LMFDB - Embedded newform 847.2.n.j.632.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(9,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 18]))

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

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

chi := DirichletCharacter("847.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			632.2
Character	$\chi$	$=$	847.632
Dual form			847.2.n.j.130.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.659236 - 0.140125i) q^{2} +(-0.224855 + 2.13935i) q^{3} +(-1.41213 - 0.628722i) q^{4} +(1.13022 + 1.25524i) q^{5} +(0.448009 - 1.37883i) q^{6} +(-2.51637 + 0.817238i) q^{7} +(1.93333 + 1.40464i) q^{8} +(-1.59182 - 0.338352i) q^{9} +O(q^{10})$	\(q+(-0.659236 - 0.140125i) q^{2} +(-0.224855 + 2.13935i) q^{3} +(-1.41213 - 0.628722i) q^{4} +(1.13022 + 1.25524i) q^{5} +(0.448009 - 1.37883i) q^{6} +(-2.51637 + 0.817238i) q^{7} +(1.93333 + 1.40464i) q^{8} +(-1.59182 - 0.338352i) q^{9} +(-0.569194 - 0.985873i) q^{10} +(1.66258 - 2.87968i) q^{12} +(1.22798 + 3.77933i) q^{13} +(1.77340 - 0.186146i) q^{14} +(-2.93954 + 2.13570i) q^{15} +(0.990954 + 1.10057i) q^{16} +(-2.51278 + 0.534107i) q^{17} +(1.00198 + 0.446108i) q^{18} +(-0.305292 + 0.135925i) q^{19} +(-0.806829 - 2.48316i) q^{20} +(-1.18254 - 5.56716i) q^{21} +(-2.11859 + 3.66950i) q^{23} +(-3.43975 + 3.82022i) q^{24} +(0.224419 - 2.13520i) q^{25} +(-0.279950 - 2.66354i) q^{26} +(-0.912429 + 2.80817i) q^{27} +(4.06727 + 0.428050i) q^{28} +(2.51823 - 1.82960i) q^{29} +(2.23711 - 0.996028i) q^{30} +(-5.11813 + 5.68426i) q^{31} +(-2.88878 - 5.00351i) q^{32} +1.73135 q^{34} +(-3.86989 - 2.23499i) q^{35} +(2.03514 + 1.47861i) q^{36} +(-1.06012 - 10.0863i) q^{37} +(0.220306 - 0.0468275i) q^{38} +(-8.36143 + 1.77728i) q^{39} +(0.421925 + 4.01435i) q^{40} +(-8.76494 - 6.36810i) q^{41} +(-0.000525269 + 3.83578i) q^{42} +6.26797 q^{43} +(-1.37440 - 2.38053i) q^{45} +(1.91084 - 2.12220i) q^{46} +(-2.15968 + 0.961554i) q^{47} +(-2.57732 + 1.87253i) q^{48} +(5.66425 - 4.11295i) q^{49} +(-0.447141 + 1.37616i) q^{50} +(-0.577633 - 5.49581i) q^{51} +(0.642079 - 6.10898i) q^{52} +(-2.93539 + 3.26008i) q^{53} +(0.995001 - 1.72339i) q^{54} +(-6.01289 - 1.95462i) q^{56} +(-0.222144 - 0.683690i) q^{57} +(-1.91648 + 0.853273i) q^{58} +(-0.0319655 - 0.0142320i) q^{59} +(5.49378 - 1.16774i) q^{60} +(2.74836 + 3.05237i) q^{61} +(4.17056 - 3.03009i) q^{62} +(4.28213 - 0.449477i) q^{63} +(0.287989 + 0.886339i) q^{64} +(-3.35608 + 5.81290i) q^{65} +(-2.72981 - 4.72817i) q^{67} +(3.88418 + 0.825608i) q^{68} +(-7.37397 - 5.35750i) q^{69} +(2.23800 + 2.01566i) q^{70} +(2.91440 - 8.96959i) q^{71} +(-2.60225 - 2.89009i) q^{72} +(0.273807 + 0.121907i) q^{73} +(-0.714481 + 6.79783i) q^{74} +(4.51749 + 0.960222i) q^{75} +0.516572 q^{76} +5.76120 q^{78} +(-13.9247 - 2.95979i) q^{79} +(-0.261475 + 2.48777i) q^{80} +(-10.2626 - 4.56919i) q^{81} +(4.88583 + 5.42627i) q^{82} +(1.43515 - 4.41695i) q^{83} +(-1.83029 + 8.60506i) q^{84} +(-3.51043 - 2.55048i) q^{85} +(-4.13208 - 0.878300i) q^{86} +(3.34793 + 5.79878i) q^{87} +(-6.99890 + 12.1225i) q^{89} +(0.572483 + 1.76192i) q^{90} +(-6.17866 - 8.50664i) q^{91} +(5.29882 - 3.84982i) q^{92} +(-11.0098 - 12.2276i) q^{93} +(1.55848 - 0.331265i) q^{94} +(-0.515666 - 0.229589i) q^{95} +(11.3538 - 5.05505i) q^{96} +(-1.02232 - 3.14637i) q^{97} +(-4.31040 + 1.91770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 3 q^{2} - 4 q^{3} - 3 q^{4} + 4 q^{5} + 16 q^{6} + 2 q^{7} + 38 q^{8} + 7 q^{9}+O(q^{10}) $ 40 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 + 4 * q^5 + 16 * q^6 + 2 * q^7 + 38 * q^8 + 7 * q^9	\( 40 q + 3 q^{2} - 4 q^{3} - 3 q^{4} + 4 q^{5} + 16 q^{6} + 2 q^{7} + 38 q^{8} + 7 q^{9} - 14 q^{10} - 18 q^{12} - 6 q^{13} - 3 q^{14} - 14 q^{15} - 5 q^{16} + 7 q^{17} - 24 q^{18} + 4 q^{19} - 30 q^{20} + 2 q^{21} - 14 q^{23} + 12 q^{24} + 21 q^{25} - 16 q^{27} - 16 q^{28} - 16 q^{30} - 17 q^{31} + 30 q^{32} + 48 q^{34} + 14 q^{35} + 14 q^{36} + 24 q^{37} + 12 q^{38} - 28 q^{39} - 10 q^{40} - 60 q^{41} - 70 q^{42} + 72 q^{43} - 16 q^{45} - 8 q^{46} + 13 q^{47} + 128 q^{48} - 10 q^{49} - 6 q^{50} + 7 q^{51} - 2 q^{52} + 33 q^{53} - 34 q^{54} + 24 q^{56} - 44 q^{57} - 17 q^{58} + 21 q^{59} - 48 q^{60} + 52 q^{62} - 24 q^{63} + 94 q^{64} + 40 q^{65} - 38 q^{67} + 23 q^{68} - 124 q^{69} - 3 q^{70} + 20 q^{71} + 38 q^{72} - 11 q^{73} + 41 q^{74} - 11 q^{75} + 96 q^{76} - 100 q^{78} - 21 q^{79} + 12 q^{80} - 58 q^{81} + 6 q^{82} + 46 q^{83} + 29 q^{84} + 78 q^{85} + 7 q^{86} - 48 q^{87} - 10 q^{89} + 18 q^{90} - 14 q^{91} - 110 q^{92} + 12 q^{93} - 37 q^{94} - 7 q^{95} + 53 q^{96} - 54 q^{97} - 116 q^{98}+O(q^{100}) \) 40 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 + 4 * q^5 + 16 * q^6 + 2 * q^7 + 38 * q^8 + 7 * q^9 - 14 * q^10 - 18 * q^12 - 6 * q^13 - 3 * q^14 - 14 * q^15 - 5 * q^16 + 7 * q^17 - 24 * q^18 + 4 * q^19 - 30 * q^20 + 2 * q^21 - 14 * q^23 + 12 * q^24 + 21 * q^25 - 16 * q^27 - 16 * q^28 - 16 * q^30 - 17 * q^31 + 30 * q^32 + 48 * q^34 + 14 * q^35 + 14 * q^36 + 24 * q^37 + 12 * q^38 - 28 * q^39 - 10 * q^40 - 60 * q^41 - 70 * q^42 + 72 * q^43 - 16 * q^45 - 8 * q^46 + 13 * q^47 + 128 * q^48 - 10 * q^49 - 6 * q^50 + 7 * q^51 - 2 * q^52 + 33 * q^53 - 34 * q^54 + 24 * q^56 - 44 * q^57 - 17 * q^58 + 21 * q^59 - 48 * q^60 + 52 * q^62 - 24 * q^63 + 94 * q^64 + 40 * q^65 - 38 * q^67 + 23 * q^68 - 124 * q^69 - 3 * q^70 + 20 * q^71 + 38 * q^72 - 11 * q^73 + 41 * q^74 - 11 * q^75 + 96 * q^76 - 100 * q^78 - 21 * q^79 + 12 * q^80 - 58 * q^81 + 6 * q^82 + 46 * q^83 + 29 * q^84 + 78 * q^85 + 7 * q^86 - 48 * q^87 - 10 * q^89 + 18 * q^90 - 14 * q^91 - 110 * q^92 + 12 * q^93 - 37 * q^94 - 7 * q^95 + 53 * q^96 - 54 * q^97 - 116 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.659236	−	0.140125i	−0.466150	−	0.0990833i	−0.0311523	−	0.999515i	$-0.509918\pi$
$2$	−0.659236	−	0.140125i	−0.466150	−	0.0990833i	−0.434998	+	0.900431i	$0.643251\pi$
$3$	−0.224855	+	2.13935i	−0.129820	+	1.23516i	0.714623	+	0.699510i	$0.246598\pi$
$3$	−0.224855	+	2.13935i	−0.129820	+	1.23516i	−0.844443	+	0.535645i	$0.820068\pi$
$4$	−1.41213	−	0.628722i	−0.706067	−	0.314361i
$5$	1.13022	+	1.25524i	0.505451	+	0.561361i	0.940827	−	0.338888i	$-0.110051\pi$
$5$	1.13022	+	1.25524i	0.505451	+	0.561361i	−0.435375	+	0.900249i	$0.643384\pi$
$6$	0.448009	−	1.37883i	0.182899	−	0.562905i
$7$	−2.51637	+	0.817238i	−0.951099	+	0.308887i
$7$	−2.51637	+	0.817238i	−0.951099	+	0.308887i
$8$	1.93333	+	1.40464i	0.683534	+	0.496617i
$9$	−1.59182	−	0.338352i	−0.530607	−	0.112784i
$10$	−0.569194	−	0.985873i	−0.179995	−	0.311760i
$11$		0			0
$11$		0			0
$12$	1.66258	−	2.87968i	0.479946	−	0.831292i
$13$	1.22798	+	3.77933i	0.340580	+	1.04820i	0.963908	+	0.266237i	$0.0857803\pi$
$13$	1.22798	+	3.77933i	0.340580	+	1.04820i	−0.623328	+	0.781961i	$0.714220\pi$
$14$	1.77340	−	0.186146i	0.473961	−	0.0497497i
$15$	−2.93954	+	2.13570i	−0.758985	+	0.551435i
$16$	0.990954	+	1.10057i	0.247738	+	0.275141i
$17$	−2.51278	+	0.534107i	−0.609438	+	0.129540i	−0.502284	−	0.864703i	$-0.667507\pi$
$17$	−2.51278	+	0.534107i	−0.609438	+	0.129540i	−0.107153	+	0.994243i	$0.534174\pi$
$18$	1.00198	+	0.446108i	0.236168	+	0.105149i
$19$	−0.305292	+	0.135925i	−0.0700388	+	0.0311833i	−0.441457	−	0.897282i	$-0.645538\pi$
$19$	−0.305292	+	0.135925i	−0.0700388	+	0.0311833i	0.371418	+	0.928466i	$0.378872\pi$
$20$	−0.806829	−	2.48316i	−0.180412	−	0.555252i
$21$	−1.18254	−	5.56716i	−0.258051	−	1.21485i
$22$		0			0
$23$	−2.11859	+	3.66950i	−0.441756	+	0.765143i	−0.997820	−	0.0659962i	$-0.978977\pi$
$23$	−2.11859	+	3.66950i	−0.441756	+	0.765143i	0.556064	+	0.831139i	$0.312311\pi$
$24$	−3.43975	+	3.82022i	−0.702135	+	0.779800i
$25$	0.224419	−	2.13520i	0.0448838	−	0.427041i
$26$	−0.279950	−	2.66354i	−0.0549026	−	0.522364i
$27$	−0.912429	+	2.80817i	−0.175597	+	0.540432i
$28$	4.06727	+	0.428050i	0.768641	+	0.0808939i
$29$	2.51823	−	1.82960i	0.467624	−	0.339749i	−0.328891	−	0.944368i	$-0.606675\pi$
$29$	2.51823	−	1.82960i	0.467624	−	0.339749i	0.796515	+	0.604619i	$0.206675\pi$
$30$	2.23711	−	0.996028i	0.408439	−	0.181849i
$31$	−5.11813	+	5.68426i	−0.919243	+	1.02092i	0.0804649	+	0.996757i	$0.474360\pi$
$31$	−5.11813	+	5.68426i	−0.919243	+	1.02092i	−0.999708	+	0.0241654i	$0.992307\pi$
$32$	−2.88878	−	5.00351i	−0.510669	−	0.884504i
$33$		0			0
$34$	1.73135			0.296925
$35$	−3.86989	−	2.23499i	−0.654131	−	0.377782i
$36$	2.03514	+	1.47861i	0.339189	+	0.246435i
$37$	−1.06012	−	10.0863i	−0.174282	−	1.65818i	−0.636395	−	0.771364i	$-0.719575\pi$
$37$	−1.06012	−	10.0863i	−0.174282	−	1.65818i	0.462112	−	0.886821i	$-0.347092\pi$
$38$	0.220306	−	0.0468275i	0.0357383	−	0.00759642i
$39$	−8.36143	+	1.77728i	−1.33890	+	0.284592i
$40$	0.421925	+	4.01435i	0.0667123	+	0.634725i
$41$	−8.76494	−	6.36810i	−1.36885	−	0.994530i	−0.997826	−	0.0659081i	$-0.979006\pi$
$41$	−8.76494	−	6.36810i	−1.36885	−	0.994530i	−0.371027	−	0.928622i	$-0.620994\pi$
$42$	−0.000525269		3.83578i	−8.10508e−5		0.591873i
$43$	6.26797			0.955857			0.477928	−	0.878399i	$-0.341388\pi$
$43$	6.26797			0.955857			0.477928	+	0.878399i	$0.341388\pi$
$44$		0			0
$45$	−1.37440	−	2.38053i	−0.204884	−	0.354869i
$46$	1.91084	−	2.12220i	0.281738	−	0.312901i
$47$	−2.15968	+	0.961554i	−0.315022	+	0.140257i	−0.558157	−	0.829736i	$-0.688491\pi$
$47$	−2.15968	+	0.961554i	−0.315022	+	0.140257i	0.243134	+	0.969993i	$0.421824\pi$
$48$	−2.57732	+	1.87253i	−0.372004	+	0.270277i
$49$	5.66425	−	4.11295i	0.809178	−	0.587564i
$50$	−0.447141	+	1.37616i	−0.0632352	+	0.194618i
$51$	−0.577633	−	5.49581i	−0.0808847	−	0.769567i
$52$	0.642079	−	6.10898i	0.0890404	−	0.847162i
$53$	−2.93539	+	3.26008i	−0.403207	+	0.447807i	−0.910216	−	0.414134i	$-0.864085\pi$
