LMFDB - Embedded newform 189.4.i.a.143.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(143,189)]

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([1, 1]))

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

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

chi := DirichletCharacter("189.143");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.i (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			143.19
Character	$\chi$	$=$	189.143
Dual form			189.4.i.a.152.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.72101i q^{2} -5.84592 q^{4} +(-1.33006 + 2.30373i) q^{5} +(8.98650 - 16.1939i) q^{7} +8.01534i q^{8} +O(q^{10})$	\(q+3.72101i q^{2} -5.84592 q^{4} +(-1.33006 + 2.30373i) q^{5} +(8.98650 - 16.1939i) q^{7} +8.01534i q^{8} +(-8.57221 - 4.94917i) q^{10} +(-58.8750 + 33.9915i) q^{11} +(-69.6961 + 40.2391i) q^{13} +(60.2577 + 33.4389i) q^{14} -76.5926 q^{16} +(29.6144 - 51.2937i) q^{17} +(-5.86312 + 3.38507i) q^{19} +(7.77543 - 13.4674i) q^{20} +(-126.483 - 219.075i) q^{22} +(-109.467 - 63.2006i) q^{23} +(58.9619 + 102.125i) q^{25} +(-149.730 - 259.340i) q^{26} +(-52.5344 + 94.6684i) q^{28} +(114.327 + 66.0067i) q^{29} +72.5745i q^{31} -220.879i q^{32} +(190.864 + 110.196i) q^{34} +(25.3539 + 42.2414i) q^{35} +(-63.8671 - 110.621i) q^{37} +(-12.5959 - 21.8167i) q^{38} +(-18.4652 - 10.6609i) q^{40} +(4.93523 + 8.54808i) q^{41} +(-108.717 + 188.303i) q^{43} +(344.179 - 198.712i) q^{44} +(235.170 - 407.327i) q^{46} +185.893 q^{47} +(-181.486 - 291.053i) q^{49} +(-380.008 + 219.398i) q^{50} +(407.438 - 235.235i) q^{52} +(-174.049 - 100.487i) q^{53} -180.843i q^{55} +(129.800 + 72.0299i) q^{56} +(-245.612 + 425.412i) q^{58} +178.469 q^{59} +225.957i q^{61} -270.051 q^{62} +209.153 q^{64} -214.082i q^{65} +438.597 q^{67} +(-173.124 + 299.859i) q^{68} +(-157.181 + 94.3420i) q^{70} +533.668i q^{71} +(287.020 + 165.711i) q^{73} +(411.622 - 237.650i) q^{74} +(34.2753 - 19.7889i) q^{76} +(21.3751 + 1258.88i) q^{77} -1007.24 q^{79} +(101.873 - 176.449i) q^{80} +(-31.8075 + 18.3641i) q^{82} +(-590.719 + 1023.16i) q^{83} +(78.7779 + 136.447i) q^{85} +(-700.677 - 404.536i) q^{86} +(-272.454 - 471.903i) q^{88} +(66.3626 + 114.943i) q^{89} +(25.3038 + 1490.26i) q^{91} +(639.934 + 369.466i) q^{92} +691.710i q^{94} -18.0094i q^{95} +(761.712 + 439.775i) q^{97} +(1083.01 - 675.310i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) $ 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7	$ 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7} - 6 q^{10} - 9 q^{11} - 36 q^{13} - 54 q^{14} + 526 q^{16} + 72 q^{17} - 6 q^{19} - 24 q^{20} + 14 q^{22} + 285 q^{23} - 349 q^{25} + 96 q^{26} - 156 q^{28} + 132 q^{29} + 24 q^{34} - 765 q^{35} + 82 q^{37} + 873 q^{38} + 420 q^{40} - 618 q^{41} + 82 q^{43} - 603 q^{44} + 266 q^{46} + 402 q^{47} - 79 q^{49} + 1845 q^{50} + 189 q^{52} - 564 q^{53} - 66 q^{56} + 269 q^{58} - 1494 q^{59} + 2904 q^{62} - 1144 q^{64} - 590 q^{67} - 3504 q^{68} - 105 q^{70} - 6 q^{73} - 1515 q^{74} - 144 q^{76} + 4443 q^{77} + 1102 q^{79} + 4239 q^{80} + 18 q^{82} - 1830 q^{83} - 237 q^{85} - 1209 q^{86} - 623 q^{88} - 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 792 q^{97} - 5667 q^{98}+O(q^{100}) $ 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7 - 6 * q^10 - 9 * q^11 - 36 * q^13 - 54 * q^14 + 526 * q^16 + 72 * q^17 - 6 * q^19 - 24 * q^20 + 14 * q^22 + 285 * q^23 - 349 * q^25 + 96 * q^26 - 156 * q^28 + 132 * q^29 + 24 * q^34 - 765 * q^35 + 82 * q^37 + 873 * q^38 + 420 * q^40 - 618 * q^41 + 82 * q^43 - 603 * q^44 + 266 * q^46 + 402 * q^47 - 79 * q^49 + 1845 * q^50 + 189 * q^52 - 564 * q^53 - 66 * q^56 + 269 * q^58 - 1494 * q^59 + 2904 * q^62 - 1144 * q^64 - 590 * q^67 - 3504 * q^68 - 105 * q^70 - 6 * q^73 - 1515 * q^74 - 144 * q^76 + 4443 * q^77 + 1102 * q^79 + 4239 * q^80 + 18 * q^82 - 1830 * q^83 - 237 * q^85 - 1209 * q^86 - 623 * q^88 - 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 792 * q^97 - 5667 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$			3.72101i			1.31558i	0.753203	+	0.657788i	$0.228508\pi$
$2$			3.72101i			1.31558i	−0.753203	+	0.657788i	$0.771492\pi$
$3$		0			0
$3$		0			0
$4$	−5.84592			−0.730740
$5$	−1.33006	+	2.30373i	−0.118964	+	0.206052i	−0.919357	−	0.393423i	$-0.871291\pi$
$5$	−1.33006	+	2.30373i	−0.118964	+	0.206052i	0.800393	+	0.599475i	$0.204624\pi$
$6$		0			0
$7$	8.98650	−	16.1939i	0.485225	−	0.874389i
$7$	8.98650	−	16.1939i	0.485225	−	0.874389i
$8$			8.01534i			0.354231i
$9$		0			0
$10$	−8.57221	−	4.94917i	−0.271077	−	0.156507i
$11$	−58.8750	+	33.9915i	−1.61377	+	0.931711i	−0.625286	+	0.780396i	$0.715018\pi$
$11$	−58.8750	+	33.9915i	−1.61377	+	0.931711i	−0.988486	+	0.151315i	$0.951649\pi$
$12$		0			0
$13$	−69.6961	+	40.2391i	−1.48694	+	0.858485i	−0.999889	−	0.0148882i	$-0.995261\pi$
$13$	−69.6961	+	40.2391i	−1.48694	+	0.858485i	−0.487051	+	0.873374i	$0.661927\pi$
$14$	60.2577	+	33.4389i	1.15033	+	0.638351i
$15$		0			0
$16$	−76.5926			−1.19676
$17$	29.6144	−	51.2937i	0.422503	−	0.731797i	−0.573681	−	0.819079i	$-0.694485\pi$
$17$	29.6144	−	51.2937i	0.422503	−	0.731797i	0.996184	+	0.0872825i	$0.0278183\pi$
$18$		0			0
$19$	−5.86312	+	3.38507i	−0.0707943	+	0.0408731i	−0.534979	−	0.844865i	$-0.679681\pi$
$19$	−5.86312	+	3.38507i	−0.0707943	+	0.0408731i	0.464185	+	0.885738i	$0.346347\pi$
$20$	7.77543	−	13.4674i	0.0869320	−	0.150571i
$21$		0			0
$22$	−126.483	−	219.075i	−1.22574	−	2.12304i
$23$	−109.467	−	63.2006i	−0.992408	−	0.572967i	−0.0864145	−	0.996259i	$-0.527541\pi$
$23$	−109.467	−	63.2006i	−0.992408	−	0.572967i	−0.905993	+	0.423293i	$0.860874\pi$
$24$		0			0
$25$	58.9619	+	102.125i	0.471695	+	0.817000i
$26$	−149.730	−	259.340i	−1.12940	−	1.95618i
$27$		0			0
$28$	−52.5344	+	94.6684i	−0.354574	+	0.638951i
$29$	114.327	+	66.0067i	0.732068	+	0.422660i	0.819178	−	0.573539i	$-0.194430\pi$
$29$	114.327	+	66.0067i	0.732068	+	0.422660i	−0.0871101	+	0.996199i	$0.527763\pi$
$30$		0			0
$31$			72.5745i			0.420476i	0.977650	+	0.210238i	$0.0674239\pi$
$31$			72.5745i			0.420476i	−0.977650	+	0.210238i	$0.932576\pi$
$32$		−	220.879i		−	1.22020i
$33$		0			0
$34$	190.864	+	110.196i	0.962734	+	0.555835i
$35$	25.3539	+	42.2414i	0.122445	+	0.204003i
$36$		0			0
$37$	−63.8671	−	110.621i	−0.283775	−	0.491513i	0.688536	−	0.725202i	$-0.258254\pi$
$37$	−63.8671	−	110.621i	−0.283775	−	0.491513i	−0.972311	+	0.233689i	$0.924920\pi$
$38$	−12.5959	−	21.8167i	−0.0537717	−	0.0931353i
$39$		0			0
$40$	−18.4652	−	10.6609i	−0.0729901	−	0.0421409i
$41$	4.93523	+	8.54808i	0.0187989	+	0.0325606i	0.875272	−	0.483631i	$-0.160682\pi$
$41$	4.93523	+	8.54808i	0.0187989	+	0.0325606i	−0.856473	+	0.516192i	$0.827349\pi$
$42$		0			0
$43$	−108.717	+	188.303i	−0.385561	+	0.667812i	−0.991847	−	0.127435i	$-0.959326\pi$
$43$	−108.717	+	188.303i	−0.385561	+	0.667812i	0.606286	+	0.795247i	$0.292659\pi$
$44$	344.179	−	198.712i	1.17925	−	0.680839i
$45$		0			0
$46$	235.170	−	407.327i	0.753781	−	1.30559i
$47$	185.893			0.576921			0.288460	−	0.957492i	$-0.406857\pi$
$47$	185.893			0.576921			0.288460	+	0.957492i	$0.406857\pi$
$48$		0			0
$49$	−181.486	−	291.053i	−0.529113	−	0.848552i
$50$	−380.008	+	219.398i	−1.07483	+	0.620551i
$51$		0			0
$52$	407.438	−	235.235i	1.08657	−	0.627330i
$53$	−174.049	−	100.487i	−0.451084	−	0.260433i	0.257204	−	0.966357i	$-0.417199\pi$
$53$	−174.049	−	100.487i	−0.451084	−	0.260433i	−0.708288	+	0.705924i	$0.750532\pi$
$54$		0			0
$55$		−	180.843i		−	0.443361i
