LMFDB - Embedded newform 189.4.h.a.37.18

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			37.18
Character	$\chi$	$=$	189.37
Dual form			189.4.h.a.46.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.37342 q^{2} +3.37993 q^{4} +(-4.87266 - 8.43970i) q^{5} +(-16.1176 - 9.12268i) q^{7} -15.5854 q^{8} +O(q^{10})$	\(q+3.37342 q^{2} +3.37993 q^{4} +(-4.87266 - 8.43970i) q^{5} +(-16.1176 - 9.12268i) q^{7} -15.5854 q^{8} +(-16.4375 - 28.4706i) q^{10} +(19.4562 - 33.6990i) q^{11} +(-31.2817 + 54.1816i) q^{13} +(-54.3713 - 30.7746i) q^{14} -79.6155 q^{16} +(-63.3614 - 109.745i) q^{17} +(22.7332 - 39.3751i) q^{19} +(-16.4692 - 28.5256i) q^{20} +(65.6337 - 113.681i) q^{22} +(76.9324 + 133.251i) q^{23} +(15.0144 - 26.0056i) q^{25} +(-105.526 + 182.777i) q^{26} +(-54.4763 - 30.8340i) q^{28} +(-27.4655 - 47.5716i) q^{29} +109.702 q^{31} -143.893 q^{32} +(-213.744 - 370.216i) q^{34} +(1.54295 + 180.479i) q^{35} +(144.482 - 250.249i) q^{37} +(76.6886 - 132.829i) q^{38} +(75.9424 + 131.536i) q^{40} +(11.3009 - 19.5738i) q^{41} +(23.9450 + 41.4740i) q^{43} +(65.7604 - 113.900i) q^{44} +(259.525 + 449.510i) q^{46} -386.770 q^{47} +(176.554 + 294.071i) q^{49} +(50.6496 - 87.7278i) q^{50} +(-105.730 + 183.130i) q^{52} +(133.617 + 231.431i) q^{53} -379.213 q^{55} +(251.199 + 142.181i) q^{56} +(-92.6525 - 160.479i) q^{58} -386.742 q^{59} +35.6817 q^{61} +370.070 q^{62} +151.514 q^{64} +609.701 q^{65} +35.7027 q^{67} +(-214.157 - 370.931i) q^{68} +(5.20500 + 608.832i) q^{70} +146.355 q^{71} +(-364.856 - 631.948i) q^{73} +(487.396 - 844.195i) q^{74} +(76.8367 - 133.085i) q^{76} +(-621.012 + 365.655i) q^{77} +501.351 q^{79} +(387.939 + 671.931i) q^{80} +(38.1227 - 66.0304i) q^{82} +(-169.622 - 293.794i) q^{83} +(-617.477 + 1069.50i) q^{85} +(80.7764 + 139.909i) q^{86} +(-303.232 + 525.214i) q^{88} +(104.209 - 180.495i) q^{89} +(998.467 - 587.903i) q^{91} +(260.026 + 450.378i) q^{92} -1304.74 q^{94} -443.085 q^{95} +(-56.7013 - 98.2095i) q^{97} +(595.588 + 992.024i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.37342			1.19268			0.596341	−	0.802731i	$-0.296621\pi$
$2$	3.37342			1.19268			0.596341	+	0.802731i	$0.296621\pi$
$3$		0			0
$3$		0			0
$4$	3.37993			0.422491
$5$	−4.87266	−	8.43970i	−0.435824	−	0.754869i	0.561538	−	0.827451i	$-0.310210\pi$
$5$	−4.87266	−	8.43970i	−0.435824	−	0.754869i	−0.997363	+	0.0725813i	$0.976876\pi$
$6$		0			0
$7$	−16.1176	−	9.12268i	−0.870268	−	0.492578i
$7$	−16.1176	−	9.12268i	−0.870268	−	0.492578i
$8$	−15.5854			−0.688785
$9$		0			0
$10$	−16.4375	−	28.4706i	−0.519800	−	0.900319i
$11$	19.4562	−	33.6990i	0.533296	−	0.923695i	−0.465948	−	0.884812i	$-0.654287\pi$
$11$	19.4562	−	33.6990i	0.533296	−	0.923695i	0.999244	−	0.0388830i	$-0.0123800\pi$
$12$		0			0
$13$	−31.2817	+	54.1816i	−0.667384	+	1.15594i	0.311249	+	0.950328i	$0.399253\pi$
$13$	−31.2817	+	54.1816i	−0.667384	+	1.15594i	−0.978633	+	0.205615i	$0.934081\pi$
$14$	−54.3713	−	30.7746i	−1.03795	−	0.587489i
$15$		0			0
$16$	−79.6155			−1.24399
$17$	−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
$23$	76.9324	+	133.251i	0.697457	+	1.20803i	0.969345	+	0.245702i	$0.0790185\pi$
$23$	76.9324	+	133.251i	0.697457	+	1.20803i	−0.271889	+	0.962329i	$0.587648\pi$
$24$		0			0
$25$	15.0144	−	26.0056i	0.120115	−	0.208045i
$26$	−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	0.764592	−	0.644514i	$-0.222940\pi$
$29$	−27.4655	−	47.5716i	−0.175869	−	0.304615i	−0.940462	+	0.339899i	$0.889607\pi$
$30$		0			0
$31$	109.702			0.635581			0.317791	−	0.948161i	$-0.397059\pi$
$31$	109.702			0.635581			0.317791	+	0.948161i	$0.397059\pi$
$32$	−143.893			−0.794903
$33$		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	$-0.0552129\pi$
$38$	76.6886	−	132.829i	0.327383	−	0.567043i
$39$		0			0
$40$	75.9424	+	131.536i	0.300189	+	0.519942i
$41$	11.3009	−	19.5738i	0.0430465	−	0.0745587i	−0.843699	−	0.536816i	$-0.819627\pi$
$41$	11.3009	−	19.5738i	0.0430465	−	0.0745587i	0.886746	+	0.462257i	$0.152960\pi$
$42$		0			0
$43$	23.9450	+	41.4740i	0.0849204	+	0.147086i	0.905357	−	0.424651i	$-0.139603\pi$
$43$	23.9450	+	41.4740i	0.0849204	+	0.147086i	−0.820437	+	0.571737i	$0.806270\pi$
$44$	65.7604	−	113.900i	0.225313	−	0.390253i
$45$		0			0
$46$	259.525	+	449.510i	0.831845	+	1.44080i
$47$	−386.770			−1.20035			−0.600173	−	0.799870i	$-0.704902\pi$
$47$	−386.770			−1.20035			−0.600173	+	0.799870i	$0.704902\pi$
$48$		0			0
$49$	176.554	+	294.071i	0.514733	+	0.857350i
$50$	50.6496	−	87.7278i	0.143259	−	0.248132i
$51$		0			0
$52$	−105.730	+	183.130i	−0.281964	+	0.488376i
$53$	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
$56$	251.199	+	142.181i	0.599427	+	0.339280i
$57$		0			0
$58$	−92.6525	−	160.479i	−0.209756	−	0.363309i
$59$	−386.742			−0.853382			−0.426691	−	0.904397i	$-0.640321\pi$
$59$	−386.742			−0.853382			−0.426691	+	0.904397i	$0.640321\pi$
$60$		0			0
$61$	35.6817			0.0748947			0.0374473	−	0.999299i	$-0.488077\pi$
$61$	35.6817			0.0748947			0.0374473	+	0.999299i	$0.488077\pi$
$62$	370.070			0.758047
$63$		0			0
$64$	151.514			0.295925
$65$	609.701			1.16345
$66$		0			0
$67$	35.7027			0.0651011			0.0325506	−	0.999470i	$-0.489637\pi$
$67$	35.7027			0.0651011			0.0325506	+	0.999470i	$0.489637\pi$
$68$	−214.157	−	370.931i	−0.381917	−	0.661499i
$69$		0			0
$70$	5.20500	+	608.832i	0.00888739	+	1.03956i
