LMFDB - Embedded newform 975.2.o.n.551.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(476,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.476"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.o (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,6,-2,0,0,4,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.619810816.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			551.3
Root			$1.18254 - 1.18254i$ of defining polynomial
Character	$\chi$	$=$	975.551
Dual form			975.2.o.n.476.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.42282 + 1.42282i) q^{2} +(-0.759725 - 1.55654i) q^{3} +2.04882i q^{4} +(1.13372 - 3.29562i) q^{6} +(0.739083 + 0.739083i) q^{7} +(-0.0694623 + 0.0694623i) q^{8} +(-1.84564 + 2.36509i) q^{9} +(0.336908 - 0.336908i) q^{11} +(3.18907 - 1.55654i) q^{12} +(-0.0370899 + 3.60536i) q^{13} +2.10316i q^{14} +3.89998 q^{16} +4.51945 q^{17} +(-5.99109 + 0.739083i) q^{18} +(1.60536 - 1.60536i) q^{19} +(0.588913 - 1.71191i) q^{21} +0.958716 q^{22} +2.68373 q^{23} +(0.160893 + 0.0553486i) q^{24} +(-5.18254 + 5.07700i) q^{26} +(5.08353 + 1.07599i) q^{27} +(-1.51425 + 1.51425i) q^{28} -4.78690i q^{29} +(2.29562 - 2.29562i) q^{31} +(5.68788 + 5.68788i) q^{32} +(-0.780367 - 0.268453i) q^{33} +(6.43035 + 6.43035i) q^{34} +(-4.84564 - 3.78137i) q^{36} +(1.60536 + 1.60536i) q^{37} +4.56827 q^{38} +(5.64007 - 2.68135i) q^{39} +(4.71090 + 4.71090i) q^{41} +(3.27365 - 1.59782i) q^{42} -1.99008i q^{43} +(0.690263 + 0.690263i) q^{44} +(3.81846 + 3.81846i) q^{46} +(-1.30735 + 1.30735i) q^{47} +(-2.96291 - 6.07047i) q^{48} -5.90751i q^{49} +(-3.43354 - 7.03471i) q^{51} +(-7.38674 - 0.0759906i) q^{52} +13.3290i q^{53} +(5.70199 + 8.76387i) q^{54} -0.102677 q^{56} +(-3.71844 - 1.27918i) q^{57} +(6.81088 - 6.81088i) q^{58} +(7.53351 - 7.53351i) q^{59} -12.8254 q^{61} +6.53251 q^{62} +(-3.11207 + 0.383917i) q^{63} +8.38568i q^{64} +(-0.728361 - 1.49228i) q^{66} +(-7.65079 + 7.65079i) q^{67} +9.25954i q^{68} +(-2.03890 - 4.17734i) q^{69} +(-3.32800 - 3.32800i) q^{71} +(-0.0360822 - 0.292486i) q^{72} +(-5.41762 - 5.41762i) q^{73} +4.56827i q^{74} +(3.28910 + 3.28910i) q^{76} +0.498005 q^{77} +(11.8399 + 4.20971i) q^{78} -11.1032 q^{79} +(-2.18726 - 8.73017i) q^{81} +13.4055i q^{82} +(9.05535 + 9.05535i) q^{83} +(3.50740 + 1.20658i) q^{84} +(2.83152 - 2.83152i) q^{86} +(-7.45100 + 3.63673i) q^{87} +0.0468047i q^{88} +(3.57819 - 3.57819i) q^{89} +(-2.69207 + 2.63725i) q^{91} +5.49849i q^{92} +(-5.31727 - 1.82919i) q^{93} -3.72025 q^{94} +(4.53219 - 13.1746i) q^{96} +(-6.51707 + 6.51707i) q^{97} +(8.40531 - 8.40531i) q^{98} +(0.175007 + 1.41862i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} - 2 q^{3} + 4 q^{6} - 14 q^{7} - 12 q^{8} - 4 q^{9} + 4 q^{11} - 14 q^{12} + 2 q^{13} - 8 q^{16} + 28 q^{17} - 30 q^{18} - 2 q^{19} + 8 q^{21} - 24 q^{22} + 36 q^{23} - 18 q^{24} - 32 q^{26}+ \cdots + 28 q^{99}+O(q^{100}) $ 8 * q + 6 * q^2 - 2 * q^3 + 4 * q^6 - 14 * q^7 - 12 * q^8 - 4 * q^9 + 4 * q^11 - 14 * q^12 + 2 * q^13 - 8 * q^16 + 28 * q^17 - 30 * q^18 - 2 * q^19 + 8 * q^21 - 24 * q^22 + 36 * q^23 - 18 * q^24 - 32 * q^26 - 14 * q^27 + 24 * q^28 - 12 * q^31 - 18 * q^32 - 18 * q^33 + 10 * q^34 - 28 * q^36 - 2 * q^37 + 24 * q^38 - 20 * q^39 + 38 * q^41 + 38 * q^42 - 10 * q^44 + 34 * q^46 + 22 * q^47 - 26 * q^48 - 26 * q^51 - 50 * q^52 + 28 * q^54 + 76 * q^56 + 6 * q^57 - 18 * q^58 - 14 * q^59 - 8 * q^61 - 16 * q^62 - 10 * q^63 + 18 * q^66 - 10 * q^71 - 4 * q^72 - 10 * q^73 + 26 * q^76 - 12 * q^77 - 6 * q^78 - 56 * q^79 + 8 * q^81 + 38 * q^83 + 74 * q^84 - 34 * q^86 - 34 * q^87 + 28 * q^89 + 8 * q^91 - 22 * q^93 + 20 * q^94 + 20 * q^96 + 4 * q^97 - 26 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.42282	+	1.42282i	1.00608	+	1.00608i	0.999981	+	0.00610264i	$0.00194254\pi$
$2$	1.42282	+	1.42282i	1.00608	+	1.00608i	0.00610264	+	0.999981i	$0.498057\pi$
$3$	−0.759725	−	1.55654i	−0.438628	−	0.898669i
$3$	−0.759725	−	1.55654i	−0.438628	−	0.898669i
$4$			2.04882i			1.02441i
$5$		0			0
$5$		0			0
$6$	1.13372	−	3.29562i	0.462840	−	1.34543i
$7$	0.739083	+	0.739083i	0.279347	+	0.279347i	0.832848	−	0.553501i	$-0.186709\pi$
$7$	0.739083	+	0.739083i	0.279347	+	0.279347i	−0.553501	+	0.832848i	$0.686709\pi$
$8$	−0.0694623	+	0.0694623i	−0.0245586	+	0.0245586i
$9$	−1.84564	+	2.36509i	−0.615212	+	0.788362i
$10$		0			0
$11$	0.336908	−	0.336908i	0.101581	−	0.101581i	−0.654490	−	0.756071i	$-0.727116\pi$
$11$	0.336908	−	0.336908i	0.101581	−	0.101581i	0.756071	+	0.654490i	$0.227116\pi$
$12$	3.18907	−	1.55654i	0.920606	−	0.449334i
$13$	−0.0370899	+	3.60536i	−0.0102869	+	0.999947i
$13$	−0.0370899	+	3.60536i	−0.0102869	+	0.999947i
$14$			2.10316i			0.562093i
$15$		0			0
$16$	3.89998			0.974994
$17$	4.51945			1.09613			0.548064	−	0.836436i	$-0.315365\pi$
$17$	4.51945			1.09613			0.548064	+	0.836436i	$0.315365\pi$
$18$	−5.99109	+	0.739083i	−1.41211	+	0.174204i
$19$	1.60536	−	1.60536i	0.368295	−	0.368295i	−0.498560	−	0.866855i	$-0.666138\pi$
$19$	1.60536	−	1.60536i	0.368295	−	0.368295i	0.866855	+	0.498560i	$0.166138\pi$
$20$		0			0
$21$	0.588913	−	1.71191i	0.128511	−	0.373570i
$22$	0.958716			0.204399
$23$	2.68373			0.559597			0.279799	−	0.960059i	$-0.409732\pi$
$23$	2.68373			0.559597			0.279799	+	0.960059i	$0.409732\pi$
$24$	0.160893	+	0.0553486i	0.0328422	+	0.0112980i
$25$		0			0
$26$	−5.18254	+	5.07700i	−1.01638	+	0.995681i
$27$	5.08353	+	1.07599i	0.978325	+	0.207074i
$28$	−1.51425	+	1.51425i	−0.286166	+	0.286166i
$29$		−	4.78690i		−	0.888904i	−0.895803	−	0.444452i	$-0.853398\pi$
$29$		−	4.78690i		−	0.888904i	0.895803	−	0.444452i	$-0.146602\pi$
$30$		0			0
$31$	2.29562	−	2.29562i	0.412306	−	0.412306i	−0.470235	−	0.882541i	$-0.655831\pi$
$31$	2.29562	−	2.29562i	0.412306	−	0.412306i	0.882541	+	0.470235i	$0.155831\pi$
$32$	5.68788	+	5.68788i	1.00548	+	1.00548i
$33$	−0.780367	−	0.268453i	−0.135844	−	0.0467317i
$34$	6.43035	+	6.43035i	1.10280	+	1.10280i
$35$		0			0
$36$	−4.84564	−	3.78137i	−0.807606	−	0.630229i
$37$	1.60536	+	1.60536i	0.263920	+	0.263920i	0.826644	−	0.562725i	$-0.190247\pi$
$37$	1.60536	+	1.60536i	0.263920	+	0.263920i	−0.562725	+	0.826644i	$0.690247\pi$
$38$	4.56827			0.741071
$39$	5.64007	−	2.68135i	0.903134	−	0.429360i
$40$		0			0
$41$	4.71090	+	4.71090i	0.735720	+	0.735720i	0.971747	−	0.236027i	$-0.0758453\pi$
$41$	4.71090	+	4.71090i	0.735720	+	0.735720i	−0.236027	+	0.971747i	$0.575845\pi$
$42$	3.27365	−	1.59782i	0.505136	−	0.246550i
$43$		−	1.99008i		−	0.303484i	−0.988420	−	0.151742i	$-0.951512\pi$
$43$		−	1.99008i		−	0.303484i	0.988420	−	0.151742i	$-0.0484884\pi$
$44$	0.690263	+	0.690263i	0.104061	+	0.104061i
$45$		0			0
$46$	3.81846	+	3.81846i	0.563002	+	0.563002i
$47$	−1.30735	+	1.30735i	−0.190697	+	0.190697i	−0.795997	−	0.605300i	$-0.793053\pi$
$47$	−1.30735	+	1.30735i	−0.190697	+	0.190697i	0.605300	+	0.795997i	$0.293053\pi$
$48$	−2.96291	−	6.07047i	−0.427659	−	0.876197i
$49$		−	5.90751i		−	0.843930i
$50$		0			0
$51$	−3.43354	−	7.03471i	−0.480792	−	0.985056i
$52$	−7.38674	−	0.0759906i	−1.02436	−	0.0105380i
$53$			13.3290i			1.83087i	0.402463	+	0.915436i	$0.368154\pi$
$53$			13.3290i			1.83087i	−0.402463	+	0.915436i	$0.631846\pi$
$54$	5.70199	+	8.76387i	0.775943	+	1.19261i
$55$		0			0
$56$	−0.102677			−0.0137208
$57$	−3.71844	−	1.27918i	−0.492520	−	0.169431i
$58$	6.81088	−	6.81088i	0.894312	−	0.894312i
$59$	7.53351	−	7.53351i	0.980780	−	0.980780i	−0.0190387	−	0.999819i	$-0.506061\pi$
$59$	7.53351	−	7.53351i	0.980780	−	0.980780i	0.999819	+	0.0190387i	$0.00606056\pi$
$60$		0			0
$61$	−12.8254			−1.64213			−0.821064	−	0.570836i	$-0.806619\pi$
$61$	−12.8254			−1.64213			−0.821064	+	0.570836i	$0.806619\pi$
$62$	6.53251			0.829629
$63$	−3.11207	+	0.383917i	−0.392084	+	0.0483690i
$64$			8.38568i			1.04821i
$65$		0			0
$66$	−0.728361	−	1.49228i	−0.0896550	−	0.183687i