$56$	129.800	+	72.0299i	0.309736	+	0.171882i
$57$		0			0
$58$	−245.612	+	425.412i	−0.556041	+	0.963092i
$59$	178.469			0.393809			0.196904	−	0.980423i	$-0.436911\pi$
$59$	178.469			0.393809			0.196904	+	0.980423i	$0.436911\pi$
$60$		0			0
$61$			225.957i			0.474275i	0.971476	+	0.237138i	$0.0762092\pi$
$61$			225.957i			0.474275i	−0.971476	+	0.237138i	$0.923791\pi$
$62$	−270.051			−0.553169
$63$		0			0
$64$	209.153			0.408502
$65$		−	214.082i		−	0.408516i
$66$		0			0
$67$	438.597			0.799748			0.399874	−	0.916570i	$-0.369054\pi$
$67$	438.597			0.799748			0.399874	+	0.916570i	$0.369054\pi$
$68$	−173.124	+	299.859i	−0.308740	+	0.534753i
$69$		0			0
$70$	−157.181	+	94.3420i	−0.268381	+	0.161086i
$71$			533.668i			0.892039i	0.895023	+	0.446019i	$0.147159\pi$
$71$			533.668i			0.892039i	−0.895023	+	0.446019i	$0.852841\pi$
$72$		0			0
$73$	287.020	+	165.711i	0.460180	+	0.265685i	0.712120	−	0.702058i	$-0.247735\pi$
$73$	287.020	+	165.711i	0.460180	+	0.265685i	−0.251940	+	0.967743i	$0.581068\pi$
$74$	411.622	−	237.650i	0.646623	−	0.373328i
$75$		0			0
$76$	34.2753	−	19.7889i	0.0517323	−	0.0298676i
$77$	21.3751	+	1258.88i	0.0316353	+	1.86315i
$78$		0			0
$79$	−1007.24			−1.43448			−0.717238	−	0.696829i	$-0.754594\pi$
$79$	−1007.24			−1.43448			−0.717238	+	0.696829i	$0.754594\pi$
$80$	101.873	−	176.449i	0.142372	−	0.246595i
$81$		0			0
$82$	−31.8075	+	18.3641i	−0.0428360	+	0.0247314i
$83$	−590.719	+	1023.16i	−0.781203	+	1.35308i	0.150039	+	0.988680i	$0.452060\pi$
$83$	−590.719	+	1023.16i	−0.781203	+	1.35308i	−0.931242	+	0.364403i	$0.881273\pi$
$84$		0			0
$85$	78.7779	+	136.447i	0.100525	+	0.174115i
$86$	−700.677	−	404.536i	−0.878557	−	0.507235i
$87$		0			0
$88$	−272.454	−	471.903i	−0.330041	−	0.571648i
$89$	66.3626	+	114.943i	0.0790385	+	0.136899i	0.902835	−	0.429986i	$-0.141482\pi$
$89$	66.3626	+	114.943i	0.0790385	+	0.136899i	−0.823797	+	0.566885i	$0.808148\pi$
$90$		0			0
$91$	25.3038	+	1490.26i	0.0291490	+	1.71672i
$92$	639.934	+	369.466i	0.725192	+	0.418690i
$93$		0			0
$94$			691.710i			0.758983i
$95$		−	18.0094i		−	0.0194498i
$96$		0			0
$97$	761.712	+	439.775i	0.797321	+	0.460333i	0.842533	−	0.538644i	$-0.181063\pi$
$97$	761.712	+	439.775i	0.797321	+	0.460333i	−0.0452127	+	0.998977i	$0.514397\pi$
$98$	1083.01	−	675.310i	1.11633	−	0.696088i
$99$		0			0
$100$	−344.687	−	597.015i	−0.344687	−	0.597015i
$101$	782.039	+	1354.53i	0.770454	+	1.33446i	0.937315	+	0.348484i	$0.113304\pi$
$101$	782.039	+	1354.53i	0.770454	+	1.33446i	−0.166861	+	0.985980i	$0.553363\pi$
$102$		0			0
$103$	678.462	+	391.710i	0.649037	+	0.374722i	0.788087	−	0.615564i	$-0.211072\pi$
$103$	678.462	+	391.710i	0.649037	+	0.374722i	−0.139050	+	0.990285i	$0.544405\pi$
$104$	−322.530	−	558.638i	−0.304102	−	0.526721i
$105$		0			0
$106$	373.914	−	647.637i	0.342620	−	0.593435i
$107$	120.873	−	69.7858i	0.109207	−	0.0630509i	−0.444401	−	0.895828i	$-0.646584\pi$
$107$	120.873	−	69.7858i	0.109207	−	0.0630509i	0.553609	+	0.832777i	$0.313250\pi$
$108$		0			0
$109$	600.318	−	1039.78i	0.527523	−	0.913697i	−0.471962	−	0.881619i	$-0.656454\pi$
$109$	600.318	−	1039.78i	0.527523	−	0.913697i	0.999485	−	0.0320783i	$-0.0102126\pi$
$110$	672.919			0.583275
$111$		0			0
$112$	−688.299	+	1240.33i	−0.580698	+	1.04643i
$113$	−682.006	+	393.756i	−0.567767	+	0.327801i	−0.756257	−	0.654275i	$-0.772974\pi$
$113$	−682.006	+	393.756i	−0.567767	+	0.327801i	0.188490	+	0.982075i	$0.439641\pi$
$114$		0			0
$115$	291.195	−	168.121i	0.236122	−	0.136325i
$116$	−668.347	−	385.870i	−0.534952	−	0.308855i
$117$		0			0
$118$			664.086i			0.518086i
$119$	−564.515	−	940.524i	−0.434866	−	0.724518i
$120$		0			0
$121$	1645.34	−	2849.82i	1.23617	−	2.14111i
$122$	−840.787			−0.623945
$123$		0			0
$124$		−	424.265i		−	0.307259i
$125$	−646.207			−0.462388
$126$		0			0
$127$	−778.835			−0.544176			−0.272088	−	0.962272i	$-0.587714\pi$
$127$	−778.835			−0.544176			−0.272088	+	0.962272i	$0.587714\pi$
$128$		−	988.772i		−	0.682781i
$129$		0			0
$130$	796.600			0.537434
$131$	−298.803	+	517.541i	−0.199286	+	0.345174i	−0.948297	−	0.317384i	$-0.897196\pi$
$131$	−298.803	+	517.541i	−0.199286	+	0.345174i	0.749011	+	0.662558i	$0.230529\pi$
$132$		0			0
$133$	2.12866	+	125.367i	0.00138780	+	0.0817344i
$134$			1632.02i			1.05213i
$135$		0			0
$136$	411.136	+	237.370i	0.259225	+	0.149664i
$137$	1018.30	−	587.917i	0.635032	−	0.366636i	−0.147666	−	0.989037i	$-0.547176\pi$
$137$	1018.30	−	587.917i	0.635032	−	0.366636i	0.782698	+	0.622401i	$0.213843\pi$
$138$		0			0
$139$	1061.55	−	612.889i	0.647769	−	0.373990i	−0.139832	−	0.990175i	$-0.544656\pi$
$139$	1061.55	−	612.889i	0.647769	−	0.373990i	0.787601	+	0.616186i	$0.211323\pi$
$140$	−148.217	−	246.940i	−0.0894757	−	0.149073i
$141$		0			0
$142$	−1985.79			−1.17354
$143$	2735.57	−	4738.15i	1.59972	−	2.77080i
$144$		0			0
$145$	−304.124	+	175.586i	−0.174180	+	0.100563i
$146$	−616.613	+	1068.01i	−0.349529	+	0.605402i
$147$		0			0
$148$	373.362	+	646.682i	0.207366	+	0.359169i
$149$	365.439	+	210.986i	0.200926	+	0.116005i	0.597087	−	0.802176i	$-0.296325\pi$
$149$	365.439	+	210.986i	0.200926	+	0.116005i	−0.396161	+	0.918181i	$0.629658\pi$
$150$		0			0
$151$	−682.760	−	1182.58i	−0.367962	−	0.637329i	0.621285	−	0.783585i	$-0.286611\pi$
$151$	−682.760	−	1182.58i	−0.367962	−	0.637329i	−0.989247	+	0.146256i	$0.953278\pi$
$152$	−27.1325	−	46.9949i	−0.0144785	−	0.0250776i
$153$		0			0
$154$	−4684.31	+	79.5369i	−2.45112	+	0.0416186i
$155$	−167.192	−	96.5285i	−0.0866400	−	0.0500217i
$156$		0			0
$157$			1168.21i			0.593844i	0.954902	+	0.296922i	$0.0959602\pi$
$157$			1168.21i			0.593844i	−0.954902	+	0.296922i	$0.904040\pi$
$158$		−	3747.96i		−	1.88716i
$159$		0			0
$160$	508.846	+	293.783i	0.251424	+	0.145160i
$161$	−2007.19	+	1204.74i	−0.982537	+	0.589732i
$162$		0			0
$163$	917.697	+	1589.50i	0.440979	+	0.763798i	0.997762	−	0.0668596i	$-0.0212979\pi$
$163$	917.697	+	1589.50i	0.440979	+	0.763798i	−0.556783	+	0.830658i	$0.687965\pi$
$164$	−28.8510	−	49.9714i	−0.0137371	−	0.0237934i
$165$		0			0
$166$	−3807.17	−	2198.07i	−1.78008	−	1.02773i
$167$	746.502	+	1292.98i	0.345905	+	0.599124i	0.985518	−	0.169573i	$-0.0542388\pi$
$167$	746.502	+	1292.98i	0.345905	+	0.599124i	−0.639613	+	0.768697i	$0.720905\pi$
$168$		0			0
$169$	2139.86	−	3706.35i	0.973994	−	1.68701i
$170$	−507.722	+	293.134i	−0.229062	+	0.132249i
$171$		0			0
$172$	635.549	−	1100.80i	0.281745	−	0.487997i
$173$	780.091			0.342828			0.171414	−	0.985199i	$-0.445166\pi$
$173$	780.091			0.342828			0.171414	+	0.985199i	$0.445166\pi$
$174$		0			0
$175$	2183.66	−	37.0774i	0.943254	−	0.0160159i
$176$	4509.39	−	2603.50i	1.93129	−	1.11503i
$177$		0			0
$178$	−427.706	+	246.936i	−0.180101	+	0.103981i
$179$	−971.797	−	561.067i	−0.405785	−	0.234280i	0.283192	−	0.959063i	$-0.408607\pi$
$179$	−971.797	−	561.067i	−0.405785	−	0.234280i	−0.688977	+	0.724783i	$0.741940\pi$
$180$		0			0
$181$			4283.84i			1.75920i	0.475715	+	0.879600i	$0.342190\pi$
$181$			4283.84i			1.75920i	−0.475715	+	0.879600i	$0.657810\pi$
$182$	−5545.28	+	94.1556i	−2.25848	+	0.0383477i
$183$		0			0
$184$	506.574	−	877.413i	0.202963	−	0.351542i
$185$	339.788			0.135036
$186$		0			0
$187$			4026.55i			1.57460i
$188$	−1086.72			−0.421579
$189$		0			0
$190$	67.0132			0.0255876
$191$		−	1025.25i		−	0.388401i	−0.980962	−	0.194200i	$-0.937789\pi$
$191$		−	1025.25i		−	0.388401i	0.980962	−	0.194200i	$-0.0622112\pi$
$192$		0			0
$193$	−4306.10			−1.60601			−0.803005	−	0.595972i	$-0.796767\pi$
