LMFDB - Embedded newform 189.4.g.a.100.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(100,189)]

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([4, 2]))

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

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

chi := DirichletCharacter("189.100");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.g (of order $3$, degree $2$, not 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:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.2
Character	$\chi$	$=$	189.100
Dual form			189.4.g.a.172.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.53999 - 4.39939i) q^{2} +(-8.90312 + 15.4206i) q^{4} -18.4700 q^{5} +(-9.68740 + 15.7846i) q^{7} +49.8155 q^{8} +O(q^{10})$	\(q+(-2.53999 - 4.39939i) q^{2} +(-8.90312 + 15.4206i) q^{4} -18.4700 q^{5} +(-9.68740 + 15.7846i) q^{7} +49.8155 q^{8} +(46.9136 + 81.2567i) q^{10} -17.1812 q^{11} +(-27.2834 - 47.2562i) q^{13} +(94.0487 + 2.52592i) q^{14} +(-55.3060 - 95.7928i) q^{16} +(7.61880 + 13.1962i) q^{17} +(43.7138 - 75.7145i) q^{19} +(164.440 - 284.819i) q^{20} +(43.6402 + 75.5870i) q^{22} +96.6913 q^{23} +216.140 q^{25} +(-138.599 + 240.061i) q^{26} +(-157.161 - 289.918i) q^{28} +(-57.3750 + 99.3765i) q^{29} +(-25.0182 + 43.3329i) q^{31} +(-81.6917 + 141.494i) q^{32} +(38.7034 - 67.0362i) q^{34} +(178.926 - 291.542i) q^{35} +(3.58236 - 6.20483i) q^{37} -444.131 q^{38} -920.091 q^{40} +(87.4719 + 151.506i) q^{41} +(-77.4059 + 134.071i) q^{43} +(152.967 - 264.946i) q^{44} +(-245.595 - 425.383i) q^{46} +(-58.8666 - 101.960i) q^{47} +(-155.308 - 305.824i) q^{49} +(-548.994 - 950.886i) q^{50} +971.628 q^{52} +(1.27556 + 2.20934i) q^{53} +317.337 q^{55} +(-482.583 + 786.319i) q^{56} +582.929 q^{58} +(206.089 - 356.957i) q^{59} +(355.968 + 616.554i) q^{61} +254.184 q^{62} -54.9116 q^{64} +(503.923 + 872.820i) q^{65} +(-18.8778 + 32.6973i) q^{67} -271.324 q^{68} +(-1737.08 - 46.6536i) q^{70} +290.205 q^{71} +(209.932 + 363.612i) q^{73} -36.3966 q^{74} +(778.378 + 1348.19i) q^{76} +(166.442 - 271.199i) q^{77} +(537.670 + 931.272i) q^{79} +(1021.50 + 1769.29i) q^{80} +(444.356 - 769.647i) q^{82} +(634.888 - 1099.66i) q^{83} +(-140.719 - 243.733i) q^{85} +786.442 q^{86} -855.892 q^{88} +(-5.74700 + 9.95410i) q^{89} +(1010.23 + 27.1322i) q^{91} +(-860.854 + 1491.04i) q^{92} +(-299.041 + 517.955i) q^{94} +(-807.393 + 1398.45i) q^{95} +(935.304 - 1619.99i) q^{97} +(-950.958 + 1460.05i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) $ 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8	$ 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} + 10 q^{11} - 14 q^{13} + 79 q^{14} - 247 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} - 186 q^{23} + 698 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} + 61 q^{31} + 163 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} - 1522 q^{38} + 36 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} + 1005 q^{47} - 277 q^{49} - 239 q^{50} + 670 q^{52} - 258 q^{53} - 870 q^{55} - 714 q^{56} - 474 q^{58} + 1665 q^{59} + 439 q^{61} - 1812 q^{62} + 872 q^{64} + 613 q^{65} + 295 q^{67} - 2748 q^{68} - 1044 q^{70} - 636 q^{71} - 338 q^{73} + 2238 q^{74} + 1006 q^{76} + 2909 q^{77} + 133 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} - 6686 q^{86} - 738 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} - 1191 q^{94} - 3083 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) $ 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 + 10 * q^11 - 14 * q^13 + 79 * q^14 - 247 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 - 186 * q^23 + 698 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 + 61 * q^31 + 163 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 - 1522 * q^38 + 36 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 + 1005 * q^47 - 277 * q^49 - 239 * q^50 + 670 * q^52 - 258 * q^53 - 870 * q^55 - 714 * q^56 - 474 * q^58 + 1665 * q^59 + 439 * q^61 - 1812 * q^62 + 872 * q^64 + 613 * q^65 + 295 * q^67 - 2748 * q^68 - 1044 * q^70 - 636 * q^71 - 338 * q^73 + 2238 * q^74 + 1006 * q^76 + 2909 * q^77 + 133 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 - 6686 * q^86 - 738 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 - 1191 * q^94 - 3083 * q^95 - 266 * q^97 - 3601 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.53999	−	4.39939i	−0.898023	−	1.55542i	−0.830018	−	0.557736i	$-0.811670\pi$
$2$	−2.53999	−	4.39939i	−0.898023	−	1.55542i	−0.0680042	−	0.997685i	$-0.521663\pi$
$3$		0			0
$3$		0			0
$4$	−8.90312	+	15.4206i	−1.11289	+	1.92758i
$5$	−18.4700			−1.65201			−0.826003	−	0.563666i	$-0.809390\pi$
$5$	−18.4700			−1.65201			−0.826003	+	0.563666i	$0.809390\pi$
$6$		0			0
$7$	−9.68740	+	15.7846i	−0.523071	+	0.852289i
$7$	−9.68740	+	15.7846i	−0.523071	+	0.852289i
$8$	49.8155			2.20155
$9$		0			0
$10$	46.9136	+	81.2567i	1.48354	+	2.56956i
$11$	−17.1812			−0.470940			−0.235470	−	0.971882i	$-0.575663\pi$
$11$	−17.1812			−0.470940			−0.235470	+	0.971882i	$0.575663\pi$
$12$		0			0
$13$	−27.2834	−	47.2562i	−0.582080	−	1.00819i	−0.995233	−	0.0975305i	$-0.968906\pi$
$13$	−27.2834	−	47.2562i	−0.582080	−	1.00819i	0.413152	−	0.910662i	$-0.364428\pi$
$14$	94.0487	+	2.52592i	1.79540	+	0.0482199i
$15$		0			0
$16$	−55.3060	−	95.7928i	−0.864156	−	1.49676i
$17$	7.61880	+	13.1962i	0.108696	+	0.188267i	0.915242	−	0.402904i	$-0.131999\pi$
$17$	7.61880	+	13.1962i	0.108696	+	0.188267i	−0.806546	+	0.591171i	$0.798666\pi$
$18$		0			0
$19$	43.7138	−	75.7145i	0.527823	−	0.914216i	−0.471651	−	0.881785i	$-0.656342\pi$
$19$	43.7138	−	75.7145i	0.527823	−	0.914216i	0.999474	−	0.0324308i	$-0.0103249\pi$
$20$	164.440	−	284.819i	1.83850	−	3.18437i
$21$		0			0
$22$	43.6402	+	75.5870i	0.422915	+	0.732510i
$23$	96.6913			0.876588			0.438294	−	0.898832i	$-0.355583\pi$
$23$	96.6913			0.876588			0.438294	+	0.898832i	$0.355583\pi$
$24$		0			0
$25$	216.140			1.72912
$26$	−138.599	+	240.061i	−1.04544	+	1.81076i
$27$		0			0
$28$	−157.161	−	289.918i	−1.06074	−	1.95676i
$29$	−57.3750	+	99.3765i	−0.367389	+	0.636336i	−0.989156	−	0.146866i	$-0.953082\pi$
$29$	−57.3750	+	99.3765i	−0.367389	+	0.636336i	0.621768	+	0.783202i	$0.286415\pi$
$30$		0			0
$31$	−25.0182	+	43.3329i	−0.144949	+	0.251058i	−0.929354	−	0.369190i	$-0.879635\pi$
$31$	−25.0182	+	43.3329i	−0.144949	+	0.251058i	0.784405	+	0.620249i	$0.212968\pi$
$32$	−81.6917	+	141.494i	−0.451287	+	0.781652i
$33$		0			0
$34$	38.7034	−	67.0362i	0.195223	−	0.338136i
$35$	178.926	−	291.542i	0.864115	−	1.40799i
$36$		0			0
$37$	3.58236	−	6.20483i	0.0159172	−	0.0275694i	−0.857957	−	0.513721i	$-0.828267\pi$
$37$	3.58236	−	6.20483i	0.0159172	−	0.0275694i	0.873874	+	0.486152i	$0.161600\pi$
$38$	−444.131			−1.89599
$39$		0			0
$40$	−920.091			−3.63698
$41$	87.4719	+	151.506i	0.333191	+	0.577103i	0.983136	−	0.182878i	$-0.0585414\pi$
$41$	87.4719	+	151.506i	0.333191	+	0.577103i	−0.649945	+	0.759981i	$0.725208\pi$
$42$		0			0
$43$	−77.4059	+	134.071i	−0.274519	+	0.475480i	−0.970014	−	0.243051i	$-0.921852\pi$
$43$	−77.4059	+	134.071i	−0.274519	+	0.475480i	0.695495	+	0.718531i	$0.255185\pi$
$44$	152.967	−	264.946i	0.524104	−	0.907775i
$45$		0			0
$46$	−245.595	−	425.383i	−0.787196	−	1.36346i
$47$	−58.8666	−	101.960i	−0.182693	−	0.316434i	0.760104	−	0.649802i	$-0.225148\pi$
$47$	−58.8666	−	101.960i	−0.182693	−	0.316434i	−0.942797	+	0.333368i	$0.891815\pi$
$48$		0			0
$49$	−155.308	−	305.824i	−0.452794	−	0.891615i
