LMFDB - Embedded newform 189.4.s.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(17,189)]

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([5, 1]))

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

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

chi := DirichletCharacter("189.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.s (of order $6$, 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 $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	189.17
Dual form			189.4.s.a.89.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.68213 - 2.12588i) q^{2} +(5.03872 + 8.72732i) q^{4} +2.97507 q^{5} +(-4.05014 - 18.0720i) q^{7} -8.83278i q^{8} +O(q^{10})$	\(q+(-3.68213 - 2.12588i) q^{2} +(5.03872 + 8.72732i) q^{4} +2.97507 q^{5} +(-4.05014 - 18.0720i) q^{7} -8.83278i q^{8} +(-10.9546 - 6.32464i) q^{10} +33.6576i q^{11} +(22.0839 + 12.7502i) q^{13} +(-23.5057 + 75.1535i) q^{14} +(21.5324 - 37.2951i) q^{16} +(55.6342 - 96.3612i) q^{17} +(66.6439 - 38.4768i) q^{19} +(14.9906 + 25.9644i) q^{20} +(71.5519 - 123.932i) q^{22} -27.8198i q^{23} -116.149 q^{25} +(-54.2106 - 93.8955i) q^{26} +(137.312 - 126.407i) q^{28} +(-87.6545 + 50.6073i) q^{29} +(-57.9504 + 33.4577i) q^{31} +(-219.765 + 126.881i) q^{32} +(-409.704 + 236.543i) q^{34} +(-12.0495 - 53.7654i) q^{35} +(-146.685 - 254.067i) q^{37} -327.188 q^{38} -26.2782i q^{40} +(62.2674 - 107.850i) q^{41} +(-151.499 - 262.404i) q^{43} +(-293.741 + 169.591i) q^{44} +(-59.1416 + 102.436i) q^{46} +(183.568 - 317.949i) q^{47} +(-310.193 + 146.388i) q^{49} +(427.676 + 246.919i) q^{50} +256.978i q^{52} +(-281.281 - 162.397i) q^{53} +100.134i q^{55} +(-159.626 + 35.7740i) q^{56} +430.340 q^{58} +(-388.659 - 673.177i) q^{59} +(162.171 + 93.6293i) q^{61} +284.508 q^{62} +734.421 q^{64} +(65.7013 + 37.9326i) q^{65} +(358.878 + 621.595i) q^{67} +1121.30 q^{68} +(-69.9311 + 223.587i) q^{70} -762.408i q^{71} +(-409.650 - 236.512i) q^{73} +1247.34i q^{74} +(671.600 + 387.748i) q^{76} +(608.259 - 136.318i) q^{77} +(353.515 - 612.306i) q^{79} +(64.0603 - 110.956i) q^{80} +(-458.553 + 264.746i) q^{82} +(406.242 + 703.632i) q^{83} +(165.516 - 286.681i) q^{85} +1288.27i q^{86} +297.290 q^{88} +(393.311 + 681.235i) q^{89} +(140.978 - 450.740i) q^{91} +(242.792 - 140.176i) q^{92} +(-1351.84 + 780.486i) q^{94} +(198.270 - 114.471i) q^{95} +(1510.29 - 871.967i) q^{97} +(1453.37 + 120.412i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−3.68213	−	2.12588i	−1.30183	−	0.751612i	−0.321112	−	0.947041i	$-0.604057\pi$
$2$	−3.68213	−	2.12588i	−1.30183	−	0.751612i	−0.980718	+	0.195430i	$0.937390\pi$
$3$		0			0
$3$		0			0
$4$	5.03872	+	8.72732i	0.629840	+	1.09092i
$5$	2.97507			0.266099			0.133049	−	0.991109i	$-0.457523\pi$
$5$	2.97507			0.266099			0.133049	+	0.991109i	$0.457523\pi$
$6$		0			0
$7$	−4.05014	−	18.0720i	−0.218687	−	0.975795i
$7$	−4.05014	−	18.0720i	−0.218687	−	0.975795i
$8$		−	8.83278i		−	0.390357i
$9$		0			0
$10$	−10.9546	−	6.32464i	−0.346415	−	0.200003i
$11$			33.6576i			0.922558i	0.887255	+	0.461279i	$0.152609\pi$
$11$			33.6576i			0.922558i	−0.887255	+	0.461279i	$0.847391\pi$
$12$		0			0
$13$	22.0839	+	12.7502i	0.471152	+	0.272020i	0.716722	−	0.697359i	$-0.245642\pi$
$13$	22.0839	+	12.7502i	0.471152	+	0.272020i	−0.245570	+	0.969379i	$0.578975\pi$
$14$	−23.5057	+	75.1535i	−0.448725	+	1.43469i
$15$		0			0
$16$	21.5324	−	37.2951i	0.336443	−	0.582736i
$17$	55.6342	−	96.3612i	0.793721	−	1.37477i	−0.129926	−	0.991524i	$-0.541474\pi$
$17$	55.6342	−	96.3612i	0.793721	−	1.37477i	0.923648	−	0.383242i	$-0.125193\pi$
$18$		0			0
$19$	66.6439	−	38.4768i	0.804692	−	0.464589i	−0.0404171	−	0.999183i	$-0.512869\pi$
$19$	66.6439	−	38.4768i	0.804692	−	0.464589i	0.845109	+	0.534594i	$0.179535\pi$
$20$	14.9906	+	25.9644i	0.167600	+	0.290291i
$21$		0			0
$22$	71.5519	−	123.932i	0.693406	−	1.20101i
$23$		−	27.8198i		−	0.252210i	−0.992017	−	0.126105i	$-0.959752\pi$
$23$		−	27.8198i		−	0.252210i	0.992017	−	0.126105i	$-0.0402476\pi$
$24$		0			0
$25$	−116.149			−0.929192
$26$	−54.2106	−	93.8955i	−0.408906	−	0.708247i
$27$		0			0
$28$	137.312	−	126.407i	0.926772	−	0.853164i
$29$	−87.6545	+	50.6073i	−0.561277	+	0.324053i	−0.753658	−	0.657267i	$-0.771712\pi$
$29$	−87.6545	+	50.6073i	−0.561277	+	0.324053i	0.192381	+	0.981320i	$0.438379\pi$
$30$		0			0
$31$	−57.9504	+	33.4577i	−0.335748	+	0.193844i	−0.658390	−	0.752677i	$-0.728762\pi$
$31$	−57.9504	+	33.4577i	−0.335748	+	0.193844i	0.322642	+	0.946521i	$0.395429\pi$
$32$	−219.765	+	126.881i	−1.21404	+	0.700928i
$33$		0			0
$34$	−409.704	+	236.543i	−2.06658	+	1.19314i
$35$	−12.0495	−	53.7654i	−0.0581923	−	0.259658i
$36$		0			0
$37$	−146.685	−	254.067i	−0.651755	−	1.12887i	−0.982697	−	0.185222i	$-0.940700\pi$
$37$	−146.685	−	254.067i	−0.651755	−	1.12887i	0.330942	−	0.943651i	$-0.392634\pi$
$38$	−327.188			−1.39676
$39$		0			0
$40$		−	26.2782i		−	0.103874i
$41$	62.2674	−	107.850i	0.237184	−	0.410814i	−0.722721	−	0.691140i	$-0.757109\pi$
$41$	62.2674	−	107.850i	0.237184	−	0.410814i	0.959905	+	0.280325i	$0.0904423\pi$
$42$		0			0
$43$	−151.499	−	262.404i	−0.537288	−	0.930610i	−0.999049	−	0.0436058i	$-0.986115\pi$
$43$	−151.499	−	262.404i	−0.537288	−	0.930610i	0.461761	−	0.887005i	$-0.347218\pi$
$44$	−293.741	+	169.591i	−1.00643	+	0.581064i
$45$		0			0
$46$	−59.1416	+	102.436i	−0.189564	+	0.328335i
$47$	183.568	−	317.949i	0.569705	−	0.986758i	−0.426890	−	0.904304i	$-0.640391\pi$
$47$	183.568	−	317.949i	0.569705	−	0.986758i	0.996595	−	0.0824542i	$-0.0262758\pi$
$48$		0			0
$49$	−310.193	+	146.388i	−0.904352	+	0.426788i
$50$	427.676	+	246.919i	1.20965	+	0.698391i
$51$		0			0
$52$			256.978i			0.685316i
$53$	−281.281	−	162.397i	−0.728997	−	0.420887i	0.0890579	−	0.996026i	$-0.471614\pi$
$53$	−281.281	−	162.397i	−0.728997	−	0.420887i	−0.818055	+	0.575140i	$0.804948\pi$
$54$		0			0
$55$			100.134i			0.245491i
$56$	−159.626	+	35.7740i	−0.380909	+	0.0853661i
$57$		0			0
$58$	430.340			0.974249
$59$	−388.659	−	673.177i	−0.857612	−	1.48543i	−0.874200	−	0.485565i	$-0.838614\pi$
$59$	−388.659	−	673.177i	−0.857612	−	1.48543i	0.0165884	−	0.999862i	$-0.494720\pi$
$60$		0			0
$61$	162.171	+	93.6293i	0.340391	+	0.196525i	0.660445	−	0.750875i	$-0.270368\pi$
$61$	162.171	+	93.6293i	0.340391	+	0.196525i	−0.320054	+	0.947399i	$0.603701\pi$
$62$	284.508			0.582783
$63$		0			0
$64$	734.421			1.43442
$65$	65.7013	+	37.9326i	0.125373	+	0.0723841i
$66$		0			0
$67$	358.878	+	621.595i	0.654387	+	1.13343i	0.982047	+	0.188635i	$0.0604065\pi$
$67$	358.878	+	621.595i	0.654387	+	1.13343i	−0.327660	+	0.944796i	$0.606260\pi$
$68$	1121.30			1.99967
$69$		0			0
$70$	−69.9311	+	223.587i	−0.119405	+	0.381768i
$71$		−	762.408i		−	1.27438i	−0.770705	−	0.637192i	$-0.780096\pi$
$71$		−	762.408i		−	1.27438i	0.770705	−	0.637192i	$-0.219904\pi$
$72$		0			0
$73$	−409.650	−	236.512i	−0.656793	−	0.379200i	0.134261	−	0.990946i	$-0.457134\pi$
$73$	−409.650	−	236.512i	−0.656793	−	0.379200i	−0.791054	+	0.611746i	$0.790467\pi$
$74$			1247.34i			1.95947i
$75$		0			0
$76$	671.600	+	387.748i	1.01365	+	0.585234i
