LMFDB - Embedded newform 273.2.by.d.202.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(76,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("273.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.by (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			202.3
Character	$\chi$	$=$	273.202
Dual form			273.2.by.d.223.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38083 + 0.369991i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.0377371 - 0.0217876i) q^{4} +(0.512287 - 0.512287i) q^{5} +(-1.38083 - 0.369991i) q^{6} +(-2.41005 + 1.09162i) q^{7} +(1.97762 - 1.97762i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.38083 + 0.369991i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.0377371 - 0.0217876i) q^{4} +(0.512287 - 0.512287i) q^{5} +(-1.38083 - 0.369991i) q^{6} +(-2.41005 + 1.09162i) q^{7} +(1.97762 - 1.97762i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.517838 + 0.896921i) q^{10} +(1.38992 + 5.18727i) q^{11} +0.0435751 q^{12} +(-0.0545462 + 3.60514i) q^{13} +(2.92397 - 2.39904i) q^{14} +(0.699797 - 0.187510i) q^{15} +(-2.04263 + 3.53793i) q^{16} +(-1.31681 - 2.28077i) q^{17} +(-1.01084 - 1.01084i) q^{18} +(-5.26328 - 1.41029i) q^{19} +(0.00817077 - 0.0304937i) q^{20} +(-2.63298 - 0.259652i) q^{21} +(-3.83849 - 6.64846i) q^{22} +(5.51236 + 3.18256i) q^{23} +(2.70148 - 0.723860i) q^{24} +4.47512i q^{25} +(-1.25855 - 4.99825i) q^{26} +1.00000i q^{27} +(-0.0671647 + 0.0937039i) q^{28} +(0.300703 - 0.520832i) q^{29} +(-0.896921 + 0.517838i) q^{30} +(-6.22737 + 6.22737i) q^{31} +(0.0637871 - 0.238057i) q^{32} +(-1.38992 + 5.18727i) q^{33} +(2.66215 + 2.66215i) q^{34} +(-0.675414 + 1.79386i) q^{35} +(0.0377371 + 0.0217876i) q^{36} +(0.172749 + 0.644708i) q^{37} +7.78948 q^{38} +(-1.84981 + 3.09487i) q^{39} -2.02622i q^{40} +(-2.11401 - 7.88960i) q^{41} +(3.73176 - 0.615645i) q^{42} +(4.10340 - 2.36910i) q^{43} +(0.165470 + 0.165470i) q^{44} +(0.699797 + 0.187510i) q^{45} +(-8.78913 - 2.35504i) q^{46} +(4.25821 + 4.25821i) q^{47} +(-3.53793 + 2.04263i) q^{48} +(4.61671 - 5.26174i) q^{49} +(-1.65576 - 6.17937i) q^{50} -2.63361i q^{51} +(0.0764887 + 0.137236i) q^{52} +0.282101 q^{53} +(-0.369991 - 1.38083i) q^{54} +(3.36941 + 1.94533i) q^{55} +(-2.60736 + 6.92500i) q^{56} +(-3.85299 - 3.85299i) q^{57} +(-0.222515 + 0.830436i) q^{58} +(-1.21690 + 4.54153i) q^{59} +(0.0223230 - 0.0223230i) q^{60} +(13.0884 - 7.55656i) q^{61} +(6.29485 - 10.9030i) q^{62} +(-2.15040 - 1.54136i) q^{63} -7.81819i q^{64} +(1.81892 + 1.87481i) q^{65} -7.67698i q^{66} +(4.48192 - 1.20093i) q^{67} +(-0.0993850 - 0.0573799i) q^{68} +(3.18256 + 5.51236i) q^{69} +(0.268916 - 2.72691i) q^{70} +(4.11194 - 15.3460i) q^{71} +(2.70148 + 0.723860i) q^{72} +(3.04327 + 3.04327i) q^{73} +(-0.477073 - 0.826314i) q^{74} +(-2.23756 + 3.87557i) q^{75} +(-0.229348 + 0.0614536i) q^{76} +(-9.01234 - 10.9843i) q^{77} +(1.40919 - 4.95789i) q^{78} +4.77147 q^{79} +(0.766026 + 2.85885i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.83817 + 10.1120i) q^{82} +(2.42351 - 2.42351i) q^{83} +(-0.105018 + 0.0475676i) q^{84} +(-1.84299 - 0.493829i) q^{85} +(-4.78954 + 4.78954i) q^{86} +(0.520832 - 0.300703i) q^{87} +(13.0072 + 7.50971i) q^{88} +(-5.75969 + 1.54330i) q^{89} -1.03568 q^{90} +(-3.80400 - 8.74812i) q^{91} +0.277361 q^{92} +(-8.50675 + 2.27938i) q^{93} +(-7.45535 - 4.30435i) q^{94} +(-3.41879 + 1.97384i) q^{95} +(0.174270 - 0.174270i) q^{96} +(-15.7347 - 4.21610i) q^{97} +(-4.42808 + 8.97370i) q^{98} +(-3.79734 + 3.79734i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q - 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 16 * q^9	$ 32 q - 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 16 q^{9} + 2 q^{10} - 4 q^{11} + 32 q^{12} + 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} - 8 q^{17} + 2 q^{18} + 2 q^{19} + 44 q^{20} - 4 q^{21} - 4 q^{22} - 18 q^{23} + 4 q^{24} - 28 q^{26} - 32 q^{28} - 18 q^{29} - 14 q^{31} - 8 q^{32} + 4 q^{33} - 66 q^{34} + 22 q^{35} + 6 q^{36} - 24 q^{37} + 24 q^{38} + 8 q^{39} - 26 q^{42} - 6 q^{43} - 20 q^{44} + 4 q^{45} - 58 q^{46} - 28 q^{47} - 60 q^{48} + 8 q^{49} + 70 q^{50} + 28 q^{52} - 80 q^{53} - 4 q^{54} + 60 q^{55} - 54 q^{56} + 16 q^{57} - 4 q^{58} - 42 q^{59} - 58 q^{60} + 36 q^{61} + 52 q^{62} + 4 q^{63} + 14 q^{65} + 26 q^{67} - 72 q^{68} + 2 q^{69} - 116 q^{70} - 4 q^{71} + 4 q^{72} + 12 q^{73} - 18 q^{74} + 16 q^{75} - 48 q^{76} + 28 q^{77} - 14 q^{78} - 4 q^{79} - 98 q^{80} - 16 q^{81} + 20 q^{82} - 36 q^{83} - 18 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} - 54 q^{89} + 4 q^{90} + 148 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} + 22 q^{96} - 40 q^{97} + 36 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 16 * q^9 + 2 * q^10 - 4 * q^11 + 32 * q^12 + 6 * q^13 + 34 * q^14 + 4 * q^15 + 14 * q^16 - 8 * q^17 + 2 * q^18 + 2 * q^19 + 44 * q^20 - 4 * q^21 - 4 * q^22 - 18 * q^23 + 4 * q^24 - 28 * q^26 - 32 * q^28 - 18 * q^29 - 14 * q^31 - 8 * q^32 + 4 * q^33 - 66 * q^34 + 22 * q^35 + 6 * q^36 - 24 * q^37 + 24 * q^38 + 8 * q^39 - 26 * q^42 - 6 * q^43 - 20 * q^44 + 4 * q^45 - 58 * q^46 - 28 * q^47 - 60 * q^48 + 8 * q^49 + 70 * q^50 + 28 * q^52 - 80 * q^53 - 4 * q^54 + 60 * q^55 - 54 * q^56 + 16 * q^57 - 4 * q^58 - 42 * q^59 - 58 * q^60 + 36 * q^61 + 52 * q^62 + 4 * q^63 + 14 * q^65 + 26 * q^67 - 72 * q^68 + 2 * q^69 - 116 * q^70 - 4 * q^71 + 4 * q^72 + 12 * q^73 - 18 * q^74 + 16 * q^75 - 48 * q^76 + 28 * q^77 - 14 * q^78 - 4 * q^79 - 98 * q^80 - 16 * q^81 + 20 * q^82 - 36 * q^83 - 18 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 - 54 * q^89 + 4 * q^90 + 148 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 + 22 * q^96 - 40 * q^97 + 36 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$

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 $

$2$	−1.38083	+	0.369991i	−0.976392	+	0.261623i	−0.711524	−	0.702661i	$-0.751995\pi$
$2$	−1.38083	+	0.369991i	−0.976392	+	0.261623i	−0.264867	+	0.964285i	$0.585328\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.0377371	−	0.0217876i	0.0188686	−	0.0108938i
$5$	0.512287	−	0.512287i	0.229102	−	0.229102i	−0.583216	−	0.812317i	$-0.698206\pi$
$5$	0.512287	−	0.512287i	0.229102	−	0.229102i	0.812317	+	0.583216i	$0.198206\pi$
$6$	−1.38083	−	0.369991i	−0.563720	−	0.151048i
$7$	−2.41005	+	1.09162i	−0.910915	+	0.412595i
$7$	−2.41005	+	1.09162i	−0.910915	+	0.412595i
$8$	1.97762	−	1.97762i	0.699195	−	0.699195i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.517838	+	0.896921i	−0.163755	+	0.283631i
$11$	1.38992	+	5.18727i	0.419078	+	1.56402i	0.776525	+	0.630086i	$0.216981\pi$
$11$	1.38992	+	5.18727i	0.419078	+	1.56402i	−0.357447	+	0.933933i	$0.616353\pi$
$12$	0.0435751			0.0125790
$13$	−0.0545462	+	3.60514i	−0.0151284	+	0.999886i
$13$	−0.0545462	+	3.60514i	−0.0151284	+	0.999886i
$14$	2.92397	−	2.39904i	0.781465	−	0.641171i
$15$	0.699797	−	0.187510i	0.180687	−	0.0484149i
$16$	−2.04263	+	3.53793i	−0.510656	+	0.884483i
$17$	−1.31681	−	2.28077i	−0.319372	−	0.553169i	0.660985	−	0.750399i	$-0.270139\pi$
$17$	−1.31681	−	2.28077i	−0.319372	−	0.553169i	−0.980357	+	0.197230i	$0.936805\pi$
$18$	−1.01084	−	1.01084i	−0.238256	−	0.238256i
$19$	−5.26328	−	1.41029i	−1.20748	−	0.323543i	−0.401707	−	0.915768i	$-0.631583\pi$
$19$	−5.26328	−	1.41029i	−1.20748	−	0.323543i	−0.805773	+	0.592225i	$0.798250\pi$
$20$	0.00817077	−	0.0304937i	0.00182704	−	0.00681861i
$21$	−2.63298	−	0.259652i	−0.574563	−	0.0566608i
$22$	−3.83849	−	6.64846i	−0.818368	−	1.41746i
$23$	5.51236	+	3.18256i	1.14941	+	0.663610i	0.948742	−	0.316051i	$-0.102357\pi$
$23$	5.51236	+	3.18256i	1.14941	+	0.663610i	0.200663	+	0.979660i	$0.435690\pi$
$24$	2.70148	−	0.723860i	0.551438	−	0.147757i
$25$			4.47512i			0.895025i
$26$	−1.25855	−	4.99825i	−0.246822	−	0.980238i
$27$			1.00000i			0.192450i
$28$	−0.0671647	+	0.0937039i	−0.0126929	+	0.0177084i
$29$	0.300703	−	0.520832i	0.0558391	−	0.0967161i	−0.836755	−	0.547578i	$-0.815550\pi$
$29$	0.300703	−	0.520832i	0.0558391	−	0.0967161i	0.892594	+	0.450862i	$0.148883\pi$
$30$	−0.896921	+	0.517838i	−0.163755	+	0.0945438i
$31$	−6.22737	+	6.22737i	−1.11847	+	1.11847i	−0.126503	+	0.991966i	$0.540375\pi$
$31$	−6.22737	+	6.22737i	−1.11847	+	1.11847i	−0.991966	+	0.126503i	$0.959625\pi$
$32$	0.0637871	−	0.238057i	0.0112761	−	0.0420829i
$33$	−1.38992	+	5.18727i	−0.241955	+	0.902987i
$34$	2.66215	+	2.66215i	0.456554	+	0.456554i
$35$	−0.675414	+	1.79386i	−0.114166	+	0.303218i
$36$	0.0377371	+	0.0217876i	0.00628952	+	0.00363126i
$37$	0.172749	+	0.644708i	0.0283998	+	0.105989i	0.978671	−	0.205435i	$-0.0658608\pi$
$37$	0.172749	+	0.644708i	0.0283998	+	0.105989i	−0.950271	+	0.311424i	$0.899194\pi$
$38$	7.78948			1.26362
$39$	−1.84981	+	3.09487i	−0.296206	+	0.495576i
$40$		−	2.02622i		−	0.320374i
$41$	−2.11401	−	7.88960i	−0.330153	−	1.23215i	−0.909029	−	0.416733i	$-0.863175\pi$
$41$	−2.11401	−	7.88960i	−0.330153	−	1.23215i	0.578876	−	0.815416i	$-0.303492\pi$
$42$	3.73176	−	0.615645i	0.575823	−	0.0949960i
$43$	4.10340	−	2.36910i	0.625762	−	0.361284i	−0.153347	−	0.988172i	$-0.549005\pi$
$43$	4.10340	−	2.36910i	0.625762	−	0.361284i	0.779109	+	0.626888i	$0.215672\pi$
$44$	0.165470	+	0.165470i	0.0249455	+	0.0249455i
$45$	0.699797	+	0.187510i	0.104320	+	0.0279524i
$46$	−8.78913	−	2.35504i	−1.29589	−	0.347232i
$47$	4.25821	+	4.25821i	0.621123	+	0.621123i	0.945819	−	0.324695i	$-0.105262\pi$
$47$	4.25821	+	4.25821i	0.621123	+	0.621123i	−0.324695	+	0.945819i	$0.605262\pi$
$48$	−3.53793	+	2.04263i	−0.510656	+	0.294828i
$49$	4.61671	−	5.26174i	0.659530	−	0.751678i
$50$	−1.65576	−	6.17937i	−0.234159	−	0.873895i
$51$		−	2.63361i		−	0.368779i
$52$	0.0764887	+	0.137236i	0.0106071	+	0.0190312i
