LMFDB - Embedded newform 841.2.d.g.574.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(190,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

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

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

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

chi := DirichletCharacter("841.190");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	12.0.4413675765625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2x^{10} - 3x^{9} + 5x^{8} - 8x^{7} + 13x^{6} + 8x^{5} + 5x^{4} + 3x^{3} + 2x^{2} + x + 1 $ x^12 - x^11 + 2x^10 - 3x^9 + 5x^8 - 8x^7 + 13x^6 + 8x^5 + 5x^4 + 3x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			574.1
Root			$0.385338 - 0.483198i$ of defining polynomial
Character	$\chi$	$=$	841.574
Dual form			841.2.d.g.778.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.385338 + 0.483198i) q^{2} +(-0.137526 + 0.602539i) q^{3} +(0.360046 + 1.57747i) q^{4} +(2.40299 - 3.01326i) q^{5} +(-0.238152 - 0.298633i) q^{6} +(0.497572 - 2.18001i) q^{7} +(-2.01463 - 0.970194i) q^{8} +(2.35877 + 1.13592i) q^{9} +O(q^{10})$	\(q+(-0.385338 + 0.483198i) q^{2} +(-0.137526 + 0.602539i) q^{3} +(0.360046 + 1.57747i) q^{4} +(2.40299 - 3.01326i) q^{5} +(-0.238152 - 0.298633i) q^{6} +(0.497572 - 2.18001i) q^{7} +(-2.01463 - 0.970194i) q^{8} +(2.35877 + 1.13592i) q^{9} +(0.530037 + 2.32225i) q^{10} +(-1.24511 + 0.599613i) q^{11} -1.00000 q^{12} +(0.212690 - 0.102426i) q^{13} +(0.861642 + 1.08046i) q^{14} +(1.48513 + 1.86230i) q^{15} +(-1.67049 + 0.804465i) q^{16} +4.38197 q^{17} +(-1.45780 + 0.702039i) q^{18} +(-1.08014 - 4.73240i) q^{19} +(5.61850 + 2.70573i) q^{20} +(1.24511 + 0.599613i) q^{21} +(0.190056 - 0.832688i) q^{22} +(-0.770676 - 0.966397i) q^{23} +(0.861642 - 1.08046i) q^{24} +(-2.19274 - 9.60704i) q^{25} +(-0.0324654 + 0.142240i) q^{26} +(-2.16484 + 2.71463i) q^{27} +3.61803 q^{28} -1.47214 q^{30} +(6.29112 - 7.88881i) q^{31} +(1.25013 - 5.47718i) q^{32} +(-0.190056 - 0.832688i) q^{33} +(-1.68854 + 2.11736i) q^{34} +(-5.37326 - 6.73785i) q^{35} +(-0.942614 + 4.12986i) q^{36} +(4.24195 + 2.04281i) q^{37} +(2.70291 + 1.30165i) q^{38} +(0.0324654 + 0.142240i) q^{39} +(-7.76458 + 3.73922i) q^{40} -3.85410 q^{41} +(-0.769519 + 0.370581i) q^{42} +(4.51161 + 5.65739i) q^{43} +(-1.39417 - 1.74823i) q^{44} +(9.09093 - 4.37796i) q^{45} +0.763932 q^{46} +(-6.30678 + 3.03719i) q^{47} +(-0.254986 - 1.11717i) q^{48} +(1.80194 + 0.867767i) q^{49} +(5.48705 + 2.64243i) q^{50} +(-0.602632 + 2.64030i) q^{51} +(0.238152 + 0.298633i) q^{52} +(-1.24698 + 1.56366i) q^{53} +(-0.477507 - 2.09210i) q^{54} +(-1.18520 + 5.19270i) q^{55} +(-3.11745 + 3.90916i) q^{56} +3.00000 q^{57} +6.09017 q^{59} +(-2.40299 + 3.01326i) q^{60} +(-0.137526 + 0.602539i) q^{61} +(1.38766 + 6.07972i) q^{62} +(3.64997 - 4.57692i) q^{63} +(-0.147186 - 0.184565i) q^{64} +(0.202456 - 0.887019i) q^{65} +(0.475589 + 0.229032i) q^{66} +(1.37656 + 0.662915i) q^{67} +(1.57771 + 6.91240i) q^{68} +(0.688279 - 0.331458i) q^{69} +5.32624 q^{70} +(-9.43507 + 4.54369i) q^{71} +(-3.64997 - 4.57692i) q^{72} +(8.54693 + 10.7175i) q^{73} +(-2.62167 + 1.26253i) q^{74} +6.09017 q^{75} +(7.07630 - 3.40777i) q^{76} +(0.687628 + 3.01269i) q^{77} +(-0.0812403 - 0.0391233i) q^{78} +(-5.48705 - 2.64243i) q^{79} +(-1.59011 + 6.96674i) q^{80} +(3.55901 + 4.46285i) q^{81} +(1.48513 - 1.86230i) q^{82} +(2.21281 + 9.69495i) q^{83} +(-0.497572 + 2.18001i) q^{84} +(10.5298 - 13.2040i) q^{85} -4.47214 q^{86} +3.09017 q^{88} +(-2.93552 + 3.68102i) q^{89} +(-1.38766 + 6.07972i) q^{90} +(-0.117461 - 0.514629i) q^{91} +(1.24698 - 1.56366i) q^{92} +(3.88812 + 4.87555i) q^{93} +(0.962679 - 4.21777i) q^{94} +(-16.8555 - 8.11719i) q^{95} +(3.12829 + 1.50650i) q^{96} +(0.792688 + 3.47299i) q^{97} +(-1.11366 + 0.536310i) q^{98} -3.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9}+O(q^{10}) $ 12 * q - q^2 + q^3 + q^4 - q^5 + 3 * q^6 + 3 * q^9	$ 12 q - q^{2} + q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9} + 7 q^{10} - 5 q^{11} - 12 q^{12} - 4 q^{13} - 5 q^{14} - 7 q^{15} + 3 q^{16} + 66 q^{17} - q^{18} - 3 q^{19} + 8 q^{20} + 5 q^{21} - 5 q^{22} - 2 q^{23} - 5 q^{24} - 13 q^{25} - 7 q^{26} - 2 q^{27} + 30 q^{28} + 36 q^{30} - 9 q^{31} + 9 q^{32} + 5 q^{33} - 8 q^{34} + 15 q^{35} - 4 q^{36} - 4 q^{37} + 6 q^{38} + 7 q^{39} - 15 q^{40} - 6 q^{41} + 5 q^{42} - 10 q^{43} + 9 q^{45} + 36 q^{46} - 14 q^{47} - 9 q^{48} + 4 q^{49} + q^{50} + 8 q^{51} - 3 q^{52} + 4 q^{53} - 11 q^{54} + 5 q^{55} + 10 q^{56} + 36 q^{57} + 6 q^{59} + q^{60} + q^{61} + 8 q^{62} - 5 q^{63} - 4 q^{64} + 13 q^{65} + 10 q^{66} + 12 q^{67} + 3 q^{68} + 6 q^{69} - 30 q^{70} - 12 q^{71} + 5 q^{72} - 14 q^{73} - 17 q^{74} + 6 q^{75} + 9 q^{76} - 5 q^{77} + 11 q^{78} - q^{79} - 21 q^{80} + 2 q^{81} - 7 q^{82} + 2 q^{83} + 2 q^{85} - 30 q^{88} - 4 q^{89} - 8 q^{90} - 10 q^{91} - 4 q^{92} - 8 q^{93} - 7 q^{94} - 24 q^{95} - 2 q^{96} - 13 q^{97} + 2 q^{98} - 30 q^{99}+O(q^{100}) $ 12 * q - q^2 + q^3 + q^4 - q^5 + 3 * q^6 + 3 * q^9 + 7 * q^10 - 5 * q^11 - 12 * q^12 - 4 * q^13 - 5 * q^14 - 7 * q^15 + 3 * q^16 + 66 * q^17 - q^18 - 3 * q^19 + 8 * q^20 + 5 * q^21 - 5 * q^22 - 2 * q^23 - 5 * q^24 - 13 * q^25 - 7 * q^26 - 2 * q^27 + 30 * q^28 + 36 * q^30 - 9 * q^31 + 9 * q^32 + 5 * q^33 - 8 * q^34 + 15 * q^35 - 4 * q^36 - 4 * q^37 + 6 * q^38 + 7 * q^39 - 15 * q^40 - 6 * q^41 + 5 * q^42 - 10 * q^43 + 9 * q^45 + 36 * q^46 - 14 * q^47 - 9 * q^48 + 4 * q^49 + q^50 + 8 * q^51 - 3 * q^52 + 4 * q^53 - 11 * q^54 + 5 * q^55 + 10 * q^56 + 36 * q^57 + 6 * q^59 + q^60 + q^61 + 8 * q^62 - 5 * q^63 - 4 * q^64 + 13 * q^65 + 10 * q^66 + 12 * q^67 + 3 * q^68 + 6 * q^69 - 30 * q^70 - 12 * q^71 + 5 * q^72 - 14 * q^73 - 17 * q^74 + 6 * q^75 + 9 * q^76 - 5 * q^77 + 11 * q^78 - q^79 - 21 * q^80 + 2 * q^81 - 7 * q^82 + 2 * q^83 + 2 * q^85 - 30 * q^88 - 4 * q^89 - 8 * q^90 - 10 * q^91 - 4 * q^92 - 8 * q^93 - 7 * q^94 - 24 * q^95 - 2 * q^96 - 13 * q^97 + 2 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{7}\right)$

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 $

$2$	−0.385338	+	0.483198i	−0.272475	+	0.341673i	−0.899176	−	0.437587i	$-0.855833\pi$
$2$	−0.385338	+	0.483198i	−0.272475	+	0.341673i	0.626701	+	0.779260i	$0.284405\pi$
$3$	−0.137526	+	0.602539i	−0.0794004	+	0.347876i	−0.998986	−	0.0450129i	$-0.985667\pi$
$3$	−0.137526	+	0.602539i	−0.0794004	+	0.347876i	0.919586	+	0.392889i	$0.128524\pi$
$4$	0.360046	+	1.57747i	0.180023	+	0.788733i
$5$	2.40299	−	3.01326i	1.07465	−	1.34757i	0.140748	−	0.990046i	$-0.455049\pi$
$5$	2.40299	−	3.01326i	1.07465	−	1.34757i	0.933904	−	0.357525i	$-0.116379\pi$
$6$	−0.238152	−	0.298633i	−0.0972251	−	0.121916i
$7$	0.497572	−	2.18001i	0.188065	−	0.823964i	−0.789571	−	0.613659i	$-0.789697\pi$
$7$	0.497572	−	2.18001i	0.188065	−	0.823964i	0.977636	−	0.210306i	$-0.0674459\pi$
$8$	−2.01463	−	0.970194i	−0.712278	−	0.343015i
$9$	2.35877	+	1.13592i	0.786256	+	0.378641i
$10$	0.530037	+	2.32225i	0.167613	+	0.734358i
$11$	−1.24511	+	0.599613i	−0.375414	+	0.180790i	−0.612070	−	0.790804i	$-0.709663\pi$
$11$	−1.24511	+	0.599613i	−0.375414	+	0.180790i	0.236656	+	0.971594i	$0.423949\pi$
$12$	−1.00000			−0.288675
$13$	0.212690	−	0.102426i	0.0589896	−	0.0284079i	−0.404156	−	0.914690i	$-0.632435\pi$
$13$	0.212690	−	0.102426i	0.0589896	−	0.0284079i	0.463146	+	0.886282i	$0.346721\pi$
$14$	0.861642	+	1.08046i	0.230283	+	0.288766i
$15$	1.48513	+	1.86230i	0.383459	+	0.480843i
$16$	−1.67049	+	0.804465i	−0.417622	+	0.201116i
$17$	4.38197			1.06278			0.531391	−	0.847126i	$-0.321669\pi$
$17$	4.38197			1.06278			0.531391	+	0.847126i	$0.321669\pi$
