LMFDB - Embedded newform 210.2.u.b.157.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(73,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("210.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.u (of order $12$, degree $4$, 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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.4
Root			$0.277956 - 0.213283i$ of defining polynomial
Character	$\chi$	$=$	210.157
Dual form			210.2.u.b.103.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.14315 + 0.637899i) q^{5} +1.00000i q^{6} +(0.153213 - 2.64131i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.14315 + 0.637899i) q^{5} +1.00000i q^{6} +(0.153213 - 2.64131i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(1.17085 - 1.90502i) q^{10} +(2.27722 - 3.94427i) q^{11} +(0.965926 + 0.258819i) q^{12} +(1.77772 + 1.77772i) q^{13} +(-2.51166 - 0.831614i) q^{14} +(-2.23522 - 0.0614757i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.06747 - 3.98386i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(1.88956 + 3.27281i) q^{19} +(-1.53707 - 1.62401i) q^{20} +(0.535629 + 2.59097i) q^{21} +(-3.22048 - 3.22048i) q^{22} +(-7.77857 - 2.08426i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.18617 + 2.73423i) q^{25} +(2.17725 - 1.25704i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.45334 + 2.21084i) q^{28} +1.55563i q^{29} +(-0.637899 + 2.14315i) q^{30} +(3.37208 + 1.94687i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-1.17878 + 4.39926i) q^{33} -4.12440 q^{34} +(2.01325 - 5.56299i) q^{35} -1.00000 q^{36} +(-2.95980 + 11.0461i) q^{37} +(3.65035 - 0.978107i) q^{38} +(-2.17725 - 1.25704i) q^{39} +(-1.96650 + 1.06437i) q^{40} +11.3796i q^{41} +(2.64131 + 0.153213i) q^{42} +(0.367260 - 0.367260i) q^{43} +(-3.94427 + 2.27722i) q^{44} +(2.17497 - 0.519137i) q^{45} +(-4.02648 + 6.97408i) q^{46} +(4.87829 + 1.30713i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-6.95305 - 0.809365i) q^{49} +(3.72452 - 3.33586i) q^{50} +(2.06220 + 3.57183i) q^{51} +(-0.650691 - 2.42841i) q^{52} +(-2.18307 - 8.14732i) q^{53} +(0.500000 + 0.866025i) q^{54} +(7.39647 - 7.00051i) q^{55} +(1.75935 + 1.97603i) q^{56} +(-2.67224 - 2.67224i) q^{57} +(1.50262 + 0.402626i) q^{58} +(-0.221511 + 0.383668i) q^{59} +(1.90502 + 1.17085i) q^{60} +(7.09442 - 4.09597i) q^{61} +(2.75329 - 2.75329i) q^{62} +(-1.18797 - 2.36405i) q^{63} -1.00000i q^{64} +(2.67591 + 4.94392i) q^{65} +(3.94427 + 2.27722i) q^{66} +(-8.99808 + 2.41103i) q^{67} +(-1.06747 + 3.98386i) q^{68} +8.05297 q^{69} +(-4.85237 - 3.38446i) q^{70} -6.68403 q^{71} +(-0.258819 + 0.965926i) q^{72} +(-4.20080 + 1.12560i) q^{73} +(9.90370 + 5.71790i) q^{74} +(-4.75120 - 1.55760i) q^{75} -3.77912i q^{76} +(-10.0691 - 6.61917i) q^{77} +(-1.77772 + 1.77772i) q^{78} +(-4.08283 + 2.35722i) q^{79} +(0.519137 + 2.17497i) q^{80} +(0.500000 - 0.866025i) q^{81} +(10.9919 + 2.94527i) q^{82} +(-3.21718 - 3.21718i) q^{83} +(0.831614 - 2.51166i) q^{84} +(0.253550 - 9.21894i) q^{85} +(-0.259692 - 0.449799i) q^{86} +(-0.402626 - 1.50262i) q^{87} +(1.17878 + 4.39926i) q^{88} +(3.02425 + 5.23816i) q^{89} +(0.0614757 - 2.23522i) q^{90} +(4.96788 - 4.42314i) q^{91} +(5.69431 + 5.69431i) q^{92} +(-3.76106 - 1.00777i) q^{93} +(2.52519 - 4.37376i) q^{94} +(1.96188 + 8.21947i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(0.462652 - 0.462652i) q^{97} +(-2.58137 + 6.50665i) q^{98} -4.55445i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 16 * q + 12 * q^5 - 4 * q^7	$ 16 q + 12 q^{5} - 4 q^{7} + 4 q^{10} + 4 q^{11} + 16 q^{13} - 16 q^{14} + 4 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{19} + 8 q^{20} + 8 q^{21} + 4 q^{22} - 40 q^{23} + 8 q^{24} + 16 q^{25} - 12 q^{26} - 4 q^{28} - 4 q^{30} - 24 q^{31} + 4 q^{33} - 16 q^{34} - 44 q^{35} - 16 q^{36} - 8 q^{37} - 20 q^{38} + 12 q^{39} + 8 q^{42} - 24 q^{43} - 4 q^{45} - 4 q^{46} - 52 q^{49} + 8 q^{51} + 8 q^{52} - 28 q^{53} + 8 q^{54} + 56 q^{55} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} + 16 q^{65} - 84 q^{67} + 12 q^{68} + 8 q^{69} + 4 q^{70} - 32 q^{71} + 16 q^{73} + 24 q^{74} - 24 q^{75} + 44 q^{77} - 16 q^{78} - 12 q^{79} + 12 q^{80} + 8 q^{81} + 36 q^{82} + 16 q^{83} - 4 q^{84} + 8 q^{85} - 8 q^{86} + 48 q^{87} - 4 q^{88} + 16 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 8 q^{94} + 72 q^{95} - 44 q^{97} + 24 q^{98}+O(q^{100}) $ 16 * q + 12 * q^5 - 4 * q^7 + 4 * q^10 + 4 * q^11 + 16 * q^13 - 16 * q^14 + 4 * q^15 + 8 * q^16 + 12 * q^17 + 8 * q^19 + 8 * q^20 + 8 * q^21 + 4 * q^22 - 40 * q^23 + 8 * q^24 + 16 * q^25 - 12 * q^26 - 4 * q^28 - 4 * q^30 - 24 * q^31 + 4 * q^33 - 16 * q^34 - 44 * q^35 - 16 * q^36 - 8 * q^37 - 20 * q^38 + 12 * q^39 + 8 * q^42 - 24 * q^43 - 4 * q^45 - 4 * q^46 - 52 * q^49 + 8 * q^51 + 8 * q^52 - 28 * q^53 + 8 * q^54 + 56 * q^55 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 + 16 * q^65 - 84 * q^67 + 12 * q^68 + 8 * q^69 + 4 * q^70 - 32 * q^71 + 16 * q^73 + 24 * q^74 - 24 * q^75 + 44 * q^77 - 16 * q^78 - 12 * q^79 + 12 * q^80 + 8 * q^81 + 36 * q^82 + 16 * q^83 - 4 * q^84 + 8 * q^85 - 8 * q^86 + 48 * q^87 - 4 * q^88 + 16 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 8 * q^94 + 72 * q^95 - 44 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	2.14315	+	0.637899i	0.958445	+	0.285277i
$5$	2.14315	+	0.637899i	0.958445	+	0.285277i
$6$			1.00000i			0.408248i
$7$	0.153213	−	2.64131i	0.0579090	−	0.998322i
$7$	0.153213	−	2.64131i	0.0579090	−	0.998322i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	1.17085	−	1.90502i	0.370256	−	0.602421i
$11$	2.27722	−	3.94427i	0.686609	−	1.18924i	−0.286319	−	0.958134i	$-0.592432\pi$
$11$	2.27722	−	3.94427i	0.686609	−	1.18924i	0.972928	−	0.231107i	$-0.0742348\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	1.77772	+	1.77772i	0.493051	+	0.493051i	0.909266	−	0.416215i	$-0.136644\pi$
$13$	1.77772	+	1.77772i	0.493051	+	0.493051i	−0.416215	+	0.909266i	$0.636644\pi$
$14$	−2.51166	−	0.831614i	−0.671268	−	0.222258i
$15$	−2.23522	−	0.0614757i	−0.577132	−	0.0158730i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.06747	−	3.98386i	−0.258900	−	0.966228i	−0.965879	−	0.258993i	$-0.916609\pi$
$17$	−1.06747	−	3.98386i	−0.258900	−	0.966228i	0.706979	−	0.707234i	$-0.250057\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	1.88956	+	3.27281i	0.433494	+	0.750834i	0.997171	−	0.0751610i	$-0.0239471\pi$
$19$	1.88956	+	3.27281i	0.433494	+	0.750834i	−0.563677	+	0.825995i	$0.690614\pi$
$20$	−1.53707	−	1.62401i	−0.343700	−	0.363140i
$21$	0.535629	+	2.59097i	0.116884	+	0.565395i
$22$	−3.22048	−	3.22048i	−0.686609	−	0.686609i
$23$	−7.77857	−	2.08426i	−1.62194	−	0.434599i	−0.670372	−	0.742025i	$-0.733866\pi$
$23$	−7.77857	−	2.08426i	−1.62194	−	0.434599i	−0.951572	+	0.307426i	$0.900532\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	4.18617	+	2.73423i	0.837234	+	0.546845i
$26$	2.17725	−	1.25704i	0.426995	−	0.246525i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.45334	+	2.21084i	−0.274656	+	0.417809i
$29$			1.55563i			0.288873i	0.989514	+	0.144436i	$0.0461369\pi$
$29$			1.55563i			0.288873i	−0.989514	+	0.144436i	$0.953863\pi$
$30$	−0.637899	+	2.14315i	−0.116464	+	0.391284i
$31$	3.37208	+	1.94687i	0.605643	+	0.349668i	0.771258	−	0.636522i	$-0.219628\pi$
$31$	3.37208	+	1.94687i	0.605643	+	0.349668i	−0.165615	+	0.986190i	$0.552961\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−1.17878	+	4.39926i	−0.205199	+	0.765813i
$34$	−4.12440			−0.707328
$35$	2.01325	−	5.56299i	0.340301	−	0.940317i
$36$	−1.00000			−0.166667
$37$	−2.95980	+	11.0461i	−0.486589	+	1.81597i	0.0862078	+	0.996277i	$0.472525\pi$
$37$	−2.95980	+	11.0461i	−0.486589	+	1.81597i	−0.572797	+	0.819697i	$0.694142\pi$
$38$	3.65035	−	0.978107i	0.592164	−	0.158670i
$39$	−2.17725	−	1.25704i	−0.348640	−	0.201287i
$40$	−1.96650	+	1.06437i	−0.310931	+	0.168292i
$41$			11.3796i			1.77720i	0.458682	+	0.888600i	$0.348322\pi$
$41$			11.3796i			1.77720i	−0.458682	+	0.888600i	$0.651678\pi$
$42$	2.64131	+	0.153213i	0.407563	+	0.0236412i
$43$	0.367260	−	0.367260i	0.0560066	−	0.0560066i	−0.678549	−	0.734555i	$-0.737391\pi$
$43$	0.367260	−	0.367260i	0.0560066	−	0.0560066i	0.734555	+	0.678549i	$0.237391\pi$
$44$	−3.94427	+	2.27722i	−0.594621	+	0.343304i
$45$	2.17497	−	0.519137i	0.324225	−	0.0773884i
$46$	−4.02648	+	6.97408i	−0.593673	+	1.02827i
$47$	4.87829	+	1.30713i	0.711572	+	0.190665i	0.596408	−	0.802681i	$-0.296594\pi$
$47$	4.87829	+	1.30713i	0.711572	+	0.190665i	0.115164	+	0.993347i	$0.463261\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	−6.95305	−	0.809365i	−0.993293	−	0.115624i
$50$	3.72452	−	3.33586i	0.526727	−	0.471762i
$51$	2.06220	+	3.57183i	0.288765	+	0.500156i
$52$	−0.650691	−	2.42841i	−0.0902346	−	0.336760i
$53$	−2.18307	−	8.14732i	−0.299868	−	1.11912i	−0.937274	−	0.348593i	$-0.886659\pi$
$53$	−2.18307	−	8.14732i	−0.299868	−	1.11912i	0.637407	−	0.770528i	$-0.280007\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	7.39647	−	7.00051i	0.997340	−	0.943949i
$56$	1.75935	+	1.97603i	0.235103	+	0.264058i
$57$	−2.67224	−	2.67224i	−0.353947	−	0.353947i
$58$	1.50262	+	0.402626i	0.197304	+	0.0528674i
$59$	−0.221511	+	0.383668i	−0.0288383	+	0.0499493i	−0.880084	−	0.474817i	$-0.842514\pi$
$59$	−0.221511	+	0.383668i	−0.0288383	+	0.0499493i	0.851246	+	0.524767i	$0.175847\pi$
$60$	1.90502	+	1.17085i	0.245937	+	0.151156i
$61$	7.09442	−	4.09597i	0.908348	−	0.524435i	0.0284488	−	0.999595i	$-0.490943\pi$
$61$	7.09442	−	4.09597i	0.908348	−	0.524435i	0.879899	+	0.475160i	$0.157610\pi$
$62$	2.75329	−	2.75329i	0.349668	−	0.349668i
