LMFDB - Embedded newform 825.2.o.a.511.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(421,825)]

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, 6, 8]))

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

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

chi := DirichletCharacter("825.421");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.o (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			511.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	825.511
Dual form			825.2.o.a.691.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(0.690983 - 2.12663i) q^{5} +(3.73607 - 2.71441i) q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(0.690983 - 2.12663i) q^{5} +(3.73607 - 2.71441i) q^{7} +(0.309017 - 0.951057i) q^{9} +(3.04508 - 1.31433i) q^{11} +(1.61803 + 1.17557i) q^{12} +(-1.42705 + 4.39201i) q^{13} +(0.690983 + 2.12663i) q^{15} +(-3.23607 + 2.35114i) q^{16} +1.76393 q^{17} +(2.30902 - 7.10642i) q^{19} -4.47214 q^{20} +(-1.42705 + 4.39201i) q^{21} +(-1.92705 + 1.40008i) q^{23} +(-4.04508 - 2.93893i) q^{25} +(0.309017 + 0.951057i) q^{27} +(-7.47214 - 5.42882i) q^{28} +(1.76393 + 5.42882i) q^{29} +(1.61803 - 1.17557i) q^{31} +(-1.69098 + 2.85317i) q^{33} +(-3.19098 - 9.82084i) q^{35} -2.00000 q^{36} -5.76393 q^{37} +(-1.42705 - 4.39201i) q^{39} +(0.545085 + 1.67760i) q^{41} +1.76393 q^{43} +(-4.38197 - 4.97980i) q^{44} +(-1.80902 - 1.31433i) q^{45} +(-2.92705 + 2.12663i) q^{47} +(1.23607 - 3.80423i) q^{48} +(4.42705 - 13.6251i) q^{49} +(-1.42705 + 1.03681i) q^{51} +9.23607 q^{52} +9.00000 q^{53} +(-0.690983 - 7.38394i) q^{55} +(2.30902 + 7.10642i) q^{57} -7.76393 q^{59} +(3.61803 - 2.62866i) q^{60} +(-1.21885 - 3.75123i) q^{61} +(-1.42705 - 4.39201i) q^{63} +(6.47214 + 4.70228i) q^{64} +(8.35410 + 6.06961i) q^{65} +(-0.690983 - 2.12663i) q^{67} +(-1.09017 - 3.35520i) q^{68} +(0.736068 - 2.26538i) q^{69} +(2.04508 + 1.48584i) q^{71} +(1.76393 - 5.42882i) q^{73} +5.00000 q^{75} -14.9443 q^{76} +(7.80902 - 13.1760i) q^{77} -12.0902 q^{79} +(2.76393 + 8.50651i) q^{80} +(-0.809017 - 0.587785i) q^{81} +12.0902 q^{83} +9.23607 q^{84} +(1.21885 - 3.75123i) q^{85} +(-4.61803 - 3.35520i) q^{87} +(-10.2812 + 7.46969i) q^{89} +(6.59017 + 20.2825i) q^{91} +(3.85410 + 2.80017i) q^{92} +(-0.618034 + 1.90211i) q^{93} +(-13.5172 - 9.82084i) q^{95} -6.61803 q^{97} +(-0.309017 - 3.30220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + q^{11} + 2 q^{12} + q^{13} + 5 q^{15} - 4 q^{16} + 16 q^{17} + 7 q^{19} + q^{21} - q^{23} - 5 q^{25} - q^{27} - 12 q^{28} + 16 q^{29} + 2 q^{31} - 9 q^{33} - 15 q^{35} - 8 q^{36} - 32 q^{37} + q^{39} - 9 q^{41} + 16 q^{43} - 22 q^{44} - 5 q^{45} - 5 q^{47} - 4 q^{48} + 11 q^{49} + q^{51} + 28 q^{52} + 36 q^{53} - 5 q^{55} + 7 q^{57} - 40 q^{59} + 10 q^{60} - 25 q^{61} + q^{63} + 8 q^{64} + 20 q^{65} - 5 q^{67} + 18 q^{68} - 6 q^{69} - 3 q^{71} + 16 q^{73} + 20 q^{75} - 24 q^{76} + 29 q^{77} - 26 q^{79} + 20 q^{80} - q^{81} + 26 q^{83} + 28 q^{84} + 25 q^{85} - 14 q^{87} - 21 q^{89} + 4 q^{91} + 2 q^{92} + 2 q^{93} - 25 q^{95} - 22 q^{97} + q^{99}+O(q^{100}) $ 4 * q - q^3 + 2 * q^4 + 5 * q^5 + 6 * q^7 - q^9 + q^11 + 2 * q^12 + q^13 + 5 * q^15 - 4 * q^16 + 16 * q^17 + 7 * q^19 + q^21 - q^23 - 5 * q^25 - q^27 - 12 * q^28 + 16 * q^29 + 2 * q^31 - 9 * q^33 - 15 * q^35 - 8 * q^36 - 32 * q^37 + q^39 - 9 * q^41 + 16 * q^43 - 22 * q^44 - 5 * q^45 - 5 * q^47 - 4 * q^48 + 11 * q^49 + q^51 + 28 * q^52 + 36 * q^53 - 5 * q^55 + 7 * q^57 - 40 * q^59 + 10 * q^60 - 25 * q^61 + q^63 + 8 * q^64 + 20 * q^65 - 5 * q^67 + 18 * q^68 - 6 * q^69 - 3 * q^71 + 16 * q^73 + 20 * q^75 - 24 * q^76 + 29 * q^77 - 26 * q^79 + 20 * q^80 - q^81 + 26 * q^83 + 28 * q^84 + 25 * q^85 - 14 * q^87 - 21 * q^89 + 4 * q^91 + 2 * q^92 + 2 * q^93 - 25 * q^95 - 22 * q^97 + q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$

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		0.587785	−	0.809017i	$-0.300000\pi$
$2$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−0.618034	−	1.90211i	−0.309017	−	0.951057i
$5$	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	0.419088	−	0.907946i	$-0.362350\pi$
$7$	3.73607	−	2.71441i	1.41210	−	1.02595i	0.993013	−	0.118006i	$-0.0376501\pi$
$8$		0			0
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	3.04508	−	1.31433i	0.918128	−	0.396285i
$11$	3.04508	−	1.31433i	0.918128	−	0.396285i
$12$	1.61803	+	1.17557i	0.467086	+	0.339358i
$13$	−1.42705	+	4.39201i	−0.395793	+	1.21812i	0.532550	+	0.846399i	$0.321234\pi$
$13$	−1.42705	+	4.39201i	−0.395793	+	1.21812i	−0.928342	+	0.371726i	$0.878766\pi$
$14$		0			0
$15$	0.690983	+	2.12663i	0.178411	+	0.549093i
$16$	−3.23607	+	2.35114i	−0.809017	+	0.587785i
$17$	1.76393			0.427816			0.213908	−	0.976854i	$-0.431381\pi$
$17$	1.76393			0.427816			0.213908	+	0.976854i	$0.431381\pi$
$18$		0			0
$19$	2.30902	−	7.10642i	0.529725	−	1.63033i	−0.225054	−	0.974346i	$-0.572256\pi$
$19$	2.30902	−	7.10642i	0.529725	−	1.63033i	0.754779	−	0.655979i	$-0.227744\pi$
$20$	−4.47214			−1.00000
$21$	−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
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−7.47214	−	5.42882i	−1.41210	−	1.02595i
$29$	1.76393	+	5.42882i	0.327554	+	1.00811i	0.970275	+	0.242007i	$0.0778056\pi$
$29$	1.76393	+	5.42882i	0.327554	+	1.00811i	−0.642721	+	0.766101i	$0.722194\pi$
$30$		0			0
$31$	1.61803	−	1.17557i	0.290607	−	0.211139i	−0.432923	−	0.901431i	$-0.642518\pi$
$31$	1.61803	−	1.17557i	0.290607	−	0.211139i	0.723531	+	0.690292i	$0.242518\pi$
$32$		0			0
$33$	−1.69098	+	2.85317i	−0.294362	+	0.496673i
$34$		0			0
$35$	−3.19098	−	9.82084i	−0.539375	−	1.66002i
$36$	−2.00000			−0.333333
$37$	−5.76393			−0.947585			−0.473792	−	0.880637i	$-0.657115\pi$
$37$	−5.76393			−0.947585			−0.473792	+	0.880637i	$0.657115\pi$
$38$		0			0
$39$	−1.42705	−	4.39201i	−0.228511	−	0.703285i
$40$		0			0
$41$	0.545085	+	1.67760i	0.0851280	+	0.261997i	0.984555	−	0.175073i	$-0.0560162\pi$
$41$	0.545085	+	1.67760i	0.0851280	+	0.261997i	−0.899427	+	0.437070i	$0.856016\pi$
$42$		0			0
$43$	1.76393			0.268997			0.134499	−	0.990914i	$-0.457058\pi$
$43$	1.76393			0.268997			0.134499	+	0.990914i	$0.457058\pi$
$44$	−4.38197	−	4.97980i	−0.660606	−	0.750733i
$45$	−1.80902	−	1.31433i	−0.269672	−	0.195928i
$46$		0			0
$47$	−2.92705	+	2.12663i	−0.426954	+	0.310200i	−0.780430	−	0.625243i	$-0.785000\pi$
$47$	−2.92705	+	2.12663i	−0.426954	+	0.310200i	0.353476	+	0.935444i	$0.385000\pi$
$48$	1.23607	−	3.80423i	0.178411	−	0.549093i
$49$	4.42705	−	13.6251i	0.632436	−	1.94644i
$50$		0			0
$51$	−1.42705	+	1.03681i	−0.199827	+	0.145183i
$52$	9.23607			1.28081
$53$	9.00000			1.23625			0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000			1.23625			0.618123	+	0.786082i	$0.287894\pi$
$54$		0			0
