LMFDB - Embedded newform 847.2.n.d.632.2

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			632.2
Character	$\chi$	$=$	847.632
Dual form			847.2.n.d.130.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642272 + 0.136519i) q^{2} +(-0.199882 + 1.90175i) q^{3} +(-1.43322 - 0.638109i) q^{4} +(-2.38803 - 2.65217i) q^{5} +(-0.388004 + 1.19415i) q^{6} +(2.59182 + 0.531487i) q^{7} +(-1.89583 - 1.37740i) q^{8} +(-0.642272 - 0.136519i) q^{9} +O(q^{10})$	\(q+(0.642272 + 0.136519i) q^{2} +(-0.199882 + 1.90175i) q^{3} +(-1.43322 - 0.638109i) q^{4} +(-2.38803 - 2.65217i) q^{5} +(-0.388004 + 1.19415i) q^{6} +(2.59182 + 0.531487i) q^{7} +(-1.89583 - 1.37740i) q^{8} +(-0.642272 - 0.136519i) q^{9} +(-1.17169 - 2.02943i) q^{10} +(1.50000 - 2.59808i) q^{12} +(1.82698 + 5.62286i) q^{13} +(1.59209 + 0.695192i) q^{14} +(5.52110 - 4.01132i) q^{15} +(1.06993 + 1.18828i) q^{16} +(-1.62042 + 0.344431i) q^{17} +(-0.393875 - 0.175365i) q^{18} +(-1.35303 + 0.602409i) q^{19} +(1.73018 + 5.32495i) q^{20} +(-1.52882 + 4.82277i) q^{21} +(-1.67169 + 2.89545i) q^{23} +(2.99843 - 3.33009i) q^{24} +(-0.808704 + 7.69431i) q^{25} +(0.405789 + 3.86082i) q^{26} +(-1.38473 + 4.26176i) q^{27} +(-3.37549 - 2.41560i) q^{28} +(2.49183 - 1.81042i) q^{29} +(4.09367 - 1.82262i) q^{30} +(-4.73749 + 5.26152i) q^{31} +(2.86834 + 4.96812i) q^{32} -1.08777 q^{34} +(-4.77974 - 8.14315i) q^{35} +(0.833400 + 0.605500i) q^{36} +(0.471551 + 4.48650i) q^{37} +(-0.951255 + 0.202195i) q^{38} +(-11.0585 + 2.35055i) q^{39} +(0.874189 + 8.31735i) q^{40} +(-1.04019 - 0.755743i) q^{41} +(-1.64031 + 2.88881i) q^{42} -1.59899 q^{43} +(1.17169 + 2.02943i) q^{45} +(-1.46896 + 1.63145i) q^{46} +(-1.51340 + 0.673808i) q^{47} +(-2.47368 + 1.79723i) q^{48} +(6.43504 + 2.75503i) q^{49} +(-1.56983 + 4.83143i) q^{50} +(-0.331129 - 3.15048i) q^{51} +(0.969543 - 9.22459i) q^{52} +(6.17304 - 6.85586i) q^{53} +(-1.47118 + 2.54817i) q^{54} +(-4.18158 - 4.57759i) q^{56} +(-0.875186 - 2.69355i) q^{57} +(1.84759 - 0.822598i) q^{58} +(8.08666 + 3.60041i) q^{59} +(-10.4726 + 2.22602i) q^{60} +(4.47432 + 4.96923i) q^{61} +(-3.76105 + 2.73256i) q^{62} +(-1.59209 - 0.695192i) q^{63} +(0.175784 + 0.541008i) q^{64} +(10.5499 - 18.2730i) q^{65} +(4.91223 + 8.50823i) q^{67} +(2.54219 + 0.540360i) q^{68} +(-5.17229 - 3.75789i) q^{69} +(-1.95819 - 5.88264i) q^{70} +(-2.66335 + 8.19694i) q^{71} +(1.02960 + 1.14349i) q^{72} +(-4.16681 - 1.85519i) q^{73} +(-0.309630 + 2.94593i) q^{74} +(-14.4710 - 3.07591i) q^{75} +2.32359 q^{76} -7.42345 q^{78} +(-6.25360 - 1.32924i) q^{79} +(0.596497 - 5.67529i) q^{80} +(-9.62759 - 4.28648i) q^{81} +(-0.564912 - 0.627399i) q^{82} +(-0.0518648 + 0.159623i) q^{83} +(5.26857 - 5.93651i) q^{84} +(4.78309 + 3.47512i) q^{85} +(-1.02698 - 0.218292i) q^{86} +(2.94490 + 5.10071i) q^{87} +(1.28442 - 2.22469i) q^{89} +(0.475488 + 1.46340i) q^{90} +(1.74672 + 15.5445i) q^{91} +(4.24350 - 3.08309i) q^{92} +(-9.05917 - 10.0612i) q^{93} +(-1.06400 + 0.226160i) q^{94} +(4.82877 + 2.14991i) q^{95} +(-10.0215 + 4.46184i) 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 $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.642272	+	0.136519i	0.454155	+	0.0965336i	0.429309	−	0.903158i	$-0.358757\pi$
$2$	0.642272	+	0.136519i	0.454155	+	0.0965336i	0.0248458	+	0.999691i	$0.492091\pi$
$3$	−0.199882	+	1.90175i	−0.115402	+	1.09798i	0.771567	+	0.636149i	$0.219473\pi$
$3$	−0.199882	+	1.90175i	−0.115402	+	1.09798i	−0.886969	+	0.461829i	$0.847193\pi$
$4$	−1.43322	−	0.638109i	−0.716608	−	0.319054i
$5$	−2.38803	−	2.65217i	−1.06796	−	1.18609i	−0.981822	−	0.189804i	$-0.939215\pi$
$5$	−2.38803	−	2.65217i	−1.06796	−	1.18609i	−0.0861359	−	0.996283i	$-0.527452\pi$
$6$	−0.388004	+	1.19415i	−0.158402	+	0.487512i
$7$	2.59182	+	0.531487i	0.979615	+	0.200883i
$7$	2.59182	+	0.531487i	0.979615	+	0.200883i
$8$	−1.89583	−	1.37740i	−0.670279	−	0.486986i
$9$	−0.642272	−	0.136519i	−0.214091	−	0.0455064i
$10$	−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	0.797872	+	0.602827i	$0.205959\pi$
$13$	1.82698	+	5.62286i	0.506713	+	1.55950i	−0.291159	+	0.956675i	$0.594041\pi$
$14$	1.59209	+	0.695192i	0.425505	+	0.185798i
$15$	5.52110	−	4.01132i	1.42554	−	1.03572i
$16$	1.06993	+	1.18828i	0.267483	+	0.297070i
$17$	−1.62042	+	0.344431i	−0.393009	+	0.0835367i	−0.400178	−	0.916438i	$-0.631052\pi$
$17$	−1.62042	+	0.344431i	−0.393009	+	0.0835367i	0.00716826	+	0.999974i	$0.497718\pi$
$18$	−0.393875	−	0.175365i	−0.0928373	−	0.0413338i
$19$	−1.35303	+	0.602409i	−0.310407	+	0.138202i	−0.556027	−	0.831164i	$-0.687675\pi$
$19$	−1.35303	+	0.602409i	−0.310407	+	0.138202i	0.245620	+	0.969366i	$0.421008\pi$
$20$	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	$0.280000\pi$
$24$	2.99843	−	3.33009i	0.612051	−	0.679752i
$25$	−0.808704	+	7.69431i	−0.161741	+	1.53886i
$26$	0.405789	+	3.86082i	0.0795818	+	0.757170i
$27$	−1.38473	+	4.26176i	−0.266491	+	0.820176i
$28$	−3.37549	−	2.41560i	−0.637907	−	0.456505i
$29$	2.49183	−	1.81042i	0.462721	−	0.336186i	−0.331877	−	0.943323i	$-0.607682\pi$
$29$	2.49183	−	1.81042i	0.462721	−	0.336186i	0.794598	+	0.607136i	$0.207682\pi$
$30$	4.09367	−	1.82262i	0.747398	−	0.332763i
$31$	−4.73749	+	5.26152i	−0.850878	+	0.944996i	−0.999033	−	0.0439682i	$-0.986000\pi$
$31$	−4.73749	+	5.26152i	−0.850878	+	0.944996i	0.148155	+	0.988964i	$0.452667\pi$
$32$	2.86834	+	4.96812i	0.507056	+	0.878247i
$33$		0			0
$34$	−1.08777			−0.186551
$35$	−4.77974	−	8.14315i	−0.807923	−	1.37644i
$36$	0.833400	+	0.605500i	0.138900	+	0.100917i
$37$	0.471551	+	4.48650i	0.0775224	+	0.737577i	0.962379	+	0.271712i	$0.0875899\pi$
$37$	0.471551	+	4.48650i	0.0775224	+	0.737577i	−0.884856	+	0.465864i	$0.845743\pi$
$38$	−0.951255	+	0.202195i	−0.154314	+	0.0328004i
$39$	−11.0585	+	2.35055i	−1.77077	+	0.376390i
$40$	0.874189	+	8.31735i	0.138221	+	1.31509i
$41$	−1.04019	−	0.755743i	−0.162451	−	0.118027i	0.503590	−	0.863943i	$-0.332012\pi$
$41$	−1.04019	−	0.755743i	−0.162451	−	0.118027i	−0.666041	+	0.745916i	$0.732012\pi$
$42$	−1.64031	+	2.88881i	−0.253106	+	0.445754i
$43$	−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
$46$	−1.46896	+	1.63145i	−0.216587	+	0.240544i
$47$	−1.51340	+	0.673808i	−0.220752	+	0.0982850i	−0.514133	−	0.857711i	$-0.671886\pi$
$47$	−1.51340	+	0.673808i	−0.220752	+	0.0982850i	0.293381	+	0.955996i	$0.405220\pi$
$48$	−2.47368	+	1.79723i	−0.357044	+	0.259408i
$49$	6.43504	+	2.75503i	0.919292	+	0.393576i
$50$	−1.56983	+	4.83143i	−0.222007	+	0.683268i
$51$	−0.331129	−	3.15048i	−0.0463674	−	0.441156i
$52$	0.969543	−	9.22459i	0.134451	−	1.27922i
$53$	6.17304	−	6.85586i	0.847933	−	0.941725i	−0.150971	−	0.988538i	$-0.548240\pi$
$53$	6.17304	−	6.85586i	0.847933	−	0.941725i	0.998904	+	0.0468134i	$0.0149066\pi$
$54$	−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
$58$	1.84759	−	0.822598i	0.242600	−	0.108012i
$59$	8.08666	+	3.60041i	1.05279	+	0.468734i	0.858822	−	0.512273i	$-0.171197\pi$
$59$	8.08666	+	3.60041i	1.05279	+	0.468734i	0.193971	+	0.981007i	$0.437863\pi$
$60$	−10.4726	+	2.22602i	−1.35200	+	0.287378i
$61$	4.47432	+	4.96923i	0.572877	+	0.636245i	0.958050	−	0.286600i	$-0.0925249\pi$
$61$	4.47432	+	4.96923i	0.572877	+	0.636245i	−0.385173	+	0.922844i	$0.625858\pi$
$62$	−3.76105	+	2.73256i	−0.477654	+	0.347036i
$63$	−1.59209	−	0.695192i	−0.200585	−	0.0875859i
$64$	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	$0.628451\pi$
$68$	2.54219	+	0.540360i	0.308286	+	0.0655283i
$69$	−5.17229	−	3.75789i	−0.622671	−	0.452397i
$70$	−1.95819	−	5.88264i	−0.234049	−	0.703110i
$71$	−2.66335	+	8.19694i	−0.316081	+	0.972798i	0.659226	+	0.751945i	$0.270884\pi$
$71$	−2.66335	+	8.19694i	−0.316081	+	0.972798i	−0.975307	+	0.220853i	$0.929116\pi$
$72$	1.02960	+	1.14349i	0.121339	+	0.134761i
$73$	−4.16681	−	1.85519i	−0.487689	−	0.217133i	0.148135	−	0.988967i	$-0.452673\pi$
$73$	−4.16681	−	1.85519i	−0.487689	−	0.217133i	−0.635824	+	0.771834i	$0.719340\pi$
$74$	−0.309630	+	2.94593i	−0.0359937	+	0.342457i
$75$	−14.4710	−	3.07591i	−1.67097	−	0.355176i