$63$	−1.18797	−	2.36405i	−0.149670	−	0.297842i
$64$		−	1.00000i		−	0.125000i
$65$	2.67591	+	4.94392i	0.331906	+	0.613218i
$66$	3.94427	+	2.27722i	0.485506	+	0.280307i
$67$	−8.99808	+	2.41103i	−1.09929	+	0.294554i	−0.762476	−	0.647017i	$-0.776016\pi$
$67$	−8.99808	+	2.41103i	−1.09929	+	0.294554i	−0.336815	+	0.941571i	$0.609350\pi$
$68$	−1.06747	+	3.98386i	−0.129450	+	0.483114i
$69$	8.05297			0.969464
$70$	−4.85237	−	3.38446i	−0.579969	−	0.404520i
$71$	−6.68403			−0.793248			−0.396624	−	0.917981i	$-0.629818\pi$
$71$	−6.68403			−0.793248			−0.396624	+	0.917981i	$0.629818\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	−4.20080	+	1.12560i	−0.491666	+	0.131742i	−0.496130	−	0.868249i	$-0.665246\pi$
$73$	−4.20080	+	1.12560i	−0.491666	+	0.131742i	0.00446349	+	0.999990i	$0.498579\pi$
$74$	9.90370	+	5.71790i	1.15128	+	0.664693i
$75$	−4.75120	−	1.55760i	−0.548621	−	0.179856i
$76$		−	3.77912i		−	0.433494i
$77$	−10.0691	−	6.61917i	−1.14748	−	0.754324i
$78$	−1.77772	+	1.77772i	−0.201287	+	0.201287i
$79$	−4.08283	+	2.35722i	−0.459354	+	0.265208i	−0.711773	−	0.702410i	$-0.752107\pi$
$79$	−4.08283	+	2.35722i	−0.459354	+	0.265208i	0.252418	+	0.967618i	$0.418774\pi$
$80$	0.519137	+	2.17497i	0.0580413	+	0.243169i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	10.9919	+	2.94527i	1.21385	+	0.325250i
$83$	−3.21718	−	3.21718i	−0.353131	−	0.353131i	0.508142	−	0.861273i	$-0.330332\pi$
$83$	−3.21718	−	3.21718i	−0.353131	−	0.353131i	−0.861273	+	0.508142i	$0.830332\pi$
$84$	0.831614	−	2.51166i	0.0907365	−	0.274044i
$85$	0.253550	−	9.21894i	0.0275014	−	0.999935i
$86$	−0.259692	−	0.449799i	−0.0280033	−	0.0485031i
$87$	−0.402626	−	1.50262i	−0.0431660	−	0.161098i
$88$	1.17878	+	4.39926i	0.125658	+	0.468963i
$89$	3.02425	+	5.23816i	0.320570	+	0.555244i	0.980606	−	0.195990i	$-0.0627921\pi$
$89$	3.02425	+	5.23816i	0.320570	+	0.555244i	−0.660035	+	0.751234i	$0.729459\pi$
$90$	0.0614757	−	2.23522i	0.00648011	−	0.235613i
$91$	4.96788	−	4.42314i	0.520775	−	0.463671i
$92$	5.69431	+	5.69431i	0.593673	+	0.593673i
$93$	−3.76106	−	1.00777i	−0.390004	−	0.104501i
$94$	2.52519	−	4.37376i	0.260453	−	0.451118i
$95$	1.96188	+	8.21947i	0.201285	+	0.843299i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	0.462652	−	0.462652i	0.0469752	−	0.0469752i	−0.683229	−	0.730204i	$-0.739425\pi$
$97$	0.462652	−	0.462652i	0.0469752	−	0.0469752i	0.730204	+	0.683229i	$0.239425\pi$
$98$	−2.58137	+	6.50665i	−0.260758	+	0.657271i
$99$		−	4.55445i		−	0.457739i
$100$	−2.25822	−	4.46099i	−0.225822	−	0.446099i
$101$	−4.85151	−	2.80102i	−0.482743	−	0.278712i	0.238816	−	0.971065i	$-0.423241\pi$
$101$	−4.85151	−	2.80102i	−0.482743	−	0.278712i	−0.721559	+	0.692353i	$0.756574\pi$
$102$	3.98386	−	1.06747i	0.394461	−	0.105695i
$103$	−1.43852	+	5.36863i	−0.141742	+	0.528987i	0.858137	+	0.513420i	$0.171622\pi$
$103$	−1.43852	+	5.36863i	−0.141742	+	0.528987i	−0.999879	+	0.0155666i	$0.995045\pi$
$104$	−2.51408			−0.246525
$105$	−0.504841	+	5.89450i	−0.0492675	+	0.575244i
$106$	−8.43473			−0.819253
$107$	1.93865	−	7.23514i	0.187416	−	0.699447i	−0.806684	−	0.590983i	$-0.798740\pi$
$107$	1.93865	−	7.23514i	0.187416	−	0.699447i	0.994100	−	0.108464i	$-0.0345932\pi$
$108$	0.965926	−	0.258819i	0.0929463	−	0.0249049i
$109$	1.27034	+	0.733433i	0.121677	+	0.0702501i	0.559603	−	0.828761i	$-0.310954\pi$
$109$	1.27034	+	0.733433i	0.121677	+	0.0702501i	−0.437926	+	0.899011i	$0.644287\pi$
$110$	−4.84763	−	8.95631i	−0.462203	−	0.853951i
$111$		−	11.4358i		−	1.08544i
$112$	2.36405	−	1.18797i	0.223382	−	0.112253i
$113$	7.08834	−	7.08834i	0.666815	−	0.666815i	−0.290163	−	0.956977i	$-0.593709\pi$
$113$	7.08834	−	7.08834i	0.666815	−	0.666815i	0.956977	+	0.290163i	$0.0937094\pi$
$114$	−3.27281	+	1.88956i	−0.306527	+	0.176973i
$115$	−15.3411	−	9.42883i	−1.43056	−	0.879243i
$116$	0.777814	−	1.34721i	0.0722182	−	0.125086i
$117$	2.42841	+	0.650691i	0.224507	+	0.0601564i
$118$	0.313264	+	0.313264i	0.0288383	+	0.0288383i
$119$	−10.6862	+	2.20915i	−0.979599	+	0.202512i
$120$	1.62401	−	1.53707i	0.148251	−	0.140315i
$121$	−4.87150	−	8.43768i	−0.442863	−	0.767062i
$122$	−2.12023	−	7.91280i	−0.191957	−	0.716391i
$123$	−2.94527	−	10.9919i	−0.265566	−	0.991105i
$124$	−1.94687	−	3.37208i	−0.174834	−	0.302821i
$125$	7.22742	+	8.53020i	0.646440	+	0.762965i
$126$	−2.59097	+	0.535629i	−0.230822	+	0.0477177i
$127$	12.9176	+	12.9176i	1.14625	+	1.14625i	0.987283	+	0.158971i	$0.0508176\pi$
$127$	12.9176	+	12.9176i	1.14625	+	1.14625i	0.158971	+	0.987283i	$0.449182\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−0.259692	+	0.449799i	−0.0228646	+	0.0396026i
$130$	5.46804	−	1.30515i	0.479579	−	0.114469i
$131$	0.323655	−	0.186862i	0.0282779	−	0.0163262i	−0.485794	−	0.874073i	$-0.661470\pi$
$131$	0.323655	−	0.186862i	0.0282779	−	0.0163262i	0.514072	+	0.857747i	$0.328136\pi$
$132$	3.22048	−	3.22048i	0.280307	−	0.280307i
$133$	8.93402	−	4.48947i	0.774677	−	0.389287i
$134$			9.31550i			0.804737i
$135$	−1.96650	+	1.06437i	−0.169249	+	0.0916065i
$136$	3.57183	+	2.06220i	0.306282	+	0.176832i
$137$	2.56800	−	0.688094i	0.219399	−	0.0587878i	−0.147445	−	0.989070i	$-0.547105\pi$
$137$	2.56800	−	0.688094i	0.219399	−	0.0587878i	0.366844	+	0.930282i	$0.380438\pi$
$138$	2.08426	−	7.77857i	0.177424	−	0.662156i
$139$	4.58070			0.388530			0.194265	−	0.980949i	$-0.437768\pi$
$139$	4.58070			0.388530			0.194265	+	0.980949i	$0.437768\pi$
$140$	−4.52502	+	3.81106i	−0.382434	+	0.322094i
$141$	−5.05038			−0.425319
$142$	−1.72995	+	6.45627i	−0.145174	+	0.541798i
$143$	11.0601	−	2.96354i	0.924889	−	0.247823i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	−0.992333	+	3.33394i	−0.0824088	+	0.276869i
$146$			4.34898i			0.359925i
$147$	6.92561	−	1.01780i	0.571215	−	0.0839463i
$148$	8.08634	−	8.08634i	0.664693	−	0.664693i
$149$	14.9338	−	8.62203i	1.22342	−	0.706344i	0.257778	−	0.966204i	$-0.417010\pi$
$149$	14.9338	−	8.62203i	1.22342	−	0.706344i	0.965646	+	0.259860i	$0.0836764\pi$
$150$	−2.73423	+	4.18617i	−0.223249	+	0.341799i
$151$	2.78385	−	4.82177i	0.226546	−	0.392390i	−0.730236	−	0.683195i	$-0.760590\pi$
$151$	2.78385	−	4.82177i	0.226546	−	0.392390i	0.956782	+	0.290805i	$0.0939231\pi$
$152$	−3.65035	−	0.978107i	−0.296082	−	0.0793350i
$153$	−2.91639	−	2.91639i	−0.235776	−	0.235776i
$154$	−8.99971	+	8.01287i	−0.725217	+	0.645696i
$155$	5.98495	+	6.32347i	0.480723	+	0.507914i
$156$	1.25704	+	2.17725i	0.100644	+	0.174320i
$157$	−1.06916	−	3.99014i	−0.0853279	−	0.318448i	0.910048	−	0.414503i	$-0.136044\pi$
$157$	−1.06916	−	3.99014i	−0.0853279	−	0.318448i	−0.995376	+	0.0960544i	$0.969378\pi$
$158$	1.22019	+	4.55381i	0.0970730	+	0.362281i
$159$	4.21737	+	7.30469i	0.334459	+	0.579300i
$160$	2.23522	+	0.0614757i	0.176710	+	0.00486008i
$161$	−6.69696	+	20.2263i	−0.527795	+	1.59406i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	20.9982	+	5.62644i	1.64470	+	0.440697i	0.958123	−	0.286357i	$-0.0924445\pi$
$163$	20.9982	+	5.62644i	1.64470	+	0.440697i	0.686580	+	0.727054i	$0.259111\pi$
$164$	5.68982	−	9.85506i	0.444300	−	0.769551i
$165$	−5.33258	+	8.67632i	−0.415141	+	0.675451i
$166$	−3.94022	+	2.27489i	−0.305821	+	0.176566i
$167$	−17.4949	+	17.4949i	−1.35380	+	1.35380i	−0.472425	+	0.881371i	$0.656621\pi$
$167$	−17.4949	+	17.4949i	−1.35380	+	1.35380i	−0.881371	+	0.472425i	$0.843379\pi$
$168$	−2.21084	−	1.45334i	−0.170570	−	0.112128i
$169$		−	6.67942i		−	0.513802i
$170$	−8.83919	−	2.63095i	−0.677935	−	0.201785i
$171$	3.27281	+	1.88956i	0.250278	+	0.144498i
$172$	−0.501686	+	0.134426i	−0.0382532	+	0.0102499i
$173$	−4.28763	+	16.0017i	−0.325982	+	1.21658i	0.587338	+	0.809342i	$0.300176\pi$
$173$	−4.28763	+	16.0017i	−0.325982	+	1.21658i	−0.913321	+	0.407241i	$0.866491\pi$
$174$	−1.55563			−0.117932
$175$	7.86331	−	10.6381i	0.594411	−	0.804162i
$176$	4.55445			0.343304
$177$	0.114663	−	0.427926i	0.00861856	−	0.0321649i
$178$	5.84241	−	1.56547i	0.437907	−	0.117337i
$179$	−11.0222	−	6.36367i	−0.823837	−	0.475643i	0.0279007	−	0.999611i	$-0.491118\pi$
$179$	−11.0222	−	6.36367i	−0.823837	−	0.475643i	−0.851738	+	0.523968i	$0.824451\pi$
$180$	−2.14315	−	0.637899i	−0.159741	−	0.0475462i
$181$		−	9.09951i		−	0.676361i	−0.941081	−	0.338180i	$-0.890189\pi$
$181$		−	9.09951i		−	0.676361i	0.941081	−	0.338180i	$-0.109811\pi$
$182$	−2.98665	−	5.94340i	−0.221385	−	0.440554i
$183$	−5.79257	+	5.79257i	−0.428199	+	0.428199i
$184$	6.97408	−	4.02648i	0.514136	−	0.296836i
$185$	−13.3896	+	21.7855i	−0.984425	+	1.60170i
$186$	−1.94687	+	3.37208i	−0.142751	+	0.247253i
$187$	−18.1443	−	4.86175i	−1.32684	−	0.355526i
$188$	−3.57116	−	3.57116i	−0.260453	−	0.260453i
$189$	1.75935	+	1.97603i	0.127974	+	0.143735i
$190$	8.44717	+	0.232324i	0.612822	+	0.0168545i
$191$	−9.10308	−	15.7670i	−0.658676	−	1.14086i	−0.980959	−	0.194216i	$-0.937784\pi$
$191$	−9.10308	−	15.7670i	−0.658676	−	1.14086i	0.322283	−	0.946643i	$-0.395550\pi$
$192$	0.258819	+	0.965926i	0.0186787	+	0.0697097i
$193$	−2.60664	−	9.72810i	−0.187630	−	0.700244i	−0.994052	−	0.108904i	$-0.965266\pi$
$193$	−2.60664	−	9.72810i	−0.187630	−	0.700244i	0.806422	−	0.591340i	$-0.201401\pi$
$194$	−0.327144	−	0.566631i	−0.0234876	−	0.0406817i
$195$	−3.86431	−	4.08289i	−0.276729	−	0.292382i
$196$	5.61684	+	4.17746i	0.401203	+	0.298390i
$197$	16.2439	+	16.2439i	1.15733	+	1.15733i	0.985048	+	0.172283i	$0.0551142\pi$
$197$	16.2439	+	16.2439i	1.15733	+	1.15733i	0.172283	+	0.985048i	$0.444886\pi$
$198$	−4.39926	−	1.17878i	−0.312642	−	0.0837721i
$199$	−12.6984	+	21.9943i	−0.900168	+	1.55914i	−0.0728933	+	0.997340i	$0.523223\pi$
$199$	−12.6984	+	21.9943i	−0.900168	+	1.55914i	−0.827275	+	0.561797i	$0.810110\pi$