$53$	−2.93539	+	3.26008i	−0.403207	+	0.447807i	0.507009	+	0.861941i	$0.330751\pi$
$54$	0.995001	−	1.72339i	0.135402	−	0.234524i
$55$		0			0
$56$	−6.01289	−	1.95462i	−0.803507	−	0.261197i
$57$	−0.222144	−	0.683690i	−0.0294237	−	0.0905570i
$58$	−1.91648	+	0.853273i	−0.251647	+	0.112040i
$59$	−0.0319655	−	0.0142320i	−0.00416155	−	0.00185284i	0.404655	−	0.914470i	$-0.367392\pi$
$59$	−0.0319655	−	0.0142320i	−0.00416155	−	0.00185284i	−0.408816	+	0.912617i	$0.634058\pi$
$60$	5.49378	−	1.16774i	0.709244	−	0.150754i
$61$	2.74836	+	3.05237i	0.351892	+	0.390815i	0.892940	−	0.450176i	$-0.148639\pi$
$61$	2.74836	+	3.05237i	0.351892	+	0.390815i	−0.541048	+	0.840992i	$0.681972\pi$
$62$	4.17056	−	3.03009i	0.529662	−	0.384822i
$63$	4.28213	−	0.449477i	0.539497	−	0.0566288i
$64$	0.287989	+	0.886339i	0.0359986	+	0.110792i
$65$	−3.35608	+	5.81290i	−0.416270	+	0.721001i
$66$		0			0
$67$	−2.72981	−	4.72817i	−0.333499	−	0.577637i	0.649696	−	0.760194i	$-0.274896\pi$
$67$	−2.72981	−	4.72817i	−0.333499	−	0.577637i	−0.983195	+	0.182557i	$0.941563\pi$
$68$	3.88418	+	0.825608i	0.471026	+	0.100120i
$69$	−7.37397	−	5.35750i	−0.887722	−	0.644968i
$70$	2.23800	+	2.01566i	0.267492	+	0.240917i
$71$	2.91440	−	8.96959i	0.345875	−	1.06449i	−0.615238	−	0.788341i	$-0.710940\pi$
$71$	2.91440	−	8.96959i	0.345875	−	1.06449i	0.961114	−	0.276154i	$-0.0890598\pi$
$72$	−2.60225	−	2.89009i	−0.306678	−	0.340600i
$73$	0.273807	+	0.121907i	0.0320467	+	0.0142681i	0.422697	−	0.906271i	$-0.361083\pi$
$73$	0.273807	+	0.121907i	0.0320467	+	0.0142681i	−0.390651	+	0.920539i	$0.627750\pi$
$74$	−0.714481	+	6.79783i	−0.0830567	+	0.790232i
$75$	4.51749	+	0.960222i	0.521635	+	0.110877i
$76$	0.516572			0.0592548
$77$		0			0
$78$	5.76120			0.652327
$79$	−13.9247	−	2.95979i	−1.56666	−	0.333003i	−0.658810	−	0.752309i	$-0.728940\pi$
$79$	−13.9247	−	2.95979i	−1.56666	−	0.333003i	−0.907845	+	0.419306i	$0.862273\pi$
$80$	−0.261475	+	2.48777i	−0.0292338	+	0.278141i
$81$	−10.2626	−	4.56919i	−1.14028	−	0.507687i
$82$	4.88583	+	5.42627i	0.539550	+	0.599231i
$83$	1.43515	−	4.41695i	0.157528	−	0.484823i	−0.840880	−	0.541222i	$-0.817962\pi$
$83$	1.43515	−	4.41695i	0.157528	−	0.484823i	0.998408	+	0.0563991i	$0.0179619\pi$
$84$	−1.83029	+	8.60506i	−0.199701	+	0.938889i
$85$	−3.51043	−	2.55048i	−0.380760	−	0.276638i
$86$	−4.13208	−	0.878300i	−0.445573	−	0.0947095i
$87$	3.34793	+	5.79878i	0.358935	+	0.621694i
$88$		0			0
$89$	−6.99890	+	12.1225i	−0.741882	+	1.28498i	0.209755	+	0.977754i	$0.432733\pi$
$89$	−6.99890	+	12.1225i	−0.741882	+	1.28498i	−0.951637	+	0.307224i	$0.900600\pi$
$90$	0.572483	+	1.76192i	0.0603450	+	0.185723i
$91$	−6.17866	−	8.50664i	−0.647700	−	0.891739i
$92$	5.29882	−	3.84982i	0.552440	−	0.401371i
$93$	−11.0098	−	12.2276i	−1.14166	−	1.26794i
$94$	1.55848	−	0.331265i	0.160745	−	0.0341674i
$95$	−0.515666	−	0.229589i	−0.0529063	−	0.0235554i
$96$	11.3538	−	5.05505i	1.15880	−	0.515929i
$97$	−1.02232	−	3.14637i	−0.103801	−	0.319465i	0.885646	−	0.464360i	$-0.153716\pi$
$97$	−1.02232	−	3.14637i	−0.103801	−	0.319465i	−0.989447	+	0.144895i	$0.953716\pi$
$98$	−4.31040	+	1.91770i	−0.435416	+	0.193717i
$99$		0			0
$100$	−1.65936	+	2.87410i	−0.165936	+	0.287410i
$101$	−6.16373	+	6.84552i	−0.613314	+	0.681155i	−0.967166	−	0.254147i	$-0.918205\pi$
$101$	−6.16373	+	6.84552i	−0.613314	+	0.681155i	0.353851	+	0.935302i	$0.384872\pi$
$102$	−0.389304	+	3.70398i	−0.0385468	+	0.366748i
$103$	1.74351	+	16.5884i	0.171793	+	1.63450i	0.652620	+	0.757685i	$0.273670\pi$
$103$	1.74351	+	16.5884i	0.171793	+	1.63450i	−0.480828	+	0.876815i	$0.659664\pi$
$104$	−2.93453	+	9.03155i	−0.287754	+	0.885616i
$105$	5.65159	−	7.77651i	0.551539	−	0.758910i
$106$	2.39194	−	1.73784i	0.232326	−	0.168794i
$107$	−1.22455	+	0.545203i	−0.118381	+	0.0527068i	−0.465073	−	0.885273i	$-0.653972\pi$
$107$	−1.22455	+	0.545203i	−0.118381	+	0.0527068i	0.346691	+	0.937979i	$0.387305\pi$
$108$	3.05403	−	3.39184i	0.293874	−	0.326380i
$109$	−3.16671	−	5.48491i	−0.303316	−	0.525359i	0.673569	−	0.739124i	$-0.264760\pi$
$109$	−3.16671	−	5.48491i	−0.303316	−	0.525359i	−0.976885	+	0.213765i	$0.931427\pi$
$110$		0			0
$111$	21.8166			2.07074
$112$	−3.39303	−	1.95959i	−0.320611	−	0.185164i
$113$	12.3099	+	8.94367i	1.15802	+	0.841349i	0.989526	−	0.144354i	$-0.0461103\pi$
$113$	12.3099	+	8.94367i	1.15802	+	0.841349i	0.168492	+	0.985703i	$0.446110\pi$
$114$	0.0506436	+	0.481841i	0.00474320	+	0.0451286i
$115$	−7.00058	+	1.48802i	−0.652807	+	0.138758i
$116$	−4.70639	+	1.00037i	−0.436978	+	0.0928824i
$117$	−0.675979	−	6.43151i	−0.0624943	−	0.594593i
$118$	0.0190786	+	0.0138614i	0.00175632	+	0.00127604i
$119$	5.88658	−	3.39755i	0.539622	−	0.311452i
$120$	−8.68298			−0.792644
$121$		0			0
$122$	−1.38411	−	2.39734i	−0.125311	−	0.217045i
$123$	15.5944	−	17.3194i	1.40610	−	1.56164i
$124$	10.8013	−	4.80905i	0.969985	−	0.431865i
$125$	9.76636	−	7.09568i	0.873530	−	0.634657i
$126$	−2.88592	−	0.303722i	−0.257098	−	0.0270577i
$127$	−1.68911	+	5.19854i	−0.149884	+	0.461296i	−0.997607	−	0.0691441i	$-0.977973\pi$
$127$	−1.68911	+	5.19854i	−0.149884	+	0.461296i	0.847723	+	0.530440i	$0.177973\pi$
$128$	1.14218	+	10.8672i	0.100956	+	0.960530i
$129$	−1.40938	+	13.4094i	−0.124089	+	1.18063i
$130$	3.02698	−	3.36180i	0.265484	−	0.294850i
$131$	2.46819	−	4.27502i	0.215646	−	0.373510i	−0.737826	−	0.674991i	$-0.764147\pi$
$131$	2.46819	−	4.27502i	0.215646	−	0.373510i	0.953472	+	0.301481i	$0.0974808\pi$
$132$		0			0
$133$	0.657145	−	0.591533i	0.0569817	−	0.0512924i
$134$	1.13705	+	3.49949i	0.0982265	+	0.302310i
$135$	−4.55618	+	2.02854i	−0.392133	+	0.174589i
$136$	−5.60825	−	2.49695i	−0.480903	−	0.214112i
$137$	−1.59960	+	0.340006i	−0.136663	+	0.0290487i	−0.275735	−	0.961234i	$-0.588921\pi$
$137$	−1.59960	+	0.340006i	−0.136663	+	0.0290487i	0.139072	+	0.990282i	$0.455588\pi$
$138$	4.11047	+	4.56514i	0.349906	+	0.388610i
$139$	−7.16508	+	5.20573i	−0.607734	+	0.441545i	−0.848616	−	0.529010i	$-0.822563\pi$
$139$	−7.16508	+	5.20573i	−0.607734	+	0.441545i	0.240882	+	0.970554i	$0.422563\pi$
$140$	4.05962	+	5.58919i	0.343100	+	0.472373i
$141$	−1.57149	−	4.83653i	−0.132343	−	0.407310i
$142$	−3.17814	+	5.50470i	−0.266704	+	0.461944i
$143$		0			0
$144$	−1.20504	−	2.08720i	−0.100420	−	0.173933i
$145$	5.14276	+	1.09313i	0.427083	+	0.0907793i
$146$	−0.163422	−	0.118733i	−0.0135249	−	0.00982639i
$147$	7.52540	+	13.0426i	0.620685	+	1.07574i
$148$	−4.84448	+	14.9098i	−0.398214	+	1.22558i
$149$	3.20622	+	3.56086i	0.262663	+	0.291717i	0.860022	−	0.510257i	$-0.170450\pi$
$149$	3.20622	+	3.56086i	0.262663	+	0.291717i	−0.597359	+	0.801974i	$0.703783\pi$
$150$	−2.84354	−	1.26603i	−0.232174	−	0.103371i
$151$	−1.68058	+	15.9897i	−0.136764	+	1.30122i	0.683802	+	0.729668i	$0.260325\pi$
$151$	−1.68058	+	15.9897i	−0.136764	+	1.30122i	−0.820566	+	0.571552i	$0.806341\pi$
$152$	−0.781155	−	0.166040i	−0.0633600	−	0.0134676i
$153$	4.18061			0.337982
$154$		0			0
$155$	−12.9197			−1.03774
$156$	12.9249	+	2.74727i	1.03482	+	0.219957i
$157$	−0.712751	+	6.78137i	−0.0568837	+	0.541212i	0.928557	+	0.371191i	$0.121050\pi$
$157$	−0.712751	+	6.78137i	−0.0568837	+	0.541212i	−0.985440	+	0.170022i	$0.945616\pi$
$158$	8.76495	+	3.90241i	0.697302	+	0.310459i
$159$	−6.31443	−	7.01288i	−0.500767	−	0.556158i
$160$	3.01565	−	9.28120i	0.238408	−	0.733743i
$161$	2.33230	−	10.9652i	0.183811	−	0.864179i
$162$	6.12520	+	4.45022i	0.481241	+	0.349642i
$163$	13.4196	+	2.85242i	1.05110	+	0.223419i	0.700904	−	0.713256i	$-0.252780\pi$
$163$	13.4196	+	2.85242i	1.05110	+	0.223419i	0.350200	+	0.936675i	$0.386114\pi$
$164$	8.37349	+	14.5033i	0.653860	+	1.13252i
$165$		0			0
$166$	−1.56503	+	2.71071i	−0.121470	+	0.210392i
$167$	6.04406	+	18.6017i	0.467703	+	1.43944i	0.855551	+	0.517719i	$0.173219\pi$
$167$	6.04406	+	18.6017i	0.467703	+	1.43944i	−0.387847	+	0.921724i	$0.626781\pi$
$168$	5.53364	−	12.4242i	0.426930	−	0.958547i
$169$	−2.25818	+	1.64066i	−0.173706	+	0.126205i
$170$	1.95682	+	2.17327i	0.150081	+	0.166682i
$171$	0.531961	−	0.113072i	0.0406801	−	0.00864681i
$172$	−8.85121	−	3.94081i	−0.674899	−	0.300484i
$173$	−3.36136	+	1.49657i	−0.255559	+	0.113782i	−0.530518	−	0.847674i	$-0.678003\pi$
$173$	−3.36136	+	1.49657i	−0.255559	+	0.113782i	0.274959	+	0.961456i	$0.411336\pi$
$174$	−1.39452	−	4.29189i	−0.105718	−	0.325368i
$175$	1.18025	+	5.55637i	0.0892183	+	0.420022i
$176$		0			0
$177$	0.0376348	−	0.0651853i	0.00282880	−	0.00489963i
$178$	6.31259	−	7.01084i	0.473149	−	0.525485i
$179$	−2.06293	+	19.6275i	−0.154191	+	1.46703i	0.594493	+	0.804101i	$0.297353\pi$
$179$	−2.06293	+	19.6275i	−0.154191	+	1.46703i	−0.748684	+	0.662927i	$0.769314\pi$
$180$	0.444144	+	4.22575i	0.0331045	+	0.314969i
$181$	−0.683681	+	2.10415i	−0.0508176	+	0.156400i	−0.973245	−	0.229770i	$-0.926202\pi$
$181$	−0.683681	+	2.10415i	−0.0508176	+	0.156400i	0.922427	+	0.386171i	$0.126202\pi$
$182$	2.88120	+	6.47367i	0.213569	+	0.479861i
$183$	−7.14806	+	5.19337i	−0.528400	+	0.383905i
$184$	−9.25026	+	4.11848i	−0.681938	+	0.303618i
$185$	11.4626	−	12.7305i	0.842749	−	0.935967i
$186$	5.54466	+	9.60363i	0.406554	+	0.704172i
$187$		0			0
$188$	3.65431			0.266518
$189$	0.00106978	−	7.81206i	7.78150e−5	−	0.568244i
$190$	0.307775	+	0.223611i	0.0223283	+	0.0162225i
$191$	−0.899407	−	8.55728i	−0.0650788	−	0.619183i	−0.977646	−	0.210257i	$-0.932570\pi$
$191$	−0.899407	−	8.55728i	−0.0650788	−	0.619183i	0.912567	−	0.408926i	$-0.134097\pi$
$192$	−1.96095	+	0.416812i	−0.141519	+	0.0300808i
$193$	0.249950	−	0.0531286i	0.0179918	−	0.00382428i	−0.198907	−	0.980018i	$-0.563739\pi$
$193$	0.249950	−	0.0531286i	0.0179918	−	0.00382428i	0.216899	+	0.976194i	$0.430406\pi$
$194$	0.233064	+	2.21745i	0.0167330	+	0.159204i
$195$	−11.6812	−	8.48689i	−0.836508	−	0.607759i
