LMFDB - Embedded newform 441.3.t.a.166.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(166,441)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("441.166");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.t (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:	$12.0163796583$
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			166.12
Character	$\chi$	$=$	441.166
Dual form			441.3.t.a.178.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.65681 q^{2} +(2.49911 + 1.65965i) q^{3} +3.05866 q^{4} +(-7.97090 + 4.60200i) q^{5} +(6.63967 + 4.40939i) q^{6} -2.50096 q^{8} +(3.49110 + 8.29531i) q^{9} +O(q^{10})$	\(q+2.65681 q^{2} +(2.49911 + 1.65965i) q^{3} +3.05866 q^{4} +(-7.97090 + 4.60200i) q^{5} +(6.63967 + 4.40939i) q^{6} -2.50096 q^{8} +(3.49110 + 8.29531i) q^{9} +(-21.1772 + 12.2267i) q^{10} +(-3.52733 + 6.10952i) q^{11} +(7.64393 + 5.07632i) q^{12} +(4.15930 + 2.40137i) q^{13} +(-27.5579 - 1.72803i) q^{15} -18.8792 q^{16} +(2.74329 - 1.58384i) q^{17} +(9.27520 + 22.0391i) q^{18} +(-1.70864 - 0.986484i) q^{19} +(-24.3803 + 14.0760i) q^{20} +(-9.37147 + 16.2319i) q^{22} +(2.51399 + 4.35435i) q^{23} +(-6.25018 - 4.15073i) q^{24} +(29.8569 - 51.7136i) q^{25} +(11.0505 + 6.38000i) q^{26} +(-5.04271 + 26.5249i) q^{27} +(22.9425 + 39.7376i) q^{29} +(-73.2162 - 4.59105i) q^{30} +15.2726i q^{31} -40.1548 q^{32} +(-18.9549 + 9.41421i) q^{33} +(7.28840 - 4.20796i) q^{34} +(10.6781 + 25.3726i) q^{36} +(17.6998 - 30.6570i) q^{37} +(-4.53954 - 2.62090i) q^{38} +(6.40909 + 12.9043i) q^{39} +(19.9349 - 11.5094i) q^{40} +(48.4509 + 27.9732i) q^{41} +(-3.45068 - 5.97676i) q^{43} +(-10.7889 + 18.6870i) q^{44} +(-66.0023 - 50.0551i) q^{45} +(6.67920 + 11.5687i) q^{46} +51.3447i q^{47} +(-47.1813 - 31.3330i) q^{48} +(79.3241 - 137.393i) q^{50} +(9.48440 + 0.594723i) q^{51} +(12.7219 + 7.34498i) q^{52} +(-10.3556 - 17.9365i) q^{53} +(-13.3975 + 70.4718i) q^{54} -64.9312i q^{55} +(-2.63286 - 5.30108i) q^{57} +(60.9540 + 105.575i) q^{58} -49.3508i q^{59} +(-84.2903 - 5.28546i) q^{60} -2.30422i q^{61} +40.5764i q^{62} -31.1668 q^{64} -44.2045 q^{65} +(-50.3596 + 25.0118i) q^{66} +30.8279 q^{67} +(8.39079 - 4.84442i) q^{68} +(-0.943990 + 15.0544i) q^{69} +81.2604 q^{71} +(-8.73110 - 20.7463i) q^{72} +(61.7481 - 35.6503i) q^{73} +(47.0251 - 81.4499i) q^{74} +(160.442 - 79.6859i) q^{75} +(-5.22615 - 3.01732i) q^{76} +(17.0278 + 34.2843i) q^{78} -29.0358 q^{79} +(150.485 - 86.8823i) q^{80} +(-56.6245 + 57.9195i) q^{81} +(128.725 + 74.3195i) q^{82} +(55.9283 - 32.2902i) q^{83} +(-14.5776 + 25.2492i) q^{85} +(-9.16783 - 15.8791i) q^{86} +(-8.61480 + 137.385i) q^{87} +(8.82172 - 15.2797i) q^{88} +(-89.0979 - 51.4407i) q^{89} +(-175.356 - 132.987i) q^{90} +(7.68944 + 13.3185i) q^{92} +(-25.3472 + 38.1679i) q^{93} +136.413i q^{94} +18.1592 q^{95} +(-100.351 - 66.6430i) q^{96} +(-48.7891 + 28.1684i) q^{97} +(-62.9946 - 7.93140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + 3 q^{3} + 46 q^{4} + 3 q^{5} + 12 q^{6} - 16 q^{8} - 15 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 + 3 * q^3 + 46 * q^4 + 3 * q^5 + 12 * q^6 - 16 * q^8 - 15 * q^9	$ 28 q - 2 q^{2} + 3 q^{3} + 46 q^{4} + 3 q^{5} + 12 q^{6} - 16 q^{8} - 15 q^{9} + 6 q^{10} + 7 q^{11} + 30 q^{12} + 15 q^{13} - 18 q^{15} + 54 q^{16} + 33 q^{17} - 42 q^{18} + 6 q^{19} + 108 q^{20} - 10 q^{22} + 34 q^{23} + 78 q^{24} + 31 q^{25} - 54 q^{26} - 81 q^{27} + 70 q^{29} - 27 q^{30} - 306 q^{32} + 3 q^{33} + 12 q^{34} - 174 q^{36} + 9 q^{37} - 87 q^{38} + 129 q^{39} + 102 q^{40} - 234 q^{41} + 30 q^{43} + 51 q^{44} - 273 q^{45} - 22 q^{46} + 147 q^{48} + 241 q^{50} + 12 q^{51} + 219 q^{52} + 148 q^{53} - 171 q^{54} + 189 q^{57} + 17 q^{58} + 33 q^{60} - 48 q^{64} - 228 q^{65} - 258 q^{66} + 68 q^{67} + 18 q^{68} + 78 q^{69} - 350 q^{71} + 162 q^{72} + 6 q^{73} + 359 q^{74} + 510 q^{75} + 72 q^{76} - 375 q^{78} + 164 q^{79} + 609 q^{80} - 435 q^{81} + 18 q^{82} + 738 q^{83} + 3 q^{85} + 17 q^{86} + 561 q^{87} + 25 q^{88} - 21 q^{89} - 543 q^{90} + 288 q^{92} - 222 q^{93} - 1014 q^{95} - 231 q^{96} - 57 q^{97} - 162 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + 3 * q^3 + 46 * q^4 + 3 * q^5 + 12 * q^6 - 16 * q^8 - 15 * q^9 + 6 * q^10 + 7 * q^11 + 30 * q^12 + 15 * q^13 - 18 * q^15 + 54 * q^16 + 33 * q^17 - 42 * q^18 + 6 * q^19 + 108 * q^20 - 10 * q^22 + 34 * q^23 + 78 * q^24 + 31 * q^25 - 54 * q^26 - 81 * q^27 + 70 * q^29 - 27 * q^30 - 306 * q^32 + 3 * q^33 + 12 * q^34 - 174 * q^36 + 9 * q^37 - 87 * q^38 + 129 * q^39 + 102 * q^40 - 234 * q^41 + 30 * q^43 + 51 * q^44 - 273 * q^45 - 22 * q^46 + 147 * q^48 + 241 * q^50 + 12 * q^51 + 219 * q^52 + 148 * q^53 - 171 * q^54 + 189 * q^57 + 17 * q^58 + 33 * q^60 - 48 * q^64 - 228 * q^65 - 258 * q^66 + 68 * q^67 + 18 * q^68 + 78 * q^69 - 350 * q^71 + 162 * q^72 + 6 * q^73 + 359 * q^74 + 510 * q^75 + 72 * q^76 - 375 * q^78 + 164 * q^79 + 609 * q^80 - 435 * q^81 + 18 * q^82 + 738 * q^83 + 3 * q^85 + 17 * q^86 + 561 * q^87 + 25 * q^88 - 21 * q^89 - 543 * q^90 + 288 * q^92 - 222 * q^93 - 1014 * q^95 - 231 * q^96 - 57 * q^97 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	2.65681			1.32841			0.664204	−	0.747552i	$-0.268771\pi$
$2$	2.65681			1.32841			0.664204	+	0.747552i	$0.268771\pi$
$3$	2.49911	+	1.65965i	0.833037	+	0.553218i
$3$	2.49911	+	1.65965i	0.833037	+	0.553218i
$4$	3.05866			0.764665
$5$	−7.97090	+	4.60200i	−1.59418	+	0.920400i	−0.601602	+	0.798796i	$0.705471\pi$
$5$	−7.97090	+	4.60200i	−1.59418	+	0.920400i	−0.992579	+	0.121604i	$0.961196\pi$
$6$	6.63967	+	4.40939i	1.10661	+	0.734899i
$7$		0			0
$7$		0			0
$8$	−2.50096			−0.312620
$9$	3.49110	+	8.29531i	0.387900	+	0.921702i
$10$	−21.1772	+	12.2267i	−2.11772	+	1.22267i
$11$	−3.52733	+	6.10952i	−0.320667	+	0.555411i	−0.980626	−	0.195891i	$-0.937240\pi$
$11$	−3.52733	+	6.10952i	−0.320667	+	0.555411i	0.659959	+	0.751301i	$0.270574\pi$
$12$	7.64393	+	5.07632i	0.636994	+	0.423027i
$13$	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	$0.607529\pi$
$14$		0			0
$15$	−27.5579	−	1.72803i	−1.83719	−	0.115202i
$16$	−18.8792			−1.17995
$17$	2.74329	−	1.58384i	0.161370	−	0.0931669i	−0.417140	−	0.908842i	$-0.636968\pi$
$17$	2.74329	−	1.58384i	0.161370	−	0.0931669i	0.578510	+	0.815675i	$0.303634\pi$
$18$	9.27520	+	22.0391i	0.515289	+	1.22439i
$19$	−1.70864	−	0.986484i	−0.0899284	−	0.0519202i	0.454361	−	0.890817i	$-0.349867\pi$
$19$	−1.70864	−	0.986484i	−0.0899284	−	0.0519202i	−0.544290	+	0.838897i	$0.683201\pi$
$20$	−24.3803	+	14.0760i	−1.21901	+	0.703798i
$21$		0			0
$22$	−9.37147	+	16.2319i	−0.425976	+	0.737812i
$23$	2.51399	+	4.35435i	0.109304	+	0.189320i	0.915488	−	0.402344i	$-0.131805\pi$
$23$	2.51399	+	4.35435i	0.109304	+	0.189320i	−0.806185	+	0.591664i	$0.798471\pi$
$24$	−6.25018	−	4.15073i	−0.260424	−	0.172947i
$25$	29.8569	−	51.7136i	1.19427	−	2.06854i
$26$	11.0505	+	6.38000i	0.425018	+	0.245384i
$27$	−5.04271	+	26.5249i	−0.186767	+	0.982404i
$28$		0			0
$29$	22.9425	+	39.7376i	0.791121	+	1.37026i	0.925273	+	0.379301i	$0.123836\pi$
$29$	22.9425	+	39.7376i	0.791121	+	1.37026i	−0.134152	+	0.990961i	$0.542831\pi$
$30$	−73.2162	−	4.59105i	−2.44054	−	0.153035i
$31$			15.2726i			0.492664i	0.969185	+	0.246332i	$0.0792254\pi$
$31$			15.2726i			0.492664i	−0.969185	+	0.246332i	$0.920775\pi$
$32$	−40.1548			−1.25484
$33$	−18.9549	+	9.41421i	−0.574390	+	0.285279i
$34$	7.28840	−	4.20796i	0.214365	−	0.123764i
$35$		0			0
$36$	10.6781	+	25.3726i	0.296614	+	0.704793i
$37$	17.6998	−	30.6570i	0.478373	−	0.828567i	−0.521319	−	0.853362i	$-0.674560\pi$
$37$	17.6998	−	30.6570i	0.478373	−	0.828567i	0.999693	+	0.0247946i	$0.00789319\pi$
$38$	−4.53954	−	2.62090i	−0.119462	−	0.0689711i
$39$	6.40909	+	12.9043i	0.164336	+	0.330879i
$40$	19.9349	−	11.5094i	0.498373	−	0.287736i
$41$	48.4509	+	27.9732i	1.18173	+	0.682272i	0.956414	−	0.292014i	$-0.0943253\pi$
$41$	48.4509	+	27.9732i	1.18173	+	0.682272i	0.225316	+	0.974286i	$0.427659\pi$
$42$		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
$45$	−66.0023	−	50.0551i	−1.46672	−	1.11234i
$46$	6.67920	+	11.5687i	0.145200	+	0.251494i
$47$			51.3447i			1.09244i	0.837642	+	0.546220i	$0.183934\pi$
