LMFDB - Embedded newform 189.3.k.a.10.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(10,189)]

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, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("189.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.14987699641$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.7
Character	$\chi$	$=$	189.10
Dual form			189.3.k.a.19.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.198068 + 0.343064i) q^{2} +(1.92154 + 3.32820i) q^{4} -2.97240i q^{5} +(2.98301 - 6.33259i) q^{7} -3.10693 q^{8} +O(q^{10})$	\(q+(-0.198068 + 0.343064i) q^{2} +(1.92154 + 3.32820i) q^{4} -2.97240i q^{5} +(2.98301 - 6.33259i) q^{7} -3.10693 q^{8} +(1.01972 + 0.588737i) q^{10} +18.6735 q^{11} +(9.50735 + 5.48907i) q^{13} +(1.58164 + 2.27765i) q^{14} +(-7.07077 + 12.2469i) q^{16} +(-5.75359 - 3.32184i) q^{17} +(-19.6578 + 11.3494i) q^{19} +(9.89274 - 5.71158i) q^{20} +(-3.69862 + 6.40621i) q^{22} +26.9112 q^{23} +16.1648 q^{25} +(-3.76620 + 2.17442i) q^{26} +(26.8081 - 2.24026i) q^{28} +(10.3714 + 17.9638i) q^{29} +(16.4381 - 9.49056i) q^{31} +(-9.01484 - 15.6142i) q^{32} +(2.27920 - 1.31590i) q^{34} +(-18.8230 - 8.86669i) q^{35} +(-3.57815 - 6.19754i) q^{37} -8.99185i q^{38} +9.23502i q^{40} +(-66.6091 - 38.4568i) q^{41} +(-14.9257 - 25.8521i) q^{43} +(35.8819 + 62.1492i) q^{44} +(-5.33024 + 9.23225i) q^{46} +(-5.23602 - 3.02302i) q^{47} +(-31.2033 - 37.7803i) q^{49} +(-3.20174 + 5.54558i) q^{50} +42.1898i q^{52} +(-19.9358 + 34.5297i) q^{53} -55.5051i q^{55} +(-9.26798 + 19.6749i) q^{56} -8.21697 q^{58} +(-30.4254 + 17.5661i) q^{59} +(-27.8338 - 16.0698i) q^{61} +7.51910i q^{62} -49.4240 q^{64} +(16.3157 - 28.2596i) q^{65} +(-0.778839 - 1.34899i) q^{67} -25.5321i q^{68} +(6.77007 - 4.70128i) q^{70} -111.763 q^{71} +(37.1401 + 21.4429i) q^{73} +2.83487 q^{74} +(-75.5465 - 43.6168i) q^{76} +(55.7032 - 118.252i) q^{77} +(-22.9975 + 39.8329i) q^{79} +(36.4028 + 21.0171i) q^{80} +(26.3863 - 15.2341i) q^{82} +(-31.3176 + 18.0812i) q^{83} +(-9.87382 + 17.1020i) q^{85} +11.8252 q^{86} -58.0172 q^{88} +(35.9830 - 20.7748i) q^{89} +(63.1205 - 43.8322i) q^{91} +(51.7108 + 89.5658i) q^{92} +(2.07418 - 1.19753i) q^{94} +(33.7351 + 58.4309i) q^{95} +(120.608 - 69.6332i) q^{97} +(19.1414 - 3.22166i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.198068	+	0.343064i	−0.0990340	+	0.171532i	−0.911285	−	0.411776i	$-0.864909\pi$
$2$	−0.198068	+	0.343064i	−0.0990340	+	0.171532i	0.812251	+	0.583308i	$0.198242\pi$
$3$		0			0
$3$		0			0
$4$	1.92154	+	3.32820i	0.480385	+	0.832050i
$5$		−	2.97240i		−	0.594480i	−0.954803	−	0.297240i	$-0.903934\pi$
$5$		−	2.97240i		−	0.594480i	0.954803	−	0.297240i	$-0.0960661\pi$
$6$		0			0
$7$	2.98301	−	6.33259i	0.426144	−	0.904655i
$7$	2.98301	−	6.33259i	0.426144	−	0.904655i
$8$	−3.10693			−0.388366
$9$		0			0
$10$	1.01972	+	0.588737i	0.101972	+	0.0588737i
$11$	18.6735			1.69759			0.848796	−	0.528721i	$-0.177328\pi$
$11$	18.6735			1.69759			0.848796	+	0.528721i	$0.177328\pi$
$12$		0			0
$13$	9.50735	+	5.48907i	0.731335	+	0.422236i	0.818910	−	0.573922i	$-0.194579\pi$
$13$	9.50735	+	5.48907i	0.731335	+	0.422236i	−0.0875755	+	0.996158i	$0.527912\pi$
$14$	1.58164	+	2.27765i	0.112975	+	0.162689i
$15$		0			0
$16$	−7.07077	+	12.2469i	−0.441923	+	0.765433i
$17$	−5.75359	−	3.32184i	−0.338446	−	0.195402i	0.321138	−	0.947032i	$-0.395935\pi$
$17$	−5.75359	−	3.32184i	−0.338446	−	0.195402i	−0.659585	+	0.751630i	$0.729268\pi$
$18$		0			0
$19$	−19.6578	+	11.3494i	−1.03462	+	0.597339i	−0.918305	−	0.395873i	$-0.870442\pi$
$19$	−19.6578	+	11.3494i	−1.03462	+	0.597339i	−0.116317	+	0.993212i	$0.537109\pi$
$20$	9.89274	−	5.71158i	0.494637	−	0.285579i
$21$		0			0
$22$	−3.69862	+	6.40621i	−0.168119	+	0.291191i
$23$	26.9112			1.17005			0.585025	−	0.811015i	$-0.301084\pi$
$23$	26.9112			1.17005			0.585025	+	0.811015i	$0.301084\pi$
$24$		0			0
$25$	16.1648			0.646594
$26$	−3.76620	+	2.17442i	−0.144854	+	0.0836315i
$27$		0			0
$28$	26.8081	−	2.24026i	0.957432	−	0.0800092i
$29$	10.3714	+	17.9638i	0.357634	+	0.619441i	0.987565	−	0.157210i	$-0.0502501\pi$
$29$	10.3714	+	17.9638i	0.357634	+	0.619441i	−0.629931	+	0.776651i	$0.716917\pi$
$30$		0			0
$31$	16.4381	−	9.49056i	0.530262	−	0.306147i	−0.210861	−	0.977516i	$-0.567627\pi$
$31$	16.4381	−	9.49056i	0.530262	−	0.306147i	0.741123	+	0.671369i	$0.234293\pi$
$32$	−9.01484	−	15.6142i	−0.281714	−	0.487942i
$33$		0			0
$34$	2.27920	−	1.31590i	0.0670354	−	0.0387029i
$35$	−18.8230	−	8.86669i	−0.537799	−	0.253334i
$36$		0			0
$37$	−3.57815	−	6.19754i	−0.0967068	−	0.167501i	0.813613	−	0.581407i	$-0.197498\pi$
$37$	−3.57815	−	6.19754i	−0.0967068	−	0.167501i	−0.910320	+	0.413906i	$0.864164\pi$
$38$		−	8.99185i		−	0.236628i
$39$		0			0
$40$			9.23502i			0.230875i
$41$	−66.6091	−	38.4568i	−1.62461	−	0.937970i	−0.985664	−	0.168721i	$-0.946036\pi$
$41$	−66.6091	−	38.4568i	−1.62461	−	0.937970i	−0.638948	−	0.769250i	$-0.720630\pi$
$42$		0			0
$43$	−14.9257	−	25.8521i	−0.347109	−	0.601211i	0.638625	−	0.769518i	$-0.279503\pi$
$43$	−14.9257	−	25.8521i	−0.347109	−	0.601211i	−0.985735	+	0.168307i	$0.946170\pi$
$44$	35.8819	+	62.1492i	0.815497	+	1.41248i
$45$		0			0
$46$	−5.33024	+	9.23225i	−0.115875	+	0.200701i
$47$	−5.23602	−	3.02302i	−0.111405	−	0.0643195i	0.443262	−	0.896392i	$-0.353821\pi$
$47$	−5.23602	−	3.02302i	−0.111405	−	0.0643195i	−0.554667	+	0.832072i	$0.687154\pi$
$48$		0			0
$49$	−31.2033	−	37.7803i	−0.636803	−	0.771027i
$50$	−3.20174	+	5.54558i	−0.0640348	+	0.110912i
$51$		0			0
$52$			42.1898i			0.811343i
$53$	−19.9358	+	34.5297i	−0.376146	+	0.651504i	−0.990498	−	0.137528i	$-0.956084\pi$
$53$	−19.9358	+	34.5297i	−0.376146	+	0.651504i	0.614352	+	0.789032i	$0.289418\pi$
$54$		0			0
$55$		−	55.5051i		−	1.00918i
$56$	−9.26798	+	19.6749i	−0.165500	+	0.351337i
$57$		0			0
$58$	−8.21697			−0.141672
$59$	−30.4254	+	17.5661i	−0.515684	+	0.297730i	−0.735167	−	0.677886i	$-0.762896\pi$
$59$	−30.4254	+	17.5661i	−0.515684	+	0.297730i	0.219483	+	0.975616i	$0.429563\pi$
$60$		0			0
$61$	−27.8338	−	16.0698i	−0.456292	−	0.263440i	0.254192	−	0.967154i	$-0.418190\pi$
$61$	−27.8338	−	16.0698i	−0.456292	−	0.263440i	−0.710484	+	0.703714i	$0.751524\pi$
$62$			7.51910i			0.121276i
$63$		0			0
$64$	−49.4240			−0.772249
$65$	16.3157	−	28.2596i	0.251011	−	0.434764i
$66$		0			0
$67$	−0.778839	−	1.34899i	−0.0116245	−	0.0201342i	0.860155	−	0.510033i	$-0.170367\pi$
$67$	−0.778839	−	1.34899i	−0.0116245	−	0.0201342i	−0.871779	+	0.489899i	$0.837034\pi$
$68$		−	25.5321i		−	0.375473i
$69$		0			0
$70$	6.77007	−	4.70128i	0.0967153	−	0.0671611i
$71$	−111.763			−1.57413			−0.787067	−	0.616868i	$-0.788401\pi$
$71$	−111.763			−1.57413			−0.787067	+	0.616868i	$0.788401\pi$
$72$		0			0
$73$	37.1401	+	21.4429i	0.508769	+	0.293738i	0.732327	−	0.680953i	$-0.238434\pi$
$73$	37.1401	+	21.4429i	0.508769	+	0.293738i	−0.223559	+	0.974690i	$0.571767\pi$
$74$	2.83487			0.0383091
$75$		0			0
$76$	−75.5465	−	43.6168i	−0.994033	−	0.573905i
$77$	55.7032	−	118.252i	0.723418	−	1.53574i
$78$		0			0
$79$	−22.9975	+	39.8329i	−0.291108	+	0.504213i	−0.974072	−	0.226238i	$-0.927357\pi$
