LMFDB - Embedded newform 847.2.n.d.9.2

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			9.2
Character	$\chi$	$=$	847.9
Dual form			847.2.n.d.753.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.439365 - 0.487964i) q^{2} +(1.74691 + 0.777774i) q^{3} +(0.163989 - 1.56026i) q^{4} +(3.49086 + 0.742006i) q^{5} +(-0.388004 - 1.19415i) q^{6} +(0.295442 + 2.62920i) q^{7} +(-1.89583 + 1.37740i) q^{8} +(0.439365 + 0.487964i) q^{9} +O(q^{10})$	\(q+(-0.439365 - 0.487964i) q^{2} +(1.74691 + 0.777774i) q^{3} +(0.163989 - 1.56026i) q^{4} +(3.49086 + 0.742006i) q^{5} +(-0.388004 - 1.19415i) q^{6} +(0.295442 + 2.62920i) q^{7} +(-1.89583 + 1.37740i) q^{8} +(0.439365 + 0.487964i) q^{9} +(-1.17169 - 2.02943i) q^{10} +(1.50000 - 2.59808i) q^{12} +(1.82698 - 5.62286i) q^{13} +(1.15315 - 1.29934i) q^{14} +(5.52110 + 4.01132i) q^{15} +(-1.56405 - 0.332448i) q^{16} +(1.10850 - 1.23111i) q^{17} +(0.0450675 - 0.428789i) q^{18} +(0.154815 + 1.47297i) q^{19} +(1.73018 - 5.32495i) q^{20} +(-1.52882 + 4.82277i) q^{21} +(-1.67169 + 2.89545i) q^{23} +(-4.38316 + 0.931669i) q^{24} +(7.06782 + 3.14679i) q^{25} +(-3.54647 + 1.57899i) q^{26} +(-1.38473 - 4.26176i) q^{27} +(4.15068 - 0.0298029i) q^{28} +(2.49183 + 1.81042i) q^{29} +(-0.468400 - 4.45653i) q^{30} +(6.92535 - 1.47203i) q^{31} +(2.86834 + 4.96812i) q^{32} -1.08777 q^{34} +(-0.919538 + 9.39741i) q^{35} +(0.833400 - 0.605500i) q^{36} +(-4.12120 + 1.83488i) q^{37} +(0.650734 - 0.722713i) q^{38} +(7.56488 - 8.40165i) q^{39} +(-7.64014 + 3.40161i) q^{40} +(-1.04019 + 0.755743i) q^{41} +(3.02504 - 1.37295i) q^{42} -1.59899 q^{43} +(1.17169 + 2.02943i) q^{45} +(2.14736 - 0.456435i) q^{46} +(0.173164 + 1.64755i) q^{47} +(-2.47368 - 1.79723i) q^{48} +(-6.82543 + 1.55355i) q^{49} +(-1.56983 - 4.83143i) q^{50} +(2.89396 - 1.28848i) q^{51} +(-8.47350 - 3.77264i) q^{52} +(-9.02387 + 1.91808i) q^{53} +(-1.47118 + 2.54817i) q^{54} +(-4.18158 - 4.57759i) q^{56} +(-0.875186 + 2.69355i) q^{57} +(-0.211402 - 2.01136i) q^{58} +(-0.925281 + 8.80346i) q^{59} +(7.16408 - 7.95652i) q^{60} +(-6.54064 - 1.39026i) q^{61} +(-3.76105 - 2.73256i) q^{62} +(-1.15315 + 1.29934i) q^{63} +(0.175784 - 0.541008i) q^{64} +(10.5499 - 18.2730i) q^{65} +(4.91223 + 8.50823i) q^{67} +(-1.73906 - 1.93142i) q^{68} +(-5.17229 + 3.75789i) q^{69} +(4.98961 - 3.68019i) q^{70} +(-2.66335 - 8.19694i) q^{71} +(-1.50509 - 0.319916i) q^{72} +(0.476770 - 4.53616i) q^{73} +(2.70607 + 1.20482i) q^{74} +(9.89933 + 10.9943i) q^{75} +2.32359 q^{76} -7.42345 q^{78} +(4.27796 + 4.75115i) q^{79} +(-5.21319 - 2.32106i) q^{80} +(1.10160 - 10.4810i) q^{81} +(0.825799 + 0.175529i) q^{82} +(-0.0518648 - 0.159623i) q^{83} +(7.27404 + 3.17623i) q^{84} +(4.78309 - 3.47512i) q^{85} +(0.702539 + 0.780249i) q^{86} +(2.94490 + 5.10071i) q^{87} +(1.28442 - 2.22469i) q^{89} +(0.475488 - 1.46340i) q^{90} +(15.3234 + 3.14227i) q^{91} +(4.24350 + 3.08309i) q^{92} +(13.2429 + 2.81486i) q^{93} +(0.727861 - 0.808371i) q^{94} +(-0.552511 + 5.25679i) q^{95} +(1.14666 + 10.9098i) q^{96} +(3.00880 - 9.26014i) q^{97} +(3.75693 + 2.64799i) 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 $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.439365	−	0.487964i	−0.310678	−	0.345043i	0.567503	−	0.823371i	$-0.307909\pi$
$2$	−0.439365	−	0.487964i	−0.310678	−	0.345043i	−0.878181	+	0.478329i	$0.841243\pi$
$3$	1.74691	+	0.777774i	1.00858	+	0.449048i	0.843440	−	0.537223i	$-0.180527\pi$
$3$	1.74691	+	0.777774i	1.00858	+	0.449048i	0.165138	+	0.986271i	$0.447193\pi$
$4$	0.163989	−	1.56026i	0.0819947	−	0.780128i
$5$	3.49086	+	0.742006i	1.56116	+	0.331835i	0.905875	−	0.423546i	$-0.139215\pi$
$5$	3.49086	+	0.742006i	1.56116	+	0.331835i	0.655286	+	0.755381i	$0.272548\pi$
$6$	−0.388004	−	1.19415i	−0.158402	−	0.487512i
$7$	0.295442	+	2.62920i	0.111666	+	0.993746i
$7$	0.295442	+	2.62920i	0.111666	+	0.993746i
$8$	−1.89583	+	1.37740i	−0.670279	+	0.486986i
$9$	0.439365	+	0.487964i	0.146455	+	0.162655i
$10$	−1.17169	−	2.02943i	−0.370521	−	0.641761i
$11$		0			0
$11$		0			0
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	1.82698	−	5.62286i	0.506713	−	1.55950i	−0.291159	−	0.956675i	$-0.594041\pi$
$13$	1.82698	−	5.62286i	0.506713	−	1.55950i	0.797872	−	0.602827i	$-0.205959\pi$
$14$	1.15315	−	1.29934i	0.308192	−	0.347264i
$15$	5.52110	+	4.01132i	1.42554	+	1.03572i
$16$	−1.56405	−	0.332448i	−0.391012	−	0.0831121i
$17$	1.10850	−	1.23111i	0.268850	−	0.298588i	−0.593569	−	0.804783i	$-0.702282\pi$
$17$	1.10850	−	1.23111i	0.268850	−	0.298588i	0.862419	+	0.506195i	$0.168948\pi$
$18$	0.0450675	−	0.428789i	0.0106225	−	0.101066i
$19$	0.154815	+	1.47297i	0.0355170	+	0.337921i	0.997823	+	0.0659518i	$0.0210084\pi$
$19$	0.154815	+	1.47297i	0.0355170	+	0.337921i	−0.962306	+	0.271970i	$0.912325\pi$
$20$	1.73018	−	5.32495i	0.386881	−	1.19070i
$21$	−1.52882	+	4.82277i	−0.333615	+	1.05241i
$22$		0			0
$23$	−1.67169	+	2.89545i	−0.348571	+	0.603743i	−0.985996	−	0.166769i	$-0.946666\pi$
$23$	−1.67169	+	2.89545i	−0.348571	+	0.603743i	0.637425	+	0.770513i	$0.280000\pi$
$24$	−4.38316	+	0.931669i	−0.894708	+	0.190176i
$25$	7.06782	+	3.14679i	1.41356	+	0.629359i
$26$	−3.54647	+	1.57899i	−0.695519	+	0.309665i
$27$	−1.38473	−	4.26176i	−0.266491	−	0.820176i
$28$	4.15068	−	0.0298029i	0.784405	−	0.00563222i
$29$	2.49183	+	1.81042i	0.462721	+	0.336186i	0.794598	−	0.607136i	$-0.207682\pi$
$29$	2.49183	+	1.81042i	0.462721	+	0.336186i	−0.331877	+	0.943323i	$0.607682\pi$
$30$	−0.468400	−	4.45653i	−0.0855178	−	0.813648i
$31$	6.92535	−	1.47203i	1.24383	−	0.264384i	0.461439	−	0.887172i	$-0.347333\pi$
$31$	6.92535	−	1.47203i	1.24383	−	0.264384i	0.782391	+	0.622788i	$0.214000\pi$
$32$	2.86834	+	4.96812i	0.507056	+	0.878247i
$33$		0			0
$34$	−1.08777			−0.186551
$35$	−0.919538	+	9.39741i	−0.155430	+	1.58845i
$36$	0.833400	−	0.605500i	0.138900	−	0.100917i
$37$	−4.12120	+	1.83488i	−0.677521	+	0.301652i	−0.716499	−	0.697588i	$-0.754257\pi$
$37$	−4.12120	+	1.83488i	−0.677521	+	0.301652i	0.0389776	+	0.999240i	$0.487590\pi$
$38$	0.650734	−	0.722713i	0.105563	−	0.117240i
$39$	7.56488	−	8.40165i	1.21135	−	1.34534i
$40$	−7.64014	+	3.40161i	−1.20801	+	0.537841i
$41$	−1.04019	+	0.755743i	−0.162451	+	0.118027i	−0.666041	−	0.745916i	$-0.732012\pi$
$41$	−1.04019	+	0.755743i	−0.162451	+	0.118027i	0.503590	+	0.863943i	$0.332012\pi$
$42$	3.02504	−	1.37295i	0.466774	−	0.211850i
$43$	−1.59899			−0.243843			−0.121922	−	0.992540i	$-0.538906\pi$
$43$	−1.59899			−0.243843			−0.121922	+	0.992540i	$0.538906\pi$
$44$		0			0
$45$	1.17169	+	2.02943i	0.174665	+	0.302529i
$46$	2.14736	−	0.456435i	0.316611	−	0.0672977i
$47$	0.173164	+	1.64755i	0.0252586	+	0.240319i	0.999866	+	0.0163969i	$0.00521952\pi$
$47$	0.173164	+	1.64755i	0.0252586	+	0.240319i	−0.974607	+	0.223922i	$0.928114\pi$
$48$	−2.47368	−	1.79723i	−0.357044	−	0.259408i
$49$	−6.82543	+	1.55355i	−0.975061	+	0.221936i
$50$	−1.56983	−	4.83143i	−0.222007	−	0.683268i
$51$	2.89396	−	1.28848i	0.405236	−	0.180423i
$52$	−8.47350	−	3.77264i	−1.17506	−	0.523172i
$53$	−9.02387	+	1.91808i	−1.23952	+	0.263469i	−0.780614	−	0.625014i	$-0.785093\pi$
$53$	−9.02387	+	1.91808i	−1.23952	+	0.263469i	−0.458910	+	0.888483i	$0.651760\pi$
$54$	−1.47118	+	2.54817i	−0.200203	+	0.346761i
$55$		0			0
$56$	−4.18158	−	4.57759i	−0.558788	−	0.611706i
$57$	−0.875186	+	2.69355i	−0.115921	+	0.356769i
$58$	−0.211402	−	2.01136i	−0.0277584	−	0.264104i
$59$	−0.925281	+	8.80346i	−0.120461	+	1.14611i	0.752592	+	0.658487i	$0.228803\pi$
$59$	−0.925281	+	8.80346i	−0.120461	+	1.14611i	−0.873053	+	0.487625i	$0.837863\pi$
$60$	7.16408	−	7.95652i	0.924879	−	1.02718i
$61$	−6.54064	−	1.39026i	−0.837443	−	0.178004i	−0.230823	−	0.972996i	$-0.574142\pi$
$61$	−6.54064	−	1.39026i	−0.837443	−	0.178004i	−0.606620	+	0.794992i	$0.707475\pi$
$62$	−3.76105	−	2.73256i	−0.477654	−	0.347036i
$63$	−1.15315	+	1.29934i	−0.145283	+	0.163702i
$64$	0.175784	−	0.541008i	0.0219730	−	0.0676260i
$65$	10.5499	−	18.2730i	1.30856	−	2.26649i
$66$		0			0
$67$	4.91223	+	8.50823i	0.600124	+	1.03945i	0.992802	+	0.119770i	$0.0382156\pi$
$67$	4.91223	+	8.50823i	0.600124	+	1.03945i	−0.392677	+	0.919676i	$0.628451\pi$
$68$	−1.73906	−	1.93142i	−0.210892	−	0.234220i
$69$	−5.17229	+	3.75789i	−0.622671	+	0.452397i
$70$	4.98961	−	3.68019i	0.596372	−	0.439867i
$71$	−2.66335	−	8.19694i	−0.316081	−	0.972798i	−0.975307	−	0.220853i	$-0.929116\pi$
$71$	−2.66335	−	8.19694i	−0.316081	−	0.972798i	0.659226	−	0.751945i	$-0.270884\pi$
$72$	−1.50509	−	0.319916i	−0.177376	−	0.0377025i
$73$	0.476770	−	4.53616i	0.0558017	−	0.530917i	−0.930538	−	0.366195i	$-0.880660\pi$
$73$	0.476770	−	4.53616i	0.0558017	−	0.530917i	0.986340	−	0.164723i	$-0.0526729\pi$
$74$	2.70607	+	1.20482i	0.314574	+	0.140057i
$75$	9.89933	+	10.9943i	1.14308	+	1.26951i
$76$	2.32359			0.266534
$77$		0			0
$78$	−7.42345			−0.840540
$79$	4.27796	+	4.75115i	0.481308	+	0.534547i	0.934072	−	0.357084i	$-0.116229\pi$
$79$	4.27796	+	4.75115i	0.481308	+	0.534547i	−0.452765	+	0.891630i	$0.649562\pi$
$80$	−5.21319	−	2.32106i	−0.582853	−	0.259503i
$81$	1.10160	−	10.4810i	0.122399	−	1.16455i
