LMFDB - Embedded newform 189.4.g.a.100.5

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			100.5
Character	$\chi$	$=$	189.100
Dual form			189.4.g.a.172.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68671 - 2.92146i) q^{2} +(-1.68996 + 2.92710i) q^{4} +9.74532 q^{5} +(0.158327 + 18.5196i) q^{7} -15.5854 q^{8} +O(q^{10})$	\(q+(-1.68671 - 2.92146i) q^{2} +(-1.68996 + 2.92710i) q^{4} +9.74532 q^{5} +(0.158327 + 18.5196i) q^{7} -15.5854 q^{8} +(-16.4375 - 28.4706i) q^{10} -38.9123 q^{11} +(-31.2817 - 54.1816i) q^{13} +(53.8372 - 31.6997i) q^{14} +(39.8078 + 68.9491i) q^{16} +(-63.3614 - 109.745i) q^{17} +(22.7332 - 39.3751i) q^{19} +(-16.4692 + 28.5256i) q^{20} +(65.6337 + 113.681i) q^{22} -153.865 q^{23} -30.0287 q^{25} +(-105.526 + 182.777i) q^{26} +(-54.4763 - 30.8340i) q^{28} +(-27.4655 + 47.5716i) q^{29} +(-54.8509 + 95.0045i) q^{31} +(71.9464 - 124.615i) q^{32} +(-213.744 + 370.216i) q^{34} +(1.54295 + 180.479i) q^{35} +(144.482 - 250.249i) q^{37} -153.377 q^{38} -151.885 q^{40} +(11.3009 + 19.5738i) q^{41} +(23.9450 - 41.4740i) q^{43} +(65.7604 - 113.900i) q^{44} +(259.525 + 449.510i) q^{46} +(193.385 + 334.953i) q^{47} +(-342.950 + 5.86430i) q^{49} +(50.6496 + 87.7278i) q^{50} +211.460 q^{52} +(133.617 + 231.431i) q^{53} -379.213 q^{55} +(-2.46759 - 288.635i) q^{56} +185.305 q^{58} +(193.371 - 334.929i) q^{59} +(-17.8409 - 30.9013i) q^{61} +370.070 q^{62} +151.514 q^{64} +(-304.851 - 528.017i) q^{65} +(-17.8513 + 30.9194i) q^{67} +428.314 q^{68} +(524.661 - 308.923i) q^{70} +146.355 q^{71} +(-364.856 - 631.948i) q^{73} -974.792 q^{74} +(76.8367 + 133.085i) q^{76} +(-6.16087 - 720.640i) q^{77} +(-250.675 - 434.183i) q^{79} +(387.939 + 671.931i) q^{80} +(38.1227 - 66.0304i) q^{82} +(-169.622 + 293.794i) q^{83} +(-617.477 - 1069.50i) q^{85} -161.553 q^{86} +606.465 q^{88} +(104.209 - 180.495i) q^{89} +(998.467 - 587.903i) q^{91} +(260.026 - 450.378i) q^{92} +(652.368 - 1129.94i) q^{94} +(221.543 - 383.723i) q^{95} +(-56.7013 + 98.2095i) q^{97} +(595.588 + 992.024i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.68671	−	2.92146i	−0.596341	−	1.03289i	−0.993356	−	0.115081i	$-0.963287\pi$
$2$	−1.68671	−	2.92146i	−0.596341	−	1.03289i	0.397015	−	0.917812i	$-0.370046\pi$
$3$		0			0
$3$		0			0
$4$	−1.68996	+	2.92710i	−0.211246	+	0.365888i
$5$	9.74532			0.871648			0.435824	−	0.900032i	$-0.356457\pi$
$5$	9.74532			0.871648			0.435824	+	0.900032i	$0.356457\pi$
$6$		0			0
$7$	0.158327	+	18.5196i	0.00854886	+	0.999963i
$7$	0.158327	+	18.5196i	0.00854886	+	0.999963i
$8$	−15.5854			−0.688785
$9$		0			0
$10$	−16.4375	−	28.4706i	−0.519800	−	0.900319i
$11$	−38.9123			−1.06659			−0.533296	−	0.845929i	$-0.679047\pi$
$11$	−38.9123			−1.06659			−0.533296	+	0.845929i	$0.679047\pi$
$12$		0			0
$13$	−31.2817	−	54.1816i	−0.667384	−	1.15594i	−0.978633	−	0.205615i	$-0.934081\pi$
$13$	−31.2817	−	54.1816i	−0.667384	−	1.15594i	0.311249	−	0.950328i	$-0.399253\pi$
$14$	53.8372	−	31.6997i	1.02776	−	0.605149i
$15$		0			0
$16$	39.8078	+	68.9491i	0.621996	+	1.07733i
$17$	−63.3614	−	109.745i	−0.903964	−	1.56571i	−0.822302	−	0.569051i	$-0.807311\pi$
$17$	−63.3614	−	109.745i	−0.903964	−	1.56571i	−0.0816621	−	0.996660i	$-0.526023\pi$
$18$		0			0
$19$	22.7332	−	39.3751i	0.274493	−	0.475435i	−0.695514	−	0.718512i	$-0.744823\pi$
$19$	22.7332	−	39.3751i	0.274493	−	0.475435i	0.970007	+	0.243077i	$0.0781568\pi$
$20$	−16.4692	+	28.5256i	−0.184132	+	0.318926i
$21$		0			0
$22$	65.6337	+	113.681i	0.636052	+	1.10167i
$23$	−153.865			−1.39491			−0.697457	−	0.716627i	$-0.745685\pi$
$23$	−153.865			−1.39491			−0.697457	+	0.716627i	$0.745685\pi$
$24$		0			0
$25$	−30.0287			−0.240230
$26$	−105.526	+	182.777i	−0.795977	+	1.37867i
$27$		0			0
$28$	−54.4763	−	30.8340i	−0.367681	−	0.208110i
$29$	−27.4655	+	47.5716i	−0.175869	+	0.304615i	−0.940462	−	0.339899i	$-0.889607\pi$
$29$	−27.4655	+	47.5716i	−0.175869	+	0.304615i	0.764592	+	0.644514i	$0.222940\pi$
$30$		0			0
$31$	−54.8509	+	95.0045i	−0.317791	+	0.550430i	−0.980027	−	0.198866i	$-0.936274\pi$
$31$	−54.8509	+	95.0045i	−0.317791	+	0.550430i	0.662236	+	0.749295i	$0.269608\pi$
$32$	71.9464	−	124.615i	0.397452	−	0.688406i
$33$		0			0
$34$	−213.744	+	370.216i	−1.07814	+	1.86740i
$35$	1.54295	+	180.479i	0.00745159	+	0.871616i
$36$		0			0
$37$	144.482	−	250.249i	0.641962	−	1.11191i	−0.343032	−	0.939324i	$-0.611454\pi$
$37$	144.482	−	250.249i	0.641962	−	1.11191i	0.984994	−	0.172588i	$-0.0552129\pi$
$38$	−153.377			−0.654765
$39$		0			0
$40$	−151.885			−0.600378
$41$	11.3009	+	19.5738i	0.0430465	+	0.0745587i	0.886746	−	0.462257i	$-0.152960\pi$
$41$	11.3009	+	19.5738i	0.0430465	+	0.0745587i	−0.843699	+	0.536816i	$0.819627\pi$
$42$		0			0
$43$	23.9450	−	41.4740i	0.0849204	−	0.147086i	−0.820437	−	0.571737i	$-0.806270\pi$
$43$	23.9450	−	41.4740i	0.0849204	−	0.147086i	0.905357	+	0.424651i	$0.139603\pi$
$44$	65.7604	−	113.900i	0.225313	−	0.390253i
$45$		0			0
$46$	259.525	+	449.510i	0.831845	+	1.44080i
$47$	193.385	+	334.953i	0.600173	+	1.03953i	0.992794	+	0.119830i	$0.0382349\pi$
$47$	193.385	+	334.953i	0.600173	+	1.03953i	−0.392622	+	0.919700i	$0.628432\pi$
$48$		0			0
$49$	−342.950	+	5.86430i	−0.999854	+	0.0170971i
$50$	50.6496	+	87.7278i	0.143259	+	0.248132i
$51$		0			0
$52$	211.460			0.563928
$53$	133.617	+	231.431i	0.346296	+	0.599802i	0.985588	−	0.169162i	$-0.0541060\pi$
$53$	133.617	+	231.431i	0.346296	+	0.599802i	−0.639293	+	0.768964i	$0.720773\pi$
$54$		0			0
$55$	−379.213			−0.929692
$56$	−2.46759	−	288.635i	−0.00588832	−	0.688759i
$57$		0			0
$58$	185.305			0.419513
$59$	193.371	−	334.929i	0.426691	−	0.739051i	−0.569886	−	0.821724i	$-0.693013\pi$
$59$	193.371	−	334.929i	0.426691	−	0.739051i	0.996577	+	0.0826735i	$0.0263458\pi$
$60$		0			0
$61$	−17.8409	−	30.9013i	−0.0374473	−	0.0648607i	0.846694	−	0.532080i	$-0.178589\pi$
$61$	−17.8409	−	30.9013i	−0.0374473	−	0.0648607i	−0.884142	+	0.467219i	$0.845256\pi$
$62$	370.070			0.758047
$63$		0			0
$64$	151.514			0.295925
$65$	−304.851	−	528.017i	−0.581724	−	1.00758i
$66$		0			0
$67$	−17.8513	+	30.9194i	−0.0325506	+	0.0563792i	−0.881842	−	0.471545i	$-0.843696\pi$
$67$	−17.8513	+	30.9194i	−0.0325506	+	0.0563792i	0.849291	+	0.527925i	$0.177030\pi$
$68$	428.314			0.763834
$69$		0			0
$70$	524.661	−	308.923i	0.895843	−	0.527477i
$71$	146.355			0.244636			0.122318	−	0.992491i	$-0.460967\pi$
$71$	146.355			0.244636			0.122318	+	0.992491i	$0.460967\pi$
$72$		0			0
$73$	−364.856	−	631.948i	−0.584974	−	1.01320i	−0.994879	−	0.101076i	$-0.967771\pi$
$73$	−364.856	−	631.948i	−0.584974	−	1.01320i	0.409905	−	0.912128i	$-0.365562\pi$
$74$	−974.792			−1.53131
$75$		0			0
$76$	76.8367	+	133.085i	0.115971	+	0.200867i
$77$	−6.16087	−	720.640i	−0.00911814	−	1.06655i
$78$		0			0
$79$	−250.675	−	434.183i	−0.357002	−	0.618346i	0.630456	−	0.776225i	$-0.282868\pi$
$79$	−250.675	−	434.183i	−0.357002	−	0.618346i	−0.987459	+	0.157879i	$0.949535\pi$
$80$	387.939	+	671.931i	0.542162	+	0.939052i
$81$		0			0
$82$	38.1227	−	66.0304i	0.0513408	−	0.0889249i
