LMFDB - Embedded newform 189.4.g.a.100.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("189.100");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.10
Character	$\chi$	$=$	189.100
Dual form			189.4.g.a.172.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.295387 - 0.511626i) q^{2} +(3.82549 - 6.62595i) q^{4} -10.9845 q^{5} +(1.43976 + 18.4642i) q^{7} -9.24621 q^{8} +O(q^{10})$	\(q+(-0.295387 - 0.511626i) q^{2} +(3.82549 - 6.62595i) q^{4} -10.9845 q^{5} +(1.43976 + 18.4642i) q^{7} -9.24621 q^{8} +(3.24467 + 5.61993i) q^{10} -45.7848 q^{11} +(37.1957 + 64.4248i) q^{13} +(9.02148 - 6.19071i) q^{14} +(-27.8727 - 48.2770i) q^{16} +(40.4681 + 70.0928i) q^{17} +(8.05953 - 13.9595i) q^{19} +(-42.0210 + 72.7824i) q^{20} +(13.5242 + 23.4247i) q^{22} +134.120 q^{23} -4.34174 q^{25} +(21.9743 - 38.0606i) q^{26} +(127.851 + 61.0949i) q^{28} +(-114.686 + 198.643i) q^{29} +(-45.8326 + 79.3844i) q^{31} +(-53.4513 + 92.5804i) q^{32} +(23.9075 - 41.4091i) q^{34} +(-15.8150 - 202.819i) q^{35} +(5.76196 - 9.98001i) q^{37} -9.52273 q^{38} +101.565 q^{40} +(-56.3705 - 97.6366i) q^{41} +(-248.834 + 430.992i) q^{43} +(-175.149 + 303.367i) q^{44} +(-39.6174 - 68.6194i) q^{46} +(-41.4773 - 71.8409i) q^{47} +(-338.854 + 53.1680i) q^{49} +(1.28250 + 2.22135i) q^{50} +569.167 q^{52} +(247.056 + 427.914i) q^{53} +502.921 q^{55} +(-13.3123 - 170.724i) q^{56} +135.508 q^{58} +(129.500 - 224.301i) q^{59} +(-80.8264 - 139.995i) q^{61} +54.1535 q^{62} -382.808 q^{64} +(-408.574 - 707.671i) q^{65} +(146.935 - 254.499i) q^{67} +619.242 q^{68} +(-99.0961 + 68.0016i) q^{70} -249.873 q^{71} +(-398.968 - 691.033i) q^{73} -6.80805 q^{74} +(-61.6633 - 106.804i) q^{76} +(-65.9190 - 845.380i) q^{77} +(-370.412 - 641.572i) q^{79} +(306.167 + 530.296i) q^{80} +(-33.3023 + 57.6813i) q^{82} +(-215.540 + 373.327i) q^{83} +(-444.520 - 769.932i) q^{85} +294.009 q^{86} +423.335 q^{88} +(224.168 - 388.270i) q^{89} +(-1136.00 + 779.545i) q^{91} +(513.076 - 888.674i) q^{92} +(-24.5038 + 42.4418i) q^{94} +(-88.5295 + 153.338i) q^{95} +(125.941 - 218.136i) q^{97} +(127.295 + 157.661i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) $ 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8	$ 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} + 10 q^{11} - 14 q^{13} + 79 q^{14} - 247 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} - 186 q^{23} + 698 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} + 61 q^{31} + 163 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} - 1522 q^{38} + 36 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} + 1005 q^{47} - 277 q^{49} - 239 q^{50} + 670 q^{52} - 258 q^{53} - 870 q^{55} - 714 q^{56} - 474 q^{58} + 1665 q^{59} + 439 q^{61} - 1812 q^{62} + 872 q^{64} + 613 q^{65} + 295 q^{67} - 2748 q^{68} - 1044 q^{70} - 636 q^{71} - 338 q^{73} + 2238 q^{74} + 1006 q^{76} + 2909 q^{77} + 133 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} - 6686 q^{86} - 738 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} - 1191 q^{94} - 3083 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) $ 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 + 10 * q^11 - 14 * q^13 + 79 * q^14 - 247 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 - 186 * q^23 + 698 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 + 61 * q^31 + 163 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 - 1522 * q^38 + 36 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 + 1005 * q^47 - 277 * q^49 - 239 * q^50 + 670 * q^52 - 258 * q^53 - 870 * q^55 - 714 * q^56 - 474 * q^58 + 1665 * q^59 + 439 * q^61 - 1812 * q^62 + 872 * q^64 + 613 * q^65 + 295 * q^67 - 2748 * q^68 - 1044 * q^70 - 636 * q^71 - 338 * q^73 + 2238 * q^74 + 1006 * q^76 + 2909 * q^77 + 133 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 - 6686 * q^86 - 738 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 - 1191 * q^94 - 3083 * q^95 - 266 * q^97 - 3601 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.295387	−	0.511626i	−0.104435	−	0.180887i	0.809072	−	0.587709i	$-0.199970\pi$
$2$	−0.295387	−	0.511626i	−0.104435	−	0.180887i	−0.913507	+	0.406822i	$0.866637\pi$
$3$		0			0
$3$		0			0
$4$	3.82549	−	6.62595i	0.478187	−	0.828243i
$5$	−10.9845			−0.982480			−0.491240	−	0.871024i	$-0.663456\pi$
$5$	−10.9845			−0.982480			−0.491240	+	0.871024i	$0.663456\pi$
$6$		0			0
$7$	1.43976	+	18.4642i	0.0777397	+	0.996974i
$7$	1.43976	+	18.4642i	0.0777397	+	0.996974i
$8$	−9.24621			−0.408629
$9$		0			0
$10$	3.24467	+	5.61993i	0.102605	+	0.177718i
$11$	−45.7848			−1.25497			−0.627483	−	0.778630i	$-0.715915\pi$
$11$	−45.7848			−1.25497			−0.627483	+	0.778630i	$0.715915\pi$
$12$		0			0
$13$	37.1957	+	64.4248i	0.793556	+	1.37448i	0.923752	+	0.382991i	$0.125106\pi$
$13$	37.1957	+	64.4248i	0.793556	+	1.37448i	−0.130196	+	0.991488i	$0.541561\pi$
$14$	9.02148	−	6.19071i	0.172221	−	0.118181i
$15$		0			0
$16$	−27.8727	−	48.2770i	−0.435511	−	0.754328i
$17$	40.4681	+	70.0928i	0.577351	+	1.00000i	0.995782	+	0.0917521i	$0.0292467\pi$
$17$	40.4681	+	70.0928i	0.577351	+	1.00000i	−0.418431	+	0.908248i	$0.637420\pi$
$18$		0			0
$19$	8.05953	−	13.9595i	0.0973149	−	0.168554i	−0.813258	−	0.581904i	$-0.802308\pi$
$19$	8.05953	−	13.9595i	0.0973149	−	0.168554i	0.910572	+	0.413350i	$0.135641\pi$
$20$	−42.0210	+	72.7824i	−0.469809	+	0.813732i
$21$		0			0
$22$	13.5242	+	23.4247i	0.131063	+	0.227007i
$23$	134.120			1.21591			0.607957	−	0.793970i	$-0.291989\pi$
$23$	134.120			1.21591			0.607957	+	0.793970i	$0.291989\pi$
$24$		0			0
$25$	−4.34174			−0.0347339
$26$	21.9743	−	38.0606i	0.165750	−	0.287088i
$27$		0			0
$28$	127.851	+	61.0949i	0.862911	+	0.412352i
$29$	−114.686	+	198.643i	−0.734370	+	1.27197i	0.220629	+	0.975358i	$0.429189\pi$
$29$	−114.686	+	198.643i	−0.734370	+	1.27197i	−0.954999	+	0.296609i	$0.904144\pi$
$30$		0			0
$31$	−45.8326	+	79.3844i	−0.265541	+	0.459931i	−0.967705	−	0.252084i	$-0.918884\pi$
$31$	−45.8326	+	79.3844i	−0.265541	+	0.459931i	0.702164	+	0.712015i	$0.252217\pi$
$32$	−53.4513	+	92.5804i	−0.295280	+	0.511440i
$33$		0			0
$34$	23.9075	−	41.4091i	0.120591	−	0.208871i
$35$	−15.8150	−	202.819i	−0.0763777	−	0.979506i
$36$		0			0
$37$	5.76196	−	9.98001i	0.0256016	−	0.0443434i	−0.852941	−	0.522008i	$-0.825183\pi$
$37$	5.76196	−	9.98001i	0.0256016	−	0.0443434i	0.878542	+	0.477664i	$0.158517\pi$
$38$	−9.52273			−0.0406524
$39$		0			0
$40$	101.565			0.401469
$41$	−56.3705	−	97.6366i	−0.214722	−	0.371909i	0.738465	−	0.674292i	$-0.235551\pi$
$41$	−56.3705	−	97.6366i	−0.214722	−	0.371909i	−0.953187	+	0.302383i	$0.902218\pi$
$42$		0			0
$43$	−248.834	+	430.992i	−0.882483	+	1.52851i	−0.0339110	+	0.999425i	$0.510796\pi$
$43$	−248.834	+	430.992i	−0.882483	+	1.52851i	−0.848572	+	0.529080i	$0.822537\pi$
$44$	−175.149	+	303.367i	−0.600108	+	1.03942i
$45$		0			0
$46$	−39.6174	−	68.6194i	−0.126984	−	0.219943i
$47$	−41.4773	−	71.8409i	−0.128725	−	0.222959i	0.794458	−	0.607320i	$-0.207755\pi$
$47$	−41.4773	−	71.8409i	−0.128725	−	0.222959i	−0.923183	+	0.384361i	$0.874422\pi$
$48$		0			0
$49$	−338.854	+	53.1680i	−0.987913	+	0.155009i
$50$	1.28250	+	2.22135i	0.00362745	+	0.00628292i
$51$		0			0
$52$	569.167			1.51787
$53$	247.056	+	427.914i	0.640298	+	1.10903i	0.985366	+	0.170451i	$0.0545226\pi$
$53$	247.056	+	427.914i	0.640298	+	1.10903i	−0.345068	+	0.938578i	$0.612144\pi$
$54$		0			0
$55$	502.921			1.23298
$56$	−13.3123	−	170.724i	−0.0317667	−	0.407392i
$57$		0			0
