624i	$0.127050\pi$
$492$		0			0
$493$	−7.13082			−0.000651432
$494$	2484.36	+	1804.99i	0.226269	+	0.164394i
$495$		0			0
$496$	−967.034	+	702.591i	−0.0875426	+	0.0636034i
$497$	13128.9	−	9538.72i	1.18493	−	0.860906i
$498$		0			0
$499$	17773.8			1.59451			0.797257	−	0.603640i	$-0.206284\pi$
$499$	17773.8			1.59451			0.797257	+	0.603640i	$0.206284\pi$
$500$	5416.26	+	505.886i	0.484445	+	0.0452478i
$501$		0			0
$502$	−1056.55	−	3251.73i	−0.0939366	−	0.289107i
$503$	1358.97	−	987.353i	0.120465	−	0.0875227i	−0.525922	−	0.850533i	$-0.676279\pi$
$503$	1358.97	−	987.353i	0.120465	−	0.0875227i	0.646386	+	0.763010i	$0.276279\pi$
$504$		0			0
$505$	2288.48	+	7866.06i	0.201655	+	0.693139i
$506$	736.708	+	535.249i	0.0647246	+	0.0470252i
$507$		0			0
$508$	−2919.21	−	2120.93i	−0.254959	−	0.185239i
$509$	−5876.65	+	18086.5i	−0.511744	+	1.57499i	0.277385	+	0.960759i	$0.410532\pi$
$509$	−5876.65	+	18086.5i	−0.511744	+	1.57499i	−0.789129	+	0.614228i	$0.789468\pi$
$510$		0			0
$511$	4223.65	+	12999.1i	0.365642	+	1.12533i
$512$	1914.02	−	5890.75i	0.165212	−	0.508470i
$513$		0			0
$514$	1314.12	+	4044.46i	0.112769	+	0.347069i
$515$	−1626.42	−	1260.61i	−0.139162	−	0.107862i
$516$		0			0
$517$	162.953	+	118.392i	0.0138620	+	0.0100714i
$518$	−6089.71			−0.516538
$519$		0			0
$520$	−11752.5	−	9109.16i	−0.991117	−	0.768198i
$521$	−1611.58	+	1170.88i	−0.135517	+	0.0984592i	−0.653479	−	0.756945i	$-0.726691\pi$
$521$	−1611.58	+	1170.88i	−0.135517	+	0.0984592i	0.517961	+	0.855404i	$0.326691\pi$
$522$		0			0
$523$	−3681.59	−	11330.8i	−0.307810	−	0.947342i	−0.978614	−	0.205707i	$-0.934051\pi$
$523$	−3681.59	−	11330.8i	−0.307810	−	0.947342i	0.670803	−	0.741635i	$-0.265949\pi$
$524$	10146.6			0.845909
$525$		0			0
$526$	−288.538			−0.0239180
$527$	−44.5235	−	137.029i	−0.00368022	−	0.0113265i
$528$		0			0
$529$	2011.12	−	1461.17i	0.165293	−	0.120093i
$530$	1552.95	−	4318.54i	0.127275	−	0.353934i
$531$		0			0
$532$	−1757.43			−0.143222
$533$	1702.96	+	1237.28i	0.138393	+	0.100549i
$534$		0			0
$535$	4566.05	+	15694.6i	0.368986	+	1.26829i
$536$	−4819.57	−	14833.1i	−0.388384	−	1.19532i
$537$		0			0
$538$	−1961.93	+	6038.21i	−0.157221	+	0.483876i
$539$	102.511	+	315.497i	0.00819196	+	0.0252123i
$540$		0			0
$541$	3650.27	−	11234.4i	0.290088	−	0.892798i	−0.694740	−	0.719261i	$-0.744480\pi$
$541$	3650.27	−	11234.4i	0.290088	−	0.892798i	0.984827	−	0.173537i	$-0.0555196\pi$
$542$	−5700.12	−	4141.38i	−0.451736	−	0.328206i
$543$		0			0
$544$	271.013	+	196.902i	0.0213595	+	0.0155186i
$545$	−19934.8	−	619.049i	−1.56681	−	0.0486553i
$546$		0			0
$547$	6225.01	−	4522.74i	0.486586	−	0.353525i	−0.317284	−	0.948331i	$-0.602771\pi$
$547$	6225.01	−	4522.74i	0.486586	−	0.353525i	0.803870	+	0.594805i	$0.202771\pi$
$548$	3513.92	+	10814.7i	0.273918	+	0.843033i
$549$		0			0
$550$	425.072	−	1075.95i	0.0329548	−	0.0834156i
$551$	91.7274			0.00709205
$552$		0			0
$553$	−13517.2	+	9820.84i	−1.03944	+	0.755198i
$554$	−5449.43	+	3959.24i	−0.417914	+	0.303632i
$555$		0			0
$556$	3142.41	+	2283.09i	0.239690	+	0.174145i
$557$	20699.8			1.57465			0.787324	−	0.616540i	$-0.211466\pi$
$557$	20699.8			1.57465			0.787324	+	0.616540i	$0.211466\pi$
$558$		0			0
$559$	4313.55	−	13275.8i	0.326375	−	1.00448i
$560$	−3254.02	−	101.049i	−0.245549	−	0.00762521i
$561$		0			0
$562$	−1795.59	+	5526.26i	−0.134773	+	0.414789i
$563$	5732.09	−	17641.6i	0.429092	−	1.32061i	−0.469929	−	0.882704i	$-0.655721\pi$
$563$	5732.09	−	17641.6i	0.429092	−	1.32061i	0.899021	−	0.437905i	$-0.144279\pi$
$564$		0			0
$565$	−21799.8	−	676.965i	−1.62323	−	0.0504073i