$53$	0.282101			0.0387495			0.0193748	−	0.999812i	$-0.493832\pi$
$53$	0.282101			0.0387495			0.0193748	+	0.999812i	$0.493832\pi$
$54$	−0.369991	−	1.38083i	−0.0503494	−	0.187907i
$55$	3.36941	+	1.94533i	0.454331	+	0.262308i
$56$	−2.60736	+	6.92500i	−0.348423	+	0.925392i
$57$	−3.85299	−	3.85299i	−0.510341	−	0.510341i
$58$	−0.222515	+	0.830436i	−0.0292176	+	0.109042i
$59$	−1.21690	+	4.54153i	−0.158427	+	0.591257i	0.840361	+	0.542028i	$0.182343\pi$
$59$	−1.21690	+	4.54153i	−0.158427	+	0.591257i	−0.998787	+	0.0492295i	$0.984323\pi$
$60$	0.0223230	−	0.0223230i	0.00288188	−	0.00288188i
$61$	13.0884	−	7.55656i	1.67579	−	0.967519i	0.711497	−	0.702690i	$-0.248018\pi$
$61$	13.0884	−	7.55656i	1.67579	−	0.967519i	0.964295	−	0.264829i	$-0.0853156\pi$
$62$	6.29485	−	10.9030i	0.799446	−	1.38468i
$63$	−2.15040	−	1.54136i	−0.270925	−	0.194193i
$64$		−	7.81819i		−	0.977273i
$65$	1.81892	+	1.87481i	0.225610	+	0.232541i
$66$		−	7.67698i		−	0.944970i
$67$	4.48192	−	1.20093i	0.547553	−	0.146716i	0.0255714	−	0.999673i	$-0.491859\pi$
$67$	4.48192	−	1.20093i	0.547553	−	0.146716i	0.521982	+	0.852957i	$0.325193\pi$
$68$	−0.0993850	−	0.0573799i	−0.0120522	−	0.00695834i
$69$	3.18256	+	5.51236i	0.383135	+	0.663610i
$70$	0.268916	−	2.72691i	0.0321416	−	0.325928i
$71$	4.11194	−	15.3460i	0.487998	−	1.82123i	−0.0781668	−	0.996940i	$-0.524907\pi$
$71$	4.11194	−	15.3460i	0.487998	−	1.82123i	0.566165	−	0.824292i	$-0.308427\pi$
$72$	2.70148	+	0.723860i	0.318373	+	0.0853077i
$73$	3.04327	+	3.04327i	0.356188	+	0.356188i	0.862406	−	0.506218i	$-0.168957\pi$
$73$	3.04327	+	3.04327i	0.356188	+	0.356188i	−0.506218	+	0.862406i	$0.668957\pi$
$74$	−0.477073	−	0.826314i	−0.0554586	−	0.0960571i
$75$	−2.23756	+	3.87557i	−0.258371	+	0.447512i
$76$	−0.229348	+	0.0614536i	−0.0263080	+	0.00704922i
$77$	−9.01234	−	10.9843i	−1.02705	−	1.25178i
$78$	1.40919	−	4.95789i	0.159559	−	0.561370i
$79$	4.77147			0.536832			0.268416	−	0.963303i	$-0.413500\pi$
$79$	4.77147			0.536832			0.268416	+	0.963303i	$0.413500\pi$
$80$	0.766026	+	2.85885i	0.0856443	+	0.319629i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.83817	+	10.1120i	0.644718	+	1.11668i
$83$	2.42351	−	2.42351i	0.266015	−	0.266015i	−0.561477	−	0.827492i	$-0.689767\pi$
$83$	2.42351	−	2.42351i	0.266015	−	0.266015i	0.827492	+	0.561477i	$0.189767\pi$
$84$	−0.105018	+	0.0475676i	−0.0114584	+	0.00519005i
$85$	−1.84299	−	0.493829i	−0.199901	−	0.0535632i
$86$	−4.78954	+	4.78954i	−0.516469	+	0.516469i
$87$	0.520832	−	0.300703i	0.0558391	−	0.0322387i
$88$	13.0072	+	7.50971i	1.38657	+	0.800538i
$89$	−5.75969	+	1.54330i	−0.610526	+	0.163590i	−0.550817	−	0.834626i	$-0.685684\pi$
$89$	−5.75969	+	1.54330i	−0.610526	+	0.163590i	−0.0597085	+	0.998216i	$0.519017\pi$
$90$	−1.03568			−0.109170
$91$	−3.80400	−	8.74812i	−0.398767	−	0.917052i
$92$	0.277361			0.0289169
$93$	−8.50675	+	2.27938i	−0.882109	+	0.236360i
$94$	−7.45535	−	4.30435i	−0.768960	−	0.443959i
$95$	−3.41879	+	1.97384i	−0.350760	+	0.202511i
$96$	0.174270	−	0.174270i	0.0177863	−	0.0177863i
$97$	−15.7347	−	4.21610i	−1.59762	−	0.428080i	−0.653296	−	0.757103i	$-0.726614\pi$
$97$	−15.7347	−	4.21610i	−1.59762	−	0.428080i	−0.944322	+	0.329022i	$0.893281\pi$
$98$	−4.42808	+	8.97370i	−0.447304	+	0.906481i
$99$	−3.79734	+	3.79734i	−0.381647	+	0.381647i
$100$	0.0975020	+	0.168878i	0.00975020	+	0.0168878i
$101$	8.39661	−	14.5434i	0.835494	−	1.44712i	−0.0581328	−	0.998309i	$-0.518515\pi$
$101$	8.39661	−	14.5434i	0.835494	−	1.44712i	0.893627	−	0.448810i	$-0.148152\pi$
$102$	0.974413	+	3.63656i	0.0964813	+	0.360073i
$103$	0.962454			0.0948334			0.0474167	−	0.998875i	$-0.484901\pi$
$103$	0.962454			0.0948334			0.0474167	+	0.998875i	$0.484901\pi$
$104$	7.02173	+	7.23748i	0.688538	+	0.709693i
$105$	−1.48186	+	1.21582i	−0.144615	+	0.118652i
$106$	−0.389532	+	0.104375i	−0.0378347	+	0.0101378i
$107$	−5.96703	+	10.3352i	−0.576854	+	0.999141i	0.418983	+	0.907994i	$0.362387\pi$
$107$	−5.96703	+	10.3352i	−0.576854	+	0.999141i	−0.995837	+	0.0911468i	$0.970947\pi$
$108$	0.0217876	+	0.0377371i	0.00209651	+	0.00363126i
$109$	3.42240	+	3.42240i	0.327807	+	0.327807i	0.851752	−	0.523945i	$-0.175540\pi$
$109$	3.42240	+	3.42240i	0.327807	+	0.327807i	−0.523945	+	0.851752i	$0.675540\pi$
$110$	−5.37233	−	1.43951i	−0.512231	−	0.137252i
$111$	−0.172749	+	0.644708i	−0.0163966	+	0.0611930i
$112$	1.06075	−	10.7564i	0.100231	−	1.01638i
$113$	6.78443	+	11.7510i	0.638226	+	1.10544i	0.985822	+	0.167795i	$0.0536647\pi$
$113$	6.78443	+	11.7510i	0.638226	+	1.10544i	−0.347596	+	0.937644i	$0.613002\pi$
$114$	6.74588	+	3.89474i	0.631810	+	0.364776i
$115$	4.45429	−	1.19352i	0.415365	−	0.111297i
$116$		−	0.0262063i		−	0.00243319i
$117$	−3.14941	+	1.75533i	−0.291163	+	0.162280i
$118$		−	6.72131i		−	0.618747i
$119$	5.66332	+	4.05933i	0.519156	+	0.372118i
$120$	1.01311	−	1.75476i	0.0924839	−	0.160187i
$121$	−15.4496	+	8.91981i	−1.40451	+	0.810892i
$122$	−15.2769	+	15.2769i	−1.38310	+	1.38310i
$123$	2.11401	−	7.88960i	0.190614	−	0.711381i
$124$	−0.0993241	+	0.370682i	−0.00891956	+	0.0332883i
$125$	4.85398	+	4.85398i	0.434153	+	0.434153i
$126$	3.53962	+	1.33271i	0.315334	+	0.118728i
$127$	11.3554	+	6.55606i	1.00763	+	0.581757i	0.910497	−	0.413515i	$-0.135699\pi$
$127$	11.3554	+	6.55606i	1.00763	+	0.581757i	0.0971344	+	0.995271i	$0.469032\pi$
$128$	3.02024	+	11.2717i	0.266954	+	0.996285i
$129$	4.73820			0.417175
$130$	−3.20528	−	1.91580i	−0.281122	−	0.168027i
$131$		−	6.96325i		−	0.608382i	−0.952611	−	0.304191i	$-0.901614\pi$
$131$		−	6.96325i		−	0.608382i	0.952611	−	0.304191i	$-0.0983861\pi$
$132$	0.0605661	+	0.226036i	0.00527160	+	0.0196739i
$133$	14.2243	−	2.34665i	1.23340	−	0.203480i
$134$	−5.74442	+	3.31654i	−0.496242	+	0.286506i
$135$	0.512287	+	0.512287i	0.0440906	+	0.0440906i
$136$	−7.11466	−	1.90637i	−0.610077	−	0.163470i
$137$	−0.989826	−	0.265223i	−0.0845665	−	0.0226595i	0.216288	−	0.976330i	$-0.430605\pi$
$137$	−0.989826	−	0.265223i	−0.0845665	−	0.0226595i	−0.300854	+	0.953670i	$0.597272\pi$
$138$	−6.43409	−	6.43409i	−0.547706	−	0.547706i
$139$	−13.5680	+	7.83346i	−1.15082	+	0.664426i	−0.949087	−	0.315015i	$-0.897990\pi$
$139$	−13.5680	+	7.83346i	−1.15082	+	0.664426i	−0.201732	+	0.979441i	$0.564657\pi$
$140$	0.0135957	+	0.0824109i	0.00114905	+	0.00696499i
$141$	1.55861	+	5.81682i	0.131259	+	0.489865i
$142$			22.7115i			1.90591i
$143$	−18.7766	+	4.72792i	−1.57018	+	0.395369i
$144$	−4.08525			−0.340438
$145$	−0.112770	−	0.420862i	−0.00936500	−	0.0349507i
$146$	−5.32821	−	3.07624i	−0.440966	−	0.254592i
$147$	6.62906	−	2.24845i	0.546756	−	0.185449i
$148$	0.0205657	+	0.0205657i	0.00169049	+	0.00169049i
$149$	3.05630	−	11.4063i	0.250382	−	0.934438i	−0.720220	−	0.693746i	$-0.755959\pi$
$149$	3.05630	−	11.4063i	0.250382	−	0.934438i	0.970602	−	0.240692i	$-0.0773743\pi$
$150$	1.65576	−	6.17937i	0.135192	−	0.504543i
$151$	−8.50103	+	8.50103i	−0.691804	+	0.691804i	−0.962629	−	0.270825i	$-0.912704\pi$
$151$	−8.50103	+	8.50103i	−0.691804	+	0.691804i	0.270825	+	0.962629i	$0.412704\pi$
$152$	−13.1978	+	7.61976i	−1.07048	+	0.618044i
$153$	1.31681	−	2.28077i	0.106457	−	0.184390i
$154$	16.5086	+	11.8329i	1.33030	+	0.953526i
$155$			6.38040i			0.512486i
$156$	−0.00237685	+	0.157094i	−0.000190301	+	0.0125776i
$157$			0.627679i			0.0500942i	0.999686	+	0.0250471i	$0.00797357\pi$
$157$			0.627679i			0.0500942i	−0.999686	+	0.0250471i	$0.992026\pi$
$158$	−6.58857	+	1.76540i	−0.524158	+	0.140448i
$159$	0.244307	+	0.141050i	0.0193748	+	0.0111860i
$160$	−0.0892761	−	0.154631i	−0.00705789	−	0.0122246i
$161$	−16.7592	−	1.65272i	−1.32081	−	0.130252i
$162$	0.369991	−	1.38083i	0.0290693	−	0.108488i
$163$	12.2260	+	3.27594i	0.957613	+	0.256592i	0.703590	−	0.710607i	$-0.251579\pi$
$163$	12.2260	+	3.27594i	0.957613	+	0.256592i	0.254023	+	0.967198i	$0.418246\pi$
$164$	−0.251672	−	0.251672i	−0.0196523	−	0.0196523i
$165$	1.94533	+	3.36941i	0.151444	+	0.262308i
$166$	−2.44977	+	4.24312i	−0.190139	+	0.329330i
$167$	14.4241	−	3.86492i	1.11617	−	0.299076i	0.346837	−	0.937926i	$-0.387256\pi$
$167$	14.4241	−	3.86492i	1.11617	−	0.299076i	0.769332	+	0.638849i	$0.220589\pi$
$168$	−5.72053	+	4.69355i	−0.441349	+	0.362115i
$169$	−12.9940	−	0.393293i	−0.999542	−	0.0302533i
$170$	2.72757			0.209195
$171$	−1.41029	−	5.26328i	−0.107848	−	0.402493i
$172$	0.103234	−	0.178806i	0.00787150	−	0.0136338i
$173$	6.31043	+	10.9300i	0.479773	+	0.830991i	0.999731	−	0.0232010i	$-0.00738576\pi$
$173$	6.31043	+	10.9300i	0.479773	+	0.830991i	−0.519958	+	0.854192i	$0.674052\pi$
$174$	−0.607922	+	0.607922i	−0.0460864	+	0.0460864i
$175$	−4.88515	−	10.7853i	−0.369283	−	0.815291i
$176$	−21.1913	−	5.67819i	−1.59735	−	0.428010i
$177$	−3.32463	+	3.32463i	−0.249895	+	0.249895i
$178$	7.38212	−	4.26207i	0.553313	−	0.319456i
$179$	−9.45522	−	5.45897i	−0.706716	−	0.408023i	0.103128	−	0.994668i	$-0.467115\pi$
$179$	−9.45522	−	5.45897i	−0.706716	−	0.408023i	−0.809844	+	0.586645i	$0.800448\pi$
$180$	0.0304937	−	0.00817077i	0.00227287	−	0.000609013i
$181$	−5.94105			−0.441595			−0.220797	−	0.975320i	$-0.570866\pi$
$181$	−5.94105			−0.441595			−0.220797	+	0.975320i	$0.570866\pi$
$182$	8.48939	+	10.6722i	0.629275	+	0.791075i
$183$	15.1131			1.11719
$184$	17.1953	−	4.60746i	1.26765	−	0.339666i
$185$	0.418773	+	0.241779i	0.0307888	+	0.0177759i
$186$	10.9030	−	6.29485i	0.799446	−	0.461560i
$187$	10.0007	−	10.0007i	0.731326	−	0.731326i
$188$	0.253469	+	0.0679167i	0.0184861	+	0.00495333i
$189$	−1.09162	−	2.41005i	−0.0794040	−	0.175306i
$190$	3.99045	−	3.99045i	0.289498	−	0.289498i
$191$	−0.805155	−	1.39457i	−0.0582590	−	0.100907i	0.835425	−	0.549604i	$-0.185222\pi$
$191$	−0.805155	−	1.39457i	−0.0582590	−	0.100907i	−0.893684	+	0.448697i	$0.851888\pi$
$192$	3.90909	−	6.77075i	0.282115	−	0.488637i