$83$	−169.622	+	293.794i	−0.224319	+	0.388532i	−0.956115	−	0.292992i	$-0.905349\pi$
$83$	−169.622	+	293.794i	−0.224319	+	0.388532i	0.731796	+	0.681524i	$0.238682\pi$
$84$		0			0
$85$	−617.477	−	1069.50i	−0.787938	−	1.36475i
$86$	−161.553			−0.202566
$87$		0			0
$88$	606.465			0.734652
$89$	104.209	−	180.495i	0.124113	−	0.214971i	−0.797273	−	0.603619i	$-0.793725\pi$
$89$	104.209	−	180.495i	0.124113	−	0.214971i	0.921386	+	0.388649i	$0.127058\pi$
$90$		0			0
$91$	998.467	−	587.903i	1.15020	−	0.677242i
$92$	260.026	−	450.378i	0.294669	−	0.510382i
$93$		0			0
$94$	652.368	−	1129.94i	0.715816	−	1.23983i
$95$	221.543	−	383.723i	0.239261	−	0.414412i
$96$		0			0
$97$	−56.7013	+	98.2095i	−0.0593520	+	0.102801i	−0.894175	−	0.447718i	$-0.852237\pi$
$97$	−56.7013	+	98.2095i	−0.0593520	+	0.102801i	0.834823	+	0.550519i	$0.185570\pi$
$98$	595.588	+	992.024i	0.613913	+	1.02255i
$99$		0			0
$100$	50.7475	−	87.8972i	0.0507475	−	0.0878972i
$101$	−1078.01			−1.06204			−0.531019	−	0.847360i	$-0.678191\pi$
$101$	−1078.01			−1.06204			−0.531019	+	0.847360i	$0.678191\pi$
$102$		0			0
$103$	1710.37			1.63619			0.818097	−	0.575080i	$-0.195029\pi$
$103$	1710.37			1.63619			0.818097	+	0.575080i	$0.195029\pi$
$104$	487.539	+	844.442i	0.459684	+	0.796196i
$105$		0			0
$106$	450.745	−	780.713i	0.413021	−	0.715373i
$107$	410.398	−	710.830i	0.370791	−	0.642229i	−0.618896	−	0.785473i	$-0.712420\pi$
$107$	410.398	−	710.830i	0.370791	−	0.642229i	0.989687	+	0.143244i	$0.0457532\pi$
$108$		0			0
$109$	1064.55	+	1843.85i	0.935460	+	1.62026i	0.773812	+	0.633416i	$0.218348\pi$
$109$	1064.55	+	1843.85i	0.935460	+	1.62026i	0.161648	+	0.986848i	$0.448319\pi$
$110$	639.621	+	1107.86i	0.554414	+	0.960273i
$111$		0			0
$112$	−1270.61	+	748.140i	−1.07197	+	0.631183i
$113$	−203.179	−	351.917i	−0.169146	−	0.292970i	0.768974	−	0.639280i	$-0.220768\pi$
$113$	−203.179	−	351.917i	−0.169146	−	0.292970i	−0.938120	+	0.346311i	$0.887434\pi$
$114$		0			0
$115$	−1499.46			−1.21587
$116$	−92.8314	−	160.789i	−0.0743033	−	0.128697i
$117$		0			0
$118$	−1304.64			−1.01781
$119$	2022.40	−	1190.80i	1.55793	−	0.917316i
$120$		0			0
$121$	183.168			0.137617
$122$	−60.1846	+	104.243i	−0.0446628	+	0.0773582i
$123$		0			0
$124$	−185.392	−	321.109i	−0.134264	−	0.232552i
$125$	−1510.80			−1.08104
$126$		0			0
$127$	−2300.05			−1.60706			−0.803529	−	0.595266i	$-0.797047\pi$
$127$	−2300.05			−1.60706			−0.803529	+	0.595266i	$0.797047\pi$
$128$	−831.131	−	1439.56i	−0.573924	−	0.994066i
$129$		0			0
$130$	−1028.39	+	1781.22i	−0.693812	+	1.20172i
$131$	583.702			0.389300			0.194650	−	0.980873i	$-0.437643\pi$
$131$	583.702			0.389300			0.194650	+	0.980873i	$0.437643\pi$
$132$		0			0
$133$	732.810	+	414.776i	0.477764	+	0.270418i
$134$	120.440			0.0776449
$135$		0			0
$136$	987.513	+	1710.42i	0.622636	+	1.07844i
$137$	168.798			0.105266			0.0526328	−	0.998614i	$-0.483239\pi$
$137$	168.798			0.105266			0.0526328	+	0.998614i	$0.483239\pi$
$138$		0			0
$139$	671.306	+	1162.74i	0.409636	+	0.709511i	0.994849	−	0.101369i	$-0.0323223\pi$
$139$	671.306	+	1162.74i	0.409636	+	0.709511i	−0.585213	+	0.810880i	$0.698989\pi$
$140$	−530.889	−	300.487i	−0.320488	−	0.181399i
$141$		0			0
$142$	−246.858	−	427.571i	−0.145887	−	0.252683i
$143$	1217.24	+	2108.33i	0.711826	+	1.23292i
$144$		0			0
$145$	−267.660	+	463.601i	−0.153296	+	0.265517i
$146$	−1230.81	+	2131.82i	−0.697688	+	1.20843i
$147$		0			0
$148$	488.337	+	845.825i	0.271223	+	0.469773i
$149$	721.359			0.396618			0.198309	−	0.980140i	$-0.436455\pi$
$149$	721.359			0.396618			0.198309	+	0.980140i	$0.436455\pi$
$150$		0			0
$151$	−2867.01			−1.54513			−0.772563	−	0.634938i	$-0.781026\pi$
$151$	−2867.01			−1.54513			−0.772563	+	0.634938i	$0.781026\pi$
$152$	−354.307	+	613.677i	−0.189066	+	0.327472i
$153$		0			0
$154$	−2094.93	+	1233.51i	−1.09620	+	0.645447i
$155$	−534.540	+	925.850i	−0.277002	+	0.479781i
$156$		0			0
$157$	375.097	−	649.686i	0.190675	−	0.330259i	−0.754799	−	0.655956i	$-0.772266\pi$
$157$	375.097	−	649.686i	0.190675	−	0.330259i	0.945474	+	0.325697i	$0.105599\pi$
$158$	−845.632	+	1464.68i	−0.425790	+	0.737491i
$159$		0			0
$160$	701.141	−	1214.41i	0.346438	−	0.600048i
$161$	−24.3610	−	2849.51i	−0.0119249	−	1.39486i
$162$		0			0
$163$	1400.06	−	2424.98i	0.672769	−	1.16527i	−0.304347	−	0.952561i	$-0.598438\pi$
$163$	1400.06	−	2424.98i	0.672769	−	1.16527i	0.977116	−	0.212709i	$-0.0682285\pi$
$164$	−76.3926			−0.0363735
$165$		0			0
$166$	1144.41			0.535082
$167$	0.0790177	+	0.136863i	3.66142e−5	+	6.34176e-5i	0.866044	−	0.499968i	$-0.166655\pi$
$167$	0.0790177	+	0.136863i	3.66142e−5	+	6.34176e-5i	−0.866007	+	0.500032i	$0.833322\pi$
$168$		0			0
$169$	−858.594	+	1487.13i	−0.390803	+	0.676890i
$170$	−2083.01	+	3607.87i	−0.939760	+	1.62771i
$171$		0			0
$172$	80.9324	+	140.179i	0.0358781	+	0.0621427i
$173$	631.310	+	1093.46i	0.277443	+	0.480545i	0.970748	−	0.240099i	$-0.0771798\pi$
$173$	631.310	+	1093.46i	0.277443	+	0.480545i	−0.693306	+	0.720644i	$0.743846\pi$
$174$		0			0
$175$	−4.75436	−	556.119i	−0.00205369	−	0.240221i
$176$	−1549.01	−	2682.97i	−0.663416	−	1.14907i
$177$		0			0
$178$	−703.078			−0.296056
$179$	−1457.18	−	2523.91i	−0.608462	−	1.05389i	−0.991494	−	0.130152i	$-0.958454\pi$
$179$	−1457.18	−	2523.91i	−0.608462	−	1.05389i	0.383032	−	0.923735i	$-0.374880\pi$
$180$		0			0
$181$	870.971			0.357673			0.178836	−	0.983879i	$-0.442767\pi$
$181$	870.971			0.357673			0.178836	+	0.983879i	$0.442767\pi$
$182$	−3401.66	−	1925.36i	−1.38543	−	0.784162i
$183$		0			0
$184$	2398.05			0.960795
$185$	1408.02	−	2438.76i	0.559565	−	0.969196i
$186$		0			0
$187$	2465.54	+	4270.44i	0.964160	+	1.66997i
$188$	−1307.26			−0.507135
$189$		0			0
$190$	−1494.71			−0.570725
$191$	1588.84	+	2751.95i	0.601907	+	1.04253i	0.992532	+	0.121983i	$0.0389255\pi$
$191$	1588.84	+	2751.95i	0.601907	+	1.04253i	−0.390625	+	0.920550i	$0.627741\pi$
$192$		0			0
$193$	851.492	−	1474.83i	0.317574	−	0.550054i	−0.662407	−	0.749144i	$-0.730465\pi$
$193$	851.492	−	1474.83i	0.317574	−	0.550054i	0.979981	+	0.199090i	$0.0637985\pi$
$194$	382.554			0.141576
$195$		0			0
$196$	562.408	−	1013.76i	0.204959	−	0.369446i
$197$	−254.870			−0.0921763			−0.0460881	−	0.998937i	$-0.514676\pi$
$197$	−254.870			−0.0921763			−0.0460881	+	0.998937i	$0.514676\pi$
$198$		0			0
$199$	−386.703	−	669.790i	−0.137752	−	0.238594i	0.788893	−	0.614530i	$-0.210654\pi$
$199$	−386.703	−	669.790i	−0.137752	−	0.238594i	−0.926645	+	0.375937i	$0.877321\pi$
$200$	468.010			0.165466
$201$		0			0
$202$	1818.28	+	3149.36i	0.633337	+	1.09697i
$203$	−885.355	−	501.118i	−0.306107	−	0.173259i
$204$		0			0
$205$	110.131	+	190.753i	0.0375214	+	0.0649890i
$206$	−2884.90	−	4996.79i	−0.975730	−	1.69001i
$207$		0			0
$208$	2490.51	−	4313.69i	0.830221	−	1.43798i
$209$	−884.602	+	1532.18i	−0.292771	+	0.507095i
$210$		0			0
$211$	−1834.55	−	3177.54i	−0.598558	−	1.03673i	−0.993034	−	0.117827i	$-0.962407\pi$
$211$	−1834.55	−	3177.54i	−0.598558	−	1.03673i	0.394476	−	0.918906i	$-0.370926\pi$