$566$	5155.18	−	15866.0i	0.382841	−	1.17826i
$567$		0			0
$568$	23788.5			1.75730
$569$	131.419	+	95.4817i	0.00968257	+	0.00703480i	0.592616	−	0.805485i	$-0.298095\pi$
$569$	131.419	+	95.4817i	0.00968257	+	0.00703480i	−0.582933	+	0.812520i	$0.698095\pi$
$570$		0			0
$571$	13305.3	−	9666.86i	0.975147	−	0.708486i	0.0185281	−	0.999828i	$-0.494102\pi$
$571$	13305.3	−	9666.86i	0.975147	−	0.708486i	0.956619	+	0.291343i	$0.0941020\pi$
$572$	793.478	−	576.495i	0.0580017	−	0.0421407i
$573$		0			0
$574$	1271.26			0.0924412
$575$	9482.44	+	7832.67i	0.687731	+	0.568078i
$576$		0			0
$577$	−1917.80	−	5902.39i	−0.138369	−	0.425857i	0.857729	−	0.514101i	$-0.171874\pi$
$577$	−1917.80	−	5902.39i	−0.138369	−	0.425857i	−0.996099	+	0.0882441i	$0.971874\pi$
$578$	−8048.11	+	5847.29i	−0.579165	+	0.420788i
$579$		0			0
$580$	−145.303	−	4.51220i	−0.0104024	−	0.000323032i
$581$	15238.2	+	11071.2i	1.08810	+	0.790552i
$582$		0			0
$583$	748.232	+	543.622i	0.0531537	+	0.0386184i
$584$	−6191.33	+	19054.9i	−0.438697	+	1.35017i
$585$		0			0
$586$	1433.11	+	4410.66i	0.101026	+	0.310926i
$587$	−4296.85	+	13224.4i	−0.302130	+	0.929860i	0.678603	+	0.734505i	$0.262586\pi$
$587$	−4296.85	+	13224.4i	−0.302130	+	0.929860i	−0.980733	+	0.195354i	$0.937414\pi$
$588$		0			0
$589$	572.729	+	1762.68i	0.0400660	+	0.123311i
$590$	745.854	+	2563.68i	0.0520446	+	0.178890i
$591$		0			0
$592$	−2618.20	−	1902.23i	−0.181769	−	0.132063i
$593$	11389.2			0.788698			0.394349	−	0.918961i	$-0.370970\pi$
$593$	11389.2			0.788698			0.394349	+	0.918961i	$0.370970\pi$
$594$		0			0
$595$	132.791	−	369.272i	0.00914939	−	0.0254431i
$596$	8213.40	−	5967.38i	0.564486	−	0.410123i
$597$		0			0
$598$	−3400.26	−	10464.9i	−0.232520	−	0.715622i
$599$	−12576.2			−0.857844			−0.428922	−	0.903342i	$-0.641106\pi$
$599$	−12576.2			−0.857844			−0.428922	+	0.903342i	$0.641106\pi$
$600$		0			0
$601$	2154.43			0.146225			0.0731124	−	0.997324i	$-0.476707\pi$
$601$	2154.43			0.146225			0.0731124	+	0.997324i	$0.476707\pi$
$602$	−2605.08	−	8017.61i	−0.176371	−	0.542813i
$603$		0			0
$604$	−1369.11	+	994.717i	−0.0922323	+	0.0670107i
$605$	−11577.4	−	8973.49i	−0.778000	−	0.603015i
$606$		0			0
$607$	9937.94			0.664528			0.332264	−	0.943186i	$-0.392187\pi$
$607$	9937.94			0.664528			0.332264	+	0.943186i	$0.392187\pi$
$608$	−3486.18	−	2532.86i	−0.232538	−	0.168949i
$609$		0			0
$610$	14385.4	+	11149.9i	0.954832	+	0.740075i
$611$	−752.106	−	2314.74i	−0.0497986	−	0.153264i
$612$		0			0
$613$	3184.38	−	9800.52i	0.209814	−	0.645741i	−0.789667	−	0.613535i	$-0.789747\pi$
$613$	3184.38	−	9800.52i	0.209814	−	0.645741i	0.999481	−	0.0322059i	$-0.0102532\pi$
$614$	1743.30	+	5365.32i	0.114583	+	0.352649i
$615$		0			0
$616$	559.236	−	1721.15i	0.0365783	−	0.112577i
$617$	13637.9	+	9908.50i	0.889854	+	0.646517i	0.935840	−	0.352425i	$-0.114643\pi$
$617$	13637.9	+	9908.50i	0.889854	+	0.646517i	−0.0459856	+	0.998942i	$0.514643\pi$
$618$		0			0
$619$	−6572.78	−	4775.40i	−0.426789	−	0.310080i	0.353575	−	0.935406i	$-0.384966\pi$
$619$	−6572.78	−	4775.40i	−0.426789	−	0.310080i	−0.780364	+	0.625326i	$0.784966\pi$
$620$	−820.537	−	2820.39i	−0.0531509	−	0.182693i
$621$		0			0
$622$	13067.6	−	9494.17i	0.842385	−	0.612028i
$623$	5739.40	+	17664.1i	0.369092	+	1.13595i
$624$		0			0
$625$	6631.74	−	14147.8i	0.424432	−	0.905460i
$626$	9770.92			0.623841
$627$		0			0
$628$	−6874.40	+	4994.54i	−0.436813	+	0.317363i
$629$	315.592	−	229.291i	0.0200055	−	0.0145348i
$630$		0			0
$631$	−9984.59	−	7254.23i	−0.629921	−	0.457665i	0.226452	−	0.974022i	$-0.427287\pi$