$193$	−6.36607	−	23.7585i	−0.458240	−	1.71017i	−0.678384	−	0.734707i	$-0.737319\pi$
$193$	−6.36607	−	23.7585i	−0.458240	−	1.71017i	0.220144	−	0.975467i	$-0.429347\pi$
$194$	23.2868			1.67190
$195$	0.637829	+	2.53309i	0.0456759	+	0.181399i
$196$	0.0595811	−	0.299150i	0.00425579	−	0.0213679i
$197$	−4.77159	+	1.27854i	−0.339962	+	0.0910925i	−0.424761	−	0.905306i	$-0.639642\pi$
$197$	−4.77159	+	1.27854i	−0.339962	+	0.0910925i	0.0847991	+	0.996398i	$0.472975\pi$
$198$	3.83849	−	6.64846i	0.272789	−	0.472485i
$199$	−2.30866	−	3.99871i	−0.163656	−	0.283461i	0.772521	−	0.634989i	$-0.218995\pi$
$199$	−2.30866	−	3.99871i	−0.163656	−	0.283461i	−0.936177	+	0.351528i	$0.885662\pi$
$200$	8.85011	+	8.85011i	0.625797	+	0.625797i
$201$	4.48192	+	1.20093i	0.316130	+	0.0847068i
$202$	−6.21335	+	23.1885i	−0.437170	+	1.63154i
$203$	−0.156156	+	1.58349i	−0.0109600	+	0.111139i
$204$	−0.0573799	−	0.0993850i	−0.00401740	−	0.00695834i
$205$	−5.12472	−	2.95876i	−0.357926	−	0.206649i
$206$	−1.32898	+	0.356100i	−0.0925946	+	0.0248106i
$207$			6.36512i			0.442406i
$208$	−12.6433	−	7.55693i	−0.876656	−	0.523979i
$209$		−	29.2623i		−	2.02411i
$210$	1.59634	−	2.22712i	0.110158	−	0.153686i
$211$	−3.39083	+	5.87308i	−0.233434	+	0.404320i	−0.958816	−	0.284026i	$-0.908330\pi$
$211$	−3.39083	+	5.87308i	−0.233434	+	0.404320i	0.725382	+	0.688346i	$0.241663\pi$
$212$	0.0106457	−	0.00614629i	0.000731149	−	0.000422129i
$213$	11.2340	−	11.2340i	0.769743	−	0.769743i
$214$	4.41550	−	16.4789i	0.301837	−	1.12647i
$215$	0.888460	−	3.31578i	0.0605924	−	0.226134i
$216$	1.97762	+	1.97762i	0.134560	+	0.134560i
$217$	8.21035	−	21.8062i	0.557355	−	1.48030i
$218$	−5.99200	−	3.45948i	−0.405830	−	0.234306i
$219$	1.11391	+	4.15718i	0.0752713	+	0.280916i
$220$	0.169536			0.0114301
$221$	8.29434	−	4.62286i	0.557937	−	0.310967i
$222$		−	0.954146i		−	0.0640381i
$223$	5.00651	+	18.6845i	0.335260	+	1.25121i	0.903587	+	0.428406i	$0.140925\pi$
$223$	5.00651	+	18.6845i	0.335260	+	1.25121i	−0.568326	+	0.822803i	$0.692409\pi$
$224$	0.106138	+	0.643361i	0.00709165	+	0.0429864i
$225$	−3.87557	+	2.23756i	−0.258371	+	0.149171i
$226$	−13.7159	−	13.7159i	−0.912367	−	0.912367i
$227$	11.5655	+	3.09897i	0.767631	+	0.205686i	0.621324	−	0.783553i	$-0.286595\pi$
$227$	11.5655	+	3.09897i	0.767631	+	0.205686i	0.146306	+	0.989239i	$0.453262\pi$
$228$	−0.229348	−	0.0614536i	−0.0151889	−	0.00406987i
$229$	−0.755536	−	0.755536i	−0.0499272	−	0.0499272i	0.681702	−	0.731630i	$-0.261240\pi$
$229$	−0.755536	−	0.755536i	−0.0499272	−	0.0499272i	−0.731630	+	0.681702i	$0.761240\pi$
$230$	−5.70901	+	3.29610i	−0.376441	+	0.217338i
$231$	−2.31276	−	14.0189i	−0.152168	−	0.922374i
$232$	−0.435333	−	1.62469i	−0.0285810	−	0.106666i
$233$		−	16.2619i		−	1.06535i	−0.846318	−	0.532677i	$-0.821186\pi$
$233$		−	16.2619i		−	1.06535i	0.846318	−	0.532677i	$-0.178814\pi$
$234$	3.69934	−	3.58906i	0.241833	−	0.234624i
$235$	4.36285			0.284601
$236$	0.0530266	+	0.197898i	0.00345173	+	0.0128820i
$237$	4.13221	+	2.38573i	0.268416	+	0.154970i
$238$	−9.32198	−	3.50985i	−0.604254	−	0.227510i
$239$	15.1795	+	15.1795i	0.981878	+	0.981878i	0.999839	−	0.0179604i	$-0.00571728\pi$
$239$	15.1795	+	15.1795i	0.981878	+	0.981878i	−0.0179604	+	0.999839i	$0.505717\pi$
$240$	−0.766026	+	2.85885i	−0.0494468	+	0.184538i
$241$	−3.31373	+	12.3670i	−0.213456	+	0.796630i	0.773248	+	0.634104i	$0.218631\pi$
$241$	−3.31373	+	12.3670i	−0.213456	+	0.796630i	−0.986704	+	0.162526i	$0.948036\pi$
$242$	18.0329	−	18.0329i	1.15920	−	1.15920i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	0.329278	−	0.570326i	0.0210799	−	0.0365114i
$245$	−0.330441	−	5.06061i	−0.0211111	−	0.323310i
$246$			11.6763i			0.744456i
$247$	5.37139	−	18.8979i	0.341773	−	1.20245i
$248$			24.6308i			1.56406i
$249$	3.31057	−	0.887065i	0.209799	−	0.0562155i
$250$	−8.49844	−	4.90658i	−0.537489	−	0.310319i
$251$	−3.61972	−	6.26954i	−0.228475	−	0.395730i	0.728881	−	0.684640i	$-0.240041\pi$
$251$	−3.61972	−	6.26954i	−0.228475	−	0.395730i	−0.957356	+	0.288910i	$0.906707\pi$
$252$	−0.114732	−	0.0113144i	−0.00722746	−	0.000712739i
$253$	−8.84703	+	33.0176i	−0.556208	+	2.07580i
$254$	−18.1056	−	4.85137i	−1.13604	−	0.304402i
$255$	−1.34917	−	1.34917i	−0.0844880	−	0.0844880i
$256$	−0.522655	−	0.905265i	−0.0326659	−	0.0565790i
$257$	−1.90293	+	3.29597i	−0.118701	+	0.205597i	−0.919253	−	0.393667i	$-0.871206\pi$
$257$	−1.90293	+	3.29597i	−0.118701	+	0.205597i	0.800552	+	0.599263i	$0.204540\pi$
$258$	−6.54263	+	1.75309i	−0.407326	+	0.109143i
$259$	−1.12011	−	1.36520i	−0.0696005	−	0.0848296i
$260$	0.109488	+	0.0311201i	0.00679019	+	0.00192999i
$261$	0.601405			0.0372261
$262$	2.57634	+	9.61504i	0.159167	+	0.594019i
$263$	2.01647	−	3.49263i	0.124341	−	0.215365i	−0.797134	−	0.603802i	$-0.793652\pi$
$263$	2.01647	−	3.49263i	0.124341	−	0.215365i	0.921475	+	0.388437i	$0.126985\pi$
$264$	7.50971	+	13.0072i	0.462191	+	0.800538i
$265$	0.144517	−	0.144517i	0.00887759	−	0.00887759i
$266$	−18.7731	+	8.50318i	−1.15105	+	0.521363i
$267$	−5.75969	−	1.54330i	−0.352487	−	0.0944486i
$268$	0.142970	−	0.142970i	0.00873325	−	0.00873325i
$269$	6.03395	−	3.48370i	0.367897	−	0.212405i	−0.304643	−	0.952467i	$-0.598537\pi$
$269$	6.03395	−	3.48370i	0.367897	−	0.212405i	0.672539	+	0.740062i	$0.265204\pi$
$270$	−0.896921	−	0.517838i	−0.0545849	−	0.0315146i
$271$	8.12317	−	2.17660i	0.493447	−	0.132219i	−0.00350987	−	0.999994i	$-0.501117\pi$
$271$	8.12317	−	2.17660i	0.493447	−	0.132219i	0.496957	+	0.867775i	$0.334451\pi$
$272$	10.7590			0.652358
$273$	1.07970	−	9.47809i	0.0653465	−	0.573640i
$274$	1.46491			0.0884983
$275$	−23.2137	+	6.22008i	−1.39984	+	0.375085i
$276$	0.240202	+	0.138680i	0.0144584	+	0.00834758i
$277$	−8.34222	+	4.81638i	−0.501236	+	0.289388i	−0.729224	−	0.684275i	$-0.760119\pi$
$277$	−8.34222	+	4.81638i	−0.501236	+	0.289388i	0.227988	+	0.973664i	$0.426785\pi$
$278$	15.8367	−	15.8367i	0.949821	−	0.949821i
$279$	−8.50675	−	2.27938i	−0.509286	−	0.136463i
$280$	2.21187	+	4.88330i	0.132185	+	0.291833i
$281$	−9.81783	+	9.81783i	−0.585683	+	0.585683i	−0.936459	−	0.350777i	$-0.885918\pi$
$281$	−9.81783	+	9.81783i	−0.585683	+	0.585683i	0.350777	+	0.936459i	$0.385918\pi$
$282$	−4.30435	−	7.45535i	−0.256320	−	0.443959i
$283$	0.916453	−	1.58734i	0.0544775	−	0.0943578i	−0.837501	−	0.546436i	$-0.815984\pi$
$283$	0.916453	−	1.58734i	0.0544775	−	0.0943578i	0.891978	+	0.452079i	$0.149317\pi$
$284$	−0.179178	−	0.668703i	−0.0106323	−	0.0396802i
$285$	−3.94767			−0.233840
$286$	24.1780	−	13.4756i	1.42967	−	0.796831i
$287$	13.7074	+	16.7067i	0.809120	+	0.986163i
$288$	0.238057	−	0.0637871i	0.0140276	−	0.00375869i
$289$	5.03204	−	8.71576i	0.296003	−	0.512692i
$290$	0.311430	+	0.539413i	0.0182878	+	0.0316754i
$291$	−11.5186	−	11.5186i	−0.675233	−	0.675233i
$292$	0.181150	+	0.0485389i	0.0106010	+	0.00284052i
$293$	7.17194	−	26.7660i	0.418989	−	1.56369i	−0.357719	−	0.933829i	$-0.616446\pi$
$293$	7.17194	−	26.7660i	0.418989	−	1.56369i	0.776709	−	0.629860i	$-0.216888\pi$
$294$	−8.32168	+	5.55741i	−0.485330	+	0.324115i
$295$	1.70317	+	2.94997i	0.0991622	+	0.171754i
$296$	1.61662	+	0.933357i	0.0939642	+	0.0542503i
$297$	−5.18727	+	1.38992i	−0.300996	+	0.0806516i
$298$			16.8809i			0.977883i
$299$	−11.7742	+	19.6992i	−0.680922	+	1.13923i
$300$			0.195004i			0.0112586i
$301$	−7.30324	+	10.1890i	−0.420952	+	0.587285i
$302$	8.59314	−	14.8838i	0.494480	−	0.856464i
$303$	14.5434	−	8.39661i	0.835494	−	0.482373i
$304$	15.7404	−	15.7404i	0.902776	−	0.902776i
$305$	2.83386	−	10.5761i	0.162267	−	0.605587i
$306$	−0.974413	+	3.63656i	−0.0557035	+	0.207888i
$307$	16.7091	+	16.7091i	0.953641	+	0.953641i	0.998972	−	0.0453311i	$-0.0144343\pi$
$307$	16.7091	+	16.7091i	0.953641	+	0.953641i	−0.0453311	+	0.998972i	$0.514434\pi$
$308$	−0.579421	−	0.218160i	−0.0330156	−	0.0124308i
$309$	0.833510	+	0.481227i	0.0474167	+	0.0273761i
$310$	−2.36069	−	8.81023i	−0.134078	−	0.500387i
$311$	−1.88740			−0.107025			−0.0535124	−	0.998567i	$-0.517042\pi$
$311$	−1.88740			−0.107025			−0.0535124	+	0.998567i	$0.517042\pi$
$312$	2.46226	+	9.77871i	0.139398	+	0.553610i
$313$			4.73972i			0.267905i	0.990988	+	0.133953i	$0.0427670\pi$
$313$			4.73972i			0.267905i	−0.990988	+	0.133953i	$0.957233\pi$
$314$	−0.232236	−	0.866715i	−0.0131058	−	0.0489116i
$315$	−1.89124	+	0.312006i	−0.106559	+	0.0175796i
$316$	0.180062	−	0.103959i	0.0101293	−	0.00584813i
$317$	12.0340	+	12.0340i	0.675897	+	0.675897i	0.959069	−	0.283172i	$-0.0913868\pi$
$317$	12.0340	+	12.0340i	0.675897	+	0.675897i	−0.283172	+	0.959069i	$0.591387\pi$
$318$	−0.389532	−	0.104375i	−0.0218439	−	0.00585305i
$319$	3.11965	+	0.835908i	0.174667	+	0.0468019i
$320$	−4.00516	−	4.00516i	−0.223895	−	0.223895i
$321$	−10.3352	+	5.96703i	−0.576854	+	0.333047i
$322$	23.7531	−	3.91865i	1.32371	−	0.218378i
$323$	3.71416	+	13.8614i	0.206662	+	0.771271i
$324$			0.0435751i			0.00242084i
$325$	−16.1334	−	0.244101i	−0.894922	−	0.0135403i
$326$	−18.0940			−1.00214
$327$	1.25269	+	4.67509i	0.0692737	+	0.258533i
$328$	−19.7834	−	11.4219i	−1.09235	−	0.630671i
$329$	−14.9109	−	5.61414i	−0.822063	−	0.309518i
$330$	−3.93281	−	3.93281i	−0.216494	−	0.216494i
$331$	−4.49452	+	16.7738i	−0.247041	+	0.921969i	0.725306	+	0.688427i	$0.241698\pi$
$331$	−4.49452	+	16.7738i	−0.247041	+	0.921969i	−0.972347	+	0.233542i	$0.924968\pi$
$332$	0.0386540	−	0.144259i	0.00212141	−	0.00791722i
$333$	−0.471959	+	0.471959i	−0.0258632	+	0.0258632i
$334$	−18.4872	+	10.6736i	−1.01157	+	0.584032i
$335$	1.68081	−	2.91125i	0.0918324	−	0.159058i
$336$	6.29682	−	8.78493i	0.343520	−	0.479257i
$337$		−	10.9597i		−	0.597011i	−0.954408	−	0.298506i	$-0.903512\pi$
$337$		−	10.9597i		−	0.597011i	0.954408	−	0.298506i	$-0.0964882\pi$
$338$	18.0880	−	4.26462i	0.983860	−	0.231965i
$339$			13.5689i			0.736960i