$71$	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	$-0.365562\pi$
$74$	487.396	−	844.195i	0.765657	−	1.32616i
$75$		0			0
$76$	76.8367	−	133.085i	0.115971	−	0.200867i
$77$	−621.012	+	365.655i	−0.919102	+	0.541173i
$78$		0			0
$79$	501.351			0.714005			0.357002	−	0.934103i	$-0.383799\pi$
$79$	501.351			0.714005			0.357002	+	0.934103i	$0.383799\pi$
$80$	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	0.731796	−	0.681524i	$-0.238682\pi$
$83$	−169.622	−	293.794i	−0.224319	−	0.388532i	−0.956115	+	0.292992i	$0.905349\pi$
$84$		0			0
$85$	−617.477	+	1069.50i	−0.787938	+	1.36475i
$86$	80.7764	+	139.909i	0.101283	+	0.175427i
$87$		0			0
$88$	−303.232	+	525.214i	−0.367326	+	0.636227i
$89$	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
$94$	−1304.74			−1.43163
$95$	−443.085			−0.478522
$96$		0			0
$97$	−56.7013	−	98.2095i	−0.0593520	−	0.102801i	0.834823	−	0.550519i	$-0.185570\pi$
$97$	−56.7013	−	98.2095i	−0.0593520	−	0.102801i	−0.894175	+	0.447718i	$0.852237\pi$
$98$	595.588	+	992.024i	0.613913	+	1.02255i
$99$		0			0
$100$	50.7475	−	87.8972i	0.0507475	−	0.0878972i
$101$	539.004	−	933.582i	0.531019	−	0.919752i	−0.468326	−	0.883556i	$-0.655143\pi$
$101$	539.004	−	933.582i	0.531019	−	0.919752i	0.999345	−	0.0361958i	$-0.0115240\pi$
$102$		0			0
$103$	−855.186	−	1481.23i	−0.818097	−	1.41699i	−0.907082	−	0.420953i	$-0.861696\pi$
$103$	−855.186	−	1481.23i	−0.818097	−	1.41699i	0.0889851	−	0.996033i	$-0.471638\pi$
$104$	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	$0.448319\pi$
$110$	−1279.24			−1.10883
$111$		0			0
$112$	1283.21	+	726.307i	1.08261	+	0.612764i
$113$	−203.179	+	351.917i	−0.169146	+	0.292970i	−0.938120	−	0.346311i	$-0.887434\pi$
$113$	−203.179	+	351.917i	−0.169146	+	0.292970i	0.768974	+	0.639280i	$0.220768\pi$
$114$		0			0
$115$	749.731	−	1298.57i	0.607937	−	1.05298i
$116$	−92.8314	−	160.789i	−0.0743033	−	0.128697i
$117$		0			0
$118$	−1304.64			−1.01781
$119$	20.0636	+	2346.85i	0.0154557	+	1.80786i
$120$		0			0
$121$	−91.5839	−	158.628i	−0.0688083	−	0.119180i
$122$	120.369			0.0893256
$123$		0			0
$124$	370.784			0.268528
$125$	−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	$0.797047\pi$
$128$	1662.26			1.14785
$129$		0			0
$130$	2056.77			1.38762
$131$	−291.851	−	505.501i	−0.194650	−	0.337144i	0.752136	−	0.659008i	$-0.229024\pi$
$131$	−291.851	−	505.501i	−0.194650	−	0.337144i	−0.946786	+	0.321865i	$0.895690\pi$
$132$		0			0
$133$	−725.611	+	427.244i	−0.473071	+	0.278547i
$134$	120.440			0.0776449
$135$		0			0
$136$	987.513	+	1710.42i	0.622636	+	1.07844i
$137$	−84.3990	+	146.183i	−0.0526328	+	0.0911626i	−0.891141	−	0.453726i	$-0.850095\pi$
$137$	−84.3990	+	146.183i	−0.0526328	+	0.0911626i	0.838509	+	0.544888i	$0.183428\pi$
$138$		0			0
$139$	671.306	−	1162.74i	0.409636	−	0.709511i	−0.585213	−	0.810880i	$-0.698989\pi$
$139$	671.306	−	1162.74i	0.409636	−	0.709511i	0.994849	+	0.101369i	$0.0323223\pi$
$140$	5.21506	+	610.007i	0.00314823	+	0.368250i
$141$		0			0
$142$	493.716			0.291773
$143$	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
$149$	−360.679	−	624.715i	−0.198309	−	0.343481i	0.749671	−	0.661810i	$-0.230212\pi$
$149$	−360.679	−	624.715i	−0.198309	−	0.343481i	−0.947980	+	0.318329i	$0.896878\pi$
$150$		0			0
$151$	1433.51	−	2482.90i	0.772563	−	1.33812i	−0.163591	−	0.986528i	$-0.552308\pi$
$151$	1433.51	−	2482.90i	0.772563	−	1.33812i	0.936154	−	0.351590i	$-0.114359\pi$
$152$	−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
$157$	−750.193			−0.381350			−0.190675	−	0.981653i	$-0.561068\pi$
$157$	−750.193			−0.381350			−0.190675	+	0.981653i	$0.561068\pi$
$158$	1691.26			0.851581
$159$		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	$-0.0682285\pi$
$164$	38.1963	−	66.1579i	0.0181868	−	0.0315004i
$165$		0			0
$166$	−572.206	−	991.090i	−0.267541	−	0.463395i
$167$	0.0790177	−	0.136863i	3.66142e−5	−	6.34176e-5i	−0.866007	−	0.500032i	$-0.833322\pi$
$167$	0.0790177	−	0.136863i	3.66142e−5	−	6.34176e-5i	0.866044	+	0.499968i	$0.166655\pi$
$168$		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
$173$	−1262.62			−0.554885			−0.277443	−	0.960742i	$-0.589487\pi$
$173$	−1262.62			−0.554885			−0.277443	+	0.960742i	$0.589487\pi$
$174$		0			0
$175$	−479.236	+	282.177i	−0.207011	+	0.121889i
$176$	−1549.01	+	2682.97i	−0.663416	+	1.14907i
$177$		0			0
$178$	351.539	−	608.884i	0.148028	−	0.256392i
$179$	−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	$0.442767\pi$
$182$	3368.24	−	1983.24i	1.37182	−	0.807734i
$183$		0			0
$184$	−1199.02	−	2076.77i	−0.480398	−	0.832073i
$185$	−2816.04			−1.11913
$186$		0			0
$187$	−4931.07			−1.92832
$188$	−1307.26			−0.507135
$189$		0			0
$190$	−1494.71			−0.570725
$191$	−3177.67			−1.20381			−0.601907	−	0.798566i	$-0.705592\pi$
$191$	−3177.67			−1.20381			−0.601907	+	0.798566i	$0.705592\pi$
$192$		0			0
$193$	−1702.98			−0.635148			−0.317574	−	0.948234i	$-0.602868\pi$
$193$	−1702.98			−0.635148			−0.317574	+	0.948234i	$0.602868\pi$
$194$	−191.277	−	331.301i	−0.0707880	−	0.122608i
$195$		0			0
$196$	596.739	+	993.940i	0.217470	+	0.362223i
$197$	−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	$0.877321\pi$
$200$	−234.005	+	405.308i	−0.0827332	+	0.143298i
$201$		0			0
$202$	1818.28	−	3149.36i	0.633337	−	1.09697i
$203$	8.69706	+	1017.30i	0.00300697	+	0.351726i
$204$		0			0