$50$	−548.994	−	950.886i	−1.55279	−	2.68951i
$51$		0			0
$52$	971.628			2.59116
$53$	1.27556	+	2.20934i	0.00330588	+	0.00572596i	0.867674	−	0.497134i	$-0.165614\pi$
$53$	1.27556	+	2.20934i	0.00330588	+	0.00572596i	−0.864368	+	0.502860i	$0.832281\pi$
$54$		0			0
$55$	317.337			0.777995
$56$	−482.583	+	786.319i	−1.15157	+	1.87636i
$57$		0			0
$58$	582.929			1.31969
$59$	206.089	−	356.957i	0.454755	−	0.787659i	−0.543919	−	0.839138i	$-0.683060\pi$
$59$	206.089	−	356.957i	0.454755	−	0.787659i	0.998674	+	0.0514786i	$0.0163934\pi$
$60$		0			0
$61$	355.968	+	616.554i	0.747163	+	1.29413i	0.949177	+	0.314742i	$0.101918\pi$
$61$	355.968	+	616.554i	0.747163	+	1.29413i	−0.202014	+	0.979383i	$0.564749\pi$
$62$	254.184			0.520669
$63$		0			0
$64$	−54.9116			−0.107249
$65$	503.923	+	872.820i	0.961599	+	1.66554i
$66$		0			0
$67$	−18.8778	+	32.6973i	−0.0344222	+	0.0596210i	−0.882723	−	0.469893i	$-0.844292\pi$
$67$	−18.8778	+	32.6973i	−0.0344222	+	0.0596210i	0.848301	+	0.529514i	$0.177626\pi$
$68$	−271.324			−0.483866
$69$		0			0
$70$	−1737.08	−	46.6536i	−2.96601	−	0.0796596i
$71$	290.205			0.485084			0.242542	−	0.970141i	$-0.422019\pi$
$71$	290.205			0.485084			0.242542	+	0.970141i	$0.422019\pi$
$72$		0			0
$73$	209.932	+	363.612i	0.336584	+	0.582981i	0.983788	−	0.179336i	$-0.0573950\pi$
$73$	209.932	+	363.612i	0.336584	+	0.582981i	−0.647204	+	0.762317i	$0.724062\pi$
$74$	−36.3966			−0.0571760
$75$		0			0
$76$	778.378	+	1348.19i	1.17482	+	2.03484i
$77$	166.442	−	271.199i	0.246335	−	0.401377i
$78$		0			0
$79$	537.670	+	931.272i	0.765729	+	1.32628i	0.939860	+	0.341560i	$0.110955\pi$
$79$	537.670	+	931.272i	0.765729	+	1.32628i	−0.174131	+	0.984723i	$0.555711\pi$
$80$	1021.50	+	1769.29i	1.42759	+	2.47266i
$81$		0			0
$82$	444.356	−	769.647i	0.598425	−	1.03650i
$83$	634.888	−	1099.66i	0.839615	−	1.45426i	−0.0506023	−	0.998719i	$-0.516114\pi$
$83$	634.888	−	1099.66i	0.839615	−	1.45426i	0.890217	−	0.455537i	$-0.150553\pi$
$84$		0			0
$85$	−140.719	−	243.733i	−0.179566	−	0.311018i
$86$	786.442			0.986095
$87$		0			0
$88$	−855.892			−1.03680
$89$	−5.74700	+	9.95410i	−0.00684473	+	0.0118554i	−0.869427	−	0.494061i	$-0.835512\pi$
$89$	−5.74700	+	9.95410i	−0.00684473	+	0.0118554i	0.862583	+	0.505916i	$0.168845\pi$
$90$		0			0
$91$	1010.23	+	27.1322i	1.16374	+	0.0312552i
$92$	−860.854	+	1491.04i	−0.975545	+	1.68969i
$93$		0			0
$94$	−299.041	+	517.955i	−0.328125	+	0.568330i
$95$	−807.393	+	1398.45i	−0.871966	+	1.51029i
$96$		0			0
$97$	935.304	−	1619.99i	0.979029	−	1.69573i	0.313085	−	0.949725i	$-0.398637\pi$
$97$	935.304	−	1619.99i	0.979029	−	1.69573i	0.665943	−	0.746002i	$-0.268029\pi$
$98$	−950.958	+	1460.05i	−0.980217	+	1.50498i
$99$		0			0
$100$	−1924.32	+	3333.02i	−1.92432	+	3.33302i
$101$	−500.879			−0.493459			−0.246729	−	0.969084i	$-0.579356\pi$
$101$	−500.879			−0.493459			−0.246729	+	0.969084i	$0.579356\pi$
$102$		0			0
$103$	675.061			0.645784			0.322892	−	0.946436i	$-0.395345\pi$
$103$	675.061			0.645784			0.322892	+	0.946436i	$0.395345\pi$
$104$	−1359.13	−	2354.09i	−1.28148	−	2.21959i
$105$		0			0
$106$	6.47983	−	11.2234i	0.00593751	−	0.0102841i
$107$	327.267	−	566.844i	0.295683	−	0.512139i	−0.679460	−	0.733712i	$-0.737786\pi$
$107$	327.267	−	566.844i	0.295683	−	0.512139i	0.975144	+	0.221574i	$0.0711193\pi$
$108$		0			0
$109$	−216.870	−	375.630i	−0.190573	−	0.330081i	0.754868	−	0.655877i	$-0.227701\pi$
$109$	−216.870	−	375.630i	−0.190573	−	0.330081i	−0.945440	+	0.325796i	$0.894368\pi$
$110$	−806.034	−	1396.09i	−0.698657	−	1.21011i
$111$		0			0
$112$	2047.83	+	54.9995i	1.72769	+	0.0464015i
$113$	929.178	+	1609.38i	0.773537	+	1.33981i	0.935613	+	0.353028i	$0.114848\pi$
$113$	929.178	+	1609.38i	0.773537	+	1.33981i	−0.162076	+	0.986778i	$0.551819\pi$
$114$		0			0
$115$	−1785.89			−1.44813
$116$	−1021.63	−	1769.52i	−0.817726	−	1.41634i
$117$		0			0
$118$	−2093.86			−1.63352
$119$	−282.103	−	7.57658i	−0.217314	−	0.00583650i
$120$		0			0
$121$	−1035.81			−0.778216
$122$	1808.31	−	3132.08i	1.34194	−	2.32431i
$123$		0			0
$124$	−445.480	−	771.595i	−0.322624	−	0.558800i
$125$	−1683.36			−1.20451
$126$		0			0
$127$	2418.53			1.68984			0.844919	−	0.534894i	$-0.179648\pi$
$127$	2418.53			1.68984			0.844919	+	0.534894i	$0.179648\pi$
$128$	793.008	+	1373.53i	0.547599	+	0.948470i
$129$		0			0
$130$	2559.92	−	4433.91i	1.72708	−	2.99138i
$131$	−733.113			−0.488950			−0.244475	−	0.969656i	$-0.578616\pi$
$131$	−733.113			−0.488950			−0.244475	+	0.969656i	$0.578616\pi$
$132$		0			0
$133$	771.652	+	1423.48i	0.503088	+	0.928057i
$134$	191.798			0.123648
$135$		0			0
$136$	379.534	+	657.373i	0.239300	+	0.414480i
$137$	−767.807			−0.478819			−0.239409	−	0.970919i	$-0.576954\pi$
$137$	−767.807			−0.478819			−0.239409	+	0.970919i	$0.576954\pi$
$138$		0			0
$139$	−839.190	−	1453.52i	−0.512080	−	0.886949i	−0.999902	−	0.0140058i	$-0.995542\pi$
$139$	−839.190	−	1453.52i	−0.512080	−	0.886949i	0.487822	−	0.872943i	$-0.337792\pi$
$140$	2902.76	+	5354.79i	1.75234	+	3.23259i
$141$		0			0
$142$	−737.118	−	1276.73i	−0.435617	−	0.754510i
$143$	468.762	+	811.919i	0.274125	+	0.474798i
$144$		0			0
$145$	1059.72	−	1835.48i	0.606928	−	1.05123i
$146$	1066.45	−	1847.14i	0.604521	−	1.04706i
$147$		0			0
$148$	63.7883	+	110.485i	0.0354281	+	0.0613633i
$149$	−3295.73			−1.81206			−0.906029	−	0.423216i	$-0.860901\pi$
$149$	−3295.73			−1.81206			−0.906029	+	0.423216i	$0.860901\pi$
$150$		0			0
$151$	−1500.72			−0.808788			−0.404394	−	0.914585i	$-0.632518\pi$
$151$	−1500.72			−0.808788			−0.404394	+	0.914585i	$0.632518\pi$
$152$	2177.62	−	3771.76i	1.16203	−	2.01270i
$153$		0			0
$154$	−1615.87	−	43.3984i	−0.845524	−	0.0227087i
$155$	462.086	−	800.357i	0.239456	−	0.414750i
$156$		0			0
$157$	209.436	−	362.754i	0.106464	−	0.184401i	−0.807871	−	0.589359i	$-0.799380\pi$
$157$	209.436	−	362.754i	0.106464	−	0.184401i	0.914335	+	0.404958i	$0.132714\pi$
$158$	2731.36	−	4730.85i	1.37528	−	2.38206i
$159$		0			0
$160$	1508.84	−	2613.39i	0.745528	−	1.29129i
$161$	−936.687	+	1526.23i	−0.458517	+	0.747107i
$162$		0			0
$163$	−1643.60	+	2846.80i	−0.789796	+	1.36797i	0.136295	+	0.990668i	$0.456481\pi$
$163$	−1643.60	+	2846.80i	−0.789796	+	1.36797i	−0.926091	+	0.377299i	$0.876853\pi$
$164$	−3115.09			−1.48322
$165$		0			0
$166$	−6450.44			−3.01597
$167$	452.893	+	784.434i	0.209856	+	0.363481i	0.951669	−	0.307126i	$-0.0993672\pi$
$167$	452.893	+	784.434i	0.209856	+	0.363481i	−0.741813	+	0.670607i	$0.766034\pi$
$168$		0			0
$169$	−390.263	+	675.956i	−0.177635	+	0.307672i
$170$	−714.851	+	1238.16i	−0.322509	+	0.558602i
$171$		0			0
$172$	−1378.31	−	2387.30i	−0.611018	−	1.05831i
$173$	−142.606	−	247.002i	−0.0626715	−	0.108550i	0.832987	−	0.553292i	$-0.186629\pi$
$173$	−142.606	−	247.002i	−0.0626715	−	0.108550i	−0.895659	+	0.444742i	$0.853295\pi$
$174$		0			0
$175$	−2093.84	+	3411.69i	−0.904453	+	1.47371i
$176$	950.226	+	1645.84i	0.406966	+	0.704885i
$177$		0			0
$178$	58.3894			0.0245869
$179$	1438.75	+	2492.00i	0.600768	+	1.04056i	0.992705	+	0.120569i	$0.0384719\pi$
$179$	1438.75	+	2492.00i	0.600768	+	1.04056i	−0.391937	+	0.919992i	$0.628195\pi$
$180$		0			0
$181$	918.462			0.377175			0.188588	−	0.982056i	$-0.439609\pi$
$181$	918.462			0.377175			0.188588	+	0.982056i	$0.439609\pi$
$182$	−2446.60	−	4513.30i	−0.996451	−	1.83817i
$183$		0			0
$184$	4816.72			1.92986
$185$	−66.1661	+	114.603i	−0.0262953	+	0.0455448i
$186$		0			0
$187$	−130.900	−	226.726i	−0.0511893	−	0.0886624i
$188$	2096.39			0.813269