$340$	−0.0803086	+	0.0215186i	−0.00435535	+	0.00116701i
$341$	−40.9586	−	23.6475i	−2.21803	−	1.28058i
$342$	3.89474	+	6.74588i	0.210603	+	0.364776i
$343$	−5.38268	+	17.7208i	−0.290637	+	0.956833i
$344$	3.42979	−	12.8002i	0.184922	−	0.690138i
$345$	4.45429	+	1.19352i	0.239811	+	0.0642572i
$346$	−12.7576	−	12.7576i	−0.685853	−	0.685853i
$347$	−1.04935	−	1.81754i	−0.0563323	−	0.0975704i	0.836484	−	0.547991i	$-0.184607\pi$
$347$	−1.04935	−	1.81754i	−0.0563323	−	0.0975704i	−0.892816	+	0.450421i	$0.851274\pi$
$348$	0.0131032	−	0.0226953i	0.000702403	−	0.00121660i
$349$	−4.33364	+	1.16119i	−0.231974	+	0.0621573i	−0.372933	−	0.927858i	$-0.621648\pi$
$349$	−4.33364	+	1.16119i	−0.231974	+	0.0621573i	0.140959	+	0.990015i	$0.454981\pi$
$350$	10.7360	+	13.0851i	0.573864	+	0.699430i
$351$	−3.60514	−	0.0545462i	−0.192428	−	0.00291146i
$352$	1.32352			0.0705440
$353$	3.60851	+	13.4671i	0.192061	+	0.716783i	0.993008	+	0.118047i	$0.0376634\pi$
$353$	3.60851	+	13.4671i	0.192061	+	0.716783i	−0.800946	+	0.598736i	$0.795670\pi$
$354$	3.36066	−	5.82083i	0.178617	−	0.309373i
$355$	−5.75505	−	9.96804i	−0.305446	−	0.529049i
$356$	−0.183729	+	0.183729i	−0.00973764	+	0.00973764i
$357$	2.87491	+	6.34714i	0.152157	+	0.335926i
$358$	15.0758	+	4.03954i	0.796780	+	0.213497i
$359$	14.5777	−	14.5777i	0.769383	−	0.769383i	−0.208615	−	0.977998i	$-0.566896\pi$
$359$	14.5777	−	14.5777i	0.769383	−	0.769383i	0.977998	+	0.208615i	$0.0668956\pi$
$360$	1.75476	−	1.01311i	0.0924839	−	0.0533956i
$361$	9.25874	+	5.34554i	0.487302	+	0.281344i
$362$	8.20356	−	2.19814i	0.431169	−	0.115531i
$363$	−17.8396			−0.936338
$364$	−0.334152	−	0.247249i	−0.0175143	−	0.0129594i
$365$	3.11805			0.163206
$366$	−20.8686	+	5.59173i	−1.09082	+	0.292284i
$367$	6.13097	+	3.53972i	0.320034	+	0.184772i	0.651408	−	0.758728i	$-0.274179\pi$
$367$	6.13097	+	3.53972i	0.320034	+	0.184772i	−0.331374	+	0.943500i	$0.607512\pi$
$368$	−22.5194	+	13.0016i	−1.17390	+	0.677753i
$369$	5.77559	−	5.77559i	0.300665	−	0.300665i
$370$	−0.667708	−	0.178912i	−0.0347125	−	0.00930119i
$371$	−0.679878	+	0.307948i	−0.0352975	+	0.0159879i
$372$	−0.271358	+	0.271358i	−0.0140693	+	0.0140693i
$373$	−8.61866	−	14.9280i	−0.446257	−	0.772941i	0.551881	−	0.833923i	$-0.313910\pi$
$373$	−8.61866	−	14.9280i	−0.446257	−	0.772941i	−0.998139	+	0.0609820i	$0.980577\pi$
$374$	−10.1091	+	17.5094i	−0.522728	+	0.905392i
$375$	1.77668	+	6.63066i	0.0917474	+	0.342406i
$376$	16.8423			0.868573
$377$	1.86127	+	1.11248i	0.0958603	+	0.0572959i
$378$	2.39904	+	2.92397i	0.123393	+	0.150393i
$379$	4.36936	−	1.17077i	0.224439	−	0.0601382i	−0.144847	−	0.989454i	$-0.546269\pi$
$379$	4.36936	−	1.17077i	0.224439	−	0.0601382i	0.369286	+	0.929316i	$0.379602\pi$
$380$	−0.0860102	+	0.148974i	−0.00441223	+	0.00764220i
$381$	6.55606	+	11.3554i	0.335877	+	0.581757i
$382$	1.62776	+	1.62776i	0.0832833	+	0.0832833i
$383$	27.6971	+	7.42141i	1.41525	+	0.379216i	0.883798	−	0.467870i	$-0.154978\pi$
$383$	27.6971	+	7.42141i	1.41525	+	0.379216i	0.531456	+	0.847086i	$0.321645\pi$
$384$	−3.02024	+	11.2717i	−0.154126	+	0.575205i
$385$	−10.2440	−	1.01022i	−0.522084	−	0.0514855i
$386$	17.5809	+	30.4510i	0.894843	+	1.54991i
$387$	4.10340	+	2.36910i	0.208587	+	0.120428i
$388$	−0.685642	+	0.183717i	−0.0348082	+	0.00932682i
$389$			6.44786i			0.326919i	0.986550	+	0.163460i	$0.0522654\pi$
$389$			6.44786i			0.326919i	−0.986550	+	0.163460i	$0.947735\pi$
$390$	−1.81795	−	3.26177i	−0.0920556	−	0.165166i
$391$		−	16.7633i		−	0.847754i
$392$	−1.27563	−	19.5359i	−0.0644290	−	0.986710i
$393$	3.48162	−	6.03035i	0.175625	−	0.304191i
$394$	6.11569	−	3.53089i	0.308104	−	0.177884i
$395$	2.44436	−	2.44436i	0.122989	−	0.122989i
$396$	−0.0605661	+	0.226036i	−0.00304356	+	0.0113587i
$397$	7.70578	−	28.7583i	0.386742	−	1.44334i	−0.448661	−	0.893702i	$-0.648099\pi$
$397$	7.70578	−	28.7583i	0.386742	−	1.44334i	0.835403	−	0.549638i	$-0.185234\pi$
$398$	4.66734	+	4.66734i	0.233953	+	0.233953i
$399$	13.4919	+	5.07990i	0.675441	+	0.254313i
$400$	−15.8327	−	9.14100i	−0.791634	−	0.457050i
$401$	−5.89581	−	22.0035i	−0.294423	−	1.09880i	−0.941675	−	0.336524i	$-0.890749\pi$
$401$	−5.89581	−	22.0035i	−0.294423	−	1.09880i	0.647252	−	0.762276i	$-0.275918\pi$
$402$	−6.63308			−0.330828
$403$	−22.1109	−	22.7902i	−1.10142	−	1.13526i
$404$		−	0.731767i		−	0.0364068i
$405$	0.187510	+	0.699797i	0.00931745	+	0.0347732i
$406$	−0.370252	−	2.24430i	−0.0183753	−	0.111383i
$407$	−3.10417	+	1.79219i	−0.153868	+	0.0888356i
$408$	−5.20829	−	5.20829i	−0.257849	−	0.257849i
$409$	−2.36322	−	0.633222i	−0.116854	−	0.0313108i	0.199918	−	0.979813i	$-0.435932\pi$
$409$	−2.36322	−	0.633222i	−0.116854	−	0.0313108i	−0.316772	+	0.948502i	$0.602599\pi$
$410$	8.17107	+	2.18943i	0.403540	+	0.108128i
$411$	−0.724603	−	0.724603i	−0.0357420	−	0.0357420i
$412$	0.0363203	−	0.0209695i	0.00178937	−	0.00103309i
$413$	−2.02485	−	12.2737i	−0.0996365	−	0.603951i
$414$	−2.35504	−	8.78913i	−0.115744	−	0.431962i
$415$		−	2.48306i		−	0.121889i
$416$	0.854748	+	0.242946i	0.0419075	+	0.0119114i
$417$	−15.6669			−0.767213
$418$	10.8268	+	40.4061i	0.529555	+	1.97633i
$419$	16.9152	+	9.76598i	0.826361	+	0.477100i	0.852605	−	0.522556i	$-0.175021\pi$
$419$	16.9152	+	9.76598i	0.826361	+	0.477100i	−0.0262443	+	0.999656i	$0.508355\pi$
$420$	−0.0294312	+	0.0781678i	−0.00143610	+	0.00381420i
$421$	14.8560	+	14.8560i	0.724035	+	0.724035i	0.969425	−	0.245389i	$-0.0789158\pi$
$421$	14.8560	+	14.8560i	0.724035	+	0.724035i	−0.245389	+	0.969425i	$0.578916\pi$
$422$	2.50915	−	9.36428i	0.122144	−	0.455846i
$423$	−1.55861	+	5.81682i	−0.0757823	+	0.282823i
$424$	0.557889	−	0.557889i	0.0270935	−	0.0270935i
$425$	10.2067	−	5.89287i	0.495100	−	0.285846i
$426$	−11.3558	+	19.6687i	−0.550188	+	0.952954i
$427$	−23.2947	+	32.4993i	−1.12731	+	1.57275i
$428$			0.520028i			0.0251365i
$429$	−18.6250	−	5.29381i	−0.899224	−	0.255588i
$430$			4.90723i			0.236648i
$431$	13.8720	−	3.71698i	0.668188	−	0.179041i	0.0912498	−	0.995828i	$-0.470914\pi$
$431$	13.8720	−	3.71698i	0.668188	−	0.179041i	0.576939	+	0.816788i	$0.304247\pi$
$432$	−3.53793	−	2.04263i	−0.170219	−	0.0982759i
$433$	18.2103	+	31.5412i	0.875131	+	1.51577i	0.856623	+	0.515943i	$0.172558\pi$
$433$	18.2103	+	31.5412i	0.875131	+	1.51577i	0.0185084	+	0.999829i	$0.494108\pi$
$434$	−3.26894	+	33.1484i	−0.156914	+	1.59117i
$435$	0.112770	−	0.420862i	0.00540689	−	0.0201788i
$436$	0.203717	+	0.0545859i	0.00975630	+	0.00261419i
$437$	−24.5248	−	24.5248i	−1.17318	−	1.17318i
$438$	−3.07624	−	5.32821i	−0.146989	−	0.254592i
$439$	−16.0130	+	27.7354i	−0.764259	+	1.32374i	0.176378	+	0.984323i	$0.443562\pi$
$439$	−16.0130	+	27.7354i	−0.764259	+	1.32374i	−0.940637	+	0.339414i	$0.889771\pi$
$440$	10.5106	−	2.81629i	0.501071	−	0.134262i
$441$	6.86516	+	1.36732i	0.326912	+	0.0651104i
$442$	−9.74262	+	9.45220i	−0.463409	+	0.449595i
$443$	13.4249			0.637834			0.318917	−	0.947783i	$-0.396681\pi$
$443$	13.4249			0.637834			0.318917	+	0.947783i	$0.396681\pi$
$444$	0.00752756	+	0.0280932i	0.000357242	+	0.00133325i
$445$	−2.16000	+	3.74123i	−0.102394	+	0.177351i
$446$	−13.8262	−	23.9477i	−0.654691	−	1.13396i
$447$	8.34997	−	8.34997i	0.394940	−	0.394940i
$448$	8.53452	+	18.8422i	0.403218	+	0.890213i
$449$	18.5886	+	4.98079i	0.877248	+	0.235058i	0.669220	−	0.743065i	$-0.266629\pi$
$449$	18.5886	+	4.98079i	0.877248	+	0.235058i	0.208029	+	0.978123i	$0.433295\pi$
$450$	4.52361	−	4.52361i	0.213245	−	0.213245i
$451$	37.9872	−	21.9319i	1.78875	−	1.03273i
$452$	0.512050	+	0.295632i	0.0240848	+	0.0139054i
$453$	−11.6126	+	3.11159i	−0.545609	+	0.146195i
$454$	−17.1166			−0.803320
$455$	−6.43029	−	2.53281i	−0.301457	−	0.118740i
$456$	−15.2395			−0.713656
$457$	24.5036	−	6.56571i	1.14623	−	0.307131i	0.364776	−	0.931095i	$-0.381146\pi$
$457$	24.5036	−	6.56571i	1.14623	−	0.307131i	0.781453	+	0.623964i	$0.214479\pi$
$458$	1.32281	+	0.763722i	0.0618107	+	0.0356864i
$459$	2.28077	−	1.31681i	0.106457	−	0.0614632i
$460$	0.142088	−	0.142088i	0.00662490	−	0.00662490i
$461$	−23.2002	−	6.21648i	−1.08054	−	0.289530i	−0.325724	−	0.945465i	$-0.605608\pi$
$461$	−23.2002	−	6.21648i	−1.08054	−	0.289530i	−0.754818	+	0.655935i	$0.772275\pi$
$462$	8.38037	+	18.5019i	0.389890	+	0.860787i
$463$	1.96489	−	1.96489i	0.0913160	−	0.0913160i	−0.659973	−	0.751289i	$-0.729432\pi$
$463$	1.96489	−	1.96489i	0.0913160	−	0.0913160i	0.751289	+	0.659973i	$0.229432\pi$
$464$	1.22845	+	2.12773i	0.0570292	+	0.0987774i
$465$	−3.19020	+	5.52559i	−0.147942	+	0.256243i
$466$	6.01678	+	22.4549i	0.278722	+	1.04020i
$467$	1.05748			0.0489341			0.0244671	−	0.999701i	$-0.492211\pi$
$467$	1.05748			0.0489341			0.0244671	+	0.999701i	$0.492211\pi$
$468$	−0.0806056	+	0.134859i	−0.00372599	+	0.00623387i
$469$	−9.49070	+	7.78687i	−0.438240	+	0.359564i
$470$	−6.02434	+	1.61422i	−0.277882	+	0.0744582i
$471$	−0.313839	+	0.543586i	−0.0144610	+	0.0250471i
$472$	6.57487	+	11.3880i	0.302633	+	0.524176i
$473$	17.9926	+	17.9926i	0.827299	+	0.827299i
$474$	−6.58857	−	1.76540i	−0.302623	−	0.0810876i
$475$	6.31123	−	23.5538i	0.289579	−	1.08072i
$476$	0.302160	+	0.0297977i	0.0138495	+	0.00136577i
$477$	0.141050	+	0.244307i	0.00645826	+	0.0111860i
$478$	−26.5765	−	15.3439i	−1.21558	−	0.701816i
$479$	−4.87277	+	1.30565i	−0.222643	+	0.0596569i	−0.368416	−	0.929661i	$-0.620100\pi$
$479$	−4.87277	+	1.30565i	−0.222643	+	0.0596569i	0.145773	+	0.989318i	$0.453433\pi$
$480$		−	0.178552i		−	0.00814975i
$481$	−2.33369	+	0.587618i	−0.106407	+	0.0267931i
$482$		−	18.3028i		−	0.833668i
$483$	−13.6876	−	9.81091i	−0.622806	−	0.446412i
$484$	−0.388682	+	0.673217i	−0.0176674	+	0.0306008i
$485$	−10.2205	+	5.90083i	−0.464091	+	0.267943i
$486$	1.01084	−	1.01084i	0.0458524	−	0.0458524i