$77$	608.259	−	136.318i	0.900228	−	0.201752i
$78$		0			0
$79$	353.515	−	612.306i	0.503462	−	0.872022i	−0.496530	−	0.868020i	$-0.665393\pi$
$79$	353.515	−	612.306i	0.503462	−	0.872022i	0.999992	−	0.00400262i	$-0.00127408\pi$
$80$	64.0603	−	110.956i	0.0895270	−	0.155065i
$81$		0			0
$82$	−458.553	+	264.746i	−0.617546	+	0.356540i
$83$	406.242	+	703.632i	0.537240	+	0.930526i	0.999051	+	0.0435485i	$0.0138663\pi$
$83$	406.242	+	703.632i	0.537240	+	0.930526i	−0.461812	+	0.886978i	$0.652800\pi$
$84$		0			0
$85$	165.516	−	286.681i	0.211208	−	0.365823i
$86$			1288.27i			1.61533i
$87$		0			0
$88$	297.290			0.360127
$89$	393.311	+	681.235i	0.468437	+	0.811356i	0.999349	−	0.0360703i	$-0.0114840\pi$
$89$	393.311	+	681.235i	0.468437	+	0.811356i	−0.530912	+	0.847427i	$0.678151\pi$
$90$		0			0
$91$	140.978	−	450.740i	0.162401	−	0.519235i
$92$	242.792	−	140.176i	0.275140	−	0.158852i
$93$		0			0
$94$	−1351.84	+	780.486i	−1.48332	+	0.856394i
$95$	198.270	−	114.471i	0.214127	−	0.123627i
$96$		0			0
$97$	1510.29	−	871.967i	1.58090	−	0.912731i	0.586167	−	0.810190i	$-0.300636\pi$
$97$	1510.29	−	871.967i	1.58090	−	0.912731i	0.994729	−	0.102540i	$-0.0326970\pi$
$98$	1453.37	+	120.412i	1.49809	+	0.124117i
$99$		0			0
$100$	−585.242	−	1013.67i	−0.585242	−	1.01367i
$101$	−1046.74			−1.03123			−0.515614	−	0.856821i	$-0.672436\pi$
$101$	−1046.74			−1.03123			−0.515614	+	0.856821i	$0.672436\pi$
$102$		0			0
$103$		−	849.490i		−	0.812648i	−0.913729	−	0.406324i	$-0.866810\pi$
$103$		−	849.490i		−	0.812648i	0.913729	−	0.406324i	$-0.133190\pi$
$104$	112.619	−	195.062i	0.106185	−	0.183918i
$105$		0			0
$106$	690.474	+	1195.94i	0.632687	+	1.09585i
$107$	−235.192	+	135.788i	−0.212494	+	0.122684i	−0.602470	−	0.798141i	$-0.705817\pi$
$107$	−235.192	+	135.788i	−0.212494	+	0.122684i	0.389976	+	0.920825i	$0.372483\pi$
$108$		0			0
$109$	−812.303	+	1406.95i	−0.713803	+	1.23634i	0.249616	+	0.968345i	$0.419695\pi$
$109$	−812.303	+	1406.95i	−0.713803	+	1.23634i	−0.963419	+	0.267998i	$0.913638\pi$
$110$	212.872	−	368.705i	0.184514	−	0.319588i
$111$		0			0
$112$	−761.206	−	238.082i	−0.642207	−	0.200862i
$113$	1403.77	+	810.466i	1.16863	+	0.674710i	0.953357	−	0.301843i	$-0.0976020\pi$
$113$	1403.77	+	810.466i	1.16863	+	0.674710i	0.215275	+	0.976554i	$0.430935\pi$
$114$		0			0
$115$		−	82.7660i		−	0.0671128i
$116$	−883.333	−	509.993i	−0.707029	−	0.408204i
$117$		0			0
$118$			3304.97i			2.57836i
$119$	−1966.76	−	615.143i	−1.51507	−	0.473866i
$120$		0			0
$121$	198.167			0.148886
$122$	−398.089	−	689.511i	−0.295421	−	0.511683i
$123$		0			0
$124$	−583.992	−	337.168i	−0.422935	−	0.244182i
$125$	−717.436			−0.513355
$126$		0			0
$127$	2812.64			1.96521			0.982605	−	0.185710i	$-0.0594585\pi$
$127$	2812.64			1.96521			0.982605	+	0.185710i	$0.0594585\pi$
$128$	−946.111	−	546.238i	−0.653322	−	0.377196i
$129$		0			0
$130$	−161.280	−	279.346i	−0.108809	−	0.188463i
$131$	−1011.28			−0.674473			−0.337236	−	0.941420i	$-0.609492\pi$
$131$	−1011.28			−0.674473			−0.337236	+	0.941420i	$0.609492\pi$
$132$		0			0
$133$	−965.270	−	1048.55i	−0.629320	−	0.683615i
$134$		−	3051.72i		−	1.96738i
$135$		0			0
$136$	−851.137	−	491.404i	−0.536650	−	0.309835i
$137$		−	2509.41i		−	1.56492i	−0.622703	−	0.782459i	$-0.713965\pi$
$137$		−	2509.41i		−	1.56492i	0.622703	−	0.782459i	$-0.286035\pi$
$138$		0			0
$139$	−1711.04	−	987.869i	−1.04409	−	0.602805i	−0.123101	−	0.992394i	$-0.539284\pi$
$139$	−1711.04	−	987.869i	−1.04409	−	0.602805i	−0.920989	+	0.389589i	$0.872617\pi$
$140$	408.514	−	376.069i	0.246613	−	0.227026i
$141$		0			0
$142$	−1620.79	+	2807.29i	−0.957842	+	1.65903i
$143$	−429.139	+	743.291i	−0.250954	+	0.434665i
$144$		0			0
$145$	−260.778	+	150.561i	−0.149355	+	0.0862301i
$146$	1005.59	+	1741.73i	0.570022	+	0.987307i
$147$		0			0
$148$	1478.21	−	2560.34i	0.821003	−	1.42202i
$149$			541.339i			0.297639i	0.988864	+	0.148819i	$0.0475473\pi$
$149$			541.339i			0.297639i	−0.988864	+	0.148819i	$0.952453\pi$
$150$		0			0
$151$	2064.71			1.11274			0.556371	−	0.830934i	$-0.312193\pi$
$151$	2064.71			1.11274			0.556371	+	0.830934i	$0.312193\pi$
$152$	−339.857	−	588.650i	−0.181356	−	0.314117i
$153$		0			0
$154$	−2529.48	−	791.144i	−1.32358	−	0.413975i
$155$	−172.407	+	99.5390i	−0.0893421	+	0.0515817i
$156$		0			0
$157$	−1623.15	+	937.128i	−0.825107	+	0.476375i	−0.852174	−	0.523258i	$-0.824716\pi$
$157$	−1623.15	+	937.128i	−0.825107	+	0.476375i	0.0270677	+	0.999634i	$0.491383\pi$
$158$	−2603.38	+	1503.06i	−1.31084	+	0.756816i
$159$		0			0
$160$	−653.817	+	377.482i	−0.323055	+	0.186516i
$161$	−502.759	+	112.674i	−0.246105	+	0.0551551i
$162$		0			0
$163$	375.825	+	650.948i	0.180594	+	0.312799i	0.942083	−	0.335380i	$-0.108865\pi$
$163$	375.825	+	650.948i	0.180594	+	0.312799i	−0.761489	+	0.648178i	$0.775531\pi$
$164$	1254.99			0.597551
$165$		0			0
$166$		−	3454.49i		−	1.61518i
$167$	768.357	−	1330.83i	0.356032	−	0.616665i	−0.631262	−	0.775569i	$-0.717463\pi$
$167$	768.357	−	1330.83i	0.356032	−	0.616665i	0.987294	+	0.158905i	$0.0507962\pi$
$168$		0			0
$169$	−773.367	−	1339.51i	−0.352010	−	0.609700i
$170$	−1218.90	+	703.732i	−0.549914	+	0.317493i
$171$		0			0
$172$	1526.72	−	2644.36i	0.676811	−	1.17227i
$173$	−1004.57	+	1739.97i	−0.441480	+	0.764667i	−0.997800	−	0.0663021i	$-0.978880\pi$
$173$	−1004.57	+	1739.97i	−0.441480	+	0.764667i	0.556319	+	0.830969i	$0.312213\pi$
$174$		0			0
$175$	470.420	+	2099.04i	0.203202	+	0.906700i
$176$	1255.26	+	724.727i	0.537608	+	0.310388i
$177$		0			0
$178$		−	3344.53i		−	1.40833i
$179$	−635.487	−	366.899i	−0.265355	−	0.153203i	0.361420	−	0.932403i	$-0.382292\pi$
$179$	−635.487	−	366.899i	−0.265355	−	0.153203i	−0.626775	+	0.779200i	$0.715625\pi$
$180$		0			0
$181$		−	14.0932i		−	0.00578751i	−0.999996	−	0.00289375i	$-0.999079\pi$
$181$		−	14.0932i		−	0.00578751i	0.999996	−	0.00289375i	$-0.000921111\pi$
$182$	−1477.32	+	1359.98i	−0.601681	+	0.553893i
$183$		0			0
$184$	−245.726			−0.0984521
$185$	−436.400	−	755.867i	−0.173431	−	0.300392i
$186$		0			0
$187$	3243.28	+	1872.51i	1.26830	+	0.732254i
$188$	3699.79			1.43529
$189$		0			0
$190$	−973.409			−0.371677
$191$	2374.42	+	1370.87i	0.899512	+	0.519333i	0.877042	−	0.480414i	$-0.159514\pi$
$191$	2374.42	+	1370.87i	0.899512	+	0.519333i	0.0224699	+	0.999748i	$0.492847\pi$
$192$		0			0
$193$	−1138.20	−	1971.42i	−0.424506	−	0.735266i	0.571868	−	0.820345i	$-0.306219\pi$
$193$	−1138.20	−	1971.42i	−0.424506	−	0.735266i	−0.996374	+	0.0850798i	$0.972885\pi$
$194$	−7414.79			−2.74408
$195$		0			0
$196$	−2840.55	−	1969.54i	−1.03519	−	0.717763i
$197$			674.789i			0.244044i	0.992527	+	0.122022i	$0.0389379\pi$
$197$			674.789i			0.244044i	−0.992527	+	0.122022i	$0.961062\pi$
$198$		0			0
$199$	2293.61	+	1324.22i	0.817033	+	0.471714i	0.849392	−	0.527762i	$-0.176969\pi$
$199$	2293.61	+	1324.22i	0.817033	+	0.471714i	−0.0323593	+	0.999476i	$0.510302\pi$
$200$			1025.92i			0.362717i
$201$		0			0
$202$	3854.22	+	2225.23i	1.34248	+	0.775083i
$203$	1269.59	+	1379.12i	0.438954	+	0.476825i
$204$		0			0
$205$	185.250	−	320.862i	0.0631143	−	0.109317i
