LMFDB - Embedded newform 108.4.i.a.13.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(13,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, 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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.9
Character	$\chi$	$=$	108.13
Dual form			108.4.i.a.25.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.19029 - 0.246754i) q^{3} +(15.7004 + 13.1742i) q^{5} +(-8.81657 - 3.20897i) q^{7} +(26.8782 - 2.56145i) q^{9} +O(q^{10})$	\(q+(5.19029 - 0.246754i) q^{3} +(15.7004 + 13.1742i) q^{5} +(-8.81657 - 3.20897i) q^{7} +(26.8782 - 2.56145i) q^{9} +(-45.7414 + 38.3816i) q^{11} +(2.61377 - 14.8234i) q^{13} +(84.7402 + 64.5036i) q^{15} +(44.8278 - 77.6441i) q^{17} +(-3.79866 - 6.57947i) q^{19} +(-46.5524 - 14.4800i) q^{21} +(126.350 - 45.9876i) q^{23} +(51.2365 + 290.577i) q^{25} +(138.874 - 19.9270i) q^{27} +(-25.0600 - 142.122i) q^{29} +(-243.712 + 88.7037i) q^{31} +(-227.940 + 210.499i) q^{33} +(-96.1478 - 166.533i) q^{35} +(113.051 - 195.811i) q^{37} +(9.90850 - 77.5829i) q^{39} +(32.6776 - 185.324i) q^{41} +(-45.0211 + 37.7772i) q^{43} +(455.743 + 313.882i) q^{45} +(-298.842 - 108.770i) q^{47} +(-195.319 - 163.892i) q^{49} +(213.510 - 414.057i) q^{51} -170.290 q^{53} -1223.80 q^{55} +(-21.3396 - 33.2120i) q^{57} +(-82.5952 - 69.3056i) q^{59} +(-324.349 - 118.053i) q^{61} +(-245.193 - 63.6682i) q^{63} +(236.323 - 198.299i) q^{65} +(1.02407 - 5.80776i) q^{67} +(644.446 - 269.867i) q^{69} +(-205.653 + 356.202i) q^{71} +(602.689 + 1043.89i) q^{73} +(337.634 + 1495.54i) q^{75} +(526.448 - 191.611i) q^{77} +(19.8089 + 112.342i) q^{79} +(715.878 - 137.694i) q^{81} +(-245.975 - 1394.99i) q^{83} +(1726.71 - 628.470i) q^{85} +(-165.138 - 731.472i) q^{87} +(683.369 + 1183.63i) q^{89} +(-70.6125 + 122.304i) q^{91} +(-1243.05 + 520.535i) q^{93} +(27.0387 - 153.344i) q^{95} +(-294.392 + 247.025i) q^{97} +(-1131.14 + 1148.79i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) $ 54 * q + 12 * q^5 - 48 * q^9	$ 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99}+O(q^{100}) $ 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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			0
$2$		0			0
$3$	5.19029	−	0.246754i	0.998872	−	0.0474878i
$3$	5.19029	−	0.246754i	0.998872	−	0.0474878i
$4$		0			0
$5$	15.7004	+	13.1742i	1.40428	+	1.17833i	0.959160	+	0.282863i	$0.0912840\pi$
$5$	15.7004	+	13.1742i	1.40428	+	1.17833i	0.445122	+	0.895470i	$0.353160\pi$
$6$		0			0
$7$	−8.81657	−	3.20897i	−0.476050	−	0.173268i	0.0928410	−	0.995681i	$-0.470405\pi$
$7$	−8.81657	−	3.20897i	−0.476050	−	0.173268i	−0.568891	+	0.822413i	$0.692627\pi$
$8$		0			0
$9$	26.8782	−	2.56145i	0.995490	−	0.0948684i
$10$		0			0
$11$	−45.7414	+	38.3816i	−1.25378	+	1.05204i	−0.257462	+	0.966288i	$0.582886\pi$
$11$	−45.7414	+	38.3816i	−1.25378	+	1.05204i	−0.996316	+	0.0857561i	$0.972669\pi$
$12$		0			0
$13$	2.61377	−	14.8234i	0.0557638	−	0.316252i	−0.944148	−	0.329521i	$-0.893113\pi$
$13$	2.61377	−	14.8234i	0.0557638	−	0.316252i	0.999912	+	0.0132689i	$0.00422374\pi$
$14$		0			0
$15$	84.7402	+	64.5036i	1.45865	+	1.11032i
$16$		0			0
$17$	44.8278	−	77.6441i	0.639550	−	1.10773i	−0.345982	−	0.938241i	$-0.612454\pi$
$17$	44.8278	−	77.6441i	0.639550	−	1.10773i	0.985532	−	0.169491i	$-0.0542124\pi$
$18$		0			0
$19$	−3.79866	−	6.57947i	−0.0458669	−	0.0794439i	0.842180	−	0.539196i	$-0.181272\pi$
$19$	−3.79866	−	6.57947i	−0.0458669	−	0.0794439i	−0.888047	+	0.459752i	$0.847938\pi$
$20$		0			0
$21$	−46.5524	−	14.4800i	−0.483741	−	0.150466i
$22$		0			0
$23$	126.350	−	45.9876i	1.14547	−	0.416917i	0.301584	−	0.953440i	$-0.402485\pi$
$23$	126.350	−	45.9876i	1.14547	−	0.416917i	0.843886	+	0.536523i	$0.180262\pi$
$24$		0			0
$25$	51.2365	+	290.577i	0.409892	+	2.32462i
$26$		0			0
$27$	138.874	−	19.9270i	0.989862	−	0.142035i
$28$		0			0
$29$	−25.0600	−	142.122i	−0.160466	−	0.910049i	−0.953617	−	0.301023i	$-0.902672\pi$
$29$	−25.0600	−	142.122i	−0.160466	−	0.910049i	0.793151	−	0.609026i	$-0.208439\pi$
$30$		0			0
$31$	−243.712	+	88.7037i	−1.41200	+	0.513925i	−0.931715	−	0.363190i	$-0.881688\pi$
$31$	−243.712	+	88.7037i	−1.41200	+	0.513925i	−0.480281	+	0.877115i	$0.659465\pi$
$32$		0			0
$33$	−227.940	+	210.499i	−1.20240	+	1.11040i
$34$		0			0
$35$	−96.1478	−	166.533i	−0.464341	−	0.804263i
$36$		0			0
$37$	113.051	−	195.811i	0.502312	−	0.870030i	−0.497684	−	0.867358i	$-0.665816\pi$
$37$	113.051	−	195.811i	0.502312	−	0.870030i	0.999996	−	0.00267179i	$-0.000850458\pi$
$38$		0			0
$39$	9.90850	−	77.5829i	0.0406828	−	0.318544i
$40$		0			0
$41$	32.6776	−	185.324i	0.124473	−	0.705921i	−0.857147	−	0.515072i	$-0.827765\pi$
$41$	32.6776	−	185.324i	0.124473	−	0.705921i	0.981620	−	0.190848i	$-0.0611238\pi$
$42$		0			0
$43$	−45.0211	+	37.7772i	−0.159667	+	0.133976i	−0.719121	−	0.694885i	$-0.755455\pi$
$43$	−45.0211	+	37.7772i	−0.159667	+	0.133976i	0.559454	+	0.828861i	$0.311011\pi$
$44$		0			0
$45$	455.743	+	313.882i	1.50974	+	1.03980i
$46$		0			0
$47$	−298.842	−	108.770i	−0.927459	−	0.337568i	−0.166257	−	0.986082i	$-0.553168\pi$
$47$	−298.842	−	108.770i	−0.927459	−	0.337568i	−0.761202	+	0.648515i	$0.775390\pi$
$48$		0			0
$49$	−195.319	−	163.892i	−0.569443	−	0.477819i
$50$		0			0
$51$	213.510	−	414.057i	0.586224	−	1.13685i
$52$		0			0
$53$	−170.290			−0.441341			−0.220671	−	0.975348i	$-0.570825\pi$
$53$	−170.290			−0.441341			−0.220671	+	0.975348i	$0.570825\pi$
$54$		0			0
$55$	−1223.80			−3.00032
$56$		0			0
$57$	−21.3396	−	33.2120i	−0.0495878	−	0.0771761i
$58$		0			0
$59$	−82.5952	−	69.3056i	−0.182254	−	0.152929i	0.547096	−	0.837070i	$-0.315733\pi$
$59$	−82.5952	−	69.3056i	−0.182254	−	0.152929i	−0.729350	+	0.684140i	$0.760178\pi$
$60$		0			0
$61$	−324.349	−	118.053i	−0.680797	−	0.247790i	−0.0216072	−	0.999767i	$-0.506878\pi$
$61$	−324.349	−	118.053i	−0.680797	−	0.247790i	−0.659190	+	0.751977i	$0.729101\pi$
$62$		0			0
$63$	−245.193	−	63.6682i	−0.490341	−	0.127324i
$64$		0			0
$65$	236.323	−	198.299i	0.450959	−	0.378399i
$66$		0			0
$67$	1.02407	−	5.80776i	0.00186731	−	0.0105900i	−0.983860	−	0.178941i	$-0.942733\pi$
$67$	1.02407	−	5.80776i	0.00186731	−	0.0105900i	0.985727	+	0.168351i	$0.0538441\pi$
$68$		0			0
$69$	644.446	−	269.867i	1.12438	−	0.470842i
$70$		0			0
$71$	−205.653	+	356.202i	−0.343754	+	0.595400i	−0.985127	−	0.171830i	$-0.945032\pi$
$71$	−205.653	+	356.202i	−0.343754	+	0.595400i	0.641372	+	0.767230i	$0.278365\pi$
$72$		0			0
$73$	602.689	+	1043.89i	0.966294	+	1.67367i	0.706098	+	0.708115i	$0.250454\pi$
$73$	602.689	+	1043.89i	0.966294	+	1.67367i	0.260196	+	0.965556i	$0.416213\pi$
$74$		0			0
$75$	337.634	+	1495.54i	0.519821	+	2.30253i
$76$		0			0
$77$	526.448	−	191.611i	0.779147	−	0.283586i
$78$		0			0
