LMFDB - Embedded newform 225.4.h.d.46.9

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			46.9
Character	$\chi$	$=$	225.46
Dual form			225.4.h.d.181.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0492832 - 0.151678i) q^{2} +(6.45156 + 4.68733i) q^{4} +(9.69768 + 5.56372i) q^{5} +29.3448 q^{7} +(2.06112 - 1.49749i) q^{8} +O(q^{10})$	\(q+(0.0492832 - 0.151678i) q^{2} +(6.45156 + 4.68733i) q^{4} +(9.69768 + 5.56372i) q^{5} +29.3448 q^{7} +(2.06112 - 1.49749i) q^{8} +(1.32183 - 1.19673i) q^{10} +(10.1644 - 31.2829i) q^{11} +(-9.02150 - 27.7653i) q^{13} +(1.44621 - 4.45096i) q^{14} +(19.5887 + 60.2877i) q^{16} +(-103.730 + 75.3644i) q^{17} +(3.24851 - 2.36018i) q^{19} +(36.4862 + 81.3509i) q^{20} +(-4.24399 - 3.08344i) q^{22} +(39.8382 - 122.609i) q^{23} +(63.0901 + 107.910i) q^{25} -4.65600 q^{26} +(189.320 + 137.549i) q^{28} +(-178.493 - 129.683i) q^{29} +(139.509 - 101.359i) q^{31} +30.4912 q^{32} +(6.31897 + 19.4478i) q^{34} +(284.577 + 163.266i) q^{35} +(64.2980 + 197.889i) q^{37} +(-0.197890 - 0.609044i) q^{38} +(28.3197 - 3.05470i) q^{40} +(78.0265 + 240.141i) q^{41} -81.1845 q^{43} +(212.210 - 154.179i) q^{44} +(-16.6338 - 12.0852i) q^{46} +(-281.870 - 204.790i) q^{47} +518.118 q^{49} +(19.4769 - 4.25122i) q^{50} +(71.9425 - 221.416i) q^{52} +(-324.991 - 236.120i) q^{53} +(272.621 - 246.820i) q^{55} +(60.4832 - 43.9436i) q^{56} +(-28.4668 + 20.6823i) q^{58} +(196.402 + 604.462i) q^{59} +(-111.080 + 341.868i) q^{61} +(-8.49851 - 26.1557i) q^{62} +(-155.207 + 477.677i) q^{64} +(66.9907 - 319.452i) q^{65} +(-72.2562 + 52.4972i) q^{67} -1022.48 q^{68} +(38.7888 - 35.1178i) q^{70} +(434.583 + 315.743i) q^{71} +(28.1745 - 86.7122i) q^{73} +33.1842 q^{74} +32.0209 q^{76} +(298.273 - 917.991i) q^{77} +(-1076.93 - 782.439i) q^{79} +(-145.459 + 693.636i) q^{80} +40.2695 q^{82} +(-148.238 + 107.701i) q^{83} +(-1425.25 + 153.734i) q^{85} +(-4.00103 + 12.3139i) q^{86} +(-25.8957 - 79.6989i) q^{88} +(-179.451 + 552.293i) q^{89} +(-264.734 - 814.768i) q^{91} +(831.729 - 604.287i) q^{92} +(-44.9536 + 32.6607i) q^{94} +(44.6344 - 4.81449i) q^{95} +(-1342.00 - 975.019i) q^{97} +(25.5345 - 78.5871i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) $ 64 * q - 72 * q^4 + 20 * q^7	$ 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) $ 64 * q - 72 * q^4 + 20 * q^7 + 50 * q^10 + 180 * q^13 - 244 * q^16 - 116 * q^19 - 210 * q^22 + 440 * q^25 + 980 * q^28 + 42 * q^31 + 40 * q^34 - 1170 * q^37 - 3040 * q^40 + 1040 * q^43 + 700 * q^46 + 4188 * q^49 + 3280 * q^52 + 2640 * q^55 - 4530 * q^58 + 88 * q^61 - 3018 * q^64 - 2860 * q^67 - 3720 * q^70 - 5280 * q^73 + 9288 * q^76 - 1144 * q^79 + 2840 * q^82 + 470 * q^85 + 7610 * q^88 - 1180 * q^91 + 2170 * q^94 + 2050 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.0492832	−	0.151678i	0.0174242	−	0.0536263i	−0.941966	−	0.335707i	$-0.891025\pi$
$2$	0.0492832	−	0.151678i	0.0174242	−	0.0536263i	0.959391	+	0.282081i	$0.0910247\pi$
$3$		0			0
$3$		0			0
$4$	6.45156	+	4.68733i	0.806445	+	0.585916i
$5$	9.69768	+	5.56372i	0.867387	+	0.497634i
$5$	9.69768	+	5.56372i	0.867387	+	0.497634i
$6$		0			0
$7$	29.3448			1.58447			0.792235	−	0.610216i	$-0.208917\pi$
$7$	29.3448			1.58447			0.792235	+	0.610216i	$0.208917\pi$
$8$	2.06112	−	1.49749i	0.0910895	−	0.0661804i
$9$		0			0
$10$	1.32183	−	1.19673i	0.0417998	−	0.0378439i
$11$	10.1644	−	31.2829i	0.278608	−	0.857468i	−0.709634	−	0.704571i	$-0.751140\pi$
$11$	10.1644	−	31.2829i	0.278608	−	0.857468i	0.988242	−	0.152897i	$-0.0488604\pi$
$12$		0			0
$13$	−9.02150	−	27.7653i	−0.192470	−	0.592362i	−0.999997	−	0.00253122i	$-0.999194\pi$
$13$	−9.02150	−	27.7653i	−0.192470	−	0.592362i	0.807527	−	0.589831i	$-0.200806\pi$
$14$	1.44621	−	4.45096i	0.0276082	−	0.0849693i
$15$		0			0
$16$	19.5887	+	60.2877i	0.306073	+	0.941995i
$17$	−103.730	+	75.3644i	−1.47990	+	1.07521i	−0.502309	+	0.864688i	$0.667516\pi$
$17$	−103.730	+	75.3644i	−1.47990	+	1.07521i	−0.977589	+	0.210520i	$0.932484\pi$
$18$		0			0
$19$	3.24851	−	2.36018i	0.0392241	−	0.0284980i	−0.568000	−	0.823028i	$-0.692283\pi$
$19$	3.24851	−	2.36018i	0.0392241	−	0.0284980i	0.607225	+	0.794530i	$0.292283\pi$
$20$	36.4862	+	81.3509i	0.407928	+	0.909531i
$21$		0			0
$22$	−4.24399	−	3.08344i	−0.0411283	−	0.0298815i
$23$	39.8382	−	122.609i	0.361167	−	1.11156i	−0.591180	−	0.806540i	$-0.701338\pi$
$23$	39.8382	−	122.609i	0.361167	−	1.11156i	0.952347	−	0.305018i	$-0.0986624\pi$
$24$		0			0
$25$	63.0901	+	107.910i	0.504721	+	0.863283i
$26$	−4.65600			−0.0351198
$27$		0			0
$28$	189.320	+	137.549i	1.27779	+	0.928368i
$29$	−178.493	−	129.683i	−1.14294	−	0.830397i	−0.155417	−	0.987849i	$-0.549672\pi$
$29$	−178.493	−	129.683i	−1.14294	−	0.830397i	−0.987527	+	0.157452i	$0.949672\pi$
$30$		0			0
$31$	139.509	−	101.359i	0.808275	−	0.587246i	−0.105055	−	0.994466i	$-0.533502\pi$
$31$	139.509	−	101.359i	0.808275	−	0.587246i	0.913330	+	0.407220i	$0.133502\pi$
$32$	30.4912			0.168442
$33$		0			0
$34$	6.31897	+	19.4478i	0.0318734	+	0.0980961i
$35$	284.577	+	163.266i	1.37435	+	0.788487i
$36$		0			0
$37$	64.2980	+	197.889i	0.285690	+	0.879263i	0.986191	+	0.165612i	$0.0529599\pi$
$37$	64.2980	+	197.889i	0.285690	+	0.879263i	−0.700501	+	0.713651i	$0.747040\pi$
$38$	−0.197890	−	0.609044i	−0.000844791	−	0.00260000i
$39$		0			0
$40$	28.3197	−	3.05470i	0.111943	−	0.0120748i
$41$	78.0265	+	240.141i	0.297212	+	0.914725i	0.982469	+	0.186424i	$0.0596897\pi$
$41$	78.0265	+	240.141i	0.297212	+	0.914725i	−0.685257	+	0.728301i	$0.740310\pi$
$42$		0			0
$43$	−81.1845			−0.287919			−0.143960	−	0.989584i	$-0.545984\pi$
$43$	−81.1845			−0.287919			−0.143960	+	0.989584i	$0.545984\pi$
$44$	212.210	−	154.179i	0.727087	−	0.528260i
$45$		0			0
$46$	−16.6338	−	12.0852i	−0.0533156	−	0.0387361i
$47$	−281.870	−	204.790i	−0.874785	−	0.635569i	0.0570816	−	0.998370i	$-0.481820\pi$
$47$	−281.870	−	204.790i	−0.874785	−	0.635569i	−0.931867	+	0.362801i	$0.881820\pi$
$48$		0			0
$49$	518.118			1.51055
$50$	19.4769	−	4.25122i	0.0550890	−	0.0120243i
$51$		0			0
$52$	71.9425	−	221.416i	0.191858	−	0.590479i
$53$	−324.991	−	236.120i	−0.842283	−	0.611955i	0.0807243	−	0.996736i	$-0.474277\pi$
$53$	−324.991	−	236.120i	−0.842283	−	0.611955i	−0.923008	+	0.384782i	$0.874277\pi$
$54$		0			0
$55$	272.621	−	246.820i	0.668367	−	0.605112i
$56$	60.4832	−	43.9436i	0.144329	−	0.104861i
$57$		0			0
$58$	−28.4668	+	20.6823i	−0.0644460	+	0.0468228i
$59$	196.402	+	604.462i	0.433379	+	1.33380i	0.894739	+	0.446589i	$0.147361\pi$
$59$	196.402	+	604.462i	0.433379	+	1.33380i	−0.461361	+	0.887213i	$0.652639\pi$
$60$		0			0
$61$	−111.080	+	341.868i	−0.233153	+	0.717570i	0.764208	+	0.644969i	$0.223130\pi$
$61$	−111.080	+	341.868i	−0.233153	+	0.717570i	−0.997361	+	0.0726007i	$0.976870\pi$
$62$	−8.49851	−	26.1557i	−0.0174083	−	0.0535771i
$63$		0			0
$64$	−155.207	+	477.677i	−0.303138	+	0.932962i
$65$	66.9907	−	319.452i	0.127834	−	0.609587i
$66$		0			0
$67$	−72.2562	+	52.4972i	−0.131754	+	0.0957247i	−0.651710	−	0.758468i	$-0.725948\pi$
$67$	−72.2562	+	52.4972i	−0.131754	+	0.0957247i	0.519956	+	0.854193i	$0.325948\pi$
$68$	−1022.48			−1.82344
$69$		0			0
$70$	38.7888	−	35.1178i	0.0662306	−	0.0599625i
$71$	434.583	+	315.743i	0.726415	+	0.527771i	0.888427	−	0.459017i	$-0.151798\pi$
$71$	434.583	+	315.743i	0.726415	+	0.527771i	−0.162012	+	0.986789i	$0.551798\pi$
$72$		0			0
$73$	28.1745	−	86.7122i	0.0451723	−	0.139026i	−0.925927	−	0.377703i	$-0.876714\pi$
