LMFDB - Embedded newform 961.2.g.b.338.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] 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("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-6,-1,6,6,2,3] 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			338.1
Root			$-0.978148 + 0.207912i$ of defining polynomial
Character	$\chi$	$=$	961.338
Dual form			961.2.g.b.816.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30902 + 0.951057i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.190983 - 0.587785i) q^{4} +(0.190983 - 0.330792i) q^{5} +(0.809017 + 1.40126i) q^{6} +(-2.93444 + 0.623735i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(1.95630 + 0.415823i) q^{9} +(0.0646021 + 0.614648i) q^{10} +(-3.50361 - 3.89116i) q^{11} +(-0.564602 - 0.251377i) q^{12} +(-1.69381 + 0.754131i) q^{13} +(3.24803 - 3.60730i) q^{14} +(-0.309017 - 0.224514i) q^{15} +(3.92705 + 2.85317i) q^{16} +(-2.83448 + 3.14801i) q^{17} +(-2.95630 + 1.31623i) q^{18} +(4.56773 + 2.03368i) q^{19} +(-0.157960 - 0.175433i) q^{20} +(0.313585 + 2.98357i) q^{21} +(8.28700 + 1.76146i) q^{22} +(1.07295 + 3.30220i) q^{23} +(-2.18720 + 0.464905i) q^{24} +(2.42705 + 4.20378i) q^{25} +(1.50000 - 2.59808i) q^{26} +(1.54508 - 4.75528i) q^{27} +(-0.193806 + 1.84395i) q^{28} +(5.16312 - 3.75123i) q^{29} +0.618034 q^{30} -3.38197 q^{32} +(-4.23607 + 3.07768i) q^{33} +(0.716449 - 6.81655i) q^{34} +(-0.354102 + 1.08981i) q^{35} +(0.618034 - 1.07047i) q^{36} +(2.11803 + 3.66854i) q^{37} +(-7.91338 + 1.68204i) q^{38} +(0.572949 + 1.76336i) q^{39} +(-0.835438 - 0.177578i) q^{40} +(0.258409 + 2.45859i) q^{41} +(-3.24803 - 3.60730i) q^{42} +(-2.17603 - 0.968833i) q^{43} +(-2.95630 + 1.31623i) q^{44} +(0.511170 - 0.567712i) q^{45} +(-4.54508 - 3.30220i) q^{46} +(4.54508 + 3.30220i) q^{47} +(3.24803 - 3.60730i) q^{48} +(1.82709 - 0.813473i) q^{49} +(-7.17508 - 3.19455i) q^{50} +(2.83448 + 3.14801i) q^{51} +(0.119779 + 1.13962i) q^{52} +(-0.692728 - 0.147244i) q^{53} +(2.50000 + 7.69421i) q^{54} +(-1.95630 + 0.415823i) q^{55} +(3.35410 + 5.80948i) q^{56} +(2.50000 - 4.33013i) q^{57} +(-3.19098 + 9.82084i) q^{58} +(-0.0551768 + 0.524972i) q^{59} +(-0.190983 + 0.138757i) q^{60} +10.9443 q^{61} -6.00000 q^{63} +(-3.42705 + 2.48990i) q^{64} +(-0.0740275 + 0.704324i) q^{65} +(2.61803 - 8.05748i) q^{66} +(-0.118034 + 0.204441i) q^{67} +(1.30902 + 2.26728i) q^{68} +(3.39626 - 0.721898i) q^{69} +(-0.572949 - 1.76336i) q^{70} +(10.8478 + 2.30578i) q^{71} +(-0.467465 - 4.44764i) q^{72} +(7.73669 + 8.59247i) q^{73} +(-6.26153 - 2.78781i) q^{74} +(4.43444 - 1.97434i) q^{75} +(2.06773 - 2.29644i) q^{76} +(12.7082 + 9.23305i) q^{77} +(-2.42705 - 1.76336i) q^{78} +(1.69381 - 0.754131i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-2.67652 - 2.97258i) q^{82} +(-0.741125 - 7.05133i) q^{83} +(1.81359 + 0.385489i) q^{84} +(0.500000 + 1.53884i) q^{85} +(3.76988 - 0.801313i) q^{86} +(-3.19098 - 5.52694i) q^{87} +(-5.85410 + 10.1396i) q^{88} +(-2.66312 + 8.19624i) q^{89} +(-0.129204 + 1.22930i) q^{90} +(4.50000 - 3.26944i) q^{91} +2.14590 q^{92} -9.09017 q^{94} +(1.54508 - 1.12257i) q^{95} +(-0.353512 + 3.36344i) q^{96} +(-5.78115 + 17.7926i) q^{97} +(-1.61803 + 2.80252i) q^{98} +(-5.23607 - 9.06914i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + 2 q^{6} + 3 q^{7} - 10 q^{8} - 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} - 6 q^{14} + 2 q^{15} + 18 q^{16} + 3 q^{17} - 6 q^{18} + 5 q^{19} + 7 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) $ 8 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + 2 * q^6 + 3 * q^7 - 10 * q^8 - 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 - 6 * q^14 + 2 * q^15 + 18 * q^16 + 3 * q^17 - 6 * q^18 + 5 * q^19 + 7 * q^20 - 3 * q^21 + 6 * q^22 + 22 * q^23 - 5 * q^24 + 6 * q^25 + 12 * q^26 - 10 * q^27 + 6 * q^28 + 10 * q^29 - 4 * q^30 - 36 * q^32 - 16 * q^33 - 11 * q^34 + 24 * q^35 - 4 * q^36 + 8 * q^37 - 10 * q^38 + 18 * q^39 - 10 * q^40 - 8 * q^41 + 6 * q^42 - q^43 - 6 * q^44 + 8 * q^45 - 14 * q^46 + 14 * q^47 - 6 * q^48 + 2 * q^49 - 12 * q^50 - 3 * q^51 + 3 * q^52 - 21 * q^53 + 20 * q^54 + 2 * q^55 + 20 * q^57 - 30 * q^58 - 5 * q^59 - 6 * q^60 + 16 * q^61 - 48 * q^63 - 14 * q^64 + 9 * q^65 + 12 * q^66 + 8 * q^67 + 6 * q^68 + 11 * q^69 - 18 * q^70 + 7 * q^71 + 10 * q^72 - 21 * q^73 - 11 * q^74 + 9 * q^75 - 15 * q^76 + 48 * q^77 - 6 * q^78 + 6 * q^80 + q^81 - 4 * q^82 + 14 * q^83 + 9 * q^84 + 4 * q^85 + 7 * q^86 - 30 * q^87 - 20 * q^88 + 10 * q^89 + 4 * q^90 + 36 * q^91 + 44 * q^92 - 28 * q^94 - 10 * q^95 + 2 * q^96 - 6 * q^97 - 4 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{8}{15}\right)$

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 $

$2$	−1.30902	+	0.951057i	−0.925615	+	0.672499i	−0.944915	−	0.327315i	$-0.893856\pi$
$2$	−1.30902	+	0.951057i	−0.925615	+	0.672499i	0.0193004	+	0.999814i	$0.493856\pi$
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i	−0.922007	−	0.387172i	$-0.873452\pi$
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i	0.982357	−	0.187015i	$-0.0598814\pi$
$4$	0.190983	−	0.587785i	0.0954915	−	0.293893i
$5$	0.190983	−	0.330792i	0.0854102	−	0.147935i	−0.820156	−	0.572140i	$-0.806113\pi$
$5$	0.190983	−	0.330792i	0.0854102	−	0.147935i	0.905566	+	0.424206i	$0.139447\pi$
$6$	0.809017	+	1.40126i	0.330280	+	0.572061i
$7$	−2.93444	+	0.623735i	−1.10912	+	0.235750i	−0.725826	−	0.687879i	$-0.758542\pi$
$7$	−2.93444	+	0.623735i	−1.10912	+	0.235750i	−0.383289	+	0.923628i	$0.625209\pi$
$8$	−0.690983	−	2.12663i	−0.244299	−	0.751876i
$9$	1.95630	+	0.415823i	0.652098	+	0.138608i
$10$	0.0646021	+	0.614648i	0.0204290	+	0.194369i
$11$	−3.50361	−	3.89116i	−1.05638	−	1.17323i	−0.984422	−	0.175820i	$-0.943742\pi$
$11$	−3.50361	−	3.89116i	−1.05638	−	1.17323i	−0.0719569	−	0.997408i	$-0.522924\pi$
$12$	−0.564602	−	0.251377i	−0.162987	−	0.0725663i
$13$	−1.69381	+	0.754131i	−0.469777	+	0.209158i	−0.627951	−	0.778253i	$-0.716106\pi$
$13$	−1.69381	+	0.754131i	−0.469777	+	0.209158i	0.158174	+	0.987411i	$0.449439\pi$
$14$	3.24803	−	3.60730i	0.868072	−	0.964092i
$15$	−0.309017	−	0.224514i	−0.0797878	−	0.0579693i
$16$	3.92705	+	2.85317i	0.981763	+	0.713292i
$17$	−2.83448	+	3.14801i	−0.687463	+	0.763505i	−0.981328	−	0.192342i	$-0.938392\pi$
$17$	−2.83448	+	3.14801i	−0.687463	+	0.763505i	0.293865	+	0.955847i	$0.405058\pi$
$18$	−2.95630	+	1.31623i	−0.696805	+	0.310238i
$19$	4.56773	+	2.03368i	1.04791	+	0.466559i	0.857144	−	0.515077i	$-0.172237\pi$
$19$	4.56773	+	2.03368i	1.04791	+	0.466559i	0.190765	+	0.981636i	$0.438903\pi$
$20$	−0.157960	−	0.175433i	−0.0353210	−	0.0392279i
$21$	0.313585	+	2.98357i	0.0684299	+	0.651067i
$22$	8.28700	+	1.76146i	1.76679	+	0.375544i
$23$	1.07295	+	3.30220i	0.223725	+	0.688556i	0.998418	+	0.0562184i	$0.0179043\pi$
$23$	1.07295	+	3.30220i	0.223725	+	0.688556i	−0.774693	+	0.632337i	$0.782096\pi$
$24$	−2.18720	+	0.464905i	−0.446461	+	0.0948983i
$25$	2.42705	+	4.20378i	0.485410	+	0.840755i
$26$	1.50000	−	2.59808i	0.294174	−	0.509525i
$27$	1.54508	−	4.75528i	0.297352	−	0.915155i
$28$	−0.193806	+	1.84395i	−0.0366260	+	0.348473i
$29$	5.16312	−	3.75123i	0.958767	−	0.696585i	0.00590304	−	0.999983i	$-0.498121\pi$
$29$	5.16312	−	3.75123i	0.958767	−	0.696585i	0.952864	+	0.303397i	$0.0981210\pi$
$30$	0.618034			0.112837
$31$		0			0
$31$		0			0
$32$	−3.38197			−0.597853
$33$	−4.23607	+	3.07768i	−0.737405	+	0.535756i
$34$	0.716449	−	6.81655i	0.122870	−	1.16903i
$35$	−0.354102	+	1.08981i	−0.0598542	+	0.184212i
$36$	0.618034	−	1.07047i	0.103006	−	0.178411i
$37$	2.11803	+	3.66854i	0.348203	+	0.603105i	0.985930	−	0.167157i	$-0.0534588\pi$
$37$	2.11803	+	3.66854i	0.348203	+	0.603105i	−0.637728	+	0.770262i	$0.720125\pi$
$38$	−7.91338	+	1.68204i	−1.28372	+	0.272863i
$39$	0.572949	+	1.76336i	0.0917453	+	0.282363i
$40$	−0.835438	−	0.177578i	−0.132094	−	0.0280775i
$41$	0.258409	+	2.45859i	0.0403566	+	0.383968i	0.995994	+	0.0894215i	$0.0285018\pi$
$41$	0.258409	+	2.45859i	0.0403566	+	0.383968i	−0.955637	+	0.294546i	$0.904832\pi$
$42$	−3.24803	−	3.60730i	−0.501182	−	0.556619i
$43$	−2.17603	−	0.968833i	−0.331842	−	0.147746i	0.234051	−	0.972224i	$-0.424802\pi$
$43$	−2.17603	−	0.968833i	−0.331842	−	0.147746i	−0.565893	+	0.824479i	$0.691468\pi$
$44$	−2.95630	+	1.31623i	−0.445678	+	0.198429i
$45$	0.511170	−	0.567712i	0.0762008	−	0.0846295i
$46$	−4.54508	−	3.30220i	−0.670136	−	0.486882i
$47$	4.54508	+	3.30220i	0.662969	+	0.481675i	0.867664	−	0.497151i	$-0.165620\pi$
$47$	4.54508	+	3.30220i	0.662969	+	0.481675i	−0.204695	+	0.978826i	$0.565620\pi$
$48$	3.24803	−	3.60730i	0.468812	−	0.520669i
$49$	1.82709	−	0.813473i	0.261013	−	0.116210i
$50$	−7.17508	−	3.19455i	−1.01471	−	0.451778i
$51$	2.83448	+	3.14801i	0.396907	+	0.440810i
$52$	0.119779	+	1.13962i	0.0166104	+	0.158037i
$53$	−0.692728	−	0.147244i	−0.0951535	−	0.0202255i	0.160089	−	0.987103i	$-0.448822\pi$
$53$	−0.692728	−	0.147244i	−0.0951535	−	0.0202255i	−0.255242	+	0.966877i	$0.582155\pi$
$54$	2.50000	+	7.69421i	0.340207	+	1.04705i
$55$	−1.95630	+	0.415823i	−0.263787	+	0.0560696i
$56$	3.35410	+	5.80948i	0.448211	+	0.776324i
$57$	2.50000	−	4.33013i	0.331133	−	0.573539i
$58$	−3.19098	+	9.82084i	−0.418997	+	1.28954i
$59$	−0.0551768	+	0.524972i	−0.00718341	+	0.0683456i	−0.997526	−	0.0702939i	$-0.977606\pi$
$59$	−0.0551768	+	0.524972i	−0.00718341	+	0.0683456i	0.990343	+	0.138640i	$0.0442729\pi$
$60$	−0.190983	+	0.138757i	−0.0246558	+	0.0179135i
$61$	10.9443			1.40127			0.700635	−	0.713520i	$-0.252900\pi$
$61$	10.9443			1.40127			0.700635	+	0.713520i	$0.252900\pi$
$62$		0			0
$63$	−6.00000			−0.755929
$64$	−3.42705	+	2.48990i	−0.428381	+	0.311237i
