LMFDB - Embedded newform 189.3.k.a.10.12

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			10.12
Character	$\chi$	$=$	189.10
Dual form			189.3.k.a.19.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32841 - 2.30087i) q^{2} +(-1.52933 - 2.64888i) q^{4} +9.20400i q^{5} +(6.96620 + 0.687028i) q^{7} +2.50096 q^{8} +O(q^{10})$	\(q+(1.32841 - 2.30087i) q^{2} +(-1.52933 - 2.64888i) q^{4} +9.20400i q^{5} +(6.96620 + 0.687028i) q^{7} +2.50096 q^{8} +(21.1772 + 12.2267i) q^{10} -7.05467 q^{11} +(4.15930 + 2.40137i) q^{13} +(10.8347 - 15.1157i) q^{14} +(9.43962 - 16.3499i) q^{16} +(2.74329 + 1.58384i) q^{17} +(1.70864 - 0.986484i) q^{19} +(24.3803 - 14.0760i) q^{20} +(-9.37147 + 16.2319i) q^{22} +5.02797 q^{23} -59.7137 q^{25} +(11.0505 - 6.38000i) q^{26} +(-8.83378 - 19.5033i) q^{28} +(-22.9425 - 39.7376i) q^{29} +(13.2265 - 7.63630i) q^{31} +(-20.0774 - 34.7751i) q^{32} +(7.28840 - 4.20796i) q^{34} +(-6.32341 + 64.1170i) q^{35} +(17.6998 + 30.6570i) q^{37} -5.24181i q^{38} +23.0189i q^{40} +(-48.4509 - 27.9732i) q^{41} +(-3.45068 - 5.97676i) q^{43} +(10.7889 + 18.6870i) q^{44} +(6.67920 - 11.5687i) q^{46} +(44.4658 + 25.6723i) q^{47} +(48.0560 + 9.57195i) q^{49} +(-79.3241 + 137.393i) q^{50} -14.6900i q^{52} +(10.3556 - 17.9365i) q^{53} -64.9312i q^{55} +(17.4222 + 1.71823i) q^{56} -121.908 q^{58} +(42.7391 - 24.6754i) q^{59} +(1.99551 + 1.15211i) q^{61} -40.5764i q^{62} -31.1668 q^{64} +(-22.1022 + 38.2822i) q^{65} +(-15.4139 - 26.6977i) q^{67} -9.68884i q^{68} +(139.125 + 99.7228i) q^{70} -81.2604 q^{71} +(-61.7481 - 35.6503i) q^{73} +94.0503 q^{74} +(-5.22615 - 3.01732i) q^{76} +(-49.1442 - 4.84675i) q^{77} +(14.5179 - 25.1458i) q^{79} +(150.485 + 86.8823i) q^{80} +(-128.725 + 74.3195i) q^{82} +(-55.9283 + 32.2902i) q^{83} +(-14.5776 + 25.2492i) q^{85} -18.3357 q^{86} -17.6434 q^{88} +(-89.0979 + 51.4407i) q^{89} +(27.3247 + 19.5860i) q^{91} +(-7.68944 - 13.3185i) q^{92} +(118.137 - 68.2067i) q^{94} +(9.07960 + 15.7263i) q^{95} +(-48.7891 + 28.1684i) q^{97} +(85.8617 - 97.8551i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.32841	−	2.30087i	0.664204	−	1.15043i	−0.315297	−	0.948993i	$-0.602104\pi$
$2$	1.32841	−	2.30087i	0.664204	−	1.15043i	0.979501	−	0.201441i	$-0.0645625\pi$
$3$		0			0
$3$		0			0
$4$	−1.52933	−	2.64888i	−0.382333	−	0.662220i
$5$			9.20400i			1.84080i	0.390977	+	0.920400i	$0.372137\pi$
$5$			9.20400i			1.84080i	−0.390977	+	0.920400i	$0.627863\pi$
$6$		0			0
$7$	6.96620	+	0.687028i	0.995172	+	0.0981468i
$7$	6.96620	+	0.687028i	0.995172	+	0.0981468i
$8$	2.50096			0.312620
$9$		0			0
$10$	21.1772	+	12.2267i	2.11772	+	1.22267i
$11$	−7.05467			−0.641333			−0.320667	−	0.947192i	$-0.603907\pi$
$11$	−7.05467			−0.641333			−0.320667	+	0.947192i	$0.603907\pi$
$12$		0			0
$13$	4.15930	+	2.40137i	0.319946	+	0.184721i	0.651368	−	0.758762i	$-0.274195\pi$
$13$	4.15930	+	2.40137i	0.319946	+	0.184721i	−0.331423	+	0.943482i	$0.607529\pi$
$14$	10.8347	−	15.1157i	0.773908	−	1.07969i
$15$		0			0
$16$	9.43962	−	16.3499i	0.589976	−	1.02187i
$17$	2.74329	+	1.58384i	0.161370	+	0.0931669i	0.578510	−	0.815675i	$-0.303634\pi$
$17$	2.74329	+	1.58384i	0.161370	+	0.0931669i	−0.417140	+	0.908842i	$0.636968\pi$
$18$		0			0
$19$	1.70864	−	0.986484i	0.0899284	−	0.0519202i	−0.454361	−	0.890817i	$-0.650133\pi$
$19$	1.70864	−	0.986484i	0.0899284	−	0.0519202i	0.544290	+	0.838897i	$0.316799\pi$
$20$	24.3803	−	14.0760i	1.21901	−	0.703798i
$21$		0			0
$22$	−9.37147	+	16.2319i	−0.425976	+	0.737812i
$23$	5.02797			0.218608			0.109304	−	0.994008i	$-0.465138\pi$
$23$	5.02797			0.218608			0.109304	+	0.994008i	$0.465138\pi$
$24$		0			0
$25$	−59.7137			−2.38855
$26$	11.0505	−	6.38000i	0.425018	−	0.245384i
$27$		0			0
$28$	−8.83378	−	19.5033i	−0.315492	−	0.696547i
$29$	−22.9425	−	39.7376i	−0.791121	−	1.37026i	−0.925273	−	0.379301i	$-0.876164\pi$
$29$	−22.9425	−	39.7376i	−0.791121	−	1.37026i	0.134152	−	0.990961i	$-0.457169\pi$
$30$		0			0
$31$	13.2265	−	7.63630i	0.426660	−	0.246332i	−0.271263	−	0.962505i	$-0.587441\pi$
$31$	13.2265	−	7.63630i	0.426660	−	0.246332i	0.697923	+	0.716173i	$0.254108\pi$
$32$	−20.0774	−	34.7751i	−0.627418	−	1.08672i
$33$		0			0
$34$	7.28840	−	4.20796i	0.214365	−	0.123764i
$35$	−6.32341	+	64.1170i	−0.180669	+	1.83191i
$36$		0			0
$37$	17.6998	+	30.6570i	0.478373	+	0.828567i	0.999693	−	0.0247946i	$-0.00789319\pi$
$37$	17.6998	+	30.6570i	0.478373	+	0.828567i	−0.521319	+	0.853362i	$0.674560\pi$
$38$		−	5.24181i		−	0.137942i
$39$		0			0
$40$			23.0189i			0.575471i
$41$	−48.4509	−	27.9732i	−1.18173	−	0.682272i	−0.225316	−	0.974286i	$-0.572341\pi$
$41$	−48.4509	−	27.9732i	−1.18173	−	0.682272i	−0.956414	+	0.292014i	$0.905675\pi$
$42$		0			0
$43$	−3.45068	−	5.97676i	−0.0802485	−	0.138994i	0.823108	−	0.567885i	$-0.192238\pi$
$43$	−3.45068	−	5.97676i	−0.0802485	−	0.138994i	−0.903357	+	0.428890i	$0.858905\pi$
$44$	10.7889	+	18.6870i	0.245203	+	0.424703i
$45$		0			0
$46$	6.67920	−	11.5687i	0.145200	−	0.251494i
$47$	44.4658	+	25.6723i	0.946081	+	0.546220i	0.891861	−	0.452309i	$-0.149400\pi$
$47$	44.4658	+	25.6723i	0.946081	+	0.546220i	0.0542197	+	0.998529i	$0.482733\pi$
$48$		0			0
$49$	48.0560	+	9.57195i	0.980734	+	0.195346i
$50$	−79.3241	+	137.393i	−1.58648	+	2.74787i
$51$		0			0
$52$		−	14.6900i		−	0.282499i
$53$	10.3556	−	17.9365i	0.195390	−	0.338425i	−0.751639	−	0.659575i	$-0.770736\pi$
$53$	10.3556	−	17.9365i	0.195390	−	0.338425i	0.947028	+	0.321151i	$0.104070\pi$
$54$		0			0
$55$		−	64.9312i		−	1.18057i
$56$	17.4222	+	1.71823i	0.311111	+	0.0306827i
$57$		0			0
$58$	−121.908			−2.10186
$59$	42.7391	−	24.6754i	0.724391	−	0.418227i	−0.0919759	−	0.995761i	$-0.529318\pi$
$59$	42.7391	−	24.6754i	0.724391	−	0.418227i	0.816367	+	0.577534i	$0.195985\pi$
$60$		0			0
$61$	1.99551	+	1.15211i	0.0327133	+	0.0188871i	0.516267	−	0.856427i	$-0.327321\pi$
$61$	1.99551	+	1.15211i	0.0327133	+	0.0188871i	−0.483554	+	0.875314i	$0.660654\pi$
$62$		−	40.5764i		−	0.654459i
$63$		0			0
$64$	−31.1668			−0.486982
$65$	−22.1022	+	38.2822i	−0.340034	+	0.588957i
$66$		0			0
$67$	−15.4139	−	26.6977i	−0.230059	−	0.398473i	0.727766	−	0.685825i	$-0.240558\pi$
$67$	−15.4139	−	26.6977i	−0.230059	−	0.398473i	−0.957825	+	0.287352i	$0.907225\pi$
$68$		−	9.68884i		−	0.142483i
$69$		0			0
$70$	139.125	+	99.7228i	1.98750	+	1.42461i
$71$	−81.2604			−1.14451			−0.572256	−	0.820075i	$-0.693932\pi$
$71$	−81.2604			−1.14451			−0.572256	+	0.820075i	$0.693932\pi$
$72$		0			0
$73$	−61.7481	−	35.6503i	−0.845864	−	0.488360i	0.0133893	−	0.999910i	$-0.495738\pi$
$73$	−61.7481	−	35.6503i	−0.845864	−	0.488360i	−0.859253	+	0.511551i	$0.829071\pi$
$74$	94.0503			1.27095
$75$		0			0
$76$	−5.22615	−	3.01732i	−0.0687651	−	0.0397016i
$77$	−49.1442	−	4.84675i	−0.638237	−	0.0629448i
$78$		0			0
$79$	14.5179	−	25.1458i	0.183771	−	0.318301i	−0.759391	−	0.650635i	$-0.774503\pi$
$79$	14.5179	−	25.1458i	0.183771	−	0.318301i	0.943162	+	0.332334i	$0.107836\pi$
$80$	150.485	+	86.8823i	1.88106	+	1.08603i
$81$		0			0
$82$	−128.725	+	74.3195i	−1.56982	+	0.906335i
$83$	−55.9283	+	32.2902i	−0.673835	+	0.389039i	−0.797528	−	0.603282i	$-0.793860\pi$