$205$	−220.262			−0.0750428
$206$	−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	0.394476	+	0.918906i	$0.370926\pi$
$211$	−1834.55	+	3177.54i	−0.598558	+	1.03673i	−0.993034	+	0.117827i	$0.962407\pi$
$212$	451.615	+	782.220i	0.146307	+	0.253411i
$213$		0			0
$214$	1384.44	−	2397.92i	0.442236	−	0.765975i
$215$	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
$220$	−1281.71			−0.392787
$221$	7928.21			2.41316
$222$		0			0
$223$	1002.18	+	1735.83i	0.300947	+	0.521256i	0.976351	−	0.216192i	$-0.0693639\pi$
$223$	1002.18	+	1735.83i	0.300947	+	0.521256i	−0.675404	+	0.737448i	$0.736031\pi$
$224$	2319.21	+	1312.69i	0.691779	+	0.391552i
$225$		0			0
$226$	−685.409	+	1187.16i	−0.201738	+	0.349420i
$227$	−1698.01	+	2941.04i	−0.496479	+	0.859927i	−0.999992	−	0.00406099i	$-0.998707\pi$
$227$	−1698.01	+	2941.04i	−0.496479	+	0.859927i	0.503513	+	0.863988i	$0.332041\pi$
$228$		0			0
$229$	2576.89	+	4463.31i	0.743606	+	1.28796i	0.950843	+	0.309673i	$0.100220\pi$
$229$	2576.89	+	4463.31i	0.743606	+	1.28796i	−0.207237	+	0.978291i	$0.566447\pi$
$230$	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
$236$	−1307.16			−0.360546
$237$		0			0
$238$	67.6830	+	7916.91i	0.0184338	+	2.15620i
$239$	1301.70	−	2254.62i	0.352302	−	0.610205i	−0.634350	−	0.773046i	$-0.718732\pi$
$239$	1301.70	−	2254.62i	0.352302	−	0.610205i	0.986652	+	0.162840i	$0.0520656\pi$
$240$		0			0
$241$	−1161.13	+	2011.14i	−0.310354	+	0.537548i	−0.978439	−	0.206536i	$-0.933781\pi$
$241$	−1161.13	+	2011.14i	−0.310354	+	0.537548i	0.668085	+	0.744085i	$0.267114\pi$
$242$	−308.950	−	535.118i	−0.0820665	−	0.142143i
$243$		0			0
$244$	120.602			0.0316423
$245$	1621.59	−	2922.97i	0.422854	−	0.762210i
$246$		0			0
$247$	1422.27	+	2463.44i	0.366384	+	0.634596i
$248$	−1709.75			−0.437779
$249$		0			0
$250$	−5096.57			−1.28934
$251$	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
$254$	−7759.02			−1.91671
$255$		0			0
$256$	4395.39			1.07309
$257$	1868.42	+	3236.21i	0.453499	+	0.785483i	0.998600	−	0.0528872i	$-0.0168424\pi$
$257$	1868.42	+	3236.21i	0.453499	+	0.785483i	−0.545102	+	0.838370i	$0.683509\pi$
$258$		0			0
$259$	−4611.64	+	2715.36i	−1.10638	+	0.651445i
$260$	2060.75			0.491546
$261$		0			0
$262$	−984.535	−	1705.26i	−0.232156	−	0.402105i
$263$	504.567	−	873.935i	0.118300	−	0.204902i	−0.800794	−	0.598940i	$-0.795589\pi$
$263$	504.567	−	873.935i	0.118300	−	0.204902i	0.919094	+	0.394038i	$0.128922\pi$
$264$		0			0
$265$	1302.14	−	2255.37i	0.301848	−	0.522816i
$266$	−2447.79	+	1441.27i	−0.564224	+	0.332218i
$267$		0			0
$268$	120.672			0.0275046
$269$	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
$275$	−584.243	−	1011.94i	−0.128113	−	0.221899i
$276$		0			0
$277$	3259.50	−	5645.62i	0.707019	−	1.22459i	−0.258939	−	0.965894i	$-0.583373\pi$
$277$	3259.50	−	5645.62i	0.707019	−	1.22459i	0.965958	−	0.258700i	$-0.0832940\pi$
$278$	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	0.978932	+	0.204185i	$0.0654545\pi$
$281$	3138.53	+	5436.10i	0.666296	+	1.15406i	−0.312636	+	0.949873i	$0.601212\pi$
$282$		0			0
$283$	806.332			0.169369			0.0846845	−	0.996408i	$-0.473012\pi$
$283$	806.332			0.169369			0.0846845	+	0.996408i	$0.473012\pi$
$284$	494.670			0.103357
$285$		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
$290$	−902.929	+	1563.92i	−0.182834	+	0.316677i
$291$		0			0
$292$	−1233.19	−	2135.94i	−0.247146	−	0.428070i
$293$	−3084.92	+	5343.24i	−0.615095	+	1.06538i	0.375272	+	0.926915i	$0.377549\pi$
$293$	−3084.92	+	5343.24i	−0.615095	+	1.06538i	−0.990368	+	0.138462i	$0.955784\pi$
$294$		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
$299$	−9626.31			−1.86189
$300$		0			0
$301$	−7.58228	−	886.903i	−0.00145195	−	0.169835i
$302$	4835.81	−	8375.87i	0.921423	−	1.59595i
$303$		0			0
$304$	−1809.92	+	3134.87i	−0.341467	+	0.591438i
$305$	−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	$0.366471\pi$
$308$	−2098.98	+	1235.89i	−0.388313	+	0.228641i
$309$		0			0
$310$	−1803.22	−	3123.28i	−0.330375	−	0.572226i
$311$	8462.60			1.54299			0.771495	−	0.636235i	$-0.219509\pi$
$311$	8462.60			1.54299			0.771495	+	0.636235i	$0.219509\pi$
$312$		0			0
$313$	5820.47			1.05109			0.525547	−	0.850765i	$-0.323861\pi$
$313$	5820.47			1.05109			0.525547	+	0.850765i	$0.323861\pi$
$314$	−2530.71			−0.454829
$315$		0			0
$316$	1694.53			0.301661
$317$	6415.18			1.13663			0.568316	−	0.822810i	$-0.307595\pi$
$317$	6415.18			1.13663			0.568316	+	0.822810i	$0.307595\pi$
$318$		0			0
$319$	−2137.49			−0.375162
$320$	−738.275	−	1278.73i	−0.128971	−	0.223385i
$321$		0			0
$322$	−82.1796	−	9612.58i	−0.0142226	−	1.66363i
$323$	−5761.63			−0.992526
$324$		0			0
$325$	939.350	+	1627.00i	0.160325	+	0.277692i
$326$	4722.99	−	8180.46i	0.802400	−	1.38980i
$327$		0			0
$328$	−176.130	+	305.065i	−0.0296498	+	0.0513549i
$329$	6233.81	+	3528.38i	1.04462	+	0.591264i
$330$		0			0
$331$	−828.837			−0.137634			−0.0688172	−	0.997629i	$-0.521923\pi$
$331$	−828.837			−0.137634			−0.0688172	+	0.997629i	$0.521923\pi$
$332$	−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	−0.999407	−	0.0344432i	$-0.989034\pi$
$337$	−2906.88	+	5034.86i	−0.469875	+	0.813847i	0.529532	+	0.848290i	$0.322368\pi$
$338$	−2896.39	−	5016.70i	−0.466104	−	0.807315i
$339$		0			0
$340$	−2087.03	+	3614.84i	−0.332897	+	0.576595i
$341$	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