$65$	−0.0740275	+	0.704324i	−0.00918198	+	0.0873607i
$66$	2.61803	−	8.05748i	0.322258	−	0.991807i
$67$	−0.118034	+	0.204441i	−0.0144201	+	0.0249764i	−0.873145	−	0.487460i	$-0.837924\pi$
$67$	−0.118034	+	0.204441i	−0.0144201	+	0.0249764i	0.858725	+	0.512436i	$0.171257\pi$
$68$	1.30902	+	2.26728i	0.158742	+	0.274949i
$69$	3.39626	−	0.721898i	0.408862	−	0.0869063i
$70$	−0.572949	−	1.76336i	−0.0684805	−	0.210761i
$71$	10.8478	+	2.30578i	1.28740	+	0.273645i	0.800246	−	0.599671i	$-0.204702\pi$
$71$	10.8478	+	2.30578i	1.28740	+	0.273645i	0.487153	+	0.873316i	$0.338035\pi$
$72$	−0.467465	−	4.44764i	−0.0550913	−	0.524159i
$73$	7.73669	+	8.59247i	0.905511	+	1.00567i	0.999949	+	0.0101415i	$0.00322818\pi$
$73$	7.73669	+	8.59247i	0.905511	+	1.00567i	−0.0944372	+	0.995531i	$0.530105\pi$
$74$	−6.26153	−	2.78781i	−0.727889	−	0.324077i
$75$	4.43444	−	1.97434i	0.512045	−	0.227977i
$76$	2.06773	−	2.29644i	0.237185	−	0.263420i
$77$	12.7082	+	9.23305i	1.44823	+	1.05220i
$78$	−2.42705	−	1.76336i	−0.274809	−	0.199661i
$79$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$79$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$80$	1.69381	−	0.754131i	0.189373	−	0.0843144i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	−2.67652	−	2.97258i	−0.295572	−	0.328266i
$83$	−0.741125	−	7.05133i	−0.0813490	−	0.773984i	−0.956814	−	0.290702i	$-0.906111\pi$
$83$	−0.741125	−	7.05133i	−0.0813490	−	0.773984i	0.875465	−	0.483282i	$-0.160555\pi$
$84$	1.81359	+	0.385489i	0.197878	+	0.0420603i
$85$	0.500000	+	1.53884i	0.0542326	+	0.166911i
$86$	3.76988	−	0.801313i	0.406517	−	0.0864078i
$87$	−3.19098	−	5.52694i	−0.342109	−	0.592551i
$88$	−5.85410	+	10.1396i	−0.624049	+	1.08089i
$89$	−2.66312	+	8.19624i	−0.282290	+	0.868799i	0.704908	+	0.709299i	$0.250988\pi$
$89$	−2.66312	+	8.19624i	−0.282290	+	0.868799i	−0.987198	+	0.159500i	$0.949012\pi$
$90$	−0.129204	+	1.22930i	−0.0136193	+	0.129579i
$91$	4.50000	−	3.26944i	0.471728	−	0.342731i
$92$	2.14590			0.223725
$93$		0			0
$94$	−9.09017			−0.937579
$95$	1.54508	−	1.12257i	0.158522	−	0.115173i
$96$	−0.353512	+	3.36344i	−0.0360801	+	0.343280i
$97$	−5.78115	+	17.7926i	−0.586987	+	1.80656i	0.00415240	+	0.999991i	$0.498678\pi$
$97$	−5.78115	+	17.7926i	−0.586987	+	1.80656i	−0.591140	+	0.806569i	$0.701322\pi$
$98$	−1.61803	+	2.80252i	−0.163446	+	0.283097i
$99$	−5.23607	−	9.06914i	−0.526245	−	0.911482i
$100$	2.93444	−	0.623735i	0.293444	−	0.0623735i
$101$	2.85410	+	8.78402i	0.283994	+	0.874043i	0.986698	+	0.162561i	$0.0519755\pi$
$101$	2.85410	+	8.78402i	0.283994	+	0.874043i	−0.702705	+	0.711482i	$0.748024\pi$
$102$	−6.70432	−	1.42505i	−0.663827	−	0.141101i
$103$	0.716449	+	6.81655i	0.0705938	+	0.671655i	0.971402	+	0.237439i	$0.0763079\pi$
$103$	0.716449	+	6.81655i	0.0705938	+	0.671655i	−0.900809	+	0.434216i	$0.857025\pi$
$104$	2.77415	+	3.08100i	0.272028	+	0.302117i
$105$	1.04683	+	0.466079i	0.102160	+	0.0454846i
$106$	1.04683	−	0.466079i	0.101677	−	0.0452696i
$107$	−6.75164	+	7.49846i	−0.652706	+	0.724903i	−0.975116	−	0.221697i	$-0.928840\pi$
$107$	−6.75164	+	7.49846i	−0.652706	+	0.724903i	0.322410	+	0.946600i	$0.395507\pi$
$108$	−2.50000	−	1.81636i	−0.240563	−	0.174779i
$109$	−14.8992	−	10.8249i	−1.42708	−	1.03684i	−0.990551	−	0.137148i	$-0.956206\pi$
$109$	−14.8992	−	10.8249i	−1.42708	−	1.03684i	−0.436533	−	0.899688i	$-0.643794\pi$
$110$	2.16535	−	2.40487i	0.206458	−	0.229295i
$111$	3.86984	−	1.72296i	0.367309	−	0.163537i
$112$	−13.3033	−	5.92302i	−1.25705	−	0.559673i
$113$	3.24803	+	3.60730i	0.305549	+	0.339346i	0.876290	−	0.481783i	$-0.160011\pi$
$113$	3.24803	+	3.60730i	0.305549	+	0.339346i	−0.570742	+	0.821130i	$0.693344\pi$
$114$	0.845653	+	8.04585i	0.0792027	+	0.753563i
$115$	1.29726	+	0.275740i	0.120970	+	0.0257129i
$116$	−1.21885	−	3.75123i	−0.113167	−	0.348293i
$117$	−3.62717	+	0.770979i	−0.335332	+	0.0712770i
$118$	−0.427051	−	0.739674i	−0.0393132	−	0.0680925i
$119$	6.35410	−	11.0056i	0.582480	−	1.00888i
$120$	−0.263932	+	0.812299i	−0.0240936	+	0.0741524i
$121$	−1.71598	+	16.3265i	−0.155998	+	1.48423i
$122$	−14.3262	+	10.4086i	−1.29704	+	0.942352i
$123$	2.47214			0.222905
$124$		0			0
$125$	3.76393			0.336656
$126$	7.85410	−	5.70634i	0.699699	−	0.508361i
$127$	−0.602495	+	5.73236i	−0.0534628	+	0.508664i	0.934720	+	0.355385i	$0.115650\pi$
$127$	−0.602495	+	5.73236i	−0.0534628	+	0.508664i	−0.988183	+	0.153280i	$0.951016\pi$
$128$	4.20820	−	12.9515i	0.371956	−	1.14476i
$129$	−1.19098	+	2.06284i	−0.104860	+	0.181623i
$130$	−0.572949	−	0.992377i	−0.0502510	−	0.0870372i
$131$	10.8478	−	2.30578i	0.947779	−	0.201457i	0.292007	−	0.956416i	$-0.405677\pi$
$131$	10.8478	−	2.30578i	0.947779	−	0.201457i	0.655771	+	0.754960i	$0.272344\pi$
$132$	1.00000	+	3.07768i	0.0870388	+	0.267878i
$133$	−14.6722	−	3.11868i	−1.27224	−	0.270423i
$134$	−0.0399263	−	0.379874i	−0.00344911	−	0.0328161i
$135$	−1.27793	−	1.41928i	−0.109986	−	0.122152i
$136$	8.65323	+	3.85266i	0.742008	+	0.330363i
$137$	2.25841	−	1.00551i	0.192949	−	0.0859064i	−0.307988	−	0.951390i	$-0.599656\pi$
$137$	2.25841	−	1.00551i	0.192949	−	0.0859064i	0.500937	+	0.865484i	$0.332989\pi$
$138$	−3.75920	+	4.17501i	−0.320004	+	0.355401i
$139$	0.690983	+	0.502029i	0.0586084	+	0.0425815i	0.616704	−	0.787195i	$-0.288468\pi$
$139$	0.690983	+	0.502029i	0.0586084	+	0.0425815i	−0.558095	+	0.829777i	$0.688468\pi$
$140$	0.572949	+	0.416272i	0.0484230	+	0.0351814i
$141$	3.75920	−	4.17501i	0.316582	−	0.351600i
$142$	−16.3929	+	7.29859i	−1.37566	+	0.612484i
$143$	8.86889	+	3.94868i	0.741653	+	0.330205i
$144$	6.49606	+	7.21460i	0.541338	+	0.601217i
$145$	−0.254808	−	2.42434i	−0.0211607	−	0.201330i
$146$	−18.2994	−	3.88965i	−1.51447	−	0.321910i
$147$	−0.618034	−	1.90211i	−0.0509746	−	0.156884i
$148$	2.56082	−	0.544320i	0.210498	−	0.0447428i
$149$	−6.01722	−	10.4221i	−0.492950	−	0.853814i	0.507017	−	0.861936i	$-0.330748\pi$
$149$	−6.01722	−	10.4221i	−0.492950	−	0.853814i	−0.999967	+	0.00812166i	$0.997415\pi$
$150$	−3.92705	+	6.80185i	−0.320642	+	0.555369i
$151$	5.71885	−	17.6008i	0.465393	−	1.43233i	−0.393094	−	0.919498i	$-0.628595\pi$
$151$	5.71885	−	17.6008i	0.465393	−	1.43233i	0.858487	−	0.512835i	$-0.171405\pi$
$152$	1.16866	−	11.1191i	0.0947911	−	0.901878i
$153$	−6.85410	+	4.97980i	−0.554121	+	0.402593i
$154$	−25.4164			−2.04811
$155$		0			0
$156$	1.14590			0.0917453
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	−0.461601	−	0.887087i	$-0.652725\pi$
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	0.701028	+	0.713134i	$0.252725\pi$
$158$		0			0
$159$	−0.218847	+	0.673542i	−0.0173557	+	0.0534154i
$160$	−0.645898	+	1.11873i	−0.0510627	+	0.0884432i
$161$	−5.20820	−	9.02087i	−0.410464	−	0.710944i
$162$	−1.58268	+	0.336408i	−0.124347	+	0.0264307i
$163$	0.218847	+	0.673542i	0.0171414	+	0.0527559i	0.959261	−	0.282520i	$-0.0911704\pi$
$163$	0.218847	+	0.673542i	0.0171414	+	0.0527559i	−0.942120	+	0.335276i	$0.891170\pi$
$164$	1.49448	+	0.317661i	0.116699	+	0.0248051i
$165$	0.209057	+	1.98904i	0.0162751	+	0.154847i
$166$	7.67636	+	8.52546i	0.595801	+	0.661704i
$167$	−4.35207	−	1.93767i	−0.336773	−	0.149941i	0.231381	−	0.972863i	$-0.425676\pi$
$167$	−4.35207	−	1.93767i	−0.336773	−	0.149941i	−0.568154	+	0.822922i	$0.692342\pi$
$168$	6.12825	−	2.72847i	0.472805	−	0.210506i
$169$	−6.39843	+	7.10618i	−0.492187	+	0.546629i
$170$	−2.11803	−	1.53884i	−0.162446	−	0.118024i
$171$	8.09017	+	5.87785i	0.618671	+	0.449491i
$172$	−0.985051	+	1.09401i	−0.0751095	+	0.0834175i
$173$	11.0449	−	4.91752i	0.839730	−	0.373872i	0.0586313	−	0.998280i	$-0.481326\pi$
$173$	11.0449	−	4.91752i	0.839730	−	0.373872i	0.781098	+	0.624408i	$0.214660\pi$
$174$	9.43349	+	4.20006i	0.715151	+	0.318406i
$175$	−9.74408	−	10.8219i	−0.736584	−	0.818059i
$176$	−2.65674	−	25.2772i	−0.200259	−	1.90534i
$177$	0.516329	+	0.109749i	0.0388097	+	0.00824925i
$178$	−4.30902	−	13.2618i	−0.322974	−	0.994013i
$179$	4.69352	−	0.997638i	0.350810	−	0.0745670i	−0.0291365	−	0.999575i	$-0.509276\pi$
$179$	4.69352	−	0.997638i	0.350810	−	0.0745670i	0.379946	+	0.925008i	$0.375942\pi$
$180$	−0.236068	−	0.408882i	−0.0175955	−	0.0304762i
$181$	−8.50000	+	14.7224i	−0.631800	+	1.09431i	0.355383	+	0.934721i	$0.384350\pi$
$181$	−8.50000	+	14.7224i	−0.631800	+	1.09431i	−0.987184	+	0.159589i	$0.948983\pi$
$182$	−2.78115	+	8.55951i	−0.206153	+	0.634473i
$183$	1.14399	−	10.8843i	0.0845660	−	0.804592i
$184$	6.28115	−	4.56352i	0.463053	−	0.336428i
$185$	1.61803			0.118960
$186$		0			0
$187$	22.1803			1.62199
$188$	2.80902	−	2.04087i	0.204869	−	0.148846i
$189$	−1.56793	+	14.9178i	−0.114050	+	1.08511i
$190$	−0.954915	+	2.93893i	−0.0692768	+	0.213212i
$191$	2.45492	−	4.25204i	0.177631	−	0.307667i	−0.763437	−	0.645882i	$-0.776490\pi$
$191$	2.45492	−	4.25204i	0.177631	−	0.307667i	0.941069	+	0.338215i	$0.109823\pi$
$192$	2.11803	+	3.66854i	0.152856	+	0.264754i
$193$	4.51712	−	0.960143i	0.325149	−	0.0691126i	−0.0424452	−	0.999099i	$-0.513515\pi$
$193$	4.51712	−	0.960143i	0.325149	−	0.0691126i	0.367594	+	0.929986i	$0.380181\pi$
$194$	−9.35410	−	28.7890i	−0.671585	−	2.06693i
$195$	0.692728	+	0.147244i	0.0496073	+	0.0105444i
$196$	−0.129204	−	1.22930i	−0.00922888	−	0.0878069i
$197$	−6.96994	−	7.74090i	−0.496587	−	0.551516i	0.441794	−	0.897116i	$-0.354342\pi$
$197$	−6.96994	−	7.74090i	−0.496587	−	0.551516i	−0.938382	+	0.345600i	$0.887675\pi$
$198$	15.4794	+	6.89186i	1.10007	+	0.489783i
$199$	−12.1427	+	5.40626i	−0.860770	+	0.383240i	−0.789156	−	0.614193i	$-0.789482\pi$
$199$	−12.1427	+	5.40626i	−0.860770	+	0.383240i	−0.0716143	+	0.997432i	$0.522815\pi$
$200$	7.26281	−	8.06617i	0.513558	−	0.570364i
$201$	0.190983	+	0.138757i	0.0134709	+	0.00978718i