$193$	−4306.10			−1.60601			−0.803005	+	0.595972i	$0.796767\pi$
$194$	−1636.41	+	2834.34i	−0.605604	+	1.04894i
$195$		0			0
$196$	1060.95	+	1701.47i	0.386644	+	0.620071i
$197$			1121.20i			0.405493i	0.979231	+	0.202747i	$0.0649868\pi$
$197$			1121.20i			0.405493i	−0.979231	+	0.202747i	$0.935013\pi$
$198$		0			0
$199$	−3579.81	−	2066.80i	−1.27521	−	0.736241i	−0.299243	−	0.954177i	$-0.596734\pi$
$199$	−3579.81	−	2066.80i	−1.27521	−	0.736241i	−0.975963	+	0.217936i	$0.930068\pi$
$200$	−818.567	+	472.600i	−0.289407	+	0.167089i
$201$		0			0
$202$	−5040.23	+	2909.98i	−1.75559	+	1.01359i
$203$	2096.31	−	1258.23i	0.724787	−	0.435027i
$204$		0			0
$205$	−26.2566			−0.00894558
$206$	−1457.56	+	2524.56i	−0.492975	+	0.853858i
$207$		0			0
$208$	5338.20	−	3082.01i	1.77951	−	1.02740i
$209$	230.127	−	398.592i	0.0761639	−	0.131920i
$210$		0			0
$211$	−157.594	−	272.960i	−0.0514179	−	0.0890585i	0.839171	−	0.543868i	$-0.183041\pi$
$211$	−157.594	−	272.960i	−0.0514179	−	0.0890585i	−0.890589	+	0.454809i	$0.849707\pi$
$212$	1017.48	+	587.440i	0.329625	+	0.190309i
$213$		0			0
$214$	259.674	+	449.768i	0.0829482	+	0.143671i
$215$	−289.200	−	500.908i	−0.0917360	−	0.158891i
$216$		0			0
$217$	1175.27	+	652.191i	0.367660	+	0.204026i
$218$	3869.04	+	2233.79i	1.20204	+	0.693997i
$219$		0			0
$220$			1057.19i			0.323982i
$221$			4766.63i			1.45085i
$222$		0			0
$223$	−2009.02	−	1159.91i	−0.603290	−	0.348310i	0.167045	−	0.985949i	$-0.446578\pi$
$223$	−2009.02	−	1159.91i	−0.603290	−	0.348310i	−0.770335	+	0.637640i	$0.779911\pi$
$224$	−3576.90	−	1984.93i	−1.06693	−	0.592070i
$225$		0			0
$226$	−1465.17	−	2537.75i	−0.431247	−	0.746941i
$227$	−2681.42	−	4644.35i	−0.784017	−	1.35796i	−0.929585	−	0.368609i	$-0.879834\pi$
$227$	−2681.42	−	4644.35i	−0.784017	−	1.35796i	0.145568	−	0.989348i	$-0.453499\pi$
$228$		0			0
$229$	−753.947	−	435.292i	−0.217564	−	0.125611i	0.387258	−	0.921972i	$-0.373422\pi$
$229$	−753.947	−	435.292i	−0.217564	−	0.125611i	−0.604822	+	0.796361i	$0.706756\pi$
$230$	625.581	+	1083.54i	0.179346	+	0.310636i
$231$		0			0
$232$	−529.066	+	916.370i	−0.149719	+	0.259322i
$233$	718.819	−	415.010i	0.202109	−	0.116688i	−0.395530	−	0.918453i	$-0.629439\pi$
$233$	718.819	−	415.010i	0.202109	−	0.116688i	0.597639	+	0.801765i	$0.296106\pi$
$234$		0			0
$235$	−247.249	+	428.248i	−0.0686329	+	0.118876i
$236$	−1043.32			−0.287772
$237$		0			0
$238$	3499.70	−	2100.57i	0.953159	−	0.572099i
$239$	−1663.03	+	960.148i	−0.450093	+	0.259861i	−0.707869	−	0.706343i	$-0.750343\pi$
$239$	−1663.03	+	960.148i	−0.450093	+	0.259861i	0.257777	+	0.966205i	$0.417010\pi$
$240$		0			0
$241$	−770.404	+	444.793i	−0.205917	+	0.118886i	−0.599413	−	0.800440i	$-0.704599\pi$
$241$	−770.404	+	444.793i	−0.205917	+	0.118886i	0.393495	+	0.919327i	$0.371266\pi$
$242$	10604.2	+	6122.34i	2.81680	+	1.62628i
$243$		0			0
$244$		−	1320.93i		−	0.346572i
$245$	911.896	−	30.9759i	0.237791	−	0.00807745i
$246$		0			0
$247$	272.424	−	471.853i	0.0701779	−	0.121552i
$248$	−581.710			−0.148946
$249$		0			0
$250$		−	2404.54i		−	0.608306i
$251$	285.392			0.0717681			0.0358840	−	0.999356i	$-0.488575\pi$
$251$	285.392			0.0717681			0.0358840	+	0.999356i	$0.488575\pi$
$252$		0			0
$253$	8593.13			2.13536
$254$		−	2898.05i		−	0.715906i
$255$		0			0
$256$	5352.46			1.30675
$257$	3521.78	−	6099.90i	0.854795	−	1.48055i	−0.0220391	−	0.999757i	$-0.507016\pi$
$257$	3521.78	−	6099.90i	0.854795	−	1.48055i	0.876835	−	0.480792i	$-0.159651\pi$
$258$		0			0
$259$	−2365.33	+	40.1619i	−0.567469	+	0.00963530i
$260$			1251.50i			0.298519i
$261$		0			0
$262$	−1925.78	−	1111.85i	−0.454103	−	0.262176i
$263$	−318.701	+	184.002i	−0.0747221	+	0.0431408i	−0.536896	−	0.843649i	$-0.680403\pi$
$263$	−318.701	+	184.002i	−0.0747221	+	0.0431408i	0.462173	+	0.886790i	$0.347070\pi$
$264$		0			0
$265$	462.991	−	267.308i	0.107326	−	0.0619645i
$266$	−466.491	+	7.92075i	−0.107528	+	0.00182576i
$267$		0			0
$268$	−2564.00			−0.584408
$269$	−4136.20	+	7164.11i	−0.937504	+	1.62380i	−0.167396	+	0.985890i	$0.553536\pi$
$269$	−4136.20	+	7164.11i	−0.937504	+	1.62380i	−0.770108	+	0.637914i	$0.779798\pi$
$270$		0			0
$271$	4457.05	−	2573.28i	0.999064	−	0.576810i	0.0910927	−	0.995842i	$-0.470964\pi$
$271$	4457.05	−	2573.28i	0.999064	−	0.576810i	0.907971	+	0.419033i	$0.137631\pi$
$272$	−2268.24	+	3928.71i	−0.505634	+	0.875784i
$273$		0			0
$274$	2187.65	+	3789.11i	0.482338	+	0.835433i
$275$	−6942.76	−	4008.41i	−1.52242	−	0.878967i
$276$		0			0
$277$	2350.90	+	4071.87i	0.509934	+	0.883231i	0.999934	+	0.0115088i	$0.00366344\pi$
$277$	2350.90	+	4071.87i	0.509934	+	0.883231i	−0.490000	+	0.871722i	$0.663003\pi$
$278$	2280.57	+	3950.06i	0.492012	+	0.852190i
$279$		0			0
$280$	−338.579	+	203.220i	−0.0722642	+	0.0433740i
$281$	−1320.09	−	762.157i	−0.280250	−	0.161802i	0.353287	−	0.935515i	$-0.385064\pi$
$281$	−1320.09	−	762.157i	−0.280250	−	0.161802i	−0.633537	+	0.773713i	$0.718397\pi$
$282$		0			0
$283$		−	1682.18i		−	0.353341i	−0.984270	−	0.176670i	$-0.943467\pi$
$283$		−	1682.18i		−	0.353341i	0.984270	−	0.176670i	$-0.0565327\pi$
$284$		−	3119.78i		−	0.651849i
$285$		0			0
$286$	17630.7	+	10179.1i	3.64520	+	2.10455i
$287$	182.777	−	3.10345i	0.0375923	−	0.000638296i
$288$		0			0
$289$	702.473	+	1216.72i	0.142982	+	0.247653i
$290$	−653.357	−	1131.65i	−0.132298	−	0.229147i
$291$		0			0
$292$	−1677.90	−	968.735i	−0.336272	−	0.194147i
$293$	2826.07	+	4894.90i	0.563484	+	0.975983i	0.997189	+	0.0749284i	$0.0238728\pi$
$293$	2826.07	+	4894.90i	0.563484	+	0.975983i	−0.433705	+	0.901055i	$0.642794\pi$
$294$		0			0
$295$	−237.375	+	411.146i	−0.0468492	+	0.0811452i
$296$	886.666	−	511.917i	0.174109	−	0.100522i
$297$		0			0
$298$	−785.082	+	1359.80i	−0.152613	+	0.264333i
$299$	10172.5			1.96753
$300$		0			0
$301$	2072.38	+	3452.73i	0.396843	+	0.661170i
$302$	4400.38	−	2540.56i	0.838454	−	0.484082i
$303$		0			0
$304$	449.071	−	259.271i	0.0847237	−	0.0489153i
$305$	−520.544	−	300.536i	−0.0977254	−	0.0564218i
$306$		0			0
$307$		−	6001.21i		−	1.11566i	−0.829956	−	0.557829i	$-0.811634\pi$
$307$		−	6001.21i		−	1.11566i	0.829956	−	0.557829i	$-0.188366\pi$
$308$	−124.957	−	7359.32i	−0.0231172	−	1.36148i
$309$		0			0
$310$	359.184	−	622.124i	0.0658073	−	0.113982i
$311$	−4485.13			−0.817776			−0.408888	−	0.912585i	$-0.634083\pi$
$311$	−4485.13			−0.817776			−0.408888	+	0.912585i	$0.634083\pi$
$312$		0			0
$313$			1310.79i			0.236709i	0.992971	+	0.118355i	$0.0377619\pi$
$313$			1310.79i			0.236709i	−0.992971	+	0.118355i	$0.962238\pi$
$314$	−4346.93			−0.781247
$315$		0			0
$316$	5888.26			1.04823
$317$		−	1942.63i		−	0.344193i	−0.985080	−	0.172097i	$-0.944946\pi$
$317$		−	1942.63i		−	0.344193i	0.985080	−	0.172097i	$-0.0550541\pi$
$318$		0			0
$319$	−8974.67			−1.57519
$320$	−278.186	+	481.832i	−0.0485971	+	0.0841726i
$321$		0			0
$322$	−4482.85	−	7468.77i	−0.775838	−	1.29260i
$323$			400.988i			0.0690760i
$324$		0			0
$325$	−8218.83	−	4745.14i	−1.40276	−	0.809886i
$326$	−5914.54	+	3414.76i	−1.00483	+	0.580142i
$327$		0			0
$328$	−68.5158	+	39.5576i	−0.0115340	+	0.00665915i
$329$	1670.53	−	3010.33i	0.279937	−	0.504453i
$330$		0			0
$331$	−9505.51			−1.57846			−0.789230	−	0.614098i	$-0.789520\pi$
$331$	−9505.51			−1.57846			−0.789230	+	0.614098i	$0.789520\pi$
$332$	3453.30	−	5981.29i	0.570856	−	0.988752i
$333$		0			0
$334$	−4811.19	+	2777.74i	−0.788194	+	0.455064i
$335$	−583.360	+	1010.41i	−0.0951414	+	0.164790i
$336$		0			0
$337$	2613.96	+	4527.51i	0.422527	+	0.731838i	0.996186	−	0.0872564i	$-0.0278099\pi$