$200$	−4.89346	+	1.02668i	−0.346020	+	0.0725972i
$201$	8.06746	−	4.65775i	0.569035	−	0.328532i
$202$	−3.96124	+	3.96124i	−0.278712	+	0.278712i
$203$	4.10890	+	0.238342i	0.288388	+	0.0167283i
$204$		−	4.12440i		−	0.288765i
$205$	−7.25906	+	24.3883i	−0.506995	+	1.70335i
$206$	4.81338	+	2.77901i	0.335364	+	0.193623i
$207$	−7.77857	+	2.08426i	−0.540648	+	0.144866i
$208$	−0.650691	+	2.42841i	−0.0451173	+	0.168380i
$209$	17.2118			1.19056
$210$	5.56299	+	2.01325i	0.383883	+	0.138927i
$211$	−13.6182			−0.937517			−0.468759	−	0.883326i	$-0.655299\pi$
$211$	−13.6182			−0.937517			−0.468759	+	0.883326i	$0.655299\pi$
$212$	−2.18307	+	8.14732i	−0.149934	+	0.559560i
$213$	6.45627	−	1.72995i	0.442377	−	0.118534i
$214$	−6.48684	−	3.74518i	−0.443432	−	0.256015i
$215$	1.02137	−	0.552817i	0.0696566	−	0.0377018i
$216$		−	1.00000i		−	0.0680414i
$217$	5.65893	−	8.60842i	0.384153	−	0.584378i
$218$	1.03723	−	1.03723i	0.0702501	−	0.0702501i
$219$	3.76633	−	2.17449i	0.254505	−	0.146939i
$220$	−9.90579	+	2.36438i	−0.667848	+	0.159407i
$221$	5.18452	−	8.97985i	0.348749	−	0.604050i
$222$	−11.0461	−	2.95980i	−0.741369	−	0.198649i
$223$	15.8412	+	15.8412i	1.06081	+	1.06081i	0.998027	+	0.0627803i	$0.0199968\pi$
$223$	15.8412	+	15.8412i	1.06081	+	1.06081i	0.0627803	+	0.998027i	$0.480003\pi$
$224$	−0.535629	−	2.59097i	−0.0357883	−	0.173116i
$225$	4.99244	+	0.274824i	0.332829	+	0.0183216i
$226$	−5.01221	−	8.68141i	−0.333407	−	0.577479i
$227$	−2.83476	−	10.5795i	−0.188150	−	0.702184i	−0.993934	−	0.109976i	$-0.964923\pi$
$227$	−2.83476	−	10.5795i	−0.188150	−	0.702184i	0.805785	−	0.592209i	$-0.201744\pi$
$228$	0.978107	+	3.65035i	0.0647767	+	0.241750i
$229$	−14.4722	−	25.0665i	−0.956347	−	1.65644i	−0.731255	−	0.682104i	$-0.761065\pi$
$229$	−14.4722	−	25.0665i	−0.956347	−	1.65644i	−0.225092	−	0.974338i	$-0.572268\pi$
$230$	−13.0781	+	12.3780i	−0.862345	+	0.816180i
$231$	11.4392	+	3.78754i	0.752645	+	0.249202i
$232$	−1.09999	−	1.09999i	−0.0722182	−	0.0722182i
$233$	−1.36397	−	0.365476i	−0.0893569	−	0.0239431i	0.213864	−	0.976864i	$-0.431395\pi$
$233$	−1.36397	−	0.365476i	−0.0893569	−	0.0239431i	−0.303220	+	0.952920i	$0.598062\pi$
$234$	1.25704	−	2.17725i	0.0821751	−	0.142332i
$235$	9.62108	+	5.91324i	0.627610	+	0.385737i
$236$	0.383668	−	0.221511i	0.0249747	−	0.0144191i
$237$	3.33362	−	3.33362i	0.216542	−	0.216542i
$238$	−0.631910	+	10.8938i	−0.0409606	+	0.706141i
$239$			4.36430i			0.282303i	0.989988	+	0.141152i	$0.0450805\pi$
$239$			4.36430i			0.282303i	−0.989988	+	0.141152i	$0.954920\pi$
$240$	−1.06437	−	1.96650i	−0.0687049	−	0.126937i
$241$	−2.65862	−	1.53496i	−0.171257	−	0.0988752i	0.411922	−	0.911219i	$-0.364858\pi$
$241$	−2.65862	−	1.53496i	−0.171257	−	0.0988752i	−0.583178	+	0.812344i	$0.698191\pi$
$242$	−9.41101	+	2.52167i	−0.604963	+	0.162099i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−8.19194			−0.524435
$245$	−14.3851	−	6.16994i	−0.919032	−	0.394183i
$246$	−11.3796			−0.725539
$247$	−2.45904	+	9.17725i	−0.156465	+	0.583934i
$248$	−3.76106	+	1.00777i	−0.238828	+	0.0639937i
$249$	3.94022	+	2.27489i	0.249701	+	0.144165i
$250$	10.1101	−	4.77337i	0.639421	−	0.301895i
$251$			1.25355i			0.0791234i	0.999217	+	0.0395617i	$0.0125962\pi$
$251$			1.25355i			0.0791234i	−0.999217	+	0.0395617i	$0.987404\pi$
$252$	−0.153213	+	2.64131i	−0.00965150	+	0.166387i
$253$	−25.9344	+	25.9344i	−1.63048	+	1.63048i
$254$	15.8208	−	9.13414i	0.992685	−	0.573127i
$255$	2.14113	+	8.97044i	0.134083	+	0.561751i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.81783	+	1.82683i	0.425285	+	0.113955i	0.465112	−	0.885252i	$-0.346014\pi$
$257$	6.81783	+	1.82683i	0.425285	+	0.113955i	−0.0398273	+	0.999207i	$0.512681\pi$
$258$	0.367260	+	0.367260i	0.0228646	+	0.0228646i
$259$	28.7228	+	9.51018i	1.78475	+	0.590934i
$260$	0.154555	−	5.61952i	0.00958507	−	0.348508i
$261$	0.777814	+	1.34721i	0.0481455	+	0.0833904i
$262$	−0.0967271	−	0.360990i	−0.00597582	−	0.0223021i
$263$	−1.47214	−	5.49409i	−0.0907758	−	0.338780i	0.905569	−	0.424198i	$-0.139444\pi$
$263$	−1.47214	−	5.49409i	−0.0907758	−	0.338780i	−0.996345	+	0.0854182i	$0.972777\pi$
$264$	−2.27722	−	3.94427i	−0.140153	−	0.242753i
$265$	0.518531	−	18.8535i	0.0318531	−	1.15816i
$266$	−2.02421	−	9.79156i	−0.124112	−	0.600359i
$267$	−4.27694	−	4.27694i	−0.261745	−	0.261745i
$268$	8.99808	+	2.41103i	0.549645	+	0.147277i
$269$	3.85391	−	6.67517i	0.234977	−	0.406992i	−0.724289	−	0.689496i	$-0.757832\pi$
$269$	3.85391	−	6.67517i	0.234977	−	0.406992i	0.959266	+	0.282504i	$0.0911652\pi$
$270$	0.519137	+	2.17497i	0.0315937	+	0.132364i
$271$	−15.4900	+	8.94316i	−0.940951	+	0.543258i	−0.890258	−	0.455456i	$-0.849476\pi$
$271$	−15.4900	+	8.94316i	−0.940951	+	0.543258i	−0.0506925	+	0.998714i	$0.516143\pi$
$272$	2.91639	−	2.91639i	0.176832	−	0.176832i
$273$	−3.65381	+	5.55821i	−0.221139	+	0.336398i
$274$		−	2.65859i		−	0.160611i
$275$	20.3174	−	10.2849i	1.22518	−	0.620205i
$276$	−6.97408	−	4.02648i	−0.419790	−	0.242366i
$277$	−14.2439	+	3.81664i	−0.855832	+	0.229319i	−0.659951	−	0.751308i	$-0.729423\pi$
$277$	−14.2439	+	3.81664i	−0.855832	+	0.229319i	−0.195881	+	0.980628i	$0.562756\pi$
$278$	1.18557	−	4.42461i	0.0711059	−	0.265371i
$279$	3.89374			0.233112
$280$	2.51004	+	5.35721i	0.150004	+	0.320154i
$281$	0.587402			0.0350415			0.0175207	−	0.999847i	$-0.494423\pi$
$281$	0.587402			0.0350415			0.0175207	+	0.999847i	$0.494423\pi$
$282$	−1.30713	+	4.87829i	−0.0778387	+	0.290498i
$283$	17.9809	−	4.81795i	1.06885	−	0.286398i	0.318830	−	0.947812i	$-0.396710\pi$
$283$	17.9809	−	4.81795i	1.06885	−	0.286398i	0.750021	+	0.661414i	$0.230043\pi$
$284$	5.78854	+	3.34201i	0.343486	+	0.198312i
$285$	−4.02238	−	7.43162i	−0.238266	−	0.440211i
$286$		−	11.4502i		−	0.677066i
$287$	30.0572	+	1.74351i	1.77422	+	0.102916i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$	−0.00921092	+	0.00531793i	−0.000541819	+	0.000312819i
$290$	2.96350	+	1.82141i	0.174023	+	0.106957i
$291$	−0.327144	+	0.566631i	−0.0191775	+	0.0332165i
$292$	4.20080	+	1.12560i	0.245833	+	0.0658708i
$293$	−20.6736	−	20.6736i	−1.20777	−	1.20777i	−0.971749	−	0.236018i	$-0.924158\pi$
$293$	−20.6736	−	20.6736i	−1.20777	−	1.20777i	−0.236018	−	0.971749i	$-0.575842\pi$
$294$	0.809365	−	6.95305i	0.0472031	−	0.405510i
$295$	−0.719472	+	0.680956i	−0.0418893	+	0.0396468i
$296$	−5.71790	−	9.90370i	−0.332346	−	0.575641i
$297$	1.17878	+	4.39926i	0.0683996	+	0.255271i
$298$	−4.46309	−	16.6565i	−0.258540	−	0.964884i
$299$	−10.1229	−	17.5334i	−0.585422	−	1.01398i
$300$	3.33586	+	3.72452i	0.192596	+	0.215035i
$301$	−0.913778	−	1.02632i	−0.0526693	−	0.0591559i
$302$	−3.93696	−	3.93696i	−0.226546	−	0.226546i
$303$	5.41115	+	1.44991i	0.310863	+	0.0832954i
$304$	−1.88956	+	3.27281i	−0.108374	+	0.187709i
$305$	17.8172	−	4.25274i	1.02021	−	0.243511i
$306$	−3.57183	+	2.06220i	−0.204188	+	0.117888i
$307$	−1.63464	+	1.63464i	−0.0932937	+	0.0932937i	−0.752213	−	0.658920i	$-0.771014\pi$
$307$	−1.63464	+	1.63464i	−0.0932937	+	0.0932937i	0.658920	+	0.752213i	$0.271014\pi$
$308$	5.41055	+	10.7669i	0.308294	+	0.613503i
$309$		−	5.55802i		−	0.316185i
$310$	7.65703	−	4.14439i	0.434890	−	0.235385i
$311$	12.0239	+	6.94197i	0.681810	+	0.393643i	0.800537	−	0.599284i	$-0.204548\pi$
$311$	12.0239	+	6.94197i	0.681810	+	0.393643i	−0.118727	+	0.992927i	$0.537881\pi$
$312$	2.42841	−	0.650691i	0.137482	−	0.0368381i
$313$	3.49157	−	13.0307i	0.197355	−	0.736540i	−0.794289	−	0.607540i	$-0.792157\pi$
$313$	3.49157	−	13.0307i	0.197355	−	0.736540i	0.991645	−	0.129000i	$-0.0411768\pi$
$314$	−4.13090			−0.233120
$315$	−1.03797	−	5.82431i	−0.0584830	−	0.328163i
$316$	4.71445			0.265208
$317$	3.55024	−	13.2497i	0.199401	−	0.744175i	−0.791682	−	0.610933i	$-0.790794\pi$
$317$	3.55024	−	13.2497i	0.199401	−	0.744175i	0.991083	−	0.133242i	$-0.0425389\pi$
$318$	8.14732	−	2.18307i	0.456879	−	0.122420i
$319$	6.13581	+	3.54251i	0.343539	+	0.198343i
$320$	0.637899	−	2.14315i	0.0356596	−	0.119806i
$321$			7.49036i			0.418071i
$322$	17.8038	+	11.7037i	0.992167	+	0.652223i
$323$	11.0214	−	11.0214i	0.613245	−	0.613245i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	2.58115	+	12.3025i	0.143176	+	0.682421i
$326$	10.8694	−	18.8264i	0.602003	−	1.04270i
$327$	−1.41688	−	0.379653i	−0.0783538	−	0.0209948i
$328$	−8.04662	−	8.04662i	−0.444300	−	0.444300i
$329$	4.19996	−	12.6848i	0.231552	−	0.699336i
$330$	7.00051	+	7.39647i	0.385365	+	0.407162i
$331$	−16.6194	−	28.7856i	−0.913483	−	1.58220i	−0.809108	−	0.587660i	$-0.800049\pi$
$331$	−16.6194	−	28.7856i	−0.913483	−	1.58220i	−0.104375	−	0.994538i	$-0.533284\pi$
$332$	1.17757	+	4.39475i	0.0646275	+	0.241193i
$333$	2.95980	+	11.0461i	0.162196	+	0.605325i
$334$	12.3708	+	21.4268i	0.676898	+	1.17242i
$335$	−20.8222	−	0.572677i	−1.13764	−	0.0312887i
$336$	−1.97603	+	1.75935i	−0.107801	+	0.0959805i
$337$	−17.0329	−	17.0329i	−0.927842	−	0.927842i	0.0697246	−	0.997566i	$-0.477788\pi$
$337$	−17.0329	−	17.0329i	−0.927842	−	0.927842i	−0.997566	+	0.0697246i	$0.977788\pi$
$338$	−6.45183	−	1.72876i	−0.350933	−	0.0940323i
$339$	−5.01221	+	8.68141i	−0.272226	+	0.471509i
$340$	−4.82905	+	7.85706i	−0.261892	+	0.426109i
$341$	15.3579	−	8.86691i	0.831679	−	0.480170i
$342$	2.67224	−	2.67224i	0.144498	−	0.144498i
$343$	−3.20308	+	18.2412i	−0.172950	+	0.984931i
$344$			0.519384i			0.0280033i
$345$	17.2587	+	5.13698i	0.929178	+	0.276566i
$346$	14.3467	+	8.28306i	0.771283	+	0.445300i
$347$	−1.98700	+	0.532414i	−0.106668	+	0.0285815i	−0.311758	−	0.950162i	$-0.600918\pi$
$347$	−1.98700	+	0.532414i	−0.106668	+	0.0285815i	0.205090	+	0.978743i	$0.434251\pi$