$79$	19.8089	+	112.342i	0.0282111	+	0.159993i	0.995659	−	0.0930777i	$-0.0296705\pi$
$79$	19.8089	+	112.342i	0.0282111	+	0.159993i	−0.967448	+	0.253071i	$0.918559\pi$
$80$		0			0
$81$	715.878	−	137.694i	0.982000	−	0.188881i
$82$		0			0
$83$	−245.975	−	1394.99i	−0.325292	−	1.84482i	−0.507616	−	0.861583i	$-0.669473\pi$
$83$	−245.975	−	1394.99i	−0.325292	−	1.84482i	0.182324	−	0.983238i	$-0.441638\pi$
$84$		0			0
$85$	1726.71	−	628.470i	2.20339	−	0.801967i
$86$		0			0
$87$	−165.138	−	731.472i	−0.203501	−	0.901402i
$88$		0			0
$89$	683.369	+	1183.63i	0.813899	+	1.40971i	0.910116	+	0.414354i	$0.135992\pi$
$89$	683.369	+	1183.63i	0.813899	+	1.40971i	−0.0962172	+	0.995360i	$0.530674\pi$
$90$		0			0
$91$	−70.6125	+	122.304i	−0.0813428	+	0.140890i
$92$		0			0
$93$	−1243.05	+	520.535i	−1.38600	+	0.580397i
$94$		0			0
$95$	27.0387	−	153.344i	0.0292012	−	0.165608i
$96$		0			0
$97$	−294.392	+	247.025i	−0.308155	+	0.258573i	−0.783729	−	0.621103i	$-0.786685\pi$
$97$	−294.392	+	247.025i	−0.308155	+	0.258573i	0.475574	+	0.879676i	$0.342240\pi$
$98$		0			0
$99$	−1131.14	+	1148.79i	−1.14832	+	1.16624i
$100$		0			0
$101$	586.611	+	213.509i	0.577920	+	0.210346i	0.614408	−	0.788988i	$-0.289395\pi$
$101$	586.611	+	213.509i	0.577920	+	0.210346i	−0.0364880	+	0.999334i	$0.511617\pi$
$102$		0			0
$103$	801.072	+	672.179i	0.766330	+	0.643027i	0.939766	−	0.341818i	$-0.111043\pi$
$103$	801.072	+	672.179i	0.766330	+	0.643027i	−0.173436	+	0.984845i	$0.555487\pi$
$104$		0			0
$105$	−540.128	−	840.629i	−0.502010	−	0.781305i
$106$		0			0
$107$	219.340			0.198172			0.0990860	−	0.995079i	$-0.468408\pi$
$107$	219.340			0.198172			0.0990860	+	0.995079i	$0.468408\pi$
$108$		0			0
$109$	−2066.92			−1.81628			−0.908142	−	0.418663i	$-0.862499\pi$
$109$	−2066.92			−1.81628			−0.908142	+	0.418663i	$0.862499\pi$
$110$		0			0
$111$	538.453	−	1044.21i	0.460430	−	0.892902i
$112$		0			0
$113$	−126.524	−	106.166i	−0.105331	−	0.0883828i	0.588601	−	0.808423i	$-0.299679\pi$
$113$	−126.524	−	106.166i	−0.105331	−	0.0883828i	−0.693932	+	0.720041i	$0.744123\pi$
$114$		0			0
$115$	2589.59	+	942.533i	2.09983	+	0.764275i
$116$		0			0
$117$	32.2841	−	405.123i	0.0255100	−	0.320116i
$118$		0			0
$119$	−644.385	+	540.703i	−0.496392	+	0.416523i
$120$		0			0
$121$	388.004	−	2200.48i	0.291513	−	1.65325i
$122$		0			0
$123$	123.877	−	969.949i	0.0908098	−	0.711035i
$124$		0			0
$125$	−1742.72	+	3018.47i	−1.24699	+	2.15984i
$126$		0			0
$127$	−801.591	−	1388.40i	−0.560077	−	0.970081i	−0.997489	−	0.0708201i	$-0.977438\pi$
$127$	−801.591	−	1388.40i	−0.560077	−	0.970081i	0.437413	−	0.899261i	$-0.355895\pi$
$128$		0			0
$129$	−224.351	+	207.184i	−0.153124	+	0.141407i
$130$		0			0
$131$	1986.87	−	723.162i	1.32514	−	0.482313i	0.420040	−	0.907505i	$-0.362016\pi$
$131$	1986.87	−	723.162i	1.32514	−	0.482313i	0.905103	+	0.425193i	$0.139794\pi$
$132$		0			0
$133$	12.3778	+	70.1981i	0.00806988	+	0.0457665i
$134$		0			0
$135$	2442.89	+	1516.68i	1.55741	+	0.966929i
$136$		0			0
$137$	174.325	+	988.647i	0.108712	+	0.616539i	0.989672	+	0.143348i	$0.0457868\pi$
$137$	174.325	+	988.647i	0.108712	+	0.616539i	−0.880960	+	0.473191i	$0.843102\pi$
$138$		0			0
$139$	−141.218	+	51.3992i	−0.0861724	+	0.0313642i	−0.384747	−	0.923022i	$-0.625711\pi$
$139$	−141.218	+	51.3992i	−0.0861724	+	0.0313642i	0.298574	+	0.954386i	$0.403489\pi$
$140$		0			0
$141$	−1577.92	−	490.805i	−0.942443	−	0.293144i
$142$		0			0
$143$	449.390	+	778.366i	0.262796	+	0.455176i
$144$		0			0
$145$	1478.89	−	2561.51i	0.847001	−	1.46705i
$146$		0			0
$147$	−1054.20	−	802.451i	−0.591491	−	0.450238i
$148$		0			0
$149$	−353.047	+	2002.23i	−0.194112	+	1.10087i	0.719565	+	0.694426i	$0.244341\pi$
$149$	−353.047	+	2002.23i	−0.194112	+	1.10087i	−0.913677	+	0.406441i	$0.866770\pi$
$150$		0			0
$151$	−998.407	+	837.763i	−0.538074	+	0.451498i	−0.870879	−	0.491498i	$-0.836450\pi$
$151$	−998.407	+	837.763i	−0.538074	+	0.451498i	0.332804	+	0.942996i	$0.392005\pi$
$152$		0			0
$153$	1006.01	−	2201.76i	0.531576	−	1.16341i
$154$		0			0
$155$	−4994.95	−	1818.01i	−2.58842	−	0.942106i
$156$		0			0
$157$	−1497.76	−	1256.77i	−0.761366	−	0.638862i	0.177116	−	0.984190i	$-0.443323\pi$
$157$	−1497.76	−	1256.77i	−0.761366	−	0.638862i	−0.938482	+	0.345328i	$0.887768\pi$
$158$		0			0
$159$	−883.853	+	42.0196i	−0.440844	+	0.0209583i
$160$		0			0
$161$	−1261.55			−0.617539
$162$		0			0
$163$	304.483			0.146312			0.0731562	−	0.997320i	$-0.476693\pi$
$163$	304.483			0.146312			0.0731562	+	0.997320i	$0.476693\pi$
$164$		0			0
$165$	−6351.89	+	301.978i	−2.99693	+	0.142478i
$166$		0			0
$167$	1927.52	+	1617.38i	0.893150	+	0.749442i	0.968839	−	0.247690i	$-0.0796714\pi$
$167$	1927.52	+	1617.38i	0.893150	+	0.749442i	−0.0756896	+	0.997131i	$0.524116\pi$
$168$		0			0
$169$	1851.60	+	673.928i	0.842787	+	0.306749i
$170$		0			0
$171$	−118.954	−	167.114i	−0.0531968	−	0.0747342i
$172$		0			0
$173$	−416.652	+	349.613i	−0.183107	+	0.153645i	−0.729734	−	0.683731i	$-0.760356\pi$
$173$	−416.652	+	349.613i	−0.183107	+	0.153645i	0.546627	+	0.837376i	$0.315912\pi$
$174$		0			0
$175$	480.722	−	2726.31i	0.207652	−	1.17765i
$176$		0			0
$177$	−445.795	−	339.336i	−0.189311	−	0.144102i
$178$		0			0
$179$	1487.78	−	2576.91i	0.621238	−	1.07602i	−0.368017	−	0.929819i	$-0.619963\pi$
$179$	1487.78	−	2576.91i	0.621238	−	1.07602i	0.989255	−	0.146197i	$-0.0467034\pi$
$180$		0			0
$181$	−6.47319	−	11.2119i	−0.00265828	−	0.00460427i	0.864693	−	0.502300i	$-0.167513\pi$
$181$	−6.47319	−	11.2119i	−0.00265828	−	0.00460427i	−0.867351	+	0.497696i	$0.834179\pi$
$182$		0			0
$183$	−1712.59	−	532.697i	−0.691796	−	0.215181i
$184$		0			0
$185$	4354.59	−	1584.94i	1.73057	−	0.629877i
$186$		0			0
$187$	929.616	+	5272.11i	0.363531	+	2.06168i
$188$		0			0
$189$	−1288.34	−	269.954i	−0.495834	−	0.103896i
$190$		0			0
$191$	107.185	+	607.875i	0.0406053	+	0.230284i	0.998356	−	0.0573151i	$-0.0182540\pi$
$191$	107.185	+	607.875i	0.0406053	+	0.230284i	−0.957751	+	0.287599i	$0.907143\pi$
$192$		0			0
$193$	1940.91	−	706.433i	0.723884	−	0.263472i	0.0463102	−	0.998927i	$-0.485254\pi$
$193$	1940.91	−	706.433i	0.723884	−	0.263472i	0.677574	+	0.735455i	$0.263032\pi$
$194$		0			0
$195$	1177.66	−	1087.54i	0.432481	−	0.399387i
$196$		0			0
$197$	−300.362	−	520.241i	−0.108629	−	0.188151i	0.806586	−	0.591116i	$-0.201313\pi$
$197$	−300.362	−	520.241i	−0.108629	−	0.188151i	−0.915215	+	0.402966i	$0.867979\pi$
$198$		0			0
$199$	−1860.07	+	3221.74i	−0.662597	+	1.14765i	0.317333	+	0.948314i	$0.397213\pi$
$199$	−1860.07	+	3221.74i	−0.662597	+	1.14765i	−0.979931	+	0.199338i	$0.936121\pi$
$200$		0			0
$201$	3.88211	−	30.3967i	0.00136230	−	0.0106667i
$202$		0			0
$203$	−235.123	+	1333.45i	−0.0812925	+	0.461033i
$204$		0			0