$67$	−7.65079	+	7.65079i	−0.934693	+	0.934693i	−0.997994	−	0.0633017i	$-0.979837\pi$
$67$	−7.65079	+	7.65079i	−0.934693	+	0.934693i	0.0633017	+	0.997994i	$0.479837\pi$
$68$			9.25954i			1.12288i
$69$	−2.03890	−	4.17734i	−0.245455	−	0.502893i
$70$		0			0
$71$	−3.32800	−	3.32800i	−0.394960	−	0.394960i	0.481491	−	0.876451i	$-0.340095\pi$
$71$	−3.32800	−	3.32800i	−0.394960	−	0.394960i	−0.876451	+	0.481491i	$0.840095\pi$
$72$	−0.0360822	−	0.292486i	−0.00425233	−	0.0344698i
$73$	−5.41762	−	5.41762i	−0.634084	−	0.634084i	0.315006	−	0.949090i	$-0.397994\pi$
$73$	−5.41762	−	5.41762i	−0.634084	−	0.634084i	−0.949090	+	0.315006i	$0.897994\pi$
$74$			4.56827i			0.531051i
$75$		0			0
$76$	3.28910	+	3.28910i	0.377285	+	0.377285i
$77$	0.498005			0.0567530
$78$	11.8399	+	4.20971i	1.34060	+	0.476656i
$79$	−11.1032			−1.24920			−0.624602	−	0.780944i	$-0.714739\pi$
$79$	−11.1032			−1.24920			−0.624602	+	0.780944i	$0.714739\pi$
$80$		0			0
$81$	−2.18726	−	8.73017i	−0.243029	−	0.970019i
$82$			13.4055i			1.48039i
$83$	9.05535	+	9.05535i	0.993954	+	0.993954i	0.999982	−	0.00602819i	$-0.00191885\pi$
$83$	9.05535	+	9.05535i	0.993954	+	0.993954i	−0.00602819	+	0.999982i	$0.501919\pi$
$84$	3.50740	+	1.20658i	0.382689	+	0.131648i
$85$		0			0
$86$	2.83152	−	2.83152i	0.305331	−	0.305331i
$87$	−7.45100	+	3.63673i	−0.798831	+	0.389898i
$88$			0.0468047i			0.00498940i
$89$	3.57819	−	3.57819i	0.379287	−	0.379287i	−0.491558	−	0.870845i	$-0.663572\pi$
$89$	3.57819	−	3.57819i	0.379287	−	0.379287i	0.870845	+	0.491558i	$0.163572\pi$
$90$		0			0
$91$	−2.69207	+	2.63725i	−0.282206	+	0.276459i
$92$			5.49849i			0.573257i
$93$	−5.31727	−	1.82919i	−0.551376	−	0.189678i
$94$	−3.72025			−0.383715
$95$		0			0
$96$	4.53219	−	13.1746i	0.462565	−	1.34463i
$97$	−6.51707	+	6.51707i	−0.661708	+	0.661708i	−0.955782	−	0.294075i	$-0.904989\pi$
$97$	−6.51707	+	6.51707i	−0.661708	+	0.661708i	0.294075	+	0.955782i	$0.404989\pi$
$98$	8.40531	−	8.40531i	0.849065	−	0.849065i
$99$	0.175007	+	1.41862i	0.0175888	+	0.142577i
$100$		0			0
$101$	−9.12424			−0.907896			−0.453948	−	0.891028i	$-0.649985\pi$
$101$	−9.12424			−0.907896			−0.453948	+	0.891028i	$0.649985\pi$
$102$	5.12380	−	14.8944i	0.507332	−	1.47477i
$103$		−	10.9512i		−	1.07905i	−0.841969	−	0.539526i	$-0.818603\pi$
$103$		−	10.9512i		−	1.07905i	0.841969	−	0.539526i	$-0.181397\pi$
$104$	−0.247860	−	0.253013i	−0.0243047	−	0.0248100i
$105$		0			0
$106$	−18.9647	+	18.9647i	−1.84201	+	1.84201i
$107$			5.02108i			0.485406i	0.970101	+	0.242703i	$0.0780340\pi$
$107$			5.02108i			0.485406i	−0.970101	+	0.242703i	$0.921966\pi$
$108$	−2.20451	+	10.4152i	−0.212129	+	1.00221i
$109$	−2.63072	+	2.63072i	−0.251977	+	0.251977i	−0.821781	−	0.569804i	$-0.807019\pi$
$109$	−2.63072	+	2.63072i	−0.251977	+	0.251977i	0.569804	+	0.821781i	$0.307019\pi$
$110$		0			0
$111$	1.27918	−	3.71844i	0.121414	−	0.352939i
$112$	2.88241	+	2.88241i	0.272362	+	0.272362i
$113$		−	1.88454i		−	0.177282i	−0.996064	−	0.0886411i	$-0.971748\pi$
$113$		−	1.88454i		−	0.177282i	0.996064	−	0.0886411i	$-0.0282524\pi$
$114$	−3.47063	−	7.11070i	−0.325054	−	0.665978i
$115$		0			0
$116$	9.80749			0.910602
$117$	−8.45853	−	6.74190i	−0.781992	−	0.623289i
$118$	21.4376			1.97349
$119$	3.34025	+	3.34025i	0.306200	+	0.306200i
$120$		0			0
$121$			10.7730i			0.979362i
$122$	−18.2482	−	18.2482i	−1.65212	−	1.65212i
$123$	3.75372	−	10.9117i	0.338462	−	0.983875i
$124$	4.70332	+	4.70332i	0.422371	+	0.422371i
$125$		0			0
$126$	−4.97416	−	3.88167i	−0.443133	−	0.345806i
$127$		−	3.73771i		−	0.331668i	−0.986154	−	0.165834i	$-0.946968\pi$
$127$		−	3.73771i		−	0.331668i	0.986154	−	0.165834i	$-0.0530316\pi$
$128$	−0.555533	+	0.555533i	−0.0491026	+	0.0491026i
$129$	−3.09764	+	1.51191i	−0.272732	+	0.133117i
$130$		0			0
$131$			10.1441i			0.886292i	0.896449	+	0.443146i	$0.146138\pi$
$131$			10.1441i			0.886292i	−0.896449	+	0.443146i	$0.853862\pi$
$132$	0.550012	−	1.59883i	0.0478724	−	0.139160i
$133$	2.37299			0.205764
$134$	−21.7714			−1.88076
$135$		0			0
$136$	−0.313931	+	0.313931i	−0.0269194	+	0.0269194i
$137$	−0.0896200	+	0.0896200i	−0.00765676	+	0.00765676i	−0.710925	−	0.703268i	$-0.751723\pi$
$137$	−0.0896200	+	0.0896200i	−0.00765676	+	0.00765676i	0.703268	+	0.710925i	$0.251723\pi$
$138$	3.04261	−	8.84458i	0.259004	−	0.752901i
$139$	−4.73017			−0.401208			−0.200604	−	0.979672i	$-0.564290\pi$
$139$	−4.73017			−0.401208			−0.200604	+	0.979672i	$0.564290\pi$
$140$		0			0
$141$	3.02818	+	1.04172i	0.255019	+	0.0877286i
$142$		−	9.47026i		−	0.794727i
$143$	1.20218	+	1.22717i	0.100531	+	0.102621i
$144$	−7.19793	+	9.22378i	−0.599828	+	0.768648i
$145$		0			0
$146$		−	15.4166i		−	1.27588i
$147$	−9.19528	+	4.48809i	−0.758414	+	0.370171i
$148$	−3.28910	+	3.28910i	−0.270362	+	0.270362i
$149$	−16.9150	−	16.9150i	−1.38573	−	1.38573i	−0.834058	−	0.551677i	$-0.813988\pi$
$149$	−16.9150	−	16.9150i	−1.38573	−	1.38573i	−0.551677	−	0.834058i	$-0.686012\pi$
$150$		0			0
$151$	−15.7855	−	15.7855i	−1.28461	−	1.28461i	−0.938016	−	0.346591i	$-0.887339\pi$
$151$	−15.7855	−	15.7855i	−1.28461	−	1.28461i	−0.346591	−	0.938016i	$-0.612661\pi$
$152$			0.223024i			0.0180896i
$153$	−8.34126	+	10.6889i	−0.674351	+	0.864145i
$154$	0.708571	+	0.708571i	0.0570983	+	0.0570983i
$155$		0			0
$156$	5.49361	+	11.5555i	0.439841	+	0.925179i
$157$	21.2079			1.69257			0.846285	−	0.532730i	$-0.178834\pi$
$157$	21.2079			1.69257			0.846285	+	0.532730i	$0.178834\pi$
$158$	−15.7978	−	15.7978i	−1.25680	−	1.25680i
$159$	20.7471	−	10.1263i	1.64535	−	0.803071i
$160$		0			0
$161$	1.98350	+	1.98350i	0.156322	+	0.156322i
$162$	9.30937	−	15.5335i	0.731413	−	1.22043i
$163$	−11.2553	−	11.2553i	−0.881587	−	0.881587i	0.112109	−	0.993696i	$-0.464239\pi$
$163$	−11.2553	−	11.2553i	−0.881587	−	0.881587i	−0.993696	+	0.112109i	$0.964239\pi$
$164$	−9.65180	+	9.65180i	−0.753679	+	0.753679i
$165$		0			0
$166$			25.7682i			2.00000i
$167$	11.2201	−	11.2201i	0.868235	−	0.868235i	−0.124042	−	0.992277i	$-0.539586\pi$
$167$	11.2201	−	11.2201i	0.868235	−	0.868235i	0.992277	+	0.124042i	$0.0395858\pi$
$168$	0.0780061	+	0.159821i	0.00601830	+	0.0123304i
$169$	−12.9972	−	0.267445i	−0.999788	−	0.0205727i
$170$		0			0
$171$	0.833905	+	6.75973i	0.0637703	+	0.516929i
$172$	4.07732			0.310893
$173$	−14.0262			−1.06639			−0.533197	−	0.845991i	$-0.679010\pi$
$173$	−14.0262			−1.06639			−0.533197	+	0.845991i	$0.679010\pi$
$174$	−15.7758	−	5.42701i	−1.19596	−	0.411421i
$175$		0			0
$176$	1.31393	−	1.31393i	0.0990413	−	0.0990413i
$177$	−17.4496	−	6.00282i	−1.31159	−	0.451199i
$178$	10.1822			0.763190
$179$	26.3524			1.96967			0.984836	−	0.173488i	$-0.0555038\pi$
$179$	26.3524			1.96967			0.984836	+	0.173488i	$0.0555038\pi$
$180$		0			0
$181$		−	0.195164i		−	0.0145065i	−0.999974	−	0.00725323i	$-0.997691\pi$
$181$		−	0.195164i		−	0.0145065i	0.999974	−	0.00725323i	$-0.00230880\pi$
$182$	−7.58265	−	0.0780061i	−0.562064	−	0.00578220i
$183$	9.74380	+	19.9633i	0.720282	+	1.47573i
$184$	−0.186418	+	0.186418i	−0.0137429	+	0.0137429i
$185$		0			0
$186$	−4.96291	−	10.1681i	−0.363898	−	0.745562i
$187$	1.52264	−	1.52264i	0.111346	−	0.111346i
$188$	−2.67853	−	2.67853i	−0.195352	−	0.195352i
$189$	2.96190	+	4.55240i	0.215447	+	0.331138i
$190$		0			0
$191$			5.64797i			0.408673i	0.978901	+	0.204336i	$0.0655036\pi$
$191$			5.64797i			0.408673i	−0.978901	+	0.204336i	$0.934496\pi$
$192$	13.0526	−	6.37081i	0.941994	−	0.459774i
$193$	−18.2430	−	18.2430i	−1.31316	−	1.31316i	−0.919071	−	0.394092i	$-0.871059\pi$
$193$	−18.2430	−	18.2430i	−1.31316	−	1.31316i	−0.394092	−	0.919071i	$-0.628941\pi$
$194$	−18.5452			−1.33147
$195$		0			0
$196$	12.1034			0.864531
$197$	0.235122	+	0.235122i	0.0167518	+	0.0167518i	0.715433	−	0.698681i	$-0.246229\pi$
$197$	0.235122	+	0.235122i	0.0167518	+	0.0167518i	−0.698681	+	0.715433i	$0.746229\pi$
$198$	−1.76944	+	2.26745i	−0.125749	+	0.161140i
$199$		−	19.6865i		−	1.39554i	−0.716322	−	0.697770i	$-0.754176\pi$