$79$	−22.9975	+	39.8329i	−0.291108	+	0.504213i	0.682964	+	0.730452i	$0.260690\pi$
$80$	36.4028	+	21.0171i	0.455035	+	0.262714i
$81$		0			0
$82$	26.3863	−	15.2341i	0.321784	−	0.185782i
$83$	−31.3176	+	18.0812i	−0.377320	+	0.217846i	−0.676652	−	0.736303i	$-0.736570\pi$
$83$	−31.3176	+	18.0812i	−0.377320	+	0.217846i	0.299332	+	0.954149i	$0.403236\pi$
$84$		0			0
$85$	−9.87382	+	17.1020i	−0.116163	+	0.201200i
$86$	11.8252			0.137502
$87$		0			0
$88$	−58.0172			−0.659286
$89$	35.9830	−	20.7748i	0.404303	−	0.233424i	−0.284036	−	0.958814i	$-0.591674\pi$
$89$	35.9830	−	20.7748i	0.404303	−	0.233424i	0.688339	+	0.725389i	$0.258340\pi$
$90$		0			0
$91$	63.1205	−	43.8322i	0.693632	−	0.481672i
$92$	51.7108	+	89.5658i	0.562074	+	0.973541i
$93$		0			0
$94$	2.07418	−	1.19753i	0.0220657	−	0.0127396i
$95$	33.7351	+	58.4309i	0.355106	+	0.615062i
$96$		0			0
$97$	120.608	−	69.6332i	1.24338	−	0.717868i	0.273602	−	0.961843i	$-0.411785\pi$
$97$	120.608	−	69.6332i	1.24338	−	0.717868i	0.969782	+	0.243975i	$0.0784514\pi$
$98$	19.1414	−	3.22166i	0.195321	−	0.0328741i
$99$		0			0
$100$	31.0614	+	53.7999i	0.310614	+	0.537999i
$101$		−	27.6001i		−	0.273268i	−0.990622	−	0.136634i	$-0.956372\pi$
$101$		−	27.6001i		−	0.273268i	0.990622	−	0.136634i	$-0.0436285\pi$
$102$		0			0
$103$			34.4030i			0.334010i	0.985956	+	0.167005i	$0.0534096\pi$
$103$			34.4030i			0.334010i	−0.985956	+	0.167005i	$0.946590\pi$
$104$	−29.5386	−	17.0541i	−0.284025	−	0.163982i
$105$		0			0
$106$	−7.89727	−	13.6785i	−0.0745026	−	0.129042i
$107$	−55.3775	−	95.9167i	−0.517547	−	0.896418i	−0.999792	−	0.0203813i	$-0.993512\pi$
$107$	−55.3775	−	95.9167i	−0.517547	−	0.896418i	0.482245	−	0.876036i	$-0.339821\pi$
$108$		0			0
$109$	−62.0687	+	107.506i	−0.569438	+	0.986295i	0.427184	+	0.904165i	$0.359506\pi$
$109$	−62.0687	+	107.506i	−0.569438	+	0.986295i	−0.996622	+	0.0821300i	$0.973828\pi$
$110$	19.0418	+	10.9938i	0.173107	+	0.0999435i
$111$		0			0
$112$	56.4626	+	81.3090i	0.504130	+	0.725973i
$113$	−17.5138	+	30.3348i	−0.154989	+	0.268449i	−0.933055	−	0.359734i	$-0.882868\pi$
$113$	−17.5138	+	30.3348i	−0.154989	+	0.268449i	0.778066	+	0.628183i	$0.216201\pi$
$114$		0			0
$115$		−	79.9907i		−	0.695571i
$116$	−39.8581	+	69.0362i	−0.343604	+	0.595140i
$117$		0			0
$118$		−	13.9171i		−	0.117942i
$119$	−38.1988	+	26.5261i	−0.320999	+	0.222908i
$120$		0			0
$121$	227.700			1.88182
$122$	11.0260	−	6.36585i	0.0903768	−	0.0521791i
$123$		0			0
$124$	63.1730	+	36.4729i	0.509459	+	0.294137i
$125$		−	122.358i		−	0.978867i
$126$		0			0
$127$	−202.854			−1.59727			−0.798637	−	0.601813i	$-0.794445\pi$
$127$	−202.854			−1.59727			−0.798637	+	0.601813i	$0.794445\pi$
$128$	45.8487	−	79.4122i	0.358193	−	0.620408i
$129$		0			0
$130$	6.46324	+	11.1947i	0.0497172	+	0.0861128i
$131$			252.088i			1.92433i	0.272461	+	0.962167i	$0.412162\pi$
$131$			252.088i			1.92433i	−0.272461	+	0.962167i	$0.587838\pi$
$132$		0			0
$133$	13.2319	+	158.340i	0.0994883	+	1.19053i
$134$	0.617052			0.00460487
$135$		0			0
$136$	17.8760	+	10.3207i	0.131441	+	0.0758875i
$137$	105.375			0.769163			0.384581	−	0.923091i	$-0.374346\pi$
$137$	105.375			0.769163			0.384581	+	0.923091i	$0.374346\pi$
$138$		0			0
$139$	−39.7883	−	22.9718i	−0.286247	−	0.165264i	0.350001	−	0.936749i	$-0.386181\pi$
$139$	−39.7883	−	22.9718i	−0.286247	−	0.165264i	−0.636248	+	0.771485i	$0.719514\pi$
$140$	−6.65894	−	79.6843i	−0.0475638	−	0.569174i
$141$		0			0
$142$	22.1368	−	38.3420i	0.155893	−	0.270014i
$143$	177.536	+	102.500i	1.24151	+	0.716785i
$144$		0			0
$145$	53.3955	−	30.8279i	0.368245	−	0.212606i
$146$	−14.7125	+	8.49429i	−0.100771	+	0.0581800i
$147$		0			0
$148$	13.7511	−	23.8176i	0.0929129	−	0.160930i
$149$	171.148			1.14865			0.574324	−	0.818628i	$-0.305265\pi$
$149$	171.148			1.14865			0.574324	+	0.818628i	$0.305265\pi$
$150$		0			0
$151$	12.8045			0.0847977			0.0423988	−	0.999101i	$-0.486500\pi$
$151$	12.8045			0.0847977			0.0423988	+	0.999101i	$0.486500\pi$
$152$	61.0754	−	35.2619i	0.401812	−	0.231986i
$153$		0			0
$154$	29.5348	+	42.5316i	0.191785	+	0.276179i
$155$	−28.2097	−	48.8607i	−0.181998	−	0.315230i
$156$		0			0
$157$	−150.664	+	86.9861i	−0.959646	+	0.554052i	−0.896064	−	0.443925i	$-0.853586\pi$
$157$	−150.664	+	86.9861i	−0.959646	+	0.554052i	−0.0635816	+	0.997977i	$0.520252\pi$
$158$	−9.11014	−	15.7792i	−0.0576591	−	0.0998686i
$159$		0			0
$160$	−46.4115	+	26.7957i	−0.290072	+	0.167473i
$161$	80.2762	−	170.417i	0.498610	−	1.05849i
$162$		0			0
$163$	82.0960	+	142.194i	0.503656	+	0.872358i	0.999991	+	0.00422710i	$0.00134553\pi$
$163$	82.0960	+	142.194i	0.503656	+	0.872358i	−0.496335	+	0.868131i	$0.665321\pi$
$164$		−	295.585i		−	1.80235i
$165$		0			0
$166$		−	14.3252i		−	0.0862966i
$167$	18.9002	+	10.9120i	0.113175	+	0.0653415i	0.555519	−	0.831504i	$-0.312520\pi$
$167$	18.9002	+	10.9120i	0.113175	+	0.0653415i	−0.442344	+	0.896845i	$0.645853\pi$
$168$		0			0
$169$	−24.2402	−	41.9852i	−0.143433	−	0.248433i
$170$	−3.91138	−	6.77470i	−0.0230081	−	0.0398512i
$171$		0			0
$172$	57.3606	−	99.3514i	0.333492	−	0.577625i
$173$	−164.382	−	94.9061i	−0.950186	−	0.548590i	−0.0570472	−	0.998371i	$-0.518169\pi$
$173$	−164.382	−	94.9061i	−0.950186	−	0.548590i	−0.893139	+	0.449781i	$0.851502\pi$
$174$		0			0
$175$	48.2199	−	102.365i	0.275542	−	0.584945i
$176$	−132.036	+	228.693i	−0.750205	+	1.29939i
$177$		0			0
$178$			16.4593i			0.0924678i
$179$	10.1668	−	17.6094i	0.0567978	−	0.0983766i	−0.836228	−	0.548381i	$-0.815244\pi$
$179$	10.1668	−	17.6094i	0.0567978	−	0.0983766i	0.893026	+	0.450005i	$0.148578\pi$
$180$		0			0
$181$		−	191.103i		−	1.05582i	−0.849302	−	0.527908i	$-0.822977\pi$
$181$		−	191.103i		−	1.05582i	0.849302	−	0.527908i	$-0.177023\pi$
$182$	2.53508	+	30.3361i	0.0139290	+	0.166682i
$183$		0			0
$184$	−83.6110			−0.454408
$185$	−18.4216	+	10.6357i	−0.0995760	+	0.0574902i
$186$		0			0
$187$	−107.440	−	62.0303i	−0.574544	−	0.331713i
$188$		−	23.2354i		−	0.123592i
$189$		0			0
$190$	−26.7274			−0.140670
$191$	−141.748	+	245.514i	−0.742134	+	1.28541i	0.209388	+	0.977833i	$0.432853\pi$
$191$	−141.748	+	245.514i	−0.742134	+	1.28541i	−0.951522	+	0.307581i	$0.900481\pi$
$192$		0			0
$193$	9.05364	+	15.6814i	0.0469100	+	0.0812506i	0.888527	−	0.458824i	$-0.151729\pi$
$193$	9.05364	+	15.6814i	0.0469100	+	0.0812506i	−0.841617	+	0.540075i	$0.818396\pi$
$194$			55.1685i			0.284373i
$195$		0			0
$196$	65.7821	−	176.447i	0.335623	−	0.900241i
$197$	94.2507			0.478430			0.239215	−	0.970967i	$-0.423110\pi$
$197$	94.2507			0.478430			0.239215	+	0.970967i	$0.423110\pi$
$198$		0			0
$199$	−12.6643	−	7.31175i	−0.0636399	−	0.0367425i	0.467842	−	0.883812i	$-0.345031\pi$
$199$	−12.6643	−	7.31175i	−0.0636399	−	0.0367425i	−0.531482	+	0.847069i	$0.678365\pi$
$200$	−50.2230			−0.251115
$201$		0			0
$202$	9.46860	+	5.46670i	0.0468742	+	0.0270629i
$203$	144.695	−	12.0917i	0.712784	−	0.0595649i
$204$		0			0
$205$	−114.309	+	197.989i	−0.557604	+	0.965799i
$206$	−11.8024	−	6.81414i	−0.0572934	−	0.0330783i
$207$		0			0
$208$	−134.449	+	77.6239i	−0.646387	+	0.373192i
$209$	−367.080	+	211.934i	−1.75637	+	1.01404i
$210$		0			0
$211$	−123.129	+	213.266i	−0.583551	+	1.01074i	0.411504	+	0.911408i	$0.365004\pi$