$196$	−10.5846	+	2.24679i	−0.756041	+	0.160485i
$197$	9.76587			0.695789			0.347895	−	0.937534i	$-0.386897\pi$
$197$	9.76587			0.695789			0.347895	+	0.937534i	$0.386897\pi$
$198$		0			0
$199$	0.176993	+	0.306561i	0.0125467	+	0.0217315i	0.872231	−	0.489095i	$-0.162673\pi$
$199$	0.176993	+	0.306561i	0.0125467	+	0.0217315i	−0.859684	+	0.510826i	$0.829339\pi$
$200$	3.43308	−	3.81282i	0.242755	−	0.269607i
$201$	10.7290	−	4.77687i	0.756767	−	0.336934i
$202$	5.02259	−	3.64912i	0.353388	−	0.256751i
$203$	−4.84159	+	6.66195i	−0.339813	+	0.467577i
$204$	−2.63964	+	8.12398i	−0.184812	+	0.568793i
$205$	−1.91284	−	18.1995i	−0.133599	−	1.27111i
$206$	1.17506	−	11.1800i	0.0818704	−	0.778945i
$207$	4.61399	−	5.12436i	0.320695	−	0.356168i
$208$	−2.94253	+	5.09661i	−0.204028	+	0.353386i
$209$		0			0
$210$	−4.81542	+	4.33463i	−0.332295	+	0.299118i
$211$	−4.60636	−	14.1769i	−0.317115	−	0.975979i	−0.974875	−	0.222751i	$-0.928496\pi$
$211$	−4.60636	−	14.1769i	−0.317115	−	0.975979i	0.657761	−	0.753227i	$-0.271504\pi$
$212$	6.19486	−	2.75813i	0.425464	−	0.189429i
$213$	18.5338	+	8.25178i	1.26991	+	0.565402i
$214$	0.883662	−	0.187828i	0.0604059	−	0.0128397i
$215$	7.08421	+	7.86782i	0.483139	+	0.536581i
$216$	−5.70850	+	4.14747i	−0.388414	+	0.282199i
$217$	8.23372	−	18.4864i	0.558941	−	1.25494i
$218$	1.31904	+	4.05959i	0.0893366	+	0.274950i
$219$	−0.322369	+	0.558359i	−0.0217837	+	0.0377304i
$220$		0			0
$221$	−5.10420	−	8.84073i	−0.343346	−	0.594692i
$222$	−14.3823	−	3.05705i	−0.965277	−	0.205176i
$223$	−23.1818	−	16.8425i	−1.55237	−	1.12786i	−0.941938	−	0.335788i	$-0.890997\pi$
$223$	−23.1818	−	16.8425i	−1.55237	−	1.12786i	−0.610428	−	0.792072i	$-0.709003\pi$
$224$	11.3583	+	10.2299i	0.758908	+	0.683512i
$225$	−1.07969	+	3.32293i	−0.0719791	+	0.221529i
$226$	−6.86190	−	7.62091i	−0.456447	−	0.506936i
$227$	19.2446	+	8.56826i	1.27731	+	0.568695i	0.929484	−	0.368863i	$-0.120253\pi$
$227$	19.2446	+	8.56826i	1.27731	+	0.568695i	0.347827	+	0.937559i	$0.386920\pi$
$228$	−0.116154	+	1.10513i	−0.00769247	+	0.0731889i
$229$	7.06001	+	1.50065i	0.466539	+	0.0991658i	0.435182	−	0.900342i	$-0.356684\pi$
$229$	7.06001	+	1.50065i	0.466539	+	0.0991658i	0.0313564	+	0.999508i	$0.490017\pi$
$230$	4.82354			0.318055
$231$		0			0
$232$	7.43851			0.488362
$233$	25.1228	+	5.34001i	1.64585	+	0.349836i	0.935312	−	0.353825i	$-0.115119\pi$
$233$	25.1228	+	5.34001i	1.64585	+	0.349836i	0.710536	+	0.703661i	$0.248452\pi$
$234$	−0.455585	+	4.33461i	−0.0297826	+	0.283362i
$235$	−3.64791	−	1.62415i	−0.237963	−	0.105948i
$236$	0.0361916	+	0.0401949i	0.00235587	+	0.00261646i
$237$	9.46309	−	29.1244i	0.614693	−	1.89183i
$238$	−4.35673	+	1.41493i	−0.282405	+	0.0917162i
$239$	−7.01845	−	5.09920i	−0.453986	−	0.329840i	0.337182	−	0.941440i	$-0.390526\pi$
$239$	−7.01845	−	5.09920i	−0.453986	−	0.329840i	−0.791167	+	0.611600i	$0.790526\pi$
$240$	−5.26342	−	1.11878i	−0.339752	−	0.0722166i
$241$	−11.0355	−	19.1141i	−0.710862	−	1.23125i	−0.964534	−	0.263959i	$-0.914972\pi$
$241$	−11.0355	−	19.1141i	−0.710862	−	1.23125i	0.253672	−	0.967290i	$-0.418362\pi$
$242$		0			0
$243$	7.65366	−	13.2565i	0.490983	−	0.850407i
$244$	−1.96196	−	6.03830i	−0.125602	−	0.386563i
$245$	11.5646	+	2.46144i	0.738835	+	0.157256i
$246$	−12.7073	+	9.23239i	−0.810188	+	0.588636i
$247$	−0.888596	−	0.986886i	−0.0565400	−	0.0627941i
$248$	−17.8794	+	3.80038i	−1.13534	+	0.241324i
$249$	9.12670	+	4.06347i	0.578381	+	0.257512i
$250$	−7.43262	+	3.30922i	−0.470080	+	0.209293i
$251$	5.32569	+	16.3908i	0.336155	+	1.03458i	0.966150	+	0.257980i	$0.0830567\pi$
$251$	5.32569	+	16.3908i	0.336155	+	1.03458i	−0.629995	+	0.776599i	$0.716943\pi$
$252$	−6.32953	−	2.05755i	−0.398723	−	0.129613i
$253$		0			0
$254$	1.84197	−	3.19038i	0.115575	−	0.200182i
$255$	6.24571	−	6.93656i	0.391121	−	0.434384i
$256$	0.964622	−	9.17777i	0.0602889	−	0.573610i
$257$	0.599439	+	5.70328i	0.0373920	+	0.355761i	0.997181	+	0.0750376i	$0.0239077\pi$
$257$	0.599439	+	5.70328i	0.0373920	+	0.355761i	−0.959789	+	0.280723i	$0.909426\pi$
$258$	2.80811	−	8.64247i	0.174825	−	0.538057i
$259$	10.9106	+	24.5146i	0.677951	+	1.52326i
$260$	8.39393	−	6.09855i	0.520569	−	0.378216i
$261$	−4.62763	+	2.06035i	−0.286443	+	0.127533i
$262$	−2.22616	+	2.47240i	−0.137532	+	0.152745i
$263$	11.2982	+	19.5691i	0.696679	+	1.20668i	0.969612	+	0.244650i	$0.0786729\pi$
$263$	11.2982	+	19.5691i	0.696679	+	1.20668i	−0.272933	+	0.962033i	$0.587994\pi$
$264$		0			0
$265$	−7.40984			−0.455183
$266$	−0.516102	+	0.297878i	−0.0316443	+	0.0182640i
$267$	−24.3605	−	17.6989i	−1.49084	−	1.08316i
$268$	0.882149	+	8.39309i	0.0538859	+	0.512690i
$269$	15.9050	−	3.38071i	0.969744	−	0.206125i	0.304302	−	0.952575i	$-0.401577\pi$
$269$	15.9050	−	3.38071i	0.969744	−	0.206125i	0.665441	+	0.746450i	$0.268243\pi$
$270$	3.28785	−	0.698853i	0.200092	−	0.0425309i
$271$	0.738626	+	7.02755i	0.0448683	+	0.426894i	0.993781	+	0.111354i	$0.0355188\pi$
$271$	0.738626	+	7.02755i	0.0448683	+	0.426894i	−0.948912	+	0.315539i	$0.897815\pi$
$272$	−3.07786	−	2.23620i	−0.186623	−	0.135590i
$273$	19.5880	−	11.3056i	1.18552	−	0.684244i
$274$	1.10216			0.0665839
$275$		0			0
$276$	7.04465	+	12.2017i	0.424038	+	0.734455i
$277$	−7.95588	+	8.83591i	−0.478023	+	0.530898i	−0.933130	−	0.359538i	$-0.882934\pi$
$277$	−7.95588	+	8.83591i	−0.478023	+	0.530898i	0.455107	+	0.890437i	$0.349601\pi$
$278$	5.45293	−	2.42780i	0.327045	−	0.145610i
$279$	10.0704	−	7.31660i	0.602901	−	0.438033i
$280$	−4.34240	−	9.75679i	−0.259508	−	0.583080i
$281$	−3.21105	+	9.88261i	−0.191555	+	0.589547i	0.808444	+	0.588573i	$0.200310\pi$
$281$	−3.21105	+	9.88261i	−0.191555	+	0.589547i	−1.00000		0.000973981i	$0.999690\pi$
$282$	0.358261	+	3.40862i	0.0213341	+	0.202981i
$283$	−2.12197	+	20.1892i	−0.126138	+	1.20012i	0.730027	+	0.683419i	$0.239508\pi$
$283$	−2.12197	+	20.1892i	−0.126138	+	1.20012i	−0.856165	+	0.516703i	$0.827159\pi$
$284$	−9.75490	+	10.8339i	−0.578847	+	0.642875i
$285$	0.607123	−	1.05157i	0.0359628	−	0.0622895i
$286$		0			0
$287$	27.2601	+	8.86146i	1.60911	+	0.523076i
$288$	2.90547	+	8.94213i	0.171207	+	0.526920i
$289$	−9.50150	+	4.23034i	−0.558912	+	0.248844i
$290$	−3.23712	−	1.44126i	−0.190090	−	0.0846336i
$291$	6.96106	−	1.47962i	0.408065	−	0.0867368i
$292$	−0.310007	−	0.344298i	−0.0181418	−	0.0201485i
$293$	19.3158	−	14.0337i	1.12844	−	0.819860i	0.142973	−	0.989727i	$-0.454334\pi$
$293$	19.3158	−	14.0337i	1.12844	−	0.819860i	0.985467	+	0.169866i	$0.0543336\pi$
$294$	−3.13342	−	9.65267i	−0.182745	−	0.562955i
$295$	−0.0182636	−	0.0562097i	−0.00106335	−	0.00327266i
$296$	12.1182	−	20.9893i	0.704354	−	1.21998i
$297$		0			0
$298$	−1.61469	−	2.79672i	−0.0935364	−	0.162010i
$299$	−16.4698	−	3.50077i	−0.952474	−	0.202455i
$300$	−5.77558	−	4.19621i	−0.333454	−	0.242268i
$301$	−15.7725	+	5.12242i	−0.909114	+	0.295252i
$302$	3.34845	−	10.3055i	0.192682	−	0.593013i
$303$	−13.2590	−	14.7256i	−0.761711	−	0.845966i
$304$	−0.452124	−	0.201299i	−0.0259311	−	0.0115453i
$305$	−0.725189	+	6.89971i	−0.0415242	+	0.395076i
$306$	−2.75601	−	0.585808i	−0.157551	−	0.0334884i
$307$	−8.73868			−0.498743			−0.249372	−	0.968408i	$-0.580224\pi$
$307$	−8.73868			−0.498743			−0.249372	+	0.968408i	$0.580224\pi$
$308$		0			0
$309$	−35.8804			−2.04116
$310$	8.51716	+	1.81038i	0.483742	+	0.102823i
$311$	−0.273671	+	2.60381i	−0.0155185	+	0.147648i	−0.999537	−	0.0304159i	$-0.990317\pi$
$311$	−0.273671	+	2.60381i	−0.0155185	+	0.147648i	0.984019	+	0.178064i	$0.0569835\pi$
$312$	−18.6618	−	8.30878i	−1.05652	−	0.470392i
$313$	−15.2251	−	16.9092i	−0.860574	−	0.955764i	0.138829	−	0.990316i	$-0.455666\pi$
$313$	−15.2251	−	16.9092i	−0.860574	−	0.955764i	−0.999403	+	0.0345523i	$0.988999\pi$
$314$	1.42011	−	4.37065i	0.0801415	−	0.246650i
$315$	5.40397	+	4.86709i	0.304479	+	0.274230i
$316$	17.8027	+	12.9344i	1.00148	+	0.727618i
$317$	−4.39006	−	0.933136i	−0.246570	−	0.0524101i	0.0829685	−	0.996552i	$-0.473560\pi$
$317$	−4.39006	−	0.933136i	−0.246570	−	0.0524101i	−0.329539	+	0.944142i	$0.606893\pi$
$318$	3.18002	+	5.50796i	0.178327	+	0.308871i
$319$		0			0
$320$	−0.787077	+	1.36326i	−0.0439989	+	0.0762084i
$321$	−0.891035	−	2.74233i	−0.0497328	−	0.153062i
$322$	−3.07403	+	6.90185i	−0.171309	+	0.384625i
$323$	0.694532	−	0.504607i	0.0386448	−	0.0280771i
$324$	11.6194	+	12.9046i	0.645520	+	0.716922i
$325$	8.34522	−	1.77383i	0.462910	−	0.0983945i
$326$	−8.44699	−	3.76084i	−0.467835	−	0.208294i
$327$	12.4462	−	5.54140i	0.688276	−	0.306440i
$328$	−8.00057	−	24.6232i	−0.441758	−	1.35959i
$329$	4.64875	−	4.18460i	0.256294	−	0.230705i
$330$		0			0
$331$	6.90068	−	11.9523i	0.379296	−	0.656960i	−0.611664	−	0.791118i	$-0.709500\pi$
$331$	6.90068	−	11.9523i	0.379296	−	0.656960i	0.990960	+	0.134158i	$0.0428330\pi$
$332$	−4.80366	+	5.33500i	−0.263635	+	0.292796i
$333$	−1.72522	+	16.4144i	−0.0945414	+	0.899501i
$334$	−1.37790	−	13.1098i	−0.0753953	−	0.717338i
$335$	2.84969	−	8.77045i	0.155695	−	0.479181i
$336$	4.95518	−	6.81826i	0.270327	−	0.371967i
$337$	−9.10560	+	6.61560i	−0.496013	+	0.360375i	−0.807492	−	0.589878i	$-0.799176\pi$
$337$	−9.10560	+	6.61560i	−0.496013	+	0.360375i	0.311479	+	0.950253i	$0.399176\pi$
$338$	1.71857	−	0.765158i	0.0934780	−	0.0416191i
$339$	−21.9016	+	24.3242i	−1.18953	+	1.32111i
$340$	3.35366	+	5.80870i	0.181877	+	0.315021i
$341$		0			0
$342$	−0.366532			−0.0198198
$343$	−10.8921	+	14.9787i	−0.588118	+	0.808775i
$344$	12.1180	+	8.80427i	0.653361	+	0.474695i
$345$	−1.60928	−	15.3113i	−0.0866408	−	0.824332i
$346$	2.42564	−	0.515585i	0.130403	−	0.0277180i
$347$	−15.1016	+	3.20994i	−0.810696	+	0.172319i	−0.594567	−	0.804046i	$-0.702677\pi$
$347$	−15.1016	+	3.20994i	−0.810696	+	0.172319i	−0.216129	+	0.976365i	$0.569343\pi$
$348$	−1.08190	−	10.2936i	−0.0579958	−	0.551793i