$58$	135.508			0.306776
$59$	129.500	−	224.301i	0.285754	−	0.494941i	−0.687038	−	0.726622i	$-0.741089\pi$
$59$	129.500	−	224.301i	0.285754	−	0.494941i	0.972792	+	0.231681i	$0.0744225\pi$
$60$		0			0
$61$	−80.8264	−	139.995i	−0.169652	−	0.293846i	0.768646	−	0.639675i	$-0.220931\pi$
$61$	−80.8264	−	139.995i	−0.169652	−	0.293846i	−0.938297	+	0.345829i	$0.887598\pi$
$62$	54.1535			0.110927
$63$		0			0
$64$	−382.808			−0.747672
$65$	−408.574	−	707.671i	−0.779652	−	1.35040i
$66$		0			0
$67$	146.935	−	254.499i	0.267925	−	0.464060i	−0.700401	−	0.713750i	$-0.746995\pi$
$67$	146.935	−	254.499i	0.267925	−	0.464060i	0.968326	+	0.249690i	$0.0803287\pi$
$68$	619.242			1.10433
$69$		0			0
$70$	−99.0961	+	68.0016i	−0.169204	+	0.116111i
$71$	−249.873			−0.417668			−0.208834	−	0.977951i	$-0.566967\pi$
$71$	−249.873			−0.417668			−0.208834	+	0.977951i	$0.566967\pi$
$72$		0			0
$73$	−398.968	−	691.033i	−0.639666	−	1.10793i	−0.985506	−	0.169641i	$-0.945739\pi$
$73$	−398.968	−	691.033i	−0.639666	−	1.10793i	0.345839	−	0.938294i	$-0.387594\pi$
$74$	−6.80805			−0.0106949
$75$		0			0
$76$	−61.6633	−	106.804i	−0.0930693	−	0.161201i
$77$	−65.9190	−	845.380i	−0.0975607	−	1.25117i
$78$		0			0
$79$	−370.412	−	641.572i	−0.527526	−	0.913702i	−0.999485	−	0.0320815i	$-0.989786\pi$
$79$	−370.412	−	641.572i	−0.527526	−	0.913702i	0.471959	−	0.881620i	$-0.343547\pi$
$80$	306.167	+	530.296i	0.427881	+	0.741112i
$81$		0			0
$82$	−33.3023	+	57.6813i	−0.0448491	+	0.0776809i
$83$	−215.540	+	373.327i	−0.285044	+	0.493710i	−0.972620	−	0.232402i	$-0.925341\pi$
$83$	−215.540	+	373.327i	−0.285044	+	0.493710i	0.687576	+	0.726112i	$0.258675\pi$
$84$		0			0
$85$	−444.520	−	769.932i	−0.567235	−	0.982480i
$86$	294.009			0.368649
$87$		0			0
$88$	423.335			0.512815
$89$	224.168	−	388.270i	0.266986	−	0.462433i	−0.701096	−	0.713067i	$-0.747306\pi$
$89$	224.168	−	388.270i	0.266986	−	0.462433i	0.968082	+	0.250634i	$0.0806390\pi$
$90$		0			0
$91$	−1136.00	+	779.545i	−1.30863	+	0.898006i
$92$	513.076	−	888.674i	0.581433	−	1.00707i
$93$		0			0
$94$	−24.5038	+	42.4418i	−0.0268869	+	0.0465695i
$95$	−88.5295	+	153.338i	−0.0956099	+	0.165601i
$96$		0			0
$97$	125.941	−	218.136i	0.131828	−	0.228333i	−0.792553	−	0.609803i	$-0.791249\pi$
$97$	125.941	−	218.136i	0.131828	−	0.228333i	0.924381	+	0.381470i	$0.124582\pi$
$98$	127.295	+	157.661i	0.131212	+	0.162512i
$99$		0			0
$100$	−16.6093	+	28.7682i	−0.0166093	+	0.0287682i
$101$	121.381			0.119583			0.0597914	−	0.998211i	$-0.480956\pi$
$101$	121.381			0.119583			0.0597914	+	0.998211i	$0.480956\pi$
$102$		0			0
$103$	−568.815			−0.544146			−0.272073	−	0.962277i	$-0.587709\pi$
$103$	−568.815			−0.544146			−0.272073	+	0.962277i	$0.587709\pi$
$104$	−343.919	−	595.685i	−0.324270	−	0.561651i
$105$		0			0
$106$	145.955	−	252.801i	0.133739	−	0.231643i
$107$	−198.198	+	343.288i	−0.179070	+	0.310158i	−0.941562	−	0.336839i	$-0.890642\pi$
$107$	−198.198	+	343.288i	−0.179070	+	0.310158i	0.762492	+	0.646997i	$0.223975\pi$
$108$		0			0
$109$	523.948	+	907.504i	0.460414	+	0.797460i	0.998981	−	0.0451222i	$-0.0143677\pi$
$109$	523.948	+	907.504i	0.460414	+	0.797460i	−0.538568	+	0.842582i	$0.681034\pi$
$110$	−148.556	−	257.307i	−0.128766	−	0.223030i
$111$		0			0
$112$	851.266	−	584.155i	0.718188	−	0.492835i
$113$	−601.187	−	1041.29i	−0.500486	−	0.866867i	−1.00000		0.000560846i	$-0.999821\pi$
$113$	−601.187	−	1041.29i	−0.500486	−	0.866867i	0.499514	−	0.866306i	$-0.333512\pi$
$114$		0			0
$115$	−1473.24			−1.19461
$116$	877.464	+	1519.81i	0.702332	+	1.21647i
$117$		0			0
$118$	−153.011			−0.119371
$119$	−1235.94	+	848.129i	−0.952091	+	0.653343i
$120$		0			0
$121$	765.244			0.574939
$122$	−47.7502	+	82.7058i	−0.0354353	+	0.0613757i
$123$		0			0
$124$	350.665	+	607.369i	0.253957	+	0.439866i
$125$	1420.75			1.01660
$126$		0			0
$127$	823.034			0.575059			0.287529	−	0.957772i	$-0.407166\pi$
$127$	823.034			0.575059			0.287529	+	0.957772i	$0.407166\pi$
$128$	540.687	+	936.498i	0.373363	+	0.646684i
$129$		0			0
$130$	−241.375	+	418.074i	−0.162846	+	0.282058i
$131$	1874.32			1.25008			0.625040	−	0.780593i	$-0.285083\pi$
$131$	1874.32			1.25008			0.625040	+	0.780593i	$0.285083\pi$
$132$		0			0
$133$	269.355	+	128.714i	0.175609	+	0.0839170i
$134$	−173.611			−0.111923
$135$		0			0
$136$	−374.177	−	648.093i	−0.235922	−	0.408629i
$137$	−2029.51			−1.26564			−0.632819	−	0.774300i	$-0.718102\pi$
$137$	−2029.51			−1.26564			−0.632819	+	0.774300i	$0.718102\pi$
$138$		0			0
$139$	1063.25	+	1841.61i	0.648805	+	1.12376i	0.983409	+	0.181405i	$0.0580644\pi$
$139$	1063.25	+	1841.61i	0.648805	+	1.12376i	−0.334603	+	0.942359i	$0.608602\pi$
$140$	−1404.37	−	671.095i	−0.847792	−	0.405127i
$141$		0			0
$142$	73.8092	+	127.841i	0.0436193	+	0.0755508i
$143$	−1703.00	−	2949.67i	−0.995885	−	1.72492i
$144$		0			0
$145$	1259.77	−	2181.98i	0.721504	−	1.24968i
$146$	−235.700	+	408.245i	−0.133607	+	0.231415i
$147$		0			0
$148$	−44.0847	−	76.3569i	−0.0244847	−	0.0424088i
$149$	−24.2344			−0.0133245			−0.00666227	−	0.999978i	$-0.502121\pi$
$149$	−24.2344			−0.0133245			−0.00666227	+	0.999978i	$0.502121\pi$
$150$		0			0
$151$	1848.69			0.996319			0.498159	−	0.867085i	$-0.334009\pi$
$151$	1848.69			0.996319			0.498159	+	0.867085i	$0.334009\pi$
$152$	−74.5201	+	129.073i	−0.0397656	+	0.0688761i
$153$		0			0
$154$	−413.047	+	283.440i	−0.216131	+	0.148313i
$155$	503.446	−	871.995i	0.260889	−	0.451873i
$156$		0			0
$157$	−722.194	+	1250.88i	−0.367117	+	0.635865i	−0.989113	−	0.147155i	$-0.952988\pi$
$157$	−722.194	+	1250.88i	−0.367117	+	0.635865i	0.621997	+	0.783020i	$0.286322\pi$
$158$	−218.830	+	379.024i	−0.110185	+	0.190845i
$159$		0			0
$160$	587.134	−	1016.95i	0.290106	−	0.502479i
$161$	193.101	+	2476.42i	0.0945247	+	1.21223i
$162$		0			0
$163$	174.373	−	302.024i	0.0837913	−	0.145131i	−0.821084	−	0.570807i	$-0.806630\pi$
$163$	174.373	−	302.024i	0.0837913	−	0.145131i	0.904876	+	0.425676i	$0.139964\pi$
$164$	−862.580			−0.410709
$165$		0			0
$166$	254.672			0.119074
$167$	1799.80	+	3117.34i	0.833968	+	1.44447i	0.894868	+	0.446331i	$0.147269\pi$
$167$	1799.80	+	3117.34i	0.833968	+	1.44447i	−0.0609003	+	0.998144i	$0.519397\pi$
$168$		0			0
$169$	−1668.54	+	2889.99i	−0.759462	+	1.31543i
$170$	−262.611	+	454.856i	−0.118479	+	0.205211i
$171$		0			0
$172$	1903.82	+	3297.52i	0.843983	+	1.46182i
$173$	1620.57	+	2806.91i	0.712194	+	1.23356i	0.964032	+	0.265787i	$0.0856319\pi$
$173$	1620.57	+	2806.91i	0.712194	+	1.23356i	−0.251837	+	0.967770i	$0.581035\pi$
$174$		0			0
$175$	−6.25106	−	80.1668i	−0.00270021	−	0.0346288i
$176$	1276.15	+	2210.35i	0.546552	+	0.946656i
$177$		0			0
$178$	−264.865			−0.111531
$179$	−580.762	−	1005.91i	−0.242504	−	0.420029i	0.718923	−	0.695090i	$-0.244635\pi$
$179$	−580.762	−	1005.91i	−0.242504	−	0.420029i	−0.961427	+	0.275061i	$0.911302\pi$
$180$		0			0
$181$	−1135.58			−0.466336			−0.233168	−	0.972437i	$-0.574909\pi$
$181$	−1135.58			−0.466336			−0.233168	+	0.972437i	$0.574909\pi$
$182$	734.396	+	350.940i	0.299105	+	0.142931i
$183$		0			0
$184$	−1240.10			−0.496857
$185$	−63.2920	+	109.625i	−0.0251531	+	0.0435664i
$186$		0			0
$187$	−1852.82	−	3209.18i	−0.724555	−	1.25497i
$188$	−634.685			−0.246219
$189$		0			0
$190$	104.602			0.0399402
$191$	−905.760	−	1568.82i	−0.343133	−	0.594324i	0.641879	−	0.766806i	$-0.278155\pi$
$191$	−905.760	−	1568.82i	−0.343133	−	0.594324i	−0.985013	+	0.172481i	$0.944822\pi$
$192$		0			0