$337$	2613.96	+	4527.51i	0.422527	+	0.731838i	−0.573659	+	0.819094i	$0.694477\pi$
$338$	13791.4	+	7962.46i	2.21939	+	1.28136i
$339$		0			0
$340$	−460.530	−	797.661i	−0.0734580	−	0.127233i
$341$	−2466.92	−	4272.82i	−0.391763	−	0.678553i
$342$		0			0
$343$	−6344.21	+	323.412i	−0.998703	+	0.0509114i
$344$	−1509.31	−	871.401i	−0.236560	−	0.136578i
$345$		0			0
$346$			2902.73i			0.451016i
$347$		−	1356.46i		−	0.209852i	−0.994480	−	0.104926i	$-0.966539\pi$
$347$		−	1356.46i		−	0.209852i	0.994480	−	0.104926i	$-0.0334606\pi$
$348$		0			0
$349$	−8379.49	−	4837.90i	−1.28523	−	0.742025i	−0.307427	−	0.951572i	$-0.599468\pi$
$349$	−8379.49	−	4837.90i	−1.28523	−	0.742025i	−0.977799	+	0.209546i	$0.932801\pi$
$350$	137.965	+	8125.44i	0.0210702	+	1.24092i
$351$		0			0
$352$	7508.01	+	13004.3i	1.13687	+	1.96912i
$353$	4696.69	+	8134.90i	0.708157	+	1.22656i	0.965540	+	0.260254i	$0.0838064\pi$
$353$	4696.69	+	8134.90i	0.708157	+	1.22656i	−0.257383	+	0.966309i	$0.582860\pi$
$354$		0			0
$355$	−1229.43	−	709.811i	−0.183806	−	0.106121i
$356$	−387.951	−	671.951i	−0.0577566	−	0.100037i
$357$		0			0
$358$	2087.74	−	3616.07i	0.308213	−	0.533841i
$359$	220.500	−	127.306i	0.0324166	−	0.0187157i	−0.483704	−	0.875232i	$-0.660709\pi$
$359$	220.500	−	127.306i	0.0324166	−	0.0187157i	0.516121	+	0.856516i	$0.327376\pi$
$360$		0			0
$361$	−3406.58	+	5900.37i	−0.496659	+	0.860238i
$362$	−15940.2			−2.31436
$363$		0			0
$364$	−147.924	−	8711.95i	−0.0213003	−	1.25448i
$365$	−763.509	+	440.812i	−0.109490	+	0.0632141i
$366$		0			0
$367$	7588.20	−	4381.05i	1.07929	−	0.623130i	0.148588	−	0.988899i	$-0.452527\pi$
$367$	7588.20	−	4381.05i	1.07929	−	0.623130i	0.930706	+	0.365769i	$0.119194\pi$
$368$	8384.33	+	4840.70i	1.18767	+	0.685703i
$369$		0			0
$370$			1264.36i			0.177651i
$371$	−3191.37	+	1915.50i	−0.446597	+	0.268054i
$372$		0			0
$373$	1785.05	−	3091.79i	0.247792	−	0.429188i	−0.715121	−	0.699001i	$-0.753628\pi$
$373$	1785.05	−	3091.79i	0.247792	−	0.429188i	0.962913	+	0.269813i	$0.0869618\pi$
$374$	−14982.9			−2.07151
$375$		0			0
$376$			1490.00i			0.204363i
$377$	−10624.2			−1.45139
$378$		0			0
$379$	−6856.36			−0.929255			−0.464628	−	0.885506i	$-0.653812\pi$
$379$	−6856.36			−0.929255			−0.464628	+	0.885506i	$0.653812\pi$
$380$			105.282i			0.0142127i
$381$		0			0
$382$	3814.97			0.510970
$383$	−1052.95	+	1823.77i	−0.140479	+	0.243316i	−0.927677	−	0.373384i	$-0.878197\pi$
$383$	−1052.95	+	1823.77i	−0.140479	+	0.243316i	0.787198	+	0.616700i	$0.211531\pi$
$384$		0			0
$385$	−2928.56	−	1625.15i	−0.387670	−	0.215130i
$386$		−	16023.0i		−	2.11283i
$387$		0			0
$388$	−4452.91	−	2570.89i	−0.582635	−	0.336384i
$389$	−6935.64	+	4004.29i	−0.903987	+	0.521917i	−0.878491	−	0.477758i	$-0.841450\pi$
$389$	−6935.64	+	4004.29i	−0.903987	+	0.521917i	−0.0254951	+	0.999675i	$0.508116\pi$
$390$		0			0
$391$	−6483.58	+	3743.30i	−0.838590	+	0.484160i
$392$	2332.89	−	1454.67i	0.300584	−	0.187428i
$393$		0			0
$394$	−4172.00			−0.533457
$395$	1339.69	−	2320.42i	0.170651	−	0.295577i
$396$		0			0
$397$	4606.90	−	2659.79i	0.582402	−	0.336250i	−0.179685	−	0.983724i	$-0.557508\pi$
$397$	4606.90	−	2659.79i	0.582402	−	0.336250i	0.762087	+	0.647474i	$0.224175\pi$
$398$	7690.60	−	13320.5i	0.968581	−	1.67763i
$399$		0			0
$400$	−4516.04	−	7822.01i	−0.564505	−	0.977752i
$401$	3579.53	+	2066.64i	0.445769	+	0.257365i	0.706042	−	0.708170i	$-0.250479\pi$
$401$	3579.53	+	2066.64i	0.445769	+	0.257365i	−0.260273	+	0.965535i	$0.583813\pi$
$402$		0			0
$403$	−2920.33	−	5058.16i	−0.360973	−	0.625223i
$404$	−4571.74	−	7918.49i	−0.563002	−	0.975147i
$405$		0			0
$406$	4681.89	+	7800.38i	0.572311	+	0.953513i
$407$	7520.35	+	4341.88i	0.915897	+	0.528793i
$408$		0			0
$409$		−	1530.28i		−	0.185007i	−0.995712	−	0.0925033i	$-0.970513\pi$
$409$		−	1530.28i		−	0.185007i	0.995712	−	0.0925033i	$-0.0294869\pi$
$410$		−	97.7013i		−	0.0117686i
$411$		0			0
$412$	−3966.23	−	2289.91i	−0.474278	−	0.273824i
$413$	1603.81	−	2890.12i	0.191086	−	0.344342i
$414$		0			0
$415$	−1571.38	−	2721.72i	−0.185870	−	0.321937i
$416$	8887.97	+	15394.4i	1.04752	+	1.81436i
$417$		0			0
$418$	1483.17	+	856.307i	0.173550	+	0.100199i
$419$	4054.18	+	7022.04i	0.472696	+	0.818733i	0.999512	−	0.0312463i	$-0.00994762\pi$
$419$	4054.18	+	7022.04i	0.472696	+	0.818733i	−0.526816	+	0.849979i	$0.676614\pi$
$420$		0			0
$421$	5593.01	−	9687.38i	0.647474	−	1.12146i	−0.336250	−	0.941773i	$-0.609159\pi$
$421$	5593.01	−	9687.38i	0.647474	−	1.12146i	0.983724	−	0.179686i	$-0.0575080\pi$
$422$	1015.69	−	586.407i	0.117163	−	0.0676442i
$423$		0			0
$424$	805.438	−	1395.06i	0.0922536	−	0.159788i
$425$	6984.49			0.797170
$426$		0			0
$427$	3659.12	+	2030.56i	0.414701	+	0.230130i
$428$	−706.611	+	407.962i	−0.0798022	+	0.0460738i
$429$		0			0
$430$	1863.89	−	1076.11i	0.209034	−	0.120686i
$431$	−8537.03	−	4928.85i	−0.954093	−	0.550846i	−0.0597429	−	0.998214i	$-0.519028\pi$
$431$	−8537.03	−	4928.85i	−0.954093	−	0.550846i	−0.894350	+	0.447368i	$0.852361\pi$
$432$		0			0
$433$			7805.42i			0.866292i	0.901324	+	0.433146i	$0.142597\pi$
$433$			7805.42i			0.866292i	−0.901324	+	0.433146i	$0.857403\pi$
$434$	−2426.81	+	4373.18i	−0.268412	+	0.483685i
$435$		0			0
$436$	−3509.41	+	6078.48i	−0.385483	+	0.667676i
$437$	855.755			0.0936757
$438$		0			0
$439$			15722.3i			1.70930i	0.519204	+	0.854650i	$0.326229\pi$
$439$			15722.3i			1.70930i	−0.519204	+	0.854650i	$0.673771\pi$
$440$	1449.52			0.157052
$441$		0			0
$442$	−17736.7			−1.90870
$443$		−	14656.0i		−	1.57184i	−0.618327	−	0.785921i	$-0.712189\pi$
$443$		−	14656.0i		−	1.57184i	0.618327	−	0.785921i	$-0.287811\pi$
$444$		0			0
$445$	−353.065			−0.0376110
$446$	4316.03	−	7475.57i	0.458228	−	0.793674i
$447$		0			0
$448$	1879.55	−	3387.00i	0.198215	−	0.357189i
$449$			2222.19i			0.233567i	0.993157	+	0.116784i	$0.0372584\pi$
$449$			2222.19i			0.233567i	−0.993157	+	0.116784i	$0.962742\pi$
$450$		0			0
$451$	−581.124	−	335.512i	−0.0606742	−	0.0350303i
$452$	3986.95	−	2301.87i	0.414891	−	0.239537i
$453$		0			0
$454$	17281.7	−	9977.58i	1.78650	−	1.03143i
$455$	−3466.82	−	1923.84i	−0.357202	−	0.198222i
$456$		0			0
$457$	10876.2			1.11327			0.556636	−	0.830757i	$-0.312092\pi$
$457$	10876.2			1.11327			0.556636	+	0.830757i	$0.312092\pi$
$458$	1619.73	−	2805.45i	0.165251	−	0.286222i
$459$		0			0
$460$	−1702.30	+	982.824i	−0.172544	+	0.0996183i
$461$	8061.39	−	13962.7i	0.814439	−	1.41065i	−0.0952903	−	0.995450i	$-0.530378\pi$
$461$	8061.39	−	13962.7i	0.814439	−	1.41065i	0.909730	−	0.415201i	$-0.136289\pi$
$462$		0			0
$463$	1001.50	+	1734.65i	0.100526	+	0.174117i	0.911902	−	0.410409i	$-0.134614\pi$
$463$	1001.50	+	1734.65i	0.100526	+	0.174117i	−0.811375	+	0.584525i	$0.801281\pi$
$464$	−8756.59	−	5055.62i	−0.876109	−	0.505822i
$465$		0			0
$466$	1544.26	+	2674.73i	0.153512	+	0.265890i
$467$	−2157.57	−	3737.02i	−0.213791	−	0.370297i	0.739107	−	0.673588i	$-0.235248\pi$
$467$	−2157.57	−	3737.02i	−0.213791	−	0.370297i	−0.952898	+	0.303291i	$0.901914\pi$
$468$		0			0
$469$	3941.45	−	7102.60i	0.388058	−	0.699291i
$470$	−1593.51	−	920.016i	−0.156390	−	0.0902919i
$471$		0			0
$472$			1430.49i			0.139499i
$473$		−	14781.8i		−	1.43693i
$474$		0			0
$475$	−691.401	−	399.181i	−0.0667866	−	0.0385593i
$476$	3300.11	+	5498.23i	0.317774	+	0.529435i
$477$		0			0
$478$	−3572.72	−	6188.14i	−0.341867	−	0.592131i
$479$	−6253.90	−	10832.1i	−0.596551	−	1.03326i	−0.993326	−	0.115340i	$-0.963204\pi$
$479$	−6253.90	−	10832.1i	−0.596551	−	1.03326i	0.396775	−	0.917916i	$-0.370129\pi$
