LMFDB - Embedded newform 522.2.k.h.343.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [522,2,Mod(181,522)] 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("522.181"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(522, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 522 = 2 \cdot 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	522.k (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,2,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.16819098551$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 9 x^{9} - 5 x^{8} + 35 x^{7} + 197 x^{6} - 140 x^{5} - 80 x^{4} + \cdots + 4096 $ x^12 - 3x^11 + 13x^10 - 9x^9 - 5x^8 + 35x^7 + 197x^6 - 140x^5 - 80x^4 + 576x^3 + 3328x^2 + 3072*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			343.1
Root			$-0.260453 + 1.14112i$ of defining polynomial
Character	$\chi$	$=$	522.343
Dual form			522.2.k.h.487.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.623490 - 0.781831i) q^{2} +(-0.222521 + 0.974928i) q^{4} +(-1.00725 - 1.26305i) q^{5} +(0.338433 + 1.48277i) q^{7} +(0.900969 - 0.433884i) q^{8} +(-0.359484 + 1.57500i) q^{10} +(1.70872 + 0.822877i) q^{11} +(2.87014 + 1.38219i) q^{13} +(0.948269 - 1.18909i) q^{14} +(-0.900969 - 0.433884i) q^{16} +1.69929 q^{17} +(0.818639 - 3.58669i) q^{19} +(1.45552 - 0.700942i) q^{20} +(-0.422020 - 1.84899i) q^{22} +(1.67782 - 2.10392i) q^{23} +(0.531856 - 2.33021i) q^{25} +(-0.708867 - 3.10575i) q^{26} -1.52091 q^{28} +(4.31703 + 3.21920i) q^{29} +(-1.11130 - 1.39353i) q^{31} +(0.222521 + 0.974928i) q^{32} +(-1.05949 - 1.32856i) q^{34} +(1.53194 - 1.92099i) q^{35} +(6.37006 - 3.06766i) q^{37} +(-3.31460 + 1.59623i) q^{38} +(-1.45552 - 0.700942i) q^{40} +5.03259 q^{41} +(-1.18247 + 1.48277i) q^{43} +(-1.18247 + 1.48277i) q^{44} -2.69101 q^{46} +(2.31606 + 1.11536i) q^{47} +(4.22270 - 2.03355i) q^{49} +(-2.15344 + 1.03704i) q^{50} +(-1.98620 + 2.49062i) q^{52} +(-5.14319 - 6.44936i) q^{53} +(-0.681776 - 2.98705i) q^{55} +(0.948269 + 1.18909i) q^{56} +(-0.174748 - 5.38233i) q^{58} -2.95027 q^{59} +(1.72363 + 7.55173i) q^{61} +(-0.396619 + 1.73770i) q^{62} +(0.623490 - 0.781831i) q^{64} +(-1.14518 - 5.01736i) q^{65} +(-2.23359 + 1.07564i) q^{67} +(-0.378127 + 1.65668i) q^{68} -2.45703 q^{70} +(5.46771 + 2.63311i) q^{71} +(2.33692 - 2.93041i) q^{73} +(-6.37006 - 3.06766i) q^{74} +(3.31460 + 1.59623i) q^{76} +(-0.641852 + 2.81214i) q^{77} +(-8.30753 + 4.00069i) q^{79} +(0.359484 + 1.57500i) q^{80} +(-3.13777 - 3.93464i) q^{82} +(-1.22901 + 5.38465i) q^{83} +(-1.71161 - 2.14629i) q^{85} +1.89654 q^{86} +1.89654 q^{88} +(-9.95740 - 12.4862i) q^{89} +(-1.07812 + 4.72355i) q^{91} +(1.67782 + 2.10392i) q^{92} +(-0.572020 - 2.50618i) q^{94} +(-5.35476 + 2.57872i) q^{95} +(-3.31730 + 14.5341i) q^{97} +(-4.22270 - 2.03355i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{4} + q^{7} + 2 q^{8} - 7 q^{10} + 2 q^{11} + q^{13} - q^{14} - 2 q^{16} + 12 q^{17} - 6 q^{19} - 7 q^{20} - 2 q^{22} - 35 q^{23} - 6 q^{25} - 8 q^{26} - 6 q^{28} + 14 q^{29} - 8 q^{31}+ \cdots - 37 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 - 2 * q^4 + q^7 + 2 * q^8 - 7 * q^10 + 2 * q^11 + q^13 - q^14 - 2 * q^16 + 12 * q^17 - 6 * q^19 - 7 * q^20 - 2 * q^22 - 35 * q^23 - 6 * q^25 - 8 * q^26 - 6 * q^28 + 14 * q^29 - 8 * q^31 + 2 * q^32 - 5 * q^34 + 18 * q^35 + 31 * q^37 - q^38 + 7 * q^40 + 30 * q^41 - 5 * q^43 - 5 * q^44 - 28 * q^46 + 33 * q^47 + 37 * q^49 - q^50 - 6 * q^52 - 13 * q^53 + 36 * q^55 - q^56 - 38 * q^59 - 5 * q^61 + 8 * q^62 - 2 * q^64 + 20 * q^65 - 7 * q^67 + 19 * q^68 - 18 * q^70 - 3 * q^71 - 22 * q^73 - 31 * q^74 + q^76 - 10 * q^77 - 60 * q^79 + 7 * q^80 + 26 * q^82 + 39 * q^83 + 38 * q^85 - 2 * q^86 - 2 * q^88 - 39 * q^89 + 61 * q^91 - 35 * q^92 + 16 * q^94 - 55 * q^95 - 19 * q^97 - 37 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/522\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{2}{7}\right)$	$1$

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 $

$2$	−0.623490	−	0.781831i	−0.440874	−	0.552838i
$2$	−0.623490	−	0.781831i	−0.440874	−	0.552838i
$3$		0			0
$3$		0			0
$4$	−0.222521	+	0.974928i	−0.111260	+	0.487464i
$5$	−1.00725	−	1.26305i	−0.450457	−	0.564855i	0.503809	−	0.863815i	$-0.331932\pi$
$5$	−1.00725	−	1.26305i	−0.450457	−	0.564855i	−0.954266	+	0.298960i	$0.903360\pi$
$6$		0			0
$7$	0.338433	+	1.48277i	0.127916	+	0.560436i	0.997747	+	0.0670866i	$0.0213704\pi$
$7$	0.338433	+	1.48277i	0.127916	+	0.560436i	−0.869831	+	0.493349i	$0.835772\pi$
$8$	0.900969	−	0.433884i	0.318541	−	0.153401i
$9$		0			0
$10$	−0.359484	+	1.57500i	−0.113679	+	0.498060i
$11$	1.70872	+	0.822877i	0.515199	+	0.248107i	0.673371	−	0.739305i	$-0.264846\pi$
$11$	1.70872	+	0.822877i	0.515199	+	0.248107i	−0.158172	+	0.987412i	$0.550560\pi$
$12$		0			0
$13$	2.87014	+	1.38219i	0.796035	+	0.383350i	0.787268	−	0.616611i	$-0.211495\pi$
$13$	2.87014	+	1.38219i	0.796035	+	0.383350i	0.00876713	+	0.999962i	$0.497209\pi$
$14$	0.948269	−	1.18909i	0.253436	−	0.317798i
$15$		0			0
$16$	−0.900969	−	0.433884i	−0.225242	−	0.108471i
$17$	1.69929			0.412138			0.206069	−	0.978537i	$-0.433933\pi$
$17$	1.69929			0.412138			0.206069	+	0.978537i	$0.433933\pi$
$18$		0			0
$19$	0.818639	−	3.58669i	0.187809	−	0.822843i	−0.789960	−	0.613158i	$-0.789899\pi$
$19$	0.818639	−	3.58669i	0.187809	−	0.822843i	0.977769	−	0.209685i	$-0.0672439\pi$
$20$	1.45552	−	0.700942i	0.325465	−	0.156735i
$21$		0			0
$22$	−0.422020	−	1.84899i	−0.0899749	−	0.394206i
$23$	1.67782	−	2.10392i	0.349849	−	0.438697i	−0.575506	−	0.817797i	$-0.695195\pi$
$23$	1.67782	−	2.10392i	0.349849	−	0.438697i	0.925356	+	0.379100i	$0.123766\pi$
$24$		0			0
$25$	0.531856	−	2.33021i	0.106371	−	0.466042i
$26$	−0.708867	−	3.10575i	−0.139020	−	0.609088i
$27$		0			0
$28$	−1.52091			−0.287424
$29$	4.31703	+	3.21920i	0.801652	+	0.597791i
$29$	4.31703	+	3.21920i	0.801652	+	0.597791i
$30$		0			0
$31$	−1.11130	−	1.39353i	−0.199596	−	0.250285i	0.671953	−	0.740594i	$-0.265456\pi$
$31$	−1.11130	−	1.39353i	−0.199596	−	0.250285i	−0.871549	+	0.490308i	$0.836884\pi$
$32$	0.222521	+	0.974928i	0.0393365	+	0.172345i
$33$		0			0
$34$	−1.05949	−	1.32856i	−0.181701	−	0.227846i
$35$	1.53194	−	1.92099i	0.258944	−	0.324706i
$36$		0			0
$37$	6.37006	−	3.06766i	1.04723	−	0.504320i	0.170529	−	0.985353i	$-0.445452\pi$
$37$	6.37006	−	3.06766i	1.04723	−	0.504320i	0.876703	+	0.481032i	$0.159738\pi$
$38$	−3.31460	+	1.59623i	−0.537699	+	0.258942i
$39$		0			0
$40$	−1.45552	−	0.700942i	−0.230138	−	0.110829i
$41$	5.03259			0.785959			0.392979	−	0.919547i	$-0.371444\pi$
$41$	5.03259			0.785959			0.392979	+	0.919547i	$0.371444\pi$
$42$		0			0
$43$	−1.18247	+	1.48277i	−0.180325	+	0.226121i	−0.863776	−	0.503876i	$-0.831907\pi$
$43$	−1.18247	+	1.48277i	−0.180325	+	0.226121i	0.683451	+	0.729997i	$0.260478\pi$
$44$	−1.18247	+	1.48277i	−0.178264	+	0.223537i
$45$		0			0
$46$	−2.69101			−0.396768
$47$	2.31606	+	1.11536i	0.337832	+	0.162691i	0.595106	−	0.803647i	$-0.297110\pi$
$47$	2.31606	+	1.11536i	0.337832	+	0.162691i	−0.257274	+	0.966339i	$0.582824\pi$
$48$		0			0
$49$	4.22270	−	2.03355i	0.603243	−	0.290507i
$50$	−2.15344	+	1.03704i	−0.304542	+	0.146660i
$51$		0			0
$52$	−1.98620	+	2.49062i	−0.275437	+	0.345387i
$53$	−5.14319	−	6.44936i	−0.706472	−	0.885888i	0.291016	−	0.956718i	$-0.406007\pi$
$53$	−5.14319	−	6.44936i	−0.706472	−	0.885888i	−0.997488	+	0.0708303i	$0.977435\pi$
$54$		0			0
$55$	−0.681776	−	2.98705i	−0.0919306	−	0.402774i
$56$	0.948269	+	1.18909i	0.126718	+	0.158899i
$57$		0			0
$58$	−0.174748	−	5.38233i	−0.0229456	−	0.706734i
$59$	−2.95027			−0.384093			−0.192046	−	0.981386i	$-0.561512\pi$
$59$	−2.95027			−0.384093			−0.192046	+	0.981386i	$0.561512\pi$
$60$		0			0
$61$	1.72363	+	7.55173i	0.220688	+	0.966899i	0.956962	+	0.290215i	$0.0937268\pi$