$206$	−1805.91	+	3127.93i	−0.610795	+	1.05793i
$207$		0			0
$208$	951.037	−	549.082i	0.317032	−	0.183038i
$209$	1295.04	+	2243.07i	0.428611	+	0.742376i
$210$		0			0
$211$	531.302	−	920.242i	0.173348	−	0.300247i	−0.766241	−	0.642554i	$-0.777875\pi$
$211$	531.302	−	920.242i	0.173348	−	0.300247i	0.939588	+	0.342307i	$0.111208\pi$
$212$		−	3273.10i		−	1.06037i
$213$		0			0
$214$	1154.68			0.368842
$215$	−450.721	−	780.671i	−0.142972	−	0.247634i
$216$		0			0
$217$	839.354	+	911.770i	0.262576	+	0.285230i
$218$	5982.01	−	3453.72i	1.85850	−	1.07301i
$219$		0			0
$220$	−873.899	+	504.546i	−0.267810	+	0.154620i
$221$	2457.24	−	1418.69i	0.747927	−	0.431816i
$222$		0			0
$223$	−2567.87	+	1482.56i	−0.771108	+	0.445199i	−0.833270	−	0.552867i	$-0.813534\pi$
$223$	−2567.87	+	1482.56i	−0.771108	+	0.445199i	0.0621620	+	0.998066i	$0.480200\pi$
$224$	3183.08	+	3457.70i	0.949457	+	1.03137i
$225$		0			0
$226$	−3445.91	−	5968.48i	−1.01424	−	1.75671i
$227$	4381.95			1.28123			0.640617	−	0.767860i	$-0.278679\pi$
$227$	4381.95			1.28123			0.640617	+	0.767860i	$0.278679\pi$
$228$		0			0
$229$			3369.93i			0.972452i	0.873833	+	0.486226i	$0.161627\pi$
$229$			3369.93i			0.972452i	−0.873833	+	0.486226i	$0.838373\pi$
$230$	−175.950	+	304.755i	−0.0504427	+	0.0873694i
$231$		0			0
$232$	447.003	+	774.233i	0.126497	+	0.219099i
$233$	−1010.94	+	583.664i	−0.284243	+	0.164108i	−0.635343	−	0.772230i	$-0.719141\pi$
$233$	−1010.94	+	583.664i	−0.284243	+	0.164108i	0.351100	+	0.936338i	$0.385808\pi$
$234$		0			0
$235$	546.128	−	945.921i	0.151598	−	0.262575i
$236$	3916.69	−	6783.91i	1.08032	−	1.87116i
$237$		0			0
$238$	5934.16	+	6446.14i	1.61620	+	1.75563i
$239$	−4756.63	−	2746.24i	−1.28737	−	0.743262i	−0.309184	−	0.951002i	$-0.600056\pi$
$239$	−4756.63	−	2746.24i	−1.28737	−	0.743262i	−0.978184	+	0.207740i	$0.933389\pi$
$240$		0			0
$241$		−	2341.14i		−	0.625752i	−0.949794	−	0.312876i	$-0.898708\pi$
$241$		−	2341.14i		−	0.625752i	0.949794	−	0.312876i	$-0.101292\pi$
$242$	−729.677	−	421.279i	−0.193824	−	0.111904i
$243$		0			0
$244$			1887.09i			0.495117i
$245$	−922.846	+	435.515i	−0.240647	+	0.113568i
$246$		0			0
$247$	1962.34			0.505510
$248$	295.524	+	511.863i	0.0756686	+	0.131062i
$249$		0			0
$250$	2641.69	+	1525.18i	0.668301	+	0.385844i
$251$	1600.54			0.402492			0.201246	−	0.979541i	$-0.435501\pi$
$251$	1600.54			0.402492			0.201246	+	0.979541i	$0.435501\pi$
$252$		0			0
$253$	936.348			0.232679
$254$	−10356.5	−	5979.33i	−2.55837	−	1.47707i
$255$		0			0
$256$	−615.212	−	1065.58i	−0.150198	−	0.260151i
$257$	3263.97			0.792221			0.396111	−	0.918203i	$-0.370360\pi$
$257$	3263.97			0.792221			0.396111	+	0.918203i	$0.370360\pi$
$258$		0			0
$259$	−3997.39	+	3679.90i	−0.959018	+	0.882849i
$260$			764.528i			0.182362i
$261$		0			0
$262$	3723.66	+	2149.86i	0.878049	+	0.506942i
$263$			131.475i			0.0308254i	0.999881	+	0.0154127i	$0.00490621\pi$
$263$			131.475i			0.0308254i	−0.999881	+	0.0154127i	$0.995094\pi$
$264$		0			0
$265$	−836.830	−	483.144i	−0.193985	−	0.111997i
$266$	1325.16	+	5912.94i	0.305454	+	1.36295i
$267$		0			0
$268$	−3616.57	+	6264.08i	−0.824318	+	1.42776i
$269$	−1332.45	+	2307.88i	−0.302011	+	0.523099i	−0.976591	−	0.215103i	$-0.930991\pi$
$269$	−1332.45	+	2307.88i	−0.302011	+	0.523099i	0.674580	+	0.738202i	$0.264325\pi$
$270$		0			0
$271$	−2504.76	+	1446.13i	−0.561453	+	0.324155i	−0.753728	−	0.657186i	$-0.771747\pi$
$271$	−2504.76	+	1446.13i	−0.561453	+	0.324155i	0.192276	+	0.981341i	$0.438413\pi$
$272$	−2395.87	−	4149.77i	−0.534084	−	0.925061i
$273$		0			0
$274$	−5334.71	+	9239.99i	−1.17621	+	2.03726i
$275$		−	3909.29i		−	0.857234i
$276$		0			0
$277$	−6346.89			−1.37671			−0.688353	−	0.725376i	$-0.741666\pi$
$277$	−6346.89			−1.37671			−0.688353	+	0.725376i	$0.741666\pi$
$278$	4200.18	+	7274.92i	0.906151	+	1.56950i
$279$		0			0
$280$	−474.898	+	106.430i	−0.101359	+	0.0227158i
$281$	−4680.87	+	2702.50i	−0.993726	+	0.573728i	−0.906386	−	0.422451i	$-0.861170\pi$
$281$	−4680.87	+	2702.50i	−0.993726	+	0.573728i	−0.0873400	+	0.996179i	$0.527837\pi$
$282$		0			0
$283$	838.390	−	484.045i	0.176103	−	0.101673i	−0.409357	−	0.912374i	$-0.634247\pi$
$283$	838.390	−	484.045i	0.176103	−	0.101673i	0.585460	+	0.810701i	$0.300914\pi$
$284$	6653.78	−	3841.56i	1.39024	−	0.802658i
$285$		0			0
$286$	3160.29	−	1824.60i	0.653399	−	0.377240i
$287$	−2201.26	−	688.486i	−0.452740	−	0.141603i
$288$		0			0
$289$	−3733.82	−	6467.16i	−0.759987	−	1.31634i
$290$	1280.29			0.259246
$291$		0			0
$292$		−	4766.86i		−	0.955341i
$293$	−1057.46	+	1831.57i	−0.210844	+	0.365192i	−0.951979	−	0.306164i	$-0.900954\pi$
$293$	−1057.46	+	1831.57i	−0.210844	+	0.365192i	0.741135	+	0.671356i	$0.234288\pi$
$294$		0			0
$295$	−1156.29	−	2002.75i	−0.228209	−	0.395270i
$296$	−2244.11	+	1295.64i	−0.440664	+	0.254417i
$297$		0			0
$298$	1150.82	−	1993.28i	0.223709	−	0.387475i
$299$	354.707	−	614.371i	0.0686061	−	0.118829i
$300$		0			0
$301$	−4128.57	+	3800.66i	−0.790587	+	0.727796i
$302$	−7602.54	−	4389.33i	−1.44860	−	0.836350i
$303$		0			0
$304$		−	3313.99i		−	0.625231i
$305$	482.470	+	278.554i	0.0905775	+	0.0522950i
$306$		0			0
$307$			2503.96i			0.465500i	0.972537	+	0.232750i	$0.0747724\pi$
$307$			2503.96i			0.465500i	−0.972537	+	0.232750i	$0.925228\pi$
$308$	4254.54	+	4621.60i	0.787094	+	0.855001i
$309$		0			0
$310$	846.431			0.155078
$311$	4633.86	+	8026.08i	0.844894	+	1.46340i	0.885713	+	0.464233i	$0.153670\pi$
$311$	4633.86	+	8026.08i	0.844894	+	1.46340i	−0.0408192	+	0.999167i	$0.512997\pi$
$312$		0			0
$313$	5500.16	+	3175.52i	0.993250	+	0.573453i	0.906244	−	0.422755i	$-0.138937\pi$
$313$	5500.16	+	3175.52i	0.993250	+	0.573453i	0.0870057	+	0.996208i	$0.472270\pi$
$314$	7968.88			1.43220
$315$		0			0
$316$	7125.05			1.26840
$317$	1749.23	+	1009.92i	0.309926	+	0.178936i	0.646893	−	0.762581i	$-0.276068\pi$
$317$	1749.23	+	1009.92i	0.309926	+	0.178936i	−0.336968	+	0.941516i	$0.609401\pi$
$318$		0			0
$319$	−1703.32	−	2950.24i	−0.298958	−	0.517811i
$320$	2184.95			0.381696
$321$		0			0
$322$	2090.76	+	653.924i	0.361842	+	0.113173i
$323$		−	8562.51i		−	1.47502i
$324$		0			0
$325$	−2565.02	−	1480.92i	−0.437791	−	0.252758i
$326$		−	3195.83i		−	0.542947i
$327$		0			0
$328$	−952.618	−	549.994i	−0.160364	−	0.0925864i
$329$	−6489.44	−	2029.70i	−1.08746	−	0.340124i
$330$		0			0
$331$	2944.01	−	5099.17i	0.488874	−	0.846754i	−0.511044	−	0.859554i	$-0.670741\pi$
$331$	2944.01	−	5099.17i	0.488874	−	0.846754i	0.999918	+	0.0128004i	$0.00407460\pi$
$332$	−4093.88	+	7090.82i	−0.676750	+	1.17217i
$333$		0			0
$334$	−5658.38	+	3266.87i	−0.926985	+	0.535195i
$335$	1067.69	+	1849.29i	0.174131	+	0.301604i
$336$		0			0
$337$	621.055	−	1075.70i	0.100389	−	0.173878i	−0.811456	−	0.584413i	$-0.801325\pi$
$337$	621.055	−	1075.70i	0.100389	−	0.173878i	0.911845	+	0.410535i	$0.134658\pi$
$338$			6576.34i			1.05830i
$339$		0			0
$340$	3335.95			0.532109
$341$	−1126.10	−	1950.47i	−0.178833	−	0.309747i
$342$		0			0
$343$	3901.85	+	5012.90i	0.614227	+	0.789129i
$344$	−2317.76	+	1338.16i	−0.363271	+	0.209734i
$345$		0			0