$47$			51.3447i			1.09244i	−0.837642	+	0.546220i	$0.816066\pi$
$48$	−47.1813	−	31.3330i	−0.982943	−	0.652771i
$49$		0			0
$50$	79.3241	−	137.393i	1.58648	−	2.74787i
$51$	9.48440	+	0.594723i	0.185969	+	0.0116612i
$52$	12.7219	+	7.34498i	0.244652	+	0.141250i
$53$	−10.3556	−	17.9365i	−0.195390	−	0.338425i	0.751639	−	0.659575i	$-0.229264\pi$
$53$	−10.3556	−	17.9365i	−0.195390	−	0.338425i	−0.947028	+	0.321151i	$0.895930\pi$
$54$	−13.3975	+	70.4718i	−0.248103	+	1.30503i
$55$		−	64.9312i		−	1.18057i
$56$		0			0
$57$	−2.63286	−	5.30108i	−0.0461905	−	0.0930014i
$58$	60.9540	+	105.575i	1.05093	+	1.82027i
$59$		−	49.3508i		−	0.836454i	−0.908342	−	0.418227i	$-0.862652\pi$
$59$		−	49.3508i		−	0.836454i	0.908342	−	0.418227i	$-0.137348\pi$
$60$	−84.2903	−	5.28546i	−1.40484	−	0.0880909i
$61$		−	2.30422i		−	0.0377741i	−0.999822	−	0.0188871i	$-0.993988\pi$
$61$		−	2.30422i		−	0.0377741i	0.999822	−	0.0188871i	$-0.00601229\pi$
$62$			40.5764i			0.654459i
$63$		0			0
$64$	−31.1668			−0.486982
$65$	−44.2045			−0.680069
$66$	−50.3596	+	25.0118i	−0.763024	+	0.378967i
$67$	30.8279			0.460117			0.230059	−	0.973177i	$-0.426108\pi$
$67$	30.8279			0.460117			0.230059	+	0.973177i	$0.426108\pi$
$68$	8.39079	−	4.84442i	0.123394	−	0.0712415i
$69$	−0.943990	+	15.0544i	−0.0136810	+	0.218179i
$70$		0			0
$71$	81.2604			1.14451			0.572256	−	0.820075i	$-0.306068\pi$
$71$	81.2604			1.14451			0.572256	+	0.820075i	$0.306068\pi$
$72$	−8.73110	−	20.7463i	−0.121265	−	0.288142i
$73$	61.7481	−	35.6503i	0.845864	−	0.488360i	−0.0133893	−	0.999910i	$-0.504262\pi$
$73$	61.7481	−	35.6503i	0.845864	−	0.488360i	0.859253	+	0.511551i	$0.170929\pi$
$74$	47.0251	−	81.4499i	0.635475	−	1.10067i
$75$	160.442	−	79.6859i	2.13923	−	1.06248i
$76$	−5.22615	−	3.01732i	−0.0687651	−	0.0397016i
$77$		0			0
$78$	17.0278	+	34.2843i	0.218305	+	0.439542i
$79$	−29.0358			−0.367542			−0.183771	−	0.982969i	$-0.558831\pi$
$79$	−29.0358			−0.367542			−0.183771	+	0.982969i	$0.558831\pi$
$80$	150.485	−	86.8823i	1.88106	−	1.08603i
$81$	−56.6245	+	57.9195i	−0.699067	+	0.715056i
$82$	128.725	+	74.3195i	1.56982	+	0.906335i
$83$	55.9283	−	32.2902i	0.673835	−	0.389039i	−0.123693	−	0.992321i	$-0.539474\pi$
$83$	55.9283	−	32.2902i	0.673835	−	0.389039i	0.797528	+	0.603282i	$0.206140\pi$
$84$		0			0
$85$	−14.5776	+	25.2492i	−0.171502	+	0.297050i
$86$	−9.16783	−	15.8791i	−0.106603	−	0.184641i
$87$	−8.61480	+	137.385i	−0.0990207	+	1.57914i
$88$	8.82172	−	15.2797i	0.100247	−	0.173633i
$89$	−89.0979	−	51.4407i	−1.00110	−	0.577985i	−0.0925265	−	0.995710i	$-0.529494\pi$
$89$	−89.0979	−	51.4407i	−1.00110	−	0.577985i	−0.908574	+	0.417725i	$0.862828\pi$
$90$	−175.356	−	132.987i	−1.94840	−	1.47763i
$91$		0			0
$92$	7.68944	+	13.3185i	0.0835808	+	0.144766i
$93$	−25.3472	+	38.1679i	−0.272551	+	0.410407i
$94$			136.413i			1.45121i
$95$	18.1592			0.191149
$96$	−100.351	−	66.6430i	−1.04532	−	0.694198i
$97$	−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	$0.427120\pi$
$98$		0			0
$99$	−62.9946	−	7.93140i	−0.636310	−	0.0801151i
$100$	91.3220	−	158.174i	0.913220	−	1.58174i
$101$	−96.9924	−	55.9986i	−0.960321	−	0.554442i	−0.0640493	−	0.997947i	$-0.520401\pi$
$101$	−96.9924	−	55.9986i	−0.960321	−	0.554442i	−0.896272	+	0.443505i	$0.853735\pi$
$102$	25.1983	+	1.58007i	0.247042	+	0.0154909i
$103$	−74.9527	+	43.2740i	−0.727696	+	0.420136i	−0.817579	−	0.575817i	$-0.804684\pi$
$103$	−74.9527	+	43.2740i	−0.727696	+	0.420136i	0.0898825	+	0.995952i	$0.471351\pi$
$104$	−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	$-0.909784\pi$
$107$	−25.4526	+	44.0852i	−0.237875	+	0.412012i	0.722229	+	0.691654i	$0.243118\pi$
$108$	−15.4239	+	81.1307i	−0.142814	+	0.751211i
$109$	21.9214	+	37.9690i	0.201114	+	0.348340i	0.948888	−	0.315614i	$-0.102211\pi$
$109$	21.9214	+	37.9690i	0.201114	+	0.348340i	−0.747774	+	0.663954i	$0.768877\pi$
$110$		−	172.510i		−	1.56827i
$111$	95.1138	−	47.2396i	0.856881	−	0.425582i
$112$		0			0
$113$	−53.2988	+	92.3163i	−0.471671	+	0.816959i	−0.999475	−	0.0324080i	$-0.989682\pi$
$113$	−53.2988	+	92.3163i	−0.471671	+	0.816959i	0.527803	+	0.849367i	$0.323016\pi$
$114$	−6.99501	−	14.0840i	−0.0613597	−	0.123544i
$115$	−40.0775	−	23.1387i	−0.348500	−	0.201207i
$116$	70.1734	+	121.544i	0.604943	+	1.04779i
$117$	−5.39961	+	42.8861i	−0.0461505	+	0.366548i
$118$		−	131.116i		−	1.11115i
$119$		0			0
$120$	68.9212	+	4.32173i	0.574343	+	0.0360144i
$121$	35.6159	+	61.6885i	0.294346	+	0.509822i
$122$		−	6.12189i		−	0.0501794i
$123$	74.6584	+	150.320i	0.606979	+	1.22211i
$124$			46.7137i			0.376723i
$125$			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	$0.757982\pi$
$128$	77.8146			0.607927
$129$	1.29571	−	20.6635i	0.0100443	−	0.160182i
$130$	−117.443			−0.903408
$131$	6.29953	−	3.63703i	0.0480880	−	0.0277636i	−0.475763	−	0.879573i	$-0.657828\pi$
$131$	6.29953	−	3.63703i	0.0480880	−	0.0277636i	0.523851	+	0.851810i	$0.324495\pi$
$132$	−57.9766	+	28.7949i	−0.439216	+	0.218143i
$133$		0			0
$134$	81.9039			0.611223
$135$	−81.8728	−	234.634i	−0.606465	−	1.73803i
$136$	−6.86085	+	3.96111i	−0.0504474	+	0.0291258i
$137$	23.6360	−	40.9388i	0.172526	−	0.298823i	−0.766777	−	0.641914i	$-0.778141\pi$
$137$	23.6360	−	40.9388i	0.172526	−	0.298823i	0.939302	+	0.343091i	$0.111474\pi$
$138$	−2.50801	+	39.9966i	−0.0181740	+	0.289831i
$139$	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	$0.301899\pi$
$140$		0			0
$141$	−85.2144	+	128.316i	−0.604358	+	0.910043i
$142$	215.894			1.52038
$143$	−29.3424	+	16.9409i	−0.205192	+	0.118468i
$144$	−65.9093	−	156.609i	−0.457703	−	1.08756i
$145$	−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
$149$	128.422	+	222.433i	0.861892	+	1.49284i	0.870100	+	0.492874i	$0.164054\pi$
$149$	128.422	+	222.433i	0.861892	+	1.49284i	−0.00820848	+	0.999966i	$0.502613\pi$
$150$	426.265	−	211.711i	2.84177	−	1.41140i
$151$	59.1932	−	102.526i	0.392008	−	0.678978i	−0.600706	−	0.799470i	$-0.705114\pi$
$151$	59.1932	−	102.526i	0.392008	−	0.678978i	0.992714	+	0.120492i	$0.0384471\pi$
$152$	4.27324	+	2.46716i	0.0281134	+	0.0162313i
$153$	22.7155	+	17.2271i	0.148467	+	0.112595i
$154$		0			0
$155$	−70.2845	−	121.736i	−0.453448	−	0.785396i
$156$	19.6032	+	39.4698i	0.125662	+	0.253012i
$157$		−	51.0244i		−	0.324996i	−0.986709	−	0.162498i	$-0.948045\pi$
$157$		−	51.0244i		−	0.324996i	0.986709	−	0.162498i	$-0.0519551\pi$
$158$	−77.1428			−0.488246
$159$	3.88849	−	62.0121i	0.0244559	−	0.390013i
$160$	320.070	−	184.792i	2.00044	−	1.15495i
$161$		0			0
$162$	−150.441	+	153.881i	−0.928646	+	0.949885i
$163$	143.157	−	247.955i	0.878263	−	1.52120i	0.0250163	−	0.999687i	$-0.492036\pi$
$163$	143.157	−	247.955i	0.878263	−	1.52120i	0.853246	−	0.521508i	$-0.174630\pi$
$164$	148.195	+	85.5604i	0.903628	+	0.521710i
$165$	107.763	−	162.270i	0.653111	−	0.983455i
$166$	148.591	−	85.7892i	0.895128	−	0.516802i
$167$	−162.132	−	93.6068i	−0.970848	−	0.560519i	−0.0713535	−	0.997451i	$-0.522732\pi$
$167$	−162.132	−	93.6068i	−0.970848	−	0.560519i	−0.899495	+	0.436932i	$0.856065\pi$
$168$		0			0
$169$	−72.9668	−	126.382i	−0.431756	−	0.747824i
$170$	−38.7301	+	67.0825i	−0.227824	+	0.394603i
$171$	2.21816	−	17.6176i	0.0129717	−	0.103027i
$172$	−10.5545	−	18.2809i	−0.0613632	−	0.106284i
$173$			148.886i			0.860613i	0.902683	+	0.430306i	$0.141594\pi$
$173$			148.886i			0.860613i	−0.902683	+	0.430306i	$0.858406\pi$
$174$	−22.8879	+	365.007i	−0.131540	+	2.09774i
$175$		0			0
$176$	66.5933	−	115.343i	0.378371	−	0.655358i
$177$	81.9053	−	123.333i	0.462742	−	0.696797i
$178$	−236.717	−	136.668i	−1.32987	−	0.767800i
$179$	98.1713	+	170.038i	0.548443	+	0.949931i	0.998381	+	0.0568718i	$0.0181126\pi$
$179$	98.1713	+	170.038i	0.548443	+	0.949931i	−0.449938	+	0.893060i	$0.648554\pi$
$180$	−201.879	−	153.102i	−1.12155	−	0.850564i
$181$		−	80.6783i		−	0.445736i	−0.974849	−	0.222868i	$-0.928458\pi$
$181$		−	80.6783i		−	0.445736i	0.974849	−	0.222868i	$-0.0715419\pi$
$182$		0			0
$183$	3.82421	−	5.75850i	0.0208973	−	0.0314672i
$184$	−6.28738	−	10.8901i	−0.0341706	−	0.0591852i
$185$			325.818i			1.76118i
$186$	−67.3429	+	101.405i	−0.362058	+	0.545188i
$187$			22.3469i			0.119502i