$76$	2.32359			0.266534
$77$		0			0
$78$	−7.42345			−0.840540
$79$	−6.25360	−	1.32924i	−0.703585	−	0.149552i	−0.157793	−	0.987472i	$-0.550438\pi$
$79$	−6.25360	−	1.32924i	−0.703585	−	0.149552i	−0.545792	+	0.837921i	$0.683771\pi$
$80$	0.596497	−	5.67529i	0.0666904	−	0.634516i
$81$	−9.62759	−	4.28648i	−1.06973	−	0.476276i
$82$	−0.564912	−	0.627399i	−0.0623841	−	0.0692846i
$83$	−0.0518648	+	0.159623i	−0.00569290	+	0.0175209i	−0.953863	−	0.300243i	$-0.902932\pi$
$83$	−0.0518648	+	0.159623i	−0.00569290	+	0.0175209i	0.948170	+	0.317764i	$0.102932\pi$
$84$	5.26857	−	5.93651i	0.574848	−	0.647726i
$85$	4.78309	+	3.47512i	0.518799	+	0.376930i
$86$	−1.02698	−	0.218292i	−0.110743	−	0.0235391i
$87$	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
$91$	1.74672	+	15.5445i	0.183106	+	1.62950i
$92$	4.24350	−	3.08309i	0.442416	−	0.321434i
$93$	−9.05917	−	10.0612i	−0.939392	−	1.04330i
$94$	−1.06400	+	0.226160i	−0.109743	+	0.0233267i
$95$	4.82877	+	2.14991i	0.495421	+	0.220576i
$96$	−10.0215	+	4.46184i	−1.02281	+	0.455385i
$97$	3.00880	+	9.26014i	0.305498	+	0.940225i	0.979491	+	0.201488i	$0.0645776\pi$
$97$	3.00880	+	9.26014i	0.305498	+	0.940225i	−0.673994	+	0.738737i	$0.735422\pi$
$98$	3.75693	+	2.64799i	0.379507	+	0.267487i
$99$		0			0
$100$	6.06885	−	10.5116i	0.606885	−	1.05116i
$101$	−1.24097	+	1.37823i	−0.123481	+	0.137139i	−0.801715	−	0.597706i	$-0.796079\pi$
$101$	−1.24097	+	1.37823i	−0.123481	+	0.137139i	0.678234	+	0.734846i	$0.262746\pi$
$102$	0.217426	−	2.06867i	0.0215284	−	0.204829i
$103$	0.331129	+	3.15048i	0.0326271	+	0.310426i	0.998649	+	0.0519656i	$0.0165486\pi$
$103$	0.331129	+	3.15048i	0.0326271	+	0.310426i	−0.966022	+	0.258461i	$0.916785\pi$
$104$	4.28131	−	13.1765i	0.419817	−	1.29206i
$105$	16.4417	−	7.46221i	1.60454	−	0.728237i
$106$	4.90073	−	3.56059i	0.476001	−	0.345835i
$107$	4.35471	−	1.93884i	0.420986	−	0.187435i	−0.185300	−	0.982682i	$-0.559326\pi$
$107$	4.35471	−	1.93884i	0.420986	−	0.187435i	0.606285	+	0.795247i	$0.292659\pi$
$108$	4.70408	−	5.22441i	0.452650	−	0.502719i
$109$	−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
$112$	2.14151	+	3.64846i	0.202354	+	0.344747i
$113$	−10.0668	−	7.31395i	−0.947004	−	0.688039i	0.00309244	−	0.999995i	$-0.499016\pi$
$113$	−10.0668	−	7.31395i	−0.947004	−	0.688039i	−0.950096	+	0.311957i	$0.899016\pi$
$114$	−0.194387	−	1.84947i	−0.0182060	−	0.173219i
$115$	11.6713	−	2.48081i	1.08835	−	0.231336i
$116$	−4.72657	+	1.00466i	−0.438851	+	0.0932806i
$117$	−0.405789	−	3.86082i	−0.0375152	−	0.356933i
$118$	4.70231	+	3.41643i	0.432883	+	0.314508i
$119$	−4.38289	+	0.0314702i	−0.401779	+	0.00288487i
$120$	−15.9923			−1.45989
$121$		0			0
$122$	2.19533	+	3.80243i	0.198756	+	0.344255i
$123$	1.64515	−	1.82713i	0.148339	−	0.164747i
$124$	10.1473	−	4.51785i	0.911251	−	0.405715i
$125$	7.90153	−	5.74080i	0.706734	−	0.513472i
$126$	−0.927650	−	0.663853i	−0.0826416	−	0.0591407i
$127$	2.04613	−	6.29735i	0.181565	−	0.558799i	−0.818307	−	0.574781i	$-0.805087\pi$
$127$	2.04613	−	6.29735i	0.181565	−	0.558799i	0.999872	+	0.0159816i	$0.00508731\pi$
$128$	−1.16025	−	11.0391i	−0.102553	−	0.975723i
$129$	0.319610	−	3.04088i	0.0281401	−	0.267735i
$130$	9.27053	−	10.2960i	0.813080	−	0.903016i
$131$	−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
$135$	14.6097	−	6.50465i	1.25740	−	0.559831i
$136$	3.54647	+	1.57899i	0.304107	+	0.135397i
$137$	7.26123	−	1.54342i	0.620368	−	0.131863i	0.113003	−	0.993595i	$-0.463953\pi$
$137$	7.26123	−	1.54342i	0.620368	−	0.131863i	0.507365	+	0.861731i	$0.330620\pi$
$138$	−2.80899	−	3.11970i	−0.239118	−	0.265567i
$139$	−8.75717	+	6.36246i	−0.742774	+	0.539657i	−0.893578	−	0.448907i	$-0.851813\pi$
$139$	−8.75717	+	6.36246i	−0.742774	+	0.539657i	0.150805	+	0.988564i	$0.451813\pi$
$140$	1.65418	+	14.7209i	0.139803	+	1.24414i
$141$	−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
$145$	−10.7521	−	2.28543i	−0.892912	−	0.189794i
$146$	−2.42296	−	1.76038i	−0.200525	−	0.145690i
$147$	−6.52565	+	11.6872i	−0.538227	+	0.963943i
$148$	2.18704	−	6.73103i	0.179774	−	0.553287i
$149$	0.669131	+	0.743145i	0.0548173	+	0.0608808i	0.769930	−	0.638129i	$-0.220291\pi$
$149$	0.669131	+	0.743145i	0.0548173	+	0.0608808i	−0.715112	+	0.699009i	$0.753625\pi$
$150$	−8.87441	−	3.95114i	−0.724593	−	0.322609i
$151$	1.71672	−	16.3335i	0.139705	−	1.32920i	−0.670000	−	0.742361i	$-0.733706\pi$
$151$	1.71672	−	16.3335i	0.139705	−	1.32920i	0.809704	−	0.586838i	$-0.199628\pi$
$152$	3.39489	+	0.721605i	0.275362	+	0.0585299i
$153$	1.08777			0.0879411
$154$		0			0
$155$	25.2677			2.02955
$156$	17.3491	+	3.68766i	1.38904	+	0.295249i
$157$	1.19695	−	11.3882i	0.0955269	−	0.908878i	−0.836860	−	0.547417i	$-0.815611\pi$
$157$	1.19695	−	11.3882i	0.0955269	−	0.908878i	0.932387	−	0.361461i	$-0.117722\pi$
$158$	−3.83504	−	1.70747i	−0.305100	−	0.135839i
$159$	11.8043	+	13.1100i	0.936140	+	1.03969i
$160$	6.32662	−	19.4713i	0.500163	−	1.53934i
$161$	−5.87161	+	6.61600i	−0.462748	+	0.521414i
$162$	−5.59834	−	4.06743i	−0.439847	−	0.319568i
$163$	8.74437	+	1.85867i	0.684912	+	0.145582i	0.537209	−	0.843449i	$-0.319479\pi$
$163$	8.74437	+	1.85867i	0.684912	+	0.145582i	0.147703	+	0.989032i	$0.452812\pi$
$164$	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	0.892438	+	0.451170i	$0.148993\pi$
$167$	5.62960	+	17.3261i	0.435631	+	1.34074i	−0.456807	+	0.889566i	$0.651007\pi$
$168$	9.54128	−	7.03736i	0.736126	−	0.542944i
$169$	−17.7615	+	12.9045i	−1.36627	+	0.992654i
$170$	2.59763	+	2.88496i	0.199229	+	0.221266i
$171$	0.951255	−	0.202195i	0.0727443	−	0.0154623i
$172$	2.29169	+	1.02033i	0.174740	+	0.0777993i
$173$	−17.8700	+	7.95623i	−1.35863	+	0.604901i	−0.951268	−	0.308365i	$-0.900218\pi$
$173$	−17.8700	+	7.95623i	−1.35863	+	0.604901i	−0.407363	+	0.913267i	$0.633551\pi$
$174$	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
$178$	1.12866	−	1.25351i	0.0845968	−	0.0939543i
$179$	−0.339499	+	3.23011i	−0.0253753	+	0.241430i	0.974481	+	0.224471i	$0.0720653\pi$
$179$	−0.339499	+	3.23011i	−0.0253753	+	0.241430i	−0.999856	+	0.0169594i	$0.994601\pi$
$180$	−0.384290	−	3.65627i	−0.0286432	−	0.272522i
$181$	−3.19546	+	9.83462i	−0.237517	+	0.731002i	0.759261	+	0.650787i	$0.225561\pi$
$181$	−3.19546	+	9.83462i	−0.237517	+	0.731002i	−0.996778	+	0.0802152i	$0.974439\pi$
$182$	−1.00025	+	10.2222i	−0.0741432	+	0.757722i
$183$	−10.3446	+	7.51578i	−0.764694	+	0.555583i
$184$	7.15745	−	3.18670i	0.527654	−	0.234927i
$185$	10.7729	−	11.9645i	0.792040	−	0.879649i
$186$	−4.44490	−	7.69879i	−0.325916	−	0.564502i
$187$		0			0
$188$	2.59899			0.189551
$189$	−5.85404	+	10.3097i	−0.425818	+	0.749923i
$190$	2.80788	+	2.04004i	0.203705	+	0.148000i
$191$	−1.04763	−	9.96753i	−0.0758038	−	0.721225i	−0.964742	−	0.263198i	$-0.915223\pi$
$191$	−1.04763	−	9.96753i	−0.0758038	−	0.721225i	0.888938	−	0.458027i	$-0.151444\pi$
$192$	−1.06400	+	0.226160i	−0.0767876	+	0.0163217i
$193$	24.7719	−	5.26543i	1.78312	−	0.379014i	0.806036	−	0.591866i	$-0.201609\pi$
$193$	24.7719	−	5.26543i	1.78312	−	0.379014i	0.977084	+	0.212852i	$0.0682752\pi$
$194$	0.668283	+	6.35828i	0.0479799	+	0.456498i
$195$	32.6420	+	23.7158i	2.33754	+	1.69833i
$196$	−7.46479	−	8.05482i	−0.533199	−	0.575344i
$197$	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	$0.896836\pi$
$200$	12.1313	−	13.4732i	0.857815	−	0.952700i
$201$	−17.1624	+	7.64121i	−1.21054	+	0.538969i
$202$	−0.985194	+	0.715785i	−0.0693180	+	0.0503625i
$203$	7.42058	−	3.36790i	0.520822	−	0.236380i
$204$	−1.53577	+	4.72662i	−0.107526	+	0.330930i
$205$	0.479643	+	4.56350i	0.0334997	+	0.318729i
$206$	−0.217426	+	2.06867i	−0.0151488	+	0.144131i
$207$	1.46896	−	1.63145i	0.102100	−	0.113394i
$208$	−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	−0.993346	−	0.115170i	$-0.963259\pi$
$211$	−3.73906	−	11.5076i	−0.257408	−	0.792219i	0.735938	−	0.677049i	$-0.236741\pi$
$212$	−13.2221	+	5.88685i	−0.908097	+	0.404311i
$213$	−15.0562	−	6.70346i	−1.03163	−	0.459313i
$214$	3.06160	−	0.650763i	0.209287	−	0.0444852i
