LMFDB - Embedded newform 105.3.t.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(11,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

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

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

chi := DirichletCharacter("105.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.t (of order $6$, degree $2$, 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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} + 7x^{4} + 36x^{2} + 81 $ x^8 + 4x^6 + 7x^4 + 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.3
Root			$0.178197 + 1.72286i$ of defining polynomial
Character	$\chi$	$=$	105.11
Dual form			105.3.t.a.86.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.711747 - 0.410927i) q^{2} +(2.83943 + 0.968306i) q^{3} +(-1.66228 + 2.87915i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(2.41886 - 0.477612i) q^{6} +7.00000 q^{7} +6.01972i q^{8} +(7.12477 + 5.49888i) q^{9} +O(q^{10})$	\(q+(0.711747 - 0.410927i) q^{2} +(2.83943 + 0.968306i) q^{3} +(-1.66228 + 2.87915i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(2.41886 - 0.477612i) q^{6} +7.00000 q^{7} +6.01972i q^{8} +(7.12477 + 5.49888i) q^{9} +(-0.918861 + 1.59151i) q^{10} +(-9.48371 - 5.47542i) q^{11} +(-7.50783 + 6.56556i) q^{12} +16.8114 q^{13} +(4.98223 - 2.87649i) q^{14} +(-6.58114 + 1.29947i) q^{15} +(-4.17544 - 7.23208i) q^{16} +(-16.7167 - 9.65138i) q^{17} +(7.33067 + 0.986053i) q^{18} +(-6.56797 - 11.3761i) q^{19} -7.43393i q^{20} +(19.8760 + 6.77814i) q^{21} -9.00000 q^{22} +(17.6594 - 10.1957i) q^{23} +(-5.82893 + 17.0926i) q^{24} +(2.50000 - 4.33013i) q^{25} +(11.9655 - 6.90826i) q^{26} +(14.9057 + 22.5127i) q^{27} +(-11.6359 + 20.1540i) q^{28} -10.8175i q^{29} +(-4.15012 + 3.62926i) q^{30} +(-8.06797 + 13.9741i) q^{31} +(-26.7966 - 15.4710i) q^{32} +(-21.6265 - 24.7302i) q^{33} -15.8641 q^{34} +(-13.5554 + 7.82624i) q^{35} +(-27.6754 + 11.3726i) q^{36} +(-22.0548 - 38.2000i) q^{37} +(-9.34947 - 5.39792i) q^{38} +(47.7348 + 16.2786i) q^{39} +(-6.73025 - 11.6571i) q^{40} -20.1246i q^{41} +(16.9320 - 3.34328i) q^{42} -9.81139 q^{43} +(31.5291 - 18.2033i) q^{44} +(-19.9450 - 2.68281i) q^{45} +(8.37936 - 14.5135i) q^{46} +(-57.0178 + 32.9192i) q^{47} +(-4.85303 - 24.5781i) q^{48} +49.0000 q^{49} -4.10927i q^{50} +(-38.1204 - 43.5913i) q^{51} +(-27.9452 + 48.4025i) q^{52} +(-2.59724 - 1.49952i) q^{53} +(19.8601 + 9.89817i) q^{54} +24.4868 q^{55} +42.1380i q^{56} +(-7.63381 - 38.6614i) q^{57} +(-4.44520 - 7.69930i) q^{58} +(74.9082 + 43.2483i) q^{59} +(7.19832 - 21.1082i) q^{60} +(55.1359 + 95.4983i) q^{61} +13.2614i q^{62} +(49.8734 + 38.4922i) q^{63} +7.97367 q^{64} +(-32.5551 + 18.7957i) q^{65} +(-25.5549 - 8.71476i) q^{66} +(29.6754 - 51.3994i) q^{67} +(55.5755 - 32.0865i) q^{68} +(60.0153 - 11.8502i) q^{69} +(-6.43203 + 11.1406i) q^{70} -48.0460i q^{71} +(-33.1017 + 42.8891i) q^{72} +(-47.0680 + 81.5241i) q^{73} +(-31.3949 - 18.1258i) q^{74} +(11.2915 - 9.87434i) q^{75} +43.6712 q^{76} +(-66.3860 - 38.3280i) q^{77} +(40.6644 - 8.02931i) q^{78} +(-47.7434 - 82.6940i) q^{79} +(16.1714 + 9.33658i) q^{80} +(20.5246 + 78.3565i) q^{81} +(-8.26975 - 14.3236i) q^{82} +114.706i q^{83} +(-52.5548 + 45.9589i) q^{84} +43.1623 q^{85} +(-6.98322 + 4.03177i) q^{86} +(10.4746 - 30.7155i) q^{87} +(32.9605 - 57.0893i) q^{88} +(45.2833 - 26.1443i) q^{89} +(-15.2982 + 6.28646i) q^{90} +117.680 q^{91} +67.7922i q^{92} +(-36.4397 + 31.8664i) q^{93} +(-27.0548 + 46.8603i) q^{94} +(25.4376 + 14.6864i) q^{95} +(-61.1066 - 69.8764i) q^{96} -40.1886 q^{97} +(34.8756 - 20.1354i) q^{98} +(-37.4605 - 91.1609i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 12 q^{4} + 32 q^{6} + 56 q^{7} + 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 12 * q^4 + 32 * q^6 + 56 * q^7 + 8 * q^9	$ 8 q - 4 q^{3} + 12 q^{4} + 32 q^{6} + 56 q^{7} + 8 q^{9} - 20 q^{10} + 52 q^{12} + 8 q^{13} - 40 q^{15} - 84 q^{16} - 52 q^{18} + 36 q^{19} - 28 q^{21} - 72 q^{22} + 24 q^{24} + 20 q^{25} + 56 q^{27} + 84 q^{28} - 40 q^{30} + 24 q^{31} - 72 q^{33} - 304 q^{34} - 272 q^{36} - 12 q^{37} + 96 q^{39} + 60 q^{40} + 224 q^{42} + 48 q^{43} + 20 q^{45} - 148 q^{46} + 328 q^{48} + 392 q^{49} - 164 q^{51} - 388 q^{52} - 160 q^{54} + 120 q^{55} - 352 q^{57} - 200 q^{58} - 20 q^{60} + 264 q^{61} + 56 q^{63} - 88 q^{64} + 36 q^{66} + 288 q^{67} + 88 q^{69} - 140 q^{70} + 348 q^{72} - 288 q^{73} + 20 q^{75} + 1336 q^{76} - 168 q^{78} - 344 q^{79} - 28 q^{81} - 180 q^{82} + 364 q^{84} + 320 q^{85} + 140 q^{87} + 36 q^{88} + 80 q^{90} + 56 q^{91} + 164 q^{93} - 52 q^{94} - 320 q^{96} - 448 q^{97} - 72 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 12 * q^4 + 32 * q^6 + 56 * q^7 + 8 * q^9 - 20 * q^10 + 52 * q^12 + 8 * q^13 - 40 * q^15 - 84 * q^16 - 52 * q^18 + 36 * q^19 - 28 * q^21 - 72 * q^22 + 24 * q^24 + 20 * q^25 + 56 * q^27 + 84 * q^28 - 40 * q^30 + 24 * q^31 - 72 * q^33 - 304 * q^34 - 272 * q^36 - 12 * q^37 + 96 * q^39 + 60 * q^40 + 224 * q^42 + 48 * q^43 + 20 * q^45 - 148 * q^46 + 328 * q^48 + 392 * q^49 - 164 * q^51 - 388 * q^52 - 160 * q^54 + 120 * q^55 - 352 * q^57 - 200 * q^58 - 20 * q^60 + 264 * q^61 + 56 * q^63 - 88 * q^64 + 36 * q^66 + 288 * q^67 + 88 * q^69 - 140 * q^70 + 348 * q^72 - 288 * q^73 + 20 * q^75 + 1336 * q^76 - 168 * q^78 - 344 * q^79 - 28 * q^81 - 180 * q^82 + 364 * q^84 + 320 * q^85 + 140 * q^87 + 36 * q^88 + 80 * q^90 + 56 * q^91 + 164 * q^93 - 52 * q^94 - 320 * q^96 - 448 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.711747	−	0.410927i	0.355873	−	0.205464i	−0.311396	−	0.950280i	$-0.600796\pi$
$2$	0.711747	−	0.410927i	0.355873	−	0.205464i	0.667269	+	0.744817i	$0.267463\pi$
$3$	2.83943	+	0.968306i	0.946478	+	0.322769i
$3$	2.83943	+	0.968306i	0.946478	+	0.322769i
$4$	−1.66228	+	2.87915i	−0.415569	+	0.719787i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$	2.41886	−	0.477612i	0.403144	−	0.0796019i
$7$	7.00000			1.00000
$7$	7.00000			1.00000
$8$			6.01972i			0.752465i
$9$	7.12477	+	5.49888i	0.791641	+	0.610987i
$10$	−0.918861	+	1.59151i	−0.0918861	+	0.159151i
$11$	−9.48371	−	5.47542i	−0.862155	−	0.497766i	0.00257807	−	0.999997i	$-0.499179\pi$
$11$	−9.48371	−	5.47542i	−0.862155	−	0.497766i	−0.864733	+	0.502231i	$0.832513\pi$
$12$	−7.50783	+	6.56556i	−0.625652	+	0.547130i
$13$	16.8114			1.29318			0.646592	−	0.762836i	$-0.276194\pi$
$13$	16.8114			1.29318			0.646592	+	0.762836i	$0.276194\pi$
$14$	4.98223	−	2.87649i	0.355873	−	0.205464i
$15$	−6.58114	+	1.29947i	−0.438743	+	0.0866311i
$16$	−4.17544	−	7.23208i	−0.260965	−	0.452005i
$17$	−16.7167	−	9.65138i	−0.983334	−	0.567728i	−0.0800590	−	0.996790i	$-0.525511\pi$
$17$	−16.7167	−	9.65138i	−0.983334	−	0.567728i	−0.903275	+	0.429062i	$0.858844\pi$
$18$	7.33067	+	0.986053i	0.407259	+	0.0547807i
$19$	−6.56797	−	11.3761i	−0.345683	−	0.598740i	0.639795	−	0.768546i	$-0.279019\pi$
$19$	−6.56797	−	11.3761i	−0.345683	−	0.598740i	−0.985478	+	0.169806i	$0.945686\pi$
$20$		−	7.43393i		−	0.371697i
$21$	19.8760	+	6.77814i	0.946478	+	0.322769i
$22$	−9.00000			−0.409091
$23$	17.6594	−	10.1957i	0.767801	−	0.443290i	−0.0642885	−	0.997931i	$-0.520478\pi$
$23$	17.6594	−	10.1957i	0.767801	−	0.443290i	0.832090	+	0.554641i	$0.187144\pi$
$24$	−5.82893	+	17.0926i	−0.242872	+	0.712191i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	11.9655	−	6.90826i	0.460210	−	0.265702i
$27$	14.9057	+	22.5127i	0.552063	+	0.833803i
$28$	−11.6359	+	20.1540i	−0.415569	+	0.719787i
$29$		−	10.8175i		−	0.373016i	−0.982453	−	0.186508i	$-0.940283\pi$
$29$		−	10.8175i		−	0.373016i	0.982453	−	0.186508i	$-0.0597171\pi$
$30$	−4.15012	+	3.62926i	−0.138337	+	0.120975i
$31$	−8.06797	+	13.9741i	−0.260257	+	0.450779i	−0.966310	−	0.257380i	$-0.917141\pi$
$31$	−8.06797	+	13.9741i	−0.260257	+	0.450779i	0.706053	+	0.708159i	$0.250474\pi$
$32$	−26.7966	−	15.4710i	−0.837395	−	0.483470i
$33$	−21.6265	−	24.7302i	−0.655348	−	0.749401i
$34$	−15.8641			−0.466590
$35$	−13.5554	+	7.82624i	−0.387298	+	0.223607i
$36$	−27.6754	+	11.3726i	−0.768762	+	0.315905i
$37$	−22.0548	−	38.2000i	−0.596076	−	1.03243i	−0.993394	−	0.114753i	$-0.963392\pi$
$37$	−22.0548	−	38.2000i	−0.596076	−	1.03243i	0.397318	−	0.917681i	$-0.369941\pi$
$38$	−9.34947	−	5.39792i	−0.246039	−	0.142050i
$39$	47.7348	+	16.2786i	1.22397	+	0.417399i
$40$	−6.73025	−	11.6571i	−0.168256	−	0.291428i
$41$		−	20.1246i		−	0.490844i	−0.969416	−	0.245422i	$-0.921073\pi$
$41$		−	20.1246i		−	0.490844i	0.969416	−	0.245422i	$-0.0789266\pi$
$42$	16.9320	−	3.34328i	0.403144	−	0.0796019i
$43$	−9.81139			−0.228172			−0.114086	−	0.993471i	$-0.536394\pi$
$43$	−9.81139			−0.228172			−0.114086	+	0.993471i	$0.536394\pi$
$44$	31.5291	−	18.2033i	0.716571	−	0.413712i
$45$	−19.9450	−	2.68281i	−0.443222	−	0.0596180i
$46$	8.37936	−	14.5135i	0.182160	−	0.315510i
$47$	−57.0178	+	32.9192i	−1.21314	+	0.700409i	−0.963443	−	0.267914i	$-0.913666\pi$
$47$	−57.0178	+	32.9192i	−1.21314	+	0.700409i	−0.249701	+	0.968323i	$0.580332\pi$
$48$	−4.85303	−	24.5781i	−0.101105	−	0.512044i
$49$	49.0000			1.00000
$50$		−	4.10927i		−	0.0821854i
$51$	−38.1204	−	43.5913i	−0.747459	−	0.854732i
$52$	−27.9452	+	48.4025i	−0.537408	+	0.930817i