$82$	0.825799	+	0.175529i	0.0911943	+	0.0193839i
$83$	−0.0518648	−	0.159623i	−0.00569290	−	0.0175209i	0.948170	−	0.317764i	$-0.102932\pi$
$83$	−0.0518648	−	0.159623i	−0.00569290	−	0.0175209i	−0.953863	+	0.300243i	$0.902932\pi$
$84$	7.27404	+	3.17623i	0.793662	+	0.346555i
$85$	4.78309	−	3.47512i	0.518799	−	0.376930i
$86$	0.702539	+	0.780249i	0.0757568	+	0.0841364i
$87$	2.94490	+	5.10071i	0.315726	+	0.546854i
$88$		0			0
$89$	1.28442	−	2.22469i	0.136149	−	0.235817i	−0.789887	−	0.613252i	$-0.789861\pi$
$89$	1.28442	−	2.22469i	0.136149	−	0.235817i	0.926036	+	0.377436i	$0.123194\pi$
$90$	0.475488	−	1.46340i	0.0501208	−	0.154256i
$91$	15.3234	+	3.14227i	1.60633	+	0.329400i
$92$	4.24350	+	3.08309i	0.442416	+	0.321434i
$93$	13.2429	+	2.81486i	1.37322	+	0.291887i
$94$	0.727861	−	0.808371i	0.0750731	−	0.0833771i
$95$	−0.552511	+	5.25679i	−0.0566864	+	0.539335i
$96$	1.14666	+	10.9098i	0.117031	+	1.11347i
$97$	3.00880	−	9.26014i	0.305498	−	0.940225i	−0.673994	−	0.738737i	$-0.735422\pi$
$97$	3.00880	−	9.26014i	0.305498	−	0.940225i	0.979491	−	0.201488i	$-0.0645776\pi$
$98$	3.75693	+	2.64799i	0.379507	+	0.267487i
$99$		0			0
$100$	6.06885	−	10.5116i	0.606885	−	1.05116i
$101$	1.81407	−	0.385592i	0.180507	−	0.0383679i	−0.116771	−	0.993159i	$-0.537254\pi$
$101$	1.81407	−	0.385592i	0.180507	−	0.0383679i	0.297278	+	0.954791i	$0.403921\pi$
$102$	−1.90024	−	0.846040i	−0.188151	−	0.0837704i
$103$	−2.89396	+	1.28848i	−0.285151	+	0.126957i	−0.544328	−	0.838872i	$-0.683215\pi$
$103$	−2.89396	+	1.28848i	−0.285151	+	0.126957i	0.259177	+	0.965830i	$0.416549\pi$
$104$	4.28131	+	13.1765i	0.419817	+	1.29206i
$105$	−8.91540	+	15.7012i	−0.870054	+	1.53228i
$106$	4.90073	+	3.56059i	0.476001	+	0.345835i
$107$	−0.498269	−	4.74071i	−0.0481695	−	0.458302i	−0.991847	−	0.127435i	$-0.959326\pi$
$107$	−0.498269	−	4.74071i	−0.0481695	−	0.458302i	0.943677	−	0.330867i	$-0.107341\pi$
$108$	−6.87651	+	1.46165i	−0.661693	+	0.140647i
$109$	−7.44105	−	12.8883i	−0.712723	−	1.23447i	−0.963831	−	0.266513i	$-0.914128\pi$
$109$	−7.44105	−	12.8883i	−0.712723	−	1.23447i	0.251108	−	0.967959i	$-0.419205\pi$
$110$		0			0
$111$	−8.62648			−0.818789
$112$	0.411990	−	4.21042i	0.0389294	−	0.397847i
$113$	−10.0668	+	7.31395i	−0.947004	+	0.688039i	−0.950096	−	0.311957i	$-0.899016\pi$
$113$	−10.0668	+	7.31395i	−0.947004	+	0.688039i	0.00309244	+	0.999995i	$0.499016\pi$
$114$	1.69888	−	0.756390i	0.159115	−	0.0708424i
$115$	−7.98408	+	8.86722i	−0.744519	+	0.826872i
$116$	3.23335	−	3.59100i	0.300209	−	0.333416i
$117$	3.54647	−	1.57899i	0.327871	−	0.145978i
$118$	4.70231	−	3.41643i	0.432883	−	0.314508i
$119$	3.56433	+	2.55074i	0.326742	+	0.233826i
$120$	−15.9923			−1.45989
$121$		0			0
$122$	2.19533	+	3.80243i	0.198756	+	0.344255i
$123$	−2.40492	+	0.511181i	−0.216844	+	0.0460916i
$124$	−1.16106	−	11.0467i	−0.104266	−	0.992024i
$125$	7.90153	+	5.74080i	0.706734	+	0.513472i
$126$	1.14069	−	0.00819041i	0.101621	−	0.000729660i
$127$	2.04613	+	6.29735i	0.181565	+	0.558799i	0.999872	−	0.0159816i	$-0.00508731\pi$
$127$	2.04613	+	6.29735i	0.181565	+	0.558799i	−0.818307	+	0.574781i	$0.805087\pi$
$128$	10.1402	−	4.51472i	0.896278	−	0.399049i
$129$	−2.79329	−	1.24365i	−0.245935	−	0.109497i
$130$	−13.5518	+	2.88053i	−1.18858	+	0.252639i
$131$	−3.02882	+	5.24606i	−0.264629	+	0.458351i	−0.967466	−	0.253000i	$-0.918583\pi$
$131$	−3.02882	+	5.24606i	−0.264629	+	0.458351i	0.702837	+	0.711351i	$0.251916\pi$
$132$		0			0
$133$	−3.82699	+	0.842215i	−0.331842	+	0.0730293i
$134$	1.99345	−	6.13521i	0.172208	−	0.530001i
$135$	−1.67165	−	15.9047i	−0.143873	−	1.36886i
$136$	−0.405789	+	3.86082i	−0.0347961	+	0.331063i
$137$	−4.96726	+	5.51670i	−0.424381	+	0.471323i	−0.916980	−	0.398933i	$-0.869380\pi$
$137$	−4.96726	+	5.51670i	−0.424381	+	0.471323i	0.492599	+	0.870257i	$0.336047\pi$
$138$	4.10624	+	0.872808i	0.349546	+	0.0742984i
$139$	−8.75717	−	6.36246i	−0.742774	−	0.539657i	0.150805	−	0.988564i	$-0.451813\pi$
$139$	−8.75717	−	6.36246i	−0.742774	−	0.539657i	−0.893578	+	0.448907i	$0.851813\pi$
$140$	14.5116	+	2.97579i	1.22645	+	0.251500i
$141$	−0.978916	+	3.01279i	−0.0824396	+	0.253723i
$142$	−2.82963	+	4.90107i	−0.237458	+	0.411288i
$143$		0			0
$144$	−0.524964	−	0.909265i	−0.0437470	−	0.0757721i
$145$	7.35528	+	8.16887i	0.610823	+	0.678388i
$146$	−2.42296	+	1.76038i	−0.200525	+	0.145690i
$147$	−13.1317	−	2.59472i	−1.08309	−	0.214009i
$148$	2.18704	+	6.73103i	0.179774	+	0.553287i
$149$	−0.978148	−	0.207912i	−0.0801330	−	0.0170328i	0.167671	−	0.985843i	$-0.446375\pi$
$149$	−0.978148	−	0.207912i	−0.0801330	−	0.0170328i	−0.247804	+	0.968810i	$0.579709\pi$
$150$	1.01542	−	9.66104i	0.0829084	−	0.788820i
$151$	−15.0036	−	6.68002i	−1.22097	−	0.543612i	−0.307904	−	0.951417i	$-0.599628\pi$
$151$	−15.0036	−	6.68002i	−1.22097	−	0.543612i	−0.913069	+	0.407805i	$0.866294\pi$
$152$	−2.32237	−	2.57925i	−0.188369	−	0.209205i
$153$	1.08777			0.0879411
$154$		0			0
$155$	25.2677			2.02955
$156$	−11.8682	−	13.1809i	−0.950213	−	1.05532i
$157$	−10.4610	−	4.65752i	−0.834875	−	0.371710i	−0.0556468	−	0.998451i	$-0.517722\pi$
$157$	−10.4610	−	4.65752i	−0.834875	−	0.371710i	−0.779228	+	0.626740i	$0.784389\pi$
$158$	0.438808	−	4.17498i	0.0349097	−	0.332144i
$159$	−17.2557	−	3.66781i	−1.36847	−	0.290877i
$160$	6.32662	+	19.4713i	0.500163	+	1.53934i
$161$	−8.10662	−	3.53978i	−0.638891	−	0.278973i
$162$	−5.59834	+	4.06743i	−0.439847	+	0.319568i
$163$	−5.98184	−	6.64351i	−0.468534	−	0.520360i	0.461844	−	0.886961i	$-0.347188\pi$
$163$	−5.98184	−	6.64351i	−0.468534	−	0.520360i	−0.930378	+	0.366601i	$0.880521\pi$
$164$	1.00857	+	1.74690i	0.0787563	+	0.136410i
$165$		0			0
$166$	−0.0551029	+	0.0954410i	−0.00427681	+	0.00740766i
$167$	5.62960	−	17.3261i	0.435631	−	1.34074i	−0.456807	−	0.889566i	$-0.651007\pi$
$167$	5.62960	−	17.3261i	0.435631	−	1.34074i	0.892438	−	0.451170i	$-0.148993\pi$
$168$	−3.74451	−	11.2490i	−0.288896	−	0.867876i
$169$	−17.7615	−	12.9045i	−1.36627	−	0.992654i
$170$	−3.79726	−	0.807132i	−0.291236	−	0.0619042i
$171$	−0.650734	+	0.722713i	−0.0497629	+	0.0552673i
$172$	−0.262217	+	2.49483i	−0.0199939	+	0.190229i
$173$	2.04470	+	19.4540i	0.155455	+	1.47906i	0.742686	+	0.669640i	$0.233551\pi$
$173$	2.04470	+	19.4540i	0.155455	+	1.47906i	−0.587231	+	0.809420i	$0.699782\pi$
$174$	1.19508	−	3.67808i	0.0905988	−	0.278834i
$175$	−6.18544	+	19.5124i	−0.467575	+	1.47500i
$176$		0			0
$177$	−8.46348	+	14.6592i	−0.636154	+	1.10185i
$178$	−1.64990	+	0.350697i	−0.123665	+	0.0262858i
$179$	2.96711	+	1.32104i	0.221772	+	0.0987393i	0.514615	−	0.857421i	$-0.327935\pi$
$179$	2.96711	+	1.32104i	0.221772	+	0.0987393i	−0.292843	+	0.956160i	$0.594601\pi$
$180$	3.35857	−	1.49533i	0.250333	−	0.111455i
$181$	−3.19546	−	9.83462i	−0.237517	−	0.731002i	−0.996778	−	0.0802152i	$-0.974439\pi$
$181$	−3.19546	−	9.83462i	−0.237517	−	0.731002i	0.759261	−	0.650787i	$-0.225561\pi$
$182$	−5.19926	−	8.85788i	−0.385395	−	0.656590i
$183$	−10.3446	−	7.51578i	−0.764694	−	0.555583i
$184$	−0.818960	−	7.79189i	−0.0603746	−	0.574426i
$185$	−15.7480	+	3.34735i	−1.15782	+	0.246102i
$186$	−4.44490	−	7.69879i	−0.325916	−	0.564502i
$187$		0			0
$188$	2.59899			0.189551
$189$	10.7959	−	4.89984i	0.785288	−	0.356411i
$190$	2.80788	−	2.04004i	0.203705	−	0.148000i
$191$	9.15595	−	4.07649i	0.662501	−	0.294965i	−0.0478056	−	0.998857i	$-0.515223\pi$
$191$	9.15595	−	4.07649i	0.662501	−	0.294965i	0.710307	+	0.703892i	$0.248556\pi$
$192$	0.727861	−	0.808371i	0.0525288	−	0.0583392i
$193$	−16.9460	+	18.8204i	−1.21980	+	1.35472i	−0.304207	+	0.952606i	$0.598391\pi$
$193$	−16.9460	+	18.8204i	−1.21980	+	1.35472i	−0.915589	+	0.402115i	$0.868275\pi$
$194$	−5.84058	+	2.60039i	−0.419329	+	0.186697i
$195$	32.6420	−	23.7158i	2.33754	−	1.69833i
$196$	1.30464	+	10.9042i	0.0931887	+	0.778870i
$197$	24.5809			1.75132			0.875660	−	0.482929i	$-0.160427\pi$
$197$	24.5809			1.75132			0.875660	+	0.482929i	$0.160427\pi$
$198$		0			0
$199$	−2.79564	−	4.84219i	−0.198178	−	0.343254i	0.749760	−	0.661710i	$-0.230169\pi$
$199$	−2.79564	−	4.84219i	−0.198178	−	0.343254i	−0.947938	+	0.318456i	$0.896836\pi$
$200$	−17.7338	+	3.76944i	−1.25397	+	0.266540i
$201$	1.96374	+	18.6837i	0.138511	+	1.31785i
$202$	−0.985194	−	0.715785i	−0.0693180	−	0.0503625i
$203$	−4.02377	+	7.08639i	−0.282413	+	0.497367i
$204$	−1.53577	−	4.72662i	−0.107526	−	0.330930i
$205$	−4.19193	+	1.86637i	−0.292777	+	0.130353i
$206$	1.90024	+	0.846040i	0.132396	+	0.0589464i
$207$	−2.14736	+	0.456435i	−0.149252	+	0.0317244i
$208$	−4.72679	+	8.18705i	−0.327744	+	0.567669i
$209$		0			0
$210$	11.5787	−	2.54817i	0.799009	−	0.175840i
$211$	−3.73906	+	11.5076i	−0.257408	+	0.792219i	0.735938	+	0.677049i	$0.236741\pi$
$211$	−3.73906	+	11.5076i	−0.257408	+	0.792219i	−0.993346	+	0.115170i	$0.963259\pi$
$212$	1.51288	+	14.3941i	0.103905	+	0.988590i
$213$	1.72274	−	16.3908i	0.118040	−	1.12308i
$214$	−2.09438	+	2.32604i	−0.143169	+	0.159005i
$215$	−5.58185	−	1.18646i	−0.380679	−	0.0809158i
$216$	8.49538	+	6.17226i	0.578037	+	0.419969i
$217$	5.91630	+	17.7733i	0.401625	+	1.20653i