$199$		−	19.6865i		−	1.39554i	0.716322	−	0.697770i	$-0.245824\pi$
$200$		0			0
$201$	17.7213	+	6.09626i	1.24996	+	0.429997i
$202$	−12.9821	−	12.9821i	−0.913419	−	0.913419i
$203$	3.53791	−	3.53791i	0.248313	−	0.248313i
$204$	14.4128	−	7.03471i	1.00910	−	0.492528i
$205$		0			0
$206$	15.5815	−	15.5815i	1.08562	−	1.08562i
$207$	−4.95320	+	6.34726i	−0.344271	+	0.441165i
$208$	−0.144650	+	14.0608i	−0.0100297	+	0.974942i
$209$		−	1.08172i		−	0.0748239i
$210$		0			0
$211$	13.4374			0.925066			0.462533	−	0.886602i	$-0.346941\pi$
$211$	13.4374			0.925066			0.462533	+	0.886602i	$0.346941\pi$
$212$	−27.3086			−1.87556
$213$	−2.65180	+	7.70852i	−0.181698	+	0.528179i
$214$	−7.14408	+	7.14408i	−0.488359	+	0.488359i
$215$		0			0
$216$	−0.427854	+	0.278373i	−0.0291118	+	0.0189409i
$217$	3.39331			0.230353
$218$	−7.48607			−0.507021
$219$	−4.31684	+	12.5486i	−0.291705	+	0.847958i
$220$		0			0
$221$	−0.167626	+	16.2942i	−0.0112758	+	1.09607i
$222$	7.11070	−	3.47063i	0.477239	−	0.232933i
$223$	−14.5482	+	14.5482i	−0.974216	+	0.974216i	−0.999676	−	0.0254595i	$-0.991895\pi$
$223$	−14.5482	+	14.5482i	−0.974216	+	0.974216i	0.0254595	+	0.999676i	$0.491895\pi$
$224$			8.40763i			0.561759i
$225$		0			0
$226$	2.68135	−	2.68135i	0.178361	−	0.178361i
$227$	10.4317	+	10.4317i	0.692375	+	0.692375i	0.962754	−	0.270379i	$-0.0871490\pi$
$227$	10.4317	+	10.4317i	0.692375	+	0.692375i	−0.270379	+	0.962754i	$0.587149\pi$
$228$	2.62080	−	7.61842i	0.173567	−	0.504542i
$229$	19.4110	+	19.4110i	1.28272	+	1.28272i	0.939115	+	0.343602i	$0.111647\pi$
$229$	19.4110	+	19.4110i	1.28272	+	1.28272i	0.343602	+	0.939115i	$0.388353\pi$
$230$		0			0
$231$	−0.378347	−	0.775165i	−0.0248934	−	0.0510021i
$232$	0.332509	+	0.332509i	0.0218303	+	0.0218303i
$233$	−14.7282			−0.964874			−0.482437	−	0.875931i	$-0.660248\pi$
$233$	−14.7282			−0.964874			−0.482437	+	0.875931i	$0.660248\pi$
$234$	−2.44245	−	21.6274i	−0.159668	−	1.41383i
$235$		0			0
$236$	15.4348	+	15.4348i	1.00472	+	1.00472i
$237$	8.43535	+	17.2825i	0.547935	+	1.12262i
$238$			9.50513i			0.616126i
$239$	1.91881	+	1.91881i	0.124117	+	0.124117i	0.766437	−	0.642320i	$-0.222028\pi$
$239$	1.91881	+	1.91881i	0.124117	+	0.124117i	−0.642320	+	0.766437i	$0.722028\pi$
$240$		0			0
$241$	1.43507	+	1.43507i	0.0924411	+	0.0924411i	0.751815	−	0.659374i	$-0.229179\pi$
$241$	1.43507	+	1.43507i	0.0924411	+	0.0924411i	−0.659374	+	0.751815i	$0.729179\pi$
$242$	−15.3280	+	15.3280i	−0.985321	+	0.985321i
$243$	−11.9271	+	10.0371i	−0.765127	+	0.643880i
$244$		−	26.2770i		−	1.68221i
$245$		0			0
$246$	20.8662	−	10.1845i	1.33038	−	0.649341i
$247$	5.72836	+	5.84745i	0.364487	+	0.372064i
$248$			0.318918i			0.0202513i
$249$	7.21544	−	20.9746i	0.457260	−	1.32921i
$250$		0			0
$251$	−26.6058			−1.67935			−0.839673	−	0.543093i	$-0.817253\pi$
$251$	−26.6058			−1.67935			−0.839673	+	0.543093i	$0.817253\pi$
$252$	−0.786577	−	6.37608i	−0.0495497	−	0.401655i
$253$	0.904170	−	0.904170i	0.0568447	−	0.0568447i
$254$	5.31808	−	5.31808i	0.333686	−	0.333686i
$255$		0			0
$256$	15.1905			0.949407
$257$	−15.6733			−0.977676			−0.488838	−	0.872375i	$-0.662579\pi$
$257$	−15.6733			−0.977676			−0.488838	+	0.872375i	$0.662579\pi$
$258$	−6.55856	−	2.25620i	−0.408318	−	0.140465i
$259$			2.37299i			0.147450i
$260$		0			0
$261$	11.3214	+	8.83486i	0.700778	+	0.546864i
$262$	−14.4332	+	14.4332i	−0.891684	+	0.891684i
$263$			0.693170i			0.0427427i	0.999772	+	0.0213713i	$0.00680323\pi$
$263$			0.693170i			0.0427427i	−0.999772	+	0.0213713i	$0.993197\pi$
$264$	0.0728534	−	0.0355587i	0.00448382	−	0.00218849i
$265$		0			0
$266$	3.37633	+	3.37633i	0.207016	+	0.207016i
$267$	−8.28804	−	2.85116i	−0.507220	−	0.174488i
$268$	−15.6751	−	15.6751i	−0.957509	−	0.957509i
$269$			3.75001i			0.228642i	0.993444	+	0.114321i	$0.0364693\pi$
$269$			3.75001i			0.228642i	−0.993444	+	0.114321i	$0.963531\pi$
$270$		0			0
$271$	3.61370	+	3.61370i	0.219517	+	0.219517i	0.808295	−	0.588778i	$-0.200391\pi$
$271$	3.61370	+	3.61370i	0.219517	+	0.219517i	−0.588778	+	0.808295i	$0.700391\pi$
$272$	17.6257			1.06872
$273$	6.15022	+	2.18674i	0.372228	+	0.132347i
$274$	−0.255026			−0.0154067
$275$		0			0
$276$	8.55862	−	4.17734i	0.515168	−	0.251446i
$277$		−	18.8952i		−	1.13530i	−0.823269	−	0.567652i	$-0.807852\pi$
$277$		−	18.8952i		−	1.13530i	0.823269	−	0.567652i	$-0.192148\pi$
$278$	−6.73017	−	6.73017i	−0.403649	−	0.403649i
$279$	1.19246	+	9.66623i	0.0713909	+	0.578702i
$280$		0			0
$281$	1.68889	−	1.68889i	0.100751	−	0.100751i	−0.654935	−	0.755685i	$-0.727304\pi$
$281$	1.68889	−	1.68889i	0.100751	−	0.100751i	0.755685	+	0.654935i	$0.227304\pi$
$282$	2.82637	+	5.79072i	0.168308	+	0.344832i
$283$			28.3106i			1.68289i	0.540340	+	0.841447i	$0.318296\pi$
$283$			28.3106i			1.68289i	−0.540340	+	0.841447i	$0.681704\pi$
$284$	6.81846	−	6.81846i	0.404601	−	0.404601i
$285$		0			0
$286$	−0.0355587	+	3.45652i	−0.00210263	+	0.204388i
$287$			6.96350i			0.411042i
$288$	−23.9501	+	2.95457i	−1.41127	+	0.174100i
$289$	3.42543			0.201496
$290$		0			0
$291$	15.0953	+	5.19290i	0.884900	+	0.304413i
$292$	11.0997	−	11.0997i	0.649562	−	0.649562i
$293$	13.7452	−	13.7452i	0.803006	−	0.803006i	−0.180559	−	0.983564i	$-0.557791\pi$
$293$	13.7452	−	13.7452i	0.803006	−	0.803006i	0.983564	+	0.180559i	$0.0577905\pi$
$294$	−19.4689	−	6.69748i	−1.13545	−	0.390605i
$295$		0			0
$296$	−0.223024			−0.0129630
$297$	2.07519	−	1.35017i	0.120415	−	0.0783448i
$298$		−	48.1341i		−	2.78833i
$299$	−0.0995396	+	9.67583i	−0.00575652	+	0.559568i
$300$		0			0
$301$	1.47083	−	1.47083i	0.0847775	−	0.0847775i
$302$		−	44.9198i		−	2.58485i
$303$	6.93191	+	14.2022i	0.398228	+	0.815898i
$304$	6.26087	−	6.26087i	0.359085	−	0.359085i
$305$		0			0
$306$	−27.0764	+	3.34025i	−1.54786	+	0.190949i
$307$	17.4791	+	17.4791i	0.997586	+	0.997586i	0.999997	−	0.00241075i	$-0.000767366\pi$
$307$	17.4791	+	17.4791i	0.997586	+	0.997586i	−0.00241075	+	0.999997i	$0.500767\pi$
$308$			1.02032i			0.0581383i
$309$	−17.0460	+	8.31989i	−0.969710	+	0.473302i
$310$		0			0
$311$	12.1718			0.690201			0.345100	−	0.938566i	$-0.387845\pi$
$311$	12.1718			0.690201			0.345100	+	0.938566i	$0.387845\pi$
$312$	−0.205519	+	0.578025i	−0.0116352	+	0.0327242i
$313$	27.7777			1.57009			0.785043	−	0.619441i	$-0.212641\pi$
$313$	27.7777			1.57009			0.785043	+	0.619441i	$0.212641\pi$
$314$	30.1749	+	30.1749i	1.70287	+	1.70287i
$315$		0			0
$316$		−	22.7484i		−	1.27970i
$317$	−10.5771	−	10.5771i	−0.594071	−	0.594071i	0.344658	−	0.938728i	$-0.387995\pi$
$317$	−10.5771	−	10.5771i	−0.594071	−	0.594071i	−0.938728	+	0.344658i	$0.887995\pi$
$318$	43.9272	+	15.1113i	2.46332	+	0.847402i
$319$	−1.61274	−	1.61274i	−0.0902962	−	0.0902962i
$320$		0			0
$321$	7.81551	−	3.81464i	0.436219	−	0.212912i
$322$			5.64433i			0.314546i
$323$	7.25535	−	7.25535i	0.403698	−	0.403698i
$324$	17.8866	−	4.48130i	0.993697	−	0.248961i
$325$		0			0
$326$		−	32.0286i		−	1.77390i
$327$	6.09345	+	2.09620i	0.336968	+	0.115920i
$328$	−0.654460			−0.0361365
$329$	−1.93249			−0.106541
$330$		0			0
$331$	2.00971	−	2.00971i	0.110464	−	0.110464i	−0.649714	−	0.760178i	$-0.725112\pi$
$331$	2.00971	−	2.00971i	0.110464	−	0.110464i	0.760178	+	0.649714i	$0.225112\pi$
$332$	−18.5528	+	18.5528i	−1.01822	+	1.01822i
$333$	−6.75973	+	0.833905i	−0.370431	+	0.0456977i
$334$	31.9282			1.74703
$335$		0			0
$336$	2.29675	−	6.67642i	0.125298	−	0.364229i
$337$		−	18.6860i		−	1.01789i	−0.860798	−	0.508946i	$-0.830035\pi$
$337$		−	18.6860i		−	1.01789i	0.860798	−	0.508946i	$-0.169965\pi$
$338$	−18.1122	−	18.8732i	−0.985173	−	1.02657i
$339$	−2.93336	+	1.43173i	−0.159318	+	0.0777609i
$340$		0			0
$341$		−	1.54683i		−	0.0837653i
$342$	−8.43136	+	10.8044i	−0.455916	+	0.584232i
$343$	9.53972	−	9.53972i	0.515097	−	0.515097i
$344$	0.138235	+	0.138235i	0.00745316	+	0.00745316i
$345$		0			0
$346$	−19.9568	−	19.9568i	−1.07288	−	1.07288i
