LMFDB - Embedded newform 147.2.m.b.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,2,Mod(4,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("147.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.m (of order $21$, degree $12$, 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:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	147.25
Dual form			147.2.m.b.100.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.380106 - 0.117247i) q^{2} +(0.365341 + 0.930874i) q^{3} +(-1.52174 + 1.03751i) q^{4} +(0.996754 + 0.150237i) q^{5} +(0.248010 + 0.310995i) q^{6} +(2.64575 + 0.00303574i) q^{7} +(-0.952800 + 1.19477i) q^{8} +(-0.733052 + 0.680173i) q^{9} +O(q^{10})$	\(q+(0.380106 - 0.117247i) q^{2} +(0.365341 + 0.930874i) q^{3} +(-1.52174 + 1.03751i) q^{4} +(0.996754 + 0.150237i) q^{5} +(0.248010 + 0.310995i) q^{6} +(2.64575 + 0.00303574i) q^{7} +(-0.952800 + 1.19477i) q^{8} +(-0.733052 + 0.680173i) q^{9} +(0.396487 - 0.0597608i) q^{10} +(1.00095 + 0.928747i) q^{11} +(-1.52174 - 1.03751i) q^{12} +(-1.26765 + 5.55392i) q^{13} +(1.00602 - 0.309053i) q^{14} +(0.224304 + 0.982740i) q^{15} +(1.12367 - 2.86306i) q^{16} +(0.594210 - 7.92918i) q^{17} +(-0.198889 + 0.344486i) q^{18} +(-1.97740 - 3.42496i) q^{19} +(-1.67268 + 0.805519i) q^{20} +(0.963775 + 2.46397i) q^{21} +(0.489360 + 0.235663i) q^{22} +(-0.416919 - 5.56340i) q^{23} +(-1.46028 - 0.450437i) q^{24} +(-3.80692 - 1.17428i) q^{25} +(0.169342 + 2.25971i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-4.02930 + 2.74037i) q^{28} +(8.45611 - 4.07225i) q^{29} +(0.200483 + 0.347246i) q^{30} +(-2.53729 + 4.39471i) q^{31} +(0.319828 - 4.26781i) q^{32} +(-0.498858 + 1.27107i) q^{33} +(-0.703810 - 3.08360i) q^{34} +(2.63671 + 0.400514i) q^{35} +(0.409833 - 1.79560i) q^{36} +(4.20461 + 2.86666i) q^{37} +(-1.15319 - 1.07000i) q^{38} +(-5.63313 + 0.849057i) q^{39} +(-1.12921 + 1.04775i) q^{40} +(-4.23188 + 5.30661i) q^{41} +(0.655230 + 0.823569i) q^{42} +(-0.406277 - 0.509456i) q^{43} +(-2.48677 - 0.374821i) q^{44} +(-0.832859 + 0.567834i) q^{45} +(-0.810766 - 2.06580i) q^{46} +(-10.4626 + 3.22730i) q^{47} +3.07567 q^{48} +(6.99998 + 0.0160636i) q^{49} -1.58471 q^{50} +(7.59815 - 2.34372i) q^{51} +(-3.83320 - 9.76685i) q^{52} +(6.20346 - 4.22945i) q^{53} +(-0.393335 - 0.0592857i) q^{54} +(0.858171 + 1.07611i) q^{55} +(-2.52450 + 3.15818i) q^{56} +(2.46578 - 3.09199i) q^{57} +(2.73676 - 2.53934i) q^{58} +(-3.22914 + 0.486714i) q^{59} +(-1.36093 - 1.26276i) q^{60} +(-0.0921568 - 0.0628315i) q^{61} +(-0.449171 + 1.96795i) q^{62} +(-1.94154 + 1.79734i) q^{63} +(0.989983 + 4.33740i) q^{64} +(-2.09794 + 5.34545i) q^{65} +(-0.0405896 + 0.541630i) q^{66} +(-2.03572 + 3.52598i) q^{67} +(7.32235 + 12.6827i) q^{68} +(5.02650 - 2.42064i) q^{69} +(1.04919 - 0.156908i) q^{70} +(1.85333 + 0.892516i) q^{71} +(-0.114200 - 1.52390i) q^{72} +(6.83997 + 2.10985i) q^{73} +(1.93430 + 0.596654i) q^{74} +(-0.297718 - 3.97277i) q^{75} +(6.56253 + 3.16035i) q^{76} +(2.64545 + 2.46027i) q^{77} +(-2.04163 + 0.983199i) q^{78} +(-2.75372 - 4.76959i) q^{79} +(1.55016 - 2.68495i) q^{80} +(0.0747301 - 0.997204i) q^{81} +(-0.986377 + 2.51325i) q^{82} +(-0.325178 - 1.42470i) q^{83} +(-4.02300 - 2.74960i) q^{84} +(1.78353 - 7.81417i) q^{85} +(-0.214161 - 0.146012i) q^{86} +(6.88011 + 6.38381i) q^{87} +(-2.06335 + 0.311000i) q^{88} +(-4.54981 + 4.22161i) q^{89} +(-0.249998 + 0.313487i) q^{90} +(-3.37074 + 14.6904i) q^{91} +(6.40651 + 8.03351i) q^{92} +(-5.01790 - 0.756326i) q^{93} +(-3.59852 + 2.45343i) q^{94} +(-1.45643 - 3.71092i) q^{95} +(4.08964 - 1.26149i) q^{96} +4.96295 q^{97} +(2.66262 - 0.814622i) q^{98} -1.36546 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9} - 34 q^{10} - 11 q^{11} + 5 q^{12} - 2 q^{13} + 40 q^{14} - 3 q^{15} - 31 q^{16} - 9 q^{17} - 6 q^{18} - 29 q^{19} - 43 q^{20} - 11 q^{21} + 9 q^{22} - 4 q^{23} - 24 q^{24} + 55 q^{25} + 36 q^{26} - 10 q^{27} - 57 q^{28} + 4 q^{29} - 20 q^{30} - 39 q^{31} - 92 q^{32} - 18 q^{33} - 36 q^{34} - 33 q^{35} - 10 q^{36} - 24 q^{37} + 118 q^{38} - 6 q^{39} + 35 q^{41} + 38 q^{42} + 2 q^{43} + 40 q^{44} + 12 q^{45} - 40 q^{46} - 5 q^{47} + 76 q^{48} + 129 q^{49} - 176 q^{50} + 54 q^{51} - 6 q^{52} + 26 q^{53} + q^{54} + 2 q^{55} + 63 q^{56} - 12 q^{57} + 11 q^{58} - 41 q^{59} + 32 q^{60} + 6 q^{61} + 36 q^{62} - q^{63} + 74 q^{64} - 51 q^{65} - 15 q^{66} - 55 q^{67} - 22 q^{68} + 8 q^{69} - 68 q^{70} - 66 q^{71} - 24 q^{72} + 24 q^{73} + 28 q^{74} + 41 q^{75} + 3 q^{76} - 34 q^{77} - 30 q^{78} - 51 q^{79} - 5 q^{80} + 5 q^{81} - 41 q^{82} + 30 q^{83} - 30 q^{84} + 68 q^{85} + 110 q^{86} + 19 q^{87} + 129 q^{88} + 75 q^{89} - 16 q^{90} + 5 q^{91} - 4 q^{93} + 38 q^{94} + 36 q^{95} - 57 q^{96} - 168 q^{97} + 227 q^{98} + 36 q^{99}+O(q^{100}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9 - 34 * q^10 - 11 * q^11 + 5 * q^12 - 2 * q^13 + 40 * q^14 - 3 * q^15 - 31 * q^16 - 9 * q^17 - 6 * q^18 - 29 * q^19 - 43 * q^20 - 11 * q^21 + 9 * q^22 - 4 * q^23 - 24 * q^24 + 55 * q^25 + 36 * q^26 - 10 * q^27 - 57 * q^28 + 4 * q^29 - 20 * q^30 - 39 * q^31 - 92 * q^32 - 18 * q^33 - 36 * q^34 - 33 * q^35 - 10 * q^36 - 24 * q^37 + 118 * q^38 - 6 * q^39 + 35 * q^41 + 38 * q^42 + 2 * q^43 + 40 * q^44 + 12 * q^45 - 40 * q^46 - 5 * q^47 + 76 * q^48 + 129 * q^49 - 176 * q^50 + 54 * q^51 - 6 * q^52 + 26 * q^53 + q^54 + 2 * q^55 + 63 * q^56 - 12 * q^57 + 11 * q^58 - 41 * q^59 + 32 * q^60 + 6 * q^61 + 36 * q^62 - q^63 + 74 * q^64 - 51 * q^65 - 15 * q^66 - 55 * q^67 - 22 * q^68 + 8 * q^69 - 68 * q^70 - 66 * q^71 - 24 * q^72 + 24 * q^73 + 28 * q^74 + 41 * q^75 + 3 * q^76 - 34 * q^77 - 30 * q^78 - 51 * q^79 - 5 * q^80 + 5 * q^81 - 41 * q^82 + 30 * q^83 - 30 * q^84 + 68 * q^85 + 110 * q^86 + 19 * q^87 + 129 * q^88 + 75 * q^89 - 16 * q^90 + 5 * q^91 - 4 * q^93 + 38 * q^94 + 36 * q^95 - 57 * q^96 - 168 * q^97 + 227 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{8}{21}\right)$

Coefficient data

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

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

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

$2$	0.380106	−	0.117247i	0.268775	−	0.0829062i	−0.157438	−	0.987529i	$-0.550323\pi$
$2$	0.380106	−	0.117247i	0.268775	−	0.0829062i	0.426213	+	0.904623i	$0.359847\pi$
$3$	0.365341	+	0.930874i	0.210930	+	0.537440i
$3$	0.365341	+	0.930874i	0.210930	+	0.537440i
$4$	−1.52174	+	1.03751i	−0.760872	+	0.518754i
$5$	0.996754	+	0.150237i	0.445762	+	0.0671878i	0.368088	−	0.929791i	$-0.380013\pi$
$5$	0.996754	+	0.150237i	0.445762	+	0.0671878i	0.0776741	+	0.996979i	$0.475251\pi$
$6$	0.248010	+	0.310995i	0.101250	+	0.126963i
$7$	2.64575	+	0.00303574i	0.999999	+	0.00114740i
$7$	2.64575	+	0.00303574i	0.999999	+	0.00114740i
$8$	−0.952800	+	1.19477i	−0.336866	+	0.422416i
$9$	−0.733052	+	0.680173i	−0.244351	+	0.226724i
$10$	0.396487	−	0.0597608i	0.125380	−	0.0188980i
$11$	1.00095	+	0.928747i	0.301798	+	0.280028i	0.816505	−	0.577339i	$-0.195909\pi$
$11$	1.00095	+	0.928747i	0.301798	+	0.280028i	−0.514707	+	0.857366i	$0.672099\pi$
$12$	−1.52174	−	1.03751i	−0.439290	−	0.299503i
$13$	−1.26765	+	5.55392i	−0.351582	+	1.54038i	0.421947	+	0.906621i	$0.361347\pi$
$13$	−1.26765	+	5.55392i	−0.351582	+	1.54038i	−0.773529	+	0.633761i	$0.781510\pi$
$14$	1.00602	−	0.309053i	0.268870	−	0.0825978i
$15$	0.224304	+	0.982740i	0.0579150	+	0.253742i
$16$	1.12367	−	2.86306i	0.280917	−	0.715766i
$17$	0.594210	−	7.92918i	0.144117	−	1.92311i	−0.192194	−	0.981357i	$-0.561560\pi$
$17$	0.594210	−	7.92918i	0.144117	−	1.92311i	0.336311	−	0.941751i	$-0.390821\pi$
$18$	−0.198889	+	0.344486i	−0.0468786	+	0.0811961i
$19$	−1.97740	−	3.42496i	−0.453647	−	0.785740i	0.544962	−	0.838461i	$-0.316544\pi$
$19$	−1.97740	−	3.42496i	−0.453647	−	0.785740i	−0.998609	+	0.0527205i	$0.983211\pi$
$20$	−1.67268	+	0.805519i	−0.374022	+	0.180119i
$21$	0.963775	+	2.46397i	0.210313	+	0.537682i
$22$	0.489360	+	0.235663i	0.104332	+	0.0502436i
$23$	−0.416919	−	5.56340i	−0.0869337	−	1.16005i	−0.854631	−	0.519236i	$-0.826217\pi$
$23$	−0.416919	−	5.56340i	−0.0869337	−	1.16005i	0.767697	−	0.640813i	$-0.221403\pi$
$24$	−1.46028	−	0.450437i	−0.298078	−	0.0919450i
$25$	−3.80692	−	1.17428i	−0.761383	−	0.234856i
$26$	0.169342	+	2.25971i	0.0332106	+	0.443165i
$27$	−0.900969	−	0.433884i	−0.173392	−	0.0835010i
$28$	−4.02930	+	2.74037i	−0.761467	+	0.517880i
$29$	8.45611	−	4.07225i	1.57026	−	0.756197i	0.572300	−	0.820044i	$-0.306051\pi$
$29$	8.45611	−	4.07225i	1.57026	−	0.756197i	0.997960	+	0.0638471i	$0.0203370\pi$
$30$	0.200483	+	0.347246i	0.0366030	+	0.0633982i
$31$	−2.53729	+	4.39471i	−0.455710	+	0.789314i	−0.998729	−	0.0504073i	$-0.983948\pi$
$31$	−2.53729	+	4.39471i	−0.455710	+	0.789314i	0.543018	+	0.839721i	$0.317281\pi$
$32$	0.319828	−	4.26781i	0.0565382	−	0.754450i
$33$	−0.498858	+	1.27107i	−0.0868400	+	0.221265i
$34$	−0.703810	−	3.08360i	−0.120703	−	0.528832i
$35$	2.63671	+	0.400514i	0.445685	+	0.0676993i
$36$	0.409833	−	1.79560i	0.0683055	−	0.299266i
$37$	4.20461	+	2.86666i	0.691234	+	0.471275i	0.857285	−	0.514842i	$-0.172149\pi$
$37$	4.20461	+	2.86666i	0.691234	+	0.471275i	−0.166051	+	0.986117i	$0.553102\pi$
$38$	−1.15319	−	1.07000i	−0.187072	−	0.173577i
$39$	−5.63313	+	0.849057i	−0.902022	+	0.135958i
$40$	−1.12921	+	1.04775i	−0.178543	+	0.165664i
$41$	−4.23188	+	5.30661i	−0.660909	+	0.828753i	−0.993442	−	0.114338i	$-0.963525\pi$
$41$	−4.23188	+	5.30661i	−0.660909	+	0.828753i	0.332533	+	0.943092i	$0.392097\pi$
$42$	0.655230	+	0.823569i	0.101104	+	0.127079i
$43$	−0.406277	−	0.509456i	−0.0619567	−	0.0776913i	0.749887	−	0.661565i	$-0.230108\pi$
$43$	−0.406277	−	0.509456i	−0.0619567	−	0.0776913i	−0.811844	+	0.583874i	$0.801536\pi$
$44$	−2.48677	−	0.374821i	−0.374895	−	0.0565064i
$45$	−0.832859	+	0.567834i	−0.124155	+	0.0846477i
$46$	−0.810766	−	2.06580i	−0.119541	−	0.304585i
$47$	−10.4626	+	3.22730i	−1.52613	+	0.470750i	−0.940491	−	0.339820i	$-0.889634\pi$
$47$	−10.4626	+	3.22730i	−1.52613	+	0.470750i	−0.585643	+	0.810569i	$0.699158\pi$