$218$	−3.01968	+	9.29361i	−0.204518	+	0.629443i
$219$	4.36098	−	7.55344i	0.294688	−	0.510414i
$220$		0			0
$221$	−4.89716	−	8.48213i	−0.329419	−	0.570570i
$222$	3.79017	+	4.20941i	0.254380	+	0.282517i
$223$	−12.6421	+	9.18502i	−0.846577	+	0.615074i	−0.924200	−	0.381909i	$-0.875267\pi$
$223$	−12.6421	+	9.18502i	−0.846577	+	0.615074i	0.0776232	+	0.996983i	$0.475267\pi$
$224$	−12.2148	+	9.00925i	−0.816133	+	0.601956i
$225$	1.56983	+	4.83143i	0.104655	+	0.322095i
$226$	7.99194	+	1.69874i	0.531616	+	0.112998i
$227$	−1.63783	+	15.5829i	−0.108706	+	1.03427i	0.795143	+	0.606421i	$0.207396\pi$
$227$	−1.63783	+	15.5829i	−0.108706	+	1.03427i	−0.903850	+	0.427850i	$0.859271\pi$
$228$	4.05910	+	1.80723i	0.268820	+	0.119687i
$229$	−3.72806	−	4.14043i	−0.246357	−	0.273607i	0.607266	−	0.794499i	$-0.292266\pi$
$229$	−3.72806	−	4.14043i	−0.246357	−	0.273607i	−0.853623	+	0.520892i	$0.825600\pi$
$230$	7.83481			0.516612
$231$		0			0
$232$	−7.21777			−0.473870
$233$	12.8978	+	14.3244i	0.844960	+	0.938423i	0.998765	−	0.0496777i	$-0.0158194\pi$
$233$	12.8978	+	14.3244i	0.844960	+	0.938423i	−0.153805	+	0.988101i	$0.549153\pi$
$234$	−2.32868	−	1.03680i	−0.152231	−	0.0677775i
$235$	−0.617996	+	5.87984i	−0.0403136	+	0.383559i
$236$	13.5839	+	2.88735i	0.884237	+	0.187950i
$237$	3.77788	+	11.6271i	0.245400	+	0.755262i
$238$	−0.321373	−	2.85997i	−0.0208315	−	0.185384i
$239$	−17.9258	+	13.0238i	−1.15952	+	0.842443i	−0.989718	−	0.143035i	$-0.954314\pi$
$239$	−17.9258	+	13.0238i	−1.15952	+	0.842443i	−0.169805	+	0.985478i	$0.554314\pi$
$240$	−7.30171	−	8.10937i	−0.471323	−	0.523457i
$241$	−9.93719	−	17.2117i	−0.640111	−	1.10870i	−0.985408	−	0.170211i	$-0.945555\pi$
$241$	−9.93719	−	17.2117i	−0.640111	−	1.10870i	0.345297	−	0.938494i	$-0.387778\pi$
$242$		0			0
$243$	3.35460	−	5.81033i	0.215198	−	0.372733i
$244$	−3.24175	+	9.97708i	−0.207532	+	0.638717i
$245$	−24.9794	+	0.358734i	−1.59587	+	0.0229187i
$246$	1.30607	+	0.948918i	0.0832722	+	0.0605008i
$247$	8.56513	+	1.82057i	0.544986	+	0.115840i
$248$	−11.1017	+	12.3297i	−0.704961	+	0.782938i
$249$	0.0335478	−	0.319186i	0.00212601	−	0.0202276i
$250$	−0.670351	−	6.37797i	−0.0423967	−	0.403378i
$251$	6.83161	−	21.0255i	0.431208	−	1.32712i	−0.465716	−	0.884934i	$-0.654203\pi$
$251$	6.83161	−	21.0255i	0.431208	−	1.32712i	0.896923	−	0.442186i	$-0.145797\pi$
$252$	1.83821	+	2.01229i	0.115796	+	0.126762i
$253$		0			0
$254$	2.17388	−	3.76527i	0.136401	−	0.236254i
$255$	11.0585	−	2.35055i	0.692509	−	0.147197i
$256$	−7.69762	−	3.42720i	−0.481101	−	0.214200i
$257$	26.6021	−	11.8440i	1.65939	−	0.738810i	0.659478	−	0.751724i	$-0.270777\pi$
$257$	26.6021	−	11.8440i	1.65939	−	0.738810i	0.999917	+	0.0129137i	$0.00411066\pi$
$258$	0.620415	+	1.90944i	0.0386253	+	0.118877i
$259$	−6.04184	−	10.2934i	−0.375422	−	0.639600i
$260$	−26.7805	−	19.4572i	−1.66086	−	1.20668i
$261$	0.211402	+	2.01136i	0.0130855	+	0.124500i
$262$	3.89065	−	0.826982i	0.240365	−	0.0510911i
$263$	−7.75176	−	13.4264i	−0.477994	−	0.827910i	0.521688	−	0.853136i	$-0.325303\pi$
$263$	−7.75176	−	13.4264i	−0.477994	−	0.827910i	−0.999682	+	0.0252268i	$0.991969\pi$
$264$		0			0
$265$	−32.9243			−2.02252
$266$	2.09241	+	1.49739i	0.128294	+	0.0918110i
$267$	3.97408	−	2.88734i	0.243210	−	0.176702i
$268$	14.0806	−	6.26907i	0.860107	−	0.382944i
$269$	1.14190	−	1.26821i	0.0696231	−	0.0773243i	−0.707327	−	0.706887i	$-0.750099\pi$
$269$	1.14190	−	1.26821i	0.0696231	−	0.0773243i	0.776950	+	0.629562i	$0.216766\pi$
$270$	−7.02645	+	7.80367i	−0.427616	+	0.474916i
$271$	18.7536	−	8.34964i	1.13920	−	0.507204i	0.251605	−	0.967830i	$-0.419042\pi$
$271$	18.7536	−	8.34964i	1.13920	−	0.507204i	0.887595	+	0.460626i	$0.152375\pi$
$272$	−2.14302	+	1.55699i	−0.129940	+	0.0944066i
$273$	24.3246	+	17.4074i	1.47219	+	1.05354i
$274$	4.87439			0.294472
$275$		0			0
$276$	5.01507	+	8.68635i	0.301872	+	0.522857i
$277$	−26.0784	+	5.54313i	−1.56690	+	0.333055i	−0.907932	−	0.419117i	$-0.862340\pi$
$277$	−26.0784	+	5.54313i	−1.56690	+	0.333055i	−0.658967	+	0.752172i	$0.729006\pi$
$278$	0.742942	+	7.06862i	0.0445587	+	0.423948i
$279$	3.76105	+	2.73256i	0.225168	+	0.163594i
$280$	−11.2007	−	19.0825i	−0.669372	−	1.14040i
$281$	−4.86528	−	14.9738i	−0.290239	−	0.893262i	−0.984779	−	0.173809i	$-0.944392\pi$
$281$	−4.86528	−	14.9738i	−0.290239	−	0.893262i	0.694541	−	0.719453i	$-0.255608\pi$
$282$	1.90024	−	0.846040i	0.113157	−	0.0503809i
$283$	14.6804	+	6.53614i	0.872660	+	0.388533i	0.793675	−	0.608342i	$-0.208165\pi$
$283$	14.6804	+	6.53614i	0.872660	+	0.388533i	0.0789856	+	0.996876i	$0.474832\pi$
$284$	−13.2261	+	2.81129i	−0.784824	+	0.166819i
$285$	−5.05378	+	8.75340i	−0.299360	+	0.518507i
$286$		0			0
$287$	−2.29432	−	2.51160i	−0.135429	−	0.148255i
$288$	−1.16401	+	3.58246i	−0.0685901	+	0.211099i
$289$	1.49012	+	14.1775i	0.0876539	+	0.833971i
$290$	0.754462	−	7.17823i	0.0443035	−	0.421520i
$291$	12.4584	−	13.8364i	0.730324	−	0.811107i
$292$	−6.99938	−	1.48776i	−0.409608	−	0.0870648i
$293$	12.4068	+	9.01408i	0.724814	+	0.526608i	0.887919	−	0.460000i	$-0.152151\pi$
$293$	12.4068	+	9.01408i	0.724814	+	0.526608i	−0.163104	+	0.986609i	$0.552151\pi$
$294$	4.50348	+	7.54783i	0.262648	+	0.440199i
$295$	−9.76224	+	30.0451i	−0.568380	+	1.74929i
$296$	5.28575	−	9.15518i	0.307228	−	0.532134i
$297$		0			0
$298$	0.328310	+	0.568650i	0.0190185	+	0.0329410i
$299$	13.2266	+	14.6896i	0.764913	+	0.849522i
$300$	18.7773	−	13.6425i	1.08411	−	0.787652i
$301$	−0.472408	−	4.20407i	−0.0272291	−	0.242318i
$302$	3.33243	+	10.2562i	0.191760	+	0.590176i
$303$	3.46892	+	0.737341i	0.199284	+	0.0423591i
$304$	0.247547	−	2.35525i	0.0141978	−	0.135083i
$305$	−21.8009	−	9.70638i	−1.24831	−	0.555786i
$306$	−0.477928	−	0.530793i	−0.0273213	−	0.0303434i
$307$	16.4707			0.940034			0.470017	−	0.882657i	$-0.344248\pi$
$307$	16.4707			0.940034			0.470017	+	0.882657i	$0.344248\pi$
$308$		0			0
$309$	−6.05763			−0.344607
$310$	−11.1017	−	12.3297i	−0.630536	−	0.700281i
$311$	19.7592	+	8.79736i	1.12044	+	0.498852i	0.881501	−	0.472182i	$-0.156533\pi$
$311$	19.7592	+	8.79736i	1.12044	+	0.498852i	0.238940	+	0.971034i	$0.423200\pi$
$312$	−2.76929	+	26.3480i	−0.156780	+	1.49166i
$313$	−16.0301	−	3.40731i	−0.906076	−	0.192592i	−0.268771	−	0.963204i	$-0.586618\pi$
$313$	−16.0301	−	3.40731i	−0.906076	−	0.192592i	−0.637305	+	0.770612i	$0.719951\pi$
$314$	2.32347	+	7.15092i	0.131121	+	0.403550i
$315$	−4.98961	+	3.68019i	−0.281133	+	0.207355i
$316$	8.11455	−	5.89557i	0.456479	−	0.331652i
$317$	2.98519	+	3.31538i	0.167665	+	0.186211i	0.821122	−	0.570753i	$-0.193349\pi$
$317$	2.98519	+	3.31538i	0.167665	+	0.186211i	−0.653457	+	0.756964i	$0.726682\pi$
$318$	5.79179	+	10.0317i	0.324787	+	0.562548i
$319$		0			0
$320$	1.01507	−	1.75815i	0.0567441	−	0.0982837i
$321$	2.81677	−	8.66913i	0.157217	−	0.483864i
$322$	1.83448	+	5.51099i	0.102232	+	0.307116i
$323$	1.98499	+	1.44218i	0.110448	+	0.0802451i
$324$	−16.1724	−	3.43754i	−0.898464	−	0.190974i
$325$	30.6067	−	33.9922i	1.69776	−	1.88555i
$326$	−0.613583	+	5.83785i	−0.0339832	+	0.323328i
$327$	−2.97467	−	28.3021i	−0.164499	−	1.56511i
$328$	0.931066	−	2.86553i	0.0514095	−	0.158222i
$329$	−4.28057	+	0.942037i	−0.235996	+	0.0519362i
$330$		0			0
$331$	−9.51979	+	16.4888i	−0.523255	+	0.906304i	0.476379	+	0.879240i	$0.341949\pi$
$331$	−9.51979	+	16.4888i	−0.523255	+	0.906304i	−0.999634	+	0.0270640i	$0.991384\pi$
$332$	−0.257558	+	0.0547457i	−0.0141354	+	0.00300456i
$333$	−2.70607	−	1.20482i	−0.148291	−	0.0660236i
$334$	−10.9280	+	4.86545i	−0.597952	+	0.266225i
$335$	10.8348	+	33.3460i	0.591966	+	1.82188i
$336$	3.99446	−	7.03478i	0.217916	−	0.383779i
$337$	21.8554	+	15.8789i	1.19054	+	0.864977i	0.993321	−	0.115383i	$-0.0368096\pi$
$337$	21.8554	+	15.8789i	1.19054	+	0.864977i	0.197217	+	0.980360i	$0.436810\pi$
$338$	1.50686	+	14.3368i	0.0819621	+	0.779818i
$339$	−23.2744	+	4.94712i	−1.26409	+	0.268691i
$340$	−4.63770	−	8.03273i	−0.251515	−	0.435636i
$341$		0			0
$342$	0.638568			0.0345298
$343$	−6.10113	−	17.4865i	−0.329430	−	0.944180i
$344$	3.03142	−	2.20245i	0.163443	−	0.118748i
$345$	−20.8441	+	9.28041i	−1.12221	+	0.499640i
$346$	8.59448	−	9.54514i	0.462042	−	0.513150i
$347$	13.5283	−	15.0247i	0.726239	−	0.806570i	−0.261081	−	0.965317i	$-0.584079\pi$
$347$	13.5283	−	15.0247i	0.726239	−	0.806570i	0.987319	+	0.158747i	$0.0507455\pi$
$348$	8.44134	−	3.75833i	0.452504	−	0.201468i
$349$	−9.72635	+	7.06661i	−0.520640	+	0.378267i	−0.816845	−	0.576857i	$-0.804279\pi$
$349$	−9.72635	+	7.06661i	−0.520640	+	0.378267i	0.296205	+	0.955124i	$0.404279\pi$
$350$	12.2390	−	5.55480i	0.654203	−	0.296917i
$351$	−26.4932			−1.41410
$352$		0			0
$353$	5.37956	+	9.31767i	0.286325	+	0.495930i	0.972930	−	0.231101i	$-0.0742329\pi$
$353$	5.37956	+	9.31767i	0.286325	+	0.495930i	−0.686605	+	0.727031i	$0.740900\pi$
$354$	10.8717	−	2.31085i	0.577825	−	0.122820i
$355$	−3.21520	−	30.5906i	−0.170645	−	1.62358i
$356$	−3.26045	−	2.36886i	−0.172804	−	0.125549i
$357$	4.24266	+	7.22815i	0.224546	+	0.382554i
$358$	−0.659022	−	2.02826i	−0.0348304	−	0.107197i
