LMFDB - Embedded newform 189.4.h.a.37.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(37,189)]

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([2, 2]))

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

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

chi := DirichletCharacter("189.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.h (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			37.19
Character	$\chi$	$=$	189.37
Dual form			189.4.h.a.46.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.30573 q^{2} +10.5394 q^{4} +(-7.99829 - 13.8535i) q^{5} +(1.84582 - 18.4280i) q^{7} +10.9338 q^{8} +O(q^{10})$	\(q+4.30573 q^{2} +10.5394 q^{4} +(-7.99829 - 13.8535i) q^{5} +(1.84582 - 18.4280i) q^{7} +10.9338 q^{8} +(-34.4385 - 59.6493i) q^{10} +(-6.17419 + 10.6940i) q^{11} +(35.8182 - 62.0390i) q^{13} +(7.94761 - 79.3463i) q^{14} -37.2369 q^{16} +(42.2423 + 73.1658i) q^{17} +(13.6505 - 23.6434i) q^{19} +(-84.2968 - 146.006i) q^{20} +(-26.5844 + 46.0455i) q^{22} +(-20.2699 - 35.1085i) q^{23} +(-65.4454 + 113.355i) q^{25} +(154.224 - 267.123i) q^{26} +(19.4537 - 194.220i) q^{28} +(99.2642 + 171.931i) q^{29} +292.232 q^{31} -247.802 q^{32} +(181.884 + 315.033i) q^{34} +(-270.055 + 121.822i) q^{35} +(58.7266 - 101.717i) q^{37} +(58.7754 - 101.802i) q^{38} +(-87.4515 - 151.470i) q^{40} +(18.6085 - 32.2308i) q^{41} +(122.917 + 212.898i) q^{43} +(-65.0719 + 112.708i) q^{44} +(-87.2767 - 151.168i) q^{46} -91.6808 q^{47} +(-336.186 - 68.0297i) q^{49} +(-281.791 + 488.076i) q^{50} +(377.501 - 653.851i) q^{52} +(-85.8330 - 148.667i) q^{53} +197.532 q^{55} +(20.1818 - 201.488i) q^{56} +(427.405 + 740.287i) q^{58} +102.569 q^{59} -581.105 q^{61} +1258.27 q^{62} -769.076 q^{64} -1145.94 q^{65} -103.147 q^{67} +(445.207 + 771.120i) q^{68} +(-1162.79 + 524.533i) q^{70} +204.144 q^{71} +(580.785 + 1005.95i) q^{73} +(252.861 - 437.968i) q^{74} +(143.867 - 249.186i) q^{76} +(185.673 + 133.517i) q^{77} +621.055 q^{79} +(297.832 + 515.860i) q^{80} +(80.1231 - 138.777i) q^{82} +(-67.9652 - 117.719i) q^{83} +(675.733 - 1170.40i) q^{85} +(529.246 + 916.681i) q^{86} +(-67.5071 + 116.926i) q^{88} +(710.607 - 1230.81i) q^{89} +(-1077.14 - 774.573i) q^{91} +(-213.631 - 370.020i) q^{92} -394.753 q^{94} -436.723 q^{95} +(-559.262 - 968.670i) q^{97} +(-1447.53 - 292.918i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) $ 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8	$ 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} - 5 q^{11} - 14 q^{13} + 52 q^{14} + 494 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} + 93 q^{23} - 349 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} - 122 q^{31} - 326 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} + 761 q^{38} - 18 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} - 2010 q^{47} + 317 q^{49} - 239 q^{50} - 335 q^{52} - 258 q^{53} - 870 q^{55} + 1752 q^{56} + 237 q^{58} - 3330 q^{59} - 878 q^{61} - 1812 q^{62} + 872 q^{64} - 1226 q^{65} - 590 q^{67} + 1374 q^{68} + 1251 q^{70} - 636 q^{71} - 338 q^{73} - 1119 q^{74} + 1006 q^{76} - 2269 q^{77} - 266 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} + 3343 q^{86} + 369 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} + 2382 q^{94} + 6166 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) $ 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 - 5 * q^11 - 14 * q^13 + 52 * q^14 + 494 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 + 93 * q^23 - 349 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 - 122 * q^31 - 326 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 + 761 * q^38 - 18 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 - 2010 * q^47 + 317 * q^49 - 239 * q^50 - 335 * q^52 - 258 * q^53 - 870 * q^55 + 1752 * q^56 + 237 * q^58 - 3330 * q^59 - 878 * q^61 - 1812 * q^62 + 872 * q^64 - 1226 * q^65 - 590 * q^67 + 1374 * q^68 + 1251 * q^70 - 636 * q^71 - 338 * q^73 - 1119 * q^74 + 1006 * q^76 - 2269 * q^77 - 266 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 + 3343 * q^86 + 369 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 + 2382 * q^94 + 6166 * q^95 - 266 * q^97 - 3601 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	4.30573			1.52231			0.761154	−	0.648572i	$-0.224633\pi$
$2$	4.30573			1.52231			0.761154	+	0.648572i	$0.224633\pi$
$3$		0			0
$3$		0			0
$4$	10.5394			1.31742
$5$	−7.99829	−	13.8535i	−0.715389	−	1.23909i	−0.962809	−	0.270182i	$-0.912916\pi$
$5$	−7.99829	−	13.8535i	−0.715389	−	1.23909i	0.247420	−	0.968908i	$-0.420417\pi$
$6$		0			0
$7$	1.84582	−	18.4280i	0.0996649	−	0.995021i
$7$	1.84582	−	18.4280i	0.0996649	−	0.995021i
$8$	10.9338			0.483209
$9$		0			0
$10$	−34.4385	−	59.6493i	−1.08904	−	1.88628i
$11$	−6.17419	+	10.6940i	−0.169235	+	0.293124i	−0.938151	−	0.346226i	$-0.887463\pi$
$11$	−6.17419	+	10.6940i	−0.169235	+	0.293124i	0.768916	+	0.639350i	$0.220796\pi$
$12$		0			0
$13$	35.8182	−	62.0390i	0.764168	−	1.32358i	−0.176517	−	0.984298i	$-0.556483\pi$
$13$	35.8182	−	62.0390i	0.764168	−	1.32358i	0.940685	−	0.339281i	$-0.110184\pi$
$14$	7.94761	−	79.3463i	0.151721	−	1.51473i
$15$		0			0
$16$	−37.2369			−0.581827
$17$	42.2423	+	73.1658i	0.602663	+	1.04384i	0.992416	+	0.122923i	$0.0392269\pi$
$17$	42.2423	+	73.1658i	0.602663	+	1.04384i	−0.389753	+	0.920919i	$0.627440\pi$
$18$		0			0
$19$	13.6505	−	23.6434i	0.164823	−	0.285482i	−0.771769	−	0.635903i	$-0.780628\pi$
$19$	13.6505	−	23.6434i	0.164823	−	0.285482i	0.936592	+	0.350421i	$0.113961\pi$
$20$	−84.2968	−	146.006i	−0.942467	−	1.63240i
$21$		0			0
$22$	−26.5844	+	46.0455i	−0.257628	+	0.446225i
$23$	−20.2699	−	35.1085i	−0.183764	−	0.318288i	0.759396	−	0.650629i	$-0.225495\pi$
$23$	−20.2699	−	35.1085i	−0.183764	−	0.318288i	−0.943159	+	0.332341i	$0.892161\pi$
$24$		0			0
$25$	−65.4454	+	113.355i	−0.523563	+	0.906838i
$26$	154.224	−	267.123i	1.16330	−	2.01489i
$27$		0			0
$28$	19.4537	−	194.220i	0.131300	−	1.31086i
$29$	99.2642	+	171.931i	0.635617	+	1.10092i	0.986384	+	0.164458i	$0.0525876\pi$
$29$	99.2642	+	171.931i	0.635617	+	1.10092i	−0.350767	+	0.936463i	$0.614079\pi$
$30$		0			0
$31$	292.232			1.69311			0.846555	−	0.532301i	$-0.178673\pi$
$31$	292.232			1.69311			0.846555	+	0.532301i	$0.178673\pi$
$32$	−247.802			−1.36893
$33$		0			0
$34$	181.884	+	315.033i	0.917438	+	1.58905i
$35$	−270.055	+	121.822i	−1.30422	+	0.588334i
$36$		0			0
$37$	58.7266	−	101.717i	0.260935	−	0.451952i	−0.705556	−	0.708654i	$-0.749303\pi$
$37$	58.7266	−	101.717i	0.260935	−	0.451952i	0.966491	+	0.256702i	$0.0826359\pi$
$38$	58.7754	−	101.802i	0.250911	−	0.434591i
$39$		0			0
$40$	−87.4515	−	151.470i	−0.345682	−	0.598739i
$41$	18.6085	−	32.2308i	0.0708818	−	0.122771i	−0.828406	−	0.560128i	$-0.810752\pi$
$41$	18.6085	−	32.2308i	0.0708818	−	0.122771i	0.899288	+	0.437357i	$0.144085\pi$
$42$		0			0
$43$	122.917	+	212.898i	0.435921	+	0.755037i	0.997370	−	0.0724738i	$-0.0230894\pi$
$43$	122.917	+	212.898i	0.435921	+	0.755037i	−0.561449	+	0.827511i	$0.689756\pi$
$44$	−65.0719	+	112.708i	−0.222954	+	0.386167i
$45$		0			0
$46$	−87.2767	−	151.168i	−0.279745	−	0.484532i
$47$	−91.6808			−0.284532			−0.142266	−	0.989828i	$-0.545439\pi$
$47$	−91.6808			−0.284532			−0.142266	+	0.989828i	$0.545439\pi$
$48$		0			0
$49$	−336.186	−	68.0297i	−0.980134	−	0.198337i
$50$	−281.791	+	488.076i	−0.797024	+	1.38049i
$51$		0			0
$52$	377.501	−	653.851i	1.00673	−	1.74371i