$18$	−1.45780	+	0.702039i	−0.343606	+	0.165472i
$19$	−1.08014	−	4.73240i	−0.247801	−	1.08569i	−0.933719	−	0.358008i	$-0.883456\pi$
$19$	−1.08014	−	4.73240i	−0.247801	−	1.08569i	0.685918	−	0.727679i	$-0.259401\pi$
$20$	5.61850	+	2.70573i	1.25634	+	0.605019i
$21$	1.24511	+	0.599613i	0.271705	+	0.130846i
$22$	0.190056	−	0.832688i	0.0405200	−	0.177530i
$23$	−0.770676	−	0.966397i	−0.160697	−	0.201508i	0.694964	−	0.719045i	$-0.255420\pi$
$23$	−0.770676	−	0.966397i	−0.160697	−	0.201508i	−0.855661	+	0.517537i	$0.826849\pi$
$24$	0.861642	−	1.08046i	0.175882	−	0.220549i
$25$	−2.19274	−	9.60704i	−0.438549	−	1.92141i
$26$	−0.0324654	+	0.142240i	−0.00636698	+	0.0278956i
$27$	−2.16484	+	2.71463i	−0.416624	+	0.522430i
$28$	3.61803			0.683744
$29$		0			0
$29$		0			0
$30$	−1.47214			−0.268774
$31$	6.29112	−	7.88881i	1.12992	−	1.41687i	0.234235	−	0.972180i	$-0.424742\pi$
$31$	6.29112	−	7.88881i	1.12992	−	1.41687i	0.895683	−	0.444693i	$-0.146687\pi$
$32$	1.25013	−	5.47718i	0.220994	−	0.968237i
$33$	−0.190056	−	0.832688i	−0.0330844	−	0.144952i
$34$	−1.68854	+	2.11736i	−0.289582	+	0.363124i
$35$	−5.37326	−	6.73785i	−0.908246	−	1.13890i
$36$	−0.942614	+	4.12986i	−0.157102	+	0.688310i
$37$	4.24195	+	2.04281i	0.697371	+	0.335836i	0.748759	−	0.662842i	$-0.230650\pi$
$37$	4.24195	+	2.04281i	0.697371	+	0.335836i	−0.0513875	+	0.998679i	$0.516364\pi$
$38$	2.70291	+	1.30165i	0.438469	+	0.211156i
$39$	0.0324654	+	0.142240i	0.00519862	+	0.0227766i
$40$	−7.76458	+	3.73922i	−1.22769	+	0.591223i
$41$	−3.85410			−0.601910			−0.300955	−	0.953638i	$-0.597305\pi$
$41$	−3.85410			−0.601910			−0.300955	+	0.953638i	$0.597305\pi$
$42$	−0.769519	+	0.370581i	−0.118739	+	0.0571819i
$43$	4.51161	+	5.65739i	0.688015	+	0.862743i	0.996065	−	0.0886269i	$-0.0282479\pi$
$43$	4.51161	+	5.65739i	0.688015	+	0.862743i	−0.308050	+	0.951370i	$0.599676\pi$
$44$	−1.39417	−	1.74823i	−0.210178	−	0.263555i
$45$	9.09093	−	4.37796i	1.35520	−	0.652628i
$46$	0.763932			0.112636
$47$	−6.30678	+	3.03719i	−0.919939	+	0.443019i	−0.833049	−	0.553199i	$-0.813407\pi$
$47$	−6.30678	+	3.03719i	−0.919939	+	0.443019i	−0.0868895	+	0.996218i	$0.527693\pi$
$48$	−0.254986	−	1.11717i	−0.0368041	−	0.161249i
$49$	1.80194	+	0.867767i	0.257420	+	0.123967i
$50$	5.48705	+	2.64243i	0.775987	+	0.373695i
$51$	−0.602632	+	2.64030i	−0.0843854	+	0.369716i
$52$	0.238152	+	0.298633i	0.0330257	+	0.0414130i
$53$	−1.24698	+	1.56366i	−0.171286	+	0.214786i	−0.860064	−	0.510187i	$-0.829576\pi$
$53$	−1.24698	+	1.56366i	−0.171286	+	0.214786i	0.688778	+	0.724973i	$0.258148\pi$
$54$	−0.477507	−	2.09210i	−0.0649805	−	0.284698i
$55$	−1.18520	+	5.19270i	−0.159812	+	0.700183i
$56$	−3.11745	+	3.90916i	−0.416587	+	0.522383i
$57$	3.00000			0.397360
$58$		0			0
$59$	6.09017			0.792873			0.396436	−	0.918062i	$-0.370247\pi$
$59$	6.09017			0.792873			0.396436	+	0.918062i	$0.370247\pi$
$60$	−2.40299	+	3.01326i	−0.310225	+	0.389010i
$61$	−0.137526	+	0.602539i	−0.0176083	+	0.0771472i	−0.982969	−	0.183773i	$-0.941169\pi$
$61$	−0.137526	+	0.602539i	−0.0176083	+	0.0771472i	0.965360	+	0.260920i	$0.0840260\pi$
$62$	1.38766	+	6.07972i	0.176232	+	0.772125i
$63$	3.64997	−	4.57692i	0.459853	−	0.576638i
$64$	−0.147186	−	0.184565i	−0.0183982	−	0.0230707i
$65$	0.202456	−	0.887019i	0.0251116	−	0.110021i
$66$	0.475589	+	0.229032i	0.0585410	+	0.0281918i
$67$	1.37656	+	0.662915i	0.168173	+	0.0809880i	0.516077	−	0.856542i	$-0.327392\pi$
$67$	1.37656	+	0.662915i	0.168173	+	0.0809880i	−0.347903	+	0.937530i	$0.613106\pi$
$68$	1.57771	+	6.91240i	0.191326	+	0.838252i
$69$	0.688279	−	0.331458i	0.0828591	−	0.0399028i
$70$	5.32624			0.636607
$71$	−9.43507	+	4.54369i	−1.11974	+	0.539237i	−0.899811	−	0.436280i	$-0.856296\pi$
$71$	−9.43507	+	4.54369i	−1.11974	+	0.539237i	−0.219926	+	0.975517i	$0.570581\pi$
$72$	−3.64997	−	4.57692i	−0.430153	−	0.539395i
$73$	8.54693	+	10.7175i	1.00034	+	1.25439i	0.966955	+	0.254947i	$0.0820579\pi$
$73$	8.54693	+	10.7175i	1.00034	+	1.25439i	0.0333868	+	0.999443i	$0.489371\pi$
$74$	−2.62167	+	1.26253i	−0.304763	+	0.146766i
$75$	6.09017			0.703232
$76$	7.07630	−	3.40777i	0.811707	−	0.390898i
$77$	0.687628	+	3.01269i	0.0783624	+	0.343328i
$78$	−0.0812403	−	0.0391233i	−0.00919865	−	0.00442984i
$79$	−5.48705	−	2.64243i	−0.617342	−	0.297296i	0.0989550	−	0.995092i	$-0.468450\pi$
$79$	−5.48705	−	2.64243i	−0.617342	−	0.297296i	−0.716297	+	0.697796i	$0.754164\pi$
$80$	−1.59011	+	6.96674i	−0.177780	+	0.778905i
$81$	3.55901	+	4.46285i	0.395445	+	0.495873i
$82$	1.48513	−	1.86230i	0.164005	−	0.205656i
$83$	2.21281	+	9.69495i	0.242887	+	1.06416i	0.938374	+	0.345620i	$0.112331\pi$
$83$	2.21281	+	9.69495i	0.242887	+	1.06416i	−0.695487	+	0.718539i	$0.744811\pi$
$84$	−0.497572	+	2.18001i	−0.0542895	+	0.237858i
$85$	10.5298	−	13.2040i	1.14212	−	1.43217i
$86$	−4.47214			−0.482243
$87$		0			0
$88$	3.09017			0.329413
$89$	−2.93552	+	3.68102i	−0.311164	+	0.390188i	−0.912681	−	0.408673i	$-0.865992\pi$
$89$	−2.93552	+	3.68102i	−0.311164	+	0.390188i	0.601517	+	0.798860i	$0.294563\pi$
$90$	−1.38766	+	6.07972i	−0.146272	+	0.640858i
$91$	−0.117461	−	0.514629i	−0.0123132	−	0.0539478i
$92$	1.24698	−	1.56366i	0.130007	−	0.163023i
$93$	3.88812	+	4.87555i	0.403180	+	0.505571i
$94$	0.962679	−	4.21777i	0.0992927	−	0.435030i
$95$	−16.8555	−	8.11719i	−1.72934	−	0.832806i
$96$	3.12829	+	1.50650i	0.319279	+	0.153757i
$97$	0.792688	+	3.47299i	0.0804852	+	0.352629i	0.999095	−	0.0425373i	$-0.0135441\pi$
$97$	0.792688	+	3.47299i	0.0804852	+	0.352629i	−0.918610	+	0.395166i	$0.870687\pi$
$98$	−1.11366	+	0.536310i	−0.112497	+	0.0541755i
$99$	−3.61803			−0.363626
$100$	14.3653	−	6.91796i	1.43653	−	0.691796i
$101$	0.385338	+	0.483198i	0.0383426	+	0.0480800i	0.800633	−	0.599155i	$-0.204497\pi$
$101$	0.385338	+	0.483198i	0.0383426	+	0.0480800i	−0.762291	+	0.647235i	$0.775925\pi$
$102$	−1.04357	−	1.30860i	−0.103329	−	0.129571i
$103$	−8.27120	+	3.98320i	−0.814986	+	0.392476i	−0.794463	−	0.607313i	$-0.792247\pi$
$103$	−8.27120	+	3.98320i	−0.814986	+	0.392476i	−0.0205229	+	0.999789i	$0.506533\pi$
$104$	−0.527864			−0.0517613
$105$	4.79877	−	2.31097i	0.468312	−	0.225527i
$106$	−0.275051	−	1.20508i	−0.0267153	−	0.117047i
$107$	−6.09409	−	2.93476i	−0.589138	−	0.283714i	0.115470	−	0.993311i	$-0.463163\pi$
$107$	−6.09409	−	2.93476i	−0.589138	−	0.283714i	−0.704608	+	0.709597i	$0.748877\pi$
$108$	−5.06167	−	2.43757i	−0.487060	−	0.234556i
$109$	3.20029	−	14.0214i	0.306532	−	1.34300i	−0.553536	−	0.832825i	$-0.686722\pi$
$109$	3.20029	−	14.0214i	0.306532	−	1.34300i	0.860068	−	0.510179i	$-0.170421\pi$
$110$	−2.05240	−	2.57363i	−0.195689	−	0.245386i
$111$	−1.81425	+	2.27500i	−0.172201	+	0.215933i
$112$	0.922549	+	4.04195i	0.0871727	+	0.381929i
$113$	1.76777	−	7.74509i	0.166298	−	0.728597i	−0.821158	−	0.570701i	$-0.806672\pi$
$113$	1.76777	−	7.74509i	0.166298	−	0.728597i	0.987456	−	0.157896i	$-0.0504712\pi$
$114$	−1.15601	+	1.44960i	−0.108271	+	0.135767i
$115$	−4.76393			−0.444239
$116$		0			0
$117$	0.618034			0.0571373
$118$	−2.34677	+	2.94276i	−0.216038	+	0.270903i
$119$	2.18034	−	9.55271i	0.199872	−	0.875695i
$120$	−1.18520	−	5.19270i	−0.108193	−	0.474026i
$121$	−5.66763	+	7.10698i	−0.515239	+	0.646089i
$122$	−0.238152	−	0.298633i	−0.0215613	−	0.0270370i
$123$	0.530037	−	2.32225i	0.0477919	−	0.209390i
$124$	14.7094	+	7.08369i	1.32095	+	0.636134i
$125$	−16.8555	−	8.11719i	−1.50760	−	0.726023i
$126$	0.805088	+	3.52732i	0.0717230	+	0.314239i
$127$	14.3653	−	6.91796i	1.27471	−	0.613870i	0.330687	−	0.943740i	$-0.392719\pi$
$127$	14.3653	−	6.91796i	1.27471	−	0.613870i	0.944026	+	0.329871i	$0.107005\pi$
$128$	11.3820			1.00603
$129$	−4.02926	+	1.94039i	−0.354756	+	0.170842i
