LMFDB - Embedded newform 294.2.p.a.257.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(5,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 29]))

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

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

chi := DirichletCharacter("294.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.p (of order $42$, degree $12$, 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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			257.18
Character	$\chi$	$=$	294.257
Dual form			294.2.p.a.143.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.563320 + 0.826239i) q^{2} +(1.68711 + 0.392004i) q^{3} +(-0.365341 + 0.930874i) q^{4} +(1.89764 + 0.585345i) q^{5} +(0.626493 + 1.61478i) q^{6} +(-2.33674 - 1.24082i) q^{7} +(-0.974928 + 0.222521i) q^{8} +(2.69267 + 1.32270i) q^{9} +O(q^{10})$	\(q+(0.563320 + 0.826239i) q^{2} +(1.68711 + 0.392004i) q^{3} +(-0.365341 + 0.930874i) q^{4} +(1.89764 + 0.585345i) q^{5} +(0.626493 + 1.61478i) q^{6} +(-2.33674 - 1.24082i) q^{7} +(-0.974928 + 0.222521i) q^{8} +(2.69267 + 1.32270i) q^{9} +(0.585345 + 1.89764i) q^{10} +(0.512629 - 0.0384162i) q^{11} +(-0.981276 + 1.42727i) q^{12} +(-0.441530 + 0.916846i) q^{13} +(-0.291117 - 2.62969i) q^{14} +(2.97207 + 1.73142i) q^{15} +(-0.733052 - 0.680173i) q^{16} +(2.74625 + 0.413931i) q^{17} +(0.423963 + 2.96989i) q^{18} +(-6.52721 - 3.76849i) q^{19} +(-1.23817 + 1.55262i) q^{20} +(-3.45593 - 3.00941i) q^{21} +(0.320515 + 0.401913i) q^{22} +(-0.417819 - 2.77205i) q^{23} +(-1.73204 - 0.00675846i) q^{24} +(-0.872773 - 0.595046i) q^{25} +(-1.00626 + 0.151669i) q^{26} +(4.02431 + 3.28708i) q^{27} +(2.00876 - 1.72189i) q^{28} +(0.493279 + 0.393377i) q^{29} +(0.243658 + 3.43099i) q^{30} +(-0.0488029 + 0.0281764i) q^{31} +(0.149042 - 0.988831i) q^{32} +(0.879919 + 0.136140i) q^{33} +(1.20501 + 2.50224i) q^{34} +(-3.70799 - 3.72244i) q^{35} +(-2.21501 + 2.02329i) q^{36} +(2.66055 + 6.77896i) q^{37} +(-0.563239 - 7.51590i) q^{38} +(-1.10432 + 1.37374i) q^{39} +(-1.98032 - 0.148404i) q^{40} +(-1.50923 - 6.61236i) q^{41} +(0.539700 - 4.55068i) q^{42} +(0.323261 - 1.41630i) q^{43} +(-0.151524 + 0.491228i) q^{44} +(4.33548 + 4.08616i) q^{45} +(2.05501 - 1.90677i) q^{46} +(-0.902273 + 0.615159i) q^{47} +(-0.970107 - 1.43488i) q^{48} +(3.92072 + 5.79896i) q^{49} -1.05632i q^{50} +(4.47096 + 1.77489i) q^{51} +(-0.692159 - 0.745970i) q^{52} +(-10.9042 - 4.27958i) q^{53} +(-0.448937 + 5.17672i) q^{54} +(0.995273 + 0.227165i) q^{55} +(2.55426 + 0.689739i) q^{56} +(-9.53485 - 8.91654i) q^{57} +(-0.0471493 + 0.629163i) q^{58} +(11.4491 - 3.53157i) q^{59} +(-2.69756 + 2.13406i) q^{60} +(-4.24886 + 1.66755i) q^{61} +(-0.0507721 - 0.0244505i) q^{62} +(-4.65082 - 6.43194i) q^{63} +(0.900969 - 0.433884i) q^{64} +(-1.37454 + 1.48140i) q^{65} +(0.383192 + 0.803714i) q^{66} +(-3.27424 - 5.67115i) q^{67} +(-1.38864 + 2.40519i) q^{68} +(0.381747 - 4.84053i) q^{69} +(0.986838 - 5.16061i) q^{70} +(-6.42198 + 5.12136i) q^{71} +(-2.91949 - 0.690367i) q^{72} +(8.41113 - 12.3369i) q^{73} +(-4.10230 + 6.01697i) q^{74} +(-1.23920 - 1.34604i) q^{75} +(5.89264 - 4.69923i) q^{76} +(-1.24555 - 0.546313i) q^{77} +(-1.75712 - 0.138575i) q^{78} +(-4.00283 + 6.93310i) q^{79} +(-0.992935 - 1.71981i) q^{80} +(5.50090 + 7.12321i) q^{81} +(4.61321 - 4.97186i) q^{82} +(13.9886 - 6.73658i) q^{83} +(4.06398 - 2.11757i) q^{84} +(4.96912 + 2.39300i) q^{85} +(1.35230 - 0.530739i) q^{86} +(0.678010 + 0.857036i) q^{87} +(-0.491228 + 0.151524i) q^{88} +(-0.954366 + 12.7351i) q^{89} +(-0.933882 + 5.88396i) q^{90} +(2.16939 - 1.59457i) q^{91} +(2.73307 + 0.623806i) q^{92} +(-0.0933810 + 0.0284057i) q^{93} +(-1.01654 - 0.398961i) q^{94} +(-10.1805 - 10.9719i) q^{95} +(0.639076 - 1.60984i) q^{96} +12.0264i q^{97} +(-2.58271 + 6.50612i) q^{98} +(1.43115 + 0.574615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9}+O(q^{10}) $ 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9	$ 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9} + 6 q^{10} - 12 q^{15} + 18 q^{16} - 4 q^{18} - 12 q^{19} + 10 q^{22} - 6 q^{24} + 16 q^{25} - 42 q^{27} + 2 q^{28} + 4 q^{30} + 6 q^{31} + 18 q^{33} - 10 q^{36} - 36 q^{37} + 4 q^{39} - 22 q^{40} + 20 q^{42} + 40 q^{43} - 14 q^{45} - 156 q^{46} - 134 q^{49} - 12 q^{51} + 16 q^{52} - 18 q^{54} - 322 q^{55} - 34 q^{57} - 164 q^{58} - 6 q^{60} + 56 q^{61} - 24 q^{63} + 36 q^{64} - 28 q^{69} - 4 q^{70} + 4 q^{72} - 24 q^{73} + 84 q^{75} + 16 q^{78} + 22 q^{79} - 52 q^{81} + 24 q^{82} + 42 q^{84} + 32 q^{85} - 94 q^{87} - 2 q^{88} + 42 q^{90} - 100 q^{91} - 266 q^{93} - 88 q^{94} - 6 q^{96} + 224 q^{99}+O(q^{100}) $ 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9 + 6 * q^10 - 12 * q^15 + 18 * q^16 - 4 * q^18 - 12 * q^19 + 10 * q^22 - 6 * q^24 + 16 * q^25 - 42 * q^27 + 2 * q^28 + 4 * q^30 + 6 * q^31 + 18 * q^33 - 10 * q^36 - 36 * q^37 + 4 * q^39 - 22 * q^40 + 20 * q^42 + 40 * q^43 - 14 * q^45 - 156 * q^46 - 134 * q^49 - 12 * q^51 + 16 * q^52 - 18 * q^54 - 322 * q^55 - 34 * q^57 - 164 * q^58 - 6 * q^60 + 56 * q^61 - 24 * q^63 + 36 * q^64 - 28 * q^69 - 4 * q^70 + 4 * q^72 - 24 * q^73 + 84 * q^75 + 16 * q^78 + 22 * q^79 - 52 * q^81 + 24 * q^82 + 42 * q^84 + 32 * q^85 - 94 * q^87 - 2 * q^88 + 42 * q^90 - 100 * q^91 - 266 * q^93 - 88 * q^94 - 6 * q^96 + 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{11}{42}\right)$

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 $

$2$	0.563320	+	0.826239i	0.398327	+	0.584239i
$2$	0.563320	+	0.826239i	0.398327	+	0.584239i
$3$	1.68711	+	0.392004i	0.974052	+	0.226323i
$3$	1.68711	+	0.392004i	0.974052	+	0.226323i
$4$	−0.365341	+	0.930874i	−0.182671	+	0.465437i
$5$	1.89764	+	0.585345i	0.848652	+	0.261774i	0.688427	−	0.725306i	$-0.258302\pi$
$5$	1.89764	+	0.585345i	0.848652	+	0.261774i	0.160225	+	0.987080i	$0.448778\pi$
$6$	0.626493	+	1.61478i	0.255765	+	0.659230i
$7$	−2.33674	−	1.24082i	−0.883205	−	0.468987i
$7$	−2.33674	−	1.24082i	−0.883205	−	0.468987i
$8$	−0.974928	+	0.222521i	−0.344689	+	0.0786730i
$9$	2.69267	+	1.32270i	0.897555	+	0.440902i
$10$	0.585345	+	1.89764i	0.185102	+	0.600088i
$11$	0.512629	−	0.0384162i	0.154563	−	0.0115829i	0.00277636	−	0.999996i	$-0.499116\pi$
$11$	0.512629	−	0.0384162i	0.154563	−	0.0115829i	0.151787	+	0.988413i	$0.451497\pi$
$12$	−0.981276	+	1.42727i	−0.283270	+	0.412017i
$13$	−0.441530	+	0.916846i	−0.122458	+	0.254287i	−0.953182	−	0.302398i	$-0.902213\pi$
$13$	−0.441530	+	0.916846i	−0.122458	+	0.254287i	0.830723	+	0.556685i	$0.187927\pi$
$14$	−0.291117	−	2.62969i	−0.0778044	−	0.702813i
$15$	2.97207	+	1.73142i	0.767386	+	0.447052i
$16$	−0.733052	−	0.680173i	−0.183263	−	0.170043i
$17$	2.74625	+	0.413931i	0.666064	+	0.100393i	0.473367	−	0.880865i	$-0.343038\pi$
$17$	2.74625	+	0.413931i	0.666064	+	0.100393i	0.192697	+	0.981258i	$0.438277\pi$
$18$	0.423963	+	2.96989i	0.0999290	+	0.700010i
$19$	−6.52721	−	3.76849i	−1.49745	−	0.864550i	−0.497449	−	0.867493i	$-0.665730\pi$
$19$	−6.52721	−	3.76849i	−1.49745	−	0.864550i	−0.999996	+	0.00294269i	$0.999063\pi$
$20$	−1.23817	+	1.55262i	−0.276863	+	0.347175i
$21$	−3.45593	−	3.00941i	−0.754145	−	0.656708i
$22$	0.320515	+	0.401913i	0.0683340	+	0.0856882i
$23$	−0.417819	−	2.77205i	−0.0871212	−	0.578011i	−0.989215	−	0.146471i	$-0.953208\pi$
$23$	−0.417819	−	2.77205i	−0.0871212	−	0.578011i	0.902094	−	0.431540i	$-0.142030\pi$
$24$	−1.73204	−	0.00675846i	−0.353551	−	0.00137956i
$25$	−0.872773	−	0.595046i	−0.174555	−	0.119009i
$26$	−1.00626	+	0.151669i	−0.197343	+	0.0297447i
$27$	4.02431	+	3.28708i	0.774479	+	0.632599i
$28$	2.00876	−	1.72189i	0.379619	−	0.325406i
$29$	0.493279	+	0.393377i	0.0915996	+	0.0730482i	0.668219	−	0.743965i	$-0.267057\pi$
$29$	0.493279	+	0.393377i	0.0915996	+	0.0730482i	−0.576619	+	0.817013i	$0.695628\pi$
$30$	0.243658	+	3.43099i	0.0444856	+	0.626410i
$31$	−0.0488029	+	0.0281764i	−0.00876526	+	0.00506063i	−0.504376	−	0.863484i	$-0.668278\pi$
$31$	−0.0488029	+	0.0281764i	−0.00876526	+	0.00506063i	0.495611	+	0.868545i	$0.334944\pi$
$32$	0.149042	−	0.988831i	0.0263472	−	0.174802i
$33$	0.879919	+	0.136140i	0.153174	+	0.0236989i
$34$	1.20501	+	2.50224i	0.206658	+	0.429130i
$35$	−3.70799	−	3.72244i	−0.626765	−	0.629207i
$36$	−2.21501	+	2.02329i	−0.369169	+	0.337216i
$37$	2.66055	+	6.77896i	0.437391	+	1.11445i	0.964366	+	0.264573i	$0.0852312\pi$
$37$	2.66055	+	6.77896i	0.437391	+	1.11445i	−0.526974	+	0.849881i	$0.676674\pi$
$38$	−0.563239	−	7.51590i	−0.0913694	−	1.21924i
$39$	−1.10432	+	1.37374i	−0.176832	+	0.219974i
$40$	−1.98032	−	0.148404i	−0.313116	−	0.0234648i