$53$	−2.59724	−	1.49952i	−0.0490046	−	0.0282928i	0.475298	−	0.879825i	$-0.342340\pi$
$53$	−2.59724	−	1.49952i	−0.0490046	−	0.0282928i	−0.524302	+	0.851532i	$0.675674\pi$
$54$	19.8601	+	9.89817i	0.367781	+	0.183299i
$55$	24.4868			0.445215
$56$			42.1380i			0.752465i
$57$	−7.63381	−	38.6614i	−0.133926	−	0.678270i
$58$	−4.44520	−	7.69930i	−0.0766413	−	0.132747i
$59$	74.9082	+	43.2483i	1.26963	+	0.733021i	0.974918	−	0.222565i	$-0.0714428\pi$
$59$	74.9082	+	43.2483i	1.26963	+	0.733021i	0.294712	+	0.955586i	$0.404776\pi$
$60$	7.19832	−	21.1082i	0.119972	−	0.351803i
$61$	55.1359	+	95.4983i	0.903868	+	1.56555i	0.822430	+	0.568867i	$0.192618\pi$
$61$	55.1359	+	95.4983i	0.903868	+	1.56555i	0.0814382	+	0.996678i	$0.474049\pi$
$62$			13.2614i			0.213893i
$63$	49.8734	+	38.4922i	0.791641	+	0.610987i
$64$	7.97367			0.124589
$65$	−32.5551	+	18.7957i	−0.500848	+	0.289165i
$66$	−25.5549	−	8.71476i	−0.387195	−	0.132042i
$67$	29.6754	−	51.3994i	0.442917	−	0.767155i	−0.554987	−	0.831859i	$-0.687277\pi$
$67$	29.6754	−	51.3994i	0.442917	−	0.767155i	0.997905	+	0.0647038i	$0.0206103\pi$
$68$	55.5755	−	32.0865i	0.817287	−	0.471861i
$69$	60.0153	−	11.8502i	0.869787	−	0.171742i
$70$	−6.43203	+	11.1406i	−0.0918861	+	0.159151i
$71$		−	48.0460i		−	0.676704i	−0.941020	−	0.338352i	$-0.890130\pi$
$71$		−	48.0460i		−	0.676704i	0.941020	−	0.338352i	$-0.109870\pi$
$72$	−33.1017	+	42.8891i	−0.459746	+	0.595682i
$73$	−47.0680	+	81.5241i	−0.644767	+	1.11677i	0.339589	+	0.940574i	$0.389712\pi$
$73$	−47.0680	+	81.5241i	−0.644767	+	1.11677i	−0.984355	+	0.176195i	$0.943621\pi$
$74$	−31.3949	−	18.1258i	−0.424255	−	0.244944i
$75$	11.2915	−	9.87434i	0.150553	−	0.131658i
$76$	43.6712			0.574621
$77$	−66.3860	−	38.3280i	−0.862155	−	0.497766i
$78$	40.6644	−	8.02931i	0.521339	−	0.102940i
$79$	−47.7434	−	82.6940i	−0.604347	−	1.04676i	−0.992154	−	0.125019i	$-0.960101\pi$
$79$	−47.7434	−	82.6940i	−0.604347	−	1.04676i	0.387807	−	0.921740i	$-0.373233\pi$
$80$	16.1714	+	9.33658i	0.202143	+	0.116707i
$81$	20.5246	+	78.3565i	0.253390	+	0.967364i
$82$	−8.26975	−	14.3236i	−0.100851	−	0.174678i
$83$			114.706i			1.38200i	0.722853	+	0.691002i	$0.242830\pi$
$83$			114.706i			1.38200i	−0.722853	+	0.691002i	$0.757170\pi$
$84$	−52.5548	+	45.9589i	−0.625652	+	0.547130i
$85$	43.1623			0.507792
$86$	−6.98322	+	4.03177i	−0.0812003	+	0.0468810i
$87$	10.4746	−	30.7155i	0.120398	−	0.353052i
$88$	32.9605	−	57.0893i	0.374551	−	0.648742i
$89$	45.2833	−	26.1443i	0.508801	−	0.293757i	−0.223540	−	0.974695i	$-0.571761\pi$
$89$	45.2833	−	26.1443i	0.508801	−	0.293757i	0.732341	+	0.680938i	$0.238428\pi$
$90$	−15.2982	+	6.28646i	−0.169980	+	0.0698495i
$91$	117.680			1.29318
$92$			67.7922i			0.736871i
$93$	−36.4397	+	31.8664i	−0.391825	+	0.342649i
$94$	−27.0548	+	46.8603i	−0.287817	+	0.498514i
$95$	25.4376	+	14.6864i	0.267765	+	0.154594i
$96$	−61.1066	−	69.8764i	−0.636527	−	0.727879i
$97$	−40.1886			−0.414316			−0.207158	−	0.978308i	$-0.566421\pi$
$97$	−40.1886			−0.414316			−0.207158	+	0.978308i	$0.566421\pi$
$98$	34.8756	−	20.1354i	0.355873	−	0.205464i
$99$	−37.4605	−	91.1609i	−0.378389	−	0.920817i
$100$	8.31139	+	14.3957i	0.0831139	+	0.143957i
$101$	−14.9279	−	8.61865i	−0.147801	−	0.0853332i	0.424276	−	0.905533i	$-0.360529\pi$
$101$	−14.9279	−	8.61865i	−0.147801	−	0.0853332i	−0.572077	+	0.820200i	$0.693862\pi$
$102$	−45.0449	−	15.3613i	−0.441617	−	0.150601i
$103$	−72.9210	−	126.303i	−0.707971	−	1.22624i	−0.965609	−	0.260000i	$-0.916277\pi$
$103$	−72.9210	−	126.303i	−0.707971	−	1.22624i	0.257638	−	0.966242i	$-0.417056\pi$
$104$			101.200i			0.973075i
$105$	−46.0680	+	9.09626i	−0.438743	+	0.0866311i
$106$	−2.46477			−0.0232526
$107$	157.992	−	91.2168i	1.47656	−	0.852493i	0.476912	−	0.878951i	$-0.341756\pi$
$107$	157.992	−	91.2168i	1.47656	−	0.852493i	0.999650	+	0.0264580i	$0.00842283\pi$
$108$	−89.5947	+	5.49341i	−0.829581	+	0.0508649i
$109$	−68.8530	+	119.257i	−0.631679	+	1.09410i	0.355529	+	0.934665i	$0.384301\pi$
$109$	−68.8530	+	119.257i	−0.631679	+	1.09410i	−0.987208	+	0.159435i	$0.949033\pi$
$110$	17.4284	−	10.0623i	0.158440	−	0.0914755i
$111$	−25.6338	−	129.822i	−0.230935	−	1.16957i
$112$	−29.2281	−	50.6246i	−0.260965	−	0.452005i
$113$			153.200i			1.35575i	0.735176	+	0.677877i	$0.237100\pi$
$113$			153.200i			1.35575i	−0.735176	+	0.677877i	$0.762900\pi$
$114$	−21.3203	−	24.3802i	−0.187021	−	0.213861i
$115$	−22.7982	+	39.4877i	−0.198245	+	0.343371i
$116$	31.1451	+	17.9816i	0.268492	+	0.155014i
$117$	119.777	+	92.4439i	1.02374	+	0.790118i
$118$	71.0875			0.602437
$119$	−117.017	−	67.5597i	−0.983334	−	0.567728i
$120$	−7.82242	−	39.6166i	−0.0651868	−	0.330138i
$121$	−0.539501	−	0.934443i	−0.00445869	−	0.00772267i
$122$	78.4857	+	45.3137i	0.643325	+	0.371424i
$123$	19.4868	−	57.1425i	0.158429	−	0.464573i
$124$	−26.8224	−	46.4578i	−0.216310	−	0.374660i
$125$			11.1803i			0.0894427i
$126$	51.3147	+	6.90237i	0.407259	+	0.0547807i
$127$	−215.868			−1.69975			−0.849875	−	0.526984i	$-0.823323\pi$
$127$	−215.868			−1.69975			−0.849875	+	0.526984i	$0.823323\pi$
$128$	112.862	−	65.1608i	0.881733	−	0.509069i
$129$	−27.8588	−	9.50043i	−0.215960	−	0.0736467i
$130$	−15.4473	+	26.7556i	−0.118826	+	0.205812i
$131$	−103.590	+	59.8079i	−0.790766	+	0.456549i	−0.840232	−	0.542227i	$-0.817581\pi$
$131$	−103.590	+	59.8079i	−0.790766	+	0.456549i	0.0494663	+	0.998776i	$0.484248\pi$
$132$	107.151	−	21.1573i	0.811752	−	0.160283i
$133$	−45.9758	−	79.6324i	−0.345683	−	0.598740i
$134$		−	48.7778i		−	0.364013i
$135$	−54.0347	−	26.9305i	−0.400257	−	0.199485i
$136$	58.0986	−	100.630i	0.427195	−	0.739924i
$137$	45.1491	+	26.0668i	0.329555	+	0.190269i	0.655644	−	0.755070i	$-0.272397\pi$
$137$	45.1491	+	26.0668i	0.329555	+	0.190269i	−0.326088	+	0.945339i	$0.605731\pi$
$138$	37.8461	−	33.0963i	0.274247	−	0.239828i
$139$	−63.6228			−0.457718			−0.228859	−	0.973460i	$-0.573499\pi$
$139$	−63.6228			−0.457718			−0.228859	+	0.973460i	$0.573499\pi$
$140$		−	52.0375i		−	0.371697i
$141$	−193.774	+	38.2613i	−1.37428	+	0.271357i
$142$	−19.7434	−	34.1966i	−0.139038	−	0.240821i
$143$	−159.434	−	92.0495i	−1.11493	−	0.643702i
$144$	10.0193	−	74.4872i	0.0695786	−	0.517272i
$145$	12.0943	+	20.9480i	0.0834090	+	0.144469i
$146$			77.3660i			0.529904i
$147$	139.132	+	47.4470i	0.946478	+	0.322769i
$148$	146.645			0.990843
$149$	−187.155	+	108.054i	−1.25607	+	0.725194i	−0.972309	−	0.233700i	$-0.924917\pi$
$149$	−187.155	+	108.054i	−1.25607	+	0.725194i	−0.283765	+	0.958894i	$0.591583\pi$
$150$	3.97903	−	11.6680i	0.0265269	−	0.0777867i
$151$	−19.5658	+	33.8890i	−0.129575	+	0.224431i	−0.923512	−	0.383570i	$-0.874695\pi$
$151$	−19.5658	+	33.8890i	−0.129575	+	0.224431i	0.793937	+	0.608000i	$0.208028\pi$
$152$	68.4807	−	39.5373i	0.450531	−	0.260114i
$153$	−66.0306	−	160.687i	−0.431573	−	1.05024i
$154$	−63.0000			−0.409091
$155$		−	36.0811i		−	0.232781i
$156$	−126.217	+	110.376i	−0.809083	+	0.707540i
$157$	23.8399	−	41.2918i	0.151846	−	0.263005i	−0.780060	−	0.625705i	$-0.784811\pi$
$157$	23.8399	−	41.2918i	0.151846	−	0.263005i	0.931906	+	0.362699i	$0.118145\pi$
$158$	−67.9624	−	39.2381i	−0.430142	−	0.248343i
$159$	−5.92270	−	6.77271i	−0.0372497	−	0.0425957i
$160$	69.1886			0.432429
$161$	123.616	−	71.3697i	0.767801	−	0.443290i
$162$	46.8071	+	47.3359i	0.288933	+	0.292197i
$163$	63.2719	+	109.590i	0.388171	+	0.672332i	0.992204	−	0.124628i	$-0.0397736\pi$
$163$	63.2719	+	109.590i	0.388171	+	0.672332i	−0.604032	+	0.796960i	$0.706440\pi$
$164$	57.9418	+	33.4527i	0.353303	+	0.203980i
$165$	69.5287	+	23.7108i	0.421386	+	0.143702i
$166$	47.1359	+	81.6418i	0.283951	+	0.491818i
$167$			54.3325i			0.325344i	0.986680	+	0.162672i	$0.0520113\pi$
$167$			54.3325i			0.325344i	−0.986680	+	0.162672i	$0.947989\pi$
$168$	−40.8025	+	119.648i	−0.242872	+	0.712191i
$169$	113.623			0.672324
$170$	30.7206	−	17.7366i	0.180709	−	0.104333i
$171$	15.7604	−	117.168i	0.0921659	−	0.685195i
$172$	16.3093	−	28.2485i	0.0948212	−	0.164235i
$173$	−241.363	+	139.351i	−1.39516	+	0.805498i	−0.993881	−	0.110457i	$-0.964769\pi$
$173$	−241.363	+	139.351i	−1.39516	+	0.805498i	−0.401282	+	0.915954i	$0.631435\pi$
$174$	−5.16655	−	26.1660i	−0.0296928	−	0.150379i
$175$	17.5000	−	30.3109i	0.100000	−	0.173205i
$176$			91.4493i			0.519598i
$177$	170.819	+	195.335i	0.965080	+	1.10359i
$178$	21.4868	−	37.2163i	0.120713	−	0.209080i
$179$	−102.629	−	59.2528i	−0.573345	−	0.331021i	0.185139	−	0.982712i	$-0.440726\pi$
$179$	−102.629	−	59.2528i	−0.573345	−	0.331021i	−0.758484	+	0.651691i	$0.774060\pi$
$180$	40.8783	−	52.9650i	0.227102	−	0.294250i
$181$	−28.9431			−0.159906			−0.0799532	−	0.996799i	$-0.525477\pi$
$181$	−28.9431			−0.159906			−0.0799532	+	0.996799i	$0.525477\pi$
$182$	83.7582	−	48.3578i	0.460210	−	0.265702i
$183$	64.0833	+	324.549i	0.350182	+	1.77349i
$184$	61.3751	+	106.305i	0.333560	+	0.577743i
$185$	85.4179	+	49.3160i	0.461718	+	0.266573i
$186$	−12.8411	+	37.6549i	−0.0690381	+	0.202445i
$187$	105.691	+	183.062i	0.565191	+	0.978940i
$188$		−	218.884i		−	1.16427i
$189$	104.340	+	157.589i	0.552063	+	0.833803i
$190$	24.1402			0.127054
$191$	268.488	−	155.011i	1.40569	−	0.811578i	0.410725	−	0.911759i	$-0.365276\pi$
