LMFDB - Embedded newform 847.2.n.e.366.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(9,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 18]))

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

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

chi := DirichletCharacter("847.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			366.3
Character	$\chi$	$=$	847.366
Dual form			847.2.n.e.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.260366 + 2.47722i) q^{2} +(-0.477450 + 0.530262i) q^{3} +(-4.11253 + 0.874144i) q^{4} +(2.01382 - 0.896611i) q^{5} +(-1.43789 - 1.04469i) q^{6} +(1.94692 + 1.79151i) q^{7} +(-1.69677 - 5.22212i) q^{8} +(0.260366 + 2.47722i) q^{9} +O(q^{10})$	\(q+(0.260366 + 2.47722i) q^{2} +(-0.477450 + 0.530262i) q^{3} +(-4.11253 + 0.874144i) q^{4} +(2.01382 - 0.896611i) q^{5} +(-1.43789 - 1.04469i) q^{6} +(1.94692 + 1.79151i) q^{7} +(-1.69677 - 5.22212i) q^{8} +(0.260366 + 2.47722i) q^{9} +(2.74543 + 4.75523i) q^{10} +(1.50000 - 2.59808i) q^{12} +(2.65880 - 1.93173i) q^{13} +(-3.93106 + 5.28938i) q^{14} +(-0.486060 + 1.49594i) q^{15} +(4.81273 - 2.14277i) q^{16} +(-0.155838 + 1.48270i) q^{17} +(-6.06882 + 1.28997i) q^{18} +(6.76677 + 1.43832i) q^{19} +(-7.49812 + 5.44770i) q^{20} +(-1.87953 + 0.177017i) q^{21} +(-3.24543 + 5.62125i) q^{23} +(3.57922 + 1.59357i) q^{24} +(-0.0940890 + 0.104496i) q^{25} +(5.47759 + 6.08348i) q^{26} +(-3.16968 - 2.30291i) q^{27} +(-9.57278 - 5.66576i) q^{28} +(-0.509801 + 1.56901i) q^{29} +(-3.83232 - 0.814585i) q^{30} +(-2.14706 - 0.955933i) q^{31} +(1.07031 + 1.85383i) q^{32} -3.71354 q^{34} +(5.52703 + 1.86216i) q^{35} +(-3.23621 - 9.96003i) q^{36} +(-3.71679 - 4.12791i) q^{37} +(-1.80120 + 17.1372i) q^{38} +(-0.245121 + 2.33217i) q^{39} +(-8.09920 - 8.99508i) q^{40} +(-3.47642 - 10.6993i) q^{41} +(-0.927875 - 4.60991i) q^{42} +5.26819 q^{43} +(2.74543 + 4.75523i) q^{45} +(-14.7701 - 6.57606i) q^{46} +(-1.45828 - 0.309968i) q^{47} +(-1.16161 + 3.57507i) q^{48} +(0.580958 + 6.97585i) q^{49} +(-0.283358 - 0.205872i) q^{50} +(-0.711813 - 0.790548i) q^{51} +(-9.24578 + 10.2685i) q^{52} +(0.278389 + 0.123947i) q^{53} +(4.87953 - 8.45159i) q^{54} +(6.05203 - 13.2068i) q^{56} +(-3.99348 + 2.90143i) q^{57} +(-4.01950 - 0.854372i) q^{58} +(12.3821 - 2.63190i) q^{59} +(0.691268 - 6.57698i) q^{60} +(-11.8594 + 5.28014i) q^{61} +(1.80903 - 5.56763i) q^{62} +(-3.93106 + 5.28938i) q^{63} +(4.21045 - 3.05907i) q^{64} +(3.62234 - 6.27408i) q^{65} +(2.28646 + 3.96027i) q^{67} +(-0.655204 - 6.23385i) q^{68} +(-1.43121 - 4.40480i) q^{69} +(-3.17393 + 14.1765i) q^{70} +(-9.16353 - 6.65769i) q^{71} +(12.4946 - 5.56293i) q^{72} +(8.38047 - 1.78132i) q^{73} +(9.25801 - 10.2821i) q^{74} +(-0.0104877 - 0.0997836i) q^{75} -29.0858 q^{76} -5.84111 q^{78} +(-0.484121 - 4.60611i) q^{79} +(7.77075 - 8.63029i) q^{80} +(-4.57479 + 0.972401i) q^{81} +(25.5994 - 11.3976i) q^{82} +(1.56643 + 1.13808i) q^{83} +(7.57486 - 2.37096i) q^{84} +(1.01557 + 3.12561i) q^{85} +(1.37166 + 13.0505i) q^{86} +(-0.588580 - 1.01945i) q^{87} +(-1.60220 + 2.77509i) q^{89} +(-11.0649 + 8.03913i) q^{90} +(8.63719 + 1.00236i) q^{91} +(8.43313 - 25.9545i) q^{92} +(1.53201 - 0.682094i) q^{93} +(0.388170 - 3.69319i) q^{94} +(14.9167 - 3.17064i) q^{95} +(-1.49403 - 0.317566i) q^{96} +(-1.50428 + 1.09292i) q^{97} +(-17.1294 + 3.25544i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8}+O(q^{10}) $ 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} + 36 q^{10} + 36 q^{12} + 22 q^{13} - 12 q^{14} + 14 q^{15} + 2 q^{16} - 3 q^{17} + 10 q^{18} - 11 q^{19} - 28 q^{20} + 40 q^{21} - 48 q^{23} + 2 q^{24} + 3 q^{25} + q^{26} - 4 q^{27} - 13 q^{28} + 18 q^{29} + 2 q^{30} - 3 q^{31} + 12 q^{32} - 80 q^{34} - 9 q^{35} + 18 q^{36} - 4 q^{37} + 8 q^{38} - 5 q^{39} - 3 q^{40} + 10 q^{41} + 2 q^{42} + 16 q^{43} + 36 q^{45} - 10 q^{46} - 3 q^{47} - 20 q^{48} + 24 q^{49} + 6 q^{50} + 2 q^{51} - 7 q^{52} + 17 q^{53} + 32 q^{54} + 12 q^{56} - 40 q^{57} - 13 q^{58} + 8 q^{59} + 6 q^{60} - 24 q^{61} - 26 q^{62} - 12 q^{63} + 14 q^{64} - 60 q^{65} + 64 q^{67} + 5 q^{68} + 6 q^{69} + 27 q^{70} - 14 q^{71} + 10 q^{72} - 20 q^{73} + 22 q^{74} + 25 q^{75} - 312 q^{76} - 48 q^{78} + 3 q^{79} + 9 q^{80} - 17 q^{81} + 41 q^{82} + 22 q^{83} - 12 q^{84} - 22 q^{85} - 21 q^{86} - 120 q^{87} - 4 q^{89} - 20 q^{90} + 15 q^{91} - 50 q^{92} - 26 q^{93} - 10 q^{94} - 17 q^{95} + 27 q^{96} - 18 q^{97} - 96 q^{98}+O(q^{100}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 + 36 * q^10 + 36 * q^12 + 22 * q^13 - 12 * q^14 + 14 * q^15 + 2 * q^16 - 3 * q^17 + 10 * q^18 - 11 * q^19 - 28 * q^20 + 40 * q^21 - 48 * q^23 + 2 * q^24 + 3 * q^25 + q^26 - 4 * q^27 - 13 * q^28 + 18 * q^29 + 2 * q^30 - 3 * q^31 + 12 * q^32 - 80 * q^34 - 9 * q^35 + 18 * q^36 - 4 * q^37 + 8 * q^38 - 5 * q^39 - 3 * q^40 + 10 * q^41 + 2 * q^42 + 16 * q^43 + 36 * q^45 - 10 * q^46 - 3 * q^47 - 20 * q^48 + 24 * q^49 + 6 * q^50 + 2 * q^51 - 7 * q^52 + 17 * q^53 + 32 * q^54 + 12 * q^56 - 40 * q^57 - 13 * q^58 + 8 * q^59 + 6 * q^60 - 24 * q^61 - 26 * q^62 - 12 * q^63 + 14 * q^64 - 60 * q^65 + 64 * q^67 + 5 * q^68 + 6 * q^69 + 27 * q^70 - 14 * q^71 + 10 * q^72 - 20 * q^73 + 22 * q^74 + 25 * q^75 - 312 * q^76 - 48 * q^78 + 3 * q^79 + 9 * q^80 - 17 * q^81 + 41 * q^82 + 22 * q^83 - 12 * q^84 - 22 * q^85 - 21 * q^86 - 120 * q^87 - 4 * q^89 - 20 * q^90 + 15 * q^91 - 50 * q^92 - 26 * q^93 - 10 * q^94 - 17 * q^95 + 27 * q^96 - 18 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.260366	+	2.47722i	0.184107	+	1.75166i	0.563219	+	0.826307i	$0.309563\pi$
$2$	0.260366	+	2.47722i	0.184107	+	1.75166i	−0.379113	+	0.925351i	$0.623771\pi$
$3$	−0.477450	+	0.530262i	−0.275656	+	0.306147i	−0.865037	−	0.501708i	$-0.832705\pi$
$3$	−0.477450	+	0.530262i	−0.275656	+	0.306147i	0.589381	+	0.807855i	$0.299372\pi$
$4$	−4.11253	+	0.874144i	−2.05626	+	0.437072i
$5$	2.01382	−	0.896611i	0.900608	−	0.400977i	0.0964126	−	0.995341i	$-0.469263\pi$
$5$	2.01382	−	0.896611i	0.900608	−	0.400977i	0.804195	+	0.594365i	$0.202596\pi$
$6$	−1.43789	−	1.04469i	−0.587015	−	0.426491i
$7$	1.94692	+	1.79151i	0.735865	+	0.677128i
$7$	1.94692	+	1.79151i	0.735865	+	0.677128i
$8$	−1.69677	−	5.22212i	−0.599899	−	1.84630i
$9$	0.260366	+	2.47722i	0.0867887	+	0.825739i
$10$	2.74543	+	4.75523i	0.868182	+	1.50373i
$11$		0			0
$11$		0			0
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	2.65880	−	1.93173i	0.737419	−	0.535767i	−0.154482	−	0.987996i	$-0.549371\pi$
$13$	2.65880	−	1.93173i	0.737419	−	0.535767i	0.891902	+	0.452229i	$0.149371\pi$
$14$	−3.93106	+	5.28938i	−1.05062	+	1.41365i
$15$	−0.486060	+	1.49594i	−0.125500	+	0.386250i
$16$	4.81273	−	2.14277i	1.20318	−	0.535691i
$17$	−0.155838	+	1.48270i	−0.0377962	+	0.359607i	0.959235	+	0.282609i	$0.0912000\pi$
$17$	−0.155838	+	1.48270i	−0.0377962	+	0.359607i	−0.997031	+	0.0769974i	$0.975467\pi$
$18$	−6.06882	+	1.28997i	−1.43043	+	0.304048i
$19$	6.76677	+	1.43832i	1.55240	+	0.329973i	0.902719	−	0.430231i	$-0.141568\pi$
$19$	6.76677	+	1.43832i	1.55240	+	0.329973i	0.649684	+	0.760205i	$0.274901\pi$
$20$	−7.49812	+	5.44770i	−1.67663	+	1.21814i
$21$	−1.87953	+	0.177017i	−0.410146	+	0.0386283i
$22$		0			0
$23$	−3.24543	+	5.62125i	−0.676719	+	1.17211i	0.299244	+	0.954177i	$0.403266\pi$
$23$	−3.24543	+	5.62125i	−0.676719	+	1.17211i	−0.975963	+	0.217936i	$0.930068\pi$
$24$	3.57922	+	1.59357i	0.730604	+	0.325286i
$25$	−0.0940890	+	0.104496i	−0.0188178	+	0.0208993i
$26$	5.47759	+	6.08348i	1.07424	+	1.19307i
$27$	−3.16968	−	2.30291i	−0.610005	−	0.443195i
$28$	−9.57278	−	5.66576i	−1.80909	−	1.07073i
$29$	−0.509801	+	1.56901i	−0.0946676	+	0.291357i	−0.987167	−	0.159692i	$-0.948950\pi$
$29$	−0.509801	+	1.56901i	−0.0946676	+	0.291357i	0.892499	+	0.451049i	$0.148950\pi$
$30$	−3.83232	−	0.814585i	−0.699683	−	0.148722i
$31$	−2.14706	−	0.955933i	−0.385623	−	0.171691i	0.204763	−	0.978812i	$-0.434358\pi$
$31$	−2.14706	−	0.955933i	−0.385623	−	0.171691i	−0.590386	+	0.807121i	$0.701024\pi$
$32$	1.07031	+	1.85383i	0.189205	+	0.327713i
$33$		0			0
$34$	−3.71354			−0.636867
$35$	5.52703	+	1.86216i	0.934238	+	0.314763i
$36$	−3.23621	−	9.96003i	−0.539368	−	1.66000i
$37$	−3.71679	−	4.12791i	−0.611036	−	0.678624i	0.355641	−	0.934623i	$-0.384263\pi$
$37$	−3.71679	−	4.12791i	−0.611036	−	0.678624i	−0.966677	+	0.255998i	$0.917596\pi$
$38$	−1.80120	+	17.1372i	−0.292193	+	2.78003i
$39$	−0.245121	+	2.33217i	−0.0392507	+	0.373446i
$40$	−8.09920	−	8.99508i	−1.28060	−	1.42225i
$41$	−3.47642	−	10.6993i	−0.542925	−	1.67095i	−0.725873	−	0.687828i	$-0.758564\pi$
$41$	−3.47642	−	10.6993i	−0.542925	−	1.67095i	0.182948	−	0.983123i	$-0.441436\pi$
$42$	−0.927875	−	4.60991i	−0.143174	−	0.711324i
$43$	5.26819			0.803391			0.401696	−	0.915773i	$-0.368421\pi$
$43$	5.26819			0.803391			0.401696	+	0.915773i	$0.368421\pi$
$44$		0			0
$45$	2.74543	+	4.75523i	0.409265	+	0.708867i
$46$	−14.7701	−	6.57606i	−2.17773	−	0.969587i
$47$	−1.45828	−	0.309968i	−0.212713	−	0.0452135i	0.100323	−	0.994955i	$-0.468012\pi$
$47$	−1.45828	−	0.309968i	−0.212713	−	0.0452135i	−0.313035	+	0.949741i	$0.601346\pi$
$48$	−1.16161	+	3.57507i	−0.167664	+	0.516017i
$49$	0.580958	+	6.97585i	0.0829940	+	0.996550i
$50$	−0.283358	−	0.205872i	−0.0400729	−	0.0291147i
$51$	−0.711813	−	0.790548i	−0.0996737	−	0.110699i
$52$	−9.24578	+	10.2685i	−1.28216	+	1.42398i
$53$	0.278389	+	0.123947i	0.0382397	+	0.0170254i	0.425767	−	0.904833i	$-0.360004\pi$
$53$	0.278389	+	0.123947i	0.0382397	+	0.0170254i	−0.387528	+	0.921858i	$0.626671\pi$
$54$	4.87953	−	8.45159i	0.664019	−	1.15012i
$55$		0			0