$73$	28.1745	−	86.7122i	0.0451723	−	0.139026i	0.971099	+	0.238677i	$0.0767139\pi$
$74$	33.1842			0.0521296
$75$		0			0
$76$	32.0209			0.0483295
$77$	298.273	−	917.991i	0.441447	−	1.35863i
$78$		0			0
$79$	−1076.93	−	782.439i	−1.53373	−	1.11432i	−0.954120	−	0.299425i	$-0.903205\pi$
$79$	−1076.93	−	782.439i	−1.53373	−	1.11432i	−0.579609	−	0.814894i	$-0.696795\pi$
$80$	−145.459	+	693.636i	−0.203285	+	0.969386i
$81$		0			0
$82$	40.2695			0.0542320
$83$	−148.238	+	107.701i	−0.196038	+	0.142430i	−0.681474	−	0.731842i	$-0.738661\pi$
$83$	−148.238	+	107.701i	−0.196038	+	0.142430i	0.485436	+	0.874272i	$0.338661\pi$
$84$		0			0
$85$	−1425.25	+	153.734i	−1.81870	+	0.196175i
$86$	−4.00103	+	12.3139i	−0.00501677	+	0.0154400i
$87$		0			0
$88$	−25.8957	−	79.6989i	−0.0313693	−	0.0965447i
$89$	−179.451	+	552.293i	−0.213728	+	0.657786i	0.785514	+	0.618844i	$0.212399\pi$
$89$	−179.451	+	552.293i	−0.213728	+	0.657786i	−0.999241	+	0.0389420i	$0.987601\pi$
$90$		0			0
$91$	−264.734	−	814.768i	−0.304963	−	0.938581i
$92$	831.729	−	604.287i	0.942541	−	0.684796i
$93$		0			0
$94$	−44.9536	+	32.6607i	−0.0493256	+	0.0358372i
$95$	44.6344	−	4.81449i	0.0482041	−	0.00519953i
$96$		0			0
$97$	−1342.00	−	975.019i	−1.40473	−	1.02060i	−0.994062	−	0.108817i	$-0.965294\pi$
$97$	−1342.00	−	975.019i	−1.40473	−	1.02060i	−0.410673	−	0.911783i	$-0.634706\pi$
$98$	25.5345	−	78.5871i	0.0263201	−	0.0810051i
$99$		0			0
$100$	−98.7821	+	991.914i	−0.0987821	+	0.991914i
$101$	1351.67			1.33165			0.665824	−	0.746109i	$-0.268080\pi$
$101$	1351.67			1.33165			0.665824	+	0.746109i	$0.268080\pi$
$102$		0			0
$103$	−727.905	−	528.854i	−0.696336	−	0.505918i	0.182401	−	0.983224i	$-0.441613\pi$
$103$	−727.905	−	528.854i	−0.696336	−	0.505918i	−0.878737	+	0.477307i	$0.841613\pi$
$104$	−60.1727	−	43.7180i	−0.0567348	−	0.0412202i
$105$		0			0
$106$	−51.8309	+	37.6573i	−0.0474930	+	0.0345057i
$107$	64.2638			0.0580619			0.0290309	−	0.999579i	$-0.490758\pi$
$107$	64.2638			0.0580619			0.0290309	+	0.999579i	$0.490758\pi$
$108$		0			0
$109$	−325.634	−	1002.20i	−0.286148	−	0.880672i	−0.986052	−	0.166436i	$-0.946774\pi$
$109$	−325.634	−	1002.20i	−0.286148	−	0.880672i	0.699905	−	0.714236i	$-0.253226\pi$
$110$	−24.0015	−	53.5146i	−0.0208041	−	0.0463856i
$111$		0			0
$112$	574.825	+	1769.13i	0.484963	+	1.49256i
$113$	−45.0297	−	138.587i	−0.0374871	−	0.115373i	0.930562	−	0.366135i	$-0.119319\pi$
$113$	−45.0297	−	138.587i	−0.0374871	−	0.115373i	−0.968049	+	0.250761i	$0.919319\pi$
$114$		0			0
$115$	1068.50	−	967.378i	0.866420	−	0.784422i
$116$	−543.693	−	1673.31i	−0.435178	−	1.33934i
$117$		0			0
$118$	101.363			0.0790781
$119$	−3043.94	+	2211.55i	−2.34486	+	1.70364i
$120$		0			0
$121$	201.498	+	146.397i	0.151388	+	0.109990i
$122$	46.3796	+	33.6967i	0.0344181	+	0.0250062i
$123$		0			0
$124$	1375.15			0.995907
$125$	11.4451	+	1397.50i	0.00818942	+	0.999966i
$126$		0			0
$127$	488.467	−	1503.35i	0.341294	−	1.05040i	−0.622243	−	0.782824i	$-0.713779\pi$
$127$	488.467	−	1503.35i	0.341294	−	1.05040i	0.963538	−	0.267572i	$-0.0862214\pi$
$128$	262.147	+	190.461i	0.181021	+	0.131520i
$129$		0			0
$130$	−45.1524	−	25.9046i	−0.0304625	−	0.0174768i
$131$	1857.49	−	1349.55i	1.23885	−	0.900080i	0.241333	−	0.970442i	$-0.422416\pi$
$131$	1857.49	−	1349.55i	1.23885	−	0.900080i	0.997522	+	0.0703622i	$0.0224155\pi$
$132$		0			0
$133$	95.3268	−	69.2590i	0.0621495	−	0.0451543i
$134$	4.40166	+	13.5469i	0.00283765	+	0.00873340i
$135$		0			0
$136$	−100.943	+	310.670i	−0.0636454	+	0.195880i
$137$	−789.846	−	2430.90i	−0.492563	−	1.51595i	−0.820721	−	0.571330i	$-0.806428\pi$
$137$	−789.846	−	2430.90i	−0.492563	−	1.51595i	0.328158	−	0.944623i	$-0.393572\pi$
$138$		0			0
$139$	−727.700	+	2239.63i	−0.444048	+	1.36664i	0.439475	+	0.898255i	$0.355164\pi$
$139$	−727.700	+	2239.63i	−0.444048	+	1.36664i	−0.883524	+	0.468386i	$0.844836\pi$
$140$	1070.68	+	2387.23i	0.646350	+	1.44112i
$141$		0			0
$142$	69.3089	−	50.3558i	0.0409597	−	0.0297589i
$143$	−960.278			−0.561556
$144$		0			0
$145$	−1009.45	−	2250.71i	−0.578141	−	1.28904i
$146$	−11.7638	−	8.54691i	−0.00666836	−	0.00484484i
$147$		0			0
$148$	−512.749	+	1578.08i	−0.284782	+	0.876468i
$149$	−2505.02			−1.37731			−0.688656	−	0.725088i	$-0.741799\pi$
$149$	−2505.02			−1.37731			−0.688656	+	0.725088i	$0.741799\pi$
$150$		0			0
$151$	−2051.97			−1.10587			−0.552936	−	0.833224i	$-0.686493\pi$
$151$	−2051.97			−1.10587			−0.552936	+	0.833224i	$0.686493\pi$
$152$	3.16121	−	9.72922i	0.00168690	−	0.00519174i
$153$		0			0
$154$	−124.539	−	90.4830i	−0.0651666	−	0.0473463i
$155$	1916.85	−	206.761i	0.993321	−	0.107145i
$156$		0			0
$157$	−743.884			−0.378143			−0.189071	−	0.981963i	$-0.560548\pi$
$157$	−743.884			−0.378143			−0.189071	+	0.981963i	$0.560548\pi$
$158$	−171.754	+	124.786i	−0.0864809	+	0.0628320i
$159$		0			0
$160$	295.694	+	169.644i	0.146104	+	0.0838222i
$161$	1169.04	−	3597.95i	0.572258	−	1.76123i
$162$		0			0
$163$	−104.751	−	322.390i	−0.0503357	−	0.154917i	0.922729	−	0.385449i	$-0.125953\pi$
$163$	−104.751	−	322.390i	−0.0503357	−	0.154917i	−0.973065	+	0.230532i	$0.925953\pi$
$164$	−622.227	+	1915.02i	−0.296267	+	0.911816i
$165$		0			0
$166$	9.03024	+	27.7922i	0.00422219	+	0.0129946i
$167$	1141.26	−	829.177i	0.528825	−	0.384214i	−0.291093	−	0.956695i	$-0.594019\pi$
$167$	1141.26	−	829.177i	0.528825	−	0.384214i	0.819918	+	0.572481i	$0.194019\pi$
$168$		0			0
$169$	1087.89	−	790.395i	0.495169	−	0.359761i
$170$	−46.9226	+	223.755i	−0.0211694	+	0.100949i
$171$		0			0
$172$	−523.767	−	380.539i	−0.232191	−	0.168697i
$173$	−229.277	+	705.642i	−0.100761	+	0.310110i	−0.988712	−	0.149828i	$-0.952128\pi$
$173$	−229.277	+	705.642i	−0.100761	+	0.310110i	0.887951	+	0.459937i	$0.152128\pi$
$174$		0			0
$175$	1851.37	+	3166.61i	0.799715	+	1.36785i
$176$	2085.08			0.893005
$177$		0			0
$178$	74.9268	+	54.4375i	0.0315506	+	0.0229228i
$179$	1687.40	+	1225.97i	0.704592	+	0.511916i	0.881425	−	0.472325i	$-0.156585\pi$
$179$	1687.40	+	1225.97i	0.704592	+	0.511916i	−0.176832	+	0.984241i	$0.556585\pi$
$180$		0			0
$181$	2664.46	−	1935.84i	1.09419	−	0.794974i	0.114086	−	0.993471i	$-0.463606\pi$
$181$	2664.46	−	1935.84i	1.09419	−	0.794974i	0.980101	+	0.198497i	$0.0636061\pi$
$182$	−136.629			−0.0556464
$183$		0			0
$184$	−101.495	−	312.370i	−0.0406648	−	0.125153i
$185$	−477.457	+	2276.80i	−0.189748	+	0.904831i
$186$		0			0
$187$	1303.26	+	4011.02i	0.509645	+	1.56853i
$188$	−858.578	−	2642.43i	−0.333076	−	1.02510i
$189$		0			0
$190$	1.46947	−	7.00732i	0.000561088	−	0.00267560i
$191$	1133.86	+	3489.66i	0.429545	+	1.32200i	0.898574	+	0.438822i	$0.144604\pi$
$191$	1133.86	+	3489.66i	0.429545	+	1.32200i	−0.469029	+	0.883183i	$0.655396\pi$
$192$		0			0
$193$	3385.06			1.26250			0.631249	−	0.775580i	$-0.282543\pi$
$193$	3385.06			1.26250			0.631249	+	0.775580i	$0.282543\pi$
$194$	−214.027	+	155.500i	−0.0792074	+	0.0575476i
$195$		0			0
$196$	3342.67	+	2428.59i	1.21817	+	0.885055i
$197$	−206.238	−	149.841i	−0.0745881	−	0.0541914i	0.549866	−	0.835253i	$-0.314679\pi$
$197$	−206.238	−	149.841i	−0.0745881	−	0.0541914i	−0.624454	+	0.781061i	$0.714679\pi$
$198$		0			0
$199$	1588.39			0.565819			0.282909	−	0.959147i	$-0.408700\pi$
$199$	1588.39			0.565819			0.282909	+	0.959147i	$0.408700\pi$
$200$	291.631	+	127.939i	0.103107	+	0.0452333i
$201$		0			0
$202$	66.6147	−	205.019i	0.0232029	−	0.0714113i