$346$	−4259.34			−0.661802
$347$	−3322.93			−0.514075			−0.257038	−	0.966401i	$-0.582746\pi$
$347$	−3322.93			−0.514075			−0.257038	+	0.966401i	$0.582746\pi$
$348$		0			0
$349$	−376.201	−	651.599i	−0.0577008	−	0.0999407i	0.835732	−	0.549137i	$-0.185044\pi$
$349$	−376.201	−	651.599i	−0.0577008	−	0.0999407i	−0.893433	+	0.449197i	$0.851710\pi$
$350$	−1616.66	+	951.900i	−0.246898	+	0.145375i
$351$		0			0
$352$	−2799.60	+	4849.05i	−0.423918	+	0.734248i
$353$	−1106.83	+	1917.08i	−0.166885	+	0.289054i	−0.937323	−	0.348461i	$-0.886704\pi$
$353$	−1106.83	+	1917.08i	−0.166885	+	0.289054i	0.770438	+	0.637515i	$0.220038\pi$
$354$		0			0
$355$	−713.139	−	1235.19i	−0.106618	−	0.184668i
$356$	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
$362$	2938.15			0.426590
$363$		0			0
$364$	3374.75	−	1987.07i	0.485947	−	0.286129i
$365$	−3555.63	+	6158.54i	−0.509892	+	0.883158i
$366$		0			0
$367$	1264.33	−	2189.89i	0.179830	−	0.311475i	−0.761992	−	0.647586i	$-0.775779\pi$
$367$	1264.33	−	2189.89i	0.179830	−	0.311475i	0.941822	+	0.336111i	$0.109112\pi$
$368$	−6125.01	−	10608.8i	−0.867631	−	1.50278i
$369$		0			0
$370$	−9499.66			−1.33477
$371$	−42.3103	−	4949.05i	−0.00592087	−	0.692566i
$372$		0			0
$373$	−2685.29	−	4651.06i	−0.372759	−	0.645637i	0.617230	−	0.786783i	$-0.288255\pi$
$373$	−2685.29	−	4651.06i	−0.372759	−	0.645637i	−0.989989	+	0.141145i	$0.954921\pi$
$374$	−16634.6			−2.29987
$375$		0			0
$376$	6027.98			0.826780
$377$	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	$0.734770\pi$
$380$	−1497.60			−0.202171
$381$		0			0
$382$	−10719.6			−1.43577
$383$	5593.82	+	9688.78i	0.746295	+	1.29262i	0.949587	+	0.313503i	$0.101502\pi$
$383$	5593.82	+	9688.78i	0.746295	+	1.29262i	−0.203293	+	0.979118i	$0.565164\pi$
$384$		0			0
$385$	6112.00	+	3459.44i	0.809081	+	0.457946i
$386$	−5744.87			−0.757529
$387$		0			0
$388$	−191.646	−	331.941i	−0.0250757	−	0.0434324i
$389$	−841.686	+	1457.84i	−0.109705	+	0.190014i	−0.915651	−	0.401975i	$-0.868324\pi$
$389$	−841.686	+	1457.84i	−0.109705	+	0.190014i	0.805946	+	0.591989i	$0.201657\pi$
$390$		0			0
$391$	9749.08	−	16885.9i	1.26095	−	2.18403i
$392$	−2751.66	−	4583.22i	−0.354540	−	0.590530i
$393$		0			0
$394$	−859.782			−0.109937
$395$	−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
$401$	−1900.83	−	3292.34i	−0.236716	−	0.410004i	0.723054	−	0.690791i	$-0.242738\pi$
$401$	−1900.83	−	3292.34i	−0.236716	−	0.410004i	−0.959770	+	0.280788i	$0.909404\pi$
$402$		0			0
$403$	−3431.66	+	5943.81i	−0.424177	+	0.734696i
$404$	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
$409$	13244.8			1.60125			0.800626	−	0.599164i	$-0.204500\pi$
$409$	13244.8			1.60125			0.800626	+	0.599164i	$0.204500\pi$
$410$	−743.036			−0.0895022
$411$		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
$416$	4501.22	−	7796.34i	0.530506	−	0.918863i
$417$		0			0
$418$	−2984.13	−	5168.67i	−0.349183	−	0.604803i
$419$	−1435.52	+	2486.39i	−0.167374	+	0.289900i	−0.937496	−	0.347997i	$-0.886862\pi$
$419$	−1435.52	+	2486.39i	−0.167374	+	0.289900i	0.770122	+	0.637897i	$0.220195\pi$
$420$		0			0
$421$	−441.098	−	764.004i	−0.0510637	−	0.0884449i	0.839364	−	0.543570i	$-0.182928\pi$
$421$	−441.098	−	764.004i	−0.0510637	−	0.0884449i	−0.890427	+	0.455125i	$0.849594\pi$
$422$	−6188.70	+	10719.1i	−0.713890	+	1.23649i
$423$		0			0
$424$	−2082.47	−	3606.95i	−0.238523	−	0.413134i
$425$	−3805.32			−0.434318
$426$		0			0
$427$	−575.103	−	325.513i	−0.0651785	−	0.0368915i
$428$	1387.12	−	2402.55i	0.156656	−	0.271336i
$429$		0			0
$430$	787.192	−	1363.46i	0.0882832	−	0.152911i
$431$	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	$0.698452\pi$
$434$	−5964.63	−	3376.03i	−0.659704	−	0.373397i
$435$		0			0
$436$	3598.09	+	6232.08i	0.395224	+	0.684547i
$437$	6995.68			0.765787
$438$		0			0
$439$	−11207.0			−1.21841			−0.609205	−	0.793013i	$-0.708511\pi$
$439$	−11207.0			−1.21841			−0.609205	+	0.793013i	$0.708511\pi$
$440$	5910.19			0.640358
$441$		0			0
$442$	26745.2			2.87814
$443$	2560.78			0.274642			0.137321	−	0.990527i	$-0.456151\pi$
$443$	2560.78			0.274642			0.137321	+	0.990527i	$0.456151\pi$
$444$		0			0
$445$	−2031.09			−0.216367
$446$	3380.78	+	5855.69i	0.358934	+	0.621693i
$447$		0			0
$448$	−2442.04	−	1382.21i	−0.257534	−	0.145766i
$449$	−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
$452$	−686.732	+	1189.46i	−0.0714628	+	0.123777i
$453$		0			0
$454$	−5728.08	+	9921.33i	−0.592142	+	1.02562i
$455$	−9826.91	−	5562.11i	−1.01251	−	0.573089i
$456$		0			0
$457$	14364.8			1.47037			0.735184	−	0.677868i	$-0.237096\pi$
$457$	14364.8			1.47037			0.735184	+	0.677868i	$0.237096\pi$
$458$	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	0.970784	−	0.239955i	$-0.0771325\pi$
$461$	2747.56	+	4758.92i	0.277585	+	0.480792i	−0.693199	+	0.720746i	$0.743799\pi$
$462$		0			0
$463$	3667.94	−	6353.05i	0.368172	−	0.637692i	−0.621108	−	0.783725i	$-0.713317\pi$
$463$	3667.94	−	6353.05i	0.368172	−	0.637692i	0.989280	+	0.146033i	$0.0466506\pi$
$464$	2186.68	+	3787.44i	0.218780	+	0.378939i
$465$		0			0
$466$	10299.5	−	17839.2i	1.02385	−	1.77336i
$467$	−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
$472$	6027.54			0.587796
$473$	1863.51			0.181151
$474$		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
$479$	5301.89	−	9183.14i	0.505740	−	0.875968i	−0.494238	−	0.869327i	$-0.664553\pi$