$48$	3.07567			0.443935
$49$	6.99998	+	0.0160636i	0.999997	+	0.00229481i
$50$	−1.58471			−0.224112
$51$	7.59815	−	2.34372i	1.06395	−	0.328186i
$52$	−3.83320	−	9.76685i	−0.531570	−	1.35442i
$53$	6.20346	−	4.22945i	0.852111	−	0.580959i	−0.0565947	−	0.998397i	$-0.518024\pi$
$53$	6.20346	−	4.22945i	0.852111	−	0.580959i	0.908705	+	0.417438i	$0.137072\pi$
$54$	−0.393335	−	0.0592857i	−0.0535261	−	0.00806777i
$55$	0.858171	+	1.07611i	0.115716	+	0.145103i
$56$	−2.52450	+	3.15818i	−0.337350	+	0.422029i
$57$	2.46578	−	3.09199i	0.326601	−	0.409544i
$58$	2.73676	−	2.53934i	0.359354	−	0.333432i
$59$	−3.22914	+	0.486714i	−0.420398	+	0.0633648i	−0.355835	−	0.934549i	$-0.615803\pi$
$59$	−3.22914	+	0.486714i	−0.420398	+	0.0633648i	−0.0645631	+	0.997914i	$0.520565\pi$
$60$	−1.36093	−	1.26276i	−0.175696	−	0.163022i
$61$	−0.0921568	−	0.0628315i	−0.0117995	−	0.00804474i	0.557406	−	0.830240i	$-0.311797\pi$
$61$	−0.0921568	−	0.0628315i	−0.0117995	−	0.00804474i	−0.569205	+	0.822195i	$0.692749\pi$
$62$	−0.449171	+	1.96795i	−0.0570447	+	0.249929i
$63$	−1.94154	+	1.79734i	−0.244611	+	0.226444i
$64$	0.989983	+	4.33740i	0.123748	+	0.542175i
$65$	−2.09794	+	5.34545i	−0.260217	+	0.663022i
$66$	−0.0405896	+	0.541630i	−0.00499623	+	0.0666701i
$67$	−2.03572	+	3.52598i	−0.248703	+	0.430767i	−0.963166	−	0.268906i	$-0.913338\pi$
$67$	−2.03572	+	3.52598i	−0.248703	+	0.430767i	0.714463	+	0.699673i	$0.246671\pi$
$68$	7.32235	+	12.6827i	0.887965	+	1.53800i
$69$	5.02650	−	2.42064i	0.605120	−	0.291410i
$70$	1.04919	−	0.156908i	0.125402	−	0.0187541i
$71$	1.85333	+	0.892516i	0.219950	+	0.105922i	0.540614	−	0.841271i	$-0.318192\pi$
$71$	1.85333	+	0.892516i	0.219950	+	0.105922i	−0.320664	+	0.947193i	$0.603906\pi$
$72$	−0.114200	−	1.52390i	−0.0134587	−	0.179593i
$73$	6.83997	+	2.10985i	0.800558	+	0.246940i	0.667928	−	0.744226i	$-0.267181\pi$
$73$	6.83997	+	2.10985i	0.800558	+	0.246940i	0.132630	+	0.991166i	$0.457658\pi$
$74$	1.93430	+	0.596654i	0.224858	+	0.0693596i
$75$	−0.297718	−	3.97277i	−0.0343775	−	0.458736i
$76$	6.56253	+	3.16035i	0.752773	+	0.362517i
$77$	2.64545	+	2.46027i	0.301477	+	0.280374i
$78$	−2.04163	+	0.983199i	−0.231170	+	0.111325i
$79$	−2.75372	−	4.76959i	−0.309818	−	0.536621i	0.668504	−	0.743708i	$-0.266935\pi$
$79$	−2.75372	−	4.76959i	−0.309818	−	0.536621i	−0.978322	+	0.207088i	$0.933602\pi$
$80$	1.55016	−	2.68495i	0.173313	−	0.300187i
$81$	0.0747301	−	0.997204i	0.00830334	−	0.110800i
$82$	−0.986377	+	2.51325i	−0.108927	+	0.277542i
$83$	−0.325178	−	1.42470i	−0.0356930	−	0.156381i	0.953941	−	0.299995i	$-0.0969849\pi$
$83$	−0.325178	−	1.42470i	−0.0356930	−	0.156381i	−0.989634	+	0.143614i	$0.954128\pi$
$84$	−4.02300	−	2.74960i	−0.438946	−	0.300006i
$85$	1.78353	−	7.81417i	0.193451	−	0.847566i
$86$	−0.214161	−	0.146012i	−0.0230935	−	0.0157449i
$87$	6.88011	+	6.38381i	0.737625	+	0.684416i
$88$	−2.06335	+	0.311000i	−0.219954	+	0.0331527i
$89$	−4.54981	+	4.22161i	−0.482279	+	0.447490i	−0.883458	−	0.468510i	$-0.844791\pi$
$89$	−4.54981	+	4.22161i	−0.482279	+	0.447490i	0.401179	+	0.916000i	$0.368601\pi$
$90$	−0.249998	+	0.313487i	−0.0263521	+	0.0330445i
$91$	−3.37074	+	14.6904i	−0.353349	+	1.53998i
$92$	6.40651	+	8.03351i	0.667925	+	0.837552i
$93$	−5.01790	−	0.756326i	−0.520332	−	0.0784274i
$94$	−3.59852	+	2.45343i	−0.371159	+	0.253052i
$95$	−1.45643	−	3.71092i	−0.149427	−	0.380733i
$96$	4.08964	−	1.26149i	0.417397	−	0.128750i
$97$	4.96295			0.503912			0.251956	−	0.967739i	$-0.418926\pi$
$97$	4.96295			0.503912			0.251956	+	0.967739i	$0.418926\pi$
$98$	2.66262	−	0.814622i	0.268965	−	0.0822892i
$99$	−1.36546			−0.137234
$100$	7.01147	−	2.16275i	0.701147	−	0.216275i
$101$	−1.86183	−	4.74387i	−0.185259	−	0.472033i	0.807827	−	0.589420i	$-0.200643\pi$
$101$	−1.86183	−	4.74387i	−0.185259	−	0.472033i	−0.993086	+	0.117387i	$0.962548\pi$
$102$	2.61331	−	1.78172i	0.258756	−	0.176417i
$103$	−7.18152	−	1.08244i	−0.707616	−	0.106656i	−0.214633	−	0.976695i	$-0.568856\pi$
$103$	−7.18152	−	1.08244i	−0.707616	−	0.106656i	−0.492983	+	0.870039i	$0.664094\pi$
$104$	−5.42787	−	6.80633i	−0.532246	−	0.667416i
$105$	0.590469	+	2.60076i	0.0576239	+	0.253809i
$106$	1.86208	−	2.33497i	0.180861	−	0.226793i
$107$	−6.63311	+	6.15463i	−0.641247	+	0.594991i	−0.932287	−	0.361721i	$-0.882189\pi$
$107$	−6.63311	+	6.15463i	−0.641247	+	0.594991i	0.291039	+	0.956711i	$0.405999\pi$
$108$	1.82120	−	0.274502i	0.175245	−	0.0264140i
$109$	−2.98074	−	2.76572i	−0.285503	−	0.264908i	0.524400	−	0.851472i	$-0.324290\pi$
$109$	−2.98074	−	2.76572i	−0.285503	−	0.264908i	−0.809903	+	0.586564i	$0.800480\pi$
$110$	0.452367	+	0.308418i	0.0431315	+	0.0294065i
$111$	−1.13238	+	4.96127i	−0.107480	+	0.470903i
$112$	2.98164	−	7.57154i	0.281738	−	0.715443i
$113$	2.81671	+	12.3408i	0.264974	+	1.16093i	0.915780	+	0.401681i	$0.131574\pi$
$113$	2.81671	+	12.3408i	0.264974	+	1.16093i	−0.650806	+	0.759244i	$0.725569\pi$
$114$	0.574731	−	1.46439i	0.0538285	−	0.137153i
$115$	0.420260	−	5.60798i	0.0391894	−	0.522947i
$116$	−8.64304	+	14.9702i	−0.802487	+	1.38995i
$117$	−2.84838	−	4.93353i	−0.263333	−	0.456105i
$118$	−1.17035	+	0.563610i	−0.107739	+	0.0518845i
$119$	1.59620	−	20.9768i	0.146323	−	1.92294i
$120$	−1.38787	−	0.668362i	−0.126694	−	0.0610128i
$121$	−0.682699	−	9.10998i	−0.0620635	−	0.828180i
$122$	−0.0423961	−	0.0130775i	−0.00383837	−	0.00118398i
$123$	−6.48586	−	2.00062i	−0.584811	−	0.180390i
$124$	−0.698444	−	9.32008i	−0.0627221	−	0.836968i
$125$	−8.15908	−	3.92921i	−0.729771	−	0.351439i
$126$	−0.527256	+	0.910819i	−0.0469717	+	0.0811422i
$127$	−4.57770	+	2.20450i	−0.406205	+	0.195618i	−0.625818	−	0.779969i	$-0.715235\pi$
$127$	−4.57770	+	2.20450i	−0.406205	+	0.195618i	0.219613	+	0.975587i	$0.429521\pi$
$128$	5.16463	+	8.94539i	0.456493	+	0.790669i
$129$	0.325809	−	0.564318i	0.0286859	−	0.0496854i
$130$	−0.170699	+	2.27781i	−0.0149713	+	0.199778i
$131$	2.28244	−	5.81557i	0.199418	−	0.508109i	−0.795826	−	0.605526i	$-0.792963\pi$
$131$	2.28244	−	5.81557i	0.199418	−	0.508109i	0.995244	+	0.0974169i	$0.0310580\pi$
$132$	−0.559610	−	2.45181i	−0.0487078	−	0.213403i
$133$	−5.22132	−	9.06760i	−0.452745	−	0.786260i
$134$	−0.360380	+	1.57893i	−0.0311321	+	0.136399i
$135$	−0.832859	−	0.567834i	−0.0716811	−	0.0488714i
$136$	8.90741	+	8.26486i	0.763804	+	0.708706i
$137$	4.49565	−	0.677611i	0.384090	−	0.0578922i	0.0458405	−	0.998949i	$-0.485403\pi$
$137$	4.49565	−	0.677611i	0.384090	−	0.0578922i	0.338249	+	0.941057i	$0.390165\pi$
$138$	1.62679	−	1.50944i	0.138482	−	0.128492i
$139$	−1.42918	+	1.79214i	−0.121222	+	0.152007i	−0.838739	−	0.544533i	$-0.816707\pi$
$139$	−1.42918	+	1.79214i	−0.121222	+	0.152007i	0.717518	+	0.696540i	$0.245278\pi$
$140$	−4.42793	+	2.12612i	−0.374228	+	0.179690i
$141$	−6.82664	−	8.56034i	−0.574907	−	0.720910i
$142$	0.809106	+	0.121953i	0.0678987	+	0.0102341i
$143$	−6.42704	+	4.38188i	−0.537456	+	0.366432i
$144$	1.12367	+	2.86306i	0.0936391	+	0.238589i
$145$	9.04046	−	2.78861i	0.750770	−	0.231582i
$146$	2.84729			0.235643
$147$	2.54243	+	6.52197i	0.209696	+	0.537923i
$148$	−9.37252			−0.770416
$149$	−8.08088	+	2.49262i	−0.662011	+	0.204203i	−0.607512	−	0.794310i	$-0.707832\pi$
$149$	−8.08088	+	2.49262i	−0.662011	+	0.204203i	−0.0544991	+	0.998514i	$0.517356\pi$
$150$	−0.578960	−	1.47517i	−0.0472719	−	0.120447i
$151$	10.1861	−	6.94477i	0.828934	−	0.565158i	−0.0728507	−	0.997343i	$-0.523210\pi$
$151$	10.1861	−	6.94477i	0.828934	−	0.565158i	0.901785	+	0.432185i	$0.142257\pi$
$152$	5.97612	+	0.900756i	0.484728	+	0.0730609i
$153$	4.95762	+	6.21666i	0.400800	+	0.502587i
$154$	1.29401	+	0.624992i	0.104274	+	0.0503633i
$155$	−3.18930	+	3.99925i	−0.256171	+	0.321228i
$156$	7.69127	−	7.13646i	0.615795	−	0.571374i
$157$	0.626460	−	0.0944237i	0.0499970	−	0.00753583i	−0.123996	−	0.992283i	$-0.539571\pi$
$157$	0.626460	−	0.0944237i	0.0499970	−	0.00753583i	0.173993	+	0.984747i	$0.444333\pi$
$158$	−1.60593	−	1.49008i	−0.127761	−	0.118545i
$159$	6.20346	+	4.22945i	0.491966	+	0.335417i
$160$	0.959972	−	4.20591i	0.0758924	−	0.332506i
$161$	−1.08617	−	14.7206i	−0.0856026	−	1.16015i
$162$	−0.0885139	−	0.387805i	−0.00695431	−	0.0304688i
$163$	−6.96803	+	17.7542i	−0.545778	+	1.39062i	0.346038	+	0.938221i	$0.387527\pi$
$163$	−6.96803	+	17.7542i	−0.545778	+	1.39062i	−0.891816	+	0.452399i	$0.850568\pi$
$164$	0.934191	−	12.4659i	0.0729480	−	0.973424i
$165$	−0.688200	+	1.19200i	−0.0535763	+	0.0927968i
$166$	−0.290644	−	0.503410i	−0.0225584	−	0.0390722i
$167$	−11.3682	+	5.47462i	−0.879694	+	0.423638i	−0.818513	−	0.574488i	$-0.805201\pi$
$167$	−11.3682	+	5.47462i	−0.879694	+	0.423638i	−0.0611814	+	0.998127i	$0.519487\pi$
$168$	−3.86217	−	1.19618i	−0.297973	−	0.0922870i
$169$	−17.5266	−	8.44035i	−1.34820	−	0.649257i
$170$	−0.238257	−	3.17933i	−0.0182735	−	0.243843i
$171$	3.77911	+	1.16570i	0.288995	+	0.0891433i
$172$	1.14681	+	0.353745i	0.0874438	+	0.0269728i
$173$	0.229875	+	3.06747i	0.0174771	+	0.233215i	0.999101	+	0.0423902i	$0.0134973\pi$
$173$	0.229875	+	3.06747i	0.0174771	+	0.233215i	−0.981624	+	0.190825i	$0.938884\pi$
$174$	3.36365	+	1.61985i	0.254998	+	0.122801i
$175$	−10.0686	−	3.11840i	−0.761113	−	0.235729i
$176$	3.78380	−	1.82218i	0.285215	−	0.137352i
$177$	−1.63281	−	2.82810i	−0.122729	−	0.212573i
$178$	−1.23444	+	2.13811i	−0.0925251	+	0.160258i
$179$	0.725492	−	9.68102i	0.0542258	−	0.723593i	−0.902144	−	0.431435i	$-0.858008\pi$
$179$	0.725492	−	9.68102i	0.0542258	−	0.723593i	0.956370	−	0.292158i	$-0.0943734\pi$
$180$	0.678267	−	1.72820i	0.0505550	−	0.128812i
$181$	−0.786784	−	3.44713i	−0.0584812	−	0.256223i	0.937233	−	0.348703i	$-0.113378\pi$
$181$	−0.786784	−	3.44713i	−0.0584812	−	0.256223i	−0.995715	+	0.0924799i	$0.970521\pi$
$182$	0.441176	+	5.97913i	0.0327021	+	0.443203i
$183$	0.0248195	−	0.108741i	0.00183471	−	0.00803839i
$184$	7.04424	+	4.80268i	0.519308	+	0.354058i
$185$	3.76029	+	3.48904i	0.276462	+	0.256519i
$186$	−1.99601	+	0.300850i	−0.146354	+	0.0220594i
$187$	7.95897	−	7.38485i	0.582018	−	0.540034i
$188$	12.5731	−	15.7662i	0.916989	−	1.14987i
