LMFDB - Embedded newform 225.4.h.d.46.16

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			46.16
Character	$\chi$	$=$	225.46
Dual form			225.4.h.d.181.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71061 - 5.26471i) q^{2} +(-18.3188 - 13.3094i) q^{4} +(11.1283 + 1.07706i) q^{5} -30.2200 q^{7} +(-65.5791 + 47.6460i) q^{8} +O(q^{10})$	\(q+(1.71061 - 5.26471i) q^{2} +(-18.3188 - 13.3094i) q^{4} +(11.1283 + 1.07706i) q^{5} -30.2200 q^{7} +(-65.5791 + 47.6460i) q^{8} +(24.7066 - 56.7450i) q^{10} +(6.53575 - 20.1150i) q^{11} +(-1.85672 - 5.71440i) q^{13} +(-51.6946 + 159.100i) q^{14} +(82.6849 + 254.478i) q^{16} +(-17.3999 + 12.6418i) q^{17} +(-85.2864 + 61.9642i) q^{19} +(-189.523 - 167.842i) q^{20} +(-94.7194 - 68.8177i) q^{22} +(-1.91808 + 5.90324i) q^{23} +(122.680 + 23.9717i) q^{25} -33.2608 q^{26} +(553.596 + 402.211i) q^{28} +(-187.176 - 135.991i) q^{29} +(142.099 - 103.241i) q^{31} +832.711 q^{32} +(36.7909 + 113.231i) q^{34} +(-336.299 - 32.5487i) q^{35} +(-90.6084 - 278.864i) q^{37} +(180.332 + 555.004i) q^{38} +(-781.104 + 459.589i) q^{40} +(-18.2039 - 56.0257i) q^{41} -379.656 q^{43} +(-387.446 + 281.496i) q^{44} +(27.7978 + 20.1962i) q^{46} +(131.812 + 95.7671i) q^{47} +570.251 q^{49} +(336.061 - 604.868i) q^{50} +(-42.0424 + 129.393i) q^{52} +(-214.314 - 155.708i) q^{53} +(94.3971 - 216.807i) q^{55} +(1981.80 - 1439.87i) q^{56} +(-1036.14 + 752.798i) q^{58} +(141.788 + 436.378i) q^{59} +(185.460 - 570.786i) q^{61} +(-300.457 - 924.713i) q^{62} +(762.963 - 2348.16i) q^{64} +(-14.5075 - 65.5916i) q^{65} +(-269.638 + 195.903i) q^{67} +487.002 q^{68} +(-746.635 + 1714.84i) q^{70} +(-715.330 - 519.718i) q^{71} +(100.853 - 310.394i) q^{73} -1623.13 q^{74} +2387.05 q^{76} +(-197.511 + 607.876i) q^{77} +(-63.7800 - 46.3389i) q^{79} +(646.058 + 2920.97i) q^{80} -326.099 q^{82} +(-1062.34 + 771.834i) q^{83} +(-207.248 + 121.941i) q^{85} +(-649.442 + 1998.78i) q^{86} +(529.790 + 1630.53i) q^{88} +(348.484 - 1072.52i) q^{89} +(56.1102 + 172.690i) q^{91} +(113.706 - 82.6120i) q^{92} +(729.664 - 530.132i) q^{94} +(-1015.83 + 597.700i) q^{95} +(40.0395 + 29.0904i) q^{97} +(975.476 - 3002.21i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.71061	−	5.26471i	0.604791	−	1.86136i	0.106571	−	0.994305i	$-0.466013\pi$
$2$	1.71061	−	5.26471i	0.604791	−	1.86136i	0.498220	−	0.867050i	$-0.333987\pi$
$3$		0			0
$3$		0			0
$4$	−18.3188	−	13.3094i	−2.28986	−	1.66368i
$5$	11.1283	+	1.07706i	0.995349	+	0.0963350i
$5$	11.1283	+	1.07706i	0.995349	+	0.0963350i
$6$		0			0
$7$	−30.2200			−1.63173			−0.815865	−	0.578243i	$-0.803739\pi$
$7$	−30.2200			−1.63173			−0.815865	+	0.578243i	$0.803739\pi$
$8$	−65.5791	+	47.6460i	−2.89822	+	2.10568i
$9$		0			0
$10$	24.7066	−	56.7450i	0.781292	−	1.79444i
$11$	6.53575	−	20.1150i	0.179146	−	0.551354i	−0.820653	−	0.571427i	$-0.806390\pi$
$11$	6.53575	−	20.1150i	0.179146	−	0.551354i	0.999799	+	0.0200732i	$0.00638993\pi$
$12$		0			0
$13$	−1.85672	−	5.71440i	−0.0396125	−	0.121915i	0.929295	−	0.369339i	$-0.120416\pi$
$13$	−1.85672	−	5.71440i	−0.0396125	−	0.121915i	−0.968907	+	0.247424i	$0.920416\pi$
$14$	−51.6946	+	159.100i	−0.986855	+	3.03723i
$15$		0			0
$16$	82.6849	+	254.478i	1.29195	+	3.97622i
$17$	−17.3999	+	12.6418i	−0.248241	+	0.180358i	−0.704947	−	0.709260i	$-0.749029\pi$
$17$	−17.3999	+	12.6418i	−0.248241	+	0.180358i	0.456706	+	0.889618i	$0.349029\pi$
$18$		0			0
$19$	−85.2864	+	61.9642i	−1.02979	+	0.748187i	−0.968267	−	0.249918i	$-0.919596\pi$
$19$	−85.2864	+	61.9642i	−1.02979	+	0.748187i	−0.0615244	+	0.998106i	$0.519596\pi$
$20$	−189.523	−	167.842i	−2.11893	−	1.87653i
$21$		0			0
$22$	−94.7194	−	68.8177i	−0.917920	−	0.666908i
$23$	−1.91808	+	5.90324i	−0.0173890	+	0.0535178i	−0.959374	−	0.282136i	$-0.908957\pi$
$23$	−1.91808	+	5.90324i	−0.0173890	+	0.0535178i	0.941985	+	0.335654i	$0.108957\pi$
$24$		0			0
$25$	122.680	+	23.9717i	0.981439	+	0.191774i
$26$	−33.2608			−0.250884
$27$		0			0
$28$	553.596	+	402.211i	3.73642	+	2.71467i
$29$	−187.176	−	135.991i	−1.19854	−	0.870791i	−0.204400	−	0.978887i	$-0.565524\pi$
$29$	−187.176	−	135.991i	−1.19854	−	0.870791i	−0.994140	+	0.108097i	$0.965524\pi$
$30$		0			0
$31$	142.099	−	103.241i	0.823280	−	0.598148i	−0.0943701	−	0.995537i	$-0.530084\pi$
$31$	142.099	−	103.241i	0.823280	−	0.598148i	0.917650	+	0.397389i	$0.130084\pi$
$32$	832.711			4.60012
$33$		0			0
$34$	36.7909	+	113.231i	0.185576	+	0.571144i
$35$	−336.299	−	32.5487i	−1.62414	−	0.157193i
$36$		0			0
$37$	−90.6084	−	278.864i	−0.402592	−	1.23905i	−0.922889	−	0.385066i	$-0.874179\pi$
$37$	−90.6084	−	278.864i	−0.402592	−	1.23905i	0.520296	−	0.853986i	$-0.325821\pi$
$38$	180.332	+	555.004i	0.769834	+	2.36930i
$39$		0			0
$40$	−781.104	+	459.589i	−3.08759	+	1.81668i
$41$	−18.2039	−	56.0257i	−0.0693406	−	0.213408i	0.910381	−	0.413770i	$-0.135788\pi$
$41$	−18.2039	−	56.0257i	−0.0693406	−	0.213408i	−0.979722	+	0.200362i	$0.935788\pi$
$42$		0			0
$43$	−379.656			−1.34644			−0.673220	−	0.739442i	$-0.735089\pi$
$43$	−379.656			−1.34644			−0.673220	+	0.739442i	$0.735089\pi$
$44$	−387.446	+	281.496i	−1.32749	+	0.964480i
$45$		0			0
$46$	27.7978	+	20.1962i	0.0890990	+	0.0647342i
$47$	131.812	+	95.7671i	0.409080	+	0.297214i	0.773229	−	0.634127i	$-0.218640\pi$
$47$	131.812	+	95.7671i	0.409080	+	0.297214i	−0.364149	+	0.931341i	$0.618640\pi$
$48$		0			0
$49$	570.251			1.66254
$50$	336.061	−	604.868i	0.950525	−	1.71082i
$51$		0			0
$52$	−42.0424	+	129.393i	−0.112120	+	0.345069i
$53$	−214.314	−	155.708i	−0.555440	−	0.403551i	0.274347	−	0.961631i	$-0.411538\pi$
$53$	−214.314	−	155.708i	−0.555440	−	0.403551i	−0.829787	+	0.558080i	$0.811538\pi$
$54$		0			0
$55$	94.3971	−	216.807i	0.231427	−	0.531532i
$56$	1981.80	−	1439.87i	4.72910	−	3.43589i
$57$		0			0
$58$	−1036.14	+	752.798i	−2.34572	+	1.70426i
$59$	141.788	+	436.378i	0.312868	+	0.962908i	0.976623	+	0.214958i	$0.0689616\pi$
$59$	141.788	+	436.378i	0.312868	+	0.962908i	−0.663755	+	0.747950i	$0.731038\pi$
$60$		0			0
$61$	185.460	−	570.786i	0.389273	−	1.19806i	−0.544059	−	0.839047i	$-0.683113\pi$
$61$	185.460	−	570.786i	0.389273	−	1.19806i	0.933333	−	0.359013i	$-0.116887\pi$
$62$	−300.457	−	924.713i	−0.615454	−	1.89417i
$63$		0			0
$64$	762.963	−	2348.16i	1.49016	−	4.58625i
$65$	−14.5075	−	65.5916i	−0.0276836	−	0.125164i
$66$		0			0
$67$	−269.638	+	195.903i	−0.491665	+	0.357215i	−0.805824	−	0.592155i	$-0.798277\pi$
$67$	−269.638	+	195.903i	−0.491665	+	0.357215i	0.314160	+	0.949370i	$0.398277\pi$
$68$	487.002			0.868494
$69$		0			0
$70$	−746.635	+	1714.84i	−1.27486	+	2.92803i
$71$	−715.330	−	519.718i	−1.19569	−	0.868721i	−0.201838	−	0.979419i	$-0.564691\pi$
$71$	−715.330	−	519.718i	−1.19569	−	0.868721i	−0.993854	+	0.110698i	$0.964691\pi$
$72$		0			0
$73$	100.853	−	310.394i	0.161698	−	0.497656i	−0.837080	−	0.547081i	$-0.815739\pi$
$73$	100.853	−	310.394i	0.161698	−	0.497656i	0.998778	+	0.0494250i	$0.0157389\pi$
$74$	−1623.13			−2.54980
$75$		0			0
$76$	2387.05			3.60281
$77$	−197.511	+	607.876i	−0.292317	+	0.899661i
$78$		0			0
$79$	−63.7800	−	46.3389i	−0.0908330	−	0.0659940i	0.541442	−	0.840738i	$-0.317879\pi$
$79$	−63.7800	−	46.3389i	−0.0908330	−	0.0659940i	−0.632275	+	0.774744i	$0.717879\pi$
$80$	646.058	+	2920.97i	0.902894	+	4.08218i