$191$	268.488	−	155.011i	1.40569	−	0.811578i	0.994969	+	0.100181i	$0.0319423\pi$
$192$	22.6407	+	7.72095i	0.117920	+	0.0402133i
$193$	−128.774	+	223.043i	−0.667223	+	1.15566i	0.311455	+	0.950261i	$0.399184\pi$
$193$	−128.774	+	223.043i	−0.667223	+	1.15566i	−0.978677	+	0.205403i	$0.934150\pi$
$194$	−28.6041	+	16.5146i	−0.147444	+	0.0851268i
$195$	−110.638	+	21.8458i	−0.567375	+	0.112030i
$196$	−81.4516	+	141.078i	−0.415569	+	0.719787i
$197$		−	83.7642i		−	0.425199i	−0.977139	−	0.212600i	$-0.931807\pi$
$197$		−	83.7642i		−	0.425199i	0.977139	−	0.212600i	$-0.0681930\pi$
$198$	−64.1229	−	49.4899i	−0.323853	−	0.249949i
$199$	139.434	−	241.507i	0.700674	−	1.21360i	−0.267556	−	0.963542i	$-0.586216\pi$
$199$	139.434	−	241.507i	0.700674	−	1.21360i	0.968230	−	0.250061i	$-0.0804507\pi$
$200$	26.0661	+	15.0493i	0.130331	+	0.0752465i
$201$	134.032	−	117.210i	0.666825	−	0.583135i
$202$	−14.1666			−0.0701314
$203$		−	75.7223i		−	0.373016i
$204$	188.873	−	37.2935i	0.925846	−	0.182811i
$205$	22.5000	+	38.9711i	0.109756	+	0.190103i
$206$	−103.803	−	59.9304i	−0.503896	−	0.290924i
$207$	181.884	+	24.4653i	0.878667	+	0.118190i
$208$	−70.1950	−	121.581i	−0.337476	−	0.584526i
$209$			143.850i			0.688276i
$210$	−29.0508	+	25.4048i	−0.138337	+	0.120975i
$211$	136.057			0.644820			0.322410	−	0.946600i	$-0.395507\pi$
$211$	136.057			0.644820			0.322410	+	0.946600i	$0.395507\pi$
$212$	8.63468	−	4.98523i	0.0407296	−	0.0235153i
$213$	46.5233	−	136.423i	0.218419	−	0.640486i
$214$	74.9669	−	129.846i	0.350313	−	0.606759i
$215$	18.9997	−	10.9695i	0.0883706	−	0.0510208i
$216$	−135.520	+	89.7281i	−0.627407	+	0.415408i
$217$	−56.4758	+	97.8190i	−0.260257	+	0.450779i
$218$			113.174i			0.519148i
$219$	−212.587	+	185.906i	−0.970716	+	0.848886i
$220$	−40.7039	+	70.5012i	−0.185018	+	0.320460i
$221$	−281.031	−	162.253i	−1.27163	−	0.734177i
$222$	−71.5923	−	81.8670i	−0.322488	−	0.368770i
$223$	−65.8861			−0.295453			−0.147727	−	0.989028i	$-0.547196\pi$
$223$	−65.8861			−0.295453			−0.147727	+	0.989028i	$0.547196\pi$
$224$	−187.576	−	108.297i	−0.837395	−	0.483470i
$225$	41.6228	−	17.1039i	0.184990	−	0.0760175i
$226$	62.9541	+	109.040i	0.278558	+	0.482476i
$227$	24.8924	+	14.3716i	0.109658	+	0.0633111i	0.553826	−	0.832632i	$-0.313167\pi$
$227$	24.8924	+	14.3716i	0.109658	+	0.0633111i	−0.444168	+	0.895944i	$0.646501\pi$
$228$	124.001	+	42.2871i	0.543866	+	0.185470i
$229$	41.3135	+	71.5571i	0.180408	+	0.312477i	0.942020	−	0.335558i	$-0.108925\pi$
$229$	41.3135	+	71.5571i	0.180408	+	0.312477i	−0.761611	+	0.648034i	$0.775591\pi$
$230$			37.4736i			0.162929i
$231$	−151.385	−	173.112i	−0.655348	−	0.749401i
$232$	65.1182			0.280682
$233$	220.261	−	127.167i	0.945324	−	0.545783i	0.0536989	−	0.998557i	$-0.482899\pi$
$233$	220.261	−	127.167i	0.945324	−	0.545783i	0.891625	+	0.452774i	$0.149566\pi$
$234$	123.239	+	16.5769i	0.526661	+	0.0708415i
$235$	73.6096	−	127.496i	0.313232	−	0.542534i
$236$	−249.036	+	143.781i	−1.05524	+	0.609243i
$237$	−55.4911	−	281.034i	−0.234140	−	1.18580i
$238$	−111.048			−0.466590
$239$		−	468.377i		−	1.95974i	−0.199641	−	0.979869i	$-0.563977\pi$
$239$		−	468.377i		−	1.95974i	0.199641	−	0.979869i	$-0.436023\pi$
$240$	36.8770	+	42.1695i	0.153654	+	0.175706i
$241$	84.3904	−	146.168i	0.350168	−	0.606508i	−0.636111	−	0.771598i	$-0.719458\pi$
$241$	84.3904	−	146.168i	0.350168	−	0.606508i	0.986279	+	0.165089i	$0.0527913\pi$
$242$	−0.767976	−	0.443391i	−0.00317346	−	0.00183220i
$243$	−17.5950	+	242.362i	−0.0724073	+	0.997375i
$244$	−366.605			−1.50248
$245$	−94.8881	+	54.7837i	−0.387298	+	0.223607i
$246$	−9.61175	−	48.6786i	−0.0390721	−	0.197881i
$247$	−110.417	−	191.247i	−0.447031	−	0.774281i
$248$	−84.1204	−	48.5669i	−0.339195	−	0.195834i
$249$	−111.071	+	325.701i	−0.446068	+	1.30804i
$250$	4.59431	+	7.95757i	0.0183772	+	0.0318303i
$251$		−	61.6391i		−	0.245574i	−0.992433	−	0.122787i	$-0.960817\pi$
$251$		−	61.6391i		−	0.245574i	0.992433	−	0.122787i	$-0.0391832\pi$
$252$	−193.728	+	79.6082i	−0.768762	+	0.315905i
$253$	−223.302			−0.882619
$254$	−153.644	+	88.7062i	−0.604896	+	0.349237i
$255$	122.556	+	41.7943i	0.480613	+	0.163899i
$256$	37.6053	−	65.1344i	0.146896	−	0.254431i
$257$	14.0039	−	8.08518i	0.0544900	−	0.0314598i	−0.472507	−	0.881327i	$-0.656651\pi$
$257$	14.0039	−	8.08518i	0.0544900	−	0.0314598i	0.526998	+	0.849867i	$0.323318\pi$
$258$	−23.7324	+	4.68603i	−0.0919860	+	0.0181629i
$259$	−154.384	−	267.400i	−0.596076	−	1.03243i
$260$		−	124.975i		−	0.480672i
$261$	59.4840	−	77.0720i	0.227908	−	0.295295i
$262$	−49.1534	+	85.1362i	−0.187608	+	0.324947i
$263$	−69.4827	−	40.1159i	−0.264193	−	0.152532i	0.362053	−	0.932158i	$-0.382076\pi$
$263$	−69.4827	−	40.1159i	−0.264193	−	0.152532i	−0.626246	+	0.779626i	$0.715409\pi$
$264$	148.869	−	130.185i	0.563898	−	0.493126i
$265$	6.70605			0.0253059
$266$	−65.4463	−	37.7854i	−0.246039	−	0.142050i
$267$	153.895	−	30.3870i	0.576385	−	0.113809i
$268$	98.6577	+	170.880i	0.368126	+	0.637612i
$269$	439.597	+	253.802i	1.63419	+	0.943500i	0.982781	+	0.184773i	$0.0591550\pi$
$269$	439.597	+	253.802i	1.63419	+	0.943500i	0.651409	+	0.758727i	$0.274178\pi$
$270$	−49.5255	+	3.03661i	−0.183428	+	0.0112467i
$271$	44.7061	+	77.4332i	0.164967	+	0.285731i	0.936644	−	0.350284i	$-0.113915\pi$
$271$	44.7061	+	77.4332i	0.164967	+	0.285731i	−0.771677	+	0.636015i	$0.780582\pi$
$272$			161.195i			0.592629i
$273$	334.144	+	113.950i	1.22397	+	0.417399i
$274$	42.8463			0.156373
$275$	−47.4185	+	27.3771i	−0.172431	+	0.0995531i
$276$	−65.6436	+	192.491i	−0.237839	+	0.697432i
$277$	4.84200	−	8.38658i	0.0174801	−	0.0302765i	−0.857153	−	0.515062i	$-0.827769\pi$
$277$	4.84200	−	8.38658i	0.0174801	−	0.0302765i	0.874633	+	0.484785i	$0.161102\pi$
$278$	−45.2833	+	26.1443i	−0.162890	+	0.0940444i
$279$	−134.325	+	55.1976i	−0.481450	+	0.197841i
$280$	−47.1117	−	81.5999i	−0.168256	−	0.291428i
$281$			290.277i			1.03301i	0.856283	+	0.516506i	$0.172768\pi$
$281$			290.277i			1.03301i	−0.856283	+	0.516506i	$0.827232\pi$
$282$	−122.195	+	106.859i	−0.433317	+	0.378934i
$283$	231.947	−	401.745i	0.819602	−	1.41959i	−0.0863740	−	0.996263i	$-0.527528\pi$
$283$	231.947	−	401.745i	0.819602	−	1.41959i	0.905976	−	0.423329i	$-0.139139\pi$
$284$	138.332	+	79.8658i	0.487083	+	0.281218i
$285$	58.0075	+	66.3326i	0.203535	+	0.232746i
$286$	−151.302			−0.529030
$287$		−	140.872i		−	0.490844i
$288$	−105.846	−	257.579i	−0.367522	−	0.894372i
$289$	41.7982	+	72.3966i	0.144631	+	0.250507i
$290$	17.2162	+	9.93976i	0.0593661	+	0.0342750i
$291$	−114.113	−	38.9149i	−0.392141	−	0.133728i
$292$	−156.480	−	271.031i	−0.535891	−	0.928190i
$293$			120.503i			0.411272i	0.978629	+	0.205636i	$0.0659262\pi$
$293$			120.503i			0.411272i	−0.978629	+	0.205636i	$0.934074\pi$
$294$	118.524	−	23.4030i	0.403144	−	0.0796019i
$295$	−193.412			−0.655634
$296$	229.953	−	132.764i	0.776870	−	0.448526i
$297$	−18.0949	−	295.119i	−0.0609256	−	0.993665i
$298$	−88.8046	+	153.814i	−0.298002	+	0.516155i
$299$	296.879	−	171.403i	0.992908	−	0.573256i
$300$	9.66014	+	48.9237i	0.0322005	+	0.163079i
$301$	−68.6797			−0.228172
$302$			32.1605i			0.106492i
$303$	−34.0414	−	38.9269i	−0.112348	−	0.128472i
$304$	−54.8484	+	95.0002i	−0.180422	+	0.312501i
$305$	−213.541	−	123.288i	−0.700133	−	0.404222i
$306$	−113.028	−	87.2346i	−0.369372	−	0.285080i
$307$	−84.7936			−0.276201			−0.138100	−	0.990418i	$-0.544100\pi$
$307$	−84.7936			−0.276201			−0.138100	+	0.990418i	$0.544100\pi$
$308$	220.704	−	127.423i	0.716571	−	0.413712i
$309$	−84.7544	−	429.238i	−0.274286	−	1.38912i
$310$	−14.8267	−	25.6806i	−0.0478280	−	0.0828406i
$311$	442.101	+	255.247i	1.42155	+	0.820730i	0.996431	−	0.0844100i	$-0.0269005\pi$
$311$	442.101	+	255.247i	1.42155	+	0.820730i	0.425114	+	0.905140i	$0.360234\pi$
$312$	−97.9924	+	287.350i	−0.314078	+	0.920994i
$313$	57.4605	+	99.5245i	0.183580	+	0.317970i	0.943097	−	0.332518i	$-0.107898\pi$
$313$	57.4605	+	99.5245i	0.183580	+	0.317970i	−0.759517	+	0.650487i	$0.774565\pi$
$314$		−	39.1858i		−	0.124795i
$315$	−139.615	−	18.7797i	−0.443222	−	0.0596180i
$316$	317.451			1.00459
$317$	−423.015	+	244.228i	−1.33443	+	0.770434i	−0.985975	−	0.166891i	$-0.946627\pi$
$317$	−423.015	+	244.228i	−1.33443	+	0.770434i	−0.348456	+	0.937325i	$0.613294\pi$
$318$	−6.99856	−	2.38665i	−0.0220080	−	0.00750520i
$319$	−59.2302	+	102.590i	−0.185675	+	0.321598i
$320$	−15.4409	+	8.91483i	−0.0482529	+	0.0278588i
$321$	536.934	−	106.019i	1.67269	−	0.330278i
$322$	58.6555	−	101.594i	0.182160	−	0.315510i
$323$			253.560i			0.785015i
$324$	−259.718	−	71.1570i	−0.801598	−	0.219620i
$325$	42.0285	−	72.7954i	0.129318	−	0.223986i
$326$	90.0671	+	52.0003i	0.276280	+	0.159510i
$327$	−310.981	+	271.951i	−0.951012	+	0.831655i
$328$	121.144			0.369343
$329$	−399.124	+	230.435i	−1.21314	+	0.700409i
$330$	59.2302	−	11.6952i	0.179486	−	0.0354400i
$331$	106.568	+	184.581i	0.321958	+	0.557647i	0.980892	−	0.194554i	$-0.0623258\pi$
$331$	106.568	+	184.581i	0.321958	+	0.557647i	−0.658934	+	0.752201i	$0.728992\pi$
$332$	−330.257	−	190.674i	−0.994749	−	0.574318i
$333$	52.9223	−	393.443i	0.158926	−	1.18151i
$334$	22.3267	+	38.6710i	0.0668464	+	0.115781i
$335$			132.713i			0.396157i
$336$	−33.9712	−	172.047i	−0.101105	−	0.512044i
