LMFDB - Embedded newform 189.4.e.f.163.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(109,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("189.109");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.e (of order $3$, degree $2$, 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:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 44 x^{12} + 23 x^{11} + 1346 x^{10} + 854 x^{9} + 20545 x^{8} + 27750 x^{7} + \cdots + 254016 $ x^14 - x^13 + 44x^12 + 23x^11 + 1346x^10 + 854x^9 + 20545x^8 + 27750x^7 + 221349x^6 + 172746x^5 + 551772x^4 + 275616x^3 + 1006128x^2 + 471744x + 254016
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.5
Root			$-0.815927 + 1.41323i$ of defining polynomial
Character	$\chi$	$=$	189.163
Dual form			189.4.e.f.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.815927 - 1.41323i) q^{2} +(2.66853 + 4.62202i) q^{4} +(-6.18949 + 10.7205i) q^{5} +(-6.28171 - 17.4224i) q^{7} +21.7641 q^{8} +(10.1003 + 17.4943i) q^{10} +(14.5026 + 25.1192i) q^{11} -52.9884 q^{13} +(-29.7472 - 5.33792i) q^{14} +(-3.59026 + 6.21851i) q^{16} +(61.0234 + 105.696i) q^{17} +(-70.5524 + 122.200i) q^{19} -66.0672 q^{20} +47.3321 q^{22} +(-30.1496 + 52.2206i) q^{23} +(-14.1195 - 24.4556i) q^{25} +(-43.2346 + 74.8846i) q^{26} +(63.7638 - 75.5263i) q^{28} -126.997 q^{29} +(-75.4244 - 130.639i) q^{31} +(92.9153 + 160.934i) q^{32} +199.163 q^{34} +(225.658 + 40.4926i) q^{35} +(170.791 - 295.818i) q^{37} +(115.131 + 199.413i) q^{38} +(-134.709 + 233.322i) q^{40} +292.082 q^{41} +290.696 q^{43} +(-77.4008 + 134.062i) q^{44} +(49.1998 + 85.2165i) q^{46} +(-142.041 + 246.022i) q^{47} +(-264.080 + 218.885i) q^{49} -46.0818 q^{50} +(-141.401 - 244.913i) q^{52} +(-193.996 - 336.011i) q^{53} -359.053 q^{55} +(-136.716 - 379.183i) q^{56} +(-103.621 + 179.476i) q^{58} +(-134.656 - 233.231i) q^{59} +(119.803 - 207.505i) q^{61} -246.163 q^{62} +245.804 q^{64} +(327.971 - 568.062i) q^{65} +(356.125 + 616.827i) q^{67} +(-325.685 + 564.103i) q^{68} +(241.345 - 285.866i) q^{70} +270.507 q^{71} +(-73.0414 - 126.511i) q^{73} +(-278.706 - 482.732i) q^{74} -753.083 q^{76} +(346.535 - 410.461i) q^{77} +(326.396 - 565.334i) q^{79} +(-44.4437 - 76.9787i) q^{80} +(238.318 - 412.779i) q^{82} -35.0239 q^{83} -1510.81 q^{85} +(237.186 - 410.819i) q^{86} +(315.635 + 546.696i) q^{88} +(697.278 - 1207.72i) q^{89} +(332.858 + 923.184i) q^{91} -321.820 q^{92} +(231.790 + 401.473i) q^{94} +(-873.366 - 1512.71i) q^{95} +805.822 q^{97} +(93.8642 + 551.800i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 31 q^{4} + q^{5} + 20 q^{7} + 168 q^{8} - 12 q^{10} - 98 q^{11} - 248 q^{13} - 134 q^{14} - 139 q^{16} - 30 q^{17} - 182 q^{19} - 220 q^{20} + 552 q^{22} + 6 q^{23} - 388 q^{25} + 245 q^{26}+ \cdots + 10160 q^{98}+O(q^{100}) $ 14 * q - q^2 - 31 * q^4 + q^5 + 20 * q^7 + 168 * q^8 - 12 * q^10 - 98 * q^11 - 248 * q^13 - 134 * q^14 - 139 * q^16 - 30 * q^17 - 182 * q^19 - 220 * q^20 + 552 * q^22 + 6 * q^23 - 388 * q^25 + 245 * q^26 + 425 * q^28 + 646 * q^29 - 26 * q^31 - 398 * q^32 + 228 * q^34 + 1025 * q^35 + 112 * q^37 - 1015 * q^38 + 147 * q^40 - 1048 * q^41 + 16 * q^43 - 937 * q^44 + 339 * q^46 - 288 * q^47 + 446 * q^49 + 5152 * q^50 + 1075 * q^52 - 1353 * q^53 + 312 * q^55 + 1980 * q^56 + 81 * q^58 - 165 * q^59 - 56 * q^61 - 2430 * q^62 - 3412 * q^64 - 1694 * q^65 + 988 * q^67 - 2625 * q^68 - 4941 * q^70 + 1584 * q^71 - 1487 * q^73 - 2736 * q^74 + 3904 * q^76 - 34 * q^77 + 1273 * q^79 + 2501 * q^80 + 2049 * q^82 - 2340 * q^83 + 432 * q^85 + 160 * q^86 - 9 * q^88 - 1058 * q^89 + 3538 * q^91 + 7668 * q^92 - 1653 * q^94 - 3260 * q^95 - 7460 * q^97 + 10160 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.815927	−	1.41323i	0.288474	−	0.499651i	−0.684972	−	0.728570i	$-0.740185\pi$
$2$	0.815927	−	1.41323i	0.288474	−	0.499651i	0.973446	+	0.228918i	$0.0735188\pi$
$3$		0			0
$3$		0			0
$4$	2.66853	+	4.62202i	0.333566	+	0.577753i
$5$	−6.18949	+	10.7205i	−0.553604	+	0.958871i	0.444406	+	0.895825i	$0.353415\pi$
$5$	−6.18949	+	10.7205i	−0.553604	+	0.958871i	−0.998011	+	0.0630456i	$0.979919\pi$
$6$		0			0
$7$	−6.28171	−	17.4224i	−0.339181	−	0.940721i
$7$	−6.28171	−	17.4224i	−0.339181	−	0.940721i
$8$	21.7641			0.961848
$9$		0			0
$10$	10.1003	+	17.4943i	0.319401	+	0.553218i
$11$	14.5026	+	25.1192i	0.397517	+	0.688519i	0.993419	−	0.114538i	$-0.0365387\pi$
$11$	14.5026	+	25.1192i	0.397517	+	0.688519i	−0.595902	+	0.803057i	$0.703205\pi$
$12$		0			0
$13$	−52.9884			−1.13049			−0.565243	−	0.824924i	$-0.691218\pi$
$13$	−52.9884			−1.13049			−0.565243	+	0.824924i	$0.691218\pi$
$14$	−29.7472	−	5.33792i	−0.567877	−	0.101901i
$15$		0			0
$16$	−3.59026	+	6.21851i	−0.0560978	+	0.0971642i
$17$	61.0234	+	105.696i	0.870609	+	1.50794i	0.861368	+	0.507982i	$0.169608\pi$
$17$	61.0234	+	105.696i	0.870609	+	1.50794i	0.00924125	+	0.999957i	$0.497058\pi$
$18$		0			0
$19$	−70.5524	+	122.200i	−0.851885	+	1.47551i	0.0276192	+	0.999619i	$0.491207\pi$
$19$	−70.5524	+	122.200i	−0.851885	+	1.47551i	−0.879505	+	0.475890i	$0.842126\pi$
$20$	−66.0672			−0.738654
$21$		0			0
$22$	47.3321			0.458693
$23$	−30.1496	+	52.2206i	−0.273332	+	0.473424i	−0.969713	−	0.244248i	$-0.921459\pi$
$23$	−30.1496	+	52.2206i	−0.273332	+	0.473424i	0.696381	+	0.717672i	$0.254792\pi$
$24$		0			0
$25$	−14.1195	−	24.4556i	−0.112956	−	0.195645i
$26$	−43.2346	+	74.8846i	−0.326116	+	0.564849i
$27$		0			0
$28$	63.7638	−	75.5263i	0.430365	−	0.509755i
$29$	−126.997			−0.813201			−0.406601	−	0.913606i	$-0.633286\pi$
$29$	−126.997			−0.813201			−0.406601	+	0.913606i	$0.633286\pi$
$30$		0			0
$31$	−75.4244	−	130.639i	−0.436988	−	0.756885i	0.560468	−	0.828176i	$-0.310621\pi$
$31$	−75.4244	−	130.639i	−0.436988	−	0.756885i	−0.997456	+	0.0712915i	$0.977288\pi$
$32$	92.9153	+	160.934i	0.513289	+	0.889043i
$33$		0			0
$34$	199.163			1.00459
$35$	225.658	+	40.4926i	1.08980	+	0.195557i
$36$		0			0
$37$	170.791	−	295.818i	0.758860	−	1.31438i	−0.184572	−	0.982819i	$-0.559090\pi$
$37$	170.791	−	295.818i	0.758860	−	1.31438i	0.943432	−	0.331565i	$-0.107577\pi$
$38$	115.131	+	199.413i	0.491493	+	0.851291i
$39$		0			0
$40$	−134.709	+	233.322i	−0.532483	+	0.922288i
$41$	292.082			1.11258			0.556288	−	0.830990i	$-0.312225\pi$
$41$	292.082			1.11258			0.556288	+	0.830990i	$0.312225\pi$
$42$		0			0
$43$	290.696			1.03095			0.515473	−	0.856906i	$-0.327616\pi$
$43$	290.696			1.03095			0.515473	+	0.856906i	$0.327616\pi$
$44$	−77.4008	+	134.062i	−0.265196	+	0.459333i
$45$		0			0
$46$	49.1998	+	85.2165i	0.157698	+	0.273141i
$47$	−142.041	+	246.022i	−0.440826	+	0.763533i	−0.997751	−	0.0670298i	$-0.978648\pi$
$47$	−142.041	+	246.022i	−0.440826	+	0.763533i	0.556925	+	0.830563i	$0.311981\pi$
$48$		0			0
$49$	−264.080	+	218.885i	−0.769913	+	0.638149i
$50$	−46.0818			−0.130339
$51$		0			0
$52$	−141.401	−	244.913i	−0.377091	−	0.653142i
$53$	−193.996	−	336.011i	−0.502782	−	0.870844i	−0.999995	−	0.00321513i	$-0.998977\pi$
$53$	−193.996	−	336.011i	−0.502782	−	0.870844i	0.497213	−	0.867628i	$-0.334357\pi$
$54$		0			0
$55$	−359.053			−0.880268
$56$	−136.716	−	379.183i	−0.326240	−	0.904831i
$57$		0			0
$58$	−103.621	+	179.476i	−0.234587	+	0.406317i
$59$	−134.656	−	233.231i	−0.297131	−	0.514646i	0.678348	−	0.734741i	$-0.262696\pi$
$59$	−134.656	−	233.231i	−0.297131	−	0.514646i	−0.975478	+	0.220096i	$0.929363\pi$