$205$	2954.54	−	2479.15i	1.00660	−	0.844641i
$206$		0			0
$207$	3278.27	−	1559.71i	1.10075	−	0.523705i
$208$		0			0
$209$	426.287	+	155.156i	0.141085	+	0.0513509i
$210$		0			0
$211$	1236.66	+	1037.68i	0.403484	+	0.338563i	0.821838	−	0.569721i	$-0.192949\pi$
$211$	1236.66	+	1037.68i	0.403484	+	0.338563i	−0.418355	+	0.908284i	$0.637393\pi$
$212$		0			0
$213$	−979.506	+	1899.54i	−0.315092	+	0.611052i
$214$		0			0
$215$	−1204.53			−0.382085
$216$		0			0
$217$	2433.35			0.761228
$218$		0			0
$219$	3385.72	+	5269.37i	1.04468	+	1.62589i
$220$		0			0
$221$	−1033.78	−	867.446i	−0.314659	−	0.264031i
$222$		0			0
$223$	−3267.43	−	1189.25i	−0.981182	−	0.357121i	−0.198882	−	0.980023i	$-0.563731\pi$
$223$	−3267.43	−	1189.25i	−0.981182	−	0.357121i	−0.782299	+	0.622902i	$0.785953\pi$
$224$		0			0
$225$	2121.45	+	7678.95i	0.628576	+	2.27524i
$226$		0			0
$227$	573.716	−	481.405i	0.167748	−	0.140758i	−0.555049	−	0.831818i	$-0.687300\pi$
$227$	573.716	−	481.405i	0.167748	−	0.140758i	0.722797	+	0.691060i	$0.242856\pi$
$228$		0			0
$229$	−628.614	+	3565.05i	−0.181397	+	1.02875i	0.749100	+	0.662457i	$0.230486\pi$
$229$	−628.614	+	3565.05i	−0.181397	+	1.02875i	−0.930498	+	0.366298i	$0.880625\pi$
$230$		0			0
$231$	2685.14	−	1124.42i	0.764801	−	0.320266i
$232$		0			0
$233$	−2041.89	+	3536.65i	−0.574113	+	0.994393i	0.422024	+	0.906585i	$0.361320\pi$
$233$	−2041.89	+	3536.65i	−0.574113	+	0.994393i	−0.996137	+	0.0878086i	$0.972014\pi$
$234$		0			0
$235$	−3258.98	−	5644.71i	−0.904648	−	1.56690i
$236$		0			0
$237$	130.535	+	578.200i	0.0357770	+	0.158473i
$238$		0			0
$239$	2769.51	−	1008.02i	0.749560	−	0.272817i	0.0611393	−	0.998129i	$-0.480527\pi$
$239$	2769.51	−	1008.02i	0.749560	−	0.272817i	0.688421	+	0.725312i	$0.258304\pi$
$240$		0			0
$241$	−17.3695	−	98.5075i	−0.00464261	−	0.0263296i	0.982398	−	0.186797i	$-0.0598108\pi$
$241$	−17.3695	−	98.5075i	−0.00464261	−	0.0263296i	−0.987041	+	0.160468i	$0.948700\pi$
$242$		0			0
$243$	3681.64	−	891.319i	0.971923	−	0.235301i
$244$		0			0
$245$	−907.435	−	5146.32i	−0.236628	−	1.34199i
$246$		0			0
$247$	−107.459	+	39.1119i	−0.0276820	+	0.0100754i
$248$		0			0
$249$	−1620.90	−	7179.72i	−0.412531	−	1.82729i
$250$		0			0
$251$	2244.88	+	3888.24i	0.564524	+	0.977783i	0.997094	+	0.0761832i	$0.0242734\pi$
$251$	2244.88	+	3888.24i	0.564524	+	0.977783i	−0.432570	+	0.901600i	$0.642393\pi$
$252$		0			0
$253$	−4014.35	+	6953.06i	−0.997549	+	1.72781i
$254$		0			0
$255$	8807.04	−	3688.01i	2.16282	−	0.905696i
$256$		0			0
$257$	−537.383	+	3047.65i	−0.130432	+	0.739717i	0.847500	+	0.530795i	$0.178107\pi$
$257$	−537.383	+	3047.65i	−0.130432	+	0.739717i	−0.977932	+	0.208922i	$0.933005\pi$
$258$		0			0
$259$	−1625.08	+	1363.60i	−0.389874	+	0.327143i
$260$		0			0
$261$	−1037.61	−	3755.80i	−0.246077	−	0.890721i
$262$		0			0
$263$	5048.21	+	1837.40i	1.18360	+	0.430794i	0.857471	−	0.514533i	$-0.172035\pi$
$263$	5048.21	+	1837.40i	1.18360	+	0.430794i	0.326125	+	0.945327i	$0.394257\pi$
$264$		0			0
$265$	−2673.61	−	2243.42i	−0.619768	−	0.520047i
$266$		0			0
$267$	3838.95	+	5974.76i	0.879925	+	1.36947i
$268$		0			0
$269$	3518.17			0.797422			0.398711	−	0.917077i	$-0.369458\pi$
$269$	3518.17			0.797422			0.398711	+	0.917077i	$0.369458\pi$
$270$		0			0
$271$	168.611			0.0377948			0.0188974	−	0.999821i	$-0.493984\pi$
$271$	168.611			0.0377948			0.0188974	+	0.999821i	$0.493984\pi$
$272$		0			0
$273$	−336.320	+	652.219i	−0.0745605	+	0.144594i
$274$		0			0
$275$	−13496.4	−	11324.9i	−2.95951	−	2.48333i
$276$		0			0
$277$	−2582.12	−	939.815i	−0.560088	−	0.203856i	0.0464347	−	0.998921i	$-0.485214\pi$
$277$	−2582.12	−	939.815i	−0.560088	−	0.203856i	−0.606523	+	0.795066i	$0.707436\pi$
$278$		0			0
$279$	−6323.32	+	3008.45i	−1.35687	+	0.645561i
$280$		0			0
$281$	3848.57	−	3229.33i	0.817034	−	0.685573i	−0.135242	−	0.990813i	$-0.543181\pi$
$281$	3848.57	−	3229.33i	0.817034	−	0.685573i	0.952275	+	0.305240i	$0.0987367\pi$
$282$		0			0
$283$	63.6653	−	361.064i	0.0133728	−	0.0758411i	−0.977391	−	0.211440i	$-0.932185\pi$
$283$	63.6653	−	361.064i	0.0133728	−	0.0758411i	0.990764	+	0.135599i	$0.0432958\pi$
$284$		0			0
$285$	102.500	−	802.572i	0.0213039	−	0.166808i
$286$		0			0
$287$	−882.804	+	1529.06i	−0.181569	+	0.314486i
$288$		0			0
$289$	−1562.57	−	2706.44i	−0.318047	−	0.550874i
$290$		0			0
$291$	−1467.03	+	1354.77i	−0.295528	+	0.272914i
$292$		0			0
$293$	−1101.03	+	400.741i	−0.219532	+	0.0799029i	−0.449445	−	0.893308i	$-0.648378\pi$
$293$	−1101.03	+	400.741i	−0.219532	+	0.0799029i	0.229913	+	0.973211i	$0.426156\pi$
$294$		0			0
$295$	−383.731	−	2176.25i	−0.0757345	−	0.429511i
$296$		0			0
$297$	−5587.45	+	6241.69i	−1.09164	+	1.21946i
$298$		0			0
$299$	−351.445	−	1993.14i	−0.0679752	−	0.385506i
$300$		0			0
$301$	518.158	−	188.594i	0.0992230	−	0.0361142i
$302$		0			0
$303$	3097.36	+	963.424i	0.587257	+	0.182664i
$304$		0			0
$305$	−3537.14	−	6126.50i	−0.664052	−	1.15017i
$306$		0			0
$307$	−4212.00	+	7295.40i	−0.783034	+	1.35626i	0.147132	+	0.989117i	$0.452996\pi$
$307$	−4212.00	+	7295.40i	−0.783034	+	1.35626i	−0.930166	+	0.367139i	$0.880337\pi$
$308$		0			0
$309$	4323.66	+	3291.14i	0.796001	+	0.605910i
$310$		0			0
$311$	1088.82	−	6175.03i	0.198526	−	1.12590i	−0.708781	−	0.705428i	$-0.750755\pi$
$311$	1088.82	−	6175.03i	0.198526	−	1.12590i	0.907307	−	0.420468i	$-0.138134\pi$
$312$		0			0
$313$	−1561.71	+	1310.43i	−0.282022	+	0.236645i	−0.772815	−	0.634632i	$-0.781152\pi$
$313$	−1561.71	+	1310.43i	−0.282022	+	0.236645i	0.490792	+	0.871277i	$0.336707\pi$
$314$		0			0
$315$	−3010.85	−	4229.83i	−0.538546	−	0.756584i
$316$		0			0
$317$	−4935.72	−	1796.45i	−0.874503	−	0.318293i	−0.134514	−	0.990912i	$-0.542947\pi$
$317$	−4935.72	−	1796.45i	−0.874503	−	0.318293i	−0.739989	+	0.672619i	$0.765170\pi$
$318$		0			0
$319$	6601.16	+	5539.03i	1.15860	+	0.972182i
$320$		0			0
$321$	1138.44	−	54.1230i	0.197948	−	0.00941075i
$322$		0			0
$323$	−681.142			−0.117337
$324$		0			0
$325$	4441.27			0.758023
$326$		0			0
$327$	−10727.9	+	510.020i	−1.81423	+	0.0862513i
$328$		0			0
$329$	2285.72	+	1917.95i	0.383027	+	0.321398i
$330$		0			0
$331$	−5265.15	−	1916.36i	−0.874317	−	0.318225i	−0.134403	−	0.990927i	$-0.542912\pi$
$331$	−5265.15	−	1916.36i	−0.874317	−	0.318225i	−0.739914	+	0.672702i	$0.765134\pi$
$332$		0			0
$333$	2537.06	−	5552.62i	0.417508	−	0.913760i
$334$		0			0
$335$	92.5906	−	77.6927i	0.0151008	−	0.0126711i
$336$		0			0
$337$	−1242.81	+	7048.32i	−0.200890	+	1.13931i	0.702886	+	0.711302i	$0.251894\pi$
$337$	−1242.81	+	7048.32i	−0.200890	+	1.13931i	−0.903777	+	0.428004i	$0.859217\pi$
$338$		0			0
$339$	−682.891	−	519.812i	−0.109409	−	0.0832812i
$340$		0			0
$341$	7743.12	−	13411.5i	1.22966	−	2.12983i
$342$		0			0
$343$	2805.20	+	4858.75i	0.441593	+	0.764862i