$349$	−8.01108	−	5.82039i	−0.428823	−	0.311558i	0.352355	−	0.935866i	$-0.385381\pi$
$349$	−8.01108	−	5.82039i	−0.428823	−	0.311558i	−0.781178	+	0.624308i	$0.785381\pi$
$350$	0.000524251	−	3.82834i	2.80224e−5	−	0.204633i
$351$	−11.7334			−0.626285
$352$		0			0
$353$	−4.91732	−	8.51704i	−0.261722	−	0.453316i	0.704977	−	0.709230i	$-0.250957\pi$
$353$	−4.91732	−	8.51704i	−0.261722	−	0.453316i	−0.966700	+	0.255913i	$0.917624\pi$
$354$	−0.0339443	+	0.0376990i	−0.00180412	+	0.00200368i
$355$	14.5529	−	6.47938i	0.772389	−	0.343890i
$356$	17.5050	−	12.7182i	0.927765	−	0.674061i
$357$	5.94492	+	13.3574i	0.314638	+	0.706950i
$358$	4.11026	−	12.6501i	0.217234	−	0.668578i
$359$	0.319789	+	3.04259i	0.0168778	+	0.160582i	0.999714	−	0.0238963i	$-0.00760716\pi$
$359$	0.319789	+	3.04259i	0.0168778	+	0.160582i	−0.982837	+	0.184478i	$0.940940\pi$
$360$	0.686635	−	6.53289i	0.0361888	−	0.344314i
$361$	−12.6388	+	14.0368i	−0.665198	+	0.738777i
$362$	0.745552	−	1.29133i	0.0391853	−	0.0678710i
$363$		0			0
$364$	3.37677	+	15.8972i	0.176991	+	0.833239i
$365$	0.156441	+	0.481476i	0.00818851	+	0.0252016i
$366$	5.43999	−	2.42204i	0.284353	−	0.126602i
$367$	−7.01601	−	3.12373i	−0.366233	−	0.163057i	0.215366	−	0.976534i	$-0.430906\pi$
$367$	−7.01601	−	3.12373i	−0.366233	−	0.163057i	−0.581598	+	0.813476i	$0.697572\pi$
$368$	−6.13794	+	1.30466i	−0.319962	+	0.0680101i
$369$	11.7976	+	13.1025i	0.614156	+	0.682090i
$370$	−9.34044	+	6.78623i	−0.485586	+	0.352799i
$371$	4.72228	−	10.6025i	0.245168	−	0.550454i
$372$	7.85952	+	24.1891i	0.407497	+	1.25415i
$373$	−3.34422	+	5.79236i	−0.173157	+	0.299917i	−0.939522	−	0.342488i	$-0.888730\pi$
$373$	−3.34422	+	5.79236i	−0.173157	+	0.299917i	0.766365	+	0.642406i	$0.222064\pi$
$374$		0			0
$375$	12.9841	+	22.4892i	0.670498	+	1.16134i
$376$	−5.52602	−	1.17459i	−0.284983	−	0.0605749i
$377$	10.0070	+	7.27052i	0.515387	+	0.374451i
$378$	−1.09537	+	5.14985i	−0.0563398	+	0.264880i
$379$	−4.17467	+	12.8483i	−0.214438	+	0.659973i	0.784755	+	0.619806i	$0.212789\pi$
$379$	−4.17467	+	12.8483i	−0.214438	+	0.659973i	−0.999193	+	0.0401666i	$0.987211\pi$
$380$	0.583842	+	0.648422i	0.0299504	+	0.0332633i
$381$	−10.7417	−	4.78251i	−0.550314	−	0.245015i
$382$	−0.606168	+	5.76730i	−0.0310142	+	0.295081i
$383$	−0.490256	−	0.104207i	−0.0250509	−	0.00532473i	0.195369	−	0.980730i	$-0.437409\pi$
$383$	−0.490256	−	0.104207i	−0.0250509	−	0.00532473i	−0.220420	+	0.975405i	$0.570743\pi$
$384$	−23.5055			−1.19951
$385$		0			0
$386$	−0.172221			−0.00876582
$387$	−9.97750	−	2.12078i	−0.507185	−	0.107805i
$388$	−0.534544	+	5.08585i	−0.0271374	+	0.258195i
$389$	−17.0893	−	7.60865i	−0.866463	−	0.385774i	−0.0751402	−	0.997173i	$-0.523940\pi$
$389$	−17.0893	−	7.60865i	−0.866463	−	0.385774i	−0.791323	+	0.611399i	$0.790607\pi$
$390$	6.51145	+	7.23169i	0.329720	+	0.366191i
$391$	3.36363	−	10.3522i	0.170106	−	0.523532i
$392$	16.7281	+	0.00458146i	0.844895	+	0.000231399i
$393$	8.59079	+	6.24158i	0.433348	+	0.314846i
$394$	−6.43802	−	1.36844i	−0.324343	−	0.0689411i
$395$	−12.0228	−	20.8241i	−0.604934	−	1.04778i
$396$		0			0
$397$	−2.36033	+	4.08821i	−0.118461	+	0.205181i	−0.919158	−	0.393889i	$-0.871130\pi$
$397$	−2.36033	+	4.08821i	−0.118461	+	0.205181i	0.800697	+	0.599070i	$0.204463\pi$
$398$	−0.0737234	−	0.226897i	−0.00369542	−	0.0113733i
$399$	1.11773	+	1.53887i	0.0559567	+	0.0770400i
$400$	2.57232	−	1.86890i	0.128616	−	0.0934450i
$401$	11.3134	+	12.5648i	0.564965	+	0.627458i	0.956158	−	0.292851i	$-0.0946040\pi$
$401$	11.3134	+	12.5648i	0.564965	+	0.627458i	−0.391193	+	0.920309i	$0.627937\pi$
$402$	−7.74232	+	1.64568i	−0.386152	+	0.0820791i
$403$	−27.7676	−	12.3629i	−1.38320	−	0.615842i
$404$	13.0079	−	5.79151i	0.647169	−	0.288138i
$405$	−5.86356	−	18.0462i	−0.291363	−	0.896722i
$406$	4.12526	−	3.71337i	0.204733	−	0.184292i
$407$		0			0
$408$	6.60290	−	11.4366i	0.326892	−	0.566194i
$409$	17.0587	−	18.9456i	0.843496	−	0.936797i	−0.155198	−	0.987883i	$-0.549602\pi$
$409$	17.0587	−	18.9456i	0.843496	−	0.936797i	0.998694	+	0.0510860i	$0.0162682\pi$
$410$	−1.28919	+	12.2658i	−0.0636684	+	0.605765i
$411$	−0.367714	−	3.49856i	−0.0181380	−	0.172571i
$412$	7.96741	−	24.5212i	0.392526	−	1.20807i
$413$	0.0920680	+	0.00968948i	0.00453037	+	0.000476788i
$414$	−3.75976	+	2.73163i	−0.184782	+	0.134252i
$415$	7.16637	−	3.19067i	0.351783	−	0.156624i
$416$	15.3626	−	17.0619i	0.753212	−	0.836526i
$417$	−9.52579	−	16.4992i	−0.466480	−	0.807967i
$418$		0			0
$419$	−22.6624			−1.10713			−0.553565	−	0.832806i	$-0.686733\pi$
$419$	−22.6624			−1.10713			−0.553565	+	0.832806i	$0.686733\pi$
$420$	−12.8701	+	7.42819i	−0.627995	+	0.362458i
$421$	15.1994	+	11.0430i	0.740774	+	0.538204i	0.892954	−	0.450149i	$-0.148629\pi$
$421$	15.1994	+	11.0430i	0.740774	+	0.538204i	−0.152179	+	0.988353i	$0.548629\pi$
$422$	1.05014	+	9.99140i	0.0511199	+	0.486374i
$423$	3.76318	−	0.799888i	0.182972	−	0.0388919i
$424$	−10.2543	+	2.17963i	−0.497994	+	0.105852i
$425$	0.576513	+	5.48515i	0.0279650	+	0.266069i
$426$	−11.0619	−	8.03692i	−0.535949	−	0.389390i
$427$	−9.41041	−	5.43482i	−0.455401	−	0.263009i
$428$	2.07200			0.100154
$429$		0			0
$430$	−3.56769	−	6.17942i	−0.172049	−	0.297998i
$431$	−22.9484	+	25.4867i	−1.10538	+	1.22765i	−0.133786	+	0.991010i	$0.542714\pi$
$431$	−22.9484	+	25.4867i	−1.10538	+	1.22765i	−0.971597	+	0.236642i	$0.923953\pi$
$432$	−3.99475	+	1.77858i	−0.192197	+	0.0855718i
$433$	−2.57803	+	1.87305i	−0.123892	+	0.0900130i	−0.648006	−	0.761635i	$-0.724397\pi$
$433$	−2.57803	+	1.87305i	−0.123892	+	0.0900130i	0.524114	+	0.851648i	$0.324397\pi$
$434$	−8.01838	+	11.0332i	−0.384895	+	0.529609i
$435$	−3.49496	+	10.7564i	−0.167570	+	0.515729i
$436$	1.02334	+	9.73641i	0.0490090	+	0.466289i
$437$	0.148012	−	1.40824i	0.00708035	−	0.0673651i
$438$	0.290757	−	0.322919i	0.0138929	−	0.0154297i
$439$	6.18390	−	10.7108i	0.295141	−	0.511200i	−0.679877	−	0.733327i	$-0.737967\pi$
$439$	6.18390	−	10.7108i	0.295141	−	0.511200i	0.975018	+	0.222127i	$0.0713000\pi$
$440$		0			0
$441$	−10.4081	+	4.63057i	−0.495624	+	0.220503i
$442$	2.12607	+	6.54336i	0.101127	+	0.311236i
$443$	−4.66181	+	2.07557i	−0.221489	+	0.0986133i	−0.514482	−	0.857501i	$-0.672016\pi$
$443$	−4.66181	+	2.07557i	−0.221489	+	0.0986133i	0.292992	+	0.956115i	$0.405349\pi$
$444$	−30.8080	−	13.7166i	−1.46208	−	0.650960i
$445$	−23.1269	+	4.91578i	−1.09632	+	0.233030i
$446$	12.9222	+	14.3516i	0.611884	+	0.679566i
$447$	−8.33887	+	6.05854i	−0.394415	+	0.286559i
$448$	−1.44904	−	1.99500i	−0.0684606	−	0.0942550i
$449$	−0.378022	−	1.16343i	−0.0178400	−	0.0549057i	0.941740	−	0.336341i	$-0.109190\pi$
$449$	−0.378022	−	1.16343i	−0.0178400	−	0.0549057i	−0.959580	+	0.281435i	$0.909190\pi$
$450$	1.17739	−	2.03931i	0.0555029	−	0.0961338i
$451$		0			0
$452$	−11.7601	−	20.3692i	−0.553150	−	0.958085i
$453$	−33.8296	−	7.19071i	−1.58945	−	0.337849i
$454$	−11.4861	−	8.34516i	−0.539071	−	0.391658i
$455$	3.69462	−	17.3701i	0.173206	−	0.814324i
$456$	0.530863	−	1.63383i	0.0248600	−	0.0765111i
$457$	−3.43531	−	3.81530i	−0.160697	−	0.178472i	0.657419	−	0.753525i	$-0.271648\pi$
$457$	−3.43531	−	3.81530i	−0.160697	−	0.178472i	−0.818116	+	0.575053i	$0.804981\pi$
$458$	−4.44394	−	1.97857i	−0.207652	−	0.0924524i
$459$	0.792868	−	7.54363i	0.0370079	−	0.352107i
$460$	10.8213	+	2.30014i	0.504546	+	0.107245i
$461$	−22.7757			−1.06077			−0.530386	−	0.847757i	$-0.677953\pi$
$461$	−22.7757			−1.06077			−0.530386	+	0.847757i	$0.677953\pi$
$462$		0			0
$463$	29.8445			1.38699			0.693496	−	0.720460i	$-0.256069\pi$
$463$	29.8445			1.38699			0.693496	+	0.720460i	$0.256069\pi$
$464$	4.50905	+	0.958428i	0.209327	+	0.0444939i
$465$	2.90507	−	27.6399i	0.134719	−	1.28177i
$466$	−15.8136	−	7.04066i	−0.732550	−	0.326152i
$467$	1.03715	+	1.15187i	0.0479936	+	0.0533022i	0.766664	−	0.642049i	$-0.221915\pi$
$467$	1.03715	+	1.15187i	0.0479936	+	0.0533022i	−0.718670	+	0.695351i	$0.755249\pi$
$468$	−3.08906	+	9.50715i	−0.142792	+	0.439468i
$469$	10.7332	+	9.66692i	0.495615	+	0.446377i
$470$	2.17725	+	1.58186i	0.100429	+	0.0729660i
$471$	−14.3475	−	3.04965i	−0.661096	−	0.140520i
$472$	−0.0418089	−	0.0724152i	−0.00192441	−	0.00333318i
$473$		0			0
$474$	−10.3195	+	17.8738i	−0.473989	+	0.820973i
$475$	0.221714	+	0.682364i	0.0101729	+	0.0313090i
$476$	−10.4488	+	1.09676i	−0.478918	+	0.0502700i
$477$	5.77568	−	4.19628i	0.264450	−	0.192134i
$478$	3.91229	+	4.34504i	0.178944	+	0.198737i
$479$	−11.4888	+	2.44202i	−0.524937	+	0.111579i	−0.462755	−	0.886486i	$-0.653139\pi$
$479$	−11.4888	+	2.44202i	−0.524937	+	0.111579i	−0.0621816	+	0.998065i	$0.519806\pi$
$480$	19.1777	+	8.53845i	0.875337	+	0.389725i
$481$	36.8178	−	16.3923i	1.67875	−	0.747427i
$482$	4.59667	+	14.1471i	0.209372	+	0.644382i
$483$	22.9340	+	7.45518i	1.04353	+	0.339222i
$484$		0			0
$485$	2.79400	−	4.83936i	0.126869	−	0.219744i
$486$	−6.90314	+	7.66672i	−0.313133	+	0.347769i
$487$	−0.767648	+	7.30368i	−0.0347854	+	0.330961i	0.963265	+	0.268552i	$0.0865451\pi$
$487$	−0.767648	+	7.30368i	−0.0347854	+	0.330961i	−0.998051	+	0.0624094i	$0.980122\pi$
$488$	1.02599	+	9.76169i	0.0464446	+	0.441891i
$489$	−9.11980	+	28.0679i	−0.412412	+	1.26927i
$490$	−7.27890	−	3.24316i	−0.328827	−	0.146511i
$491$	−10.4859	+	7.61845i	−0.473222	+	0.343816i	−0.798696	−	0.601735i	$-0.794476\pi$
$491$	−10.4859	+	7.61845i	−0.473222	+	0.343816i	0.325474	+	0.945551i	$0.394476\pi$
$492$	−32.9105	+	14.6527i	−1.48372	+	0.660595i
$493$	−5.35055	+	5.94239i	−0.240977	+	0.267632i
$494$	0.447507	+	0.775106i	0.0201343	+	0.0348737i
$495$		0			0
$496$	−11.3277			−0.508630
$497$	−0.00341699	+	24.9526i	−0.000153273	+	1.11928i
$498$	−5.44726	−	3.95766i	−0.244097	−	0.177347i
$499$	−0.457159	−	4.34958i	−0.0204653	−	0.194714i	0.979512	−	0.201383i	$-0.0645437\pi$
