LMFDB - Embedded newform 189.3.n.b.170.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(170,189)]

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([1, 2]))

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

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

chi := DirichletCharacter("189.170");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.n (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:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			170.10
Character	$\chi$	$=$	189.170
Dual form			189.3.n.b.179.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.79169 - 1.61178i) q^{2} +(3.19568 - 5.53509i) q^{4} -5.53294i q^{5} +(3.31972 + 6.16275i) q^{7} -7.70873i q^{8} +O(q^{10})$	\(q+(2.79169 - 1.61178i) q^{2} +(3.19568 - 5.53509i) q^{4} -5.53294i q^{5} +(3.31972 + 6.16275i) q^{7} -7.70873i q^{8} +(-8.91790 - 15.4463i) q^{10} -17.6887i q^{11} +(2.03775 + 3.52949i) q^{13} +(19.2006 + 11.8538i) q^{14} +(0.357941 + 0.619972i) q^{16} +(-14.3348 + 8.27617i) q^{17} +(-3.92096 + 6.79130i) q^{19} +(-30.6253 - 17.6815i) q^{20} +(-28.5103 - 49.3813i) q^{22} +10.0676i q^{23} -5.61347 q^{25} +(11.3775 + 6.56882i) q^{26} +(44.7201 + 1.31926i) q^{28} +(39.9040 + 23.0386i) q^{29} +(-14.8117 + 25.6547i) q^{31} +(28.7023 + 16.5713i) q^{32} +(-26.6788 + 46.2090i) q^{34} +(34.0981 - 18.3678i) q^{35} +(15.5948 - 27.0110i) q^{37} +25.2789i q^{38} -42.6520 q^{40} +(-27.8184 + 16.0609i) q^{41} +(3.35243 - 5.80658i) q^{43} +(-97.9085 - 56.5275i) q^{44} +(16.2267 + 28.1055i) q^{46} +(14.2377 - 8.22012i) q^{47} +(-26.9589 + 40.9172i) q^{49} +(-15.6711 + 9.04769i) q^{50} +26.0480 q^{52} +(-32.5897 + 18.8157i) q^{53} -97.8706 q^{55} +(47.5070 - 25.5908i) q^{56} +148.533 q^{58} +(-82.3206 - 47.5278i) q^{59} +(36.8839 + 63.8848i) q^{61} +95.4932i q^{62} +103.974 q^{64} +(19.5285 - 11.2748i) q^{65} +(6.09545 - 10.5576i) q^{67} +105.792i q^{68} +(65.5865 - 106.236i) q^{70} +20.0140i q^{71} +(-11.4932 - 19.9068i) q^{73} -100.542i q^{74} +(25.0603 + 43.4057i) q^{76} +(109.011 - 58.7215i) q^{77} +(-69.4400 - 120.274i) q^{79} +(3.43027 - 1.98047i) q^{80} +(-51.7735 + 89.6743i) q^{82} +(-13.6928 - 7.90552i) q^{83} +(45.7916 + 79.3134i) q^{85} -21.6136i q^{86} -136.357 q^{88} +(-46.9444 - 27.1034i) q^{89} +(-14.9866 + 24.2750i) q^{91} +(55.7249 + 32.1728i) q^{92} +(26.4981 - 45.8960i) q^{94} +(37.5759 + 21.6944i) q^{95} +(86.1189 - 149.162i) q^{97} +(-9.31136 + 157.680i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 6 q^{2} + 12 q^{4} + 3 q^{7}+O(q^{10}) $ 22 * q + 6 * q^2 + 12 * q^4 + 3 * q^7	$ 22 q + 6 q^{2} + 12 q^{4} + 3 q^{7} + 25 q^{10} - 18 q^{13} + 90 q^{14} + 12 q^{16} - 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 114 q^{25} + 3 q^{26} + 34 q^{28} + 63 q^{29} - 29 q^{31} - 246 q^{32} - 99 q^{34} + 27 q^{35} - 20 q^{37} + 210 q^{40} + 51 q^{41} + 65 q^{43} - 54 q^{44} + 75 q^{46} - 261 q^{47} - 131 q^{49} - 63 q^{50} + 92 q^{52} + 63 q^{53} - 100 q^{55} - 153 q^{56} - 80 q^{58} + 102 q^{59} + 78 q^{61} + 106 q^{64} + 225 q^{65} - 132 q^{67} + 179 q^{70} + q^{73} + 233 q^{76} + 447 q^{77} + 140 q^{79} - 96 q^{80} - 157 q^{82} - 255 q^{83} + 102 q^{85} - 816 q^{88} + 720 q^{89} - 70 q^{91} + 1239 q^{92} + 261 q^{94} - 642 q^{95} + 178 q^{97} - 483 q^{98}+O(q^{100}) $ 22 * q + 6 * q^2 + 12 * q^4 + 3 * q^7 + 25 * q^10 - 18 * q^13 + 90 * q^14 + 12 * q^16 - 6 * q^17 + 3 * q^19 + 39 * q^20 - 59 * q^22 - 114 * q^25 + 3 * q^26 + 34 * q^28 + 63 * q^29 - 29 * q^31 - 246 * q^32 - 99 * q^34 + 27 * q^35 - 20 * q^37 + 210 * q^40 + 51 * q^41 + 65 * q^43 - 54 * q^44 + 75 * q^46 - 261 * q^47 - 131 * q^49 - 63 * q^50 + 92 * q^52 + 63 * q^53 - 100 * q^55 - 153 * q^56 - 80 * q^58 + 102 * q^59 + 78 * q^61 + 106 * q^64 + 225 * q^65 - 132 * q^67 + 179 * q^70 + q^73 + 233 * q^76 + 447 * q^77 + 140 * q^79 - 96 * q^80 - 157 * q^82 - 255 * q^83 + 102 * q^85 - 816 * q^88 + 720 * q^89 - 70 * q^91 + 1239 * q^92 + 261 * q^94 - 642 * q^95 + 178 * q^97 - 483 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	2.79169	−	1.61178i	1.39584	−	0.805891i	0.401890	−	0.915688i	$-0.368353\pi$
$2$	2.79169	−	1.61178i	1.39584	−	0.805891i	0.993954	+	0.109797i	$0.0350200\pi$
$3$		0			0
$3$		0			0
$4$	3.19568	−	5.53509i	0.798921	−	1.38377i
$5$		−	5.53294i		−	1.10659i	−0.832986	−	0.553294i	$-0.813370\pi$
$5$		−	5.53294i		−	1.10659i	0.832986	−	0.553294i	$-0.186630\pi$
$6$		0			0
$7$	3.31972	+	6.16275i	0.474246	+	0.880393i
$7$	3.31972	+	6.16275i	0.474246	+	0.880393i
$8$		−	7.70873i		−	0.963591i
$9$		0			0
$10$	−8.91790	−	15.4463i	−0.891790	−	1.54463i
$11$		−	17.6887i		−	1.60806i	−0.594587	−	0.804032i	$-0.702684\pi$
$11$		−	17.6887i		−	1.60806i	0.594587	−	0.804032i	$-0.297316\pi$
$12$		0			0
$13$	2.03775	+	3.52949i	0.156750	+	0.271499i	0.933695	−	0.358070i	$-0.116565\pi$
$13$	2.03775	+	3.52949i	0.156750	+	0.271499i	−0.776945	+	0.629569i	$0.783232\pi$
$14$	19.2006	+	11.8538i	1.37147	+	0.846701i
$15$		0			0
$16$	0.357941	+	0.619972i	0.0223713	+	0.0387483i
$17$	−14.3348	+	8.27617i	−0.843221	+	0.486834i	−0.858358	−	0.513052i	$-0.828515\pi$
$17$	−14.3348	+	8.27617i	−0.843221	+	0.486834i	0.0151370	+	0.999885i	$0.495182\pi$
$18$		0			0
$19$	−3.92096	+	6.79130i	−0.206366	+	0.357437i	−0.950567	−	0.310519i	$-0.899497\pi$
$19$	−3.92096	+	6.79130i	−0.206366	+	0.357437i	0.744201	+	0.667956i	$0.232830\pi$
$20$	−30.6253	−	17.6815i	−1.53127	−	0.884077i
$21$		0			0
$22$	−28.5103	−	49.3813i	−1.29592	−	2.24461i
$23$			10.0676i			0.437720i	0.975756	+	0.218860i	$0.0702339\pi$
$23$			10.0676i			0.437720i	−0.975756	+	0.218860i	$0.929766\pi$
$24$		0			0
$25$	−5.61347			−0.224539
$26$	11.3775	+	6.56882i	0.437597	+	0.252647i
$27$		0			0
$28$	44.7201	+	1.31926i	1.59715	+	0.0471165i
$29$	39.9040	+	23.0386i	1.37600	+	0.794434i	0.991675	−	0.128764i	$-0.0411011\pi$
$29$	39.9040	+	23.0386i	1.37600	+	0.794434i	0.384324	+	0.923198i	$0.374434\pi$
$30$		0			0
$31$	−14.8117	+	25.6547i	−0.477798	+	0.827570i	−0.999676	−	0.0254498i	$-0.991898\pi$
$31$	−14.8117	+	25.6547i	−0.477798	+	0.827570i	0.521878	+	0.853020i	$0.325232\pi$
$32$	28.7023	+	16.5713i	0.896948	+	0.517853i
$33$		0			0
$34$	−26.6788	+	46.2090i	−0.784670	+	1.35909i
$35$	34.0981	−	18.3678i	0.974233	−	0.524795i
$36$		0			0
$37$	15.5948	−	27.0110i	0.421481	−	0.730026i	−0.574604	−	0.818432i	$-0.694844\pi$
$37$	15.5948	−	27.0110i	0.421481	−	0.730026i	0.996085	+	0.0884059i	$0.0281772\pi$
$38$			25.2789i			0.665235i
$39$		0			0
$40$	−42.6520			−1.06630
$41$	−27.8184	+	16.0609i	−0.678497	+	0.391730i	−0.799288	−	0.600948i	$-0.794790\pi$
$41$	−27.8184	+	16.0609i	−0.678497	+	0.391730i	0.120792	+	0.992678i	$0.461457\pi$
$42$		0			0
$43$	3.35243	−	5.80658i	0.0779635	−	0.135037i	−0.824408	−	0.565997i	$-0.808492\pi$
$43$	3.35243	−	5.80658i	0.0779635	−	0.135037i	0.902371	+	0.430960i	$0.141825\pi$
$44$	−97.9085	−	56.5275i	−2.22519	−	1.28472i
$45$		0			0
$46$	16.2267	+	28.1055i	0.352755	+	0.610990i
$47$	14.2377	−	8.22012i	0.302929	−	0.174896i	−0.340829	−	0.940125i	$-0.610708\pi$
$47$	14.2377	−	8.22012i	0.302929	−	0.174896i	0.643758	+	0.765229i	$0.277374\pi$
$48$		0			0
$49$	−26.9589	+	40.9172i	−0.550182	+	0.835045i
$50$	−15.6711	+	9.04769i	−0.313421	+	0.180954i
$51$		0			0
$52$	26.0480			0.500924
$53$	−32.5897	+	18.8157i	−0.614900	+	0.355013i	−0.774881	−	0.632108i	$-0.782190\pi$
$53$	−32.5897	+	18.8157i	−0.614900	+	0.355013i	0.159981	+	0.987120i	$0.448857\pi$
$54$		0			0
$55$	−97.8706			−1.77946
$56$	47.5070	−	25.5908i	0.848339	−	0.456979i
$57$		0			0
$58$	148.533			2.56091