$211$	−123.129	+	213.266i	−0.583551	+	1.01074i	−0.995054	+	0.0993314i	$0.968330\pi$
$212$	−153.229			−0.722779
$213$		0			0
$214$	43.8741			0.205019
$215$	−76.8426	+	44.3651i	−0.357408	+	0.206349i
$216$		0			0
$217$	−11.0647	−	132.406i	−0.0509895	−	0.610167i
$218$	−24.5876	−	42.5871i	−0.112787	−	0.195353i
$219$		0			0
$220$	184.732	−	106.655i	0.839692	−	0.484796i
$221$	−36.4676	−	63.1637i	−0.165012	−	0.285809i
$222$		0			0
$223$	−33.4633	+	19.3201i	−0.150060	+	0.0866371i	−0.573150	−	0.819451i	$-0.694279\pi$
$223$	−33.4633	+	19.3201i	−0.150060	+	0.0866371i	0.423090	+	0.906088i	$0.360945\pi$
$224$	−125.769	+	10.5101i	−0.561470	+	0.0469201i
$225$		0			0
$226$	−6.93784	−	12.0167i	−0.0306984	−	0.0531712i
$227$			147.896i			0.651523i	0.945452	+	0.325761i	$0.105621\pi$
$227$			147.896i			0.651523i	−0.945452	+	0.325761i	$0.894379\pi$
$228$		0			0
$229$		−	312.033i		−	1.36259i	−0.732010	−	0.681294i	$-0.761417\pi$
$229$		−	312.033i		−	1.36259i	0.732010	−	0.681294i	$-0.238583\pi$
$230$	27.4419	+	15.8436i	0.119313	+	0.0688852i
$231$		0			0
$232$	−32.2232	−	55.8121i	−0.138893	−	0.240570i
$233$	72.0190	+	124.741i	0.309094	+	0.535367i	0.978164	−	0.207832i	$-0.0666408\pi$
$233$	72.0190	+	124.741i	0.309094	+	0.535367i	−0.669070	+	0.743199i	$0.733307\pi$
$234$		0			0
$235$	−8.98561	+	15.5635i	−0.0382366	+	0.0662278i
$236$	−116.927	−	67.5078i	−0.495453	−	0.286050i
$237$		0			0
$238$	−1.53416	−	18.3586i	−0.00644607	−	0.0771370i
$239$	14.2206	−	24.6308i	0.0595004	−	0.103058i	−0.834741	−	0.550643i	$-0.814383\pi$
$239$	14.2206	−	24.6308i	0.0595004	−	0.103058i	0.894241	+	0.447585i	$0.147716\pi$
$240$		0			0
$241$			125.629i			0.521283i	0.965436	+	0.260641i	$0.0839340\pi$
$241$			125.629i			0.521283i	−0.965436	+	0.260641i	$0.916066\pi$
$242$	−45.1001	+	78.1156i	−0.186364	+	0.322792i
$243$		0			0
$244$		−	123.515i		−	0.506210i
$245$	−112.298	+	92.7487i	−0.458360	+	0.378566i
$246$		0			0
$247$	−249.192			−1.00887
$248$	−51.0720	+	29.4864i	−0.205936	+	0.118897i
$249$		0			0
$250$	41.9767	+	24.2353i	0.167907	+	0.0969411i
$251$		−	393.359i		−	1.56717i	−0.621287	−	0.783583i	$-0.713390\pi$
$251$		−	393.359i		−	1.56717i	0.621287	−	0.783583i	$-0.286610\pi$
$252$		0			0
$253$	502.526			1.98627
$254$	40.1789	−	69.5918i	0.158184	−	0.273984i
$255$		0			0
$256$	−80.6856	−	139.752i	−0.315178	−	0.545905i
$257$		−	191.543i		−	0.745302i	−0.927971	−	0.372651i	$-0.878449\pi$
$257$		−	191.543i		−	0.745302i	0.927971	−	0.372651i	$-0.121551\pi$
$258$		0			0
$259$	−49.9201	+	4.17165i	−0.192742	+	0.0161068i
$260$	125.405			0.482327
$261$		0			0
$262$	−86.4822	−	49.9305i	−0.330085	−	0.190574i
$263$	314.217			1.19474			0.597371	−	0.801965i	$-0.296212\pi$
$263$	314.217			1.19474			0.597371	+	0.801965i	$0.296212\pi$
$264$		0			0
$265$	102.636	+	59.2570i	0.387306	+	0.223611i
$266$	−56.9417	−	26.8228i	−0.214066	−	0.100837i
$267$		0			0
$268$	2.99314	−	5.18426i	0.0111684	−	0.0193443i
$269$	125.315	+	72.3509i	0.465856	+	0.268962i	0.714504	−	0.699632i	$-0.246653\pi$
$269$	125.315	+	72.3509i	0.465856	+	0.268962i	−0.248647	+	0.968594i	$0.579986\pi$
$270$		0			0
$271$	−198.530	+	114.621i	−0.732583	+	0.422957i	−0.819366	−	0.573270i	$-0.805675\pi$
$271$	−198.530	+	114.621i	−0.732583	+	0.422957i	0.0867835	+	0.996227i	$0.472341\pi$
$272$	81.3646	−	46.9759i	0.299135	−	0.172705i
$273$		0			0
$274$	−20.8715	+	36.1505i	−0.0761733	+	0.131936i
$275$	301.854			1.09765
$276$		0			0
$277$	−85.8627			−0.309974			−0.154987	−	0.987917i	$-0.549534\pi$
$277$	−85.8627			−0.309974			−0.154987	+	0.987917i	$0.549534\pi$
$278$	15.7616	−	9.09995i	0.0566963	−	0.0327336i
$279$		0			0
$280$	58.4816	+	27.5481i	0.208863	+	0.0983862i
$281$	−133.707	−	231.588i	−0.475827	−	0.824157i	0.523789	−	0.851848i	$-0.324518\pi$
$281$	−133.707	−	231.588i	−0.475827	−	0.824157i	−0.999617	+	0.0276910i	$0.991185\pi$
$282$		0			0
$283$	20.1566	−	11.6374i	0.0712248	−	0.0411217i	−0.463965	−	0.885854i	$-0.653574\pi$
$283$	20.1566	−	11.6374i	0.0712248	−	0.0411217i	0.535189	+	0.844732i	$0.320240\pi$
$284$	−214.758	−	371.971i	−0.756189	−	1.30976i
$285$		0			0
$286$	−70.3282	+	40.6040i	−0.245903	+	0.141972i
$287$	−442.226	+	307.091i	−1.54086	+	1.07000i
$288$		0			0
$289$	−122.431	−	212.056i	−0.423636	−	0.733759i
$290$			24.4241i			0.0842211i
$291$		0			0
$292$			164.813i			0.564428i
$293$	441.759	+	255.049i	1.50771	+	0.870476i	0.999960	+	0.00897082i	$0.00285554\pi$
$293$	441.759	+	255.049i	1.50771	+	0.870476i	0.507749	+	0.861505i	$0.330478\pi$
$294$		0			0
$295$	52.2134	+	90.4363i	0.176995	+	0.306564i
$296$	11.1171	+	19.2553i	0.0375576	+	0.0650517i
$297$		0			0
$298$	−33.8990	+	58.7148i	−0.113755	+	0.197030i
$299$	255.854	+	147.717i	0.855699	+	0.494038i
$300$		0			0
$301$	−208.234	+	17.4014i	−0.691807	+	0.0578119i
$302$	−2.53615	+	4.39275i	−0.00839786	+	0.0145455i
$303$		0			0
$304$		−	320.997i		−	1.05591i
$305$	−47.7660	+	82.7331i	−0.156610	+	0.271256i
$306$		0			0
$307$			593.354i			1.93275i	0.257139	+	0.966374i	$0.417220\pi$
$307$			593.354i			1.93275i	−0.257139	+	0.966374i	$0.582780\pi$
$308$	500.601	−	41.8335i	1.62533	−	0.135823i
$309$		0			0
$310$	22.3498			0.0720960
$311$	−412.180	+	237.972i	−1.32534	+	0.765183i	−0.984574	−	0.174966i	$-0.944018\pi$
$311$	−412.180	+	237.972i	−1.32534	+	0.765183i	−0.340762	+	0.940150i	$0.610685\pi$
$312$		0			0
$313$	352.264	+	203.379i	1.12544	+	0.649775i	0.942785	−	0.333402i	$-0.108197\pi$
$313$	352.264	+	203.379i	1.12544	+	0.649775i	0.182658	+	0.983177i	$0.441530\pi$
$314$		−	68.9167i		−	0.219480i
$315$		0			0
$316$	−176.762			−0.559375
$317$	40.1465	−	69.5359i	0.126645	−	0.219356i	−0.795730	−	0.605652i	$-0.792912\pi$
$317$	40.1465	−	69.5359i	0.126645	−	0.219356i	0.922375	+	0.386296i	$0.126246\pi$
$318$		0			0
$319$	193.670	+	335.447i	0.607117	+	1.05156i
$320$			146.908i			0.459086i
$321$		0			0
$322$	42.5639	+	61.2941i	0.132186	+	0.190354i
$323$	150.804			0.466886
$324$		0			0
$325$	153.685	+	88.7300i	0.472877	+	0.273015i
$326$	−65.0424			−0.199516
$327$		0			0
$328$	206.950	+	119.482i	0.630944	+	0.364275i
$329$	−34.7626	+	24.1399i	−0.105661	+	0.0733734i
$330$		0			0
$331$	237.985	−	412.202i	0.718987	−	1.24532i	−0.242414	−	0.970173i	$-0.577939\pi$
$331$	237.985	−	412.202i	0.718987	−	1.24532i	0.961401	−	0.275150i	$-0.0887275\pi$
$332$	−120.356	−	69.4874i	−0.362517	−	0.209299i
$333$		0			0
$334$	−7.48705	+	4.32265i	−0.0224163	+	0.0129421i
$335$	−4.00973	+	2.31502i	−0.0119693	+	0.00691050i
$336$		0			0
$337$	260.519	−	451.233i	0.773055	−	1.33897i	−0.162827	−	0.986655i	$-0.552061\pi$
$337$	260.519	−	451.233i	0.773055	−	1.33897i	0.935881	−	0.352315i	$-0.114605\pi$
$338$	19.2048			0.0568190
$339$		0			0
$340$	−75.8917			−0.223211
$341$	306.957	−	177.222i	0.900168	−	0.519712i
$342$		0			0
$343$	−332.327	+	84.8989i	−0.968883	+	0.247519i
$344$	46.3730	+	80.3204i	0.134805	+	0.233490i
$345$		0			0
$346$	65.1177	−	37.5957i	0.188201	−	0.108658i
$347$	−129.806	−	224.830i	−0.374080	−	0.647925i	0.616109	−	0.787661i	$-0.288708\pi$
$347$	−129.806	−	224.830i	−0.374080	−	0.647925i	−0.990189	+	0.139736i	$0.955375\pi$
$348$		0			0
$349$	79.9285	−	46.1468i	0.229022	−	0.132226i	−0.381099	−	0.924534i	$-0.624454\pi$