$189$		0			0
$190$	8203.09			3.13218
$191$	1581.23	+	2738.77i	0.599024	+	1.03754i	0.992965	+	0.118405i	$0.0377781\pi$
$191$	1581.23	+	2738.77i	0.599024	+	1.03754i	−0.393941	+	0.919136i	$0.628889\pi$
$192$		0			0
$193$	−894.024	+	1548.50i	−0.333437	+	0.577529i	−0.983183	−	0.182622i	$-0.941542\pi$
$193$	−894.024	+	1548.50i	−0.333437	+	0.577529i	0.649747	+	0.760151i	$0.274875\pi$
$194$	−9502.66			−3.51676
$195$		0			0
$196$	6098.73	+	327.830i	2.22257	+	0.119472i
$197$	5091.77			1.84149			0.920746	−	0.390163i	$-0.127581\pi$
$197$	5091.77			1.84149			0.920746	+	0.390163i	$0.127581\pi$
$198$		0			0
$199$	−1275.06	−	2208.47i	−0.454205	−	0.786706i	0.544437	−	0.838802i	$-0.316743\pi$
$199$	−1275.06	−	2208.47i	−0.454205	−	0.786706i	−0.998642	+	0.0520957i	$0.983410\pi$
$200$	10767.1			3.80675
$201$		0			0
$202$	1272.23	+	2203.57i	0.443137	+	0.767536i
$203$	−1012.80	−	1868.34i	−0.350172	−	0.645970i
$204$		0			0
$205$	−1615.60	−	2798.31i	−0.550432	−	0.953377i
$206$	−1714.65	−	2969.86i	−0.579928	−	1.00447i
$207$		0			0
$208$	−3017.87	+	5227.10i	−1.00602	+	1.74247i
$209$	−751.057	+	1300.87i	−0.248573	+	0.430541i
$210$		0			0
$211$	−1457.71	−	2524.82i	−0.475605	−	0.823771i	0.524005	−	0.851715i	$-0.324437\pi$
$211$	−1457.71	−	2524.82i	−0.475605	−	0.823771i	−0.999609	+	0.0279438i	$0.991104\pi$
$212$	−45.4259			−0.0147163
$213$		0			0
$214$	−3325.03			−1.06212
$215$	1429.69	−	2476.29i	0.453506	−	0.785495i
$216$		0			0
$217$	−441.631	−	814.686i	−0.138156	−	0.254859i
$218$	−1101.70	+	1908.20i	−0.342277	+	0.592841i
$219$		0			0
$220$	−2825.29	+	4893.54i	−0.865822	+	1.49965i
$221$	415.733	−	720.071i	0.126540	−	0.219173i
$222$		0			0
$223$	−337.754	+	585.007i	−0.101425	+	0.175673i	−0.912272	−	0.409585i	$-0.865673\pi$
$223$	−337.754	+	585.007i	−0.101425	+	0.175673i	0.810847	+	0.585258i	$0.199007\pi$
$224$	−1442.05	−	2660.18i	−0.430139	−	0.793486i
$225$		0			0
$226$	4720.21	−	8175.64i	1.38931	−	2.40635i
$227$	643.309			0.188097			0.0940483	−	0.995568i	$-0.470019\pi$
$227$	643.309			0.188097			0.0940483	+	0.995568i	$0.470019\pi$
$228$		0			0
$229$	3663.97			1.05730			0.528651	−	0.848839i	$-0.322698\pi$
$229$	3663.97			1.05730			0.528651	+	0.848839i	$0.322698\pi$
$230$	4536.13	+	7856.82i	1.30045	+	2.25245i
$231$		0			0
$232$	−2858.17	+	4950.49i	−0.808827	+	1.40093i
$233$	2093.55	−	3626.13i	0.588639	−	1.01955i	−0.405772	−	0.913974i	$-0.632997\pi$
$233$	2093.55	−	3626.13i	0.588639	−	1.01955i	0.994411	−	0.105578i	$-0.0336693\pi$
$234$		0			0
$235$	1087.27	+	1883.20i	0.301810	+	0.522750i
$236$	3669.68	+	6356.07i	1.01218	+	1.75316i
$237$		0			0
$238$	683.206	+	1260.33i	0.186074	+	0.343255i
$239$	62.9867	+	109.096i	0.0170472	+	0.0295266i	0.874423	−	0.485164i	$-0.161240\pi$
$239$	62.9867	+	109.096i	0.0170472	+	0.0295266i	−0.857376	+	0.514691i	$0.827907\pi$
$240$		0			0
$241$	6606.50			1.76582			0.882909	−	0.469545i	$-0.155582\pi$
$241$	6606.50			1.76582			0.882909	+	0.469545i	$0.155582\pi$
$242$	2630.94	+	4556.92i	0.698855	+	1.21045i
$243$		0			0
$244$	−12676.9			−3.32604
$245$	2868.54	+	5648.56i	0.748018	+	1.47295i
$246$		0			0
$247$	−4770.64			−1.22894
$248$	−1246.30	+	2158.65i	−0.319112	+	0.552719i
$249$		0			0
$250$	4275.71	+	7405.75i	1.08168	+	1.87352i
$251$	−7221.02			−1.81588			−0.907942	−	0.419095i	$-0.862347\pi$
$251$	−7221.02			−1.81588			−0.907942	+	0.419095i	$0.862347\pi$
$252$		0			0
$253$	−1661.28			−0.412820
$254$	−6143.04	−	10640.1i	−1.51751	−	2.62841i
$255$		0			0
$256$	3808.82	−	6597.08i	0.929888	−	1.61061i
$257$	4312.85			1.04680			0.523401	−	0.852087i	$-0.324663\pi$
$257$	4312.85			1.04680			0.523401	+	0.852087i	$0.324663\pi$
$258$		0			0
$259$	63.2371	+	116.655i	0.0151713	+	0.0279868i
$260$	−17945.9			−4.28062
$261$		0			0
$262$	1862.10	+	3225.26i	0.439088	+	0.760523i
$263$	−4264.54			−0.999860			−0.499930	−	0.866066i	$-0.666641\pi$
$263$	−4264.54			−0.999860			−0.499930	+	0.866066i	$0.666641\pi$
$264$		0			0
$265$	−23.5596	−	40.8064i	−0.00546133	−	0.00945931i
$266$	4302.47	−	7010.44i	0.991736	−	1.61593i
$267$		0			0
$268$	−336.142	−	582.215i	−0.0766162	−	0.132703i
$269$	−329.686	−	571.032i	−0.0747260	−	0.129429i	0.826241	−	0.563317i	$-0.190475\pi$
$269$	−329.686	−	571.032i	−0.0747260	−	0.129429i	−0.900967	+	0.433887i	$0.857142\pi$
$270$		0			0
$271$	−1808.63	+	3132.63i	−0.405410	+	0.702191i	−0.994369	−	0.105972i	$-0.966205\pi$
$271$	−1808.63	+	3132.63i	−0.405410	+	0.702191i	0.588959	+	0.808163i	$0.299538\pi$
$272$	842.731	−	1459.65i	0.187861	−	0.325384i
$273$		0			0
$274$	1950.22	+	3377.89i	0.429990	+	0.744765i
$275$	−3713.55			−0.814312
$276$		0			0
$277$	−674.716			−0.146353			−0.0731765	−	0.997319i	$-0.523314\pi$
$277$	−674.716			−0.146353			−0.0731765	+	0.997319i	$0.523314\pi$
$278$	−4263.07	+	7383.86i	−0.919719	+	1.59300i
$279$		0			0
$280$	8913.30	−	14523.3i	1.90240	−	3.09976i
$281$	4209.37	−	7290.84i	0.893630	−	1.54781i	0.0581382	−	0.998309i	$-0.481484\pi$
$281$	4209.37	−	7290.84i	0.893630	−	1.54781i	0.835491	−	0.549503i	$-0.185183\pi$
$282$		0			0
$283$	3239.12	−	5610.32i	0.680373	−	1.17844i	−0.294493	−	0.955653i	$-0.595151\pi$
$283$	3239.12	−	5610.32i	0.680373	−	1.17844i	0.974867	−	0.222788i	$-0.0715157\pi$
$284$	−2583.73	+	4475.15i	−0.539845	+	0.935039i
$285$		0			0
$286$	2381.30	−	4124.54i	0.492340	−	0.852759i
$287$	−3238.84	−	86.9871i	−0.666141	−	0.0178909i
$288$		0			0
$289$	2340.41	−	4053.71i	0.476370	−	0.825098i
$290$	−10766.7			−2.18014
$291$		0			0
$292$	−7476.19			−1.49832
$293$	−565.462	−	979.409i	−0.112746	−	0.195282i	0.804130	−	0.594453i	$-0.202631\pi$
$293$	−565.462	−	979.409i	−0.112746	−	0.195282i	−0.916877	+	0.399171i	$0.869298\pi$
$294$		0			0
$295$	−3806.47	+	6593.00i	−0.751258	+	1.30122i
$296$	178.457	−	309.096i	0.0350426	−	0.0606955i
$297$		0			0
$298$	8371.12	+	14499.2i	1.62727	+	2.81851i
$299$	−2638.06	−	4569.26i	−0.510244	−	0.883769i
$300$		0			0
$301$	−1366.40	−	2520.62i	−0.261654	−	0.482679i
$302$	3811.82	+	6602.27i	0.726310	+	1.25801i
$303$		0			0
$304$	−9670.55			−1.82449
$305$	−6574.71	−	11387.7i	−1.23432	−	2.13790i
$306$		0			0
$307$	−1352.97			−0.251525			−0.125763	−	0.992060i	$-0.540138\pi$
$307$	−1352.97			−0.251525			−0.125763	+	0.992060i	$0.540138\pi$
$308$	2700.22	+	4981.16i	0.499543	+	0.921519i
$309$		0			0
$310$	−4694.78			−0.860147
$311$	−4797.72	+	8309.89i	−0.874770	+	1.51515i	−0.0177633	+	0.999842i	$0.505655\pi$
$311$	−4797.72	+	8309.89i	−0.874770	+	1.51515i	−0.857007	+	0.515305i	$0.827679\pi$
$312$		0			0
$313$	655.136	+	1134.73i	0.118308	+	0.204916i	0.919097	−	0.394031i	$-0.128920\pi$
$313$	655.136	+	1134.73i	0.118308	+	0.204916i	−0.800789	+	0.598946i	$0.795586\pi$
$314$	−2127.87			−0.382428
$315$		0			0
$316$	−19147.8			−3.40869
$317$	3322.72	+	5755.12i	0.588714	+	1.01968i	0.994401	+	0.105671i	$0.0336991\pi$
$317$	3322.72	+	5755.12i	0.588714	+	1.01968i	−0.405687	+	0.914012i	$0.632968\pi$
$318$		0			0
$319$	985.774	−	1707.41i	0.173018	−	0.299676i
$320$	1014.22			0.177176
$321$		0			0
$322$	9093.69	+	244.234i	1.57382	+	0.0422690i
$323$	1332.19			0.229489
$324$		0			0
$325$	−5897.03	−	10214.0i	−1.00649	−	1.74329i
$326$	16698.9			2.83702
$327$		0			0
$328$	4357.45	+	7547.33i	0.733537	+	1.27052i
$329$	2179.66	+	58.5404i	0.365255	+	0.00980984i
$330$		0			0
$331$	1311.16	+	2271.00i	0.217728	+	0.377117i	0.954113	−	0.299446i	$-0.0968020\pi$
$331$	1311.16	+	2271.00i	0.217728	+	0.377117i	−0.736385	+	0.676563i	$0.763469\pi$
$332$	11305.0	+	19580.8i	1.86880	+	3.23685i
$333$		0			0