$631$	−9984.59	−	7254.23i	−0.629921	−	0.457665i	−0.856373	+	0.516358i	$0.827287\pi$
$632$	−24492.1			−1.54152
$633$		0			0
$634$	5408.87	−	16646.8i	0.338823	−	1.04279i
$635$	−8569.99	+	5828.83i	−0.535574	+	0.364268i
$636$		0			0
$637$	1238.69	−	3812.30i	0.0770466	−	0.237125i
$638$	−9.55357	+	29.4029i	−0.000592836	+	0.00182456i
$639$		0			0
$640$	2860.41	+	2217.05i	0.176668	+	0.136932i
$641$	4664.84	−	14356.9i	0.287442	−	0.884654i	−0.698215	−	0.715889i	$-0.746022\pi$
$641$	4664.84	−	14356.9i	0.287442	−	0.884654i	0.985656	−	0.168766i	$-0.0539781\pi$
$642$		0			0
$643$	21379.1			1.31121			0.655606	−	0.755103i	$-0.272413\pi$
$643$	21379.1			1.31121			0.655606	+	0.755103i	$0.272413\pi$
$644$	5094.58	+	3701.43i	0.311731	+	0.226486i
$645$		0			0
$646$	−96.1107	+	69.8285i	−0.00585360	+	0.00425289i
$647$	7903.05	−	5741.90i	0.480218	−	0.348899i	−0.321192	−	0.947014i	$-0.604084\pi$
$647$	7903.05	−	5741.90i	0.480218	−	0.348899i	0.801410	+	0.598115i	$0.204084\pi$
$648$		0			0
$649$	−538.074			−0.0325443
$650$	−11797.3	+	7499.12i	−0.711889	+	0.452522i
$651$		0			0
$652$	−6.07770	−	18.7052i	−0.000365063	−	0.00112355i
$653$	10418.9	−	7569.74i	0.624382	−	0.453640i	−0.230068	−	0.973175i	$-0.573895\pi$
$653$	10418.9	−	7569.74i	0.624382	−	0.453640i	0.854449	+	0.519535i	$0.173895\pi$
$654$		0			0
$655$	9862.10	−	27425.1i	0.588312	−	1.63601i
$656$	546.562	+	397.100i	0.0325300	+	0.0236344i
$657$		0			0
$658$	−1189.16	−	863.974i	−0.0704532	−	0.0511873i
$659$	1499.44	−	4614.81i	0.0886343	−	0.272788i	−0.896908	−	0.442217i	$-0.854192\pi$
$659$	1499.44	−	4614.81i	0.0886343	−	0.272788i	0.985542	+	0.169429i	$0.0541922\pi$
$660$		0			0
$661$	−2892.29	−	8901.56i	−0.170192	−	0.523798i	0.829189	−	0.558968i	$-0.188803\pi$
$661$	−2892.29	−	8901.56i	−0.170192	−	0.523798i	−0.999381	+	0.0351704i	$0.988803\pi$
$662$	1204.57	−	3707.27i	0.0707202	−	0.217655i
$663$		0			0
$664$	8532.07	+	26259.0i	0.498657	+	1.53471i
$665$	−1708.16	+	4750.13i	−0.0996081	+	0.276996i
$666$		0			0
$667$	−265.907	−	193.192i	−0.0154362	−	0.0112151i
$668$	−877.838			−0.0508452
$669$		0			0
$670$	−14655.5	−	455.107i	−0.845062	−	0.0262423i
$671$	−2967.40	+	2155.95i	−0.170723	+	0.124038i
$672$		0			0
$673$	−8985.41	−	27654.2i	−0.514654	−	1.58394i	−0.783911	−	0.620873i	$-0.786778\pi$
$673$	−8985.41	−	27654.2i	−0.514654	−	1.58394i	0.269257	−	0.963068i	$-0.413222\pi$
$674$	−4733.99			−0.270544
$675$		0			0
$676$	−3299.71			−0.187740
$677$	−1446.09	−	4450.60i	−0.0820940	−	0.252659i	0.901582	−	0.432608i	$-0.142407\pi$
$677$	−1446.09	−	4450.60i	−0.0820940	−	0.252659i	−0.983676	+	0.179949i	$0.942407\pi$
$678$		0			0
$679$	−7527.72	+	5469.21i	−0.425460	+	0.309115i
$680$	475.649	−	323.510i	0.0268240	−	0.0182442i
$681$		0			0
$682$	−624.671			−0.0350731
$683$	−13511.7	−	9816.80i	−0.756968	−	0.549970i	0.141011	−	0.990008i	$-0.454965\pi$
$683$	−13511.7	−	9816.80i	−0.756968	−	0.549970i	−0.897979	+	0.440038i	$0.854965\pi$
$684$		0			0
$685$	32646.3	+	1013.79i	1.82095	+	0.0565472i
$686$	−4280.21	−	13173.1i	−0.238220	−	0.733166i
$687$		0			0
$688$	1384.42	−	4260.82i	0.0767161	−	0.236108i
$689$	−3453.45	−	10628.6i	−0.190952	−	0.587689i
$690$		0			0
$691$	−3623.18	+	11151.0i	−0.199468	+	0.613899i	0.800428	+	0.599429i	$0.204606\pi$
$691$	−3623.18	+	11151.0i	−0.199468	+	0.613899i	−0.999895	+	0.0144691i	$0.995394\pi$
$692$	−10411.1	−	7564.14i	−0.571925	−	0.415528i
$693$		0			0
$694$	−10648.4	−	7736.52i	−0.582432	−	0.423162i
$695$	9225.23	−	6274.48i	0.503501	−	0.342453i
$696$		0			0
$697$	−65.8813	+	47.8656i	−0.00358025	+	0.00260120i
