LMFDB - Embedded newform 825.2.m.b.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(16,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("825.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.m (of order $5$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	825.361
Dual form			825.2.m.b.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{3} +(1.61803 - 1.17557i) q^{4} +(0.690983 + 2.12663i) q^{5} +(3.73607 + 2.71441i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{3} +(1.61803 - 1.17557i) q^{4} +(0.690983 + 2.12663i) q^{5} +(3.73607 + 2.71441i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(2.19098 - 2.48990i) q^{11} +(1.61803 + 1.17557i) q^{12} +(3.73607 - 2.71441i) q^{13} +(-1.80902 + 1.31433i) q^{15} +(1.23607 - 3.80423i) q^{16} +(-1.42705 + 1.03681i) q^{17} +(-6.04508 - 4.39201i) q^{19} +(3.61803 + 2.62866i) q^{20} +(-1.42705 + 4.39201i) q^{21} +(-1.92705 + 1.40008i) q^{23} +(-4.04508 + 2.93893i) q^{25} +(-0.809017 - 0.587785i) q^{27} +9.23607 q^{28} +(-4.61803 + 3.35520i) q^{29} -2.00000 q^{31} +(3.04508 + 1.31433i) q^{33} +(-3.19098 + 9.82084i) q^{35} +(-0.618034 + 1.90211i) q^{36} +(-1.78115 - 5.48183i) q^{37} +(3.73607 + 2.71441i) q^{39} +1.76393 q^{41} +1.76393 q^{43} +(0.618034 - 6.60440i) q^{44} +(-1.80902 - 1.31433i) q^{45} +(1.11803 + 3.44095i) q^{47} +4.00000 q^{48} +(4.42705 + 13.6251i) q^{49} +(-1.42705 - 1.03681i) q^{51} +(2.85410 - 8.78402i) q^{52} +(-7.28115 - 5.29007i) q^{53} +(6.80902 + 2.93893i) q^{55} +(2.30902 - 7.10642i) q^{57} +(-2.39919 - 7.38394i) q^{59} +(-1.38197 + 4.25325i) q^{60} +(3.19098 + 2.31838i) q^{61} -4.61803 q^{63} +(-2.47214 - 7.60845i) q^{64} +(8.35410 + 6.06961i) q^{65} +(-0.690983 - 2.12663i) q^{67} +(-1.09017 + 3.35520i) q^{68} +(-1.92705 - 1.40008i) q^{69} -2.52786 q^{71} +5.70820 q^{73} +(-4.04508 - 2.93893i) q^{75} -14.9443 q^{76} +(14.9443 - 3.35520i) q^{77} +(9.78115 + 7.10642i) q^{79} +8.94427 q^{80} +(0.309017 - 0.951057i) q^{81} +(-9.78115 + 7.10642i) q^{83} +(2.85410 + 8.78402i) q^{84} +(-3.19098 - 2.31838i) q^{85} +(-4.61803 - 3.35520i) q^{87} +(-10.2812 + 7.46969i) q^{89} +21.3262 q^{91} +(-1.47214 + 4.53077i) q^{92} +(-0.618034 - 1.90211i) q^{93} +(5.16312 - 15.8904i) q^{95} +(5.35410 + 3.88998i) q^{97} +(-0.309017 + 3.30220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 2 q^{4} + 5 q^{5} + 6 q^{7} - q^{9}+O(q^{10}) $ 4 * q - q^3 + 2 * q^4 + 5 * q^5 + 6 * q^7 - q^9	$ 4 q - q^{3} + 2 q^{4} + 5 q^{5} + 6 q^{7} - q^{9} + 11 q^{11} + 2 q^{12} + 6 q^{13} - 5 q^{15} - 4 q^{16} + q^{17} - 13 q^{19} + 10 q^{20} + q^{21} - q^{23} - 5 q^{25} - q^{27} + 28 q^{28} - 14 q^{29} - 8 q^{31} + q^{33} - 15 q^{35} + 2 q^{36} + 13 q^{37} + 6 q^{39} + 16 q^{41} + 16 q^{43} - 2 q^{44} - 5 q^{45} + 16 q^{48} + 11 q^{49} + q^{51} - 2 q^{52} - 9 q^{53} + 25 q^{55} + 7 q^{57} + 15 q^{59} - 10 q^{60} + 15 q^{61} - 14 q^{63} + 8 q^{64} + 20 q^{65} - 5 q^{67} + 18 q^{68} - q^{69} - 28 q^{71} - 4 q^{73} - 5 q^{75} - 24 q^{76} + 24 q^{77} + 19 q^{79} - q^{81} - 19 q^{83} - 2 q^{84} - 15 q^{85} - 14 q^{87} - 21 q^{89} + 54 q^{91} + 12 q^{92} + 2 q^{93} + 5 q^{95} + 8 q^{97} + q^{99}+O(q^{100}) $ 4 * q - q^3 + 2 * q^4 + 5 * q^5 + 6 * q^7 - q^9 + 11 * q^11 + 2 * q^12 + 6 * q^13 - 5 * q^15 - 4 * q^16 + q^17 - 13 * q^19 + 10 * q^20 + q^21 - q^23 - 5 * q^25 - q^27 + 28 * q^28 - 14 * q^29 - 8 * q^31 + q^33 - 15 * q^35 + 2 * q^36 + 13 * q^37 + 6 * q^39 + 16 * q^41 + 16 * q^43 - 2 * q^44 - 5 * q^45 + 16 * q^48 + 11 * q^49 + q^51 - 2 * q^52 - 9 * q^53 + 25 * q^55 + 7 * q^57 + 15 * q^59 - 10 * q^60 + 15 * q^61 - 14 * q^63 + 8 * q^64 + 20 * q^65 - 5 * q^67 + 18 * q^68 - q^69 - 28 * q^71 - 4 * q^73 - 5 * q^75 - 24 * q^76 + 24 * q^77 + 19 * q^79 - q^81 - 19 * q^83 - 2 * q^84 - 15 * q^85 - 14 * q^87 - 21 * q^89 + 54 * q^91 + 12 * q^92 + 2 * q^93 + 5 * q^95 + 8 * q^97 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$

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			0		0.951057	−	0.309017i	$-0.100000\pi$
$2$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	1.61803	−	1.17557i	0.809017	−	0.587785i
$5$	0.690983	+	2.12663i	0.309017	+	0.951057i
$5$	0.690983	+	2.12663i	0.309017	+	0.951057i
$6$		0			0
$7$	3.73607	+	2.71441i	1.41210	+	1.02595i	0.993013	+	0.118006i	$0.0376501\pi$
$7$	3.73607	+	2.71441i	1.41210	+	1.02595i	0.419088	+	0.907946i	$0.362350\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	2.19098	−	2.48990i	0.660606	−	0.750733i
$11$	2.19098	−	2.48990i	0.660606	−	0.750733i
$12$	1.61803	+	1.17557i	0.467086	+	0.339358i
$13$	3.73607	−	2.71441i	1.03620	−	0.752843i	0.0666589	−	0.997776i	$-0.478766\pi$
$13$	3.73607	−	2.71441i	1.03620	−	0.752843i	0.969540	+	0.244933i	$0.0787661\pi$
$14$		0			0
$15$	−1.80902	+	1.31433i	−0.467086	+	0.339358i
$16$	1.23607	−	3.80423i	0.309017	−	0.951057i
$17$	−1.42705	+	1.03681i	−0.346111	+	0.251464i	−0.747236	−	0.664559i	$-0.768619\pi$
$17$	−1.42705	+	1.03681i	−0.346111	+	0.251464i	0.401125	+	0.916023i	$0.368619\pi$
$18$		0			0
$19$	−6.04508	−	4.39201i	−1.38684	−	1.00760i	−0.996204	−	0.0870503i	$-0.972256\pi$
$19$	−6.04508	−	4.39201i	−1.38684	−	1.00760i	−0.390634	−	0.920546i	$-0.627744\pi$
$20$	3.61803	+	2.62866i	0.809017	+	0.587785i
$21$	−1.42705	+	4.39201i	−0.311408	+	0.958415i
$22$		0			0
$23$	−1.92705	+	1.40008i	−0.401818	+	0.291938i	−0.770281	−	0.637705i	$-0.779884\pi$
$23$	−1.92705	+	1.40008i	−0.401818	+	0.291938i	0.368463	+	0.929642i	$0.379884\pi$
$24$		0			0
$25$	−4.04508	+	2.93893i	−0.809017	+	0.587785i
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	9.23607			1.74545
$29$	−4.61803	+	3.35520i	−0.857547	+	0.623045i	−0.927217	−	0.374526i	$-0.877806\pi$
$29$	−4.61803	+	3.35520i	−0.857547	+	0.623045i	0.0696692	+	0.997570i	$0.477806\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$		0			0
$33$	3.04508	+	1.31433i	0.530081	+	0.228795i
$34$		0			0
$35$	−3.19098	+	9.82084i	−0.539375	+	1.66002i
$36$	−0.618034	+	1.90211i	−0.103006	+	0.317019i
$37$	−1.78115	−	5.48183i	−0.292820	−	0.901206i	−0.983945	−	0.178472i	$-0.942885\pi$
$37$	−1.78115	−	5.48183i	−0.292820	−	0.901206i	0.691125	−	0.722735i	$-0.257115\pi$
$38$		0			0
$39$	3.73607	+	2.71441i	0.598250	+	0.434654i
$40$		0			0
$41$	1.76393			0.275480			0.137740	−	0.990468i	$-0.456016\pi$
$41$	1.76393			0.275480			0.137740	+	0.990468i	$0.456016\pi$
$42$		0			0
$43$	1.76393			0.268997			0.134499	−	0.990914i	$-0.457058\pi$
$43$	1.76393			0.268997			0.134499	+	0.990914i	$0.457058\pi$
$44$	0.618034	−	6.60440i	0.0931721	−	0.995650i
$45$	−1.80902	−	1.31433i	−0.269672	−	0.195928i
$46$		0			0
$47$	1.11803	+	3.44095i	0.163082	+	0.501915i	0.998890	−	0.0471073i	$-0.0150003\pi$
$47$	1.11803	+	3.44095i	0.163082	+	0.501915i	−0.835808	+	0.549022i	$0.815000\pi$
$48$	4.00000			0.577350
$49$	4.42705	+	13.6251i	0.632436	+	1.94644i
$50$		0			0
$51$	−1.42705	−	1.03681i	−0.199827	−	0.145183i
$52$	2.85410	−	8.78402i	0.395793	−	1.21812i
$53$	−7.28115	−	5.29007i	−1.00014	−	0.726647i	−0.0380244	−	0.999277i	$-0.512106\pi$
$53$	−7.28115	−	5.29007i	−1.00014	−	0.726647i	−0.962119	+	0.272630i	$0.912106\pi$
$54$		0			0
$55$	6.80902	+	2.93893i	0.918128	+	0.396285i
$56$		0			0
$57$	2.30902	−	7.10642i	0.305837	−	0.941269i
$58$		0			0
$59$	−2.39919	−	7.38394i	−0.312348	−	0.961307i	−0.976833	−	0.214005i	$-0.931349\pi$
$59$	−2.39919	−	7.38394i	−0.312348	−	0.961307i	0.664485	−	0.747302i	$-0.268651\pi$
$60$	−1.38197	+	4.25325i	−0.178411	+	0.549093i
$61$	3.19098	+	2.31838i	0.408564	+	0.296839i	0.773020	−	0.634382i	$-0.218745\pi$
$61$	3.19098	+	2.31838i	0.408564	+	0.296839i	−0.364456	+	0.931220i	$0.618745\pi$
$62$		0			0
$63$	−4.61803			−0.581818