$479$	5301.89	−	9183.14i	0.505740	−	0.875968i	0.999978	−	0.00664089i	$-0.00211388\pi$
$480$		0			0
$481$	9039.26	+	15656.5i	0.856871	+	1.48414i
$482$	−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	$0.601213\pi$
$488$	−556.114			−0.0515863
$489$		0			0
$490$	5470.28	−	9860.38i	0.504331	−	0.909075i
$491$	2111.73	−	3657.62i	0.194096	−	0.336184i	−0.752508	−	0.658583i	$-0.771156\pi$
$491$	2111.73	−	3657.62i	0.194096	−	0.336184i	0.946604	+	0.322399i	$0.104489\pi$
$492$		0			0
$493$	−3480.50	+	6028.41i	−0.317959	+	0.550722i
$494$	4797.91	+	8310.22i	0.436980	+	0.756871i
$495$		0			0
$496$	−8733.96			−0.790658
$497$	−2358.89	−	1335.15i	−0.212899	−	0.120502i
$498$		0			0
$499$	−9348.72	−	16192.5i	−0.838690	−	1.45265i	−0.890991	−	0.454022i	$-0.849989\pi$
$499$	−9348.72	−	16192.5i	−0.838690	−	1.45265i	0.0523011	−	0.998631i	$-0.483344\pi$
$500$	−5106.41			−0.456731
$501$		0			0
$502$	1608.74			0.143031
$503$	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
$506$	20197.4			1.77448
$507$		0			0
$508$	−7774.00			−0.678967
$509$	−3209.87	−	5559.65i	−0.279518	−	0.484140i	0.691747	−	0.722140i	$-0.256841\pi$
$509$	−3209.87	−	5559.65i	−0.279518	−	0.484140i	−0.971265	+	0.238000i	$0.923508\pi$
$510$		0			0
$511$	115.533	+	13513.9i	0.0100017	+	1.16991i
$512$	1529.38			0.132011
$513$		0			0
$514$	6302.97	+	10917.1i	0.540880	+	0.936831i
$515$	−8334.07	+	14435.0i	−0.713093	+	1.23511i
$516$		0			0
$517$	−7525.06	+	13033.8i	−0.640139	+	1.10875i
$518$	−15557.0	+	9160.03i	−1.31956	+	0.776966i
$519$		0			0
$520$	−9502.45			−0.801365
$521$	−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
$527$	−6950.86	−	12039.2i	−0.574543	−	0.995137i
$528$		0			0
$529$	−5753.68	+	9965.67i	−0.472892	+	0.819073i
$530$	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
$535$	−7998.92			−0.646399
$536$	−556.441			−0.0448406
$537$		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	$-0.133555\pi$
$542$	11418.0	−	19776.5i	0.904878	−	1.56729i
$543$		0			0
$544$	9117.25	+	15791.5i	0.718564	+	1.24459i
$545$	10374.4	−	17968.9i	0.815392	−	1.41230i
$546$		0			0
$547$	−1046.82	−	1813.14i	−0.0818258	−	0.141726i	0.822208	−	0.569187i	$-0.192742\pi$
$547$	−1046.82	−	1813.14i	−0.0818258	−	0.141726i	−0.904034	+	0.427460i	$0.859408\pi$
$548$	−285.263	+	494.089i	−0.0222369	+	0.0385154i
$549$		0			0
$550$	−1970.89	−	3413.69i	−0.152799	−	0.264655i
$551$	−2497.52			−0.193100
$552$		0			0
$553$	−8080.57	−	4573.66i	−0.621376	−	0.351703i
$554$	10995.6	−	19045.0i	0.843249	−	1.46055i
$555$		0			0
$556$	2268.97	−	3929.97i	0.173068	−	0.299762i
$557$	−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
$560$	−122.843	−	14369.0i	−0.00926973	−	1.08428i
$561$		0			0
$562$	10587.6	+	18338.2i	0.794679	+	1.37642i
$563$	−12909.2			−0.966356			−0.483178	−	0.875522i	$-0.660518\pi$
$563$	−12909.2			−0.966356			−0.483178	+	0.875522i	$0.660518\pi$
$564$		0			0
$565$	3960.10			0.294872
$566$	2720.09			0.202004
$567$		0			0
$568$	−2281.01			−0.168501
$569$	26422.8			1.94675			0.973377	−	0.229211i	$-0.0736147\pi$
$569$	26422.8			1.94675			0.973377	+	0.229211i	$0.0736147\pi$
$570$		0			0
$571$	−12785.6			−0.937057			−0.468528	−	0.883448i	$-0.655216\pi$
$571$	−12785.6			−0.937057			−0.468528	+	0.883448i	$0.655216\pi$
$572$	4114.20	+	7126.00i	0.300740	+	0.520897i
$573$		0			0
$574$	−1216.82	+	716.471i	−0.0884827	+	0.0520991i
$575$	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	$0.886264\pi$
$578$	−18799.5	+	32561.6i	−1.35286	+	2.34323i
$579$		0			0
$580$	−904.672	+	1566.94i	−0.0647663	+	0.112179i
$581$	53.7116	+	6282.67i	0.00383534	+	0.448621i
$582$		0			0
$583$	10398.7			0.738712
$584$	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	−0.959339	−	0.282256i	$-0.908917\pi$
$587$	−10298.2	−	17837.0i	−0.724111	−	1.25420i	0.235228	−	0.971940i	$-0.424416\pi$
$588$		0			0
$589$	2493.88	−	4319.52i	0.174462	−	0.302178i
$590$	6357.08	+	11010.8i	0.443588	+	0.768316i
$591$		0			0
$592$	−11503.0	+	19923.7i	−0.798596	+	1.38321i
$593$	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
$598$	−32473.5			−2.22064
$599$	−21873.9			−1.49206			−0.746031	−	0.665912i	$-0.768043\pi$
$599$	−21873.9			−1.49206			−0.746031	+	0.665912i	$0.768043\pi$
$600$		0			0
$601$	−13992.6	−	24235.9i	−0.949702	−	1.64493i	−0.746052	−	0.665888i	$-0.768053\pi$
$601$	−13992.6	−	24235.9i	−0.949702	−	1.64493i	−0.203650	−	0.979044i	$-0.565281\pi$
$602$	−25.5782	−	2991.89i	−0.00173171	−	0.202559i
$603$		0			0
$604$	4845.15	−	8392.04i	0.326401	−	0.565343i
$605$	−892.514	+	1545.88i	−0.0599766	+	0.103883i
$606$		0			0
$607$	2341.73	+	4055.99i	0.156586	+	0.271215i	0.933635	−	0.358225i	$-0.116618\pi$
$607$	2341.73	+	4055.99i	0.156586	+	0.271215i	−0.777049	+	0.629440i	$0.783284\pi$
$608$	−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	$-0.500036\pi$
$614$	14781.5			0.971555
$615$		0			0
$616$	9678.73	−	5698.89i	0.633063	−	0.372751i
$617$	215.459	−	373.186i	0.0140584	−	0.0243499i	−0.858911	−	0.512126i	$-0.828858\pi$
$617$	215.459	−	373.186i	0.0140584	−	0.0243499i	0.872969	+	0.487776i	$0.162192\pi$
$618$		0			0
$619$	8689.07	−	15049.9i	0.564205	−	0.977232i	−0.432918	−	0.901433i	$-0.642516\pi$
$619$	8689.07	−	15049.9i	0.564205	−	0.977232i	0.997123	−	0.0757988i	$-0.0241507\pi$
$620$	−1806.71	−	3129.31i	−0.117031	−	0.202703i