$212$	−903.230			−0.292614
$213$		0			0
$214$	−2768.88			−0.884472
$215$	233.352	−	404.177i	0.0740207	−	0.128208i
$216$		0			0
$217$	−1768.13	−	1000.77i	−0.553126	−	0.313074i
$218$	3591.16	−	6220.07i	1.11571	−	1.93246i
$219$		0			0
$220$	640.857	−	1110.00i	0.196393	−	0.340163i
$221$	−3964.11	+	6866.03i	−1.20658	+	2.08986i
$222$		0			0
$223$	1002.18	−	1735.83i	0.300947	−	0.521256i	−0.675404	−	0.737448i	$-0.736031\pi$
$223$	1002.18	−	1735.83i	0.300947	−	0.521256i	0.976351	+	0.216192i	$0.0693639\pi$
$224$	2319.21	+	1312.69i	0.691779	+	0.391552i
$225$		0			0
$226$	−685.409	+	1187.16i	−0.201738	+	0.349420i
$227$	3396.02			0.992958			0.496479	−	0.868049i	$-0.334626\pi$
$227$	3396.02			0.992958			0.496479	+	0.868049i	$0.334626\pi$
$228$		0			0
$229$	−5153.79			−1.48721			−0.743606	−	0.668618i	$-0.766886\pi$
$229$	−5153.79			−1.48721			−0.743606	+	0.668618i	$0.766886\pi$
$230$	2529.15	+	4380.62i	0.725076	+	1.25587i
$231$		0			0
$232$	428.061	−	741.424i	0.121136	−	0.209814i
$233$	3053.12	−	5288.16i	0.858441	−	1.48686i	−0.0149746	−	0.999888i	$-0.504767\pi$
$233$	3053.12	−	5288.16i	0.858441	−	1.48686i	0.873416	−	0.486976i	$-0.161900\pi$
$234$		0			0
$235$	1884.60	+	3264.22i	0.523139	+	0.906104i
$236$	653.581	+	1132.03i	0.180273	+	0.312242i
$237$		0			0
$238$	−6890.08	−	3899.84i	−1.87655	−	1.06214i
$239$	1301.70	+	2254.62i	0.352302	+	0.610205i	0.986652	−	0.162840i	$-0.0520656\pi$
$239$	1301.70	+	2254.62i	0.352302	+	0.610205i	−0.634350	+	0.773046i	$0.718732\pi$
$240$		0			0
$241$	2322.27			0.620707			0.310354	−	0.950621i	$-0.399553\pi$
$241$	2322.27			0.620707			0.310354	+	0.950621i	$0.399553\pi$
$242$	−308.950	−	535.118i	−0.0820665	−	0.142143i
$243$		0			0
$244$	120.602			0.0316423
$245$	−3342.16	+	57.1495i	−0.871521	+	0.0149026i
$246$		0			0
$247$	−2844.54			−0.732768
$248$	854.874	−	1480.69i	0.218889	−	0.379127i
$249$		0			0
$250$	2548.29	+	4413.76i	0.644671	+	1.11660i
$251$	476.889			0.119924			0.0599621	−	0.998201i	$-0.480902\pi$
$251$	476.889			0.119924			0.0599621	+	0.998201i	$0.480902\pi$
$252$		0			0
$253$	5987.23			1.48780
$254$	3879.51	+	6719.51i	0.958354	+	1.65992i
$255$		0			0
$256$	−2197.69	+	3806.52i	−0.536546	+	0.929326i
$257$	−3736.85			−0.906997			−0.453499	−	0.891257i	$-0.649824\pi$
$257$	−3736.85			−0.906997			−0.453499	+	0.891257i	$0.649824\pi$
$258$		0			0
$259$	4657.39	+	2636.12i	1.11736	+	0.632433i
$260$	2060.75			0.491546
$261$		0			0
$262$	−984.535	−	1705.26i	−0.232156	−	0.402105i
$263$	−1009.13			−0.236600			−0.118300	−	0.992978i	$-0.537744\pi$
$263$	−1009.13			−0.236600			−0.118300	+	0.992978i	$0.537744\pi$
$264$		0			0
$265$	1302.14	+	2255.37i	0.301848	+	0.522816i
$266$	−24.2838	−	2840.48i	−0.00559749	−	0.654741i
$267$		0			0
$268$	−60.3362	−	104.505i	−0.0137523	−	0.0238197i
$269$	4069.36	+	7048.33i	0.922354	+	1.59756i	0.795763	+	0.605608i	$0.207070\pi$
$269$	4069.36	+	7048.33i	0.922354	+	1.59756i	0.126591	+	0.991955i	$0.459597\pi$
$270$		0			0
$271$	3384.69	−	5862.46i	0.758692	−	1.31409i	−0.184826	−	0.982771i	$-0.559172\pi$
$271$	3384.69	−	5862.46i	0.758692	−	1.31409i	0.943518	−	0.331321i	$-0.107494\pi$
$272$	5044.55	−	8737.41i	1.12452	−	1.94773i
$273$		0			0
$274$	−284.713	−	493.137i	−0.0627742	−	0.108728i
$275$	1168.49			0.256227
$276$		0			0
$277$	−6519.00			−1.41404			−0.707019	−	0.707194i	$-0.749961\pi$
$277$	−6519.00			−1.41404			−0.707019	+	0.707194i	$0.749961\pi$
$278$	2264.59	−	3922.39i	0.488566	−	0.846221i
$279$		0			0
$280$	−24.0475	−	2812.84i	−0.00513254	−	0.600356i
$281$	3138.53	−	5436.10i	0.666296	−	1.15406i	−0.312636	−	0.949873i	$-0.601212\pi$
$281$	3138.53	−	5436.10i	0.666296	−	1.15406i	0.978932	−	0.204185i	$-0.0654545\pi$
$282$		0			0
$283$	−403.166	+	698.304i	−0.0846845	+	0.146678i	−0.905257	−	0.424865i	$-0.860322\pi$
$283$	−403.166	+	698.304i	−0.0846845	+	0.146678i	0.820572	+	0.571543i	$0.193655\pi$
$284$	−247.335	+	428.397i	−0.0516783	+	0.0895094i
$285$		0			0
$286$	4106.27	−	7112.27i	0.848982	−	1.47048i
$287$	−360.709	+	212.387i	−0.0741880	+	0.0436823i
$288$		0			0
$289$	−5572.82	+	9652.42i	−1.13430	+	1.96467i
$290$	1805.86			0.365668
$291$		0			0
$292$	2466.37			0.494293
$293$	−3084.92	−	5343.24i	−0.615095	−	1.06538i	−0.990368	−	0.138462i	$-0.955784\pi$
$293$	−3084.92	−	5343.24i	−0.615095	−	1.06538i	0.375272	−	0.926915i	$-0.377549\pi$
$294$		0			0
$295$	1884.46	−	3263.99i	0.371924	−	0.644192i
$296$	−2251.80	+	3900.24i	−0.442174	+	0.765868i
$297$		0			0
$298$	−1216.72	−	2107.42i	−0.236519	−	0.409664i
$299$	4813.16	+	8336.63i	0.930943	+	1.61244i
$300$		0			0
$301$	771.871	+	436.885i	0.147807	+	0.0836599i
$302$	4835.81	+	8375.87i	0.921423	+	1.59595i
$303$		0			0
$304$	3619.84			0.682933
$305$	−173.865	−	301.143i	−0.0326409	−	0.0565357i
$306$		0			0
$307$	4381.77			0.814596			0.407298	−	0.913295i	$-0.366471\pi$
$307$	4381.77			0.814596			0.407298	+	0.913295i	$0.366471\pi$
$308$	2119.80	+	1199.82i	0.392165	+	0.221968i
$309$		0			0
$310$	3606.45			0.660750
$311$	−4231.30	+	7328.83i	−0.771495	+	1.33627i	0.165248	+	0.986252i	$0.447157\pi$
$311$	−4231.30	+	7328.83i	−0.771495	+	1.33627i	−0.936743	+	0.350017i	$0.886176\pi$
$312$		0			0
$313$	−2910.23	−	5040.67i	−0.525547	−	0.910273i	−0.999557	−	0.0297543i	$-0.990528\pi$
$313$	−2910.23	−	5040.67i	−0.525547	−	0.910273i	0.474011	−	0.880519i	$-0.342806\pi$
$314$	−2530.71			−0.454829
$315$		0			0
$316$	1694.53			0.301661
$317$	−3207.59	−	5555.71i	−0.568316	−	0.984353i	−0.996733	−	0.0807714i	$-0.974262\pi$
$317$	−3207.59	−	5555.71i	−0.568316	−	0.984353i	0.428416	−	0.903582i	$-0.359072\pi$
$318$		0			0
$319$	1068.75	−	1851.12i	0.187581	−	0.324900i
$320$	1476.55			0.257943
$321$		0			0
$322$	−8283.65	+	4877.46i	−1.43363	+	0.844131i
$323$	−5761.63			−0.992526
$324$		0			0
$325$	939.350	+	1627.00i	0.160325	+	0.277692i
$326$	−9445.98			−1.60480
$327$		0			0
$328$	−176.130	−	305.065i	−0.0296498	−	0.0513549i
$329$	−6172.57	+	3634.44i	−1.03436	+	0.609038i
$330$		0			0
$331$	414.418	+	717.794i	0.0688172	+	0.119195i	0.898381	−	0.439217i	$-0.144744\pi$
$331$	414.418	+	717.794i	0.0688172	+	0.119195i	−0.829564	+	0.558412i	$0.811411\pi$
$332$	−573.311	−	993.004i	−0.0947727	−	0.164151i
$333$		0			0
$334$	0.266559	−	0.461694i	4.36691e−5	−	7.56371e-5i
$335$	−173.967	+	301.320i	−0.0283726	+	0.0491428i
$336$		0			0
$337$	−2906.88	−	5034.86i	−0.469875	−	0.813847i	0.529532	−	0.848290i	$-0.322368\pi$
$337$	−2906.88	−	5034.86i	−0.469875	−	0.813847i	−0.999407	+	0.0344432i	$0.989034\pi$
$338$	5792.79			0.932207
$339$		0			0
$340$	4174.06			0.665794
$341$	2134.37	−	3696.85i	0.338953	−	0.587083i
$342$		0			0
$343$	−162.903	−	6350.36i	−0.0256441	−	0.999671i
$344$	−373.193	+	646.389i	−0.0584919	+	0.101311i
$345$		0			0
$346$	2129.67	−	3688.70i	0.330901	−	0.573137i
$347$	1661.46	−	2877.74i	0.257038	−	0.445202i	−0.708409	−	0.705802i	$-0.750587\pi$
$347$	1661.46	−	2877.74i	0.257038	−	0.445202i	0.965447	+	0.260600i	$0.0839203\pi$
$348$		0			0
$349$	−376.201	+	651.599i	−0.0577008	+	0.0999407i	−0.893433	−	0.449197i	$-0.851710\pi$