$41$	−1.50923	−	6.61236i	−0.235702	−	1.03268i	−0.944820	−	0.327589i	$-0.893764\pi$
$41$	−1.50923	−	6.61236i	−0.235702	−	1.03268i	0.709119	−	0.705089i	$-0.249093\pi$
$42$	0.539700	−	4.55068i	0.0832775	−	0.702186i
$43$	0.323261	−	1.41630i	0.0492968	−	0.215984i	−0.944280	−	0.329143i	$-0.893240\pi$
$43$	0.323261	−	1.41630i	0.0492968	−	0.215984i	0.993577	+	0.113160i	$0.0360972\pi$
$44$	−0.151524	+	0.491228i	−0.0228431	+	0.0740554i
$45$	4.33548	+	4.08616i	0.646295	+	0.609129i
$46$	2.05501	−	1.90677i	0.302994	−	0.281137i
$47$	−0.902273	+	0.615159i	−0.131610	+	0.0897302i	−0.627336	−	0.778749i	$-0.715855\pi$
$47$	−0.902273	+	0.615159i	−0.131610	+	0.0897302i	0.495726	+	0.868479i	$0.334902\pi$
$48$	−0.970107	−	1.43488i	−0.140023	−	0.207108i
$49$	3.92072	+	5.79896i	0.560103	+	0.828423i
$50$		−	1.05632i		−	0.149386i
$51$	4.47096	+	1.77489i	0.626060	+	0.248534i
$52$	−0.692159	−	0.745970i	−0.0959852	−	0.103447i
$53$	−10.9042	−	4.27958i	−1.49781	−	0.587845i	−0.531915	−	0.846797i	$-0.678528\pi$
$53$	−10.9042	−	4.27958i	−1.49781	−	0.587845i	−0.965890	+	0.258952i	$0.916623\pi$
$54$	−0.448937	+	5.17672i	−0.0610926	+	0.704463i
$55$	0.995273	+	0.227165i	0.134203	+	0.0306309i
$56$	2.55426	+	0.689739i	0.341328	+	0.0921702i
$57$	−9.53485	−	8.91654i	−1.26292	−	1.18102i
$58$	−0.0471493	+	0.629163i	−0.00619100	+	0.0826132i
$59$	11.4491	−	3.53157i	1.49054	−	0.459772i	0.560791	−	0.827958i	$-0.310497\pi$
$59$	11.4491	−	3.53157i	1.49054	−	0.459772i	0.929752	+	0.368186i	$0.120021\pi$
$60$	−2.69756	+	2.13406i	−0.348253	+	0.275506i
$61$	−4.24886	+	1.66755i	−0.544011	+	0.213508i	−0.621401	−	0.783492i	$-0.713436\pi$
$61$	−4.24886	+	1.66755i	−0.544011	+	0.213508i	0.0773907	+	0.997001i	$0.475341\pi$
$62$	−0.0507721	−	0.0244505i	−0.00644806	−	0.00310522i
$63$	−4.65082	−	6.43194i	−0.585949	−	0.810348i
$64$	0.900969	−	0.433884i	0.112621	−	0.0542355i
$65$	−1.37454	+	1.48140i	−0.170491	+	0.183745i
$66$	0.383192	+	0.803714i	0.0471677	+	0.0989303i
$67$	−3.27424	−	5.67115i	−0.400012	−	0.692842i	0.593715	−	0.804676i	$-0.297661\pi$
$67$	−3.27424	−	5.67115i	−0.400012	−	0.692842i	−0.993727	+	0.111834i	$0.964328\pi$
$68$	−1.38864	+	2.40519i	−0.168397	+	0.291672i
$69$	0.381747	−	4.84053i	0.0459569	−	0.582731i
$70$	0.986838	−	5.16061i	0.117950	−	0.616811i
$71$	−6.42198	+	5.12136i	−0.762149	+	0.607793i	−0.925488	−	0.378777i	$-0.876345\pi$
$71$	−6.42198	+	5.12136i	−0.762149	+	0.607793i	0.163339	+	0.986570i	$0.447773\pi$
$72$	−2.91949	−	0.690367i	−0.344065	−	0.0813606i
$73$	8.41113	−	12.3369i	0.984449	−	1.44392i	0.0904237	−	0.995903i	$-0.471178\pi$
$73$	8.41113	−	12.3369i	0.984449	−	1.44392i	0.894025	−	0.448017i	$-0.147870\pi$
$74$	−4.10230	+	6.01697i	−0.476883	+	0.699459i
$75$	−1.23920	−	1.34604i	−0.143091	−	0.155427i
$76$	5.89264	−	4.69923i	0.675933	−	0.539038i
$77$	−1.24555	−	0.546313i	−0.141943	−	0.0622581i
$78$	−1.75712	−	0.138575i	−0.198955	−	0.0156905i
$79$	−4.00283	+	6.93310i	−0.450353	+	0.780035i	−0.998408	−	0.0564076i	$-0.982035\pi$
$79$	−4.00283	+	6.93310i	−0.450353	+	0.780035i	0.548054	+	0.836443i	$0.315369\pi$
$80$	−0.992935	−	1.71981i	−0.111014	−	0.192281i
$81$	5.50090	+	7.12321i	0.611212	+	0.791467i
$82$	4.61321	−	4.97186i	0.509444	−	0.549050i
$83$	13.9886	−	6.73658i	1.53545	−	0.739435i	0.540650	−	0.841248i	$-0.318178\pi$
$83$	13.9886	−	6.73658i	1.53545	−	0.739435i	0.994804	+	0.101812i	$0.0324641\pi$
$84$	4.06398	−	2.11757i	0.443416	−	0.231046i
$85$	4.96912	+	2.39300i	0.538976	+	0.259557i
$86$	1.35230	−	0.530739i	0.145822	−	0.0572310i
$87$	0.678010	+	0.857036i	0.0726903	+	0.0918839i
$88$	−0.491228	+	0.151524i	−0.0523650	+	0.0161525i
$89$	−0.954366	+	12.7351i	−0.101163	+	1.34992i	0.683479	+	0.729970i	$0.260466\pi$
$89$	−0.954366	+	12.7351i	−0.101163	+	1.34992i	−0.784641	+	0.619950i	$0.787153\pi$
$90$	−0.933882	+	5.88396i	−0.0984398	+	0.620224i
$91$	2.16939	−	1.59457i	0.227413	−	0.167157i
$92$	2.73307	+	0.623806i	0.284942	+	0.0650362i
$93$	−0.0933810	+	0.0284057i	−0.00968316	+	0.00294553i
$94$	−1.01654	−	0.398961i	−0.104848	−	0.0411497i
$95$	−10.1805	−	10.9719i	−1.04449	−	1.12570i
$96$	0.639076	−	1.60984i	0.0652254	−	0.164304i
$97$			12.0264i			1.22110i	0.791979	+	0.610548i	$0.209051\pi$
$97$			12.0264i			1.22110i	−0.791979	+	0.610548i	$0.790949\pi$
$98$	−2.58271	+	6.50612i	−0.260893	+	0.657218i
$99$	1.43115	+	0.574615i	0.143836	+	0.0577509i
$100$	0.872773	−	0.595046i	0.0872773	−	0.0595046i
$101$	4.01337	−	3.72387i	0.399346	−	0.370539i	−0.454781	−	0.890603i	$-0.650283\pi$
$101$	4.01337	−	3.72387i	0.399346	−	0.370539i	0.854127	+	0.520065i	$0.174092\pi$
$102$	1.05210	+	4.69391i	0.104174	+	0.464767i
$103$	0.376008	−	1.21899i	0.0370491	−	0.120110i	−0.935159	−	0.354228i	$-0.884744\pi$
$103$	0.376008	−	1.21899i	0.0370491	−	0.120110i	0.972208	+	0.234117i	$0.0752200\pi$
$104$	0.226442	−	0.992109i	0.0222045	−	0.0972843i
$105$	−4.79657	−	7.73370i	−0.468098	−	0.754732i
$106$	−2.60659	−	11.4202i	−0.253175	−	1.10923i
$107$	−11.6291	−	0.871480i	−1.12423	−	0.0842491i	−0.500387	−	0.865802i	$-0.666809\pi$
$107$	−11.6291	−	0.871480i	−1.12423	−	0.0842491i	−0.623839	+	0.781553i	$0.714428\pi$
$108$	−4.53010	+	2.54522i	−0.435909	+	0.244914i
$109$	−0.619690	−	8.26918i	−0.0593555	−	0.792044i	−0.944873	−	0.327438i	$-0.893815\pi$
$109$	−0.619690	−	8.26918i	−0.0593555	−	0.792044i	0.885517	−	0.464606i	$-0.153804\pi$
$110$	0.372965	+	0.950300i	0.0355608	+	0.0906075i
$111$	1.83125	+	12.4798i	0.173815	+	1.18453i
$112$	0.868979	+	2.49897i	0.0821108	+	0.236131i
$113$	2.26695	+	4.70737i	0.213257	+	0.442832i	0.979967	−	0.199162i	$-0.0638218\pi$
$113$	2.26695	+	4.70737i	0.213257	+	0.442832i	−0.766710	+	0.641994i	$0.778108\pi$
$114$	1.99602	−	12.9009i	0.186944	−	1.20828i
$115$	0.829733	−	5.50492i	0.0773730	−	0.513337i
$116$	−0.546399	+	0.315464i	−0.0507319	+	0.0292901i
$117$	−2.40161	+	1.88475i	−0.222029	+	0.174245i
$118$	9.36742	+	7.47026i	0.862340	+	0.687694i
$119$	−5.90367	−	4.37486i	−0.541188	−	0.401043i
$120$	−3.28283	−	1.02667i	−0.299680	−	0.0937213i
$121$	−10.6158	+	1.60008i	−0.965075	+	0.145462i
$122$	−3.77127	−	2.57121i	−0.341434	−	0.232786i
$123$	0.0458387	−	11.7474i	0.00413313	−	1.05923i
$124$	−0.00839894	−	0.0557233i	−0.000754247	−	0.00500410i
$125$	−7.49875	−	9.40314i	−0.670709	−	0.841042i
$126$	2.69442	−	7.46593i	0.240038	−	0.665118i
$127$	−12.2100	+	15.3108i	−1.08346	+	1.35862i	−0.154689	+	0.987963i	$0.549437\pi$
$127$	−12.2100	+	15.3108i	−1.08346	+	1.35862i	−0.928771	+	0.370653i	$0.879134\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	1.10057	−	2.26273i	0.0968998	−	0.199222i
$130$	−1.99830	−	0.301195i	−0.175262	−	0.0264165i
$131$	13.3016	+	12.3421i	1.16217	+	1.07834i	0.995733	+	0.0922842i	$0.0294168\pi$
$131$	13.3016	+	12.3421i	1.16217	+	1.07834i	0.166437	+	0.986052i	$0.446774\pi$
$132$	−0.448200	+	0.769356i	−0.0390108	+	0.0669639i
$133$	10.5764	+	16.9051i	0.917088	+	1.46586i
$134$	2.84128	−	5.89998i	0.245449	−	0.509681i
$135$	5.71263	+	8.59332i	0.491665	+	0.739595i
$136$	−2.76951	+	0.207546i	−0.237483	+	0.0177969i
$137$	4.78311	+	15.5065i	0.408649	+	1.32481i	0.893048	+	0.449961i	$0.148562\pi$
$137$	4.78311	+	15.5065i	0.408649	+	1.32481i	−0.484399	+	0.874847i	$0.660962\pi$
$138$	4.21448	−	2.41135i	0.358760	−	0.205268i
$139$	−11.7826	+	2.68931i	−0.999391	+	0.228104i	−0.690765	−	0.723079i	$-0.742726\pi$
$139$	−11.7826	+	2.68931i	−0.999391	+	0.228104i	−0.308626	+	0.951184i	$0.599869\pi$
$140$	4.81980	−	2.09171i	0.407348	−	0.176782i
$141$	−1.76338	+	0.684146i	−0.148503	+	0.0576155i
$142$	−7.84909	−	2.42112i	−0.658681	−	0.203176i
$143$	−0.191119	+	0.486964i	−0.0159822	+	0.0407220i
$144$	−1.07420	−	2.80109i	−0.0895164	−	0.233424i
$145$	0.705806	+	1.03523i	0.0586140	+	0.0859710i
$146$	14.9314			1.23573
$147$	4.34146	+	11.3204i	0.358078	+	0.933692i
$148$	−7.28237			−0.598607
$149$	12.1947	+	17.8863i	0.999025	+	1.46530i	0.881474	+	0.472233i	$0.156552\pi$
$149$	12.1947	+	17.8863i	0.999025	+	1.46530i	0.117551	+	0.993067i	$0.462496\pi$
$150$	0.414081	−	1.78213i	0.0338096	−	0.145510i
$151$	1.24279	−	3.16658i	0.101137	−	0.257693i	−0.871345	−	0.490671i	$-0.836752\pi$
$151$	1.24279	−	3.16658i	0.101137	−	0.257693i	0.972482	+	0.232978i	$0.0748470\pi$
$152$	7.20213	+	2.22156i	0.584170	+	0.180192i
$153$	6.84724	+	4.74706i	0.553566	+	0.383777i
$154$	−0.250258	−	1.33687i	−0.0201663	−	0.107728i
$155$	−0.109103	+	0.0249021i	−0.00876340	+	0.00200019i
$156$	−0.875324	−	1.52986i	−0.0700820	−	0.122487i
$157$	6.31164	+	20.4618i	0.503724	+	1.63303i	0.748269	+	0.663395i	$0.230885\pi$
$157$	6.31164	+	20.4618i	0.503724	+	1.63303i	−0.244545	+	0.969638i	$0.578639\pi$
$158$	−7.98327	+	0.598264i	−0.635115	+	0.0475953i
$159$	−16.7189	−	11.4946i	−1.32590	−	0.911581i