$55$	−0.690983	−	7.38394i	−0.0931721	−	0.995650i
$56$		0			0
$57$	2.30902	+	7.10642i	0.305837	+	0.941269i
$58$		0			0
$59$	−7.76393			−1.01078			−0.505389	−	0.862892i	$-0.668651\pi$
$59$	−7.76393			−1.01078			−0.505389	+	0.862892i	$0.668651\pi$
$60$	3.61803	−	2.62866i	0.467086	−	0.339358i
$61$	−1.21885	−	3.75123i	−0.156057	−	0.480295i	0.842209	−	0.539151i	$-0.181255\pi$
$61$	−1.21885	−	3.75123i	−0.156057	−	0.480295i	−0.998266	+	0.0588558i	$0.981255\pi$
$62$		0			0
$63$	−1.42705	−	4.39201i	−0.179792	−	0.553341i
$64$	6.47214	+	4.70228i	0.809017	+	0.587785i
$65$	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
$69$	0.736068	−	2.26538i	0.0886122	−	0.272720i
$70$		0			0
$71$	2.04508	+	1.48584i	0.242707	+	0.176337i	0.702488	−	0.711695i	$-0.252072\pi$
$71$	2.04508	+	1.48584i	0.242707	+	0.176337i	−0.459781	+	0.888032i	$0.652072\pi$
$72$		0			0
$73$	1.76393	−	5.42882i	0.206453	−	0.635396i	−0.793198	−	0.608964i	$-0.791585\pi$
$73$	1.76393	−	5.42882i	0.206453	−	0.635396i	0.999651	−	0.0264320i	$-0.00841455\pi$
$74$		0			0
$75$	5.00000			0.577350
$76$	−14.9443			−1.71423
$77$	7.80902	−	13.1760i	0.889920	−	1.50155i
$78$		0			0
$79$	−12.0902			−1.36025			−0.680125	−	0.733096i	$-0.738075\pi$
$79$	−12.0902			−1.36025			−0.680125	+	0.733096i	$0.738075\pi$
$80$	2.76393	+	8.50651i	0.309017	+	0.951057i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	12.0902			1.32707			0.663534	−	0.748146i	$-0.269056\pi$
$83$	12.0902			1.32707			0.663534	+	0.748146i	$0.269056\pi$
$84$	9.23607			1.00774
$85$	1.21885	−	3.75123i	0.132203	−	0.406878i
$86$		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
$91$	6.59017	+	20.2825i	0.690838	+	2.12618i
$92$	3.85410	+	2.80017i	0.401818	+	0.291938i
$93$	−0.618034	+	1.90211i	−0.0640871	+	0.197240i
$94$		0			0
$95$	−13.5172	−	9.82084i	−1.38684	−	1.00760i
$96$		0			0
$97$	−6.61803			−0.671960			−0.335980	−	0.941869i	$-0.609067\pi$
$97$	−6.61803			−0.671960			−0.335980	+	0.941869i	$0.609067\pi$
$98$		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	−0.974707	−	0.223487i	$-0.928256\pi$
$101$	−3.19098	−	9.82084i	−0.317515	−	0.977210i	0.657192	−	0.753723i	$-0.271744\pi$
$102$		0			0
$103$	4.44427	+	13.6781i	0.437907	+	1.34774i	0.890078	+	0.455808i	$0.150650\pi$
$103$	4.44427	+	13.6781i	0.437907	+	1.34774i	−0.452171	+	0.891931i	$0.649350\pi$
$104$		0			0
$105$	8.35410	+	6.06961i	0.815277	+	0.592333i
$106$		0			0
$107$	8.89919	+	6.46564i	0.860317	+	0.625057i	0.927971	−	0.372652i	$-0.121551\pi$
$107$	8.89919	+	6.46564i	0.860317	+	0.625057i	−0.0676543	+	0.997709i	$0.521551\pi$
$108$	1.61803	−	1.17557i	0.155695	−	0.113119i
$109$	−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
$112$	−5.70820	+	17.5680i	−0.539375	+	1.66002i
$113$	2.59017	+	7.97172i	0.243663	+	0.749917i	0.995854	+	0.0909713i	$0.0289972\pi$
$113$	2.59017	+	7.97172i	0.243663	+	0.749917i	−0.752191	+	0.658945i	$0.771003\pi$
$114$		0			0
$115$	1.64590	+	5.06555i	0.153481	+	0.472365i
$116$	9.23607	−	6.71040i	0.857547	−	0.623045i
$117$	3.73607	+	2.71441i	0.345400	+	0.250948i
$118$		0			0
$119$	6.59017	−	4.78804i	0.604120	−	0.438919i
$120$		0			0
$121$	7.54508	−	8.00448i	0.685917	−	0.727680i
$122$		0			0
$123$	−1.42705	−	1.03681i	−0.128673	−	0.0934863i
$124$	−3.23607	−	2.35114i	−0.290607	−	0.211139i
$125$	−9.04508	+	6.57164i	−0.809017	+	0.587785i
$126$		0			0
$127$	3.52786	+	10.8576i	0.313047	+	0.963461i	0.976551	+	0.215287i	$0.0690688\pi$
$127$	3.52786	+	10.8576i	0.313047	+	0.963461i	−0.663503	+	0.748173i	$0.730931\pi$
$128$		0			0
$129$	−1.42705	+	1.03681i	−0.125645	+	0.0912863i
$130$		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
$135$	2.23607			0.192450
$136$		0			0
$137$	2.07295	−	1.50609i	0.177104	−	0.128674i	−0.495702	−	0.868493i	$-0.665089\pi$
$137$	2.07295	−	1.50609i	0.177104	−	0.128674i	0.672806	+	0.739819i	$0.265089\pi$
$138$		0			0
$139$	−0.545085	+	1.67760i	−0.0462335	+	0.142292i	−0.971508	−	0.237005i	$-0.923834\pi$
$139$	−0.545085	+	1.67760i	−0.0462335	+	0.142292i	0.925275	+	0.379297i	$0.123834\pi$
$140$	−16.7082	+	12.1392i	−1.41210	+	1.02595i
$141$	1.11803	−	3.44095i	0.0941554	−	0.289781i
$142$		0			0
$143$	1.42705	+	15.2497i	0.119336	+	1.27524i
$144$	1.23607	+	3.80423i	0.103006	+	0.317019i
$145$	12.7639			1.05999
$146$		0			0
$147$	4.42705	+	13.6251i	0.365137	+	1.12378i
$148$	3.56231	+	10.9637i	0.292820	+	0.901206i
$149$	−0.673762	+	2.07363i	−0.0551967	+	0.169878i	−0.974854	−	0.222843i	$-0.928466\pi$
$149$	−0.673762	+	2.07363i	−0.0551967	+	0.169878i	0.919658	+	0.392721i	$0.128466\pi$
$150$		0			0
$151$	−11.2082	−	8.14324i	−0.912111	−	0.662687i	0.0294371	−	0.999567i	$-0.490629\pi$
$151$	−11.2082	−	8.14324i	−0.912111	−	0.662687i	−0.941548	+	0.336879i	$0.890629\pi$
$152$		0			0
$153$	0.545085	−	1.67760i	0.0440675	−	0.135626i
$154$		0			0
$155$	−1.38197	−	4.25325i	−0.111002	−	0.341630i
$156$	−7.47214	+	5.42882i	−0.598250	+	0.434654i
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	0.701028	−	0.713134i	$-0.252725\pi$
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	−0.461601	+	0.887087i	$0.652725\pi$
$158$		0			0
$159$	−7.28115	+	5.29007i	−0.577433	+	0.419530i
$160$		0			0
$161$	−3.39919	+	10.4616i	−0.267893	+	0.824491i
$162$		0			0
$163$	3.11803	−	9.59632i	0.244223	−	0.751642i	−0.751540	−	0.659688i	$-0.770689\pi$
$163$	3.11803	−	9.59632i	0.244223	−	0.751642i	0.995763	−	0.0919544i	$-0.0293114\pi$
$164$	2.85410	−	2.07363i	0.222868	−	0.161923i
$165$	4.89919	+	5.56758i	0.381401	+	0.433436i
$166$		0			0
$167$	−16.7082	+	12.1392i	−1.29292	+	0.939361i	−0.999860	−	0.0167331i	$-0.994673\pi$
$167$	−16.7082	+	12.1392i	−1.29292	+	0.939361i	−0.293060	+	0.956094i	$0.594673\pi$
$168$		0			0
$169$	−6.73607	−	4.89404i	−0.518159	−	0.376465i
$170$		0			0
$171$	−6.04508	−	4.39201i	−0.462279	−	0.335865i
$172$	−1.09017	−	3.35520i	−0.0831247	−	0.255831i
$173$	18.8885			1.43607			0.718035	−	0.696007i	$-0.245042\pi$
$173$	18.8885			1.43607			0.718035	+	0.696007i	$0.245042\pi$
$174$		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
$179$	16.5172	−	12.0005i	1.23456	−	0.896957i	0.237332	−	0.971429i	$-0.423727\pi$
$179$	16.5172	−	12.0005i	1.23456	−	0.896957i	0.997223	+	0.0744719i	$0.0237271\pi$
$180$	−1.38197	+	4.25325i	−0.103006	+	0.317019i
$181$	−18.6180			−1.38387			−0.691934	−	0.721961i	$-0.743241\pi$
$181$	−18.6180			−1.38387			−0.691934	+	0.721961i	$0.743241\pi$
$182$		0			0
$183$	3.19098	+	2.31838i	0.235884	+	0.171380i
$184$		0			0
$185$	−3.98278	+	12.2577i	−0.292820	+	0.901206i
$186$		0			0
$187$	5.37132	−	2.31838i	0.392790	−	0.169537i
$188$	5.85410	+	4.25325i	0.426954	+	0.310200i
$189$	3.73607	+	2.71441i	0.271759	+	0.197444i
$190$		0			0
$191$	−2.32624			−0.168321			−0.0841603	−	0.996452i	$-0.526821\pi$
$191$	−2.32624			−0.168321			−0.0841603	+	0.996452i	$0.526821\pi$