$698$	−2952.16	−	9085.80i	−0.160087	−	0.492697i
$699$		0			0
$700$	2939.51	−	7440.54i	0.158719	−	0.401751i
$701$	−19249.4			−1.03714			−0.518572	−	0.855034i	$-0.673536\pi$
$701$	−19249.4			−1.03714			−0.518572	+	0.855034i	$0.673536\pi$
$702$		0			0
$703$	−4059.62	+	2949.49i	−0.217797	+	0.158239i
$704$	1698.39	−	1233.95i	0.0909242	−	0.0660603i
$705$		0			0
$706$	−6456.48	−	4690.90i	−0.344182	−	0.250063i
$707$	12047.9			0.640890
$708$		0			0
$709$	1993.96	−	6136.79i	0.105620	−	0.325066i	−0.884255	−	0.467004i	$-0.845333\pi$
$709$	1993.96	−	6136.79i	0.105620	−	0.325066i	0.989876	+	0.141938i	$0.0453334\pi$
$710$	7567.74	−	21044.8i	0.400017	−	1.11239i
$711$		0			0
$712$	−8413.23	+	25893.3i	−0.442836	+	1.36291i
$713$	2052.21	−	6316.05i	0.107792	−	0.331750i
$714$		0			0
$715$	−786.969	−	2705.01i	−0.0411622	−	0.141485i
$716$	2177.77	−	6702.48i	0.113669	−	0.349837i
$717$		0			0
$718$	19109.3			0.993251
$719$	−17508.2	−	12720.5i	−0.908132	−	0.659797i	0.0324096	−	0.999475i	$-0.489682\pi$
$719$	−17508.2	−	12720.5i	−0.908132	−	0.659797i	−0.940542	+	0.339678i	$0.889682\pi$
$720$		0			0
$721$	−2448.30	+	1778.79i	−0.126462	+	0.0918803i
$722$	−10010.0	+	7272.70i	−0.515975	+	0.374878i
$723$		0			0
$724$	−6963.96			−0.357477
$725$	−153.425	+	388.352i	−0.00785939	+	0.0198938i
$726$		0			0
$727$	−6051.62	−	18625.0i	−0.308724	−	0.950155i	−0.978261	−	0.207376i	$-0.933508\pi$
$727$	−6051.62	−	18625.0i	−0.308724	−	0.950155i	0.669537	−	0.742778i	$-0.266492\pi$
$728$	−17691.4	+	12853.5i	−0.900668	+	0.654374i
$729$		0			0
$730$	14887.6	+	11539.1i	0.754813	+	0.585043i
$731$	436.885	+	317.416i	0.0221050	+	0.0160603i
$732$		0			0
$733$	8314.98	+	6041.19i	0.418992	+	0.304415i	0.777232	−	0.629214i	$-0.216623\pi$
$733$	8314.98	+	6041.19i	0.418992	+	0.304415i	−0.358240	+	0.933629i	$0.616623\pi$
$734$	1600.87	−	4926.97i	0.0805029	−	0.247762i
$735$		0			0
$736$	4771.40	+	14684.9i	0.238962	+	0.735450i
$737$	913.119	−	2810.29i	0.0456380	−	0.140459i
$738$		0			0
$739$	8283.58	+	25494.2i	0.412336	+	1.26904i	0.914612	+	0.404333i	$0.132496\pi$
$739$	8283.58	+	25494.2i	0.412336	+	1.26904i	−0.502276	+	0.864707i	$0.667504\pi$
$740$	6575.83	−	4472.51i	0.326665	−	0.222179i
$741$		0			0
$742$	−5460.26	−	3967.11i	−0.270152	−	0.196277i
$743$	3369.02			0.166349			0.0831746	−	0.996535i	$-0.473494\pi$
$743$	3369.02			0.166349			0.0831746	+	0.996535i	$0.473494\pi$
$744$		0			0
$745$	−8146.03	−	27999.9i	−0.400601	−	1.37696i
$746$	−17831.6	+	12955.5i	−0.875151	+	0.635835i
$747$		0			0
$748$	11.7251	+	36.0861i	0.000573144	+	0.00176396i
$749$	24038.4			1.17269
$750$		0			0
$751$	6458.58			0.313817			0.156909	−	0.987613i	$-0.449847\pi$
$751$	6458.58			0.313817			0.156909	+	0.987613i	$0.449847\pi$
$752$	−241.386	−	742.911i	−0.0117054	−	0.0360255i
$753$		0			0
$754$	302.227	−	219.581i	0.0145974	−	0.0106056i
$755$	1357.88	+	4667.37i	0.0654548	+	0.224984i
$756$		0			0
$757$	−5810.90			−0.278997			−0.139499	−	0.990222i	$-0.544549\pi$
$757$	−5810.90			−0.278997			−0.139499	+	0.990222i	$0.544549\pi$
$758$	12138.5	+	8819.17i	0.581651	+	0.422594i
$759$		0			0
$760$	−6118.52	+	4161.47i	−0.292029	+	0.198622i
$761$	10479.9	+	32253.9i	0.499208	+	1.53640i	0.810295	+	0.586023i	$0.199307\pi$
$761$	10479.9	+	32253.9i	0.499208	+	1.53640i	−0.311087	+	0.950382i	$0.600693\pi$
$762$		0			0
$763$	−9063.92	+	27895.9i	−0.430060	+	1.32359i
$764$	5474.11	+	16847.6i	0.259223	+	0.797806i
$765$		0			0
$766$	3906.83	−	12024.0i	0.184281	−	0.567160i
$767$	5260.07	+	3821.66i	0.247627	+	0.179912i
$768$		0			0
$769$	−29641.8	−	21536.0i	−1.39000	−	1.00990i	−0.995865	−	0.0908440i	$-0.971044\pi$