$160$	0.861637	−	1.78921i	0.0681184	−	0.141449i
$161$	−2.46328	+	6.99599i	−0.194134	+	0.551361i
$162$	−2.78670	+	8.55770i	−0.218944	+	0.672357i
$163$	−2.70134	−	2.50648i	−0.211586	−	0.196323i	0.567259	−	0.823539i	$-0.308004\pi$
$163$	−2.70134	−	2.50648i	−0.211586	−	0.196323i	−0.778845	+	0.627216i	$0.784194\pi$
$164$	6.70666	+	1.01087i	0.523702	+	0.0789354i
$165$	1.59008	+	0.773402i	0.123788	+	0.0602093i
$166$	13.4461	+	7.76311i	1.04362	+	0.602534i
$167$	0.807224	−	1.01223i	0.0624649	−	0.0783285i	−0.749617	−	0.661871i	$-0.769763\pi$
$167$	0.807224	−	1.01223i	0.0624649	−	0.0783285i	0.812082	+	0.583543i	$0.198334\pi$
$168$	4.03894	+	2.16494i	0.311611	+	0.167029i
$169$	7.45971	+	9.35418i	0.573824	+	0.719552i
$170$	0.822013	+	5.45370i	0.0630456	+	0.418280i
$171$	−12.5910	−	18.7809i	−0.962858	−	1.43621i
$172$	1.20030	+	0.818347i	0.0915216	+	0.0623984i
$173$	8.53457	−	1.28638i	0.648871	−	0.0978016i	0.183644	−	0.982993i	$-0.441211\pi$
$173$	8.53457	−	1.28638i	0.648871	−	0.0978016i	0.465227	+	0.885191i	$0.345973\pi$
$174$	−0.326180	+	1.04298i	−0.0247277	+	0.0790684i
$175$	1.30110	+	2.47342i	0.0983537	+	0.186973i
$176$	−0.401913	−	0.320515i	−0.0302953	−	0.0241597i
$177$	20.7002	−	1.47006i	1.55592	−	0.110497i
$178$	−11.0599	+	6.38542i	−0.828972	+	0.478607i
$179$	1.49638	−	9.92781i	0.111844	−	0.742039i	−0.860664	−	0.509173i	$-0.829951\pi$
$179$	1.49638	−	9.92781i	0.111844	−	0.742039i	0.972509	−	0.232866i	$-0.0748105\pi$
$180$	−5.38763	+	2.54294i	−0.401570	+	0.189540i
$181$	0.334269	+	0.694117i	0.0248460	+	0.0515933i	0.913022	−	0.407909i	$-0.133742\pi$
$181$	0.334269	+	0.694117i	0.0248460	+	0.0515933i	−0.888176	+	0.459503i	$0.848028\pi$
$182$	2.53956	+	0.894175i	0.188244	+	0.0662807i
$183$	−7.82197	+	1.14778i	−0.578217	+	0.0848461i
$184$	1.02418	+	2.60957i	0.0755036	+	0.192380i
$185$	1.08073	+	14.4214i	0.0794571	+	1.06028i
$186$	−0.0760733	−	0.0611535i	−0.00557796	−	0.00448400i
$187$	1.42371	+	0.106692i	0.104112	+	0.00780212i
$188$	−0.242998	−	1.06465i	−0.0177225	−	0.0776473i
$189$	−5.32510	−	12.6745i	−0.387344	−	0.921935i
$190$	3.33057	−	14.5922i	0.241625	−	1.05863i
$191$	−6.50517	+	21.0892i	−0.470698	+	1.52596i	0.339958	+	0.940441i	$0.389587\pi$
$191$	−6.50517	+	21.0892i	−0.470698	+	1.52596i	−0.810656	+	0.585523i	$0.800889\pi$
$192$	1.69012	−	0.378826i	0.121974	−	0.0273394i
$193$	14.1257	−	13.1067i	1.01679	−	0.943441i	0.0183785	−	0.999831i	$-0.494150\pi$
$193$	14.1257	−	13.1067i	1.01679	−	0.943441i	0.998409	+	0.0563903i	$0.0179591\pi$
$194$	−9.93668	+	6.77472i	−0.713412	+	0.486396i
$195$	−2.89971	+	1.96046i	−0.207652	+	0.140391i
$196$	−6.83050	+	1.53110i	−0.487893	+	0.109364i
$197$			2.81895i			0.200842i	0.994945	+	0.100421i	$0.0320190\pi$
$197$			2.81895i			0.200842i	−0.994945	+	0.100421i	$0.967981\pi$
$198$	0.331428	+	1.50616i	0.0235535	+	0.107038i
$199$	−14.2214	−	15.3270i	−1.00813	−	1.08650i	−0.996245	−	0.0865735i	$-0.972408\pi$
$199$	−14.2214	−	15.3270i	−1.00813	−	1.08650i	−0.0118820	−	0.999929i	$-0.503782\pi$
$200$	0.983301	+	0.385917i	0.0695298	+	0.0272885i
$201$	−3.30089	−	10.8514i	−0.232827	−	0.765396i
$202$	5.33762	+	1.21828i	0.375553	+	0.0857176i
$203$	−0.664554	−	1.53129i	−0.0466426	−	0.107476i
$204$	−3.28562	+	3.51346i	−0.230040	+	0.245992i
$205$	1.00654	−	13.4313i	0.0702997	−	0.938085i
$206$	1.21899	−	0.376008i	0.0849308	−	0.0261977i
$207$	2.54155	−	8.01684i	0.176650	−	0.557209i
$208$	0.947278	−	0.371779i	0.0656819	−	0.0257783i
$209$	−3.49081	−	1.68108i	−0.241464	−	0.116283i
$210$	3.68788	−	8.31966i	0.254488	−	0.574111i
$211$	−22.8241	+	10.9915i	−1.57128	+	0.756686i	−0.998032	−	0.0626992i	$-0.980029\pi$
$211$	−22.8241	+	10.9915i	−1.57128	+	0.756686i	−0.573243	+	0.819386i	$0.694315\pi$
$212$	7.96750	−	8.58692i	0.547210	−	0.589752i
$213$	−12.8422	+	6.12284i	−0.879930	+	0.419530i
$214$	−5.83085	−	10.0993i	−0.398589	−	0.690376i
$215$	1.44246	−	2.49841i	0.0983749	−	0.170390i
$216$	−4.65486	−	2.30917i	−0.316723	−	0.157119i
$217$	0.149002	−	0.00528514i	0.0101149	−	0.000358779i
$218$	6.48324	−	5.17021i	0.439100	−	0.350171i
$219$	19.0266	−	17.5164i	1.28570	−	1.18365i
$220$	−0.575076	+	0.843481i	−0.0387716	+	0.0568675i
$221$	−1.59206	+	2.33513i	−0.107094	+	0.157078i
$222$	−9.27970	+	8.54316i	−0.622813	+	0.573380i
$223$	20.0953	−	16.0255i	1.34568	−	1.07314i	0.355303	−	0.934751i	$-0.384378\pi$
$223$	20.0953	−	16.0255i	1.34568	−	1.07314i	0.990377	−	0.138393i	$-0.0441938\pi$
$224$	−1.57524	+	2.12571i	−0.105250	+	0.142030i
$225$	−1.56301	−	2.75668i	−0.104201	−	0.183779i
$226$	−2.61239	+	4.52480i	−0.173774	+	0.300985i
$227$	−0.198289	−	0.343447i	−0.0131609	−	0.0227954i	0.859370	−	0.511354i	$-0.170856\pi$
$227$	−0.198289	−	0.343447i	−0.0131609	−	0.0227954i	−0.872531	+	0.488559i	$0.837523\pi$
$228$	11.7836	−	5.61817i	0.780391	−	0.372072i
$229$	−5.05452	+	5.44748i	−0.334012	+	0.359980i	−0.877618	−	0.479361i	$-0.840868\pi$
$229$	−5.05452	+	5.44748i	−0.334012	+	0.359980i	0.543605	+	0.839341i	$0.317059\pi$
$230$	5.01579	−	2.41547i	0.330731	−	0.159272i
$231$	−1.88722	−	1.40995i	−0.124170	−	0.0927678i
$232$	−0.568446	−	0.273749i	−0.0373203	−	0.0179725i
$233$	5.37159	−	2.10819i	0.351904	−	0.138112i	−0.182803	−	0.983150i	$-0.558517\pi$
$233$	5.37159	−	2.10819i	0.351904	−	0.138112i	0.534707	+	0.845037i	$0.320422\pi$
$234$	−2.91013	−	0.922587i	−0.190241	−	0.0603114i
$235$	−2.07227	+	0.639212i	−0.135180	+	0.0416976i
$236$	−0.895369	+	11.9479i	−0.0582836	+	0.777740i
$237$	−9.47101	+	10.1278i	−0.615208	+	0.657869i
$238$	0.289027	−	7.34229i	0.0187348	−	0.475930i
$239$	−1.56800	−	0.357886i	−0.101426	−	0.0231497i	0.171507	−	0.985183i	$-0.445136\pi$
$239$	−1.56800	−	0.357886i	−0.101426	−	0.0231497i	−0.272932	+	0.962033i	$0.587994\pi$
$240$	−1.00102	−	3.29075i	−0.0646153	−	0.212417i
$241$	1.67626	+	0.657884i	0.107977	+	0.0423780i	0.418715	−	0.908118i	$-0.362481\pi$
$241$	1.67626	+	0.657884i	0.107977	+	0.0423780i	−0.310737	+	0.950496i	$0.600576\pi$
$242$	−7.30215	−	7.86985i	−0.469400	−	0.505893i
$243$	6.48830	+	14.1740i	0.416224	+	0.909262i
$244$		−	4.56438i		−	0.292204i
$245$	4.04573	+	13.2993i	0.258472	+	0.849664i
$246$	9.73198	−	6.57967i	0.620488	−	0.419504i
$247$	6.33708	−	4.32055i	0.403219	−	0.274910i
$248$	0.0413095	−	0.0383296i	0.00262316	−	0.00243393i
$249$	26.2411	−	5.88173i	1.66296	−	0.372740i
$250$	3.54504	−	11.4927i	0.224208	−	0.726864i
$251$	0.0838110	−	0.367200i	0.00529010	−	0.0231774i	−0.972214	−	0.234094i	$-0.924788\pi$
$251$	0.0838110	−	0.367200i	0.00529010	−	0.0231774i	0.977504	+	0.210916i	$0.0676448\pi$
$252$	7.68646	−	1.97948i	0.484201	−	0.124695i
$253$	−0.320677	−	1.40498i	−0.0201608	−	0.0883303i
$254$	−19.5285	−	1.46346i	−1.22533	−	0.0918257i
$255$	7.44537	+	5.98516i	0.466247	+	0.374805i
$256$	0.0747301	+	0.997204i	0.00467063	+	0.0623252i
$257$	−4.07547	−	10.3841i	−0.254221	−	0.647744i	0.745605	−	0.666388i	$-0.232160\pi$
$257$	−4.07547	−	10.3841i	−0.254221	−	0.647744i	−0.999826	+	0.0186435i	$0.994065\pi$
$258$	2.48953	−	0.365307i	0.154991	−	0.0227430i
$259$	2.19448	−	19.1419i	0.136358	−	1.18942i
$260$	−0.876821	−	1.82074i	−0.0543781	−	0.112917i
$261$	0.807914	+	1.71169i	0.0500086	+	0.105951i
$262$	−2.70446	+	17.9429i	−0.167082	+	1.10852i
$263$	10.1596	−	5.86565i	0.626468	−	0.361692i	−0.152915	−	0.988239i	$-0.548866\pi$
$263$	10.1596	−	5.86565i	0.626468	−	0.361692i	0.779383	+	0.626548i	$0.215533\pi$
$264$	−0.888152	+	0.0630738i	−0.0546620	+	0.00388192i
$265$	−18.1872	−	14.5038i	−1.11723	−	0.890963i
$266$	−8.00975	+	18.2616i	−0.491110	+	1.11969i
$267$	−6.60233	+	21.1114i	−0.404056	+	1.29200i
$268$	6.47534	−	0.976001i	0.395545	−	0.0596188i
$269$	−8.79226	−	5.99446i	−0.536073	−	0.365489i	0.264818	−	0.964298i	$-0.414688\pi$
$269$	−8.79226	−	5.99446i	−0.536073	−	0.365489i	−0.800891	+	0.598810i	$0.795641\pi$
$270$	−3.88209	+	9.56079i	−0.236257	+	0.581851i
$271$	−1.75869	−	11.6681i	−0.106833	−	0.708788i	−0.976558	−	0.215253i	$-0.930943\pi$
$271$	−1.75869	−	11.6681i	−0.106833	−	0.708788i	0.869726	−	0.493535i	$-0.164296\pi$
$272$	−1.73160	−	2.17136i	−0.104994	−	0.131658i
$273$	4.28507	−	1.83981i	0.259344	−	0.111350i
$274$	−10.1176	+	12.6871i	−0.611228	+	0.766456i
$275$	−0.470268	−	0.271509i	−0.0283582	−	0.0163726i
$276$	4.36645	+	2.12380i	0.262829	+	0.127838i
$277$	−0.521677	−	0.0786301i	−0.0313445	−	0.00472442i	0.133351	−	0.991069i	$-0.457426\pi$
$277$	−0.521677	−	0.0786301i	−0.0313445	−	0.00472442i	−0.164696	+	0.986344i	$0.552664\pi$
$278$	−8.85941	−	8.22033i	−0.531352	−	0.493023i
$279$	−0.168679	+	0.0113177i	−0.0100985	+	0.000677574i
$280$	4.44335	+	2.80400i	0.265541	+	0.167571i
$281$	10.8711	−	22.5742i	0.648518	−	1.34666i	−0.274381	−	0.961621i	$-0.588473\pi$