$349$	79.9285	−	46.1468i	0.229022	−	0.132226i	0.610121	+	0.792309i	$0.291121\pi$
$350$	25.5670	+	36.8178i	0.0730487	+	0.105194i
$351$		0			0
$352$	−168.339	−	291.571i	−0.478235	−	0.828327i
$353$		−	402.801i		−	1.14108i	−0.821270	−	0.570539i	$-0.806734\pi$
$353$		−	402.801i		−	1.14108i	0.821270	−	0.570539i	$-0.193266\pi$
$354$		0			0
$355$			332.206i			0.935790i
$356$	138.285	+	79.8390i	0.388442	+	0.224267i
$357$		0			0
$358$	4.02744	+	6.97573i	0.0112498	+	0.0194853i
$359$	−238.980	−	413.925i	−0.665682	−	1.15299i	−0.979100	−	0.203379i	$-0.934807\pi$
$359$	−238.980	−	413.925i	−0.665682	−	1.15299i	0.313418	−	0.949615i	$-0.398526\pi$
$360$		0			0
$361$	77.1198	−	133.575i	0.213628	−	0.370015i
$362$	65.5604	+	37.8513i	0.181106	+	0.104562i
$363$		0			0
$364$	267.171	+	125.853i	0.733986	+	0.345749i
$365$	63.7367	−	110.395i	0.174621	−	0.302453i
$366$		0			0
$367$			236.707i			0.644979i	0.946573	+	0.322489i	$0.104520\pi$
$367$			236.707i			0.644979i	−0.946573	+	0.322489i	$0.895480\pi$
$368$	−190.283	+	329.579i	−0.517073	+	0.895596i
$369$		0			0
$370$		−	8.42636i		−	0.0227740i
$371$	159.194	+	229.247i	0.429095	+	0.617917i
$372$		0			0
$373$	82.7790			0.221928			0.110964	−	0.993824i	$-0.464606\pi$
$373$	82.7790			0.221928			0.110964	+	0.993824i	$0.464606\pi$
$374$	42.5607	−	24.5725i	0.113799	−	0.0657018i
$375$		0			0
$376$	16.2679	+	9.39229i	0.0432657	+	0.0249795i
$377$			227.717i			0.604025i
$378$		0			0
$379$	238.538			0.629387			0.314694	−	0.949193i	$-0.398098\pi$
$379$	238.538			0.629387			0.314694	+	0.949193i	$0.398098\pi$
$380$	−129.646	+	224.554i	−0.341175	+	0.590932i
$381$		0			0
$382$	−56.1513	−	97.2569i	−0.146993	−	0.254599i
$383$		−	588.452i		−	1.53643i	−0.640193	−	0.768214i	$-0.721146\pi$
$383$		−	588.452i		−	1.53643i	0.640193	−	0.768214i	$-0.278854\pi$
$384$		0			0
$385$	−351.491	−	165.572i	−0.912963	−	0.430057i
$386$	−7.17295			−0.0185828
$387$		0			0
$388$	463.507	+	267.606i	1.19460	+	0.689705i
$389$	603.675			1.55186			0.775932	−	0.630817i	$-0.217280\pi$
$389$	603.675			1.55186			0.775932	+	0.630817i	$0.217280\pi$
$390$		0			0
$391$	−154.836	−	89.3945i	−0.396000	−	0.228631i
$392$	96.9464	+	117.381i	0.247312	+	0.299440i
$393$		0			0
$394$	−18.6681	+	32.3340i	−0.0473809	+	0.0820661i
$395$	118.399	+	68.3578i	0.299745	+	0.173058i
$396$		0			0
$397$	265.409	−	153.234i	0.668537	−	0.385980i	−0.126985	−	0.991905i	$-0.540530\pi$
$397$	265.409	−	153.234i	0.668537	−	0.385980i	0.795522	+	0.605925i	$0.207197\pi$
$398$	5.01680	−	2.89645i	0.0126050	−	0.00727751i
$399$		0			0
$400$	−114.298	+	197.970i	−0.285745	+	0.494925i
$401$	−457.696			−1.14139			−0.570693	−	0.821164i	$-0.693325\pi$
$401$	−457.696			−1.14139			−0.570693	+	0.821164i	$0.693325\pi$
$402$		0			0
$403$	208.377			0.517065
$404$	91.8587	−	53.0346i	0.227373	−	0.131274i
$405$		0			0
$406$	−24.5113	+	52.0347i	−0.0603726	+	0.128164i
$407$	−66.8166	−	115.730i	−0.164169	−	0.284348i
$408$		0			0
$409$	−287.215	+	165.823i	−0.702236	+	0.405436i	−0.808180	−	0.588936i	$-0.799547\pi$
$409$	−287.215	+	165.823i	−0.702236	+	0.405436i	0.105944	+	0.994372i	$0.466214\pi$
$410$	−45.2819	−	78.4305i	−0.110444	−	0.191294i
$411$		0			0
$412$	−114.500	+	66.1067i	−0.277913	+	0.160453i
$413$	20.4797	+	245.071i	0.0495877	+	0.593392i
$414$		0			0
$415$	53.7445	+	93.0882i	0.129505	+	0.224309i
$416$		−	197.932i		−	0.475799i
$417$		0			0
$418$		−	167.909i		−	0.401697i
$419$	444.173	+	256.443i	1.06008	+	0.612037i	0.925454	−	0.378860i	$-0.123684\pi$
$419$	444.173	+	256.443i	1.06008	+	0.612037i	0.134625	+	0.990897i	$0.457017\pi$
$420$		0			0
$421$	69.3423	+	120.104i	0.164709	+	0.285284i	0.936552	−	0.350529i	$-0.113998\pi$
$421$	69.3423	+	120.104i	0.164709	+	0.285284i	−0.771843	+	0.635813i	$0.780665\pi$
$422$	−48.7759	−	84.4824i	−0.115583	−	0.200195i
$423$		0			0
$424$	61.9389	−	107.281i	0.146082	−	0.253022i
$425$	−93.0059	−	53.6970i	−0.218837	−	0.126346i
$426$		0			0
$427$	−184.792	+	128.323i	−0.432769	+	0.300523i
$428$	212.820	−	368.615i	0.497243	−	0.861250i
$429$		0			0
$430$		−	35.1492i		−	0.0817424i
$431$	−279.301	+	483.764i	−0.648030	+	1.12242i	0.335562	+	0.942018i	$0.391074\pi$
$431$	−279.301	+	483.764i	−0.648030	+	1.12242i	−0.983593	+	0.180403i	$0.942260\pi$
$432$		0			0
$433$			462.936i			1.06914i	0.845125	+	0.534568i	$0.179526\pi$
$433$			462.936i			1.06914i	−0.845125	+	0.534568i	$0.820474\pi$
$434$	47.6154	+	22.4295i	0.109713	+	0.0516810i
$435$		0			0
$436$	−477.069			−1.09420
$437$	−529.015	+	305.427i	−1.21056	+	0.698917i
$438$		0			0
$439$	−553.220	−	319.401i	−1.26018	−	0.727566i	−0.287072	−	0.957909i	$-0.592682\pi$
$439$	−553.220	−	319.401i	−1.26018	−	0.727566i	−0.973109	+	0.230343i	$0.926015\pi$
$440$			172.450i			0.391932i
$441$		0			0
$442$	28.8923			0.0653671
$443$	−91.5065	+	158.494i	−0.206561	+	0.357774i	−0.950629	−	0.310330i	$-0.899561\pi$
$443$	−91.5065	+	158.494i	−0.206561	+	0.357774i	0.744068	+	0.668104i	$0.232894\pi$
$444$		0			0
$445$	−61.7509	−	106.956i	−0.138766	−	0.240350i
$446$		−	15.3067i		−	0.0343201i
$447$		0			0
$448$	−147.432	+	312.982i	−0.329089	+	0.698619i
$449$	−52.9818			−0.118000			−0.0589998	−	0.998258i	$-0.518791\pi$
$449$	−52.9818			−0.118000			−0.0589998	+	0.998258i	$0.518791\pi$
$450$		0			0
$451$	−1243.83	−	718.123i	−2.75793	−	1.59229i
$452$	−134.614			−0.297818
$453$		0			0
$454$	−50.7377	−	29.2934i	−0.111757	−	0.0645229i
$455$	−130.287	−	187.619i	−0.286344	−	0.412350i
$456$		0			0
$457$	177.522	−	307.478i	0.388451	−	0.672817i	−0.603790	−	0.797143i	$-0.706344\pi$
$457$	177.522	−	307.478i	0.388451	−	0.672817i	0.992241	+	0.124326i	$0.0396769\pi$
$458$	107.047	+	61.8037i	0.233727	+	0.134943i
$459$		0			0
$460$	266.225	−	153.705i	0.578751	−	0.334142i
$461$	203.793	−	117.660i	0.442068	−	0.255228i	−0.262406	−	0.964957i	$-0.584516\pi$
$461$	203.793	−	117.660i	0.442068	−	0.255228i	0.704474	+	0.709729i	$0.251183\pi$
$462$		0			0
$463$	353.885	−	612.947i	0.764331	−	1.32386i	−0.176268	−	0.984342i	$-0.556403\pi$
$463$	353.885	−	612.947i	0.764331	−	1.32386i	0.940600	−	0.339518i	$-0.110264\pi$
$464$	−293.335			−0.632188
$465$		0			0
$466$	−57.0586			−0.122443
$467$	−620.830	+	358.436i	−1.32940	+	0.767529i	−0.985207	−	0.171370i	$-0.945181\pi$
$467$	−620.830	+	358.436i	−1.32940	+	0.767529i	−0.344193	+	0.938899i	$0.611847\pi$
$468$		0			0
$469$	−10.8659	+	0.908022i	−0.0231682	+	0.00193608i
$470$	−3.55952	−	6.16528i	−0.00757345	−	0.0131176i
$471$		0			0
$472$	94.5293	−	54.5765i	0.200274	−	0.115628i
$473$	−278.715	−	482.749i	−0.589250	−	1.02061i
$474$		0			0
$475$	−317.766	+	183.462i	−0.668980	+	0.386236i
$476$	−161.685	−	76.1626i	−0.339673	−	0.160005i
$477$		0			0
$478$	5.63329	+	9.75715i	0.0117851	+	0.0204124i
$479$			401.396i			0.837988i	0.907989	+	0.418994i	$0.137617\pi$
$479$			401.396i			0.837988i	−0.907989	+	0.418994i	$0.862383\pi$
$480$		0			0
$481$		−	78.5629i		−	0.163332i
$482$	−43.0988	−	24.8831i	−0.0894166	−	0.0516247i
$483$		0			0
$484$	437.534	+	757.831i	0.903996	+	1.56577i
$485$	−206.978	−	358.496i	−0.426758	−	0.739167i
$486$		0			0
$487$	244.577	−	423.619i	0.502211	−	0.869854i	−0.497786	−	0.867300i	$-0.665854\pi$