$203$	−5237.85	−	3805.52i	−1.81096	−	1.31574i
$204$		0			0
$205$	−579.400	+	2762.93i	−0.197400	+	0.941323i
$206$	−116.089	+	84.3436i	−0.0392636	+	0.0285267i
$207$		0			0
$208$	1497.19	−	1087.77i	0.499092	−	0.362612i
$209$	−40.8140	−	125.613i	−0.0135080	−	0.0415732i
$210$		0			0
$211$	−391.821	+	1205.90i	−0.127839	+	0.393448i	−0.994408	−	0.105610i	$-0.966321\pi$
$211$	−391.821	+	1205.90i	−0.127839	+	0.393448i	0.866569	+	0.499058i	$0.166321\pi$
$212$	−989.928	−	3046.69i	−0.320701	−	0.987015i
$213$		0			0
$214$	3.16713	−	9.74741i	0.00101168	−	0.00311364i
$215$	−787.302	−	451.688i	−0.249737	−	0.143278i
$216$		0			0
$217$	4093.86	−	2974.36i	1.28069	−	0.930475i
$218$	−168.060			−0.0522131
$219$		0			0
$220$	2915.75	−	314.508i	0.893546	−	0.0963823i
$221$	3028.32	+	2200.20i	0.921750	+	0.669690i
$222$		0			0
$223$	−325.421	+	1001.54i	−0.0977211	+	0.300755i	−0.987953	−	0.154752i	$-0.950542\pi$
$223$	−325.421	+	1001.54i	−0.0977211	+	0.300755i	0.890232	+	0.455507i	$0.150542\pi$
$224$	894.758			0.266891
$225$		0			0
$226$	−23.2399			−0.00684023
$227$	1421.01	−	4373.43i	0.415489	−	1.27874i	−0.496325	−	0.868137i	$-0.665317\pi$
$227$	1421.01	−	4373.43i	0.415489	−	1.27874i	0.911813	−	0.410605i	$-0.134683\pi$
$228$		0			0
$229$	−955.043	−	693.879i	−0.275594	−	0.200231i	0.441399	−	0.897311i	$-0.354482\pi$
$229$	−955.043	−	693.879i	−0.275594	−	0.200231i	−0.716993	+	0.697080i	$0.754482\pi$
$230$	−94.0709	−	209.744i	−0.0269689	−	0.0601309i
$231$		0			0
$232$	−562.095			−0.159066
$233$	−5377.93	+	3907.29i	−1.51210	+	1.09861i	−0.546869	+	0.837218i	$0.684180\pi$
$233$	−5377.93	+	3907.29i	−1.51210	+	1.09861i	−0.965234	+	0.261388i	$0.915820\pi$
$234$		0			0
$235$	−1594.09	−	3554.23i	−0.442497	−	0.986607i
$236$	−1566.22	+	4820.33i	−0.432001	+	1.32956i
$237$		0			0
$238$	185.429	+	570.692i	0.0505024	+	0.155430i
$239$	−500.005	+	1538.86i	−0.135325	+	0.416487i	−0.995640	−	0.0932750i	$-0.970266\pi$
$239$	−500.005	+	1538.86i	−0.135325	+	0.416487i	0.860316	+	0.509762i	$0.170266\pi$
$240$		0			0
$241$	−237.696	−	731.554i	−0.0635326	−	0.195533i	0.914252	−	0.405147i	$-0.132779\pi$
$241$	−237.696	−	731.554i	−0.0635326	−	0.195533i	−0.977784	+	0.209613i	$0.932779\pi$
$242$	32.1356	−	23.3479i	0.00853617	−	0.00620189i
$243$		0			0
$244$	−2319.09	+	1684.92i	−0.608461	+	0.442073i
$245$	5024.54	+	2882.66i	1.31023	+	0.751700i
$246$		0			0
$247$	−94.8375	−	68.9035i	−0.0244306	−	0.0177499i
$248$	135.760	−	417.826i	0.0347612	−	0.106984i
$249$		0			0
$250$	212.533	+	67.1371i	0.0537672	+	0.0169845i
$251$	−1218.11			−0.306321			−0.153160	−	0.988201i	$-0.548945\pi$
$251$	−1218.11			−0.306321			−0.153160	+	0.988201i	$0.548945\pi$
$252$		0			0
$253$	−3430.64	−	2492.51i	−0.852501	−	0.619378i
$254$	−203.951	−	148.179i	−0.0503821	−	0.0366047i
$255$		0			0
$256$	−3208.88	+	2331.39i	−0.783418	+	0.569186i
$257$	492.212			0.119468			0.0597342	−	0.998214i	$-0.480975\pi$
$257$	492.212			0.119468			0.0597342	+	0.998214i	$0.480975\pi$
$258$		0			0
$259$	1886.81	+	5807.01i	0.452667	+	1.39317i
$260$	1929.57	−	1746.96i	0.460258	−	0.416699i
$261$		0			0
$262$	−113.154	−	348.251i	−0.0266819	−	0.0821184i
$263$	−862.074	−	2653.19i	−0.202121	−	0.622064i	−0.999819	−	0.0190075i	$-0.993949\pi$
$263$	−862.074	−	2653.19i	−0.202121	−	0.622064i	0.797699	−	0.603056i	$-0.206051\pi$
$264$		0			0
$265$	−1837.96	−	4097.98i	−0.426056	−	0.949950i
$266$	−5.80706	−	17.8723i	−0.00133855	−	0.00411963i
$267$		0			0
$268$	−712.237			−0.162339
$269$	4837.44	−	3514.61i	1.09645	−	0.796615i	0.115970	−	0.993253i	$-0.463002\pi$
$269$	4837.44	−	3514.61i	1.09645	−	0.796615i	0.980476	+	0.196638i	$0.0630023\pi$
$270$		0			0
$271$	−886.592	−	644.146i	−0.198733	−	0.144388i	0.483968	−	0.875085i	$-0.339195\pi$
$271$	−886.592	−	644.146i	−0.198733	−	0.144388i	−0.682701	+	0.730698i	$0.739195\pi$
$272$	−6575.48	−	4777.36i	−1.46580	−	1.06496i
$273$		0			0
$274$	−407.640			−0.0898774
$275$	4017.02	−	876.794i	0.880857	−	0.192264i
$276$		0			0
$277$	−722.301	+	2223.01i	−0.156675	+	0.482195i	−0.998327	−	0.0578254i	$-0.981583\pi$
$277$	−722.301	+	2223.01i	−0.156675	+	0.482195i	0.841652	+	0.540020i	$0.181583\pi$
$278$	303.840	+	220.752i	0.0655507	+	0.0476253i
$279$		0			0
$280$	831.036	−	89.6397i	0.177371	−	0.0191321i
$281$	3090.76	−	2245.57i	0.656154	−	0.476724i	−0.209208	−	0.977871i	$-0.567089\pi$
$281$	3090.76	−	2245.57i	0.656154	−	0.476724i	0.865362	+	0.501148i	$0.167089\pi$
$282$		0			0
$283$	−2933.95	+	2131.64i	−0.616274	+	0.447749i	−0.851618	−	0.524163i	$-0.824378\pi$
$283$	−2933.95	+	2131.64i	−0.616274	+	0.447749i	0.235344	+	0.971912i	$0.424378\pi$
$284$	1323.74	+	4074.07i	0.276584	+	0.851237i
$285$		0			0
$286$	−47.3255	+	145.653i	−0.00978468	+	0.0301141i
$287$	2289.67	+	7046.89i	0.470924	+	1.44935i
$288$		0			0
$289$	3561.96	−	10962.6i	0.725007	−	2.23134i
$290$	−391.132	+	42.1895i	−0.0792003	+	0.00854294i
$291$		0			0
$292$	588.218	−	427.366i	0.117887	−	0.0856496i
$293$	−1795.61			−0.358024			−0.179012	−	0.983847i	$-0.557290\pi$
$293$	−1795.61			−0.358024			−0.179012	+	0.983847i	$0.557290\pi$
$294$		0			0
$295$	−1458.42	+	6954.61i	−0.287838	+	1.37259i
$296$	428.863	+	311.587i	0.0842133	+	0.0611846i
$297$		0			0
$298$	−123.456	+	379.957i	−0.0239986	+	0.0738601i
$299$	−3763.69			−0.727959
$300$		0			0
$301$	−2382.35			−0.456200
$302$	−101.128	+	311.238i	−0.0192690	+	0.0593038i
$303$		0			0
$304$	205.924	+	149.612i	0.0388504	+	0.0282265i
$305$	−2979.28	+	2697.32i	−0.559321	+	0.506386i
$306$		0			0
$307$	−9971.47			−1.85375			−0.926876	−	0.375367i	$-0.877517\pi$
$307$	−9971.47			−1.85375			−0.926876	+	0.375367i	$0.877517\pi$
$308$	6227.25	−	4524.37i	1.15205	−	0.837012i
$309$		0			0
$310$	63.1072	−	300.933i	0.0115621	−	0.0551351i
$311$	1060.97	−	3265.34i	0.193448	−	0.595371i	−0.806543	−	0.591175i	$-0.798664\pi$
$311$	1060.97	−	3265.34i	0.193448	−	0.595371i	0.999991	−	0.00419632i	$-0.00133573\pi$
$312$		0			0
$313$	−702.374	−	2161.68i	−0.126839	−	0.390370i	0.867393	−	0.497624i	$-0.165794\pi$
$313$	−702.374	−	2161.68i	−0.126839	−	0.390370i	−0.994232	+	0.107254i	$0.965794\pi$
$314$	−36.6610	+	112.831i	−0.00658885	+	0.0202784i
$315$		0			0
$316$	−3280.36	−	10095.9i	−0.583970	−	1.79727i
$317$	−3669.22	+	2665.84i	−0.650106	+	0.472330i	−0.863307	−	0.504678i	$-0.831611\pi$
$317$	−3669.22	+	2665.84i	−0.650106	+	0.472330i	0.213201	+	0.977008i	$0.431611\pi$
$318$		0			0
$319$	−5871.14	+	4265.63i	−1.03047	+	0.748682i
$320$	−4162.80	+	3768.83i	−0.727211	+	0.658387i
$321$		0			0
$322$	−488.116	−	354.637i	−0.0844771	−	0.0613762i
$323$	−159.095	+	489.643i	−0.0274064	+	0.0843483i
$324$		0			0
$325$	2427.00	−	2725.23i	0.414232	−	0.465134i
$326$	−54.0619			−0.00918470
$327$		0			0
$328$	520.431	+	378.115i	0.0876097	+	0.0636522i
$329$	−8271.41	−	6009.53i	−1.38607	−	1.00704i
$330$		0			0
$331$	4593.10	−	3337.08i	0.762717	−	0.554146i	−0.137025	−	0.990568i	$-0.543754\pi$
$331$	4593.10	−	3337.08i	0.762717	−	0.554146i	0.899743	+	0.436421i	$0.143754\pi$
$332$	−1461.19			−0.241546
$333$		0			0
$334$	−69.5228	−	213.969i	−0.0113896	−	0.0350535i
$335$	−992.798	+	107.088i	−0.161917	+	0.0174652i
$336$		0			0
$337$	−467.461	−	1438.70i	−0.0755615	−	0.232554i	0.906141	−	0.422976i	$-0.139015\pi$
$337$	−467.461	−	1438.70i	−0.0755615	−	0.232554i	−0.981702	+	0.190422i	$0.939015\pi$
$338$	−66.2711	−	203.962i	−0.0106647	−	0.0328226i
$339$		0			0
$340$	−9915.68	−	5688.79i	−1.58163	−	0.907405i