$189$	−2.38242	−	1.15068i	−0.173296	−	0.0836999i
$190$	−0.988693	−	1.23978i	−0.0717273	−	0.0899432i
$191$	−20.4764	−	3.08632i	−1.48162	−	0.223318i	−0.642088	−	0.766631i	$-0.721932\pi$
$191$	−20.4764	−	3.08632i	−1.48162	−	0.223318i	−0.839531	+	0.543313i	$0.817170\pi$
$192$	−3.67589	+	2.50618i	−0.265284	+	0.180868i
$193$	9.43715	+	24.0455i	0.679301	+	1.73083i	0.682554	+	0.730836i	$0.260869\pi$
$193$	9.43715	+	24.0455i	0.679301	+	1.73083i	−0.00325269	+	0.999995i	$0.501035\pi$
$194$	1.88645	−	0.581892i	0.135439	−	0.0417774i
$195$	−5.74240			−0.411222
$196$	−10.6688	+	7.23809i	−0.762060	+	0.517006i
$197$	10.3126			0.734741			0.367370	−	0.930075i	$-0.380258\pi$
$197$	10.3126			0.734741			0.367370	+	0.930075i	$0.380258\pi$
$198$	−0.519018	+	0.160096i	−0.0368850	+	0.0113775i
$199$	5.10580	+	13.0094i	0.361941	+	0.922210i	0.989616	+	0.143735i	$0.0459113\pi$
$199$	5.10580	+	13.0094i	0.361941	+	0.922210i	−0.627675	+	0.778475i	$0.715993\pi$
$200$	5.03023	−	3.42955i	0.355691	−	0.242506i
$201$	−4.02597	−	0.606818i	−0.283970	−	0.0428016i
$202$	−1.26390	−	1.58488i	−0.0889275	−	0.111512i
$203$	22.3851	−	10.7485i	1.57113	−	0.754395i
$204$	−9.13081	+	11.4497i	−0.639285	+	0.801638i
$205$	−5.01539	+	4.65360i	−0.350290	+	0.325022i
$206$	−2.85665	+	0.430571i	−0.199032	+	0.0299993i
$207$	4.08970	+	3.79468i	0.284254	+	0.263749i
$208$	14.4768	+	9.87013i	1.00379	+	0.684370i
$209$	1.20164	−	5.26473i	0.0831192	−	0.364169i
$210$	0.529373	+	0.919335i	0.0365302	+	0.0634401i
$211$	−1.25847	−	5.51370i	−0.0866364	−	0.379579i	0.912958	−	0.408053i	$-0.133792\pi$
$211$	−1.25847	−	5.51370i	−0.0866364	−	0.379579i	−0.999595	+	0.0284745i	$0.990935\pi$
$212$	−5.05199	+	12.8723i	−0.346972	+	0.884071i
$213$	−0.153723	+	2.05129i	−0.0105329	+	0.140552i
$214$	−1.79967	+	3.11712i	−0.123023	+	0.213082i
$215$	−0.328420	−	0.568840i	−0.0223981	−	0.0387946i
$216$	1.37684	−	0.663049i	0.0936818	−	0.0451148i
$217$	−6.72637	+	11.6196i	−0.456616	+	0.788790i
$218$	−1.45727	−	0.701785i	−0.0986988	−	0.0475309i
$219$	0.534917	+	7.13797i	0.0361463	+	0.482339i
$220$	−2.42239	−	0.747209i	−0.163318	−	0.0503768i
$221$	43.2848	+	13.3516i	2.91165	+	0.898125i
$222$	0.151271	+	2.01858i	0.0101527	+	0.135478i
$223$	6.54971	+	3.15417i	0.438601	+	0.211219i	0.640135	−	0.768262i	$-0.278878\pi$
$223$	6.54971	+	3.15417i	0.438601	+	0.211219i	−0.201534	+	0.979482i	$0.564593\pi$
$224$	0.859142	−	11.2906i	0.0574038	−	0.754384i
$225$	3.58938	−	1.72855i	0.239292	−	0.115237i
$226$	2.51757	+	4.36056i	0.167466	+	0.290060i
$227$	−12.3789	+	21.4410i	−0.821619	+	1.42309i	0.0828563	+	0.996562i	$0.473596\pi$
$227$	−12.3789	+	21.4410i	−0.821619	+	1.42309i	−0.904476	+	0.426525i	$0.859738\pi$
$228$	−0.544323	+	7.26349i	−0.0360487	+	0.481036i
$229$	3.91641	−	9.97884i	0.258803	−	0.659420i	−0.741125	−	0.671367i	$-0.765708\pi$
$229$	3.91641	−	9.97884i	0.258803	−	0.659420i	0.999929	+	0.0119465i	$0.00380279\pi$
$230$	−0.497776	−	2.18090i	−0.0328224	−	0.143804i
$231$	−1.32371	+	3.36141i	−0.0870938	+	0.221165i
$232$	−3.19157	+	13.9832i	−0.209537	+	0.918040i
$233$	24.7796	+	16.8944i	1.62336	+	1.10679i	0.916958	+	0.398984i	$0.130637\pi$
$233$	24.7796	+	16.8944i	1.62336	+	1.10679i	0.706406	+	0.707807i	$0.250315\pi$
$234$	−1.66113	−	1.54130i	−0.108591	−	0.100758i
$235$	−10.9135	+	1.64495i	−0.711921	+	0.107305i
$236$	4.40895	−	4.09091i	0.286998	−	0.266296i
$237$	3.43384	−	4.30590i	0.223052	−	0.279698i
$238$	−1.85275	−	8.16056i	−0.120096	−	0.528970i
$239$	−7.40228	−	9.28217i	−0.478814	−	0.600413i	0.482491	−	0.875901i	$-0.339732\pi$
$239$	−7.40228	−	9.28217i	−0.478814	−	0.600413i	−0.961305	+	0.275488i	$0.911161\pi$
$240$	3.06569	+	0.462078i	0.197889	+	0.0298270i
$241$	−14.7941	+	10.0865i	−0.952975	+	0.649727i	−0.936697	−	0.350140i	$-0.886134\pi$
$241$	−14.7941	+	10.0865i	−0.952975	+	0.649727i	−0.0162775	+	0.999868i	$0.505182\pi$
$242$	−1.32762	−	3.38271i	−0.0853424	−	0.217449i
$243$	0.955573	−	0.294755i	0.0613000	−	0.0189086i
$244$	0.205427			0.0131511
$245$	6.97485	+	1.06766i	0.445607	+	0.0682106i
$246$	−2.69988			−0.172138
$247$	21.5286	−	6.64070i	1.36983	−	0.422538i
$248$	−2.83316	−	7.21877i	−0.179906	−	0.458392i
$249$	1.20741	−	0.823201i	0.0765168	−	0.0521682i
$250$	−3.56200	−	0.536885i	−0.225281	−	0.0339556i
$251$	−5.65700	−	7.09366i	−0.357067	−	0.447748i	0.570560	−	0.821256i	$-0.306726\pi$
$251$	−5.65700	−	7.09366i	−0.357067	−	0.447748i	−0.927627	+	0.373508i	$0.878155\pi$
$252$	1.08977	−	4.74945i	0.0686488	−	0.299187i
$253$	4.74967	−	5.95590i	0.298610	−	0.374444i
$254$	−1.48154	+	1.37467i	−0.0929600	+	0.0862543i
$255$	7.92560	−	1.19459i	0.496320	−	0.0748083i
$256$	−3.51069	−	3.25744i	−0.219418	−	0.203590i
$257$	−19.8528	−	13.5354i	−1.23838	−	0.844314i	−0.246212	−	0.969216i	$-0.579186\pi$
$257$	−19.8528	−	13.5354i	−1.23838	−	0.844314i	−0.992169	+	0.124902i	$0.960138\pi$
$258$	0.0576773	−	0.252701i	0.00359083	−	0.0157325i
$259$	11.1156	+	7.59722i	0.690693	+	0.472068i
$260$	−2.35343	−	10.3110i	−0.145953	−	0.639463i
$261$	−3.42893	+	8.73678i	−0.212246	+	0.540793i
$262$	0.185711	−	2.47814i	0.0114733	−	0.153100i
$263$	5.42343	−	9.39366i	0.334423	−	0.579238i	−0.648951	−	0.760831i	$-0.724792\pi$
$263$	5.42343	−	9.39366i	0.334423	−	0.579238i	0.983374	+	0.181592i	$0.0581251\pi$
$264$	−1.04333	−	1.80710i	−0.0642124	−	0.111219i
$265$	6.81874	−	3.28373i	0.418872	−	0.201718i
$266$	−3.04780	−	2.83446i	−0.186873	−	0.173792i
$267$	−5.59202	−	2.69298i	−0.342226	−	0.164807i
$268$	−0.560377	−	7.47772i	−0.0342305	−	0.456774i
$269$	17.5711	+	5.41995i	1.07133	+	0.330460i	0.779752	−	0.626088i	$-0.215345\pi$
$269$	17.5711	+	5.41995i	1.07133	+	0.330460i	0.291574	+	0.956548i	$0.405821\pi$
$270$	−0.383152	−	0.118187i	−0.0233179	−	0.00719261i
$271$	0.829511	+	11.0691i	0.0503892	+	0.672397i	0.964016	+	0.265844i	$0.0856505\pi$
$271$	0.829511	+	11.0691i	0.0503892	+	0.672397i	−0.913627	+	0.406553i	$0.866730\pi$
$272$	−22.0340	−	10.6110i	−1.33601	−	0.643388i
$273$	−14.9064	+	2.22929i	−0.902178	+	0.134923i
$274$	1.62938	−	0.784666i	0.0984342	−	0.0474034i
$275$	−2.71993	−	4.71106i	−0.164018	−	0.284087i
$276$	−5.13762	+	8.89863i	−0.309249	+	0.535634i
$277$	2.32241	−	30.9904i	0.139540	−	1.86203i	−0.287476	−	0.957788i	$-0.592816\pi$
$277$	2.32241	−	30.9904i	0.139540	−	1.86203i	0.427016	−	0.904244i	$-0.359565\pi$
$278$	−0.333118	+	0.848770i	−0.0199791	+	0.0509058i
$279$	−1.12920	−	4.94735i	−0.0676034	−	0.296190i
$280$	−2.99078	+	2.76866i	−0.178733	+	0.165459i
$281$	−0.779955	+	3.41721i	−0.0465282	+	0.203853i	−0.992849	−	0.119375i	$-0.961911\pi$
$281$	−0.779955	+	3.41721i	−0.0465282	+	0.203853i	0.946321	+	0.323228i	$0.104768\pi$
$282$	−3.59852	−	2.45343i	−0.214289	−	0.146100i
$283$	13.8112	+	12.8149i	0.820988	+	0.761765i	0.974022	−	0.226456i	$-0.0727138\pi$
$283$	13.8112	+	12.8149i	0.820988	+	0.761765i	−0.153034	+	0.988221i	$0.548904\pi$
$284$	−3.74629	+	0.564662i	−0.222301	+	0.0335065i
$285$	2.92231	−	2.71151i	0.173103	−	0.160616i
$286$	−1.92919	+	2.41913i	−0.114076	+	0.143046i
$287$	−11.2126	+	14.0271i	−0.661859	+	0.827994i
$288$	2.66840	+	3.34607i	0.157237	+	0.197169i
$289$	−45.7086	−	6.88947i	−2.68874	−	0.405263i
$290$	3.10938	−	2.11994i	0.182589	−	0.124487i
$291$	1.81317	+	4.61988i	0.106290	+	0.270822i
$292$	−12.5977	+	3.88587i	−0.737223	+	0.227403i
$293$	15.1796			0.886800			0.443400	−	0.896324i	$-0.353772\pi$
$293$	15.1796			0.886800			0.443400	+	0.896324i	$0.353772\pi$
$294$	1.73107	+	2.18095i	0.100958	+	0.127195i
$295$	−3.29178			−0.191655
$296$	−7.43116	+	2.29221i	−0.431927	+	0.133232i
$297$	−0.498858	−	1.27107i	−0.0289467	−	0.0737549i
$298$	−2.77934	+	1.89492i	−0.161003	+	0.109770i
$299$	31.4272	+	4.73689i	1.81748	+	0.273941i
$300$	4.57483	+	5.73665i	0.264128	+	0.331206i
$301$	−1.07336	−	1.34913i	−0.0618675	−	0.0777623i
$302$	3.05755	−	3.83404i	0.175942	−	0.220624i
$303$	3.73574	−	3.46626i	0.214613	−	0.199131i
$304$	−12.0278	+	1.81290i	−0.689843	+	0.103977i
$305$	−0.0824181	−	0.0764728i	−0.00471925	−	0.00437882i
$306$	2.61331	+	1.78172i	0.149393	+	0.101854i
$307$	3.37078	−	14.7683i	0.192381	−	0.842874i	−0.782943	−	0.622093i	$-0.786282\pi$
$307$	3.37078	−	14.7683i	0.192381	−	0.842874i	0.975323	−	0.220781i	$-0.0708605\pi$
$308$	−6.57824	−	0.999231i	−0.374830	−	0.0569365i
$309$	−1.61609	−	7.08055i	−0.0919361	−	0.402798i
$310$	−0.743370	+	1.89408i	−0.0422206	+	0.107576i
$311$	1.31048	−	17.4871i	0.0743103	−	0.991603i	−0.828059	−	0.560640i	$-0.810555\pi$
$311$	1.31048	−	17.4871i	0.0743103	−	0.991603i	0.902370	−	0.430962i	$-0.141826\pi$
$312$	4.35281	−	7.53929i	0.246429	−	0.426828i
$313$	−2.61668	−	4.53221i	−0.147903	−	0.256176i	0.782549	−	0.622589i	$-0.213919\pi$
$313$	−2.61668	−	4.53221i	−0.147903	−	0.256176i	−0.930452	+	0.366413i	$0.880586\pi$
$314$	0.227050	−	0.109342i	0.0128132	−	0.00617051i
$315$	−2.20526	+	1.49982i	−0.124252	+	0.0845052i
$316$	9.13895	+	4.40109i	0.514106	+	0.247580i
$317$	−1.03999	−	13.8777i	−0.0584115	−	0.779447i	−0.947101	−	0.320937i	$-0.896002\pi$
$317$	−1.03999	−	13.8777i	−0.0584115	−	0.779447i	0.888689	−	0.458510i	$-0.151617\pi$
$318$	2.85386	+	0.880300i	0.160037	+	0.0493648i
$319$	12.2462	+	3.77746i	0.685658	+	0.211497i
$320$	0.335134	+	4.47205i	0.0187346	+	0.249995i
$321$	−8.15253	−	3.92605i	−0.455030	−	0.219131i
$322$	−2.13881	−	5.46804i	−0.119191	−	0.304722i
$323$	−28.3321	+	13.6440i	−1.57644	+	0.759174i
$324$	0.920886	+	1.59502i	0.0511604	+	0.0886123i
$325$	11.3477	−	19.6548i	0.629456	−	1.09025i
$326$	−0.566954	+	7.56547i	−0.0314007	+	0.419013i
$327$	1.48555	−	3.78513i	0.0821513	−	0.209318i
$328$	−2.30806	−	10.1123i	−0.127441	−	0.558357i
$329$	−27.6913	+	8.50686i	−1.52667	+	0.468998i
$330$	−0.121830	+	0.533774i	−0.00670655	+	0.0293833i
$331$	−16.9929	−	11.5855i	−0.934012	−	0.636799i	−0.00230028	−	0.999997i	$-0.500732\pi$
$331$	−16.9929	−	11.5855i	−0.934012	−	0.636799i	−0.931712	+	0.363199i	$0.881685\pi$
$332$	1.97297	+	1.83065i	0.108281	+	0.100470i
$333$	−5.03202	+	0.758455i	−0.275753	+	0.0415631i
$334$	−3.67922	+	3.41382i	−0.201318	+	0.186796i
$335$	−2.55885	+	3.20869i	−0.139805	+	0.175310i