$53$	−85.8330	−	148.667i	−0.222454	−	0.385302i	0.733098	−	0.680123i	$-0.238073\pi$
$53$	−85.8330	−	148.667i	−0.222454	−	0.385302i	−0.955553	+	0.294821i	$0.904740\pi$
$54$		0			0
$55$	197.532			0.484276
$56$	20.1818	−	201.488i	0.0481589	−	0.480803i
$57$		0			0
$58$	427.405	+	740.287i	0.967604	+	1.67594i
$59$	102.569			0.226329			0.113164	−	0.993576i	$-0.463901\pi$
$59$	102.569			0.226329			0.113164	+	0.993576i	$0.463901\pi$
$60$		0			0
$61$	−581.105			−1.21972			−0.609859	−	0.792510i	$-0.708774\pi$
$61$	−581.105			−1.21972			−0.609859	+	0.792510i	$0.708774\pi$
$62$	1258.27			2.57743
$63$		0			0
$64$	−769.076			−1.50210
$65$	−1145.94			−2.18671
$66$		0			0
$67$	−103.147			−0.188081			−0.0940406	−	0.995568i	$-0.529978\pi$
$67$	−103.147			−0.188081			−0.0940406	+	0.995568i	$0.529978\pi$
$68$	445.207	+	771.120i	0.793959	+	1.37518i
$69$		0			0
$70$	−1162.79	+	524.533i	−1.98542	+	0.895624i
$71$	204.144			0.341231			0.170616	−	0.985338i	$-0.445424\pi$
$71$	204.144			0.341231			0.170616	+	0.985338i	$0.445424\pi$
$72$		0			0
$73$	580.785	+	1005.95i	0.931174	+	1.61284i	0.781318	+	0.624133i	$0.214548\pi$
$73$	580.785	+	1005.95i	0.931174	+	1.61284i	0.149856	+	0.988708i	$0.452119\pi$
$74$	252.861	−	437.968i	0.397223	−	0.688010i
$75$		0			0
$76$	143.867	−	249.186i	0.217141	−	0.376099i
$77$	185.673	+	133.517i	0.274798	+	0.197607i
$78$		0			0
$79$	621.055			0.884482			0.442241	−	0.896896i	$-0.354184\pi$
$79$	621.055			0.884482			0.442241	+	0.896896i	$0.354184\pi$
$80$	297.832	+	515.860i	0.416232	+	0.720936i
$81$		0			0
$82$	80.1231	−	138.777i	0.107904	−	0.186895i
$83$	−67.9652	−	117.719i	−0.0898813	−	0.155679i	0.817579	−	0.575816i	$-0.195315\pi$
$83$	−67.9652	−	117.719i	−0.0898813	−	0.155679i	−0.907461	+	0.420137i	$0.861982\pi$
$84$		0			0
$85$	675.733	−	1170.40i	0.862277	−	1.49351i
$86$	529.246	+	916.681i	0.663606	+	1.14940i
$87$		0			0
$88$	−67.5071	+	116.926i	−0.0817759	+	0.141640i
$89$	710.607	−	1230.81i	0.846339	−	1.46590i	−0.0381134	−	0.999273i	$-0.512135\pi$
$89$	710.607	−	1230.81i	0.846339	−	1.46590i	0.884453	−	0.466630i	$-0.154532\pi$
$90$		0			0
$91$	−1077.14	−	774.573i	−1.24083	−	0.892278i
$92$	−213.631	−	370.020i	−0.242094	−	0.419318i
$93$		0			0
$94$	−394.753			−0.433146
$95$	−436.723			−0.471651
$96$		0			0
$97$	−559.262	−	968.670i	−0.585407	−	1.01395i	−0.994825	−	0.101607i	$-0.967602\pi$
$97$	−559.262	−	968.670i	−0.585407	−	1.01395i	0.409418	−	0.912347i	$-0.365732\pi$
$98$	−1447.53	−	292.918i	−1.49206	−	0.301930i
$99$		0			0
$100$	−689.752	+	1194.69i	−0.689752	+	1.19469i
$101$	483.103	−	836.759i	0.475946	−	0.824362i	−0.523674	−	0.851918i	$-0.675439\pi$
$101$	483.103	−	836.759i	0.475946	−	0.824362i	0.999620	+	0.0275561i	$0.00877248\pi$
$102$		0			0
$103$	385.116	+	667.040i	0.368413	+	0.638111i	0.989318	−	0.145776i	$-0.0465678\pi$
$103$	385.116	+	667.040i	0.368413	+	0.638111i	−0.620904	+	0.783886i	$0.713234\pi$
$104$	391.628	−	678.320i	0.369253	−	0.639565i
$105$		0			0
$106$	−369.574	−	640.121i	−0.338644	−	0.586548i
$107$	−638.529	+	1105.96i	−0.576905	+	0.999230i	0.418926	+	0.908020i	$0.362407\pi$
$107$	−638.529	+	1105.96i	−0.576905	+	0.999230i	−0.995832	+	0.0912094i	$0.970927\pi$
$108$		0			0
$109$	496.710	+	860.327i	0.436479	+	0.756003i	0.997415	−	0.0718556i	$-0.0228921\pi$
$109$	496.710	+	860.327i	0.436479	+	0.756003i	−0.560936	+	0.827859i	$0.689559\pi$
$110$	850.520			0.737217
$111$		0			0
$112$	−68.7326	+	686.203i	−0.0579877	+	0.578930i
$113$	172.393	−	298.593i	0.143516	−	0.248577i	−0.785302	−	0.619113i	$-0.787492\pi$
$113$	172.393	−	298.593i	0.143516	−	0.248577i	0.928818	+	0.370535i	$0.120826\pi$
$114$		0			0
$115$	−324.249	+	561.615i	−0.262925	+	0.455399i
$116$	1046.18	+	1812.04i	0.837374	+	1.45037i
$117$		0			0
$118$	441.637			0.344542
$119$	1426.28	−	643.393i	1.09871	−	0.495628i
$120$		0			0
$121$	589.259	+	1020.63i	0.442719	+	0.766812i
$122$	−2502.08			−1.85679
$123$		0			0
$124$	3079.94			2.23053
$125$	94.2335			0.0674280
$126$		0			0
$127$	1096.49			0.766121			0.383060	−	0.923723i	$-0.374870\pi$
$127$	1096.49			0.766121			0.383060	+	0.923723i	$0.374870\pi$
$128$	−1329.02			−0.917732
$129$		0			0
$130$	−4934.11			−3.32885
$131$	−218.366	−	378.221i	−0.145639	−	0.252255i	0.783972	−	0.620796i	$-0.213191\pi$
$131$	−218.366	−	378.221i	−0.145639	−	0.252255i	−0.929611	+	0.368542i	$0.879857\pi$
$132$		0			0
$133$	−410.505	−	295.193i	−0.267634	−	0.192455i
$134$	−444.125			−0.286317
$135$		0			0
$136$	461.868	+	799.978i	0.291212	+	0.504394i
$137$	−1134.52	+	1965.04i	−0.707506	+	1.22544i	0.258273	+	0.966072i	$0.416847\pi$
$137$	−1134.52	+	1965.04i	−0.707506	+	1.22544i	−0.965779	+	0.259365i	$0.916487\pi$
$138$		0			0
$139$	315.251	−	546.031i	0.192369	−	0.333192i	−0.753666	−	0.657257i	$-0.771716\pi$
$139$	315.251	−	546.031i	0.192369	−	0.333192i	0.946035	+	0.324065i	$0.105050\pi$
$140$	−2846.21	+	1283.92i	−1.71820	+	0.775082i
$141$		0			0
$142$	878.989			0.519459
$143$	442.297	+	766.081i	0.258648	+	0.447992i
$144$		0			0
$145$	1587.89	−	2750.30i	0.909427	−	1.57517i
$146$	2500.70	+	4331.35i	1.41753	+	2.45524i
$147$		0			0
$148$	618.940	−	1072.04i	0.343760	−	0.595410i
$149$	721.803	+	1250.20i	0.396862	+	0.687385i	0.993337	−	0.115247i	$-0.0367659\pi$
$149$	721.803	+	1250.20i	0.396862	+	0.687385i	−0.596475	+	0.802632i	$0.703433\pi$
$150$		0			0
$151$	330.218	−	571.955i	0.177965	−	0.308245i	−0.763218	−	0.646141i	$-0.776382\pi$
$151$	330.218	−	571.955i	0.177965	−	0.308245i	0.941184	+	0.337896i	$0.109715\pi$
$152$	149.251	−	258.511i	0.0796440	−	0.137947i
$153$		0			0
$154$	799.459	+	574.890i	0.418326	+	0.300818i
$155$	−2337.36	−	4048.42i	−1.21123	−	2.09792i
$156$		0			0
$157$	−1992.11			−1.01266			−0.506331	−	0.862339i	$-0.668999\pi$
$157$	−1992.11			−1.01266			−0.506331	+	0.862339i	$0.668999\pi$
$158$	2674.10			1.34645
$159$		0			0
$160$	1982.00	+	3432.92i	0.979316	+	1.69622i
$161$	−684.395	+	308.730i	−0.335018	+	0.151126i
$162$		0			0
$163$	187.561	−	324.866i	0.0901285	−	0.156107i	−0.817437	−	0.576019i	$-0.804606\pi$
$163$	187.561	−	324.866i	0.0901285	−	0.156107i	0.907565	+	0.419911i	$0.137939\pi$
$164$	196.121	−	339.692i	0.0933810	−	0.161741i
$165$		0			0
$166$	−292.640	−	506.867i	−0.136827	−	0.236991i
$167$	1404.71	−	2433.03i	0.650896	−	1.12738i	−0.332010	−	0.943276i	$-0.607727\pi$
$167$	1404.71	−	2433.03i	0.650896	−	1.12738i	0.982906	−	0.184109i	$-0.0589399\pi$
$168$		0			0
$169$	−1467.39	−	2541.60i	−0.667907	−	1.15685i
$170$	2909.53	−	5039.45i	1.31265	−	2.27358i
$171$		0			0
$172$	1295.46	+	2243.80i	0.574291	+	0.994700i
$173$	−663.878			−0.291756			−0.145878	−	0.989303i	$-0.546601\pi$
$173$	−663.878			−0.291756			−0.145878	+	0.989303i	$0.546601\pi$
$174$		0			0
$175$	1968.11	+	1415.26i	0.850142	+	0.611337i
$176$	229.908	−	398.212i	0.0984655	−	0.170547i
$177$		0			0
$178$	3059.69	−	5299.53i	1.28839	−	2.23155i
$179$	−2169.02	−	3756.85i	−0.905698	−	1.56872i	−0.819977	−	0.572396i	$-0.806014\pi$
$179$	−2169.02	−	3756.85i	−0.905698	−	1.56872i	−0.0857207	−	0.996319i	$-0.527319\pi$
$180$		0			0
$181$	−523.330			−0.214911			−0.107455	−	0.994210i	$-0.534270\pi$
$181$	−523.330			−0.214911			−0.107455	+	0.994210i	$0.534270\pi$
$182$	−4637.89	−	3335.10i	−1.88892	−	1.35832i
$183$		0			0
$184$	−221.626	−	383.868i	−0.0887962	−	0.153799i
$185$	−1878.85			−0.746680
$186$		0			0
$187$	−1043.25			−0.407967
$188$	−966.256			−0.374848
$189$		0			0
$190$	−1880.41			−0.717997
$191$	2934.87			1.11183			0.555916	−	0.831239i	$-0.312368\pi$