$621$		0			0
$622$	28547.9			1.84030
$623$	−3326.19	+	1958.48i	−0.213902	+	0.125947i
$624$		0			0
$625$	5484.84	+	9500.03i	0.351030	+	0.608002i
$626$	19634.8			1.25362
$627$		0			0
$628$	−2535.60			−0.161117
$629$	−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	$0.501777\pi$
$632$	−7813.76			−0.491795
$633$		0			0
$634$	21641.1			1.35564
$635$	11207.4	+	19411.7i	0.700394	+	1.21312i
$636$		0			0
$637$	−21456.1	+	366.891i	−1.33457	+	0.0228206i
$638$	−7210.65			−0.447449
$639$		0			0
$640$	−8099.64	−	14029.0i	−0.500260	−	0.866475i
$641$	−10514.9	+	18212.4i	−0.647917	+	1.12223i	0.335702	+	0.941968i	$0.391026\pi$
$641$	−10514.9	+	18212.4i	−0.647917	+	1.12223i	−0.983619	+	0.180257i	$0.942307\pi$
$642$		0			0
$643$	−6304.53	+	10919.8i	−0.386666	+	0.669725i	−0.991999	−	0.126247i	$-0.959707\pi$
$643$	−6304.53	+	10919.8i	−0.386666	+	0.669725i	0.605333	+	0.795973i	$0.293040\pi$
$644$	−82.3383	−	9631.15i	−0.00503817	−	0.589317i
$645$		0			0
$646$	−19436.4			−1.18377
$647$	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
$653$	8663.76	+	15006.1i	0.519203	+	0.899285i	0.999751	+	0.0223171i	$0.00710434\pi$
$653$	8663.76	+	15006.1i	0.519203	+	0.899285i	−0.480548	+	0.876968i	$0.659562\pi$
$654$		0			0
$655$	−2844.18	+	4926.27i	−0.169666	+	0.293871i
$656$	−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	0.558367	−	0.829594i	$-0.311428\pi$
$659$	−7431.15	−	12871.1i	−0.439266	−	0.760831i	−0.997633	+	0.0687629i	$0.978095\pi$
$660$		0			0
$661$	31289.4			1.84118			0.920588	−	0.390535i	$-0.127710\pi$
$661$	31289.4			1.84118			0.920588	+	0.390535i	$0.127710\pi$
$662$	−2796.01			−0.164154
$663$		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
$668$	0.267074	−	0.462586i	1.54692e−5	−	2.67934e-5i
$669$		0			0
$670$	−586.863	−	1016.48i	−0.0338395	−	0.0586118i
$671$	694.229	−	1202.44i	0.0399410	−	0.0691798i
$672$		0			0
$673$	2162.02	+	3744.73i	0.123833	+	0.214485i	0.921276	−	0.388909i	$-0.127148\pi$
$673$	2162.02	+	3744.73i	0.123833	+	0.214485i	−0.797443	+	0.603394i	$0.793815\pi$
$674$	−9806.11	+	16984.7i	−0.560411	+	0.970661i
$675$		0			0
$676$	−2901.99	−	5026.39i	−0.165111	−	0.285980i
$677$	4809.41			0.273029			0.136514	−	0.990638i	$-0.456410\pi$
$677$	4809.41			0.273029			0.136514	+	0.990638i	$0.456410\pi$
$678$		0			0
$679$	17.9547	+	2100.17i	0.00101478	+	0.118700i
$680$	9623.63	−	16668.6i	0.542720	−	0.940018i
$681$		0			0
$682$	7200.13	−	12471.0i	0.404263	−	0.700204i
$683$	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
$686$	−549.538	−	21422.4i	−0.0305852	−	1.19229i
$687$		0			0
$688$	−1906.39	−	3301.97i	−0.105640	−	0.182974i
$689$	−16719.1			−0.924449
$690$		0			0
$691$	2191.19			0.120632			0.0603161	−	0.998179i	$-0.480789\pi$
$691$	2191.19			0.120632			0.0603161	+	0.998179i	$0.480789\pi$
$692$	−4267.56			−0.234434
$693$		0			0
$694$	−11209.6			−0.613128
$695$	−13084.2			−0.714117
$696$		0			0
$697$	−2864.17			−0.155650
$698$	−1269.08	−	2198.11i	−0.0688187	−	0.119198i
$699$		0			0
$700$	−1619.78	+	953.738i	−0.0874601	+	0.0514970i
$701$	−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
$704$	2947.88	−	5105.87i	0.157816	−	0.273345i
$705$		0			0
$706$	−3733.79	+	6467.11i	−0.199041	+	0.344749i
$707$	−17204.2	+	10129.9i	−0.915178	+	0.538862i
$708$		0			0
$709$	22878.6			1.21188			0.605940	−	0.795510i	$-0.292797\pi$
$709$	22878.6			1.21188			0.605940	+	0.795510i	$0.292797\pi$
$710$	−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
$716$	−4925.16	−	8530.63i	−0.257070	−	0.445258i
$717$		0			0
$718$	1467.74	−	2542.20i	0.0762891	−	0.132137i
$719$	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
$724$	2943.82			0.151114
$725$	−1649.51			−0.0844981
$726$		0			0
$727$	−9053.60	−	15681.3i	−0.461870	−	0.799982i	0.537184	−	0.843465i	$-0.319488\pi$
$727$	−9053.60	−	15681.3i	−0.461870	−	0.799982i	−0.999054	+	0.0434827i	$0.986155\pi$
$728$	−15561.5	+	9162.71i	−0.792237	+	0.466474i
$729$		0			0
$730$	−11994.6	+	20775.3i	−0.608139	+	1.05333i
$731$	3034.38	−	5255.69i	0.153530	−	0.265922i
$732$		0			0
$733$	−11550.6	−	20006.1i	−0.582032	−	1.00811i	−0.995238	−	0.0974713i	$-0.968925\pi$
$733$	−11550.6	−	20006.1i	−0.582032	−	1.00811i	0.413207	−	0.910637i	$-0.364409\pi$
$734$	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	$0.921272\pi$
$740$	−9518.01			−0.472823
$741$		0			0
$742$	−142.730	−	16695.2i	−0.00706171	−	0.826011i
$743$	2774.77	−	4806.05i	0.137008	−	0.237304i	−0.789355	−	0.613937i	$-0.789585\pi$
$743$	2774.77	−	4806.05i	0.137008	−	0.237304i	0.926363	+	0.376633i	$0.122918\pi$
$744$		0			0
$745$	−3514.94	+	6088.05i	−0.172855	+	0.299394i
$746$	−9058.60	−	15690.0i	−0.444583	−	0.770040i
$747$		0			0
$748$	−16666.7			−0.814698
$749$	−13099.3	+	7712.94i	−0.639036	+	0.376268i
$750$		0			0
$751$	8301.78	+	14379.1i	0.403377	+	0.698670i	0.994131	−	0.108182i	$-0.0345029\pi$
$751$	8301.78	+	14379.1i	0.403377	+	0.698670i	−0.590754	+	0.806852i	$0.701170\pi$
$752$	30792.9			1.49322
$753$		0			0
$754$	11593.3			0.559952
$755$	−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	$0.482138\pi$
$758$	−33476.2			−1.60410
$759$		0			0
$760$	6905.67			0.329599
$761$	5034.41	+	8719.85i	0.239812	+	0.415367i	0.960660	−	0.277726i	$-0.0895807\pi$
$761$	5034.41	+	8719.85i	0.239812	+	0.415367i	−0.720848	+	0.693093i	$0.756247\pi$
$762$		0			0
$763$	−337.093	−	39429.9i	−0.0159942	−	1.87085i