$348$	−0.402626	+	1.50262i	−0.0215830	+	0.0805489i
$349$	−11.7250			−0.627627			−0.313814	−	0.949485i	$-0.601607\pi$
$349$	−11.7250			−0.627627			−0.313814	+	0.949485i	$0.601607\pi$
$350$	−8.24040	−	10.3487i	−0.440468	−	0.553162i
$351$	−2.51408			−0.134191
$352$	1.17878	−	4.39926i	0.0628291	−	0.234481i
$353$	−11.0334	+	2.95640i	−0.587250	+	0.157353i	−0.540196	−	0.841539i	$-0.681650\pi$
$353$	−11.0334	+	2.95640i	−0.587250	+	0.157353i	−0.0470542	+	0.998892i	$0.514983\pi$
$354$	−0.383668	−	0.221511i	−0.0203917	−	0.0117732i
$355$	−14.3249	−	4.26373i	−0.760285	−	0.226296i
$356$		−	6.04851i		−	0.320570i
$357$	9.75027	−	4.89966i	0.516039	−	0.259317i
$358$	−8.99958	+	8.99958i	−0.475643	+	0.475643i
$359$	2.08846	−	1.20577i	0.110225	−	0.0636383i	−0.443874	−	0.896089i	$-0.646396\pi$
$359$	2.08846	−	1.20577i	0.110225	−	0.0636383i	0.554099	+	0.832451i	$0.313063\pi$
$360$	−1.17085	+	1.90502i	−0.0617093	+	0.100403i
$361$	2.35914	−	4.08615i	0.124165	−	0.215061i
$362$	−8.78945	−	2.35513i	−0.461963	−	0.123783i
$363$	6.88934	+	6.88934i	0.361596	+	0.361596i
$364$	−6.51388	+	1.34661i	−0.341420	+	0.0705817i
$365$	−9.72095	−	0.267357i	−0.508818	−	0.0139941i
$366$	4.09597	+	7.09442i	0.214100	+	0.370832i
$367$	1.34815	+	5.03135i	0.0703727	+	0.262635i	0.992144	−	0.125099i	$-0.0399248\pi$
$367$	1.34815	+	5.03135i	0.0703727	+	0.262635i	−0.921772	+	0.387733i	$0.873258\pi$
$368$	−2.08426	−	7.77857i	−0.108650	−	0.405486i
$369$	5.68982	+	9.85506i	0.296200	+	0.513034i
$370$	17.5777	+	18.5719i	0.913819	+	0.965506i
$371$	−21.8541	+	4.51789i	−1.13461	+	0.234557i
$372$	2.75329	+	2.75329i	0.142751	+	0.142751i
$373$	0.141659	+	0.0379573i	0.00733480	+	0.00196535i	0.262485	−	0.964936i	$-0.415458\pi$
$373$	0.141659	+	0.0379573i	0.00733480	+	0.00196535i	−0.255150	+	0.966902i	$0.582125\pi$
$374$	−9.39217	+	16.2677i	−0.485658	+	0.841184i
$375$	−9.18893	−	6.36895i	−0.474514	−	0.328891i
$376$	−4.37376	+	2.52519i	−0.225559	+	0.130227i
$377$	−2.76547	+	2.76547i	−0.142429	+	0.142429i
$378$	2.36405	−	1.18797i	0.121594	−	0.0611026i
$379$		−	18.5438i		−	0.952530i	−0.879302	−	0.476265i	$-0.841990\pi$
$379$		−	18.5438i		−	0.952530i	0.879302	−	0.476265i	$-0.158010\pi$
$380$	2.41069	−	8.09921i	0.123666	−	0.415481i
$381$	−15.8208	−	9.13414i	−0.810524	−	0.467956i
$382$	−17.5858	+	4.71210i	−0.899768	+	0.241092i
$383$	−0.996351	+	3.71843i	−0.0509112	+	0.190003i	−0.986698	−	0.162563i	$-0.948024\pi$
$383$	−0.996351	+	3.71843i	−0.0509112	+	0.190003i	0.935787	+	0.352566i	$0.114691\pi$
$384$	1.00000			0.0510310
$385$	−17.3573	−	20.6090i	−0.884610	−	1.05033i
$386$	−10.0713			−0.512614
$387$	0.134426	−	0.501686i	0.00683328	−	0.0255021i
$388$	−0.631994	+	0.169342i	−0.0320847	+	0.00859706i
$389$	−15.4340	−	8.91085i	−0.782537	−	0.451798i	0.0547917	−	0.998498i	$-0.482551\pi$
$389$	−15.4340	−	8.91085i	−0.782537	−	0.451798i	−0.837329	+	0.546700i	$0.815884\pi$
$390$	−4.94392	+	2.67591i	−0.250345	+	0.135500i
$391$			33.2136i			1.67969i
$392$	5.48886	−	4.34424i	0.277229	−	0.219417i
$393$	−0.264263	+	0.264263i	−0.0133303	+	0.0133303i
$394$	19.8946	−	11.4862i	1.00228	−	0.578665i
$395$	−10.2538	+	2.44745i	−0.515924	+	0.123144i
$396$	−2.27722	+	3.94427i	−0.114435	+	0.198207i
$397$	24.7725	+	6.63778i	1.24330	+	0.333141i	0.819744	−	0.572730i	$-0.194116\pi$
$397$	24.7725	+	6.63778i	1.24330	+	0.333141i	0.423554	+	0.905871i	$0.360782\pi$
$398$	17.9583	+	17.9583i	0.900168	+	0.900168i
$399$	−7.46764	+	6.64879i	−0.373849	+	0.332856i
$400$	−0.274824	+	4.99244i	−0.0137412	+	0.249622i
$401$	2.63060	+	4.55632i	0.131366	+	0.227532i	0.924203	−	0.381901i	$-0.124730\pi$
$401$	2.63060	+	4.55632i	0.131366	+	0.227532i	−0.792838	+	0.609433i	$0.791397\pi$
$402$	−2.41103	−	8.99808i	−0.120251	−	0.448784i
$403$	2.53362	+	9.45560i	0.126209	+	0.471017i
$404$	2.80102	+	4.85151i	0.139356	+	0.241371i
$405$	1.62401	−	1.53707i	0.0806978	−	0.0763777i
$406$	1.29368	−	3.90720i	0.0642043	−	0.193911i
$407$	36.8288	+	36.8288i	1.82554	+	1.82554i
$408$	−3.98386	−	1.06747i	−0.197230	−	0.0528477i
$409$	−4.18773	+	7.25336i	−0.207070	+	0.358655i	−0.950790	−	0.309835i	$-0.899726\pi$
$409$	−4.18773	+	7.25336i	−0.207070	+	0.358655i	0.743720	+	0.668491i	$0.233059\pi$
$410$	21.6785	+	13.3239i	1.07062	+	0.658018i
$411$	−2.30241	+	1.32929i	−0.113569	+	0.0655693i
$412$	3.93011	−	3.93011i	0.193623	−	0.193623i
$413$	0.979449	+	0.643862i	0.0481955	+	0.0316824i
$414$			8.05297i			0.395782i
$415$	−4.84265	−	8.94712i	−0.237717	−	0.439197i
$416$	2.17725	+	1.25704i	0.106749	+	0.0616313i
$417$	−4.42461	+	1.18557i	−0.216674	+	0.0580577i
$418$	4.45474	−	16.6253i	0.217888	−	0.813170i
$419$	−9.53078			−0.465609			−0.232805	−	0.972524i	$-0.574790\pi$
$419$	−9.53078			−0.465609			−0.232805	+	0.972524i	$0.574790\pi$
$420$	3.38446	−	4.85237i	0.165145	−	0.236771i
$421$	16.8461			0.821027			0.410514	−	0.911854i	$-0.365349\pi$
$421$	16.8461			0.821027			0.410514	+	0.911854i	$0.365349\pi$
$422$	−3.52466	+	13.1542i	−0.171578	+	0.640336i
$423$	4.87829	−	1.30713i	0.237191	−	0.0635550i
$424$	7.30469	+	4.21737i	0.354747	+	0.204813i
$425$	6.42415	−	19.5958i	0.311617	−	0.950537i
$426$		−	6.68403i		−	0.323842i
$427$	−9.73177	−	19.3661i	−0.470953	−	0.937193i
$428$	−5.29649	+	5.29649i	−0.256015	+	0.256015i
$429$	−9.91619	+	5.72511i	−0.478758	+	0.276411i
$430$	−0.269631	−	1.12964i	−0.0130028	−	0.0544763i
$431$	−10.7791	+	18.6699i	−0.519209	+	0.899297i	0.480541	+	0.876972i	$0.340440\pi$
$431$	−10.7791	+	18.6699i	−0.519209	+	0.899297i	−0.999751	+	0.0223251i	$0.992893\pi$
$432$	−0.965926	−	0.258819i	−0.0464731	−	0.0124524i
$433$	−25.8823	−	25.8823i	−1.24382	−	1.24382i	−0.958402	−	0.285422i	$-0.907866\pi$
$433$	−25.8823	−	25.8823i	−1.24382	−	1.24382i	−0.285422	−	0.958402i	$-0.592134\pi$
$434$	−6.85045	−	7.69413i	−0.328832	−	0.369330i
$435$	0.0956333	−	3.47717i	0.00458526	−	0.166718i
$436$	−0.733433	−	1.27034i	−0.0351251	−	0.0608384i
$437$	−7.87667	−	29.3961i	−0.376792	−	1.40621i
$438$	−1.12560	−	4.20080i	−0.0537832	−	0.200722i
$439$	−10.5899	−	18.3422i	−0.505426	−	0.875424i	−0.999980	−	0.00627716i	$-0.998002\pi$
$439$	−10.5899	−	18.3422i	−0.505426	−	0.875424i	0.494554	−	0.869147i	$-0.335331\pi$
$440$	−0.279988	+	10.1802i	−0.0133479	+	0.485322i
$441$	−6.42620	+	2.77559i	−0.306010	+	0.132171i
$442$	−7.33202	−	7.33202i	−0.348749	−	0.348749i
$443$	4.00895	+	1.07420i	0.190471	+	0.0510366i	0.352794	−	0.935701i	$-0.385232\pi$
$443$	4.00895	+	1.07420i	0.190471	+	0.0510366i	−0.162322	+	0.986738i	$0.551898\pi$
$444$	−5.71790	+	9.90370i	−0.271360	+	0.470009i
$445$	3.14001	+	13.1553i	0.148851	+	0.623622i
$446$	19.4015	−	11.2014i	0.918686	−	0.530404i
$447$	−12.1934	+	12.1934i	−0.576728	+	0.576728i
$448$	−2.64131	−	0.153213i	−0.124790	−	0.00723862i
$449$		−	29.3795i		−	1.38651i	−0.720694	−	0.693253i	$-0.756177\pi$
$449$		−	29.3795i		−	1.38651i	0.720694	−	0.693253i	$-0.243823\pi$
$450$	1.55760	−	4.75120i	0.0734259	−	0.223974i
$451$	44.8843	+	25.9140i	2.11352	+	1.22024i
$452$	−9.68285	+	2.59451i	−0.455443	+	0.122036i
$453$	−1.44103	+	5.37799i	−0.0677053	+	0.252680i
$454$	−10.9527			−0.514035
$455$	13.4684	−	6.31044i	0.631410	−	0.295838i
$456$	3.77912			0.176973
$457$	−0.121995	+	0.455291i	−0.00570668	+	0.0212976i	−0.968720	−	0.248155i	$-0.920176\pi$
$457$	−0.121995	+	0.455291i	−0.00570668	+	0.0212976i	0.963014	+	0.269452i	$0.0868426\pi$
$458$	−27.9581	+	7.49134i	−1.30639	+	0.350047i
$459$	3.57183	+	2.06220i	0.166719	+	0.0962551i
$460$	8.57135	+	15.8361i	0.399641	+	0.738364i
$461$			26.3199i			1.22584i	0.790145	+	0.612920i	$0.210005\pi$
$461$			26.3199i			1.22584i	−0.790145	+	0.612920i	$0.789995\pi$
$462$	6.61917	−	10.0691i	0.307952	−	0.468459i
$463$	−1.02619	+	1.02619i	−0.0476909	+	0.0476909i	−0.730550	−	0.682859i	$-0.760736\pi$
$463$	−1.02619	+	1.02619i	−0.0476909	+	0.0476909i	0.682859	+	0.730550i	$0.260736\pi$
$464$	−1.34721	+	0.777814i	−0.0625428	+	0.0361091i
$465$	−7.41766	−	4.55899i	−0.343986	−	0.211418i
$466$	−0.706045	+	1.22291i	−0.0327069	+	0.0566500i
$467$	−29.9569	−	8.02693i	−1.38624	−	0.371442i	−0.512856	−	0.858475i	$-0.671413\pi$
$467$	−29.9569	−	8.02693i	−1.38624	−	0.371442i	−0.873384	+	0.487033i	$0.838079\pi$
$468$	−1.77772	−	1.77772i	−0.0821751	−	0.0821751i
$469$	4.98966	+	24.1361i	0.230401	+	1.11450i
$470$	8.20187	−	7.76279i	0.378324	−	0.358071i
$471$	2.06545	+	3.57747i	0.0951709	+	0.164841i
$472$	−0.114663	−	0.427926i	−0.00527777	−	0.0196969i
$473$	−0.612238	−	2.28490i	−0.0281507	−	0.105060i
$474$	−2.35722	−	4.08283i	−0.108271	−	0.187531i
$475$	−1.03859	+	18.8670i	−0.0476538	+	0.865678i
$476$	10.3591	+	3.42990i	0.474807	+	0.157209i
$477$	−5.96425	−	5.96425i	−0.273084	−	0.273084i
$478$	4.21559	+	1.12956i	0.192817	+	0.0516650i
$479$	−16.6760	+	28.8837i	−0.761945	+	1.31973i	0.179901	+	0.983685i	$0.442422\pi$
$479$	−16.6760	+	28.8837i	−0.761945	+	1.31973i	−0.941847	+	0.336043i	$0.890911\pi$
$480$	−2.17497	+	0.519137i	−0.0992734	+	0.0236953i
$481$	−24.8987	+	14.3752i	−1.13528	+	0.655455i
$482$	−2.17075	+	2.17075i	−0.0988752	+	0.0988752i
$483$	1.23382	−	21.2704i	0.0561407	−	0.967837i
$484$			9.74299i			0.442863i
$485$	1.28666	−	0.696407i	0.0584241	−	0.0316222i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	3.19111	−	0.855056i	0.144603	−	0.0387463i	−0.185791	−	0.982589i	$-0.559485\pi$
$487$	3.19111	−	0.855056i	0.144603	−	0.0387463i	0.330395	+	0.943843i	$0.392818\pi$
$488$	−2.12023	+	7.91280i	−0.0959783	+	0.358196i
$489$	−21.7389			−0.983067
$490$	−9.68285	+	12.2981i	−0.437426	+	0.555570i
$491$	3.61649			0.163210			0.0816051	−	0.996665i	$-0.473995\pi$
$491$	3.61649			0.163210			0.0816051	+	0.996665i	$0.473995\pi$