$341$	−1752.78	−	5394.50i	−0.278353	−	0.856682i
$342$		0			0
$343$	5138.80			0.808948
$344$	−167.331	+	121.573i	−0.0262264	+	0.0190546i
$345$		0			0
$346$	95.7309	+	69.5525i	0.0148743	+	0.0108068i
$347$	7811.23	+	5675.19i	1.20844	+	0.877983i	0.995088	−	0.0989921i	$-0.0315618\pi$
$347$	7811.23	+	5675.19i	1.20844	+	0.877983i	0.213352	+	0.976975i	$0.431562\pi$
$348$		0			0
$349$	−7346.82			−1.12684			−0.563419	−	0.826171i	$-0.690514\pi$
$349$	−7346.82			−1.12684			−0.563419	+	0.826171i	$0.690514\pi$
$350$	571.546	−	124.751i	0.0872869	−	0.0190521i
$351$		0			0
$352$	309.925	−	953.852i	0.0469292	−	0.144433i
$353$	7714.51	+	5604.92i	1.16318	+	0.845099i	0.990177	−	0.139822i	$-0.0446532\pi$
$353$	7714.51	+	5604.92i	1.16318	+	0.845099i	0.173002	+	0.984921i	$0.444653\pi$
$354$		0			0
$355$	2457.74	+	5479.87i	0.367446	+	0.819271i
$356$	−3746.52	+	2722.01i	−0.557767	+	0.405242i
$357$		0			0
$358$	269.113	−	195.522i	0.0397292	−	0.0288649i
$359$	−775.270	−	2386.04i	−0.113975	−	0.350780i	0.877756	−	0.479107i	$-0.159039\pi$
$359$	−775.270	−	2386.04i	−0.113975	−	0.350780i	−0.991732	+	0.128327i	$0.959039\pi$
$360$		0			0
$361$	−2114.57	+	6507.96i	−0.308291	+	0.948821i
$362$	−162.312	−	499.545i	−0.0235661	−	0.0725290i
$363$		0			0
$364$	2111.14	−	6497.42i	0.303994	−	0.935597i
$365$	755.670	−	684.153i	0.108366	−	0.0981101i
$366$		0			0
$367$	4863.50	−	3533.54i	0.691751	−	0.502587i	−0.185484	−	0.982647i	$-0.559385\pi$
$367$	4863.50	−	3533.54i	0.691751	−	0.502587i	0.877235	+	0.480061i	$0.159385\pi$
$368$	8172.21			1.15762
$369$		0			0
$370$	321.810	+	184.628i	0.0452165	+	0.0259414i
$371$	−9536.81	−	6928.90i	−1.33457	−	0.969624i
$372$		0			0
$373$	−2343.48	+	7212.50i	−0.325311	+	1.00120i	0.645989	+	0.763347i	$0.276445\pi$
$373$	−2343.48	+	7212.50i	−0.325311	+	1.00120i	−0.971300	+	0.237858i	$0.923555\pi$
$374$	672.612			0.0929945
$375$		0			0
$376$	−887.638			−0.121746
$377$	−1990.41	+	6125.85i	−0.271913	+	0.836863i
$378$		0			0
$379$	2308.85	+	1677.48i	0.312923	+	0.227352i	0.733150	−	0.680067i	$-0.238050\pi$
$379$	2308.85	+	1677.48i	0.312923	+	0.227352i	−0.420227	+	0.907419i	$0.638050\pi$
$380$	310.528	+	178.155i	0.0419204	+	0.0240504i
$381$		0			0
$382$	585.185			0.0783787
$383$	1443.06	−	1048.45i	0.192525	−	0.139878i	−0.487347	−	0.873208i	$-0.662035\pi$
$383$	1443.06	−	1048.45i	0.192525	−	0.139878i	0.679872	+	0.733331i	$0.262035\pi$
$384$		0			0
$385$	8000.00	−	7242.87i	1.05901	−	0.958782i
$386$	166.827	−	513.440i	0.0219981	−	0.0677031i
$387$		0			0
$388$	−4087.74	−	12580.8i	−0.534855	−	1.64611i
$389$	737.976	−	2271.26i	0.0961873	−	0.296034i	−0.891374	−	0.453269i	$-0.850258\pi$
$389$	737.976	−	2271.26i	0.0961873	−	0.296034i	0.987561	+	0.157234i	$0.0502578\pi$
$390$		0			0
$391$	5107.96	+	15720.7i	0.660666	+	2.03332i
$392$	1067.90	−	775.877i	0.137595	−	0.0999686i
$393$		0			0
$394$	−32.8916	+	23.8972i	−0.00420573	+	0.00305564i
$395$	−6090.50	−	13579.6i	−0.775814	−	1.72978i
$396$		0			0
$397$	6647.72	+	4829.85i	0.840402	+	0.610588i	0.922483	−	0.386038i	$-0.126157\pi$
$397$	6647.72	+	4829.85i	0.840402	+	0.610588i	−0.0820812	+	0.996626i	$0.526157\pi$
$398$	78.2809	−	240.924i	0.00985896	−	0.0303428i
$399$		0			0
$400$	−5269.81	+	5917.37i	−0.658727	+	0.739672i
$401$	7475.11			0.930896			0.465448	−	0.885075i	$-0.345893\pi$
$401$	7475.11			0.930896			0.465448	+	0.885075i	$0.345893\pi$
$402$		0			0
$403$	−4072.85	−	2959.10i	−0.503432	−	0.365764i
$404$	8720.39	+	6335.73i	1.07390	+	0.780234i
$405$		0			0
$406$	−835.352	+	606.919i	−0.102113	+	0.0741893i
$407$	6844.09			0.833536
$408$		0			0
$409$	3838.20	+	11812.8i	0.464026	+	1.42813i	0.860203	+	0.509951i	$0.170337\pi$
$409$	3838.20	+	11812.8i	0.464026	+	1.42813i	−0.396177	+	0.918174i	$0.629663\pi$
$410$	390.521	+	224.048i	0.0470401	+	0.0269877i
$411$		0			0
$412$	−2217.21	−	6823.86i	−0.265131	−	0.815989i
$413$	5763.37	+	17737.8i	0.686676	+	2.11337i
$414$		0			0
$415$	−2036.78	+	219.697i	−0.240919	+	0.0259868i
$416$	−275.076	−	846.597i	−0.0324200	−	0.0997784i
$417$		0			0
$418$	−21.0641			−0.00246478
$419$	−4073.98	+	2959.92i	−0.475004	+	0.345111i	−0.799388	−	0.600815i	$-0.794843\pi$
$419$	−4073.98	+	2959.92i	−0.475004	+	0.345111i	0.324384	+	0.945925i	$0.394843\pi$
$420$		0			0
$421$	−7971.21	−	5791.42i	−0.922786	−	0.670443i	0.0214300	−	0.999770i	$-0.493178\pi$
$421$	−7971.21	−	5791.42i	−0.922786	−	0.670443i	−0.944216	+	0.329327i	$0.893178\pi$
$422$	163.598	+	118.861i	0.0188717	+	0.0137111i
$423$		0			0
$424$	−1023.43			−0.117222
$425$	−14676.9	−	6438.81i	−1.67514	−	0.734890i
$426$		0			0
$427$	−3259.62	+	10032.1i	−0.369424	+	1.13697i
$428$	414.602	+	301.226i	0.0468237	+	0.0340194i
$429$		0			0
$430$	−107.312	+	97.1558i	−0.0120350	+	0.0108960i
$431$	−6931.59	+	5036.09i	−0.774670	+	0.562831i	−0.903375	−	0.428852i	$-0.858918\pi$
$431$	−6931.59	+	5036.09i	−0.774670	+	0.562831i	0.128704	+	0.991683i	$0.458918\pi$
$432$		0			0
$433$	6367.30	−	4626.12i	0.706681	−	0.513434i	−0.175420	−	0.984494i	$-0.556128\pi$
$433$	6367.30	−	4626.12i	0.706681	−	0.513434i	0.882101	+	0.471060i	$0.156128\pi$
$434$	−249.387	−	767.535i	−0.0275829	−	0.0848914i
$435$		0			0
$436$	2596.79	−	7992.10i	0.285238	−	0.877872i
$437$	−159.965	−	492.323i	−0.0175107	−	0.0538924i
$438$		0			0
$439$	2487.25	−	7654.97i	0.270410	−	0.832236i	−0.719987	−	0.693987i	$-0.755852\pi$
$439$	2487.25	−	7654.97i	0.270410	−	0.832236i	0.990397	−	0.138249i	$-0.0441475\pi$
$440$	192.294	−	916.971i	0.0208346	−	0.0993520i
$441$		0			0
$442$	482.967	−	350.896i	0.0519738	−	0.0377612i
$443$	−4305.60			−0.461773			−0.230886	−	0.972981i	$-0.574163\pi$
$443$	−4305.60			−0.461773			−0.230886	+	0.972981i	$0.574163\pi$
$444$		0			0
$445$	−4813.06	+	4357.55i	−0.512721	+	0.464197i
$446$	135.874	+	98.7184i	0.0144256	+	0.0104808i
$447$		0			0
$448$	−4554.51	+	14017.3i	−0.480313	+	1.47825i
$449$	9905.44			1.04113			0.520564	−	0.853822i	$-0.325722\pi$
$449$	9905.44			1.04113			0.520564	+	0.853822i	$0.325722\pi$
$450$		0			0
$451$	8305.40			0.867153
$452$	359.093	−	1105.17i	0.0373679	−	0.115007i
$453$		0			0
$454$	−593.321	−	431.073i	−0.0613346	−	0.0445622i
$455$	1965.83	−	9374.26i	0.202548	−	0.965873i
$456$		0			0
$457$	6073.04			0.621630			0.310815	−	0.950470i	$-0.399398\pi$
$457$	6073.04			0.621630			0.310815	+	0.950470i	$0.399398\pi$
$458$	−152.314	+	110.662i	−0.0155396	+	0.0112902i
$459$		0			0
$460$	11427.9	−	1232.67i	1.15833	−	0.124943i
$461$	−2488.37	+	7658.41i	−0.251399	+	0.773726i	0.743119	+	0.669159i	$0.233346\pi$
$461$	−2488.37	+	7658.41i	−0.251399	+	0.773726i	−0.994518	+	0.104567i	$0.966654\pi$
$462$		0			0
$463$	2624.36	+	8076.94i	0.263422	+	0.810728i	0.992053	+	0.125822i	$0.0401568\pi$
$463$	2624.36	+	8076.94i	0.263422	+	0.810728i	−0.728631	+	0.684906i	$0.759843\pi$
$464$	4321.84	−	13301.3i	0.432406	−	1.33081i
$465$		0			0
$466$	327.609	+	1008.28i	0.0325670	+	0.100231i
$467$	655.875	−	476.521i	0.0649899	−	0.0472179i	−0.554816	−	0.831973i	$-0.687211\pi$
$467$	655.875	−	476.521i	0.0649899	−	0.0472179i	0.619806	+	0.784755i	$0.287211\pi$
$468$		0			0
$469$	−2120.35	+	1540.52i	−0.208760	+	0.151673i
$470$	−617.661	+	66.6240i	−0.0606182	+	0.00653859i
$471$		0			0
$472$	1309.98	+	951.759i	0.127748	+	0.0928141i
$473$	−825.195	+	2539.69i	−0.0802167	+	0.246882i
$474$		0			0
$475$	459.636	+	201.644i	0.0443991	+	0.0194780i
$476$	−30004.5			−2.88919
$477$		0			0