$130$	0.350592	+	0.439628i	0.0307490	+	0.0385580i
$131$	−8.93226	−	11.2007i	−0.780415	−	0.978610i	−0.999995	−	0.00301554i	$-0.999040\pi$
$131$	−8.93226	−	11.2007i	−0.780415	−	0.978610i	0.219580	−	0.975594i	$-0.429531\pi$
$132$	1.24511	−	0.599613i	0.108373	−	0.0521896i
$133$	−10.8541			−0.941170
$134$	−0.850760	+	0.409704i	−0.0734944	+	0.0353931i
$135$	2.97777	+	13.0465i	0.256285	+	1.12286i
$136$	−8.82803	−	4.25136i	−0.756997	−	0.364551i
$137$	6.43823	+	3.10049i	0.550055	+	0.264893i	0.688202	−	0.725519i	$-0.258400\pi$
$137$	6.43823	+	3.10049i	0.550055	+	0.264893i	−0.138147	+	0.990412i	$0.544115\pi$
$138$	−0.105060	+	0.460299i	−0.00894331	+	0.0391832i
$139$	0.805422	+	1.00997i	0.0683150	+	0.0856643i	0.814815	−	0.579721i	$-0.196839\pi$
$139$	0.805422	+	1.00997i	0.0683150	+	0.0856643i	−0.746500	+	0.665386i	$0.768267\pi$
$140$	8.69411	−	10.9021i	0.734787	−	0.921393i
$141$	−0.962679	−	4.21777i	−0.0810722	−	0.355200i
$142$	1.44019	−	6.30987i	0.120858	−	0.529512i
$143$	−0.203406	+	0.255063i	−0.0170097	+	0.0213294i
$144$	−4.85410			−0.404508
$145$		0			0
$146$	−8.47214			−0.701159
$147$	−0.770676	+	0.966397i	−0.0635643	+	0.0797071i
$148$	−1.69517	+	7.42703i	−0.139342	+	0.610498i
$149$	−2.14021	−	9.37689i	−0.175333	−	0.768185i	−0.983746	−	0.179568i	$-0.942530\pi$
$149$	−2.14021	−	9.37689i	−0.175333	−	0.768185i	0.808412	−	0.588617i	$-0.200327\pi$
$150$	−2.34677	+	2.94276i	−0.191613	+	0.240275i
$151$	1.66706	+	2.09043i	0.135664	+	0.170117i	0.845023	−	0.534731i	$-0.179587\pi$
$151$	1.66706	+	2.09043i	0.135664	+	0.170117i	−0.709359	+	0.704847i	$0.751015\pi$
$152$	−2.41526	+	10.5820i	−0.195904	+	0.858311i
$153$	10.3360	+	4.97757i	0.835619	+	0.402413i
$154$	−1.72070	−	0.828644i	−0.138658	−	0.0667741i
$155$	−8.65352	−	37.9135i	−0.695067	−	3.04529i
$156$	−0.212690	+	0.102426i	−0.0170288	+	0.00820065i
$157$	−14.5623			−1.16220			−0.581099	−	0.813833i	$-0.697377\pi$
$157$	−14.5623			−1.16220			−0.581099	+	0.813833i	$0.697377\pi$
$158$	3.39119	−	1.63311i	0.269788	−	0.129923i
$159$	−0.770676	−	0.966397i	−0.0611186	−	0.0766403i
$160$	−13.5001	−	16.9286i	−1.06728	−	1.33832i
$161$	−2.49022	+	1.19923i	−0.196257	+	0.0945122i
$162$	−3.52786			−0.277175
$163$	−5.43684	+	2.61825i	−0.425847	+	0.205077i	−0.634517	−	0.772909i	$-0.718801\pi$
$163$	−5.43684	+	2.61825i	−0.425847	+	0.205077i	0.208670	+	0.977986i	$0.433087\pi$
$164$	−1.38766	−	6.07972i	−0.108358	−	0.474746i
$165$	−2.96581	−	1.42826i	−0.230888	−	0.111190i
$166$	−5.53726	−	2.66661i	−0.429775	−	0.206969i
$167$	−2.34267	+	10.2639i	−0.181281	+	0.794245i	0.799740	+	0.600346i	$0.204971\pi$
$167$	−2.34267	+	10.2639i	−0.181281	+	0.794245i	−0.981022	+	0.193899i	$0.937887\pi$
$168$	−1.92669	−	2.41599i	−0.148647	−	0.186398i
$169$	−8.07062	+	10.1202i	−0.620817	+	0.778480i
$170$	2.32261	+	10.1760i	0.178136	+	0.780464i
$171$	2.82784	−	12.3896i	0.216250	−	0.947455i
$172$	−7.29995	+	9.15384i	−0.556616	+	0.697974i
$173$	4.09017			0.310970			0.155485	−	0.987838i	$-0.450306\pi$
$173$	4.09017			0.310970			0.155485	+	0.987838i	$0.450306\pi$
$174$		0			0
$175$	−22.0344			−1.66565
$176$	1.59757	−	2.00329i	0.120421	−	0.151004i
$177$	−0.837554	+	3.66956i	−0.0629544	+	0.275821i
$178$	−0.647498	−	2.83687i	−0.0485320	−	0.212633i
$179$	−9.97584	+	12.5093i	−0.745629	+	0.934989i	−0.999480	−	0.0322542i	$-0.989731\pi$
$179$	−9.97584	+	12.5093i	−0.745629	+	0.934989i	0.253851	+	0.967243i	$0.418303\pi$
$180$	10.1792	+	12.7644i	0.758716	+	0.951400i
$181$	−1.32272	+	5.79524i	−0.0983174	+	0.430757i	−0.999999	−	0.00164474i	$-0.999476\pi$
$181$	−1.32272	+	5.79524i	−0.0983174	+	0.430757i	0.901681	+	0.432401i	$0.142334\pi$
$182$	0.293930	+	0.141549i	0.0217876	+	0.0104923i
$183$	−0.344139	−	0.165729i	−0.0254395	−	0.0122510i
$184$	0.615033	+	2.69463i	0.0453408	+	0.198651i
$185$	16.3489	−	7.87321i	1.20199	−	0.578850i
$186$	−3.85410			−0.282596
$187$	−5.45602	+	2.62748i	−0.398984	+	0.192141i
$188$	−7.06179	−	8.85521i	−0.515034	−	0.645833i
$189$	4.84073	+	6.07009i	0.352111	+	0.441534i
$190$	10.4173	−	5.01670i	0.755749	−	0.363949i
$191$	−17.0344			−1.23257			−0.616284	−	0.787524i	$-0.711363\pi$
$191$	−17.0344			−1.23257			−0.616284	+	0.787524i	$0.711363\pi$
$192$	0.131450	−	0.0633028i	0.00948656	−	0.00456848i
$193$	2.77531	+	12.1594i	0.199771	+	0.875255i	0.971072	+	0.238785i	$0.0767491\pi$
$193$	2.77531	+	12.1594i	0.199771	+	0.875255i	−0.771301	+	0.636470i	$0.780394\pi$
$194$	−1.98360	−	0.955250i	−0.142414	−	0.0685829i
$195$	0.506620	+	0.243975i	0.0362798	+	0.0174714i
$196$	−0.720093	+	3.15493i	−0.0514352	+	0.225352i
$197$	−3.92287	−	4.91912i	−0.279493	−	0.350473i	0.622194	−	0.782863i	$-0.286242\pi$
$197$	−3.92287	−	4.91912i	−0.279493	−	0.350473i	−0.901687	+	0.432390i	$0.857670\pi$
$198$	1.39417	−	1.74823i	0.0990790	−	0.124241i
$199$	1.30266	+	5.70733i	0.0923431	+	0.404582i	0.999882	−	0.0153872i	$-0.00489810\pi$
$199$	1.30266	+	5.70733i	0.0923431	+	0.404582i	−0.907538	+	0.419969i	$0.862041\pi$
$200$	−4.90312	+	21.4820i	−0.346703	+	1.51901i
$201$	−0.588744	+	0.738262i	−0.0415268	+	0.0520730i
$202$	−0.381966			−0.0268750
$203$		0			0
$204$	−4.38197			−0.306799
$205$	−9.26138	+	11.6134i	−0.646843	+	0.811115i
$206$	1.26253	−	5.53151i	0.0879647	−	0.385398i
$207$	−0.720093	−	3.15493i	−0.0500499	−	0.219283i
$208$	−0.272898	+	0.342203i	−0.0189221	+	0.0237275i
$209$	4.18250	+	5.24469i	0.289309	+	0.362782i
$210$	−0.732494	+	3.20926i	−0.0505469	+	0.221460i
$211$	−10.4985	−	5.05582i	−0.722748	−	0.348057i	0.0360795	−	0.999349i	$-0.488513\pi$
$211$	−10.4985	−	5.05582i	−0.722748	−	0.348057i	−0.758827	+	0.651292i	$0.774227\pi$
$212$	−2.91560	−	1.40408i	−0.200244	−	0.0964324i
$213$	−1.44019	−	6.30987i	−0.0986799	−	0.432345i
$214$	3.76636	−	1.81378i	0.257463	−	0.123988i
$215$	27.8885			1.90198
$216$	6.99506	−	3.36864i	0.475954	−	0.229207i
$217$	−14.0674	−	17.6399i	−0.954955	−	1.19748i
$218$	5.54192	+	6.94934i	0.375346	+	0.470669i
$219$	−7.63313	+	3.67592i	−0.515799	+	0.248396i
$220$	−8.61803			−0.581028
$221$	0.932000	−	0.448827i	0.0626931	−	0.0301914i
$222$	−0.400176	−	1.75328i	−0.0268580	−	0.117673i
$223$	−2.40898	−	1.16010i	−0.161317	−	0.0776862i	0.351483	−	0.936194i	$-0.385677\pi$
$223$	−2.40898	−	1.16010i	−0.161317	−	0.0776862i	−0.512800	+	0.858508i	$0.671392\pi$
$224$	−11.3182	−	5.45058i	−0.756232	−	0.364182i
$225$	5.74068	−	25.1516i	0.382712	−	1.67677i
$226$	3.06123	+	3.83866i	0.203630	+	0.255344i
$227$	−13.0238	+	16.3313i	−0.864420	+	1.08395i	0.131284	+	0.991345i	$0.458090\pi$
$227$	−13.0238	+	16.3313i	−0.864420	+	1.08395i	−0.995703	+	0.0926030i	$0.970481\pi$
$228$	1.08014	+	4.73240i	0.0715340	+	0.313411i
$229$	0.509973	−	2.23434i	0.0336999	−	0.147649i	−0.955279	−	0.295707i	$-0.904445\pi$
$229$	0.509973	−	2.23434i	0.0336999	−	0.147649i	0.988979	+	0.148058i	$0.0473021\pi$
$230$	1.83572	−	2.30192i	0.121044	−	0.151784i
$231$	−1.90983			−0.125658
$232$		0			0
$233$	15.2361			0.998148			0.499074	−	0.866559i	$-0.333674\pi$
$233$	15.2361			0.998148			0.499074	+	0.866559i	$0.333674\pi$
$234$	−0.238152	+	0.298633i	−0.0155685	+	0.0195223i
$235$	−6.00333	+	26.3023i	−0.391614	+	1.71577i
$236$	2.19274	+	9.60704i	0.142735	+	0.625365i
$237$	2.34677	−	2.94276i	0.152439	−	0.191153i
$238$	3.77568	+	4.73456i	0.244741	+	0.306896i
$239$	6.17332	−	27.0471i	0.399319	−	1.74953i	−0.230771	−	0.973008i	$-0.574125\pi$
$239$	6.17332	−	27.0471i	0.399319	−	1.74953i	0.630090	−	0.776522i	$-0.283018\pi$
$240$	−3.97905	−	1.91621i	−0.256846	−	0.123691i
$241$	4.19174	+	2.01863i	0.270013	+	0.130032i	0.563992	−	0.825781i	$-0.309265\pi$
$241$	4.19174	+	2.01863i	0.270013	+	0.130032i	−0.293978	+	0.955812i	$0.594979\pi$
$242$	−1.25013	−	5.47718i	−0.0803614	−	0.352086i