$191$	2934.87			1.11183			0.555916	+	0.831239i	$0.312368\pi$
$192$		0			0
$193$	−1574.06			−0.587065			−0.293533	−	0.955949i	$-0.594831\pi$
$193$	−1574.06			−0.587065			−0.293533	+	0.955949i	$0.594831\pi$
$194$	−2408.03	−	4170.84i	−0.891169	−	1.54355i
$195$		0			0
$196$	−3543.18	−	716.989i	−1.29125	−	0.261293i
$197$	9.28789			0.00335906			0.00167953	−	0.999999i	$-0.499465\pi$
$197$	9.28789			0.00335906			0.00167953	+	0.999999i	$0.499465\pi$
$198$		0			0
$199$	−1767.58	−	3061.55i	−0.629652	−	1.09059i	−0.987621	−	0.156856i	$-0.949864\pi$
$199$	−1767.58	−	3061.55i	−0.629652	−	1.09059i	0.357969	−	0.933733i	$-0.383469\pi$
$200$	−715.565	+	1239.40i	−0.252990	+	0.438192i
$201$		0			0
$202$	2080.11	−	3602.86i	0.724536	−	1.25493i
$203$	3351.57	−	1511.89i	1.15879	−	0.522729i
$204$		0			0
$205$	−595.344			−0.202832
$206$	1658.21	+	2872.10i	0.560838	+	0.971400i
$207$		0			0
$208$	−1333.76	+	2310.14i	−0.444613	+	0.770093i
$209$	168.561	+	291.957i	0.0557877	+	0.0966272i
$210$		0			0
$211$	435.806	−	754.838i	0.142190	−	0.246280i	−0.786131	−	0.618060i	$-0.787919\pi$
$211$	435.806	−	754.838i	0.142190	−	0.246280i	0.928321	+	0.371779i	$0.121252\pi$
$212$	−904.624	−	1566.86i	−0.293065	−	0.507604i
$213$		0			0
$214$	−2749.33	+	4761.99i	−0.878227	+	1.52113i
$215$	1966.25	−	3405.64i	0.623706	−	1.08029i
$216$		0			0
$217$	539.407	−	5385.26i	0.168744	−	1.68468i
$218$	2138.70	+	3704.34i	0.664455	+	1.15087i
$219$		0			0
$220$	2081.86			0.637994
$221$	6052.18			1.84214
$222$		0			0
$223$	1217.61	+	2108.95i	0.365636	+	0.633300i	0.988878	−	0.148729i	$-0.0475181\pi$
$223$	1217.61	+	2108.95i	0.365636	+	0.633300i	−0.623242	+	0.782029i	$0.714185\pi$
$224$	−457.398	+	4566.51i	−0.136434	+	1.36211i
$225$		0			0
$226$	742.276	−	1285.66i	0.218476	−	0.378411i
$227$	144.839	−	250.869i	0.0423494	−	0.0733513i	−0.844074	−	0.536227i	$-0.819849\pi$
$227$	144.839	−	250.869i	0.0423494	−	0.0733513i	0.886423	+	0.462876i	$0.153182\pi$
$228$		0			0
$229$	2452.29	+	4247.50i	0.707651	+	1.22569i	0.965726	+	0.259563i	$0.0835784\pi$
$229$	2452.29	+	4247.50i	0.707651	+	1.22569i	−0.258075	+	0.966125i	$0.583088\pi$
$230$	−1396.13	+	2418.17i	−0.400252	+	0.693258i
$231$		0			0
$232$	1085.33	+	1879.85i	0.307136	+	0.531975i
$233$	−2698.04	+	4673.15i	−0.758604	+	1.31394i	0.184959	+	0.982746i	$0.440785\pi$
$233$	−2698.04	+	4673.15i	−0.758604	+	1.31394i	−0.943563	+	0.331194i	$0.892549\pi$
$234$		0			0
$235$	733.290	+	1270.10i	0.203551	+	0.352561i
$236$	1081.02			0.298170
$237$		0			0
$238$	6141.16	−	2770.28i	1.67257	−	0.754498i
$239$	−1692.03	+	2930.68i	−0.457943	+	0.793181i	−0.998852	−	0.0479004i	$-0.984747\pi$
$239$	−1692.03	+	2930.68i	−0.457943	+	0.793181i	0.540909	+	0.841081i	$0.318080\pi$
$240$		0			0
$241$	−2611.16	+	4522.66i	−0.697923	+	1.20884i	0.271262	+	0.962505i	$0.412559\pi$
$241$	−2611.16	+	4522.66i	−0.697923	+	1.20884i	−0.969185	+	0.246332i	$0.920774\pi$
$242$	2537.19	+	4394.55i	0.673954	+	1.16732i
$243$		0			0
$244$	−6124.47			−1.60688
$245$	1746.47	+	5201.46i	0.455419	+	1.35636i
$246$		0			0
$247$	−977.873	−	1693.73i	−0.251905	−	0.436313i
$248$	3195.20			0.818126
$249$		0			0
$250$	405.744			0.102646
$251$	−2776.49			−0.698208			−0.349104	−	0.937084i	$-0.613514\pi$
$251$	−2776.49			−0.698208			−0.349104	+	0.937084i	$0.613514\pi$
$252$		0			0
$253$	500.600			0.124397
$254$	4721.17			1.16627
$255$		0			0
$256$	430.208			0.105031
$257$	841.709	+	1457.88i	0.204297	+	0.353853i	0.949909	−	0.312528i	$-0.101176\pi$
$257$	841.709	+	1457.88i	0.204297	+	0.353853i	−0.745611	+	0.666381i	$0.767842\pi$
$258$		0			0
$259$	−1766.05	−	1269.97i	−0.423696	−	0.304679i
$260$	−12077.5			−2.88081
$261$		0			0
$262$	−940.227	−	1628.52i	−0.221708	−	0.384009i
$263$	−3723.30	+	6448.94i	−0.872959	+	1.51201i	−0.0140388	+	0.999901i	$0.504469\pi$
$263$	−3723.30	+	6448.94i	−0.872959	+	1.51201i	−0.858921	+	0.512109i	$0.828864\pi$
$264$		0			0
$265$	−1373.04	+	2378.17i	−0.318283	+	0.551282i
$266$	−1767.52	−	1271.02i	−0.407420	−	0.292976i
$267$		0			0
$268$	−1087.11			−0.247782
$269$	−3697.25	−	6403.83i	−0.838013	−	1.45148i	−0.891553	−	0.452916i	$-0.850384\pi$
$269$	−3697.25	−	6403.83i	−0.838013	−	1.45148i	0.0535400	−	0.998566i	$-0.482950\pi$
$270$		0			0
$271$	614.965	−	1065.15i	0.137847	−	0.238757i	−0.788835	−	0.614606i	$-0.789315\pi$
$271$	614.965	−	1065.15i	0.137847	−	0.238757i	0.926681	+	0.375848i	$0.122649\pi$
$272$	−1572.97	−	2724.47i	−0.350645	−	0.607335i
$273$		0			0
$274$	−4884.93	+	8460.95i	−1.07704	+	1.86549i
$275$	−808.144	−	1399.75i	−0.177211	−	0.306938i
$276$		0			0
$277$	−865.305	+	1498.75i	−0.187694	+	0.325095i	−0.944481	−	0.328566i	$-0.893435\pi$
$277$	−865.305	+	1498.75i	−0.187694	+	0.325095i	0.756787	+	0.653661i	$0.226768\pi$
$278$	1357.39	−	2351.06i	0.292844	−	0.507221i
$279$		0			0
$280$	−2952.72	+	1331.97i	−0.630211	+	0.284288i
$281$	2590.08	+	4486.16i	0.549863	+	0.952391i	0.998283	+	0.0585679i	$0.0186534\pi$
$281$	2590.08	+	4486.16i	0.549863	+	0.952391i	−0.448420	+	0.893823i	$0.648013\pi$
$282$		0			0
$283$	4630.21			0.972570			0.486285	−	0.873800i	$-0.338352\pi$
$283$	4630.21			0.972570			0.486285	+	0.873800i	$0.338352\pi$
$284$	2151.54			0.449544
$285$		0			0
$286$	1904.41	+	3298.54i	0.393742	+	0.681982i
$287$	−559.603	−	402.410i	−0.115095	−	0.0827648i
$288$		0			0
$289$	−1112.33	+	1926.61i	−0.226405	+	0.392145i
$290$	6837.02	−	11842.1i	1.38443	−	2.39790i
$291$		0			0
$292$	6121.09	+	10602.0i	1.22675	+	2.12479i
$293$	−2109.17	+	3653.19i	−0.420543	+	0.728401i	−0.995993	−	0.0894358i	$-0.971494\pi$
$293$	−2109.17	+	3653.19i	−0.420543	+	0.728401i	0.575450	+	0.817837i	$0.304827\pi$
$294$		0			0
$295$	−820.381	−	1420.94i	−0.161913	−	0.280442i
$296$	642.103	−	1112.15i	0.126086	−	0.218387i
$297$		0			0
$298$	3107.89	+	5383.03i	0.604145	+	1.04641i
$299$	−2904.12			−0.561705
$300$		0			0
$301$	4150.17	−	1872.14i	0.794724	−	0.358500i
$302$	1421.83	−	2462.69i	0.270918	−	0.469244i
$303$		0			0
$304$	−508.302	+	880.405i	−0.0958984	+	0.166101i
$305$	4647.85	+	8050.31i	0.872573	+	1.51134i
$306$		0			0
$307$	−5634.20			−1.04743			−0.523715	−	0.851894i	$-0.675454\pi$
$307$	−5634.20			−1.04743			−0.523715	+	0.851894i	$0.675454\pi$
$308$	1956.87	+	1407.19i	0.362024	+	0.260331i
$309$		0			0
$310$	−10064.0	−	17431.4i	−1.84387	−	3.19367i
$311$	−1631.73			−0.297514			−0.148757	−	0.988874i	$-0.547527\pi$
$311$	−1631.73			−0.297514			−0.148757	+	0.988874i	$0.547527\pi$
$312$		0			0
$313$	−3258.72			−0.588478			−0.294239	−	0.955732i	$-0.595066\pi$
$313$	−3258.72			−0.588478			−0.294239	+	0.955732i	$0.595066\pi$
$314$	−8577.51			−1.54158
$315$		0			0
$316$	6545.51			1.16523
$317$	1697.52			0.300764			0.150382	−	0.988628i	$-0.451950\pi$
$317$	1697.52			0.300764			0.150382	+	0.988628i	$0.451950\pi$
$318$		0			0
$319$	−2451.50			−0.430275
$320$	6151.30	+	10654.4i	1.07459	+	1.86124i
$321$		0			0
$322$	−2946.82	+	1329.31i	−0.510000	+	0.230061i
$323$	2306.51			0.397331
$324$		0			0
$325$	4688.28	+	8120.34i	0.800181	+	1.38595i
$326$	807.590	−	1398.79i	0.137203	−	0.237643i
$327$		0			0
$328$	203.461	−	352.404i	0.0342507	−	0.0593240i
$329$	−169.226	+	1689.50i	−0.0283579	+	0.283116i
$330$		0			0
$331$	7928.23			1.31654			0.658270	−	0.752782i	$-0.271289\pi$
$331$	7928.23			1.31654			0.658270	+	0.752782i	$0.271289\pi$
$332$	−716.309	−	1240.68i	−0.118411	−	0.205094i
$333$		0			0
$334$	6048.30	−	10476.0i	0.990864	−	1.71623i
$335$	825.002	+	1428.95i	0.134551	+	0.233050i
$336$		0			0