$60$		0			0
$61$	119.803	−	207.505i	0.251462	−	0.435546i	−0.712466	−	0.701706i	$-0.752422\pi$
$61$	119.803	−	207.505i	0.251462	−	0.435546i	0.963929	+	0.266161i	$0.0857552\pi$
$62$	−246.163			−0.504238
$63$		0			0
$64$	245.804			0.480087
$65$	327.971	−	568.062i	0.625842	−	1.08399i
$66$		0			0
$67$	356.125	+	616.827i	0.649367	+	1.12474i	0.983274	+	0.182131i	$0.0582994\pi$
$67$	356.125	+	616.827i	0.649367	+	1.12474i	−0.333907	+	0.942606i	$0.608367\pi$
$68$	−325.685	+	564.103i	−0.580811	+	1.00599i
$69$		0			0
$70$	241.345	−	285.866i	0.412090	−	0.488108i
$71$	270.507			0.452160			0.226080	−	0.974109i	$-0.427409\pi$
$71$	270.507			0.452160			0.226080	+	0.974109i	$0.427409\pi$
$72$		0			0
$73$	−73.0414	−	126.511i	−0.117108	−	0.202836i	0.801513	−	0.597978i	$-0.204029\pi$
$73$	−73.0414	−	126.511i	−0.117108	−	0.202836i	−0.918620	+	0.395142i	$0.870696\pi$
$74$	−278.706	−	482.732i	−0.437823	−	0.758331i
$75$		0			0
$76$	−753.083			−1.13664
$77$	346.535	−	410.461i	0.512875	−	0.607485i
$78$		0			0
$79$	326.396	−	565.334i	0.464841	−	0.805128i	−0.534354	−	0.845261i	$-0.679445\pi$
$79$	326.396	−	565.334i	0.464841	−	0.805128i	0.999194	+	0.0401334i	$0.0127783\pi$
$80$	−44.4437	−	76.9787i	−0.0621120	−	0.107581i
$81$		0			0
$82$	238.318	−	412.779i	0.320949	−	0.555900i
$83$	−35.0239			−0.0463178			−0.0231589	−	0.999732i	$-0.507372\pi$
$83$	−35.0239			−0.0463178			−0.0231589	+	0.999732i	$0.507372\pi$
$84$		0			0
$85$	−1510.81			−1.92789
$86$	237.186	−	410.819i	0.297401	−	0.515113i
$87$		0			0
$88$	315.635	+	546.696i	0.382350	+	0.662250i
$89$	697.278	−	1207.72i	0.830465	−	1.43841i	−0.0672053	−	0.997739i	$-0.521408\pi$
$89$	697.278	−	1207.72i	0.830465	−	1.43841i	0.897670	−	0.440668i	$-0.145258\pi$
$90$		0			0
$91$	332.858	+	923.184i	0.383439	+	1.06347i
$92$	−321.820			−0.364696
$93$		0			0
$94$	231.790	+	401.473i	0.254334	+	0.440519i
$95$	−873.366	−	1512.71i	−0.943215	−	1.63370i
$96$		0			0
$97$	805.822			0.843493			0.421746	−	0.906714i	$-0.361417\pi$
$97$	805.822			0.843493			0.421746	+	0.906714i	$0.361417\pi$
$98$	93.8642	+	551.800i	0.0967522	+	0.568777i
$99$		0			0
$100$	75.3563	−	130.521i	0.0753563	−	0.130521i
$101$	507.406	+	878.853i	0.499889	+	0.865833i	1.00000		0.000128157i	$-4.07938e-5\pi$
$101$	507.406	+	878.853i	0.499889	+	0.865833i	−0.500111	+	0.865961i	$0.666707\pi$
$102$		0			0
$103$	−519.694	+	900.137i	−0.497155	+	0.861098i	−0.999995	−	0.00328180i	$-0.998955\pi$
$103$	−519.694	+	900.137i	−0.497155	+	0.861098i	0.502839	+	0.864380i	$0.332289\pi$
$104$	−1153.25			−1.08736
$105$		0			0
$106$	−633.147			−0.580158
$107$	−304.169	+	526.836i	−0.274814	+	0.475992i	−0.970088	−	0.242753i	$-0.921950\pi$
$107$	−304.169	+	526.836i	−0.274814	+	0.475992i	0.695274	+	0.718745i	$0.255283\pi$
$108$		0			0
$109$	−538.856	−	933.326i	−0.473514	−	0.820151i	0.526026	−	0.850468i	$-0.323681\pi$
$109$	−538.856	−	933.326i	−0.473514	−	0.820151i	−0.999540	+	0.0303176i	$0.990348\pi$
$110$	−292.961	+	507.424i	−0.253934	+	0.439827i
$111$		0			0
$112$	130.894	+	23.4880i	0.110432	+	0.0198162i
$113$	2064.78			1.71893			0.859463	−	0.511199i	$-0.170798\pi$
$113$	2064.78			1.71893			0.859463	+	0.511199i	$0.170798\pi$
$114$		0			0
$115$	−373.221	−	646.438i	−0.302635	−	0.524180i
$116$	−338.896	−	586.985i	−0.271256	−	0.469829i
$117$		0			0
$118$	−439.478			−0.342858
$119$	1458.14	−	1727.12i	1.12326	−	1.33046i
$120$		0			0
$121$	244.852	−	424.096i	0.183961	−	0.318630i
$122$	−195.501	−	338.618i	−0.145081	−	0.251287i
$123$		0			0
$124$	402.544	−	697.226i	0.291528	−	0.504941i
$125$	−1197.80			−0.857078
$126$		0			0
$127$	−130.430			−0.0911320			−0.0455660	−	0.998961i	$-0.514509\pi$
$127$	−130.430			−0.0911320			−0.0455660	+	0.998961i	$0.514509\pi$
$128$	−542.764	+	940.094i	−0.374797	+	0.649167i
$129$		0			0
$130$	−535.200	−	926.994i	−0.361078	−	0.625406i
$131$	−952.534	+	1649.84i	−0.635292	+	1.10036i	0.351161	+	0.936315i	$0.385787\pi$
$131$	−952.534	+	1649.84i	−0.635292	+	1.10036i	−0.986453	+	0.164043i	$0.947546\pi$
$132$		0			0
$133$	2572.21	+	461.565i	1.67699	+	0.300923i
$134$	1162.29			0.749302
$135$		0			0
$136$	1328.12	+	2300.37i	0.837393	+	1.45041i
$137$	279.649	+	484.367i	0.174394	+	0.302060i	0.939952	−	0.341308i	$-0.110870\pi$
$137$	279.649	+	484.367i	0.174394	+	0.302060i	−0.765557	+	0.643368i	$0.777537\pi$
$138$		0			0
$139$	−699.079			−0.426583			−0.213292	−	0.976989i	$-0.568418\pi$
$139$	−699.079			−0.426583			−0.213292	+	0.976989i	$0.568418\pi$
$140$	415.015	+	1151.05i	0.250537	+	0.694867i
$141$		0			0
$142$	220.714	−	382.289i	0.130436	−	0.225922i
$143$	−768.466	−	1331.02i	−0.449387	−	0.778362i
$144$		0			0
$145$	786.049	−	1361.48i	0.450192	−	0.779755i
$146$	−238.386			−0.135130
$147$		0			0
$148$	1823.04			1.01252
$149$	−807.450	+	1398.54i	−0.443952	+	0.768948i	−0.997979	−	0.0635514i	$-0.979757\pi$
$149$	−807.450	+	1398.54i	−0.443952	+	0.768948i	0.554026	+	0.832499i	$0.313091\pi$
$150$		0			0
$151$	1.79636	+	3.11138i	0.000968116	+	0.00167683i	0.866509	−	0.499161i	$-0.166359\pi$
$151$	1.79636	+	3.11138i	0.000968116	+	0.00167683i	−0.865541	+	0.500838i	$0.833025\pi$
$152$	−1535.51	+	2659.58i	−0.819384	+	1.41921i
$153$		0			0
$154$	−297.327	−	824.639i	−0.155580	−	0.431502i
$155$	1867.35			0.967673
$156$		0			0
$157$	−348.873	−	604.266i	−0.177345	−	0.307170i	0.763626	−	0.645659i	$-0.223417\pi$
$157$	−348.873	−	604.266i	−0.177345	−	0.307170i	−0.940970	+	0.338490i	$0.890084\pi$
$158$	−532.631	−	922.543i	−0.268189	−	0.464517i
$159$		0			0
$160$	−2300.39			−1.13664
$161$	1099.20	+	197.243i	0.538069	+	0.0965525i
$162$		0			0
$163$	−72.9541	+	126.360i	−0.0350565	+	0.0607196i	−0.883021	−	0.469333i	$-0.844494\pi$
$163$	−72.9541	+	126.360i	−0.0350565	+	0.0607196i	0.847965	+	0.530052i	$0.177828\pi$
$164$	779.429	+	1350.01i	0.371117	+	0.642793i
$165$		0			0
$166$	−28.5770	+	49.4968i	−0.0133615	+	0.0231427i
$167$	1816.18			0.841556			0.420778	−	0.907164i	$-0.361757\pi$
$167$	1816.18			0.841556			0.420778	+	0.907164i	$0.361757\pi$
$168$		0			0
$169$	610.766			0.278000
$170$	−1232.71	+	2135.12i	−0.556146	+	0.963274i
$171$		0			0
$172$	775.729	+	1343.60i	0.343888	+	0.595632i
$173$	−1212.34	+	2099.84i	−0.532790	+	0.922819i	0.466477	+	0.884533i	$0.345523\pi$
$173$	−1212.34	+	2099.84i	−0.532790	+	0.922819i	−0.999267	+	0.0382860i	$0.987810\pi$
$174$		0			0
$175$	−337.382	+	399.618i	−0.145735	+	0.172619i
$176$	−208.272			−0.0891992
$177$		0			0
$178$	−1137.86	−	1970.83i	−0.479135	−	0.829886i
$179$	−1417.68	−	2455.50i	−0.591969	−	1.02532i	−0.993967	−	0.109680i	$-0.965017\pi$
$179$	−1417.68	−	2455.50i	−0.591969	−	1.02532i	0.401998	−	0.915641i	$-0.368316\pi$
$180$		0			0
$181$	−219.212			−0.0900214			−0.0450107	−	0.998987i	$-0.514332\pi$
$181$	−219.212			−0.0900214			−0.0450107	+	0.998987i	$0.514332\pi$
$182$	1576.26	+	282.848i	0.641978	+	0.115198i
$183$		0			0
$184$	−656.180	+	1136.54i	−0.262903	+	0.455362i
$185$	2114.21	+	3661.93i	0.840217	+	1.45530i
$186$		0			0
$187$	−1769.99	+	3065.71i	−0.692163	+	1.19886i
$188$	−1516.16			−0.588178
$189$		0			0
$190$	−2850.41			−1.08837
$191$	−111.712	+	193.491i	−0.0423205	+	0.0733012i	−0.886410	−	0.462901i	$-0.846808\pi$
$191$	−111.712	+	193.491i	−0.0423205	+	0.0733012i	0.844089	+	0.536203i	$0.180142\pi$
$192$		0			0
$193$	176.079	+	304.978i	0.0656708	+	0.113745i	0.896991	−	0.442048i	$-0.145748\pi$