$83$	−55.9283	+	32.2902i	−0.673835	+	0.389039i	0.123693	+	0.992321i	$0.460526\pi$
$84$		0			0
$85$	−14.5776	+	25.2492i	−0.171502	+	0.297050i
$86$	−18.3357			−0.213205
$87$		0			0
$88$	−17.6434			−0.200494
$89$	−89.0979	+	51.4407i	−1.00110	+	0.577985i	−0.908574	−	0.417725i	$-0.862828\pi$
$89$	−89.0979	+	51.4407i	−1.00110	+	0.577985i	−0.0925265	+	0.995710i	$0.529494\pi$
$90$		0			0
$91$	27.3247	+	19.5860i	0.300271	+	0.215231i
$92$	−7.68944	−	13.3185i	−0.0835808	−	0.144766i
$93$		0			0
$94$	118.137	−	68.2067i	1.25678	−	0.725603i
$95$	9.07960	+	15.7263i	0.0955747	+	0.165540i
$96$		0			0
$97$	−48.7891	+	28.1684i	−0.502981	+	0.290396i	−0.729944	−	0.683507i	$-0.760454\pi$
$97$	−48.7891	+	28.1684i	−0.502981	+	0.290396i	0.226963	+	0.973903i	$0.427120\pi$
$98$	85.8617	−	97.8551i	0.876140	−	0.998521i
$99$		0			0
$100$	91.3220	+	158.174i	0.913220	+	1.58174i
$101$		−	111.997i		−	1.10888i	−0.832223	−	0.554442i	$-0.812932\pi$
$101$		−	111.997i		−	1.10888i	0.832223	−	0.554442i	$-0.187068\pi$
$102$		0			0
$103$		−	86.5479i		−	0.840271i	−0.907461	−	0.420136i	$-0.861982\pi$
$103$		−	86.5479i		−	0.840271i	0.907461	−	0.420136i	$-0.138018\pi$
$104$	10.4022	+	6.00573i	0.100022	+	0.0577474i
$105$		0			0
$106$	−27.5130	−	47.6540i	−0.259557	−	0.449566i
$107$	25.4526	+	44.0852i	0.237875	+	0.412012i	0.960104	−	0.279642i	$-0.0902158\pi$
$107$	25.4526	+	44.0852i	0.237875	+	0.412012i	−0.722229	+	0.691654i	$0.756882\pi$
$108$		0			0
$109$	21.9214	−	37.9690i	0.201114	−	0.348340i	−0.747774	−	0.663954i	$-0.768877\pi$
$109$	21.9214	−	37.9690i	0.201114	−	0.348340i	0.948888	+	0.315614i	$0.102211\pi$
$110$	−149.398	−	86.2550i	−1.35816	−	0.784137i
$111$		0			0
$112$	76.9911	−	107.411i	0.687421	−	0.959031i
$113$	53.2988	−	92.3163i	0.471671	−	0.816959i	−0.527803	−	0.849367i	$-0.676984\pi$
$113$	53.2988	−	92.3163i	0.471671	−	0.816959i	0.999475	+	0.0324080i	$0.0103176\pi$
$114$		0			0
$115$			46.2775i			0.402413i
$116$	−70.1734	+	121.544i	−0.604943	+	1.04779i
$117$		0			0
$118$		−	131.116i		−	1.11115i
$119$	18.0222	+	12.9180i	0.151447	+	0.108555i
$120$		0			0
$121$	−71.2317			−0.588692
$122$	5.30171	−	3.06094i	0.0434566	−	0.0250897i
$123$		0			0
$124$	−40.4553	−	23.3568i	−0.326252	−	0.188362i
$125$		−	319.505i		−	2.55604i
$126$		0			0
$127$	−184.052			−1.44923			−0.724614	−	0.689155i	$-0.757982\pi$
$127$	−184.052			−1.44923			−0.724614	+	0.689155i	$0.757982\pi$
$128$	38.9073	−	67.3894i	0.303963	−	0.526480i
$129$		0			0
$130$	58.7215	+	101.709i	0.451704	+	0.782374i
$131$		−	7.27407i		−	0.0555272i	−0.999615	−	0.0277636i	$-0.991161\pi$
$131$		−	7.27407i		−	0.0555272i	0.999615	−	0.0277636i	$-0.00883857\pi$
$132$		0			0
$133$	12.5805	−	5.69816i	0.0945900	−	0.0428433i
$134$	−81.9039			−0.611223
$135$		0			0
$136$	6.86085	+	3.96111i	0.0504474	+	0.0291258i
$137$	47.2720			0.345051			0.172526	−	0.985005i	$-0.444807\pi$
$137$	47.2720			0.345051			0.172526	+	0.985005i	$0.444807\pi$
$138$		0			0
$139$	219.353	+	126.643i	1.57808	+	0.911103i	0.995128	+	0.0985934i	$0.0314343\pi$
$139$	219.353	+	126.643i	1.57808	+	0.911103i	0.582948	+	0.812509i	$0.301899\pi$
$140$	179.509	−	81.3061i	1.28220	−	0.580758i
$141$		0			0
$142$	−107.947	+	186.970i	−0.760190	+	1.31669i
$143$	−29.3424	−	16.9409i	−0.205192	−	0.118468i
$144$		0			0
$145$	365.745	−	211.163i	2.52238	−	1.45630i
$146$	−164.053	+	94.7161i	−1.12365	+	0.648741i
$147$		0			0
$148$	54.1378	−	93.7693i	0.365796	−	0.633577i
$149$	256.844			1.72378			0.861892	−	0.507092i	$-0.169280\pi$
$149$	256.844			1.72378			0.861892	+	0.507092i	$0.169280\pi$
$150$		0			0
$151$	−118.386			−0.784016			−0.392008	−	0.919962i	$-0.628220\pi$
$151$	−118.386			−0.784016			−0.392008	+	0.919962i	$0.628220\pi$
$152$	4.27324	−	2.46716i	0.0281134	−	0.0162313i
$153$		0			0
$154$	−76.4353	+	106.636i	−0.496333	+	0.692441i
$155$	70.2845	+	121.736i	0.453448	+	0.785396i
$156$		0			0
$157$	−44.1884	+	25.5122i	−0.281455	+	0.162498i	−0.634082	−	0.773266i	$-0.718622\pi$
$157$	−44.1884	+	25.5122i	−0.281455	+	0.162498i	0.352627	+	0.935764i	$0.385288\pi$
$158$	−38.5714	−	66.8077i	−0.244123	−	0.422833i
$159$		0			0
$160$	320.070	−	184.792i	2.00044	−	1.15495i
$161$	35.0259	+	3.45436i	0.217552	+	0.0214556i
$162$		0			0
$163$	143.157	+	247.955i	0.878263	+	1.52120i	0.853246	+	0.521508i	$0.174630\pi$
$163$	143.157	+	247.955i	0.878263	+	1.52120i	0.0250163	+	0.999687i	$0.492036\pi$
$164$			171.121i			1.04342i
$165$		0			0
$166$			171.578i			1.03360i
$167$	162.132	+	93.6068i	0.970848	+	0.560519i	0.899495	−	0.436932i	$-0.143935\pi$
$167$	162.132	+	93.6068i	0.970848	+	0.560519i	0.0713535	+	0.997451i	$0.477268\pi$
$168$		0			0
$169$	−72.9668	−	126.382i	−0.431756	−	0.747824i
$170$	38.7301	+	67.0825i	0.227824	+	0.394603i
$171$		0			0
$172$	−10.5545	+	18.2809i	−0.0613632	+	0.106284i
$173$	128.939	+	74.4430i	0.745313	+	0.430306i	0.823998	−	0.566593i	$-0.191739\pi$
$173$	128.939	+	74.4430i	0.745313	+	0.430306i	−0.0786851	+	0.996900i	$0.525072\pi$
$174$		0			0
$175$	−415.978	−	41.0250i	−2.37702	−	0.234428i
$176$	−66.5933	+	115.343i	−0.378371	+	0.655358i
$177$		0			0
$178$			273.337i			1.53560i
$179$	−98.1713	+	170.038i	−0.548443	+	0.949931i	0.449938	+	0.893060i	$0.351446\pi$
$179$	−98.1713	+	170.038i	−0.548443	+	0.949931i	−0.998381	+	0.0568718i	$0.981887\pi$
$180$		0			0
$181$		−	80.6783i		−	0.445736i	−0.974849	−	0.222868i	$-0.928458\pi$
$181$		−	80.6783i		−	0.445736i	0.974849	−	0.222868i	$-0.0715419\pi$
$182$	81.3631	−	36.8524i	0.447050	−	0.202486i
$183$		0			0
$184$	12.5748			0.0683411
$185$	−282.167	+	162.909i	−1.52523	+	0.880590i
$186$		0			0
$187$	−19.3530	−	11.1734i	−0.103492	−	0.0597510i
$188$		−	157.046i		−	0.835351i
$189$		0			0
$190$	48.2456			0.253924
$191$	13.7811	−	23.8695i	0.0721521	−	0.124971i	−0.827692	−	0.561182i	$-0.810347\pi$
$191$	13.7811	−	23.8695i	0.0721521	−	0.124971i	0.899844	+	0.436211i	$0.143680\pi$
$192$		0			0
$193$	62.2668	+	107.849i	0.322626	+	0.558804i	0.981029	−	0.193861i	$-0.0621012\pi$
$193$	62.2668	+	107.849i	0.322626	+	0.558804i	−0.658403	+	0.752665i	$0.728768\pi$
$194$			149.676i			0.771528i
$195$		0			0
$196$	−48.1386	−	141.933i	−0.245605	−	0.724149i
$197$	115.102			0.584274			0.292137	−	0.956376i	$-0.405634\pi$
$197$	115.102			0.584274			0.292137	+	0.956376i	$0.405634\pi$
$198$		0			0
$199$	−104.660	−	60.4253i	−0.525928	−	0.303645i	0.213429	−	0.976959i	$-0.431537\pi$
$199$	−104.660	−	60.4253i	−0.525928	−	0.303645i	−0.739357	+	0.673314i	$0.764870\pi$
$200$	−149.342			−0.746708
$201$		0			0
$202$	−257.691	−	148.778i	−1.27570	−	0.736524i
$203$	−132.521	−	292.582i	−0.652815	−	1.44129i
$204$		0			0
$205$	257.465	−	445.943i	1.25593	−	2.17533i
$206$	−199.135	−	114.971i	−0.966677	−	0.558111i
$207$		0			0
$208$	78.5243	−	45.3360i	0.377521	−	0.217962i
$209$	−12.0539	+	6.95931i	−0.0576741	+	0.0332981i
$210$		0			0
$211$	60.1908	−	104.254i	0.285264	−	0.494092i	−0.687409	−	0.726271i	$-0.741252\pi$
$211$	60.1908	−	104.254i	0.285264	−	0.494092i	0.972673	+	0.232178i	$0.0745853\pi$
$212$	−63.3488			−0.298815
$213$		0			0
$214$	135.246			0.631990
$215$	55.0101	−	31.7601i	0.255861	−	0.147721i