$478$	208.769	+	151.679i	0.0199767	+	0.0145139i
$479$	5393.84	+	3918.85i	0.514511	+	0.373814i	0.814532	−	0.580118i	$-0.196994\pi$
$479$	5393.84	+	3918.85i	0.514511	+	0.373814i	−0.300021	+	0.953933i	$0.596994\pi$
$480$		0			0
$481$	4914.38	−	3570.51i	0.465856	−	0.338464i
$482$	−122.675			−0.0115927
$483$		0			0
$484$	613.764	+	1888.97i	0.0576412	+	0.177402i
$485$	−7589.54	−	16921.9i	−0.710564	−	1.58430i
$486$		0			0
$487$	−1201.19	−	3696.88i	−0.111768	−	0.343987i	0.879491	−	0.475915i	$-0.157883\pi$
$487$	−1201.19	−	3696.88i	−0.111768	−	0.343987i	−0.991259	+	0.131928i	$0.957883\pi$
$488$	282.996	+	870.973i	0.0262513	+	0.0807932i
$489$		0			0
$490$	684.862	−	620.046i	0.0631406	−	0.0571650i
$491$	3440.60	+	10589.1i	0.316236	+	0.973275i	0.975243	+	0.221138i	$0.0709770\pi$
$491$	3440.60	+	10589.1i	0.316236	+	0.973275i	−0.659006	+	0.752137i	$0.729023\pi$
$492$		0			0
$493$	28288.6			2.58429
$494$	−15.1250	+	10.9890i	−0.00137755	+	0.00100085i
$495$		0			0
$496$	8843.50	+	6425.18i	0.800574	+	0.581651i
$497$	12752.7	+	9265.41i	1.15098	+	0.836238i
$498$		0			0
$499$	18600.7			1.66870			0.834351	−	0.551233i	$-0.185842\pi$
$499$	18600.7			1.66870			0.834351	+	0.551233i	$0.185842\pi$
$500$	−6476.69	+	9069.67i	−0.579292	+	0.811216i
$501$		0			0
$502$	−60.0324	+	184.761i	−0.00533740	+	0.0164268i
$503$	9096.52	+	6609.01i	0.806349	+	0.585847i	0.912770	−	0.408474i	$-0.133939\pi$
$503$	9096.52	+	6609.01i	0.806349	+	0.585847i	−0.106421	+	0.994321i	$0.533939\pi$
$504$		0			0
$505$	13108.1	+	7520.32i	1.15505	+	0.662673i
$506$	−547.132	+	397.515i	−0.0480691	+	0.0349243i
$507$		0			0
$508$	10198.0	−	7409.32i	0.890680	−	0.647117i
$509$	−3557.97	−	10950.3i	−0.309832	−	0.953565i	−0.977830	−	0.209401i	$-0.932848\pi$
$509$	−3557.97	−	10950.3i	−0.309832	−	0.953565i	0.667998	−	0.744163i	$-0.267152\pi$
$510$		0			0
$511$	826.776	−	2544.55i	0.0715742	−	0.220283i
$512$	996.526	+	3066.99i	0.0860169	+	0.264733i
$513$		0			0
$514$	24.2578	−	74.6578i	0.00208164	−	0.00640664i
$515$	−4116.60	−	9178.51i	−0.352231	−	0.785347i
$516$		0			0
$517$	−9271.47	+	6736.12i	−0.788702	+	0.573026i
$518$	973.785			0.0825978
$519$		0			0
$520$	−340.301	−	758.747i	−0.0286984	−	0.0639870i
$521$	7391.15	+	5369.99i	0.621521	+	0.451561i	0.853452	−	0.521171i	$-0.174505\pi$
$521$	7391.15	+	5369.99i	0.621521	+	0.451561i	−0.231932	+	0.972732i	$0.574505\pi$
$522$		0			0
$523$	−6777.77	+	20859.8i	−0.566675	+	1.74405i	0.0962456	+	0.995358i	$0.469317\pi$
$523$	−6777.77	+	20859.8i	−0.566675	+	1.74405i	−0.662921	+	0.748690i	$0.730683\pi$
$524$	18309.5			1.52644
$525$		0			0
$526$	−444.917			−0.0368808
$527$	−6832.41	+	21028.0i	−0.564752	+	1.73813i
$528$		0			0
$529$	−3602.67	−	2617.49i	−0.296101	−	0.215130i
$530$	−712.154	+	76.8165i	−0.0583660	+	0.00629565i
$531$		0			0
$532$	939.646			0.0765768
$533$	5963.67	−	4332.86i	0.484644	−	0.352114i
$534$		0			0
$535$	623.210	+	357.546i	0.0503621	+	0.0288936i
$536$	−70.3146	+	216.406i	−0.00566628	+	0.0174390i
$537$		0			0
$538$	−294.684	−	906.945i	−0.0236148	−	0.0726788i
$539$	5266.37	−	16208.2i	0.420851	−	1.29525i
$540$		0			0
$541$	−1587.67	−	4886.34i	−0.126172	−	0.388318i	0.867941	−	0.496668i	$-0.165443\pi$
$541$	−1587.67	−	4886.34i	−0.126172	−	0.388318i	−0.994113	+	0.108350i	$0.965443\pi$
$542$	−141.397	+	102.731i	−0.0112058	+	0.00814146i
$543$		0			0
$544$	−3162.86	+	2297.95i	−0.249276	+	0.181110i
$545$	2418.05	−	11530.7i	0.190051	−	0.906280i
$546$		0			0
$547$	2450.34	+	1780.28i	0.191534	+	0.139157i	0.679419	−	0.733750i	$-0.262232\pi$
$547$	2450.34	+	1780.28i	0.191534	+	0.139157i	−0.487886	+	0.872908i	$0.662232\pi$
$548$	6298.68	−	19385.3i	0.490997	−	1.51113i
$549$		0			0
$550$	64.9813	−	652.505i	0.00503784	−	0.0505871i
$551$	−885.911			−0.0684956
$552$		0			0
$553$	−31602.4	−	22960.5i	−2.43015	−	1.76561i
$554$	301.585	+	219.114i	0.0231284	+	0.0168037i
$555$		0			0
$556$	−15192.7	+	11038.1i	−1.15884	+	0.841945i
$557$	−20769.3			−1.57994			−0.789968	−	0.613148i	$-0.789903\pi$
$557$	−20769.3			−1.57994			−0.789968	+	0.613148i	$0.789903\pi$
$558$		0			0
$559$	732.406	+	2254.11i	0.0554159	+	0.170553i
$560$	−4268.47	+	20354.6i	−0.322099	+	1.53596i
$561$		0			0
$562$	−188.281	−	579.469i	−0.0141319	−	0.0434936i
$563$	−555.456	−	1709.52i	−0.0415803	−	0.127971i	0.928112	−	0.372302i	$-0.121432\pi$
$563$	−555.456	−	1709.52i	−0.0415803	−	0.127971i	−0.969692	+	0.244331i	$0.921432\pi$
$564$		0			0
$565$	334.376	−	1594.51i	0.0248979	−	0.118728i
$566$	178.729	+	550.071i	0.0132730	+	0.0408502i
$567$		0			0
$568$	1368.55			0.101097
$569$	10255.6	−	7451.12i	0.755600	−	0.548976i	−0.141958	−	0.989873i	$-0.545340\pi$
$569$	10255.6	−	7451.12i	0.755600	−	0.548976i	0.897558	+	0.440897i	$0.145340\pi$
$570$		0			0
$571$	−4944.23	−	3592.20i	−0.362364	−	0.263273i	0.391674	−	0.920104i	$-0.371896\pi$
$571$	−4944.23	−	3592.20i	−0.362364	−	0.263273i	−0.754037	+	0.656832i	$0.771896\pi$
$572$	−6195.29	−	4501.14i	−0.452864	−	0.329025i
$573$		0			0
$574$	1181.70			0.0859290
$575$	15744.2	−	3436.48i	1.14188	−	0.249237i
$576$		0			0
$577$	4174.86	−	12848.9i	0.301216	−	0.927047i	−0.679846	−	0.733354i	$-0.737954\pi$
$577$	4174.86	−	12848.9i	0.301216	−	0.927047i	0.981062	−	0.193692i	$-0.0620464\pi$
$578$	−1487.24	−	1080.54i	−0.107026	−	0.0777589i
$579$		0			0
$580$	4037.29	−	19252.2i	0.289033	−	1.37828i
$581$	−4350.00	+	3160.46i	−0.310617	+	0.225677i
$582$		0			0
$583$	−10689.9	+	7766.65i	−0.759399	+	0.551735i
$584$	−71.7797	−	220.915i	−0.00508607	−	0.0156533i
$585$		0			0
$586$	−88.4936	+	272.355i	−0.00623829	+	0.0191995i
$587$	7283.42	+	22416.1i	0.512128	+	1.57617i	0.788448	+	0.615101i	$0.210885\pi$
$587$	7283.42	+	22416.1i	0.512128	+	1.57617i	−0.276320	+	0.961066i	$0.589115\pi$
$588$		0			0
$589$	213.970	−	658.532i	0.0149685	−	0.0460685i
$590$	982.986	+	563.955i	0.0685914	+	0.0393520i
$591$		0			0
$592$	−10670.8	+	7752.76i	−0.740820	+	0.538237i
$593$	18418.6			1.27548			0.637741	−	0.770251i	$-0.279869\pi$
$593$	18418.6			1.27548			0.637741	+	0.770251i	$0.279869\pi$
$594$		0			0
$595$	−41823.7	+	4511.31i	−2.88169	+	0.310833i
$596$	−16161.3	−	11741.9i	−1.11073	−	0.806990i
$597$		0			0
$598$	−185.487	+	570.869i	−0.0126841	+	0.0390377i
$599$	−20376.6			−1.38992			−0.694962	−	0.719047i	$-0.744579\pi$
$599$	−20376.6			−1.38992			−0.694962	+	0.719047i	$0.744579\pi$
$600$		0			0
$601$	6750.30			0.458154			0.229077	−	0.973408i	$-0.426429\pi$
$601$	6750.30			0.458154			0.229077	+	0.973408i	$0.426429\pi$
$602$	−117.410	+	361.349i	−0.00794893	+	0.0244643i
$603$		0			0
$604$	−13238.4	−	9618.25i	−0.891825	−	0.647949i
$605$	1139.55	+	2540.78i	0.0765774	+	0.170740i
$606$		0			0
$607$	24863.6			1.66258			0.831288	−	0.555842i	$-0.187604\pi$
$607$	24863.6			1.66258			0.831288	+	0.555842i	$0.187604\pi$
$608$	99.0508	−	71.9646i	0.00660697	−	0.00480025i
$609$		0			0
$610$	262.295	+	584.823i	0.0174099	+	0.0388177i
$611$	−3143.18	+	9673.71i	−0.208117	+	0.640518i
$612$		0			0
$613$	−4288.32	−	13198.1i	−0.282551	−	0.869602i	−0.987122	−	0.159969i	$-0.948861\pi$
$613$	−4288.32	−	13198.1i	−0.282551	−	0.869602i	0.704571	−	0.709633i	$-0.251139\pi$
$614$	−491.426	+	1512.45i	−0.0323002	+	0.0994099i
$615$		0			0
$616$	−759.906	−	2338.75i	−0.0497037	−	0.152972i
$617$	−19426.7	+	14114.3i	−1.26757	+	0.920943i	−0.999103	−	0.0423456i	$-0.986517\pi$
$617$	−19426.7	+	14114.3i	−1.26757	+	0.920943i	−0.268467	+	0.963289i	$0.586517\pi$
$618$		0			0