$193$	176.079	+	304.978i	0.0656708	+	0.113745i	−0.831321	+	0.555793i	$0.812415\pi$
$194$	657.492	−	1138.81i	0.243326	−	0.421452i
$195$		0			0
$196$	−1716.40	−	636.484i	−0.625509	−	0.231955i
$197$	5347.45			1.93396			0.966981	−	0.254850i	$-0.0820261\pi$
$197$	5347.45			1.93396			0.966981	+	0.254850i	$0.0820261\pi$
$198$		0			0
$199$	−291.114	−	504.224i	−0.103701	−	0.179616i	0.809506	−	0.587112i	$-0.199735\pi$
$199$	−291.114	−	504.224i	−0.103701	−	0.179616i	−0.913207	+	0.407496i	$0.866402\pi$
$200$	−307.298	−	532.256i	−0.108646	−	0.188181i
$201$		0			0
$202$	1656.03			0.576820
$203$	797.762	+	2212.60i	0.275822	+	0.764996i
$204$		0			0
$205$	−1807.84	+	3131.27i	−0.615927	+	1.06682i
$206$	848.065	+	1468.89i	0.286833	+	0.496809i
$207$		0			0
$208$	190.242	−	329.509i	0.0634178	−	0.109843i
$209$	−4092.76			−1.35455
$210$		0			0
$211$	5467.96			1.78403			0.892014	−	0.452008i	$-0.149292\pi$
$211$	5467.96			1.78403			0.892014	+	0.452008i	$0.149292\pi$
$212$	1035.37	−	1793.31i	0.335421	−	0.580967i
$213$		0			0
$214$	496.359	+	859.720i	0.158553	+	0.274623i
$215$	−1799.26	+	3116.40i	−0.570736	+	0.988544i
$216$		0			0
$217$	−1802.25	+	2134.71i	−0.563800	+	0.667804i
$218$	−1758.67			−0.546386
$219$		0			0
$220$	−958.143	−	1659.55i	−0.293627	−	0.508577i
$221$	−3233.53	−	5600.64i	−0.984212	−	1.70470i
$222$		0			0
$223$	4368.05			1.31169			0.655844	−	0.754897i	$-0.272313\pi$
$223$	4368.05			1.31169			0.655844	+	0.754897i	$0.272313\pi$
$224$	2220.19	−	2629.75i	0.662244	−	0.784408i
$225$		0			0
$226$	1684.71	−	2918.01i	0.495865	−	0.858863i
$227$	−318.476	−	551.617i	−0.0931189	−	0.161287i	0.815703	−	0.578471i	$-0.196350\pi$
$227$	−318.476	−	551.617i	−0.0931189	−	0.161287i	−0.908822	+	0.417184i	$0.863017\pi$
$228$		0			0
$229$	−491.748	+	851.732i	−0.141902	+	0.245782i	−0.928213	−	0.372049i	$-0.878655\pi$
$229$	−491.748	+	851.732i	−0.141902	+	0.245782i	0.786311	+	0.617831i	$0.211989\pi$
$230$	−1218.09			−0.349209
$231$		0			0
$232$	−2763.99			−0.782176
$233$	838.684	−	1452.64i	0.235811	−	0.408437i	−0.723697	−	0.690118i	$-0.757559\pi$
$233$	838.684	−	1452.64i	0.235811	−	0.408437i	0.959508	+	0.281681i	$0.0908919\pi$
$234$		0			0
$235$	−1758.32	−	3045.50i	−0.488086	−	0.845390i
$236$	718.666	−	1244.77i	0.198225	−	0.343336i
$237$		0			0
$238$	−1251.08	−	3469.89i	−0.340738	−	0.945041i
$239$	−2705.18			−0.732148			−0.366074	−	0.930586i	$-0.619298\pi$
$239$	−2705.18			−0.732148			−0.366074	+	0.930586i	$0.619298\pi$
$240$		0			0
$241$	1070.36	+	1853.93i	0.286092	+	0.495527i	0.972873	−	0.231338i	$-0.0743102\pi$
$241$	1070.36	+	1853.93i	0.286092	+	0.495527i	−0.686781	+	0.726864i	$0.740977\pi$
$242$	−399.563	−	692.063i	−0.106136	−	0.183833i
$243$		0			0
$244$	1278.79			0.335517
$245$	−712.038	−	4185.86i	−0.185675	−	1.09153i
$246$		0			0
$247$	3738.45	−	6475.19i	0.963045	−	1.66804i
$248$	−1641.55	−	2843.24i	−0.420315	−	0.728008i
$249$		0			0
$250$	−977.320	+	1692.77i	−0.247244	+	0.428240i
$251$	918.484			0.230973			0.115486	−	0.993309i	$-0.463157\pi$
$251$	918.484			0.230973			0.115486	+	0.993309i	$0.463157\pi$
$252$		0			0
$253$	−1748.98			−0.434616
$254$	−106.421	+	184.327i	−0.0262892	+	0.0455343i
$255$		0			0
$256$	1868.93	+	3237.08i	0.456281	+	0.790303i
$257$	−2116.09	+	3665.17i	−0.513611	+	0.889600i	0.486265	+	0.873812i	$0.338359\pi$
$257$	−2116.09	+	3665.17i	−0.513611	+	0.889600i	−0.999875	+	0.0157883i	$0.994974\pi$
$258$		0			0
$259$	−6226.72	−	1117.34i	−1.49386	−	0.268062i
$260$	3500.79			0.835038
$261$		0			0
$262$	1554.40	+	2692.29i	0.366530	+	0.634849i
$263$	−2912.53	−	5044.64i	−0.682867	−	1.18276i	−0.974102	−	0.226109i	$-0.927399\pi$
$263$	−2912.53	−	5044.64i	−0.682867	−	1.18276i	0.291235	−	0.956652i	$-0.405934\pi$
$264$		0			0
$265$	4802.95			1.11337
$266$	2751.03	−	3258.52i	0.634123	−	0.751100i
$267$		0			0
$268$	−1900.66	+	3292.03i	−0.433213	+	0.750347i
$269$	1296.11	+	2244.93i	0.293775	+	0.508833i	0.974699	−	0.223521i	$-0.0717551\pi$
$269$	1296.11	+	2244.93i	0.293775	+	0.508833i	−0.680924	+	0.732354i	$0.738422\pi$
$270$		0			0
$271$	1854.95	−	3212.86i	0.415793	−	0.720175i	−0.579718	−	0.814817i	$-0.696837\pi$
$271$	1854.95	−	3212.86i	0.415793	−	0.720175i	0.995511	+	0.0946424i	$0.0301708\pi$
$272$	−876.359			−0.195357
$273$		0			0
$274$	912.694			0.201233
$275$	409.537	−	709.338i	0.0898036	−	0.155544i
$276$		0			0
$277$	161.690	+	280.055i	0.0350722	+	0.0607469i	0.883029	−	0.469319i	$-0.155501\pi$
$277$	161.690	+	280.055i	0.0350722	+	0.0607469i	−0.847956	+	0.530066i	$0.822167\pi$
$278$	−570.397	+	987.957i	−0.123058	+	0.213143i
$279$		0			0
$280$	4911.24	+	881.286i	1.04822	+	0.188096i
$281$	4990.53			1.05947			0.529733	−	0.848165i	$-0.322292\pi$
$281$	4990.53			1.05947			0.529733	+	0.848165i	$0.322292\pi$
$282$		0			0
$283$	−1229.34	−	2129.27i	−0.258221	−	0.447251i	0.707545	−	0.706669i	$-0.249803\pi$
$283$	−1229.34	−	2129.27i	−0.258221	−	0.447251i	−0.965765	+	0.259417i	$0.916470\pi$
$284$	721.856	+	1250.29i	0.150825	+	0.261236i
$285$		0			0
$286$	−2508.05			−0.518546
$287$	−1834.78	−	5088.77i	−0.377364	−	1.04662i
$288$		0			0
$289$	−4991.22	+	8645.04i	−1.01592	+	1.75963i
$290$	−1282.72	−	2221.73i	−0.259737	−	0.449878i
$291$		0			0
$292$	389.826	−	675.198i	0.0781261	−	0.135318i
$293$	3028.06			0.603758			0.301879	−	0.953346i	$-0.402386\pi$
$293$	3028.06			0.603758			0.301879	+	0.953346i	$0.402386\pi$
$294$		0			0
$295$	3333.80			0.657972
$296$	3717.11	−	6438.23i	0.729908	−	1.26424i
$297$		0			0
$298$	1317.64	+	2282.22i	0.256137	+	0.443643i
$299$	1597.58	−	2767.09i	0.308998	−	0.535200i
$300$		0			0
$301$	−1826.07	−	5064.62i	−0.349677	−	0.969833i
$302$	5.86279			0.00111710
$303$		0			0
$304$	−506.602	−	877.461i	−0.0955777	−	0.165546i
$305$	1483.04	+	2568.70i	0.278421	+	0.482240i
$306$		0			0
$307$	−8277.86			−1.53890			−0.769450	−	0.638707i	$-0.779470\pi$
$307$	−8277.86			−1.53890			−0.769450	+	0.638707i	$0.779470\pi$
$308$	2821.90	+	506.368i	0.522053	+	0.0936786i
$309$		0			0
$310$	1523.62	−	2638.99i	0.279148	−	0.483499i
$311$	−412.036	−	713.667i	−0.0751267	−	0.130123i	0.826015	−	0.563649i	$-0.190603\pi$
$311$	−412.036	−	713.667i	−0.0751267	−	0.130123i	−0.901141	+	0.433525i	$0.857269\pi$
$312$		0			0
$313$	1213.90	−	2102.54i	0.219213	−	0.379688i	−0.735355	−	0.677683i	$-0.762984\pi$
$313$	1213.90	−	2102.54i	0.219213	−	0.379688i	0.954568	+	0.297994i	$0.0963177\pi$
$314$	−1138.62			−0.204637
$315$		0			0
$316$	3483.98			0.620219
$317$	−3985.18	+	6902.53i	−0.706088	+	1.22298i	0.260210	+	0.965552i	$0.416208\pi$
$317$	−3985.18	+	6902.53i	−0.706088	+	1.22298i	−0.966298	+	0.257428i	$0.917125\pi$
$318$		0			0
$319$	−1841.79	−	3190.07i	−0.323261	−	0.559905i
$320$	−1521.40	+	2635.15i	−0.265778	+	0.460341i
$321$		0			0
$322$	1175.62	−	1392.48i	0.203461	−	0.240994i
$323$	−17221.4			−2.96664
$324$		0			0
$325$	748.168	+	1295.86i	0.127695	+	0.221174i
$326$	119.051	+	206.202i	0.0202258	+	0.0350321i
$327$		0			0
$328$	6356.92			1.07013
$329$	5178.56	+	929.255i	0.867791	+	0.155719i
$330$		0			0
$331$	−1136.83	+	1969.05i	−0.188779	+	0.326975i	−0.944843	−	0.327523i	$-0.893786\pi$
$331$	−1136.83	+	1969.05i	−0.188779	+	0.326975i	0.756065	+	0.654497i	$0.227120\pi$
$332$	−93.4622	−	161.881i	−0.0154500	−	0.0267602i
$333$		0			0
$334$	1481.87	−	2566.67i	0.242767	−	0.420485i
$335$	−8816.92			−1.43797