$347$		−	22.6674i		−	1.21685i	−0.793611	−	0.608426i	$-0.791801\pi$
$347$		−	22.6674i		−	1.21685i	0.793611	−	0.608426i	$-0.208199\pi$
$348$	−7.45100	−	15.2658i	−0.399415	−	0.818330i
$349$	1.89063	+	1.89063i	0.101203	+	0.101203i	0.755895	−	0.654692i	$-0.227202\pi$
$349$	1.89063	+	1.89063i	0.101203	+	0.101203i	−0.654692	+	0.755895i	$0.727202\pi$
$350$		0			0
$351$	−4.06788	+	18.2880i	−0.217127	+	0.976143i
$352$	3.83258			0.204277
$353$	−13.8077	−	13.8077i	−0.734909	−	0.734909i	0.236679	−	0.971588i	$-0.423941\pi$
$353$	−13.8077	−	13.8077i	−0.734909	−	0.734909i	−0.971588	+	0.236679i	$0.923941\pi$
$354$	−16.2867	−	33.3685i	−0.865629	−	1.77352i
$355$		0			0
$356$	7.33107	+	7.33107i	0.388546	+	0.388546i
$357$	2.66156	−	7.73690i	0.140865	−	0.409480i
$358$	37.4947	+	37.4947i	1.98166	+	1.98166i
$359$	−9.48985	+	9.48985i	−0.500855	+	0.500855i	−0.911704	−	0.410849i	$-0.865232\pi$
$359$	−9.48985	+	9.48985i	−0.500855	+	0.500855i	0.410849	+	0.911704i	$0.365232\pi$
$360$		0			0
$361$			13.8456i			0.728718i
$362$	0.277683	−	0.277683i	0.0145947	−	0.0145947i
$363$	16.7686	−	8.18451i	0.880123	−	0.429575i
$364$	−5.40325	−	5.51557i	−0.283207	−	0.289095i
$365$		0			0
$366$	−14.5405	+	42.2678i	−0.760043	+	2.20937i
$367$	−13.2306			−0.690630			−0.345315	−	0.938487i	$-0.612228\pi$
$367$	−13.2306			−0.690630			−0.345315	+	0.938487i	$0.612228\pi$
$368$	10.4665			0.545604
$369$	−19.8363	+	2.44708i	−1.03264	+	0.127390i
$370$		0			0
$371$	−9.85121	+	9.85121i	−0.511449	+	0.511449i
$372$	3.74768	−	10.8941i	0.194308	−	0.564835i
$373$	−18.5810			−0.962086			−0.481043	−	0.876697i	$-0.659742\pi$
$373$	−18.5810			−0.962086			−0.481043	+	0.876697i	$0.659742\pi$
$374$	4.33287			0.224047
$375$		0			0
$376$		−	0.181623i		−	0.00936652i
$377$	17.2585	+	0.177546i	0.888857	+	0.00914407i
$378$	−2.26298	+	10.6915i	−0.116395	+	0.549910i
$379$	8.12344	−	8.12344i	0.417273	−	0.417273i	−0.466990	−	0.884263i	$-0.654662\pi$
$379$	8.12344	−	8.12344i	0.417273	−	0.417273i	0.884263	+	0.466990i	$0.154662\pi$
$380$		0			0
$381$	−5.81789	+	2.83963i	−0.298060	+	0.145479i
$382$	−8.03603	+	8.03603i	−0.411159	+	0.411159i
$383$	−7.48628	−	7.48628i	−0.382531	−	0.382531i	0.489482	−	0.872013i	$-0.337186\pi$
$383$	−7.48628	−	7.48628i	−0.382531	−	0.382531i	−0.872013	+	0.489482i	$0.837186\pi$
$384$	1.28676	+	0.442657i	0.0656647	+	0.0225892i
$385$		0			0
$386$		−	51.9131i		−	2.64230i
$387$	4.70671	+	3.67296i	0.239256	+	0.186707i
$388$	−13.3523	−	13.3523i	−0.677860	−	0.677860i
$389$	5.90034			0.299159			0.149580	−	0.988750i	$-0.452208\pi$
$389$	5.90034			0.299159			0.149580	+	0.988750i	$0.452208\pi$
$390$		0			0
$391$	12.1290			0.613390
$392$	0.410349	+	0.410349i	0.0207258	+	0.0207258i
$393$	15.7897	−	7.70671i	0.796483	−	0.388752i
$394$			0.669072i			0.0337074i
$395$		0			0
$396$	−2.90650	+	0.358557i	−0.146057	+	0.0180182i
$397$	−10.4992	−	10.4992i	−0.526942	−	0.526942i	0.392717	−	0.919659i	$-0.371535\pi$
$397$	−10.4992	−	10.4992i	−0.526942	−	0.526942i	−0.919659	+	0.392717i	$0.871535\pi$
$398$	28.0103	−	28.0103i	1.40403	−	1.40403i
$399$	−1.80282	−	3.69365i	−0.0902539	−	0.184914i
$400$		0			0
$401$	5.06797	−	5.06797i	0.253082	−	0.253082i	−0.569151	−	0.822233i	$-0.692728\pi$
$401$	5.06797	−	5.06797i	0.253082	−	0.253082i	0.822233	+	0.569151i	$0.192728\pi$
$402$	16.5402	+	33.8880i	0.824953	+	1.69018i
$403$	8.19141	+	8.36169i	0.408043	+	0.416526i
$404$		−	18.6939i		−	0.930057i
$405$		0			0
$406$	10.0676			0.499647
$407$	1.08172			0.0536187
$408$	0.727148	+	0.250145i	0.0359992	+	0.0123840i
$409$	−9.73150	+	9.73150i	−0.481192	+	0.481192i	−0.905512	−	0.424320i	$-0.860513\pi$
$409$	−9.73150	+	9.73150i	−0.481192	+	0.481192i	0.424320	+	0.905512i	$0.360513\pi$
$410$		0			0
$411$	0.207584	+	0.0714106i	0.0102394	+	0.00352243i
$412$	22.4370			1.10539
$413$	11.1358			0.547956
$414$	−16.0785	+	1.98350i	−0.790215	+	0.0974838i
$415$		0			0
$416$	−20.7178	+	20.2959i	−1.01577	+	0.995088i
$417$	3.59363	+	7.36270i	0.175981	+	0.360553i
$418$	1.53908	−	1.53908i	0.0752791	−	0.0752791i
$419$			18.6219i			0.909738i	0.890558	+	0.454869i	$0.150314\pi$
$419$			18.6219i			0.909738i	−0.890558	+	0.454869i	$0.849686\pi$
$420$		0			0
$421$	−16.6790	+	16.6790i	−0.812883	+	0.812883i	−0.985065	−	0.172182i	$-0.944918\pi$
$421$	−16.6790	+	16.6790i	−0.812883	+	0.812883i	0.172182	+	0.985065i	$0.444918\pi$
$422$	19.1189	+	19.1189i	0.930695	+	0.930695i
$423$	−0.679105	−	5.50490i	−0.0330192	−	0.267657i
$424$	−0.925859	−	0.925859i	−0.0449637	−	0.0449637i
$425$		0			0
$426$	−14.7408	+	7.19480i	−0.714196	+	0.348589i
$427$	−9.47906	−	9.47906i	−0.458724	−	0.458724i
$428$	−10.2873			−0.497255
$429$	0.996814	−	2.80355i	0.0481266	−	0.135357i
$430$		0			0
$431$	−16.5554	−	16.5554i	−0.797445	−	0.797445i	0.185247	−	0.982692i	$-0.440692\pi$
$431$	−16.5554	−	16.5554i	−0.797445	−	0.797445i	−0.982692	+	0.185247i	$0.940692\pi$
$432$	19.8256	+	4.19634i	0.953861	+	0.201896i
$433$			28.3639i			1.36308i	0.731779	+	0.681542i	$0.238690\pi$
$433$			28.3639i			1.36308i	−0.731779	+	0.681542i	$0.761310\pi$
$434$	4.82807	+	4.82807i	0.231755	+	0.231755i
$435$		0			0
$436$	−5.38987	−	5.38987i	−0.258128	−	0.258128i
$437$	4.30836	−	4.30836i	0.206097	−	0.206097i
$438$	−23.9965	+	11.7123i	−1.14660	+	0.559638i
$439$			26.5091i			1.26521i	0.774475	+	0.632604i	$0.218014\pi$
$439$			26.5091i			1.26521i	−0.774475	+	0.632604i	$0.781986\pi$
$440$		0			0
$441$	13.9718	+	10.9031i	0.665323	+	0.519196i
$442$	−23.4222	+	22.9452i	−1.11408	+	1.09139i
$443$			12.9703i			0.616237i	0.951348	+	0.308118i	$0.0996993\pi$
$443$			12.9703i			0.616237i	−0.951348	+	0.308118i	$0.900301\pi$
$444$	7.61842	+	2.62080i	0.361554	+	0.124378i
$445$		0			0
$446$	−41.3987			−1.96029
$447$	−13.4782	+	39.1797i	−0.637495	+	1.85314i
$448$	−6.19771	+	6.19771i	−0.292814	+	0.292814i
$449$	−22.8445	+	22.8445i	−1.07810	+	1.07810i	−0.0814181	+	0.996680i	$0.525945\pi$
$449$	−22.8445	+	22.8445i	−1.07810	+	1.07810i	−0.996680	+	0.0814181i	$0.974055\pi$
$450$		0			0
$451$	3.17428			0.149471
$452$	3.86108			0.181610
$453$	−12.5781	+	36.5635i	−0.590973	+	1.71790i
$454$			29.6848i			1.39317i
$455$		0			0
$456$	0.347146	−	0.169437i	0.0162566	−	0.00793461i
$457$	−15.3590	+	15.3590i	−0.718463	+	0.718463i	−0.968290	−	0.249827i	$-0.919626\pi$
$457$	−15.3590	+	15.3590i	−0.718463	+	0.718463i	0.249827	+	0.968290i	$0.419626\pi$
$458$			55.2367i			2.58104i
$459$	22.9747	+	4.86289i	1.07237	+	0.226980i
$460$		0			0
$461$	−7.50039	−	7.50039i	−0.349328	−	0.349328i	0.510531	−	0.859859i	$-0.329449\pi$
$461$	−7.50039	−	7.50039i	−0.349328	−	0.349328i	−0.859859	+	0.510531i	$0.829449\pi$
$462$	0.564600	−	1.64124i	0.0262676	−	0.0763573i
$463$	7.89441	+	7.89441i	0.366884	+	0.366884i	0.866340	−	0.499455i	$-0.166467\pi$
$463$	7.89441	+	7.89441i	0.366884	+	0.366884i	−0.499455	+	0.866340i	$0.666467\pi$
$464$		−	18.6688i		−	0.866676i
$465$		0			0
$466$	−20.9555	−	20.9555i	−0.970744	−	0.970744i
$467$	36.8758			1.70641			0.853204	−	0.521578i	$-0.174656\pi$
$467$	36.8758			1.70641			0.853204	+	0.521578i	$0.174656\pi$
$468$	13.8129	−	17.3300i	0.638504	−	0.801080i
$469$	−11.3091			−0.522208
$470$		0			0
$471$	−16.1121	−	33.0109i	−0.742408	−	1.52106i
$472$			1.04659i			0.0481732i
$473$	−0.670473	−	0.670473i	−0.0308284	−	0.0308284i
$474$	−12.5879	+	36.5918i	−0.578182	+	1.68072i
$475$		0			0
$476$	−6.84357	+	6.84357i	−0.313675	+	0.313675i
$477$	−31.5241	−	24.6004i	−1.44339	−	1.12637i
$478$			5.46023i			0.249745i
$479$	30.1150	−	30.1150i	1.37599	−	1.37599i	0.524711	−	0.851280i	$-0.324173\pi$
$479$	30.1150	−	30.1150i	1.37599	−	1.37599i	0.851280	−	0.524711i	$-0.175827\pi$
$480$		0			0
$481$	−5.84745	+	5.72836i	−0.266621	+	0.261191i
$482$			4.08369i			0.186007i
$483$	1.58049	−	4.59432i	0.0719146	−	0.209049i
$484$	−22.0719			−1.00327
$485$		0			0
$486$	−31.2511	−	2.68921i	−1.41758	−	0.121985i
$487$	−14.5278	+	14.5278i	−0.658317	+	0.658317i	−0.954982	−	0.296665i	$-0.904126\pi$