$337$	−2899.12	+	5021.42i	−0.468620	+	0.811674i	−0.999357	−	0.0358626i	$-0.988582\pi$
$337$	−2899.12	+	5021.42i	−0.468620	+	0.811674i	0.530736	+	0.847537i	$0.321915\pi$
$338$	−6318.20	−	10943.4i	−1.01676	−	1.76108i
$339$		0			0
$340$	7121.79	−	12335.3i	1.13598	−	1.96757i
$341$	−1804.29	+	3125.13i	−0.286534	+	0.496291i
$342$		0			0
$343$	−1874.19	+	6069.68i	−0.295035	+	0.955487i
$344$	1343.94	+	2327.78i	0.210641	+	0.364841i
$345$		0			0
$346$	−2858.48			−0.444142
$347$	−8450.14			−1.30728			−0.653642	−	0.756804i	$-0.726760\pi$
$347$	−8450.14			−1.30728			−0.653642	+	0.756804i	$0.726760\pi$
$348$		0			0
$349$	4344.69	+	7525.22i	0.666378	+	1.15420i	0.978910	+	0.204293i	$0.0654895\pi$
$349$	4344.69	+	7525.22i	0.666378	+	1.15420i	−0.312532	+	0.949907i	$0.601177\pi$
$350$	8474.15	+	6093.75i	1.29418	+	0.930642i
$351$		0			0
$352$	1529.98	−	2650.00i	0.231671	−	0.401265i
$353$	−2161.42	+	3743.68i	−0.325894	+	0.564465i	−0.981693	−	0.190471i	$-0.938999\pi$
$353$	−2161.42	+	3743.68i	−0.325894	+	0.564465i	0.655799	+	0.754936i	$0.272332\pi$
$354$		0			0
$355$	−1632.80	−	2828.10i	−0.244113	−	0.422816i
$356$	7489.34	−	12971.9i	1.11498	−	1.93121i
$357$		0			0
$358$	−9339.21	−	16176.0i	−1.37875	−	2.38807i
$359$	3205.46	−	5552.03i	0.471248	−	0.816225i	−0.528211	−	0.849113i	$-0.677137\pi$
$359$	3205.46	−	5552.03i	0.471248	−	0.816225i	0.999459	+	0.0328880i	$0.0104705\pi$
$360$		0			0
$361$	3056.83	+	5294.58i	0.445667	+	0.771917i
$362$	−2253.32			−0.327160
$363$		0			0
$364$	−11352.4	−	8163.49i	−1.63469	−	1.17550i
$365$	9290.57	−	16091.7i	1.33230	−	2.30762i
$366$		0			0
$367$	−2570.52	+	4452.28i	−0.365614	+	0.633261i	−0.988874	−	0.148753i	$-0.952474\pi$
$367$	−2570.52	+	4452.28i	−0.365614	+	0.633261i	0.623261	+	0.782014i	$0.285808\pi$
$368$	754.787	+	1307.33i	0.106918	+	0.185188i
$369$		0			0
$370$	−8089.83			−1.13668
$371$	−2898.08	+	1307.32i	−0.405554	+	0.182946i
$372$		0			0
$373$	2446.20	+	4236.94i	0.339569	+	0.588151i	0.984352	−	0.176215i	$-0.0563853\pi$
$373$	2446.20	+	4236.94i	0.339569	+	0.588151i	−0.644782	+	0.764366i	$0.723052\pi$
$374$	−4491.95			−0.621051
$375$		0			0
$376$	−1002.42			−0.137489
$377$	14221.9			1.94287
$378$		0			0
$379$	−7875.22			−1.06734			−0.533671	−	0.845692i	$-0.679188\pi$
$379$	−7875.22			−1.06734			−0.533671	+	0.845692i	$0.679188\pi$
$380$	−4602.77			−0.621361
$381$		0			0
$382$	12636.8			1.69255
$383$	2289.71	+	3965.89i	0.305480	+	0.529106i	0.977368	−	0.211546i	$-0.0678499\pi$
$383$	2289.71	+	3965.89i	0.305480	+	0.529106i	−0.671888	+	0.740652i	$0.734517\pi$
$384$		0			0
$385$	364.608	−	3640.13i	0.0482653	−	0.481865i
$386$	−6777.50			−0.893694
$387$		0			0
$388$	−5894.26	−	10209.2i	−0.771226	−	1.33580i
$389$	743.851	−	1288.39i	0.0969531	−	0.167928i	−0.813469	−	0.581608i	$-0.802424\pi$
$389$	743.851	−	1288.39i	0.0969531	−	0.167928i	0.910422	+	0.413681i	$0.135757\pi$
$390$		0			0
$391$	1712.49	−	2966.13i	0.221495	−	0.383640i
$392$	−3675.78	−	743.821i	−0.473609	−	0.0958383i
$393$		0			0
$394$	39.9912			0.00511352
$395$	−4967.38	−	8603.75i	−0.632749	−	1.09595i
$396$		0			0
$397$	210.748	−	365.026i	0.0266426	−	0.0461464i	−0.852397	−	0.522896i	$-0.824852\pi$
$397$	210.748	−	365.026i	0.0266426	−	0.0461464i	0.879039	+	0.476749i	$0.158185\pi$
$398$	−7610.75	−	13182.2i	−0.958524	−	1.66021i
$399$		0			0
$400$	2436.98	−	4220.98i	0.304623	−	0.527623i
$401$	1682.69	+	2914.50i	0.209550	+	0.362951i	0.951573	−	0.307423i	$-0.0994668\pi$
$401$	1682.69	+	2914.50i	0.209550	+	0.362951i	−0.742023	+	0.670375i	$0.766133\pi$
$402$		0			0
$403$	10467.2	−	18129.8i	1.29382	−	2.24096i
$404$	5091.59	−	8818.89i	0.627020	−	1.08603i
$405$		0			0
$406$	14431.0	−	6509.81i	1.76403	−	0.795754i
$407$	725.177	+	1256.04i	0.0883187	+	0.152972i
$408$		0			0
$409$	−12776.9			−1.54468			−0.772341	−	0.635208i	$-0.780915\pi$
$409$	−12776.9			−1.54468			−0.772341	+	0.635208i	$0.780915\pi$
$410$	−2563.39			−0.308773
$411$		0			0
$412$	4058.87	+	7030.17i	0.485355	+	0.840659i
$413$	189.325	−	1890.16i	0.0225570	−	0.225202i
$414$		0			0
$415$	−1087.21	+	1883.11i	−0.128600	+	0.222742i
$416$	−8875.84	+	15373.4i	−1.04609	+	1.81188i
$417$		0			0
$418$	725.781	+	1257.09i	0.0849261	+	0.147096i
$419$	−2968.34	+	5141.32i	−0.346093	+	0.599451i	−0.985552	−	0.169375i	$-0.945825\pi$
$419$	−2968.34	+	5141.32i	−0.346093	+	0.599451i	0.639459	+	0.768825i	$0.279158\pi$
$420$		0			0
$421$	3097.28	+	5364.64i	0.358556	+	0.621037i	0.987720	−	0.156236i	$-0.0499359\pi$
$421$	3097.28	+	5364.64i	0.358556	+	0.621037i	−0.629164	+	0.777273i	$0.716603\pi$
$422$	1876.46	−	3250.13i	0.216457	−	0.374915i
$423$		0			0
$424$	−938.479	−	1625.49i	−0.107492	−	0.186181i
$425$	−11058.3			−1.26213
$426$		0			0
$427$	−1072.61	+	10708.6i	−0.121563	+	1.21365i
$428$	−6729.68	+	11656.1i	−0.760026	+	1.31640i
$429$		0			0
$430$	8466.13	−	14663.8i	0.949473	−	1.64453i
$431$	−6203.14	−	10744.2i	−0.693259	−	1.20076i	−0.970764	−	0.240036i	$-0.922841\pi$
$431$	−6203.14	−	10744.2i	−0.693259	−	1.20076i	0.277505	−	0.960724i	$-0.410493\pi$
$432$		0			0
$433$	6906.51			0.766525			0.383263	−	0.923639i	$-0.374800\pi$
$433$	6906.51			0.766525			0.383263	+	0.923639i	$0.374800\pi$
$434$	2322.54	−	23187.5i	0.256880	−	2.56460i
$435$		0			0
$436$	5235.00	+	9067.29i	0.575025	+	0.995973i
$437$	−1106.78			−0.121154
$438$		0			0
$439$	−6034.84			−0.656098			−0.328049	−	0.944661i	$-0.606391\pi$
$439$	−6034.84			−0.656098			−0.328049	+	0.944661i	$0.606391\pi$
$440$	2159.77			0.234007
$441$		0			0
$442$	26059.1			2.80431
$443$	9440.28			1.01246			0.506231	−	0.862398i	$-0.331038\pi$
$443$	9440.28			1.01246			0.506231	+	0.862398i	$0.331038\pi$
$444$		0			0
$445$	−22734.6			−2.42185
$446$	5242.68	+	9080.60i	0.556611	+	0.964078i
$447$		0			0
$448$	−1419.58	+	14172.6i	−0.149707	+	1.49462i
$449$	−1036.72			−0.108966			−0.0544830	−	0.998515i	$-0.517351\pi$
$449$	−1036.72			−0.108966			−0.0544830	+	0.998515i	$0.517351\pi$
$450$		0			0
$451$	229.784	+	397.998i	0.0239914	+	0.0415543i
$452$	1816.91	−	3146.97i	0.189071	−	0.327480i
$453$		0			0
$454$	623.639	−	1080.17i	0.0644688	−	0.111663i
$455$	−2115.20	+	21117.4i	−0.217938	+	2.17582i
$456$		0			0
$457$	8605.86			0.880887			0.440443	−	0.897780i	$-0.354821\pi$
$457$	8605.86			0.880887			0.440443	+	0.897780i	$0.354821\pi$
$458$	10558.9	+	18288.6i	1.07726	+	1.86587i
$459$		0			0
$460$	−3417.37	+	5919.06i	−0.346382	+	0.599952i
$461$	2742.73	+	4750.55i	0.277097	+	0.479946i	0.970662	−	0.240448i	$-0.0772944\pi$
$461$	2742.73	+	4750.55i	0.277097	+	0.479946i	−0.693565	+	0.720394i	$0.743961\pi$
$462$		0			0
$463$	9424.66	−	16324.0i	0.946007	−	1.63853i	0.192285	−	0.981339i	$-0.438410\pi$
$463$	9424.66	−	16324.0i	0.946007	−	1.63853i	0.753722	−	0.657193i	$-0.228256\pi$
$464$	−3696.29	−	6402.16i	−0.369819	−	0.640545i
$465$		0			0
$466$	−11617.1	+	20121.3i	−1.15483	+	2.00022i
$467$	1996.29	−	3457.67i	0.197810	−	0.342616i	−0.750008	−	0.661428i	$-0.769951\pi$
$467$	1996.29	−	3457.67i	0.197810	−	0.342616i	0.947818	+	0.318812i	$0.103284\pi$
$468$		0			0
$469$	−190.391	+	1900.80i	−0.0187451	+	0.187145i
$470$	3157.35	+	5468.69i	0.309868	+	0.536706i
$471$		0			0
$472$	1121.47			0.109364
$473$	−3035.64			−0.295093
$474$		0			0
$475$	1786.73	+	3094.70i	0.172591	+	0.298936i
$476$	15032.0	−	6780.94i	1.44746	−	0.652949i
$477$		0			0
$478$	−7285.44	+	12618.7i	−0.697130	+	1.20746i
$479$	−2017.44	+	3494.31i	−0.192441	+	0.333318i	−0.946059	−	0.323995i	$-0.894974\pi$
$479$	−2017.44	+	3494.31i	−0.192441	+	0.333318i	0.753618	+	0.657313i	$0.228307\pi$