$202$	−12.0902	−	8.78402i	−0.850661	−	0.618042i
$203$	−12.8111	+	14.2282i	−0.899163	+	0.998622i
$204$	2.39169	−	1.06485i	0.167452	−	0.0745544i
$205$	0.862635	+	0.384070i	0.0602491	+	0.0268246i
$206$	−7.42077	−	8.24160i	−0.517030	−	0.574220i
$207$	0.725874	+	6.90623i	0.0504517	+	0.480016i
$208$	−8.80333	−	1.87121i	−0.610401	−	0.129745i
$209$	−8.09017	−	24.8990i	−0.559609	−	1.72230i
$210$	−1.81359	+	0.385489i	−0.125149	+	0.0266013i
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$	−0.218847	+	0.379054i	−0.0150305	+	0.0260336i
$213$	3.42705	−	10.5474i	0.234818	−	0.722694i
$214$	1.70656	−	16.2368i	0.116658	−	1.10992i
$215$	−0.736068	+	0.534785i	−0.0501994	+	0.0364720i
$216$	−11.1803			−0.760726
$217$		0			0
$218$	29.7984			2.01820
$219$	9.35410	−	6.79615i	0.632092	−	0.459241i
$220$	−0.129204	+	1.22930i	−0.00871095	+	0.0828792i
$221$	2.42705	−	7.46969i	0.163261	−	0.502466i
$222$	−3.42705	+	5.93583i	−0.230009	+	0.398387i
$223$	6.35410	+	11.0056i	0.425502	+	0.736991i	0.996467	−	0.0839830i	$-0.0267642\pi$
$223$	6.35410	+	11.0056i	0.425502	+	0.736991i	−0.570965	+	0.820974i	$0.693431\pi$
$224$	9.92419	−	2.10945i	0.663088	−	0.140944i
$225$	3.00000	+	9.23305i	0.200000	+	0.615537i
$226$	−7.68247	−	1.63296i	−0.511030	−	0.108623i
$227$	−2.27273	−	21.6235i	−0.150846	−	1.43520i	−0.763987	−	0.645231i	$-0.776761\pi$
$227$	−2.27273	−	21.6235i	−0.150846	−	1.43520i	0.613141	−	0.789973i	$-0.289906\pi$
$228$	−2.06773	−	2.29644i	−0.136939	−	0.152086i
$229$	−2.52498	−	1.12419i	−0.166855	−	0.0742887i	0.321609	−	0.946872i	$-0.395776\pi$
$229$	−2.52498	−	1.12419i	−0.166855	−	0.0742887i	−0.488465	+	0.872584i	$0.662443\pi$
$230$	−1.96038	+	0.872815i	−0.129263	+	0.0575517i
$231$	10.5108	−	11.6735i	0.691563	−	0.768058i
$232$	−11.5451	−	8.38800i	−0.757972	−	0.550699i
$233$	4.69098	+	3.40820i	0.307317	+	0.223279i	0.730744	−	0.682651i	$-0.239173\pi$
$233$	4.69098	+	3.40820i	0.307317	+	0.223279i	−0.423428	+	0.905930i	$0.639173\pi$
$234$	4.01478	−	4.45887i	0.262455	−	0.291485i
$235$	1.96038	−	0.872815i	0.127881	−	0.0569362i
$236$	0.298033	+	0.132693i	0.0194003	+	0.00863757i
$237$		0			0
$238$	2.14935	+	20.4497i	0.139321	+	1.32555i
$239$	−13.1232	−	2.78943i	−0.848871	−	0.180433i	−0.237117	−	0.971481i	$-0.576202\pi$
$239$	−13.1232	−	2.78943i	−0.848871	−	0.180433i	−0.611754	+	0.791048i	$0.709536\pi$
$240$	−0.572949	−	1.76336i	−0.0369837	−	0.113824i
$241$	17.0903	−	3.63266i	1.10088	−	0.234000i	0.378575	−	0.925570i	$-0.376414\pi$
$241$	17.0903	−	3.63266i	1.10088	−	0.234000i	0.722309	+	0.691570i	$0.243081\pi$
$242$	−13.2812	−	23.0036i	−0.853745	−	1.47873i
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	2.09017	−	6.43288i	0.133809	−	0.411823i
$245$	0.0798526	−	0.759747i	0.00510160	−	0.0485385i
$246$	−3.23607	+	2.35114i	−0.206324	+	0.149903i
$247$	−9.27051			−0.589868
$248$		0			0
$249$	−7.09017			−0.449321
$250$	−4.92705	+	3.57971i	−0.311614	+	0.226401i
$251$	1.77116	−	16.8514i	0.111795	−	1.06365i	−0.784480	−	0.620154i	$-0.787070\pi$
$251$	1.77116	−	16.8514i	0.111795	−	1.06365i	0.896274	−	0.443500i	$-0.146263\pi$
$252$	−1.14590	+	3.52671i	−0.0721848	+	0.222162i
$253$	9.09017	−	15.7446i	0.571494	−	0.989857i
$254$	−4.66312	−	8.07676i	−0.292590	−	0.506781i
$255$	1.58268	−	0.336408i	0.0991110	−	0.0210667i
$256$	4.19098	+	12.8985i	0.261936	+	0.806157i
$257$	24.8610	+	5.28437i	1.55079	+	0.329630i	0.902134	−	0.431455i	$-0.142000\pi$
$257$	24.8610	+	5.28437i	1.55079	+	0.329630i	0.648652	+	0.761085i	$0.275333\pi$
$258$	−0.402863	−	3.83299i	−0.0250812	−	0.238631i
$259$	−8.50345	−	9.44404i	−0.528379	−	0.586824i
$260$	0.399853	+	0.178026i	0.0247979	+	0.0110407i
$261$	11.6604	−	5.19156i	0.721763	−	0.321349i
$262$	−12.0071	+	13.3352i	−0.741799	+	0.823851i
$263$	−11.1631	−	8.11048i	−0.688347	−	0.500114i	0.187769	−	0.982213i	$-0.439874\pi$
$263$	−11.1631	−	8.11048i	−0.688347	−	0.500114i	−0.876116	+	0.482100i	$0.839874\pi$
$264$	9.47214	+	6.88191i	0.582970	+	0.423552i
$265$	−0.181006	+	0.201028i	−0.0111191	+	0.0123491i
$266$	22.1722	−	9.87171i	1.35947	−	0.605273i
$267$	7.87297	+	3.50527i	0.481818	+	0.214519i
$268$	0.0976248	+	0.108423i	0.00596339	+	0.00662301i
$269$	0.378188	+	3.59821i	0.0230585	+	0.219387i	0.999983	+	0.00580280i	$0.00184710\pi$
$269$	0.378188	+	3.59821i	0.0230585	+	0.219387i	−0.976925	+	0.213584i	$0.931486\pi$
$270$	3.02264	+	0.642482i	0.183952	+	0.0391002i
$271$	−3.26393	−	10.0453i	−0.198270	−	0.610212i	−0.999923	−	0.0124220i	$-0.996046\pi$
$271$	−3.26393	−	10.0453i	−0.198270	−	0.610212i	0.801653	−	0.597790i	$-0.203954\pi$
$272$	−20.1130	+	4.27514i	−1.21953	+	0.259219i
$273$	−2.78115	−	4.81710i	−0.168323	−	0.291544i
$274$	−2.00000	+	3.46410i	−0.120824	+	0.209274i
$275$	7.85410	−	24.1724i	0.473620	−	1.45765i
$276$	0.224307	−	2.13414i	0.0135017	−	0.128460i
$277$	1.88197	−	1.36733i	0.113076	−	0.0821548i	−0.529810	−	0.848116i	$-0.677737\pi$
$277$	1.88197	−	1.36733i	0.113076	−	0.0821548i	0.642886	+	0.765962i	$0.277737\pi$
$278$	−1.38197			−0.0828848
$279$		0			0
$280$	2.56231			0.153127
$281$	8.11803	−	5.89810i	0.484281	−	0.351851i	−0.318700	−	0.947856i	$-0.603246\pi$
$281$	8.11803	−	5.89810i	0.484281	−	0.351851i	0.802981	+	0.596005i	$0.203246\pi$
$282$	−0.950181	+	9.04037i	−0.0565825	+	0.538346i
$283$	−4.19098	+	12.8985i	−0.249128	+	0.766737i	0.745802	+	0.666168i	$0.232067\pi$
$283$	−4.19098	+	12.8985i	−0.249128	+	0.766737i	−0.994930	+	0.100570i	$0.967933\pi$
$284$	3.42705	−	5.93583i	0.203358	−	0.352226i
$285$	−0.954915	−	1.65396i	−0.0565643	−	0.0979722i
$286$	−15.3649	+	3.26592i	−0.908548	+	0.193118i
$287$	−2.29180	−	7.05342i	−0.135280	−	0.416350i
$288$	−6.61612	−	1.40630i	−0.389859	−	0.0828671i
$289$	−0.0987033	−	0.939099i	−0.00580608	−	0.0552411i
$290$	2.63923	+	2.93117i	0.154981	+	0.172124i
$291$	17.0908	+	7.60931i	1.00188	+	0.446066i
$292$	6.52810	−	2.90650i	0.382028	−	0.170090i
$293$	−2.51856	+	2.79715i	−0.147136	+	0.163411i	−0.812208	−	0.583369i	$-0.801734\pi$
$293$	−2.51856	+	2.79715i	−0.147136	+	0.163411i	0.665072	+	0.746780i	$0.268401\pi$
$294$	2.61803	+	1.90211i	0.152687	+	0.110933i
$295$	0.163119	+	0.118513i	0.00949715	+	0.00690009i
$296$	6.33810	−	7.03917i	0.368394	−	0.409143i
$297$	−23.9169	+	10.6485i	−1.38780	+	0.617889i
$298$	17.7887	+	7.92003i	1.03047	+	0.458795i
$299$	−4.30766	−	4.78414i	−0.249118	−	0.276674i
$300$	−0.313585	−	2.98357i	−0.0181049	−	0.172256i
$301$	6.98974	+	1.48572i	0.402882	+	0.0856352i
$302$	9.25329	+	28.4787i	0.532467	+	1.63876i
$303$	9.03424	−	1.92029i	0.519003	−	0.110318i
$304$	12.1353	+	21.0189i	0.696005	+	1.20552i
$305$	2.09017	−	3.62028i	0.119683	−	0.207297i
$306$	4.23607	−	13.0373i	0.242160	−	0.745292i
$307$	0.532068	−	5.06229i	0.0303667	−	0.288920i	−0.968791	−	0.247880i	$-0.920266\pi$
$307$	0.532068	−	5.06229i	0.0303667	−	0.288920i	0.999158	−	0.0410401i	$-0.0130671\pi$
$308$	7.85410	−	5.70634i	0.447529	−	0.325149i
$309$	6.85410			0.389916
$310$		0			0
$311$	7.52786			0.426866			0.213433	−	0.976958i	$-0.431535\pi$
$311$	7.52786			0.426866			0.213433	+	0.976958i	$0.431535\pi$
$312$	3.35410	−	2.43690i	0.189889	−	0.137962i
$313$	0.338261	−	3.21834i	0.0191197	−	0.181911i	−0.980794	−	0.195046i	$-0.937514\pi$
$313$	0.338261	−	3.21834i	0.0191197	−	0.181911i	0.999914	+	0.0131347i	$0.00418103\pi$
$314$	−1.85410	+	5.70634i	−0.104633	+	0.322027i
$315$	−1.14590	+	1.98475i	−0.0645640	+	0.111828i
$316$		0			0
$317$	9.67246	−	2.05594i	0.543259	−	0.115473i	0.0718954	−	0.997412i	$-0.477095\pi$
$317$	9.67246	−	2.05594i	0.543259	−	0.115473i	0.471364	+	0.881939i	$0.343762\pi$
$318$	−0.354102	−	1.08981i	−0.0198571	−	0.0611137i
$319$	−32.6862	−	6.94766i	−1.83007	−	0.388994i
$320$	0.169131	+	1.60917i	0.00945469	+	0.0899554i
$321$	6.75164	+	7.49846i	0.376840	+	0.418523i
$322$	15.3970	+	6.85518i	0.858041	+	0.382024i
$323$	−19.3492	+	8.61482i	−1.07662	+	0.479341i
$324$	0.413545	−	0.459289i	0.0229747	−	0.0255160i
$325$	−7.28115	−	5.29007i	−0.403886	−	0.293440i
$326$	−0.927051	−	0.673542i	−0.0513446	−	0.0373040i
$327$	−12.3230	+	13.6861i	−0.681462	+	0.756841i
$328$	5.04996	−	2.24838i	0.278837	−	0.124146i
$329$	−15.3970	−	6.85518i	−0.848863	−	0.377938i
$330$	−2.16535	−	2.40487i	−0.119199	−	0.132384i
$331$	2.32790	+	22.1485i	0.127953	+	1.21739i	0.850464	+	0.526033i	$0.176321\pi$
$331$	2.32790	+	22.1485i	0.127953	+	1.21739i	−0.722511	+	0.691359i	$0.757012\pi$
$332$	−4.28621	−	0.911062i	−0.235236	−	0.0500010i
$333$	2.61803	+	8.05748i	0.143467	+	0.441547i
$334$	7.53976	−	1.60263i	0.412557	−	0.0876918i
$335$	0.0450850	+	0.0780895i	0.00246326	+	0.00426648i
$336$	−7.28115	+	12.6113i	−0.397219	+	0.688004i
$337$	−8.64590	+	26.6093i	−0.470972	+	1.44950i	0.380342	+	0.924846i	$0.375806\pi$
$337$	−8.64590	+	26.6093i	−0.470972	+	1.44950i	−0.851314	+	0.524657i	$0.824194\pi$
$338$	1.61728	−	15.3874i	0.0879684	−	0.836963i
$339$	3.92705	−	2.85317i	0.213288	−	0.154963i
$340$	1.00000			0.0542326
$341$		0			0
$342$	−16.1803			−0.874933
$343$	12.1353	−	8.81678i	0.655242	−	0.476061i
$344$	−0.556743	+	5.29706i	−0.0300176	+	0.285598i
$345$	0.409830	−	1.26133i	0.0220645	−	0.0679076i
$346$	−9.78115	+	16.9415i	−0.525838	+	0.910778i
$347$	16.0623	+	27.8207i	0.862270	+	1.49350i	0.869733	+	0.493523i	$0.164291\pi$
$347$	16.0623	+	27.8207i	0.862270	+	1.49350i	−0.00746305	+	0.999972i	$0.502376\pi$
$348$	−3.85808	+	0.820060i	−0.206815	+	0.0439598i
$349$	−1.01722	−	3.13068i	−0.0544506	−	0.167582i	0.920133	−	0.391606i	$-0.128080\pi$
$349$	−1.01722	−	3.13068i	−0.0544506	−	0.167582i	−0.974584	+	0.224025i	$0.928080\pi$
$350$	23.0474	+	4.89888i	1.23194	+	0.261856i
$351$	0.969032	+	9.21973i	0.0517231	+	0.492113i
$352$	11.8491	+	13.1598i	0.631559	+	0.701418i