$193$	−1333.91	+	2310.41i	−0.497498	+	0.861692i	−0.999996	−	0.00288635i	$-0.999081\pi$
$193$	−1333.91	+	2310.41i	−0.497498	+	0.861692i	0.502498	+	0.864579i	$0.332415\pi$
$194$	−148.805			−0.0550700
$195$		0			0
$196$	−943.996	+	2448.62i	−0.344022	+	0.892356i
$197$	−3360.97			−1.21553			−0.607765	−	0.794117i	$-0.707934\pi$
$197$	−3360.97			−1.21553			−0.607765	+	0.794117i	$0.707934\pi$
$198$		0			0
$199$	690.248	+	1195.54i	0.245881	+	0.425879i	0.962379	−	0.271711i	$-0.0875894\pi$
$199$	690.248	+	1195.54i	0.245881	+	0.425879i	−0.716498	+	0.697589i	$0.754256\pi$
$200$	40.1447			0.0141933
$201$		0			0
$202$	−35.8544	−	62.1016i	−0.0124886	−	0.0216310i
$203$	−3832.90	−	1831.60i	−1.32521	−	0.633265i
$204$		0			0
$205$	619.200	+	1072.49i	0.210960	+	0.365393i
$206$	168.021	+	291.021i	0.0568280	+	0.0984290i
$207$		0			0
$208$	2073.49	−	3591.39i	0.691205	−	1.19720i
$209$	−369.004	+	639.133i	−0.122127	+	0.211530i
$210$		0			0
$211$	−1002.20	−	1735.86i	−0.326987	−	0.566359i	0.654925	−	0.755694i	$-0.272700\pi$
$211$	−1002.20	−	1735.86i	−0.326987	−	0.566359i	−0.981913	+	0.189335i	$0.939367\pi$
$212$	3780.45			1.22473
$213$		0			0
$214$	234.180			0.0748048
$215$	2733.30	−	4734.22i	0.867021	−	1.50172i
$216$		0			0
$217$	−1531.76	−	731.969i	−0.479182	−	0.228983i
$218$	309.535	−	536.131i	0.0961668	−	0.166566i
$219$		0			0
$220$	1923.92	−	3332.33i	0.589594	−	1.02121i
$221$	−3010.48	+	5214.30i	−0.916320	+	1.58711i
$222$		0			0
$223$	702.905	−	1217.47i	0.211076	−	0.365595i	−0.740975	−	0.671532i	$-0.765636\pi$
$223$	702.905	−	1217.47i	0.211076	−	0.365595i	0.952052	+	0.305937i	$0.0989698\pi$
$224$	−1786.38	−	853.643i	−0.532847	−	0.254627i
$225$		0			0
$226$	−355.166	+	615.165i	−0.104537	+	0.181063i
$227$	4980.85			1.45635			0.728174	−	0.685392i	$-0.240369\pi$
$227$	4980.85			1.45635			0.728174	+	0.685392i	$0.240369\pi$
$228$		0			0
$229$	4259.52			1.22916			0.614579	−	0.788855i	$-0.289326\pi$
$229$	4259.52			1.22916			0.614579	+	0.788855i	$0.289326\pi$
$230$	435.176	+	753.747i	0.124759	+	0.216090i
$231$		0			0
$232$	1060.41	−	1836.69i	0.300085	−	0.519762i
$233$	928.994	−	1609.06i	0.261203	−	0.452418i	−0.705359	−	0.708851i	$-0.749214\pi$
$233$	928.994	−	1609.06i	0.261203	−	0.452418i	0.966562	+	0.256433i	$0.0825473\pi$
$234$		0			0
$235$	455.606	+	789.133i	0.126470	+	0.219052i
$236$	−990.805	−	1716.12i	−0.273288	−	0.473348i
$237$		0			0
$238$	799.007	+	381.815i	0.217613	+	0.103989i
$239$	−1822.76	−	3157.12i	−0.493325	−	0.854464i	0.506645	−	0.862155i	$-0.330885\pi$
$239$	−1822.76	−	3157.12i	−0.493325	−	0.854464i	−0.999970	+	0.00769024i	$0.997552\pi$
$240$		0			0
$241$	656.573			0.175492			0.0877460	−	0.996143i	$-0.472034\pi$
$241$	656.573			0.175492			0.0877460	+	0.996143i	$0.472034\pi$
$242$	−226.044	−	391.519i	−0.0600439	−	0.103999i
$243$		0			0
$244$	−1236.80			−0.324501
$245$	3722.13	−	584.022i	0.970604	−	0.152293i
$246$		0			0
$247$	1199.12			0.308899
$248$	423.778	−	734.005i	0.108508	−	0.187941i
$249$		0			0
$250$	−419.671	−	726.892i	−0.106169	−	0.183891i
$251$	4591.82			1.15471			0.577357	−	0.816492i	$-0.304084\pi$
$251$	4591.82			1.15471			0.577357	+	0.816492i	$0.304084\pi$
$252$		0			0
$253$	−6140.66			−1.52593
$254$	−243.114	−	421.086i	−0.0600564	−	0.104021i
$255$		0			0
$256$	−1211.81	+	2098.91i	−0.295852	+	0.512430i
$257$	−6878.86			−1.66962			−0.834809	−	0.550540i	$-0.814422\pi$
$257$	−6878.86			−1.66962			−0.834809	+	0.550540i	$0.814422\pi$
$258$		0			0
$259$	192.569	+	92.0213i	0.0461994	+	0.0220769i
$260$	−6251.99			−1.49128
$261$		0			0
$262$	−553.651	−	958.953i	−0.130552	−	0.226123i
$263$	4565.64			1.07045			0.535227	−	0.844708i	$-0.320226\pi$
$263$	4565.64			1.07045			0.535227	+	0.844708i	$0.320226\pi$
$264$		0			0
$265$	−2713.78	−	4700.41i	−0.629080	−	1.08960i
$266$	−13.7104	−	175.830i	−0.00316031	−	0.0405294i
$267$		0			0
$268$	−1124.20	−	1947.17i	−0.256236	−	0.443814i
$269$	231.632	+	401.198i	0.0525013	+	0.0909349i	0.891082	−	0.453843i	$-0.149947\pi$
$269$	231.632	+	401.198i	0.0525013	+	0.0909349i	−0.838580	+	0.544778i	$0.816614\pi$
$270$		0			0
$271$	180.602	−	312.811i	0.0404825	−	0.0701178i	−0.845074	−	0.534649i	$-0.820444\pi$
$271$	180.602	−	312.811i	0.0404825	−	0.0701178i	0.885557	+	0.464531i	$0.153777\pi$
$272$	2255.91	−	3907.36i	0.502885	−	0.871023i
$273$		0			0
$274$	599.490	+	1038.35i	0.132177	+	0.228938i
$275$	198.786			0.0435899
$276$		0			0
$277$	4992.38			1.08290			0.541450	−	0.840733i	$-0.317876\pi$
$277$	4992.38			1.08290			0.541450	+	0.840733i	$0.317876\pi$
$278$	628.143	−	1087.98i	0.135516	−	0.234721i
$279$		0			0
$280$	146.229	+	1875.31i	0.0312101	+	0.400254i
$281$	795.782	−	1378.34i	0.168941	−	0.292614i	−0.769107	−	0.639120i	$-0.779299\pi$
$281$	795.782	−	1378.34i	0.168941	−	0.292614i	0.938048	+	0.346506i	$0.112632\pi$
$282$		0			0
$283$	−552.562	+	957.066i	−0.116065	+	0.201031i	−0.918205	−	0.396105i	$-0.870361\pi$
$283$	−552.562	+	957.066i	−0.116065	+	0.201031i	0.802140	+	0.597136i	$0.203695\pi$
$284$	−955.886	+	1655.64i	−0.199723	+	0.345931i
$285$		0			0
$286$	−1006.09	+	1742.59i	−0.208011	+	0.360286i
$287$	1721.62	−	1181.41i	0.354091	−	0.242984i
$288$		0			0
$289$	−818.837	+	1418.27i	−0.166667	+	0.288676i
$290$	−1488.48			−0.301402
$291$		0			0
$292$	−6104.99			−1.22352
$293$	−748.863	−	1297.07i	−0.149314	−	0.258620i	0.781660	−	0.623705i	$-0.214373\pi$
$293$	−748.863	−	1297.07i	−0.149314	−	0.258620i	−0.930974	+	0.365085i	$0.881040\pi$
$294$		0			0
$295$	−1422.49	+	2463.83i	−0.280748	+	0.486269i
$296$	−53.2763	+	92.2773i	−0.0104616	+	0.0181200i
$297$		0			0
$298$	7.15853	+	12.3989i	0.00139155	+	0.00241024i
$299$	4988.69	+	8640.67i	0.964895	+	1.67125i
$300$		0			0
$301$	−8316.19	−	3973.99i	−1.59248	−	0.760987i
$302$	−546.079	−	945.837i	−0.104051	−	0.180221i
$303$		0			0
$304$	−898.564			−0.169527
$305$	887.834	+	1537.77i	0.166679	+	0.288697i
$306$		0			0
$307$	8007.68			1.48867			0.744336	−	0.667805i	$-0.232766\pi$
$307$	8007.68			1.48867			0.744336	+	0.667805i	$0.232766\pi$
$308$	−5853.61	−	2797.22i	−1.08292	−	0.517488i
$309$		0			0
$310$	−594.847			−0.108984
$311$	3018.76	−	5228.65i	0.550413	−	0.953343i	−0.447832	−	0.894118i	$-0.647804\pi$
$311$	3018.76	−	5228.65i	0.550413	−	0.953343i	0.998245	−	0.0592252i	$-0.0188630\pi$
$312$		0			0
$313$	1661.10	+	2877.11i	0.299971	+	0.519565i	0.976129	−	0.217192i	$-0.0696896\pi$
$313$	1661.10	+	2877.11i	0.299971	+	0.519565i	−0.676158	+	0.736757i	$0.736356\pi$
$314$	853.308			0.153360
$315$		0			0
$316$	−5668.03			−1.00902
$317$	39.4267	+	68.2890i	0.00698556	+	0.0120993i	0.869497	−	0.493938i	$-0.164443\pi$
$317$	39.4267	+	68.2890i	0.00698556	+	0.0120993i	−0.862511	+	0.506037i	$0.831110\pi$
$318$		0			0
$319$	5250.89	−	9094.81i	0.921610	−	1.59627i
$320$	4204.94			0.734573
$321$		0			0
$322$	1209.96	−	830.300i	0.209406	−	0.143698i
$323$	1304.62			0.224739
$324$		0			0
$325$	−161.494	−	279.716i	−0.0275633	−	0.0477411i
$326$	−206.031			−0.0350031
$327$		0			0
$328$	521.214	+	902.769i	0.0877415	+	0.151973i
$329$	1266.77	−	869.280i	0.212277	−	0.145669i
$330$		0			0
$331$	−1278.50	−	2214.42i	−0.212303	−	0.367720i	0.740132	−	0.672462i	$-0.234763\pi$
$331$	−1278.50	−	2214.42i	−0.212303	−	0.367720i	−0.952435	+	0.304742i	$0.901430\pi$
$332$	1649.10	+	2856.32i	0.272608	+	0.472171i
$333$		0			0
$334$	1063.28	−	1841.65i	0.174191	−	0.301708i
$335$	−1614.00	+	2795.53i	−0.263231	+	0.455929i
$336$		0			0
$337$	3802.94	+	6586.88i	0.614716	+	1.06472i	0.990434	+	0.137985i	$0.0440627\pi$