$346$	7397.92	−	4271.19i	1.14946	−	0.663644i
$347$	4680.20	−	2702.11i	0.724052	−	0.418032i	−0.0921900	−	0.995741i	$-0.529387\pi$
$347$	4680.20	−	2702.11i	0.724052	−	0.418032i	0.816242	+	0.577710i	$0.196053\pi$
$348$		0			0
$349$	−653.852	+	377.501i	−0.100286	+	0.0579002i	−0.549304	−	0.835622i	$-0.685107\pi$
$349$	−653.852	+	377.501i	−0.100286	+	0.0579002i	0.449018	+	0.893523i	$0.351774\pi$
$350$	2730.16	−	8729.00i	0.416952	−	1.33310i
$351$		0			0
$352$	−4270.52	−	7396.76i	−0.646647	−	1.12002i
$353$	9168.28			1.38238			0.691188	−	0.722675i	$-0.257088\pi$
$353$	9168.28			1.38238			0.691188	+	0.722675i	$0.257088\pi$
$354$		0			0
$355$		−	2268.22i		−	0.339112i
$356$	−3963.57	+	6865.10i	−0.590081	+	1.02205i
$357$		0			0
$358$	1559.96	+	2701.94i	0.230298	+	0.398888i
$359$	6409.04	−	3700.26i	0.942218	−	0.543990i	0.0515634	−	0.998670i	$-0.483580\pi$
$359$	6409.04	−	3700.26i	0.942218	−	0.543990i	0.890655	+	0.454680i	$0.150246\pi$
$360$		0			0
$361$	−468.564	+	811.577i	−0.0683138	+	0.118323i
$362$	−29.9604	+	51.8930i	−0.00434996	+	0.00753435i
$363$		0			0
$364$	4644.10	−	1040.80i	0.668728	−	0.149870i
$365$	−1218.74	−	703.639i	−0.174772	−	0.100905i
$366$		0			0
$367$		−	2187.54i		−	0.311141i	−0.987825	−	0.155571i	$-0.950278\pi$
$367$		−	2187.54i		−	0.311141i	0.987825	−	0.155571i	$-0.0497216\pi$
$368$	−1037.54	−	599.026i	−0.146972	−	0.0848543i
$369$		0			0
$370$			3710.93i			0.521411i
$371$	−1795.62	+	5741.03i	−0.251277	+	0.803395i
$372$		0			0
$373$	9692.28			1.34543			0.672717	−	0.739899i	$-0.265127\pi$
$373$	9692.28			1.34543			0.672717	+	0.739899i	$0.265127\pi$
$374$	−7961.46	−	13789.7i	−1.10074	−	1.90654i
$375$		0			0
$376$	−2808.37	−	1621.41i	−0.385188	−	0.222388i
$377$	−2581.01			−0.352596
$378$		0			0
$379$	−820.518			−0.111206			−0.0556031	−	0.998453i	$-0.517708\pi$
$379$	−820.518			−0.111206			−0.0556031	+	0.998453i	$0.517708\pi$
$380$	1998.06	+	1153.58i	0.269732	+	0.155730i
$381$		0			0
$382$	−5828.61	−	10095.4i	−0.780674	−	1.35217i
$383$	−4380.73			−0.584451			−0.292226	−	0.956349i	$-0.594396\pi$
$383$	−4380.73			−0.584451			−0.292226	+	0.956349i	$0.594396\pi$
$384$		0			0
$385$	1809.61	−	405.556i	0.239549	−	0.0536858i
$386$			9678.72i			1.27625i
$387$		0			0
$388$	15219.9	+	8787.20i	1.99142	+	1.14975i
$389$			4234.63i			0.551940i	0.961166	+	0.275970i	$0.0889990\pi$
$389$			4234.63i			0.551940i	−0.961166	+	0.275970i	$0.911001\pi$
$390$		0			0
$391$	−2680.75	−	1547.73i	−0.346730	−	0.200185i
$392$	1293.01	+	2739.86i	0.166600	+	0.353020i
$393$		0			0
$394$	1434.52	−	2484.66i	0.183426	−	0.317704i
$395$	1051.73	−	1821.65i	0.133971	−	0.232044i
$396$		0			0
$397$	−12000.8	+	6928.65i	−1.51713	+	0.875916i	−0.517334	+	0.855784i	$0.673076\pi$
$397$	−12000.8	+	6928.65i	−1.51713	+	0.875916i	−0.999797	+	0.0201327i	$0.993591\pi$
$398$	−5630.24	−	9751.86i	−0.709092	−	1.22818i
$399$		0			0
$400$	−2500.96	+	4331.79i	−0.312620	+	0.541474i
$401$			3811.86i			0.474701i	0.971424	+	0.237351i	$0.0762791\pi$
$401$			3811.86i			0.474701i	−0.971424	+	0.237351i	$0.923721\pi$
$402$		0			0
$403$	−1706.36			−0.210918
$404$	−5274.21	−	9135.20i	−0.649509	−	1.12498i
$405$		0			0
$406$	−1742.94	−	7777.10i	−0.213056	−	0.950667i
$407$	8551.27	−	4937.08i	1.04145	−	0.601282i
$408$		0			0
$409$	−10108.2	+	5835.97i	−1.22205	+	0.705550i	−0.965354	−	0.260943i	$-0.915967\pi$
$409$	−10108.2	+	5835.97i	−1.22205	+	0.705550i	−0.256694	+	0.966493i	$0.582633\pi$
$410$	−1364.23	+	787.638i	−0.164328	+	0.0948748i
$411$		0			0
$412$	7413.77	−	4280.34i	0.886530	−	0.511838i
$413$	−10591.5	+	9750.30i	−1.26192	+	1.16170i
$414$		0			0
$415$	1208.60	+	2093.36i	0.142959	+	0.247612i
$416$	−6471.03			−0.762665
$417$		0			0
$418$		−	11012.4i		−	1.28860i
$419$	1542.12	−	2671.02i	0.179803	−	0.311427i	−0.762010	−	0.647565i	$-0.775787\pi$
$419$	1542.12	−	2671.02i	0.179803	−	0.311427i	0.941813	+	0.336138i	$0.109121\pi$
$420$		0			0
$421$	−3318.59	−	5747.97i	−0.384176	−	0.665413i	0.607478	−	0.794336i	$-0.292181\pi$
$421$	−3318.59	−	5747.97i	−0.384176	−	0.665413i	−0.991655	+	0.128923i	$0.958848\pi$
$422$	−3912.65	+	2258.97i	−0.451338	+	0.260580i
$423$		0			0
$424$	−1434.42	+	2484.49i	−0.164296	+	0.284569i
$425$	−6461.85	+	11192.2i	−0.737519	+	1.27742i
$426$		0			0
$427$	1035.25	−	3309.96i	0.117329	−	0.375129i
$428$	−2370.14	−	1368.40i	−0.267675	−	0.154542i
$429$		0			0
$430$			3832.71i			0.429836i
$431$	−11162.7	−	6444.81i	−1.24754	−	0.720268i	−0.276923	−	0.960892i	$-0.589315\pi$
$431$	−11162.7	−	6444.81i	−1.24754	−	0.720268i	−0.970618	+	0.240624i	$0.922648\pi$
$432$		0			0
$433$		−	3882.87i		−	0.430945i	−0.976510	−	0.215472i	$-0.930871\pi$
$433$		−	3882.87i		−	0.430945i	0.976510	−	0.215472i	$-0.0691291\pi$
$434$	−1152.30	−	5141.62i	−0.127447	−	0.568676i
$435$		0			0
$436$	−16371.9			−1.79833
$437$	−1070.42	−	1854.02i	−0.117174	−	0.202951i
$438$		0			0
$439$	3834.56	+	2213.88i	0.416887	+	0.240690i	0.693745	−	0.720221i	$-0.255960\pi$
$439$	3834.56	+	2213.88i	0.416887	+	0.240690i	−0.276857	+	0.960911i	$0.589293\pi$
$440$	884.459			0.0958294
$441$		0			0
$442$	−12063.8			−1.29823
$443$	7319.03	+	4225.64i	0.784961	+	0.453197i	0.838186	−	0.545385i	$-0.183617\pi$
$443$	7319.03	+	4225.64i	0.784961	+	0.453197i	−0.0532246	+	0.998583i	$0.516950\pi$
$444$		0			0
$445$	1170.13	+	2026.72i	0.124650	+	0.215901i
$446$	12607.0			1.33847
$447$		0			0
$448$	−2974.51	−	13272.4i	−0.313688	−	1.39970i
$449$			6114.22i			0.642646i	0.946970	+	0.321323i	$0.104127\pi$
$449$			6114.22i			0.642646i	−0.946970	+	0.321323i	$0.895873\pi$
$450$		0			0
$451$	3629.98	+	2095.77i	0.379000	+	0.218816i
$452$			16334.8i			1.69984i
$453$		0			0
$454$	−16134.9	−	9315.49i	−1.66795	−	0.962991i
$455$	419.418	−	1340.98i	0.0432146	−	0.138168i
$456$		0			0
$457$	−8336.20	+	14438.7i	−0.853285	+	1.47793i	0.0249425	+	0.999689i	$0.492060\pi$
$457$	−8336.20	+	14438.7i	−0.853285	+	1.47793i	−0.878227	+	0.478244i	$0.841274\pi$
$458$	7164.07	−	12408.5i	0.730906	−	1.26597i
$459$		0			0
$460$	722.325	−	417.035i	0.0732143	−	0.0422703i
$461$	−6164.70	−	10677.6i	−0.622817	−	1.07875i	−0.988959	−	0.148192i	$-0.952655\pi$
$461$	−6164.70	−	10677.6i	−0.622817	−	1.07875i	0.366142	−	0.930559i	$-0.380679\pi$
$462$		0			0
$463$	5479.45	−	9490.69i	0.550004	−	0.952635i	−0.448270	−	0.893898i	$-0.647960\pi$
$463$	5479.45	−	9490.69i	0.550004	−	0.952635i	0.998274	−	0.0587364i	$-0.0187071\pi$
$464$			4358.78i			0.436102i
$465$		0			0
$466$	4963.20			0.493381
$467$	652.506	+	1130.17i	0.0646561	+	0.111988i	0.896541	−	0.442960i	$-0.146072\pi$
$467$	652.506	+	1130.17i	0.0646561	+	0.111988i	−0.831885	+	0.554948i	$0.812738\pi$
$468$		0			0
$469$	9779.94	−	9003.18i	0.962890	−	0.886414i
$470$	−4021.83	+	2322.00i	−0.394709	+	0.227885i
$471$		0			0
$472$	−5946.03	+	3432.94i	−0.579848	+	0.334775i
$473$	8831.89	−	5099.09i	0.858542	−	0.495680i
$474$		0			0
$475$	−7740.61	+	4469.05i	−0.747713	+	0.431692i
$476$	−4541.42	−	20264.1i	−0.437302	−	1.95127i
$477$		0			0
$478$	11676.4	+	20224.0i	1.11729	+	1.93520i
$479$	−6071.45			−0.579147			−0.289574	−	0.957156i	$-0.593513\pi$