$336$	8.13746	+	0.00933695i	0.443935	+	0.000509373i
$337$	10.8161	+	13.5630i	0.589193	+	0.738825i	0.983650	−	0.180090i	$-0.0576388\pi$
$337$	10.8161	+	13.5630i	0.589193	+	0.738825i	−0.394457	+	0.918914i	$0.629067\pi$
$338$	−7.65155	−	1.15329i	−0.416190	−	0.0627305i
$339$	−10.4587	+	7.13060i	−0.568037	+	0.387281i
$340$	5.39318	+	13.7416i	0.292486	+	0.745243i
$341$	−6.62128	+	2.04239i	−0.358562	+	0.110602i
$342$	1.57313			0.0850654
$343$	18.5201	+	0.0637505i	0.999994	+	0.00344220i
$344$	0.995785			0.0536891
$345$	5.37386	−	1.65762i	0.289319	−	0.0892430i
$346$	0.447028	+	1.13901i	0.0240324	+	0.0612336i
$347$	−16.0754	+	10.9600i	−0.862970	+	0.588363i	−0.911888	−	0.410440i	$-0.865375\pi$
$347$	−16.0754	+	10.9600i	−0.862970	+	0.588363i	0.0489174	+	0.998803i	$0.484423\pi$
$348$	−17.0930	−	2.57636i	−0.916282	−	0.138107i
$349$	5.27482	+	6.61442i	0.282355	+	0.354062i	0.902703	−	0.430265i	$-0.141580\pi$
$349$	5.27482	+	6.61442i	0.282355	+	0.354062i	−0.620348	+	0.784327i	$0.713008\pi$
$350$	−4.19275	−	0.00481078i	−0.224112	−	0.000257147i
$351$	3.55187	−	4.45390i	0.189585	−	0.237732i
$352$	4.28385	−	3.97483i	0.228330	−	0.211859i
$353$	−14.7637	+	2.22526i	−0.785790	+	0.118439i	−0.529668	−	0.848205i	$-0.677683\pi$
$353$	−14.7637	+	2.22526i	−0.785790	+	0.118439i	−0.256123	+	0.966644i	$0.582445\pi$
$354$	−0.952226	−	0.883537i	−0.0506103	−	0.0469595i
$355$	1.71323	+	1.16806i	0.0909286	+	0.0619940i
$356$	2.54370	−	11.1447i	0.134816	−	0.590667i
$357$	20.1099	−	6.17783i	1.06433	−	0.326965i
$358$	−0.859308	−	3.76487i	−0.0454158	−	0.198980i
$359$	7.10880	−	18.1129i	0.375188	−	0.955964i	−0.611192	−	0.791482i	$-0.709310\pi$
$359$	7.10880	−	18.1129i	0.375188	−	0.955964i	0.986380	−	0.164481i	$-0.0525950\pi$
$360$	0.115116	−	1.53611i	0.00606712	−	0.0809601i
$361$	1.67975	−	2.90942i	0.0884081	−	0.153127i
$362$	−0.703227	−	1.21802i	−0.0369608	−	0.0640179i
$363$	8.23082	−	3.96376i	0.432006	−	0.208043i
$364$	−10.1120	−	25.8523i	−0.530015	−	1.35503i
$365$	6.50080	+	3.13062i	0.340267	+	0.163864i
$366$	−0.00331557	−	0.0442432i	−0.000173308	−	0.00231263i
$367$	32.7692	+	10.1080i	1.71054	+	0.527632i	0.986730	−	0.162367i	$-0.0519130\pi$
$367$	32.7692	+	10.1080i	1.71054	+	0.527632i	0.723810	+	0.689999i	$0.242389\pi$
$368$	−16.3968	−	5.05776i	−0.854744	−	0.263654i
$369$	−0.507224	−	6.76843i	−0.0264050	−	0.352350i
$370$	1.83839	+	0.885320i	0.0955732	+	0.0460256i
$371$	16.4256	−	11.1712i	0.852777	−	0.579981i
$372$	8.42065	−	4.05517i	0.436590	−	0.210251i
$373$	14.9819	+	25.9493i	0.775731	+	1.34361i	0.934383	+	0.356271i	$0.115952\pi$
$373$	14.9819	+	25.9493i	0.775731	+	1.34361i	−0.158652	+	0.987335i	$0.550715\pi$
$374$	2.15940	−	3.74019i	0.111660	−	0.193401i
$375$	0.676748	−	9.03058i	0.0349471	−	0.466337i
$376$	6.11292	−	15.5755i	0.315250	−	0.803243i
$377$	11.8976	+	52.1268i	0.612757	+	2.68466i
$378$	−1.04049	−	0.158049i	−0.0535168	−	0.00812918i
$379$	3.91090	−	17.1348i	0.200890	−	0.880154i	−0.769507	−	0.638638i	$-0.779498\pi$
$379$	3.91090	−	17.1348i	0.200890	−	0.880154i	0.970397	−	0.241516i	$-0.0776447\pi$
$380$	6.06643	+	4.13602i	0.311201	+	0.212173i
$381$	−3.72454	−	3.45586i	−0.190814	−	0.177049i
$382$	−8.14505	+	1.22767i	−0.416737	+	0.0628130i
$383$	−1.59085	+	1.47609i	−0.0812885	+	0.0754247i	−0.719771	−	0.694212i	$-0.755753\pi$
$383$	−1.59085	+	1.47609i	−0.0812885	+	0.0754247i	0.638482	+	0.769637i	$0.279563\pi$
$384$	−6.44018	+	8.07573i	−0.328649	+	0.412113i
$385$	2.26724	+	2.84973i	0.115549	+	0.145236i
$386$	6.40638	+	8.03334i	0.326076	+	0.408886i
$387$	0.644340	+	0.0971187i	0.0327537	+	0.00493682i
$388$	−7.55234	+	5.14910i	−0.383412	+	0.261406i
$389$	3.91342	+	9.97122i	0.198418	+	0.505561i	0.995104	−	0.0988324i	$-0.0315108\pi$
$389$	3.91342	+	9.97122i	0.198418	+	0.505561i	−0.796686	+	0.604393i	$0.793416\pi$
$390$	−2.18272	+	0.673280i	−0.110526	+	0.0340929i
$391$	−44.3609			−2.24343
$392$	−6.68877	+	8.34809i	−0.337834	+	0.421642i
$393$	6.24744			0.315141
$394$	3.91987	−	1.20912i	0.197480	−	0.0609146i
$395$	−2.02822	−	5.16782i	−0.102051	−	0.260021i
$396$	2.07788	−	1.41667i	0.104417	−	0.0711905i
$397$	−0.141604	−	0.0213434i	−0.00710690	−	0.00107119i	0.145488	−	0.989360i	$-0.453525\pi$
$397$	−0.141604	−	0.0213434i	−0.00710690	−	0.00107119i	−0.152595	+	0.988289i	$0.548763\pi$
$398$	3.46606	+	4.34630i	0.173738	+	0.217860i
$399$	6.53323	−	8.17315i	0.327070	−	0.409169i
$400$	−7.63975	+	9.57994i	−0.381987	+	0.478997i
$401$	−4.01812	+	3.72827i	−0.200655	+	0.186181i	−0.774100	−	0.633063i	$-0.781797\pi$
$401$	−4.01812	+	3.72827i	−0.200655	+	0.186181i	0.573445	+	0.819244i	$0.305607\pi$
$402$	−1.60144	+	0.241379i	−0.0798728	+	0.0120389i
$403$	−21.1915	−	19.6629i	−1.05562	−	0.979476i
$404$	7.75503	+	5.28729i	0.385827	+	0.263053i
$405$	0.224304	−	0.982740i	0.0111458	−	0.0488327i
$406$	7.24848	−	6.71015i	0.359736	−	0.333019i
$407$	1.54621	+	6.77440i	0.0766429	+	0.335795i
$408$	−4.43930	+	11.3112i	−0.219778	+	0.559986i
$409$	−0.268348	+	3.58086i	−0.0132690	+	0.177062i	0.986632	+	0.162966i	$0.0521061\pi$
$409$	−0.268348	+	3.58086i	−0.0132690	+	0.177062i	−0.999901	+	0.0140960i	$0.995513\pi$
$410$	−1.36076	+	2.35690i	−0.0672030	+	0.116399i
$411$	2.27322	+	3.93733i	0.112130	+	0.194214i
$412$	12.0515	−	5.80368i	0.593733	−	0.285927i
$413$	−8.54497	+	1.27792i	−0.420471	+	0.0628824i
$414$	1.99943	+	0.962876i	0.0982668	+	0.0473228i
$415$	−0.110081	−	1.46893i	−0.00540366	−	0.0721069i
$416$	23.2977	+	7.18638i	1.14226	+	0.352341i
$417$	−2.19039	−	0.675647i	−0.107264	−	0.0330866i
$418$	−0.160524	−	2.14204i	−0.00785148	−	0.104771i
$419$	25.6645	+	12.3594i	1.25379	+	0.603796i	0.938527	−	0.345207i	$-0.112191\pi$
$419$	25.6645	+	12.3594i	1.25379	+	0.603796i	0.315268	+	0.949003i	$0.397906\pi$
$420$	−3.59686	−	3.34508i	−0.175509	−	0.163223i
$421$	−0.0411916	+	0.0198368i	−0.00200755	+	0.000966787i	−0.434887	−	0.900485i	$-0.643212\pi$
$421$	−0.0411916	+	0.0198368i	−0.00200755	+	0.000966787i	0.432880	+	0.901452i	$0.357497\pi$
$422$	−1.12482	−	1.94824i	−0.0547552	−	0.0948387i
$423$	5.47454	−	9.48218i	0.266181	−	0.461039i
$424$	−0.857425	+	11.4415i	−0.0416403	+	0.555651i
$425$	−11.5732	+	29.4879i	−0.561381	+	1.43038i
$426$	0.182077	+	0.797730i	0.00882164	+	0.0386502i
$427$	−0.243633	−	0.166516i	−0.0117902	−	0.00805828i
$428$	3.70843	−	16.2477i	0.179254	−	0.785361i
$429$	−6.42704	−	4.38188i	−0.310301	−	0.211559i
$430$	−0.191529	−	0.177713i	−0.00923636	−	0.00857009i
$431$	7.07224	−	1.06597i	0.340658	−	0.0513459i	0.0235143	−	0.999723i	$-0.492514\pi$
$431$	7.07224	−	1.06597i	0.340658	−	0.0513459i	0.317143	+	0.948378i	$0.397276\pi$
$432$	−2.25463	+	2.09199i	−0.108476	+	0.100651i
$433$	6.03880	−	7.57242i	0.290206	−	0.363907i	−0.615261	−	0.788324i	$-0.710949\pi$
$433$	6.03880	−	7.57242i	0.290206	−	0.363907i	0.905467	+	0.424416i	$0.139521\pi$
$434$	−1.19437	+	5.20533i	−0.0573315	+	0.249864i
$435$	5.89870	+	7.39673i	0.282821	+	0.354646i
$436$	7.40539	+	1.11618i	0.354654	+	0.0534555i
$437$	−18.2300	+	12.4290i	−0.872060	+	0.594560i
$438$	1.04023	+	2.65047i	0.0497042	+	0.126644i
$439$	12.7903	−	3.94527i	0.610446	−	0.188298i	0.0259083	−	0.999664i	$-0.491752\pi$
$439$	12.7903	−	3.94527i	0.610446	−	0.188298i	0.584537	+	0.811367i	$0.301276\pi$
$440$	−2.10338			−0.100274
$441$	−5.14228	+	4.74942i	−0.244870	+	0.226163i
$442$	18.0182			0.857040
$443$	20.5617	−	6.34243i	0.976914	−	0.301338i	0.235120	−	0.971966i	$-0.424452\pi$
$443$	20.5617	−	6.34243i	0.976914	−	0.301338i	0.741794	+	0.670628i	$0.233975\pi$
$444$	−3.42417	−	8.72463i	−0.162504	−	0.414053i
$445$	−5.16929	+	3.52436i	−0.245048	+	0.167071i
$446$	2.85940	+	0.430985i	0.135397	+	0.0204077i
$447$	−5.27259	−	6.61162i	−0.249385	−	0.312719i
$448$	2.60608	+	11.4787i	0.123126	+	0.542316i
$449$	2.87263	−	3.60216i	0.135568	−	0.169996i	−0.709414	−	0.704792i	$-0.751040\pi$
$449$	2.87263	−	3.60216i	0.135568	−	0.169996i	0.844981	+	0.534796i	$0.179612\pi$
$450$	1.16168	−	1.07788i	0.0547619	−	0.0508116i
$451$	−9.16440	+	1.38131i	−0.431535	+	0.0650434i
$452$	−17.0900	−	15.8572i	−0.803845	−	0.745859i
$453$	10.1861	+	6.94477i	0.478585	+	0.326294i
$454$	−2.19142	+	9.60123i	−0.102848	+	0.450608i
$455$	−5.56684	+	14.1364i	−0.260977	+	0.662723i
$456$	1.34483	+	5.89210i	0.0629776	+	0.275923i
$457$	−6.17651	+	15.7375i	−0.288925	+	0.736169i	0.710546	+	0.703651i	$0.248448\pi$
$457$	−6.17651	+	15.7375i	−0.288925	+	0.736169i	−0.999471	+	0.0325182i	$0.989647\pi$
$458$	0.318658	−	4.25220i	0.0148899	−	0.198692i
$459$	−3.97571	+	6.88612i	−0.185570	+	0.321417i
$460$	5.17879	+	8.96993i	0.241462	+	0.418225i
$461$	−26.1377	+	12.5873i	−1.21735	+	0.586247i	−0.928574	−	0.371148i	$-0.878964\pi$
$461$	−26.1377	+	12.5873i	−1.21735	+	0.586247i	−0.288781	+	0.957395i	$0.593250\pi$
$462$	−0.109034	+	1.43289i	−0.00507272	+	0.0666643i
$463$	13.6146	+	6.55643i	0.632723	+	0.304703i	0.722618	−	0.691248i	$-0.242939\pi$
$463$	13.6146	+	6.55643i	0.632723	+	0.304703i	−0.0898947	+	0.995951i	$0.528653\pi$
$464$	−2.15723	−	28.7862i	−0.100147	−	1.33637i
$465$	−4.88798	−	1.50774i	−0.226675	−	0.0699199i
$466$	11.3997	+	3.51634i	0.528080	+	0.162891i
$467$	−1.52638	−	20.3681i	−0.0706324	−	0.942523i	−0.914138	−	0.405403i	$-0.867131\pi$
$467$	−1.52638	−	20.3681i	−0.0706324	−	0.942523i	0.843506	−	0.537120i	$-0.180488\pi$
$468$	9.45308	+	4.55236i	0.436969	+	0.210433i
$469$	−5.39672	+	9.32268i	−0.249197	+	0.430481i
$470$	−3.95544	+	1.90484i	−0.182451	+	0.0878636i
$471$	0.316768	+	0.548659i	0.0145959	+	0.0252809i
$472$	2.49521	−	4.32183i	0.114851	−	0.198928i
$473$	0.0664916	−	0.887269i	0.00305729	−	0.0407967i
$474$	0.800368	−	2.03930i	0.0367621	−	0.0936683i
$475$	3.50595	+	15.3606i	0.160864	+	0.704791i
$476$	19.3346	+	33.5774i	0.886199	+	1.53902i
$477$	−1.67070	+	7.31983i	−0.0764962	+	0.335152i
$478$	−3.90196	−	2.66031i	−0.178471	−	0.121680i
$479$	−1.30910	−	1.21467i	−0.0598143	−	0.0554996i	0.649699	−	0.760191i	$-0.274895\pi$
$479$	−1.30910	−	1.21467i	−0.0598143	−	0.0554996i	−0.709514	+	0.704692i	$0.751085\pi$
$480$	4.26589	−	0.642979i	0.194710	−	0.0293479i