$59$	−82.3206	−	47.5278i	−1.39527	−	0.805557i	−0.401373	−	0.915915i	$-0.631467\pi$
$59$	−82.3206	−	47.5278i	−1.39527	−	0.805557i	−0.993892	+	0.110358i	$0.964800\pi$
$60$		0			0
$61$	36.8839	+	63.8848i	0.604655	+	1.04729i	0.992106	+	0.125402i	$0.0400222\pi$
$61$	36.8839	+	63.8848i	0.604655	+	1.04729i	−0.387451	+	0.921890i	$0.626644\pi$
$62$			95.4932i			1.54021i
$63$		0			0
$64$	103.974			1.62459
$65$	19.5285	−	11.2748i	0.300438	−	0.173458i
$66$		0			0
$67$	6.09545	−	10.5576i	0.0909769	−	0.157577i	−0.816946	−	0.576715i	$-0.804334\pi$
$67$	6.09545	−	10.5576i	0.0909769	−	0.157577i	0.907922	+	0.419138i	$0.137668\pi$
$68$			105.792i			1.55577i
$69$		0			0
$70$	65.5865	−	106.236i	0.936950	−	1.51766i
$71$			20.0140i			0.281887i	0.990018	+	0.140944i	$0.0450136\pi$
$71$			20.0140i			0.281887i	−0.990018	+	0.140944i	$0.954986\pi$
$72$		0			0
$73$	−11.4932	−	19.9068i	−0.157441	−	0.272696i	0.776504	−	0.630112i	$-0.216991\pi$
$73$	−11.4932	−	19.9068i	−0.157441	−	0.272696i	−0.933945	+	0.357416i	$0.883658\pi$
$74$		−	100.542i		−	1.35867i
$75$		0			0
$76$	25.0603	+	43.4057i	0.329741	+	0.571128i
$77$	109.011	−	58.7215i	1.41573	−	0.762617i
$78$		0			0
$79$	−69.4400	−	120.274i	−0.878988	−	1.52245i	−0.852453	−	0.522804i	$-0.824886\pi$
$79$	−69.4400	−	120.274i	−0.878988	−	1.52245i	−0.0265350	−	0.999648i	$-0.508447\pi$
$80$	3.43027	−	1.98047i	0.0428784	−	0.0247559i
$81$		0			0
$82$	−51.7735	+	89.6743i	−0.631384	+	1.09359i
$83$	−13.6928	−	7.90552i	−0.164973	−	0.0952472i	0.415240	−	0.909712i	$-0.363697\pi$
$83$	−13.6928	−	7.90552i	−0.164973	−	0.0952472i	−0.580213	+	0.814465i	$0.697031\pi$
$84$		0			0
$85$	45.7916	+	79.3134i	0.538725	+	0.933099i
$86$		−	21.6136i		−	0.251320i
$87$		0			0
$88$	−136.357			−1.54952
$89$	−46.9444	−	27.1034i	−0.527466	−	0.304532i	0.212518	−	0.977157i	$-0.431834\pi$
$89$	−46.9444	−	27.1034i	−0.527466	−	0.304532i	−0.739984	+	0.672625i	$0.765167\pi$
$90$		0			0
$91$	−14.9866	+	24.2750i	−0.164688	+	0.266759i
$92$	55.7249	+	32.1728i	0.605705	+	0.349704i
$93$		0			0
$94$	26.4981	−	45.8960i	0.281894	−	0.488256i
$95$	37.5759	+	21.6944i	0.395536	+	0.228363i
$96$		0			0
$97$	86.1189	−	149.162i	0.887823	−	1.53776i	0.0453802	−	0.998970i	$-0.485550\pi$
$97$	86.1189	−	149.162i	0.887823	−	1.53776i	0.842443	−	0.538785i	$-0.181117\pi$
$98$	−9.31136	+	157.680i	−0.0950139	+	1.60898i
$99$		0			0
$100$	−17.9389	+	31.0710i	−0.179389	+	0.310710i
$101$			17.3176i			0.171461i	0.996318	+	0.0857307i	$0.0273225\pi$
$101$			17.3176i			0.171461i	−0.996318	+	0.0857307i	$0.972678\pi$
$102$		0			0
$103$	−27.5997			−0.267958			−0.133979	−	0.990984i	$-0.542776\pi$
$103$	−27.5997			−0.267958			−0.133979	+	0.990984i	$0.542776\pi$
$104$	27.2079	−	15.7085i	0.261614	−	0.151043i
$105$		0			0
$106$	−60.6535	+	105.055i	−0.572203	+	0.991085i
$107$	−106.089	−	61.2506i	−0.991488	−	0.572436i	−0.0857691	−	0.996315i	$-0.527335\pi$
$107$	−106.089	−	61.2506i	−0.991488	−	0.572436i	−0.905719	+	0.423879i	$0.860668\pi$
$108$		0			0
$109$	−17.0725	−	29.5705i	−0.156629	−	0.271289i	0.777022	−	0.629473i	$-0.216729\pi$
$109$	−17.0725	−	29.5705i	−0.156629	−	0.271289i	−0.933651	+	0.358184i	$0.883396\pi$
$110$	−273.224	+	157.746i	−2.48386	+	1.43405i
$111$		0			0
$112$	−2.63247	+	4.26403i	−0.0235042	+	0.0380717i
$113$	−67.4250	+	38.9278i	−0.596681	+	0.344494i	−0.767735	−	0.640768i	$-0.778616\pi$
$113$	−67.4250	+	38.9278i	−0.596681	+	0.344494i	0.171054	+	0.985262i	$0.445283\pi$
$114$		0			0
$115$	55.7033			0.484377
$116$	255.041	−	147.248i	2.19863	−	1.26938i
$117$		0			0
$118$	−306.418			−2.59676
$119$	−98.5913	−	60.8669i	−0.828498	−	0.511487i
$120$		0			0
$121$	−191.890			−1.58587
$122$	205.937	+	118.898i	1.68801	+	0.974572i
$123$		0			0
$124$	94.6673	+	163.968i	0.763446	+	1.32233i
$125$		−	107.265i		−	0.858117i
$126$		0			0
$127$	14.0742			0.110821			0.0554103	−	0.998464i	$-0.482353\pi$
$127$	14.0742			0.110821			0.0554103	+	0.998464i	$0.482353\pi$
$128$	175.453	−	101.298i	1.37073	−	0.791390i
$129$		0			0
$130$	36.3449	−	62.9512i	0.279576	−	0.484240i
$131$			22.2699i			0.169999i	0.996381	+	0.0849995i	$0.0270889\pi$
$131$			22.2699i			0.169999i	−0.996381	+	0.0849995i	$0.972911\pi$
$132$		0			0
$133$	−54.8695	−	1.61868i	−0.412553	−	0.0121705i
$134$		−	39.2982i		−	0.293270i
$135$		0			0
$136$	63.7988	+	110.503i	0.469109	+	0.812520i
$137$		−	37.0861i		−	0.270701i	−0.990798	−	0.135351i	$-0.956784\pi$
$137$		−	37.0861i		−	0.270701i	0.990798	−	0.135351i	$-0.0432161\pi$
$138$		0			0
$139$	70.5358	+	122.172i	0.507451	+	0.878932i	0.999963	+	0.00862568i	$0.00274567\pi$
$139$	70.5358	+	122.172i	0.507451	+	0.878932i	−0.492511	+	0.870306i	$0.663921\pi$
$140$	7.29941	−	247.434i	0.0521386	−	1.76739i
$141$		0			0
$142$	32.2582	+	55.8728i	0.227170	+	0.393471i
$143$	62.4320	−	36.0451i	0.436587	−	0.252064i
$144$		0			0
$145$	127.471	−	220.787i	0.879111	−	1.52267i
$146$	−64.1710	−	37.0491i	−0.439527	−	0.253761i
$147$		0			0
$148$	−99.6720	−	172.637i	−0.673459	−	1.16647i
$149$			115.718i			0.776631i	0.921526	+	0.388315i	$0.126943\pi$
$149$			115.718i			0.776631i	−0.921526	+	0.388315i	$0.873057\pi$
$150$		0			0
$151$	−150.316			−0.995469			−0.497734	−	0.867330i	$-0.665835\pi$
$151$	−150.316			−0.995469			−0.497734	+	0.867330i	$0.665835\pi$
$152$	52.3523	+	30.2256i	0.344423	+	0.198853i
$153$		0			0
$154$	209.678	−	339.634i	1.36155	−	2.20542i
$155$	141.946	+	81.9525i	0.915780	+	0.528726i
$156$		0			0
$157$	137.028	−	237.339i	0.872788	−	1.51171i	0.0136883	−	0.999906i	$-0.495643\pi$
$157$	137.028	−	237.339i	0.872788	−	1.51171i	0.859100	−	0.511808i	$-0.171024\pi$
$158$	−387.710	−	223.844i	−2.45386	−	1.41674i
$159$		0			0
$160$	91.6881	−	158.808i	0.573051	−	0.992553i
$161$	−62.0439	+	33.4215i	−0.385366	+	0.207587i
$162$		0			0
$163$	−111.326	+	192.822i	−0.682981	+	1.18296i	0.291085	+	0.956697i	$0.405984\pi$
$163$	−111.326	+	192.822i	−0.682981	+	1.18296i	−0.974067	+	0.226261i	$0.927350\pi$
$164$			205.303i			1.25185i
$165$		0			0
$166$	−50.9679			−0.307035
$167$	−62.7878	+	36.2506i	−0.375975	+	0.217069i	−0.676066	−	0.736841i	$-0.736316\pi$
$167$	−62.7878	+	36.2506i	−0.375975	+	0.217069i	0.300091	+	0.953911i	$0.402983\pi$
$168$		0			0
$169$	76.1951	−	131.974i	0.450859	−	0.780910i
$170$	255.672	+	147.612i	1.50395	+	0.868307i
$171$		0			0
$172$	−21.4266	−	37.1120i	−0.124573	−	0.215768i
$173$	182.881	−	105.587i	1.05712	−	0.610328i	0.132485	−	0.991185i	$-0.457704\pi$
$173$	182.881	−	105.587i	1.05712	−	0.610328i	0.924634	+	0.380857i	$0.124371\pi$
$174$		0			0
$175$	−18.6351	−	34.5944i	−0.106487	−	0.197682i
$176$	10.9665	−	6.33151i	0.0623096	−	0.0359745i
$177$		0			0
$178$	−174.739			−0.981680
$179$	69.5967	−	40.1817i	0.388809	−	0.224479i	−0.292835	−	0.956163i	$-0.594599\pi$
$179$	69.5967	−	40.1817i	0.388809	−	0.224479i	0.681644	+	0.731684i	$0.261265\pi$
$180$		0			0
$181$	122.944			0.679250			0.339625	−	0.940561i	$-0.389700\pi$
$181$	122.944			0.679250			0.339625	+	0.940561i	$0.389700\pi$
$182$	−2.71178	+	91.9235i	−0.0148999	+	0.505074i
$183$		0			0
$184$	77.6082			0.421784
$185$	−149.450	−	86.2850i	−0.807838	−	0.466406i
$186$		0			0
$187$	146.395	+	253.563i	0.782859	+	1.35595i
$188$		−	105.076i		−	0.558913i
$189$		0			0
$190$	139.867			0.736141
$191$	−307.863	+	177.745i	−1.61185	+	0.930602i	−0.622909	+	0.782294i	$0.714049\pi$
$191$	−307.863	+	177.745i	−1.61185	+	0.930602i	−0.988941	+	0.148308i	$0.952617\pi$
$192$		0			0
$193$	19.8296	−	34.3459i	0.102744	−	0.177958i	−0.810070	−	0.586333i	$-0.800571\pi$
$193$	19.8296	−	34.3459i	0.102744	−	0.177958i	0.912814	+	0.408375i	$0.133904\pi$