$769$	−29641.8	−	21536.0i	−1.39000	−	1.00990i	−0.394137	−	0.919052i	$-0.628956\pi$
$770$	−1344.73	−	1042.28i	−0.0629359	−	0.0487806i
$771$		0			0
$772$	11131.7	−	8087.64i	0.518961	−	0.377047i
$773$	136.048	+	418.714i	0.00633030	+	0.0194827i	0.954172	−	0.299259i	$-0.0967396\pi$
$773$	136.048	+	418.714i	0.00633030	+	0.0194827i	−0.947841	+	0.318742i	$0.896740\pi$
$774$		0			0
$775$	−8420.71	−	523.493i	−0.390298	−	0.0242638i
$776$	−13639.6			−0.630971
$777$		0			0
$778$	−12824.1	+	9317.29i	−0.590961	+	0.429359i
$779$	847.465	−	615.720i	0.0389777	−	0.0283189i
$780$		0			0
$781$	3646.23	+	2649.14i	0.167058	+	0.121375i
$782$	425.683			0.0194660
$783$		0			0
$784$	397.554	−	1223.55i	0.0181102	−	0.0557374i
$785$	6818.01	+	23435.2i	0.309994	+	1.06553i
$786$		0			0
$787$	7874.56	−	24235.4i	0.356668	−	1.09771i	−0.598368	−	0.801222i	$-0.704184\pi$
$787$	7874.56	−	24235.4i	0.356668	−	1.09771i	0.955036	−	0.296490i	$-0.0958163\pi$
$788$	−200.921	+	618.372i	−0.00908316	+	0.0279551i
$789$		0			0
$790$	−7791.57	+	21667.2i	−0.350901	+	0.975804i
$791$	−9911.90	+	30505.7i	−0.445546	+	1.37125i
$792$		0			0
$793$	44321.1			1.98473
$794$	13258.4	+	9632.79i	0.592598	+	0.430548i
$795$		0			0
$796$	−9993.29	+	7260.55i	−0.444979	+	0.323296i
$797$	11704.4	−	8503.78i	0.520192	−	0.377941i	−0.296484	−	0.955038i	$-0.595814\pi$
$797$	11704.4	−	8503.78i	0.520192	−	0.377941i	0.816676	+	0.577096i	$0.195814\pi$
$798$		0			0
$799$	94.1572			0.00416901
$800$	16554.5	−	10523.1i	0.731614	−	0.465061i
$801$		0			0
$802$	842.761	+	2593.75i	0.0371059	+	0.114200i
$803$	−3070.99	+	2231.20i	−0.134960	+	0.0980541i
$804$		0			0
$805$	14956.3	−	10172.4i	0.654831	−	0.445379i
$806$	6106.61	+	4436.71i	0.266869	+	0.193892i
$807$		0			0
$808$	14287.8	+	10380.7i	0.622084	+	0.451970i
$809$	9487.61	−	29199.8i	0.412319	−	1.26899i	−0.502307	−	0.864689i	$-0.667515\pi$
$809$	9487.61	−	29199.8i	0.412319	−	1.26899i	0.914627	−	0.404300i	$-0.132485\pi$
$810$		0			0
$811$	9430.64	+	29024.5i	0.408329	+	1.25671i	0.918084	+	0.396387i	$0.129736\pi$
$811$	9430.64	+	29024.5i	0.408329	+	1.25671i	−0.509755	+	0.860320i	$0.670264\pi$
$812$	−66.0661	+	203.331i	−0.00285525	+	0.00878757i
$813$		0			0
$814$	−522.630	−	1608.49i	−0.0225039	−	0.0692598i
$815$	−56.4653	−	1.75346i	−0.00242686	−	7.53630e-5i
$816$		0			0
$817$	−5619.88	−	4083.08i	−0.240654	−	0.174846i
$818$	−6020.12			−0.257321
$819$		0			0
$820$	−1372.74	+	933.658i	−0.0584610	+	0.0397619i
$821$	−9950.34	+	7229.34i	−0.422983	+	0.307315i	−0.778837	−	0.627226i	$-0.784190\pi$
$821$	−9950.34	+	7229.34i	−0.422983	+	0.307315i	0.355854	+	0.934542i	$0.384190\pi$
$822$		0			0
$823$	−13521.5	−	41614.9i	−0.572697	−	1.76258i	−0.643891	−	0.765117i	$-0.722681\pi$
$823$	−13521.5	−	41614.9i	−0.572697	−	1.76258i	0.0711940	−	0.997462i	$-0.477319\pi$
$824$	−4436.11			−0.187548
$825$		0			0
$826$	3926.63			0.165405
$827$	10223.8	+	31465.7i	0.429888	+	1.32306i	0.898235	+	0.439515i	$0.144850\pi$
$827$	10223.8	+	31465.7i	0.429888	+	1.32306i	−0.468347	+	0.883545i	$0.655150\pi$
$828$		0			0
$829$	−16695.2	+	12129.7i	−0.699454	+	0.508183i	−0.879754	−	0.475429i	$-0.842293\pi$
$829$	−16695.2	+	12129.7i	−0.699454	+	0.508183i	0.180301	+	0.983612i	$0.442293\pi$
$830$	25944.6	+	805.675i	1.08500	+	0.0336933i
$831$		0			0
$832$	−25367.2			−1.05703
$833$	125.457	+	91.1499i	0.00521828	+	0.00379130i
$834$		0			0
$835$	−853.224	+	2372.69i	−0.0353617	+	0.0983358i
$836$	−150.826	−	464.195i	−0.00623974	−	0.0192040i
$837$		0			0
$838$	−9709.90	+	29884.0i	−0.400266	+	1.23189i