$336$		0			0
$337$	3142.92			0.508030			0.254015	−	0.967200i	$-0.418249\pi$
$337$	3142.92			0.508030			0.254015	+	0.967200i	$0.418249\pi$
$338$	498.340	−	863.151i	0.0801957	−	0.138903i
$339$		0			0
$340$	−4031.65	−	6983.02i	−0.643079	−	1.11384i
$341$	2187.69	−	3789.19i	0.347420	−	0.601749i
$342$		0			0
$343$	5472.38	+	3225.94i	0.861460	+	0.507826i
$344$	6326.74			0.991613
$345$		0			0
$346$	1978.37	+	3426.63i	0.307392	+	0.532419i
$347$	−4483.37	−	7765.42i	−0.693602	−	1.20135i	−0.970650	−	0.240498i	$-0.922689\pi$
$347$	−4483.37	−	7765.42i	−0.693602	−	1.20135i	0.277048	−	0.960856i	$-0.410644\pi$
$348$		0			0
$349$	−140.981			−0.0216234			−0.0108117	−	0.999942i	$-0.503442\pi$
$349$	−140.981			−0.0216234			−0.0108117	+	0.999942i	$0.503442\pi$
$350$	289.473	+	802.856i	0.0442085	+	0.122613i
$351$		0			0
$352$	−2695.02	+	4667.91i	−0.408082	+	0.706819i
$353$	4104.49	+	7109.18i	0.618867	+	1.07191i	0.989693	+	0.143206i	$0.0457412\pi$
$353$	4104.49	+	7109.18i	0.618867	+	1.07191i	−0.370826	+	0.928702i	$0.620925\pi$
$354$		0			0
$355$	−1674.30	+	2899.98i	−0.250318	+	0.433563i
$356$	7442.82			1.10806
$357$		0			0
$358$	−4626.90			−0.683070
$359$	−4374.52	+	7576.90i	−0.643116	+	1.11391i	0.341618	+	0.939839i	$0.389025\pi$
$359$	−4374.52	+	7576.90i	−0.643116	+	1.11391i	−0.984733	+	0.174070i	$0.944308\pi$
$360$		0			0
$361$	−6525.77	−	11303.0i	−0.951418	−	1.64790i
$362$	−178.861	+	309.796i	−0.0259688	+	0.0449793i
$363$		0			0
$364$	−3378.74	+	4002.02i	−0.486522	+	0.576271i
$365$	1808.36			0.259325
$366$		0			0
$367$	2958.95	+	5125.05i	0.420860	+	0.728952i	0.996024	−	0.0890869i	$-0.0283949\pi$
$367$	2958.95	+	5125.05i	0.420860	+	0.728952i	−0.575163	+	0.818038i	$0.695062\pi$
$368$	−216.490	−	374.971i	−0.0306666	−	0.0531161i
$369$		0			0
$370$	6900.18			0.969522
$371$	−4635.50	+	5490.61i	−0.648687	+	0.768351i
$372$		0			0
$373$	−5830.36	+	10098.5i	−0.809342	+	1.40182i	0.103979	+	0.994579i	$0.466842\pi$
$373$	−5830.36	+	10098.5i	−0.809342	+	1.40182i	−0.913321	+	0.407241i	$0.866491\pi$
$374$	2888.37	+	5002.80i	0.399342	+	0.691681i
$375$		0			0
$376$	−3091.40	+	5354.46i	−0.424007	+	0.734402i
$377$	6729.39			0.919313
$378$		0			0
$379$	−14306.7			−1.93902			−0.969508	−	0.245060i	$-0.921192\pi$
$379$	−14306.7			−1.93902			−0.969508	+	0.245060i	$0.921192\pi$
$380$	4661.20	−	8073.43i	0.629248	−	1.08989i
$381$		0			0
$382$	182.298	+	315.750i	0.0244167	+	0.0422910i
$383$	−5420.24	+	9388.13i	−0.723136	+	1.25251i	0.236600	+	0.971607i	$0.423967\pi$
$383$	−5420.24	+	9388.13i	−0.723136	+	1.25251i	−0.959737	+	0.280902i	$0.909366\pi$
$384$		0			0
$385$	2255.47	+	6255.57i	0.298570	+	0.828087i
$386$	574.671			0.0757772
$387$		0			0
$388$	2150.36	+	3724.53i	0.281360	+	0.487330i
$389$	5587.73	+	9678.23i	0.728301	+	1.26145i	0.957601	+	0.288099i	$0.0930231\pi$
$389$	5587.73	+	9678.23i	0.728301	+	1.26145i	−0.229300	+	0.973356i	$0.573644\pi$
$390$		0			0
$391$	−7359.33			−0.951860
$392$	−5747.47	+	4763.84i	−0.740539	+	0.613802i
$393$		0			0
$394$	4363.13	−	7557.17i	0.557897	−	0.966306i
$395$	4040.45	+	6998.26i	0.514676	+	0.891444i
$396$		0			0
$397$	6538.94	−	11325.8i	0.826650	−	1.43180i	−0.0740015	−	0.997258i	$-0.523577\pi$
$397$	6538.94	−	11325.8i	0.826650	−	1.43180i	0.900652	−	0.434542i	$-0.143090\pi$
$398$	−950.111			−0.119660
$399$		0			0
$400$	202.770			0.0253463
$401$	−1366.82	+	2367.40i	−0.170213	+	0.294818i	−0.938494	−	0.345294i	$-0.887779\pi$
$401$	−1366.82	+	2367.40i	−0.170213	+	0.294818i	0.768281	+	0.640113i	$0.221112\pi$
$402$		0			0
$403$	3996.61	+	6922.34i	0.494009	+	0.855648i
$404$	−2708.05	+	4690.48i	−0.333492	+	0.577624i
$405$		0			0
$406$	3777.82	+	677.903i	0.461799	+	0.0828664i
$407$	9907.60			1.20664
$408$		0			0
$409$	−5760.54	−	9977.55i	−0.696431	−	1.20625i	−0.969696	−	0.244316i	$-0.921437\pi$
$409$	−5760.54	−	9977.55i	−0.696431	−	1.20625i	0.273264	−	0.961939i	$-0.411897\pi$
$410$	2950.13	+	5109.78i	0.355357	+	0.615497i
$411$		0			0
$412$	−5547.27			−0.663336
$413$	−3217.57	+	3811.12i	−0.383357	+	0.454075i
$414$		0			0
$415$	216.780	−	375.474i	0.0256417	−	0.0444128i
$416$	−4923.43	−	8527.63i	−0.580267	−	1.00505i
$417$		0			0
$418$	−3339.39	+	5784.00i	−0.390754	+	0.676805i
$419$	−2426.62			−0.282931			−0.141465	−	0.989943i	$-0.545181\pi$
$419$	−2426.62			−0.282931			−0.141465	+	0.989943i	$0.545181\pi$
$420$		0			0
$421$	10188.2			1.17943			0.589716	−	0.807611i	$-0.299240\pi$
$421$	10188.2			1.17943			0.589716	+	0.807611i	$0.299240\pi$
$422$	4461.46	−	7727.47i	0.514645	−	0.891392i
$423$		0			0
$424$	−4222.16	−	7312.99i	−0.483599	−	0.837619i
$425$	1723.24	−	2984.73i	0.196681	−	0.340661i
$426$		0			0
$427$	−4367.80	−	783.770i	−0.495018	−	0.0888274i
$428$	−3246.73			−0.366674
$429$		0			0
$430$	2936.12	+	5085.52i	0.329285	+	0.570338i
$431$	3390.20	+	5872.00i	0.378887	+	0.656251i	0.990901	−	0.134596i	$-0.0429737\pi$
$431$	3390.20	+	5872.00i	0.378887	+	0.656251i	−0.612014	+	0.790847i	$0.709640\pi$
$432$		0			0
$433$	6122.85			0.679550			0.339775	−	0.940507i	$-0.389649\pi$
$433$	6122.85			0.679550			0.339775	+	0.940507i	$0.389649\pi$
$434$	1546.33	+	4288.75i	0.171028	+	0.474347i
$435$		0			0
$436$	2875.90	−	4981.21i	0.315896	−	0.547148i
$437$	−4254.25	−	7368.58i	−0.465694	−	0.806606i
$438$		0			0
$439$	7873.75	−	13637.7i	0.856022	−	1.48267i	−0.0196718	−	0.999806i	$-0.506262\pi$
$439$	7873.75	−	13637.7i	0.856022	−	1.48267i	0.875694	−	0.482867i	$-0.160405\pi$
$440$	−7814.48			−0.846684
$441$		0			0
$442$	−10553.3			−1.13568
$443$	−7531.88	+	13045.6i	−0.807789	+	1.39913i	0.106604	+	0.994302i	$0.466002\pi$
$443$	−7531.88	+	13045.6i	−0.807789	+	1.39913i	−0.914392	+	0.404829i	$0.867331\pi$
$444$		0			0
$445$	8631.59	+	14950.4i	0.919498	+	1.59262i
$446$	3564.01	−	6173.05i	0.378388	−	0.655387i
$447$		0			0
$448$	−1544.07	−	4282.50i	−0.162836	−	0.451628i
$449$	−175.064			−0.0184004			−0.00920020	−	0.999958i	$-0.502929\pi$
$449$	−175.064			−0.0184004			−0.00920020	+	0.999958i	$0.502929\pi$
$450$		0			0
$451$	4235.94	+	7336.86i	0.442267	+	0.766029i
$452$	5509.93	+	9543.48i	0.573374	+	0.993114i
$453$		0			0
$454$	−1039.41			−0.107450
$455$	−11957.2	−	2145.63i	−1.23201	−	0.221075i
$456$		0			0
$457$	6296.73	−	10906.3i	0.644527	−	1.11635i	−0.339884	−	0.940467i	$-0.610388\pi$
$457$	6296.73	−	10906.3i	0.644527	−	1.11635i	0.984411	−	0.175886i	$-0.0562790\pi$
$458$	802.461	+	1389.90i	0.0818701	+	0.141803i
$459$		0			0
$460$	1991.90	−	3450.07i	0.201897	−	0.349697i
$461$	13781.7			1.39236			0.696182	−	0.717865i	$-0.254881\pi$
$461$	13781.7			1.39236			0.696182	+	0.717865i	$0.254881\pi$
$462$		0			0
$463$	8867.45			0.890076			0.445038	−	0.895512i	$-0.353190\pi$
$463$	8867.45			0.890076			0.445038	+	0.895512i	$0.353190\pi$
$464$	455.954	−	789.735i	0.0456188	−	0.0790141i
$465$		0			0
$466$	−1368.61	−	2370.50i	−0.136051	−	0.235647i
$467$	6419.52	−	11118.9i	0.636103	−	1.10176i	−0.350177	−	0.936683i	$-0.613879\pi$
$467$	6419.52	−	11118.9i	0.636103	−	1.10176i	0.986280	−	0.165079i	$-0.0527880\pi$
$468$		0			0
$469$	8509.53	−	10079.3i	0.837811	−	0.992362i
$470$	−5738.65			−0.563201
$471$		0			0
$472$	−2930.67	−	5076.07i	−0.285794	−	0.495011i
$473$	4215.83	+	7302.03i	0.409818	+	0.709826i
$474$		0			0
$475$	3984.65			0.384902
$476$	11873.9	+	2130.68i	1.14336	+	0.205167i
$477$		0			0
$478$	−2207.23	+	3823.03i	−0.211206	+	0.365819i