$194$		−	555.219i		−	2.86196i
$195$		0			0
$196$	140.328	+	279.978i	0.715959	+	1.42846i
$197$		−	130.634i		−	0.663119i	−0.943434	−	0.331559i	$-0.892425\pi$
$197$		−	130.634i		−	0.663119i	0.943434	−	0.331559i	$-0.107575\pi$
$198$		0			0
$199$	108.521	+	187.964i	0.545331	+	0.944540i	0.998586	+	0.0531596i	$0.0169292\pi$
$199$	108.521	+	187.964i	0.545331	+	0.944540i	−0.453255	+	0.891381i	$0.649737\pi$
$200$			43.2727i			0.216364i
$201$		0			0
$202$	27.9122	+	48.3454i	0.138179	+	0.239333i
$203$	−9.51093	+	322.400i	−0.0468519	+	1.58818i
$204$		0			0
$205$	88.8643	+	153.917i	0.433484	+	0.750817i
$206$	−77.0498	+	44.4847i	−0.374028	+	0.215945i
$207$		0			0
$208$	−1.45879	+	2.52670i	−0.00701341	+	0.0121476i
$209$	120.129	+	69.3566i	0.574781	+	0.331850i
$210$		0			0
$211$	54.6113	+	94.5895i	0.258821	+	0.448292i	0.965926	−	0.258817i	$-0.0833326\pi$
$211$	54.6113	+	94.5895i	0.258821	+	0.448292i	−0.707105	+	0.707108i	$0.749999\pi$
$212$			240.516i			1.13451i
$213$		0			0
$214$	−394.891			−1.84528
$215$	−32.1275	−	18.5488i	−0.149430	−	0.0862736i
$216$		0			0
$217$	−207.274	−	6.11468i	−0.955180	−	0.0281782i
$218$	−95.3224	−	55.0344i	−0.437259	−	0.252451i
$219$		0			0
$220$	−312.763	+	541.722i	−1.42165	+	2.46237i
$221$	−58.4213	−	33.7295i	−0.264350	−	0.152622i
$222$		0			0
$223$	−93.3685	+	161.719i	−0.418693	+	0.725197i	−0.995808	−	0.0914653i	$-0.970845\pi$
$223$	−93.3685	+	161.719i	−0.418693	+	0.725197i	0.577115	+	0.816663i	$0.304178\pi$
$224$	−6.84107	+	231.897i	−0.0305405	+	1.03526i
$225$		0			0
$226$	−125.486	+	217.349i	−0.555249	+	0.961720i
$227$		−	202.548i		−	0.892280i	−0.894963	−	0.446140i	$-0.852798\pi$
$227$		−	202.548i		−	0.892280i	0.894963	−	0.446140i	$-0.147202\pi$
$228$		0			0
$229$	−79.2731			−0.346171			−0.173085	−	0.984907i	$-0.555374\pi$
$229$	−79.2731			−0.346171			−0.173085	+	0.984907i	$0.555374\pi$
$230$	155.506	−	89.7816i	0.676114	−	0.390355i
$231$		0			0
$232$	177.598	−	307.609i	0.765509	−	1.32590i
$233$	282.430	+	163.061i	1.21215	+	0.699833i	0.963227	−	0.268690i	$-0.0865909\pi$
$233$	282.430	+	163.061i	1.21215	+	0.699833i	0.248921	+	0.968524i	$0.419924\pi$
$234$		0			0
$235$	−45.4814	−	78.7762i	−0.193538	−	0.335218i
$236$	−526.142	+	303.768i	−2.22941	+	1.28715i
$237$		0			0
$238$	−373.340	−	11.0137i	−1.56866	−	0.0462761i
$239$	210.918	−	121.774i	0.882503	−	0.509514i	0.0110203	−	0.999939i	$-0.496492\pi$
$239$	210.918	−	121.774i	0.882503	−	0.509514i	0.871483	+	0.490426i	$0.163159\pi$
$240$		0			0
$241$	28.3405			0.117595			0.0587976	−	0.998270i	$-0.481273\pi$
$241$	28.3405			0.117595			0.0587976	+	0.998270i	$0.481273\pi$
$242$	−535.697	+	309.285i	−2.21362	+	1.27804i
$243$		0			0
$244$	471.478			1.93229
$245$	226.392	+	149.162i	0.924051	+	0.608826i
$246$		0			0
$247$	−31.9597			−0.129392
$248$	197.765	+	114.180i	0.797440	+	0.460402i
$249$		0			0
$250$	−172.887	−	299.449i	−0.691549	−	1.19780i
$251$			140.132i			0.558294i	0.960248	+	0.279147i	$0.0900516\pi$
$251$			140.132i			0.558294i	−0.960248	+	0.279147i	$0.909948\pi$
$252$		0			0
$253$	178.082			0.703882
$254$	39.2909	−	22.6846i	0.154688	−	0.0893094i
$255$		0			0
$256$	118.593	−	205.409i	0.463253	−	0.802378i
$257$			110.672i			0.430629i	0.976545	+	0.215315i	$0.0690777\pi$
$257$			110.672i			0.430629i	−0.976545	+	0.215315i	$0.930922\pi$
$258$		0			0
$259$	218.232	+	6.43794i	0.842595	+	0.0248569i
$260$		−	144.122i		−	0.554316i
$261$		0			0
$262$	35.8942	+	62.1705i	0.137001	+	0.237292i
$263$			49.3684i			0.187713i	0.995586	+	0.0938563i	$0.0299194\pi$
$263$			49.3684i			0.187713i	−0.995586	+	0.0938563i	$0.970081\pi$
$264$		0			0
$265$	104.106	+	180.317i	0.392853	+	0.680441i
$266$	−155.788	+	83.9189i	−0.585668	+	0.315485i
$267$		0			0
$268$	−38.9583	−	67.4777i	−0.145367	−	0.251783i
$269$	−162.040	+	93.5538i	−0.602379	+	0.347784i	−0.769977	−	0.638072i	$-0.779732\pi$
$269$	−162.040	+	93.5538i	−0.602379	+	0.347784i	0.167598	+	0.985855i	$0.446399\pi$
$270$		0			0
$271$	108.146	−	187.315i	0.399064	−	0.691199i	−0.594547	−	0.804061i	$-0.702668\pi$
$271$	108.146	−	187.315i	0.399064	−	0.691199i	0.993611	+	0.112862i	$0.0360018\pi$
$272$	−10.2620	−	5.92476i	−0.0377279	−	0.0217822i
$273$		0			0
$274$	−59.7747	−	103.533i	−0.218156	−	0.377857i
$275$			99.2950i			0.361073i
$276$		0			0
$277$	78.1235			0.282034			0.141017	−	0.990007i	$-0.454963\pi$
$277$	78.1235			0.282034			0.141017	+	0.990007i	$0.454963\pi$
$278$	393.828	+	227.377i	1.41665	+	0.817901i
$279$		0			0
$280$	−141.593	−	262.853i	−0.505688	−	0.938762i
$281$	385.051	+	222.309i	1.37029	+	0.791135i	0.990964	−	0.134129i	$-0.0428237\pi$
$281$	385.051	+	222.309i	1.37029	+	0.791135i	0.379323	+	0.925264i	$0.376157\pi$
$282$		0			0
$283$	64.2122	−	111.219i	0.226898	−	0.392999i	−0.729989	−	0.683459i	$-0.760475\pi$
$283$	64.2122	−	111.219i	0.226898	−	0.392999i	0.956887	+	0.290460i	$0.0938082\pi$
$284$	110.779	+	63.9584i	0.390068	+	0.225206i
$285$		0			0
$286$	116.194	−	201.254i	0.406272	−	0.703684i
$287$	−191.329	−	118.120i	−0.666650	−	0.411567i
$288$		0			0
$289$	−7.50994	+	13.0076i	−0.0259859	+	0.0450090i
$290$		−	821.823i		−	2.83387i
$291$		0			0
$292$	−146.915			−0.503133
$293$	42.6510	−	24.6246i	0.145567	−	0.0840429i	−0.425448	−	0.904983i	$-0.639883\pi$
$293$	42.6510	−	24.6246i	0.145567	−	0.0840429i	0.571014	+	0.820940i	$0.306550\pi$
$294$		0			0
$295$	−262.969	+	455.475i	−0.891420	+	1.54398i
$296$	−208.220	−	120.216i	−0.703446	−	0.406135i
$297$		0			0
$298$	186.512	+	323.049i	0.625880	+	1.08406i
$299$	−35.5334	+	20.5152i	−0.118841	+	0.0686127i
$300$		0			0
$301$	46.9136	+	1.38397i	0.155859	+	0.00459792i
$302$	−419.635	+	242.276i	−1.38952	+	0.802239i
$303$		0			0
$304$	−5.61389			−0.0184667
$305$	353.471	−	204.077i	1.15892	−	0.669104i
$306$		0			0
$307$	−387.296			−1.26155			−0.630776	−	0.775965i	$-0.717263\pi$
$307$	−387.296			−1.26155			−0.630776	+	0.775965i	$0.717263\pi$
$308$	23.3360	−	791.041i	0.0757664	−	2.56831i
$309$		0			0
$310$	528.358			1.70438
$311$	87.5525	+	50.5485i	0.281519	+	0.162535i	0.634111	−	0.773242i	$-0.281366\pi$
$311$	87.5525	+	50.5485i	0.281519	+	0.162535i	−0.352592	+	0.935777i	$0.614700\pi$
$312$		0			0
$313$	−182.396	−	315.918i	−0.582733	−	1.00932i	−0.995154	−	0.0983303i	$-0.968650\pi$
$313$	−182.396	−	315.918i	−0.582733	−	1.00932i	0.412420	−	0.910994i	$-0.364684\pi$
$314$		−	883.436i		−	2.81349i
$315$		0			0
$316$	−887.634			−2.80897
$317$	−28.7096	+	16.5755i	−0.0905665	+	0.0522886i	−0.544599	−	0.838696i	$-0.683318\pi$
$317$	−28.7096	+	16.5755i	−0.0905665	+	0.0522886i	0.454033	+	0.890985i	$0.349985\pi$
$318$		0			0
$319$	407.522	−	705.849i	1.27750	−	2.21269i
$320$		−	575.281i		−	1.79775i
$321$		0			0
$322$	−119.339	+	193.304i	−0.370618	+	0.600322i
$323$		−	129.802i		−	0.401864i
$324$		0			0
$325$	−11.4388	−	19.8127i	−0.0351965	−	0.0609621i
$326$			717.733i			2.20163i
$327$		0			0
$328$	123.809	+	214.444i	0.377468	+	0.653794i
$329$	97.9235	+	60.4546i	0.297640	+	0.183753i
$330$		0			0
$331$	45.2538	+	78.3820i	0.136719	+	0.236804i	0.926253	−	0.376903i	$-0.123011\pi$
$331$	45.2538	+	78.3820i	0.136719	+	0.236804i	−0.789534	+	0.613707i	$0.789678\pi$
$332$	−87.5154	+	50.5271i	−0.263601	+	0.152190i
$333$		0			0
$334$	−116.856	+	202.401i	−0.349869	+	0.605990i
$335$	−58.4148	−	33.7258i	−0.174373	−	0.100674i
$336$		0			0
$337$	216.839	+	375.576i	0.643438	+	1.11447i	0.984660	+	0.174485i	$0.0558261\pi$
$337$	216.839	+	375.576i	0.643438	+	1.11447i	−0.341221	+	0.939983i	$0.610841\pi$
$338$		−	491.240i		−	1.45337i
$339$		0			0
$340$	585.342			1.72159