$353$	−31.6251	−	14.0804i	−1.68324	−	0.749425i	−0.999812	−	0.0194046i	$-0.993823\pi$
$353$	−31.6251	−	14.0804i	−1.68324	−	0.749425i	−0.683425	−	0.730021i	$-0.739510\pi$
$354$	−0.780261	+	0.347395i	−0.0414704	+	0.0184638i
$355$	2.83448	−	3.14801i	0.150439	−	0.167079i
$356$	4.30902	+	3.13068i	0.228377	+	0.165926i
$357$	−10.2812	−	7.46969i	−0.544136	−	0.395338i
$358$	−5.19508	+	5.76973i	−0.274569	+	0.304939i
$359$	−8.83742	+	3.93467i	−0.466421	+	0.207664i	−0.626471	−	0.779445i	$-0.715501\pi$
$359$	−8.83742	+	3.93467i	−0.466421	+	0.207664i	0.160050	+	0.987109i	$0.448835\pi$
$360$	−1.56052	−	0.694789i	−0.0822467	−	0.0366186i
$361$	4.01478	+	4.45887i	0.211304	+	0.234677i
$362$	−2.87522	−	27.3559i	−0.151118	−	1.43779i
$363$	16.0577	+	3.41316i	0.842809	+	0.179145i
$364$	−1.06231	−	3.26944i	−0.0556800	−	0.171365i
$365$	4.31990	−	0.918223i	0.226114	−	0.0480620i
$366$	8.85410	+	15.3358i	0.462811	+	0.801613i
$367$	1.36475	−	2.36381i	0.0712391	−	0.123390i	−0.828206	−	0.560425i	$-0.810638\pi$
$367$	1.36475	−	2.36381i	0.0712391	−	0.123390i	0.899445	+	0.437035i	$0.143971\pi$
$368$	−5.20820	+	16.0292i	−0.271496	+	0.835580i
$369$	−0.516817	+	4.91719i	−0.0269044	+	0.255979i
$370$	−2.11803	+	1.53884i	−0.110111	+	0.0800006i
$371$	2.12461			0.110304
$372$		0			0
$373$	−31.6525			−1.63890			−0.819452	−	0.573148i	$-0.805722\pi$
$373$	−31.6525			−1.63890			−0.819452	+	0.573148i	$0.805722\pi$
$374$	−29.0344	+	21.0948i	−1.50134	+	1.09078i
$375$	0.393438	−	3.74331i	0.0203171	−	0.193304i
$376$	3.88197	−	11.9475i	0.200197	−	0.616143i
$377$	−5.91641	+	10.2475i	−0.304711	+	0.527774i
$378$	−12.1353	−	21.0189i	−0.624170	−	1.08109i
$379$	−8.23249	+	1.74987i	−0.422875	+	0.0898848i	−0.414433	−	0.910080i	$-0.636020\pi$
$379$	−8.23249	+	1.74987i	−0.422875	+	0.0898848i	−0.00844109	+	0.999964i	$0.502687\pi$
$380$	−0.364745	−	1.12257i	−0.0187110	−	0.0575866i
$381$	5.63798	+	1.19839i	0.288842	+	0.0613953i
$382$	0.830403	+	7.90075i	0.0424871	+	0.404238i
$383$	−6.78893	−	7.53987i	−0.346898	−	0.385269i	0.544295	−	0.838894i	$-0.316797\pi$
$383$	−6.78893	−	7.53987i	−0.346898	−	0.385269i	−0.891193	+	0.453625i	$0.850131\pi$
$384$	−12.4407	−	5.53895i	−0.634861	−	0.282659i
$385$	5.48127	−	2.44042i	0.279352	−	0.124375i
$386$	−4.99983	+	5.55288i	−0.254485	+	0.282634i
$387$	−3.85410	−	2.80017i	−0.195915	−	0.142341i
$388$	9.35410	+	6.79615i	0.474883	+	0.345022i
$389$	19.4509	−	21.6024i	0.986199	−	1.09528i	−0.00924722	−	0.999957i	$-0.502944\pi$
$389$	19.4509	−	21.6024i	0.986199	−	1.09528i	0.995446	−	0.0953274i	$-0.0303898\pi$
$390$	−1.04683	+	0.466079i	−0.0530083	+	0.0236008i
$391$	−13.4366	−	5.98237i	−0.679519	−	0.302541i
$392$	−2.99244	−	3.32344i	−0.151141	−	0.167859i
$393$	−1.15924	−	11.0294i	−0.0584758	−	0.556360i
$394$	16.4858	+	3.50416i	0.830543	+	0.176537i
$395$		0			0
$396$	−6.33070	+	1.34563i	−0.318130	+	0.0676206i
$397$	−14.8541	−	25.7281i	−0.745506	−	1.29125i	−0.949958	−	0.312378i	$-0.898875\pi$
$397$	−14.8541	−	25.7281i	−0.745506	−	1.29125i	0.204452	−	0.978877i	$-0.434459\pi$
$398$	10.7533	−	18.6252i	0.539014	−	0.933599i
$399$	−4.63525	+	14.2658i	−0.232053	+	0.714186i
$400$	−2.46293	+	23.4332i	−0.123147	+	1.17166i
$401$	−19.2812	+	14.0086i	−0.962855	+	0.699555i	−0.953812	−	0.300404i	$-0.902878\pi$
$401$	−19.2812	+	14.0086i	−0.962855	+	0.699555i	−0.00904282	+	0.999959i	$0.502878\pi$
$402$	−0.381966			−0.0190507
$403$		0			0
$404$	5.70820			0.283994
$405$	0.309017	−	0.224514i	0.0153552	−	0.0111562i
$406$	3.23816	−	30.8090i	0.160707	−	1.52903i
$407$	6.85410	−	21.0948i	0.339745	−	1.04563i
$408$	4.73607	−	8.20311i	0.234470	−	0.406114i
$409$	−8.09017	−	14.0126i	−0.400033	−	0.692878i	0.593696	−	0.804689i	$-0.297668\pi$
$409$	−8.09017	−	14.0126i	−0.400033	−	0.692878i	−0.993729	+	0.111811i	$0.964335\pi$
$410$	−1.49448	+	0.317661i	−0.0738069	+	0.0156881i
$411$	−0.763932	−	2.35114i	−0.0376820	−	0.115973i
$412$	4.14350	+	0.880728i	0.204136	+	0.0433904i
$413$	−0.165530	−	1.57492i	−0.00814522	−	0.0774966i
$414$	−7.51840	−	8.35003i	−0.369509	−	0.410381i
$415$	−2.47407	−	1.10153i	−0.121447	−	0.0540718i
$416$	5.72840	−	2.55045i	0.280858	−	0.125046i
$417$	0.571506	−	0.634721i	0.0279868	−	0.0310824i
$418$	34.2705	+	24.8990i	1.67623	+	1.21785i
$419$	3.61803	+	2.62866i	0.176753	+	0.128418i	0.672644	−	0.739966i	$-0.265159\pi$
$419$	3.61803	+	2.62866i	0.176753	+	0.128418i	−0.495891	+	0.868385i	$0.665159\pi$
$420$	0.473881	−	0.526298i	0.0231230	−	0.0256807i
$421$	17.5730	−	7.82401i	0.856457	−	0.381319i	0.0689462	−	0.997620i	$-0.478036\pi$
$421$	17.5730	−	7.82401i	0.856457	−	0.381319i	0.787510	+	0.616301i	$0.211370\pi$
$422$	−11.8252	−	5.26491i	−0.575641	−	0.256292i
$423$	7.51840	+	8.35003i	0.365557	+	0.405992i
$424$	0.165530	+	1.57492i	0.00803887	+	0.0764847i
$425$	−20.1130	−	4.27514i	−0.975622	−	0.207375i
$426$	5.54508	+	17.0660i	0.268660	+	0.826851i
$427$	−32.1153	+	6.82633i	−1.55417	+	0.330349i
$428$	3.11803	+	5.40059i	0.150716	+	0.261048i
$429$	4.85410	−	8.40755i	0.234358	−	0.405920i
$430$	0.454915	−	1.40008i	0.0219380	−	0.0675181i
$431$	−2.58854	+	24.6283i	−0.124685	+	1.18630i	0.735934	+	0.677053i	$0.236743\pi$
$431$	−2.58854	+	24.6283i	−0.124685	+	1.18630i	−0.860619	+	0.509249i	$0.829923\pi$
$432$	19.6353	−	14.2658i	0.944702	−	0.686366i
$433$	27.4164			1.31755			0.658774	−	0.752341i	$-0.271075\pi$
$433$	27.4164			1.31755			0.658774	+	0.752341i	$0.271075\pi$
$434$		0			0
$435$	−2.43769			−0.116878
$436$	−9.20820	+	6.69015i	−0.440993	+	0.320400i
$437$	−1.81469	+	17.2656i	−0.0868082	+	0.825925i
$438$	−5.78115	+	17.7926i	−0.276234	+	0.850161i
$439$	5.91641	−	10.2475i	0.282375	−	0.489087i	−0.689594	−	0.724196i	$-0.742211\pi$
$439$	5.91641	−	10.2475i	0.282375	−	0.489087i	0.971969	+	0.235108i	$0.0755445\pi$
$440$	2.23607	+	3.87298i	0.106600	+	0.184637i
$441$	3.91259	−	0.831647i	0.186314	−	0.0396022i
$442$	3.92705	+	12.0862i	0.186791	+	0.574883i
$443$	0.856259	+	0.182003i	0.0406821	+	0.00864724i	0.228208	−	0.973612i	$-0.426713\pi$
$443$	0.856259	+	0.182003i	0.0406821	+	0.00864724i	−0.187526	+	0.982260i	$0.560047\pi$
$444$	−0.273659	−	2.60369i	−0.0129873	−	0.123566i
$445$	2.20264	+	2.44628i	0.104415	+	0.115965i
$446$	−18.7846	−	8.36344i	−0.889477	−	0.396021i
$447$	−10.9940	+	4.89485i	−0.519999	+	0.231518i
$448$	8.50345	−	9.44404i	0.401750	−	0.446189i
$449$	27.5623	+	20.0252i	1.30075	+	0.945047i	0.999963	−	0.00864558i	$-0.00275201\pi$
$449$	27.5623	+	20.0252i	1.30075	+	0.945047i	0.300783	+	0.953693i	$0.402752\pi$
$450$	−12.7082	−	9.23305i	−0.599070	−	0.435250i
$451$	8.66141	−	9.61947i	0.407850	−	0.452963i
$452$	2.74064	−	1.22021i	0.128909	−	0.0573938i
$453$	−16.9066	−	7.52730i	−0.794341	−	0.353664i
$454$	23.5402	+	26.1441i	1.10480	+	1.22700i
$455$	−0.222082	−	2.11297i	−0.0104114	−	0.0990577i
$456$	−10.9360	−	2.32452i	−0.512126	−	0.108856i
$457$	8.26393	+	25.4338i	0.386570	+	1.18974i	0.935335	+	0.353764i	$0.115098\pi$
$457$	8.26393	+	25.4338i	0.386570	+	1.18974i	−0.548764	+	0.835977i	$0.684902\pi$
$458$	4.37441	−	0.929809i	0.204403	−	0.0434471i
$459$	10.5902	+	18.3427i	0.494307	+	0.856164i
$460$	0.409830	−	0.709846i	0.0191084	−	0.0330968i
$461$	−9.80902	+	30.1891i	−0.456851	+	1.40604i	0.412096	+	0.911140i	$0.364797\pi$
$461$	−9.80902	+	30.1891i	−0.456851	+	1.40604i	−0.868948	+	0.494904i	$0.835203\pi$
$462$	−2.65674	+	25.2772i	−0.123603	+	1.17600i
$463$	−7.38197	+	5.36331i	−0.343069	+	0.249254i	−0.745956	−	0.665996i	$-0.768007\pi$
$463$	−7.38197	+	5.36331i	−0.343069	+	0.249254i	0.402887	+	0.915250i	$0.368007\pi$
$464$	30.9787			1.43815
$465$		0			0
$466$	−9.38197			−0.434611
$467$	−31.3713	+	22.7926i	−1.45169	+	1.05472i	−0.466259	+	0.884648i	$0.654399\pi$
$467$	−31.3713	+	22.7926i	−1.45169	+	1.05472i	−0.985432	+	0.170068i	$0.945601\pi$
$468$	−0.239558	+	2.27924i	−0.0110736	+	0.105358i
$469$	0.218847	−	0.673542i	0.0101054	−	0.0311013i
$470$	−1.73607	+	3.00696i	−0.0800788	+	0.138701i
$471$	−1.85410	−	3.21140i	−0.0854325	−	0.147973i
$472$	1.15455	−	0.245406i	0.0531423	−	0.0112957i
$473$	3.85410	+	11.8617i	0.177212	+	0.545402i
$474$		0			0
$475$	2.53696	+	24.1376i	0.116404	+	1.10751i
$476$	−5.25542	−	5.83674i	−0.240882	−	0.267526i
$477$	−1.29395	−	0.576105i	−0.0592460	−	0.0263780i
$478$	19.8314	−	8.82952i	0.907069	−	0.403853i
$479$	5.98489	−	6.64689i	0.273456	−	0.303704i	−0.590737	−	0.806864i	$-0.701163\pi$
$479$	5.98489	−	6.64689i	0.273456	−	0.303704i	0.864193	+	0.503160i	$0.167829\pi$
$480$	1.04508	+	0.759299i	0.0477014	+	0.0346571i
$481$	−6.35410	−	4.61653i	−0.289722	−	0.210495i
$482$	−18.9167	+	21.0091i	−0.861630	+	0.956938i
$483$	−9.51586	+	4.23673i	−0.432987	+	0.192778i
$484$	9.26874	+	4.12671i	0.421306	+	0.187578i
$485$	4.78154	+	5.31044i	0.217119	+	0.241135i
$486$	2.70609	+	25.7467i	0.122751	+	1.16790i
$487$	41.0069	+	8.71628i	1.85820	+	0.394972i	0.994111	−	0.108369i	$-0.0345627\pi$
$487$	41.0069	+	8.71628i	1.85820	+	0.394972i	0.864088	+	0.503341i	$0.167896\pi$
$488$	−7.56231	−	23.2744i	−0.342330	−	1.05358i
$489$	0.692728	−	0.147244i	0.0313262	−	0.00665860i
$490$	0.618034	+	1.07047i	0.0279199	+	0.0483587i
$491$	−10.7984	+	18.7033i	−0.487324	+	0.844070i	−0.999894	−	0.0145759i	$-0.995360\pi$
$491$	−10.7984	+	18.7033i	−0.487324	+	0.844070i	0.512570	+	0.858645i	$0.328694\pi$
$492$	0.472136	−	1.45309i	0.0212855	−	0.0655101i
$493$	−2.82587	+	26.8863i	−0.127271	+	1.21090i
$494$	12.1353	−	8.81678i	0.545991	−	0.396686i
$495$	−4.00000			−0.179787
$496$		0			0
$497$	−33.2705			−1.49239
$498$	9.28115	−	6.74315i	0.415898	−	0.302168i
$499$	−1.13456	+	10.7946i	−0.0507900	+	0.483235i	0.939330	+	0.343014i	$0.111448\pi$
$499$	−1.13456	+	10.7946i	−0.0507900	+	0.483235i	−0.990120	+	0.140221i	$0.955219\pi$