$188$			157.046i			0.835351i
$189$		0			0
$190$	48.2456			0.253924
$191$	27.5621			0.144304			0.0721521	−	0.997394i	$-0.477013\pi$
$191$	27.5621			0.144304			0.0721521	+	0.997394i	$0.477013\pi$
$192$	−77.8893	−	51.7262i	−0.405674	−	0.269407i
$193$	−124.534			−0.645251			−0.322626	−	0.946527i	$-0.604565\pi$
$193$	−124.534			−0.645251			−0.322626	+	0.946527i	$0.604565\pi$
$194$	−129.624	+	74.8382i	−0.668163	+	0.385764i
$195$	−110.472	−	73.3641i	−0.566522	−	0.376226i
$196$		0			0
$197$	−115.102			−0.584274			−0.292137	−	0.956376i	$-0.594366\pi$
$197$	−115.102			−0.584274			−0.292137	+	0.956376i	$0.594366\pi$
$198$	−167.365	−	21.0723i	−0.845278	−	0.106426i
$199$	104.660	−	60.4253i	0.525928	−	0.303645i	−0.213429	−	0.976959i	$-0.568463\pi$
$199$	104.660	−	60.4253i	0.525928	−	0.303645i	0.739357	+	0.673314i	$0.235130\pi$
$200$	−74.6708	+	129.334i	−0.373354	+	0.646668i
$201$	77.0422	+	51.1636i	0.383295	+	0.254545i
$202$	−257.691	−	148.778i	−1.27570	−	0.736524i
$203$		0			0
$204$	29.0096	+	1.81906i	0.142204	+	0.00891694i
$205$	−514.930			−2.51185
$206$	−199.135	+	114.971i	−0.966677	+	0.558111i
$207$	−27.3442	+	36.0558i	−0.132097	+	0.174183i
$208$	−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	$0.0745853\pi$
$212$	−31.6744	−	54.8617i	−0.149408	−	0.258782i
$213$	203.079	+	134.864i	0.953421	+	0.633165i
$214$	−67.6229	+	117.126i	−0.315995	+	0.547319i
$215$	55.0101	+	31.7601i	0.255861	+	0.147721i
$216$	12.6116	−	66.3378i	0.0583872	−	0.307119i
$217$		0			0
$218$	58.2411	+	100.877i	0.267161	+	0.462737i
$219$	213.482	+	13.3865i	0.974805	+	0.0611256i
$220$		−	198.602i		−	0.902739i
$221$	15.2135			0.0688395
$222$	252.700	−	125.507i	1.13829	−	0.565346i
$223$	−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	$0.510077\pi$
$224$		0			0
$225$	533.214	+	67.1348i	2.36984	+	0.298377i
$226$	−141.605	+	245.267i	−0.626571	+	1.08525i
$227$	130.976	+	75.6193i	0.576989	+	0.333125i	0.759936	−	0.649998i	$-0.225230\pi$
$227$	130.976	+	75.6193i	0.576989	+	0.333125i	−0.182947	+	0.983123i	$0.558564\pi$
$228$	−8.05302	−	16.2142i	−0.0353203	−	0.0711150i
$229$	358.522	−	206.993i	1.56560	−	0.903899i	0.568927	−	0.822388i	$-0.307359\pi$
$229$	358.522	−	206.993i	1.56560	−	0.903899i	0.996672	−	0.0815115i	$-0.0259747\pi$
$230$	−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	−0.246731	−	0.969084i	$-0.579356\pi$
$233$	166.801	−	288.909i	0.715886	−	1.23995i	0.962617	−	0.270867i	$-0.0873103\pi$
$234$	−14.3458	+	113.940i	−0.0613067	+	0.486925i
$235$	−236.288	−	409.264i	−1.00548	−	1.74155i
$236$		−	150.947i		−	0.639608i
$237$	−72.5637	−	48.1894i	−0.306176	−	0.203331i
$238$		0			0
$239$	−104.819	+	181.552i	−0.438573	+	0.759631i	−0.997580	−	0.0695323i	$-0.977849\pi$
$239$	−104.819	+	181.552i	−0.438573	+	0.759631i	0.559007	+	0.829163i	$0.311183\pi$
$240$	520.272	+	32.6239i	2.16780	+	0.135933i
$241$	−197.233	−	113.873i	−0.818394	−	0.472500i	0.0314682	−	0.999505i	$-0.489982\pi$
$241$	−197.233	−	113.873i	−0.818394	−	0.472500i	−0.849862	+	0.527005i	$0.823315\pi$
$242$	94.6247	+	163.895i	0.391011	+	0.677251i
$243$	−237.637	+	50.7702i	−0.977930	+	0.208931i
$244$		−	7.04783i		−	0.0288846i
$245$		0			0
$246$	198.354	+	399.372i	0.806315	+	1.62346i
$247$	−4.73783	−	8.20615i	−0.0191815	−	0.0332233i
$248$		−	38.1962i		−	0.154017i
$249$	193.362	+	12.1248i	0.776553	+	0.0486941i
$250$			848.866i			3.39546i
$251$		−	422.578i		−	1.68358i	−0.539808	−	0.841788i	$-0.681503\pi$
$251$		−	422.578i		−	1.68358i	0.539808	−	0.841788i	$-0.318497\pi$
$252$		0			0
$253$	−35.4707			−0.140200
$254$	−488.992			−1.92516
$255$	−78.3361	+	38.9067i	−0.307200	+	0.152575i
$256$	331.406			1.29456
$257$	−75.4797	+	43.5782i	−0.293695	+	0.169565i	−0.639607	−	0.768702i	$-0.720903\pi$
$257$	−75.4797	+	43.5782i	−0.293695	+	0.169565i	0.345912	+	0.938267i	$0.387570\pi$
$258$	3.44247	−	54.8991i	0.0133429	−	0.212787i
$259$		0			0
$260$	−135.206			−0.520025
$261$	−249.541	+	329.043i	−0.956097	+	1.26070i
$262$	16.7367	−	9.66292i	0.0638804	−	0.0368814i
$263$	22.0938	−	38.2676i	0.0840069	−	0.145504i	−0.820961	−	0.570985i	$-0.806562\pi$
$263$	22.0938	−	38.2676i	0.0840069	−	0.145504i	0.904968	+	0.425481i	$0.139895\pi$
$264$	47.4054	−	23.5446i	0.179566	−	0.0891840i
$265$	165.088	+	95.3134i	0.622972	+	0.359673i
$266$		0			0
$267$	−137.292	−	276.428i	−0.514201	−	1.03531i
$268$	94.2920			0.351836
$269$	169.996	−	98.1474i	0.631957	−	0.364860i	−0.149553	−	0.988754i	$-0.547783\pi$
$269$	169.996	−	98.1474i	0.631957	−	0.364860i	0.781509	+	0.623893i	$0.214450\pi$
$270$	−217.521	−	623.379i	−0.805632	−	2.30881i
$271$	146.761	+	84.7324i	0.541553	+	0.312666i	0.745708	−	0.666273i	$-0.232111\pi$
$271$	146.761	+	84.7324i	0.541553	+	0.312666i	−0.204155	+	0.978938i	$0.565445\pi$
$272$	−51.7912	+	29.9016i	−0.190409	+	0.109932i
$273$		0			0
$274$	62.7965	−	108.767i	0.229184	−	0.396959i
$275$	210.630	+	364.822i	0.765928	+	1.32663i
$276$	−2.88735	+	46.0462i	−0.0104614	+	0.166834i
$277$	−185.050	+	320.517i	−0.668052	+	1.15710i	0.310396	+	0.950607i	$0.399538\pi$
$277$	−185.050	+	320.517i	−0.668052	+	1.15710i	−0.978448	+	0.206493i	$0.933795\pi$
$278$	582.779	+	336.468i	2.09633	+	1.21032i
$279$	−126.691	+	53.3181i	−0.454089	+	0.191104i
$280$		0			0
$281$	61.5023	+	106.525i	0.218869	+	0.379093i	0.954463	−	0.298331i	$-0.0964298\pi$
$281$	61.5023	+	106.525i	0.218869	+	0.379093i	−0.735593	+	0.677424i	$0.763096\pi$
$282$	−226.399	+	340.912i	−0.802833	+	1.20891i
$283$			150.448i			0.531617i	0.964026	+	0.265809i	$0.0856389\pi$
$283$			150.448i			0.531617i	−0.964026	+	0.265809i	$0.914361\pi$
$284$	248.548			0.875169
$285$	45.3818	+	30.1380i	0.159234	+	0.105747i
$286$	−77.9574	+	45.0087i	−0.272578	+	0.157373i
$287$		0			0
$288$	−140.184	−	333.096i	−0.486751	−	1.15658i
$289$	−139.483	+	241.592i	−0.482640	+	0.835957i
$290$	−971.717	−	561.021i	−3.35075	−	1.93456i
$291$	−168.679	−	10.5771i	−0.579653	−	0.0363474i
$292$	188.866	−	109.042i	0.646803	−	0.373432i
$293$	373.737	+	215.777i	1.27555	+	0.736440i	0.976027	−	0.217648i	$-0.0698385\pi$
$293$	373.737	+	215.777i	1.27555	+	0.736440i	0.299525	+	0.954088i	$0.403172\pi$
$294$		0			0
$295$	227.113	+	393.370i	0.769873	+	1.33346i
$296$	−44.2666	+	76.6719i	−0.149549	+	0.259027i
$297$	−144.267	−	124.371i	−0.485748	−	0.418757i
$298$	341.193	+	590.964i	1.14494	+	1.98310i
$299$			24.1481i			0.0807627i
$300$	490.738	−	243.732i	1.63579	−	0.812441i
$301$		0			0
$302$	157.265	−	272.392i	0.520746	−	0.901959i
$303$	−149.456	−	300.921i	−0.493256	−	0.993137i
$304$	32.2578	+	18.6241i	0.106111	+	0.0612633i
$305$	10.6040	+	18.3667i	0.0347673	+	0.0602187i
$306$	60.3509	+	45.7692i	0.197225	+	0.149572i
$307$			157.167i			0.511946i	0.966684	+	0.255973i	$0.0823958\pi$
$307$			157.167i			0.511946i	−0.966684	+	0.255973i	$0.917604\pi$
$308$		0			0
$309$	−259.135	−	16.2492i	−0.838624	−	0.0525863i
$310$	−186.733	−	323.431i	−0.602364	−	1.04333i
$311$			331.813i			1.06692i	0.845825	+	0.533461i	$0.179109\pi$
$311$			331.813i			1.06692i	−0.845825	+	0.533461i	$0.820891\pi$
$312$	−16.0289	−	32.2731i	−0.0513747	−	0.103439i
$313$		−	408.491i		−	1.30508i	−0.757753	−	0.652541i	$-0.773703\pi$
$313$		−	408.491i		−	1.30508i	0.757753	−	0.652541i	$-0.226297\pi$
$314$		−	135.562i		−	0.431727i
$315$		0			0
$316$	−88.8108			−0.281047
$317$	38.7454			0.122225			0.0611126	−	0.998131i	$-0.480535\pi$
$317$	38.7454			0.122225			0.0611126	+	0.998131i	$0.480535\pi$
$318$	10.3310	−	164.755i	0.0324874	−	0.518096i
$319$	−323.704			−1.01474
$320$	248.428	−	143.430i	0.776337	−	0.448218i
$321$	−136.775	+	67.9313i	−0.426091	+	0.211624i
$322$		0			0
$323$	−6.24972			−0.0193490
$324$	−173.195	+	177.156i	−0.534553	+	0.546778i
$325$	248.367	−	143.395i	0.764206	−	0.441215i
$326$	380.341	−	658.770i	1.16669	−	2.02077i
$327$	−8.23139	+	131.271i	−0.0251724	+	0.401439i
$328$	−121.174	−	69.9598i	−0.369433	−	0.213292i
$329$		0			0
$330$	286.307	−	431.122i	0.867597	−	1.30643i
$331$	285.046			0.861167			0.430583	−	0.902551i	$-0.358308\pi$
$331$	285.046			0.861167			0.430583	+	0.902551i	$0.358308\pi$
$332$	171.066	−	98.7649i	0.515259	−	0.297485i
$333$	316.101	+	39.7990i	0.949253	+	0.119517i