$341$	453.798	+	262.000i	1.33079	+	0.768329i
$342$		0			0
$343$	−341.658	−	30.3076i	−0.996089	−	0.0883603i
$344$	−44.7614	−	25.8430i	−0.130120	−	0.0751250i
$345$		0			0
$346$	340.365	−	589.530i	0.983715	−	1.70384i
$347$	10.1281	+	5.84745i	0.0291876	+	0.0168514i	0.514523	−	0.857477i	$-0.327969\pi$
$347$	10.1281	+	5.84745i	0.0291876	+	0.0168514i	−0.485335	+	0.874328i	$0.661302\pi$
$348$		0			0
$349$	91.7075	−	158.842i	0.262772	−	0.455135i	−0.704205	−	0.709996i	$-0.748697\pi$
$349$	91.7075	−	158.842i	0.262772	−	0.455135i	0.966978	+	0.254862i	$0.0820299\pi$
$350$	−107.782	−	66.5410i	−0.307949	−	0.190117i
$351$		0			0
$352$	293.125	−	507.707i	0.832741	−	1.44235i
$353$			68.0833i			0.192871i	0.995339	+	0.0964353i	$0.0307441\pi$
$353$			68.0833i			0.192871i	−0.995339	+	0.0964353i	$0.969256\pi$
$354$		0			0
$355$	110.736			0.311933
$356$	−300.039	+	173.228i	−0.842807	+	0.486595i
$357$		0			0
$358$	129.528	−	224.350i	0.361811	−	0.626675i
$359$	−386.169	−	222.955i	−1.07568	−	0.621044i	−0.145952	−	0.989292i	$-0.546625\pi$
$359$	−386.169	−	222.955i	−1.07568	−	0.621044i	−0.929728	+	0.368247i	$0.879958\pi$
$360$		0			0
$361$	149.752	+	259.378i	0.414826	+	0.718500i
$362$	343.222	−	198.159i	0.948127	−	0.547401i
$363$		0			0
$364$	86.4721	+	160.527i	0.237561	+	0.441009i
$365$	−110.143	+	63.5913i	−0.301763	+	0.174223i
$366$		0			0
$367$	126.685			0.345190			0.172595	−	0.984993i	$-0.444785\pi$
$367$	126.685			0.345190			0.172595	+	0.984993i	$0.444785\pi$
$368$	−6.24161	+	3.60360i	−0.0169609	+	0.00979238i
$369$		0			0
$370$	−556.291			−1.50349
$371$	−224.145	−	138.379i	−0.604164	−	0.372990i
$372$		0			0
$373$	−612.329			−1.64163			−0.820817	−	0.571192i	$-0.806481\pi$
$373$	−612.329			−1.64163			−0.820817	+	0.571192i	$0.806481\pi$
$374$	817.377	+	471.913i	2.18550	+	1.26180i
$375$		0			0
$376$	−63.3667	−	109.754i	−0.168528	−	0.291900i
$377$			187.787i			0.498110i
$378$		0			0
$379$	410.847			1.08403			0.542015	−	0.840369i	$-0.317662\pi$
$379$	410.847			1.08403			0.542015	+	0.840369i	$0.317662\pi$
$380$	240.161	−	138.657i	0.632003	−	0.364887i
$381$		0			0
$382$	−572.973	+	992.418i	−1.49993	+	2.59795i
$383$			220.118i			0.574720i	0.957823	+	0.287360i	$0.0927775\pi$
$383$			220.118i			0.574720i	−0.957823	+	0.287360i	$0.907222\pi$
$384$		0			0
$385$	−324.903	−	603.152i	−0.843903	−	1.56663i
$386$		−	127.844i		−	0.331203i
$387$		0			0
$388$	−550.417	−	953.351i	−1.41860	−	2.45709i
$389$		−	172.259i		−	0.442824i	−0.975180	−	0.221412i	$-0.928933\pi$
$389$		−	172.259i		−	0.442824i	0.975180	−	0.221412i	$-0.0710666\pi$
$390$		0			0
$391$	−83.3209	−	144.316i	−0.213097	−	0.369095i
$392$	315.420	+	207.819i	0.804642	+	0.530151i
$393$		0			0
$394$	−210.554	−	364.691i	−0.534402	−	0.925611i
$395$	−665.468	+	384.208i	−1.68473	+	0.972678i
$396$		0			0
$397$	−185.521	+	321.332i	−0.467308	+	0.809401i	−0.999302	−	0.0373470i	$-0.988109\pi$
$397$	−185.521	+	321.332i	−0.467308	+	0.809401i	0.531995	+	0.846748i	$0.321443\pi$
$398$	605.912	+	349.824i	1.52239	+	0.878954i
$399$		0			0
$400$	−2.00929	−	3.48020i	−0.00502323	−	0.00870049i
$401$		−	299.417i		−	0.746675i	−0.927696	−	0.373338i	$-0.878213\pi$
$401$		−	299.417i		−	0.746675i	0.927696	−	0.373338i	$-0.121787\pi$
$402$		0			0
$403$	−120.730			−0.299579
$404$	95.8544	+	55.3416i	0.237263	+	0.136984i
$405$		0			0
$406$	493.087	+	915.370i	1.21450	+	2.25460i
$407$	−477.788	−	275.851i	−1.17393	−	0.677767i
$408$		0			0
$409$	187.201	−	324.241i	0.457703	−	0.792766i	−0.541136	−	0.840935i	$-0.682005\pi$
$409$	187.201	−	324.241i	0.457703	−	0.792766i	0.998839	+	0.0481696i	$0.0153388\pi$
$410$	496.163	+	286.460i	1.21015	+	0.698682i
$411$		0			0
$412$	−88.2000	+	152.767i	−0.214078	+	0.370793i
$413$	19.6208	−	665.100i	0.0475079	−	1.61041i
$414$		0			0
$415$	−43.7408	+	75.7613i	−0.105399	+	0.182557i
$416$			135.073i			0.324694i
$417$		0			0
$418$	447.151			1.06974
$419$	−350.317	+	202.256i	−0.836080	+	0.482711i	−0.855930	−	0.517092i	$-0.827014\pi$
$419$	−350.317	+	202.256i	−0.836080	+	0.482711i	0.0198501	+	0.999803i	$0.493681\pi$
$420$		0			0
$421$	−231.002	+	400.107i	−0.548698	+	0.950372i	0.449666	+	0.893197i	$0.351543\pi$
$421$	−231.002	+	400.107i	−0.548698	+	0.950372i	−0.998364	+	0.0571757i	$0.981790\pi$
$422$	304.916	+	176.043i	0.722549	+	0.417164i
$423$		0			0
$424$	145.045	+	251.225i	0.342087	+	0.592512i
$425$	80.4677	−	46.4580i	0.189336	−	0.109313i
$426$		0			0
$427$	−271.262	+	439.386i	−0.635274	+	1.02901i
$428$	−678.055	+	391.475i	−1.58424	+	0.914662i
$429$		0			0
$430$	−119.587			−0.278108
$431$	197.559	−	114.061i	0.458374	−	0.264643i	−0.252986	−	0.967470i	$-0.581413\pi$
$431$	197.559	−	114.061i	0.458374	−	0.264643i	0.711360	+	0.702827i	$0.248079\pi$
$432$		0			0
$433$	777.626			1.79590			0.897951	−	0.440095i	$-0.145055\pi$
$433$	777.626			1.79590			0.897951	+	0.440095i	$0.145055\pi$
$434$	−588.500	+	317.010i	−1.35599	+	0.730439i
$435$		0			0
$436$	−218.234			−0.500536
$437$	−68.3719	−	39.4745i	−0.156457	−	0.0903307i
$438$		0			0
$439$	−34.4006	−	59.5836i	−0.0783612	−	0.135726i	0.824182	−	0.566325i	$-0.191635\pi$
$439$	−34.4006	−	59.5836i	−0.0783612	−	0.135726i	−0.902543	+	0.430600i	$0.858302\pi$
$440$			754.458i			1.71468i
$441$		0			0
$442$	−217.459			−0.491988
$443$	180.419	−	104.165i	0.407267	−	0.235136i	−0.282348	−	0.959312i	$-0.591113\pi$
$443$	180.419	−	104.165i	0.407267	−	0.235136i	0.689615	+	0.724176i	$0.257780\pi$
$444$		0			0
$445$	−149.961	+	259.741i	−0.336992	+	0.583687i
$446$			601.959i			1.34968i
$447$		0			0
$448$	345.164	+	640.765i	0.770455	+	1.43028i
$449$			259.045i			0.576937i	0.957489	+	0.288469i	$0.0931461\pi$
$449$			259.045i			0.576937i	−0.957489	+	0.288469i	$0.906854\pi$
$450$		0			0
$451$	284.097	+	492.071i	0.629927	+	1.09107i
$452$			497.604i			1.10089i
$453$		0			0
$454$	−326.463	−	565.450i	−0.719081	−	1.24548i
$455$	134.312	+	82.9199i	0.295192	+	0.182242i
$456$		0			0
$457$	−79.7186	−	138.077i	−0.174439	−	0.302137i	0.765528	−	0.643403i	$-0.222478\pi$
$457$	−79.7186	−	138.077i	−0.174439	−	0.302137i	−0.939967	+	0.341265i	$0.889144\pi$
$458$	−221.306	+	127.771i	−0.483201	+	0.278976i
$459$		0			0
$460$	178.010	−	308.323i	0.386979	−	0.670267i
$461$	176.910	+	102.139i	0.383752	+	0.221559i	0.679449	−	0.733722i	$-0.262219\pi$
$461$	176.910	+	102.139i	0.383752	+	0.221559i	−0.295697	+	0.955282i	$0.595552\pi$
$462$		0			0
$463$	−381.105	−	660.092i	−0.823120	−	1.42569i	−0.903348	−	0.428909i	$-0.858898\pi$
$463$	−381.105	−	660.092i	−0.823120	−	1.42569i	0.0802276	−	0.996777i	$-0.474435\pi$
$464$			32.9858i			0.0710901i
$465$		0			0
$466$	1051.28			2.25596
$467$	−462.046	−	266.762i	−0.989391	−	0.571225i	−0.0842988	−	0.996441i	$-0.526865\pi$
$467$	−462.046	−	266.762i	−0.989391	−	0.571225i	−0.905092	+	0.425215i	$0.860198\pi$
$468$		0			0
$469$	85.2993	+	2.51636i	0.181875	+	0.00536538i
$470$	−253.940	−	146.612i	−0.540298	−	0.311941i
$471$		0			0
$472$	−366.379	+	634.588i	−0.776227	+	1.34447i
$473$	−102.711	−	59.3001i	−0.217148	−	0.125370i
$474$		0			0
$475$	22.0102	−	38.1228i	0.0463372	−	0.0802584i
$476$	−651.970	+	351.200i	−1.36969	+	0.737815i
$477$		0			0
$478$	392.545	−	679.909i	0.821225	−	1.42240i
$479$		−	604.516i		−	1.26204i	−0.775768	−	0.631019i	$-0.782637\pi$
$479$		−	604.516i		−	1.26204i	0.775768	−	0.631019i	$-0.217363\pi$
$480$		0			0
$481$	127.113			0.264268
$482$	79.1177	−	45.6787i	0.164145	−	0.0947690i
$483$		0			0
$484$	−613.220	+	1062.13i	−1.26698	+	2.19448i
$485$	−825.306	−	476.491i	−1.70166	−	0.982455i
$486$		0			0
