LMFDB - Embedded newform 189.4.h.a.37.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("189.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			37.13
Character	$\chi$	$=$	189.37
Dual form			189.4.h.a.46.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.590775 q^{2} -7.65099 q^{4} +(5.49223 + 9.51282i) q^{5} +(-16.7104 - 7.98524i) q^{7} -9.24621 q^{8} +O(q^{10})$	\(q+0.590775 q^{2} -7.65099 q^{4} +(5.49223 + 9.51282i) q^{5} +(-16.7104 - 7.98524i) q^{7} -9.24621 q^{8} +(3.24467 + 5.61993i) q^{10} +(22.8924 - 39.6508i) q^{11} +(37.1957 - 64.4248i) q^{13} +(-9.87206 - 4.71748i) q^{14} +55.7455 q^{16} +(40.4681 + 70.0928i) q^{17} +(8.05953 - 13.9595i) q^{19} +(-42.0210 - 72.7824i) q^{20} +(13.5242 - 23.4247i) q^{22} +(-67.0601 - 116.152i) q^{23} +(2.17087 - 3.76006i) q^{25} +(21.9743 - 38.0606i) q^{26} +(127.851 + 61.0949i) q^{28} +(-114.686 - 198.643i) q^{29} +91.6652 q^{31} +106.903 q^{32} +(23.9075 + 41.4091i) q^{34} +(-15.8150 - 202.819i) q^{35} +(5.76196 - 9.98001i) q^{37} +(4.76137 - 8.24693i) q^{38} +(-50.7823 - 87.9575i) q^{40} +(-56.3705 + 97.6366i) q^{41} +(-248.834 - 430.992i) q^{43} +(-175.149 + 303.367i) q^{44} +(-39.6174 - 68.6194i) q^{46} +82.9547 q^{47} +(215.472 + 266.872i) q^{49} +(1.28250 - 2.22135i) q^{50} +(-284.584 + 492.913i) q^{52} +(247.056 + 427.914i) q^{53} +502.921 q^{55} +(154.507 + 73.8332i) q^{56} +(-67.7539 - 117.353i) q^{58} -259.001 q^{59} +161.653 q^{61} +54.1535 q^{62} -382.808 q^{64} +817.149 q^{65} -293.870 q^{67} +(-309.621 - 536.279i) q^{68} +(-9.34309 - 119.821i) q^{70} -249.873 q^{71} +(-398.968 - 691.033i) q^{73} +(3.40402 - 5.89594i) q^{74} +(-61.6633 + 106.804i) q^{76} +(-699.161 + 479.777i) q^{77} +740.823 q^{79} +(306.167 + 530.296i) q^{80} +(-33.3023 + 57.6813i) q^{82} +(-215.540 - 373.327i) q^{83} +(-444.520 + 769.932i) q^{85} +(-147.005 - 254.619i) q^{86} +(-211.668 + 366.619i) q^{88} +(224.168 - 388.270i) q^{89} +(-1136.00 + 779.545i) q^{91} +(513.076 + 888.674i) q^{92} +49.0075 q^{94} +177.059 q^{95} +(125.941 + 218.136i) q^{97} +(127.295 + 157.661i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) $ 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8	$ 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} - 5 q^{11} - 14 q^{13} + 52 q^{14} + 494 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} + 93 q^{23} - 349 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} - 122 q^{31} - 326 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} + 761 q^{38} - 18 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} - 2010 q^{47} + 317 q^{49} - 239 q^{50} - 335 q^{52} - 258 q^{53} - 870 q^{55} + 1752 q^{56} + 237 q^{58} - 3330 q^{59} - 878 q^{61} - 1812 q^{62} + 872 q^{64} - 1226 q^{65} - 590 q^{67} + 1374 q^{68} + 1251 q^{70} - 636 q^{71} - 338 q^{73} - 1119 q^{74} + 1006 q^{76} - 2269 q^{77} - 266 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} + 3343 q^{86} + 369 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} + 2382 q^{94} + 6166 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) $ 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 - 5 * q^11 - 14 * q^13 + 52 * q^14 + 494 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 + 93 * q^23 - 349 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 - 122 * q^31 - 326 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 + 761 * q^38 - 18 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 - 2010 * q^47 + 317 * q^49 - 239 * q^50 - 335 * q^52 - 258 * q^53 - 870 * q^55 + 1752 * q^56 + 237 * q^58 - 3330 * q^59 - 878 * q^61 - 1812 * q^62 + 872 * q^64 - 1226 * q^65 - 590 * q^67 + 1374 * q^68 + 1251 * q^70 - 636 * q^71 - 338 * q^73 - 1119 * q^74 + 1006 * q^76 - 2269 * q^77 - 266 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 + 3343 * q^86 + 369 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 + 2382 * q^94 + 6166 * q^95 - 266 * q^97 - 3601 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.590775			0.208870			0.104435	−	0.994532i	$-0.466697\pi$
$2$	0.590775			0.208870			0.104435	+	0.994532i	$0.466697\pi$
$3$		0			0
$3$		0			0
$4$	−7.65099			−0.956373
$5$	5.49223	+	9.51282i	0.491240	+	0.850852i	0.999949	−	0.0100861i	$-0.00321055\pi$
$5$	5.49223	+	9.51282i	0.491240	+	0.850852i	−0.508709	+	0.860938i	$0.669877\pi$
$6$		0			0
$7$	−16.7104	−	7.98524i	−0.902274	−	0.431162i
$7$	−16.7104	−	7.98524i	−0.902274	−	0.431162i
$8$	−9.24621			−0.408629
$9$		0			0
$10$	3.24467	+	5.61993i	0.102605	+	0.177718i
$11$	22.8924	−	39.6508i	0.627483	−	1.08683i	−0.360572	−	0.932731i	$-0.617419\pi$
$11$	22.8924	−	39.6508i	0.627483	−	1.08683i	0.988055	−	0.154101i	$-0.0492481\pi$
$12$		0			0
$13$	37.1957	−	64.4248i	0.793556	−	1.37448i	−0.130196	−	0.991488i	$-0.541561\pi$
$13$	37.1957	−	64.4248i	0.793556	−	1.37448i	0.923752	−	0.382991i	$-0.125106\pi$
$14$	−9.87206	−	4.71748i	−0.188458	−	0.0900571i
$15$		0			0
$16$	55.7455			0.871023
$17$	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
$23$	−67.0601	−	116.152i	−0.607957	−	1.05301i	−0.991577	−	0.129521i	$-0.958656\pi$
$23$	−67.0601	−	116.152i	−0.607957	−	1.05301i	0.383620	−	0.923491i	$-0.374677\pi$
$24$		0			0
$25$	2.17087	−	3.76006i	0.0173670	−	0.0300805i
$26$	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	−0.954999	−	0.296609i	$-0.904144\pi$
$29$	−114.686	−	198.643i	−0.734370	−	1.27197i	0.220629	−	0.975358i	$-0.429189\pi$
$30$		0			0
$31$	91.6652			0.531083			0.265541	−	0.964099i	$-0.414449\pi$
$31$	91.6652			0.531083			0.265541	+	0.964099i	$0.414449\pi$
$32$	106.903			0.590559
$33$		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	$0.158517\pi$
$38$	4.76137	−	8.24693i	0.0203262	−	0.0352060i
$39$		0			0
$40$	−50.7823	−	87.9575i	−0.200735	−	0.347683i
$41$	−56.3705	+	97.6366i	−0.214722	+	0.371909i	−0.953187	−	0.302383i	$-0.902218\pi$