$487$	0.725342	−	2.70701i	0.0328684	−	0.122666i	−0.947542	−	0.319630i	$-0.896441\pi$
$487$	0.725342	−	2.70701i	0.0328684	−	0.122666i	0.980411	+	0.196964i	$0.0631081\pi$
$488$	10.9398	−	40.8279i	0.495221	−	1.84819i
$489$	8.95004	+	8.95004i	0.404735	+	0.404735i
$490$	2.32866	+	6.86556i	0.105198	+	0.310154i
$491$	−10.7778	−	6.22255i	−0.486394	−	0.280820i	0.236683	−	0.971587i	$-0.423940\pi$
$491$	−10.7778	−	6.22255i	−0.486394	−	0.280820i	−0.723077	+	0.690767i	$0.757273\pi$
$492$	−0.0921183	−	0.343790i	−0.00415301	−	0.0154993i
$493$	−1.58387			−0.0713338
$494$	−0.424886	+	28.0821i	−0.0191165	+	1.26348i
$495$			3.89066i			0.174872i
$496$	−9.31182	−	34.7522i	−0.418113	−	1.56042i
$497$	6.84204	+	41.4733i	0.306907	+	1.86033i
$498$	−4.24312	+	2.44977i	−0.190139	+	0.109777i
$499$	−6.23994	−	6.23994i	−0.279338	−	0.279338i	0.553507	−	0.832845i	$-0.313289\pi$
$499$	−6.23994	−	6.23994i	−0.279338	−	0.279338i	−0.832845	+	0.553507i	$0.813289\pi$
$500$	0.288932	+	0.0774191i	0.0129214	+	0.00346229i
$501$	14.4241	+	3.86492i	0.644420	+	0.172672i
$502$	7.31788	+	7.31788i	0.326613	+	0.326613i
$503$	−13.6723	+	7.89370i	−0.609617	+	0.351963i	−0.772816	−	0.634631i	$-0.781152\pi$
$503$	−13.6723	+	7.89370i	−0.609617	+	0.351963i	0.163198	+	0.986593i	$0.447819\pi$
$504$	−7.30090	+	1.20446i	−0.325208	+	0.0536510i
$505$	−3.14890	−	11.7519i	−0.140124	−	0.522951i
$506$		−	48.8649i		−	2.17231i
$507$	−11.0565	−	6.83763i	−0.491038	−	0.303670i
$508$	0.571362			0.0253501
$509$	6.32401	+	23.6015i	0.280307	+	1.04612i	0.952201	+	0.305472i	$0.0988142\pi$
$509$	6.32401	+	23.6015i	0.280307	+	1.04612i	−0.671894	+	0.740647i	$0.734519\pi$
$510$	2.36214	+	1.36378i	0.104597	+	0.0603893i
$511$	−10.6565	−	4.01233i	−0.471418	−	0.177495i
$512$	−15.4462	−	15.4462i	−0.682634	−	0.682634i
$513$	1.41029	−	5.26328i	0.0622659	−	0.232380i
$514$	1.40813	−	5.25523i	0.0621101	−	0.231798i
$515$	0.493053	−	0.493053i	0.0217265	−	0.0217265i
$516$	0.178806	−	0.103234i	0.00787150	−	0.00454461i
$517$	−16.1699	+	28.0070i	−0.711150	+	1.23175i
$518$	2.05180	+	1.47068i	0.0901507	+	0.0646179i
$519$			12.6209i			0.553994i
$520$	7.30481	+	0.110523i	0.320337	+	0.00484674i
$521$			2.98806i			0.130909i	0.997856	+	0.0654547i	$0.0208498\pi$
$521$			2.98806i			0.130909i	−0.997856	+	0.0654547i	$0.979150\pi$
$522$	−0.830436	+	0.222515i	−0.0363472	+	0.00973921i
$523$	−23.5900	−	13.6197i	−1.03152	−	0.595547i	−0.114099	−	0.993469i	$-0.536398\pi$
$523$	−23.5900	−	13.6197i	−1.03152	−	0.595547i	−0.917419	+	0.397922i	$0.869731\pi$
$524$	−0.151712	−	0.262773i	−0.00662757	−	0.0114793i
$525$	1.16198	−	11.7829i	0.0507128	−	0.514248i
$526$	−1.49215	+	5.56879i	−0.0650610	+	0.242811i
$527$	22.4035	+	6.00299i	0.975910	+	0.261494i
$528$	−15.5131	−	15.5131i	−0.675121	−	0.675121i
$529$	8.75738	+	15.1682i	0.380756	+	0.659488i
$530$	−0.146083	+	0.253022i	−0.00634542	+	0.0109906i
$531$	−4.54153	+	1.21690i	−0.197086	+	0.0528090i
$532$	0.485657	−	0.398468i	0.0210559	−	0.0172758i
$533$	28.5584	−	7.19096i	1.23700	−	0.311475i
$534$	8.52414			0.368875
$535$	2.23776	+	8.35142i	0.0967466	+	0.361063i
$536$	6.48856	−	11.2385i	0.280263	−	0.485430i
$537$	−5.45897	−	9.45522i	−0.235572	−	0.408023i
$538$	−7.04290	+	7.04290i	−0.303641	+	0.303641i
$539$	33.7110	+	16.6347i	1.45203	+	0.716507i
$540$	0.0304937	+	0.00817077i	0.00131224	+	0.000351614i
$541$	−5.00068	+	5.00068i	−0.214996	+	0.214996i	−0.806386	−	0.591390i	$-0.798579\pi$
$541$	−5.00068	+	5.00068i	−0.214996	+	0.214996i	0.591390	+	0.806386i	$0.298579\pi$
$542$	−10.4114	+	6.01100i	−0.447206	+	0.258195i
$543$	−5.14510	−	2.97052i	−0.220797	−	0.127477i
$544$	−0.626949	+	0.167990i	−0.0268802	+	0.00720253i
$545$	3.50650			0.150202
$546$	2.01593	+	13.4871i	0.0862739	+	0.577194i
$547$	−23.2544			−0.994288			−0.497144	−	0.867668i	$-0.665618\pi$
$547$	−23.2544			−0.994288			−0.497144	+	0.867668i	$0.665618\pi$
$548$	−0.0431318	+	0.0115571i	−0.00184250	+	0.000493696i
$549$	13.0884	+	7.55656i	0.558597	+	0.322506i
$550$	29.7527	−	17.1777i	1.26866	−	0.732460i
$551$	−2.31721	+	2.31721i	−0.0987164	+	0.0987164i
$552$	17.1953	+	4.60746i	0.731879	+	0.196106i
$553$	−11.4995	+	5.20865i	−0.489008	+	0.221494i
$554$	9.73714	−	9.73714i	0.413691	−	0.413691i
$555$	0.241779	+	0.418773i	0.0102629	+	0.0177759i
$556$	−0.341344	+	0.591225i	−0.0144762	+	0.0250735i
$557$	−4.49356	−	16.7702i	−0.190398	−	0.710576i	−0.993410	−	0.114613i	$-0.963437\pi$
$557$	−4.49356	−	16.7702i	−0.190398	−	0.710576i	0.803012	−	0.595963i	$-0.203230\pi$
$558$	12.5897			0.532964
$559$	8.31710	+	14.9225i	0.351776	+	0.631156i
$560$	−4.96695	−	6.05376i	−0.209892	−	0.255818i
$561$	13.6612	−	3.66052i	0.576778	−	0.154547i
$562$	9.92421	−	17.1892i	0.418627	−	0.725084i
$563$	−9.17267	−	15.8875i	−0.386582	−	0.669579i	0.605405	−	0.795917i	$-0.293011\pi$
$563$	−9.17267	−	15.8875i	−0.386582	−	0.669579i	−0.991987	+	0.126338i	$0.959678\pi$
$564$	0.185552	+	0.185552i	0.00781314	+	0.00781314i
$565$	9.49545	+	2.54430i	0.399477	+	0.107039i
$566$	−0.678159	+	2.53093i	−0.0285052	+	0.106383i
$567$	0.259652	−	2.63298i	0.0109044	−	0.110575i
$568$	−22.2167	−	38.4804i	−0.932191	−	1.61460i
$569$	−12.1394	−	7.00867i	−0.508909	−	0.293819i	0.223476	−	0.974709i	$-0.428260\pi$
$569$	−12.1394	−	7.00867i	−0.508909	−	0.293819i	−0.732385	+	0.680891i	$0.761593\pi$
$570$	5.45105	−	1.46061i	0.228319	−	0.0611780i
$571$		−	10.4239i		−	0.436226i	−0.975924	−	0.218113i	$-0.930010\pi$
$571$		−	10.4239i		−	0.436226i	0.975924	−	0.218113i	$-0.0699901\pi$
$572$	−0.605567	+	0.587515i	−0.0253200	+	0.0245652i
$573$		−	1.61031i		−	0.0672716i
$574$	−25.1088	−	17.9974i	−1.04802	−	0.751196i
$575$	−14.2424	+	24.6685i	−0.593947	+	1.02875i
$576$	6.77075	−	3.90909i	0.282115	−	0.162879i
$577$	11.2444	−	11.2444i	0.468111	−	0.468111i	−0.433191	−	0.901302i	$-0.642612\pi$
$577$	11.2444	−	11.2444i	0.468111	−	0.468111i	0.901302	+	0.433191i	$0.142612\pi$
$578$	−3.72363	+	13.8968i	−0.154882	+	0.578029i
$579$	6.36607	−	23.7585i	0.264565	−	0.987370i
$580$	−0.0134252	−	0.0134252i	−0.000557449	−	0.000557449i
$581$	−3.19522	+	8.48634i	−0.132560	+	0.352073i
$582$	20.1670	+	11.6434i	0.835948	+	0.482635i
$583$	0.392099	+	1.46333i	0.0162391	+	0.0606051i
$584$	12.0369			0.498090
$585$	−0.714171	+	2.51264i	−0.0295273	+	0.103885i
$586$			39.6128i			1.63639i
$587$	−10.3083	−	38.4710i	−0.425468	−	1.58787i	−0.762900	−	0.646517i	$-0.776225\pi$
$587$	−10.3083	−	38.4710i	−0.425468	−	1.58787i	0.337432	−	0.941350i	$-0.390442\pi$
$588$	0.201174	−	0.229281i	0.00829627	−	0.00945539i
$589$	41.5588	−	23.9940i	1.71240	−	0.988656i
$590$	−3.44324	−	3.44324i	−0.141756	−	0.141756i
$591$	−4.77159	−	1.27854i	−0.196277	−	0.0525923i
$592$	−2.63379	−	0.705723i	−0.108248	−	0.0290050i
$593$	23.4934	+	23.4934i	0.964759	+	0.964759i	0.999400	−	0.0346408i	$-0.0110287\pi$
$593$	23.4934	+	23.4934i	0.964759	+	0.964759i	−0.0346408	+	0.999400i	$0.511029\pi$
$594$	6.64846	−	3.83849i	0.272789	−	0.157495i
$595$	4.98079	−	0.821703i	0.204192	−	0.0336865i
$596$	−0.133179	−	0.497029i	−0.00545521	−	0.0203591i
$597$		−	4.61731i		−	0.188974i
$598$	8.96966	−	31.5576i	0.366797	−	1.29048i
$599$	−45.3452			−1.85276			−0.926378	−	0.376594i	$-0.877095\pi$
$599$	−45.3452			−1.85276			−0.926378	+	0.376594i	$0.877095\pi$
$600$	3.23936	+	12.0895i	0.132246	+	0.493551i
$601$	24.8361	+	14.3392i	1.01309	+	0.584906i	0.912094	−	0.409981i	$-0.134465\pi$
$601$	24.8361	+	14.3392i	1.01309	+	0.584906i	0.100993	+	0.994887i	$0.467798\pi$
$602$	6.31466	−	16.7714i	0.257366	−	0.683552i
$603$	3.28099	+	3.28099i	0.133612	+	0.133612i
$604$	−0.135588	+	0.506021i	−0.00551700	+	0.0205897i
$605$	−3.34511	+	12.4841i	−0.135998	+	0.507552i
$606$	−16.9752	+	16.9752i	−0.689570	+	0.689570i
$607$	−8.50843	+	4.91234i	−0.345347	+	0.199386i	−0.662634	−	0.748944i	$-0.730561\pi$
$607$	−8.50843	+	4.91234i	−0.345347	+	0.199386i	0.317287	+	0.948329i	$0.397228\pi$
$608$	−0.671459	+	1.16300i	−0.0272313	+	0.0471659i
$609$	−0.926979	+	1.29326i	−0.0375631	+	0.0524057i
$610$			15.6523i			0.633743i
$611$	−15.5837	+	15.1192i	−0.630449	+	0.611656i
$612$		−	0.114760i		−	0.00463889i
$613$	−24.7029	+	6.61912i	−0.997741	+	0.267344i	−0.720499	−	0.693456i	$-0.756087\pi$
$613$	−24.7029	+	6.61912i	−0.997741	+	0.267344i	−0.277242	+	0.960800i	$0.589420\pi$
$614$	−29.2547	−	16.8902i	−1.18062	−	0.681632i
$615$	−2.95876	−	5.12472i	−0.119309	−	0.206649i
$616$	−39.5458	−	3.89983i	−1.59335	−	0.157129i
$617$	1.62469	−	6.06341i	0.0654074	−	0.244104i	−0.925480	−	0.378796i	$-0.876338\pi$
$617$	1.62469	−	6.06341i	0.0654074	−	0.244104i	0.990887	+	0.134693i	$0.0430047\pi$
$618$	−1.32898	−	0.356100i	−0.0534595	−	0.0143244i
$619$	−28.4665	−	28.4665i	−1.14416	−	1.14416i	−0.987680	−	0.156484i	$-0.949984\pi$
$619$	−28.4665	−	28.4665i	−1.14416	−	1.14416i	−0.156484	−	0.987680i	$-0.550016\pi$
$620$	0.139013	+	0.240778i	0.00558291	+	0.00966989i
$621$	−3.18256	+	5.51236i	−0.127712	+	0.221203i
$622$	2.60617	−	0.698322i	0.104498	−	0.0280002i
$623$	12.1964	−	10.0069i	0.488640	−	0.400916i
$624$	−7.17097	−	12.8662i	−0.287068	−	0.515058i
$625$	−17.4024			−0.696094
$626$	−1.75366	−	6.54474i	−0.0700902	−	0.261580i
$627$	14.6311	−	25.3419i	0.584311	−	1.01206i
$628$	0.0136756	+	0.0236868i	0.000545715	+	0.000945206i
$629$	1.24296	−	1.24296i	0.0495599	−	0.0495599i
$630$	2.49603	−	1.13057i	0.0994443	−	0.0450429i
$631$	12.2380	+	3.27917i	0.487188	+	0.130542i	0.494048	−	0.869435i	$-0.335517\pi$
$631$	12.2380	+	3.27917i	0.487188	+	0.130542i	−0.00685968	+	0.999976i	$0.502184\pi$
$632$	9.43616	−	9.43616i	0.375350	−	0.375350i
$633$	−5.87308	+	3.39083i	−0.233434	+	0.134773i
$634$	−21.0693	−	12.1644i	−0.836771	−	0.483110i
$635$	9.17583	−	2.45866i	0.364132	−	0.0975688i
$636$	0.0122926			0.000487432
$637$	18.7175	+	16.9309i	0.741614	+	0.670827i
$638$	−4.61697			−0.182788