$215$	3.81843	+	4.24079i	0.260415	+	0.289220i
$216$	8.49538	−	6.17226i	0.578037	−	0.419969i
$217$	−15.0751	+	11.1190i	−1.02337	+	0.754805i
$218$	−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
$222$	−5.54055	−	1.17768i	−0.371857	−	0.0790407i
$223$	−12.6421	−	9.18502i	−0.846577	−	0.615074i	0.0776232	−	0.996983i	$-0.475267\pi$
$223$	−12.6421	−	9.18502i	−0.846577	−	0.615074i	−0.924200	+	0.381909i	$0.875267\pi$
$224$	4.79374	+	14.4009i	0.320295	+	0.962204i
$225$	1.56983	−	4.83143i	0.104655	−	0.322095i
$226$	−5.46712	−	6.07185i	−0.363667	−	0.403894i
$227$	14.3141	+	6.37304i	0.950059	+	0.422993i	0.822454	−	0.568832i	$-0.192604\pi$
$227$	14.3141	+	6.37304i	0.950059	+	0.422993i	0.127605	+	0.991825i	$0.459271\pi$
$228$	−0.464445	+	4.41890i	−0.0307586	+	0.292649i
$229$	5.44974	+	1.15838i	0.360129	+	0.0765478i	0.384423	−	0.923157i	$-0.374400\pi$
$229$	5.44974	+	1.15838i	0.360129	+	0.0765478i	−0.0242938	+	0.999705i	$0.507734\pi$
$230$	7.83481			0.516612
$231$		0			0
$232$	−7.21777			−0.473870
$233$	−18.8542	−	4.00758i	−1.23518	−	0.262545i	−0.456360	−	0.889795i	$-0.650847\pi$
$233$	−18.8542	−	4.00758i	−1.23518	−	0.262545i	−0.778818	+	0.627250i	$0.784181\pi$
$234$	0.266449	−	2.53510i	0.0174183	−	0.165724i
$235$	5.40109	+	2.40472i	0.352328	+	0.156867i
$236$	−9.29247	−	10.3203i	−0.604888	−	0.671797i
$237$	3.77788	−	11.6271i	0.245400	−	0.755262i
$238$	−2.81930	−	0.578136i	−0.182748	−	0.0374750i
$239$	−17.9258	−	13.0238i	−1.15952	−	0.842443i	−0.169805	−	0.985478i	$-0.554314\pi$
$239$	−17.9258	−	13.0238i	−1.15952	−	0.842443i	−0.989718	+	0.143035i	$0.954314\pi$
$240$	10.6738	+	2.26878i	0.688989	+	0.146449i
$241$	−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
$245$	−8.06023	−	23.6459i	−0.514949	−	1.51068i
$246$	1.30607	−	0.948918i	0.0832722	−	0.0605008i
$247$	−5.85923	−	6.50733i	−0.372814	−	0.414052i
$248$	16.2287	−	3.44952i	1.03053	−	0.219045i
$249$	−0.293197	−	0.130540i	−0.0185806	−	0.00827263i
$250$	5.85866	−	2.60844i	0.370534	−	0.164972i
$251$	6.83161	+	21.0255i	0.431208	+	1.32712i	0.896923	+	0.442186i	$0.145797\pi$
$251$	6.83161	+	21.0255i	0.431208	+	1.32712i	−0.465716	+	0.884934i	$0.654203\pi$
$252$	1.83821	+	2.01229i	0.115796	+	0.126762i
$253$		0			0
$254$	2.17388	−	3.76527i	0.136401	−	0.236254i
$255$	−7.56488	+	8.40165i	−0.473731	+	0.526132i
$256$	0.880766	−	8.37993i	0.0550479	−	0.523746i
$257$	−3.04383	−	28.9601i	−0.189869	−	1.80648i	−0.511142	−	0.859496i	$-0.670777\pi$
$257$	−3.04383	−	28.9601i	−0.189869	−	1.80648i	0.321273	−	0.946987i	$-0.395889\pi$
$258$	0.620415	−	1.90944i	0.0386253	−	0.118877i
$259$	−1.16234	+	11.8788i	−0.0722246	+	0.738114i
$260$	−26.7805	+	19.4572i	−1.66086	+	1.20668i
$261$	−1.84759	+	0.822598i	−0.114363	+	0.0509176i
$262$	−2.66151	+	2.95591i	−0.164429	+	0.182617i
$263$	−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
$266$	−2.57294	+	0.0184744i	−0.157757	+	0.00113274i
$267$	3.97408	+	2.88734i	0.243210	+	0.176702i
$268$	−1.61111	−	15.3287i	−0.0984140	−	0.936347i
$269$	−1.66926	+	0.354811i	−0.101776	+	0.0216332i	−0.258518	−	0.966006i	$-0.583234\pi$
$269$	−1.66926	+	0.354811i	−0.101776	+	0.0216332i	0.156742	+	0.987640i	$0.449901\pi$
$270$	10.2714	−	2.18325i	0.625097	−	0.132869i
$271$	−2.14580	−	20.4159i	−0.130348	−	1.24018i	−0.842711	−	0.538367i	$-0.819042\pi$
$271$	−2.14580	−	20.4159i	−0.130348	−	1.24018i	0.712363	−	0.701811i	$-0.247625\pi$
$272$	−2.14302	−	1.55699i	−0.129940	−	0.0944066i
$273$	−29.9109	+	0.214767i	−1.81029	+	0.0129983i
$274$	4.87439			0.294472
$275$		0			0
$276$	5.01507	+	8.68635i	0.301872	+	0.522857i
$277$	17.8397	−	19.8130i	1.07188	−	1.19045i	0.0909998	−	0.995851i	$-0.470994\pi$
$277$	17.8397	−	19.8130i	1.07188	−	1.19045i	0.980883	−	0.194596i	$-0.0623396\pi$
$278$	−6.49308	+	2.89091i	−0.389429	+	0.173385i
$279$	3.76105	−	2.73256i	0.225168	−	0.163594i
$280$	−2.15483	+	22.0217i	−0.128775	+	1.31605i
$281$	−4.86528	+	14.9738i	−0.290239	+	0.893262i	0.694541	+	0.719453i	$0.255608\pi$
$281$	−4.86528	+	14.9738i	−0.290239	+	0.893262i	−0.984779	+	0.173809i	$0.944392\pi$
$282$	−0.217426	−	2.06867i	−0.0129475	−	0.123188i
$283$	−1.67974	+	15.9817i	−0.0998504	+	0.950013i	0.823827	+	0.566841i	$0.191835\pi$
$283$	−1.67974	+	15.9817i	−0.0998504	+	0.950013i	−0.923677	+	0.383171i	$0.874832\pi$
$284$	9.04769	−	10.0485i	0.536882	−	0.596268i
$285$	−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
$289$	−13.0231	+	5.79828i	−0.766067	+	0.341075i
$290$	−6.59376	−	2.93573i	−0.387199	−	0.172392i
$291$	−18.2119	+	3.87106i	−1.06760	+	0.226926i
$292$	4.78813	+	5.31776i	0.280204	+	0.311198i
$293$	12.4068	−	9.01408i	0.724814	−	0.526608i	−0.163104	−	0.986609i	$-0.552151\pi$
$293$	12.4068	−	9.01408i	0.724814	−	0.526608i	0.887919	+	0.460000i	$0.152151\pi$
$294$	−5.78676	+	6.61547i	−0.337491	+	0.385822i
$295$	−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
$299$	−19.3349	−	4.10975i	−1.11816	−	0.237673i
$300$	18.7773	+	13.6425i	1.08411	+	0.787652i
$301$	−4.14429	−	0.849841i	−0.238873	−	0.0489840i
$302$	3.33243	−	10.2562i	0.191760	−	0.590176i
$303$	−2.37301	−	2.63550i	−0.136326	−	0.151406i
$304$	−2.16348	−	0.963245i	−0.124084	−	0.0552459i
$305$	2.49447	−	23.7333i	0.142833	−	1.35897i
$306$	0.698644	+	0.148501i	0.0399388	+	0.00848926i
$307$	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
$310$	16.2287	+	3.44952i	0.921730	+	0.195920i
$311$	−2.26086	+	21.5106i	−0.128202	+	1.21976i	0.721471	+	0.692445i	$0.243467\pi$
$311$	−2.26086	+	21.5106i	−0.128202	+	1.21976i	−0.849672	+	0.527311i	$0.823200\pi$
$312$	24.2027	+	10.7757i	1.37021	+	0.610056i
$313$	10.9659	+	12.1788i	0.619828	+	0.688389i	0.968545	−	0.248839i	$-0.0800491\pi$
$313$	10.9659	+	12.1788i	0.619828	+	0.688389i	−0.348717	+	0.937228i	$0.613382\pi$
$314$	2.32347	−	7.15092i	0.131121	−	0.403550i
$315$	1.95819	+	5.88264i	0.110332	+	0.331449i
$316$	8.11455	+	5.89557i	0.456479	+	0.331652i
$317$	−4.36380	−	0.927554i	−0.245095	−	0.0520966i	0.0837258	−	0.996489i	$-0.473318\pi$
$317$	−4.36380	−	0.927554i	−0.245095	−	0.0520966i	−0.328821	+	0.944392i	$0.606651\pi$
$318$	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
$322$	−4.67438	+	3.44768i	−0.260493	+	0.192132i
$323$	1.98499	−	1.44218i	0.110448	−	0.0802451i
$324$	11.0632	+	12.2869i	0.614621	+	0.682605i
$325$	−44.7415	+	9.51010i	−2.48181	+	0.527526i
$326$	5.36252	+	2.38755i	0.297002	+	0.132234i
$327$	25.9976	−	11.5749i	1.43767	−	0.640093i
$328$	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	$0.991384\pi$
$332$	0.176190	−	0.195679i	0.00966971	−	0.0107393i
$333$	0.309630	−	2.94593i	0.0169676	−	0.161436i
$334$	1.25039	+	11.8966i	0.0684181	+	0.650955i
$335$	10.8348	−	33.3460i	0.591966	−	1.82188i
$336$	−7.36652	+	3.34337i	−0.401877	+	0.182396i
$337$	21.8554	−	15.8789i	1.19054	−	0.864977i	0.197217	−	0.980360i	$-0.436810\pi$
$337$	21.8554	−	15.8789i	1.19054	−	0.864977i	0.993321	+	0.115383i	$0.0368096\pi$
$338$	−13.1694	+	5.86341i	−0.716323	+	0.318928i
$339$	15.9215	−	17.6826i	0.864738	−	0.960388i
$340$	−4.63770	−	8.03273i	−0.251515	−	0.435636i
$341$		0			0
$342$	0.638568			0.0345298
$343$	15.2142	+	10.5607i	0.821489	+	0.570224i
$344$	3.03142	+	2.20245i	0.163443	+	0.118748i
$345$	2.38500	+	22.6918i	0.128404	+	1.22168i
$346$	−12.5636	+	2.67047i	−0.675422	+	0.143565i
$347$	−19.7760	+	4.20351i	−1.06163	+	0.225656i	−0.705449	−	0.708761i	$-0.749254\pi$
$347$	−19.7760	+	4.20351i	−1.06163	+	0.225656i	−0.356180	+	0.934417i	$0.615921\pi$
$348$	−0.965864	−	9.18958i	−0.0517757	−	0.492613i
$349$	−9.72635	−	7.06661i	−0.520640	−	0.378267i	0.296205	−	0.955124i	$-0.404279\pi$
$349$	−9.72635	−	7.06661i	−0.520640	−	0.378267i	−0.816845	+	0.576857i	$0.804279\pi$
$350$	−6.63655	+	11.6878i	−0.354738	+	0.624742i
$351$	−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	$0.740900\pi$
$354$	−7.43711	+	8.25975i	−0.395278	+	0.439001i
$355$	28.0999	−	12.5109i	1.49139	−	0.664008i
$356$	−3.26045	+	2.36886i	−0.172804	+	0.125549i
$357$	0.816214	−	8.34147i	0.0431986	−	0.441478i
$358$	−0.659022	+	2.02826i	−0.0348304	+	0.107197i