$216$		0			0
$217$	97.3845	−	44.1091i	0.448777	−	0.203268i
$218$	−58.2411	−	100.877i	−0.267161	−	0.462737i
$219$		0			0
$220$	−171.995	+	99.3012i	−0.781795	+	0.451369i
$221$	7.60676	+	13.1753i	0.0344197	+	0.0596167i
$222$		0			0
$223$	−203.615	+	117.557i	−0.913072	+	0.527162i	−0.881418	−	0.472336i	$-0.843411\pi$
$223$	−203.615	+	117.557i	−0.913072	+	0.527162i	−0.0316538	+	0.999499i	$0.510077\pi$
$224$	−115.972	−	256.044i	−0.517731	−	1.14305i
$225$		0			0
$226$	−141.605	−	245.267i	−0.626571	−	1.08525i
$227$			151.239i			0.666249i	0.942883	+	0.333125i	$0.108103\pi$
$227$			151.239i			0.666249i	−0.942883	+	0.333125i	$0.891897\pi$
$228$		0			0
$229$			413.986i			1.80780i	0.427745	+	0.903899i	$0.359308\pi$
$229$			413.986i			1.80780i	−0.427745	+	0.903899i	$0.640692\pi$
$230$	106.478	+	61.4754i	0.462950	+	0.267284i
$231$		0			0
$232$	−57.3783	−	99.3822i	−0.247320	−	0.428372i
$233$	−166.801	−	288.909i	−0.715886	−	1.23995i	−0.962617	−	0.270867i	$-0.912690\pi$
$233$	−166.801	−	288.909i	−0.715886	−	1.23995i	0.246731	−	0.969084i	$-0.420644\pi$
$234$		0			0
$235$	−236.288	+	409.264i	−1.00548	+	1.74155i
$236$	−130.724	−	75.4737i	−0.553917	−	0.319804i
$237$		0			0
$238$	53.6635	−	24.3062i	0.225477	−	0.102127i
$239$	104.819	−	181.552i	0.438573	−	0.759631i	−0.559007	−	0.829163i	$-0.688817\pi$
$239$	104.819	−	181.552i	0.438573	−	0.759631i	0.997580	+	0.0695323i	$0.0221507\pi$
$240$		0			0
$241$			227.745i			0.945000i	0.881331	+	0.472500i	$0.156648\pi$
$241$			227.745i			0.945000i	−0.881331	+	0.472500i	$0.843352\pi$
$242$	−94.6247	+	163.895i	−0.391011	+	0.677251i
$243$		0			0
$244$		−	7.04783i		−	0.0288846i
$245$	−88.1003	+	442.308i	−0.359593	+	1.80534i
$246$		0			0
$247$	9.47565			0.0383630
$248$	33.0788	−	19.0981i	0.133382	−	0.0770084i
$249$		0			0
$250$	−735.139	−	424.433i	−2.94056	−	1.69773i
$251$			422.578i			1.68358i	0.539808	+	0.841788i	$0.318497\pi$
$251$			422.578i			1.68358i	−0.539808	+	0.841788i	$0.681503\pi$
$252$		0			0
$253$	−35.4707			−0.140200
$254$	−244.496	+	423.479i	−0.962582	+	1.66724i
$255$		0			0
$256$	−165.703	−	287.006i	−0.647278	−	1.12112i
$257$			87.1564i			0.339130i	0.985519	+	0.169565i	$0.0542363\pi$
$257$			87.1564i			0.339130i	−0.985519	+	0.169565i	$0.945764\pi$
$258$		0			0
$259$	102.238	+	225.723i	0.394743	+	0.871518i
$260$	135.206			0.520025
$261$		0			0
$262$	−16.7367	−	9.66292i	−0.0638804	−	0.0368814i
$263$	44.1876			0.168014			0.0840069	−	0.996465i	$-0.473228\pi$
$263$	44.1876			0.168014			0.0840069	+	0.996465i	$0.473228\pi$
$264$		0			0
$265$	165.088	+	95.3134i	0.622972	+	0.359673i
$266$	3.60127	−	36.5155i	0.0135386	−	0.137276i
$267$		0			0
$268$	−47.1460	+	81.6593i	−0.175918	+	0.304699i
$269$	169.996	+	98.1474i	0.631957	+	0.364860i	0.781509	−	0.623893i	$-0.214450\pi$
$269$	169.996	+	98.1474i	0.631957	+	0.364860i	−0.149553	+	0.988754i	$0.547783\pi$
$270$		0			0
$271$	−146.761	+	84.7324i	−0.541553	+	0.312666i	−0.745708	−	0.666273i	$-0.767889\pi$
$271$	−146.761	+	84.7324i	−0.541553	+	0.312666i	0.204155	+	0.978938i	$0.434555\pi$
$272$	51.7912	−	29.9016i	0.190409	−	0.109932i
$273$		0			0
$274$	62.7965	−	108.767i	0.229184	−	0.396959i
$275$	421.260			1.53186
$276$		0			0
$277$	370.101			1.33610			0.668052	−	0.744114i	$-0.267128\pi$
$277$	370.101			1.33610			0.668052	+	0.744114i	$0.267128\pi$
$278$	582.779	−	336.468i	2.09633	−	1.21032i
$279$		0			0
$280$	−15.8146	+	160.354i	−0.0564807	+	0.572693i
$281$	−61.5023	−	106.525i	−0.218869	−	0.379093i	0.735593	−	0.677424i	$-0.236904\pi$
$281$	−61.5023	−	106.525i	−0.218869	−	0.379093i	−0.954463	+	0.298331i	$0.903570\pi$
$282$		0			0
$283$	130.292	−	75.2239i	0.460394	−	0.265809i	−0.251816	−	0.967775i	$-0.581028\pi$
$283$	130.292	−	75.2239i	0.460394	−	0.265809i	0.712210	+	0.701967i	$0.247694\pi$
$284$	124.274	+	215.249i	0.437585	+	0.757919i
$285$		0			0
$286$	−77.9574	+	45.0087i	−0.272578	+	0.157373i
$287$	−318.301	−	228.154i	−1.10906	−	0.794961i
$288$		0			0
$289$	−139.483	−	241.592i	−0.482640	−	0.835957i
$290$		−	1122.04i		−	3.86911i
$291$		0			0
$292$			218.084i			0.746864i
$293$	−373.737	−	215.777i	−1.27555	−	0.736440i	−0.299525	−	0.954088i	$-0.596828\pi$
$293$	−373.737	−	215.777i	−1.27555	−	0.736440i	−0.976027	+	0.217648i	$0.930162\pi$
$294$		0			0
$295$	227.113	+	393.370i	0.769873	+	1.33346i
$296$	44.2666	+	76.6719i	0.149549	+	0.259027i
$297$		0			0
$298$	341.193	−	590.964i	1.14494	−	1.98310i
$299$	20.9128	+	12.0740i	0.0699426	+	0.0403814i
$300$		0			0
$301$	−19.9320	−	44.0060i	−0.0662192	−	0.146199i
$302$	−157.265	+	272.392i	−0.520746	+	0.901959i
$303$		0			0
$304$		−	37.2481i		−	0.122527i
$305$	−10.6040	+	18.3667i	−0.0347673	+	0.0602187i
$306$		0			0
$307$			157.167i			0.511946i	0.966684	+	0.255973i	$0.0823958\pi$
$307$			157.167i			0.511946i	−0.966684	+	0.255973i	$0.917604\pi$
$308$	62.3193	+	137.589i	0.202336	+	0.446719i
$309$		0			0
$310$	373.466			1.20473
$311$	−287.358	+	165.906i	−0.923982	+	0.533461i	−0.884903	−	0.465775i	$-0.845776\pi$
$311$	−287.358	+	165.906i	−0.923982	+	0.533461i	−0.0390787	+	0.999236i	$0.512442\pi$
$312$		0			0
$313$	353.763	+	204.245i	1.13023	+	0.652541i	0.943994	−	0.329963i	$-0.107036\pi$
$313$	353.763	+	204.245i	1.13023	+	0.652541i	0.186241	+	0.982504i	$0.440370\pi$
$314$			135.562i			0.431727i
$315$		0			0
$316$	−88.8108			−0.281047
$317$	19.3727	−	33.5545i	0.0611126	−	0.105850i	−0.833850	−	0.551991i	$-0.813868\pi$
$317$	19.3727	−	33.5545i	0.0611126	−	0.105850i	0.894963	+	0.446140i	$0.147202\pi$
$318$		0			0
$319$	161.852	+	280.335i	0.507372	+	0.878795i
$320$		−	286.860i		−	0.896437i
$321$		0			0
$322$	54.4767	−	76.0012i	0.169182	−	0.236029i
$323$	6.24972			0.0193490
$324$		0			0
$325$	−248.367	−	143.395i	−0.764206	−	0.441215i
$326$	760.682			2.33338
$327$		0			0
$328$	−121.174	−	69.9598i	−0.369433	−	0.213292i
$329$	292.120	+	209.388i	0.887904	+	0.636438i
$330$		0			0
$331$	−142.523	+	246.857i	−0.430583	+	0.745792i	−0.996924	−	0.0783792i	$-0.975026\pi$
$331$	−142.523	+	246.857i	−0.430583	+	0.745792i	0.566340	+	0.824172i	$0.308359\pi$
$332$	171.066	+	98.7649i	0.515259	+	0.297485i
$333$		0			0
$334$	430.754	−	248.696i	1.28968	−	0.744598i
$335$	245.726	−	141.870i	0.733510	−	0.423492i
$336$		0			0
$337$	298.113	−	516.347i	0.884608	−	1.53219i	0.0384451	−	0.999261i	$-0.487760\pi$
$337$	298.113	−	516.347i	0.884608	−	1.53219i	0.846163	−	0.532925i	$-0.178907\pi$
$338$	−387.719			−1.14710
$339$		0			0
$340$	89.1762			0.262283
$341$	−93.3082	+	53.8715i	−0.273631	+	0.157981i
$342$		0			0
$343$	328.192	+	99.6959i	0.956827	+	0.290659i
$344$	−8.63003	−	14.9476i	−0.0250873	−	0.0434525i
$345$		0			0
$346$	342.567	−	197.781i	0.990079	−	0.571622i
$347$	−145.285	−	251.641i	−0.418690	−	0.725192i	0.577118	−	0.816660i	$-0.304177\pi$
$347$	−145.285	−	251.641i	−0.418690	−	0.725192i	−0.995808	+	0.0914690i	$0.970844\pi$
$348$		0			0
$349$	−283.473	+	163.663i	−0.812243	+	0.468949i	−0.847734	−	0.530421i	$-0.822034\pi$
$349$	−283.473	+	163.663i	−0.812243	+	0.468949i	0.0354909	+	0.999370i	$0.488701\pi$
$350$	−646.981	+	902.612i	−1.84852	+	2.57889i
$351$		0			0
$352$	141.639	+	245.326i	0.402384	+	0.696950i