$61$	1.72363	+	7.55173i	0.220688	+	0.966899i	−0.736273	+	0.676685i	$0.763416\pi$
$62$	−0.396619	+	1.73770i	−0.0503707	+	0.220688i
$63$		0			0
$64$	0.623490	−	0.781831i	0.0779362	−	0.0977289i
$65$	−1.14518	−	5.01736i	−0.142042	−	0.622327i
$66$		0			0
$67$	−2.23359	+	1.07564i	−0.272876	+	0.131410i	−0.565318	−	0.824873i	$-0.691246\pi$
$67$	−2.23359	+	1.07564i	−0.272876	+	0.131410i	0.292442	+	0.956283i	$0.405532\pi$
$68$	−0.378127	+	1.65668i	−0.0458546	+	0.200902i
$69$		0			0
$70$	−2.45703			−0.293672
$71$	5.46771	+	2.63311i	0.648898	+	0.312493i	0.729223	−	0.684276i	$-0.239882\pi$
$71$	5.46771	+	2.63311i	0.648898	+	0.312493i	−0.0803250	+	0.996769i	$0.525596\pi$
$72$		0			0
$73$	2.33692	−	2.93041i	0.273516	−	0.342978i	−0.626034	−	0.779796i	$-0.715323\pi$
$73$	2.33692	−	2.93041i	0.273516	−	0.342978i	0.899550	+	0.436817i	$0.143894\pi$
$74$	−6.37006	−	3.06766i	−0.740505	−	0.356608i
$75$		0			0
$76$	3.31460	+	1.59623i	0.380211	+	0.183100i
$77$	−0.641852	+	2.81214i	−0.0731458	+	0.320473i
$78$		0			0
$79$	−8.30753	+	4.00069i	−0.934670	+	0.450113i	−0.838286	−	0.545231i	$-0.816442\pi$
$79$	−8.30753	+	4.00069i	−0.934670	+	0.450113i	−0.0963841	+	0.995344i	$0.530728\pi$
$80$	0.359484	+	1.57500i	0.0401915	+	0.176091i
$81$		0			0
$82$	−3.13777	−	3.93464i	−0.346509	−	0.434508i
$83$	−1.22901	+	5.38465i	−0.134902	+	0.591042i	0.861609	+	0.507573i	$0.169457\pi$
$83$	−1.22901	+	5.38465i	−0.134902	+	0.591042i	−0.996510	+	0.0834694i	$0.973400\pi$
$84$		0			0
$85$	−1.71161	−	2.14629i	−0.185650	−	0.232798i
$86$	1.89654			0.204509
$87$		0			0
$88$	1.89654			0.202172
$89$	−9.95740	−	12.4862i	−1.05548	−	1.32353i	−0.944065	−	0.329759i	$-0.893032\pi$
$89$	−9.95740	−	12.4862i	−1.05548	−	1.32353i	−0.111417	−	0.993774i	$-0.535539\pi$
$90$		0			0
$91$	−1.07812	+	4.72355i	−0.113018	+	0.495163i
$92$	1.67782	+	2.10392i	0.174925	+	0.219348i
$93$		0			0
$94$	−0.572020	−	2.50618i	−0.0589994	−	0.258493i
$95$	−5.35476	+	2.57872i	−0.549387	+	0.264571i
$96$		0			0
$97$	−3.31730	+	14.5341i	−0.336821	+	1.47571i	0.468814	+	0.883297i	$0.344682\pi$
$97$	−3.31730	+	14.5341i	−0.336821	+	1.47571i	−0.805635	+	0.592412i	$0.798176\pi$
$98$	−4.22270	−	2.03355i	−0.426557	−	0.205419i
$99$		0			0
$100$	2.15344	+	1.03704i	0.215344	+	0.103704i
$101$	−0.114672	+	0.143794i	−0.0114102	+	0.0143080i	−0.787504	−	0.616310i	$-0.788627\pi$
$101$	−0.114672	+	0.143794i	−0.0114102	+	0.0143080i	0.776094	+	0.630618i	$0.217198\pi$
$102$		0			0
$103$	13.5567	+	6.52856i	1.33578	+	0.643279i	0.959101	−	0.283065i	$-0.0913511\pi$
$103$	13.5567	+	6.52856i	1.33578	+	0.643279i	0.376681	+	0.926343i	$0.377065\pi$
$104$	3.18562			0.312376
$105$		0			0
$106$	−1.83558	+	8.04222i	−0.178288	+	0.781130i
$107$	−0.273899	+	0.131903i	−0.0264789	+	0.0127515i	−0.447076	−	0.894496i	$-0.647535\pi$
$107$	−0.273899	+	0.131903i	−0.0264789	+	0.0127515i	0.420597	+	0.907247i	$0.361820\pi$
$108$		0			0
$109$	−2.00800	−	8.79762i	−0.192332	−	0.842660i	−0.975350	−	0.220662i	$-0.929178\pi$
$109$	−2.00800	−	8.79762i	−0.192332	−	0.842660i	0.783019	−	0.621998i	$-0.213679\pi$
$110$	−1.91029	+	2.39543i	−0.182139	+	0.228395i
$111$		0			0
$112$	0.338433	−	1.48277i	0.0319790	−	0.140109i
$113$	1.80183	+	7.89435i	0.169502	+	0.742638i	0.986198	+	0.165570i	$0.0529463\pi$
$113$	1.80183	+	7.89435i	0.169502	+	0.742638i	−0.816696	+	0.577069i	$0.804197\pi$
$114$		0			0
$115$	−4.34735			−0.405392
$116$	−4.09912	+	3.49245i	−0.380594	+	0.324266i
$117$		0			0
$118$	1.83946	+	2.30662i	0.169336	+	0.212341i
$119$	0.575096	+	2.51966i	0.0527189	+	0.230977i
$120$		0			0
$121$	−4.61578	−	5.78801i	−0.419617	−	0.526183i
$122$	4.82951	−	6.05601i	0.437243	−	0.548286i
$123$		0			0
$124$	1.60588	−	0.773350i	0.144212	−	0.0694489i
$125$	−10.7565	+	5.18006i	−0.962091	+	0.463319i
$126$		0			0
$127$	8.57262	+	4.12836i	0.760697	+	0.366332i	0.773674	−	0.633583i	$-0.218417\pi$
$127$	8.57262	+	4.12836i	0.760697	+	0.366332i	−0.0129773	+	0.999916i	$0.504131\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−3.20872	+	4.02361i	−0.281424	+	0.352894i
$131$	−8.88757	+	11.1447i	−0.776511	+	0.973714i	−1.00000		0.000992917i	$-0.999684\pi$
$131$	−8.88757	+	11.1447i	−0.776511	+	0.973714i	0.223489	+	0.974706i	$0.428255\pi$
$132$		0			0
$133$	5.59530			0.485174
$134$	2.23359	+	1.07564i	0.192952	+	0.0929210i
$135$		0			0
$136$	1.53101	−	0.737293i	0.131283	−	0.0632224i
$137$	5.82435	−	2.80486i	0.497608	−	0.239635i	−0.168208	−	0.985752i	$-0.553798\pi$
$137$	5.82435	−	2.80486i	0.497608	−	0.239635i	0.665816	+	0.746116i	$0.268084\pi$
$138$		0			0
$139$	−8.88930	+	11.1468i	−0.753980	+	0.945462i	−0.999715	−	0.0238756i	$-0.992399\pi$
$139$	−8.88930	+	11.1468i	−0.753980	+	0.945462i	0.245734	+	0.969337i	$0.420971\pi$
$140$	1.53194	+	1.92099i	0.129472	+	0.162353i
$141$		0			0
$142$	−1.35041	−	5.91655i	−0.113324	−	0.496506i
$143$	3.76691	+	4.72355i	0.315005	+	0.395003i
$144$		0			0
$145$	−0.282307	−	8.69519i	−0.0234443	−	0.722096i
$146$	−3.74813			−0.310198
$147$		0			0
$148$	1.57328	+	6.89297i	0.129322	+	0.566599i
$149$	−1.83339	+	8.03260i	−0.150197	+	0.658056i	0.842630	+	0.538493i	$0.181006\pi$
$149$	−1.83339	+	8.03260i	−0.150197	+	0.658056i	−0.992827	+	0.119563i	$0.961851\pi$
$150$		0			0
$151$	−13.7186	+	17.2026i	−1.11640	+	1.39992i	−0.209900	+	0.977723i	$0.567314\pi$
$151$	−13.7186	+	17.2026i	−1.11640	+	1.39992i	−0.906502	+	0.422201i	$0.861258\pi$
$152$	−0.818639	−	3.58669i	−0.0664004	−	0.290919i
$153$		0			0
$154$	2.59881	−	1.25152i	0.209418	−	0.100850i
$155$	−0.640741	+	2.80727i	−0.0514655	+	0.225485i
$156$		0			0
$157$	0.135585			0.0108208			0.00541041	−	0.999985i	$-0.498278\pi$
$157$	0.135585			0.0108208			0.00541041	+	0.999985i	$0.498278\pi$
$158$	8.30753	+	4.00069i	0.660911	+	0.318278i
$159$		0			0
$160$	1.00725	−	1.26305i	0.0796303	−	0.0998532i
$161$	3.68746	+	1.77579i	0.290613	+	0.139952i
$162$		0			0
$163$	−9.23815	−	4.44886i	−0.723587	−	0.348461i	0.0355711	−	0.999367i	$-0.488675\pi$
$163$	−9.23815	−	4.44886i	−0.723587	−	0.348461i	−0.759158	+	0.650906i	$0.774389\pi$
$164$	−1.11986	+	4.90641i	−0.0874461	+	0.383127i
$165$		0			0
$166$	4.97617	−	2.39640i	0.386225	−	0.185996i
$167$	3.73573	+	16.3673i	0.289079	+	1.26654i	0.885791	+	0.464084i	$0.153616\pi$
$167$	3.73573	+	16.3673i	0.289079	+	1.26654i	−0.596712	+	0.802456i	$0.703526\pi$
$168$		0			0
$169$	−1.77808	−	2.22965i	−0.136776	−	0.171511i
$170$	−0.610867	+	2.67638i	−0.0468513	+	0.205269i
$171$		0			0
$172$	−1.18247	−	1.48277i	−0.0901627	−	0.113060i
$173$	−4.15473			−0.315878			−0.157939	−	0.987449i	$-0.550485\pi$
$173$	−4.15473			−0.315878			−0.157939	+	0.987449i	$0.550485\pi$
$174$		0			0
$175$	3.63517			0.274793
$176$	−1.18247	−	1.48277i	−0.0891322	−	0.111768i
$177$		0			0
$178$	−3.55376	+	15.5700i	−0.266365	+	1.16702i
$179$	−6.60922	−	8.28770i	−0.493996	−	0.619452i	0.470867	−	0.882204i	$-0.343941\pi$
$179$	−6.60922	−	8.28770i	−0.493996	−	0.619452i	−0.964863	+	0.262753i	$0.915370\pi$
$180$		0			0
$181$	−4.84352	−	21.2209i	−0.360016	−	1.57733i	−0.753147	−	0.657852i	$-0.771465\pi$
$181$	−4.84352	−	21.2209i	−0.360016	−	1.57733i	0.393131	−	0.919483i	$-0.371392\pi$
$182$	4.36522	−	2.10218i	0.323572	−	0.155824i
$183$		0			0
$184$	0.598806	−	2.62354i	0.0441446	−	0.193410i
$185$	−10.2909	−	4.95583i	−0.756601	−	0.364360i
$186$		0			0
$187$	2.90361	+	1.39831i	0.212333	+	0.102254i
$188$	−1.60276	+	2.00980i	−0.116894	+	0.146580i
$189$		0			0
$190$	5.35476	+	2.57872i	0.388475	+	0.187080i
$191$	14.5209			1.05069			0.525346	−	0.850888i	$-0.323936\pi$
$191$	14.5209			1.05069			0.525346	+	0.850888i	$0.323936\pi$
$192$		0			0
$193$	1.06926	−	4.68476i	0.0769674	−	0.337216i	−0.921754	−	0.387776i	$-0.873243\pi$
$193$	1.06926	−	4.68476i	0.0769674	−	0.337216i	0.998721	+	0.0505599i	$0.0161006\pi$