$499$	−0.457159	−	4.34958i	−0.0204653	−	0.194714i	−0.999978	+	0.00666940i	$0.997877\pi$
$500$	−18.2526	+	3.87971i	−0.816282	+	0.173506i
$501$	−41.1546	+	8.74768i	−1.83865	+	0.390818i
$502$	−1.21413	−	11.5517i	−0.0541893	−	0.515577i
$503$	25.8970	+	18.8153i	1.15469	+	0.838931i	0.989097	−	0.147263i	$-0.0470464\pi$
$503$	25.8970	+	18.8153i	1.15469	+	0.838931i	0.165592	+	0.986194i	$0.447046\pi$
$504$	8.91011	+	5.14588i	0.396888	+	0.229216i
$505$	−15.5592			−0.692374
$506$		0			0
$507$	−3.00219	−	5.19995i	−0.133332	−	0.230938i
$508$	5.65368	−	6.27905i	0.250842	−	0.278588i
$509$	−19.7525	+	8.79440i	−0.875516	+	0.389805i	−0.794756	−	0.606929i	$-0.792401\pi$
$509$	−19.7525	+	8.79440i	−0.875516	+	0.389805i	−0.0807597	+	0.996734i	$0.525735\pi$
$510$	−5.08938	+	3.69765i	−0.225362	+	0.163735i
$511$	−0.788628	−	0.0829973i	−0.0348869	−	0.00367159i
$512$	4.83132	−	14.8693i	0.213516	−	0.657135i
$513$	−0.103142	−	0.981333i	−0.00455384	−	0.0433269i
$514$	0.404000	−	3.84381i	0.0178197	−	0.169543i
$515$	−18.8518	+	20.9371i	−0.830711	+	0.922598i
$516$	10.4210	−	18.0497i	0.458760	−	0.794596i
$517$		0			0
$518$	−3.75755	−	17.6898i	−0.165097	−	0.777244i
$519$	−2.44588	−	7.52764i	−0.107362	−	0.330427i
$520$	−14.6534	+	6.52413i	−0.642596	+	0.286102i
$521$	1.34423	+	0.598491i	0.0588919	+	0.0262204i	0.435971	−	0.899961i	$-0.356405\pi$
$521$	1.34423	+	0.598491i	0.0588919	+	0.0262204i	−0.377079	+	0.926181i	$0.623072\pi$
$522$	3.33941	−	0.709813i	0.146162	−	0.0310677i
$523$	−23.1035	−	25.6590i	−1.01025	−	1.12199i	−0.992512	−	0.122149i	$-0.961021\pi$
$523$	−23.1035	−	25.6590i	−1.01025	−	1.12199i	−0.0177343	−	0.999843i	$-0.505645\pi$
$524$	−6.17321	+	4.48510i	−0.269678	+	0.195932i
$525$	−12.1524	+	1.27559i	−0.530375	+	0.0556712i
$526$	−4.70608	−	14.4838i	−0.205195	−	0.631525i
$527$	9.82471	−	17.0169i	0.427971	−	0.741267i
$528$		0			0
$529$	2.52319	+	4.37030i	0.109704	+	0.190013i
$530$	4.88484	+	1.03830i	0.212184	+	0.0451011i
$531$	0.0460680	+	0.0334703i	0.00199918	+	0.00145249i
$532$	−1.29989	+	0.422162i	−0.0563572	+	0.0183030i
$533$	13.3040	−	40.9455i	0.576260	−	1.77355i
$534$	13.5792	+	15.0813i	0.587631	+	0.652630i
$535$	−2.06837	−	0.920898i	−0.0894235	−	0.0398139i
$536$	1.36378	−	12.9755i	0.0589063	−	0.560456i
$537$	−41.5262	−	8.82668i	−1.79199	−	0.380899i
$538$	−10.9589			−0.472470
$539$		0			0
$540$	7.70932			0.331756
$541$	−5.98408	−	1.27195i	−0.257276	−	0.0546856i	0.0774681	−	0.996995i	$-0.475316\pi$
$541$	−5.98408	−	1.27195i	−0.257276	−	0.0546856i	−0.334744	+	0.942309i	$0.608650\pi$
$542$	0.497807	−	4.73632i	0.0213827	−	0.203442i
$543$	−4.34779	−	1.93576i	−0.186582	−	0.0830715i
$544$	9.93126	+	11.0298i	0.425799	+	0.472898i
$545$	3.30579	−	10.1742i	0.141604	−	0.435813i
$546$	−14.4973	+	4.70827i	−0.620428	+	0.201495i
$547$	−20.2909	−	14.7422i	−0.867575	−	0.630330i	0.0623603	−	0.998054i	$-0.480137\pi$
$547$	−20.2909	−	14.7422i	−0.867575	−	0.630330i	−0.929935	+	0.367724i	$0.880137\pi$
$548$	2.47262	+	0.525572i	0.105625	+	0.0224513i
$549$	−3.34213	−	5.78874i	−0.142639	−	0.247057i
$550$		0			0
$551$	−0.520108	+	0.900853i	−0.0221573	+	0.0383776i
$552$	−6.73091	−	20.7156i	−0.286487	−	0.881715i
$553$	37.4587	−	3.93188i	1.59290	−	0.167200i
$554$	6.48294	−	4.71013i	0.275434	−	0.200114i
$555$	24.6577	+	27.3851i	1.04666	+	1.16243i
$556$	13.3910	−	2.84635i	0.567905	−	0.120712i
$557$	28.0427	+	12.4854i	1.18821	+	0.529023i	0.903082	−	0.429468i	$-0.141299\pi$
$557$	28.0427	+	12.4854i	1.18821	+	0.529023i	0.285123	+	0.958491i	$0.407965\pi$
$558$	−7.66403	+	3.41225i	−0.324444	+	0.144452i
$559$	7.69694	+	23.6887i	0.325546	+	1.00193i
$560$	−1.37513	−	6.47384i	−0.0581099	−	0.273570i
$561$		0			0
$562$	3.50164	−	6.06502i	0.147708	−	0.255838i
$563$	11.6914	−	12.9846i	0.492733	−	0.547235i	−0.444573	−	0.895742i	$-0.646645\pi$
$563$	11.6914	−	12.9846i	0.492733	−	0.547235i	0.937306	+	0.348507i	$0.113311\pi$
$564$	−0.821690	+	7.81786i	−0.0345994	+	0.329191i
$565$	2.68649	+	25.5602i	0.113021	+	1.07533i
$566$	4.22789	−	13.0121i	0.177711	−	0.546939i
$567$	29.5585	+	3.11082i	1.24134	+	0.130642i
$568$	18.2336	−	13.2475i	0.765063	−	0.555851i
$569$	−21.3265	+	9.49519i	−0.894055	+	0.398059i	−0.801742	−	0.597671i	$-0.796093\pi$
$569$	−21.3265	+	9.49519i	−0.894055	+	0.398059i	−0.0923138	+	0.995730i	$0.529426\pi$
$570$	−0.547588	+	0.608158i	−0.0229359	+	0.0254729i
$571$	7.38432	+	12.7900i	0.309024	+	0.535245i	0.978149	−	0.207905i	$-0.0666643\pi$
$571$	7.38432	+	12.7900i	0.309024	+	0.535245i	−0.669125	+	0.743150i	$0.733331\pi$
$572$		0			0
$573$	18.5093			0.773236
$574$	−16.7291	−	9.66162i	−0.698260	−	0.403268i
$575$	7.35967	+	5.34712i	0.306920	+	0.222990i
$576$	−0.158532	−	1.50834i	−0.00660552	−	0.0628473i
$577$	35.4430	−	7.53363i	1.47551	−	0.313629i	0.601240	−	0.799069i	$-0.294674\pi$
$577$	35.4430	−	7.53363i	1.47551	−	0.313629i	0.874270	+	0.485439i	$0.161340\pi$
$578$	6.85651	−	1.45740i	0.285193	−	0.0606197i
$579$	0.0574582	+	0.546678i	0.00238788	+	0.0227192i
$580$	−6.57499	−	4.77701i	−0.273011	−	0.198354i
$581$	−0.00168265	+	12.2875i	−6.98079e−5	+	0.509773i
$582$	−4.79632			−0.198814
$583$		0			0
$584$	0.358123	+	0.620288i	0.0148193	+	0.0256677i
$585$	7.30908	−	8.11756i	0.302193	−	0.335620i
$586$	−14.7001	+	6.54493i	−0.607258	+	0.270368i
$587$	14.7176	−	10.6930i	0.607461	−	0.441346i	−0.241058	−	0.970511i	$-0.577494\pi$
$587$	14.7176	−	10.6930i	0.607461	−	0.441346i	0.848519	+	0.529164i	$0.177494\pi$
$588$	−2.42668	−	23.1493i	−0.100075	−	0.954662i
$589$	0.789892	−	2.43104i	0.0325469	−	0.100169i
$590$	0.00416367	+	0.0396147i	0.000171416	+	0.00163091i
$591$	−2.19590	+	20.8926i	−0.0903274	+	0.859408i
$592$	10.0502	−	11.1618i	0.413059	−	0.458748i
$593$	−21.2413	+	36.7910i	−0.872276	+	1.51083i	−0.0126393	+	0.999920i	$0.504023\pi$
$593$	−21.2413	+	36.7910i	−0.872276	+	1.51083i	−0.859637	+	0.510906i	$0.829310\pi$
$594$		0			0
$595$	10.9179	+	3.54909i	0.447590	+	0.145499i
$596$	−2.28881	−	7.04423i	−0.0937533	−	0.288543i
$597$	−0.695639	+	0.309719i	−0.0284706	+	0.0126759i
$598$	10.3670	+	4.61567i	0.423936	+	0.188749i
$599$	17.2038	−	3.65677i	0.702927	−	0.149412i	0.157437	−	0.987529i	$-0.449677\pi$
$599$	17.2038	−	3.65677i	0.702927	−	0.149412i	0.545490	+	0.838117i	$0.316344\pi$
$600$	7.38501	+	8.20189i	0.301492	+	0.334841i
$601$	24.8322	−	18.0416i	1.01293	−	0.735934i	0.0481049	−	0.998842i	$-0.484682\pi$
$601$	24.8322	−	18.0416i	1.01293	−	0.735934i	0.964821	+	0.262909i	$0.0846818\pi$
$602$	11.1156	−	1.16676i	0.453039	−	0.0475536i
$603$	2.74558	+	8.45003i	0.111809	+	0.344112i
$604$	12.4263	−	21.5229i	0.505617	−	0.875755i
$605$		0			0
$606$	6.67740	+	11.5656i	0.271251	+	0.469820i
$607$	34.6965	+	7.37497i	1.40829	+	0.299341i	0.848456	−	0.529266i	$-0.177532\pi$
$607$	34.6965	+	7.37497i	1.40829	+	0.299341i	0.559832	+	0.828606i	$0.310866\pi$
$608$	1.56202	+	1.13488i	0.0633484	+	0.0460253i
$609$	−13.1636	−	11.8558i	−0.533416	−	0.480422i
$610$	1.44489	−	4.44692i	0.0585020	−	0.180051i
$611$	−6.28607	−	6.98139i	−0.254307	−	0.282437i
$612$	−5.90358	−	2.62844i	−0.238638	−	0.106248i
$613$	1.43644	−	13.6668i	0.0580172	−	0.551997i	−0.926449	−	0.376421i	$-0.877155\pi$
$613$	1.43644	−	13.6668i	0.0580172	−	0.551997i	0.984466	−	0.175576i	$-0.0561787\pi$
$614$	5.76086	+	1.22451i	0.232489	+	0.0494171i
$615$	39.3652			1.58736
$616$		0			0
$617$	2.42135			0.0974798			0.0487399	−	0.998812i	$-0.484479\pi$
$617$	2.42135			0.0974798			0.0487399	+	0.998812i	$0.484479\pi$
$618$	23.6536	+	5.02774i	0.951489	+	0.202245i
$619$	1.45422	−	13.8360i	0.0584499	−	0.556114i	−0.925635	−	0.378417i	$-0.876469\pi$
$619$	1.45422	−	13.8360i	0.0584499	−	0.556114i	0.984085	−	0.177697i	$-0.0568648\pi$
$620$	18.2444	+	8.12293i	0.732713	+	0.326225i
$621$	−8.37151	−	9.29750i	−0.335937	−	0.373096i
$622$	0.545273	−	1.67818i	0.0218634	−	0.0672887i
$623$	7.70491	−	36.2244i	0.308691	−	1.45130i
$624$	−10.2418	−	7.44111i	−0.410000	−	0.297883i
$625$	9.44472	+	2.00754i	0.377789	+	0.0803015i
$626$	7.66754	+	13.2806i	0.306457	+	0.530798i
$627$		0			0
$628$	5.27010	−	9.12808i	0.210300	−	0.364250i
$629$	8.05102	+	24.7785i	0.321015	+	0.987984i
$630$	−2.88049	−	3.96579i	−0.114761	−	0.158001i
$631$	−31.3804	+	22.7992i	−1.24923	+	0.907620i	−0.998177	−	0.0603525i	$-0.980778\pi$
$631$	−31.3804	+	22.7992i	−1.24923	+	0.907620i	−0.251055	+	0.967973i	$0.580778\pi$
$632$	−22.7636	−	25.2816i	−0.905488	−	1.00565i
$633$	31.3651	−	6.66687i	1.24665	−	0.264984i
$634$	2.76333	+	1.23031i	0.109746	+	0.0488620i
$635$	−8.43449	+	3.75527i	−0.334712	+	0.149024i
$636$	4.50766	+	13.8732i	0.178740	+	0.550106i
$637$	22.4997	+	16.3564i	0.891473	+	0.648066i
$638$		0			0
$639$	−7.67408	+	13.2919i	−0.303582	+	0.525819i
$640$	−12.3500	+	13.7160i	−0.488175	+	0.542174i
$641$	2.64384	−	25.1545i	0.104426	−	0.993543i	−0.809351	−	0.587326i	$-0.800181\pi$
$641$	2.64384	−	25.1545i	0.104426	−	0.993543i	0.913776	−	0.406218i	$-0.133152\pi$
$642$	0.203135	+	1.93270i	0.00801708	+	0.0762775i
$643$	−0.0277191	+	0.0853105i	−0.00109313	+	0.00336432i	−0.951602	−	0.307334i	$-0.900563\pi$
$643$	−0.0277191	+	0.0853105i	−0.00109313	+	0.00336432i	0.950508	+	0.310699i	$0.100563\pi$
$644$	−10.1876	+	14.0180i	−0.401447	+	0.552385i
$645$	−18.4249	+	13.3865i	−0.725481	+	0.527093i
$646$	−0.528569	+	0.235334i	−0.0207963	+	0.00925909i
$647$	−2.90392	+	3.22513i	−0.114165	+	0.126793i	−0.797518	−	0.603295i	$-0.793854\pi$
$647$	−2.90392	+	3.22513i	−0.114165	+	0.126793i	0.683353	+	0.730088i	$0.260521\pi$
$648$	−13.4228	−	23.2490i	−0.527298	−	0.913306i
$649$		0			0
$650$	−5.75003			−0.225535
$651$	37.6976	+	21.7716i	1.47748	+	0.853296i
$652$	−17.1569	−	12.4652i	−0.671915	−	0.488175i
$653$	2.21857	+	21.1083i	0.0868195	+	0.826032i	0.948115	+	0.317928i	$0.102987\pi$