$41$	−56.3705	+	97.6366i	−0.214722	+	0.371909i	0.738465	+	0.674292i	$0.235551\pi$
$42$		0			0
$43$	−248.834	−	430.992i	−0.882483	−	1.52851i	−0.848572	−	0.529080i	$-0.822537\pi$
$43$	−248.834	−	430.992i	−0.882483	−	1.52851i	−0.0339110	−	0.999425i	$-0.510796\pi$
$44$	−175.149	+	303.367i	−0.600108	+	1.03942i
$45$		0			0
$46$	−39.6174	−	68.6194i	−0.126984	−	0.219943i
$47$	82.9547			0.257451			0.128725	−	0.991680i	$-0.458911\pi$
$47$	82.9547			0.257451			0.128725	+	0.991680i	$0.458911\pi$
$48$		0			0
$49$	215.472	+	266.872i	0.628198	+	0.778053i
$50$	1.28250	−	2.22135i	0.00362745	−	0.00628292i
$51$		0			0
$52$	−284.584	+	492.913i	−0.758935	+	1.31451i
$53$	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
$56$	154.507	+	73.8332i	0.368695	+	0.176185i
$57$		0			0
$58$	−67.7539	−	117.353i	−0.153388	−	0.265676i
$59$	−259.001			−0.571509			−0.285754	−	0.958303i	$-0.592244\pi$
$59$	−259.001			−0.571509			−0.285754	+	0.958303i	$0.592244\pi$
$60$		0			0
$61$	161.653			0.339304			0.169652	−	0.985504i	$-0.445736\pi$
$61$	161.653			0.339304			0.169652	+	0.985504i	$0.445736\pi$
$62$	54.1535			0.110927
$63$		0			0
$64$	−382.808			−0.747672
$65$	817.149			1.55930
$66$		0			0
$67$	−293.870			−0.535850			−0.267925	−	0.963440i	$-0.586338\pi$
$67$	−293.870			−0.535850			−0.267925	+	0.963440i	$0.586338\pi$
$68$	−309.621	−	536.279i	−0.552163	−	0.956374i
$69$		0			0
$70$	−9.34309	−	119.821i	−0.0159530	−	0.204590i
$71$	−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	$-0.387594\pi$
$74$	3.40402	−	5.89594i	0.00534743	−	0.00926202i
$75$		0			0
$76$	−61.6633	+	106.804i	−0.0930693	+	0.161201i
$77$	−699.161	+	479.777i	−1.03476	+	0.710074i
$78$		0			0
$79$	740.823			1.05505			0.527526	−	0.849539i	$-0.323120\pi$
$79$	740.823			1.05505			0.527526	+	0.849539i	$0.323120\pi$
$80$	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	0.687576	−	0.726112i	$-0.258675\pi$
$83$	−215.540	−	373.327i	−0.285044	−	0.493710i	−0.972620	+	0.232402i	$0.925341\pi$
$84$		0			0
$85$	−444.520	+	769.932i	−0.567235	+	0.982480i
$86$	−147.005	−	254.619i	−0.184325	−	0.319260i
$87$		0			0
$88$	−211.668	+	366.619i	−0.256407	+	0.444111i
$89$	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
$94$	49.0075			0.0537738
$95$	177.059			0.191220
$96$		0			0
$97$	125.941	+	218.136i	0.131828	+	0.228333i	0.924381	−	0.381470i	$-0.124582\pi$
$97$	125.941	+	218.136i	0.131828	+	0.228333i	−0.792553	+	0.609803i	$0.791249\pi$
$98$	127.295	+	157.661i	0.131212	+	0.162512i
$99$		0			0
$100$	−16.6093	+	28.7682i	−0.0166093	+	0.0287682i
$101$	−60.6905	+	105.119i	−0.0597914	+	0.103562i	−0.894372	−	0.447325i	$-0.852377\pi$
$101$	−60.6905	+	105.119i	−0.0597914	+	0.103562i	0.834580	+	0.550886i	$0.185710\pi$
$102$		0			0
$103$	284.408	+	492.608i	0.272073	+	0.471244i	0.969392	−	0.245516i	$-0.0789575\pi$
$103$	284.408	+	492.608i	0.272073	+	0.471244i	−0.697320	+	0.716760i	$0.745624\pi$
$104$	−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	$0.681034\pi$
$110$	297.113			0.257533
$111$		0			0
$112$	−931.526	−	445.141i	−0.785901	−	0.375552i
$113$	−601.187	+	1041.29i	−0.500486	+	0.866867i	0.499514	+	0.866306i	$0.333512\pi$
$113$	−601.187	+	1041.29i	−0.500486	+	0.866867i	−1.00000		0.000560846i	$0.999821\pi$
$114$		0			0
$115$	736.619	−	1275.86i	0.597305	−	1.03456i
$116$	877.464	+	1519.81i	0.702332	+	1.21647i
$117$		0			0
$118$	−153.011			−0.119371
$119$	−116.529	−	1494.42i	−0.0897661	−	1.15121i
$120$		0			0
$121$	−382.622	−	662.721i	−0.287470	−	0.497912i
$122$	95.5004			0.0708705
$123$		0			0
$124$	−701.329			−0.507913
$125$	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	$0.407166\pi$
$128$	−1081.37			−0.746726
$129$		0			0
$130$	482.751			0.325693
$131$	−937.162	−	1623.21i	−0.625040	−	1.08260i	−0.988533	−	0.151004i	$-0.951749\pi$
$131$	−937.162	−	1623.21i	−0.625040	−	1.08260i	0.363494	−	0.931597i	$-0.381584\pi$
$132$		0			0
$133$	−246.148	+	168.911i	−0.160479	+	0.110124i
$134$	−173.611			−0.111923
$135$		0			0
$136$	−374.177	−	648.093i	−0.235922	−	0.408629i
$137$	1014.75	−	1757.60i	0.632819	−	1.09607i	−0.354154	−	0.935187i	$-0.615231\pi$
$137$	1014.75	−	1757.60i	0.632819	−	1.09607i	0.986973	−	0.160887i	$-0.0514356\pi$
$138$		0			0
$139$	1063.25	−	1841.61i	0.648805	−	1.12376i	−0.334603	−	0.942359i	$-0.608602\pi$
$139$	1063.25	−	1841.61i	0.648805	−	1.12376i	0.983409	−	0.181405i	$-0.0580644\pi$
$140$	121.000	+	1551.77i	0.0730455	+	0.936773i
$141$		0			0
$142$	−147.618			−0.0872385
$143$	−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
$149$	12.1172	+	20.9876i	0.00666227	+	0.0115394i	0.869337	−	0.494219i	$-0.164546\pi$
$149$	12.1172	+	20.9876i	0.00666227	+	0.0115394i	−0.862675	+	0.505759i	$0.831213\pi$
$150$		0			0
$151$	−924.344	+	1601.01i	−0.498159	+	0.862837i	−0.999998	−	0.00212404i	$-0.999324\pi$
$151$	−924.344	+	1601.01i	−0.498159	+	0.862837i	0.501838	+	0.864961i	$0.332657\pi$
$152$	−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
$157$	1444.39			0.734233			0.367117	−	0.930175i	$-0.380345\pi$
$157$	1444.39			0.734233			0.367117	+	0.930175i	$0.380345\pi$
$158$	437.660			0.220369
$159$		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	$0.139964\pi$
$164$	431.290	−	747.016i	0.205354	−	0.355684i
$165$		0			0
$166$	−127.336	−	220.552i	−0.0595372	−	0.103121i
$167$	1799.80	−	3117.34i	0.833968	−	1.44447i	−0.0609003	−	0.998144i	$-0.519397\pi$
$167$	1799.80	−	3117.34i	0.833968	−	1.44447i	0.894868	−	0.446331i	$-0.147269\pi$
$168$		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
$173$	−3241.14			−1.42439			−0.712194	−	0.701982i	$-0.752299\pi$
$173$	−3241.14			−1.42439			−0.712194	+	0.701982i	$0.752299\pi$
$174$		0			0
$175$	−66.3010	+	45.4970i	−0.0286393	+	0.0196529i
$176$	1276.15	−	2210.35i	0.546552	−	0.946656i
$177$		0			0