$487$	−78.1017	−	135.276i	−0.160373	−	0.277774i	0.774629	−	0.632415i	$-0.217936\pi$
$487$	−78.1017	−	135.276i	−0.160373	−	0.277774i	−0.935002	+	0.354641i	$0.884603\pi$
$488$	492.471	−	284.328i	1.00916	−	0.582640i
$489$		0			0
$490$	872.434	+	51.5192i	1.78048	+	0.105141i
$491$	346.903	−	200.285i	0.706523	−	0.407911i	−0.103249	−	0.994656i	$-0.532924\pi$
$491$	346.903	−	200.285i	0.706523	−	0.407911i	0.809772	+	0.586744i	$0.199591\pi$
$492$		0			0
$493$	−762.685			−1.54703
$494$	−89.2216	+	51.5121i	−0.180611	+	0.104276i
$495$		0			0
$496$	−21.2069			−0.0427559
$497$	−123.341	+	66.4408i	−0.248171	+	0.133684i
$498$		0			0
$499$	−122.289			−0.245068			−0.122534	−	0.992464i	$-0.539102\pi$
$499$	−122.289			−0.245068			−0.122534	+	0.992464i	$0.539102\pi$
$500$	−593.719	−	342.784i	−1.18744	−	0.685567i
$501$		0			0
$502$	225.862	+	391.204i	0.449924	+	0.779291i
$503$			786.814i			1.56424i	0.623126	+	0.782121i	$0.285862\pi$
$503$			786.814i			1.56424i	−0.623126	+	0.782121i	$0.714138\pi$
$504$		0			0
$505$	95.8173			0.189737
$506$	497.150	−	287.030i	0.982510	−	0.567252i
$507$		0			0
$508$	44.9768	−	77.9021i	0.0885370	−	0.153351i
$509$		−	902.823i		−	1.77372i	−0.462040	−	0.886859i	$-0.652882\pi$
$509$		−	902.823i		−	1.77372i	0.462040	−	0.886859i	$-0.347118\pi$
$510$		0			0
$511$	84.5265	−	136.915i	0.165414	−	0.267935i
$512$			45.8004i			0.0894539i
$513$		0			0
$514$	178.379	+	308.961i	0.347040	+	0.601092i
$515$			152.708i			0.296520i
$516$		0			0
$517$	−145.403	−	251.846i	−0.281244	−	0.487129i
$518$	619.612	−	333.770i	1.19616	−	0.644343i
$519$		0			0
$520$	−86.9141	−	150.540i	−0.167142	−	0.289499i
$521$	442.743	−	255.618i	0.849795	−	0.490630i	−0.0107865	−	0.999942i	$-0.503434\pi$
$521$	442.743	−	255.618i	0.849795	−	0.490630i	0.860582	+	0.509312i	$0.170100\pi$
$522$		0			0
$523$	489.654	−	848.105i	0.936240	−	1.62162i	0.163833	−	0.986488i	$-0.447614\pi$
$523$	489.654	−	848.105i	0.936240	−	1.62162i	0.772407	−	0.635128i	$-0.219053\pi$
$524$	123.266	+	71.1675i	0.235240	+	0.135816i
$525$		0			0
$526$	79.5711	+	137.821i	0.151276	+	0.262018i
$527$		−	490.338i		−	0.930432i
$528$		0			0
$529$	427.644			0.808401
$530$	581.263	+	335.592i	1.09672	+	0.633193i
$531$		0			0
$532$	−184.305	+	298.535i	−0.346438	+	0.561156i
$533$	−113.374	−	65.4564i	−0.212709	−	0.122807i
$534$		0			0
$535$	−338.896	+	586.986i	−0.633451	+	1.09717i
$536$	−81.3860	−	46.9882i	−0.151840	−	0.0876646i
$537$		0			0
$538$	−301.577	+	522.346i	−0.560552	+	0.970904i
$539$	723.772	+	476.868i	1.34280	+	0.884728i
$540$		0			0
$541$	350.265	−	606.676i	0.647439	−	1.12140i	−0.336293	−	0.941757i	$-0.609173\pi$
$541$	350.265	−	606.676i	0.647439	−	1.12140i	0.983732	−	0.179640i	$-0.0574934\pi$
$542$		−	697.234i		−	1.28641i
$543$		0			0
$544$	−548.588			−1.00843
$545$	−163.612	+	94.4613i	−0.300205	+	0.173324i
$546$		0			0
$547$	294.015	−	509.248i	0.537504	−	0.930984i	−0.461534	−	0.887123i	$-0.652701\pi$
$547$	294.015	−	509.248i	0.537504	−	0.930984i	0.999038	−	0.0438616i	$-0.0139660\pi$
$548$	−205.275	−	118.515i	−0.374589	−	0.216269i
$549$		0			0
$550$	160.042	+	277.201i	0.290985	+	0.504001i
$551$	−312.924	+	180.667i	−0.567920	+	0.327889i
$552$		0			0
$553$	510.695	−	827.216i	0.923499	−	1.49587i
$554$	218.097	−	125.918i	0.393676	−	0.227289i
$555$		0			0
$556$	901.640			1.62165
$557$	347.042	−	200.365i	0.623055	−	0.359721i	−0.155002	−	0.987914i	$-0.549539\pi$
$557$	347.042	−	200.365i	0.623055	−	0.359721i	0.778057	+	0.628193i	$0.216205\pi$
$558$		0			0
$559$	27.3257			0.0488831
$560$	23.5927	+	14.5653i	0.0421298	+	0.0260095i
$561$		0			0
$562$	1433.26			2.55028
$563$	78.9486	+	45.5810i	0.140228	+	0.0809609i	0.568473	−	0.822702i	$-0.307534\pi$
$563$	78.9486	+	45.5810i	0.140228	+	0.0809609i	−0.428244	+	0.903663i	$0.640868\pi$
$564$		0			0
$565$	215.385	+	373.058i	0.381213	+	0.660281i
$566$		−	413.984i		−	0.731421i
$567$		0			0
$568$	154.282			0.271624
$569$	−255.596	+	147.568i	−0.449202	+	0.259347i	−0.707493	−	0.706720i	$-0.750174\pi$
$569$	−255.596	+	147.568i	−0.449202	+	0.259347i	0.258291	+	0.966067i	$0.416841\pi$
$570$		0			0
$571$	−457.407	+	792.252i	−0.801062	+	1.38748i	0.117855	+	0.993031i	$0.462398\pi$
$571$	−457.407	+	792.252i	−0.801062	+	1.38748i	−0.918917	+	0.394450i	$0.870935\pi$
$572$		−	460.756i		−	0.805517i
$573$		0			0
$574$	−724.513	−	21.3735i	−1.26222	−	0.0372360i
$575$		−	56.5140i		−	0.0982852i
$576$		0			0
$577$	−267.301	−	462.978i	−0.463259	−	0.802389i	0.535862	−	0.844306i	$-0.319987\pi$
$577$	−267.301	−	462.978i	−0.463259	−	0.802389i	−0.999121	+	0.0419171i	$0.986653\pi$
$578$			48.4175i			0.0837674i
$579$		0			0
$580$	−814.715	−	1411.13i	−1.40468	−	2.43298i
$581$	3.26361	−	110.629i	0.00561722	−	0.190412i
$582$		0			0
$583$	332.825	+	576.469i	0.570883	+	0.988798i
$584$	−153.456	+	88.5981i	−0.262768	+	0.151709i
$585$		0			0
$586$	79.3789	−	137.488i	0.135459	−	0.234622i
$587$	−299.889	−	173.141i	−0.510884	−	0.294959i	0.222313	−	0.974975i	$-0.428639\pi$
$587$	−299.889	−	173.141i	−0.510884	−	0.294959i	−0.733197	+	0.680016i	$0.761973\pi$
$588$		0			0
$589$	−116.152	−	201.182i	−0.197203	−	0.341565i
$590$			1695.39i			2.87355i
$591$		0			0
$592$	22.3281			0.0377163
$593$	3.55214	+	2.05083i	0.00599012	+	0.00345840i	0.502992	−	0.864291i	$-0.332232\pi$
$593$	3.55214	+	2.05083i	0.00599012	+	0.00345840i	−0.497002	+	0.867749i	$0.665566\pi$
$594$		0			0
$595$	−336.773	+	545.500i	−0.566005	+	0.916807i
$596$	640.509	+	369.798i	1.07468	+	0.620467i
$597$		0			0
$598$	−66.1320	+	114.544i	−0.110589	+	0.191545i
$599$	−146.853	−	84.7858i	−0.245164	−	0.141546i	0.372384	−	0.928079i	$-0.378541\pi$
$599$	−146.853	−	84.7858i	−0.245164	−	0.141546i	−0.617548	+	0.786533i	$0.711874\pi$
$600$		0			0
$601$	−312.975	+	542.089i	−0.520757	+	0.901978i	0.478951	+	0.877841i	$0.341017\pi$
$601$	−312.975	+	542.089i	−0.520757	+	0.901978i	−0.999709	+	0.0241366i	$0.992316\pi$
$602$	133.199	−	71.7510i	0.221261	−	0.119188i
$603$		0			0
$604$	−480.362	+	832.011i	−0.795301	+	1.37750i
$605$			1061.72i			1.75490i
$606$		0			0
$607$	−37.6117			−0.0619633			−0.0309817	−	0.999520i	$-0.509863\pi$
$607$	−37.6117			−0.0619633			−0.0309817	+	0.999520i	$0.509863\pi$
$608$	−225.081	+	129.951i	−0.370200	+	0.213735i
$609$		0			0
$610$	657.855	−	1139.44i	1.07845	−	1.86793i
$611$	58.0256	+	33.5011i	0.0949682	+	0.0548299i
$612$		0			0
$613$	−149.019	−	258.108i	−0.243098	−	0.421057i	0.718497	−	0.695530i	$-0.244830\pi$
$613$	−149.019	−	258.108i	−0.243098	−	0.421057i	−0.961595	+	0.274472i	$0.911497\pi$
$614$	−1081.21	+	624.238i	−1.76093	+	1.01667i
$615$		0			0
$616$	−452.668	−	840.336i	−0.734851	−	1.36418i
$617$	−818.560	+	472.596i	−1.32668	+	0.765957i	−0.984784	−	0.173782i	$-0.944401\pi$
$617$	−818.560	+	472.596i	−1.32668	+	0.765957i	−0.341893	+	0.939739i	$0.611068\pi$
$618$		0			0
$619$	−1193.60			−1.92827			−0.964133	−	0.265418i	$-0.914490\pi$
$619$	−1193.60			−1.92827			−0.964133	+	0.265418i	$0.914490\pi$
$620$	907.229	−	523.789i	1.46327	−	0.844820i
$621$		0			0
$622$	325.892			0.523943
$623$	11.1890	−	379.282i	0.0179599	−	0.608800i
$624$		0			0
$625$	−733.826			−1.17412
$626$	−1018.38	−	587.964i	−1.62681	−	0.939239i
$627$		0			0
$628$	−875.795	−	1516.92i	−1.39458	−	2.41548i
$629$			516.260i			0.820764i
$630$		0			0
$631$	−823.055			−1.30437			−0.652183	−	0.758062i	$-0.726147\pi$
$631$	−823.055			−1.30437			−0.652183	+	0.758062i	$0.726147\pi$
$632$	−927.158	+	535.295i	−1.46702	+	0.846985i
$633$		0			0
$634$	−53.4322	+	92.5472i	−0.0842779	+	0.145974i
$635$		−	77.8719i		−	0.122633i
$636$		0			0