$64$	−2.47214	−	7.60845i	−0.309017	−	0.951057i
$65$	8.35410	+	6.06961i	1.03620	+	0.752843i
$66$		0			0
$67$	−0.690983	−	2.12663i	−0.0844170	−	0.259809i	0.899934	−	0.436025i	$-0.143614\pi$
$67$	−0.690983	−	2.12663i	−0.0844170	−	0.259809i	−0.984351	+	0.176216i	$0.943614\pi$
$68$	−1.09017	+	3.35520i	−0.132203	+	0.406878i
$69$	−1.92705	−	1.40008i	−0.231990	−	0.168550i
$70$		0			0
$71$	−2.52786			−0.300002			−0.150001	−	0.988686i	$-0.547928\pi$
$71$	−2.52786			−0.300002			−0.150001	+	0.988686i	$0.547928\pi$
$72$		0			0
$73$	5.70820			0.668095			0.334047	−	0.942556i	$-0.391585\pi$
$73$	5.70820			0.668095			0.334047	+	0.942556i	$0.391585\pi$
$74$		0			0
$75$	−4.04508	−	2.93893i	−0.467086	−	0.339358i
$76$	−14.9443			−1.71423
$77$	14.9443	−	3.35520i	1.70306	−	0.382360i
$78$		0			0
$79$	9.78115	+	7.10642i	1.10047	+	0.799535i	0.981136	−	0.193320i	$-0.0619254\pi$
$79$	9.78115	+	7.10642i	1.10047	+	0.799535i	0.119330	+	0.992855i	$0.461925\pi$
$80$	8.94427			1.00000
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	−9.78115	+	7.10642i	−1.07362	+	0.780031i	−0.976560	−	0.215247i	$-0.930944\pi$
$83$	−9.78115	+	7.10642i	−1.07362	+	0.780031i	−0.0970614	+	0.995278i	$0.530944\pi$
$84$	2.85410	+	8.78402i	0.311408	+	0.958415i
$85$	−3.19098	−	2.31838i	−0.346111	−	0.251464i
$86$		0			0
$87$	−4.61803	−	3.35520i	−0.495105	−	0.359715i
$88$		0			0
$89$	−10.2812	+	7.46969i	−1.08980	+	0.791786i	−0.979365	−	0.202097i	$-0.935224\pi$
$89$	−10.2812	+	7.46969i	−1.08980	+	0.791786i	−0.110435	+	0.993883i	$0.535224\pi$
$90$		0			0
$91$	21.3262			2.23560
$92$	−1.47214	+	4.53077i	−0.153481	+	0.472365i
$93$	−0.618034	−	1.90211i	−0.0640871	−	0.197240i
$94$		0			0
$95$	5.16312	−	15.8904i	0.529725	−	1.63033i
$96$		0			0
$97$	5.35410	+	3.88998i	0.543627	+	0.394968i	0.825430	−	0.564504i	$-0.190933\pi$
$97$	5.35410	+	3.88998i	0.543627	+	0.394968i	−0.281803	+	0.959472i	$0.590933\pi$
$98$		0			0
$99$	−0.309017	+	3.30220i	−0.0310574	+	0.331883i
$100$	−3.09017	+	9.51057i	−0.309017	+	0.951057i
$101$	−3.19098	+	9.82084i	−0.317515	+	0.977210i	0.657192	+	0.753723i	$0.271744\pi$
$101$	−3.19098	+	9.82084i	−0.317515	+	0.977210i	−0.974707	+	0.223487i	$0.928256\pi$
$102$		0			0
$103$	−11.6353	+	8.45351i	−1.14646	+	0.832949i	−0.988006	−	0.154418i	$-0.950650\pi$
$103$	−11.6353	+	8.45351i	−1.14646	+	0.832949i	−0.158450	+	0.987367i	$0.550650\pi$
$104$		0			0
$105$	−10.3262			−1.00774
$106$		0			0
$107$	8.89919	−	6.46564i	0.860317	−	0.625057i	−0.0676543	−	0.997709i	$-0.521551\pi$
$107$	8.89919	−	6.46564i	0.860317	−	0.625057i	0.927971	+	0.372652i	$0.121551\pi$
$108$	−2.00000			−0.192450
$109$	−12.0902	−	8.78402i	−1.15803	−	0.841357i	−0.168501	−	0.985702i	$-0.553893\pi$
$109$	−12.0902	−	8.78402i	−1.15803	−	0.841357i	−0.989527	+	0.144345i	$0.953893\pi$
$110$		0			0
$111$	4.66312	−	3.38795i	0.442604	−	0.321570i
$112$	14.9443	−	10.8576i	1.41210	−	1.02595i
$113$	8.38197			0.788509			0.394255	−	0.919001i	$-0.371003\pi$
$113$	8.38197			0.788509			0.394255	+	0.919001i	$0.371003\pi$
$114$		0			0
$115$	−4.30902	−	3.13068i	−0.401818	−	0.291938i
$116$	−3.52786	+	10.8576i	−0.327554	+	1.00811i
$117$	−1.42705	+	4.39201i	−0.131931	+	0.406042i
$118$		0			0
$119$	−8.14590			−0.746733
$120$		0			0
$121$	−1.39919	−	10.9106i	−0.127199	−	0.991877i
$122$		0			0
$123$	0.545085	+	1.67760i	0.0491487	+	0.151264i
$124$	−3.23607	+	2.35114i	−0.290607	+	0.211139i
$125$	−9.04508	−	6.57164i	−0.809017	−	0.587785i
$126$		0			0
$127$	−9.23607	−	6.71040i	−0.819569	−	0.595451i	0.0970204	−	0.995282i	$-0.469069\pi$
$127$	−9.23607	−	6.71040i	−0.819569	−	0.595451i	−0.916589	+	0.399831i	$0.869069\pi$
$128$		0			0
$129$	0.545085	+	1.67760i	0.0479921	+	0.147704i
$130$		0			0
$131$	6.25329	+	19.2456i	0.546352	+	1.68150i	0.717753	+	0.696298i	$0.245171\pi$
$131$	6.25329	+	19.2456i	0.546352	+	1.68150i	−0.171400	+	0.985201i	$0.554829\pi$
$132$	6.47214	−	1.45309i	0.563327	−	0.126475i
$133$	−10.6631	−	32.8177i	−0.924610	−	2.84566i
$134$		0			0
$135$	0.690983	−	2.12663i	0.0594703	−	0.183031i
$136$		0			0
$137$	−0.791796	+	2.43690i	−0.0676477	+	0.208198i	−0.979166	−	0.203061i	$-0.934911\pi$
$137$	−0.791796	+	2.43690i	−0.0676477	+	0.208198i	0.911518	+	0.411259i	$0.134911\pi$
$138$		0			0
$139$	−1.76393			−0.149615			−0.0748074	−	0.997198i	$-0.523834\pi$
$139$	−1.76393			−0.149615			−0.0748074	+	0.997198i	$0.523834\pi$
$140$	6.38197	+	19.6417i	0.539375	+	1.66002i
$141$	−2.92705	+	2.12663i	−0.246502	+	0.179094i
$142$		0			0
$143$	1.42705	−	15.2497i	0.119336	−	1.27524i
$144$	1.23607	+	3.80423i	0.103006	+	0.317019i
$145$	−10.3262	−	7.50245i	−0.857547	−	0.623045i
$146$		0			0
$147$	−11.5902	+	8.42075i	−0.955941	+	0.694532i
$148$	−9.32624	−	6.77591i	−0.766612	−	0.556976i
$149$	−0.673762	−	2.07363i	−0.0551967	−	0.169878i	0.919658	−	0.392721i	$-0.128466\pi$
$149$	−0.673762	−	2.07363i	−0.0551967	−	0.169878i	−0.974854	+	0.222843i	$0.928466\pi$
$150$		0			0
$151$	−11.2082	+	8.14324i	−0.912111	+	0.662687i	−0.941548	−	0.336879i	$-0.890629\pi$
$151$	−11.2082	+	8.14324i	−0.912111	+	0.662687i	0.0294371	+	0.999567i	$0.490629\pi$
$152$		0			0
$153$	0.545085	−	1.67760i	0.0440675	−	0.135626i
$154$		0			0
$155$	−1.38197	−	4.25325i	−0.111002	−	0.341630i
$156$	9.23607			0.739477
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	−0.461601	−	0.887087i	$-0.652725\pi$
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	0.701028	+	0.713134i	$0.252725\pi$
$158$		0			0
$159$	2.78115	−	8.55951i	0.220560	−	0.678813i
$160$		0			0
$161$	−11.0000			−0.866921
$162$		0			0
$163$	−8.16312	+	5.93085i	−0.639385	+	0.464540i	−0.859639	−	0.510902i	$-0.829311\pi$
$163$	−8.16312	+	5.93085i	−0.639385	+	0.464540i	0.220254	+	0.975443i	$0.429311\pi$
$164$	2.85410	−	2.07363i	0.222868	−	0.161923i
$165$	−0.690983	+	7.38394i	−0.0537930	+	0.574839i
$166$		0			0
$167$	20.6525			1.59814			0.799068	−	0.601240i	$-0.205327\pi$
$167$	20.6525			1.59814			0.799068	+	0.601240i	$0.205327\pi$
$168$		0			0
$169$	2.57295	−	7.91872i	0.197919	−	0.609133i
$170$		0			0
$171$	7.47214			0.571409
$172$	2.85410	−	2.07363i	0.217623	−	0.158113i
$173$	5.83688	−	17.9641i	0.443770	−	1.36578i	−0.440057	−	0.897970i	$-0.645042\pi$
$173$	5.83688	−	17.9641i	0.443770	−	1.36578i	0.883827	−	0.467813i	$-0.154958\pi$
$174$		0			0
$175$	−23.0902			−1.74545
$176$	−6.76393	−	11.4127i	−0.509851	−	0.860263i
$177$	6.28115	−	4.56352i	0.472120	−	0.343016i
$178$		0			0
$179$	−6.30902	−	19.4172i	−0.471558	−	1.45131i	−0.850544	−	0.525904i	$-0.823727\pi$
$179$	−6.30902	−	19.4172i	−0.471558	−	1.45131i	0.378986	−	0.925402i	$-0.376273\pi$
$180$	−4.47214			−0.333333
$181$	15.0623	−	10.9434i	1.11957	−	0.813417i	0.135428	−	0.990787i	$-0.456759\pi$
$181$	15.0623	−	10.9434i	1.11957	−	0.813417i	0.984144	+	0.177370i	$0.0567590\pi$
$182$		0			0
$183$	−1.21885	+	3.75123i	−0.0900998	+	0.277299i
$184$		0			0
$185$	10.4271	−	7.57570i	0.766612	−	0.556976i
$186$		0			0
$187$	−0.545085	+	5.82485i	−0.0398606	+	0.425955i
$188$	5.85410	+	4.25325i	0.426954	+	0.310200i
$189$	−1.42705	−	4.39201i	−0.103803	−	0.319472i
$190$		0			0
$191$	−0.718847	−	2.21238i	−0.0520139	−	0.160082i	0.921675	−	0.387962i	$-0.126821\pi$
$191$	−0.718847	−	2.21238i	−0.0520139	−	0.160082i	−0.973689	+	0.227879i	$0.926821\pi$
$192$	6.47214	−	4.70228i	0.467086	−	0.339358i
$193$	2.30902	+	7.10642i	0.166207	+	0.511532i	0.999123	−	0.0418671i	$-0.0133306\pi$
$193$	2.30902	+	7.10642i	0.166207	+	0.511532i	−0.832917	+	0.553399i	$0.813331\pi$
$194$		0			0
$195$	−3.19098	+	9.82084i	−0.228511	+	0.703285i
$196$	23.1803	+	16.8415i	1.65574	+	1.20296i
$197$	−5.37132	+	16.5312i	−0.382691	+	1.17780i	0.555451	+	0.831550i	$0.312546\pi$