$500$	0.718847	−	2.21238i	0.0321478	−	0.0989408i
$501$	−2.38197	+	4.12569i	−0.106418	+	0.184322i
$502$	13.7082	+	23.7433i	0.611827	+	1.05972i
$503$	−19.4202	+	4.12790i	−0.865906	+	0.184054i	−0.619389	−	0.785084i	$-0.712619\pi$
$503$	−19.4202	+	4.12790i	−0.865906	+	0.184054i	−0.246517	+	0.969138i	$0.579286\pi$
$504$	4.14590	+	12.7598i	0.184673	+	0.568365i
$505$	3.45077	+	0.733484i	0.153557	+	0.0326396i
$506$	3.07485	+	29.2553i	0.136694	+	1.30056i
$507$	6.39843	+	7.10618i	0.284164	+	0.315596i
$508$	3.25433	+	1.44892i	0.144387	+	0.0642854i
$509$	−11.9585	+	5.32425i	−0.530050	+	0.235993i	−0.654270	−	0.756261i	$-0.727024\pi$
$509$	−11.9585	+	5.32425i	−0.530050	+	0.235993i	0.124220	+	0.992255i	$0.460357\pi$
$510$	−1.75181	+	1.94558i	−0.0775713	+	0.0861517i
$511$	−28.0623	−	20.3885i	−1.24140	−	0.901932i
$512$	4.28115	+	3.11044i	0.189202	+	0.137463i
$513$	16.7283	−	18.5786i	0.738571	−	0.820266i
$514$	−37.5692	+	16.7269i	−1.65711	+	0.737791i
$515$	2.39169	+	1.06485i	0.105391	+	0.0469229i
$516$	0.985051	+	1.09401i	0.0433645	+	0.0481611i
$517$	−3.07485	−	29.2553i	−0.135232	−	1.28664i
$518$	20.1130	+	4.27514i	0.883713	+	0.187839i
$519$	−3.73607	−	11.4984i	−0.163995	−	0.504725i
$520$	1.54899	−	0.329247i	0.0679276	−	0.0144385i
$521$	13.5344	+	23.4423i	0.592955	+	1.02703i	0.993832	+	0.110896i	$0.0353720\pi$
$521$	13.5344	+	23.4423i	0.592955	+	1.02703i	−0.400877	+	0.916132i	$0.631295\pi$
$522$	−10.3262	+	17.8856i	−0.451967	+	0.782830i
$523$	−1.89261	+	5.82485i	−0.0827580	+	0.254703i	−0.983870	−	0.178883i	$-0.942752\pi$
$523$	−1.89261	+	5.82485i	−0.0827580	+	0.254703i	0.901112	+	0.433586i	$0.142752\pi$
$524$	0.716449	−	6.81655i	0.0312982	−	0.297783i
$525$	−11.7812	+	8.55951i	−0.514172	+	0.373568i
$526$	22.3262			0.973470
$527$		0			0
$528$	−25.4164			−1.10611
$529$	8.85410	−	6.43288i	0.384961	−	0.279691i
$530$	0.0457515	−	0.435296i	0.00198732	−	0.0189081i
$531$	−0.326238	+	1.00406i	−0.0141575	+	0.0435724i
$532$	−4.63525	+	8.02850i	−0.200964	+	0.348079i
$533$	−2.29180	−	3.96951i	−0.0992687	−	0.171938i
$534$	−13.6396	+	2.89918i	−0.590241	+	0.125460i
$535$	1.19098	+	3.66547i	0.0514907	+	0.158472i
$536$	0.516329	+	0.109749i	0.0223020	+	0.00474044i
$537$	−0.501567	−	4.77209i	−0.0216442	−	0.205931i
$538$	−3.91716	−	4.35045i	−0.168881	−	0.187561i
$539$	−9.56677	−	4.25940i	−0.412070	−	0.183465i
$540$	−1.07829	+	0.480087i	−0.0464024	+	0.0206597i
$541$	14.7209	−	16.3492i	0.632900	−	0.702906i	−0.338336	−	0.941025i	$-0.609864\pi$
$541$	14.7209	−	16.3492i	0.632900	−	0.702906i	0.971236	+	0.238119i	$0.0765308\pi$
$542$	13.8262	+	10.0453i	0.593888	+	0.431485i
$543$	13.7533	+	9.99235i	0.590210	+	0.428813i
$544$	9.58612	−	10.6465i	0.411002	−	0.456464i
$545$	−6.42628	+	2.86117i	−0.275272	+	0.122559i
$546$	8.22191	+	3.66063i	0.351865	+	0.156660i
$547$	−6.88656	−	7.64829i	−0.294448	−	0.327017i	0.577710	−	0.816242i	$-0.303946\pi$
$547$	−6.88656	−	7.64829i	−0.294448	−	0.327017i	−0.872158	+	0.489225i	$0.837280\pi$
$548$	−0.159705	−	1.51949i	−0.00682227	−	0.0649096i
$549$	21.4102	+	4.55088i	0.913766	+	0.194227i
$550$	12.7082	+	39.1118i	0.541880	+	1.66773i
$551$	31.2125	−	6.63443i	1.32970	−	0.282636i
$552$	−3.88197	−	6.72376i	−0.165227	−	0.286182i
$553$		0			0
$554$	−1.16312	+	3.57971i	−0.0494162	+	0.152087i
$555$	0.169131	−	1.60917i	0.00717919	−	0.0683055i
$556$	0.427051	−	0.310271i	0.0181110	−	0.0131584i
$557$	0.111456			0.00472255			0.00236127	−	0.999997i	$-0.499248\pi$
$557$	0.111456			0.00472255			0.00236127	+	0.999997i	$0.499248\pi$
$558$		0			0
$559$	4.41641			0.186794
$560$	−4.50000	+	3.26944i	−0.190160	+	0.138159i
$561$	2.31848	−	22.0588i	0.0978862	−	0.931325i
$562$	−5.01722	+	15.4414i	−0.211639	+	0.651357i
$563$	−5.78115	+	10.0133i	−0.243647	+	0.422008i	−0.961750	−	0.273928i	$-0.911677\pi$
$563$	−5.78115	+	10.0133i	−0.243647	+	0.422008i	0.718104	+	0.695936i	$0.245010\pi$
$564$	−1.73607	−	3.00696i	−0.0731016	−	0.126616i
$565$	1.81359	−	0.385489i	0.0762981	−	0.0162177i
$566$	−6.78115	−	20.8702i	−0.285033	−	0.877242i
$567$	−2.93444	−	0.623735i	−0.123235	−	0.0261944i
$568$	−2.59214	−	24.6625i	−0.108764	−	1.03482i
$569$	16.3751	+	18.1863i	0.686478	+	0.762411i	0.981163	−	0.193183i	$-0.0618813\pi$
$569$	16.3751	+	18.1863i	0.686478	+	0.762411i	−0.294685	+	0.955595i	$0.595215\pi$
$570$	2.82301	+	1.25689i	0.118243	+	0.0526451i
$571$	6.39482	−	2.84716i	0.267615	−	0.119150i	−0.268543	−	0.963268i	$-0.586542\pi$
$571$	6.39482	−	2.84716i	0.267615	−	0.119150i	0.536157	+	0.844118i	$0.319875\pi$
$572$	4.01478	−	4.45887i	0.167867	−	0.186435i
$573$	−3.97214	−	2.88593i	−0.165938	−	0.120561i
$574$	9.70820	+	7.05342i	0.405213	+	0.294404i
$575$	−11.2776	+	12.5250i	−0.470308	+	0.522330i
$576$	−7.73968	+	3.44593i	−0.322487	+	0.143580i
$577$	−7.28892	−	3.24524i	−0.303442	−	0.135101i	0.249367	−	0.968409i	$-0.419777\pi$
$577$	−7.28892	−	3.24524i	−0.303442	−	0.135101i	−0.552809	+	0.833308i	$0.686444\pi$
$578$	1.02234	+	1.13542i	0.0425238	+	0.0472274i
$579$	−0.482716	−	4.59274i	−0.0200610	−	0.190868i
$580$	−1.47366	−	0.313235i	−0.0611902	−	0.0130064i
$581$	6.57295	+	20.2295i	0.272692	+	0.839259i
$582$	−29.6090	+	6.29359i	−1.22733	+	0.260878i
$583$	1.85410	+	3.21140i	0.0767891	+	0.133003i
$584$	12.9271	−	22.3903i	0.534925	−	0.926518i
$585$	−0.437694	+	1.34708i	−0.0180964	+	0.0556951i
$586$	0.636596	−	6.05681i	0.0262975	−	0.250204i
$587$	32.3713	−	23.5191i	1.33611	−	0.970739i	0.336530	−	0.941673i	$-0.390747\pi$
$587$	32.3713	−	23.5191i	1.33611	−	0.970739i	0.999577	−	0.0290662i	$-0.00925335\pi$
$588$	−1.23607			−0.0509746
$589$		0			0
$590$	−0.326238			−0.0134310
$591$	−8.42705	+	6.12261i	−0.346643	+	0.251851i
$592$	−2.14935	+	20.4497i	−0.0883376	+	0.840476i
$593$	12.9443	−	39.8384i	0.531558	−	1.63597i	−0.219414	−	0.975632i	$-0.570415\pi$
$593$	12.9443	−	39.8384i	0.531558	−	1.63597i	0.750972	−	0.660334i	$-0.229585\pi$
$594$	21.1803	−	36.6854i	0.869040	−	1.50522i
$595$	−2.42705	−	4.20378i	−0.0994994	−	0.172338i
$596$	−7.27516	+	1.54638i	−0.298002	+	0.0633423i
$597$	4.10739	+	12.6412i	0.168104	+	0.517372i
$598$	10.1888	+	2.16569i	0.416650	+	0.0885618i
$599$	−0.543718	−	5.17313i	−0.0222157	−	0.211368i	−0.999998	−	0.00174761i	$-0.999444\pi$
$599$	−0.543718	−	5.17313i	−0.0222157	−	0.211368i	0.977783	−	0.209621i	$-0.0672229\pi$
$600$	−7.26281	−	8.06617i	−0.296503	−	0.329300i
$601$	20.0980	+	8.94821i	0.819815	+	0.365005i	0.773401	−	0.633917i	$-0.218554\pi$
$601$	20.0980	+	8.94821i	0.819815	+	0.365005i	0.0464137	+	0.998922i	$0.485221\pi$
$602$	−10.5627	+	4.70281i	−0.430503	+	0.191672i
$603$	−0.315921	+	0.350865i	−0.0128653	+	0.0142883i
$604$	−9.25329	−	6.72291i	−0.376511	−	0.273551i
$605$	5.07295	+	3.68571i	0.206245	+	0.149846i
$606$	−9.99967	+	11.1058i	−0.406209	+	0.451141i
$607$	1.29395	−	0.576105i	0.0525199	−	0.0233834i	−0.380309	−	0.924860i	$-0.624182\pi$
$607$	1.29395	−	0.576105i	0.0525199	−	0.0233834i	0.432829	+	0.901476i	$0.357516\pi$
$608$	−15.4479	−	6.87785i	−0.626495	−	0.278934i
$609$	12.8111	+	14.2282i	0.519132	+	0.576555i
$610$	0.707023	+	6.72688i	0.0286265	+	0.272363i
$611$	−10.1888	−	2.16569i	−0.412194	−	0.0876146i
$612$	1.61803	+	4.97980i	0.0654051	+	0.201296i
$613$	−42.0058	+	8.92862i	−1.69660	+	0.360623i	−0.951813	−	0.306679i	$-0.900782\pi$
$613$	−42.0058	+	8.92862i	−1.69660	+	0.360623i	−0.744787	+	0.667303i	$0.767449\pi$
$614$	4.11803	+	7.13264i	0.166190	+	0.287850i
$615$	0.472136	−	0.817763i	0.0190384	−	0.0329754i
$616$	10.8541	−	33.4055i	0.437324	−	1.34595i
$617$	1.02061	−	9.71044i	0.0410882	−	0.390928i	−0.954580	−	0.297954i	$-0.903696\pi$
$617$	1.02061	−	9.71044i	0.0410882	−	0.390928i	0.995669	−	0.0929742i	$-0.0296374\pi$
$618$	−8.97214	+	6.51864i	−0.360912	+	0.262218i
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$		0			0
$621$	17.3607			0.696660
$622$	−9.85410	+	7.15942i	−0.395113	+	0.287067i
$623$	2.70249	−	25.7125i	0.108273	−	1.03015i
$624$	−2.78115	+	8.55951i	−0.111335	+	0.342655i
$625$	−11.4164	+	19.7738i	−0.456656	+	0.790952i
$626$	2.61803	+	4.53457i	0.104638	+	0.181238i
$627$	−25.6082	+	5.44320i	−1.02269	+	0.217380i
$628$	−0.708204	−	2.17963i	−0.0282604	−	0.0869766i
$629$	−17.5521	−	3.73082i	−0.699850	−	0.148758i
$630$	−0.387613	−	3.68789i	−0.0154429	−	0.146929i
$631$	−28.2845	−	31.4131i	−1.12599	−	1.25054i	−0.964621	−	0.263642i	$-0.915076\pi$
$631$	−28.2845	−	31.4131i	−1.12599	−	1.25054i	−0.161367	−	0.986894i	$-0.551590\pi$
$632$		0			0
$633$	7.30836	−	3.25389i	0.290481	−	0.129331i
$634$	−10.7061	+	11.8903i	−0.425193	+	0.472225i
$635$	1.78115	+	1.29408i	0.0706829	+	0.0513541i
$636$	0.354102	+	0.257270i	0.0140411	+	0.0102014i
$637$	−2.48127	+	2.75573i	−0.0983116	+	0.109186i
$638$	49.3944	−	21.9918i	1.95554	−	0.870664i
$639$	20.2627	+	9.02156i	0.801582	+	0.356887i
$640$	−3.48057	−	3.86556i	−0.137582	−	0.152800i
$641$	3.12643	+	29.7460i	0.123487	+	1.17490i	0.864226	+	0.503103i	$0.167809\pi$
$641$	3.12643	+	29.7460i	0.123487	+	1.17490i	−0.740740	+	0.671792i	$0.765525\pi$
$642$	−15.9695	−	3.39442i	−0.630265	−	0.133967i
$643$	4.59017	+	14.1271i	0.181019	+	0.557118i	0.999857	−	0.0169060i	$-0.00538159\pi$
$643$	4.59017	+	14.1271i	0.181019	+	0.557118i	−0.818838	+	0.574024i	$0.805382\pi$
$644$	−6.29702	+	1.33847i	−0.248137	+	0.0527432i
$645$	0.454915	+	0.787936i	0.0179123	+	0.0310249i
$646$	17.1353	−	29.6791i	0.674178	−	1.16771i
$647$	1.81966	−	5.60034i	0.0715382	−	0.220172i	−0.908895	−	0.417026i	$-0.863072\pi$
$647$	1.81966	−	5.60034i	0.0715382	−	0.220172i	0.980433	+	0.196854i	$0.0630724\pi$
$648$	0.233733	−	2.22382i	0.00918189	−	0.0873598i
$649$	2.23607	−	1.62460i	0.0877733	−	0.0637711i
$650$	14.5623			0.571181
$651$		0			0
$652$	0.437694			0.0171414