$487$	244.577	−	423.619i	0.502211	−	0.869854i	0.999997	−	0.00255441i	$-0.000813093\pi$
$488$	86.4775	+	49.9278i	0.177208	+	0.102311i
$489$		0			0
$490$	−9.57607	−	56.8960i	−0.0195430	−	0.116114i
$491$	229.841	−	398.097i	0.468109	−	0.810788i	−0.531227	−	0.847230i	$-0.678269\pi$
$491$	229.841	−	398.097i	0.468109	−	0.810788i	0.999336	+	0.0364412i	$0.0116022\pi$
$492$		0			0
$493$		−	137.808i		−	0.279530i
$494$	49.3569	−	85.4887i	0.0999128	−	0.173054i
$495$		0			0
$496$			268.422i			0.541174i
$497$	−333.391	+	707.752i	−0.670808	+	1.42405i
$498$		0			0
$499$	492.176			0.986326			0.493163	−	0.869937i	$-0.335841\pi$
$499$	492.176			0.986326			0.493163	+	0.869937i	$0.335841\pi$
$500$	407.233	−	235.116i	0.814466	−	0.470232i
$501$		0			0
$502$	134.947	+	77.9118i	0.268819	+	0.155203i
$503$			26.5745i			0.0528321i	0.999651	+	0.0264160i	$0.00840947\pi$
$503$			26.5745i			0.0528321i	−0.999651	+	0.0264160i	$0.991591\pi$
$504$		0			0
$505$	−82.0385			−0.162452
$506$	−99.5343	+	172.399i	−0.196708	+	0.340709i
$507$		0			0
$508$	−389.791	−	675.138i	−0.767306	−	1.32901i
$509$			222.332i			0.436802i	0.975859	+	0.218401i	$0.0700841\pi$
$509$			222.332i			0.436802i	−0.975859	+	0.218401i	$0.929916\pi$
$510$		0			0
$511$	246.578	−	171.229i	0.482540	−	0.335086i
$512$	430.714			0.841239
$513$		0			0
$514$	65.7114	+	37.9385i	0.127843	+	0.0738103i
$515$	102.259			0.198562
$516$		0			0
$517$	−97.7748	−	56.4503i	−0.189120	−	0.109188i
$518$	8.45644	−	17.9521i	0.0163252	−	0.0346565i
$519$		0			0
$520$	−50.6917	+	87.8006i	−0.0974840	+	0.168847i
$521$	377.408	+	217.896i	0.724391	+	0.418227i	0.816367	−	0.577534i	$-0.195985\pi$
$521$	377.408	+	217.896i	0.724391	+	0.418227i	−0.0919757	+	0.995761i	$0.529318\pi$
$522$		0			0
$523$	452.836	−	261.445i	0.865843	−	0.499895i	−0.000121417	−	1.00000i	$-0.500039\pi$
$523$	452.836	−	261.445i	0.865843	−	0.499895i	0.865965	+	0.500105i	$0.166705\pi$
$524$	−838.999	+	484.396i	−1.60114	+	0.924420i
$525$		0			0
$526$	−62.2363	+	107.796i	−0.118320	+	0.204936i
$527$	−126.104			−0.239287
$528$		0			0
$529$	195.211			0.369019
$530$	−40.6579	+	23.4738i	−0.0767130	+	0.0442903i
$531$		0			0
$532$	−501.563	+	348.296i	−0.942787	+	0.654691i
$533$	−422.184	−	731.244i	−0.792090	−	1.37194i
$534$		0			0
$535$	−285.103	+	164.604i	−0.532902	+	0.307671i
$536$	2.41979	+	4.19121i	0.00451454	+	0.00781941i
$537$		0			0
$538$	−49.6419	+	28.6608i	−0.0922713	+	0.0532728i
$539$	−582.676	−	705.491i	−1.08103	−	1.30889i
$540$		0			0
$541$	−195.417	−	338.472i	−0.361214	−	0.625642i	0.626947	−	0.779062i	$-0.284304\pi$
$541$	−195.417	−	338.472i	−0.361214	−	0.625642i	−0.988161	+	0.153421i	$0.950971\pi$
$542$		−	90.8113i		−	0.167548i
$543$		0			0
$544$			119.783i			0.220190i
$545$	319.551	+	184.493i	0.586332	+	0.338519i
$546$		0			0
$547$	−383.668	−	664.533i	−0.701405	−	1.21487i	−0.967973	−	0.251053i	$-0.919223\pi$
$547$	−383.668	−	664.533i	−0.701405	−	1.21487i	0.266568	−	0.963816i	$-0.414110\pi$
$548$	202.483	+	350.710i	0.369494	+	0.639982i
$549$		0			0
$550$	−59.7877	+	103.555i	−0.108705	+	0.188282i
$551$	−407.758	−	235.419i	−0.740033	−	0.427258i
$552$		0			0
$553$	183.643	+	264.455i	0.332086	+	0.478220i
$554$	17.0067	−	29.4564i	0.0306979	−	0.0531704i
$555$		0			0
$556$		−	176.564i		−	0.317562i
$557$	240.211	−	416.057i	0.431258	−	0.746961i	−0.565724	−	0.824595i	$-0.691403\pi$
$557$	240.211	−	416.057i	0.431258	−	0.746961i	0.996982	+	0.0776337i	$0.0247365\pi$
$558$		0			0
$559$		−	327.713i		−	0.586248i
$560$	241.683	−	167.829i	0.431576	−	0.299695i
$561$		0			0
$562$	105.933			0.188492
$563$	−110.169	+	63.6063i	−0.195683	+	0.112977i	−0.594640	−	0.803992i	$-0.702705\pi$
$563$	−110.169	+	63.6063i	−0.195683	+	0.112977i	0.398957	+	0.916969i	$0.369372\pi$
$564$		0			0
$565$	90.1670	+	52.0579i	0.159588	+	0.0921379i
$566$			9.22001i			0.0162898i
$567$		0			0
$568$	347.241			0.611339
$569$	87.7076	−	151.914i	0.154143	−	0.266984i	−0.778603	−	0.627516i	$-0.784072\pi$
$569$	87.7076	−	151.914i	0.154143	−	0.266984i	0.932747	+	0.360532i	$0.117405\pi$
$570$		0			0
$571$	281.695	+	487.910i	0.493336	+	0.854483i	0.999971	−	0.00767812i	$-0.00244404\pi$
$571$	281.695	+	487.910i	0.493336	+	0.854483i	−0.506635	+	0.862161i	$0.669111\pi$
$572$			787.832i			1.37733i
$573$		0			0
$574$	−17.7610	−	212.537i	−0.0309424	−	0.370273i
$575$	435.015			0.756548
$576$		0			0
$577$	582.279	+	336.179i	1.00915	+	0.582632i	0.910942	−	0.412534i	$-0.135356\pi$
$577$	582.279	+	336.179i	1.00915	+	0.582632i	0.0982060	+	0.995166i	$0.468690\pi$
$578$	96.9985			0.167817
$579$		0			0
$580$	205.203	+	118.474i	0.353798	+	0.204266i
$581$	21.0803	+	252.257i	0.0362827	+	0.434178i
$582$		0			0
$583$	−372.270	+	644.791i	−0.638543	+	1.10599i
$584$	−115.392	−	66.6213i	−0.197588	−	0.114078i
$585$		0			0
$586$	−174.997	+	101.034i	−0.298629	+	0.172413i
$587$	771.927	−	445.672i	1.31504	−	0.759237i	0.332112	−	0.943240i	$-0.392239\pi$
$587$	771.927	−	445.672i	1.31504	−	0.759237i	0.982926	+	0.184003i	$0.0589055\pi$
$588$		0			0
$589$	−215.425	+	373.127i	−0.365747	+	0.633493i
$590$	−41.3672			−0.0701139
$591$		0			0
$592$	101.201			0.170948
$593$	244.839	−	141.358i	0.412882	−	0.238378i	−0.279145	−	0.960249i	$-0.590051\pi$
$593$	244.839	−	141.358i	0.412882	−	0.238378i	0.692027	+	0.721871i	$0.256718\pi$
$594$		0			0
$595$	78.8460	+	113.542i	0.132514	+	0.190827i
$596$	328.868	+	569.616i	0.551792	+	0.955732i
$597$		0			0
$598$	−101.353	+	58.5162i	−0.169487	+	0.0978531i
$599$	144.808	+	250.816i	0.241750	+	0.418724i	0.961213	−	0.275807i	$-0.0889452\pi$
$599$	144.808	+	250.816i	0.241750	+	0.418724i	−0.719463	+	0.694531i	$0.755612\pi$
$600$		0			0
$601$	231.175	−	133.469i	0.384651	−	0.222078i	−0.295189	−	0.955439i	$-0.595383\pi$
$601$	231.175	−	133.469i	0.384651	−	0.222078i	0.679840	+	0.733361i	$0.262049\pi$
$602$	35.2747	−	74.8842i	0.0585958	−	0.124392i
$603$		0			0
$604$	24.6042	+	42.6158i	0.0407355	+	0.0705560i
$605$		−	676.814i		−	1.11870i
$606$		0			0
$607$		−	590.249i		−	0.972404i	−0.873846	−	0.486202i	$-0.838382\pi$
$607$		−	590.249i		−	0.972404i	0.873846	−	0.486202i	$-0.161618\pi$
$608$	354.424	+	204.627i	0.582934	+	0.336557i
$609$		0			0
$610$	−18.9218	−	32.7736i	−0.0310194	−	0.0537272i
$611$	−33.1871	−	57.4818i	−0.0543160	−	0.0940782i
$612$		0			0
$613$	−363.910	+	630.310i	−0.593654	+	1.02824i	0.400081	+	0.916480i	$0.368982\pi$
$613$	−363.910	+	630.310i	−0.593654	+	1.02824i	−0.993735	+	0.111759i	$0.964351\pi$
$614$	−203.558	−	117.524i	−0.331528	−	0.191408i
$615$		0			0
$616$	−173.066	+	367.399i	−0.280951	+	0.596427i
$617$	−224.856	+	389.462i	−0.364434	+	0.631219i	−0.988685	−	0.150005i	$-0.952071\pi$
$617$	−224.856	+	389.462i	−0.364434	+	0.631219i	0.624251	+	0.781224i	$0.285404\pi$
$618$		0			0
$619$			626.724i			1.01248i	0.862393	+	0.506239i	$0.168965\pi$
$619$			626.724i			1.01248i	−0.862393	+	0.506239i	$0.831035\pi$
$620$	108.412	−	187.775i	0.174858	−	0.302863i
$621$		0			0
$622$		−	188.539i		−	0.303117i
$623$	−24.2206	−	289.837i	−0.0388774	−	0.465227i
$624$		0			0
$625$	40.4236			0.0646777
$626$	−139.544	+	80.5660i	−0.222914	+	0.128700i
$627$		0			0
$628$	−579.015	−	334.294i	−0.921998	−	0.532316i