$178$	132.433	−	229.380i	0.0557655	−	0.0965886i
$179$	−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	$0.574909\pi$
$182$	−671.120	+	460.536i	−0.273334	+	0.187567i
$183$		0			0
$184$	620.052	+	1073.96i	0.248428	+	0.430291i
$185$	126.584			0.0503062
$186$		0			0
$187$	3705.65			1.44911
$188$	−634.685			−0.246219
$189$		0			0
$190$	104.602			0.0399402
$191$	1811.52			0.686267			0.343133	−	0.939287i	$-0.388512\pi$
$191$	1811.52			0.686267			0.343133	+	0.939287i	$0.388512\pi$
$192$		0			0
$193$	2667.83			0.994997			0.497498	−	0.867465i	$-0.334252\pi$
$193$	2667.83			0.994997			0.497498	+	0.867465i	$0.334252\pi$
$194$	74.4025	+	128.869i	0.0275350	+	0.0476920i
$195$		0			0
$196$	−1648.57	−	2041.84i	−0.600792	−	0.744109i
$197$	−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	$0.754256\pi$
$200$	−20.0723	+	34.7663i	−0.00709664	+	0.0122917i
$201$		0			0
$202$	−35.8544	+	62.1016i	−0.0124886	+	0.0216310i
$203$	330.242	+	4235.19i	0.114179	+	1.46430i
$204$		0			0
$205$	−1238.40			−0.421920
$206$	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	−0.981913	−	0.189335i	$-0.939367\pi$
$211$	−1002.20	+	1735.86i	−0.326987	+	0.566359i	0.654925	+	0.755694i	$0.272700\pi$
$212$	−1890.22	−	3273.97i	−0.612364	−	1.06065i
$213$		0			0
$214$	−117.090	+	202.806i	−0.0374024	+	0.0647829i
$215$	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
$220$	−3847.84			−1.17919
$221$	6020.96			1.83264
$222$		0			0
$223$	702.905	+	1217.47i	0.211076	+	0.365595i	0.952052	−	0.305937i	$-0.0989698\pi$
$223$	702.905	+	1217.47i	0.211076	+	0.365595i	−0.740975	+	0.671532i	$0.765636\pi$
$224$	−1786.38	−	853.643i	−0.532847	−	0.254627i
$225$		0			0
$226$	−355.166	+	615.165i	−0.104537	+	0.181063i
$227$	−2490.43	+	4313.55i	−0.728174	+	1.26123i	0.229480	+	0.973313i	$0.426297\pi$
$227$	−2490.43	+	4313.55i	−0.728174	+	1.26123i	−0.957654	+	0.287921i	$0.907036\pi$
$228$		0			0
$229$	−2129.76	−	3688.85i	−0.614579	−	1.06448i	−0.990458	−	0.137813i	$-0.955993\pi$
$229$	−2129.76	−	3688.85i	−0.614579	−	1.06448i	0.375879	−	0.926669i	$-0.377341\pi$
$230$	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
$236$	1981.61			0.546576
$237$		0			0
$238$	−68.8422	−	882.868i	−0.0187495	−	0.240453i
$239$	−1822.76	+	3157.12i	−0.493325	+	0.854464i	−0.999970	−	0.00769024i	$-0.997552\pi$
$239$	−1822.76	+	3157.12i	−0.493325	+	0.854464i	0.506645	+	0.862155i	$0.330885\pi$
$240$		0			0
$241$	−328.286	+	568.609i	−0.0877460	+	0.151981i	−0.906558	−	0.422081i	$-0.861300\pi$
$241$	−328.286	+	568.609i	−0.0877460	+	0.151981i	0.818812	+	0.574062i	$0.194633\pi$
$242$	−226.044	−	391.519i	−0.0600439	−	0.103999i
$243$		0			0
$244$	−1236.80			−0.324501
$245$	−1355.29	+	3515.47i	−0.353413	+	0.916715i
$246$		0			0
$247$	−599.559	−	1038.47i	−0.154450	−	0.267514i
$248$	−847.556			−0.217016
$249$		0			0
$250$	839.343			0.212339
$251$	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
$254$	486.228			0.120113
$255$		0			0
$256$	2423.62			0.591703
$257$	3439.43	+	5957.27i	0.834809	+	1.44593i	0.894186	+	0.447696i	$0.147755\pi$
$257$	3439.43	+	5957.27i	0.834809	+	1.44593i	−0.0593769	+	0.998236i	$0.518911\pi$
$258$		0			0
$259$	−175.977	+	120.759i	−0.0422189	+	0.0289714i
$260$	−6251.99			−1.49128
$261$		0			0
$262$	−553.651	−	958.953i	−0.130552	−	0.226123i
$263$	−2282.82	+	3953.96i	−0.535227	+	0.927041i	0.463925	+	0.885875i	$0.346441\pi$
$263$	−2282.82	+	3953.96i	−0.535227	+	0.927041i	−0.999152	+	0.0411665i	$0.986893\pi$
$264$		0			0
$265$	−2713.78	+	4700.41i	−0.629080	+	1.08960i
$266$	−145.418	+	99.7885i	−0.0335193	+	0.0230016i
$267$		0			0
$268$	2248.40			0.512473
$269$	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
$275$	−99.3928	−	172.153i	−0.0217950	−	0.0377500i
$276$		0			0
$277$	−2496.19	+	4323.53i	−0.541450	+	0.937819i	0.457371	+	0.889276i	$0.348791\pi$
$277$	−2496.19	+	4323.53i	−0.541450	+	0.937819i	−0.998821	+	0.0485429i	$0.984542\pi$
$278$	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	0.938048	−	0.346506i	$-0.112632\pi$
$281$	795.782	+	1378.34i	0.168941	+	0.292614i	−0.769107	+	0.639120i	$0.779299\pi$
$282$		0			0
$283$	1105.12			0.232130			0.116065	−	0.993242i	$-0.462972\pi$
$283$	1105.12			0.232130			0.116065	+	0.993242i	$0.462972\pi$
$284$	1911.77			0.399446
$285$		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
$290$	744.239	−	1289.06i	0.150701	−	0.261021i
$291$		0			0
$292$	3052.50	+	5287.08i	0.611760	+	1.05960i
$293$	−748.863	+	1297.07i	−0.149314	+	0.258620i	−0.930974	−	0.365085i	$-0.881040\pi$
$293$	−748.863	+	1297.07i	−0.149314	+	0.258620i	0.781660	+	0.623705i	$0.214373\pi$
$294$		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
$299$	−9977.39			−1.92979
$300$		0			0
$301$	716.521	+	9189.03i	0.137208	+	1.75962i
$302$	−546.079	+	945.837i	−0.104051	+	0.180221i
$303$		0			0
$304$	449.282	−	778.179i	0.0847635	−	0.146815i
$305$	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	$0.232766\pi$
$308$	5349.27	−	3670.77i	0.989619	−	0.679096i
$309$		0			0
$310$	297.423	+	515.152i	0.0544920	+	0.0943829i
$311$	−6037.53			−1.10083			−0.550413	−	0.834893i	$-0.685530\pi$
$311$	−6037.53			−1.10083			−0.550413	+	0.834893i	$0.685530\pi$
$312$		0			0
$313$	−3322.20			−0.599942			−0.299971	−	0.953948i	$-0.596977\pi$
$313$	−3322.20			−0.599942			−0.299971	+	0.953948i	$0.596977\pi$
$314$	853.308			0.153360
$315$		0			0
$316$	−5668.03			−1.00902
$317$	−78.8533			−0.0139711			−0.00698556	−	0.999976i	$-0.502224\pi$
$317$	−78.8533			−0.0139711			−0.00698556	+	0.999976i	$0.502224\pi$
$318$		0			0
$319$	−10501.8			−1.84322
$320$	−2102.47	−	3641.58i	−0.367286	−	0.636159i
$321$		0			0
$322$	114.079	+	1463.01i	0.0197434	+	0.253200i
$323$	1304.62			0.224739
$324$		0			0
$325$	−161.494	−	279.716i	−0.0275633	−	0.0477411i
$326$	103.015	−	178.428i	0.0175015	−	0.0303135i