$344$		0			0
$345$	13673.3	+	4253.03i	2.13375	+	0.663697i
$346$		0			0
$347$	6609.62	−	2405.70i	1.02254	−	0.372176i	0.224307	−	0.974519i	$-0.427988\pi$
$347$	6609.62	−	2405.70i	1.02254	−	0.372176i	0.798237	+	0.602343i	$0.205766\pi$
$348$		0			0
$349$	−2117.69	−	12010.0i	−0.324806	−	1.84207i	−0.511032	−	0.859562i	$-0.670737\pi$
$349$	−2117.69	−	12010.0i	−0.324806	−	1.84207i	0.186226	−	0.982507i	$-0.440374\pi$
$350$		0			0
$351$	67.5982	−	2110.67i	0.0102796	−	0.320967i
$352$		0			0
$353$	1121.15	+	6358.37i	0.169045	+	0.958702i	0.944795	+	0.327662i	$0.106261\pi$
$353$	1121.15	+	6358.37i	0.169045	+	0.958702i	−0.775750	+	0.631040i	$0.782628\pi$
$354$		0			0
$355$	−7921.49	+	2883.19i	−1.18431	+	0.431053i
$356$		0			0
$357$	−3211.12	+	2965.41i	−0.476053	+	0.439625i
$358$		0			0
$359$	−2838.30	−	4916.07i	−0.417269	−	0.722731i	0.578395	−	0.815757i	$-0.303679\pi$
$359$	−2838.30	−	4916.07i	−0.417269	−	0.722731i	−0.995664	+	0.0930261i	$0.970346\pi$
$360$		0			0
$361$	3400.64	−	5890.08i	0.495792	−	0.858738i
$362$		0			0
$363$	1470.88	−	11516.9i	0.212675	−	1.66523i
$364$		0			0
$365$	−4289.92	+	24329.3i	−0.615191	+	3.48892i
$366$		0			0
$367$	−5167.88	+	4336.37i	−0.735045	+	0.616776i	−0.931502	−	0.363737i	$-0.881501\pi$
$367$	−5167.88	+	4336.37i	−0.735045	+	0.616776i	0.196457	+	0.980512i	$0.437056\pi$
$368$		0			0
$369$	403.619	−	5064.88i	0.0569419	−	0.714545i
$370$		0			0
$371$	1501.37	+	546.455i	0.210101	+	0.0764704i
$372$		0			0
$373$	−6570.17	−	5513.03i	−0.912039	−	0.765292i	0.0604669	−	0.998170i	$-0.480741\pi$
$373$	−6570.17	−	5513.03i	−0.912039	−	0.765292i	−0.972506	+	0.232879i	$0.925185\pi$
$374$		0			0
$375$	−8300.38	+	16096.8i	−1.14301	+	2.21662i
$376$		0			0
$377$	−2172.24			−0.296754
$378$		0			0
$379$	2072.06			0.280830			0.140415	−	0.990093i	$-0.455156\pi$
$379$	2072.06			0.280830			0.140415	+	0.990093i	$0.455156\pi$
$380$		0			0
$381$	−4503.08	−	7008.39i	−0.605512	−	0.942390i
$382$		0			0
$383$	−8567.05	−	7188.61i	−1.14297	−	0.959062i	−0.143434	−	0.989660i	$-0.545815\pi$
$383$	−8567.05	−	7188.61i	−1.14297	−	0.959062i	−0.999532	+	0.0305975i	$0.990259\pi$
$384$		0			0
$385$	10789.7	+	3927.14i	1.42830	+	0.519859i
$386$		0			0
$387$	−1113.32	+	1130.70i	−0.146236	+	0.148519i
$388$		0			0
$389$	−7629.67	+	6402.06i	−0.994447	+	0.834440i	−0.986205	−	0.165526i	$-0.947068\pi$
$389$	−7629.67	+	6402.06i	−0.994447	+	0.834440i	−0.00824146	+	0.999966i	$0.502623\pi$
$390$		0			0
$391$	2093.33	−	11871.9i	0.270752	−	1.53551i
$392$		0			0
$393$	10134.0	−	4243.69i	1.30074	−	0.544697i
$394$		0			0
$395$	−1169.00	+	2024.78i	−0.148909	+	0.257918i
$396$		0			0
$397$	1696.82	+	2938.98i	0.214511	+	0.371545i	0.953121	−	0.302588i	$-0.0978508\pi$
$397$	1696.82	+	2938.98i	0.214511	+	0.371545i	−0.738610	+	0.674133i	$0.764517\pi$
$398$		0			0
$399$	81.5662	+	361.294i	0.0102341	+	0.0453317i
$400$		0			0
$401$	4357.03	−	1585.83i	0.542593	−	0.197488i	−0.0561597	−	0.998422i	$-0.517886\pi$
$401$	4357.03	−	1585.83i	0.542593	−	0.197488i	0.598752	+	0.800934i	$0.295663\pi$
$402$		0			0
$403$	677.888	+	3844.49i	0.0837916	+	0.475206i
$404$		0			0
$405$	13053.5	+	7269.24i	1.60157	+	0.891880i
$406$		0			0
$407$	2344.40	+	13295.8i	0.285523	+	1.61928i
$408$		0			0
$409$	−12927.5	+	4705.22i	−1.56289	+	0.568846i	−0.971397	−	0.237463i	$-0.923684\pi$
$409$	−12927.5	+	4705.22i	−1.56289	+	0.568846i	−0.591495	+	0.806309i	$0.701462\pi$
$410$		0			0
$411$	1148.75	+	5088.35i	0.137868	+	0.610681i
$412$		0			0
$413$	505.807	+	876.083i	0.0602643	+	0.104381i
$414$		0			0
$415$	14516.0	−	25142.4i	1.71701	−	2.97395i
$416$		0			0
$417$	−720.280	+	301.623i	−0.0845858	+	0.0354209i
$418$		0			0
$419$	−2243.12	+	12721.3i	−0.261536	+	1.48324i	0.517186	+	0.855873i	$0.326979\pi$
$419$	−2243.12	+	12721.3i	−0.261536	+	1.48324i	−0.778722	+	0.627369i	$0.784132\pi$
$420$		0			0
$421$	9277.02	−	7784.35i	1.07395	−	0.901154i	0.0785486	−	0.996910i	$-0.474971\pi$
$421$	9277.02	−	7784.35i	1.07395	−	0.901154i	0.995405	+	0.0957563i	$0.0305270\pi$
$422$		0			0
$423$	−8310.95	−	2158.07i	−0.955301	−	0.248058i
$424$		0			0
$425$	24858.4	+	9047.71i	2.83720	+	1.03266i
$426$		0			0
$427$	2480.81	+	2081.65i	0.281159	+	0.235921i
$428$		0			0
$429$	2524.53	+	3929.06i	0.284115	+	0.442183i
$430$		0			0
$431$	8454.10			0.944826			0.472413	−	0.881377i	$-0.343383\pi$
$431$	8454.10			0.944826			0.472413	+	0.881377i	$0.343383\pi$
$432$		0			0
$433$	16108.8			1.78785			0.893926	−	0.448214i	$-0.147940\pi$
$433$	16108.8			1.78785			0.893926	+	0.448214i	$0.147940\pi$
$434$		0			0
$435$	7043.80	−	13659.9i	0.776378	−	1.50562i
$436$		0			0
$437$	−782.535	−	656.625i	−0.0856607	−	0.0718778i
$438$		0			0
$439$	4859.34	+	1768.65i	0.528300	+	0.192285i	0.592379	−	0.805659i	$-0.298189\pi$
$439$	4859.34	+	1768.65i	0.528300	+	0.192285i	−0.0640794	+	0.997945i	$0.520411\pi$
$440$		0			0
$441$	−5669.62	−	3904.83i	−0.612204	−	0.421642i
$442$		0			0
$443$	−4319.54	+	3624.52i	−0.463267	+	0.388728i	−0.844332	−	0.535821i	$-0.820002\pi$
$443$	−4319.54	+	3624.52i	−0.463267	+	0.388728i	0.381064	+	0.924549i	$0.375558\pi$
$444$		0			0
$445$	−4864.20	+	27586.2i	−0.518169	+	2.93868i
$446$		0			0
$447$	−1338.36	+	10479.3i	−0.141616	+	1.10884i
$448$		0			0
$449$	1788.29	−	3097.40i	0.187961	−	0.325558i	−0.756609	−	0.653867i	$-0.773146\pi$
$449$	1788.29	−	3097.40i	0.187961	−	0.325558i	0.944570	+	0.328309i	$0.106479\pi$
$450$		0			0
$451$	5618.31	+	9731.20i	0.586599	+	1.01602i
$452$		0			0
$453$	−4975.30	+	4594.59i	−0.516027	+	0.476541i
$454$		0			0
$455$	−2719.90	+	989.962i	−0.280244	+	0.102000i
$456$		0			0
$457$	−1008.03	−	5716.82i	−0.103181	−	0.585168i	−0.991931	−	0.126776i	$-0.959537\pi$
$457$	−1008.03	−	5716.82i	−0.103181	−	0.585168i	0.888750	−	0.458391i	$-0.151574\pi$
$458$		0			0
$459$	4678.20	−	11676.0i	0.475729	−	1.18734i
$460$		0			0
$461$	−1782.29	−	10107.9i	−0.180065	−	1.02120i	−0.932134	−	0.362113i	$-0.882055\pi$
$461$	−1782.29	−	10107.9i	−0.180065	−	1.02120i	0.752070	−	0.659084i	$-0.229056\pi$
$462$		0			0
$463$	4506.47	−	1640.22i	0.452340	−	0.164638i	−0.105796	−	0.994388i	$-0.533739\pi$
$463$	4506.47	−	1640.22i	0.452340	−	0.164638i	0.558136	+	0.829750i	$0.311517\pi$
$464$		0			0
$465$	−26373.9	−	8203.50i	−2.63023	−	0.818125i
$466$		0			0
$467$	−517.986	−	897.177i	−0.0513266	−	0.0889003i	0.839221	−	0.543791i	$-0.183012\pi$
$467$	−517.986	−	897.177i	−0.0513266	−	0.0889003i	−0.890547	+	0.454891i	$0.849678\pi$
$468$		0			0
$469$	−27.6657	+	47.9184i	−0.00272384	+	0.00471783i
$470$		0			0
$471$	−8083.94	−	6153.44i	−0.790846	−	0.601986i
$472$		0			0
$473$	609.380	−	3455.97i	0.0592375	−	0.335953i
$474$		0			0
$475$	1717.21	−	1440.91i	0.165876	−	0.139186i
$476$		0			0
$477$	−4577.09	+	436.188i	−0.439351	+	0.0418694i