$334$	−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	$-0.178907\pi$
$338$	−193.859	−	335.774i	−0.573548	−	0.993415i
$339$	−286.413	+	142.251i	−0.844875	+	0.419619i
$340$	−44.5881	+	77.2288i	−0.131141	+	0.227144i
$341$	−93.3082	−	53.8715i	−0.273631	−	0.157981i
$342$	5.89324	−	46.8067i	0.0172317	−	0.136862i
$343$		0			0
$344$	8.63003	+	14.9476i	0.0250873	+	0.0434525i
$345$	−61.7557	−	124.341i	−0.179002	−	0.360409i
$346$			395.562i			1.14324i
$347$	−290.571			−0.837379			−0.418690	−	0.908129i	$-0.637510\pi$
$347$	−290.571			−0.837379			−0.418690	+	0.908129i	$0.637510\pi$
$348$	−26.3498	+	420.215i	−0.0757177	+	1.20751i
$349$	−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	$0.488701\pi$
$350$		0			0
$351$	−84.6703	+	98.2155i	−0.241226	+	0.279816i
$352$	141.639	−	245.326i	0.402384	−	0.696950i
$353$	72.8629	+	42.0674i	0.206411	+	0.119171i	0.599642	−	0.800268i	$-0.295310\pi$
$353$	72.8629	+	42.0674i	0.206411	+	0.119171i	−0.393232	+	0.919439i	$0.628643\pi$
$354$	217.607	−	327.673i	0.614709	−	0.925630i
$355$	−647.719	+	373.961i	−1.82456	+	1.05341i
$356$	−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	$-0.928918\pi$
$359$	−106.191	+	183.928i	−0.295796	+	0.512334i	0.679374	+	0.733792i	$0.262252\pi$
$360$	165.069	+	125.186i	0.458525	+	0.347738i
$361$	−178.554	−	309.264i	−0.494609	−	0.856687i
$362$		−	214.347i		−	0.592119i
$363$	−13.3736	+	213.276i	−0.0368418	+	0.587538i
$364$		0			0
$365$	−328.125	+	568.329i	−0.898973	+	1.55707i
$366$	10.1602	−	15.2993i	0.0277601	−	0.0418013i
$367$	363.389	+	209.803i	0.990162	+	0.571670i	0.905323	−	0.424724i	$-0.139629\pi$
$367$	363.389	+	209.803i	0.990162	+	0.571670i	0.0848392	+	0.996395i	$0.472962\pi$
$368$	−47.4622	−	82.2069i	−0.128973	−	0.223388i
$369$	−62.8992	+	499.573i	−0.170458	+	1.35386i
$370$			865.639i			2.33957i
$371$		0			0
$372$	−77.5286	+	116.743i	−0.208410	+	0.313824i
$373$	110.530	+	191.443i	0.296326	+	0.513252i	0.975292	−	0.220918i	$-0.0709052\pi$
$373$	110.530	+	191.443i	0.296326	+	0.513252i	−0.678966	+	0.734169i	$0.737572\pi$
$374$			59.3715i			0.158747i
$375$	−530.268	+	798.478i	−1.41405	+	2.12928i
$376$		−	128.411i		−	0.341519i
$377$			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	$0.362631\pi$
$380$	55.5428			0.146165
$381$	−459.966	−	305.462i	−1.20726	−	0.801739i
$382$	73.2274			0.191695
$383$	−240.396	+	138.793i	−0.627666	+	0.362383i	−0.779847	−	0.625970i	$-0.784703\pi$
$383$	−240.396	+	138.793i	−0.627666	+	0.362383i	0.152182	+	0.988353i	$0.451370\pi$
$384$	194.467	+	129.145i	0.506425	+	0.336316i
$385$		0			0
$386$	−330.862			−0.857156
$387$	37.5324	−	49.4900i	0.0969830	−	0.127881i
$388$	−149.229	+	86.1576i	−0.384612	+	0.222056i
$389$	36.2173	−	62.7303i	0.0931037	−	0.161260i	−0.815712	−	0.578458i	$-0.803655\pi$
$389$	36.2173	−	62.7303i	0.0931037	−	0.161260i	0.908816	+	0.417198i	$0.136988\pi$
$390$	−293.503	−	194.915i	−0.752572	−	0.499781i
$391$	13.7932	+	7.96349i	0.0352767	+	0.0203670i
$392$		0			0
$393$	21.7794	+	1.36569i	0.0554184	+	0.00347503i
$394$	−305.805			−0.776154
$395$	231.442	−	133.623i	0.585929	−	0.338286i
$396$	−192.679	−	24.2595i	−0.486564	−	0.0612613i
$397$	590.904	+	341.158i	1.48842	+	0.859341i	0.999913	−	0.0132172i	$-0.00420730\pi$
$397$	590.904	+	341.158i	1.48842	+	0.859341i	0.488510	+	0.872558i	$0.337541\pi$
$398$	278.061	−	160.539i	0.698647	−	0.403364i
$399$		0			0
$400$	−563.675	+	976.313i	−1.40919	+	2.44078i
$401$	−224.827	−	389.411i	−0.560665	−	0.971100i	−0.997439	−	0.0715286i	$-0.977212\pi$
$401$	−224.827	−	389.411i	−0.560665	−	0.971100i	0.436774	−	0.899571i	$-0.356121\pi$
$402$	204.687	+	135.932i	0.509171	+	0.338140i
$403$	−36.6752	+	63.5232i	−0.0910054	+	0.157626i
$404$	−296.667	−	171.281i	−0.734324	−	0.423962i
$405$	184.802	−	722.257i	0.456302	−	1.78335i
$406$		0			0
$407$	124.866	+	216.275i	0.306797	+	0.531388i
$408$	−23.7201	−	1.48738i	−0.0581375	−	0.00364554i
$409$		−	148.908i		−	0.364079i	−0.983291	−	0.182040i	$-0.941730\pi$
$409$		−	148.908i		−	0.364079i	0.983291	−	0.182040i	$-0.0582699\pi$
$410$	−1368.07			−3.33676
$411$	127.013	−	63.0829i	0.309035	−	0.153486i
$412$	−229.255	+	132.360i	−0.556444	+	0.321263i
$413$		0			0
$414$	−72.6483	+	95.7935i	−0.175479	+	0.231385i
$415$	−297.199	+	514.765i	−0.716143	+	1.24040i
$416$	−167.016	−	96.4265i	−0.401480	−	0.231794i
$417$	338.002	+	680.545i	0.810557	+	1.63200i
$418$	32.0249	−	18.4896i	0.0766146	−	0.0442335i
$419$	−399.171	−	230.461i	−0.952675	−	0.550027i	−0.0587641	−	0.998272i	$-0.518716\pi$
$419$	−399.171	−	230.461i	−0.952675	−	0.550027i	−0.893911	+	0.448245i	$0.852049\pi$
$420$		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
$423$	−425.920	+	179.249i	−1.00690	+	0.423757i
$424$	25.8991	+	44.8585i	0.0610827	+	0.105798i
$425$		−	189.154i		−	0.445067i
$426$	539.542	+	358.309i	1.26653	+	0.841101i
$427$		0			0
$428$	−77.8510	+	134.842i	−0.181895	+	0.315051i
$429$	−101.446	−	6.36121i	−0.236471	−	0.0148280i
$430$	146.152	+	84.3807i	0.339888	+	0.196234i
$431$	−104.431	−	180.879i	−0.242298	−	0.419673i	0.719070	−	0.694937i	$-0.244568\pi$
$431$	−104.431	−	180.879i	−0.242298	−	0.419673i	−0.961369	+	0.275264i	$0.911235\pi$
$432$	95.2025	−	500.770i	0.220376	−	1.15919i
$433$		−	492.194i		−	1.13671i	−0.822784	−	0.568354i	$-0.807581\pi$
$433$		−	492.194i		−	1.13671i	0.822784	−	0.568354i	$-0.192419\pi$
$434$		0			0
$435$	−563.580	−	1134.73i	−1.29559	−	2.60857i
$436$	67.0502	+	116.134i	0.153785	+	0.266363i
$437$		−	9.92003i		−	0.0227003i
$438$	567.183	+	35.5654i	1.29494	+	0.0811996i
$439$			70.4474i			0.160472i	0.996776	+	0.0802362i	$0.0255675\pi$
$439$			70.4474i			0.160472i	−0.996776	+	0.0802362i	$0.974433\pi$
$440$			162.390i			0.369069i
$441$		0			0
$442$	40.4195			0.0914468
$443$	716.071			1.61641			0.808206	−	0.588900i	$-0.200439\pi$
$443$	716.071			1.61641			0.808206	+	0.588900i	$0.200439\pi$
$444$	290.921	−	144.490i	0.655227	−	0.325428i
$445$	946.921			2.12791
$446$	−540.967	+	312.328i	−1.21293	+	0.700286i
$447$	−48.2218	+	769.021i	−0.107879	+	1.72041i
$448$		0			0
$449$	−130.350			−0.290313			−0.145156	−	0.989409i	$-0.546369\pi$
$449$	−130.350			−0.290313			−0.145156	+	0.989409i	$0.546369\pi$
$450$	1416.65	+	178.365i	3.14811	+	0.396366i
$451$	−341.805	+	197.341i	−0.757883	+	0.437564i
$452$	−163.023	+	282.364i	−0.360671	+	0.624700i
$453$	318.088	−	157.983i	0.702180	−	0.348748i
$454$	347.980	+	200.906i	0.766476	+	0.442525i
$455$		0			0
$456$	6.58467	+	13.2578i	0.0144401	+	0.0290741i
$457$	−211.530			−0.462866			−0.231433	−	0.972851i	$-0.574341\pi$
$457$	−211.530			−0.462866			−0.231433	+	0.972851i	$0.574341\pi$
$458$	952.527	−	549.942i	2.07975	−	1.20075i
$459$	28.1775	+	80.7523i	0.0613890	+	0.175931i
$460$	−122.583	−	70.7736i	−0.266486	−	0.153856i
$461$	457.027	−	263.865i	0.991381	−	0.572374i	0.0856943	−	0.996321i	$-0.472689\pi$
$461$	457.027	−	263.865i	0.991381	−	0.572374i	0.905687	+	0.423947i	$0.139356\pi$
$462$		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	$0.875289\pi$
$464$	−433.137	−	750.216i	−0.933485	−	1.61684i
$465$	26.3915	−	420.880i	0.0567559	−	0.905119i
$466$	443.160	−	767.576i	0.950988	−	1.64716i
$467$	−280.938	−	162.200i	−0.601581	−	0.347323i	0.168082	−	0.985773i	$-0.446243\pi$
$467$	−280.938	−	162.200i	−0.601581	−	0.347323i	−0.769663	+	0.638450i	$0.779576\pi$
$468$	−16.5156	+	131.174i	−0.0352897	+	0.280286i
$469$		0			0
$470$	−627.774	−	1087.34i	−1.33569	−	2.31348i
$471$	84.6828	−	127.516i	0.179794	−	0.270734i
$472$			123.424i			0.261492i
$473$	48.6868			0.102932
$474$	−192.788	−	128.030i	−0.406727	−	0.270106i
$475$	−102.029	+	58.9066i	−0.214798	+	0.124014i
$476$		0			0
$477$	112.636	−	148.521i	0.236135	−	0.311366i
$478$	−278.485	+	482.349i	−0.582604	+	1.00910i
$479$	364.187	+	210.264i	0.760307	+	0.438964i	0.829406	−	0.558646i	$-0.188679\pi$
$479$	364.187	+	210.264i	0.760307	+	0.438964i	−0.0690988	+	0.997610i	$0.522012\pi$
$480$	1106.58	+	69.3886i	2.30538	+	0.144560i
$481$	147.238	−	85.0077i	0.306107	−	0.176731i
$482$	−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
$486$	−631.358	+	134.887i	−1.29909	+	0.277545i
$487$	19.3349	+	33.4890i	0.0397020	+	0.0687658i	0.885194	−	0.465223i	$-0.154026\pi$