$192$	−8.00000			−0.577350
$193$	2.30902	−	7.10642i	0.166207	−	0.511532i	−0.832917	−	0.553399i	$-0.813331\pi$
$193$	2.30902	−	7.10642i	0.166207	−	0.511532i	0.999123	+	0.0418671i	$0.0133306\pi$
$194$		0			0
$195$	−10.3262			−0.739477
$196$	−28.6525			−2.04661
$197$	−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
$203$	21.3262	+	15.4944i	1.49681	+	1.08750i
$204$	2.85410	+	2.07363i	0.199827	+	0.145183i
$205$	3.94427			0.275480
$206$		0			0
$207$	0.736068	+	2.26538i	0.0511603	+	0.157455i
$208$	−5.70820	−	17.5680i	−0.395793	−	1.21812i
$209$	−2.30902	−	24.6745i	−0.159718	−	1.70677i
$210$		0			0
$211$	−8.35410	−	6.06961i	−0.575120	−	0.417849i	0.261841	−	0.965111i	$-0.415670\pi$
$211$	−8.35410	−	6.06961i	−0.575120	−	0.417849i	−0.836962	+	0.547262i	$0.815670\pi$
$212$	−5.56231	−	17.1190i	−0.382021	−	1.17574i
$213$	−2.52786			−0.173206
$214$		0			0
$215$	1.21885	−	3.75123i	0.0831247	−	0.255831i
$216$		0			0
$217$	2.85410	−	8.78402i	0.193749	−	0.596298i
$218$		0			0
$219$	1.76393	+	5.42882i	0.119195	+	0.366846i
$220$	−13.6180	+	5.87785i	−0.918128	+	0.396285i
$221$	−2.51722	+	7.74721i	−0.169327	+	0.521134i
$222$		0			0
$223$	29.2705			1.96010			0.980049	−	0.198755i	$-0.0636899\pi$
$223$	29.2705			1.96010			0.980049	+	0.198755i	$0.0636899\pi$
$224$		0			0
$225$	−4.04508	+	2.93893i	−0.269672	+	0.195928i
$226$		0			0
$227$	6.59017	−	20.2825i	0.437405	−	1.34619i	−0.453197	−	0.891410i	$-0.649717\pi$
$227$	6.59017	−	20.2825i	0.437405	−	1.34619i	0.890602	−	0.454784i	$-0.150283\pi$
$228$	12.0902	−	8.78402i	0.800691	−	0.581736i
$229$	19.2361			1.27116			0.635578	−	0.772037i	$-0.280762\pi$
$229$	19.2361			1.27116			0.635578	+	0.772037i	$0.280762\pi$
$230$		0			0
$231$	1.42705	+	15.2497i	0.0938931	+	1.00335i
$232$		0			0
$233$	6.04508	−	4.39201i	0.396027	−	0.287730i	−0.371894	−	0.928275i	$-0.621292\pi$
$233$	6.04508	−	4.39201i	0.396027	−	0.287730i	0.767921	+	0.640545i	$0.221292\pi$
$234$		0			0
$235$	2.50000	+	7.69421i	0.163082	+	0.501915i
$236$	4.79837	+	14.7679i	0.312348	+	0.961307i
$237$	9.78115	−	7.10642i	0.635354	−	0.461612i
$238$		0			0
$239$	14.2705			0.923083			0.461541	−	0.887119i	$-0.347297\pi$
$239$	14.2705			0.923083			0.461541	+	0.887119i	$0.347297\pi$
$240$	−7.23607	−	5.25731i	−0.467086	−	0.339358i
$241$	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
$244$	−6.38197	+	4.63677i	−0.408564	+	0.296839i
$245$	−25.9164	−	18.8294i	−1.65574	−	1.20296i
$246$		0			0
$247$	27.9164	+	20.2825i	1.77628	+	1.29054i
$248$		0			0
$249$	−9.78115	+	7.10642i	−0.619855	+	0.450351i
$250$		0			0
$251$	5.09017	+	15.6659i	0.321289	+	0.988825i	0.973088	+	0.230433i	$0.0740144\pi$
$251$	5.09017	+	15.6659i	0.321289	+	0.988825i	−0.651799	+	0.758391i	$0.725986\pi$
$252$	−7.47214	+	5.42882i	−0.470700	+	0.341984i
$253$	−4.02786	+	6.79615i	−0.253230	+	0.427270i
$254$		0			0
$255$	1.21885	+	3.75123i	0.0763272	+	0.234911i
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$	−18.5623	+	13.4863i	−1.15788	+	0.841253i	−0.989509	−	0.144470i	$-0.953852\pi$
$257$	−18.5623	+	13.4863i	−1.15788	+	0.841253i	−0.168376	+	0.985723i	$0.553852\pi$
$258$		0			0
$259$	−21.5344	+	15.6457i	−1.33809	+	0.972176i
$260$	6.38197	−	19.6417i	0.395793	−	1.21812i
$261$	5.70820			0.353329
$262$		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
$267$	3.92705	−	12.0862i	0.240332	−	0.739665i
$268$	−3.61803	+	2.62866i	−0.221007	+	0.160571i
$269$	28.0000			1.70719			0.853595	−	0.520937i	$-0.174417\pi$
$269$	28.0000			1.70719			0.853595	+	0.520937i	$0.174417\pi$
$270$		0			0
$271$	1.76393	+	5.42882i	0.107151	+	0.329778i	0.990229	−	0.139448i	$-0.0445329\pi$
$271$	1.76393	+	5.42882i	0.107151	+	0.329778i	−0.883078	+	0.469226i	$0.844533\pi$
$272$	−5.70820	+	4.14725i	−0.346111	+	0.251464i
$273$	−17.2533	−	12.5352i	−1.04422	−	0.758668i
$274$		0			0
$275$	−16.1803	−	3.63271i	−0.975711	−	0.219061i
$276$	−4.76393			−0.286755
$277$	0.881966	+	0.640786i	0.0529922	+	0.0385011i	0.613966	−	0.789332i	$-0.289573\pi$
$277$	0.881966	+	0.640786i	0.0529922	+	0.0385011i	−0.560974	+	0.827834i	$0.689573\pi$
$278$		0			0
$279$	−0.618034	−	1.90211i	−0.0370007	−	0.113877i
$280$		0			0
$281$	−11.4164			−0.681046			−0.340523	−	0.940236i	$-0.610604\pi$
$281$	−11.4164			−0.681046			−0.340523	+	0.940236i	$0.610604\pi$
$282$		0			0
$283$	−7.34346	+	22.6008i	−0.436523	+	1.34348i	0.454994	+	0.890494i	$0.349641\pi$
$283$	−7.34346	+	22.6008i	−0.436523	+	1.34348i	−0.891518	+	0.452986i	$0.850359\pi$
$284$	1.56231	−	4.80828i	0.0927058	−	0.285319i
$285$	16.7082			0.989709
$286$		0			0
$287$	6.59017	+	4.78804i	0.389005	+	0.282629i
$288$		0			0
$289$	−13.8885			−0.816973
$290$		0			0
$291$	5.35410	−	3.88998i	0.313863	−	0.228035i
$292$	−11.4164			−0.668095
$293$	7.47214	−	5.42882i	0.436527	−	0.317155i	−0.347727	−	0.937596i	$-0.613046\pi$
$293$	7.47214	−	5.42882i	0.436527	−	0.317155i	0.784253	+	0.620441i	$0.213046\pi$
$294$		0			0
$295$	−5.36475	+	16.5110i	−0.312348	+	0.961307i
$296$		0			0
$297$	2.19098	+	2.48990i	0.127134	+	0.144479i
$298$		0			0
$299$	−3.39919	−	10.4616i	−0.196580	−	0.605011i
$300$	−3.09017	−	9.51057i	−0.178411	−	0.549093i
$301$	6.59017	−	4.78804i	0.379851	−	0.275978i
$302$		0			0
$303$	8.35410	+	6.06961i	0.479931	+	0.348690i
$304$	9.23607	+	28.4257i	0.529725	+	1.63033i
$305$	−8.81966			−0.505012
$306$		0			0
$307$	24.5967			1.40381			0.701905	−	0.712270i	$-0.252333\pi$
$307$	24.5967			1.40381			0.701905	+	0.712270i	$0.252333\pi$
$308$	−29.8885	−	6.71040i	−1.70306	−	0.382360i
$309$	−11.6353	−	8.45351i	−0.661907	−	0.480903i
$310$		0			0
$311$	33.6525			1.90826			0.954128	−	0.299398i	$-0.0967857\pi$
$311$	33.6525			1.90826			0.954128	+	0.299398i	$0.0967857\pi$
$312$		0			0
$313$	16.4721	−	11.9677i	0.931060	−	0.676455i	−0.0151920	−	0.999885i	$-0.504836\pi$
$313$	16.4721	−	11.9677i	0.931060	−	0.676455i	0.946252	+	0.323430i	$0.104836\pi$
$314$		0			0
$315$	−10.3262			−0.581818
$316$	7.47214	+	22.9969i	0.420340	+	1.29367i
$317$	7.66312	−	5.56758i	0.430404	−	0.312707i	−0.351407	−	0.936223i	$-0.614297\pi$
$317$	7.66312	−	5.56758i	0.430404	−	0.312707i	0.781810	+	0.623516i	$0.214297\pi$
$318$		0			0
$319$	12.5066	+	14.2128i	0.700234	+	0.795767i
$320$	14.4721	−	10.5146i	0.809017	−	0.587785i
$321$	−11.0000			−0.613960
$322$		0			0
$323$	4.07295	−	12.5352i	0.226625	−	0.697480i
$324$	−0.618034	+	1.90211i	−0.0343352	+	0.105673i
$325$	18.6803	−	13.5721i	1.03620	−	0.752843i
$326$		0			0
$327$	14.9443			0.826420
$328$		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
$333$	−1.78115	+	5.48183i	−0.0976066	+	0.300402i
$334$		0			0
$335$	−5.00000			−0.273179
$336$	−5.70820	−	17.5680i	−0.311408	−	0.958415i
$337$	9.23607			0.503121			0.251560	−	0.967842i	$-0.419056\pi$
$337$	9.23607			0.503121			0.251560	+	0.967842i	$0.419056\pi$
$338$		0			0
