LMFDB - Embedded newform 189.3.k.a.10.8

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			10.8
Character	$\chi$	$=$	189.10
Dual form			189.3.k.a.19.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.178911 - 0.309883i) q^{2} +(1.93598 + 3.35322i) q^{4} +4.59004i q^{5} +(-6.01934 + 3.57317i) q^{7} +2.81677 q^{8} +O(q^{10})$	\(q+(0.178911 - 0.309883i) q^{2} +(1.93598 + 3.35322i) q^{4} +4.59004i q^{5} +(-6.01934 + 3.57317i) q^{7} +2.81677 q^{8} +(1.42238 + 0.821210i) q^{10} -13.4737 q^{11} +(-13.4065 - 7.74026i) q^{13} +(0.0303368 + 2.50457i) q^{14} +(-7.23997 + 12.5400i) q^{16} +(17.6163 + 10.1708i) q^{17} +(0.149161 - 0.0861184i) q^{19} +(-15.3914 + 8.88623i) q^{20} +(-2.41061 + 4.17529i) q^{22} +31.6842 q^{23} +3.93154 q^{25} +(-4.79716 + 2.76964i) q^{26} +(-23.6349 - 13.2666i) q^{28} +(15.1613 + 26.2601i) q^{29} +(7.57687 - 4.37451i) q^{31} +(8.22416 + 14.2447i) q^{32} +(6.30353 - 3.63934i) q^{34} +(-16.4010 - 27.6290i) q^{35} +(29.3450 + 50.8271i) q^{37} -0.0616302i q^{38} +12.9291i q^{40} +(-14.5072 - 8.37576i) q^{41} +(7.44584 + 12.8966i) q^{43} +(-26.0849 - 45.1804i) q^{44} +(5.66866 - 9.81842i) q^{46} +(-38.6426 - 22.3103i) q^{47} +(23.4650 - 43.0162i) q^{49} +(0.703397 - 1.21832i) q^{50} -59.9400i q^{52} +(23.1656 - 40.1240i) q^{53} -61.8450i q^{55} +(-16.9551 + 10.0648i) q^{56} +10.8501 q^{58} +(-6.83327 + 3.94519i) q^{59} +(35.9531 + 20.7575i) q^{61} -3.13060i q^{62} -52.0342 q^{64} +(35.5281 - 61.5365i) q^{65} +(27.6189 + 47.8373i) q^{67} +78.7619i q^{68} +(-11.4961 + 0.139247i) q^{70} -4.91318 q^{71} +(-9.44921 - 5.45550i) q^{73} +21.0006 q^{74} +(0.577548 + 0.333447i) q^{76} +(81.1031 - 48.1439i) q^{77} +(54.1512 - 93.7926i) q^{79} +(-57.5591 - 33.2318i) q^{80} +(-5.19102 + 2.99703i) q^{82} +(-98.3122 + 56.7606i) q^{83} +(-46.6844 + 80.8597i) q^{85} +5.32858 q^{86} -37.9524 q^{88} +(105.603 - 60.9700i) q^{89} +(108.356 - 1.31246i) q^{91} +(61.3401 + 106.244i) q^{92} +(-13.8272 + 7.98314i) q^{94} +(0.395287 + 0.684657i) q^{95} +(-85.6452 + 49.4473i) q^{97} +(-9.13187 - 14.9675i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.178911	−	0.309883i	0.0894556	−	0.154942i	−0.817826	−	0.575466i	$-0.804821\pi$
$2$	0.178911	−	0.309883i	0.0894556	−	0.154942i	0.907281	+	0.420525i	$0.138154\pi$
$3$		0			0
$3$		0			0
$4$	1.93598	+	3.35322i	0.483995	+	0.838305i
$5$			4.59004i			0.918008i	0.888434	+	0.459004i	$0.151794\pi$
$5$			4.59004i			0.918008i	−0.888434	+	0.459004i	$0.848206\pi$
$6$		0			0
$7$	−6.01934	+	3.57317i	−0.859906	+	0.510452i
$7$	−6.01934	+	3.57317i	−0.859906	+	0.510452i
$8$	2.81677			0.352096
$9$		0			0
$10$	1.42238	+	0.821210i	0.142238	+	0.0821210i
$11$	−13.4737			−1.22489			−0.612443	−	0.790515i	$-0.709813\pi$
$11$	−13.4737			−1.22489			−0.612443	+	0.790515i	$0.709813\pi$
$12$		0			0
$13$	−13.4065	−	7.74026i	−1.03127	−	0.595405i	−0.113923	−	0.993490i	$-0.536342\pi$
$13$	−13.4065	−	7.74026i	−1.03127	−	0.595405i	−0.917349	+	0.398085i	$0.869675\pi$
$14$	0.0303368	+	2.50457i	0.00216691	+	0.178898i
$15$		0			0
$16$	−7.23997	+	12.5400i	−0.452498	+	0.783750i
$17$	17.6163	+	10.1708i	1.03626	+	0.598282i	0.918770	−	0.394792i	$-0.129183\pi$
$17$	17.6163	+	10.1708i	1.03626	+	0.598282i	0.117485	+	0.993075i	$0.462517\pi$
$18$		0			0
$19$	0.149161	−	0.0861184i	0.00785060	−	0.00453255i	−0.496070	−	0.868283i	$-0.665224\pi$
$19$	0.149161	−	0.0861184i	0.00785060	−	0.00453255i	0.503920	+	0.863750i	$0.331891\pi$
$20$	−15.3914	+	8.88623i	−0.769570	+	0.444312i
$21$		0			0
$22$	−2.41061	+	4.17529i	−0.109573	+	0.189786i
$23$	31.6842			1.37757			0.688787	−	0.724963i	$-0.258143\pi$
$23$	31.6842			1.37757			0.688787	+	0.724963i	$0.258143\pi$
$24$		0			0
$25$	3.93154			0.157262
$26$	−4.79716	+	2.76964i	−0.184506	+	0.106525i
$27$		0			0
$28$	−23.6349	−	13.2666i	−0.844105	−	0.473807i
$29$	15.1613	+	26.2601i	0.522802	+	0.905520i	0.999648	+	0.0265331i	$0.00844675\pi$
$29$	15.1613	+	26.2601i	0.522802	+	0.905520i	−0.476846	+	0.878987i	$0.658220\pi$
$30$		0			0
$31$	7.57687	−	4.37451i	0.244415	−	0.141113i	−0.372789	−	0.927916i	$-0.621599\pi$
$31$	7.57687	−	4.37451i	0.244415	−	0.141113i	0.617204	+	0.786803i	$0.288265\pi$
$32$	8.22416	+	14.2447i	0.257005	+	0.445146i
$33$		0			0
$34$	6.30353	−	3.63934i	0.185398	−	0.107039i
$35$	−16.4010	−	27.6290i	−0.468599	−	0.789401i
$36$		0			0
$37$	29.3450	+	50.8271i	0.793109	+	1.37370i	0.924033	+	0.382312i	$0.124872\pi$
$37$	29.3450	+	50.8271i	0.793109	+	1.37370i	−0.130924	+	0.991392i	$0.541794\pi$
$38$		−	0.0616302i		−	0.00162185i
$39$		0			0
$40$			12.9291i			0.323227i
$41$	−14.5072	−	8.37576i	−0.353835	−	0.204287i	0.312538	−	0.949905i	$-0.398821\pi$
$41$	−14.5072	−	8.37576i	−0.353835	−	0.204287i	−0.666373	+	0.745618i	$0.732154\pi$
$42$		0			0
$43$	7.44584	+	12.8966i	0.173159	+	0.299920i	0.939523	−	0.342487i	$-0.111269\pi$
$43$	7.44584	+	12.8966i	0.173159	+	0.299920i	−0.766364	+	0.642407i	$0.777936\pi$
$44$	−26.0849	−	45.1804i	−0.592839	−	1.02683i
$45$		0			0
$46$	5.66866	−	9.81842i	0.123232	−	0.213444i
$47$	−38.6426	−	22.3103i	−0.822184	−	0.474688i	0.0289853	−	0.999580i	$-0.490772\pi$
$47$	−38.6426	−	22.3103i	−0.822184	−	0.474688i	−0.851169	+	0.524892i	$0.824106\pi$
$48$		0			0
$49$	23.4650	−	43.0162i	0.478877	−	0.877882i
$50$	0.703397	−	1.21832i	0.0140679	−	0.0243664i
$51$		0			0
$52$		−	59.9400i		−	1.15269i
$53$	23.1656	−	40.1240i	0.437087	−	0.757056i	−0.560377	−	0.828238i	$-0.689344\pi$
$53$	23.1656	−	40.1240i	0.437087	−	0.757056i	0.997463	+	0.0711817i	$0.0226770\pi$
$54$		0			0
$55$		−	61.8450i		−	1.12446i
$56$	−16.9551	+	10.0648i	−0.302769	+	0.179728i
$57$		0			0
$58$	10.8501			0.187070
$59$	−6.83327	+	3.94519i	−0.115818	+	0.0668676i	−0.556790	−	0.830653i	$-0.687967\pi$
$59$	−6.83327	+	3.94519i	−0.115818	+	0.0668676i	0.440972	+	0.897521i	$0.354634\pi$
$60$		0			0
$61$	35.9531	+	20.7575i	0.589395	+	0.340287i	0.764858	−	0.644199i	$-0.222809\pi$
$61$	35.9531	+	20.7575i	0.589395	+	0.340287i	−0.175463	+	0.984486i	$0.556142\pi$
$62$		−	3.13060i		−	0.0504935i
$63$		0			0
$64$	−52.0342			−0.813035
$65$	35.5281	−	61.5365i	0.546586	−	0.946715i
$66$		0			0
$67$	27.6189	+	47.8373i	0.412222	+	0.713990i	0.995132	−	0.0985469i	$-0.0314194\pi$
$67$	27.6189	+	47.8373i	0.412222	+	0.713990i	−0.582910	+	0.812537i	$0.698086\pi$
$68$			78.7619i			1.15826i
$69$		0			0
$70$	−11.4961	+	0.139247i	−0.164230	+	0.00198924i
$71$	−4.91318			−0.0691998			−0.0345999	−	0.999401i	$-0.511016\pi$
$71$	−4.91318			−0.0691998			−0.0345999	+	0.999401i	$0.511016\pi$
$72$		0			0
$73$	−9.44921	−	5.45550i	−0.129441	−	0.0747329i	0.433881	−	0.900970i	$-0.357144\pi$
$73$	−9.44921	−	5.45550i	−0.129441	−	0.0747329i	−0.563322	+	0.826237i	$0.690477\pi$
$74$	21.0006			0.283792
$75$		0			0
$76$	0.577548	+	0.333447i	0.00759931	+	0.00438746i
$77$	81.1031	−	48.1439i	1.05329	−	0.625246i
$78$		0			0
$79$	54.1512	−	93.7926i	0.685458	−	1.18725i	−0.287834	−	0.957680i	$-0.592935\pi$
$79$	54.1512	−	93.7926i	0.685458	−	1.18725i	0.973293	−	0.229568i	$-0.0737314\pi$
$80$	−57.5591	−	33.2318i	−0.719489	−	0.415397i
$81$		0			0
$82$	−5.19102	+	2.99703i	−0.0633051	+	0.0365492i
$83$	−98.3122	+	56.7606i	−1.18448	+	0.683862i	−0.957048	−	0.289930i	$-0.906368\pi$