$639$	15.3460	−	4.11194i	0.607078	−	0.162666i
$640$	7.32156	+	4.22710i	0.289410	+	0.167091i
$641$	24.0436	−	13.8816i	0.949666	−	0.548290i	0.0566885	−	0.998392i	$-0.481946\pi$
$641$	24.0436	−	13.8816i	0.949666	−	0.548290i	0.892977	+	0.450102i	$0.148612\pi$
$642$	12.0634	−	12.0634i	0.476103	−	0.476103i
$643$	−17.1125	−	4.58528i	−0.674851	−	0.180826i	−0.0949121	−	0.995486i	$-0.530257\pi$
$643$	−17.1125	−	4.58528i	−0.674851	−	0.180826i	−0.579939	+	0.814660i	$0.696924\pi$
$644$	−0.668454	+	0.302774i	−0.0263408	+	0.0119310i
$645$	2.42732	−	2.42732i	0.0955755	−	0.0955755i
$646$	−10.2572	−	17.7660i	−0.403565	−	0.698995i
$647$	−3.33450	+	5.77553i	−0.131093	+	0.227059i	−0.924098	−	0.382155i	$-0.875182\pi$
$647$	−3.33450	+	5.77553i	−0.131093	+	0.227059i	0.793005	+	0.609215i	$0.208515\pi$
$648$	0.723860	+	2.70148i	0.0284359	+	0.106124i
$649$	−25.2495			−0.991131
$650$	22.3678	−	5.63217i	0.877337	−	0.220912i
$651$	18.0135	−	14.7796i	0.706004	−	0.579258i
$652$	0.532748	−	0.142749i	0.0208640	−	0.00559050i
$653$	−0.491840	+	0.851891i	−0.0192472	+	0.0333371i	−0.875489	−	0.483239i	$-0.839460\pi$
$653$	−0.491840	+	0.851891i	−0.0192472	+	0.0333371i	0.856241	+	0.516576i	$0.172794\pi$
$654$	−3.45948	−	5.99200i	−0.135277	−	0.234306i
$655$	−3.56718	−	3.56718i	−0.139381	−	0.139381i
$656$	32.2310	+	8.63627i	1.25841	+	0.337190i
$657$	−1.11391	+	4.15718i	−0.0434579	+	0.162187i
$658$	22.6665	+	2.23527i	0.883632	+	0.0871398i
$659$	−10.5833	−	18.3308i	−0.412267	−	0.714067i	0.582871	−	0.812565i	$-0.301929\pi$
$659$	−10.5833	−	18.3308i	−0.412267	−	0.714067i	−0.995137	+	0.0984983i	$0.968596\pi$
$660$	0.146822	+	0.0847679i	0.00571505	+	0.00329959i
$661$	16.8983	−	4.52790i	0.657270	−	0.176115i	0.0852561	−	0.996359i	$-0.472829\pi$
$661$	16.8983	−	4.52790i	0.657270	−	0.176115i	0.572013	+	0.820244i	$0.306163\pi$
$662$		−	24.8246i		−	0.964835i
$663$	9.49454	+	0.143653i	0.368737	+	0.00557904i
$664$		−	9.58557i		−	0.371992i
$665$	6.08477	−	8.48908i	0.235957	−	0.329193i
$666$	0.477073	−	0.826314i	0.0184862	−	0.0320190i
$667$	3.31516	−	1.91401i	0.128364	−	0.0741107i
$668$	0.460116	−	0.460116i	0.0178024	−	0.0178024i
$669$	−5.00651	+	18.6845i	−0.193563	+	0.722386i
$670$	−1.24377	+	4.64181i	−0.0480510	+	0.179329i
$671$	57.3897	+	57.3897i	2.21551	+	2.21551i
$672$	−0.229762	+	0.610236i	−0.00886327	+	0.0235404i
$673$	21.4934	+	12.4092i	0.828511	+	0.478341i	0.853343	−	0.521351i	$-0.174572\pi$
$673$	21.4934	+	12.4092i	0.828511	+	0.478341i	−0.0248316	+	0.999692i	$0.507905\pi$
$674$	4.05498	+	15.1334i	0.156192	+	0.582917i
$675$	−4.47512			−0.172248
$676$	−0.498927	+	0.268267i	−0.0191895	+	0.0103180i
$677$			18.0191i			0.692531i	0.938137	+	0.346266i	$0.112550\pi$
$677$			18.0191i			0.692531i	−0.938137	+	0.346266i	$0.887450\pi$
$678$	−5.02036	−	18.7362i	−0.192806	−	0.719561i
$679$	42.5239	−	7.01536i	1.63192	−	0.269225i
$680$	−4.62135	+	2.66814i	−0.177221	+	0.102318i
$681$	8.46655	+	8.46655i	0.324439	+	0.324439i
$682$	65.3061	+	17.4987i	2.50070	+	0.670060i
$683$	−31.7978	−	8.52018i	−1.21671	−	0.326016i	−0.407317	−	0.913287i	$-0.633536\pi$
$683$	−31.7978	−	8.52018i	−1.21671	−	0.326016i	−0.809390	+	0.587271i	$0.800202\pi$
$684$	−0.167894	−	0.167894i	−0.00641961	−	0.00641961i
$685$	−0.642945	+	0.371205i	−0.0245657	+	0.0141830i
$686$	0.876001	−	26.4609i	0.0334459	−	1.01028i
$687$	−0.276545	−	1.03208i	−0.0105509	−	0.0393764i
$688$			19.3567i			0.737968i
$689$	−0.0153875	+	1.01701i	−0.000586218	+	0.0387451i
$690$	−6.59220			−0.250961
$691$	4.58957	+	17.1285i	0.174595	+	0.651599i	0.996620	+	0.0821472i	$0.0261778\pi$
$691$	4.58957	+	17.1285i	0.174595	+	0.651599i	−0.822025	+	0.569452i	$0.807156\pi$
$692$	0.476275	+	0.274977i	0.0181053	+	0.0104531i
$693$	5.00653	−	13.2971i	0.190182	−	0.505114i
$694$	2.12145	+	2.12145i	0.0805291	+	0.0805291i
$695$	−2.93771	+	10.9637i	−0.111434	+	0.415876i
$696$	0.435333	−	1.62469i	0.0165013	−	0.0615836i
$697$	−15.2107	+	15.2107i	−0.576145	+	0.576145i
$698$	5.55437	−	3.20682i	0.210236	−	0.121380i
$699$	8.13097	−	14.0833i	0.307541	−	0.532677i
$700$	−0.419337	−	0.300570i	−0.0158494	−	0.0113605i
$701$		−	41.2421i		−	1.55769i	−0.627214	−	0.778847i	$-0.715805\pi$
$701$		−	41.2421i		−	1.55769i	0.627214	−	0.778847i	$-0.284195\pi$
$702$	4.99825	−	1.25855i	0.188647	−	0.0475010i
$703$		−	3.63691i		−	0.137169i
$704$	40.5550	−	10.8667i	1.52848	−	0.409554i
$705$	3.77834	+	2.18142i	0.142300	+	0.0821572i
$706$	−9.96545	−	17.2607i	−0.375054	−	0.649613i
$707$	−4.36040	+	44.2162i	−0.163990	+	1.66292i
$708$	−0.0530266	+	0.197898i	−0.00199286	+	0.00743745i
$709$	−23.1654	−	6.20716i	−0.869996	−	0.233115i	−0.203910	−	0.978990i	$-0.565365\pi$
$709$	−23.1654	−	6.20716i	−0.869996	−	0.233115i	−0.666086	+	0.745875i	$0.732032\pi$
$710$	11.6348	+	11.6348i	0.436647	+	0.436647i
$711$	2.38573	+	4.13221i	0.0894720	+	0.154970i
$712$	−8.33842	+	14.4426i	−0.312495	+	0.541258i
$713$	−54.1465	+	14.5085i	−2.02780	+	0.543348i
$714$	−6.31815	−	7.70061i	−0.236451	−	0.288188i
$715$	−7.19697	+	12.0411i	−0.269151	+	0.450311i
$716$	−0.475751			−0.0177796
$717$	5.55607	+	20.7355i	0.207495	+	0.774383i
$718$	−14.7357	+	25.5229i	−0.549930	+	0.952507i
$719$	−10.7383	−	18.5992i	−0.400469	−	0.693633i	0.593313	−	0.804972i	$-0.297820\pi$
$719$	−10.7383	−	18.5992i	−0.400469	−	0.693633i	−0.993783	+	0.111338i	$0.964486\pi$
$720$	−2.09282	+	2.09282i	−0.0779948	+	0.0779948i
$721$	−2.31957	+	1.05064i	−0.0863851	+	0.0391278i
$722$	−14.7625	−	3.95561i	−0.549404	−	0.147212i
$723$	−9.05329	+	9.05329i	−0.336696	+	0.336696i
$724$	−0.224198	+	0.129441i	−0.00833226	+	0.00481063i
$725$	2.33079	+	1.34568i	0.0865633	+	0.0499774i
$726$	24.6334	−	6.60051i	0.914232	−	0.244968i
$727$	−16.2550			−0.602863			−0.301431	−	0.953488i	$-0.597464\pi$
$727$	−16.2550			−0.602863			−0.301431	+	0.953488i	$0.597464\pi$
$728$	−24.8234	−	9.77761i	−0.920015	−	0.362382i
$729$	−1.00000			−0.0370370
$730$	−4.30549	+	1.15365i	−0.159353	+	0.0426986i
$731$	−10.8068	−	6.23928i	−0.399702	−	0.230768i
$732$	0.570326	−	0.329278i	0.0210799	−	0.0121705i
$733$	37.7313	−	37.7313i	1.39364	−	1.39364i	0.576637	−	0.817001i	$-0.304365\pi$
$733$	37.7313	−	37.7313i	1.39364	−	1.39364i	0.817001	−	0.576637i	$-0.195635\pi$
$734$	−9.77547	−	2.61933i	−0.360819	−	0.0966812i
$735$	2.24413	−	4.54783i	0.0827761	−	0.167749i
$736$	1.10925	−	1.10925i	0.0408874	−	0.0408874i
$737$	12.4591	+	21.5797i	0.458935	+	0.794899i
$738$	−5.83817	+	10.1120i	−0.214906	+	0.372228i
$739$	−11.5735	−	43.1929i	−0.425738	−	1.58888i	−0.762305	−	0.647218i	$-0.775932\pi$
$739$	−11.5735	−	43.1929i	−0.425738	−	1.58888i	0.336567	−	0.941660i	$-0.390734\pi$
$740$	0.0210711			0.000774587
$741$	14.1007	−	13.6804i	0.518003	−	0.502562i
$742$	0.824856	−	0.676772i	0.0302814	−	0.0248451i
$743$	−43.8408	+	11.7471i	−1.60836	+	0.430959i	−0.947554	−	0.319596i	$-0.896453\pi$
$743$	−43.8408	+	11.7471i	−1.60836	+	0.430959i	−0.660808	+	0.750555i	$0.729786\pi$
$744$	−12.3154	+	21.3309i	−0.451504	+	0.782028i
$745$	−4.27758	−	7.40899i	−0.156718	−	0.271444i
$746$	17.4241	+	17.4241i	0.637941	+	0.637941i
$747$	3.31057	+	0.887065i	0.121128	+	0.0324560i
$748$	0.159508	−	0.595290i	0.00583217	−	0.0217660i
$749$	3.09870	−	31.4221i	0.113224	−	1.14814i
$750$	−4.90658	−	8.49844i	−0.179163	−	0.310319i
$751$	27.9904	+	16.1603i	1.02138	+	0.589696i	0.914505	−	0.404575i	$-0.132581\pi$
$751$	27.9904	+	16.1603i	1.02138	+	0.589696i	0.106880	+	0.994272i	$0.465914\pi$
$752$	−23.7632	+	6.36732i	−0.866554	+	0.232192i
$753$		−	7.23944i		−	0.263820i
$754$	−2.98170	−	0.847494i	−0.108587	−	0.0308639i
$755$			8.70994i			0.316987i
$756$	−0.0937039	−	0.0671647i	−0.00340798	−	0.00244276i
$757$	−14.5363	+	25.1776i	−0.528331	+	0.915097i	0.471123	+	0.882068i	$0.343849\pi$
$757$	−14.5363	+	25.1776i	−0.528331	+	0.915097i	−0.999454	+	0.0330294i	$0.989484\pi$
$758$	−5.60015	+	3.23325i	−0.203407	+	0.117437i
$759$	−24.1705	+	24.1705i	−0.877335	+	0.877335i
$760$	−2.85756	+	10.6646i	−0.103655	+	0.386845i
$761$	−7.58218	+	28.2971i	−0.274854	+	1.02577i	0.681086	+	0.732204i	$0.261508\pi$
$761$	−7.58218	+	28.2971i	−0.274854	+	1.02577i	−0.955939	+	0.293564i	$0.905159\pi$
$762$	−13.2542	−	13.2542i	−0.480149	−	0.480149i
$763$	−11.9841	−	4.51219i	−0.433855	−	0.163352i
$764$	−0.0607685	−	0.0350847i	−0.00219853	−	0.00126932i
$765$	−0.493829	−	1.84299i	−0.0178544	−	0.0666336i
$766$	−40.9907			−1.48105
$767$	−16.3065	−	4.63482i	−0.588793	−	0.167354i
$768$		−	1.04531i		−	0.0377194i
$769$	−13.2029	−	49.2739i	−0.476109	−	1.77686i	−0.617136	−	0.786857i	$-0.711707\pi$
$769$	−13.2029	−	49.2739i	−0.476109	−	1.77686i	0.141027	−	0.990006i	$-0.454960\pi$
$770$	14.5190	−	2.39526i	0.523228	−	0.0863193i
$771$	−3.29597	+	1.90293i	−0.118701	+	0.0685323i
$772$	−0.757877	−	0.757877i	−0.0272766	−	0.0272766i
$773$	7.92985	+	2.12480i	0.285217	+	0.0764236i	0.398591	−	0.917129i	$-0.369499\pi$
$773$	7.92985	+	2.12480i	0.285217	+	0.0764236i	−0.113374	+	0.993552i	$0.536166\pi$
$774$	−6.54263	−	1.75309i	−0.235170	−	0.0630136i
$775$	−27.8683	−	27.8683i	−1.00106	−	1.00106i
$776$	−39.4552	+	22.7795i	−1.41636	+	0.817735i
$777$	−0.287445	−	1.74236i	−0.0103120	−	0.0625067i
$778$	−2.38565	−	8.90337i	−0.0855298	−	0.319201i
$779$			44.5066i			1.59461i
$780$	0.0792597	+	0.0816950i	0.00283795	+	0.00292515i
$781$	85.3190			3.05295
$782$	6.20226	+	23.1471i	0.221792	+	0.827740i
$783$	0.520832	+	0.300703i	0.0186130	+	0.0107462i
$784$	9.18548	+	27.0814i	0.328053	+	0.967193i
$785$	0.321552	+	0.321552i	0.0114767	+	0.0114767i
$786$	−2.57634	+	9.61504i	−0.0918951	+	0.342957i
$787$	0.450270	−	1.68043i	0.0160504	−	0.0599009i	−0.957436	−	0.288645i	$-0.906795\pi$
$787$	0.450270	−	1.68043i	0.0160504	−	0.0599009i	0.973487	+	0.228744i	$0.0734619\pi$
$788$	−0.152210	+	0.152210i	−0.00542225	+	0.00542225i
$789$	3.49263	−	2.01647i	0.124341	−	0.0717883i