$480$		0			0
$481$	8902.58	+	5139.91i	0.843914	+	0.487234i
$482$	−1655.08	−	2866.68i	−0.156404	−	0.270900i
$483$		0			0
$484$	−9618.56	+	16659.8i	−0.903321	+	1.56460i
$485$	−2026.25	+	1169.85i	−0.189705	+	0.109526i
$486$		0			0
$487$	−3487.77	+	6041.00i	−0.324530	+	0.562102i	−0.981417	−	0.191887i	$-0.938539\pi$
$487$	−3487.77	+	6041.00i	−0.324530	+	0.562102i	0.656887	+	0.753989i	$0.271873\pi$
$488$	−1811.12			−0.168003
$489$		0			0
$490$	115.262	+	3393.17i	0.0106265	+	0.312833i
$491$	−17281.9	+	9977.72i	−1.58844	+	0.917084i	−0.594871	+	0.803821i	$0.702797\pi$
$491$	−17281.9	+	9977.72i	−1.58844	+	0.917084i	−0.993565	+	0.113263i	$0.963870\pi$
$492$		0			0
$493$	6771.45	−	3909.50i	0.618602	−	0.357150i
$494$	1755.77	+	1013.69i	0.159911	+	0.0923244i
$495$		0			0
$496$		−	5558.67i		−	0.503209i
$497$	8642.18	+	4795.81i	0.779989	+	0.432840i
$498$		0			0
$499$	5387.18	−	9330.87i	0.483293	−	0.837088i	−0.516523	−	0.856273i	$-0.672774\pi$
$499$	5387.18	−	9330.87i	0.483293	−	0.837088i	0.999816	+	0.0191853i	$0.00610723\pi$
$500$	3777.67			0.337886
$501$		0			0
$502$			1061.95i			0.0944163i
$503$	2784.15			0.246798			0.123399	−	0.992357i	$-0.460621\pi$
$503$	2784.15			0.246798			0.123399	+	0.992357i	$0.460621\pi$
$504$		0			0
$505$	−4160.64			−0.366626
$506$			31975.1i			2.80923i
$507$		0			0
$508$	4553.01			0.397652
$509$	−8393.47	+	14537.9i	−0.730911	+	1.26598i	0.225583	+	0.974224i	$0.427571\pi$
$509$	−8393.47	+	14537.9i	−0.730911	+	1.26598i	−0.956494	+	0.291751i	$0.905762\pi$
$510$		0			0
$511$	5262.82	−	3158.82i	0.455604	−	0.273460i
$512$			12006.4i			1.03635i
$513$		0			0
$514$	22697.8	+	13104.6i	1.94778	+	1.12455i
$515$	−1804.79	+	1042.00i	−0.154424	+	0.0891570i
$516$		0			0
$517$	−10944.5	+	6318.78i	−0.931018	+	0.537524i
$518$	−149.443	−	8801.42i	−0.0126760	−	0.746548i
$519$		0			0
$520$	1715.94			0.144709
$521$	11145.0	−	19303.7i	0.937181	−	1.62324i	0.166482	−	0.986045i	$-0.446759\pi$
$521$	11145.0	−	19303.7i	0.937181	−	1.62324i	0.770699	−	0.637200i	$-0.219907\pi$
$522$		0			0
$523$	13575.4	−	7837.78i	1.13501	−	0.655301i	0.189823	−	0.981818i	$-0.439209\pi$
$523$	13575.4	−	7837.78i	1.13501	−	0.655301i	0.945191	+	0.326517i	$0.105875\pi$
$524$	1746.78	−	3025.51i	0.145627	−	0.252233i
$525$		0			0
$526$	−684.673	−	1185.89i	−0.0567551	−	0.0983027i
$527$	3722.61	+	2149.25i	0.307703	+	0.177653i
$528$		0			0
$529$	1905.13	+	3299.78i	0.156582	+	0.271208i
$530$	994.655	+	1722.79i	0.0815190	+	0.141195i
$531$		0			0
$532$	−12.4440	−	732.885i	−0.00101412	−	0.0597267i
$533$	−687.933	−	397.178i	−0.0559056	−	0.0322771i
$534$		0			0
$535$			371.277i			0.0300032i
$536$			3515.50i			0.283296i
$537$		0			0
$538$	−26657.7	−	15390.8i	−2.13624	−	1.23336i
$539$	20578.3	+	10966.8i	1.64447	+	0.876388i
$540$		0			0
$541$	7285.01	+	12618.0i	0.578941	+	1.00275i	0.995601	+	0.0936925i	$0.0298671\pi$
$541$	7285.01	+	12618.0i	0.578941	+	1.00275i	−0.416660	+	0.909062i	$0.636800\pi$
$542$	9575.19	+	16584.7i	0.758837	+	1.31434i
$543$		0			0
$544$	−11329.7	−	6541.20i	−0.892935	−	0.515536i
$545$	1596.92	+	2765.94i	0.125513	+	0.217395i
$546$		0			0
$547$	−2097.03	+	3632.16i	−0.163917	+	0.283912i	−0.936270	−	0.351281i	$-0.885746\pi$
$547$	−2097.03	+	3632.16i	−0.163917	+	0.283912i	0.772353	+	0.635193i	$0.219079\pi$
$548$	−5952.92	+	3436.92i	−0.464044	+	0.267916i
$549$		0			0
$550$	14915.3	−	25834.1i	1.15635	−	2.00285i
$551$	−893.750			−0.0691017
$552$		0			0
$553$	−9051.58	+	16311.2i	−0.696044	+	1.25429i
$554$	−15151.5	+	8747.71i	−1.16196	+	0.670857i
$555$		0			0
$556$	−6205.77	+	3582.90i	−0.473351	+	0.273289i
$557$	−6775.49	−	3911.83i	−0.515416	−	0.297575i	0.219641	−	0.975581i	$-0.429511\pi$
$557$	−6775.49	−	3911.83i	−0.515416	−	0.297575i	−0.735057	+	0.678005i	$0.762845\pi$
$558$		0			0
$559$		−	17498.6i		−	1.32399i
$560$	−1941.92	−	3235.38i	−0.146537	−	0.244142i
$561$		0			0
$562$	2836.00	−	4912.09i	0.212863	−	0.368690i
$563$	5309.54			0.397461			0.198731	−	0.980054i	$-0.436318\pi$
$563$	5309.54			0.397461			0.198731	+	0.980054i	$0.436318\pi$
$564$		0			0
$565$		−	2094.88i		−	0.155986i
$566$	6259.42			0.464847
$567$		0			0
$568$	−4277.53			−0.315988
$569$			9561.83i			0.704486i	0.935909	+	0.352243i	$0.114581\pi$
$569$			9561.83i			0.704486i	−0.935909	+	0.352243i	$0.885419\pi$
$570$		0			0
$571$	−4660.92			−0.341600			−0.170800	−	0.985306i	$-0.554635\pi$
$571$	−4660.92			−0.341600			−0.170800	+	0.985306i	$0.554635\pi$
$572$	−15991.9	+	27698.9i	−1.16898	+	2.02473i
$573$		0			0
$574$	11.5480	+	680.116i	0.000839727	+	0.0494556i
$575$		−	14905.7i		−	1.08106i
$576$		0			0
$577$	11960.4	+	6905.37i	0.862946	+	0.498222i	0.864998	−	0.501776i	$-0.167320\pi$
$577$	11960.4	+	6905.37i	0.862946	+	0.498222i	−0.00205155	+	0.999998i	$0.500653\pi$
$578$	−4527.42	+	2613.91i	−0.325806	+	0.188104i
$579$		0			0
$580$	1777.88	−	1026.46i	0.127280	−	0.0734853i
$581$	11260.4	+	18760.6i	0.804061	+	1.33963i
$582$		0			0
$583$	13662.8			0.970594
$584$	−1328.23	+	2300.57i	−0.0941141	+	0.163010i
$585$		0			0
$586$	−18214.0	+	10515.8i	−1.28398	+	0.741307i
$587$	−2615.61	+	4530.36i	−0.183914	+	0.318549i	−0.943210	−	0.332197i	$-0.892210\pi$
$587$	−2615.61	+	4530.36i	−0.183914	+	0.318549i	0.759296	+	0.650745i	$0.225544\pi$
$588$		0			0
$589$	−245.670	−	425.513i	−0.0171862	−	0.0297673i
$590$	−1529.88	−	883.275i	−0.106753	−	0.0616337i
$591$		0			0
$592$	4891.75	+	8472.75i	0.339611	+	0.588223i
$593$	8934.43	+	15474.9i	0.618707	+	1.07163i	0.989722	+	0.143005i	$0.0456765\pi$
$593$	8934.43	+	15474.9i	0.618707	+	1.07163i	−0.371015	+	0.928627i	$0.620990\pi$
$594$		0			0
$595$	2917.55	−	49.5384i	0.201022	−	0.00341324i
$596$	−2136.33	−	1233.41i	−0.146825	−	0.0847692i
$597$		0			0
$598$			37852.1i			2.58844i
$599$		−	14019.3i		−	0.956280i	−0.878284	−	0.478140i	$-0.841311\pi$
$599$		−	14019.3i		−	0.956280i	0.878284	−	0.478140i	$-0.158689\pi$
$600$		0			0
$601$	16180.5	+	9341.82i	1.09820	+	0.634045i	0.935747	−	0.352672i	$-0.114727\pi$
$601$	16180.5	+	9341.82i	1.09820	+	0.634045i	0.162450	+	0.986717i	$0.448060\pi$
$602$	−12847.7	+	7711.34i	−0.869819	+	0.522077i
$603$		0			0
$604$	3991.36	+	6913.25i	0.268885	+	0.465722i
$605$	4376.82	+	7580.87i	0.294120	+	0.509432i
$606$		0			0
$607$	−17484.5	−	10094.7i	−1.16915	−	0.675008i	−0.215668	−	0.976467i	$-0.569193\pi$
$607$	−17484.5	−	10094.7i	−1.16915	−	0.675008i	−0.953479	+	0.301459i	$0.902526\pi$
$608$	747.692	+	1295.04i	0.0498732	+	0.0863829i
$609$		0			0
$610$	1118.30	−	1936.95i	0.0742271	−	0.128565i
$611$	−12956.0	+	7480.16i	−0.857847	+	0.495278i
$612$		0			0
$613$	9593.06	−	16615.7i	0.632072	−	1.09478i	−0.355056	−	0.934845i	$-0.615538\pi$
$613$	9593.06	−	16615.7i	0.632072	−	1.09478i	0.987128	−	0.159935i	$-0.0511285\pi$
$614$	22330.6			1.46773
$615$		0			0
$616$	−10090.4	+	171.329i	−0.659988	+	0.0112062i
$617$	−2177.62	+	1257.25i	−0.142087	+	0.0820340i	−0.569358	−	0.822090i	$-0.692808\pi$
$617$	−2177.62	+	1257.25i	−0.142087	+	0.0820340i	0.427271	+	0.904123i	$0.359475\pi$
$618$		0			0
$619$	−13808.1	+	7972.14i	−0.896601	+	0.517653i	−0.876096	−	0.482137i	$-0.839861\pi$
$619$	−13808.1	+	7972.14i	−0.896601	+	0.517653i	−0.0205054	+	0.999790i	$0.506528\pi$
$620$	977.393	+	564.298i	0.0633114	+	0.0365528i
$621$		0			0
$622$		−	16689.2i		−	1.07585i
$623$	2457.75	−	41.7312i	0.158054	−	0.00268367i
$624$		0			0
$625$	−6510.74	+	11276.9i	−0.416687	+	0.721724i
$626$	−4877.45			−0.311409
$627$		0			0
$628$		−	6829.28i		−	0.433946i
$629$	−7565.55			−0.479584