$839$	−10488.9	−	32281.4i	−0.431605	−	1.32834i	−0.896526	−	0.442991i	$-0.853918\pi$
$839$	−10488.9	−	32281.4i	−0.431605	−	1.32834i	0.464922	−	0.885352i	$-0.346082\pi$
$840$		0			0
$841$	−7533.17	+	23184.7i	−0.308876	+	0.950621i
$842$	3964.47	+	2880.35i	0.162262	+	0.117890i
$843$		0			0
$844$	8588.00	+	6239.55i	0.350250	+	0.254472i
$845$	−3207.19	+	8918.73i	−0.130569	+	0.363093i
$846$		0			0
$847$	−17427.9	+	12662.1i	−0.707001	+	0.513666i
$848$	−1108.37	−	3411.22i	−0.0448841	−	0.138139i
$849$		0			0
$850$	−134.880	−	523.706i	−0.00544278	−	0.0211329i
$851$	17980.4			0.724278
$852$		0			0
$853$	−28353.2	+	20599.8i	−1.13809	+	0.826873i	−0.986852	−	0.161624i	$-0.948327\pi$
$853$	−28353.2	+	20599.8i	−1.13809	+	0.826873i	−0.151241	+	0.988497i	$0.548327\pi$
$854$	21654.8	−	15733.1i	0.867695	−	0.630417i
$855$		0			0
$856$	28507.5	+	20711.9i	1.13828	+	0.827008i
$857$	−39687.9			−1.58193			−0.790965	−	0.611862i	$-0.790421\pi$
$857$	−39687.9			−1.58193			−0.790965	+	0.611862i	$0.790421\pi$
$858$		0			0
$859$	1637.70	−	5040.34i	0.0650498	−	0.200203i	−0.913249	−	0.407402i	$-0.866435\pi$
$859$	1637.70	−	5040.34i	0.0650498	−	0.200203i	0.978299	+	0.207199i	$0.0664348\pi$
$860$	8701.46	+	6744.36i	0.345020	+	0.267419i
$861$		0			0
$862$	−4972.21	+	15302.9i	−0.196466	+	0.604662i
$863$	347.117	−	1068.32i	0.0136918	−	0.0421390i	−0.943977	−	0.330011i	$-0.892948\pi$
$863$	347.117	−	1068.32i	0.0136918	−	0.0421390i	0.957669	+	0.287872i	$0.0929477\pi$
$864$		0			0
$865$	−30564.2	+	20788.0i	−1.20140	+	0.817127i
$866$	887.467	−	2731.34i	0.0348237	−	0.107176i
$867$		0			0
$868$	−4319.80			−0.168921
$869$	−3754.07	−	2727.49i	−0.146546	−	0.106472i
$870$		0			0
$871$	−28886.5	+	20987.2i	−1.12374	+	0.816447i
$872$	−34784.6	+	25272.5i	−1.35087	+	0.981462i
$873$		0			0
$874$	−5475.78			−0.211923
$875$	−17253.8	−	15177.1i	−0.666611	−	0.586375i
$876$		0			0
$877$	−6273.14	−	19306.7i	−0.241538	−	0.743378i	−0.996187	−	0.0872483i	$-0.972193\pi$
$877$	−6273.14	−	19306.7i	−0.241538	−	0.743378i	0.754649	−	0.656129i	$-0.227807\pi$
$878$	22041.7	−	16014.2i	0.847234	−	0.615551i
$879$		0			0
$880$	−252.576	−	868.165i	−0.00967537	−	0.0332566i
$881$	−15364.5	−	11163.0i	−0.587563	−	0.426890i	0.253880	−	0.967236i	$-0.418293\pi$
$881$	−15364.5	−	11163.0i	−0.587563	−	0.426890i	−0.841443	+	0.540346i	$0.818293\pi$
$882$		0			0
$883$	18914.0	+	13741.8i	0.720845	+	0.523725i	0.886654	−	0.462433i	$-0.153024\pi$
$883$	18914.0	+	13741.8i	0.720845	+	0.523725i	−0.165809	+	0.986158i	$0.553024\pi$
$884$	141.680	−	436.046i	0.00539051	−	0.0165903i
$885$		0			0
$886$	−8359.44	−	25727.7i	−0.316976	−	0.975553i
$887$	1134.58	−	3491.86i	0.0429485	−	0.132182i	−0.927283	−	0.374361i	$-0.877862\pi$
$887$	1134.58	−	3491.86i	0.0429485	−	0.132182i	0.970232	+	0.242179i	$0.0778621\pi$
$888$		0			0
$889$	4710.17	+	14496.4i	0.177699	+	0.546901i
$890$	20230.3	+	15680.2i	0.761934	+	0.590563i
$891$		0			0
$892$	−118.589	−	86.1601i	−0.00445141	−	0.00323414i
$893$	−1211.19			−0.0453875
$894$		0			0
$895$	−15999.3	−	12400.8i	−0.597539	−	0.463143i
$896$	4305.86	−	3128.39i	0.160545	−	0.116643i
$897$		0			0
$898$	−1918.88	−	5905.70i	−0.0713071	−	0.219461i
$899$	225.468			0.00836460
$900$		0			0
$901$	432.342			0.0159860
$902$	109.102	+	335.780i	0.00402737	+	0.0123950i
$903$		0			0
$904$	−38038.9	+	27636.9i	−1.39951	+	1.01680i
$905$	−6768.70	+	18822.8i	−0.248618	+	0.691370i
$906$		0			0
$907$	9274.11			0.339517			0.169758	−	0.985486i	$-0.445701\pi$
$907$	9274.11			0.339517			0.169758	+	0.985486i	$0.445701\pi$
$908$	−10445.7	−	7589.22i	−0.381775	−	0.277376i