$337$	137.925			0.409274			0.204637	−	0.978838i	$-0.434399\pi$
$337$	137.925			0.409274			0.204637	+	0.978838i	$0.434399\pi$
$338$	80.8706	−	46.6907i	0.239262	−	0.138138i
$339$	−148.345	+	435.001i	−0.437595	+	1.28319i
$340$	−71.7477	+	124.271i	−0.211023	+	0.365502i
$341$	153.029	−	88.3511i	0.448764	−	0.259094i
$342$	−36.9302	−	89.8705i	−0.107983	−	0.262779i
$343$	343.000			1.00000
$344$		−	59.0618i		−	0.171691i
$345$	−102.970	+	90.0470i	−0.298464	+	0.261006i
$346$	−114.526	+	198.365i	−0.331001	+	0.573310i
$347$	−19.3327	−	11.1617i	−0.0557137	−	0.0321663i	0.471884	−	0.881660i	$-0.343574\pi$
$347$	−19.3327	−	11.1617i	−0.0557137	−	0.0321663i	−0.527598	+	0.849494i	$0.676907\pi$
$348$	71.0228	+	81.2157i	0.204088	+	0.233379i
$349$	360.302			1.03239			0.516193	−	0.856472i	$-0.327349\pi$
$349$	360.302			1.03239			0.516193	+	0.856472i	$0.327349\pi$
$350$		−	28.7649i		−	0.0821854i
$351$	250.585	+	378.469i	0.713919	+	1.07826i
$352$	169.421	+	293.446i	0.481310	+	0.833653i
$353$	−64.2507	−	37.0952i	−0.182013	−	0.105085i	0.406225	−	0.913773i	$-0.366845\pi$
$353$	−64.2507	−	37.0952i	−0.182013	−	0.105085i	−0.588238	+	0.808688i	$0.700178\pi$
$354$	201.848	+	68.8345i	0.570193	+	0.194448i
$355$	53.7171	+	93.0407i	0.151316	+	0.262087i
$356$			173.837i			0.488305i
$357$	−266.843	−	305.139i	−0.747459	−	0.854732i
$358$	−97.3943			−0.272051
$359$	258.985	−	149.525i	0.721407	−	0.416505i	−0.0938632	−	0.995585i	$-0.529922\pi$
$359$	258.985	−	149.525i	0.721407	−	0.416505i	0.815270	+	0.579080i	$0.196588\pi$
$360$	16.1498	−	120.063i	0.0448605	−	0.333509i
$361$	94.2235	−	163.200i	0.261007	−	0.452077i
$362$	−20.6001	+	11.8935i	−0.0569064	+	0.0328549i
$363$	−0.627050	−	3.17569i	−0.00172741	−	0.00874846i
$364$	−195.616	+	338.817i	−0.537408	+	0.930817i
$365$		−	210.494i		−	0.576697i
$366$	178.977	+	204.663i	0.489009	+	0.559190i
$367$	−37.8246	+	65.5141i	−0.103064	+	0.178512i	−0.912946	−	0.408081i	$-0.866198\pi$
$367$	−37.8246	+	65.5141i	−0.103064	+	0.178512i	0.809881	+	0.586594i	$0.199531\pi$
$368$	−147.472	−	85.1429i	−0.400739	−	0.231367i
$369$	110.663	−	143.383i	0.299899	−	0.388572i
$370$	81.0612			0.219084
$371$	−18.1807	−	10.4966i	−0.0490046	−	0.0282928i
$372$	−31.1751	−	157.886i	−0.0838040	−	0.424425i
$373$	40.6712	+	70.4445i	0.109038	+	0.188859i	0.915381	−	0.402589i	$-0.131890\pi$
$373$	40.6712	+	70.4445i	0.109038	+	0.188859i	−0.806343	+	0.591448i	$0.798556\pi$
$374$	150.450	+	86.8624i	0.402273	+	0.232252i
$375$	−10.8260	+	31.7458i	−0.0288693	+	0.0846556i
$376$	−198.164	−	343.231i	−0.527033	−	0.912848i
$377$		−	181.857i		−	0.482379i
$378$	139.021	+	69.2872i	0.367781	+	0.183299i
$379$	195.302			0.515310			0.257655	−	0.966237i	$-0.417050\pi$
$379$	195.302			0.515310			0.257655	+	0.966237i	$0.417050\pi$
$380$	−84.5689	+	48.8259i	−0.222550	+	0.128489i
$381$	−612.944	−	209.027i	−1.60878	−	0.548626i
$382$	127.397	−	220.658i	0.333499	−	0.577638i
$383$	146.198	−	84.4077i	0.381719	−	0.220386i	−0.296847	−	0.954925i	$-0.595935\pi$
$383$	146.198	−	84.4077i	0.381719	−	0.220386i	0.678566	+	0.734540i	$0.262602\pi$
$384$	383.559	−	75.7349i	0.998852	−	0.197226i
$385$	171.408			0.445215
$386$			211.667i			0.548360i
$387$	−69.9038	−	53.9517i	−0.180630	−	0.139410i
$388$	66.8046	−	115.709i	0.172177	−	0.298219i
$389$	561.384	+	324.115i	1.44315	+	0.833201i	0.998058	−	0.0622862i	$-0.0198391\pi$
$389$	561.384	+	324.115i	1.44315	+	0.833201i	0.445088	+	0.895487i	$0.353172\pi$
$390$	−69.7693	+	61.0129i	−0.178896	+	0.156443i
$391$	−393.609			−1.00667
$392$			294.966i			0.752465i
$393$	−352.050	+	69.5134i	−0.895802	+	0.176879i
$394$	−34.4210	−	59.6189i	−0.0873629	−	0.151317i
$395$	184.909	+	106.758i	0.468125	+	0.270272i
$396$	324.736	+	43.6804i	0.820039	+	0.110304i
$397$	25.3552	+	43.9164i	0.0638669	+	0.110621i	0.896191	−	0.443669i	$-0.146323\pi$
$397$	25.3552	+	43.9164i	0.0638669	+	0.110621i	−0.832324	+	0.554290i	$0.812990\pi$
$398$		−	229.189i		−	0.575852i
$399$	−53.4366	−	270.630i	−0.133926	−	0.678270i
$400$	−41.7544			−0.104386
$401$	16.4294	−	9.48555i	0.0409712	−	0.0236547i	−0.479374	−	0.877610i	$-0.659136\pi$
$401$	16.4294	−	9.48555i	0.0409712	−	0.0236547i	0.520346	+	0.853956i	$0.325803\pi$
$402$	47.2318	−	138.501i	0.117492	−	0.344531i
$403$	−135.634	+	234.925i	−0.336560	+	0.582940i
$404$	49.6288	−	28.6532i	0.122843	−	0.0709237i
$405$	−127.351	−	128.790i	−0.314447	−	0.317999i
$406$	−31.1164	−	53.8951i	−0.0766413	−	0.132747i
$407$			483.037i			1.18682i
$408$	262.407	−	229.474i	0.643155	−	0.562437i
$409$	24.0527	−	41.6604i	0.0588085	−	0.101859i	−0.835122	−	0.550064i	$-0.814603\pi$
$409$	24.0527	−	41.6604i	0.0588085	−	0.101859i	0.893931	+	0.448205i	$0.147937\pi$
$410$	32.0286	+	18.4917i	0.0781186	+	0.0451018i
$411$	102.957	+	117.733i	0.250504	+	0.286455i
$412$	484.860			1.17684
$413$	524.357	+	302.738i	1.26963	+	0.733021i
$414$	139.509	−	57.3280i	0.336978	−	0.138473i
$415$	−128.246	−	222.128i	−0.309025	−	0.535248i
$416$	−450.489	−	260.090i	−1.08291	−	0.625216i
$417$	−180.653	−	61.6063i	−0.433220	−	0.147737i
$418$	59.1117	+	102.385i	0.141416	+	0.244939i
$419$			257.824i			0.615332i	0.951494	+	0.307666i	$0.0995480\pi$
$419$			257.824i			0.615332i	−0.951494	+	0.307666i	$0.900452\pi$
$420$	50.3883	−	147.757i	0.119972	−	0.351803i
$421$	−640.719			−1.52190			−0.760949	−	0.648812i	$-0.775266\pi$
$421$	−640.719			−1.52190			−0.760949	+	0.648812i	$0.775266\pi$
$422$	96.8381	−	55.9095i	0.229474	−	0.132487i
$423$	−587.257	−	78.9923i	−1.38831	−	0.186743i
$424$	9.02668	−	15.6347i	0.0212893	−	0.0368742i
$425$	−83.5834	+	48.2569i	−0.196667	+	0.113546i
$426$	−22.9473	−	116.217i	−0.0538670	−	0.272809i
$427$	385.952	+	668.488i	0.903868	+	1.56555i
$428$			606.510i			1.41708i
$429$	−363.571	−	415.750i	−0.847485	−	0.969113i
$430$	9.01530	−	15.6150i	0.0209658	−	0.0363139i
$431$	−237.998	−	137.408i	−0.552200	−	0.318813i	0.197809	−	0.980241i	$-0.436617\pi$
$431$	−237.998	−	137.408i	−0.552200	−	0.318813i	−0.750009	+	0.661428i	$0.769951\pi$
$432$	100.576	−	201.800i	0.232814	−	0.467129i
$433$	−57.2456			−0.132207			−0.0661034	−	0.997813i	$-0.521057\pi$
$433$	−57.2456			−0.132207			−0.0661034	+	0.997813i	$0.521057\pi$
$434$			92.8298i			0.213893i
$435$	14.0569	+	71.1913i	0.0323148	+	0.163658i
$436$	−228.906	−	396.476i	−0.525013	−	0.909349i
$437$	−231.973	−	133.930i	−0.530831	−	0.306476i
$438$	−74.9140	+	219.676i	−0.171037	+	0.501543i
$439$	101.958	+	176.597i	0.232251	+	0.402271i	0.958470	−	0.285192i	$-0.0920575\pi$
$439$	101.958	+	176.597i	0.232251	+	0.402271i	−0.726219	+	0.687464i	$0.758724\pi$
$440$			147.404i			0.335009i
$441$	349.114	+	269.445i	0.791641	+	0.610987i
$442$	−266.697			−0.603386
$443$	230.300	−	132.964i	0.519865	−	0.300144i	−0.217015	−	0.976168i	$-0.569632\pi$
$443$	230.300	−	132.964i	0.519865	−	0.300144i	0.736879	+	0.676024i	$0.236299\pi$
$444$	416.388	+	141.997i	0.937811	+	0.319813i
$445$	−58.4605	+	101.257i	−0.131372	+	0.227543i
$446$	−46.8942	+	27.0744i	−0.105144	+	0.0607049i
$447$	−636.043	+	125.589i	−1.42292	+	0.280959i
$448$	55.8157			0.124589
$449$		−	281.215i		−	0.626313i	−0.949702	−	0.313157i	$-0.898614\pi$
$449$		−	281.215i		−	0.626313i	0.949702	−	0.313157i	$-0.101386\pi$
$450$	22.5964	−	29.2776i	0.0502142	−	0.0650613i
$451$	−110.191	+	190.856i	−0.244325	+	0.423184i
$452$	−441.086	−	254.661i	−0.975854	−	0.563410i
$453$	−88.3708	+	77.2799i	−0.195079	+	0.170596i
$454$	23.6228			0.0520325
$455$	−227.886	+	131.570i	−0.500848	+	0.289165i
$456$	232.731	−	45.9534i	0.510374	−	0.100775i
$457$	−345.228	−	597.952i	−0.755422	−	1.30843i	−0.945164	−	0.326595i	$-0.894099\pi$
$457$	−345.228	−	597.952i	−0.755422	−	1.30843i	0.189743	−	0.981834i	$-0.439235\pi$
$458$	58.8095	+	33.9537i	0.128405	+	0.0741347i
$459$	−31.8954	−	520.198i	−0.0694889	−	1.13333i
$460$	−75.7939	−	131.279i	−0.164769	−	0.285389i
$461$		−	1.75543i		−	0.00380788i	−0.999998	−	0.00190394i	$-0.999394\pi$
$461$		−	1.75543i		−	0.00380788i	0.999998	−	0.00190394i	$-0.000606044\pi$
$462$	−178.884	−	61.0033i	−0.387195	−	0.132042i
$463$	−635.491			−1.37255			−0.686275	−	0.727342i	$-0.740756\pi$
$463$	−635.491			−1.37255			−0.686275	+	0.727342i	$0.740756\pi$
$464$	−78.2329	+	45.1678i	−0.168605	+	0.0973443i
$465$	34.9375	−	102.450i	0.0751345	−	0.220322i
$466$	104.513	−	181.022i	0.224277	−	0.388459i
$467$	181.111	−	104.565i	0.387819	−	0.223907i	−0.293396	−	0.955991i	$-0.594785\pi$
$467$	181.111	−	104.565i	0.387819	−	0.223907i	0.681215	+	0.732084i	$0.261452\pi$
$468$	−465.263	+	191.189i	−0.994151	+	0.408524i
$469$	207.728	−	359.796i	0.442917	−	0.767155i
$470$		−	120.993i		−	0.257431i
$471$	107.675	−	94.1612i	0.228609	−	0.199918i
$472$	−260.342	+	450.926i	−0.551573	+	0.955352i
$473$	93.0484	+	53.7215i	0.196720	+	0.113576i
$474$	−154.980	−	177.223i	−0.326963	−	0.373887i
$475$	−65.6797			−0.138273
$476$	389.029	−	224.606i	0.817287	−	0.471861i
$477$	−10.2591	−	24.9657i	−0.0215075	−	0.0523389i
$478$	−192.469	−	333.366i	−0.402655	−	0.697419i
$479$	−133.986	−	77.3570i	−0.279721	−	0.161497i	0.353576	−	0.935406i	$-0.384965\pi$
$479$	−133.986	−	77.3570i	−0.279721	−	0.161497i	−0.633297	+	0.773909i	$0.718299\pi$
$480$	196.456	+	66.9958i	0.409284	+	0.139575i