$56$	6.05203	−	13.2068i	0.808737	−	1.76483i
$57$	−3.99348	+	2.90143i	−0.528949	+	0.384304i
$58$	−4.01950	−	0.854372i	−0.527787	−	0.112185i
$59$	12.3821	−	2.63190i	1.61201	−	0.342644i	0.688209	−	0.725513i	$-0.258397\pi$
$59$	12.3821	−	2.63190i	1.61201	−	0.342644i	0.923803	+	0.382869i	$0.125064\pi$
$60$	0.691268	−	6.57698i	0.0892423	−	0.849084i
$61$	−11.8594	+	5.28014i	−1.51844	+	0.676053i	−0.985434	−	0.170058i	$-0.945604\pi$
$61$	−11.8594	+	5.28014i	−1.51844	+	0.676053i	−0.533006	+	0.846111i	$0.678938\pi$
$62$	1.80903	−	5.56763i	0.229747	−	0.707090i
$63$	−3.93106	+	5.28938i	−0.495267	+	0.666400i
$64$	4.21045	−	3.05907i	0.526306	−	0.382384i
$65$	3.62234	−	6.27408i	0.449296	−	0.778204i
$66$		0			0
$67$	2.28646	+	3.96027i	0.279336	+	0.483824i	0.971220	−	0.238185i	$-0.0765524\pi$
$67$	2.28646	+	3.96027i	0.279336	+	0.483824i	−0.691884	+	0.722009i	$0.743219\pi$
$68$	−0.655204	−	6.23385i	−0.0794552	−	0.755966i
$69$	−1.43121	−	4.40480i	−0.172297	−	0.530275i
$70$	−3.17393	+	14.1765i	−0.379357	+	1.69442i
$71$	−9.16353	−	6.65769i	−1.08751	−	0.790123i	−0.108533	−	0.994093i	$-0.534615\pi$
$71$	−9.16353	−	6.65769i	−1.08751	−	0.790123i	−0.978977	+	0.203970i	$0.934615\pi$
$72$	12.4946	−	5.56293i	1.47250	−	0.655598i
$73$	8.38047	−	1.78132i	0.980859	−	0.208488i	0.310540	−	0.950560i	$-0.399490\pi$
$73$	8.38047	−	1.78132i	0.980859	−	0.208488i	0.670320	+	0.742072i	$0.266157\pi$
$74$	9.25801	−	10.2821i	1.07622	−	1.19527i
$75$	−0.0104877	−	0.0997836i	−0.00121101	−	0.0115220i
$76$	−29.0858			−3.33637
$77$		0			0
$78$	−5.84111			−0.661376
$79$	−0.484121	−	4.60611i	−0.0544679	−	0.518227i	−0.987408	−	0.158195i	$-0.949432\pi$
$79$	−0.484121	−	4.60611i	−0.0544679	−	0.518227i	0.932940	−	0.360032i	$-0.117234\pi$
$80$	7.77075	−	8.63029i	0.868796	−	0.964896i
$81$	−4.57479	+	0.972401i	−0.508310	+	0.108045i
$82$	25.5994	−	11.3976i	2.82698	−	1.25865i
$83$	1.56643	+	1.13808i	0.171938	+	0.124920i	0.670426	−	0.741976i	$-0.266111\pi$
$83$	1.56643	+	1.13808i	0.171938	+	0.124920i	−0.498488	+	0.866896i	$0.666111\pi$
$84$	7.57486	−	2.37096i	0.826485	−	0.258693i
$85$	1.01557	+	3.12561i	0.110154	+	0.339020i
$86$	1.37166	+	13.0505i	0.147910	+	1.40727i
$87$	−0.588580	−	1.01945i	−0.0631024	−	0.109297i
$88$		0			0
$89$	−1.60220	+	2.77509i	−0.169833	+	0.294159i	−0.938361	−	0.345657i	$-0.887656\pi$
$89$	−1.60220	+	2.77509i	−0.169833	+	0.294159i	0.768528	+	0.639816i	$0.220989\pi$
$90$	−11.0649	+	8.03913i	−1.16634	+	0.847399i
$91$	8.63719	+	1.00236i	0.905424	+	0.105076i
$92$	8.43313	−	25.9545i	0.879215	−	2.70595i
$93$	1.53201	−	0.682094i	0.158862	−	0.0707299i
$94$	0.388170	−	3.69319i	0.0400367	−	0.380924i
$95$	14.9167	−	3.17064i	1.53042	−	0.325300i
$96$	−1.49403	−	0.317566i	−0.152484	−	0.0324115i
$97$	−1.50428	+	1.09292i	−0.152736	+	0.110969i	−0.661529	−	0.749920i	$-0.730092\pi$
$97$	−1.50428	+	1.09292i	−0.152736	+	0.110969i	0.508793	+	0.860889i	$0.330092\pi$
$98$	−17.1294	+	3.25544i	−1.73034	+	0.328849i
$99$		0			0
$100$	0.295598	−	0.511992i	0.0295598	−	0.0511992i
$101$	5.52285	+	2.45893i	0.549544	+	0.244673i	0.662675	−	0.748907i	$-0.269421\pi$
$101$	5.52285	+	2.45893i	0.549544	+	0.244673i	−0.113130	+	0.993580i	$0.536088\pi$
$102$	1.77303	−	1.96915i	0.175556	−	0.194975i
$103$	−0.711813	−	0.790548i	−0.0701370	−	0.0778950i	0.707055	−	0.707159i	$-0.250023\pi$
$103$	−0.711813	−	0.790548i	−0.0701370	−	0.0778950i	−0.777192	+	0.629263i	$0.783357\pi$
$104$	−14.5991	−	10.6069i	−1.43156	−	1.04009i
$105$	−3.62631	+	2.04168i	−0.353892	+	0.199248i
$106$	−0.234560	+	0.721902i	−0.0227825	+	0.0701173i
$107$	6.19361	+	1.31649i	0.598759	+	0.127270i	0.497313	−	0.867571i	$-0.334320\pi$
$107$	6.19361	+	1.31649i	0.598759	+	0.127270i	0.101445	+	0.994841i	$0.467653\pi$
$108$	15.0485	+	6.70001i	1.44804	+	0.644708i
$109$	1.40694	+	2.43688i	0.134760	+	0.233411i	0.925506	−	0.378734i	$-0.123640\pi$
$109$	1.40694	+	2.43688i	0.134760	+	0.233411i	−0.790746	+	0.612145i	$0.790307\pi$
$110$		0			0
$111$	3.96345			0.376194
$112$	13.2088	+	4.45029i	1.24811	+	0.420513i
$113$	−3.94115	−	12.1296i	−0.370752	−	1.14106i	−0.946300	−	0.323289i	$-0.895211\pi$
$113$	−3.94115	−	12.1296i	−0.370752	−	1.14106i	0.575548	−	0.817768i	$-0.304789\pi$
$114$	−8.22725	−	9.13729i	−0.770553	−	0.855785i
$115$	−1.49564	+	14.2301i	−0.139469	+	1.32696i
$116$	0.725032	−	6.89821i	0.0673175	−	0.640483i
$117$	5.47759	+	6.08348i	0.506403	+	0.562418i
$118$	9.74366	+	29.9879i	0.896977	+	2.76061i
$119$	−2.95967	+	2.60750i	−0.271313	+	0.239029i
$120$	8.63671			0.788420
$121$		0			0
$122$	−16.1679	−	28.0035i	−1.46377	−	2.53532i
$123$	7.33325	+	3.26497i	0.661217	+	0.294393i
$124$	9.66546	+	2.05446i	0.867984	+	0.184496i
$125$	−3.50177	+	10.7774i	−0.313208	+	0.963956i
$126$	−14.1265	−	8.36092i	−1.25849	−	0.744850i
$127$	10.0136	+	7.27531i	0.888563	+	0.645579i	0.935503	−	0.353319i	$-0.114947\pi$
$127$	10.0136	+	7.27531i	0.888563	+	0.645579i	−0.0469396	+	0.998898i	$0.514947\pi$
$128$	11.5389	+	12.8153i	1.01991	+	1.13272i
$129$	−2.51530	+	2.79352i	−0.221460	+	0.245956i
$130$	16.4854	+	7.33977i	1.44587	+	0.643741i
$131$	−0.379526	+	0.657359i	−0.0331594	+	0.0574337i	−0.882129	−	0.471008i	$-0.843890\pi$
$131$	−0.379526	+	0.657359i	−0.0331594	+	0.0574337i	0.848969	+	0.528442i	$0.177224\pi$
$132$		0			0
$133$	10.5975	+	14.9230i	0.918924	+	1.29399i
$134$	−9.21513	+	6.69519i	−0.796066	+	0.578376i
$135$	−8.44798	−	1.79567i	−0.727086	−	0.154547i
$136$	8.00724	−	1.70199i	0.686615	−	0.145945i
$137$	0.610563	−	5.80912i	0.0521639	−	0.496306i	−0.936983	−	0.349375i	$-0.886394\pi$
$137$	0.610563	−	5.80912i	0.0521639	−	0.496306i	0.989147	−	0.146931i	$-0.0469395\pi$
$138$	10.5390	−	4.69227i	0.897140	−	0.399432i
$139$	−1.72213	+	5.30017i	−0.146069	+	0.449554i	−0.997147	−	0.0754852i	$-0.975949\pi$
$139$	−1.72213	+	5.30017i	−0.146069	+	0.449554i	0.851078	+	0.525039i	$0.175949\pi$
$140$	−24.3578	−	2.82677i	−2.05861	−	0.238906i
$141$	0.860622	−	0.625279i	0.0724775	−	0.0526580i
$142$	14.1067	−	24.4335i	1.18381	−	2.05041i
$143$		0			0
$144$	6.56117	+	11.3643i	0.546764	+	0.947023i
$145$	0.380140	+	3.61679i	0.0315689	+	0.300358i
$146$	6.59472	+	20.2964i	0.545783	+	1.67975i
$147$	−3.97641	−	3.02256i	−0.327969	−	0.249297i
$148$	18.8938	+	13.7271i	1.55306	+	1.12836i
$149$	−0.913545	+	0.406737i	−0.0748406	+	0.0333212i	−0.443816	−	0.896118i	$-0.646375\pi$
$149$	−0.913545	+	0.406737i	−0.0748406	+	0.0333212i	0.368975	+	0.929439i	$0.379709\pi$
$150$	0.244455	−	0.0519606i	0.0199597	−	0.00424256i
$151$	9.93064	−	11.0291i	0.808144	−	0.897535i	−0.188272	−	0.982117i	$-0.560289\pi$
$151$	9.93064	−	11.0291i	0.808144	−	0.897535i	0.996417	+	0.0845817i	$0.0269554\pi$
$152$	−3.97056	−	37.7774i	−0.322055	−	3.06415i
$153$	−3.71354			−0.300222
$154$		0			0
$155$	−5.18089			−0.416139
$156$	−1.03059	−	9.80538i	−0.0825130	−	0.785058i
$157$	4.27610	−	4.74909i	0.341270	−	0.379019i	−0.547940	−	0.836517i	$-0.684588\pi$
$157$	4.27610	−	4.74909i	0.341270	−	0.379019i	0.889210	+	0.457499i	$0.151255\pi$
$158$	11.2843	−	2.39855i	0.897729	−	0.190818i
$159$	−0.198641	+	0.0884408i	−0.0157533	+	0.00701381i
$160$	3.81757	+	2.77362i	0.301805	+	0.219274i
$161$	−16.3891	+	5.12987i	−1.29164	+	0.404290i
$162$	−3.59997	−	11.0796i	−0.282840	−	0.870493i
$163$	−1.03955	−	9.89070i	−0.0814242	−	0.774699i	−0.956700	−	0.291076i	$-0.905987\pi$
$163$	−1.03955	−	9.89070i	−0.0814242	−	0.774699i	0.875276	−	0.483624i	$-0.160680\pi$
$164$	23.6496	+	40.9623i	1.84672	+	3.19862i
$165$		0			0
$166$	−2.41142	+	4.17670i	−0.187163	+	0.324175i
$167$	1.57066	−	1.14115i	0.121542	−	0.0883051i	−0.525354	−	0.850884i	$-0.676067\pi$
$167$	1.57066	−	1.14115i	0.121542	−	0.0883051i	0.646895	+	0.762579i	$0.276067\pi$
$168$	4.11353	+	9.51476i	0.317366	+	0.734080i
$169$	−0.679580	+	2.09153i	−0.0522754	+	0.160887i
$170$	−7.47840	+	3.32960i	−0.573567	+	0.255369i
$171$	−1.80120	+	17.1372i	−0.137741	+	1.31052i
$172$	−21.6656	+	4.60516i	−1.65198	+	0.351140i
$173$	−6.29175	−	1.33735i	−0.478353	−	0.101677i	−0.0375760	−	0.999294i	$-0.511964\pi$
$173$	−6.29175	−	1.33735i	−0.478353	−	0.101677i	−0.440777	+	0.897617i	$0.645297\pi$
$174$	2.37215	−	1.72347i	0.179833	−	0.130656i
$175$	−0.370390	+	0.0348840i	−0.0279989	+	0.00263698i
$176$		0			0
$177$	−4.51624	+	7.82235i	−0.339461	+	0.587964i
$178$	−7.29167	−	3.24646i	−0.546534	−	0.243333i
$179$	−2.39948	+	2.66489i	−0.179345	+	0.199183i	−0.826114	−	0.563503i	$-0.809453\pi$
$179$	−2.39948	+	2.66489i	−0.179345	+	0.199183i	0.646769	+	0.762686i	$0.276120\pi$
$180$	−15.4474	−	17.1561i	−1.15138	−	1.27874i
$181$	−9.88082	−	7.17884i	−0.734436	−	0.533599i	0.156528	−	0.987674i	$-0.449970\pi$
$181$	−9.88082	−	7.17884i	−0.734436	−	0.533599i	−0.890964	+	0.454075i	$0.849970\pi$
$182$	−0.234234	+	21.6572i	−0.0173625	+	1.60534i
$183$	2.86241	−	8.80959i	0.211595	−	0.651224i
$184$	34.8616	+	7.41007i	2.57003	+	0.546277i
$185$	−11.1861	−	4.98036i	−0.822416	−	0.366163i
$186$	2.08858	+	3.61753i	0.153142	+	0.265250i
$187$		0			0
$188$	6.26819			0.457155
$189$	−2.04541	−	10.1621i	−0.148782	−	0.739183i
$190$	11.7382	+	36.1263i	0.851575	+	2.62088i
$191$	8.10271	+	8.99897i	0.586291	+	0.651142i	0.961178	−	0.275928i	$-0.0889852\pi$
$191$	8.10271	+	8.99897i	0.586291	+	0.651142i	−0.374887	+	0.927070i	$0.622319\pi$
$192$	−0.388170	+	3.69319i	−0.0280138	+	0.266533i
$193$	1.24806	−	11.8745i	0.0898376	−	0.854748i	−0.853093	−	0.521759i	$-0.825276\pi$
$193$	1.24806	−	11.8745i	0.0898376	−	0.854748i	0.942931	−	0.332989i	$-0.108057\pi$
$194$	−3.09906	−	3.44186i	−0.222500	−	0.247111i
$195$	1.59742	+	4.91635i	0.114394	+	0.352067i
$196$	−8.48710	−	28.1805i	−0.606222	−	2.01289i
$197$	12.1626			0.866551			0.433275	−	0.901262i	$-0.357358\pi$