$197$	−5.37132	+	16.5312i	−0.382691	+	1.17780i	−0.938142	+	0.346252i	$0.887454\pi$
$198$		0			0
$199$	10.2705			0.728057			0.364029	−	0.931388i	$-0.381401\pi$
$199$	10.2705			0.728057			0.364029	+	0.931388i	$0.381401\pi$
$200$		0			0
$201$	1.80902	−	1.31433i	0.127598	−	0.0927055i
$202$		0			0
$203$	−26.3607			−1.85016
$204$	−3.52786			−0.247000
$205$	1.21885	+	3.75123i	0.0851280	+	0.261997i
$206$		0			0
$207$	0.736068	−	2.26538i	0.0511603	−	0.157455i
$208$	−5.70820	−	17.5680i	−0.395793	−	1.21812i
$209$	−24.1803	+	5.42882i	−1.67259	+	0.375520i
$210$		0			0
$211$	3.19098	+	9.82084i	0.219676	+	0.676094i	0.998788	+	0.0492096i	$0.0156702\pi$
$211$	3.19098	+	9.82084i	0.219676	+	0.676094i	−0.779112	+	0.626885i	$0.784330\pi$
$212$	−18.0000			−1.23625
$213$	−0.781153	−	2.40414i	−0.0535237	−	0.164729i
$214$		0			0
$215$	1.21885	+	3.75123i	0.0831247	+	0.255831i
$216$		0			0
$217$	−7.47214	−	5.42882i	−0.507242	−	0.368533i
$218$		0			0
$219$	1.76393	+	5.42882i	0.119195	+	0.366846i
$220$	14.4721	−	3.24920i	0.975711	−	0.219061i
$221$	−2.51722	+	7.74721i	−0.169327	+	0.521134i
$222$		0			0
$223$	9.04508	−	27.8379i	0.605704	−	1.86416i	0.113824	−	0.993501i	$-0.463690\pi$
$223$	9.04508	−	27.8379i	0.605704	−	1.86416i	0.491879	−	0.870663i	$-0.336310\pi$
$224$		0			0
$225$	1.54508	−	4.75528i	0.103006	−	0.317019i
$226$		0			0
$227$	21.3262			1.41547			0.707736	−	0.706477i	$-0.249717\pi$
$227$	21.3262			1.41547			0.707736	+	0.706477i	$0.249717\pi$
$228$	−4.61803	−	14.2128i	−0.305837	−	0.941269i
$229$	−15.5623	−	11.3067i	−1.02839	−	0.747166i	−0.0604011	−	0.998174i	$-0.519238\pi$
$229$	−15.5623	−	11.3067i	−1.02839	−	0.747166i	−0.967985	+	0.251008i	$0.919238\pi$
$230$		0			0
$231$	7.80902	+	13.1760i	0.513796	+	0.866919i
$232$		0			0
$233$	−7.47214			−0.489516			−0.244758	−	0.969584i	$-0.578708\pi$
$233$	−7.47214			−0.489516			−0.244758	+	0.969584i	$0.578708\pi$
$234$		0			0
$235$	−6.54508	+	4.75528i	−0.426954	+	0.310200i
$236$	−12.5623	−	9.12705i	−0.817736	−	0.594120i
$237$	−3.73607	+	11.4984i	−0.242684	+	0.746904i
$238$		0			0
$239$	4.40983	−	13.5721i	0.285248	−	0.877904i	−0.701076	−	0.713087i	$-0.747297\pi$
$239$	4.40983	−	13.5721i	0.285248	−	0.877904i	0.986324	−	0.164817i	$-0.0527034\pi$
$240$	2.76393	+	8.50651i	0.178411	+	0.549093i
$241$	22.7533	+	16.5312i	1.46567	+	1.06487i	0.981841	+	0.189707i	$0.0607538\pi$
$241$	22.7533	+	16.5312i	1.46567	+	1.06487i	0.483827	+	0.875163i	$0.339246\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	7.88854			0.505012
$245$	−25.9164	+	18.8294i	−1.65574	+	1.20296i
$246$		0			0
$247$	−34.5066			−2.19560
$248$		0			0
$249$	−9.78115	−	7.10642i	−0.619855	−	0.450351i
$250$		0			0
$251$	5.09017	−	15.6659i	0.321289	−	0.988825i	−0.651799	−	0.758391i	$-0.725986\pi$
$251$	5.09017	−	15.6659i	0.321289	−	0.988825i	0.973088	−	0.230433i	$-0.0740144\pi$
$252$	−7.47214	+	5.42882i	−0.470700	+	0.341984i
$253$	−0.736068	+	7.86572i	−0.0462762	+	0.494514i
$254$		0			0
$255$	1.21885	−	3.75123i	0.0763272	−	0.234911i
$256$	−12.9443	−	9.40456i	−0.809017	−	0.587785i
$257$	−18.5623	−	13.4863i	−1.15788	−	0.841253i	−0.168376	−	0.985723i	$-0.553852\pi$
$257$	−18.5623	−	13.4863i	−1.15788	−	0.841253i	−0.989509	+	0.144470i	$0.953852\pi$
$258$		0			0
$259$	8.22542	−	25.3153i	0.511103	−	1.57301i
$260$	20.6525			1.28081
$261$	1.76393	−	5.42882i	0.109185	−	0.336036i
$262$		0			0
$263$	−4.28115	−	3.11044i	−0.263987	−	0.191798i	0.447916	−	0.894076i	$-0.352166\pi$
$263$	−4.28115	−	3.11044i	−0.263987	−	0.191798i	−0.711903	+	0.702278i	$0.752166\pi$
$264$		0			0
$265$	6.21885	−	19.1396i	0.382021	−	1.17574i
$266$		0			0
$267$	−10.2812	−	7.46969i	−0.629196	−	0.457138i
$268$	−3.61803	−	2.62866i	−0.221007	−	0.160571i
$269$	−22.6525	+	16.4580i	−1.38115	+	1.00346i	−0.384374	+	0.923178i	$0.625583\pi$
$269$	−22.6525	+	16.4580i	−1.38115	+	1.00346i	−0.996772	+	0.0802836i	$0.974417\pi$
$270$		0			0
$271$	−4.61803	+	3.35520i	−0.280526	+	0.203814i	−0.719147	−	0.694858i	$-0.755467\pi$
$271$	−4.61803	+	3.35520i	−0.280526	+	0.203814i	0.438621	+	0.898672i	$0.355467\pi$
$272$	2.18034	+	6.71040i	0.132203	+	0.406878i
$273$	6.59017	+	20.2825i	0.398855	+	1.22755i
$274$		0			0
$275$	−1.54508	+	16.5110i	−0.0931721	+	0.995650i
$276$	−4.76393			−0.286755
$277$	−0.336881	−	1.03681i	−0.0202412	−	0.0622961i	0.940426	−	0.339999i	$-0.110427\pi$
$277$	−0.336881	−	1.03681i	−0.0202412	−	0.0622961i	−0.960667	+	0.277703i	$0.910427\pi$
$278$		0			0
$279$	1.61803	−	1.17557i	0.0968692	−	0.0703796i
$280$		0			0
$281$	9.23607	−	6.71040i	0.550978	−	0.400309i	−0.277168	−	0.960821i	$-0.589396\pi$
$281$	9.23607	−	6.71040i	0.550978	−	0.400309i	0.828146	+	0.560513i	$0.189396\pi$
$282$		0			0
$283$	19.2254	+	13.9681i	1.14283	+	0.830317i	0.987511	−	0.157547i	$-0.0503587\pi$
$283$	19.2254	+	13.9681i	1.14283	+	0.830317i	0.155321	+	0.987864i	$0.450359\pi$
$284$	−4.09017	+	2.97168i	−0.242707	+	0.176337i
$285$	16.7082			0.989709
$286$		0			0
$287$	6.59017	+	4.78804i	0.389005	+	0.282629i
$288$		0			0
$289$	−4.29180	+	13.2088i	−0.252459	+	0.776988i
$290$		0			0
$291$	−2.04508	+	6.29412i	−0.119885	+	0.368968i
$292$	9.23607	−	6.71040i	0.540500	−	0.392696i
$293$	7.47214	+	5.42882i	0.436527	+	0.317155i	0.784253	−	0.620441i	$-0.213046\pi$
$293$	7.47214	+	5.42882i	0.436527	+	0.317155i	−0.347727	+	0.937596i	$0.613046\pi$
$294$		0			0
$295$	14.0451	−	10.2044i	0.817736	−	0.594120i
$296$		0			0
$297$	−3.23607	+	0.726543i	−0.187776	+	0.0421583i
$298$		0			0
$299$	−3.39919	+	10.4616i	−0.196580	+	0.605011i
$300$	−10.0000			−0.577350
$301$	6.59017	+	4.78804i	0.379851	+	0.275978i
$302$		0			0
$303$	−10.3262			−0.593227
$304$	−24.1803	+	17.5680i	−1.38684	+	1.00760i
$305$	−2.72542	+	8.38800i	−0.156057	+	0.480295i
$306$		0			0
$307$	24.5967			1.40381			0.701905	−	0.712270i	$-0.252333\pi$
$307$	24.5967			1.40381			0.701905	+	0.712270i	$0.252333\pi$
$308$	20.2361	−	22.9969i	1.15306	−	1.31037i
$309$	−11.6353	−	8.45351i	−0.661907	−	0.480903i
$310$		0			0
$311$	10.3992	−	32.0054i	0.589684	−	1.81486i	0.0100978	−	0.999949i	$-0.496786\pi$
$311$	10.3992	−	32.0054i	0.589684	−	1.81486i	0.579586	−	0.814911i	$-0.303214\pi$
$312$		0			0
$313$	−6.29180	+	19.3642i	−0.355633	+	1.09453i	0.600008	+	0.799994i	$0.295164\pi$
$313$	−6.29180	+	19.3642i	−0.355633	+	1.09453i	−0.955641	+	0.294533i	$0.904836\pi$
$314$		0			0
$315$	−3.19098	−	9.82084i	−0.179792	−	0.553341i
$316$	24.1803			1.36025
$317$	−9.47214			−0.532008			−0.266004	−	0.963972i	$-0.585703\pi$
$317$	−9.47214			−0.532008			−0.266004	+	0.963972i	$0.585703\pi$
$318$		0			0
$319$	−1.76393	+	18.8496i	−0.0987612	+	1.05538i
$320$	14.4721	−	10.5146i	0.809017	−	0.587785i
$321$	8.89919	+	6.46564i	0.496704	+	0.360877i
$322$		0			0
$323$	13.1803			0.733374
$324$	−0.618034	−	1.90211i	−0.0343352	−	0.105673i
$325$	−7.13525	+	21.9601i	−0.395793	+	1.21812i
$326$		0			0
$327$	4.61803	−	14.2128i	0.255378	−	0.785972i
$328$		0			0
$329$	−5.16312	+	15.8904i	−0.284652	+	0.876069i
$330$		0			0
$331$	3.92705	+	12.0862i	0.215850	+	0.664319i	0.999092	+	0.0426017i	$0.0135646\pi$
$331$	3.92705	+	12.0862i	0.215850	+	0.664319i	−0.783242	+	0.621717i	$0.786435\pi$
$332$	−7.47214	+	22.9969i	−0.410087	+	1.26212i
$333$	4.66312	+	3.38795i	0.255537	+	0.185659i
$334$		0			0
$335$	4.04508	−	2.93893i	0.221007	−	0.160571i
$336$	14.9443	+	10.8576i	0.815277	+	0.592333i
$337$	2.85410	+	8.78402i	0.155473	+	0.478496i	0.998208	−	0.0598314i	$-0.0190563\pi$
$337$	2.85410	+	8.78402i	0.155473	+	0.478496i	−0.842736	+	0.538328i	$0.819056\pi$
$338$		0			0
$339$	2.59017	+	7.97172i	0.140679	+	0.432965i
$340$	−7.88854			−0.427816