$479$	−6071.45			−0.579147			−0.289574	+	0.957156i	$0.593513\pi$
$480$		0			0
$481$		−	7481.05i		−	0.709161i
$482$	−4976.99	+	8620.40i	−0.470323	+	0.814623i
$483$		0			0
$484$	998.509	+	1729.47i	0.0937743	+	0.162422i
$485$	4493.23	−	2594.17i	0.420674	−	0.242876i
$486$		0			0
$487$	1357.44	−	2351.16i	0.126307	−	0.218771i	−0.795936	−	0.605381i	$-0.793021\pi$
$487$	1357.44	−	2351.16i	0.126307	−	0.218771i	0.922243	+	0.386610i	$0.126354\pi$
$488$	827.007	−	1432.42i	0.0767149	−	0.132874i
$489$		0			0
$490$	4323.89	+	358.234i	0.398640	+	0.0330272i
$491$	8766.69	+	5061.45i	0.805774	+	0.465214i	0.845486	−	0.533997i	$-0.179311\pi$
$491$	8766.69	+	5061.45i	0.805774	+	0.465214i	−0.0397122	+	0.999211i	$0.512644\pi$
$492$		0			0
$493$			11262.0i			1.02883i
$494$	−7225.60	−	4171.70i	−0.658088	−	0.379947i
$495$		0			0
$496$			2881.69i			0.260870i
$497$	−13778.2	+	3087.86i	−1.24354	+	0.278691i
$498$		0			0
$499$	8993.59			0.806830			0.403415	−	0.915017i	$-0.367823\pi$
$499$	8993.59			0.806830			0.403415	+	0.915017i	$0.367823\pi$
$500$	−3614.96	−	6261.29i	−0.323332	−	0.560027i
$501$		0			0
$502$	−5893.41	−	3402.56i	−0.523975	−	0.302517i
$503$	18029.3			1.59818			0.799091	−	0.601210i	$-0.205315\pi$
$503$	18029.3			1.59818			0.799091	+	0.601210i	$0.205315\pi$
$504$		0			0
$505$	−3114.11			−0.274408
$506$	−3447.75	−	1990.56i	−0.302908	−	0.174884i
$507$		0			0
$508$	14172.1	+	24546.8i	1.23777	+	2.14388i
$509$	−2837.22			−0.247068			−0.123534	−	0.992340i	$-0.539423\pi$
$509$	−2837.22			−0.247068			−0.123534	+	0.992340i	$0.539423\pi$
$510$		0			0
$511$	−2615.09	+	8361.09i	−0.226389	+	0.723822i
$512$			13971.3i			1.20595i
$513$		0			0
$514$	−12018.4	−	6938.80i	−1.03134	−	0.595443i
$515$		−	2527.29i		−	0.216244i
$516$		0			0
$517$	10701.4	+	6178.45i	0.910342	+	0.525586i
$518$	22541.9	−	5051.91i	1.91204	−	0.428510i
$519$		0			0
$520$	335.051	−	580.325i	0.0282557	−	0.0489402i
$521$	−4220.64	+	7310.36i	−0.354913	+	0.614727i	−0.987103	−	0.160086i	$-0.948823\pi$
$521$	−4220.64	+	7310.36i	−0.354913	+	0.614727i	0.632190	+	0.774813i	$0.282156\pi$
$522$		0			0
$523$	3141.63	−	1813.82i	0.262665	−	0.151650i	−0.362884	−	0.931834i	$-0.618208\pi$
$523$	3141.63	−	1813.82i	0.262665	−	0.151650i	0.625550	+	0.780184i	$0.284875\pi$
$524$	−5095.56	−	8825.76i	−0.424810	−	0.735793i
$525$		0			0
$526$	279.499	−	484.107i	0.0231687	−	0.0401294i
$527$			7445.56i			0.615434i
$528$		0			0
$529$	11393.1			0.936390
$530$	2054.21	+	3558.00i	0.168357	+	0.291603i
$531$		0			0
$532$	4287.30	−	13707.6i	0.349395	−	1.11710i
$533$	2750.22	−	1587.84i	0.223499	−	0.129037i
$534$		0			0
$535$	−699.714	+	403.980i	−0.0565444	+	0.0326460i
$536$	5490.41	−	3169.89i	0.442443	−	0.255445i
$537$		0			0
$538$	9812.53	−	5665.26i	0.786335	−	0.453991i
$539$	−4927.07	−	10440.3i	−0.393737	−	0.834317i
$540$		0			0
$541$	−2781.66	−	4817.98i	−0.221059	−	0.382886i	0.734071	−	0.679073i	$-0.237618\pi$
$541$	−2781.66	−	4817.98i	−0.221059	−	0.382886i	−0.955130	+	0.296187i	$0.904285\pi$
$542$	12297.2			0.974554
$543$		0			0
$544$			28235.8i			2.22537i
$545$	−2416.66	+	4185.78i	−0.189942	+	0.328989i
$546$		0			0
$547$	1520.34	+	2633.31i	0.118839	+	0.205836i	0.919308	−	0.393539i	$-0.128749\pi$
$547$	1520.34	+	2633.31i	0.118839	+	0.205836i	−0.800469	+	0.599375i	$0.795416\pi$
$548$	21900.5	−	12644.2i	1.70719	−	0.985648i
$549$		0			0
$550$	−8310.68	+	14394.5i	−0.644307	+	1.11597i
$551$	−3894.42	+	6745.34i	−0.301103	+	0.521526i
$552$		0			0
$553$	−12497.4	−	3908.79i	−0.961016	−	0.300576i
$554$	23370.1	+	13492.7i	1.79224	+	1.03475i
$555$		0			0
$556$		−	19910.4i		−	1.51868i
$557$	160.380	+	92.5957i	0.0122002	+	0.00704382i	0.506088	−	0.862482i	$-0.331091\pi$
$557$	160.380	+	92.5957i	0.0122002	+	0.00704382i	−0.493887	+	0.869526i	$0.664425\pi$
$558$		0			0
$559$		−	7726.55i		−	0.584612i
$560$	−2264.64	−	708.310i	−0.170890	−	0.0534492i
$561$		0			0
$562$	22980.7			1.72488
$563$	4709.64	+	8157.33i	0.352553	+	0.610640i	0.986696	−	0.162576i	$-0.0519802\pi$
$563$	4709.64	+	8157.33i	0.352553	+	0.610640i	−0.634143	+	0.773216i	$0.718647\pi$
$564$		0			0
$565$	4176.31	+	2411.20i	0.310971	+	0.179539i
$566$	−4116.08			−0.305675
$567$		0			0
$568$	−6734.18			−0.497465
$569$	5199.71	+	3002.05i	0.383099	+	0.221182i	0.679166	−	0.733985i	$-0.262342\pi$
$569$	5199.71	+	3002.05i	0.383099	+	0.221182i	−0.296067	+	0.955167i	$0.595675\pi$
$570$		0			0
$571$	11218.1	+	19430.4i	0.822179	+	1.42406i	0.904056	+	0.427414i	$0.140575\pi$
$571$	11218.1	+	19430.4i	0.822179	+	1.42406i	−0.0818770	+	0.996642i	$0.526091\pi$
$572$	−8649.26			−0.632244
$573$		0			0
$574$	6641.69	+	7214.71i	0.482959	+	0.524627i
$575$			3231.24i			0.234352i
$576$		0			0
$577$	−13610.9	−	7858.26i	−0.982027	−	0.566974i	−0.0791455	−	0.996863i	$-0.525219\pi$
$577$	−13610.9	−	7858.26i	−0.982027	−	0.566974i	−0.902882	+	0.429890i	$0.858553\pi$
$578$			31750.6i			2.28486i
$579$		0			0
$580$	−2627.98	−	1517.26i	−0.188140	−	0.108622i
$581$	11070.7	−	10191.4i	0.790516	−	0.727730i
$582$		0			0
$583$	5465.90	−	9467.23i	0.388293	−	0.672543i
$584$	−2089.05	+	3618.35i	−0.148023	+	0.256384i
$585$		0			0
$586$	7787.38	−	4496.04i	0.548965	−	0.316945i
$587$	−7664.92	−	13276.0i	−0.538952	−	0.933493i	−0.998961	−	0.0455781i	$-0.985487\pi$
$587$	−7664.92	−	13276.0i	−0.538952	−	0.933493i	0.460009	−	0.887914i	$-0.347846\pi$
$588$		0			0
$589$	−2574.69	+	4459.50i	−0.180116	+	0.311970i
$590$			9832.52i			0.686099i
$591$		0			0
$592$	−12633.9			−0.877114
$593$	7150.47	+	12385.0i	0.495168	+	0.857656i	0.999984	−	0.00557046i	$-0.00177314\pi$
$593$	7150.47	+	12385.0i	0.495168	+	0.857656i	−0.504816	+	0.863227i	$0.668440\pi$
$594$		0			0
$595$	−5851.26	−	1830.09i	−0.403157	−	0.126095i
$596$	−4724.44	+	2727.66i	−0.324699	+	0.187465i
$597$		0			0
$598$	−2612.15	+	1508.13i	−0.178627	+	0.103130i
$599$	3218.52	−	1858.22i	0.219541	−	0.126752i	−0.386196	−	0.922417i	$-0.626211\pi$
$599$	3218.52	−	1858.22i	0.219541	−	0.126752i	0.605738	+	0.795664i	$0.292878\pi$
$600$		0			0
$601$	904.706	−	522.332i	0.0614039	−	0.0354515i	−0.468984	−	0.883207i	$-0.655380\pi$
$601$	904.706	−	522.332i	0.0614039	−	0.0354515i	0.530388	+	0.847755i	$0.322046\pi$
$602$	23281.7	−	5217.70i	1.57623	−	0.353252i
$603$		0			0
$604$	10403.5	+	18019.4i	0.700849	+	1.21391i
$605$	589.561			0.0396183
$606$		0			0
$607$			397.834i			0.0266023i	0.999912	+	0.0133011i	$0.00423401\pi$
$607$			397.834i			0.0266023i	−0.999912	+	0.0133011i	$0.995766\pi$
$608$	−9764.00	+	16911.7i	−0.651287	+	1.12806i
$609$		0			0
$610$	−1184.34	−	2051.34i	−0.0786110	−	0.136158i
$611$	8107.80	−	4681.04i	0.536835	−	0.309942i
$612$		0			0
$613$	−6825.91	+	11822.8i	−0.449749	+	0.778988i	−0.998369	−	0.0570835i	$-0.981820\pi$
$613$	−6825.91	+	11822.8i	−0.449749	+	0.778988i	0.548620	+	0.836071i	$0.315153\pi$
$614$	5323.11	−	9219.90i	0.349875	−	0.606002i
$615$		0			0
$616$	−1204.07	−	5372.62i	−0.0787553	−	0.351411i
$617$	−10813.0	−	6242.87i	−0.705533	−	0.407340i	0.103872	−	0.994591i	$-0.466877\pi$
$617$	−10813.0	−	6242.87i	−0.705533	−	0.407340i	−0.809405	+	0.587251i	$0.800210\pi$
$618$		0			0