$81$		0			0
$82$	−326.099			−0.439165
$83$	−1062.34	+	771.834i	−1.40490	+	1.02072i	−0.410862	+	0.911698i	$0.634772\pi$
$83$	−1062.34	+	771.834i	−1.40490	+	1.02072i	−0.994039	+	0.109023i	$0.965228\pi$
$84$		0			0
$85$	−207.248	+	121.941i	−0.264462	+	0.155605i
$86$	−649.442	+	1998.78i	−0.814315	+	2.50620i
$87$		0			0
$88$	529.790	+	1630.53i	0.641770	+	1.97517i
$89$	348.484	−	1072.52i	0.415047	−	1.27738i	−0.497161	−	0.867658i	$-0.665624\pi$
$89$	348.484	−	1072.52i	0.415047	−	1.27738i	0.912209	−	0.409726i	$-0.134376\pi$
$90$		0			0
$91$	56.1102	+	172.690i	0.0646368	+	0.198932i
$92$	113.706	−	82.6120i	0.128855	−	0.0936184i
$93$		0			0
$94$	729.664	−	530.132i	0.800629	−	0.581691i
$95$	−1015.83	+	597.700i	−1.09708	+	0.645502i
$96$		0			0
$97$	40.0395	+	29.0904i	0.0419113	+	0.0304503i	0.608544	−	0.793520i	$-0.291754\pi$
$97$	40.0395	+	29.0904i	0.0419113	+	0.0304503i	−0.566632	+	0.823971i	$0.691754\pi$
$98$	975.476	−	3002.21i	1.00549	−	3.09458i
$99$		0			0
$100$	−1928.30	−	2071.93i	−1.92830	−	2.07193i
$101$	−790.998			−0.779279			−0.389640	−	0.920967i	$-0.627400\pi$
$101$	−790.998			−0.779279			−0.389640	+	0.920967i	$0.627400\pi$
$102$		0			0
$103$	46.4033	+	33.7140i	0.0443908	+	0.0322518i	0.609759	−	0.792587i	$-0.291266\pi$
$103$	46.4033	+	33.7140i	0.0443908	+	0.0322518i	−0.565369	+	0.824838i	$0.691266\pi$
$104$	394.031	+	286.280i	0.371518	+	0.269924i
$105$		0			0
$106$	−1186.37	+	861.946i	−1.08708	+	0.789808i
$107$	−470.946			−0.425496			−0.212748	−	0.977107i	$-0.568241\pi$
$107$	−470.946			−0.425496			−0.212748	+	0.977107i	$0.568241\pi$
$108$		0			0
$109$	−71.2432	−	219.264i	−0.0626042	−	0.192676i	0.914863	−	0.403765i	$-0.132299\pi$
$109$	−71.2432	−	219.264i	−0.0626042	−	0.192676i	−0.977467	+	0.211090i	$0.932299\pi$
$110$	−979.949	−	867.845i	−0.849404	−	0.752234i
$111$		0			0
$112$	−2498.74	−	7690.33i	−2.10811	−	6.48811i
$113$	−54.7705	−	168.566i	−0.0455962	−	0.140331i	0.925667	−	0.378340i	$-0.123505\pi$
$113$	−54.7705	−	168.566i	−0.0455962	−	0.140331i	−0.971263	+	0.238009i	$0.923505\pi$
$114$		0			0
$115$	−27.7032	+	63.6274i	−0.0224638	+	0.0515938i
$116$	1618.88	+	4982.40i	1.29577	+	3.98797i
$117$		0			0
$118$	2539.95			1.98153
$119$	525.827	−	382.036i	0.405063	−	0.294295i
$120$		0			0
$121$	714.905	+	519.409i	0.537119	+	0.390240i
$122$	−2687.77	−	1952.78i	−1.99459	−	1.44915i
$123$		0			0
$124$	−3977.16			−2.88032
$125$	1339.40	+	398.899i	0.958400	+	0.285429i
$126$		0			0
$127$	−250.813	+	771.924i	−0.175245	+	0.539348i	−0.999645	−	0.0266600i	$-0.991513\pi$
$127$	−250.813	+	771.924i	−0.175245	+	0.539348i	0.824400	+	0.566008i	$0.191513\pi$
$128$	−5667.82	−	4117.91i	−3.91382	−	2.84356i
$129$		0			0
$130$	−370.137	−	35.8238i	−0.249717	−	0.0241689i
$131$	1053.96	−	765.747i	0.702938	−	0.510714i	−0.177950	−	0.984040i	$-0.556946\pi$
$131$	1053.96	−	765.747i	0.702938	−	0.510714i	0.880888	+	0.473325i	$0.156946\pi$
$132$		0			0
$133$	2577.36	−	1872.56i	1.68034	−	1.22084i
$134$	570.130	+	1754.68i	0.367550	+	1.13120i
$135$		0			0
$136$	538.741	−	1658.08i	0.339682	−	1.04543i
$137$	343.611	+	1057.53i	0.214282	+	0.659493i	0.999204	+	0.0398976i	$0.0127032\pi$
$137$	343.611	+	1057.53i	0.214282	+	0.659493i	−0.784922	+	0.619595i	$0.787297\pi$
$138$		0			0
$139$	7.34441	−	22.6038i	0.00448162	−	0.0137930i	−0.948791	−	0.315905i	$-0.897692\pi$
$139$	7.34441	−	22.6038i	0.00448162	−	0.0137930i	0.953272	+	0.302112i	$0.0976918\pi$
$140$	5727.40	+	5072.20i	3.45753	+	3.06199i
$141$		0			0
$142$	−3959.81	+	2876.97i	−2.34014	+	1.70021i
$143$	−127.080			−0.0743146
$144$		0			0
$145$	−1936.49	−	1714.96i	−1.10908	−	0.982202i
$146$	−1461.62	−	1061.93i	−0.828521	−	0.601956i
$147$		0			0
$148$	−2051.68	+	6314.41i	−1.13950	+	3.50703i
$149$	2190.65			1.20446			0.602232	−	0.798321i	$-0.294278\pi$
$149$	2190.65			1.20446			0.602232	+	0.798321i	$0.294278\pi$
$150$		0			0
$151$	891.600			0.480513			0.240256	−	0.970709i	$-0.422769\pi$
$151$	891.600			0.480513			0.240256	+	0.970709i	$0.422769\pi$
$152$	2640.66	−	8127.11i	1.40912	−	4.33681i
$153$		0			0
$154$	2862.42	+	2079.67i	1.49780	+	1.08821i
$155$	1692.52	−	995.850i	0.877074	−	0.516055i
$156$		0			0
$157$	2339.90			1.18946			0.594728	−	0.803927i	$-0.297260\pi$
$157$	2339.90			1.18946			0.594728	+	0.803927i	$0.297260\pi$
$158$	−353.063	+	256.515i	−0.177773	+	0.129160i
$159$		0			0
$160$	9266.69	+	896.878i	4.57873	+	0.443153i
$161$	57.9644	−	178.396i	0.0283741	−	0.0873266i
$162$		0			0
$163$	−687.964	−	2117.34i	−0.330586	−	1.01744i	−0.968856	−	0.247626i	$-0.920350\pi$
$163$	−687.964	−	2117.34i	−0.330586	−	1.01744i	0.638270	−	0.769813i	$-0.279650\pi$
$164$	−412.196	+	1268.61i	−0.196263	+	0.604035i
$165$		0			0
$166$	2246.24	+	6913.21i	1.05025	+	3.23234i
$167$	−501.922	+	364.668i	−0.232574	+	0.168975i	−0.697969	−	0.716128i	$-0.745913\pi$
$167$	−501.922	+	364.668i	−0.232574	+	0.168975i	0.465394	+	0.885103i	$0.345913\pi$
$168$		0			0
$169$	1748.20	−	1270.14i	0.795723	−	0.578127i
$170$	287.466	+	1299.70i	0.129692	+	0.586366i
$171$		0			0
$172$	6954.85	+	5052.99i	3.08315	+	2.24004i
$173$	774.704	−	2384.29i	0.340461	−	1.04783i	−0.623509	−	0.781816i	$-0.714293\pi$
$173$	774.704	−	2384.29i	0.340461	−	1.04783i	0.963969	−	0.266013i	$-0.0857066\pi$
$174$		0			0
$175$	−3707.39	−	724.427i	−1.60144	−	0.312923i
$176$	5659.23			2.42375
$177$		0			0
$178$	−5050.40	−	3669.33i	−2.12665	−	1.54510i
$179$	−1412.93	−	1026.56i	−0.589987	−	0.428651i	0.252324	−	0.967643i	$-0.418805\pi$
$179$	−1412.93	−	1026.56i	−0.589987	−	0.428651i	−0.842311	+	0.538992i	$0.818805\pi$
$180$		0			0
$181$	275.217	−	199.957i	0.113020	−	0.0821142i	−0.529839	−	0.848098i	$-0.677748\pi$
$181$	275.217	−	199.957i	0.113020	−	0.0821142i	0.642860	+	0.765984i	$0.277748\pi$
$182$	1005.14			0.409374
$183$		0			0
$184$	−155.480	−	478.518i	−0.0622942	−	0.191722i
$185$	−707.968	−	3200.88i	−0.281356	−	1.27207i
$186$		0			0
$187$	140.568	+	432.623i	0.0549697	+	0.169179i
$188$	−1140.04	−	3508.68i	−0.442266	−	1.36115i
$189$		0			0
$190$	1409.02	+	6370.50i	0.538006	+	2.43245i
$191$	754.426	+	2321.89i	0.285803	+	0.879611i	0.986157	+	0.165815i	$0.0530256\pi$
$191$	754.426	+	2321.89i	0.285803	+	0.879611i	−0.700354	+	0.713796i	$0.746974\pi$
$192$		0			0
$193$	−2643.56			−0.985946			−0.492973	−	0.870045i	$-0.664090\pi$
$193$	−2643.56			−0.985946			−0.492973	+	0.870045i	$0.664090\pi$
$194$	221.644	−	161.034i	0.0820264	−	0.0595957i
$195$		0			0
$196$	−10446.3	−	7589.71i	−3.80698	−	2.76593i
$197$	2093.75	+	1521.20i	0.757225	+	0.550156i	0.898058	−	0.439877i	$-0.144978\pi$
$197$	2093.75	+	1521.20i	0.757225	+	0.550156i	−0.140833	+	0.990033i	$0.544978\pi$
$198$		0			0
$199$	772.004			0.275005			0.137502	−	0.990501i	$-0.456093\pi$
$199$	772.004			0.275005			0.137502	+	0.990501i	$0.456093\pi$
$200$	−9187.40	+	4273.16i	−3.24824	+	1.51079i
$201$		0			0
$202$	−1353.09	+	4164.37i	−0.471301	+	1.45052i
$203$	5656.46	+	4109.66i	1.95569	+	1.42089i
$204$		0			0
$205$	−142.236	−	643.080i	−0.0484594	−	0.219096i
$206$	256.872	−	186.628i	0.0868792	−	0.0631215i
$207$		0			0
$208$	1300.67	−	944.990i	0.433582	−	0.315016i
$209$	688.997	+	2120.52i	0.228033	+	0.701814i
$210$		0			0
$211$	1842.83	−	5671.63i	0.601257	−	1.85048i	0.0805394	−	0.996751i	$-0.474336\pi$