$341$	−4.38197	+	4.97980i	−0.237297	+	0.269671i
$342$		0			0
$343$	−10.4549	+	32.1769i	−0.564512	+	1.73739i
$344$		0			0
$345$	1.64590	−	5.06555i	0.0886122	−	0.272720i
$346$		0			0
$347$	22.4164			1.20338			0.601688	−	0.798731i	$-0.294495\pi$
$347$	22.4164			1.20338			0.601688	+	0.798731i	$0.294495\pi$
$348$	−11.4164			−0.611984
$349$	−16.7082	+	12.1392i	−0.894370	+	0.649798i	−0.937014	−	0.349293i	$-0.886422\pi$
$349$	−16.7082	+	12.1392i	−0.894370	+	0.649798i	0.0426440	+	0.999090i	$0.486422\pi$
$350$		0			0
$351$	−4.61803			−0.246492
$352$		0			0
$353$	9.43769	−	29.0462i	0.502318	−	1.54598i	−0.302916	−	0.953017i	$-0.597960\pi$
$353$	9.43769	−	29.0462i	0.502318	−	1.54598i	0.805234	−	0.592958i	$-0.202040\pi$
$354$		0			0
$355$	−1.74671	−	5.37582i	−0.0927058	−	0.285319i
$356$	−7.85410	+	24.1724i	−0.416267	+	1.28114i
$357$	−2.51722	−	7.74721i	−0.133225	−	0.410026i
$358$		0			0
$359$	−0.545085	−	1.67760i	−0.0287685	−	0.0885403i	0.935641	−	0.352952i	$-0.114822\pi$
$359$	−0.545085	−	1.67760i	−0.0287685	−	0.0885403i	−0.964410	+	0.264412i	$0.914822\pi$
$360$		0			0
$361$	11.3820	+	35.0301i	0.599051	+	1.84369i
$362$		0			0
$363$	9.94427	−	4.70228i	0.521939	−	0.246806i
$364$	34.5066	−	25.0705i	1.80864	−	1.31405i
$365$	3.94427	+	12.1392i	0.206453	+	0.635396i
$366$		0			0
$367$	3.69098	−	11.3597i	0.192668	−	0.592970i	−0.807328	−	0.590103i	$-0.799087\pi$
$367$	3.69098	−	11.3597i	0.192668	−	0.592970i	0.999996	−	0.00286759i	$-0.000912782\pi$
$368$	2.94427	+	9.06154i	0.153481	+	0.472365i
$369$	−1.42705	+	1.03681i	−0.0742893	+	0.0539743i
$370$		0			0
$371$	−12.8435	−	39.5281i	−0.666799	−	2.05220i
$372$	−3.23607	−	2.35114i	−0.167782	−	0.121901i
$373$	−11.0000	+	7.99197i	−0.569558	+	0.413808i	−0.834945	−	0.550334i	$-0.814500\pi$
$373$	−11.0000	+	7.99197i	−0.569558	+	0.413808i	0.265386	+	0.964142i	$0.414500\pi$
$374$		0			0
$375$	3.45492	−	10.6331i	0.178411	−	0.549093i
$376$		0			0
$377$	−8.14590	+	25.0705i	−0.419535	+	1.29120i
$378$		0			0
$379$	−5.18034			−0.266096			−0.133048	−	0.991110i	$-0.542476\pi$
$379$	−5.18034			−0.266096			−0.133048	+	0.991110i	$0.542476\pi$
$380$	−10.3262	−	31.7809i	−0.529725	−	1.63033i
$381$	3.52786	−	10.8576i	0.180738	−	0.556254i
$382$		0			0
$383$	33.5967			1.71671			0.858357	−	0.513053i	$-0.171486\pi$
$383$	33.5967			1.71671			0.858357	+	0.513053i	$0.171486\pi$
$384$		0			0
$385$	17.4615	+	29.4625i	0.889920	+	1.50155i
$386$		0			0
$387$	−1.42705	+	1.03681i	−0.0725411	+	0.0527042i
$388$	13.2361			0.671960
$389$	17.7639			0.900667			0.450334	−	0.892860i	$-0.351305\pi$
$389$	17.7639			0.900667			0.450334	+	0.892860i	$0.351305\pi$
$390$		0			0
$391$	1.29837	−	3.99598i	0.0656616	−	0.202086i
$392$		0			0
$393$	−16.3713	+	11.8945i	−0.825824	+	0.599996i
$394$		0			0
$395$	−8.35410	+	25.7113i	−0.420340	+	1.29367i
$396$	3.38197	+	5.70634i	0.169950	+	0.286754i
$397$	0.527864	−	1.62460i	0.0264927	−	0.0815363i	−0.936936	−	0.349501i	$-0.886351\pi$
$397$	0.527864	−	1.62460i	0.0264927	−	0.0815363i	0.963429	+	0.267965i	$0.0863511\pi$
$398$		0			0
$399$	27.9164	−	20.2825i	1.39757	−	1.01539i
$400$	6.18034	+	19.0211i	0.309017	+	0.951057i
$401$	−2.20820	−	6.79615i	−0.110272	−	0.339384i	0.880659	−	0.473750i	$-0.157100\pi$
$401$	−2.20820	−	6.79615i	−0.110272	−	0.339384i	−0.990932	+	0.134367i	$0.957100\pi$
$402$		0			0
$403$	−7.47214	+	5.42882i	−0.372214	+	0.270429i
$404$	6.38197	+	19.6417i	0.317515	+	0.977210i
$405$	2.23607			0.111111
$406$		0			0
$407$	−17.5517	−	7.57570i	−0.870004	−	0.375513i
$408$		0			0
$409$	25.9443	−	18.8496i	1.28286	−	0.932054i	0.283226	−	0.959053i	$-0.408595\pi$
$409$	25.9443	−	18.8496i	1.28286	−	0.932054i	0.999635	+	0.0269996i	$0.00859527\pi$
$410$		0			0
$411$	−2.56231			−0.126389
$412$	−8.88854	+	27.3561i	−0.437907	+	1.34774i
$413$	11.0795	−	34.0993i	0.545188	−	1.67792i
$414$		0			0
$415$	−21.8713	−	15.8904i	−1.07362	−	0.780031i
$416$		0			0
$417$	−0.545085	−	1.67760i	−0.0266929	−	0.0821524i
$418$		0			0
$419$	−2.80902	−	8.64527i	−0.137229	−	0.422349i	0.858701	−	0.512477i	$-0.171272\pi$
$419$	−2.80902	−	8.64527i	−0.137229	−	0.422349i	−0.995930	+	0.0901286i	$0.971272\pi$
$420$	−16.7082	+	12.1392i	−0.815277	+	0.592333i
$421$	−7.86475	−	24.2052i	−0.383304	−	1.17969i	−0.937703	−	0.347438i	$-0.887052\pi$
$421$	−7.86475	−	24.2052i	−0.383304	−	1.17969i	0.554399	−	0.832251i	$-0.312948\pi$
$422$		0			0
$423$	−2.92705	−	2.12663i	−0.142318	−	0.103400i
$424$		0			0
$425$	2.72542	−	8.38800i	0.132203	−	0.406878i
$426$		0			0
$427$	5.62868	+	17.3233i	0.272391	+	0.838333i
$428$	6.79837	−	20.9232i	0.328612	−	1.01136i
$429$	14.9443	−	3.35520i	0.721516	−	0.161990i
$430$		0			0
$431$	19.1459			0.922225			0.461113	−	0.887342i	$-0.347450\pi$
$431$	19.1459			0.922225			0.461113	+	0.887342i	$0.347450\pi$
$432$	−3.23607	+	2.35114i	−0.155695	+	0.113119i
$433$	−6.39919	+	19.6947i	−0.307525	+	0.946466i	0.671197	+	0.741279i	$0.265780\pi$
$433$	−6.39919	+	19.6947i	−0.307525	+	0.946466i	−0.978723	+	0.205187i	$0.934220\pi$
$434$		0			0
$435$	3.94427	−	12.1392i	0.189113	−	0.582031i
$436$	−29.8885			−1.43140
$437$	17.7984			0.851412
$438$		0			0
$439$	−7.13525	+	5.18407i	−0.340547	+	0.247422i	−0.744893	−	0.667184i	$-0.767499\pi$
$439$	−7.13525	+	5.18407i	−0.340547	+	0.247422i	0.404346	+	0.914606i	$0.367499\pi$
$440$		0			0
$441$	−11.5902	−	8.42075i	−0.551913	−	0.400988i
$442$		0			0
$443$	−3.02786	+	2.19987i	−0.143858	+	0.104519i	−0.657387	−	0.753554i	$-0.728338\pi$
$443$	−3.02786	+	2.19987i	−0.143858	+	0.104519i	0.513528	+	0.858073i	$0.328338\pi$
$444$	3.56231	−	10.9637i	0.169060	−	0.520312i
$445$	−22.9894	−	16.7027i	−1.08980	−	0.791786i
$446$		0			0
$447$	1.76393	−	1.28157i	0.0834311	−	0.0606163i
$448$	11.4164	−	35.1361i	0.539375	−	1.66002i
$449$	−9.41641	+	28.9807i	−0.444388	+	1.36768i	0.438766	+	0.898601i	$0.355416\pi$
$449$	−9.41641	+	28.9807i	−0.444388	+	1.36768i	−0.883154	+	0.469084i	$0.844584\pi$
$450$		0			0
$451$	3.86475	−	4.39201i	0.181984	−	0.206812i
$452$	13.5623	−	9.85359i	0.637917	−	0.463474i
$453$	−11.2082	−	8.14324i	−0.526607	−	0.382603i
$454$		0			0
$455$	14.7361	+	45.3530i	0.690838	+	2.12618i
$456$		0			0
$457$	−1.01064	−	3.11044i	−0.0472759	−	0.145500i	0.924632	−	0.380862i	$-0.124373\pi$
$457$	−1.01064	−	3.11044i	−0.0472759	−	0.145500i	−0.971908	+	0.235361i	$0.924373\pi$
$458$		0			0
$459$	1.76393			0.0823333
$460$	−10.6525			−0.496674
$461$	−4.95492	+	3.59996i	−0.230773	+	0.167667i	−0.697163	−	0.716913i	$-0.745555\pi$
$461$	−4.95492	+	3.59996i	−0.230773	+	0.167667i	0.466389	+	0.884580i	$0.345555\pi$
$462$		0			0
$463$	−12.2533	−	8.90254i	−0.569459	−	0.413736i	0.265450	−	0.964125i	$-0.414480\pi$
$463$	−12.2533	−	8.90254i	−0.569459	−	0.413736i	−0.834909	+	0.550389i	$0.814480\pi$
$464$	7.05573	+	21.7153i	0.327554	+	1.00811i
$465$	3.61803	−	2.62866i	0.167782	−	0.121901i
$466$		0			0
$467$	27.4894	−	19.9722i	1.27206	−	0.924203i	0.272773	−	0.962078i	$-0.412059\pi$
$467$	27.4894	−	19.9722i	1.27206	−	0.924203i	0.999282	+	0.0378758i	$0.0120591\pi$
$468$	2.85410	+	8.78402i	0.131931	+	0.406042i
$469$	3.19098	−	9.82084i	0.147346	−	0.453484i
$470$		0			0
$471$	3.00000	+	2.17963i	0.138233	+	0.100432i
$472$		0			0
$473$	3.86475	−	4.39201i	0.177701	−	0.201945i
$474$		0			0
$475$	37.3607			1.71423
$476$	−13.1803	+	9.57608i	−0.604120	+	0.438919i
$477$	9.00000			0.412082
$478$		0			0
$479$	−14.9443			−0.682821			−0.341411	−	0.939914i	$-0.610905\pi$
$479$	−14.9443			−0.682821			−0.341411	+	0.939914i	$0.610905\pi$
$480$		0			0
$481$	−21.5344	−	15.6457i	−0.981886	−	0.713382i
$482$		0			0
$483$	−3.39919	−	10.4616i	−0.154668	−	0.476020i
$484$	−15.0902	−	16.0090i	−0.685917	−	0.727680i