$637$	−199.352	−	11.7722i	−0.312955	−	0.0184807i
$638$		−	2627.35i		−	4.11810i
$639$		0			0
$640$	−560.476	−	970.773i	−0.875744	−	1.51683i
$641$			712.531i			1.11159i	0.831319	+	0.555796i	$0.187587\pi$
$641$			712.531i			1.11159i	−0.831319	+	0.555796i	$0.812413\pi$
$642$		0			0
$643$	534.902	+	926.478i	0.831885	+	1.44087i	0.896542	+	0.442960i	$0.146072\pi$
$643$	534.902	+	926.478i	0.831885	+	1.44087i	−0.0646564	+	0.997908i	$0.520595\pi$
$644$	−13.2818	+	450.223i	−0.0206239	+	0.699104i
$645$		0			0
$646$	−209.213	−	362.367i	−0.323859	−	0.560940i
$647$	973.422	−	562.006i	1.50452	−	0.868633i	0.504531	−	0.863394i	$-0.331666\pi$
$647$	973.422	−	562.006i	1.50452	−	0.868633i	0.999986	−	0.00523936i	$-0.00166775\pi$
$648$		0			0
$649$	−840.705	+	1456.14i	−1.29539	+	2.24367i
$650$	−63.8674	−	36.8739i	−0.0982576	−	0.0567290i
$651$		0			0
$652$	711.525	+	1232.40i	1.09130	+	1.89018i
$653$			48.4318i			0.0741682i	0.999312	+	0.0370841i	$0.0118069\pi$
$653$			48.4318i			0.0741682i	−0.999312	+	0.0370841i	$0.988193\pi$
$654$		0			0
$655$	123.218			0.188119
$656$	−19.9147	−	11.4977i	−0.0303577	−	0.0175270i
$657$		0			0
$658$	370.812	+	10.9391i	0.563544	+	0.0166248i
$659$	818.128	+	472.346i	1.24147	+	0.716762i	0.969393	−	0.245514i	$-0.0789566\pi$
$659$	818.128	+	472.346i	1.24147	+	0.716762i	0.272076	+	0.962276i	$0.412290\pi$
$660$		0			0
$661$	−140.597	+	243.521i	−0.212703	+	0.368413i	−0.952560	−	0.304352i	$-0.901560\pi$
$661$	−140.597	+	243.521i	−0.212703	+	0.368413i	0.739856	+	0.672765i	$0.234893\pi$
$662$	252.669	+	145.879i	0.381676	+	0.220361i
$663$		0			0
$664$	−60.9415	+	105.554i	−0.0917794	+	0.158967i
$665$	−8.95604	+	303.590i	−0.0134677	+	0.456526i
$666$		0			0
$667$	−231.942	+	401.736i	−0.347740	+	0.602303i
$668$			463.382i			0.693685i
$669$		0			0
$670$	−217.435			−0.324529
$671$	1130.04	−	652.429i	1.68411	−	0.972323i
$672$		0			0
$673$	246.892	−	427.630i	0.366854	−	0.635409i	−0.622218	−	0.782844i	$-0.713768\pi$
$673$	246.892	−	427.630i	0.366854	−	0.635409i	0.989072	+	0.147435i	$0.0471017\pi$
$674$	1210.69	+	698.994i	1.79628	+	1.03708i
$675$		0			0
$676$	−486.991	−	843.494i	−0.720401	−	1.24777i
$677$	611.085	−	352.810i	0.902636	−	0.521137i	0.0245816	−	0.999698i	$-0.492175\pi$
$677$	611.085	−	352.810i	0.902636	−	0.521137i	0.878055	+	0.478561i	$0.158841\pi$
$678$		0			0
$679$	1205.14	+	35.5521i	1.77487	+	0.0523596i
$680$	611.405	−	352.995i	0.899126	−	0.519110i
$681$		0			0
$682$	1689.15			2.47676
$683$	−1010.24	+	583.260i	−1.47912	+	0.853968i	−0.999721	−	0.0236320i	$-0.992477\pi$
$683$	−1010.24	+	583.260i	−1.47912	+	0.853968i	−0.479394	+	0.877600i	$0.659144\pi$
$684$		0			0
$685$	−205.195			−0.299555
$686$	−1002.65	+	466.070i	−1.46159	+	0.679402i
$687$		0			0
$688$	4.79989			0.00697659
$689$	−132.819	−	76.6832i	−0.192771	−	0.111296i
$690$		0			0
$691$	−182.834	−	316.677i	−0.264593	−	0.458289i	0.702864	−	0.711324i	$-0.251904\pi$
$691$	−182.834	−	316.677i	−0.264593	−	0.458289i	−0.967457	+	0.253036i	$0.918571\pi$
$692$		−	1349.69i		−	1.95041i
$693$		0			0
$694$	37.6993			0.0543217
$695$	675.968	−	390.270i	0.972616	−	0.561540i
$696$		0			0
$697$	265.846	−	460.459i	0.381415	−	0.660630i
$698$		−	591.250i		−	0.847063i
$699$		0			0
$700$	−251.035	−	7.40564i	−0.358622	−	0.0105795i
$701$			254.519i			0.363080i	0.983384	+	0.181540i	$0.0581083\pi$
$701$			254.519i			0.363080i	−0.983384	+	0.181540i	$0.941892\pi$
$702$		0			0
$703$	122.293	+	211.818i	0.173959	+	0.301305i
$704$		−	1839.16i		−	2.61245i
$705$		0			0
$706$	109.735	+	190.067i	0.155433	+	0.269217i
$707$	−106.724	+	57.4896i	−0.150953	+	0.0813148i
$708$		0			0
$709$	520.494	+	901.522i	0.734124	+	1.27154i	0.955107	+	0.296263i	$0.0957403\pi$
$709$	520.494	+	901.522i	0.734124	+	1.27154i	−0.220982	+	0.975278i	$0.570926\pi$
$710$	309.141	−	178.483i	0.435410	−	0.251384i
$711$		0			0
$712$	−208.933	+	361.882i	−0.293445	+	0.508261i
$713$	−258.280	−	149.118i	−0.362244	−	0.209142i
$714$		0			0
$715$	−199.436	−	345.433i	−0.278931	−	0.483123i
$716$		−	513.632i		−	0.717363i
$717$		0			0
$718$	−1437.42			−2.00198
$719$	653.543	+	377.323i	0.908961	+	0.524789i	0.880097	−	0.474795i	$-0.157478\pi$
$719$	653.543	+	377.323i	0.908961	+	0.524789i	0.0288642	+	0.999583i	$0.490811\pi$
$720$		0			0
$721$	−91.6233	−	170.090i	−0.127078	−	0.235909i
$722$	836.123	+	482.736i	1.15807	+	0.668609i
$723$		0			0
$724$	392.891	−	680.507i	0.542667	−	0.939927i
$725$	−224.000	−	129.326i	−0.308965	−	0.178381i
$726$		0			0
$727$	698.773	−	1210.31i	0.961174	−	1.66480i	0.241612	−	0.970373i	$-0.422324\pi$
$727$	698.773	−	1210.31i	0.961174	−	1.66480i	0.719561	−	0.694429i	$-0.244343\pi$
$728$	187.130	+	115.528i	0.257046	+	0.158692i
$729$		0			0
$730$	−204.991	+	355.054i	−0.280809	+	0.486376i
$731$			110.981i			0.151821i
$732$		0			0
$733$	1253.49			1.71008			0.855039	−	0.518564i	$-0.173533\pi$
$733$	1253.49			1.71008			0.855039	+	0.518564i	$0.173533\pi$
$734$	353.664	−	204.188i	0.481832	−	0.278186i
$735$		0			0
$736$	−166.833	+	288.963i	−0.226675	+	0.392613i
$737$	−186.751	−	107.821i	−0.253393	−	0.146297i
$738$		0			0
$739$	−534.999	−	926.646i	−0.723950	−	1.25392i	−0.959405	−	0.282033i	$-0.908991\pi$
$739$	−534.999	−	926.646i	−0.723950	−	1.25392i	0.235454	−	0.971885i	$-0.424342\pi$
$740$	−955.191	+	551.480i	−1.29080	+	0.745243i
$741$		0			0
$742$	−848.780	−	25.0394i	−1.14391	−	0.0337458i
$743$	620.266	−	358.111i	0.834813	−	0.481980i	−0.0206847	−	0.999786i	$-0.506585\pi$
$743$	620.266	−	358.111i	0.834813	−	0.481980i	0.855498	+	0.517806i	$0.173251\pi$
$744$		0			0
$745$	640.261			0.859411
$746$	−1709.43	+	986.941i	−2.29146	+	1.32298i
$747$		0			0
$748$	1871.32			2.50177
$749$	25.2859	−	857.136i	0.0337595	−	1.14437i
$750$		0			0
$751$	−120.642			−0.160642			−0.0803208	−	0.996769i	$-0.525594\pi$
$751$	−120.642			−0.160642			−0.0803208	+	0.996769i	$0.525594\pi$
$752$	10.1925	+	5.88464i	0.0135538	+	0.00782531i
$753$		0			0
$754$	302.672	+	524.244i	0.401422	+	0.695284i
$755$			831.689i			1.10157i
$756$		0			0
$757$	−369.403			−0.487983			−0.243992	−	0.969777i	$-0.578457\pi$
$757$	−369.403			−0.487983			−0.243992	+	0.969777i	$0.578457\pi$
$758$	1146.96	−	662.196i	1.51314	−	0.873610i
$759$		0			0
$760$	167.237	−	289.662i	0.220048	−	0.381135i
$761$			1145.54i			1.50531i	0.658415	+	0.752655i	$0.271227\pi$
$761$			1145.54i			1.50531i	−0.658415	+	0.752655i	$0.728773\pi$
$762$		0			0
$763$	125.559	−	203.379i	0.164560	−	0.266552i
$764$			2272.07i			2.97391i
$765$		0			0
$766$	354.782	+	614.500i	0.463161	+	0.802219i
$767$		−	387.399i		−	0.505084i
$768$		0			0
$769$	319.295	+	553.035i	0.415208	+	0.719162i	0.995450	−	0.0952822i	$-0.0303754\pi$
$769$	319.295	+	553.035i	0.415208	+	0.719162i	−0.580242	+	0.814444i	$0.697042\pi$
$770$	−1879.18	−	1160.14i	−2.44049	−	1.50667i
$771$		0			0
$772$	−126.738	−	219.517i	−0.164169	−	0.284349i
$773$	169.438	−	97.8250i	0.219195	−	0.126552i	−0.386382	−	0.922339i	$-0.626275\pi$
$773$	169.438	−	97.8250i	0.219195	−	0.126552i	0.605578	+	0.795786i	$0.292942\pi$
$774$		0			0
$775$	83.1452	−	144.012i	0.107284	−	0.185822i
$776$	−1149.85	−	663.867i	−1.48177	−	0.855499i
$777$		0			0
$778$	−277.643	−	480.892i	−0.356868	−	0.618114i
$779$		−	251.897i		−	0.323360i
$780$		0			0
$781$	354.021			0.453292
$782$	−465.212	−	268.590i	−0.594901	−	0.343466i
$783$		0			0
$784$	−35.0172	−	2.06785i	−0.0446648	−	0.00263756i
$785$	−1313.18	−	758.167i	−1.67285	−	0.965818i
$786$		0			0
$787$	8.68274	−	15.0389i	0.0110327	−	0.0191092i	−0.860456	−	0.509524i	$-0.829821\pi$