$211$	1842.83	−	5671.63i	0.601257	−	1.85048i	0.520718	−	0.853729i	$-0.325664\pi$
$212$	1853.60	+	5704.80i	0.600499	+	1.84815i
$213$		0			0
$214$	−805.603	+	2479.39i	−0.257336	+	0.791998i
$215$	−4224.94	−	408.911i	−1.34018	−	0.129709i
$216$		0			0
$217$	−4294.23	+	3119.94i	−1.34337	+	0.976016i
$218$	−1276.23			−0.396501
$219$		0			0
$220$	−4614.82	+	2715.28i	−1.41423	+	0.832110i
$221$	104.547	+	75.9580i	0.0318217	+	0.0231198i
$222$		0			0
$223$	1435.00	−	4416.46i	0.430917	−	1.32623i	−0.466297	−	0.884628i	$-0.654412\pi$
$223$	1435.00	−	4416.46i	0.430917	−	1.32623i	0.897213	−	0.441597i	$-0.145588\pi$
$224$	−25164.6			−7.50615
$225$		0			0
$226$	−981.143			−0.288782
$227$	418.007	−	1286.49i	0.122221	−	0.376156i	−0.871164	−	0.490992i	$-0.836634\pi$
$227$	418.007	−	1286.49i	0.122221	−	0.376156i	0.993384	+	0.114836i	$0.0366343\pi$
$228$		0			0
$229$	2577.13	+	1872.40i	0.743675	+	0.540312i	0.893860	−	0.448346i	$-0.147987\pi$
$229$	2577.13	+	1872.40i	0.743675	+	0.540312i	−0.150185	+	0.988658i	$0.547987\pi$
$230$	287.590	+	254.690i	0.0824484	+	0.0730165i
$231$		0			0
$232$	18754.3			5.30723
$233$	−1720.35	+	1249.91i	−0.483708	+	0.351434i	−0.802759	−	0.596303i	$-0.796636\pi$
$233$	−1720.35	+	1249.91i	−0.483708	+	0.351434i	0.319052	+	0.947737i	$0.396636\pi$
$234$		0			0
$235$	1363.70	+	1207.70i	0.378545	+	0.335240i
$236$	3210.55	−	9881.05i	0.885546	−	2.72543i
$237$		0			0
$238$	−1111.82	−	3421.84i	−0.302810	−	0.931953i
$239$	1449.47	−	4461.01i	0.392295	−	1.20736i	−0.538754	−	0.842463i	$-0.681105\pi$
$239$	1449.47	−	4461.01i	0.392295	−	1.20736i	0.931049	−	0.364895i	$-0.118895\pi$
$240$		0			0
$241$	−1069.17	−	3290.58i	−0.285774	−	0.879522i	−0.986166	−	0.165763i	$-0.946991\pi$
$241$	−1069.17	−	3290.58i	−0.285774	−	0.879522i	0.700391	−	0.713759i	$-0.253009\pi$
$242$	3957.46	−	2875.26i	1.05122	−	0.763756i
$243$		0			0
$244$	−10994.2	+	7987.78i	−2.88456	+	2.09576i
$245$	6345.95	+	614.194i	1.65481	+	0.160161i
$246$		0			0
$247$	512.442	+	372.311i	0.132008	+	0.0959091i
$248$	−4399.70	+	13540.9i	−1.12654	+	3.46712i
$249$		0			0
$250$	4391.28	−	6369.22i	1.11092	−	1.61130i
$251$	5528.48			1.39026			0.695128	−	0.718886i	$-0.255348\pi$
$251$	5528.48			1.39026			0.695128	+	0.718886i	$0.255348\pi$
$252$		0			0
$253$	106.207	+	77.1642i	0.0263921	+	0.0191750i
$254$	3634.91	+	2640.92i	0.897932	+	0.652386i
$255$		0			0
$256$	−15395.3	+	11185.4i	−3.75862	+	2.73080i
$257$	2290.19			0.555869			0.277934	−	0.960600i	$-0.410350\pi$
$257$	2290.19			0.555869			0.277934	+	0.960600i	$0.410350\pi$
$258$		0			0
$259$	2738.19	+	8427.28i	0.656922	+	2.02180i
$260$	−607.226	+	1394.65i	−0.144841	+	0.332663i
$261$		0			0
$262$	−2228.52	−	6858.68i	−0.525491	−	1.61729i
$263$	651.760	+	2005.91i	0.152811	+	0.470304i	0.997933	−	0.0642705i	$-0.0204720\pi$
$263$	651.760	+	2005.91i	0.152811	+	0.470304i	−0.845122	+	0.534574i	$0.820472\pi$
$264$		0			0
$265$	−2217.26	−	1963.61i	−0.513981	−	0.455182i
$266$	−5449.64	−	16772.3i	−1.25616	−	3.86606i
$267$		0			0
$268$	7546.82			1.72013
$269$	−6952.97	+	5051.63i	−1.57595	+	1.14499i	−0.654787	+	0.755814i	$0.727242\pi$
$269$	−6952.97	+	5051.63i	−1.57595	+	1.14499i	−0.921162	+	0.389180i	$0.872758\pi$
$270$		0			0
$271$	3304.58	+	2400.92i	0.740734	+	0.538175i	0.892941	−	0.450174i	$-0.148638\pi$
$271$	3304.58	+	2400.92i	0.740734	+	0.538175i	−0.152207	+	0.988349i	$0.548638\pi$
$272$	−4655.77	−	3382.61i	−1.03786	−	0.754048i
$273$		0			0
$274$	6155.35			1.35715
$275$	1284.00	−	2311.03i	0.281556	−	0.506765i
$276$		0			0
$277$	−1157.41	+	3562.16i	−0.251055	+	0.772669i	0.743526	+	0.668707i	$0.233152\pi$
$277$	−1157.41	+	3562.16i	−0.251055	+	0.772669i	−0.994581	+	0.103962i	$0.966848\pi$
$278$	−106.439	−	77.3324i	−0.0229632	−	0.0166838i
$279$		0			0
$280$	23605.0	−	13888.8i	5.03810	−	2.96434i
$281$	−3085.22	+	2241.55i	−0.654978	+	0.475870i	−0.864963	−	0.501835i	$-0.832658\pi$
$281$	−3085.22	+	2241.55i	−0.654978	+	0.475870i	0.209985	+	0.977705i	$0.432658\pi$
$282$		0			0
$283$	−2689.86	+	1954.30i	−0.565003	+	0.410499i	−0.833287	−	0.552841i	$-0.813544\pi$
$283$	−2689.86	+	1954.30i	−0.565003	+	0.410499i	0.268284	+	0.963340i	$0.413544\pi$
$284$	6186.88	+	19041.3i	1.29269	+	3.97849i
$285$		0			0
$286$	−217.384	+	669.040i	−0.0449448	+	0.138326i
$287$	550.121	+	1693.10i	0.113145	+	0.348225i
$288$		0			0
$289$	−1375.26	+	4232.61i	−0.279922	+	0.861512i
$290$	−12341.3	+	7261.42i	−2.49899	+	1.47036i
$291$		0			0
$292$	−5978.68	+	4343.77i	−1.19820	+	0.870547i
$293$	−6316.24			−1.25938			−0.629691	−	0.776846i	$-0.716818\pi$
$293$	−6316.24			−1.25938			−0.629691	+	0.776846i	$0.716818\pi$
$294$		0			0
$295$	1107.86	+	5008.88i	0.218651	+	0.988570i
$296$	19228.8	+	13970.5i	3.77584	+	2.74331i
$297$		0			0
$298$	3747.34	−	11533.1i	0.728449	−	2.24193i
$299$	37.2948			0.00721343
$300$		0			0
$301$	11473.2			2.19703
$302$	1525.18	−	4694.02i	0.290610	−	0.894405i
$303$		0			0
$304$	−22820.4	−	16580.0i	−4.30539	−	3.12805i
$305$	2678.63	−	6152.15i	0.502878	−	1.15499i
$306$		0			0
$307$	−8592.04			−1.59731			−0.798655	−	0.601790i	$-0.794455\pi$
$307$	−8592.04			−1.59731			−0.798655	+	0.601790i	$0.794455\pi$
$308$	11708.6	−	8506.82i	2.16611	−	1.57377i
$309$		0			0
$310$	−2347.62	−	10614.1i	−0.430116	−	1.94465i
$311$	−140.125	+	431.260i	−0.0255490	+	0.0786319i	−0.963018	−	0.269437i	$-0.913162\pi$
$311$	−140.125	+	431.260i	−0.0255490	+	0.0786319i	0.937469	+	0.348069i	$0.113162\pi$
$312$		0			0
$313$	−1961.96	−	6038.28i	−0.354302	−	1.09043i	−0.956413	−	0.292016i	$-0.905674\pi$
$313$	−1961.96	−	6038.28i	−0.354302	−	1.09043i	0.602112	−	0.798412i	$-0.294326\pi$
$314$	4002.65	−	12318.9i	0.719372	−	2.21400i
$315$		0			0
$316$	551.632	+	1697.75i	0.0982017	+	0.302234i
$317$	−5897.27	+	4284.62i	−1.04487	+	0.759143i	−0.971230	−	0.238142i	$-0.923462\pi$
$317$	−5897.27	+	4284.62i	−1.04487	+	0.759143i	−0.0736400	+	0.997285i	$0.523462\pi$
$318$		0			0
$319$	−3958.79	+	2876.23i	−0.694827	+	0.504822i
$320$	11019.6	−	25309.4i	1.92505	−	4.42136i
$321$		0			0
$322$	−840.049	−	610.332i	−0.145385	−	0.105629i
$323$	700.639	−	2156.35i	0.120695	−	0.371462i
$324$		0			0
$325$	−90.7984	−	745.551i	−0.0154972	−	0.127248i
$326$	−12324.0			−2.09375
$327$		0			0
$328$	3863.19	+	2806.77i	0.650333	+	0.472494i
$329$	−3983.37	−	2894.09i	−0.667508	−	0.484973i
$330$		0			0
$331$	−3531.10	+	2565.49i	−0.586365	+	0.426019i	−0.841013	−	0.541015i	$-0.818040\pi$
$331$	−3531.10	+	2565.49i	−0.586365	+	0.426019i	0.254648	+	0.967034i	$0.418040\pi$
$332$	29733.5			4.91517
$333$		0			0
$334$	1061.28	+	3266.28i	0.173864	+	0.535098i
$335$	−3211.62	+	1889.66i	−0.523790	+	0.308189i
$336$		0			0
$337$	663.043	+	2040.64i	0.107176	+	0.329853i	0.990235	−	0.139408i	$-0.0445201\pi$
$337$	663.043	+	2040.64i	0.107176	+	0.329853i	−0.883059	+	0.469262i	$0.844520\pi$
$338$	−3696.45	−	11376.5i	−0.594853	−	1.83077i
$339$		0			0
$340$	5419.52	+	524.529i	0.864455	+	0.0836664i
$341$	−1147.96	−	3533.07i	−0.182304	−	0.561075i
$342$		0			0
$343$	−6867.55			−1.08109
$344$	24897.5	−	18089.1i	3.90227	−	2.83517i
$345$		0			0
$346$	−11227.4	−	8157.18i	−1.74448	−	1.26744i
$347$	−6185.75	−	4494.21i	−0.956970	−	0.695279i	−0.00452493	−	0.999990i	$-0.501440\pi$
$347$	−6185.75	−	4494.21i	−0.956970	−	0.695279i	−0.952445	+	0.304710i	$0.901440\pi$
$348$		0			0