$197$	12.1626			0.866551			0.433275	+	0.901262i	$0.357358\pi$
$198$		0			0
$199$	−0.952451	−	1.64969i	−0.0675174	−	0.116944i	0.830290	−	0.557331i	$-0.188174\pi$
$199$	−0.952451	−	1.64969i	−0.0675174	−	0.116944i	−0.897808	+	0.440387i	$0.854841\pi$
$200$	0.705340	+	0.314038i	0.0498751	+	0.0222058i
$201$	−3.19165	−	0.678406i	−0.225122	−	0.0478511i
$202$	−4.65335	+	14.3215i	−0.327408	+	1.00766i
$203$	−3.80343	+	2.14141i	−0.266949	+	0.150297i
$204$	3.61840	+	2.62892i	0.253339	+	0.184061i
$205$	−16.5940	−	18.4295i	−1.15897	−	1.28717i
$206$	1.77303	−	1.96915i	0.123533	−	0.137197i
$207$	−14.7701	−	6.57606i	−1.02659	−	0.457068i
$208$	8.65685	−	14.9941i	0.600245	−	1.03965i
$209$		0			0
$210$	−6.00187	−	8.45159i	−0.414168	−	0.583215i
$211$	13.1422	−	9.54838i	0.904748	−	0.657338i	−0.0349331	−	0.999390i	$-0.511122\pi$
$211$	13.1422	−	9.54838i	0.904748	−	0.657338i	0.939681	+	0.342052i	$0.111122\pi$
$212$	−1.25323	−	0.266382i	−0.0860722	−	0.0182952i
$213$	7.90545	−	1.68035i	0.541672	−	0.115136i
$214$	−1.64863	+	15.6857i	−0.112698	+	1.07225i
$215$	10.6092	−	4.72352i	0.723541	−	0.322141i
$216$	−6.64784	+	20.4600i	−0.452328	+	1.39212i
$217$	−2.46758	−	5.70761i	−0.167510	−	0.387458i
$218$	−5.67038	+	4.11977i	−0.384046	+	0.279026i
$219$	−3.05669	+	5.29434i	−0.206552	+	0.357758i
$220$		0			0
$221$	2.44983	+	4.24324i	0.164794	+	0.285431i
$222$	1.03195	+	9.81834i	0.0692599	+	0.658964i
$223$	0.938344	+	2.88793i	0.0628362	+	0.193390i	0.977546	−	0.210721i	$-0.0675811\pi$
$223$	0.938344	+	2.88793i	0.0628362	+	0.193390i	−0.914710	+	0.404111i	$0.867581\pi$
$224$	−1.23736	+	5.52671i	−0.0826744	+	0.369269i
$225$	−0.283358	−	0.205872i	−0.0188905	−	0.0137248i
$226$	29.0215	−	12.9212i	1.93048	−	0.859507i
$227$	−18.0459	+	3.83578i	−1.19775	+	0.254590i	−0.763263	−	0.646088i	$-0.776404\pi$
$227$	−18.0459	+	3.83578i	−1.19775	+	0.254590i	−0.434487	+	0.900678i	$0.643070\pi$
$228$	13.8870	−	15.4231i	0.919690	−	1.02142i
$229$	2.66546	+	25.3601i	0.176138	+	1.67585i	0.623755	+	0.781620i	$0.285606\pi$
$229$	2.66546	+	25.3601i	0.176138	+	1.67585i	−0.447617	+	0.894226i	$0.647727\pi$
$230$	−35.6404			−2.35006
$231$		0			0
$232$	9.05855			0.594723
$233$	−0.399049	−	3.79669i	−0.0261425	−	0.248730i	−0.999787	−	0.0206568i	$-0.993424\pi$
$233$	−0.399049	−	3.79669i	−0.0261425	−	0.248730i	0.973644	−	0.228073i	$-0.0732424\pi$
$234$	−13.6439	+	15.1531i	−0.891931	+	0.990590i
$235$	−3.21464	+	0.683294i	−0.209700	+	0.0445732i
$236$	−48.6210	+	21.6475i	−3.16496	+	1.40913i
$237$	2.67359	+	1.94247i	0.173668	+	0.126177i
$238$	−7.22994	−	6.65285i	−0.468648	−	0.431240i
$239$	4.01838	+	12.3673i	0.259927	+	0.799973i	0.992819	+	0.119628i	$0.0381702\pi$
$239$	4.01838	+	12.3673i	0.259927	+	0.799973i	−0.732892	+	0.680345i	$0.761830\pi$
$240$	0.866171	+	8.24107i	0.0559111	+	0.531959i
$241$	0.225292	+	0.390216i	0.0145123	+	0.0251360i	0.873190	−	0.487379i	$-0.162047\pi$
$241$	0.225292	+	0.390216i	0.0145123	+	0.0251360i	−0.858678	+	0.512515i	$0.828714\pi$
$242$		0			0
$243$	7.54551	−	13.0692i	0.484045	−	0.838391i
$244$	44.1565	−	32.0816i	2.82683	−	2.05381i
$245$	7.42457	+	13.5272i	0.474338	+	0.864222i
$246$	−6.17872	+	19.0162i	−0.393941	+	1.21243i
$247$	20.7700	−	9.24738i	1.32156	−	0.588397i
$248$	−1.34893	+	12.8342i	−0.0856571	+	0.814973i
$249$	−1.35137	+	0.287243i	−0.0856396	+	0.0182033i
$250$	−27.6096	−	5.86860i	−1.74618	−	0.371163i
$251$	−0.904971	+	0.657500i	−0.0571213	+	0.0415010i	−0.615980	−	0.787762i	$-0.711240\pi$
$251$	−0.904971	+	0.657500i	−0.0571213	+	0.0415010i	0.558858	+	0.829263i	$0.311240\pi$
$252$	11.5429	−	25.1890i	0.727134	−	1.58676i
$253$		0			0
$254$	−15.4153	+	26.7001i	−0.967243	+	1.67531i
$255$	−2.14228	−	0.953804i	−0.134155	−	0.0597295i
$256$	−21.7771	+	24.1859i	−1.36107	+	1.51162i
$257$	−15.2827	−	16.9731i	−0.953308	−	1.05876i	−0.998213	−	0.0597642i	$-0.980965\pi$
$257$	−15.2827	−	16.9731i	−0.953308	−	1.05876i	0.0449048	−	0.998991i	$-0.485702\pi$
$258$	−7.57506	−	5.50360i	−0.471603	−	0.342639i
$259$	0.158938	−	14.6954i	0.00987592	−	0.913126i
$260$	−9.41252	+	28.9688i	−0.583740	+	1.79657i
$261$	−4.01950	−	0.854372i	−0.248801	−	0.0528843i
$262$	−1.72724	−	0.769016i	−0.106709	−	0.0475100i
$263$	4.59568	+	7.95995i	0.283382	+	0.490832i	0.972215	−	0.234088i	$-0.0752103\pi$
$263$	4.59568	+	7.95995i	0.283382	+	0.490832i	−0.688834	+	0.724919i	$0.741877\pi$
$264$		0			0
$265$	0.671758			0.0412658
$266$	−34.2084	+	30.1379i	−2.09745	+	1.84787i
$267$	−0.706556	−	2.17455i	−0.0432405	−	0.133081i
$268$	−12.8650	−	14.2880i	−0.785854	−	0.872779i
$269$	1.63202	−	15.5277i	0.0995063	−	0.946739i	−0.824887	−	0.565298i	$-0.808761\pi$
$269$	1.63202	−	15.5277i	0.0995063	−	0.946739i	0.924393	−	0.381441i	$-0.124572\pi$
$270$	2.24871	−	21.3950i	0.136852	−	1.30206i
$271$	18.5647	+	20.6182i	1.12773	+	1.25247i	0.963983	+	0.265963i	$0.0856899\pi$
$271$	18.5647	+	20.6182i	1.12773	+	1.25247i	0.163742	+	0.986503i	$0.447643\pi$
$272$	2.42707	+	7.46974i	0.147163	+	0.452920i
$273$	−4.65534	+	4.10140i	−0.281754	+	0.248228i
$274$	14.5494			0.878962
$275$		0			0
$276$	9.73630	+	16.8638i	0.586056	+	1.01508i
$277$	13.5318	+	6.02473i	0.813046	+	0.361991i	0.770769	−	0.637115i	$-0.219872\pi$
$277$	13.5318	+	6.02473i	0.813046	+	0.361991i	0.0422766	+	0.999106i	$0.486539\pi$
$278$	−13.5781	−	2.88610i	−0.814357	−	0.173097i
$279$	1.80903	−	5.56763i	0.108304	−	0.333325i
$280$	0.346339	−	32.0225i	0.0206977	−	1.91371i
$281$	−12.3154	−	8.94766i	−0.734675	−	0.533773i	0.156364	−	0.987700i	$-0.450023\pi$
$281$	−12.3154	−	8.94766i	−0.734675	−	0.533773i	−0.891039	+	0.453927i	$0.850023\pi$
$282$	1.77303	+	1.96915i	0.105582	+	0.117261i
$283$	14.5317	−	16.1391i	0.863819	−	0.959369i	−0.135688	−	0.990752i	$-0.543324\pi$
$283$	14.5317	−	16.1391i	0.863819	−	0.959369i	0.999507	+	0.0313830i	$0.00999114\pi$
$284$	43.5050	+	19.3697i	2.58155	+	1.14938i
$285$	−5.44070	+	9.42356i	−0.322279	+	0.558204i
$286$		0			0
$287$	12.3997	−	27.0587i	0.731929	−	1.59722i
$288$	−4.31366	+	3.13406i	−0.254185	+	0.184676i
$289$	14.4544	+	3.07238i	0.850259	+	0.180728i
$290$	−8.86060	+	1.88338i	−0.520312	+	0.110596i
$291$	0.138682	−	1.31947i	0.00812970	−	0.0773490i
$292$	−32.9077	+	14.6515i	−1.92578	+	0.857412i
$293$	3.43861	−	10.5830i	0.200886	−	0.618263i	−0.798972	−	0.601369i	$-0.794622\pi$
$293$	3.43861	−	10.5830i	0.200886	−	0.618263i	0.999857	−	0.0168939i	$-0.00537775\pi$
$294$	6.45222	−	10.6374i	0.376301	−	0.620386i
$295$	22.5755	−	16.4021i	1.31440	−	0.954967i
$296$	−15.2499	+	26.4136i	−0.886383	+	1.53526i
$297$		0			0
$298$	−1.24543	−	2.15715i	−0.0721459	−	0.124960i
$299$	2.22980	+	21.2151i	0.128953	+	1.22690i
$300$	0.130356	+	0.401195i	0.00752612	+	0.0231630i
$301$	10.2567	+	9.43803i	0.591187	+	0.543999i
$302$	29.9071	+	21.7288i	1.72096	+	1.25035i
$303$	−3.94076	+	1.75454i	−0.226391	+	0.100796i
$304$	35.6486	−	7.57734i	2.04459	−	0.434591i
$305$	−19.1485	+	21.2665i	−1.09644	+	1.21772i
$306$	−0.966880	−	9.19924i	−0.0552728	−	0.525886i
$307$	24.9855			1.42600			0.712998	−	0.701166i	$-0.247337\pi$
$307$	24.9855			1.42600			0.712998	+	0.701166i	$0.247337\pi$
$308$		0			0
$309$	0.759053			0.0431810
$310$	−1.34893	−	12.8342i	−0.0766140	−	0.728934i
$311$	23.2461	−	25.8174i	1.31817	−	1.46397i	0.530784	−	0.847507i	$-0.321897\pi$
$311$	23.2461	−	25.8174i	1.31817	−	1.46397i	0.787382	−	0.616465i	$-0.211436\pi$
$312$	12.5948	−	2.67710i	0.713039	−	0.151561i
$313$	21.6597	−	9.64351i	1.22428	−	0.545083i	0.310219	−	0.950665i	$-0.399598\pi$
$313$	21.6597	−	9.64351i	1.22428	−	0.545083i	0.914059	+	0.405582i	$0.132931\pi$
$314$	12.8779	+	9.35633i	0.726741	+	0.528008i
$315$	−3.17393	+	14.1765i	−0.178831	+	0.798755i
$316$	6.01736	+	18.5195i	0.338503	+	1.04181i
$317$	−2.05681	−	19.5692i	−0.115522	−	1.09912i	−0.886652	−	0.462438i	$-0.846975\pi$
$317$	−2.05681	−	19.5692i	−0.115522	−	1.09912i	0.771130	−	0.636678i	$-0.219692\pi$
$318$	−0.270807	−	0.469051i	−0.0151861	−	0.0263031i
$319$		0			0
$320$	5.73630	−	9.93556i	0.320669	−	0.555414i
$321$	−3.65522	+	2.65568i	−0.204015	+	0.148225i
$322$	−16.9750	−	39.2638i	−0.945979	−	2.18809i
$323$	−3.18711	+	9.80892i	−0.177336	+	0.545783i
$324$	17.9639	−	7.99805i	0.997995	−	0.444336i
$325$	−0.0483049	+	0.459590i	−0.00267947	+	0.0254935i
$326$	24.2308	−	5.15041i	1.34202	−	0.285255i
$327$	−1.96393	−	0.417446i	−0.108605	−	0.0230848i
$328$	−49.9744	+	36.3085i	−2.75937	+	2.00480i
$329$	−2.28384	−	3.21602i	−0.125912	−	0.177305i
$330$		0			0
$331$	14.0949	−	24.4131i	0.774728	−	1.34187i	−0.160220	−	0.987081i	$-0.551220\pi$
$331$	14.0949	−	24.4131i	0.774728	−	1.34187i	0.934947	−	0.354786i	$-0.115446\pi$
$332$	−7.43682	−	3.31109i	−0.408149	−	0.181719i
$333$	9.25801	−	10.2821i	0.507336	−	0.563454i
$334$	3.23583	+	3.59376i	0.177057	+	0.196642i
$335$	8.15535	+	5.92521i	0.445574	+	0.323729i
$336$	−8.66635	+	4.87932i	−0.472788	+	0.266189i
$337$	6.71989	−	20.6817i	0.366056	−	1.12660i	−0.583262	−	0.812284i	$-0.698224\pi$
$337$	6.71989	−	20.6817i	0.366056	−	1.12660i	0.949317	−	0.314319i	$-0.101776\pi$
$338$	−5.35812	−	1.13890i	−0.291443	−	0.0619482i
$339$	8.31357	+	3.70144i	0.451531	+	0.201035i
$340$	−6.90880	−	11.9664i	−0.374682	−	0.648969i
$341$		0			0
$342$	−42.9217			−2.32094
$343$	−11.3663	+	14.6222i	−0.613720	+	0.789524i
$344$	−8.93891	−	27.5111i	−0.481954	−	1.48330i
$345$	−6.83158	−	7.58724i	−0.367800	−	0.408483i
$346$	1.67476	−	15.9342i	0.0900354	−	0.856630i
$347$	0.411993	−	3.91986i	0.0221170	−	0.210429i	−0.977882	−	0.209156i	$-0.932928\pi$
$347$	0.411993	−	3.91986i	0.0221170	−	0.210429i	0.999999	−	0.00127257i	$-0.000405070\pi$