$353$			84.1348i			0.238342i	0.992874	+	0.119171i	$0.0380237\pi$
$353$			84.1348i			0.238342i	−0.992874	+	0.119171i	$0.961976\pi$
$354$		0			0
$355$		−	747.921i		−	2.10682i
$356$	272.520	+	157.340i	0.765507	+	0.441965i
$357$		0			0
$358$	260.823	+	451.759i	0.728556	+	1.26190i
$359$	106.191	+	183.928i	0.295796	+	0.512334i	0.975170	−	0.221459i	$-0.0710818\pi$
$359$	106.191	+	183.928i	0.295796	+	0.512334i	−0.679374	+	0.733792i	$0.737748\pi$
$360$		0			0
$361$	−178.554	+	309.264i	−0.494609	+	0.856687i
$362$	−185.630	−	107.174i	−0.512790	−	0.296060i
$363$		0			0
$364$	10.0924	−	102.333i	0.0277264	−	0.281135i
$365$	328.125	−	568.329i	0.898973	−	1.55707i
$366$		0			0
$367$		−	419.606i		−	1.14334i	−0.820484	−	0.571670i	$-0.806296\pi$
$367$		−	419.606i		−	1.14334i	0.820484	−	0.571670i	$-0.193704\pi$
$368$	47.4622	−	82.2069i	0.128973	−	0.223388i
$369$		0			0
$370$			865.639i			2.33957i
$371$	84.4624	−	117.835i	0.227661	−	0.317614i
$372$		0			0
$373$	−221.059			−0.592652			−0.296326	−	0.955087i	$-0.595761\pi$
$373$	−221.059			−0.592652			−0.296326	+	0.955087i	$0.595761\pi$
$374$	−51.4172	+	29.6858i	−0.137479	+	0.0793737i
$375$		0			0
$376$	111.207	+	64.2055i	0.295764	+	0.170759i
$377$		−	220.374i		−	0.584546i
$378$		0			0
$379$	317.062			0.836575			0.418287	−	0.908315i	$-0.362631\pi$
$379$	317.062			0.836575			0.418287	+	0.908315i	$0.362631\pi$
$380$	27.7714	−	48.1015i	0.0730827	−	0.126583i
$381$		0			0
$382$	−36.6137	−	63.4168i	−0.0958474	−	0.166013i
$383$			277.585i			0.724766i	0.932029	+	0.362383i	$0.118037\pi$
$383$			277.585i			0.724766i	−0.932029	+	0.362383i	$0.881963\pi$
$384$		0			0
$385$	44.6095	−	452.324i	0.115869	−	1.17487i
$386$	330.862			0.857156
$387$		0			0
$388$	149.229	+	86.1576i	0.384612	+	0.222056i
$389$	72.4347			0.186207			0.0931037	−	0.995656i	$-0.470321\pi$
$389$	72.4347			0.186207			0.0931037	+	0.995656i	$0.470321\pi$
$390$		0			0
$391$	13.7932	+	7.96349i	0.0352767	+	0.0203670i
$392$	120.186	+	23.9391i	0.306597	+	0.0610691i
$393$		0			0
$394$	152.902	−	264.834i	0.388077	−	0.672169i
$395$	231.442	+	133.623i	0.585929	+	0.338286i
$396$		0			0
$397$	−590.904	+	341.158i	−1.48842	+	0.859341i	−0.999913	−	0.0132172i	$-0.995793\pi$
$397$	−590.904	+	341.158i	−1.48842	+	0.859341i	−0.488510	+	0.872558i	$0.662459\pi$
$398$	−278.061	+	160.539i	−0.698647	+	0.403364i
$399$		0			0
$400$	−563.675	+	976.313i	−1.40919	+	2.44078i
$401$	−449.653			−1.12133			−0.560665	−	0.828043i	$-0.689454\pi$
$401$	−449.653			−1.12133			−0.560665	+	0.828043i	$0.689454\pi$
$402$		0			0
$403$	73.3503			0.182011
$404$	−296.667	+	171.281i	−0.734324	+	0.423962i
$405$		0			0
$406$	−849.236	−	83.7542i	−2.09171	−	0.206291i
$407$	−124.866	−	216.275i	−0.306797	−	0.531388i
$408$		0			0
$409$	−128.958	+	74.4542i	−0.315302	+	0.182040i	−0.649296	−	0.760535i	$-0.724937\pi$
$409$	−128.958	+	74.4542i	−0.315302	+	0.182040i	0.333995	+	0.942575i	$0.391603\pi$
$410$	−684.037	−	1184.79i	−1.66838	−	2.88972i
$411$		0			0
$412$	−229.255	+	132.360i	−0.556444	+	0.321263i
$413$	314.682	−	142.531i	0.761941	−	0.345111i
$414$		0			0
$415$	−297.199	−	514.765i	−0.716143	−	1.24040i
$416$		−	192.853i		−	0.463589i
$417$		0			0
$418$			36.9792i			0.0884670i
$419$	399.171	+	230.461i	0.952675	+	0.550027i	0.893911	−	0.448245i	$-0.147951\pi$
$419$	399.171	+	230.461i	0.952675	+	0.550027i	0.0587641	+	0.998272i	$0.481284\pi$
$420$		0			0
$421$	−63.9001	−	110.678i	−0.151782	−	0.262894i	0.780101	−	0.625654i	$-0.215168\pi$
$421$	−63.9001	−	110.678i	−0.151782	−	0.262894i	−0.931883	+	0.362760i	$0.881834\pi$
$422$	−159.916	−	276.982i	−0.378947	−	0.656356i
$423$		0			0
$424$	25.8991	−	44.8585i	0.0610827	−	0.105798i
$425$	−163.812	−	94.5768i	−0.385440	−	0.222534i
$426$		0			0
$427$	13.1096	+	9.39681i	0.0307017	+	0.0220066i
$428$	77.8510	−	134.842i	0.181895	−	0.315051i
$429$		0			0
$430$		−	168.761i		−	0.392468i
$431$	104.431	−	180.879i	0.242298	−	0.419673i	−0.719070	−	0.694937i	$-0.755432\pi$
$431$	104.431	−	180.879i	0.242298	−	0.419673i	0.961369	+	0.275264i	$0.0887654\pi$
$432$		0			0
$433$		−	492.194i		−	1.13671i	−0.822784	−	0.568354i	$-0.807581\pi$
$433$		−	492.194i		−	1.13671i	0.822784	−	0.568354i	$-0.192419\pi$
$434$	27.8771	−	282.664i	0.0642330	−	0.651299i
$435$		0			0
$436$	−134.100			−0.307570
$437$	8.59100	−	4.96001i	0.0196590	−	0.0113501i
$438$		0			0
$439$	−61.0093	−	35.2237i	−0.138973	−	0.0802362i	0.428901	−	0.903351i	$-0.358901\pi$
$439$	−61.0093	−	35.2237i	−0.138973	−	0.0802362i	−0.567875	+	0.823115i	$0.692234\pi$
$440$		−	162.390i		−	0.369069i
$441$		0			0
$442$	40.4195			0.0914468
$443$	358.035	−	620.135i	0.808206	−	1.39985i	−0.105899	−	0.994377i	$-0.533772\pi$
$443$	358.035	−	620.135i	0.808206	−	1.39985i	0.914105	−	0.405477i	$-0.132895\pi$
$444$		0			0
$445$	−473.460	−	820.058i	−1.06396	−	1.84283i
$446$			624.655i			1.40057i
$447$		0			0
$448$	−217.115	−	21.4125i	−0.484631	−	0.0477957i
$449$	130.350			0.290313			0.145156	−	0.989409i	$-0.453631\pi$
$449$	130.350			0.290313			0.145156	+	0.989409i	$0.453631\pi$
$450$		0			0
$451$	341.805	+	197.341i	0.757883	+	0.437564i
$452$	−326.046			−0.721341
$453$		0			0
$454$	347.980	+	200.906i	0.766476	+	0.442525i
$455$	−180.270	+	251.497i	−0.396197	+	0.552740i
$456$		0			0
$457$	105.765	−	183.190i	0.231433	−	0.400854i	−0.726797	−	0.686852i	$-0.758992\pi$
$457$	105.765	−	183.190i	0.231433	−	0.400854i	0.958230	+	0.285998i	$0.0923252\pi$
$458$	952.527	+	549.942i	2.07975	+	1.20075i
$459$		0			0
$460$	122.583	−	70.7736i	0.266486	−	0.153856i
$461$	−457.027	+	263.865i	−0.991381	+	0.572374i	−0.905687	−	0.423947i	$-0.860644\pi$
$461$	−457.027	+	263.865i	−0.991381	+	0.572374i	−0.0856943	+	0.996321i	$0.527311\pi$
$462$		0			0
$463$	−367.066	+	635.777i	−0.792800	+	1.37317i	0.131428	+	0.991326i	$0.458044\pi$
$463$	−367.066	+	635.777i	−0.792800	+	1.37317i	−0.924227	+	0.381843i	$0.875289\pi$
$464$	−866.274			−1.86697
$465$		0			0
$466$	−886.321			−1.90198
$467$	−280.938	+	162.200i	−0.601581	+	0.347323i	−0.769663	−	0.638450i	$-0.779576\pi$
$467$	−280.938	+	162.200i	−0.601581	+	0.347323i	0.168082	+	0.985773i	$0.446243\pi$
$468$		0			0
$469$	−89.0345	−	196.571i	−0.189839	−	0.419129i
$470$	627.774	+	1087.34i	1.33569	+	2.31348i
$471$		0			0
$472$	106.889	−	61.7122i	0.226459	−	0.130746i
$473$	24.3434	+	42.1640i	0.0514660	+	0.0891417i
$474$		0			0
$475$	−102.029	+	58.9066i	−0.214798	+	0.124014i
$476$	6.65650	−	67.4945i	0.0139843	−	0.141795i
$477$		0			0
$478$	−278.485	−	482.349i	−0.582604	−	1.00910i
$479$			420.527i			0.877927i	0.898505	+	0.438964i	$0.144654\pi$
$479$			420.527i			0.877927i	−0.898505	+	0.438964i	$0.855346\pi$
$480$		0			0
$481$			170.015i			0.353462i
$482$	524.011	+	302.538i	1.08716	+	0.627672i
$483$		0			0
$484$	108.937	+	188.684i	0.225076	+	0.389843i
$485$	−259.262	−	449.055i	−0.534561	−	0.925887i
$486$		0			0
$487$	19.3349	−	33.4890i	0.0397020	−	0.0687658i	−0.845492	−	0.533989i	$-0.820692\pi$
$487$	19.3349	−	33.4890i	0.0397020	−	0.0687658i	0.885194	+	0.465223i	$0.154026\pi$
$488$	4.99070	+	2.88138i	0.0102268	+	0.00590447i
$489$		0			0
$490$	900.659	+	790.272i	1.83808	+	1.61280i