$349$	−376.201	+	651.599i	−0.0577008	+	0.0999407i	0.835732	+	0.549137i	$0.185044\pi$
$350$	−1616.66	+	951.900i	−0.246898	+	0.145375i
$351$		0			0
$352$	−2799.60	+	4849.05i	−0.423918	+	0.734248i
$353$	2213.65			0.333770			0.166885	−	0.985976i	$-0.446629\pi$
$353$	2213.65			0.333770			0.166885	+	0.985976i	$0.446629\pi$
$354$		0			0
$355$	1426.28			0.213236
$356$	352.218	+	610.060i	0.0524368	+	0.0908233i
$357$		0			0
$358$	−4915.67	+	8514.19i	−0.725702	+	1.25695i
$359$	435.090	−	753.599i	0.0639643	−	0.110789i	−0.832270	−	0.554371i	$-0.812959\pi$
$359$	435.090	−	753.599i	0.0639643	−	0.110789i	0.896234	+	0.443581i	$0.146292\pi$
$360$		0			0
$361$	2395.90	+	4149.82i	0.349308	+	0.605018i
$362$	−1469.07	−	2544.51i	−0.213295	−	0.369438i
$363$		0			0
$364$	33.4799	+	3916.15i	0.00482094	+	0.563907i
$365$	−3555.63	−	6158.54i	−0.509892	−	0.883158i
$366$		0			0
$367$	−2528.67			−0.359660			−0.179830	−	0.983698i	$-0.557555\pi$
$367$	−2528.67			−0.359660			−0.179830	+	0.983698i	$0.557555\pi$
$368$	−6125.01	−	10608.8i	−0.867631	−	1.50278i
$369$		0			0
$370$	−9499.66			−1.33477
$371$	−4264.85	+	2511.17i	−0.596819	+	0.351411i
$372$		0			0
$373$	5370.58			0.745518			0.372759	−	0.927928i	$-0.378412\pi$
$373$	5370.58			0.745518			0.372759	+	0.927928i	$0.378412\pi$
$374$	8317.28	−	14406.0i	1.14994	−	1.99175i
$375$		0			0
$376$	−3013.99	−	5220.38i	−0.413390	−	0.716012i
$377$	3436.67			0.469490
$378$		0			0
$379$	−9923.53			−1.34495			−0.672477	−	0.740118i	$-0.734770\pi$
$379$	−9923.53			−1.34495			−0.672477	+	0.740118i	$0.734770\pi$
$380$	748.798	+	1296.96i	0.101086	+	0.175085i
$381$		0			0
$382$	5359.81	−	9283.46i	0.717884	−	1.24341i
$383$	−11187.6			−1.49259			−0.746295	−	0.665616i	$-0.768169\pi$
$383$	−11187.6			−1.49259			−0.746295	+	0.665616i	$0.768169\pi$
$384$		0			0
$385$	−60.0397	−	7022.87i	−0.00794781	−	0.929658i
$386$	−5744.87			−0.757529
$387$		0			0
$388$	−191.646	−	331.941i	−0.0250757	−	0.0434324i
$389$	1683.37			0.219410			0.109705	−	0.993964i	$-0.465009\pi$
$389$	1683.37			0.219410			0.109705	+	0.993964i	$0.465009\pi$
$390$		0			0
$391$	9749.08	+	16885.9i	1.26095	+	2.18403i
$392$	5345.02	−	91.3976i	0.688684	−	0.0117762i
$393$		0			0
$394$	429.891	+	744.593i	0.0549685	+	0.0952083i
$395$	−2442.91	−	4231.25i	−0.311180	−	0.538980i
$396$		0			0
$397$	−1775.41	+	3075.09i	−0.224446	+	0.388752i	−0.956153	−	0.292867i	$-0.905391\pi$
$397$	−1775.41	+	3075.09i	−0.224446	+	0.388752i	0.731707	+	0.681619i	$0.238724\pi$
$398$	−1304.51	+	2259.48i	−0.164295	+	0.284566i
$399$		0			0
$400$	−1195.38	−	2070.45i	−0.149422	−	0.258806i
$401$	3801.66			0.473431			0.236716	−	0.971579i	$-0.423929\pi$
$401$	3801.66			0.473431			0.236716	+	0.971579i	$0.423929\pi$
$402$		0			0
$403$	6863.32			0.848354
$404$	1821.80	−	3155.44i	0.224351	−	0.388587i
$405$		0			0
$406$	29.3388	+	3431.77i	0.00358636	+	0.419498i
$407$	−5622.11	+	9737.78i	−0.684712	+	1.18596i
$408$		0			0
$409$	−6622.39	+	11470.3i	−0.800626	+	1.38673i	0.118578	+	0.992945i	$0.462166\pi$
$409$	−6622.39	+	11470.3i	−0.800626	+	1.38673i	−0.919204	+	0.393781i	$0.871167\pi$
$410$	371.518	−	643.488i	0.0447511	−	0.0775112i
$411$		0			0
$412$	−2890.47	+	5006.44i	−0.345639	+	0.598664i
$413$	6233.35	+	3528.12i	0.742671	+	0.420357i
$414$		0			0
$415$	−1653.02	+	2863.12i	−0.195527	+	0.338663i
$416$	−9002.44			−1.06101
$417$		0			0
$418$	5968.26			0.698367
$419$	−1435.52	−	2486.39i	−0.167374	−	0.289900i	0.770122	−	0.637897i	$-0.220195\pi$
$419$	−1435.52	−	2486.39i	−0.167374	−	0.289900i	−0.937496	+	0.347997i	$0.886862\pi$
$420$		0			0
$421$	−441.098	+	764.004i	−0.0510637	+	0.0884449i	−0.890427	−	0.455125i	$-0.849594\pi$
$421$	−441.098	+	764.004i	−0.0510637	+	0.0884449i	0.839364	+	0.543570i	$0.182928\pi$
$422$	−6188.70	+	10719.1i	−0.713890	+	1.23649i
$423$		0			0
$424$	−2082.47	−	3606.95i	−0.238523	−	0.413134i
$425$	1902.66	+	3295.50i	0.217159	+	0.376130i
$426$		0			0
$427$	569.454	−	335.298i	0.0645382	−	0.0380005i
$428$	1387.12	+	2402.55i	0.156656	+	0.271336i
$429$		0			0
$430$	−1574.38			−0.176566
$431$	4337.40	+	7512.59i	0.484745	+	0.839603i	0.999846	−	0.0175265i	$-0.00557915\pi$
$431$	4337.40	+	7512.59i	0.484745	+	0.839603i	−0.515102	+	0.857129i	$0.672246\pi$
$432$		0			0
$433$	−10521.0			−1.16769			−0.583843	−	0.811866i	$-0.698452\pi$
$433$	−10521.0			−1.16769			−0.583843	+	0.811866i	$0.698452\pi$
$434$	58.5920	+	6853.54i	0.00648043	+	0.758019i
$435$		0			0
$436$	−7196.19			−0.790447
$437$	−3497.84	+	6058.44i	−0.382894	+	0.663191i
$438$		0			0
$439$	5603.51	+	9705.56i	0.609205	+	1.05517i	0.991372	+	0.131080i	$0.0418445\pi$
$439$	5603.51	+	9705.56i	0.609205	+	1.05517i	−0.382167	+	0.924093i	$0.624822\pi$
$440$	5910.19			0.640358
$441$		0			0
$442$	26745.2			2.87814
$443$	−1280.39	−	2217.70i	−0.137321	−	0.237847i	0.789161	−	0.614187i	$-0.210516\pi$
$443$	−1280.39	−	2217.70i	−0.137321	−	0.237847i	−0.926482	+	0.376340i	$0.877183\pi$
$444$		0			0
$445$	1015.55	−	1758.98i	0.108183	−	0.187379i
$446$	−6761.57			−0.717869
$447$		0			0
$448$	23.9887	+	2805.97i	0.00252982	+	0.295915i
$449$	−10296.7			−1.08225			−0.541126	−	0.840941i	$-0.682002\pi$
$449$	−10296.7			−1.08225			−0.541126	+	0.840941i	$0.682002\pi$
$450$		0			0
$451$	−439.745	−	761.660i	−0.0459130	−	0.0795237i
$452$	1373.46			0.142926
$453$		0			0
$454$	−5728.08	−	9921.33i	−0.592142	−	1.02562i
$455$	9730.38	−	5729.30i	1.00257	−	0.590316i
$456$		0			0
$457$	−7182.41	−	12440.3i	−0.735184	−	1.27338i	−0.954643	−	0.297754i	$-0.903762\pi$
$457$	−7182.41	−	12440.3i	−0.735184	−	1.27338i	0.219459	−	0.975622i	$-0.429571\pi$
$458$	8692.93	+	15056.6i	0.886886	+	1.53613i
$459$		0			0
$460$	2534.04	−	4389.08i	0.256848	−	0.444874i
$461$	2747.56	−	4758.92i	0.277585	−	0.480792i	−0.693199	−	0.720746i	$-0.743799\pi$
$461$	2747.56	−	4758.92i	0.277585	−	0.480792i	0.970784	+	0.239955i	$0.0771325\pi$
$462$		0			0
$463$	3667.94	+	6353.05i	0.368172	+	0.637692i	0.989280	−	0.146033i	$-0.0466506\pi$
$463$	3667.94	+	6353.05i	0.368172	+	0.637692i	−0.621108	+	0.783725i	$0.713317\pi$
$464$	−4373.36			−0.437561
$465$		0			0
$466$	−20598.9			−2.04769
$467$	−1503.29	+	2603.77i	−0.148959	+	0.258004i	−0.930843	−	0.365420i	$-0.880926\pi$
$467$	−1503.29	+	2603.77i	−0.148959	+	0.258004i	0.781884	+	0.623424i	$0.214259\pi$
$468$		0			0
$469$	−575.441	−	325.704i	−0.0566554	−	0.0320674i
$470$	6357.54	−	11011.6i	0.623939	−	1.08069i
$471$		0			0
$472$	−3013.77	+	5220.00i	−0.293898	+	0.509047i
$473$	−931.755	+	1613.85i	−0.0905754	+	0.156881i
$474$		0			0
$475$	−682.649	+	1182.38i	−0.0659413	+	0.114214i
$476$	67.8137	+	7932.19i	0.00652990	+	0.763806i
$477$		0			0
$478$	4391.19	−	7605.76i	0.420185	−	0.727781i
$479$	−10603.8			−1.01148			−0.505740	−	0.862686i	$-0.668781\pi$
$479$	−10603.8			−1.01148			−0.505740	+	0.862686i	$0.668781\pi$
$480$		0			0
$481$	−18078.5			−1.71374
$482$	−3916.99	−	6784.42i	−0.370153	−	0.641124i
$483$		0			0
$484$	−309.547	+	536.151i	−0.0290709	+	0.0503523i
$485$	−552.572	+	957.083i	−0.0517340	+	0.0896060i