$790$	−2.47085	+	4.27963i	−0.0879088	+	0.152262i
$791$	−29.1785	−	20.9144i	−1.03747	−	0.743632i
$792$			15.0194i			0.533692i
$793$	26.5285	+	47.5975i	0.942056	+	1.69024i
$794$			42.5614i			1.51045i
$795$	0.197413	−	0.0528968i	0.00700153	−	0.00187606i
$796$	−0.174244	−	0.100600i	−0.00617592	−	0.00356567i
$797$	−0.464274	−	0.804146i	−0.0164454	−	0.0284843i	0.857686	−	0.514175i	$-0.171902\pi$
$797$	−0.464274	−	0.804146i	−0.0164454	−	0.0284843i	−0.874131	+	0.485690i	$0.838568\pi$
$798$	−20.5095	−	2.02256i	−0.726030	−	0.0715977i
$799$	4.10478	−	15.3192i	0.145217	−	0.541956i
$800$	1.06533	+	0.285455i	0.0376652	+	0.0100924i
$801$	−4.21638	−	4.21638i	−0.148979	−	0.148979i
$802$	16.2822	+	28.2016i	0.574944	+	0.995832i
$803$	−11.5563	+	20.0162i	−0.407814	+	0.706355i
$804$	0.195300	−	0.0523305i	0.00688770	−	0.00184555i
$805$	−9.43220	+	7.73887i	−0.332442	+	0.272759i
$806$	38.9634	+	23.2885i	1.37243	+	0.820303i
$807$	6.96741			0.245264
$808$	−12.1560	−	45.3666i	−0.427645	−	1.59599i
$809$	−27.3761	+	47.4168i	−0.962492	+	1.66709i	−0.246286	+	0.969197i	$0.579210\pi$
$809$	−27.3761	+	47.4168i	−0.962492	+	1.66709i	−0.716207	+	0.697888i	$0.754123\pi$
$810$	−0.517838	−	0.896921i	−0.0181950	−	0.0315146i
$811$	15.2089	−	15.2089i	0.534055	−	0.534055i	−0.387721	−	0.921777i	$-0.626738\pi$
$811$	15.2089	−	15.2089i	0.534055	−	0.534055i	0.921777	+	0.387721i	$0.126738\pi$
$812$	0.0286074	+	0.0631586i	0.00100392	+	0.00221643i
$813$	8.12317	+	2.17660i	0.284892	+	0.0763366i
$814$	3.62322	−	3.62322i	0.126994	−	0.126994i
$815$	7.94143	−	4.58499i	0.278176	−	0.160605i
$816$	9.31754	+	5.37948i	0.326179	+	0.188320i
$817$	−24.9385	+	6.68224i	−0.872487	+	0.233782i
$818$	3.49748			0.122287
$819$	5.67410	−	7.66842i	0.198269	−	0.267956i
$820$	−0.257857			−0.00900474
$821$	−25.5931	+	6.85765i	−0.893206	+	0.239334i	−0.676096	−	0.736814i	$-0.736330\pi$
$821$	−25.5931	+	6.85765i	−0.893206	+	0.239334i	−0.217110	+	0.976147i	$0.569663\pi$
$822$	1.26865	+	0.732454i	0.0442492	+	0.0255473i
$823$	34.5953	−	19.9736i	1.20592	−	0.696237i	0.244053	−	0.969762i	$-0.421523\pi$
$823$	34.5953	−	19.9736i	1.20592	−	0.696237i	0.961865	+	0.273525i	$0.0881897\pi$
$824$	1.90337	−	1.90337i	0.0663071	−	0.0663071i
$825$	−23.2137	−	6.22008i	−0.808196	−	0.216555i
$826$	7.33715	+	16.1987i	0.255292	+	0.563626i
$827$	−16.8364	+	16.8364i	−0.585458	+	0.585458i	−0.936398	−	0.350940i	$-0.885862\pi$
$827$	−16.8364	+	16.8364i	−0.585458	+	0.585458i	0.350940	+	0.936398i	$0.385862\pi$
$828$	0.138680	+	0.240202i	0.00481948	+	0.00834758i
$829$	1.41086	−	2.44368i	0.0490011	−	0.0848724i	−0.840485	−	0.541836i	$-0.817730\pi$
$829$	1.41086	−	2.44368i	0.0490011	−	0.0848724i	0.889486	+	0.456963i	$0.151063\pi$
$830$	0.918712	+	3.42868i	0.0318890	+	0.119011i
$831$	−9.63277			−0.334157
$832$	28.1856	+	0.426452i	0.977162	+	0.0147846i
$833$	−18.0802	−	3.60099i	−0.626441	−	0.124767i
$834$	21.6333	−	5.79663i	0.749100	−	0.200721i
$835$	5.40932	−	9.36922i	0.187197	−	0.324235i
$836$	−0.637553	−	1.10427i	−0.0220502	−	0.0381921i
$837$	−6.22737	−	6.22737i	−0.215249	−	0.215249i
$838$	−26.9703	−	7.22666i	−0.931672	−	0.249641i
$839$	−3.56318	+	13.2980i	−0.123015	+	0.459097i	−0.999761	−	0.0218557i	$-0.993043\pi$
$839$	−3.56318	+	13.2980i	−0.123015	+	0.459097i	0.876746	+	0.480953i	$0.159709\pi$
$840$	−0.526113	+	5.33500i	−0.0181526	+	0.184075i
$841$	14.3192	+	24.8015i	0.493764	+	0.855224i
$842$	−26.0101	−	15.0169i	−0.896367	−	0.517517i
$843$	−13.4114	+	3.59357i	−0.461913	+	0.123769i
$844$			0.295511i			0.0101719i
$845$	−6.85816	+	6.45520i	−0.235928	+	0.222066i
$846$		−	8.60869i		−	0.295973i
$847$	27.4972	−	38.3624i	0.944815	−	1.31815i
$848$	−0.576227	+	0.998054i	−0.0197877	+	0.0342733i
$849$	1.58734	−	0.916453i	0.0544775	−	0.0314526i
$850$	−11.9134	+	11.9134i	−0.408628	+	0.408628i
$851$	−1.09957	+	4.10365i	−0.0376927	+	0.140671i
$852$	0.179178	−	0.668703i	0.00613855	−	0.0229094i
$853$	23.8704	+	23.8704i	0.817307	+	0.817307i	0.985717	−	0.168410i	$-0.0538632\pi$
$853$	23.8704	+	23.8704i	0.817307	+	0.817307i	−0.168410	+	0.985717i	$0.553863\pi$
$854$	20.1415	−	53.4947i	0.689227	−	1.83055i
$855$	−3.41879	−	1.97384i	−0.116920	−	0.0675038i
$856$	8.63859	+	32.2396i	0.295261	+	1.10193i
$857$	−10.9745			−0.374882			−0.187441	−	0.982276i	$-0.560019\pi$
$857$	−10.9745			−0.374882			−0.187441	+	0.982276i	$0.560019\pi$
$858$	27.6766	+	0.418750i	0.944862	+	0.0142959i
$859$		−	29.4072i		−	1.00336i	−0.865053	−	0.501681i	$-0.832715\pi$
$859$		−	29.4072i		−	1.00336i	0.865053	−	0.501681i	$-0.167285\pi$
$860$	−0.0387147	−	0.144485i	−0.00132016	−	0.00492691i
$861$	3.51760	+	21.3221i	0.119879	+	0.726654i
$862$	−17.7795	+	10.2650i	−0.605572	+	0.349627i
$863$	−16.1604	−	16.1604i	−0.550105	−	0.550105i	0.376366	−	0.926471i	$-0.377173\pi$
$863$	−16.1604	−	16.1604i	−0.550105	−	0.550105i	−0.926471	+	0.376366i	$0.877173\pi$
$864$	0.238057	+	0.0637871i	0.00809885	+	0.00217008i
$865$	8.83204	+	2.36654i	0.300298	+	0.0804647i
$866$	−36.8152	−	36.8152i	−1.25103	−	1.25103i
$867$	8.71576	−	5.03204i	0.296003	−	0.170897i
$868$	−0.165270	−	1.00179i	−0.00560962	−	0.0340029i
$869$	6.63198	+	24.7509i	0.224974	+	0.839616i
$870$			0.622861i			0.0211170i
$871$	4.08503	+	16.2234i	0.138416	+	0.549710i
$872$	13.5364			0.458402
$873$	−4.21610	−	15.7347i	−0.142693	−	0.532539i
$874$	42.9384	+	24.7905i	1.45241	+	0.838550i
$875$	−16.9971	−	6.39963i	−0.574606	−	0.216347i
$876$	0.132611	+	0.132611i	0.00448050	+	0.00448050i
$877$	−10.5333	+	39.3110i	−0.355686	+	1.32744i	0.523934	+	0.851759i	$0.324464\pi$
$877$	−10.5333	+	39.3110i	−0.355686	+	1.32744i	−0.879620	+	0.475678i	$0.842203\pi$
$878$	11.8494	−	44.2224i	0.399896	−	1.49243i
$879$	19.5941	−	19.5941i	0.660893	−	0.660893i
$880$	−13.7649	+	7.94716i	−0.464014	+	0.267899i
$881$	−11.2270	+	19.4458i	−0.378248	+	0.655145i	−0.990807	−	0.135280i	$-0.956807\pi$
$881$	−11.2270	+	19.4458i	−0.378248	+	0.655145i	0.612559	+	0.790425i	$0.290140\pi$
$882$	−9.98549	+	0.652020i	−0.336229	+	0.0219547i
$883$			0.128296i			0.00431752i	0.999998	+	0.00215876i	$0.000687155\pi$
$883$			0.128296i			0.00431752i	−0.999998	+	0.00215876i	$0.999313\pi$
$884$	0.212284	−	0.355167i	0.00713987	−	0.0119456i
$885$			3.40633i			0.114503i
$886$	−18.5374	+	4.96708i	−0.622776	+	0.166872i
$887$	7.73247	+	4.46434i	0.259631	+	0.149898i	0.624166	−	0.781292i	$-0.285439\pi$
$887$	7.73247	+	4.46434i	0.259631	+	0.149898i	−0.364535	+	0.931190i	$0.618772\pi$
$888$	0.933357	+	1.61662i	0.0313214	+	0.0542503i
$889$	−34.5240	−	3.40459i	−1.15790	−	0.114186i
$890$	1.59836	−	5.96517i	0.0535772	−	0.199953i
$891$	−5.18727	−	1.38992i	−0.173780	−	0.0465642i
$892$	0.596022	+	0.596022i	0.0199563	+	0.0199563i
$893$	−16.4068	−	28.4175i	−0.549034	−	0.950954i
$894$	−8.44044	+	14.6193i	−0.282291	+	0.488942i
$895$	−7.64035	+	2.04722i	−0.255389	+	0.0684312i
$896$	−19.5834	−	23.8684i	−0.654234	−	0.797386i
$897$	−20.0464	+	11.1729i	−0.669330	+	0.373052i
$898$	−27.5104			−0.918035
$899$	1.37083	+	5.11600i	0.0457197	+	0.170628i
$900$	−0.0975020	+	0.168878i	−0.00325007	+	0.00562928i
$901$	−0.371472	−	0.643409i	−0.0123755	−	0.0214350i
$902$	−44.3391	+	44.3391i	−1.47633	+	1.47633i
$903$	−11.4193	+	5.17233i	−0.380011	+	0.172124i
$904$	36.6561	+	9.82196i	1.21916	+	0.326674i
$905$	−3.04352	+	3.04352i	−0.101170	+	0.101170i
$906$	14.8838	−	8.59314i	0.494480	−	0.285488i
$907$	−29.2036	−	16.8607i	−0.969690	−	0.559851i	−0.0705480	−	0.997508i	$-0.522475\pi$
$907$	−29.2036	−	16.8607i	−0.969690	−	0.559851i	−0.899142	+	0.437658i	$0.855808\pi$
$908$	0.503969	−	0.135038i	0.0167248	−	0.00448139i
$909$	16.7932			0.556996
$910$	9.81623	+	1.11822i	0.325405	+	0.0370687i
$911$	12.1553			0.402724			0.201362	−	0.979517i	$-0.435463\pi$
$911$	12.1553			0.402724			0.201362	+	0.979517i	$0.435463\pi$
$912$	21.5018	−	5.76140i	0.711997	−	0.190779i
$913$	15.9399	+	9.20289i	0.527533	+	0.304571i
$914$	−31.4059	+	18.1322i	−1.03882	+	0.599760i
$915$	7.74226	−	7.74226i	0.255951	−	0.255951i
$916$	−0.0449731	−	0.0120505i	−0.00148595	−	0.000398160i
$917$	7.60125	+	16.7818i	0.251015	+	0.554184i
$918$	−2.66215	+	2.66215i	−0.0878639	+	0.0878639i
$919$	27.1965	+	47.1057i	0.897129	+	1.55387i	0.831148	+	0.556052i	$0.187684\pi$
$919$	27.1965	+	47.1057i	0.897129	+	1.55387i	0.0659808	+	0.997821i	$0.478982\pi$
$920$	6.44857	−	11.1693i	0.212603	−	0.368239i
$921$	6.11597	+	22.8251i	0.201528	+	0.752113i
$922$	34.3355			1.13078
$923$	55.1001	+	15.6612i	1.81364	+	0.515494i
$924$	−0.392714	−	0.478643i	−0.0129193	−	0.0157462i
$925$	−2.88515	+	0.773073i	−0.0948631	+	0.0254185i
$926$	−1.98617	+	3.44016i	−0.0652698	+	0.113051i
$927$	0.481227	+	0.833510i	0.0158056	+	0.0273761i
$928$	−0.104807	−	0.104807i	−0.00344045	−	0.00344045i
$929$	11.3587	+	3.04356i	0.372667	+	0.0998559i	0.440291	−	0.897855i	$-0.354875\pi$
$929$	11.3587	+	3.04356i	0.372667	+	0.0998559i	−0.0676240	+	0.997711i	$0.521542\pi$
$930$	2.36069	−	8.81023i	0.0774102	−	0.288899i
$931$	−31.7197	+	21.1831i	−1.03957	+	0.694249i
$932$	−0.354308	−	0.613679i	−0.0116057	−	0.0201017i
$933$	−1.63454	−	0.943701i	−0.0535124	−	0.0308954i
$934$	−1.46019	+	0.391257i	−0.0477789	+	0.0128023i
$935$		−	10.2465i		−	0.335096i
$936$	−2.75697	+	9.69974i	−0.0901144	+	0.317046i
$937$		−	23.7187i		−	0.774857i	−0.921900	−	0.387428i	$-0.873363\pi$
$937$		−	23.7187i		−	0.774857i	0.921900	−	0.387428i	$-0.126637\pi$
$938$	10.2239	−	14.2638i	0.333823	−	0.465729i
$939$	−2.36986	+	4.10472i	−0.0773375	+	0.133953i
$940$	0.164641	−	0.0950558i	0.00537001	−	0.00310038i
$941$	−8.77975	+	8.77975i	−0.286212	+	0.286212i	−0.835580	−	0.549368i	$-0.814868\pi$
$941$	−8.77975	+	8.77975i	−0.286212	+	0.286212i	0.549368	+	0.835580i	$0.314868\pi$
$942$	0.232236	−	0.866715i	0.00756665	−	0.0282391i