$359$	−22.1901	+	9.87969i	−1.17115	+	0.521430i	−0.897765	−	0.440475i	$-0.854810\pi$
$359$	−22.1901	+	9.87969i	−1.17115	+	0.521430i	−0.273386	+	0.961905i	$0.588144\pi$
$360$	−5.01667	−	2.23356i	−0.264402	−	0.117719i
$361$	16.4391	−	3.49425i	0.865218	−	0.183908i
$362$	−3.39497	+	5.88026i	−0.178436	+	0.309060i
$363$		0			0
$364$	7.41563	−	23.3932i	0.388684	−	1.22613i
$365$	5.03019	−	15.4813i	0.263292	−	0.810330i
$366$	0.877616	+	8.34996i	0.0458737	+	0.436459i
$367$	−1.13353	+	10.7848i	−0.0591699	+	0.562964i	0.924271	+	0.381736i	$0.124674\pi$
$367$	−1.13353	+	10.7848i	−0.0591699	+	0.562964i	−0.983441	+	0.181228i	$0.941993\pi$
$368$	3.57719	−	3.97287i	0.186474	−	0.207100i
$369$	−0.825799	−	0.175529i	−0.0429894	−	0.00913768i
$370$	8.55252	+	6.21377i	0.444624	+	0.323038i
$371$	−7.70906	−	23.1589i	−0.400234	−	1.20235i
$372$	6.56358	−	20.2006i	0.340306	−	1.04735i
$373$	−16.5121	+	28.5998i	−0.854963	+	1.48084i	0.0217156	+	0.999764i	$0.493087\pi$
$373$	−16.5121	+	28.5998i	−0.854963	+	1.48084i	−0.876679	+	0.481076i	$0.840246\pi$
$374$		0			0
$375$	9.33821	+	16.1742i	0.482223	+	0.835234i
$376$	−2.59763	−	2.88496i	−0.133962	−	0.148780i
$377$	14.7323	−	10.7036i	0.758749	−	0.551264i
$378$	−7.13430	−	3.11521i	−0.366949	−	0.160229i
$379$	−6.77737	−	20.8586i	−0.348130	−	1.07143i	−0.959887	−	0.280388i	$-0.909537\pi$
$379$	−6.77737	−	20.8586i	−0.348130	−	1.07143i	0.611757	−	0.791046i	$-0.290463\pi$
$380$	8.11133	+	1.72412i	0.416102	+	0.0884453i
$381$	−1.32351	+	12.5923i	−0.0678053	+	0.645124i
$382$	−6.01198	−	2.67671i	−0.307600	−	0.136952i
$383$	24.3985	+	27.0973i	1.24671	+	1.38461i	0.893500	+	0.449062i	$0.148242\pi$
$383$	24.3985	+	27.0973i	1.24671	+	1.38461i	0.353206	+	0.935546i	$0.385091\pi$
$384$	21.2255			1.08316
$385$		0			0
$386$	16.6291			0.846400
$387$	−0.702539	−	0.780249i	−0.0357121	−	0.0396623i
$388$	−13.9548	−	6.21306i	−0.708446	−	0.315421i
$389$	−2.03580	+	19.3693i	−0.103219	+	0.982064i	0.813238	+	0.581931i	$0.197703\pi$
$389$	−2.03580	+	19.3693i	−0.103219	+	0.982064i	−0.916457	+	0.400133i	$0.868964\pi$
$390$	−25.9142	−	5.50824i	−1.31222	−	0.278921i
$391$	1.71156	+	5.26763i	0.0865571	+	0.266395i
$392$	10.8000	−	12.3467i	0.545483	−	0.623600i
$393$	−9.37131	+	6.80866i	−0.472720	+	0.343451i
$394$	−10.8000	−	11.9946i	−0.544096	−	0.604280i
$395$	11.4084	+	19.7599i	0.574018	+	0.994228i
$396$		0			0
$397$	3.91993	−	6.78952i	0.196736	−	0.340756i	−0.750732	−	0.660606i	$-0.770299\pi$
$397$	3.91993	−	6.78952i	0.196736	−	0.340756i	0.947468	+	0.319850i	$0.103633\pi$
$398$	−1.13451	+	3.49166i	−0.0568679	+	0.175021i
$399$	−7.34045	−	1.50526i	−0.367482	−	0.0753571i
$400$	−10.0082	−	7.27142i	−0.500412	−	0.363571i
$401$	23.9117	+	5.08258i	1.19409	+	0.253812i	0.761734	−	0.647890i	$-0.224348\pi$
$401$	23.9117	+	5.08258i	1.19409	+	0.253812i	0.432358	+	0.901702i	$0.357682\pi$
$402$	8.25418	−	9.16719i	0.411681	−	0.457218i
$403$	4.37545	−	41.6297i	0.217957	−	2.07372i
$404$	−0.304134	−	2.89364i	−0.0151312	−	0.143964i
$405$	11.6225	−	35.7703i	0.577525	−	1.77744i
$406$	5.22581	−	1.15006i	0.259353	−	0.0570764i
$407$		0			0
$408$	−3.71172	+	6.42889i	−0.183758	+	0.318278i
$409$	−2.30229	+	0.489368i	−0.113841	+	0.0241977i	−0.264480	−	0.964391i	$-0.585200\pi$
$409$	−2.30229	+	0.489368i	−0.113841	+	0.0241977i	0.150639	+	0.988589i	$0.451867\pi$
$410$	2.75251	+	1.22550i	0.135937	+	0.0605229i
$411$	−12.9681	+	5.77376i	−0.639668	+	0.284799i
$412$	1.53577	+	4.72662i	0.0756620	+	0.232864i
$413$	−23.4195	+	0.168157i	−1.15240	+	0.00827448i
$414$	1.16620	+	0.847292i	0.0573155	+	0.0416421i
$415$	−0.0626113	−	0.595707i	−0.00307347	−	0.0292421i
$416$	33.1755	−	7.05166i	1.62656	−	0.345736i
$417$	−10.3494	−	17.9257i	−0.506813	−	0.877827i
$418$		0			0
$419$	9.29081			0.453886			0.226943	−	0.973908i	$-0.427127\pi$
$419$	9.29081			0.453886			0.226943	+	0.973908i	$0.427127\pi$
$420$	23.0359	+	16.4851i	1.12404	+	0.804392i
$421$	31.5775	−	22.9424i	1.53899	−	1.11814i	0.588026	−	0.808842i	$-0.299905\pi$
$421$	31.5775	−	22.9424i	1.53899	−	1.11814i	0.950964	−	0.309301i	$-0.100095\pi$
$422$	7.25813	−	3.23153i	0.353320	−	0.157308i
$423$	−0.727861	+	0.808371i	−0.0353898	+	0.0393044i
$424$	14.4658	−	16.0659i	0.702521	−	0.780228i
$425$	11.7087	−	5.21304i	0.567955	−	0.252870i
$426$	−8.75503	+	6.36090i	−0.424183	+	0.308187i
$427$	1.72289	−	17.6074i	0.0833764	−	0.852082i
$428$	−7.47843			−0.361484
$429$		0			0
$430$	1.87352	+	3.24503i	0.0903491	+	0.156489i
$431$	−3.71894	+	0.790485i	−0.179135	+	0.0380763i	−0.296606	−	0.955000i	$-0.595855\pi$
$431$	−3.71894	+	0.790485i	−0.179135	+	0.0380763i	0.117471	+	0.993076i	$0.462521\pi$
$432$	0.748967	+	7.12594i	0.0360347	+	0.342847i
$433$	−6.65045	−	4.83184i	−0.319600	−	0.232203i	0.416405	−	0.909179i	$-0.363290\pi$
$433$	−6.65045	−	4.83184i	−0.319600	−	0.232203i	−0.736005	+	0.676976i	$0.763290\pi$
$434$	6.07330	−	10.6959i	0.291528	−	0.513419i
$435$	6.49547	+	19.9910i	0.311434	+	0.958495i
$436$	−21.3292	+	9.49639i	−1.02149	+	0.454795i
$437$	−4.52370	−	2.01408i	−0.216398	−	0.0963466i
$438$	−5.60187	+	1.19071i	−0.267667	+	0.0568945i
$439$	2.27068	−	3.93293i	0.108374	−	0.187708i	−0.806738	−	0.590909i	$-0.798769\pi$
$439$	2.27068	−	3.93293i	0.108374	−	0.187708i	0.915112	+	0.403201i	$0.132102\pi$
$440$		0			0
$441$	−3.75693	−	2.64799i	−0.178901	−	0.126095i
$442$	−1.98733	+	6.11639i	−0.0945279	+	0.290927i
$443$	−1.43668	−	13.6691i	−0.0682587	−	0.649438i	−0.974146	−	0.225919i	$-0.927461\pi$
$443$	−1.43668	−	13.6691i	−0.0682587	−	0.649438i	0.905887	−	0.423519i	$-0.139205\pi$
$444$	−1.41465	+	13.4595i	−0.0671364	+	0.638760i
$445$	6.13448	−	6.81303i	0.290802	−	0.322969i
$446$	10.0364	+	2.13331i	0.475240	+	0.101015i
$447$	−1.54703	−	1.12398i	−0.0731718	−	0.0531624i
$448$	1.47435	+	0.302336i	0.0696567	+	0.0142840i
$449$	6.66432	−	20.5107i	0.314509	−	0.967959i	−0.661447	−	0.749992i	$-0.730057\pi$
$449$	6.66432	−	20.5107i	0.314509	−	0.967959i	0.975956	−	0.217967i	$-0.0699425\pi$
$450$	1.66784	−	2.88878i	0.0786226	−	0.136178i
$451$		0			0
$452$	9.76078	+	16.9062i	0.459109	+	0.795199i
$453$	−21.0143	−	23.3388i	−0.987338	−	1.09655i
$454$	8.32348	−	6.04737i	0.390640	−	0.283817i
$455$	51.1604	+	22.3393i	2.39844	+	1.04728i
$456$	−2.05089	−	6.31200i	−0.0960419	−	0.295587i
$457$	−3.23330	−	0.687260i	−0.151248	−	0.0321487i	0.131666	−	0.991294i	$-0.457967\pi$
$457$	−3.23330	−	0.687260i	−0.151248	−	0.0321487i	−0.282913	+	0.959146i	$0.591301\pi$
$458$	−0.382402	+	3.63832i	−0.0178685	+	0.170007i
$459$	−6.78166	−	3.01939i	−0.316541	−	0.140933i
$460$	12.5258	+	13.9113i	0.584019	+	0.648619i
$461$	32.1524			1.49749			0.748744	−	0.662859i	$-0.230657\pi$
$461$	32.1524			1.49749			0.748744	+	0.662859i	$0.230657\pi$
$462$		0			0
$463$	5.82181			0.270563			0.135281	−	0.990807i	$-0.456806\pi$
$463$	5.82181			0.270563			0.135281	+	0.990807i	$0.456806\pi$
$464$	−3.29546	−	3.65998i	−0.152988	−	0.169910i
$465$	44.1403	+	19.6525i	2.04696	+	0.911365i
$466$	1.32298	−	12.5873i	0.0612857	−	0.583095i
$467$	5.88329	+	1.25053i	0.272246	+	0.0578678i	0.342012	−	0.939696i	$-0.388892\pi$
$467$	5.88329	+	1.25053i	0.272246	+	0.0578678i	−0.0697654	+	0.997563i	$0.522225\pi$
$468$	−1.88204	−	5.79233i	−0.0869974	−	0.267751i
$469$	−20.9186	+	15.4289i	−0.965931	+	0.712442i
$470$	3.14068	−	2.28184i	0.144869	−	0.105253i
$471$	−14.6518	−	16.2725i	−0.675121	−	0.749798i
$472$	−10.3717	−	17.9644i	−0.477398	−	0.826878i
$473$		0			0
$474$	4.01375	−	6.95201i	0.184357	−	0.319317i
$475$	−3.54092	+	10.8978i	−0.162468	+	0.500026i
$476$	4.56432	−	5.14297i	0.209205	−	0.235728i
$477$	−4.90073	−	3.56059i	−0.224389	−	0.163028i
$478$	14.2311	+	3.02492i	0.650917	+	0.138357i
$479$	−11.4656	+	12.7338i	−0.523876	+	0.581823i	−0.945776	−	0.324819i	$-0.894697\pi$
$479$	−11.4656	+	12.7338i	−0.523876	+	0.581823i	0.421900	+	0.906642i	$0.361363\pi$
$480$	−4.09227	+	38.9353i	−0.186786	+	1.77715i
$481$	2.78792	+	26.5252i	0.127118	+	1.20945i
$482$	−4.03265	+	12.4112i	−0.183682	+	0.565316i
$483$	−11.4084	−	12.4888i	−0.519099	−	0.568259i
$484$		0			0
$485$	17.3744	−	30.0933i	0.788930	−	1.36647i
$486$	−4.30913	+	0.915933i	−0.195466	+	0.0415476i
$487$	5.22023	+	2.32420i	0.236551	+	0.105319i	0.521589	−	0.853197i	$-0.325339\pi$
$487$	5.22023	+	2.32420i	0.236551	+	0.105319i	−0.285038	+	0.958516i	$0.592006\pi$
$488$	14.3149	−	6.37341i	0.648005	−	0.288511i
$489$	−5.28258	−	16.2581i	−0.238887	−	0.735218i
$490$	11.1501	+	12.0314i	0.503710	+	0.543524i
$491$	19.4709	+	14.1464i	0.878708	+	0.638418i	0.932909	−	0.360112i	$-0.117261\pi$
$491$	19.4709	+	14.1464i	0.878708	+	0.638418i	−0.0542017	+	0.998530i	$0.517261\pi$
$492$	0.403192	+	3.83611i	0.0181773	+	0.172945i
$493$	4.99100	−	1.06087i	0.224783	−	0.0477792i
$494$	−2.87484	−	4.97937i	−0.129345	−	0.224032i
$495$		0			0
$496$	−11.3209			−0.508325
$497$	20.7646	−	9.42421i	0.931419	−	0.422733i
$498$	−0.170491	+	0.123869i	−0.00763990	+	0.00555071i
$499$	9.85648	−	4.38839i	0.441237	−	0.196451i	−0.174080	−	0.984732i	$-0.555695\pi$
$499$	9.85648	−	4.38839i	0.441237	−	0.196451i	0.615316	+	0.788280i	$0.289028\pi$
$500$	10.2529	−	11.3870i	0.458523	−	0.509241i
$501$	23.3102	−	25.8886i	1.04142	−	1.15662i