$334$	2300.69	−	3984.91i	0.376910	−	0.652828i
$335$	348.672	−	603.918i	0.0568657	−	0.0984942i
$336$		0			0
$337$	5564.34	+	9637.71i	0.899432	+	1.55786i	0.828221	+	0.560401i	$0.189353\pi$
$337$	5564.34	+	9637.71i	0.899432	+	1.55786i	0.0712112	+	0.997461i	$0.477314\pi$
$338$	3965.06			0.638080
$339$		0			0
$340$	5011.35			0.799350
$341$	429.844	−	744.512i	0.0682621	−	0.118233i
$342$		0			0
$343$	6331.85	+	511.157i	0.996757	+	0.0804661i
$344$	−3856.02	+	6678.81i	−0.604367	+	1.04680i
$345$		0			0
$346$	−724.438	+	1254.76i	−0.112561	+	0.194961i
$347$	4288.52	−	7427.93i	0.663458	−	1.14914i	−0.316244	−	0.948678i	$-0.602422\pi$
$347$	4288.52	−	7427.93i	0.663458	−	1.14914i	0.979701	−	0.200464i	$-0.0642450\pi$
$348$		0			0
$349$	−368.128	+	637.616i	−0.0564626	+	0.0977960i	−0.892875	−	0.450304i	$-0.851315\pi$
$349$	−368.128	+	637.616i	−0.0564626	+	0.0977960i	0.836413	+	0.548100i	$0.184649\pi$
$350$	20327.7	+	545.952i	3.10446	+	0.0833781i
$351$		0			0
$352$	1403.56	−	2431.04i	0.212529	−	0.368111i
$353$	9198.17			1.38688			0.693441	−	0.720514i	$-0.256094\pi$
$353$	9198.17			1.38688			0.693441	+	0.720514i	$0.256094\pi$
$354$		0			0
$355$	−5360.08			−0.801361
$356$	−102.332	−	177.245i	−0.0152349	−	0.0263876i
$357$		0			0
$358$	7308.85	−	12659.3i	1.07901	−	1.86890i
$359$	731.205	−	1266.48i	0.107497	−	0.186191i	−0.807258	−	0.590198i	$-0.799050\pi$
$359$	731.205	−	1266.48i	0.107497	−	0.186191i	0.914756	+	0.404007i	$0.132383\pi$
$360$		0			0
$361$	−392.294	−	679.472i	−0.0571940	−	0.0990629i
$362$	−2332.89	−	4040.68i	−0.338712	−	0.586666i
$363$		0			0
$364$	−9412.55	+	15336.8i	−1.35536	+	2.20842i
$365$	−3877.43	−	6715.91i	−0.556039	−	0.963088i
$366$		0			0
$367$	−5111.37			−0.727007			−0.363503	−	0.931593i	$-0.618419\pi$
$367$	−5111.37			−0.727007			−0.363503	+	0.931593i	$0.618419\pi$
$368$	−5347.61	−	9262.33i	−0.757509	−	1.31204i
$369$		0			0
$370$	672.245			0.0944550
$371$	−47.2304	−	1.26849i	−0.00660938	−	0.000177512i
$372$		0			0
$373$	12431.0			1.72560			0.862802	−	0.505541i	$-0.168707\pi$
$373$	12431.0			1.72560			0.862802	+	0.505541i	$0.168707\pi$
$374$	−664.972	+	1151.77i	−0.0919382	+	0.159242i
$375$		0			0
$376$	−2932.47	−	5079.19i	−0.402209	−	0.696646i
$377$	6261.54			0.855399
$378$		0			0
$379$	10316.4			1.39820			0.699102	−	0.715022i	$-0.253583\pi$
$379$	10316.4			1.39820			0.699102	+	0.715022i	$0.253583\pi$
$380$	−14376.6	−	24901.0i	−1.94080	−	3.36157i
$381$		0			0
$382$	8032.61	−	13912.9i	1.07587	−	1.86347i
$383$	−2019.95			−0.269489			−0.134745	−	0.990880i	$-0.543021\pi$
$383$	−2019.95			−0.269489			−0.134745	+	0.990880i	$0.543021\pi$
$384$		0			0
$385$	−3074.17	+	5009.05i	−0.406946	+	0.663077i
$386$	9083.26			1.19773
$387$		0			0
$388$	16654.2	+	28846.0i	2.17910	+	3.77431i
$389$	4498.04			0.586271			0.293136	−	0.956071i	$-0.405301\pi$
$389$	4498.04			0.586271			0.293136	+	0.956071i	$0.405301\pi$
$390$		0			0
$391$	736.672	+	1275.95i	0.0952816	+	0.165032i
$392$	−7736.76	−	15234.8i	−0.996851	−	1.96294i
$393$		0			0
$394$	−12933.1	−	22400.7i	−1.65370	−	2.86429i
$395$	−9930.76	−	17200.6i	−1.26499	−	2.19103i
$396$		0			0
$397$	331.900	−	574.868i	0.0419587	−	0.0726746i	−0.844283	−	0.535897i	$-0.819974\pi$
$397$	331.900	−	574.868i	0.0419587	−	0.0726746i	0.886242	+	0.463222i	$0.153307\pi$
$398$	−6477.30	+	11219.0i	−0.815773	+	1.41296i
$399$		0			0
$400$	−11953.8	−	20704.7i	−1.49423	−	2.58808i
$401$	1746.87			0.217542			0.108771	−	0.994067i	$-0.465308\pi$
$401$	1746.87			0.217542			0.108771	+	0.994067i	$0.465308\pi$
$402$		0			0
$403$	2730.33			0.337487
$404$	4459.39	−	7723.88i	0.549165	−	0.951182i
$405$		0			0
$406$	−5647.06	+	9201.30i	−0.690293	+	1.12476i
$407$	−61.5493	+	106.607i	−0.00749604	+	0.0129835i
$408$		0			0
$409$	5159.64	−	8936.77i	0.623785	−	1.08043i	−0.364990	−	0.931012i	$-0.618927\pi$
$409$	5159.64	−	8936.77i	0.623785	−	1.08043i	0.988775	−	0.149415i	$-0.0477392\pi$
$410$	−8207.24	+	14215.4i	−0.988602	+	1.71231i
$411$		0			0
$412$	−6010.14	+	10409.9i	−0.718686	+	1.24480i
$413$	3637.96	+	6711.03i	0.433444	+	0.799585i
$414$		0			0
$415$	−11726.4	+	20310.7i	−1.38705	+	2.40244i
$416$	8915.29			1.05074
$417$		0			0
$418$	7630.72			0.892896
$419$	205.621	+	356.146i	0.0239743	+	0.0415248i	0.877764	−	0.479094i	$-0.159035\pi$
$419$	205.621	+	356.146i	0.0239743	+	0.0415248i	−0.853789	+	0.520619i	$0.825701\pi$
$420$		0			0
$421$	1545.97	−	2677.70i	0.178969	−	0.309983i	−0.762559	−	0.646919i	$-0.776057\pi$
$421$	1545.97	−	2677.70i	0.178969	−	0.309983i	0.941528	+	0.336936i	$0.109390\pi$
$422$	−7405.12	+	12826.0i	−0.854208	+	1.47953i
$423$		0			0
$424$	63.5427	+	110.059i	0.00727808	+	0.0126060i
$425$	1646.73	+	2852.22i	0.187948	+	0.325536i
$426$		0			0
$427$	−13180.5	−	353.995i	−1.49379	−	0.0401195i
$428$	5827.40	+	10093.4i	0.658126	+	1.13991i
$429$		0			0
$430$	−14525.6			−1.62903
$431$	3186.48	+	5519.14i	0.356119	+	0.616816i	0.987309	−	0.158812i	$-0.0507665\pi$
$431$	3186.48	+	5519.14i	0.356119	+	0.616816i	−0.631190	+	0.775628i	$0.717433\pi$
$432$		0			0
$433$	−15703.9			−1.74292			−0.871458	−	0.490471i	$-0.836825\pi$
$433$	−15703.9			−1.74292			−0.871458	+	0.490471i	$0.836825\pi$
$434$	−2462.39	+	4012.20i	−0.272347	+	0.443760i
$435$		0			0
$436$	7723.29			0.848345
$437$	4226.74	−	7320.93i	0.462683	−	0.801391i
$438$		0			0
$439$	−3172.32	−	5494.62i	−0.344890	−	0.597366i	0.640444	−	0.768005i	$-0.278750\pi$
$439$	−3172.32	−	5494.62i	−0.344890	−	0.597366i	−0.985334	+	0.170638i	$0.945417\pi$
$440$	15808.3			1.71280
$441$		0			0
$442$	−4223.83			−0.454541
$443$	4008.55	+	6943.01i	0.429914	+	0.744632i	0.996865	−	0.0791187i	$-0.0252106\pi$
$443$	4008.55	+	6943.01i	0.429914	+	0.744632i	−0.566951	+	0.823751i	$0.691877\pi$
$444$		0			0
$445$	106.147	−	183.852i	0.0113075	−	0.0195852i
$446$	3431.57			0.364326
$447$		0			0
$448$	531.951	−	866.759i	0.0560990	−	0.0914074i
$449$	−3077.02			−0.323416			−0.161708	−	0.986839i	$-0.551700\pi$
$449$	−3077.02			−0.323416			−0.161708	+	0.986839i	$0.551700\pi$
$450$		0			0
$451$	−1502.88	−	2603.06i	−0.156913	−	0.271781i
$452$	−33090.3			−3.44345
$453$		0			0
$454$	−1634.00	−	2830.17i	−0.168915	−	0.292570i
$455$	−18658.8	−	501.130i	−1.92251	−	0.0516337i
$456$		0			0
$457$	2207.33	+	3823.20i	0.225940	+	0.391339i	0.956601	−	0.291401i	$-0.0941214\pi$
$457$	2207.33	+	3823.20i	0.225940	+	0.391339i	−0.730661	+	0.682740i	$0.760788\pi$
$458$	−9306.46	−	16119.3i	−0.949481	−	1.64455i
$459$		0			0
$460$	15899.9	−	27539.5i	1.61161	−	2.79138i
$461$	−1139.72	+	1974.05i	−0.115146	+	0.199438i	−0.917838	−	0.396955i	$-0.870067\pi$
$461$	−1139.72	+	1974.05i	−0.115146	+	0.199438i	0.802692	+	0.596393i	$0.203400\pi$
$462$		0			0
$463$	3230.05	+	5594.62i	0.324219	+	0.561563i	0.981354	−	0.192209i	$-0.0615653\pi$
$463$	3230.05	+	5594.62i	0.324219	+	0.561563i	−0.657135	+	0.753773i	$0.728232\pi$
$464$	12692.7			1.26993
$465$		0			0
$466$	−21270.4			−2.11444
$467$	7609.58	−	13180.2i	0.754024	−	1.30601i	−0.191834	−	0.981427i	$-0.561443\pi$
$467$	7609.58	−	13180.2i	0.754024	−	1.30601i	0.945858	−	0.324581i	$-0.105223\pi$
$468$		0			0
$469$	−333.237	−	614.730i	−0.0328091	−	0.0605237i
$470$	5523.29	−	9566.62i	0.542065	−	0.938883i
$471$		0			0
$472$	10266.4	−	17782.0i	1.00117	−	1.73407i
$473$	1329.93	−	2303.51i	0.129282	−	0.223922i
$474$		0			0
$475$	9448.31	−	16364.9i	0.912670	−	1.58079i
$476$	2628.43	−	4282.75i	0.253096	−	0.412394i
$477$		0			0
$478$	319.972	−	554.207i	0.0306175	−	0.0530311i