$348$	3.31170	+	3.67801i	0.177525	+	0.197162i
$349$	−4.36001	−	13.4187i	−0.233386	−	0.718289i	−0.997331	−	0.0730077i	$-0.976740\pi$
$349$	−4.36001	−	13.4187i	−0.233386	−	0.718289i	0.763945	−	0.645281i	$-0.223260\pi$
$350$	−0.182852	−	0.908454i	−0.00977386	−	0.0485589i
$351$	−12.8762			−0.687279
$352$		0			0
$353$	2.48434	+	4.30301i	0.132228	+	0.229026i	0.924535	−	0.381097i	$-0.124453\pi$
$353$	2.48434	+	4.30301i	0.132228	+	0.229026i	−0.792307	+	0.610123i	$0.791120\pi$
$354$	−20.5536	−	9.15103i	−1.09241	−	0.486372i
$355$	−24.4231	−	5.19128i	−1.29624	−	0.275525i
$356$	4.16326	−	12.8132i	0.220652	−	0.679098i
$357$	0.0304387	−	2.81435i	0.00161098	−	0.148951i
$358$	−7.22626	−	5.25018i	−0.381919	−	0.277481i
$359$	−2.72443	−	3.02578i	−0.143790	−	0.159695i	0.666948	−	0.745104i	$-0.267600\pi$
$359$	−2.72443	−	3.02578i	−0.143790	−	0.159695i	−0.810738	+	0.585410i	$0.800934\pi$
$360$	20.1740	−	22.4055i	1.06326	−	1.18087i
$361$	26.3630	+	11.7376i	1.38753	+	0.617766i
$362$	15.2109	−	26.3461i	0.799468	−	1.38472i
$363$		0			0
$364$	−36.3969	+	3.42792i	−1.90772	+	0.179672i
$365$	15.2796	−	11.1013i	0.799771	−	0.581068i
$366$	22.5686	+	4.79710i	1.17968	+	0.250748i
$367$	17.6282	−	3.74699i	0.920184	−	0.195591i	0.276616	−	0.960980i	$-0.410787\pi$
$367$	17.6282	−	3.74699i	0.920184	−	0.195591i	0.643567	+	0.765389i	$0.277454\pi$
$368$	−3.57436	+	34.0078i	−0.186326	+	1.77278i
$369$	25.5994	−	11.3976i	1.33265	−	0.593334i
$370$	9.42497	−	29.0071i	0.489981	−	1.50801i
$371$	0.319948	+	0.740052i	0.0166109	+	0.0384216i
$372$	−5.70418	+	4.14433i	−0.295748	+	0.214873i
$373$	−14.4582	+	25.0424i	−0.748618	+	1.29664i	0.199867	+	0.979823i	$0.435949\pi$
$373$	−14.4582	+	25.0424i	−0.748618	+	1.29664i	−0.948485	+	0.316822i	$0.897384\pi$
$374$		0			0
$375$	−4.04290	−	7.00250i	−0.208774	−	0.361608i
$376$	0.855683	+	8.14128i	0.0441285	+	0.419855i
$377$	1.67544	+	5.15648i	0.0862896	+	0.265572i
$378$	24.6412	−	7.71279i	1.26740	−	0.396703i
$379$	−3.48563	−	2.53246i	−0.179045	−	0.130083i	0.494653	−	0.869090i	$-0.335295\pi$
$379$	−3.48563	−	2.53246i	−0.179045	−	0.130083i	−0.673698	+	0.739007i	$0.735295\pi$
$380$	−58.5736	+	26.0786i	−3.00476	+	1.33781i
$381$	−8.63881	+	1.83624i	−0.442580	+	0.0940732i
$382$	−20.1827	+	22.4152i	−1.03264	+	1.14686i
$383$	1.29080	+	12.2811i	0.0659566	+	0.627535i	0.976707	+	0.214578i	$0.0688375\pi$
$383$	1.29080	+	12.2811i	0.0659566	+	0.627535i	−0.910750	+	0.412957i	$0.864496\pi$
$384$	−12.3047			−0.627923
$385$		0			0
$386$	29.7408			1.51377
$387$	1.37166	+	13.0505i	0.0697253	+	0.663392i
$388$	5.23100	−	5.80961i	0.265564	−	0.294938i
$389$	−28.7800	+	6.11739i	−1.45921	+	0.310164i	−0.868084	−	0.496418i	$-0.834648\pi$
$389$	−28.7800	+	6.11739i	−1.45921	+	0.310164i	−0.591122	+	0.806582i	$0.701315\pi$
$390$	−11.7630	+	5.23721i	−0.595640	+	0.265196i
$391$	−7.82885	−	5.68799i	−0.395922	−	0.287654i
$392$	35.4430	−	14.8702i	1.79014	−	0.751061i
$393$	−0.167368	−	0.515105i	−0.00844258	−	0.0259836i
$394$	3.16673	+	30.1295i	0.159538	+	1.51790i
$395$	−5.10482	−	8.84180i	−0.256851	−	0.444879i
$396$		0			0
$397$	8.64975	−	14.9818i	0.434119	−	0.751915i	−0.563105	−	0.826386i	$-0.690393\pi$
$397$	8.64975	−	14.9818i	0.434119	−	0.751915i	0.997223	+	0.0744702i	$0.0237266\pi$
$398$	3.83866	−	2.78895i	0.192415	−	0.139798i
$399$	−12.9729	−	1.50553i	−0.649458	−	0.0753707i
$400$	−0.228914	+	0.704524i	−0.0114457	+	0.0352262i
$401$	−22.7933	+	10.1482i	−1.13825	+	0.506779i	−0.887287	−	0.461219i	$-0.847412\pi$
$401$	−22.7933	+	10.1482i	−1.13825	+	0.506779i	−0.250958	+	0.967998i	$0.580746\pi$
$402$	0.849563	−	8.08305i	0.0423724	−	0.403146i
$403$	−7.55522	+	1.60591i	−0.376352	+	0.0799961i
$404$	−24.8623	−	5.28465i	−1.23695	−	0.262921i
$405$	−8.34094	+	6.06005i	−0.414465	+	0.301126i
$406$	−6.29502	−	8.86439i	−0.312416	−	0.439932i
$407$		0			0
$408$	−2.92056	+	5.05855i	−0.144589	+	0.250436i
$409$	−35.2248	−	15.6831i	−1.74176	−	0.775480i	−0.993729	−	0.111811i	$-0.964335\pi$
$409$	−35.2248	−	15.6831i	−1.74176	−	0.775480i	−0.748027	−	0.663669i	$-0.768999\pi$
$410$	41.3334	−	45.9054i	2.04131	−	2.26710i
$411$	2.78884	+	3.09732i	0.137563	+	0.152780i
$412$	3.61840	+	2.62892i	0.178266	+	0.129518i
$413$	28.8220	+	17.0586i	1.41824	+	0.839400i
$414$	12.4447	−	38.3009i	0.611624	−	1.88239i
$415$	4.17492	+	0.887406i	0.204939	+	0.0435611i
$416$	6.42683	+	2.86141i	0.315101	+	0.140292i
$417$	−1.98825	−	3.44374i	−0.0973648	−	0.168641i
$418$		0			0
$419$	0.908970			0.0444061			0.0222030	−	0.999753i	$-0.492932\pi$
$419$	0.908970			0.0444061			0.0222030	+	0.999753i	$0.492932\pi$
$420$	13.1286	−	11.5664i	0.640609	−	0.564383i
$421$	4.80619	+	14.7919i	0.234239	+	0.720914i	0.997221	+	0.0744948i	$0.0237344\pi$
$421$	4.80619	+	14.7919i	0.234239	+	0.720914i	−0.762982	+	0.646420i	$0.776266\pi$
$422$	27.0752	+	30.0701i	1.31800	+	1.46379i
$423$	0.388170	−	3.69319i	0.0188735	−	0.179569i
$424$	0.174903	−	1.66409i	0.00849404	−	0.0808154i
$425$	−0.140274	−	0.155790i	−0.00680428	−	0.00755692i
$426$	6.22092	+	19.1460i	0.301404	+	0.927627i
$427$	−32.5487	−	10.9663i	−1.57514	−	0.530695i
$428$	−26.6222			−1.28683
$429$		0			0
$430$	14.4635	+	25.0514i	0.697490	+	1.20809i
$431$	3.23064	+	1.43837i	0.155615	+	0.0692841i	0.483066	−	0.875584i	$-0.339523\pi$
$431$	3.23064	+	1.43837i	0.155615	+	0.0692841i	−0.327451	+	0.944868i	$0.606190\pi$
$432$	−20.1894	−	4.29139i	−0.971363	−	0.206470i
$433$	5.45282	−	16.7820i	0.262046	−	0.806493i	−0.730314	−	0.683112i	$-0.760626\pi$
$433$	5.45282	−	16.7820i	0.262046	−	0.806493i	0.992359	−	0.123381i	$-0.0393739\pi$
$434$	13.4965	−	7.59880i	0.647854	−	0.364754i
$435$	−2.09934	−	1.52526i	−0.100656	−	0.0731307i
$436$	−7.91625	−	8.79188i	−0.379119	−	0.421055i
$437$	−30.0462	+	33.3697i	−1.43731	+	1.59629i
$438$	−13.9111	−	6.19361i	−0.664697	−	0.295942i
$439$	−7.51362	+	13.0140i	−0.358606	+	0.621123i	−0.987728	−	0.156183i	$-0.950081\pi$
$439$	−7.51362	+	13.0140i	−0.358606	+	0.621123i	0.629123	+	0.777306i	$0.283414\pi$
$440$		0			0
$441$	−17.1294	+	3.25544i	−0.815688	+	0.155021i
$442$	−9.87357	+	7.17357i	−0.469638	+	0.341212i
$443$	−12.9337	−	2.74915i	−0.614500	−	0.130616i	−0.109862	−	0.993947i	$-0.535041\pi$
$443$	−12.9337	−	2.74915i	−0.614500	−	0.130616i	−0.504638	+	0.863331i	$0.668374\pi$
$444$	−16.2998	+	3.46463i	−0.773555	+	0.164424i
$445$	−0.738367	+	7.02509i	−0.0350019	+	0.333021i
$446$	−6.90971	+	3.07640i	−0.327184	+	0.145672i
$447$	0.220495	−	0.678615i	0.0104291	−	0.0320974i
$448$	13.6778	+	1.58733i	0.646213	+	0.0749941i
$449$	8.01626	−	5.82415i	0.378310	−	0.274859i	−0.382338	−	0.924022i	$-0.624881\pi$
$449$	8.01626	−	5.82415i	0.378310	−	0.274859i	0.760649	+	0.649164i	$0.224881\pi$
$450$	0.436212	−	0.755542i	0.0205632	−	0.0356166i
$451$		0			0
$452$	26.8111	+	46.4382i	1.26109	+	2.18427i
$453$	1.10692	+	10.5317i	0.0520079	+	0.494822i
$454$	−14.2006	−	43.7050i	−0.666468	−	2.05118i
$455$	18.2925	−	5.72563i	0.857565	−	0.268422i
$456$	21.9277	+	15.9314i	1.02686	+	0.746055i
$457$	9.45064	−	4.20770i	0.442082	−	0.196828i	−0.173610	−	0.984815i	$-0.555543\pi$
$457$	9.45064	−	4.20770i	0.442082	−	0.196828i	0.615692	+	0.787987i	$0.288876\pi$
$458$	−62.1286	+	13.2058i	−2.90308	+	0.617069i
$459$	3.90847	−	4.34079i	0.182432	−	0.202611i
$460$	−6.28828	−	59.8290i	−0.293193	−	2.78954i
$461$	−15.3372			−0.714325			−0.357163	−	0.934042i	$-0.616256\pi$
$461$	−15.3372			−0.714325			−0.357163	+	0.934042i	$0.616256\pi$
$462$		0			0
$463$	−25.1313			−1.16795			−0.583976	−	0.811771i	$-0.698504\pi$
$463$	−25.1313			−1.16795			−0.583976	+	0.811771i	$0.698504\pi$
$464$	0.908477	+	8.64359i	0.0421750	+	0.401268i
$465$	2.47362	−	2.74723i	0.114711	−	0.127400i
$466$	9.30134	−	1.97706i	0.430876	−	0.0915856i
$467$	−0.681518	+	0.303431i	−0.0315369	+	0.0140411i	−0.422445	−	0.906389i	$-0.638828\pi$
$467$	−0.681518	+	0.303431i	−0.0315369	+	0.0140411i	0.390908	+	0.920430i	$0.372161\pi$
$468$	−27.8446	−	20.2303i	−1.28712	−	0.935144i
$469$	−2.64333	+	11.8065i	−0.122057	+	0.545175i
$470$	−2.52965	−	7.78547i	−0.116684	−	0.359117i
$471$	0.476638	+	4.53491i	0.0219623	+	0.208957i
$472$	−34.7537	−	60.1951i	−1.59967	−	2.77070i
$473$		0			0
$474$	−4.11582	+	7.12881i	−0.189046	+	0.327437i
$475$	−0.786978	+	0.571773i	−0.0361090	+	0.0262347i
$476$	9.89240	−	13.3106i	0.453418	−	0.610090i
$477$	−0.234560	+	0.721902i	−0.0107398	+	0.0330536i
$478$	−29.5902	+	13.1744i	−1.35343	+	0.602584i
$479$	2.10238	−	20.0029i	0.0960604	−	0.913954i	−0.835285	−	0.549817i	$-0.814697\pi$
$479$	2.10238	−	20.0029i	0.0960604	−	0.913954i	0.931345	−	0.364137i	$-0.118636\pi$
$480$	−3.29345	+	0.700043i	−0.150325	+	0.0319525i
$481$	−17.8562	−	3.79546i	−0.814174	−	0.173058i
$482$	−0.907993	+	0.659696i	−0.0413579	+	0.0300483i
$483$	5.10482	−	11.1398i	0.232277	−	0.506878i
$484$		0			0
$485$	−2.04942	+	3.54969i	−0.0930592	+	0.161183i
$486$	34.3399	+	15.2891i	1.55769	+	0.693528i
$487$	−2.84375	+	3.15830i	−0.128863	+	0.143116i	−0.804123	−	0.594463i	$-0.797365\pi$
$487$	−2.84375	+	3.15830i	−0.128863	+	0.143116i	0.675260	+	0.737579i	$0.264031\pi$
$488$	47.6962	+	52.9720i	2.15911	+	2.39793i
$489$	5.74100	+	4.17108i	0.259617	+	0.188623i
$490$	−31.5768	+	21.9143i	−1.42649	+	0.989988i
$491$	9.37184	−	28.8436i	0.422945	−	1.30169i	−0.482003	−	0.876170i	$-0.660091\pi$
$491$	9.37184	−	28.8436i	0.422945	−	1.30169i	0.904948	−	0.425522i	$-0.139909\pi$
$492$	−33.0122	−	7.01697i	−1.48831	−	0.316349i
$493$	−2.24691	−	1.00039i	−0.101196	−	0.0450553i
$494$	28.3156	+	49.0440i	1.27398	+	2.20659i
$495$		0			0
$496$	−12.3816			−0.555948
$497$	−5.91326	−	29.3785i	−0.265246	−	1.31781i
$498$	−1.06341	−	3.27285i	−0.0476527	−	0.146660i