$653$	−6.75329	+	4.90655i	−0.264277	+	0.192008i	−0.712030	−	0.702149i	$-0.752224\pi$
$653$	−6.75329	+	4.90655i	−0.264277	+	0.192008i	0.447754	+	0.894157i	$0.352224\pi$
$654$	3.11478	−	29.6351i	0.121797	−	1.15883i
$655$	1.30902	−	4.02874i	0.0511475	−	0.157416i
$656$	−6.00000	+	10.3923i	−0.234261	+	0.405751i
$657$	11.5623	+	20.0265i	0.451089	+	0.781308i
$658$	26.6746	−	5.66986i	1.03988	−	0.221034i
$659$	−11.6459	−	35.8424i	−0.453660	−	1.39622i	−0.872701	−	0.488254i	$-0.837634\pi$
$659$	−11.6459	−	35.8424i	−0.453660	−	1.39622i	0.419042	−	0.907967i	$-0.362366\pi$
$660$	1.20906	+	0.256993i	0.0470625	+	0.0100034i
$661$	1.50332	+	14.3032i	0.0584726	+	0.556329i	0.984065	+	0.177808i	$0.0569006\pi$
$661$	1.50332	+	14.3032i	0.0584726	+	0.556329i	−0.925593	+	0.378521i	$0.876433\pi$
$662$	−24.1117	−	26.7788i	−0.937130	−	1.04079i
$663$	−7.17508	−	3.19455i	−0.278657	−	0.124066i
$664$	−14.4834	+	6.44844i	−0.562067	+	0.250248i
$665$	−3.83378	+	4.25784i	−0.148668	+	0.165112i
$666$	−11.0902	−	8.05748i	−0.429735	−	0.312221i
$667$	17.9271	+	13.0248i	0.694138	+	0.504321i
$668$	−1.97010	+	2.18802i	−0.0762256	+	0.0846571i
$669$	11.6095	−	5.16889i	0.448850	−	0.199841i
$670$	−0.133284	−	0.0593421i	−0.00514923	−	0.00229258i
$671$	−38.3445	−	42.5859i	−1.48027	−	1.64401i
$672$	−1.06054	−	10.0903i	−0.0409110	−	0.389242i
$673$	−21.9266	−	4.66063i	−0.845207	−	0.179654i	−0.235098	−	0.971972i	$-0.575541\pi$
$673$	−21.9266	−	4.66063i	−0.845207	−	0.179654i	−0.610109	+	0.792318i	$0.708874\pi$
$674$	−13.9894	−	43.0548i	−0.538850	−	1.65841i
$675$	23.7401	−	5.04612i	0.913758	−	0.194225i
$676$	2.95492	+	5.11806i	0.113651	+	0.196849i
$677$	1.32624	−	2.29711i	0.0509715	−	0.0882852i	−0.839414	−	0.543493i	$-0.817102\pi$
$677$	1.32624	−	2.29711i	0.0509715	−	0.0882852i	0.890385	+	0.455207i	$0.150435\pi$
$678$	−2.42705	+	7.46969i	−0.0932103	+	0.286872i
$679$	5.86662	−	55.8172i	0.225140	−	2.14207i
$680$	2.92705	−	2.12663i	0.112247	−	0.0815524i
$681$	−21.7426			−0.833180
$682$		0			0
$683$	27.9443			1.06926			0.534629	−	0.845087i	$-0.320451\pi$
$683$	27.9443			1.06926			0.534629	+	0.845087i	$0.320451\pi$
$684$	5.00000	−	3.63271i	0.191180	−	0.138900i
$685$	0.0987033	−	0.939099i	0.00377126	−	0.0358811i
$686$	−7.50000	+	23.0826i	−0.286351	+	0.881299i
$687$	−1.38197	+	2.39364i	−0.0527253	+	0.0913229i
$688$	−5.78115	−	10.0133i	−0.220404	−	0.381752i
$689$	1.28439	−	0.273005i	0.0489313	−	0.0104007i
$690$	0.663119	+	2.04087i	0.0252445	+	0.0776946i
$691$	48.7438	+	10.3608i	1.85430	+	0.394144i	0.993407	−	0.114637i	$-0.0365704\pi$
$691$	48.7438	+	10.3608i	1.85430	+	0.394144i	0.860896	+	0.508781i	$0.169904\pi$
$692$	−0.781051	−	7.43120i	−0.0296911	−	0.282492i
$693$	21.0217	+	23.3469i	0.798548	+	0.886877i
$694$	−47.4849	−	21.1416i	−1.80250	−	0.802526i
$695$	0.298033	−	0.132693i	0.0113050	−	0.00503333i
$696$	−9.54883	+	10.6051i	−0.361948	+	0.401984i
$697$	−8.47214	−	6.15537i	−0.320905	−	0.233151i
$698$	4.30902	+	3.13068i	0.163099	+	0.118498i
$699$	3.87987	−	4.30903i	0.146750	−	0.162983i
$700$	−8.22191	+	3.66063i	−0.310759	+	0.138359i
$701$	−0.882081	−	0.392728i	−0.0333157	−	0.0148331i	0.390011	−	0.920810i	$-0.372471\pi$
$701$	−0.882081	−	0.392728i	−0.0333157	−	0.0148331i	−0.423327	+	0.905977i	$0.639138\pi$
$702$	−10.0370	−	11.1472i	−0.378821	−	0.420723i
$703$	2.21395	+	21.0643i	0.0835006	+	0.794456i
$704$	21.6956	+	4.61155i	0.817685	+	0.173804i
$705$	−0.663119	−	2.04087i	−0.0249745	−	0.0768636i
$706$	54.7891	−	11.6458i	2.06202	−	0.438295i
$707$	−13.8541	−	23.9960i	−0.521037	−	0.902463i
$708$	0.163119	−	0.282530i	0.00613039	−	0.0106181i
$709$	3.35410	−	10.3229i	0.125966	−	0.387683i	−0.868110	−	0.496372i	$-0.834665\pi$
$709$	3.35410	−	10.3229i	0.125966	−	0.387683i	0.994076	+	0.108689i	$0.0346652\pi$
$710$	−0.716449	+	6.81655i	−0.0268878	+	0.255821i
$711$		0			0
$712$	19.2705			0.722193
$713$		0			0
$714$	20.5623			0.769525
$715$	3.00000	−	2.17963i	0.112194	−	0.0815134i
$716$	0.309985	−	2.94931i	0.0115847	−	0.110221i
$717$	−4.14590	+	12.7598i	−0.154831	+	0.476522i
$718$	7.82624	−	13.5554i	0.292073	−	0.505885i
$719$	21.8090	+	37.7743i	0.813339	+	1.40874i	0.910514	+	0.413477i	$0.135686\pi$
$719$	21.8090	+	37.7743i	0.813339	+	1.40874i	−0.0971753	+	0.995267i	$0.530981\pi$
$720$	3.62717	−	0.770979i	0.135177	−	0.0287327i
$721$	−6.35410	−	19.5559i	−0.236639	−	0.728300i
$722$	−9.49606	−	2.01845i	−0.353407	−	0.0751189i
$723$	−1.82634	−	17.3764i	−0.0679221	−	0.646236i
$724$	7.03027	+	7.80791i	0.261278	+	0.290179i
$725$	28.3005	+	12.6002i	1.05105	+	0.467959i
$726$	−24.2659	+	10.8039i	−0.900591	+	0.400969i
$727$	19.9621	−	22.1701i	0.740351	−	0.822244i	−0.248891	−	0.968532i	$-0.580066\pi$
$727$	19.9621	−	22.1701i	0.740351	−	0.822244i	0.989242	+	0.146288i	$0.0467326\pi$
$728$	−10.0623	−	7.31069i	−0.372934	−	0.270952i
$729$	−10.5172	−	7.64121i	−0.389527	−	0.283008i
$730$	−4.78154	+	5.31044i	−0.176973	+	0.196548i
$731$	9.21783	−	4.10404i	0.340934	−	0.151793i
$732$	−6.17916	−	2.75114i	−0.228388	−	0.101685i
$733$	6.72860	+	7.47286i	0.248526	+	0.276016i	0.854481	−	0.519483i	$-0.173875\pi$
$733$	6.72860	+	7.47286i	0.248526	+	0.276016i	−0.605955	+	0.795499i	$0.707209\pi$
$734$	0.461640	+	4.39221i	0.0170395	+	0.162120i
$735$	−0.747238	−	0.158830i	−0.0275623	−	0.00585855i
$736$	−3.62868	−	11.1679i	−0.133755	−	0.411655i
$737$	1.20906	−	0.256993i	0.0445362	−	0.00946646i
$738$	−4.00000	−	6.92820i	−0.147242	−	0.255031i
$739$	−4.14590	+	7.18091i	−0.152509	+	0.264154i	−0.932149	−	0.362074i	$-0.882069\pi$
$739$	−4.14590	+	7.18091i	−0.152509	+	0.264154i	0.779640	+	0.626228i	$0.215402\pi$
$740$	0.309017	−	0.951057i	0.0113597	−	0.0349615i
$741$	−0.969032	+	9.21973i	−0.0355983	+	0.338695i
$742$	−2.78115	+	2.02063i	−0.102099	+	0.0741795i
$743$	−23.5623			−0.864417			−0.432209	−	0.901774i	$-0.642266\pi$
$743$	−23.5623			−0.864417			−0.432209	+	0.901774i	$0.642266\pi$
$744$		0			0
$745$	−4.59675			−0.168412
$746$	41.4336	−	30.1033i	1.51699	−	1.10216i
$747$	1.48225	−	14.1027i	0.0542327	−	0.515989i
$748$	4.23607	−	13.0373i	0.154886	−	0.476690i
$749$	15.1353	−	26.2150i	0.553030	−	0.957876i
$750$	3.04508	+	5.27424i	0.111191	+	0.192588i
$751$	−13.5305	+	2.87600i	−0.493736	+	0.104947i	−0.448049	−	0.894009i	$-0.647881\pi$
$751$	−13.5305	+	2.87600i	−0.493736	+	0.104947i	−0.0456871	+	0.998956i	$0.514548\pi$
$752$	8.42705	+	25.9358i	0.307303	+	0.945781i
$753$	−16.5740	−	3.52291i	−0.603990	−	0.128382i
$754$	−2.00129	−	19.0410i	−0.0728827	−	0.693433i
$755$	−4.73001	−	5.25320i	−0.172143	−	0.191184i
$756$	8.46903	+	3.77066i	0.308016	+	0.137137i
$757$	2.62680	−	1.16953i	0.0954726	−	0.0425071i	−0.358445	−	0.933551i	$-0.616693\pi$
$757$	2.62680	−	1.16953i	0.0954726	−	0.0425071i	0.453917	+	0.891044i	$0.350026\pi$
$758$	9.11224	−	10.1202i	0.330972	−	0.367581i
$759$	−14.7082	−	10.6861i	−0.533874	−	0.387882i
$760$	−3.45492	−	2.51014i	−0.125323	−	0.0910524i
$761$	−23.0894	+	25.6434i	−0.836990	+	0.929572i	−0.998356	−	0.0573228i	$-0.981744\pi$
$761$	−23.0894	+	25.6434i	−0.836990	+	0.929572i	0.161365	+	0.986895i	$0.448410\pi$
$762$	−8.51994	+	3.79332i	−0.308645	+	0.137418i
$763$	50.4727	+	22.4719i	1.82723	+	0.813537i
$764$	−2.03044	−	2.25503i	−0.0734587	−	0.0815841i
$765$	0.338261	+	3.21834i	0.0122299	+	0.116359i
$766$	16.0577	+	3.41316i	0.580187	+	0.123323i
$767$	−0.302439	−	0.930812i	−0.0109204	−	0.0336097i
$768$	13.2659	−	2.81976i	0.478693	−	0.101749i
$769$	5.62868	+	9.74915i	0.202975	+	0.351564i	0.949486	−	0.313810i	$-0.101606\pi$
$769$	5.62868	+	9.74915i	0.202975	+	0.351564i	−0.746510	+	0.665374i	$0.768272\pi$
$770$	−4.85410	+	8.40755i	−0.174930	+	0.302987i
$771$	7.85410	−	24.1724i	0.282859	−	0.870549i
$772$	0.298335	−	2.83847i	0.0107373	−	0.102159i
$773$	6.39919	−	4.64928i	0.230163	−	0.167223i	−0.466727	−	0.884402i	$-0.654567\pi$
$773$	6.39919	−	4.64928i	0.230163	−	0.167223i	0.696889	+	0.717179i	$0.254567\pi$
$774$	7.70820			0.277066
$775$		0			0
$776$	41.8328			1.50171
$777$	−10.2812	+	7.46969i	−0.368834	+	0.267974i
$778$	−4.91644	+	46.7768i	−0.176263	+	1.67703i
$779$	−3.81966	+	11.7557i	−0.136854	+	0.421192i
$780$	0.218847	−	0.379054i	0.00783598	−	0.0135723i
$781$	−29.0344	−	50.2891i	−1.03893	−	1.79949i
$782$	23.2783	−	4.94796i	0.832431	−	0.176939i
$783$	−9.86068	−	30.3481i	−0.352392	−	1.08455i
$784$	9.49606	+	2.01845i	0.339145	+	0.0720875i
$785$	−0.148055	−	1.40865i	−0.00528431	−	0.0502768i
$786$	12.0071	+	13.3352i	0.428278	+	0.475651i
$787$	40.8430	+	18.1845i	1.45589	+	0.648206i	0.973695	−	0.227855i	$-0.0731712\pi$
$787$	40.8430	+	18.1845i	1.45589	+	0.648206i	0.482200	+	0.876061i	$0.339838\pi$
$788$	−5.88113	+	2.61845i	−0.209506	+	0.0932783i
$789$	−9.23291	+	10.2542i	−0.328700	+	0.365059i
$790$		0			0
$791$	−11.7812	−	8.55951i	−0.418890	−	0.304341i
$792$	−15.6686	+	17.4018i	−0.556761	+	0.618345i
$793$	−18.5375	+	8.25342i	−0.658285	+	0.293087i
$794$	43.9131	+	19.5514i	1.55842	+	0.693852i
$795$	0.181006	+	0.201028i	0.00641964	+	0.00712973i
$796$	0.858679	+	8.16978i	0.0304351	+	0.289570i
$797$	−26.3555	−	5.60203i	−0.933559	−	0.198434i	−0.284069	−	0.958804i	$-0.591684\pi$
$797$	−26.3555	−	5.60203i	−0.933559	−	0.198434i	−0.649490	+	0.760370i	$0.725018\pi$
$798$	−7.50000	−	23.0826i	−0.265497	−	0.817116i
$799$	−23.2783	+	4.94796i	−0.823528	+	0.175046i
$800$	−8.20820	−	14.2170i	−0.290204	−	0.502648i
$801$	−8.61803	+	14.9269i	−0.304503	+	0.527415i
$802$	11.9164	−	36.6749i	0.420783	−	1.29504i
$803$	6.32826	−	60.2094i	0.223319	−	2.12474i
$804$	0.118034	−	0.0857567i	0.00416274	−	0.00302441i
$805$	−3.97871			−0.140231
$806$		0			0
$807$	3.61803			0.127361
$808$	16.7082	−	12.1392i	0.587793	−	0.427056i
$809$	−3.15693	+	30.0362i	−0.110992	+	1.05602i	0.787286	+	0.616588i	$0.211485\pi$