$479$	−19222.0			−1.83356			−0.916779	−	0.399394i	$-0.869220\pi$
$479$	−19222.0			−1.83356			−0.916779	+	0.399394i	$0.869220\pi$
$480$		0			0
$481$	−390.955			−0.0370603
$482$	−16780.5	−	29064.6i	−1.58574	−	2.74659i
$483$		0			0
$484$	9221.89	−	15972.8i	0.866068	−	1.50007i
$485$	−17275.1	+	29921.3i	−1.61736	+	2.80135i
$486$		0			0
$487$	−4166.80	−	7217.11i	−0.387712	−	0.671537i	0.604430	−	0.796659i	$-0.293401\pi$
$487$	−4166.80	−	7217.11i	−0.387712	−	0.671537i	−0.992141	+	0.125122i	$0.960068\pi$
$488$	17732.7	+	30713.9i	1.64492	+	2.84909i
$489$		0			0
$490$	17564.2	−	26967.2i	1.61932	−	2.48623i
$491$	5352.23	+	9270.34i	0.491941	+	0.852066i	0.999957	−	0.00928128i	$-0.00295437\pi$
$491$	5352.23	+	9270.34i	0.491941	+	0.852066i	−0.508016	+	0.861347i	$0.669621\pi$
$492$		0			0
$493$	−1748.52			−0.159735
$494$	12117.4	+	20987.9i	1.10362	+	1.91152i
$495$		0			0
$496$	5534.64			0.501033
$497$	−2811.33	+	4580.77i	−0.253733	+	0.413432i
$498$		0			0
$499$	10892.1			0.977151			0.488575	−	0.872522i	$-0.337517\pi$
$499$	10892.1			0.977151			0.488575	+	0.872522i	$0.337517\pi$
$500$	14987.1	−	25958.4i	1.34049	−	2.32179i
$501$		0			0
$502$	18341.3	+	31768.1i	1.63071	+	2.82446i
$503$	13166.9			1.16716			0.583581	−	0.812055i	$-0.301651\pi$
$503$	13166.9			1.16716			0.583581	+	0.812055i	$0.301651\pi$
$504$		0			0
$505$	9251.23			0.815197
$506$	4219.63	+	7308.61i	0.370722	+	0.642109i
$507$		0			0
$508$	−21532.4	+	37295.3i	−1.88060	+	3.25730i
$509$	4149.07			0.361305			0.180653	−	0.983547i	$-0.442179\pi$
$509$	4149.07			0.361305			0.180653	+	0.983547i	$0.442179\pi$
$510$		0			0
$511$	−7773.18	−	208.768i	−0.672926	−	0.0180731i
$512$	−26009.4			−2.24505
$513$		0			0
$514$	−10954.6	−	18973.9i	−0.940052	−	1.62822i
$515$	−12468.4			−1.06684
$516$		0			0
$517$	1011.40	+	1751.80i	0.0860375	+	0.149021i
$518$	352.589	−	574.507i	0.0299071	−	0.0487305i
$519$		0			0
$520$	25103.2	+	43480.0i	2.11701	+	3.66678i
$521$	1219.25	+	2111.80i	0.102526	+	0.177580i	0.912725	−	0.408575i	$-0.133974\pi$
$521$	1219.25	+	2111.80i	0.102526	+	0.177580i	−0.810199	+	0.586155i	$0.800641\pi$
$522$		0			0
$523$	−610.745	+	1057.84i	−0.0510631	+	0.0884439i	−0.890427	−	0.455126i	$-0.849594\pi$
$523$	−610.745	+	1057.84i	−0.0510631	+	0.0884439i	0.839364	+	0.543570i	$0.182928\pi$
$524$	6526.99	−	11305.1i	0.544147	−	0.942490i
$525$		0			0
$526$	10831.9	+	18761.4i	0.897897	+	1.55520i
$527$	−762.436			−0.0630213
$528$		0			0
$529$	−2817.80			−0.231594
$530$	−119.682	+	207.296i	−0.00980881	+	0.0169893i
$531$		0			0
$532$	−28821.1	−	774.064i	−2.34879	−	0.0630826i
$533$	4773.05	−	8267.17i	0.387887	−	0.671840i
$534$		0			0
$535$	−6044.62	+	10469.6i	−0.488471	+	0.846056i
$536$	−940.406	+	1628.83i	−0.0757824	+	0.131259i
$537$		0			0
$538$	−1674.80	+	2900.83i	−0.134211	+	0.232461i
$539$	2668.39	+	5254.43i	0.213239	+	0.419897i
$540$		0			0
$541$	−4410.12	+	7638.56i	−0.350473	+	0.607037i	−0.986332	−	0.164768i	$-0.947313\pi$
$541$	−4410.12	+	7638.56i	−0.350473	+	0.607037i	0.635859	+	0.771805i	$0.280646\pi$
$542$	18375.6			1.45627
$543$		0			0
$544$	−2489.57			−0.196212
$545$	4005.59	+	6937.89i	0.314827	+	0.545296i
$546$		0			0
$547$	6262.47	−	10846.9i	0.489514	−	0.847862i	−0.510414	−	0.859929i	$-0.670508\pi$
$547$	6262.47	−	10846.9i	0.489514	−	0.847862i	0.999927	+	0.0120667i	$0.00384105\pi$
$548$	6835.87	−	11840.1i	0.532872	−	0.922962i
$549$		0			0
$550$	9432.40	+	16337.4i	0.731271	+	1.26660i
$551$	5016.16	+	8688.25i	0.387833	+	0.671746i
$552$		0			0
$553$	−19908.4	−	534.691i	−1.53091	−	0.0411164i
$554$	1713.77	+	2968.34i	0.131428	+	0.227641i
$555$		0			0
$556$	29885.6			2.27956
$557$	−4686.71	−	8117.61i	−0.356521	−	0.617512i	0.630856	−	0.775900i	$-0.282704\pi$
$557$	−4686.71	−	8117.61i	−0.356521	−	0.617512i	−0.987377	+	0.158388i	$0.949370\pi$
$558$		0			0
$559$	8447.58			0.639167
$560$	−37823.3	−	1015.84i	−2.85415	−	0.0766555i
$561$		0			0
$562$	−42767.1			−3.21000
$563$	−8085.56	+	14004.6i	−0.605268	+	1.04835i	0.386741	+	0.922188i	$0.373601\pi$
$563$	−8085.56	+	14004.6i	−0.605268	+	1.04835i	−0.992009	+	0.126166i	$0.959733\pi$
$564$		0			0
$565$	−17161.9	−	29725.3i	−1.27789	−	2.21337i
$566$	−32909.4			−2.44396
$567$		0			0
$568$	14456.7			1.06794
$569$	−7951.37	−	13772.2i	−0.585833	−	1.01469i	−0.994771	−	0.102130i	$-0.967434\pi$
$569$	−7951.37	−	13772.2i	−0.585833	−	1.01469i	0.408938	−	0.912562i	$-0.365899\pi$
$570$		0			0
$571$	−6608.04	+	11445.5i	−0.484304	+	0.838839i	−0.999837	−	0.0180301i	$-0.994261\pi$
$571$	−6608.04	+	11445.5i	−0.484304	+	0.838839i	0.515533	+	0.856870i	$0.327594\pi$
$572$	−16693.8			−1.22028
$573$		0			0
$574$	7843.93	+	14469.9i	0.570382	+	1.05220i
$575$	20898.9			1.51573
$576$		0			0
$577$	3146.59	+	5450.06i	0.227027	+	0.393222i	0.956926	−	0.290334i	$-0.0937662\pi$
$577$	3146.59	+	5450.06i	0.227027	+	0.393222i	−0.729899	+	0.683555i	$0.760433\pi$
$578$	−23778.5			−1.71117
$579$		0			0
$580$	18869.5	+	32683.0i	1.35089	+	2.33981i
$581$	11207.3	+	20674.3i	0.800268	+	1.47627i
$582$		0			0
$583$	−21.9157	−	37.9591i	−0.00155687	−	0.00269658i
$584$	10457.9	+	18113.5i	0.741009	+	1.28346i
$585$		0			0
$586$	−2872.54	+	4975.38i	−0.202497	+	0.350736i
$587$	7722.40	−	13375.6i	0.542994	−	0.940493i	−0.455736	−	0.890115i	$-0.650624\pi$
$587$	7722.40	−	13375.6i	0.542994	−	0.940493i	0.998730	−	0.0503782i	$-0.0160427\pi$
$588$		0			0
$589$	2187.28	+	3788.49i	0.153014	+	0.265029i
$590$	38673.6			2.69859
$591$		0			0
$592$	−792.504			−0.0550198
$593$	−4163.34	+	7211.12i	−0.288310	+	0.499368i	−0.973407	−	0.229085i	$-0.926427\pi$
$593$	−4163.34	+	7211.12i	−0.288310	+	0.499368i	0.685096	+	0.728453i	$0.259760\pi$
$594$		0			0
$595$	5210.43	+	139.939i	0.359003	+	0.00964193i
$596$	29342.3	−	50822.3i	2.01662	−	3.49289i
$597$		0			0
$598$	−13401.3	+	23211.8i	−0.916422	+	1.58729i
$599$	−2972.96	+	5149.31i	−0.202791	+	0.351244i	−0.949427	−	0.313989i	$-0.898334\pi$
$599$	−2972.96	+	5149.31i	−0.202791	+	0.351244i	0.746636	+	0.665233i	$0.231668\pi$
$600$		0			0
$601$	−867.852	+	1503.16i	−0.0589025	+	0.102022i	−0.893973	−	0.448121i	$-0.852093\pi$
$601$	−867.852	+	1503.16i	−0.0589025	+	0.102022i	0.835071	+	0.550143i	$0.185427\pi$
$602$	−7618.58	+	12413.7i	−0.515798	+	0.840439i
$603$		0			0
$604$	13361.1	−	23142.1i	0.900092	−	1.55900i
$605$	19131.3			1.28562
$606$		0			0
$607$	14460.8			0.966961			0.483481	−	0.875355i	$-0.339372\pi$
$607$	14460.8			0.966961			0.483481	+	0.875355i	$0.339372\pi$
$608$	7142.11	+	12370.5i	0.476399	+	0.825148i
$609$		0			0
$610$	−33399.4	+	57849.5i	−2.21689	+	3.83977i
$611$	−3212.16	+	5563.62i	−0.212684	+	0.368380i
$612$		0			0
$613$	−9264.27	−	16046.2i	−0.610408	−	1.05726i	−0.991172	−	0.132586i	$-0.957672\pi$
$613$	−9264.27	−	16046.2i	−0.610408	−	1.05726i	0.380763	−	0.924673i	$-0.375661\pi$
$614$	3436.54	+	5952.26i	0.225875	+	0.391227i
$615$		0			0
$616$	8291.37	−	13509.9i	0.542320	−	0.883653i
$617$	−3589.01	−	6216.34i	−0.234178	−	0.405609i	0.724855	−	0.688901i	$-0.241907\pi$
$617$	−3589.01	−	6216.34i	−0.234178	−	0.405609i	−0.959034	+	0.283292i	$0.908573\pi$
$618$		0			0
$619$	9082.53			0.589754			0.294877	−	0.955535i	$-0.404721\pi$
$619$	9082.53			0.589754			0.294877	+	0.955535i	$0.404721\pi$
$620$	8228.02	+	14251.3i	0.532976	+	0.923141i
$621$		0			0
$622$	48744.7			3.14225
$623$	−101.448	−	187.144i	−0.00652397	−	0.0120349i
$624$		0			0
$625$	4074.04			0.260738
$626$	3328.08	−	5764.40i	0.212487	−	0.368038i
$627$		0			0
$628$	3729.27	+	6459.29i	0.236965	+	0.410436i
$629$	109.173			0.00692054