$337$	3802.94	+	6586.88i	0.614716	+	1.06472i	−0.375718	+	0.926734i	$0.622604\pi$
$338$	1971.46			0.317258
$339$		0			0
$340$	−6802.04			−1.08498
$341$	2098.44	−	3634.60i	0.333245	−	0.577198i
$342$		0			0
$343$	−1469.57	−	6180.13i	−0.231340	−	0.972873i
$344$	2300.77	−	3985.05i	0.360608	−	0.624591i
$345$		0			0
$346$	957.392	−	1658.25i	0.148756	−	0.257654i
$347$	−4582.47	+	7937.07i	−0.708933	+	1.22791i	0.256320	+	0.966592i	$0.417490\pi$
$347$	−4582.47	+	7937.07i	−0.708933	+	1.22791i	−0.965253	+	0.261317i	$0.915843\pi$
$348$		0			0
$349$	2641.65	−	4575.47i	0.405170	−	0.701775i	−0.589171	−	0.808008i	$-0.700546\pi$
$349$	2641.65	−	4575.47i	0.405170	−	0.701775i	0.994341	+	0.106233i	$0.0338790\pi$
$350$	−39.1690	+	26.8785i	−0.00598191	+	0.00410490i
$351$		0			0
$352$	2447.26	−	4238.77i	0.370566	−	0.641839i
$353$	−4987.97			−0.752076			−0.376038	−	0.926604i	$-0.622714\pi$
$353$	−4987.97			−0.752076			−0.376038	+	0.926604i	$0.622714\pi$
$354$		0			0
$355$	2744.71			0.410350
$356$	−1715.10	−	2970.65i	−0.255338	−	0.442259i
$357$		0			0
$358$	−343.099	+	594.266i	−0.0506519	+	0.0877316i
$359$	149.472	−	258.894i	0.0219745	−	0.0380610i	−0.854829	−	0.518910i	$-0.826338\pi$
$359$	149.472	−	258.894i	0.0219745	−	0.0380610i	0.876804	+	0.480849i	$0.159671\pi$
$360$		0			0
$361$	3299.59	+	5715.05i	0.481060	+	0.833220i
$362$	335.435	+	580.991i	0.0487019	+	0.0843541i
$363$		0			0
$364$	819.464	+	10509.2i	0.117999	+	1.51328i
$365$	4382.44	+	7590.62i	0.628459	+	1.08852i
$366$		0			0
$367$	2869.17			0.408091			0.204045	−	0.978961i	$-0.434591\pi$
$367$	2869.17			0.408091			0.204045	+	0.978961i	$0.434591\pi$
$368$	−3738.30	−	6474.92i	−0.529544	−	0.917197i
$369$		0			0
$370$	74.7827			0.0105075
$371$	−7545.40	+	5177.80i	−1.05590	+	0.724576i
$372$		0			0
$373$	−260.708			−0.0361902			−0.0180951	−	0.999836i	$-0.505760\pi$
$373$	−260.708			−0.0361902			−0.0180951	+	0.999836i	$0.505760\pi$
$374$	−1094.60	+	1895.91i	−0.151338	+	0.262125i
$375$		0			0
$376$	383.508	+	664.256i	0.0526009	+	0.0911073i
$377$	−17063.4			−2.33105
$378$		0			0
$379$	8599.02			1.16544			0.582720	−	0.812673i	$-0.301988\pi$
$379$	8599.02			1.16544			0.582720	+	0.812673i	$0.301988\pi$
$380$	677.338	+	1173.18i	0.0914387	+	0.158376i
$381$		0			0
$382$	−535.100	+	926.821i	−0.0716704	+	0.124137i
$383$	−1240.58			−0.165511			−0.0827553	−	0.996570i	$-0.526372\pi$
$383$	−1240.58			−0.165511			−0.0827553	+	0.996570i	$0.526372\pi$
$384$		0			0
$385$	724.085	+	9286.03i	0.0958513	+	1.22925i
$386$	1576.08			0.207825
$387$		0			0
$388$	−963.570	−	1668.95i	−0.126077	−	0.218372i
$389$	7915.50			1.03170			0.515851	−	0.856679i	$-0.327476\pi$
$389$	7915.50			1.03170			0.515851	+	0.856679i	$0.327476\pi$
$390$		0			0
$391$	5427.59	+	9400.87i	0.702008	+	1.21591i
$392$	3133.12	−	491.603i	0.403690	−	0.0633410i
$393$		0			0
$394$	992.789	+	1719.56i	0.126944	+	0.219874i
$395$	4068.77	+	7047.32i	0.518284	+	0.897693i
$396$		0			0
$397$	−7325.46	+	12688.1i	−0.926081	+	1.60402i	−0.136268	+	0.990672i	$0.543511\pi$
$397$	−7325.46	+	12688.1i	−0.926081	+	1.60402i	−0.789813	+	0.613347i	$0.789823\pi$
$398$	407.781	−	706.297i	0.0513573	−	0.0889535i
$399$		0			0
$400$	121.016	+	209.606i	0.0151270	+	0.0262008i
$401$	−13980.3			−1.74101			−0.870505	−	0.492160i	$-0.836208\pi$
$401$	−13980.3			−1.74101			−0.870505	+	0.492160i	$0.836208\pi$
$402$		0			0
$403$	−6819.10			−0.842887
$404$	464.342	−	804.264i	0.0571828	−	0.0990436i
$405$		0			0
$406$	195.098	+	2502.04i	0.0238487	+	0.305848i
$407$	−263.810	+	456.933i	−0.0321292	+	0.0556494i
$408$		0			0
$409$	−236.972	+	410.448i	−0.0286492	+	0.0496219i	−0.879995	−	0.474984i	$-0.842454\pi$
$409$	−236.972	+	410.448i	−0.0286492	+	0.0496219i	0.851345	+	0.524606i	$0.175787\pi$
$410$	365.808	−	633.597i	0.0440633	−	0.0763199i
$411$		0			0
$412$	−2176.00	+	3768.94i	−0.260203	+	0.450685i
$413$	4327.99	+	2068.18i	0.515658	+	0.246413i
$414$		0			0
$415$	2367.59	−	4100.79i	0.280049	−	0.485060i
$416$	−7952.64			−0.937284
$417$		0			0
$418$	435.996			0.0510174
$419$	4736.18	+	8203.31i	0.552214	+	0.956462i	0.998114	+	0.0613799i	$0.0195501\pi$
$419$	4736.18	+	8203.31i	0.552214	+	0.956462i	−0.445901	+	0.895082i	$0.647117\pi$
$420$		0			0
$421$	6733.40	−	11662.6i	0.779491	−	1.35012i	−0.152744	−	0.988266i	$-0.548811\pi$
$421$	6733.40	−	11662.6i	0.779491	−	1.35012i	0.932235	−	0.361853i	$-0.117856\pi$
$422$	−592.075	+	1025.50i	−0.0682980	+	0.118296i
$423$		0			0
$424$	−2284.34	−	3956.58i	−0.261644	−	0.453181i
$425$	−175.702	−	304.325i	−0.0200537	−	0.0347340i
$426$		0			0
$427$	2468.54	−	1693.96i	0.279768	−	0.191982i
$428$	1516.41	+	2626.49i	0.171258	+	0.296627i
$429$		0			0
$430$	−3229.53			−0.362190
$431$	4108.46	+	7116.07i	0.459159	+	0.795287i	0.998917	−	0.0465334i	$-0.0148174\pi$
$431$	4108.46	+	7116.07i	0.459159	+	0.795287i	−0.539757	+	0.841821i	$0.681484\pi$
$432$		0			0
$433$	−834.867			−0.0926585			−0.0463293	−	0.998926i	$-0.514752\pi$
$433$	−834.867			−0.0926585			−0.0463293	+	0.998926i	$0.514752\pi$
$434$	77.9680	+	999.902i	0.00862347	+	0.110592i
$435$		0			0
$436$	8017.43			0.880655
$437$	1080.95	−	1872.25i	0.118326	−	0.204947i
$438$		0			0
$439$	−1945.40	−	3369.53i	−0.211501	−	0.366330i	0.740684	−	0.671854i	$-0.234502\pi$
$439$	−1945.40	−	3369.53i	−0.211501	−	0.366330i	−0.952184	+	0.305524i	$0.901168\pi$
$440$	−4650.11			−0.503830
$441$		0			0
$442$	3557.03			0.382784
$443$	1125.36	+	1949.17i	0.120694	+	0.209048i	0.920041	−	0.391821i	$-0.128155\pi$
$443$	1125.36	+	1949.17i	0.120694	+	0.209048i	−0.799348	+	0.600869i	$0.794821\pi$
$444$		0			0
$445$	−2462.36	+	4264.93i	−0.262308	+	0.454331i
$446$	−830.518			−0.0881752
$447$		0			0
$448$	−551.152	−	7068.25i	−0.0581238	−	0.745410i
$449$	−2354.72			−0.247497			−0.123749	−	0.992314i	$-0.539492\pi$
$449$	−2354.72			−0.247497			−0.123749	+	0.992314i	$0.539492\pi$
$450$		0			0
$451$	2580.91	+	4470.27i	0.269469	+	0.466733i
$452$	−9199.34			−0.957302
$453$		0			0
$454$	−1471.28	−	2548.34i	−0.152094	−	0.263435i
$455$	12478.3	−	8562.88i	1.28570	−	0.882272i
$456$		0			0
$457$	5450.34	+	9440.26i	0.557891	+	0.966295i	0.997672	+	0.0681905i	$0.0217226\pi$
$457$	5450.34	+	9440.26i	0.557891	+	0.966295i	−0.439781	+	0.898105i	$0.644944\pi$
$458$	−1258.21	−	2179.28i	−0.128367	−	0.222339i
$459$		0			0
$460$	−5635.86	+	9761.60i	−0.571246	+	0.989428i
$461$	844.836	−	1463.30i	0.0853534	−	0.147836i	−0.820188	−	0.572094i	$-0.806131\pi$
$461$	844.836	−	1463.30i	0.0853534	−	0.147836i	0.905542	+	0.424257i	$0.139465\pi$
$462$		0			0
$463$	−4861.63	−	8420.59i	−0.487989	−	0.845222i	0.511915	−	0.859036i	$-0.328936\pi$
$463$	−4861.63	−	8420.59i	−0.487989	−	0.845222i	−0.999905	+	0.0138136i	$0.995603\pi$
$464$	12786.5			1.27931
$465$		0			0
$466$	−1097.65			−0.109115
$467$	3287.11	−	5693.44i	0.325716	−	0.564156i	−0.655941	−	0.754812i	$-0.727728\pi$
$467$	3287.11	−	5693.44i	0.325716	−	0.564156i	0.981657	+	0.190656i	$0.0610614\pi$
$468$		0			0
$469$	4910.68	+	2346.62i	0.483484	+	0.231038i
$470$	269.161	−	466.200i	0.0264159	−	0.0457536i
$471$		0			0
$472$	−1197.39	+	2073.94i	−0.116767	+	0.202247i
$473$	11392.8	−	19732.9i	1.10749	−	1.91822i
$474$		0			0
$475$	−34.9924	+	60.6086i	−0.00338013	+	0.00585455i
$476$	891.559	+	11433.8i	0.0858499	+	1.10098i
$477$		0			0
$478$	−1076.84	+	1865.15i	−0.103041	+	0.178472i
$479$	−17828.4			−1.70063			−0.850313	−	0.526277i	$-0.823588\pi$
$479$	−17828.4			−1.70063			−0.850313	+	0.526277i	$0.823588\pi$
$480$		0			0
$481$	857.281			0.0812653