$83$	−98.3122	+	56.7606i	−1.18448	+	0.683862i	−0.227437	+	0.973793i	$0.573034\pi$
$84$		0			0
$85$	−46.6844	+	80.8597i	−0.549228	+	0.951291i
$86$	5.32858			0.0619602
$87$		0			0
$88$	−37.9524			−0.431277
$89$	105.603	−	60.9700i	1.18655	−	0.685056i	0.229031	−	0.973419i	$-0.426444\pi$
$89$	105.603	−	60.9700i	1.18655	−	0.685056i	0.957521	+	0.288363i	$0.0931110\pi$
$90$		0			0
$91$	108.356	−	1.31246i	1.19072	−	0.0144227i
$92$	61.3401	+	106.244i	0.666740	+	1.15483i
$93$		0			0
$94$	−13.8272	+	7.98314i	−0.147098	+	0.0849270i
$95$	0.395287	+	0.684657i	0.00416091	+	0.00720692i
$96$		0			0
$97$	−85.6452	+	49.4473i	−0.882940	+	0.509766i	−0.871627	−	0.490170i	$-0.836935\pi$
$97$	−85.6452	+	49.4473i	−0.882940	+	0.509766i	−0.0113135	+	0.999936i	$0.503601\pi$
$98$	−9.13187	−	14.9675i	−0.0931823	−	0.152729i
$99$		0			0
$100$	7.61139	+	13.1833i	0.0761139	+	0.131833i
$101$		−	132.682i		−	1.31368i	−0.754029	−	0.656842i	$-0.771892\pi$
$101$		−	132.682i		−	1.31368i	0.754029	−	0.656842i	$-0.228108\pi$
$102$		0			0
$103$		−	56.1007i		−	0.544667i	−0.962203	−	0.272334i	$-0.912205\pi$
$103$		−	56.1007i		−	0.544667i	0.962203	−	0.272334i	$-0.0877955\pi$
$104$	−37.7630	−	21.8025i	−0.363106	−	0.209639i
$105$		0			0
$106$	−8.28917	−	14.3573i	−0.0781997	−	0.135446i
$107$	24.1951	+	41.9072i	0.226123	+	0.391656i	0.956656	−	0.291222i	$-0.0940617\pi$
$107$	24.1951	+	41.9072i	0.226123	+	0.391656i	−0.730533	+	0.682877i	$0.760728\pi$
$108$		0			0
$109$	−31.1327	+	53.9234i	−0.285621	+	0.494710i	−0.972760	−	0.231816i	$-0.925533\pi$
$109$	−31.1327	+	53.9234i	−0.285621	+	0.494710i	0.687139	+	0.726526i	$0.258866\pi$
$110$	−19.1648	−	11.0648i	−0.174225	−	0.100589i
$111$		0			0
$112$	−1.22763	−	101.352i	−0.0109610	−	0.904930i
$113$	−72.2659	+	125.168i	−0.639521	+	1.10768i	0.346017	+	0.938228i	$0.387534\pi$
$113$	−72.2659	+	125.168i	−0.639521	+	1.10768i	−0.985538	+	0.169455i	$0.945799\pi$
$114$		0			0
$115$			145.432i			1.26462i
$116$	−58.7039	+	101.678i	−0.506068	+	0.876535i
$117$		0			0
$118$			2.82336i			0.0239267i
$119$	−142.381	+	1.72459i	−1.19648	+	0.0144924i
$120$		0			0
$121$	60.5419			0.500346
$122$	12.8648	−	7.42751i	0.105449	−	0.0608813i
$123$		0			0
$124$	29.3374	+	16.9379i	0.236592	+	0.136596i
$125$			132.797i			1.06238i
$126$		0			0
$127$	6.23227			0.0490730			0.0245365	−	0.999699i	$-0.492189\pi$
$127$	6.23227			0.0490730			0.0245365	+	0.999699i	$0.492189\pi$
$128$	−42.2061	+	73.1032i	−0.329735	+	0.571119i
$129$		0			0
$130$	−12.7128	−	22.0191i	−0.0977904	−	0.169378i
$131$		−	48.9225i		−	0.373454i	−0.982412	−	0.186727i	$-0.940212\pi$
$131$		−	48.9225i		−	0.373454i	0.982412	−	0.186727i	$-0.0597880\pi$
$132$		0			0
$133$	−0.590138	+	1.05135i	−0.00443713	+	0.00790492i
$134$	19.7653			0.147502
$135$		0			0
$136$	49.6211	+	28.6488i	0.364861	+	0.210653i
$137$	238.567			1.74137			0.870684	−	0.491843i	$-0.163676\pi$
$137$	238.567			1.74137			0.870684	+	0.491843i	$0.163676\pi$
$138$		0			0
$139$	−177.385	−	102.413i	−1.27615	−	0.736786i	−0.300012	−	0.953935i	$-0.596991\pi$
$139$	−177.385	−	102.413i	−1.27615	−	0.736786i	−0.976138	+	0.217149i	$0.930324\pi$
$140$	60.8941	−	108.485i	0.434958	−	0.774895i
$141$		0			0
$142$	−0.879024	+	1.52251i	−0.00619031	+	0.0107219i
$143$	180.636	+	104.290i	1.26319	+	0.729303i
$144$		0			0
$145$	−120.535	+	69.5908i	−0.831275	+	0.479937i
$146$	−3.38114	+	1.95210i	−0.0231585	+	0.0133706i
$147$		0			0
$148$	−113.623	+	196.801i	−0.767722	+	1.32973i
$149$	−4.07337			−0.0273380			−0.0136690	−	0.999907i	$-0.504351\pi$
$149$	−4.07337			−0.0273380			−0.0136690	+	0.999907i	$0.504351\pi$
$150$		0			0
$151$	20.7285			0.137275			0.0686374	−	0.997642i	$-0.478135\pi$
$151$	20.7285			0.137275			0.0686374	+	0.997642i	$0.478135\pi$
$152$	0.420153	−	0.242575i	0.00276416	−	0.00159589i
$153$		0			0
$154$	−0.408750	−	33.7460i	−0.00265422	−	0.219130i
$155$	20.0792	+	34.7781i	0.129543	+	0.224375i
$156$		0			0
$157$	88.7587	−	51.2448i	0.565342	−	0.326400i	−0.189945	−	0.981795i	$-0.560831\pi$
$157$	88.7587	−	51.2448i	0.565342	−	0.326400i	0.755287	+	0.655395i	$0.227498\pi$
$158$	−19.3765	−	33.5611i	−0.122636	−	0.212412i
$159$		0			0
$160$	−65.3835	+	37.7492i	−0.408647	+	0.235933i
$161$	−190.718	+	113.213i	−1.18458	+	0.703186i
$162$		0			0
$163$	−15.4290	−	26.7238i	−0.0946563	−	0.163950i	0.814809	−	0.579730i	$-0.196842\pi$
$163$	−15.4290	−	26.7238i	−0.0946563	−	0.163950i	−0.909465	+	0.415780i	$0.863509\pi$
$164$		−	64.8612i		−	0.395495i
$165$		0			0
$166$			40.6204i			0.244701i
$167$	−80.8401	−	46.6730i	−0.484072	−	0.279479i	0.238040	−	0.971255i	$-0.423495\pi$
$167$	−80.8401	−	46.6730i	−0.484072	−	0.279479i	−0.722112	+	0.691776i	$0.756828\pi$
$168$		0			0
$169$	35.3233	+	61.1817i	0.209014	+	0.362022i
$170$	16.7047	+	28.9334i	0.0982631	+	0.170197i
$171$		0			0
$172$	−28.8300	+	49.9350i	−0.167616	+	0.290320i
$173$	174.637	+	100.827i	1.00946	+	0.582814i	0.911034	−	0.412331i	$-0.135285\pi$
$173$	174.637	+	100.827i	1.00946	+	0.582814i	0.0984284	+	0.995144i	$0.468618\pi$
$174$		0			0
$175$	−23.6653	+	14.0480i	−0.135230	+	0.0802745i
$176$	97.5496	−	168.961i	0.554259	−	0.960005i
$177$		0			0
$178$		−	43.6329i		−	0.245128i
$179$	−64.1067	+	111.036i	−0.358138	+	0.620313i	−0.987650	−	0.156678i	$-0.949922\pi$
$179$	−64.1067	+	111.036i	−0.358138	+	0.620313i	0.629512	+	0.776991i	$0.283255\pi$
$180$		0			0
$181$		−	160.637i		−	0.887496i	−0.896152	−	0.443748i	$-0.853648\pi$
$181$		−	160.637i		−	0.887496i	0.896152	−	0.443748i	$-0.146352\pi$
$182$	18.9793	−	33.8125i	0.104282	−	0.185783i
$183$		0			0
$184$	89.2470			0.485038
$185$	−233.298	+	134.695i	−1.26107	+	0.728080i
$186$		0			0
$187$	−237.358	−	137.039i	−1.26930	−	0.732828i
$188$		−	172.770i		−	0.918987i
$189$		0			0
$190$	0.282885			0.00148887
$191$	110.157	−	190.797i	0.576736	−	0.998936i	−0.419115	−	0.907933i	$-0.637660\pi$
$191$	110.157	−	190.797i	0.576736	−	0.998936i	0.995851	−	0.0910025i	$-0.0290071\pi$
$192$		0			0
$193$	98.6654	+	170.894i	0.511220	+	0.885459i	0.999915	+	0.0130044i	$0.00413953\pi$
$193$	98.6654	+	170.894i	0.511220	+	0.885459i	−0.488696	+	0.872454i	$0.662527\pi$
$194$			35.3867i			0.182406i
$195$		0			0
$196$	189.671	−	4.59546i	0.967707	−	0.0234462i
$197$	−58.7408			−0.298177			−0.149088	−	0.988824i	$-0.547634\pi$
$197$	−58.7408			−0.298177			−0.149088	+	0.988824i	$0.547634\pi$
$198$		0			0
$199$	5.03827	+	2.90884i	0.0253179	+	0.0146173i	0.512606	−	0.858624i	$-0.328680\pi$
$199$	5.03827	+	2.90884i	0.0253179	+	0.0146173i	−0.487288	+	0.873242i	$0.662014\pi$
$200$	11.0742			0.0553711
$201$		0			0
$202$	−41.1160	−	23.7383i	−0.203544	−	0.117516i
$203$	−185.093	−	103.895i	−0.911786	−	0.511797i
$204$		0			0
$205$	38.4451	−	66.5888i	0.187537	−	0.324823i
$206$	−17.3847	−	10.0371i	−0.0843917	−	0.0487236i
$207$		0			0
$208$	194.126	−	112.079i	0.933297	−	0.538839i
$209$	−2.00976	+	1.16034i	−0.00961610	+	0.00555186i
$210$		0			0
$211$	154.119	−	266.942i	0.730423	−	1.26513i	−0.226280	−	0.974062i	$-0.572656\pi$
$211$	154.119	−	266.942i	0.730423	−	1.26513i	0.956703	−	0.291067i	$-0.0940102\pi$
$212$	179.393			0.846192
$213$		0			0
$214$	17.3151			0.0809117
$215$	−59.1958	+	34.1767i	−0.275329	+	0.158961i