$194$	13.4315	−	6.46826i	0.964324	−	0.464394i
$195$		0			0
$196$	1.04292	+	4.56934i	0.0744944	+	0.326381i
$197$	9.49108	−	11.9014i	0.676212	−	0.847943i	−0.318787	−	0.947826i	$-0.603276\pi$
$197$	9.49108	−	11.9014i	0.676212	−	0.847943i	0.994999	+	0.0998835i	$0.0318470\pi$
$198$		0			0
$199$	2.71330	−	11.8877i	0.192341	−	0.842699i	−0.783005	−	0.622015i	$-0.786314\pi$
$199$	2.71330	−	11.8877i	0.192341	−	0.842699i	0.975345	−	0.220683i	$-0.0708288\pi$
$200$	−0.531856	−	2.33021i	−0.0376079	−	0.164771i
$201$		0			0
$202$	0.183919			0.0129405
$203$	−3.31232	+	7.49066i	−0.232480	+	0.525741i
$204$		0			0
$205$	−5.06909	−	6.35644i	−0.354040	−	0.443953i
$206$	−3.34823	−	14.6696i	−0.233282	−	1.02208i
$207$		0			0
$208$	−1.98620	−	2.49062i	−0.137718	−	0.172693i
$209$	4.35023	−	5.45502i	0.300912	−	0.377332i
$210$		0			0
$211$	−12.9606	+	6.24151i	−0.892246	+	0.429683i	−0.823082	−	0.567922i	$-0.807747\pi$
$211$	−12.9606	+	6.24151i	−0.892246	+	0.429683i	−0.0691638	+	0.997605i	$0.522033\pi$
$212$	7.43213	−	3.57912i	0.510441	−	0.245815i
$213$		0			0
$214$	0.273899	+	0.131903i	0.0187234	+	0.00901670i
$215$	3.06387			0.208954
$216$		0			0
$217$	1.69019	−	2.11943i	0.114737	−	0.143876i
$218$	−5.62629	+	7.05515i	−0.381061	+	0.477835i
$219$		0			0
$220$	3.06387			0.206566
$221$	4.87720	+	2.34874i	0.328076	+	0.157993i
$222$		0			0
$223$	11.5189	−	5.54720i	0.771362	−	0.371468i	−0.00643891	−	0.999979i	$-0.502050\pi$
$223$	11.5189	−	5.54720i	0.771362	−	0.371468i	0.777801	+	0.628511i	$0.216335\pi$
$224$	−1.37029	+	0.659896i	−0.0915563	+	0.0440912i
$225$		0			0
$226$	5.04863	−	6.33078i	0.335830	−	0.421117i
$227$	−16.4768	−	20.6612i	−1.09360	−	1.37133i	−0.922462	−	0.386088i	$-0.873826\pi$
$227$	−16.4768	−	20.6612i	−1.09360	−	1.37133i	−0.171141	−	0.985246i	$-0.554745\pi$
$228$		0			0
$229$	−4.27284	−	18.7206i	−0.282358	−	1.23709i	−0.894762	−	0.446544i	$-0.852655\pi$
$229$	−4.27284	−	18.7206i	−0.282358	−	1.23709i	0.612404	−	0.790545i	$-0.290203\pi$
$230$	2.71053	+	3.39889i	0.178727	+	0.224116i
$231$		0			0
$232$	5.28627	+	1.02731i	0.347060	+	0.0674464i
$233$	8.12368			0.532200			0.266100	−	0.963945i	$-0.414265\pi$
$233$	8.12368			0.532200			0.266100	+	0.963945i	$0.414265\pi$
$234$		0			0
$235$	−0.924102	−	4.04876i	−0.0602818	−	0.264112i
$236$	0.656497	−	2.87630i	0.0427343	−	0.187231i
$237$		0			0
$238$	1.61138	−	2.02061i	0.104450	−	0.130977i
$239$	−6.74549	−	29.5539i	−0.436329	−	1.91168i	−0.410131	−	0.912027i	$-0.634517\pi$
$239$	−6.74549	−	29.5539i	−0.436329	−	1.91168i	−0.0261983	−	0.999657i	$-0.508340\pi$
$240$		0			0
$241$	−4.12092	+	1.98453i	−0.265452	+	0.127835i	−0.561876	−	0.827222i	$-0.689920\pi$
$241$	−4.12092	+	1.98453i	−0.265452	+	0.127835i	0.296424	+	0.955056i	$0.404206\pi$
$242$	−1.64735	+	7.21753i	−0.105896	+	0.463960i
$243$		0			0
$244$	−7.74593			−0.495883
$245$	−6.82180	−	3.28521i	−0.435829	−	0.209884i
$246$		0			0
$247$	7.30709	−	9.16281i	0.464939	−	0.583015i
$248$	−1.60588	−	0.773350i	−0.101973	−	0.0491078i
$249$		0			0
$250$	10.7565	+	5.18006i	0.680301	+	0.327616i
$251$	−2.96313	+	12.9823i	−0.187031	+	0.819438i	0.791139	+	0.611636i	$0.209488\pi$
$251$	−2.96313	+	12.9823i	−0.187031	+	0.819438i	−0.978171	+	0.207802i	$0.933369\pi$
$252$		0			0
$253$	4.59819	−	2.21437i	0.289086	−	0.139216i
$254$	−2.11726	−	9.27633i	−0.132849	−	0.582049i
$255$		0			0
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$	4.33421	−	18.9894i	0.270360	−	1.18453i	−0.639228	−	0.769017i	$-0.720746\pi$
$257$	4.33421	−	18.9894i	0.270360	−	1.18453i	0.909589	−	0.415510i	$-0.136397\pi$
$258$		0			0
$259$	6.70449	+	8.40716i	0.416597	+	0.522396i
$260$	5.14639			0.319166
$261$		0			0
$262$	14.2546			0.880649
$263$	−6.26071	−	7.85069i	−0.386052	−	0.484094i	0.550394	−	0.834905i	$-0.314477\pi$
$263$	−6.26071	−	7.85069i	−0.386052	−	0.484094i	−0.936446	+	0.350811i	$0.885906\pi$
$264$		0			0
$265$	−2.96540	+	12.9923i	−0.182163	+	0.798108i
$266$	−3.48862	−	4.37459i	−0.213901	−	0.268223i
$267$		0			0
$268$	−0.551650	−	2.41694i	−0.0336974	−	0.147638i
$269$	−5.34815	+	2.57553i	−0.326083	+	0.157033i	−0.589762	−	0.807577i	$-0.700778\pi$
$269$	−5.34815	+	2.57553i	−0.326083	+	0.157033i	0.263679	+	0.964610i	$0.415064\pi$
$270$		0			0
$271$	−4.22317	+	18.5029i	−0.256540	+	1.12397i	0.668383	+	0.743817i	$0.266987\pi$
$271$	−4.22317	+	18.5029i	−0.256540	+	1.12397i	−0.924922	+	0.380156i	$0.875870\pi$
$272$	−1.53101	−	0.737293i	−0.0928308	−	0.0447050i
$273$		0			0
$274$	−5.82435	−	2.80486i	−0.351862	−	0.169448i
$275$	2.82627	−	3.54403i	0.170431	−	0.213713i
$276$		0			0
$277$	23.2546	+	11.1988i	1.39723	+	0.672872i	0.972598	−	0.232494i	$-0.0746884\pi$
$277$	23.2546	+	11.1988i	1.39723	+	0.672872i	0.424634	+	0.905365i	$0.360403\pi$
$278$	14.2573			0.855098
$279$		0			0
$280$	0.546742	−	2.39543i	0.0326741	−	0.143154i
$281$	22.7311	−	10.9467i	1.35602	−	0.653027i	0.392278	−	0.919847i	$-0.371687\pi$
$281$	22.7311	−	10.9467i	1.35602	−	0.653027i	0.963747	+	0.266820i	$0.0859728\pi$
$282$		0			0
$283$	−2.74754	−	12.0378i	−0.163324	−	0.715571i	−0.988566	−	0.150791i	$-0.951818\pi$
$283$	−2.74754	−	12.0378i	−0.163324	−	0.715571i	0.825241	−	0.564780i	$-0.191039\pi$
$284$	−3.78378	+	4.74470i	−0.224526	+	0.281546i
$285$		0			0
$286$	1.34439	−	5.89017i	0.0794957	−	0.348293i
$287$	1.70320	+	7.46219i	0.100537	+	0.440479i
$288$		0			0
$289$	−14.1124			−0.830142
$290$	−6.62216	+	5.64208i	−0.388866	+	0.331314i
$291$		0			0
$292$	2.33692	+	2.93041i	0.136758	+	0.171489i
$293$	2.74795	+	12.0396i	0.160537	+	0.703359i	0.989557	+	0.144140i	$0.0460416\pi$
$293$	2.74795	+	12.0396i	0.160537	+	0.703359i	−0.829020	+	0.559219i	$0.811101\pi$
$294$		0			0
$295$	2.97167	+	3.72635i	0.173017	+	0.216957i
$296$	4.40822	−	5.52773i	0.256223	−	0.321293i
$297$		0			0
$298$	7.42324	−	3.57484i	0.430016	−	0.207085i
$299$	7.72359	−	3.71948i	0.446667	−	0.215103i
$300$		0			0
$301$	−2.59881	−	1.25152i	−0.149793	−	0.0721364i
$302$	22.0029			1.26612
$303$		0			0
$304$	−2.29377	+	2.87630i	−0.131557	+	0.164967i
$305$	7.80211	−	9.78353i	0.446747	−	0.560203i
$306$		0			0
$307$	11.8371			0.675579			0.337790	−	0.941222i	$-0.390321\pi$
$307$	11.8371			0.675579			0.337790	+	0.941222i	$0.390321\pi$
$308$	−2.59881	−	1.25152i	−0.148081	−	0.0713119i
$309$		0			0
$310$	2.59431	−	1.24935i	0.147347	−	0.0709584i
$311$	−9.16959	+	4.41584i	−0.519960	+	0.250400i	−0.675408	−	0.737445i	$-0.736032\pi$
$311$	−9.16959	+	4.41584i	−0.519960	+	0.250400i	0.155448	+	0.987844i	$0.450318\pi$
$312$		0			0
$313$	−8.31868	+	10.4313i	−0.470200	+	0.589612i	−0.959220	−	0.282661i	$-0.908783\pi$
$313$	−8.31868	+	10.4313i	−0.470200	+	0.589612i	0.489020	+	0.872272i	$0.337354\pi$
$314$	−0.0845356	−	0.106004i	−0.00477062	−	0.00598217i
$315$		0			0
$316$	−2.05179	−	8.98948i	−0.115422	−	0.505698i
$317$	7.46575	+	9.36176i	0.419318	+	0.525809i	0.945962	−	0.324278i	$-0.105121\pi$
$317$	7.46575	+	9.36176i	0.419318	+	0.525809i	−0.526644	+	0.850086i	$0.676550\pi$
$318$		0			0
$319$	4.72759	+	9.05311i	0.264694	+	0.506877i
$320$	−1.61551			−0.0903096
$321$		0			0
$322$	−0.910728	−	3.99016i	−0.0507529	−	0.222363i
$323$	1.39110	−	6.09482i	0.0774030	−	0.339125i
$324$		0			0
$325$	4.74729	−	5.95292i	0.263332	−	0.330208i
$326$	2.28163	+	9.99649i	0.126368	+	0.553654i
$327$		0			0
$328$	4.53421	−	2.18356i	0.250360	−	0.120567i
$329$	−0.869989	+	3.81167i	−0.0479640	+	0.210144i
$330$		0			0
$331$	−23.3952			−1.28592			−0.642958	−	0.765902i	$-0.722293\pi$
$331$	−23.3952			−1.28592			−0.642958	+	0.765902i	$0.722293\pi$
$332$	−4.97617	−	2.39640i	−0.273103	−	0.131519i
$333$		0			0
$334$	10.4673	−	13.1256i	0.572744	−	0.718198i
$335$	3.60837	+	1.73770i	0.197147	+	0.0949408i
$336$		0			0
$337$	−20.5917	−	9.91642i	−1.12170	−	0.540182i	−0.221282	−	0.975210i	$-0.571024\pi$