$630$		0			0
$631$	−15257.6			−0.962595			−0.481297	−	0.876557i	$-0.659834\pi$
$631$	−15257.6			−0.962595			−0.481297	+	0.876557i	$0.659834\pi$
$632$	26784.3	+	46391.8i	1.68580	+	2.91988i
$633$		0			0
$634$	16879.4	−	29235.9i	1.05736	−	1.83140i
$635$	−44670.1			−2.79162
$636$		0			0
$637$	−10214.7	+	15683.2i	−0.635357	+	0.975495i
$638$	−10015.4			−0.621497
$639$		0			0
$640$	−14646.8	−	25369.1i	−0.904637	−	1.56688i
$641$	15441.5			0.951488			0.475744	−	0.879584i	$-0.342179\pi$
$641$	15441.5			0.951488			0.475744	+	0.879584i	$0.342179\pi$
$642$		0			0
$643$	−5388.32	−	9332.85i	−0.330474	−	0.572398i	0.652131	−	0.758106i	$-0.273875\pi$
$643$	−5388.32	−	9332.85i	−0.330474	−	0.572398i	−0.982605	+	0.185709i	$0.940542\pi$
$644$	−15196.1	−	28032.6i	−0.929829	−	1.71528i
$645$		0			0
$646$	−3383.74	−	5860.82i	−0.206086	−	0.356952i
$647$	4762.72	+	8249.27i	0.289400	+	0.501255i	0.973667	−	0.227977i	$-0.0732109\pi$
$647$	4762.72	+	8249.27i	0.289400	+	0.501255i	−0.684267	+	0.729232i	$0.739878\pi$
$648$		0			0
$649$	−3540.87	+	6132.97i	−0.214162	+	0.370940i
$650$	−29956.8	+	51886.7i	−1.80770	+	3.13102i
$651$		0			0
$652$	−29266.4	−	50690.8i	−1.75791	−	3.04479i
$653$	21397.9			1.28234			0.641169	−	0.767400i	$-0.278450\pi$
$653$	21397.9			1.28234			0.641169	+	0.767400i	$0.278450\pi$
$654$		0			0
$655$	13540.6			0.807748
$656$	9675.44	−	16758.4i	0.575858	−	0.997414i
$657$		0			0
$658$	−5278.79	−	9737.89i	−0.312749	−	0.576934i
$659$	−5564.91	+	9638.70i	−0.328950	+	0.569758i	−0.982304	−	0.187295i	$-0.940028\pi$
$659$	−5564.91	+	9638.70i	−0.328950	+	0.569758i	0.653354	+	0.757053i	$0.273361\pi$
$660$		0			0
$661$	6263.54	−	10848.8i	0.368568	−	0.638379i	−0.620774	−	0.783990i	$-0.713181\pi$
$661$	6263.54	−	10848.8i	0.368568	−	0.638379i	0.989342	+	0.145611i	$0.0465148\pi$
$662$	6660.69	−	11536.7i	0.391050	−	0.677319i
$663$		0			0
$664$	31627.3	−	54780.0i	1.84846	−	3.20162i
$665$	−14252.4	−	26291.7i	−0.831104	−	1.53316i
$666$		0			0
$667$	−5547.67	+	9608.84i	−0.322049	+	0.557805i
$668$	−16128.6			−0.934185
$669$		0			0
$670$	−3542.50			−0.204267
$671$	−6115.96	−	10593.2i	−0.351869	−	0.609455i
$672$		0			0
$673$	4494.06	−	7783.93i	0.257404	−	0.445837i	−0.708141	−	0.706071i	$-0.750466\pi$
$673$	4494.06	−	7783.93i	0.257404	−	0.445837i	0.965546	+	0.260233i	$0.0837994\pi$
$674$	28266.7	−	48959.4i	1.61542	−	2.79799i
$675$		0			0
$676$	−6949.12	−	12036.2i	−0.395376	−	0.684811i
$677$	−8243.31	−	14277.8i	−0.467971	−	0.810549i	0.531359	−	0.847146i	$-0.321681\pi$
$677$	−8243.31	−	14277.8i	−0.467971	−	0.810549i	−0.999330	+	0.0365976i	$0.988348\pi$
$678$		0			0
$679$	16510.3	+	30457.0i	0.933149	+	1.72140i
$680$	−7009.99	−	12141.7i	−0.395325	−	0.684723i
$681$		0			0
$682$	−4367.20			−0.245204
$683$	−7398.40	−	12814.4i	−0.414483	−	0.717905i	0.580891	−	0.813981i	$-0.302704\pi$
$683$	−7398.40	−	12814.4i	−0.414483	−	0.717905i	−0.995374	+	0.0960760i	$0.969371\pi$
$684$		0			0
$685$	14181.4			0.791011
$686$	−13834.1	−	29154.6i	−0.769952	−	1.62264i
$687$		0			0
$688$	17124.1			0.948908
$689$	69.6032	−	120.556i	0.00384858	−	0.00666593i
$690$		0			0
$691$	4373.33	+	7574.83i	0.240766	+	0.417019i	0.960933	−	0.276782i	$-0.0892681\pi$
$691$	4373.33	+	7574.83i	0.240766	+	0.417019i	−0.720167	+	0.693801i	$0.755935\pi$
$692$	5078.57			0.278986
$693$		0			0
$694$	−43571.2			−2.38320
$695$	15499.8	+	26846.5i	0.845959	+	1.46524i
$696$		0			0
$697$	−1332.86	+	2308.58i	−0.0724329	+	0.125457i
$698$	3740.17			0.202819
$699$		0			0
$700$	−33968.8	−	62663.0i	−1.83414	−	3.38348i
$701$	−6101.34			−0.328737			−0.164368	−	0.986399i	$-0.552559\pi$
$701$	−6101.34			−0.328737			−0.164368	+	0.986399i	$0.552559\pi$
$702$		0			0
$703$	−313.197	−	542.473i	−0.0168029	−	0.0291035i
$704$	943.450			0.0505080
$705$		0			0
$706$	−23363.3	−	40466.4i	−1.24545	−	2.15718i
$707$	4852.22	−	7906.19i	0.258114	−	0.420570i
$708$		0			0
$709$	−5146.65	−	8914.25i	−0.272618	−	0.472189i	0.696913	−	0.717156i	$-0.254556\pi$
$709$	−5146.65	−	8914.25i	−0.272618	−	0.472189i	−0.969531	+	0.244967i	$0.921223\pi$
$710$	13614.6	+	23581.1i	0.719641	+	1.24645i
$711$		0			0
$712$	−286.290	+	495.868i	−0.0150691	+	0.0261004i
$713$	−2419.04	+	4189.91i	−0.127060	+	0.220075i
$714$		0			0
$715$	−8658.02	−	14996.1i	−0.452855	−	0.784369i
$716$	−51237.6			−2.67436
$717$		0			0
$718$	−7429.02			−0.386140
$719$	3415.37	−	5915.59i	0.177151	−	0.306835i	−0.763752	−	0.645509i	$-0.776645\pi$
$719$	3415.37	−	5915.59i	0.177151	−	0.306835i	0.940904	+	0.338674i	$0.109979\pi$
$720$		0			0
$721$	−6539.59	+	10655.6i	−0.337791	+	0.550395i
$722$	−1992.84	+	3451.71i	−0.102723	+	0.177921i
$723$		0			0
$724$	−8177.17	+	14163.3i	−0.419754	+	0.727036i
$725$	−12401.0	+	21479.2i	−0.635260	+	1.10030i
$726$		0			0
$727$	−4704.28	+	8148.05i	−0.239989	+	0.415673i	−0.960711	−	0.277551i	$-0.910477\pi$
$727$	−4704.28	+	8148.05i	−0.239989	+	0.415673i	0.720722	+	0.693224i	$0.243810\pi$
$728$	50324.9	+	1351.60i	2.56204	+	0.0688100i
$729$		0			0
$730$	−19697.3	+	34116.7i	−0.998671	+	1.72975i
$731$	−2358.96			−0.119356
$732$		0			0
$733$	28361.0			1.42911			0.714554	−	0.699580i	$-0.246630\pi$
$733$	28361.0			1.42911			0.714554	+	0.699580i	$0.246630\pi$
$734$	12982.8	+	22486.9i	0.652869	+	1.13080i
$735$		0			0
$736$	−7898.87	+	13681.2i	−0.395593	+	0.685187i
$737$	324.344	−	561.780i	0.0162108	−	0.0280779i
$738$		0			0
$739$	11135.5	+	19287.2i	0.554296	+	0.960069i	0.997958	+	0.0638750i	$0.0203459\pi$
$739$	11135.5	+	19287.2i	0.554296	+	0.960069i	−0.443662	+	0.896194i	$0.646321\pi$
$740$	−1178.17	−	2040.65i	−0.0585275	−	0.101373i
$741$		0			0
$742$	114.384	+	211.007i	0.00565927	+	0.0104398i
$743$	−1289.88	−	2234.14i	−0.0636892	−	0.110313i	0.832423	−	0.554141i	$-0.186953\pi$
$743$	−1289.88	−	2234.14i	−0.0636892	−	0.110313i	−0.896112	+	0.443828i	$0.853620\pi$
$744$		0			0
$745$	60872.0			2.99353
$746$	−31574.5	−	54688.7i	−1.54963	−	2.68404i
$747$		0			0
$748$	4661.69			0.227872
$749$	5777.04	+	10657.0i	0.281827	+	0.519893i
$750$		0			0
$751$	8600.27			0.417881			0.208940	−	0.977928i	$-0.432999\pi$
$751$	8600.27			0.417881			0.208940	+	0.977928i	$0.432999\pi$
$752$	−6511.36	+	11278.0i	−0.315751	+	0.546897i
$753$		0			0
$754$	−15904.2	−	27547.0i	−0.768168	−	1.33051i
$755$	27718.3			1.33612
$756$		0			0
$757$	16640.3			0.798947			0.399474	−	0.916745i	$-0.369193\pi$
$757$	16640.3			0.798947			0.399474	+	0.916745i	$0.369193\pi$
$758$	−26203.7	−	45386.1i	−1.25562	−	2.17480i
$759$		0			0
$760$	−40220.7	+	69664.3i	−1.91968	+	3.32499i
$761$	29490.1			1.40475			0.702376	−	0.711806i	$-0.252122\pi$
$761$	29490.1			1.40475			0.702376	+	0.711806i	$0.252122\pi$
$762$		0			0
$763$	8030.09	+	215.668i	0.381008	+	0.0102329i
$764$	−56311.4			−2.66659
$765$		0			0
$766$	5130.64	+	8886.54i	0.242007	+	0.419169i
$767$	−22491.3			−1.05882
$768$		0			0
$769$	−7237.30	−	12535.4i	−0.339381	−	0.587825i	0.644936	−	0.764237i	$-0.276884\pi$
$769$	−7237.30	−	12535.4i	−0.339381	−	0.587825i	−0.984316	+	0.176412i	$0.943551\pi$
$770$	29845.1	+	801.567i	1.39681	+	0.0375149i
$771$		0			0
$772$	−15919.2	−	27572.9i	−0.742156	−	1.28545i
$773$	12775.8	+	22128.4i	0.594455	+	1.02963i	0.993623	+	0.112749i	$0.0359657\pi$
$773$	12775.8	+	22128.4i	0.594455	+	1.02963i	−0.399168	+	0.916878i	$0.630701\pi$
$774$		0			0
$775$	−5407.44	+	9365.97i	−0.250634	+	0.434110i
$776$	46592.7	−	80700.8i	2.15538	−	3.73324i
$777$		0			0
$778$	−11425.0	−	19788.6i	−0.526485	−	0.911899i
$779$	15294.9			0.703462