$764$	−10740.3			−0.508601
$765$		0			0
$766$	18870.3	+	32684.3i	0.890093	+	1.54169i
$767$	12098.0	−	20954.3i	0.569534	−	0.986461i
$768$		0			0
$769$	−1220.38	+	2113.76i	−0.0572277	+	0.0991213i	−0.893220	−	0.449620i	$-0.851559\pi$
$769$	−1220.38	+	2113.76i	−0.0572277	+	0.0991213i	0.835992	+	0.548741i	$0.184893\pi$
$770$	20618.3	+	11670.1i	0.964977	+	0.546184i
$771$		0			0
$772$	−5755.97			−0.268344
$773$	−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
$779$	−513.813	−	889.950i	−0.0236319	−	0.0409317i
$780$		0			0
$781$	2847.51	−	4932.03i	0.130463	−	0.225969i
$782$	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
$787$	19481.8			0.882404			0.441202	−	0.897408i	$-0.354552\pi$
$787$	19481.8			0.882404			0.441202	+	0.897408i	$0.354552\pi$
$788$	−861.442			−0.0389437
$789$		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
$794$	−5989.18	+	10373.6i	−0.267693	+	0.463657i
$795$		0			0
$796$	−1307.03	−	2263.84i	−0.0581991	−	0.100804i
$797$	−1644.31	+	2848.02i	−0.0730794	+	0.126577i	−0.900249	−	0.435374i	$-0.856616\pi$
$797$	−1644.31	+	2848.02i	−0.0730794	+	0.126577i	0.827170	+	0.561952i	$0.189949\pi$
$798$		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
$803$	−28394.7			−1.24786
$804$		0			0
$805$	−23930.3	+	14090.3i	−1.04774	+	0.616916i
$806$	−11576.4	+	20050.9i	−0.505908	+	0.876259i
$807$		0			0
$808$	−8400.60	+	14550.3i	−0.365758	+	0.633511i
$809$	−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	$0.513171\pi$
$812$	29.3955	+	3438.40i	0.00127042	+	0.148601i
$813$		0			0
$814$	−18965.7	−	32849.6i	−0.816643	−	1.41447i
$815$	−27288.1			−1.17284
$816$		0			0
$817$	2177.39			0.0932401
$818$	44680.1			1.90979
$819$		0			0
$820$	−744.471			−0.0317049
$821$	33565.6			1.42686			0.713428	−	0.700729i	$-0.247142\pi$
$821$	33565.6			1.42686			0.713428	+	0.700729i	$0.247142\pi$
$822$		0			0
$823$	−39336.6			−1.66608			−0.833042	−	0.553209i	$-0.813403\pi$
$823$	−39336.6			−1.66608			−0.833042	+	0.553209i	$0.813403\pi$
$824$	13328.4	+	23085.5i	0.563493	+	0.975998i
$825$		0			0
$826$	21027.7	+	11901.8i	0.885771	+	0.501353i
$827$	−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	$0.851371\pi$
$830$	−5576.33	+	9658.50i	−0.233202	+	0.403917i
$831$		0			0
$832$	−4739.61	+	8209.25i	−0.197496	+	0.342073i
$833$	21086.2	−	38008.6i	0.877063	−	1.58094i
$834$		0			0
$835$	−1.54010			−6.38294e−5
$836$	−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	0.991482	+	0.130245i	$0.0415765\pi$
$839$	14788.7	+	25614.8i	0.608537	+	1.05402i	−0.382945	+	0.923771i	$0.625090\pi$
$840$		0			0
$841$	10685.8	−	18508.3i	0.438140	−	0.758880i
$842$	−1488.01	−	2577.30i	−0.0609027	−	0.105487i
$843$		0			0
$844$	−6200.65	+	10739.8i	−0.252885	+	0.438010i
$845$	−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
$850$	−12836.9			−0.518003
$851$	44461.2			1.79096
$852$		0			0
$853$	1776.98	+	3077.82i	0.0713279	+	0.123544i	0.899484	−	0.436955i	$-0.143943\pi$
$853$	1776.98	+	3077.82i	0.0713279	+	0.123544i	−0.828156	+	0.560498i	$0.810610\pi$
$854$	−1940.06	−	1098.09i	−0.0777372	−	0.0439998i
$855$		0			0
$856$	−6396.22	+	11078.6i	−0.255395	+	0.442357i
$857$	6638.83	−	11498.8i	0.264619	−	0.458333i	−0.702845	−	0.711343i	$-0.748087\pi$
$857$	6638.83	−	11498.8i	0.264619	−	0.458333i	0.967464	+	0.253010i	$0.0814206\pi$
$858$		0			0
$859$	−18099.1	−	31348.5i	−0.718896	−	1.24517i	−0.961437	−	0.275024i	$-0.911314\pi$
$859$	−18099.1	−	31348.5i	−0.718896	−	1.24517i	0.242541	−	0.970141i	$-0.422019\pi$
$860$	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
$866$	−35491.8			−1.39268
$867$		0			0
$868$	−5976.15	−	3382.55i	−0.233691	−	0.132271i
$869$	9754.36	−	16895.0i	0.380776	−	0.659523i
$870$		0			0
$871$	−1116.84	+	1934.43i	−0.0434474	+	0.0752532i
$872$	−16591.4	−	28737.2i	−0.644330	−	1.11601i
$873$		0			0
$874$	23599.3			0.913341
$875$	24350.5	+	13782.6i	0.940798	+	0.532499i
$876$		0			0
$877$	5469.19	+	9472.91i	0.210583	+	0.364741i	0.951897	−	0.306418i	$-0.0991304\pi$
$877$	5469.19	+	9472.91i	0.210583	+	0.364741i	−0.741314	+	0.671158i	$0.765797\pi$
$878$	−37805.9			−1.45317
$879$		0			0
$880$	30191.2			1.15653
$881$	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	$0.743518\pi$
$884$	26796.8			1.01954
$885$		0			0
$886$	8638.59			0.327561
$887$	12337.8	+	21369.7i	0.467038	+	0.808934i	0.999291	−	0.0376515i	$-0.0119877\pi$
$887$	12337.8	+	21369.7i	0.467038	+	0.808934i	−0.532253	+	0.846586i	$0.678654\pi$
$888$		0			0
$889$	37071.2	+	20982.6i	1.39857	+	0.791601i
$890$	−6851.72			−0.258057
$891$		0			0
$892$	3387.31	+	5867.00i	0.127148	+	0.220226i
$893$	−8792.54	+	15229.1i	−0.329486	+	0.570687i
$894$		0			0
$895$	−14200.7	+	24596.3i	−0.530365	+	0.918618i
$896$	−26791.7	−	15164.3i	−0.998936	−	0.565405i
$897$		0			0
$898$	−34735.1			−1.29078
$899$	−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
$905$	−4243.95	−	7350.73i	−0.155882	−	0.269996i
$906$		0			0
$907$	8450.81	−	14637.2i	0.309377	−	0.535856i	−0.668850	−	0.743398i	$-0.733213\pi$
$907$	8450.81	−	14637.2i	0.309377	−	0.535856i	0.978226	+	0.207542i	$0.0665463\pi$
$908$	−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	0.983224	+	0.182401i	$0.0583868\pi$
$911$	17861.1	+	30936.3i	0.649576	+	1.12510i	−0.333649	+	0.942698i	$0.608280\pi$
$912$		0			0
$913$	−13200.8			−0.478513
$914$	48458.5			1.75368