$337$	−20.5917	−	9.91642i	−1.12170	−	0.540182i	−0.900417	+	0.435028i	$0.856738\pi$
$338$	−0.634591	+	2.78033i	−0.0345172	+	0.151230i
$339$		0			0
$340$	2.47335	−	1.19110i	0.134136	−	0.0645966i
$341$	−0.752203	−	3.29562i	−0.0407341	−	0.178468i
$342$		0			0
$343$	11.0823	+	13.8967i	0.598387	+	0.750353i
$344$	−0.422020	+	1.84899i	−0.0227538	+	0.0996908i
$345$		0			0
$346$	2.59043	+	3.24830i	0.139262	+	0.174630i
$347$	−6.48177			−0.347960			−0.173980	−	0.984749i	$-0.555663\pi$
$347$	−6.48177			−0.347960			−0.173980	+	0.984749i	$0.555663\pi$
$348$		0			0
$349$	−11.7835			−0.630754			−0.315377	−	0.948966i	$-0.602131\pi$
$349$	−11.7835			−0.630754			−0.315377	+	0.948966i	$0.602131\pi$
$350$	−2.26649	−	2.84209i	−0.121149	−	0.151916i
$351$		0			0
$352$	−0.422020	+	1.84899i	−0.0224937	+	0.0985514i
$353$	11.9204	+	14.9477i	0.634457	+	0.795584i	0.990298	−	0.138963i	$-0.0443768\pi$
$353$	11.9204	+	14.9477i	0.634457	+	0.795584i	−0.355841	+	0.934547i	$0.615805\pi$
$354$		0			0
$355$	−2.18160	−	9.55823i	−0.115787	−	0.507298i
$356$	14.3889	−	6.92931i	0.762608	−	0.367253i
$357$		0			0
$358$	−2.35880	+	10.3346i	−0.124667	+	0.546200i
$359$	−7.46972	−	3.59723i	−0.394237	−	0.189854i	0.226254	−	0.974068i	$-0.427352\pi$
$359$	−7.46972	−	3.59723i	−0.394237	−	0.189854i	−0.620490	+	0.784214i	$0.713066\pi$
$360$		0			0
$361$	4.92423	+	2.37138i	0.259170	+	0.124810i
$362$	−13.5713	+	17.0178i	−0.713289	+	0.894437i
$363$		0			0
$364$	−4.36522	−	2.10218i	−0.228800	−	0.110184i
$365$	−6.05514			−0.316940
$366$		0			0
$367$	−6.42229	+	28.1379i	−0.335241	+	1.46879i	0.473590	+	0.880746i	$0.342958\pi$
$367$	−6.42229	+	28.1379i	−0.335241	+	1.46879i	−0.808831	+	0.588041i	$0.799899\pi$
$368$	−2.42452	+	1.16759i	−0.126387	+	0.0608646i
$369$		0			0
$370$	2.54164	+	11.1356i	0.132133	+	0.578915i
$371$	7.82231	−	9.80887i	0.406114	−	0.509251i
$372$		0			0
$373$	4.97759	−	21.8082i	0.257730	−	1.12919i	−0.665942	−	0.746004i	$-0.731970\pi$
$373$	4.97759	−	21.8082i	0.257730	−	1.12919i	0.923672	−	0.383185i	$-0.125173\pi$
$374$	−0.717133	−	3.14196i	−0.0370820	−	0.162467i
$375$		0			0
$376$	2.57063			0.132570
$377$	7.94095	+	15.2065i	0.408980	+	0.783176i
$378$		0			0
$379$	−9.28671	−	11.6452i	−0.477026	−	0.598172i	0.483850	−	0.875151i	$-0.339238\pi$
$379$	−9.28671	−	11.6452i	−0.477026	−	0.598172i	−0.960876	+	0.276979i	$0.910667\pi$
$380$	−1.32252	−	5.79432i	−0.0678437	−	0.297243i
$381$		0			0
$382$	−9.05361	−	11.3529i	−0.463223	−	0.580863i
$383$	−6.81614	+	8.54717i	−0.348289	+	0.436740i	−0.924861	−	0.380306i	$-0.875819\pi$
$383$	−6.81614	+	8.54717i	−0.348289	+	0.436740i	0.576572	+	0.817046i	$0.304390\pi$
$384$		0			0
$385$	4.19839	−	2.02184i	0.213970	−	0.103042i
$386$	−4.32937	+	2.08491i	−0.220359	+	0.106119i
$387$		0			0
$388$	−13.4315	−	6.46826i	−0.681880	−	0.328376i
$389$	−15.6282			−0.792380			−0.396190	−	0.918169i	$-0.629668\pi$
$389$	−15.6282			−0.792380			−0.396190	+	0.918169i	$0.629668\pi$
$390$		0			0
$391$	2.85109	−	3.57516i	0.144186	−	0.180804i
$392$	2.92220	−	3.66432i	0.147593	−	0.185076i
$393$		0			0
$394$	−15.2225			−0.766899
$395$	13.4209	+	6.46315i	0.675277	+	0.325196i
$396$		0			0
$397$	6.90371	−	3.32465i	0.346487	−	0.166859i	−0.252543	−	0.967586i	$-0.581267\pi$
$397$	6.90371	−	3.32465i	0.346487	−	0.166859i	0.599031	+	0.800726i	$0.295553\pi$
$398$	−10.9859	+	5.29054i	−0.550674	+	0.265191i
$399$		0			0
$400$	−1.49023	+	1.86868i	−0.0745113	+	0.0934342i
$401$	−2.93903	−	3.68543i	−0.146768	−	0.184042i	0.703013	−	0.711177i	$-0.251838\pi$
$401$	−2.93903	−	3.68543i	−0.146768	−	0.184042i	−0.849781	+	0.527135i	$0.823266\pi$
$402$		0			0
$403$	−1.26348	−	5.53566i	−0.0629383	−	0.275751i
$404$	−0.114672	−	0.143794i	−0.00570512	−	0.00715400i
$405$		0			0
$406$	7.92163	−	2.08067i	0.393144	−	0.103262i
$407$	13.4090			0.664658
$408$		0			0
$409$	1.71367	+	7.50807i	0.0847354	+	0.371250i	0.999461	−	0.0328253i	$-0.0104505\pi$
$409$	1.71367	+	7.50807i	0.0847354	+	0.371250i	−0.914726	+	0.404075i	$0.867593\pi$
$410$	−1.80914	+	7.92635i	−0.0893469	+	0.391454i
$411$		0			0
$412$	−9.38153	+	11.7641i	−0.462195	+	0.579574i
$413$	−0.998471	−	4.37459i	−0.0491315	−	0.215259i
$414$		0			0
$415$	8.03903	−	3.87139i	0.394621	−	0.190039i
$416$	−0.708867	+	3.10575i	−0.0347551	+	0.152272i
$417$		0			0
$418$	−6.97723			−0.341268
$419$	−23.2064	−	11.1756i	−1.13370	−	0.545963i	−0.229605	−	0.973284i	$-0.573743\pi$
$419$	−23.2064	−	11.1756i	−1.13370	−	0.545963i	−0.904100	+	0.427321i	$0.859458\pi$
$420$		0			0
$421$	3.59860	−	4.51250i	0.175385	−	0.219926i	−0.686367	−	0.727255i	$-0.740796\pi$
$421$	3.59860	−	4.51250i	0.175385	−	0.219926i	0.861752	+	0.507329i	$0.169367\pi$
$422$	12.9606	+	6.24151i	0.630913	+	0.303832i
$423$		0			0
$424$	−7.43213	−	3.57912i	−0.360936	−	0.173818i
$425$	0.903775	−	3.95970i	0.0438395	−	0.192074i
$426$		0			0
$427$	−10.6142	+	5.11151i	−0.513655	+	0.247363i
$428$	−0.0676476	−	0.296383i	−0.00326987	−	0.0143262i
$429$		0			0
$430$	−1.91029	−	2.39543i	−0.0921225	−	0.115518i
$431$	−3.64058	+	15.9504i	−0.175361	+	0.768305i	0.808373	+	0.588671i	$0.200349\pi$
$431$	−3.64058	+	15.9504i	−0.175361	+	0.768305i	−0.983733	+	0.179634i	$0.942509\pi$
$432$		0			0
$433$	15.7575	+	19.7592i	0.757255	+	0.949568i	0.999788	−	0.0205753i	$-0.00654978\pi$
$433$	15.7575	+	19.7592i	0.757255	+	0.949568i	−0.242533	+	0.970143i	$0.577978\pi$
$434$	−2.71085			−0.130125
$435$		0			0
$436$	9.02387			0.432165
$437$	−6.17257	−	7.74016i	−0.295274	−	0.370262i
$438$		0			0
$439$	−1.44144	+	6.31536i	−0.0687961	+	0.301415i	−0.997607	−	0.0691384i	$-0.977975\pi$
$439$	−1.44144	+	6.31536i	−0.0687961	+	0.301415i	0.928811	+	0.370554i	$0.120832\pi$
$440$	−1.91029	−	2.39543i	−0.0910696	−	0.114198i
$441$		0			0
$442$	−1.20457	−	5.27756i	−0.0572955	−	0.251028i
$443$	−23.3182	+	11.2295i	−1.10788	+	0.533528i	−0.896128	−	0.443795i	$-0.853632\pi$
$443$	−23.3182	+	11.2295i	−1.10788	+	0.533528i	−0.211754	+	0.977323i	$0.567918\pi$
$444$		0			0
$445$	−5.74112	+	25.1535i	−0.272155	+	1.19239i
$446$	−11.5189	−	5.54720i	−0.545435	−	0.262668i
$447$		0			0
$448$	1.37029	+	0.659896i	0.0647401	+	0.0311772i
$449$	−5.52744	+	6.93120i	−0.260856	+	0.327103i	−0.894962	−	0.446143i	$-0.852797\pi$
$449$	−5.52744	+	6.93120i	−0.260856	+	0.327103i	0.634105	+	0.773247i	$0.281369\pi$
$450$		0			0
$451$	8.59930	+	4.14120i	0.404925	+	0.195002i
$452$	−8.09737			−0.380868
$453$		0			0
$454$	−5.88050	+	25.7641i	−0.275985	+	1.20917i
$455$	7.05204	−	3.39608i	0.330605	−	0.159211i
$456$		0			0
$457$	−4.93294	−	21.6126i	−0.230753	−	1.01100i	−0.949017	−	0.315225i	$-0.897920\pi$
$457$	−4.93294	−	21.6126i	−0.230753	−	1.01100i	0.718263	−	0.695771i	$-0.244937\pi$
$458$	−11.9722	+	15.0127i	−0.559426	+	0.701498i
$459$		0			0
$460$	0.967375	−	4.23835i	0.0451041	−	0.197614i
$461$	8.58503	+	37.6135i	0.399845	+	1.75183i	0.628003	+	0.778211i	$0.283872\pi$
$461$	8.58503	+	37.6135i	0.399845	+	1.75183i	−0.228159	+	0.973624i	$0.573270\pi$
$462$		0			0
$463$	30.1073			1.39921			0.699603	−	0.714531i	$-0.253360\pi$
$463$	30.1073			1.39921			0.699603	+	0.714531i	$0.253360\pi$
$464$	−2.49275	−	4.77349i	−0.115723	−	0.221604i
$465$		0			0
$466$	−5.06503	−	6.35135i	−0.234633	−	0.294220i
$467$	1.25558	+	5.50105i	0.0581012	+	0.254558i	0.995635	−	0.0933375i	$-0.0297535\pi$
$467$	1.25558	+	5.50105i	0.0581012	+	0.254558i	−0.937533	+	0.347895i	$0.886896\pi$
$468$		0			0
$469$	−2.35085	−	2.94787i	−0.108552	−	0.136120i
$470$	−2.58928	+	3.24685i	−0.119434	+	0.149766i
$471$		0			0
$472$	−2.65810	+	1.28007i	−0.122349	+	0.0589202i
$473$	−3.24066	+	1.56062i	−0.149006	+	0.0717573i
$474$		0			0
$475$	−7.92235	−	3.81520i	−0.363502	−	0.175053i
$476$	−2.58446			−0.118458
$477$		0			0
$478$	−18.9004	+	23.7004i	−0.864486	+	1.08403i
$479$	13.3395	−	16.7271i	0.609495	−	0.764283i	−0.377329	−	0.926079i	$-0.623157\pi$