$479$	−4977.61	−	8621.47i	−0.474807	−	0.822390i	0.524777	−	0.851240i	$-0.324149\pi$
$479$	−4977.61	−	8621.47i	−0.474807	−	0.822390i	−0.999584	+	0.0288499i	$0.990816\pi$
$480$		0			0
$481$	−9049.92	+	15674.9i	−0.857881	+	1.48589i
$482$	3493.36			0.330121
$483$		0			0
$484$	2613.58			0.245452
$485$	−4987.62	+	8638.82i	−0.466961	+	0.808801i
$486$		0			0
$487$	8357.99	+	14476.5i	0.777693	+	1.34700i	0.933268	+	0.359180i	$0.116944\pi$
$487$	8357.99	+	14476.5i	0.777693	+	1.34700i	−0.155575	+	0.987824i	$0.549723\pi$
$488$	2607.41	−	4516.16i	0.241869	−	0.418929i
$489$		0			0
$490$	−6496.54	−	2409.08i	−0.598947	−	0.222105i
$491$	−2981.39			−0.274029			−0.137014	−	0.990569i	$-0.543751\pi$
$491$	−2981.39			−0.274029			−0.137014	+	0.990569i	$0.543751\pi$
$492$		0			0
$493$	−7749.82	−	13423.1i	−0.707981	−	1.22626i
$494$	−6100.61	−	10566.6i	−0.555627	−	0.962374i
$495$		0			0
$496$	1083.17			0.0980561
$497$	−1699.25	−	4712.89i	−0.153364	−	0.425356i
$498$		0			0
$499$	−4084.74	+	7074.97i	−0.366449	+	0.634708i	−0.989008	−	0.147865i	$-0.952760\pi$
$499$	−4084.74	+	7074.97i	−0.366449	+	0.634708i	0.622559	+	0.782573i	$0.286093\pi$
$500$	−3196.37	−	5536.27i	−0.285892	−	0.495179i
$501$		0			0
$502$	749.416	−	1298.03i	0.0666296	−	0.115406i
$503$	−1858.71			−0.164763			−0.0823814	−	0.996601i	$-0.526253\pi$
$503$	−1858.71			−0.164763			−0.0823814	+	0.996601i	$0.526253\pi$
$504$		0			0
$505$	−12562.3			−1.10696
$506$	−1427.04	+	2471.71i	−0.125375	+	0.217156i
$507$		0			0
$508$	−348.055	−	602.849i	−0.0303985	−	0.0526518i
$509$	7374.51	−	12773.0i	0.642179	−	1.11229i	−0.342766	−	0.939421i	$-0.611364\pi$
$509$	7374.51	−	12773.0i	0.642179	−	1.11229i	0.984945	−	0.172866i	$-0.0553029\pi$
$510$		0			0
$511$	−1745.31	+	2067.27i	−0.151092	+	0.178964i
$512$	−2584.58			−0.223093
$513$		0			0
$514$	3453.15	+	5981.03i	0.296327	+	0.513253i
$515$	−6433.28	−	11142.8i	−0.550455	−	0.953415i
$516$		0			0
$517$	−8239.83			−0.700943
$518$	−6659.61	+	7888.11i	−0.564877	+	0.669080i
$519$		0			0
$520$	7138.00	−	12363.4i	0.601965	−	1.04263i
$521$	−6616.05	−	11459.3i	−0.556342	−	0.963613i	−0.997798	−	0.0663300i	$-0.978871\pi$
$521$	−6616.05	−	11459.3i	−0.556342	−	0.963613i	0.441455	−	0.897283i	$-0.354462\pi$
$522$		0			0
$523$	8050.47	−	13943.8i	0.673083	−	1.16581i	−0.303942	−	0.952691i	$-0.598303\pi$
$523$	8050.47	−	13943.8i	0.673083	−	1.16581i	0.977025	−	0.213124i	$-0.0683639\pi$
$524$	−10167.4			−0.847646
$525$		0			0
$526$	−9505.64			−0.787958
$527$	9205.30	−	15944.1i	0.760891	−	1.31790i
$528$		0			0
$529$	4265.50	+	7388.07i	0.350580	+	0.607222i
$530$	3918.86	−	6787.66i	0.321178	−	0.556296i
$531$		0			0
$532$	4730.65	+	13120.5i	0.385526	+	1.06926i
$533$	−15477.0			−1.25775
$534$		0			0
$535$	−3765.30	−	6521.69i	−0.304277	−	0.527023i
$536$	7750.75	+	13424.7i	0.624592	+	1.08183i
$537$		0			0
$538$	4230.14			0.338986
$539$	−9328.04	−	3459.08i	−0.745431	−	0.276425i
$540$		0			0
$541$	−1811.31	+	3137.28i	−0.143945	+	0.249320i	−0.928979	−	0.370133i	$-0.879312\pi$
$541$	−1811.31	+	3137.28i	−0.143945	+	0.249320i	0.785034	+	0.619453i	$0.212646\pi$
$542$	−3027.00	−	5242.92i	−0.239891	−	0.415503i
$543$		0			0
$544$	−11340.0	+	19641.5i	−0.893749	+	1.54802i
$545$	13341.0			1.04856
$546$		0			0
$547$	14543.8			1.13683			0.568417	−	0.822741i	$-0.307556\pi$
$547$	14543.8			1.13683			0.568417	+	0.822741i	$0.307556\pi$
$548$	−1492.50	+	2585.09i	−0.116344	+	0.201514i
$549$		0			0
$550$	−668.304	−	1157.54i	−0.0518120	−	0.0897410i
$551$	8959.97	−	15519.1i	0.692754	−	1.19989i
$552$		0			0
$553$	−11899.8	−	2135.33i	−0.915066	−	0.164202i
$554$	527.709			0.0404697
$555$		0			0
$556$	−1865.51	−	3231.16i	−0.142294	−	0.246460i
$557$	5766.65	+	9988.14i	0.438673	+	0.759804i	0.997587	−	0.0694212i	$-0.0221153\pi$
$557$	5766.65	+	9988.14i	0.438673	+	0.759804i	−0.558914	+	0.829225i	$0.688782\pi$
$558$		0			0
$559$	−15403.5			−1.16547
$560$	−1061.97	+	1257.87i	−0.0801366	+	0.0949194i
$561$		0			0
$562$	4071.91	−	7052.75i	0.305628	−	0.529363i
$563$	138.157	+	239.294i	0.0103421	+	0.0179131i	0.871150	−	0.491017i	$-0.163375\pi$
$563$	138.157	+	239.294i	0.0103421	+	0.0179131i	−0.860808	+	0.508930i	$0.830041\pi$
$564$		0			0
$565$	−12780.0	+	22135.5i	−0.951605	+	1.64823i
$566$	−4012.20			−0.297960
$567$		0			0
$568$	5887.36			0.434909
$569$	7864.76	−	13622.2i	0.579452	−	1.00364i	−0.416091	−	0.909323i	$-0.636600\pi$
$569$	7864.76	−	13622.2i	0.579452	−	1.00364i	0.995542	−	0.0943164i	$-0.0300665\pi$
$570$		0			0
$571$	−3859.15	−	6684.25i	−0.282838	−	0.489890i	0.689245	−	0.724529i	$-0.257943\pi$
$571$	−3859.15	−	6684.25i	−0.282838	−	0.489890i	−0.972083	+	0.234639i	$0.924609\pi$
$572$	4101.34	−	7103.74i	0.299800	−	0.519269i
$573$		0			0
$574$	−8688.64	−	1559.11i	−0.631806	−	0.113373i
$575$	1702.79			0.123498
$576$		0			0
$577$	−7819.21	−	13543.3i	−0.564156	−	0.977146i	−0.997128	−	0.0757390i	$-0.975868\pi$
$577$	−7819.21	−	13543.3i	−0.564156	−	0.977146i	0.432972	−	0.901407i	$-0.357465\pi$
$578$	8144.94	+	14107.4i	0.586133	+	1.01521i
$579$		0			0
$580$	8390.37			0.600674
$581$	220.010	+	610.201i	0.0157101	+	0.0435721i
$582$		0			0
$583$	5626.88	−	9746.04i	0.399728	−	0.692350i
$584$	−1589.68	−	2753.41i	−0.112640	−	0.195098i
$585$		0			0
$586$	2470.67	−	4279.33i	0.174168	−	0.301668i
$587$	14520.1			1.02097			0.510484	−	0.859888i	$-0.329466\pi$
$587$	14520.1			1.02097			0.510484	+	0.859888i	$0.329466\pi$
$588$		0			0
$589$	21285.5			1.48905
$590$	2720.14	−	4711.42i	0.189808	−	0.328756i
$591$		0			0
$592$	1226.37	+	2124.13i	0.0851407	+	0.147468i
$593$	2969.35	−	5143.07i	0.205627	−	0.356156i	−0.744706	−	0.667393i	$-0.767410\pi$
$593$	2969.35	−	5143.07i	0.205627	−	0.356156i	0.950332	+	0.311237i	$0.100743\pi$
$594$		0			0
$595$	9490.50	+	26322.0i	0.653904	+	1.81361i
$596$	−8618.80			−0.592349
$597$		0			0
$598$	−2607.01	−	4515.48i	−0.178276	−	0.308782i
$599$	−3632.41	−	6291.52i	−0.247774	−	0.429156i	0.715134	−	0.698987i	$-0.246366\pi$
$599$	−3632.41	−	6291.52i	−0.247774	−	0.429156i	−0.962908	+	0.269831i	$0.913032\pi$
$600$		0			0
$601$	−1691.27			−0.114789			−0.0573945	−	0.998352i	$-0.518279\pi$
$601$	−1691.27			−0.114789			−0.0573945	+	0.998352i	$0.518279\pi$
$602$	−8647.39	−	1551.71i	−0.585451	−	0.105055i
$603$		0			0
$604$	−9.58725	+	16.6056i	−0.000645860	+	0.00111866i
$605$	3031.02	+	5249.87i	0.203683	+	0.352790i
$606$		0			0
$607$	−8705.22	+	15077.9i	−0.582099	+	1.00822i	0.413131	+	0.910671i	$0.364435\pi$
$607$	−8705.22	+	15077.9i	−0.582099	+	1.00822i	−0.995230	+	0.0975534i	$0.968898\pi$
$608$	−26221.6			−1.74905
$609$		0			0
$610$	4840.21			0.321269
$611$	7526.52	−	13036.3i	0.498348	−	0.863164i
$612$		0			0
$613$	−5102.70	−	8838.13i	−0.336209	−	0.582331i	0.647507	−	0.762059i	$-0.275812\pi$
$613$	−5102.70	−	8838.13i	−0.336209	−	0.582331i	−0.983716	+	0.179728i	$0.942478\pi$
$614$	−6754.13	+	11698.5i	−0.443933	+	0.768914i
$615$		0			0
$616$	7542.03	−	8933.32i	0.493307	−	0.584308i
$617$	8936.08			0.583068			0.291534	−	0.956560i	$-0.405834\pi$
$617$	8936.08			0.583068			0.291534	+	0.956560i	$0.405834\pi$
$618$		0			0
$619$	9280.11	+	16073.6i	0.602584	+	1.04371i	0.992428	+	0.122825i	$0.0391953\pi$
$619$	9280.11	+	16073.6i	0.602584	+	1.04371i	−0.389845	+	0.920881i	$0.627471\pi$
$620$	4983.08	+	8630.94i	0.322782	+	0.559076i
$621$		0			0
$622$	−1344.76			−0.0866883