$359$	2.53901	+	24.1571i	0.134004	+	1.27496i	0.830345	+	0.557250i	$0.188144\pi$
$359$	2.53901	+	24.1571i	0.134004	+	1.27496i	−0.696341	+	0.717711i	$0.745190\pi$
$360$	0.574011	−	5.46135i	0.0302530	−	0.287838i
$361$	−11.2457	+	12.4896i	−0.591878	+	0.657347i
$362$	−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
$366$	−7.67008	+	3.41494i	−0.400922	+	0.178502i
$367$	9.90671	+	4.41075i	0.517126	+	0.230239i	0.648668	−	0.761071i	$-0.275326\pi$
$367$	9.90671	+	4.41075i	0.517126	+	0.230239i	−0.131542	+	0.991311i	$0.541993\pi$
$368$	−5.22920	+	1.11150i	−0.272591	+	0.0579410i
$369$	0.564912	+	0.627399i	0.0294082	+	0.0326611i
$370$	8.55252	−	6.21377i	0.444624	−	0.323038i
$371$	19.6432	−	14.4883i	1.01982	−	0.752193i
$372$	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
$376$	3.79726	+	0.807132i	0.195829	+	0.0416247i
$377$	14.7323	+	10.7036i	0.758749	+	0.551264i
$378$	−5.16736	+	5.82247i	−0.265780	+	0.299475i
$379$	−6.77737	+	20.8586i	−0.348130	+	1.07143i	0.611757	+	0.791046i	$0.290463\pi$
$379$	−6.77737	+	20.8586i	−0.348130	+	1.07143i	−0.959887	+	0.280388i	$0.909537\pi$
$380$	−5.54879	−	6.16256i	−0.284647	−	0.316133i
$381$	11.5670	+	5.14997i	0.592596	+	0.263841i
$382$	0.687895	−	6.54488i	0.0351958	−	0.334865i
$383$	−35.6662	−	7.58109i	−1.82246	−	0.387376i	−0.835650	−	0.549263i	$-0.814909\pi$
$383$	−35.6662	−	7.58109i	−1.82246	−	0.387376i	−0.986809	+	0.161887i	$0.948242\pi$
$384$	21.2255			1.08316
$385$		0			0
$386$	16.6291			0.846400
$387$	1.02698	+	0.218292i	0.0522046	+	0.0110964i
$388$	1.59671	−	15.1917i	0.0810609	−	0.771243i
$389$	17.7922	+	7.92161i	0.902102	+	0.401642i	0.804754	−	0.593609i	$-0.202297\pi$
$389$	17.7922	+	7.92161i	0.902102	+	0.401642i	0.0973481	+	0.995250i	$0.468964\pi$
$390$	17.7274	+	19.6883i	0.897661	+	0.996954i
$391$	1.71156	−	5.26763i	0.0865571	−	0.266395i
$392$	−8.40498	−	14.0867i	−0.424515	−	0.711488i
$393$	−9.37131	−	6.80866i	−0.472720	−	0.343451i
$394$	15.7876	+	3.35577i	0.795370	+	0.169061i
$395$	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
$399$	−0.836739	−	7.44633i	−0.0418893	−	0.372783i
$400$	−10.0082	+	7.27142i	−0.500412	+	0.363571i
$401$	−16.3575	−	18.1668i	−0.816854	−	0.907208i	0.180222	−	0.983626i	$-0.442318\pi$
$401$	−16.3575	−	18.1668i	−0.816854	−	0.907208i	−0.997076	+	0.0764178i	$0.975652\pi$
$402$	−12.0661	+	2.56473i	−0.601803	+	0.127917i
$403$	−38.2401	−	17.0256i	−1.90487	−	0.848105i
$404$	2.65804	−	1.18343i	0.132242	−	0.0588781i
$405$	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
$409$	1.57495	−	1.74916i	0.0778764	−	0.0864905i	−0.702947	−	0.711242i	$-0.748133\pi$
$409$	1.57495	−	1.74916i	0.0778764	−	0.0864905i	0.780824	+	0.624751i	$0.214800\pi$
$410$	−0.314944	+	2.99649i	−0.0155540	+	0.147986i
$411$	1.48382	+	14.1176i	0.0731913	+	0.696368i
$412$	1.53577	−	4.72662i	0.0756620	−	0.232864i
$413$	19.0456	+	13.6296i	0.937172	+	0.670667i
$414$	1.16620	−	0.847292i	0.0573155	−	0.0416421i
$415$	0.547203	−	0.243630i	0.0268611	−	0.0119594i
$416$	−22.6946	+	25.2050i	−1.11270	+	1.23577i
$417$	−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	$0.427127\pi$
$420$	−28.3261	+	0.203389i	−1.38217	+	0.00992434i
$421$	31.5775	+	22.9424i	1.53899	+	1.11814i	0.950964	+	0.309301i	$0.100095\pi$
$421$	31.5775	+	22.9424i	1.53899	+	1.11814i	0.588026	+	0.808842i	$0.299905\pi$
$422$	−0.830480	−	7.90149i	−0.0404271	−	0.384638i
$423$	1.06400	−	0.226160i	0.0517335	−	0.0109963i
$424$	−21.1464	+	4.49480i	−1.02696	+	0.218287i
$425$	−1.33972	−	12.7465i	−0.0649858	−	0.618298i
$426$	−8.75503	−	6.36090i	−0.424183	−	0.308187i
$427$	8.95553	+	15.2574i	0.433389	+	0.738356i
$428$	−7.47843			−0.361484
$429$		0			0
$430$	1.87352	+	3.24503i	0.0903491	+	0.156489i
$431$	2.54405	−	2.82545i	0.122543	−	0.136097i	−0.678751	−	0.734368i	$-0.737479\pi$
$431$	2.54405	−	2.82545i	0.122543	−	0.136097i	0.801294	+	0.598271i	$0.204145\pi$
$432$	−6.54573	+	2.91435i	−0.314932	+	0.140217i
$433$	−6.65045	+	4.83184i	−0.319600	+	0.232203i	−0.736005	−	0.676976i	$-0.763290\pi$
$433$	−6.65045	+	4.83184i	−0.319600	+	0.232203i	0.416405	+	0.909179i	$0.363290\pi$
$434$	−11.2003	+	5.08336i	−0.537631	+	0.244009i
$435$	6.49547	−	19.9910i	0.311434	−	0.958495i
$436$	2.44051	+	23.2199i	0.116879	+	1.11203i
$437$	0.517605	−	4.92468i	0.0247604	−	0.235579i
$438$	3.83212	−	4.25600i	0.183106	−	0.203360i
$439$	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
$443$	12.5561	−	5.59035i	0.596560	−	0.265605i	−0.0861655	−	0.996281i	$-0.527461\pi$
$443$	12.5561	−	5.59035i	0.596560	−	0.265605i	0.682725	+	0.730675i	$0.260795\pi$
$444$	12.3636	+	5.50463i	0.586751	+	0.261238i
$445$	−8.96750	+	1.90610i	−0.425100	+	0.0903578i
$446$	−6.86573	−	7.62516i	−0.325102	−	0.361062i
$447$	−1.54703	+	1.12398i	−0.0731718	+	0.0531624i
$448$	0.168062	+	1.49562i	0.00794018	+	0.0706615i
$449$	6.66432	+	20.5107i	0.314509	+	0.967959i	0.975956	+	0.217967i	$0.0699425\pi$
$449$	6.66432	+	20.5107i	0.314509	+	0.967959i	−0.661447	+	0.749992i	$0.730057\pi$
$450$	1.66784	−	2.88878i	0.0786226	−	0.136178i
$451$		0			0
$452$	9.76078	+	16.9062i	0.459109	+	0.795199i
$453$	30.7191	+	6.52955i	1.44331	+	0.306785i
$454$	8.32348	+	6.04737i	0.390640	+	0.283817i
$455$	37.0554	−	41.7532i	1.73718	−	1.95742i
$456$	−2.05089	+	6.31200i	−0.0960419	+	0.295587i
$457$	2.21184	+	2.45649i	0.103465	+	0.114910i	0.792653	−	0.609673i	$-0.208699\pi$
$457$	2.21184	+	2.45649i	0.103465	+	0.114910i	−0.689188	+	0.724583i	$0.742033\pi$
$458$	3.34208	+	1.48799i	0.156165	+	0.0695291i
$459$	0.775961	−	7.38278i	0.0362188	−	0.344599i
$460$	−18.3105	−	3.89201i	−0.853730	−	0.181466i
$461$	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	$0.456806\pi$
$464$	4.81737	+	1.02396i	0.223641	+	0.0475363i
$465$	−5.05057	+	48.0529i	−0.234214	+	2.22840i
$466$	−11.5624	−	5.14791i	−0.535618	−	0.238472i
$467$	−4.02464	−	4.46982i	−0.186238	−	0.206838i	0.642794	−	0.766039i	$-0.277775\pi$
$467$	−4.02464	−	4.46982i	−0.186238	−	0.206838i	−0.829033	+	0.559200i	$0.811108\pi$
$468$	−1.88204	+	5.79233i	−0.0869974	+	0.267751i
$469$	8.20959	+	24.6626i	0.379084	+	1.13881i
$470$	3.14068	+	2.28184i	0.144869	+	0.105253i
$471$	21.4183	+	4.55261i	0.986904	+	0.209773i
$472$	−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
$476$	6.30171	+	2.75166i	0.288838	+	0.126122i
$477$	−4.90073	+	3.56059i	−0.224389	+	0.163028i
$478$	−9.73522	−	10.8121i	−0.445279	−	0.494532i
$479$	16.7606	−	3.56258i	0.765812	−	0.162778i	0.191587	−	0.981476i	$-0.438637\pi$
$479$	16.7606	−	3.56258i	0.765812	−	0.162778i	0.574225	+	0.818697i	$0.305303\pi$
$480$	35.7651	+	15.9237i	1.63245	+	0.726812i
$481$	−24.3655	+	10.8482i	−1.11097	+	0.494636i
$482$	−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
$486$	2.94778	−	3.27385i	0.133714	−	0.148505i
$487$	−0.597302	+	5.68295i	−0.0270663	+	0.257519i	0.972618	+	0.232408i	$0.0746605\pi$
$487$	−0.597302	+	5.68295i	−0.0270663	+	0.257519i	−0.999685	+	0.0251108i	$0.992006\pi$
$488$	−1.63792	−	15.5838i	−0.0741452	−	0.705444i
$489$	−5.28258	+	16.2581i	−0.238887	+	0.735218i
$490$	−1.94873	−	16.2875i	−0.0880348	−	0.735794i
$491$	19.4709	−	14.1464i	0.878708	−	0.638418i	−0.0542017	−	0.998530i	$-0.517261\pi$
$491$	19.4709	−	14.1464i	0.878708	−	0.638418i	0.932909	+	0.360112i	$0.117261\pi$
$492$	−3.52377	+	1.56888i	−0.158864	+	0.0707307i
$493$	−3.41424	+	3.79190i	−0.153770	+	0.170778i
$494$	−2.87484	−	4.97937i	−0.129345	−	0.224032i
$495$		0			0
$496$	−11.3209			−0.508325
$497$	−11.2595	+	19.8295i	−0.505057	+	0.889473i
$498$	−0.170491	−	0.123869i	−0.00763990	−	0.00555071i
$499$	−1.12778	−	10.7302i	−0.0504866	−	0.480348i	−0.990329	−	0.138739i	$-0.955695\pi$
$499$	−1.12778	−	10.7302i	−0.0504866	−	0.480348i	0.939842	−	0.341608i	$-0.110972\pi$
$500$	−14.9878	+	3.18576i	−0.670277	+	0.142472i
$501$	−34.0753	+	7.24292i	−1.52237	+	0.323590i
$502$	1.51736	+	14.4368i	0.0677233	+	0.644344i
$503$	22.6623	+	16.4651i	1.01046	+	0.734142i	0.964305	−	0.264792i	$-0.0853034\pi$
$503$	22.6623	+	16.4651i	1.01046	+	0.734142i	0.0461544	+	0.998934i	$0.485303\pi$