$479$	13.3395	−	16.7271i	0.609495	−	0.764283i	0.986824	+	0.161797i	$0.0517288\pi$
$480$		0			0
$481$	22.5231			1.02696
$482$	4.12092	+	1.98453i	0.187703	+	0.0903928i
$483$		0			0
$484$	6.67000	−	3.21210i	0.303182	−	0.146005i
$485$	21.6987	−	10.4495i	0.985285	−	0.474488i
$486$		0			0
$487$	7.91124	−	9.92038i	0.358492	−	0.449535i	−0.569580	−	0.821936i	$-0.692894\pi$
$487$	7.91124	−	9.92038i	0.358492	−	0.449535i	0.928072	+	0.372401i	$0.121465\pi$
$488$	4.82951	+	6.05601i	0.218622	+	0.274143i
$489$		0			0
$490$	1.68485	+	7.38179i	0.0761136	+	0.333475i
$491$	7.68443	+	9.63597i	0.346794	+	0.434865i	0.924385	−	0.381460i	$-0.124579\pi$
$491$	7.68443	+	9.63597i	0.346794	+	0.434865i	−0.577592	+	0.816326i	$0.696007\pi$
$492$		0			0
$493$	7.33587	+	5.47035i	0.330391	+	0.246372i
$494$	−11.7197			−0.527293
$495$		0			0
$496$	0.396619	+	1.73770i	0.0178087	+	0.0780251i
$497$	−2.05385	+	8.99852i	−0.0921279	+	0.403639i
$498$		0			0
$499$	−2.40764	+	3.01909i	−0.107781	+	0.135153i	−0.832796	−	0.553580i	$-0.813261\pi$
$499$	−2.40764	+	3.01909i	−0.107781	+	0.135153i	0.725015	+	0.688733i	$0.241833\pi$
$500$	−2.65664	−	11.6395i	−0.118808	−	0.520534i
$501$		0			0
$502$	11.9975	−	5.77769i	0.535474	−	0.257871i
$503$	−8.65503	+	37.9202i	−0.385909	+	1.69078i	0.292642	+	0.956222i	$0.405466\pi$
$503$	−8.65503	+	37.9202i	−0.385909	+	1.69078i	−0.678550	+	0.734554i	$0.737391\pi$
$504$		0			0
$505$	0.297122			0.0132218
$506$	−4.59819	−	2.21437i	−0.204414	−	0.0984408i
$507$		0			0
$508$	−5.93244	+	7.43904i	−0.263209	+	0.330054i
$509$	−29.1230	−	14.0249i	−1.29085	−	0.621642i	−0.342697	−	0.939446i	$-0.611340\pi$
$509$	−29.1230	−	14.0249i	−1.29085	−	0.621642i	−0.948156	+	0.317804i	$0.897055\pi$
$510$		0			0
$511$	5.13603	+	2.47338i	0.227204	+	0.109416i
$512$	0.222521	−	0.974928i	0.00983413	−	0.0430861i
$513$		0			0
$514$	−17.5489	+	8.45108i	−0.774047	+	0.372761i
$515$	−5.40909	−	23.6988i	−0.238353	−	1.04429i
$516$		0			0
$517$	3.03970	+	3.81167i	0.133686	+	0.167637i
$518$	2.39280	−	10.4836i	0.105134	−	0.460621i
$519$		0			0
$520$	−3.20872	−	4.02361i	−0.140712	−	0.176447i
$521$	−7.79081			−0.341321			−0.170661	−	0.985330i	$-0.554590\pi$
$521$	−7.79081			−0.341321			−0.170661	+	0.985330i	$0.554590\pi$
$522$		0			0
$523$	−34.8524			−1.52399			−0.761995	−	0.647582i	$-0.775780\pi$
$523$	−34.8524			−1.52399			−0.761995	+	0.647582i	$0.775780\pi$
$524$	−8.88757	−	11.1447i	−0.388255	−	0.486857i
$525$		0			0
$526$	−2.23442	+	9.78965i	−0.0974255	+	0.426849i
$527$	−1.88842	−	2.36801i	−0.0822609	−	0.103152i
$528$		0			0
$529$	3.50659	+	15.3634i	0.152460	+	0.667972i
$530$	12.0067	−	5.78210i	0.521536	−	0.251158i
$531$		0			0
$532$	−1.24507	+	5.45502i	−0.0539807	+	0.236505i
$533$	14.4443	+	6.95599i	0.625650	+	0.301297i
$534$		0			0
$535$	0.442486	+	0.213090i	0.0191304	+	0.00921269i
$536$	−1.54569	+	1.93823i	−0.0667636	+	0.0837189i
$537$		0			0
$538$	5.34815	+	2.57553i	0.230575	+	0.111039i
$539$	8.88878			0.382867
$540$		0			0
$541$	−2.73274	+	11.9729i	−0.117490	+	0.514757i	0.881596	+	0.472005i	$0.156470\pi$
$541$	−2.73274	+	11.9729i	−0.117490	+	0.514757i	−0.999086	+	0.0427517i	$0.986388\pi$
$542$	17.0993	−	8.23458i	0.734477	−	0.353705i
$543$		0			0
$544$	0.378127	+	1.65668i	0.0162121	+	0.0710297i
$545$	−9.08931	+	11.3976i	−0.389343	+	0.488221i
$546$		0			0
$547$	−0.742753	+	3.25421i	−0.0317578	+	0.139140i	−0.988321	−	0.152384i	$-0.951305\pi$
$547$	−0.742753	+	3.25421i	−0.0317578	+	0.139140i	0.956564	+	0.291524i	$0.0941622\pi$
$548$	1.43850	+	6.30246i	0.0614495	+	0.269228i
$549$		0			0
$550$	−4.53299			−0.193287
$551$	15.0804	−	12.8485i	0.642445	−	0.547364i
$552$		0			0
$553$	−8.74367	−	10.9642i	−0.371819	−	0.466246i
$554$	−5.74341	−	25.1635i	−0.244014	−	1.06909i
$555$		0			0
$556$	−8.88930	−	11.1468i	−0.376990	−	0.472731i
$557$	−5.15315	+	6.46185i	−0.218346	+	0.273797i	−0.878926	−	0.476959i	$-0.841739\pi$
$557$	−5.15315	+	6.46185i	−0.218346	+	0.273797i	0.660580	+	0.750756i	$0.270311\pi$
$558$		0			0
$559$	−5.44334	+	2.62137i	−0.230229	+	0.110872i
$560$	−2.21371	+	1.06607i	−0.0935464	+	0.0450496i
$561$		0			0
$562$	−22.7311	−	10.9467i	−0.958854	−	0.461760i
$563$	−16.4004			−0.691193			−0.345596	−	0.938383i	$-0.612323\pi$
$563$	−16.4004			−0.691193			−0.345596	+	0.938383i	$0.612323\pi$
$564$		0			0
$565$	8.15610	−	10.2274i	0.343130	−	0.430271i
$566$	−7.69844	+	9.65354i	−0.323590	+	0.405769i
$567$		0			0
$568$	6.06870			0.254637
$569$	−16.8135	−	8.09698i	−0.704861	−	0.339443i	0.0468812	−	0.998900i	$-0.485072\pi$
$569$	−16.8135	−	8.09698i	−0.704861	−	0.339443i	−0.751742	+	0.659457i	$0.770786\pi$
$570$		0			0
$571$	35.3010	−	17.0001i	1.47730	−	0.711430i	0.490211	−	0.871604i	$-0.336920\pi$
$571$	35.3010	−	17.0001i	1.47730	−	0.711430i	0.987089	+	0.160174i	$0.0512055\pi$
$572$	−5.44334	+	2.62137i	−0.227597	+	0.109605i
$573$		0			0
$574$	4.77225	−	5.98421i	0.199190	−	0.249776i
$575$	−4.01021	−	5.02865i	−0.167237	−	0.209709i
$576$		0			0
$577$	−1.73944	−	7.62100i	−0.0724140	−	0.317266i	0.925729	−	0.378189i	$-0.123453\pi$
$577$	−1.73944	−	7.62100i	−0.0724140	−	0.317266i	−0.998143	+	0.0609223i	$0.980596\pi$
$578$	8.79895	+	11.0335i	0.365988	+	0.458935i
$579$		0			0
$580$	8.54000	+	1.65963i	0.354604	+	0.0689125i
$581$	−8.40016			−0.348497
$582$		0			0
$583$	−3.48126	−	15.2524i	−0.144179	−	0.631689i
$584$	0.834038	−	3.65416i	0.0345127	−	0.151210i
$585$		0			0
$586$	7.69959	−	9.65498i	0.318067	−	0.398844i
$587$	−1.70127	−	7.45375i	−0.0702189	−	0.307649i	0.927607	−	0.373558i	$-0.121862\pi$
$587$	−1.70127	−	7.45375i	−0.0702189	−	0.307649i	−0.997826	+	0.0659091i	$0.979005\pi$
$588$		0			0
$589$	−5.90791	+	2.84510i	−0.243431	+	0.117230i
$590$	1.06058	−	4.64669i	0.0436632	−	0.191301i
$591$		0			0
$592$	−7.07024			−0.290585
$593$	8.78740	+	4.23179i	0.360855	+	0.173779i	0.605522	−	0.795828i	$-0.292964\pi$
$593$	8.78740	+	4.23179i	0.360855	+	0.173779i	−0.244667	+	0.969607i	$0.578679\pi$
$594$		0			0
$595$	2.60320	−	3.26431i	0.106721	−	0.133824i
$596$	−7.42324	−	3.57484i	−0.304068	−	0.146431i
$597$		0			0
$598$	−7.72359	−	3.71948i	−0.315841	−	0.152101i
$599$	−4.77068	+	20.9017i	−0.194925	+	0.854022i	0.778977	+	0.627052i	$0.215739\pi$
$599$	−4.77068	+	20.9017i	−0.194925	+	0.854022i	−0.973902	+	0.226969i	$0.927118\pi$
$600$		0			0
$601$	−24.6258	+	11.8592i	−1.00451	+	0.483745i	−0.862465	−	0.506116i	$-0.831081\pi$
$601$	−24.6258	+	11.8592i	−1.00451	+	0.483745i	−0.142041	+	0.989861i	$0.545367\pi$
$602$	0.641852	+	2.81214i	0.0261599	+	0.114614i
$603$		0			0
$604$	−13.7186	−	17.2026i	−0.558201	−	0.699962i
$605$	−2.66131	+	11.6600i	−0.108198	+	0.474045i
$606$		0			0
$607$	20.7591	+	26.0310i	0.842584	+	1.05657i	0.997640	+	0.0686611i	$0.0218727\pi$
$607$	20.7591	+	26.0310i	0.842584	+	1.05657i	−0.155056	+	0.987906i	$0.549556\pi$
$608$	3.67893			0.149200
$609$		0			0
$610$	−12.5136			−0.506661
$611$	5.10580	+	6.40247i	0.206558	+	0.259016i
$612$		0			0
$613$	−6.67444	+	29.2426i	−0.269578	+	1.18110i	0.640928	+	0.767601i	$0.278550\pi$
$613$	−6.67444	+	29.2426i	−0.269578	+	1.18110i	−0.910506	+	0.413497i	$0.864307\pi$
$614$	−7.38031	−	9.25462i	−0.297845	−	0.373486i
$615$		0			0
$616$	0.641852	+	2.81214i	0.0258610	+	0.113304i
$617$	−17.1426	+	8.25544i	−0.690135	+	0.332352i	−0.745868	−	0.666094i	$-0.767965\pi$
$617$	−17.1426	+	8.25544i	−0.690135	+	0.332352i	0.0557324	+	0.998446i	$0.482251\pi$
$618$		0			0
$619$	9.12639	−	39.9853i	0.366820	−	1.60715i	−0.368636	−	0.929574i	$-0.620175\pi$
$619$	9.12639	−	39.9853i	0.366820	−	1.60715i	0.735457	−	0.677572i	$-0.236968\pi$
$620$	−2.59431	−	1.24935i	−0.104190	−	0.0501752i
$621$		0			0
$622$	9.16959	+	4.41584i	0.367667	+	0.177059i
$623$	15.1443	−	18.9903i	0.606742	−	0.760831i
$624$		0			0
$625$	6.61001	+	3.18321i	0.264400	+	0.127329i