$491$	−435.683	+	754.625i	−0.887338	+	1.53691i	−0.0443266	+	0.999017i	$0.514114\pi$
$491$	−435.683	+	754.625i	−0.887338	+	1.53691i	−0.843011	+	0.537897i	$0.819219\pi$
$492$		0			0
$493$		−	145.349i		−	0.294825i
$494$	12.5875	−	21.8022i	0.0254808	−	0.0441341i
$495$		0			0
$496$		−	288.335i		−	0.581320i
$497$	−566.077	−	55.8281i	−1.13899	−	0.112330i
$498$		0			0
$499$	−368.253			−0.737982			−0.368991	−	0.929433i	$-0.620297\pi$
$499$	−368.253			−0.737982			−0.368991	+	0.929433i	$0.620297\pi$
$500$	−846.330	+	488.629i	−1.69266	+	0.977258i
$501$		0			0
$502$	972.296	+	561.355i	1.93684	+	1.11824i
$503$			603.853i			1.20050i	0.799811	+	0.600251i	$0.204933\pi$
$503$			603.853i			1.20050i	−0.799811	+	0.600251i	$0.795067\pi$
$504$		0			0
$505$	1030.82			2.04123
$506$	−47.1195	+	81.6134i	−0.0931215	+	0.161291i
$507$		0			0
$508$	281.476	+	487.531i	0.554087	+	0.959707i
$509$		−	228.276i		−	0.448479i	−0.974534	−	0.224240i	$-0.928010\pi$
$509$		−	228.276i		−	0.448479i	0.974534	−	0.224240i	$-0.0719898\pi$
$510$		0			0
$511$	−405.657	−	290.770i	−0.793849	−	0.569021i
$512$	−569.227			−1.11177
$513$		0			0
$514$	200.535	+	115.779i	0.390147	+	0.225251i
$515$	796.588			1.54677
$516$		0			0
$517$	−313.691	−	181.110i	−0.606753	−	0.350309i
$518$	655.173	+	64.6151i	1.26481	+	0.124740i
$519$		0			0
$520$	−55.2768	+	95.7422i	−0.106302	+	0.184120i
$521$	−409.376	−	236.354i	−0.785751	−	0.453654i	0.0527134	−	0.998610i	$-0.483213\pi$
$521$	−409.376	−	236.354i	−0.785751	−	0.453654i	−0.838465	+	0.544956i	$0.816546\pi$
$522$		0			0
$523$	242.231	−	139.852i	0.463156	−	0.267403i	−0.250214	−	0.968190i	$-0.580501\pi$
$523$	242.231	−	139.852i	0.463156	−	0.267403i	0.713370	+	0.700787i	$0.247168\pi$
$524$	−19.2681	+	11.1245i	−0.0367712	+	0.0212299i
$525$		0			0
$526$	58.6991	−	101.670i	0.111595	−	0.193289i
$527$	48.3786			0.0918000
$528$		0			0
$529$	−503.719			−0.952211
$530$	438.607	−	253.230i	0.827561	−	0.477792i
$531$		0			0
$532$	−34.3334	−	24.6098i	−0.0645366	−	0.0462590i
$533$	−134.348	−	232.697i	−0.252060	−	0.436580i
$534$		0			0
$535$	−405.761	+	234.266i	−0.758431	+	0.437881i
$536$	−38.5496	−	66.7699i	−0.0719210	−	0.124571i
$537$		0			0
$538$	451.649	−	260.759i	0.839496	−	0.484683i
$539$	−339.019	−	67.5269i	−0.628978	−	0.125282i
$540$		0			0
$541$	508.919	+	881.473i	0.940700	+	1.62934i	0.764139	+	0.645051i	$0.223164\pi$
$541$	508.919	+	881.473i	0.940700	+	1.62934i	0.176561	+	0.984290i	$0.443503\pi$
$542$			450.236i			0.830694i
$543$		0			0
$544$		−	127.197i		−	0.233818i
$545$	349.467	+	201.765i	0.641224	+	0.370211i
$546$		0			0
$547$	−195.785	−	339.109i	−0.357924	−	0.619943i	0.629690	−	0.776847i	$-0.283182\pi$
$547$	−195.785	−	339.109i	−0.357924	−	0.619943i	−0.987614	+	0.156904i	$0.949849\pi$
$548$	−72.2946	−	125.218i	−0.131924	−	0.228500i
$549$		0			0
$550$	559.605	−	969.264i	1.01746	−	1.76230i
$551$	−78.4010	−	45.2648i	−0.142289	−	0.0821503i
$552$		0			0
$553$	118.411	−	165.196i	0.214124	−	0.298728i
$554$	491.645	−	851.554i	0.887445	−	1.53710i
$555$		0			0
$556$		−	774.718i		−	1.39338i
$557$	−249.913	+	432.862i	−0.448677	+	0.777131i	−0.998300	−	0.0582814i	$-0.981438\pi$
$557$	−249.913	+	432.862i	−0.448677	+	0.777131i	0.549623	+	0.835413i	$0.314771\pi$
$558$		0			0
$559$		−	33.1455i		−	0.0592942i
$560$	988.615	+	708.627i	1.76538	+	1.26540i
$561$		0			0
$562$	−326.800			−0.581495
$563$	279.885	−	161.592i	0.497132	−	0.287019i	−0.230397	−	0.973097i	$-0.574002\pi$
$563$	279.885	−	161.592i	0.497132	−	0.287019i	0.727528	+	0.686078i	$0.240669\pi$
$564$		0			0
$565$	849.680	+	490.563i	1.50386	+	0.868253i
$566$		−	399.712i		−	0.706204i
$567$		0			0
$568$	−203.229			−0.357798
$569$	88.4404	−	153.183i	0.155431	−	0.269215i	−0.777785	−	0.628531i	$-0.783657\pi$
$569$	88.4404	−	153.183i	0.155431	−	0.269215i	0.933216	+	0.359316i	$0.116990\pi$
$570$		0			0
$571$	278.796	+	482.889i	0.488260	+	0.845691i	0.999909	−	0.0135039i	$-0.00429856\pi$
$571$	278.796	+	482.889i	0.488260	+	0.845691i	−0.511649	+	0.859194i	$0.670965\pi$
$572$			103.633i			0.181176i
$573$		0			0
$574$	−947.785	+	429.287i	−1.65119	+	0.747887i
$575$	−300.239			−0.522155
$576$		0			0
$577$	−640.283	−	369.668i	−1.10968	−	0.640672i	−0.170931	−	0.985283i	$-0.554677\pi$
$577$	−640.283	−	369.668i	−1.10968	−	0.640672i	−0.938745	+	0.344611i	$0.888011\pi$
$578$	−741.160			−1.28228
$579$		0			0
$580$	−1118.69	−	645.876i	−1.92878	−	1.11358i
$581$	−411.792	+	186.516i	−0.708765	+	0.321026i
$582$		0			0
$583$	−73.0556	+	126.536i	−0.125310	+	0.217043i
$584$	−154.430	−	89.1599i	−0.264434	−	0.152671i
$585$		0			0
$586$	−992.949	+	573.280i	−1.69445	+	0.978293i
$587$	47.8551	−	27.6292i	0.0815249	−	0.0470684i	−0.458683	−	0.888600i	$-0.651679\pi$
$587$	47.8551	−	27.6292i	0.0815249	−	0.0470684i	0.540208	+	0.841531i	$0.318345\pi$
$588$		0			0
$589$	15.0662	−	26.0954i	0.0255792	−	0.0443045i
$590$	1206.79			2.04541
$591$		0			0
$592$	668.318			1.12892
$593$	663.928	−	383.319i	1.11961	−	0.646406i	0.178307	−	0.983975i	$-0.442938\pi$
$593$	663.928	−	383.319i	1.11961	−	0.646406i	0.941301	+	0.337569i	$0.109605\pi$
$594$		0			0
$595$	−118.898	+	165.876i	−0.199828	+	0.278783i
$596$	−392.799	−	680.348i	−0.659059	−	1.14152i
$597$		0			0
$598$	55.5615	−	32.0785i	0.0929122	−	0.0536429i
$599$	−453.133	−	784.849i	−0.756482	−	1.31027i	−0.944634	−	0.328126i	$-0.893583\pi$
$599$	−453.133	−	784.849i	−0.756482	−	1.31027i	0.188152	−	0.982140i	$-0.439750\pi$
$600$		0			0
$601$	−192.859	+	111.347i	−0.320897	+	0.185270i	−0.651793	−	0.758397i	$-0.725983\pi$
$601$	−192.859	+	111.347i	−0.320897	+	0.185270i	0.330895	+	0.943668i	$0.392649\pi$
$602$	−127.730	−	12.5971i	−0.212176	−	0.0209254i
$603$		0			0
$604$	181.052	+	313.591i	0.299755	+	0.519191i
$605$		−	655.617i		−	1.08366i
$606$		0			0
$607$		−	599.115i		−	0.987010i	−0.869743	−	0.493505i	$-0.835715\pi$
$607$		−	599.115i		−	0.987010i	0.869743	−	0.493505i	$-0.164285\pi$
$608$	−68.6100	−	39.6120i	−0.112845	−	0.0651514i
$609$		0			0
$610$	28.1729	+	48.7970i	0.0461851	+	0.0799950i
$611$	123.298	+	213.558i	0.201796	+	0.349522i
$612$		0			0
$613$	−270.643	+	468.768i	−0.441506	+	0.764711i	−0.997801	−	0.0662736i	$-0.978889\pi$
$613$	−270.643	+	468.768i	−0.441506	+	0.764711i	0.556295	+	0.830985i	$0.312222\pi$
$614$	361.622	+	208.782i	0.588960	+	0.340036i
$615$		0			0
$616$	−122.908	−	12.1215i	−0.199526	−	0.0196778i
$617$	−331.635	+	574.409i	−0.537497	+	0.930972i	0.461541	+	0.887119i	$0.347297\pi$
$617$	−331.635	+	574.409i	−0.537497	+	0.930972i	−0.999038	+	0.0438529i	$0.986037\pi$
$618$		0			0
$619$		−	978.753i		−	1.58118i	−0.612343	−	0.790592i	$-0.709773\pi$
$619$		−	978.753i		−	1.58118i	0.612343	−	0.790592i	$-0.290227\pi$
$620$	214.977	−	372.350i	0.346736	−	0.600565i
$621$		0			0
$622$			881.565i			1.41731i
$623$	−656.015	+	297.134i	−1.05299	+	0.476940i
$624$		0			0
$625$	1447.88			2.31661
$626$	939.884	−	542.642i	1.50141	−	0.866840i
$627$		0			0
$628$	135.157	+	78.0331i	0.215219	+	0.124257i
$629$			112.135i			0.178274i
$630$		0			0
$631$	256.500			0.406498			0.203249	−	0.979127i	$-0.434850\pi$