$327$		0			0
$328$	521.214	−	902.769i	0.0877415	−	0.151973i
$329$	−1386.20	−	662.413i	−0.232291	−	0.111003i
$330$		0			0
$331$	2556.99			0.424607			0.212303	−	0.977204i	$-0.431903\pi$
$331$	2556.99			0.424607			0.212303	+	0.977204i	$0.431903\pi$
$332$	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	−0.375718	−	0.926734i	$-0.622604\pi$
$337$	3802.94	−	6586.88i	0.614716	−	1.06472i	0.990434	−	0.137985i	$-0.0440627\pi$
$338$	−985.730	−	1707.33i	−0.158629	−	0.274754i
$339$		0			0
$340$	3401.02	−	5890.74i	0.542488	−	0.939618i
$341$	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
$346$	−1914.78			−0.297513
$347$	9164.94			1.41787			0.708933	−	0.705275i	$-0.249177\pi$
$347$	9164.94			1.41787			0.708933	+	0.705275i	$0.249177\pi$
$348$		0			0
$349$	2641.65	+	4575.47i	0.405170	+	0.701775i	0.994341	−	0.106233i	$-0.0338790\pi$
$349$	2641.65	+	4575.47i	0.405170	+	0.701775i	−0.589171	+	0.808008i	$0.700546\pi$
$350$	−39.1690	+	26.8785i	−0.00598191	+	0.00410490i
$351$		0			0
$352$	2447.26	−	4238.77i	0.370566	−	0.641839i
$353$	2493.99	−	4319.71i	0.376038	−	0.651317i	−0.614444	−	0.788961i	$-0.710620\pi$
$353$	2493.99	−	4319.71i	0.376038	−	0.651317i	0.990482	+	0.137644i	$0.0439529\pi$
$354$		0			0
$355$	−1372.36	−	2376.99i	−0.205175	−	0.355374i
$356$	−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
$362$	−670.870			−0.0974037
$363$		0			0
$364$	8691.52	−	5964.29i	1.25154	−	0.858829i
$365$	4382.44	−	7590.62i	0.628459	−	1.08852i
$366$		0			0
$367$	−1434.58	+	2484.77i	−0.204045	+	0.353417i	−0.949828	−	0.312772i	$-0.898742\pi$
$367$	−1434.58	+	2484.77i	−0.204045	+	0.353417i	0.745783	+	0.666189i	$0.232076\pi$
$368$	−3738.30	−	6474.92i	−0.529544	−	0.917197i
$369$		0			0
$370$	74.7827			0.0105075
$371$	−711.403	−	9123.40i	−0.0995532	−	1.27672i
$372$		0			0
$373$	130.354	+	225.780i	0.0180951	+	0.0313417i	0.874931	−	0.484247i	$-0.160906\pi$
$373$	130.354	+	225.780i	0.0180951	+	0.0313417i	−0.856836	+	0.515589i	$0.827573\pi$
$374$	2189.20			0.302676
$375$		0			0
$376$	−767.016			−0.105202
$377$	−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	$0.301988\pi$
$380$	−1354.68			−0.182877
$381$		0			0
$382$	1070.20			0.143341
$383$	620.289	+	1074.37i	0.0827553	+	0.143336i	0.904433	−	0.426617i	$-0.140295\pi$
$383$	620.289	+	1074.37i	0.0827553	+	0.143336i	−0.821677	+	0.569953i	$0.806961\pi$
$384$		0			0
$385$	−8403.98	−	4015.94i	−1.11248	−	0.531614i
$386$	1576.08			0.207825
$387$		0			0
$388$	−963.570	−	1668.95i	−0.126077	−	0.218372i
$389$	−3957.75	+	6855.02i	−0.515851	+	0.893479i	0.483980	+	0.875079i	$0.339191\pi$
$389$	−3957.75	+	6855.02i	−0.515851	+	0.893479i	−0.999831	+	0.0184004i	$0.994143\pi$
$390$		0			0
$391$	5427.59	−	9400.87i	0.702008	−	1.21591i
$392$	−1992.30	−	2467.56i	−0.256700	−	0.317935i
$393$		0			0
$394$	−1985.58			−0.253888
$395$	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
$401$	6990.17	+	12107.3i	0.870505	+	1.50776i	0.861475	+	0.507799i	$0.169541\pi$
$401$	6990.17	+	12107.3i	0.870505	+	1.50776i	0.00902952	+	0.999959i	$0.497126\pi$
$402$		0			0
$403$	3409.55	−	5905.51i	0.421444	−	0.729962i
$404$	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
$409$	473.945			0.0572984			0.0286492	−	0.999590i	$-0.490879\pi$
$409$	473.945			0.0572984			0.0286492	+	0.999590i	$0.490879\pi$
$410$	−731.615			−0.0881266
$411$		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
$416$	3976.32	−	6887.18i	0.468642	−	0.811712i
$417$		0			0
$418$	−217.998	−	377.584i	−0.0255087	−	0.0441823i
$419$	4736.18	−	8203.31i	0.552214	−	0.956462i	−0.445901	−	0.895082i	$-0.647117\pi$
$419$	4736.18	−	8203.31i	0.552214	−	0.956462i	0.998114	−	0.0613799i	$-0.0195501\pi$
$420$		0			0
$421$	6733.40	+	11662.6i	0.779491	+	1.35012i	0.932235	+	0.361853i	$0.117856\pi$
$421$	6733.40	+	11662.6i	0.779491	+	1.35012i	−0.152744	+	0.988266i	$0.548811\pi$
$422$	−592.075	+	1025.50i	−0.0682980	+	0.118296i
$423$		0			0
$424$	−2284.34	−	3956.58i	−0.261644	−	0.453181i
$425$	351.404			0.0401073
$426$		0			0
$427$	−2701.28	−	1290.84i	−0.306145	−	0.146295i
$428$	1516.41	−	2626.49i	0.171258	−	0.296627i
$429$		0			0
$430$	1614.77	−	2796.86i	0.181095	−	0.313666i
$431$	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	$0.514752\pi$
$434$	−904.924	−	432.429i	−0.100087	−	0.0478277i
$435$		0			0
$436$	−4008.72	−	6943.30i	−0.440327	−	0.762669i
$437$	−2161.89			−0.236653
$438$		0			0
$439$	3890.80			0.423001			0.211501	−	0.977378i	$-0.432165\pi$
$439$	3890.80			0.423001			0.211501	+	0.977378i	$0.432165\pi$
$440$	−4650.11			−0.503830
$441$		0			0
$442$	3557.03			0.382784
$443$	−2250.71			−0.241387			−0.120694	−	0.992690i	$-0.538512\pi$
$443$	−2250.71			−0.241387			−0.120694	+	0.992690i	$0.538512\pi$
$444$		0			0
$445$	4924.72			0.524616
$446$	415.259	+	719.250i	0.0440876	+	0.0763620i
$447$		0			0
$448$	6396.86	+	3056.81i	0.674606	+	0.322368i
$449$	−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
$452$	4599.67	−	7966.86i	0.478651	−	0.829048i
$453$		0			0
$454$	−1471.28	+	2548.34i	−0.152094	+	0.263435i
$455$	−13654.8	−	6525.13i	−1.40692	−	0.672313i
$456$		0			0
$457$	−10900.7			−1.11578			−0.557891	−	0.829914i	$-0.688389\pi$
$457$	−10900.7			−1.11578			−0.557891	+	0.829914i	$0.688389\pi$
$458$	−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	0.905542	−	0.424257i	$-0.139465\pi$
$461$	844.836	+	1463.30i	0.0853534	+	0.147836i	−0.820188	+	0.572094i	$0.806131\pi$
$462$		0			0
$463$	−4861.63	+	8420.59i	−0.487989	+	0.845222i	−0.999905	−	0.0138136i	$-0.995603\pi$
$463$	−4861.63	+	8420.59i	−0.487989	+	0.845222i	0.511915	+	0.859036i	$0.328936\pi$
$464$	−6393.25	−	11073.4i	−0.639653	−	1.10791i
$465$		0			0
$466$	548.826	−	950.595i	0.0545577	−	0.0944967i
$467$	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
$472$	2394.77			0.233535