$339$	−6.78115	−	4.92680i	−0.368302	−	0.267587i
$340$	−7.88854			−0.427816
$341$	3.38197	−	5.70634i	0.183144	−	0.309016i
$342$		0			0
$343$	−10.4549	−	32.1769i	−0.564512	−	1.73739i
$344$		0			0
$345$	−4.30902	−	3.13068i	−0.231990	−	0.168550i
$346$		0			0
$347$	−18.1353	−	13.1760i	−0.973551	−	0.707327i	−0.0172933	−	0.999850i	$-0.505505\pi$
$347$	−18.1353	−	13.1760i	−0.973551	−	0.707327i	−0.956258	+	0.292524i	$0.905505\pi$
$348$	−3.52786	+	10.8576i	−0.189113	+	0.582031i
$349$	−16.7082	−	12.1392i	−0.894370	−	0.649798i	0.0426440	−	0.999090i	$-0.486422\pi$
$349$	−16.7082	−	12.1392i	−0.894370	−	0.649798i	−0.937014	+	0.349293i	$0.886422\pi$
$350$		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
$355$	4.57295	−	3.32244i	0.242707	−	0.176337i
$356$	20.5623	+	14.9394i	1.08980	+	0.791786i
$357$	−2.51722	+	7.74721i	−0.133225	+	0.410026i
$358$		0			0
$359$	−1.76393			−0.0930968			−0.0465484	−	0.998916i	$-0.514822\pi$
$359$	−1.76393			−0.0930968			−0.0465484	+	0.998916i	$0.514822\pi$
$360$		0			0
$361$	−29.7984	−	21.6498i	−1.56834	−	1.13946i
$362$		0			0
$363$	−1.39919	+	10.9106i	−0.0734383	+	0.572661i
$364$	34.5066	−	25.0705i	1.80864	−	1.31405i
$365$	−10.3262	−	7.50245i	−0.540500	−	0.392696i
$366$		0			0
$367$	−9.66312	−	7.02067i	−0.504411	−	0.366476i	0.306288	−	0.951939i	$-0.400913\pi$
$367$	−9.66312	−	7.02067i	−0.504411	−	0.366476i	−0.810699	+	0.585463i	$0.800913\pi$
$368$	2.94427	−	9.06154i	0.153481	−	0.472365i
$369$	1.76393			0.0918266
$370$		0			0
$371$	33.6246	−	24.4297i	1.74570	−	1.26833i
$372$	4.00000			0.207390
$373$	−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
$377$	−26.3607			−1.35764
$378$		0			0
$379$	4.19098	+	3.04493i	0.215276	+	0.156407i	0.690198	−	0.723621i	$-0.257524\pi$
$379$	4.19098	+	3.04493i	0.215276	+	0.156407i	−0.474921	+	0.880028i	$0.657524\pi$
$380$	−10.3262	+	31.7809i	−0.529725	+	1.63033i
$381$	−9.23607	−	6.71040i	−0.473178	−	0.343784i
$382$		0			0
$383$	−27.1803	+	19.7477i	−1.38885	+	1.00906i	−0.392860	+	0.919598i	$0.628514\pi$
$383$	−27.1803	+	19.7477i	−1.38885	+	1.00906i	−0.995990	+	0.0894607i	$0.971486\pi$
$384$		0			0
$385$	−22.6246	−	25.7113i	−1.15306	−	1.31037i
$386$		0			0
$387$	0.545085	−	1.67760i	0.0277082	−	0.0852772i
$388$	4.09017	+	12.5882i	0.207647	+	0.639072i
$389$	5.48936	−	16.8945i	0.278321	−	0.856585i	−0.710000	−	0.704202i	$-0.751305\pi$
$389$	5.48936	−	16.8945i	0.278321	−	0.856585i	0.988321	−	0.152384i	$-0.0486949\pi$
$390$		0			0
$391$	−3.39919	+	2.46965i	−0.171904	+	0.124896i
$392$		0			0
$393$	−16.3713	−	11.8945i	−0.825824	−	0.599996i
$394$		0			0
$395$	−8.35410	+	25.7113i	−0.420340	+	1.29367i
$396$	−6.09017	+	2.62866i	−0.306043	+	0.132095i
$397$	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
$400$	20.0000			1.00000
$401$	−2.20820	+	6.79615i	−0.110272	+	0.339384i	−0.990932	−	0.134367i	$-0.957100\pi$
$401$	−2.20820	+	6.79615i	−0.110272	+	0.339384i	0.880659	+	0.473750i	$0.157100\pi$
$402$		0			0
$403$	2.85410	+	8.78402i	0.142173	+	0.437563i
$404$	−16.7082	+	12.1392i	−0.831264	+	0.603949i
$405$	−1.80902	+	1.31433i	−0.0898908	+	0.0653095i
$406$		0			0
$407$	−17.5517	+	7.57570i	−0.870004	+	0.375513i
$408$		0			0
$409$	−9.90983	+	30.4993i	−0.490010	+	1.50809i	0.334582	+	0.942366i	$0.391405\pi$
$409$	−9.90983	+	30.4993i	−0.490010	+	1.50809i	−0.824592	+	0.565728i	$0.808595\pi$
$410$		0			0
$411$	−0.791796	+	2.43690i	−0.0390564	+	0.120203i
$412$	23.2705	−	16.9070i	1.14646	−	0.832949i
$413$	−29.0066	+	21.0745i	−1.42732	+	1.03701i
$414$		0			0
$415$	8.35410	−	25.7113i	0.410087	−	1.26212i
$416$		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	$0.971272\pi$
$420$	6.38197	−	19.6417i	0.311408	−	0.958415i
$421$	20.5902	−	14.9596i	1.00350	−	0.729088i	0.0406669	−	0.999173i	$-0.487052\pi$
$421$	20.5902	−	14.9596i	1.00350	−	0.729088i	0.962837	+	0.270085i	$0.0870517\pi$
$422$		0			0
$423$	1.11803	+	3.44095i	0.0543607	+	0.167305i
$424$		0			0
$425$	−7.13525	−	5.18407i	−0.346111	−	0.251464i
$426$		0			0
$427$	−14.7361	−	10.7064i	−0.713128	−	0.518118i
$428$	6.79837	−	20.9232i	0.328612	−	1.01136i
$429$	−10.1180	−	11.4984i	−0.488503	−	0.555150i
$430$		0			0
$431$	−15.4894	+	11.2537i	−0.746096	+	0.542071i	−0.894614	−	0.446839i	$-0.852550\pi$
$431$	−15.4894	+	11.2537i	−0.746096	+	0.542071i	0.148518	+	0.988910i	$0.452550\pi$
$432$	−3.23607	−	2.35114i	−0.155695	−	0.113119i
$433$	16.7533	+	12.1720i	0.805112	+	0.584948i	0.912409	−	0.409279i	$-0.134220\pi$
$433$	16.7533	+	12.1720i	0.805112	+	0.584948i	−0.107298	+	0.994227i	$0.534220\pi$
$434$		0			0
$435$	−10.3262	+	7.50245i	−0.495105	+	0.359715i
$436$	−9.23607	+	28.4257i	−0.442327	+	1.36134i
$437$	5.50000	+	16.9273i	0.263101	+	0.809741i
$438$		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	0.513528	−	0.858073i	$-0.328338\pi$
$443$	−3.02786	−	2.19987i	−0.143858	−	0.104519i	−0.657387	+	0.753554i	$0.728338\pi$
$444$	−9.32624	−	6.77591i	−0.442604	−	0.321570i
$445$	8.78115	+	27.0256i	0.416267	+	1.28114i
$446$		0			0
$447$	−0.673762	−	2.07363i	−0.0318679	−	0.0980792i
$448$	36.9443			1.74545
$449$	−9.41641	−	28.9807i	−0.444388	−	1.36768i	−0.883154	−	0.469084i	$-0.844584\pi$
$449$	−9.41641	−	28.9807i	−0.444388	−	1.36768i	0.438766	−	0.898601i	$-0.355416\pi$
$450$		0			0
$451$	3.86475	+	4.39201i	0.181984	+	0.206812i
$452$	13.5623	−	9.85359i	0.637917	−	0.463474i
$453$	13.8541			0.650922
$454$		0			0
$455$	47.6869			2.23560
$456$		0			0
$457$	−1.01064	+	3.11044i	−0.0472759	+	0.145500i	−0.971908	−	0.235361i	$-0.924373\pi$
$457$	−1.01064	+	3.11044i	−0.0472759	+	0.145500i	0.924632	+	0.380862i	$0.124373\pi$
$458$		0			0
$459$	0.545085	+	1.67760i	0.0254424	+	0.0783036i
$460$	8.61803	−	6.26137i	0.401818	−	0.291938i
$461$	−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	$0.814480\pi$
$464$	−18.4721	−	13.4208i	−0.857547	−	0.623045i
$465$	3.61803	+	2.62866i	0.167782	+	0.121901i
$466$		0			0
$467$	−33.9787			−1.57235			−0.786174	−	0.618006i	$-0.787941\pi$
$467$	−33.9787			−1.57235			−0.786174	+	0.618006i	$0.787941\pi$
$468$	2.85410	−	8.78402i	0.131931	−	0.406042i
$469$	−8.35410	−	6.06961i	−0.385757	−	0.280269i
$470$		0			0
$471$	−3.70820			−0.170865
$472$		0			0
$473$	5.37132	−	2.31838i	0.246974	−	0.106599i
$474$		0			0
$475$	−30.2254	+	21.9601i	−1.38684	+	1.00760i
$476$	−13.1803	−	9.57608i	−0.604120	−	0.438919i
$477$	2.78115	−	8.55951i	0.127340	−	0.391913i
$478$		0			0
$479$	12.0902	+	8.78402i	0.552414	+	0.401352i	0.828675	−	0.559730i	$-0.189095\pi$
$479$	12.0902	+	8.78402i	0.552414	+	0.401352i	−0.276261	+	0.961083i	$0.589095\pi$
$480$		0			0
$481$	8.22542	−	25.3153i	0.375047	−	1.15428i
$482$		0			0
$483$	−3.39919	−	10.4616i	−0.154668	−	0.476020i
$484$	−19.8885	−	9.40456i	−0.904025	−	0.427480i
$485$	−4.57295	+	14.0741i	−0.207647	+	0.639072i
$486$		0			0