$216$		0			0
$217$	−29.9769	+	53.4051i	−0.138143	+	0.246106i
$218$	11.1400	+	19.2950i	0.0511008	+	0.0885092i
$219$		0			0
$220$	207.380	−	119.731i	0.942636	−	0.544231i
$221$	−157.449	−	272.710i	−0.712440	−	1.23398i
$222$		0			0
$223$	207.191	−	119.622i	0.929109	−	0.536421i	0.0425791	−	0.999093i	$-0.486443\pi$
$223$	207.191	−	119.622i	0.929109	−	0.536421i	0.886530	+	0.462672i	$0.153109\pi$
$224$	−100.403	−	56.3572i	−0.448226	−	0.251595i
$225$		0			0
$226$	25.8584	+	44.7880i	0.114418	+	0.198177i
$227$		−	246.262i		−	1.08486i	−0.840102	−	0.542428i	$-0.817505\pi$
$227$		−	246.262i		−	1.08486i	0.840102	−	0.542428i	$-0.182495\pi$
$228$		0			0
$229$			243.735i			1.06434i	0.846636	+	0.532172i	$0.178624\pi$
$229$			243.735i			1.06434i	−0.846636	+	0.532172i	$0.821376\pi$
$230$	45.0669	+	26.0194i	0.195943	+	0.113128i
$231$		0			0
$232$	42.7057	+	73.9685i	0.184076	+	0.318830i
$233$	−104.972	−	181.817i	−0.450524	−	0.780331i	0.547894	−	0.836548i	$-0.315430\pi$
$233$	−104.972	−	181.817i	−0.450524	−	0.780331i	−0.998419	+	0.0562167i	$0.982096\pi$
$234$		0			0
$235$	102.405	−	177.371i	0.435767	−	0.754771i
$236$	−26.4582	−	15.2756i	−0.112111	−	0.0647272i
$237$		0			0
$238$	−24.9391	+	44.4300i	−0.104786	+	0.186681i
$239$	−128.716	+	222.942i	−0.538560	+	0.932812i	0.460422	+	0.887700i	$0.347698\pi$
$239$	−128.716	+	222.942i	−0.538560	+	0.932812i	−0.998982	+	0.0451125i	$0.985635\pi$
$240$		0			0
$241$		−	37.7730i		−	0.156734i	−0.996925	−	0.0783672i	$-0.975029\pi$
$241$		−	37.7730i		−	0.156734i	0.996925	−	0.0783672i	$-0.0249707\pi$
$242$	10.8316	−	18.7609i	0.0447588	−	0.0775245i
$243$		0			0
$244$			160.745i			0.658790i
$245$	197.446	+	107.705i	0.805903	+	0.439613i
$246$		0			0
$247$	−2.66632			−0.0107948
$248$	21.3423	−	12.3220i	0.0860575	−	0.0496853i
$249$		0			0
$250$	41.1516	+	23.7589i	0.164606	+	0.0950355i
$251$		−	173.737i		−	0.692179i	−0.938202	−	0.346089i	$-0.887509\pi$
$251$		−	173.737i		−	0.692179i	0.938202	−	0.346089i	$-0.112491\pi$
$252$		0			0
$253$	−426.905			−1.68737
$254$	1.11502	−	1.93128i	0.00438985	−	0.00760345i
$255$		0			0
$256$	−88.9661	−	154.094i	−0.347524	−	0.601929i
$257$			169.568i			0.659796i	0.944017	+	0.329898i	$0.107014\pi$
$257$			169.568i			0.659796i	−0.944017	+	0.329898i	$0.892986\pi$
$258$		0			0
$259$	−358.251	−	201.091i	−1.38321	−	0.776413i
$260$	275.127			1.05818
$261$		0			0
$262$	−15.1603	−	8.75279i	−0.0578637	−	0.0334076i
$263$	215.562			0.819627			0.409814	−	0.912169i	$-0.365594\pi$
$263$	215.562			0.819627			0.409814	+	0.912169i	$0.365594\pi$
$264$		0			0
$265$	184.171	+	106.331i	0.694984	+	0.401249i
$266$	0.220215	+	0.370973i	0.000827876	+	0.00139464i
$267$		0			0
$268$	−106.939	+	185.224i	−0.399027	+	0.691135i
$269$	362.108	+	209.063i	1.34613	+	0.777186i	0.987698	−	0.156372i	$-0.0499797\pi$
$269$	362.108	+	209.063i	1.34613	+	0.777186i	0.358427	+	0.933558i	$0.383313\pi$
$270$		0			0
$271$	15.1120	−	8.72489i	0.0557637	−	0.0321952i	−0.471859	−	0.881674i	$-0.656417\pi$
$271$	15.1120	−	8.72489i	0.0557637	−	0.0321952i	0.527623	+	0.849479i	$0.323084\pi$
$272$	−255.084	+	147.273i	−0.937808	+	0.541444i
$273$		0			0
$274$	42.6824	−	73.9281i	0.155775	−	0.269811i
$275$	−52.9726			−0.192627
$276$		0			0
$277$	344.133			1.24236			0.621178	−	0.783670i	$-0.286654\pi$
$277$	344.133			1.24236			0.621178	+	0.783670i	$0.286654\pi$
$278$	−63.4723	+	36.6458i	−0.228318	+	0.131819i
$279$		0			0
$280$	−46.1977	−	77.8245i	−0.164992	−	0.277945i
$281$	−199.841	−	346.135i	−0.711178	−	1.23180i	−0.964415	−	0.264392i	$-0.914829\pi$
$281$	−199.841	−	346.135i	−0.711178	−	1.23180i	0.253238	−	0.967404i	$-0.418505\pi$
$282$		0			0
$283$	−463.108	+	267.376i	−1.63643	+	0.944791i	−0.654376	+	0.756170i	$0.727069\pi$
$283$	−463.108	+	267.376i	−1.63643	+	0.944791i	−0.982050	+	0.188621i	$0.939598\pi$
$284$	−9.51184	−	16.4750i	−0.0334924	−	0.0580105i
$285$		0			0
$286$	64.6357	−	37.3174i	0.225999	−	0.130481i
$287$	117.252	−	1.42022i	0.408544	−	0.00494850i
$288$		0			0
$289$	62.3904	+	108.063i	0.215884	+	0.373921i
$290$			49.8023i			0.171732i
$291$		0			0
$292$		−	42.2470i		−	0.144682i
$293$	369.137	+	213.121i	1.25985	+	0.727377i	0.973046	−	0.230612i	$-0.0740727\pi$
$293$	369.137	+	213.121i	1.25985	+	0.727377i	0.286807	+	0.957988i	$0.407406\pi$
$294$		0			0
$295$	−18.1086	−	31.3650i	−0.0613850	−	0.106322i
$296$	82.6581	+	143.168i	0.279250	+	0.483676i
$297$		0			0
$298$	−0.728772	+	1.26227i	−0.00244554	+	0.00423580i
$299$	−424.775	−	245.244i	−1.42065	−	0.820215i
$300$		0			0
$301$	−90.9006	−	51.0236i	−0.301995	−	0.169514i
$302$	3.70856	−	6.42342i	0.0122800	−	0.0212696i
$303$		0			0
$304$			2.49398i			0.00820388i
$305$	−95.2779	+	165.026i	−0.312387	+	0.541069i
$306$		0			0
$307$			76.0021i			0.247564i	0.992309	+	0.123782i	$0.0395023\pi$
$307$			76.0021i			0.247564i	−0.992309	+	0.123782i	$0.960498\pi$
$308$	318.451	+	178.751i	1.03393	+	0.580359i
$309$		0			0
$310$	14.3696			0.0463534
$311$	−130.914	+	75.5833i	−0.420945	+	0.243033i	−0.695482	−	0.718544i	$-0.744809\pi$
$311$	−130.914	+	75.5833i	−0.420945	+	0.243033i	0.274536	+	0.961577i	$0.411476\pi$
$312$		0			0
$313$	142.393	+	82.2104i	0.454928	+	0.262653i	0.709909	−	0.704293i	$-0.248736\pi$
$313$	142.393	+	82.2104i	0.454928	+	0.262653i	−0.254981	+	0.966946i	$0.582069\pi$
$314$		−	36.6731i		−	0.116793i
$315$		0			0
$316$	419.343			1.32703
$317$	−202.862	+	351.367i	−0.639942	+	1.10841i	0.345503	+	0.938418i	$0.387708\pi$
$317$	−202.862	+	351.367i	−0.639942	+	1.10841i	−0.985445	+	0.169994i	$0.945625\pi$
$318$		0			0
$319$	−204.279	−	353.822i	−0.640373	−	1.10916i
$320$		−	238.839i		−	0.746372i
$321$		0			0
$322$	0.961197	+	79.3555i	0.00298509	+	0.246446i
$323$	3.50357			0.0108470
$324$		0			0
$325$	−52.7083	−	30.4311i	−0.162179	−	0.0936343i
$326$	−11.0417			−0.0338702
$327$		0			0
$328$	−40.8635	−	23.5925i	−0.124584	−	0.0719285i
$329$	312.322	−	3.78301i	0.949306	−	0.0114985i
$330$		0			0
$331$	−168.599	+	292.022i	−0.509362	+	0.882242i	0.490579	+	0.871397i	$0.336785\pi$
$331$	−168.599	+	292.022i	−0.509362	+	0.882242i	−0.999941	+	0.0108447i	$0.996548\pi$
$332$	−380.661	−	219.775i	−1.14657	−	0.661973i
$333$		0			0
$334$	−28.9264	+	16.7007i	−0.0866060	+	0.0500020i
$335$	−219.575	+	126.772i	−0.655448	+	0.378423i
$336$		0			0
$337$	26.0635	−	45.1433i	0.0773397	−	0.133956i	−0.824762	−	0.565481i	$-0.808691\pi$
$337$	26.0635	−	45.1433i	0.0773397	−	0.133956i	0.902101	+	0.431524i	$0.142024\pi$
$338$	25.2789			0.0747898
$339$		0			0
$340$	−361.520			−1.06330
$341$	−102.089	+	58.9410i	−0.299381	+	0.172848i
$342$		0			0
$343$	12.4605	+	342.774i	0.0363279	+	0.999340i
$344$	20.9732	+	36.3266i	0.0609686	+	0.105601i
$345$		0			0
$346$	62.4891	−	36.0781i	0.180604	−	0.104272i
$347$	−130.618	−	226.237i	−0.376421	−	0.651981i	0.614117	−	0.789215i	$-0.289512\pi$
$347$	−130.618	−	226.237i	−0.376421	−	0.651981i	−0.990539	+	0.137234i	$0.956179\pi$
$348$		0			0
$349$	−211.722	+	122.238i	−0.606653	+	0.350251i	−0.771654	−	0.636042i	$-0.780570\pi$
$349$	−211.722	+	122.238i	−0.606653	+	0.350251i	0.165001	+	0.986293i	$0.447237\pi$
$350$	0.119270	+	9.84683i	0.000340772	+	0.0281338i
$351$		0			0