$481$	−370.772	−	642.196i	−0.770836	−	1.33513i
$482$		−	138.713i		−	0.287787i
$483$	420.107	−	82.9514i	0.869787	−	0.171742i
$484$	3.58720			0.00741157
$485$	77.8249	−	44.9322i	0.160464	−	0.0926438i
$486$	87.0700	+	179.731i	0.179156	+	0.369816i
$487$	161.895	−	280.410i	0.332433	−	0.575790i	−0.650556	−	0.759459i	$-0.725464\pi$
$487$	161.895	−	280.410i	0.332433	−	0.575790i	0.982988	+	0.183668i	$0.0587973\pi$
$488$	−574.873	+	331.903i	−1.17802	+	0.680129i
$489$	73.5395	+	372.440i	0.150388	+	0.761637i
$490$	−45.0242	+	77.9842i	−0.0918861	+	0.159151i
$491$		−	473.929i		−	0.965231i	−0.875832	−	0.482616i	$-0.839687\pi$
$491$		−	473.929i		−	0.965231i	0.875832	−	0.482616i	$-0.160313\pi$
$492$	132.129	+	151.092i	0.268556	+	0.307098i
$493$	−104.404	+	180.832i	−0.211772	+	0.366800i
$494$	−157.178	−	90.7465i	−0.318173	−	0.183697i
$495$	174.463	+	134.650i	0.352450	+	0.272021i
$496$	134.749			0.271672
$497$		−	336.322i		−	0.676704i
$498$	54.7851	+	277.459i	0.110010	+	0.557146i
$499$	279.302	+	483.766i	0.559724	+	0.969471i	0.997519	+	0.0703962i	$0.0224263\pi$
$499$	279.302	+	483.766i	0.559724	+	0.969471i	−0.437795	+	0.899075i	$0.644240\pi$
$500$	−32.1899	−	18.5848i	−0.0643797	−	0.0371697i
$501$	−52.6105	+	154.273i	−0.105011	+	0.307931i
$502$	−25.3292	−	43.8714i	−0.0504565	−	0.0873933i
$503$		−	549.856i		−	1.09315i	−0.837409	−	0.546577i	$-0.815931\pi$
$503$		−	549.856i		−	1.09315i	0.837409	−	0.546577i	$-0.184069\pi$
$504$	−231.712	+	300.224i	−0.459746	+	0.595682i
$505$	38.5438			0.0763243
$506$	−158.935	+	91.7611i	−0.314100	+	0.181346i
$507$	322.624	+	110.022i	0.636340	+	0.217005i
$508$	358.833	−	621.517i	0.706364	−	1.22346i
$509$	394.701	−	227.881i	0.775444	−	0.447703i	−0.0593694	−	0.998236i	$-0.518909\pi$
$509$	394.701	−	227.881i	0.775444	−	0.447703i	0.834813	+	0.550533i	$0.185576\pi$
$510$	104.404	−	20.6148i	0.204713	−	0.0404212i
$511$	−329.476	+	570.669i	−0.644767	+	1.11677i
$512$			459.474i			0.897410i
$513$	158.205	−	317.431i	0.308392	−	0.618773i
$514$	6.64484	−	11.5092i	0.0129277	−	0.0223914i
$515$	282.422	+	163.056i	0.548392	+	0.316614i
$516$	73.6622	−	64.4173i	0.142756	−	0.124840i
$517$	720.986			1.39456
$518$	−219.764	−	126.881i	−0.424255	−	0.244944i
$519$	−820.269	+	161.965i	−1.58048	+	0.312071i
$520$	−113.145	−	195.973i	−0.217586	−	0.376870i
$521$	−183.521	−	105.956i	−0.352248	−	0.203371i	0.313427	−	0.949612i	$-0.398523\pi$
$521$	−183.521	−	105.956i	−0.352248	−	0.203371i	−0.665675	+	0.746242i	$0.731856\pi$
$522$	10.6666	−	79.2993i	0.0204341	−	0.151914i
$523$	306.427	+	530.748i	0.585903	+	1.01481i	0.994762	+	0.102217i	$0.0325935\pi$
$523$	306.427	+	530.748i	0.585903	+	1.01481i	−0.408859	+	0.912598i	$0.634073\pi$
$524$		−	397.669i		−	0.758911i
$525$	79.0403	−	69.1204i	0.150553	−	0.131658i
$526$	−65.9388			−0.125359
$527$	269.739	−	155.734i	0.511839	−	0.295511i
$528$	−88.5509	+	259.664i	−0.167710	+	0.491788i
$529$	−56.5964	+	98.0279i	−0.106988	+	0.185308i
$530$	4.77301	−	2.75570i	0.00900568	−	0.00519943i
$531$	295.886	+	720.045i	0.557224	+	1.35602i
$532$	305.698			0.574621
$533$		−	338.323i		−	0.634752i
$534$	97.0472	−	84.8673i	0.181736	−	0.158928i
$535$	−203.967	+	353.281i	−0.381247	+	0.660338i
$536$	309.410	+	178.638i	0.577257	+	0.333280i
$537$	−234.033	−	267.620i	−0.435815	−	0.498362i
$538$	417.176			0.775420
$539$	−464.702	−	268.296i	−0.862155	−	0.497766i
$540$	167.358	−	110.808i	0.309922	−	0.205200i
$541$	−147.985	−	256.317i	−0.273539	−	0.473784i	0.696226	−	0.717822i	$-0.254861\pi$
$541$	−147.985	−	256.317i	−0.273539	−	0.473784i	−0.969766	+	0.244039i	$0.921528\pi$
$542$	63.6388	+	36.7419i	0.117415	+	0.0677894i
$543$	−82.1819	−	28.0257i	−0.151348	−	0.0516128i
$544$	298.634	+	517.249i	0.548959	+	0.950825i
$545$		−	307.920i		−	0.564991i
$546$	284.651	−	56.2052i	0.521339	−	0.102940i
$547$	517.246			0.945604			0.472802	−	0.881169i	$-0.343243\pi$
$547$	517.246			0.945604			0.472802	+	0.881169i	$0.343243\pi$
$548$	−150.101	+	86.6606i	−0.273906	+	0.158140i
$549$	−132.303	+	983.589i	−0.240989	+	1.79160i
$550$	−22.5000	+	38.9711i	−0.0409091	+	0.0708566i
$551$	−123.060	+	71.0489i	−0.223340	+	0.128945i
$552$	71.3349	+	361.275i	0.129230	+	0.654484i
$553$	−334.204	−	578.858i	−0.604347	−	1.04676i
$554$		−	7.95883i		−	0.0143661i
$555$	194.785	+	222.740i	0.350965	+	0.401334i
$556$	105.759	−	183.179i	0.190214	−	0.329459i
$557$	521.373	+	301.015i	0.936038	+	0.540422i	0.888716	−	0.458458i	$-0.151598\pi$
$557$	521.373	+	301.015i	0.936038	+	0.540422i	0.0473217	+	0.998880i	$0.484931\pi$
$558$	−72.9229	+	94.4843i	−0.130686	+	0.169327i
$559$	−164.943			−0.295068
$560$	113.200	+	65.3560i	0.202143	+	0.116707i
$561$	122.842	+	622.133i	0.218970	+	1.10897i
$562$	119.283	+	206.603i	0.212247	+	0.367622i
$563$	−314.754	−	181.723i	−0.559066	−	0.322777i	0.193704	−	0.981060i	$-0.437950\pi$
$563$	−314.754	−	181.723i	−0.559066	−	0.322777i	−0.752771	+	0.658283i	$0.771283\pi$
$564$	211.946	−	621.505i	0.375791	−	1.10196i
$565$	−171.283	−	296.671i	−0.303156	−	0.525081i
$566$		−	381.254i		−	0.673593i
$567$	143.672	+	548.496i	0.253390	+	0.967364i
$568$	289.223			0.509196
$569$	−922.402	+	532.549i	−1.62109	+	0.935938i	−0.634464	+	0.772952i	$0.718779\pi$
$569$	−922.402	+	532.549i	−1.62109	+	0.935938i	−0.986628	+	0.162986i	$0.947888\pi$
$570$	68.5445	+	23.3751i	0.120254	+	0.0410090i
$571$	−49.9125	+	86.4509i	−0.0874123	+	0.151403i	−0.906417	−	0.422385i	$-0.861193\pi$
$571$	−49.9125	+	86.4509i	−0.0874123	+	0.151403i	0.819004	+	0.573787i	$0.194526\pi$
$572$	530.048	−	306.023i	0.926658	−	0.535006i
$573$	912.451	−	180.166i	1.59241	−	0.314426i
$574$	−57.8883	−	100.265i	−0.100851	−	0.174678i
$575$		−	101.957i		−	0.177316i
$576$	56.8105	+	43.8463i	0.0986293	+	0.0761220i
$577$	−464.160	+	803.948i	−0.804436	+	1.39332i	0.112235	+	0.993682i	$0.464199\pi$
$577$	−464.160	+	803.948i	−0.804436	+	1.39332i	−0.916671	+	0.399643i	$0.869134\pi$
$578$	59.4995	+	34.3521i	0.102940	+	0.0594326i
$579$	−581.619	+	508.623i	−1.00452	+	0.878452i
$580$	−80.4164			−0.138649
$581$			802.944i			1.38200i
$582$	−97.2107	+	19.1945i	−0.167029	+	0.0329803i
$583$	16.4210	+	28.4420i	0.0281664	+	0.0487856i
$584$	−490.752	−	283.336i	−0.840329	−	0.485164i
$585$	−335.303	−	45.1018i	−0.573167	−	0.0770971i
$586$	49.5178	+	85.7673i	0.0845013	+	0.146361i
$587$			524.505i			0.893535i	0.894650	+	0.446768i	$0.147425\pi$
$587$			524.505i			0.893535i	−0.894650	+	0.446768i	$0.852575\pi$
$588$	−367.883	+	321.712i	−0.625652	+	0.547130i
$589$	211.961			0.359866
$590$	−137.660	+	79.4783i	−0.233323	+	0.134709i
$591$	81.1094	−	237.843i	0.137241	−	0.402442i
$592$	−184.177	+	319.004i	−0.311110	+	0.538859i
$593$	−8.04147	+	4.64275i	−0.0135607	+	0.00782925i	−0.506765	−	0.862084i	$-0.669159\pi$
$593$	−8.04147	+	4.64275i	−0.0135607	+	0.00782925i	0.493204	+	0.869913i	$0.335825\pi$
$594$	−134.151	−	202.614i	−0.225844	−	0.341101i
$595$	302.136			0.507792
$596$		−	718.463i		−	1.20547i
$597$	629.767	−	550.728i	1.05489	−	0.922493i
$598$	140.869	−	243.992i	0.235566	−	0.408013i
$599$	−362.110	−	209.065i	−0.604525	−	0.349023i	0.166295	−	0.986076i	$-0.446820\pi$
$599$	−362.110	−	209.065i	−0.604525	−	0.349023i	−0.770820	+	0.637053i	$0.780153\pi$
$600$	59.4408	+	67.9715i	0.0990679	+	0.113286i
$601$	500.377			0.832574			0.416287	−	0.909233i	$-0.363331\pi$
$601$	500.377			0.832574			0.416287	+	0.909233i	$0.363331\pi$
$602$	−48.8826	+	28.2224i	−0.0812003	+	0.0468810i
$603$	494.070	−	203.027i	0.819353	−	0.336694i
$604$	−65.0477	−	112.666i	−0.107695	−	0.186533i
$605$	2.08948	+	1.20636i	0.00345368	+	0.00199399i
$606$	−40.2250	−	13.7176i	−0.0663779	−	0.0226362i
$607$	−196.368	−	340.120i	−0.323506	−	0.560329i	0.657703	−	0.753278i	$-0.271528\pi$
$607$	−196.368	−	340.120i	−0.323506	−	0.560329i	−0.981209	+	0.192948i	$0.938195\pi$
$608$			406.454i			0.668509i
$609$	73.3224	−	215.009i	0.120398	−	0.353052i
$610$	−202.649			−0.332212
$611$	−958.548	+	553.418i	−1.56882	+	0.905757i
$612$	572.403	+	76.9942i	0.935299	+	0.125808i
$613$	−104.735	+	181.406i	−0.170856	+	0.295931i	−0.938719	−	0.344683i	$-0.887987\pi$
$613$	−104.735	+	181.406i	−0.170856	+	0.295931i	0.767864	+	0.640613i	$0.221320\pi$
$614$	−60.3516	+	34.8440i	−0.0982925	+	0.0567492i
$615$	26.1512	+	132.443i	0.0425224	+	0.215354i
$616$	230.723	−	399.625i	0.374551	−	0.648742i
$617$		−	1002.43i		−	1.62469i	−0.583176	−	0.812346i	$-0.698190\pi$
$617$		−	1002.43i		−	1.62469i	0.583176	−	0.812346i	$-0.301810\pi$
$618$	−236.709	−	270.681i	−0.383025	−	0.437995i
$619$	272.870	−	472.626i	0.440825	−	0.763531i	−0.556926	−	0.830562i	$-0.688019\pi$
$619$	272.870	−	472.626i	0.440825	−	0.763531i	0.997751	+	0.0670313i	$0.0213527\pi$
$620$	103.883	+	59.9768i	0.167553	+	0.0967367i
$621$	492.758	+	245.587i	0.793491	+	0.395471i
$622$	419.552			0.674520
$623$	316.983	−	183.010i	0.508801	−	0.293757i
$624$	−81.5861	−	413.192i	−0.130747	−	0.662167i
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	81.7947	+	47.2242i	0.130662	+	0.0754380i
$627$	−139.291	+	408.452i	−0.222154	+	0.651438i
$628$	79.2569	+	137.277i	0.126205	+	0.218594i
$629$			851.437i			1.35364i
$630$	−107.088	+	44.0052i	−0.169980	+	0.0698495i
$631$	−101.662			−0.161112			−0.0805562	−	0.996750i	$-0.525670\pi$