$243$	−12.5634	+	6.05019i	−0.805940	+	0.388120i
$244$	−1.00000			−0.0640184
$245$	6.94485	−	3.34446i	0.443690	−	0.213670i
$246$	0.917862	+	1.15096i	0.0585207	+	0.0733827i
$247$	−0.714456	−	0.895899i	−0.0454597	−	0.0570047i
$248$	−20.3279	+	9.78942i	−1.29083	+	0.621629i
$249$	−6.14590			−0.389480
$250$	10.4173	−	5.01670i	0.658846	−	0.317284i
$251$	−4.37309	−	19.1597i	−0.276027	−	1.20935i	−0.902769	−	0.430126i	$-0.858469\pi$
$251$	−4.37309	−	19.1597i	−0.276027	−	1.20935i	0.626742	−	0.779227i	$-0.284388\pi$
$252$	8.53410	+	4.10981i	0.537598	+	0.258893i
$253$	1.53904	+	0.741162i	0.0967585	+	0.0465965i
$254$	−2.19274	+	9.60704i	−0.137585	+	0.602799i
$255$	6.50780	+	8.16052i	0.407534	+	0.511031i
$256$	−4.09153	+	5.13062i	−0.255721	+	0.320664i
$257$	5.15811	+	22.5992i	0.321754	+	1.40970i	0.834430	+	0.551114i	$0.185797\pi$
$257$	5.15811	+	22.5992i	0.321754	+	1.40970i	−0.512676	+	0.858582i	$0.671346\pi$
$258$	0.615033	−	2.69463i	0.0382903	−	0.167761i
$259$	6.56402	−	8.23102i	0.407868	−	0.511450i
$260$	1.47214			0.0912980
$261$		0			0
$262$	8.85410			0.547008
$263$	10.4174	−	13.0630i	0.642364	−	0.805499i	−0.348932	−	0.937148i	$-0.613456\pi$
$263$	10.4174	−	13.0630i	0.642364	−	0.805499i	0.991296	+	0.131649i	$0.0420271\pi$
$264$	−0.424977	+	1.86195i	−0.0261555	+	0.114595i
$265$	1.71524	+	7.51494i	0.105366	+	0.461639i
$266$	4.18250	−	5.24469i	0.256445	−	0.321572i
$267$	−1.81425	−	2.27500i	−0.111030	−	0.139228i
$268$	−0.550102	+	2.41015i	−0.0336028	+	0.147224i
$269$	−5.40581	−	2.60330i	−0.329598	−	0.158726i	0.261765	−	0.965132i	$-0.415696\pi$
$269$	−5.40581	−	2.60330i	−0.329598	−	0.158726i	−0.591363	+	0.806406i	$0.701410\pi$
$270$	−7.45147	−	3.58844i	−0.453482	−	0.218385i
$271$	2.26534	+	9.92510i	0.137610	+	0.602907i	0.995956	+	0.0898370i	$0.0286346\pi$
$271$	2.26534	+	9.92510i	0.137610	+	0.602907i	−0.858347	+	0.513070i	$0.828508\pi$
$272$	−7.32002	+	3.52514i	−0.443842	+	0.213743i
$273$	0.326238			0.0197448
$274$	−3.97905	+	1.91621i	−0.240383	+	0.115762i
$275$	8.49071	+	10.6470i	0.512009	+	0.642039i
$276$	0.770676	+	0.966397i	0.0463892	+	0.0581703i
$277$	19.2645	−	9.27729i	1.15749	−	0.557418i	0.246215	−	0.969215i	$-0.420813\pi$
$277$	19.2645	−	9.27729i	1.15749	−	0.557418i	0.911276	+	0.411797i	$0.135099\pi$
$278$	−0.798374			−0.0478833
$279$	23.8004	−	11.4616i	1.42489	−	0.686191i
$280$	4.28809	+	18.7874i	0.256263	+	1.12276i
$281$	−20.8346	−	10.0334i	−1.24289	−	0.598542i	−0.307290	−	0.951616i	$-0.599422\pi$
$281$	−20.8346	−	10.0334i	−1.24289	−	0.598542i	−0.935595	+	0.353074i	$0.885136\pi$
$282$	2.40898	+	1.16010i	0.143452	+	0.0690831i
$283$	1.16513	−	5.10479i	0.0692601	−	0.303448i	−0.928419	−	0.371534i	$-0.878832\pi$
$283$	1.16513	−	5.10479i	0.0692601	−	0.303448i	0.997679	+	0.0680857i	$0.0216891\pi$
$284$	−10.5646	−	13.2476i	−0.626893	−	0.786098i
$285$	7.20898	−	9.03977i	0.427023	−	0.535470i
$286$	−0.0448660	−	0.196571i	−0.00265298	−	0.0116235i
$287$	−1.91769	+	8.40196i	−0.113198	+	0.495952i
$288$	9.17042	−	11.4993i	0.540372	−	0.677605i
$289$	2.20163			0.129507
$290$		0			0
$291$	−2.20163			−0.129062
$292$	−13.8292	+	17.3413i	−0.809294	+	1.01482i
$293$	1.89763	−	8.31405i	0.110861	−	0.485712i	−0.888765	−	0.458363i	$-0.848436\pi$
$293$	1.89763	−	8.31405i	0.110861	−	0.485712i	0.999626	−	0.0273496i	$-0.00870673\pi$
$294$	−0.169991	−	0.744779i	−0.00991407	−	0.0434364i
$295$	14.6346	−	18.3513i	0.852062	−	1.06845i
$296$	−6.56402	−	8.23102i	−0.381526	−	0.478418i
$297$	1.06774	−	4.67807i	0.0619565	−	0.271449i
$298$	5.35560	+	2.57912i	0.310242	+	0.149405i
$299$	−0.262899	−	0.126606i	−0.0152039	−	0.00732179i
$300$	2.19274	+	9.60704i	0.126598	+	0.554663i
$301$	14.5780	−	7.02039i	0.840261	−	0.404648i
$302$	−1.65248			−0.0950893
$303$	−0.344139	+	0.165729i	−0.0197703	+	0.00952087i
$304$	5.61141	+	7.03648i	0.321836	+	0.403570i
$305$	1.48513	+	1.86230i	0.0850384	+	0.106635i
$306$	−6.38802	+	3.07631i	−0.365179	+	0.175861i
$307$	19.1803			1.09468			0.547340	−	0.836910i	$-0.315640\pi$
$307$	19.1803			1.09468			0.547340	+	0.836910i	$0.315640\pi$
$308$	−4.50484	+	2.16942i	−0.256687	+	0.123614i
$309$	−1.26253	−	5.53151i	−0.0718229	−	0.314677i
$310$	21.6543	+	10.4282i	1.22988	+	0.592279i
$311$	1.88318	+	0.906891i	0.106785	+	0.0514251i	0.486514	−	0.873673i	$-0.338268\pi$
$311$	1.88318	+	0.906891i	0.106785	+	0.0514251i	−0.379729	+	0.925098i	$0.623983\pi$
$312$	0.0725948	−	0.318058i	0.00410987	−	0.0180065i
$313$	−8.04915	−	10.0933i	−0.454965	−	0.570508i	0.500454	−	0.865763i	$-0.333167\pi$
$313$	−8.04915	−	10.0933i	−0.454965	−	0.570508i	−0.955418	+	0.295256i	$0.904595\pi$
$314$	5.61141	−	7.03648i	0.316670	−	0.397092i
$315$	−5.02059	−	21.9966i	−0.282878	−	1.23937i
$316$	2.19274	−	9.60704i	0.123351	−	0.540438i
$317$	−17.2758	+	21.6631i	−0.970305	+	1.21672i	0.00592451	+	0.999982i	$0.498114\pi$
$317$	−17.2758	+	21.6631i	−0.970305	+	1.21672i	−0.976229	+	0.216741i	$0.930457\pi$
$318$	0.763932			0.0428392
$319$		0			0
$320$	−0.909830			−0.0508610
$321$	2.60640	−	3.26832i	0.145475	−	0.182420i
$322$	0.380111	−	1.66538i	0.0211828	−	0.0928078i
$323$	−4.73313	−	20.7372i	−0.263359	−	1.15385i
$324$	−5.75859	+	7.22105i	−0.319922	+	0.401169i
$325$	−1.45039	−	1.81873i	−0.0804529	−	0.100885i
$326$	0.829890	−	3.63598i	0.0459633	−	0.201379i
$327$	8.00830	+	3.85659i	0.442860	+	0.213270i
$328$	7.76458	+	3.73922i	0.428727	+	0.206464i
$329$	3.48300	+	15.2600i	0.192024	+	0.841313i
$330$	1.83297	−	0.882711i	0.100902	−	0.0485917i
$331$	−21.1803			−1.16418			−0.582088	−	0.813126i	$-0.697764\pi$
$331$	−21.1803			−1.16418			−0.582088	+	0.813126i	$0.697764\pi$
$332$	−14.4967	+	6.98126i	−0.795612	+	0.383147i
$333$	7.68528	+	9.63704i	0.421151	+	0.528107i
$334$	−4.05678	−	5.08705i	−0.221977	−	0.278351i
$335$	5.30539	−	2.55494i	0.289865	−	0.139591i
$336$	−2.56231			−0.139785
$337$	−30.6950	+	14.7819i	−1.67206	+	0.805223i	−0.674294	+	0.738463i	$0.735552\pi$
$337$	−30.6950	+	14.7819i	−1.67206	+	0.805223i	−0.997769	+	0.0667606i	$0.978734\pi$
$338$	−1.78017	−	7.79942i	−0.0968283	−	0.424233i
$339$	4.42360	+	2.13030i	0.240257	+	0.115702i
$340$	24.6201	+	11.8564i	1.33521	+	0.643004i
$341$	−3.10289	+	13.5947i	−0.168031	+	0.736192i
$342$	4.89695	+	6.14058i	0.264797	+	0.332045i
$343$	12.5475	−	15.7341i	0.677501	−	0.849559i
$344$	−3.60046	−	15.7747i	−0.194124	−	0.850513i
$345$	0.655162	−	2.87045i	0.0352727	−	0.154540i
$346$	−1.57610	+	1.97636i	−0.0847315	+	0.106250i
$347$	−32.1246			−1.72454			−0.862270	−	0.506449i	$-0.830958\pi$
$347$	−32.1246			−1.72454			−0.862270	+	0.506449i	$0.830958\pi$
$348$		0			0
$349$	4.52786			0.242371			0.121186	−	0.992630i	$-0.461330\pi$
$349$	4.52786			0.242371			0.121186	+	0.992630i	$0.461330\pi$
$350$	8.49071	−	10.6470i	0.453847	−	0.569107i
$351$	−0.182392	+	0.799110i	−0.00973534	+	0.0426533i
$352$	1.72764	+	7.56927i	0.0920834	+	0.403444i
$353$	−11.9240	+	14.9522i	−0.634651	+	0.795827i	−0.990323	−	0.138784i	$-0.955681\pi$
$353$	−11.9240	+	14.9522i	−0.634651	+	0.795827i	0.355672	+	0.934611i	$0.384252\pi$
$354$	−1.45039	−	1.81873i	−0.0770871	−	0.0966642i
$355$	−8.98110	+	39.3488i	−0.476667	+	2.08841i
$356$	−6.86361	−	3.30534i	−0.363771	−	0.175183i
$357$	5.45602	+	2.62748i	0.288763	+	0.139061i
$358$	−2.20041	−	9.64062i	−0.116295	−	0.509522i
$359$	−21.4106	+	10.3108i	−1.13001	+	0.544182i	−0.902970	−	0.429704i	$-0.858618\pi$
$359$	−21.4106	+	10.3108i	−1.13001	+	0.544182i	−0.227036	+	0.973886i	$0.572904\pi$
$360$	−22.5623			−1.18914
$361$	−4.11050	+	1.97951i	−0.216342	+	0.104185i
$362$	−2.29055	−	2.87226i	−0.120389	−	0.150963i
$363$	−3.50279	−	4.39236i	−0.183849	−	0.230539i
$364$	0.769519	−	0.370581i	0.0403338	−	0.0194237i
$365$	52.8328			2.76540