$504$	2.06078	+	3.51092i	0.0917947	+	0.156389i
$505$	6.61878			0.294532
$506$		0			0
$507$	−20.9910	−	36.3574i	−0.932242	−	1.61469i
$508$	−6.95094	+	7.71980i	−0.308398	+	0.342511i
$509$	−1.74932	+	0.778850i	−0.0775375	+	0.0345219i	−0.445139	−	0.895462i	$-0.646846\pi$
$509$	−1.74932	+	0.778850i	−0.0775375	+	0.0345219i	0.367601	+	0.929983i	$0.380179\pi$
$510$	−6.00569	+	4.36339i	−0.265937	+	0.193214i
$511$	−9.81362	−	7.02291i	−0.434129	−	0.310675i
$512$	−5.15038	+	15.8512i	−0.227617	+	0.700532i
$513$	−0.693738	−	6.60047i	−0.0306293	−	0.291418i
$514$	1.99864	−	19.0158i	0.0881563	−	0.838751i
$515$	7.56488	−	8.40165i	0.333348	−	0.370221i
$516$	−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
$520$	−45.1702	+	20.1111i	−1.98085	+	0.881929i
$521$	1.44267	+	0.642318i	0.0632045	+	0.0281405i	0.438095	−	0.898928i	$-0.355653\pi$
$521$	1.44267	+	0.642318i	0.0632045	+	0.0281405i	−0.374891	+	0.927069i	$0.622320\pi$
$522$	−1.29895	+	0.276101i	−0.0568536	+	0.0120846i
$523$	6.00201	+	6.66591i	0.262450	+	0.291480i	0.859939	−	0.510397i	$-0.170502\pi$
$523$	6.00201	+	6.66591i	0.262450	+	0.291480i	−0.597489	+	0.801877i	$0.703835\pi$
$524$	7.68850	−	5.58603i	0.335874	−	0.244027i
$525$	−35.8715	−	15.6634i	−1.56556	−	0.683605i
$526$	−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
$530$	−21.1464	−	4.49480i	−0.918539	−	0.195241i
$531$	−4.70231	−	3.41643i	−0.204063	−	0.148260i
$532$	6.02232	+	1.23496i	0.261101	+	0.0535422i
$533$	2.34903	−	7.22958i	0.101748	−	0.313148i
$534$	2.15826	+	2.39699i	0.0933971	+	0.103728i
$535$	−15.5413	−	6.91944i	−0.671910	−	0.299153i
$536$	2.40650	−	22.8963i	0.103945	−	0.988970i
$537$	−6.07502	−	1.29129i	−0.262156	−	0.0557231i
$538$	−1.12055			−0.0483105
$539$		0			0
$540$	−25.0895			−1.07968
$541$	17.7069	+	3.76372i	0.761280	+	0.161815i	0.572163	−	0.820140i	$-0.306104\pi$
$541$	17.7069	+	3.76372i	0.761280	+	0.161815i	0.189116	+	0.981955i	$0.439438\pi$
$542$	1.40897	−	13.4055i	0.0605207	−	0.575816i
$543$	−18.0643	−	8.04275i	−0.775214	−	0.345147i
$544$	−6.35909	−	7.06249i	−0.272644	−	0.302802i
$545$	−16.4125	+	50.5125i	−0.703034	+	2.16372i
$546$	−19.2402	−	3.94546i	−0.823406	−	0.168850i
$547$	18.3554	+	13.3360i	0.784819	+	0.570205i	0.906422	−	0.422374i	$-0.138803\pi$
$547$	18.3554	+	13.3360i	0.784819	+	0.570205i	−0.121602	+	0.992579i	$0.538803\pi$
$548$	−11.3918	−	2.42140i	−0.486632	−	0.103437i
$549$	−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
$553$	−15.5017	−	6.76886i	−0.659200	−	0.287841i
$554$	14.1628	−	10.2899i	0.601719	−	0.437174i
$555$	20.6003	+	22.8789i	0.874433	+	0.971156i
$556$	16.6109	−	3.53075i	0.704457	−	0.149737i
$557$	−35.0395	−	15.6006i	−1.48467	−	0.661018i	−0.505272	−	0.862960i	$-0.668608\pi$
$557$	−35.0395	−	15.6006i	−1.48467	−	0.661018i	−0.979397	+	0.201942i	$0.935275\pi$
$558$	2.78866	−	1.24159i	0.118054	−	0.0525608i
$559$	−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
$563$	27.9522	−	31.0440i	1.17804	−	1.30835i	0.236432	−	0.971648i	$-0.424022\pi$
$563$	27.9522	−	31.0440i	1.17804	−	1.30835i	0.941611	−	0.336702i	$-0.109311\pi$
$564$	−0.519492	+	4.94264i	−0.0218746	+	0.208123i
$565$	4.64190	+	44.1648i	0.195286	+	1.85803i
$566$	−3.26066	+	10.0353i	−0.137056	+	0.421814i
$567$	−22.6748	−	16.2267i	−0.952250	−	0.681458i
$568$	16.3398	−	11.8715i	0.685602	−	0.498119i
$569$	10.8438	−	4.82797i	0.454595	−	0.202399i	−0.166648	−	0.986016i	$-0.553294\pi$
$569$	10.8438	−	4.82797i	0.454595	−	0.202399i	0.621244	+	0.783618i	$0.286628\pi$
$570$	−4.44091	+	4.93213i	−0.186009	+	0.206584i
$571$	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
$574$	−1.13070	−	1.92635i	−0.0471943	−	0.0804041i
$575$	−20.9266	−	15.2041i	−0.872699	−	0.634053i
$576$	−0.0390433	−	0.371472i	−0.00162680	−	0.0154780i
$577$	−28.0523	+	5.96271i	−1.16783	+	0.248231i	−0.750718	−	0.660622i	$-0.770293\pi$
$577$	−28.0523	+	5.96271i	−1.16783	+	0.248231i	−0.417116	+	0.908853i	$0.636959\pi$
$578$	−9.15597	+	1.94616i	−0.380838	+	0.0809497i
$579$	5.06209	+	48.1625i	0.210373	+	2.00157i
$580$	13.9517	+	10.1365i	0.579313	+	0.420896i
$581$	−0.219262	+	0.386149i	−0.00909651	+	0.0160202i
$582$	−12.2255			−0.506762
$583$		0			0
$584$	5.34425	+	9.25651i	0.221147	+	0.383037i
$585$	−9.27053	+	10.2960i	−0.383289	+	0.425686i
$586$	9.19915	−	4.09572i	0.380013	−	0.169193i
$587$	−0.818795	+	0.594889i	−0.0337953	+	0.0245537i	−0.604555	−	0.796564i	$-0.706649\pi$
$587$	−0.818795	+	0.594889i	−0.0337953	+	0.0245537i	0.570759	+	0.821117i	$0.306649\pi$
$588$	16.8104	−	12.5862i	0.693247	−	0.519045i
$589$	3.24039	−	9.97291i	0.133518	−	0.410927i
$590$	−2.16828	−	20.6298i	−0.0892669	−	0.849317i
$591$	−4.91330	+	46.7469i	−0.202106	+	1.92291i
$592$	−4.82670	+	5.36059i	−0.198376	+	0.220319i
$593$	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
$597$	9.76746	−	4.34875i	0.399756	−	0.177983i
$598$	−11.8572	−	5.27916i	−0.484876	−	0.215881i
$599$	25.9657	−	5.51917i	1.06093	−	0.225507i	0.355782	−	0.934569i	$-0.384215\pi$
$599$	25.9657	−	5.51917i	1.06093	−	0.225507i	0.705146	+	0.709062i	$0.250881\pi$
$600$	23.1979	+	25.7639i	0.947050	+	1.05181i
$601$	−9.83421	+	7.14497i	−0.401146	+	0.291449i	−0.770008	−	0.638035i	$-0.779748\pi$
$601$	−9.83421	+	7.14497i	−0.401146	+	0.291449i	0.368862	+	0.929484i	$0.379748\pi$
$602$	−2.54574	−	1.11160i	−0.103757	−	0.0453056i
$603$	−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
$607$	13.6620	+	2.90395i	0.554523	+	0.117868i	0.476646	−	0.879095i	$-0.341852\pi$
$607$	13.6620	+	2.90395i	0.554523	+	0.117868i	0.0778775	+	0.996963i	$0.475186\pi$
$608$	−6.87380	−	4.99411i	−0.278769	−	0.202538i
$609$	4.92168	+	14.7853i	0.199436	+	0.599130i
$610$	4.84218	−	14.9027i	0.196054	−	0.603392i
$611$	−6.55368	−	7.27860i	−0.265133	−	0.294461i
$612$	−1.55901	−	0.694116i	−0.0630192	−	0.0280580i
$613$	0.485210	−	4.61646i	0.0195974	−	0.186457i	−0.980344	−	0.197297i	$-0.936784\pi$
$613$	0.485210	−	4.61646i	0.0195974	−	0.186457i	0.999941	+	0.0108396i	$0.00345043\pi$
$614$	10.5787	+	2.24857i	0.426921	+	0.0907448i
$615$	−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	$0.678308\pi$
$618$	−3.89065	−	0.826982i	−0.156505	−	0.0332661i
$619$	−1.53463	+	14.6010i	−0.0616820	+	0.586865i	0.919407	+	0.393308i	$0.128669\pi$
$619$	−1.53463	+	14.6010i	−0.0616820	+	0.586865i	−0.981089	+	0.193558i	$0.937997\pi$
$620$	−36.2141	−	16.1235i	−1.45439	−	0.647537i
$621$	−10.0249	−	11.1338i	−0.402285	−	0.446782i
$622$	−4.38870	+	13.5070i	−0.175971	+	0.541582i
$623$	4.51139	−	5.08333i	0.180745	−	0.203659i
$624$	−14.6249	−	10.6256i	−0.585466	−	0.425366i
$625$	3.74347	+	0.795700i	0.149739	+	0.0318280i
$626$	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
$630$	0.454599	+	4.04559i	0.0181117	+	0.161180i
$631$	24.3917	−	17.7216i	0.971018	−	0.705486i	0.0153345	−	0.999882i	$-0.495119\pi$
$631$	24.3917	−	17.7216i	0.971018	−	0.705486i	0.955683	+	0.294397i	$0.0951187\pi$
$632$	10.0249	+	11.1338i	0.398768	+	0.442877i
$633$	22.6321	−	4.81060i	0.899545	−	0.191204i
$634$	−2.67612	−	1.19148i	−0.106282	−	0.0473199i
$635$	−21.5879	+	9.61154i	−0.856688	+	0.381422i
$636$	−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
$640$	−26.5068	+	29.4387i	−1.04777	+	1.16367i
$641$	1.69108	−	16.0896i	0.0667937	−	0.635499i	−0.908998	−	0.416799i	$-0.863152\pi$
$641$	1.69108	−	16.0896i	0.0667937	−	0.635499i	0.975792	−	0.218700i	$-0.0701816\pi$
$642$	0.625631	+	5.95248i	0.0246917	+	0.234926i
$643$	−0.721764	+	2.22136i	−0.0284636	+	0.0876019i	−0.964279	−	0.264888i	$-0.914665\pi$
$643$	−0.721764	+	2.22136i	−0.0284636	+	0.0876019i	0.935816	+	0.352490i	$0.114665\pi$
$644$	12.6370	−	5.73543i	0.497968	−	0.226008i
$645$	−8.82818	+	6.41405i	−0.347609	+	0.252553i
$646$	1.47179	−	0.655283i	0.0579068	−	0.0257818i
$647$	10.0116	−	11.1190i	0.393598	−	0.437135i	−0.513477	−	0.858103i	$-0.671643\pi$
$647$	10.0116	−	11.1190i	0.393598	−	0.437135i	0.907075	+	0.420968i	$0.138310\pi$
$648$	12.3481	+	21.3875i	0.485079	+	0.840182i
$649$		0			0
$650$	−30.0345			−1.17805