$486$		0			0
$487$	7160.77	+	12402.8i	0.666294	+	1.15406i	0.978933	+	0.204183i	$0.0654538\pi$
$487$	7160.77	+	12402.8i	0.666294	+	1.15406i	−0.312638	+	0.949872i	$0.601213\pi$
$488$	278.057	+	481.609i	0.0257932	+	0.0446751i
$489$		0			0
$490$	5804.20	+	9667.59i	0.535116	+	0.891301i
$491$	2111.73	+	3657.62i	0.194096	+	0.336184i	0.946604	−	0.322399i	$-0.104489\pi$
$491$	2111.73	+	3657.62i	0.194096	+	0.336184i	−0.752508	+	0.658583i	$0.771156\pi$
$492$		0			0
$493$	6961.01			0.635919
$494$	4797.91	+	8310.22i	0.436980	+	0.756871i
$495$		0			0
$496$	−8733.96			−0.790658
$497$	23.1720	+	2710.44i	0.00209136	+	0.244627i
$498$		0			0
$499$	18697.4			1.67738			0.838690	−	0.544610i	$-0.183322\pi$
$499$	18697.4			1.67738			0.838690	+	0.544610i	$0.183322\pi$
$500$	2553.21	−	4422.28i	0.228366	−	0.395541i
$501$		0			0
$502$	−804.372	−	1393.21i	−0.0715157	−	0.123869i
$503$	7096.25			0.629038			0.314519	−	0.949251i	$-0.398157\pi$
$503$	7096.25			0.629038			0.314519	+	0.949251i	$0.398157\pi$
$504$		0			0
$505$	−10505.5			−0.925723
$506$	−10098.7	−	17491.5i	−0.887238	−	1.53674i
$507$		0			0
$508$	3887.00	−	6732.48i	0.339484	−	0.588003i
$509$	6419.73			0.559037			0.279518	−	0.960140i	$-0.409825\pi$
$509$	6419.73			0.559037			0.279518	+	0.960140i	$0.409825\pi$
$510$		0			0
$511$	11645.7	−	6857.03i	1.00817	−	0.593614i
$512$	1529.38			0.132011
$513$		0			0
$514$	6302.97	+	10917.1i	0.540880	+	0.936831i
$515$	16668.1			1.42619
$516$		0			0
$517$	−7525.06	−	13033.8i	−0.640139	−	1.10875i
$518$	−154.336	−	18052.7i	−0.0130910	−	1.53126i
$519$		0			0
$520$	4751.22	+	8229.36i	0.400682	+	0.694002i
$521$	−4877.13	−	8447.45i	−0.410117	−	0.710344i	0.584785	−	0.811188i	$-0.301179\pi$
$521$	−4877.13	−	8447.45i	−0.410117	−	0.710344i	−0.994902	+	0.100844i	$0.967846\pi$
$522$		0			0
$523$	−2134.28	+	3696.68i	−0.178443	+	0.309072i	−0.941347	−	0.337439i	$-0.890439\pi$
$523$	−2134.28	+	3696.68i	−0.178443	+	0.309072i	0.762905	+	0.646511i	$0.223773\pi$
$524$	−986.436	+	1708.56i	−0.0822379	+	0.142440i
$525$		0			0
$526$	1702.11	+	2948.15i	0.141094	+	0.244383i
$527$	13901.7			1.14909
$528$		0			0
$529$	11507.4			0.945784
$530$	4392.65	−	7608.30i	0.360009	−	0.623553i
$531$		0			0
$532$	−2452.51	+	1444.05i	−0.199868	+	0.117684i
$533$	707.025	−	1224.60i	0.0574571	−	0.0995186i
$534$		0			0
$535$	3999.46	−	6927.26i	0.323199	−	0.559798i
$536$	278.220	−	481.892i	0.0224203	−	0.0388331i
$537$		0			0
$538$	13727.6	−	23777.0i	1.10007	−	1.90539i
$539$	13345.0	−	228.194i	1.06644	−	0.0182356i
$540$		0			0
$541$	10185.3	−	17641.4i	0.809426	−	1.40197i	−0.103836	−	0.994594i	$-0.533112\pi$
$541$	10185.3	−	17641.4i	0.809426	−	1.40197i	0.913262	−	0.407373i	$-0.133555\pi$
$542$	−22835.9			−1.80976
$543$		0			0
$544$	−18234.5			−1.43713
$545$	10374.4	+	17968.9i	0.815392	+	1.41230i
$546$		0			0
$547$	−1046.82	+	1813.14i	−0.0818258	+	0.141726i	−0.904034	−	0.427460i	$-0.859408\pi$
$547$	−1046.82	+	1813.14i	−0.0818258	+	0.141726i	0.822208	+	0.569187i	$0.192742\pi$
$548$	−285.263	+	494.089i	−0.0222369	+	0.0385154i
$549$		0			0
$550$	−1970.89	−	3413.69i	−0.152799	−	0.264655i
$551$	1248.76	+	2162.91i	0.0965498	+	0.167229i
$552$		0			0
$553$	8001.19	−	4711.15i	0.615272	−	0.362275i
$554$	10995.6	+	19045.0i	0.843249	+	1.46055i
$555$		0			0
$556$	−4537.94			−0.346135
$557$	−844.740	−	1463.13i	−0.0642599	−	0.111301i	0.832106	−	0.554617i	$-0.187135\pi$
$557$	−844.740	−	1463.13i	−0.0642599	−	0.111301i	−0.896365	+	0.443316i	$0.853802\pi$
$558$		0			0
$559$	−2996.16			−0.226698
$560$	−12382.5	+	7290.86i	−0.934383	+	0.550170i
$561$		0			0
$562$	−21175.1			−1.58936
$563$	6454.60	−	11179.7i	0.483178	−	0.836888i	−0.516636	−	0.856205i	$-0.672816\pi$
$563$	6454.60	−	11179.7i	0.483178	−	0.836888i	0.999813	+	0.0193169i	$0.00614915\pi$
$564$		0			0
$565$	−1980.05	−	3429.55i	−0.147436	−	0.255367i
$566$	2720.09			0.202004
$567$		0			0
$568$	−2281.01			−0.168501
$569$	−13211.4	−	22882.8i	−0.973377	−	1.68594i	−0.685191	−	0.728363i	$-0.740281\pi$
$569$	−13211.4	−	22882.8i	−0.973377	−	1.68594i	−0.288185	−	0.957575i	$-0.593052\pi$
$570$		0			0
$571$	6392.78	−	11072.6i	0.468528	−	0.811515i	−0.530825	−	0.847482i	$-0.678118\pi$
$571$	6392.78	−	11072.6i	0.468528	−	0.811515i	0.999353	+	0.0359669i	$0.0114511\pi$
$572$	−8228.40			−0.601480
$573$		0			0
$574$	1228.89	+	695.562i	0.0893606	+	0.0505787i
$575$	4620.36			0.335100
$576$		0			0
$577$	−2294.12	−	3973.54i	−0.165521	−	0.286691i	0.771319	−	0.636449i	$-0.219597\pi$
$577$	−2294.12	−	3973.54i	−0.165521	−	0.286691i	−0.936840	+	0.349758i	$0.886264\pi$
$578$	37598.9			2.70572
$579$		0			0
$580$	−904.672	−	1566.94i	−0.0647663	−	0.112179i
$581$	−5467.81	−	3094.82i	−0.390435	−	0.220989i
$582$		0			0
$583$	−5199.34	−	9005.52i	−0.369356	−	0.639743i
$584$	5686.43	+	9849.18i	0.402921	+	0.697880i
$585$		0			0
$586$	−10406.7	+	18025.0i	−0.733613	+	1.27066i
$587$	−10298.2	+	17837.0i	−0.724111	+	1.25420i	0.235228	+	0.971940i	$0.424416\pi$
$587$	−10298.2	+	17837.0i	−0.724111	+	1.25420i	−0.959339	+	0.282256i	$0.908917\pi$
$588$		0			0
$589$	2493.88	+	4319.52i	0.174462	+	0.302178i
$590$	−12714.2			−0.887175
$591$		0			0
$592$	23005.9			1.59719
$593$	3894.55	−	6745.56i	0.269697	−	0.467128i	−0.699087	−	0.715037i	$-0.746410\pi$
$593$	3894.55	−	6745.56i	0.269697	−	0.467128i	0.968783	+	0.247909i	$0.0797433\pi$
$594$		0			0
$595$	19709.0	−	11604.7i	1.35796	−	0.799577i
$596$	−1219.07	+	2111.49i	−0.0837837	+	0.145118i
$597$		0			0
$598$	16236.8	−	28122.9i	1.11032	−	1.92313i
$599$	10937.0	−	18943.4i	0.746031	−	1.29216i	−0.203681	−	0.979037i	$-0.565291\pi$
$599$	10937.0	−	18943.4i	0.746031	−	1.29216i	0.949712	−	0.313126i	$-0.101376\pi$
$600$		0			0
$601$	−13992.6	+	24235.9i	−0.949702	+	1.64493i	−0.203650	+	0.979044i	$0.565281\pi$
$601$	−13992.6	+	24235.9i	−0.949702	+	1.64493i	−0.746052	+	0.665888i	$0.768053\pi$
$602$	−25.5782	−	2991.89i	−0.00173171	−	0.202559i
$603$		0			0
$604$	4845.15	−	8392.04i	0.326401	−	0.565343i
$605$	1785.03			0.119953
$606$		0			0
$607$	−4683.46			−0.313172			−0.156586	−	0.987664i	$-0.550049\pi$
$607$	−4683.46			−0.313172			−0.156586	+	0.987664i	$0.550049\pi$
$608$	−3271.15	−	5665.80i	−0.218195	−	0.377925i
$609$		0			0
$610$	−586.518	+	1015.88i	−0.0389302	+	0.0674291i
$611$	12098.8	−	20955.8i	0.801091	−	1.38753i
$612$		0			0
$613$	−13144.7	−	22767.2i	−0.866082	−	1.50010i	−0.865968	−	0.500099i	$-0.833297\pi$
$613$	−13144.7	−	22767.2i	−0.866082	−	1.50010i	−0.000113990	−	1.00000i	$-0.500036\pi$
$614$	−7390.77	−	12801.2i	−0.485777	−	0.841391i
$615$		0			0
$616$	96.0197	+	11231.5i	0.00628043	+	0.734625i
$617$	215.459	+	373.186i	0.0140584	+	0.0243499i	0.872969	−	0.487776i	$-0.162192\pi$
$617$	215.459	+	373.186i	0.0140584	+	0.0243499i	−0.858911	+	0.512126i	$0.828858\pi$
$618$		0			0
$619$	−17378.1			−1.12841			−0.564205	−	0.825635i	$-0.690817\pi$
$619$	−17378.1			−1.12841			−0.564205	+	0.825635i	$0.690817\pi$
$620$	−1806.71	−	3129.31i	−0.117031	−	0.202703i
$621$		0			0
$622$	28547.9			1.84030