$626$	13.3421			0.533259
$627$		0			0
$628$	−0.0301704	+	0.132185i	−0.00120393	+	0.00527476i
$629$	10.8246	−	5.21284i	0.431604	−	0.207849i
$630$		0			0
$631$	−6.01242	−	26.3421i	−0.239350	−	1.04866i	−0.941600	−	0.336732i	$-0.890678\pi$
$631$	−6.01242	−	26.3421i	−0.239350	−	1.04866i	0.702250	−	0.711931i	$-0.252179\pi$
$632$	−5.74899	+	7.20900i	−0.228682	+	0.286759i
$633$		0			0
$634$	2.66450	−	11.6739i	0.105821	−	0.463631i
$635$	−3.42045	−	14.9860i	−0.135737	−	0.594701i
$636$		0			0
$637$	14.9305			0.591568
$638$	4.13040	−	9.34070i	0.163524	−	0.369802i
$639$		0			0
$640$	1.00725	+	1.26305i	0.0398151	+	0.0499266i
$641$	6.88451	+	30.1630i	0.271922	+	1.19137i	0.907742	+	0.419529i	$0.137805\pi$
$641$	6.88451	+	30.1630i	0.271922	+	1.19137i	−0.635820	+	0.771837i	$0.719338\pi$
$642$		0			0
$643$	−1.31321	−	1.64672i	−0.0517881	−	0.0649403i	0.755263	−	0.655422i	$-0.227509\pi$
$643$	−1.31321	−	1.64672i	−0.0517881	−	0.0649403i	−0.807051	+	0.590482i	$0.798938\pi$
$644$	−2.55180	+	3.19986i	−0.100555	+	0.126092i
$645$		0			0
$646$	−5.63246	+	2.71245i	−0.221606	+	0.106720i
$647$	−14.0227	+	6.75299i	−0.551291	+	0.265488i	−0.688724	−	0.725023i	$-0.741829\pi$
$647$	−14.0227	+	6.75299i	−0.551291	+	0.265488i	0.137434	+	0.990511i	$0.456115\pi$
$648$		0			0
$649$	−5.04120	−	2.42771i	−0.197884	−	0.0952960i
$650$	−7.61407			−0.298648
$651$		0			0
$652$	6.39299	−	8.01656i	0.250369	−	0.313953i
$653$	28.0153	−	35.1301i	1.09633	−	1.37475i	0.175634	−	0.984455i	$-0.443802\pi$
$653$	28.0153	−	35.1301i	1.09633	−	1.37475i	0.920691	−	0.390293i	$-0.127626\pi$
$654$		0			0
$655$	23.0283			0.899792
$656$	−4.53421	−	2.18356i	−0.177031	−	0.0852537i
$657$		0			0
$658$	3.52251	−	1.69635i	0.137322	−	0.0661307i
$659$	7.73847	−	3.72665i	0.301448	−	0.145170i	−0.277045	−	0.960857i	$-0.589355\pi$
$659$	7.73847	−	3.72665i	0.301448	−	0.145170i	0.578493	+	0.815687i	$0.303641\pi$
$660$		0			0
$661$	−1.97142	+	2.47208i	−0.0766794	+	0.0961529i	−0.818692	−	0.574233i	$-0.805300\pi$
$661$	−1.97142	+	2.47208i	−0.0766794	+	0.0961529i	0.742012	+	0.670386i	$0.233872\pi$
$662$	14.5867	+	18.2911i	0.566927	+	0.710903i
$663$		0			0
$664$	1.22901	+	5.38465i	0.0476949	+	0.208965i
$665$	−5.63588	−	7.06717i	−0.218550	−	0.274053i
$666$		0			0
$667$	14.0161	−	3.68143i	0.542706	−	0.142546i
$668$	−16.7882			−0.649555
$669$		0			0
$670$	−0.891195	−	3.90458i	−0.0344299	−	0.150847i
$671$	−3.26894	+	14.3221i	−0.126196	+	0.552900i
$672$		0			0
$673$	10.9959	−	13.7885i	0.423862	−	0.531506i	−0.523349	−	0.852119i	$-0.675317\pi$
$673$	10.9959	−	13.7885i	0.423862	−	0.531506i	0.947210	+	0.320613i	$0.103889\pi$
$674$	5.08572	+	22.2820i	0.195895	+	0.858270i
$675$		0			0
$676$	2.56941	−	1.23736i	0.0988233	−	0.0475908i
$677$	−0.959235	+	4.20268i	−0.0368664	+	0.161522i	−0.990010	−	0.140995i	$-0.954970\pi$
$677$	−0.959235	+	4.20268i	−0.0368664	+	0.161522i	0.953144	+	0.302517i	$0.0978270\pi$
$678$		0			0
$679$	−22.6734			−0.870125
$680$	−2.47335	−	1.19110i	−0.0948486	−	0.0456767i
$681$		0			0
$682$	−2.10763	+	2.64288i	−0.0807052	+	0.101201i
$683$	35.8251	+	17.2525i	1.37081	+	0.660148i	0.967019	−	0.254703i	$-0.0819778\pi$
$683$	35.8251	+	17.2525i	1.37081	+	0.660148i	0.403791	+	0.914851i	$0.367692\pi$
$684$		0			0
$685$	−9.40928	−	4.53127i	−0.359510	−	0.173131i
$686$	3.95522	−	17.3289i	0.151011	−	0.661622i
$687$		0			0
$688$	1.70872	−	0.822877i	0.0651444	−	0.0313719i
$689$	−5.84747	−	25.6195i	−0.222771	−	0.976024i
$690$		0			0
$691$	−11.5115	−	14.4349i	−0.437916	−	0.549130i	0.513076	−	0.858343i	$-0.328506\pi$
$691$	−11.5115	−	14.4349i	−0.437916	−	0.549130i	−0.950993	+	0.309213i	$0.899934\pi$
$692$	0.924514	−	4.05056i	0.0351448	−	0.153979i
$693$		0			0
$694$	4.04132	+	5.06765i	0.153406	+	0.192365i
$695$	23.0328			0.873684
$696$		0			0
$697$	8.55182			0.323923
$698$	7.34687	+	9.21268i	0.278083	+	0.348705i
$699$		0			0
$700$	−0.808902	+	3.54403i	−0.0305736	+	0.133952i
$701$	−12.1339	−	15.2154i	−0.458291	−	0.574679i	0.497970	−	0.867195i	$-0.334079\pi$
$701$	−12.1339	−	15.2154i	−0.458291	−	0.574679i	−0.956261	+	0.292515i	$0.905508\pi$
$702$		0			0
$703$	−5.78797	−	25.3588i	−0.218297	−	0.956423i
$704$	1.70872	−	0.822877i	0.0643999	−	0.0310134i
$705$		0			0
$706$	4.25433	−	18.6394i	0.160114	−	0.701504i
$707$	−0.252022	−	0.121367i	−0.00947826	−	0.00456449i
$708$		0			0
$709$	−5.96289	−	2.87158i	−0.223941	−	0.107844i	0.318549	−	0.947906i	$-0.396804\pi$
$709$	−5.96289	−	2.87158i	−0.223941	−	0.107844i	−0.542491	+	0.840062i	$0.682519\pi$
$710$	−6.11272	+	7.66510i	−0.229406	+	0.287666i
$711$		0			0
$712$	−14.3889	−	6.92931i	−0.539245	−	0.259687i
$713$	−4.79643			−0.179628
$714$		0			0
$715$	2.17188	−	9.51562i	0.0812236	−	0.355864i
$716$	9.55060	−	4.59933i	0.356923	−	0.171885i
$717$		0			0
$718$	1.84487	+	8.08289i	0.0688498	+	0.301651i
$719$	11.3027	−	14.1732i	0.421521	−	0.528571i	−0.525047	−	0.851073i	$-0.675952\pi$
$719$	11.3027	−	14.1732i	0.421521	−	0.528571i	0.946569	+	0.322502i	$0.104524\pi$
$720$		0			0
$721$	−5.09234	+	22.3110i	−0.189649	+	0.830905i
$722$	−1.21618	−	5.32845i	−0.0452617	−	0.198304i
$723$		0			0
$724$	21.7666			0.808949
$725$	9.79746	−	8.34744i	0.363868	−	0.310016i
$726$		0			0
$727$	−8.87894	−	11.1338i	−0.329302	−	0.412931i	0.589426	−	0.807822i	$-0.299354\pi$
$727$	−8.87894	−	11.1338i	−0.329302	−	0.412931i	−0.918728	+	0.394891i	$0.870782\pi$
$728$	1.07812	+	4.72355i	0.0399578	+	0.175067i
$729$		0			0
$730$	3.77532	+	4.73410i	0.139731	+	0.175217i
$731$	−2.00936	+	2.51966i	−0.0743189	+	0.0931929i
$732$		0			0
$733$	−17.0908	+	8.23048i	−0.631262	+	0.304000i	−0.722019	−	0.691873i	$-0.756786\pi$
$733$	−17.0908	+	8.23048i	−0.631262	+	0.304000i	0.0907571	+	0.995873i	$0.471071\pi$
$734$	26.0033	−	12.5225i	0.959801	−	0.462216i
$735$		0			0
$736$	2.42452	+	1.16759i	0.0893689	+	0.0430378i
$737$	−4.70170			−0.173189
$738$		0			0
$739$	−27.5316	+	34.5236i	−1.01277	+	1.26997i	−0.0502534	+	0.998737i	$0.516003\pi$
$739$	−27.5316	+	34.5236i	−1.01277	+	1.26997i	−0.962514	+	0.271233i	$0.912569\pi$
$740$	7.12151	−	8.93009i	0.261792	−	0.328277i
$741$		0			0
$742$	−12.5460			−0.460579
$743$	29.1694	+	14.0473i	1.07012	+	0.515344i	0.884146	−	0.467210i	$-0.154741\pi$
$743$	29.1694	+	14.0473i	1.07012	+	0.515344i	0.185977	+	0.982554i	$0.440455\pi$
$744$		0			0
$745$	11.9923	−	5.77518i	0.439363	−	0.211586i
$746$	−20.1538	+	9.70558i	−0.737885	+	0.355347i
$747$		0			0
$748$	−2.00936	+	2.51966i	−0.0734695	+	0.0921278i
$749$	−0.288279	−	0.361490i	−0.0105335	−	0.0132086i
$750$		0			0
$751$	6.02269	+	26.3871i	0.219771	+	0.962881i	0.957647	+	0.287944i	$0.0929718\pi$
$751$	6.02269	+	26.3871i	0.219771	+	0.962881i	−0.737876	+	0.674936i	$0.764171\pi$
$752$	−1.60276	−	2.00980i	−0.0584468	−	0.0732900i
$753$		0			0
$754$	6.93784	−	15.6896i	0.252661	−	0.571381i
$755$	35.5458			1.29364
$756$		0			0
$757$	11.1140	+	48.6936i	0.403945	+	1.76980i	0.611162	+	0.791505i	$0.290702\pi$
$757$	11.1140	+	48.6936i	0.403945	+	1.76980i	−0.207217	+	0.978295i	$0.566441\pi$
$758$	−3.31439	+	14.5213i	−0.120384	+	0.527437i
$759$		0			0
$760$	−3.70561	+	4.64669i	−0.134417	+	0.168553i
$761$	−1.94753	−	8.53268i	−0.0705979	−	0.309309i	0.927284	−	0.374358i	$-0.122137\pi$
$761$	−1.94753	−	8.53268i	−0.0705979	−	0.309309i	−0.997882	+	0.0650486i	$0.979280\pi$
$762$		0			0
$763$	12.3653	−	5.95482i	0.447654	−	0.215579i
$764$	−3.23120	+	14.1568i	−0.116901	+	0.512175i
$765$		0			0
$766$	10.9322			0.394998
$767$	−8.46771	−	4.07783i	−0.305751	−	0.147242i
$768$		0			0
$769$	13.7625	−	17.2576i	0.496287	−	0.622325i	−0.469100	−	0.883145i	$-0.655422\pi$
$769$	13.7625	−	17.2576i	0.496287	−	0.622325i	0.965387	+	0.260820i	$0.0839931\pi$
$770$	−4.19839	−	2.02184i	−0.151299	−	0.0728620i
$771$		0			0
$772$	4.32937	+	2.08491i	0.155817	+	0.0750376i