$623$	−25421.5	−	4561.70i	−1.63482	−	0.293356i
$624$		0			0
$625$	9178.71	−	15898.0i	0.587438	−	1.01747i
$626$	−1980.91	−	3431.03i	−0.126474	−	0.219060i
$627$		0			0
$628$	1861.95	−	3225.00i	0.118312	−	0.204923i
$629$	41688.9			2.64268
$630$		0			0
$631$	−6191.13			−0.390594			−0.195297	−	0.980744i	$-0.562567\pi$
$631$	−6191.13			−0.390594			−0.195297	+	0.980744i	$0.562567\pi$
$632$	7103.72	−	12304.0i	0.447106	−	0.774410i
$633$		0			0
$634$	6503.23	+	11263.9i	0.407376	+	0.705595i
$635$	807.293	−	1398.27i	0.0504511	−	0.0873839i
$636$		0			0
$637$	13993.2	−	11598.4i	0.870376	−	0.721419i
$638$	−6011.06			−0.373010
$639$		0			0
$640$	−6718.86	−	11637.4i	−0.414978	−	0.718764i
$641$	−796.266	−	1379.17i	−0.0490649	−	0.0849829i	0.840450	−	0.541889i	$-0.182291\pi$
$641$	−796.266	−	1379.17i	−0.0490649	−	0.0849829i	−0.889515	+	0.456906i	$0.848957\pi$
$642$		0			0
$643$	−20101.4			−1.23285			−0.616426	−	0.787413i	$-0.711420\pi$
$643$	−20101.4			−1.23285			−0.616426	+	0.787413i	$0.711420\pi$
$644$	2021.58	+	5606.88i	0.123698	+	0.343077i
$645$		0			0
$646$	−14051.4	+	24337.7i	−0.855797	+	1.48228i
$647$	−6976.66	−	12083.9i	−0.423927	−	0.734264i	0.572392	−	0.819980i	$-0.306015\pi$
$647$	−6976.66	−	12083.9i	−0.423927	−	0.734264i	−0.996320	+	0.0857162i	$0.972682\pi$
$648$		0			0
$649$	3905.71	−	6764.89i	0.236229	−	0.409160i
$650$	2441.80			0.147347
$651$		0			0
$652$	−778.720			−0.0467746
$653$	−16020.0	+	27747.5i	−0.960049	+	1.66285i	−0.237683	+	0.971343i	$0.576388\pi$
$653$	−16020.0	+	27747.5i	−0.960049	+	1.66285i	−0.722366	+	0.691511i	$0.756945\pi$
$654$		0			0
$655$	−11791.4	−	20423.3i	−0.703401	−	1.21833i
$656$	−1048.65	+	1816.32i	−0.0624130	+	0.108102i
$657$		0			0
$658$	5538.58	−	6560.28i	0.328140	−	0.388672i
$659$	−22240.2			−1.31465			−0.657325	−	0.753607i	$-0.728312\pi$
$659$	−22240.2			−1.31465			−0.657325	+	0.753607i	$0.728312\pi$
$660$		0			0
$661$	−456.916	−	791.402i	−0.0268865	−	0.0465688i	0.852269	−	0.523104i	$-0.175226\pi$
$661$	−456.916	−	791.402i	−0.0268865	−	0.0465688i	−0.879156	+	0.476535i	$0.841893\pi$
$662$	1855.14	+	3213.20i	0.108916	+	0.188647i
$663$		0			0
$664$	−762.265			−0.0445506
$665$	−20868.9	+	24718.6i	−1.21693	+	1.44142i
$666$		0			0
$667$	3828.92	−	6631.89i	0.222274	−	0.384989i
$668$	4846.51	+	8394.40i	0.280714	+	0.486211i
$669$		0			0
$670$	−7193.97	+	12460.3i	−0.414817	+	0.718484i
$671$	6949.80			0.399842
$672$		0			0
$673$	−7951.84			−0.455454			−0.227727	−	0.973725i	$-0.573129\pi$
$673$	−7951.84			−0.455454			−0.227727	+	0.973725i	$0.573129\pi$
$674$	2564.40	−	4441.67i	0.146553	−	0.253838i
$675$		0			0
$676$	1629.84	+	2822.97i	0.0927312	+	0.160615i
$677$	1316.70	−	2280.59i	0.0747488	−	0.129469i	−0.826228	−	0.563336i	$-0.809518\pi$
$677$	1316.70	−	2280.59i	0.0747488	−	0.129469i	0.900977	+	0.433867i	$0.142851\pi$
$678$		0			0
$679$	−5061.94	−	14039.4i	−0.286096	−	0.793492i
$680$	−32881.6			−1.85434
$681$		0			0
$682$	−3569.99	−	6183.41i	−0.200443	−	0.347177i
$683$	15620.8	+	27056.0i	0.875129	+	1.51577i	0.856625	+	0.515939i	$0.172557\pi$
$683$	15620.8	+	27056.0i	0.875129	+	1.51577i	0.0185036	+	0.999829i	$0.494110\pi$
$684$		0			0
$685$	−6923.54			−0.386182
$686$	9024.05	−	5101.59i	0.502244	−	0.283935i
$687$		0			0
$688$	−1043.67	+	1807.69i	−0.0578338	+	0.100171i
$689$	10279.5	+	17804.7i	0.568388	+	0.984477i
$690$		0			0
$691$	2886.75	−	5000.00i	0.158925	−	0.275266i	−0.775556	−	0.631278i	$-0.782531\pi$
$691$	2886.75	−	5000.00i	0.158925	−	0.275266i	0.934481	+	0.356012i	$0.115864\pi$
$692$	−12940.7			−0.710882
$693$		0			0
$694$	−14632.4			−0.800344
$695$	4326.94	−	7494.48i	0.236158	−	0.409038i
$696$		0			0
$697$	17823.9	+	30871.8i	0.968618	+	1.67770i
$698$	−115.031	+	199.239i	−0.00623778	+	0.0108042i
$699$		0			0
$700$	−2747.36	−	492.993i	−0.148343	−	0.0266191i
$701$	18643.2			1.00449			0.502243	−	0.864726i	$-0.332508\pi$
$701$	18643.2			1.00449			0.502243	+	0.864726i	$0.332508\pi$
$702$		0			0
$703$	24099.4	+	41741.4i	1.29292	+	2.23941i
$704$	3564.79	+	6174.40i	0.190842	+	0.330549i
$705$		0			0
$706$	13395.9			0.714107
$707$	12124.4	−	14360.9i	0.644955	−	0.763930i
$708$		0			0
$709$	−5210.20	+	9024.33i	−0.275985	+	0.478020i	−0.970383	−	0.241571i	$-0.922337\pi$
$709$	−5210.20	+	9024.33i	−0.275985	+	0.478020i	0.694398	+	0.719591i	$0.255671\pi$
$710$	2732.22	+	4732.34i	0.144420	+	0.250143i
$711$		0			0
$712$	15175.7	−	26285.0i	0.798781	−	1.38353i
$713$	9096.06			0.477770
$714$		0			0
$715$	19025.6			0.995131
$716$	7566.24	−	13105.1i	0.394921	−	0.684024i
$717$		0			0
$718$	7138.58	+	12364.4i	0.371044	+	0.642667i
$719$	4134.92	−	7161.90i	0.214474	−	0.371479i	−0.738636	−	0.674105i	$-0.764530\pi$
$719$	4134.92	−	7161.90i	0.214474	−	0.371479i	0.953110	+	0.302625i	$0.0978630\pi$
$720$		0			0
$721$	18947.1	+	3399.92i	0.978679	+	0.175617i
$722$	−21298.2			−1.09784
$723$		0			0
$724$	−584.972	−	1013.20i	−0.0300281	−	0.0520101i
$725$	1793.14	+	3105.81i	0.0918558	+	0.159099i
$726$		0			0
$727$	−4112.34			−0.209791			−0.104896	−	0.994483i	$-0.533451\pi$
$727$	−4112.34			−0.209791			−0.104896	+	0.994483i	$0.533451\pi$
$728$	7244.36	+	20092.3i	0.368810	+	1.02290i
$729$		0			0
$730$	1475.49	−	2555.62i	0.0748085	−	0.129572i
$731$	17739.2	+	30725.3i	0.897551	+	1.55460i
$732$		0			0
$733$	14281.3	−	24736.0i	0.719636	−	1.24645i	−0.241508	−	0.970399i	$-0.577642\pi$
$733$	14281.3	−	24736.0i	0.719636	−	1.24645i	0.961144	−	0.276047i	$-0.0890246\pi$
$734$	9657.14			0.485629
$735$		0			0
$736$	−11205.4			−0.561193
$737$	−10329.4	+	17891.1i	−0.516269	+	0.894203i
$738$		0			0
$739$	−11592.0	−	20077.9i	−0.577019	−	0.999426i	−0.995819	−	0.0913478i	$-0.970883\pi$
$739$	−11592.0	−	20077.9i	−0.577019	−	0.999426i	0.418800	−	0.908078i	$-0.362451\pi$
$740$	−11283.7	+	19543.9i	−0.560535	+	0.970875i
$741$		0			0
$742$	3977.25	+	11030.9i	0.196778	+	0.545767i
$743$	−7212.11			−0.356106			−0.178053	−	0.984021i	$-0.556980\pi$
$743$	−7212.11			−0.356106			−0.178053	+	0.984021i	$0.556980\pi$
$744$		0			0
$745$	−9995.40	−	17312.5i	−0.491548	−	0.851386i
$746$	9514.29	+	16479.2i	0.466948	+	0.808777i
$747$		0			0
$748$	−18893.1			−0.923528
$749$	11089.5	+	1989.92i	0.540988	+	0.0970762i
$750$		0			0
$751$	10881.1	−	18846.6i	0.528703	−	0.915741i	−0.470736	−	0.882274i	$-0.656012\pi$
$751$	10881.1	−	18846.6i	0.528703	−	0.915741i	0.999440	−	0.0334672i	$-0.0106549\pi$
$752$	−1019.93	−	1766.57i	−0.0494587	−	0.0856650i
$753$		0			0
$754$	5490.69	−	9510.16i	0.265198	−	0.459336i
$755$	−44.4741			−0.00214381
$756$		0			0
$757$	−29737.8			−1.42779			−0.713896	−	0.700252i	$-0.753071\pi$
$757$	−29737.8			−1.42779			−0.713896	+	0.700252i	$0.753071\pi$
$758$	−11673.2	+	20218.7i	−0.559355	+	0.968832i
$759$		0			0
$760$	−19008.0	−	32922.9i	−0.907229	−	1.57137i
$761$	15269.9	−	26448.3i	0.727378	−	1.25986i	−0.230609	−	0.973046i	$-0.574072\pi$
$761$	15269.9	−	26448.3i	0.727378	−	1.25986i	0.957988	−	0.286810i	$-0.0925947\pi$
$762$		0			0
$763$	−12875.8	+	15251.1i	−0.610926	+	0.723624i
$764$	−1192.43			−0.0564667
$765$		0			0
$766$	8845.04	+	15320.1i	0.417212	+	0.722632i
$767$	7135.20	+	12358.5i	0.335902	+	0.581800i
$768$		0			0
$769$	39801.3			1.86642			0.933208	−	0.359338i	$-0.116997\pi$
$769$	39801.3			1.86642			0.933208	+	0.359338i	$0.116997\pi$
$770$	10680.8	+	1916.60i	0.499884	+	0.0897006i
$771$		0			0