$651$	−18.1323	−	30.8917i	−0.710661	−	1.21074i
$652$	−11.3465	−	8.24374i	−0.444364	−	0.322850i
$653$	2.39264	+	22.7644i	0.0936310	+	0.890840i	0.936015	+	0.351961i	$0.114485\pi$
$653$	2.39264	+	22.7644i	0.0936310	+	0.890840i	−0.842383	+	0.538879i	$0.818848\pi$
$654$	18.2777	−	3.88506i	0.714716	−	0.151918i
$655$	21.1464	−	4.49480i	0.826256	−	0.175626i
$656$	−0.214900	−	2.04463i	−0.00839042	−	0.0798295i
$657$	2.42296	+	1.76038i	0.0945286	+	0.0686791i
$658$	−2.87790	+	0.0206640i	−0.112192	+	0.000805567i
$659$	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	$0.829109\pi$
$662$	−8.36532	+	9.29063i	−0.325127	+	0.361091i
$663$	17.1098	−	7.61776i	0.664489	−	0.295849i
$664$	0.318193	−	0.231181i	0.0123483	−	0.00897155i
$665$	11.3726	+	8.13860i	0.441012	+	0.315601i
$666$	0.601042	−	1.84982i	0.0232899	−	0.0716790i
$667$	1.07642	+	10.2414i	0.0416790	+	0.396549i
$668$	2.98752	−	28.4244i	0.115591	−	1.09977i
$669$	19.9946	−	22.2062i	0.773035	−	0.858542i
$670$	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	0.994724	−	0.102586i	$-0.0327118\pi$
$673$	3.36411	+	10.3537i	0.129677	+	0.399104i	−0.865047	+	0.501690i	$0.832712\pi$
$674$	16.2049	−	7.21487i	0.624188	−	0.277906i
$675$	−31.6714	−	14.1010i	−1.21903	−	0.542749i
$676$	33.6906	−	7.16115i	1.29579	−	0.275429i
$677$	−30.5561	−	33.9360i	−1.17437	−	1.30427i	−0.943535	−	0.331272i	$-0.892522\pi$
$677$	−30.5561	−	33.9360i	−1.17437	−	1.30427i	−0.230831	−	0.972994i	$-0.574145\pi$
$678$	12.6399	−	9.18346i	0.485434	−	0.352689i
$679$	2.87662	+	25.5997i	0.110395	+	0.982428i
$680$	−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	$0.872921\pi$
$684$	−1.49238	−	0.317214i	−0.0570624	−	0.0121290i
$685$	−21.4334	−	15.5723i	−0.818929	−	0.594987i
$686$	8.32991	+	8.85986i	0.318038	+	0.338271i
$687$	−3.29226	+	10.1325i	−0.125608	+	0.386580i
$688$	−1.71081	−	1.90005i	−0.0652240	−	0.0724386i
$689$	49.8276	+	22.1847i	1.89828	+	0.845169i
$690$	−1.56604	+	14.8999i	−0.0596181	+	0.567229i
$691$	−10.7075	−	2.27596i	−0.407334	−	0.0865815i	−0.000312141	−	1.00000i	$-0.500099\pi$
$691$	−10.7075	−	2.27596i	−0.407334	−	0.0865815i	−0.407022	+	0.913418i	$0.633433\pi$
$692$	30.6885			1.16660
$693$		0			0
$694$	−13.2754			−0.503927
$695$	37.7867	+	8.03181i	1.43333	+	0.304664i
$696$	1.44270	−	13.7264i	0.0546856	−	0.520298i
$697$	1.94585	+	0.866347i	0.0737042	+	0.0328152i
$698$	−5.28224	−	5.86652i	−0.199936	−	0.222051i
$699$	11.3901	−	35.0550i	0.430811	−	1.32590i
$700$	21.3161	−	24.0185i	0.805673	−	0.907815i
$701$	−0.740149	−	0.537750i	−0.0279550	−	0.0203105i	0.573720	−	0.819052i	$-0.305500\pi$
$701$	−0.740149	−	0.537750i	−0.0279550	−	0.0203105i	−0.601675	+	0.798741i	$0.705500\pi$
$702$	−17.0158	−	3.61682i	−0.642220	−	0.136508i
$703$	−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
$707$	−3.94888	+	2.91257i	−0.148513	+	0.109539i
$708$	21.4841	−	15.6091i	0.807423	−	0.586627i
$709$	29.6507	+	32.9305i	1.11356	+	1.23673i	0.968954	+	0.247240i	$0.0795237\pi$
$709$	29.6507	+	32.9305i	1.11356	+	1.23673i	0.144603	+	0.989490i	$0.453810\pi$
$710$	19.7557	−	4.19921i	0.741419	−	0.157593i
$711$	3.83504	+	1.70747i	0.143825	+	0.0640352i
$712$	−5.49935	+	2.44847i	−0.206097	+	0.0917603i
$713$	−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
$717$	28.3512	−	31.4872i	1.05879	−	1.17591i
$718$	−1.66717	+	15.8620i	−0.0622181	+	0.591965i
$719$	0.543795	+	5.17386i	0.0202801	+	0.192952i	0.999971	−	0.00755926i	$-0.00240621\pi$
$719$	0.543795	+	5.17386i	0.0202801	+	0.192952i	−0.979691	+	0.200512i	$0.935740\pi$
$720$	−1.15790	+	3.56364i	−0.0431523	+	0.132809i
$721$	−0.816214	+	8.34147i	−0.0303974	+	0.310653i
$722$	−8.92785	+	6.48646i	−0.332260	+	0.241401i
$723$	34.7187	−	15.4578i	1.29120	−	0.574881i
$724$	10.8553	−	12.0561i	0.403436	−	0.448061i
$725$	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	$0.120830\pi$
$728$	18.0995	−	31.8756i	0.670812	−	1.18139i
$729$	−15.1987	−	11.0425i	−0.562915	−	0.408981i
$730$	1.11725	+	10.6299i	0.0413514	+	0.393432i
$731$	2.59103	−	0.550741i	0.0958328	−	0.0203699i
$732$	19.6219	−	4.17077i	0.725247	−	0.154156i
$733$	−4.92013	−	46.8119i	−0.181729	−	1.72904i	−0.582477	−	0.812847i	$-0.697916\pi$
$733$	−4.92013	−	46.8119i	−0.181729	−	1.72904i	0.400748	−	0.916188i	$-0.368750\pi$
$734$	5.76065	+	4.18536i	0.212629	+	0.154484i
$735$	46.5799	−	10.6022i	1.71812	−	0.391067i
$736$	−19.1799			−0.706981
$737$		0			0
$738$	0.277175	+	0.480082i	0.0102030	+	0.0176720i
$739$	−31.4434	+	34.9214i	−1.15666	+	1.28460i	−0.204551	+	0.978856i	$0.565573\pi$
$739$	−31.4434	+	34.9214i	−1.15666	+	1.28460i	−0.952112	+	0.305749i	$0.901093\pi$
$740$	−23.0746	+	10.2735i	−0.848238	+	0.377660i
$741$	13.5465	−	9.84211i	0.497643	−	0.361559i
$742$	14.5942	−	6.62372i	0.535770	−	0.243164i
$743$	1.60545	−	4.94105i	0.0588981	−	0.181270i	−0.917279	−	0.398245i	$-0.869619\pi$
$743$	1.60545	−	4.94105i	0.0588981	−	0.181270i	0.976177	+	0.216976i	$0.0696192\pi$
$744$	3.31631	+	31.5525i	0.121582	+	1.15677i
$745$	0.373046	−	3.54930i	0.0136674	−	0.130036i
$746$	−14.5097	+	16.1146i	−0.531236	+	0.589998i
$747$	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
$751$	30.5614	−	13.6068i	1.11520	−	0.496519i	0.235417	−	0.971894i	$-0.424354\pi$
$751$	30.5614	−	13.6068i	1.11520	−	0.496519i	0.879783	+	0.475375i	$0.157688\pi$
$752$	−2.41991	−	1.07741i	−0.0882449	−	0.0392892i
$753$	−41.3509	+	8.78941i	−1.50691	+	0.320304i
$754$	8.00086	+	8.88586i	0.291374	+	0.323604i
$755$	−47.4188	+	34.4517i	−1.72575	+	1.25383i
$756$	14.9688	−	11.0406i	0.544411	−	0.401542i
$757$	12.3743	+	38.0841i	0.449750	+	1.38419i	0.877189	+	0.480145i	$0.159416\pi$
$757$	12.3743	+	38.0841i	0.449750	+	1.38419i	−0.427439	+	0.904044i	$0.640584\pi$
$758$	−7.20051	+	12.4716i	−0.261534	+	0.452990i
$759$		0			0
$760$	−6.19326	−	10.7270i	−0.224653	−	0.389110i
$761$	−7.39333	−	1.57150i	−0.268008	−	0.0569669i	0.0719474	−	0.997408i	$-0.477079\pi$
$761$	−7.39333	−	1.57150i	−0.268008	−	0.0569669i	−0.339955	+	0.940442i	$0.610412\pi$
$762$	6.72610	+	4.88680i	0.243661	+	0.177030i
$763$	−12.4359	−	37.3589i	−0.450209	−	1.35248i
$764$	−4.85889	+	14.9541i	−0.175788	+	0.541021i
$765$	−2.59763	−	2.88496i	−0.0939174	−	0.104306i
$766$	−21.8724	−	9.73824i	−0.790283	−	0.351857i
$767$	−5.47047	+	52.0481i	−0.197527	+	1.87935i
$768$	15.7605	+	3.35000i	0.568709	+	0.120883i
$769$	−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
$772$	−38.8634	−	8.26067i	−1.39872	−	0.297308i
$773$	1.61660	−	15.3809i	0.0581452	−	0.553214i	−0.926209	−	0.377011i	$-0.876952\pi$
$773$	1.61660	−	15.3809i	0.0581452	−	0.553214i	0.984354	−	0.176203i	$-0.0563815\pi$
$774$	0.629802	+	0.280406i	0.0226378	+	0.0100790i
$775$	−36.6525	−	40.7067i	−1.31660	−	1.46223i
$776$	7.05076	−	21.7000i	0.253108	−	0.778985i
$777$	−22.3583	−	4.58486i	−0.802099	−	0.164481i
$778$	10.3460	+	7.51681i	0.370922	+	0.269491i
$779$	1.86268	+	0.395925i	0.0667374	+	0.0141855i
$780$	−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
$784$	3.61131	+	10.5943i	0.128975	+	0.378369i
$785$	−33.0618	+	24.0208i	−1.18003	+	0.857340i
$786$	−5.08942	−	5.65237i	−0.181534	−	0.201613i
$787$	21.4721	−	4.56404i	0.765398	−	0.162690i	0.191361	−	0.981520i	$-0.438710\pi$
$787$	21.4721	−	4.56404i	0.765398	−	0.162690i	0.574037	+	0.818829i	$0.305377\pi$
$788$	−35.2298	−	15.6853i	−1.25501	−	0.558766i
$789$	27.0832	−	12.0582i	0.964188	−	0.429284i
$790$	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
$794$	3.44456	−	3.82557i	0.122243	−	0.135765i
$795$	6.58099	−	62.6139i	0.233404	−	2.22069i
$796$	0.916912	+	8.72383i	0.0324991	+	0.309208i
$797$	13.1721	−	40.5396i	0.466580	−	1.43598i	−0.390405	−	0.920643i	$-0.627665\pi$
$797$	13.1721	−	40.5396i	0.466580	−	1.43598i	0.856985	−	0.515341i	$-0.172335\pi$
$798$	0.479153	−	4.89680i	0.0169618	−	0.173345i
$799$	2.22026	−	1.61311i	0.0785471	−	0.0570678i
$800$	−40.5459	+	18.0522i	−1.43351	+	0.638241i
$801$	−1.12866	+	1.25351i	−0.0398793	+	0.0442905i
$802$	−8.02583	−	13.9011i	−0.283402	−	0.490867i
$803$		0			0
$804$	29.4734			1.03945