$943$	13.4559	−	50.2183i	0.438186	−	1.63533i
$944$	−13.5820	−	13.5820i	−0.442055	−	0.442055i
$945$	−1.79386	−	0.675414i	−0.0583544	−	0.0219712i
$946$	−31.5017	−	18.1875i	−1.02421	−	0.591327i
$947$	−3.45357	−	12.8889i	−0.112226	−	0.418833i	0.886838	−	0.462080i	$-0.152897\pi$
$947$	−3.45357	−	12.8889i	−0.112226	−	0.418833i	−0.999064	+	0.0432464i	$0.986230\pi$
$948$	0.207917			0.00675284
$949$	−11.1374	+	10.8054i	−0.361535	+	0.350758i
$950$			34.8589i			1.13097i
$951$	4.40475	+	16.4388i	0.142834	+	0.533063i
$952$	19.2277	−	3.17209i	0.623175	−	0.102808i
$953$	2.94104	−	1.69801i	0.0952697	−	0.0550040i	−0.451608	−	0.892216i	$-0.649150\pi$
$953$	2.94104	−	1.69801i	0.0952697	−	0.0550040i	0.546878	+	0.837212i	$0.315816\pi$
$954$	−0.285158	−	0.285158i	−0.00923232	−	0.00923232i
$955$	−1.12689	−	0.301949i	−0.0364653	−	0.00977085i
$956$	0.903553	+	0.242106i	0.0292230	+	0.00783028i
$957$	2.28374	+	2.28374i	0.0738229	+	0.0738229i
$958$	6.24537	−	3.60577i	0.201779	−	0.116497i
$959$	2.67506	−	0.441316i	0.0863821	−	0.0142508i
$960$	−1.46599	−	5.47114i	−0.0473146	−	0.176580i
$961$		−	46.5603i		−	1.50195i
$962$	3.00500	−	1.67484i	0.0968851	−	0.0539991i
$963$	−11.9341			−0.384569
$964$	0.144396	+	0.538894i	0.00465069	+	0.0173566i
$965$	−15.4324	−	8.90992i	−0.496788	−	0.286820i
$966$	22.5301	+	8.48289i	0.724894	+	0.272932i
$967$	−32.6551	−	32.6551i	−1.05012	−	1.05012i	−0.998676	−	0.0514398i	$-0.983619\pi$
$967$	−32.6551	−	32.6551i	−1.05012	−	1.05012i	−0.0514398	−	0.998676i	$-0.516381\pi$
$968$	−12.9134	+	48.1935i	−0.415052	+	1.54900i
$969$	−3.71416	+	13.8614i	−0.119316	+	0.445294i
$970$	11.9295	−	11.9295i	0.383034	−	0.383034i
$971$	−8.75213	+	5.05305i	−0.280869	+	0.162160i	−0.633817	−	0.773483i	$-0.718513\pi$
$971$	−8.75213	+	5.05305i	−0.280869	+	0.162160i	0.352948	+	0.935643i	$0.385179\pi$
$972$	−0.0217876	+	0.0377371i	−0.000698836	+	0.00121042i
$973$	24.1483	−	33.6902i	0.774159	−	1.08006i
$974$			4.00629i			0.128370i
$975$	−13.8499	−	8.27812i	−0.443552	−	0.265112i
$976$			61.7409i			1.97628i
$977$	57.0790	−	15.2943i	1.82612	−	0.489307i	0.828608	−	0.559829i	$-0.189133\pi$
$977$	57.0790	−	15.2943i	1.82612	−	0.489307i	0.997510	+	0.0705222i	$0.0224666\pi$
$978$	−15.6699	−	9.04701i	−0.501068	−	0.289292i
$979$	−16.0111	−	27.7320i	−0.511716	−	0.886317i
$980$	−0.122728	−	0.183773i	−0.00392041	−	0.00587042i
$981$	−1.25269	+	4.67509i	−0.0399952	+	0.149264i
$982$	17.1845	+	4.60458i	0.548380	+	0.146938i
$983$	32.3474	+	32.3474i	1.03172	+	1.03172i	0.999480	+	0.0322405i	$0.0102642\pi$
$983$	32.3474	+	32.3474i	1.03172	+	1.03172i	0.0322405	+	0.999480i	$0.489736\pi$
$984$	−11.4219	−	19.7834i	−0.364118	−	0.630671i
$985$	−1.78944	+	3.09940i	−0.0570164	+	0.0987552i
$986$	2.18705	−	0.586018i	0.0696498	−	0.0186626i
$987$	−10.1061	−	12.3174i	−0.321681	−	0.392068i
$988$	−0.209039	−	0.830184i	−0.00665041	−	0.0264117i
$989$	30.1592			0.959007
$990$	−1.43951	−	5.37233i	−0.0457506	−	0.170744i
$991$	−1.26677	+	2.19411i	−0.0402402	+	0.0696981i	−0.885444	−	0.464746i	$-0.846146\pi$
$991$	−1.26677	+	2.19411i	−0.0402402	+	0.0696981i	0.845204	+	0.534444i	$0.179479\pi$
$992$	1.08524	+	1.87969i	0.0344565	+	0.0596803i
$993$	−12.2792	+	12.2792i	−0.389670	+	0.389670i
$994$	−24.7924	−	54.7360i	−0.786368	−	1.73612i
$995$	−3.23118	−	0.865793i	−0.102435	−	0.0274475i
$996$	0.105605	−	0.105605i	0.00334621	−	0.00334621i
$997$	−10.4694	+	6.04452i	−0.331570	+	0.191432i	−0.656538	−	0.754293i	$-0.727980\pi$
$997$	−10.4694	+	6.04452i	−0.331570	+	0.191432i	0.324968	+	0.945725i	$0.394646\pi$
$998$	10.9250	+	6.30755i	0.345825	+	0.199662i
$999$	−0.644708	+	0.172749i	−0.0203977	+	0.00546554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.by.d.202.3	yes	32
3.2	odd	2		819.2.fm.e.748.6		32
7.6	odd	2		273.2.by.c.202.3	✓	32
13.2	odd	12		273.2.by.c.223.3	yes	32
21.20	even	2		819.2.fm.f.748.6		32
39.2	even	12		819.2.fm.f.496.6		32
91.41	even	12	inner	273.2.by.d.223.3	yes	32
273.41	odd	12		819.2.fm.e.496.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.3	✓	32	7.6	odd	2
273.2.by.c.223.3	yes	32	13.2	odd	12
273.2.by.d.202.3	yes	32	1.1	even	1	trivial
273.2.by.d.223.3	yes	32	91.41	even	12	inner
819.2.fm.e.496.6		32	273.41	odd	12
819.2.fm.e.748.6		32	3.2	odd	2
819.2.fm.f.496.6		32	39.2	even	12
819.2.fm.f.748.6		32	21.20	even	2

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38083 + 0.369991i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.0377371 - 0.0217876i) q^{4} +(0.512287 - 0.512287i) q^{5} +(-1.38083 - 0.369991i) q^{6} +(-2.41005 + 1.09162i) q^{7} +(1.97762 - 1.97762i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.38083 + 0.369991i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.0377371 - 0.0217876i) q^{4} +(0.512287 - 0.512287i) q^{5} +(-1.38083 - 0.369991i) q^{6} +(-2.41005 + 1.09162i) q^{7} +(1.97762 - 1.97762i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.517838 + 0.896921i) q^{10} +(1.38992 + 5.18727i) q^{11} +0.0435751 q^{12} +(-0.0545462 + 3.60514i) q^{13} +(2.92397 - 2.39904i) q^{14} +(0.699797 - 0.187510i) q^{15} +(-2.04263 + 3.53793i) q^{16} +(-1.31681 - 2.28077i) q^{17} +(-1.01084 - 1.01084i) q^{18} +(-5.26328 - 1.41029i) q^{19} +(0.00817077 - 0.0304937i) q^{20} +(-2.63298 - 0.259652i) q^{21} +(-3.83849 - 6.64846i) q^{22} +(5.51236 + 3.18256i) q^{23} +(2.70148 - 0.723860i) q^{24} +4.47512i q^{25} +(-1.25855 - 4.99825i) q^{26} +1.00000i q^{27} +(-0.0671647 + 0.0937039i) q^{28} +(0.300703 - 0.520832i) q^{29} +(-0.896921 + 0.517838i) q^{30} +(-6.22737 + 6.22737i) q^{31} +(0.0637871 - 0.238057i) q^{32} +(-1.38992 + 5.18727i) q^{33} +(2.66215 + 2.66215i) q^{34} +(-0.675414 + 1.79386i) q^{35} +(0.0377371 + 0.0217876i) q^{36} +(0.172749 + 0.644708i) q^{37} +7.78948 q^{38} +(-1.84981 + 3.09487i) q^{39} -2.02622i q^{40} +(-2.11401 - 7.88960i) q^{41} +(3.73176 - 0.615645i) q^{42} +(4.10340 - 2.36910i) q^{43} +(0.165470 + 0.165470i) q^{44} +(0.699797 + 0.187510i) q^{45} +(-8.78913 - 2.35504i) q^{46} +(4.25821 + 4.25821i) q^{47} +(-3.53793 + 2.04263i) q^{48} +(4.61671 - 5.26174i) q^{49} +(-1.65576 - 6.17937i) q^{50} -2.63361i q^{51} +(0.0764887 + 0.137236i) q^{52} +0.282101 q^{53} +(-0.369991 - 1.38083i) q^{54} +(3.36941 + 1.94533i) q^{55} +(-2.60736 + 6.92500i) q^{56} +(-3.85299 - 3.85299i) q^{57} +(-0.222515 + 0.830436i) q^{58} +(-1.21690 + 4.54153i) q^{59} +(0.0223230 - 0.0223230i) q^{60} +(13.0884 - 7.55656i) q^{61} +(6.29485 - 10.9030i) q^{62} +(-2.15040 - 1.54136i) q^{63} -7.81819i q^{64} +(1.81892 + 1.87481i) q^{65} -7.67698i q^{66} +(4.48192 - 1.20093i) q^{67} +(-0.0993850 - 0.0573799i) q^{68} +(3.18256 + 5.51236i) q^{69} +(0.268916 - 2.72691i) q^{70} +(4.11194 - 15.3460i) q^{71} +(2.70148 + 0.723860i) q^{72} +(3.04327 + 3.04327i) q^{73} +(-0.477073 - 0.826314i) q^{74} +(-2.23756 + 3.87557i) q^{75} +(-0.229348 + 0.0614536i) q^{76} +(-9.01234 - 10.9843i) q^{77} +(1.40919 - 4.95789i) q^{78} +4.77147 q^{79} +(0.766026 + 2.85885i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.83817 + 10.1120i) q^{82} +(2.42351 - 2.42351i) q^{83} +(-0.105018 + 0.0475676i) q^{84} +(-1.84299 - 0.493829i) q^{85} +(-4.78954 + 4.78954i) q^{86} +(0.520832 - 0.300703i) q^{87} +(13.0072 + 7.50971i) q^{88} +(-5.75969 + 1.54330i) q^{89} -1.03568 q^{90} +(-3.80400 - 8.74812i) q^{91} +0.277361 q^{92} +(-8.50675 + 2.27938i) q^{93} +(-7.45535 - 4.30435i) q^{94} +(-3.41879 + 1.97384i) q^{95} +(0.174270 - 0.174270i) q^{96} +(-15.7347 - 4.21610i) q^{97} +(-4.42808 + 8.97370i) q^{98} +(-3.79734 + 3.79734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q - 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 16 * q^9	\( 32 q - 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 16 q^{9} + 2 q^{10} - 4 q^{11} + 32 q^{12} + 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} - 8 q^{17} + 2 q^{18} + 2 q^{19} + 44 q^{20} - 4 q^{21} - 4 q^{22} - 18 q^{23} + 4 q^{24} - 28 q^{26} - 32 q^{28} - 18 q^{29} - 14 q^{31} - 8 q^{32} + 4 q^{33} - 66 q^{34} + 22 q^{35} + 6 q^{36} - 24 q^{37} + 24 q^{38} + 8 q^{39} - 26 q^{42} - 6 q^{43} - 20 q^{44} + 4 q^{45} - 58 q^{46} - 28 q^{47} - 60 q^{48} + 8 q^{49} + 70 q^{50} + 28 q^{52} - 80 q^{53} - 4 q^{54} + 60 q^{55} - 54 q^{56} + 16 q^{57} - 4 q^{58} - 42 q^{59} - 58 q^{60} + 36 q^{61} + 52 q^{62} + 4 q^{63} + 14 q^{65} + 26 q^{67} - 72 q^{68} + 2 q^{69} - 116 q^{70} - 4 q^{71} + 4 q^{72} + 12 q^{73} - 18 q^{74} + 16 q^{75} - 48 q^{76} + 28 q^{77} - 14 q^{78} - 4 q^{79} - 98 q^{80} - 16 q^{81} + 20 q^{82} - 36 q^{83} - 18 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} - 54 q^{89} + 4 q^{90} + 148 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} + 22 q^{96} - 40 q^{97} + 36 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 16 * q^9 + 2 * q^10 - 4 * q^11 + 32 * q^12 + 6 * q^13 + 34 * q^14 + 4 * q^15 + 14 * q^16 - 8 * q^17 + 2 * q^18 + 2 * q^19 + 44 * q^20 - 4 * q^21 - 4 * q^22 - 18 * q^23 + 4 * q^24 - 28 * q^26 - 32 * q^28 - 18 * q^29 - 14 * q^31 - 8 * q^32 + 4 * q^33 - 66 * q^34 + 22 * q^35 + 6 * q^36 - 24 * q^37 + 24 * q^38 + 8 * q^39 - 26 * q^42 - 6 * q^43 - 20 * q^44 + 4 * q^45 - 58 * q^46 - 28 * q^47 - 60 * q^48 + 8 * q^49 + 70 * q^50 + 28 * q^52 - 80 * q^53 - 4 * q^54 + 60 * q^55 - 54 * q^56 + 16 * q^57 - 4 * q^58 - 42 * q^59 - 58 * q^60 + 36 * q^61 + 52 * q^62 + 4 * q^63 + 14 * q^65 + 26 * q^67 - 72 * q^68 + 2 * q^69 - 116 * q^70 - 4 * q^71 + 4 * q^72 + 12 * q^73 - 18 * q^74 + 16 * q^75 - 48 * q^76 + 28 * q^77 - 14 * q^78 - 4 * q^79 - 98 * q^80 - 16 * q^81 + 20 * q^82 - 36 * q^83 - 18 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 - 54 * q^89 + 4 * q^90 + 148 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 + 22 * q^96 - 40 * q^97 + 36 * q^98 + 4 * q^99

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