$480$		0			0
$481$	−4206.96	−	7286.67i	−0.398796	−	0.690735i
$482$	−11242.9	+	19473.4i	−1.06245	+	1.84022i
$483$		0			0
$484$	6210.41	+	10756.7i	0.583246	+	1.01021i
$485$	−8946.28	+	15495.4i	−0.837587	+	1.45074i
$486$		0			0
$487$	−2594.34	−	4493.53i	−0.241398	−	0.418114i	0.719715	−	0.694270i	$-0.244273\pi$
$487$	−2594.34	−	4493.53i	−0.241398	−	0.418114i	−0.961113	+	0.276156i	$0.910939\pi$
$488$	−6353.66			−0.589379
$489$		0			0
$490$	7519.83	+	22396.1i	0.693288	+	2.06480i
$491$	9858.14	−	17074.8i	0.906093	−	1.56940i	0.0866491	−	0.996239i	$-0.472384\pi$
$491$	9858.14	−	17074.8i	0.906093	−	1.56940i	0.819444	−	0.573160i	$-0.194283\pi$
$492$		0			0
$493$	−8386.30	+	14525.5i	−0.766125	+	1.32697i
$494$	−4210.46	−	7292.74i	−0.383477	−	0.664202i
$495$		0			0
$496$	−10881.8			−0.985096
$497$	376.812	−	3761.97i	0.0340088	−	0.339532i
$498$		0			0
$499$	−4602.18	−	7971.20i	−0.412869	−	0.715110i	0.582333	−	0.812950i	$-0.302140\pi$
$499$	−4602.18	−	7971.20i	−0.412869	−	0.715110i	−0.995202	+	0.0978399i	$0.968807\pi$
$500$	993.159			0.0888309
$501$		0			0
$502$	−11954.8			−1.06289
$503$	−15889.6			−1.40852			−0.704258	−	0.709944i	$-0.748720\pi$
$503$	−15889.6			−1.40852			−0.704258	+	0.709944i	$0.748720\pi$
$504$		0			0
$505$	−15456.0			−1.36195
$506$	2155.45			0.189370
$507$		0			0
$508$	11556.2			1.00930
$509$	−6094.85	−	10556.6i	−0.530746	−	0.919278i	−0.999356	−	0.0358735i	$-0.988579\pi$
$509$	−6094.85	−	10556.6i	−0.530746	−	0.919278i	0.468611	−	0.883405i	$-0.344755\pi$
$510$		0			0
$511$	19609.7	−	8845.93i	1.69762	−	0.765794i
$512$	12484.5			1.07762
$513$		0			0
$514$	3624.18	+	6277.26i	0.311003	+	0.538673i
$515$	6160.54	−	10670.4i	0.527118	−	0.912995i
$516$		0			0
$517$	566.054	−	980.435i	0.0481529	−	0.0834032i
$518$	−7604.16	−	5468.14i	−0.644995	−	0.463816i
$519$		0			0
$520$	−12529.4			−1.05664
$521$	4945.29	+	8565.50i	0.415849	+	0.720271i	0.995517	−	0.0945813i	$-0.0301512\pi$
$521$	4945.29	+	8565.50i	0.415849	+	0.720271i	−0.579668	+	0.814852i	$0.696818\pi$
$522$		0			0
$523$	3592.36	−	6222.15i	0.300350	−	0.520221i	−0.675865	−	0.737025i	$-0.736230\pi$
$523$	3592.36	−	6222.15i	0.300350	−	0.520221i	0.976215	+	0.216804i	$0.0695632\pi$
$524$	−2301.44	−	3986.21i	−0.191868	−	0.332325i
$525$		0			0
$526$	−16031.5	+	27767.4i	−1.32891	+	2.30174i
$527$	12344.6	+	21381.4i	1.02037	+	1.76734i
$528$		0			0
$529$	5261.76	−	9113.64i	0.432462	−	0.749046i
$530$	−5911.93	+	10239.8i	−0.484524	+	0.839220i
$531$		0			0
$532$	−4326.45	−	3111.15i	−0.352585	−	0.253544i
$533$	−1333.04	−	2308.90i	−0.108331	−	0.187635i
$534$		0			0
$535$	20428.6			1.65085
$536$	−1127.79			−0.0908825
$537$		0			0
$538$	−15919.4	−	27573.2i	−1.27571	−	2.20960i
$539$	2803.18	−	3175.15i	0.224011	−	0.253735i
$540$		0			0
$541$	−8256.26	+	14300.3i	−0.656126	+	1.13644i	0.325484	+	0.945548i	$0.394473\pi$
$541$	−8256.26	+	14300.3i	−0.656126	+	1.13644i	−0.981610	+	0.190896i	$0.938861\pi$
$542$	2647.87	−	4586.25i	0.209845	−	0.363462i
$543$		0			0
$544$	−10467.7	−	18130.7i	−0.825002	−	1.42894i
$545$	7945.66	−	13762.3i	0.624504	−	1.08167i
$546$		0			0
$547$	−7742.69	−	13410.7i	−0.605217	−	1.04827i	−0.992017	−	0.126103i	$-0.959753\pi$
$547$	−7742.69	−	13410.7i	−0.605217	−	1.04827i	0.386801	−	0.922163i	$-0.373580\pi$
$548$	−11957.1	+	20710.3i	−0.932082	+	1.61441i
$549$		0			0
$550$	−3479.66	−	6026.94i	−0.269769	−	0.467254i
$551$	5420.02			0.419057
$552$		0			0
$553$	1146.35	−	11444.8i	0.0881518	−	0.880079i
$554$	−3725.77	+	6453.23i	−0.285727	+	0.494894i
$555$		0			0
$556$	3322.54	−	5754.81i	0.253430	−	0.438954i
$557$	−2735.23	−	4737.56i	−0.208071	−	0.360390i	0.743036	−	0.669252i	$-0.233385\pi$
$557$	−2735.23	−	4737.56i	−0.208071	−	0.360390i	−0.951107	+	0.308862i	$0.900052\pi$
$558$		0			0
$559$	17610.6			1.33247
$560$	10056.0	−	4536.27i	0.758830	−	0.342308i
$561$		0			0
$562$	11152.2	+	19316.2i	0.837060	+	1.44983i
$563$	13295.9			0.995305			0.497652	−	0.867377i	$-0.334196\pi$
$563$	13295.9			0.995305			0.497652	+	0.867377i	$0.334196\pi$
$564$		0			0
$565$	−5515.38			−0.410680
$566$	19936.4			1.48055
$567$		0			0
$568$	2232.06			0.164886
$569$	−6809.71			−0.501719			−0.250859	−	0.968024i	$-0.580713\pi$
$569$	−6809.71			−0.501719			−0.250859	+	0.968024i	$0.580713\pi$
$570$		0			0
$571$	−96.2117			−0.00705138			−0.00352569	−	0.999994i	$-0.501122\pi$
$571$	−96.2117			−0.00705138			−0.00352569	+	0.999994i	$0.501122\pi$
$572$	4661.52	+	8073.99i	0.340748	+	0.590193i
$573$		0			0
$574$	−2409.50	−	1732.67i	−0.175210	−	0.125993i
$575$	5306.28			0.384847
$576$		0			0
$577$	−2412.03	−	4177.76i	−0.174028	−	0.301425i	0.765797	−	0.643083i	$-0.222345\pi$
$577$	−2412.03	−	4177.76i	−0.174028	−	0.301425i	−0.939824	+	0.341658i	$0.889012\pi$
$578$	−4789.39	+	8295.46i	−0.344658	+	0.596965i
$579$		0			0
$580$	16735.3	−	28986.4i	1.19810	−	2.07516i
$581$	−2294.79	+	1035.18i	−0.163862	+	0.0739181i
$582$		0			0
$583$	2119.80			0.150588
$584$	6350.17	+	10998.8i	0.449952	+	0.779339i
$585$		0			0
$586$	−9081.52	+	15729.7i	−0.640195	+	1.10885i
$587$	1727.26	+	2991.70i	0.121451	+	0.210359i	0.920340	−	0.391119i	$-0.127912\pi$
$587$	1727.26	+	2991.70i	0.121451	+	0.210359i	−0.798889	+	0.601478i	$0.794579\pi$
$588$		0			0
$589$	3989.11	−	6909.34i	0.279064	−	0.483352i
$590$	−3532.34	−	6118.20i	−0.246482	−	0.426919i
$591$		0			0
$592$	−2186.79	+	3787.64i	−0.151819	+	0.262958i
$593$	2016.99	−	3493.53i	0.139676	−	0.241926i	−0.787698	−	0.616061i	$-0.788727\pi$
$593$	2016.99	−	3493.53i	0.139676	−	0.241926i	0.927374	+	0.374136i	$0.122061\pi$
$594$		0			0
$595$	−20321.0	−	14612.8i	−1.40013	−	1.00683i
$596$	7607.33	+	13176.3i	0.522833	+	0.905574i
$597$		0			0
$598$	−12504.4			−0.855088
$599$	4837.66			0.329986			0.164993	−	0.986295i	$-0.447240\pi$
$599$	4837.66			0.329986			0.164993	+	0.986295i	$0.447240\pi$
$600$		0			0
$601$	−4800.07	−	8313.96i	−0.325788	−	0.564282i	0.655883	−	0.754862i	$-0.272296\pi$
$601$	−4800.07	−	8313.96i	−0.325788	−	0.564282i	−0.981672	+	0.190580i	$0.938963\pi$
$602$	17869.5	−	8060.95i	1.20981	−	0.545747i
$603$		0			0
$604$	3480.29	−	6028.03i	0.234455	−	0.406088i
$605$	9426.13	−	16326.5i	0.633433	−	1.09714i
$606$		0			0
$607$	3843.94	+	6657.90i	0.257036	+	0.445199i	0.965446	−	0.260602i	$-0.0839209\pi$
$607$	3843.94	+	6657.90i	0.257036	+	0.445199i	−0.708411	+	0.705800i	$0.750588\pi$
$608$	−3382.63	+	5858.88i	−0.225631	+	0.390804i
$609$		0			0
$610$	20012.4	+	34662.5i	1.32832	+	2.30073i
$611$	−3283.84	+	5687.78i	−0.217431	+	0.376601i
$612$		0			0
$613$	−7582.86	−	13133.9i	−0.499623	−	0.865372i	0.500377	−	0.865808i	$-0.333195\pi$
$613$	−7582.86	−	13133.9i	−0.499623	−	0.865372i	−1.00000		0.000435446i	$0.999861\pi$
$614$	−24259.4			−1.59451
$615$		0			0
$616$	2030.11	+	1459.85i	0.132785	+	0.0954853i
$617$	−1488.76	+	2578.61i	−0.0971397	+	0.168251i	−0.910500	−	0.413510i	$-0.864303\pi$
$617$	−1488.76	+	2578.61i	−0.0971397	+	0.168251i	0.813360	+	0.581761i	$0.197636\pi$
$618$		0			0
$619$	−3810.52	+	6600.02i	−0.247428	+	0.428558i	−0.962811	−	0.270174i	$-0.912919\pi$
$619$	−3810.52	+	6600.02i	−0.247428	+	0.428558i	0.715384	+	0.698732i	$0.246252\pi$
$620$	−24634.2	−	42667.7i	−1.59570	−	2.76383i
$621$		0			0
$622$	−7025.80			−0.452908
$623$	−21369.7	−	15367.0i	−1.37425	−	0.988225i
$624$		0			0
$625$	7426.97	+	12863.9i	0.475326	+	0.823289i
$626$	−14031.2			−0.895845
$627$		0			0
$628$	−20995.6			−1.33410
$629$	9922.98			0.629023
$630$		0			0