$349$	7655.39			1.17416			0.587082	−	0.809527i	$-0.300276\pi$
$349$	7655.39			1.17416			0.587082	+	0.809527i	$0.300276\pi$
$350$	−10155.8	+	18279.1i	−1.55100	+	2.79160i
$351$		0			0
$352$	5442.39	−	16750.0i	0.824093	−	2.53630i
$353$	5076.69	+	3688.43i	0.765453	+	0.556134i	0.900578	−	0.434694i	$-0.143144\pi$
$353$	5076.69	+	3688.43i	0.765453	+	0.556134i	−0.135125	+	0.990829i	$0.543144\pi$
$354$		0			0
$355$	−7400.67	−	6554.05i	−1.10644	−	0.979867i
$356$	−20658.5	+	15009.3i	−3.07555	+	2.23452i
$357$		0			0
$358$	−7821.50	+	5682.65i	−1.15469	+	0.838931i
$359$	−2156.39	−	6636.67i	−0.317019	−	0.975683i	−0.974916	−	0.222575i	$-0.928554\pi$
$359$	−2156.39	−	6636.67i	−0.317019	−	0.975683i	0.657897	−	0.753108i	$-0.271446\pi$
$360$		0			0
$361$	1314.66	−	4046.10i	0.191669	−	0.589897i
$362$	−581.926	−	1790.98i	−0.0844899	−	0.260033i
$363$		0			0
$364$	1270.52	−	3910.27i	0.182949	−	0.563060i
$365$	1456.64	−	3345.55i	0.208888	−	0.479764i
$366$		0			0
$367$	−1972.27	+	1432.94i	−0.280522	+	0.203811i	−0.719145	−	0.694860i	$-0.755466\pi$
$367$	−1972.27	+	1432.94i	−0.280522	+	0.203811i	0.438623	+	0.898671i	$0.355466\pi$
$368$	−1660.84			−0.235264
$369$		0			0
$370$	−18062.8	−	1748.21i	−2.53794	−	0.245635i
$371$	6476.59	+	4705.52i	0.906328	+	0.658486i
$372$		0			0
$373$	697.469	−	2146.59i	0.0968193	−	0.297979i	−0.890904	−	0.454191i	$-0.849928\pi$
$373$	697.469	−	2146.59i	0.0968193	−	0.297979i	0.987724	+	0.156212i	$0.0499283\pi$
$374$	2518.09			0.348148
$375$		0			0
$376$	−13207.0			−1.81144
$377$	−429.575	+	1322.10i	−0.0586850	+	0.180614i
$378$		0			0
$379$	7532.09	+	5472.38i	1.02084	+	0.741682i	0.966454	−	0.256838i	$-0.0826807\pi$
$379$	7532.09	+	5472.38i	1.02084	+	0.741682i	0.0543834	+	0.998520i	$0.482681\pi$
$380$	26564.0	+	2571.00i	3.58606	+	0.347077i
$381$		0			0
$382$	13514.6			1.81012
$383$	−5295.40	+	3847.33i	−0.706481	+	0.513289i	−0.882037	−	0.471181i	$-0.843828\pi$
$383$	−5295.40	+	3847.33i	−0.706481	+	0.513289i	0.175555	+	0.984470i	$0.443828\pi$
$384$		0			0
$385$	−2852.68	+	6551.92i	−0.377627	+	0.867316i
$386$	−4522.09	+	13917.6i	−0.596291	+	1.83520i
$387$		0			0
$388$	−346.301	−	1065.80i	−0.0453112	−	0.139454i
$389$	−1760.54	+	5418.39i	−0.229468	+	0.706230i	0.768339	+	0.640043i	$0.221083\pi$
$389$	−1760.54	+	5418.39i	−0.229468	+	0.706230i	−0.997807	+	0.0661869i	$0.978917\pi$
$390$		0			0
$391$	−41.2531	−	126.964i	−0.00533570	−	0.0164216i
$392$	−37396.6	+	27170.2i	−4.81840	+	3.50077i
$393$		0			0
$394$	11590.2	−	8420.80i	1.48200	−	1.07674i
$395$	−659.856	−	584.369i	−0.0840530	−	0.0744375i
$396$		0			0
$397$	7305.74	+	5307.93i	0.923589	+	0.671026i	0.944415	−	0.328757i	$-0.106630\pi$
$397$	7305.74	+	5307.93i	0.923589	+	0.671026i	−0.0208261	+	0.999783i	$0.506630\pi$
$398$	1320.60	−	4064.38i	0.166320	−	0.511881i
$399$		0			0
$400$	4043.50	+	33201.4i	0.505437	+	4.15018i
$401$	−1291.00			−0.160772			−0.0803859	−	0.996764i	$-0.525615\pi$
$401$	−1291.00			−0.160772			−0.0803859	+	0.996764i	$0.525615\pi$
$402$		0			0
$403$	−853.797	−	620.320i	−0.105535	−	0.0766758i
$404$	14490.2	+	10527.7i	1.78444	+	1.29647i
$405$		0			0
$406$	31312.1	−	22749.6i	3.82758	−	2.78090i
$407$	−6201.53			−0.755279
$408$		0			0
$409$	−1299.63	−	3999.85i	−0.157121	−	0.483570i	0.841248	−	0.540649i	$-0.181821\pi$
$409$	−1299.63	−	3999.85i	−0.157121	−	0.483570i	−0.998370	+	0.0570792i	$0.981821\pi$
$410$	−3628.94	−	351.227i	−0.437123	−	0.0423070i
$411$		0			0
$412$	−401.341	−	1235.20i	−0.0479919	−	0.147704i
$413$	−4284.83	−	13187.4i	−0.510515	−	1.57121i
$414$		0			0
$415$	−12653.4	+	7445.03i	−1.49670	+	0.880632i
$416$	−1546.11	−	4758.45i	−0.182222	−	0.560822i
$417$		0			0
$418$	12342.5			1.44424
$419$	4482.54	−	3256.76i	0.522641	−	0.379721i	−0.294957	−	0.955510i	$-0.595305\pi$
$419$	4482.54	−	3256.76i	0.522641	−	0.379721i	0.817598	+	0.575790i	$0.195305\pi$
$420$		0			0
$421$	5750.48	+	4177.97i	0.665704	+	0.483662i	0.868584	−	0.495541i	$-0.165030\pi$
$421$	5750.48	+	4177.97i	0.665704	+	0.483662i	−0.202881	+	0.979203i	$0.565030\pi$
$422$	−26707.1	−	19403.9i	−3.08077	−	2.23831i
$423$		0			0
$424$	21473.4			2.45953
$425$	−2437.67	+	1133.79i	−0.278222	+	0.129404i
$426$		0			0
$427$	−5604.60	+	17249.2i	−0.635188	+	1.95491i
$428$	8627.18	+	6268.01i	0.974323	+	0.707887i
$429$		0			0
$430$	−9380.00	+	21543.6i	−1.05196	+	2.41610i
$431$	4596.49	−	3339.54i	0.513701	−	0.373225i	−0.300525	−	0.953774i	$-0.597162\pi$
$431$	4596.49	−	3339.54i	0.513701	−	0.373225i	0.814226	+	0.580549i	$0.197162\pi$
$432$		0			0
$433$	12267.7	−	8913.00i	1.36154	−	0.989218i	0.363196	−	0.931713i	$-0.381685\pi$
$433$	12267.7	−	8913.00i	1.36154	−	0.989218i	0.998345	−	0.0575050i	$-0.0183145\pi$
$434$	9079.84	+	27944.9i	1.00425	+	3.09078i
$435$		0			0
$436$	−1613.18	+	4964.87i	−0.177196	+	0.545353i
$437$	−202.203	−	622.318i	−0.0221343	−	0.0681224i
$438$		0			0
$439$	583.950	−	1797.21i	0.0634861	−	0.195390i	−0.914282	−	0.405077i	$-0.867245\pi$
$439$	583.950	−	1797.21i	0.0634861	−	0.195390i	0.977769	+	0.209687i	$0.0672446\pi$
$440$	4139.51	+	18715.7i	0.448508	+	2.02780i
$441$		0			0
$442$	578.736	−	420.476i	0.0622798	−	0.0452489i
$443$	−14518.3			−1.55707			−0.778536	−	0.627600i	$-0.784037\pi$
$443$	−14518.3			−1.55707			−0.778536	+	0.627600i	$0.784037\pi$
$444$		0			0
$445$	5033.22	−	11560.1i	0.536174	−	1.23146i
$446$	−20796.7	−	15109.7i	−2.20796	−	1.60418i
$447$		0			0
$448$	−23056.8	+	70961.5i	−2.43154	+	7.48351i
$449$	−15727.5			−1.65307			−0.826535	−	0.562885i	$-0.809691\pi$
$449$	−15727.5			−1.65307			−0.826535	+	0.562885i	$0.809691\pi$
$450$		0			0
$451$	−1245.93			−0.130086
$452$	−1240.19	+	3816.90i	−0.129056	+	0.397194i
$453$		0			0
$454$	−6057.96	−	4401.37i	−0.626243	−	0.454992i
$455$	438.417	+	1982.18i	0.0451721	+	0.204233i
$456$		0			0
$457$	−3024.30			−0.309564			−0.154782	−	0.987949i	$-0.549468\pi$
$457$	−3024.30			−0.309564			−0.154782	+	0.987949i	$0.549468\pi$
$458$	14266.1	−	10364.9i	1.45548	−	1.05747i
$459$		0			0
$460$	1354.33	−	796.867i	0.137274	−	0.0807698i
$461$	−1738.63	+	5350.95i	−0.175653	+	0.540604i	−0.999663	−	0.0259714i	$-0.991732\pi$
$461$	−1738.63	+	5350.95i	−0.175653	+	0.540604i	0.824010	+	0.566576i	$0.191732\pi$
$462$		0			0
$463$	−1365.98	−	4204.05i	−0.137111	−	0.421985i	0.858801	−	0.512309i	$-0.171210\pi$
$463$	−1365.98	−	4204.05i	−0.137111	−	0.421985i	−0.995912	+	0.0903241i	$0.971210\pi$
$464$	19130.1	−	58876.5i	1.91400	−	5.89068i
$465$		0			0
$466$	3637.55	+	11195.2i	0.361602	+	1.11290i
$467$	4026.97	−	2925.76i	0.399028	−	0.289911i	−0.370117	−	0.928985i	$-0.620682\pi$
$467$	4026.97	−	2925.76i	0.399028	−	0.289911i	0.769145	+	0.639075i	$0.220682\pi$
$468$		0			0
$469$	8148.47	−	5920.21i	0.802263	−	0.582878i
$470$	8690.94	−	5113.60i	0.852942	−	0.501857i
$471$		0			0
$472$	−30090.0	−	21861.7i	−2.93433	−	2.13192i
$473$	−2481.34	+	7636.76i	−0.241209	+	0.742365i
$474$		0			0
$475$	−11948.3	+	5557.30i	−1.15416	+	0.536813i
$476$	−14717.2			−1.41715
$477$		0			0
$478$	−21006.4	−	15262.1i	−2.01007	−	1.46040i
$479$	−5836.76	−	4240.66i	−0.556761	−	0.404511i	0.273511	−	0.961869i	$-0.411815\pi$
$479$	−5836.76	−	4240.66i	−0.556761	−	0.404511i	−0.830272	+	0.557358i	$0.811815\pi$
$480$		0			0
$481$	−1425.31	+	1035.55i	−0.135111	+	0.0981639i
$482$	−19152.9			−1.80994