$619$			7621.70i			0.494898i	0.968901	+	0.247449i	$0.0795923\pi$
$619$			7621.70i			0.494898i	−0.968901	+	0.247449i	$0.920408\pi$
$620$	−1737.42	−	1003.10i	−0.112543	−	0.0649764i
$621$		0			0
$622$		−	39404.1i		−	2.54013i
$623$	10718.3	−	9867.00i	0.689276	−	0.634532i
$624$		0			0
$625$	12384.2			0.792588
$626$	−13501.5	−	23385.3i	−0.862028	−	1.49308i
$627$		0			0
$628$	−16357.2	−	9443.85i	−1.03937	−	0.600081i
$629$	−32642.9			−2.06925
$630$		0			0
$631$	24538.8			1.54813			0.774067	−	0.633103i	$-0.218219\pi$
$631$	24538.8			1.54813			0.774067	+	0.633103i	$0.218219\pi$
$632$	−5408.36	−	3122.52i	−0.340400	−	0.196530i
$633$		0			0
$634$	−4293.92	−	7437.29i	−0.268980	−	0.465887i
$635$	8367.81			0.522939
$636$		0			0
$637$	−8716.74	−	722.181i	−0.542182	−	0.0449197i
$638$			14484.2i			0.898802i
$639$		0			0
$640$	−2814.75	−	1625.10i	−0.173848	−	0.100371i
$641$			11594.1i			0.714414i	0.934025	+	0.357207i	$0.116271\pi$
$641$			11594.1i			0.714414i	−0.934025	+	0.357207i	$0.883729\pi$
$642$		0			0
$643$	20426.2	+	11793.1i	1.25277	+	0.723286i	0.971659	−	0.236389i	$-0.0759639\pi$
$643$	20426.2	+	11793.1i	1.25277	+	0.723286i	0.281110	+	0.959675i	$0.409297\pi$
$644$	−3516.61	−	3820.01i	−0.215177	−	0.233741i
$645$		0			0
$646$	−18202.9	+	31528.3i	−1.10864	+	1.92022i
$647$	2126.86	−	3683.82i	0.129235	−	0.223842i	−0.794145	−	0.607728i	$-0.792081\pi$
$647$	2126.86	−	3683.82i	0.129235	−	0.223842i	0.923381	+	0.383886i	$0.125414\pi$
$648$		0			0
$649$	22657.5	−	13081.3i	1.37039	−	0.791197i
$650$	6296.50	+	10905.9i	0.379952	+	0.658097i
$651$		0			0
$652$	−3787.35	+	6559.89i	−0.227491	+	0.394026i
$653$		−	25340.6i		−	1.51862i	−0.650732	−	0.759308i	$-0.725538\pi$
$653$		−	25340.6i		−	1.51862i	0.650732	−	0.759308i	$-0.274462\pi$
$654$		0			0
$655$	−3008.63			−0.179476
$656$	−2681.53	−	4644.54i	−0.159598	−	0.276431i
$657$		0			0
$658$	19580.1	+	21269.4i	1.16005	+	1.26013i
$659$	−1230.18	+	710.247i	−0.0727180	+	0.0419837i	−0.535918	−	0.844270i	$-0.680034\pi$
$659$	−1230.18	+	710.247i	−0.0727180	+	0.0419837i	0.463200	+	0.886254i	$0.346701\pi$
$660$		0			0
$661$	844.855	−	487.777i	0.0497141	−	0.0287025i	−0.474937	−	0.880020i	$-0.657529\pi$
$661$	844.855	−	487.777i	0.0497141	−	0.0287025i	0.524651	+	0.851317i	$0.324196\pi$
$662$	−21680.4	+	12517.2i	−1.27286	+	0.734886i
$663$		0			0
$664$	6215.03	−	3588.25i	0.363238	−	0.209715i
$665$	−2871.75	−	3119.51i	−0.167461	−	0.181909i
$666$		0			0
$667$	1407.89	+	2438.53i	0.0817295	+	0.141560i
$668$	15486.1			0.896972
$669$		0			0
$670$		−	9079.10i		−	0.523517i
$671$	−3151.34	+	5458.28i	−0.181306	+	0.314030i
$672$		0			0
$673$	−8197.75	−	14198.9i	−0.469539	−	0.813266i	0.529854	−	0.848089i	$-0.322247\pi$
$673$	−8197.75	−	14198.9i	−0.469539	−	0.813266i	−0.999394	+	0.0348227i	$0.988913\pi$
$674$	−4573.61	+	2640.57i	−0.261378	+	0.150907i
$675$		0			0
$676$	7793.56	−	13498.8i	0.443421	−	0.768027i
$677$	7847.68	−	13592.6i	0.445511	−	0.771648i	−0.552577	−	0.833462i	$-0.686355\pi$
$677$	7847.68	−	13592.6i	0.445511	−	0.771648i	0.998088	+	0.0618144i	$0.0196887\pi$
$678$		0			0
$679$	−21875.1	−	23762.4i	−1.23636	−	1.34303i
$680$	−2532.19	−	1461.96i	−0.142802	−	0.0824466i
$681$		0			0
$682$			9575.84i			0.537651i
$683$	4500.99	+	2598.65i	0.252160	+	0.145585i	0.620753	−	0.784006i	$-0.286827\pi$
$683$	4500.99	+	2598.65i	0.252160	+	0.145585i	−0.368593	+	0.929591i	$0.620160\pi$
$684$		0			0
$685$		−	7465.69i		−	0.416422i
$686$	−3710.29	−	26753.0i	−0.206501	−	1.48897i
$687$		0			0
$688$	−13048.5			−0.723067
$689$	−4141.19	−	7172.74i	−0.228979	−	0.396603i
$690$		0			0
$691$	4854.95	+	2803.01i	0.267281	+	0.154315i	0.627651	−	0.778495i	$-0.284016\pi$
$691$	4854.95	+	2803.01i	0.267281	+	0.154315i	−0.360370	+	0.932809i	$0.617350\pi$
$692$	−20247.0			−1.11225
$693$		0			0
$694$	−22977.5			−1.25679
$695$	−5090.47	−	2938.98i	−0.277831	−	0.160406i
$696$		0			0
$697$	−6928.39	−	12000.3i	−0.376516	−	0.652144i
$698$	3210.09			0.174074
$699$		0			0
$700$	−15948.7	+	14682.0i	−0.861148	+	0.792753i
$701$		−	8629.57i		−	0.464956i	−0.972602	−	0.232478i	$-0.925317\pi$
$701$		−	8629.57i		−	0.464956i	0.972602	−	0.232478i	$-0.0746834\pi$
$702$		0			0
$703$	−19551.4	−	11288.0i	−1.04892	−	0.605597i
$704$			24718.8i			1.32333i
$705$		0			0
$706$	−33758.8	−	19490.7i	−1.79962	−	1.03901i
$707$	4239.43	+	18916.6i	0.225516	+	1.00627i
$708$		0			0
$709$	17662.3	−	30592.0i	0.935574	−	1.62046i	0.161966	−	0.986796i	$-0.448216\pi$
$709$	17662.3	−	30592.0i	0.935574	−	1.62046i	0.773608	−	0.633665i	$-0.218450\pi$
$710$	−4821.96	+	8351.88i	−0.254880	+	0.441466i
$711$		0			0
$712$	6017.19	−	3474.03i	0.316719	−	0.182858i
$713$	930.786	+	1612.17i	0.0488895	+	0.0846791i
$714$		0			0
$715$	−1276.72	+	2211.35i	−0.0667785	+	0.115664i
$716$		−	7394.80i		−	0.385973i
$717$		0			0
$718$	−31465.2			−1.63548
$719$	1378.95	+	2388.42i	0.0715248	+	0.123885i	0.899570	−	0.436777i	$-0.143880\pi$
$719$	1378.95	+	2388.42i	0.0715248	+	0.123885i	−0.828045	+	0.560662i	$0.810547\pi$
$720$		0			0
$721$	−15352.0	+	3440.55i	−0.792977	+	0.177716i
$722$	3450.63	−	1992.22i	0.177866	−	0.102691i
$723$		0			0
$724$	122.996	−	71.0116i	0.00631368	−	0.00364520i
$725$	10181.0	−	5877.99i	0.521534	−	0.301108i
$726$		0			0
$727$	−12443.7	+	7184.36i	−0.634814	+	0.366510i	−0.782614	−	0.622507i	$-0.786114\pi$
$727$	−12443.7	+	7184.36i	−0.634814	+	0.366510i	0.147800	+	0.989017i	$0.452781\pi$
$728$	−3981.29	−	1245.22i	−0.202687	−	0.0633943i
$729$		0			0
$730$	2991.70	+	5181.78i	0.151682	+	0.262721i
$731$	−33714.1			−1.70583
$732$		0			0
$733$			2888.16i			0.145534i	0.997349	+	0.0727672i	$0.0231830\pi$
$733$			2888.16i			0.145534i	−0.997349	+	0.0727672i	$0.976817\pi$
$734$	−4650.45	+	8054.82i	−0.233857	+	0.405053i
$735$		0			0
$736$	3529.82	+	6113.83i	0.176781	+	0.306194i
$737$	−20921.4	+	12079.0i	−1.04566	+	0.603710i
$738$		0			0
$739$	−12636.6	+	21887.2i	−0.629017	+	1.08949i	0.358733	+	0.933440i	$0.383209\pi$
$739$	−12636.6	+	21887.2i	−0.629017	+	1.08949i	−0.987749	+	0.156048i	$0.950124\pi$
$740$	4397.79	−	7617.20i	0.218468	−	0.378397i
$741$		0			0
$742$	18816.4	−	17322.0i	0.930960	−	0.857020i
$743$	−21111.2	−	12188.6i	−1.04239	−	0.601824i	−0.121880	−	0.992545i	$-0.538892\pi$
$743$	−21111.2	−	12188.6i	−1.04239	−	0.601824i	−0.920509	+	0.390721i	$0.872226\pi$
$744$		0			0
$745$			1610.52i			0.0792013i
$746$	−35688.2	−	20604.6i	−1.75153	−	1.01124i
$747$		0			0
$748$			37740.2i			1.84481i
$749$	3406.53	+	3700.43i	0.166184	+	0.180522i
$750$		0			0
$751$	1695.52			0.0823839			0.0411919	−	0.999151i	$-0.486884\pi$
$751$	1695.52			0.0823839			0.0411919	+	0.999151i	$0.486884\pi$
$752$	−7905.30	−	13692.4i	−0.383346	−	0.663976i
$753$		0			0
$754$	9503.60	+	5486.91i	0.459020	+	0.265015i
$755$	6142.67			0.296099
$756$		0			0
$757$	−23361.6			−1.12165			−0.560827	−	0.827933i	$-0.689517\pi$
$757$	−23361.6			−1.12165			−0.560827	+	0.827933i	$0.689517\pi$
$758$	3021.25	+	1744.32i	0.144772	+	0.0835839i
$759$		0			0
$760$	−1011.10	−	1751.28i	−0.0482585	−	0.0835862i
$761$	−31128.0			−1.48277			−0.741386	−	0.671079i	$-0.765831\pi$
$761$	−31128.0			−1.48277			−0.741386	+	0.671079i	$0.765831\pi$