$487$	9.13525	+	28.1154i	0.413958	+	1.27403i	0.913180	+	0.407557i	$0.133619\pi$
$487$	9.13525	+	28.1154i	0.413958	+	1.27403i	−0.499222	+	0.866474i	$0.666381\pi$
$488$		0			0
$489$	3.11803	+	9.59632i	0.141002	+	0.433961i
$490$		0			0
$491$	−31.3951			−1.41684			−0.708421	−	0.705790i	$-0.750592\pi$
$491$	−31.3951			−1.41684			−0.708421	+	0.705790i	$0.750592\pi$
$492$	−1.09017	+	3.35520i	−0.0491487	+	0.151264i
$493$	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
$497$	11.6738			0.523640
$498$		0			0
$499$	35.4164	−	25.7315i	1.58546	−	1.15190i	0.675372	−	0.737477i	$-0.263983\pi$
$499$	35.4164	−	25.7315i	1.58546	−	1.15190i	0.910084	−	0.414425i	$-0.136017\pi$
$500$	18.0902	+	13.1433i	0.809017	+	0.587785i
$501$	6.38197	−	19.6417i	0.285125	−	0.877525i
$502$		0			0
$503$	−30.7705	+	22.3561i	−1.37199	+	0.996809i	−0.374410	+	0.927263i	$0.622155\pi$
$503$	−30.7705	+	22.3561i	−1.37199	+	0.996809i	−0.997579	+	0.0695454i	$0.977845\pi$
$504$		0			0
$505$	−23.0902			−1.02750
$506$		0			0
$507$	8.32624			0.369781
$508$	18.4721	−	13.4208i	0.819569	−	0.595451i
$509$	−7.19098	−	22.1316i	−0.318735	−	0.980965i	−0.974190	−	0.225730i	$-0.927523\pi$
$509$	−7.19098	−	22.1316i	−0.318735	−	0.980965i	0.655455	−	0.755234i	$-0.272477\pi$
$510$		0			0
$511$	−8.14590	−	25.0705i	−0.360353	−	1.10905i
$512$		0			0
$513$	7.47214			0.329903
$514$		0			0
$515$	32.1591			1.41710
$516$	2.85410	+	2.07363i	0.125645	+	0.0912863i
$517$	−6.11803	+	10.3229i	−0.269071	+	0.453999i
$518$		0			0
$519$	−15.2812	+	11.1024i	−0.670768	+	0.487342i
$520$		0			0
$521$	−0.253289	−	0.779543i	−0.0110968	−	0.0341524i	0.945355	−	0.326043i	$-0.105716\pi$
$521$	−0.253289	−	0.779543i	−0.0110968	−	0.0341524i	−0.956452	+	0.291891i	$0.905716\pi$
$522$		0			0
$523$	−7.00658	−	21.5640i	−0.306376	−	0.942929i	−0.979160	−	0.203090i	$-0.934902\pi$
$523$	−7.00658	−	21.5640i	−0.306376	−	0.942929i	0.672784	−	0.739839i	$-0.265098\pi$
$524$	32.7426	−	23.7889i	1.43037	−	1.03922i
$525$	18.6803	−	13.5721i	0.815277	−	0.592333i
$526$		0			0
$527$	2.85410	−	2.07363i	0.124327	−	0.0903286i
$528$	−1.23607	−	13.2088i	−0.0537930	−	0.574839i
$529$	−5.35410	+	16.4782i	−0.232787	+	0.716445i
$530$		0			0
$531$	−2.39919	+	7.38394i	−0.104116	+	0.320436i
$532$	−55.8328	+	40.5649i	−2.42066	+	1.75871i
$533$	−8.14590			−0.352838
$534$		0			0
$535$	19.8992	−	14.4576i	0.860317	−	0.625057i
$536$		0			0
$537$	−6.30902	+	19.4172i	−0.272254	+	0.837912i
$538$		0			0
$539$	−4.42705	−	47.3081i	−0.190687	−	2.03770i
$540$	−1.38197	−	4.25325i	−0.0594703	−	0.183031i
$541$	7.47214	−	22.9969i	0.321252	−	0.988713i	−0.651852	−	0.758346i	$-0.726008\pi$
$541$	7.47214	−	22.9969i	0.321252	−	0.988713i	0.973104	−	0.230366i	$-0.0739924\pi$
$542$		0			0
$543$	15.0623	−	10.9434i	0.646385	−	0.469626i
$544$		0			0
$545$	−27.0344	+	19.6417i	−1.15803	+	0.841357i
$546$		0			0
$547$	19.5623	−	14.2128i	0.836424	−	0.607697i	−0.0849456	−	0.996386i	$-0.527072\pi$
$547$	19.5623	−	14.2128i	0.836424	−	0.607697i	0.921369	+	0.388688i	$0.127072\pi$
$548$	−4.14590	−	3.01217i	−0.177104	−	0.128674i
$549$	−3.94427			−0.168337
$550$		0			0
$551$	42.6525			1.81706
$552$		0			0
$553$	−45.1697	+	32.8177i	−1.92081	+	1.39555i
$554$		0			0
$555$	−3.98278	−	12.2577i	−0.169060	−	0.520312i
$556$	3.52786			0.149615
$557$	2.30902	−	1.67760i	0.0978362	−	0.0710822i	−0.537792	−	0.843078i	$-0.680741\pi$
$557$	2.30902	−	1.67760i	0.0978362	−	0.0710822i	0.635628	+	0.771996i	$0.280741\pi$
$558$		0			0
$559$	−2.51722	+	7.74721i	−0.106467	+	0.327672i
$560$	33.4164	+	24.2784i	1.41210	+	1.02595i
$561$	−2.98278	+	5.03280i	−0.125933	+	0.212485i
$562$		0			0
$563$	−5.16312	+	15.8904i	−0.217600	+	0.669702i	0.781359	+	0.624081i	$0.214527\pi$
$563$	−5.16312	+	15.8904i	−0.217600	+	0.669702i	−0.998959	+	0.0456210i	$0.985473\pi$
$564$	−7.23607			−0.304693
$565$	18.7426			0.788509
$566$		0			0
$567$	−4.61803			−0.193939
$568$		0			0
$569$	−2.43769	+	7.50245i	−0.102193	+	0.314519i	−0.989062	−	0.147504i	$-0.952876\pi$
$569$	−2.43769	+	7.50245i	−0.102193	+	0.314519i	0.886868	+	0.462023i	$0.152876\pi$
$570$		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	$0.0719792\pi$
$572$	28.1246	−	12.1392i	1.17595	−	0.507566i
$573$	1.88197	−	1.36733i	0.0786203	−	0.0571210i
$574$		0			0
$575$	11.9098			0.496674
$576$	6.47214	−	4.70228i	0.269672	−	0.195928i
$577$	3.08359	+	9.49032i	0.128372	+	0.395087i	0.994500	−	0.104734i	$-0.0333991\pi$
$577$	3.08359	+	9.49032i	0.128372	+	0.395087i	−0.866129	+	0.499821i	$0.833399\pi$
$578$		0			0
$579$	2.30902	+	7.10642i	0.0959595	+	0.295333i
$580$	−7.88854	−	24.2784i	−0.327554	−	1.00811i
$581$	45.1697	−	32.8177i	1.87395	−	1.36151i
$582$		0			0
$583$	27.4058	−	11.8290i	1.13503	−	0.489905i
$584$		0			0
$585$	8.35410	−	6.06961i	0.345400	−	0.250948i
$586$		0			0
$587$	18.1803			0.750383			0.375191	−	0.926947i	$-0.377577\pi$
$587$	18.1803			0.750383			0.375191	+	0.926947i	$0.377577\pi$
$588$	23.1803	−	16.8415i	0.955941	−	0.694532i
$589$	−4.61803	−	14.2128i	−0.190283	−	0.585630i
$590$		0			0
$591$	−5.37132	−	16.5312i	−0.220947	−	0.680004i
$592$	18.6525	−	13.5518i	0.766612	−	0.556976i
$593$	−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
$596$	4.36068			0.178620
$597$	−8.30902	+	6.03685i	−0.340065	+	0.247072i
$598$		0			0
$599$	−0.236068	+	0.726543i	−0.00964548	+	0.0296857i	−0.955763	−	0.294136i	$-0.904968\pi$
$599$	−0.236068	+	0.726543i	−0.00964548	+	0.0296857i	0.946118	+	0.323822i	$0.104968\pi$
$600$		0			0
$601$	−10.6631	+	7.74721i	−0.434958	+	0.316015i	−0.783628	−	0.621230i	$-0.786633\pi$
$601$	−10.6631	+	7.74721i	−0.434958	+	0.316015i	0.348671	+	0.937245i	$0.386633\pi$
$602$		0			0
$603$	−2.23607			−0.0910597
$604$	−8.56231	+	26.3521i	−0.348395	+	1.07225i
$605$	−11.8090	−	21.5765i	−0.480105	−	0.877211i
$606$		0			0
$607$	−4.69756	−	14.4576i	−0.190668	−	0.586816i	0.809332	−	0.587352i	$-0.199829\pi$
$607$	−4.69756	−	14.4576i	−0.190668	−	0.586816i	−1.00000		0.000535683i	$0.999829\pi$
$608$		0			0
$609$	−26.3607			−1.06819
$610$		0			0
$611$	−5.16312	−	15.8904i	−0.208877	−	0.642859i
$612$	−3.52786			−0.142605
$613$	2.98278	+	9.18005i	0.120473	+	0.370779i	0.993049	−	0.117700i	$-0.0375521\pi$
$613$	2.98278	+	9.18005i	0.120473	+	0.370779i	−0.872576	+	0.488479i	$0.837552\pi$
$614$		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
$619$	6.73607	−	20.7315i	0.270745	−	0.833269i	−0.719568	−	0.694422i	$-0.755660\pi$
$619$	6.73607	−	20.7315i	0.270745	−	0.833269i	0.990314	−	0.138847i	$-0.0443397\pi$
$620$	−7.23607	+	5.25731i	−0.290607	+	0.211139i
$621$	−1.92705	−	1.40008i	−0.0773299	−	0.0561835i
$622$		0			0
$623$	−18.1353	+	55.8146i	−0.726574	+	2.23616i
$624$	14.9443	+	10.8576i	0.598250	+	0.434654i
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$		0			0
$627$	16.3713	+	18.6049i	0.653808	+	0.743006i
$628$	2.29180	−	7.05342i	0.0914526	−	0.281462i