$482$	−193.943	−	335.920i	−0.0183275	−	0.0317442i
$483$		0			0
$484$	2927.44	−	5070.47i	0.274928	−	0.476190i
$485$	−1383.39	+	2396.10i	−0.129518	+	0.224333i
$486$		0			0
$487$	−10447.7	−	18095.9i	−0.972133	−	1.68378i	−0.689088	−	0.724677i	$-0.741989\pi$
$487$	−10447.7	−	18095.9i	−0.972133	−	1.68378i	−0.283045	−	0.959107i	$-0.591345\pi$
$488$	747.338	+	1294.43i	0.0693246	+	0.120074i
$489$		0			0
$490$	−1398.27	−	1731.83i	−0.128913	−	0.159665i
$491$	3811.67	+	6602.01i	0.350343	+	0.606811i	0.986309	−	0.164905i	$-0.0527318\pi$
$491$	3811.67	+	6602.01i	0.350343	+	0.606811i	−0.635967	+	0.771717i	$0.719398\pi$
$492$		0			0
$493$	−18564.6			−1.69596
$494$	−354.205	−	613.500i	−0.0322600	−	0.0558759i
$495$		0			0
$496$	5109.92			0.462585
$497$	−359.756	−	4613.70i	−0.0324694	−	0.416404i
$498$		0			0
$499$	−12461.9			−1.11798			−0.558990	−	0.829174i	$-0.688811\pi$
$499$	−12461.9			−1.11798			−0.558990	+	0.829174i	$0.688811\pi$
$500$	5435.06	−	9413.81i	0.486127	−	0.841996i
$501$		0			0
$502$	−1356.37	−	2349.30i	−0.120593	−	0.208873i
$503$	4132.51			0.366321			0.183161	−	0.983083i	$-0.441367\pi$
$503$	4132.51			0.366321			0.183161	+	0.983083i	$0.441367\pi$
$504$		0			0
$505$	−1333.30			−0.117488
$506$	1813.87	+	3141.72i	0.159361	+	0.276021i
$507$		0			0
$508$	3148.51	−	5453.38i	0.274985	−	0.476288i
$509$	−19651.3			−1.71125			−0.855625	−	0.517596i	$-0.826827\pi$
$509$	−19651.3			−1.71125			−0.855625	+	0.517596i	$0.826827\pi$
$510$		0			0
$511$	12185.0	−	8361.55i	1.05485	−	0.723861i
$512$	10082.8			0.870315
$513$		0			0
$514$	2031.93	+	3519.41i	0.174367	+	0.302012i
$515$	6248.13			0.534612
$516$		0			0
$517$	1899.03	+	3289.22i	0.161546	+	0.279806i
$518$	−9.80195	−	125.705i	−0.000831415	−	0.0106625i
$519$		0			0
$520$	3777.76	+	6543.28i	0.318588	+	0.551811i
$521$	10838.1	+	18772.1i	0.911370	+	1.57854i	0.812130	+	0.583476i	$0.198308\pi$
$521$	10838.1	+	18772.1i	0.911370	+	1.57854i	0.0992403	+	0.995064i	$0.468359\pi$
$522$		0			0
$523$	8815.06	−	15268.1i	0.737009	−	1.27654i	−0.216828	−	0.976210i	$-0.569571\pi$
$523$	8815.06	−	15268.1i	0.737009	−	1.27654i	0.953836	−	0.300327i	$-0.0970957\pi$
$524$	7170.21	−	12419.2i	0.597771	−	1.03537i
$525$		0			0
$526$	−1348.63	−	2335.90i	−0.111793	−	0.193631i
$527$	−7419.04			−0.613242
$528$		0			0
$529$	5821.24			0.478445
$530$	−1603.23	+	2776.88i	−0.131396	+	0.227585i
$531$		0			0
$532$	1883.27	−	1292.34i	0.153478	−	0.105319i
$533$	4193.48	−	7263.32i	0.340788	−	0.590261i
$534$		0			0
$535$	2177.09	−	3770.83i	0.175932	−	0.304724i
$536$	−1358.59	+	2353.15i	−0.109482	+	0.189628i
$537$		0			0
$538$	136.842	−	237.018i	0.0109660	−	0.0189936i
$539$	15514.4	−	2434.29i	1.23980	−	0.194531i
$540$		0			0
$541$	−6631.61	+	11486.3i	−0.527015	+	0.912817i	0.472489	+	0.881336i	$0.343355\pi$
$541$	−6631.61	+	11486.3i	−0.527015	+	0.912817i	−0.999504	+	0.0314803i	$0.989978\pi$
$542$	−213.390			−0.0169112
$543$		0			0
$544$	−8652.30			−0.681920
$545$	−5755.28	−	9968.44i	−0.452347	−	0.783488i
$546$		0			0
$547$	−8982.32	+	15557.8i	−0.702114	+	1.21610i	0.265609	+	0.964081i	$0.414427\pi$
$547$	−8982.32	+	15557.8i	−0.702114	+	1.21610i	−0.967723	+	0.252016i	$0.918906\pi$
$548$	−7763.86	+	13447.4i	−0.605211	+	1.04826i
$549$		0			0
$550$	−58.7188	−	101.704i	−0.00455232	−	0.00788485i
$551$	1848.64	+	3201.93i	0.142930	+	0.247562i
$552$		0			0
$553$	11312.8	−	7763.07i	0.869927	−	0.596960i
$554$	−1474.69	−	2554.23i	−0.113093	−	0.195883i
$555$		0			0
$556$	16269.9			1.24100
$557$	−11038.9	−	19119.9i	−0.839733	−	1.45446i	−0.890118	−	0.455730i	$-0.849378\pi$
$557$	−11038.9	−	19119.9i	−0.839733	−	1.45446i	0.0503851	−	0.998730i	$-0.483955\pi$
$558$		0			0
$559$	−37022.1			−2.80120
$560$	−9350.70	+	6416.63i	−0.705605	+	0.484200i
$561$		0			0
$562$	−940.256			−0.0705735
$563$	10860.3	−	18810.6i	0.812981	−	1.40812i	−0.0977882	−	0.995207i	$-0.531177\pi$
$563$	10860.3	−	18810.6i	0.812981	−	1.40812i	0.910769	−	0.412917i	$-0.135490\pi$
$564$		0			0
$565$	6603.71	+	11438.0i	0.491717	+	0.851679i
$566$	652.880			0.0484851
$567$		0			0
$568$	2310.37			0.170671
$569$	−9704.18	−	16808.1i	−0.714974	−	1.23837i	−0.962970	−	0.269610i	$-0.913105\pi$
$569$	−9704.18	−	16808.1i	−0.714974	−	1.23837i	0.247996	−	0.968761i	$-0.420228\pi$
$570$		0			0
$571$	−1197.39	+	2073.95i	−0.0877572	+	0.152000i	−0.906563	−	0.422071i	$-0.861303\pi$
$571$	−1197.39	+	2073.95i	−0.0877572	+	0.152000i	0.818806	+	0.574071i	$0.194637\pi$
$572$	−26059.2			−1.90488
$573$		0			0
$574$	−1112.99	−	531.853i	−0.0809323	−	0.0386745i
$575$	−582.315			−0.0422334
$576$		0			0
$577$	6386.16	+	11061.2i	0.460762	+	0.798062i	0.998999	−	0.0447307i	$-0.0142430\pi$
$577$	6386.16	+	11061.2i	0.460762	+	0.798062i	−0.538237	+	0.842793i	$0.680910\pi$
$578$	967.497			0.0696238
$579$		0			0
$580$	−9638.47	−	16694.3i	−0.690027	−	1.19516i
$581$	−7203.51	−	3442.28i	−0.514375	−	0.245800i
$582$		0			0
$583$	−11311.4	−	19592.0i	−0.803553	−	1.39179i
$584$	3688.94	+	6389.43i	0.261386	+	0.452734i
$585$		0			0
$586$	−442.409	+	766.276i	−0.0311873	+	0.0540180i
$587$	−1742.96	+	3018.90i	−0.122555	+	0.212271i	−0.920774	−	0.390095i	$-0.872442\pi$
$587$	−1742.96	+	3018.90i	−0.122555	+	0.212271i	0.798220	+	0.602366i	$0.205775\pi$
$588$		0			0
$589$	738.778	+	1279.60i	0.0516822	+	0.0895163i
$590$	1680.74			0.117280
$591$		0			0
$592$	−642.407			−0.0445992
$593$	3891.11	−	6739.60i	0.269458	−	0.466715i	−0.699264	−	0.714864i	$-0.746489\pi$
$593$	3891.11	−	6739.60i	0.269458	−	0.466715i	0.968722	+	0.248148i	$0.0798221\pi$
$594$		0			0
$595$	13576.2	−	9316.23i	0.935410	−	0.641896i
$596$	−92.7084	+	160.576i	−0.00637162	+	0.0110360i
$597$		0			0
$598$	2947.19	−	5104.69i	0.201538	−	0.349074i
$599$	7646.47	−	13244.1i	0.521580	−	0.903403i	−0.478105	−	0.878303i	$-0.658676\pi$
$599$	7646.47	−	13244.1i	0.521580	−	0.903403i	0.999685	−	0.0251002i	$-0.00799049\pi$
$600$		0			0
$601$	−9098.78	+	15759.5i	−0.617549	+	1.06963i	0.372383	+	0.928079i	$0.378541\pi$
$601$	−9098.78	+	15759.5i	−0.617549	+	1.06963i	−0.989932	+	0.141547i	$0.954792\pi$
$602$	423.302	+	5428.65i	0.0286587	+	0.367534i
$603$		0			0
$604$	7072.14	−	12249.3i	0.476426	−	0.825195i
$605$	−8405.79			−0.564866
$606$		0			0
$607$	1623.65			0.108570			0.0542848	−	0.998525i	$-0.482712\pi$
$607$	1623.65			0.108570			0.0542848	+	0.998525i	$0.482712\pi$
$608$	861.585	+	1492.31i	0.0574702	+	0.0995413i
$609$		0			0
$610$	524.510	−	908.478i	0.0348144	−	0.0603003i
$611$	3085.56	−	5344.34i	0.204301	−	0.353861i
$612$		0			0
$613$	−9187.65	−	15913.5i	−0.605360	−	1.04851i	−0.991994	−	0.126281i	$-0.959696\pi$
$613$	−9187.65	−	15913.5i	−0.605360	−	1.04851i	0.386634	−	0.922233i	$-0.373638\pi$
$614$	−2365.37	−	4096.94i	−0.155470	−	0.269282i
$615$		0			0
$616$	609.501	+	7816.56i	0.0398661	+	0.511263i
$617$	13260.3	+	22967.5i	0.865218	+	1.49860i	0.866831	+	0.498602i	$0.166153\pi$
$617$	13260.3	+	22967.5i	0.865218	+	1.49860i	−0.00161310	+	0.999999i	$0.500513\pi$
$618$		0			0
$619$	22293.5			1.44758			0.723788	−	0.690022i	$-0.242399\pi$
$619$	22293.5			1.44758			0.723788	+	0.690022i	$0.242399\pi$
$620$	−3851.86	−	6671.62i	−0.249507	−	0.432159i
$621$		0			0
$622$	−3566.82			−0.229930
$623$	7491.85	+	3580.07i	0.481789	+	0.230228i
$624$		0			0
$625$	−15063.4			−0.964060
$626$	981.337	−	1699.72i	0.0626551	−	0.108522i
$627$		0			0
$628$	5525.49	+	9570.43i	0.351101	+	0.608124i
$629$	932.703			0.0591245
$630$		0			0
$631$	22214.9			1.40152			0.700762	−	0.713396i	$-0.252844\pi$