$630$		0			0
$631$	−17578.2			−1.10900			−0.554500	−	0.832184i	$-0.687090\pi$
$631$	−17578.2			−1.10900			−0.554500	+	0.832184i	$0.687090\pi$
$632$		−	8073.39i		−	0.508136i
$633$		0			0
$634$	7228.56			0.452812
$635$	1035.90	−	1794.23i	0.0647375	−	0.112129i
$636$		0			0
$637$	24360.5	+	12982.5i	1.51523	+	0.807510i
$638$		−	33394.8i		−	2.07228i
$639$		0			0
$640$	2277.87	+	1315.13i	0.140688	+	0.0812265i
$641$	−22423.0	+	12945.9i	−1.38168	+	0.797712i	−0.992358	−	0.123390i	$-0.960623\pi$
$641$	−22423.0	+	12945.9i	−1.38168	+	0.797712i	−0.389320	+	0.921102i	$0.627290\pi$
$642$		0			0
$643$	17292.0	−	9983.55i	1.06054	−	0.612306i	0.134962	−	0.990851i	$-0.456909\pi$
$643$	17292.0	−	9983.55i	1.06054	−	0.612306i	0.925583	+	0.378545i	$0.123575\pi$
$644$	11733.9	−	7042.82i	0.717980	−	0.430941i
$645$		0			0
$646$	−1492.08			−0.0908748
$647$	9164.51	−	15873.4i	0.556869	−	0.964525i	−0.440887	−	0.897563i	$-0.645336\pi$
$647$	9164.51	−	15873.4i	0.556869	−	0.964525i	0.997756	−	0.0669620i	$-0.0213306\pi$
$648$		0			0
$649$	−10507.4	+	6066.44i	−0.635517	+	0.366916i
$650$	17656.7	−	30582.3i	1.06547	−	1.84544i
$651$		0			0
$652$	−5364.79	−	9292.09i	−0.322241	−	0.558138i
$653$	−6907.42	−	3988.00i	−0.413948	−	0.238993i	0.278537	−	0.960426i	$-0.410151\pi$
$653$	−6907.42	−	3988.00i	−0.413948	−	0.238993i	−0.692485	+	0.721433i	$0.743484\pi$
$654$		0			0
$655$	−794.851	−	1376.72i	−0.0474159	−	0.0821267i
$656$	−378.002	−	654.719i	−0.0224977	−	0.0389672i
$657$		0			0
$658$	11201.5	+	6216.05i	0.663647	+	0.368278i
$659$	−14842.8	−	8569.48i	−0.877378	−	0.506554i	−0.00758502	−	0.999971i	$-0.502414\pi$
$659$	−14842.8	−	8569.48i	−0.877378	−	0.506554i	−0.869793	+	0.493417i	$0.835748\pi$
$660$		0			0
$661$		−	30361.4i		−	1.78657i	−0.449493	−	0.893284i	$-0.648395\pi$
$661$		−	30361.4i		−	1.78657i	0.449493	−	0.893284i	$-0.351605\pi$
$662$		−	35370.1i		−	2.07658i
$663$		0			0
$664$	−8200.94	−	4734.81i	−0.479304	−	0.276727i
$665$	−291.643	−	161.842i	−0.0170067	−	0.00943752i
$666$		0			0
$667$	−8343.32	−	14451.1i	−0.484340	−	0.838902i
$668$	−4363.99	−	7558.66i	−0.252766	−	0.437804i
$669$		0			0
$670$	−3759.75	−	2170.69i	−0.216793	−	0.125166i
$671$	−7680.61	−	13303.2i	−0.441887	−	0.765372i
$672$		0			0
$673$	−14629.3	+	25338.6i	−0.837914	+	1.45131i	0.0537214	+	0.998556i	$0.482892\pi$
$673$	−14629.3	+	25338.6i	−0.837914	+	1.45131i	−0.891636	+	0.452754i	$0.850442\pi$
$674$	−16846.9	+	9726.57i	−0.962788	+	0.555866i
$675$		0			0
$676$	−12509.5	+	21667.1i	−0.711737	+	1.23276i
$677$	6426.03			0.364804			0.182402	−	0.983224i	$-0.441613\pi$
$677$	6426.03			0.364804			0.182402	+	0.983224i	$0.441613\pi$
$678$		0			0
$679$	13966.8	−	8383.06i	0.789391	−	0.473803i
$680$	−1093.67	+	631.432i	−0.0616771	+	0.0356093i
$681$		0			0
$682$	15899.2	−	9179.42i	0.892688	−	0.515393i
$683$	25125.5	+	14506.2i	1.40761	+	0.812686i	0.995158	−	0.0982922i	$-0.0313380\pi$
$683$	25125.5	+	14506.2i	1.40761	+	0.812686i	0.412455	+	0.910978i	$0.364671\pi$
$684$		0			0
$685$			3127.86i			0.174466i
$686$	−1203.42	−	23606.9i	−0.0669778	−	1.31387i
$687$		0			0
$688$	8326.89	−	14422.6i	0.461424	−	0.799210i
$689$	16174.0			0.894312
$690$		0			0
$691$		−	9279.68i		−	0.510877i	−0.966825	−	0.255438i	$-0.917780\pi$
$691$		−	9279.68i		−	0.510877i	0.966825	−	0.255438i	$-0.0822198\pi$
$692$	−4560.35			−0.250518
$693$		0			0
$694$	5047.41			0.276076
$695$			3260.72i			0.177966i
$696$		0			0
$697$	584.616			0.0317703
$698$	18001.9	−	31180.2i	0.976191	−	1.69081i
$699$		0			0
$700$	−12765.5	+	216.751i	−0.689274	+	0.0117035i
$701$			12950.9i			0.697784i	0.937163	+	0.348892i	$0.113442\pi$
$701$			12950.9i			0.697784i	−0.937163	+	0.348892i	$0.886558\pi$
$702$		0			0
$703$	748.921	+	432.390i	0.0401794	+	0.0231976i
$704$	−12313.9	+	7109.42i	−0.659228	+	0.380606i
$705$		0			0
$706$	−30270.1	+	17476.4i	−1.61364	+	0.931634i
$707$	28963.0	−	491.775i	1.54069	−	0.0261600i
$708$		0			0
$709$	7871.41			0.416949			0.208475	−	0.978028i	$-0.433150\pi$
$709$	7871.41			0.416949			0.208475	+	0.978028i	$0.433150\pi$
$710$	2641.21	−	4574.72i	0.139610	−	0.241811i
$711$		0			0
$712$	−921.311	+	531.919i	−0.0484938	+	0.0279979i
$713$	4586.75	−	7944.49i	0.240919	−	0.417284i
$714$		0			0
$715$	7276.95	+	12604.1i	0.380619	+	0.659252i
$716$	5681.05	+	3279.96i	0.296523	+	0.171198i
$717$		0			0
$718$	473.706	+	820.484i	0.0246220	+	0.0426465i
$719$	−7688.81	−	13317.4i	−0.398810	−	0.690759i	0.594769	−	0.803896i	$-0.297243\pi$
$719$	−7688.81	−	13317.4i	−0.398810	−	0.690759i	−0.993579	+	0.113137i	$0.963910\pi$
$720$		0			0
$721$	12440.3	−	7466.85i	0.642582	−	0.385686i
$722$	−21955.4	−	12675.9i	−1.13171	−	0.653392i
$723$		0			0
$724$		−	25043.0i		−	1.28552i
$725$			15567.5i			0.797466i
$726$		0			0
$727$	3867.48	+	2232.89i	0.197300	+	0.113911i	0.595395	−	0.803433i	$-0.296995\pi$
$727$	3867.48	+	2232.89i	0.197300	+	0.113911i	−0.398096	+	0.917344i	$0.630329\pi$
$728$	−11945.0	+	202.818i	−0.608117	+	0.0103255i
$729$		0			0
$730$	−1640.27	−	2841.02i	−0.0831630	−	0.144042i
$731$	6439.16	+	11153.0i	0.325802	+	0.564305i
$732$		0			0
$733$	15250.8	+	8805.07i	0.768488	+	0.443687i	0.832335	−	0.554273i	$-0.187004\pi$
$733$	15250.8	+	8805.07i	0.768488	+	0.443687i	−0.0638468	+	0.997960i	$0.520337\pi$
$734$	16301.9	+	28235.8i	0.819776	+	1.41989i
$735$		0			0
$736$	−13959.7	+	24178.9i	−0.699132	+	1.21093i
$737$	−25822.4	+	14908.6i	−1.29061	+	0.745134i
$738$		0			0
$739$	−17415.2	+	30164.1i	−0.866887	+	1.50149i	−0.00172595	+	0.999999i	$0.500549\pi$
$739$	−17415.2	+	30164.1i	−0.866887	+	1.50149i	−0.865161	+	0.501494i	$0.832784\pi$
$740$	−1986.38			−0.0986766
$741$		0			0
$742$	−7127.61	−	11875.1i	−0.352645	−	0.587533i
$743$	−7577.11	+	4374.65i	−0.374128	+	0.216003i	−0.675260	−	0.737579i	$-0.735969\pi$
$743$	−7577.11	+	4374.65i	−0.374128	+	0.216003i	0.301132	+	0.953582i	$0.402635\pi$
$744$		0			0
$745$	−972.112	+	561.249i	−0.0478059	+	0.0276008i
$746$	11504.6	+	6642.18i	0.564629	+	0.325989i
$747$		0			0
$748$		−	23538.9i		−	1.15063i
$749$	−43.8838	−	2584.53i	−0.00214083	−	0.126084i
$750$		0			0
$751$	−6654.76	+	11526.4i	−0.323350	+	0.560058i	−0.981177	−	0.193111i	$-0.938142\pi$
$751$	−6654.76	+	11526.4i	−0.323350	+	0.560058i	0.657827	+	0.753169i	$0.271476\pi$
$752$	−14238.0			−0.690435
$753$		0			0
$754$		−	39532.7i		−	1.90941i
$755$	3632.45			0.175097
$756$		0			0
$757$	−828.798			−0.0397929			−0.0198964	−	0.999802i	$-0.506334\pi$
$757$	−828.798			−0.0397929			−0.0198964	+	0.999802i	$0.506334\pi$
$758$		−	25512.6i		−	1.22251i
$759$		0			0
$760$	144.352			0.00688971
$761$	−505.175	+	874.989i	−0.0240638	+	0.0416798i	−0.877807	−	0.479015i	$-0.840994\pi$
$761$	−505.175	+	874.989i	−0.0240638	+	0.0416798i	0.853743	+	0.520695i	$0.174327\pi$
$762$		0			0
$763$	−11443.4	−	19065.5i	−0.542959	−	0.904610i
$764$			5993.53i			0.283820i
$765$		0			0
$766$	−6786.26	−	3918.05i	−0.320101	−	0.184810i
$767$	−12438.6	+	7181.44i	−0.585570	+	0.338079i
$768$		0			0
$769$	23020.8	−	13291.1i	1.07952	−	0.623263i	0.148755	−	0.988874i	$-0.452473\pi$
$769$	23020.8	−	13291.1i	1.07952	−	0.623263i	0.930768	+	0.365611i	$0.119140\pi$
$770$	6047.19	−	10897.2i	0.283020	−	0.510010i
$771$		0			0
$772$	25173.1			1.17358
$773$	−3029.80	+	5247.77i	−0.140976	+	0.244177i	−0.927864	−	0.372918i	$-0.878357\pi$
$773$	−3029.80	+	5247.77i	−0.140976	+	0.244177i	0.786889	+	0.617095i	$0.211691\pi$
$774$		0			0
$775$	−7411.67	+	4279.13i	−0.343529	+	0.198337i
$776$	−3524.94	+	6105.38i	−0.163065	+	0.282436i
$777$		0			0