$485$	−4.57295	+	14.0741i	−0.207647	+	0.639072i
$486$		0			0
$487$	29.5623			1.33960			0.669798	−	0.742543i	$-0.266381\pi$
$487$	29.5623			1.33960			0.669798	+	0.742543i	$0.266381\pi$
$488$		0			0
$489$	−8.16312	−	5.93085i	−0.369149	−	0.268202i
$490$		0			0
$491$	−9.70163	−	29.8585i	−0.437828	−	1.34750i	−0.890160	−	0.455647i	$-0.849408\pi$
$491$	−9.70163	−	29.8585i	−0.437828	−	1.34750i	0.452332	−	0.891850i	$-0.350592\pi$
$492$	2.85410	+	2.07363i	0.128673	+	0.0934863i
$493$	3.11146	−	9.57608i	0.140133	−	0.431285i
$494$		0			0
$495$	−7.23607	+	1.62460i	−0.325237	+	0.0730203i
$496$	−2.47214	+	7.60845i	−0.111002	+	0.341630i
$497$	−9.44427	−	6.86167i	−0.423633	−	0.307788i
$498$		0			0
$499$	35.4164	+	25.7315i	1.58546	+	1.15190i	0.910084	+	0.414425i	$0.136017\pi$
$499$	35.4164	+	25.7315i	1.58546	+	1.15190i	0.675372	+	0.737477i	$0.263983\pi$
$500$	−22.3607			−1.00000
$501$	6.38197	+	19.6417i	0.285125	+	0.877525i
$502$		0			0
$503$	11.7533	+	36.1729i	0.524053	+	1.61287i	0.766180	+	0.642626i	$0.222155\pi$
$503$	11.7533	+	36.1729i	0.524053	+	1.61287i	−0.242127	+	0.970245i	$0.577845\pi$
$504$		0			0
$505$	−23.0902			−1.02750
$506$		0			0
$507$	8.32624			0.369781
$508$	−22.8328			−1.01304
$509$	−23.2705			−1.03145			−0.515724	−	0.856755i	$-0.672477\pi$
$509$	−23.2705			−1.03145			−0.515724	+	0.856755i	$0.672477\pi$
$510$		0			0
$511$	21.3262	+	15.4944i	0.943417	+	0.685433i
$512$		0			0
$513$	2.30902	+	7.10642i	0.101946	+	0.313756i
$514$		0			0
$515$	−26.0172	−	18.9026i	−1.14646	−	0.832949i
$516$	2.85410	+	2.07363i	0.125645	+	0.0912863i
$517$	11.0172	+	4.75528i	0.484537	+	0.209137i
$518$		0			0
$519$	18.8885			0.829115
$520$		0			0
$521$	0.663119	−	0.481784i	0.0290518	−	0.0211073i	−0.573165	−	0.819440i	$-0.694284\pi$
$521$	0.663119	−	0.481784i	0.0290518	−	0.0211073i	0.602216	+	0.798333i	$0.294284\pi$
$522$		0			0
$523$	18.3435	+	13.3273i	0.802103	+	0.582762i	0.911530	−	0.411233i	$-0.134902\pi$
$523$	18.3435	+	13.3273i	0.802103	+	0.582762i	−0.109427	+	0.993995i	$0.534902\pi$
$524$	32.7426	+	23.7889i	1.43037	+	1.03922i
$525$	−7.13525	−	21.9601i	−0.311408	−	0.958415i
$526$		0			0
$527$	2.85410	−	2.07363i	0.124327	−	0.0903286i
$528$	8.76393	−	9.95959i	0.381401	−	0.433436i
$529$	−5.35410	+	16.4782i	−0.232787	+	0.716445i
$530$		0			0
$531$	6.28115	+	4.56352i	0.272579	+	0.198040i
$532$	−55.8328	−	40.5649i	−2.42066	−	1.75871i
$533$	6.59017	−	4.78804i	0.285452	−	0.207393i
$534$		0			0
$535$	19.8992	+	14.4576i	0.860317	+	0.625057i
$536$		0			0
$537$	16.5172	−	12.0005i	0.712771	−	0.517858i
$538$		0			0
$539$	43.6246	+	18.8294i	1.87905	+	0.811038i
$540$	−1.38197	−	4.25325i	−0.0594703	−	0.183031i
$541$	−19.5623	+	14.2128i	−0.841049	+	0.611058i	−0.922664	−	0.385606i	$-0.873992\pi$
$541$	−19.5623	+	14.2128i	−0.841049	+	0.611058i	0.0816143	+	0.996664i	$0.473992\pi$
$542$		0			0
$543$	15.0623	+	10.9434i	0.646385	+	0.469626i
$544$		0			0
$545$	10.3262	−	31.7809i	0.442327	−	1.36134i
$546$		0			0
$547$	−7.47214	−	22.9969i	−0.319485	−	0.983275i	−0.973869	−	0.227112i	$-0.927072\pi$
$547$	−7.47214	−	22.9969i	−0.319485	−	0.983275i	0.654383	−	0.756163i	$-0.272928\pi$
$548$	1.58359	+	4.87380i	0.0676477	+	0.208198i
$549$	−3.94427			−0.168337
$550$		0			0
$551$	42.6525			1.81706
$552$		0			0
$553$	17.2533	+	53.1002i	0.733684	+	2.25805i
$554$		0			0
$555$	10.4271	+	7.57570i	0.442604	+	0.321570i
$556$	−2.85410	+	2.07363i	−0.121041	+	0.0879414i
$557$	2.30902	+	1.67760i	0.0978362	+	0.0710822i	0.635628	−	0.771996i	$-0.280741\pi$
$557$	2.30902	+	1.67760i	0.0978362	+	0.0710822i	−0.537792	+	0.843078i	$0.680741\pi$
$558$		0			0
$559$	6.59017	−	4.78804i	0.278734	−	0.202512i
$560$	33.4164	+	24.2784i	1.41210	+	1.02595i
$561$	−5.70820	+	1.28157i	−0.241001	+	0.0541080i
$562$		0			0
$563$	13.5172	−	9.82084i	0.569683	−	0.413899i	−0.265307	−	0.964164i	$-0.585473\pi$
$563$	13.5172	−	9.82084i	0.569683	−	0.413899i	0.834990	+	0.550265i	$0.185473\pi$
$564$	−2.23607	+	6.88191i	−0.0941554	+	0.289781i
$565$	5.79180	+	17.8253i	0.243663	+	0.749917i
$566$		0			0
$567$	3.73607	−	2.71441i	0.156900	−	0.113995i
$568$		0			0
$569$	6.38197	+	4.63677i	0.267546	+	0.194383i	0.713467	−	0.700689i	$-0.247124\pi$
$569$	6.38197	+	4.63677i	0.267546	+	0.194383i	−0.445921	+	0.895072i	$0.647124\pi$
$570$		0			0
$571$	1.29837	−	3.99598i	0.0543353	−	0.167227i	−0.920206	−	0.391434i	$-0.871979\pi$
$571$	1.29837	−	3.99598i	0.0543353	−	0.167227i	0.974542	+	0.224207i	$0.0719792\pi$
$572$	−15.6180	−	26.3521i	−0.653023	−	1.10184i
$573$	1.88197	−	1.36733i	0.0786203	−	0.0571210i
$574$		0			0
$575$	3.68034	−	11.3269i	0.153481	−	0.472365i
$576$	6.47214	+	4.70228i	0.269672	+	0.195928i
$577$	−8.07295	−	5.86534i	−0.336081	−	0.244177i	0.406925	−	0.913461i	$-0.366601\pi$
$577$	−8.07295	−	5.86534i	−0.336081	−	0.244177i	−0.743007	+	0.669284i	$0.766601\pi$
$578$		0			0
$579$	−6.04508	+	4.39201i	−0.251225	+	0.182526i
$580$	−25.5279			−1.05999
$581$	−55.8328			−2.31634
$582$		0			0
$583$	−29.1246	+	6.53888i	−1.20622	+	0.270813i
$584$		0			0
$585$	−10.3262			−0.426937
$586$		0			0
$587$	5.61803	+	17.2905i	0.231881	+	0.713657i	0.997520	+	0.0703858i	$0.0224230\pi$
$587$	5.61803	+	17.2905i	0.231881	+	0.713657i	−0.765639	+	0.643271i	$0.777577\pi$
$588$	−8.85410	+	27.2501i	−0.365137	+	1.12378i
$589$	12.0902	+	8.78402i	0.498167	+	0.361939i
$590$		0			0
$591$	−17.3820			−0.714999
$592$	−23.0557			−0.947585
$593$	−18.4721			−0.758560			−0.379280	−	0.925282i	$-0.623828\pi$
$593$	−18.4721			−0.758560			−0.379280	+	0.925282i	$0.623828\pi$
$594$		0			0
$595$	−5.62868	−	17.3233i	−0.230753	−	0.710186i
$596$	−3.52786	−	2.56314i	−0.144507	−	0.104990i
$597$	3.17376	+	9.76784i	0.129893	+	0.399771i
$598$		0			0
$599$	−0.236068	−	0.726543i	−0.00964548	−	0.0296857i	0.946118	−	0.323822i	$-0.104968\pi$
$599$	−0.236068	−	0.726543i	−0.00964548	−	0.0296857i	−0.955763	+	0.294136i	$0.904968\pi$
$600$		0			0
$601$	−10.6631	−	7.74721i	−0.434958	−	0.316015i	0.348671	−	0.937245i	$-0.386633\pi$
$601$	−10.6631	−	7.74721i	−0.434958	−	0.316015i	−0.783628	+	0.621230i	$0.786633\pi$
$602$		0			0
$603$	1.80902	+	1.31433i	0.0736689	+	0.0535236i
$604$	−8.56231	+	26.3521i	−0.348395	+	1.07225i
$605$	22.2361	−	10.5146i	0.904025	−	0.427480i
$606$		0			0
$607$	−4.69756	+	14.4576i	−0.190668	+	0.586816i	−1.00000		0.000535683i	$-0.999829\pi$
$607$	−4.69756	+	14.4576i	−0.190668	+	0.586816i	0.809332	+	0.587352i	$0.199829\pi$
$608$		0			0
$609$	−8.14590	−	25.0705i	−0.330088	−	1.01591i
$610$		0			0
$611$	13.5172	+	9.82084i	0.546848	+	0.397308i
$612$	−1.09017	−	3.35520i	−0.0440675	−	0.135626i
$613$	9.65248			0.389860			0.194930	−	0.980817i	$-0.437552\pi$
$613$	9.65248			0.389860			0.194930	+	0.980817i	$0.437552\pi$
$614$		0			0
$615$	−3.19098	+	2.31838i	−0.128673	+	0.0934863i
$616$		0			0
$617$	6.63525	+	20.4212i	0.267125	+	0.822127i	0.991196	+	0.132402i	$0.0422688\pi$
$617$	6.63525	+	20.4212i	0.267125	+	0.822127i	−0.724071	+	0.689726i	$0.757731\pi$
$618$		0			0
$619$	−17.6353	−	12.8128i	−0.708821	−	0.514988i	0.173972	−	0.984751i	$-0.444340\pi$
$619$	−17.6353	−	12.8128i	−0.708821	−	0.514988i	−0.882793	+	0.469762i	$0.844340\pi$
$620$	−7.23607	−	5.25731i	−0.290607	−	0.211139i
$621$	2.38197			0.0955850
$622$		0			0
$623$	−58.6869			−2.35124
$624$	14.9443	−	10.8576i	0.598250	−	0.434654i
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$		0			0
$627$	−12.6353	−	21.3193i	−0.504603	−	0.851410i
$628$	2.29180	−	7.05342i	0.0914526	−	0.281462i
$629$	8.22542	+	5.97612i	0.327969	+	0.238284i
$630$		0			0
$631$	−10.2426	+	31.5236i	−0.407753	+	1.25494i	0.510821	+	0.859687i	$0.329342\pi$