$366$	0.212690	−	0.102426i	0.0111175	−	0.00535390i
$367$	6.06826	+	26.5868i	0.316761	+	1.38782i	0.843197	+	0.537604i	$0.180671\pi$
$367$	6.06826	+	26.5868i	0.316761	+	1.38782i	−0.526437	+	0.850214i	$0.676472\pi$
$368$	2.06484	+	0.994373i	0.107637	+	0.0518353i
$369$	−9.09093	−	4.37796i	−0.473255	−	0.227908i
$370$	−2.49552	+	10.9336i	−0.129736	+	0.568411i
$371$	2.78833	+	3.49646i	0.144763	+	0.181527i
$372$	−6.29112	+	7.88881i	−0.326179	+	0.409016i
$373$	−4.58794	−	20.1011i	−0.237555	−	1.04080i	−0.943199	−	0.332229i	$-0.892199\pi$
$373$	−4.58794	−	20.1011i	−0.237555	−	1.04080i	0.705644	−	0.708566i	$-0.250658\pi$
$374$	0.832817	−	3.64881i	0.0430639	−	0.188675i
$375$	7.20898	−	9.03977i	0.372270	−	0.466812i
$376$	15.6525			0.807215
$377$		0			0
$378$	−4.79837			−0.246802
$379$	15.1457	−	18.9921i	0.777982	−	0.975558i	−0.222018	−	0.975043i	$-0.571264\pi$
$379$	15.1457	−	18.9921i	0.777982	−	0.975558i	1.00000		0.000515656i	$-0.000164138\pi$
$380$	6.73582	−	29.5116i	0.345540	−	1.51391i
$381$	2.19274	+	9.60704i	0.112338	+	0.492184i
$382$	6.56402	−	8.23102i	0.335844	−	0.421135i
$383$	−17.9902	−	22.5590i	−0.919258	−	1.15271i	−0.987903	−	0.155072i	$-0.950439\pi$
$383$	−17.9902	−	22.5590i	−0.919258	−	1.15271i	0.0686449	−	0.997641i	$-0.478132\pi$
$384$	−1.56531	+	6.85807i	−0.0798794	+	0.349975i
$385$	10.7304	+	5.16748i	0.546871	+	0.263359i
$386$	−6.94485	−	3.34446i	−0.353484	−	0.170229i
$387$	4.21550	+	18.4693i	0.214286	+	0.938847i
$388$	−5.19312	+	2.50088i	−0.263641	+	0.126963i
$389$	19.1246			0.969656			0.484828	−	0.874609i	$-0.338882\pi$
$389$	19.1246			0.969656			0.484828	+	0.874609i	$0.338882\pi$
$390$	−0.313108	+	0.150785i	−0.0158549	+	0.00763530i
$391$	−3.37708	−	4.23472i	−0.170786	−	0.214159i
$392$	−2.78833	−	3.49646i	−0.140832	−	0.176598i
$393$	7.97727	−	3.84165i	0.402400	−	0.193786i
$394$	3.88854			0.195902
$395$	−21.1477	+	10.1842i	−1.06405	+	0.512422i
$396$	−1.30266	−	5.70733i	−0.0654611	−	0.286804i
$397$	12.6638	+	6.09855i	0.635577	+	0.306078i	0.723786	−	0.690024i	$-0.242400\pi$
$397$	12.6638	+	6.09855i	0.635577	+	0.306078i	−0.0882095	+	0.996102i	$0.528115\pi$
$398$	−3.25974	−	1.56981i	−0.163396	−	0.0786873i
$399$	1.49272	−	6.54002i	0.0747293	−	0.327410i
$400$	11.3915	+	14.2845i	0.569574	+	0.714223i
$401$	15.6302	−	19.5996i	0.780535	−	0.978759i	−0.219460	−	0.975621i	$-0.570430\pi$
$401$	15.6302	−	19.5996i	0.780535	−	0.978759i	0.999995	−	0.00313805i	$-0.000998873\pi$
$402$	−0.129861	−	0.568960i	−0.00647690	−	0.0283772i
$403$	0.530037	−	2.32225i	0.0264030	−	0.115679i
$404$	−0.623490	+	0.781831i	−0.0310198	+	0.0388976i
$405$	22.0000			1.09319
$406$		0			0
$407$	−6.50658			−0.322519
$408$	3.77568	−	4.73456i	0.186924	−	0.234396i
$409$	6.10072	−	26.7290i	0.301661	−	1.32167i	−0.565957	−	0.824435i	$-0.691493\pi$
$409$	6.10072	−	26.7290i	0.301661	−	1.32167i	0.867619	−	0.497230i	$-0.165650\pi$
$410$	−2.04282	−	8.95017i	−0.100888	−	0.442017i
$411$	−2.75359	+	3.45289i	−0.135824	+	0.170318i
$412$	−9.26138	−	11.6134i	−0.456275	−	0.572151i
$413$	3.03030	−	13.2766i	0.149111	−	0.653299i
$414$	1.80194	+	0.867767i	0.0885604	+	0.0426484i
$415$	34.5307	+	16.6291i	1.69505	+	0.816292i
$416$	−0.295116	−	1.29299i	−0.0144692	−	0.0633939i
$417$	−0.719310	+	0.346401i	−0.0352248	+	0.0169634i
$418$	−4.14590			−0.202783
$419$	15.8231	−	7.62000i	0.773009	−	0.372261i	−0.00542744	−	0.999985i	$-0.501728\pi$
$419$	15.8231	−	7.62000i	0.773009	−	0.372261i	0.778436	+	0.627724i	$0.216013\pi$
$420$	5.37326	+	6.73785i	0.262188	+	0.328773i
$421$	19.3497	+	24.2637i	0.943045	+	1.18254i	0.983049	+	0.183341i	$0.0586913\pi$
$421$	19.3497	+	24.2637i	0.943045	+	1.18254i	−0.0400047	+	0.999199i	$0.512737\pi$
$422$	6.48844	−	3.12467i	0.315852	−	0.152106i
$423$	−18.3262			−0.891052
$424$	4.02926	−	1.94039i	0.195678	−	0.0942335i
$425$	−9.60853	−	42.0977i	−0.466082	−	2.04204i
$426$	3.60388	+	1.73553i	0.174608	+	0.0840869i
$427$	1.24511	+	0.599613i	0.0602550	+	0.0290173i
$428$	2.43533	−	10.6699i	0.117716	−	0.515748i
$429$	−0.125712	−	0.157638i	−0.00606942	−	0.00761082i
$430$	−10.7465	+	13.4757i	−0.518243	+	0.649856i
$431$	−3.24808	−	14.2308i	−0.156455	−	0.685472i	−0.990925	−	0.134419i	$-0.957083\pi$
$431$	−3.24808	−	14.2308i	−0.156455	−	0.685472i	0.834470	−	0.551053i	$-0.185774\pi$
$432$	1.43252	−	6.27629i	0.0689222	−	0.301968i
$433$	−6.47305	+	8.11695i	−0.311075	+	0.390076i	−0.912651	−	0.408740i	$-0.865968\pi$
$433$	−6.47305	+	8.11695i	−0.311075	+	0.390076i	0.601576	+	0.798816i	$0.294540\pi$
$434$	13.9443			0.669346
$435$		0			0
$436$	23.2705			1.11446
$437$	−3.74094	+	4.69099i	−0.178953	+	0.224400i
$438$	1.16513	−	5.10479i	0.0556723	−	0.243916i
$439$	4.66054	+	20.4192i	0.222435	+	0.974553i	0.955638	+	0.294543i	$0.0951674\pi$
$439$	4.66054	+	20.4192i	0.222435	+	0.974553i	−0.733203	+	0.680010i	$0.761975\pi$
$440$	7.42566	−	9.31148i	0.354004	−	0.443907i
$441$	3.26463	+	4.09372i	0.155459	+	0.194939i
$442$	−0.142262	+	0.623291i	−0.00676672	+	0.0296469i
$443$	−1.72070	−	0.828644i	−0.0817528	−	0.0393701i	0.392561	−	0.919726i	$-0.371589\pi$
$443$	−1.72070	−	0.828644i	−0.0817528	−	0.0393701i	−0.474313	+	0.880356i	$0.657304\pi$
$444$	−4.24195	−	2.04281i	−0.201314	−	0.0969476i
$445$	4.03784	+	17.6909i	0.191412	+	0.838631i
$446$	1.48883	−	0.716982i	0.0704981	−	0.0339501i
$447$	5.94427			0.281154
$448$	−0.475589	+	0.229032i	−0.0224695	+	0.0108207i
$449$	16.2884	+	20.4250i	0.768698	+	0.963917i	0.999960	−	0.00897427i	$-0.00285664\pi$
$449$	16.2884	+	20.4250i	0.768698	+	0.963917i	−0.231261	+	0.972892i	$0.574285\pi$
$450$	9.94109	+	12.4657i	0.468628	+	0.587640i
$451$	4.79877	−	2.31097i	0.225965	−	0.108819i
$452$	12.8541			0.604606
$453$	−1.48883	+	0.716982i	−0.0699513	+	0.0336868i
$454$	−2.87271	−	12.5862i	−0.134823	−	0.590697i
$455$	−1.83297	−	0.882711i	−0.0859309	−	0.0413821i
$456$	−6.04388	−	2.91058i	−0.283031	−	0.136300i
$457$	−4.16297	+	18.2392i	−0.194735	+	0.853191i	0.779274	+	0.626683i	$0.215588\pi$
$457$	−4.16297	+	18.2392i	−0.194735	+	0.853191i	−0.974009	+	0.226508i	$0.927269\pi$
$458$	0.883116	+	1.10739i	0.0412653	+	0.0517450i
$459$	−9.48626	+	11.8954i	−0.442781	+	0.555230i
$460$	−1.71524	−	7.51494i	−0.0799733	−	0.350386i
$461$	−8.67358	+	38.0014i	−0.403969	+	1.76990i	0.207094	+	0.978321i	$0.433599\pi$
$461$	−8.67358	+	38.0014i	−0.403969	+	1.76990i	−0.611063	+	0.791582i	$0.709258\pi$
$462$	0.735930	−	0.922827i	0.0342386	−	0.0429338i
$463$	10.7082			0.497652			0.248826	−	0.968548i	$-0.419955\pi$
$463$	10.7082			0.497652			0.248826	+	0.968548i	$0.419955\pi$
$464$		0			0
$465$	24.0344			1.11457
$466$	−5.87103	+	7.36204i	−0.271970	+	0.341040i
$467$	−3.99298	+	17.4944i	−0.184773	+	0.809543i	0.794543	+	0.607207i	$0.207710\pi$
$467$	−3.99298	+	17.4944i	−0.184773	+	0.809543i	−0.979316	+	0.202336i	$0.935147\pi$
$468$	0.222521	+	0.974928i	0.0102860	+	0.0450661i
$469$	2.13010	−	2.67106i	0.0983587	−	0.123338i
$470$	−10.3959	−	13.0361i	−0.479528	−	0.601309i
$471$	2.00269	−	8.77435i	0.0922790	−	0.404301i
$472$	−12.2694	−	5.90864i	−0.564746	−	0.271967i
$473$	−9.00969	−	4.33884i	−0.414266	−	0.199500i
$474$	0.517637	+	2.26791i	0.0237758	+	0.104169i
$475$	−43.0959	+	20.7539i	−1.97737	+	0.952253i
$476$	15.8541			0.726672
$477$	−4.71753	+	2.27184i	−0.216001	+	0.104021i
$478$	10.6903	+	13.4052i	0.488963	+	0.613140i
$479$	6.97083	+	8.74114i	0.318505	+	0.399393i	0.915151	−	0.403112i	$-0.132072\pi$
$479$	6.97083	+	8.74114i	0.318505	+	0.399393i	−0.596645	+	0.802505i	$0.703500\pi$
$480$	12.0567	−	5.80622i	0.550312	−	0.265016i
$481$	1.11146			0.0506780
$482$	−2.59064	+	1.24758i	−0.118000	+	0.0568259i
$483$	−0.380111	−	1.66538i	−0.0172957	−	0.0757772i