$909$		0			0
$910$	5742.95	+	19739.9i	0.209205	+	0.719091i
$911$	9464.91	+	29130.0i	0.344222	+	1.05941i	0.961999	+	0.273054i	$0.0880337\pi$
$911$	9464.91	+	29130.0i	0.344222	+	1.05941i	−0.617776	+	0.786354i	$0.711966\pi$
$912$		0			0
$913$	−1616.49	+	4975.05i	−0.0585959	+	0.180340i
$914$	115.907	+	356.725i	0.00419460	+	0.0129097i
$915$		0			0
$916$	−5929.32	+	18248.6i	−0.213876	+	0.658242i
$917$	−34675.6	−	25193.3i	−1.24874	−	0.907260i
$918$		0			0
$919$	−10928.5	−	7940.03i	−0.392272	−	0.285003i	0.374114	−	0.927383i	$-0.377947\pi$
$919$	−10928.5	−	7940.03i	−0.392272	−	0.285003i	−0.766386	+	0.642380i	$0.777947\pi$
$920$	26501.6	+	822.971i	0.949707	+	0.0294919i
$921$		0			0
$922$	−12677.5	+	9210.77i	−0.452833	+	0.329003i
$923$	−16829.1	−	51794.6i	−0.600148	−	1.84706i
$924$		0			0
$925$	−5697.21	−	22120.8i	−0.202511	−	0.786300i
$926$	29908.4			1.06139
$927$		0			0
$928$	−424.099	+	308.126i	−0.0150019	+	0.0108995i
$929$	5704.34	−	4144.45i	0.201457	−	0.146367i	−0.482483	−	0.875905i	$-0.660265\pi$
$929$	5704.34	−	4144.45i	0.201457	−	0.146367i	0.683940	+	0.729538i	$0.260265\pi$
$930$		0			0
$931$	−1613.82	−	1172.51i	−0.0568107	−	0.0412754i
$932$	−27.7916			−0.000976764
$933$		0			0
$934$	8911.56	−	27427.0i	0.312200	−	0.960854i
$935$	108.933	+	3.38277i	0.00381015	+	0.000118319i
$936$		0			0
$937$	3108.74	−	9567.73i	0.108387	−	0.333579i	−0.882124	−	0.471018i	$-0.843887\pi$
$937$	3108.74	−	9567.73i	0.108387	−	0.333579i	0.990510	+	0.137438i	$0.0438868\pi$
$938$	−6663.54	+	20508.3i	−0.231953	+	0.713879i
$939$		0			0
$940$	1918.62	+	59.5802i	0.0665729	+	0.00206733i
$941$	−17066.8	+	52526.1i	−0.591244	+	1.81966i	−0.0186448	+	0.999826i	$0.505935\pi$
$941$	−17066.8	+	52526.1i	−0.591244	+	1.81966i	−0.572599	+	0.819835i	$0.694065\pi$
$942$		0			0
$943$	−3753.50			−0.129619
$944$	1688.21	+	1226.55i	0.0582059	+	0.0422891i
$945$		0			0
$946$	1894.14	−	1376.17i	0.0650990	−	0.0472972i
$947$	−34518.5	+	25079.2i	−1.18448	+	0.860574i	−0.992670	−	0.120858i	$-0.961435\pi$
$947$	−34518.5	+	25079.2i	−1.18448	+	0.860574i	−0.191809	+	0.981432i	$0.561435\pi$
$948$		0			0
$949$	45868.3			1.56896
$950$	1735.04	+	6736.70i	0.0592548	+	0.230071i
$951$		0			0
$952$	−261.423	−	804.577i	−0.00889996	−	0.0273913i
$953$	15050.9	−	10935.1i	0.511592	−	0.371694i	−0.301835	−	0.953360i	$-0.597599\pi$
$953$	15050.9	−	10935.1i	0.511592	−	0.371694i	0.813427	+	0.581667i	$0.197599\pi$
$954$		0			0
$955$	50857.6	+	1579.32i	1.72326	+	0.0535136i
$956$	−22704.3	−	16495.6i	−0.768106	−	0.558061i
$957$		0			0
$958$	26862.8	+	19517.0i	0.905947	+	0.658209i
$959$	14843.5	−	45683.7i	0.499816	−	1.53827i
$960$		0			0
$961$	−7798.15	−	24000.2i	−0.261762	−	0.805620i
$962$	−6315.18	+	19436.1i	−0.211652	+	0.651399i
$963$		0			0
$964$	4133.02	+	12720.1i	0.138087	+	0.424988i
$965$	−11040.4	−	37948.5i	−0.368293	−	1.26591i
$966$		0			0
$967$	182.356	+	132.489i	0.00606428	+	0.00440596i	0.590813	−	0.806808i	$-0.298807\pi$
$967$	182.356	+	132.489i	0.00606428	+	0.00440596i	−0.584749	+	0.811214i	$0.698807\pi$
$968$	−31577.9			−1.04850
$969$		0			0
$970$	−4339.11	+	12066.4i	−0.143629	+	0.399412i
$971$	30228.7	−	21962.4i	0.999058	−	0.725858i	0.0371718	−	0.999309i	$-0.488165\pi$
$971$	30228.7	−	21962.4i	0.999058	−	0.725858i	0.961886	+	0.273451i	$0.0881651\pi$
$972$		0			0
$973$	−5070.30	−	15604.8i	−0.167057	−	0.514148i
$974$	26555.8			0.873617
$975$		0			0
$976$	14224.7			0.466520
$977$	−2795.31	−	8603.08i	−0.0915352	−	0.281716i	0.894800	−	0.446467i	$-0.147318\pi$
$977$	−2795.31	−	8603.08i	−0.0915352	−	0.281716i	−0.986335	+	0.164751i	$0.947318\pi$