$487$	−14.5278	+	14.5278i	−0.658317	+	0.658317i	0.296665	+	0.954982i	$0.404126\pi$
$488$	0.890883	−	0.890883i	0.0403284	−	0.0403284i
$489$	−8.96843	+	26.0704i	−0.405566	+	1.17894i
$490$		0			0
$491$	11.0154			0.497120			0.248560	−	0.968617i	$-0.420043\pi$
$491$	11.0154			0.497120			0.248560	+	0.968617i	$0.420043\pi$
$492$	22.3561	+	7.69070i	1.00789	+	0.346723i
$493$		−	21.6341i		−	0.974353i
$494$	−0.169437	+	16.4703i	−0.00762333	+	0.741032i
$495$		0			0
$496$	8.95288	−	8.95288i	0.401996	−	0.401996i
$497$		−	4.91933i		−	0.220662i
$498$	40.1093	−	19.5768i	1.79734	−	0.877256i
$499$	0.885544	−	0.885544i	0.0396424	−	0.0396424i	−0.687008	−	0.726650i	$-0.741076\pi$
$499$	0.885544	−	0.885544i	0.0396424	−	0.0396424i	0.726650	+	0.687008i	$0.241076\pi$
$500$		0			0
$501$	−25.9887	−	8.94032i	−1.16109	−	0.399424i
$502$	−37.8553	−	37.8553i	−1.68956	−	1.68956i
$503$			15.6004i			0.695587i	0.937571	+	0.347793i	$0.113069\pi$
$503$			15.6004i			0.695587i	−0.937571	+	0.347793i	$0.886931\pi$
$504$	0.189504	−	0.242839i	0.00844117	−	0.0108169i
$505$		0			0
$506$	2.57294			0.114381
$507$	9.45805	+	20.4339i	0.420047	+	0.907503i
$508$	7.65789			0.339764
$509$	−16.9597	−	16.9597i	−0.751724	−	0.751724i	0.223077	−	0.974801i	$-0.428390\pi$
$509$	−16.9597	−	16.9597i	−0.751724	−	0.751724i	−0.974801	+	0.223077i	$0.928390\pi$
$510$		0			0
$511$		−	8.00814i		−	0.354259i
$512$	22.7244	+	22.7244i	1.00429	+	1.00429i
$513$	9.88825	−	6.43354i	0.436577	−	0.284048i
$514$	−22.3003	−	22.3003i	−0.983624	−	0.983624i
$515$		0			0
$516$	−3.09764	−	6.34651i	−0.136366	−	0.279389i
$517$			0.880915i			0.0387426i
$518$	−3.37633	+	3.37633i	−0.148347	+	0.148347i
$519$	10.6561	+	21.8324i	0.467750	+	0.958336i
$520$		0			0
$521$		−	9.51106i		−	0.416687i	−0.978056	−	0.208344i	$-0.933193\pi$
$521$		−	9.51106i		−	0.416687i	0.978056	−	0.208344i	$-0.0668072\pi$
$522$	3.53791	+	28.6787i	0.154850	+	1.25523i
$523$	−14.6147			−0.639057			−0.319528	−	0.947577i	$-0.603524\pi$
$523$	−14.6147			−0.639057			−0.319528	+	0.947577i	$0.603524\pi$
$524$	−20.7834			−0.907927
$525$		0			0
$526$	−0.986254	+	0.986254i	−0.0430027	+	0.0430027i
$527$	10.3750	−	10.3750i	0.451940	−	0.451940i
$528$	−3.04341	−	1.04696i	−0.132448	−	0.0455631i
$529$	−15.7976			−0.686851
$530$		0			0
$531$	3.91329	+	31.7215i	0.169822	+	1.37660i
$532$			4.86183i			0.210787i
$533$	−17.1592	+	16.8098i	−0.743249	+	0.728113i
$534$	−7.73569	−	15.8490i	−0.334756	−	0.685855i
$535$		0			0
$536$		−	1.06288i		−	0.0459095i
$537$	−20.0206	−	41.0186i	−0.863952	−	1.77008i
$538$	−5.33558	+	5.33558i	−0.230033	+	0.230033i
$539$	−1.99029	−	1.99029i	−0.0857277	−	0.0857277i
$540$		0			0
$541$	−21.2823	−	21.2823i	−0.914998	−	0.914998i	0.0816620	−	0.996660i	$-0.473977\pi$
$541$	−21.2823	−	21.2823i	−0.914998	−	0.914998i	−0.996660	+	0.0816620i	$0.973977\pi$
$542$			10.2833i			0.441704i
$543$	−0.303781	+	0.148271i	−0.0130365	+	0.00636293i
$544$	25.7061	+	25.7061i	1.10214	+	1.10214i
$545$		0			0
$546$	5.63931	+	11.8620i	0.241340	+	0.507645i
$547$	16.9541			0.724903			0.362452	−	0.932003i	$-0.381940\pi$
$547$	16.9541			0.724903			0.362452	+	0.932003i	$0.381940\pi$
$548$	−0.183615	−	0.183615i	−0.00784366	−	0.00784366i
$549$	23.6711	−	30.3332i	1.01026	−	1.29459i
$550$		0			0
$551$	−7.68469	−	7.68469i	−0.327379	−	0.327379i
$552$	0.431794	+	0.148541i	0.0183784	+	0.00632232i
$553$	−8.20616	−	8.20616i	−0.348961	−	0.348961i
$554$	26.8844	−	26.8844i	1.14221	−	1.14221i
$555$		0			0
$556$		−	9.69127i		−	0.411001i
$557$	−10.4018	+	10.4018i	−0.440739	+	0.440739i	−0.892260	−	0.451522i	$-0.850881\pi$
$557$	−10.4018	+	10.4018i	−0.440739	+	0.440739i	0.451522	+	0.892260i	$0.350881\pi$
$558$	−12.0566	+	15.4499i	−0.510398	+	0.654048i
$559$	7.17496	+	0.0738120i	0.303468	+	0.00312191i
$560$		0			0
$561$	−3.52683	−	1.21326i	−0.148903	−	0.0512239i
$562$	4.80596			0.202727
$563$	9.46463			0.398886			0.199443	−	0.979909i	$-0.436087\pi$
$563$	9.46463			0.398886			0.199443	+	0.979909i	$0.436087\pi$
$564$	−2.13430	+	6.20419i	−0.0898700	+	0.261244i
$565$		0			0
$566$	−40.2809	+	40.2809i	−1.69313	+	1.69313i
$567$	4.83576	−	8.06889i	0.203083	−	0.338862i
$568$	0.462340			0.0193994
$569$	26.1992			1.09833			0.549164	−	0.835715i	$-0.314946\pi$
$569$	26.1992			1.09833			0.549164	+	0.835715i	$0.314946\pi$
$570$		0			0
$571$		−	2.01935i		−	0.0845074i	−0.999107	−	0.0422537i	$-0.986546\pi$
$571$		−	2.01935i		−	0.0845074i	0.999107	−	0.0422537i	$-0.0134538\pi$
$572$	−2.51425	+	2.46304i	−0.105126	+	0.102985i
$573$	8.79129	−	4.29091i	0.367262	−	0.179255i
$574$	−9.90779	+	9.90779i	−0.413543	+	0.413543i
$575$		0			0
$576$	−19.8328	−	15.4769i	−0.826369	−	0.644871i
$577$	14.1048	−	14.1048i	0.587191	−	0.587191i	−0.349679	−	0.936870i	$-0.613709\pi$
$577$	14.1048	−	14.1048i	0.587191	−	0.587191i	0.936870	+	0.349679i	$0.113709\pi$
$578$	4.87376	+	4.87376i	0.202722	+	0.202722i
$579$	−14.5363	+	42.2557i	−0.604109	+	1.75609i
$580$		0			0
$581$			13.3853i			0.555316i
$582$	14.0893	+	28.8663i	0.584018	+	1.19655i
$583$	4.49062	+	4.49062i	0.185983	+	0.185983i
$584$	0.752640			0.0311445
$585$		0			0
$586$	39.1140			1.61578
$587$	29.5091	+	29.5091i	1.21797	+	1.21797i	0.968341	+	0.249630i	$0.0803091\pi$
$587$	29.5091	+	29.5091i	1.21797	+	1.21797i	0.249630	+	0.968341i	$0.419691\pi$
$588$	−9.19528	−	18.8395i	−0.379207	−	0.776927i
$589$		−	7.37061i		−	0.303701i
$590$		0			0
$591$	0.187349	−	0.544605i	0.00770650	−	0.0224021i
$592$	6.26087	+	6.26087i	0.257320	+	0.257320i
$593$	12.1679	−	12.1679i	0.499676	−	0.499676i	−0.411661	−	0.911337i	$-0.635051\pi$
$593$	12.1679	−	12.1679i	0.499676	−	0.499676i	0.911337	+	0.411661i	$0.135051\pi$
$594$	4.87366	+	1.03157i	0.199969	+	0.0423258i
$595$		0			0
$596$	34.6559	−	34.6559i	1.41956	−	1.41956i
$597$	−30.6428	+	14.9563i	−1.25413	+	0.612122i
$598$	−13.9086	+	13.6253i	−0.568764	+	0.557181i
$599$		−	32.6782i		−	1.33520i	−0.744522	−	0.667598i	$-0.767322\pi$
$599$		−	32.6782i		−	1.33520i	0.744522	−	0.667598i	$-0.232678\pi$
$600$		0			0
$601$	8.63691			0.352307			0.176153	−	0.984363i	$-0.443635\pi$
$601$	8.63691			0.352307			0.176153	+	0.984363i	$0.443635\pi$
$602$	4.18546			0.170587
$603$	−3.97421	−	32.2153i	−0.161842	−	1.31191i
$604$	32.3417	−	32.3417i	1.31596	−	1.31596i
$605$		0			0
$606$	−10.3444	+	30.0701i	−0.420211	+	1.22151i
$607$	20.1069			0.816114			0.408057	−	0.912956i	$-0.366206\pi$
$607$	20.1069			0.816114			0.408057	+	0.912956i	$0.366206\pi$
$608$	18.2622			0.740630
$609$	−8.19475	−	2.81906i	−0.332068	−	0.114234i
$610$		0			0
$611$	−4.66499	−	4.76197i	−0.188725	−	0.192649i
$612$	−21.8996	−	17.0897i	−0.885239	−	0.690812i
$613$	14.6949	−	14.6949i	0.593521	−	0.593521i	−0.345060	−	0.938581i	$-0.612141\pi$
$613$	14.6949	−	14.6949i	0.593521	−	0.593521i	0.938581	+	0.345060i	$0.112141\pi$
$614$			49.7392i			2.00731i
$615$		0			0
$616$	−0.0345926	+	0.0345926i	−0.00139377	+	0.00139377i
$617$	−29.8552	−	29.8552i	−1.20192	−	1.20192i	−0.973581	−	0.228343i	$-0.926669\pi$
$617$	−29.8552	−	29.8552i	−1.20192	−	1.20192i	−0.228343	−	0.973581i	$-0.573331\pi$
$618$	−36.0910	−	12.4156i	−1.45179	−	0.499429i
$619$	2.01564	+	2.01564i	0.0810156	+	0.0810156i	0.746453	−	0.665438i	$-0.231755\pi$
$619$	2.01564	+	2.01564i	0.0810156	+	0.0810156i	−0.665438	+	0.746453i	$0.731755\pi$
$620$		0			0
$621$	13.6428	+	2.88767i	0.547468	+	0.115878i
$622$	17.3183	+	17.3183i	0.694400	+	0.694400i
$623$	5.28916			0.211906
$624$	21.9961	−	10.4572i	0.880550	−	0.418623i
$625$		0			0
$626$	39.5225	+	39.5225i	1.57964	+	1.57964i
$627$	−1.68373	+	0.821807i	−0.0672419	+	0.0328198i
$628$			43.4511i			1.73389i
$629$	7.25535	+	7.25535i	0.289290	+	0.289290i
$630$		0			0
$631$	−24.5399	−	24.5399i	−0.976917	−	0.976917i	0.0228223	−	0.999740i	$-0.492735\pi$
$631$	−24.5399	−	24.5399i	−0.976917	−	0.976917i	−0.999740	+	0.0228223i	$0.992735\pi$
$632$	0.771251	−	0.771251i	0.0306787	−	0.0306787i