$492$	−2.94527	+	10.9919i	−0.132783	+	0.495552i
$493$	6.19740	−	1.66059i	0.279117	−	0.0747891i
$494$	8.22809	+	4.75049i	0.370199	+	0.213735i
$495$	2.90528	−	9.76086i	0.130583	−	0.438718i
$496$			3.89374i			0.174834i
$497$	−1.02408	+	17.6546i	−0.0459362	+	0.791917i
$498$	3.21718	−	3.21718i	0.144165	−	0.144165i
$499$	0.561004	−	0.323896i	0.0251140	−	0.0144996i	−0.487390	−	0.873184i	$-0.662051\pi$
$499$	0.561004	−	0.323896i	0.0251140	−	0.0144996i	0.512504	+	0.858685i	$0.328718\pi$
$500$	−1.99403	−	11.0011i	−0.0891757	−	0.491983i
$501$	12.3708	−	21.4268i	0.552685	−	0.957278i
$502$	1.21084	+	0.324443i	0.0540423	+	0.0144806i
$503$	12.9189	+	12.9189i	0.576027	+	0.576027i	0.933806	−	0.357779i	$-0.116466\pi$
$503$	12.9189	+	12.9189i	0.576027	+	0.576027i	−0.357779	+	0.933806i	$0.616466\pi$
$504$	2.51166	+	0.831614i	0.111878	+	0.0370430i
$505$	−8.61073	−	9.09777i	−0.383172	−	0.404845i
$506$	18.3384	+	31.7631i	0.815242	+	1.41204i
$507$	1.72876	+	6.45183i	0.0767770	+	0.286536i
$508$	−4.72818	−	17.6458i	−0.209779	−	0.782906i
$509$	10.1554	+	17.5896i	0.450128	+	0.779645i	0.998394	−	0.0566595i	$-0.0180449\pi$
$509$	10.1554	+	17.5896i	0.450128	+	0.779645i	−0.548265	+	0.836304i	$0.684712\pi$
$510$	9.21894	+	0.253550i	0.408222	+	0.0112274i
$511$	2.32944	+	11.2681i	0.103049	+	0.498470i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−3.65035	−	0.978107i	−0.161167	−	0.0431845i
$514$	3.52917	−	6.11270i	0.155665	−	0.269620i
$515$	−6.50761	+	10.5881i	−0.286760	+	0.466569i
$516$	0.449799	−	0.259692i	0.0198013	−	0.0114323i
$517$	16.2646	−	16.2646i	0.715318	−	0.715318i
$518$	16.6201	−	25.2827i	0.730247	−	1.11086i
$519$		−	16.5661i		−	0.727172i
$520$	−5.38804	−	1.60373i	−0.236281	−	0.0703281i
$521$	1.07875	+	0.622814i	0.0472607	+	0.0272860i	0.523444	−	0.852060i	$-0.324647\pi$
$521$	1.07875	+	0.622814i	0.0472607	+	0.0272860i	−0.476183	+	0.879346i	$0.657980\pi$
$522$	1.50262	−	0.402626i	0.0657679	−	0.0176225i
$523$	5.25224	−	19.6016i	0.229664	−	0.857119i	−0.750818	−	0.660509i	$-0.770340\pi$
$523$	5.25224	−	19.6016i	0.229664	−	0.857119i	0.980482	−	0.196609i	$-0.0629930\pi$
$524$	−0.373725			−0.0163262
$525$	−4.84205	+	12.3108i	−0.211324	+	0.537285i
$526$	−5.68790			−0.248004
$527$	4.15646	−	15.5121i	0.181058	−	0.675718i
$528$	−4.39926	+	1.17878i	−0.191453	+	0.0512997i
$529$	36.2434	+	20.9252i	1.57580	+	0.909790i
$530$	−18.0769	−	5.38051i	−0.785209	−	0.233714i
$531$			0.443022i			0.0192255i
$532$	−9.98182	−	0.579009i	−0.432767	−	0.0251032i
$533$	−20.2298	+	20.2298i	−0.876250	+	0.876250i
$534$	−5.23816	+	3.02425i	−0.226677	+	0.130872i
$535$	8.77010	−	14.2693i	0.379164	−	0.616916i
$536$	4.65775	−	8.06746i	0.201184	−	0.348461i
$537$	12.2937	+	3.29408i	0.530510	+	0.142150i
$538$	−5.45025	−	5.45025i	−0.234977	−	0.234977i
$539$	−19.0260	+	25.5816i	−0.819508	+	1.10188i
$540$	2.23522	+	0.0614757i	0.0961887	+	0.00264549i
$541$	17.0068	+	29.4566i	0.731178	+	1.26644i	0.956380	+	0.292126i	$0.0943625\pi$
$541$	17.0068	+	29.4566i	0.731178	+	1.26644i	−0.225202	+	0.974312i	$0.572304\pi$
$542$	4.62932	+	17.2769i	0.198846	+	0.742104i
$543$	2.35513	+	8.78945i	0.101068	+	0.377191i
$544$	−2.06220	−	3.57183i	−0.0884160	−	0.153141i
$545$	2.25468	+	2.38221i	0.0965798	+	0.102043i
$546$	4.42314	+	4.96788i	0.189293	+	0.212606i
$547$	27.8171	+	27.8171i	1.18937	+	1.18937i	0.977241	+	0.212132i	$0.0680407\pi$
$547$	27.8171	+	27.8171i	1.18937	+	1.18937i	0.212132	+	0.977241i	$0.431959\pi$
$548$	−2.56800	−	0.688094i	−0.109700	−	0.0293939i
$549$	4.09597	−	7.09442i	0.174812	−	0.302783i
$550$	−4.67596	−	22.2870i	−0.199384	−	0.950321i
$551$	−5.09127	+	2.93945i	−0.216896	+	0.125225i
$552$	−5.69431	+	5.69431i	−0.242366	+	0.242366i
$553$	5.60062	+	11.1452i	0.238163	+	0.473941i
$554$			14.7464i			0.626512i
$555$	7.29489	−	24.5086i	0.309651	−	1.04033i
$556$	−3.96700	−	2.29035i	−0.168238	−	0.0971324i
$557$	−1.36512	+	0.365782i	−0.0578419	+	0.0154987i	−0.287624	−	0.957743i	$-0.592865\pi$
$557$	−1.36512	+	0.365782i	−0.0578419	+	0.0154987i	0.229782	+	0.973242i	$0.426199\pi$
$558$	1.00777	−	3.76106i	0.0426625	−	0.159218i
$559$	1.30577			0.0552282
$560$	5.82431	−	1.03797i	0.246122	−	0.0438622i
$561$	18.7843			0.793076
$562$	0.152031	−	0.567387i	0.00641303	−	0.0239338i
$563$	36.9530	−	9.90152i	1.55738	−	0.417299i	0.625548	−	0.780185i	$-0.284875\pi$
$563$	36.9530	−	9.90152i	1.55738	−	0.417299i	0.931834	+	0.362886i	$0.118209\pi$
$564$	4.37376	+	2.52519i	0.184168	+	0.106330i
$565$	19.7130	−	10.6697i	0.829332	−	0.448878i
$566$		−	18.6151i		−	0.782453i
$567$	−2.21084	−	1.45334i	−0.0928464	−	0.0610346i
$568$	4.72632	−	4.72632i	0.198312	−	0.198312i
$569$	−31.1820	+	18.0029i	−1.30722	+	0.754723i	−0.981631	−	0.190789i	$-0.938895\pi$
$569$	−31.1820	+	18.0029i	−1.30722	+	0.754723i	−0.325587	+	0.945512i	$0.605562\pi$
$570$	−8.21947	+	1.96188i	−0.344276	+	0.0821741i
$571$	17.1990	−	29.7895i	0.719756	−	1.24665i	−0.241341	−	0.970440i	$-0.577587\pi$
$571$	17.1990	−	29.7895i	0.719756	−	1.24665i	0.961096	−	0.276213i	$-0.0890795\pi$
$572$	−11.0601	−	2.96354i	−0.462445	−	0.123912i
$573$	12.8737	+	12.8737i	0.537806	+	0.537806i
$574$	9.46346	−	28.5817i	0.394997	−	1.19298i
$575$	−26.8636	−	29.9934i	−1.12029	−	1.25081i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−11.5727	−	43.1900i	−0.481779	−	1.79802i	−0.594148	−	0.804355i	$-0.702511\pi$
$577$	−11.5727	−	43.1900i	−0.481779	−	1.79802i	0.112370	−	0.993666i	$-0.464156\pi$
$578$	0.00275276	+	0.0102734i	0.000114500	+	0.000427319i
$579$	5.03564	+	8.72198i	0.209274	+	0.362473i
$580$	2.52636	−	2.39111i	0.104901	−	0.0992854i
$581$	−8.99048	+	8.00466i	−0.372988	+	0.332089i
$582$	0.462652	+	0.462652i	0.0191775	+	0.0191775i
$583$	−37.1066	−	9.94267i	−1.53680	−	0.411783i
$584$	2.17449	−	3.76633i	0.0899811	−	0.155852i
$585$	4.78937	+	2.94361i	0.198016	+	0.121703i
$586$	−25.3199	+	14.6185i	−1.04596	+	0.603883i
$587$	19.7182	−	19.7182i	0.813859	−	0.813859i	−0.171351	−	0.985210i	$-0.554813\pi$
$587$	19.7182	−	19.7182i	0.813859	−	0.813859i	0.985210	+	0.171351i	$0.0548132\pi$
$588$	−6.50665	−	2.58137i	−0.268330	−	0.106454i
$589$			14.7149i			0.606316i
$590$	0.471540	+	0.871201i	0.0194130	+	0.0358668i
$591$	−19.8946	−	11.4862i	−0.818356	−	0.472478i
$592$	−11.0461	+	2.95980i	−0.453994	+	0.121647i
$593$	−2.57961	+	9.62724i	−0.105932	+	0.395343i	−0.998449	−	0.0556699i	$-0.982271\pi$
$593$	−2.57961	+	9.62724i	−0.105932	+	0.395343i	0.892517	+	0.451013i	$0.148937\pi$
$594$	4.55445			0.186871
$595$	−24.3112	−	2.08216i	−0.996664	−	0.0853604i
$596$	−17.2441			−0.706344
$597$	6.57319	−	24.5315i	0.269023	−	1.00401i
$598$	−19.5559	+	5.23999i	−0.799701	+	0.214279i
$599$	14.2556	+	8.23048i	0.582469	+	0.336288i	0.762114	−	0.647443i	$-0.224162\pi$
$599$	14.2556	+	8.23048i	0.582469	+	0.336288i	−0.179645	+	0.983731i	$0.557495\pi$
$600$	4.46099	−	2.25822i	0.182119	−	0.0921913i
$601$		−	34.0216i		−	1.38777i	−0.720086	−	0.693885i	$-0.755898\pi$
$601$		−	34.0216i		−	1.38777i	0.720086	−	0.693885i	$-0.244102\pi$
$602$	−1.22785	+	0.617012i	−0.0500434	+	0.0251475i
$603$	−6.58705	+	6.58705i	−0.268246	+	0.268246i
$604$	−4.82177	+	2.78385i	−0.196195	+	0.113273i
$605$	−5.05795	−	21.1907i	−0.205635	−	0.861525i
$606$	2.80102	−	4.85151i	0.113784	−	0.197079i
$607$	34.7707	+	9.31678i	1.41130	+	0.378156i	0.882389	−	0.470521i	$-0.155934\pi$
$607$	34.7707	+	9.31678i	1.41130	+	0.378156i	0.528910	+	0.848678i	$0.322601\pi$
$608$	2.67224	+	2.67224i	0.108374	+	0.108374i
$609$	−4.03058	+	0.833240i	−0.163327	+	0.0337646i
$610$	0.503605	−	18.3108i	0.0203904	−	0.741383i
$611$	6.34852	+	10.9960i	0.256833	+	0.444849i
$612$	1.06747	+	3.98386i	0.0431500	+	0.161038i
$613$	−8.52125	−	31.8017i	−0.344170	−	1.28446i	−0.893579	−	0.448906i	$-0.851814\pi$
$613$	−8.52125	−	31.8017i	−0.344170	−	1.28446i	0.549409	−	0.835554i	$-0.314853\pi$
$614$	1.15586	+	2.00201i	0.0466469	+	0.0807947i
$615$	0.699571	−	25.4360i	0.0282094	−	1.02568i
$616$	11.8004	−	2.43950i	0.475452	−	0.0982901i
$617$	−10.3705	−	10.3705i	−0.417499	−	0.417499i	0.466842	−	0.884341i	$-0.345392\pi$
$617$	−10.3705	−	10.3705i	−0.417499	−	0.417499i	−0.884341	+	0.466842i	$0.845392\pi$
$618$	−5.36863	−	1.43852i	−0.215958	−	0.0578658i
$619$	−2.58828	+	4.48304i	−0.104032	+	0.180188i	−0.913342	−	0.407193i	$-0.866508\pi$
$619$	−2.58828	+	4.48304i	−0.104032	+	0.180188i	0.809310	+	0.587381i	$0.199841\pi$
$620$	−2.02138	−	8.46877i	−0.0811808	−	0.340114i
$621$	6.97408	−	4.02648i	0.279860	−	0.161577i
$622$	9.81743	−	9.81743i	0.393643	−	0.393643i
$623$	14.2990	−	7.18544i	0.572876	−	0.287879i
$624$		−	2.51408i		−	0.100644i
$625$	10.0480	+	22.8919i	0.401921	+	0.915674i
$626$	−11.6830	−	6.74520i	−0.466948	−	0.269592i
$627$	−16.6253	+	4.45474i	−0.663951	+	0.177905i
$628$	−1.06916	+	3.99014i	−0.0426640	+	0.159224i
$629$	47.1658			1.88062
$630$	−5.89450	−	0.504841i	−0.234843	−	0.0201134i
$631$	14.5385			0.578769			0.289384	−	0.957213i	$-0.406549\pi$
$631$	14.5385			0.578769			0.289384	+	0.957213i	$0.406549\pi$
$632$	1.22019	−	4.55381i	0.0485365	−	0.181141i
$633$	13.1542	−	3.52466i	0.522832	−	0.140093i
$634$	−11.8793	−	6.85853i	−0.471788	−	0.272387i
$635$	19.4442	+	35.9245i	0.771621	+	1.42562i
$636$		−	8.43473i		−	0.334459i
$637$	−10.9218	−	13.7994i	−0.432736	−	0.546752i
$638$	5.00987	−	5.00987i	0.198343	−	0.198343i
$639$	−5.78854	+	3.34201i	−0.228991	+	0.132208i
$640$	−1.90502	−	1.17085i	−0.0753026	−	0.0462819i
$641$	−20.8743	+	36.1553i	−0.824484	+	1.42805i	0.0778281	+	0.996967i	$0.475201\pi$
$641$	−20.8743	+	36.1553i	−0.824484	+	1.42805i	−0.902313	+	0.431082i	$0.858132\pi$
$642$	7.23514	+	1.93865i	0.285548	+	0.0765124i