$653$	2.21857	+	21.1083i	0.0868195	+	0.826032i	−0.861295	+	0.508104i	$0.830346\pi$
$654$	−8.98148	+	1.90907i	−0.351203	+	0.0746506i
$655$	8.15578	−	1.73357i	0.318673	−	0.0677360i
$656$	−1.67714	−	15.9569i	−0.0654812	−	0.623012i
$657$	−0.394605	−	0.286698i	−0.0153950	−	0.0111851i
$658$	−3.65099	+	2.10723i	−0.142331	+	0.0821486i
$659$	25.4606			0.991805			0.495902	−	0.868378i	$-0.334837\pi$
$659$	25.4606			0.991805			0.495902	+	0.868378i	$0.334837\pi$
$660$		0			0
$661$	−4.77124	−	8.26403i	−0.185580	−	0.321433i	0.758192	−	0.652031i	$-0.226083\pi$
$661$	−4.77124	−	8.26403i	−0.185580	−	0.321433i	−0.943772	+	0.330598i	$0.892750\pi$
$662$	−6.22400	+	6.91245i	−0.241903	+	0.268660i
$663$	20.0611	−	8.93180i	0.779110	−	0.346882i
$664$	8.97885	−	6.52352i	0.348447	−	0.253162i
$665$	1.48524	+	0.156310i	0.0575950	+	0.00606146i
$666$	3.43739	−	10.5792i	0.133196	−	0.409935i
$667$	1.37863	+	13.1168i	0.0533809	+	0.507885i
$668$	3.16029	−	30.0681i	0.122275	−	1.16337i
$669$	41.2446	−	45.8068i	1.59461	−	1.77099i
$670$	−3.10758	+	5.38249i	−0.120056	+	0.207944i
$671$		0			0
$672$	−24.4393	+	21.9992i	−0.942765	+	0.848636i
$673$	−5.11101	−	15.7301i	−0.197015	−	0.606350i	−0.999947	−	0.0102793i	$-0.996728\pi$
$673$	−5.11101	−	15.7301i	−0.197015	−	0.606350i	0.802932	−	0.596070i	$-0.203272\pi$
$674$	6.92975	−	3.08532i	0.266924	−	0.118842i
$675$	5.79124	+	2.57843i	0.222905	+	0.0992438i
$676$	4.22037	−	0.897068i	0.162322	−	0.0345026i
$677$	1.62842	+	1.80854i	0.0625852	+	0.0695079i	0.773624	−	0.633645i	$-0.218442\pi$
$677$	1.62842	+	1.80854i	0.0625852	+	0.0695079i	−0.711039	+	0.703152i	$0.751775\pi$
$678$	17.8467	−	12.9664i	0.685400	−	0.497972i
$679$	5.14386	+	7.08196i	0.197403	+	0.271781i
$680$	−3.20430	−	9.86181i	−0.122879	−	0.378183i
$681$	−22.6578	+	39.2444i	−0.868248	+	1.50385i
$682$		0			0
$683$	2.64045	+	4.57339i	0.101034	+	0.174996i	0.912111	−	0.409944i	$-0.134452\pi$
$683$	2.64045	+	4.57339i	0.101034	+	0.174996i	−0.811077	+	0.584939i	$0.801118\pi$
$684$	−0.822290	−	0.174783i	−0.0314411	−	0.00668300i
$685$	−2.23470	−	1.62360i	−0.0853834	−	0.0620347i
$686$	9.27936	−	8.34827i	0.354287	−	0.318738i
$687$	−4.79790	+	14.7664i	−0.183051	+	0.563374i
$688$	6.21127	+	6.89832i	0.236803	+	0.262996i
$689$	−15.9255	−	7.09051i	−0.606715	−	0.270127i
$690$	−1.08460	+	10.3193i	−0.0412899	+	0.392847i
$691$	20.6370	+	4.38653i	0.785069	+	0.166872i	0.582970	−	0.812494i	$-0.301890\pi$
$691$	20.6370	+	4.38653i	0.785069	+	0.166872i	0.202099	+	0.979365i	$0.435224\pi$
$692$	5.68761			0.216211
$693$		0			0
$694$	10.4053			0.394980
$695$	−14.6326	−	3.11025i	−0.555046	−	0.117979i
$696$	−1.67258	+	15.9136i	−0.0633992	+	0.603203i
$697$	25.4256	+	11.3202i	0.963062	+	0.428783i
$698$	4.46561	+	4.95957i	0.169026	+	0.187722i
$699$	−17.0731	+	52.5457i	−0.645766	+	1.98746i
$700$	1.82675	−	8.58838i	0.0690445	−	0.324610i
$701$	22.7280	+	16.5128i	0.858423	+	0.623681i	0.927456	−	0.373934i	$-0.121991\pi$
$701$	22.7280	+	16.5128i	0.858423	+	0.623681i	−0.0690324	+	0.997614i	$0.521991\pi$
$702$	7.73511	+	1.64415i	0.291943	+	0.0620544i
$703$	1.69463	+	2.93518i	0.0639141	+	0.110703i
$704$		0			0
$705$	4.29489	−	7.43896i	0.161755	−	0.280167i
$706$	2.04822	+	6.30378i	0.0770859	+	0.237246i
$707$	9.91582	−	22.2631i	0.372923	−	0.837290i
$708$	−0.0941288	+	0.0683886i	−0.00353758	+	0.00257020i
$709$	−3.41227	−	3.78971i	−0.128150	−	0.142325i	0.675655	−	0.737218i	$-0.263861\pi$
$709$	−3.41227	−	3.78971i	−0.128150	−	0.142325i	−0.803805	+	0.594893i	$0.797194\pi$
$710$	−10.5017	+	2.23221i	−0.394123	+	0.0837735i
$711$	21.1643	+	9.42293i	0.793721	+	0.353388i
$712$	−30.5589	+	13.6057i	−1.14524	+	0.509895i
$713$	−10.0152	−	30.8235i	−0.375071	−	1.15435i
$714$	−2.04740	−	9.63873i	−0.0766219	−	0.360720i
$715$		0			0
$716$	15.2534	−	26.4196i	0.570046	−	0.987348i
$717$	12.4871	−	13.8683i	0.466340	−	0.517923i
$718$	0.215527	−	2.05060i	0.00804338	−	0.0765276i
$719$	−2.51282	−	23.9079i	−0.0937123	−	0.891613i	−0.935862	−	0.352368i	$-0.885377\pi$
$719$	−2.51282	−	23.9079i	−0.0937123	−	0.891613i	0.842149	−	0.539244i	$-0.181290\pi$
$720$	1.25796	−	3.87162i	0.0468816	−	0.144287i
$721$	−17.9439	−	40.3176i	−0.668267	−	1.50151i
$722$	10.2988	−	7.48254i	0.383283	−	0.278471i
$723$	43.3732	−	19.3110i	1.61307	−	0.718184i
$724$	2.28838	−	2.54150i	0.0850468	−	0.0944541i
$725$	−3.34144	−	5.78754i	−0.124098	−	0.214944i
$726$		0			0
$727$	14.6738			0.544221			0.272111	−	0.962266i	$-0.412278\pi$
$727$	14.6738			0.544221			0.272111	+	0.962266i	$0.412278\pi$
$728$	0.00344059	−	25.1249i	0.000127517	−	0.931192i
$729$	−0.625530	−	0.454474i	−0.0231678	−	0.0168324i
$730$	−0.0356648	−	0.339328i	−0.00132001	−	0.0125591i
$731$	−15.7500	+	3.34777i	−0.582535	+	0.123822i
$732$	13.3592	−	2.83959i	0.493771	−	0.104954i
$733$	5.07226	+	48.2593i	0.187348	+	1.78250i	0.534977	+	0.844867i	$0.320320\pi$
$733$	5.07226	+	48.2593i	0.187348	+	1.78250i	−0.347628	+	0.937632i	$0.613013\pi$
$734$	4.18750	+	3.04239i	0.154563	+	0.112297i
$735$	−7.86625	+	24.1873i	−0.290151	+	0.892161i
$736$	24.4805			0.902363
$737$		0			0
$738$	−5.94139	−	10.2908i	−0.218706	−	0.378809i
$739$	7.55017	−	8.38531i	0.277737	−	0.308459i	−0.588096	−	0.808791i	$-0.700122\pi$
$739$	7.55017	−	8.38531i	0.277737	−	0.308459i	0.865833	+	0.500333i	$0.166789\pi$
$740$	−24.1907	+	10.7704i	−0.889268	+	0.395928i
$741$	2.31110	−	1.67911i	0.0849004	−	0.0616838i
$742$	−4.59877	+	6.32784i	−0.168826	+	0.232302i
$743$	−1.07005	+	3.29327i	−0.0392562	+	0.120818i	−0.968764	−	0.247984i	$-0.920232\pi$
$743$	−1.07005	+	3.29327i	−0.0392562	+	0.120818i	0.929508	+	0.368802i	$0.120232\pi$
$744$	−4.11008	−	39.1048i	−0.150683	−	1.43365i
$745$	−0.845999	+	8.04914i	−0.0309950	+	0.294898i
$746$	3.01629	−	3.34993i	0.110434	−	0.122650i
$747$	−3.77899	+	6.54540i	−0.138266	+	0.239484i
$748$		0			0
$749$	2.63585	−	2.37268i	0.0963119	−	0.0866957i
$750$	−5.40832	−	16.6451i	−0.197484	−	0.607793i
$751$	1.95566	−	0.870716i	0.0713630	−	0.0317729i	−0.370745	−	0.928735i	$-0.620898\pi$
$751$	1.95566	−	0.870716i	0.0713630	−	0.0317729i	0.442108	+	0.896962i	$0.354231\pi$
$752$	−3.19840	−	1.42402i	−0.116634	−	0.0519287i
$753$	−36.2632	+	7.70798i	−1.32150	+	0.280894i
$754$	−5.57820	−	6.19522i	−0.203146	−	0.225617i
$755$	−21.9703	+	15.9624i	−0.799581	+	0.580930i
$756$	−4.91313	+	11.0310i	−0.178689	+	0.401194i
$757$	−11.3705	−	34.9949i	−0.413269	−	1.27191i	−0.913790	−	0.406186i	$-0.866858\pi$
$757$	−11.3705	−	34.9949i	−0.413269	−	1.27191i	0.500522	−	0.865724i	$-0.333142\pi$
$758$	4.55246	−	7.88509i	0.165353	−	0.286399i
$759$		0			0
$760$	−0.674460	−	1.16820i	−0.0244652	−	0.0423750i
$761$	28.7562	+	6.11232i	1.04241	+	0.221571i	0.697143	−	0.716933i	$-0.254454\pi$
$761$	28.7562	+	6.11232i	1.04241	+	0.221571i	0.345269	+	0.938504i	$0.387788\pi$
$762$	6.41117	+	4.65799i	0.232252	+	0.168741i
$763$	12.4511	+	11.2141i	0.450760	+	0.405978i
$764$	−4.11007	+	12.6495i	−0.148697	+	0.457643i
$765$	4.72502	+	5.24767i	0.170834	+	0.189730i
$766$	0.308592	+	0.137394i	0.0111499	+	0.00496425i
$767$	0.0145343	−	0.138285i	0.000524804	−	0.00499317i
$768$	19.4176	+	4.12733i	0.700671	+	0.148932i
$769$	1.47798			0.0532972			0.0266486	−	0.999645i	$-0.491516\pi$
$769$	1.47798			0.0532972			0.0266486	+	0.999645i	$0.491516\pi$
$770$		0			0
$771$	−12.3361			−0.444274
$772$	−0.386366	−	0.0821247i	−0.0139056	−	0.00295573i
$773$	−1.96111	+	18.6587i	−0.0705363	+	0.671108i	0.900936	+	0.433953i	$0.142882\pi$
$773$	−1.96111	+	18.6587i	−0.0705363	+	0.671108i	−0.971472	+	0.237155i	$0.923785\pi$
$774$	6.28035	+	2.79619i	0.225743	+	0.100507i
$775$	10.9884	+	12.2039i	0.394717	+	0.438377i
$776$	2.44306	−	7.51895i	0.0877006	−	0.269915i
$777$	−54.8987	+	17.8294i	−1.96948	+	0.639624i
$778$	10.1997	+	7.41054i	0.365678	+	0.265681i
$779$	3.54145	+	0.752758i	0.126885	+	0.0269703i
$780$	11.1595	+	19.3288i	0.399575	+	0.692084i
$781$		0			0
$782$	−3.66802	+	6.35320i	−0.131168	+	0.227190i
$783$	2.84012	+	8.74100i	0.101498	+	0.312378i
$784$	10.1396	+	2.15814i	0.362128	+	0.0770763i
$785$	−9.31782	+	6.76979i	−0.332567	+	0.241624i
$786$	−4.78876	−	5.31846i	−0.170809	−	0.189703i
$787$	−18.5419	+	3.94120i	−0.660946	+	0.140488i	−0.526159	−	0.850386i	$-0.676368\pi$
$787$	−18.5419	+	3.94120i	−0.660946	+	0.140488i	−0.134787	+	0.990875i	$0.543035\pi$
$788$	−13.7907	−	6.14002i	−0.491274	−	0.218729i
$789$	−44.4057	+	19.7707i	−1.58088	+	0.703855i
$790$	5.00790	+	15.4127i	0.178173	+	0.548360i
$791$	−38.2854	−	12.4455i	−1.36127	−	0.442510i
$792$		0			0
$793$	−8.16096	+	14.1352i	−0.289804	+	0.501956i
$794$	2.12887	−	2.36435i	0.0755509	−	0.0839077i
$795$	1.66614	−	15.8523i	0.0590919	−	0.562222i
$796$	−0.0571961	−	0.544184i	−0.00202726	−	0.0192881i
$797$	−12.2905	+	37.8263i	−0.435352	+	1.33988i	0.457373	+	0.889275i	$0.348790\pi$
$797$	−12.2905	+	37.8263i	−0.435352	+	1.33988i	−0.892725	+	0.450601i	$0.851210\pi$
$798$	−0.521217	−	1.17110i	−0.0184509	−	0.0414566i
$799$	4.91323	−	3.56967i	0.173818	−	0.126286i
$800$	−11.3318	+	5.04525i	−0.400640	+	0.178376i
$801$	15.2427	−	16.9287i	0.538573	−	0.598146i
$802$	−5.69757	−	9.86849i	−0.201188	−	0.348468i
$803$		0			0
$804$	−18.1541			−0.640247
$805$	16.4000	−	9.46554i	0.578024	−	0.333617i
$806$	16.5731	+	12.0410i	0.583762	+	0.424128i
$807$	3.65621	+	34.7865i	0.128705	+	1.22454i
$808$	−21.5320	+	4.57677i	−0.757494	+	0.161010i
$809$	54.8176	−	11.6518i	1.92728	−	0.409657i	0.927968	−	0.372661i	$-0.121555\pi$
$809$	54.8176	−	11.6518i	1.92728	−	0.409657i	0.999315	−	0.0369956i	$-0.0117788\pi$
$810$	1.33675	+	12.7183i	0.0469686	+	0.446877i
$811$	−16.9878	−	12.3423i	−0.596521	−	0.433398i	0.248121	−	0.968729i	$-0.420187\pi$
$811$	−16.9878	−	12.3423i	−0.596521	−	0.433398i	−0.844642	+	0.535331i	$0.820187\pi$
$812$	11.0255	−	6.36355i	0.386919	−	0.223317i