$631$	256.500			0.406498			0.203249	+	0.979127i	$0.434850\pi$
$632$	36.3088	−	62.8886i	0.0574506	−	0.0995073i
$633$		0			0
$634$	−51.4697	−	89.1481i	−0.0811824	−	0.140612i
$635$		−	1694.01i		−	2.66774i
$636$		0			0
$637$	176.893	+	155.213i	0.277697	+	0.243662i
$638$	860.020			1.34799
$639$		0			0
$640$	620.253	+	358.103i	0.969145	+	0.559536i
$641$	336.160			0.524431			0.262215	−	0.965009i	$-0.415547\pi$
$641$	336.160			0.524431			0.262215	+	0.965009i	$0.415547\pi$
$642$		0			0
$643$	754.603	+	435.671i	1.17357	+	0.677559i	0.954518	−	0.298155i	$-0.0963711\pi$
$643$	754.603	+	435.671i	1.17357	+	0.677559i	0.219049	+	0.975714i	$0.429704\pi$
$644$	−44.4160	−	98.0622i	−0.0689690	−	0.152270i
$645$		0			0
$646$	8.30217	−	14.3798i	0.0128517	−	0.0222597i
$647$	707.666	+	408.571i	1.09376	+	0.631485i	0.934576	−	0.355763i	$-0.115779\pi$
$647$	707.666	+	408.571i	1.09376	+	0.631485i	0.159189	+	0.987248i	$0.449112\pi$
$648$		0			0
$649$	−301.510	+	174.077i	−0.464576	+	0.268223i
$650$	−659.865	+	380.973i	−1.01518	+	0.586113i
$651$		0			0
$652$	437.868	−	758.410i	0.671577	−	1.16321i
$653$	360.836			0.552582			0.276291	−	0.961074i	$-0.410895\pi$
$653$	360.836			0.552582			0.276291	+	0.961074i	$0.410895\pi$
$654$		0			0
$655$	66.9506			0.102215
$656$	−914.716	+	528.112i	−1.39438	+	0.805048i
$657$		0			0
$658$	869.829	−	393.978i	1.32193	−	0.598750i
$659$	−515.473	−	892.826i	−0.782205	−	1.35482i	−0.930654	−	0.365899i	$-0.880761\pi$
$659$	−515.473	−	892.826i	−0.782205	−	1.35482i	0.148449	−	0.988920i	$-0.452572\pi$
$660$		0			0
$661$	−287.835	+	166.182i	−0.435455	+	0.251410i	−0.701668	−	0.712504i	$-0.747561\pi$
$661$	−287.835	+	166.182i	−0.435455	+	0.251410i	0.266213	+	0.963914i	$0.414228\pi$
$662$	378.657	+	655.854i	0.571990	+	0.990716i
$663$		0			0
$664$	−139.875	+	80.7566i	−0.210654	+	0.121621i
$665$	52.4459	+	115.791i	0.0788660	+	0.174121i
$666$		0			0
$667$	−115.354	−	199.800i	−0.172945	−	0.299550i
$668$		−	572.623i		−	0.857220i
$669$		0			0
$670$		−	753.844i		−	1.12514i
$671$	−14.0777	−	8.12775i	−0.0209801	−	0.0121129i
$672$		0			0
$673$	−241.240	−	417.840i	−0.358455	−	0.620862i	0.629248	−	0.777204i	$-0.283363\pi$
$673$	−241.240	−	417.840i	−0.358455	−	0.620862i	−0.987703	+	0.156343i	$0.950030\pi$
$674$	−792.030	−	1371.84i	−1.17512	−	2.03537i
$675$		0			0
$676$	−223.181	+	386.561i	−0.330149	+	0.571835i
$677$	−538.899	−	311.134i	−0.796011	−	0.459577i	0.0460636	−	0.998939i	$-0.485332\pi$
$677$	−538.899	−	311.134i	−0.796011	−	0.459577i	−0.842074	+	0.539362i	$0.818666\pi$
$678$		0			0
$679$	−359.227	+	162.707i	−0.529054	+	0.239628i
$680$	−36.4581	+	63.1473i	−0.0536149	+	0.0928637i
$681$		0			0
$682$			286.253i			0.419726i
$683$	−235.625	+	408.115i	−0.344986	+	0.597533i	−0.985351	−	0.170538i	$-0.945450\pi$
$683$	−235.625	+	408.115i	−0.344986	+	0.597533i	0.640366	+	0.768070i	$0.278783\pi$
$684$		0			0
$685$			435.092i			0.635171i
$686$	665.359	−	622.689i	0.969911	−	0.907710i
$687$		0			0
$688$	−130.293			−0.189379
$689$	86.1444	−	49.7355i	0.125028	−	0.0721850i
$690$		0			0
$691$	−449.921	−	259.762i	−0.651115	−	0.375921i	0.137768	−	0.990464i	$-0.456007\pi$
$691$	−449.921	−	259.762i	−0.651115	−	0.375921i	−0.788883	+	0.614543i	$0.789340\pi$
$692$		−	455.392i		−	0.658081i
$693$		0			0
$694$	−771.992			−1.11238
$695$	−1165.63	+	2018.92i	−1.67716	+	2.90492i
$696$		0			0
$697$	−88.6098	−	153.477i	−0.127130	−	0.220196i
$698$			869.645i			1.24591i
$699$		0			0
$700$	527.498	+	1164.62i	0.753568	+	1.66374i
$701$	985.712			1.40615			0.703076	−	0.711115i	$-0.251809\pi$
$701$	985.712			1.40615			0.703076	+	0.711115i	$0.251809\pi$
$702$		0			0
$703$	60.4852	+	34.9212i	0.0860387	+	0.0496745i
$704$	219.872			0.312318
$705$		0			0
$706$	193.583	+	111.765i	0.274197	+	0.158308i
$707$	76.9452	−	780.195i	0.108833	−	1.10353i
$708$		0			0
$709$	−295.114	+	511.152i	−0.416240	+	0.720948i	−0.995558	−	0.0941533i	$-0.969986\pi$
$709$	−295.114	+	511.152i	−0.416240	+	0.720948i	0.579318	+	0.815102i	$0.303319\pi$
$710$	−1720.87	−	993.544i	−2.42376	−	1.39936i
$711$		0			0
$712$	−222.830	+	128.651i	−0.312964	+	0.180690i
$713$	66.5023	−	38.3951i	0.0932711	−	0.0538501i
$714$		0			0
$715$	155.924	−	270.068i	0.218075	−	0.377717i
$716$	600.546			0.838751
$717$		0			0
$718$	564.258			0.785875
$719$	−320.943	+	185.297i	−0.446375	+	0.257715i	−0.706298	−	0.707915i	$-0.749636\pi$
$719$	−320.943	+	185.297i	−0.446375	+	0.257715i	0.259923	+	0.965629i	$0.416303\pi$
$720$		0			0
$721$	59.4608	−	602.911i	0.0824699	−	0.836214i
$722$	474.384	+	821.657i	0.657042	+	1.13803i
$723$		0			0
$724$	−213.707	+	123.384i	−0.295175	+	0.170420i
$725$	1369.98	+	2372.88i	1.88963	+	3.27294i
$726$		0			0
$727$	98.4688	−	56.8510i	0.135445	−	0.0781995i	−0.430746	−	0.902473i	$-0.641750\pi$
$727$	98.4688	−	56.8510i	0.135445	−	0.0781995i	0.566192	+	0.824274i	$0.308416\pi$
$728$	68.3380	+	48.9838i	0.0938709	+	0.0672854i
$729$		0			0
$730$	−871.768	−	1509.95i	−1.19420	−	2.06842i
$731$		−	21.8613i		−	0.0299060i
$732$		0			0
$733$		−	608.247i		−	0.829805i	−0.909866	−	0.414903i	$-0.863816\pi$
$733$		−	608.247i		−	0.829805i	0.909866	−	0.414903i	$-0.136184\pi$
$734$	−965.458	−	557.407i	−1.31534	−	0.759411i
$735$		0			0
$736$	−100.949	−	174.848i	−0.137158	−	0.237565i
$737$	108.740	+	188.343i	0.147544	+	0.255554i
$738$		0			0
$739$	605.973	−	1049.58i	0.819990	−	1.42026i	−0.0856983	−	0.996321i	$-0.527312\pi$
$739$	605.973	−	1049.58i	0.819990	−	1.42026i	0.905689	−	0.423944i	$-0.139355\pi$
$740$	863.054	+	498.284i	1.16629	+	0.673357i
$741$		0			0
$742$	−158.922	−	350.869i	−0.214180	−	0.472870i
$743$	−82.8636	+	143.524i	−0.111526	+	0.193168i	−0.916386	−	0.400297i	$-0.868907\pi$
$743$	−82.8636	+	143.524i	−0.111526	+	0.193168i	0.804860	+	0.593465i	$0.202240\pi$
$744$		0			0
$745$			2363.99i			3.17314i
$746$	−293.657	+	508.628i	−0.393642	+	0.681807i
$747$		0			0
$748$			68.3515i			0.0913791i
$749$	147.020	+	324.593i	0.196289	+	0.433369i
$750$		0			0
$751$	1353.18			1.80183			0.900916	−	0.433993i	$-0.142896\pi$
$751$	1353.18			1.80183			0.900916	+	0.433993i	$0.142896\pi$
$752$	839.480	−	484.674i	1.11633	−	0.644514i
$753$		0			0
$754$	−507.051	−	292.746i	−0.672482	−	0.388258i
$755$		−	1089.63i		−	1.44322i
$756$		0			0
$757$	128.108			0.169231			0.0846155	−	0.996414i	$-0.473034\pi$
$757$	128.108			0.169231			0.0846155	+	0.996414i	$0.473034\pi$
$758$	421.187	−	729.518i	0.555656	−	0.962424i
$759$		0			0
$760$	22.7077	+	39.3309i	0.0298786	+	0.0517512i
$761$			805.339i			1.05826i	0.848540	+	0.529132i	$0.177482\pi$
$761$			805.339i			1.05826i	−0.848540	+	0.529132i	$0.822518\pi$
$762$		0			0
$763$	178.795	−	249.439i	0.234331	−	0.326919i
$764$	−84.3032			−0.110344
$765$		0			0
$766$	638.687	+	368.746i	0.833795	+	0.481392i
$767$	237.019			0.309021
$768$		0			0
$769$	501.209	+	289.373i	0.651767	+	0.376298i	0.789133	−	0.614222i	$-0.210530\pi$
$769$	501.209	+	289.373i	0.651767	+	0.376298i	−0.137366	+	0.990520i	$0.543864\pi$
$770$	−981.478	−	703.511i	−1.27465	−	0.913650i
$771$		0			0
$772$	190.453	−	329.874i	0.246701	−	0.427298i
$773$	−685.032	−	395.504i	−0.886200	−	0.511648i	−0.0135021	−	0.999909i	$-0.504298\pi$