$483$		0			0
$484$	−6183.20	−	19029.9i	−0.580692	−	1.78718i
$485$	414.241	+	366.852i	0.0387829	+	0.0343462i
$486$		0			0
$487$	4846.33	+	14915.5i	0.450941	+	1.38785i	0.875835	+	0.482610i	$0.160311\pi$
$487$	4846.33	+	14915.5i	0.450941	+	1.38785i	−0.424894	+	0.905243i	$0.639689\pi$
$488$	15033.4	+	46268.0i	1.39453	+	4.29192i
$489$		0			0
$490$	14089.0	−	32358.9i	1.29893	−	2.98332i
$491$	4177.42	+	12856.8i	0.383960	+	1.18171i	0.937232	+	0.348707i	$0.113379\pi$
$491$	4177.42	+	12856.8i	0.383960	+	1.18171i	−0.553271	+	0.833001i	$0.686621\pi$
$492$		0			0
$493$	4976.02			0.454581
$494$	2836.69	−	2060.98i	0.258358	−	0.187708i
$495$		0			0
$496$	38021.9	+	27624.5i	3.44200	+	2.50076i
$497$	21617.3	+	15705.9i	1.95104	+	1.41752i
$498$		0			0
$499$	−19053.5			−1.70932			−0.854660	−	0.519188i	$-0.826234\pi$
$499$	−19053.5			−1.70932			−0.854660	+	0.519188i	$0.826234\pi$
$500$	−19227.2	−	25134.1i	−1.71974	−	2.24806i
$501$		0			0
$502$	9457.05	−	29105.8i	0.840815	−	2.58776i
$503$	−12244.1	−	8895.89i	−1.08537	−	0.788565i	−0.106756	−	0.994285i	$-0.534046\pi$
$503$	−12244.1	−	8895.89i	−1.08537	−	0.788565i	−0.978611	+	0.205720i	$0.934046\pi$
$504$		0			0
$505$	−8802.49	−	851.950i	−0.775655	−	0.0750719i
$506$	587.926	−	427.153i	0.0516532	−	0.0375282i
$507$		0			0
$508$	14868.5	−	10802.6i	1.29859	−	0.943478i
$509$	2000.14	+	6155.78i	0.174174	+	0.536052i	0.999595	−	0.0284660i	$-0.00906222\pi$
$509$	2000.14	+	6155.78i	0.174174	+	0.536052i	−0.825421	+	0.564518i	$0.809062\pi$
$510$		0			0
$511$	−3047.79	+	9380.13i	−0.263848	+	0.812040i
$512$	15233.0	+	46882.2i	1.31486	+	4.04672i
$513$		0			0
$514$	3917.62	−	12057.2i	0.336185	−	1.03467i
$515$	480.080	+	425.160i	0.0410774	+	0.0363782i
$516$		0			0
$517$	2787.84	−	2025.49i	0.237155	−	0.172303i
$518$	49051.1			4.16059
$519$		0			0
$520$	4076.57	+	3610.22i	0.343787	+	0.304459i
$521$	−12414.6	−	9019.77i	−1.04395	−	0.758471i	−0.0728937	−	0.997340i	$-0.523223\pi$
$521$	−12414.6	−	9019.77i	−1.04395	−	0.758471i	−0.971052	+	0.238869i	$0.923223\pi$
$522$		0			0
$523$	−1899.57	+	5846.27i	−0.158819	+	0.488795i	−0.998528	−	0.0542423i	$-0.982726\pi$
$523$	−1899.57	+	5846.27i	−0.158819	+	0.488795i	0.839709	+	0.543037i	$0.182726\pi$
$524$	−29499.0			−2.45929
$525$		0			0
$526$	11675.5			0.967821
$527$	−1167.36	+	3592.77i	−0.0964915	+	0.296970i
$528$		0			0
$529$	9812.14	+	7128.94i	0.806455	+	0.585924i
$530$	−14130.7	+	8314.24i	−1.15811	+	0.681411i
$531$		0			0
$532$	−72136.9			−5.87882
$533$	−286.354	+	208.048i	−0.0232709	+	0.0169073i
$534$		0			0
$535$	−5240.84	−	507.236i	−0.423517	−	0.0409901i
$536$	8348.60	−	25694.4i	0.672770	−	2.07057i
$537$		0			0
$538$	14701.6	+	45246.7i	1.17812	+	3.62588i
$539$	3727.02	−	11470.6i	0.297837	−	0.916648i
$540$		0			0
$541$	−3280.78	−	10097.2i	−0.260724	−	0.802425i	−0.992648	−	0.121039i	$-0.961377\pi$
$541$	−3280.78	−	10097.2i	−0.260724	−	0.802425i	0.731924	−	0.681386i	$-0.238623\pi$
$542$	18293.0	−	13290.6i	1.44972	−	1.05329i
$543$		0			0
$544$	−14489.1	+	10527.0i	−1.14194	+	0.829669i
$545$	−556.658	−	2516.78i	−0.0437516	−	0.197811i
$546$		0			0
$547$	−16829.3	−	12227.2i	−1.31548	−	0.955754i	−0.999977	−	0.00683023i	$-0.997826\pi$
$547$	−16829.3	−	12227.2i	−1.31548	−	0.955754i	−0.315506	−	0.948924i	$-0.602174\pi$
$548$	7780.50	−	23945.9i	0.606508	−	1.86664i
$549$		0			0
$550$	−9970.49	−	10713.1i	−0.772987	−	0.830563i
$551$	24390.1			1.88576
$552$		0			0
$553$	1927.43	+	1400.36i	0.148215	+	0.107684i
$554$	16773.8	+	12186.9i	1.28637	+	0.934606i
$555$		0			0
$556$	−435.384	+	316.325i	−0.0332094	+	0.0241280i
$557$	8938.79			0.679980			0.339990	−	0.940429i	$-0.389576\pi$
$557$	8938.79			0.679980			0.339990	+	0.940429i	$0.389576\pi$
$558$		0			0
$559$	704.915	+	2169.51i	0.0533358	+	0.164151i
$560$	−19523.9	−	88271.9i	−1.47328	−	6.66102i
$561$		0			0
$562$	6523.48	+	20077.2i	0.489638	+	1.50695i
$563$	3016.21	+	9282.93i	0.225787	+	0.694900i	0.998211	+	0.0597931i	$0.0190441\pi$
$563$	3016.21	+	9282.93i	0.225787	+	0.694900i	−0.772424	+	0.635107i	$0.780956\pi$
$564$		0			0
$565$	−427.949	−	1934.85i	−0.0318654	−	0.144071i
$566$	5687.52	+	17504.4i	0.422375	+	1.29994i
$567$		0			0
$568$	71673.2			5.29462
$569$	11079.9	−	8050.05i	0.816336	−	0.593103i	−0.0993244	−	0.995055i	$-0.531668\pi$
$569$	11079.9	−	8050.05i	0.816336	−	0.593103i	0.915661	+	0.401952i	$0.131668\pi$
$570$		0			0
$571$	9324.33	+	6774.52i	0.683382	+	0.496506i	0.874478	−	0.485065i	$-0.161204\pi$
$571$	9324.33	+	6774.52i	0.683382	+	0.496506i	−0.191096	+	0.981571i	$0.561204\pi$
$572$	2327.96	+	1691.36i	0.170170	+	0.123635i
$573$		0			0
$574$	9854.71			0.716599
$575$	−376.820	+	678.229i	−0.0273296	+	0.0491897i
$576$		0			0
$577$	4919.30	−	15140.0i	0.354927	−	1.09235i	−0.601125	−	0.799155i	$-0.705280\pi$
$577$	4919.30	−	15140.0i	0.354927	−	1.09235i	0.956052	−	0.293198i	$-0.0947195\pi$
$578$	19930.9	+	14480.7i	1.43429	+	1.04207i
$579$		0			0
$580$	12649.1	+	57189.5i	0.905562	+	4.09425i
$581$	32103.9	−	23324.9i	2.29242	−	1.66554i
$582$		0			0
$583$	−4532.78	+	3293.26i	−0.322004	+	0.233950i
$584$	8175.19	+	25160.6i	0.579267	+	1.78280i
$585$		0			0
$586$	−10804.6	+	33253.2i	−0.761663	+	2.34416i
$587$	5556.96	+	17102.6i	0.390733	+	1.20255i	0.932235	+	0.361853i	$0.117856\pi$
$587$	5556.96	+	17102.6i	0.390733	+	1.20255i	−0.541502	+	0.840700i	$0.682144\pi$
$588$		0			0
$589$	−5721.86	+	17610.1i	−0.400280	+	1.23194i
$590$	28265.4	+	2735.67i	1.97232	+	0.190891i
$591$		0			0
$592$	63472.7	−	46115.6i	4.40661	−	3.20159i
$593$	−230.646			−0.0159721			−0.00798607	−	0.999968i	$-0.502542\pi$
$593$	−230.646			−0.0159721			−0.00798607	+	0.999968i	$0.502542\pi$
$594$		0			0
$595$	6263.05	−	3685.08i	0.431530	−	0.253905i
$596$	−40130.2	−	29156.3i	−2.75805	−	2.00384i
$597$		0			0
$598$	63.7968	−	196.346i	0.00436262	−	0.0134268i
$599$	−11209.1			−0.764597			−0.382298	−	0.924039i	$-0.624867\pi$
$599$	−11209.1			−0.764597			−0.382298	+	0.924039i	$0.624867\pi$
$600$		0			0
$601$	8219.09			0.557843			0.278922	−	0.960314i	$-0.410023\pi$
$601$	8219.09			0.557843			0.278922	+	0.960314i	$0.410023\pi$
$602$	19626.2	−	60403.1i	1.32874	−	4.08945i
$603$		0			0
$604$	−16333.1	−	11866.7i	−1.10030	−	0.799418i
$605$	7396.28	+	6550.16i	0.497027	+	0.440168i
$606$		0			0
$607$	9305.08			0.622210			0.311105	−	0.950376i	$-0.399301\pi$
$607$	9305.08			0.622210			0.311105	+	0.950376i	$0.399301\pi$
$608$	−71018.9	+	51598.3i	−4.73717	+	3.44175i
$609$		0			0
$610$	−27807.2	−	24626.1i	−1.84570	−	1.63456i
$611$	302.513	−	931.040i	0.0200301	−	0.0616463i
$612$		0			0
$613$	−2405.39	−	7403.03i	−0.158487	−	0.487774i	0.840010	−	0.542571i	$-0.182549\pi$
$613$	−2405.39	−	7403.03i	−0.158487	−	0.487774i	−0.998498	+	0.0547965i	$0.982549\pi$
$614$	−14697.6	+	45234.6i	−0.966038	+	2.97316i
$615$		0			0
$616$	−16010.3	−	49274.6i	−1.04720	−	3.22294i
$617$	745.708	−	541.789i	0.0486565	−	0.0353510i	−0.563191	−	0.826327i	$-0.690427\pi$
$617$	745.708	−	541.789i	0.0486565	−	0.0353510i	0.611848	+	0.790976i	$0.290427\pi$
$618$		0			0
$619$	6014.72	−	4369.95i	0.390553	−	0.283753i	−0.375129	−	0.926972i	$-0.622402\pi$
$619$	6014.72	−	4369.95i	0.390553	−	0.283753i	0.765682	+	0.643219i	$0.222402\pi$
$620$	−44259.2	−	4283.63i	−2.86692	−	0.277475i
$621$		0			0