$473$	−22785.6			−2.21497
$474$		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
$479$	8914.20	−	15439.8i	0.850313	−	1.47279i	−0.0306124	−	0.999531i	$-0.509746\pi$
$479$	8914.20	−	15439.8i	0.850313	−	1.47279i	0.880926	−	0.473255i	$-0.156921\pi$
$480$		0			0
$481$	−428.640	−	742.427i	−0.0406327	−	0.0703779i
$482$	−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	$-0.591345\pi$
$488$	−1494.68			−0.138649
$489$		0			0
$490$	−800.669	+	2076.85i	−0.0738174	+	0.191475i
$491$	3811.67	−	6602.01i	0.350343	−	0.606811i	−0.635967	−	0.771717i	$-0.719398\pi$
$491$	3811.67	−	6602.01i	0.350343	−	0.606811i	0.986309	+	0.164905i	$0.0527318\pi$
$492$		0			0
$493$	9282.29	−	16077.4i	0.847978	−	1.46874i
$494$	−354.205	−	613.500i	−0.0322600	−	0.0558759i
$495$		0			0
$496$	5109.92			0.462585
$497$	4175.46	+	1995.29i	0.376851	+	0.180083i
$498$		0			0
$499$	6230.96	+	10792.3i	0.558990	+	0.968199i	0.997581	+	0.0695126i	$0.0221444\pi$
$499$	6230.96	+	10792.3i	0.558990	+	0.968199i	−0.438591	+	0.898687i	$0.644522\pi$
$500$	−10870.1			−0.972254
$501$		0			0
$502$	2712.73			0.241186
$503$	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
$506$	−3627.75			−0.318722
$507$		0			0
$508$	−6297.02			−0.549971
$509$	9825.63	+	17018.5i	0.855625	+	1.48199i	0.876064	+	0.482196i	$0.160161\pi$
$509$	9825.63	+	17018.5i	0.855625	+	1.48199i	−0.0204383	+	0.999791i	$0.506506\pi$
$510$		0			0
$511$	1148.84	+	14733.3i	0.0994549	+	1.27546i
$512$	10082.8			0.870315
$513$		0			0
$514$	2031.93	+	3519.41i	0.174367	+	0.302012i
$515$	−3124.06	+	5411.04i	−0.267306	+	0.462988i
$516$		0			0
$517$	1899.03	−	3289.22i	0.161546	−	0.279806i
$518$	−103.963	+	71.3413i	−0.00881828	+	0.00605127i
$519$		0			0
$520$	−7555.53			−0.637176
$521$	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
$527$	3709.52	+	6425.08i	0.306621	+	0.531083i
$528$		0			0
$529$	−2910.62	+	5041.34i	−0.239222	+	0.414345i
$530$	−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
$535$	−4354.18			−0.351865
$536$	2717.19			0.218964
$537$		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	$0.989978\pi$
$542$	106.695	−	184.801i	0.00845560	−	0.0146455i
$543$		0			0
$544$	4326.15	+	7493.11i	0.340960	+	0.590560i
$545$	−5755.28	+	9968.44i	−0.452347	+	0.783488i
$546$		0			0
$547$	−8982.32	−	15557.8i	−0.702114	−	1.21610i	−0.967723	−	0.252016i	$-0.918906\pi$
$547$	−8982.32	−	15557.8i	−0.702114	−	1.21610i	0.265609	−	0.964081i	$-0.414427\pi$
$548$	−7763.86	+	13447.4i	−0.605211	+	1.04826i
$549$		0			0
$550$	−58.7188	−	101.704i	−0.00455232	−	0.00788485i
$551$	−3697.27			−0.285861
$552$		0			0
$553$	−12379.4	−	5915.65i	−0.951946	−	0.454899i
$554$	−1474.69	+	2554.23i	−0.113093	+	0.195883i
$555$		0			0
$556$	−8134.93	+	14090.1i	−0.620500	+	1.07474i
$557$	−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
$560$	−881.613	−	11306.3i	−0.0665267	−	0.853172i
$561$		0			0
$562$	470.128	+	814.286i	0.0352868	+	0.0611185i
$563$	−21720.6			−1.62596			−0.812981	−	0.582291i	$-0.802157\pi$
$563$	−21720.6			−1.62596			−0.812981	+	0.582291i	$0.802157\pi$
$564$		0			0
$565$	−13207.4			−0.983434
$566$	652.880			0.0484851
$567$		0			0
$568$	2310.37			0.170671
$569$	19408.4			1.42995			0.714974	−	0.699151i	$-0.246438\pi$
$569$	19408.4			1.42995			0.714974	+	0.699151i	$0.246438\pi$
$570$		0			0
$571$	2394.79			0.175514			0.0877572	−	0.996142i	$-0.472030\pi$
$571$	2394.79			0.175514			0.0877572	+	0.996142i	$0.472030\pi$
$572$	13029.6	+	22567.9i	0.952438	+	1.64967i
$573$		0			0
$574$	1017.09	−	697.948i	0.0739592	−	0.0507522i
$575$	−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	$0.680910\pi$
$578$	−483.748	+	837.877i	−0.0348119	+	0.0602960i
$579$		0			0
$580$	−9638.47	+	16694.3i	−0.690027	+	1.19516i
$581$	620.652	+	7959.56i	0.0443184	+	0.568362i
$582$		0			0
$583$	22622.8			1.60711
$584$	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	0.798220	−	0.602366i	$-0.205775\pi$
$587$	−1742.96	−	3018.90i	−0.122555	−	0.212271i	−0.920774	+	0.390095i	$0.872442\pi$
$588$		0			0
$589$	738.778	−	1279.60i	0.0516822	−	0.0895163i
$590$	−840.372	−	1455.57i	−0.0586399	−	0.101567i
$591$		0			0
$592$	321.203	−	556.340i	0.0222996	−	0.0386241i
$593$	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
$598$	−5894.39			−0.403076
$599$	−15292.9			−1.04316			−0.521580	−	0.853202i	$-0.674657\pi$
$599$	−15292.9			−1.04316			−0.521580	+	0.853202i	$0.674657\pi$
$600$		0			0
$601$	−9098.78	−	15759.5i	−0.617549	−	1.06963i	−0.989932	−	0.141547i	$-0.954792\pi$
$601$	−9098.78	−	15759.5i	−0.617549	−	1.06963i	0.372383	−	0.928079i	$-0.378541\pi$
$602$	423.302	+	5428.65i	0.0286587	+	0.367534i
$603$		0			0
$604$	7072.14	−	12249.3i	0.476426	−	0.825195i
$605$	4202.90	−	7279.63i	0.282433	−	0.489189i
$606$		0			0
$607$	−811.823	−	1406.12i	−0.0542848	−	0.0940240i	0.837606	−	0.546275i	$-0.183955\pi$
$607$	−811.823	−	1406.12i	−0.0542848	−	0.0940240i	−0.891891	+	0.452251i	$0.850621\pi$
$608$	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	$-0.373638\pi$
$614$	4730.74			0.310940
$615$		0			0
$616$	6464.59	−	4436.12i	0.422834	−	0.290157i
$617$	13260.3	−	22967.5i	0.865218	−	1.49860i	−0.00161310	−	0.999999i	$-0.500513\pi$
$617$	13260.3	−	22967.5i	0.865218	−	1.49860i	0.866831	−	0.498602i	$-0.166153\pi$
$618$		0			0
$619$	−11146.7	+	19306.7i	−0.723788	+	1.25364i	0.235683	+	0.971830i	$0.424267\pi$
$619$	−11146.7	+	19306.7i	−0.723788	+	1.25364i	−0.959471	+	0.281808i	$0.909066\pi$
$620$	−3851.86	−	6671.62i	−0.249507	−	0.432159i
$621$		0			0
$622$	−3566.82			−0.229930
$623$	−6846.35	+	4698.10i	−0.440278	+	0.302127i
$624$		0			0
$625$	7531.72	+	13045.3i	0.482030	+	0.834900i
$626$	−1962.67			−0.125310
$627$		0			0
$628$	−11051.0			−0.702201
$629$	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	$0.252844\pi$
$632$	−6849.81			−0.431124