$631$	22214.9			1.40152			0.700762	+	0.713396i	$0.252844\pi$
$632$	3424.90	+	5932.11i	0.215562	+	0.373365i
$633$		0			0
$634$	23.2923	−	40.3434i	0.00145908	−	0.00252719i
$635$	−9040.58			−0.564983
$636$		0			0
$637$	−16029.3	−	19853.0i	−0.997021	−	1.23486i
$638$	−6204.19			−0.384994
$639$		0			0
$640$	−5939.16	−	10286.9i	−0.366822	−	0.635354i
$641$	3760.55			0.231721			0.115860	−	0.993266i	$-0.463037\pi$
$641$	3760.55			0.231721			0.115860	+	0.993266i	$0.463037\pi$
$642$		0			0
$643$	−722.264	−	1251.00i	−0.0442975	−	0.0767255i	0.843027	−	0.537872i	$-0.180772\pi$
$643$	−722.264	−	1251.00i	−0.0442975	−	0.0767255i	−0.887324	+	0.461146i	$0.847438\pi$
$644$	17147.4	+	8194.07i	1.04922	+	0.501384i
$645$		0			0
$646$	−385.367	−	667.475i	−0.0234707	−	0.0406524i
$647$	5590.74	+	9683.45i	0.339714	+	0.588401i	0.984379	−	0.176064i	$-0.0563365\pi$
$647$	5590.74	+	9683.45i	0.339714	+	0.588401i	−0.644665	+	0.764465i	$0.723003\pi$
$648$		0			0
$649$	−5929.14	+	10269.6i	−0.358612	+	0.621134i
$650$	−95.4066	+	165.249i	−0.00575716	+	0.00997170i
$651$		0			0
$652$	−1334.13	−	2310.78i	−0.0801357	−	0.138799i
$653$	21837.5			1.30868			0.654339	−	0.756201i	$-0.272947\pi$
$653$	21837.5			1.30868			0.654339	+	0.756201i	$0.272947\pi$
$654$		0			0
$655$	−20588.4			−1.22818
$656$	−3142.40	+	5442.80i	−0.187028	+	0.323941i
$657$		0			0
$658$	−818.933	−	391.337i	−0.0485188	−	0.0231853i
$659$	−4540.44	+	7864.27i	−0.268392	+	0.464868i	−0.968447	−	0.249221i	$-0.919826\pi$
$659$	−4540.44	+	7864.27i	−0.268392	+	0.464868i	0.700055	+	0.714089i	$0.253159\pi$
$660$		0			0
$661$	−12766.1	+	22111.5i	−0.751200	+	1.30112i	0.196042	+	0.980596i	$0.437191\pi$
$661$	−12766.1	+	22111.5i	−0.751200	+	1.30112i	−0.947242	+	0.320521i	$0.896142\pi$
$662$	−755.303	+	1308.22i	−0.0443439	+	0.0768059i
$663$		0			0
$664$	1992.93	−	3451.86i	0.116477	−	0.201744i
$665$	−2958.72	−	1413.86i	−0.172533	−	0.0824467i
$666$		0			0
$667$	−15381.8	+	26642.0i	−0.892930	+	1.54660i
$668$	27540.5			1.59517
$669$		0			0
$670$	1907.02			0.109962
$671$	3700.62	+	6409.66i	0.212907	+	0.368766i
$672$		0			0
$673$	7674.86	−	13293.3i	0.439590	−	0.761393i	−0.558068	−	0.829795i	$-0.688457\pi$
$673$	7674.86	−	13293.3i	0.439590	−	0.761393i	0.997658	+	0.0684030i	$0.0217904\pi$
$674$	2246.68	−	3891.37i	0.128396	−	0.222388i
$675$		0			0
$676$	12766.0	+	22111.3i	0.726329	+	1.25804i
$677$	12738.6	+	22063.8i	0.723165	+	1.25256i	0.959725	+	0.280941i	$0.0906466\pi$
$677$	12738.6	+	22063.8i	0.723165	+	1.25256i	−0.236560	+	0.971617i	$0.576020\pi$
$678$		0			0
$679$	4209.02	+	2011.33i	0.237890	+	0.113679i
$680$	4110.13	+	7118.95i	0.231788	+	0.401469i
$681$		0			0
$682$	−2479.41			−0.139210
$683$	−16833.0	−	29155.7i	−0.943043	−	1.63340i	−0.759623	−	0.650363i	$-0.774617\pi$
$683$	−16833.0	−	29155.7i	−0.943043	−	1.63340i	−0.183420	−	0.983035i	$-0.558717\pi$
$684$		0			0
$685$	22293.0			1.24346
$686$	−2727.82	+	2577.40i	−0.151820	+	0.143449i
$687$		0			0
$688$	27742.7			1.53733
$689$	−18378.9	+	31833.1i	−1.01622	+	1.76015i
$690$		0			0
$691$	2056.92	+	3562.70i	0.113240	+	0.196138i	0.917075	−	0.398715i	$-0.130544\pi$
$691$	2056.92	+	3562.70i	0.113240	+	0.196138i	−0.803835	+	0.594853i	$0.797210\pi$
$692$	24797.9			1.36225
$693$		0			0
$694$	5414.42			0.296151
$695$	−11679.3	−	20229.1i	−0.637438	−	1.10408i
$696$		0			0
$697$	4562.42	−	7902.34i	0.247940	−	0.429444i
$698$	−3121.24			−0.169256
$699$		0			0
$700$	−555.095	−	265.258i	−0.0299723	−	0.0143226i
$701$	−33029.9			−1.77963			−0.889817	−	0.456317i	$-0.849168\pi$
$701$	−33029.9			−1.77963			−0.889817	+	0.456317i	$0.849168\pi$
$702$		0			0
$703$	−92.8774	−	160.868i	−0.00498284	−	0.00863054i
$704$	17526.8			0.938303
$705$		0			0
$706$	1473.38	+	2551.98i	0.0785432	+	0.136041i
$707$	174.759	+	2241.20i	0.00929632	+	0.119221i
$708$		0			0
$709$	44.0712	+	76.3336i	0.00233446	+	0.00404340i	0.867190	−	0.497977i	$-0.165924\pi$
$709$	44.0712	+	76.3336i	0.00233446	+	0.00404340i	−0.864856	+	0.502020i	$0.832590\pi$
$710$	−810.754	−	1404.27i	−0.0428550	−	0.0742271i
$711$		0			0
$712$	−2072.70	+	3590.03i	−0.109098	+	0.188963i
$713$	−6147.08	+	10647.1i	−0.322875	+	0.559236i
$714$		0			0
$715$	18706.5	+	32400.6i	0.978437	+	1.69470i
$716$	−8886.80			−0.463848
$717$		0			0
$718$	−176.609			−0.00917965
$719$	−7868.86	+	13629.3i	−0.408149	+	0.706934i	−0.994682	−	0.102991i	$-0.967159\pi$
$719$	−7868.86	+	13629.3i	−0.408149	+	0.706934i	0.586534	+	0.809925i	$0.300492\pi$
$720$		0			0
$721$	−818.957	−	10502.7i	−0.0423017	−	0.542499i
$722$	1949.31	−	3376.31i	0.100479	−	0.174035i
$723$		0			0
$724$	−4344.14	+	7524.27i	−0.222995	+	0.386239i
$725$	497.939	−	862.455i	0.0255076	−	0.0441804i
$726$		0			0
$727$	4457.88	−	7721.27i	0.227419	−	0.393901i	−0.729624	−	0.683849i	$-0.760305\pi$
$727$	4457.88	−	7721.27i	0.227419	−	0.393901i	0.957042	+	0.289948i	$0.0936380\pi$
$728$	10503.7	−	7207.84i	0.534743	−	0.366951i
$729$		0			0
$730$	2589.04	−	4484.35i	0.131267	−	0.227360i
$731$	−40279.3			−2.03801
$732$		0			0
$733$	−6474.72			−0.326261			−0.163130	−	0.986605i	$-0.552159\pi$
$733$	−6474.72			−0.326261			−0.163130	+	0.986605i	$0.552159\pi$
$734$	−847.516	−	1467.94i	−0.0426191	−	0.0738184i
$735$		0			0
$736$	−7168.91	+	12416.9i	−0.359035	+	0.621866i
$737$	−6727.39	+	11652.2i	−0.336237	+	0.582379i
$738$		0			0
$739$	−4530.08	−	7846.32i	−0.225496	−	0.390571i	0.730972	−	0.682407i	$-0.239067\pi$
$739$	−4530.08	−	7846.32i	−0.225496	−	0.390571i	−0.956468	+	0.291837i	$0.905734\pi$
$740$	484.246	+	838.739i	0.0240557	+	0.0416658i
$741$		0			0
$742$	4877.91	+	2330.97i	0.241339	+	0.115327i
$743$	−1098.47	−	1902.60i	−0.0542381	−	0.0939431i	0.837632	−	0.546236i	$-0.183940\pi$
$743$	−1098.47	−	1902.60i	−0.0542381	−	0.0939431i	−0.891870	+	0.452292i	$0.850606\pi$
$744$		0			0
$745$	266.201			0.0130911
$746$	77.0099	+	133.385i	0.00377953	+	0.00654635i
$747$		0			0
$748$	−28351.8			−1.38589
$749$	−6623.90	−	3165.31i	−0.323140	−	0.154416i
$750$		0			0
$751$	3270.42			0.158907			0.0794536	−	0.996839i	$-0.474682\pi$
$751$	3270.42			0.158907			0.0794536	+	0.996839i	$0.474682\pi$
$752$	−2312.17	+	4004.80i	−0.112123	+	0.194202i
$753$		0			0
$754$	5040.30	+	8730.06i	0.243444	+	0.421658i
$755$	−20306.8			−0.978863
$756$		0			0
$757$	3374.70			0.162029			0.0810143	−	0.996713i	$-0.474184\pi$
$757$	3374.70			0.162029			0.0810143	+	0.996713i	$0.474184\pi$
$758$	−2540.04	−	4399.48i	−0.121713	−	0.210813i
$759$		0			0
$760$	818.563	−	1417.79i	0.0390689	−	0.0676694i
$761$	−15409.2			−0.734014			−0.367007	−	0.930218i	$-0.619617\pi$
$761$	−15409.2			−0.734014			−0.367007	+	0.930218i	$0.619617\pi$
$762$		0			0
$763$	−16002.0	+	10980.9i	−0.759254	+	0.521015i
$764$	−13859.9			−0.656327
$765$		0			0
$766$	366.451	+	634.712i	0.0172851	+	0.0299388i
$767$	19267.4			0.907048
$768$		0			0
$769$	9472.98	+	16407.7i	0.444219	+	0.769410i	0.997997	−	0.0632543i	$-0.0201479\pi$
$769$	9472.98	+	16407.7i	0.444219	+	0.769410i	−0.553779	+	0.832664i	$0.686815\pi$
$770$	4537.09	−	3113.44i	0.212345	−	0.145715i
$771$		0			0
$772$	10205.7	+	17676.9i	0.475794	+	0.824099i
$773$	−13493.2	−	23370.8i	−0.627833	−	1.08744i	−0.987986	−	0.154545i	$-0.950609\pi$
$773$	−13493.2	−	23370.8i	−0.627833	−	1.08744i	0.360153	−	0.932893i	$-0.382725\pi$
$774$		0			0
$775$	198.993	−	344.667i	0.00922329	−	0.0159752i
$776$	−1164.47	+	2016.93i	−0.0538687	+	0.0933034i
$777$		0			0
$778$	−2338.14	−	4049.78i	−0.107746	−	0.186621i
$779$	−1817.28			−0.0835825
$780$		0			0