$499$	9.66310	+	10.7320i	0.432580	+	0.480429i	0.919540	−	0.392995i	$-0.128561\pi$
$499$	9.66310	+	10.7320i	0.432580	+	0.480429i	−0.486961	+	0.873424i	$0.661894\pi$
$500$	4.98017	−	47.3832i	0.222720	−	2.11904i
$501$	−0.144803	+	1.37771i	−0.00646931	+	0.0615514i
$502$	−1.86440	−	2.07062i	−0.0832120	−	0.0924163i
$503$	−0.914140	−	2.81343i	−0.0407595	−	0.125445i	0.928606	−	0.371067i	$-0.121008\pi$
$503$	−0.914140	−	2.81343i	−0.0407595	−	0.125445i	−0.969366	+	0.245622i	$0.921008\pi$
$504$	34.2919	+	11.5536i	1.52748	+	0.514638i
$505$	13.3267			0.593032
$506$		0			0
$507$	−0.784595	−	1.35896i	−0.0348451	−	0.0603534i
$508$	−47.5409	−	21.1666i	−2.10928	−	0.939114i
$509$	24.4446	+	5.19586i	1.08349	+	0.230302i	0.714855	−	0.699273i	$-0.246493\pi$
$509$	24.4446	+	5.19586i	1.08349	+	0.230302i	0.368633	+	0.929575i	$0.379826\pi$
$510$	1.80500	−	5.55523i	0.0799269	−	0.245990i
$511$	19.5073	+	11.5456i	0.862953	+	0.510749i
$512$	−37.6813	−	27.3771i	−1.66529	−	1.20991i
$513$	−18.1362	−	20.1422i	−0.800731	−	0.889302i
$514$	38.0671	−	42.2778i	1.67907	−	1.86479i
$515$	−2.14228	−	0.953804i	−0.0944001	−	0.0420296i
$516$	7.90228	−	13.6872i	0.347879	−	0.602544i
$517$		0			0
$518$	36.4450	−	3.43245i	1.60130	−	0.150813i
$519$	3.71314	−	2.69776i	0.162989	−	0.118418i
$520$	−38.9103	−	8.27064i	−1.70633	−	0.362691i
$521$	−28.2324	+	6.00098i	−1.23688	+	0.262908i	−0.779523	−	0.626374i	$-0.784538\pi$
$521$	−28.2324	+	6.00098i	−1.23688	+	0.262908i	−0.457361	+	0.889281i	$0.651205\pi$
$522$	1.06992	−	10.1796i	0.0468293	−	0.445551i
$523$	0.431733	−	0.192220i	0.0188784	−	0.00840519i	−0.397276	−	0.917699i	$-0.630044\pi$
$523$	0.431733	−	0.192220i	0.0188784	−	0.00840519i	0.416154	+	0.909294i	$0.363378\pi$
$524$	0.986185	−	3.03517i	0.0430817	−	0.132592i
$525$	0.158345	−	0.213059i	0.00691075	−	0.00929866i
$526$	−18.5220	+	13.4570i	−0.807597	+	0.586754i
$527$	1.75195	−	3.03447i	0.0763162	−	0.132184i
$528$		0			0
$529$	−9.56566	−	16.5682i	−0.415898	−	0.720357i
$530$	0.174903	+	1.66409i	0.00759730	+	0.0722835i
$531$	9.74366	+	29.9879i	0.422839	+	1.30136i
$532$	−56.6276	−	52.1076i	−2.45512	−	2.25915i
$533$	−29.9113	−	21.7318i	−1.29560	−	0.941311i
$534$	5.20288	−	2.31647i	0.225151	−	0.100244i
$535$	13.6532	−	2.90208i	0.590279	−	0.125468i
$536$	16.8014	−	18.6598i	0.725710	−	0.805983i
$537$	−0.267459	−	2.54470i	−0.0115417	−	0.109812i
$538$	38.8904			1.67668
$539$		0			0
$540$	36.3122			1.56263
$541$	−1.61596	−	15.3749i	−0.0694757	−	0.661017i	−0.972735	−	0.231921i	$-0.925499\pi$
$541$	−1.61596	−	15.3749i	−0.0694757	−	0.661017i	0.903259	−	0.429096i	$-0.141168\pi$
$542$	−46.2421	+	51.3571i	−1.98627	+	2.20598i
$543$	8.52427	−	1.81189i	0.365811	−	0.0777556i
$544$	−2.91546	+	1.29804i	−0.124999	+	0.0556532i
$545$	5.01825	+	3.64597i	0.214958	+	0.156176i
$546$	−11.3722	−	10.4644i	−0.486683	−	0.447836i
$547$	−10.8292	−	33.3288i	−0.463023	−	1.42504i	−0.861452	−	0.507839i	$-0.830444\pi$
$547$	−10.8292	−	33.3288i	−0.463023	−	1.42504i	0.398429	−	0.917199i	$-0.369556\pi$
$548$	2.56705	+	24.4239i	0.109659	+	1.04334i
$549$	−16.1679	−	28.0035i	−0.690027	−	1.19516i
$550$		0			0
$551$	−5.70644	+	9.88384i	−0.243102	+	0.421066i
$552$	−20.5740	+	14.9479i	−0.875686	+	0.636223i
$553$	7.30936	−	9.83501i	0.310826	−	0.418227i
$554$	−11.4014	+	35.0898i	−0.484398	+	1.49082i
$555$	7.98169	−	3.55368i	0.338804	−	0.150845i
$556$	2.44919	−	23.3025i	0.103869	−	0.988244i
$557$	−10.3025	+	2.18986i	−0.436530	+	0.0927873i	−0.420934	−	0.907091i	$-0.638298\pi$
$557$	−10.3025	+	2.18986i	−0.436530	+	0.0927873i	−0.0155956	+	0.999878i	$0.504964\pi$
$558$	14.2632	+	3.03175i	0.603811	+	0.128344i
$559$	14.0071	−	10.1767i	0.592436	−	0.430430i
$560$	30.5903	−	2.88104i	1.29268	−	0.121746i
$561$		0			0
$562$	18.9588	−	32.8376i	0.799729	−	1.38517i
$563$	−28.0593	−	12.4928i	−1.18256	−	0.526509i	−0.281227	−	0.959641i	$-0.590742\pi$
$563$	−28.0593	−	12.4928i	−1.18256	−	0.526509i	−0.901330	+	0.433133i	$0.857408\pi$
$564$	−2.99275	+	3.32378i	−0.126017	+	0.139957i
$565$	−18.8123	−	20.8932i	−0.791439	−	0.878982i
$566$	43.7636	+	31.7961i	1.83952	+	1.33649i
$567$	−10.6488	−	6.30261i	−0.447207	−	0.264685i
$568$	−19.2189	+	59.1496i	−0.806406	+	2.48186i
$569$	30.0996	+	6.39788i	1.26184	+	0.268213i	0.789801	−	0.613363i	$-0.210184\pi$
$569$	30.0996	+	6.39788i	1.26184	+	0.268213i	0.472042	+	0.881576i	$0.343517\pi$
$570$	−24.7608	−	11.0242i	−1.03712	−	0.461754i
$571$	3.75847	+	6.50986i	0.157287	+	0.272429i	0.933889	−	0.357562i	$-0.116392\pi$
$571$	3.75847	+	6.50986i	0.157287	+	0.272429i	−0.776602	+	0.629991i	$0.783059\pi$
$572$		0			0
$573$	−8.64045			−0.360960
$574$	70.2587	+	23.6715i	2.93254	+	0.988030i
$575$	−0.282041	−	0.868034i	−0.0117619	−	0.0361995i
$576$	8.67424	+	9.63372i	0.361427	+	0.401405i
$577$	−2.88691	+	27.4671i	−0.120184	+	1.14347i	0.753660	+	0.657265i	$0.228287\pi$
$577$	−2.88691	+	27.4671i	−0.120184	+	1.14347i	−0.873843	+	0.486207i	$0.838380\pi$
$578$	−3.84752	+	36.6067i	−0.160036	+	1.52264i
$579$	5.70073	+	6.33130i	0.236914	+	0.263120i
$580$	−4.72493	−	14.5418i	−0.196192	−	0.603817i
$581$	1.01082	+	5.02202i	0.0419360	+	0.208348i
$582$	3.30473			0.136986
$583$		0			0
$584$	−23.5220	−	40.7413i	−0.973348	−	1.68589i
$585$	16.4854	+	7.33977i	0.681587	+	0.303462i
$586$	27.1116	+	5.76275i	1.11997	+	0.238057i
$587$	−9.25760	+	28.4920i	−0.382102	+	1.17599i	0.556459	+	0.830875i	$0.312160\pi$
$587$	−9.25760	+	28.4920i	−0.382102	+	1.17599i	−0.938561	+	0.345114i	$0.887840\pi$
$588$	18.9952	+	8.95440i	0.783350	+	0.369273i
$589$	−13.1537	−	9.55673i	−0.541989	−	0.393778i
$590$	46.5095	+	51.6540i	1.91476	+	2.12656i
$591$	−5.80704	+	6.44938i	−0.238870	+	0.265292i
$592$	−26.7330	−	11.9023i	−1.09872	−	0.489182i
$593$	−6.33401	+	10.9708i	−0.260107	+	0.450518i	−0.966270	−	0.257531i	$-0.917091\pi$
$593$	−6.33401	+	10.9708i	−0.260107	+	0.450518i	0.706163	+	0.708049i	$0.250424\pi$
$594$		0			0
$595$	−3.62234	+	7.90471i	−0.148502	+	0.324062i
$596$	3.40143	−	2.47129i	0.139328	−	0.101228i
$597$	1.32952	+	0.282598i	0.0544135	+	0.0115659i
$598$	−51.9739	+	11.0474i	−2.12537	+	0.451762i
$599$	−0.135288	+	1.28718i	−0.00552770	+	0.0525926i	−0.996938	−	0.0781956i	$-0.975084\pi$
$599$	−0.135288	+	1.28718i	−0.00552770	+	0.0525926i	0.991410	+	0.130788i	$0.0417508\pi$
$600$	−0.503287	+	0.224078i	−0.0205466	+	0.00914794i
$601$	−12.6765	+	39.0142i	−0.517085	+	1.59142i	0.262371	+	0.964967i	$0.415496\pi$
$601$	−12.6765	+	39.0142i	−0.517085	+	1.59142i	−0.779456	+	0.626457i	$0.784504\pi$
$602$	−20.7096	+	27.8655i	−0.844059	+	1.13571i
$603$	−9.21513	+	6.69519i	−0.375269	+	0.272649i
$604$	−31.1990	+	54.0383i	−1.26947	+	2.19879i
$605$		0			0
$606$	−5.37242	−	9.30531i	−0.218240	−	0.378002i
$607$	2.21358	+	21.0608i	0.0898465	+	0.854832i	0.942915	+	0.333033i	$0.108072\pi$
$607$	2.21358	+	21.0608i	0.0898465	+	0.854832i	−0.853069	+	0.521799i	$0.825261\pi$
$608$	4.57612	+	14.0839i	0.185586	+	0.571176i
$609$	0.680444	−	3.03923i	0.0275730	−	0.123156i
$610$	−57.6675	−	41.8979i	−2.33489	−	1.69639i
$611$	−4.47607	+	1.99287i	−0.181082	+	0.0806231i
$612$	15.2720	−	3.24617i	0.617335	−	0.131219i
$613$	4.52541	−	5.02598i	0.182780	−	0.202997i	−0.644791	−	0.764359i	$-0.723056\pi$
$613$	4.52541	−	5.02598i	0.182780	−	0.202997i	0.827571	+	0.561362i	$0.189722\pi$
$614$	6.50537	+	61.8944i	0.262535	+	2.49786i
$615$	17.6953			0.713542
$616$		0			0
$617$	−41.0728			−1.65353			−0.826763	−	0.562550i	$-0.809820\pi$
$617$	−41.0728			−1.65353			−0.826763	+	0.562550i	$0.809820\pi$
$618$	0.197632	+	1.88034i	0.00794991	+	0.0756384i
$619$	−20.3595	+	22.6115i	−0.818316	+	0.908832i	−0.997180	−	0.0750418i	$-0.976091\pi$
$619$	−20.3595	+	22.6115i	−0.818316	+	0.908832i	0.178864	+	0.983874i	$0.442758\pi$
$620$	21.3066	−	4.52885i	0.855692	−	0.181883i
$621$	23.2322	−	10.3436i	0.932276	−	0.415076i
$622$	70.0079	+	50.8637i	2.80706	+	2.03945i
$623$	−8.09097	+	2.53251i	−0.324158	+	0.101463i
$624$	3.81759	+	11.7493i	0.152826	+	0.470350i
$625$	2.53765	+	24.1442i	0.101506	+	0.965767i
$626$	29.5285	+	51.1449i	1.18020	+	2.04416i
$627$		0			0
$628$	−13.4342	+	23.2687i	−0.536082	+	0.928521i
$629$	6.69965	−	4.86758i	0.267133	−	0.194083i
$630$	−35.9447	−	4.17144i	−1.43207	−	0.166194i
$631$	3.82162	−	11.7617i	0.152136	−	0.468227i	−0.845723	−	0.533622i	$-0.820831\pi$
$631$	3.82162	−	11.7617i	0.152136	−	0.468227i	0.997859	+	0.0653945i	$0.0208306\pi$
$632$	−23.2322	+	10.3436i	−0.924127	+	0.411448i
$633$	−1.21161	+	11.5277i	−0.0481572	+	0.458185i
$634$	47.9417	−	10.1903i	1.90401	−	0.404709i
$635$	26.6887	+	5.67286i	1.05911	+	0.225121i
$636$	0.739607	−	0.537356i	0.0293273	−	0.0213075i
$637$	15.0201	+	17.4252i	0.595120	+	0.690410i
$638$		0			0
$639$	14.1067	−	24.4335i	0.558052	−	0.966574i
$640$	34.7277	+	15.4618i	1.37273	+	0.611180i
$641$	−31.5370	+	35.0254i	−1.24564	+	1.38342i	−0.351154	+	0.936318i	$0.614211\pi$
$641$	−31.5370	+	35.0254i	−1.24564	+	1.38342i	−0.894483	+	0.447102i	$0.852456\pi$
$642$	−7.53039	−	8.36334i	−0.297201	−	0.330075i
$643$	−1.51482	−	1.10058i	−0.0597388	−	0.0434028i	0.557515	−	0.830167i	$-0.311755\pi$
$643$	−1.51482	−	1.10058i	−0.0597388	−	0.0434028i	−0.617254	+	0.786764i	$0.711755\pi$
$644$	62.9165	−	35.4232i	2.47926	−	1.39587i
$645$	−2.56066	+	7.88089i	−0.100826	+	0.310310i
$646$	−25.1286	−	5.34126i	−0.988673	−	0.210149i
$647$	−1.67716	−	0.746719i	−0.0659359	−	0.0293566i	0.373504	−	0.927629i	$-0.378156\pi$
$647$	−1.67716	−	0.746719i	−0.0659359	−	0.0293566i	−0.439440	+	0.898272i	$0.644823\pi$
$648$	12.8404	+	22.2402i	0.504417	+	0.873676i
$649$		0			0
$650$	−1.15108			−0.0451492
$651$	4.20467	+	1.41663i	0.164794	+	0.0555223i