$780$		0			0
$781$	−4986.08			−0.228445
$782$	3742.28	−	6481.82i	0.171130	−	0.296406i
$783$		0			0
$784$	−20706.3	+	31791.3i	−0.943251	+	1.44822i
$785$	−3868.28	+	6700.06i	−0.175879	+	0.304631i
$786$		0			0
$787$	−12413.4	+	21500.6i	−0.562248	+	0.973841i	0.435052	+	0.900405i	$0.356730\pi$
$787$	−12413.4	+	21500.6i	−0.562248	+	0.973841i	−0.997300	+	0.0734362i	$0.976603\pi$
$788$	−45332.7	+	78518.5i	−2.04938	+	3.54962i
$789$		0			0
$790$	−50448.1	+	87378.6i	−2.27198	+	3.93518i
$791$	−34404.8	−	924.029i	−1.54652	−	0.0415356i
$792$		0			0
$793$	19424.0	−	33643.3i	0.869818	−	1.50657i
$794$	−3372.10			−0.150719
$795$		0			0
$796$	45408.1			2.02192
$797$	12558.2	+	21751.5i	0.558138	+	0.966723i	0.997652	+	0.0684876i	$0.0218174\pi$
$797$	12558.2	+	21751.5i	0.558138	+	0.966723i	−0.439514	+	0.898236i	$0.644849\pi$
$798$		0			0
$799$	896.986	−	1553.63i	0.0397160	−	0.0687902i
$800$	−17656.8	+	30582.6i	−0.780330	+	1.35157i
$801$		0			0
$802$	−4437.02	−	7685.15i	−0.195358	−	0.338369i
$803$	−3606.89	−	6247.31i	−0.158511	−	0.274549i
$804$		0			0
$805$	17300.6	−	28189.5i	0.757473	−	1.23422i
$806$	−6935.01	−	12011.8i	−0.303071	−	0.524934i
$807$		0			0
$808$	−24951.5			−1.08638
$809$	8165.63	+	14143.3i	0.354868	+	0.614650i	0.987095	−	0.160133i	$-0.0511924\pi$
$809$	8165.63	+	14143.3i	0.354868	+	0.614650i	−0.632227	+	0.774783i	$0.717859\pi$
$810$		0			0
$811$	562.583			0.0243588			0.0121794	−	0.999926i	$-0.496123\pi$
$811$	562.583			0.0243588			0.0121794	+	0.999926i	$0.496123\pi$
$812$	37828.2	+	1015.97i	1.63486	+	0.0439084i
$813$		0			0
$814$	625.339			0.0269265
$815$	30357.3	−	52580.4i	1.30475	−	2.25989i
$816$		0			0
$817$	6767.42	+	11721.5i	0.289794	+	0.501938i
$818$	−52421.8			−2.24069
$819$		0			0
$820$	57535.6			2.45028
$821$	−13832.1	−	23957.9i	−0.587995	−	1.01844i	−0.994495	−	0.104786i	$-0.966584\pi$
$821$	−13832.1	−	23957.9i	−0.587995	−	1.01844i	0.406500	−	0.913651i	$-0.366749\pi$
$822$		0			0
$823$	−1862.34	+	3225.66i	−0.0788784	+	0.136621i	−0.902766	−	0.430131i	$-0.858467\pi$
$823$	−1862.34	+	3225.66i	−0.0788784	+	0.136621i	0.823888	+	0.566753i	$0.191801\pi$
$824$	33628.5			1.42173
$825$		0			0
$826$	20284.1	−	33050.8i	0.854448	−	1.39223i
$827$	35662.0			1.49950			0.749751	−	0.661720i	$-0.230173\pi$
$827$	35662.0			1.49950			0.749751	+	0.661720i	$0.230173\pi$
$828$		0			0
$829$	14890.1	+	25790.4i	0.623828	+	1.08050i	0.988766	+	0.149470i	$0.0477568\pi$
$829$	14890.1	+	25790.4i	0.623828	+	1.08050i	−0.364938	+	0.931032i	$0.618910\pi$
$830$	119140.			4.98240
$831$		0			0
$832$	1498.17	+	2594.91i	0.0624277	+	0.108128i
$833$	2852.44	−	4379.49i	0.118645	−	0.182161i
$834$		0			0
$835$	−8364.92	−	14488.5i	−0.346683	−	0.600472i
$836$	−13373.5	−	23163.6i	−0.553268	−	0.958289i
$837$		0			0
$838$	1044.55	−	1809.22i	0.0430590	−	0.0745804i
$839$	3127.04	−	5416.20i	0.128674	−	0.222870i	−0.794489	−	0.607278i	$-0.792261\pi$
$839$	3127.04	−	5416.20i	0.128674	−	0.222870i	0.923163	+	0.384409i	$0.125595\pi$
$840$		0			0
$841$	5610.71	+	9718.03i	0.230051	+	0.398460i
$842$	−15707.0			−0.642873
$843$		0			0
$844$	51912.5			2.11718
$845$	7208.16	−	12484.9i	0.293453	−	0.508276i
$846$		0			0
$847$	10034.3	−	16349.8i	0.407062	−	0.663265i
$848$	141.092	−	244.379i	0.00571360	−	0.00989624i
$849$		0			0
$850$	8365.36	−	14489.2i	0.337564	−	0.584678i
$851$	346.383	−	599.952i	0.0139528	−	0.0241670i
$852$		0			0
$853$	−6712.59	+	11626.5i	−0.269443	+	0.466688i	−0.968718	−	0.248164i	$-0.920173\pi$
$853$	−6712.59	+	11626.5i	−0.269443	+	0.466688i	0.699275	+	0.714852i	$0.253506\pi$
$854$	31920.9	+	58885.2i	1.27905	+	2.35950i
$855$		0			0
$856$	16303.0	−	28237.6i	0.650963	−	1.12750i
$857$	−27929.4			−1.11325			−0.556623	−	0.830765i	$-0.687903\pi$
$857$	−27929.4			−1.11325			−0.556623	+	0.830765i	$0.687903\pi$
$858$		0			0
$859$	9520.49			0.378155			0.189077	−	0.981962i	$-0.439450\pi$
$859$	9520.49			0.378155			0.189077	+	0.981962i	$0.439450\pi$
$860$	25457.3	+	44093.4i	1.00940	+	1.74834i
$861$		0			0
$862$	16187.3	−	28037.1i	0.639606	−	1.10783i
$863$	−15835.9	+	27428.6i	−0.624635	+	1.08190i	0.363977	+	0.931408i	$0.381419\pi$
$863$	−15835.9	+	27428.6i	−0.624635	+	1.08190i	−0.988611	+	0.150491i	$0.951915\pi$
$864$		0			0
$865$	2633.94	+	4562.11i	0.103534	+	0.179325i
$866$	39887.8	+	69087.8i	1.56518	+	2.71097i
$867$		0			0
$868$	16494.9	+	443.012i	0.645015	+	0.0173235i
$869$	−9237.84	−	16000.4i	−0.360613	−	0.624599i
$870$		0			0
$871$	2060.20			0.0801460
$872$	−10803.5	−	18712.2i	−0.419556	−	0.726692i
$873$		0			0
$874$	−42943.6			−1.66200
$875$	16307.4	−	26571.1i	0.630045	−	1.02659i
$876$		0			0
$877$	11843.9			0.456031			0.228015	−	0.973658i	$-0.426776\pi$
$877$	11843.9			0.456031			0.228015	+	0.973658i	$0.426776\pi$
$878$	−16115.3	+	27912.6i	−0.619437	+	1.07290i
$879$		0			0
$880$	−17550.7	−	30398.6i	−0.672309	−	1.16447i
$881$	−23747.9			−0.908156			−0.454078	−	0.890962i	$-0.650031\pi$
$881$	−23747.9			−0.908156			−0.454078	+	0.890962i	$0.650031\pi$
$882$		0			0
$883$	−35595.0			−1.35659			−0.678294	−	0.734790i	$-0.737281\pi$
$883$	−35595.0			−1.35659			−0.678294	+	0.734790i	$0.737281\pi$
$884$	7402.64	+	12821.7i	0.281649	+	0.487830i
$885$		0			0
$886$	20363.4	−	35270.4i	0.772145	−	1.33739i
$887$	20604.7			0.779974			0.389987	−	0.920820i	$-0.372480\pi$
$887$	20604.7			0.779974			0.389987	+	0.920820i	$0.372480\pi$
$888$		0			0
$889$	−23429.2	+	38175.5i	−0.883905	+	1.44023i
$890$	−1078.45			−0.0406177
$891$		0			0
$892$	−6014.13	−	10416.8i	−0.225749	−	0.391008i
$893$	−10293.1			−0.385719
$894$		0			0
$895$	−26573.8	−	46027.1i	−0.992472	−	1.71901i
$896$	−29362.9	−	788.614i	−1.09480	−	0.0294037i
$897$		0			0
$898$	7815.61	+	13537.0i	0.290435	+	0.503048i
$899$	−2870.84	−	4972.45i	−0.106505	−	0.184472i
$900$		0			0
$901$	−19.4365	+	33.6650i	−0.000718672	+	0.00124478i
$902$	−7634.58	+	13223.5i	−0.281822	+	0.488131i
$903$		0			0
$904$	46287.5	+	80172.2i	1.70298	+	2.94966i
$905$	−16964.0			−0.623096
$906$		0			0
$907$	−51597.3			−1.88893			−0.944466	−	0.328610i	$-0.893420\pi$
$907$	−51597.3			−1.88893			−0.944466	+	0.328610i	$0.893420\pi$
$908$	−5727.46	+	9920.25i	−0.209331	+	0.362572i
$909$		0			0
$910$	45188.6	+	83360.5i	1.64614	+	3.03667i
$911$	−17019.3	+	29478.3i	−0.618962	+	1.07207i	0.370714	+	0.928747i	$0.379113\pi$
$911$	−17019.3	+	29478.3i	−0.618962	+	1.07207i	−0.989675	+	0.143326i	$0.954220\pi$
$912$		0			0
$913$	−10908.2	+	18893.5i	−0.395408	+	0.684867i
$914$	11213.2	−	19421.8i	0.405798	−	0.702863i
$915$		0			0
$916$	−32620.8	+	56500.8i	−1.17666	+	2.03803i
$917$	7101.97	−	11571.9i	0.255755	−	0.416727i
$918$		0			0
$919$	−6325.21	+	10955.6i	−0.227040	+	0.393244i	−0.956929	−	0.290321i	$-0.906238\pi$
$919$	−6325.21	+	10955.6i	−0.227040	+	0.393244i	0.729890	+	0.683565i	$0.239571\pi$
$920$	−88964.8			−3.18813
$921$		0			0
$922$	11579.5			0.413613
$923$	−7917.76	−	13714.0i	−0.282358	−	0.489058i
$924$		0			0
$925$	774.291	−	1341.11i	0.0275227	−	0.0476708i
$926$	16408.6	−	28420.6i	0.582312	−	1.00859i
$927$		0			0
$928$	−9374.13	−	16236.5i	−0.331596	−	0.574340i
$929$	−11635.1	−	20152.6i	−0.410909	−	0.711716i	0.584080	−	0.811696i	$-0.301455\pi$
$929$	−11635.1	−	20152.6i	−0.410909	−	0.711716i	−0.994989	+	0.0999801i	$0.968122\pi$
$930$		0			0
$931$	−29944.4	−	1609.63i	−1.05412	−	0.0566632i
$932$	37278.2	+	64567.7i	1.31018	+	2.26930i
$933$		0			0
$934$	−77313.1			−2.70852
$935$	2417.73	+	4187.63i	0.0845649	+	0.146471i
$936$		0			0
$937$	21381.0			0.745451			0.372725	−	0.927942i	$-0.378423\pi$