$622$	2030.76	+	1475.43i	0.130910	+	0.0951117i
$623$	−10531.2	+	32411.7i	−0.677245	+	2.08435i
$624$		0			0
$625$	14475.7	+	5881.70i	0.926446	+	0.376429i
$626$	−35145.9			−2.24395
$627$		0			0
$628$	−42864.3	−	31142.7i	−2.72368	−	1.97887i
$629$	5101.92	+	3706.76i	0.323413	+	0.234973i
$630$		0			0
$631$	5821.33	−	4229.44i	0.367264	−	0.266833i	−0.388812	−	0.921317i	$-0.627114\pi$
$631$	5821.33	−	4229.44i	0.367264	−	0.266833i	0.756075	+	0.654485i	$0.227114\pi$
$632$	6390.50			0.402216
$633$		0			0
$634$	12469.4	+	38376.7i	0.781106	+	2.40400i
$635$	−3622.54	+	8320.09i	−0.226388	+	0.519957i
$636$		0			0
$637$	−1058.80	−	3258.65i	−0.0658573	−	0.202688i
$638$	8370.58	+	25762.0i	0.519427	+	1.59863i
$639$		0			0
$640$	−58638.2	−	51930.1i	−3.62169	−	3.20737i
$641$	467.168	+	1437.79i	0.0287863	+	0.0885951i	0.964417	−	0.264384i	$-0.0851687\pi$
$641$	467.168	+	1437.79i	0.0287863	+	0.0885951i	−0.935631	+	0.352979i	$0.885169\pi$
$642$		0			0
$643$	−22396.8			−1.37363			−0.686813	−	0.726834i	$-0.740991\pi$
$643$	−22396.8			−1.37363			−0.686813	+	0.726834i	$0.740991\pi$
$644$	−3436.19	+	2496.54i	−0.210256	+	0.152760i
$645$		0			0
$646$	−10154.0	−	7377.32i	−0.618428	−	0.449314i
$647$	−1561.70	−	1134.64i	−0.0948944	−	0.0689448i	0.539326	−	0.842097i	$-0.318679\pi$
$647$	−1561.70	−	1134.64i	−0.0948944	−	0.0689448i	−0.634221	+	0.773152i	$0.718679\pi$
$648$		0			0
$649$	9704.42			0.586952
$650$	−4080.43	−	797.319i	−0.246227	−	0.0481130i
$651$		0			0
$652$	−15577.8	+	47943.5i	−0.935696	+	2.87978i
$653$	−23581.3	−	17132.8i	−1.41318	−	1.02674i	−0.992850	−	0.119368i	$-0.961913\pi$
$653$	−23581.3	−	17132.8i	−1.41318	−	1.02674i	−0.420333	−	0.907370i	$-0.638087\pi$
$654$		0			0
$655$	12553.6	−	7386.31i	0.748868	−	0.440622i
$656$	12752.1	−	9264.95i	0.758973	−	0.551426i
$657$		0			0
$658$	−22050.5	+	16020.6i	−1.30641	+	0.949162i
$659$	−5189.79	−	15972.5i	−0.306776	−	0.944161i	−0.979008	−	0.203820i	$-0.934664\pi$
$659$	−5189.79	−	15972.5i	−0.306776	−	0.944161i	0.672232	−	0.740341i	$-0.265336\pi$
$660$		0			0
$661$	7008.62	−	21570.3i	0.412411	−	1.26927i	−0.502135	−	0.864789i	$-0.667452\pi$
$661$	7008.62	−	21570.3i	0.412411	−	1.26927i	0.914546	−	0.404482i	$-0.132548\pi$
$662$	7466.26	+	22978.8i	0.438345	+	1.34909i
$663$		0			0
$664$	32892.4	−	101232.i	1.92240	−	5.91654i
$665$	30698.6	−	18062.5i	1.79013	−	1.05329i
$666$		0			0
$667$	1161.81	−	844.102i	0.0674442	−	0.0490011i
$668$	14048.2			0.813682
$669$		0			0
$670$	4454.71	+	20140.7i	0.256866	+	1.16135i
$671$	−10269.2	−	7461.03i	−0.590818	−	0.429255i
$672$		0			0
$673$	1787.87	−	5502.51i	0.102403	−	0.315165i	−0.886709	−	0.462328i	$-0.847014\pi$
$673$	1787.87	−	5502.51i	0.102403	−	0.315165i	0.989112	+	0.147163i	$0.0470142\pi$
$674$	11877.6			0.678793
$675$		0			0
$676$	−48929.9			−2.78391
$677$	−2989.08	+	9199.45i	−0.169690	+	0.522251i	−0.999351	−	0.0360158i	$-0.988533\pi$
$677$	−2989.08	+	9199.45i	−0.169690	+	0.522251i	0.829662	+	0.558267i	$0.188533\pi$
$678$		0			0
$679$	−1209.99	−	879.113i	−0.0683878	−	0.0496867i
$680$	7781.14	−	17871.4i	0.438813	−	1.00785i
$681$		0			0
$682$	−20564.3			−1.15462
$683$	23680.4	−	17204.8i	1.32666	−	0.963872i	0.326832	−	0.945082i	$-0.394019\pi$
$683$	23680.4	−	17204.8i	1.32666	−	0.963872i	0.999823	−	0.0187892i	$-0.00598113\pi$
$684$		0			0
$685$	2684.80	+	12138.6i	0.149753	+	0.677068i
$686$	−11747.7	+	36155.6i	−0.653831	+	2.01229i
$687$		0			0
$688$	−31391.8	−	96613.9i	−1.73954	−	5.35374i
$689$	−491.859	+	1513.79i	−0.0271964	+	0.0837020i
$690$		0			0
$691$	−6623.67	−	20385.6i	−0.364654	−	1.12229i	−0.950197	−	0.311650i	$-0.899119\pi$
$691$	−6623.67	−	20385.6i	−0.364654	−	1.12229i	0.585543	−	0.810642i	$-0.300881\pi$
$692$	−45925.3	+	33366.7i	−2.52286	+	1.83296i
$693$		0			0
$694$	−34242.1	+	24878.4i	−1.87293	+	1.36076i
$695$	106.077	−	243.632i	0.00578952	−	0.0132971i
$696$		0			0
$697$	1025.01	+	744.714i	0.0557031	+	0.0404707i
$698$	13095.4	−	40303.4i	0.710124	−	2.18554i
$699$		0			0
$700$	58273.4	+	62613.9i	3.14647	+	3.38083i
$701$	16727.9			0.901292			0.450646	−	0.892703i	$-0.351194\pi$
$701$	16727.9			0.901292			0.450646	+	0.892703i	$0.351194\pi$
$702$		0			0
$703$	25007.2	+	18168.8i	1.34163	+	0.974751i
$704$	−42246.6	−	30694.0i	−2.26169	−	1.64321i
$705$		0			0
$706$	28102.7	−	20417.8i	1.49810	−	1.08844i
$707$	23904.0			1.27157
$708$		0			0
$709$	−5241.61	−	16132.0i	−0.277648	−	0.854514i	−0.988506	−	0.151178i	$-0.951693\pi$
$709$	−5241.61	−	16132.0i	−0.277648	−	0.854514i	0.710858	−	0.703335i	$-0.248307\pi$
$710$	−47164.8	+	27751.0i	−2.49305	+	1.46687i
$711$		0			0
$712$	28248.2	+	86939.0i	1.48686	+	4.57609i
$713$	336.898	+	1036.87i	0.0176956	+	0.0544614i
$714$		0			0
$715$	−1414.19	−	136.873i	−0.0739689	−	0.00715909i
$716$	12220.4	+	37610.7i	0.637848	+	1.96310i
$717$		0			0
$718$	−38628.9			−2.00782
$719$	−6363.32	+	4623.22i	−0.330058	+	0.239801i	−0.740455	−	0.672106i	$-0.765390\pi$
$719$	−6363.32	+	4623.22i	−0.330058	+	0.239801i	0.410397	+	0.911907i	$0.365390\pi$
$720$		0			0
$721$	−1402.31	−	1018.84i	−0.0724338	−	0.0526262i
$722$	−19052.7	−	13842.6i	−0.982088	−	0.713529i
$723$		0			0
$724$	−7702.96			−0.395412
$725$	−19702.8	−	21170.3i	−1.00930	−	1.08448i
$726$		0			0
$727$	2605.34	−	8018.41i	0.132912	−	0.409060i	−0.862348	−	0.506316i	$-0.831007\pi$
$727$	2605.34	−	8018.41i	0.132912	−	0.409060i	0.995259	+	0.0972567i	$0.0310068\pi$
$728$	−11907.6	−	8651.40i	−0.606217	−	0.440443i
$729$		0			0
$730$	−15121.6	−	13391.7i	−0.766679	−	0.678972i
$731$	6605.98	−	4799.53i	0.334242	−	0.242841i
$732$		0			0
$733$	−17055.7	+	12391.7i	−0.859435	+	0.624416i	−0.927731	−	0.373249i	$-0.878244\pi$
$733$	−17055.7	+	12391.7i	−0.859435	+	0.624416i	0.0682959	+	0.997665i	$0.478244\pi$
$734$	4170.22	+	12834.6i	0.209708	+	0.645414i
$735$		0			0
$736$	−1597.21	+	4915.69i	−0.0799915	+	0.246189i
$737$	2178.31	+	6704.14i	0.108872	+	0.335075i
$738$		0			0
$739$	−1688.56	+	5196.84i	−0.0840522	+	0.258686i	−0.984246	−	0.176803i	$-0.943424\pi$
$739$	−1688.56	+	5196.84i	−0.0840522	+	0.258686i	0.900194	+	0.435489i	$0.143424\pi$
$740$	−29632.7	+	68059.1i	−1.47205	+	3.38095i
$741$		0			0
$742$	35852.1	−	26048.1i	1.77382	−	1.28875i
$743$	12400.7			0.612300			0.306150	−	0.951983i	$-0.400959\pi$
$743$	12400.7			0.612300			0.306150	+	0.951983i	$0.400959\pi$
$744$		0			0
$745$	24378.3	+	2359.46i	1.19886	+	0.116032i
$746$	−10108.1	−	7343.95i	−0.496090	−	0.360430i
$747$		0			0
$748$	3182.92	−	9796.03i	0.155587	−	0.478848i
$749$	14232.0			0.694293
$750$		0			0
$751$	−29073.8			−1.41267			−0.706336	−	0.707876i	$-0.749653\pi$
$751$	−29073.8			−1.41267			−0.706336	+	0.707876i	$0.749653\pi$
$752$	−13471.7	+	41461.7i	−0.653276	+	2.01058i
$753$		0			0
$754$	6225.62	+	4523.18i	0.300694	+	0.218467i
$755$	9922.03	+	960.305i	0.478278	+	0.0462902i
$756$		0			0
$757$	−17652.4			−0.847539			−0.423770	−	0.905770i	$-0.639293\pi$
$757$	−17652.4			−0.847539			−0.423770	+	0.905770i	$0.639293\pi$
$758$	41695.0	−	30293.2i	1.99793	−	1.45158i
$759$		0			0
$760$	38139.5	−	87597.1i	1.82035	−	4.18090i
$761$	−9492.07	+	29213.6i	−0.452151	+	1.39158i	0.422296	+	0.906458i	$0.361224\pi$
$761$	−9492.07	+	29213.6i	−0.452151	+	1.39158i	−0.874447	+	0.485121i	$0.838776\pi$
$762$		0			0
$763$	2152.97	+	6626.17i	0.102153	+	0.314395i