$281$	10.8711	−	22.5742i	0.648518	−	1.34666i	0.922899	−	0.385041i	$-0.125813\pi$
$282$	−1.55861	−	1.07158i	−0.0928141	−	0.0638115i
$283$	−2.13943	+	0.160328i	−0.127176	+	0.00953052i	−0.138166	−	0.990409i	$-0.544121\pi$
$283$	−2.13943	+	0.160328i	−0.127176	+	0.00953052i	0.0109900	+	0.999940i	$0.496502\pi$
$284$	−2.42112	−	7.84909i	−0.143667	−	0.465758i
$285$	−12.8745	−	22.5016i	−0.762619	−	1.33288i
$286$	−0.510010	+	0.116406i	−0.0301575	+	0.00688325i
$287$	−4.67809	+	17.3241i	−0.276139	+	1.02261i
$288$	1.70925	−	2.46545i	0.100719	−	0.145278i
$289$	−8.87417	−	2.73732i	−0.522010	−	0.161019i
$290$	−0.457750	+	1.16633i	−0.0268800	+	0.0684892i
$291$	−4.71440	+	20.2898i	−0.276363	+	1.18941i
$292$	8.41113	+	12.3369i	0.492224	+	0.721960i
$293$	−29.4244			−1.71899			−0.859495	−	0.511144i	$-0.829222\pi$
$293$	−29.4244			−1.71899			−0.859495	+	0.511144i	$0.829222\pi$
$294$	−6.90773	+	9.96410i	−0.402867	+	0.581118i
$295$	23.7935			1.38531
$296$	−4.10230	−	6.01697i	−0.238441	−	0.349729i
$297$	2.18926	+	1.53045i	0.127034	+	0.0888059i
$298$	−7.90884	+	20.1514i	−0.458147	+	1.16734i
$299$	2.72602	+	0.840866i	0.157650	+	0.0486285i
$300$	1.70572	−	0.661777i	0.0984799	−	0.0382077i
$301$	−2.51275	+	2.90841i	−0.144833	+	0.167638i
$302$	3.31645	−	0.756957i	0.190840	−	0.0435580i
$303$	8.23076	−	4.70931i	0.472845	−	0.270543i
$304$	2.22156	+	7.20213i	0.127415	+	0.413070i
$305$	−9.03892	+	0.677373i	−0.517567	+	0.0387863i
$306$	−0.0650210	+	8.33157i	−0.00371700	+	0.476284i
$307$	4.90166	−	10.1784i	0.279753	−	0.580912i	−0.712990	−	0.701175i	$-0.752659\pi$
$307$	4.90166	−	10.1784i	0.279753	−	0.580912i	0.992742	+	0.120262i	$0.0383736\pi$
$308$	0.963598	−	0.959858i	0.0549061	−	0.0546930i
$309$	1.11221	−	1.90917i	0.0632716	−	0.108609i
$310$	−0.0820353	−	0.0761176i	−0.00465929	−	0.00432319i
$311$	14.3646	+	2.16511i	0.814541	+	0.122772i	0.543084	−	0.839678i	$-0.317256\pi$
$311$	14.3646	+	2.16511i	0.814541	+	0.122772i	0.271457	+	0.962451i	$0.412494\pi$
$312$	0.770943	−	1.58503i	0.0436461	−	0.0897346i
$313$	8.18447	+	4.72531i	0.462614	+	0.267090i	0.713143	−	0.701019i	$-0.247271\pi$
$313$	8.18447	+	4.72531i	0.462614	+	0.267090i	−0.250529	+	0.968109i	$0.580605\pi$
$314$	−13.3509	+	16.7415i	−0.753435	+	0.944777i
$315$	−5.06070	−	14.9279i	−0.285138	−	0.841090i
$316$	−4.99145	−	6.25908i	−0.280791	−	0.352101i
$317$	−4.72383	−	31.3406i	−0.265317	−	1.76026i	−0.583387	−	0.812194i	$-0.698273\pi$
$317$	−4.72383	−	31.3406i	−0.265317	−	1.76026i	0.318070	−	0.948067i	$-0.396965\pi$
$318$	0.0791681	−	20.2890i	0.00443953	−	1.13775i
$319$	0.267981	+	0.182706i	0.0150041	+	0.0102296i
$320$	1.96369	−	0.295979i	0.109774	−	0.0165457i
$321$	−19.2779	−	6.02893i	−1.07599	−	0.336502i
$322$	−7.16798	+	1.90572i	−0.399456	+	0.106202i
$323$	−16.3655	−	13.0510i	−0.910600	−	0.726179i
$324$	−8.64051	+	2.51825i	−0.480028	+	0.139903i
$325$	0.930921	−	0.537468i	0.0516382	−	0.0298133i
$326$	0.549230	−	3.64390i	0.0304191	−	0.201817i
$327$	2.19607	−	14.1939i	0.121443	−	0.784926i
$328$	2.94278	+	6.11074i	0.162488	+	0.337409i
$329$	2.87168	−	0.317908i	0.158321	−	0.0175268i
$330$	0.256712	+	1.74946i	0.0141315	+	0.0963047i
$331$	6.32053	+	16.1044i	0.347408	+	0.885180i	0.992630	+	0.121185i	$0.0386696\pi$
$331$	6.32053	+	16.1044i	0.347408	+	0.885180i	−0.645222	+	0.763995i	$0.723235\pi$
$332$	1.16028	+	15.4828i	0.0636784	+	0.849730i
$333$	−1.80260	+	21.7726i	−0.0987820	+	1.19313i
$334$	1.29107	+	0.0967521i	0.0706440	+	0.00529404i
$335$	−2.89376	−	12.6784i	−0.158103	−	0.692695i
$336$	0.486454	+	4.55668i	0.0265382	+	0.248587i
$337$	4.88153	−	21.3874i	0.265914	−	1.16504i	−0.648805	−	0.760955i	$-0.724731\pi$
$337$	4.88153	−	21.3874i	0.265914	−	1.16504i	0.914719	−	0.404090i	$-0.132412\pi$
$338$	−3.52658	+	11.4329i	−0.191821	+	0.621868i
$339$	1.97928	+	8.83049i	0.107500	+	0.479607i
$340$	−4.04300	+	3.75136i	−0.219263	+	0.203446i
$341$	−0.0239353	+	0.0163188i	−0.00129617	+	0.000883715i
$342$	8.42470	−	20.9828i	0.455556	−	1.13462i
$343$	−1.96622	−	18.4156i	−0.106166	−	0.994348i
$344$			1.45272i			0.0783255i
$345$	3.55780	−	8.96214i	0.191545	−	0.482505i
$346$	5.87055	+	6.32695i	0.315603	+	0.340139i
$347$	14.1067	+	5.53648i	0.757288	+	0.297214i	0.712396	−	0.701778i	$-0.247610\pi$
$347$	14.1067	+	5.53648i	0.757288	+	0.297214i	0.0448928	+	0.998992i	$0.485705\pi$
$348$	−1.04550	+	0.318031i	−0.0560445	+	0.0170482i
$349$	−21.1907	−	4.83665i	−1.13431	−	0.258900i	−0.386165	−	0.922430i	$-0.626200\pi$
$349$	−21.1907	−	4.83665i	−1.13431	−	0.258900i	−0.748150	+	0.663530i	$0.769058\pi$
$350$	−1.31071	+	2.46835i	−0.0700602	+	0.131939i
$351$	−4.79060	+	2.23833i	−0.255704	+	0.119473i
$352$	0.0384162	−	0.512629i	0.00204759	−	0.0273232i
$353$	31.8300	−	9.81826i	1.69414	−	0.522573i	0.710653	−	0.703543i	$-0.248400\pi$
$353$	31.8300	−	9.81826i	1.69414	−	0.522573i	0.983489	+	0.180969i	$0.0579235\pi$
$354$	12.8755	+	16.2752i	0.684324	+	0.865017i
$355$	−15.1844	+	5.95943i	−0.805904	+	0.316294i
$356$	−11.5061	−	5.54106i	−0.609823	−	0.293675i
$357$	−8.24516	−	9.69513i	−0.436380	−	0.513120i
$358$	9.04568	−	4.35617i	0.478079	−	0.230231i
$359$	−13.6603	+	14.7223i	−0.720965	+	0.777016i	−0.982115	−	0.188283i	$-0.939708\pi$
$359$	−13.6603	+	14.7223i	−0.720965	+	0.777016i	0.261150	+	0.965298i	$0.415898\pi$
$360$	−5.13604	−	3.01898i	−0.270693	−	0.159114i
$361$	18.9030	+	32.7409i	0.994894	+	1.72321i
$362$	−0.385206	+	0.667196i	−0.0202460	+	0.0350670i
$363$	−18.5373	−	1.46194i	−0.972955	−	0.0767318i
$364$	0.691780	+	2.60199i	0.0362591	+	0.136381i
$365$	23.1827	−	18.4876i	1.21344	−	0.967683i
$366$	−5.35461	−	5.81625i	−0.279890	−	0.304020i
$367$	8.78662	−	12.8876i	0.458658	−	0.672728i	−0.525343	−	0.850890i	$-0.676063\pi$
$367$	8.78662	−	12.8876i	0.458658	−	0.672728i	0.984001	+	0.178163i	$0.0570154\pi$
$368$	−1.57919	+	2.31624i	−0.0823208	+	0.120742i
$369$	4.68236	−	19.8012i	0.243754	−	1.03081i
$370$	−11.3067	+	9.01680i	−0.587808	+	0.468761i
$371$	20.1701	+	23.5304i	1.04718	+	1.22164i
$372$	0.00767383	−	0.0973037i	0.000397870	−	0.00504496i
$373$	−0.0111660	+	0.0193401i	−0.000578155	+	0.00100139i	−0.866314	−	0.499499i	$-0.833517\pi$
$373$	−0.0111660	+	0.0193401i	−0.000578155	+	0.00100139i	0.865736	+	0.500501i	$0.166851\pi$
$374$	0.713851	+	1.23643i	0.0369124	+	0.0639341i
$375$	−8.96514	−	18.8036i	−0.462958	−	0.971016i
$376$	0.742765	−	0.800511i	0.0383052	−	0.0412832i
$377$	−0.578464	+	0.278573i	−0.0297924	+	0.0143473i
$378$	7.47244	−	11.5396i	0.384341	−	0.593533i
$379$	11.3791	+	5.47988i	0.584504	+	0.281482i	0.702675	−	0.711511i	$-0.251989\pi$
$379$	11.3791	+	5.47988i	0.584504	+	0.281482i	−0.118171	+	0.992993i	$0.537703\pi$
$380$	13.9328	−	5.46822i	0.714738	−	0.280514i
$381$	−26.6014	+	21.0447i	−1.36283	+	1.07815i
$382$	−21.0892	+	6.50517i	−1.07902	+	0.332833i
$383$	0.966746	−	12.9003i	0.0493984	−	0.659176i	−0.916463	−	0.400118i	$-0.868969\pi$
$383$	0.966746	−	12.9003i	0.0493984	−	0.659176i	0.965862	−	0.259058i	$-0.0834120\pi$
$384$	1.26508	+	1.18304i	0.0645582	+	0.0603717i
$385$	−2.04383	−	1.76578i	−0.104163	−	0.0899926i
$386$	18.7865	+	4.28790i	0.956209	+	0.218249i
$387$	2.74378	−	3.38604i	0.139474	−	0.172122i
$388$	−11.1951	−	4.39374i	−0.568343	−	0.223058i
$389$	−8.75093	−	9.43126i	−0.443690	−	0.478184i	0.471120	−	0.882069i	$-0.343850\pi$
$389$	−8.75093	−	9.43126i	−0.443690	−	0.478184i	−0.914810	+	0.403885i	$0.867659\pi$
$390$	−3.25327	−	1.29149i	−0.164736	−	0.0653970i
$391$		−	7.78569i		−	0.393739i
$392$	−5.11281	−	4.78113i	−0.258236	−	0.241483i
$393$	17.6032	+	26.0368i	0.887962	+	1.31338i
$394$	−2.32913	+	1.58797i	−0.117340	+	0.0800010i
$395$	−11.6542	+	10.8135i	−0.586387	+	0.544087i
$396$	−1.05775	+	1.12229i	−0.0531540	+	0.0563973i
$397$	5.95016	−	19.2900i	0.298630	−	0.968135i	−0.674577	−	0.738205i	$-0.735674\pi$
$397$	5.95016	−	19.2900i	0.298630	−	0.968135i	0.973207	−	0.229931i	$-0.0738499\pi$
$398$	4.65258	−	20.3843i	0.233213	−	1.02177i
$399$	11.2166	+	32.6667i	0.561534	+	1.63538i
$400$	0.235053	+	1.02984i	0.0117527	+	0.0514918i
$401$	−9.83940	−	0.737361i	−0.491356	−	0.0368221i	−0.173251	−	0.984878i	$-0.555427\pi$
$401$	−9.83940	−	0.737361i	−0.491356	−	0.0368221i	−0.318105	+	0.948056i	$0.603046\pi$
$402$	7.10636	−	8.84011i	0.354433	−	0.440905i
$403$	−0.00428546	−	0.0571855i	−0.000213474	−	0.00284861i
$404$	2.00020	+	5.09643i	0.0995137	+	0.253557i
$405$	6.26922	+	16.7372i	0.311520	+	0.831680i
$406$	0.890855	−	1.41169i	0.0442124	−	0.0700609i
$407$	1.62430	+	3.37288i	0.0805133	+	0.167188i
$408$	−4.75382	−	0.735505i	−0.235349	−	0.0364129i
$409$	0.488628	−	3.24183i	0.0241611	−	0.160298i	−0.973497	−	0.228701i	$-0.926552\pi$