$633$	−10.2087	−	20.9158i	−0.405760	−	0.831329i
$634$		−	30.0987i		−	1.19537i
$635$		0			0
$636$	20.7471	+	42.5070i	0.822674	+	1.68551i
$637$	21.2987	+	0.219109i	0.843886	+	0.00868143i
$638$		−	4.58927i		−	0.181691i
$639$	14.0133	−	1.72873i	0.554356	−	0.0683874i
$640$		0			0
$641$	−22.3667			−0.883433			−0.441716	−	0.897155i	$-0.645630\pi$
$641$	−22.3667			−0.883433			−0.441716	+	0.897155i	$0.645630\pi$
$642$	16.5476	+	5.69251i	0.653081	+	0.224665i
$643$	−24.8057	+	24.8057i	−0.978240	+	0.978240i	−0.999768	−	0.0215278i	$-0.993147\pi$
$643$	−24.8057	+	24.8057i	−0.978240	+	0.978240i	0.0215278	+	0.999768i	$0.493147\pi$
$644$	−4.06384	+	4.06384i	−0.160138	+	0.160138i
$645$		0			0
$646$	20.6461			0.812309
$647$	−5.70359			−0.224231			−0.112116	−	0.993695i	$-0.535763\pi$
$647$	−5.70359			−0.224231			−0.112116	+	0.993695i	$0.535763\pi$
$648$	0.758350	+	0.454485i	0.0297908	+	0.0178539i
$649$		−	5.07620i		−	0.199258i
$650$		0			0
$651$	−2.57799	−	5.28183i	−0.101039	−	0.207011i
$652$	23.0602	−	23.0602i	0.903106	−	0.903106i
$653$			17.5389i			0.686351i	0.939271	+	0.343176i	$0.111503\pi$
$653$			17.5389i			0.686351i	−0.939271	+	0.343176i	$0.888497\pi$
$654$	5.68736	+	11.6524i	0.222393	+	0.455644i
$655$		0			0
$656$	18.3724	+	18.3724i	0.717322	+	0.717322i
$657$	22.8121	−	2.81418i	0.889984	−	0.109792i
$658$	−2.74958	−	2.74958i	−0.107190	−	0.107190i
$659$			23.7592i			0.925525i	0.886482	+	0.462763i	$0.153142\pi$
$659$			23.7592i			0.925525i	−0.886482	+	0.462763i	$0.846858\pi$
$660$		0			0
$661$	9.44470	+	9.44470i	0.367356	+	0.367356i	0.866512	−	0.499156i	$-0.166357\pi$
$661$	9.44470	+	9.44470i	0.367356	+	0.367356i	−0.499156	+	0.866512i	$0.666357\pi$
$662$	5.71892			0.222272
$663$	25.4900	−	12.1182i	0.989950	−	0.470633i
$664$	−1.25801			−0.0488203
$665$		0			0
$666$	−10.8044	−	8.43136i	−0.418660	−	0.326709i
$667$		−	12.8468i		−	0.497428i
$668$	22.9879	+	22.9879i	0.889429	+	0.889429i
$669$	33.6974	+	11.5922i	1.30282	+	0.448180i
$670$		0			0
$671$	−4.32098	+	4.32098i	−0.166810	+	0.166810i
$672$	13.0868	−	6.38749i	0.504835	−	0.246403i
$673$			8.66064i			0.333843i	0.985970	+	0.166922i	$0.0533827\pi$
$673$			8.66064i			0.333843i	−0.985970	+	0.166922i	$0.946617\pi$
$674$	26.5868	−	26.5868i	1.02409	−	1.02409i
$675$		0			0
$676$	0.547947	−	26.6290i	0.0210749	−	1.02419i
$677$		−	0.0318488i		−	0.00122405i	−1.00000		0.000612025i	$-0.999805\pi$
$677$		−	0.0318488i		−	0.00122405i	1.00000		0.000612025i	$-0.000194814\pi$
$678$	−6.21072	−	2.13654i	−0.238521	−	0.0820534i
$679$	−9.63331			−0.369692
$680$		0			0
$681$	8.31212	−	24.1625i	0.318521	−	0.925911i
$682$	2.20085	−	2.20085i	0.0842749	−	0.0842749i
$683$	12.2599	−	12.2599i	0.469111	−	0.469111i	−0.432516	−	0.901626i	$-0.642374\pi$
$683$	12.2599	−	12.2599i	0.469111	−	0.469111i	0.901626	+	0.432516i	$0.142374\pi$
$684$	−13.8495	+	1.70852i	−0.529547	+	0.0653270i
$685$		0			0
$686$	27.1466			1.03646
$687$	15.4670	−	44.9611i	0.590103	−	1.71537i
$688$		−	7.76127i		−	0.295896i
$689$	−48.0557	−	0.494370i	−1.83078	−	0.0188340i
$690$		0			0
$691$	10.4049	−	10.4049i	0.395820	−	0.395820i	−0.480936	−	0.876756i	$-0.659703\pi$
$691$	10.4049	−	10.4049i	0.395820	−	0.395820i	0.876756	+	0.480936i	$0.159703\pi$
$692$		−	28.7372i		−	1.09243i
$693$	−0.919136	+	1.17783i	−0.0349151	+	0.0447419i
$694$	32.2516	−	32.2516i	1.22426	−	1.22426i
$695$		0			0
$696$	0.264948	−	0.770178i	0.0100428	−	0.0291935i
$697$	21.2907	+	21.2907i	0.806443	+	0.806443i
$698$			5.38004i			0.203638i
$699$	11.1894	+	22.9250i	0.423220	+	0.867102i
$700$		0			0
$701$	38.4849			1.45355			0.726776	−	0.686874i	$-0.241018\pi$
$701$	38.4849			1.45355			0.726776	+	0.686874i	$0.241018\pi$
$702$	−31.8084	+	20.2327i	−1.20053	+	0.763634i
$703$	5.15436			0.194401
$704$	2.82520	+	2.82520i	0.106479	+	0.106479i
$705$		0			0
$706$		−	39.2917i		−	1.47876i
$707$	−6.74357	−	6.74357i	−0.253618	−	0.253618i
$708$	12.2987	−	35.7511i	0.462213	−	1.34361i
$709$	−30.5927	−	30.5927i	−1.14893	−	1.14893i	−0.986763	−	0.162170i	$-0.948151\pi$
$709$	−30.5927	−	30.5927i	−1.14893	−	1.14893i	−0.162170	−	0.986763i	$-0.551849\pi$
$710$		0			0
$711$	20.4924	−	26.2599i	0.768525	−	0.984824i
$712$			0.497098i			0.0186295i
$713$	6.16084	−	6.16084i	0.230725	−	0.230725i
$714$	14.7951	−	7.22129i	0.553693	−	0.270250i
$715$		0			0
$716$			53.9914i			2.01775i
$717$	1.52893	−	4.44447i	0.0570991	−	0.165982i
$718$	−27.0046			−1.00780
$719$	10.3484			0.385930			0.192965	−	0.981206i	$-0.438190\pi$
$719$	10.3484			0.385930			0.192965	+	0.981206i	$0.438190\pi$
$720$		0			0
$721$	8.09383	−	8.09383i	0.301430	−	0.301430i
$722$	−19.6998	+	19.6998i	−0.733151	+	0.733151i
$723$	1.14349	−	3.32401i	0.0425267	−	0.123621i
$724$	0.399857			0.0148606
$725$		0			0
$726$	35.5037	+	12.2136i	1.31767	+	0.453288i
$727$		−	38.3639i		−	1.42284i	−0.702769	−	0.711419i	$-0.748053\pi$
$727$		−	38.3639i		−	1.42284i	0.702769	−	0.711419i	$-0.251947\pi$
$728$	0.00380828	−	0.370187i	0.000141144	−	0.0137200i
$729$	24.6845	+	10.9397i	0.914240	+	0.405172i
$730$		0			0
$731$		−	8.99407i		−	0.332658i
$732$	−40.9012	+	19.9633i	−1.51175	+	0.737865i
$733$	−15.1762	+	15.1762i	−0.560546	+	0.560546i	−0.929462	−	0.368917i	$-0.879729\pi$
$733$	−15.1762	+	15.1762i	−0.560546	+	0.560546i	0.368917	+	0.929462i	$0.379729\pi$
$734$	−18.8247	−	18.8247i	−0.694831	−	0.694831i
$735$		0			0
$736$	15.2648	+	15.2648i	0.562666	+	0.562666i
$737$			5.15522i			0.189895i
$738$	−31.7052	−	24.7417i	−1.16708	−	0.910754i
$739$	−20.4670	−	20.4670i	−0.752889	−	0.752889i	0.222128	−	0.975017i	$-0.428700\pi$
$739$	−20.4670	−	20.4670i	−0.752889	−	0.752889i	−0.975017	+	0.222128i	$0.928700\pi$
$740$		0			0
$741$	4.74981	−	13.3589i	0.174488	−	0.490751i
$742$	−28.0329			−1.02912
$743$	−8.05943	−	8.05943i	−0.295672	−	0.295672i	0.543644	−	0.839316i	$-0.317044\pi$
$743$	−8.05943	−	8.05943i	−0.295672	−	0.295672i	−0.839316	+	0.543644i	$0.817044\pi$
$744$	0.496409	−	0.242290i	0.0181992	−	0.00888279i
$745$		0			0
$746$	−26.4373	−	26.4373i	−0.967939	−	0.967939i
$747$	−38.1295	+	4.70380i	−1.39509	+	0.172103i
$748$	3.11961	+	3.11961i	0.114064	+	0.114064i
$749$	−3.71099	+	3.71099i	−0.135597	+	0.135597i
$750$		0			0
$751$		−	12.8622i		−	0.469350i	−0.972074	−	0.234675i	$-0.924597\pi$
$751$		−	12.8622i		−	0.469350i	0.972074	−	0.234675i	$-0.0754025\pi$
$752$	−5.09865	+	5.09865i	−0.185929	+	0.185929i
$753$	20.2131	+	41.4131i	0.736607	+	1.50918i
$754$	24.3031	+	24.8083i	0.885065	+	0.903465i
$755$		0			0
$756$	−9.32704	+	6.06841i	−0.339221	+	0.220706i
$757$	5.31615			0.193219			0.0966094	−	0.995322i	$-0.469200\pi$
$757$	5.31615			0.193219			0.0966094	+	0.995322i	$0.469200\pi$
$758$	23.1163			0.839623
$759$	−2.09430	−	0.720457i	−0.0760182	−	0.0261509i
$760$		0			0
$761$	23.9765	−	23.9765i	0.869146	−	0.869146i	−0.123232	−	0.992378i	$-0.539326\pi$
$761$	23.9765	−	23.9765i	0.869146	−	0.869146i	0.992378	+	0.123232i	$0.0393260\pi$
$762$	−12.3181	−	4.23752i	−0.446237	−	0.153509i
$763$	−3.88864			−0.140778
$764$	−11.5717			−0.418649
$765$		0			0
$766$		−	21.3032i		−	0.769716i
$767$	26.8816	+	27.4405i	0.970639	+	0.990817i
$768$	−11.5406	−	23.6446i	−0.416436	−	0.853203i
$769$	−18.4441	+	18.4441i	−0.665109	+	0.665109i	−0.956580	−	0.291470i	$-0.905856\pi$
$769$	−18.4441	+	18.4441i	−0.665109	+	0.665109i	0.291470	+	0.956580i	$0.405856\pi$
$770$		0			0
$771$	11.9074	+	24.3962i	0.428835	+	0.878607i
$772$	37.3767	−	37.3767i	1.34522	−	1.34522i
$773$	−17.3271	−	17.3271i	−0.623211	−	0.623211i	0.323140	−	0.946351i	$-0.395261\pi$
$773$	−17.3271	−	17.3271i	−0.623211	−	0.623211i	−0.946351	+	0.323140i	$0.895261\pi$
$774$	1.47083	+	11.9227i	0.0528681	+	0.428554i
$775$		0			0
$776$		−	0.905380i		−	0.0325013i
$777$	3.69365	−	1.80282i	0.132509	−	0.0646758i
$778$	8.39511	+	8.39511i	0.300979	+	0.300979i
$779$	15.1254			0.541924
$780$		0			0
$781$	−2.24245			−0.0802413
$782$	17.2574	+	17.2574i	0.617122	+	0.617122i