$633$		0			0
$634$	−46.5846			−0.00291815
$635$	4520.29	+	7829.37i	0.282492	+	0.489290i
$636$		0			0
$637$	25207.8	−	3955.24i	1.56793	−	0.246016i
$638$	−6204.19			−0.384994
$639$		0			0
$640$	−5939.16	−	10286.9i	−0.366822	−	0.635354i
$641$	−1880.28	+	3256.74i	−0.115860	+	0.200676i	−0.918123	−	0.396295i	$-0.870296\pi$
$641$	−1880.28	+	3256.74i	−0.115860	+	0.200676i	0.802263	+	0.596971i	$0.203629\pi$
$642$		0			0
$643$	−722.264	+	1251.00i	−0.0442975	+	0.0767255i	−0.887324	−	0.461146i	$-0.847438\pi$
$643$	−722.264	+	1251.00i	−0.0442975	+	0.0767255i	0.843027	+	0.537872i	$0.180772\pi$
$644$	−1477.41	−	18947.1i	−0.0904009	−	1.15935i
$645$		0			0
$646$	770.734			0.0469414
$647$	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
$653$	−10918.7	−	18911.8i	−0.654339	−	1.13335i	−0.982059	−	0.188574i	$-0.939614\pi$
$653$	−10918.7	−	18911.8i	−0.654339	−	1.13335i	0.327720	−	0.944775i	$-0.393720\pi$
$654$		0			0
$655$	10294.2	−	17830.1i	0.614089	−	1.06363i
$656$	−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	0.700055	−	0.714089i	$-0.253159\pi$
$659$	−4540.44	−	7864.27i	−0.268392	−	0.464868i	−0.968447	+	0.249221i	$0.919826\pi$
$660$		0			0
$661$	25532.2			1.50240			0.751200	−	0.660075i	$-0.229475\pi$
$661$	25532.2			1.50240			0.751200	+	0.660075i	$0.229475\pi$
$662$	1510.61			0.0886879
$663$		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
$668$	−13770.2	+	23850.7i	−0.797584	+	1.38146i
$669$		0			0
$670$	−953.512	−	1651.53i	−0.0549812	−	0.0952302i
$671$	3700.62	−	6409.66i	0.212907	−	0.368766i
$672$		0			0
$673$	7674.86	+	13293.3i	0.439590	+	0.761393i	0.997658	−	0.0684030i	$-0.0217904\pi$
$673$	7674.86	+	13293.3i	0.439590	+	0.761393i	−0.558068	+	0.829795i	$0.688457\pi$
$674$	2246.68	−	3891.37i	0.128396	−	0.222388i
$675$		0			0
$676$	12766.0	+	22111.3i	0.726329	+	1.25804i
$677$	−25477.1			−1.44633			−0.723165	−	0.690676i	$-0.757313\pi$
$677$	−25477.1			−1.44633			−0.723165	+	0.690676i	$0.757313\pi$
$678$		0			0
$679$	−362.648	−	4650.79i	−0.0204966	−	0.262858i
$680$	4110.13	−	7118.95i	0.231788	−	0.401469i
$681$		0			0
$682$	1239.70	−	2147.23i	0.0696051	−	0.120560i
$683$	−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
$686$	−868.188	−	3651.06i	−0.0483200	−	0.203204i
$687$		0			0
$688$	−13871.3	−	24025.9i	−0.768663	−	1.33136i
$689$	36757.7			2.03245
$690$		0			0
$691$	−4113.85			−0.226481			−0.113240	−	0.993568i	$-0.536123\pi$
$691$	−4113.85			−0.226481			−0.113240	+	0.993568i	$0.536123\pi$
$692$	24797.9			1.36225
$693$		0			0
$694$	5414.42			0.296151
$695$	23358.5			1.27488
$696$		0			0
$697$	−9124.84			−0.495879
$698$	1560.62	+	2703.07i	0.0846280	+	0.146580i
$699$		0			0
$700$	507.268	−	348.097i	0.0273899	−	0.0187955i
$701$	−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
$704$	−8763.39	+	15178.6i	−0.469152	+	0.812594i
$705$		0			0
$706$	1473.38	−	2551.98i	0.0785432	−	0.136041i
$707$	1853.56	−	1271.95i	0.0986001	−	0.0676613i
$708$		0			0
$709$	−88.1425			−0.00466891			−0.00233446	−	0.999997i	$-0.500743\pi$
$709$	−88.1425			−0.00466891			−0.00233446	+	0.999997i	$0.500743\pi$
$710$	−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
$716$	4443.40	+	7696.19i	0.231924	+	0.401704i
$717$		0			0
$718$	88.3045	−	152.948i	0.00458982	−	0.00794981i
$719$	−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
$724$	8688.28			0.445991
$725$	−995.878			−0.0510151
$726$		0			0
$727$	4457.88	+	7721.27i	0.227419	+	0.393901i	0.957042	−	0.289948i	$-0.0936380\pi$
$727$	4457.88	+	7721.27i	0.227419	+	0.393901i	−0.729624	+	0.683849i	$0.760305\pi$
$728$	10503.7	−	7207.84i	0.534743	−	0.366951i
$729$		0			0
$730$	2589.04	−	4484.35i	0.131267	−	0.227360i
$731$	20139.6	−	34882.9i	1.01900	−	1.76497i
$732$		0			0
$733$	3237.36	+	5607.27i	0.163130	+	0.282550i	0.935990	−	0.352027i	$-0.114508\pi$
$733$	3237.36	+	5607.27i	0.163130	+	0.282550i	−0.772859	+	0.634577i	$0.781174\pi$
$734$	−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	$0.905734\pi$
$740$	−968.493			−0.0481115
$741$		0			0
$742$	−420.279	−	5389.88i	−0.0207937	−	0.266669i
$743$	−1098.47	+	1902.60i	−0.0542381	+	0.0939431i	−0.891870	−	0.452292i	$-0.850606\pi$
$743$	−1098.47	+	1902.60i	−0.0542381	+	0.0939431i	0.837632	+	0.546236i	$0.183940\pi$
$744$		0			0
$745$	−133.101	+	230.537i	−0.00654555	+	0.0113372i
$746$	77.0099	+	133.385i	0.00377953	+	0.00654635i
$747$		0			0
$748$	−28351.8			−1.38589
$749$	6053.19	−	4153.81i	0.295299	−	0.202640i
$750$		0			0
$751$	−1635.21	−	2832.27i	−0.0794536	−	0.137618i	0.823561	−	0.567228i	$-0.191984\pi$
$751$	−1635.21	−	2832.27i	−0.0794536	−	0.137618i	−0.903014	+	0.429610i	$0.858651\pi$
$752$	4624.35			0.224245
$753$		0			0
$754$	−10080.6			−0.486888
$755$	−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	$0.474184\pi$
$758$	5080.09			0.243426
$759$		0			0
$760$	−1637.13			−0.0781378
$761$	7704.62	+	13344.8i	0.367007	+	0.635674i	0.989096	−	0.147272i	$-0.0470492\pi$
$761$	7704.62	+	13344.8i	0.367007	+	0.635674i	−0.622089	+	0.782946i	$0.713716\pi$
$762$		0			0
$763$	−1508.72	−	19348.6i	−0.0715848	−	0.918041i
$764$	−13859.9			−0.656327
$765$		0			0
$766$	366.451	+	634.712i	0.0172851	+	0.0299388i
$767$	−9633.70	+	16686.1i	−0.453524	+	0.785527i
$768$		0			0
$769$	9472.98	−	16407.7i	0.444219	−	0.769410i	−0.553779	−	0.832664i	$-0.686815\pi$
$769$	9472.98	−	16407.7i	0.444219	−	0.769410i	0.997997	+	0.0632543i	$0.0201479\pi$
$770$	−4964.86	−	2372.52i	−0.232365	−	0.111038i
$771$		0			0
$772$	−20411.5			−0.951588
$773$	−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
$779$	908.640	+	1573.81i	0.0417913	+	0.0723846i
$780$		0			0
$781$	−5720.18	+	9907.64i	−0.262080	+	0.453935i
$782$	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
$787$	−9694.98			−0.439122			−0.219561	−	0.975599i	$-0.570462\pi$