$805$	31.5683	−	0.226668i	1.11264	−	0.00798901i
$806$	−22.2362	−	16.1555i	−0.783237	−	0.569055i
$807$	−0.341109	−	3.24544i	−0.0120076	−	0.114245i
$808$	4.25105	−	0.903589i	0.149552	−	0.0317882i
$809$	3.88075	−	0.824879i	0.136440	−	0.0290012i	−0.139185	−	0.990266i	$-0.544448\pi$
$809$	3.88075	−	0.824879i	0.136440	−	0.0290012i	0.275625	+	0.961265i	$0.411115\pi$
$810$	2.58146	+	24.5609i	0.0907031	+	0.862982i
$811$	−37.9604	−	27.5799i	−1.33297	−	0.968460i	−0.999671	−	0.0256391i	$-0.991838\pi$
$811$	−37.9604	−	27.5799i	−1.33297	−	0.968460i	−0.333300	−	0.942821i	$-0.608162\pi$
$812$	−12.7844	+	0.0917949i	−0.448643	+	0.00322137i
$813$	39.2549			1.37673
$814$		0			0
$815$	−15.9523	−	27.6301i	−0.558783	−	0.967841i
$816$	3.38937	−	3.76428i	0.118652	−	0.131776i
$817$	2.16348	−	0.963245i	0.0756907	−	0.0336997i
$818$	1.25034	−	0.908426i	0.0437171	−	0.0317624i
$819$	1.00025	−	10.2222i	0.0349514	−	0.357193i
$820$	2.22458	−	6.84655i	0.0776856	−	0.239092i
$821$	−5.28915	−	50.3229i	−0.184592	−	1.75628i	−0.559141	−	0.829073i	$-0.688869\pi$
$821$	−5.28915	−	50.3229i	−0.184592	−	1.75628i	0.374549	−	0.927207i	$-0.377798\pi$
$822$	−0.974304	+	9.26988i	−0.0339828	+	0.323324i
$823$	0.266714	−	0.296216i	0.00929708	−	0.0103255i	−0.738478	−	0.674277i	$-0.764455\pi$
$823$	0.266714	−	0.296216i	0.00929708	−	0.0103255i	0.747775	+	0.663952i	$0.231122\pi$
$824$	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	0.998807	+	0.0488385i	$0.0155520\pi$
$827$	6.31119	+	19.4239i	0.219462	+	0.675434i	−0.779345	+	0.626595i	$0.784448\pi$
$828$	−3.14638	+	1.40086i	−0.109344	+	0.0486832i
$829$	−21.2521	−	9.46204i	−0.738116	−	0.328630i	0.00301099	−	0.999995i	$-0.499042\pi$
$829$	−21.2521	−	9.46204i	−0.738116	−	0.328630i	−0.741127	+	0.671365i	$0.765708\pi$
$830$	0.384713	−	0.0817733i	0.0133536	−	0.00283839i
$831$	34.1136	+	37.8870i	1.18339	+	1.31428i
$832$	−2.72086	+	1.97682i	−0.0943289	+	0.0685339i
$833$	−11.3764	−	2.24789i	−0.394168	−	0.0778846i
$834$	−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
$838$	5.96722	+	1.26837i	0.206134	+	0.0438152i
$839$	13.3376	+	9.69031i	0.460464	+	0.334547i	0.793713	−	0.608292i	$-0.208145\pi$
$839$	13.3376	+	9.69031i	0.460464	+	0.334547i	−0.333249	+	0.942839i	$0.608145\pi$
$840$	−41.4491	−	8.49970i	−1.43013	−	0.293267i
$841$	−6.02991	+	18.5581i	−0.207928	+	0.639936i
$842$	17.1492	+	19.0462i	0.591002	+	0.656374i
$843$	−27.5040	−	12.2456i	−0.947288	−	0.421760i
$844$	−1.98425	+	18.8789i	−0.0683007	+	0.649837i
$845$	76.6400	+	16.2903i	2.63649	+	0.560404i
$846$	0.714253			0.0245565
$847$		0			0
$848$	14.7514			0.506566
$849$	−30.0575	−	6.38891i	−1.03157	−	0.219267i
$850$	0.879685	−	8.36964i	0.0301729	−	0.287076i
$851$	−13.7787	−	6.13469i	−0.472329	−	0.210295i
$852$	17.3013	+	19.2150i	0.592732	+	0.658295i
$853$	4.58318	−	14.1056i	0.156925	−	0.482966i	−0.841426	−	0.540373i	$-0.818283\pi$
$853$	4.58318	−	14.1056i	0.156925	−	0.482966i	0.998351	+	0.0574069i	$0.0182832\pi$
$854$	3.66896	+	11.0220i	0.125549	+	0.377165i
$855$	−2.80788	−	2.04004i	−0.0960274	−	0.0697680i
$856$	−10.9264	−	2.32247i	−0.373456	−	0.0793805i
$857$	−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
$861$	5.23503	−	3.86121i	0.178409	−	0.131590i
$862$	2.01970	−	1.46740i	0.0687912	−	0.0499798i
$863$	−24.4072	−	27.1070i	−0.830831	−	0.922732i	0.167170	−	0.985928i	$-0.446537\pi$
$863$	−24.4072	−	27.1070i	−0.830831	−	0.922732i	−0.998001	+	0.0631963i	$0.979871\pi$
$864$	−25.1448	+	5.34469i	−0.855443	+	0.181830i
$865$	63.7753	+	28.3946i	2.16843	+	0.965446i
$866$	−4.93104	+	2.19544i	−0.167563	+	0.0746040i
$867$	−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
$871$	−38.8661	+	43.1652i	−1.31693	+	1.46260i
$872$	−3.64537	+	34.6833i	−0.123448	+	1.17453i
$873$	−0.668283	−	6.35828i	−0.0226179	−	0.215195i
$874$	1.00476	−	3.09232i	0.0339864	−	0.104599i
$875$	23.5305	−	10.6795i	0.795476	−	0.361034i
$876$	−11.0701	+	8.04292i	−0.374025	+	0.271745i
$877$	6.04414	−	2.69102i	0.204096	−	0.0908694i	−0.302143	−	0.953263i	$-0.597702\pi$
$877$	6.04414	−	2.69102i	0.204096	−	0.0908694i	0.506239	+	0.862393i	$0.331035\pi$
$878$	1.99531	−	2.21602i	0.0673385	−	0.0747870i
$879$	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	$0.623905\pi$
$882$	−2.05147	−	2.21362i	−0.0690766	−	0.0745365i
$883$	41.3935	+	30.0741i	1.39300	+	1.01208i	0.995528	+	0.0944622i	$0.0301131\pi$
$883$	41.3935	+	30.0741i	1.39300	+	1.01208i	0.397474	+	0.917613i	$0.369887\pi$
$884$	1.60616	+	15.2816i	0.0540212	+	0.513977i
$885$	59.0897	−	12.5599i	1.98628	−	0.422196i
$886$	8.82763	−	1.87637i	0.296570	−	0.0630379i
$887$	−0.662511	−	6.30337i	−0.0222449	−	0.211646i	−0.999998	−	0.00188817i	$-0.999399\pi$
$887$	−0.662511	−	6.30337i	−0.0222449	−	0.211646i	0.977753	−	0.209758i	$-0.0672677\pi$
$888$	16.3544	+	11.8822i	0.548817	+	0.398739i
$889$	8.65016	−	15.2341i	0.290117	−	0.510935i
$890$	−6.01979			−0.201784
$891$		0			0
$892$	12.2578	+	21.2311i	0.410421	+	0.710871i
$893$	1.64177	−	1.82337i	0.0549397	−	0.0610167i
$894$	−1.14706	+	0.510702i	−0.0383633	+	0.0170804i
$895$	9.37755	−	6.81319i	0.313457	−	0.227740i
$896$	2.85995	−	29.2279i	0.0955443	−	0.976435i
$897$	11.6804	−	35.9487i	0.389999	−	1.20029i
$898$	1.48021	+	14.0832i	0.0493952	+	0.469964i
$899$	−2.27946	+	21.6876i	−0.0760243	+	0.723323i
$900$	−5.33288	+	5.92276i	−0.177763	+	0.197425i
$901$	−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
$905$	33.7140	−	15.0104i	1.12069	−	0.498963i
$906$	18.8386	+	8.38749i	0.625871	+	0.278656i
$907$	6.73429	−	1.43142i	0.223608	−	0.0475294i	−0.0947449	−	0.995502i	$-0.530204\pi$
$907$	6.73429	−	1.43142i	0.223608	−	0.0475294i	0.318353	+	0.947972i	$0.396870\pi$
$908$	−16.4485	−	18.2679i	−0.545861	−	0.606241i
$909$	0.985194	−	0.715785i	0.0326768	−	0.0237411i
$910$	29.4997	−	21.7581i	0.977906	−	0.721275i
$911$	−12.6950	−	39.0711i	−0.420603	−	1.29448i	−0.907142	−	0.420825i	$-0.861741\pi$
$911$	−12.6950	−	39.0711i	−0.420603	−	1.29448i	0.486539	−	0.873659i	$-0.338259\pi$
$912$	2.26430	−	3.92188i	0.0749784	−	0.129866i
$913$		0			0
$914$	1.08524	+	1.87969i	0.0358966	+	0.0621747i
$915$	44.6363	+	9.48774i	1.47563	+	0.313655i
$916$	−7.07149	−	5.13774i	−0.233648	−	0.169756i
$917$	−10.6384	+	11.9871i	−0.351309	+	0.395848i
$918$	1.50627	−	4.63582i	0.0497143	−	0.153005i
$919$	7.77963	+	8.64016i	0.256626	+	0.285013i	0.857667	−	0.514206i	$-0.171913\pi$
$919$	7.77963	+	8.64016i	0.256626	+	0.285013i	−0.601040	+	0.799219i	$0.705247\pi$
$920$	−25.5439	−	11.3729i	−0.842157	−	0.374952i
$921$	−3.29221	+	31.3233i	−0.108482	+	1.03214i
$922$	20.6506	+	4.38942i	0.680091	+	0.144558i
$923$	−50.9562			−1.67724
$924$		0			0
$925$	−34.9019			−1.14757
$926$	3.73919	+	0.794788i	0.122877	+	0.0261184i
$927$	0.217426	−	2.06867i	0.00714121	−	0.0679441i
$928$	16.1418	+	7.18679i	0.529880	+	0.235918i
$929$	16.5722	+	18.4053i	0.543718	+	0.603860i	0.950904	−	0.309485i	$-0.100157\pi$
$929$	16.5722	+	18.4053i	0.543718	+	0.603860i	−0.407187	+	0.913345i	$0.633490\pi$
$930$	−9.80398	+	30.1735i	−0.321485	+	0.989429i
$931$	−10.3665	+	0.148875i	−0.339748	+	0.00487919i
$932$	24.4648	+	17.7747i	0.801372	+	0.582231i
$933$	−40.4560	−	8.59920i	−1.32447	−	0.281525i
$934$	−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	0.945082	−	0.326835i	$-0.105982\pi$
$937$	−0.355512	−	1.09415i	−0.0116141	−	0.0357444i	−0.956696	+	0.291090i	$0.905982\pi$
$938$	1.90588	+	16.9608i	0.0622291	+	0.553791i
$939$	−25.3530	+	18.4201i	−0.827365	+	0.601116i
$940$	−6.20645	−	6.89296i	−0.202432	−	0.224824i
$941$	9.88927	−	2.10203i	0.322381	−	0.0685242i	−0.0438787	−	0.999037i	$-0.513971\pi$
$941$	9.88927	−	2.10203i	0.322381	−	0.0685242i	0.366260	+	0.930513i	$0.380638\pi$
$942$	13.1349	+	5.84802i	0.427957	+	0.190539i
$943$	3.92710	−	1.74846i	0.127884	−	0.0569376i
$944$	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	$0.0365981\pi$
$948$	−12.8339	+	14.2535i	−0.416825	+	0.462931i
$949$	2.81877	−	26.8188i	0.0915012	−	0.870576i
$950$	−0.786470	−	7.48276i	−0.0255165	−	0.242773i
$951$	2.63623	−	8.11347i	0.0854855	−	0.263097i