$631$	−101.662			−0.161112			−0.0805562	+	0.996750i	$0.525670\pi$
$632$	497.795	−	287.402i	0.787650	−	0.454750i
$633$	386.325	+	131.745i	0.610307	+	0.208128i
$634$	−200.720	+	347.656i	−0.316592	+	0.548354i
$635$	418.027	−	241.348i	0.658311	−	0.380076i
$636$	29.3448	−	5.79423i	0.0461397	−	0.00911042i
$637$	823.758			1.29318
$638$			97.3573i			0.152598i
$639$	264.199	−	342.317i	0.413458	−	0.535707i
$640$	−145.704	+	252.367i	−0.227662	+	0.394323i
$641$	296.558	+	171.218i	0.462649	+	0.267110i	0.713157	−	0.701004i	$-0.247265\pi$
$641$	296.558	+	171.218i	0.462649	+	0.267110i	−0.250509	+	0.968114i	$0.580598\pi$
$642$	338.595	−	296.100i	0.527406	−	0.461214i
$643$	−362.904			−0.564392			−0.282196	−	0.959357i	$-0.591063\pi$
$643$	−362.904			−0.564392			−0.282196	+	0.959357i	$0.591063\pi$
$644$			474.545i			0.736871i
$645$	64.5701	−	12.7496i	0.100109	−	0.0197668i
$646$	104.195	+	180.470i	0.161292	+	0.279366i
$647$	399.162	+	230.456i	0.616942	+	0.356192i	0.775678	−	0.631129i	$-0.217408\pi$
$647$	399.162	+	230.456i	0.616942	+	0.356192i	−0.158735	+	0.987321i	$0.550742\pi$
$648$	−471.684	+	123.552i	−0.727908	+	0.190667i
$649$	−473.605	−	820.308i	−0.729746	−	1.26396i
$650$		−	69.0826i		−	0.106281i
$651$	−255.078	+	223.065i	−0.391825	+	0.342649i
$652$	−420.702			−0.645248
$653$	−636.951	+	367.744i	−0.975422	+	0.563160i	−0.900885	−	0.434058i	$-0.857081\pi$
$653$	−636.951	+	367.744i	−0.975422	+	0.563160i	−0.0745371	+	0.997218i	$0.523748\pi$
$654$	−109.587	+	321.351i	−0.167565	+	0.491362i
$655$	133.735	−	231.635i	0.204175	−	0.353641i
$656$	−145.543	+	84.0292i	−0.221864	+	0.128093i
$657$	−783.640	+	322.019i	−1.19275	+	0.490135i
$658$	−189.384	+	328.022i	−0.287817	+	0.498514i
$659$		−	959.450i		−	1.45592i	−0.685621	−	0.727959i	$-0.740469\pi$
$659$		−	959.450i		−	1.45592i	0.685621	−	0.727959i	$-0.259531\pi$
$660$	−183.843	+	160.770i	−0.278550	+	0.243591i
$661$	−124.816	+	216.187i	−0.188829	+	0.327061i	−0.944860	−	0.327475i	$-0.893802\pi$
$661$	−124.816	+	216.187i	−0.188829	+	0.327061i	0.756031	+	0.654535i	$0.227136\pi$
$662$	151.699	+	87.5834i	0.229152	+	0.132301i
$663$	−640.857	−	732.831i	−0.966602	−	1.10533i
$664$	−690.500			−1.03991
$665$	178.064	+	102.805i	0.267765	+	0.154594i
$666$	−124.009	−	301.779i	−0.186200	−	0.453122i
$667$	−110.291	−	191.030i	−0.165355	−	0.286402i
$668$	−156.431	−	90.3157i	−0.234179	−	0.135203i
$669$	−187.079	−	63.7979i	−0.279640	−	0.0953632i
$670$	54.5352	+	94.4578i	0.0813959	+	0.140982i
$671$		−	1207.57i		−	1.79966i
$672$	−427.746	−	489.134i	−0.636527	−	0.727879i
$673$	527.512			0.783822			0.391911	−	0.920003i	$-0.371814\pi$
$673$	527.512			0.783822			0.391911	+	0.920003i	$0.371814\pi$
$674$	98.1679	−	56.6772i	0.145650	−	0.0840909i
$675$	134.747	−	8.26188i	0.199625	−	0.0122398i
$676$	−188.873	+	327.137i	−0.279397	+	0.483930i
$677$	−433.266	+	250.146i	−0.639980	+	0.369493i	−0.784607	−	0.619994i	$-0.787135\pi$
$677$	−433.266	+	250.146i	−0.639980	+	0.369493i	0.144627	+	0.989486i	$0.453802\pi$
$678$	73.1701	+	370.570i	0.107921	+	0.546563i
$679$	−281.320			−0.414316
$680$			259.825i			0.382095i
$681$	56.7642	+	64.9108i	0.0833541	+	0.0953168i
$682$	72.6117	−	125.767i	0.106469	−	0.184409i
$683$	12.3930	+	7.15511i	0.0181450	+	0.0104760i	0.509045	−	0.860740i	$-0.329999\pi$
$683$	12.3930	+	7.15511i	0.0181450	+	0.0104760i	−0.490900	+	0.871216i	$0.663332\pi$
$684$	311.147	+	240.143i	0.454893	+	0.351086i
$685$	−116.574			−0.170182
$686$	244.129	−	140.948i	0.355873	−	0.205464i
$687$	48.0178	+	243.186i	0.0698949	+	0.353982i
$688$	40.9669	+	70.9568i	0.0595449	+	0.103135i
$689$	−43.6633	−	25.2090i	−0.0633719	−	0.0365878i
$690$	−36.2860	+	106.404i	−0.0525884	+	0.154209i
$691$	268.562	+	465.162i	0.388656	+	0.673173i	0.992269	−	0.124105i	$-0.0396060\pi$
$691$	268.562	+	465.162i	0.388656	+	0.673173i	−0.603613	+	0.797278i	$0.706273\pi$
$692$		−	926.561i		−	1.33896i
$693$	−262.223	−	638.126i	−0.378389	−	0.920817i
$694$	−18.3466			−0.0264360
$695$	123.205	−	71.1324i	0.177273	−	0.102349i
$696$	184.899	+	63.0543i	0.265659	+	0.0905953i
$697$	−194.230	+	336.417i	−0.278666	+	0.482664i
$698$	256.444	−	148.058i	0.367398	−	0.212118i
$699$	748.552	−	147.804i	1.07089	−	0.211451i
$700$	58.1797	+	100.770i	0.0831139	+	0.143957i
$701$			618.842i			0.882799i	0.897311	+	0.441399i	$0.145518\pi$
$701$			618.842i			0.882799i	−0.897311	+	0.441399i	$0.854482\pi$
$702$	333.877	+	166.402i	0.475608	+	0.237040i
$703$	−289.711	+	501.794i	−0.412106	+	0.713789i
$704$	−75.6199	−	43.6592i	−0.107415	−	0.0620159i
$705$	332.464	−	290.739i	0.471581	−	0.412395i
$706$	−60.9737			−0.0863650
$707$	−104.496	−	60.3305i	−0.147801	−	0.0853332i
$708$	−846.347	+	167.114i	−1.19540	+	0.236036i
$709$	242.721	+	420.406i	0.342343	+	0.592956i	0.984867	−	0.173310i	$-0.0554461\pi$
$709$	242.721	+	420.406i	0.342343	+	0.592956i	−0.642524	+	0.766265i	$0.722113\pi$
$710$	76.4659	+	44.1476i	0.107698	+	0.0621797i
$711$	114.564	−	851.711i	0.161131	−	1.19791i
$712$	157.381	+	272.593i	0.221041	+	0.382855i
$713$			329.034i			0.461478i
$714$	−315.315	−	107.529i	−0.441617	−	0.150601i
$715$	411.658			0.575745
$716$	341.195	−	196.989i	0.476530	−	0.275125i
$717$	453.533	−	1329.93i	0.632542	−	1.85485i
$718$	122.888	−	212.848i	0.171153	−	0.296446i
$719$	−750.521	+	433.314i	−1.04384	+	0.602661i	−0.920919	−	0.389755i	$-0.872560\pi$
$719$	−750.521	+	433.314i	−1.04384	+	0.602661i	−0.122922	+	0.992416i	$0.539226\pi$
$720$	63.8769	+	155.446i	0.0887179	+	0.215897i
$721$	−510.447	−	884.120i	−0.707971	−	1.22624i
$722$		−	154.876i		−	0.214510i
$723$	381.157	−	333.320i	0.527188	−	0.461023i
$724$	48.1114	−	83.3314i	0.0664522	−	0.115099i
$725$	−46.8410	−	27.0437i	−0.0646083	−	0.0373016i
$726$	−1.75128	−	2.00262i	−0.00241223	−	0.00275843i
$727$	−823.719			−1.13304			−0.566519	−	0.824049i	$-0.691710\pi$
$727$	−823.719			−1.13304			−0.566519	+	0.824049i	$0.691710\pi$
$728$			708.399i			0.973075i
$729$	−284.641	+	671.134i	−0.390453	+	0.920623i
$730$	−86.4979	−	149.819i	−0.118490	−	0.205231i
$731$	164.014	+	94.6934i	0.224369	+	0.129540i
$732$	−1040.95	−	354.986i	−1.42206	−	0.484953i
$733$	−385.164	−	667.124i	−0.525463	−	0.910129i	−0.999560	−	0.0296561i	$-0.990559\pi$
$733$	−385.164	−	667.124i	−0.525463	−	0.910129i	0.474097	−	0.880473i	$-0.342775\pi$
$734$			62.1726i			0.0847038i
$735$	−322.476	+	63.6738i	−0.438743	+	0.0866311i
$736$	−630.951			−0.857270
$737$	−562.867	+	324.971i	−0.763727	+	0.440938i
$738$	19.8439	−	147.527i	0.0268888	−	0.199901i
$739$	473.730	−	820.525i	0.641042	−	1.11032i	−0.344158	−	0.938912i	$-0.611836\pi$
$739$	473.730	−	820.525i	0.641042	−	1.11032i	0.985200	−	0.171406i	$-0.0548310\pi$
$740$	−283.977	+	163.954i	−0.383752	+	0.221559i
$741$	−128.335	−	649.951i	−0.173191	−	0.877127i
$742$	−17.2534			−0.0232526
$743$		−	453.804i		−	0.610773i	−0.952229	−	0.305386i	$-0.901214\pi$
$743$		−	453.804i		−	0.610773i	0.952229	−	0.305386i	$-0.0987856\pi$
$744$	−191.827	−	219.357i	−0.257831	−	0.294834i
$745$	241.616	−	418.491i	0.324317	−	0.561733i
$746$	57.8952	+	33.4258i	0.0776074	+	0.0448067i
$747$	−630.757	+	817.256i	−0.844386	+	1.09405i
$748$	−702.749			−0.939505
$749$	1105.94	−	638.517i	1.47656	−	0.852493i
$750$	5.33986	+	27.0437i	0.00711981	+	0.0360583i
$751$	−284.698	−	493.111i	−0.379091	−	0.656605i	0.611839	−	0.790982i	$-0.290430\pi$
$751$	−284.698	−	493.111i	−0.379091	−	0.656605i	−0.990930	+	0.134377i	$0.957097\pi$
$752$	476.149	+	274.905i	0.633177	+	0.365565i
$753$	59.6855	−	175.020i	0.0792636	−	0.232430i
$754$	−74.7299	−	129.436i	−0.0991113	−	0.171666i
$755$		−	87.5011i		−	0.115895i
$756$	−627.163	+	38.4539i	−0.829581	+	0.0508649i
$757$	58.6050			0.0774174			0.0387087	−	0.999251i	$-0.487676\pi$
$757$	58.6050			0.0774174			0.0387087	+	0.999251i	$0.487676\pi$
$758$	139.006	−	80.2551i	0.183385	−	0.105877i
$759$	−634.053	−	216.225i	−0.835379	−	0.284882i
$760$	−88.4082	+	153.127i	−0.116327	+	0.201483i
$761$	−211.873	+	122.325i	−0.278413	+	0.160742i	−0.632705	−	0.774393i	$-0.718055\pi$
$761$	−211.873	+	122.325i	−0.278413	+	0.160742i	0.354292	+	0.935135i	$0.384722\pi$
$762$	−522.156	+	103.101i	−0.685243	+	0.135303i
$763$	−481.971	+	834.799i	−0.631679	+	1.09410i
$764$			1030.69i			1.34907i
$765$	307.521	+	237.344i	0.401988	+	0.310254i
$766$	69.3708	−	120.154i	0.0905624	−	0.156859i
$767$	1259.31	+	727.063i	1.64187	+	0.947931i
$768$	169.848	−	148.531i	0.221156	−	0.193400i
$769$	113.790			0.147971			0.0739857	−	0.997259i	$-0.476428\pi$
$769$	113.790			0.147971			0.0739857	+	0.997259i	$0.476428\pi$
$770$	121.999	−	70.4361i	0.158440	−	0.0914755i
$771$	47.5922	−	9.39722i	0.0617278	−	0.0121884i
$772$	−428.116	−	741.519i	−0.554555	−	0.960517i
$773$	47.5310	+	27.4420i	0.0614890	+	0.0355007i	0.530429	−	0.847729i	$-0.322031\pi$
$773$	47.5310	+	27.4420i	0.0614890	+	0.0355007i	−0.468940	+	0.883230i	$0.655364\pi$
$774$	−71.9240	−	9.67454i	−0.0929251	−	0.0124994i
$775$	40.3399	+	69.8707i	0.0520514	+	0.0901557i
$776$		−	241.924i		−	0.311758i
$777$	−179.437	−	908.756i	−0.230935	−	1.16957i
$778$	532.751			0.684770
$779$	−228.939	+	132.178i	−0.293888	+	0.169676i
$780$	121.014	−	354.857i	0.155146	−	0.454945i
$781$	−263.072	+	455.654i	−0.336840	+	0.583424i