$778$	−14900.0	−	25807.6i	−0.686621	−	1.18926i
$779$	−57.8717	−	33.4123i	−0.00266171	−	0.00153674i
$780$		0			0
$781$	−18140.2	−	31419.7i	−0.831123	−	1.43955i
$782$	−13928.9	−	24125.5i	−0.636950	−	1.10323i
$783$		0			0
$784$	13900.4	+	22292.5i	0.633220	+	1.01551i
$785$	−2691.25	−	1553.79i	−0.122363	−	0.0706462i
$786$		0			0
$787$			16971.1i			0.768683i	0.923191	+	0.384342i	$0.125572\pi$
$787$			16971.1i			0.768683i	−0.923191	+	0.384342i	$0.874428\pi$
$788$		−	6554.45i		−	0.296310i
$789$		0			0
$790$	8634.29	+	4985.01i	0.388854	+	0.224505i
$791$	247.608	+	14582.8i	0.0111301	+	0.655507i
$792$		0			0
$793$	−9092.28	−	15748.3i	−0.407158	−	0.705219i
$794$	9897.13	+	17142.3i	0.442363	+	0.766194i
$795$		0			0
$796$	20927.3	+	12082.4i	0.931845	+	0.538001i
$797$	−2055.29	−	3559.87i	−0.0913453	−	0.158215i	0.816732	−	0.577017i	$-0.195783\pi$
$797$	−2055.29	−	3559.87i	−0.0913453	−	0.158215i	−0.908077	+	0.418802i	$0.862450\pi$
$798$		0			0
$799$	5505.11	−	9535.13i	0.243751	−	0.422189i
$800$	22557.3	−	13023.4i	0.996900	−	0.575560i
$801$		0			0
$802$	−7690.00	+	13319.5i	−0.338583	+	0.586443i
$803$	−22531.1			−0.990168
$804$		0			0
$805$	−105.721	−	6226.40i	−0.00462878	−	0.272611i
$806$	18821.5	−	10866.6i	0.822529	−	0.474887i
$807$		0			0
$808$	−10857.0	+	6268.31i	−0.472709	+	0.272919i
$809$	−15968.0	−	9219.15i	−0.693951	−	0.400653i	0.111140	−	0.993805i	$-0.464550\pi$
$809$	−15968.0	−	9219.15i	−0.693951	−	0.400653i	−0.805090	+	0.593152i	$0.797883\pi$
$810$		0			0
$811$			36653.8i			1.58704i	0.608544	+	0.793520i	$0.291754\pi$
$811$			36653.8i			1.58704i	−0.608544	+	0.793520i	$0.708246\pi$
$812$	−12254.8	+	7355.52i	−0.529631	+	0.317892i
$813$		0			0
$814$	−16156.2	+	27983.3i	−0.695668	+	1.20493i
$815$	−4882.37			−0.209843
$816$		0			0
$817$		−	1472.06i		−	0.0630364i
$818$	5694.20			0.243390
$819$		0			0
$820$	153.494			0.00653690
$821$			17274.6i			0.734334i	0.930155	+	0.367167i	$0.119672\pi$
$821$			17274.6i			0.734334i	−0.930155	+	0.367167i	$0.880328\pi$
$822$		0			0
$823$	−10420.9			−0.441374			−0.220687	−	0.975345i	$-0.570830\pi$
$823$	−10420.9			−0.441374			−0.220687	+	0.975345i	$0.570830\pi$
$824$	−3139.69	+	5438.10i	−0.132738	+	0.229909i
$825$		0			0
$826$	10754.2	+	5967.81i	0.453008	+	0.251388i
$827$			28826.1i			1.21207i	0.795438	+	0.606034i	$0.207241\pi$
$827$			28826.1i			1.21207i	−0.795438	+	0.606034i	$0.792759\pi$
$828$		0			0
$829$	4447.48	+	2567.75i	0.186330	+	0.107577i	0.590263	−	0.807211i	$-0.299024\pi$
$829$	4447.48	+	2567.75i	0.186330	+	0.107577i	−0.403934	+	0.914788i	$0.632357\pi$
$830$	10127.5	−	5847.14i	0.423532	−	0.244527i
$831$		0			0
$832$	−14577.1	+	8416.12i	−0.607418	+	0.350693i
$833$	−20303.8	+	689.692i	−0.844519	+	0.0286872i
$834$		0			0
$835$	−3971.57			−0.164601
$836$	−1345.31	+	2330.14i	−0.0556560	+	0.0963991i
$837$		0			0
$838$	−26129.1	+	15085.6i	−1.07711	+	0.621867i
$839$	−4274.18	+	7403.10i	−0.175877	+	0.304629i	−0.940465	−	0.339892i	$-0.889610\pi$
$839$	−4274.18	+	7403.10i	−0.175877	+	0.304629i	0.764587	+	0.644520i	$0.222943\pi$
$840$		0			0
$841$	−3480.73	−	6028.81i	−0.142717	−	0.247194i
$842$	36046.8	+	20811.7i	1.47536	+	0.851802i
$843$		0			0
$844$	921.280	+	1595.70i	0.0375732	+	0.0650786i
$845$	5692.30	+	9859.35i	0.231741	+	0.401387i
$846$		0			0
$847$	−31363.8	−	52254.5i	−1.27234	−	2.11982i
$848$	13330.8	+	7696.56i	0.539838	+	0.311676i
$849$		0			0
$850$			25989.3i			1.04874i
$851$			16145.8i			0.650375i
$852$		0			0
$853$	−37121.9	−	21432.3i	−1.49007	−	0.860292i	−0.490133	−	0.871648i	$-0.663052\pi$
$853$	−37121.9	−	21432.3i	−1.49007	−	0.860292i	−0.999936	+	0.0113561i	$0.996385\pi$
$854$	−7555.73	+	13615.6i	−0.302754	+	0.545571i
$855$		0			0
$856$	559.357	+	968.835i	0.0223346	+	0.0386847i
$857$	−9985.95	−	17296.2i	−0.398032	−	0.689412i	0.595451	−	0.803392i	$-0.296973\pi$
$857$	−9985.95	−	17296.2i	−0.398032	−	0.689412i	−0.993483	+	0.113980i	$0.963640\pi$
$858$		0			0
$859$	29246.4	+	16885.4i	1.16167	+	0.670690i	0.951704	−	0.307018i	$-0.0993313\pi$
$859$	29246.4	+	16885.4i	1.16167	+	0.670690i	0.209966	+	0.977709i	$0.432665\pi$
$860$	1690.64	+	2928.27i	0.0670352	+	0.116108i
$861$		0			0
$862$	18340.3	−	31766.4i	0.724680	−	1.25518i
$863$	36583.9	−	21121.7i	1.44302	−	0.833130i	0.444974	−	0.895544i	$-0.353213\pi$
$863$	36583.9	−	21121.7i	1.44302	−	0.833130i	0.998050	+	0.0624134i	$0.0198797\pi$
$864$		0			0
$865$	−1037.57	+	1797.12i	−0.0407843	+	0.0706404i
$866$	−29044.1			−1.13967
$867$		0			0
$868$	−6870.51	−	3812.66i	−0.268664	−	0.149090i
$869$	59301.4	−	34237.7i	2.31491	−	1.33652i
$870$		0			0
$871$	−30568.5	+	17648.7i	−1.18918	+	0.686572i
$872$	8334.20	+	4811.75i	0.323660	+	0.186865i
$873$		0			0
$874$			3184.27i			0.123238i
$875$	−5807.14	+	10464.6i	−0.224362	+	0.404307i
$876$		0			0
$877$	−17959.7	+	31107.0i	−0.691510	+	1.19773i	0.279833	+	0.960049i	$0.409721\pi$
$877$	−17959.7	+	31107.0i	−0.691510	+	1.19773i	−0.971343	+	0.237682i	$0.923612\pi$
$878$	−58502.7			−2.24872
$879$		0			0
$880$			13851.2i			0.530597i
$881$	−1190.21			−0.0455154			−0.0227577	−	0.999741i	$-0.507245\pi$
$881$	−1190.21			−0.0455154			−0.0227577	+	0.999741i	$0.507245\pi$
$882$		0			0
$883$	26696.9			1.01747			0.508733	−	0.860924i	$-0.330114\pi$
$883$	26696.9			1.01747			0.508733	+	0.860924i	$0.330114\pi$
$884$		−	27865.3i		−	1.06020i
$885$		0			0
$886$	54535.0			2.06788
$887$	−4987.96	+	8639.39i	−0.188815	+	0.327038i	−0.944856	−	0.327487i	$-0.893798\pi$
$887$	−4987.96	+	8639.39i	−0.188815	+	0.327038i	0.756040	+	0.654525i	$0.227131\pi$
$888$		0			0
$889$	−6999.00	+	12612.4i	−0.264048	+	0.475822i
$890$		−	1313.76i		−	0.0494802i
$891$		0			0
$892$	11744.6	+	6780.72i	0.440849	+	0.254524i
$893$	−1089.91	+	629.261i	−0.0408427	+	0.0235805i
$894$		0			0
$895$	2585.10	−	1492.51i	0.0965478	−	0.0557419i
$896$	−16012.1	−	8885.60i	−0.597016	−	0.331303i
$897$		0			0
$898$	−8268.80			−0.307276
$899$	−4790.40	+	8297.22i	−0.177718	+	0.307817i
$900$		0			0
$901$	−10308.7	+	5951.73i	−0.381168	+	0.220068i
$902$	1248.44	−	2162.37i	0.0460850	−	0.0798215i
$903$		0			0
$904$	−3156.09	−	5466.51i	−0.116117	−	0.201121i
$905$	−9868.82	−	5697.76i	−0.362487	−	0.209282i
$906$		0			0
$907$	23272.0	+	40308.3i	0.851968	+	1.47565i	0.879429	+	0.476029i	$0.157924\pi$
$907$	23272.0	+	40308.3i	0.851968	+	1.47565i	−0.0274610	+	0.999623i	$0.508742\pi$
$908$	15675.4	+	27150.5i	0.572913	+	0.992314i
$909$		0			0
$910$	7158.65	−	12900.1i	0.260777	−	0.469927i
$911$	15539.5	+	8971.75i	0.565145	+	0.326287i	0.755208	−	0.655485i	$-0.227536\pi$
$911$	15539.5	+	8971.75i	0.565145	+	0.326287i	−0.190063	+	0.981772i	$0.560869\pi$
$912$		0			0
$913$		−	80317.7i		−	2.91142i
$914$			40470.3i			1.46459i
$915$		0			0
$916$	4407.52	+	2544.68i	0.158983	+	0.0917889i
$917$	5695.83	+	9489.67i	0.205118	+	0.341741i
$918$		0			0
$919$	23381.4	+	40497.8i	0.839262	+	1.45364i	0.890513	+	0.454959i	$0.150346\pi$
$919$	23381.4	+	40497.8i	0.839262	+	1.45364i	−0.0512505	+	0.998686i	$0.516321\pi$
$920$	1347.55	+	2334.02i	0.0482906	+	0.0836418i
$921$		0			0
$922$	51955.5	+	29996.5i	1.85582	+	1.07146i
$923$	−21474.3	−	37194.6i	−0.765802	−	1.32641i
$924$		0			0
$925$	7531.45	−	13044.9i	0.267711	−	0.463689i
$926$	−6454.65	+	3726.59i	−0.229064	+	0.132250i
$927$		0			0
$928$	14579.5	−	25252.4i	0.515728	−	0.893267i
$929$	32305.0			1.14090			0.570448	−	0.821334i	$-0.306770\pi$
$929$	32305.0			1.14090			0.570448	+	0.821334i	$0.306770\pi$
$930$		0			0
$931$	2049.31	+	1092.14i	0.0721411	+	0.0384461i