$629$	−10.1672			−0.405392
$630$		0			0
$631$	26.8156	+	19.4827i	1.06751	+	0.775593i	0.975463	−	0.220162i	$-0.0706585\pi$
$631$	26.8156	+	19.4827i	1.06751	+	0.775593i	0.0920486	+	0.995755i	$0.470658\pi$
$632$		0			0
$633$	10.3262			0.410431
$634$		0			0
$635$	25.5279			1.01304
$636$	14.5623	+	10.5801i	0.577433	+	0.419530i
$637$	53.5238	+	38.8873i	2.12069	+	1.54077i
$638$		0			0
$639$	2.04508	−	1.48584i	0.0809023	−	0.0587790i
$640$		0			0
$641$	−12.6976	−	39.0791i	−0.501523	−	1.54353i	−0.806538	−	0.591183i	$-0.798661\pi$
$641$	−12.6976	−	39.0791i	−0.501523	−	1.54353i	0.305014	−	0.952348i	$-0.401339\pi$
$642$		0			0
$643$	1.27051	−	3.91023i	0.0501040	−	0.154204i	−0.922874	−	0.385102i	$-0.874166\pi$
$643$	1.27051	−	3.91023i	0.0501040	−	0.154204i	0.972978	+	0.230898i	$0.0741663\pi$
$644$	22.0000			0.866921
$645$	1.21885	+	3.75123i	0.0479921	+	0.147704i
$646$		0			0
$647$	−25.1803			−0.989941			−0.494971	−	0.868910i	$-0.664821\pi$
$647$	−25.1803			−0.989941			−0.494971	+	0.868910i	$0.664821\pi$
$648$		0			0
$649$	−23.6418	+	10.2044i	−0.928023	+	0.400556i
$650$		0			0
$651$	2.85410	+	8.78402i	0.111861	+	0.344273i
$652$	−20.1803			−0.790323
$653$	4.94427	+	15.2169i	0.193484	+	0.595483i	0.999991	+	0.00425842i	$0.00135550\pi$
$653$	4.94427	+	15.2169i	0.193484	+	0.595483i	−0.806507	+	0.591225i	$0.798644\pi$
$654$		0			0
$655$	45.2492			1.76803
$656$	−5.70820	−	4.14725i	−0.222868	−	0.161923i
$657$	−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
$663$	−2.51722	−	7.74721i	−0.0977608	−	0.300877i
$664$		0			0
$665$	−77.1591			−2.99210
$666$		0			0
$667$	−11.0000	−	7.99197i	−0.425922	−	0.309450i
$668$	33.4164	+	24.2784i	1.29292	+	0.939361i
$669$	−23.6803	+	17.2048i	−0.915535	+	0.665175i
$670$		0			0
$671$	−8.64183	−	9.82084i	−0.333614	−	0.379129i
$672$		0			0
$673$	−21.5344	−	15.6457i	−0.830092	−	0.603097i	0.0894935	−	0.995987i	$-0.471475\pi$
$673$	−21.5344	−	15.6457i	−0.830092	−	0.603097i	−0.919585	+	0.392890i	$0.871475\pi$
$674$		0			0
$675$	1.54508	−	4.75528i	0.0594703	−	0.183031i
$676$	−5.14590	+	15.8374i	−0.197919	+	0.609133i
$677$	−0.465558	−	1.43284i	−0.0178929	−	0.0550685i	0.941711	−	0.336422i	$-0.109217\pi$
$677$	−0.465558	−	1.43284i	−0.0178929	−	0.0550685i	−0.959604	+	0.281353i	$0.909217\pi$
$678$		0			0
$679$	−24.7254	+	17.9641i	−0.948875	+	0.689398i
$680$		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	$0.785385\pi$
$684$	−4.61803	+	14.2128i	−0.176575	+	0.543442i
$685$	−1.77051	−	5.44907i	−0.0676477	−	0.208198i
$686$		0			0
$687$	−15.5623	+	11.3067i	−0.593739	+	0.431377i
$688$	−5.70820	+	4.14725i	−0.217623	+	0.158113i
$689$	−12.8435	+	39.5281i	−0.489297	+	1.50590i
$690$		0			0
$691$	−10.9721	+	33.7688i	−0.417400	+	1.28462i	0.492687	+	0.870207i	$0.336015\pi$
$691$	−10.9721	+	33.7688i	−0.417400	+	1.28462i	−0.910087	+	0.414418i	$0.863985\pi$
$692$	−11.6738	−	35.9281i	−0.443770	−	1.36578i
$693$	−10.1180	−	11.4984i	−0.384352	−	0.436789i
$694$		0			0
$695$	3.19098	+	2.31838i	0.121041	+	0.0879414i
$696$		0			0
$697$	0.961493	+	2.95917i	0.0364191	+	0.112087i
$698$		0			0
$699$	−2.30902	+	7.10642i	−0.0873350	+	0.268790i
$700$	14.2705	+	43.9201i	0.539375	+	1.66002i
$701$	1.76393	+	1.28157i	0.0666228	+	0.0484043i	0.620598	−	0.784129i	$-0.286890\pi$
$701$	1.76393	+	1.28157i	0.0666228	+	0.0484043i	−0.553975	+	0.832533i	$0.686890\pi$
$702$		0			0
$703$	−13.3090	+	40.9609i	−0.501959	+	1.54487i
$704$	25.8885	+	5.81234i	0.975711	+	0.219061i
$705$	−6.54508	−	4.75528i	−0.246502	−	0.179094i
$706$		0			0
$707$	−38.5795	−	28.0297i	−1.45093	−	1.05416i
$708$	−12.5623	−	9.12705i	−0.472120	−	0.343016i
$709$	−5.76393	+	4.18774i	−0.216469	+	0.157274i	−0.690736	−	0.723107i	$-0.742713\pi$
$709$	−5.76393	+	4.18774i	−0.216469	+	0.157274i	0.474267	+	0.880381i	$0.342713\pi$
$710$		0			0
$711$	−3.73607	+	11.4984i	−0.140113	+	0.431225i
$712$		0			0
$713$	−1.47214	+	4.53077i	−0.0551319	+	0.169679i
$714$		0			0
$715$	33.4164	+	7.50245i	1.24970	+	0.280576i
$716$	−33.0344	−	24.0009i	−1.23456	−	0.896957i
$717$	−11.5451	+	8.38800i	−0.431159	+	0.313255i
$718$		0			0
$719$	12.4164	+	9.02105i	0.463054	+	0.336428i	0.794728	−	0.606966i	$-0.207613\pi$
$719$	12.4164	+	9.02105i	0.463054	+	0.336428i	−0.331674	+	0.943394i	$0.607613\pi$
$720$	8.94427			0.333333
$721$	53.7320	+	39.0386i	2.00108	+	1.45387i
$722$		0			0
$723$	−28.1246			−1.04597
$724$	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
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	3.11146			0.115081
$732$	2.43769	−	7.50245i	0.0900998	−	0.277299i
$733$	26.8262	+	19.4904i	0.990850	+	0.719894i	0.960107	−	0.279633i	$-0.0902128\pi$
$733$	26.8262	+	19.4904i	0.990850	+	0.719894i	0.0307427	+	0.999527i	$0.490213\pi$
$734$		0			0
$735$	32.0344			1.18161
$736$		0			0
$737$	−4.89919	−	5.56758i	−0.180464	−	0.205085i
$738$		0			0
$739$	15.6180	+	11.3472i	0.574519	+	0.417412i	0.836744	−	0.547594i	$-0.184456\pi$
$739$	15.6180	+	11.3472i	0.574519	+	0.417412i	−0.262225	+	0.965007i	$0.584456\pi$
$740$	25.7771			0.947585
$741$	−34.5066			−1.26763
$742$		0			0
$743$	−12.2188	+	37.6057i	−0.448266	+	1.37962i	0.430596	+	0.902545i	$0.358303\pi$
$743$	−12.2188	+	37.6057i	−0.448266	+	1.37962i	−0.878862	+	0.477076i	$0.841697\pi$
$744$		0			0
$745$	3.94427	+	2.86568i	0.144507	+	0.104990i
$746$		0			0
$747$	3.73607	−	11.4984i	0.136696	−	0.420706i
$748$	−7.72949	−	8.78402i	−0.282618	−	0.321176i
$749$	50.7984			1.85613
$750$		0			0
$751$	−22.2705	−	16.1805i	−0.812662	−	0.590434i	0.101939	−	0.994791i	$-0.467495\pi$
$751$	−22.2705	−	16.1805i	−0.812662	−	0.590434i	−0.914601	+	0.404357i	$0.867495\pi$
$752$	4.47214	−	13.7638i	0.163082	−	0.501915i
$753$	−13.3262	−	9.68208i	−0.485635	−	0.352835i
$754$		0			0
$755$	−25.0623	+	18.2088i	−0.912111	+	0.662687i
$756$	2.85410	−	8.78402i	0.103803	−	0.319472i
$757$	0.343459	+	1.05706i	0.0124832	+	0.0384194i	0.957104	−	0.289744i	$-0.0935703\pi$
$757$	0.343459	+	1.05706i	0.0124832	+	0.0384194i	−0.944621	+	0.328164i	$0.893570\pi$
$758$		0			0
$759$	−0.736068	−	7.86572i	−0.0267176	−	0.285508i
$760$		0			0
$761$	13.5172	+	9.82084i	0.489999	+	0.356005i	0.805184	−	0.593025i	$-0.202067\pi$
$761$	13.5172	+	9.82084i	0.489999	+	0.356005i	−0.315185	+	0.949030i	$0.602067\pi$
$762$		0			0
$763$	−69.0132			−2.49844
$764$	1.43769	+	4.42477i	0.0520139	+	0.160082i
$765$	−3.19098	−	2.31838i	−0.115370	−	0.0838214i
$766$		0			0
$767$	11.0795	−	34.0993i	0.400059	−	1.23125i
$768$	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
$772$	−14.9443			−0.537856
$773$	−10.1115			−0.363684			−0.181842	−	0.983328i	$-0.558206\pi$
$773$	−10.1115			−0.363684			−0.181842	+	0.983328i	$0.558206\pi$
$774$		0			0
$775$	−10.0000			−0.359211
$776$		0			0
$777$	8.22542	−	25.3153i	0.295085	−	0.908180i
$778$		0			0
$779$	13.1803			0.472235