$487$	19.3349	+	33.4890i	0.0397020	+	0.0687658i	−0.845492	+	0.533989i	$0.820692\pi$
$488$			5.76277i			0.0118089i
$489$	769.284	−	382.076i	1.57318	−	0.781341i
$490$		0			0
$491$	435.683	−	754.625i	0.887338	−	1.53691i	0.0443266	−	0.999017i	$-0.485886\pi$
$491$	435.683	−	754.625i	0.887338	−	1.53691i	0.843011	−	0.537897i	$-0.180781\pi$
$492$	228.355	+	459.777i	0.464136	+	0.934507i
$493$	125.876	+	72.6744i	0.255326	+	0.147413i
$494$	−12.5875	−	21.8022i	−0.0254808	−	0.0441341i
$495$	538.624	−	226.681i	1.08813	−	0.457942i
$496$		−	288.335i		−	0.581320i
$497$		0			0
$498$	513.726	+	32.2134i	1.03158	+	0.0646856i
$499$	184.126	+	318.916i	0.368991	+	0.639111i	0.989408	−	0.145161i	$-0.0463700\pi$
$499$	184.126	+	318.916i	0.368991	+	0.639111i	−0.620417	+	0.784272i	$0.713037\pi$
$500$			977.258i			1.95452i
$501$	−249.830	−	503.016i	−0.498663	−	1.00402i
$502$		−	1122.71i		−	2.23648i
$503$		−	603.853i		−	1.20050i	−0.799811	−	0.600251i	$-0.795067\pi$
$503$		−	603.853i		−	1.20050i	0.799811	−	0.600251i	$-0.204933\pi$
$504$		0			0
$505$	1030.82			2.04123
$506$	−94.2390			−0.186243
$507$	27.3987	−	436.943i	0.0540408	−	0.861820i
$508$	−562.953			−1.10817
$509$	197.693	−	114.138i	0.388394	−	0.224240i	−0.293070	−	0.956091i	$-0.594677\pi$
$509$	197.693	−	114.138i	0.388394	−	0.224240i	0.681464	+	0.731851i	$0.261344\pi$
$510$	−208.124	+	103.368i	−0.408087	+	0.202682i
$511$		0			0
$512$	569.227			1.11177
$513$	34.7826	−	40.3470i	0.0678023	−	0.0786491i
$514$	−200.535	+	115.779i	−0.390147	+	0.225251i
$515$	398.294	−	689.865i	0.773386	−	1.33954i
$516$	3.96315	−	63.2027i	0.00768053	−	0.122486i
$517$	−313.691	−	181.110i	−0.606753	−	0.350309i
$518$		0			0
$519$	−247.099	+	372.082i	−0.476106	+	0.716922i
$520$	110.554			0.212603
$521$	−409.376	+	236.354i	−0.785751	+	0.453654i	−0.838465	−	0.544956i	$-0.816546\pi$
$521$	−409.376	+	236.354i	−0.785751	+	0.453654i	0.0527134	+	0.998610i	$0.483213\pi$
$522$	−662.985	+	874.207i	−1.27009	+	1.67473i
$523$	−242.231	−	139.852i	−0.463156	−	0.267403i	0.250214	−	0.968190i	$-0.419499\pi$
$523$	−242.231	−	139.852i	−0.463156	−	0.267403i	−0.713370	+	0.700787i	$0.752832\pi$
$524$	19.2681	−	11.1245i	0.0367712	−	0.0212299i
$525$		0			0
$526$	58.6991	−	101.670i	0.111595	−	0.193289i
$527$	24.1893	+	41.8971i	0.0459000	+	0.0795011i
$528$	357.854	−	177.733i	0.677753	−	0.336616i
$529$	251.860	−	436.234i	0.476105	−	0.824639i
$530$	438.607	+	253.230i	0.827561	+	0.477792i
$531$	409.380	−	172.289i	0.770961	−	0.324460i
$532$		0			0
$533$	134.348	+	232.697i	0.252060	+	0.436580i
$534$	−364.759	−	734.417i	−0.683068	−	1.37531i
$535$		−	468.532i		−	0.875761i
$536$	−77.0993			−0.143842
$537$	−36.8628	+	587.873i	−0.0686459	+	1.09474i
$538$	451.649	−	260.759i	0.839496	−	0.484683i
$539$		0			0
$540$	−250.421	−	717.666i	−0.463743	−	1.32901i
$541$	508.919	−	881.473i	0.940700	−	1.62934i	0.176561	−	0.984290i	$-0.443503\pi$
$541$	508.919	−	881.473i	0.940700	−	1.62934i	0.764139	−	0.645051i	$-0.223164\pi$
$542$	389.916	+	225.118i	0.719402	+	0.415347i
$543$	133.898	−	201.624i	0.246589	−	0.371315i
$544$	−110.156	+	63.5986i	−0.202493	+	0.116909i
$545$	−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
$549$	19.1142	−	8.04426i	0.0348165	−	0.0146526i
$550$	559.605	+	969.264i	1.01746	+	1.76230i
$551$		−	90.5297i		−	0.164301i
$552$	2.36088	−	37.6504i	0.00427696	−	0.0682072i
$553$		0			0
$554$	−491.645	+	851.554i	−0.887445	+	1.53710i
$555$	−540.746	+	814.256i	−0.974317	+	1.46713i
$556$	670.925	+	387.359i	1.20670	+	0.696689i
$557$	249.913	+	432.862i	0.448677	+	0.777131i	0.998300	−	0.0582814i	$-0.0185621\pi$
$557$	249.913	+	432.862i	0.448677	+	0.777131i	−0.549623	+	0.835413i	$0.685229\pi$
$558$	−336.594	+	141.656i	−0.603216	+	0.253864i
$559$		−	33.1455i		−	0.0592942i
$560$		0			0
$561$	−37.0881	+	55.8473i	−0.0661107	+	0.0995496i
$562$	163.400	+	283.018i	0.290748	+	0.503590i
$563$		−	323.183i		−	0.574038i	−0.957925	−	0.287019i	$-0.907336\pi$
$563$		−	323.183i		−	0.574038i	0.957925	−	0.287019i	$-0.0926643\pi$
$564$	−260.642	+	392.475i	−0.462131	+	0.695878i
$565$		−	981.126i		−	1.73651i
$566$			399.712i			0.706204i
$567$		0			0
$568$	−203.229			−0.357798
$569$	176.881			0.310863			0.155431	−	0.987847i	$-0.450323\pi$
$569$	176.881			0.310863			0.155431	+	0.987847i	$0.450323\pi$
$570$	120.571	+	80.0710i	0.211528	+	0.140475i
$571$	−557.593			−0.976519			−0.488260	−	0.872698i	$-0.662368\pi$
$571$	−557.593			−0.976519			−0.488260	+	0.872698i	$0.662368\pi$
$572$	−89.7486	+	51.8164i	−0.156903	+	0.0905881i
$573$	68.8807	+	45.7436i	0.120211	+	0.0798317i
$574$		0			0
$575$	300.239			0.522155
$576$	−108.807	−	258.539i	−0.188900	−	0.448852i
$577$	640.283	−	369.668i	1.10968	−	0.640672i	0.170931	−	0.985283i	$-0.445323\pi$
$577$	640.283	−	369.668i	1.10968	−	0.640672i	0.938745	+	0.344611i	$0.111989\pi$
$578$	−370.580	+	641.864i	−0.641142	+	1.11049i
$579$	−311.223	−	206.683i	−0.537518	−	0.356965i
$580$	−1118.69	−	645.876i	−1.92878	−	1.11358i
$581$		0			0
$582$	−448.149	−	28.1014i	−0.770016	−	0.0482842i
$583$	146.111			0.250620
$584$	−154.430	+	89.1599i	−0.264434	+	0.152671i
$585$	−154.322	−	366.690i	−0.263798	−	0.626820i
$586$	992.949	+	573.280i	1.69445	+	0.978293i
$587$	−47.8551	+	27.6292i	−0.0815249	+	0.0470684i	−0.540208	−	0.841531i	$-0.681655\pi$
$587$	−47.8551	+	27.6292i	−0.0815249	+	0.0470684i	0.458683	+	0.888600i	$0.348321\pi$
$588$		0			0
$589$	15.0662	−	26.0954i	0.0255792	−	0.0443045i
$590$	603.396	+	1045.11i	1.02270	+	1.77138i
$591$	−287.652	−	191.029i	−0.486722	−	0.323231i
$592$	−334.159	+	578.780i	−0.564458	+	0.977670i
$593$	663.928	+	383.319i	1.11961	+	0.646406i	0.941301	−	0.337569i	$-0.109605\pi$
$593$	663.928	+	383.319i	1.11961	+	0.646406i	0.178307	+	0.983975i	$0.442938\pi$
$594$	−383.291	−	330.430i	−0.645271	−	0.556279i
$595$		0			0
$596$	392.799	+	680.348i	0.659059	+	1.14152i
$597$	361.841	+	22.6894i	0.606099	+	0.0380057i
$598$			64.1569i			0.107286i
$599$	−906.266			−1.51296			−0.756482	−	0.654014i	$-0.773084\pi$
$599$	−906.266			−1.51296			−0.756482	+	0.654014i	$0.773084\pi$
$600$	−401.260	+	199.291i	−0.668766	+	0.332152i
$601$	−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	$0.392649\pi$
$602$		0			0
$603$	107.623	+	255.727i	0.178479	+	0.424091i
$604$	181.052	−	313.591i	0.299755	−	0.519191i
$605$	−567.781	−	327.808i	−0.938481	−	0.541832i
$606$	−397.078	−	799.490i	−0.655244	−	1.31929i
$607$	−518.849	+	299.558i	−0.854776	+	0.493505i	−0.862259	−	0.506467i	$-0.830951\pi$
$607$	−518.849	+	299.558i	−0.854776	+	0.493505i	0.00748365	+	0.999972i	$0.497618\pi$
$608$	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
$612$	69.4791	+	52.6918i	0.113528	+	0.0860978i
$613$	−270.643	−	468.768i	−0.441506	−	0.764711i	0.556295	−	0.830985i	$-0.312222\pi$
$613$	−270.643	−	468.768i	−0.441506	−	0.764711i	−0.997801	+	0.0662736i	$0.978889\pi$
$614$			417.565i			0.680073i
$615$	−1286.87	−	854.606i	−2.09247	−	1.38960i
$616$		0			0
$617$	331.635	−	574.409i	0.537497	−	0.930972i	−0.461541	−	0.887119i	$-0.652703\pi$
$617$	331.635	−	574.409i	0.537497	−	0.930972i	0.999038	−	0.0438529i	$-0.0139633\pi$
$618$	−688.473	−	43.1710i	−1.11403	−	0.0698560i
$619$	847.625	+	489.377i	1.36935	+	0.790592i	0.990844	−	0.135008i	$-0.0431061\pi$
$619$	847.625	+	489.377i	1.36935	+	0.790592i	0.378502	+	0.925601i	$0.376439\pi$
$620$	−214.977	−	372.350i	−0.346736	−	0.600565i
$621$	−128.176	+	44.7255i	−0.206403	+	0.0720218i
$622$			881.565i			1.41731i
$623$		0			0
$624$	−120.999	−	243.623i	−0.193908	−	0.390421i
$625$	−723.942	−	1253.90i	−1.15831	−	2.00625i
$626$		−	1085.28i		−	1.73368i
$627$	41.6740	+	2.61319i	0.0664657	+	0.00416776i
$628$		−	156.066i		−	0.248513i
$629$		−	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	$0.434850\pi$
$632$	72.6175			0.114901
$633$	323.448	−	160.645i	0.510977	−	0.253784i
$634$	102.939			0.162365
$635$	1467.06	−	847.007i	2.31033	−	1.33387i
$636$	11.8936	−	189.674i	0.0187006	−	0.298229i
$637$		0			0
$638$	−860.020			−1.34799
$639$	283.688	+	674.081i	0.443956	+	1.05490i
$640$	−620.253	+	358.103i	−0.969145	+	0.559536i
$641$	168.080	−	291.123i	0.262215	−	0.454170i	−0.704615	−	0.709590i	$-0.748880\pi$