$481$	−21.2512	+	19.7182i	−0.968969	+	0.899072i
$482$	−4.44073	+	5.56850i	−0.202270	+	0.253638i
$483$	13.3062	−	6.38914i	0.605454	−	0.290716i
$484$	10.4906	+	13.1548i	0.476844	+	0.597943i
$485$	4.94685	+	0.745617i	0.224625	+	0.0338567i
$486$	0.328660	−	0.224076i	0.0149083	−	0.0101643i
$487$	−5.04193	−	12.8466i	−0.228472	−	0.582136i	0.769962	−	0.638090i	$-0.220275\pi$
$487$	−5.04193	−	12.8466i	−0.228472	−	0.582136i	−0.998433	+	0.0559540i	$0.982180\pi$
$488$	0.162876	−	0.0502407i	0.00737307	−	0.00227429i
$489$	−19.0727			−0.862496
$490$	2.77636	−	0.411955i	0.125423	−	0.0186102i
$491$	−1.39136			−0.0627913			−0.0313956	−	0.999507i	$-0.509995\pi$
$491$	−1.39136			−0.0627913			−0.0313956	+	0.999507i	$0.509995\pi$
$492$	11.9455	−	3.68469i	0.538544	−	0.166119i
$493$	−27.2649	−	69.4697i	−1.22795	−	3.12876i
$494$	7.40455	−	5.04834i	0.333147	−	0.227136i
$495$	−1.36103	−	0.205142i	−0.0611736	−	0.00922043i
$496$	9.73126	+	12.2026i	0.436947	+	0.547914i
$497$	4.90074	+	2.36700i	0.219828	+	0.106175i
$498$	0.362427	−	0.454469i	0.0162408	−	0.0203653i
$499$	27.3747	−	25.4000i	1.22546	−	1.13706i	0.239354	−	0.970932i	$-0.423064\pi$
$499$	27.3747	−	25.4000i	1.22546	−	1.13706i	0.986104	−	0.166127i	$-0.0531262\pi$
$500$	16.4926	−	2.48586i	0.737572	−	0.111171i
$501$	−9.24943	−	8.58222i	−0.413234	−	0.383425i
$502$	−2.98197	−	2.03307i	−0.133092	−	0.0907405i
$503$	1.34751	−	5.90385i	0.0600827	−	0.263240i	−0.935961	−	0.352104i	$-0.885467\pi$
$503$	1.34751	−	5.90385i	0.0600827	−	0.263240i	0.996044	+	0.0888640i	$0.0283236\pi$
$504$	−0.297520	−	4.03220i	−0.0132526	−	0.179609i
$505$	−1.14309	−	5.00819i	−0.0508667	−	0.222861i
$506$	1.10707	−	2.82076i	0.0492151	−	0.125398i
$507$	1.45373	−	19.3986i	0.0645622	−	0.861523i
$508$	4.67890	−	8.10409i	0.207592	−	0.359561i
$509$	−7.16090	−	12.4030i	−0.317401	−	0.549755i	0.662544	−	0.749023i	$-0.269477\pi$
$509$	−7.16090	−	12.4030i	−0.317401	−	0.549755i	−0.979945	+	0.199268i	$0.936144\pi$
$510$	2.87250	−	1.38333i	0.127197	−	0.0612547i
$511$	18.0905	+	5.60291i	0.800274	+	0.247858i
$512$	−20.3290	−	9.78994i	−0.898424	−	0.432658i
$513$	0.295543	+	3.94375i	0.0130485	+	0.174121i
$514$	−9.13313	−	2.81720i	−0.402845	−	0.124261i
$515$	−6.99559	−	2.15785i	−0.308262	−	0.0950864i
$516$	0.0896860	+	1.19678i	0.00394821	+	0.0526852i
$517$	−13.4699	−	6.48678i	−0.592407	−	0.285288i
$518$	5.11587	+	1.58447i	0.224779	+	0.0696176i
$519$	−2.77144	+	1.33466i	−0.121653	+	0.0585849i
$520$	−4.38769	−	7.59970i	−0.192413	−	0.333269i
$521$	1.04267	−	1.80596i	0.0456804	−	0.0791207i	−0.842281	−	0.539038i	$-0.818788\pi$
$521$	1.04267	−	1.80596i	0.0456804	−	0.0791207i	0.887962	+	0.459918i	$0.152121\pi$
$522$	−0.278995	+	3.72293i	−0.0122113	+	0.162948i
$523$	−12.9190	+	32.9170i	−0.564907	+	1.43936i	0.307959	+	0.951400i	$0.400354\pi$
$523$	−12.9190	+	32.9170i	−0.564907	+	1.43936i	−0.872866	+	0.487960i	$0.837741\pi$
$524$	2.56041	+	11.2179i	0.111852	+	0.490055i
$525$	−0.775627	−	10.5119i	−0.0338511	−	0.458775i
$526$	0.960099	−	4.20647i	0.0418623	−	0.183411i
$527$	33.3388	+	22.7300i	1.45226	+	0.990134i
$528$	3.07860	+	2.85652i	0.133979	+	0.124314i
$529$	−8.03448	+	1.21100i	−0.349325	+	0.0526523i
$530$	2.20684	−	2.04764i	0.0958588	−	0.0889440i
$531$	2.03608	−	2.55316i	0.0883582	−	0.110798i
$532$	17.3532	+	8.38141i	0.752357	+	0.363380i
$533$	−24.1080	−	30.2305i	−1.04423	−	1.30943i
$534$	−2.44130	−	0.367967i	−0.105646	−	0.0159235i
$535$	−7.53624	+	5.13812i	−0.325820	+	0.222140i
$536$	−2.27311	−	5.79178i	−0.0981833	−	0.250167i
$537$	9.27686	−	2.86153i	0.400326	−	0.123484i
$538$	7.31433			0.315343
$539$	6.99172	+	6.51729i	0.301155	+	0.280720i
$540$	1.85653			0.0798924
$541$	10.1158	−	3.12030i	0.434910	−	0.134152i	−0.0695665	−	0.997577i	$-0.522162\pi$
$541$	10.1158	−	3.12030i	0.434910	−	0.134152i	0.504477	+	0.863425i	$0.331685\pi$
$542$	1.61312	+	4.11015i	0.0692893	+	0.176546i
$543$	2.92139	−	1.99177i	0.125369	−	0.0854752i
$544$	−33.6502	−	5.07195i	−1.44274	−	0.217458i
$545$	−2.55556	−	3.20456i	−0.109468	−	0.137268i
$546$	−5.40464	+	2.59510i	−0.231297	+	0.111060i
$547$	0.686842	−	0.861272i	0.0293672	−	0.0368253i	−0.766931	−	0.641730i	$-0.778217\pi$
$547$	0.686842	−	0.861272i	0.0293672	−	0.0368253i	0.796298	+	0.604904i	$0.206789\pi$
$548$	−6.13821	+	5.69543i	−0.262211	+	0.243297i
$549$	0.110292	−	0.0166238i	0.00470715	−	0.000709488i
$550$	−1.58622	−	1.47180i	−0.0676366	−	0.0627576i
$551$	−30.6684	−	20.9094i	−1.30652	−	0.890769i
$552$	−1.89714	+	8.31192i	−0.0807477	+	0.353779i
$553$	−7.27119	−	12.6275i	−0.309202	−	0.536976i
$554$	−2.75077	−	12.0519i	−0.116869	−	0.512037i
$555$	−1.87407	+	4.77504i	−0.0795497	+	0.202689i
$556$	0.315493	−	4.20996i	0.0133799	−	0.178542i
$557$	−19.2070	+	33.2675i	−0.813826	+	1.40959i	0.0963414	+	0.995348i	$0.469286\pi$
$557$	−19.2070	+	33.2675i	−0.813826	+	1.40959i	−0.910168	+	0.414240i	$0.864047\pi$
$558$	−1.00928	−	1.74812i	−0.0427261	−	0.0740038i
$559$	3.34450	−	1.61062i	0.141457	−	0.0681221i
$560$	4.10948	−	7.09901i	0.173657	−	0.299988i
$561$	9.78210	+	4.71081i	0.413001	+	0.198891i
$562$	0.104192	+	1.39035i	0.00439508	+	0.0586483i
$563$	−2.87966	−	0.888257i	−0.121363	−	0.0374356i	0.233479	−	0.972362i	$-0.424989\pi$
$563$	−2.87966	−	0.888257i	−0.121363	−	0.0374356i	−0.354842	+	0.934926i	$0.615465\pi$
$564$	19.2698	+	5.94395i	0.811405	+	0.250285i
$565$	0.953526	+	12.7239i	0.0401151	+	0.535299i
$566$	6.75221	+	3.25169i	0.283816	+	0.136679i
$567$	0.200744	−	2.63812i	0.00843047	−	0.110791i
$568$	−2.83221	+	1.36392i	−0.118837	+	0.0572288i
$569$	7.49635	+	12.9841i	0.314263	+	0.544320i	0.979281	−	0.202508i	$-0.0649092\pi$
$569$	7.49635	+	12.9841i	0.314263	+	0.544320i	−0.665017	+	0.746828i	$0.731576\pi$
$570$	0.792870	−	1.37329i	0.0332097	−	0.0575208i
$571$	−0.977645	+	13.0458i	−0.0409132	+	0.545948i	0.938658	+	0.344850i	$0.112070\pi$
$571$	−0.977645	+	13.0458i	−0.0409132	+	0.545948i	−0.979571	+	0.201098i	$0.935549\pi$
$572$	5.23408	−	13.3362i	0.218848	−	0.557615i
$573$	−4.60789	−	20.1885i	−0.192497	−	0.843386i
$574$	−2.61734	+	6.64643i	−0.109246	+	0.277417i
$575$	−4.94580	+	21.6690i	−0.206254	+	0.903659i
$576$	−3.67589	−	2.50618i	−0.153162	−	0.104424i
$577$	−23.4625	−	21.7700i	−0.976755	−	0.906296i	0.0188617	−	0.999822i	$-0.493996\pi$
$577$	−23.4625	−	21.7700i	−0.976755	−	0.906296i	−0.995617	+	0.0935257i	$0.970186\pi$
$578$	−18.1819	+	2.74048i	−0.756267	+	0.113989i
$579$	−18.9355	+	17.5696i	−0.786933	+	0.730167i
$580$	−10.8641	+	13.6231i	−0.451106	+	0.565669i
$581$	−0.856015	−	3.77038i	−0.0355135	−	0.156422i
$582$	1.23086	+	1.54346i	0.0510210	+	0.0639783i
$583$	10.1374	+	1.52797i	0.419850	+	0.0632822i
$584$	−9.03792	+	6.16195i	−0.373992	+	0.254983i
$585$	−2.09794	−	5.34545i	−0.0867389	−	0.221007i
$586$	5.76984	−	1.77976i	0.238350	−	0.0735212i
$587$	29.2589			1.20765			0.603823	−	0.797119i	$-0.293644\pi$
$587$	29.2589			1.20765			0.603823	+	0.797119i	$0.293644\pi$
$588$	−10.6355	−	7.28698i	−0.438601	−	0.300510i
$589$	20.0690			0.826927
$590$	−1.25122	+	0.385952i	−0.0515121	+	0.0158894i
$591$	3.76761	+	9.59971i	0.154979	+	0.394879i
$592$	12.9320	−	8.81689i	0.531502	−	0.362372i
$593$	−17.3139	−	2.60966i	−0.710999	−	0.107166i	−0.216422	−	0.976300i	$-0.569439\pi$
$593$	−17.3139	−	2.60966i	−0.710999	−	0.107166i	−0.494577	+	0.869134i	$0.664677\pi$
$594$	−0.338648	−	0.424651i	−0.0138949	−	0.0174236i
$595$	4.74250	−	20.6689i	0.194424	−	0.847343i
$596$	9.71091	−	12.1771i	0.397775	−	0.498793i
$597$	−10.2447	+	9.50572i	−0.419289	+	0.389043i
$598$	12.5011	−	1.88423i	0.511206	−	0.0770519i
$599$	−22.2846	−	20.6771i	−0.910524	−	0.844843i	0.0778376	−	0.996966i	$-0.475198\pi$
$599$	−22.2846	−	20.6771i	−0.910524	−	0.844843i	−0.988362	+	0.152123i	$0.951389\pi$
$600$	5.03023	+	3.42955i	0.205358	+	0.140011i
$601$	−1.25465	+	5.49697i	−0.0511781	+	0.224226i	−0.994049	−	0.108932i	$-0.965257\pi$
$601$	−1.25465	+	5.49697i	−0.0511781	+	0.224226i	0.942871	+	0.333158i	$0.108114\pi$
$602$	−0.566172	−	0.386962i	−0.0230755	−	0.0157714i
$603$	−0.905983	−	3.96937i	−0.0368945	−	0.161645i
$604$	−8.29540	+	21.1363i	−0.337535	+	0.860025i
$605$	0.688169	−	9.18298i	0.0279781	−	0.373341i
$606$	1.01357	−	1.75555i	0.0411734	−	0.0713144i
$607$	−3.14210	−	5.44228i	−0.127534	−	0.220895i	0.795187	−	0.606365i	$-0.207373\pi$
$607$	−3.14210	−	5.44228i	−0.127534	−	0.220895i	−0.922721	+	0.385469i	$0.874040\pi$
$608$	−15.2495	+	7.34378i	−0.618450	+	0.297830i
$609$	18.1837	+	16.9108i	0.736839	+	0.685262i
$610$	−0.0402938	−	0.0194045i	−0.00163145	−	0.000785665i
$611$	−4.66123	−	62.1998i	−0.188573	−	2.51633i
$612$	−13.9941	−	4.31660i	−0.565677	−	0.174488i
$613$	−26.8309	−	8.27625i	−1.08369	−	0.334274i	−0.299058	−	0.954235i	$-0.596672\pi$
$613$	−26.8309	−	8.27625i	−1.08369	−	0.334274i	−0.784633	+	0.619960i	$0.787149\pi$
$614$	−0.450293	−	6.00875i	−0.0181724	−	0.242493i
$615$	−6.16425	−	2.96854i	−0.248566	−	0.119703i
$616$	−5.46005	+	0.816564i	−0.219992	+	0.0329003i
$617$	17.3508	−	8.35568i	0.698515	−	0.336387i	−0.0507000	−	0.998714i	$-0.516145\pi$
$617$	17.3508	−	8.35568i	0.698515	−	0.336387i	0.749215	+	0.662327i	$0.230431\pi$
$618$	−1.44446	−	2.50188i	−0.0581046	−	0.100640i
$619$	−8.88783	+	15.3942i	−0.357232	+	0.618744i	−0.987497	−	0.157636i	$-0.949613\pi$
$619$	−8.88783	+	15.3942i	−0.357232	+	0.618744i	0.630265	+	0.776380i	$0.282946\pi$
$620$	0.704040	−	9.39476i	0.0282749	−	0.377303i
$621$	−2.03824	+	5.19334i	−0.0817916	+	0.208402i
$622$	−1.55219	−	6.80060i	−0.0622372	−	0.272679i
$623$	−12.0505	+	11.1555i	−0.482793	+	0.446936i
$624$	−3.89887	+	17.0821i	−0.156080	+	0.683829i
$625$	8.91601	+	6.07883i	0.356641	+	0.243153i
$626$	−1.52600	−	1.41592i	−0.0609913	−	0.0565917i
$627$	5.33980	−	0.804846i	0.213251	−	0.0321425i
$628$	−0.855347	+	0.793646i	−0.0341321	+	0.0316699i
$629$	25.2286	−	31.6357i	1.00593	−	1.26140i
$630$	−0.662383	+	0.828650i	−0.0263900	+	0.0330142i
$631$	−10.9711	−	13.7573i	−0.436752	−	0.547670i	0.513932	−	0.857831i	$-0.328189\pi$
$631$	−10.9711	−	13.7573i	−0.436752	−	0.547670i	−0.950684	+	0.310161i	$0.899617\pi$