$484$	−13.2516	−	6.38165i	−0.602347	−	0.290075i
$485$	12.3698	+	5.95700i	0.561686	+	0.270494i
$486$	1.91769	−	8.40196i	0.0869883	−	0.381121i
$487$	26.5372	+	33.2766i	1.20251	+	1.50790i	0.808178	+	0.588938i	$0.200454\pi$
$487$	26.5372	+	33.2766i	1.20251	+	1.50790i	0.394335	+	0.918967i	$0.370975\pi$
$488$	0.861642	−	1.08046i	0.0390047	−	0.0489103i
$489$	−0.829890	−	3.63598i	−0.0375289	−	0.164425i
$490$	−1.06007	+	4.64449i	−0.0478893	+	0.209817i
$491$	9.43004	−	11.8249i	0.425572	−	0.533650i	−0.522105	−	0.852881i	$-0.674853\pi$
$491$	9.43004	−	11.8249i	0.425572	−	0.533650i	0.947677	+	0.319231i	$0.103425\pi$
$492$	3.85410			0.173756
$493$		0			0
$494$	0.708204			0.0318636
$495$	−8.69411	+	10.9021i	−0.390771	+	0.490012i
$496$	−4.16297	+	18.2392i	−0.186923	+	0.818962i
$497$	5.21064	+	22.8293i	0.233729	+	1.02403i
$498$	2.36825	−	2.96969i	0.106124	−	0.133075i
$499$	15.3920	+	19.3010i	0.689042	+	0.864032i	0.996152	−	0.0876423i	$-0.0279332\pi$
$499$	15.3920	+	19.3010i	0.689042	+	0.864032i	−0.307110	+	0.951674i	$0.599362\pi$
$500$	6.73582	−	29.5116i	0.301235	−	1.31980i
$501$	−5.86222	−	2.82310i	−0.261905	−	0.126127i
$502$	10.9431	+	5.26991i	0.488413	+	0.235207i
$503$	3.17549	+	13.9127i	0.141588	+	0.620337i	0.995067	+	0.0992095i	$0.0316314\pi$
$503$	3.17549	+	13.9127i	0.141588	+	0.620337i	−0.853479	+	0.521128i	$0.825511\pi$
$504$	−11.7938	+	5.67961i	−0.525339	+	0.252990i
$505$	2.38197			0.105996
$506$	−0.951178	+	0.458063i	−0.0422850	+	0.0203634i
$507$	−4.98792	−	6.25465i	−0.221521	−	0.277779i
$508$	16.0850	+	20.1700i	0.713657	+	0.894898i
$509$	−28.4367	+	13.6944i	−1.26043	+	0.606992i	−0.940289	−	0.340377i	$-0.889445\pi$
$509$	−28.4367	+	13.6944i	−1.26043	+	0.606992i	−0.320143	+	0.947369i	$0.603731\pi$
$510$	−6.45085			−0.285648
$511$	27.6169	−	13.2996i	1.22170	−	0.588340i
$512$	4.16297	+	18.2392i	0.183979	+	0.806064i
$513$	15.1850	+	7.31272i	0.670435	+	0.322865i
$514$	−12.9075	−	6.21592i	−0.569325	−	0.274173i
$515$	−7.87323	+	34.4949i	−0.346936	+	1.52003i
$516$	−4.51161	−	5.65739i	−0.198613	−	0.249053i
$517$	6.03149	−	7.56325i	0.265265	−	0.332631i
$518$	1.44785	+	6.34344i	0.0636149	+	0.278715i
$519$	−0.562503	+	2.46449i	−0.0246911	+	0.108179i
$520$	−1.26845	+	1.59059i	−0.0556254	+	0.0697520i
$521$	4.09017			0.179194			0.0895968	−	0.995978i	$-0.471442\pi$
$521$	4.09017			0.179194			0.0895968	+	0.995978i	$0.471442\pi$
$522$		0			0
$523$	−20.3820			−0.891241			−0.445621	−	0.895222i	$-0.647017\pi$
$523$	−20.3820			−0.891241			−0.445621	+	0.895222i	$0.647017\pi$
$524$	14.4527	−	18.1231i	0.631369	−	0.791712i
$525$	3.03030	−	13.2766i	0.132253	−	0.579438i
$526$	2.29780	+	10.0673i	0.100189	+	0.438957i
$527$	27.5675	−	34.5685i	1.20086	−	1.50583i
$528$	0.987354	+	1.23810i	0.0429690	+	0.0538815i
$529$	4.77800	−	20.9338i	0.207739	−	0.910165i
$530$	−4.29215	−	2.06699i	−0.186439	−	0.0897844i
$531$	14.3653	+	6.91796i	0.623401	+	0.300214i
$532$	−3.90798	−	17.1220i	−0.169432	−	0.742332i
$533$	−0.819729	+	0.394760i	−0.0355064	+	0.0170990i
$534$	1.79837			0.0778232
$535$	−23.4873	+	11.3109i	−1.01544	+	0.489011i
$536$	−2.13010	−	2.67106i	−0.0920061	−	0.115372i
$537$	−6.16541	−	7.73117i	−0.266057	−	0.333625i
$538$	3.34098	−	1.60893i	0.144040	−	0.0693659i
$539$	−2.76393			−0.119051
$540$	−19.5082	+	9.39466i	−0.839500	+	0.404282i
$541$	−3.24808	−	14.2308i	−0.139646	−	0.611829i	−0.995512	−	0.0946319i	$-0.969833\pi$
$541$	−3.24808	−	14.2308i	−0.139646	−	0.611829i	0.855866	−	0.517197i	$-0.173025\pi$
$542$	−5.66871	−	2.72991i	−0.243492	−	0.117260i
$543$	−3.30995	−	1.59399i	−0.142043	−	0.0684045i
$544$	5.47803	−	24.0008i	0.234869	−	1.02903i
$545$	−34.5598	−	43.3366i	−1.48038	−	1.85634i
$546$	−0.125712	+	0.157638i	−0.00537997	+	0.00674627i
$547$	−1.64264	−	7.19688i	−0.0702343	−	0.307717i	0.927594	−	0.373591i	$-0.121874\pi$
$547$	−1.64264	−	7.19688i	−0.0702343	−	0.307717i	−0.997828	+	0.0658742i	$0.979016\pi$
$548$	−2.57286	+	11.2724i	−0.109907	+	0.481534i
$549$	−1.00883	+	1.26503i	−0.0430557	+	0.0539902i
$550$	−8.41641			−0.358877
$551$		0			0
$552$	−1.70820			−0.0727060
$553$	−8.49071	+	10.6470i	−0.361062	+	0.452757i
$554$	−2.94057	+	12.8835i	−0.124933	+	0.547366i
$555$	2.49552	+	10.9336i	0.105929	+	0.464106i
$556$	−1.30320	+	1.63416i	−0.0552680	+	0.0693038i
$557$	−3.43330	−	4.30522i	−0.145473	−	0.182418i	0.703756	−	0.710441i	$-0.251505\pi$
$557$	−3.43330	−	4.30522i	−0.145473	−	0.182418i	−0.849230	+	0.528024i	$0.822933\pi$
$558$	−3.63293	+	15.9169i	−0.153794	+	0.673816i
$559$	1.53904	+	0.741162i	0.0650944	+	0.0313478i
$560$	14.3963	+	6.93290i	0.608356	+	0.292969i
$561$	−0.832817	−	3.64881i	−0.0351616	−	0.154053i
$562$	12.8765	−	6.20098i	0.543161	−	0.261572i
$563$	−28.3951			−1.19671			−0.598356	−	0.801230i	$-0.704179\pi$
$563$	−28.3951			−1.19671			−0.598356	+	0.801230i	$0.704179\pi$
$564$	6.30678	−	3.03719i	0.265563	−	0.127889i
$565$	−19.0900	−	23.9381i	−0.803124	−	1.00709i
$566$	2.01766	+	2.53006i	0.0848084	+	0.106346i
$567$	11.4999	−	5.53806i	0.482951	−	0.232577i
$568$	23.4164			0.982531
$569$	−1.75173	+	0.843588i	−0.0734363	+	0.0353650i	−0.470241	−	0.882538i	$-0.655833\pi$
$569$	−1.75173	+	0.843588i	−0.0734363	+	0.0353650i	0.396805	+	0.917903i	$0.370119\pi$
$570$	1.59011	+	6.96674i	0.0666025	+	0.291804i
$571$	31.0894	+	14.9718i	1.30105	+	0.626552i	0.950713	−	0.310072i	$-0.100353\pi$
$571$	31.0894	+	14.9718i	1.30105	+	0.626552i	0.350336	+	0.936624i	$0.386067\pi$
$572$	−0.475589	−	0.229032i	−0.0198854	−	0.00957629i
$573$	2.34267	−	10.2639i	0.0978664	−	0.428781i
$574$	−3.32086	−	4.16422i	−0.138610	−	0.173811i
$575$	−7.59432	+	9.52297i	−0.316705	+	0.397135i
$576$	−0.137526	−	0.602539i	−0.00573023	−	0.0251058i
$577$	−0.615033	+	2.69463i	−0.0256041	+	0.112179i	−0.986115	−	0.166063i	$-0.946895\pi$
$577$	−0.615033	+	2.69463i	−0.0256041	+	0.112179i	0.960511	+	0.278242i	$0.0897517\pi$
$578$	−0.848370	+	1.06382i	−0.0352875	+	0.0442492i
$579$	−7.70820			−0.320342
$580$		0			0
$581$	22.2361			0.922508
$582$	0.848370	−	1.06382i	0.0351661	−	0.0440969i
$583$	0.615033	−	2.69463i	0.0254721	−	0.111600i
$584$	−6.82082	−	29.8840i	−0.282247	−	1.23661i
$585$	1.48513	−	1.86230i	0.0614026	−	0.0769965i
$586$	3.28611	+	4.12065i	0.135748	+	0.170223i
$587$	−10.3735	+	45.4492i	−0.428160	+	1.87589i	0.0518966	+	0.998652i	$0.483473\pi$
$587$	−10.3735	+	45.4492i	−0.428160	+	1.87589i	−0.480056	+	0.877238i	$0.659384\pi$
$588$	−1.80194	−	0.867767i	−0.0743107	−	0.0357861i
$589$	−44.1283	−	21.2511i	−1.81827	−	0.875635i
$590$	3.22802	+	14.1429i	0.132895	+	0.582253i
$591$	3.50346	−	1.68718i	0.144113	−	0.0694011i
$592$	−8.72949			−0.358780
$593$	13.0079	−	6.26428i	0.534171	−	0.257243i	−0.147295	−	0.989093i	$-0.547057\pi$
$593$	13.0079	−	6.26428i	0.534171	−	0.257243i	0.681466	+	0.731849i	$0.261343\pi$
$594$	1.84900	+	2.31857i	0.0758652	+	0.0951319i
$595$	−23.5454	−	29.5250i	−0.965268	−	1.21041i
$596$	14.0212	−	6.75223i	0.574329	−	0.276582i
$597$	−3.61803			−0.148076
$598$	0.162481	−	0.0782465i	0.00664433	−	0.00319974i
$599$	2.90810	+	12.7412i	0.118822	+	0.520592i	0.998948	+	0.0458528i	$0.0146005\pi$
$599$	2.90810	+	12.7412i	0.118822	+	0.520592i	−0.880126	+	0.474739i	$0.842542\pi$
$600$	−12.2694	−	5.90864i	−0.500897	−	0.241219i
$601$	26.2714	+	12.6516i	1.07163	+	0.516071i	0.884633	−	0.466289i	$-0.154409\pi$
$601$	26.2714	+	12.6516i	1.07163	+	0.516071i	0.187000	+	0.982360i	$0.440124\pi$
$602$	−2.22521	+	9.74928i	−0.0906928	+	0.397351i
$603$	2.49396	+	3.12733i	0.101562	+	0.127355i
$604$	−2.69737	+	3.38239i	−0.109754	+	0.137627i
$605$	7.79590	+	34.1561i	0.316948	+	1.38864i
$606$	0.0525301	−	0.230149i	0.00213389	−	0.00934917i
$607$	−6.84512	+	8.58350i	−0.277835	+	0.348394i	−0.901096	−	0.433620i	$-0.857236\pi$