$631$	−10.2426	+	31.5236i	−0.407753	+	1.25494i	−0.918574	+	0.395248i	$0.870658\pi$
$632$		0			0
$633$	−8.35410	+	6.06961i	−0.332046	+	0.241245i
$634$		0			0
$635$	7.88854	−	24.2784i	0.313047	−	0.963461i
$636$	−5.56231	−	17.1190i	−0.220560	−	0.678813i
$637$	53.5238	+	38.8873i	2.12069	+	1.54077i
$638$		0			0
$639$	2.04508	−	1.48584i	0.0809023	−	0.0587790i
$640$		0			0
$641$	−41.0902			−1.62296			−0.811482	−	0.584377i	$-0.801339\pi$
$641$	−41.0902			−1.62296			−0.811482	+	0.584377i	$0.801339\pi$
$642$		0			0
$643$	1.27051	+	3.91023i	0.0501040	+	0.154204i	0.972978	−	0.230898i	$-0.0741663\pi$
$643$	1.27051	+	3.91023i	0.0501040	+	0.154204i	−0.922874	+	0.385102i	$0.874166\pi$
$644$	−17.7984	+	12.9313i	−0.701354	+	0.509564i
$645$	−3.19098	+	2.31838i	−0.125645	+	0.0912863i
$646$		0			0
$647$	20.3713	+	14.8006i	0.800879	+	0.581873i	0.911172	−	0.412026i	$-0.135179\pi$
$647$	20.3713	+	14.8006i	0.800879	+	0.581873i	−0.110293	+	0.993899i	$0.535179\pi$
$648$		0			0
$649$	−23.6418	−	10.2044i	−0.928023	−	0.400556i
$650$		0			0
$651$	2.85410	−	8.78402i	0.111861	−	0.344273i
$652$	−6.23607	+	19.1926i	−0.244223	+	0.751642i
$653$	−12.9443	+	9.40456i	−0.506549	+	0.368029i	−0.811513	−	0.584335i	$-0.801356\pi$
$653$	−12.9443	+	9.40456i	−0.506549	+	0.368029i	0.304964	+	0.952364i	$0.401356\pi$
$654$		0			0
$655$	−36.6074	+	26.5968i	−1.43037	+	1.03922i
$656$	2.18034	−	6.71040i	0.0851280	−	0.261997i
$657$	−4.61803	+	3.35520i	−0.180167	+	0.130899i
$658$		0			0
$659$	−32.7426	−	23.7889i	−1.27547	−	0.926685i	−0.276066	−	0.961139i	$-0.589031\pi$
$659$	−32.7426	−	23.7889i	−1.27547	−	0.926685i	−0.999406	+	0.0344537i	$0.989031\pi$
$660$	7.56231	+	12.7598i	0.294362	+	0.496673i
$661$	1.26393	−	0.918300i	0.0491613	−	0.0357177i	−0.562933	−	0.826502i	$-0.690327\pi$
$661$	1.26393	−	0.918300i	0.0491613	−	0.0357177i	0.612095	+	0.790785i	$0.290327\pi$
$662$		0			0
$663$	−8.14590			−0.316360
$664$		0			0
$665$	62.4230	−	45.3530i	2.42066	−	1.75871i
$666$		0			0
$667$	4.20163	−	12.9313i	0.162688	−	0.500701i
$668$	33.4164	−	24.2784i	1.29292	−	0.939361i
$669$	29.2705			1.13166
$670$		0			0
$671$	12.7639	−	2.86568i	0.492746	−	0.110628i
$672$		0			0
$673$	8.22542	+	25.3153i	0.317067	+	0.975831i	0.974895	+	0.222664i	$0.0714752\pi$
$673$	8.22542	+	25.3153i	0.317067	+	0.975831i	−0.657829	+	0.753168i	$0.728525\pi$
$674$		0			0
$675$	5.00000			0.192450
$676$	−5.14590	−	15.8374i	−0.197919	−	0.609133i
$677$	1.21885	+	0.885544i	0.0468441	+	0.0340342i	0.610961	−	0.791661i	$-0.290783\pi$
$677$	1.21885	+	0.885544i	0.0468441	+	0.0340342i	−0.564117	+	0.825695i	$0.690783\pi$
$678$		0			0
$679$	9.44427	+	29.0665i	0.362438	+	1.11547i
$680$		0			0
$681$	6.59017	+	20.2825i	0.252536	+	0.777225i
$682$		0			0
$683$	5.69098	+	17.5150i	0.217759	+	0.670195i	0.998946	+	0.0458972i	$0.0146147\pi$
$683$	5.69098	+	17.5150i	0.217759	+	0.670195i	−0.781187	+	0.624297i	$0.785385\pi$
$684$	12.0902	−	8.78402i	0.462279	−	0.335865i
$685$	−5.72949			−0.218913
$686$		0			0
$687$	5.94427	−	18.2946i	0.226788	−	0.697982i
$688$	2.18034	−	6.71040i	0.0831247	−	0.255831i
$689$	−41.5623			−1.58340
$690$		0			0
$691$	28.7254	−	20.8702i	1.09277	−	0.793941i	0.112902	−	0.993606i	$-0.463985\pi$
$691$	28.7254	−	20.8702i	1.09277	−	0.793941i	0.979864	+	0.199665i	$0.0639853\pi$
$692$	−11.6738	−	35.9281i	−0.443770	−	1.36578i
$693$	−10.1180	+	11.4984i	−0.384352	+	0.436789i
$694$		0			0
$695$	−1.21885	−	3.75123i	−0.0462335	−	0.142292i
$696$		0			0
$697$	−2.51722	+	1.82887i	−0.0953465	+	0.0692733i
$698$		0			0
$699$	−2.30902	−	7.10642i	−0.0873350	−	0.268790i
$700$	−37.3607	+	27.1441i	−1.41210	+	1.02595i
$701$	1.76393	−	1.28157i	0.0666228	−	0.0484043i	−0.553975	−	0.832533i	$-0.686890\pi$
$701$	1.76393	−	1.28157i	0.0666228	−	0.0484043i	0.620598	+	0.784129i	$0.286890\pi$
$702$		0			0
$703$	−13.3090	+	40.9609i	−0.501959	+	1.54487i
$704$	−24.3607	−	10.5146i	−0.918128	−	0.396285i
$705$	−6.54508	−	4.75528i	−0.246502	−	0.179094i
$706$		0			0
$707$	−38.5795	+	28.0297i	−1.45093	+	1.05416i
$708$	4.79837	−	14.7679i	0.180334	−	0.555011i
$709$	2.20163	−	6.77591i	0.0826838	−	0.254475i	−0.901165	−	0.433476i	$-0.857287\pi$
$709$	2.20163	−	6.77591i	0.0826838	−	0.254475i	0.983849	+	0.179002i	$0.0572868\pi$
$710$		0			0
$711$	−12.0902			−0.453417
$712$		0			0
$713$	3.85410	−	2.80017i	0.144337	−	0.104867i
$714$		0			0
$715$	33.4164	−	7.50245i	1.24970	−	0.280576i
$716$	−33.0344	−	24.0009i	−1.23456	−	0.896957i
$717$	14.2705			0.532942
$718$		0			0
$719$	−4.74265	+	14.5964i	−0.176871	+	0.544352i	−0.999714	−	0.0239161i	$-0.992387\pi$
$719$	−4.74265	+	14.5964i	−0.176871	+	0.544352i	0.822843	+	0.568269i	$0.192387\pi$
$720$	−7.23607	+	5.25731i	−0.269672	+	0.195928i
$721$	−66.4164			−2.47348
$722$		0			0
$723$	−8.69098	+	26.7481i	−0.323221	+	0.994772i
$724$	11.5066	−	35.4136i	0.427639	−	1.31614i
$725$	8.81966	−	27.1441i	0.327554	−	1.00811i
$726$		0			0
$727$	−26.6074	+	19.3314i	−0.986814	+	0.716962i	−0.959221	−	0.282657i	$-0.908784\pi$
$727$	−26.6074	+	19.3314i	−0.986814	+	0.716962i	−0.0275925	+	0.999619i	$0.508784\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−2.51722	+	1.82887i	−0.0931028	+	0.0676431i
$732$	2.43769	+	7.50245i	0.0900998	+	0.277299i
$733$	−10.2467	+	31.5361i	−0.378471	+	1.16481i	0.562636	+	0.826705i	$0.309787\pi$
$733$	−10.2467	+	31.5361i	−0.378471	+	1.16481i	−0.941107	+	0.338109i	$0.890213\pi$
$734$		0			0
$735$	−25.9164	−	18.8294i	−0.955941	−	0.694532i
$736$		0			0
$737$	−6.80902	−	2.93893i	−0.250813	−	0.108257i
$738$		0			0
$739$	−5.96556	−	18.3601i	−0.219447	−	0.675387i	−0.998808	−	0.0488125i	$-0.984456\pi$
$739$	−5.96556	−	18.3601i	−0.219447	−	0.675387i	0.779361	−	0.626575i	$-0.215544\pi$
$740$	7.96556	−	24.5155i	0.292820	−	0.901206i
$741$	−10.6631	−	32.8177i	−0.391719	−	1.20559i
$742$		0			0
$743$	−12.2188	−	37.6057i	−0.448266	−	1.37962i	−0.878862	−	0.477076i	$-0.841697\pi$
$743$	−12.2188	−	37.6057i	−0.448266	−	1.37962i	0.430596	−	0.902545i	$-0.358303\pi$
$744$		0			0
$745$	3.94427	−	2.86568i	0.144507	−	0.104990i
$746$		0			0
$747$	3.73607	−	11.4984i	0.136696	−	0.420706i
$748$	5.96556	+	10.0656i	0.218122	+	0.368035i
$749$	50.7984			1.85613
$750$		0			0
$751$	−22.2705	+	16.1805i	−0.812662	+	0.590434i	−0.914601	−	0.404357i	$-0.867495\pi$
$751$	−22.2705	+	16.1805i	−0.812662	+	0.590434i	0.101939	+	0.994791i	$0.467495\pi$
$752$	14.4721			0.527744
$753$	16.4721			0.600278
$754$		0			0
$755$	−25.0623	−	18.2088i	−0.912111	−	0.662687i
$756$	−7.47214	−	5.42882i	−0.271759	−	0.197444i
$757$	0.343459	−	1.05706i	0.0124832	−	0.0384194i	−0.944621	−	0.328164i	$-0.893570\pi$
$757$	0.343459	−	1.05706i	0.0124832	−	0.0384194i	0.957104	+	0.289744i	$0.0935703\pi$
$758$		0			0
$759$	−7.70820	+	1.73060i	−0.279790	+	0.0628168i
$760$		0			0
$761$	−5.16312	−	15.8904i	−0.187163	−	0.576028i	0.812816	−	0.582521i	$-0.197933\pi$
$761$	−5.16312	−	15.8904i	−0.187163	−	0.576028i	−0.999979	+	0.00649228i	$0.997933\pi$
$762$		0			0
$763$	−21.3262	−	65.6354i	−0.772062	−	2.37616i
$764$	−3.76393	−	2.73466i	−0.136174	−	0.0989364i
$765$	3.94427			0.142605
$766$		0			0
$767$	−29.0066	−	21.0745i	−1.04737	−	0.760957i
$768$	4.94427	−	15.2169i	0.178411	−	0.549093i
$769$	−9.31559	−	28.6705i	−0.335929	−	1.03388i	−0.966263	−	0.257559i	$-0.917082\pi$
$769$	−9.31559	−	28.6705i	−0.335929	−	1.03388i	0.630334	−	0.776324i	$-0.282918\pi$
$770$		0			0
$771$	7.09017	−	21.8213i	0.255346	−	0.785875i
$772$	12.0902	+	8.78402i	0.435135	+	0.316144i
$773$	−3.12461	+	9.61657i	−0.112384	+	0.345884i	−0.991393	−	0.130923i	$-0.958206\pi$
$773$	−3.12461	+	9.61657i	−0.112384	+	0.345884i	0.879008	+	0.476807i	$0.158206\pi$
$774$		0			0