$632$	8.32233	+	1.25439i	0.331044	+	0.0498969i
$633$	4.67279	−	3.18585i	0.185727	−	0.126626i
$634$	−2.02242	−	5.15305i	−0.0803206	−	0.204654i
$635$	−4.89404	+	1.50961i	−0.194214	+	0.0599071i
$636$	−13.8282			−0.548322
$637$	−8.96272	+	38.8570i	−0.355116	+	1.53957i
$638$	5.09776			0.201822
$639$	−1.96565	+	0.606323i	−0.0777600	+	0.0239858i
$640$	3.80394	+	9.69227i	0.150364	+	0.383121i
$641$	0.935184	−	0.637597i	0.0369375	−	0.0251836i	−0.544711	−	0.838624i	$-0.683360\pi$
$641$	0.935184	−	0.637597i	0.0369375	−	0.0251836i	0.581648	+	0.813441i	$0.302408\pi$
$642$	−3.55914	−	0.536455i	−0.140468	−	0.0211722i
$643$	−3.09397	−	3.87972i	−0.122014	−	0.153001i	0.717073	−	0.696998i	$-0.245482\pi$
$643$	−3.09397	−	3.87972i	−0.122014	−	0.153001i	−0.839087	+	0.543997i	$0.816910\pi$
$644$	16.9256	+	21.2741i	0.666964	+	0.838317i
$645$	0.409533	−	0.513538i	0.0161253	−	0.0202205i
$646$	−9.16948	+	8.50803i	−0.360768	+	0.334744i
$647$	1.08809	−	0.164004i	0.0427774	−	0.00644765i	−0.127619	−	0.991823i	$-0.540733\pi$
$647$	1.08809	−	0.164004i	0.0427774	−	0.00644765i	0.170396	+	0.985376i	$0.445495\pi$
$648$	1.12023	+	1.03942i	0.0440068	+	0.0408323i
$649$	−3.68425	−	2.51188i	−0.144619	−	0.0985997i
$650$	2.00885	−	8.80137i	0.0787938	−	0.345218i
$651$	−13.2738	−	2.01628i	−0.520241	−	0.0790244i
$652$	−7.81661	−	34.2468i	−0.306122	−	1.34121i
$653$	14.4254	−	36.7552i	0.564508	−	1.43834i	−0.308777	−	0.951134i	$-0.599920\pi$
$653$	14.4254	−	36.7552i	0.564508	−	1.43834i	0.873286	−	0.487209i	$-0.161985\pi$
$654$	0.120872	−	1.61293i	0.00472647	−	0.0630704i
$655$	3.14875	−	5.45379i	0.123032	−	0.213097i
$656$	10.4379	+	18.0790i	0.407532	+	0.705867i
$657$	−6.44912	+	3.10573i	−0.251604	+	0.121166i
$658$	−9.52823	+	6.48024i	−0.371449	+	0.252626i
$659$	27.8454	+	13.4096i	1.08470	+	0.522365i	0.888817	−	0.458262i	$-0.151528\pi$
$659$	27.8454	+	13.4096i	1.08470	+	0.522365i	0.195884	+	0.980627i	$0.437242\pi$
$660$	−0.189442	−	2.52793i	−0.00737401	−	0.0983994i
$661$	16.0825	+	4.96079i	0.625536	+	0.192952i	0.591287	−	0.806461i	$-0.298620\pi$
$661$	16.0825	+	4.96079i	0.625536	+	0.192952i	0.0342490	+	0.999413i	$0.489096\pi$
$662$	−7.81745	−	2.41137i	−0.303834	−	0.0937204i
$663$	3.38507	+	45.1706i	0.131465	+	1.75428i
$664$	2.01202	+	0.968939i	0.0780816	+	0.0376021i
$665$	−3.84209	−	9.82260i	−0.148990	−	0.380904i
$666$	−1.82377	+	0.878283i	−0.0706698	+	0.0340328i
$667$	−26.1810	−	45.3469i	−1.01373	−	1.75584i
$668$	11.6195	−	20.1255i	0.449571	−	0.778679i
$669$	−0.543260	+	7.24930i	−0.0210037	+	0.280274i
$670$	−0.596423	+	1.51966i	−0.0230418	+	0.0587096i
$671$	−0.0338900	−	0.148482i	−0.00130831	−	0.00573207i
$672$	10.8240	−	3.32516i	0.417545	−	0.128271i
$673$	−5.81855	+	25.4927i	−0.224289	+	0.982672i	0.729921	+	0.683532i	$0.239557\pi$
$673$	−5.81855	+	25.4927i	−0.224289	+	0.982672i	−0.954209	+	0.299140i	$0.903300\pi$
$674$	5.70150	+	3.88722i	0.219614	+	0.149730i
$675$	2.92041	+	2.70975i	0.112407	+	0.104298i
$676$	35.4279	−	5.33989i	1.36261	−	0.205380i
$677$	31.1247	−	28.8795i	1.19622	−	1.10993i	0.204856	−	0.978792i	$-0.434328\pi$
$677$	31.1247	−	28.8795i	1.19622	−	1.10993i	0.991364	−	0.131137i	$-0.0418629\pi$
$678$	−3.13936	+	3.93663i	−0.120566	+	0.151185i
$679$	13.1307	+	0.0150663i	0.503911	+	0.000578190i
$680$	7.63681	+	9.57626i	0.292858	+	0.367233i
$681$	−24.4814	−	3.68997i	−0.938128	−	0.141400i
$682$	−2.27732	+	1.55265i	−0.0872031	+	0.0594541i
$683$	1.74948	+	4.45761i	0.0669421	+	0.170566i	0.960430	−	0.278522i	$-0.0898444\pi$
$683$	1.74948	+	4.45761i	0.0669421	+	0.170566i	−0.893488	+	0.449087i	$0.851749\pi$
$684$	−6.96025	+	2.14695i	−0.266132	+	0.0820908i
$685$	4.58287			0.175102
$686$	7.04709	−	2.14720i	0.269059	−	0.0819806i
$687$	10.7199			0.408988
$688$	−1.91513	+	0.590738i	−0.0730135	+	0.0225217i
$689$	15.6262	+	39.8150i	0.595312	+	1.51683i
$690$	1.84828	−	1.26014i	0.0703630	−	0.0479727i
$691$	42.1121	+	6.34738i	1.60202	+	0.241466i	0.888401	−	0.459069i	$-0.151817\pi$
$691$	42.1121	+	6.34738i	1.60202	+	0.241466i	0.713619	+	0.700534i	$0.247055\pi$
$692$	−3.53233	−	4.42940i	−0.134279	−	0.168381i
$693$	−3.61266	−	0.00414518i	−0.137234	−	0.000157462i
$694$	−4.82531	+	6.05075i	−0.183166	+	0.229683i
$695$	−1.69379	+	1.57161i	−0.0642491	+	0.0596144i
$696$	−14.1826	+	2.13768i	−0.537589	+	0.0810285i
$697$	39.5624	+	36.7086i	1.49853	+	1.39044i
$698$	2.78051	+	1.89572i	0.105244	+	0.0717541i
$699$	−6.67358	+	29.2389i	−0.252418	+	1.10592i
$700$	18.5572	−	5.70082i	0.701395	−	0.215471i
$701$	−4.15804	−	18.2176i	−0.157047	−	0.688068i	−0.990732	−	0.135828i	$-0.956630\pi$
$701$	−4.15804	−	18.2176i	−0.157047	−	0.688068i	0.833685	−	0.552240i	$-0.186227\pi$
$702$	0.827879	−	2.10940i	0.0312463	−	0.0796142i
$703$	1.50398	−	20.0692i	0.0567235	−	0.756923i
$704$	−3.03742	+	5.26097i	−0.114477	+	0.198280i
$705$	−5.51841	−	9.55816i	−0.207835	−	0.359981i
$706$	−5.35085	+	2.57683i	−0.201382	+	0.0969804i
$707$	−4.91154	−	12.5567i	−0.184717	−	0.472245i
$708$	5.41889	+	2.60960i	0.203654	+	0.0980748i
$709$	3.90476	+	52.1054i	0.146646	+	1.95686i	0.265914	+	0.963997i	$0.414326\pi$
$709$	3.90476	+	52.1054i	0.146646	+	1.95686i	−0.119268	+	0.992862i	$0.538055\pi$
$710$	0.788158	+	0.243115i	0.0295791	+	0.00912393i
$711$	5.26277	+	1.62335i	0.197369	+	0.0608803i
$712$	−0.708805	−	9.45835i	−0.0265636	−	0.354467i
$713$	25.5074	+	12.2837i	0.955259	+	0.460028i
$714$	6.91956	−	4.70606i	0.258958	−	0.176120i
$715$	−7.06450	+	3.40209i	−0.264197	+	0.127231i
$716$	8.94011	+	15.4847i	0.334108	+	0.578692i
$717$	5.93617	−	10.2817i	0.221690	−	0.383979i
$718$	0.578408	−	7.71831i	0.0215860	−	0.288045i
$719$	4.20535	−	10.7150i	0.156833	−	0.399604i	−0.830762	−	0.556628i	$-0.812095\pi$
$719$	4.20535	−	10.7150i	0.156833	−	0.399604i	0.987595	+	0.157024i	$0.0501901\pi$
$720$	0.689886	+	3.02259i	0.0257105	+	0.112645i
$721$	−18.9972	−	2.88567i	−0.707493	−	0.107468i
$722$	0.297363	−	1.30283i	0.0110667	−	0.0484865i
$723$	−14.7941	−	10.0865i	−0.550200	−	0.375120i
$724$	4.77370	+	4.42935i	0.177413	+	0.164615i
$725$	−36.9736	+	5.57288i	−1.37317	+	0.206972i
$726$	2.66384	−	2.47169i	0.0988646	−	0.0917329i
$727$	−23.5336	+	29.5103i	−0.872815	+	1.09447i	0.121976	+	0.992533i	$0.461077\pi$
$727$	−23.5336	+	29.5103i	−0.872815	+	1.09447i	−0.994790	+	0.101942i	$0.967494\pi$
$728$	−14.3401	−	18.0243i	−0.531480	−	0.668026i
$729$	0.623490	+	0.781831i	0.0230922	+	0.0289567i
$730$	2.83805	+	0.427767i	0.105041	+	0.0158324i
$731$	−4.28098	+	2.91872i	−0.158338	+	0.107953i
$732$	0.0750510	+	0.191227i	0.00277396	+	0.00706795i
$733$	−10.3408	+	3.18970i	−0.381945	+	0.117814i	−0.479781	−	0.877388i	$-0.659284\pi$
$733$	−10.3408	+	3.18970i	−0.381945	+	0.117814i	0.0978366	+	0.995202i	$0.468808\pi$
$734$	13.6409			0.503495
$735$	1.55434	+	6.88277i	0.0573326	+	0.253875i
$736$	−23.8769			−0.880114
$737$	−5.31240	+	1.63866i	−0.195685	+	0.0603608i
$738$	−0.986377	−	2.51325i	−0.0363091	−	0.0925140i
$739$	3.98669	−	2.71808i	0.146653	−	0.0999862i	−0.487771	−	0.872972i	$-0.662190\pi$
$739$	3.98669	−	2.71808i	0.146653	−	0.0999862i	0.634424	+	0.772986i	$0.281237\pi$
$740$	−9.34210	−	1.40809i	−0.343422	−	0.0517626i
$741$	14.0469	+	17.6143i	0.516028	+	0.647078i
$742$	4.93369	−	6.17211i	0.181121	−	0.226585i
$743$	−26.2741	+	32.9467i	−0.963905	+	1.20870i	0.0140543	+	0.999901i	$0.495526\pi$
$743$	−26.2741	+	32.9467i	−0.963905	+	1.20870i	−0.977959	+	0.208797i	$0.933045\pi$
$744$	5.68469	−	5.27462i	0.208411	−	0.193377i
$745$	−8.42913	+	1.27049i	−0.308820	+	0.0465471i
$746$	8.73717	+	8.10691i	0.319891	+	0.296815i
$747$	1.20741	+	0.823201i	0.0441770	+	0.0301194i
$748$	−4.44969	+	19.4953i	−0.162697	+	0.712820i
$749$	−17.5682	+	16.2635i	−0.641930	+	0.594254i
$750$	−0.801573	−	3.51192i	−0.0292693	−	0.128237i
$751$	−1.01302	+	2.58112i	−0.0369655	+	0.0941865i	−0.948164	−	0.317780i	$-0.897063\pi$
$751$	−1.01302	+	2.58112i	−0.0369655	+	0.0941865i	0.911199	+	0.411966i	$0.135158\pi$
$752$	−2.51659	+	33.5816i	−0.0917707	+	1.22460i
$753$	4.53656	−	7.85756i	0.165322	−	0.286345i
$754$	10.6341	+	18.4187i	0.387269	+	0.670770i
$755$	11.1964	−	5.39191i	0.407479	−	0.196232i
$756$	4.81928	−	0.720735i	0.175275	−	0.0262129i
$757$	31.0570	+	14.9563i	1.12879	+	0.543595i	0.902596	−	0.430488i	$-0.141659\pi$
$757$	31.0570	+	14.9563i	1.12879	+	0.543595i	0.226190	+	0.974083i	$0.427373\pi$
$758$	−0.522447	−	6.97157i	−0.0189761	−	0.253219i
$759$	7.27945	+	2.24541i	0.264227	+	0.0815033i
$760$	5.82140	+	1.79566i	0.211164	+	0.0651356i
$761$	−1.51238	−	20.1813i	−0.0548236	−	0.731571i	−0.955106	−	0.296264i	$-0.904259\pi$
$761$	−1.51238	−	20.1813i	−0.0548236	−	0.731571i	0.900282	−	0.435306i	$-0.143360\pi$
$762$	−1.82091	−	0.876903i	−0.0659645	−	0.0317668i
$763$	−7.87790	−	7.32646i	−0.285199	−	0.265236i
$764$	34.3619	−	16.5478i	1.24317	−	0.598679i
$765$	4.00756	+	6.94130i	0.144894	+	0.250963i
$766$	−0.431623	+	0.747593i	−0.0155952	+	0.0270116i
$767$	1.39023	−	18.5514i	0.0501984	−	0.669851i
$768$	1.74967	−	4.45808i	0.0631357	−	0.160867i
$769$	−6.29534	−	27.5817i	−0.227016	−	0.994621i	−0.952058	−	0.305917i	$-0.901037\pi$
$769$	−6.29534	−	27.5817i	−0.227016	−	0.994621i	0.725042	−	0.688704i	$-0.241820\pi$
$770$	1.19591	+	0.817371i	0.0430977	+	0.0294560i
$771$	5.34671	−	23.4254i	0.192557	−	0.843647i
$772$	−39.3083	−	26.7999i	−1.41474	−	0.964550i
$773$	19.6942	+	18.2736i	0.708352	+	0.657255i	0.949692	−	0.313186i	$-0.101396\pi$
$773$	19.6942	+	18.2736i	0.708352	+	0.657255i	−0.241340	+	0.970441i	$0.577587\pi$
$774$	0.256304	−	0.0386317i	0.00921267	−	0.00138859i
$775$	14.8199	−	13.7508i	0.532345	−	0.493944i
$776$	−4.72870	+	5.92960i	−0.169750	+	0.212860i
$777$	−3.01105	+	13.1228i	−0.108021	+	0.470779i
$778$	2.65661	+	3.33128i	0.0952441	+	0.119432i
$779$	26.5431	+	4.00072i	0.951004	+	0.143341i
$780$	8.73847	−	5.95779i	0.312887	−	0.213323i
$781$	1.02617	+	2.61464i	0.0367193	+	0.0935592i
$782$	−16.8618	+	5.20119i	−0.602978	+	0.185994i
$783$	−9.38557			−0.335413
$784$	7.91165	−	20.0233i	0.282559	−	0.715119i
$785$	0.638613			0.0227931
$786$	2.37469	−	0.732494i	0.0847023	−	0.0261272i