$787$	−9694.98			−0.439122			−0.219561	+	0.975599i	$0.570462\pi$
$788$	25714.8			1.16250
$789$		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
$794$	−4327.70	+	7495.79i	−0.193431	+	0.335032i
$795$		0			0
$796$	−5281.07	−	9147.09i	−0.235154	−	0.407299i
$797$	10265.5	−	17780.4i	0.456240	−	0.790231i	−0.542519	−	0.840044i	$-0.682529\pi$
$797$	10265.5	−	17780.4i	0.456240	−	0.790231i	0.998759	+	0.0498132i	$0.0158626\pi$
$798$		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
$803$	−36533.3			−1.60552
$804$		0			0
$805$	−22497.2	+	15438.0i	−0.984997	+	0.675924i
$806$	2014.28	−	3488.83i	0.0880271	−	0.152467i
$807$		0			0
$808$	561.157	−	971.952i	0.0244325	−	0.0423183i
$809$	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	$0.210629\pi$
$812$	−2526.67	−	32403.4i	−0.109198	−	1.40041i
$813$		0			0
$814$	−155.852	−	269.944i	−0.00671084	−	0.0116235i
$815$	3830.79			0.164646
$816$		0			0
$817$	−8021.92			−0.343515
$818$	279.995			0.0119680
$819$		0			0
$820$	9474.97			0.403513
$821$	−8125.35			−0.345404			−0.172702	−	0.984974i	$-0.555250\pi$
$821$	−8125.35			−0.345404			−0.172702	+	0.984974i	$0.555250\pi$
$822$		0			0
$823$	32747.6			1.38701			0.693505	−	0.720451i	$-0.256065\pi$
$823$	32747.6			1.38701			0.693505	+	0.720451i	$0.256065\pi$
$824$	−2629.69	−	4554.76i	−0.111177	−	0.192564i
$825$		0			0
$826$	2556.87	+	1221.83i	0.107706	+	0.0514684i
$827$	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	$0.974109\pi$
$830$	1398.71	−	2422.64i	0.0584941	−	0.101315i
$831$		0			0
$832$	−14238.8	+	24662.3i	−0.593320	+	1.02766i
$833$	−9986.09	+	25902.9i	−0.415363	+	1.07741i
$834$		0			0
$835$	39539.6			1.63871
$836$	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	0.997227	−	0.0744142i	$-0.0237087\pi$
$839$	10551.2	+	18275.2i	0.434169	+	0.752003i	−0.563058	+	0.826417i	$0.690375\pi$
$840$		0			0
$841$	−14111.5	+	24441.8i	−0.578599	+	1.00216i
$842$	3977.92	+	6889.97i	0.162813	+	0.282000i
$843$		0			0
$844$	7667.82	−	13281.1i	0.312722	−	0.541650i
$845$	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
$850$	207.601			0.00837723
$851$	−1545.59			−0.0622588
$852$		0			0
$853$	−15303.6	−	26506.6i	−0.614285	−	1.06397i	−0.990510	−	0.137444i	$-0.956111\pi$
$853$	−15303.6	−	26506.6i	−0.614285	−	1.06397i	0.376225	−	0.926528i	$-0.377222\pi$
$854$	−1595.85	−	762.594i	−0.0639447	−	0.0305567i
$855$		0			0
$856$	1832.58	−	3174.11i	0.0731731	−	0.126739i
$857$	−18701.7	+	32392.2i	−0.745434	+	1.29113i	0.204558	+	0.978854i	$0.434424\pi$
$857$	−18701.7	+	32392.2i	−0.745434	+	1.29113i	−0.949992	+	0.312275i	$0.898909\pi$
$858$		0			0
$859$	10176.5	+	17626.2i	0.404212	+	0.700116i	0.994229	−	0.107275i	$-0.0342125\pi$
$859$	10176.5	+	17626.2i	0.404212	+	0.700116i	−0.590017	+	0.807391i	$0.700879\pi$
$860$	−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
$866$	−493.218			−0.0193536
$867$		0			0
$868$	11719.5	+	5600.28i	0.458277	+	0.218993i
$869$	16959.2	−	29374.2i	0.662027	−	1.14666i
$870$		0			0
$871$	−10930.7	+	18932.5i	−0.425227	+	0.736515i
$872$	−4844.53	−	8390.97i	−0.188138	−	0.325865i
$873$		0			0
$874$	−1277.19			−0.0494298
$875$	−23741.2	−	11345.0i	−0.917257	−	0.438322i
$876$		0			0
$877$	7562.65	+	13098.9i	0.291189	+	0.504354i	0.974091	−	0.226156i	$-0.0726159\pi$
$877$	7562.65	+	13098.9i	0.291189	+	0.504354i	−0.682902	+	0.730510i	$0.739283\pi$
$878$	2298.59			0.0883525
$879$		0			0
$880$	28035.5			1.07395
$881$	−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	$0.779621\pi$
$884$	−46066.2			−1.75269
$885$		0			0
$886$	−1329.66			−0.0504187
$887$	−425.110	−	736.313i	−0.0160922	−	0.0278726i	0.857867	−	0.513872i	$-0.171789\pi$
$887$	−425.110	−	736.313i	−0.0160922	−	0.0278726i	−0.873959	+	0.485999i	$0.838456\pi$
$888$		0			0
$889$	−13753.2	−	6572.12i	−0.518861	−	0.247944i
$890$	2909.40			0.109577
$891$		0			0
$892$	−5377.92	−	9314.83i	−0.201868	−	0.349645i
$893$	668.576	−	1158.01i	0.0250538	−	0.0433944i
$894$		0			0
$895$	6379.35	−	11049.4i	0.238255	−	0.412670i
$896$	18070.2	+	8635.04i	0.673752	+	0.321960i
$897$		0			0
$898$	−1391.11			−0.0516948
$899$	−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
$905$	−6236.85	−	10802.5i	−0.229083	−	0.396783i
$906$		0			0
$907$	−18321.1	+	31733.1i	−0.670719	+	1.16172i	0.306982	+	0.951715i	$0.400681\pi$
$907$	−18321.1	+	31733.1i	−0.670719	+	1.16172i	−0.977701	+	0.210004i	$0.932652\pi$
$908$	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	0.982682	−	0.185300i	$-0.0593256\pi$
$911$	9097.68	+	15757.6i	0.330867	+	0.573078i	−0.651815	+	0.758378i	$0.725992\pi$
$912$		0			0
$913$	−19736.9			−0.715440
$914$	−6439.85			−0.233054
$915$		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	$0.224407\pi$
$920$	−6810.93	+	11796.9i	−0.244076	+	0.422752i
$921$		0			0
$922$	499.108	+	864.480i	0.0178278	+	0.0308787i
$923$	−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
$929$	49820.3			1.75947			0.879736	−	0.475463i	$-0.157719\pi$
$929$	49820.3			1.75947			0.879736	+	0.475463i	$0.157719\pi$
$930$		0			0
$931$	5462.01	−	857.019i	0.192277	−	0.0301693i
$932$	−7107.72	+	12310.9i	−0.249808	+	0.432680i
$933$		0			0
$934$	1941.94	−	3363.54i	0.0680324	−	0.117836i
$935$	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	$0.398297\pi$
$938$	2901.10	+	1386.33i	0.100986	+	0.0482571i
$939$		0			0
$940$	−3485.83	−	6037.64i	−0.120953	−	0.209496i
$941$	−2876.36			−0.0996457			−0.0498229	−	0.998758i	$-0.515866\pi$
$941$	−2876.36			−0.0996457			−0.0498229	+	0.998758i	$0.515866\pi$
$942$		0			0
$943$	15120.9			0.522166
$944$	−14438.1			−0.497797
$945$		0			0
$946$	−13461.1			−0.462642
$947$	41168.7			1.41267			0.706337	−	0.707876i	$-0.250346\pi$
$947$	41168.7			1.41267			0.706337	+	0.707876i	$0.250346\pi$
$948$		0			0
$949$	−59359.5			−2.03044
$950$	−20.6726	−	35.8060i	−0.000706009	−	0.00122284i