$352$	−110.810	−	191.929i	−0.314802	−	0.545253i
$353$			532.054i			1.50724i	0.657313	+	0.753618i	$0.271693\pi$
$353$			532.054i			1.50724i	−0.657313	+	0.753618i	$0.728307\pi$
$354$		0			0
$355$		−	22.5517i		−	0.0635260i
$356$	408.891	+	236.074i	1.14857	+	0.663128i
$357$		0			0
$358$	22.9388	+	39.7312i	0.0640749	+	0.110981i
$359$	−132.455	−	229.420i	−0.368957	−	0.639052i	0.620446	−	0.784249i	$-0.286952\pi$
$359$	−132.455	−	229.420i	−0.368957	−	0.639052i	−0.989403	+	0.145197i	$0.953618\pi$
$360$		0			0
$361$	−180.485	+	312.609i	−0.499959	+	0.865954i
$362$	−49.7787	−	28.7397i	−0.137510	−	0.0793915i
$363$		0			0
$364$	214.176	+	360.799i	0.588395	+	0.991207i
$365$	25.0410	−	43.3722i	0.0686054	−	0.118828i
$366$		0			0
$367$		−	121.137i		−	0.330073i	−0.986287	−	0.165036i	$-0.947226\pi$
$367$		−	121.137i		−	0.330073i	0.986287	−	0.165036i	$-0.0527741\pi$
$368$	−229.393	+	397.320i	−0.623350	+	1.07967i
$369$		0			0
$370$			96.3937i			0.260523i
$371$	3.92803	+	324.294i	0.0105877	+	0.874109i
$372$		0			0
$373$	−510.590			−1.36887			−0.684437	−	0.729072i	$-0.739952\pi$
$373$	−510.590			−1.36887			−0.684437	+	0.729072i	$0.739952\pi$
$374$	−84.9321	+	49.0356i	−0.227091	+	0.131111i
$375$		0			0
$376$	−108.847	−	62.8430i	−0.289487	−	0.167136i
$377$		−	469.409i		−	1.24512i
$378$		0			0
$379$	352.243			0.929402			0.464701	−	0.885468i	$-0.346162\pi$
$379$	352.243			0.929402			0.464701	+	0.885468i	$0.346162\pi$
$380$	−1.53054	+	2.65097i	−0.00402773	+	0.00697623i
$381$		0			0
$382$	−39.4165	−	68.2714i	−0.103185	−	0.178721i
$383$			139.893i			0.365256i	0.983182	+	0.182628i	$0.0584604\pi$
$383$			139.893i			0.365256i	−0.983182	+	0.182628i	$0.941540\pi$
$384$		0			0
$385$	220.983	+	372.266i	0.573981	+	0.966926i
$386$	70.6094			0.182926
$387$		0			0
$388$	−331.615	−	191.458i	−0.854678	−	0.493449i
$389$	239.114			0.614689			0.307345	−	0.951598i	$-0.400560\pi$
$389$	239.114			0.614689			0.307345	+	0.951598i	$0.400560\pi$
$390$		0			0
$391$	558.160	+	322.254i	1.42752	+	0.824179i
$392$	66.0953	−	121.167i	0.168610	−	0.309099i
$393$		0			0
$394$	−10.5094	+	18.2028i	−0.0266736	+	0.0462000i
$395$	430.512	+	248.556i	1.08990	+	0.629256i
$396$		0			0
$397$	627.183	−	362.104i	1.57981	−	0.912102i	0.584921	−	0.811090i	$-0.301126\pi$
$397$	627.183	−	362.104i	1.57981	−	0.912102i	0.994885	−	0.101011i	$-0.0322078\pi$
$398$	1.80281	−	1.04085i	0.00452966	−	0.00261520i
$399$		0			0
$400$	−28.4642	+	49.3015i	−0.0711606	+	0.123254i
$401$	46.8372			0.116801			0.0584005	−	0.998293i	$-0.481400\pi$
$401$	46.8372			0.116801			0.0584005	+	0.998293i	$0.481400\pi$
$402$		0			0
$403$	−135.439			−0.336078
$404$	444.912	−	256.870i	1.10127	−	0.635817i
$405$		0			0
$406$	−65.3104	+	38.7692i	−0.160863	+	0.0954906i
$407$	−395.388	−	684.831i	−0.971468	−	1.68263i
$408$		0			0
$409$	155.795	−	89.9485i	0.380918	−	0.219923i	−0.297300	−	0.954784i	$-0.596086\pi$
$409$	155.795	−	89.9485i	0.380918	−	0.219923i	0.678217	+	0.734861i	$0.262753\pi$
$410$	−13.7565	−	23.8270i	−0.0335525	−	0.0581146i
$411$		0			0
$412$	188.118	−	108.610i	0.456597	−	0.263616i
$413$	27.0350	−	48.1638i	0.0654600	−	0.116619i
$414$		0			0
$415$	−260.533	−	451.257i	−0.627791	−	1.08737i
$416$		−	254.629i		−	0.612088i
$417$		0			0
$418$			0.830390i			0.00198658i
$419$	530.561	+	306.320i	1.26626	+	0.731073i	0.974278	−	0.225352i	$-0.0723531\pi$
$419$	530.561	+	306.320i	1.26626	+	0.731073i	0.291979	+	0.956425i	$0.405686\pi$
$420$		0			0
$421$	−413.302	−	715.860i	−0.981715	−	1.70038i	−0.655711	−	0.755012i	$-0.727631\pi$
$421$	−413.302	−	715.860i	−0.981715	−	1.70038i	−0.326004	−	0.945368i	$-0.605702\pi$
$422$	−55.1473	−	95.5180i	−0.130681	−	0.226346i
$423$		0			0
$424$	65.2520	−	113.020i	0.153896	−	0.266556i
$425$	69.2593	+	39.9869i	0.162963	+	0.0940868i
$426$		0			0
$427$	−290.584	+	3.51972i	−0.680525	+	0.00824289i
$428$	−93.6826	+	162.263i	−0.218885	+	0.379119i
$429$		0			0
$430$			24.4584i			0.0568800i
$431$	23.6677	−	40.9937i	0.0549135	−	0.0951130i	−0.837262	−	0.546802i	$-0.815845\pi$
$431$	23.6677	−	40.9937i	0.0549135	−	0.0951130i	0.892175	+	0.451689i	$0.149178\pi$
$432$		0			0
$433$			190.256i			0.439390i	0.975569	+	0.219695i	$0.0705061\pi$
$433$			190.256i			0.439390i	−0.975569	+	0.219695i	$0.929494\pi$
$434$	11.1861	+	18.8441i	0.0257745	+	0.0434196i
$435$		0			0
$436$	−241.089			−0.552957
$437$	4.72606	−	2.72859i	0.0108148	−	0.00624392i
$438$		0			0
$439$	308.042	+	177.848i	0.701691	+	0.405122i	0.807977	−	0.589214i	$-0.200563\pi$
$439$	308.042	+	177.848i	0.701691	+	0.405122i	−0.106286	+	0.994336i	$0.533896\pi$
$440$		−	174.203i		−	0.395916i
$441$		0			0
$442$	−112.678			−0.254927
$443$	−424.488	+	735.235i	−0.958212	+	1.65967i	−0.231372	+	0.972865i	$0.574321\pi$
$443$	−424.488	+	735.235i	−0.958212	+	1.65967i	−0.726840	+	0.686807i	$0.759012\pi$
$444$		0			0
$445$	279.855	+	484.722i	0.628887	+	1.08926i
$446$		−	85.6068i		−	0.191944i
$447$		0			0
$448$	313.212	−	185.927i	0.699133	−	0.415015i
$449$	−41.6583			−0.0927802			−0.0463901	−	0.998923i	$-0.514772\pi$
$449$	−41.6583			−0.0927802			−0.0463901	+	0.998923i	$0.514772\pi$
$450$		0			0
$451$	195.467	+	112.853i	0.433408	+	0.250228i
$452$	−559.622			−1.23810
$453$		0			0
$454$	−76.3126	−	44.0591i	−0.168089	−	0.0970464i
$455$	6.02426	+	497.357i	0.0132401	+	1.09309i
$456$		0			0
$457$	325.501	−	563.785i	0.712257	−	1.23367i	−0.251751	−	0.967792i	$-0.581006\pi$
$457$	325.501	−	563.785i	0.712257	−	1.23367i	0.964008	−	0.265873i	$-0.0856603\pi$
$458$	75.5294	+	43.6069i	0.164911	+	0.0952116i
$459$		0			0
$460$	−487.665	+	281.553i	−1.06014	+	0.612072i
$461$	478.318	−	276.157i	1.03757	−	0.599039i	0.118424	−	0.992963i	$-0.462216\pi$
$461$	478.318	−	276.157i	1.03757	−	0.599039i	0.919143	+	0.393924i	$0.128883\pi$
$462$		0			0
$463$	263.978	−	457.223i	0.570146	−	0.987522i	−0.426404	−	0.904533i	$-0.640220\pi$
$463$	263.978	−	457.223i	0.570146	−	0.987522i	0.996550	−	0.0829895i	$-0.0264468\pi$
$464$	−439.069			−0.946269
$465$		0			0
$466$	−75.1228			−0.161208
$467$	137.783	−	79.5489i	0.295038	−	0.170340i	−0.345174	−	0.938539i	$-0.612180\pi$
$467$	137.783	−	79.5489i	0.295038	−	0.170340i	0.640212	+	0.768199i	$0.278847\pi$
$468$		0			0
$469$	−337.178	−	189.262i	−0.718930	−	0.403544i
$470$	−36.6429	−	63.4674i	−0.0779637	−	0.135037i
$471$		0			0
$472$	−19.2477	+	11.1127i	−0.0407791	+	0.0235438i
$473$	−100.323	−	173.765i	−0.212100	−	0.367368i
$474$		0			0
$475$	0.586434	−	0.338578i	0.00123460	−	0.000712795i
$476$	−281.429	−	474.095i	−0.591238	−	0.995998i
$477$		0			0
$478$	46.0574	+	79.7737i	0.0963544	+	0.166891i
$479$		−	937.084i		−	1.95633i	−0.207820	−	0.978167i	$-0.566637\pi$
$479$		−	937.084i		−	1.95633i	0.207820	−	0.978167i	$-0.433363\pi$
$480$		0			0
$481$		−	908.553i		−	1.88888i
$482$	−11.7052	−	6.75801i	−0.0242847	−	0.0140208i
$483$		0			0
$484$	117.208	+	203.010i	0.242165	+	0.419443i
$485$	−226.965	−	393.115i	−0.467969	−	0.810546i
$486$		0			0
$487$	167.657	−	290.390i	0.344264	−	0.596283i	−0.640956	−	0.767578i	$-0.721462\pi$
$487$	167.657	−	290.390i	0.344264	−	0.596283i	0.985220	+	0.171295i	$0.0547951\pi$
$488$	101.271	+	58.4691i	0.207524	+	0.119814i
$489$		0			0
$490$	68.7014	−	41.9156i	0.140207	−	0.0855421i