$787$	8.68274	−	15.0389i	0.0110327	−	0.0191092i	0.871489	+	0.490415i	$0.163155\pi$
$788$	−723.073	−	417.466i	−0.917605	−	0.529780i
$789$		0			0
$790$	−1238.52	+	2145.18i	−1.56775	+	2.71542i
$791$	−463.734	−	286.294i	−0.586263	−	0.361939i
$792$		0			0
$793$	−150.320	+	260.363i	−0.189559	+	0.328326i
$794$			1196.08i			1.50640i
$795$		0			0
$796$	1387.19			1.74270
$797$	871.920	−	503.403i	1.09400	−	0.631622i	0.159363	−	0.987220i	$-0.449056\pi$
$797$	871.920	−	503.403i	1.09400	−	0.631622i	0.934639	+	0.355598i	$0.115723\pi$
$798$		0			0
$799$	−136.062	+	235.667i	−0.170291	+	0.294952i
$800$	−161.120	−	93.0225i	−0.201400	−	0.116278i
$801$		0			0
$802$	−482.595	−	835.879i	−0.601739	−	1.04224i
$803$	−352.126	+	203.300i	−0.438513	+	0.253176i
$804$		0			0
$805$	184.919	+	343.285i	0.229713	+	0.426442i
$806$	−337.042	+	194.591i	−0.418166	+	0.241428i
$807$		0			0
$808$	133.497			0.165219
$809$	364.210	−	210.277i	0.450198	−	0.259922i	−0.257716	−	0.966221i	$-0.582970\pi$
$809$	364.210	−	210.277i	0.450198	−	0.259922i	0.707914	+	0.706299i	$0.249636\pi$
$810$		0			0
$811$	1318.39			1.62564			0.812819	−	0.582517i	$-0.197932\pi$
$811$	1318.39			1.62564			0.812819	+	0.582517i	$0.197932\pi$
$812$	1754.12	+	1082.93i	2.16024	+	1.33366i
$813$		0			0
$814$	−1778.45			−2.18483
$815$	1066.87	+	615.960i	1.30905	+	0.755780i
$816$		0			0
$817$	26.2895	+	45.5347i	0.0321781	+	0.0557341i
$818$		−	1206.91i		−	1.47544i
$819$		0			0
$820$	1135.93			1.38528
$821$	−668.380	+	385.889i	−0.814104	+	0.470023i	−0.848379	−	0.529389i	$-0.822421\pi$
$821$	−668.380	+	385.889i	−0.814104	+	0.470023i	0.0342747	+	0.999412i	$0.489088\pi$
$822$		0			0
$823$	−453.227	+	785.013i	−0.550702	+	0.953843i	0.447522	+	0.894273i	$0.352306\pi$
$823$	−453.227	+	785.013i	−0.550702	+	0.953843i	−0.998224	+	0.0595705i	$0.981027\pi$
$824$			212.759i			0.258202i
$825$		0			0
$826$	−1017.22	−	1888.38i	−1.23150	−	2.28617i
$827$			509.463i			0.616038i	0.951380	+	0.308019i	$0.0996660\pi$
$827$			509.463i			0.616038i	−0.951380	+	0.308019i	$0.900334\pi$
$828$		0			0
$829$	332.585	+	576.054i	0.401188	+	0.694878i	0.993870	−	0.110559i	$-0.0352641\pi$
$829$	332.585	+	576.054i	0.401188	+	0.694878i	−0.592682	+	0.805437i	$0.701931\pi$
$830$			282.002i			0.339762i
$831$		0			0
$832$	211.873	+	366.974i	0.254655	+	0.441075i
$833$	47.8119	−	809.654i	0.0573973	−	0.971974i
$834$		0			0
$835$	200.572	+	347.402i	0.240207	+	0.416050i
$836$	767.790	−	443.284i	0.918409	−	0.530244i
$837$		0			0
$838$	−651.985	+	1129.27i	−0.778025	+	1.34758i
$839$	−1237.78	−	714.635i	−1.47531	−	0.851770i	−0.475696	−	0.879610i	$-0.657804\pi$
$839$	−1237.78	−	714.635i	−1.47531	−	0.851770i	−0.999612	+	0.0278396i	$0.991137\pi$
$840$		0			0
$841$	641.052	+	1110.33i	0.762250	+	1.32026i
$842$			1489.30i			1.76876i
$843$		0			0
$844$	698.082			0.827111
$845$	−730.204	−	421.583i	−0.864147	−	0.498915i
$846$		0			0
$847$	−637.020	−	1182.57i	−0.752090	−	1.39619i
$848$	−23.3304	−	13.4698i	−0.0275122	−	0.0158842i
$849$		0			0
$850$	149.761	−	259.393i	0.176189	−	0.305168i
$851$	271.935	+	157.002i	0.319547	+	0.184491i
$852$		0			0
$853$	485.171	−	840.341i	0.568782	−	0.985159i	−0.427905	−	0.903824i	$-0.640748\pi$
$853$	485.171	−	840.341i	0.568782	−	0.985159i	0.996687	−	0.0813353i	$-0.0259185\pi$
$854$	−49.0841	+	1663.84i	−0.0574756	+	1.94830i
$855$		0			0
$856$	−472.165	+	817.813i	−0.551594	+	0.955389i
$857$			1510.42i			1.76245i	0.472700	+	0.881223i	$0.343279\pi$
$857$			1510.42i			1.76245i	−0.472700	+	0.881223i	$0.656721\pi$
$858$		0			0
$859$	−1228.38			−1.43001			−0.715007	−	0.699118i	$-0.753576\pi$
$859$	−1228.38			−1.43001			−0.715007	+	0.699118i	$0.753576\pi$
$860$	−205.339	+	118.552i	−0.238766	+	0.137852i
$861$		0			0
$862$	367.683	−	636.845i	0.426546	−	0.738800i
$863$	1292.69	+	746.335i	1.49790	+	0.864815i	0.999997	−	0.00241587i	$-0.000768995\pi$
$863$	1292.69	+	746.335i	1.49790	+	0.864815i	0.497906	+	0.867231i	$0.334102\pi$
$864$		0			0
$865$	−584.205	−	1011.87i	−0.675382	−	1.16980i
$866$	2170.89	−	1253.36i	2.50680	−	1.44730i
$867$		0			0
$868$	−696.228	+	1127.74i	−0.802106	+	1.29924i
$869$	−2127.48	+	1228.30i	−2.44820	+	1.41347i
$870$		0			0
$871$	49.6841			0.0570425
$872$	−227.951	+	131.608i	−0.261412	+	0.150926i
$873$		0			0
$874$	−254.497			−0.291187
$875$	661.045	−	356.088i	0.755480	−	0.406958i
$876$		0			0
$877$	−346.948			−0.395608			−0.197804	−	0.980242i	$-0.563381\pi$
$877$	−346.948			−0.395608			−0.197804	+	0.980242i	$0.563381\pi$
$878$	−192.071	−	110.892i	−0.218760	−	0.126301i
$879$		0			0
$880$	−35.0319	−	60.6770i	−0.0398090	−	0.0689512i
$881$		−	738.403i		−	0.838142i	−0.907953	−	0.419071i	$-0.862356\pi$
$881$		−	738.403i		−	0.838142i	0.907953	−	0.419071i	$-0.137644\pi$
$882$		0			0
$883$	872.215			0.987786			0.493893	−	0.869523i	$-0.335573\pi$
$883$	872.215			0.987786			0.493893	+	0.869523i	$0.335573\pi$
$884$	−373.392	+	215.578i	−0.422389	+	0.243866i
$885$		0			0
$886$	335.783	−	581.593i	0.378987	−	0.656426i
$887$			633.281i			0.713958i	0.934112	+	0.356979i	$0.116193\pi$
$887$			633.281i			0.713958i	−0.934112	+	0.356979i	$0.883807\pi$
$888$		0			0
$889$	46.7225	+	86.7359i	0.0525562	+	0.0975657i
$890$			966.821i			1.08632i
$891$		0			0
$892$	596.753	+	1033.61i	0.669005	+	1.15875i
$893$			128.923i			0.144371i
$894$		0			0
$895$	−222.323	−	385.075i	−0.248406	−	0.430251i
$896$	1206.73	+	744.993i	1.34680	+	0.831466i
$897$		0			0
$898$	417.524	+	723.172i	0.464949	+	0.805314i
$899$	−1182.09	+	682.483i	−1.31490	+	0.759158i
$900$		0			0
$901$	311.443	−	539.436i	0.345664	−	0.598708i
$902$	1586.22	+	915.805i	1.75856	+	1.01531i
$903$		0			0
$904$	300.084	+	519.761i	0.331951	+	0.574957i
$905$		−	680.244i		−	0.751650i
$906$		0			0
$907$	1121.71			1.23672			0.618361	−	0.785894i	$-0.287797\pi$
$907$	1121.71			1.23672			0.618361	+	0.785894i	$0.287797\pi$
$908$	−1121.12	−	647.278i	−1.23471	−	0.712861i
$909$		0			0
$910$	508.607	+	15.0041i	0.558909	+	0.0164881i
$911$	770.852	+	445.052i	0.846160	+	0.488531i	0.859353	−	0.511382i	$-0.170866\pi$
$911$	770.852	+	445.052i	0.846160	+	0.488531i	−0.0131931	+	0.999913i	$0.504200\pi$
$912$		0			0
$913$	−139.838	+	242.207i	−0.153163	+	0.265287i
$914$	−445.099	−	256.978i	−0.486979	−	0.281158i
$915$		0			0
$916$	−253.332	+	438.784i	−0.276563	+	0.479021i
$917$	−137.244	+	73.9297i	−0.149666	+	0.0806213i
$918$		0			0
$919$	567.953	−	983.724i	0.618012	−	1.07043i	−0.371836	−	0.928299i	$-0.621271\pi$
$919$	567.953	−	983.724i	0.618012	−	1.07043i	0.989848	−	0.142130i	$-0.0453952\pi$
$920$		−	429.402i		−	0.466741i
$921$		0			0
$922$	658.502			0.714211
$923$	−70.6391	+	40.7835i	−0.0765321	+	0.0441858i
$924$		0			0
$925$	−87.5408	+	151.625i	−0.0946387	+	0.163919i
$926$	−2127.85	−	1228.52i	−2.29790	−	1.32669i
$927$		0			0
$928$	763.559	+	1322.52i	0.822800	+	1.42513i
$929$	−622.843	+	359.598i	−0.670444	+	0.387081i	−0.796245	−	0.604974i	$-0.793183\pi$
$929$	−622.843	+	359.598i	−0.670444	+	0.387081i	0.125801	+	0.992056i	$0.459850\pi$
$930$		0			0
$931$	−172.176	−	343.521i	−0.184937	−	0.368980i
$932$	1805.12	−	1042.18i	1.93682	−	1.11822i
$933$		0			0
$934$	−1719.85			−1.84138
$935$	1402.95	−	809.994i	1.50048	−	0.866303i
$936$		0			0
$937$	−1522.34			−1.62470			−0.812348	−	0.583172i	$-0.801811\pi$
$937$	−1522.34			−1.62470			−0.812348	+	0.583172i	$0.801811\pi$
$938$	242.185	−	130.459i	0.258193	−	0.139082i
$939$		0			0
$940$	−581.377			−0.618487
$941$	886.384	+	511.754i	0.941960	+	0.543841i	0.890574	−	0.454838i	$-0.150303\pi$
$941$	886.384	+	511.754i	0.941960	+	0.543841i	0.0513858	+	0.998679i	$0.483636\pi$