$607$	−6.84512	+	8.58350i	−0.277835	+	0.348394i	0.623261	+	0.782014i	$0.285807\pi$
$608$	−27.2705			−1.10597
$609$		0			0
$610$	−1.47214			−0.0596050
$611$	−1.03030	+	1.29196i	−0.0416816	+	0.0522670i
$612$	−4.13050	+	18.0969i	−0.166966	+	0.731524i
$613$	−6.12845	−	26.8505i	−0.247526	−	1.08448i	−0.933985	−	0.357313i	$-0.883693\pi$
$613$	−6.12845	−	26.8505i	−0.247526	−	1.08448i	0.686459	−	0.727169i	$-0.259164\pi$
$614$	−7.39091	+	9.26791i	−0.298273	+	0.374022i
$615$	−5.72385	−	7.17748i	−0.230808	−	0.289424i
$616$	1.53758	−	6.73659i	0.0619509	−	0.271425i
$617$	−12.7760	−	6.15262i	−0.514344	−	0.247695i	0.158661	−	0.987333i	$-0.449282\pi$
$617$	−12.7760	−	6.15262i	−0.514344	−	0.247695i	−0.673005	+	0.739638i	$0.734997\pi$
$618$	3.15932	+	1.52145i	0.127086	+	0.0612016i
$619$	1.57005	+	6.87883i	0.0631055	+	0.276483i	0.996630	−	0.0820308i	$-0.0261406\pi$
$619$	1.57005	+	6.87883i	0.0631055	+	0.276483i	−0.933524	+	0.358514i	$0.883283\pi$
$620$	56.6917	−	27.3013i	2.27679	−	1.09644i
$621$	4.29180			0.172224
$622$	−1.16387	+	0.560489i	−0.0466669	+	0.0224736i
$623$	6.56402	+	8.23102i	0.262982	+	0.329769i
$624$	−0.168660	−	0.211493i	−0.00675181	−	0.00846650i
$625$	−20.5717	+	9.90679i	−0.822866	+	0.396271i
$626$	7.97871			0.318894
$627$	−3.73533	+	1.79884i	−0.149175	+	0.0718387i
$628$	−5.24311	−	22.9715i	−0.209223	−	0.916665i
$629$	18.5881	+	8.95154i	0.741154	+	0.356921i
$630$	12.5634	+	6.05019i	0.500536	+	0.241045i
$631$	6.27838	−	27.5074i	0.249938	−	1.09505i	−0.681691	−	0.731641i	$-0.738755\pi$
$631$	6.27838	−	27.5074i	0.249938	−	1.09505i	0.931629	−	0.363411i	$-0.118388\pi$
$632$	8.49071	+	10.6470i	0.337742	+	0.423515i
$633$	4.49014	−	5.63046i	0.178467	−	0.223791i
$634$	−3.81058	−	16.6953i	−0.151338	−	0.663054i
$635$	13.6741	−	59.9101i	0.542640	−	2.37746i
$636$	1.24698	−	1.56366i	0.0494460	−	0.0620033i
$637$	0.472136			0.0187067
$638$		0			0
$639$	−27.4164			−1.08458
$640$	27.3508	−	34.2968i	1.08113	−	1.35570i
$641$	2.46013	−	10.7785i	0.0971693	−	0.425727i	−0.902821	−	0.430016i	$-0.858508\pi$
$641$	2.46013	−	10.7785i	0.0971693	−	0.425727i	0.999991	+	0.00428892i	$0.00136521\pi$
$642$	0.574903	+	2.51882i	0.0226896	+	0.0994097i
$643$	−23.3287	+	29.2533i	−0.919996	+	1.15364i	0.0677709	+	0.997701i	$0.478411\pi$
$643$	−23.3287	+	29.2533i	−0.919996	+	1.15364i	−0.987767	+	0.155938i	$0.950160\pi$
$644$	−2.78833	−	3.49646i	−0.109876	−	0.137780i
$645$	−3.83539	+	16.8039i	−0.151018	+	0.661654i
$646$	11.8440	+	5.70379i	0.465998	+	0.224413i
$647$	27.5047	+	13.2455i	1.08132	+	0.520736i	0.887738	−	0.460348i	$-0.152275\pi$
$647$	27.5047	+	13.2455i	1.08132	+	0.520736i	0.193581	+	0.981084i	$0.437990\pi$
$648$	−2.84024	−	12.4439i	−0.111575	−	0.488843i
$649$	−7.58292	+	3.65174i	−0.297656	+	0.143343i
$650$	1.43769			0.0563910
$651$	12.5634	−	6.05019i	0.492397	−	0.237126i
$652$	−6.08771	−	7.63375i	−0.238413	−	0.298961i
$653$	−29.9357	−	37.5382i	−1.17147	−	1.46898i	−0.853660	−	0.520830i	$-0.825622\pi$
$653$	−29.9357	−	37.5382i	−1.17147	−	1.46898i	−0.317815	−	0.948153i	$-0.602949\pi$
$654$	−4.94940	+	2.38351i	−0.193537	+	0.0932025i
$655$	−55.2148			−2.15742
$656$	6.43823	−	3.10049i	0.251371	−	0.121054i
$657$	7.98595	+	34.9887i	0.311562	+	1.36504i
$658$	−8.71576	−	4.19729i	−0.339776	−	0.163627i
$659$	−6.35699	−	3.06137i	−0.247633	−	0.119254i	0.305950	−	0.952047i	$-0.401026\pi$
$659$	−6.35699	−	3.06137i	−0.247633	−	0.119254i	−0.553584	+	0.832794i	$0.686740\pi$
$660$	1.18520	−	5.19270i	0.0461338	−	0.202125i
$661$	−23.3502	−	29.2803i	−0.908218	−	1.13887i	−0.989837	−	0.142206i	$-0.954580\pi$
$661$	−23.3502	−	29.2803i	−0.908218	−	1.13887i	0.0816186	−	0.996664i	$-0.473991\pi$
$662$	8.16159	−	10.2343i	0.317209	−	0.397768i
$663$	0.142262	+	0.623291i	0.00552500	+	0.0242066i
$664$	4.94799	−	21.6786i	0.192019	−	0.841291i
$665$	−26.0823	+	32.7062i	−1.01143	+	1.26829i
$666$	−7.61803			−0.295193
$667$		0			0
$668$	−17.0344			−0.659082
$669$	1.03030	−	1.29196i	0.0398338	−	0.0499500i
$670$	−0.809825	+	3.54807i	−0.0312863	+	0.137074i
$671$	−0.190056	−	0.832688i	−0.00733701	−	0.0321456i
$672$	4.84073	−	6.07009i	0.186735	−	0.234159i
$673$	−4.03531	−	5.06012i	−0.155550	−	0.195053i	0.697950	−	0.716147i	$-0.254096\pi$
$673$	−4.03531	−	5.06012i	−0.155550	−	0.195053i	−0.853500	+	0.521093i	$0.825524\pi$
$674$	4.68534	−	20.5278i	0.180473	−	0.790702i
$675$	30.8265	+	14.8452i	1.18651	+	0.571393i
$676$	−18.8701	−	9.08738i	−0.725774	−	0.349515i
$677$	−9.08616	−	39.8091i	−0.349209	−	1.52999i	−0.778980	−	0.627048i	$-0.784263\pi$
$677$	−9.08616	−	39.8091i	−0.349209	−	1.52999i	0.429771	−	0.902938i	$-0.358594\pi$
$678$	−2.73394	+	1.31659i	−0.104996	+	0.0505635i
$679$	7.96556			0.305690
$680$	−34.0241	+	16.3852i	−1.30477	+	0.628342i
$681$	−8.04915	−	10.0933i	−0.308444	−	0.386777i
$682$	−5.37326	−	6.73785i	−0.205753	−	0.258006i
$683$	−18.7889	+	9.04826i	−0.718937	+	0.346222i	−0.757322	−	0.653041i	$-0.773493\pi$
$683$	−18.7889	+	9.04826i	−0.718937	+	0.346222i	0.0383853	+	0.999263i	$0.487779\pi$
$684$	20.5623			0.786219
$685$	24.8136	−	11.9496i	0.948079	−	0.456571i
$686$	2.76765	+	12.1259i	0.105669	+	0.462967i
$687$	1.27614	+	0.614556i	0.0486878	+	0.0234468i
$688$	−12.0878	−	5.82116i	−0.460842	−	0.221930i
$689$	−0.105060	+	0.460299i	−0.00400247	+	0.0175360i
$690$	1.13454	+	1.42267i	0.0431912	+	0.0541600i
$691$	7.37764	−	9.25127i	0.280659	−	0.351935i	−0.621442	−	0.783460i	$-0.713453\pi$
$691$	7.37764	−	9.25127i	0.280659	−	0.351935i	0.902101	+	0.431525i	$0.142024\pi$
$692$	1.47265	+	6.45211i	0.0559818	+	0.245272i
$693$	−1.80023	+	7.88733i	−0.0683852	+	0.299615i
$694$	12.3788	−	15.5226i	0.469894	−	0.589228i
$695$	4.97871			0.188853
$696$		0			0
$697$	−16.8885			−0.639699
$698$	−1.74476	+	2.18786i	−0.0660400	+	0.0828116i
$699$	−2.09535	+	9.18032i	−0.0792533	+	0.347232i
$700$	−7.93342	−	34.7586i	−0.299855	−	1.31375i
$701$	−13.1280	+	16.4620i	−0.495839	+	0.621762i	−0.965285	−	0.261199i	$-0.915882\pi$
$701$	−13.1280	+	16.4620i	−0.495839	+	0.621762i	0.469446	+	0.882961i	$0.344454\pi$
$702$	−0.315846	−	0.396058i	−0.0119208	−	0.0149483i
$703$	5.08552	−	22.2811i	0.191804	−	0.840348i
$704$	0.293930	+	0.141549i	0.0110779	+	0.00533484i
$705$	−15.0225	−	7.23447i	−0.565782	−	0.272466i
$706$	−2.63012	−	11.5233i	−0.0989859	−	0.433686i
$707$	1.24511	−	0.599613i	0.0468271	−	0.0225508i
$708$	−6.09017			−0.228883
$709$	37.3961	−	18.0090i	1.40444	−	0.676343i	0.430384	−	0.902646i	$-0.358378\pi$
$709$	37.3961	−	18.0090i	1.40444	−	0.676343i	0.974057	+	0.226302i	$0.0726638\pi$
$710$	−15.5525	−	19.5022i	−0.583675	−	0.731905i
$711$	−9.94109	−	12.4657i	−0.372820	−	0.467502i
$712$	9.48528	−	4.56787i	0.355476	−	0.171188i
$713$	−12.4721			−0.467085
$714$	−3.37201	+	1.62387i	−0.126194	+	0.0607719i
$715$	0.279788	+	1.22583i	0.0104635	+	0.0458434i
$716$	−23.3248	−	11.2326i	−0.871688	−	0.419783i
$717$	15.4479	+	7.43933i	0.576913	+	0.277827i
$718$	3.26815	−	14.3187i	0.121966	−	0.534369i
$719$	5.30376	+	6.65071i	0.197797	+	0.248030i	0.870832	−	0.491581i	$-0.163581\pi$
$719$	5.30376	+	6.65071i	0.197797	+	0.248030i	−0.673035	+	0.739611i	$0.735010\pi$
$720$	−11.6644	+	14.6267i	−0.434706	+	0.545104i
$721$	4.56788	+	20.0132i	0.170117	+	0.745330i
$722$	0.627433	−	2.74897i	0.0233507	−	0.102306i
$723$	−1.79278	+	2.24807i	−0.0666740	+	0.0836066i
$724$	−9.61803			−0.357451
$725$		0			0
$726$	3.47214			0.128863
$727$	−17.4925	+	21.9349i	−0.648759	+	0.813519i	−0.992068	−	0.125704i	$-0.959881\pi$
$727$	−17.4925	+	21.9349i	−0.648759	+	0.813519i	0.343308	+	0.939223i	$0.388452\pi$
$728$	−0.262650	+	1.15075i	−0.00973447	+	0.0426495i
$729$	1.89289	+	8.29330i	0.0701071	+	0.307159i