$491$	176.727	−	306.100i	0.359933	−	0.623422i	−0.628017	−	0.778200i	$-0.716133\pi$
$491$	176.727	−	306.100i	0.359933	−	0.623422i	0.987949	+	0.154778i	$0.0494663\pi$
$492$		0			0
$493$			616.809i			1.25113i
$494$	−0.477034	+	0.826247i	−0.000965656	+	0.00167256i
$495$		0			0
$496$			126.685i			0.255414i
$497$	29.5741	−	17.5556i	0.0595053	−	0.0353232i
$498$		0			0
$499$	363.463			0.728382			0.364191	−	0.931324i	$-0.381346\pi$
$499$	363.463			0.728382			0.364191	+	0.931324i	$0.381346\pi$
$500$	−445.297	+	257.092i	−0.890594	+	0.514185i
$501$		0			0
$502$	−53.8382	−	31.0835i	−0.107247	−	0.0619193i
$503$		−	903.205i		−	1.79564i	−0.440366	−	0.897819i	$-0.645151\pi$
$503$		−	903.205i		−	1.79564i	0.440366	−	0.897819i	$-0.354849\pi$
$504$		0			0
$505$	609.016			1.20597
$506$	−76.3782	+	132.291i	−0.150945	+	0.261444i
$507$		0			0
$508$	12.0656	+	20.8981i	0.0237511	+	0.0411381i
$509$		−	92.9997i		−	0.182711i	−0.995818	−	0.0913553i	$-0.970880\pi$
$509$		−	92.9997i		−	0.182711i	0.995818	−	0.0913553i	$-0.0291199\pi$
$510$		0			0
$511$	76.3714	−	0.925053i	0.149455	−	0.00181028i
$512$	−401.317			−0.783823
$513$		0			0
$514$	52.5462	+	30.3375i	0.102230	+	0.0590224i
$515$	257.505			0.500009
$516$		0			0
$517$	520.661	+	300.604i	1.00708	+	0.581439i
$518$	−126.410	+	75.0387i	−0.244035	+	0.144862i
$519$		0			0
$520$	100.074	−	173.334i	0.192451	−	0.333334i
$521$	35.5126	+	20.5032i	0.0681625	+	0.0393536i	0.533694	−	0.845678i	$-0.320803\pi$
$521$	35.5126	+	20.5032i	0.0681625	+	0.0393536i	−0.465531	+	0.885031i	$0.654137\pi$
$522$		0			0
$523$	−848.580	+	489.928i	−1.62252	+	0.936765i	−0.636283	+	0.771456i	$0.719529\pi$
$523$	−848.580	+	489.928i	−1.62252	+	0.936765i	−0.986242	+	0.165309i	$0.947138\pi$
$524$	164.048	−	94.7131i	0.313068	−	0.180750i
$525$		0			0
$526$	38.5665	−	66.7991i	0.0733203	−	0.126994i
$527$	177.969			0.337702
$528$		0			0
$529$	474.890			0.897713
$530$	65.9004	−	38.0476i	0.124340	−	0.0717880i
$531$		0			0
$532$	−4.66792	+	0.0565404i	−0.00877428	+	0.000106279i
$533$	129.661	+	224.580i	0.243267	+	0.421350i
$534$		0			0
$535$	−192.356	+	111.057i	−0.359543	+	0.207582i
$536$	77.7959	+	134.746i	0.145142	+	0.251393i
$537$		0			0
$538$	129.570	−	74.8075i	0.240837	−	0.139047i
$539$	−316.161	+	579.590i	−0.586570	+	1.07531i
$540$		0			0
$541$	−23.4697	−	40.6506i	−0.0433820	−	0.0751398i	0.843519	−	0.537099i	$-0.180480\pi$
$541$	−23.4697	−	40.6506i	−0.0433820	−	0.0751398i	−0.886901	+	0.461959i	$0.847147\pi$
$542$		−	6.24393i		−	0.0115202i
$543$		0			0
$544$			334.585i			0.615046i
$545$	−247.510	−	142.900i	−0.454148	−	0.262202i
$546$		0			0
$547$	238.708	+	413.454i	0.436395	+	0.755858i	0.997408	−	0.0719485i	$-0.0229217\pi$
$547$	238.708	+	413.454i	0.436395	+	0.755858i	−0.561013	+	0.827807i	$0.689588\pi$
$548$	461.862	+	799.969i	0.842814	+	1.45980i
$549$		0			0
$550$	−9.47739	+	16.4153i	−0.0172316	+	0.0298460i
$551$	4.52295	+	2.61133i	0.00820863	+	0.00473925i
$552$		0			0
$553$	9.18206	+	758.061i	0.0166041	+	1.37082i
$554$	61.5692	−	106.641i	0.111136	−	0.192493i
$555$		0			0
$556$		−	793.081i		−	1.42640i
$557$	−60.4347	+	104.676i	−0.108500	+	0.187928i	−0.915163	−	0.403084i	$-0.867938\pi$
$557$	−60.4347	+	104.676i	−0.108500	+	0.187928i	0.806663	+	0.591012i	$0.201272\pi$
$558$		0			0
$559$		−	230.531i		−	0.412399i
$560$	465.211	−	5.63489i	0.830733	−	0.0100623i
$561$		0			0
$562$	−143.015			−0.254475
$563$	23.0895	−	13.3307i	0.0410116	−	0.0236780i	−0.479354	−	0.877622i	$-0.659129\pi$
$563$	23.0895	−	13.3307i	0.0410116	−	0.0236780i	0.520366	+	0.853944i	$0.325796\pi$
$564$		0			0
$565$	−574.527	−	331.703i	−1.01686	−	0.587086i
$566$			191.346i			0.338067i
$567$		0			0
$568$	−13.8393			−0.0243650
$569$	−7.82917	+	13.5605i	−0.0137595	+	0.0238322i	−0.872823	−	0.488037i	$-0.837713\pi$
$569$	−7.82917	+	13.5605i	−0.0137595	+	0.0238322i	0.859064	+	0.511869i	$0.171047\pi$
$570$		0			0
$571$	−201.516	−	349.036i	−0.352917	−	0.611271i	0.633842	−	0.773463i	$-0.281477\pi$
$571$	−201.516	−	349.036i	−0.352917	−	0.611271i	−0.986759	+	0.162192i	$0.948144\pi$
$572$			807.617i			1.41192i
$573$		0			0
$574$	20.5376	−	36.5885i	0.0357798	−	0.0637431i
$575$	124.568			0.216640
$576$		0			0
$577$	468.261	+	270.350i	0.811544	+	0.468545i	0.847492	−	0.530809i	$-0.178112\pi$
$577$	468.261	+	270.350i	0.811544	+	0.468545i	−0.0359480	+	0.999354i	$0.511445\pi$
$578$	44.6494			0.0772480
$579$		0			0
$580$	−466.706	−	269.453i	−0.804666	−	0.464574i
$581$	388.960	−	692.947i	0.669466	−	1.19268i
$582$		0			0
$583$	−312.127	+	540.620i	−0.535381	+	0.927308i
$584$	−26.6162	−	15.3669i	−0.0455757	−	0.0263131i
$585$		0			0
$586$	132.086	−	76.2596i	0.225402	−	0.130136i
$587$	−20.2716	+	11.7038i	−0.0345342	+	0.0199383i	−0.517168	−	0.855884i	$-0.673014\pi$
$587$	−20.2716	+	11.7038i	−0.0345342	+	0.0199383i	0.482633	+	0.875822i	$0.339680\pi$
$588$		0			0
$589$	0.753451	−	1.30502i	0.00127920	−	0.00221565i
$590$	−12.9593			−0.0219649
$591$		0			0
$592$	−849.829			−1.43552
$593$	−338.337	+	195.339i	−0.570551	+	0.329408i	−0.757370	−	0.652987i	$-0.773516\pi$
$593$	−338.337	+	195.339i	−0.570551	+	0.329408i	0.186818	+	0.982395i	$0.440182\pi$
$594$		0			0
$595$	−7.91596	−	653.533i	−0.0133041	−	1.09838i
$596$	−7.88597	−	13.6589i	−0.0132315	−	0.0229176i
$597$		0			0
$598$	−151.994	+	87.7539i	−0.254171	+	0.146746i
$599$	−425.272	−	736.592i	−0.709969	−	1.22970i	−0.964868	−	0.262735i	$-0.915375\pi$
$599$	−425.272	−	736.592i	−0.709969	−	1.22970i	0.254899	−	0.966968i	$-0.417958\pi$
$600$		0			0
$601$	−296.410	+	171.132i	−0.493194	+	0.284746i	−0.725899	−	0.687802i	$-0.758576\pi$
$601$	−296.410	+	171.132i	−0.493194	+	0.284746i	0.232705	+	0.972547i	$0.425242\pi$
$602$	−32.0745	+	19.0399i	−0.0532800	+	0.0316277i
$603$		0			0
$604$	40.1300	+	69.5072i	0.0664404	+	0.115078i
$605$			277.890i			0.459322i
$606$		0			0
$607$		−	97.6497i		−	0.160873i	−0.996760	−	0.0804364i	$-0.974369\pi$
$607$		−	97.6497i		−	0.160873i	0.996760	−	0.0804364i	$-0.0256314\pi$
$608$	2.45345	+	1.41650i	0.00403529	+	0.00232977i
$609$		0			0
$610$	34.0926	+	59.0501i	0.0558895	+	0.0968034i
$611$	345.376	+	598.208i	0.565263	+	0.979064i
$612$		0			0
$613$	249.196	−	431.620i	0.406519	−	0.704111i	−0.587978	−	0.808877i	$-0.700076\pi$
$613$	249.196	−	431.620i	0.406519	−	0.704111i	0.994497	+	0.104766i	$0.0334093\pi$
$614$	23.5518	+	13.5976i	0.0383579	+	0.0221460i
$615$		0			0
$616$	228.448	−	135.610i	0.370858	−	0.220146i
$617$	433.173	−	750.277i	0.702063	−	1.21601i	−0.265678	−	0.964062i	$-0.585596\pi$
$617$	433.173	−	750.277i	0.702063	−	1.21601i	0.967741	−	0.251947i	$-0.0810707\pi$
$618$		0			0
$619$			432.541i			0.698775i	0.936978	+	0.349387i	$0.113610\pi$
$619$			432.541i			0.698775i	−0.936978	+	0.349387i	$0.886390\pi$
$620$	−77.7458	+	134.660i	−0.125396	+	0.217193i
$621$		0			0
$622$			54.0908i			0.0869627i
$623$	−417.805	+	744.337i	−0.670635	+	1.19476i
$624$		0			0
$625$	−511.255			−0.818007
$626$	50.9513	−	29.4167i	0.0813918	−	0.0469916i
$627$		0			0
$628$	343.670	+	198.418i	0.547246	+	0.315952i
$629$			1193.85i			1.89801i
$630$		0			0
$631$	−315.748			−0.500393			−0.250197	−	0.968195i	$-0.580495\pi$