$782$	−280.150	+	161.745i	−0.358248	+	0.206835i
$783$	243.530	−	161.242i	0.311022	−	0.205928i
$784$	−204.597	−	354.372i	−0.260965	−	0.452005i
$785$			106.615i			0.135815i
$786$	−222.006	+	194.143i	−0.282450	+	0.247001i
$787$	76.6100	−	132.692i	0.0973443	−	0.168605i	−0.813240	−	0.581928i	$-0.802299\pi$
$787$	76.6100	−	132.692i	0.0973443	−	0.168605i	0.910585	+	0.413323i	$0.135632\pi$
$788$	241.170	+	139.239i	0.306053	+	0.176700i
$789$	−158.447	−	181.187i	−0.200820	−	0.229641i
$790$	175.478			0.222124
$791$			1072.40i			1.35575i
$792$	548.763	−	225.502i	0.692883	−	0.284724i
$793$	926.912	+	1605.46i	1.16887	+	2.02454i
$794$	36.0929	+	20.8383i	0.0454571	+	0.0262447i
$795$	19.0414	+	6.49351i	0.0239514	+	0.00816794i
$796$	463.557	+	802.904i	0.582358	+	1.00867i
$797$		−	137.401i		−	0.172398i	−0.996278	−	0.0861990i	$-0.972528\pi$
$797$		−	137.401i		−	0.172398i	0.996278	−	0.0861990i	$-0.0274721\pi$
$798$	−149.242	−	170.661i	−0.187021	−	0.213861i
$799$	1270.86			1.59057
$800$	−133.983	+	77.3552i	−0.167479	+	0.0966940i
$801$	466.398	+	62.7354i	0.582269	+	0.0783214i
$802$	7.79574	−	13.5026i	0.00972037	−	0.0168362i
$803$	892.758	−	515.434i	1.11178	−	0.641885i
$804$	114.668	+	580.733i	0.142621	+	0.722305i
$805$	−159.588	+	276.414i	−0.198245	+	0.343371i
$806$			222.942i			0.276604i
$807$	1002.45	+	1146.32i	1.24219	+	1.42047i
$808$	51.8818	−	89.8620i	0.0642102	−	0.111215i
$809$	673.166	+	388.652i	0.832096	+	0.480411i	0.854570	−	0.519337i	$-0.173821\pi$
$809$	673.166	+	388.652i	0.832096	+	0.480411i	−0.0224739	+	0.999747i	$0.507154\pi$
$810$	−143.565	−	39.3336i	−0.177240	−	0.0485600i
$811$	−592.584			−0.730683			−0.365341	−	0.930874i	$-0.619048\pi$
$811$	−592.584			−0.730683			−0.365341	+	0.930874i	$0.619048\pi$
$812$	218.016	+	125.872i	0.268492	+	0.155014i
$813$	51.9608	+	263.155i	0.0639125	+	0.323684i
$814$	198.493	+	343.800i	0.243849	+	0.422359i
$815$	−245.051	−	141.480i	−0.300676	−	0.173595i
$816$	−156.086	+	457.703i	−0.191282	+	0.560911i
$817$	64.4409	+	111.615i	0.0788751	+	0.136616i
$818$		−	39.5356i		−	0.0483320i
$819$	838.440	+	647.107i	1.02374	+	0.790118i
$820$	−149.605			−0.182445
$821$	486.079	−	280.638i	0.592057	−	0.341824i	−0.173853	−	0.984772i	$-0.555622\pi$
$821$	486.079	−	280.638i	0.592057	−	0.341824i	0.765911	+	0.642947i	$0.222289\pi$
$822$	121.659	+	41.4883i	0.148004	+	0.0504724i
$823$	477.065	−	826.302i	0.579666	−	1.00401i	−0.415851	−	0.909433i	$-0.636516\pi$
$823$	477.065	−	826.302i	0.579666	−	1.00401i	0.995517	−	0.0945789i	$-0.0301505\pi$
$824$	760.308	−	438.964i	0.922704	−	0.532723i
$825$	−161.151	+	31.8198i	−0.195335	+	0.0385695i
$826$	497.613			0.602437
$827$			803.925i			0.972097i	0.873932	+	0.486049i	$0.161562\pi$
$827$			803.925i			0.972097i	−0.873932	+	0.486049i	$0.838438\pi$
$828$	−372.781	+	483.003i	−0.450219	+	0.583337i
$829$	647.028	−	1120.69i	0.780492	−	1.35185i	−0.151163	−	0.988509i	$-0.548302\pi$
$829$	647.028	−	1120.69i	0.780492	−	1.35185i	0.931655	−	0.363343i	$-0.118365\pi$
$830$	−182.557	−	105.399i	−0.219948	−	0.126987i
$831$	21.8693	−	19.1246i	0.0263169	−	0.0230140i
$832$	134.048			0.161116
$833$	−819.117	−	472.918i	−0.983334	−	0.567728i
$834$	−153.895	+	30.3870i	−0.184526	+	0.0364352i
$835$	−60.7456	−	105.214i	−0.0727492	−	0.126005i
$836$	−414.165	−	239.118i	−0.495412	−	0.286026i
$837$	−434.854	+	26.6626i	−0.519539	+	0.0318550i
$838$	105.947	+	183.506i	0.126428	+	0.218980i
$839$		−	763.470i		−	0.909976i	−0.890498	−	0.454988i	$-0.849644\pi$
$839$		−	763.470i		−	0.909976i	0.890498	−	0.454988i	$-0.150356\pi$
$840$	−54.7569	−	277.316i	−0.0651868	−	0.330138i
$841$	723.982			0.860859
$842$	−456.030	+	263.289i	−0.541603	+	0.312695i
$843$	−281.077	+	824.221i	−0.333424	+	0.977724i
$844$	−226.164	+	391.728i	−0.267967	+	0.464133i
$845$	−220.030	+	127.034i	−0.260390	+	0.150336i
$846$	−450.438	+	185.097i	−0.532433	+	0.218791i
$847$	−3.77651	−	6.54110i	−0.00445869	−	0.00772267i
$848$			25.0446i			0.0295338i
$849$	1047.61	−	916.131i	1.23394	−	1.07907i
$850$	−39.6601	+	68.6934i	−0.0466590	+	0.0808157i
$851$	−778.950	−	449.727i	−0.915335	−	0.528469i
$852$	315.449	+	360.721i	0.370245	+	0.423382i
$853$	−697.530			−0.817738			−0.408869	−	0.912593i	$-0.634077\pi$
$853$	−697.530			−0.817738			−0.408869	+	0.912593i	$0.634077\pi$
$854$	549.400	+	317.196i	0.643325	+	0.371424i
$855$	100.478	+	244.516i	0.117518	+	0.285984i
$856$	549.099	+	951.068i	0.641471	+	1.11106i
$857$	−864.347	−	499.031i	−1.00857	−	0.582300i	−0.0977997	−	0.995206i	$-0.531180\pi$
$857$	−864.347	−	499.031i	−1.00857	−	0.582300i	−0.910774	+	0.412906i	$0.864514\pi$
$858$	−429.613	−	146.507i	−0.500715	−	0.170754i
$859$	774.157	+	1340.88i	0.901231	+	1.56098i	0.825898	+	0.563819i	$0.190669\pi$
$859$	774.157	+	1340.88i	0.901231	+	1.56098i	0.0753326	+	0.997158i	$0.475998\pi$
$860$			72.9372i			0.0848107i
$861$	136.408	−	399.997i	0.158429	−	0.464573i
$862$	−225.859			−0.262018
$863$	−633.732	+	365.885i	−0.734336	+	0.423969i	−0.820006	−	0.572354i	$-0.806030\pi$
$863$	−633.732	+	365.885i	−0.734336	+	0.423969i	0.0856701	+	0.996324i	$0.472697\pi$
$864$	−51.1279	−	833.870i	−0.0591759	−	0.965128i
$865$	311.599	−	539.705i	0.360230	−	0.623936i
$866$	−40.7443	+	23.5238i	−0.0470489	+	0.0271637i
$867$	48.5811	+	246.039i	0.0560336	+	0.283782i
$868$	−187.757	−	325.205i	−0.216310	−	0.374660i
$869$			1045.66i			1.20329i
$870$	39.2594	+	44.8938i	0.0451258	+	0.0516021i
$871$	498.885	−	864.095i	0.572773	−	0.992072i
$872$	−717.893	−	414.476i	−0.823272	−	0.475316i
$873$	−286.334	−	220.992i	−0.327989	−	0.253141i
$874$	−220.142			−0.251878
$875$			78.2624i			0.0894427i
$876$	−181.873	−	921.096i	−0.207618	−	1.05148i
$877$	−71.6249	−	124.058i	−0.0816704	−	0.141457i	0.822297	−	0.569058i	$-0.192692\pi$
$877$	−71.6249	−	124.058i	−0.0816704	−	0.141457i	−0.903968	+	0.427601i	$0.859359\pi$
$878$	145.137	+	83.7949i	0.165304	+	0.0954384i
$879$	−116.683	+	342.159i	−0.132746	+	0.389259i
$880$	−102.243	−	177.091i	−0.116186	−	0.201240i
$881$			1661.69i			1.88614i	0.332591	+	0.943071i	$0.392077\pi$
$881$			1661.69i			1.88614i	−0.332591	+	0.943071i	$0.607923\pi$
$882$	359.203	+	48.3166i	0.407259	+	0.0547807i
$883$	565.057			0.639929			0.319964	−	0.947430i	$-0.396329\pi$
$883$	565.057			0.639929			0.319964	+	0.947430i	$0.396329\pi$
$884$	934.302	−	539.419i	1.05690	−	0.610203i
$885$	−549.181	−	187.282i	−0.620543	−	0.211618i
$886$	109.277	−	189.273i	0.123337	−	0.213626i
$887$	110.302	−	63.6829i	0.124354	−	0.0717958i	−0.436533	−	0.899688i	$-0.643794\pi$
$887$	110.302	−	63.6829i	0.124354	−	0.0717958i	0.560887	+	0.827893i	$0.310460\pi$
$888$	781.494	−	154.308i	0.880060	−	0.173771i
$889$	−1511.08			−1.69975
$890$			96.0920i			0.107969i
$891$	234.386	−	855.491i	0.263059	−	0.960147i
$892$	109.521	−	189.696i	0.122781	−	0.212664i
$893$	748.982	+	432.425i	0.838726	+	0.484239i
$894$	−401.094	+	350.755i	−0.448651	+	0.392343i
$895$	264.986			0.296074
$896$	790.032	−	456.125i	0.881733	−	0.509069i
$897$	1008.94	−	199.218i	1.12479	−	0.222094i
$898$	−115.559	−	200.154i	−0.128685	−	0.222888i
$899$	151.165	+	87.2751i	0.168148	+	0.0970802i
$900$	−19.9438	+	148.270i	−0.0221598	+	0.164744i
$901$	28.9448	+	50.1339i	0.0321252	+	0.0556426i
$902$			181.122i			0.200800i
$903$	−195.011	−	66.5030i	−0.215960	−	0.0736467i
$904$	−922.221			−1.02016
$905$	56.0480	−	32.3593i	0.0619315	−	0.0357562i
$906$	−31.1413	+	91.3177i	−0.0343722	+	0.100792i
$907$	−16.7189	+	28.9579i	−0.0184332	+	0.0319272i	−0.875095	−	0.483951i	$-0.839201\pi$
$907$	−16.7189	+	28.9579i	−0.0184332	+	0.0319272i	0.856662	+	0.515879i	$0.172534\pi$
$908$	−82.7561	+	47.7793i	−0.0911411	+	0.0526204i
$909$	−58.9651	−	143.493i	−0.0648681	−	0.157858i
$910$	−108.131	+	187.289i	−0.118826	+	0.205812i
$911$		−	105.154i		−	0.115427i	−0.998333	−	0.0577135i	$-0.981619\pi$
$911$		−	105.154i		−	0.115427i	0.998333	−	0.0577135i	$-0.0183810\pi$
$912$	−247.728	+	216.637i	−0.271631	+	0.237540i
$913$	628.065	−	1087.84i	0.687914	−	1.19150i
$914$	−491.430	−	283.727i	−0.537669	−	0.310423i
$915$	−486.954	−	556.840i	−0.532190	−	0.608568i
$916$	−274.698			−0.299889
$917$	−725.132	+	418.655i	−0.790766	+	0.456549i
$918$	−236.465	−	357.142i	−0.257587	−	0.389044i
$919$	62.4231	+	108.120i	0.0679251	+	0.117650i	0.897988	−	0.440020i	$-0.145029\pi$
$919$	62.4231	+	108.120i	0.0679251	+	0.117650i	−0.830063	+	0.557670i	$0.811695\pi$
$920$	−237.705	−	137.239i	−0.258375	−	0.149173i
$921$	−240.766	−	82.1062i	−0.261418	−	0.0891490i
$922$	−0.721356	−	1.24943i	−0.000782382	−	0.00135512i
$923$		−	807.720i		−	0.875103i
$924$	750.059	−	148.101i	0.811752	−	0.160283i
$925$	−220.548			−0.238430
$926$	−452.309	+	261.141i	−0.488454	+	0.282009i
$927$	174.980	−	1300.86i	0.188759	−	1.40330i
$928$	−167.358	+	289.872i	−0.180342	+	0.312362i
$929$	−362.569	+	209.330i	−0.390279	+	0.225328i	−0.682281	−	0.731090i	$-0.739012\pi$
$929$	−362.569	+	209.330i	−0.390279	+	0.225328i	0.292002	+	0.956418i	$0.405679\pi$
$930$	−17.2327	−	87.2751i	−0.0185298	−	0.0938442i
$931$	−321.831	−	557.427i	−0.345683	−	0.598740i
$932$			845.551i			0.907243i
$933$	1008.16	+	1152.85i	1.08056	+	1.23563i
$934$	85.9370	−	148.847i	0.0920096	−	0.159365i
$935$	−409.339	−	236.332i	−0.437795	−	0.252761i