$781$	11440.4			0.524159
$782$	3206.49	−	5553.80i	0.146629	−	0.253968i
$783$		0			0
$784$	12011.6	+	14876.9i	0.547175	+	0.677702i
$785$	7932.90	−	13740.2i	0.360685	−	0.624724i
$786$		0			0
$787$	4847.49	−	8396.10i	0.219561	−	0.380291i	−0.735113	−	0.677945i	$-0.762871\pi$
$787$	4847.49	−	8396.10i	0.219561	−	0.380291i	0.954674	+	0.297654i	$0.0962042\pi$
$788$	−12857.4	+	22269.6i	−0.581250	+	1.00675i
$789$		0			0
$790$	2403.73	−	4163.38i	0.108254	−	0.187502i
$791$	18361.0	−	12599.6i	0.825336	−	0.566361i
$792$		0			0
$793$	6012.79	−	10414.5i	0.269256	−	0.466366i
$794$	8655.39			0.386862
$795$		0			0
$796$	10562.1			0.470308
$797$	10265.5	+	17780.4i	0.456240	+	0.790231i	0.998759	−	0.0498132i	$-0.0158626\pi$
$797$	10265.5	+	17780.4i	0.456240	+	0.790231i	−0.542519	+	0.840044i	$0.682529\pi$
$798$		0			0
$799$	3357.02	−	5814.53i	0.148639	−	0.257451i
$800$	232.072	−	401.960i	0.0102562	−	0.0177643i
$801$		0			0
$802$	4129.62	+	7152.71i	0.181823	+	0.314926i
$803$	18266.6	+	31638.8i	0.802760	+	1.39042i
$804$		0			0
$805$	−2121.11	−	27202.2i	−0.0928686	−	1.19099i
$806$	2014.28	+	3488.83i	0.0880271	+	0.152467i
$807$		0			0
$808$	−1122.31			−0.0488649
$809$	8716.50	+	15097.4i	0.378808	+	0.656115i	0.990889	−	0.134680i	$-0.0430007\pi$
$809$	8716.50	+	15097.4i	0.378808	+	0.656115i	−0.612081	+	0.790795i	$0.709667\pi$
$810$		0			0
$811$	36442.4			1.57789			0.788943	−	0.614466i	$-0.210629\pi$
$811$	36442.4			1.57789			0.788943	+	0.614466i	$0.210629\pi$
$812$	−26798.8	+	18389.8i	−1.15819	+	0.794775i
$813$		0			0
$814$	311.705			0.0134217
$815$	−1915.40	+	3317.56i	−0.0823232	+	0.142588i
$816$		0			0
$817$	4010.96	+	6947.19i	0.171757	+	0.297493i
$818$	279.995			0.0119680
$819$		0			0
$820$	9474.97			0.403513
$821$	4062.67	+	7036.76i	0.172702	+	0.299129i	0.939364	−	0.342923i	$-0.111417\pi$
$821$	4062.67	+	7036.76i	0.172702	+	0.299129i	−0.766662	+	0.642051i	$0.778084\pi$
$822$		0			0
$823$	−16373.8	+	28360.3i	−0.693505	+	1.20119i	0.277177	+	0.960819i	$0.410601\pi$
$823$	−16373.8	+	28360.3i	−0.693505	+	1.20119i	−0.970682	+	0.240368i	$0.922732\pi$
$824$	5259.38			0.222354
$825$		0			0
$826$	−220.299	−	2825.23i	−0.00927989	−	0.119010i
$827$	21269.1			0.894314			0.447157	−	0.894456i	$-0.352437\pi$
$827$	21269.1			0.894314			0.447157	+	0.894456i	$0.352437\pi$
$828$		0			0
$829$	−10215.5	−	17693.7i	−0.427982	−	0.741287i	0.568711	−	0.822537i	$-0.307442\pi$
$829$	−10215.5	−	17693.7i	−0.427982	−	0.741287i	−0.996694	+	0.0812500i	$0.974109\pi$
$830$	−2797.43			−0.116988
$831$		0			0
$832$	−14238.8	−	24662.3i	−0.593320	−	1.02766i
$833$	−17439.5	−	21599.6i	−0.725381	−	0.898419i
$834$		0			0
$835$	−19769.8	−	34242.3i	−0.819356	−	1.41917i
$836$	2823.24	+	4890.00i	0.116799	+	0.202302i
$837$		0			0
$838$	2798.02	−	4846.31i	0.115341	−	0.199777i
$839$	10551.2	−	18275.2i	0.434169	−	0.752003i	−0.563058	−	0.826417i	$-0.690375\pi$
$839$	10551.2	−	18275.2i	0.434169	−	0.752003i	0.997227	+	0.0744142i	$0.0237087\pi$
$840$		0			0
$841$	−14111.5	−	24441.8i	−0.578599	−	1.00216i
$842$	−7955.85			−0.325625
$843$		0			0
$844$	−15335.6			−0.625444
$845$	18328.0	−	31745.0i	0.746155	−	1.29238i
$846$		0			0
$847$	1101.77	+	14129.6i	0.0446956	+	0.573200i
$848$	13772.3	−	23854.3i	0.557714	−	0.965990i
$849$		0			0
$850$	−103.800	+	179.788i	−0.00418862	+	0.00725490i
$851$	772.796	−	1338.52i	0.0311294	−	0.0539177i
$852$		0			0
$853$	−15303.6	+	26506.6i	−0.614285	+	1.06397i	0.376225	+	0.926528i	$0.377222\pi$
$853$	−15303.6	+	26506.6i	−0.614285	+	1.06397i	−0.990510	+	0.137444i	$0.956111\pi$
$854$	−1595.85	−	762.594i	−0.0639447	−	0.0305567i
$855$		0			0
$856$	1832.58	−	3174.11i	0.0731731	−	0.126739i
$857$	37403.3			1.49087			0.745434	−	0.666580i	$-0.232242\pi$
$857$	37403.3			1.49087			0.745434	+	0.666580i	$0.232242\pi$
$858$		0			0
$859$	−20353.0			−0.808424			−0.404212	−	0.914665i	$-0.632454\pi$
$859$	−20353.0			−0.808424			−0.404212	+	0.914665i	$0.632454\pi$
$860$	−20912.4	−	36221.4i	−0.829196	−	1.43621i
$861$		0			0
$862$	2427.18	−	4203.99i	0.0959048	−	0.166112i
$863$	10955.2	−	18974.9i	0.432119	−	0.748451i	−0.564937	−	0.825134i	$-0.691099\pi$
$863$	10955.2	−	18974.9i	0.432119	−	0.748451i	0.997056	+	0.0766826i	$0.0244328\pi$
$864$		0			0
$865$	−17801.1	−	30832.4i	−0.699716	−	1.21194i
$866$	246.609	+	427.140i	0.00967681	+	0.0167607i
$867$		0			0
$868$	−10709.7	+	7349.21i	−0.418792	+	0.287383i
$869$	16959.2	+	29374.2i	0.662027	+	1.14666i
$870$		0			0
$871$	21861.4			0.850454
$872$	−4844.53	−	8390.97i	−0.188138	−	0.325865i
$873$		0			0
$874$	−1277.19			−0.0494298
$875$	2045.54	+	26233.0i	0.0790305	+	1.01353i
$876$		0			0
$877$	−15125.3			−0.582377			−0.291189	−	0.956666i	$-0.594051\pi$
$877$	−15125.3			−0.582377			−0.291189	+	0.956666i	$0.594051\pi$
$878$	−1149.29	+	1990.63i	−0.0441763	+	0.0765155i
$879$		0			0
$880$	−14017.8	−	24279.5i	−0.536976	−	0.930070i
$881$	−27570.4			−1.05434			−0.527169	−	0.849761i	$-0.676746\pi$
$881$	−27570.4			−1.05434			−0.527169	+	0.849761i	$0.676746\pi$
$882$		0			0
$883$	−40394.6			−1.53951			−0.769755	−	0.638340i	$-0.779621\pi$
$883$	−40394.6			−1.53951			−0.769755	+	0.638340i	$0.779621\pi$
$884$	23033.1	+	39894.5i	0.876344	+	1.51787i
$885$		0			0
$886$	664.832	−	1151.52i	0.0252093	−	0.0436639i
$887$	850.221			0.0321845			0.0160922	−	0.999871i	$-0.494877\pi$
$887$	850.221			0.0321845			0.0160922	+	0.999871i	$0.494877\pi$
$888$		0			0
$889$	1184.97	+	15196.7i	0.0447049	+	0.573318i
$890$	2909.40			0.109577
$891$		0			0
$892$	−5377.92	−	9314.83i	−0.201868	−	0.349645i
$893$	−1337.15			−0.0501076
$894$		0			0
$895$	6379.35	+	11049.4i	0.238255	+	0.412670i
$896$	−16513.2	+	11331.7i	−0.615702	+	0.422506i
$897$		0			0
$898$	695.555	+	1204.74i	0.0258474	+	0.0447690i
$899$	−10512.8	−	18208.6i	−0.390011	−	0.675519i
$900$		0			0
$901$	−19995.8	+	34633.8i	−0.739353	+	1.28060i
$902$	1524.74	−	2640.92i	0.0562840	−	0.0974868i
$903$		0			0
$904$	5558.70	+	9627.95i	0.204513	+	0.354226i
$905$	12473.7			0.458165
$906$		0			0
$907$	36642.2			1.34144			0.670719	−	0.741712i	$-0.265986\pi$
$907$	36642.2			1.34144			0.670719	+	0.741712i	$0.265986\pi$
$908$	19054.2	−	33002.9i	0.696406	−	1.20621i
$909$		0			0
$910$	−8066.94	−	3854.88i	−0.293864	−	0.140426i
$911$	9097.68	−	15757.6i	0.330867	−	0.573078i	−0.651815	−	0.758378i	$-0.725992\pi$
$911$	9097.68	−	15757.6i	0.330867	−	0.573078i	0.982682	+	0.185300i	$0.0593256\pi$
$912$		0			0
$913$	9868.46	−	17092.7i	0.357720	−	0.619589i
$914$	3219.92	−	5577.07i	0.116527	−	0.201831i
$915$		0			0
$916$	16294.8	−	28223.4i	0.587767	−	1.01804i
$917$	2698.57	+	34607.9i	0.0971808	+	1.24630i
$918$		0			0
$919$	−5025.98	+	8705.25i	−0.180404	+	0.312470i	−0.942018	−	0.335561i	$-0.891074\pi$
$919$	−5025.98	+	8705.25i	−0.180404	+	0.312470i	0.761614	+	0.648031i	$0.224407\pi$
$920$	13621.9			0.488152
$921$		0			0
$922$	−998.215			−0.0356556
$923$	−9294.18	−	16098.0i	−0.331443	−	0.574076i
$924$		0			0
$925$	−25.0170	+	43.3306i	−0.000889246	+	0.00154022i
$926$	−2872.13	+	4974.67i	−0.101927	+	0.176542i
$927$		0			0
$928$	−12260.3	−	21235.4i	−0.433689	−	0.751172i
$929$	−24910.1	−	43145.6i	−0.879736	−	1.52375i	−0.851631	−	0.524142i	$-0.824386\pi$
$929$	−24910.1	−	43145.6i	−0.879736	−	1.52375i	−0.0281053	−	0.999605i	$-0.508947\pi$
$930$		0			0
$931$	−1988.81	+	5158.75i	−0.0700112	+	0.181602i
$932$	−7107.72	−	12310.9i	−0.249808	−	0.432680i
$933$		0			0
$934$	−3883.88			−0.136065
$935$	20352.3	+	35251.1i	0.711861	+	1.23298i
$936$		0			0