$619$	−15028.7	+	10919.0i	−0.975858	+	0.709002i	−0.956779	−	0.290816i	$-0.906073\pi$
$619$	−15028.7	+	10919.0i	−0.975858	+	0.709002i	−0.0190786	+	0.999818i	$0.506073\pi$
$620$	13335.8	+	7650.97i	0.863837	+	0.495597i
$621$		0			0
$622$	−442.992	−	321.853i	−0.0285569	−	0.0207478i
$623$	−5265.95	+	16206.9i	−0.338645	+	1.04224i
$624$		0			0
$625$	−7664.28	+	13616.1i	−0.490514	+	0.871433i
$626$	−362.495			−0.0231441
$627$		0			0
$628$	−4799.21	−	3486.83i	−0.304951	−	0.221560i
$629$	−21583.4	−	15681.3i	−1.36818	−	0.994044i
$630$		0			0
$631$	−13503.0	+	9810.53i	−0.851897	+	0.618940i	−0.925669	−	0.378335i	$-0.876497\pi$
$631$	−13503.0	+	9810.53i	−0.851897	+	0.618940i	0.0737711	+	0.997275i	$0.476497\pi$
$632$	−3391.39			−0.213453
$633$		0			0
$634$	223.519	+	687.921i	0.0140017	+	0.0430928i
$635$	13101.2	−	11861.3i	0.818747	−	0.741260i
$636$		0			0
$637$	−4674.20	−	14385.7i	−0.290735	−	0.894792i
$638$	357.654	+	1100.75i	0.0221938	+	0.0683056i
$639$		0			0
$640$	1482.55	+	3305.54i	0.0915669	+	0.204161i
$641$	−6734.41	−	20726.4i	−0.414966	−	1.27713i	−0.912281	−	0.409565i	$-0.865681\pi$
$641$	−6734.41	−	20726.4i	−0.414966	−	1.27713i	0.497315	−	0.867570i	$-0.334319\pi$
$642$		0			0
$643$	27264.8			1.67219			0.836095	−	0.548585i	$-0.184833\pi$
$643$	27264.8			1.67219			0.836095	+	0.548585i	$0.184833\pi$
$644$	24406.9	−	17732.7i	1.49343	−	1.08504i
$645$		0			0
$646$	66.4275	+	48.2624i	0.00404575	+	0.00293941i
$647$	−11895.8	−	8642.84i	−0.722834	−	0.525170i	0.164454	−	0.986385i	$-0.447414\pi$
$647$	−11895.8	−	8642.84i	−0.722834	−	0.525170i	−0.887288	+	0.461215i	$0.847414\pi$
$648$		0			0
$649$	20905.7			1.26444
$650$	−293.747	−	502.430i	−0.0177257	−	0.0303184i
$651$		0			0
$652$	835.342	−	2570.92i	0.0501756	−	0.154425i
$653$	2577.82	+	1872.90i	0.154484	+	0.112239i	0.662342	−	0.749202i	$-0.269563\pi$
$653$	2577.82	+	1872.90i	0.154484	+	0.112239i	−0.507858	+	0.861441i	$0.669563\pi$
$654$		0			0
$655$	25521.9	−	2752.92i	1.52248	−	0.164222i
$656$	−12949.1	+	9408.07i	−0.770697	+	0.559944i
$657$		0			0
$658$	−1319.16	+	958.422i	−0.0781551	+	0.0567830i
$659$	169.519	+	521.726i	0.0100205	+	0.0308400i	0.955942	−	0.293556i	$-0.0948388\pi$
$659$	169.519	+	521.726i	0.0100205	+	0.0308400i	−0.945921	+	0.324396i	$0.894839\pi$
$660$		0			0
$661$	6862.63	−	21121.0i	0.403820	−	1.24283i	−0.518056	−	0.855347i	$-0.673344\pi$
$661$	6862.63	−	21121.0i	0.403820	−	1.24283i	0.921876	−	0.387484i	$-0.126656\pi$
$662$	−279.799	−	861.134i	−0.0164271	−	0.0505573i
$663$		0			0
$664$	−144.254	+	443.969i	−0.00843095	+	0.0259478i
$665$	1309.79	−	141.280i	0.0763780	−	0.00823851i
$666$		0			0
$667$	−23011.2	+	16718.6i	−1.33583	+	0.970535i
$668$	11249.6			0.651585
$669$		0			0
$670$	−32.6853	+	155.863i	−0.00188469	+	0.00898735i
$671$	9565.57	+	6949.80i	0.550335	+	0.399842i
$672$		0			0
$673$	−1118.05	+	3441.00i	−0.0640381	+	0.197089i	−0.977956	−	0.208809i	$-0.933041\pi$
$673$	−1118.05	+	3441.00i	−0.0640381	+	0.197089i	0.913918	+	0.405898i	$0.133041\pi$
$674$	−241.257			−0.0137876
$675$		0			0
$676$	10723.4			0.610116
$677$	−381.095	+	1172.89i	−0.0216347	+	0.0665847i	−0.961291	−	0.275535i	$-0.911145\pi$
$677$	−381.095	+	1172.89i	−0.0216347	+	0.0665847i	0.939656	+	0.342120i	$0.111145\pi$
$678$		0			0
$679$	−39380.7	−	28611.7i	−2.22576	−	1.61711i
$680$	−2707.39	+	2451.16i	−0.152682	+	0.138232i
$681$		0			0
$682$	−904.610			−0.0507908
$683$	8454.62	−	6142.64i	0.473656	−	0.344131i	−0.325209	−	0.945642i	$-0.605435\pi$
$683$	8454.62	−	6142.64i	0.473656	−	0.344131i	0.798864	+	0.601511i	$0.205435\pi$
$684$		0			0
$685$	5865.14	−	27968.5i	0.327147	−	1.56003i
$686$	253.257	−	779.443i	0.0140953	−	0.0433809i
$687$		0			0
$688$	−1590.30	−	4894.43i	−0.0881242	−	0.271218i
$689$	−3624.04	+	11153.6i	−0.200384	+	0.616720i
$690$		0			0
$691$	5157.67	+	15873.7i	0.283947	+	0.873898i	0.986712	+	0.162477i	$0.0519482\pi$
$691$	5157.67	+	15873.7i	0.283947	+	0.873898i	−0.702766	+	0.711421i	$0.748052\pi$
$692$	−4786.77	+	3477.79i	−0.262956	+	0.191049i
$693$		0			0
$694$	1245.76	−	905.101i	0.0681391	−	0.0495060i
$695$	−19517.7	+	17670.5i	−1.06525	+	0.964433i
$696$		0			0
$697$	−26191.8	−	19029.4i	−1.42336	−	1.03413i
$698$	−362.075	+	1114.35i	−0.0196343	+	0.0604282i
$699$		0			0
$700$	−2898.74	+	29107.5i	−0.156517	+	1.57166i
$701$	16107.7			0.867872			0.433936	−	0.900944i	$-0.357124\pi$
$701$	16107.7			0.867872			0.433936	+	0.900944i	$0.357124\pi$
$702$		0			0
$703$	675.926	+	491.089i	0.0362632	+	0.0263468i
$704$	13365.5	+	9710.62i	0.715528	+	0.519862i
$705$		0			0
$706$	1230.34	−	893.894i	0.0655870	−	0.0476518i
$707$	39664.6			2.10996
$708$		0			0
$709$	−1080.15	−	3324.37i	−0.0572158	−	0.176092i	0.918364	−	0.395736i	$-0.129510\pi$
$709$	−1080.15	−	3324.37i	−0.0572158	−	0.176092i	−0.975580	+	0.219644i	$0.929510\pi$
$710$	952.301	−	102.720i	0.0503369	−	0.00542959i
$711$		0			0
$712$	457.184	+	1407.07i	0.0240642	+	0.0740620i
$713$	−6869.80	−	21143.1i	−0.360836	−	1.11054i
$714$		0			0
$715$	−9312.47	−	5342.71i	−0.487086	−	0.279449i
$716$	5139.84	+	15818.8i	0.268275	+	0.825665i
$717$		0			0
$718$	−400.117			−0.0207970
$719$	−4561.98	+	3314.47i	−0.236625	+	0.171918i	−0.699778	−	0.714360i	$-0.746718\pi$
$719$	−4561.98	+	3314.47i	−0.236625	+	0.171918i	0.463153	+	0.886278i	$0.346718\pi$
$720$		0			0
$721$	−21360.2	−	15519.1i	−1.10332	−	0.801612i
$722$	882.903	+	641.466i	0.0455100	+	0.0330650i
$723$		0			0
$724$	26263.9			1.34819
$725$	2732.97	−	27443.0i	0.140000	−	1.40580i
$726$		0			0
$727$	−1371.30	+	4220.44i	−0.0699572	+	0.215306i	−0.979923	−	0.199378i	$-0.936108\pi$
$727$	−1371.30	+	4220.44i	−0.0699572	+	0.215306i	0.909966	+	0.414684i	$0.136108\pi$
$728$	−1765.76	−	1282.90i	−0.0898946	−	0.0653122i
$729$		0			0
$730$	−66.5291	−	148.336i	−0.00337309	−	0.00752076i
$731$	8421.29	−	6118.42i	0.426091	−	0.309573i
$732$		0			0
$733$	−1276.36	+	927.332i	−0.0643159	+	0.0467282i	−0.619479	−	0.785013i	$-0.712656\pi$
$733$	−1276.36	+	927.332i	−0.0643159	+	0.0467282i	0.555163	+	0.831742i	$0.312656\pi$
$734$	−296.272	−	911.830i	−0.0148986	−	0.0458532i
$735$		0			0
$736$	1214.71	−	3738.50i	0.0608355	−	0.187232i
$737$	907.822	+	2793.99i	0.0453732	+	0.139644i
$738$		0			0
$739$	−4924.32	+	15155.5i	−0.245120	+	0.754403i	0.750496	+	0.660875i	$0.229815\pi$
$739$	−4924.32	+	15155.5i	−0.245120	+	0.754403i	−0.995617	+	0.0935283i	$0.970185\pi$
$740$	−13752.5	+	12450.9i	−0.683176	+	0.618520i
$741$		0			0
$742$	−1520.97	+	1105.05i	−0.0752513	+	0.0546732i
$743$	−23105.8			−1.14088			−0.570438	−	0.821341i	$-0.693226\pi$
$743$	−23105.8			−1.14088			−0.570438	+	0.821341i	$0.693226\pi$
$744$		0			0
$745$	−24292.9	−	13937.2i	−1.19466	−	0.685397i
$746$	978.484	+	710.910i	0.0480226	+	0.0348904i
$747$		0			0
$748$	−10392.9	+	31986.1i	−0.508025	+	1.56354i
$749$	1885.81			0.0919973
$750$		0			0
$751$	−24402.0			−1.18567			−0.592837	−	0.805323i	$-0.701992\pi$
$751$	−24402.0			−1.18567			−0.592837	+	0.805323i	$0.701992\pi$
$752$	6824.88	−	21004.8i	0.330954	−	1.01857i
$753$		0			0
$754$	831.064	+	603.803i	0.0401400	+	0.0291634i
$755$	−19899.3	−	11416.6i	−0.959220	−	0.550320i
$756$		0			0
$757$	17698.1			0.849736			0.424868	−	0.905255i	$-0.360321\pi$
$757$	17698.1			0.849736			0.424868	+	0.905255i	$0.360321\pi$
$758$	368.224	−	267.531i	0.0176445	−	0.0128195i
$759$		0			0
$760$	84.7871	−	76.7628i	0.00404678	−	0.00366379i
$761$	2428.43	−	7473.92i	0.115677	−	0.356018i	−0.876410	−	0.481565i	$-0.840069\pi$