$643$	−15.5128	−	15.5128i	−0.611766	−	0.611766i	0.331640	−	0.943406i	$-0.392398\pi$
$643$	−15.5128	−	15.5128i	−0.611766	−	0.611766i	−0.943406	+	0.331640i	$0.892398\pi$
$644$	15.9129	−	14.1680i	0.627056	−	0.558298i
$645$	−0.843485	+	0.798330i	−0.0332122	+	0.0314342i
$646$	−7.79328	−	13.4984i	−0.306623	−	0.531086i
$647$	−3.70148	−	13.8141i	−0.145520	−	0.543089i	−0.999732	−	0.0231633i	$-0.992626\pi$
$647$	−3.70148	−	13.8141i	−0.145520	−	0.543089i	0.854211	−	0.519926i	$-0.174040\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	1.00886	+	1.74740i	0.0396012	+	0.0685913i
$650$	12.5514	+	0.690928i	0.492305	+	0.0271004i
$651$	−3.23809	+	9.77973i	−0.126911	+	0.383298i
$652$	−15.3717	−	15.3717i	−0.602003	−	0.602003i
$653$	−14.7451	−	3.95094i	−0.577021	−	0.154612i	−0.0415062	−	0.999138i	$-0.513216\pi$
$653$	−14.7451	−	3.95094i	−0.577021	−	0.154612i	−0.535515	+	0.844526i	$0.679882\pi$
$654$	−0.733433	+	1.27034i	−0.0286795	+	0.0496743i
$655$	0.812840	−	0.194014i	0.0317603	−	0.00758077i
$656$	−9.85506	+	5.68982i	−0.384775	+	0.222150i
$657$	−3.07520	+	3.07520i	−0.119975	+	0.119975i
$658$	−11.1656	−	7.33993i	−0.435279	−	0.286140i
$659$		−	18.9116i		−	0.736690i	−0.929689	−	0.368345i	$-0.879924\pi$
$659$		−	18.9116i		−	0.736690i	0.929689	−	0.368345i	$-0.120076\pi$
$660$	8.95631	−	4.84763i	0.348624	−	0.188694i
$661$	19.5815	+	11.3054i	0.761632	+	0.439728i	0.829881	−	0.557940i	$-0.188408\pi$
$661$	19.5815	+	11.3054i	0.761632	+	0.439728i	−0.0682495	+	0.997668i	$0.521741\pi$
$662$	−32.1061	+	8.60281i	−1.24784	+	0.334358i
$663$	−2.68371	+	10.0157i	−0.104226	+	0.388979i
$664$	4.54978			0.176566
$665$	22.0108	−	3.92261i	0.853540	−	0.152112i
$666$	11.4358			0.443129
$667$	3.24233	−	12.1006i	0.125544	−	0.468535i
$668$	23.8985	−	6.40358i	0.924660	−	0.247762i
$669$	−19.4015	−	11.2014i	−0.750104	−	0.433073i
$670$	−5.94235	+	19.9645i	−0.229573	+	0.771296i
$671$		−	37.3097i		−	1.44033i
$672$	1.18797	+	2.36405i	0.0458269	+	0.0911952i
$673$	−24.2623	+	24.2623i	−0.935243	+	0.935243i	−0.998027	−	0.0627838i	$-0.980002\pi$
$673$	−24.2623	+	24.2623i	−0.935243	+	0.935243i	0.0627838	+	0.998027i	$0.480002\pi$
$674$	−20.8610	+	12.0441i	−0.803534	+	0.463921i
$675$	−4.89346	+	1.02668i	−0.188349	+	0.0395169i
$676$	−3.33971	+	5.78455i	−0.128450	+	0.222483i
$677$	8.59870	+	2.30402i	0.330475	+	0.0885505i	0.420241	−	0.907412i	$-0.361945\pi$
$677$	8.59870	+	2.30402i	0.330475	+	0.0885505i	−0.0897664	+	0.995963i	$0.528612\pi$
$678$	7.08834	+	7.08834i	0.272226	+	0.272226i
$679$	−1.15112	−	1.29289i	−0.0441761	−	0.0496166i
$680$	6.33949	+	6.69806i	0.243108	+	0.256859i
$681$	5.47634	+	9.48530i	0.209854	+	0.363477i
$682$	−4.58985	−	17.1296i	−0.175755	−	0.655925i
$683$	12.3979	+	46.2697i	0.474394	+	1.77046i	0.623693	+	0.781669i	$0.285632\pi$
$683$	12.3979	+	46.2697i	0.474394	+	1.77046i	−0.149299	+	0.988792i	$0.547702\pi$
$684$	−1.88956	−	3.27281i	−0.0722491	−	0.125139i
$685$	5.94254	+	0.163439i	0.227053	+	0.00624467i
$686$	16.7906	+	7.81510i	0.641068	+	0.298382i
$687$	20.4667	+	20.4667i	0.780854	+	0.780854i
$688$	0.501686	+	0.134426i	0.0191266	+	0.00512496i
$689$	10.6028	−	18.3645i	0.403934	−	0.699633i
$690$	9.42883	−	15.3411i	0.358949	−	0.584025i
$691$	−22.3848	+	12.9239i	−0.851559	+	0.491648i	−0.861177	−	0.508306i	$-0.830272\pi$
$691$	−22.3848	+	12.9239i	−0.851559	+	0.491648i	0.00961738	+	0.999954i	$0.496939\pi$
$692$	11.7140	−	11.7140i	0.445300	−	0.445300i
$693$	−12.0297	−	0.697800i	−0.456971	−	0.0265072i
$694$			2.05709i			0.0780861i
$695$	9.81711	+	2.92202i	0.372384	+	0.110839i
$696$	1.34721	+	0.777814i	0.0510660	+	0.0294829i
$697$	45.3349	−	12.1474i	1.71718	−	0.460117i
$698$	−3.03467	+	11.3255i	−0.114864	+	0.428677i
$699$	1.41209			0.0534102
$700$	−12.1289	+	5.28117i	−0.458428	+	0.199610i
$701$	3.95788			0.149487			0.0747435	−	0.997203i	$-0.476186\pi$
$701$	3.95788			0.149487			0.0747435	+	0.997203i	$0.476186\pi$
$702$	−0.650691	+	2.42841i	−0.0245587	+	0.0916544i
$703$	−41.7447	+	11.1854i	−1.57443	+	0.421867i
$704$	−3.94427	−	2.27722i	−0.148655	−	0.0858261i
$705$	−10.8237	−	3.22163i	−0.407644	−	0.121334i
$706$			11.4227i			0.429897i
$707$	−8.14167	+	12.3852i	−0.306199	+	0.465793i
$708$	−0.313264	+	0.313264i	−0.0117732	+	0.0117732i
$709$	−25.1665	+	14.5299i	−0.945148	+	0.545682i	−0.891570	−	0.452882i	$-0.850396\pi$
$709$	−25.1665	+	14.5299i	−0.945148	+	0.545682i	−0.0535778	+	0.998564i	$0.517063\pi$
$710$	−7.82600	+	12.7332i	−0.293704	+	0.477869i
$711$	−2.35722	+	4.08283i	−0.0884028	+	0.153118i
$712$	−5.84241	−	1.56547i	−0.218954	−	0.0586684i
$713$	−22.1722	−	22.1722i	−0.830354	−	0.830354i
$714$	−2.20915	−	10.6862i	−0.0826753	−	0.399920i
$715$	25.5938	+	0.703911i	0.957154	+	0.0263248i
$716$	6.36367	+	11.0222i	0.237821	+	0.411919i
$717$	−1.12956	−	4.21559i	−0.0421843	−	0.157434i
$718$	−0.624155	−	2.32938i	−0.0232932	−	0.0869316i
$719$	−10.1319	−	17.5490i	−0.377857	−	0.654467i	0.612893	−	0.790166i	$-0.290005\pi$
$719$	−10.1319	−	17.5490i	−0.377857	−	0.654467i	−0.990750	+	0.135699i	$0.956672\pi$
$720$	1.53707	+	1.62401i	0.0572833	+	0.0605233i
$721$	13.9598	+	4.62212i	0.519891	+	0.172137i
$722$	−3.33633	−	3.33633i	−0.124165	−	0.124165i
$723$	2.96531	+	0.794551i	0.110281	+	0.0295497i
$724$	−4.54975	+	7.88040i	−0.169090	+	0.292873i
$725$	−4.25343	+	6.51212i	−0.157969	+	0.241854i
$726$	8.43768	−	4.87150i	0.313152	−	0.180798i
$727$	−2.80940	+	2.80940i	−0.104195	+	0.104195i	−0.757282	−	0.653088i	$-0.773473\pi$
$727$	−2.80940	+	2.80940i	−0.104195	+	0.104195i	0.653088	+	0.757282i	$0.273473\pi$
$728$	−0.385189	+	6.64046i	−0.0142760	+	0.246112i
$729$		−	1.00000i		−	0.0370370i
$730$	−2.77421	+	9.32052i	−0.102678	+	0.344968i
$731$	−1.85515	−	1.07107i	−0.0686152	−	0.0396150i
$732$	7.91280	−	2.12023i	0.292466	−	0.0783659i
$733$	−0.451275	+	1.68418i	−0.0166682	+	0.0622066i	−0.973759	−	0.227582i	$-0.926918\pi$
$733$	−0.451275	+	1.68418i	−0.0166682	+	0.0622066i	0.957091	+	0.289788i	$0.0935848\pi$
$734$	5.20884			0.192262
$735$	15.4919	+	2.23656i	0.571426	+	0.0824966i
$736$	−8.05297			−0.296836
$737$	−10.9809	+	40.9813i	−0.404487	+	1.50957i
$738$	10.9919	−	2.94527i	0.404617	−	0.108417i
$739$	−20.2692	−	11.7024i	−0.745615	−	0.430481i	0.0784926	−	0.996915i	$-0.474989\pi$
$739$	−20.2692	−	11.7024i	−0.745615	−	0.430481i	−0.824107	+	0.566434i	$0.808323\pi$
$740$	22.4885	−	12.1720i	0.826693	−	0.447450i
$741$		−	9.50098i		−	0.349027i
$742$	−1.29231	+	22.2787i	−0.0474421	+	0.817879i
$743$	1.84057	−	1.84057i	0.0675240	−	0.0675240i	−0.672538	−	0.740062i	$-0.734796\pi$
$743$	1.84057	−	1.84057i	0.0675240	−	0.0675240i	0.740062	+	0.672538i	$0.234796\pi$
$744$	3.37208	−	1.94687i	0.123626	−	0.0713757i
$745$	37.5053	−	8.95203i	1.37409	−	0.327977i
$746$	0.0733279	−	0.127008i	0.00268472	−	0.00465008i
$747$	−4.39475	−	1.17757i	−0.160795	−	0.0430850i
$748$	13.2825	+	13.2825i	0.485658	+	0.485658i
$749$	−18.8132	−	6.22909i	−0.687420	−	0.227606i
$750$	−8.53020	+	7.22742i	−0.311479	+	0.263908i
$751$	−21.1862	−	36.6956i	−0.773096	−	1.33904i	−0.935858	−	0.352376i	$-0.885374\pi$
$751$	−21.1862	−	36.6956i	−0.773096	−	1.33904i	0.162762	−	0.986665i	$-0.447960\pi$
$752$	1.30713	+	4.87829i	0.0476663	+	0.177893i
$753$	−0.324443	−	1.21084i	−0.0118234	−	0.0441254i
$754$	1.95548	+	3.38699i	0.0712145	+	0.123347i
$755$	9.04201	−	8.55795i	0.329072	−	0.311456i
$756$	−0.535629	−	2.59097i	−0.0194807	−	0.0942325i
$757$	10.2470	+	10.2470i	0.372434	+	0.372434i	0.868363	−	0.495929i	$-0.165172\pi$
$757$	10.2470	+	10.2470i	0.372434	+	0.372434i	−0.495929	+	0.868363i	$0.665172\pi$
$758$	−17.9119	−	4.79948i	−0.650590	−	0.174325i
$759$	18.3384	−	31.7631i	0.665642	−	1.15293i
$760$	−7.19930	−	4.42478i	−0.261146	−	0.160504i
$761$	13.4082	−	7.74124i	0.486048	−	0.280620i	−0.236886	−	0.971538i	$-0.576127\pi$
$761$	13.4082	−	7.74124i	0.486048	−	0.280620i	0.722933	+	0.690918i	$0.242793\pi$
$762$	−12.9176	+	12.9176i	−0.467956	+	0.467956i
$763$	2.13186	−	3.24300i	0.0771784	−	0.117404i
$764$			18.2062i			0.658676i
$765$	−4.38989	−	8.11061i	−0.158717	−	0.293240i
$766$	3.33386	+	1.92480i	0.120457	+	0.0695460i
$767$	−1.07584	+	0.288270i	−0.0388463	+	0.0104088i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	15.9644			0.575691			0.287846	−	0.957677i	$-0.407061\pi$
$769$	15.9644			0.575691			0.287846	+	0.957677i	$0.407061\pi$
$770$	−24.3991	+	11.4319i	−0.879283	+	0.411976i
$771$	−7.05834			−0.254200
$772$	−2.60664	+	9.72810i	−0.0938149	+	0.350122i
$773$	22.3797	−	5.99662i	0.804941	−	0.215683i	0.167189	−	0.985925i	$-0.446531\pi$
$773$	22.3797	−	5.99662i	0.804941	−	0.215683i	0.637752	+	0.770241i	$0.279864\pi$
$774$	−0.449799	−	0.259692i	−0.0161677	−	0.00933443i
$775$	8.79290	+	17.3699i	0.315850	+	0.623947i
$776$			0.654289i			0.0234876i
$777$	−30.2055	−	1.75211i	−1.08362	−	0.0628567i
$778$	−12.6018	+	12.6018i	−0.451798	+	0.451798i
$779$	−37.2434	+	21.5025i	−1.33438	+	0.770406i
$780$	1.30515	+	5.46804i	0.0467319	+	0.195787i
$781$	−15.2210	+	26.3636i	−0.544651	+	0.943363i
$782$	32.0819	+	8.59632i	1.14725	+	0.307404i
$783$	−1.09999	−	1.09999i	−0.0393106	−	0.0393106i
$784$	−2.77559	−	6.42620i	−0.0991284	−	0.229507i
$785$	0.253950	−	9.23348i	0.00906386	−	0.329557i
$786$	0.186862	+	0.323655i	0.00666516	+	0.0115444i
$787$	−0.544910	−	2.03363i	−0.0194239	−	0.0724912i	0.955534	−	0.294882i	$-0.0952805\pi$
$787$	−0.544910	−	2.03363i	−0.0194239	−	0.0724912i	−0.974958	+	0.222391i	$0.928614\pi$
$788$	−5.94568	−	22.1896i	−0.211806	−	0.790471i
$789$	2.84395	+	4.92586i	0.101247	+	0.175365i
$790$	−0.289824	+	10.5378i	−0.0103115	+	0.374920i
$791$	−17.6365	−	19.8085i	−0.627081	−	0.704310i