$409$	0.488628	−	3.24183i	0.0241611	−	0.160298i	0.997658	+	0.0684027i	$0.0217903\pi$
$410$	11.6645	−	6.73450i	0.576068	−	0.332593i
$411$	1.99104	+	28.0361i	0.0982105	+	1.38292i
$412$	0.997352	+	0.795361i	0.0491360	+	0.0391846i
$413$	−31.1356	−	5.95390i	−1.53208	−	0.292972i
$414$	8.05553	−	2.41612i	0.395908	−	0.118746i
$415$	30.4887	−	4.59543i	1.49663	−	0.225581i
$416$	0.840799	+	0.573247i	0.0412236	+	0.0281058i
$417$	−20.9328	−	0.0816804i	−1.02508	−	0.00399991i
$418$	−0.577465	−	3.83123i	−0.0282447	−	0.187392i
$419$	21.6520	+	27.1507i	1.05777	+	1.32640i	0.942921	+	0.333016i	$0.108066\pi$
$419$	21.6520	+	27.1507i	1.05777	+	1.32640i	0.114847	+	0.993383i	$0.463362\pi$
$420$	8.95149	−	1.63956i	0.436788	−	0.0800025i
$421$	−5.82082	+	7.29907i	−0.283689	+	0.355735i	−0.903175	−	0.429273i	$-0.858770\pi$
$421$	−5.82082	+	7.29907i	−0.283689	+	0.355735i	0.619486	+	0.785008i	$0.287341\pi$
$422$	−21.9389	−	12.6664i	−1.06797	−	0.616591i
$423$	−3.24320	+	0.462978i	−0.157690	+	0.0225108i
$424$	11.5831	+	1.74587i	0.562525	+	0.0847870i
$425$	−2.15055	−	1.99542i	−0.104317	−	0.0967919i
$426$	−12.2932	−	7.16157i	−0.595606	−	0.346979i
$427$	11.9976	+	1.37544i	0.580606	+	0.0665621i
$428$	5.05982	−	10.5068i	0.244576	−	0.507867i
$429$	−0.513330	+	0.746641i	−0.0247838	+	0.0360482i
$430$	2.87685	−	0.215590i	0.138734	−	0.0103967i
$431$	2.52762	+	8.19436i	0.121751	+	0.394708i	0.995847	−	0.0910462i	$-0.0290211\pi$
$431$	2.52762	+	8.19436i	0.121751	+	0.394708i	−0.874095	+	0.485755i	$0.838545\pi$
$432$	−0.714248	−	5.14683i	−0.0343643	−	0.247627i
$433$	2.32897	−	0.531571i	0.111923	−	0.0255457i	−0.166193	−	0.986093i	$-0.553147\pi$
$433$	2.32897	−	0.531571i	0.111923	−	0.0255457i	0.278116	+	0.960548i	$0.410290\pi$
$434$	0.0883024	+	0.120134i	0.00423865	+	0.00576660i
$435$	0.784958	+	2.02322i	0.0376359	+	0.0970059i
$436$	7.92396	+	2.44422i	0.379489	+	0.117057i
$437$	−7.71923	+	19.6683i	−0.369261	+	0.940861i
$438$	25.1908	+	5.85315i	1.20366	+	0.279674i
$439$	8.93579	+	13.1064i	0.426482	+	0.625534i	0.977994	−	0.208633i	$-0.0669013\pi$
$439$	8.93579	+	13.1064i	0.426482	+	0.625534i	−0.551512	+	0.834167i	$0.685949\pi$
$440$	−1.02087			−0.0486680
$441$	2.88687	+	20.8006i	0.137470	+	0.990506i
$442$	−2.82622			−0.134429
$443$	−10.5963	−	15.5420i	−0.503447	−	0.738422i	0.487434	−	0.873160i	$-0.337933\pi$
$443$	−10.5963	−	15.5420i	−0.503447	−	0.738422i	−0.990881	+	0.134738i	$0.956981\pi$
$444$	−12.2861	−	2.85471i	−0.583074	−	0.135479i
$445$	−9.26549	+	23.6081i	−0.439226	+	1.11913i
$446$	24.5609	+	7.57605i	1.16299	+	0.358736i
$447$	13.5622	+	34.9564i	0.641471	+	1.65338i
$448$	−2.64370	−	0.104068i	−0.124903	−	0.00491677i
$449$	7.21822	−	1.64751i	0.340649	−	0.0777508i	−0.0487744	−	0.998810i	$-0.515532\pi$
$449$	7.21822	−	1.64751i	0.340649	−	0.0777508i	0.389423	+	0.921059i	$0.372674\pi$
$450$	1.39720	−	2.84432i	0.0658646	−	0.134082i
$451$	−1.02770	−	3.33171i	−0.0483923	−	0.156884i
$452$	−5.21018	+	0.390449i	−0.245066	+	0.0183652i
$453$	3.33804	−	4.85519i	0.156835	−	0.228117i
$454$	0.172069	−	0.357305i	0.00807560	−	0.0167692i
$455$	5.05010	−	1.75609i	0.236752	−	0.0823268i
$456$	11.2799	+	6.57128i	0.528230	+	0.307728i
$457$	2.78654	+	2.58553i	0.130349	+	0.120946i	0.742654	−	0.669676i	$-0.233567\pi$
$457$	2.78654	+	2.58553i	0.130349	+	0.120946i	−0.612305	+	0.790622i	$0.709757\pi$
$458$	−7.34824	−	1.10757i	−0.343360	−	0.0517533i
$459$	9.69116	+	10.6929i	0.452345	+	0.499104i
$460$	4.82125	+	2.78355i	0.224792	+	0.129784i
$461$	6.85067	−	8.59046i	0.319067	−	0.400098i	−0.596271	−	0.802783i	$-0.703352\pi$
$461$	6.85067	−	8.59046i	0.319067	−	0.400098i	0.915338	+	0.402685i	$0.131923\pi$
$462$	0.101846	−	2.35354i	0.00473829	−	0.109497i
$463$	15.4269	+	19.3448i	0.716951	+	0.899028i	0.998161	−	0.0606180i	$-0.0193071\pi$
$463$	15.4269	+	19.3448i	0.716951	+	0.899028i	−0.281210	+	0.959646i	$0.590736\pi$
$464$	−0.0940348	−	0.623880i	−0.00436546	−	0.0289629i
$465$	−0.193831		0.000756334i	−0.00898870		3.50742e-5i
$466$	4.76779	+	3.25063i	0.220864	+	0.150582i
$467$	13.4939	−	2.03388i	0.624423	−	0.0941166i	0.170793	−	0.985307i	$-0.445367\pi$
$467$	13.4939	−	2.03388i	0.624423	−	0.0941166i	0.453630	+	0.891190i	$0.350129\pi$
$468$	−0.877055	−	2.92417i	−0.0405419	−	0.135170i
$469$	0.614161	+	17.3148i	0.0283593	+	0.799522i
$470$	−1.69549	−	1.35211i	−0.0782073	−	0.0623683i
$471$	2.62731	+	36.9955i	0.121060	+	1.70466i
$472$	−10.3762	+	5.99069i	−0.477602	+	0.275744i
$473$	0.111304	−	0.738454i	0.00511777	−	0.0339542i
$474$	−13.7032	−	2.12014i	−0.629407	−	0.0973811i
$475$	3.45435	+	7.17302i	0.158496	+	0.329121i
$476$	6.22930	−	3.89725i	0.285519	−	0.178630i
$477$	−23.7007	−	25.9465i	−1.08518	−	1.18801i
$478$	−0.587587	−	1.49715i	−0.0268756	−	0.0684780i
$479$	2.18508	+	29.1579i	0.0998391	+	1.33226i	0.792002	+	0.610519i	$0.209039\pi$
$479$	2.18508	+	29.1579i	0.0998391	+	1.33226i	−0.692163	+	0.721741i	$0.743342\pi$
$480$	2.15505	−	2.68082i	0.0983641	−	0.122362i
$481$	−7.38998	−	0.553802i	−0.336954	−	0.0252512i
$482$	0.400702	+	1.75559i	0.0182515	+	0.0799650i
$483$	−6.89828	+	10.8374i	−0.313882	+	0.493118i
$484$	2.38893	−	10.4666i	0.108588	−	0.475753i
$485$	−7.03960	+	22.8218i	−0.319652	+	1.03629i
$486$	−8.05611	+	13.3454i	−0.365433	+	0.605358i
$487$	−5.05956	+	4.69459i	−0.229271	+	0.212732i	−0.786440	−	0.617667i	$-0.788078\pi$
$487$	−5.05956	+	4.69459i	−0.229271	+	0.212732i	0.557169	+	0.830399i	$0.311888\pi$
$488$	3.77127	−	2.57121i	0.170717	−	0.116393i
$489$	−3.57491	−	5.28764i	−0.161663	−	0.239115i
$490$	−8.70939	+	10.8345i	−0.393450	+	0.489454i
$491$		−	40.9751i		−	1.84918i	−0.380962	−	0.924591i	$-0.624407\pi$
$491$		−	40.9751i		−	1.84918i	0.380962	−	0.924591i	$-0.375593\pi$
$492$	10.9186	+	4.33448i	0.492248	+	0.195413i
$493$	1.19184	+	1.28450i	0.0536777	+	0.0578508i
$494$	7.13961	+	2.80209i	0.321226	+	0.126072i
$495$	2.37947	+	1.92813i	0.106949	+	0.0866631i
$496$	0.0549399	+	0.0125397i	0.00246687	+	0.000563048i
$497$	21.3612	−	3.99875i	0.958181	−	0.179368i
$498$	19.6419	+	18.3681i	0.880173	+	0.823096i
$499$	2.84993	−	38.0297i	0.127581	−	1.70244i	−0.455667	−	0.890150i	$-0.650599\pi$
$499$	2.84993	−	38.0297i	0.127581	−	1.70244i	0.583248	−	0.812294i	$-0.301782\pi$
$500$	11.4927	−	3.54504i	0.513971	−	0.158539i
$501$	1.75867	−	1.39130i	0.0785716	−	0.0621588i
$502$	0.350607	−	0.137603i	0.0156484	−	0.00614153i
$503$	−15.6255	−	7.52484i	−0.696706	−	0.335516i	0.0517872	−	0.998658i	$-0.483508\pi$
$503$	−15.6255	−	7.52484i	−0.696706	−	0.335516i	−0.748494	+	0.663142i	$0.769223\pi$
$504$	5.96546	+	5.23577i	0.265723	+	0.233220i
$505$	9.79570	−	4.71736i	0.435903	−	0.209920i
$506$	0.980204	−	1.05641i	0.0435754	−	0.0469631i
$507$	8.91846	+	18.7057i	0.396083	+	0.830751i
$508$	−9.79164	−	16.9596i	−0.434434	−	0.752461i
$509$	11.5561	−	20.0158i	0.512217	−	0.887186i	−0.487683	−	0.873021i	$-0.662158\pi$
$509$	11.5561	−	20.0158i	0.512217	−	0.887186i	0.999900	−	0.0141649i	$-0.00450899\pi$
$510$	−0.751046	+	9.52322i	−0.0332569	+	0.421695i
$511$	−34.9625	+	18.3913i	−1.54665	+	0.813585i
$512$	−0.781831	+	0.623490i	−0.0345524	+	0.0275546i
$513$	−13.8802	−	36.6210i	−0.612827	−	1.61686i
$514$	6.28398	−	9.21690i	0.277174	−	0.406540i
$515$	1.42706	−	2.09311i	0.0628836	−	0.0922333i
$516$	1.70423	+	1.85116i	0.0750246	+	0.0814928i
$517$	−0.438899	+	0.350010i	−0.0193028	+	0.0153934i
$518$	17.0520	−	8.96988i	0.749223	−	0.394114i
$519$	14.9030	+	1.17532i	0.654169	+	0.0515909i
$520$	1.01043	−	1.75012i	0.0443104	−	0.0767479i
$521$	−11.2753	−	19.5294i	−0.493981	−	0.855601i	0.505995	−	0.862537i	$-0.331126\pi$
$521$	−11.2753	−	19.5294i	−0.493981	−	0.855601i	−0.999976	+	0.00693600i	$0.997792\pi$
$522$	−0.959154	+	1.63176i	−0.0419810	+	0.0714203i
$523$	−8.63167	+	9.30273i	−0.377436	+	0.406780i	−0.892989	−	0.450078i	$-0.851396\pi$
$523$	−8.63167	+	9.30273i	−0.377436	+	0.406780i	0.515553	+	0.856858i	$0.327587\pi$
$524$	−16.3486	+	7.87307i	−0.714192	+	0.343937i
$525$	1.22550	+	4.68297i	0.0534852	+	0.204382i
$526$	10.5695	+	5.09002i	0.460854	+	0.221936i
$527$	−0.145688	+	0.0571784i	−0.00634628	+	0.00249073i
$528$	−0.552428	−	0.698295i	−0.0240413	−	0.0303894i
$529$	14.4685	−	4.46294i	0.629066	−	0.194041i
$530$	1.73840	−	23.1973i	0.0755111	−	1.00763i
$531$	35.4998	+	5.63440i	1.54056	+	0.244512i
$532$	−19.6005	+	3.66915i	−0.849789	+	0.159078i
$533$	6.72889	+	1.53583i	0.291461	+	0.0665240i
$534$	−21.1623	+	6.43738i	−0.915782	+	0.278573i
$535$	−21.5577	−	8.46079i	−0.932023	−	0.365792i
$536$	4.45410	+	4.80038i	0.192388	+	0.207345i
$537$	6.41628	−	16.1627i	0.276883	−	0.697472i
$538$		−	10.6413i		−	0.458779i
$539$	2.23265	+	2.82210i	0.0961669	+	0.121556i