$730$	−20.3585	+	25.5287i	−0.753501	+	0.944861i
$731$	19.7697	+	24.7905i	0.731210	+	0.916909i
$732$	0.137526	−	0.602539i	0.00508309	−	0.0222705i
$733$	13.3521	+	6.43001i	0.493169	+	0.237498i	0.663902	−	0.747820i	$-0.268899\pi$
$733$	13.3521	+	6.43001i	0.493169	+	0.237498i	−0.170733	+	0.985317i	$0.554613\pi$
$734$	−15.1850	−	7.31272i	−0.560489	−	0.269917i
$735$	1.06007	+	4.64449i	0.0391014	+	0.171315i
$736$	−6.25657	+	3.01301i	−0.230620	+	0.111061i
$737$	−2.11146			−0.0777765
$738$	5.61850	−	2.70573i	0.206820	−	0.0995992i
$739$	31.2174	+	39.1454i	1.14835	+	1.43999i	0.878920	+	0.476968i	$0.158264\pi$
$739$	31.2174	+	39.1454i	1.14835	+	1.43999i	0.269432	+	0.963020i	$0.413164\pi$
$740$	18.3061	+	22.9551i	0.672945	+	0.843846i
$741$	0.638070	−	0.307278i	0.0234401	−	0.0112881i
$742$	−2.76393			−0.101467
$743$	31.7466	−	15.2884i	1.16467	−	0.560875i	0.251261	−	0.967919i	$-0.419155\pi$
$743$	31.7466	−	15.2884i	1.16467	−	0.560875i	0.913409	+	0.407044i	$0.133440\pi$
$744$	−3.10289	−	13.5947i	−0.113758	−	0.498404i
$745$	−33.3979	−	16.0836i	−1.22360	−	0.589257i
$746$	11.4807	+	5.52883i	0.420339	+	0.202425i
$747$	−5.79321	+	25.3817i	−0.211962	+	0.928668i
$748$	−6.10919	−	7.66068i	−0.223374	−	0.280102i
$749$	−9.43004	+	11.8249i	−0.344566	+	0.432072i
$750$	1.59011	+	6.96674i	0.0580627	+	0.254389i
$751$	−4.12284	+	18.0633i	−0.150444	+	0.659140i	0.842311	+	0.538991i	$0.181194\pi$
$751$	−4.12284	+	18.0633i	−0.150444	+	0.659140i	−0.992756	+	0.120149i	$0.961663\pi$
$752$	8.09210	−	10.1472i	0.295088	−	0.370029i
$753$	12.1459			0.442621
$754$		0			0
$755$	10.3050			0.375036
$756$	−7.83247	+	9.82161i	−0.284864	+	0.357208i
$757$	−0.00473663	+	0.0207525i	−0.000172156	+	0.000754264i	−0.975014	−	0.222144i	$-0.928695\pi$
$757$	−0.00473663	+	0.0207525i	−0.000172156	+	0.000754264i	0.974842	+	0.222898i	$0.0715517\pi$
$758$	3.34074	+	14.6367i	0.121341	+	0.531630i
$759$	−0.658236	+	0.825401i	−0.0238924	+	0.0299602i
$760$	26.0823	+	32.7062i	0.946106	+	1.18638i
$761$	−5.60789	+	24.5698i	−0.203286	+	0.890653i	0.765634	+	0.643277i	$0.222426\pi$
$761$	−5.60789	+	24.5698i	−0.203286	+	0.890653i	−0.968919	+	0.247377i	$0.920432\pi$
$762$	−5.48705	−	2.64243i	−0.198775	−	0.0957250i
$763$	−28.9743	−	13.9533i	−1.04894	−	0.505143i
$764$	−6.13319	−	26.8713i	−0.221891	−	0.972168i
$765$	39.8361	−	19.1841i	1.44028	−	0.693602i
$766$	17.8328			0.644326
$767$	1.29532	−	0.623792i	0.0467712	−	0.0225238i
$768$

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.385338 + 0.483198i) q^{2} +(-0.137526 + 0.602539i) q^{3} +(0.360046 + 1.57747i) q^{4} +(2.40299 - 3.01326i) q^{5} +(-0.238152 - 0.298633i) q^{6} +(0.497572 - 2.18001i) q^{7} +(-2.01463 - 0.970194i) q^{8} +(2.35877 + 1.13592i) q^{9} +O(q^{10})\)	\(q+(-0.385338 + 0.483198i) q^{2} +(-0.137526 + 0.602539i) q^{3} +(0.360046 + 1.57747i) q^{4} +(2.40299 - 3.01326i) q^{5} +(-0.238152 - 0.298633i) q^{6} +(0.497572 - 2.18001i) q^{7} +(-2.01463 - 0.970194i) q^{8} +(2.35877 + 1.13592i) q^{9} +(0.530037 + 2.32225i) q^{10} +(-1.24511 + 0.599613i) q^{11} -1.00000 q^{12} +(0.212690 - 0.102426i) q^{13} +(0.861642 + 1.08046i) q^{14} +(1.48513 + 1.86230i) q^{15} +(-1.67049 + 0.804465i) q^{16} +4.38197 q^{17} +(-1.45780 + 0.702039i) q^{18} +(-1.08014 - 4.73240i) q^{19} +(5.61850 + 2.70573i) q^{20} +(1.24511 + 0.599613i) q^{21} +(0.190056 - 0.832688i) q^{22} +(-0.770676 - 0.966397i) q^{23} +(0.861642 - 1.08046i) q^{24} +(-2.19274 - 9.60704i) q^{25} +(-0.0324654 + 0.142240i) q^{26} +(-2.16484 + 2.71463i) q^{27} +3.61803 q^{28} -1.47214 q^{30} +(6.29112 - 7.88881i) q^{31} +(1.25013 - 5.47718i) q^{32} +(-0.190056 - 0.832688i) q^{33} +(-1.68854 + 2.11736i) q^{34} +(-5.37326 - 6.73785i) q^{35} +(-0.942614 + 4.12986i) q^{36} +(4.24195 + 2.04281i) q^{37} +(2.70291 + 1.30165i) q^{38} +(0.0324654 + 0.142240i) q^{39} +(-7.76458 + 3.73922i) q^{40} -3.85410 q^{41} +(-0.769519 + 0.370581i) q^{42} +(4.51161 + 5.65739i) q^{43} +(-1.39417 - 1.74823i) q^{44} +(9.09093 - 4.37796i) q^{45} +0.763932 q^{46} +(-6.30678 + 3.03719i) q^{47} +(-0.254986 - 1.11717i) q^{48} +(1.80194 + 0.867767i) q^{49} +(5.48705 + 2.64243i) q^{50} +(-0.602632 + 2.64030i) q^{51} +(0.238152 + 0.298633i) q^{52} +(-1.24698 + 1.56366i) q^{53} +(-0.477507 - 2.09210i) q^{54} +(-1.18520 + 5.19270i) q^{55} +(-3.11745 + 3.90916i) q^{56} +3.00000 q^{57} +6.09017 q^{59} +(-2.40299 + 3.01326i) q^{60} +(-0.137526 + 0.602539i) q^{61} +(1.38766 + 6.07972i) q^{62} +(3.64997 - 4.57692i) q^{63} +(-0.147186 - 0.184565i) q^{64} +(0.202456 - 0.887019i) q^{65} +(0.475589 + 0.229032i) q^{66} +(1.37656 + 0.662915i) q^{67} +(1.57771 + 6.91240i) q^{68} +(0.688279 - 0.331458i) q^{69} +5.32624 q^{70} +(-9.43507 + 4.54369i) q^{71} +(-3.64997 - 4.57692i) q^{72} +(8.54693 + 10.7175i) q^{73} +(-2.62167 + 1.26253i) q^{74} +6.09017 q^{75} +(7.07630 - 3.40777i) q^{76} +(0.687628 + 3.01269i) q^{77} +(-0.0812403 - 0.0391233i) q^{78} +(-5.48705 - 2.64243i) q^{79} +(-1.59011 + 6.96674i) q^{80} +(3.55901 + 4.46285i) q^{81} +(1.48513 - 1.86230i) q^{82} +(2.21281 + 9.69495i) q^{83} +(-0.497572 + 2.18001i) q^{84} +(10.5298 - 13.2040i) q^{85} -4.47214 q^{86} +3.09017 q^{88} +(-2.93552 + 3.68102i) q^{89} +(-1.38766 + 6.07972i) q^{90} +(-0.117461 - 0.514629i) q^{91} +(1.24698 - 1.56366i) q^{92} +(3.88812 + 4.87555i) q^{93} +(0.962679 - 4.21777i) q^{94} +(-16.8555 - 8.11719i) q^{95} +(3.12829 + 1.50650i) q^{96} +(0.792688 + 3.47299i) q^{97} +(-1.11366 + 0.536310i) q^{98} -3.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9}+O(q^{10}) \) 12 * q - q^2 + q^3 + q^4 - q^5 + 3 * q^6 + 3 * q^9	\( 12 q - q^{2} + q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9} + 7 q^{10} - 5 q^{11} - 12 q^{12} - 4 q^{13} - 5 q^{14} - 7 q^{15} + 3 q^{16} + 66 q^{17} - q^{18} - 3 q^{19} + 8 q^{20} + 5 q^{21} - 5 q^{22} - 2 q^{23} - 5 q^{24} - 13 q^{25} - 7 q^{26} - 2 q^{27} + 30 q^{28} + 36 q^{30} - 9 q^{31} + 9 q^{32} + 5 q^{33} - 8 q^{34} + 15 q^{35} - 4 q^{36} - 4 q^{37} + 6 q^{38} + 7 q^{39} - 15 q^{40} - 6 q^{41} + 5 q^{42} - 10 q^{43} + 9 q^{45} + 36 q^{46} - 14 q^{47} - 9 q^{48} + 4 q^{49} + q^{50} + 8 q^{51} - 3 q^{52} + 4 q^{53} - 11 q^{54} + 5 q^{55} + 10 q^{56} + 36 q^{57} + 6 q^{59} + q^{60} + q^{61} + 8 q^{62} - 5 q^{63} - 4 q^{64} + 13 q^{65} + 10 q^{66} + 12 q^{67} + 3 q^{68} + 6 q^{69} - 30 q^{70} - 12 q^{71} + 5 q^{72} - 14 q^{73} - 17 q^{74} + 6 q^{75} + 9 q^{76} - 5 q^{77} + 11 q^{78} - q^{79} - 21 q^{80} + 2 q^{81} - 7 q^{82} + 2 q^{83} + 2 q^{85} - 30 q^{88} - 4 q^{89} - 8 q^{90} - 10 q^{91} - 4 q^{92} - 8 q^{93} - 7 q^{94} - 24 q^{95} - 2 q^{96} - 13 q^{97} + 2 q^{98} - 30 q^{99}+O(q^{100}) \) 12 * q - q^2 + q^3 + q^4 - q^5 + 3 * q^6 + 3 * q^9 + 7 * q^10 - 5 * q^11 - 12 * q^12 - 4 * q^13 - 5 * q^14 - 7 * q^15 + 3 * q^16 + 66 * q^17 - q^18 - 3 * q^19 + 8 * q^20 + 5 * q^21 - 5 * q^22 - 2 * q^23 - 5 * q^24 - 13 * q^25 - 7 * q^26 - 2 * q^27 + 30 * q^28 + 36 * q^30 - 9 * q^31 + 9 * q^32 + 5 * q^33 - 8 * q^34 + 15 * q^35 - 4 * q^36 - 4 * q^37 + 6 * q^38 + 7 * q^39 - 15 * q^40 - 6 * q^41 + 5 * q^42 - 10 * q^43 + 9 * q^45 + 36 * q^46 - 14 * q^47 - 9 * q^48 + 4 * q^49 + q^50 + 8 * q^51 - 3 * q^52 + 4 * q^53 - 11 * q^54 + 5 * q^55 + 10 * q^56 + 36 * q^57 + 6 * q^59 + q^60 + q^61 + 8 * q^62 - 5 * q^63 - 4 * q^64 + 13 * q^65 + 10 * q^66 + 12 * q^67 + 3 * q^68 + 6 * q^69 - 30 * q^70 - 12 * q^71 + 5 * q^72 - 14 * q^73 - 17 * q^74 + 6 * q^75 + 9 * q^76 - 5 * q^77 + 11 * q^78 - q^79 - 21 * q^80 + 2 * q^81 - 7 * q^82 + 2 * q^83 + 2 * q^85 - 30 * q^88 - 4 * q^89 - 8 * q^90 - 10 * q^91 - 4 * q^92 - 8 * q^93 - 7 * q^94 - 24 * q^95 - 2 * q^96 - 13 * q^97 + 2 * q^98 - 30 * q^99

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