$631$	12459.3			0.786046			0.393023	−	0.919529i	$-0.371429\pi$
$631$	12459.3			0.786046			0.393023	+	0.919529i	$0.371429\pi$
$632$	6790.47			0.427390
$633$		0			0
$634$	7309.07			0.457855
$635$	−8770.01	−	15190.1i	−0.548074	−	0.949293i
$636$		0			0
$637$	−16262.1	+	18419.9i	−1.01150	+	1.14572i
$638$	−10555.5			−0.655011
$639$		0			0
$640$	10629.9	+	18411.5i	0.656536	+	1.13715i
$641$	797.185	−	1380.76i	0.0491215	−	0.0850810i	−0.840419	−	0.541937i	$-0.817691\pi$
$641$	797.185	−	1380.76i	0.0491215	−	0.0850810i	0.889541	+	0.456856i	$0.151024\pi$
$642$		0			0
$643$	−1235.02	+	2139.11i	−0.0757453	+	0.131195i	−0.901410	−	0.432966i	$-0.857467\pi$
$643$	−1235.02	+	2139.11i	−0.0757453	+	0.131195i	0.825665	+	0.564161i	$0.190800\pi$
$644$	−7213.08	+	3253.82i	−0.441359	+	0.199097i
$645$		0			0
$646$	9931.24			0.604860
$647$	10177.5	+	17628.0i	0.618422	+	1.07114i	0.989774	+	0.142646i	$0.0455611\pi$
$647$	10177.5	+	17628.0i	0.618422	+	1.07114i	−0.371352	+	0.928492i	$0.621106\pi$
$648$		0			0
$649$	−633.283	+	1096.88i	−0.0383028	+	0.0663424i
$650$	20186.5	+	34964.0i	1.21812	+	2.10985i
$651$		0			0
$652$	1976.78	−	3423.88i	0.118737	−	0.205659i
$653$	4640.39	+	8037.40i	0.278090	+	0.481666i	0.970910	−	0.239445i	$-0.0769654\pi$
$653$	4640.39	+	8037.40i	0.278090	+	0.481666i	−0.692820	+	0.721110i	$0.743632\pi$
$654$		0			0
$655$	−3493.12	+	6050.25i	−0.208378	+	0.360921i
$656$	−692.921	+	1200.17i	−0.0412409	+	0.0714313i
$657$		0			0
$658$	−728.643	+	7274.53i	−0.0431694	+	0.430989i
$659$	−3539.92	−	6131.31i	−0.209250	−	0.362431i	0.742229	−	0.670147i	$-0.233769\pi$
$659$	−3539.92	−	6131.31i	−0.209250	−	0.362431i	−0.951478	+	0.307716i	$0.900435\pi$
$660$		0			0
$661$	11986.2			0.705310			0.352655	−	0.935753i	$-0.385279\pi$
$661$	11986.2			0.705310			0.352655	+	0.935753i	$0.385279\pi$
$662$	34136.8			2.00418
$663$		0			0
$664$	−743.116	−	1287.11i	−0.0434314	−	0.0752255i
$665$	−806.111	+	8047.95i	−0.0470070	+	0.469302i
$666$		0			0
$667$	4024.14	−	6970.02i	0.233606	−	0.404618i
$668$	14804.7	−	25642.5i	0.857503	−	1.48524i
$669$		0			0
$670$	3552.24	+	6152.66i	0.204828	+	0.354773i
$671$	3587.85	−	6214.34i	0.206419	−	0.357529i
$672$		0			0
$673$	12138.4	+	21024.4i	0.695248	+	1.20421i	0.970097	+	0.242718i	$0.0780389\pi$
$673$	12138.4	+	21024.4i	0.695248	+	1.20421i	−0.274849	+	0.961488i	$0.588628\pi$
$674$	−12482.8	+	21620.9i	−0.713384	+	1.23562i
$675$		0			0
$676$	−15465.3	−	26786.8i	−0.879913	−	1.52405i
$677$	−3453.71			−0.196066			−0.0980331	−	0.995183i	$-0.531255\pi$
$677$	−3453.71			−0.196066			−0.0980331	+	0.995183i	$0.531255\pi$
$678$		0			0
$679$	−18883.0	+	8518.12i	−1.06725	+	0.481436i
$680$	7388.31	−	12796.9i	0.416660	−	0.721676i
$681$		0			0
$682$	−7768.81	+	13456.0i	−0.436192	+	0.755507i
$683$	−15514.6	−	26872.1i	−0.869179	−	1.50546i	−0.862837	−	0.505483i	$-0.831314\pi$
$683$	−15514.6	−	26872.1i	−0.869179	−	1.50546i	−0.00634267	−	0.999980i	$-0.502019\pi$
$684$		0			0
$685$	36296.8			2.02457
$686$	−8069.78	+	26134.4i	−0.449133	+	1.45454i
$687$		0			0
$688$	−4577.03	−	7927.65i	−0.253630	−	0.439301i
$689$	−12297.5			−0.679970
$690$		0			0
$691$	15119.5			0.832379			0.416190	−	0.909278i	$-0.363365\pi$
$691$	15119.5			0.832379			0.416190	+	0.909278i	$0.363365\pi$
$692$	−6996.85			−0.384365
$693$		0			0
$694$	−36384.1			−1.99009
$695$	−10085.9			−0.550474
$696$		0			0
$697$	3144.26			0.170871
$698$	18707.1	+	32401.6i	1.01443	+	1.75705i
$699$		0			0
$700$	20742.6	+	14916.0i	1.11999	+	0.805386i
$701$	−5945.15			−0.320321			−0.160161	−	0.987091i	$-0.551201\pi$
$701$	−5945.15			−0.320321			−0.160161	+	0.987091i	$0.551201\pi$
$702$		0			0
$703$	−1603.29	−	2776.99i	−0.0860162	−	0.148984i
$704$	4748.42	−	8224.50i	0.254208	−	0.440302i
$705$		0			0
$706$	−9306.48	+	16119.3i	−0.496111	+	0.859289i
$707$	−14528.1	−	10447.1i	−0.772823	−	0.555736i
$708$		0			0
$709$	−21769.7			−1.15314			−0.576572	−	0.817047i	$-0.695610\pi$
$709$	−21769.7			−1.15314			−0.576572	+	0.817047i	$0.695610\pi$
$710$	−7030.41	−	12177.0i	−0.371615	−	0.643656i
$711$		0			0
$712$	7769.61	−	13457.4i	0.408959	−	0.708337i
$713$	−5923.51	−	10259.8i	−0.311132	−	0.538896i
$714$		0			0
$715$	7075.24	−	12254.7i	0.370069	−	0.640977i
$716$	−22860.0	−	39594.7i	−1.19318	−	2.06665i
$717$		0			0
$718$	13801.9	−	23905.6i	0.717384	−	1.24254i
$719$	14530.9	−	25168.3i	0.753701	−	1.30545i	−0.192316	−	0.981333i	$-0.561600\pi$
$719$	14530.9	−	25168.3i	0.753701	−	1.30545i	0.946017	−	0.324116i	$-0.105067\pi$
$720$		0			0
$721$	13003.1	−	5865.70i	0.671651	−	0.302982i
$722$	13161.9	+	22797.1i	0.678442	+	1.17510i
$723$		0			0
$724$	−5515.56			−0.283127
$725$	−25985.5			−1.33114
$726$		0			0
$727$	−9889.43	−	17129.0i	−0.504510	−	0.873837i	−0.999986	−	0.00521564i	$-0.998340\pi$
$727$	−9889.43	−	17129.0i	−0.504510	−	0.873837i	0.495476	−	0.868621i	$-0.334994\pi$
$728$	−11777.2	−	8469.00i	−0.599579	−	0.431157i
$729$		0			0
$730$	40002.7	−	69286.8i	2.02818	−	3.51290i
$731$	−10384.6	+	17986.6i	−0.525427	+	0.910066i
$732$		0			0
$733$	−7505.17	−	12999.3i	−0.378185	−	0.655036i	0.612613	−	0.790383i	$-0.290118\pi$
$733$	−7505.17	−	12999.3i	−0.378185	−	0.655036i	−0.990798	+	0.135347i	$0.956785\pi$
$734$	−11068.0	+	19170.3i	−0.556576	+	0.964018i
$735$		0			0
$736$	5022.92	+	8699.96i	0.251559	+	0.435713i
$737$	636.850	−	1103.06i	0.0318300	−	0.0551311i
$738$		0			0
$739$	12605.7	+	21833.6i	0.627478	+	1.08682i	0.988056	+	0.154095i	$0.0492463\pi$
$739$	12605.7	+	21833.6i	0.627478	+	1.08682i	−0.360578	+	0.932729i	$0.617420\pi$
$740$	−19801.9			−0.983690
$741$		0			0
$742$	−12478.4	+	5628.98i	−0.617378	+	0.278499i
$743$	−5901.36	+	10221.5i	−0.291386	+	0.504696i	−0.974138	−	0.225955i	$-0.927450\pi$
$743$	−5901.36	+	10221.5i	−0.291386	+	0.504696i	0.682752	+	0.730651i	$0.260783\pi$
$744$		0			0
$745$	11546.4	−	19998.9i	0.567821	−	0.983495i
$746$	10532.7	+	18243.1i	0.516929	+	0.895347i
$747$		0			0
$748$	−10995.2			−0.537463
$749$	19202.1	+	13808.2i	0.936757	+	0.673621i
$750$		0			0
$751$	4171.09	+	7224.54i	0.202670	+	0.351035i	0.949388	−	0.314106i	$-0.101705\pi$
$751$	4171.09	+	7224.54i	0.202670	+	0.351035i	−0.746718	+	0.665141i	$0.768371\pi$
$752$	3413.91			0.165548
$753$		0			0
$754$	61235.6			2.95765
$755$	−10564.7			−0.509258
$756$		0			0
$757$	−16769.4			−0.805147			−0.402573	−	0.915388i	$-0.631884\pi$
$757$	−16769.4			−0.805147			−0.402573	+	0.915388i	$0.631884\pi$
$758$	−33908.6			−1.62482
$759$		0			0
$760$	−4775.03			−0.227906
$761$	16281.8	+	28200.9i	0.775577	+	1.34334i	0.934470	+	0.356042i	$0.115874\pi$
$761$	16281.8	+	28200.9i	0.775577	+	1.34334i	−0.158893	+	0.987296i	$0.550793\pi$
$762$		0			0
$763$	16771.0	−	7565.39i	0.795741	−	0.358959i
$764$	30931.6			1.46475
$765$		0			0
$766$	9858.88	+	17076.1i	0.465034	+	0.805462i
$767$	3673.86	−	6363.31i	0.172953	−	0.299564i
$768$		0			0
$769$	10652.9	−	18451.3i	0.499547	−	0.865242i	−0.500452	−	0.865764i	$-0.666833\pi$
$769$	10652.9	−	18451.3i	0.499547	−	0.865242i	1.00000		0.000522521i	$0.000166324\pi$
$770$	1569.91	−	15673.4i	0.0734746	−	0.733546i
$771$		0			0
$772$	−16589.6			−0.773411
$773$	−7055.10	−	12219.8i	−0.328272	−	0.568584i	0.653897	−	0.756584i	$-0.273133\pi$
$773$	−7055.10	−	12219.8i	−0.328272	−	0.568584i	−0.982169	+	0.188000i	$0.939800\pi$
$774$		0			0
$775$	−19125.2	+	33125.9i	−0.886450	+	1.53538i
$776$	−6114.84	−	10591.2i	−0.282874	−	0.489952i
$777$		0			0
$778$	3202.83	−	5547.46i	0.147592	−	0.255638i
$779$	−508.029	−	879.933i	−0.0233659	−	0.0404709i