$809$	−3.15693	+	30.0362i	−0.110992	+	1.05602i	−0.898278	+	0.439428i	$0.855181\pi$
$810$	−0.190983	+	0.587785i	−0.00671046	+	0.0206527i
$811$	14.3885	−	24.9217i	0.505250	−	0.875119i	−0.494731	−	0.869046i	$-0.664734\pi$
$811$	14.3885	−	24.9217i	0.505250	−	0.875119i	0.999982	−	0.00607295i	$-0.00193309\pi$
$812$	5.91641	+	10.2475i	0.207625	+	0.359617i
$813$	−10.3315	+	2.19603i	−0.362341	+	0.0770180i
$814$	11.0902	+	34.1320i	0.388710	+	1.19633i
$815$	0.264599	+	0.0562422i	0.00926848	+	0.00197008i
$816$	2.14935	+	20.4497i	0.0752422	+	0.715881i
$817$	−7.96923	−	8.85073i	−0.278808	−	0.309648i
$818$	23.9169	+	10.6485i	0.836236	+	0.372316i
$819$	10.1628	−	4.52479i	0.355118	−	0.158109i
$820$	0.390499	−	0.433693i	0.0136368	−	0.0151452i
$821$	19.0344	+	13.8293i	0.664307	+	0.482647i	0.868115	−	0.496364i	$-0.165332\pi$
$821$	19.0344	+	13.8293i	0.664307	+	0.482647i	−0.203808	+	0.979011i	$0.565332\pi$
$822$	3.23607	+	2.35114i	0.112871	+	0.0820055i
$823$	22.8338	−	25.3595i	0.795937	−	0.883978i	−0.199451	−	0.979908i	$-0.563916\pi$
$823$	22.8338	−	25.3595i	0.795937	−	0.883978i	0.995388	+	0.0959302i	$0.0305826\pi$
$824$	14.0012	−	6.23374i	0.487755	−	0.217163i
$825$	−23.2190	−	10.3378i	−0.808383	−	0.359915i
$826$	1.71452	+	1.90416i	0.0596557	+	0.0662544i
$827$	−1.91561	−	18.2258i	−0.0666124	−	0.633775i	−0.975992	−	0.217807i	$-0.930110\pi$
$827$	−1.91561	−	18.2258i	−0.0666124	−	0.633775i	0.909379	−	0.415968i	$-0.136557\pi$
$828$	4.19801	+	0.892315i	0.145891	+	0.0310101i
$829$	−2.56231	−	7.88597i	−0.0889926	−	0.273891i	0.896649	−	0.442742i	$-0.145994\pi$
$829$	−2.56231	−	7.88597i	−0.0889926	−	0.273891i	−0.985642	+	0.168851i	$0.945994\pi$
$830$	4.28621	−	0.911062i	0.148777	−	0.0316234i
$831$	−1.16312	−	2.01458i	−0.0403481	−	0.0698850i
$832$	3.92705	−	6.80185i	0.136146	−	0.235812i
$833$	−2.61803	+	8.05748i	−0.0907095	+	0.279175i
$834$	−0.144455	+	1.37440i	−0.00500206	+	0.0475914i
$835$	−1.47214	+	1.06957i	−0.0509454	+	0.0370140i
$836$	−16.1803			−0.559609
$837$		0			0
$838$	−7.23607			−0.249966
$839$	9.04508	−	6.57164i	0.312271	−	0.226878i	−0.420599	−	0.907246i	$-0.638180\pi$
$839$	9.04508	−	6.57164i	0.312271	−	0.226878i	0.732870	+	0.680368i	$0.238180\pi$
$840$	0.267834	−	2.54827i	0.00924115	−	0.0879236i
$841$	3.62461	−	11.1554i	0.124987	−	0.384669i
$842$	−15.5623	+	26.9547i	−0.536312	+	0.928920i
$843$	−5.01722	−	8.69008i	−0.172802	−	0.299302i
$844$	4.83623	−	1.02797i	0.166470	−	0.0353843i
$845$	1.12868	+	3.47371i	0.0388277	+	0.119499i
$846$	−17.7831	−	3.77991i	−0.611394	−	0.129956i
$847$	−5.14795	−	48.9794i	−0.176886	−	1.68295i
$848$	−2.30027	−	2.55470i	−0.0789915	−	0.0877289i
$849$	12.3898	+	5.51629i	0.425216	+	0.189318i
$850$	30.3941	−	13.5323i	1.04251	−	0.464155i
$851$	−9.84171	+	10.9303i	−0.337369	+	0.374687i
$852$	−5.54508	−	4.02874i	−0.189971	−	0.138022i
$853$	−3.23607	−	2.35114i	−0.110801	−	0.0805015i	0.531005	−	0.847369i	$-0.321815\pi$
$853$	−3.23607	−	2.35114i	−0.110801	−	0.0805015i	−0.641806	+	0.766867i	$0.721815\pi$
$854$	35.5473	−	39.4793i	1.21640	−	1.35095i
$855$	3.48943	−	1.55360i	0.119336	−	0.0531319i
$856$	20.6117	+	9.17692i	0.704493	+	0.313661i
$857$	9.48850	+	10.5380i	0.324121	+	0.359973i	0.883080	−	0.469222i	$-0.155466\pi$
$857$	9.48850	+	10.5380i	0.324121	+	0.359973i	−0.558959	+	0.829195i	$0.688799\pi$
$858$	1.64195	+	15.6222i	0.0560554	+	0.533332i
$859$	−55.4690	−	11.7903i	−1.89258	−	0.402280i	−0.893658	−	0.448749i	$-0.851870\pi$
$859$	−55.4690	−	11.7903i	−1.89258	−	0.402280i	−0.998920	+	0.0464691i	$0.985203\pi$
$860$	0.173762	+	0.534785i	0.00592524	+	0.0182360i
$861$	−7.25434	+	1.54196i	−0.247227	+	0.0525498i
$862$	−20.0344	−	34.7007i	−0.682376	−	1.18191i
$863$	−20.2533	+	35.0797i	−0.689430	+	1.19413i	0.282593	+	0.959240i	$0.408806\pi$
$863$	−20.2533	+	35.0797i	−0.689430	+	1.19413i	−0.972023	+	0.234888i	$0.924528\pi$
$864$	−5.22542	+	16.0822i	−0.177773	+	0.547128i
$865$	0.482716	−	4.59274i	0.0164128	−	0.156158i
$866$	−35.8885	+	26.0746i	−1.21954	+	0.886049i
$867$	−0.944272			−0.0320692
$868$		0			0
$869$		0			0
$870$	3.19098	−	2.31838i	0.108184	−	0.0786006i
$871$	0.0457515	−	0.435296i	0.00155023	−	0.0147495i
$872$	−12.7254	+	39.1648i	−0.430937	+	1.32629i
$873$	−18.7082	+	32.4036i	−0.633177	+	1.09669i
$874$	−14.0451	−	24.3268i	−0.475082	−	0.822866i
$875$	−11.0450	+	2.34770i	−0.373391	+	0.0793666i
$876$	−2.20820	−	6.79615i	−0.0746083	−	0.229621i
$877$	−29.0590	−	6.17668i	−0.981253	−	0.208572i	−0.310761	−	0.950488i	$-0.600584\pi$
$877$	−29.0590	−	6.17668i	−0.981253	−	0.208572i	−0.670492	+	0.741916i	$0.733917\pi$
$878$	2.00129	+	19.0410i	0.0675403	+	0.642603i
$879$	2.51856	+	2.79715i	0.0849490	+	0.0943454i
$880$	−8.86889	−	3.94868i	−0.298970	−	0.133110i
$881$	26.8223	−	11.9421i	0.903667	−	0.402338i	0.0983286	−	0.995154i	$-0.468650\pi$
$881$	26.8223	−	11.9421i	0.903667	−	0.402338i	0.805338	+	0.592816i	$0.201984\pi$
$882$	−4.33070	+	4.80973i	−0.145822	+	0.161952i
$883$	0.809017	+	0.587785i	0.0272256	+	0.0197805i	0.601315	−	0.799012i	$-0.294644\pi$
$883$	0.809017	+	0.587785i	0.0272256	+	0.0197805i	−0.574089	+	0.818793i	$0.694644\pi$
$884$	−3.92705	−	2.85317i	−0.132081	−	0.0959625i
$885$	0.134914	−	0.149837i	0.00453509	−	0.00503673i
$886$	−1.29395	+	0.576105i	−0.0434712	+	0.0193546i
$887$	−43.9446	−	19.5654i	−1.47551	−	0.656941i	−0.497879	−	0.867247i	$-0.665888\pi$
$887$	−43.9446	−	19.5654i	−1.47551	−	0.656941i	−0.977636	+	0.210305i	$0.932554\pi$
$888$	−6.33810	−	7.03917i	−0.212693	−	0.236219i
$889$	−1.80748	−	17.1971i	−0.0606211	−	0.576771i
$890$	−5.20985	−	1.10739i	−0.174634	−	0.0371197i
$891$	−1.61803	−	4.97980i	−0.0542062	−	0.166829i
$892$	7.68247	−	1.63296i	0.257228	−	0.0546755i
$893$	14.0451	+	24.3268i	0.470001	+	0.814065i
$894$	9.73607	−	16.8634i	0.325623	−	0.563995i
$895$	0.566371	−	1.74311i	0.0189317	−	0.0582658i
$896$	−4.27042	+	40.6303i	−0.142665	+	1.35736i
$897$	−5.20820	+	3.78398i	−0.173897	+	0.126343i
$898$	−55.1246			−1.83953
$899$		0			0
$900$	6.00000			0.200000
$901$	2.42705	−	1.76336i	0.0808568	−	0.0587459i
$902$	−2.18927	+	20.8295i	−0.0728948	+	0.693548i
$903$	2.20820	−	6.79615i	0.0734844	−	0.226162i
$904$	5.42705	−	9.39993i	0.180501	−	0.312637i
$905$	3.24671	+	5.62347i	0.107924	+	0.186930i
$906$	29.2899	−	6.22576i	0.973092	−	0.206837i
$907$	−3.68441	−	11.3394i	−0.122339	−	0.376520i	0.871068	−	0.491162i	$-0.163428\pi$
$907$	−3.68441	−	11.3394i	−0.122339	−	0.376520i	−0.993407	+	0.114642i	$0.963428\pi$
$908$	−13.1440	−	2.79385i	−0.436201	−	0.0927173i
$909$	1.93086	+	18.3709i	0.0640427	+	0.609326i
$910$	2.30027	+	2.55470i	0.0762531	+	0.0846876i
$911$	−12.9544	−	5.76766i	−0.429198	−	0.191091i	0.180756	−	0.983528i	$-0.442145\pi$
$911$	−12.9544	−	5.76766i	−0.429198	−	0.191091i	−0.609954	+	0.792437i	$0.708812\pi$
$912$	22.1722	−	9.87171i	0.734195	−	0.326885i
$913$	−24.8412	+	27.5890i	−0.822124	+	0.913061i
$914$	−35.0066	−	25.4338i	−1.15791	−	0.841274i
$915$	−3.38197	−	2.45714i	−0.111804	−	0.0812306i
$916$	−1.14301	+	1.26944i	−0.0377662	+	0.0419436i
$917$	−30.3941	+	13.5323i	−1.00370	+	0.446877i
$918$	−31.3077	−	13.9391i	−1.03331	−	0.460058i
$919$	33.5399	+	37.2498i	1.10638	+	1.22876i	0.971283	+	0.237927i	$0.0764678\pi$
$919$	33.5399	+	37.2498i	1.10638	+	1.22876i	0.135096	+	0.990832i	$0.456866\pi$
$920$	−0.309985	−	2.94931i	−0.0102199	−	0.0972360i
$921$	−4.97894	−	1.05831i	−0.164062	−	0.0348724i
$922$	−15.8713	−	48.8469i	−0.522694	−	1.60869i
$923$	−20.1130	+	4.27514i	−0.662026	+	0.140718i
$924$	−4.85410	−	8.40755i	−0.159688	−	0.276588i
$925$	−10.2812	+	17.8075i	−0.338042	+	0.585506i
$926$	4.56231	−	14.0413i	0.149927	−	0.461427i
$927$	−1.43290	+	13.6331i	−0.0470625	+	0.447770i
$928$	−17.4615	+	12.6865i	−0.573202	+	0.416455i
$929$	−33.5410			−1.10045			−0.550223	−	0.835018i	$-0.685457\pi$
$929$	−33.5410			−1.10045			−0.550223	+	0.835018i	$0.685457\pi$
$930$		0			0
$931$	10.0000			0.327737
$932$	2.89919	−	2.10638i	0.0949660	−	0.0689969i
$933$	0.786876	−	7.48663i	0.0257612	−	0.245101i
$934$	19.3885	−	59.6718i	0.634413	−	1.95252i
$935$	4.23607	−	7.33708i	0.138534	−	0.239948i
$936$	4.14590	+	7.18091i	0.135513	+	0.234715i
$937$	43.5132	−	9.24901i	1.42151	−	0.302152i	0.567917	−	0.823086i	$-0.307750\pi$
$937$	43.5132	−	9.24901i	1.42151	−	0.302152i	0.853597	+	0.520934i	$0.174416\pi$
$938$	0.354102	+	1.08981i	0.0115618	+	0.0355837i
$939$	−3.16535	−	0.672816i	−0.103297	−	0.0219565i
$940$	−0.138630	−	1.31897i	−0.00452160	−	0.0430201i
$941$	37.0808	+	41.1824i	1.20880	+	1.34251i	0.923276	+	0.384137i	$0.125501\pi$
$941$	37.0808	+	41.1824i	1.20880	+	1.34251i	0.285524	+	0.958372i	$0.407832\pi$
$942$	5.48127	+	2.44042i	0.178590	+	0.0795132i
$943$	−7.84150	+	3.49126i	−0.255354	+	0.113691i
$944$	−1.71452	+	1.90416i	−0.0558028	+	0.0619753i
$945$	4.63525	+	3.36771i	0.150785	+	0.109552i
$946$	−16.3262	−	11.8617i	−0.530812	−	0.385657i
$947$	−24.1348	+	26.8044i	−0.784275	+	0.871026i	−0.994294	−	0.106671i	$-0.965981\pi$
$947$	−24.1348	+	26.8044i	−0.784275	+	0.871026i	0.210019	+	0.977697i	$0.432647\pi$
$948$		0			0
$949$	−19.5843	−	8.71950i	−0.635734	−	0.283047i
$950$	−26.2771	−	29.1837i	−0.852542	−	0.946843i
$951$	−1.03363	−	9.83437i	−0.0335179	−	0.318901i
$952$	−27.7954	−	5.90810i	−0.900855	−	0.191483i
$953$	−2.84752	−	8.76378i	−0.0922404	−	0.283887i	0.894284	−	0.447499i	$-0.147685\pi$
$953$	−2.84752	−	8.76378i	−0.0922404	−	0.283887i	−0.986525	+	0.163613i	$0.947685\pi$
$954$	2.24171	−	0.476491i	0.0725782	−	0.0154270i
$955$	−0.937694	−	1.62413i	−0.0303431	−	0.0525557i
$956$	−4.14590	+	7.18091i	−0.134088	+	0.232247i
$957$	−10.3262	+	31.7809i	−0.333800	+	1.02733i
$958$	−1.51275	+	14.3929i	−0.0488747	+	0.465012i