$478$		0			0
$479$	−7302.87	−	2658.03i	−0.696611	−	0.253546i	−0.0306475	−	0.999530i	$-0.509757\pi$
$479$	−7302.87	−	2658.03i	−0.696611	−	0.253546i	−0.665963	+	0.745985i	$0.731979\pi$
$480$		0			0
$481$	−2607.10	−	2187.62i	−0.247138	−	0.207374i
$482$		0			0
$483$	−6547.79	+	311.292i	−0.616843	+	0.0293256i
$484$		0			0
$485$	−7876.40			−0.737421
$486$		0			0
$487$	−6402.34			−0.595724			−0.297862	−	0.954609i	$-0.596274\pi$
$487$	−6402.34			−0.595724			−0.297862	+	0.954609i	$0.596274\pi$
$488$		0			0
$489$	1580.35	−	75.1323i	0.146147	−	0.00694806i
$490$		0			0
$491$	−1539.64	−	1291.91i	−0.141513	−	0.118743i	0.569283	−	0.822141i	$-0.307221\pi$
$491$	−1539.64	−	1291.91i	−0.141513	−	0.118743i	−0.710796	+	0.703398i	$0.751665\pi$
$492$		0			0
$493$	−12158.3	−	4425.27i	−1.11072	−	0.404268i
$494$		0			0
$495$	−32893.6	+	3134.70i	−2.98678	+	0.284635i
$496$		0			0
$497$	2956.20	−	2480.55i	0.266808	−	0.223879i
$498$		0			0
$499$	1717.87	−	9742.54i	0.154113	−	0.874020i	−0.805479	−	0.592625i	$-0.798092\pi$
$499$	1717.87	−	9742.54i	0.154113	−	0.874020i	0.959592	−	0.281395i	$-0.0907972\pi$
$500$		0			0
$501$	10403.5	+	7919.06i	0.927731	+	0.706182i
$502$		0			0
$503$	3388.43	−	5868.93i	0.300363	−	0.520244i	−0.675855	−	0.737034i	$-0.736226\pi$
$503$	3388.43	−	5868.93i	0.300363	−	0.520244i	0.976218	+	0.216791i	$0.0695589\pi$
$504$		0			0
$505$	6397.19	+	11080.3i	0.563706	+	0.976367i
$506$		0			0
$507$	9776.65	+	3040.99i	0.856403	+	0.266381i
$508$		0			0
$509$	−1383.55	+	503.573i	−0.120481	+	0.0438516i	−0.401557	−	0.915834i	$-0.631531\pi$
$509$	−1383.55	+	503.573i	−0.120481	+	0.0438516i	0.281076	+	0.959686i	$0.409309\pi$
$510$		0			0
$511$	−1963.85	−	11137.5i	−0.170011	−	0.964179i
$512$		0			0
$513$	−658.643	−	838.020i	−0.0566857	−	0.0721237i
$514$		0			0
$515$	3721.72	+	21106.9i	0.318444	+	1.80598i
$516$		0			0
$517$	17844.2	−	6494.76i	1.51796	−	0.552494i
$518$		0			0
$519$	−2076.28	+	1917.40i	−0.175604	+	0.162167i
$520$		0			0
$521$	−6864.02	−	11888.8i	−0.577194	−	0.999730i	−0.995799	−	0.0915615i	$-0.970814\pi$
$521$	−6864.02	−	11888.8i	−0.577194	−	0.999730i	0.418605	−	0.908168i	$-0.362519\pi$
$522$		0			0
$523$	2877.17	−	4983.40i	0.240554	−	0.416652i	−0.720318	−	0.693644i	$-0.756004\pi$
$523$	2877.17	−	4983.40i	0.240554	−	0.416652i	0.960872	+	0.276992i	$0.0893376\pi$
$524$		0			0
$525$	1822.36	−	14269.0i	0.151494	−	1.18619i
$526$		0			0
$527$	−4037.74	+	22899.1i	−0.333751	+	1.89279i
$528$		0			0
$529$	4529.00	−	3800.28i	0.372236	−	0.312343i
$530$		0			0
$531$	−2397.54	−	1651.25i	−0.195940	−	0.134949i
$532$		0			0
$533$	−2661.73	−	968.789i	−0.216308	−	0.0787297i
$534$		0			0
$535$	3443.72	+	2889.62i	0.278289	+	0.233513i
$536$		0			0
$537$	7086.13	−	13742.0i	0.569440	−	1.10430i
$538$		0			0
$539$	15224.6			1.21664
$540$		0			0
$541$	−17020.2			−1.35260			−0.676298	−	0.736628i	$-0.736417\pi$
$541$	−17020.2			−1.35260			−0.676298	+	0.736628i	$0.736417\pi$
$542$		0			0
$543$	−36.3643	−	56.5957i	−0.00287393	−	0.00447284i
$544$		0			0
$545$	−32451.3	−	27229.9i	−2.55057	−	2.14019i
$546$		0			0
$547$	−18304.3	−	6662.21i	−1.43078	−	0.520760i	−0.493623	−	0.869676i	$-0.664328\pi$
$547$	−18304.3	−	6662.21i	−1.43078	−	0.520760i	−0.937154	+	0.348916i	$0.886550\pi$
$548$		0			0
$549$	−9020.31	−	2342.26i	−0.701234	−	0.182086i
$550$		0			0
$551$	−839.894	+	704.755i	−0.0649377	+	0.0544892i
$552$		0			0
$553$	185.855	−	1054.04i	0.0142918	−	0.0810529i
$554$		0			0
$555$	22210.5	−	9300.82i	1.69871	−	0.711347i
$556$		0			0
$557$	−2898.44	+	5020.24i	−0.220486	+	0.381893i	−0.954956	−	0.296748i	$-0.904098\pi$
$557$	−2898.44	+	5020.24i	−0.220486	+	0.381893i	0.734469	+	0.678642i	$0.237431\pi$
$558$		0			0
$559$	442.313	+	766.109i	0.0334667	+	0.0579660i
$560$		0			0
$561$	6125.89	+	27134.4i	0.461025	+	2.04210i
$562$		0			0
$563$	8296.09	−	3019.53i	0.621027	−	0.226035i	−0.0122940	−	0.999924i	$-0.503913\pi$
$563$	8296.09	−	3019.53i	0.621027	−	0.226035i	0.633321	+	0.773889i	$0.281691\pi$
$564$		0			0
$565$	−587.819	−	3333.69i	−0.0437694	−	0.248229i
$566$		0			0
$567$	−6753.45	−	1083.24i	−0.500208	−	0.0802324i
$568$		0			0
$569$	1083.07	+	6142.40i	0.0797973	+	0.452553i	0.998358	+	0.0572742i	$0.0182409\pi$
$569$	1083.07	+	6142.40i	0.0797973	+	0.452553i	−0.918561	+	0.395279i	$0.870648\pi$
$570$		0			0
$571$	4348.11	−	1582.58i	0.318674	−	0.115988i	−0.177730	−	0.984079i	$-0.556876\pi$
$571$	4348.11	−	1582.58i	0.318674	−	0.115988i	0.496404	+	0.868091i	$0.334653\pi$
$572$		0			0
$573$	706.316	+	3128.60i	0.0514952	+	0.228096i
$574$		0			0
$575$	19836.7	+	34358.1i	1.43869	+	2.49188i
$576$		0			0
$577$	−3232.20	+	5598.33i	−0.233203	+	0.403920i	−0.958749	−	0.284254i	$-0.908254\pi$
$577$	−3232.20	+	5598.33i	−0.233203	+	0.403920i	0.725546	+	0.688174i	$0.241587\pi$
$578$		0			0
$579$	9899.56	−	4145.52i	0.710555	−	0.297551i
$580$		0			0
$581$	−2307.83	+	13088.4i	−0.164793	+	0.934590i
$582$		0			0
$583$	7789.30	−	6536.00i	0.553344	−	0.464311i
$584$		0			0
$585$	5844.02	−	5935.25i	0.413027	−	0.419474i
$586$		0			0
$587$	−1888.52	−	687.365i	−0.132790	−	0.0483315i	0.274771	−	0.961510i	$-0.411398\pi$
$587$	−1888.52	−	687.365i	−0.132790	−	0.0483315i	−0.407560	+	0.913178i	$0.633620\pi$
$588$		0			0
$589$	1509.40	+	1266.54i	0.105592	+	0.0886023i
$590$		0			0
$591$	−1687.34	−	2626.09i	−0.117441	−	0.182780i
$592$		0			0
$593$	−22078.4			−1.52892			−0.764460	−	0.644671i	$-0.776994\pi$
$593$	−22078.4			−1.52892			−0.764460	+	0.644671i	$0.776994\pi$
$594$		0			0
$595$	−17240.4			−1.18788
$596$		0			0
$597$	−8859.33	+	17180.7i	−0.607350	+	1.17782i
$598$		0			0
$599$	512.637	+	430.153i	0.0349679	+	0.0293415i	0.660104	−	0.751174i	$-0.270512\pi$
$599$	512.637	+	430.153i	0.0349679	+	0.0293415i	−0.625136	+	0.780516i	$0.714957\pi$
$600$		0			0
$601$	−25139.4	−	9150.01i	−1.70626	−	0.621026i	−0.709742	−	0.704462i	$-0.751188\pi$
$601$	−25139.4	−	9150.01i	−1.70626	−	0.621026i	−0.996513	+	0.0834358i	$0.973411\pi$
$602$		0			0
$603$	12.6488	−	158.725i	0.000854225	−	0.0107194i
$604$		0			0
$605$	35081.3	−	29436.7i	2.35745	−	1.97813i
$606$		0			0
$607$	−768.770	+	4359.91i	−0.0514059	+	0.291538i	−0.999663	−	0.0259666i	$-0.991734\pi$
$607$	−768.770	+	4359.91i	−0.0514059	+	0.291538i	0.948257	+	0.317504i	$0.102845\pi$
$608$		0			0
$609$	−891.322	+	6978.99i	−0.0593074	+	0.464373i
$610$		0			0
$611$	−2393.44	+	4145.57i	−0.158475	+	0.274487i
$612$		0			0
$613$	12641.3	+	21895.3i	0.832915	+	1.44265i	0.895717	+	0.444624i	$0.146663\pi$
$613$	12641.3	+	21895.3i	0.832915	+	1.44265i	−0.0628026	+	0.998026i	$0.520004\pi$
$614$		0			0
$615$	14723.2	−	13596.6i	0.965359	−	0.891490i
$616$		0			0
$617$	−5179.38	+	1885.14i	−0.337948	+	0.123003i	−0.505419	−	0.862874i	$-0.668662\pi$