$952$	8.35258	+	5.97735i	0.270709	+	0.193727i
$953$	−13.0815	+	9.50424i	−0.423750	+	0.307872i	−0.779145	−	0.626844i	$-0.784346\pi$
$953$	−13.0815	+	9.50424i	−0.423750	+	0.307872i	0.355395	+	0.934716i	$0.384346\pi$
$954$	−3.63369	+	1.61782i	−0.117645	+	0.0523789i
$955$	−23.9338	+	26.5812i	−0.774481	+	0.860148i
$956$	17.3809	+	30.1046i	0.562138	+	0.973652i
$957$		0			0
$958$	11.2512			0.363511
$959$	19.6401	−	0.141021i	0.634212	−	0.00455379i
$960$	3.14068	+	2.28184i	0.101365	+	0.0736459i
$961$	−1.99935	−	19.0226i	−0.0644952	−	0.613631i
$962$	−17.1303	+	3.64115i	−0.552302	+	0.117395i
$963$	−3.06160	+	0.650763i	−0.0986586	+	0.0209705i
$964$	3.25919	+	31.0091i	0.104971	+	0.998736i
$965$	−73.1208	−	53.1254i	−2.35384	−	1.71017i
$966$	−5.62232	−	9.57865i	−0.180895	−	0.308188i
$967$	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
$970$	15.2674	−	16.9562i	0.490206	−	0.544429i
$971$	−8.26510	+	3.67986i	−0.265240	+	0.118092i	−0.535048	−	0.844822i	$-0.679706\pi$
$971$	−8.26510	+	3.67986i	−0.265240	+	0.118092i	0.269808	+	0.962914i	$0.413040\pi$
$972$	−8.51548	+	6.18686i	−0.273134	+	0.198444i
$973$	−26.0786	+	11.8360i	−0.836040	+	0.379445i
$974$	−1.15946	+	3.56845i	−0.0371515	+	0.114341i
$975$	−9.14283	−	86.9883i	−0.292805	−	2.78585i
$976$	−1.11762	+	10.6335i	−0.0357743	+	0.340369i
$977$	−4.52097	+	5.02104i	−0.144639	+	0.160637i	−0.811111	−	0.584892i	$-0.801137\pi$
$977$	−4.52097	+	5.02104i	−0.144639	+	0.160637i	0.666472	+	0.745530i	$0.267803\pi$
$978$	−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
$982$	14.4368	−	6.42769i	0.460698	−	0.205116i
$983$	24.1454	+	10.7502i	0.770120	+	0.342879i	0.753900	−	0.656989i	$-0.228170\pi$
$983$	24.1454	+	10.7502i	0.770120	+	0.342879i	0.0162197	+	0.999868i	$0.494837\pi$
$984$	−5.63563	+	1.19789i	−0.179657	+	0.0381874i
$985$	−58.6999	−	65.1929i	−1.87034	−	2.07722i
$986$	−2.71054	+	1.96932i	−0.0863211	+	0.0627159i
$987$	−0.935912	−	8.32889i	−0.0297904	−	0.265112i
$988$	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	$0.830127\pi$
$992$	−39.7286	−	8.44457i	−1.26138	−	0.268115i
$993$	−29.4547	−	21.4001i	−0.934717	−	0.679112i
$994$	−9.93875	+	11.1988i	−0.315238	+	0.355203i
$995$	−6.16627	+	18.9778i	−0.195484	+	0.601637i
$996$	0.336916	+	0.374184i	0.0106756	+	0.0118565i
$997$	−9.25179	−	4.11916i	−0.293007	−	0.130455i	0.254969	−	0.966949i	$-0.417935\pi$
$997$	−9.25179	−	4.11916i	−0.293007	−	0.130455i	−0.547976	+	0.836494i	$0.684601\pi$
$998$	0.740527	−	7.04564i	0.0234410	−	0.223026i
$999$	−19.7734	−	4.20296i	−0.625602	−	0.132976i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.d.632.2		24
7.4	even	3	inner	847.2.n.d.753.2		24
11.2	odd	10		847.2.n.e.9.2		24
11.3	even	5		847.2.e.d.485.2		6
11.4	even	5	inner	847.2.n.d.366.2		24
11.5	even	5	inner	847.2.n.d.807.2		24
11.6	odd	10		847.2.n.e.807.2		24
11.7	odd	10		847.2.n.e.366.2		24
11.8	odd	10		77.2.e.b.23.2	✓	6
11.9	even	5	inner	847.2.n.d.9.2		24
11.10	odd	2		847.2.n.e.632.2		24
33.8	even	10		693.2.i.g.100.2		6
44.19	even	10		1232.2.q.k.177.3		6
77.4	even	15	inner	847.2.n.d.487.2		24
77.18	odd	30		847.2.n.e.487.2		24
77.19	even	30		539.2.a.i.1.2		3
77.25	even	15		847.2.e.d.606.2		6
77.30	odd	30		539.2.a.h.1.2		3
77.32	odd	6		847.2.n.e.753.2		24
77.39	odd	30		847.2.n.e.81.2		24
77.41	even	10		539.2.e.l.177.2		6
77.46	odd	30		847.2.n.e.130.2		24
77.47	odd	30		5929.2.a.w.1.2		3
77.52	even	30		539.2.e.l.67.2		6
77.53	even	15	inner	847.2.n.d.130.2		24
77.58	even	15		5929.2.a.v.1.2		3
77.60	even	15	inner	847.2.n.d.81.2		24
77.74	odd	30		77.2.e.b.67.2	yes	6
231.74	even	30		693.2.i.g.298.2		6
231.107	even	30		4851.2.a.bo.1.2		3
231.173	odd	30		4851.2.a.bn.1.2		3
308.19	odd	30		8624.2.a.ck.1.3		3
308.107	even	30		8624.2.a.cl.1.1		3
308.151	even	30		1232.2.q.k.529.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.2	✓	6	11.8	odd	10
77.2.e.b.67.2	yes	6	77.74	odd	30
539.2.a.h.1.2		3	77.30	odd	30
539.2.a.i.1.2		3	77.19	even	30
539.2.e.l.67.2		6	77.52	even	30
539.2.e.l.177.2		6	77.41	even	10
693.2.i.g.100.2		6	33.8	even	10
693.2.i.g.298.2		6	231.74	even	30
847.2.e.d.485.2		6	11.3	even	5
847.2.e.d.606.2		6	77.25	even	15
847.2.n.d.9.2		24	11.9	even	5	inner
847.2.n.d.81.2		24	77.60	even	15	inner
847.2.n.d.130.2		24	77.53	even	15	inner
847.2.n.d.366.2		24	11.4	even	5	inner
847.2.n.d.487.2		24	77.4	even	15	inner
847.2.n.d.632.2		24	1.1	even	1	trivial
847.2.n.d.753.2		24	7.4	even	3	inner
847.2.n.d.807.2		24	11.5	even	5	inner
847.2.n.e.9.2		24	11.2	odd	10
847.2.n.e.81.2		24	77.39	odd	30
847.2.n.e.130.2		24	77.46	odd	30
847.2.n.e.366.2		24	11.7	odd	10
847.2.n.e.487.2		24	77.18	odd	30
847.2.n.e.632.2		24	11.10	odd	2
847.2.n.e.753.2		24	77.32	odd	6
847.2.n.e.807.2		24	11.6	odd	10
1232.2.q.k.177.3		6	44.19	even	10
1232.2.q.k.529.3		6	308.151	even	30
4851.2.a.bn.1.2		3	231.173	odd	30
4851.2.a.bo.1.2		3	231.107	even	30
5929.2.a.v.1.2		3	77.58	even	15
5929.2.a.w.1.2		3	77.47	odd	30
8624.2.a.ck.1.3		3	308.19	odd	30
8624.2.a.cl.1.1		3	308.107	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)

\(f(q)\)	\(=\)	\(q+(0.642272 + 0.136519i) q^{2} +(-0.199882 + 1.90175i) q^{3} +(-1.43322 - 0.638109i) q^{4} +(-2.38803 - 2.65217i) q^{5} +(-0.388004 + 1.19415i) q^{6} +(2.59182 + 0.531487i) q^{7} +(-1.89583 - 1.37740i) q^{8} +(-0.642272 - 0.136519i) q^{9} +O(q^{10})\)	\(q+(0.642272 + 0.136519i) q^{2} +(-0.199882 + 1.90175i) q^{3} +(-1.43322 - 0.638109i) q^{4} +(-2.38803 - 2.65217i) q^{5} +(-0.388004 + 1.19415i) q^{6} +(2.59182 + 0.531487i) q^{7} +(-1.89583 - 1.37740i) q^{8} +(-0.642272 - 0.136519i) q^{9} +(-1.17169 - 2.02943i) q^{10} +(1.50000 - 2.59808i) q^{12} +(1.82698 + 5.62286i) q^{13} +(1.59209 + 0.695192i) q^{14} +(5.52110 - 4.01132i) q^{15} +(1.06993 + 1.18828i) q^{16} +(-1.62042 + 0.344431i) q^{17} +(-0.393875 - 0.175365i) q^{18} +(-1.35303 + 0.602409i) q^{19} +(1.73018 + 5.32495i) q^{20} +(-1.52882 + 4.82277i) q^{21} +(-1.67169 + 2.89545i) q^{23} +(2.99843 - 3.33009i) q^{24} +(-0.808704 + 7.69431i) q^{25} +(0.405789 + 3.86082i) q^{26} +(-1.38473 + 4.26176i) q^{27} +(-3.37549 - 2.41560i) q^{28} +(2.49183 - 1.81042i) q^{29} +(4.09367 - 1.82262i) q^{30} +(-4.73749 + 5.26152i) q^{31} +(2.86834 + 4.96812i) q^{32} -1.08777 q^{34} +(-4.77974 - 8.14315i) q^{35} +(0.833400 + 0.605500i) q^{36} +(0.471551 + 4.48650i) q^{37} +(-0.951255 + 0.202195i) q^{38} +(-11.0585 + 2.35055i) q^{39} +(0.874189 + 8.31735i) q^{40} +(-1.04019 - 0.755743i) q^{41} +(-1.64031 + 2.88881i) q^{42} -1.59899 q^{43} +(1.17169 + 2.02943i) q^{45} +(-1.46896 + 1.63145i) q^{46} +(-1.51340 + 0.673808i) q^{47} +(-2.47368 + 1.79723i) q^{48} +(6.43504 + 2.75503i) q^{49} +(-1.56983 + 4.83143i) q^{50} +(-0.331129 - 3.15048i) q^{51} +(0.969543 - 9.22459i) q^{52} +(6.17304 - 6.85586i) q^{53} +(-1.47118 + 2.54817i) q^{54} +(-4.18158 - 4.57759i) q^{56} +(-0.875186 - 2.69355i) q^{57} +(1.84759 - 0.822598i) q^{58} +(8.08666 + 3.60041i) q^{59} +(-10.4726 + 2.22602i) q^{60} +(4.47432 + 4.96923i) q^{61} +(-3.76105 + 2.73256i) q^{62} +(-1.59209 - 0.695192i) q^{63} +(0.175784 + 0.541008i) q^{64} +(10.5499 - 18.2730i) q^{65} +(4.91223 + 8.50823i) q^{67} +(2.54219 + 0.540360i) q^{68} +(-5.17229 - 3.75789i) q^{69} +(-1.95819 - 5.88264i) q^{70} +(-2.66335 + 8.19694i) q^{71} +(1.02960 + 1.14349i) q^{72} +(-4.16681 - 1.85519i) q^{73} +(-0.309630 + 2.94593i) q^{74} +(-14.4710 - 3.07591i) q^{75} +2.32359 q^{76} -7.42345 q^{78} +(-6.25360 - 1.32924i) q^{79} +(0.596497 - 5.67529i) q^{80} +(-9.62759 - 4.28648i) q^{81} +(-0.564912 - 0.627399i) q^{82} +(-0.0518648 + 0.159623i) q^{83} +(5.26857 - 5.93651i) q^{84} +(4.78309 + 3.47512i) q^{85} +(-1.02698 - 0.218292i) q^{86} +(2.94490 + 5.10071i) q^{87} +(1.28442 - 2.22469i) q^{89} +(0.475488 + 1.46340i) q^{90} +(1.74672 + 15.5445i) q^{91} +(4.24350 - 3.08309i) q^{92} +(-9.05917 - 10.0612i) q^{93} +(-1.06400 + 0.226160i) q^{94} +(4.82877 + 2.14991i) q^{95} +(-10.0215 + 4.46184i) 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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