$780$	6.38197	+	19.6417i	0.228511	+	0.703285i
$781$	8.18034	+	1.83660i	0.292716	+	0.0657187i
$782$		0			0
$783$	−4.61803	+	3.35520i	−0.165035	+	0.119905i
$784$	17.7082	+	54.5002i	0.632436	+	1.94644i
$785$	6.70820	−	4.87380i	0.239426	−	0.173953i
$786$		0			0
$787$	15.4894	−	11.2537i	0.552136	−	0.401150i	−0.276436	−	0.961032i	$-0.589154\pi$
$787$	15.4894	−	11.2537i	0.552136	−	0.401150i	0.828572	+	0.559882i	$0.189154\pi$
$788$	34.7639			1.23841
$789$	5.29180			0.188393
$790$		0			0
$791$	31.3156	+	22.7521i	1.11345	+	0.808972i
$792$		0			0
$793$	18.2148			0.646826
$794$		0			0
$795$	6.21885	+	19.1396i	0.220560	+	0.678813i
$796$	−6.34752	−	19.5357i	−0.224982	−	0.692423i
$797$	27.1353	+	19.7149i	0.961180	+	0.698338i	0.953425	−	0.301632i	$-0.0975313\pi$
$797$	27.1353	+	19.7149i	0.961180	+	0.698338i	0.00775554	+	0.999970i	$0.497531\pi$
$798$		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
$803$	−1.76393	−	18.8496i	−0.0622478	−	0.665189i
$804$	1.38197	−	4.25325i	0.0487382	−	0.150001i
$805$	19.8992	+	14.4576i	0.701354	+	0.509564i
$806$		0			0
$807$	−22.6525	+	16.4580i	−0.797405	+	0.579349i
$808$		0			0
$809$	−42.8607	+	31.1401i	−1.50690	+	1.09483i	−0.539372	+	0.842067i	$0.681338\pi$
$809$	−42.8607	+	31.1401i	−1.50690	+	1.09483i	−0.967529	+	0.252760i	$0.918662\pi$
$810$		0			0
$811$	15.3607			0.539386			0.269693	−	0.962946i	$-0.413078\pi$
$811$	15.3607			0.539386			0.269693	+	0.962946i	$0.413078\pi$
$812$	16.2918	−	50.1410i	0.571730	−	1.75960i
$813$	−4.61803	−	3.35520i	−0.161962	−	0.117672i
$814$		0			0
$815$	−18.2533	−	13.2618i	−0.639385	−	0.464540i
$816$	2.18034	−	6.71040i	0.0763272	−	0.234911i
$817$	4.07295	−	12.5352i	0.142494	−	0.438553i
$818$		0			0
$819$	21.3262			0.745199
$820$	−2.43769	−	7.50245i	−0.0851280	−	0.261997i
$821$	−5.16312	−	15.8904i	−0.180194	−	0.554580i	0.819638	−	0.572881i	$-0.194174\pi$
$821$	−5.16312	−	15.8904i	−0.180194	−	0.554580i	−0.999833	+	0.0183008i	$0.994174\pi$
$822$		0			0
$823$	−5.30902	−	3.85723i	−0.185061	−	0.134454i	0.491398	−	0.870935i	$-0.336486\pi$
$823$	−5.30902	−	3.85723i	−0.185061	−	0.134454i	−0.676458	+	0.736481i	$0.736486\pi$
$824$		0			0
$825$	15.2254	−	6.57164i	0.530081	−	0.228795i
$826$		0			0
$827$	−20.9894	−	15.2497i	−0.729871	−	0.530283i	0.159651	−	0.987173i	$-0.448963\pi$
$827$	−20.9894	−	15.2497i	−0.729871	−	0.530283i	−0.889523	+	0.456891i	$0.848963\pi$
$828$	3.85410	−	2.80017i	0.133939	−	0.0973126i
$829$	0.583592	+	1.79611i	0.0202690	+	0.0623815i	0.960679	−	0.277660i	$-0.0895589\pi$
$829$	0.583592	+	1.79611i	0.0202690	+	0.0623815i	−0.940410	+	0.340042i	$0.889559\pi$
$830$		0			0
$831$	−1.09017			−0.0378176
$832$	−29.8885	+	21.7153i	−1.03620	+	0.752843i
$833$	7.80902	−	24.0337i	0.270566	−	0.832718i
$834$		0			0
$835$	14.2705	+	43.9201i	0.493851	+	1.51992i
$836$	−45.5066	+	19.6417i	−1.57388	+	0.679321i
$837$	1.61803	+	1.17557i	0.0559274	+	0.0406337i
$838$		0			0
$839$	31.6312			1.09203			0.546015	−	0.837775i	$-0.316144\pi$
$839$	31.6312			1.09203			0.546015	+	0.837775i	$0.316144\pi$
$840$		0			0
$841$	−2.89919	+	2.10638i	−0.0999720	+	0.0726339i
$842$		0			0
$843$	9.23607	−	6.71040i	0.318107	−	0.231118i
$844$	−6.38197	+	19.6417i	−0.219676	+	0.676094i
$845$	−15.0623	+	10.9434i	−0.518159	+	0.376465i
$846$		0			0
$847$	6.46149	−	50.3858i	0.222020	−	1.73127i
$848$	−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
$852$	1.56231	+	4.80828i	0.0535237	+	0.164729i
$853$	−33.9615	−	24.6745i	−1.16282	−	0.844838i	−0.172688	−	0.984977i	$-0.555245\pi$
$853$	−33.9615	−	24.6745i	−1.16282	−	0.844838i	−0.990132	+	0.140139i	$0.955245\pi$
$854$		0			0
$855$	−13.5172	+	9.82084i	−0.462279	+	0.335865i
$856$		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	$0.533223\pi$
$860$	−7.88854			−0.268997
$861$	−8.14590			−0.277611
$862$		0			0
$863$	−18.6074	+	13.5191i	−0.633403	+	0.460194i	−0.857577	−	0.514355i	$-0.828031\pi$
$863$	−18.6074	+	13.5191i	−0.633403	+	0.460194i	0.224175	+	0.974549i	$0.428031\pi$
$864$		0			0
$865$	13.0517	−	40.1689i	0.443770	−	1.36578i
$866$		0			0
$867$	11.2361	−	8.16348i	0.381597	−	0.277246i
$868$	−18.4721			−0.626985
$869$	−36.8156	+	15.8904i	−1.24888	+	0.539046i
$870$		0			0
$871$	10.3262			0.349891
$872$		0			0
$873$	−2.04508	+	6.29412i	−0.0692156	+	0.213024i
$874$		0			0
$875$	−15.9549	+	49.1042i	−0.539375	+	1.66002i
$876$	9.23607	−	6.71040i	0.312058	−	0.226723i
$877$	−11.6738			−0.394195			−0.197097	−	0.980384i	$-0.563152\pi$
$877$	−11.6738			−0.394195			−0.197097	+	0.980384i	$0.563152\pi$
$878$		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
$883$	−15.2148	+	46.8263i	−0.512018	+	1.57583i	0.276624	+	0.960978i	$0.410784\pi$
$883$	−15.2148	+	46.8263i	−0.512018	+	1.57583i	−0.788643	+	0.614852i	$0.789216\pi$
$884$	16.2918			0.547952
$885$	−5.36475	−	16.5110i	−0.180334	−	0.555011i
$886$		0			0
$887$	27.2918			0.916369			0.458184	−	0.888857i	$-0.348500\pi$
$887$	27.2918			0.916369			0.458184	+	0.888857i	$0.348500\pi$
$888$		0			0
$889$	42.6525	+	30.9888i	1.43052	+	1.03933i
$890$		0			0
$891$	−3.23607	−	0.726543i	−0.108412	−	0.0243401i
$892$	−18.0902	−	55.6758i	−0.605704	−	1.86416i
$893$	8.35410	+	25.7113i	0.279559	+	0.860395i
$894$		0			0
$895$	−14.1074	−	43.4181i	−0.471558	−	1.45131i
$896$		0			0
$897$	8.89919	+	6.46564i	0.297135	+	0.215881i
$898$		0			0
$899$	9.23607	+	6.71040i	0.308040	+	0.223804i
$900$	8.09017	+	5.87785i	0.269672	+	0.195928i
$901$	15.8754			0.528886
$902$		0			0
$903$	−2.51722	+	7.74721i	−0.0837679	+	0.257811i
$904$		0			0
$905$	−12.8647	+	39.5936i	−0.427639	+	1.31614i
$906$		0			0
$907$	−5.75329	+	17.7068i	−0.191035	+	0.587945i	0.808965	+	0.587857i	$0.200028\pi$
$907$	−5.75329	+	17.7068i	−0.191035	+	0.587945i	−1.00000		8.81575e-5i	$0.999972\pi$
$908$	−42.6525			−1.41547
$909$	−10.3262			−0.342500
$910$		0			0
$911$	25.3262	+	18.4006i	0.839096	+	0.609639i	0.922118	−	0.386909i	$-0.126457\pi$
$911$	25.3262	+	18.4006i	0.839096	+	0.609639i	−0.0830222	+	0.996548i	$0.526457\pi$
$912$	−24.1803	−	17.5680i	−0.800691	−	0.581736i
$913$	36.8156	−	15.8904i	1.21842	−	0.525897i
$914$		0			0
$915$	7.13525	−	5.18407i	0.235884	−	0.171380i
$916$	−11.8885	−	36.5892i	−0.392809	−	1.20894i
$917$	75.6033	+	54.9290i	2.49664	+	1.81392i
$918$		0			0
$919$	18.0557			0.595604			0.297802	−	0.954628i	$-0.403747\pi$
$919$	18.0557			0.595604			0.297802	+	0.954628i	$0.403747\pi$
$920$		0			0
$921$	−19.8992	+	14.4576i	−0.655701	+	0.476394i
$922$		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
$927$	14.3820			0.472366
$928$		0			0
$929$	22.1803	+	16.1150i	0.727713	+	0.528715i	0.888839	−	0.458219i	$-0.151513\pi$
$929$	22.1803	+	16.1150i	0.727713	+	0.528715i	−0.161126	+	0.986934i	$0.551513\pi$
$930$		0			0
$931$	−86.6033	−	62.9210i	−2.83831	−	2.06215i
$932$	−12.0902	−	8.78402i	−0.396027	−	0.287730i