$773$	2.56666	−	11.2453i	0.0923162	−	0.404464i	−0.907564	−	0.419913i	$-0.862061\pi$
$773$	2.56666	−	11.2453i	0.0923162	−	0.404464i	0.999881	+	0.0154490i	$0.00491777\pi$
$774$		0			0
$775$	−3.83827	+	1.84841i	−0.137875	+	0.0663969i
$776$	3.31730	+	14.5341i	0.119084	+	0.521742i
$777$		0			0
$778$	9.74401	+	12.2186i	0.349340	+	0.438058i
$779$	4.11987	−	18.0503i	0.147610	−	0.646721i
$780$		0			0
$781$	7.17608	+	8.99852i	0.256780	+	0.321992i
$782$	−4.57280			−0.163523
$783$		0			0
$784$	−4.68684			−0.167387
$785$	−0.136568	−	0.171251i	−0.00487432	−	0.00611220i
$786$		0			0
$787$	−1.09728	+	4.80749i	−0.0391137	+	0.171368i	−0.990712	−	0.135976i	$-0.956583\pi$
$787$	−1.09728	+	4.80749i	−0.0391137	+	0.171368i	0.951598	+	0.307344i	$0.0994402\pi$
$788$	9.49108	+	11.9014i	0.338106	+	0.423971i
$789$		0			0
$790$	−3.31468	−	14.5226i	−0.117931	−	0.516690i
$791$	−11.0957	+	5.34343i	−0.394519	+	0.189990i
$792$		0			0
$793$	−5.49084	+	24.0569i	−0.194985	+	0.854287i
$794$	−6.90371	−	3.32465i	−0.245003	−	0.117987i
$795$		0			0
$796$	10.9859	+	5.29054i	0.389385	+	0.187518i
$797$	−14.5094	+	18.1942i	−0.513950	+	0.644473i	−0.969312	−	0.245833i	$-0.920938\pi$
$797$	−14.5094	+	18.1942i	−0.513950	+	0.644473i	0.455362	+	0.890306i	$0.349510\pi$
$798$		0			0
$799$	3.93565	+	1.89531i	0.139233	+	0.0670513i
$800$	2.39014			0.0845041
$801$		0			0
$802$	−1.04893	+	4.59566i	−0.0370389	+	0.162278i
$803$	6.40452	−	3.08425i	0.226011	−	0.108841i
$804$		0			0
$805$	−1.47129	−	6.44613i	−0.0518561	−	0.227196i
$806$	−3.54019	+	4.43925i	−0.124698	+	0.156366i
$807$		0			0
$808$	−0.0409258	+	0.179308i	−0.00143976	+	0.00630802i
$809$	−7.86490	−	34.4584i	−0.276515	−	1.21149i	−0.902166	−	0.431389i	$-0.858024\pi$
$809$	−7.86490	−	34.4584i	−0.276515	−	1.21149i	0.625651	−	0.780103i	$-0.284833\pi$
$810$		0			0
$811$	−9.47070			−0.332561			−0.166281	−	0.986078i	$-0.553176\pi$
$811$	−9.47070			−0.332561			−0.166281	+	0.986078i	$0.553176\pi$
$812$	−6.56579	−	4.89611i	−0.230414	−	0.171820i
$813$		0			0
$814$	−8.36036	−	10.4836i	−0.293031	−	0.367449i
$815$	3.68599	+	16.1494i	0.129115	+	0.565689i
$816$		0			0
$817$	4.35023	+	5.45502i	0.152195	+	0.190847i
$818$	4.80159	−	6.02100i	0.167884	−	0.210519i
$819$		0			0
$820$	7.32504	−	3.52756i	0.255802	−	0.123188i
$821$	26.5108	−	12.7669i	0.925234	−	0.445569i	0.0902971	−	0.995915i	$-0.471218\pi$
$821$	26.5108	−	12.7669i	0.925234	−	0.445569i	0.834937	+	0.550346i	$0.185504\pi$
$822$		0			0
$823$	−26.5320	−	12.7772i	−0.924849	−	0.445384i	−0.0900492	−	0.995937i	$-0.528702\pi$
$823$	−26.5320	−	12.7772i	−0.924849	−	0.445384i	−0.834800	+	0.550553i	$0.814417\pi$
$824$	15.0468			0.524180
$825$		0			0
$826$	−2.79765	+	3.50815i	−0.0973428	+	0.122064i
$827$	9.42602	−	11.8199i	0.327775	−	0.411017i	−0.590451	−	0.807073i	$-0.701050\pi$
$827$	9.42602	−	11.8199i	0.327775	−	0.411017i	0.918226	+	0.396057i	$0.129622\pi$
$828$		0			0
$829$	44.2208			1.53585			0.767925	−	0.640539i	$-0.221289\pi$
$829$	44.2208			1.53585			0.767925	+	0.640539i	$0.221289\pi$
$830$	−8.03903	−	3.87139i	−0.279039	−	0.134378i
$831$		0			0
$832$	2.87014	−	1.38219i	0.0995043	−	0.0479188i
$833$	7.17558	−	3.45558i	0.248619	−	0.119729i
$834$		0			0
$835$	16.9100	−	21.2044i	0.585193	−	0.733809i
$836$	4.35023	+	5.45502i	0.150456	+	0.188666i
$837$		0			0
$838$	5.73150	+	25.1113i	0.197991	+	0.867456i
$839$	−2.97931	−	3.73593i	−0.102857	−	0.128979i	0.727739	−	0.685854i	$-0.240571\pi$
$839$	−2.97931	−	3.73593i	−0.102857	−	0.128979i	−0.830596	+	0.556876i	$0.812000\pi$
$840$		0			0
$841$	8.27346	+	27.7948i	0.285292	+	0.958441i
$842$	−5.77170			−0.198906
$843$		0			0
$844$	−3.20101	−	14.0245i	−0.110183	−	0.482744i
$845$	−1.02519	+	4.49164i	−0.0352675	+	0.154517i
$846$		0			0
$847$	7.02017	−	8.80302i	0.241216	−	0.302475i
$848$	1.83558	+	8.04222i	0.0630342	+	0.276171i
$849$		0			0
$850$	−3.65931	+	1.76223i	−0.125513	+	0.0604441i
$851$	4.23370	−	18.5491i	0.145129	−	0.635854i
$852$		0			0
$853$	7.44372			0.254868			0.127434	−	0.991847i	$-0.459326\pi$
$853$	7.44372			0.254868			0.127434	+	0.991847i	$0.459326\pi$
$854$	10.6142	+	5.11151i	0.363209	+	0.174912i
$855$		0			0
$856$	−0.189544	+	0.237681i	−0.00647849	+	0.00812377i
$857$	11.4490	+	5.51356i	0.391092	+	0.188340i	0.619087	−	0.785322i	$-0.287503\pi$
$857$	11.4490	+	5.51356i	0.391092	+	0.188340i	−0.227995	+	0.973662i	$0.573217\pi$
$858$		0			0
$859$	−15.5600	−	7.49332i	−0.530902	−	0.255669i	0.149174	−	0.988811i	$-0.452339\pi$
$859$	−15.5600	−	7.49332i	−0.530902	−	0.255669i	−0.680075	+	0.733142i	$0.738053\pi$
$860$	−0.681776	+	2.98705i	−0.0232484	+	0.101858i
$861$		0			0
$862$	14.7404	−	7.09861i	0.502060	−	0.241780i
$863$	−8.10854	−	35.5258i	−0.276018	−	1.20931i	−0.902780	−	0.430103i	$-0.858477\pi$
$863$	−8.10854	−	35.5258i	−0.276018	−	1.20931i	0.626762	−	0.779211i	$-0.284380\pi$
$864$		0			0
$865$	4.18486	+	5.24765i	0.142290	+	0.178425i
$866$	5.62377	−	24.6394i	0.191104	−	0.837279i
$867$		0			0
$868$	1.69019	+	2.11943i	0.0573686	+	0.0719380i
$869$	−17.4873			−0.593217
$870$		0			0
$871$	−7.89745			−0.267595
$872$	−5.62629	−	7.05515i	−0.190530	−	0.238917i
$873$		0			0
$874$	−2.20296	+	9.65182i	−0.0745164	+	0.326478i
$875$	−11.3212	−	14.1964i	−0.382727	−	0.479924i
$876$		0			0
$877$	−1.92576	−	8.43729i	−0.0650282	−	0.284907i	0.931950	−	0.362586i	$-0.118106\pi$
$877$	−1.92576	−	8.43729i	−0.0650282	−	0.284907i	−0.996978	+	0.0776791i	$0.975249\pi$
$878$	5.83627	−	2.81060i	0.196964	−	0.0948531i
$879$		0			0
$880$	−0.681776	+	2.98705i	−0.0229827	+	0.100694i
$881$	6.87863	+	3.31257i	0.231747	+	0.111603i	0.546154	−	0.837685i	$-0.316091\pi$
$881$	6.87863	+	3.31257i	0.231747	+	0.111603i	−0.314407	+	0.949288i	$0.601806\pi$
$882$		0			0
$883$	0.556272	+	0.267887i	0.0187201	+	0.00901510i	0.443220	−	0.896413i	$-0.353836\pi$
$883$	0.556272	+	0.267887i	0.0187201	+	0.00901510i	−0.424500	+	0.905428i	$0.639550\pi$
$884$	−3.37513	+	4.23228i	−0.113518	+	0.142347i
$885$		0			0
$886$	23.3182	+	11.2295i	0.783391	+	0.377261i
$887$	20.0952			0.674732			0.337366	−	0.941374i	$-0.390464\pi$
$887$	20.0952			0.674732			0.337366	+	0.941374i	$0.390464\pi$
$888$		0			0
$889$	−3.22016	+	14.1084i	−0.108001	+	0.473182i
$890$	23.2453	−	11.1944i	0.779185	−	0.375235i
$891$		0			0
$892$	2.84493	+	12.4645i	0.0952553	+	0.417341i
$893$	5.89646	−	7.39392i	0.197317	−	0.247428i
$894$		0			0
$895$	−3.81066	+	16.6956i	−0.127376	+	0.558073i
$896$	−0.338433	−	1.48277i	−0.0113063	−	0.0495360i
$897$		0			0
$898$	8.86533			0.295840
$899$	−0.311470	−	9.59341i	−0.0103881	−	0.319958i
$900$		0			0
$901$	−8.73976	−	10.9593i	−0.291164	−	0.365108i
$902$	−2.12385	−	9.30520i	−0.0707165	−	0.309829i
$903$		0			0
$904$	5.04863	+	6.33078i	0.167915	+	0.210559i
$905$	−21.9245	+	27.4924i	−0.728794	+	0.913878i
$906$		0			0
$907$	−0.161465	+	0.0777573i	−0.00536135	+	0.00258189i	−0.436562	−	0.899674i	$-0.643804\pi$
$907$	−0.161465	+	0.0777573i	−0.00536135	+	0.00258189i	0.431201	+	0.902256i	$0.358090\pi$
$908$	23.8097	−	11.4661i	0.790151	−	0.380517i
$909$		0			0
$910$	−7.05204	−	3.39608i	−0.233773	−	0.112579i
$911$	−43.3911			−1.43761			−0.718806	−	0.695211i	$-0.755311\pi$
$911$	−43.3911			−1.43761			−0.718806	+	0.695211i	$0.755311\pi$
$912$		0			0
$913$	−6.53095	+	8.18955i	−0.216143	+	0.271035i
$914$	−13.8218	+	17.3320i	−0.457185	+	0.573291i
$915$		0			0
$916$	19.2020			0.634452
$917$	−19.5329	−	9.40653i	−0.645032	−	0.310631i
$918$		0			0
$919$	16.9880	−	8.18100i	0.560383	−	0.269866i	−0.132177	−	0.991226i	$-0.542197\pi$
$919$	16.9880	−	8.18100i	0.560383	−	0.269866i	0.692561	+	0.721360i	$0.256483\pi$
$920$	−3.91682	+	1.88624i	−0.129134	+	0.0621876i
$921$		0			0
$922$	24.0547	−	30.1637i	0.792200	−	0.993388i
$923$	12.0537	+	15.1148i	0.396751	+	0.497511i
$924$		0			0
$925$	−3.76034	−	16.4751i	−0.123639	−	0.541700i