$652$	12.9211	+	39.7670i	0.506029	+	1.55740i
$653$	−12.1629	−	13.5083i	−0.475971	−	0.528619i	0.456568	−	0.889688i	$-0.349078\pi$
$653$	−12.1629	−	13.5083i	−0.475971	−	0.528619i	−0.932539	+	0.361069i	$0.882412\pi$
$654$	0.522764	−	4.97377i	0.0204417	−	0.194490i
$655$	−0.174903	+	1.66409i	−0.00683403	+	0.0650214i
$656$	−39.6572	−	44.0437i	−1.54835	−	1.71962i
$657$	6.59472	+	20.2964i	0.257284	+	0.791840i
$658$	7.37214	−	6.49492i	0.287396	−	0.253199i
$659$	−16.8997			−0.658318			−0.329159	−	0.944275i	$-0.606765\pi$
$659$	−16.8997			−0.658318			−0.329159	+	0.944275i	$0.606765\pi$
$660$		0			0
$661$	22.6516	+	39.2338i	0.881046	+	1.52602i	0.850180	+	0.526493i	$0.176493\pi$
$661$	22.6516	+	39.2338i	0.881046	+	1.52602i	0.0308661	+	0.999524i	$0.490173\pi$
$662$	64.1465	+	28.5599i	2.49313	+	1.11001i
$663$	−3.41970	−	0.726880i	−0.132810	−	0.0282297i
$664$	3.28531	−	10.1111i	0.127495	−	0.392388i
$665$	34.7217	+	20.5505i	1.34645	+	0.796913i
$666$	27.8814	+	20.2570i	1.08038	+	0.784943i
$667$	−7.16525	−	7.95782i	−0.277440	−	0.308128i
$668$	−5.46186	+	6.06601i	−0.211326	+	0.234701i
$669$	−1.97937	−	0.881272i	−0.0765269	−	0.0340720i
$670$	−12.5547	+	21.7453i	−0.485028	+	0.840094i
$671$		0			0
$672$	−2.33983	−	3.29485i	−0.0902609	−	0.127102i
$673$	−31.9623	+	23.2220i	−1.23206	+	0.895143i	−0.997043	−	0.0768491i	$-0.975514\pi$
$673$	−31.9623	+	23.2220i	−1.23206	+	0.895143i	−0.235015	+	0.971992i	$0.575514\pi$
$674$	52.9827	+	11.2618i	2.04082	+	0.433789i
$675$	0.538878	−	0.114542i	0.0207414	−	0.00440872i
$676$	0.966489	−	9.19553i	0.0371727	−	0.353674i
$677$	−31.1829	+	13.8835i	−1.19845	+	0.533586i	−0.906239	−	0.422766i	$-0.861059\pi$
$677$	−31.1829	+	13.8835i	−1.19845	+	0.533586i	−0.292216	+	0.956352i	$0.594392\pi$
$678$	−7.00470	+	21.5583i	−0.269014	+	0.827940i
$679$	−4.88668	−	0.567107i	−0.187533	−	0.0217636i
$680$	14.5991	−	10.6069i	0.559851	−	0.406756i
$681$	6.58206	−	11.4005i	0.252225	−	0.436867i
$682$		0			0
$683$	−11.8931	−	20.5995i	−0.455079	−	0.788219i	0.543614	−	0.839335i	$-0.317056\pi$
$683$	−11.8931	−	20.5995i	−0.455079	−	0.788219i	−0.998693	+	0.0511160i	$0.983722\pi$
$684$	−7.57296	−	72.0519i	−0.289559	−	2.75497i
$685$	−3.97895	−	12.2460i	−0.152028	−	0.467894i
$686$	−39.1817	−	24.3496i	−1.49597	−	0.929671i
$687$	−14.7201	−	10.6948i	−0.561609	−	0.408032i
$688$	25.3544	−	11.2885i	0.966626	−	0.430370i
$689$	0.979614	−	0.208223i	0.0373203	−	0.00793268i
$690$	17.0165	−	18.8988i	0.647808	−	0.719464i
$691$	2.14936	+	20.4498i	0.0817656	+	0.777948i	0.956182	+	0.292772i	$0.0945777\pi$
$691$	2.14936	+	20.4498i	0.0817656	+	0.777948i	−0.874417	+	0.485176i	$0.838756\pi$
$692$	27.0440			1.02806
$693$		0			0
$694$	9.81761			0.372671
$695$	1.28413	+	12.2177i	0.0487098	+	0.463442i
$696$	−4.32501	+	4.80341i	−0.163939	+	0.182073i
$697$	16.4056	−	3.48711i	0.621406	−	0.132084i
$698$	32.1060	−	14.2945i	1.21523	−	0.541055i
$699$	2.20377	+	1.60113i	0.0833542	+	0.0605603i
$700$	1.49274	−	0.467235i	0.0564205	−	0.0176598i
$701$	−7.41353	−	22.8165i	−0.280005	−	0.861768i	−0.987851	−	0.155401i	$-0.950333\pi$
$701$	−7.41353	−	22.8165i	−0.280005	−	0.861768i	0.707846	−	0.706367i	$-0.249667\pi$
$702$	−3.35252	−	31.8971i	−0.126533	−	1.20388i
$703$	−19.2134	−	33.2785i	−0.724646	−	1.25512i
$704$		0			0
$705$	1.17251	−	2.03084i	0.0441592	−	0.0764860i
$706$	−10.0127	+	7.27462i	−0.376831	+	0.273784i
$707$	6.34732	+	14.6816i	0.238715	+	0.552158i
$708$	11.7353	−	36.1175i	0.441039	−	1.35738i
$709$	−47.2410	+	21.0330i	−1.77417	+	0.789913i	−0.789905	+	0.613229i	$0.789870\pi$
$709$	−47.2410	+	21.0330i	−1.77417	+	0.789913i	−0.984268	+	0.176683i	$0.943463\pi$
$710$	6.50100	−	61.8529i	0.243978	−	2.32130i
$711$	11.2843	−	2.39855i	0.423194	−	0.0899526i
$712$	17.2104	+	3.65819i	0.644989	+	0.137097i
$713$	12.3417	−	8.96675i	0.462199	−	0.335808i
$714$	6.97969	−	0.657359i	0.261208	−	0.0246010i
$715$		0			0
$716$	7.53841	−	13.0569i	0.281724	−	0.487960i
$717$	−8.47648	−	3.77397i	−0.316560	−	0.140942i
$718$	6.78617	−	7.53681i	0.253258	−	0.281271i
$719$	17.2536	+	19.1621i	0.643451	+	0.714625i	0.973333	−	0.229397i	$-0.0736755\pi$
$719$	17.2536	+	19.1621i	0.643451	+	0.714625i	−0.329881	+	0.944022i	$0.607009\pi$
$720$	23.4024	+	17.0028i	0.872154	+	0.633657i
$721$	0.0304387	−	2.81435i	0.00113359	−	0.104812i
$722$	−22.2125	+	68.3630i	−0.826663	+	2.54421i
$723$	−0.314482	−	0.0668453i	−0.0116957	−	0.00248600i
$724$	46.9105	+	20.8859i	1.74341	+	0.776218i
$725$	−0.115989	−	0.200899i	−0.00430772	−	0.00746118i
$726$		0			0
$727$	32.7330			1.21400			0.606999	−	0.794702i	$-0.292373\pi$
$727$	32.7330			1.21400			0.606999	+	0.794702i	$0.292373\pi$
$728$	−9.42088	−	46.8052i	−0.349161	−	1.73472i
$729$	−1.00831	−	3.10325i	−0.0373448	−	0.114935i
$730$	31.4786	+	34.9605i	1.16507	+	1.29395i
$731$	−0.820982	+	7.81113i	−0.0303651	+	0.288905i
$732$	−4.07088	+	38.7318i	−0.150464	+	1.43157i
$733$	−6.21136	−	6.89841i	−0.229422	−	0.254799i	0.617432	−	0.786624i	$-0.288173\pi$
$733$	−6.21136	−	6.89841i	−0.229422	−	0.254799i	−0.846854	+	0.531825i	$0.821506\pi$
$734$	13.8719	+	42.6933i	0.512021	+	1.57584i
$735$	−10.7178	−	2.52161i	−0.395333	−	0.0930108i
$736$	−13.8944			−0.512156
$737$		0			0
$738$	34.8995	+	60.4477i	1.28467	+	2.22511i
$739$	−45.7625	−	20.3748i	−1.68340	−	0.749498i	−0.999807	−	0.0196341i	$-0.993750\pi$
$739$	−45.7625	−	20.3748i	−1.68340	−	0.749498i	−0.683593	−	0.729864i	$-0.739583\pi$
$740$	50.3566	+	10.7036i	1.85114	+	0.393473i
$741$	−5.01308	+	15.4287i	−0.184160	+	0.566787i
$742$	−1.74997	+	0.985265i	−0.0642433	+	0.0361702i
$743$	−10.6530	−	7.73987i	−0.390821	−	0.283948i	0.374971	−	0.927037i	$-0.377653\pi$
$743$	−10.6530	−	7.73987i	−0.390821	−	0.283948i	−0.765792	+	0.643088i	$0.777653\pi$
$744$	−6.16145	−	6.84298i	−0.225890	−	0.250876i
$745$	−1.47503	+	1.63819i	−0.0540410	+	0.0600186i
$746$	−65.7999	−	29.2960i	−2.40910	−	1.07260i
$747$	−2.41142	+	4.17670i	−0.0882293	+	0.152818i
$748$		0			0
$749$	9.69992	+	13.6590i	0.354427	+	0.499090i
$750$	16.2941	−	11.8384i	0.594976	−	0.432276i
$751$	−40.4109	−	8.58960i	−1.47461	−	0.313439i	−0.600683	−	0.799487i	$-0.705105\pi$
$751$	−40.4109	−	8.58960i	−1.47461	−	0.313439i	−0.873932	+	0.486048i	$0.838438\pi$
$752$	−7.68252	+	1.63297i	−0.280153	+	0.0595483i
$753$	0.0834313	−	0.793795i	0.00304040	−	0.0289275i
$754$	−12.3375	+	5.49301i	−0.449305	+	0.200043i
$755$	10.1097	−	31.1145i	0.367931	−	1.13237i
$756$	17.2949	+	40.0039i	0.629010	+	1.45493i
$757$	36.8195	−	26.7509i	1.33823	−	0.972278i	0.338719	−	0.940887i	$-0.390006\pi$
$757$	36.8195	−	26.7509i	1.33823	−	0.972278i	0.999507	−	0.0313910i	$-0.00999371\pi$
$758$	5.36591	−	9.29402i	0.194898	−	0.337574i
$759$		0			0
$760$	−41.8676	−	72.5168i	−1.51870	−	2.63046i
$761$	−3.26881	−	31.1006i	−0.118494	−	1.12740i	−0.878587	−	0.477582i	$-0.841513\pi$
$761$	−3.26881	−	31.1006i	−0.118494	−	1.12740i	0.760093	−	0.649814i	$-0.225153\pi$
$762$	−6.79801	−	20.9221i	−0.246266	−	0.757929i
$763$	−1.62653	+	7.26495i	−0.0588842	+	0.263009i
$764$	−41.1890	−	29.9255i	−1.49016	−	1.08267i
$765$	−7.47840	+	3.32960i	−0.270382	+	0.120382i
$766$	−30.0869	+	6.39517i	−1.08708	+	0.231067i
$767$	27.8374	−	30.9166i	1.00515	−	1.11633i
$768$	−2.42740	−	23.0951i	−0.0875911	−	0.833374i
$769$	42.0467			1.51624			0.758121	−	0.652114i	$-0.226118\pi$
$769$	42.0467			1.51624			0.758121	+	0.652114i	$0.226118\pi$
$770$		0			0
$771$	16.2969			0.586920
$772$	5.24736	+	49.9253i	0.188857	+	1.79685i
$773$	5.11518	−	5.68098i	0.183980	−	0.204331i	−0.644099	−	0.764943i	$-0.722767\pi$
$773$	5.11518	−	5.68098i	0.183980	−	0.204331i	0.828079	+	0.560612i	$0.189434\pi$
$774$	−31.9717	+	6.79579i	−1.14920	+	0.244270i
$775$	0.301906	−	0.134417i	0.0108448	−	0.00482841i
$776$	8.25977	+	6.00107i	0.296508	+	0.215426i
$777$	7.71651	+	7.10058i	0.276828	+	0.254732i
$778$	−22.6475	−	69.7017i	−0.811951	−	2.49893i
$779$	−8.13506	−	77.3999i	−0.291469	−	2.77314i
$780$	−10.8670	−	18.8222i	−0.389102	−	0.673944i
$781$		0			0
$782$	12.0520	−	20.8747i	0.430980	−	0.746479i
$783$	5.22918	−	3.79922i	0.186876	−	0.135773i
$784$	17.7436	+	32.3280i	0.633700	+	1.15457i
$785$	4.35321	−	13.3978i	0.155373	−	0.478188i
$786$	1.23245	−	0.548722i	0.0439600	−	0.0195723i
$787$	2.91670	−	27.7505i	0.103969	−	0.989200i	−0.810827	−	0.585285i	$-0.800983\pi$
$787$	2.91670	−	27.7505i	0.103969	−	0.989200i	0.914797	−	0.403915i	$-0.132351\pi$
$788$	−50.0191	+	10.6319i	−1.78186	+	0.378745i
$789$	−6.41507	−	1.36357i	−0.228383	−	0.0485442i
$790$	20.5740	−	14.9479i	0.731989	−	0.531821i
$791$	14.0573	−	30.6759i	0.499819	−	1.09071i
$792$		0			0
$793$	−21.3320	+	36.9481i	−0.757521	+	1.31206i
$794$	39.3653	+	17.5266i	1.39702	+	0.621995i
$795$	−0.320731	+	0.356208i	−0.0113752	+	0.0126334i
$796$	5.35905	+	5.95182i	0.189946	+	0.210957i
$797$	−8.13546	−	5.91076i	−0.288173	−	0.209370i	0.434301	−	0.900768i	$-0.356995\pi$
$797$	−8.13546	−	5.91076i	−0.288173	−	0.209370i	−0.722474	+	0.691398i	$0.756995\pi$
$798$	0.351815	−	32.5288i	0.0124541	−	1.15151i
$799$	0.686844	−	2.11389i	0.0242988	−	0.0747840i
$800$	−0.294422	−	0.0625814i	−0.0104094	−	0.00221259i
$801$	−7.29167	−	3.24646i	−0.257639	−	0.114708i
$802$	−31.0740	−	53.8218i	−1.09726	−	1.90051i
$803$		0			0
$804$	13.7188			0.483824
$805$	−28.4053	+	25.0253i	−1.00115	+	0.882026i
$806$	−5.94532	−	18.2978i	−0.209415	−	0.644513i
$807$	7.45453	+	8.27909i	0.262412	+	0.291438i
$808$	3.46983	−	33.0133i	0.122068	−	1.16140i
$809$	−4.03193	+	38.3613i	−0.141755	+	1.34871i	0.660093	+	0.751184i	$0.270517\pi$
$809$	−4.03193	+	38.3613i	−0.141755	+	1.34871i	−0.801849	+	0.597527i	$0.796150\pi$
$810$	−17.1838	−	19.0845i	−0.603776	−	0.670561i