$959$	−6.00000	+	4.35926i	−0.193750	+	0.140768i
$960$	1.61803			0.0522218
$961$		0			0
$962$	12.7082			0.409729
$963$	−16.3262	+	11.8617i	−0.526106	+	0.382238i
$964$	1.12874	−	10.7392i	0.0363542	−	0.345887i
$965$	0.545085	−	1.67760i	0.0175469	−	0.0540038i
$966$	8.42705	−	14.5961i	0.271136	−	0.469621i
$967$	−6.17376	−	10.6933i	−0.198535	−	0.343872i	0.749519	−	0.661983i	$-0.230285\pi$
$967$	−6.17376	−	10.6933i	−0.198535	−	0.343872i	−0.948054	+	0.318111i	$0.896952\pi$
$968$	35.9060	−	7.63206i	1.15406	−	0.245304i
$969$	6.54508	+	20.1437i	0.210258	+	0.647109i
$970$	−11.3096	−	2.40394i	−0.363131	−	0.0771858i
$971$	0.0457515	+	0.435296i	0.00146824	+	0.0139693i	0.995231	−	0.0975412i	$-0.0310978\pi$
$971$	0.0457515	+	0.435296i	0.00146824	+	0.0139693i	−0.993763	+	0.111511i	$0.964431\pi$
$972$	−6.61673	−	7.34862i	−0.212232	−	0.235707i
$973$	−2.34078	−	1.04218i	−0.0750421	−	0.0334109i
$974$	−61.9684	+	27.5901i	−1.98559	+	0.884044i
$975$	−6.02218	+	6.68830i	−0.192864	+	0.214197i
$976$	42.9787	+	31.2259i	1.37572	+	0.999516i
$977$	−42.1246	−	30.6053i	−1.34769	−	0.979151i	−0.999123	−	0.0418654i	$-0.986670\pi$
$977$	−42.1246	−	30.6053i	−1.34769	−	0.979151i	−0.348562	−	0.937286i	$-0.613330\pi$
$978$	−0.766755	+	0.851568i	−0.0245181	+	0.0272301i
$979$	41.2234	−	18.3538i	1.31751	−	0.586591i
$980$	−0.431318	−	0.192035i	−0.0137779	−	0.00613433i
$981$	−24.6460	−	27.3721i	−0.786885	−	0.873924i
$982$	−3.65267	−	34.7528i	−0.116561	−	1.10901i
$983$	7.85887	+	1.67045i	0.250659	+	0.0532792i	0.331527	−	0.943446i	$-0.392436\pi$
$983$	7.85887	+	1.67045i	0.250659	+	0.0532792i	−0.0808685	+	0.996725i	$0.525769\pi$
$984$	−1.70820	−	5.25731i	−0.0544556	−	0.167597i
$985$	−3.89177	+	0.827221i	−0.124002	+	0.0263575i
$986$	−21.8713	−	37.8822i	−0.696525	−	1.20642i
$987$	−8.42705	+	14.5961i	−0.268236	+	0.464598i
$988$	−1.77051	+	5.44907i	−0.0563274	+	0.173358i
$989$	0.864504	−	8.22520i	0.0274896	−	0.261546i
$990$	5.23607	−	3.80423i	0.166413	−	0.120906i
$991$	16.2705			0.516850			0.258425	−	0.966031i	$-0.416797\pi$
$991$	16.2705			0.516850			0.258425	+	0.966031i	$0.416797\pi$
$992$		0			0
$993$	22.2705			0.706733
$994$	43.5517	−	31.6421i	1.38137	−	1.00363i
$995$	−0.530693	+	5.04920i	−0.0168241	+	0.160070i
$996$	−1.35410	+	4.16750i	−0.0429064	+	0.132052i
$997$	−26.6246	+	46.1152i	−0.843210	+	1.46048i	0.0439568	+	0.999033i	$0.486004\pi$
$997$	−26.6246	+	46.1152i	−0.843210	+	1.46048i	−0.887167	+	0.461449i	$0.847330\pi$
$998$	−8.78115	−	15.2094i	−0.277963	−	0.481445i
$999$	20.7175	−	4.40364i	0.655473	−	0.139325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.b.338.1		8
31.2	even	5	inner	961.2.g.b.732.1		8
31.3	odd	30		961.2.d.e.531.1		4
31.4	even	5		961.2.g.f.448.1		8
31.5	even	3	inner	961.2.g.b.235.1		8
31.6	odd	6		961.2.d.b.388.1		4
31.7	even	15		961.2.d.f.628.1		4
31.8	even	5		961.2.c.f.521.2		4
31.9	even	15		961.2.c.f.439.2		4
31.10	even	15	inner	961.2.g.b.816.1		8
31.11	odd	30		961.2.g.g.846.1		8
31.12	odd	30		961.2.d.b.374.1		4
31.13	odd	30		961.2.g.g.547.1		8
31.14	even	15		961.2.a.d.1.2		2
31.15	odd	10		961.2.g.g.844.1		8
31.16	even	5		961.2.g.f.844.1		8
31.17	odd	30		961.2.a.e.1.2		2
31.18	even	15		961.2.g.f.547.1		8
31.19	even	15		31.2.d.a.2.1	✓	4
31.20	even	15		961.2.g.f.846.1		8
31.21	odd	30		961.2.g.c.816.1		8
31.22	odd	30		961.2.c.d.439.2		4
31.23	odd	10		961.2.c.d.521.2		4
31.24	odd	30		961.2.d.e.628.1		4
31.25	even	3		31.2.d.a.16.1	yes	4
31.26	odd	6		961.2.g.c.235.1		8
31.27	odd	10		961.2.g.g.448.1		8
31.28	even	15		961.2.d.f.531.1		4
31.29	odd	10		961.2.g.c.732.1		8
31.30	odd	2		961.2.g.c.338.1		8
93.14	odd	30		8649.2.a.g.1.1		2
93.17	even	30		8649.2.a.f.1.1		2
93.50	odd	30		279.2.i.a.64.1		4
93.56	odd	6		279.2.i.a.109.1		4
124.19	odd	30		496.2.n.b.33.1		4
124.87	odd	6		496.2.n.b.481.1		4
155.19	even	30		775.2.k.c.126.1		4
155.87	odd	12		775.2.bf.a.574.1		8
155.112	odd	60		775.2.bf.a.374.2		8
155.118	odd	12		775.2.bf.a.574.2		8
155.143	odd	60		775.2.bf.a.374.1		8
155.149	even	6		775.2.k.c.326.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.2.1	✓	4	31.19	even	15
31.2.d.a.16.1	yes	4	31.25	even	3
279.2.i.a.64.1		4	93.50	odd	30
279.2.i.a.109.1		4	93.56	odd	6
496.2.n.b.33.1		4	124.19	odd	30
496.2.n.b.481.1		4	124.87	odd	6
775.2.k.c.126.1		4	155.19	even	30
775.2.k.c.326.1		4	155.149	even	6
775.2.bf.a.374.1		8	155.143	odd	60
775.2.bf.a.374.2		8	155.112	odd	60
775.2.bf.a.574.1		8	155.87	odd	12
775.2.bf.a.574.2		8	155.118	odd	12
961.2.a.d.1.2		2	31.14	even	15
961.2.a.e.1.2		2	31.17	odd	30
961.2.c.d.439.2		4	31.22	odd	30
961.2.c.d.521.2		4	31.23	odd	10
961.2.c.f.439.2		4	31.9	even	15
961.2.c.f.521.2		4	31.8	even	5
961.2.d.b.374.1		4	31.12	odd	30
961.2.d.b.388.1		4	31.6	odd	6
961.2.d.e.531.1		4	31.3	odd	30
961.2.d.e.628.1		4	31.24	odd	30
961.2.d.f.531.1		4	31.28	even	15
961.2.d.f.628.1		4	31.7	even	15
961.2.g.b.235.1		8	31.5	even	3	inner
961.2.g.b.338.1		8	1.1	even	1	trivial
961.2.g.b.732.1		8	31.2	even	5	inner
961.2.g.b.816.1		8	31.10	even	15	inner
961.2.g.c.235.1		8	31.26	odd	6
961.2.g.c.338.1		8	31.30	odd	2
961.2.g.c.732.1		8	31.29	odd	10
961.2.g.c.816.1		8	31.21	odd	30
961.2.g.f.448.1		8	31.4	even	5
961.2.g.f.547.1		8	31.18	even	15
961.2.g.f.844.1		8	31.16	even	5
961.2.g.f.846.1		8	31.20	even	15
961.2.g.g.448.1		8	31.27	odd	10
961.2.g.g.547.1		8	31.13	odd	30
961.2.g.g.844.1		8	31.15	odd	10
961.2.g.g.846.1		8	31.11	odd	30
8649.2.a.f.1.1		2	93.17	even	30
8649.2.a.g.1.1		2	93.14	odd	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30902 + 0.951057i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.190983 - 0.587785i) q^{4} +(0.190983 - 0.330792i) q^{5} +(0.809017 + 1.40126i) q^{6} +(-2.93444 + 0.623735i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(1.95630 + 0.415823i) q^{9} +(0.0646021 + 0.614648i) q^{10} +(-3.50361 - 3.89116i) q^{11} +(-0.564602 - 0.251377i) q^{12} +(-1.69381 + 0.754131i) q^{13} +(3.24803 - 3.60730i) q^{14} +(-0.309017 - 0.224514i) q^{15} +(3.92705 + 2.85317i) q^{16} +(-2.83448 + 3.14801i) q^{17} +(-2.95630 + 1.31623i) q^{18} +(4.56773 + 2.03368i) q^{19} +(-0.157960 - 0.175433i) q^{20} +(0.313585 + 2.98357i) q^{21} +(8.28700 + 1.76146i) q^{22} +(1.07295 + 3.30220i) q^{23} +(-2.18720 + 0.464905i) q^{24} +(2.42705 + 4.20378i) q^{25} +(1.50000 - 2.59808i) q^{26} +(1.54508 - 4.75528i) q^{27} +(-0.193806 + 1.84395i) q^{28} +(5.16312 - 3.75123i) q^{29} +0.618034 q^{30} -3.38197 q^{32} +(-4.23607 + 3.07768i) q^{33} +(0.716449 - 6.81655i) q^{34} +(-0.354102 + 1.08981i) q^{35} +(0.618034 - 1.07047i) q^{36} +(2.11803 + 3.66854i) q^{37} +(-7.91338 + 1.68204i) q^{38} +(0.572949 + 1.76336i) q^{39} +(-0.835438 - 0.177578i) q^{40} +(0.258409 + 2.45859i) q^{41} +(-3.24803 - 3.60730i) q^{42} +(-2.17603 - 0.968833i) q^{43} +(-2.95630 + 1.31623i) q^{44} +(0.511170 - 0.567712i) q^{45} +(-4.54508 - 3.30220i) q^{46} +(4.54508 + 3.30220i) q^{47} +(3.24803 - 3.60730i) q^{48} +(1.82709 - 0.813473i) q^{49} +(-7.17508 - 3.19455i) q^{50} +(2.83448 + 3.14801i) q^{51} +(0.119779 + 1.13962i) q^{52} +(-0.692728 - 0.147244i) q^{53} +(2.50000 + 7.69421i) q^{54} +(-1.95630 + 0.415823i) q^{55} +(3.35410 + 5.80948i) q^{56} +(2.50000 - 4.33013i) q^{57} +(-3.19098 + 9.82084i) q^{58} +(-0.0551768 + 0.524972i) q^{59} +(-0.190983 + 0.138757i) q^{60} +10.9443 q^{61} -6.00000 q^{63} +(-3.42705 + 2.48990i) q^{64} +(-0.0740275 + 0.704324i) q^{65} +(2.61803 - 8.05748i) q^{66} +(-0.118034 + 0.204441i) q^{67} +(1.30902 + 2.26728i) q^{68} +(3.39626 - 0.721898i) q^{69} +(-0.572949 - 1.76336i) q^{70} +(10.8478 + 2.30578i) q^{71} +(-0.467465 - 4.44764i) q^{72} +(7.73669 + 8.59247i) q^{73} +(-6.26153 - 2.78781i) q^{74} +(4.43444 - 1.97434i) q^{75} +(2.06773 - 2.29644i) q^{76} +(12.7082 + 9.23305i) q^{77} +(-2.42705 - 1.76336i) q^{78} +(1.69381 - 0.754131i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-2.67652 - 2.97258i) q^{82} +(-0.741125 - 7.05133i) q^{83} +(1.81359 + 0.385489i) q^{84} +(0.500000 + 1.53884i) q^{85} +(3.76988 - 0.801313i) q^{86} +(-3.19098 - 5.52694i) q^{87} +(-5.85410 + 10.1396i) q^{88} +(-2.66312 + 8.19624i) q^{89} +(-0.129204 + 1.22930i) q^{90} +(4.50000 - 3.26944i) q^{91} +2.14590 q^{92} -9.09017 q^{94} +(1.54508 - 1.12257i) q^{95} +(-0.353512 + 3.36344i) q^{96} +(-5.78115 + 17.7926i) q^{97} +(-1.61803 + 2.80252i) q^{98} +(-5.23607 - 9.06914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + 2 q^{6} + 3 q^{7} - 10 q^{8} - 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} - 6 q^{14} + 2 q^{15} + 18 q^{16} + 3 q^{17} - 6 q^{18} + 5 q^{19} + 7 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + 2 * q^6 + 3 * q^7 - 10 * q^8 - 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 - 6 * q^14 + 2 * q^15 + 18 * q^16 + 3 * q^17 - 6 * q^18 + 5 * q^19 + 7 * q^20 - 3 * q^21 + 6 * q^22 + 22 * q^23 - 5 * q^24 + 6 * q^25 + 12 * q^26 - 10 * q^27 + 6 * q^28 + 10 * q^29 - 4 * q^30 - 36 * q^32 - 16 * q^33 - 11 * q^34 + 24 * q^35 - 4 * q^36 + 8 * q^37 - 10 * q^38 + 18 * q^39 - 10 * q^40 - 8 * q^41 + 6 * q^42 - q^43 - 6 * q^44 + 8 * q^45 - 14 * q^46 + 14 * q^47 - 6 * q^48 + 2 * q^49 - 12 * q^50 - 3 * q^51 + 3 * q^52 - 21 * q^53 + 20 * q^54 + 2 * q^55 + 20 * q^57 - 30 * q^58 - 5 * q^59 - 6 * q^60 + 16 * q^61 - 48 * q^63 - 14 * q^64 + 9 * q^65 + 12 * q^66 + 8 * q^67 + 6 * q^68 + 11 * q^69 - 18 * q^70 + 7 * q^71 + 10 * q^72 - 21 * q^73 - 11 * q^74 + 9 * q^75 - 15 * q^76 + 48 * q^77 - 6 * q^78 + 6 * q^80 + q^81 - 4 * q^82 + 14 * q^83 + 9 * q^84 + 4 * q^85 + 7 * q^86 - 30 * q^87 - 20 * q^88 + 10 * q^89 + 4 * q^90 + 36 * q^91 + 44 * q^92 - 28 * q^94 - 10 * q^95 + 2 * q^96 - 6 * q^97 - 4 * q^98 - 24 * q^99

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