$783$	5.15065	−	24.3343i	0.184069	−	0.869637i
$784$		−	23.0392i		−	0.822827i
$785$		0			0
$786$	33.4311	+	11.5006i	1.19245	+	0.410212i
$787$	19.8254	+	19.8254i	0.706698	+	0.706698i	0.965839	−	0.259141i	$-0.0834394\pi$
$787$	19.8254	+	19.8254i	0.706698	+	0.706698i	−0.259141	+	0.965839i	$0.583439\pi$
$788$	−0.481723	+	0.481723i	−0.0171607	+	0.0171607i
$789$	1.07895	−	0.526619i	0.0384115	−	0.0187481i
$790$		0			0
$791$	1.39283	−	1.39283i	0.0495233	−	0.0495233i
$792$	−0.110697	−	0.0863844i	−0.00393345	−	0.00306954i
$793$	0.475694	−	46.2403i	0.0168924	−	1.64204i
$794$		−	29.8770i		−	1.06030i
$795$		0			0
$796$	40.3341			1.42960
$797$	−14.1984			−0.502933			−0.251467	−	0.967866i	$-0.580913\pi$
$797$	−14.1984			−0.502933			−0.251467	+	0.967866i	$0.580913\pi$
$798$	2.69031	−	7.82048i	0.0952360	−	0.276842i
$799$	−5.90852	+	5.90852i	−0.209028	+	0.209028i
$800$		0			0
$801$	1.85869	+	15.0668i	0.0656737	+	0.532358i
$802$	14.4216			0.509244
$803$	−3.65047			−0.128822
$804$	−12.4902	+	36.3077i	−0.440494	+	1.28047i
$805$		0			0
$806$	−0.242290	+	23.5520i	−0.00853431	+	0.829585i
$807$	5.83704	−	2.84898i	0.205474	−	0.100289i
$808$	0.633790	−	0.633790i	0.0222967	−	0.0222967i
$809$			29.7074i			1.04446i	0.852806	+	0.522228i	$0.174899\pi$
$809$			29.7074i			1.04446i	−0.852806	+	0.522228i	$0.825101\pi$
$810$		0			0
$811$	32.4832	−	32.4832i	1.14064	−	1.14064i	0.152305	−	0.988333i	$-0.451330\pi$
$811$	32.4832	−	32.4832i	1.14064	−	1.14064i	0.988333	−	0.152305i	$-0.0486697\pi$
$812$	7.24855	+	7.24855i	0.254374	+	0.254374i
$813$	2.87945	−	8.37029i	0.100987	−	0.293559i
$814$	1.53908	+	1.53908i	0.0539449	+	0.0539449i
$815$		0			0
$816$	−13.3907	−	27.4352i	−0.468769	−	0.960424i
$817$	−3.19480	−	3.19480i	−0.111772	−	0.111772i
$818$	−27.6923			−0.968238
$819$	−1.26873	−	11.2344i	−0.0443331	−	0.392561i
$820$		0			0
$821$	31.5279	+	31.5279i	1.10033	+	1.10033i	0.994370	+	0.105963i	$0.0337924\pi$
$821$	31.5279	+	31.5279i	1.10033	+	1.10033i	0.105963	+	0.994370i	$0.466208\pi$
$822$	0.193750	+	0.396958i	0.00675779	+	0.0138455i
$823$		−	19.2920i		−	0.672478i	−0.941777	−	0.336239i	$-0.890845\pi$
$823$		−	19.2920i		−	0.672478i	0.941777	−	0.336239i	$-0.109155\pi$
$824$	0.760694	+	0.760694i	0.0265000	+	0.0265000i
$825$		0			0
$826$	15.8442	+	15.8442i	0.551290	+	0.551290i
$827$	−9.30756	+	9.30756i	−0.323656	+	0.323656i	−0.850168	−	0.526512i	$-0.823499\pi$
$827$	−9.30756	+	9.30756i	−0.323656	+	0.323656i	0.526512	+	0.850168i	$0.323499\pi$
$828$	−13.0044	−	10.1482i	−0.451934	−	0.352675i
$829$		−	27.8662i		−	0.967835i	−0.875114	−	0.483917i	$-0.839214\pi$
$829$		−	27.8662i		−	0.967835i	0.875114	−	0.483917i	$-0.160786\pi$
$830$		0			0
$831$	−29.4112	+	14.3552i	−1.02026	+	0.497975i
$832$	−30.2334	−	0.311024i	−1.04815	−	0.0107828i
$833$		−	26.6987i		−	0.925055i
$834$	−5.36270	+	15.5889i	−0.185695	+	0.539798i
$835$		0			0
$836$	2.21624			0.0766503
$837$	14.1399	−	9.19979i	0.488748	−	0.317991i
$838$	−26.4955	+	26.4955i	−0.915273	+	0.915273i
$839$	−5.90142	+	5.90142i	−0.203740	+	0.203740i	−0.801600	−	0.597861i	$-0.796018\pi$
$839$	−5.90142	+	5.90142i	−0.203740	+	0.203740i	0.597861	+	0.801600i	$0.296018\pi$
$840$		0			0
$841$	6.08563			0.209849
$842$	−47.4623			−1.63566
$843$	−3.91191	−	1.34573i	−0.134733	−	0.0463494i
$844$			27.5307i			0.947647i
$845$		0			0
$846$	6.86623	−	8.79871i	0.236066	−	0.302506i
$847$	−7.96213	+	7.96213i	−0.273582	+	0.273582i
$848$			51.9826i			1.78509i
$849$	44.0667	−	21.5083i	1.51236	−	0.738163i
$850$		0			0
$851$	4.30836	+	4.30836i	0.147689	+	0.147689i
$852$	−15.7934	−	5.43306i	−0.541072	−	0.186133i
$853$	0.0178236	+	0.0178236i	0.000610267	+	0.000610267i	0.707412	−	0.706802i	$-0.249863\pi$
$853$	0.0178236	+	0.0178236i	0.000610267	+	0.000610267i	−0.706802	+	0.707412i	$0.749863\pi$
$854$		−	26.9739i		−	0.923029i
$855$		0			0
$856$	−0.348775	−	0.348775i	−0.0119209	−	0.0119209i
$857$	−15.5955			−0.532734			−0.266367	−	0.963872i	$-0.585823\pi$
$857$	−15.5955			−0.532734			−0.266367	+	0.963872i	$0.585823\pi$
$858$	5.40722	−	2.57065i	0.184600	−	0.0877607i
$859$	−1.89170			−0.0645441			−0.0322721	−	0.999479i	$-0.510274\pi$
$859$	−1.89170			−0.0645441			−0.0322721	+	0.999479i	$0.510274\pi$
$860$		0			0
$861$	10.8390	−	5.29035i	0.369391	−	0.180295i
$862$		−	47.1106i		−	1.60459i
$863$	35.3417	+	35.3417i	1.20305	+	1.20305i	0.973236	+	0.229810i	$0.0738103\pi$
$863$	35.3417	+	35.3417i	1.20305	+	1.20305i	0.229810	+	0.973236i	$0.426190\pi$
$864$	22.7944	+	35.0346i	0.775481	+	1.19190i
$865$		0			0
$866$	−40.3567	+	40.3567i	−1.37138	+	1.37138i
$867$	−2.60239	−	5.33182i	−0.0883817	−	0.181078i
$868$			6.95229i			0.235976i
$869$	−3.74074	+	3.74074i	−0.126896	+	0.126896i
$870$		0			0
$871$	−27.3001	−	27.8676i	−0.925028	−	0.944258i
$872$		−	0.365472i		−	0.0123764i
$873$	−3.38529	−	27.4416i	−0.114575	−	0.928756i
$874$	12.2600			0.414702
$875$		0			0
$876$	−25.7099	−	8.84443i	−0.868657	−	0.298825i
$877$	−17.4575	+	17.4575i	−0.589497	+	0.589497i	−0.937495	−	0.347998i	$-0.886862\pi$
$877$	−17.4575	+	17.4575i	−0.589497	+	0.589497i	0.347998	+	0.937495i	$0.386862\pi$
$878$	−37.7176	+	37.7176i	−1.27291	+	1.27291i
$879$	−31.8376	−	10.9524i	−1.07386	−	0.369416i
$880$		0			0
$881$	31.4060			1.05810			0.529048	−	0.848592i	$-0.322549\pi$
$881$	31.4060			1.05810			0.529048	+	0.848592i	$0.322549\pi$
$882$	4.36614	+	35.3924i	0.147016	+	1.19173i
$883$			17.2791i			0.581488i	0.956801	+	0.290744i	$0.0939027\pi$
$883$			17.2791i			0.581488i	−0.956801	+	0.290744i	$0.906097\pi$
$884$	−33.3840	−	0.343436i	−1.12282	−	0.0115510i
$885$		0			0
$886$	−18.4543	+	18.4543i	−0.619986	+	0.619986i
$887$		−	41.1922i		−	1.38310i	−0.722329	−	0.691550i	$-0.756928\pi$
$887$		−	41.1922i		−	1.38310i	0.722329	−	0.691550i	$-0.243072\pi$
$888$	0.169437	+	0.347146i	0.00568593	+	0.0116494i
$889$	2.76248	−	2.76248i	0.0926505	−	0.0926505i
$890$		0			0
$891$	−3.67816	−	2.20436i	−0.123223	−	0.0738487i
$892$	−29.8065	−	29.8065i	−0.997997	−	0.997997i
$893$			4.19755i			0.140466i
$894$	−74.9226	+	36.5687i	−2.50579	+	1.22304i
$895$		0			0
$896$	−0.821169			−0.0274333
$897$	15.1364	−	7.19603i	0.505391	−	0.240269i
$898$	−65.0071			−2.16931
$899$	−10.9889	−	10.9889i	−0.366501	−	0.366501i
$900$		0			0
$901$			60.2395i			2.00687i
$902$	4.51642	+	4.51642i	0.150380	+	0.150380i
$903$	−3.40684	−	1.17198i	−0.113373	−	0.0390012i
$904$	0.130904	+	0.130904i	0.00435381	+	0.00435381i
$905$		0			0
$906$	−69.9195	+	34.1267i	−2.32292	+	1.13378i
$907$			19.4678i			0.646416i	0.946328	+	0.323208i	$0.104761\pi$
$907$			19.4678i			0.646416i	−0.946328	+	0.323208i	$0.895239\pi$
$908$	−21.3726	+	21.3726i	−0.709276	+	0.709276i
$909$	16.8400	−	21.5796i	0.558548	−	0.715750i
$910$		0			0
$911$		−	46.0411i		−	1.52541i	−0.646747	−	0.762705i	$-0.723871\pi$
$911$		−	46.0411i		−	1.52541i	0.646747	−	0.762705i	$-0.276129\pi$
$912$	−14.5018	−	4.98875i	−0.480204	−	0.165194i
$913$	6.10163			0.201934
$914$	−43.7061			−1.44567
$915$		0			0
$916$	−39.7697	+	39.7697i	−1.31403	+	1.31403i
$917$	−7.49732	+	7.49732i	−0.247583	+	0.247583i
$918$	25.7699	+	39.6079i	0.850533	+	1.30725i
$919$	−46.0338			−1.51852			−0.759258	−	0.650790i	$-0.774438\pi$
$919$	−46.0338			−1.51852			−0.759258	+	0.650790i	$0.774438\pi$
$920$		0			0
$921$	13.9276	−	40.4863i	0.458931	−	1.33407i
$922$		−	21.3434i		−	0.702906i
$923$	12.1221	−	11.8752i	0.399002	−	0.390877i
$924$	1.58817	−	0.775165i	0.0522471	−	0.0255011i
$925$		0			0
$926$			22.4646i			0.738233i
$927$	25.9005	+	20.2119i	0.850683	+	0.663845i
$928$	27.2273	−	27.2273i	0.893779	−	0.893779i
$929$	−31.1332	−	31.1332i	−1.02145	−	1.02145i	−0.999765	−	0.0216819i	$-0.993098\pi$
$929$	−31.1332	−	31.1332i	−1.02145	−	1.02145i	−0.0216819	−	0.999765i	$-0.506902\pi$
$930$		0			0
$931$	−9.48369	−	9.48369i	−0.310815	−	0.310815i
$932$		−	30.1753i		−	0.988426i
$933$	−9.24724	−	18.9459i	−0.302741	−	0.620262i
$934$	52.4675	+	52.4675i	1.71679	+	1.71679i