$926$	−18.7716	−	23.5389i	−0.616874	−	0.773535i
$927$		0			0
$928$	−2.17786	+	4.92513i	−0.0714918	+	0.161675i
$929$	−44.1780			−1.44943			−0.724717	−	0.689047i	$-0.758030\pi$
$929$	−44.1780			−1.44943			−0.724717	+	0.689047i	$0.758030\pi$
$930$		0			0
$931$	−3.83683	−	16.8103i	−0.125747	−	0.550934i
$932$	−1.80769	+	7.92000i	−0.0592128	+	0.259428i
$933$		0			0
$934$	3.51805	−	4.41150i	0.115114	−	0.144349i
$935$	−1.15853	−	5.07586i	−0.0378881	−	0.165998i
$936$		0			0
$937$	−47.4638	+	22.8573i	−1.55057	+	0.746717i	−0.996327	−	0.0856358i	$-0.972708\pi$
$937$	−47.4638	+	22.8573i	−1.55057	+	0.746717i	−0.554247	+	0.832352i	$0.686994\pi$
$938$	−0.839008	+	3.67594i	−0.0273946	+	0.120024i
$939$		0			0
$940$	4.15288			0.135452
$941$	19.7537	+	9.51288i	0.643952	+	0.310111i	0.727208	−	0.686417i	$-0.240818\pi$
$941$	19.7537	+	9.51288i	0.643952	+	0.310111i	−0.0832559	+	0.996528i	$0.526532\pi$
$942$		0			0
$943$	8.44377	−	10.5882i	0.274967	−	0.344798i
$944$	2.65810	+	1.28007i	0.0865139	+	0.0416629i
$945$		0			0
$946$	3.24066	+	1.56062i	0.105363	+	0.0507401i
$947$	1.47868	−	6.47853i	0.0480507	−	0.210524i	−0.945203	−	0.326482i	$-0.894137\pi$
$947$	1.47868	−	6.47853i	0.0480507	−	0.210524i	0.993254	+	0.115958i	$0.0369938\pi$
$948$		0			0
$949$	10.7577	−	5.18063i	0.349209	−	0.168170i
$950$	1.95666	+	8.57268i	0.0634824	+	0.278135i
$951$		0			0
$952$	1.61138	+	2.02061i	0.0522252	+	0.0654883i
$953$	0.663211	−	2.90572i	0.0214835	−	0.0941255i	−0.963050	−	0.269324i	$-0.913200\pi$
$953$	0.663211	−	2.90572i	0.0214835	−	0.0941255i	0.984533	+	0.175199i	$0.0560568\pi$
$954$		0			0
$955$	−14.6262	−	18.3406i	−0.473292	−	0.593489i
$956$	30.3139			0.980423
$957$		0			0
$958$	−21.3948			−0.691235
$959$	6.13013	+	7.68693i	0.197952	+	0.248224i
$960$		0			0
$961$	6.19122	−	27.1255i	0.199717	−	0.875016i
$962$	−14.0429	−	17.6093i	−0.452762	−	0.567745i
$963$		0			0
$964$	−1.01778	−	4.45920i	−0.0327806	−	0.143621i
$965$	−6.99412	+	3.36819i	−0.225149	+	0.108426i
$966$		0			0
$967$	−1.40773	+	6.16768i	−0.0452696	+	0.198339i	−0.992506	−	0.122197i	$-0.961006\pi$
$967$	−1.40773	+	6.16768i	−0.0452696	+	0.198339i	0.947236	+	0.320536i	$0.103863\pi$
$968$	−6.67000	−	3.21210i	−0.214382	−	0.103241i
$969$		0			0
$970$	−21.6987	−	10.4495i	−0.696702	−	0.335514i
$971$	−12.5515	+	15.7391i	−0.402797	+	0.505092i	−0.941318	−	0.337520i	$-0.890412\pi$
$971$	−12.5515	+	15.7391i	−0.402797	+	0.505092i	0.538521	+	0.842612i	$0.318983\pi$
$972$		0			0
$973$	−19.5367	−	9.40836i	−0.626317	−	0.301618i
$974$	−12.6886			−0.406570
$975$		0			0
$976$	1.72363	−	7.55173i	0.0551721	−	0.241725i
$977$	−24.9341	+	12.0076i	−0.797713	+	0.384158i	−0.787907	−	0.615794i	$-0.788835\pi$
$977$	−24.9341	+	12.0076i	−0.797713	+	0.384158i	−0.00980533	+	0.999952i	$0.503121\pi$
$978$		0			0
$979$	−6.73984	−	29.5291i	−0.215406	−	0.943756i
$980$	4.72083	−	5.91974i	0.150802	−	0.189099i
$981$		0			0
$982$	2.74254	−	12.0159i	0.0875180	−	0.383442i
$983$	−1.31895	−	5.77869i	−0.0420679	−	0.184312i	0.949529	−	0.313680i	$-0.101562\pi$
$983$	−1.31895	−	5.77869i	−0.0420679	−	0.184312i	−0.991597	+	0.129369i	$0.958705\pi$
$984$		0			0
$985$	−24.5921			−0.783569
$986$	−0.296948	−	9.14612i	−0.00945675	−	0.291272i
$987$		0			0
$988$	7.30709	+	9.16281i	0.232470	+	0.291508i
$989$	1.13566	+	4.97565i	0.0361119	+	0.158216i
$990$		0			0
$991$	38.4258	+	48.1844i	1.22064	+	1.53063i	0.770175	+	0.637833i	$0.220169\pi$
$991$	38.4258	+	48.1844i	1.22064	+	1.53063i	0.450461	+	0.892796i	$0.351259\pi$
$992$	1.11130	−	1.39353i	0.0352839	−	0.0442446i
$993$		0			0
$994$	8.31588	−	4.00472i	0.263764	−	0.127022i
$995$	−17.7478	+	8.54690i	−0.562644	+	0.270955i
$996$		0			0
$997$	−43.8638	−	21.1237i	−1.38918	−	0.668994i	−0.418245	−	0.908334i	$-0.637355\pi$
$997$	−43.8638	−	21.1237i	−1.38918	−	0.668994i	−0.970936	+	0.239340i	$0.923069\pi$
$998$	3.86155			0.122235
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	522.2.k.h.343.1		12
3.2	odd	2		58.2.d.b.53.1	yes	12
12.11	even	2		464.2.u.h.401.2		12
29.23	even	7	inner	522.2.k.h.487.1		12
87.8	even	28		1682.2.b.i.1681.12		12
87.20	odd	14		1682.2.a.t.1.6		6
87.23	odd	14		58.2.d.b.23.1	✓	12
87.38	odd	14		1682.2.a.q.1.1		6
87.50	even	28		1682.2.b.i.1681.1		12
348.23	even	14		464.2.u.h.81.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.d.b.23.1	✓	12	87.23	odd	14
58.2.d.b.53.1	yes	12	3.2	odd	2
464.2.u.h.81.2		12	348.23	even	14
464.2.u.h.401.2		12	12.11	even	2
522.2.k.h.343.1		12	1.1	even	1	trivial
522.2.k.h.487.1		12	29.23	even	7	inner
1682.2.a.q.1.1		6	87.38	odd	14
1682.2.a.t.1.6		6	87.20	odd	14
1682.2.b.i.1681.1		12	87.50	even	28
1682.2.b.i.1681.12		12	87.8	even	28

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:	\( N \)	\(=\)	\( 522 = 2 \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	522.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.623490 - 0.781831i) q^{2} +(-0.222521 + 0.974928i) q^{4} +(-1.00725 - 1.26305i) q^{5} +(0.338433 + 1.48277i) q^{7} +(0.900969 - 0.433884i) q^{8} +(-0.359484 + 1.57500i) q^{10} +(1.70872 + 0.822877i) q^{11} +(2.87014 + 1.38219i) q^{13} +(0.948269 - 1.18909i) q^{14} +(-0.900969 - 0.433884i) q^{16} +1.69929 q^{17} +(0.818639 - 3.58669i) q^{19} +(1.45552 - 0.700942i) q^{20} +(-0.422020 - 1.84899i) q^{22} +(1.67782 - 2.10392i) q^{23} +(0.531856 - 2.33021i) q^{25} +(-0.708867 - 3.10575i) q^{26} -1.52091 q^{28} +(4.31703 + 3.21920i) q^{29} +(-1.11130 - 1.39353i) q^{31} +(0.222521 + 0.974928i) q^{32} +(-1.05949 - 1.32856i) q^{34} +(1.53194 - 1.92099i) q^{35} +(6.37006 - 3.06766i) q^{37} +(-3.31460 + 1.59623i) q^{38} +(-1.45552 - 0.700942i) q^{40} +5.03259 q^{41} +(-1.18247 + 1.48277i) q^{43} +(-1.18247 + 1.48277i) q^{44} -2.69101 q^{46} +(2.31606 + 1.11536i) q^{47} +(4.22270 - 2.03355i) q^{49} +(-2.15344 + 1.03704i) q^{50} +(-1.98620 + 2.49062i) q^{52} +(-5.14319 - 6.44936i) q^{53} +(-0.681776 - 2.98705i) q^{55} +(0.948269 + 1.18909i) q^{56} +(-0.174748 - 5.38233i) q^{58} -2.95027 q^{59} +(1.72363 + 7.55173i) q^{61} +(-0.396619 + 1.73770i) q^{62} +(0.623490 - 0.781831i) q^{64} +(-1.14518 - 5.01736i) q^{65} +(-2.23359 + 1.07564i) q^{67} +(-0.378127 + 1.65668i) q^{68} -2.45703 q^{70} +(5.46771 + 2.63311i) q^{71} +(2.33692 - 2.93041i) q^{73} +(-6.37006 - 3.06766i) q^{74} +(3.31460 + 1.59623i) q^{76} +(-0.641852 + 2.81214i) q^{77} +(-8.30753 + 4.00069i) q^{79} +(0.359484 + 1.57500i) q^{80} +(-3.13777 - 3.93464i) q^{82} +(-1.22901 + 5.38465i) q^{83} +(-1.71161 - 2.14629i) q^{85} +1.89654 q^{86} +1.89654 q^{88} +(-9.95740 - 12.4862i) q^{89} +(-1.07812 + 4.72355i) q^{91} +(1.67782 + 2.10392i) q^{92} +(-0.572020 - 2.50618i) q^{94} +(-5.35476 + 2.57872i) q^{95} +(-3.31730 + 14.5341i) q^{97} +(-4.22270 - 2.03355i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{4} + q^{7} + 2 q^{8} - 7 q^{10} + 2 q^{11} + q^{13} - q^{14} - 2 q^{16} + 12 q^{17} - 6 q^{19} - 7 q^{20} - 2 q^{22} - 35 q^{23} - 6 q^{25} - 8 q^{26} - 6 q^{28} + 14 q^{29} - 8 q^{31}+ \cdots - 37 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^4 + q^7 + 2 * q^8 - 7 * q^10 + 2 * q^11 + q^13 - q^14 - 2 * q^16 + 12 * q^17 - 6 * q^19 - 7 * q^20 - 2 * q^22 - 35 * q^23 - 6 * q^25 - 8 * q^26 - 6 * q^28 + 14 * q^29 - 8 * q^31 + 2 * q^32 - 5 * q^34 + 18 * q^35 + 31 * q^37 - q^38 + 7 * q^40 + 30 * q^41 - 5 * q^43 - 5 * q^44 - 28 * q^46 + 33 * q^47 + 37 * q^49 - q^50 - 6 * q^52 - 13 * q^53 + 36 * q^55 - q^56 - 38 * q^59 - 5 * q^61 + 8 * q^62 - 2 * q^64 + 20 * q^65 - 7 * q^67 + 19 * q^68 - 18 * q^70 - 3 * q^71 - 22 * q^73 - 31 * q^74 + q^76 - 10 * q^77 - 60 * q^79 + 7 * q^80 + 26 * q^82 + 39 * q^83 + 38 * q^85 - 2 * q^86 - 2 * q^88 - 39 * q^89 + 61 * q^91 - 35 * q^92 + 16 * q^94 - 55 * q^95 - 19 * q^97 - 37 * q^98

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