$629$			47.5441i			0.0755869i
$630$		0			0
$631$	261.737			0.414797			0.207398	−	0.978257i	$-0.433500\pi$
$631$	261.737			0.414797			0.207398	+	0.978257i	$0.433500\pi$
$632$	71.4515	−	123.758i	0.113056	−	0.195819i
$633$		0			0
$634$	15.9035	+	27.5457i	0.0250844	+	0.0434474i
$635$			602.962i			0.949547i
$636$		0			0
$637$	−89.2822	−	530.468i	−0.140160	−	0.832760i
$638$	−153.440			−0.240501
$639$		0			0
$640$	−236.045	−	136.280i	−0.368820	−	0.212938i
$641$	207.935			0.324391			0.162196	−	0.986759i	$-0.448142\pi$
$641$	207.935			0.324391			0.162196	+	0.986759i	$0.448142\pi$
$642$		0			0
$643$	682.131	+	393.828i	1.06086	+	0.612486i	0.925669	−	0.378334i	$-0.123503\pi$
$643$	682.131	+	393.828i	1.06086	+	0.612486i	0.135187	+	0.990820i	$0.456836\pi$
$644$	721.437	−	60.2880i	1.12024	−	0.0936149i
$645$		0			0
$646$	−29.8695	+	51.7354i	−0.0462376	+	0.0800858i
$647$	154.488	+	89.1939i	0.238777	+	0.137858i	0.614614	−	0.788828i	$-0.289312\pi$
$647$	154.488	+	89.1939i	0.238777	+	0.137858i	−0.375838	+	0.926685i	$0.622645\pi$
$648$		0			0
$649$	−568.148	+	328.020i	−0.875421	+	0.505424i
$650$	−60.8801	+	35.1492i	−0.0936617	+	0.0540756i
$651$		0			0
$652$	−315.501	+	546.464i	−0.483897	+	0.838135i
$653$	197.089			0.301821			0.150911	−	0.988547i	$-0.451779\pi$
$653$	197.089			0.301821			0.150911	+	0.988547i	$0.451779\pi$
$654$		0			0
$655$	749.305			1.14398
$656$	941.955	−	543.838i	1.43591	−	0.829022i
$657$		0			0
$658$	−1.39616	−	16.7071i	−0.00212182	−	0.0253908i
$659$	211.121	+	365.673i	0.320366	+	0.554890i	0.980564	−	0.196202i	$-0.0628607\pi$
$659$	211.121	+	365.673i	0.320366	+	0.554890i	−0.660197	+	0.751092i	$0.729527\pi$
$660$		0			0
$661$	277.079	−	159.972i	0.419181	−	0.242014i	−0.275546	−	0.961288i	$-0.588859\pi$
$661$	277.079	−	159.972i	0.419181	−	0.242014i	0.694727	+	0.719274i	$0.255525\pi$
$662$	94.2744	+	163.288i	0.142408	+	0.246659i
$663$		0			0
$664$	97.3013	−	56.1769i	0.146538	−	0.0846038i
$665$	470.651	−	39.3306i	0.707745	−	0.0591438i
$666$		0			0
$667$	279.106	+	483.427i	0.418450	+	0.724777i
$668$			83.8716i			0.125556i
$669$		0			0
$670$		−	1.83413i		−	0.00273750i
$671$	−519.755	−	300.080i	−0.774597	−	0.447214i
$672$		0			0
$673$	142.474	+	246.772i	0.211700	+	0.366675i	0.952247	−	0.305330i	$-0.0987668\pi$
$673$	142.474	+	246.772i	0.211700	+	0.366675i	−0.740547	+	0.672005i	$0.765433\pi$
$674$	103.201	+	178.750i	0.153117	+	0.265207i
$675$		0			0
$676$	93.1569	−	161.352i	0.137806	−	0.238687i
$677$	−571.045	−	329.693i	−0.843493	−	0.486991i	0.0149568	−	0.999888i	$-0.495239\pi$
$677$	−571.045	−	329.693i	−0.843493	−	0.486991i	−0.858450	+	0.512897i	$0.828572\pi$
$678$		0			0
$679$	−81.1831	−	971.479i	−0.119563	−	1.43075i
$680$	30.6772	−	53.1345i	0.0451136	−	0.0781390i
$681$		0			0
$682$			140.408i			0.205877i
$683$	13.3455	−	23.1150i	0.0195395	−	0.0338434i	−0.856090	−	0.516826i	$-0.827113\pi$
$683$	13.3455	−	23.1150i	0.0195395	−	0.0338434i	0.875630	+	0.482983i	$0.160447\pi$
$684$		0			0
$685$		−	313.217i		−	0.457252i
$686$	36.6976	−	130.825i	0.0534950	−	0.190707i
$687$		0			0
$688$	422.145			0.613582
$689$	−379.072	+	218.858i	−0.550178	+	0.317645i
$690$		0			0
$691$	398.277	+	229.945i	0.576378	+	0.332772i	0.759692	−	0.650283i	$-0.225349\pi$
$691$	398.277	+	229.945i	0.576378	+	0.332772i	−0.183315	+	0.983054i	$0.558683\pi$
$692$		−	729.463i		−	1.05414i
$693$		0			0
$694$	102.841			0.148186
$695$	−68.2812	+	118.267i	−0.0982464	+	0.170168i
$696$		0			0
$697$	255.494	+	442.529i	0.366563	+	0.634906i
$698$			36.5608i			0.0523794i
$699$		0			0
$700$	433.349	−	36.2134i	0.619070	−	0.0517335i
$701$	−430.145			−0.613616			−0.306808	−	0.951771i	$-0.599261\pi$
$701$	−430.145			−0.613616			−0.306808	+	0.951771i	$0.599261\pi$
$702$		0			0
$703$	140.677	+	81.2201i	0.200110	+	0.115534i
$704$	−922.918			−1.31096
$705$		0			0
$706$	138.186	+	79.7820i	0.195732	+	0.113006i
$707$	−174.780	−	82.3313i	−0.247214	−	0.116452i
$708$		0			0
$709$	308.259	−	533.921i	0.434780	−	0.753062i	−0.562497	−	0.826799i	$-0.690159\pi$
$709$	308.259	−	533.921i	0.434780	−	0.753062i	0.997278	+	0.0737374i	$0.0234927\pi$
$710$	−113.968	−	65.7993i	−0.160518	−	0.0926751i
$711$		0			0
$712$	−111.796	+	64.5457i	−0.157017	+	0.0906540i
$713$	442.369	−	255.402i	0.620434	−	0.358208i
$714$		0			0
$715$	304.671	−	527.706i	0.426114	−	0.738051i
$716$	78.1436			0.109139
$717$		0			0
$718$	189.337			0.263701
$719$	153.601	−	88.6813i	0.213631	−	0.123340i	−0.389367	−	0.921083i	$-0.627306\pi$
$719$	153.601	−	88.6813i	0.213631	−	0.123340i	0.602998	+	0.797743i	$0.293973\pi$
$720$		0			0
$721$	217.860	+	102.624i	0.302164	+	0.142336i
$722$	30.5499	+	52.9141i	0.0423129	+	0.0732882i
$723$		0			0
$724$	636.028	−	367.211i	0.878491	−	0.507197i
$725$	167.652	+	290.382i	0.231244	+	0.400527i
$726$		0			0
$727$	−233.524	+	134.825i	−0.321216	+	0.185454i	−0.651935	−	0.758275i	$-0.726042\pi$
$727$	−233.524	+	134.825i	−0.321216	+	0.185454i	0.330718	+	0.943730i	$0.392709\pi$
$728$	−196.111	+	136.183i	−0.269383	+	0.187065i
$729$		0			0
$730$	25.2484	+	43.7315i	0.0345869	+	0.0599062i
$731$			198.323i			0.271304i
$732$		0			0
$733$			1113.36i			1.51890i	0.650563	+	0.759452i	$0.274533\pi$
$733$			1113.36i			1.51890i	−0.650563	+	0.759452i	$0.725467\pi$
$734$	−81.2057	−	46.8841i	−0.110634	−	0.0638748i
$735$		0			0
$736$	−242.600	−	420.195i	−0.329619	−	0.570918i
$737$	−14.5436	−	25.1903i	−0.0197336	−	0.0341796i
$738$		0			0
$739$	−132.705	+	229.851i	−0.179573	+	0.311030i	−0.941734	−	0.336357i	$-0.890805\pi$
$739$	−132.705	+	229.851i	−0.179573	+	0.311030i	0.762161	+	0.647387i	$0.224138\pi$
$740$	−70.7955	−	40.8738i	−0.0956695	−	0.0552348i
$741$		0			0
$742$	−110.178	+	9.20717i	−0.148488	+	0.0124086i
$743$	−131.196	+	227.238i	−0.176576	+	0.305838i	−0.940706	−	0.339224i	$-0.889835\pi$
$743$	−131.196	+	227.238i	−0.176576	+	0.305838i	0.764130	+	0.645063i	$0.223169\pi$
$744$		0			0
$745$		−	508.721i		−	0.682847i
$746$	−16.3959	+	28.3985i	−0.0219784	+	0.0380677i
$747$		0			0
$748$		−	476.775i		−	0.637399i
$749$	−772.592	+	64.5628i	−1.03150	+	0.0861987i
$750$		0			0
$751$	−1440.92			−1.91867			−0.959335	−	0.282271i	$-0.908912\pi$
$751$	−1440.92			−1.91867			−0.959335	+	0.282271i	$0.908912\pi$
$752$	74.0453	−	42.7501i	0.0984646	−	0.0568485i
$753$		0			0
$754$	−78.1216	−	45.1035i	−0.103610	−	0.0598190i
$755$		−	38.0599i		−	0.0504105i
$756$		0			0
$757$	−843.445			−1.11419			−0.557097	−	0.830447i	$-0.688085\pi$
$757$	−843.445			−1.11419			−0.557097	+	0.830447i	$0.688085\pi$
$758$	−47.2467	+	81.8337i	−0.0623307	+	0.107960i
$759$		0			0
$760$	−104.812	−	181.540i	−0.137911	−	0.238869i
$761$		−	334.968i		−	0.440168i	−0.975481	−	0.220084i	$-0.929367\pi$
$761$		−	334.968i		−	0.440168i	0.975481	−	0.220084i	$-0.0706331\pi$
$762$		0			0
$763$	495.641	+	713.747i	0.649594	+	0.935448i
$764$	−1089.49			−1.42604
$765$		0			0
$766$	201.877	+	116.554i	0.263547	+	0.152159i
$767$	−385.686			−0.502850
$768$		0			0
$769$	−1021.25	−	589.617i	−1.32802	−	0.766732i	−0.343025	−	0.939326i	$-0.611452\pi$
$769$	−1021.25	−	589.617i	−1.32802	−	0.766732i	−0.984993	+	0.172595i	$0.944785\pi$
$770$	126.421	−	87.7893i	0.164183	−	0.114012i
$771$		0			0