$623$	3359.19	+	1901.32i	0.216024	+	0.122271i
$624$		0			0
$625$	−10969.7			−0.702060
$626$	−9817.42	+	17004.3i	−0.626810	+	1.08567i
$627$		0			0
$628$	1267.80	+	2195.89i	0.0805585	+	0.139531i
$629$	−36618.2			−2.32124
$630$		0			0
$631$	−176.931			−0.0111625			−0.00558123	−	0.999984i	$-0.501777\pi$
$631$	−176.931			−0.0111625			−0.00558123	+	0.999984i	$0.501777\pi$
$632$	3906.88	+	6766.92i	0.245898	+	0.425907i
$633$		0			0
$634$	−10820.5	+	18741.7i	−0.677821	+	1.17402i
$635$	−22414.7			−1.40079
$636$		0			0
$637$	11045.8	+	18398.1i	0.687050	+	1.14436i
$638$	−7210.65			−0.447449
$639$		0			0
$640$	−8099.64	−	14029.0i	−0.500260	−	0.866475i
$641$	21029.9			1.29583			0.647917	−	0.761711i	$-0.275640\pi$
$641$	21029.9			1.29583			0.647917	+	0.761711i	$0.275640\pi$
$642$		0			0
$643$	−6304.53	−	10919.8i	−0.386666	−	0.669725i	0.605333	−	0.795973i	$-0.293040\pi$
$643$	−6304.53	−	10919.8i	−0.386666	−	0.669725i	−0.991999	+	0.126247i	$0.959707\pi$
$644$	8381.99	+	4744.27i	0.512883	+	0.290295i
$645$		0			0
$646$	9718.19	+	16832.4i	0.591884	+	1.02517i
$647$	5084.38	+	8806.41i	0.308945	+	0.535109i	0.978132	−	0.207985i	$-0.0666906\pi$
$647$	5084.38	+	8806.41i	0.308945	+	0.535109i	−0.669187	+	0.743094i	$0.733357\pi$
$648$		0			0
$649$	−7524.52	+	13032.8i	−0.455105	+	0.788265i
$650$	3168.82	−	5488.55i	0.191217	−	0.331198i
$651$		0			0
$652$	4732.11	+	8196.26i	0.284239	+	0.492316i
$653$	−17327.5			−1.03841			−0.519203	−	0.854651i	$-0.673771\pi$
$653$	−17327.5			−1.03841			−0.519203	+	0.854651i	$0.673771\pi$
$654$		0			0
$655$	5688.36			0.339333
$656$	−899.728	+	1558.38i	−0.0535495	+	0.0927505i
$657$		0			0
$658$	21029.2	+	11902.7i	1.24590	+	0.705190i
$659$	−7431.15	+	12871.1i	−0.439266	+	0.760831i	−0.997633	−	0.0687629i	$-0.978095\pi$
$659$	−7431.15	+	12871.1i	−0.439266	+	0.760831i	0.558367	+	0.829594i	$0.311428\pi$
$660$		0			0
$661$	−15644.7	+	27097.4i	−0.920588	+	1.59451i	−0.122081	+	0.992520i	$0.538957\pi$
$661$	−15644.7	+	27097.4i	−0.920588	+	1.59451i	−0.798507	+	0.601985i	$0.794377\pi$
$662$	1398.01	−	2421.42i	0.0820771	−	0.142162i
$663$		0			0
$664$	2643.63	−	4578.91i	0.154507	−	0.267615i
$665$	7141.47	+	4042.12i	0.416442	+	0.235709i
$666$		0			0
$667$	4225.97	−	7319.60i	0.245323	−	0.424911i
$668$	−0.534148			−3.09383e−5
$669$		0			0
$670$	1173.73			0.0676791
$671$	694.229	+	1202.44i	0.0399410	+	0.0691798i
$672$		0			0
$673$	2162.02	−	3744.73i	0.123833	−	0.214485i	−0.797443	−	0.603394i	$-0.793815\pi$
$673$	2162.02	−	3744.73i	0.123833	−	0.214485i	0.921276	+	0.388909i	$0.127148\pi$
$674$	−9806.11	+	16984.7i	−0.560411	+	0.970661i
$675$		0			0
$676$	−2901.99	−	5026.39i	−0.165111	−	0.285980i
$677$	−2404.70	−	4165.07i	−0.136514	−	0.236450i	0.789661	−	0.613544i	$-0.210257\pi$
$677$	−2404.70	−	4165.07i	−0.136514	−	0.236450i	−0.926175	+	0.377094i	$0.876923\pi$
$678$		0			0
$679$	−1827.78	−	1034.53i	−0.103304	−	0.0584710i
$680$	9623.63	+	16668.6i	0.542720	+	0.940018i
$681$		0			0
$682$	−14400.3			−0.808526
$683$	13158.2	+	22790.8i	0.737169	+	1.27681i	0.953765	+	0.300553i	$0.0971711\pi$
$683$	13158.2	+	22790.8i	0.737169	+	1.27681i	−0.216596	+	0.976261i	$0.569496\pi$
$684$		0			0
$685$	1644.99			0.0917545
$686$	−18277.6	+	11187.1i	−1.01726	+	0.622633i
$687$		0			0
$688$	3812.79			0.211281
$689$	8359.53	−	14479.1i	0.462224	−	0.800596i
$690$		0			0
$691$	−1095.59	−	1897.63i	−0.0603161	−	0.104470i	0.834291	−	0.551325i	$-0.185878\pi$
$691$	−1095.59	−	1897.63i	−0.0603161	−	0.104470i	−0.894607	+	0.446854i	$0.852544\pi$
$692$	−4267.56			−0.234434
$693$		0			0
$694$	−11209.6			−0.613128
$695$	6542.10	+	11331.2i	0.357059	+	0.618444i
$696$		0			0
$697$	1432.08	−	2480.44i	0.0778250	−	0.134797i
$698$	2538.16			0.137637
$699$		0			0
$700$	1635.85	+	925.905i	0.0883278	+	0.0499942i
$701$	−7938.38			−0.427715			−0.213858	−	0.976865i	$-0.568603\pi$
$701$	−7938.38			−0.427715			−0.213858	+	0.976865i	$0.568603\pi$
$702$		0			0
$703$	−6569.06	−	11377.9i	−0.352428	−	0.610423i
$704$	−5895.75			−0.315631
$705$		0			0
$706$	−3733.79	−	6467.11i	−0.199041	−	0.344749i
$707$	−170.678	−	19964.3i	−0.00907921	−	1.06200i
$708$		0			0
$709$	−11439.3	−	19813.4i	−0.605940	−	1.04952i	−0.991902	−	0.127004i	$-0.959464\pi$
$709$	−11439.3	−	19813.4i	−0.605940	−	1.04952i	0.385962	−	0.922515i	$-0.373870\pi$
$710$	−2405.71	−	4166.82i	−0.127162	−	0.220251i
$711$		0			0
$712$	−1624.14	+	2813.09i	−0.0854875	+	0.148069i
$713$	8439.62	−	14617.8i	0.443291	−	0.767802i
$714$		0			0
$715$	11862.4	+	20546.3i	0.620462	+	1.07467i
$716$	9850.32			0.514139
$717$		0			0
$718$	−2935.48			−0.152578
$719$	5773.81	−	10000.5i	0.299481	−	0.518716i	−0.676536	−	0.736409i	$-0.736520\pi$
$719$	5773.81	−	10000.5i	0.299481	−	0.518716i	0.976017	+	0.217693i	$0.0698531\pi$
$720$		0			0
$721$	270.798	+	31675.4i	0.0139876	+	1.63613i
$722$	8082.37	−	13999.1i	0.416613	−	0.721595i
$723$		0			0
$724$	−1471.91	+	2549.42i	−0.0755568	+	0.130868i
$725$	824.753	−	1428.51i	0.0422491	−	0.0731775i
$726$		0			0
$727$	−9053.60	+	15681.3i	−0.461870	+	0.799982i	−0.999054	−	0.0434827i	$-0.986155\pi$
$727$	−9053.60	+	15681.3i	−0.461870	+	0.799982i	0.537184	+	0.843465i	$0.319488\pi$
$728$	−15561.5	+	9162.71i	−0.792237	+	0.466474i
$729$		0			0
$730$	−11994.6	+	20775.3i	−0.608139	+	1.05333i
$731$	−6068.75			−0.307060
$732$		0			0
$733$	23101.1			1.16406			0.582032	−	0.813166i	$-0.302258\pi$
$733$	23101.1			1.16406			0.582032	+	0.813166i	$0.302258\pi$
$734$	4265.12	+	7387.41i	0.214480	+	0.371491i
$735$		0			0
$736$	−11070.0	+	19173.8i	−0.554411	+	0.960267i
$737$	694.636	−	1203.15i	0.0347181	−	0.0601336i
$738$		0			0
$739$	−5479.70	−	9491.12i	−0.272766	−	0.472444i	0.696803	−	0.717262i	$-0.254605\pi$
$739$	−5479.70	−	9491.12i	−0.272766	−	0.472444i	−0.969569	+	0.244818i	$0.921272\pi$
$740$	4759.00	+	8242.84i	0.236411	+	0.409477i
$741$		0			0
$742$	14529.8	+	8224.00i	0.718878	+	0.406890i
$743$	2774.77	+	4806.05i	0.137008	+	0.237304i	0.926363	−	0.376633i	$-0.122918\pi$
$743$	2774.77	+	4806.05i	0.137008	+	0.237304i	−0.789355	+	0.613937i	$0.789585\pi$
$744$		0			0
$745$	7029.87			0.345711
$746$	−9058.60	−	15690.0i	−0.444583	−	0.770040i
$747$		0			0
$748$	−16666.7			−0.814698
$749$	13229.2	+	7487.85i	0.645375	+	0.365287i
$750$		0			0
$751$	−16603.6			−0.806754			−0.403377	−	0.915034i	$-0.632164\pi$
$751$	−16603.6			−0.806754			−0.403377	+	0.915034i	$0.632164\pi$
$752$	−15396.5	+	26667.4i	−0.746610	+	1.29317i
$753$		0			0
$754$	−5796.66	−	10040.1i	−0.279976	−	0.484933i
$755$	−27939.9			−1.34681
$756$		0			0
$757$	2336.31			0.112172			0.0560862	−	0.998426i	$-0.482138\pi$
$757$	2336.31			0.112172			0.0560862	+	0.998426i	$0.482138\pi$
$758$	16738.1	+	28991.2i	0.802052	+	1.38919i
$759$		0			0
$760$	−3452.83	+	5980.48i	−0.164799	+	0.285441i
$761$	−10068.8			−0.479625			−0.239812	−	0.970819i	$-0.577086\pi$
$761$	−10068.8			−0.479625			−0.239812	+	0.970819i	$0.577086\pi$
$762$		0			0
$763$	−33978.8	+	20006.9i	−1.61221	+	0.949277i
$764$	−10740.3			−0.508601
$765$		0			0
$766$	18870.3	+	32684.3i	0.890093	+	1.54169i