$932$	−4202.16	+	2426.12i	−0.147689	+	0.0852684i
$933$		0			0
$934$	13905.5	−	8028.34i	0.487154	−	0.281258i
$935$	−9276.10	−	5355.56i	−0.324450	−	0.187321i
$936$		0			0
$937$			41840.0i			1.45875i	0.684112	+	0.729377i	$0.260190\pi$
$937$			41840.0i			1.45875i	−0.684112	+	0.729377i	$0.739810\pi$
$938$	26428.8	+	14666.2i	0.919970	+	0.510520i
$939$		0			0
$940$	1445.40	−	2503.50i	0.0501529	−	0.0868673i
$941$	11715.2			0.405851			0.202925	−	0.979194i	$-0.434955\pi$
$941$	11715.2			0.405851			0.202925	+	0.979194i	$0.434955\pi$
$942$		0			0
$943$		−	1247.64i		−	0.0430845i
$944$	−13669.4			−0.471294
$945$		0			0
$946$	55003.1			1.89039
$947$			21808.2i			0.748334i	0.927361	+	0.374167i	$0.122071\pi$
$947$			21808.2i			0.748334i	−0.927361	+	0.374167i	$0.877929\pi$
$948$		0			0
$949$	−26672.3			−0.912348
$950$	1485.36	−	2572.71i	0.0507277	−	0.0878629i
$951$		0			0
$952$	7538.62	−	4524.78i	0.256647	−	0.154043i
$953$			55925.7i			1.90096i	0.310793	+	0.950478i	$0.399406\pi$
$953$			55925.7i			1.90096i	−0.310793	+	0.950478i	$0.600594\pi$
$954$		0			0
$955$	2361.90	+	1363.64i	0.0800307	+	0.0462058i
$956$	9721.92	−	5612.95i	0.328901	−	0.189891i
$957$		0			0
$958$	40306.2	−	23270.8i	1.35933	−	0.784808i
$959$	−369.703	−	21773.6i	−0.0124487	−	0.733166i
$960$		0			0
$961$	24523.9			0.823200
$962$	−19125.6	+	33126.6i	−0.640993	+	1.11023i
$963$		0			0
$964$	4503.72	−	2600.23i	0.150472	−	0.0868751i
$965$	5727.37	−	9920.10i	0.191058	−	0.330922i
$966$		0			0
$967$	26409.9	+	45743.3i	0.878268	+	1.52121i	0.853240	+	0.521519i	$0.174634\pi$
$967$	26409.9	+	45743.3i	0.878268	+	1.52121i	0.0250283	+	0.999687i	$0.492032\pi$
$968$	22842.3	+	13188.0i	0.758449	+	0.437891i
$969$		0			0
$970$	−4353.04	−	7539.68i	−0.144090	−	0.249572i
$971$	−11419.3	−	19778.9i	−0.377409	−	0.653691i	0.613276	−	0.789869i	$-0.289852\pi$
$971$	−11419.3	−	19778.9i	−0.377409	−	0.653691i	−0.990684	+	0.136178i	$0.956518\pi$
$972$		0			0
$973$	−385.407	−	22698.5i	−0.0126984	−	0.747871i
$974$	−22478.6	−	12978.0i	−0.739488	−	0.426944i
$975$		0			0
$976$		−	17306.6i		−	0.567593i
$977$		−	22509.2i		−	0.737087i	−0.929610	−	0.368544i	$-0.879857\pi$
$977$		−	22509.2i		−	0.737087i	0.929610	−	0.368544i	$-0.120143\pi$
$978$		0			0
$979$	−7814.20	−	4511.53i	−0.255100	−	0.147282i
$980$	−5330.87	+	181.083i	−0.173764	+	0.00590252i
$981$		0			0
$982$	−37127.2	−	64306.2i	−1.20649	−	2.08971i
$983$	−10425.4	−	18057.4i	−0.338271	−	0.585902i	0.645837	−	0.763475i	$-0.276509\pi$
$983$	−10425.4	−	18057.4i	−0.338271	−	0.585902i	−0.984108	+	0.177574i	$0.943175\pi$
$984$		0			0
$985$	−2582.94	−	1491.26i	−0.0835528	−	0.0482392i
$986$	14547.3	+	25196.6i	0.469858	+	0.813818i
$987$		0			0
$988$	−1592.57	+	2758.42i	−0.0512818	+	0.0888228i
$989$	23801.7	−	13741.9i	0.765268	−	0.441828i
$990$		0			0
$991$	961.363	−	1665.13i	0.0308160	−	0.0533749i	−0.850206	−	0.526450i	$-0.823523\pi$
$991$	961.363	−	1665.13i	0.0308160	−	0.0533749i	0.881022	+	0.473075i	$0.156856\pi$
$992$	16030.2			0.513064
$993$		0			0
$994$	−17845.3	+	32157.6i	−0.569434	+	1.02613i
$995$	9522.73	−	5497.95i	0.303408	−	0.175173i
$996$		0			0
$997$	−22391.7	+	12927.9i	−0.711287	+	0.410662i	−0.811537	−	0.584301i	$-0.801369\pi$
$997$	−22391.7	+	12927.9i	−0.711287	+	0.410662i	0.100251	+	0.994962i	$0.468036\pi$
$998$	34720.3	+	20045.8i	1.10125	+	0.635809i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.i.a.143.19		44
3.2	odd	2		63.4.i.a.38.4	yes	44
7.5	odd	6		189.4.s.a.89.19		44
9.4	even	3		63.4.s.a.59.4	yes	44
9.5	odd	6		189.4.s.a.17.19		44
21.5	even	6		63.4.s.a.47.4	yes	44
63.5	even	6	inner	189.4.i.a.152.4		44
63.40	odd	6		63.4.i.a.5.19	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.19	✓	44	63.40	odd	6
63.4.i.a.38.4	yes	44	3.2	odd	2
63.4.s.a.47.4	yes	44	21.5	even	6
63.4.s.a.59.4	yes	44	9.4	even	3
189.4.i.a.143.19		44	1.1	even	1	trivial
189.4.i.a.152.4		44	63.5	even	6	inner
189.4.s.a.17.19		44	9.5	odd	6
189.4.s.a.89.19		44	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+3.72101i q^{2} -5.84592 q^{4} +(-1.33006 + 2.30373i) q^{5} +(8.98650 - 16.1939i) q^{7} +8.01534i q^{8} +O(q^{10})\)	\(q+3.72101i q^{2} -5.84592 q^{4} +(-1.33006 + 2.30373i) q^{5} +(8.98650 - 16.1939i) q^{7} +8.01534i q^{8} +(-8.57221 - 4.94917i) q^{10} +(-58.8750 + 33.9915i) q^{11} +(-69.6961 + 40.2391i) q^{13} +(60.2577 + 33.4389i) q^{14} -76.5926 q^{16} +(29.6144 - 51.2937i) q^{17} +(-5.86312 + 3.38507i) q^{19} +(7.77543 - 13.4674i) q^{20} +(-126.483 - 219.075i) q^{22} +(-109.467 - 63.2006i) q^{23} +(58.9619 + 102.125i) q^{25} +(-149.730 - 259.340i) q^{26} +(-52.5344 + 94.6684i) q^{28} +(114.327 + 66.0067i) q^{29} +72.5745i q^{31} -220.879i q^{32} +(190.864 + 110.196i) q^{34} +(25.3539 + 42.2414i) q^{35} +(-63.8671 - 110.621i) q^{37} +(-12.5959 - 21.8167i) q^{38} +(-18.4652 - 10.6609i) q^{40} +(4.93523 + 8.54808i) q^{41} +(-108.717 + 188.303i) q^{43} +(344.179 - 198.712i) q^{44} +(235.170 - 407.327i) q^{46} +185.893 q^{47} +(-181.486 - 291.053i) q^{49} +(-380.008 + 219.398i) q^{50} +(407.438 - 235.235i) q^{52} +(-174.049 - 100.487i) q^{53} -180.843i q^{55} +(129.800 + 72.0299i) q^{56} +(-245.612 + 425.412i) q^{58} +178.469 q^{59} +225.957i q^{61} -270.051 q^{62} +209.153 q^{64} -214.082i q^{65} +438.597 q^{67} +(-173.124 + 299.859i) q^{68} +(-157.181 + 94.3420i) q^{70} +533.668i q^{71} +(287.020 + 165.711i) q^{73} +(411.622 - 237.650i) q^{74} +(34.2753 - 19.7889i) q^{76} +(21.3751 + 1258.88i) q^{77} -1007.24 q^{79} +(101.873 - 176.449i) q^{80} +(-31.8075 + 18.3641i) q^{82} +(-590.719 + 1023.16i) q^{83} +(78.7779 + 136.447i) q^{85} +(-700.677 - 404.536i) q^{86} +(-272.454 - 471.903i) q^{88} +(66.3626 + 114.943i) q^{89} +(25.3038 + 1490.26i) q^{91} +(639.934 + 369.466i) q^{92} +691.710i q^{94} -18.0094i q^{95} +(761.712 + 439.775i) q^{97} +(1083.01 - 675.310i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) \) 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7	\( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7} - 6 q^{10} - 9 q^{11} - 36 q^{13} - 54 q^{14} + 526 q^{16} + 72 q^{17} - 6 q^{19} - 24 q^{20} + 14 q^{22} + 285 q^{23} - 349 q^{25} + 96 q^{26} - 156 q^{28} + 132 q^{29} + 24 q^{34} - 765 q^{35} + 82 q^{37} + 873 q^{38} + 420 q^{40} - 618 q^{41} + 82 q^{43} - 603 q^{44} + 266 q^{46} + 402 q^{47} - 79 q^{49} + 1845 q^{50} + 189 q^{52} - 564 q^{53} - 66 q^{56} + 269 q^{58} - 1494 q^{59} + 2904 q^{62} - 1144 q^{64} - 590 q^{67} - 3504 q^{68} - 105 q^{70} - 6 q^{73} - 1515 q^{74} - 144 q^{76} + 4443 q^{77} + 1102 q^{79} + 4239 q^{80} + 18 q^{82} - 1830 q^{83} - 237 q^{85} - 1209 q^{86} - 623 q^{88} - 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 792 q^{97} - 5667 q^{98}+O(q^{100}) \) 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7 - 6 * q^10 - 9 * q^11 - 36 * q^13 - 54 * q^14 + 526 * q^16 + 72 * q^17 - 6 * q^19 - 24 * q^20 + 14 * q^22 + 285 * q^23 - 349 * q^25 + 96 * q^26 - 156 * q^28 + 132 * q^29 + 24 * q^34 - 765 * q^35 + 82 * q^37 + 873 * q^38 + 420 * q^40 - 618 * q^41 + 82 * q^43 - 603 * q^44 + 266 * q^46 + 402 * q^47 - 79 * q^49 + 1845 * q^50 + 189 * q^52 - 564 * q^53 - 66 * q^56 + 269 * q^58 - 1494 * q^59 + 2904 * q^62 - 1144 * q^64 - 590 * q^67 - 3504 * q^68 - 105 * q^70 - 6 * q^73 - 1515 * q^74 - 144 * q^76 + 4443 * q^77 + 1102 * q^79 + 4239 * q^80 + 18 * q^82 - 1830 * q^83 - 237 * q^85 - 1209 * q^86 - 623 * q^88 - 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 792 * q^97 - 5667 * q^98

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