$813$	−15.2005			−0.533105
$814$		0			0
$815$	11.5867	+	20.0687i	0.405863	+	0.702976i
$816$	5.47609	−	6.08181i	0.191701	−	0.212906i
$817$	−1.91356	+	0.851972i	−0.0669470	+	0.0298067i
$818$	−13.9004	+	10.0993i	−0.486017	+	0.353112i
$819$	6.95708	+	15.6316i	0.243100	+	0.546213i
$820$	−8.74123	+	26.9027i	−0.305257	+	0.939485i
$821$	3.38979	+	32.2517i	0.118304	+	1.12559i	0.879112	+	0.476615i	$0.158136\pi$
$821$	3.38979	+	32.2517i	0.118304	+	1.12559i	−0.760808	+	0.648977i	$0.775197\pi$
$822$	−0.247826	+	2.35791i	−0.00864392	+	0.0822414i
$823$	1.17404	−	1.30391i	0.0409246	−	0.0454514i	−0.722335	−	0.691543i	$-0.756931\pi$
$823$	1.17404	−	1.30391i	0.0409246	−	0.0454514i	0.763260	+	0.646092i	$0.223598\pi$
$824$	−19.9300	+	34.5197i	−0.694294	+	1.20255i
$825$		0			0
$826$	−0.0593368	−	0.0192887i	−0.00206459	−	0.000671139i
$827$	−3.60014	−	11.0801i	−0.125189	−	0.385293i	0.868746	−	0.495257i	$-0.164926\pi$
$827$	−3.60014	−	11.0801i	−0.125189	−	0.385293i	−0.993935	+	0.109965i	$0.964926\pi$
$828$	−9.73737	+	4.33536i	−0.338397	+	0.150664i
$829$	17.9410	+	7.98784i	0.623116	+	0.277429i	0.693910	−	0.720062i	$-0.255887\pi$
$829$	17.9410	+	7.98784i	0.623116	+	0.277429i	−0.0707938	+	0.997491i	$0.522553\pi$
$830$	−5.17143	+	1.09922i	−0.179503	+	0.0381545i
$831$	−17.1142	−	19.0072i	−0.593685	−	0.659354i
$832$	−2.99612	+	2.17681i	−0.103872	+	0.0754673i
$833$	−12.0362	+	13.3602i	−0.417030	+	0.462904i
$834$	3.96780	+	12.2116i	0.137394	+	0.422855i
$835$	−16.5185	+	28.6108i	−0.571645	+	0.990119i
$836$		0			0
$837$	−11.2924	−	19.5590i	−0.390323	−	0.676060i
$838$	14.9399	+	3.17557i	0.516089	+	0.109698i
$839$	35.8478	+	26.0450i	1.23760	+	0.899173i	0.997436	−	0.0715587i	$-0.0227973\pi$
$839$	35.8478	+	26.0450i	1.23760	+	0.899173i	0.240168	+	0.970731i	$0.422797\pi$
$840$	21.8496	−	7.09606i	0.753883	−	0.244837i
$841$	−5.96745	+	18.3659i	−0.205774	+	0.633307i
$842$	−8.47261	−	9.40978i	−0.291985	−	0.324283i
$843$	−20.4203	−	9.09172i	−0.703314	−	0.313136i
$844$	−2.40855	+	22.9158i	−0.0829056	+	0.788794i
$845$	−4.61168	−	0.980242i	−0.158646	−	0.0337213i
$846$	−2.59291			−0.0891460
$847$		0			0
$848$	−6.49678			−0.223100
$849$	−42.7146	−	9.07927i	−1.46596	−	0.311600i
$850$	0.388549	−	3.69679i	0.0133271	−	0.126799i
$851$	39.2578	+	17.4787i	1.34574	+	0.599162i
$852$	−20.9841	−	23.3052i	−0.718904	−	0.798424i
$853$	−6.10569	+	18.7914i	−0.209055	+	0.643405i	0.790468	+	0.612504i	$0.209838\pi$
$853$	−6.10569	+	18.7914i	−0.209055	+	0.643405i	−0.999522	+	0.0309007i	$0.990162\pi$
$854$	5.44213	+	4.90146i	0.186226	+	0.167725i
$855$	0.743167	+	0.539942i	0.0254158	+	0.0184656i
$856$	−3.13326	−	0.665996i	−0.107093	−	0.0227633i
$857$	−1.69370	−	2.93357i	−0.0578556	−	0.100209i	0.835647	−	0.549267i	$-0.185093\pi$
$857$	−1.69370	−	2.93357i	−0.0578556	−	0.100209i	−0.893503	+	0.449058i	$0.851760\pi$
$858$		0			0
$859$	−8.04855	+	13.9405i	−0.274613	+	0.475643i	−0.970037	−	0.242956i	$-0.921883\pi$
$859$	−8.04855	+	13.9405i	−0.274613	+	0.475643i	0.695425	+	0.718599i	$0.255216\pi$
$860$	−5.05718	−	15.5644i	−0.172448	−	0.530742i
$861$	−25.0874	+	56.3264i	−0.854975	+	1.91960i
$862$	18.6997	−	13.5861i	0.636915	−	0.462746i
$863$	−30.1671	−	33.5040i	−1.02690	−	1.14049i	−0.989985	−	0.141170i	$-0.954913\pi$
$863$	−30.1671	−	33.5040i	−1.02690	−	1.14049i	−0.0369155	−	0.999318i	$-0.511753\pi$
$864$	16.6865	−	3.54683i	0.567687	−	0.120666i
$865$	−5.67764	−	2.52785i	−0.193046	−	0.0859495i
$866$	1.96199	−	0.873535i	0.0666712	−	0.0296839i
$867$	−6.91373	−	21.2783i	−0.234803	−	0.722648i
$868$	−23.2499	+	20.9286i	−0.789154	+	0.710362i
$869$		0			0
$870$	3.81124	−	6.60126i	0.129213	−	0.223804i
$871$	14.5172	−	16.1229i	0.491895	−	0.546305i
$872$	1.58205	−	15.0522i	0.0535751	−	0.509733i
$873$	0.562766	+	5.35436i	0.0190467	+	0.181218i
$874$	−0.294904	+	0.907620i	−0.00997527	+	0.0307007i
$875$	−18.7769	+	25.8368i	−0.634776	+	0.873443i
$876$	0.806280	−	0.585797i	0.0272417	−	0.0197922i
$877$	51.2988	−	22.8397i	1.73224	−	0.771241i	0.736769	−	0.676145i	$-0.236351\pi$
$877$	51.2988	−	22.8397i	1.73224	−	0.771241i	0.995468	−	0.0950966i	$-0.0303160\pi$
$878$	−5.57750	+	6.19444i	−0.188232	+	0.209052i
$879$	25.6799	+	44.4788i	0.866160	+	1.50023i
$880$		0			0
$881$	20.4943			0.690469			0.345235	−	0.938516i	$-0.387799\pi$
$881$	20.4943			0.690469			0.345235	+	0.938516i	$0.387799\pi$
$882$	7.51025	−	1.59420i	0.252883	−	0.0536796i
$883$	−14.6613	−	10.6521i	−0.493393	−	0.358471i	0.313095	−	0.949722i	$-0.398634\pi$
$883$	−14.6613	−	10.6521i	−0.493393	−	0.358471i	−0.806488	+	0.591251i	$0.798634\pi$
$884$	1.64945	+	15.6934i	0.0554768	+	0.527827i
$885$	0.124359	−	0.0264333i	0.00418028	−	0.000888546i
$886$	3.36407	−	0.715056i	0.113018	−	0.0240228i
$887$	−1.57543	−	14.9892i	−0.0528977	−	0.503288i	−0.988607	−	0.150517i	$-0.951906\pi$
$887$	−1.57543	−	14.9892i	−0.0528977	−	0.503288i	0.935710	−	0.352771i	$-0.114761\pi$
$888$	42.1786	+	30.6446i	1.41542	+	1.02836i
$889$	0.00198040	−	14.4619i	6.64204e−5	−	0.485035i
$890$	15.9349			0.534140
$891$		0			0
$892$	22.1465	+	38.3588i	0.741518	+	1.28435i
$893$	0.528635	−	0.587109i	0.0176901	−	0.0196469i
$894$	6.34624	−	2.82553i	0.212250	−	0.0944998i
$895$	−26.9688	+	19.5940i	−0.901468	+	0.654955i
$896$	−11.7552	−	26.4124i	−0.392714	−	0.882375i
$897$	11.1927	−	34.4476i	0.373713	−	1.15017i
$898$	0.0861799	+	0.819947i	0.00287586	+	0.0273620i
$899$	−2.48870	+	23.6784i	−0.0830029	+	0.789720i
$900$	3.61386	−	4.01360i	0.120462	−	0.133787i
$901$	5.63475	−	9.75967i	0.187721	−	0.325142i
$902$		0			0
$903$	−7.41213	−	34.8948i	−0.246660	−	1.16123i
$904$	11.2364	+	34.5821i	0.373717	+	1.15018i
$905$	−3.41393	+	1.51998i	−0.113483	+	0.0505258i
$906$	21.2941	+	9.48075i	0.707450	+	0.314977i
$907$	−15.9214	+	3.38419i	−0.528661	+	0.112370i	−0.464507	−	0.885570i	$-0.653768\pi$
$907$	−15.9214	+	3.38419i	−0.528661	+	0.112370i	−0.0641543	+	0.997940i	$0.520435\pi$
$908$	−21.7889	−	24.1991i	−0.723091	−	0.803074i
$909$	12.1278	−	8.81134i	0.402253	−	0.292254i
$910$	−4.86961	+	10.9333i	−0.161426	+	0.362436i
$911$	−2.55183	−	7.85372i	−0.0845459	−	0.260206i	0.899843	−	0.436215i	$-0.143681\pi$
$911$	−2.55183	−	7.85372i	−0.0845459	−	0.260206i	−0.984389	+	0.176009i	$0.943681\pi$
$912$	0.532311	−	0.921990i	0.0176266	−	0.0305301i
$913$		0			0
$914$	1.73006	+	2.99655i	0.0572253	+	0.0991172i
$915$	−14.5978	−	3.10287i	−0.482590	−	0.102578i
$916$	−9.02618	−	6.55791i	−0.298233	−	0.216679i
$917$	−2.71716	+	12.7746i	−0.0897286	+	0.421856i
$918$	−1.57974	+	4.86193i	−0.0521391	+	0.160468i
$919$	25.0498	+	27.8206i	0.826316	+	0.917717i	0.997720	−	0.0674841i	$-0.0214972\pi$
$919$	25.0498	+	27.8206i	0.826316	+	0.917717i	−0.171405	+	0.985201i	$0.554831\pi$
$920$	−15.6245	−	6.95649i	−0.515126	−	0.229349i
$921$	1.96494	−	18.6951i	0.0647468	−	0.616025i
$922$	15.0146	+	3.19145i	0.494479	+	0.105105i
$923$	37.4779			1.23360
$924$		0			0
$925$	−21.7743			−0.715935
$926$	−19.6746	−	4.18196i	−0.646547	−	0.137428i
$927$	2.83736	−	26.9956i	0.0931910	−	0.886653i
$928$	−16.4291	−	7.31469i	−0.539310	−	0.240116i
$929$	36.2760	+	40.2886i	1.19018	+	1.32183i	0.934880	+	0.354965i	$0.115507\pi$
$929$	36.2760	+	40.2886i	1.19018	+	1.32183i	0.255299	+	0.966862i	$0.417826\pi$
$930$	−5.78816	+	17.8141i	−0.189801	+	0.584148i
$931$	−1.17020	+	2.02556i	−0.0383517	+	0.0663850i
$932$	−32.1193	−	23.3361i	−1.05210	−	0.764398i
$933$	−5.50892	−	1.17096i	−0.180354	−	0.0383354i
$934$	−0.522321	−	0.904686i	−0.0170909	−	0.0296022i
$935$		0			0
$936$	7.72709	−	13.3837i	0.252568	−	0.437460i
$937$	−7.25100	−	22.3163i	−0.236880	−	0.729042i	−0.996866	−	0.0791027i	$-0.974794\pi$
$937$	−7.25100	−	22.3163i	−0.236880	−	0.729042i	0.759987	−	0.649939i	$-0.225206\pi$
$938$	−5.72117	−	7.87678i	−0.186803	−	0.257186i
$939$	39.5981	−	28.7697i	1.29224	−	0.938865i
$940$	4.13019	+	4.58704i	0.134712	+	0.149613i
$941$	41.9748	−	8.92202i	1.36834	−	0.290850i	0.535580	−	0.844484i	$-0.320093\pi$
$941$	41.9748	−	8.92202i	1.36834	−	0.290850i	0.832760	+	0.553635i	$0.186760\pi$
$942$	9.03104	+	4.02088i	0.294247	+	0.131007i
$943$	41.9370	−	18.6716i	1.36566	−	0.608029i
$944$	−0.0160131	−	0.0492834i	−0.000521183	−	0.00160404i
$945$	9.80723	−	8.82804i	0.319029	−	0.287176i
$946$		0			0
$947$	−26.8719	+	46.5435i	−0.873219	+	1.51246i	−0.0145710	+	0.999894i	$0.504638\pi$
$947$	−26.8719	+	46.5435i	−0.873219	+	1.51246i	−0.858648	+	0.512566i	$0.828695\pi$
$948$	−31.6743	+	35.1779i	−1.02873	+	1.14252i
$949$	−0.124497	+	1.18451i	−0.00404134	+	0.0384508i
$950$	−0.0505454	−	0.480907i	−0.00163991	−	0.0156027i
$951$	2.98343	−	9.18206i	0.0967444	−	0.297749i
$952$	16.1530	+	1.69999i	0.523523	+	0.0550969i
$953$	7.73653	−	5.62092i	0.250611	−	0.182079i	−0.455387	−	0.890294i	$-0.650499\pi$
$953$	7.73653	−	5.62092i	0.250611	−	0.182079i	0.705998	+	0.708214i	$0.250499\pi$
$954$	−4.39554	+	1.95702i	−0.142311	+	0.0633609i
$955$	9.72492	−	10.8006i	0.314691	−	0.349500i
$956$	6.70500	+	11.6134i	0.216855	+	0.375604i
$957$		0			0
$958$	7.91603			0.255755
$959$	3.74733	−	2.16284i	0.121007	−	0.0698416i
$960$	−2.73951	−	1.99037i	−0.0884172	−	0.0642389i
$961$	−2.87516	−	27.3554i	−0.0927472	−	0.882431i
$962$	−26.5686	+	5.64734i	−0.856607	+	0.182077i
$963$	2.13373	−	0.453538i	0.0687585	−	0.0146151i
$964$	3.56619	+	33.9300i	0.114859	+	1.09281i
$965$	0.349189	+	0.253701i	0.0112408	+	0.00816692i
$966$	−14.0743	−	8.12835i	−0.452832	−	0.261525i
$967$	−34.7245			−1.11666			−0.558332	−	0.829618i	$-0.688558\pi$
$967$	−34.7245			−1.11666			−0.558332	+	0.829618i	$0.688558\pi$
$968$		0			0
$969$	0.923362	+	1.59931i	0.0296627	+	0.0513773i
$970$	−2.52002	+	2.79877i	−0.0809131	+	0.0898631i
$971$	−7.48903	+	3.33433i	−0.240334	+	0.107004i	−0.523370	−	0.852106i	$-0.675325\pi$
$971$	−7.48903	+	3.33433i	−0.240334	+	0.107004i	0.283035	+	0.959110i	$0.408659\pi$