$762$		0			0
$763$	28716.3	+	8981.57i	1.36252	+	0.426153i
$764$			27629.7i			1.30839i
$765$		0			0
$766$	16130.4	+	9312.90i	0.760856	+	0.439281i
$767$		−	19821.9i		−	0.933150i
$768$		0			0
$769$	−312.046	−	180.160i	−0.0146329	−	0.00844829i	0.492666	−	0.870219i	$-0.336023\pi$
$769$	−312.046	−	180.160i	−0.0146329	−	0.00844829i	−0.507299	+	0.861770i	$0.669356\pi$
$770$	−7525.40	−	2353.71i	−0.352203	−	0.110158i
$771$		0			0
$772$	11470.2	−	19866.9i	0.534742	−	0.926200i
$773$	−10038.7	+	17387.6i	−0.467099	+	0.809039i	−0.999294	−	0.0375828i	$-0.988034\pi$
$773$	−10038.7	+	17387.6i	−0.467099	+	0.809039i	0.532194	+	0.846622i	$0.321368\pi$
$774$		0			0
$775$	6730.88	−	3886.07i	0.311974	−	0.180119i
$776$	−7701.89	−	13340.1i	−0.356291	−	0.617114i
$777$		0			0
$778$	9002.32	−	15592.5i	0.414844	−	0.718531i
$779$		−	9583.41i		−	0.440772i
$780$		0			0
$781$	25660.8			1.17569
$782$	6580.58	+	11397.9i	0.300922	+	0.521212i
$783$		0			0
$784$	−1219.61	+	14720.8i	−0.0555581	+	0.670588i
$785$	−4829.00	+	2788.02i	−0.219560	+	0.126763i
$786$		0			0
$787$	17031.2	−	9832.94i	0.771404	−	0.445370i	−0.0619712	−	0.998078i	$-0.519739\pi$
$787$	17031.2	−	9832.94i	0.771404	−	0.445370i	0.833375	+	0.552708i	$0.186405\pi$
$788$	−5889.10	+	3400.07i	−0.266231	+	0.153709i
$789$		0			0
$790$	−7745.23	+	4471.71i	−0.348814	+	0.201388i
$791$	8961.26	−	28651.4i	0.402814	−	1.28790i
$792$		0			0
$793$	2387.58	+	4135.41i	0.106917	+	0.185186i
$794$	58917.8			2.63340
$795$		0			0
$796$			26689.4i			1.18842i
$797$	6523.01	−	11298.2i	0.289908	−	0.502136i	−0.683879	−	0.729595i	$-0.739709\pi$
$797$	6523.01	−	11298.2i	0.289908	−	0.502136i	0.973788	+	0.227459i	$0.0730419\pi$
$798$		0			0
$799$	−20425.3	−	35377.6i	−0.904374	−	1.56642i
$800$	25525.5	−	14737.1i	1.12808	−	0.651296i
$801$		0			0
$802$	8103.56	−	14035.8i	0.356791	−	0.617980i
$803$	7960.41	−	13787.8i	0.349834	−	0.605930i
$804$		0			0
$805$	−1495.74	+	335.214i	−0.0654883	+	0.0146767i
$806$	6283.05	+	3627.52i	0.274579	+	0.158528i
$807$		0			0
$808$			9245.58i			0.402548i
$809$	31834.0	+	18379.4i	1.38347	+	0.798745i	0.992568	−	0.121690i	$-0.0388312\pi$
$809$	31834.0	+	18379.4i	1.38347	+	0.798745i	0.390898	+	0.920434i	$0.372165\pi$
$810$		0			0
$811$		−	36262.6i		−	1.57010i	−0.619433	−	0.785050i	$-0.712637\pi$
$811$		−	36262.6i		−	1.57010i	0.619433	−	0.785050i	$-0.287363\pi$
$812$	−5638.95	+	18029.1i	−0.243705	+	0.779185i
$813$		0			0
$814$	−41982.5			−1.80772
$815$	1118.11	+	1936.62i	0.0480559	+	0.0832352i
$816$		0			0
$817$	−20193.0	−	11658.4i	−0.864703	−	0.499237i
$818$	49626.2			2.12120
$819$		0			0
$820$	3733.69			0.159008
$821$	4949.61	+	2857.66i	0.210405	+	0.121477i	0.601500	−	0.798873i	$-0.294570\pi$
$821$	4949.61	+	2857.66i	0.210405	+	0.121477i	−0.391095	+	0.920350i	$0.627903\pi$
$822$		0			0
$823$	1847.06	+	3199.21i	0.0782316	+	0.135501i	0.902487	−	0.430717i	$-0.141739\pi$
$823$	1847.06	+	3199.21i	0.0782316	+	0.135501i	−0.824255	+	0.566218i	$0.808406\pi$
$824$	−7503.35			−0.317223
$825$		0			0
$826$	59727.3	−	13385.6i	2.51596	−	0.563855i
$827$		−	13440.0i		−	0.565120i	−0.959250	−	0.282560i	$-0.908816\pi$
$827$		−	13440.0i		−	0.565120i	0.959250	−	0.282560i	$-0.0911837\pi$
$828$		0			0
$829$	25750.2	+	14866.9i	1.07882	+	0.622857i	0.930578	−	0.366094i	$-0.119305\pi$
$829$	25750.2	+	14866.9i	1.07882	+	0.622857i	0.148243	+	0.988951i	$0.452638\pi$
$830$		−	10277.4i		−	0.429798i
$831$		0			0
$832$	16218.9	+	9363.98i	0.675828	+	0.390189i
$833$	−3151.17	+	38034.7i	−0.131070	+	1.58202i
$834$		0			0
$835$	2285.92	−	3959.33i	0.0947395	−	0.164094i
$836$	−13050.7	+	22604.4i	−0.539912	+	0.935156i
$837$		0			0
$838$	−11356.5	+	6556.70i	−0.468144	+	0.270283i
$839$	3183.53	+	5514.04i	0.130998	+	0.226896i	0.924062	−	0.382243i	$-0.124848\pi$
$839$	3183.53	+	5514.04i	0.130998	+	0.226896i	−0.793063	+	0.609139i	$0.791515\pi$
$840$		0			0
$841$	−7072.29	+	12249.6i	−0.289979	+	0.502258i
$842$			28219.7i			1.15501i
$843$		0			0
$844$	10708.3			0.436725
$845$	−2300.82	−	3985.14i	−0.0936695	−	0.162240i
$846$		0			0
$847$	−802.605	−	3581.27i	−0.0325594	−	0.145282i
$848$	−12113.3	+	6993.60i	−0.490532	+	0.283209i
$849$		0			0
$850$	47586.7	−	27474.2i	1.92025	−	1.10866i
$851$	−7068.09	+	4080.76i	−0.284713	+	0.164379i
$852$		0			0
$853$	10454.7	−	6036.03i	0.419651	−	0.242286i	−0.275277	−	0.961365i	$-0.588770\pi$
$853$	10454.7	−	6036.03i	0.419651	−	0.242286i	0.694928	+	0.719079i	$0.255436\pi$
$854$	−10848.5	+	9986.88i	−0.434693	+	0.400169i
$855$		0			0
$856$	1199.39	+	2077.40i	0.0478905	+	0.0829487i
$857$	38582.4			1.53786			0.768932	−	0.639331i	$-0.220788\pi$
$857$	38582.4			1.53786			0.768932	+	0.639331i	$0.220788\pi$
$858$		0			0
$859$		−	12251.5i		−	0.486632i	−0.969947	−	0.243316i	$-0.921765\pi$
$859$		−	12251.5i		−	0.486632i	0.969947	−	0.243316i	$-0.0782352\pi$
$860$	4542.11	−	7867.17i	0.180099	−	0.311940i
$861$		0			0
$862$	27401.8	+	47461.3i	1.08272	+	1.87533i
$863$	12177.5	−	7030.66i	0.480331	−	0.277319i	−0.240224	−	0.970718i	$-0.577221\pi$
$863$	12177.5	−	7030.66i	0.480331	−	0.277319i	0.720554	+	0.693399i	$0.243887\pi$
$864$		0			0
$865$	−2988.67	+	5176.53i	−0.117477	+	0.203477i
$866$	−8254.52	+	14297.2i	−0.323903	+	0.561016i
$867$		0			0
$868$	−3728.04	+	11919.5i	−0.145781	+	0.466098i
$869$	20608.7	+	11898.5i	0.804492	+	0.464473i
$870$		0			0
$871$			18303.0i			0.712025i
$872$	12427.3	+	7174.89i	0.482616	+	0.278638i
$873$		0			0
$874$			9102.32i			0.352278i
$875$	2905.72	+	12965.5i	0.112264	+	0.500929i
$876$		0			0
$877$	−19100.5			−0.735435			−0.367717	−	0.929938i	$-0.619861\pi$
$877$	−19100.5			−0.735435			−0.367717	+	0.929938i	$0.619861\pi$
$878$	−9412.90	−	16303.6i	−0.361811	−	0.626675i
$879$		0			0
$880$	3734.50	+	2156.12i	0.143057	+	0.0825939i
$881$	32516.6			1.24349			0.621744	−	0.783220i	$-0.286424\pi$
$881$	32516.6			1.24349			0.621744	+	0.783220i	$0.286424\pi$
$882$		0			0
$883$	−4515.64			−0.172099			−0.0860494	−	0.996291i	$-0.527424\pi$
$883$	−4515.64			−0.172099			−0.0860494	+	0.996291i	$0.527424\pi$
$884$	24762.7	+	14296.7i	0.942149	+	0.543950i
$885$		0			0
$886$	−17966.4	−	31118.7i	−0.681257	−	1.17997i
$887$	−37636.4			−1.42470			−0.712349	−	0.701826i	$-0.752369\pi$
$887$	−37636.4			−1.42470			−0.712349	+	0.701826i	$0.752369\pi$
$888$		0			0
$889$	−11391.6	−	50830.0i	−0.429766	−	1.91764i
$890$		−	9950.21i		−	0.374755i
$891$		0			0
$892$	−25877.5	−	14940.4i	−0.971349	−	0.560809i
$893$		−	28252.5i		−	1.05871i
$894$		0			0
$895$	−1890.62	−	1091.55i	−0.0706105	−	0.0407670i
$896$	−6039.71	+	19310.4i	−0.225193	+	0.719996i
$897$		0			0
$898$	12998.1	−	22513.4i	0.483020	−	0.836615i
$899$	3386.41	−	5865.43i	0.125632	−	0.217601i
$900$		0			0
$901$	−31297.6	+	18069.7i	−1.15724	+	0.668134i
$902$	−8910.71	−	15433.8i	−0.328929	−	0.569722i
$903$		0			0
$904$	7158.67	−	12399.2i	0.263378	−	0.456184i
$905$		−	41.9283i		−	0.00154005i
$906$		0			0
$907$	27528.4			1.00779			0.503896	−	0.863764i	$-0.331900\pi$
$907$	27528.4			1.00779			0.503896	+	0.863764i	$0.331900\pi$
$908$	22079.4	+	38242.7i	0.806973	+	1.39772i