$617$	−5179.38	+	1885.14i	−0.337948	+	0.123003i	0.167471	+	0.985877i	$0.446440\pi$
$618$		0			0
$619$	2252.52	+	12774.7i	0.146263	+	0.829497i	0.966345	+	0.257251i	$0.0828166\pi$
$619$	2252.52	+	12774.7i	0.146263	+	0.829497i	−0.820082	+	0.572246i	$0.806072\pi$
$620$		0			0
$621$	16630.3	−	8904.25i	1.07464	−	0.575387i
$622$		0			0
$623$	−2226.74	−	12628.5i	−0.143198	−	0.812117i
$624$		0			0
$625$	−32468.9	+	11817.7i	−2.07801	+	0.756334i
$626$		0			0
$627$	2250.84	+	700.115i	0.143365	+	0.0445931i
$628$		0			0
$629$	−10135.7	−	17555.5i	−0.642507	−	1.11285i
$630$		0			0
$631$	7534.06	−	13049.4i	0.475319	−	0.823276i	−0.524282	−	0.851545i	$-0.675666\pi$
$631$	7534.06	−	13049.4i	0.475319	−	0.823276i	0.999600	+	0.0282687i	$0.00899939\pi$
$632$		0			0
$633$	6674.67	+	5080.71i	0.419106	+	0.319021i
$634$		0			0
$635$	5705.70	−	32358.6i	0.356573	−	2.02222i
$636$		0			0
$637$	−2939.96	+	2466.92i	−0.182866	+	0.153443i
$638$		0			0
$639$	−4615.20	+	10100.8i	−0.285719	+	0.625326i
$640$		0			0
$641$	859.168	+	312.712i	0.0529409	+	0.0192689i	0.368355	−	0.929685i	$-0.379921\pi$
$641$	859.168	+	312.712i	0.0529409	+	0.0192689i	−0.315414	+	0.948954i	$0.602143\pi$
$642$		0			0
$643$	15011.2	+	12595.9i	0.920657	+	0.772523i	0.974116	−	0.226047i	$-0.0725804\pi$
$643$	15011.2	+	12595.9i	0.920657	+	0.772523i	−0.0534597	+	0.998570i	$0.517025\pi$
$644$		0			0
$645$	−6251.87	+	297.223i	−0.381654	+	0.0181444i
$646$		0			0
$647$	13286.6			0.807339			0.403670	−	0.914905i	$-0.367735\pi$
$647$	13286.6			0.807339			0.403670	+	0.914905i	$0.367735\pi$
$648$		0			0
$649$	6438.08			0.389394
$650$		0			0
$651$	12629.8	−	600.438i	0.760369	−	0.0361490i
$652$		0			0
$653$	4349.80	+	3649.92i	0.260675	+	0.218733i	0.763753	−	0.645509i	$-0.223355\pi$
$653$	4349.80	+	3649.92i	0.260675	+	0.218733i	−0.503078	+	0.864241i	$0.667799\pi$
$654$		0			0
$655$	40721.6	+	14821.5i	2.42920	+	0.884156i
$656$		0			0
$657$	18873.1	+	26514.1i	1.12071	+	1.57445i
$658$		0			0
$659$	−9412.25	+	7897.82i	−0.556372	+	0.466852i	−0.877092	−	0.480322i	$-0.840520\pi$
$659$	−9412.25	+	7897.82i	−0.556372	+	0.466852i	0.320720	+	0.947174i	$0.396075\pi$
$660$		0			0
$661$	1355.06	−	7684.91i	0.0797362	−	0.452206i	−0.918633	−	0.395113i	$-0.870706\pi$
$661$	1355.06	−	7684.91i	0.0797362	−	0.452206i	0.998369	−	0.0570936i	$-0.0181833\pi$
$662$		0			0
$663$	−5579.68	−	4247.21i	−0.326843	−	0.248790i
$664$		0			0
$665$	−730.465	+	1265.20i	−0.0425958	+	0.0737781i
$666$		0			0
$667$	−9702.19	−	16804.7i	−0.563224	−	0.975533i
$668$		0			0
$669$	−17252.4	−	5366.29i	−0.997034	−	0.310124i
$670$		0			0
$671$	19367.3	−	7049.10i	1.11425	−	0.405555i
$672$		0			0
$673$	4431.14	+	25130.2i	0.253800	+	1.43937i	0.799133	+	0.601154i	$0.205292\pi$
$673$	4431.14	+	25130.2i	0.253800	+	1.43937i	−0.545333	+	0.838220i	$0.683597\pi$
$674$		0			0
$675$	12905.7	+	39332.5i	0.735914	+	2.24283i
$676$		0			0
$677$	−4224.47	−	23958.2i	−0.239822	−	1.36010i	−0.832216	−	0.554451i	$-0.812928\pi$
$677$	−4224.47	−	23958.2i	−0.239822	−	1.36010i	0.592394	−	0.805648i	$-0.298183\pi$
$678$		0			0
$679$	3388.23	−	1233.21i	0.191499	−	0.0697001i
$680$		0			0
$681$	2858.97	−	2640.20i	0.160875	−	0.148565i
$682$		0			0
$683$	−12807.8	−	22183.8i	−0.717535	−	1.24281i	−0.961973	−	0.273143i	$-0.911937\pi$
$683$	−12807.8	−	22183.8i	−0.717535	−	1.24281i	0.244438	−	0.969665i	$-0.421397\pi$
$684$		0			0
$685$	−10287.6	+	17818.7i	−0.573825	+	0.993894i
$686$		0			0
$687$	−2383.00	+	18658.7i	−0.132339	+	1.03621i
$688$		0			0
$689$	−445.099	+	2524.28i	−0.0246109	+	0.139575i
$690$		0			0
$691$	−7664.03	+	6430.89i	−0.421930	+	0.354041i	−0.828897	−	0.559402i	$-0.811031\pi$
$691$	−7664.03	+	6430.89i	−0.421930	+	0.354041i	0.406967	+	0.913443i	$0.366586\pi$
$692$		0			0
$693$	13659.2	−	6498.64i	0.748729	−	0.356224i
$694$		0			0
$695$	−2894.31	−	1053.44i	−0.157968	−	0.0574956i
$696$		0			0
$697$	−12924.4	−	10844.9i	−0.702365	−	0.589354i
$698$		0			0
$699$	−9725.30	+	18860.1i	−0.526244	+	1.02053i
$700$		0			0
$701$	18295.6			0.985758			0.492879	−	0.870098i	$-0.335945\pi$
$701$	18295.6			0.985758			0.492879	+	0.870098i	$0.335945\pi$
$702$		0			0
$703$	−1717.78			−0.0921581
$704$		0			0
$705$	−18307.9	−	28493.5i	−0.978035	−	1.52217i
$706$		0			0
$707$	−4486.75	−	3764.83i	−0.238673	−	0.200270i
$708$		0			0
$709$	8676.97	+	3158.16i	0.459620	+	0.167288i	0.561445	−	0.827514i	$-0.310246\pi$
$709$	8676.97	+	3158.16i	0.459620	+	0.167288i	−0.101824	+	0.994802i	$0.532468\pi$
$710$		0			0
$711$	820.187	+	2968.81i	0.0432622	+	0.156595i
$712$		0			0
$713$	−26713.7	+	22415.4i	−1.40313	+	1.17737i
$714$		0			0
$715$	−3198.74	+	18141.0i	−0.167309	+	0.948858i
$716$		0			0
$717$	14125.8	−	5915.30i	0.735759	−	0.308105i
$718$		0			0
$719$	8925.75	−	15459.9i	0.462968	−	0.801885i	−0.536139	−	0.844130i	$-0.680118\pi$
$719$	8925.75	−	15459.9i	0.462968	−	0.801885i	0.999107	+	0.0422449i	$0.0134510\pi$
$720$		0			0
$721$	−4905.71	−	8496.93i	−0.253395	−	0.438894i
$722$		0			0
$723$	−114.460	−	506.997i	−0.00588771	−	0.0260794i
$724$		0			0
$725$	40013.4	−	14563.7i	2.04974	−	0.746044i
$726$		0			0
$727$	−1140.17	−	6466.24i	−0.0581660	−	0.329876i	0.941814	−	0.336133i	$-0.109119\pi$
$727$	−1140.17	−	6466.24i	−0.0581660	−	0.329876i	−0.999980	+	0.00625749i	$0.998008\pi$
$728$		0			0
$729$	18888.8	−	5534.66i	0.959652	−	0.281190i
$730$		0			0
$731$	914.977	+	5189.09i	0.0462950	+	0.262552i
$732$		0			0
$733$	−11643.6	+	4237.94i	−0.586723	+	0.213550i	−0.618287	−	0.785952i	$-0.712173\pi$
$733$	−11643.6	+	4237.94i	−0.586723	+	0.213550i	0.0315647	+	0.999502i	$0.489951\pi$
$734$		0			0
$735$	−5979.73	−	26487.0i	−0.300089	−	1.32923i
$736$		0			0
$737$	176.069	+	304.961i	0.00879998	+	0.0152420i
$738$		0			0
$739$	−14098.2	+	24418.8i	−0.701773	+	1.21551i	0.266070	+	0.963954i	$0.414275\pi$
$739$	−14098.2	+	24418.8i	−0.701773	+	1.21551i	−0.967843	+	0.251554i	$0.919059\pi$
$740$		0			0
$741$	−548.093	+	229.518i	−0.0271723	+	0.0113786i
$742$		0			0
$743$	−4020.09	+	22799.1i	−0.198497	+	1.12573i	0.708854	+	0.705355i	$0.249213\pi$
$743$	−4020.09	+	22799.1i	−0.198497	+	1.12573i	−0.907351	+	0.420375i	$0.861899\pi$
$744$		0			0
$745$	−31920.7	+	26784.6i	−1.56978	+	1.31720i
$746$		0			0
$747$	−10184.6	−	36864.8i	−0.498840	−	1.80564i
$748$		0			0
$749$	−1933.83	−	703.855i	−0.0943398	−	0.0343369i
$750$		0			0
$751$	−16955.6	−	14227.4i	−0.823859	−	0.691300i	0.130013	−	0.991512i	$-0.458498\pi$
$751$	−16955.6	−	14227.4i	−0.823859	−	0.691300i	−0.953872	+	0.300212i	$0.902942\pi$
$752$		0			0
$753$	12611.0	+	19627.2i	0.610319	+	0.949872i
$754$		0			0
$755$	−26712.2			−1.28762
$756$		0			0
$757$	22131.8			1.06261			0.531303	−	0.847182i	$-0.321703\pi$
$757$	22131.8			1.06261			0.531303	+	0.847182i	$0.321703\pi$
$758$		0			0