$502$	−13.2613	+	5.90430i	−0.591880	+	0.263522i
$503$	22.6623	−	16.4651i	1.01046	−	0.734142i	0.0461544	−	0.998934i	$-0.485303\pi$
$503$	22.6623	−	16.4651i	1.01046	−	0.734142i	0.964305	+	0.264792i	$0.0853034\pi$
$504$	0.396459	−	4.05170i	0.0176597	−	0.180477i
$505$	6.61878			0.294532
$506$		0			0
$507$	−20.9910	−	36.3574i	−0.932242	−	1.61469i
$508$	10.1610	−	2.15979i	0.450822	−	0.0958252i
$509$	0.200159	+	1.90438i	0.00887189	+	0.0844104i	0.998062	−	0.0622291i	$-0.0198209\pi$
$509$	0.200159	+	1.90438i	0.00887189	+	0.0844104i	−0.989190	+	0.146639i	$0.953154\pi$
$510$	−6.00569	−	4.36339i	−0.265937	−	0.193214i
$511$	12.0673	−	0.0866465i	0.533828	−	0.00383301i
$512$	−5.15038	−	15.8512i	−0.227617	−	0.700532i
$513$	6.06305	−	2.69944i	0.267690	−	0.119183i
$514$	−17.4675	−	7.77703i	−0.770458	−	0.343030i
$515$	−11.0585	+	2.35055i	−0.487295	+	0.103578i
$516$	−2.39848	+	4.15429i	−0.105587	+	0.182883i
$517$		0			0
$518$	−2.36823	+	7.47075i	−0.104054	+	0.328246i
$519$	−11.5589	+	35.5746i	−0.507380	+	1.56155i
$520$	5.16841	+	49.1741i	0.226650	+	2.15643i
$521$	−0.165071	+	1.57055i	−0.00723190	+	0.0688069i	−0.997543	−	0.0700624i	$-0.977680\pi$
$521$	−0.165071	+	1.57055i	−0.00723190	+	0.0688069i	0.990311	+	0.138869i	$0.0443468\pi$
$522$	0.888587	−	0.986876i	0.0388924	−	0.0431944i
$523$	−8.77385	−	1.86494i	−0.383654	−	0.0815481i	0.0120475	−	0.999927i	$-0.496165\pi$
$523$	−8.77385	−	1.86494i	−0.383654	−	0.0815481i	−0.395701	+	0.918379i	$0.629498\pi$
$524$	7.68850	+	5.58603i	0.335874	+	0.244027i
$525$	−25.9816	+	29.2755i	−1.13393	+	1.27769i
$526$	−3.14577	+	9.68168i	−0.137162	+	0.422141i
$527$	5.86449	−	10.1576i	0.255461	−	0.442472i
$528$		0			0
$529$	5.91091	+	10.2380i	0.256996	+	0.445130i
$530$	14.4658	+	16.0659i	0.628354	+	0.697857i
$531$	−4.70231	+	3.41643i	−0.204063	+	0.148260i
$532$	0.686486	+	6.10919i	0.0297629	+	0.264867i
$533$	2.34903	+	7.22958i	0.101748	+	0.313148i
$534$	−3.15499	−	0.670613i	−0.136530	−	0.0290203i
$535$	1.77825	−	16.9189i	0.0768803	−	0.731467i
$536$	−21.0320	−	9.36407i	−0.908446	−	0.404466i
$537$	4.15580	+	4.61548i	0.179336	+	0.199173i
$538$	−1.12055			−0.0483105
$539$		0			0
$540$	−25.0895			−1.07968
$541$	−12.1129	−	13.4528i	−0.520776	−	0.578380i	0.424180	−	0.905578i	$-0.360562\pi$
$541$	−12.1129	−	13.4528i	−0.520776	−	0.578380i	−0.944956	+	0.327198i	$0.893896\pi$
$542$	−12.3140	−	5.48254i	−0.528931	−	0.235495i
$543$	2.06693	−	19.6655i	0.0887005	−	0.843929i
$544$	9.29584	+	1.97589i	0.398556	+	0.0847157i
$545$	−16.4125	−	50.5125i	−0.703034	−	2.16372i
$546$	−2.19320	−	19.5178i	−0.0938601	−	0.835283i
$547$	18.3554	−	13.3360i	0.784819	−	0.570205i	−0.121602	−	0.992579i	$-0.538803\pi$
$547$	18.3554	−	13.3360i	0.784819	−	0.570205i	0.906422	+	0.422374i	$0.138803\pi$
$548$	7.79288	+	8.65487i	0.332895	+	0.369718i
$549$	−2.19533	−	3.80243i	−0.0936945	−	0.162284i
$550$		0			0
$551$	−2.28091	+	3.95065i	−0.0971701	+	0.168304i
$552$	4.62968	−	14.2487i	0.197052	−	0.606464i
$553$	−11.2279	+	12.6513i	−0.477457	+	0.537989i
$554$	14.1628	+	10.2899i	0.601719	+	0.437174i
$555$	−30.1139	−	6.40090i	−1.27826	−	0.271703i
$556$	−11.3631	+	12.6200i	−0.481905	+	0.535209i
$557$	4.00924	−	38.1454i	0.169877	−	1.61627i	−0.494709	−	0.869059i	$-0.664725\pi$
$557$	4.00924	−	38.1454i	0.169877	−	1.61627i	0.664586	−	0.747212i	$-0.268608\pi$
$558$	−0.319081	−	3.03585i	−0.0135078	−	0.128518i
$559$	−2.92132	+	8.99089i	−0.123559	+	0.380274i
$560$	4.56235	−	14.3923i	0.192795	−	0.608185i
$561$		0			0
$562$	−5.16904	+	8.95305i	−0.218043	+	0.377662i
$563$	−40.8610	+	8.68527i	−1.72209	+	0.366041i	−0.959688	−	0.281068i	$-0.909311\pi$
$563$	−40.8610	+	8.68527i	−1.72209	+	0.366041i	−0.762398	+	0.647109i	$0.775978\pi$
$564$	4.54019	+	2.02142i	0.191177	+	0.0851173i
$565$	−40.5688	+	18.0624i	−1.70674	+	0.759890i
$566$	−3.26066	−	10.0353i	−0.137056	−	0.421814i
$567$	27.8821	−	0.200200i	1.17094	−	0.00840762i
$568$	16.3398	+	11.8715i	0.685602	+	0.498119i
$569$	−1.24075	−	11.8050i	−0.0520151	−	0.494890i	−0.989254	−	0.146204i	$-0.953294\pi$
$569$	−1.24075	−	11.8050i	−0.0520151	−	0.494890i	0.937239	−	0.348687i	$-0.113372\pi$
$570$	6.49180	−	1.37987i	0.271912	−	0.0577966i
$571$	9.90067	+	17.1485i	0.414330	+	0.717641i	0.995358	−	0.0962427i	$-0.0306825\pi$
$571$	9.90067	+	17.1485i	0.414330	+	0.717641i	−0.581028	+	0.813884i	$0.697349\pi$
$572$		0			0
$573$	19.1652			0.800637
$574$	−0.217526	+	2.22305i	−0.00907936	+	0.0927884i
$575$	−20.9266	+	15.2041i	−0.872699	+	0.634053i
$576$	0.341226	−	0.151924i	0.0142177	−	0.00633015i
$577$	19.1900	−	21.3127i	0.798892	−	0.887259i	−0.196756	−	0.980452i	$-0.563041\pi$
$577$	19.1900	−	21.3127i	0.798892	−	0.887259i	0.995648	+	0.0931934i	$0.0297075\pi$
$578$	6.26341	−	6.95622i	0.260524	−	0.289341i
$579$	−44.2410	+	19.6974i	−1.83859	+	0.818595i
$580$	13.9517	−	10.1365i	0.579313	−	0.420896i
$581$	0.404359	−	0.183522i	0.0167757	−	0.00761380i
$582$	−12.2255			−0.506762
$583$		0			0
$584$	5.34425	+	9.25651i	0.221147	+	0.383037i
$585$	13.5518	−	2.88053i	0.560300	−	0.119095i
$586$	−1.05257	−	10.0146i	−0.0434814	−	0.413697i
$587$	−0.818795	−	0.594889i	−0.0337953	−	0.0245537i	0.570759	−	0.821117i	$-0.306649\pi$
$587$	−0.818795	−	0.594889i	−0.0337953	−	0.0245537i	−0.604555	+	0.796564i	$0.706649\pi$
$588$	−6.20189	+	20.0633i	−0.255762	+	0.827397i
$589$	3.24039	+	9.97291i	0.133518	+	0.410927i
$590$	18.9501	−	8.43713i	0.780164	−	0.347351i
$591$	42.9406	+	19.1184i	1.76634	+	0.786426i
$592$	7.05575	−	1.49975i	0.289990	−	0.0616392i
$593$	7.11659	−	12.3263i	0.292243	−	0.506180i	−0.682097	−	0.731262i	$-0.738932\pi$
$593$	7.11659	−	12.3263i	0.292243	−	0.506180i	0.974340	+	0.225082i	$0.0722650\pi$
$594$		0			0
$595$	10.5499	+	11.5490i	0.432505	+	0.473464i
$596$	−0.484801	+	1.49206i	−0.0198582	+	0.0611173i
$597$	−1.11760	−	10.6332i	−0.0457403	−	0.435190i
$598$	1.35671	−	12.9082i	0.0554799	−	0.527856i
$599$	−17.7626	+	19.7273i	−0.725759	+	0.806037i	−0.987251	−	0.159169i	$-0.949119\pi$
$599$	−17.7626	+	19.7273i	−0.725759	+	0.806037i	0.261493	+	0.965205i	$0.415785\pi$
$600$	−33.9111	−	7.20803i	−1.38442	−	0.294267i
$601$	−9.83421	−	7.14497i	−0.401146	−	0.291449i	0.368862	−	0.929484i	$-0.379748\pi$
$601$	−9.83421	−	7.14497i	−0.401146	−	0.291449i	−0.770008	+	0.638035i	$0.779748\pi$
$602$	−1.84387	+	2.07764i	−0.0751507	+	0.0846782i
$603$	−1.99345	+	6.13521i	−0.0811796	+	0.249845i
$604$	−12.8830	+	22.3139i	−0.524200	+	0.907941i
$605$		0			0
$606$	−1.16432	−	2.01667i	−0.0472974	−	0.0819216i
$607$	−9.34589	−	10.3797i	−0.379338	−	0.421298i	0.522996	−	0.852335i	$-0.324814\pi$
$607$	−9.34589	−	10.3797i	−0.379338	−	0.421298i	−0.902334	+	0.431038i	$0.858148\pi$
$608$	−6.87380	+	4.99411i	−0.278769	+	0.202538i
$609$	−12.5408	+	9.24970i	−0.508177	+	0.374817i
$610$	4.84218	+	14.9027i	0.196054	+	0.603392i
$611$	9.58029	+	2.03635i	0.387577	+	0.0823820i
$612$	0.178383	−	1.69720i	0.00721070	−	0.0686053i
$613$	−4.24058	−	1.88803i	−0.171275	−	0.0762567i	0.319308	−	0.947651i	$-0.396550\pi$
$613$	−4.24058	−	1.88803i	−0.171275	−	0.0762567i	−0.490583	+	0.871394i	$0.663216\pi$
$614$	−7.23666	−	8.03712i	−0.292048	−	0.324352i
$615$	−8.77453			−0.353823
$616$		0			0
$617$	−26.3960			−1.06266			−0.531331	−	0.847165i	$-0.678308\pi$
$617$	−26.3960			−1.06266			−0.531331	+	0.847165i	$0.678308\pi$
$618$	2.66151	+	2.95591i	0.107062	+	0.118904i
$619$	13.4122	+	5.97149i	0.539081	+	0.240014i	0.658170	−	0.752869i	$-0.271331\pi$
$619$	13.4122	+	5.97149i	0.539081	+	0.240014i	−0.119089	+	0.992884i	$0.537997\pi$
$620$	4.14364	−	39.4241i	0.166412	−	1.58331i
$621$	14.6546	+	3.11492i	0.588067	+	0.124998i
$622$	−4.38870	−	13.5070i	−0.175971	−	0.541582i
$623$	6.22863	+	2.71975i	0.249545	+	0.108964i
$624$	−14.6249	+	10.6256i	−0.585466	+	0.425366i
$625$	−2.56083	−	2.84409i	−0.102433	−	0.113764i
$626$	5.38043	+	9.31918i	0.215045	+	0.372469i
$627$		0			0
$628$	−8.98240	+	15.5580i	−0.358437	+	0.620831i
$629$	−2.30940	+	7.10760i	−0.0920818	+	0.283399i
$630$	3.98806	+	0.817805i	0.158888	+	0.0325821i
$631$	24.3917	+	17.7216i	0.971018	+	0.705486i	0.955683	−	0.294397i	$-0.0951187\pi$
$631$	24.3917	+	17.7216i	0.971018	+	0.705486i	0.0153345	+	0.999882i	$0.495119\pi$
$632$	−14.6546	−	3.11492i	−0.582927	−	0.123905i
$633$	−15.4821	+	17.1947i	−0.615360	+	0.683426i
$634$	0.306203	−	2.91333i	0.0121609	−	0.115703i
$635$	2.47010	+	23.5014i	0.0980228	+	0.932625i
$636$	−8.55248	+	26.3218i	−0.339128	+	1.04373i
$637$	−3.73450	+	41.2168i	−0.147966	+	1.63307i
$638$		0			0
$639$	2.82963	−	4.90107i	0.111939	−	0.193883i
$640$	38.7481	−	8.23616i	1.53165	−	0.325563i
$641$	−14.7795	−	6.58026i	−0.583756	−	0.259905i	0.0935403	−	0.995615i	$-0.470182\pi$
$641$	−14.7795	−	6.58026i	−0.583756	−	0.259905i	−0.677296	+	0.735711i	$0.736848\pi$
$642$	−5.46782	+	2.43443i	−0.215797	+	0.0960792i
$643$	−0.721764	−	2.22136i	−0.0284636	−	0.0876019i	0.935816	−	0.352490i	$-0.114665\pi$
$643$	−0.721764	−	2.22136i	−0.0284636	−	0.0876019i	−0.964279	+	0.264888i	$0.914665\pi$
$644$	−6.85235	+	12.0679i	−0.270021	+	0.475542i
$645$	−8.82818	−	6.41405i	−0.347609	−	0.252553i