$951$		0			0
$952$	1077.45	+	13817.8i	0.0366810	+	0.470416i
$953$	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
$956$	13945.9	−	24155.1i	0.471803	−	0.817187i
$957$		0			0
$958$	5266.28	−	9121.47i	0.177605	−	0.307621i
$959$	−30991.8	+	21267.1i	−1.04356	+	0.716112i
$960$		0			0
$961$	−21388.5			−0.717951
$962$	−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	−0.145283	+	0.989390i	$0.546409\pi$
$967$	−27949.8	+	48410.5i	−0.929478	+	1.60990i	−0.784196	+	0.620514i	$0.786924\pi$
$968$	3537.80	+	6127.66i	0.117468	+	0.203461i
$969$		0			0
$970$	−817.271	+	1415.56i	−0.0270526	+	0.0468564i
$971$	−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
$976$	9011.41			0.295541
$977$	20934.3			0.685513			0.342756	−	0.939424i	$-0.388639\pi$
$977$	20934.3			0.685513			0.342756	+	0.939424i	$0.388639\pi$
$978$		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
$983$	−449.641	+	778.802i	−0.0145894	+	0.0252695i	−0.873228	−	0.487312i	$-0.837977\pi$
$983$	−449.641	+	778.802i	−0.0145894	+	0.0252695i	0.858639	+	0.512582i	$0.171311\pi$
$984$		0			0
$985$	−18459.2	−	31972.3i	−0.597117	−	1.03424i
$986$	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	$0.623474\pi$
$992$	9799.26			0.313636
$993$		0			0
$994$	2466.76	+	1178.77i	0.0787131	+	0.0376140i
$995$	−7581.99	+	13132.4i	−0.241573	+	0.418417i
$996$		0			0
$997$	26528.4	−	45948.6i	0.842692	−	1.45959i	−0.0449179	−	0.998991i	$-0.514303\pi$
$997$	26528.4	−	45948.6i	0.842692	−	1.45959i	0.887610	−	0.460595i	$-0.152364\pi$
$998$	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.h.a.37.13		44
3.2	odd	2		63.4.h.a.58.10	yes	44
7.4	even	3		189.4.g.a.172.10		44
9.2	odd	6		63.4.g.a.16.13	yes	44
9.7	even	3		189.4.g.a.100.10		44
21.11	odd	6		63.4.g.a.4.13	✓	44
63.11	odd	6		63.4.h.a.25.10	yes	44
63.25	even	3	inner	189.4.h.a.46.13		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.13	✓	44	21.11	odd	6
63.4.g.a.16.13	yes	44	9.2	odd	6
63.4.h.a.25.10	yes	44	63.11	odd	6
63.4.h.a.58.10	yes	44	3.2	odd	2
189.4.g.a.100.10		44	9.7	even	3
189.4.g.a.172.10		44	7.4	even	3
189.4.h.a.37.13		44	1.1	even	1	trivial
189.4.h.a.46.13		44	63.25	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.590775 q^{2} -7.65099 q^{4} +(5.49223 + 9.51282i) q^{5} +(-16.7104 - 7.98524i) q^{7} -9.24621 q^{8} +O(q^{10})\)	\(q+0.590775 q^{2} -7.65099 q^{4} +(5.49223 + 9.51282i) q^{5} +(-16.7104 - 7.98524i) q^{7} -9.24621 q^{8} +(3.24467 + 5.61993i) q^{10} +(22.8924 - 39.6508i) q^{11} +(37.1957 - 64.4248i) q^{13} +(-9.87206 - 4.71748i) q^{14} +55.7455 q^{16} +(40.4681 + 70.0928i) q^{17} +(8.05953 - 13.9595i) q^{19} +(-42.0210 - 72.7824i) q^{20} +(13.5242 - 23.4247i) q^{22} +(-67.0601 - 116.152i) q^{23} +(2.17087 - 3.76006i) q^{25} +(21.9743 - 38.0606i) q^{26} +(127.851 + 61.0949i) q^{28} +(-114.686 - 198.643i) q^{29} +91.6652 q^{31} +106.903 q^{32} +(23.9075 + 41.4091i) q^{34} +(-15.8150 - 202.819i) q^{35} +(5.76196 - 9.98001i) q^{37} +(4.76137 - 8.24693i) q^{38} +(-50.7823 - 87.9575i) q^{40} +(-56.3705 + 97.6366i) q^{41} +(-248.834 - 430.992i) q^{43} +(-175.149 + 303.367i) q^{44} +(-39.6174 - 68.6194i) q^{46} +82.9547 q^{47} +(215.472 + 266.872i) q^{49} +(1.28250 - 2.22135i) q^{50} +(-284.584 + 492.913i) q^{52} +(247.056 + 427.914i) q^{53} +502.921 q^{55} +(154.507 + 73.8332i) q^{56} +(-67.7539 - 117.353i) q^{58} -259.001 q^{59} +161.653 q^{61} +54.1535 q^{62} -382.808 q^{64} +817.149 q^{65} -293.870 q^{67} +(-309.621 - 536.279i) q^{68} +(-9.34309 - 119.821i) q^{70} -249.873 q^{71} +(-398.968 - 691.033i) q^{73} +(3.40402 - 5.89594i) q^{74} +(-61.6633 + 106.804i) q^{76} +(-699.161 + 479.777i) q^{77} +740.823 q^{79} +(306.167 + 530.296i) q^{80} +(-33.3023 + 57.6813i) q^{82} +(-215.540 - 373.327i) q^{83} +(-444.520 + 769.932i) q^{85} +(-147.005 - 254.619i) q^{86} +(-211.668 + 366.619i) q^{88} +(224.168 - 388.270i) q^{89} +(-1136.00 + 779.545i) q^{91} +(513.076 + 888.674i) q^{92} +49.0075 q^{94} +177.059 q^{95} +(125.941 + 218.136i) q^{97} +(127.295 + 157.661i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} - 5 q^{11} - 14 q^{13} + 52 q^{14} + 494 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} + 93 q^{23} - 349 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} - 122 q^{31} - 326 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} + 761 q^{38} - 18 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} - 2010 q^{47} + 317 q^{49} - 239 q^{50} - 335 q^{52} - 258 q^{53} - 870 q^{55} + 1752 q^{56} + 237 q^{58} - 3330 q^{59} - 878 q^{61} - 1812 q^{62} + 872 q^{64} - 1226 q^{65} - 590 q^{67} + 1374 q^{68} + 1251 q^{70} - 636 q^{71} - 338 q^{73} - 1119 q^{74} + 1006 q^{76} - 2269 q^{77} - 266 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} + 3343 q^{86} + 369 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} + 2382 q^{94} + 6166 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) \) 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 - 5 * q^11 - 14 * q^13 + 52 * q^14 + 494 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 + 93 * q^23 - 349 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 - 122 * q^31 - 326 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 + 761 * q^38 - 18 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 - 2010 * q^47 + 317 * q^49 - 239 * q^50 - 335 * q^52 - 258 * q^53 - 870 * q^55 + 1752 * q^56 + 237 * q^58 - 3330 * q^59 - 878 * q^61 - 1812 * q^62 + 872 * q^64 - 1226 * q^65 - 590 * q^67 + 1374 * q^68 + 1251 * q^70 - 636 * q^71 - 338 * q^73 - 1119 * q^74 + 1006 * q^76 - 2269 * q^77 - 266 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 + 3343 * q^86 + 369 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 + 2382 * q^94 + 6166 * q^95 - 266 * q^97 - 3601 * q^98

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