$773$	−685.032	−	395.504i	−0.886200	−	0.511648i	−0.872698	+	0.488261i	$0.837631\pi$
$774$		0			0
$775$	−789.801	+	455.992i	−1.01910	+	0.588376i
$776$	−122.020	+	70.4481i	−0.157242	+	0.0907836i
$777$		0			0
$778$	96.2228	−	166.663i	0.123680	−	0.214219i
$779$	−110.380			−0.141695
$780$		0			0
$781$	573.265			0.734014
$782$	36.6459	−	21.1575i	0.0468618	−	0.0270557i
$783$		0			0
$784$	610.131	−	695.355i	0.778228	−	0.886932i
$785$	−234.814	−	406.710i	−0.299126	−	0.518102i
$786$		0			0
$787$	−856.846	+	494.700i	−1.08875	+	0.628590i	−0.933243	−	0.359245i	$-0.883034\pi$
$787$	−856.846	+	494.700i	−1.08875	+	0.628590i	−0.155506	+	0.987835i	$0.549701\pi$
$788$	−176.029	−	304.891i	−0.223387	−	0.386918i
$789$		0			0
$790$	614.898	−	355.011i	0.778352	−	0.449382i
$791$	434.714	−	606.476i	0.549576	−	0.766721i
$792$		0			0
$793$	5.53329	+	9.58394i	0.00697766	+	0.0120857i
$794$			1812.79i			2.28311i
$795$		0			0
$796$			369.641i			0.464373i
$797$	104.384	+	60.2662i	0.130971	+	0.0756163i	0.564054	−	0.825738i	$-0.309241\pi$
$797$	104.384	+	60.2662i	0.130971	+	0.0756163i	−0.433083	+	0.901354i	$0.642574\pi$
$798$		0			0
$799$	81.3216	+	140.853i	0.101779	+	0.176287i
$800$	1198.90	+	2076.55i	1.49862	+	2.59568i
$801$		0			0
$802$	−597.323	+	1034.59i	−0.744791	+	1.29002i
$803$	435.612	+	251.501i	0.542481	+	0.313201i
$804$		0			0
$805$	−31.7939	+	322.378i	−0.0394956	+	0.400470i
$806$	97.4391	−	168.769i	0.120892	−	0.209391i
$807$		0			0
$808$		−	280.101i		−	0.346659i
$809$	94.3098	−	163.349i	0.116576	−	0.201915i	−0.801833	−	0.597548i	$-0.796142\pi$
$809$	94.3098	−	163.349i	0.116576	−	0.201915i	0.918409	+	0.395633i	$0.129475\pi$
$810$		0			0
$811$		−	1191.68i		−	1.46940i	−0.678394	−	0.734699i	$-0.737324\pi$
$811$		−	1191.68i		−	1.46940i	0.678394	−	0.734699i	$-0.262676\pi$
$812$	−572.346	+	798.488i	−0.704860	+	0.983360i
$813$		0			0
$814$	−663.493			−0.815102
$815$	−2282.18	+	1317.62i	−2.80022	+	1.61671i
$816$		0			0
$817$	−11.7920	−	6.80809i	−0.0144332	−	0.00833303i
$818$			395.622i			0.483645i
$819$		0			0
$820$	−1575.00			−1.92073
$821$	−338.613	+	586.495i	−0.412440	+	0.714366i	−0.995156	−	0.0983094i	$-0.968657\pi$
$821$	−338.613	+	586.495i	−0.412440	+	0.714366i	0.582716	+	0.812676i	$0.301990\pi$
$822$		0			0
$823$	805.395	+	1394.98i	0.978608	+	1.69500i	0.667473	+	0.744634i	$0.267376\pi$
$823$	805.395	+	1394.98i	0.978608	+	1.69500i	0.311135	+	0.950366i	$0.399291\pi$
$824$		−	216.453i		−	0.262686i
$825$		0			0
$826$	90.0803	−	913.380i	0.109056	−	1.10579i
$827$	626.312			0.757331			0.378665	−	0.925534i	$-0.376383\pi$
$827$	626.312			0.757331			0.378665	+	0.925534i	$0.376383\pi$
$828$		0			0
$829$	−469.693	−	271.178i	−0.566578	−	0.327114i	0.189203	−	0.981938i	$-0.439409\pi$
$829$	−469.693	−	271.178i	−0.566578	−	0.327114i	−0.755782	+	0.654824i	$0.772743\pi$
$830$	−1579.21			−1.90266
$831$		0			0
$832$	−129.632	−	74.8431i	−0.155808	−	0.0899557i
$833$	116.671	+	102.371i	0.140061	+	0.122895i
$834$		0			0
$835$	−861.557	+	1492.26i	−1.03180	+	1.78714i
$836$	36.8687	+	21.2862i	0.0441014	+	0.0254619i
$837$		0			0
$838$	1060.52	−	612.293i	1.26554	−	0.730660i
$839$	1281.98	−	740.153i	1.52799	−	0.882185i	0.528543	−	0.848906i	$-0.322738\pi$
$839$	1281.98	−	740.153i	1.52799	−	0.882185i	0.999446	−	0.0332790i	$-0.0105950\pi$
$840$		0			0
$841$	−632.218	+	1095.03i	−0.751746	+	1.30206i
$842$	−339.541			−0.403256
$843$		0			0
$844$	−368.207			−0.436264
$845$	1163.22	−	671.587i	1.37660	−	0.794778i
$846$		0			0
$847$	−496.215	−	48.9381i	−0.585850	−	0.0577782i
$848$	−195.507	−	338.627i	−0.230550	−	0.399325i
$849$		0			0
$850$	−435.218	+	251.273i	−0.512021	+	0.295615i
$851$	88.9942	+	154.143i	0.104576	+	0.181131i
$852$		0			0
$853$	744.542	−	429.861i	0.872851	−	0.503941i	0.00455615	−	0.999990i	$-0.498550\pi$
$853$	744.542	−	429.861i	0.872851	−	0.503941i	0.868294	+	0.496049i	$0.165216\pi$
$854$	39.0357	−	17.6807i	0.0457093	−	0.0207034i
$855$		0			0
$856$	63.6560	+	110.255i	0.0743645	+	0.128803i
$857$		−	442.777i		−	0.516659i	−0.966057	−	0.258330i	$-0.916828\pi$
$857$		−	442.777i		−	0.516659i	0.966057	−	0.258330i	$-0.0831720\pi$
$858$		0			0
$859$		−	501.048i		−	0.583293i	−0.956526	−	0.291646i	$-0.905797\pi$
$859$		−	501.048i		−	0.583293i	0.956526	−	0.291646i	$-0.0942030\pi$
$860$	−168.257	−	97.1434i	−0.195648	−	0.112957i
$861$		0			0
$862$	−277.453	−	480.562i	−0.321871	−	0.557497i
$863$	182.251	+	315.667i	0.211183	+	0.365779i	0.952085	−	0.305834i	$-0.0989352\pi$
$863$	182.251	+	315.667i	0.211183	+	0.365779i	−0.740902	+	0.671613i	$0.765602\pi$
$864$		0			0
$865$	−685.174	+	1186.76i	−0.792108	+	1.37197i
$866$	−1132.47	−	653.834i	−1.30771	−	0.755005i
$867$		0			0
$868$	−265.773	−	190.502i	−0.306190	−	0.219473i
$869$	−102.419	+	177.395i	−0.117859	+	0.204137i
$870$		0			0
$871$		−	148.058i		−	0.169986i
$872$	54.8246	−	94.9590i	0.0628723	−	0.108898i
$873$		0			0
$874$		−	26.3557i		−	0.0301552i
$875$	219.509	−	2225.74i	0.250867	−	2.54370i
$876$		0			0
$877$	−782.479			−0.892223			−0.446111	−	0.894977i	$-0.647192\pi$
$877$	−782.479			−0.892223			−0.446111	+	0.894977i	$0.647192\pi$
$878$	−162.090	+	93.5829i	−0.184613	+	0.106586i
$879$		0			0
$880$	−1061.62	−	612.925i	−1.20638	−	0.696506i
$881$			337.263i			0.382818i	0.981510	+	0.191409i	$0.0613058\pi$
$881$			337.263i			0.382818i	−0.981510	+	0.191409i	$0.938694\pi$
$882$		0			0
$883$	556.002			0.629674			0.314837	−	0.949146i	$-0.398050\pi$
$883$	556.002			0.629674			0.314837	+	0.949146i	$0.398050\pi$
$884$	23.2665	−	40.2988i	0.0263196	−	0.0455868i
$885$		0			0
$886$	−951.233	−	1647.58i	−1.07363	−	1.85958i
$887$		−	722.908i		−	0.815004i	−0.913204	−	0.407502i	$-0.866400\pi$
$887$		−	722.908i		−	0.815004i	0.913204	−	0.407502i	$-0.133600\pi$
$888$		0			0
$889$	−1282.14	−	126.449i	−1.44223	−	0.142237i
$890$	−2515.79			−2.82673
$891$		0			0
$892$	622.790	+	359.568i	0.698195	+	0.403103i
$893$	101.301			0.113439
$894$		0			0
$895$	−1565.03	−	903.569i	−1.74863	−	1.00957i
$896$	317.335	−	442.718i	0.354168	−	0.494105i
$897$		0			0
$898$	173.158	−	299.919i	0.192827	−	0.333986i
$899$	−606.896	−	350.392i	−0.675079	−	0.389757i
$900$		0			0
$901$	56.8170	−	32.8033i	0.0630599	−	0.0364077i
$902$	908.113	−	524.299i	1.00678	−	0.581263i
$903$		0			0
$904$	133.298	−	230.879i	0.147454	−	0.255398i
$905$	742.563			0.820512
$906$		0			0
$907$	1127.74			1.24338			0.621688	−	0.783265i	$-0.286447\pi$
$907$	1127.74			1.24338			0.621688	+	0.783265i	$0.286447\pi$
$908$	400.613	−	231.294i	0.441203	−	0.254729i
$909$		0			0
$910$	339.189	+	748.866i	0.372736	+	0.822930i
$911$	890.109	+	1541.71i	0.977068	+	1.69233i	0.672933	+	0.739703i	$0.265034\pi$
$911$	890.109	+	1541.71i	0.977068	+	1.69233i	0.304136	+	0.952629i	$0.401632\pi$
$912$		0			0
$913$	394.556	−	227.797i	0.432153	−	0.249504i
$914$	−280.998	−	486.702i	−0.307437	−	0.532497i
$915$		0			0
$916$	1096.60	−	633.121i	1.19716	−	0.691181i
$917$	4.99748	−	50.6726i	0.00544982	−	0.0552591i
$918$		0			0
$919$	−350.534	−	607.142i	−0.381429	−	0.660655i	0.609837	−	0.792527i	$-0.291235\pi$
$919$	−350.534	−	607.142i	−0.381429	−	0.660655i	−0.991267	+	0.131871i	$0.957901\pi$