$761$	2428.43	−	7473.92i	0.115677	−	0.356018i	0.992088	+	0.125547i	$0.0400686\pi$
$762$		0			0
$763$	−9555.67	−	29409.3i	−0.453393	−	1.39540i
$764$	−9042.03	+	27828.5i	−0.428180	+	1.31780i
$765$		0			0
$766$	−87.9077	−	270.552i	−0.00414652	−	0.0127617i
$767$	15011.2	−	10906.3i	0.706682	−	0.513434i
$768$		0			0
$769$	−8164.74	+	5932.03i	−0.382871	+	0.278172i	−0.762528	−	0.646955i	$-0.776042\pi$
$769$	−8164.74	+	5932.03i	−0.382871	+	0.278172i	0.379657	+	0.925127i	$0.376042\pi$
$770$	−704.320	−	1570.38i	−0.0329635	−	0.0734967i
$771$		0			0
$772$	21838.9	+	15866.9i	1.01813	+	0.739718i
$773$	−11235.0	+	34577.6i	−0.522760	+	1.60889i	0.245944	+	0.969284i	$0.420902\pi$
$773$	−11235.0	+	34577.6i	−0.522760	+	1.60889i	−0.768704	+	0.639605i	$0.779098\pi$
$774$		0			0
$775$	19739.3	+	8659.69i	0.914913	+	0.401375i
$776$	−4226.10			−0.195500
$777$		0			0
$778$	−308.130	−	223.870i	−0.0141992	−	0.0103163i
$779$	820.245	+	595.943i	0.0377257	+	0.0274093i
$780$		0			0
$781$	14294.6	−	10385.7i	0.654932	−	0.475836i
$782$	2636.22			0.120551
$783$		0			0
$784$	10149.2	+	31236.1i	0.462337	+	1.42293i
$785$	−7213.95	−	4138.76i	−0.327996	−	0.188177i
$786$		0			0
$787$	470.813	+	1449.01i	0.0213248	+	0.0656311i	0.961153	−	0.276017i	$-0.0890148\pi$
$787$	470.813	+	1449.01i	0.0213248	+	0.0656311i	−0.939828	+	0.341649i	$0.889015\pi$
$788$	−628.204	−	1933.41i	−0.0283995	−	0.0874048i
$789$		0			0
$790$	−2359.89	+	254.549i	−0.106280	+	0.0114639i
$791$	−1321.39	−	4066.82i	−0.0593972	−	0.182806i
$792$		0			0
$793$	10494.2			0.469936
$794$	1060.20	−	770.283i	0.0473869	−	0.0344286i
$795$		0			0
$796$	10247.6	+	7445.31i	0.456301	+	0.331522i
$797$	14386.0	+	10452.0i	0.639370	+	0.464529i	0.859634	−	0.510911i	$-0.170692\pi$
$797$	14386.0	+	10452.0i	0.639370	+	0.464529i	−0.220264	+	0.975440i	$0.570692\pi$
$798$		0			0
$799$	44672.3			1.97796
$800$	1923.69	+	3290.31i	0.0850159	+	0.145413i
$801$		0			0
$802$	368.397	−	1133.81i	0.0162202	−	0.0499205i
$803$	−2426.23	−	1762.76i	−0.106625	−	0.0774676i
$804$		0			0
$805$	31355.0	−	28387.5i	1.37282	−	1.24289i
$806$	−649.553	+	471.928i	−0.0283865	+	0.0206240i
$807$		0			0
$808$	2785.96	−	2024.12i	0.121299	−	0.0881289i
$809$	7339.29	+	22588.0i	0.318956	+	0.981646i	0.974095	+	0.226138i	$0.0726100\pi$
$809$	7339.29	+	22588.0i	0.318956	+	0.981646i	−0.655139	+	0.755508i	$0.727390\pi$
$810$		0			0
$811$	−5412.05	+	16656.6i	−0.234331	+	0.721198i	0.762878	+	0.646543i	$0.223786\pi$
$811$	−5412.05	+	16656.6i	−0.234331	+	0.721198i	−0.997209	+	0.0746556i	$0.976214\pi$
$812$	−15954.6	−	49103.1i	−0.689526	−	2.12214i
$813$		0			0
$814$	337.299	−	1038.10i	0.0145237	−	0.0446994i
$815$	777.846	−	3709.24i	0.0334316	−	0.159422i
$816$		0			0
$817$	−263.729	+	191.610i	−0.0112934	+	0.00820512i
$818$	1980.89			0.0846704
$819$		0			0
$820$	−16688.8	+	15109.4i	−0.710729	+	0.643465i
$821$	−7100.21	−	5158.61i	−0.301826	−	0.219289i	0.426555	−	0.904462i	$-0.359727\pi$
$821$	−7100.21	−	5158.61i	−0.301826	−	0.219289i	−0.728381	+	0.685172i	$0.759727\pi$
$822$		0			0
$823$	−11194.8	+	34453.9i	−0.474149	+	1.45928i	0.372953	+	0.927850i	$0.378345\pi$
$823$	−11194.8	+	34453.9i	−0.474149	+	1.45928i	−0.847102	+	0.531430i	$0.821655\pi$
$824$	−2292.25			−0.0969107
$825$		0			0
$826$	2974.48			0.125297
$827$	9416.50	−	28981.0i	0.395942	−	1.21858i	−0.532284	−	0.846566i	$-0.678666\pi$
$827$	9416.50	−	28981.0i	0.395942	−	1.21858i	0.928226	−	0.372018i	$-0.121334\pi$
$828$		0			0
$829$	−19031.7	−	13827.4i	−0.797345	−	0.579305i	0.112789	−	0.993619i	$-0.464022\pi$
$829$	−19031.7	−	13827.4i	−0.797345	−	0.579305i	−0.910134	+	0.414314i	$0.864022\pi$
$830$	−67.0557	+	319.762i	−0.00280426	+	0.0133724i
$831$		0			0
$832$	14663.0			0.610997
$833$	−53744.5	+	39047.6i	−2.23546	+	1.62415i
$834$		0			0
$835$	15680.9	−	1691.42i	0.649893	−	0.0701008i
$836$	325.474	−	1001.71i	0.0134650	−	0.0414410i
$837$		0			0
$838$	248.176	+	763.807i	0.0102304	+	0.0314860i
$839$	−650.522	+	2002.10i	−0.0267682	+	0.0823841i	−0.963548	−	0.267535i	$-0.913791\pi$
$839$	−650.522	+	2002.10i	−0.0267682	+	0.0823841i	0.936780	+	0.349919i	$0.113791\pi$
$840$		0			0
$841$	7505.55	+	23099.7i	0.307743	+	0.947137i
$842$	−1271.28	+	923.637i	−0.0520322	+	0.0378036i
$843$		0			0
$844$	−8180.30	+	5943.34i	−0.333623	+	0.242391i
$845$	14947.5	−	1612.31i	0.608532	−	0.0656393i
$846$		0			0
$847$	5912.91	+	4295.98i	0.239870	+	0.174276i
$848$	7868.99	−	24218.3i	0.318658	−	0.980729i
$849$		0			0
$850$	−1699.95	+	1908.85i	−0.0685975	+	0.0770269i
$851$	26824.6			1.08053
$852$		0			0
$853$	−20202.4	−	14677.9i	−0.810924	−	0.589171i	0.103174	−	0.994663i	$-0.467100\pi$
$853$	−20202.4	−	14677.9i	−0.810924	−	0.589171i	−0.914098	+	0.405493i	$0.867100\pi$
$854$	1361.00	+	988.824i	0.0545345	+	0.0396216i
$855$		0			0
$856$	132.455	−	96.2345i	0.00528882	−	0.00384255i
$857$	1789.44			0.0713258			0.0356629	−	0.999364i	$-0.488646\pi$
$857$	1789.44			0.0713258			0.0356629	+	0.999364i	$0.488646\pi$
$858$		0			0
$859$	2369.32	+	7292.01i	0.0941095	+	0.289639i	0.987021	−	0.160594i	$-0.0513409\pi$
$859$	2369.32	+	7292.01i	0.0941095	+	0.289639i	−0.892911	+	0.450233i	$0.851341\pi$
$860$	−2962.11	−	6604.44i	−0.117450	−	0.261871i
$861$		0			0
$862$	422.254	+	1299.56i	0.0166845	+	0.0513496i
$863$	2788.93	+	8583.43i	0.110007	+	0.338567i	0.990873	−	0.134799i	$-0.0430388\pi$
$863$	2788.93	+	8583.43i	0.110007	+	0.338567i	−0.880866	+	0.473366i	$0.843039\pi$
$864$		0			0
$865$	−6149.45	+	5567.46i	−0.241720	+	0.218843i
$866$	−387.879	−	1193.77i	−0.0152202	−	0.0468429i
$867$		0			0
$868$	40353.6			1.57799
$869$	−35423.4	+	25736.6i	−1.38280	+	1.00467i
$870$		0			0
$871$	2109.46	+	1532.61i	0.0820624	+	0.0596218i
$872$	−2171.95	−	1578.02i	−0.0843482	−	0.0612826i
$873$		0			0
$874$	−82.5581			−0.00319516
$875$	335.853	+	41009.2i	0.0129759	+	1.58442i
$876$		0			0
$877$	7135.55	−	21961.0i	0.274744	−	0.845575i	−0.714543	−	0.699591i	$-0.753365\pi$
$877$	7135.55	−	21961.0i	0.274744	−	0.845575i	0.989287	−	0.145983i	$-0.0466346\pi$
$878$	−1038.51	−	754.523i	−0.0399181	−	0.0290022i
$879$		0			0
$880$	20220.4	+	11600.8i	0.774581	+	0.444390i
$881$	40232.0	−	29230.2i	1.53853	−	1.11781i	0.587289	−	0.809378i	$-0.300195\pi$
$881$	40232.0	−	29230.2i	1.53853	−	1.11781i	0.951246	−	0.308433i	$-0.0998047\pi$
$882$		0			0
$883$	35069.6	−	25479.6i	1.33657	−	0.971071i	0.337002	−	0.941504i	$-0.390587\pi$
$883$	35069.6	−	25479.6i	1.33657	−	0.971071i	0.999563	−	0.0295676i	$-0.00941303\pi$
$884$	9224.29	+	28389.5i	0.350958	+	1.08014i
$885$		0			0
$886$	−212.194	+	653.066i	−0.00804604	+	0.0247632i
$887$	5550.36	+	17082.2i	0.210105	+	0.646635i	0.999465	+	0.0327054i	$0.0104123\pi$
$887$	5550.36	+	17082.2i	0.210105	+	0.646635i	−0.789360	+	0.613930i	$0.789588\pi$
$888$		0			0
$889$	14334.0	−	44115.4i	0.540771	−	1.66432i
$890$	423.742	+	944.790i	0.0159594	+	0.0355836i
$891$		0			0
$892$	−6794.04	+	4936.16i	−0.255024	+	0.185286i
$893$	−1399.00			−0.0524251
$894$		0			0
$895$	9542.92	+	21277.2i	0.356407	+	0.794659i
$896$	7692.65	+	5589.04i	0.286823	+	0.208389i
$897$		0			0
$898$	488.172	−	1502.44i	0.0181409	−	0.0558319i
$899$	−38045.9			−1.41146
$900$		0			0
$901$	51506.5			1.90447
$902$	409.317	−	1259.75i	0.0151095	−	0.0465022i
$903$		0			0
$904$	−300.345	−	218.213i	−0.0110501	−	0.00802839i
$905$	36609.6	−	3948.90i	1.34469	−	0.145045i
$906$		0			0
$907$	−12383.8			−0.453360			−0.226680	−	0.973969i	$-0.572787\pi$