$915$		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	$0.174735\pi$
$920$	−11684.9	+	20238.8i	−0.418738	+	0.725275i
$921$		0			0
$922$	9268.68	+	16053.8i	0.331071	+	0.573432i
$923$	−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
$929$	12591.4			0.444685			0.222342	−	0.974969i	$-0.428630\pi$
$929$	12591.4			0.444685			0.222342	+	0.974969i	$0.428630\pi$
$930$		0			0
$931$	15592.7	−	266.629i	0.548905	−	0.00938605i
$932$	10319.3	−	17873.6i	0.362684	−	0.628187i
$933$		0			0
$934$	−5071.21	+	8783.59i	−0.177661	+	0.307717i
$935$	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	$0.181271\pi$
$938$	−1941.20	−	1098.73i	−0.0675719	−	0.0382462i
$939$		0			0
$940$	6369.82	+	11032.8i	0.221022	+	0.382821i
$941$	21014.4			0.728001			0.364000	−	0.931399i	$-0.381411\pi$
$941$	21014.4			0.728001			0.364000	+	0.931399i	$0.381411\pi$
$942$		0			0
$943$	3477.63			0.120092
$944$	30790.7			1.06160
$945$		0			0
$946$	6286.39			0.216055
$947$	−51981.0			−1.78369			−0.891845	−	0.452341i	$-0.850589\pi$
$947$	−51981.0			−1.78369			−0.891845	+	0.452341i	$0.850589\pi$
$948$		0			0
$949$	45653.3			1.56161
$950$	−2302.86	−	3988.67i	−0.0786470	−	0.136221i
$951$		0			0
$952$	−312.700	−	36576.7i	−0.0106457	−	1.24523i
$953$	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
$956$	4399.67	−	7620.45i	0.148845	−	0.257806i
$957$		0			0
$958$	17885.5	−	30978.6i	0.603187	−	1.04475i
$959$	2693.89	−	1586.18i	0.0907094	−	0.0534102i
$960$		0			0
$961$	−17756.5			−0.596036
$962$	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	0.416194	+	0.909276i	$0.363364\pi$
$967$	−17421.6	+	30175.0i	−0.579359	+	1.00348i	−0.995553	+	0.0942029i	$0.969970\pi$
$968$	1427.37	+	2472.28i	0.0473941	+	0.0820890i
$969$		0			0
$970$	−1864.05	+	3228.64i	−0.0617023	+	0.106871i
$971$	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
$976$	−2840.82			−0.0931684
$977$	6244.07			0.204468			0.102234	−	0.994760i	$-0.467401\pi$
$977$	6244.07			0.204468			0.102234	+	0.994760i	$0.467401\pi$
$978$		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
$983$	4190.06	−	7257.40i	0.135953	−	0.235478i	−0.790008	−	0.613097i	$-0.789924\pi$
$983$	4190.06	−	7257.40i	0.135953	−	0.235478i	0.925961	+	0.377619i	$0.123257\pi$
$984$		0			0
$985$	1241.89	+	2151.02i	0.0401726	+	0.0695811i
$986$	−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	$0.782386\pi$
$992$	−15785.3			−0.505226
$993$		0			0
$994$	−7957.52	−	4504.02i	−0.253921	−	0.143721i
$995$	−3768.55	+	6527.32i	−0.120071	+	0.207970i
$996$		0			0
$997$	−17473.4	+	30264.8i	−0.555053	+	0.961380i	0.442846	+	0.896598i	$0.353969\pi$
$997$	−17473.4	+	30264.8i	−0.555053	+	0.961380i	−0.997899	+	0.0647828i	$0.979365\pi$
$998$	−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.h.a.37.18		44
3.2	odd	2		63.4.h.a.58.5	yes	44
7.4	even	3		189.4.g.a.172.5		44
9.2	odd	6		63.4.g.a.16.18	yes	44
9.7	even	3		189.4.g.a.100.5		44
21.11	odd	6		63.4.g.a.4.18	✓	44
63.11	odd	6		63.4.h.a.25.5	yes	44
63.25	even	3	inner	189.4.h.a.46.18		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.18	✓	44	21.11	odd	6
63.4.g.a.16.18	yes	44	9.2	odd	6
63.4.h.a.25.5	yes	44	63.11	odd	6
63.4.h.a.58.5	yes	44	3.2	odd	2
189.4.g.a.100.5		44	9.7	even	3
189.4.g.a.172.5		44	7.4	even	3
189.4.h.a.37.18		44	1.1	even	1	trivial
189.4.h.a.46.18		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)

\(f(q)\)	\(=\)	\(q+3.37342 q^{2} +3.37993 q^{4} +(-4.87266 - 8.43970i) q^{5} +(-16.1176 - 9.12268i) q^{7} -15.5854 q^{8} +O(q^{10})\)	\(q+3.37342 q^{2} +3.37993 q^{4} +(-4.87266 - 8.43970i) q^{5} +(-16.1176 - 9.12268i) q^{7} -15.5854 q^{8} +(-16.4375 - 28.4706i) q^{10} +(19.4562 - 33.6990i) q^{11} +(-31.2817 + 54.1816i) q^{13} +(-54.3713 - 30.7746i) q^{14} -79.6155 q^{16} +(-63.3614 - 109.745i) q^{17} +(22.7332 - 39.3751i) q^{19} +(-16.4692 - 28.5256i) q^{20} +(65.6337 - 113.681i) q^{22} +(76.9324 + 133.251i) q^{23} +(15.0144 - 26.0056i) q^{25} +(-105.526 + 182.777i) q^{26} +(-54.4763 - 30.8340i) q^{28} +(-27.4655 - 47.5716i) q^{29} +109.702 q^{31} -143.893 q^{32} +(-213.744 - 370.216i) q^{34} +(1.54295 + 180.479i) q^{35} +(144.482 - 250.249i) q^{37} +(76.6886 - 132.829i) q^{38} +(75.9424 + 131.536i) q^{40} +(11.3009 - 19.5738i) q^{41} +(23.9450 + 41.4740i) q^{43} +(65.7604 - 113.900i) q^{44} +(259.525 + 449.510i) q^{46} -386.770 q^{47} +(176.554 + 294.071i) q^{49} +(50.6496 - 87.7278i) q^{50} +(-105.730 + 183.130i) q^{52} +(133.617 + 231.431i) q^{53} -379.213 q^{55} +(251.199 + 142.181i) q^{56} +(-92.6525 - 160.479i) q^{58} -386.742 q^{59} +35.6817 q^{61} +370.070 q^{62} +151.514 q^{64} +609.701 q^{65} +35.7027 q^{67} +(-214.157 - 370.931i) q^{68} +(5.20500 + 608.832i) q^{70} +146.355 q^{71} +(-364.856 - 631.948i) q^{73} +(487.396 - 844.195i) q^{74} +(76.8367 - 133.085i) q^{76} +(-621.012 + 365.655i) q^{77} +501.351 q^{79} +(387.939 + 671.931i) q^{80} +(38.1227 - 66.0304i) q^{82} +(-169.622 - 293.794i) q^{83} +(-617.477 + 1069.50i) q^{85} +(80.7764 + 139.909i) q^{86} +(-303.232 + 525.214i) q^{88} +(104.209 - 180.495i) q^{89} +(998.467 - 587.903i) q^{91} +(260.026 + 450.378i) q^{92} -1304.74 q^{94} -443.085 q^{95} +(-56.7013 - 98.2095i) q^{97} +(595.588 + 992.024i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 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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