$759$	−19119.9	+	37078.9i	−0.914374	+	1.77323i
$760$		0			0
$761$	29295.5	+	24581.8i	1.39548	+	1.17095i	0.963064	+	0.269274i	$0.0867837\pi$
$761$	29295.5	+	24581.8i	1.39548	+	1.17095i	0.432417	+	0.901674i	$0.357661\pi$
$762$		0			0
$763$	18223.1	+	6632.68i	0.864642	+	0.314704i
$764$		0			0
$765$	44801.0	−	21315.0i	2.11737	−	1.00738i
$766$		0			0
$767$	−1243.23	+	1043.20i	−0.0585274	+	0.0491103i
$768$		0			0
$769$	7186.45	−	40756.4i	0.336996	−	1.91120i	−0.0695665	−	0.997577i	$-0.522162\pi$
$769$	7186.45	−	40756.4i	0.336996	−	1.91120i	0.406563	−	0.913623i	$-0.366727\pi$
$770$		0			0
$771$	−2037.15	+	15950.8i	−0.0951573	+	0.745076i
$772$		0			0
$773$	−11033.1	+	19110.0i	−0.513370	+	0.889182i	0.486510	+	0.873675i	$0.338270\pi$
$773$	−11033.1	+	19110.0i	−0.513370	+	0.889182i	−0.999880	+	0.0155073i	$0.995064\pi$
$774$		0			0
$775$	−38262.2	−	66272.1i	−1.77344	−	3.07169i
$776$		0			0
$777$	−8098.15	+	7478.48i	−0.373899	+	0.345288i
$778$		0			0
$779$	−1343.46	+	488.981i	−0.0617903	+	0.0224898i
$780$		0			0
$781$	−4264.73	−	24186.5i	−0.195396	−	1.10814i
$782$		0			0
$783$	−6312.24	−	19237.7i	−0.288098	−	0.878031i
$784$		0			0
$785$	−6958.49	−	39463.5i	−0.316381	−	1.79429i
$786$		0			0
$787$	30214.2	−	10997.1i	1.36851	−	0.498098i	0.449838	−	0.893110i	$-0.351482\pi$
$787$	30214.2	−	10997.1i	1.36851	−	0.498098i	0.918676	+	0.395012i	$0.129260\pi$
$788$		0			0
$789$	26655.0	+	8290.96i	1.20272	+	0.374101i
$790$		0			0
$791$	774.822	+	1342.03i	0.0348287	+	0.0603250i
$792$		0			0
$793$	−2597.73	+	4499.40i	−0.116328	+	0.201486i
$794$		0			0
$795$	−14430.4	−	10984.3i	−0.643765	−	0.490029i
$796$		0			0
$797$	2366.52	−	13421.2i	0.105178	−	0.596492i	−0.885972	−	0.463740i	$-0.846507\pi$
$797$	2366.52	−	13421.2i	0.105178	−	0.596492i	0.991149	−	0.132753i	$-0.0423816\pi$
$798$		0			0
$799$	−21841.7	+	18327.4i	−0.967091	+	0.811485i
$800$		0			0
$801$	21399.6	+	30063.5i	0.943965	+	1.32614i
$802$		0			0
$803$	−67634.0	−	24616.8i	−2.97229	−	1.08183i
$804$		0			0
$805$	−19806.7	−	16619.8i	−0.867199	−	0.727667i
$806$		0			0
$807$	18260.3	−	868.122i	0.796522	−	0.0378678i
$808$		0			0
$809$	−36411.3			−1.58239			−0.791194	−	0.611565i	$-0.790540\pi$
$809$	−36411.3			−1.58239			−0.791194	+	0.611565i	$0.790540\pi$
$810$		0			0
$811$	1772.50			0.0767460			0.0383730	−	0.999263i	$-0.487782\pi$
$811$	1772.50			0.0767460			0.0383730	+	0.999263i	$0.487782\pi$
$812$		0			0
$813$	875.141	−	41.6055i	0.0377522	−	0.00179479i
$814$		0			0
$815$	4780.49	+	4011.30i	0.205464	+	0.172405i
$816$		0			0
$817$	419.574	+	152.712i	0.0179670	+	0.00653945i
$818$		0			0
$819$	−1584.66	+	3468.20i	−0.0676100	+	0.147971i
$820$		0			0
$821$	−17618.5	+	14783.6i	−0.748951	+	0.628444i	−0.935225	−	0.354053i	$-0.884803\pi$
$821$	−17618.5	+	14783.6i	−0.748951	+	0.628444i	0.186274	+	0.982498i	$0.440359\pi$
$822$		0			0
$823$	150.455	−	853.275i	0.00637248	−	0.0361401i	−0.981456	−	0.191689i	$-0.938604\pi$
$823$	150.455	−	853.275i	0.00637248	−	0.0361401i	0.987828	+	0.155549i	$0.0497146\pi$
$824$		0			0
$825$	−72844.9	−	55449.0i	−3.07410	−	2.33998i
$826$		0			0
$827$	4302.27	−	7451.75i	0.180900	−	0.313328i	−0.761287	−	0.648415i	$-0.775432\pi$
$827$	4302.27	−	7451.75i	0.180900	−	0.313328i	0.942187	+	0.335086i	$0.108766\pi$
$828$		0			0
$829$	−178.808	−	309.705i	−0.00749127	−	0.0129753i	0.862255	−	0.506474i	$-0.169051\pi$
$829$	−178.808	−	309.705i	−0.00749127	−	0.0129753i	−0.869747	+	0.493498i	$0.835718\pi$
$830$		0			0
$831$	−13633.9	−	4240.76i	−0.569137	−	0.177028i
$832$		0			0
$833$	−21480.9	+	7818.43i	−0.893482	+	0.325201i
$834$		0			0
$835$	8955.10	+	50786.9i	0.371143	+	2.10486i
$836$		0			0
$837$	−32077.5	+	17175.1i	−1.32469	+	0.709267i
$838$		0			0
$839$	5844.26	+	33144.5i	0.240484	+	1.36385i	0.830750	+	0.556645i	$0.187912\pi$
$839$	5844.26	+	33144.5i	0.240484	+	1.36385i	−0.590266	+	0.807209i	$0.700977\pi$
$840$		0			0
$841$	3347.45	−	1218.37i	0.137253	−	0.0499558i
$842$		0			0
$843$	19178.3	−	17710.8i	0.783555	−	0.723598i
$844$		0			0
$845$	20192.4	+	34974.2i	0.822058	+	1.42385i
$846$		0			0
$847$	−10482.1	+	18155.6i	−0.425231	+	0.736521i
$848$		0			0
$849$	241.348	−	1889.74i	0.00975621	−	0.0763906i
$850$		0			0
$851$	5279.17	−	29939.7i	0.212653	−	1.20602i
$852$		0			0
$853$	23937.0	−	20085.6i	0.960830	−	0.806232i	−0.0202575	−	0.999795i	$-0.506449\pi$
$853$	23937.0	−	20085.6i	0.960830	−	0.806232i	0.981088	+	0.193562i	$0.0620042\pi$
$854$		0			0
$855$	333.969	−	4190.88i	0.0133585	−	0.167631i
$856$		0			0
$857$	22316.3	+	8122.48i	0.889511	+	0.323756i	0.746042	−	0.665899i	$-0.231952\pi$
$857$	22316.3	+	8122.48i	0.889511	+	0.323756i	0.143469	+	0.989655i	$0.454174\pi$
$858$		0			0
$859$	5888.94	+	4941.40i	0.233909	+	0.196273i	0.752207	−	0.658927i	$-0.228990\pi$
$859$	5888.94	+	4941.40i	0.233909	+	0.196273i	−0.518297	+	0.855200i	$0.673434\pi$
$860$		0			0
$861$	−4204.71	+	8154.10i	−0.166430	+	0.322754i
$862$		0			0
$863$	48145.1			1.89905			0.949525	−	0.313692i	$-0.101566\pi$
$863$	48145.1			1.89905			0.949525	+	0.313692i	$0.101566\pi$
$864$		0			0
$865$	−11147.4			−0.438178
$866$		0			0
$867$	−8778.00	−	13661.7i	−0.343848	−	0.535149i
$868$		0			0
$869$	−5217.96	−	4378.39i	−0.203690	−	0.170917i
$870$		0			0
$871$	−83.4143	−	30.3603i	−0.00324499	−	0.00118108i
$872$		0			0
$873$	−7280.00	+	7393.65i	−0.282235	+	0.286641i
$874$		0			0
$875$	25051.0	−	21020.2i	0.967859	−	0.812130i
$876$		0			0
$877$	2077.55	−	11782.4i	0.0799929	−	0.453662i	−0.918332	−	0.395810i	$-0.870464\pi$
$877$	2077.55	−	11782.4i	0.0799929	−	0.453662i	0.998325	−	0.0578519i	$-0.0184251\pi$
$878$		0			0
$879$	−5615.77	+	2351.65i	−0.215489	+	0.0902379i
$880$		0			0
$881$	−2602.29	+	4507.29i	−0.0995156	+	0.172366i	−0.911484	−	0.411335i	$-0.865063\pi$
$881$	−2602.29	+	4507.29i	−0.0995156	+	0.172366i	0.811969	+	0.583701i	$0.198396\pi$
$882$		0			0
$883$	558.434	+	967.235i	0.0212829	+	0.0368630i	0.876471	−	0.481455i	$-0.159892\pi$
$883$	558.434	+	967.235i	0.0212829	+	0.0368630i	−0.855188	+	0.518318i	$0.826558\pi$
$884$		0			0
$885$	−2528.67	−	11200.7i	−0.0960456	−	0.425430i
$886$		0			0
$887$	36086.5	−	13134.4i	1.36603	−	0.497193i	0.448114	−	0.893977i	$-0.352096\pi$
$887$	36086.5	−	13134.4i	1.36603	−	0.497193i	0.917912	+	0.396784i	$0.129874\pi$
$888$		0			0
$889$	2611.96	+	14813.2i	0.0985404	+	0.558851i
$890$		0			0
$891$	−27460.3	+	33774.9i	−1.03250	+	1.26992i
$892$		0			0
$893$	419.552	+	2379.40i	0.0157220	+	0.0891642i
$894$		0			0
$895$	57307.2	−	20858.1i	2.14030	−	0.779005i
$896$		0			0
$897$	−2315.92	−	10258.3i	−0.0862054	−	0.381844i
$898$		0			0
$899$	18714.2	+	32413.9i	0.694274	+	1.20252i
$900$		0			0
$901$	−7633.72	+	13222.0i	−0.282260	+	0.488888i
$902$		0			0
$903$	2642.85	−	1106.72i	0.0973961	−	0.0407854i
$904$		0			0