$787$	8.86710	+	22.5930i	0.316078	+	0.805353i	0.997311	+	0.0732866i	$0.0233488\pi$
$787$	8.86710	+	22.5930i	0.316078	+	0.805353i	−0.681233	+	0.732067i	$0.738556\pi$
$788$	−15.6931	+	10.6994i	−0.559044	+	0.381150i
$789$	10.7257	+	1.61664i	0.381846	+	0.0575540i
$790$	−1.37685	−	1.72652i	−0.0489861	−	0.0614267i
$791$	7.41484	+	32.6592i	0.263641	+	1.16123i
$792$	1.30101	−	1.63141i	0.0462293	−	0.0579697i
$793$	0.465784	−	0.432184i	0.0165405	−	0.0153473i
$794$	−0.0563270	+	0.00848992i	−0.00199897	+	0.000301296i
$795$	5.54791	+	5.14771i	0.196764	+	0.182570i
$796$	−21.2670	−	14.4996i	−0.753791	−	0.513926i
$797$	5.23766	−	22.9477i	0.185527	−	0.812849i	−0.793410	−	0.608688i	$-0.791696\pi$
$797$	5.23766	−	22.9477i	0.185527	−	0.812849i	0.978937	−	0.204161i	$-0.0654466\pi$
$798$	1.52504	−	3.87266i	0.0539858	−	0.137091i
$799$	19.3728	+	84.8778i	0.685361	+	3.00276i
$800$	−6.22916	+	15.8716i	−0.220234	+	0.561147i
$801$	0.463825	−	6.18932i	0.0163885	−	0.218689i
$802$	−1.09018	+	1.88825i	−0.0384957	+	0.0666765i
$803$	4.88696	+	8.46446i	0.172457	+	0.298704i
$804$	6.75608	−	3.25356i	0.238269	−	0.114744i
$805$	1.12893	−	14.8360i	0.0397894	−	0.522901i
$806$	−10.3604	−	4.98932i	−0.364931	−	0.175741i
$807$	1.37414	+	18.3366i	0.0483719	+	0.645478i
$808$	7.44180	+	2.29549i	0.261802	+	0.0807551i
$809$	−31.6351	−	9.75813i	−1.11223	−	0.343077i	−0.316417	−	0.948620i	$-0.602480\pi$
$809$	−31.6351	−	9.75813i	−1.11223	−	0.343077i	−0.795813	+	0.605543i	$0.792956\pi$
$810$	−0.0299642	−	0.399844i	−0.00105283	−	0.0140491i
$811$	−21.1430	−	10.1819i	−0.742431	−	0.357536i	0.0241288	−	0.999709i	$-0.492319\pi$
$811$	−21.1430	−	10.1819i	−0.742431	−	0.357536i	−0.766560	+	0.642173i	$0.778033\pi$
$812$	−22.9128	+	39.5811i	−0.804081	+	1.38903i
$813$	−10.0008	+	4.81615i	−0.350745	+	0.168910i
$814$	1.38200	+	2.39370i	0.0484392	+	0.0838992i
$815$	−9.61275	+	16.6498i	−0.336720	+	0.583216i
$816$	1.82759	−	24.3875i	0.0639786	−	0.853735i
$817$	−0.941493	+	2.39888i	−0.0329387	+	0.0839263i
$818$	0.317845	+	1.39257i	0.0111132	+	0.0486900i
$819$	−7.52112	−	13.0615i	−0.262809	−	0.456407i
$820$	2.80399	−	12.2851i	0.0979197	−	0.429014i
$821$	4.31123	+	2.93935i	0.150463	+	0.102584i	0.636212	−	0.771515i	$-0.280501\pi$
$821$	4.31123	+	2.93935i	0.150463	+	0.102584i	−0.485749	+	0.874099i	$0.661453\pi$
$822$	1.32570	+	1.23007i	0.0462392	+	0.0429037i
$823$	−21.4715	+	3.23631i	−0.748449	+	0.112811i	−0.512181	−	0.858877i	$-0.671162\pi$
$823$	−21.4715	+	3.23631i	−0.748449	+	0.112811i	−0.236268	+	0.971688i	$0.575924\pi$
$824$	8.13582	−	7.54894i	0.283425	−	0.262980i
$825$	3.39170	−	4.25305i	0.118084	−	0.148072i
$826$	−3.09816	+	1.48762i	−0.107799	+	0.0517609i
$827$	−5.84177	−	7.32535i	−0.203138	−	0.254727i	0.669819	−	0.742525i	$-0.266372\pi$
$827$	−5.84177	−	7.32535i	−0.203138	−	0.254727i	−0.872957	+	0.487797i	$0.837800\pi$
$828$	−10.1605	−	1.53145i	−0.353101	−	0.0532214i
$829$	28.2068	−	19.2311i	0.979663	−	0.667923i	0.0361805	−	0.999345i	$-0.488481\pi$
$829$	28.2068	−	19.2311i	0.979663	−	0.667923i	0.943483	+	0.331422i	$0.107528\pi$
$830$	−0.214070	−	0.545442i	−0.00743048	−	0.0189326i
$831$	29.6966	−	9.16019i	1.03016	−	0.317763i
$832$	−25.3445			−0.878664
$833$	4.28683	−	55.4945i	0.148530	−	1.92277i
$834$	−0.911799			−0.0315730
$835$	−12.1537	+	3.74893i	−0.420598	+	0.129737i
$836$	3.63361	+	9.25828i	0.125671	+	0.320204i
$837$	4.19281	−	2.85861i	0.144925	−	0.0988080i
$838$	11.2043	+	1.68878i	0.387048	+	0.0583380i
$839$	−16.6247	−	20.8467i	−0.573948	−	0.719708i	0.407120	−	0.913375i	$-0.366533\pi$
$839$	−16.6247	−	20.8467i	−0.573948	−	0.719708i	−0.981067	+	0.193667i	$0.937962\pi$
$840$	−3.66992	−	1.77253i	−0.126624	−	0.0611582i
$841$	36.8414	−	46.1976i	1.27039	−	1.59302i
$842$	−0.0133313	+	0.0123697i	−0.000459429	+	0.000426287i
$843$	−3.46594	+	0.522406i	−0.119373	+	0.0179926i
$844$	7.63557	+	7.08477i	0.262827	+	0.243868i
$845$	−16.2016	−	11.0461i	−0.557353	−	0.379997i
$846$	0.969146	−	4.24611i	0.0333199	−	0.145984i
$847$	−1.77859	−	24.1048i	−0.0611132	−	0.828251i
$848$	−5.13853	−	22.5134i	−0.176458	−	0.773113i
$849$	−6.88325	+	17.5382i	−0.236233	+	0.601911i
$850$	−0.941651	+	12.5655i	−0.0322984	+	0.430992i
$851$	14.1954	−	24.5871i	0.486611	−	0.842835i
$852$	−1.89430	−	3.28102i	−0.0648977	−	0.112406i
$853$	49.9659	−	24.0623i	1.71080	−	0.823878i	0.719161	−	0.694844i	$-0.244527\pi$
$853$	49.9659	−	24.0623i	1.71080	−	0.823878i	0.991640	−	0.129034i	$-0.0411878\pi$
$854$	−0.112130	−	0.0347284i	−0.00383701	−	0.00118838i
$855$	3.59171	+	1.72968i	0.122834	+	0.0591537i
$856$	−1.03336	−	13.7892i	−0.0353194	−	0.471305i
$857$	−20.5020	−	6.32402i	−0.700334	−	0.216025i	−0.0759155	−	0.997114i	$-0.524188\pi$
$857$	−20.5020	−	6.32402i	−0.700334	−	0.216025i	−0.624419	+	0.781090i	$0.714664\pi$
$858$	−2.95672	−	0.912027i	−0.100941	−	0.0311361i
$859$	3.04723	+	40.6625i	0.103970	+	1.38739i	0.768369	+	0.640008i	$0.221069\pi$
$859$	3.04723	+	40.6625i	0.103970	+	1.38739i	−0.664398	+	0.747379i	$0.731312\pi$
$860$	1.08995	+	0.524891i	0.0371669	+	0.0178986i
$861$	−17.1539	−	5.31284i	−0.584603	−	0.181061i
$862$	2.56322	−	1.23438i	0.0873035	−	0.0420432i
$863$	8.51832	+	14.7542i	0.289967	+	0.502238i	0.973802	−	0.227399i	$-0.0730223\pi$
$863$	8.51832	+	14.7542i	0.289967	+	0.502238i	−0.683834	+	0.729637i	$0.739689\pi$
$864$	−2.13989	+	3.70640i	−0.0728005	+	0.126094i
$865$	−0.231717	+	3.09205i	−0.00787861	+	0.105133i
$866$	1.40754	−	3.58635i	0.0478301	−	0.121869i
$867$	−10.2860	−	45.0660i	−0.349331	−	1.53052i
$868$	−1.81961	−	24.6607i	−0.0617617	−	0.837040i
$869$	1.67340	−	7.33164i	0.0567662	−	0.248709i
$870$	3.10938	+	2.11994i	0.105418	+	0.0718726i
$871$	−17.0024	−	15.7760i	−0.576106	−	0.534548i
$872$	6.14447	−	0.926129i	0.208078	−	0.0313627i
$873$	−3.63810	+	3.37567i	−0.123131	+	0.114249i
$874$	−5.47207	+	6.86176i	−0.185095	+	0.232102i
$875$	−21.5750	−	10.4205i	−0.729367	−	0.352276i
$876$	−8.21970	−	10.3072i	−0.277718	−	0.348247i
$877$	−9.84241	−	1.48351i	−0.332355	−	0.0500944i	−0.0192548	−	0.999815i	$-0.506129\pi$
$877$	−9.84241	−	1.48351i	−0.332355	−	0.0500944i	−0.313100	+	0.949720i	$0.601367\pi$
$878$	4.39908	−	2.99924i	0.148462	−	0.101220i
$879$	5.54572	+	14.1303i	0.187052	+	0.476602i
$880$	4.04528	−	1.24780i	0.136366	−	0.0420634i
$881$	20.5389			0.691973			0.345986	−	0.938240i	$-0.387544\pi$
$881$	20.5389			0.691973			0.345986	+	0.938240i	$0.387544\pi$
$882$	−1.39775	+	2.40820i	−0.0470648	+	0.0810883i
$883$	−46.0187			−1.54865			−0.774326	−	0.632787i	$-0.781911\pi$
$883$	−46.0187			−1.54865			−0.774326	+	0.632787i	$0.781911\pi$
$884$	−79.7208	+	24.5906i	−2.68130	+	0.827071i
$885$	−1.20262	−	3.06423i	−0.0404257	−	0.103003i
$886$	7.07197	−	4.82159i	0.237588	−	0.161984i
$887$	30.3587	+	4.57583i	1.01934	+	0.153641i	0.637391	−	0.770540i	$-0.280014\pi$
$887$	30.3587	+	4.57583i	1.01934	+	0.153641i	0.381953	+	0.924182i	$0.375252\pi$
$888$	−4.84866	−	6.08003i	−0.162710	−	0.204032i
$889$	−12.1181	+	5.81867i	−0.406429	+	0.195152i
$890$	−1.55166	+	1.94571i	−0.0520116	+	0.0652205i
$891$	1.00095	−	0.928747i	0.0335331	−	0.0311142i
$892$	−13.2395	+	1.99553i	−0.443290	+	0.0668152i
$893$	31.7422	+	29.4525i	1.06221	+	0.985590i
$894$	−2.77934	−	1.89492i	−0.0929549	−	0.0633756i
$895$	2.17758	−	9.54060i	0.0727885	−	0.318907i
$896$	13.6371	+	23.6829i	0.455585	+	0.791192i
$897$	7.07220	+	30.9853i	0.236134	+	1.03457i
$898$	0.669559	−	1.70601i	0.0223435	−	0.0569302i
$899$	−3.55923	+	47.4946i	−0.118707	+	1.58403i
$900$	−3.66873	+	6.35442i	−0.122291	+	0.211814i
$901$	−29.8499	−	51.7015i	−0.994444	−	1.72243i
$902$	−3.32149	+	1.59954i	−0.110593	+	0.0532590i
$903$	0.863723	−	1.49206i	0.0287429	−	0.0496525i
$904$	−17.4282	−	8.39299i	−0.579654	−	0.279147i
$905$	−0.266346	−	3.55414i	−0.00885364	−	0.118144i
$906$	4.68606	+	1.44546i	0.155684	+	0.0480221i
$907$	36.9726	+	11.4045i	1.22765	+	0.378681i	0.839727	−	0.543008i	$-0.182715\pi$
$907$	36.9726	+	11.4045i	1.22765	+	0.378681i	0.387928	+	0.921690i	$0.373191\pi$
$908$	−3.40757	−	45.4709i	−0.113084	−	1.50900i
$909$	4.59147	+	2.21114i	0.152289	+	0.0733387i
$910$	−0.458541	+	6.02601i	−0.0152005	+	0.199760i
$911$	−24.2426	+	11.6746i	−0.803194	+	0.386798i	−0.789994	−	0.613115i	$-0.789916\pi$
$911$	−24.2426	+	11.6746i	−0.803194	+	0.386798i	−0.0132004	+	0.999913i	$0.504202\pi$
$912$	−6.08184	−	10.5341i	−0.201390	−	0.348818i
$913$	0.997698	−	1.72806i	0.0330190	−	0.0571905i
$914$	−0.502552	+	6.70609i	−0.0166229	+	0.221818i
$915$	0.0410758	−	0.104660i	0.00135793	−	0.00345994i
$916$	4.39335	+	19.2485i	0.145160	+	0.635990i
$917$	6.05643	−	15.3796i	0.200001	−	0.507880i
$918$	−0.703810	+	3.08360i	−0.0232292	+	0.101774i
$919$	24.6678	+	16.8182i	0.813714	+	0.554781i	0.897147	−	0.441732i	$-0.145636\pi$
$919$	24.6678	+	16.8182i	0.813714	+	0.554781i	−0.0834326	+	0.996513i	$0.526588\pi$
$920$	6.29984	+	5.84540i	0.207700	+	0.192717i
$921$	14.9790	−	2.25771i	0.493573	−	0.0743942i
$922$	−8.45927	+	7.84906i	−0.278591	+	0.258495i
$923$	−7.30634	+	9.16186i	−0.240491	+	0.301566i
$924$	−1.47314	−	6.48857i	−0.0484629	−	0.213458i
$925$	−12.6404	−	15.8505i	−0.415612	−	0.521161i
$926$	5.94370	+	0.895869i	0.195322	+	0.0294401i
$927$	6.00067	−	4.09119i	0.197088	−	0.134372i
$928$	−14.6751	−	37.3915i	−0.481733	−	1.22744i
$929$	1.77568	−	0.547724i	0.0582581	−	0.0179702i	−0.265489	−	0.964114i	$-0.585533\pi$
$929$	1.77568	−	0.547724i	0.0582581	−	0.0179702i	0.323747	+	0.946144i	$0.395057\pi$
$930$	−2.03473			−0.0667214
$931$	−13.7868	−	24.0064i	−0.451843	−	0.786779i
$932$	−55.2363			−1.80932
$933$	16.7571	−	5.16887i	0.548601	−	0.169221i
$934$	−2.96829	−	7.56307i	−0.0971253	−	0.247471i
$935$	9.04262	−	6.16515i	0.295725	−	0.201622i
$936$	8.60839	+	1.29751i	0.281374	+	0.0424103i
$937$	−6.17885	−	7.74803i	−0.201854	−	0.253117i	0.670593	−	0.741825i	$-0.266040\pi$
$937$	−6.17885	−	7.74803i	−0.201854	−	0.253117i	−0.872447	+	0.488708i	$0.837468\pi$
$938$	−0.958268	+	4.17635i	−0.0312886	+	0.136363i
$939$	3.26294	−	4.09160i	0.106482	−	0.133524i
$940$	14.9010	−	13.8261i	0.486016	−	0.450957i