$540$	−10.0864	+	2.17825i	−0.434048	+	0.0937369i
$541$	−27.2436	+	18.5744i	−1.17129	+	0.798575i	−0.983012	−	0.183540i	$-0.941244\pi$
$541$	−27.2436	+	18.5744i	−1.17129	+	0.798575i	−0.188282	+	0.982115i	$0.560292\pi$
$542$	8.64995	−	8.02598i	0.371547	−	0.344745i
$543$	0.291852	+	1.30208i	0.0125246	+	0.0558778i
$544$	0.818616	−	2.65389i	0.0350979	−	0.113784i
$545$	3.66438	−	16.0547i	0.156965	−	0.687707i
$546$	3.93398	+	2.50409i	0.168359	+	0.107165i
$547$	−1.09922	−	4.81598i	−0.0469991	−	0.205917i	0.945977	−	0.324235i	$-0.105107\pi$
$547$	−1.09922	−	4.81598i	−0.0469991	−	0.205917i	−0.992976	+	0.118318i	$0.962250\pi$
$548$	−16.1820	−	1.21268i	−0.691262	−	0.0518030i
$549$	−13.6464	−	1.12982i	−0.582416	−	0.0482195i
$550$	−0.0405798	−	0.541500i	−0.00173033	−	0.0230896i
$551$	−1.73730	−	4.42657i	−0.0740115	−	0.188578i
$552$	0.704943	+	4.80411i	0.0300044	+	0.204477i
$553$	17.9563	−	11.2341i	0.763581	−	0.477721i
$554$	−0.228904	−	0.475323i	−0.00972519	−	0.0201946i
$555$	−3.82992	+	24.7541i	−0.162571	+	1.05075i
$556$	1.80127	−	11.9507i	0.0763910	−	0.506821i
$557$	−1.22592	+	0.707783i	−0.0519437	+	0.0299897i	−0.525747	−	0.850641i	$-0.676214\pi$
$557$	−1.22592	+	0.707783i	−0.0519437	+	0.0299897i	0.473803	+	0.880631i	$0.342881\pi$
$558$	−0.104371	−	0.132994i	−0.00441839	−	0.00563007i
$559$	1.15580	+	0.921719i	0.0488851	+	0.0389846i
$560$	0.186248	+	5.25082i	0.00787043	+	0.221887i
$561$	2.36013	+	0.738101i	0.0996447	+	0.0311627i
$562$	24.7756	−	3.73432i	1.04510	−	0.157523i
$563$	−11.6221	−	7.92380i	−0.489812	−	0.333948i	0.293099	−	0.956082i	$-0.405314\pi$
$563$	−11.6221	−	7.92380i	−0.489812	−	0.333948i	−0.782911	+	0.622134i	$0.786266\pi$
$564$	0.00738041	−	1.89143i	0.000310771	−	0.0796435i
$565$	1.54642	+	10.2599i	0.0650586	+	0.431635i
$566$	−1.33765	−	1.67737i	−0.0562258	−	0.0705049i
$567$	−4.01555	−	23.4707i	−0.168637	−	0.985678i
$568$	5.12136	−	6.42198i	0.214887	−	0.269460i
$569$	−24.1005	−	13.9144i	−1.01034	−	0.583322i	−0.0990514	−	0.995082i	$-0.531581\pi$
$569$	−24.1005	−	13.9144i	−1.01034	−	0.583322i	−0.911292	+	0.411760i	$0.864914\pi$
$570$	11.3392	−	23.3130i	0.474948	−	0.976474i
$571$	−4.34322	−	0.654635i	−0.181758	−	0.0273956i	0.0575325	−	0.998344i	$-0.481677\pi$
$571$	−4.34322	−	0.654635i	−0.181758	−	0.0273956i	−0.239291	+	0.970948i	$0.576915\pi$
$572$	−0.383478	−	0.355816i	−0.0160340	−	0.0148774i
$573$	−19.2420	+	33.0298i	−0.803845	+	1.37984i
$574$	−16.9491	+	5.89377i	−0.707441	+	0.246001i
$575$	−1.28483	+	2.66799i	−0.0535813	+	0.111263i
$576$	2.99991	+	0.0234118i	0.124996	+	0.000975492i
$577$	−1.85167	+	0.138763i	−0.0770859	+	0.00577679i	−0.113217	−	0.993570i	$-0.536116\pi$
$577$	−1.85167	+	0.138763i	−0.0770859	+	0.00577679i	0.0361313	+	0.999347i	$0.488497\pi$
$578$	−2.73732	−	8.87417i	−0.113857	−	0.369117i
$579$	28.9694	−	16.5751i	1.20393	−	0.688838i
$580$	−1.22153	+	0.278805i	−0.0507211	+	0.0115768i
$581$	−41.0467	−	1.61579i	−1.70291	−	0.0670343i
$582$	−19.4200	+	7.53446i	−0.804984	+	0.312313i
$583$	−5.75421	−	1.77494i	−0.238315	−	0.0735104i
$584$	−5.45504	+	13.8992i	−0.225731	+	0.575153i
$585$	−5.66063	+	2.17081i	−0.234038	+	0.0897518i
$586$	−16.5753	−	24.3116i	−0.684721	−	1.00430i
$587$	−19.5665			−0.807598			−0.403799	−	0.914848i	$-0.632310\pi$
$587$	−19.5665			−0.807598			−0.403799	+	0.914848i	$0.632310\pi$
$588$	−12.1240	−	0.0944582i	−0.499985	−	0.00389539i
$589$	0.424729			0.0175007
$590$	13.4033	+	19.6591i	0.551806	+	0.809351i
$591$	−1.10504	+	4.75588i	−0.0454553	+	0.195631i
$592$	2.66055	−	6.77896i	0.109348	−	0.278614i
$593$	−18.0477	−	5.56697i	−0.741129	−	0.228608i	−0.0988747	−	0.995100i	$-0.531524\pi$
$593$	−18.0477	−	5.56697i	−0.741129	−	0.228608i	−0.642254	+	0.766492i	$0.722000\pi$
$594$	−0.0312680	+	2.67098i	−0.00128294	+	0.109592i
$595$	−8.64225	−	11.7576i	−0.354298	−	0.482015i
$596$	−21.1051	+	4.81709i	−0.864497	+	0.197316i
$597$	−17.9848	−	31.4332i	−0.736068	−	1.28647i
$598$	0.840866	+	2.72602i	0.0343856	+	0.111475i
$599$	−17.7159	+	1.32763i	−0.723853	+	0.0542453i	−0.431561	−	0.902084i	$-0.642037\pi$
$599$	−17.7159	+	1.32763i	−0.723853	+	0.0542453i	−0.292292	+	0.956329i	$0.594418\pi$
$600$	1.50765	+	1.03654i	0.0615497	+	0.0423166i
$601$	0.605658	−	1.25766i	0.0247053	−	0.0513011i	−0.888251	−	0.459358i	$-0.848079\pi$
$601$	0.605658	−	1.25766i	0.0247053	−	0.0513011i	0.912956	+	0.408057i	$0.133794\pi$
$602$	−3.81853	−	0.437766i	−0.155632	−	0.0178420i
$603$	−1.31518	−	19.6014i	−0.0535582	−	0.798230i
$604$	2.49365	+	2.31377i	0.101465	+	0.0941458i
$605$	−21.0817	−	3.17755i	−0.857091	−	0.129186i
$606$	8.52757	+	4.14773i	0.346409	+	0.168490i
$607$	7.60649	+	4.39161i	0.308738	+	0.178250i	0.646362	−	0.763031i	$-0.276290\pi$
$607$	7.60649	+	4.39161i	0.308738	+	0.178250i	−0.337624	+	0.941281i	$0.609623\pi$
$608$	−4.69923	+	5.89264i	−0.190579	+	0.238978i
$609$	−0.520903	−	2.84396i	−0.0211081	−	0.115243i
$610$	−5.65148	−	7.08673i	−0.228822	−	0.286933i
$611$	−0.165626	−	1.09886i	−0.00670051	−	0.0444550i
$612$	−6.92049	+	4.63962i	−0.279744	+	0.187545i
$613$	2.26309	+	1.54295i	0.0914054	+	0.0623191i	0.608160	−	0.793814i	$-0.291908\pi$
$613$	2.26309	+	1.54295i	0.0914054	+	0.0623191i	−0.516755	+	0.856133i	$0.672860\pi$
$614$	11.1710	−	1.68376i	0.450825	−	0.0679509i
$615$	6.96327	−	22.2655i	0.280786	−	0.897833i
$616$	1.33589	+	0.255455i	0.0538244	+	0.0102926i
$617$	30.4538	+	24.2861i	1.22602	+	0.977722i	0.999994	+	0.00360206i	$0.00114657\pi$
$617$	30.4538	+	24.2861i	1.22602	+	0.977722i	0.226031	+	0.974120i	$0.427425\pi$
$618$	2.20396	−	0.156518i	0.0886562	−	0.00629608i
$619$	12.3701	−	7.14187i	0.497196	−	0.287056i	−0.230359	−	0.973106i	$-0.573990\pi$
$619$	12.3701	−	7.14187i	0.497196	−	0.287056i	0.727555	+	0.686050i	$0.240657\pi$
$620$	0.0166792	−	0.110659i	0.000669853	−	0.00444418i
$621$	7.43050	−	12.5290i	0.298176	−	0.502771i
$622$	6.30296	+	13.0882i	0.252726	+	0.524790i
$623$	18.0321	−	28.5745i	0.722442	−	1.14481i
$624$	1.74390	−	0.255895i	0.0698119	−	0.0102440i
$625$	−6.79629	−	17.3167i	−0.271852	−	0.692666i
$626$	0.706245	+	9.42418i	0.0282272	+	0.376666i
$627$	−5.23038	−	4.20458i	−0.208881	−	0.167915i
$628$	−21.3533	−	1.60021i	−0.852089	−	0.0638553i
$629$	4.50051	+	19.7180i	0.179447	+	0.786209i
$630$	9.48319	−	12.5905i	0.377819	−	0.501618i
$631$	−3.18027	+	13.9337i	−0.126605	+	0.554691i	0.871344	+	0.490673i	$0.163249\pi$
$631$	−3.18027	+	13.9337i	−0.126605	+	0.554691i	−0.997949	+	0.0640188i	$0.979608\pi$
$632$	2.35971	−	7.64999i	0.0938642	−	0.304300i
$633$	−42.8154	+	9.59673i	−1.70176	+	0.381436i
$634$	23.2338	−	21.5578i	0.922731	−	0.856169i
$635$	−32.1323	+	21.9074i	−1.27513	+	0.869370i
$636$	16.8081	−	11.3638i	0.666486	−	0.450603i
$637$	−7.04787	+	1.03428i	−0.279247	+	0.0409797i
$638$			0.324338i			0.0128407i
$639$	−24.0663	+	5.29572i	−0.952048	+	0.209496i
$640$	1.35073	+	1.45575i	0.0533925	+	0.0575434i
$641$	27.2719	+	10.7034i	1.07718	+	0.422761i	0.836569	−	0.547862i	$-0.184558\pi$
$641$	27.2719	+	10.7034i	1.07718	+	0.422761i	0.240608	+	0.970622i	$0.422653\pi$
$642$	−5.87830	−	19.3244i	−0.231998	−	0.762672i
$643$	−22.6384	−	5.16708i	−0.892773	−	0.203770i	−0.248561	−	0.968616i	$-0.579958\pi$
$643$	−22.6384	−	5.16708i	−0.892773	−	0.203770i	−0.644212	+	0.764847i	$0.722815\pi$
$644$	−5.61245	−	4.84893i	−0.221161	−	0.191075i
$645$	3.41297	−	3.64964i	0.134386	−	0.143704i
$646$	1.56427	−	20.8737i	0.0615453	−	0.821265i
$647$	22.6064	−	6.97316i	0.888750	−	0.274143i	0.183431	−	0.983033i	$-0.441280\pi$
$647$	22.6064	−	6.97316i	0.888750	−	0.274143i	0.705320	+	0.708890i	$0.250804\pi$
$648$	−6.94805	−	5.72055i	−0.272945	−	0.224724i
$649$	5.73346	−	2.25022i	0.225058	−	0.0883287i
$650$	0.968483	+	0.466397i	0.0379870	+	0.0182936i
$651$	0.253454	+	0.0494926i	0.00993363	+	0.00193977i
$652$	3.32013	−	1.59889i	0.130026	−	0.0626173i
$653$	30.1825	−	32.5289i	1.18113	−	1.27296i	0.226889	−	0.973921i	$-0.427145\pi$
$653$	30.1825	−	32.5289i	1.18113	−	1.27296i	0.954242	−	0.299035i	$-0.0966648\pi$
$654$	12.9647	−	6.18125i	0.506958	−	0.241706i
$655$	18.0174	+	31.2070i	0.703997	+	1.21936i
$656$	−3.39121	+	5.87374i	−0.132404	+	0.229331i
$657$	38.9664	−	22.0936i	1.52022	−	0.861954i
$658$	1.88034	+	2.19361i	0.0733034	+	0.0855159i
$659$	−30.5464	+	24.3600i	−1.18992	+	0.948930i	−0.999463	−	0.0327659i	$-0.989568\pi$
$659$	−30.5464	+	24.3600i	−1.18992	+	0.948930i	−0.190457	+	0.981696i	$0.560997\pi$
$660$	−1.30086	+	1.19761i	−0.0506360	+	0.0466170i
$661$	6.96860	−	10.2211i	0.271047	−	0.397553i	−0.666448	−	0.745551i	$-0.732186\pi$
$661$	6.96860	−	10.2211i	0.271047	−	0.397553i	0.937495	+	0.347998i	$0.113139\pi$
$662$	−9.74564	+	14.2942i	−0.378775	+	0.555561i