$905$	46.0759	−	261.309i	0.00169239	−	0.00959803i
$906$		0			0
$907$	26611.2	−	22329.4i	0.974211	−	0.817460i	−0.00899504	−	0.999960i	$-0.502863\pi$
$907$	26611.2	−	22329.4i	0.974211	−	0.817460i	0.983206	+	0.182500i	$0.0584188\pi$
$908$		0			0
$909$	16313.9	+	4236.16i	0.595269	+	0.154571i
$910$		0			0
$911$	7266.12	+	2644.65i	0.264256	+	0.0961814i	0.470750	−	0.882266i	$-0.343983\pi$
$911$	7266.12	+	2644.65i	0.264256	+	0.0961814i	−0.206494	+	0.978448i	$0.566205\pi$
$912$		0			0
$913$	64793.2	+	54368.0i	2.34868	+	1.97078i
$914$		0			0
$915$	−19870.5	−	30925.5i	−0.717922	−	1.11734i
$916$		0			0
$917$	−19838.0			−0.714404
$918$		0			0
$919$	3458.97			0.124158			0.0620788	−	0.998071i	$-0.480227\pi$
$919$	3458.97			0.124158			0.0620788	+	0.998071i	$0.480227\pi$
$920$		0			0
$921$	−20061.3	+	38904.6i	−0.717745	+	1.39191i
$922$		0			0
$923$	4742.61	+	3979.52i	0.169128	+	0.141915i
$924$		0			0
$925$	62690.5	+	22817.5i	2.22838	+	0.811064i
$926$		0			0
$927$	23253.1	+	16015.1i	0.823877	+	0.567426i
$928$		0			0
$929$	26175.9	−	21964.2i	0.924440	−	0.775697i	−0.0503710	−	0.998731i	$-0.516040\pi$
$929$	26175.9	−	21964.2i	0.924440	−	0.775697i	0.974811	+	0.223033i	$0.0715959\pi$
$930$		0			0
$931$	−336.373	+	1907.66i	−0.0118412	+	0.0671548i
$932$		0			0
$933$	4127.60	−	32318.9i	0.144836	−	1.13405i
$934$		0			0
$935$	−54860.4	+	95020.9i	−1.91885	+	3.32355i
$936$		0			0
$937$	−10113.2	−	17516.6i	−0.352598	−	0.610717i	0.634106	−	0.773246i	$-0.281368\pi$
$937$	−10113.2	−	17516.6i	−0.352598	−	0.610717i	−0.986704	+	0.162529i	$0.948035\pi$
$938$		0			0
$939$	−7782.37	+	7186.87i	−0.270466	+	0.249771i
$940$		0			0
$941$	−10035.5	+	3652.62i	−0.347659	+	0.126538i	−0.509947	−	0.860206i	$-0.670335\pi$
$941$	−10035.5	+	3652.62i	−0.347659	+	0.126538i	0.162288	+	0.986744i	$0.448113\pi$
$942$		0			0
$943$	−4393.80	−	24918.5i	−0.151730	−	0.860505i
$944$		0			0
$945$	−16670.9	−	21211.1i	−0.573867	−	0.730156i
$946$		0			0
$947$	−7980.48	−	45259.5i	−0.273844	−	1.55305i	−0.742608	−	0.669726i	$-0.766412\pi$
$947$	−7980.48	−	45259.5i	−0.273844	−	1.55305i	0.468764	−	0.883323i	$-0.344699\pi$
$948$		0			0
$949$	17049.3	−	6205.44i	0.583187	−	0.212263i
$950$		0			0
$951$	−26061.1	−	8106.21i	−0.888632	−	0.276406i
$952$		0			0
$953$	11800.2	+	20438.5i	0.401096	+	0.694718i	0.993858	−	0.110659i	$-0.0352961\pi$
$953$	11800.2	+	20438.5i	0.401096	+	0.694718i	−0.592763	+	0.805377i	$0.701963\pi$
$954$		0			0
$955$	−6325.40	+	10955.9i	−0.214330	+	0.371231i
$956$		0			0
$957$	35628.7	+	27120.3i	1.20346	+	0.916066i
$958$		0			0
$959$	1635.59	−	9275.88i	0.0550739	−	0.312340i
$960$		0			0
$961$	28705.7	−	24087.0i	0.963571	−	0.808532i
$962$		0			0
$963$	5895.47	−	561.828i	0.197278	−	0.0188003i
$964$		0			0
$965$	39779.6	+	14478.6i	1.32699	+	0.482987i
$966$		0			0
$967$	−30114.9	−	25269.4i	−1.00148	−	0.840339i	−0.0142886	−	0.999898i	$-0.504548\pi$
$967$	−30114.9	−	25269.4i	−1.00148	−	0.840339i	−0.987188	+	0.159559i	$0.948993\pi$
$968$		0			0
$969$	−3535.33	+	168.074i	−0.117204	+	0.00557206i
$970$		0			0
$971$	−20618.9			−0.681455			−0.340728	−	0.940162i	$-0.610673\pi$
$971$	−20618.9			−0.681455			−0.340728	+	0.940162i	$0.610673\pi$
$972$		0			0
$973$	1410.00			0.0464568
$974$		0			0
$975$	23051.5	−	1095.90i	0.757167	−	0.0359968i
$976$		0			0
$977$	26281.1	+	22052.5i	0.860602	+	0.722131i	0.962098	−	0.272705i	$-0.0879184\pi$
$977$	26281.1	+	22052.5i	0.860602	+	0.722131i	−0.101496	+	0.994836i	$0.532363\pi$
$978$		0			0
$979$	−76687.9	−	27912.1i	−2.50353	−	0.911211i
$980$		0			0
$981$	−55555.1	+	5294.30i	−1.80809	+	0.172308i
$982$		0			0
$983$	−30850.4	+	25886.6i	−1.00099	+	0.839932i	−0.987122	−	0.159971i	$-0.948860\pi$
$983$	−30850.4	+	25886.6i	−1.00099	+	0.839932i	−0.0138709	+	0.999904i	$0.504415\pi$
$984$		0			0
$985$	2137.96	−	12125.0i	0.0691585	−	0.392217i
$986$		0			0
$987$	12336.8	+	9390.71i	0.397858	+	0.302846i
$988$		0			0
$989$	−3951.14	+	6843.57i	−0.127036	+	0.220033i
$990$		0			0
$991$	10507.4	+	18199.3i	0.336809	+	0.583370i	0.983831	−	0.179102i	$-0.0573192\pi$
$991$	10507.4	+	18199.3i	0.336809	+	0.583370i	−0.647022	+	0.762471i	$0.723986\pi$
$992$		0			0
$993$	−27800.5	−	8647.26i	−0.888442	−	0.276347i
$994$		0			0
$995$	−71647.4	+	26077.5i	−2.28279	+	0.830868i
$996$		0			0
$997$	−1859.20	−	10544.0i	−0.0590586	−	0.334938i	0.940935	−	0.338588i	$-0.109949\pi$
$997$	−1859.20	−	10544.0i	−0.0590586	−	0.334938i	−0.999993	+	0.00365000i	$0.998838\pi$
$998$		0			0
$999$	11798.0	−	29445.8i	0.373645	−	0.932555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.i.a.13.9	✓	54
3.2	odd	2		324.4.i.a.253.1		54
27.2	odd	18		324.4.i.a.73.1		54
27.25	even	9	inner	108.4.i.a.25.9	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.13.9	✓	54	1.1	even	1	trivial
108.4.i.a.25.9	yes	54	27.25	even	9	inner
324.4.i.a.73.1		54	27.2	odd	18
324.4.i.a.253.1		54	3.2	odd	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(5.19029 - 0.246754i) q^{3} +(15.7004 + 13.1742i) q^{5} +(-8.81657 - 3.20897i) q^{7} +(26.8782 - 2.56145i) q^{9} +O(q^{10})\)	\(q+(5.19029 - 0.246754i) q^{3} +(15.7004 + 13.1742i) q^{5} +(-8.81657 - 3.20897i) q^{7} +(26.8782 - 2.56145i) q^{9} +(-45.7414 + 38.3816i) q^{11} +(2.61377 - 14.8234i) q^{13} +(84.7402 + 64.5036i) q^{15} +(44.8278 - 77.6441i) q^{17} +(-3.79866 - 6.57947i) q^{19} +(-46.5524 - 14.4800i) q^{21} +(126.350 - 45.9876i) q^{23} +(51.2365 + 290.577i) q^{25} +(138.874 - 19.9270i) q^{27} +(-25.0600 - 142.122i) q^{29} +(-243.712 + 88.7037i) q^{31} +(-227.940 + 210.499i) q^{33} +(-96.1478 - 166.533i) q^{35} +(113.051 - 195.811i) q^{37} +(9.90850 - 77.5829i) q^{39} +(32.6776 - 185.324i) q^{41} +(-45.0211 + 37.7772i) q^{43} +(455.743 + 313.882i) q^{45} +(-298.842 - 108.770i) q^{47} +(-195.319 - 163.892i) q^{49} +(213.510 - 414.057i) q^{51} -170.290 q^{53} -1223.80 q^{55} +(-21.3396 - 33.2120i) q^{57} +(-82.5952 - 69.3056i) q^{59} +(-324.349 - 118.053i) q^{61} +(-245.193 - 63.6682i) q^{63} +(236.323 - 198.299i) q^{65} +(1.02407 - 5.80776i) q^{67} +(644.446 - 269.867i) q^{69} +(-205.653 + 356.202i) q^{71} +(602.689 + 1043.89i) q^{73} +(337.634 + 1495.54i) q^{75} +(526.448 - 191.611i) q^{77} +(19.8089 + 112.342i) q^{79} +(715.878 - 137.694i) q^{81} +(-245.975 - 1394.99i) q^{83} +(1726.71 - 628.470i) q^{85} +(-165.138 - 731.472i) q^{87} +(683.369 + 1183.63i) q^{89} +(-70.6125 + 122.304i) q^{91} +(-1243.05 + 520.535i) q^{93} +(27.0387 - 153.344i) q^{95} +(-294.392 + 247.025i) q^{97} +(-1131.14 + 1148.79i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 54 * q + 12 * q^5 - 48 * q^9	\( 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99}+O(q^{100}) \) 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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