$772$	−34.7938	+	60.2647i	−0.0450697	+	0.0780630i
$773$	861.613	+	497.452i	1.11463	+	0.643535i	0.940026	−	0.341103i	$-0.110801\pi$
$773$	861.613	+	497.452i	1.11463	+	0.643535i	0.174609	+	0.984638i	$0.444134\pi$
$774$		0			0
$775$	265.720	−	153.413i	0.342864	−	0.197953i
$776$	−374.721	+	216.345i	−0.482888	+	0.278795i
$777$		0			0
$778$	−119.569	+	207.099i	−0.153687	+	0.266194i
$779$	1745.85			2.24115
$780$		0			0
$781$	−2087.02			−2.67224
$782$	61.3361	−	35.4124i	0.0784349	−	0.0452844i
$783$		0			0
$784$	683.325	−	115.009i	0.871587	−	0.146695i
$785$	258.557	+	447.834i	0.329372	+	0.570490i
$786$		0			0
$787$	144.261	−	83.2892i	0.183305	−	0.105831i	−0.405539	−	0.914078i	$-0.632916\pi$
$787$	144.261	−	83.2892i	0.183305	−	0.105831i	0.588845	+	0.808246i	$0.299583\pi$
$788$	181.106	+	313.685i	0.229830	+	0.398078i
$789$		0			0
$790$	−46.9022	+	27.0790i	−0.0593698	+	0.0342772i
$791$	139.854	+	201.396i	0.176806	+	0.254610i
$792$		0			0
$793$	−176.417	−	305.563i	−0.222468	−	0.385326i
$794$			121.403i			0.152901i
$795$		0			0
$796$		−	56.1993i		−	0.0706021i
$797$	−1281.62	−	739.941i	−1.60805	−	0.928408i	−0.989806	−	0.142422i	$-0.954511\pi$
$797$	−1281.62	−	739.941i	−1.60805	−	0.928408i	−0.618244	−	0.785986i	$-0.712156\pi$
$798$		0			0
$799$	20.0839	+	34.7864i	0.0251363	+	0.0435374i
$800$	−145.723	−	252.400i	−0.182154	−	0.315501i
$801$		0			0
$802$	90.6549	−	157.019i	0.113036	−	0.195784i
$803$	693.536	+	400.413i	0.863681	+	0.498647i
$804$		0			0
$805$	−506.548	−	238.613i	−0.629252	−	0.296414i
$806$	−41.2729	+	71.4868i	−0.0512071	+	0.0886932i
$807$		0			0
$808$			85.7515i			0.106128i
$809$	33.1490	−	57.4158i	0.0409753	−	0.0709713i	−0.844810	−	0.535066i	$-0.820287\pi$
$809$	33.1490	−	57.4158i	0.0409753	−	0.0709713i	0.885786	+	0.464094i	$0.153620\pi$
$810$		0			0
$811$			193.287i			0.238331i	0.992874	+	0.119166i	$0.0380220\pi$
$811$			193.287i			0.238331i	−0.992874	+	0.119166i	$0.961978\pi$
$812$	318.281	+	458.340i	0.391972	+	0.564458i
$813$		0			0
$814$	52.9370			0.0650331
$815$	422.658	−	244.022i	0.518599	−	0.299413i
$816$		0			0
$817$	586.813	+	338.797i	0.718254	+	0.414684i
$818$		−	131.377i		−	0.160608i
$819$		0			0
$820$	−878.595			−1.07146
$821$	128.230	−	222.100i	0.156187	−	0.270524i	−0.777303	−	0.629126i	$-0.783413\pi$
$821$	128.230	−	222.100i	0.156187	−	0.270524i	0.933491	+	0.358602i	$0.116746\pi$
$822$		0			0
$823$	−325.963	−	564.585i	−0.396067	−	0.686008i	0.597170	−	0.802115i	$-0.296292\pi$
$823$	−325.963	−	564.585i	−0.396067	−	0.686008i	−0.993237	+	0.116107i	$0.962959\pi$
$824$		−	106.888i		−	0.129718i
$825$		0			0
$826$	−88.1314	−	41.5149i	−0.106697	−	0.0502601i
$827$	−371.783			−0.449556			−0.224778	−	0.974410i	$-0.572166\pi$
$827$	−371.783			−0.449556			−0.224778	+	0.974410i	$0.572166\pi$
$828$		0			0
$829$	−81.4198	−	47.0078i	−0.0982145	−	0.0567042i	0.450088	−	0.892984i	$-0.351393\pi$
$829$	−81.4198	−	47.0078i	−0.0982145	−	0.0567042i	−0.548303	+	0.836280i	$0.684726\pi$
$830$	−42.5803			−0.0513015
$831$		0			0
$832$	−469.891	−	271.292i	−0.564773	−	0.326072i
$833$	54.0311	+	321.025i	0.0648633	+	0.385384i
$834$		0			0
$835$	32.4349	−	56.1789i	0.0388442	−	0.0672801i
$836$	−1410.72	−	814.478i	−1.68746	−	0.974256i
$837$		0			0
$838$	−175.953	+	101.586i	−0.209968	+	0.121225i
$839$	−1071.22	+	618.469i	−1.27678	+	0.737150i	−0.976255	−	0.216624i	$-0.930496\pi$
$839$	−1071.22	+	618.469i	−1.27678	+	0.737150i	−0.300526	+	0.953774i	$0.597162\pi$
$840$		0			0
$841$	205.368	−	355.708i	0.244195	−	0.422959i
$842$	−54.9380			−0.0652470
$843$		0			0
$844$	−946.390			−1.12131
$845$	−124.797	+	72.0515i	−0.147689	+	0.0852680i
$846$		0			0
$847$	679.230	−	1441.93i	0.801925	−	1.70240i
$848$	−281.922	−	488.304i	−0.332455	−	0.575830i
$849$		0			0
$850$	36.8430	−	21.2713i	0.0433447	−	0.0250251i
$851$	−96.2923	−	166.783i	−0.113152	−	0.195985i
$852$		0			0
$853$	29.3797	−	16.9623i	0.0344427	−	0.0198855i	−0.482680	−	0.875797i	$-0.660336\pi$
$853$	29.3797	−	16.9623i	0.0344427	−	0.0198855i	0.517122	+	0.855911i	$0.327003\pi$
$854$	−7.42173	−	88.8123i	−0.00869055	−	0.103996i
$855$		0			0
$856$	172.054	+	298.006i	0.200997	+	0.348138i
$857$		−	516.188i		−	0.602319i	−0.953574	−	0.301160i	$-0.902626\pi$
$857$		−	516.188i		−	0.602319i	0.953574	−	0.301160i	$-0.0973737\pi$
$858$		0			0
$859$			234.815i			0.273358i	0.990615	+	0.136679i	$0.0436429\pi$
$859$			234.815i			0.273358i	−0.990615	+	0.136679i	$0.956357\pi$
$860$	−295.312	−	170.499i	−0.343386	−	0.198254i
$861$		0			0
$862$	−110.641	−	191.636i	−0.128354	−	0.222316i
$863$	596.793	+	1033.68i	0.691533	+	1.19777i	0.971336	+	0.237712i	$0.0763975\pi$
$863$	596.793	+	1033.68i	0.691533	+	1.19777i	−0.279803	+	0.960057i	$0.590269\pi$
$864$		0			0
$865$	−282.099	+	488.609i	−0.326126	+	0.564866i
$866$	−158.817	−	91.6929i	−0.183391	−	0.105881i
$867$		0			0
$868$	419.413	−	291.249i	0.483195	−	0.335541i
$869$	−429.444	+	743.819i	−0.494182	+	0.855948i
$870$		0			0
$871$		−	17.1004i		−	0.0196331i
$872$	192.843	−	334.014i	0.221150	−	0.383043i
$873$		0			0
$874$		−	241.981i		−	0.276866i
$875$	−774.845	−	364.996i	−0.885537	−	0.417138i
$876$		0			0
$877$	575.791			0.656546			0.328273	−	0.944583i	$-0.393533\pi$
$877$	575.791			0.656546			0.328273	+	0.944583i	$0.393533\pi$
$878$	219.150	−	126.526i	0.249602	−	0.144108i
$879$		0			0
$880$	679.767	+	392.464i	0.772463	+	0.445982i
$881$			1501.94i			1.70481i	0.522881	+	0.852406i	$0.324857\pi$
$881$			1501.94i			1.70481i	−0.522881	+	0.852406i	$0.675143\pi$
$882$		0			0
$883$	−9.73009			−0.0110194			−0.00550968	−	0.999985i	$-0.501754\pi$
$883$	−9.73009			−0.0110194			−0.00550968	+	0.999985i	$0.501754\pi$
$884$	140.148	−	242.743i	0.158538	−	0.274596i
$885$		0			0
$886$	−36.2490	−	62.7852i	−0.0409131	−	0.0708636i
$887$		−	1546.15i		−	1.74312i	−0.490289	−	0.871560i	$-0.663109\pi$
$887$		−	1546.15i		−	1.74312i	0.490289	−	0.871560i	$-0.336891\pi$
$888$		0			0
$889$	−605.114	+	1284.59i	−0.680669	+	1.44498i
$890$	48.9235			0.0549702
$891$		0			0
$892$	−128.602	−	74.2485i	−0.144173	−	0.0832382i
$893$	137.238			0.153682
$894$		0			0
$895$	−52.3422	−	30.2198i	−0.0584829	−	0.0337651i
$896$	−366.118	−	527.228i	−0.408614	−	0.588424i
$897$		0			0
$898$	10.4940	−	18.1761i	0.0116860	−	0.0202407i
$899$	340.973	+	196.861i	0.379280	+	0.218977i
$900$		0			0
$901$	229.404	−	132.447i	0.254611	−	0.147000i
$902$	492.724	−	284.474i	0.546257	−	0.315382i
$903$		0			0
$904$	54.4140	−	94.2478i	0.0601925	−	0.104256i
$905$	−568.033			−0.627661
$906$		0			0
$907$	1258.76			1.38782			0.693912	−	0.720060i	$-0.255886\pi$
$907$	1258.76			1.38782			0.693912	+	0.720060i	$0.255886\pi$
$908$	−492.227	+	284.187i	−0.542100	+	0.312981i
$909$		0			0
$910$	90.1711	−	7.53528i	0.0990891	−	0.00828053i
$911$	260.246	+	450.759i	0.285671	+	0.494796i	0.972772	−	0.231766i	$-0.0744504\pi$
$911$	260.246	+	450.759i	0.285671	+	0.494796i	−0.687101	+	0.726562i	$0.741117\pi$
$912$		0			0
$913$	−584.808	+	337.639i	−0.640535	+	0.369813i
$914$	70.3230	+	121.803i	0.0769398	+	0.133264i
$915$		0			0
$916$	1038.51	−	599.583i	1.13374	−	0.654566i
$917$	1596.37	+	751.980i	1.74086	+	0.820043i
$918$		0			0