$941$	−7.71531	+	1.16290i	−0.251512	+	0.0379093i	−0.273588	−	0.961847i	$-0.588210\pi$
$941$	−7.71531	+	1.16290i	−0.251512	+	0.0379093i	0.0220762	+	0.999756i	$0.492972\pi$
$942$	0.184734	+	0.171408i	0.00601896	+	0.00558478i
$943$	31.2871	+	21.3312i	1.01885	+	0.694640i
$944$	−2.23499	+	9.79213i	−0.0727427	+	0.318707i
$945$	−2.20181	−	1.50487i	−0.0716250	−	0.0489536i
$946$	−0.0787559	−	0.345052i	−0.00256058	−	0.0112186i
$947$	2.57368	−	6.55763i	0.0836333	−	0.213094i	−0.882939	−	0.469487i	$-0.844439\pi$
$947$	2.57368	−	6.55763i	0.0836333	−	0.213094i	0.966573	+	0.256393i	$0.0825341\pi$
$948$	−0.758022	+	10.1151i	−0.0246194	+	0.328523i
$949$	−20.3886	+	35.3141i	−0.661843	+	1.14635i
$950$	3.13361	+	5.42758i	0.101668	+	0.176094i
$951$	12.5384	−	6.03818i	0.406586	−	0.195801i
$952$	23.5417	+	21.8938i	0.762990	+	0.709582i
$953$	−33.9873	−	16.3674i	−1.10096	−	0.530193i	−0.206997	−	0.978341i	$-0.566369\pi$
$953$	−33.9873	−	16.3674i	−1.10096	−	0.530193i	−0.893959	+	0.448149i	$0.852083\pi$
$954$	0.223185	+	2.97819i	0.00722587	+	0.0964226i
$955$	−19.9462	−	6.15260i	−0.645445	−	0.199094i
$956$	20.8947	+	6.44516i	0.675783	+	0.208451i
$957$	0.957711	+	12.7798i	0.0309584	+	0.413111i
$958$	−0.640013	−	0.308214i	−0.0206779	−	0.00995794i
$959$	11.8964	−	1.77914i	0.384156	−	0.0574515i
$960$	−4.04048	+	1.94579i	−0.130406	+	0.0628001i
$961$	2.62434	+	4.54549i	0.0846561	+	0.146629i
$962$	−5.76579	+	9.98663i	−0.185896	+	0.321982i
$963$	0.676205	−	9.02333i	0.0217904	−	0.290773i
$964$	12.0481	−	30.6981i	0.388043	−	0.988718i
$965$	5.79401	+	25.3852i	0.186516	+	0.817179i
$966$	4.30866	−	3.98867i	0.138629	−	0.128333i
$967$	8.74956	−	38.3343i	0.281367	−	1.23275i	−0.614675	−	0.788780i	$-0.710713\pi$
$967$	8.74956	−	38.3343i	0.281367	−	1.23275i	0.896042	−	0.443969i	$-0.146430\pi$
$968$	11.5348	+	7.86432i	0.370744	+	0.252769i
$969$	−23.0518	−	21.3889i	−0.740529	−	0.687111i
$970$	1.96775	−	0.296590i	0.0631805	−	0.00952293i
$971$	16.4568	−	15.2697i	0.528124	−	0.490028i	−0.370448	−	0.928853i	$-0.620796\pi$
$971$	16.4568	−	15.2697i	0.528124	−	0.490028i	0.898572	+	0.438825i	$0.144605\pi$
$972$	−1.14833	+	1.43996i	−0.0368326	+	0.0461866i
$973$	−3.78670	+	4.73721i	−0.121396	+	0.151868i
$974$	−3.42270	−	4.29192i	−0.109670	−	0.137522i
$975$	22.4419	+	3.38257i	0.718715	+	0.108329i
$976$	−0.283444	+	0.193249i	−0.00907283	+	0.00618575i
$977$	14.8655	+	37.8766i	0.475588	+	1.21178i	0.944493	+	0.328531i	$0.106553\pi$
$977$	14.8655	+	37.8766i	0.475588	+	1.21178i	−0.468905	+	0.883249i	$0.655351\pi$
$978$	−7.24963	+	2.23621i	−0.231818	+	0.0715063i
$979$	−8.47495			−0.270861
$980$	−11.7216	+	5.61175i	−0.374434	+	0.179261i
$981$	4.06621			0.129824
$982$	−0.528865	+	0.163133i	−0.0168767	+	0.00520579i
$983$	−12.7054	−	32.3729i	−0.405240	−	1.03253i	−0.977213	−	0.212262i	$-0.931917\pi$
$983$	−12.7054	−	32.3729i	−0.405240	−	1.03253i	0.571973	−	0.820273i	$-0.306178\pi$
$984$	8.57002	−	5.84294i	0.273202	−	0.186266i
$985$	10.2791	+	1.54933i	0.327520	+	0.0493656i
$986$	−18.5087	−	23.2091i	−0.589436	−	0.739129i
$987$	−18.0356	−	22.6692i	−0.574079	−	0.721569i
$988$	−25.8713	+	32.4416i	−0.823075	+	1.03210i
$989$	−2.66492	+	2.47269i	−0.0847396	+	0.0786268i
$990$	−0.541386	+	0.0816008i	−0.0172064	+	0.00259344i
$991$	−5.90508	−	5.47911i	−0.187581	−	0.174050i	0.580792	−	0.814052i	$-0.302743\pi$
$991$	−5.90508	−	5.47911i	−0.187581	−	0.174050i	−0.768373	+	0.640002i	$0.778933\pi$
$992$	17.9443	+	12.2342i	0.569732	+	0.388437i
$993$	4.57648	−	20.0509i	0.145230	−	0.636295i
$994$	2.14032	+	0.325114i	0.0678869	+	0.0103120i
$995$	3.13475	+	13.7342i	0.0993782	+	0.435404i
$996$	−0.983298	+	2.50540i	−0.0311570	+	0.0793867i
$997$	−1.37466	+	18.3435i	−0.0435358	+	0.580944i	0.932193	+	0.361962i	$0.117893\pi$
$997$	−1.37466	+	18.3435i	−0.0435358	+	0.580944i	−0.975729	+	0.218983i	$0.929726\pi$
$998$	7.42720	−	12.8643i	0.235104	−	0.407212i
$999$	−2.54443	−	4.40708i	−0.0805022	−	0.139434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.2.m.b.25.3	✓	60
3.2	odd	2		441.2.bb.e.172.3		60
49.2	even	21	inner	147.2.m.b.100.3	yes	60
49.10	odd	42		7203.2.a.m.1.17		30
49.39	even	21		7203.2.a.n.1.17		30
147.2	odd	42		441.2.bb.e.100.3		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.25.3	✓	60	1.1	even	1	trivial
147.2.m.b.100.3	yes	60	49.2	even	21	inner
441.2.bb.e.100.3		60	147.2	odd	42
441.2.bb.e.172.3		60	3.2	odd	2
7203.2.a.m.1.17		30	49.10	odd	42
7203.2.a.n.1.17		30	49.39	even	21

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.380106 - 0.117247i) q^{2} +(0.365341 + 0.930874i) q^{3} +(-1.52174 + 1.03751i) q^{4} +(0.996754 + 0.150237i) q^{5} +(0.248010 + 0.310995i) q^{6} +(2.64575 + 0.00303574i) q^{7} +(-0.952800 + 1.19477i) q^{8} +(-0.733052 + 0.680173i) q^{9} +O(q^{10})\)	\(q+(0.380106 - 0.117247i) q^{2} +(0.365341 + 0.930874i) q^{3} +(-1.52174 + 1.03751i) q^{4} +(0.996754 + 0.150237i) q^{5} +(0.248010 + 0.310995i) q^{6} +(2.64575 + 0.00303574i) q^{7} +(-0.952800 + 1.19477i) q^{8} +(-0.733052 + 0.680173i) q^{9} +(0.396487 - 0.0597608i) q^{10} +(1.00095 + 0.928747i) q^{11} +(-1.52174 - 1.03751i) q^{12} +(-1.26765 + 5.55392i) q^{13} +(1.00602 - 0.309053i) q^{14} +(0.224304 + 0.982740i) q^{15} +(1.12367 - 2.86306i) q^{16} +(0.594210 - 7.92918i) q^{17} +(-0.198889 + 0.344486i) q^{18} +(-1.97740 - 3.42496i) q^{19} +(-1.67268 + 0.805519i) q^{20} +(0.963775 + 2.46397i) q^{21} +(0.489360 + 0.235663i) q^{22} +(-0.416919 - 5.56340i) q^{23} +(-1.46028 - 0.450437i) q^{24} +(-3.80692 - 1.17428i) q^{25} +(0.169342 + 2.25971i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-4.02930 + 2.74037i) q^{28} +(8.45611 - 4.07225i) q^{29} +(0.200483 + 0.347246i) q^{30} +(-2.53729 + 4.39471i) q^{31} +(0.319828 - 4.26781i) q^{32} +(-0.498858 + 1.27107i) q^{33} +(-0.703810 - 3.08360i) q^{34} +(2.63671 + 0.400514i) q^{35} +(0.409833 - 1.79560i) q^{36} +(4.20461 + 2.86666i) q^{37} +(-1.15319 - 1.07000i) q^{38} +(-5.63313 + 0.849057i) q^{39} +(-1.12921 + 1.04775i) q^{40} +(-4.23188 + 5.30661i) q^{41} +(0.655230 + 0.823569i) q^{42} +(-0.406277 - 0.509456i) q^{43} +(-2.48677 - 0.374821i) q^{44} +(-0.832859 + 0.567834i) q^{45} +(-0.810766 - 2.06580i) q^{46} +(-10.4626 + 3.22730i) q^{47} +3.07567 q^{48} +(6.99998 + 0.0160636i) q^{49} -1.58471 q^{50} +(7.59815 - 2.34372i) q^{51} +(-3.83320 - 9.76685i) q^{52} +(6.20346 - 4.22945i) q^{53} +(-0.393335 - 0.0592857i) q^{54} +(0.858171 + 1.07611i) q^{55} +(-2.52450 + 3.15818i) q^{56} +(2.46578 - 3.09199i) q^{57} +(2.73676 - 2.53934i) q^{58} +(-3.22914 + 0.486714i) q^{59} +(-1.36093 - 1.26276i) q^{60} +(-0.0921568 - 0.0628315i) q^{61} +(-0.449171 + 1.96795i) q^{62} +(-1.94154 + 1.79734i) q^{63} +(0.989983 + 4.33740i) q^{64} +(-2.09794 + 5.34545i) q^{65} +(-0.0405896 + 0.541630i) q^{66} +(-2.03572 + 3.52598i) q^{67} +(7.32235 + 12.6827i) q^{68} +(5.02650 - 2.42064i) q^{69} +(1.04919 - 0.156908i) q^{70} +(1.85333 + 0.892516i) q^{71} +(-0.114200 - 1.52390i) q^{72} +(6.83997 + 2.10985i) q^{73} +(1.93430 + 0.596654i) q^{74} +(-0.297718 - 3.97277i) q^{75} +(6.56253 + 3.16035i) q^{76} +(2.64545 + 2.46027i) q^{77} +(-2.04163 + 0.983199i) q^{78} +(-2.75372 - 4.76959i) q^{79} +(1.55016 - 2.68495i) q^{80} +(0.0747301 - 0.997204i) q^{81} +(-0.986377 + 2.51325i) q^{82} +(-0.325178 - 1.42470i) q^{83} +(-4.02300 - 2.74960i) q^{84} +(1.78353 - 7.81417i) q^{85} +(-0.214161 - 0.146012i) q^{86} +(6.88011 + 6.38381i) q^{87} +(-2.06335 + 0.311000i) q^{88} +(-4.54981 + 4.22161i) q^{89} +(-0.249998 + 0.313487i) q^{90} +(-3.37074 + 14.6904i) q^{91} +(6.40651 + 8.03351i) q^{92} +(-5.01790 - 0.756326i) q^{93} +(-3.59852 + 2.45343i) q^{94} +(-1.45643 - 3.71092i) q^{95} +(4.08964 - 1.26149i) q^{96} +4.96295 q^{97} +(2.66262 - 0.814622i) q^{98} -1.36546 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9} - 34 q^{10} - 11 q^{11} + 5 q^{12} - 2 q^{13} + 40 q^{14} - 3 q^{15} - 31 q^{16} - 9 q^{17} - 6 q^{18} - 29 q^{19} - 43 q^{20} - 11 q^{21} + 9 q^{22} - 4 q^{23} - 24 q^{24} + 55 q^{25} + 36 q^{26} - 10 q^{27} - 57 q^{28} + 4 q^{29} - 20 q^{30} - 39 q^{31} - 92 q^{32} - 18 q^{33} - 36 q^{34} - 33 q^{35} - 10 q^{36} - 24 q^{37} + 118 q^{38} - 6 q^{39} + 35 q^{41} + 38 q^{42} + 2 q^{43} + 40 q^{44} + 12 q^{45} - 40 q^{46} - 5 q^{47} + 76 q^{48} + 129 q^{49} - 176 q^{50} + 54 q^{51} - 6 q^{52} + 26 q^{53} + q^{54} + 2 q^{55} + 63 q^{56} - 12 q^{57} + 11 q^{58} - 41 q^{59} + 32 q^{60} + 6 q^{61} + 36 q^{62} - q^{63} + 74 q^{64} - 51 q^{65} - 15 q^{66} - 55 q^{67} - 22 q^{68} + 8 q^{69} - 68 q^{70} - 66 q^{71} - 24 q^{72} + 24 q^{73} + 28 q^{74} + 41 q^{75} + 3 q^{76} - 34 q^{77} - 30 q^{78} - 51 q^{79} - 5 q^{80} + 5 q^{81} - 41 q^{82} + 30 q^{83} - 30 q^{84} + 68 q^{85} + 110 q^{86} + 19 q^{87} + 129 q^{88} + 75 q^{89} - 16 q^{90} + 5 q^{91} - 4 q^{93} + 38 q^{94} + 36 q^{95} - 57 q^{96} - 168 q^{97} + 227 q^{98} + 36 q^{99}+O(q^{100}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9 - 34 * q^10 - 11 * q^11 + 5 * q^12 - 2 * q^13 + 40 * q^14 - 3 * q^15 - 31 * q^16 - 9 * q^17 - 6 * q^18 - 29 * q^19 - 43 * q^20 - 11 * q^21 + 9 * q^22 - 4 * q^23 - 24 * q^24 + 55 * q^25 + 36 * q^26 - 10 * q^27 - 57 * q^28 + 4 * q^29 - 20 * q^30 - 39 * q^31 - 92 * q^32 - 18 * q^33 - 36 * q^34 - 33 * q^35 - 10 * q^36 - 24 * q^37 + 118 * q^38 - 6 * q^39 + 35 * q^41 + 38 * q^42 + 2 * q^43 + 40 * q^44 + 12 * q^45 - 40 * q^46 - 5 * q^47 + 76 * q^48 + 129 * q^49 - 176 * q^50 + 54 * q^51 - 6 * q^52 + 26 * q^53 + q^54 + 2 * q^55 + 63 * q^56 - 12 * q^57 + 11 * q^58 - 41 * q^59 + 32 * q^60 + 6 * q^61 + 36 * q^62 - q^63 + 74 * q^64 - 51 * q^65 - 15 * q^66 - 55 * q^67 - 22 * q^68 + 8 * q^69 - 68 * q^70 - 66 * q^71 - 24 * q^72 + 24 * q^73 + 28 * q^74 + 41 * q^75 + 3 * q^76 - 34 * q^77 - 30 * q^78 - 51 * q^79 - 5 * q^80 + 5 * q^81 - 41 * q^82 + 30 * q^83 - 30 * q^84 + 68 * q^85 + 110 * q^86 + 19 * q^87 + 129 * q^88 + 75 * q^89 - 16 * q^90 + 5 * q^91 - 4 * q^93 + 38 * q^94 + 36 * q^95 - 57 * q^96 - 168 * q^97 + 227 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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