$978$		0			0
$979$	−4173.08	+	3031.92i	−0.136233	+	0.0989793i
$980$	2498.73	+	1936.73i	0.0814480	+	0.0631290i
$981$		0			0
$982$	3743.11			0.121637
$983$	−21087.0	−	15320.6i	−0.684201	−	0.497101i	0.190548	−	0.981678i	$-0.438974\pi$
$983$	−21087.0	−	15320.6i	−0.684201	−	0.497101i	−0.874749	+	0.484577i	$0.838974\pi$
$984$		0			0
$985$	1476.10	+	1144.10i	0.0477487	+	0.0370092i
$986$	4.46596	+	13.7448i	0.000144244	+	0.000443939i
$987$		0			0
$988$	−1822.50	+	5609.08i	−0.0586857	+	0.180616i
$989$	7691.73	+	23672.7i	0.247303	+	0.761120i
$990$		0			0
$991$	13152.5	−	40479.4i	0.421599	−	1.29755i	−0.484615	−	0.874727i	$-0.661040\pi$
$991$	13152.5	−	40479.4i	0.421599	−	1.29755i	0.906214	−	0.422820i	$-0.138960\pi$
$992$	−8569.10	−	6225.81i	−0.274263	−	0.199264i
$993$		0			0
$994$	−26608.6	−	19332.3i	−0.849067	−	0.616883i
$995$	9911.32	+	34067.7i	0.315789	+	1.08544i
$996$		0			0
$997$	18242.6	−	13254.0i	0.579487	−	0.421022i	−0.259052	−	0.965863i	$-0.583410\pi$
$997$	18242.6	−	13254.0i	0.579487	−	0.421022i	0.838539	+	0.544841i	$0.183410\pi$
$998$	−11131.5	−	34259.3i	−0.353068	−	1.08663i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.d.181.6	yes	64
3.2	odd	2	inner	225.4.h.d.181.11	yes	64
25.21	even	5	inner	225.4.h.d.46.6	✓	64
75.71	odd	10	inner	225.4.h.d.46.11	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.h.d.46.6	✓	64	25.21	even	5	inner
225.4.h.d.46.11	yes	64	75.71	odd	10	inner
225.4.h.d.181.6	yes	64	1.1	even	1	trivial
225.4.h.d.181.11	yes	64	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.626289 - 1.92752i) q^{2} +(3.14904 - 2.28791i) q^{4} +(-3.12321 - 10.7352i) q^{5} -16.4425 q^{7} +(-19.4994 - 14.1671i) q^{8} +O(q^{10})\)	\(q+(-0.626289 - 1.92752i) q^{2} +(3.14904 - 2.28791i) q^{4} +(-3.12321 - 10.7352i) q^{5} -16.4425 q^{7} +(-19.4994 - 14.1671i) q^{8} +(-18.7364 + 12.7434i) q^{10} +(-1.41112 - 4.34299i) q^{11} +(-17.0513 + 52.4784i) q^{13} +(10.2977 + 31.6932i) q^{14} +(-5.47256 + 16.8428i) q^{16} +(-1.72699 - 1.25473i) q^{17} +(22.2151 + 16.1402i) q^{19} +(-34.3964 - 26.6601i) q^{20} +(-7.48743 + 5.43993i) q^{22} +(-30.4050 - 93.5770i) q^{23} +(-105.491 + 67.0569i) q^{25} +111.832 q^{26} +(-51.7780 + 37.6189i) q^{28} +(2.70250 - 1.96348i) q^{29} +(54.6052 + 39.6730i) q^{31} -156.928 q^{32} +(-1.33692 + 4.11462i) q^{34} +(51.3533 + 176.514i) q^{35} +(-56.4702 + 173.797i) q^{37} +(17.1975 - 52.9285i) q^{38} +(-91.1869 + 253.578i) q^{40} +(11.7884 - 36.2811i) q^{41} -252.976 q^{43} +(-14.3801 - 10.4477i) q^{44} +(-161.329 + 117.213i) q^{46} +(-35.6846 + 25.9263i) q^{47} -72.6451 q^{49} +(195.321 + 161.339i) q^{50} +(66.3708 + 204.268i) q^{52} +(-163.853 + 119.046i) q^{53} +(-42.2158 + 28.7128i) q^{55} +(320.618 + 232.943i) q^{56} +(-5.47720 - 3.97942i) q^{58} +(36.4118 - 112.064i) q^{59} +(-248.210 - 763.911i) q^{61} +(42.2718 - 130.099i) q^{62} +(142.063 + 437.225i) q^{64} +(616.623 + 19.1484i) q^{65} +(523.504 + 380.348i) q^{67} -8.30906 q^{68} +(308.072 - 209.533i) q^{70} +(-798.476 + 580.127i) q^{71} +(-256.874 - 790.578i) q^{73} +370.365 q^{74} +106.884 q^{76} +(23.2023 + 71.4095i) q^{77} +(822.092 - 597.285i) q^{79} +(197.904 + 6.14563i) q^{80} -77.3154 q^{82} +(-926.758 - 673.329i) q^{83} +(-8.07608 + 22.4584i) q^{85} +(158.436 + 487.616i) q^{86} +(-34.0117 + 104.677i) q^{88} +(-349.060 - 1074.29i) q^{89} +(280.365 - 862.874i) q^{91} +(-309.843 - 225.114i) q^{92} +(72.3224 + 52.5453i) q^{94} +(103.887 - 288.894i) q^{95} +(457.822 - 332.627i) q^{97} +(45.4968 + 140.025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more