$942$		0			0
$943$	−161.695	−	280.063i	−0.171468	−	0.296992i
$944$		−	68.0487i		−	0.0720855i
$945$		0			0
$946$	−382.316			−0.404139
$947$	−1361.76	+	786.215i	−1.43798	+	0.830217i	−0.997709	−	0.0676499i	$-0.978450\pi$
$947$	−1361.76	+	786.215i	−1.43798	+	0.830217i	−0.440268	+	0.897866i	$0.645117\pi$
$948$		0			0
$949$	46.8406	−	81.1303i	0.0493578	−	0.0854903i
$950$		−	141.902i		−	0.149371i
$951$		0			0
$952$	−469.207	+	760.014i	−0.492864	+	0.798334i
$953$		−	1342.92i		−	1.40915i	−0.709629	−	0.704576i	$-0.751137\pi$
$953$		−	1342.92i		−	1.40915i	0.709629	−	0.704576i	$-0.248863\pi$
$954$		0			0
$955$	983.453	+	1703.39i	1.02979	+	1.78366i
$956$		−	1556.60i		−	1.62824i
$957$		0			0
$958$	−974.348	−	1687.62i	−1.01706	−	1.76161i
$959$	228.552	−	123.115i	0.238323	−	0.128379i
$960$		0			0
$961$	41.7250	+	72.2699i	0.0434183	+	0.0752028i
$962$	354.860	−	204.879i	0.368877	−	0.212971i
$963$		0			0
$964$	90.5672	−	156.867i	0.0939493	−	0.162725i
$965$	−190.034	−	109.716i	−0.196927	−	0.113696i
$966$		0			0
$967$	−867.804	−	1503.08i	−0.897418	−	1.55437i	−0.830783	−	0.556597i	$-0.812107\pi$
$967$	−867.804	−	1503.08i	−0.897418	−	1.55437i	−0.0666355	−	0.997777i	$-0.521226\pi$
$968$			1479.23i			1.52813i
$969$		0			0
$970$	−3072.00			−3.16701
$971$	−43.8474	−	25.3153i	−0.0451569	−	0.0260714i	0.477252	−	0.878767i	$-0.341633\pi$
$971$	−43.8474	−	25.3153i	−0.0451569	−	0.0260714i	−0.522409	+	0.852695i	$0.674966\pi$
$972$		0			0
$973$	−518.753	+	840.269i	−0.533148	+	0.863586i
$974$	−436.071	−	251.766i	−0.447712	−	0.258486i
$975$		0			0
$976$	−26.4045	+	45.7340i	−0.0270538	+	0.0468586i
$977$	−506.717	−	292.553i	−0.518646	−	0.299440i	0.217734	−	0.976008i	$-0.430133\pi$
$977$	−506.717	−	292.553i	−0.518646	−	0.299440i	−0.736381	+	0.676568i	$0.763467\pi$
$978$		0			0
$979$	−479.423	+	830.386i	−0.489707	+	0.848198i
$980$	1549.11	−	776.427i	1.58072	−	0.792272i
$981$		0			0
$982$	645.630	−	1118.26i	0.657464	−	1.13876i
$983$		−	968.896i		−	0.985653i	−0.870128	−	0.492826i	$-0.835964\pi$
$983$		−	968.896i		−	0.985653i	0.870128	−	0.492826i	$-0.164036\pi$
$984$		0			0
$985$	−722.793			−0.733800
$986$	−2129.18	+	1229.28i	−2.15941	+	1.24674i
$987$		0			0
$988$	−102.133	+	176.900i	−0.103374	+	0.179048i
$989$	58.4582	+	33.7508i	0.0591084	+	0.0341262i
$990$		0			0
$991$	−104.448	−	180.910i	−0.105397	−	0.182553i	0.808503	−	0.588492i	$-0.200278\pi$
$991$	−104.448	−	180.910i	−0.105397	−	0.182553i	−0.913900	+	0.405939i	$0.866945\pi$
$992$	−850.263	+	490.900i	−0.857120	+	0.494859i
$993$		0			0
$994$	−237.242	+	384.281i	−0.238674	+	0.386601i
$995$	1039.99	−	600.439i	1.04522	−	0.603457i
$996$		0			0
$997$	152.170			0.152628			0.0763140	−	0.997084i	$-0.475685\pi$
$997$	152.170			0.152628			0.0763140	+	0.997084i	$0.475685\pi$
$998$	−341.392	+	197.103i	−0.342077	+	0.197498i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.n.b.170.10		22
3.2	odd	2		63.3.n.b.2.2	yes	22
7.4	even	3		189.3.j.b.116.10		22
9.4	even	3		63.3.j.b.23.10	yes	22
9.5	odd	6		189.3.j.b.44.2		22
21.2	odd	6		441.3.r.g.344.10		22
21.5	even	6		441.3.r.f.344.10		22
21.11	odd	6		63.3.j.b.11.2	✓	22
21.17	even	6		441.3.j.f.263.2		22
21.20	even	2		441.3.n.f.128.2		22
63.4	even	3		63.3.n.b.32.2	yes	22
63.13	odd	6		441.3.j.f.275.10		22
63.31	odd	6		441.3.n.f.410.2		22
63.32	odd	6	inner	189.3.n.b.179.10		22
63.40	odd	6		441.3.r.f.50.10		22
63.58	even	3		441.3.r.g.50.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.2	✓	22	21.11	odd	6
63.3.j.b.23.10	yes	22	9.4	even	3
63.3.n.b.2.2	yes	22	3.2	odd	2
63.3.n.b.32.2	yes	22	63.4	even	3
189.3.j.b.44.2		22	9.5	odd	6
189.3.j.b.116.10		22	7.4	even	3
189.3.n.b.170.10		22	1.1	even	1	trivial
189.3.n.b.179.10		22	63.32	odd	6	inner
441.3.j.f.263.2		22	21.17	even	6
441.3.j.f.275.10		22	63.13	odd	6
441.3.n.f.128.2		22	21.20	even	2
441.3.n.f.410.2		22	63.31	odd	6
441.3.r.f.50.10		22	63.40	odd	6
441.3.r.f.344.10		22	21.5	even	6
441.3.r.g.50.10		22	63.58	even	3
441.3.r.g.344.10		22	21.2	odd	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.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.79169 - 1.61178i) q^{2} +(3.19568 - 5.53509i) q^{4} -5.53294i q^{5} +(3.31972 + 6.16275i) q^{7} -7.70873i q^{8} +O(q^{10})\)	\(q+(2.79169 - 1.61178i) q^{2} +(3.19568 - 5.53509i) q^{4} -5.53294i q^{5} +(3.31972 + 6.16275i) q^{7} -7.70873i q^{8} +(-8.91790 - 15.4463i) q^{10} -17.6887i q^{11} +(2.03775 + 3.52949i) q^{13} +(19.2006 + 11.8538i) q^{14} +(0.357941 + 0.619972i) q^{16} +(-14.3348 + 8.27617i) q^{17} +(-3.92096 + 6.79130i) q^{19} +(-30.6253 - 17.6815i) q^{20} +(-28.5103 - 49.3813i) q^{22} +10.0676i q^{23} -5.61347 q^{25} +(11.3775 + 6.56882i) q^{26} +(44.7201 + 1.31926i) q^{28} +(39.9040 + 23.0386i) q^{29} +(-14.8117 + 25.6547i) q^{31} +(28.7023 + 16.5713i) q^{32} +(-26.6788 + 46.2090i) q^{34} +(34.0981 - 18.3678i) q^{35} +(15.5948 - 27.0110i) q^{37} +25.2789i q^{38} -42.6520 q^{40} +(-27.8184 + 16.0609i) q^{41} +(3.35243 - 5.80658i) q^{43} +(-97.9085 - 56.5275i) q^{44} +(16.2267 + 28.1055i) q^{46} +(14.2377 - 8.22012i) q^{47} +(-26.9589 + 40.9172i) q^{49} +(-15.6711 + 9.04769i) q^{50} +26.0480 q^{52} +(-32.5897 + 18.8157i) q^{53} -97.8706 q^{55} +(47.5070 - 25.5908i) q^{56} +148.533 q^{58} +(-82.3206 - 47.5278i) q^{59} +(36.8839 + 63.8848i) q^{61} +95.4932i q^{62} +103.974 q^{64} +(19.5285 - 11.2748i) q^{65} +(6.09545 - 10.5576i) q^{67} +105.792i q^{68} +(65.5865 - 106.236i) q^{70} +20.0140i q^{71} +(-11.4932 - 19.9068i) q^{73} -100.542i q^{74} +(25.0603 + 43.4057i) q^{76} +(109.011 - 58.7215i) q^{77} +(-69.4400 - 120.274i) q^{79} +(3.43027 - 1.98047i) q^{80} +(-51.7735 + 89.6743i) q^{82} +(-13.6928 - 7.90552i) q^{83} +(45.7916 + 79.3134i) q^{85} -21.6136i q^{86} -136.357 q^{88} +(-46.9444 - 27.1034i) q^{89} +(-14.9866 + 24.2750i) q^{91} +(55.7249 + 32.1728i) q^{92} +(26.4981 - 45.8960i) q^{94} +(37.5759 + 21.6944i) q^{95} +(86.1189 - 149.162i) q^{97} +(-9.31136 + 157.680i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 6 q^{2} + 12 q^{4} + 3 q^{7}+O(q^{10}) \) 22 * q + 6 * q^2 + 12 * q^4 + 3 * q^7	\( 22 q + 6 q^{2} + 12 q^{4} + 3 q^{7} + 25 q^{10} - 18 q^{13} + 90 q^{14} + 12 q^{16} - 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 114 q^{25} + 3 q^{26} + 34 q^{28} + 63 q^{29} - 29 q^{31} - 246 q^{32} - 99 q^{34} + 27 q^{35} - 20 q^{37} + 210 q^{40} + 51 q^{41} + 65 q^{43} - 54 q^{44} + 75 q^{46} - 261 q^{47} - 131 q^{49} - 63 q^{50} + 92 q^{52} + 63 q^{53} - 100 q^{55} - 153 q^{56} - 80 q^{58} + 102 q^{59} + 78 q^{61} + 106 q^{64} + 225 q^{65} - 132 q^{67} + 179 q^{70} + q^{73} + 233 q^{76} + 447 q^{77} + 140 q^{79} - 96 q^{80} - 157 q^{82} - 255 q^{83} + 102 q^{85} - 816 q^{88} + 720 q^{89} - 70 q^{91} + 1239 q^{92} + 261 q^{94} - 642 q^{95} + 178 q^{97} - 483 q^{98}+O(q^{100}) \) 22 * q + 6 * q^2 + 12 * q^4 + 3 * q^7 + 25 * q^10 - 18 * q^13 + 90 * q^14 + 12 * q^16 - 6 * q^17 + 3 * q^19 + 39 * q^20 - 59 * q^22 - 114 * q^25 + 3 * q^26 + 34 * q^28 + 63 * q^29 - 29 * q^31 - 246 * q^32 - 99 * q^34 + 27 * q^35 - 20 * q^37 + 210 * q^40 + 51 * q^41 + 65 * q^43 - 54 * q^44 + 75 * q^46 - 261 * q^47 - 131 * q^49 - 63 * q^50 + 92 * q^52 + 63 * q^53 - 100 * q^55 - 153 * q^56 - 80 * q^58 + 102 * q^59 + 78 * q^61 + 106 * q^64 + 225 * q^65 - 132 * q^67 + 179 * q^70 + q^73 + 233 * q^76 + 447 * q^77 + 140 * q^79 - 96 * q^80 - 157 * q^82 - 255 * q^83 + 102 * q^85 - 816 * q^88 + 720 * q^89 - 70 * q^91 + 1239 * q^92 + 261 * q^94 - 642 * q^95 + 178 * q^97 - 483 * q^98

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