$972$	−19.1427	+	13.9080i	−0.614001	+	0.446098i
$973$	13.7757	−	18.9551i	0.441628	−	0.607674i
$974$	1.52949	−	4.70729i	0.0490080	−	0.150831i
$975$	1.91838	+	18.2522i	0.0614375	+	0.584539i
$976$	−0.635829	+	6.04951i	−0.0203524	+	0.193640i
$977$	1.26495	−	1.40487i	0.0404694	−	0.0449458i	−0.722570	−	0.691297i	$-0.757039\pi$
$977$	1.26495	−	1.40487i	0.0404694	−	0.0449458i	0.763040	+	0.646352i	$0.223706\pi$
$978$	9.94511	−	17.2254i	0.318010	−	0.550809i
$979$		0			0
$980$	−14.7832	−	10.7468i	−0.472232	−	0.343294i
$981$	3.18501	+	9.80246i	0.101690	+	0.312969i
$982$	7.98022	−	3.55302i	0.254659	−	0.113382i
$983$	−36.7543	−	16.3641i	−1.17228	−	0.521933i	−0.274160	−	0.961684i	$-0.588400\pi$
$983$	−36.7543	−	16.3641i	−1.17228	−	0.521933i	−0.898119	+	0.439752i	$0.855067\pi$
$984$	54.4767	−	11.5794i	1.73665	−	0.369137i
$985$	11.0376	+	12.2585i	0.351688	+	0.390589i
$986$	4.35995	−	3.16769i	0.138849	−	0.100880i
$987$	7.90704	+	10.8862i	0.251684	+	0.346513i
$988$	0.634339	+	1.95230i	0.0201810	+	0.0621108i
$989$	−13.2792	+	23.0003i	−0.422255	+	0.731367i
$990$		0			0
$991$	−12.7333	−	22.0548i	−0.404487	−	0.700592i	0.589774	−	0.807568i	$-0.299217\pi$
$991$	−12.7333	−	22.0548i	−0.404487	−	0.700592i	−0.994262	+	0.106976i	$0.965883\pi$
$992$	43.2264	+	9.18805i	1.37244	+	0.291721i
$993$	24.0186	+	17.4505i	0.762207	+	0.553776i
$994$	3.49873	−	16.4492i	0.110973	−	0.521736i
$995$	−0.184766	+	0.568651i	−0.00585748	+	0.0180275i
$996$	−10.3333	−	11.4763i	−0.327424	−	0.363641i
$997$	15.0671	+	6.70832i	0.477181	+	0.212455i	0.631210	−	0.775612i	$-0.282558\pi$
$997$	15.0671	+	6.70832i	0.477181	+	0.212455i	−0.154030	+	0.988066i	$0.549225\pi$
$998$	−0.308109	+	2.93146i	−0.00975302	+	0.0927938i
$999$	29.2914	+	6.22609i	0.926740	+	0.196985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.j.632.2		40
7.4	even	3	inner	847.2.n.j.753.4		40
11.2	odd	10		77.2.m.b.9.2	✓	40
11.3	even	5		847.2.e.h.485.4		20
11.4	even	5		847.2.n.h.366.2		40
11.5	even	5		847.2.n.h.807.4		40
11.6	odd	10		847.2.n.i.807.2		40
11.7	odd	10		847.2.n.i.366.4		40
11.8	odd	10		847.2.e.i.485.7		20
11.9	even	5	inner	847.2.n.j.9.4		40
11.10	odd	2		77.2.m.b.16.4	yes	40
33.2	even	10		693.2.by.b.163.4		40
33.32	even	2		693.2.by.b.478.2		40
77.2	odd	30		539.2.f.h.295.2		20
77.4	even	15		847.2.n.h.487.4		40
77.10	even	6		539.2.q.h.214.2		40
77.13	even	10		539.2.q.h.471.2		40
77.18	odd	30		847.2.n.i.487.2		40
77.19	even	30		5929.2.a.bx.1.4		10
77.24	even	30		539.2.q.h.361.4		40
77.25	even	15		847.2.e.h.606.4		20
77.30	odd	30		5929.2.a.bw.1.4		10
77.32	odd	6		77.2.m.b.60.2	yes	40
77.39	odd	30		847.2.n.i.81.4		40
77.46	odd	30		77.2.m.b.53.4	yes	40
77.47	odd	30		5929.2.a.bz.1.7		10
77.53	even	15	inner	847.2.n.j.130.2		40
77.54	even	6		539.2.f.g.148.2		20
77.58	even	15		5929.2.a.by.1.7		10
77.60	even	15		847.2.n.h.81.2		40
77.65	odd	6		539.2.f.h.148.2		20
77.68	even	30		539.2.f.g.295.2		20
77.74	odd	30		847.2.e.i.606.7		20
77.76	even	2		539.2.q.h.324.4		40
231.32	even	6		693.2.by.b.676.4		40
231.200	even	30		693.2.by.b.361.2		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.9.2	✓	40	11.2	odd	10
77.2.m.b.16.4	yes	40	11.10	odd	2
77.2.m.b.53.4	yes	40	77.46	odd	30
77.2.m.b.60.2	yes	40	77.32	odd	6
539.2.f.g.148.2		20	77.54	even	6
539.2.f.g.295.2		20	77.68	even	30
539.2.f.h.148.2		20	77.65	odd	6
539.2.f.h.295.2		20	77.2	odd	30
539.2.q.h.214.2		40	77.10	even	6
539.2.q.h.324.4		40	77.76	even	2
539.2.q.h.361.4		40	77.24	even	30
539.2.q.h.471.2		40	77.13	even	10
693.2.by.b.163.4		40	33.2	even	10
693.2.by.b.361.2		40	231.200	even	30
693.2.by.b.478.2		40	33.32	even	2
693.2.by.b.676.4		40	231.32	even	6
847.2.e.h.485.4		20	11.3	even	5
847.2.e.h.606.4		20	77.25	even	15
847.2.e.i.485.7		20	11.8	odd	10
847.2.e.i.606.7		20	77.74	odd	30
847.2.n.h.81.2		40	77.60	even	15
847.2.n.h.366.2		40	11.4	even	5
847.2.n.h.487.4		40	77.4	even	15
847.2.n.h.807.4		40	11.5	even	5
847.2.n.i.81.4		40	77.39	odd	30
847.2.n.i.366.4		40	11.7	odd	10
847.2.n.i.487.2		40	77.18	odd	30
847.2.n.i.807.2		40	11.6	odd	10
847.2.n.j.9.4		40	11.9	even	5	inner
847.2.n.j.130.2		40	77.53	even	15	inner
847.2.n.j.632.2		40	1.1	even	1	trivial
847.2.n.j.753.4		40	7.4	even	3	inner
5929.2.a.bw.1.4		10	77.30	odd	30
5929.2.a.bx.1.4		10	77.19	even	30
5929.2.a.by.1.7		10	77.58	even	15
5929.2.a.bz.1.7		10	77.47	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.659236 - 0.140125i) q^{2} +(-0.224855 + 2.13935i) q^{3} +(-1.41213 - 0.628722i) q^{4} +(1.13022 + 1.25524i) q^{5} +(0.448009 - 1.37883i) q^{6} +(-2.51637 + 0.817238i) q^{7} +(1.93333 + 1.40464i) q^{8} +(-1.59182 - 0.338352i) q^{9} +O(q^{10})\)	\(q+(-0.659236 - 0.140125i) q^{2} +(-0.224855 + 2.13935i) q^{3} +(-1.41213 - 0.628722i) q^{4} +(1.13022 + 1.25524i) q^{5} +(0.448009 - 1.37883i) q^{6} +(-2.51637 + 0.817238i) q^{7} +(1.93333 + 1.40464i) q^{8} +(-1.59182 - 0.338352i) q^{9} +(-0.569194 - 0.985873i) q^{10} +(1.66258 - 2.87968i) q^{12} +(1.22798 + 3.77933i) q^{13} +(1.77340 - 0.186146i) q^{14} +(-2.93954 + 2.13570i) q^{15} +(0.990954 + 1.10057i) q^{16} +(-2.51278 + 0.534107i) q^{17} +(1.00198 + 0.446108i) q^{18} +(-0.305292 + 0.135925i) q^{19} +(-0.806829 - 2.48316i) q^{20} +(-1.18254 - 5.56716i) q^{21} +(-2.11859 + 3.66950i) q^{23} +(-3.43975 + 3.82022i) q^{24} +(0.224419 - 2.13520i) q^{25} +(-0.279950 - 2.66354i) q^{26} +(-0.912429 + 2.80817i) q^{27} +(4.06727 + 0.428050i) q^{28} +(2.51823 - 1.82960i) q^{29} +(2.23711 - 0.996028i) q^{30} +(-5.11813 + 5.68426i) q^{31} +(-2.88878 - 5.00351i) q^{32} +1.73135 q^{34} +(-3.86989 - 2.23499i) q^{35} +(2.03514 + 1.47861i) q^{36} +(-1.06012 - 10.0863i) q^{37} +(0.220306 - 0.0468275i) q^{38} +(-8.36143 + 1.77728i) q^{39} +(0.421925 + 4.01435i) q^{40} +(-8.76494 - 6.36810i) q^{41} +(-0.000525269 + 3.83578i) q^{42} +6.26797 q^{43} +(-1.37440 - 2.38053i) q^{45} +(1.91084 - 2.12220i) q^{46} +(-2.15968 + 0.961554i) q^{47} +(-2.57732 + 1.87253i) q^{48} +(5.66425 - 4.11295i) q^{49} +(-0.447141 + 1.37616i) q^{50} +(-0.577633 - 5.49581i) q^{51} +(0.642079 - 6.10898i) q^{52} +(-2.93539 + 3.26008i) q^{53} +(0.995001 - 1.72339i) q^{54} +(-6.01289 - 1.95462i) q^{56} +(-0.222144 - 0.683690i) q^{57} +(-1.91648 + 0.853273i) q^{58} +(-0.0319655 - 0.0142320i) q^{59} +(5.49378 - 1.16774i) q^{60} +(2.74836 + 3.05237i) q^{61} +(4.17056 - 3.03009i) q^{62} +(4.28213 - 0.449477i) q^{63} +(0.287989 + 0.886339i) q^{64} +(-3.35608 + 5.81290i) q^{65} +(-2.72981 - 4.72817i) q^{67} +(3.88418 + 0.825608i) q^{68} +(-7.37397 - 5.35750i) q^{69} +(2.23800 + 2.01566i) q^{70} +(2.91440 - 8.96959i) q^{71} +(-2.60225 - 2.89009i) q^{72} +(0.273807 + 0.121907i) q^{73} +(-0.714481 + 6.79783i) q^{74} +(4.51749 + 0.960222i) q^{75} +0.516572 q^{76} +5.76120 q^{78} +(-13.9247 - 2.95979i) q^{79} +(-0.261475 + 2.48777i) q^{80} +(-10.2626 - 4.56919i) q^{81} +(4.88583 + 5.42627i) q^{82} +(1.43515 - 4.41695i) q^{83} +(-1.83029 + 8.60506i) q^{84} +(-3.51043 - 2.55048i) q^{85} +(-4.13208 - 0.878300i) q^{86} +(3.34793 + 5.79878i) q^{87} +(-6.99890 + 12.1225i) q^{89} +(0.572483 + 1.76192i) q^{90} +(-6.17866 - 8.50664i) q^{91} +(5.29882 - 3.84982i) q^{92} +(-11.0098 - 12.2276i) q^{93} +(1.55848 - 0.331265i) q^{94} +(-0.515666 - 0.229589i) q^{95} +(11.3538 - 5.05505i) q^{96} +(-1.02232 - 3.14637i) q^{97} +(-4.31040 + 1.91770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 3 q^{2} - 4 q^{3} - 3 q^{4} + 4 q^{5} + 16 q^{6} + 2 q^{7} + 38 q^{8} + 7 q^{9}+O(q^{10}) \) 40 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 + 4 * q^5 + 16 * q^6 + 2 * q^7 + 38 * q^8 + 7 * q^9	\( 40 q + 3 q^{2} - 4 q^{3} - 3 q^{4} + 4 q^{5} + 16 q^{6} + 2 q^{7} + 38 q^{8} + 7 q^{9} - 14 q^{10} - 18 q^{12} - 6 q^{13} - 3 q^{14} - 14 q^{15} - 5 q^{16} + 7 q^{17} - 24 q^{18} + 4 q^{19} - 30 q^{20} + 2 q^{21} - 14 q^{23} + 12 q^{24} + 21 q^{25} - 16 q^{27} - 16 q^{28} - 16 q^{30} - 17 q^{31} + 30 q^{32} + 48 q^{34} + 14 q^{35} + 14 q^{36} + 24 q^{37} + 12 q^{38} - 28 q^{39} - 10 q^{40} - 60 q^{41} - 70 q^{42} + 72 q^{43} - 16 q^{45} - 8 q^{46} + 13 q^{47} + 128 q^{48} - 10 q^{49} - 6 q^{50} + 7 q^{51} - 2 q^{52} + 33 q^{53} - 34 q^{54} + 24 q^{56} - 44 q^{57} - 17 q^{58} + 21 q^{59} - 48 q^{60} + 52 q^{62} - 24 q^{63} + 94 q^{64} + 40 q^{65} - 38 q^{67} + 23 q^{68} - 124 q^{69} - 3 q^{70} + 20 q^{71} + 38 q^{72} - 11 q^{73} + 41 q^{74} - 11 q^{75} + 96 q^{76} - 100 q^{78} - 21 q^{79} + 12 q^{80} - 58 q^{81} + 6 q^{82} + 46 q^{83} + 29 q^{84} + 78 q^{85} + 7 q^{86} - 48 q^{87} - 10 q^{89} + 18 q^{90} - 14 q^{91} - 110 q^{92} + 12 q^{93} - 37 q^{94} - 7 q^{95} + 53 q^{96} - 54 q^{97} - 116 q^{98}+O(q^{100}) \) 40 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 + 4 * q^5 + 16 * q^6 + 2 * q^7 + 38 * q^8 + 7 * q^9 - 14 * q^10 - 18 * q^12 - 6 * q^13 - 3 * q^14 - 14 * q^15 - 5 * q^16 + 7 * q^17 - 24 * q^18 + 4 * q^19 - 30 * q^20 + 2 * q^21 - 14 * q^23 + 12 * q^24 + 21 * q^25 - 16 * q^27 - 16 * q^28 - 16 * q^30 - 17 * q^31 + 30 * q^32 + 48 * q^34 + 14 * q^35 + 14 * q^36 + 24 * q^37 + 12 * q^38 - 28 * q^39 - 10 * q^40 - 60 * q^41 - 70 * q^42 + 72 * q^43 - 16 * q^45 - 8 * q^46 + 13 * q^47 + 128 * q^48 - 10 * q^49 - 6 * q^50 + 7 * q^51 - 2 * q^52 + 33 * q^53 - 34 * q^54 + 24 * q^56 - 44 * q^57 - 17 * q^58 + 21 * q^59 - 48 * q^60 + 52 * q^62 - 24 * q^63 + 94 * q^64 + 40 * q^65 - 38 * q^67 + 23 * q^68 - 124 * q^69 - 3 * q^70 + 20 * q^71 + 38 * q^72 - 11 * q^73 + 41 * q^74 - 11 * q^75 + 96 * q^76 - 100 * q^78 - 21 * q^79 + 12 * q^80 - 58 * q^81 + 6 * q^82 + 46 * q^83 + 29 * q^84 + 78 * q^85 + 7 * q^86 - 48 * q^87 - 10 * q^89 + 18 * q^90 - 14 * q^91 - 110 * q^92 + 12 * q^93 - 37 * q^94 - 7 * q^95 + 53 * q^96 - 54 * q^97 - 116 * q^98

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