$631$	−315.748			−0.500393			−0.250197	+	0.968195i	$0.580495\pi$
$632$	152.531	−	264.192i	0.241347	−	0.418025i
$633$		0			0
$634$	72.5885	+	125.727i	0.114493	+	0.198307i
$635$			28.6063i			0.0450494i
$636$		0			0
$637$	−647.540	+	395.073i	−1.01655	+	0.620209i
$638$	−146.191			−0.229140
$639$		0			0
$640$	−335.546	−	193.728i	−0.524291	−	0.302700i
$641$	124.330			0.193963			0.0969816	−	0.995286i	$-0.469081\pi$
$641$	124.330			0.193963			0.0969816	+	0.995286i	$0.469081\pi$
$642$		0			0
$643$	−57.8499	−	33.3997i	−0.0899687	−	0.0519435i	0.454341	−	0.890828i	$-0.349875\pi$
$643$	−57.8499	−	33.3997i	−0.0899687	−	0.0519435i	−0.544309	+	0.838885i	$0.683208\pi$
$644$	−748.855	−	420.341i	−1.16282	−	0.652704i
$645$		0			0
$646$	0.626829	−	1.08570i	0.000970323	−	0.00168065i
$647$	594.628	+	343.308i	0.919054	+	0.530616i	0.883333	−	0.468746i	$-0.155294\pi$
$647$	594.628	+	343.308i	0.919054	+	0.530616i	0.0357206	+	0.999362i	$0.488627\pi$
$648$		0			0
$649$	92.0697	−	53.1565i	0.141864	−	0.0819052i
$650$	−18.8602	+	10.8889i	−0.0290157	+	0.0167522i
$651$		0			0
$652$	59.7404	−	103.473i	0.0916264	−	0.158702i
$653$	372.859			0.570994			0.285497	−	0.958380i	$-0.407841\pi$
$653$	372.859			0.570994			0.285497	+	0.958380i	$0.407841\pi$
$654$		0			0
$655$	224.556			0.342834
$656$	210.064	−	121.281i	0.320220	−	0.184879i
$657$		0			0
$658$	54.7056	−	97.4602i	0.0831392	−	0.148116i
$659$	191.042	+	330.895i	0.289897	+	0.502116i	0.973785	−	0.227471i	$-0.0730456\pi$
$659$	191.042	+	330.895i	0.289897	+	0.502116i	−0.683888	+	0.729587i	$0.739712\pi$
$660$		0			0
$661$	−391.836	+	226.227i	−0.592793	+	0.342249i	−0.766201	−	0.642601i	$-0.777855\pi$
$661$	−391.836	+	226.227i	−0.592793	+	0.342249i	0.173408	+	0.984850i	$0.444522\pi$
$662$	60.3285	+	104.492i	0.0911307	+	0.157843i
$663$		0			0
$664$	−276.922	+	159.881i	−0.417052	+	0.240785i
$665$	−4.82576	−	2.70876i	−0.00725678	−	0.00407332i
$666$		0			0
$667$	480.373	+	832.030i	0.720199	+	1.24742i
$668$		−	361.432i		−	0.541067i
$669$		0			0
$670$			90.7236i			0.135408i
$671$	−484.423	−	279.682i	−0.721942	−	0.416813i
$672$		0			0
$673$	−132.251	−	229.065i	−0.196509	−	0.340364i	0.750885	−	0.660433i	$-0.229627\pi$
$673$	−132.251	−	229.065i	−0.196509	−	0.340364i	−0.947394	+	0.320069i	$0.896294\pi$
$674$	−9.32610	−	16.1533i	−0.0138369	−	0.0239663i
$675$		0			0
$676$	−136.770	+	236.893i	−0.202323	+	0.350434i
$677$	113.566	+	65.5672i	0.167749	+	0.0968497i	0.581524	−	0.813529i	$-0.302457\pi$
$677$	113.566	+	65.5672i	0.167749	+	0.0968497i	−0.413775	+	0.910379i	$0.635790\pi$
$678$		0			0
$679$	338.844	−	603.665i	0.499035	−	0.889050i
$680$	−131.499	+	227.763i	−0.193381	+	0.334945i
$681$		0			0
$682$			42.1809i			0.0618488i
$683$	122.100	−	211.484i	0.178771	−	0.309640i	−0.762689	−	0.646765i	$-0.776121\pi$
$683$	122.100	−	211.484i	0.178771	−	0.309640i	0.941460	+	0.337125i	$0.109455\pi$
$684$		0			0
$685$			1095.03i			1.59859i
$686$	108.449	+	57.4648i	0.158089	+	0.0837679i
$687$		0			0
$688$	−215.631			−0.313417
$689$	−621.140	+	358.615i	−0.901510	+	0.520487i
$690$		0			0
$691$	391.262	+	225.895i	0.566226	+	0.326911i	0.755641	−	0.654986i	$-0.227326\pi$
$691$	391.262	+	225.895i	0.566226	+	0.326911i	−0.189414	+	0.981897i	$0.560659\pi$
$692$			780.795i			1.12832i
$693$		0			0
$694$	−93.4762			−0.134692
$695$	470.081	−	814.204i	0.676375	−	1.17152i
$696$		0			0
$697$	−170.376	−	295.100i	−0.244442	−	0.423387i
$698$			87.4788i			0.125328i
$699$		0			0
$700$	−92.9217	−	52.1581i	−0.132745	−	0.0745116i
$701$	−688.406			−0.982034			−0.491017	−	0.871150i	$-0.663375\pi$
$701$	−688.406			−0.982034			−0.491017	+	0.871150i	$0.663375\pi$
$702$		0			0
$703$	8.75429	+	5.05429i	0.0124528	+	0.00718961i
$704$	701.096			0.995875
$705$		0			0
$706$	164.875	+	95.1905i	0.233534	+	0.134831i
$707$	474.095	+	798.658i	0.670573	+	1.12964i
$708$		0			0
$709$	253.142	−	438.455i	0.357041	−	0.618413i	−0.630424	−	0.776251i	$-0.717119\pi$
$709$	253.142	−	438.455i	0.357041	−	0.618413i	0.987465	+	0.157838i	$0.0504523\pi$
$710$	−6.98840	−	4.03476i	−0.00984282	−	0.00568275i
$711$		0			0
$712$	297.459	−	171.738i	0.417780	−	0.241205i
$713$	240.067	−	138.603i	0.336700	−	0.194394i
$714$		0			0
$715$	−478.697	+	829.127i	−0.669506	+	1.15962i
$716$	−496.437			−0.693348
$717$		0			0
$718$	−94.7911			−0.132021
$719$	−253.574	+	146.401i	−0.352676	+	0.203618i	−0.665863	−	0.746074i	$-0.731937\pi$
$719$	−253.574	+	146.401i	−0.352676	+	0.203618i	0.313187	+	0.949691i	$0.398603\pi$
$720$		0			0
$721$	200.457	+	337.690i	0.278027	+	0.468363i
$722$	64.5817	+	111.859i	0.0894483	+	0.154929i
$723$		0			0
$724$	538.650	−	310.990i	0.743992	−	0.429544i
$725$	59.6071	+	103.243i	0.0822167	+	0.142403i
$726$		0			0
$727$	876.993	−	506.332i	1.20632	−	0.696468i	0.244365	−	0.969683i	$-0.421421\pi$
$727$	876.993	−	506.332i	1.20632	−	0.696468i	0.961953	+	0.273216i	$0.0880872\pi$
$728$	305.213	−	3.69690i	0.419248	−	0.00507817i
$729$		0			0
$730$	−8.96022	−	15.5196i	−0.0122743	−	0.0212597i
$731$			302.921i			0.414392i
$732$		0			0
$733$			526.755i			0.718628i	0.933217	+	0.359314i	$0.116989\pi$
$733$			526.755i			0.718628i	−0.933217	+	0.359314i	$0.883011\pi$
$734$	−37.5382	−	21.6727i	−0.0511420	−	0.0295269i
$735$		0			0
$736$	260.576	+	451.331i	0.354044	+	0.613221i
$737$	−372.130	−	644.548i	−0.504925	−	0.874556i
$738$		0			0
$739$	35.6298	−	61.7126i	0.0482135	−	0.0835082i	−0.840912	−	0.541173i	$-0.817981\pi$
$739$	35.6298	−	61.7126i	0.0482135	−	0.0835082i	0.889125	+	0.457664i	$0.151314\pi$
$740$	−903.322	−	521.533i	−1.22071	−	0.704775i
$741$		0			0
$742$	101.196	+	56.8027i	0.136383	+	0.0765535i
$743$	−276.074	+	478.175i	−0.371567	+	0.643573i	−0.989807	−	0.142417i	$-0.954513\pi$
$743$	−276.074	+	478.175i	−0.371567	+	0.643573i	0.618240	+	0.785989i	$0.287846\pi$
$744$		0			0
$745$		−	18.6969i		−	0.0250965i
$746$	−91.3503	+	158.223i	−0.122453	+	0.212096i
$747$		0			0
$748$		−	1061.22i		−	1.41874i
$749$	−295.380	−	165.800i	−0.394366	−	0.221362i
$750$		0			0
$751$	1350.32			1.79802			0.899012	−	0.437925i	$-0.144286\pi$
$751$	1350.32			1.79802			0.899012	+	0.437925i	$0.144286\pi$
$752$	559.543	−	323.053i	0.744074	−	0.429591i
$753$		0			0
$754$	−145.462	−	83.9825i	−0.192920	−	0.111383i
$755$			95.1446i			0.126019i
$756$		0			0
$757$	−741.980			−0.980158			−0.490079	−	0.871678i	$-0.663032\pi$
$757$	−741.980			−0.980158			−0.490079	+	0.871678i	$0.663032\pi$
$758$	63.0203	−	109.154i	0.0831402	−	0.144003i
$759$		0			0
$760$	1.11343	+	1.92852i	0.00146504	+	0.00253752i
$761$		−	858.680i		−	1.12836i	−0.825653	−	0.564179i	$-0.809193\pi$
$761$		−	858.680i		−	1.12836i	0.825653	−	0.564179i	$-0.190807\pi$
$762$		0			0
$763$	−5.27896	−	435.825i	−0.00691869	−	0.571200i
$764$	853.044			1.11655
$765$		0			0
$766$	43.3506	+	25.0285i	0.0565934	+	0.0326742i
$767$	122.147			0.159253
$768$		0			0
$769$	−1317.96	−	760.924i	−1.71386	−	0.989499i	−0.929202	−	0.369572i	$-0.879504\pi$
$769$	−1317.96	−	760.924i	−1.71386	−	0.989499i	−0.784659	−	0.619927i	$-0.787162\pi$
$770$	154.895	−	1.87618i	0.201163	−	0.00243660i
$771$		0			0
$772$	−382.029	+	661.693i	−0.494856	+	0.857116i
$773$	−649.981	−	375.267i	−0.840855	−	0.485468i	0.0166997	−	0.999861i	$-0.494684\pi$