$775$	8.09017	−	5.87785i	0.290607	−	0.211139i
$776$		0			0
$777$	26.6180			0.954917
$778$		0			0
$779$	−10.6631	−	7.74721i	−0.382046	−	0.277573i
$780$	6.38197	+	19.6417i	0.228511	+	0.703285i
$781$	−5.53851	+	6.29412i	−0.198183	+	0.225221i
$782$		0			0
$783$	5.70820			0.203995
$784$	57.3050			2.04661
$785$	6.70820	+	4.87380i	0.239426	+	0.173953i
$786$		0			0
$787$	−5.91641	+	18.2088i	−0.210897	+	0.649075i	0.788522	+	0.615006i	$0.210846\pi$
$787$	−5.91641	+	18.2088i	−0.210897	+	0.649075i	−0.999419	+	0.0340686i	$0.989154\pi$
$788$	10.7426	+	33.0625i	0.382691	+	1.17780i
$789$	1.63525	−	5.03280i	0.0582166	−	0.179172i
$790$		0			0
$791$	31.3156	+	22.7521i	1.11345	+	0.808972i
$792$		0			0
$793$	18.2148			0.646826
$794$		0			0
$795$	20.1246			0.713746
$796$	16.6180	−	12.0737i	0.589011	−	0.427941i
$797$	−33.5410			−1.18808			−0.594042	−	0.804434i	$-0.702469\pi$
$797$	−33.5410			−1.18808			−0.594042	+	0.804434i	$0.702469\pi$
$798$		0			0
$799$	−5.16312	−	3.75123i	−0.182658	−	0.132709i
$800$		0			0
$801$	3.92705	−	12.0862i	0.138756	−	0.427046i
$802$		0			0
$803$	12.5066	−	14.2128i	0.441348	−	0.501560i
$804$	1.38197	−	4.25325i	0.0487382	−	0.150001i
$805$	−7.60081	−	23.3929i	−0.267893	−	0.824491i
$806$		0			0
$807$	−22.6525	−	16.4580i	−0.797405	−	0.579349i
$808$		0			0
$809$	16.3713	−	50.3858i	0.575585	−	1.77147i	−0.0585934	−	0.998282i	$-0.518662\pi$
$809$	16.3713	−	50.3858i	0.575585	−	1.77147i	0.634178	−	0.773187i	$-0.281338\pi$
$810$		0			0
$811$	4.74671	−	14.6089i	0.166680	−	0.512987i	−0.832477	−	0.554060i	$-0.813078\pi$
$811$	4.74671	−	14.6089i	0.166680	−	0.512987i	0.999156	+	0.0410733i	$0.0130777\pi$
$812$	−42.6525	+	30.9888i	−1.49681	+	1.08750i
$813$	−4.61803	−	3.35520i	−0.161962	−	0.117672i
$814$		0			0
$815$	−18.2533	−	13.2618i	−0.639385	−	0.464540i
$816$	−5.70820	+	4.14725i	−0.199827	+	0.145183i
$817$	−10.6631	−	7.74721i	−0.373055	−	0.271041i
$818$		0			0
$819$	−17.2533	+	12.5352i	−0.602879	+	0.438017i
$820$	6.38197	+	4.63677i	0.222868	+	0.161923i
$821$	13.5172	−	9.82084i	0.471754	−	0.342750i	−0.326370	−	0.945242i	$-0.605826\pi$
$821$	13.5172	−	9.82084i	0.471754	−	0.342750i	0.798125	+	0.602492i	$0.205826\pi$
$822$		0			0
$823$	2.02786	+	6.24112i	0.0706869	+	0.217552i	0.980159	−	0.198213i	$-0.0635138\pi$
$823$	2.02786	+	6.24112i	0.0706869	+	0.217552i	−0.909472	+	0.415765i	$0.863514\pi$
$824$		0			0
$825$	−16.1803	+	3.63271i	−0.563327	+	0.126475i
$826$		0			0
$827$	8.01722	+	24.6745i	0.278786	+	0.858015i	0.988193	+	0.153216i	$0.0489630\pi$
$827$	8.01722	+	24.6745i	0.278786	+	0.858015i	−0.709407	+	0.704799i	$0.751037\pi$
$828$	−1.47214	−	4.53077i	−0.0511603	−	0.157455i
$829$	−1.52786	+	1.11006i	−0.0530649	+	0.0385539i	−0.614002	−	0.789305i	$-0.710441\pi$
$829$	−1.52786	+	1.11006i	−0.0530649	+	0.0385539i	0.560937	+	0.827859i	$0.310441\pi$
$830$		0			0
$831$	0.881966	−	0.640786i	0.0305951	−	0.0222286i
$832$	−29.8885	−	21.7153i	−1.03620	−	0.752843i
$833$	−20.4443	−	14.8536i	−0.708352	−	0.514648i
$834$		0			0
$835$	14.2705	+	43.9201i	0.493851	+	1.51992i
$836$	−32.7426	+	37.2097i	−1.13243	+	1.28692i
$837$	1.61803	+	1.17557i	0.0559274	+	0.0406337i
$838$		0			0
$839$	9.77458	−	30.0830i	0.337456	−	1.03858i	−0.628044	−	0.778178i	$-0.716144\pi$
$839$	9.77458	−	30.0830i	0.337456	−	1.03858i	0.965500	−	0.260404i	$-0.0838558\pi$
$840$		0			0
$841$	1.10739	−	3.40820i	0.0381859	−	0.117524i
$842$		0			0
$843$	9.23607	+	6.71040i	0.318107	+	0.231118i
$844$	16.7082	+	12.1392i	0.575120	+	0.417849i
$845$	18.6180			0.640480
$846$		0			0
$847$	24.3885	−	44.5609i	0.838000	−	1.53113i
$848$	−29.1246	+	21.1603i	−1.00014	+	0.726647i
$849$	−7.34346	+	22.6008i	−0.252027	+	0.775659i
$850$		0			0
$851$	11.1074	+	8.06999i	0.380756	+	0.276636i
$852$	−4.09017	−	2.97168i	−0.140127	−	0.101808i
$853$	41.9787			1.43732			0.718662	−	0.695360i	$-0.244755\pi$
$853$	41.9787			1.43732			0.718662	+	0.695360i	$0.244755\pi$
$854$		0			0
$855$	5.16312	+	15.8904i	0.176575	+	0.543442i
$856$		0			0
$857$	3.94427			0.134734			0.0673669	−	0.997728i	$-0.478540\pi$
$857$	3.94427			0.134734			0.0673669	+	0.997728i	$0.478540\pi$
$858$		0			0
$859$	23.7254	+	17.2375i	0.809501	+	0.588137i	0.913686	−	0.406421i	$-0.133223\pi$
$859$	23.7254	+	17.2375i	0.809501	+	0.588137i	−0.104185	+	0.994558i	$0.533223\pi$
$860$	6.38197	+	4.63677i	0.217623	+	0.158113i
$861$	−2.51722	+	7.74721i	−0.0857867	+	0.264024i
$862$		0			0
$863$	7.10739	−	21.8743i	0.241938	−	0.744610i	−0.754187	−	0.656660i	$-0.771969\pi$
$863$	7.10739	−	21.8743i	0.241938	−	0.744610i	0.996125	−	0.0879496i	$-0.0280314\pi$
$864$		0			0
$865$	42.2361			1.43607
$866$		0			0
$867$	−13.8885			−0.471680
$868$	−18.4721			−0.626985
$869$	39.1246	−	8.78402i	1.32721	−	0.297978i
$870$		0			0
$871$	−8.35410	−	6.06961i	−0.283068	−	0.205661i
$872$		0			0
$873$	−6.61803			−0.223987
$874$		0			0
$875$	−15.9549	−	49.1042i	−0.539375	−	1.66002i
$876$	9.23607	+	6.71040i	0.312058	+	0.226723i
$877$	−3.60739	+	11.1024i	−0.121813	+	0.374902i	−0.993307	−	0.115504i	$-0.963152\pi$
$877$	−3.60739	+	11.1024i	−0.121813	+	0.374902i	0.871494	+	0.490406i	$0.163152\pi$
$878$		0			0
$879$	−2.85410	+	8.78402i	−0.0962665	+	0.296278i
$880$	19.5967	−	22.2703i	0.660606	−	0.750733i
$881$	−7.01064	−	21.5765i	−0.236195	−	0.726932i	−0.996961	−	0.0779060i	$-0.975177\pi$
$881$	−7.01064	−	21.5765i	−0.236195	−	0.726932i	0.760766	−	0.649026i	$-0.224823\pi$
$882$		0			0
$883$	39.8328	+	28.9402i	1.34048	+	0.973916i	0.999426	+	0.0338730i	$0.0107842\pi$
$883$	39.8328	+	28.9402i	1.34048	+	0.973916i	0.341055	+	0.940043i	$0.389216\pi$
$884$	5.03444	+	15.4944i	0.169327	+	0.521134i
$885$	14.0451	+	10.2044i	0.472120	+	0.343016i
$886$		0			0
$887$	8.43363	+	25.9560i	0.283174	+	0.871519i	0.986940	+	0.161087i	$0.0515001\pi$
$887$	8.43363	+	25.9560i	0.283174	+	0.871519i	−0.703767	+	0.710431i	$0.748500\pi$
$888$		0			0
$889$	−16.2918	−	50.1410i	−0.546409	−	1.68167i
$890$		0			0
$891$	−1.69098	−	2.85317i	−0.0566501	−	0.0955848i
$892$	−18.0902	−	55.6758i	−0.605704	−	1.86416i
$893$	8.35410	−	25.7113i	0.279559	−	0.860395i
$894$		0			0
$895$	36.9336	−	26.8339i	1.23456	−	0.896957i
$896$		0			0
$897$	−11.0000			−0.367279
$898$		0			0
$899$	9.23607	−	6.71040i	0.308040	−	0.223804i
$900$	−3.09017	−	9.51057i	−0.103006	−	0.317019i
$901$	15.8754			0.528886
$902$		0			0
$903$	−2.51722	+	7.74721i	−0.0837679	+	0.257811i
$904$		0			0
$905$	33.6803	+	24.4702i	1.11957	+	0.813417i
$906$		0			0
$907$	−5.75329	−	17.7068i	−0.191035	−	0.587945i	−1.00000		8.81575e-5i	$-0.999972\pi$
$907$	−5.75329	−	17.7068i	−0.191035	−	0.587945i	0.808965	−	0.587857i	$-0.200028\pi$
$908$	34.5066	−	25.0705i	1.14514	−	0.831994i
$909$	−3.19098	−	9.82084i	−0.105838	−	0.325737i
$910$		0			0
$911$	−9.67376	−	29.7728i	−0.320506	−	0.986416i	−0.973428	−	0.228991i	$-0.926457\pi$
$911$	−9.67376	−	29.7728i	−0.320506	−	0.986416i	0.652922	−	0.757425i	$-0.273543\pi$
$912$	−24.1803	−	17.5680i	−0.800691	−	0.581736i
$913$	−3.73607	+	39.9241i	−0.123646	+	1.32130i
$914$		0			0
$915$	−8.81966			−0.291569
$916$	−38.4721			−1.27116
$917$	−28.8779	+	88.8770i	−0.953632	+	2.93498i
$918$		0			0
$919$	−14.6074	+	10.6129i	−0.481853	+	0.350087i	−0.802043	−	0.597267i	$-0.796253\pi$
$919$	−14.6074	+	10.6129i	−0.481853	+	0.350087i	0.320189	+	0.947354i	$0.396253\pi$
$920$		0			0
$921$	7.60081	+	23.3929i	0.250455	+	0.770822i
$922$		0			0
$923$	−9.44427	+	6.86167i	−0.310862	+	0.225854i
$924$	28.1246	+	12.1392i	0.925232	+	0.399351i
$925$	23.3156	+	16.9398i	0.766612	+	0.556976i
$926$		0			0
$927$	4.44427	−	13.6781i	0.145969	−	0.449247i
$928$		0			0
$929$	−27.4164			−0.899503			−0.449752	−	0.893154i	$-0.648487\pi$