$937$	18018.2			0.628205			0.314102	−	0.949389i	$-0.398297\pi$
$937$	18018.2			0.628205			0.314102	+	0.949389i	$0.398297\pi$
$938$	−249.958	−	3205.59i	−0.00870088	−	0.111585i
$939$		0			0
$940$	6971.67			0.241905
$941$	1438.18	−	2491.00i	0.0498229	−	0.0862957i	−0.840038	−	0.542527i	$-0.817468\pi$
$941$	1438.18	−	2491.00i	0.0498229	−	0.0862957i	0.889861	+	0.456231i	$0.150801\pi$
$942$		0			0
$943$	−7560.43	−	13095.0i	−0.261083	−	0.452209i
$944$	−14438.1			−0.497797
$945$		0			0
$946$	−13461.1			−0.462642
$947$	−20584.3	−	35653.1i	−0.706337	−	1.22341i	−0.966207	−	0.257768i	$-0.917013\pi$
$947$	−20584.3	−	35653.1i	−0.706337	−	1.22341i	0.259870	−	0.965644i	$-0.416320\pi$
$948$		0			0
$949$	29679.8	−	51406.8i	1.01522	−	1.75842i
$950$	41.3453			0.00141202
$951$		0			0
$952$	11427.8	−	7841.97i	0.389052	−	0.266975i
$953$	2186.86			0.0743329			0.0371665	−	0.999309i	$-0.488167\pi$
$953$	2186.86			0.0743329			0.0371665	+	0.999309i	$0.488167\pi$
$954$		0			0
$955$	9949.28	+	17232.7i	0.337122	+	0.583912i
$956$	−27891.9			−0.943606
$957$		0			0
$958$	5266.28	+	9121.47i	0.177605	+	0.307621i
$959$	−2922.00	−	37473.2i	−0.0983903	−	1.26181i
$960$		0			0
$961$	10694.2	+	18523.0i	0.358976	+	0.621764i
$962$	−253.230	−	438.607i	−0.00848697	−	0.0146999i
$963$		0			0
$964$	2511.71	−	4350.42i	0.0839179	−	0.145350i
$965$	14652.3	−	25378.5i	0.488782	−	0.846595i
$966$		0			0
$967$	−27949.8	−	48410.5i	−0.929478	−	1.60990i	−0.784196	−	0.620514i	$-0.786924\pi$
$967$	−27949.8	−	48410.5i	−0.929478	−	1.60990i	−0.145283	−	0.989390i	$-0.546409\pi$
$968$	−7075.61			−0.234937
$969$		0			0
$970$	1634.54			0.0541052
$971$	−10078.7	+	17456.9i	−0.333102	+	0.576949i	−0.983118	−	0.182971i	$-0.941429\pi$
$971$	−10078.7	+	17456.9i	−0.333102	+	0.576949i	0.650016	+	0.759920i	$0.274762\pi$
$972$		0			0
$973$	−32473.0	+	22283.6i	−1.06993	+	0.734203i
$974$	−6172.22	+	10690.6i	−0.203050	+	0.351693i
$975$		0			0
$976$	−4505.71	+	7804.11i	−0.147771	+	0.255946i
$977$	−10467.1	+	18129.6i	−0.342756	+	0.593672i	−0.984944	−	0.172876i	$-0.944694\pi$
$977$	−10467.1	+	18129.6i	−0.342756	+	0.593672i	0.642187	+	0.766548i	$0.278027\pi$
$978$		0			0
$979$	−10263.5	+	17776.9i	−0.335058	+	0.580338i
$980$	10369.3	−	26896.8i	0.337994	−	0.876721i
$981$		0			0
$982$	2251.84	−	3900.30i	0.0731763	−	0.126745i
$983$	899.283			0.0291787			0.0145894	−	0.999894i	$-0.495356\pi$
$983$	899.283			0.0291787			0.0145894	+	0.999894i	$0.495356\pi$
$984$		0			0
$985$	36918.5			1.19423
$986$	5483.74	+	9498.12i	0.177118	+	0.306777i
$987$		0			0
$988$	4587.22	−	7945.30i	0.147711	−	0.255844i
$989$	−33373.6	+	57804.8i	−1.07302	+	1.85853i
$990$		0			0
$991$	19109.8	+	33099.2i	0.612557	+	1.06098i	0.990808	+	0.135277i	$0.0431924\pi$
$991$	19109.8	+	33099.2i	0.612557	+	1.06098i	−0.378251	+	0.925703i	$0.623474\pi$
$992$	−4899.63	−	8486.41i	−0.156818	−	0.271617i
$993$		0			0
$994$	−2254.22	+	1546.89i	−0.0719312	+	0.0493605i
$995$	−7581.99	−	13132.4i	−0.241573	−	0.418417i
$996$		0			0
$997$	−53056.9			−1.68538			−0.842692	−	0.538395i	$-0.819031\pi$
$997$	−53056.9			−1.68538			−0.842692	+	0.538395i	$0.819031\pi$
$998$	3681.09	+	6375.84i	0.116757	+	0.202228i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.g.a.100.10		44
3.2	odd	2		63.4.g.a.16.13	yes	44
7.4	even	3		189.4.h.a.46.13		44
9.4	even	3		189.4.h.a.37.13		44
9.5	odd	6		63.4.h.a.58.10	yes	44
21.11	odd	6		63.4.h.a.25.10	yes	44
63.4	even	3	inner	189.4.g.a.172.10		44
63.32	odd	6		63.4.g.a.4.13	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.13	✓	44	63.32	odd	6
63.4.g.a.16.13	yes	44	3.2	odd	2
63.4.h.a.25.10	yes	44	21.11	odd	6
63.4.h.a.58.10	yes	44	9.5	odd	6
189.4.g.a.100.10		44	1.1	even	1	trivial
189.4.g.a.172.10		44	63.4	even	3	inner
189.4.h.a.37.13		44	9.4	even	3
189.4.h.a.46.13		44	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.295387 - 0.511626i) q^{2} +(3.82549 - 6.62595i) q^{4} -10.9845 q^{5} +(1.43976 + 18.4642i) q^{7} -9.24621 q^{8} +O(q^{10})\)	\(q+(-0.295387 - 0.511626i) q^{2} +(3.82549 - 6.62595i) q^{4} -10.9845 q^{5} +(1.43976 + 18.4642i) q^{7} -9.24621 q^{8} +(3.24467 + 5.61993i) q^{10} -45.7848 q^{11} +(37.1957 + 64.4248i) q^{13} +(9.02148 - 6.19071i) q^{14} +(-27.8727 - 48.2770i) q^{16} +(40.4681 + 70.0928i) q^{17} +(8.05953 - 13.9595i) q^{19} +(-42.0210 + 72.7824i) q^{20} +(13.5242 + 23.4247i) q^{22} +134.120 q^{23} -4.34174 q^{25} +(21.9743 - 38.0606i) q^{26} +(127.851 + 61.0949i) q^{28} +(-114.686 + 198.643i) q^{29} +(-45.8326 + 79.3844i) q^{31} +(-53.4513 + 92.5804i) q^{32} +(23.9075 - 41.4091i) q^{34} +(-15.8150 - 202.819i) q^{35} +(5.76196 - 9.98001i) q^{37} -9.52273 q^{38} +101.565 q^{40} +(-56.3705 - 97.6366i) q^{41} +(-248.834 + 430.992i) q^{43} +(-175.149 + 303.367i) q^{44} +(-39.6174 - 68.6194i) q^{46} +(-41.4773 - 71.8409i) q^{47} +(-338.854 + 53.1680i) q^{49} +(1.28250 + 2.22135i) q^{50} +569.167 q^{52} +(247.056 + 427.914i) q^{53} +502.921 q^{55} +(-13.3123 - 170.724i) q^{56} +135.508 q^{58} +(129.500 - 224.301i) q^{59} +(-80.8264 - 139.995i) q^{61} +54.1535 q^{62} -382.808 q^{64} +(-408.574 - 707.671i) q^{65} +(146.935 - 254.499i) q^{67} +619.242 q^{68} +(-99.0961 + 68.0016i) q^{70} -249.873 q^{71} +(-398.968 - 691.033i) q^{73} -6.80805 q^{74} +(-61.6633 - 106.804i) q^{76} +(-65.9190 - 845.380i) q^{77} +(-370.412 - 641.572i) q^{79} +(306.167 + 530.296i) q^{80} +(-33.3023 + 57.6813i) q^{82} +(-215.540 + 373.327i) q^{83} +(-444.520 - 769.932i) q^{85} +294.009 q^{86} +423.335 q^{88} +(224.168 - 388.270i) q^{89} +(-1136.00 + 779.545i) q^{91} +(513.076 - 888.674i) q^{92} +(-24.5038 + 42.4418i) q^{94} +(-88.5295 + 153.338i) q^{95} +(125.941 - 218.136i) q^{97} +(127.295 + 157.661i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} + 10 q^{11} - 14 q^{13} + 79 q^{14} - 247 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} - 186 q^{23} + 698 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} + 61 q^{31} + 163 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} - 1522 q^{38} + 36 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} + 1005 q^{47} - 277 q^{49} - 239 q^{50} + 670 q^{52} - 258 q^{53} - 870 q^{55} - 714 q^{56} - 474 q^{58} + 1665 q^{59} + 439 q^{61} - 1812 q^{62} + 872 q^{64} + 613 q^{65} + 295 q^{67} - 2748 q^{68} - 1044 q^{70} - 636 q^{71} - 338 q^{73} + 2238 q^{74} + 1006 q^{76} + 2909 q^{77} + 133 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} - 6686 q^{86} - 738 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} - 1191 q^{94} - 3083 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) \) 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 + 10 * q^11 - 14 * q^13 + 79 * q^14 - 247 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 - 186 * q^23 + 698 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 + 61 * q^31 + 163 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 - 1522 * q^38 + 36 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 + 1005 * q^47 - 277 * q^49 - 239 * q^50 + 670 * q^52 - 258 * q^53 - 870 * q^55 - 714 * q^56 - 474 * q^58 + 1665 * q^59 + 439 * q^61 - 1812 * q^62 + 872 * q^64 + 613 * q^65 + 295 * q^67 - 2748 * q^68 - 1044 * q^70 - 636 * q^71 - 338 * q^73 + 2238 * q^74 + 1006 * q^76 + 2909 * q^77 + 133 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 - 6686 * q^86 - 738 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 - 1191 * q^94 - 3083 * q^95 - 266 * q^97 - 3601 * q^98

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