$646$	−0.168403	−	1.60225i	−0.00662573	−	0.0630396i
$647$	−14.6352	+	3.11081i	−0.575369	+	0.122298i	−0.486400	−	0.873736i	$-0.661690\pi$
$647$	−14.6352	+	3.11081i	−0.575369	+	0.122298i	−0.0889685	+	0.996034i	$0.528357\pi$
$648$	12.3481	+	21.3875i	0.485079	+	0.840182i
$649$		0			0
$650$	−30.0345			−1.17805
$651$	−3.48834	+	35.6498i	−0.136719	+	1.39723i
$652$	−11.3465	+	8.24374i	−0.444364	+	0.322850i
$653$	−20.9109	+	9.31012i	−0.818305	+	0.364333i	−0.772815	−	0.634632i	$-0.781152\pi$
$653$	−20.9109	+	9.31012i	−0.818305	+	0.364333i	−0.0454907	+	0.998965i	$0.514485\pi$
$654$	−12.5034	+	13.8865i	−0.488923	+	0.543004i
$655$	−14.4658	+	16.0659i	−0.565225	+	0.627746i
$656$	1.87815	−	0.836208i	0.0733296	−	0.0326484i
$657$	2.42296	−	1.76038i	0.0945286	−	0.0686791i
$658$	2.34041	+	1.67487i	0.0912388	+	0.0652931i
$659$	2.20568			0.0859211			0.0429606	−	0.999077i	$-0.486321\pi$
$659$	2.20568			0.0859211			0.0429606	+	0.999077i	$0.486321\pi$
$660$		0			0
$661$	0.341188	+	0.590956i	0.0132707	+	0.0229855i	0.872584	−	0.488463i	$-0.162442\pi$
$661$	0.341188	+	0.590956i	0.0132707	+	0.0229855i	−0.859314	+	0.511449i	$0.829109\pi$
$662$	12.2286	−	2.59927i	0.475277	−	0.101023i
$663$	−1.95771	−	18.6264i	−0.0760312	−	0.723389i
$664$	0.318193	+	0.231181i	0.0123483	+	0.00897155i
$665$	−13.9844	+	0.100411i	−0.542292	+	0.00389379i
$666$	0.601042	+	1.84982i	0.0232899	+	0.0716790i
$667$	−9.40754	+	4.18851i	−0.364261	+	0.162180i
$668$	−26.1100	−	11.6249i	−1.01023	−	0.449781i
$669$	−29.2284	+	6.21270i	−1.13004	+	0.240197i
$670$	11.5112	−	19.9380i	0.444717	−	0.770273i
$671$		0			0
$672$	−28.3452	+	6.23801i	−1.09344	+	0.240637i
$673$	3.36411	−	10.3537i	0.129677	−	0.399104i	−0.865047	−	0.501690i	$-0.832712\pi$
$673$	3.36411	−	10.3537i	0.129677	−	0.399104i	0.994724	+	0.102586i	$0.0327118\pi$
$674$	−1.85417	−	17.6413i	−0.0714200	−	0.679516i
$675$	3.62387	−	34.4788i	0.139483	−	1.32709i
$676$	−23.0470	+	25.5963i	−0.886424	+	0.984474i
$677$	44.6675	+	9.49437i	1.71671	+	0.364898i	0.958053	−	0.286591i	$-0.0925221\pi$
$677$	44.6675	+	9.49437i	1.71671	+	0.364898i	0.758658	+	0.651489i	$0.225855\pi$
$678$	12.6399	+	9.18346i	0.485434	+	0.352689i
$679$	25.2357	+	5.17492i	0.968458	+	0.198595i
$680$	−4.28131	+	13.1765i	−0.164181	+	0.505296i
$681$	−14.9811	+	25.9480i	−0.574076	+	0.994329i
$682$		0			0
$683$	−3.24186	−	5.61507i	−0.124046	−	0.214855i	0.797313	−	0.603566i	$-0.206254\pi$
$683$	−3.24186	−	5.61507i	−0.124046	−	0.214855i	−0.921360	+	0.388711i	$0.872921\pi$
$684$	1.02090	+	1.13383i	0.0390352	+	0.0433530i
$685$	−21.4334	+	15.5723i	−0.818929	+	0.594987i
$686$	−5.85214	+	10.6601i	−0.223436	+	0.407003i
$687$	−3.29226	−	10.1325i	−0.125608	−	0.386580i
$688$	2.50089	+	0.531581i	0.0953456	+	0.0202663i
$689$	−5.70131	+	54.2443i	−0.217202	+	2.06654i
$690$	13.6867	+	6.09371i	0.521043	+	0.231983i
$691$	7.32481	+	8.13502i	0.278649	+	0.309471i	0.866181	−	0.499730i	$-0.166567\pi$
$691$	7.32481	+	8.13502i	0.278649	+	0.309471i	−0.587533	+	0.809200i	$0.699901\pi$
$692$	30.6885			1.16660
$693$		0			0
$694$	−13.2754			−0.503927
$695$	−25.8491	−	28.7083i	−0.980512	−	1.08897i
$696$	−12.6088	−	5.61379i	−0.477934	−	0.212790i
$697$	−0.222645	+	2.11833i	−0.00843329	+	0.0802374i
$698$	7.72167	+	1.64129i	0.292270	+	0.0621238i
$699$	11.3901	+	35.0550i	0.430811	+	1.32590i
$700$	29.4300	+	12.8507i	1.11235	+	0.485710i
$701$	−0.740149	+	0.537750i	−0.0279550	+	0.0203105i	−0.601675	−	0.798741i	$-0.705500\pi$
$701$	−0.740149	+	0.537750i	−0.0279550	+	0.0203105i	0.573720	+	0.819052i	$0.305500\pi$
$702$	11.6402	+	12.9277i	0.439330	+	0.487925i
$703$	−3.34073	−	5.78632i	−0.125998	−	0.218235i
$704$		0			0
$705$	−5.65277	+	9.79088i	−0.212896	+	0.368746i
$706$	2.18310	−	6.71889i	0.0821620	−	0.252869i
$707$	1.54975	+	4.65564i	0.0582845	+	0.175093i
$708$	21.4841	+	15.6091i	0.807423	+	0.586627i
$709$	−43.3440	−	9.21305i	−1.62782	−	0.346003i	−0.698594	−	0.715519i	$-0.746190\pi$
$709$	−43.3440	−	9.21305i	−1.62782	−	0.346003i	−0.929225	+	0.369515i	$0.879524\pi$
$710$	−13.5145	+	15.0093i	−0.507189	+	0.563291i
$711$	−0.438808	+	4.17498i	−0.0164566	+	0.156574i
$712$	0.629239	+	5.98681i	0.0235817	+	0.224365i
$713$	−7.31485	+	22.5128i	−0.273943	+	0.843111i
$714$	1.66300	−	5.24606i	0.0622363	−	0.196329i
$715$		0			0
$716$	2.54774	−	4.41281i	0.0952134	−	0.164914i
$717$	−41.4443	+	8.80926i	−1.54777	+	0.328988i
$718$	14.5705	+	6.48720i	0.543766	+	0.242100i
$719$	−4.75259	+	2.11599i	−0.177242	+	0.0789131i	−0.493439	−	0.869780i	$-0.664260\pi$
$719$	−4.75259	+	2.11599i	−0.177242	+	0.0789131i	0.316197	+	0.948693i	$0.397594\pi$
$720$	−1.15790	−	3.56364i	−0.0431523	−	0.132809i
$721$	−4.24266	−	7.22815i	−0.158005	−	0.269190i
$722$	−8.92785	−	6.48646i	−0.332260	−	0.241401i
$723$	−3.97254	−	37.7962i	−0.147740	−	1.40566i
$724$	−15.8685	+	3.37296i	−0.589750	+	0.125355i
$725$	11.9148	+	20.6370i	0.442503	+	0.766438i
$726$		0			0
$727$	50.0871			1.85763			0.928814	−	0.370547i	$-0.120830\pi$
$727$	50.0871			1.85763			0.928814	+	0.370547i	$0.120830\pi$
$728$	−33.3788	+	15.1493i	−1.23710	+	0.561471i
$729$	−15.1987	+	11.0425i	−0.562915	+	0.408981i
$730$	−9.76443	+	4.34740i	−0.361398	+	0.160905i
$731$	−1.77247	+	1.96853i	−0.0655572	+	0.0728087i
$732$	−13.4229	+	14.9077i	−0.496126	+	0.551004i
$733$	43.0003	−	19.1450i	1.58825	−	0.707136i	0.593068	−	0.805152i	$-0.297916\pi$
$733$	43.0003	−	19.1450i	1.58825	−	0.707136i	0.995185	+	0.0980161i	$0.0312497\pi$
$734$	5.76065	−	4.18536i	0.212629	−	0.154484i
$735$	−43.9157	−	18.8016i	−1.61985	−	0.693508i
$736$	−19.1799			−0.706981
$737$		0			0
$738$	0.277175	+	0.480082i	0.0102030	+	0.0176720i
$739$	45.9645	−	9.77006i	1.69083	−	0.359397i	0.740842	−	0.671679i	$-0.234427\pi$
$739$	45.9645	−	9.77006i	1.69083	−	0.359397i	0.949990	+	0.312282i	$0.101093\pi$
$740$	2.64021	+	25.1199i	0.0970559	+	0.923425i
$741$	13.5465	+	9.84211i	0.497643	+	0.361559i
$742$	−7.91363	+	13.9370i	−0.290518	+	0.511642i
$743$	1.60545	+	4.94105i	0.0588981	+	0.181270i	0.976177	−	0.216976i	$-0.0696192\pi$
$743$	1.60545	+	4.94105i	0.0588981	+	0.181270i	−0.917279	+	0.398245i	$0.869619\pi$
$744$	−28.9835	+	12.9043i	−1.06258	+	0.473093i
$745$	−3.26031	−	1.45158i	−0.119448	−	0.0531818i
$746$	21.2105	−	4.50843i	0.776571	−	0.165065i
$747$	0.0551029	−	0.0954410i	0.00201611	−	0.00349200i
$748$		0			0
$749$	12.3171	−	2.71066i	0.450057	−	0.0990452i
$750$	3.78957	−	11.6631i	0.138376	−	0.425876i
$751$	−3.49685	−	33.2703i	−0.127602	−	1.21405i	−0.851579	−	0.524227i	$-0.824354\pi$
$751$	−3.49685	−	33.2703i	−0.127602	−	1.21405i	0.723977	−	0.689824i	$-0.242312\pi$
$752$	0.276887	−	2.63441i	0.0100970	−	0.0960669i
$753$	28.2873	−	31.4162i	1.03085	−	1.14487i
$754$	−11.6958	−	2.48602i	−0.425936	−	0.0905355i
$755$	−47.4188	−	34.4517i	−1.72575	−	1.25383i
$756$	−5.87458	−	17.6479i	−0.213656	−	0.641849i
$757$	12.3743	−	38.0841i	0.449750	−	1.38419i	−0.427439	−	0.904044i	$-0.640584\pi$
$757$	12.3743	−	38.0841i	0.449750	−	1.38419i	0.877189	−	0.480145i	$-0.159416\pi$
$758$	−7.20051	+	12.4716i	−0.261534	+	0.452990i
$759$		0			0
$760$	−6.19326	−	10.7270i	−0.224653	−	0.389110i
$761$	5.05762	+	5.61706i	0.183339	+	0.203618i	0.827807	−	0.561012i	$-0.189588\pi$
$761$	5.05762	+	5.61706i	0.183339	+	0.203618i	−0.644469	+	0.764631i	$0.722921\pi$
$762$	6.72610	−	4.88680i	0.243661	−	0.177030i
$763$	31.6875	−	23.3718i	1.14716	−	0.846115i
$764$	−4.85889	−	14.9541i	−0.175788	−	0.541021i
$765$	3.79726	+	0.807132i	0.137290	+	0.0291819i
$766$	2.50266	−	23.8112i	0.0904247	−	0.860334i
$767$	47.8102	+	21.2865i	1.72633	+	0.768610i
$768$	−10.7814	−	11.9740i	−0.389042	−	0.432075i
$769$	−51.5407			−1.85860			−0.929302	−	0.369320i	$-0.879591\pi$
$769$	−51.5407			−1.85860			−0.929302	+	0.369320i	$0.879591\pi$
$770$		0			0
$771$	55.6834			2.00539
$772$	26.5856	+	29.5264i	0.956838	+	1.06268i
$773$	−14.1286	−	6.29046i	−0.508170	−	0.226252i	0.136603	−	0.990626i	$-0.456382\pi$
$773$	−14.1286	−	6.29046i	−0.508170	−	0.226252i	−0.644773	+	0.764374i	$0.723048\pi$
$774$	−0.0720624	+	0.685628i	−0.00259023	+	0.0246444i
$775$	53.5793	+	11.3886i	1.92462	+	0.409092i
$776$	7.05076	+	21.7000i	0.253108	+	0.778985i
$777$	−2.54862	−	22.6808i	−0.0914313	−	0.813668i
$778$	10.3460	−	7.51681i	0.370922	−	0.269491i
$779$	−1.27422	−	1.41517i	−0.0456537	−	0.0507036i
$780$	−31.6498	−	54.8190i	−1.13324	−	1.96284i
$781$		0			0
$782$	1.81842	−	3.14959i	0.0650264	−	0.112629i
$783$	4.26506	−	13.1265i	0.152421	−	0.469103i
$784$	11.1918	−	0.160727i	0.399706	−	0.00574027i
$785$	−33.0618	−	24.0208i	−1.18003	−	0.857340i
$786$	7.43981	+	1.58138i	0.265369	+	0.0564059i
$787$	−14.6886	+	16.3134i	−0.523593	+	0.581509i	−0.945702	−	0.325036i	$-0.894623\pi$
$787$	−14.6886	+	16.3134i	−0.523593	+	0.581509i	0.422109	+	0.906545i	$0.361290\pi$
$788$	4.03101	−	38.3525i	0.143599	−	1.36625i
$789$	−3.09888	−	29.4839i	−0.110323	−	1.04965i
$790$	4.62968	−	14.2487i	0.164716	−	0.506945i
$791$	−22.2040	−	24.3068i	−0.789484	−	0.864250i
$792$		0			0
$793$	−19.7668	+	34.2371i	−0.701941	+	1.21580i
$794$	−5.03532	+	1.07029i	−0.178697	+	0.0379832i
$795$	−57.5158	−	25.6077i	−2.03987	−	0.908210i