$764$	17082.7	−	52575.2i	0.808942	−	2.48967i
$765$		0			0
$766$	11196.7	+	34460.0i	0.528139	+	1.62545i
$767$	2230.38	−	1620.47i	0.104999	−	0.0762863i
$768$		0			0
$769$	−1813.75	+	1317.77i	−0.0850527	+	0.0617944i	−0.629499	−	0.777001i	$-0.716740\pi$
$769$	−1813.75	+	1317.77i	−0.0850527	+	0.0617944i	0.544446	+	0.838796i	$0.316740\pi$
$770$	29614.1	+	26226.3i	1.38600	+	1.22744i
$771$		0			0
$772$	48426.9	+	35184.2i	2.25767	+	1.64030i
$773$	−10264.5	+	31590.8i	−0.477604	+	1.46991i	0.364810	+	0.931082i	$0.381134\pi$
$773$	−10264.5	+	31590.8i	−0.477604	+	1.46991i	−0.842414	+	0.538831i	$0.818866\pi$
$774$		0			0
$775$	19907.5	−	9259.21i	0.922708	−	0.429162i
$776$	−4011.79			−0.185586
$777$		0			0
$778$	25514.6	+	18537.5i	1.17576	+	0.854243i
$779$	5024.13	+	3650.24i	0.231076	+	0.167886i
$780$		0			0
$781$	−15129.3	+	10992.1i	−0.693176	+	0.503622i
$782$	−738.996			−0.0337934
$783$		0			0
$784$	47151.2	+	145116.i	2.14792	+	6.61062i
$785$	26039.2	+	2520.21i	1.18392	+	0.114586i
$786$		0			0
$787$	−715.273	−	2201.38i	−0.0323973	−	0.0997088i	0.933550	−	0.358447i	$-0.116693\pi$
$787$	−715.273	−	2201.38i	−0.0323973	−	0.0997088i	−0.965948	+	0.258738i	$0.916693\pi$
$788$	−18108.8	−	55733.1i	−0.818653	−	2.51956i
$789$		0			0
$790$	−4205.29	+	2474.32i	−0.189389	+	0.111433i
$791$	1655.17	+	5094.08i	0.0744007	+	0.228982i
$792$		0			0
$793$	−3606.05			−0.161481
$794$	40442.0	−	29382.8i	1.80760	−	1.31330i
$795$		0			0
$796$	−14142.2	−	10274.9i	−0.629721	−	0.457519i
$797$	−23009.0	−	16717.0i	−1.02261	−	0.742970i	−0.0557946	−	0.998442i	$-0.517769\pi$
$797$	−23009.0	−	16717.0i	−1.02261	−	0.742970i	−0.966817	+	0.255472i	$0.917769\pi$
$798$		0			0
$799$	−3504.19			−0.155156
$800$	102157.	+	19961.5i	4.51474	+	0.882183i
$801$		0			0
$802$	−2208.40	+	6796.74i	−0.0972334	+	0.299254i
$803$	−5584.42	−	4057.32i	−0.245417	−	0.178306i
$804$		0			0
$805$	837.191	−	1922.82i	0.0366548	−	0.0841870i
$806$	−4726.32	+	3433.87i	−0.206548	+	0.150066i
$807$		0			0
$808$	51872.9	−	37687.9i	2.25852	−	1.64091i
$809$	−9126.05	−	28087.1i	−0.396607	−	1.22063i	−0.927703	−	0.373319i	$-0.878220\pi$
$809$	−9126.05	−	28087.1i	−0.396607	−	1.22063i	0.531096	−	0.847311i	$-0.321780\pi$
$810$		0			0
$811$	−4761.77	+	14655.2i	−0.206175	+	0.634543i	0.793488	+	0.608586i	$0.208263\pi$
$811$	−4761.77	+	14655.2i	−0.206175	+	0.634543i	−0.999663	+	0.0259564i	$0.991737\pi$
$812$	−48922.6	−	150568.i	−2.11435	−	6.50728i
$813$		0			0
$814$	−10608.4	+	32649.3i	−0.456786	+	1.40584i
$815$	−5375.41	−	24303.4i	−0.231033	−	1.04455i
$816$		0			0
$817$	32379.4	−	23525.0i	1.38655	−	1.00739i
$818$	−23281.2			−0.995121
$819$		0			0
$820$	−5953.42	+	13673.5i	−0.253540	+	0.582318i
$821$	12992.6	+	9439.64i	0.552306	+	0.401274i	0.828635	−	0.559789i	$-0.189118\pi$
$821$	12992.6	+	9439.64i	0.552306	+	0.401274i	−0.276329	+	0.961063i	$0.589118\pi$
$822$		0			0
$823$	4778.17	−	14705.7i	0.202377	−	0.622854i	−0.797433	−	0.603407i	$-0.793810\pi$
$823$	4778.17	−	14705.7i	0.202377	−	0.622854i	0.999811	−	0.0194468i	$-0.00619048\pi$
$824$	−4649.42			−0.196566
$825$		0			0
$826$	−76757.3			−3.23333
$827$	−7301.12	+	22470.5i	−0.306995	+	0.944833i	0.671930	+	0.740614i	$0.265465\pi$
$827$	−7301.12	+	22470.5i	−0.306995	+	0.944833i	−0.978925	+	0.204219i	$0.934535\pi$
$828$		0			0
$829$	−33429.1	−	24287.7i	−1.40053	−	1.01755i	−0.994615	−	0.103637i	$-0.966952\pi$
$829$	−33429.1	−	24287.7i	−1.40053	−	1.01755i	−0.405917	−	0.913910i	$-0.633048\pi$
$830$	17551.0	+	79351.9i	0.733980	+	3.31849i
$831$		0			0
$832$	−14834.9			−0.618160
$833$	−9922.34	+	7209.00i	−0.412711	+	0.299852i
$834$		0			0
$835$	−5978.33	+	3517.55i	−0.247771	+	0.145784i
$836$	15601.2	−	48015.6i	0.645429	−	1.98643i
$837$		0			0
$838$	−9478.00	−	29170.3i	−0.390707	−	1.20247i
$839$	−7593.13	+	23369.2i	−0.312448	+	0.961616i	0.664344	+	0.747427i	$0.268711\pi$
$839$	−7593.13	+	23369.2i	−0.312448	+	0.961616i	−0.976792	+	0.214189i	$0.931289\pi$
$840$		0			0
$841$	9004.56	+	27713.2i	0.369206	+	1.13630i
$842$	31832.6	−	23127.7i	1.30288	−	0.946597i
$843$		0			0
$844$	−109245.	+	79370.8i	−4.45539	+	3.23703i
$845$	20822.6	−	12251.7i	0.847716	−	0.498782i
$846$		0			0
$847$	−21604.5	−	15696.6i	−0.876433	−	0.636766i
$848$	21903.8	−	67413.0i	0.887004	−	2.72992i
$849$		0			0
$850$	1799.17	+	14773.1i	0.0726011	+	0.596132i
$851$	1819.99			0.0733121
$852$		0			0
$853$	10526.6	+	7648.06i	0.422539	+	0.306992i	0.778658	−	0.627448i	$-0.215901\pi$
$853$	10526.6	+	7648.06i	0.422539	+	0.306992i	−0.356120	+	0.934440i	$0.615901\pi$
$854$	81224.6	+	59013.1i	3.25462	+	2.36462i
$855$		0			0
$856$	30884.2	−	22438.7i	1.23318	−	0.895956i
$857$	−46342.7			−1.84718			−0.923592	−	0.383377i	$-0.874761\pi$
$857$	−46342.7			−1.84718			−0.923592	+	0.383377i	$0.874761\pi$
$858$		0			0
$859$	−7665.49	−	23591.9i	−0.304474	−	0.937074i	−0.979873	−	0.199622i	$-0.936029\pi$
$859$	−7665.49	−	23591.9i	−0.304474	−	0.937074i	0.675399	−	0.737452i	$-0.263971\pi$
$860$	71953.6	+	63722.2i	2.85302	+	2.52664i
$861$		0			0
$862$	−9718.93	−	29911.8i	−0.384023	−	1.18190i
$863$	−9182.33	−	28260.3i	−0.362190	−	1.11471i	−0.951722	−	0.306961i	$-0.900688\pi$
$863$	−9182.33	−	28260.3i	−0.362190	−	1.11471i	0.589532	−	0.807745i	$-0.299312\pi$
$864$		0			0
$865$	11189.2	−	25698.8i	0.439820	−	1.01016i
$866$	−25939.1	−	79832.4i	−1.01784	−	3.13258i
$867$		0			0
$868$	120190.			4.69990
$869$	−1348.96	+	980.074i	−0.0526584	+	0.0382586i
$870$		0			0
$871$	1620.11	+	1177.08i	0.0630258	+	0.0457909i
$872$	15119.1	+	10984.7i	0.587154	+	0.426592i
$873$		0			0
$874$	−3622.21			−0.140187
$875$	−40476.9	−	12054.7i	−1.56385	−	0.465743i
$876$		0			0
$877$	6997.55	−	21536.2i	0.269430	−	0.829221i	−0.721209	−	0.692717i	$-0.756413\pi$
$877$	6997.55	−	21536.2i	0.269430	−	0.829221i	0.990640	−	0.136504i	$-0.0435866\pi$
$878$	−8462.90	−	6148.65i	−0.325295	−	0.236341i
$879$		0			0
$880$	62977.8	+	6095.31i	2.41248	+	0.233492i
$881$	−3906.80	+	2838.45i	−0.149402	+	0.108547i	−0.659975	−	0.751287i	$-0.729433\pi$
$881$	−3906.80	+	2838.45i	−0.149402	+	0.108547i	0.510573	+	0.859834i	$0.329433\pi$
$882$		0			0
$883$	26636.5	−	19352.6i	1.01516	−	0.737560i	0.0498783	−	0.998755i	$-0.484117\pi$
$883$	26636.5	−	19352.6i	1.01516	−	0.737560i	0.965286	+	0.261195i	$0.0841167\pi$
$884$	−904.227	−	2782.92i	−0.0344032	−	0.105882i
$885$		0			0
$886$	−24835.0	+	76434.4i	−0.941703	+	2.89826i
$887$	−101.793	−	313.285i	−0.00385328	−	0.0118592i	0.949111	−	0.314941i	$-0.101985\pi$
$887$	−101.793	−	313.285i	−0.00385328	−	0.0118592i	−0.952965	+	0.303081i	$0.901985\pi$
$888$		0			0
$889$	7579.59	−	23327.6i	0.285952	−	0.880070i
$890$	−52250.5	−	46273.1i	−1.96791	−	1.74279i
$891$		0			0
$892$	−85068.0	+	61805.5i	−3.19315	+	2.31996i
$893$	−17175.9			−0.643639
$894$		0			0
$895$	−14618.0	−	12945.7i	−0.545949	−	0.483493i
$896$	171282.	+	124444.i	6.38630	+	4.63992i
$897$		0			0
$898$	−26903.6	+	82800.9i	−0.999762	+	3.07695i
$899$	−40637.3			−1.50760
$900$		0			0
$901$	5697.49			0.210667
$902$	−2131.30	+	6559.47i	−0.0786746	+	0.242136i
$903$		0			0
$904$	11623.3	+	8444.83i	0.427639	+	0.310698i
$905$	3278.07	−	1928.76i	0.120405	−	0.0708444i
$906$		0			0
$907$	41937.4			1.53529			0.767646	−	0.640874i	$-0.221428\pi$
$907$	41937.4			1.53529			0.767646	+	0.640874i	$0.221428\pi$