$773$	−649.981	−	375.267i	−0.840855	−	0.485468i	−0.857555	+	0.514393i	$0.828017\pi$
$774$		0			0
$775$	29.7888	−	17.1985i	0.0384371	−	0.0221917i
$776$	−241.243	+	139.281i	−0.310880	+	0.179486i
$777$		0			0
$778$	42.7802	−	74.0975i	0.0549874	−	0.0952410i
$779$	−2.88523			−0.00370376
$780$		0			0
$781$	66.1990			0.0847619
$782$	199.722	−	115.310i	0.255399	−	0.147455i
$783$		0			0
$784$	369.538	+	605.687i	0.471349	+	0.772560i
$785$	235.216	+	407.406i	0.299638	+	0.518988i
$786$		0			0
$787$	66.1879	−	38.2136i	0.0841015	−	0.0485560i	−0.457359	−	0.889282i	$-0.651205\pi$
$787$	66.1879	−	38.2136i	0.0841015	−	0.0485560i	0.541461	+	0.840726i	$0.317871\pi$
$788$	−113.721	−	196.971i	−0.144316	−	0.249963i
$789$		0			0
$790$	154.047	−	88.9390i	0.194996	−	0.112581i
$791$	−12.2536	−	1011.65i	−0.0154913	−	1.27895i
$792$		0			0
$793$	−321.337	−	556.573i	−0.405218	−	0.701857i
$794$		−	259.138i		−	0.326370i
$795$		0			0
$796$			22.5259i			0.0282988i
$797$	−1074.42	−	620.318i	−1.34808	−	0.778317i	−0.360106	−	0.932911i	$-0.617259\pi$
$797$	−1074.42	−	620.318i	−1.34808	−	0.778317i	−0.987978	+	0.154595i	$0.950593\pi$
$798$		0			0
$799$	−453.828	−	786.053i	−0.567995	−	0.983796i
$800$	32.3336	+	56.0034i	0.0404170	+	0.0700043i
$801$		0			0
$802$	8.37970	−	14.5141i	0.0104485	−	0.0180973i
$803$	127.316	+	73.5061i	0.158551	+	0.0915393i
$804$		0			0
$805$	−519.652	−	875.404i	−0.645531	−	1.08746i
$806$	−24.2316	+	41.9704i	−0.0300641	+	0.0520725i
$807$		0			0
$808$		−	373.734i		−	0.462542i
$809$	−18.4466	+	31.9504i	−0.0228017	+	0.0394937i	−0.877201	−	0.480123i	$-0.840592\pi$
$809$	−18.4466	+	31.9504i	−0.0228017	+	0.0394937i	0.854399	+	0.519617i	$0.173925\pi$
$810$		0			0
$811$		−	750.736i		−	0.925692i	−0.886439	−	0.462846i	$-0.846828\pi$
$811$		−	750.736i		−	0.925692i	0.886439	−	0.462846i	$-0.153172\pi$
$812$	−9.95402	−	821.794i	−0.0122586	−	1.01206i
$813$		0			0
$814$	−282.957			−0.347613
$815$	122.663	−	70.8196i	0.150507	−	0.0868953i
$816$		0			0
$817$	2.22126	+	1.28245i	0.00271881	+	0.00156970i
$818$		−	64.3712i		−	0.0786934i
$819$		0			0
$820$	297.716			0.363068
$821$	182.354	−	315.847i	0.222112	−	0.384710i	−0.733337	−	0.679865i	$-0.762038\pi$
$821$	182.354	−	315.847i	0.222112	−	0.384710i	0.955449	+	0.295156i	$0.0953715\pi$
$822$		0			0
$823$	532.747	+	922.745i	0.647323	+	1.12120i	0.983760	+	0.179491i	$0.0574449\pi$
$823$	532.747	+	922.745i	0.647323	+	1.12120i	−0.336436	+	0.941706i	$0.609222\pi$
$824$		−	158.023i		−	0.191775i
$825$		0			0
$826$	−10.0883	−	16.9947i	−0.0122135	−	0.0205747i
$827$	275.145			0.332703			0.166351	−	0.986067i	$-0.446801\pi$
$827$	275.145			0.332703			0.166351	+	0.986067i	$0.446801\pi$
$828$		0			0
$829$	−761.832	−	439.844i	−0.918977	−	0.530572i	−0.0356684	−	0.999364i	$-0.511356\pi$
$829$	−761.832	−	439.844i	−0.918977	−	0.530572i	−0.883309	+	0.468792i	$0.844689\pi$
$830$	−186.449			−0.224638
$831$		0			0
$832$	697.598	+	402.758i	0.838459	+	0.484085i
$833$	850.876	−	519.131i	1.02146	−	0.623207i
$834$		0			0
$835$	214.231	−	371.059i	0.256564	−	0.444382i
$836$	−7.78173	−	4.49279i	−0.00930829	−	0.00537414i
$837$		0			0
$838$	189.847	−	109.608i	0.226547	−	0.130797i
$839$	−312.536	+	180.443i	−0.372510	+	0.215069i	−0.674554	−	0.738225i	$-0.735664\pi$
$839$	−312.536	+	180.443i	−0.372510	+	0.215069i	0.302045	+	0.953294i	$0.402331\pi$
$840$		0			0
$841$	−39.2281	+	67.9450i	−0.0466446	+	0.0807907i
$842$	−295.778			−0.351280
$843$		0			0
$844$	1193.49			1.41408
$845$	−280.827	+	162.135i	−0.332339	+	0.191876i
$846$		0			0
$847$	−364.423	+	216.326i	−0.430251	+	0.255403i
$848$	335.437	+	580.993i	0.395562	+	0.685133i
$849$		0			0
$850$	24.7826	−	14.3082i	0.0291559	−	0.0168332i
$851$	929.774	+	1610.42i	1.09257	+	1.89238i
$852$		0			0
$853$	−19.1927	+	11.0809i	−0.0225002	+	0.0129905i	−0.511208	−	0.859457i	$-0.670802\pi$
$853$	−19.1927	+	11.0809i	−0.0225002	+	0.0129905i	0.488708	+	0.872448i	$0.337468\pi$
$854$	−50.8981	+	90.6769i	−0.0595996	+	0.106179i
$855$		0			0
$856$	68.1520	+	118.043i	0.0796168	+	0.137900i
$857$			611.164i			0.713143i	0.934268	+	0.356572i	$0.116054\pi$
$857$			611.164i			0.713143i	−0.934268	+	0.356572i	$0.883946\pi$
$858$		0			0
$859$			103.261i			0.120210i	0.998192	+	0.0601051i	$0.0191436\pi$
$859$			103.261i			0.120210i	−0.998192	+	0.0601051i	$0.980856\pi$
$860$	−229.204	−	132.331i	−0.266516	−	0.153873i
$861$		0			0
$862$	−8.46885	−	14.6685i	−0.00982465	−	0.0170168i
$863$	−740.119	−	1281.92i	−0.857612	−	1.48543i	−0.874200	−	0.485565i	$-0.838614\pi$
$863$	−740.119	−	1281.92i	−0.857612	−	1.48543i	0.0165884	−	0.999862i	$-0.494720\pi$
$864$		0			0
$865$	−462.799	+	801.591i	−0.535027	+	0.926695i
$866$	58.9571	+	34.0389i	0.0680798	+	0.0393059i
$867$		0			0
$868$	−237.114	+	2.87205i	−0.273172	+	0.00330882i
$869$	−729.620	+	1263.74i	−0.839608	+	1.45424i
$870$		0			0
$871$		−	855.109i		−	0.981756i
$872$	−87.6935	+	151.890i	−0.100566	+	0.174185i
$873$		0			0
$874$		−	1.95271i		−	0.00223422i
$875$	−474.505	−	799.350i	−0.542292	−	0.913543i
$876$		0			0
$877$	1030.05			1.17451			0.587257	−	0.809401i	$-0.300208\pi$
$877$	1030.05			1.17451			0.587257	+	0.809401i	$0.300208\pi$
$878$	110.225	−	63.6382i	0.125540	−	0.0724808i
$879$		0			0
$880$	775.537	+	447.757i	0.881292	+	0.508814i
$881$		−	163.160i		−	0.185199i	−0.995703	−	0.0925993i	$-0.970482\pi$
$881$		−	163.160i		−	0.185199i	0.995703	−	0.0925993i	$-0.0295176\pi$
$882$		0			0
$883$	−703.475			−0.796688			−0.398344	−	0.917236i	$-0.630415\pi$
$883$	−703.475			−0.796688			−0.398344	+	0.917236i	$0.630415\pi$
$884$	609.638	−	1055.92i	0.689636	−	1.19448i
$885$		0			0
$886$	151.891	+	263.084i	0.171435	+	0.296934i
$887$			624.219i			0.703742i	0.936048	+	0.351871i	$0.114454\pi$
$887$			624.219i			0.703742i	−0.936048	+	0.351871i	$0.885546\pi$
$888$		0			0
$889$	−37.5141	+	22.2689i	−0.0421981	+	0.0250494i
$890$	200.277			0.225030
$891$		0			0
$892$	802.237	+	463.172i	0.899369	+	0.519251i
$893$	−7.68532			−0.00860618
$894$		0			0
$895$	−509.660	−	294.252i	−0.569452	−	0.328773i
$896$	−7.15661	−	590.843i	−0.00798729	−	0.659423i
$897$		0			0
$898$	−7.45314	+	12.9092i	−0.00829971	+	0.0143755i
$899$	229.750	+	132.646i	0.255562	+	0.147549i
$900$		0			0
$901$	816.186	−	471.225i	0.905867	−	0.523002i
$902$	69.9425	−	40.3813i	0.0775415	−	0.0447686i
$903$		0			0
$904$	−203.556	+	352.570i	−0.225173	+	0.390011i
$905$	737.329			0.814729
$906$		0			0
$907$	259.346			0.285938			0.142969	−	0.989727i	$-0.454335\pi$
$907$	259.346			0.285938			0.142969	+	0.989727i	$0.454335\pi$
$908$	825.771	−	476.759i	0.909439	−	0.525065i
$909$		0			0
$910$	155.200	+	87.1160i	0.170550	+	0.0957318i
$911$	229.255	+	397.081i	0.251652	+	0.435874i	0.963981	−	0.265972i	$-0.0856929\pi$
$911$	229.255	+	397.081i	0.251652	+	0.435874i	−0.712329	+	0.701846i	$0.752360\pi$
$912$		0			0
$913$	1324.63	−	764.778i	1.45086	−	0.837654i
$914$	−116.472	−	201.735i	−0.127431	−	0.220717i
$915$		0			0
$916$	−817.296	+	471.866i	−0.892245	+	0.515138i
$917$	174.808	+	294.481i	0.190631	+	0.321136i
$918$		0			0
$919$	−200.059	−	346.512i	−0.217692	−	0.377053i	0.736410	−	0.676535i	$-0.236519\pi$
$919$	−200.059	−	346.512i	−0.217692	−	0.377053i	−0.954102	+	0.299482i	$0.903186\pi$