$772$	−939.743	+	1627.68i	−0.0438110	+	0.0758829i
$773$	−7581.96	−	13132.3i	−0.352787	−	0.611045i	0.633950	−	0.773374i	$-0.281433\pi$
$773$	−7581.96	−	13132.3i	−0.352787	−	0.611045i	−0.986737	+	0.162329i	$0.948099\pi$
$774$		0			0
$775$	−2129.90	+	3689.10i	−0.0987205	+	0.170989i
$776$	17538.0			0.811312
$777$		0			0
$778$	18236.7			0.840383
$779$	−20607.1	+	35692.5i	−0.947787	+	1.64161i
$780$		0			0
$781$	3923.05	+	6794.92i	0.179741	+	0.311320i
$782$	−6004.68	+	10400.4i	−0.274587	+	0.475598i
$783$		0			0
$784$	−413.023	−	2428.04i	−0.0188148	−	0.110607i
$785$	8637.38			0.392715
$786$		0			0
$787$	−10958.7	−	18981.0i	−0.496359	−	0.859718i	0.503633	−	0.863918i	$-0.331997\pi$
$787$	−10958.7	−	18981.0i	−0.496359	−	0.859718i	−0.999991	+	0.00419972i	$0.998663\pi$
$788$	14269.8	+	24716.0i	0.645103	+	1.11735i
$789$		0			0
$790$	13186.8			0.593882
$791$	−12970.4	−	35973.5i	−0.583026	−	1.61703i
$792$		0			0
$793$	−6348.17	+	10995.3i	−0.284275	+	0.492378i
$794$	−10670.6	−	18482.0i	−0.476934	−	0.826074i
$795$		0			0
$796$	1553.69	−	2691.07i	0.0691822	−	0.119827i
$797$	−3205.98			−0.142486			−0.0712431	−	0.997459i	$-0.522697\pi$
$797$	−3205.98			−0.142486			−0.0712431	+	0.997459i	$0.522697\pi$
$798$		0			0
$799$	−34671.3			−1.53515
$800$	2623.83	−	4544.61i	0.115958	−	0.200845i
$801$		0			0
$802$	2230.45	+	3863.25i	0.0982042	+	0.170095i
$803$	2118.57	−	3669.48i	0.0931044	−	0.161262i
$804$		0			0
$805$	−8918.03	+	10563.1i	−0.390459	+	0.462487i
$806$	13043.8			0.570034
$807$		0			0
$808$	11043.2	+	19127.5i	0.480817	+	0.832800i
$809$	−19605.9	−	33958.4i	−0.852048	−	1.47579i	−0.879357	−	0.476163i	$-0.842027\pi$
$809$	−19605.9	−	33958.4i	−0.852048	−	1.47579i	0.0273088	−	0.999627i	$-0.491306\pi$
$810$		0			0
$811$	14711.3			0.636973			0.318486	−	0.947927i	$-0.396825\pi$
$811$	14711.3			0.636973			0.318486	+	0.947927i	$0.396825\pi$
$812$	−8097.84	+	9591.65i	−0.349974	+	0.414533i
$813$		0			0
$814$	8083.88	−	14001.7i	0.348084	−	0.602898i
$815$	−903.097	−	1564.21i	−0.0388149	−	0.0672293i
$816$		0			0
$817$	−20509.3	+	35523.1i	−0.878248	+	1.52117i
$818$	−18800.7			−0.803609
$819$		0			0
$820$	−19297.1			−0.821808
$821$	21458.1	−	37166.5i	0.912171	−	1.57993i	0.101180	−	0.994868i	$-0.467738\pi$
$821$	21458.1	−	37166.5i	0.912171	−	1.57993i	0.810991	−	0.585059i	$-0.198928\pi$
$822$		0			0
$823$	−3441.07	−	5960.10i	−0.145745	−	0.252438i	0.783906	−	0.620880i	$-0.213225\pi$
$823$	−3441.07	−	5960.10i	−0.145745	−	0.252438i	−0.929651	+	0.368442i	$0.879891\pi$
$824$	−11310.7	+	19590.7i	−0.478188	+	0.828245i
$825$		0			0
$826$	2760.67	+	7656.76i	0.116291	+	0.322534i
$827$	−6598.74			−0.277461			−0.138731	−	0.990330i	$-0.544302\pi$
$827$	−6598.74			−0.277461			−0.138731	+	0.990330i	$0.544302\pi$
$828$		0			0
$829$	11792.8	+	20425.8i	0.494067	+	0.855749i	0.999977	−	0.00683736i	$-0.00217642\pi$
$829$	11792.8	+	20425.8i	0.494067	+	0.855749i	−0.505910	+	0.862586i	$0.668843\pi$
$830$	−353.753	−	612.719i	−0.0147939	−	0.0256238i
$831$		0			0
$832$	−13024.8			−0.542731
$833$	−39250.3	−	14555.0i	−1.63258	−	0.605404i
$834$		0			0
$835$	−11241.2	+	19470.3i	−0.465889	+	0.806944i
$836$	−10921.6	−	18916.8i	−0.451833	−	0.782598i
$837$		0			0
$838$	−1979.94	+	3429.36i	−0.0816181	+	0.141367i
$839$	656.729			0.0270236			0.0135118	−	0.999909i	$-0.495699\pi$
$839$	656.729			0.0270236			0.0135118	+	0.999909i	$0.495699\pi$
$840$		0			0
$841$	−8260.64			−0.338703
$842$	8312.80	−	14398.2i	0.340235	−	0.589304i
$843$		0			0
$844$	14591.4	+	25273.0i	0.595090	+	1.03073i
$845$	−3780.33	+	6547.72i	−0.153902	+	0.266566i
$846$		0			0
$847$	−8926.86	−	1601.86i	−0.362138	−	0.0649830i
$848$	2785.99			0.112820
$849$		0			0
$850$	−2812.07	−	4870.65i	−0.113474	−	0.196544i
$851$	10298.5	+	17837.6i	0.414841	+	0.718525i
$852$		0			0
$853$	−26201.7			−1.05173			−0.525867	−	0.850567i	$-0.676259\pi$
$853$	−26201.7			−1.05173			−0.525867	+	0.850567i	$0.676259\pi$
$854$	−4671.45	+	5533.20i	−0.187183	+	0.221712i
$855$		0			0
$856$	−6619.97	+	11466.1i	−0.264329	+	0.457832i
$857$	11604.2	+	20099.1i	0.462536	+	0.801136i	0.999087	−	0.0427325i	$-0.0136063\pi$
$857$	11604.2	+	20099.1i	0.462536	+	0.801136i	−0.536551	+	0.843868i	$0.680273\pi$
$858$		0			0
$859$	13087.7	−	22668.6i	0.519845	−	0.900398i	−0.479889	−	0.877329i	$-0.659323\pi$
$859$	13087.7	−	22668.6i	0.519845	−	0.900398i	0.999734	−	0.0230690i	$-0.00734373\pi$
$860$	−19205.4			−0.761512
$861$		0			0
$862$	11064.6			0.437196
$863$	−2825.92	+	4894.64i	−0.111466	+	0.193065i	−0.916362	−	0.400351i	$-0.868888\pi$
$863$	−2825.92	+	4894.64i	−0.111466	+	0.193065i	0.804895	+	0.593417i	$0.202221\pi$
$864$		0			0
$865$	−15007.6	−	25993.8i	−0.589910	−	1.02175i
$866$	4995.80	−	8652.98i	0.196033	−	0.339538i
$867$		0			0
$868$	−14676.0	−	2633.50i	−0.573890	−	0.102980i
$869$	18934.3			0.739128
$870$		0			0
$871$	−18870.5	−	32684.6i	−0.734101	−	1.27150i
$872$	−11727.7	−	20313.0i	−0.455449	−	0.788860i
$873$		0			0
$874$	−13884.6			−0.537363
$875$	7524.25	+	20868.6i	0.290704	+	0.806271i
$876$		0			0
$877$	−18755.1	+	32484.8i	−0.722138	+	1.25078i	0.238003	+	0.971264i	$0.423507\pi$
$877$	−18755.1	+	32484.8i	−0.722138	+	1.25078i	−0.960141	+	0.279515i	$0.909826\pi$
$878$	−12848.8	−	22254.8i	−0.493880	−	0.855425i
$879$		0			0
$880$	1289.09	−	2232.78i	0.0493811	−	0.0855305i
$881$	−22133.8			−0.846434			−0.423217	−	0.906028i	$-0.639099\pi$
$881$	−22133.8			−0.846434			−0.423217	+	0.906028i	$0.639099\pi$
$882$		0			0
$883$	20678.1			0.788080			0.394040	−	0.919093i	$-0.371077\pi$
$883$	20678.1			0.788080			0.394040	+	0.919093i	$0.371077\pi$
$884$	17257.5	−	29890.9i	0.656599	−	1.13726i
$885$		0			0
$886$	12290.9	+	21288.5i	0.466052	+	0.807225i
$887$	18734.9	−	32449.8i	0.709196	−	1.22836i	−0.255960	−	0.966687i	$-0.582392\pi$
$887$	18734.9	−	32449.8i	0.709196	−	1.22836i	0.965156	−	0.261676i	$-0.0842751\pi$
$888$		0			0
$889$	819.322	+	2272.40i	0.0309102	+	0.0857299i
$890$	28171.0			1.06100
$891$		0			0
$892$	11656.3	+	20189.2i	0.437534	+	0.757831i
$893$	−20042.7	−	34714.9i	−0.751066	−	1.30089i
$894$		0			0
$895$	35098.9			1.31087
$896$	19788.2	+	3550.84i	0.737809	+	0.132394i
$897$		0			0
$898$	−142.839	+	247.405i	−0.00530803	+	0.00919378i
$899$	9578.70	+	16590.8i	0.355359	+	0.615500i
$900$		0			0
$901$	23676.6	−	41009.1i	0.875453	−	1.51633i
$902$	13824.9			0.510330
$903$		0			0
$904$	44938.2			1.65334
$905$	1356.81	−	2350.06i	0.0498363	−	0.0863189i
$906$		0			0
$907$	−10252.0	−	17756.9i	−0.375315	−	0.650064i	0.615059	−	0.788481i	$-0.289132\pi$
$907$	−10252.0	−	17756.9i	−0.375315	−	0.650064i	−0.990374	+	0.138417i	$0.955799\pi$
$908$	1699.72	−	2944.01i	0.0621226	−	0.107599i
$909$		0			0
$910$	−12788.5	+	15147.6i	−0.465862	+	0.551800i
$911$	3533.81			0.128519			0.0642593	−	0.997933i	$-0.479532\pi$
$911$	3533.81			0.128519			0.0642593	+	0.997933i	$0.479532\pi$
$912$		0			0
$913$	−507.936	−	879.771i	−0.0184121	−	0.0318907i
$914$	−10275.4	−	17797.4i	−0.371858	−	0.644077i
$915$		0			0
$916$	−5248.96			−0.189335
$917$	34727.7	+	6231.62i	1.25061	+	0.224413i
$918$		0			0
$919$	−14901.9	+	25810.8i	−0.534895	+	0.926465i	0.464274	+	0.885692i	$0.346315\pi$
$919$	−14901.9	+	25810.8i	−0.534895	+	0.926465i	−0.999168	+	0.0407730i	$0.987018\pi$
$920$	−8122.83	−	14069.2i	−0.291089	−	0.504181i
$921$		0			0
$922$	11244.9	−	19476.7i	0.401661	−	0.695697i
$923$	−14333.7			−0.511160