$908$	−24779.9	+	18003.6i	−0.905671	+	0.658008i
$909$		0			0
$910$	11185.6	+	1082.60i	0.407470	+	0.0394371i
$911$	−14872.0	+	45771.2i	−0.540867	+	1.66462i	0.189751	+	0.981832i	$0.439232\pi$
$911$	−14872.0	+	45771.2i	−0.540867	+	1.66462i	−0.730618	+	0.682786i	$0.760768\pi$
$912$		0			0
$913$	8582.25	+	26413.4i	0.311096	+	0.957456i
$914$	−5173.39	+	15922.1i	−0.187222	+	0.576209i
$915$		0			0
$916$	−22289.6	−	68600.2i	−0.804004	−	2.47447i
$917$	−31850.7	+	23140.9i	−1.14700	+	0.833348i
$918$		0			0
$919$	11669.3	−	8478.28i	0.418864	−	0.304323i	−0.358316	−	0.933600i	$-0.616649\pi$
$919$	11669.3	−	8478.28i	0.418864	−	0.304323i	0.777181	+	0.629277i	$0.216649\pi$
$920$	−1214.84	−	5492.57i	−0.0435349	−	0.196831i
$921$		0			0
$922$	25197.1	+	18306.7i	0.900023	+	0.653905i
$923$	−1641.71	+	5052.66i	−0.0585455	+	0.180185i
$924$		0			0
$925$	−4430.98	−	36383.0i	−0.157502	−	1.29326i
$926$	−24469.8			−0.868388
$927$		0			0
$928$	−155863.	−	113241.i	−5.51343	−	4.00574i
$929$	−25185.6	−	18298.4i	−0.889466	−	0.646235i	0.0462726	−	0.998929i	$-0.485266\pi$
$929$	−25185.6	−	18298.4i	−0.889466	−	0.646235i	−0.935739	+	0.352694i	$0.885266\pi$
$930$		0			0
$931$	−48634.7	+	35335.2i	−1.71207	+	1.24389i
$932$	48150.4			1.69229
$933$		0			0
$934$	−8514.73	−	26205.7i	−0.298298	−	0.918068i
$935$	1098.33	+	4965.78i	0.0384161	+	0.173688i
$936$		0			0
$937$	−1847.93	−	5687.35i	−0.0644282	−	0.198290i	0.913660	−	0.406478i	$-0.133243\pi$
$937$	−1847.93	−	5687.35i	−0.0644282	−	0.198290i	−0.978089	+	0.208188i	$0.933243\pi$
$938$	−17229.4	−	53026.5i	−0.599742	−	1.84582i
$939$		0			0
$940$	−8907.70	−	40273.7i	−0.309082	−	1.39743i
$941$	799.362	+	2460.18i	0.0276923	+	0.0852281i	0.963947	−	0.266093i	$-0.0857327\pi$
$941$	799.362	+	2460.18i	0.0276923	+	0.0852281i	−0.936255	+	0.351321i	$0.885733\pi$
$942$		0			0
$943$	365.649			0.0126269
$944$	−99324.8	+	72163.7i	−3.42452	+	2.48806i
$945$		0			0
$946$	35960.7	+	26127.0i	1.23592	+	0.897952i
$947$	26622.7	+	19342.5i	0.913539	+	0.663725i	0.941907	−	0.335873i	$-0.109031\pi$
$947$	26622.7	+	19342.5i	0.913539	+	0.663725i	−0.0283684	+	0.999598i	$0.509031\pi$
$948$		0			0
$949$	−1960.98			−0.0670769
$950$	8818.68	+	72410.7i	0.301174	+	2.47296i
$951$		0			0
$952$	−16280.8	+	50107.1i	−0.554268	+	1.70586i
$953$	41562.9	+	30197.2i	1.41276	+	1.02643i	0.992915	+	0.118829i	$0.0379141\pi$
$953$	41562.9	+	30197.2i	1.41276	+	1.02643i	0.419841	+	0.907598i	$0.362086\pi$
$954$		0			0
$955$	5894.71	+	26651.3i	0.199736	+	0.903053i
$956$	−85926.0	+	62428.9i	−2.90695	+	2.11202i
$957$		0			0
$958$	−32310.2	+	23474.8i	−1.08966	+	0.791686i
$959$	−10383.9	−	31958.5i	−0.349650	−	1.07611i
$960$		0			0
$961$	327.466	−	1007.84i	0.0109921	−	0.0338302i
$962$	3013.71	+	9275.23i	0.101004	+	0.310858i
$963$		0			0
$964$	−24209.7	+	74509.7i	−0.808860	+	2.48941i
$965$	−29418.4	−	2847.27i	−0.981360	−	0.0949811i
$966$		0			0
$967$	15375.5	−	11170.9i	0.511315	−	0.371492i	−0.302007	−	0.953306i	$-0.597657\pi$
$967$	15375.5	−	11170.9i	0.511315	−	0.371492i	0.813322	+	0.581814i	$0.197657\pi$
$968$	−71630.6			−2.37840
$969$		0			0
$970$	2639.97	−	1553.32i	0.0873861	−	0.0514165i
$971$	−27125.9	−	19708.1i	−0.896510	−	0.651353i	0.0410573	−	0.999157i	$-0.486927\pi$
$971$	−27125.9	−	19708.1i	−0.896510	−	0.651353i	−0.937567	+	0.347804i	$0.886927\pi$
$972$		0			0
$973$	−221.949	+	683.087i	−0.00731279	+	0.0225064i
$974$	86815.8			2.85601
$975$		0			0
$976$	160587.			5.26667
$977$	3924.47	−	12078.3i	0.128511	−	0.395515i	−0.866014	−	0.500020i	$-0.833326\pi$
$977$	3924.47	−	12078.3i	0.128511	−	0.395515i	0.994524	+	0.104505i	$0.0333259\pi$
$978$		0			0
$979$	−19296.2	−	14019.5i	−0.629937	−	0.457676i
$980$	−108076.	−	95712.2i	−3.52281	−	3.11981i
$981$		0			0
$982$	74833.2			2.43179
$983$	33720.8	−	24499.6i	1.09413	−	0.794930i	0.114036	−	0.993477i	$-0.463622\pi$
$983$	33720.8	−	24499.6i	1.09413	−	0.794930i	0.980091	+	0.198547i	$0.0636222\pi$
$984$		0			0
$985$	21661.5	+	19183.5i	0.700704	+	0.620544i
$986$	8512.02	−	26197.3i	0.274927	−	0.846138i
$987$		0			0
$988$	−4432.10	−	13640.6i	−0.142716	−	0.439236i
$989$	728.209	−	2241.20i	0.0234133	−	0.0720586i
$990$		0			0
$991$	−2227.57	−	6855.76i	−0.0714037	−	0.219758i	0.908986	−	0.416827i	$-0.136858\pi$
$991$	−2227.57	−	6855.76i	−0.0714037	−	0.219758i	−0.980390	+	0.197069i	$0.936858\pi$
$992$	118327.	−	85969.7i	3.78719	−	2.75155i
$993$		0			0
$994$	119666.	−	86942.3i	3.81848	−	2.77429i
$995$	8591.12	+	831.493i	0.273726	+	0.0264926i
$996$		0			0
$997$	34106.5	+	24779.8i	1.08341	+	0.787147i	0.978275	−	0.207311i	$-0.0664710\pi$
$997$	34106.5	+	24779.8i	1.08341	+	0.787147i	0.105140	+	0.994457i	$0.466471\pi$
$998$	−32593.0	+	100311.i	−1.03378	+	3.18165i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.d.46.16	yes	64
3.2	odd	2	inner	225.4.h.d.46.1	✓	64
25.6	even	5	inner	225.4.h.d.181.16	yes	64
75.56	odd	10	inner	225.4.h.d.181.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.h.d.46.1	✓	64	3.2	odd	2	inner
225.4.h.d.46.16	yes	64	1.1	even	1	trivial
225.4.h.d.181.1	yes	64	75.56	odd	10	inner
225.4.h.d.181.16	yes	64	25.6	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71061 - 5.26471i) q^{2} +(-18.3188 - 13.3094i) q^{4} +(11.1283 + 1.07706i) q^{5} -30.2200 q^{7} +(-65.5791 + 47.6460i) q^{8} +O(q^{10})\)	\(q+(1.71061 - 5.26471i) q^{2} +(-18.3188 - 13.3094i) q^{4} +(11.1283 + 1.07706i) q^{5} -30.2200 q^{7} +(-65.5791 + 47.6460i) q^{8} +(24.7066 - 56.7450i) q^{10} +(6.53575 - 20.1150i) q^{11} +(-1.85672 - 5.71440i) q^{13} +(-51.6946 + 159.100i) q^{14} +(82.6849 + 254.478i) q^{16} +(-17.3999 + 12.6418i) q^{17} +(-85.2864 + 61.9642i) q^{19} +(-189.523 - 167.842i) q^{20} +(-94.7194 - 68.8177i) q^{22} +(-1.91808 + 5.90324i) q^{23} +(122.680 + 23.9717i) q^{25} -33.2608 q^{26} +(553.596 + 402.211i) q^{28} +(-187.176 - 135.991i) q^{29} +(142.099 - 103.241i) q^{31} +832.711 q^{32} +(36.7909 + 113.231i) q^{34} +(-336.299 - 32.5487i) q^{35} +(-90.6084 - 278.864i) q^{37} +(180.332 + 555.004i) q^{38} +(-781.104 + 459.589i) q^{40} +(-18.2039 - 56.0257i) q^{41} -379.656 q^{43} +(-387.446 + 281.496i) q^{44} +(27.7978 + 20.1962i) q^{46} +(131.812 + 95.7671i) q^{47} +570.251 q^{49} +(336.061 - 604.868i) q^{50} +(-42.0424 + 129.393i) q^{52} +(-214.314 - 155.708i) q^{53} +(94.3971 - 216.807i) q^{55} +(1981.80 - 1439.87i) q^{56} +(-1036.14 + 752.798i) q^{58} +(141.788 + 436.378i) q^{59} +(185.460 - 570.786i) q^{61} +(-300.457 - 924.713i) q^{62} +(762.963 - 2348.16i) q^{64} +(-14.5075 - 65.5916i) q^{65} +(-269.638 + 195.903i) q^{67} +487.002 q^{68} +(-746.635 + 1714.84i) q^{70} +(-715.330 - 519.718i) q^{71} +(100.853 - 310.394i) q^{73} -1623.13 q^{74} +2387.05 q^{76} +(-197.511 + 607.876i) q^{77} +(-63.7800 - 46.3389i) q^{79} +(646.058 + 2920.97i) q^{80} -326.099 q^{82} +(-1062.34 + 771.834i) q^{83} +(-207.248 + 121.941i) q^{85} +(-649.442 + 1998.78i) q^{86} +(529.790 + 1630.53i) q^{88} +(348.484 - 1072.52i) q^{89} +(56.1102 + 172.690i) q^{91} +(113.706 - 82.6120i) q^{92} +(729.664 - 530.132i) q^{94} +(-1015.83 + 597.700i) q^{95} +(40.0395 + 29.0904i) q^{97} +(975.476 - 3002.21i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) 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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