$935$		0			0
$936$	1.05586	−	0.119241i	0.0345117	−	0.00389751i
$937$	−9.36435			−0.305920			−0.152960	−	0.988232i	$-0.548881\pi$
$937$	−9.36435			−0.305920			−0.152960	+	0.988232i	$0.548881\pi$
$938$	−16.0908	−	16.0908i	−0.525385	−	0.525385i
$939$	−21.1034	−	43.2370i	−0.688683	−	1.41099i
$940$		0			0
$941$	7.95452	+	7.95452i	0.259310	+	0.259310i	0.824773	−	0.565463i	$-0.191303\pi$
$941$	7.95452	+	7.95452i	0.259310	+	0.259310i	−0.565463	+	0.824773i	$0.691303\pi$
$942$	24.0438	−	69.8931i	0.783390	−	2.27724i
$943$	12.6428	+	12.6428i	0.411707	+	0.411707i
$944$	29.3805	−	29.3805i	0.956255	−	0.956255i
$945$		0			0
$946$		−	1.90792i		−	0.0620319i
$947$	−26.7873	+	26.7873i	−0.870471	+	0.870471i	−0.992524	−	0.122052i	$-0.961052\pi$
$947$	−26.7873	+	26.7873i	−0.870471	+	0.870471i	0.122052	+	0.992524i	$0.461052\pi$
$948$	−35.4088	+	17.2825i	−1.15002	+	0.561310i
$949$	19.7334	−	19.3315i	0.640573	−	0.627528i
$950$		0			0
$951$	−8.42802	+	24.4994i	−0.273297	+	0.794449i
$952$	−0.464043			−0.0150397
$953$	33.2009			1.07548			0.537741	−	0.843110i	$-0.319278\pi$
$953$	33.2009			1.07548			0.537741	+	0.843110i	$0.319278\pi$
$954$	−9.85121	−	79.8549i	−0.318945	−	2.58540i
$955$		0			0
$956$	−3.93129	+	3.93129i	−0.127147	+	0.127147i
$957$	−1.28506	+	3.73554i	−0.0415400	+	0.120753i
$958$	85.6964			2.76873
$959$	−0.132473			−0.00427779
$960$		0			0
$961$			20.4602i			0.660007i
$962$	−16.4703	−	0.169437i	−0.531023	−	0.00546287i
$963$	−11.8753	−	9.26708i	−0.382675	−	0.298627i
$964$	−2.94020	+	2.94020i	−0.0946976	+	0.0946976i
$965$		0			0
$966$	8.78562	−	4.28814i	0.282673	−	0.137969i
$967$	4.58302	−	4.58302i	0.147380	−	0.147380i	−0.629566	−	0.776947i	$-0.716767\pi$
$967$	4.58302	−	4.58302i	0.147380	−	0.147380i	0.776947	+	0.629566i	$0.216767\pi$
$968$	−0.748316	−	0.748316i	−0.0240518	−	0.0240518i
$969$	−16.8053	−	5.78117i	−0.539864	−	0.185718i
$970$		0			0
$971$			31.4545i			1.00942i	0.863288	+	0.504712i	$0.168401\pi$
$971$			31.4545i			1.00942i	−0.863288	+	0.504712i	$0.831599\pi$
$972$	−20.5642	−	24.4366i	−0.659597	−	0.783804i
$973$	−3.49599	−	3.49599i	−0.112076	−	0.112076i
$974$	−41.3408			−1.32464
$975$		0			0
$976$	−50.0189			−1.60106
$977$	−20.0536	−	20.0536i	−0.641572	−	0.641572i	0.309370	−	0.950942i	$-0.399882\pi$
$977$	−20.0536	−	20.0536i	−0.641572	−	0.641572i	−0.950942	+	0.309370i	$0.899882\pi$
$978$	−49.8538	+	24.3329i	−1.59415	+	0.778082i
$979$		−	2.41104i		−	0.0770571i
$980$		0			0
$981$	−1.36653	−	11.0772i	−0.0436299	−	0.353669i
$982$	15.6730	+	15.6730i	0.500144	+	0.500144i
$983$	−35.7334	+	35.7334i	−1.13972	+	1.13972i	−0.151217	+	0.988501i	$0.548319\pi$
$983$	−35.7334	+	35.7334i	−1.13972	+	1.13972i	−0.988501	+	0.151217i	$0.951681\pi$
$984$	0.497210	+	1.01869i	0.0158505	+	0.0324748i
$985$		0			0
$986$	30.7814	−	30.7814i	0.980281	−	0.980281i
$987$	1.46816	+	3.00799i	0.0467320	+	0.0957455i
$988$	−11.9804	+	11.7364i	−0.381146	+	0.373384i
$989$		−	5.34085i		−	0.169829i
$990$		0			0
$991$	−17.9023			−0.568685			−0.284342	−	0.958723i	$-0.591775\pi$
$991$	−17.9023			−0.568685			−0.284342	+	0.958723i	$0.591775\pi$
$992$	26.1145			0.829135
$993$	−4.65503	−	1.60137i	−0.147723	−	0.0508180i
$994$	6.99931	−	6.99931i	0.222005	−	0.222005i
$995$		0			0
$996$	42.9732	+	14.7831i	1.36166	+	0.468422i
$997$	−29.1464			−0.923075			−0.461538	−	0.887121i	$-0.652702\pi$
$997$	−29.1464			−0.923075			−0.461538	+	0.887121i	$0.652702\pi$
$998$	2.51993			0.0797671
$999$	6.43354	+	9.88825i	0.203548	+	0.312850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.o.n.551.3	yes	8
3.2	odd	2		975.2.o.l.551.2	yes	8
5.2	odd	4		975.2.n.n.824.2		8
5.3	odd	4		975.2.n.p.824.3		8
5.4	even	2		975.2.o.m.551.2	yes	8
13.8	odd	4		975.2.o.l.476.2	✓	8
15.2	even	4		975.2.n.o.824.3		8
15.8	even	4		975.2.n.m.824.2		8
15.14	odd	2		975.2.o.o.551.3	yes	8
39.8	even	4	inner	975.2.o.n.476.3	yes	8
65.8	even	4		975.2.n.o.749.3		8
65.34	odd	4		975.2.o.o.476.3	yes	8
65.47	even	4		975.2.n.m.749.2		8
195.8	odd	4		975.2.n.n.749.2		8
195.47	odd	4		975.2.n.p.749.3		8
195.164	even	4		975.2.o.m.476.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.n.m.749.2		8	65.47	even	4
975.2.n.m.824.2		8	15.8	even	4
975.2.n.n.749.2		8	195.8	odd	4
975.2.n.n.824.2		8	5.2	odd	4
975.2.n.o.749.3		8	65.8	even	4
975.2.n.o.824.3		8	15.2	even	4
975.2.n.p.749.3		8	195.47	odd	4
975.2.n.p.824.3		8	5.3	odd	4
975.2.o.l.476.2	✓	8	13.8	odd	4
975.2.o.l.551.2	yes	8	3.2	odd	2
975.2.o.m.476.2	yes	8	195.164	even	4
975.2.o.m.551.2	yes	8	5.4	even	2
975.2.o.n.476.3	yes	8	39.8	even	4	inner
975.2.o.n.551.3	yes	8	1.1	even	1	trivial
975.2.o.o.476.3	yes	8	65.34	odd	4
975.2.o.o.551.3	yes	8	15.14	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.42282 + 1.42282i) q^{2} +(-0.759725 - 1.55654i) q^{3} +2.04882i q^{4} +(1.13372 - 3.29562i) q^{6} +(0.739083 + 0.739083i) q^{7} +(-0.0694623 + 0.0694623i) q^{8} +(-1.84564 + 2.36509i) q^{9} +(0.336908 - 0.336908i) q^{11} +(3.18907 - 1.55654i) q^{12} +(-0.0370899 + 3.60536i) q^{13} +2.10316i q^{14} +3.89998 q^{16} +4.51945 q^{17} +(-5.99109 + 0.739083i) q^{18} +(1.60536 - 1.60536i) q^{19} +(0.588913 - 1.71191i) q^{21} +0.958716 q^{22} +2.68373 q^{23} +(0.160893 + 0.0553486i) q^{24} +(-5.18254 + 5.07700i) q^{26} +(5.08353 + 1.07599i) q^{27} +(-1.51425 + 1.51425i) q^{28} -4.78690i q^{29} +(2.29562 - 2.29562i) q^{31} +(5.68788 + 5.68788i) q^{32} +(-0.780367 - 0.268453i) q^{33} +(6.43035 + 6.43035i) q^{34} +(-4.84564 - 3.78137i) q^{36} +(1.60536 + 1.60536i) q^{37} +4.56827 q^{38} +(5.64007 - 2.68135i) q^{39} +(4.71090 + 4.71090i) q^{41} +(3.27365 - 1.59782i) q^{42} -1.99008i q^{43} +(0.690263 + 0.690263i) q^{44} +(3.81846 + 3.81846i) q^{46} +(-1.30735 + 1.30735i) q^{47} +(-2.96291 - 6.07047i) q^{48} -5.90751i q^{49} +(-3.43354 - 7.03471i) q^{51} +(-7.38674 - 0.0759906i) q^{52} +13.3290i q^{53} +(5.70199 + 8.76387i) q^{54} -0.102677 q^{56} +(-3.71844 - 1.27918i) q^{57} +(6.81088 - 6.81088i) q^{58} +(7.53351 - 7.53351i) q^{59} -12.8254 q^{61} +6.53251 q^{62} +(-3.11207 + 0.383917i) q^{63} +8.38568i q^{64} +(-0.728361 - 1.49228i) q^{66} +(-7.65079 + 7.65079i) q^{67} +9.25954i q^{68} +(-2.03890 - 4.17734i) q^{69} +(-3.32800 - 3.32800i) q^{71} +(-0.0360822 - 0.292486i) q^{72} +(-5.41762 - 5.41762i) q^{73} +4.56827i q^{74} +(3.28910 + 3.28910i) q^{76} +0.498005 q^{77} +(11.8399 + 4.20971i) q^{78} -11.1032 q^{79} +(-2.18726 - 8.73017i) q^{81} +13.4055i q^{82} +(9.05535 + 9.05535i) q^{83} +(3.50740 + 1.20658i) q^{84} +(2.83152 - 2.83152i) q^{86} +(-7.45100 + 3.63673i) q^{87} +0.0468047i q^{88} +(3.57819 - 3.57819i) q^{89} +(-2.69207 + 2.63725i) q^{91} +5.49849i q^{92} +(-5.31727 - 1.82919i) q^{93} -3.72025 q^{94} +(4.53219 - 13.1746i) q^{96} +(-6.51707 + 6.51707i) q^{97} +(8.40531 - 8.40531i) q^{98} +(0.175007 + 1.41862i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} - 2 q^{3} + 4 q^{6} - 14 q^{7} - 12 q^{8} - 4 q^{9} + 4 q^{11} - 14 q^{12} + 2 q^{13} - 8 q^{16} + 28 q^{17} - 30 q^{18} - 2 q^{19} + 8 q^{21} - 24 q^{22} + 36 q^{23} - 18 q^{24} - 32 q^{26}+ \cdots + 28 q^{99}+O(q^{100}) \) 8 * q + 6 * q^2 - 2 * q^3 + 4 * q^6 - 14 * q^7 - 12 * q^8 - 4 * q^9 + 4 * q^11 - 14 * q^12 + 2 * q^13 - 8 * q^16 + 28 * q^17 - 30 * q^18 - 2 * q^19 + 8 * q^21 - 24 * q^22 + 36 * q^23 - 18 * q^24 - 32 * q^26 - 14 * q^27 + 24 * q^28 - 12 * q^31 - 18 * q^32 - 18 * q^33 + 10 * q^34 - 28 * q^36 - 2 * q^37 + 24 * q^38 - 20 * q^39 + 38 * q^41 + 38 * q^42 - 10 * q^44 + 34 * q^46 + 22 * q^47 - 26 * q^48 - 26 * q^51 - 50 * q^52 + 28 * q^54 + 76 * q^56 + 6 * q^57 - 18 * q^58 - 14 * q^59 - 8 * q^61 - 16 * q^62 - 10 * q^63 + 18 * q^66 - 10 * q^71 - 4 * q^72 - 10 * q^73 + 26 * q^76 - 12 * q^77 - 6 * q^78 - 56 * q^79 + 8 * q^81 + 38 * q^83 + 74 * q^84 - 34 * q^86 - 34 * q^87 + 28 * q^89 + 8 * q^91 - 22 * q^93 + 20 * q^94 + 20 * q^96 + 4 * q^97 - 26 * q^98 + 28 * q^99

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