$933$	−27.2254	+	19.7804i	−0.891320	+	0.647582i
$934$		0			0
$935$	−1.21885	−	13.0248i	−0.0398606	−	0.425955i
$936$		0			0
$937$	5.50000	−	16.9273i	0.179677	−	0.552989i	−0.820139	−	0.572164i	$-0.806104\pi$
$937$	5.50000	−	16.9273i	0.179677	−	0.552989i	0.999816	+	0.0191749i	$0.00610393\pi$
$938$		0			0
$939$	−6.29180	+	19.3642i	−0.205325	+	0.631925i
$940$	13.0902	−	9.51057i	0.426954	−	0.310200i
$941$	−2.51722	+	1.82887i	−0.0820591	+	0.0596194i	−0.628058	−	0.778166i	$-0.716150\pi$
$941$	−2.51722	+	1.82887i	−0.0820591	+	0.0596194i	0.545999	+	0.837786i	$0.316150\pi$
$942$		0			0
$943$	−3.39919	−	2.46965i	−0.110693	−	0.0804230i
$944$	25.1246	−	18.2541i	0.817736	−	0.594120i
$945$	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	$0.771448\pi$
$948$	−19.5623	−	14.2128i	−0.635354	−	0.461612i
$949$	21.3262	+	15.4944i	0.692279	+	0.502970i
$950$		0			0
$951$	−2.92705	+	9.00854i	−0.0949161	+	0.292122i
$952$		0			0
$953$	0.881966	+	2.71441i	0.0285697	+	0.0879284i	0.964325	−	0.264722i	$-0.0852803\pi$
$953$	0.881966	+	2.71441i	0.0285697	+	0.0879284i	−0.935755	+	0.352651i	$0.885280\pi$
$954$		0			0
$955$	−1.60739	+	4.94704i	−0.0520139	+	0.160082i
$956$	−8.81966	−	27.1441i	−0.285248	−	0.877904i
$957$	−18.4721	−	4.14725i	−0.597119	−	0.134062i
$958$		0			0
$959$	3.65654	−	11.2537i	0.118076	−	0.363400i
$960$	−5.52786	+	17.0130i	−0.178411	+	0.549093i
$961$	−8.34346	+	25.6785i	−0.269144	+	0.828340i
$962$		0			0
$963$	8.89919	−	6.46564i	0.286772	−	0.208352i
$964$	17.3820	−	53.4962i	0.559835	−	1.72300i
$965$	−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
$971$	20.6074	−	14.9721i	0.661323	−	0.480479i	−0.205787	−	0.978597i	$-0.565975\pi$
$971$	20.6074	−	14.9721i	0.661323	−	0.480479i	0.867109	+	0.498118i	$0.165975\pi$
$972$	−0.618034	−	1.90211i	−0.0198234	−	0.0610103i
$973$	2.51722	+	7.74721i	0.0806984	+	0.248364i
$974$		0			0
$975$	−7.13525	+	21.9601i	−0.228511	+	0.703285i
$976$	12.7639	+	9.27354i	0.408564	+	0.296839i
$977$	−39.3607	−	28.5972i	−1.25926	−	0.914906i	−0.260539	−	0.965463i	$-0.583900\pi$
$977$	−39.3607	−	28.5972i	−1.25926	−	0.914906i	−0.998721	+	0.0505577i	$0.983900\pi$
$978$		0			0
$979$	−21.4894	+	36.2587i	−0.686803	+	1.15883i
$980$	−19.7984	+	60.9331i	−0.632436	+	1.94644i
$981$	−12.0902	+	8.78402i	−0.386009	+	0.280452i
$982$		0			0
$983$	26.6074	+	19.3314i	0.848644	+	0.616576i	0.924772	−	0.380522i	$-0.124256\pi$
$983$	26.6074	+	19.3314i	0.848644	+	0.616576i	−0.0761278	+	0.997098i	$0.524256\pi$
$984$		0			0
$985$	31.4443	+	22.8456i	1.00190	+	0.727921i
$986$		0			0
$987$	−5.16312	−	15.8904i	−0.164344	−	0.505798i
$988$	21.3262	−	65.6354i	0.678478	−	2.08814i
$989$	−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
$996$	19.5623	+	14.2128i	0.619855	+	0.450351i
$997$	5.16312	+	15.8904i	0.163518	+	0.503255i	0.998924	−	0.0463773i	$-0.0147676\pi$
$997$	5.16312	+	15.8904i	0.163518	+	0.503255i	−0.835406	+	0.549633i	$0.814768\pi$
$998$		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.o.a.511.1	yes	4
11.9	even	5		825.2.m.b.361.1	yes	4
25.16	even	5		825.2.m.b.16.1	✓	4
275.141	even	5	inner	825.2.o.a.691.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.m.b.16.1	✓	4	25.16	even	5
825.2.m.b.361.1	yes	4	11.9	even	5
825.2.o.a.511.1	yes	4	1.1	even	1	trivial
825.2.o.a.691.1	yes	4	275.141	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(0.690983 - 2.12663i) q^{5} +(3.73607 - 2.71441i) q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(0.690983 - 2.12663i) q^{5} +(3.73607 - 2.71441i) q^{7} +(0.309017 - 0.951057i) q^{9} +(3.04508 - 1.31433i) q^{11} +(1.61803 + 1.17557i) q^{12} +(-1.42705 + 4.39201i) q^{13} +(0.690983 + 2.12663i) q^{15} +(-3.23607 + 2.35114i) q^{16} +1.76393 q^{17} +(2.30902 - 7.10642i) q^{19} -4.47214 q^{20} +(-1.42705 + 4.39201i) q^{21} +(-1.92705 + 1.40008i) q^{23} +(-4.04508 - 2.93893i) q^{25} +(0.309017 + 0.951057i) q^{27} +(-7.47214 - 5.42882i) q^{28} +(1.76393 + 5.42882i) q^{29} +(1.61803 - 1.17557i) q^{31} +(-1.69098 + 2.85317i) q^{33} +(-3.19098 - 9.82084i) q^{35} -2.00000 q^{36} -5.76393 q^{37} +(-1.42705 - 4.39201i) q^{39} +(0.545085 + 1.67760i) q^{41} +1.76393 q^{43} +(-4.38197 - 4.97980i) q^{44} +(-1.80902 - 1.31433i) q^{45} +(-2.92705 + 2.12663i) q^{47} +(1.23607 - 3.80423i) q^{48} +(4.42705 - 13.6251i) q^{49} +(-1.42705 + 1.03681i) q^{51} +9.23607 q^{52} +9.00000 q^{53} +(-0.690983 - 7.38394i) q^{55} +(2.30902 + 7.10642i) q^{57} -7.76393 q^{59} +(3.61803 - 2.62866i) q^{60} +(-1.21885 - 3.75123i) q^{61} +(-1.42705 - 4.39201i) q^{63} +(6.47214 + 4.70228i) q^{64} +(8.35410 + 6.06961i) q^{65} +(-0.690983 - 2.12663i) q^{67} +(-1.09017 - 3.35520i) q^{68} +(0.736068 - 2.26538i) q^{69} +(2.04508 + 1.48584i) q^{71} +(1.76393 - 5.42882i) q^{73} +5.00000 q^{75} -14.9443 q^{76} +(7.80902 - 13.1760i) q^{77} -12.0902 q^{79} +(2.76393 + 8.50651i) q^{80} +(-0.809017 - 0.587785i) q^{81} +12.0902 q^{83} +9.23607 q^{84} +(1.21885 - 3.75123i) q^{85} +(-4.61803 - 3.35520i) q^{87} +(-10.2812 + 7.46969i) q^{89} +(6.59017 + 20.2825i) q^{91} +(3.85410 + 2.80017i) q^{92} +(-0.618034 + 1.90211i) q^{93} +(-13.5172 - 9.82084i) q^{95} -6.61803 q^{97} +(-0.309017 - 3.30220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 2 q^{4} + 5 q^{5} + 6 q^{7} - q^{9}+O(q^{10}) \) 4 * q - q^3 + 2 * q^4 + 5 * q^5 + 6 * q^7 - q^9	\( 4 q - q^{3} + 2 q^{4} + 5 q^{5} + 6 q^{7} - q^{9} + q^{11} + 2 q^{12} + q^{13} + 5 q^{15} - 4 q^{16} + 16 q^{17} + 7 q^{19} + q^{21} - q^{23} - 5 q^{25} - q^{27} - 12 q^{28} + 16 q^{29} + 2 q^{31} - 9 q^{33} - 15 q^{35} - 8 q^{36} - 32 q^{37} + q^{39} - 9 q^{41} + 16 q^{43} - 22 q^{44} - 5 q^{45} - 5 q^{47} - 4 q^{48} + 11 q^{49} + q^{51} + 28 q^{52} + 36 q^{53} - 5 q^{55} + 7 q^{57} - 40 q^{59} + 10 q^{60} - 25 q^{61} + q^{63} + 8 q^{64} + 20 q^{65} - 5 q^{67} + 18 q^{68} - 6 q^{69} - 3 q^{71} + 16 q^{73} + 20 q^{75} - 24 q^{76} + 29 q^{77} - 26 q^{79} + 20 q^{80} - q^{81} + 26 q^{83} + 28 q^{84} + 25 q^{85} - 14 q^{87} - 21 q^{89} + 4 q^{91} + 2 q^{92} + 2 q^{93} - 25 q^{95} - 22 q^{97} + q^{99}+O(q^{100}) \) 4 * q - q^3 + 2 * q^4 + 5 * q^5 + 6 * q^7 - q^9 + q^11 + 2 * q^12 + q^13 + 5 * q^15 - 4 * q^16 + 16 * q^17 + 7 * q^19 + q^21 - q^23 - 5 * q^25 - q^27 - 12 * q^28 + 16 * q^29 + 2 * q^31 - 9 * q^33 - 15 * q^35 - 8 * q^36 - 32 * q^37 + q^39 - 9 * q^41 + 16 * q^43 - 22 * q^44 - 5 * q^45 - 5 * q^47 - 4 * q^48 + 11 * q^49 + q^51 + 28 * q^52 + 36 * q^53 - 5 * q^55 + 7 * q^57 - 40 * q^59 + 10 * q^60 - 25 * q^61 + q^63 + 8 * q^64 + 20 * q^65 - 5 * q^67 + 18 * q^68 - 6 * q^69 - 3 * q^71 + 16 * q^73 + 20 * q^75 - 24 * q^76 + 29 * q^77 - 26 * q^79 + 20 * q^80 - q^81 + 26 * q^83 + 28 * q^84 + 25 * q^85 - 14 * q^87 - 21 * q^89 + 4 * q^91 + 2 * q^92 + 2 * q^93 - 25 * q^95 - 22 * q^97 + q^99

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