$937$	21381.0			0.745451			0.372725	+	0.927942i	$0.378423\pi$
$938$	−1858.02	+	3027.45i	−0.0646765	+	0.105384i
$939$		0			0
$940$	−38720.2			−1.34352
$941$	7917.28	−	13713.1i	0.274279	−	0.475064i	−0.695674	−	0.718357i	$-0.744894\pi$
$941$	7917.28	−	13713.1i	0.274279	−	0.475064i	0.969953	+	0.243293i	$0.0782276\pi$
$942$		0			0
$943$	8457.77	+	14649.3i	0.292071	+	0.505881i
$944$	−45591.9			−1.57192
$945$		0			0
$946$	−13512.0			−0.464392
$947$	1707.66	+	2957.76i	0.0585973	+	0.101494i	0.893836	−	0.448394i	$-0.148004\pi$
$947$	1707.66	+	2957.76i	0.0585973	+	0.101494i	−0.835239	+	0.549888i	$0.814671\pi$
$948$		0			0
$949$	11455.3	−	19841.1i	0.391838	−	0.678683i
$950$	−95994.5			−3.27839
$951$		0			0
$952$	−14053.1	−	377.431i	−0.478428	−	0.0128494i
$953$	2616.58			0.0889394			0.0444697	−	0.999011i	$-0.485840\pi$
$953$	2616.58			0.0889394			0.0444697	+	0.999011i	$0.485840\pi$
$954$		0			0
$955$	−29205.2	−	50585.0i	−0.989591	−	1.71402i
$956$	−2243.11			−0.0758865
$957$		0			0
$958$	48823.7	+	84565.1i	1.64658	+	2.85196i
$959$	7438.06	−	12119.5i	0.250456	−	0.408092i
$960$		0			0
$961$	13643.7	+	23631.5i	0.457980	+	0.793244i
$962$	993.023	+	1719.97i	0.0332810	+	0.0576444i
$963$		0			0
$964$	−58818.4	+	101876.i	−1.96516	+	3.40376i
$965$	16512.6	−	28600.7i	0.550839	−	0.954081i
$966$		0			0
$967$	−4230.23	−	7326.98i	−0.140677	−	0.243660i	0.787074	−	0.616858i	$-0.211595\pi$
$967$	−4230.23	−	7326.98i	−0.140677	−	0.243660i	−0.927752	+	0.373198i	$0.878261\pi$
$968$	−51599.1			−1.71328
$969$		0			0
$970$	175514.			5.80971
$971$	−14358.9	+	24870.3i	−0.474561	+	0.821963i	−0.999576	−	0.0291297i	$-0.990726\pi$
$971$	−14358.9	+	24870.3i	−0.474561	+	0.821963i	0.525015	+	0.851093i	$0.324060\pi$
$972$		0			0
$973$	31072.8	+	834.539i	1.02379	+	0.0274965i
$974$	−21167.3	+	36662.8i	−0.696348	+	1.20611i
$975$		0			0
$976$	39374.3	−	68198.3i	1.29133	−	2.23665i
$977$	12884.2	−	22316.2i	0.421907	−	0.730765i	−0.574219	−	0.818702i	$-0.694694\pi$
$977$	12884.2	−	22316.2i	0.421907	−	0.730765i	0.996126	+	0.0879373i	$0.0280275\pi$
$978$		0			0
$979$	98.7406	−	171.024i	0.00322346	−	0.00558319i
$980$	−112643.	−	6055.02i	−3.67170	−	0.197368i
$981$		0			0
$982$	27189.3	−	47093.2i	0.883548	−	1.53035i
$983$	−10589.0			−0.343579			−0.171789	−	0.985134i	$-0.554955\pi$
$983$	−10589.0			−0.343579			−0.171789	+	0.985134i	$0.554955\pi$
$984$		0			0
$985$	−94045.0			−3.04215
$986$	4441.22	+	7692.41i	0.143445	+	0.248455i
$987$		0			0
$988$	42473.5	−	73566.3i	1.36768	−	2.36888i
$989$	−7484.48	+	12963.5i	−0.240640	+	0.416800i
$990$		0			0
$991$	−18671.0	−	32339.1i	−0.598489	−	1.03661i	−0.993044	−	0.117741i	$-0.962435\pi$
$991$	−18671.0	−	32339.1i	−0.598489	−	1.03661i	0.394555	−	0.918872i	$-0.370899\pi$
$992$	−4087.56	−	7079.87i	−0.130827	−	0.226599i
$993$		0			0
$994$	27293.4	+	733.033i	0.870919	+	0.0233907i
$995$	23550.4	+	40790.4i	0.750349	+	1.29964i
$996$		0			0
$997$	−6476.45			−0.205728			−0.102864	−	0.994695i	$-0.532801\pi$
$997$	−6476.45			−0.205728			−0.102864	+	0.994695i	$0.532801\pi$
$998$	−27665.9	−	47918.7i	−0.877504	−	1.51988i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.g.a.100.2		44
3.2	odd	2		63.4.g.a.16.21	yes	44
7.4	even	3		189.4.h.a.46.21		44
9.4	even	3		189.4.h.a.37.21		44
9.5	odd	6		63.4.h.a.58.2	yes	44
21.11	odd	6		63.4.h.a.25.2	yes	44
63.4	even	3	inner	189.4.g.a.172.2		44
63.32	odd	6		63.4.g.a.4.21	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.21	✓	44	63.32	odd	6
63.4.g.a.16.21	yes	44	3.2	odd	2
63.4.h.a.25.2	yes	44	21.11	odd	6
63.4.h.a.58.2	yes	44	9.5	odd	6
189.4.g.a.100.2		44	1.1	even	1	trivial
189.4.g.a.172.2		44	63.4	even	3	inner
189.4.h.a.37.21		44	9.4	even	3
189.4.h.a.46.21		44	7.4	even	3

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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.53999 - 4.39939i) q^{2} +(-8.90312 + 15.4206i) q^{4} -18.4700 q^{5} +(-9.68740 + 15.7846i) q^{7} +49.8155 q^{8} +O(q^{10})\)	\(q+(-2.53999 - 4.39939i) q^{2} +(-8.90312 + 15.4206i) q^{4} -18.4700 q^{5} +(-9.68740 + 15.7846i) q^{7} +49.8155 q^{8} +(46.9136 + 81.2567i) q^{10} -17.1812 q^{11} +(-27.2834 - 47.2562i) q^{13} +(94.0487 + 2.52592i) q^{14} +(-55.3060 - 95.7928i) q^{16} +(7.61880 + 13.1962i) q^{17} +(43.7138 - 75.7145i) q^{19} +(164.440 - 284.819i) q^{20} +(43.6402 + 75.5870i) q^{22} +96.6913 q^{23} +216.140 q^{25} +(-138.599 + 240.061i) q^{26} +(-157.161 - 289.918i) q^{28} +(-57.3750 + 99.3765i) q^{29} +(-25.0182 + 43.3329i) q^{31} +(-81.6917 + 141.494i) q^{32} +(38.7034 - 67.0362i) q^{34} +(178.926 - 291.542i) q^{35} +(3.58236 - 6.20483i) q^{37} -444.131 q^{38} -920.091 q^{40} +(87.4719 + 151.506i) q^{41} +(-77.4059 + 134.071i) q^{43} +(152.967 - 264.946i) q^{44} +(-245.595 - 425.383i) q^{46} +(-58.8666 - 101.960i) q^{47} +(-155.308 - 305.824i) q^{49} +(-548.994 - 950.886i) q^{50} +971.628 q^{52} +(1.27556 + 2.20934i) q^{53} +317.337 q^{55} +(-482.583 + 786.319i) q^{56} +582.929 q^{58} +(206.089 - 356.957i) q^{59} +(355.968 + 616.554i) q^{61} +254.184 q^{62} -54.9116 q^{64} +(503.923 + 872.820i) q^{65} +(-18.8778 + 32.6973i) q^{67} -271.324 q^{68} +(-1737.08 - 46.6536i) q^{70} +290.205 q^{71} +(209.932 + 363.612i) q^{73} -36.3966 q^{74} +(778.378 + 1348.19i) q^{76} +(166.442 - 271.199i) q^{77} +(537.670 + 931.272i) q^{79} +(1021.50 + 1769.29i) q^{80} +(444.356 - 769.647i) q^{82} +(634.888 - 1099.66i) q^{83} +(-140.719 - 243.733i) q^{85} +786.442 q^{86} -855.892 q^{88} +(-5.74700 + 9.95410i) q^{89} +(1010.23 + 27.1322i) q^{91} +(-860.854 + 1491.04i) q^{92} +(-299.041 + 517.955i) q^{94} +(-807.393 + 1398.45i) q^{95} +(935.304 - 1619.99i) q^{97} +(-950.958 + 1460.05i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} + 10 q^{11} - 14 q^{13} + 79 q^{14} - 247 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} - 186 q^{23} + 698 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} + 61 q^{31} + 163 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} - 1522 q^{38} + 36 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} + 1005 q^{47} - 277 q^{49} - 239 q^{50} + 670 q^{52} - 258 q^{53} - 870 q^{55} - 714 q^{56} - 474 q^{58} + 1665 q^{59} + 439 q^{61} - 1812 q^{62} + 872 q^{64} + 613 q^{65} + 295 q^{67} - 2748 q^{68} - 1044 q^{70} - 636 q^{71} - 338 q^{73} + 2238 q^{74} + 1006 q^{76} + 2909 q^{77} + 133 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} - 6686 q^{86} - 738 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} - 1191 q^{94} - 3083 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) \) 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 + 10 * q^11 - 14 * q^13 + 79 * q^14 - 247 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 - 186 * q^23 + 698 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 + 61 * q^31 + 163 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 - 1522 * q^38 + 36 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 + 1005 * q^47 - 277 * q^49 - 239 * q^50 + 670 * q^52 - 258 * q^53 - 870 * q^55 - 714 * q^56 - 474 * q^58 + 1665 * q^59 + 439 * q^61 - 1812 * q^62 + 872 * q^64 + 613 * q^65 + 295 * q^67 - 2748 * q^68 - 1044 * q^70 - 636 * q^71 - 338 * q^73 + 2238 * q^74 + 1006 * q^76 + 2909 * q^77 + 133 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 - 6686 * q^86 - 738 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 - 1191 * q^94 - 3083 * q^95 - 266 * q^97 - 3601 * q^98

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