$909$		0			0
$910$	−4395.12	+	4046.05i	−0.160106	+	0.147390i
$911$	−11771.3	+	6796.18i	−0.428103	+	0.247165i	−0.698538	−	0.715573i	$-0.746166\pi$
$911$	−11771.3	+	6796.18i	−0.428103	+	0.247165i	0.270435	+	0.962738i	$0.412832\pi$
$912$		0			0
$913$	−23682.6	+	13673.1i	−0.858465	+	0.495635i
$914$	61390.0	−	35443.5i	2.22166	−	1.28268i
$915$		0			0
$916$	−29410.5	+	16980.2i	−1.06086	+	0.612489i
$917$	4095.83	+	18275.8i	0.147499	+	0.658147i
$918$		0			0
$919$	22074.4	+	38234.0i	0.792347	+	1.37239i	0.924510	+	0.381157i	$0.124474\pi$
$919$	22074.4	+	38234.0i	0.792347	+	1.37239i	−0.132163	+	0.991228i	$0.542192\pi$
$920$	−731.053			−0.0261980
$921$		0			0
$922$			52421.6i			1.87247i
$923$	9720.83	−	16837.0i	0.346658	−	0.600428i
$924$		0			0
$925$	17037.4	+	29509.6i	0.605605	+	1.04894i
$926$	−40352.1	+	23297.3i	−1.43202	+	0.826779i
$927$		0			0
$928$	12842.3	−	22243.5i	0.454276	−	0.786829i
$929$	8136.78	−	14093.3i	0.287362	−	0.497725i	−0.685817	−	0.727774i	$-0.740555\pi$
$929$	8136.78	−	14093.3i	0.287362	−	0.497725i	0.973179	+	0.230049i	$0.0738885\pi$
$930$		0			0
$931$	−15039.9	+	21691.1i	−0.529444	+	0.763585i
$932$	−10187.7	−	5881.84i	−0.358055	−	0.206723i
$933$		0			0
$934$		−	5548.60i		−	0.194385i
$935$	9649.01	+	5570.86i	0.337493	+	0.194852i
$936$		0			0
$937$			5025.51i			0.175215i	0.996155	+	0.0876074i	$0.0279221\pi$
$937$			5025.51i			0.175215i	−0.996155	+	0.0876074i	$0.972078\pi$
$938$	−55150.7	+	12359.9i	−1.91976	+	0.430240i
$939$		0			0
$940$	11007.1			0.381929
$941$	6244.86	+	10816.4i	0.216341	+	0.374713i	0.953687	−	0.300802i	$-0.0972544\pi$
$941$	6244.86	+	10816.4i	0.216341	+	0.374713i	−0.737346	+	0.675516i	$0.763921\pi$
$942$		0			0
$943$	−3000.38	−	1732.27i	−0.103612	−	0.0598201i
$944$	−33475.0			−1.15415
$945$		0			0
$946$	−43360.2			−1.49023
$947$	−41127.9	−	23745.2i	−1.41127	−	0.814800i	−0.415766	−	0.909472i	$-0.636486\pi$
$947$	−41127.9	−	23745.2i	−1.41127	−	0.814800i	−0.995509	+	0.0946719i	$0.969820\pi$
$948$		0			0
$949$	−6031.12	−	10446.2i	−0.206300	−	0.357322i
$950$	38002.6			1.29786
$951$		0			0
$952$	−5433.42	+	17372.0i	−0.184977	+	0.591417i
$953$		−	43069.8i		−	1.46398i	−0.681318	−	0.731988i	$-0.738593\pi$
$953$		−	43069.8i		−	1.46398i	0.681318	−	0.731988i	$-0.261407\pi$
$954$		0			0
$955$	7064.06	+	4078.44i	0.239359	+	0.138194i
$956$		−	55350.2i		−	1.87254i
$957$		0			0
$958$	22355.9	+	12907.2i	0.753951	+	0.435294i
$959$	−45350.1	+	10163.5i	−1.52704	+	0.342227i
$960$		0			0
$961$	−12656.7	+	21922.0i	−0.424849	+	0.735860i
$962$	−15903.8	+	27546.2i	−0.533014	+	0.923207i
$963$		0			0
$964$	20431.9	−	11796.4i	0.682643	−	0.394124i
$965$	−3386.24	−	5865.13i	−0.112960	−	0.195653i
$966$		0			0
$967$	−9076.30	+	15720.6i	−0.301835	+	0.522793i	−0.976552	−	0.215284i	$-0.930932\pi$
$967$	−9076.30	+	15720.6i	−0.301835	+	0.522793i	0.674717	+	0.738077i	$0.264266\pi$
$968$		−	1750.37i		−	0.0581187i
$969$		0			0
$970$	−22059.5			−0.730195
$971$	15023.9	+	26022.2i	0.496541	+	0.860034i	0.999992	−	0.00398964i	$-0.00126995\pi$
$971$	15023.9	+	26022.2i	0.496541	+	0.860034i	−0.503451	+	0.864024i	$0.667937\pi$
$972$		0			0
$973$	−10922.8	+	34922.9i	−0.359886	+	1.15064i
$974$	−9996.57	+	5771.52i	−0.328861	+	0.189868i
$975$		0			0
$976$	6983.84	−	4032.12i	0.229044	−	0.132239i
$977$	48207.3	−	27832.5i	1.57859	−	0.911402i	0.583539	−	0.812085i	$-0.301668\pi$
$977$	48207.3	−	27832.5i	1.57859	−	0.911402i	0.995056	−	0.0993169i	$-0.0316657\pi$
$978$		0			0
$979$	−22928.7	+	13237.9i	−0.748524	+	0.432160i
$980$	−8450.84	−	5859.53i	−0.275462	−	0.190996i
$981$		0			0
$982$	−21520.1	−	37273.8i	−0.699320	−	1.21126i
$983$	6851.73			0.222316			0.111158	−	0.993803i	$-0.464544\pi$
$983$	6851.73			0.222316			0.111158	+	0.993803i	$0.464544\pi$
$984$		0			0
$985$			2007.55i			0.0649398i
$986$	23941.6	−	41468.1i	0.773282	−	1.33936i
$987$		0			0
$988$	9887.70	+	17126.0i	0.318390	+	0.551468i
$989$	−7300.03	+	4214.68i	−0.234709	+	0.135510i
$990$		0			0
$991$	14361.8	−	24875.3i	0.460359	−	0.797366i	−0.538619	−	0.842549i	$-0.681054\pi$
$991$	14361.8	−	24875.3i	0.460359	−	0.797366i	0.998979	+	0.0451834i	$0.0143872\pi$
$992$	8490.31	−	14705.7i	0.271742	−	0.470670i
$993$		0			0
$994$	57297.6	+	17920.9i	1.82834	+	0.571848i
$995$	6823.65	+	3939.64i	0.217411	+	0.125522i
$996$		0			0
$997$			45897.8i			1.45797i	0.684529	+	0.728985i	$0.260008\pi$
$997$			45897.8i			1.45797i	−0.684529	+	0.728985i	$0.739992\pi$
$998$	−33115.6	−	19119.3i	−1.05036	−	0.606423i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.s.a.17.3		44
3.2	odd	2		63.4.s.a.59.20	yes	44
7.5	odd	6		189.4.i.a.152.20		44
9.2	odd	6		189.4.i.a.143.3		44
9.7	even	3		63.4.i.a.38.20	yes	44
21.5	even	6		63.4.i.a.5.3	✓	44
63.47	even	6	inner	189.4.s.a.89.3		44
63.61	odd	6		63.4.s.a.47.20	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.3	✓	44	21.5	even	6
63.4.i.a.38.20	yes	44	9.7	even	3
63.4.s.a.47.20	yes	44	63.61	odd	6
63.4.s.a.59.20	yes	44	3.2	odd	2
189.4.i.a.143.3		44	9.2	odd	6
189.4.i.a.152.20		44	7.5	odd	6
189.4.s.a.17.3		44	1.1	even	1	trivial
189.4.s.a.89.3		44	63.47	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.68213 - 2.12588i) q^{2} +(5.03872 + 8.72732i) q^{4} +2.97507 q^{5} +(-4.05014 - 18.0720i) q^{7} -8.83278i q^{8} +O(q^{10})\)	\(q+(-3.68213 - 2.12588i) q^{2} +(5.03872 + 8.72732i) q^{4} +2.97507 q^{5} +(-4.05014 - 18.0720i) q^{7} -8.83278i q^{8} +(-10.9546 - 6.32464i) q^{10} +33.6576i q^{11} +(22.0839 + 12.7502i) q^{13} +(-23.5057 + 75.1535i) q^{14} +(21.5324 - 37.2951i) q^{16} +(55.6342 - 96.3612i) q^{17} +(66.6439 - 38.4768i) q^{19} +(14.9906 + 25.9644i) q^{20} +(71.5519 - 123.932i) q^{22} -27.8198i q^{23} -116.149 q^{25} +(-54.2106 - 93.8955i) q^{26} +(137.312 - 126.407i) q^{28} +(-87.6545 + 50.6073i) q^{29} +(-57.9504 + 33.4577i) q^{31} +(-219.765 + 126.881i) q^{32} +(-409.704 + 236.543i) q^{34} +(-12.0495 - 53.7654i) q^{35} +(-146.685 - 254.067i) q^{37} -327.188 q^{38} -26.2782i q^{40} +(62.2674 - 107.850i) q^{41} +(-151.499 - 262.404i) q^{43} +(-293.741 + 169.591i) q^{44} +(-59.1416 + 102.436i) q^{46} +(183.568 - 317.949i) q^{47} +(-310.193 + 146.388i) q^{49} +(427.676 + 246.919i) q^{50} +256.978i q^{52} +(-281.281 - 162.397i) q^{53} +100.134i q^{55} +(-159.626 + 35.7740i) q^{56} +430.340 q^{58} +(-388.659 - 673.177i) q^{59} +(162.171 + 93.6293i) q^{61} +284.508 q^{62} +734.421 q^{64} +(65.7013 + 37.9326i) q^{65} +(358.878 + 621.595i) q^{67} +1121.30 q^{68} +(-69.9311 + 223.587i) q^{70} -762.408i q^{71} +(-409.650 - 236.512i) q^{73} +1247.34i q^{74} +(671.600 + 387.748i) q^{76} +(608.259 - 136.318i) q^{77} +(353.515 - 612.306i) q^{79} +(64.0603 - 110.956i) q^{80} +(-458.553 + 264.746i) q^{82} +(406.242 + 703.632i) q^{83} +(165.516 - 286.681i) q^{85} +1288.27i q^{86} +297.290 q^{88} +(393.311 + 681.235i) q^{89} +(140.978 - 450.740i) q^{91} +(242.792 - 140.176i) q^{92} +(-1351.84 + 780.486i) q^{94} +(198.270 - 114.471i) q^{95} +(1510.29 - 871.967i) q^{97} +(1453.37 + 120.412i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

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