$919$	425.602	+	737.163i	0.463114	+	0.802136i	0.999114	−	0.0420812i	$-0.0133988\pi$
$919$	425.602	+	737.163i	0.463114	+	0.802136i	−0.536000	+	0.844218i	$0.680065\pi$
$920$			248.525i			0.270136i
$921$		0			0
$922$			93.2189i			0.101105i
$923$	−1062.57	−	613.478i	−1.15122	−	0.664656i
$924$		0			0
$925$	−57.8403	−	100.182i	−0.0625300	−	0.108305i
$926$	140.187	+	242.811i	0.151390	+	0.262214i
$927$		0			0
$928$	186.993	−	323.881i	0.201501	−	0.349010i
$929$	1123.30	+	648.539i	1.20915	+	0.698105i	0.962574	−	0.271018i	$-0.0873604\pi$
$929$	1123.30	+	648.539i	1.20915	+	0.698105i	0.246578	+	0.969123i	$0.420694\pi$
$930$		0			0
$931$	1042.17	+	388.538i	1.11941	+	0.417334i
$932$	−276.774	+	479.387i	−0.296968	+	0.514364i
$933$		0			0
$934$		−	283.979i		−	0.304046i
$935$	−184.379	+	319.354i	−0.197197	+	0.341555i
$936$		0			0
$937$		−	380.172i		−	0.405734i	−0.979206	−	0.202867i	$-0.934974\pi$
$937$		−	380.172i		−	0.405734i	0.979206	−	0.202867i	$-0.0650259\pi$
$938$	1.84067	−	3.90754i	0.00196234	−	0.00416582i
$939$		0			0
$940$	−69.0647			−0.0734731
$941$	−627.989	+	362.570i	−0.667363	+	0.385302i	−0.795077	−	0.606509i	$-0.792570\pi$
$941$	−627.989	+	362.570i	−0.667363	+	0.385302i	0.127714	+	0.991811i	$0.459236\pi$
$942$		0			0
$943$	−1792.53	−	1034.92i	−1.90088	−	1.09747i
$944$		−	496.823i		−	0.526296i
$945$		0			0
$946$	220.818			0.233423
$947$	377.017	−	653.013i	0.398118	−	0.689560i	−0.595376	−	0.803447i	$-0.702997\pi$
$947$	377.017	−	653.013i	0.398118	−	0.689560i	0.993494	+	0.113887i	$0.0363302\pi$
$948$		0			0
$949$	235.403	+	407.729i	0.248053	+	0.429641i
$950$		−	145.352i		−	0.153002i
$951$		0			0
$952$	118.681	−	82.4145i	0.124665	−	0.0865698i
$953$	−259.877			−0.272693			−0.136347	−	0.990661i	$-0.543536\pi$
$953$	−259.877			−0.272693			−0.136347	+	0.990661i	$0.543536\pi$
$954$		0			0
$955$	729.765	+	421.330i	0.764152	+	0.441183i
$956$	109.302			0.114332
$957$		0			0
$958$	−137.705	−	79.5038i	−0.143742	−	0.0829893i
$959$	314.335	−	667.298i	0.327774	−	0.695827i
$960$		0			0
$961$	−300.359	+	520.237i	−0.312548	+	0.541349i
$962$	26.9521	+	15.5608i	0.0280167	+	0.0161755i
$963$		0			0
$964$	−418.119	+	241.401i	−0.433733	+	0.250416i
$965$	46.6113	−	26.9110i	0.0483018	−	0.0278871i
$966$		0			0
$967$	−477.519	+	827.088i	−0.493815	+	0.855313i	−0.999975	−	0.00712679i	$-0.997731\pi$
$967$	−477.519	+	827.088i	−0.493815	+	0.855313i	0.506159	+	0.862440i	$0.331065\pi$
$968$	−707.446			−0.730833
$969$		0			0
$970$	163.983			0.169054
$971$	−644.335	+	372.007i	−0.663579	+	0.383117i	−0.793639	−	0.608389i	$-0.791816\pi$
$971$	−644.335	+	372.007i	−0.663579	+	0.383117i	0.130061	+	0.991506i	$0.458483\pi$
$972$		0			0
$973$	−264.159	+	183.438i	−0.271490	+	0.188528i
$974$	96.8856	+	167.811i	0.0994719	+	0.172290i
$975$		0			0
$976$	393.613	−	227.252i	0.403292	−	0.232841i
$977$	651.392	+	1128.24i	0.666726	+	1.15480i	0.978814	+	0.204750i	$0.0656383\pi$
$977$	651.392	+	1128.24i	0.666726	+	1.15480i	−0.312088	+	0.950053i	$0.601028\pi$
$978$		0			0
$979$	671.928	−	387.938i	0.686341	−	0.396259i
$980$	−524.472	−	195.531i	−0.535175	−	0.199521i
$981$		0			0
$982$	91.0485	+	157.701i	0.0927174	+	0.160591i
$983$			298.437i			0.303598i	0.988411	+	0.151799i	$0.0485067\pi$
$983$			298.437i			0.303598i	−0.988411	+	0.151799i	$0.951493\pi$
$984$		0			0
$985$		−	280.151i		−	0.284417i
$986$	47.2771	+	27.2954i	0.0479484	+	0.0276830i
$987$		0			0
$988$	−478.831	−	829.360i	−0.484647	−	0.839433i
$989$	−401.668	−	695.709i	−0.406135	−	0.703447i
$990$		0			0
$991$	223.032	−	386.303i	0.225057	−	0.389811i	−0.731279	−	0.682078i	$-0.761076\pi$
$991$	223.032	−	386.303i	0.225057	−	0.389811i	0.956337	+	0.292267i	$0.0944097\pi$
$992$	−296.374	−	171.112i	−0.298764	−	0.172492i
$993$		0			0
$994$	−176.770	−	254.558i	−0.177837	−	0.256094i
$995$	−21.7334	+	37.6434i	−0.0218427	+	0.0378326i
$996$		0			0
$997$			499.585i			0.501088i	0.968105	+	0.250544i	$0.0806095\pi$
$997$			499.585i			0.501088i	−0.968105	+	0.250544i	$0.919390\pi$
$998$	−97.4844	+	168.848i	−0.0976798	+	0.169186i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.k.a.10.7		28
3.2	odd	2		63.3.k.a.31.8	✓	28
7.5	odd	6		189.3.t.a.145.8		28
9.2	odd	6		63.3.t.a.52.7	yes	28
9.7	even	3		189.3.t.a.73.8		28
21.2	odd	6		441.3.t.a.166.7		28
21.5	even	6		63.3.t.a.40.7	yes	28
21.11	odd	6		441.3.l.a.391.8		28
21.17	even	6		441.3.l.b.391.8		28
21.20	even	2		441.3.k.b.31.8		28
63.2	odd	6		441.3.k.b.313.8		28
63.11	odd	6		441.3.l.b.97.8		28
63.20	even	6		441.3.t.a.178.7		28
63.38	even	6		441.3.l.a.97.8		28
63.47	even	6		63.3.k.a.61.8	yes	28
63.61	odd	6	inner	189.3.k.a.19.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.8	✓	28	3.2	odd	2
63.3.k.a.61.8	yes	28	63.47	even	6
63.3.t.a.40.7	yes	28	21.5	even	6
63.3.t.a.52.7	yes	28	9.2	odd	6
189.3.k.a.10.7		28	1.1	even	1	trivial
189.3.k.a.19.7		28	63.61	odd	6	inner
189.3.t.a.73.8		28	9.7	even	3
189.3.t.a.145.8		28	7.5	odd	6
441.3.k.b.31.8		28	21.20	even	2
441.3.k.b.313.8		28	63.2	odd	6
441.3.l.a.97.8		28	63.38	even	6
441.3.l.a.391.8		28	21.11	odd	6
441.3.l.b.97.8		28	63.11	odd	6
441.3.l.b.391.8		28	21.17	even	6
441.3.t.a.166.7		28	21.2	odd	6
441.3.t.a.178.7		28	63.20	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.198068 + 0.343064i) q^{2} +(1.92154 + 3.32820i) q^{4} -2.97240i q^{5} +(2.98301 - 6.33259i) q^{7} -3.10693 q^{8} +O(q^{10})\)	\(q+(-0.198068 + 0.343064i) q^{2} +(1.92154 + 3.32820i) q^{4} -2.97240i q^{5} +(2.98301 - 6.33259i) q^{7} -3.10693 q^{8} +(1.01972 + 0.588737i) q^{10} +18.6735 q^{11} +(9.50735 + 5.48907i) q^{13} +(1.58164 + 2.27765i) q^{14} +(-7.07077 + 12.2469i) q^{16} +(-5.75359 - 3.32184i) q^{17} +(-19.6578 + 11.3494i) q^{19} +(9.89274 - 5.71158i) q^{20} +(-3.69862 + 6.40621i) q^{22} +26.9112 q^{23} +16.1648 q^{25} +(-3.76620 + 2.17442i) q^{26} +(26.8081 - 2.24026i) q^{28} +(10.3714 + 17.9638i) q^{29} +(16.4381 - 9.49056i) q^{31} +(-9.01484 - 15.6142i) q^{32} +(2.27920 - 1.31590i) q^{34} +(-18.8230 - 8.86669i) q^{35} +(-3.57815 - 6.19754i) q^{37} -8.99185i q^{38} +9.23502i q^{40} +(-66.6091 - 38.4568i) q^{41} +(-14.9257 - 25.8521i) q^{43} +(35.8819 + 62.1492i) q^{44} +(-5.33024 + 9.23225i) q^{46} +(-5.23602 - 3.02302i) q^{47} +(-31.2033 - 37.7803i) q^{49} +(-3.20174 + 5.54558i) q^{50} +42.1898i q^{52} +(-19.9358 + 34.5297i) q^{53} -55.5051i q^{55} +(-9.26798 + 19.6749i) q^{56} -8.21697 q^{58} +(-30.4254 + 17.5661i) q^{59} +(-27.8338 - 16.0698i) q^{61} +7.51910i q^{62} -49.4240 q^{64} +(16.3157 - 28.2596i) q^{65} +(-0.778839 - 1.34899i) q^{67} -25.5321i q^{68} +(6.77007 - 4.70128i) q^{70} -111.763 q^{71} +(37.1401 + 21.4429i) q^{73} +2.83487 q^{74} +(-75.5465 - 43.6168i) q^{76} +(55.7032 - 118.252i) q^{77} +(-22.9975 + 39.8329i) q^{79} +(36.4028 + 21.0171i) q^{80} +(26.3863 - 15.2341i) q^{82} +(-31.3176 + 18.0812i) q^{83} +(-9.87382 + 17.1020i) q^{85} +11.8252 q^{86} -58.0172 q^{88} +(35.9830 - 20.7748i) q^{89} +(63.1205 - 43.8322i) q^{91} +(51.7108 + 89.5658i) q^{92} +(2.07418 - 1.19753i) q^{94} +(33.7351 + 58.4309i) q^{95} +(120.608 - 69.6332i) q^{97} +(19.1414 - 3.22166i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

Introduction

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