$641$	168.080	−	291.123i	0.262215	−	0.454170i	0.966830	+	0.255419i	$0.0822136\pi$
$642$	−363.386	+	180.481i	−0.566022	+	0.281123i
$643$	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	$0.429704\pi$
$644$		0			0
$645$	84.7656	+	170.670i	0.131419	+	0.264604i
$646$	−16.6043			−0.0257033
$647$	707.666	−	408.571i	1.09376	−	0.631485i	0.159189	−	0.987248i	$-0.449112\pi$
$647$	707.666	−	408.571i	1.09376	−	0.631485i	0.934576	+	0.355763i	$0.115779\pi$
$648$	141.616	−	144.854i	0.218543	−	0.223541i
$649$	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
$653$	180.418	+	312.493i	0.276291	+	0.478550i	0.970460	−	0.241262i	$-0.0775613\pi$
$653$	180.418	+	312.493i	0.276291	+	0.478550i	−0.694169	+	0.719812i	$0.744228\pi$
$654$	−21.8693	+	348.762i	−0.0334392	+	0.533275i
$655$	−33.4753	+	57.9809i	−0.0511073	+	0.0885204i
$656$	−914.716	−	528.112i	−1.39438	−	0.805048i
$657$	511.299	+	387.761i	0.778232	+	0.590199i
$658$		0			0
$659$	515.473	+	892.826i	0.782205	+	1.35482i	0.930654	+	0.365899i	$0.119239\pi$
$659$	515.473	+	892.826i	0.782205	+	1.35482i	−0.148449	+	0.988920i	$0.547428\pi$
$660$	329.611	−	496.329i	0.499411	−	0.752014i
$661$		−	332.364i		−	0.502820i	−0.967881	−	0.251410i	$-0.919106\pi$
$661$		−	332.364i		−	0.502820i	0.967881	−	0.251410i	$-0.0808942\pi$
$662$	757.315			1.14398
$663$	38.0203	+	25.2492i	0.0573458	+	0.0380832i
$664$	−139.875	+	80.7566i	−0.210654	+	0.121621i
$665$		0			0
$666$	839.822	+	105.739i	1.26099	+	0.158767i
$667$	−115.354	+	199.800i	−0.172945	+	0.299550i
$668$	−495.906	−	286.311i	−0.742374	−	0.428610i
$669$	−703.961	−	44.1422i	−1.05226	−	0.0659823i
$670$	−652.848	+	376.922i	−0.974400	+	0.562570i
$671$	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
$675$	1221.14	+	1052.73i	1.80909	+	1.55960i
$676$	−223.181	−	386.561i	−0.330149	−	0.571835i
$677$		−	622.267i		−	0.919154i	−0.888138	−	0.459577i	$-0.848001\pi$
$677$		−	622.267i		−	0.919154i	0.888138	−	0.459577i	$-0.151999\pi$
$678$	−760.946	+	377.934i	−1.12234	+	0.557425i
$679$		0			0
$680$	36.4581	−	63.1473i	0.0536149	−	0.0928637i
$681$	201.823	+	406.356i	0.296362	+	0.596705i
$682$	−247.903	−	143.127i	−0.363494	−	0.209863i
$683$	235.625	+	408.115i	0.344986	+	0.597533i	0.985351	−	0.170538i	$-0.0545505\pi$
$683$	235.625	+	408.115i	0.344986	+	0.597533i	−0.640366	+	0.768070i	$0.721217\pi$
$684$	6.78461	−	53.8863i	0.00991901	−	0.0787812i
$685$			435.092i			0.635171i
$686$		0			0
$687$	1239.52	+	77.7248i	1.80426	+	0.113137i
$688$	65.1463	+	112.837i	0.0946894	+	0.164007i
$689$		−	99.4710i		−	0.144370i
$690$	−164.073	−	330.351i	−0.237788	−	0.478770i
$691$			519.523i			0.751843i	0.926652	+	0.375921i	$0.122674\pi$
$691$			519.523i			0.751843i	−0.926652	+	0.375921i	$0.877326\pi$
$692$			455.392i			0.658081i
$693$		0			0
$694$	−771.992			−1.11238
$695$	−2331.25			−3.35432
$696$	21.5453	−	343.595i	0.0309559	−	0.493671i
$697$	177.220			0.254261
$698$	−753.135	+	434.823i	−1.07899	+	0.622955i
$699$	896.343	−	445.182i	1.28232	−	0.636883i
$700$		0			0
$701$	−985.712			−1.40615			−0.703076	−	0.711115i	$-0.748191\pi$
$701$	−985.712			−1.40615			−0.703076	+	0.711115i	$0.748191\pi$
$702$	−224.953	+	260.940i	−0.320446	+	0.371710i
$703$	−60.4852	+	34.9212i	−0.0860387	+	0.0496745i
$704$	109.936	−	190.414i	0.156159	−	0.270475i
$705$	88.7251	−	1414.95i	0.125851	−	2.00702i
$706$	193.583	+	111.765i	0.274197	+	0.158308i
$707$		0			0
$708$	250.520	−	377.234i	0.353842	−	0.532817i
$709$	590.228			0.832479			0.416240	−	0.909255i	$-0.363348\pi$
$709$	590.228			0.832479			0.416240	+	0.909255i	$0.363348\pi$
$710$	−1720.87	+	993.544i	−2.42376	+	1.39936i
$711$	−101.367	−	240.861i	−0.142570	−	0.338764i
$712$	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
$716$	300.273	+	520.088i	0.419376	+	0.726380i
$717$	−563.267	+	279.755i	−0.785589	+	0.390174i
$718$	−282.129	+	488.662i	−0.392938	+	0.680588i
$719$	−320.943	−	185.297i	−0.446375	−	0.257715i	0.259923	−	0.965629i	$-0.416303\pi$
$719$	−320.943	−	185.297i	−0.446375	−	0.257715i	−0.706298	+	0.707915i	$0.749636\pi$
$720$	1246.07	+	945.002i	1.73066	+	1.31250i
$721$		0			0
$722$	−474.384	−	821.657i	−0.657042	−	1.13803i
$723$	−303.918	−	611.918i	−0.420357	−	0.846360i
$724$		−	246.768i		−	0.340839i
$725$	2739.97			3.77926
$726$	−35.5311	+	566.635i	−0.0489409	+	0.780489i
$727$	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	$0.308416\pi$
$728$		0			0
$729$	−678.142	−	267.515i	−0.930236	−	0.366962i
$730$	−871.768	+	1509.95i	−1.19420	+	2.06842i
$731$	−18.9324	−	10.9306i	−0.0258994	−	0.0149530i
$732$	11.6970	−	17.6133i	0.0159795	−	0.0240619i
$733$	−526.757	+	304.124i	−0.718632	+	0.414903i	−0.814249	−	0.580516i	$-0.802851\pi$
$733$	−526.757	+	304.124i	−0.718632	+	0.414903i	0.0956168	+	0.995418i	$0.469518\pi$
$734$	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
$738$	−167.111	+	1327.27i	−0.226438	+	1.79847i
$739$	605.973	+	1049.58i	0.819990	+	1.42026i	0.905689	+	0.423944i	$0.139355\pi$
$739$	605.973	+	1049.58i	0.819990	+	1.42026i	−0.0856983	+	0.996321i	$0.527312\pi$
$740$			996.568i			1.34671i
$741$	1.77903	−	28.3712i	0.00240085	−	0.0382878i
$742$		0			0
$743$	82.8636	−	143.524i	0.111526	−	0.193168i	−0.804860	−	0.593465i	$-0.797760\pi$
$743$	82.8636	−	143.524i	0.111526	−	0.193168i	0.916386	+	0.400297i	$0.131093\pi$
$744$	63.3924	−	95.4564i	0.0852048	−	0.128302i
$745$	−2047.28	−	1182.00i	−2.74802	−	1.58657i
$746$	293.657	+	508.628i	0.393642	+	0.681807i
$747$	463.109	+	351.215i	0.619958	+	0.470167i
$748$			68.3515i			0.0913791i
$749$		0			0
$750$	−1408.82	+	2121.41i	−1.87843	+	2.82854i
$751$	−676.588	−	1171.89i	−0.900916	−	1.56043i	−0.826307	−	0.563220i	$-0.809562\pi$
$751$	−676.588	−	1171.89i	−0.900916	−	1.56043i	−0.0746094	−	0.997213i	$-0.523771\pi$
$752$		−	969.349i		−	1.28903i
$753$	701.333	−	1056.07i	0.931385	−	1.40248i
$754$			585.493i			0.776515i
$755$			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	$0.473034\pi$
$758$	842.374			1.11131
$759$	−88.6451	−	58.8690i	−0.116792	−	0.0775613i
$760$	−45.4154			−0.0597572
$761$	−697.444	+	402.669i	−0.916483	+	0.529132i	−0.882511	−	0.470291i	$-0.844149\pi$
$761$	−697.444	+	402.669i	−0.916483	+	0.529132i	−0.0339717	+	0.999423i	$0.510816\pi$
$762$	−1222.04	−	811.557i	−1.60373	−	1.06504i
$763$		0			0
$764$	84.3032			0.110344
$765$	−260.342	−	32.7786i	−0.340317	−	0.0428479i
$766$	−638.687	+	368.746i	−0.833795	+	0.481392i
$767$	118.510	−	205.265i	0.154511	−	0.267620i
$768$	828.221	+	550.020i	1.07841	+	0.716172i
$769$	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	$0.543864\pi$
$770$		0			0
$771$	−260.957	−	16.3634i	−0.338465	−	0.0212236i
$772$	−380.906			−0.493401
$773$	−685.032	+	395.504i	−0.886200	+	0.511648i	−0.872698	−	0.488261i	$-0.837631\pi$
$773$	−685.032	+	395.504i	−0.886200	+	0.511648i	−0.0135021	+	0.999909i	$0.504298\pi$
$774$	99.7167	−	131.486i	0.128833	−	0.169878i
$775$	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
$779$	−55.1901	−	95.5921i	−0.0708474	−	0.122711i
$780$	−337.896	−	224.396i	−0.433200	−	0.287687i
$781$	−286.633	+	496.462i	−0.367007	+	0.635675i
$782$	36.6459	+	21.1575i	0.0468618	+	0.0270557i
$783$	−1169.73	+	408.163i	−1.49391	+	0.521281i
$784$		0			0
$785$	234.814	+	406.710i	0.299126	+	0.518102i
$786$	57.8639	+	3.62838i	0.0736182	+	0.00461626i
$787$		−	989.401i		−	1.25718i	−0.777737	−	0.628590i	$-0.783632\pi$
$787$		−	989.401i		−	1.25718i	0.777737	−	0.628590i	$-0.216368\pi$
$788$	−352.058			−0.446774
$789$	118.726	−	58.9668i	0.150476	−	0.0747362i
$790$	614.898	−	355.011i	0.778352	−	0.449382i
$791$		0			0
$792$	157.547	+	19.8361i	0.198923	+	0.0250456i
$793$	5.53329	−	9.58394i	0.00697766	−	0.0120857i
$794$	1569.92	+	906.395i	1.97723	+	1.14155i
$795$	254.385	+	512.187i	0.319981	+	0.644260i
$796$	320.119	−	184.821i	0.402159	−	0.232187i
$797$	−104.384	−	60.2662i	−0.130971	−	0.0756163i	0.433083	−	0.901354i	$-0.357426\pi$
$797$	−104.384	−	60.2662i	−0.130971	−	0.0756163i	−0.564054	+	0.825738i	$0.690759\pi$
$798$		0			0
$799$	81.3216	+	140.853i	0.101779	+	0.176287i
$800$	−1198.90	+	2076.55i	−1.49862	+	2.59568i
$801$	115.667	−	918.680i	0.144404	−	1.14692i