$920$			115.738i			0.125802i
$921$		0			0
$922$			1402.08i			1.52069i
$923$	−337.986	−	195.136i	−0.366182	−	0.211415i
$924$		0			0
$925$	−1056.92	−	1830.64i	−1.14262	−	1.97907i
$926$	975.227	+	1689.14i	1.05316	+	1.82413i
$927$		0			0
$928$	−921.252	+	1595.65i	−0.992728	+	1.71946i
$929$	849.720	+	490.586i	0.914661	+	0.528080i	0.881928	−	0.471385i	$-0.156246\pi$
$929$	849.720	+	490.586i	0.914661	+	0.528080i	0.0327329	+	0.999464i	$0.489579\pi$
$930$		0			0
$931$	91.5529	−	31.0514i	0.0983383	−	0.0333528i
$932$	−510.189	+	883.674i	−0.547413	+	0.948148i
$933$		0			0
$934$			861.870i			0.922773i
$935$	102.840	−	178.125i	0.109990	−	0.190508i
$936$		0			0
$937$		−	949.998i		−	1.01387i	−0.861984	−	0.506936i	$-0.830778\pi$
$937$		−	949.998i		−	1.01387i	0.861984	−	0.506936i	$-0.169222\pi$
$938$	−570.559	−	56.2702i	−0.608272	−	0.0599896i
$939$		0			0
$940$	1445.45			1.53772
$941$	329.267	−	190.102i	0.349912	−	0.202022i	−0.314735	−	0.949180i	$-0.601916\pi$
$941$	329.267	−	190.102i	0.349912	−	0.202022i	0.664646	+	0.747158i	$0.268582\pi$
$942$		0			0
$943$	−243.610	−	140.648i	−0.258335	−	0.149150i
$944$		−	931.705i		−	0.986976i
$945$		0			0
$946$	129.352			0.136736
$947$	163.034	−	282.383i	0.172159	−	0.298187i	−0.767016	−	0.641628i	$-0.778259\pi$
$947$	163.034	−	282.383i	0.172159	−	0.298187i	0.939174	+	0.343441i	$0.111593\pi$
$948$		0			0
$949$	−171.219	−	296.560i	−0.180420	−	0.312497i
$950$			313.008i			0.329482i
$951$		0			0
$952$	45.0727	+	32.3075i	0.0473453	+	0.0339365i
$953$	−1009.14			−1.05891			−0.529455	−	0.848338i	$-0.677603\pi$
$953$	−1009.14			−1.05891			−0.529455	+	0.848338i	$0.677603\pi$
$954$		0			0
$955$	219.695	+	126.841i	0.230047	+	0.132818i
$956$	−641.212			−0.670723
$957$		0			0
$958$	967.578	+	558.631i	1.01000	+	0.583122i
$959$	329.307	+	32.4772i	0.343385	+	0.0338657i
$960$		0			0
$961$	−363.874	+	630.248i	−0.378641	+	0.655825i
$962$	391.183	+	225.850i	0.406635	+	0.234771i
$963$		0			0
$964$	603.269	−	348.298i	0.625798	−	0.361304i
$965$	−992.644	+	573.103i	−1.02865	+	0.593890i
$966$		0			0
$967$	277.066	−	479.892i	0.286521	−	0.496269i	−0.686456	−	0.727172i	$-0.740834\pi$
$967$	277.066	−	479.892i	0.286521	−	0.496269i	0.972977	+	0.230902i	$0.0741678\pi$
$968$	−178.148			−0.184037
$969$		0			0
$970$	−1377.62			−1.42023
$971$	−1334.71	+	770.592i	−1.37457	+	0.793607i	−0.991499	−	0.130113i	$-0.958466\pi$
$971$	−1334.71	+	770.592i	−1.37457	+	0.793607i	−0.383069	+	0.923720i	$0.625133\pi$
$972$		0			0
$973$	1441.05	+	1032.92i	1.48104	+	1.06159i
$974$	−51.3691	−	88.9739i	−0.0527404	−	0.0913490i
$975$		0			0
$976$	37.6738	−	21.7510i	0.0386002	−	0.0222858i
$977$	−812.692	−	1407.62i	−0.831824	−	1.44076i	−0.896590	−	0.442861i	$-0.853963\pi$
$977$	−812.692	−	1407.62i	−0.831824	−	1.44076i	0.0647660	−	0.997900i	$-0.479370\pi$
$978$		0			0
$979$	628.556	−	362.897i	0.642039	−	0.370681i
$980$	1306.35	−	443.068i	1.33301	−	0.452110i
$981$		0			0
$982$	1157.53	+	2004.90i	1.17875	+	2.04165i
$983$		−	35.2712i		−	0.0358812i	−0.999839	−	0.0179406i	$-0.994289\pi$
$983$		−	35.2712i		−	0.0358812i	0.999839	−	0.0179406i	$-0.00571098\pi$
$984$		0			0
$985$			1059.40i			1.07553i
$986$	−334.429	−	193.082i	−0.339177	−	0.195824i
$987$		0			0
$988$	−14.4914	−	25.0998i	−0.0146674	−	0.0254047i
$989$	−17.3499	−	30.0510i	−0.0175429	−	0.0303852i
$990$		0			0
$991$	567.488	−	982.918i	0.572642	−	0.991845i	−0.423652	−	0.905825i	$-0.639252\pi$
$991$	567.488	−	982.918i	0.572642	−	0.991845i	0.996293	−	0.0860197i	$-0.0274148\pi$
$992$	−531.105	−	306.634i	−0.535388	−	0.309107i
$993$		0			0
$994$	−880.433	+	1228.31i	−0.885748	+	1.23572i
$995$	556.155	−	963.288i	0.558950	−	0.968129i
$996$		0			0
$997$		−	51.2724i		−	0.0514267i	−0.999669	−	0.0257133i	$-0.991814\pi$
$997$		−	51.2724i		−	0.0514267i	0.999669	−	0.0257133i	$-0.00818571\pi$
$998$	−489.190	+	847.301i	−0.490170	+	0.848999i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.k.a.10.12		28
3.2	odd	2		63.3.k.a.31.3	✓	28
7.5	odd	6		189.3.t.a.145.3		28
9.2	odd	6		63.3.t.a.52.12	yes	28
9.7	even	3		189.3.t.a.73.3		28
21.2	odd	6		441.3.t.a.166.12		28
21.5	even	6		63.3.t.a.40.12	yes	28
21.11	odd	6		441.3.l.a.391.3		28
21.17	even	6		441.3.l.b.391.3		28
21.20	even	2		441.3.k.b.31.3		28
63.2	odd	6		441.3.k.b.313.3		28
63.11	odd	6		441.3.l.b.97.3		28
63.20	even	6		441.3.t.a.178.12		28
63.38	even	6		441.3.l.a.97.3		28
63.47	even	6		63.3.k.a.61.3	yes	28
63.61	odd	6	inner	189.3.k.a.19.12		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.3	✓	28	3.2	odd	2
63.3.k.a.61.3	yes	28	63.47	even	6
63.3.t.a.40.12	yes	28	21.5	even	6
63.3.t.a.52.12	yes	28	9.2	odd	6
189.3.k.a.10.12		28	1.1	even	1	trivial
189.3.k.a.19.12		28	63.61	odd	6	inner
189.3.t.a.73.3		28	9.7	even	3
189.3.t.a.145.3		28	7.5	odd	6
441.3.k.b.31.3		28	21.20	even	2
441.3.k.b.313.3		28	63.2	odd	6
441.3.l.a.97.3		28	63.38	even	6
441.3.l.a.391.3		28	21.11	odd	6
441.3.l.b.97.3		28	63.11	odd	6
441.3.l.b.391.3		28	21.17	even	6
441.3.t.a.166.12		28	21.2	odd	6
441.3.t.a.178.12		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)

\(f(q)\)	\(=\)	\(q+(1.32841 - 2.30087i) q^{2} +(-1.52933 - 2.64888i) q^{4} +9.20400i q^{5} +(6.96620 + 0.687028i) q^{7} +2.50096 q^{8} +O(q^{10})\)	\(q+(1.32841 - 2.30087i) q^{2} +(-1.52933 - 2.64888i) q^{4} +9.20400i q^{5} +(6.96620 + 0.687028i) q^{7} +2.50096 q^{8} +(21.1772 + 12.2267i) q^{10} -7.05467 q^{11} +(4.15930 + 2.40137i) q^{13} +(10.8347 - 15.1157i) q^{14} +(9.43962 - 16.3499i) q^{16} +(2.74329 + 1.58384i) q^{17} +(1.70864 - 0.986484i) q^{19} +(24.3803 - 14.0760i) q^{20} +(-9.37147 + 16.2319i) q^{22} +5.02797 q^{23} -59.7137 q^{25} +(11.0505 - 6.38000i) q^{26} +(-8.83378 - 19.5033i) q^{28} +(-22.9425 - 39.7376i) q^{29} +(13.2265 - 7.63630i) q^{31} +(-20.0774 - 34.7751i) q^{32} +(7.28840 - 4.20796i) q^{34} +(-6.32341 + 64.1170i) q^{35} +(17.6998 + 30.6570i) q^{37} -5.24181i q^{38} +23.0189i q^{40} +(-48.4509 - 27.9732i) q^{41} +(-3.45068 - 5.97676i) q^{43} +(10.7889 + 18.6870i) q^{44} +(6.67920 - 11.5687i) q^{46} +(44.4658 + 25.6723i) q^{47} +(48.0560 + 9.57195i) q^{49} +(-79.3241 + 137.393i) q^{50} -14.6900i q^{52} +(10.3556 - 17.9365i) q^{53} -64.9312i q^{55} +(17.4222 + 1.71823i) q^{56} -121.908 q^{58} +(42.7391 - 24.6754i) q^{59} +(1.99551 + 1.15211i) q^{61} -40.5764i q^{62} -31.1668 q^{64} +(-22.1022 + 38.2822i) q^{65} +(-15.4139 - 26.6977i) q^{67} -9.68884i q^{68} +(139.125 + 99.7228i) q^{70} -81.2604 q^{71} +(-61.7481 - 35.6503i) q^{73} +94.0503 q^{74} +(-5.22615 - 3.01732i) q^{76} +(-49.1442 - 4.84675i) q^{77} +(14.5179 - 25.1458i) q^{79} +(150.485 + 86.8823i) q^{80} +(-128.725 + 74.3195i) q^{82} +(-55.9283 + 32.2902i) q^{83} +(-14.5776 + 25.2492i) q^{85} -18.3357 q^{86} -17.6434 q^{88} +(-89.0979 + 51.4407i) q^{89} +(27.3247 + 19.5860i) q^{91} +(-7.68944 - 13.3185i) q^{92} +(118.137 - 68.2067i) q^{94} +(9.07960 + 15.7263i) q^{95} +(-48.7891 + 28.1684i) q^{97} +(85.8617 - 97.8551i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) \) 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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