$796$	−8.01352	+	3.56785i	−0.284032	+	0.126459i
$797$	13.1721	+	40.5396i	0.466580	+	1.43598i	0.856985	+	0.515341i	$0.172335\pi$
$797$	13.1721	+	40.5396i	0.466580	+	1.43598i	−0.390405	+	0.920643i	$0.627665\pi$
$798$	2.49062	+	4.24323i	0.0881671	+	0.150209i
$799$	2.22026	+	1.61311i	0.0785471	+	0.0570678i
$800$	4.63928	+	44.1398i	0.164023	+	1.56058i
$801$	1.64990	−	0.350697i	0.0582963	−	0.0123913i
$802$	−8.02583	−	13.9011i	−0.283402	−	0.490867i
$803$		0			0
$804$	29.4734			1.03945
$805$	−25.6726	−	18.3720i	−0.904839	−	0.647529i
$806$	−22.2362	+	16.1555i	−0.783237	+	0.569055i
$807$	2.98118	−	1.32731i	0.104943	−	0.0467235i
$808$	−2.90806	+	3.22973i	−0.102305	+	0.113621i
$809$	−2.65474	+	2.94839i	−0.0933357	+	0.103660i	−0.788003	−	0.615671i	$-0.788885\pi$
$809$	−2.65474	+	2.94839i	−0.0933357	+	0.103660i	0.694667	+	0.719331i	$0.255552\pi$
$810$	−22.5611	+	10.0448i	−0.792716	+	0.352940i
$811$	−37.9604	+	27.5799i	−1.33297	+	0.968460i	−0.333300	+	0.942821i	$0.608162\pi$
$811$	−37.9604	+	27.5799i	−1.33297	+	0.968460i	−0.999671	+	0.0256391i	$0.991838\pi$
$812$	10.3967	+	7.44020i	0.364854	+	0.261100i
$813$	39.2549			1.37673
$814$		0			0
$815$	−15.9523	−	27.6301i	−0.558783	−	0.967841i
$816$	−4.95465	+	1.05314i	−0.173447	+	0.0368674i
$817$	−0.247547	−	2.35525i	−0.00866058	−	0.0823999i
$818$	1.25034	+	0.908426i	0.0437171	+	0.0317624i
$819$	5.19926	+	8.85788i	0.181677	+	0.309520i
$820$	2.22458	+	6.84655i	0.0776856	+	0.239092i
$821$	46.2254	−	20.5809i	1.61328	−	0.718278i	0.615711	−	0.787972i	$-0.288869\pi$
$821$	46.2254	−	20.5809i	1.61328	−	0.718278i	0.997568	+	0.0696941i	$0.0222023\pi$
$822$	8.51511	+	3.79117i	0.296998	+	0.132232i
$823$	−0.389888	+	0.0828733i	−0.0135906	+	0.00288878i	−0.214702	−	0.976680i	$-0.568878\pi$
$823$	−0.389888	+	0.0828733i	−0.0135906	+	0.00288878i	0.201111	+	0.979568i	$0.435545\pi$
$824$	3.71172	−	6.42889i	0.129304	−	0.223961i
$825$		0			0
$826$	10.3717	+	11.3540i	0.360879	+	0.395055i
$827$	6.31119	−	19.4239i	0.219462	−	0.675434i	−0.779345	−	0.626595i	$-0.784448\pi$
$827$	6.31119	−	19.4239i	0.219462	−	0.675434i	0.998807	−	0.0488385i	$-0.0155520\pi$
$828$	0.360011	+	3.42528i	0.0125113	+	0.119037i
$829$	2.43168	−	23.1359i	0.0844557	−	0.803542i	−0.867527	−	0.497390i	$-0.834292\pi$
$829$	2.43168	−	23.1359i	0.0844557	−	0.803542i	0.951983	−	0.306152i	$-0.0990416\pi$
$830$	−0.263174	+	0.292285i	−0.00913492	+	0.0101454i
$831$	−49.8679	−	10.5997i	−1.72990	−	0.367701i
$832$	−2.72086	−	1.97682i	−0.0943289	−	0.0685339i
$833$	−5.65336	+	10.1250i	−0.195877	+	0.350809i
$834$	−4.19994	+	12.9261i	−0.145432	+	0.447594i
$835$	32.5082	−	56.3059i	1.12499	−	1.94855i
$836$		0			0
$837$	−15.8632	−	27.4758i	−0.548311	−	0.949703i
$838$	−4.08205	−	4.53358i	−0.141012	−	0.156610i
$839$	13.3376	−	9.69031i	0.460464	−	0.334547i	−0.333249	−	0.942839i	$-0.608145\pi$
$839$	13.3376	−	9.69031i	0.460464	−	0.334547i	0.793713	+	0.608292i	$0.208145\pi$
$840$	−4.72479	−	42.0470i	−0.163021	−	1.45076i
$841$	−6.02991	−	18.5581i	−0.207928	−	0.639936i
$842$	−25.0691	−	5.32860i	−0.863937	−	0.183636i
$843$	3.14703	−	29.9420i	0.108389	−	1.03126i
$844$	17.3417	+	7.72102i	0.596926	+	0.265769i
$845$	−52.4278	−	58.2270i	−1.80357	−	2.00307i
$846$	0.714253			0.0245565
$847$		0			0
$848$	14.7514			0.506566
$849$	20.5617	+	22.8361i	0.705676	+	0.783732i
$850$	−7.68816	−	3.42299i	−0.263702	−	0.117408i
$851$	1.57657	−	15.0001i	0.0540442	−	0.514196i
$852$	−25.2913	−	5.37583i	−0.866466	−	0.184173i
$853$	4.58318	+	14.1056i	0.156925	+	0.482966i	0.998351	−	0.0574069i	$-0.0182832\pi$
$853$	4.58318	+	14.1056i	0.156925	+	0.482966i	−0.841426	+	0.540373i	$0.818283\pi$
$854$	−9.34876	+	6.89537i	−0.319908	+	0.235955i
$855$	−2.80788	+	2.04004i	−0.0960274	+	0.0697680i
$856$	7.47451	+	8.30129i	0.255474	+	0.283732i
$857$	−2.51594	−	4.35773i	−0.0859428	−	0.148857i	0.819850	−	0.572579i	$-0.194057\pi$
$857$	−2.51594	−	4.35773i	−0.0859428	−	0.148857i	−0.905793	+	0.423721i	$0.860724\pi$
$858$		0			0
$859$	28.0181	−	48.5288i	0.955966	−	1.65578i	0.223825	−	0.974629i	$-0.428146\pi$
$859$	28.0181	−	48.5288i	0.955966	−	1.65578i	0.732141	−	0.681153i	$-0.238521\pi$
$860$	−2.76654	+	8.51454i	−0.0943383	+	0.290343i
$861$	−2.05451	−	6.17199i	−0.0700176	−	0.210341i
$862$	2.01970	+	1.46740i	0.0687912	+	0.0499798i
$863$	35.6789	+	7.58379i	1.21452	+	0.258155i	0.770254	−	0.637737i	$-0.220129\pi$
$863$	35.6789	+	7.58379i	1.21452	+	0.258155i	0.444271	+	0.895892i	$0.353463\pi$
$864$	17.2010	−	19.1037i	0.585191	−	0.649921i
$865$	−7.29721	+	69.4284i	−0.248113	+	2.36063i
$866$	0.564212	+	5.36812i	0.0191727	+	0.182416i
$867$	−8.42380	+	25.9258i	−0.286087	+	0.880486i
$868$	28.7010	−	6.31631i	0.974177	−	0.214390i
$869$		0			0
$870$	6.90101	−	11.9529i	0.233966	−	0.405241i
$871$	56.8152	−	12.0764i	1.92511	−	0.409194i
$872$	31.8593	+	14.1847i	1.07889	+	0.480354i
$873$	5.84058	−	2.60039i	0.197674	−	0.0880100i
$874$	1.00476	+	3.09232i	0.0339864	+	0.104599i
$875$	−12.7593	+	22.4708i	−0.431343	+	0.759652i
$876$	−11.0701	−	8.04292i	−0.374025	−	0.271745i
$877$	−0.691574	−	6.57989i	−0.0233528	−	0.222187i	−0.999974	−	0.00721927i	$-0.997702\pi$
$877$	−0.691574	−	6.57989i	−0.0233528	−	0.222187i	0.976621	−	0.214968i	$-0.0689647\pi$
$878$	−2.91678	+	0.619982i	−0.0984367	+	0.0209234i
$879$	14.6627	+	25.3965i	0.494559	+	0.856602i
$880$		0			0
$881$	−22.5286			−0.759008			−0.379504	−	0.925190i	$-0.623905\pi$
$881$	−22.5286			−0.759008			−0.379504	+	0.925190i	$0.623905\pi$
$882$	0.358541	+	2.99668i	0.0120727	+	0.100903i
$883$	41.3935	−	30.0741i	1.39300	−	1.01208i	0.397474	−	0.917613i	$-0.369887\pi$
$883$	41.3935	−	30.0741i	1.39300	−	1.01208i	0.995528	−	0.0944622i	$-0.0301131\pi$
$884$	−14.0374	+	6.24984i	−0.472128	+	0.210205i
$885$	−40.4220	+	44.8932i	−1.35877	+	1.50907i
$886$	−6.03880	+	6.70677i	−0.202878	+	0.225318i
$887$	5.79013	−	2.57793i	0.194414	−	0.0865585i	−0.307221	−	0.951638i	$-0.599399\pi$
$887$	5.79013	−	2.57793i	0.194414	−	0.0865585i	0.501634	+	0.865080i	$0.332732\pi$
$888$	16.3544	−	11.8822i	0.548817	−	0.398739i
$889$	−15.9525	+	7.24020i	−0.535030	+	0.242828i
$890$	−6.01979			−0.201784
$891$		0			0
$892$	12.2578	+	21.2311i	0.410421	+	0.710871i
$893$	−2.39997	+	0.510129i	−0.0803119	+	0.0170708i
$894$	0.131247	+	1.24873i	0.00438955	+	0.0417638i
$895$	9.37755	+	6.81319i	0.313457	+	0.227740i
$896$	14.8660	+	25.3269i	0.496637	+	0.846112i
$897$	11.6804	+	35.9487i	0.389999	+	1.20029i
$898$	−12.9365	+	5.75972i	−0.431698	+	0.192204i
$899$	19.9218	+	8.86974i	0.664428	+	0.295822i
$900$	7.79570	−	1.65703i	0.259857	−	0.0552342i
$901$	−7.64155	+	13.2356i	−0.254577	+	0.440940i
$902$		0			0
$903$	2.44456	−	7.71155i	0.0813498	−	0.256624i
$904$	9.01070	−	27.7321i	0.299691	−	0.922355i
$905$	−3.85757	−	36.7024i	−0.128230	−	1.22003i
$906$	−2.15553	+	20.5085i	−0.0716125	+	0.681348i
$907$	−4.60679	+	5.11636i	−0.152966	+	0.169886i	−0.814757	−	0.579802i	$-0.803130\pi$
$907$	−4.60679	+	5.11636i	−0.152966	+	0.169886i	0.661791	+	0.749688i	$0.269796\pi$
$908$	24.0447	+	5.11085i	0.797950	+	0.169610i
$909$	0.985194	+	0.715785i	0.0326768	+	0.0237411i
$910$	−11.5773	−	34.7795i	−0.383783	−	1.15293i
$911$	−12.6950	+	39.0711i	−0.420603	+	1.29448i	0.486539	+	0.873659i	$0.338259\pi$
$911$	−12.6950	+	39.0711i	−0.420603	+	1.29448i	−0.907142	+	0.420825i	$0.861741\pi$
$912$	2.26430	−	3.92188i	0.0749784	−	0.129866i
$913$		0			0
$914$	1.08524	+	1.87969i	0.0358966	+	0.0621747i
$915$	−30.5348	−	33.9123i	−1.00945	−	1.12111i
$916$	−7.07149	+	5.13774i	−0.233648	+	0.169756i
$917$	−14.6878	−	6.41347i	−0.485034	−	0.211791i
$918$	1.50627	+	4.63582i	0.0497143	+	0.153005i
$919$	−11.3724	−	2.41728i	−0.375141	−	0.0797388i	0.0164825	−	0.999864i	$-0.494753\pi$
$919$	−11.3724	−	2.41728i	−0.375141	−	0.0797388i	−0.391624	+	0.920125i	$0.628087\pi$
$920$	2.92275	−	27.8081i	0.0963601	−	0.916805i
$921$	28.7729	+	12.8105i	0.948098	+	0.422120i
$922$	−14.1266	−	15.6892i	−0.465236	−	0.516697i
$923$	−50.9562			−1.67724
$924$		0			0
$925$	−34.9019			−1.14757
$926$	−2.55790	−	2.84084i	−0.0840578	−	0.0933557i
$927$	−1.90024	−	0.846040i	−0.0624119	−	0.0277876i
$928$	−1.84695	+	17.5726i	−0.0606292	+	0.576848i
$929$	−24.2256	−	5.14931i	−0.794817	−	0.168943i	−0.207430	−	0.978250i	$-0.566510\pi$
$929$	−24.2256	−	5.14931i	−0.794817	−	0.168943i	−0.587387	+	0.809306i	$0.699843\pi$
$930$	−9.80398	−	30.1735i	−0.321485	−	0.989429i
$931$	−3.34501	−	9.81311i	−0.109628	−	0.321612i
$932$	24.4648	−	17.7747i	0.801372	−	0.582231i
$933$	27.6751	+	30.7364i	0.906043	+	1.00626i
$934$	−1.97470	−	3.42028i	−0.0646141	−	0.111915i
$935$		0			0
$936$	−4.54861	+	7.87842i	−0.148676	+	0.257514i
$937$	−0.355512	+	1.09415i	−0.0116141	+	0.0357444i	−0.956696	−	0.291090i	$-0.905982\pi$
$937$	−0.355512	+	1.09415i	−0.0116141	+	0.0357444i	0.945082	+	0.326835i	$0.105982\pi$
$938$	16.7197	+	3.42859i	0.545916	+	0.111947i
$939$	−25.3530	−	18.4201i	−0.827365	−	0.601116i
$940$	9.07271	+	1.92846i	0.295919	+	0.0628996i
$941$	−6.76505	+	7.51335i	−0.220534	+	0.244928i	−0.843252	−	0.537518i	$-0.819362\pi$
$941$	−6.76505	+	7.51335i	−0.220534	+	0.244928i	0.622718	+	0.782447i	$0.286029\pi$