$792$	3.22048	+	3.22048i	0.114435	+	0.114435i
$793$	19.8934	+	5.33042i	0.706435	+	0.189289i
$794$	12.8232	−	22.2105i	0.455079	−	0.788219i
$795$	4.37878	+	18.3453i	0.155299	+	0.650640i
$796$	21.9943	−	12.6984i	0.779569	−	0.450084i
$797$	−23.6759	+	23.6759i	−0.838642	+	0.838642i	−0.988680	−	0.150038i	$-0.952060\pi$
$797$	−23.6759	+	23.6759i	−0.838642	+	0.838642i	0.150038	+	0.988680i	$0.452060\pi$
$798$	4.48947	+	8.93402i	0.158926	+	0.316261i
$799$		−	20.8298i		−	0.736904i
$800$	4.75120	+	1.55760i	0.167980	+	0.0550694i
$801$	5.23816	+	3.02425i	0.185081	+	0.106857i
$802$	5.08192	−	1.36170i	0.179449	−	0.0480832i
$803$	−5.12649	+	19.1323i	−0.180910	+	0.675164i
$804$	−9.31550			−0.328532
$805$	−27.2549	+	39.0760i	−0.960610	+	1.37725i
$806$	9.78915			0.344808
$807$	−1.99493	+	7.44518i	−0.0702249	+	0.262083i
$808$	5.41115	−	1.44991i	0.190364	−	0.0510078i
$809$	1.15441	+	0.666500i	0.0405869	+	0.0234329i	0.520156	−	0.854071i	$-0.325874\pi$
$809$	1.15441	+	0.666500i	0.0405869	+	0.0234329i	−0.479569	+	0.877504i	$0.659207\pi$
$810$	−1.06437	−	1.96650i	−0.0373982	−	0.0690957i
$811$			41.6705i			1.46325i	0.681708	+	0.731624i	$0.261237\pi$
$811$			41.6705i			1.46325i	−0.681708	+	0.731624i	$0.738763\pi$
$812$	−3.43924	−	2.26086i	−0.120694	−	0.0793406i
$813$	12.6475	−	12.6475i	0.443568	−	0.443568i
$814$	45.1059	−	26.0419i	1.58096	−	0.912768i
$815$	41.4131	+	25.4530i	1.45064	+	0.891580i
$816$	−2.06220	+	3.57183i	−0.0721914	+	0.125039i
$817$	1.89593	+	0.508013i	0.0663302	+	0.0177731i
$818$	5.92234	+	5.92234i	0.207070	+	0.207070i
$819$	2.09074	−	6.31449i	0.0730564	−	0.220646i
$820$	18.4807	−	17.4913i	0.645373	−	0.610823i
$821$	16.0833	+	27.8571i	0.561312	+	0.972221i	0.997382	+	0.0723083i	$0.0230366\pi$
$821$	16.0833	+	27.8571i	0.561312	+	0.972221i	−0.436070	+	0.899913i	$0.643630\pi$
$822$	0.688094	+	2.56800i	0.0240000	+	0.0895693i
$823$	3.82988	+	14.2933i	0.133501	+	0.498233i	1.00000		0.000946758i	$-0.000301363\pi$
$823$	3.82988	+	14.2933i	0.133501	+	0.498233i	−0.866498	+	0.499180i	$0.833635\pi$
$824$	−2.77901	−	4.81338i	−0.0968113	−	0.167682i
$825$	−16.9631	+	15.1930i	−0.590580	+	0.528952i
$826$	0.875423	−	0.779431i	0.0304599	−	0.0271199i
$827$	−34.2632	−	34.2632i	−1.19145	−	1.19145i	−0.976661	−	0.214788i	$-0.931094\pi$
$827$	−34.2632	−	34.2632i	−1.19145	−	1.19145i	−0.214788	−	0.976661i	$-0.568906\pi$
$828$	7.77857	+	2.08426i	0.270324	+	0.0724331i
$829$	25.2456	−	43.7267i	0.876817	−	1.51869i	0.0220025	−	0.999758i	$-0.492996\pi$
$829$	25.2456	−	43.7267i	0.876817	−	1.51869i	0.854814	−	0.518934i	$-0.173671\pi$
$830$	−9.89563	+	2.36196i	−0.343482	+	0.0819848i
$831$	12.7707	−	7.37318i	0.443011	−	0.255773i
$832$	1.77772	−	1.77772i	0.0616313	−	0.0616313i
$833$	4.19779	+	28.5640i	0.145445	+	0.989682i
$834$			4.58070i			0.158617i
$835$	−48.6541	+	26.3342i	−1.68375	+	0.911332i
$836$	−14.9058	−	8.60589i	−0.515529	−	0.297641i
$837$	−3.76106	+	1.00777i	−0.130001	+	0.0348338i
$838$	−2.46675	+	9.20603i	−0.0852124	+	0.318017i
$839$	−22.4313			−0.774414			−0.387207	−	0.921993i	$-0.626560\pi$
$839$	−22.4313			−0.774414			−0.387207	+	0.921993i	$0.626560\pi$
$840$	−3.81106	−	4.52502i	−0.131494	−	0.156128i
$841$	26.5800			0.916553
$842$	4.36008	−	16.2721i	0.150258	−	0.560772i
$843$	−0.567387	+	0.152031i	−0.0195418	+	0.00523622i
$844$	11.7937	+	6.80911i	0.405957	+	0.234379i
$845$	4.26080	−	14.3150i	0.146576	−	0.492451i
$846$		−	5.05038i		−	0.173636i
$847$	−23.0329	+	11.5744i	−0.791420	+	0.397700i
$848$	5.96425	−	5.96425i	0.204813	−	0.204813i
$849$	−16.1212	+	9.30757i	−0.553278	+	0.319435i
$850$	−17.2654	−	11.2770i	−0.592199	−	0.386799i
$851$	46.0461	−	79.7542i	1.57844	−	2.73394i
$852$	−6.45627	−	1.72995i	−0.221188	−	0.0592672i
$853$	24.4497	+	24.4497i	0.837140	+	0.837140i	0.988482	−	0.151341i	$-0.0483592\pi$
$853$	24.4497	+	24.4497i	0.837140	+	0.837140i	−0.151341	+	0.988482i	$0.548359\pi$
$854$	−21.2250	+	4.38784i	−0.726305	+	0.150149i
$855$	5.80877	+	6.13733i	0.198656	+	0.209892i
$856$	3.74518	+	6.48684i	0.128008	+	0.221716i
$857$	3.75655	+	14.0196i	0.128321	+	0.478901i	0.999936	−	0.0112896i	$-0.00359368\pi$
$857$	3.75655	+	14.0196i	0.128321	+	0.478901i	−0.871615	+	0.490191i	$0.836927\pi$
$858$	2.96354	+	11.0601i	0.101173	+	0.377585i
$859$	8.65502	+	14.9909i	0.295306	+	0.511484i	0.975056	−	0.221959i	$-0.0712452\pi$
$859$	8.65502	+	14.9909i	0.295306	+	0.511484i	−0.679750	+	0.733444i	$0.737912\pi$
$860$	−1.16094	−	0.0319295i	−0.0395877	−	0.00108879i
$861$	−29.4842	+	6.09527i	−1.00482	+	0.207726i
$862$	15.2439	+	15.2439i	0.519209	+	0.519209i
$863$	9.04469	+	2.42352i	0.307885	+	0.0824975i	0.409453	−	0.912331i	$-0.365719\pi$
$863$	9.04469	+	2.42352i	0.307885	+	0.0824975i	−0.101568	+	0.994829i	$0.532386\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−19.3965	+	31.5588i	−0.659500	+	1.07303i
$866$	−31.6992	+	18.3016i	−1.07718	+	0.621912i
$867$	0.00752068	−	0.00752068i	0.000255416	−	0.000255416i
$868$	−9.20499	+	4.62564i	−0.312438	+	0.157005i
$869$			21.4717i			0.728378i
$870$	−3.33394	−	0.992333i	−0.113031	−	0.0336432i
$871$	−20.2822	−	11.7099i	−0.687236	−	0.396776i
$872$	−1.41688	+	0.379653i	−0.0479817	+	0.0128567i
$873$	0.169342	−	0.631994i	0.00573137	−	0.0213898i
$874$	−30.4331			−1.02942
$875$	23.6383	−	17.7829i	0.799119	−	0.601173i
$876$	−4.34898			−0.146939
$877$	−9.68626	+	36.1496i	−0.327082	+	1.22069i	0.585120	+	0.810946i	$0.301047\pi$
$877$	−9.68626	+	36.1496i	−0.327082	+	1.22069i	−0.912202	+	0.409740i	$0.865619\pi$
$878$	−20.4580	+	5.48171i	−0.690425	+	0.184999i
$879$	25.3199	+	14.6185i	0.854020	+	0.493069i
$880$	9.76086	+	2.90528i	0.329038	+	0.0979369i
$881$		−	49.1425i		−	1.65565i	−0.560984	−	0.827827i	$-0.689577\pi$
$881$		−	49.1425i		−	1.65565i	0.560984	−	0.827827i	$-0.310423\pi$
$882$	1.01780	+	6.92561i	0.0342709	+	0.233197i
$883$	22.9167	−	22.9167i	0.771207	−	0.771207i	−0.207110	−	0.978318i	$-0.566406\pi$
$883$	22.9167	−	22.9167i	0.771207	−	0.771207i	0.978318	+	0.207110i	$0.0664060\pi$
$884$	−8.97985	+	5.18452i	−0.302025	+	0.174374i
$885$	0.518713	−	0.843966i	0.0174363	−	0.0283696i
$886$	2.07519	−	3.59433i	0.0697173	−	0.120754i
$887$	−25.3392	−	6.78961i	−0.850806	−	0.227973i	−0.193036	−	0.981192i	$-0.561833\pi$
$887$	−25.3392	−	6.78961i	−0.850806	−	0.227973i	−0.657770	+	0.753219i	$0.728500\pi$
$888$	8.08634	+	8.08634i	0.271360	+	0.271360i
$889$	36.0986	−	32.1403i	1.21071	−	1.07795i
$890$	13.5198	+	0.371836i	0.453184	+	0.0124640i
$891$	−2.27722	−	3.94427i	−0.0762899	−	0.132138i
$892$	−5.79830	−	21.6395i	−0.194141	−	0.724545i
$893$	4.93981	+	18.4356i	0.165304	+	0.616925i
$894$	8.62203	+	14.9338i	0.288364	+	0.499461i
$895$	−19.5628	−	20.6693i	−0.653913	−	0.690899i
$896$	−0.831614	+	2.51166i	−0.0277823	+	0.0839086i
$897$	14.3159	+	14.3159i	0.477995	+	0.477995i
$898$	−28.3785	−	7.60399i	−0.947002	−	0.253748i
$899$	−3.02860	+	5.24569i	−0.101010	+	0.174954i
$900$	−4.18617	−	2.73423i	−0.139539	−	0.0911408i
$901$	−30.1274	+	17.3941i	−1.00369	+	0.579481i
$902$	36.6479	−	36.6479i	1.22024	−	1.22024i
$903$	1.14827	+	0.754842i	0.0382121	+	0.0251196i
$904$			10.0244i			0.333407i
$905$	5.80457	−	19.5016i	0.192950	−	0.648255i
$906$	4.82177	+	2.78385i	0.160193	+	0.0924872i
$907$	−1.22193	+	0.327416i	−0.0405736	+	0.0108717i	−0.279049	−	0.960277i	$-0.590019\pi$
$907$	−1.22193	+	0.327416i	−0.0405736	+	0.0108717i	0.238475	+	0.971149i	$0.423352\pi$
$908$	−2.83476	+	10.5795i	−0.0940749	+	0.351092i
$909$	−5.60204			−0.185808
$910$	−2.60953	−	14.6428i	−0.0865052	−	0.485403i
$911$	−49.7996			−1.64993			−0.824967	−	0.565182i	$-0.808806\pi$
$911$	−49.7996			−1.64993			−0.824967	+	0.565182i	$0.808806\pi$
$912$	0.978107	−	3.65035i	0.0323884	−	0.120875i
$913$	−20.0156	+	5.36318i	−0.662421	+	0.177495i
$914$	0.408203	+	0.235676i	0.0135021	+	0.00779547i
$915$	−16.1094	+	8.71927i	−0.532561	+	0.288250i
$916$			28.9443i			0.956347i
$917$	−0.443974	−	0.883504i	−0.0146613	−	0.0291759i
$918$	2.91639	−	2.91639i	0.0962551	−	0.0962551i
$919$	43.6221	−	25.1852i	1.43896	−	0.830784i	0.441182	−	0.897418i	$-0.354559\pi$
$919$	43.6221	−	25.1852i	1.43896	−	0.830784i	0.997777	+	0.0666338i	$0.0212259\pi$
$920$	17.5150	−	4.18060i	0.577452	−	0.137830i
$921$	1.15586	−	2.00201i	0.0380870	−	0.0659686i
$922$	25.4231	+	6.81209i	0.837264	+	0.224344i
$923$	−11.8823	−	11.8823i	−0.391112	−	0.391112i
$924$	−8.01287	−	8.99971i	−0.263604	−	0.296069i
$925$	−42.5929	+	38.1482i	−1.40045	+	1.25431i
$926$	0.725623	+	1.25682i	0.0238455	+	0.0413015i
$927$	1.43852	+	5.36863i	0.0472472	+	0.176329i
$928$	0.402626	+	1.50262i	0.0132168	+	0.0493259i
$929$	11.4115	+	19.7652i	0.374398	+	0.648476i	0.990237	−	0.139396i	$-0.0445161\pi$
$929$	11.4115	+	19.7652i	0.374398	+	0.648476i	−0.615839	+	0.787872i	$0.711183\pi$
$930$	−6.32347	+	5.98495i	−0.207355	+	0.196254i
$931$	−10.4893	−	24.2854i	−0.343773	−	0.795921i
$932$	0.998499	+	0.998499i	0.0327069	+	0.0327069i
$933$	−13.4109	−	3.59343i	−0.439052	−	0.117644i
$934$	−15.5068	+	26.8586i	−0.507399	+	0.878841i
$935$	−35.7846	−	21.9937i	−1.17028	−	0.719270i
$936$	−2.17725	+	1.25704i	−0.0711658	+	0.0410876i
$937$	−24.9461	+	24.9461i	−0.814954	+	0.814954i	−0.985372	−	0.170418i	$-0.945488\pi$
$937$	−24.9461	+	24.9461i	−0.814954	+	0.814954i	0.170418	+	0.985372i	$0.445488\pi$
$938$	24.6051	+	1.42725i	0.803386	+	0.0466015i
$939$			13.4904i			0.440242i
$940$	−5.37548	−	9.93156i	−0.175329	−	0.323932i
$941$	−16.1409	−	9.31896i	−0.526179	−	0.303789i	0.213280	−	0.976991i	$-0.431585\pi$
$941$	−16.1409	−	9.31896i	−0.526179	−	0.303789i	−0.739459	+	0.673202i	$0.764919\pi$
$942$	3.99014	−	1.06916i	0.130006	−	0.0348350i
$943$	23.7181	−	88.5173i	0.772369	−	2.88252i