$663$	−3.60136	+	3.31552i	−0.139865	+	0.128764i
$664$	−12.1389	+	9.68044i	−0.471080	+	0.375674i
$665$	10.1749	+	38.2707i	0.394565	+	1.48407i
$666$	−19.0048	+	10.7756i	−0.736421	+	0.417545i
$667$	0.884357	−	1.53175i	0.0342424	−	0.0593097i
$668$	0.647344	+	1.12123i	0.0250465	+	0.0433818i
$669$	40.1850	−	19.1593i	1.55364	−	0.740740i
$670$	8.84527	−	9.53293i	0.341722	−	0.368289i
$671$	−2.11403	+	1.01806i	−0.0816111	+	0.0393018i
$672$	−3.49088	+	2.96880i	−0.134664	+	0.114524i
$673$	5.61564	+	2.70435i	0.216467	+	0.104245i	0.538975	−	0.842322i	$-0.318812\pi$
$673$	5.61564	+	2.70435i	0.216467	+	0.104245i	−0.322508	+	0.946567i	$0.604526\pi$
$674$	20.4209	−	8.01463i	0.786585	−	0.308712i
$675$	−1.55635	−	5.26353i	−0.0599038	−	0.202593i
$676$	−11.4329	+	3.52658i	−0.439727	+	0.135638i
$677$	−1.55171	+	20.7061i	−0.0596370	+	0.795801i	0.884561	+	0.466424i	$0.154458\pi$
$677$	−1.55171	+	20.7061i	−0.0596370	+	0.795801i	−0.944198	+	0.329377i	$0.893161\pi$
$678$	−6.18113	+	6.60975i	−0.237385	+	0.253846i
$679$	14.9226	−	28.1026i	0.572678	−	1.07848i
$680$	−5.37702	−	1.22727i	−0.206199	−	0.0470637i
$681$	−0.199903	−	0.657163i	−0.00766030	−	0.0251825i
$682$	−0.0269665	−	0.0105836i	−0.00103260	−	0.000405266i
$683$	−23.3891	−	25.2075i	−0.894959	−	0.964537i	0.104591	−	0.994515i	$-0.466647\pi$
$683$	−23.3891	−	25.2075i	−0.894959	−	0.964537i	−0.999551	+	0.0299785i	$0.990456\pi$
$684$	22.0826	−	4.85922i	0.844350	−	0.185797i
$685$			32.2255i			1.23127i
$686$	14.1081	−	11.9984i	0.538648	−	0.458103i
$687$	−10.6630	+	7.20910i	−0.406817	+	0.275044i
$688$	−1.20030	+	0.818347i	−0.0457608	+	0.0311992i
$689$	8.73824	−	8.10791i	0.332901	−	0.308887i
$690$	9.40905	−	2.10896i	0.358196	−	0.0802868i
$691$	−3.64767	+	11.8255i	−0.138764	+	0.449862i	−0.998104	−	0.0615419i	$-0.980398\pi$
$691$	−3.64767	+	11.8255i	−0.138764	+	0.449862i	0.859340	+	0.511404i	$0.170874\pi$
$692$	−1.92057	+	8.41457i	−0.0730092	+	0.319874i
$693$	−2.63124	−	3.11853i	−0.0999524	−	0.118463i
$694$	3.37214	+	14.7743i	0.128005	+	0.560826i
$695$	−23.9334	−	1.79356i	−0.907847	−	0.0680337i
$696$	−0.851719	−	0.684677i	−0.0322843	−	0.0259526i
$697$	−1.40766	−	18.7839i	−0.0533190	−	0.711493i
$698$	−7.94095	−	20.2332i	−0.300569	−	0.765838i
$699$	9.88887	−	1.45107i	0.374031	−	0.0548844i
$700$	−2.77779	+	0.307513i	−0.104991	+	0.0116229i
$701$	−0.466426	−	0.968544i	−0.0176167	−	0.0365814i	0.891975	−	0.452085i	$-0.149320\pi$
$701$	−0.466426	−	0.968544i	−0.0176167	−	0.0365814i	−0.909592	+	0.415504i	$0.863605\pi$
$702$	−4.54804	−	2.69728i	−0.171655	−	0.101802i
$703$	8.18048	−	54.2740i	0.308533	−	2.04698i
$704$	0.445194	−	0.257033i	0.0167789	−	0.00968730i
$705$	−3.74672	+	0.266080i	−0.141110	+	0.0100212i
$706$	26.0427	+	20.7684i	0.980131	+	0.781628i
$707$	−13.9989	+	3.72183i	−0.526482	+	0.139974i
$708$	−6.19419	+	19.8064i	−0.232792	+	0.744369i
$709$	−40.5033	+	6.10489i	−1.52113	+	0.229274i	−0.855813	−	0.517285i	$-0.826943\pi$
$709$	−40.5033	+	6.10489i	−1.52113	+	0.229274i	−0.665320	+	0.746559i	$0.731705\pi$
$710$	−13.4776	−	9.18886i	−0.505805	−	0.344852i
$711$	−19.9487	+	13.3740i	−0.748136	+	0.501563i
$712$	−1.90339	−	12.6282i	−0.0713327	−	0.473262i
$713$	0.0984970	+	0.123511i	0.00368874	+	0.00462553i
$714$	3.36582	−	12.2739i	0.125963	−	0.459340i
$715$	−0.647718	+	0.812213i	−0.0242233	+	0.0303750i
$716$	8.69485	+	5.01997i	0.324942	+	0.187605i
$717$	−2.50510	−	1.21846i	−0.0935545	−	0.0455040i
$718$	−19.8593	−	2.99331i	−0.741143	−	0.111709i
$719$	−1.58058	−	1.46656i	−0.0589456	−	0.0546935i	0.650150	−	0.759806i	$-0.274706\pi$
$719$	−1.58058	−	1.46656i	−0.0589456	−	0.0546935i	−0.709096	+	0.705112i	$0.750897\pi$
$720$	−0.398836	−	5.94425i	−0.0148638	−	0.221529i
$721$	−2.39118	+	2.38190i	−0.0890521	+	0.0887065i
$722$	−16.4034	+	34.0620i	−0.610471	+	1.26766i
$723$	2.57014	+	1.76702i	0.0955846	+	0.0657163i
$724$	−0.768257	+	0.0575729i	−0.0285521	+	0.00213968i
$725$	−0.196443	−	0.636852i	−0.00729571	−	0.0236521i
$726$	−9.23451	−	16.1398i	−0.342725	−	0.599003i
$727$	41.1463	−	9.39138i	1.52603	−	0.348307i	0.624502	−	0.781023i	$-0.285302\pi$
$727$	41.1463	−	9.39138i	1.52603	−	0.348307i	0.901530	+	0.432716i	$0.142445\pi$
$728$	−1.76017	+	2.03733i	−0.0652362	+	0.0755084i
$729$	5.39020	+	26.4565i	0.199637	+	0.979870i
$730$	28.3344	+	8.74000i	1.04870	+	0.323482i
$731$	1.47401	−	3.75571i	0.0545181	−	0.138910i
$732$	1.78925	−	7.70060i	0.0661327	−	0.284622i
$733$	2.77489	+	4.07001i	0.102493	+	0.150329i	0.874059	−	0.485820i	$-0.161479\pi$
$733$	2.77489	+	4.07001i	0.102493	+	0.150329i	−0.771566	+	0.636149i	$0.780526\pi$
$734$	15.5979			0.575730
$735$	1.61219	+	24.0234i	0.0594667	+	0.886115i
$736$	−2.80336			−0.103333
$737$	−1.89634	−	2.78141i	−0.0698524	−	0.102455i
$738$	18.9981	−	7.28564i	0.699331	−	0.268188i
$739$	−3.13150	+	7.97893i	−0.115194	+	0.293510i	−0.976830	−	0.214017i	$-0.931345\pi$
$739$	−3.13150	+	7.97893i	−0.115194	+	0.293510i	0.861636	+	0.507527i	$0.169440\pi$
$740$	−13.8193	−	4.26270i	−0.508009	−	0.156700i
$741$	12.3850	−	4.80508i	0.454975	−	0.176519i
$742$	−8.07955	+	29.9205i	−0.296610	+	1.09841i
$743$	47.9547	−	10.9454i	1.75929	−	0.401546i	0.783698	−	0.621142i	$-0.213331\pi$
$743$	47.9547	−	10.9454i	1.75929	−	0.401546i	0.975591	+	0.219596i	$0.0704740\pi$
$744$	0.0847189	−	0.0484727i	0.00310595	−	0.00177710i
$745$	12.6715	+	41.0798i	0.464246	+	1.50505i
$746$	−0.0222696	+	0.00166888i	−0.000815348	+	6.11019e-5i
$747$	46.5773	+	0.363497i	1.70417	+	0.0132997i
$748$	−0.619457	+	1.28632i	−0.0226496	+	0.0470323i
$749$	26.0928	+	16.4661i	0.953411	+	0.601657i
$750$	10.4861	−	17.9998i	0.382897	−	0.657260i
$751$	−4.32295	−	4.01111i	−0.157747	−	0.146368i	0.597351	−	0.801980i	$-0.296220\pi$
$751$	−4.32295	−	4.01111i	−0.157747	−	0.146368i	−0.755098	+	0.655612i	$0.772411\pi$
$752$	1.07983	+	0.162758i	0.0393773	+	0.00593517i
$753$	0.285342	−	0.586652i	0.0103984	−	0.0213788i
$754$	−0.556028	−	0.321023i	−0.0202494	−	0.0116910i
$755$	4.21192	−	5.28159i	0.153288	−	0.192217i
$756$	13.7439	−	0.326470i	0.499859	−	0.0118736i
$757$	−9.73697	−	12.2098i	−0.353896	−	0.443772i	0.572737	−	0.819739i	$-0.305882\pi$
$757$	−9.73697	−	12.2098i	−0.353896	−	0.443772i	−0.926633	+	0.375968i	$0.877310\pi$
$758$	1.88238	+	12.4888i	0.0683710	+	0.453612i
$759$	0.00973969	−	2.49606i	0.000353528	−	0.0906012i
$760$	12.3667	+	8.43147i	0.448587	+	0.305841i
$761$	−2.92129	+	0.440313i	−0.105897	+	0.0159613i	−0.201777	−	0.979432i	$-0.564672\pi$
$761$	−2.92129	+	0.440313i	−0.105897	+	0.0159613i	0.0958801	+	0.995393i	$0.469433\pi$
$762$	−32.3730	−	10.1243i	−1.17275	−	0.366764i
$763$	−8.81253	+	20.0919i	−0.319035	+	0.727374i
$764$	−17.2548	−	13.7603i	−0.624257	−	0.497829i
$765$	10.2149	+	13.0162i	0.369322	+	0.470603i
$766$	11.2033	−	6.46825i	0.404793	−	0.233707i
$767$	−1.81720	+	12.0563i	−0.0656153	+	0.435329i
$768$	−0.264830	+	1.71168i	−0.00955622	+	0.0617651i
$769$	−22.2397	−	46.1813i	−0.801985	−	1.66534i	−0.745094	−	0.666959i	$-0.767595\pi$
$769$	−22.2397	−	46.1813i	−0.801985	−	1.66534i	−0.0568912	−	0.998380i	$-0.518119\pi$
$770$	0.307630	−	2.68339i	0.0110862	−	0.0967026i
$771$	−2.80514	−	19.1167i	−0.101025	−	0.688473i
$772$	7.04000	+	17.9376i	0.253375	+	0.645589i
$773$	−0.199899	−	2.66746i	−0.00718985	−	0.0959419i	0.992454	−	0.122615i	$-0.0391279\pi$
$773$	−0.199899	−	2.66746i	−0.00718985	−	0.0959419i	−0.999644	+	0.0266726i	$0.991509\pi$
$774$	4.34331	+	0.359592i	0.156117	+	0.0129253i
$775$	0.0593601	+	0.00444842i	0.00213228	+	0.000159792i
$776$	−2.67613	−	11.7249i	−0.0960674	−	0.420899i
$777$	11.2060	−	31.4343i	0.402014	−	1.12770i
$778$	2.86290	−	12.5432i	0.102640	−	0.449694i
$779$	−15.0676	+	48.8478i	−0.539851	+	1.75015i
$780$	−0.765556	−	3.41550i	−0.0274113	−	0.122294i
$781$	−3.09535	+	2.87206i	−0.110760	+	0.102771i
$782$	6.43284	−	4.38583i	0.230038	−	0.156837i
$783$	0.692048	+	3.20452i	0.0247318	+	0.114520i
$784$	1.07021	−	6.91771i	0.0382216	−	0.247061i
$785$			42.5238i			1.51774i
$786$	−11.5964	+	29.2115i	−0.413630	+	1.04194i
$787$	23.6667	+	25.5067i	0.843628	+	0.909215i	0.996877	−	0.0789728i	$-0.0251640\pi$
$787$	23.6667	+	25.5067i	0.843628	+	0.909215i	−0.153249	+	0.988188i	$0.548974\pi$
$788$	−2.62409	−	1.02988i	−0.0934794	−	0.0366879i
$789$	19.4397	−	5.91339i	0.692072	−	0.210522i
$790$	−15.4996	−	3.53768i	−0.551451	−	0.125865i
$791$	0.543736	−	13.8128i	0.0193330	−	0.491126i
$792$	−1.52313	−	0.241747i	−0.0541222	−	0.00859009i
$793$	0.347108	−	4.63183i	0.0123261	−	0.164481i
$794$	19.2900	−	5.95016i	0.684575	−	0.211163i
$795$	−24.9983	−	31.5990i	−0.886597	−	1.12070i
$796$	19.4632	−	7.63873i	0.689854	−	0.270748i