$767$	−24195.9			−1.13907
$768$		0			0
$769$	−1220.38	−	2113.76i	−0.0572277	−	0.0991213i	0.835992	−	0.548741i	$-0.184893\pi$
$769$	−1220.38	−	2113.76i	−0.0572277	−	0.0991213i	−0.893220	+	0.449620i	$0.851559\pi$
$770$	−20415.8	+	12020.9i	−0.955498	+	0.562603i
$771$		0			0
$772$	2877.98	+	4984.81i	0.134172	+	0.232393i
$773$	−5436.01	−	9415.44i	−0.252936	−	0.438098i	0.711397	−	0.702791i	$-0.248063\pi$
$773$	−5436.01	−	9415.44i	−0.252936	−	0.438098i	−0.964333	+	0.264692i	$0.914730\pi$
$774$		0			0
$775$	1647.10	−	2852.86i	0.0763428	−	0.132230i
$776$	883.713	−	1530.64i	0.0408807	−	0.0708075i
$777$		0			0
$778$	−2839.35	−	4917.91i	−0.130843	−	0.226627i
$779$	1027.63			0.0472638
$780$		0			0
$781$	−5695.01			−0.260927
$782$	32887.7	−	56963.2i	1.50391	−	2.60486i
$783$		0			0
$784$	−14056.4	−	23412.6i	−0.640324	−	1.06654i
$785$	3655.44	−	6331.40i	0.166201	−	0.287869i
$786$		0			0
$787$	−9740.91	+	16871.7i	−0.441202	+	0.764184i	−0.997779	−	0.0666120i	$-0.978781\pi$
$787$	−9740.91	+	16871.7i	−0.441202	+	0.764184i	0.556577	+	0.830796i	$0.312114\pi$
$788$	430.721	−	746.031i	0.0194718	−	0.0337262i
$789$		0			0
$790$	−8240.96	+	14273.8i	−0.371139	+	0.642832i
$791$	6485.19	−	3818.52i	0.291513	−	0.171645i
$792$		0			0
$793$	−1116.19	+	1933.29i	−0.0499835	+	0.0865740i
$794$	11978.4			0.535385
$795$		0			0
$796$	2614.06			0.116398
$797$	−1644.31	−	2848.02i	−0.0730794	−	0.126577i	0.827170	−	0.561952i	$-0.189949\pi$
$797$	−1644.31	−	2848.02i	−0.0730794	−	0.126577i	−0.900249	+	0.435374i	$0.856616\pi$
$798$		0			0
$799$	24506.3	−	42446.1i	1.08507	−	1.87939i
$800$	−2160.46	+	3742.02i	−0.0954797	+	0.165376i
$801$		0			0
$802$	−6412.29	−	11106.4i	−0.282327	−	0.489004i
$803$	14197.4	+	24590.6i	0.623928	+	1.08068i
$804$		0			0
$805$	−237.405	−	27769.4i	−0.0103943	−	1.21583i
$806$	−11576.4	−	20050.9i	−0.505908	−	0.876259i
$807$		0			0
$808$	16801.2			0.731515
$809$	−14785.3	−	25608.8i	−0.642549	−	1.11293i	−0.984862	−	0.173341i	$-0.944544\pi$
$809$	−14785.3	−	25608.8i	−0.642549	−	1.11293i	0.342313	−	0.939586i	$-0.388790\pi$
$810$		0			0
$811$	−1910.74			−0.0827313			−0.0413656	−	0.999144i	$-0.513171\pi$
$811$	−1910.74			−0.0827313			−0.0413656	+	0.999144i	$0.513171\pi$
$812$	2963.04	−	1744.66i	0.128057	−	0.0754008i
$813$		0			0
$814$	37931.4			1.63329
$815$	13644.1	−	23632.2i	0.586418	−	1.01571i
$816$		0			0
$817$	−1088.69	−	1885.67i	−0.0466201	−	0.0807483i
$818$	44680.1			1.90979
$819$		0			0
$820$	−744.471			−0.0317049
$821$	−16782.8	−	29068.7i	−0.713428	−	1.23569i	−0.963563	−	0.267482i	$-0.913808\pi$
$821$	−16782.8	−	29068.7i	−0.713428	−	1.23569i	0.250135	−	0.968211i	$-0.419525\pi$
$822$		0			0
$823$	19668.3	−	34066.5i	0.833042	−	1.44287i	−0.0625721	−	0.998040i	$-0.519930\pi$
$823$	19668.3	−	34066.5i	0.833042	−	1.44287i	0.895614	−	0.444831i	$-0.146736\pi$
$824$	−26656.9			−1.12699
$825$		0			0
$826$	−206.560	−	24161.4i	−0.00870114	−	1.01778i
$827$	−36017.5			−1.51445			−0.757226	−	0.653153i	$-0.773446\pi$
$827$	−36017.5			−1.51445			−0.757226	+	0.653153i	$0.773446\pi$
$828$		0			0
$829$	−1351.86	−	2341.49i	−0.0566369	−	0.0980980i	0.836317	−	0.548246i	$-0.184704\pi$
$829$	−1351.86	−	2341.49i	−0.0566369	−	0.0980980i	−0.892954	+	0.450148i	$0.851371\pi$
$830$	11152.7			0.466403
$831$		0			0
$832$	−4739.61	−	8209.25i	−0.197496	−	0.342073i
$833$	22373.3	+	37265.5i	0.930601	+	1.55003i
$834$		0			0
$835$	0.770052	+	1.33377i	3.19147e−5	+	5.52779e-5i
$836$	−2989.89	−	5178.65i	−0.123693	−	0.214243i
$837$		0			0
$838$	−4842.59	+	8387.62i	−0.199624	+	0.345758i
$839$	14788.7	−	25614.8i	0.608537	−	1.05402i	−0.382945	−	0.923771i	$-0.625090\pi$
$839$	14788.7	−	25614.8i	0.608537	−	1.05402i	0.991482	−	0.130245i	$-0.0415765\pi$
$840$		0			0
$841$	10685.8	+	18508.3i	0.438140	+	0.758880i
$842$	2976.01			0.121805
$843$		0			0
$844$	12401.3			0.505771
$845$	−8367.27	+	14492.5i	−0.340642	+	0.590010i
$846$		0			0
$847$	29.0004	+	3392.19i	0.00117647	+	0.137612i
$848$	−10638.0	+	18425.5i	−0.430789	+	0.746149i
$849$		0			0
$850$	6418.46	−	11117.1i	0.259002	−	0.448604i
$851$	−22230.6	+	38504.5i	−0.895482	+	1.55102i
$852$		0			0
$853$	1776.98	−	3077.82i	0.0713279	−	0.123544i	−0.828156	−	0.560498i	$-0.810610\pi$
$853$	1776.98	−	3077.82i	0.0713279	−	0.123544i	0.899484	+	0.436955i	$0.143943\pi$
$854$	−1940.06	−	1098.09i	−0.0777372	−	0.0439998i
$855$		0			0
$856$	−6396.22	+	11078.6i	−0.255395	+	0.442357i
$857$	−13277.7			−0.529237			−0.264619	−	0.964353i	$-0.585246\pi$
$857$	−13277.7			−0.529237			−0.264619	+	0.964353i	$0.585246\pi$
$858$		0			0
$859$	36198.1			1.43779			0.718896	−	0.695117i	$-0.244648\pi$
$859$	36198.1			1.43779			0.718896	+	0.695117i	$0.244648\pi$
$860$	788.712	+	1366.09i	0.0312731	+	0.0541666i
$861$		0			0
$862$	14631.8	−	25343.1i	0.578147	−	1.00138i
$863$	−8941.47	+	15487.1i	−0.352689	+	0.610876i	−0.986720	−	0.162432i	$-0.948066\pi$
$863$	−8941.47	+	15487.1i	−0.352689	+	0.610876i	0.634030	+	0.773308i	$0.281399\pi$
$864$		0			0
$865$	6152.32	+	10656.1i	0.241832	+	0.418866i
$866$	17745.9	+	30736.8i	0.696340	+	1.20610i
$867$		0			0
$868$	5917.45	−	3484.23i	0.231395	−	0.136247i
$869$	9754.36	+	16895.0i	0.380776	+	0.659523i
$870$		0			0
$871$	2233.68			0.0868949
$872$	−16591.4	−	28737.2i	−0.644330	−	1.11601i
$873$		0			0
$874$	23599.3			0.913341
$875$	−239.201	−	27979.5i	−0.00924169	−	1.08100i
$876$		0			0
$877$	−10938.4			−0.421166			−0.210583	−	0.977576i	$-0.567536\pi$
$877$	−10938.4			−0.421166			−0.210583	+	0.977576i	$0.567536\pi$
$878$	18903.0	−	32740.9i	0.726587	−	1.25849i
$879$		0			0
$880$	−15095.6	−	26146.4i	−0.578265	−	1.00158i
$881$	16145.8			0.617442			0.308721	−	0.951153i	$-0.400099\pi$
$881$	16145.8			0.617442			0.308721	+	0.951153i	$0.400099\pi$
$882$		0			0
$883$	−36343.7			−1.38512			−0.692562	−	0.721359i	$-0.743518\pi$
$883$	−36343.7			−1.38512			−0.692562	+	0.721359i	$0.743518\pi$
$884$	−13398.4	−	23206.7i	−0.509770	−	0.882948i
$885$		0			0
$886$	−4319.29	+	7481.23i	−0.163780	+	0.283676i
$887$	−24675.6			−0.934077			−0.467038	−	0.884237i	$-0.654679\pi$
$887$	−24675.6			−0.934077			−0.467038	+	0.884237i	$0.654679\pi$
$888$		0			0
$889$	−364.160	−	42595.9i	−0.0137385	−	1.60700i
$890$	−6851.72			−0.258057
$891$		0			0
$892$	3387.31	+	5867.00i	0.127148	+	0.220226i
$893$	17585.1			0.658972
$894$		0			0
$895$	−14200.7	−	24596.3i	−0.530365	−	0.918618i
$896$	26528.5	−	15620.1i	0.989123	−	0.582401i
$897$		0			0
$898$	17367.5	+	30081.4i	0.645392	+	1.11785i
$899$	−3013.01	−	5218.69i	−0.111779	−	0.193608i
$900$		0			0
$901$	16932.3	−	29327.6i	0.626078	−	1.08440i
$902$	−1483.44	+	2569.40i	−0.0547597	+	0.0948465i
$903$		0			0
$904$	3166.64	+	5484.78i	0.116505	+	0.201793i
$905$	8487.89			0.311765
$906$		0			0
$907$	−16901.6			−0.618753			−0.309377	−	0.950940i	$-0.600120\pi$
$907$	−16901.6			−0.618753			−0.309377	+	0.950940i	$0.600120\pi$
$908$	−5739.15	+	9940.49i	−0.209758	+	0.363311i
$909$		0			0
$910$	−33150.3	−	18763.3i	−1.20760	−	0.683513i
$911$	17861.1	−	30936.3i	0.649576	−	1.12510i	−0.333649	−	0.942698i	$-0.608280\pi$