$936$	−556.486	+	721.025i	−0.594536	+	0.770326i
$937$	991.740			1.05842			0.529210	−	0.848491i	$-0.322488\pi$
$937$	991.740			1.05842			0.529210	+	0.848491i	$0.322488\pi$
$938$		−	341.445i		−	0.364013i
$939$	66.7851	+	338.233i	0.0711236	+	0.360205i
$940$	244.719	+	423.866i	0.260340	+	0.450921i
$941$	666.760	+	384.954i	0.708565	+	0.409090i	0.810530	−	0.585698i	$-0.199179\pi$
$941$	666.760	+	384.954i	0.708565	+	0.409090i	−0.101964	+	0.994788i	$0.532513\pi$
$942$	37.9438	−	111.265i	0.0402801	−	0.118116i
$943$	−205.184	−	355.389i	−0.217586	−	0.376871i
$944$		−	722.323i		−	0.765173i
$945$	−378.243	−	188.514i	−0.400257	−	0.199485i
$946$	88.3025			0.0933430
$947$	−1200.26	+	692.971i	−1.26743	+	0.731754i	−0.974502	−	0.224379i	$-0.927964\pi$
$947$	−1200.26	+	692.971i	−1.26743	+	0.731754i	−0.292933	+	0.956133i	$0.594631\pi$
$948$	901.382	+	307.390i	0.950825	+	0.324251i
$949$	−791.278	+	1370.53i	−0.833802	+	1.44419i
$950$	−46.7473	+	26.9896i	−0.0492077	+	0.0284101i
$951$	−1437.61	+	283.860i	−1.51168	+	0.298486i
$952$	406.690	−	704.408i	0.427195	−	0.739924i
$953$		−	665.132i		−	0.697935i	−0.937135	−	0.348968i	$-0.886532\pi$
$953$		−	665.132i		−	0.697935i	0.937135	−	0.348968i	$-0.113468\pi$
$954$	−17.5609	−	13.5535i	−0.0184077	−	0.0142070i
$955$	−346.616	+	600.357i	−0.362949	+	0.628646i
$956$	1348.53	+	778.573i	1.41059	+	0.814407i
$957$	−267.519	+	233.944i	−0.279539	+	0.244455i
$958$	−127.152			−0.132727
$959$	316.043	+	182.468i	0.329555	+	0.190269i
$960$	−52.4758	+	10.3615i	−0.0546623	+	0.0107932i
$961$	350.316	+	606.765i	0.364532	+	0.631389i
$962$	−527.791	−	304.721i	−0.548640	−	0.316757i
$963$	1627.25	+	218.882i	1.68977	+	0.227292i
$964$	280.561	+	485.945i	0.291038	+	0.504092i
$965$		−	575.895i		−	0.596782i
$966$	264.923	−	231.674i	0.274247	−	0.239828i
$967$	−1158.19			−1.19772			−0.598858	−	0.800855i	$-0.704379\pi$
$967$	−1158.19			−1.19772			−0.598858	+	0.800855i	$0.704379\pi$
$968$	5.62508	−	3.24764i	0.00581104	−	0.00335500i
$969$	−245.524	+	719.967i	−0.253378	+	0.743000i
$970$	36.9278	−	63.9607i	0.0380699	−	0.0659389i
$971$	1639.61	−	946.628i	1.68858	−	0.974900i	0.732967	−	0.680264i	$-0.238135\pi$
$971$	1639.61	−	946.628i	1.68858	−	0.974900i	0.955610	−	0.294636i	$-0.0951983\pi$
$972$	−668.549	−	453.532i	−0.687808	−	0.466596i
$973$	−445.359			−0.457718
$974$		−	266.108i		−	0.273211i
$975$	189.825	−	166.001i	0.194693	−	0.170258i
$976$	460.434	−	797.495i	0.471756	−	0.817106i
$977$	−1319.18	−	761.632i	−1.35024	−	0.779561i	−0.361957	−	0.932195i	$-0.617891\pi$
$977$	−1319.18	−	761.632i	−1.35024	−	0.779561i	−0.988283	+	0.152633i	$0.951225\pi$
$978$	205.387	+	234.864i	0.210008	+	0.240147i
$979$	−572.605			−0.584888
$980$		−	364.263i		−	0.371697i
$981$	−1146.34	+	471.063i	−1.16854	+	0.480187i
$982$	−194.750	−	337.317i	−0.198320	−	0.343500i
$983$	329.604	+	190.297i	0.335304	+	0.193588i	0.658194	−	0.752849i	$-0.271321\pi$
$983$	329.604	+	190.297i	0.335304	+	0.193588i	−0.322889	+	0.946437i	$0.604654\pi$
$984$	343.982	+	117.305i	0.349575	+	0.119212i
$985$	93.6512	+	162.209i	0.0950774	+	0.164679i
$986$			171.609i			0.174046i
$987$	−1356.42	+	267.829i	−1.37428	+	0.271357i
$988$	734.173			0.743090
$989$	−173.263	+	100.034i	−0.175191	+	0.101146i
$990$	179.505	+	24.1453i	0.181318	+	0.0243892i
$991$	−643.339	+	1114.30i	−0.649182	+	1.12442i	0.334137	+	0.942525i	$0.391555\pi$
$991$	−643.339	+	1114.30i	−0.649182	+	1.12442i	−0.983319	+	0.181891i	$0.941778\pi$
$992$	432.389	−	249.640i	0.435876	−	0.251653i
$993$	123.862	+	627.296i	0.124735	+	0.631718i
$994$	−138.204	−	239.376i	−0.139038	−	0.240821i
$995$			623.569i			0.626702i
$996$	−753.111	−	861.195i	−0.756136	−	0.864654i
$997$	−948.355	+	1642.60i	−0.951209	+	1.64754i	−0.208394	+	0.978045i	$0.566824\pi$
$997$	−948.355	+	1642.60i	−0.951209	+	1.64754i	−0.742815	+	0.669497i	$0.766510\pi$
$998$	397.585	+	229.546i	0.398382	+	0.230006i
$999$	531.243	−	1065.91i	0.531775	−	1.06698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.t.a.11.3	yes	8
3.2	odd	2	inner	105.3.t.a.11.2	✓	8
7.2	even	3	inner	105.3.t.a.86.2	yes	8
21.2	odd	6	inner	105.3.t.a.86.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.t.a.11.2	✓	8	3.2	odd	2	inner
105.3.t.a.11.3	yes	8	1.1	even	1	trivial
105.3.t.a.86.2	yes	8	7.2	even	3	inner
105.3.t.a.86.3	yes	8	21.2	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.711747 - 0.410927i) q^{2} +(2.83943 + 0.968306i) q^{3} +(-1.66228 + 2.87915i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(2.41886 - 0.477612i) q^{6} +7.00000 q^{7} +6.01972i q^{8} +(7.12477 + 5.49888i) q^{9} +O(q^{10})\)	\(q+(0.711747 - 0.410927i) q^{2} +(2.83943 + 0.968306i) q^{3} +(-1.66228 + 2.87915i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(2.41886 - 0.477612i) q^{6} +7.00000 q^{7} +6.01972i q^{8} +(7.12477 + 5.49888i) q^{9} +(-0.918861 + 1.59151i) q^{10} +(-9.48371 - 5.47542i) q^{11} +(-7.50783 + 6.56556i) q^{12} +16.8114 q^{13} +(4.98223 - 2.87649i) q^{14} +(-6.58114 + 1.29947i) q^{15} +(-4.17544 - 7.23208i) q^{16} +(-16.7167 - 9.65138i) q^{17} +(7.33067 + 0.986053i) q^{18} +(-6.56797 - 11.3761i) q^{19} -7.43393i q^{20} +(19.8760 + 6.77814i) q^{21} -9.00000 q^{22} +(17.6594 - 10.1957i) q^{23} +(-5.82893 + 17.0926i) q^{24} +(2.50000 - 4.33013i) q^{25} +(11.9655 - 6.90826i) q^{26} +(14.9057 + 22.5127i) q^{27} +(-11.6359 + 20.1540i) q^{28} -10.8175i q^{29} +(-4.15012 + 3.62926i) q^{30} +(-8.06797 + 13.9741i) q^{31} +(-26.7966 - 15.4710i) q^{32} +(-21.6265 - 24.7302i) q^{33} -15.8641 q^{34} +(-13.5554 + 7.82624i) q^{35} +(-27.6754 + 11.3726i) q^{36} +(-22.0548 - 38.2000i) q^{37} +(-9.34947 - 5.39792i) q^{38} +(47.7348 + 16.2786i) q^{39} +(-6.73025 - 11.6571i) q^{40} -20.1246i q^{41} +(16.9320 - 3.34328i) q^{42} -9.81139 q^{43} +(31.5291 - 18.2033i) q^{44} +(-19.9450 - 2.68281i) q^{45} +(8.37936 - 14.5135i) q^{46} +(-57.0178 + 32.9192i) q^{47} +(-4.85303 - 24.5781i) q^{48} +49.0000 q^{49} -4.10927i q^{50} +(-38.1204 - 43.5913i) q^{51} +(-27.9452 + 48.4025i) q^{52} +(-2.59724 - 1.49952i) q^{53} +(19.8601 + 9.89817i) q^{54} +24.4868 q^{55} +42.1380i q^{56} +(-7.63381 - 38.6614i) q^{57} +(-4.44520 - 7.69930i) q^{58} +(74.9082 + 43.2483i) q^{59} +(7.19832 - 21.1082i) q^{60} +(55.1359 + 95.4983i) q^{61} +13.2614i q^{62} +(49.8734 + 38.4922i) q^{63} +7.97367 q^{64} +(-32.5551 + 18.7957i) q^{65} +(-25.5549 - 8.71476i) q^{66} +(29.6754 - 51.3994i) q^{67} +(55.5755 - 32.0865i) q^{68} +(60.0153 - 11.8502i) q^{69} +(-6.43203 + 11.1406i) q^{70} -48.0460i q^{71} +(-33.1017 + 42.8891i) q^{72} +(-47.0680 + 81.5241i) q^{73} +(-31.3949 - 18.1258i) q^{74} +(11.2915 - 9.87434i) q^{75} +43.6712 q^{76} +(-66.3860 - 38.3280i) q^{77} +(40.6644 - 8.02931i) q^{78} +(-47.7434 - 82.6940i) q^{79} +(16.1714 + 9.33658i) q^{80} +(20.5246 + 78.3565i) q^{81} +(-8.26975 - 14.3236i) q^{82} +114.706i q^{83} +(-52.5548 + 45.9589i) q^{84} +43.1623 q^{85} +(-6.98322 + 4.03177i) q^{86} +(10.4746 - 30.7155i) q^{87} +(32.9605 - 57.0893i) q^{88} +(45.2833 - 26.1443i) q^{89} +(-15.2982 + 6.28646i) q^{90} +117.680 q^{91} +67.7922i q^{92} +(-36.4397 + 31.8664i) q^{93} +(-27.0548 + 46.8603i) q^{94} +(25.4376 + 14.6864i) q^{95} +(-61.1066 - 69.8764i) q^{96} -40.1886 q^{97} +(34.8756 - 20.1354i) q^{98} +(-37.4605 - 91.1609i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 12 q^{4} + 32 q^{6} + 56 q^{7} + 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 12 * q^4 + 32 * q^6 + 56 * q^7 + 8 * q^9	\( 8 q - 4 q^{3} + 12 q^{4} + 32 q^{6} + 56 q^{7} + 8 q^{9} - 20 q^{10} + 52 q^{12} + 8 q^{13} - 40 q^{15} - 84 q^{16} - 52 q^{18} + 36 q^{19} - 28 q^{21} - 72 q^{22} + 24 q^{24} + 20 q^{25} + 56 q^{27} + 84 q^{28} - 40 q^{30} + 24 q^{31} - 72 q^{33} - 304 q^{34} - 272 q^{36} - 12 q^{37} + 96 q^{39} + 60 q^{40} + 224 q^{42} + 48 q^{43} + 20 q^{45} - 148 q^{46} + 328 q^{48} + 392 q^{49} - 164 q^{51} - 388 q^{52} - 160 q^{54} + 120 q^{55} - 352 q^{57} - 200 q^{58} - 20 q^{60} + 264 q^{61} + 56 q^{63} - 88 q^{64} + 36 q^{66} + 288 q^{67} + 88 q^{69} - 140 q^{70} + 348 q^{72} - 288 q^{73} + 20 q^{75} + 1336 q^{76} - 168 q^{78} - 344 q^{79} - 28 q^{81} - 180 q^{82} + 364 q^{84} + 320 q^{85} + 140 q^{87} + 36 q^{88} + 80 q^{90} + 56 q^{91} + 164 q^{93} - 52 q^{94} - 320 q^{96} - 448 q^{97} - 72 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 12 * q^4 + 32 * q^6 + 56 * q^7 + 8 * q^9 - 20 * q^10 + 52 * q^12 + 8 * q^13 - 40 * q^15 - 84 * q^16 - 52 * q^18 + 36 * q^19 - 28 * q^21 - 72 * q^22 + 24 * q^24 + 20 * q^25 + 56 * q^27 + 84 * q^28 - 40 * q^30 + 24 * q^31 - 72 * q^33 - 304 * q^34 - 272 * q^36 - 12 * q^37 + 96 * q^39 + 60 * q^40 + 224 * q^42 + 48 * q^43 + 20 * q^45 - 148 * q^46 + 328 * q^48 + 392 * q^49 - 164 * q^51 - 388 * q^52 - 160 * q^54 + 120 * q^55 - 352 * q^57 - 200 * q^58 - 20 * q^60 + 264 * q^61 + 56 * q^63 - 88 * q^64 + 36 * q^66 + 288 * q^67 + 88 * q^69 - 140 * q^70 + 348 * q^72 - 288 * q^73 + 20 * q^75 + 1336 * q^76 - 168 * q^78 - 344 * q^79 - 28 * q^81 - 180 * q^82 + 364 * q^84 + 320 * q^85 + 140 * q^87 + 36 * q^88 + 80 * q^90 + 56 * q^91 + 164 * q^93 - 52 * q^94 - 320 * q^96 - 448 * q^97 - 72 * q^99

Introduction

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