$802$	−597.323	−	1034.59i	−0.744791	−	1.29002i
$803$			503.001i			0.626403i
$804$	235.646	+	156.492i	0.293092	+	0.194642i
$805$		0			0
$806$	−97.4391	+	168.769i	−0.120892	+	0.209391i
$807$	587.730	+	36.8539i	0.728290	+	0.0456677i
$808$	242.574	+	140.050i	0.300216	+	0.173330i
$809$	−94.3098	−	163.349i	−0.116576	−	0.201915i	0.801833	−	0.597548i	$-0.203858\pi$
$809$	−94.3098	−	163.349i	−0.116576	−	0.201915i	−0.918409	+	0.395633i	$0.870525\pi$
$810$	490.985	−	1918.90i	0.606155	−	2.36901i
$811$		−	1191.68i		−	1.46940i	−0.678394	−	0.734699i	$-0.737324\pi$
$811$		−	1191.68i		−	1.46940i	0.678394	−	0.734699i	$-0.262676\pi$
$812$		0			0
$813$	226.145	+	455.327i	0.278161	+	0.560058i
$814$	331.747	+	574.602i	0.407551	+	0.705899i
$815$			2635.23i			3.23341i
$816$	−179.058	−	11.2279i	−0.219434	−	0.0137597i
$817$			13.6162i			0.0166661i
$818$		−	395.622i		−	0.483645i
$819$		0			0
$820$	−1575.00			−1.92073
$821$	−677.226			−0.824879			−0.412440	−	0.910985i	$-0.635323\pi$
$821$	−677.226			−0.824879			−0.412440	+	0.910985i	$0.635323\pi$
$822$	337.450	−	167.600i	0.410524	−	0.203892i
$823$	−1610.79			−1.95722			−0.978608	−	0.205732i	$-0.934043\pi$
$823$	−1610.79			−1.95722			−0.978608	+	0.205732i	$0.934043\pi$
$824$	187.454	−	108.227i	0.227493	−	0.131343i
$825$	−79.0906	+	1261.30i	−0.0958674	+	1.52885i
$826$		0			0
$827$	−626.312			−0.757331			−0.378665	−	0.925534i	$-0.623617\pi$
$827$	−626.312			−0.757331			−0.378665	+	0.925534i	$0.623617\pi$
$828$	−83.6365	+	110.282i	−0.101010	+	0.133191i
$829$	469.693	−	271.178i	0.566578	−	0.327114i	−0.189203	−	0.981938i	$-0.560591\pi$
$829$	469.693	−	271.178i	0.566578	−	0.327114i	0.755782	+	0.654824i	$0.227257\pi$
$830$	−789.604	+	1367.63i	−0.951330	+	1.64775i
$831$	−994.408	+	493.887i	−1.19664	+	0.594329i
$832$	−129.632	−	74.8431i	−0.155808	−	0.0899557i
$833$		0			0
$834$	898.009	+	1808.08i	1.07675	+	2.16796i
$835$	1723.11			2.06361
$836$	36.8687	−	21.2862i	0.0441014	−	0.0254619i
$837$	−405.104	−	77.0153i	−0.483996	−	0.0920135i
$838$	−1060.52	−	612.293i	−1.26554	−	0.730660i
$839$	−1281.98	+	740.153i	−1.52799	+	0.882185i	−0.528543	+	0.848906i	$0.677262\pi$
$839$	−1281.98	+	740.153i	−1.52799	+	0.882185i	−0.999446	+	0.0332790i	$0.989405\pi$
$840$		0			0
$841$	−632.218	+	1095.03i	−0.751746	+	1.30206i
$842$	−169.771	−	294.051i	−0.201628	−	0.349230i
$843$	−23.0938	+	368.291i	−0.0273948	+	0.436881i
$844$	184.103	−	318.876i	0.218132	−	0.377815i
$845$	1163.22	+	671.587i	1.37660	+	0.794778i
$846$	−1131.59	+	476.232i	−1.33758	+	0.562922i
$847$		0			0
$848$	195.507	+	338.627i	0.230550	+	0.399325i
$849$	−249.691	+	375.985i	−0.294100	+	0.442857i
$850$		−	502.546i		−	0.591230i
$851$	177.988			0.209152
$852$	621.149	+	412.504i	0.729048	+	0.484159i
$853$	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	$0.165216\pi$
$854$		0			0
$855$	63.3955	+	150.636i	0.0741468	+	0.176183i
$856$	63.6560	−	110.255i	0.0743645	−	0.128803i
$857$	−383.456	−	221.388i	−0.447440	−	0.258330i	0.259308	−	0.965795i	$-0.416505\pi$
$857$	−383.456	−	221.388i	−0.447440	−	0.258330i	−0.706748	+	0.707465i	$0.749839\pi$
$858$	−269.523	−	16.9006i	−0.314129	−	0.0196976i
$859$	−433.921	+	250.524i	−0.505146	+	0.291646i	−0.730836	−	0.682553i	$-0.760870\pi$
$859$	−433.921	+	250.524i	−0.505146	+	0.291646i	0.225690	+	0.974199i	$0.427536\pi$
$860$	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	$-0.901065\pi$
$863$	−182.251	+	315.667i	−0.211183	+	0.365779i	0.740902	+	0.671613i	$0.234398\pi$
$864$	202.489	−	1065.10i	0.234362	−	1.23276i
$865$	−685.174	−	1186.76i	−0.792108	−	1.37197i
$866$		−	1307.67i		−	1.51001i
$867$	−749.541	+	372.270i	−0.864523	+	0.429378i
$868$		0			0
$869$	102.419	−	177.395i	0.117859	−	0.204137i
$870$	−1497.33	−	3014.77i	−1.72106	−	3.46525i
$871$	128.222	+	74.0291i	0.147213	+	0.0849932i
$872$	−54.8246	−	94.9590i	−0.0628723	−	0.108898i
$873$	−403.993	−	306.382i	−0.462764	−	0.350953i
$874$		−	26.3557i		−	0.0301552i
$875$		0			0
$876$	652.970	+	40.9448i	0.745400	+	0.0467406i
$877$	391.240	+	677.647i	0.446111	+	0.772688i	0.998129	−	0.0611449i	$-0.0194752\pi$
$877$	391.240	+	677.647i	0.446111	+	0.772688i	−0.552017	+	0.833833i	$0.686142\pi$
$878$			187.166i			0.213173i
$879$	575.894	+	1159.52i	0.655170	+	1.31914i
$880$			1225.85i			1.39301i
$881$		−	337.263i		−	0.382818i	−0.981510	−	0.191409i	$-0.938694\pi$
$881$		−	337.263i		−	0.382818i	0.981510	−	0.191409i	$-0.0613058\pi$
$882$		0			0
$883$	556.002			0.629674			0.314837	−	0.949146i	$-0.398050\pi$
$883$	556.002			0.629674			0.314837	+	0.949146i	$0.398050\pi$
$884$	46.5330			0.0526392
$885$	−85.2796	+	1360.00i	−0.0963612	+	1.53673i
$886$	1902.47			2.14725
$887$	626.057	−	361.454i	0.705814	−	0.407502i	−0.103695	−	0.994609i	$-0.533067\pi$
$887$	626.057	−	361.454i	0.705814	−	0.407502i	0.809509	+	0.587107i	$0.199733\pi$
$888$	−237.876	+	118.144i	−0.267878	+	0.133045i
$889$		0			0
$890$	2515.79			2.82673
$891$	−154.127	−	550.250i	−0.172982	−	0.617564i
$892$	−622.790	+	359.568i	−0.698195	+	0.403103i
$893$	50.6507	−	87.7296i	0.0567197	−	0.0982414i
$894$	−128.116	+	2043.15i	−0.143307	+	2.28540i
$895$	−1565.03	−	903.569i	−1.74863	−	1.00957i
$896$		0			0
$897$	−40.0774	+	60.3486i	−0.0446794	+	0.0672783i
$898$	−346.317			−0.385653
$899$	−606.896	+	350.392i	−0.675079	+	0.389757i
$900$	1630.92	+	205.342i	1.81213	+	0.228158i
$901$	−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
$905$	371.282	+	643.079i	0.410256	+	0.710584i
$906$	845.100	−	419.731i	0.932781	−	0.463279i
$907$	−563.871	+	976.653i	−0.621688	+	1.07679i	0.367484	+	0.930030i	$0.380219\pi$
$907$	−563.871	+	976.653i	−0.621688	+	1.07679i	−0.989171	+	0.146765i	$0.953114\pi$
$908$	400.613	+	231.294i	0.441203	+	0.254729i
$909$	125.916	−	1000.08i	0.138521	−	1.10020i
$910$		0			0
$911$	−890.109	−	1541.71i	−0.977068	−	1.69233i	−0.672933	−	0.739703i	$-0.734966\pi$
$911$	−890.109	−	1541.71i	−0.977068	−	1.69233i	−0.304136	−	0.952629i	$-0.598368\pi$
$912$	49.7063	+	100.080i	0.0545025	+	0.109737i
$913$			455.594i			0.499007i
$914$	−561.995			−0.614875
$915$	−3.98176	+	63.4995i	−0.00435165	+	0.0693983i
$916$	1096.60	−	633.121i	1.19716	−	0.691181i
$917$		0			0
$918$	74.8625	+	214.544i	0.0815496	+	0.233708i
$919$	−350.534	+	607.142i	−0.381429	+	0.660655i	−0.991267	−	0.131871i	$-0.957901\pi$
$919$	−350.534	+	607.142i	−0.381429	+	0.660655i	0.609837	+	0.792527i	$0.291235\pi$
$920$	100.232	+	57.8691i	0.108948	+	0.0629012i
$921$	−260.844	+	392.779i	−0.283218	+	0.426470i
$922$	1214.24	−	701.039i	1.31696	−	0.760346i
$923$	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
$927$	−620.638	−	470.683i	−0.669513	−	0.507748i
$928$	−921.252	−	1595.65i	−0.992728	−	1.71946i
$929$			981.172i			1.05616i	0.849195	+	0.528080i	$0.177088\pi$
$929$			981.172i			1.05616i	−0.849195	+	0.528080i	$0.822912\pi$
$930$	70.1173	−	1118.20i	0.0753949	−	1.20237i
$931$		0			0
$932$	510.189	−	883.674i	0.547413	−	0.948148i
$933$	−550.695	+	829.237i	−0.590241	+	0.888785i
$934$	−746.401	−	430.935i	−0.799145	−	0.461386i
$935$	−102.840	−	178.125i	−0.109990	−	0.190508i
$936$	13.5042	−	107.256i	0.0144276	−	0.114590i
$937$		−	949.998i		−	1.01387i	−0.861984	−	0.506936i	$-0.830778\pi$
$937$		−	949.998i		−	1.01387i	0.861984	−	0.506936i	$-0.169222\pi$
$938$		0			0
$939$	677.953	−	1020.86i	0.721995	−	1.08718i
$940$	−722.726	−	1251.80i	−0.768858	−	1.33170i
$941$		−	380.205i		−	0.404043i	−0.979381	−	0.202022i	$-0.935249\pi$
$941$		−	380.205i		−	0.404043i	0.979381	−	0.202022i	$-0.0647512\pi$
$942$	224.986	−	338.785i	0.238839	−	0.359644i
$943$			281.297i			0.298300i
$944$			931.705i			0.986976i
$945$		0			0
$946$	129.352			0.136736
$947$	326.068			0.344317			0.172159	−	0.985069i	$-0.444926\pi$
$947$	326.068			0.344317			0.172159	+	0.985069i	$0.444926\pi$
$948$	−221.948	−	147.395i	−0.234122	−	0.155480i
$949$	342.438			0.360841
$950$	−271.073	+	156.504i	−0.285340	+	0.164741i
$951$	96.8290	+	64.3039i	0.101818	+	0.0676172i
$952$		0			0
$953$	1009.14			1.05891			0.529455	−	0.848338i	$-0.322397\pi$
$953$	1009.14			1.05891			0.529455	+	0.848338i	$0.322397\pi$
$954$	299.254	−	394.594i	0.313683	−	0.413620i