$907$	−12383.8			−0.453360			−0.226680	+	0.973969i	$0.572787\pi$
$908$	29667.4	−	21554.7i	1.08430	−	0.787794i
$909$		0			0
$910$	−1324.99	−	760.167i	−0.0482669	−	0.0276915i
$911$	11233.4	−	34572.8i	0.408539	−	1.25735i	−0.509366	−	0.860550i	$-0.670120\pi$
$911$	11233.4	−	34572.8i	0.408539	−	1.25735i	0.917904	−	0.396802i	$-0.129880\pi$
$912$		0			0
$913$	1862.45	+	5732.02i	0.0675115	+	0.207779i
$914$	299.299	−	921.147i	0.0108314	−	0.0333357i
$915$		0			0
$916$	−2909.07	−	8953.21i	−0.104933	−	0.322950i
$917$	54507.8	−	39602.2i	1.96293	−	1.42615i
$918$		0			0
$919$	−24485.4	+	17789.7i	−0.878888	+	0.638550i	−0.932957	−	0.359988i	$-0.882781\pi$
$919$	−24485.4	+	17789.7i	−0.878888	+	0.638550i	0.0540689	+	0.998537i	$0.482781\pi$
$920$	753.670	−	3593.95i	0.0270084	−	0.128793i
$921$		0			0
$922$	1038.98	+	754.862i	0.0371116	+	0.0269632i
$923$	4846.11	−	14914.8i	0.172819	−	0.531881i
$924$		0			0
$925$	−17297.7	+	19423.3i	−0.614859	+	0.690414i
$926$	1354.43			0.0480663
$927$		0			0
$928$	−5442.47	−	3954.18i	−0.192519	−	0.139873i
$929$	12249.3	+	8899.62i	0.432601	+	0.314303i	0.782688	−	0.622414i	$-0.213848\pi$
$929$	12249.3	+	8899.62i	0.432601	+	0.314303i	−0.350087	+	0.936717i	$0.613848\pi$
$930$		0			0
$931$	1683.11	−	1222.85i	0.0592499	−	0.0430476i
$932$	−53010.8			−1.86312
$933$		0			0
$934$	−39.9542	−	122.966i	−0.00139972	−	0.00430790i
$935$	−9677.58	+	46148.5i	−0.338493	+	1.61414i
$936$		0			0
$937$	12281.9	+	37799.9i	0.428211	+	1.31790i	0.899886	+	0.436126i	$0.143650\pi$
$937$	12281.9	+	37799.9i	0.428211	+	1.31790i	−0.471675	+	0.881773i	$0.656350\pi$
$938$	129.166	+	397.532i	0.00449618	+	0.0138378i
$939$		0			0
$940$	6375.53	−	30402.4i	0.221220	−	1.05491i
$941$	−202.289	−	622.581i	−0.00700789	−	0.0215681i	0.947491	−	0.319781i	$-0.103609\pi$
$941$	−202.289	−	622.581i	−0.00700789	−	0.0215681i	−0.954499	+	0.298213i	$0.903609\pi$
$942$		0			0
$943$	32552.0			1.12411
$944$	−32594.4	+	23681.2i	−1.12379	+	0.816481i
$945$		0			0
$946$	344.547	+	250.328i	0.0118416	+	0.00860345i
$947$	−23454.4	−	17040.6i	−0.804820	−	0.584736i	0.107504	−	0.994205i	$-0.465714\pi$
$947$	−23454.4	−	17040.6i	−0.804820	−	0.584736i	−0.912324	+	0.409468i	$0.865714\pi$
$948$		0			0
$949$	−2661.77			−0.0910481
$950$	53.2372	−	59.7791i	0.00181815	−	0.00204157i
$951$		0			0
$952$	−2962.15	+	9116.55i	−0.100844	+	0.310367i
$953$	−40357.9	−	29321.7i	−1.37179	−	0.996667i	−0.997595	−	0.0693187i	$-0.977917\pi$
$953$	−40357.9	−	29321.7i	−1.37179	−	0.996667i	−0.374200	−	0.927348i	$-0.622083\pi$
$954$		0			0
$955$	−8419.68	+	40150.1i	−0.285292	+	1.36045i
$956$	−10438.9	+	7584.33i	−0.353158	+	0.256585i
$957$		0			0
$958$	860.229	−	624.993i	0.0290112	−	0.0210779i
$959$	−23177.9	−	71334.2i	−0.780451	−	2.40198i
$960$		0			0
$961$	−16.8730	+	51.9297i	−0.000566378	+	0.00174313i
$962$	−299.371	−	921.370i	−0.0100334	−	0.0308796i
$963$		0			0
$964$	1895.52	−	5833.82i	0.0633306	−	0.194912i
$965$	32827.3	+	18833.5i	1.09507	+	0.628262i
$966$		0			0
$967$	32490.0	−	23605.4i	1.08046	−	0.785002i	0.102699	−	0.994712i	$-0.467252\pi$
$967$	32490.0	−	23605.4i	1.08046	−	0.785002i	0.977764	+	0.209711i	$0.0672522\pi$
$968$	634.538			0.0210690
$969$		0			0
$970$	−2940.72	+	317.201i	−0.0973411	+	0.0104997i
$971$	28722.9	+	20868.4i	0.949291	+	0.689701i	0.950639	−	0.310299i	$-0.100429\pi$
$971$	28722.9	+	20868.4i	0.949291	+	0.689701i	−0.00134777	+	0.999999i	$0.500429\pi$
$972$		0			0
$973$	−21354.2	+	65721.6i	−0.703582	+	2.16540i
$974$	−619.934			−0.0203942
$975$		0			0
$976$	−22786.4			−0.747309
$977$	−14940.7	+	45982.6i	−0.489247	+	1.50575i	0.336488	+	0.941688i	$0.390761\pi$
$977$	−14940.7	+	45982.6i	−0.489247	+	1.50575i	−0.825735	+	0.564059i	$0.809239\pi$
$978$		0			0
$979$	15453.3	+	11227.5i	0.504484	+	0.366529i
$980$	18904.1	+	42149.4i	0.616195	+	1.37389i
$981$		0			0
$982$	1775.69			0.0577033
$983$	3916.78	−	2845.71i	0.127086	−	0.0923336i	−0.522426	−	0.852684i	$-0.674973\pi$
$983$	3916.78	−	2845.71i	0.127086	−	0.0923336i	0.649513	+	0.760351i	$0.274973\pi$
$984$		0			0
$985$	−1166.36	−	2600.56i	−0.0377293	−	0.0841225i
$986$	1394.15	−	4290.76i	0.0450293	−	0.138586i
$987$		0			0
$988$	−288.876	−	889.069i	−0.00930200	−	0.0286286i
$989$	−3234.25	+	9953.99i	−0.103987	+	0.320039i
$990$		0			0
$991$	−13338.1	−	41050.3i	−0.427545	−	1.31585i	−0.900536	−	0.434782i	$-0.856826\pi$
$991$	−13338.1	−	41050.3i	−0.427545	−	1.31585i	0.472991	−	0.881068i	$-0.343174\pi$
$992$	4253.79	−	3090.56i	0.136147	−	0.0989167i
$993$		0			0
$994$	2033.86	−	1477.68i	0.0648994	−	0.0471522i
$995$	15403.7	+	8837.35i	0.490784	+	0.281571i
$996$		0			0
$997$	−16995.7	−	12348.1i	−0.539880	−	0.392246i	0.284161	−	0.958777i	$-0.408285\pi$
$997$	−16995.7	−	12348.1i	−0.539880	−	0.392246i	−0.824040	+	0.566531i	$0.808285\pi$
$998$	916.703	−	2821.32i	0.0290759	−	0.0894863i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.d.46.9	yes	64
3.2	odd	2	inner	225.4.h.d.46.8	✓	64
25.6	even	5	inner	225.4.h.d.181.9	yes	64
75.56	odd	10	inner	225.4.h.d.181.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.h.d.46.8	✓	64	3.2	odd	2	inner
225.4.h.d.46.9	yes	64	1.1	even	1	trivial
225.4.h.d.181.8	yes	64	75.56	odd	10	inner
225.4.h.d.181.9	yes	64	25.6	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.0492832 - 0.151678i) q^{2} +(6.45156 + 4.68733i) q^{4} +(9.69768 + 5.56372i) q^{5} +29.3448 q^{7} +(2.06112 - 1.49749i) q^{8} +O(q^{10})\)	\(q+(0.0492832 - 0.151678i) q^{2} +(6.45156 + 4.68733i) q^{4} +(9.69768 + 5.56372i) q^{5} +29.3448 q^{7} +(2.06112 - 1.49749i) q^{8} +(1.32183 - 1.19673i) q^{10} +(10.1644 - 31.2829i) q^{11} +(-9.02150 - 27.7653i) q^{13} +(1.44621 - 4.45096i) q^{14} +(19.5887 + 60.2877i) q^{16} +(-103.730 + 75.3644i) q^{17} +(3.24851 - 2.36018i) q^{19} +(36.4862 + 81.3509i) q^{20} +(-4.24399 - 3.08344i) q^{22} +(39.8382 - 122.609i) q^{23} +(63.0901 + 107.910i) q^{25} -4.65600 q^{26} +(189.320 + 137.549i) q^{28} +(-178.493 - 129.683i) q^{29} +(139.509 - 101.359i) q^{31} +30.4912 q^{32} +(6.31897 + 19.4478i) q^{34} +(284.577 + 163.266i) q^{35} +(64.2980 + 197.889i) q^{37} +(-0.197890 - 0.609044i) q^{38} +(28.3197 - 3.05470i) q^{40} +(78.0265 + 240.141i) q^{41} -81.1845 q^{43} +(212.210 - 154.179i) q^{44} +(-16.6338 - 12.0852i) q^{46} +(-281.870 - 204.790i) q^{47} +518.118 q^{49} +(19.4769 - 4.25122i) q^{50} +(71.9425 - 221.416i) q^{52} +(-324.991 - 236.120i) q^{53} +(272.621 - 246.820i) q^{55} +(60.4832 - 43.9436i) q^{56} +(-28.4668 + 20.6823i) q^{58} +(196.402 + 604.462i) q^{59} +(-111.080 + 341.868i) q^{61} +(-8.49851 - 26.1557i) q^{62} +(-155.207 + 477.677i) q^{64} +(66.9907 - 319.452i) q^{65} +(-72.2562 + 52.4972i) q^{67} -1022.48 q^{68} +(38.7888 - 35.1178i) q^{70} +(434.583 + 315.743i) q^{71} +(28.1745 - 86.7122i) q^{73} +33.1842 q^{74} +32.0209 q^{76} +(298.273 - 917.991i) q^{77} +(-1076.93 - 782.439i) q^{79} +(-145.459 + 693.636i) q^{80} +40.2695 q^{82} +(-148.238 + 107.701i) q^{83} +(-1425.25 + 153.734i) q^{85} +(-4.00103 + 12.3139i) q^{86} +(-25.8957 - 79.6989i) q^{88} +(-179.451 + 552.293i) q^{89} +(-264.734 - 814.768i) q^{91} +(831.729 - 604.287i) q^{92} +(-44.9536 + 32.6607i) q^{94} +(44.6344 - 4.81449i) q^{95} +(-1342.00 - 975.019i) q^{97} +(25.5345 - 78.5871i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) 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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