$911$	17861.1	−	30936.3i	0.649576	−	1.12510i	0.983224	−	0.182401i	$-0.0583868\pi$
$912$		0			0
$913$	6600.39	−	11432.2i	0.239256	−	0.414404i
$914$	−24229.3	+	41966.3i	−0.876841	+	1.51873i
$915$		0			0
$916$	8709.71	−	15085.7i	0.314167	−	0.544153i
$917$	92.4158	+	10809.9i	0.00332807	+	0.389286i
$918$		0			0
$919$	−706.061	+	1222.93i	−0.0253436	+	0.0438965i	−0.878419	−	0.477891i	$-0.841401\pi$
$919$	−706.061	+	1222.93i	−0.0253436	+	0.0438965i	0.853075	+	0.521788i	$0.174735\pi$
$920$	23369.7			0.837475
$921$		0			0
$922$	−18537.4			−0.662142
$923$	−4578.24	−	7929.75i	−0.163266	−	0.282785i
$924$		0			0
$925$	−4338.59	+	7514.66i	−0.154218	+	0.267114i
$926$	12373.5	−	21431.5i	0.439112	−	0.760564i
$927$		0			0
$928$	3952.09	+	6845.22i	0.139799	+	0.242139i
$929$	−6295.72	−	10904.5i	−0.222342	−	0.385108i	0.733177	−	0.680038i	$-0.238037\pi$
$929$	−6295.72	−	10904.5i	−0.222342	−	0.385108i	−0.955519	+	0.294930i	$0.904704\pi$
$930$		0			0
$931$	−7565.45	+	13637.0i	−0.266324	+	0.480059i
$932$	10319.3	+	17873.6i	0.362684	+	0.628187i
$933$		0			0
$934$	10142.4			0.355321
$935$	24027.4	+	41616.8i	0.840408	+	1.45563i
$936$		0			0
$937$	48310.9			1.68436			0.842182	−	0.539193i	$-0.181271\pi$
$937$	48310.9			1.68436			0.842182	+	0.539193i	$0.181271\pi$
$938$	19.0689	+	2230.50i	0.000663776	+	0.0776421i
$939$		0			0
$940$	−12739.6			−0.442044
$941$	−10507.2	+	18199.0i	−0.364000	+	0.630467i	−0.988615	−	0.150466i	$-0.951923\pi$
$941$	−10507.2	+	18199.0i	−0.364000	+	0.630467i	0.624615	+	0.780933i	$0.285256\pi$
$942$		0			0
$943$	−1738.81	−	3011.71i	−0.0600462	−	0.104003i
$944$	30790.7			1.06160
$945$		0			0
$946$	6286.39			0.216055
$947$	25990.5	+	45016.9i	0.891845	+	1.54472i	0.837661	+	0.546190i	$0.183923\pi$
$947$	25990.5	+	45016.9i	0.891845	+	1.54472i	0.0541843	+	0.998531i	$0.482744\pi$
$948$		0			0
$949$	−22826.6	+	39536.9i	−0.780805	+	1.35239i
$950$	4605.72			0.157294
$951$		0			0
$952$	−31520.0	+	18559.1i	−1.07308	+	0.631833i
$953$	26692.5			0.907296			0.453648	−	0.891181i	$-0.350122\pi$
$953$	26692.5			0.907296			0.453648	+	0.891181i	$0.350122\pi$
$954$		0			0
$955$	15483.7	+	26818.6i	0.524651	+	0.908722i
$956$	−8799.33			−0.297689
$957$		0			0
$958$	17885.5	+	30978.6i	0.603187	+	1.04475i
$959$	26.7253	+	3126.07i	0.000899900	+	0.105262i
$960$		0			0
$961$	8878.26	+	15377.6i	0.298018	+	0.516183i
$962$	30493.2	+	52815.8i	1.02197	+	1.77011i
$963$		0			0
$964$	−3924.55	+	6797.52i	−0.131122	+	0.227109i
$965$	8298.07	−	14372.7i	0.276813	−	0.479454i
$966$		0			0
$967$	−17421.6	−	30175.0i	−0.579359	−	1.00348i	−0.995553	−	0.0942029i	$-0.969970\pi$
$967$	−17421.6	−	30175.0i	−0.579359	−	1.00348i	0.416194	−	0.909276i	$-0.363364\pi$
$968$	−2854.75			−0.0947882
$969$		0			0
$970$	3728.11			0.123405
$971$	3963.58	−	6865.13i	0.130996	−	0.226892i	−0.793065	−	0.609138i	$-0.791516\pi$
$971$	3963.58	−	6865.13i	0.130996	−	0.226892i	0.924061	+	0.382245i	$0.124849\pi$
$972$		0			0
$973$	−21427.1	+	12616.4i	−0.705983	+	0.415687i
$974$	24156.2	−	41839.8i	0.794677	−	1.37642i
$975$		0			0
$976$	1420.41	−	2460.22i	0.0465842	−	0.0806862i
$977$	−3122.04	+	5407.52i	−0.102234	+	0.177075i	−0.912605	−	0.408843i	$-0.865932\pi$
$977$	−3122.04	+	5407.52i	−0.102234	+	0.177075i	0.810371	+	0.585918i	$0.199266\pi$
$978$		0			0
$979$	−4055.00	+	7023.47i	−0.132378	+	0.229286i
$980$	5480.84	−	9879.42i	0.178652	−	0.322027i
$981$		0			0
$982$	7123.74	−	12338.7i	0.231495	−	0.400961i
$983$	−8380.12			−0.271907			−0.135953	−	0.990715i	$-0.543410\pi$
$983$	−8380.12			−0.271907			−0.135953	+	0.990715i	$0.543410\pi$
$984$		0			0
$985$	−2483.79			−0.0803453
$986$	−11741.2	−	20336.3i	−0.379225	−	0.656836i
$987$		0			0
$988$	4807.17	−	8326.26i	0.154794	−	0.268111i
$989$	−3684.29	+	6381.38i	−0.118457	+	0.205173i
$990$		0			0
$991$	4971.94	+	8611.66i	0.159373	+	0.276043i	0.934643	−	0.355588i	$-0.115719\pi$
$991$	4971.94	+	8611.66i	0.159373	+	0.276043i	−0.775269	+	0.631631i	$0.782386\pi$
$992$	7892.65	+	13670.5i	0.252613	+	0.437538i
$993$		0			0
$994$	7879.35	−	4639.41i	0.251426	−	0.148041i
$995$	−3768.55	−	6527.32i	−0.120071	−	0.207970i
$996$		0			0
$997$	34946.8			1.11011			0.555053	−	0.831815i	$-0.312698\pi$
$997$	34946.8			1.11011			0.555053	+	0.831815i	$0.312698\pi$
$998$	−31537.1	−	54623.9i	−1.00029	−	1.73255i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.g.a.100.5		44
3.2	odd	2		63.4.g.a.16.18	yes	44
7.4	even	3		189.4.h.a.46.18		44
9.4	even	3		189.4.h.a.37.18		44
9.5	odd	6		63.4.h.a.58.5	yes	44
21.11	odd	6		63.4.h.a.25.5	yes	44
63.4	even	3	inner	189.4.g.a.172.5		44
63.32	odd	6		63.4.g.a.4.18	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.18	✓	44	63.32	odd	6
63.4.g.a.16.18	yes	44	3.2	odd	2
63.4.h.a.25.5	yes	44	21.11	odd	6
63.4.h.a.58.5	yes	44	9.5	odd	6
189.4.g.a.100.5		44	1.1	even	1	trivial
189.4.g.a.172.5		44	63.4	even	3	inner
189.4.h.a.37.18		44	9.4	even	3
189.4.h.a.46.18		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)

\(f(q)\)	\(=\)	\(q+(-1.68671 - 2.92146i) q^{2} +(-1.68996 + 2.92710i) q^{4} +9.74532 q^{5} +(0.158327 + 18.5196i) q^{7} -15.5854 q^{8} +O(q^{10})\)	\(q+(-1.68671 - 2.92146i) q^{2} +(-1.68996 + 2.92710i) q^{4} +9.74532 q^{5} +(0.158327 + 18.5196i) q^{7} -15.5854 q^{8} +(-16.4375 - 28.4706i) q^{10} -38.9123 q^{11} +(-31.2817 - 54.1816i) q^{13} +(53.8372 - 31.6997i) q^{14} +(39.8078 + 68.9491i) q^{16} +(-63.3614 - 109.745i) q^{17} +(22.7332 - 39.3751i) q^{19} +(-16.4692 + 28.5256i) q^{20} +(65.6337 + 113.681i) q^{22} -153.865 q^{23} -30.0287 q^{25} +(-105.526 + 182.777i) q^{26} +(-54.4763 - 30.8340i) q^{28} +(-27.4655 + 47.5716i) q^{29} +(-54.8509 + 95.0045i) q^{31} +(71.9464 - 124.615i) q^{32} +(-213.744 + 370.216i) q^{34} +(1.54295 + 180.479i) q^{35} +(144.482 - 250.249i) q^{37} -153.377 q^{38} -151.885 q^{40} +(11.3009 + 19.5738i) q^{41} +(23.9450 - 41.4740i) q^{43} +(65.7604 - 113.900i) q^{44} +(259.525 + 449.510i) q^{46} +(193.385 + 334.953i) q^{47} +(-342.950 + 5.86430i) q^{49} +(50.6496 + 87.7278i) q^{50} +211.460 q^{52} +(133.617 + 231.431i) q^{53} -379.213 q^{55} +(-2.46759 - 288.635i) q^{56} +185.305 q^{58} +(193.371 - 334.929i) q^{59} +(-17.8409 - 30.9013i) q^{61} +370.070 q^{62} +151.514 q^{64} +(-304.851 - 528.017i) q^{65} +(-17.8513 + 30.9194i) q^{67} +428.314 q^{68} +(524.661 - 308.923i) q^{70} +146.355 q^{71} +(-364.856 - 631.948i) q^{73} -974.792 q^{74} +(76.8367 + 133.085i) q^{76} +(-6.16087 - 720.640i) q^{77} +(-250.675 - 434.183i) q^{79} +(387.939 + 671.931i) q^{80} +(38.1227 - 66.0304i) q^{82} +(-169.622 + 293.794i) q^{83} +(-617.477 - 1069.50i) q^{85} -161.553 q^{86} +606.465 q^{88} +(104.209 - 180.495i) q^{89} +(998.467 - 587.903i) q^{91} +(260.026 - 450.378i) q^{92} +(652.368 - 1129.94i) q^{94} +(221.543 - 383.723i) q^{95} +(-56.7013 + 98.2095i) q^{97} +(595.588 + 992.024i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 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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