$942$	−1.50290	+	14.2991i	−0.0489671	+	0.465891i
$943$	−0.449341	−	4.27519i	−0.0146326	−	0.139219i
$944$	4.37388	−	13.4614i	0.142358	−	0.438132i
$945$	41.3228	−	9.09402i	1.34423	−	0.295828i
$946$		0			0
$947$	12.2277	−	21.1789i	0.397346	−	0.688223i	−0.596052	−	0.802946i	$-0.703265\pi$
$947$	12.2277	−	21.1789i	0.397346	−	0.688223i	0.993398	+	0.114723i	$0.0365981\pi$
$948$	18.7608	−	3.98773i	0.609322	−	0.129515i
$949$	−24.6352	−	10.9683i	−0.799691	−	0.356045i
$950$	6.87350	−	3.06028i	0.223006	−	0.0992885i
$951$	2.63623	+	8.11347i	0.0854855	+	0.263097i
$952$	−10.2708	+	0.0737467i	−0.332878	+	0.00239014i
$953$	−13.0815	−	9.50424i	−0.423750	−	0.307872i	0.355395	−	0.934716i	$-0.384346\pi$
$953$	−13.0815	−	9.50424i	−0.423750	−	0.307872i	−0.779145	+	0.626844i	$0.784346\pi$
$954$	0.415769	+	3.95578i	0.0134610	+	0.128073i
$955$	34.9869	−	7.43670i	1.13215	−	0.240646i
$956$	17.3809	+	30.1046i	0.562138	+	0.973652i
$957$		0			0
$958$	11.2512			0.363511
$959$	−15.9721	−	11.4301i	−0.515765	−	0.369096i
$960$	3.14068	−	2.28184i	0.101365	−	0.0736459i
$961$	17.4737	−	7.77979i	0.563668	−	0.250961i
$962$	11.7185	−	13.0147i	0.377818	−	0.419610i
$963$	2.09438	−	2.32604i	0.0674903	−	0.0749556i
$964$	−28.4843	+	12.6820i	−0.917417	+	0.408460i
$965$	−73.1208	+	53.1254i	−2.35384	+	1.71017i
$966$	−1.08164	+	11.0540i	−0.0348011	+	0.355657i
$967$	1.55941			0.0501472			0.0250736	−	0.999686i	$-0.492018\pi$
$967$	1.55941			0.0501472			0.0250736	+	0.999686i	$0.492018\pi$
$968$		0			0
$969$	2.34591	+	4.06323i	0.0753614	+	0.130530i
$970$	−22.3182	+	4.74387i	−0.716593	+	0.152316i
$971$	0.945699	+	8.99772i	0.0303489	+	0.288751i	0.999161	+	0.0409542i	$0.0130398\pi$
$971$	0.945699	+	8.99772i	0.0303489	+	0.288751i	−0.968812	+	0.247796i	$0.920294\pi$
$972$	−8.51548	−	6.18686i	−0.273134	−	0.198444i
$973$	14.1410	−	24.9041i	0.453338	−	0.798390i
$974$	−1.15946	−	3.56845i	−0.0371515	−	0.114341i
$975$	79.9055	−	35.5762i	2.55902	−	1.13935i
$976$	9.76767	+	4.34885i	0.312656	+	0.139203i
$977$	6.60883	−	1.40475i	0.211435	−	0.0449420i	−0.100976	−	0.994889i	$-0.532197\pi$
$977$	6.60883	−	1.40475i	0.211435	−	0.0449420i	0.312411	+	0.949947i	$0.398863\pi$
$978$	−5.61240	+	9.72096i	−0.179465	+	0.310842i
$979$		0			0
$980$	−3.53664	+	39.0330i	−0.112974	+	1.24686i
$981$	3.01968	−	9.29361i	0.0964109	−	0.296722i
$982$	−1.65187	−	15.7165i	−0.0527134	−	0.501534i
$983$	−2.76274	+	26.2857i	−0.0881176	+	0.838383i	0.857802	+	0.513981i	$0.171830\pi$
$983$	−2.76274	+	26.2857i	−0.0881176	+	0.838383i	−0.945919	+	0.324402i	$0.894837\pi$
$984$	3.85522	−	4.28166i	0.122900	−	0.136494i
$985$	85.8086	+	18.2392i	2.73409	+	0.581149i
$986$	−2.71054	−	1.96932i	−0.0863211	−	0.0627159i
$987$	−8.21046	−	1.68366i	−0.261342	−	0.0535916i
$988$	4.24515	−	13.0652i	0.135056	−	0.415660i
$989$	2.67301	−	4.62979i	0.0849969	−	0.147219i
$990$		0			0
$991$	0.317093	+	0.549221i	0.0100728	+	0.0174466i	0.871018	−	0.491251i	$-0.163460\pi$
$991$	0.317093	+	0.549221i	0.0100728	+	0.0174466i	−0.860945	+	0.508698i	$0.830127\pi$
$992$	27.1775	+	30.1837i	0.862886	+	0.958332i
$993$	−29.4547	+	21.4001i	−0.934717	+	0.679112i
$994$	−13.7219	−	5.99170i	−0.435232	−	0.190045i
$995$	−6.16627	−	18.9778i	−0.195484	−	0.601637i
$996$	−0.492511	−	0.104686i	−0.0156058	−	0.00331712i
$997$	1.05860	−	10.0719i	0.0335261	−	0.318979i	−0.964887	−	0.262665i	$-0.915399\pi$
$997$	1.05860	−	10.0719i	0.0335261	−	0.318979i	0.998413	−	0.0563141i	$-0.0179348\pi$
$998$	−6.47197	−	2.88151i	−0.204867	−	0.0912125i
$999$	13.5266	+	15.0228i	0.427961	+	0.475299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.d.9.2		24
7.4	even	3	inner	847.2.n.d.130.2		24
11.2	odd	10		847.2.n.e.366.2		24
11.3	even	5	inner	847.2.n.d.807.2		24
11.4	even	5		847.2.e.d.485.2		6
11.5	even	5	inner	847.2.n.d.632.2		24
11.6	odd	10		847.2.n.e.632.2		24
11.7	odd	10		77.2.e.b.23.2	✓	6
11.8	odd	10		847.2.n.e.807.2		24
11.9	even	5	inner	847.2.n.d.366.2		24
11.10	odd	2		847.2.n.e.9.2		24
33.29	even	10		693.2.i.g.100.2		6
44.7	even	10		1232.2.q.k.177.3		6
77.4	even	15		847.2.e.d.606.2		6
77.18	odd	30		77.2.e.b.67.2	yes	6
77.25	even	15	inner	847.2.n.d.81.2		24
77.26	odd	30		5929.2.a.w.1.2		3
77.32	odd	6		847.2.n.e.130.2		24
77.37	even	15		5929.2.a.v.1.2		3
77.39	odd	30		847.2.n.e.753.2		24
77.40	even	30		539.2.a.i.1.2		3
77.46	odd	30		847.2.n.e.487.2		24
77.51	odd	30		539.2.a.h.1.2		3
77.53	even	15	inner	847.2.n.d.487.2		24
77.60	even	15	inner	847.2.n.d.753.2		24
77.62	even	10		539.2.e.l.177.2		6
77.73	even	30		539.2.e.l.67.2		6
77.74	odd	30		847.2.n.e.81.2		24
231.95	even	30		693.2.i.g.298.2		6
231.128	even	30		4851.2.a.bo.1.2		3
231.194	odd	30		4851.2.a.bn.1.2		3
308.51	even	30		8624.2.a.cl.1.1		3
308.95	even	30		1232.2.q.k.529.3		6
308.271	odd	30		8624.2.a.ck.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.2	✓	6	11.7	odd	10
77.2.e.b.67.2	yes	6	77.18	odd	30
539.2.a.h.1.2		3	77.51	odd	30
539.2.a.i.1.2		3	77.40	even	30
539.2.e.l.67.2		6	77.73	even	30
539.2.e.l.177.2		6	77.62	even	10
693.2.i.g.100.2		6	33.29	even	10
693.2.i.g.298.2		6	231.95	even	30
847.2.e.d.485.2		6	11.4	even	5
847.2.e.d.606.2		6	77.4	even	15
847.2.n.d.9.2		24	1.1	even	1	trivial
847.2.n.d.81.2		24	77.25	even	15	inner
847.2.n.d.130.2		24	7.4	even	3	inner
847.2.n.d.366.2		24	11.9	even	5	inner
847.2.n.d.487.2		24	77.53	even	15	inner
847.2.n.d.632.2		24	11.5	even	5	inner
847.2.n.d.753.2		24	77.60	even	15	inner
847.2.n.d.807.2		24	11.3	even	5	inner
847.2.n.e.9.2		24	11.10	odd	2
847.2.n.e.81.2		24	77.74	odd	30
847.2.n.e.130.2		24	77.32	odd	6
847.2.n.e.366.2		24	11.2	odd	10
847.2.n.e.487.2		24	77.46	odd	30
847.2.n.e.632.2		24	11.6	odd	10
847.2.n.e.753.2		24	77.39	odd	30
847.2.n.e.807.2		24	11.8	odd	10
1232.2.q.k.177.3		6	44.7	even	10
1232.2.q.k.529.3		6	308.95	even	30
4851.2.a.bn.1.2		3	231.194	odd	30
4851.2.a.bo.1.2		3	231.128	even	30
5929.2.a.v.1.2		3	77.37	even	15
5929.2.a.w.1.2		3	77.26	odd	30
8624.2.a.ck.1.3		3	308.271	odd	30
8624.2.a.cl.1.1		3	308.51	even	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)

\(f(q)\)	\(=\)	\(q+(-0.439365 - 0.487964i) q^{2} +(1.74691 + 0.777774i) q^{3} +(0.163989 - 1.56026i) q^{4} +(3.49086 + 0.742006i) q^{5} +(-0.388004 - 1.19415i) q^{6} +(0.295442 + 2.62920i) q^{7} +(-1.89583 + 1.37740i) q^{8} +(0.439365 + 0.487964i) q^{9} +O(q^{10})\)	\(q+(-0.439365 - 0.487964i) q^{2} +(1.74691 + 0.777774i) q^{3} +(0.163989 - 1.56026i) q^{4} +(3.49086 + 0.742006i) q^{5} +(-0.388004 - 1.19415i) q^{6} +(0.295442 + 2.62920i) q^{7} +(-1.89583 + 1.37740i) q^{8} +(0.439365 + 0.487964i) q^{9} +(-1.17169 - 2.02943i) q^{10} +(1.50000 - 2.59808i) q^{12} +(1.82698 - 5.62286i) q^{13} +(1.15315 - 1.29934i) q^{14} +(5.52110 + 4.01132i) q^{15} +(-1.56405 - 0.332448i) q^{16} +(1.10850 - 1.23111i) q^{17} +(0.0450675 - 0.428789i) q^{18} +(0.154815 + 1.47297i) q^{19} +(1.73018 - 5.32495i) q^{20} +(-1.52882 + 4.82277i) q^{21} +(-1.67169 + 2.89545i) q^{23} +(-4.38316 + 0.931669i) q^{24} +(7.06782 + 3.14679i) q^{25} +(-3.54647 + 1.57899i) q^{26} +(-1.38473 - 4.26176i) q^{27} +(4.15068 - 0.0298029i) q^{28} +(2.49183 + 1.81042i) q^{29} +(-0.468400 - 4.45653i) q^{30} +(6.92535 - 1.47203i) q^{31} +(2.86834 + 4.96812i) q^{32} -1.08777 q^{34} +(-0.919538 + 9.39741i) q^{35} +(0.833400 - 0.605500i) q^{36} +(-4.12120 + 1.83488i) q^{37} +(0.650734 - 0.722713i) q^{38} +(7.56488 - 8.40165i) q^{39} +(-7.64014 + 3.40161i) q^{40} +(-1.04019 + 0.755743i) q^{41} +(3.02504 - 1.37295i) q^{42} -1.59899 q^{43} +(1.17169 + 2.02943i) q^{45} +(2.14736 - 0.456435i) q^{46} +(0.173164 + 1.64755i) q^{47} +(-2.47368 - 1.79723i) q^{48} +(-6.82543 + 1.55355i) q^{49} +(-1.56983 - 4.83143i) q^{50} +(2.89396 - 1.28848i) q^{51} +(-8.47350 - 3.77264i) q^{52} +(-9.02387 + 1.91808i) q^{53} +(-1.47118 + 2.54817i) q^{54} +(-4.18158 - 4.57759i) q^{56} +(-0.875186 + 2.69355i) q^{57} +(-0.211402 - 2.01136i) q^{58} +(-0.925281 + 8.80346i) q^{59} +(7.16408 - 7.95652i) q^{60} +(-6.54064 - 1.39026i) q^{61} +(-3.76105 - 2.73256i) q^{62} +(-1.15315 + 1.29934i) q^{63} +(0.175784 - 0.541008i) q^{64} +(10.5499 - 18.2730i) q^{65} +(4.91223 + 8.50823i) q^{67} +(-1.73906 - 1.93142i) q^{68} +(-5.17229 + 3.75789i) q^{69} +(4.98961 - 3.68019i) q^{70} +(-2.66335 - 8.19694i) q^{71} +(-1.50509 - 0.319916i) q^{72} +(0.476770 - 4.53616i) q^{73} +(2.70607 + 1.20482i) q^{74} +(9.89933 + 10.9943i) q^{75} +2.32359 q^{76} -7.42345 q^{78} +(4.27796 + 4.75115i) q^{79} +(-5.21319 - 2.32106i) q^{80} +(1.10160 - 10.4810i) q^{81} +(0.825799 + 0.175529i) q^{82} +(-0.0518648 - 0.159623i) q^{83} +(7.27404 + 3.17623i) q^{84} +(4.78309 - 3.47512i) q^{85} +(0.702539 + 0.780249i) q^{86} +(2.94490 + 5.10071i) q^{87} +(1.28442 - 2.22469i) q^{89} +(0.475488 - 1.46340i) q^{90} +(15.3234 + 3.14227i) q^{91} +(4.24350 + 3.08309i) q^{92} +(13.2429 + 2.81486i) q^{93} +(0.727861 - 0.808371i) q^{94} +(-0.552511 + 5.25679i) q^{95} +(1.14666 + 10.9098i) q^{96} +(3.00880 - 9.26014i) q^{97} +(3.75693 + 2.64799i) 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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