$944$	−0.443022			−0.0144191
$945$	2.51004	+	5.35721i	0.0816518	+	0.174270i
$946$	−2.36551			−0.0769092
$947$	0.657006	−	2.45198i	0.0213498	−	0.0796786i	−0.954429	−	0.298438i	$-0.903534\pi$
$947$	0.657006	−	2.45198i	0.0213498	−	0.0796786i	0.975779	+	0.218760i	$0.0702010\pi$
$948$	−4.55381	+	1.22019i	−0.147901	+	0.0396299i
$949$	−9.46884	−	5.46684i	−0.307372	−	0.177461i
$950$	17.9553	+	5.88634i	0.582548	+	0.190978i
$951$			13.7171i			0.444806i
$952$	5.99416	−	9.11836i	0.194272	−	0.295528i
$953$	31.1031	−	31.1031i	1.00753	−	1.00753i	0.00755624	−	0.999971i	$-0.497595\pi$
$953$	31.1031	−	31.1031i	1.00753	−	1.00753i	0.999971	−	0.00755624i	$-0.00240525\pi$
$954$	−7.30469	+	4.21737i	−0.236498	+	0.136542i
$955$	−9.45149	−	39.5979i	−0.305843	−	1.28136i
$956$	2.18215	−	3.77959i	0.0705758	−	0.122241i
$957$	−6.84361	−	1.83374i	−0.221222	−	0.0592764i
$958$	23.5834	+	23.5834i	0.761945	+	0.761945i
$959$	−1.42402	−	6.88831i	−0.0459840	−	0.222435i
$960$	−0.0614757	+	2.23522i	−0.00198412	+	0.0721415i
$961$	−7.91940	−	13.7168i	−0.255465	−	0.442477i
$962$	7.44117	+	27.7708i	0.239913	+	0.895368i
$963$	−1.93865	−	7.23514i	−0.0624721	−	0.233149i
$964$	1.53496	+	2.65862i	0.0494376	+	0.0856284i
$965$	0.619139	−	22.5115i	0.0199308	−	0.724672i
$966$	−20.2263	−	6.69696i	−0.650770	−	0.215471i
$967$	−14.7707	−	14.7707i	−0.474993	−	0.474993i	0.428533	−	0.903526i	$-0.359031\pi$
$967$	−14.7707	−	14.7707i	−0.474993	−	0.474993i	−0.903526	+	0.428533i	$0.859031\pi$
$968$	9.41101	+	2.52167i	0.302481	+	0.0810496i
$969$	−7.79328	+	13.4984i	−0.250356	+	0.433630i
$970$	−0.339666	−	1.42306i	−0.0109060	−	0.0456917i
$971$	9.39194	−	5.42244i	0.301402	−	0.174014i	−0.341671	−	0.939820i	$-0.610993\pi$
$971$	9.39194	−	5.42244i	0.301402	−	0.174014i	0.643072	+	0.765805i	$0.277659\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	0.701821	−	12.0990i	0.0224994	−	0.387878i
$974$		−	3.30368i		−	0.105857i
$975$	−5.67733	−	11.2153i	−0.181820	−	0.359176i
$976$	7.09442	+	4.09597i	0.227087	+	0.131109i
$977$	−16.5560	+	4.43616i	−0.529673	+	0.141925i	−0.513737	−	0.857948i	$-0.671739\pi$
$977$	−16.5560	+	4.43616i	−0.529673	+	0.141925i	−0.0159356	+	0.999873i	$0.505073\pi$
$978$	−5.62644	+	20.9982i	−0.179914	+	0.671447i
$979$	27.5476			0.880426
$980$	9.37292	+	12.5359i	0.299407	+	0.400444i
$981$	1.46687			0.0468334
$982$	0.936018	−	3.49327i	0.0298695	−	0.111475i
$983$	−1.62331	+	0.434966i	−0.0517757	+	0.0138732i	−0.284614	−	0.958642i	$-0.591865\pi$
$983$	−1.62331	+	0.434966i	−0.0517757	+	0.0138732i	0.232838	+	0.972515i	$0.425199\pi$
$984$	9.85506	+	5.68982i	0.314168	+	0.181385i
$985$	24.4511	+	45.1751i	0.779077	+	1.43940i
$986$		−	6.41602i		−	0.204328i
$987$	−0.773782	+	13.3396i	−0.0246298	+	0.424605i
$988$	6.71821	−	6.71821i	0.213735	−	0.213735i
$989$	−3.62222	+	2.09129i	−0.115180	+	0.0664992i
$990$	−8.67632	−	5.33258i	−0.275752	−	0.169480i
$991$	8.40392	−	14.5560i	0.266959	−	0.462387i	−0.701116	−	0.713047i	$-0.747314\pi$
$991$	8.40392	−	14.5560i	0.266959	−	0.462387i	0.968075	+	0.250660i	$0.0806478\pi$
$992$	3.76106	+	1.00777i	0.119414	+	0.0319968i
$993$	23.5033	+	23.5033i	0.745855	+	0.745855i
$994$	16.7880	+	5.55853i	0.532482	+	0.176306i
$995$	−41.2448	+	39.0368i	−1.30755	+	1.23755i
$996$	−2.27489	−	3.94022i	−0.0720826	−	0.124851i
$997$	4.51978	+	16.8680i	0.143143	+	0.534216i	0.999831	+	0.0183818i	$0.00585143\pi$
$997$	4.51978	+	16.8680i	0.143143	+	0.534216i	−0.856688	+	0.515835i	$0.827482\pi$
$998$	−0.167661	−	0.625718i	−0.00530721	−	0.0198068i
$999$	−5.71790	−	9.90370i	−0.180906	−	0.313339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.u.b.157.4	yes	16
3.2	odd	2		630.2.bv.b.577.1		16
5.2	odd	4		1050.2.bc.h.493.4		16
5.3	odd	4		210.2.u.a.73.2	✓	16
5.4	even	2		1050.2.bc.g.157.1		16
7.3	odd	6		1470.2.m.d.97.8		16
7.4	even	3		1470.2.m.e.97.5		16
7.5	odd	6		210.2.u.a.187.2	yes	16
15.8	even	4		630.2.bv.a.73.3		16
21.5	even	6		630.2.bv.a.397.3		16
35.3	even	12		1470.2.m.e.1273.5		16
35.12	even	12		1050.2.bc.g.943.1		16
35.18	odd	12		1470.2.m.d.1273.8		16
35.19	odd	6		1050.2.bc.h.607.4		16
35.33	even	12	inner	210.2.u.b.103.4	yes	16
105.68	odd	12		630.2.bv.b.523.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.2	✓	16	5.3	odd	4
210.2.u.a.187.2	yes	16	7.5	odd	6
210.2.u.b.103.4	yes	16	35.33	even	12	inner
210.2.u.b.157.4	yes	16	1.1	even	1	trivial
630.2.bv.a.73.3		16	15.8	even	4
630.2.bv.a.397.3		16	21.5	even	6
630.2.bv.b.523.1		16	105.68	odd	12
630.2.bv.b.577.1		16	3.2	odd	2
1050.2.bc.g.157.1		16	5.4	even	2
1050.2.bc.g.943.1		16	35.12	even	12
1050.2.bc.h.493.4		16	5.2	odd	4
1050.2.bc.h.607.4		16	35.19	odd	6
1470.2.m.d.97.8		16	7.3	odd	6
1470.2.m.d.1273.8		16	35.18	odd	12
1470.2.m.e.97.5		16	7.4	even	3
1470.2.m.e.1273.5		16	35.3	even	12

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.14315 + 0.637899i) q^{5} +1.00000i q^{6} +(0.153213 - 2.64131i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.14315 + 0.637899i) q^{5} +1.00000i q^{6} +(0.153213 - 2.64131i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(1.17085 - 1.90502i) q^{10} +(2.27722 - 3.94427i) q^{11} +(0.965926 + 0.258819i) q^{12} +(1.77772 + 1.77772i) q^{13} +(-2.51166 - 0.831614i) q^{14} +(-2.23522 - 0.0614757i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.06747 - 3.98386i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(1.88956 + 3.27281i) q^{19} +(-1.53707 - 1.62401i) q^{20} +(0.535629 + 2.59097i) q^{21} +(-3.22048 - 3.22048i) q^{22} +(-7.77857 - 2.08426i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.18617 + 2.73423i) q^{25} +(2.17725 - 1.25704i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.45334 + 2.21084i) q^{28} +1.55563i q^{29} +(-0.637899 + 2.14315i) q^{30} +(3.37208 + 1.94687i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-1.17878 + 4.39926i) q^{33} -4.12440 q^{34} +(2.01325 - 5.56299i) q^{35} -1.00000 q^{36} +(-2.95980 + 11.0461i) q^{37} +(3.65035 - 0.978107i) q^{38} +(-2.17725 - 1.25704i) q^{39} +(-1.96650 + 1.06437i) q^{40} +11.3796i q^{41} +(2.64131 + 0.153213i) q^{42} +(0.367260 - 0.367260i) q^{43} +(-3.94427 + 2.27722i) q^{44} +(2.17497 - 0.519137i) q^{45} +(-4.02648 + 6.97408i) q^{46} +(4.87829 + 1.30713i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-6.95305 - 0.809365i) q^{49} +(3.72452 - 3.33586i) q^{50} +(2.06220 + 3.57183i) q^{51} +(-0.650691 - 2.42841i) q^{52} +(-2.18307 - 8.14732i) q^{53} +(0.500000 + 0.866025i) q^{54} +(7.39647 - 7.00051i) q^{55} +(1.75935 + 1.97603i) q^{56} +(-2.67224 - 2.67224i) q^{57} +(1.50262 + 0.402626i) q^{58} +(-0.221511 + 0.383668i) q^{59} +(1.90502 + 1.17085i) q^{60} +(7.09442 - 4.09597i) q^{61} +(2.75329 - 2.75329i) q^{62} +(-1.18797 - 2.36405i) q^{63} -1.00000i q^{64} +(2.67591 + 4.94392i) q^{65} +(3.94427 + 2.27722i) q^{66} +(-8.99808 + 2.41103i) q^{67} +(-1.06747 + 3.98386i) q^{68} +8.05297 q^{69} +(-4.85237 - 3.38446i) q^{70} -6.68403 q^{71} +(-0.258819 + 0.965926i) q^{72} +(-4.20080 + 1.12560i) q^{73} +(9.90370 + 5.71790i) q^{74} +(-4.75120 - 1.55760i) q^{75} -3.77912i q^{76} +(-10.0691 - 6.61917i) q^{77} +(-1.77772 + 1.77772i) q^{78} +(-4.08283 + 2.35722i) q^{79} +(0.519137 + 2.17497i) q^{80} +(0.500000 - 0.866025i) q^{81} +(10.9919 + 2.94527i) q^{82} +(-3.21718 - 3.21718i) q^{83} +(0.831614 - 2.51166i) q^{84} +(0.253550 - 9.21894i) q^{85} +(-0.259692 - 0.449799i) q^{86} +(-0.402626 - 1.50262i) q^{87} +(1.17878 + 4.39926i) q^{88} +(3.02425 + 5.23816i) q^{89} +(0.0614757 - 2.23522i) q^{90} +(4.96788 - 4.42314i) q^{91} +(5.69431 + 5.69431i) q^{92} +(-3.76106 - 1.00777i) q^{93} +(2.52519 - 4.37376i) q^{94} +(1.96188 + 8.21947i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(0.462652 - 0.462652i) q^{97} +(-2.58137 + 6.50665i) q^{98} -4.55445i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 - 4 * q^7	\( 16 q + 12 q^{5} - 4 q^{7} + 4 q^{10} + 4 q^{11} + 16 q^{13} - 16 q^{14} + 4 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{19} + 8 q^{20} + 8 q^{21} + 4 q^{22} - 40 q^{23} + 8 q^{24} + 16 q^{25} - 12 q^{26} - 4 q^{28} - 4 q^{30} - 24 q^{31} + 4 q^{33} - 16 q^{34} - 44 q^{35} - 16 q^{36} - 8 q^{37} - 20 q^{38} + 12 q^{39} + 8 q^{42} - 24 q^{43} - 4 q^{45} - 4 q^{46} - 52 q^{49} + 8 q^{51} + 8 q^{52} - 28 q^{53} + 8 q^{54} + 56 q^{55} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} + 16 q^{65} - 84 q^{67} + 12 q^{68} + 8 q^{69} + 4 q^{70} - 32 q^{71} + 16 q^{73} + 24 q^{74} - 24 q^{75} + 44 q^{77} - 16 q^{78} - 12 q^{79} + 12 q^{80} + 8 q^{81} + 36 q^{82} + 16 q^{83} - 4 q^{84} + 8 q^{85} - 8 q^{86} + 48 q^{87} - 4 q^{88} + 16 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 8 q^{94} + 72 q^{95} - 44 q^{97} + 24 q^{98}+O(q^{100}) \) 16 * q + 12 * q^5 - 4 * q^7 + 4 * q^10 + 4 * q^11 + 16 * q^13 - 16 * q^14 + 4 * q^15 + 8 * q^16 + 12 * q^17 + 8 * q^19 + 8 * q^20 + 8 * q^21 + 4 * q^22 - 40 * q^23 + 8 * q^24 + 16 * q^25 - 12 * q^26 - 4 * q^28 - 4 * q^30 - 24 * q^31 + 4 * q^33 - 16 * q^34 - 44 * q^35 - 16 * q^36 - 8 * q^37 - 20 * q^38 + 12 * q^39 + 8 * q^42 - 24 * q^43 - 4 * q^45 - 4 * q^46 - 52 * q^49 + 8 * q^51 + 8 * q^52 - 28 * q^53 + 8 * q^54 + 56 * q^55 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 + 16 * q^65 - 84 * q^67 + 12 * q^68 + 8 * q^69 + 4 * q^70 - 32 * q^71 + 16 * q^73 + 24 * q^74 - 24 * q^75 + 44 * q^77 - 16 * q^78 - 12 * q^79 + 12 * q^80 + 8 * q^81 + 36 * q^82 + 16 * q^83 - 4 * q^84 + 8 * q^85 - 8 * q^86 + 48 * q^87 - 4 * q^88 + 16 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 8 * q^94 + 72 * q^95 - 44 * q^97 + 24 * q^98

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