$780$		0			0
$781$	−1260.42	+	2183.11i	−0.0577483	+	0.100023i
$782$	7373.54	−	12771.3i	0.337183	−	0.584018i
$783$		0			0
$784$	12518.5	+	2533.21i	0.570268	+	0.115398i
$785$	15933.5	+	27597.6i	0.724447	+	1.25478i
$786$		0			0
$787$	−881.916			−0.0399453			−0.0199726	−	0.999801i	$-0.506358\pi$
$787$	−881.916			−0.0399453			−0.0199726	+	0.999801i	$0.506358\pi$
$788$	97.8883			0.00442529
$789$		0			0
$790$	−21388.2	−	37045.5i	−0.963238	−	1.66838i
$791$	−5184.27	−	3728.01i	−0.233036	−	0.167576i
$792$		0			0
$793$	−20814.1	+	36051.1i	−0.932070	+	1.61439i
$794$	907.424	−	1571.70i	0.0405583	−	0.0702490i
$795$		0			0
$796$	−18629.2	−	32266.7i	−0.829515	−	1.43676i
$797$	19639.3	−	34016.3i	0.872849	−	1.51182i	0.0138121	−	0.999905i	$-0.495603\pi$
$797$	19639.3	−	34016.3i	0.872849	−	1.51182i	0.859037	−	0.511914i	$-0.171063\pi$
$798$		0			0
$799$	−3872.81	−	6707.90i	−0.171477	−	0.297007i
$800$	16217.5	−	28089.6i	0.716720	−	1.24140i
$801$		0			0
$802$	7245.21	+	12549.1i	0.318999	+	0.552523i
$803$	−14343.5			−0.630350
$804$		0			0
$805$	9750.97	+	7011.91i	0.426927	+	0.307003i
$806$	45069.1	−	78062.0i	1.96959	−	3.41144i
$807$		0			0
$808$	5282.14	−	9148.93i	0.229981	−	0.398339i
$809$	21346.5	+	36973.2i	0.927692	+	1.60681i	0.787174	+	0.616731i	$0.211543\pi$
$809$	21346.5	+	36973.2i	0.927692	+	1.60681i	0.140517	+	0.990078i	$0.455123\pi$
$810$		0			0
$811$	19800.2			0.857312			0.428656	−	0.903468i	$-0.358987\pi$
$811$	19800.2			0.857312			0.428656	+	0.903468i	$0.358987\pi$
$812$	35323.4	−	15934.4i	1.52661	−	0.688653i
$813$		0			0
$814$	3122.42	+	5408.19i	0.134448	+	0.232871i
$815$	−6000.69			−0.257908
$816$		0			0
$817$	6711.49			0.287399
$818$	−55013.8			−2.35148
$819$		0			0
$820$	−6274.54			−0.267215
$821$	15893.3			0.675616			0.337808	−	0.941215i	$-0.390314\pi$
$821$	15893.3			0.675616			0.337808	+	0.941215i	$0.390314\pi$
$822$		0			0
$823$	−4347.59			−0.184140			−0.0920702	−	0.995753i	$-0.529348\pi$
$823$	−4347.59			−0.184140			−0.0920702	+	0.995753i	$0.529348\pi$
$824$	4210.77	+	7293.26i	0.178021	+	0.308341i
$825$		0			0
$826$	815.182	−	8138.51i	0.0343387	−	0.342827i
$827$	858.141			0.0360828			0.0180414	−	0.999837i	$-0.494257\pi$
$827$	858.141			0.0360828			0.0180414	+	0.999837i	$0.494257\pi$
$828$		0			0
$829$	−12706.4	−	22008.1i	−0.532342	−	0.922043i	−0.999287	−	0.0377569i	$-0.987979\pi$
$829$	−12706.4	−	22008.1i	−0.532342	−	0.922043i	0.466945	−	0.884286i	$-0.345355\pi$
$830$	−4681.24	+	8108.15i	−0.195769	+	0.339082i
$831$		0			0
$832$	−27546.9	+	47712.7i	−1.14786	+	1.98815i
$833$	−9223.82	−	27471.1i	−0.383657	−	1.14264i
$834$		0			0
$835$	−44941.1			−1.86258
$836$	1776.53	+	3077.04i	0.0734958	+	0.127298i
$837$		0			0
$838$	−12780.9	+	22137.1i	−0.526860	+	0.912548i
$839$	−6817.03	−	11807.4i	−0.280513	−	0.485862i	0.690998	−	0.722856i	$-0.257171\pi$
$839$	−6817.03	−	11807.4i	−0.280513	−	0.485862i	−0.971511	+	0.236994i	$0.923838\pi$
$840$		0			0
$841$	−7512.25	+	13011.6i	−0.308018	+	0.533503i
$842$	13336.1	+	23098.7i	0.545832	+	0.945409i
$843$		0			0
$844$	4593.11	−	7955.50i	0.187324	−	0.324455i
$845$	−23473.3	+	40656.9i	−0.955627	+	1.65519i
$846$		0			0
$847$	19895.8	−	8975.00i	0.807117	−	0.364090i
$848$	3196.16	+	5535.90i	0.129430	+	0.224179i
$849$		0			0
$850$	−47614.0			−1.92135
$851$	−4761.52			−0.191801
$852$		0			0
$853$	3331.23	+	5769.86i	0.133715	+	0.231602i	0.925106	−	0.379709i	$-0.123976\pi$
$853$	3331.23	+	5769.86i	0.133715	+	0.231602i	−0.791391	+	0.611311i	$0.790643\pi$
$854$	−4618.39	+	46108.5i	−0.185056	+	1.84754i
$855$		0			0
$856$	−6981.52	+	12092.4i	−0.278766	+	0.482837i
$857$	−4871.38	+	8437.49i	−0.194170	+	0.336312i	−0.946628	−	0.322328i	$-0.895535\pi$
$857$	−4871.38	+	8437.49i	−0.194170	+	0.336312i	0.752458	+	0.658640i	$0.228868\pi$
$858$		0			0
$859$	−1861.77	−	3224.69i	−0.0739498	−	0.128085i	0.826679	−	0.562673i	$-0.190227\pi$
$859$	−1861.77	−	3224.69i	−0.0739498	−	0.128085i	−0.900629	+	0.434589i	$0.856894\pi$
$860$	20723.0	−	35893.2i	0.821683	−	1.42320i
$861$		0			0
$862$	−26709.1	−	46261.5i	−1.05535	−	1.82793i
$863$	9867.40	−	17090.8i	0.389212	−	0.674135i	−0.603132	−	0.797642i	$-0.706081\pi$
$863$	9867.40	−	17090.8i	0.389212	−	0.674135i	0.992344	+	0.123506i	$0.0394140\pi$
$864$		0			0
$865$	5309.90	+	9197.01i	0.208719	+	0.361512i
$866$	29737.6			1.16689
$867$		0			0
$868$	5685.00	−	56757.2i	0.222306	−	2.21943i
$869$	−3834.51	+	6641.56i	−0.149686	+	0.259263i
$870$		0			0
$871$	−3694.55	+	6399.15i	−0.143726	+	0.248940i
$872$	5430.91	+	9406.61i	0.210910	+	0.365308i
$873$		0			0
$874$	−4765.48			−0.184433
$875$	173.938	−	1736.54i	0.00672020	−	0.0670923i
$876$		0			0
$877$	−21001.0	−	36374.7i	−0.808611	−	1.40056i	−0.913826	−	0.406106i	$-0.866886\pi$
$877$	−21001.0	−	36374.7i	−0.808611	−	1.40056i	0.105215	−	0.994450i	$-0.466447\pi$
$878$	−25984.4			−0.998783
$879$		0			0
$880$	−7355.47			−0.281765
$881$	−25676.7			−0.981917			−0.490959	−	0.871183i	$-0.663353\pi$
$881$	−25676.7			−0.981917			−0.490959	+	0.871183i	$0.663353\pi$
$882$		0			0
$883$	46381.0			1.76766			0.883830	−	0.467809i	$-0.154956\pi$
$883$	46381.0			1.76766			0.883830	+	0.467809i	$0.154956\pi$
$884$	63786.1			2.42687
$885$		0			0
$886$	40647.3			1.54128
$887$	−14791.4	−	25619.5i	−0.559918	−	0.969806i	−0.997503	−	0.0706288i	$-0.977499\pi$
$887$	−14791.4	−	25619.5i	−0.559918	−	0.969806i	0.437585	−	0.899177i	$-0.355834\pi$
$888$		0			0
$889$	2023.91	−	20206.1i	0.0763553	−	0.762306i
$890$	−97889.1			−3.68680
$891$		0			0
$892$	12832.8	+	22227.0i	0.481696	+	0.834322i
$893$	−1251.49	+	2167.64i	−0.0468975	+	0.0812288i
$894$		0			0
$895$	−34696.9	+	60096.8i	−1.29585	+	2.24448i
$896$	−2453.13	+	24491.2i	−0.0914657	+	0.913163i
$897$		0			0
$898$	−4463.83			−0.165880
$899$	29008.2	+	50243.6i	1.07617	+	1.86398i
$900$		0			0
$901$	7251.57	−	12560.1i	0.268130	−	0.464414i
$902$	989.390	+	1713.67i	0.0365222	+	0.0632584i
$903$		0			0
$904$	1884.90	−	3264.74i	0.0693483	−	0.120115i
$905$	4185.75	+	7249.93i	0.153745	+	0.266294i
$906$		0			0
$907$	−5988.78	+	10372.9i	−0.219244	+	0.379742i	−0.954577	−	0.297964i	$-0.903692\pi$
$907$	−5988.78	+	10372.9i	−0.219244	+	0.379742i	0.735333	+	0.677706i	$0.237026\pi$
$908$	1526.51	−	2643.99i	0.0557919	−	0.0966344i
$909$		0			0
$910$	−9107.47	+	90926.0i	−0.331769	+	3.31227i
$911$	−6965.20	−	12064.1i	−0.253312	−	0.438750i	0.711123	−	0.703067i	$-0.248187\pi$
$911$	−6965.20	−	12064.1i	−0.253312	−	0.438750i	−0.964436	+	0.264317i	$0.914853\pi$
$912$		0			0
$913$	1678.52			0.0608443
$914$	37054.6			1.34098
$915$		0			0
$916$	25845.6	+	44765.9i	0.932273	+	1.61474i
$917$	−7372.95	+	3325.94i	−0.265514	+	0.119773i
$918$		0			0
$919$	−20470.4	+	35455.7i	−0.734772	+	1.27266i	0.220052	+	0.975488i	$0.429377\pi$
$919$	−20470.4	+	35455.7i	−0.734772	+	1.27266i	−0.954823	+	0.297174i	$0.903956\pi$
$920$	−3545.26	+	6140.57i	−0.127048	+	0.220053i
$921$		0			0
$922$	11809.5	+	20454.6i	0.421826	+	0.730625i
$923$	7312.07	−	12664.9i	0.260758	−	0.451646i
$924$		0			0
$925$	7686.77	+	13313.9i	0.273232	+	0.473251i
$926$	40580.1	−	70286.8i	1.44011	−	2.49435i
$927$		0			0
$928$	−24597.9	−	42604.8i	−0.870114	−	1.50708i
$929$	24417.0			0.862322			0.431161	−	0.902275i	$-0.358104\pi$
$929$	24417.0			0.862322			0.431161	+	0.902275i	$0.358104\pi$
$930$		0			0
$931$	−6197.55	+	7019.92i	−0.218170	+	0.247120i
$932$	−28435.6	+	49251.9i	−0.999399	+	1.73101i
$933$		0			0
$934$	8595.48	−	14887.8i	0.301127	−	0.521567i