$955$	−219.695	+	126.841i	−0.230047	+	0.132818i
$956$	−320.606	+	555.306i	−0.335362	+	0.580864i
$957$	−808.971	−	537.236i	−0.845319	−	0.561375i
$958$	967.578	+	558.631i	1.01000	+	0.583122i
$959$		0			0
$960$	858.892	+	53.8572i	0.894679	+	0.0561013i
$961$	727.748			0.757282
$962$	391.183	−	225.850i	0.406635	−	0.234771i
$963$	−454.559	−	57.2316i	−0.472023	−	0.0594305i
$964$	−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	$0.0741678\pi$
$968$	−89.0739	−	154.280i	−0.0920184	−	0.159381i
$969$	−15.6187	−	10.3724i	−0.0161184	−	0.0107042i
$970$	688.811	−	1193.06i	0.710115	−	1.22995i
$971$	−1334.71	−	770.592i	−1.37457	−	0.793607i	−0.383069	−	0.923720i	$-0.625133\pi$
$971$	−1334.71	−	770.592i	−1.37457	−	0.793607i	−0.991499	+	0.130113i	$0.958466\pi$
$972$	−726.851	+	155.289i	−0.747790	+	0.159762i
$973$		0			0
$974$	51.3691	+	88.9739i	0.0527404	+	0.0913490i
$975$	858.682	+	53.8440i	0.880699	+	0.0552246i
$976$			43.5019i			0.0445716i
$977$	−1625.38			−1.66365			−0.831824	−	0.555039i	$-0.812703\pi$
$977$	−1625.38			−1.66365			−0.831824	+	0.555039i	$0.812703\pi$
$978$	2043.84	−	1015.10i	2.08982	−	1.03794i
$979$	628.556	−	362.897i	0.642039	−	0.370681i
$980$		0			0
$981$	−238.435	+	314.399i	−0.243053	+	0.320488i
$982$	1157.53	−	2004.90i	1.17875	−	2.04165i
$983$	−30.5458	−	17.6356i	−0.0310740	−	0.0179406i	0.484383	−	0.874856i	$-0.339044\pi$
$983$	−30.5458	−	17.6356i	−0.0310740	−	0.0179406i	−0.515457	+	0.856916i	$0.672378\pi$
$984$	−186.718	−	375.944i	−0.189754	−	0.382057i
$985$	917.466	−	529.699i	0.931438	−	0.537766i
$986$	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
$990$	1431.03	−	602.250i	1.44548	−	0.608333i
$991$	567.488	+	982.918i	0.572642	+	0.991845i	0.996293	+	0.0860197i	$0.0274148\pi$
$991$	567.488	+	982.918i	0.572642	+	0.991845i	−0.423652	+	0.905825i	$0.639252\pi$
$992$		−	613.268i		−	0.618213i
$993$	712.362	+	473.078i	0.717384	+	0.476413i
$994$		0			0
$995$	−556.155	+	963.288i	−0.558950	+	0.968129i
$996$	591.428	+	37.0857i	0.593803	+	0.0372347i
$997$	44.4032	+	25.6362i	0.0445368	+	0.0257133i	0.522103	−	0.852882i	$-0.325148\pi$
$997$	44.4032	+	25.6362i	0.0445368	+	0.0257133i	−0.477566	+	0.878596i	$0.658481\pi$
$998$	489.190	+	847.301i	0.490170	+	0.848999i
$999$	723.919	+	624.081i	0.724643	+	0.624705i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.t.a.166.12		28
7.2	even	3		441.3.l.a.391.3		28
7.3	odd	6		441.3.k.b.31.3		28
7.4	even	3		63.3.k.a.31.3	✓	28
7.5	odd	6		441.3.l.b.391.3		28
7.6	odd	2		63.3.t.a.40.12	yes	28
9.7	even	3		441.3.k.b.313.3		28
21.11	odd	6		189.3.k.a.10.12		28
21.20	even	2		189.3.t.a.145.3		28
63.11	odd	6		189.3.t.a.73.3		28
63.16	even	3		441.3.l.b.97.3		28
63.20	even	6		189.3.k.a.19.12		28
63.25	even	3		63.3.t.a.52.12	yes	28
63.34	odd	6		63.3.k.a.61.3	yes	28
63.52	odd	6	inner	441.3.t.a.178.12		28
63.61	odd	6		441.3.l.a.97.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.3	✓	28	7.4	even	3
63.3.k.a.61.3	yes	28	63.34	odd	6
63.3.t.a.40.12	yes	28	7.6	odd	2
63.3.t.a.52.12	yes	28	63.25	even	3
189.3.k.a.10.12		28	21.11	odd	6
189.3.k.a.19.12		28	63.20	even	6
189.3.t.a.73.3		28	63.11	odd	6
189.3.t.a.145.3		28	21.20	even	2
441.3.k.b.31.3		28	7.3	odd	6
441.3.k.b.313.3		28	9.7	even	3
441.3.l.a.97.3		28	63.61	odd	6
441.3.l.a.391.3		28	7.2	even	3
441.3.l.b.97.3		28	63.16	even	3
441.3.l.b.391.3		28	7.5	odd	6
441.3.t.a.166.12		28	1.1	even	1	trivial
441.3.t.a.178.12		28	63.52	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.65681 q^{2} +(2.49911 + 1.65965i) q^{3} +3.05866 q^{4} +(-7.97090 + 4.60200i) q^{5} +(6.63967 + 4.40939i) q^{6} -2.50096 q^{8} +(3.49110 + 8.29531i) q^{9} +O(q^{10})\)	\(q+2.65681 q^{2} +(2.49911 + 1.65965i) q^{3} +3.05866 q^{4} +(-7.97090 + 4.60200i) q^{5} +(6.63967 + 4.40939i) q^{6} -2.50096 q^{8} +(3.49110 + 8.29531i) q^{9} +(-21.1772 + 12.2267i) q^{10} +(-3.52733 + 6.10952i) q^{11} +(7.64393 + 5.07632i) q^{12} +(4.15930 + 2.40137i) q^{13} +(-27.5579 - 1.72803i) q^{15} -18.8792 q^{16} +(2.74329 - 1.58384i) q^{17} +(9.27520 + 22.0391i) q^{18} +(-1.70864 - 0.986484i) q^{19} +(-24.3803 + 14.0760i) q^{20} +(-9.37147 + 16.2319i) q^{22} +(2.51399 + 4.35435i) q^{23} +(-6.25018 - 4.15073i) q^{24} +(29.8569 - 51.7136i) q^{25} +(11.0505 + 6.38000i) q^{26} +(-5.04271 + 26.5249i) q^{27} +(22.9425 + 39.7376i) q^{29} +(-73.2162 - 4.59105i) q^{30} +15.2726i q^{31} -40.1548 q^{32} +(-18.9549 + 9.41421i) q^{33} +(7.28840 - 4.20796i) q^{34} +(10.6781 + 25.3726i) q^{36} +(17.6998 - 30.6570i) q^{37} +(-4.53954 - 2.62090i) q^{38} +(6.40909 + 12.9043i) q^{39} +(19.9349 - 11.5094i) q^{40} +(48.4509 + 27.9732i) q^{41} +(-3.45068 - 5.97676i) q^{43} +(-10.7889 + 18.6870i) q^{44} +(-66.0023 - 50.0551i) q^{45} +(6.67920 + 11.5687i) q^{46} +51.3447i q^{47} +(-47.1813 - 31.3330i) q^{48} +(79.3241 - 137.393i) q^{50} +(9.48440 + 0.594723i) q^{51} +(12.7219 + 7.34498i) q^{52} +(-10.3556 - 17.9365i) q^{53} +(-13.3975 + 70.4718i) q^{54} -64.9312i q^{55} +(-2.63286 - 5.30108i) q^{57} +(60.9540 + 105.575i) q^{58} -49.3508i q^{59} +(-84.2903 - 5.28546i) q^{60} -2.30422i q^{61} +40.5764i q^{62} -31.1668 q^{64} -44.2045 q^{65} +(-50.3596 + 25.0118i) q^{66} +30.8279 q^{67} +(8.39079 - 4.84442i) q^{68} +(-0.943990 + 15.0544i) q^{69} +81.2604 q^{71} +(-8.73110 - 20.7463i) q^{72} +(61.7481 - 35.6503i) q^{73} +(47.0251 - 81.4499i) q^{74} +(160.442 - 79.6859i) q^{75} +(-5.22615 - 3.01732i) q^{76} +(17.0278 + 34.2843i) q^{78} -29.0358 q^{79} +(150.485 - 86.8823i) q^{80} +(-56.6245 + 57.9195i) q^{81} +(128.725 + 74.3195i) q^{82} +(55.9283 - 32.2902i) q^{83} +(-14.5776 + 25.2492i) q^{85} +(-9.16783 - 15.8791i) q^{86} +(-8.61480 + 137.385i) q^{87} +(8.82172 - 15.2797i) q^{88} +(-89.0979 - 51.4407i) q^{89} +(-175.356 - 132.987i) q^{90} +(7.68944 + 13.3185i) q^{92} +(-25.3472 + 38.1679i) q^{93} +136.413i q^{94} +18.1592 q^{95} +(-100.351 - 66.6430i) q^{96} +(-48.7891 + 28.1684i) q^{97} +(-62.9946 - 7.93140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + 3 q^{3} + 46 q^{4} + 3 q^{5} + 12 q^{6} - 16 q^{8} - 15 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 + 3 * q^3 + 46 * q^4 + 3 * q^5 + 12 * q^6 - 16 * q^8 - 15 * q^9	\( 28 q - 2 q^{2} + 3 q^{3} + 46 q^{4} + 3 q^{5} + 12 q^{6} - 16 q^{8} - 15 q^{9} + 6 q^{10} + 7 q^{11} + 30 q^{12} + 15 q^{13} - 18 q^{15} + 54 q^{16} + 33 q^{17} - 42 q^{18} + 6 q^{19} + 108 q^{20} - 10 q^{22} + 34 q^{23} + 78 q^{24} + 31 q^{25} - 54 q^{26} - 81 q^{27} + 70 q^{29} - 27 q^{30} - 306 q^{32} + 3 q^{33} + 12 q^{34} - 174 q^{36} + 9 q^{37} - 87 q^{38} + 129 q^{39} + 102 q^{40} - 234 q^{41} + 30 q^{43} + 51 q^{44} - 273 q^{45} - 22 q^{46} + 147 q^{48} + 241 q^{50} + 12 q^{51} + 219 q^{52} + 148 q^{53} - 171 q^{54} + 189 q^{57} + 17 q^{58} + 33 q^{60} - 48 q^{64} - 228 q^{65} - 258 q^{66} + 68 q^{67} + 18 q^{68} + 78 q^{69} - 350 q^{71} + 162 q^{72} + 6 q^{73} + 359 q^{74} + 510 q^{75} + 72 q^{76} - 375 q^{78} + 164 q^{79} + 609 q^{80} - 435 q^{81} + 18 q^{82} + 738 q^{83} + 3 q^{85} + 17 q^{86} + 561 q^{87} + 25 q^{88} - 21 q^{89} - 543 q^{90} + 288 q^{92} - 222 q^{93} - 1014 q^{95} - 231 q^{96} - 57 q^{97} - 162 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + 3 * q^3 + 46 * q^4 + 3 * q^5 + 12 * q^6 - 16 * q^8 - 15 * q^9 + 6 * q^10 + 7 * q^11 + 30 * q^12 + 15 * q^13 - 18 * q^15 + 54 * q^16 + 33 * q^17 - 42 * q^18 + 6 * q^19 + 108 * q^20 - 10 * q^22 + 34 * q^23 + 78 * q^24 + 31 * q^25 - 54 * q^26 - 81 * q^27 + 70 * q^29 - 27 * q^30 - 306 * q^32 + 3 * q^33 + 12 * q^34 - 174 * q^36 + 9 * q^37 - 87 * q^38 + 129 * q^39 + 102 * q^40 - 234 * q^41 + 30 * q^43 + 51 * q^44 - 273 * q^45 - 22 * q^46 + 147 * q^48 + 241 * q^50 + 12 * q^51 + 219 * q^52 + 148 * q^53 - 171 * q^54 + 189 * q^57 + 17 * q^58 + 33 * q^60 - 48 * q^64 - 228 * q^65 - 258 * q^66 + 68 * q^67 + 18 * q^68 + 78 * q^69 - 350 * q^71 + 162 * q^72 + 6 * q^73 + 359 * q^74 + 510 * q^75 + 72 * q^76 - 375 * q^78 + 164 * q^79 + 609 * q^80 - 435 * q^81 + 18 * q^82 + 738 * q^83 + 3 * q^85 + 17 * q^86 + 561 * q^87 + 25 * q^88 - 21 * q^89 - 543 * q^90 + 288 * q^92 - 222 * q^93 - 1014 * q^95 - 231 * q^96 - 57 * q^97 - 162 * q^99

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