$929$	−27.4164			−0.899503			−0.449752	+	0.893154i	$0.648487\pi$
$930$		0			0
$931$	33.0795	−	101.808i	1.08414	−	3.33663i
$932$	−12.0902	+	8.78402i	−0.396027	+	0.287730i
$933$	33.6525			1.10173
$934$		0			0
$935$	−12.7639	+	2.86568i	−0.417425	+	0.0937178i
$936$		0			0
$937$	−14.3992	+	10.4616i	−0.470401	+	0.341766i	−0.797598	−	0.603190i	$-0.793896\pi$
$937$	−14.3992	+	10.4616i	−0.470401	+	0.341766i	0.327197	+	0.944956i	$0.393896\pi$
$938$		0			0
$939$	−20.3607			−0.664446
$940$	−5.00000	+	15.3884i	−0.163082	+	0.501915i
$941$	0.961493	−	2.95917i	0.0313438	−	0.0964662i	−0.934161	−	0.356852i	$-0.883850\pi$
$941$	0.961493	−	2.95917i	0.0313438	−	0.0964662i	0.965505	+	0.260386i	$0.0838499\pi$
$942$		0			0
$943$	−3.39919	+	2.46965i	−0.110693	+	0.0804230i
$944$	−31.0557			−1.01078
$945$	8.35410	−	6.06961i	0.271759	−	0.197444i
$946$		0			0
$947$	−16.3262	+	50.2470i	−0.530531	+	1.63281i	0.222580	+	0.974915i	$0.428552\pi$
$947$	−16.3262	+	50.2470i	−0.530531	+	1.63281i	−0.753111	+	0.657893i	$0.771448\pi$
$948$	7.47214	+	22.9969i	0.242684	+	0.746904i
$949$	21.3262	−	15.4944i	0.692279	−	0.502970i
$950$		0			0
$951$	−2.92705	−	9.00854i	−0.0949161	−	0.292122i
$952$		0			0
$953$	−2.30902	+	1.67760i	−0.0747964	+	0.0543428i	−0.624555	−	0.780981i	$-0.714720\pi$
$953$	−2.30902	+	1.67760i	−0.0747964	+	0.0543428i	0.549759	+	0.835324i	$0.314720\pi$
$954$		0			0
$955$	4.20820	−	3.05744i	0.136174	−	0.0989364i
$956$	−8.81966	−	27.1441i	−0.285248	−	0.877904i
$957$	−18.4721	+	4.14725i	−0.597119	+	0.134062i
$958$		0			0
$959$	−9.57295	+	6.95515i	−0.309127	+	0.224594i
$960$	14.4721	+	10.5146i	0.467086	+	0.339358i
$961$	−27.0000			−0.870968
$962$		0			0
$963$	−3.39919	+	10.4616i	−0.109537	+	0.337121i
$964$	56.2492			1.81167
$965$	−13.5172	+	9.82084i	−0.435135	+	0.316144i
$966$		0			0
$967$	−6.04508	−	18.6049i	−0.194397	−	0.598292i	−0.999983	−	0.00581343i	$-0.998150\pi$
$967$	−6.04508	−	18.6049i	−0.194397	−	0.598292i	0.805586	−	0.592478i	$-0.201850\pi$
$968$		0			0
$969$	4.07295	+	12.5352i	0.130842	+	0.402690i
$970$		0			0
$971$	−7.87132	−	24.2254i	−0.252603	−	0.777431i	−0.994293	−	0.106688i	$-0.965975\pi$
$971$	−7.87132	−	24.2254i	−0.252603	−	0.777431i	0.741690	−	0.670743i	$-0.234025\pi$
$972$	1.61803	−	1.17557i	0.0518985	−	0.0377064i
$973$	−6.59017	−	4.78804i	−0.211271	−	0.153497i
$974$		0			0
$975$	−23.0902			−0.739477
$976$	12.7639	−	9.27354i	0.408564	−	0.296839i
$977$	15.0344	+	46.2713i	0.480994	+	1.48035i	0.837699	+	0.546132i	$0.183900\pi$
$977$	15.0344	+	46.2713i	0.480994	+	1.48035i	−0.356705	+	0.934217i	$0.616100\pi$
$978$		0			0
$979$	−3.92705	+	41.9650i	−0.125509	+	1.34121i
$980$	−19.7984	+	60.9331i	−0.632436	+	1.94644i
$981$	14.9443			0.477134
$982$		0			0
$983$	−10.1631	+	31.2789i	−0.324153	+	0.997641i	0.647668	+	0.761922i	$0.275744\pi$
$983$	−10.1631	+	31.2789i	−0.324153	+	0.997641i	−0.971821	+	0.235718i	$0.924256\pi$
$984$		0			0
$985$	−38.8673			−1.23841
$986$		0			0
$987$	−16.7082			−0.531828
$988$	−55.8328	+	40.5649i	−1.77628	+	1.29054i
$989$	−3.39919	+	2.46965i	−0.108088	+	0.0785304i
$990$		0			0
$991$	13.1910	+	9.58381i	0.419025	+	0.304440i	0.777246	−	0.629197i	$-0.216616\pi$
$991$	13.1910	+	9.58381i	0.419025	+	0.304440i	−0.358220	+	0.933637i	$0.616616\pi$
$992$		0			0
$993$	−10.2812	+	7.46969i	−0.326263	+	0.237044i
$994$		0			0
$995$	7.09675	+	21.8415i	0.224982	+	0.692423i
$996$	−24.1803			−0.766183
$997$	−13.5172	+	9.82084i	−0.428095	+	0.311029i	−0.780887	−	0.624673i	$-0.785232\pi$
$997$	−13.5172	+	9.82084i	−0.428095	+	0.311029i	0.352792	+	0.935702i	$0.385232\pi$
$998$		0			0
$999$	−1.78115	+	5.48183i	−0.0563532	+	0.173437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.m.b.361.1	yes	4
11.5	even	5		825.2.o.a.511.1	yes	4
25.16	even	5		825.2.o.a.691.1	yes	4
275.16	even	5	inner	825.2.m.b.16.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.m.b.16.1	✓	4	275.16	even	5	inner
825.2.m.b.361.1	yes	4	1.1	even	1	trivial
825.2.o.a.511.1	yes	4	11.5	even	5
825.2.o.a.691.1	yes	4	25.16	even	5

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{3} +(1.61803 - 1.17557i) q^{4} +(0.690983 + 2.12663i) q^{5} +(3.73607 + 2.71441i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{3} +(1.61803 - 1.17557i) q^{4} +(0.690983 + 2.12663i) q^{5} +(3.73607 + 2.71441i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(2.19098 - 2.48990i) q^{11} +(1.61803 + 1.17557i) q^{12} +(3.73607 - 2.71441i) q^{13} +(-1.80902 + 1.31433i) q^{15} +(1.23607 - 3.80423i) q^{16} +(-1.42705 + 1.03681i) q^{17} +(-6.04508 - 4.39201i) q^{19} +(3.61803 + 2.62866i) q^{20} +(-1.42705 + 4.39201i) q^{21} +(-1.92705 + 1.40008i) q^{23} +(-4.04508 + 2.93893i) q^{25} +(-0.809017 - 0.587785i) q^{27} +9.23607 q^{28} +(-4.61803 + 3.35520i) q^{29} -2.00000 q^{31} +(3.04508 + 1.31433i) q^{33} +(-3.19098 + 9.82084i) q^{35} +(-0.618034 + 1.90211i) q^{36} +(-1.78115 - 5.48183i) q^{37} +(3.73607 + 2.71441i) q^{39} +1.76393 q^{41} +1.76393 q^{43} +(0.618034 - 6.60440i) q^{44} +(-1.80902 - 1.31433i) q^{45} +(1.11803 + 3.44095i) q^{47} +4.00000 q^{48} +(4.42705 + 13.6251i) q^{49} +(-1.42705 - 1.03681i) q^{51} +(2.85410 - 8.78402i) q^{52} +(-7.28115 - 5.29007i) q^{53} +(6.80902 + 2.93893i) q^{55} +(2.30902 - 7.10642i) q^{57} +(-2.39919 - 7.38394i) q^{59} +(-1.38197 + 4.25325i) q^{60} +(3.19098 + 2.31838i) q^{61} -4.61803 q^{63} +(-2.47214 - 7.60845i) q^{64} +(8.35410 + 6.06961i) q^{65} +(-0.690983 - 2.12663i) q^{67} +(-1.09017 + 3.35520i) q^{68} +(-1.92705 - 1.40008i) q^{69} -2.52786 q^{71} +5.70820 q^{73} +(-4.04508 - 2.93893i) q^{75} -14.9443 q^{76} +(14.9443 - 3.35520i) q^{77} +(9.78115 + 7.10642i) q^{79} +8.94427 q^{80} +(0.309017 - 0.951057i) q^{81} +(-9.78115 + 7.10642i) q^{83} +(2.85410 + 8.78402i) q^{84} +(-3.19098 - 2.31838i) q^{85} +(-4.61803 - 3.35520i) q^{87} +(-10.2812 + 7.46969i) q^{89} +21.3262 q^{91} +(-1.47214 + 4.53077i) q^{92} +(-0.618034 - 1.90211i) q^{93} +(5.16312 - 15.8904i) q^{95} +(5.35410 + 3.88998i) q^{97} +(-0.309017 + 3.30220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 2 q^{4} + 5 q^{5} + 6 q^{7} - q^{9}+O(q^{10}) \) 4 * q - q^3 + 2 * q^4 + 5 * q^5 + 6 * q^7 - q^9	\( 4 q - q^{3} + 2 q^{4} + 5 q^{5} + 6 q^{7} - q^{9} + 11 q^{11} + 2 q^{12} + 6 q^{13} - 5 q^{15} - 4 q^{16} + q^{17} - 13 q^{19} + 10 q^{20} + q^{21} - q^{23} - 5 q^{25} - q^{27} + 28 q^{28} - 14 q^{29} - 8 q^{31} + q^{33} - 15 q^{35} + 2 q^{36} + 13 q^{37} + 6 q^{39} + 16 q^{41} + 16 q^{43} - 2 q^{44} - 5 q^{45} + 16 q^{48} + 11 q^{49} + q^{51} - 2 q^{52} - 9 q^{53} + 25 q^{55} + 7 q^{57} + 15 q^{59} - 10 q^{60} + 15 q^{61} - 14 q^{63} + 8 q^{64} + 20 q^{65} - 5 q^{67} + 18 q^{68} - q^{69} - 28 q^{71} - 4 q^{73} - 5 q^{75} - 24 q^{76} + 24 q^{77} + 19 q^{79} - q^{81} - 19 q^{83} - 2 q^{84} - 15 q^{85} - 14 q^{87} - 21 q^{89} + 54 q^{91} + 12 q^{92} + 2 q^{93} + 5 q^{95} + 8 q^{97} + q^{99}+O(q^{100}) \) 4 * q - q^3 + 2 * q^4 + 5 * q^5 + 6 * q^7 - q^9 + 11 * q^11 + 2 * q^12 + 6 * q^13 - 5 * q^15 - 4 * q^16 + q^17 - 13 * q^19 + 10 * q^20 + q^21 - q^23 - 5 * q^25 - q^27 + 28 * q^28 - 14 * q^29 - 8 * q^31 + q^33 - 15 * q^35 + 2 * q^36 + 13 * q^37 + 6 * q^39 + 16 * q^41 + 16 * q^43 - 2 * q^44 - 5 * q^45 + 16 * q^48 + 11 * q^49 + q^51 - 2 * q^52 - 9 * q^53 + 25 * q^55 + 7 * q^57 + 15 * q^59 - 10 * q^60 + 15 * q^61 - 14 * q^63 + 8 * q^64 + 20 * q^65 - 5 * q^67 + 18 * q^68 - q^69 - 28 * q^71 - 4 * q^73 - 5 * q^75 - 24 * q^76 + 24 * q^77 + 19 * q^79 - q^81 - 19 * q^83 - 2 * q^84 - 15 * q^85 - 14 * q^87 - 21 * q^89 + 54 * q^91 + 12 * q^92 + 2 * q^93 + 5 * q^95 + 8 * q^97 + q^99

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