$924$		0			0
$925$	−9645.90			−0.342870
$926$	7235.19	−	12531.7i	0.256764	−	0.444728i
$927$		0			0
$928$	−11800.0	−	20438.2i	−0.417408	−	0.722971i
$929$	−7223.19	+	12510.9i	−0.255097	+	0.441841i	−0.964922	−	0.262537i	$-0.915441\pi$
$929$	−7223.19	+	12510.9i	−0.255097	+	0.441841i	0.709825	+	0.704378i	$0.248774\pi$
$930$		0			0
$931$	−8116.34	−	47713.5i	−0.285717	−	1.67964i
$932$	8952.20			0.314634
$933$		0			0
$934$	−10475.7	−	18144.5i	−0.366998	−	0.635660i
$935$	−21910.7	−	37950.4i	−0.766369	−	1.32739i
$936$		0			0
$937$	29384.8			1.02450			0.512251	−	0.858836i	$-0.328812\pi$
$937$	29384.8			1.02450			0.512251	+	0.858836i	$0.328812\pi$
$938$	−7301.16	−	20249.9i	−0.254149	−	0.704884i
$939$		0			0
$940$	9384.26	−	16254.0i	0.325618	−	0.563986i
$941$	−2329.98	−	4035.65i	−0.0807176	−	0.139807i	0.822841	−	0.568272i	$-0.192388\pi$
$941$	−2329.98	−	4035.65i	−0.0807176	−	0.139807i	−0.903558	+	0.428465i	$0.859055\pi$
$942$		0			0
$943$	−8806.17	+	15252.7i	−0.304102	+	0.526720i
$944$	1933.80			0.0666735
$945$		0			0
$946$	13759.2			0.472887
$947$	−27160.9	+	47044.1i	−0.932008	+	1.61429i	−0.152125	+	0.988361i	$0.548612\pi$
$947$	−27160.9	+	47044.1i	−0.932008	+	1.61429i	−0.779884	+	0.625925i	$0.784722\pi$
$948$		0			0
$949$	3870.34	+	6703.63i	0.132388	+	0.229304i
$950$	3251.18	−	5631.22i	0.111034	−	0.192317i
$951$		0			0
$952$	31735.2	−	37589.4i	1.08040	−	1.27970i
$953$	−23606.5			−0.802404			−0.401202	−	0.915990i	$-0.631407\pi$
$953$	−23606.5			−0.802404			−0.401202	+	0.915990i	$0.631407\pi$
$954$		0			0
$955$	−1382.88	−	2395.22i	−0.0468576	−	0.0811598i
$956$	−7218.84	−	12503.4i	−0.244219	−	0.423001i
$957$		0			0
$958$	−16245.5			−0.547878
$959$	6682.15	−	7914.81i	0.225003	−	0.266509i
$960$		0			0
$961$	3517.83	−	6093.07i	0.118084	−	0.204527i
$962$	14768.2	+	25579.2i	0.494953	+	0.857283i
$963$		0			0
$964$	−5712.59	+	9894.50i	−0.190861	+	0.330581i
$965$	−4359.36			−0.145422
$966$		0			0
$967$	7021.95			0.233517			0.116758	−	0.993160i	$-0.462750\pi$
$967$	7021.95			0.233517			0.116758	+	0.993160i	$0.462750\pi$
$968$	5328.99	−	9230.08i	0.176942	−	0.306473i
$969$		0			0
$970$	8139.08	+	14097.3i	0.269412	+	0.466636i
$971$	741.741	−	1284.73i	0.0245145	−	0.0424604i	−0.853508	−	0.521080i	$-0.825529\pi$
$971$	741.741	−	1284.73i	0.0245145	−	0.0424604i	0.878022	+	0.478620i	$0.158863\pi$
$972$		0			0
$973$	4391.41	+	12179.6i	0.144689	+	0.401296i
$974$	27278.1			0.897377
$975$		0			0
$976$	860.247	+	1489.99i	0.0282130	+	0.0488663i
$977$	−13076.0	−	22648.3i	−0.428187	−	0.741642i	0.568525	−	0.822666i	$-0.307514\pi$
$977$	−13076.0	−	22648.3i	−0.428187	−	0.741642i	−0.996712	+	0.0810237i	$0.974181\pi$
$978$		0			0
$979$	40449.3			1.32049
$980$	17447.0	−	14461.1i	0.568699	−	0.471371i
$981$		0			0
$982$	−2432.60	+	4213.38i	−0.0790502	+	0.136919i
$983$	−19592.6	−	33935.5i	−0.635716	−	1.10109i	−0.986363	−	0.164584i	$-0.947372\pi$
$983$	−19592.6	−	33935.5i	−0.635716	−	1.10109i	0.350647	−	0.936508i	$-0.385962\pi$
$984$		0			0
$985$	−33098.0	+	57327.4i	−1.07065	+	1.85442i
$986$	−25293.2			−0.816936
$987$		0			0
$988$	39904.6			1.28496
$989$	−8764.36	+	15180.3i	−0.281790	+	0.488075i
$990$		0			0
$991$	11504.8	+	19927.0i	0.368782	+	0.638749i	0.989375	−	0.145383i	$-0.0464415\pi$
$991$	11504.8	+	19927.0i	0.368782	+	0.638749i	−0.620593	+	0.784133i	$0.713108\pi$
$992$	14016.2	−	24276.7i	0.448602	−	0.777002i
$993$		0			0
$994$	−8046.85	−	1443.95i	−0.256771	−	0.0460757i
$995$	7207.38			0.229638
$996$		0			0
$997$	5577.10	+	9659.81i	0.177160	+	0.306850i	0.940907	−	0.338666i	$-0.109976\pi$
$997$	5577.10	+	9659.81i	0.177160	+	0.306850i	−0.763747	+	0.645516i	$0.776642\pi$
$998$	6665.70	+	11545.3i	0.211422	+	0.366193i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.e.f.163.5	yes	14
3.2	odd	2		189.4.e.g.163.3	yes	14
7.2	even	3		1323.4.a.bj.1.3		7
7.4	even	3	inner	189.4.e.f.109.5	✓	14
7.5	odd	6		1323.4.a.bk.1.3		7
21.2	odd	6		1323.4.a.bi.1.5		7
21.5	even	6		1323.4.a.bh.1.5		7
21.11	odd	6		189.4.e.g.109.3	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.4.e.f.109.5	✓	14	7.4	even	3	inner
189.4.e.f.163.5	yes	14	1.1	even	1	trivial
189.4.e.g.109.3	yes	14	21.11	odd	6
189.4.e.g.163.3	yes	14	3.2	odd	2
1323.4.a.bh.1.5		7	21.5	even	6
1323.4.a.bi.1.5		7	21.2	odd	6
1323.4.a.bj.1.3		7	7.2	even	3
1323.4.a.bk.1.3		7	7.5	odd	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.815927 - 1.41323i) q^{2} +(2.66853 + 4.62202i) q^{4} +(-6.18949 + 10.7205i) q^{5} +(-6.28171 - 17.4224i) q^{7} +21.7641 q^{8} +(10.1003 + 17.4943i) q^{10} +(14.5026 + 25.1192i) q^{11} -52.9884 q^{13} +(-29.7472 - 5.33792i) q^{14} +(-3.59026 + 6.21851i) q^{16} +(61.0234 + 105.696i) q^{17} +(-70.5524 + 122.200i) q^{19} -66.0672 q^{20} +47.3321 q^{22} +(-30.1496 + 52.2206i) q^{23} +(-14.1195 - 24.4556i) q^{25} +(-43.2346 + 74.8846i) q^{26} +(63.7638 - 75.5263i) q^{28} -126.997 q^{29} +(-75.4244 - 130.639i) q^{31} +(92.9153 + 160.934i) q^{32} +199.163 q^{34} +(225.658 + 40.4926i) q^{35} +(170.791 - 295.818i) q^{37} +(115.131 + 199.413i) q^{38} +(-134.709 + 233.322i) q^{40} +292.082 q^{41} +290.696 q^{43} +(-77.4008 + 134.062i) q^{44} +(49.1998 + 85.2165i) q^{46} +(-142.041 + 246.022i) q^{47} +(-264.080 + 218.885i) q^{49} -46.0818 q^{50} +(-141.401 - 244.913i) q^{52} +(-193.996 - 336.011i) q^{53} -359.053 q^{55} +(-136.716 - 379.183i) q^{56} +(-103.621 + 179.476i) q^{58} +(-134.656 - 233.231i) q^{59} +(119.803 - 207.505i) q^{61} -246.163 q^{62} +245.804 q^{64} +(327.971 - 568.062i) q^{65} +(356.125 + 616.827i) q^{67} +(-325.685 + 564.103i) q^{68} +(241.345 - 285.866i) q^{70} +270.507 q^{71} +(-73.0414 - 126.511i) q^{73} +(-278.706 - 482.732i) q^{74} -753.083 q^{76} +(346.535 - 410.461i) q^{77} +(326.396 - 565.334i) q^{79} +(-44.4437 - 76.9787i) q^{80} +(238.318 - 412.779i) q^{82} -35.0239 q^{83} -1510.81 q^{85} +(237.186 - 410.819i) q^{86} +(315.635 + 546.696i) q^{88} +(697.278 - 1207.72i) q^{89} +(332.858 + 923.184i) q^{91} -321.820 q^{92} +(231.790 + 401.473i) q^{94} +(-873.366 - 1512.71i) q^{95} +805.822 q^{97} +(93.8642 + 551.800i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 31 q^{4} + q^{5} + 20 q^{7} + 168 q^{8} - 12 q^{10} - 98 q^{11} - 248 q^{13} - 134 q^{14} - 139 q^{16} - 30 q^{17} - 182 q^{19} - 220 q^{20} + 552 q^{22} + 6 q^{23} - 388 q^{25} + 245 q^{26}+ \cdots + 10160 q^{98}+O(q^{100}) \) 14 * q - q^2 - 31 * q^4 + q^5 + 20 * q^7 + 168 * q^8 - 12 * q^10 - 98 * q^11 - 248 * q^13 - 134 * q^14 - 139 * q^16 - 30 * q^17 - 182 * q^19 - 220 * q^20 + 552 * q^22 + 6 * q^23 - 388 * q^25 + 245 * q^26 + 425 * q^28 + 646 * q^29 - 26 * q^31 - 398 * q^32 + 228 * q^34 + 1025 * q^35 + 112 * q^37 - 1015 * q^38 + 147 * q^40 - 1048 * q^41 + 16 * q^43 - 937 * q^44 + 339 * q^46 - 288 * q^47 + 446 * q^49 + 5152 * q^50 + 1075 * q^52 - 1353 * q^53 + 312 * q^55 + 1980 * q^56 + 81 * q^58 - 165 * q^59 - 56 * q^61 - 2430 * q^62 - 3412 * q^64 - 1694 * q^65 + 988 * q^67 - 2625 * q^68 - 4941 * q^70 + 1584 * q^71 - 1487 * q^73 - 2736 * q^74 + 3904 * q^76 - 34 * q^77 + 1273 * q^79 + 2501 * q^80 + 2049 * q^82 - 2340 * q^83 + 432 * q^85 + 160 * q^86 - 9 * q^88 - 1058 * q^89 + 3538 * q^91 + 7668 * q^92 - 1653 * q^94 - 3260 * q^95 - 7460 * q^97 + 10160 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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