$811$	3.82439	+	11.7703i	0.134293	+	0.413310i	0.995479	−	0.0949787i	$-0.0302783\pi$
$811$	3.82439	+	11.7703i	0.134293	+	0.413310i	−0.861187	+	0.508289i	$0.830278\pi$
$812$	13.7698	−	12.1313i	0.483226	−	0.425726i
$813$	−19.7968			−0.694303
$814$		0			0
$815$	−10.9616	−	18.9860i	−0.383968	−	0.665051i
$816$	−5.11972	−	2.27945i	−0.179226	−	0.0797966i
$817$	35.6486	+	7.57734i	1.24719	+	0.265098i
$818$	29.6791	−	91.3430i	1.03771	−	3.19373i
$819$	−0.234234	+	21.6572i	−0.00818478	+	0.756764i
$820$	84.3533	+	61.2862i	2.94574	+	2.14021i
$821$	19.8987	+	22.0997i	0.694469	+	0.771286i	0.982485	−	0.186340i	$-0.0596625\pi$
$821$	19.8987	+	22.0997i	0.694469	+	0.771286i	−0.288017	+	0.957625i	$0.592996\pi$
$822$	−6.94662	+	7.71500i	−0.242291	+	0.269092i
$823$	37.2516	+	16.5855i	1.29851	+	0.578134i	0.935393	−	0.353609i	$-0.115046\pi$
$823$	37.2516	+	16.5855i	1.29851	+	0.578134i	0.363117	+	0.931743i	$0.381712\pi$
$824$	−2.92056	+	5.05855i	−0.101742	+	0.176223i
$825$		0			0
$826$	−34.7537	+	75.8398i	−1.20923	+	2.63880i
$827$	15.2428	−	11.0745i	0.530043	−	0.385099i	−0.290331	−	0.956926i	$-0.593765\pi$
$827$	15.2428	−	11.0745i	0.530043	−	0.385099i	0.820374	+	0.571827i	$0.193765\pi$
$828$	66.4907	+	14.1330i	2.31071	+	0.491157i
$829$	30.4601	−	6.47450i	1.05792	−	0.224869i	0.354074	−	0.935217i	$-0.384796\pi$
$829$	30.4601	−	6.47450i	1.05792	−	0.224869i	0.703850	+	0.710349i	$0.251463\pi$
$830$	−1.11129	+	10.5732i	−0.0385735	+	0.367002i
$831$	−9.65543	+	4.29888i	−0.334943	+	0.149126i
$832$	5.28545	−	16.2669i	0.183240	−	0.563955i
$833$	−10.4336	−	0.225716i	−0.361503	−	0.00782059i
$834$	8.01323	−	5.82195i	0.277476	−	0.201598i
$835$	2.13986	−	3.70635i	0.0740530	−	0.128264i
$836$		0			0
$837$	4.60407	+	7.97448i	0.159140	+	0.275638i
$838$	0.236665	+	2.25172i	0.00817546	+	0.0777843i
$839$	3.17017	+	9.75678i	0.109446	+	0.336841i	0.990748	−	0.135712i	$-0.0433323\pi$
$839$	3.17017	+	9.75678i	0.109446	+	0.336841i	−0.881302	+	0.472554i	$0.843332\pi$
$840$	16.8149	+	15.4728i	0.580171	+	0.533862i
$841$	21.2596	+	15.4460i	0.733090	+	0.532621i
$842$	−35.3915	+	15.7573i	−1.21967	+	0.543032i
$843$	10.6246	−	2.25833i	0.365931	−	0.0777809i
$844$	−45.7011	+	50.7562i	−1.57310	+	1.74710i
$845$	0.506738	+	4.82129i	0.0174323	+	0.165857i
$846$	9.24992			0.318019
$847$		0			0
$848$	1.60540			0.0551297
$849$	1.61978	+	15.4112i	0.0555908	+	0.528911i
$850$	0.349403	−	0.388051i	0.0119844	−	0.0133101i
$851$	35.2666	−	7.49615i	1.20892	−	0.256965i
$852$	−31.0425	+	13.8210i	−1.06350	+	0.473500i
$853$	−2.46293	−	1.78942i	−0.0843291	−	0.0612687i	0.544822	−	0.838552i	$-0.316597\pi$
$853$	−2.46293	−	1.78942i	−0.0843291	−	0.0612687i	−0.629151	+	0.777283i	$0.716597\pi$
$854$	18.6913	−	83.4855i	0.639603	−	2.85681i
$855$	11.7382	+	36.1263i	0.401436	+	1.23549i
$856$	−3.63425	−	34.5776i	−0.124216	−	1.18184i
$857$	−24.7766	−	42.9143i	−0.846352	−	1.46592i	−0.884442	−	0.466650i	$-0.845461\pi$
$857$	−24.7766	−	42.9143i	−0.846352	−	1.46592i	0.0380904	−	0.999274i	$-0.487873\pi$
$858$		0			0
$859$	−18.4373	+	31.9344i	−0.629074	+	1.08959i	0.358664	+	0.933467i	$0.383232\pi$
$859$	−18.4373	+	31.9344i	−0.629074	+	1.08959i	−0.987738	+	0.156121i	$0.950101\pi$
$860$	−39.5015	+	28.6995i	−1.34699	+	0.978646i
$861$	8.42797	+	19.4942i	0.287225	+	0.664362i
$862$	−2.72202	+	8.37751i	−0.0927123	+	0.285339i
$863$	−42.4095	+	18.8819i	−1.44364	+	0.642749i	−0.971124	−	0.238575i	$-0.923320\pi$
$863$	−42.4095	+	18.8819i	−1.44364	+	0.642749i	−0.472513	+	0.881324i	$0.656653\pi$
$864$	0.876659	−	8.34085i	0.0298245	−	0.283762i
$865$	−13.8695	+	2.94806i	−0.471579	+	0.100237i
$866$	42.9925	+	9.13834i	1.46094	+	0.310533i
$867$	−8.53042	+	6.19771i	−0.289708	+	0.210485i
$868$	15.1372	+	21.3157i	0.513792	+	0.723501i
$869$		0			0
$870$	3.23181	−	5.59766i	0.109569	−	0.189778i
$871$	13.7294	+	6.11274i	0.465204	+	0.207122i
$872$	10.3385	−	11.4820i	0.350104	−	0.388830i
$873$	−3.09906	−	3.44186i	−0.104887	−	0.116489i
$874$	−90.4871	−	65.7428i	−3.06077	−	2.22378i
$875$	−26.1254	+	14.7091i	−0.883201	+	0.497259i
$876$	7.94269	−	24.4451i	0.268358	−	0.825922i
$877$	−38.1781	−	8.11500i	−1.28918	−	0.274024i	−0.488210	−	0.872726i	$-0.662350\pi$
$877$	−38.1781	−	8.11500i	−1.28918	−	0.274024i	−0.800972	+	0.598702i	$0.795683\pi$
$878$	−34.1947	−	15.2245i	−1.15402	−	0.513801i
$879$	3.96997	+	6.87620i	0.133904	+	0.231928i
$880$		0			0
$881$	−44.0049			−1.48256			−0.741281	−	0.671194i	$-0.765782\pi$
$881$	−44.0049			−1.48256			−0.741281	+	0.671194i	$0.765782\pi$
$882$	−12.5244	−	41.5858i	−0.421717	−	1.40027i
$883$	−7.21850	−	22.2163i	−0.242922	−	0.747637i	−0.995971	−	0.0896726i	$-0.971418\pi$
$883$	−7.21850	−	22.2163i	−0.242922	−	0.747637i	0.753049	−	0.657964i	$-0.228582\pi$
$884$	−13.7842	−	15.3089i	−0.463613	−	0.514894i
$885$	−2.08129	+	19.8021i	−0.0699617	+	0.665641i
$886$	3.44274	−	32.7555i	0.115661	−	1.10044i
$887$	28.0484	+	31.1509i	0.941772	+	1.04594i	0.998868	+	0.0475746i	$0.0151492\pi$
$887$	28.0484	+	31.1509i	0.941772	+	1.04594i	−0.0570962	+	0.998369i	$0.518184\pi$
$888$	−6.72507	−	20.6976i	−0.225679	−	0.694567i
$889$	6.46182	+	32.1039i	0.216723	+	1.07673i
$890$	−17.5949			−0.589783
$891$		0			0
$892$	−6.38343	−	11.0564i	−0.213733	−	0.370196i
$893$	−9.42204	−	4.19496i	−0.315296	−	0.140379i
$894$	1.73849	+	0.369527i	0.0581437	+	0.0123588i
$895$	−2.44275	+	7.51801i	−0.0816521	+	0.251299i
$896$	−0.493430	+	45.6225i	−0.0164843	+	1.52414i
$897$	−12.3142	−	8.94678i	−0.411159	−	0.298724i
$898$	16.5149	+	18.3416i	0.551108	+	0.612067i
$899$	2.59444	−	2.88141i	0.0865293	−	0.0961005i
$900$	1.34528	+	0.598957i	0.0448426	+	0.0199652i
$901$	−0.227159	+	0.393451i	−0.00756776	+	0.0131078i
$902$		0			0
$903$	−9.90170	+	0.932559i	−0.329508	+	0.0310336i
$904$	−56.6550	+	41.1623i	−1.88432	+	1.36904i
$905$	−26.3348	−	5.59764i	−0.875400	−	0.186072i
$906$	−25.8011	+	5.48419i	−0.857183	+	0.182200i
$907$	2.14473	−	20.4057i	0.0712145	−	0.677560i	−0.899434	−	0.437057i	$-0.856021\pi$
$907$	2.14473	−	20.4057i	0.0712145	−	0.677560i	0.970648	−	0.240503i	$-0.0773125\pi$
$908$	70.8613	−	31.5495i	2.35162	−	1.04701i
$909$	−4.65335	+	14.3215i	−0.154342	+	0.475015i
$910$	18.9464	+	43.8237i	0.628066	+	1.45274i
$911$	−22.3899	+	16.2672i	−0.741812	+	0.538958i	−0.893278	−	0.449505i	$-0.851601\pi$
$911$	−22.3899	+	16.2672i	−0.741812	+	0.538958i	0.151466	+	0.988462i	$0.451601\pi$
$912$	−13.0025	+	22.5209i	−0.430554	+	0.745742i
$913$		0			0
$914$	12.8840	+	22.3158i	0.426165	+	0.738140i
$915$	−2.13440	−	20.3074i	−0.0705609	−	0.671342i
$916$	−33.1302	−	101.964i	−1.09465	−	3.36899i
$917$	−1.91657	+	0.599896i	−0.0632908	+	0.0198103i
$918$	11.7707	+	8.55193i	0.388492	+	0.282256i
$919$	0.880159	−	0.391872i	0.0290338	−	0.0129267i	−0.392168	−	0.919893i	$-0.628275\pi$
$919$	0.880159	−	0.391872i	0.0290338	−	0.0129267i	0.421202	+	0.906967i	$0.361608\pi$
$920$	76.8490	−	16.3348i	2.53364	−	0.538541i
$921$	−11.9293	+	13.2488i	−0.393084	+	0.436564i
$922$	−3.99329	−	37.9936i	−0.131512	−	1.25125i
$923$	−37.2249			−1.22527
$924$		0			0
$925$	0.781061			0.0256811
$926$	−6.54334	−	62.2557i	−0.215028	−	2.04585i
$927$	1.77303	−	1.96915i	0.0582339	−	0.0646753i
$928$	−3.45431	+	0.734236i	−0.113393	+	0.0241025i
$929$	24.0555	−	10.7102i	0.789234	−	0.351390i	0.0277846	−	0.999614i	$-0.491155\pi$
$929$	24.0555	−	10.7102i	0.789234	−	0.351390i	0.761449	+	0.648224i	$0.224488\pi$
$930$	7.44954	+	5.41241i	0.244280	+	0.177480i
$931$	−6.10230	+	48.0396i	−0.199995	+	1.57443i
$932$	4.95995	+	15.2652i	0.162469	+	0.500027i
$933$	2.59114	+	24.6531i	0.0848302	+	0.807105i
$934$	−0.929110	−	1.60927i	−0.0304014	−	0.0526568i
$935$		0			0
$936$	22.4745	−	38.9269i	0.734601	−	1.27237i
$937$	17.3020	−	12.5706i	0.565232	−	0.410665i	−0.268138	−	0.963381i	$-0.586408\pi$
$937$	17.3020	−	12.5706i	0.565232	−	0.410665i	0.833370	+	0.552715i	$0.186408\pi$
$938$	−29.9356	−	3.47408i	−0.977432	−	0.113433i
$939$	−5.22783	+	16.0896i	−0.170604	+	0.525064i
$940$	12.6230	−	5.62013i	0.411717	−	0.183308i
$941$	−1.54941	+	14.7416i	−0.0505093	+	0.480564i	0.939804	+	0.341714i	$0.111007\pi$
$941$	−1.54941	+	14.7416i	−0.0505093	+	0.480564i	−0.990313	+	0.138850i	$0.955659\pi$
$942$	−11.1099	+	2.36147i	−0.361979	+	0.0769409i
$943$	71.4260	+	15.1821i	2.32595	+	0.494396i
$944$	53.9522	−	39.1985i	1.75599	−	1.27580i
$945$	−13.2305	−	18.6307i	−0.430389	−	0.606056i
$946$		0			0
$947$	−15.8560	+	27.4634i	−0.515251	+	0.892442i	0.484592	+	0.874740i	$0.338968\pi$
$947$	−15.8560	+	27.4634i	−0.515251	+	0.892442i	−0.999843	+	0.0177013i	$0.994365\pi$
$948$	−12.6932	−	5.65137i	−0.412256	−	0.183548i
$949$	18.8410	−	20.9250i	0.611604	−	0.679255i
$950$	−1.62131	−	1.80065i	−0.0526022	−	0.0584206i
$951$	11.3588	+	8.25267i	0.368335	+	0.267611i
$952$	18.6386	+	11.0314i	0.604079	+	0.357531i
$953$	15.4391	−	47.5166i	0.500121	−	1.53922i	−0.308699	−	0.951160i	$-0.599894\pi$
$953$	15.4391	−	47.5166i	0.500121	−	1.53922i	0.808821	−	0.588055i	$-0.200106\pi$
$954$	−1.84938	−	0.393098i	−0.0598759	−	0.0127270i
$955$	24.3860	+	10.8573i	0.789111	+	0.351335i
$956$	−27.3365	−	47.3481i	−0.884124	−	1.53135i
$957$		0			0
$958$	50.0988			1.61862
$959$	11.5958	−	10.2160i	0.374449	−	0.329893i
$960$	2.52965	+	7.78547i	0.0816442	+	0.251275i
$961$	−17.0470	−	18.9326i	−0.549903	−	0.610729i
$962$	4.75302	−	45.2220i	0.153244	−	1.45802i
$963$	−1.64863	+	15.6857i	−0.0531264	+	0.505464i
$964$	−1.26762	−	1.40784i	−0.0408274	−	0.0453434i
$965$	−8.13346	−	25.0322i	−0.261825	−	0.805816i
$966$	28.9248	+	9.74532i	0.930641	+	0.313551i
$967$	−52.4581			−1.68694			−0.843469	−	0.537178i	$-0.819490\pi$
$967$	−52.4581			−1.68694			−0.843469	+	0.537178i	$0.819490\pi$