$935$	8344.20	+	14452.6i	0.291855	+	0.505508i
$936$		0			0
$937$	19817.4			0.690935			0.345468	−	0.938431i	$-0.387720\pi$
$937$	19817.4			0.690935			0.345468	+	0.938431i	$0.387720\pi$
$938$	−819.774	+	8184.35i	−0.0285358	+	0.284892i
$939$		0			0
$940$	7728.40	+	13386.0i	0.268162	+	0.464471i
$941$	2827.44			0.0979510			0.0489755	−	0.998800i	$-0.484404\pi$
$941$	2827.44			0.0979510			0.0489755	+	0.998800i	$0.484404\pi$
$942$		0			0
$943$	−1508.76			−0.0521019
$944$	−3819.37			−0.131684
$945$		0			0
$946$	−13070.7			−0.449222
$947$	12569.6			0.431317			0.215659	−	0.976469i	$-0.430810\pi$
$947$	12569.6			0.431317			0.215659	+	0.976469i	$0.430810\pi$
$948$		0			0
$949$	83210.7			2.84630
$950$	7693.16	+	13325.0i	0.262736	+	0.455072i
$951$		0			0
$952$	15594.6	−	7034.71i	0.530906	−	0.239492i
$953$	−1901.47			−0.0646325			−0.0323162	−	0.999478i	$-0.510288\pi$
$953$	−1901.47			−0.0646325			−0.0323162	+	0.999478i	$0.510288\pi$
$954$		0			0
$955$	−23474.0	−	40658.1i	−0.795392	−	1.37766i
$956$	−17832.9	+	30887.5i	−0.603303	+	1.04495i
$957$		0			0
$958$	−8686.57	+	15045.6i	−0.292955	+	0.507412i
$959$	34117.8	+	24534.1i	1.14882	+	0.826117i
$960$		0			0
$961$	55608.5			1.86662
$962$	−18114.1	−	31374.5i	−0.607090	−	1.05151i
$963$		0			0
$964$	−27519.9	+	47665.9i	−0.919457	+	1.59255i
$965$	12589.8	+	21806.2i	0.419980	+	0.727427i
$966$		0			0
$967$	3584.61	−	6208.73i	0.119207	−	0.206473i	−0.800246	−	0.599671i	$-0.795298\pi$
$967$	3584.61	−	6208.73i	0.119207	−	0.206473i	0.919454	+	0.393198i	$0.128631\pi$
$968$	6442.82	+	11159.3i	0.213926	+	0.370530i
$969$		0			0
$970$	−38520.3	+	66719.2i	−1.27506	+	2.20848i
$971$	15360.2	−	26604.6i	0.507653	−	0.879281i	−0.492308	−	0.870421i	$-0.663847\pi$
$971$	15360.2	−	26604.6i	0.507653	−	0.879281i	0.999961	−	0.00885954i	$-0.00282012\pi$
$972$		0			0
$973$	−9480.38	−	6817.33i	−0.312361	−	0.224618i
$974$	−11170.6	−	19348.0i	−0.367482	−	0.636498i
$975$		0			0
$976$	21638.5			0.709665
$977$	−56051.5			−1.83546			−0.917730	−	0.397204i	$-0.869980\pi$
$977$	−56051.5			−1.83546			−0.917730	+	0.397204i	$0.869980\pi$
$978$		0			0
$979$	8774.84	+	15198.5i	0.286461	+	0.496165i
$980$	18406.6	+	54820.0i	0.599978	+	1.78690i
$981$		0			0
$982$	42446.5	−	73519.5i	1.37935	−	2.38911i
$983$	19385.3	−	33576.4i	0.628989	−	1.08944i	−0.358766	−	0.933427i	$-0.616802\pi$
$983$	19385.3	−	33576.4i	0.628989	−	1.08944i	0.987755	−	0.156013i	$-0.0498642\pi$
$984$		0			0
$985$	−74.2873	−	128.669i	−0.00240303	−	0.00416218i
$986$	−36109.2	+	62542.9i	−1.16628	+	2.02005i
$987$		0			0
$988$	−10306.1	−	17850.8i	−0.331865	−	0.574806i
$989$	4983.01	−	8630.82i	0.160213	−	0.277497i
$990$		0			0
$991$	−18797.3	−	32557.9i	−0.602538	−	1.04363i	−0.992435	−	0.122768i	$-0.960823\pi$
$991$	−18797.3	−	32557.9i	−0.602538	−	1.04363i	0.389897	−	0.920858i	$-0.372511\pi$
$992$	−72415.8			−2.31774
$993$		0			0
$994$	1622.45	−	16198.0i	0.0517718	−	0.516872i
$995$	−28275.3	+	48974.3i	−0.900892	+	1.56039i
$996$		0			0
$997$	−17576.7	+	30443.7i	−0.558335	+	0.967064i	0.439301	+	0.898340i	$0.355226\pi$
$997$	−17576.7	+	30443.7i	−0.558335	+	0.967064i	−0.997636	+	0.0687241i	$0.978107\pi$
$998$	−19815.8	−	34321.9i	−0.628514	−	1.08862i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.h.a.37.19		44
3.2	odd	2		63.4.h.a.58.4	yes	44
7.4	even	3		189.4.g.a.172.4		44
9.2	odd	6		63.4.g.a.16.19	yes	44
9.7	even	3		189.4.g.a.100.4		44
21.11	odd	6		63.4.g.a.4.19	✓	44
63.11	odd	6		63.4.h.a.25.4	yes	44
63.25	even	3	inner	189.4.h.a.46.19		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.19	✓	44	21.11	odd	6
63.4.g.a.16.19	yes	44	9.2	odd	6
63.4.h.a.25.4	yes	44	63.11	odd	6
63.4.h.a.58.4	yes	44	3.2	odd	2
189.4.g.a.100.4		44	9.7	even	3
189.4.g.a.172.4		44	7.4	even	3
189.4.h.a.37.19		44	1.1	even	1	trivial
189.4.h.a.46.19		44	63.25	even	3	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+4.30573 q^{2} +10.5394 q^{4} +(-7.99829 - 13.8535i) q^{5} +(1.84582 - 18.4280i) q^{7} +10.9338 q^{8} +O(q^{10})\)	\(q+4.30573 q^{2} +10.5394 q^{4} +(-7.99829 - 13.8535i) q^{5} +(1.84582 - 18.4280i) q^{7} +10.9338 q^{8} +(-34.4385 - 59.6493i) q^{10} +(-6.17419 + 10.6940i) q^{11} +(35.8182 - 62.0390i) q^{13} +(7.94761 - 79.3463i) q^{14} -37.2369 q^{16} +(42.2423 + 73.1658i) q^{17} +(13.6505 - 23.6434i) q^{19} +(-84.2968 - 146.006i) q^{20} +(-26.5844 + 46.0455i) q^{22} +(-20.2699 - 35.1085i) q^{23} +(-65.4454 + 113.355i) q^{25} +(154.224 - 267.123i) q^{26} +(19.4537 - 194.220i) q^{28} +(99.2642 + 171.931i) q^{29} +292.232 q^{31} -247.802 q^{32} +(181.884 + 315.033i) q^{34} +(-270.055 + 121.822i) q^{35} +(58.7266 - 101.717i) q^{37} +(58.7754 - 101.802i) q^{38} +(-87.4515 - 151.470i) q^{40} +(18.6085 - 32.2308i) q^{41} +(122.917 + 212.898i) q^{43} +(-65.0719 + 112.708i) q^{44} +(-87.2767 - 151.168i) q^{46} -91.6808 q^{47} +(-336.186 - 68.0297i) q^{49} +(-281.791 + 488.076i) q^{50} +(377.501 - 653.851i) q^{52} +(-85.8330 - 148.667i) q^{53} +197.532 q^{55} +(20.1818 - 201.488i) q^{56} +(427.405 + 740.287i) q^{58} +102.569 q^{59} -581.105 q^{61} +1258.27 q^{62} -769.076 q^{64} -1145.94 q^{65} -103.147 q^{67} +(445.207 + 771.120i) q^{68} +(-1162.79 + 524.533i) q^{70} +204.144 q^{71} +(580.785 + 1005.95i) q^{73} +(252.861 - 437.968i) q^{74} +(143.867 - 249.186i) q^{76} +(185.673 + 133.517i) q^{77} +621.055 q^{79} +(297.832 + 515.860i) q^{80} +(80.1231 - 138.777i) q^{82} +(-67.9652 - 117.719i) q^{83} +(675.733 - 1170.40i) q^{85} +(529.246 + 916.681i) q^{86} +(-67.5071 + 116.926i) q^{88} +(710.607 - 1230.81i) q^{89} +(-1077.14 - 774.573i) q^{91} +(-213.631 - 370.020i) q^{92} -394.753 q^{94} -436.723 q^{95} +(-559.262 - 968.670i) q^{97} +(-1447.53 - 292.918i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} - 5 q^{11} - 14 q^{13} + 52 q^{14} + 494 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} + 93 q^{23} - 349 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} - 122 q^{31} - 326 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} + 761 q^{38} - 18 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} - 2010 q^{47} + 317 q^{49} - 239 q^{50} - 335 q^{52} - 258 q^{53} - 870 q^{55} + 1752 q^{56} + 237 q^{58} - 3330 q^{59} - 878 q^{61} - 1812 q^{62} + 872 q^{64} - 1226 q^{65} - 590 q^{67} + 1374 q^{68} + 1251 q^{70} - 636 q^{71} - 338 q^{73} - 1119 q^{74} + 1006 q^{76} - 2269 q^{77} - 266 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} + 3343 q^{86} + 369 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} + 2382 q^{94} + 6166 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) \) 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 - 5 * q^11 - 14 * q^13 + 52 * q^14 + 494 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 + 93 * q^23 - 349 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 - 122 * q^31 - 326 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 + 761 * q^38 - 18 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 - 2010 * q^47 + 317 * q^49 - 239 * q^50 - 335 * q^52 - 258 * q^53 - 870 * q^55 + 1752 * q^56 + 237 * q^58 - 3330 * q^59 - 878 * q^61 - 1812 * q^62 + 872 * q^64 - 1226 * q^65 - 590 * q^67 + 1374 * q^68 + 1251 * q^70 - 636 * q^71 - 338 * q^73 - 1119 * q^74 + 1006 * q^76 - 2269 * q^77 - 266 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 + 3343 * q^86 + 369 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 + 2382 * q^94 + 6166 * q^95 - 266 * q^97 - 3601 * q^98

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