$920$			409.647i			0.445269i
$921$		0			0
$922$		−	197.631i		−	0.214350i
$923$	65.8687	+	38.0293i	0.0713638	+	0.0412019i
$924$		0			0
$925$	115.371	+	199.829i	0.124726	+	0.216031i
$926$	−94.4572	−	163.605i	−0.102006	−	0.176679i
$927$		0			0
$928$	−249.377	+	431.934i	−0.268726	+	0.465446i
$929$	376.857	+	217.578i	0.405658	+	0.234207i	0.688923	−	0.724835i	$-0.258084\pi$
$929$	376.857	+	217.578i	0.405658	+	0.234207i	−0.283264	+	0.959042i	$0.591417\pi$
$930$		0			0
$931$	−0.204420	−	8.43713i	−0.000219571	−	0.00906244i
$932$	406.448	−	703.989i	0.436103	−	0.755353i
$933$		0			0
$934$		−	56.9288i		−	0.0609516i
$935$	629.014	−	1089.48i	0.672742	−	1.16522i
$936$		0			0
$937$		−	1259.27i		−	1.34394i	−0.740577	−	0.671971i	$-0.765448\pi$
$937$		−	1259.27i		−	1.34394i	0.740577	−	0.671971i	$-0.234552\pi$
$938$	−118.974	+	70.6248i	−0.126838	+	0.0752929i
$939$		0			0
$940$	793.019			0.843637
$941$	152.288	−	87.9235i	0.161836	−	0.0934363i	−0.416894	−	0.908955i	$-0.636882\pi$
$941$	152.288	−	87.9235i	0.161836	−	0.0934363i	0.578731	+	0.815519i	$0.303548\pi$
$942$		0			0
$943$	−459.651	−	265.379i	−0.487434	−	0.281420i
$944$		−	114.252i		−	0.121030i
$945$		0			0
$946$	−71.7959			−0.0758942
$947$	−254.298	+	440.456i	−0.268530	+	0.465107i	−0.968482	−	0.249082i	$-0.919871\pi$
$947$	−254.298	+	440.456i	−0.268530	+	0.465107i	0.699953	+	0.714189i	$0.253204\pi$
$948$		0			0
$949$	84.4540	+	146.279i	0.0889927	+	0.154140i
$950$		−	0.242302i		−	0.000255054i
$951$		0			0
$952$	−401.053	+	4.85778i	−0.421274	+	0.00510271i
$953$	−998.497			−1.04774			−0.523871	−	0.851798i	$-0.675512\pi$
$953$	−998.497			−1.04774			−0.523871	+	0.851798i	$0.675512\pi$
$954$		0			0
$955$	875.764	+	505.623i	0.917031	+	0.529448i
$956$	−996.765			−1.04264
$957$		0			0
$958$	−290.387	−	167.655i	−0.303118	−	0.175005i
$959$	−1436.02	+	852.441i	−1.49741	+	0.888885i
$960$		0			0
$961$	−442.227	+	765.960i	−0.460174	+	0.797045i
$962$	−281.545	−	162.550i	−0.292667	−	0.168971i
$963$		0			0
$964$	126.661	−	73.1278i	0.131391	−	0.0758587i
$965$	−784.408	+	452.878i	−0.812858	+	0.469304i
$966$		0			0
$967$	−864.440	+	1497.25i	−0.893940	+	1.54835i	−0.0588282	+	0.998268i	$0.518736\pi$
$967$	−864.440	+	1497.25i	−0.893940	+	1.54835i	−0.835111	+	0.550081i	$0.814597\pi$
$968$	170.532			0.176170
$969$		0			0
$970$	−162.426			−0.167450
$971$	−830.451	+	479.461i	−0.855253	+	0.493781i	−0.862420	−	0.506193i	$-0.831052\pi$
$971$	−830.451	+	479.461i	−0.855253	+	0.493781i	0.00716646	+	0.999974i	$0.497719\pi$
$972$		0			0
$973$	1433.68	−	17.3655i	1.47346	−	0.0178474i
$974$	−59.9913	−	103.908i	−0.0615927	−	0.106682i
$975$		0			0
$976$	−520.599	+	300.568i	−0.533401	+	0.307959i
$977$	210.021	+	363.766i	0.214965	+	0.372330i	0.953262	−	0.302146i	$-0.0977030\pi$
$977$	210.021	+	363.766i	0.214965	+	0.372330i	−0.738297	+	0.674476i	$0.764370\pi$
$978$		0			0
$979$	−1422.87	+	821.494i	−1.45339	+	0.839116i
$980$	21.0934	+	870.595i	0.0215238	+	0.888362i
$981$		0			0
$982$	−63.2369	−	109.530i	−0.0643960	−	0.111537i
$983$			360.270i			0.366501i	0.983066	+	0.183250i	$0.0586619\pi$
$983$			360.270i			0.366501i	−0.983066	+	0.183250i	$0.941338\pi$
$984$		0			0
$985$		−	269.623i		−	0.273728i
$986$	191.139	+	110.354i	0.193853	+	0.111921i
$987$		0			0
$988$	−5.16194	−	8.94074i	−0.00522463	−	0.00904933i
$989$	235.916	+	408.618i	0.238540	+	0.413163i
$990$		0			0
$991$	−341.859	+	592.117i	−0.344964	+	0.597495i	−0.985347	−	0.170561i	$-0.945442\pi$
$991$	−341.859	+	592.117i	−0.344964	+	0.597495i	0.640383	+	0.768055i	$0.278775\pi$
$992$	124.627	+	71.9533i	0.125632	+	0.0725336i
$993$		0			0
$994$	−0.149050	−	12.3054i	−0.000149950	−	0.0123797i
$995$	−13.3517	+	23.1258i	−0.0134188	+	0.0232421i
$996$		0			0
$997$			393.230i			0.394414i	0.980362	+	0.197207i	$0.0631871\pi$
$997$			393.230i			0.394414i	−0.980362	+	0.197207i	$0.936813\pi$
$998$	65.0275	−	112.631i	0.0651579	−	0.112857i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.k.a.10.8		28
3.2	odd	2		63.3.k.a.31.7	✓	28
7.5	odd	6		189.3.t.a.145.7		28
9.2	odd	6		63.3.t.a.52.8	yes	28
9.7	even	3		189.3.t.a.73.7		28
21.2	odd	6		441.3.t.a.166.8		28
21.5	even	6		63.3.t.a.40.8	yes	28
21.11	odd	6		441.3.l.a.391.7		28
21.17	even	6		441.3.l.b.391.7		28
21.20	even	2		441.3.k.b.31.7		28
63.2	odd	6		441.3.k.b.313.7		28
63.11	odd	6		441.3.l.b.97.7		28
63.20	even	6		441.3.t.a.178.8		28
63.38	even	6		441.3.l.a.97.7		28
63.47	even	6		63.3.k.a.61.7	yes	28
63.61	odd	6	inner	189.3.k.a.19.8		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.7	✓	28	3.2	odd	2
63.3.k.a.61.7	yes	28	63.47	even	6
63.3.t.a.40.8	yes	28	21.5	even	6
63.3.t.a.52.8	yes	28	9.2	odd	6
189.3.k.a.10.8		28	1.1	even	1	trivial
189.3.k.a.19.8		28	63.61	odd	6	inner
189.3.t.a.73.7		28	9.7	even	3
189.3.t.a.145.7		28	7.5	odd	6
441.3.k.b.31.7		28	21.20	even	2
441.3.k.b.313.7		28	63.2	odd	6
441.3.l.a.97.7		28	63.38	even	6
441.3.l.a.391.7		28	21.11	odd	6
441.3.l.b.97.7		28	63.11	odd	6
441.3.l.b.391.7		28	21.17	even	6
441.3.t.a.166.8		28	21.2	odd	6
441.3.t.a.178.8		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)

\(f(q)\)	\(=\)	\(q+(0.178911 - 0.309883i) q^{2} +(1.93598 + 3.35322i) q^{4} +4.59004i q^{5} +(-6.01934 + 3.57317i) q^{7} +2.81677 q^{8} +O(q^{10})\)	\(q+(0.178911 - 0.309883i) q^{2} +(1.93598 + 3.35322i) q^{4} +4.59004i q^{5} +(-6.01934 + 3.57317i) q^{7} +2.81677 q^{8} +(1.42238 + 0.821210i) q^{10} -13.4737 q^{11} +(-13.4065 - 7.74026i) q^{13} +(0.0303368 + 2.50457i) q^{14} +(-7.23997 + 12.5400i) q^{16} +(17.6163 + 10.1708i) q^{17} +(0.149161 - 0.0861184i) q^{19} +(-15.3914 + 8.88623i) q^{20} +(-2.41061 + 4.17529i) q^{22} +31.6842 q^{23} +3.93154 q^{25} +(-4.79716 + 2.76964i) q^{26} +(-23.6349 - 13.2666i) q^{28} +(15.1613 + 26.2601i) q^{29} +(7.57687 - 4.37451i) q^{31} +(8.22416 + 14.2447i) q^{32} +(6.30353 - 3.63934i) q^{34} +(-16.4010 - 27.6290i) q^{35} +(29.3450 + 50.8271i) q^{37} -0.0616302i q^{38} +12.9291i q^{40} +(-14.5072 - 8.37576i) q^{41} +(7.44584 + 12.8966i) q^{43} +(-26.0849 - 45.1804i) q^{44} +(5.66866 - 9.81842i) q^{46} +(-38.6426 - 22.3103i) q^{47} +(23.4650 - 43.0162i) q^{49} +(0.703397 - 1.21832i) q^{50} -59.9400i q^{52} +(23.1656 - 40.1240i) q^{53} -61.8450i q^{55} +(-16.9551 + 10.0648i) q^{56} +10.8501 q^{58} +(-6.83327 + 3.94519i) q^{59} +(35.9531 + 20.7575i) q^{61} -3.13060i q^{62} -52.0342 q^{64} +(35.5281 - 61.5365i) q^{65} +(27.6189 + 47.8373i) q^{67} +78.7619i q^{68} +(-11.4961 + 0.139247i) q^{70} -4.91318 q^{71} +(-9.44921 - 5.45550i) q^{73} +21.0006 q^{74} +(0.577548 + 0.333447i) q^{76} +(81.1031 - 48.1439i) q^{77} +(54.1512 - 93.7926i) q^{79} +(-57.5591 - 33.2318i) q^{80} +(-5.19102 + 2.99703i) q^{82} +(-98.3122 + 56.7606i) q^{83} +(-46.6844 + 80.8597i) q^{85} +5.32858 q^{86} -37.9524 q^{88} +(105.603 - 60.9700i) q^{89} +(108.356 - 1.31246i) q^{91} +(61.3401 + 106.244i) q^{92} +(-13.8272 + 7.98314i) q^{94} +(0.395287 + 0.684657i) q^{95} +(-85.6452 + 49.4473i) q^{97} +(-9.13187 - 14.9675i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) \) 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

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