$968$		0			0
$969$	−3.67961	−	6.37327i	−0.118206	−	0.204739i
$970$	−9.32697	−	4.15263i	−0.299471	−	0.133333i
$971$	−30.1529	−	6.40921i	−0.967654	−	0.205681i	−0.303131	−	0.952949i	$-0.598032\pi$
$971$	−30.1529	−	6.40921i	−0.967654	−	0.205681i	−0.664523	+	0.747268i	$0.731365\pi$
$972$	−19.6067	+	60.3433i	−0.628887	+	1.93551i
$973$	−12.8482	+	7.23376i	−0.411893	+	0.231904i
$974$	−8.56422	−	6.22227i	−0.274415	−	0.199374i
$975$	−0.220640	−	0.245046i	−0.00706614	−	0.00784774i
$976$	−45.7620	+	50.8238i	−1.46481	+	1.62683i
$977$	22.5970	+	10.0609i	0.722944	+	0.321875i	0.735014	−	0.678052i	$-0.237176\pi$
$977$	22.5970	+	10.0609i	0.722944	+	0.321875i	−0.0120704	+	0.999927i	$0.503842\pi$
$978$	−8.83791	+	15.3077i	−0.282605	+	0.489487i
$979$		0			0
$980$	−42.3585	−	49.1409i	−1.35309	−	1.56975i
$981$	−5.67038	+	4.11977i	−0.181041	+	0.131534i
$982$	73.8919	+	15.7062i	2.35799	+	0.501205i
$983$	−11.9567	+	2.54148i	−0.381360	+	0.0810606i	−0.394603	−	0.918852i	$-0.629118\pi$
$983$	−11.9567	+	2.54148i	−0.381360	+	0.0810606i	0.0132429	+	0.999912i	$0.495785\pi$
$984$	4.60725	−	43.8350i	0.146874	−	1.39741i
$985$	24.4933	−	10.9051i	0.780423	−	0.347467i
$986$	1.89316	−	5.82656i	0.0602906	−	0.185556i
$987$	2.79575	+	0.324452i	0.0889898	+	0.0103274i
$988$	−77.3334	+	56.1860i	−2.46030	+	1.78752i
$989$	−17.0975	+	29.6138i	−0.543670	+	0.941665i
$990$		0			0
$991$	−2.30008	−	3.98386i	−0.0730645	−	0.126552i	0.827178	−	0.561939i	$-0.189945\pi$
$991$	−2.30008	−	3.98386i	−0.0730645	−	0.126552i	−0.900243	+	0.435388i	$0.856611\pi$
$992$	−0.525880	−	5.00342i	−0.0166967	−	0.158859i
$993$	6.21573	+	19.1301i	0.197250	+	0.607074i
$994$	71.2375	−	22.2976i	2.25952	−	0.707238i
$995$	−3.39720	−	2.46821i	−0.107698	−	0.0782475i
$996$	5.30645	−	2.36259i	0.168141	−	0.0748614i
$997$	33.7229	−	7.16803i	1.06802	−	0.227014i	0.359814	−	0.933024i	$-0.382840\pi$
$997$	33.7229	−	7.16803i	1.06802	−	0.227014i	0.708202	+	0.706010i	$0.249507\pi$
$998$	−24.0695	+	26.7319i	−0.761906	+	0.846182i
$999$	2.27483	+	21.6436i	0.0719725	+	0.684772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.e.366.3		24
7.4	even	3	inner	847.2.n.e.487.1		24
11.2	odd	10		847.2.e.d.485.1		6
11.3	even	5	inner	847.2.n.e.632.3		24
11.4	even	5	inner	847.2.n.e.807.1		24
11.5	even	5	inner	847.2.n.e.9.1		24
11.6	odd	10		847.2.n.d.9.3		24
11.7	odd	10		847.2.n.d.807.3		24
11.8	odd	10		847.2.n.d.632.1		24
11.9	even	5		77.2.e.b.23.3	✓	6
11.10	odd	2		847.2.n.d.366.1		24
33.20	odd	10		693.2.i.g.100.1		6
44.31	odd	10		1232.2.q.k.177.2		6
77.2	odd	30		5929.2.a.v.1.3		3
77.4	even	15	inner	847.2.n.e.81.3		24
77.9	even	15		539.2.a.h.1.1		3
77.18	odd	30		847.2.n.d.81.1		24
77.20	odd	10		539.2.e.l.177.3		6
77.25	even	15	inner	847.2.n.e.753.1		24
77.31	odd	30		539.2.e.l.67.3		6
77.32	odd	6		847.2.n.d.487.3		24
77.39	odd	30		847.2.n.d.130.1		24
77.46	odd	30		847.2.e.d.606.1		6
77.53	even	15		77.2.e.b.67.3	yes	6
77.60	even	15	inner	847.2.n.e.130.3		24
77.68	even	30		5929.2.a.w.1.3		3
77.74	odd	30		847.2.n.d.753.3		24
77.75	odd	30		539.2.a.i.1.1		3
231.53	odd	30		693.2.i.g.298.1		6
231.86	odd	30		4851.2.a.bo.1.3		3
231.152	even	30		4851.2.a.bn.1.3		3
308.75	even	30		8624.2.a.ck.1.2		3
308.163	odd	30		8624.2.a.cl.1.2		3
308.207	odd	30		1232.2.q.k.529.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.3	✓	6	11.9	even	5
77.2.e.b.67.3	yes	6	77.53	even	15
539.2.a.h.1.1		3	77.9	even	15
539.2.a.i.1.1		3	77.75	odd	30
539.2.e.l.67.3		6	77.31	odd	30
539.2.e.l.177.3		6	77.20	odd	10
693.2.i.g.100.1		6	33.20	odd	10
693.2.i.g.298.1		6	231.53	odd	30
847.2.e.d.485.1		6	11.2	odd	10
847.2.e.d.606.1		6	77.46	odd	30
847.2.n.d.9.3		24	11.6	odd	10
847.2.n.d.81.1		24	77.18	odd	30
847.2.n.d.130.1		24	77.39	odd	30
847.2.n.d.366.1		24	11.10	odd	2
847.2.n.d.487.3		24	77.32	odd	6
847.2.n.d.632.1		24	11.8	odd	10
847.2.n.d.753.3		24	77.74	odd	30
847.2.n.d.807.3		24	11.7	odd	10
847.2.n.e.9.1		24	11.5	even	5	inner
847.2.n.e.81.3		24	77.4	even	15	inner
847.2.n.e.130.3		24	77.60	even	15	inner
847.2.n.e.366.3		24	1.1	even	1	trivial
847.2.n.e.487.1		24	7.4	even	3	inner
847.2.n.e.632.3		24	11.3	even	5	inner
847.2.n.e.753.1		24	77.25	even	15	inner
847.2.n.e.807.1		24	11.4	even	5	inner
1232.2.q.k.177.2		6	44.31	odd	10
1232.2.q.k.529.2		6	308.207	odd	30
4851.2.a.bn.1.3		3	231.152	even	30
4851.2.a.bo.1.3		3	231.86	odd	30
5929.2.a.v.1.3		3	77.2	odd	30
5929.2.a.w.1.3		3	77.68	even	30
8624.2.a.ck.1.2		3	308.75	even	30
8624.2.a.cl.1.2		3	308.163	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.260366 + 2.47722i) q^{2} +(-0.477450 + 0.530262i) q^{3} +(-4.11253 + 0.874144i) q^{4} +(2.01382 - 0.896611i) q^{5} +(-1.43789 - 1.04469i) q^{6} +(1.94692 + 1.79151i) q^{7} +(-1.69677 - 5.22212i) q^{8} +(0.260366 + 2.47722i) q^{9} +O(q^{10})\)	\(q+(0.260366 + 2.47722i) q^{2} +(-0.477450 + 0.530262i) q^{3} +(-4.11253 + 0.874144i) q^{4} +(2.01382 - 0.896611i) q^{5} +(-1.43789 - 1.04469i) q^{6} +(1.94692 + 1.79151i) q^{7} +(-1.69677 - 5.22212i) q^{8} +(0.260366 + 2.47722i) q^{9} +(2.74543 + 4.75523i) q^{10} +(1.50000 - 2.59808i) q^{12} +(2.65880 - 1.93173i) q^{13} +(-3.93106 + 5.28938i) q^{14} +(-0.486060 + 1.49594i) q^{15} +(4.81273 - 2.14277i) q^{16} +(-0.155838 + 1.48270i) q^{17} +(-6.06882 + 1.28997i) q^{18} +(6.76677 + 1.43832i) q^{19} +(-7.49812 + 5.44770i) q^{20} +(-1.87953 + 0.177017i) q^{21} +(-3.24543 + 5.62125i) q^{23} +(3.57922 + 1.59357i) q^{24} +(-0.0940890 + 0.104496i) q^{25} +(5.47759 + 6.08348i) q^{26} +(-3.16968 - 2.30291i) q^{27} +(-9.57278 - 5.66576i) q^{28} +(-0.509801 + 1.56901i) q^{29} +(-3.83232 - 0.814585i) q^{30} +(-2.14706 - 0.955933i) q^{31} +(1.07031 + 1.85383i) q^{32} -3.71354 q^{34} +(5.52703 + 1.86216i) q^{35} +(-3.23621 - 9.96003i) q^{36} +(-3.71679 - 4.12791i) q^{37} +(-1.80120 + 17.1372i) q^{38} +(-0.245121 + 2.33217i) q^{39} +(-8.09920 - 8.99508i) q^{40} +(-3.47642 - 10.6993i) q^{41} +(-0.927875 - 4.60991i) q^{42} +5.26819 q^{43} +(2.74543 + 4.75523i) q^{45} +(-14.7701 - 6.57606i) q^{46} +(-1.45828 - 0.309968i) q^{47} +(-1.16161 + 3.57507i) q^{48} +(0.580958 + 6.97585i) q^{49} +(-0.283358 - 0.205872i) q^{50} +(-0.711813 - 0.790548i) q^{51} +(-9.24578 + 10.2685i) q^{52} +(0.278389 + 0.123947i) q^{53} +(4.87953 - 8.45159i) q^{54} +(6.05203 - 13.2068i) q^{56} +(-3.99348 + 2.90143i) q^{57} +(-4.01950 - 0.854372i) q^{58} +(12.3821 - 2.63190i) q^{59} +(0.691268 - 6.57698i) q^{60} +(-11.8594 + 5.28014i) q^{61} +(1.80903 - 5.56763i) q^{62} +(-3.93106 + 5.28938i) q^{63} +(4.21045 - 3.05907i) q^{64} +(3.62234 - 6.27408i) q^{65} +(2.28646 + 3.96027i) q^{67} +(-0.655204 - 6.23385i) q^{68} +(-1.43121 - 4.40480i) q^{69} +(-3.17393 + 14.1765i) q^{70} +(-9.16353 - 6.65769i) q^{71} +(12.4946 - 5.56293i) q^{72} +(8.38047 - 1.78132i) q^{73} +(9.25801 - 10.2821i) q^{74} +(-0.0104877 - 0.0997836i) q^{75} -29.0858 q^{76} -5.84111 q^{78} +(-0.484121 - 4.60611i) q^{79} +(7.77075 - 8.63029i) q^{80} +(-4.57479 + 0.972401i) q^{81} +(25.5994 - 11.3976i) q^{82} +(1.56643 + 1.13808i) q^{83} +(7.57486 - 2.37096i) q^{84} +(1.01557 + 3.12561i) q^{85} +(1.37166 + 13.0505i) q^{86} +(-0.588580 - 1.01945i) q^{87} +(-1.60220 + 2.77509i) q^{89} +(-11.0649 + 8.03913i) q^{90} +(8.63719 + 1.00236i) q^{91} +(8.43313 - 25.9545i) q^{92} +(1.53201 - 0.682094i) q^{93} +(0.388170 - 3.69319i) q^{94} +(14.9167 - 3.17064i) q^{95} +(-1.49403 - 0.317566i) q^{96} +(-1.50428 + 1.09292i) q^{97} +(-17.1294 + 3.25544i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8}+O(q^{10}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} + 36 q^{10} + 36 q^{12} + 22 q^{13} - 12 q^{14} + 14 q^{15} + 2 q^{16} - 3 q^{17} + 10 q^{18} - 11 q^{19} - 28 q^{20} + 40 q^{21} - 48 q^{23} + 2 q^{24} + 3 q^{25} + q^{26} - 4 q^{27} - 13 q^{28} + 18 q^{29} + 2 q^{30} - 3 q^{31} + 12 q^{32} - 80 q^{34} - 9 q^{35} + 18 q^{36} - 4 q^{37} + 8 q^{38} - 5 q^{39} - 3 q^{40} + 10 q^{41} + 2 q^{42} + 16 q^{43} + 36 q^{45} - 10 q^{46} - 3 q^{47} - 20 q^{48} + 24 q^{49} + 6 q^{50} + 2 q^{51} - 7 q^{52} + 17 q^{53} + 32 q^{54} + 12 q^{56} - 40 q^{57} - 13 q^{58} + 8 q^{59} + 6 q^{60} - 24 q^{61} - 26 q^{62} - 12 q^{63} + 14 q^{64} - 60 q^{65} + 64 q^{67} + 5 q^{68} + 6 q^{69} + 27 q^{70} - 14 q^{71} + 10 q^{72} - 20 q^{73} + 22 q^{74} + 25 q^{75} - 312 q^{76} - 48 q^{78} + 3 q^{79} + 9 q^{80} - 17 q^{81} + 41 q^{82} + 22 q^{83} - 12 q^{84} - 22 q^{85} - 21 q^{86} - 120 q^{87} - 4 q^{89} - 20 q^{90} + 15 q^{91} - 50 q^{92} - 26 q^{93} - 10 q^{94} - 17 q^{95} + 27 q^{96} - 18 q^{97} - 96 q^{98}+O(q^{100}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 + 36 * q^10 + 36 * q^12 + 22 * q^13 - 12 * q^14 + 14 * q^15 + 2 * q^16 - 3 * q^17 + 10 * q^18 - 11 * q^19 - 28 * q^20 + 40 * q^21 - 48 * q^23 + 2 * q^24 + 3 * q^25 + q^26 - 4 * q^27 - 13 * q^28 + 18 * q^29 + 2 * q^30 - 3 * q^31 + 12 * q^32 - 80 * q^34 - 9 * q^35 + 18 * q^36 - 4 * q^37 + 8 * q^38 - 5 * q^39 - 3 * q^40 + 10 * q^41 + 2 * q^42 + 16 * q^43 + 36 * q^45 - 10 * q^46 - 3 * q^47 - 20 * q^48 + 24 * q^49 + 6 * q^50 + 2 * q^51 - 7 * q^52 + 17 * q^53 + 32 * q^54 + 12 * q^56 - 40 * q^57 - 13 * q^58 + 8 * q^59 + 6 * q^60 - 24 * q^61 - 26 * q^62 - 12 * q^63 + 14 * q^64 - 60 * q^65 + 64 * q^67 + 5 * q^68 + 6 * q^69 + 27 * q^70 - 14 * q^71 + 10 * q^72 - 20 * q^73 + 22 * q^74 + 25 * q^75 - 312 * q^76 - 48 * q^78 + 3 * q^79 + 9 * q^80 - 17 * q^81 + 41 * q^82 + 22 * q^83 - 12 * q^84 - 22 * q^85 - 21 * q^86 - 120 * q^87 - 4 * q^89 - 20 * q^90 + 15 * q^91 - 50 * q^92 - 26 * q^93 - 10 * q^94 - 17 * q^95 + 27 * q^96 - 18 * q^97 - 96 * q^98

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