$797$	3.21002	+	1.54586i	0.113705	+	0.0547573i	0.489871	−	0.871795i	$-0.337044\pi$
$797$	3.21002	+	1.54586i	0.113705	+	0.0547573i	−0.376167	+	0.926552i	$0.622758\pi$
$798$	−20.6719	+	27.6694i	−0.731778	+	0.979487i
$799$	−2.73250	+	1.31590i	−0.0966691	+	0.0465534i
$800$	−0.718480	+	0.774337i	−0.0254021	+	0.0273770i
$801$	−19.4146	+	33.0291i	−0.685981	+	1.16703i
$802$	−4.93350	−	8.54507i	−0.174208	−	0.301737i
$803$	3.83785	−	6.64736i	0.135435	−	0.234580i
$804$	11.3072	+	0.891739i	0.398774	+	0.0314492i
$805$	−8.76950	+	11.8340i	−0.309084	+	0.417095i
$806$	0.0448348	−	0.0357545i	0.00157924	−	0.00125940i
$807$	−12.4836	−	13.5599i	−0.439445	−	0.477331i
$808$	−3.08411	+	4.52356i	−0.108499	+	0.159138i
$809$	−2.35444	+	3.45333i	−0.0827778	+	0.121413i	−0.865394	−	0.501091i	$-0.832932\pi$
$809$	−2.35444	+	3.45333i	−0.0827778	+	0.121413i	0.782617	+	0.622504i	$0.213885\pi$
$810$	−10.2974	+	14.6083i	−0.361813	+	0.513283i
$811$	−26.0360	+	20.7630i	−0.914246	+	0.729087i	−0.962937	−	0.269727i	$-0.913067\pi$
$811$	−26.0360	+	20.7630i	−0.914246	+	0.729087i	0.0486908	+	0.998814i	$0.484495\pi$
$812$	1.66823	−	0.0591726i	0.0585433	−	0.00207655i
$813$	1.60685	−	20.3748i	0.0563548	−	0.714575i
$814$	−1.87181	+	3.24207i	−0.0656069	+	0.113634i
$815$	−3.65903	−	6.33762i	−0.128170	−	0.221997i
$816$	−2.07022	−	4.34211i	−0.0724721	−	0.152004i
$817$	−7.44730	+	8.02628i	−0.260548	+	0.280804i
$818$	2.95378	−	1.42247i	0.103277	−	0.0497354i
$819$	7.95058	−	1.42420i	0.277816	−	0.0497654i
$820$	12.1351	+	5.84398i	0.423778	+	0.204081i
$821$	36.4729	−	14.3146i	1.27291	−	0.499582i	0.369851	−	0.929091i	$-0.379409\pi$
$821$	36.4729	−	14.3146i	1.27291	−	0.499582i	0.903062	+	0.429510i	$0.141314\pi$
$822$	−22.0429	+	17.4384i	−0.768835	+	0.608233i
$823$	−1.02072	+	0.314852i	−0.0355802	+	0.0109750i	−0.312494	−	0.949920i	$-0.601164\pi$
$823$	−1.02072	+	0.314852i	−0.0355802	+	0.0109750i	0.276914	+	0.960895i	$0.410688\pi$
$824$	−0.0953302	+	1.27209i	−0.00332099	+	0.0443155i
$825$	−0.686960	−	0.642412i	−0.0239169	−	0.0223659i
$826$	−12.6200	−	29.0794i	−0.439104	−	1.01180i
$827$	3.92065	+	0.894863i	0.136334	+	0.0311174i	0.290144	−	0.956983i	$-0.406297\pi$
$827$	3.92065	+	0.894863i	0.136334	+	0.0311174i	−0.153809	+	0.988101i	$0.549154\pi$
$828$	6.53414	+	5.29475i	0.227077	+	0.184005i
$829$	−20.6436	−	8.10203i	−0.716983	−	0.281395i	−0.0213295	−	0.999773i	$-0.506790\pi$
$829$	−20.6436	−	8.10203i	−0.716983	−	0.281395i	−0.695654	+	0.718377i	$0.744885\pi$
$830$	20.9718	+	22.6022i	0.727942	+	0.784535i
$831$	−0.849301	−	0.337157i	−0.0294619	−	0.0116958i
$832$			1.01762i			0.0352797i
$833$	8.36692	+	17.5483i	0.289896	+	0.608014i
$834$	−11.7244	−	17.3415i	−0.405982	−	0.600488i
$835$	2.12433	−	1.44834i	0.0735153	−	0.0501219i
$836$	2.84021	−	2.63533i	0.0982308	−	0.0911449i
$837$	−0.289016	−	0.0470286i	−0.00998986	−	0.00162554i
$838$	−10.2360	+	33.1842i	−0.353596	+	1.14633i
$839$	0.723544	−	3.17005i	0.0249795	−	0.109442i	−0.960901	−	0.276891i	$-0.910696\pi$
$839$	0.723544	−	3.17005i	0.0249795	−	0.109442i	0.985881	+	0.167449i	$0.0535529\pi$
$840$	6.39722	+	6.47247i	0.220725	+	0.223321i
$841$	−6.36453	−	27.8848i	−0.219466	−	0.961546i
$842$	−9.30976	−	0.697670i	−0.320835	−	0.0240433i
$843$	27.1900	−	33.8235i	0.936472	−	1.16494i
$844$	−1.89312	−	25.2620i	−0.0651640	−	0.869554i
$845$	8.68044	+	22.1174i	0.298616	+	0.760862i
$846$	−2.20949	−	2.41885i	−0.0759637	−	0.0831617i
$847$	26.7919	+	9.43339i	0.920579	+	0.324135i
$848$	5.08248	+	10.5539i	0.174533	+	0.362422i
$849$	−3.67230	−	0.568174i	−0.126033	−	0.0194997i
$850$	0.437244	−	2.90092i	0.0149973	−	0.0995008i
$851$	17.6800	−	10.2075i	0.606061	−	0.349910i
$852$	−1.00783	−	14.1914i	−0.0345275	−	0.486188i
$853$	−8.42437	−	6.71821i	−0.288445	−	0.230027i	0.468567	−	0.883428i	$-0.344770\pi$
$853$	−8.42437	−	6.71821i	−0.288445	−	0.230027i	−0.757012	+	0.653401i	$0.773342\pi$
$854$	5.62206	+	10.6877i	0.192383	+	0.365726i
$855$	−12.9000	−	43.0095i	−0.441169	−	1.47089i
$856$	11.5314	−	1.73809i	0.394137	−	0.0594065i
$857$	4.40953	+	3.00637i	0.150627	+	0.102696i	0.636288	−	0.771451i	$-0.280469\pi$
$857$	4.40953	+	3.00637i	0.150627	+	0.102696i	−0.485662	+	0.874147i	$0.661421\pi$
$858$	−0.906073	−	0.00353552i	−0.0309328	−	0.000120701i
$859$	8.19646	+	54.3800i	0.279660	+	1.85542i	0.482086	+	0.876124i	$0.339879\pi$
$859$	8.19646	+	54.3800i	0.279660	+	1.85542i	−0.202427	+	0.979297i	$0.564883\pi$
$860$	1.79872	+	2.25552i	0.0613357	+	0.0769126i
$861$	−14.6835	+	27.3937i	−0.500414	+	0.933576i
$862$	−5.34663	+	6.70447i	−0.182107	+	0.228355i
$863$	31.2434	+	18.0384i	1.06354	+	0.614035i	0.926409	−	0.376519i	$-0.122879\pi$
$863$	31.2434	+	18.0384i	1.06354	+	0.614035i	0.137130	+	0.990553i	$0.456212\pi$
$864$	3.85016	−	3.48945i	0.130985	−	0.118714i
$865$	16.9485	+	2.55458i	0.576268	+	0.0868584i
$866$	1.75116	+	1.62484i	0.0595068	+	0.0552142i
$867$	−13.8986	−	8.09686i	−0.472023	−	0.274984i
$868$	−0.0495166	+	0.140633i	−0.00168070	+	0.00477338i
$869$	−1.78562	+	3.70788i	−0.0605731	+	0.125781i
$870$	−1.22948	+	1.78828i	−0.0416833	+	0.0606285i
$871$	6.64525	−	0.497993i	0.225166	−	0.0168738i
$872$	2.44422	+	7.92396i	0.0827717	+	0.268339i
$873$	−15.9074	+	32.3831i	−0.538383	+	1.09600i
$874$	−20.5991	+	4.70161i	−0.696774	+	0.159034i
$875$	5.85502	+	31.2773i	0.197936	+	1.05737i
$876$	9.35439	+	24.1108i	0.316056	+	0.814629i
$877$	−3.65040	−	1.12600i	−0.123265	−	0.0380223i	0.232509	−	0.972594i	$-0.425307\pi$
$877$	−3.65040	−	1.12600i	−0.123265	−	0.0380223i	−0.355774	+	0.934572i	$0.615783\pi$
$878$	−5.79531	+	14.7662i	−0.195582	+	0.498335i
$879$	−49.6421	−	11.5345i	−1.67439	−	0.389048i
$880$	−0.575076	−	0.843481i	−0.0193858	−	0.0284338i
$881$	29.9681			1.00965			0.504826	−	0.863221i	$-0.331557\pi$
$881$	29.9681			1.00965			0.504826	+	0.863221i	$0.331557\pi$
$882$	−15.5600	+	14.1027i	−0.523934	+	0.474861i
$883$	−57.9111			−1.94887			−0.974433	−	0.224680i	$-0.927866\pi$
$883$	−57.9111			−1.94887			−0.974433	+	0.224680i	$0.927866\pi$
$884$	−1.59206	−	2.33513i	−0.0535469	−	0.0785389i
$885$	40.1421	+	9.32712i	1.34936	+	0.313528i
$886$	6.87225	−	17.5102i	0.230878	−	0.588267i
$887$	2.18880	+	0.675154i	0.0734926	+	0.0226695i	0.331283	−	0.943531i	$-0.392518\pi$
$887$	2.18880	+	0.675154i	0.0734926	+	0.0226695i	−0.257791	+	0.966201i	$0.582995\pi$
$888$	−4.56235	−	11.7594i	−0.153103	−	0.394620i
$889$	47.5296	−	20.6270i	1.59409	−	0.691808i
$890$	−24.7254	+	5.64340i	−0.828796	+	0.189167i
$891$	3.09357	+	3.44024i	0.103638	+	0.115252i
$892$	7.57605	+	24.5609i	0.253665	+	0.822361i
$893$	8.20755	−	0.615071i	0.274655	−	0.0205826i
$894$	−21.2425	+	30.8973i	−0.710455	+	1.03336i
$895$	8.65078	−	17.9635i	0.289164	−	0.600455i
$896$	−1.40327	−	2.24295i	−0.0468798	−	0.0749318i
$897$	4.26947	+	2.48724i	0.142553	+	0.0830465i
$898$	5.42740	+	5.03589i	0.181115	+	0.168050i
$899$	−0.0351574	−	0.00529912i	−0.00117256	−	0.000176736i
$900$	3.13716	−	0.447840i	0.104572	−	0.0149280i
$901$	−28.1742	−	16.2664i	−0.938619	−	0.541912i
$902$	2.17387	−	2.72594i	0.0723818	−	0.0907639i
$903$	−5.37940	+	3.92180i	−0.179015	+	0.130509i
$904$	−3.25760	−	4.08490i	−0.108346	−	0.135862i
$905$	0.228025	+	1.51285i	0.00757982	+	0.0502888i
$906$	5.89193	+	0.0229905i	0.195746	+	0.000763808i
$907$	−31.1958	−	21.2690i	−1.03584	−	0.706224i	−0.0790109	−	0.996874i	$-0.525176\pi$
$907$	−31.1958	−	21.2690i	−1.03584	−	0.706224i	−0.956830	+	0.290650i	$0.906129\pi$
$908$	0.392149	−	0.0591070i	0.0130139	−	0.00196153i
$909$	15.7323	−	4.71862i	0.521806	−	0.156507i
$910$	4.29577	+	3.18334i	0.142403	+	0.105527i
$911$	−5.10976	−	4.07490i	−0.169294	−	0.135007i	0.535178	−	0.844739i	$-0.320245\pi$
$911$	−5.10976	−	4.07490i	−0.169294	−	0.135007i	−0.704472	+	0.709732i	$0.748816\pi$
$912$	0.924755	+	13.0216i	0.0306217	+	0.431189i
$913$	6.91219	−	3.99075i	0.228760	−	0.132075i
$914$	−0.566553	+	3.75883i	−0.0187399	+	0.124331i
$915$	−15.5152	−	2.40049i	−0.512915	−	0.0793576i
$916$	−3.22429	−	6.69531i	−0.106534	−	0.221219i
$917$	−15.7681	−	45.3453i	−0.520709	−	1.49743i
$918$	−3.37570	+	14.0308i	−0.111415	+	0.463084i
$919$	11.8069	+	30.0834i	0.389473	+	0.992361i	0.982347	+	0.187066i	$0.0598979\pi$
$919$	11.8069	+	30.0834i	0.389473	+	0.992361i	−0.592874	+	0.805295i	$0.702007\pi$
$920$	0.416030	+	5.55154i	0.0137161	+	0.183029i
$921$	12.2596	−	15.2506i	0.403968	−	0.502524i
$922$	10.9569	+	0.821105i	0.360846	+	0.0270417i
$923$	−1.86000	−	8.14920i	−0.0612227	−	0.268234i
$924$	2.00196	−	1.24165i	0.0658597	−	0.0408473i
$925$	1.71174	−	7.49964i	0.0562818	−	0.246587i
$926$	−7.29310	+	23.6436i	−0.239666	+	0.776978i
$927$	2.62482	−	2.78498i	0.0862105	−	0.0914707i
$928$	0.462502	−	0.429140i	0.0151824	−	0.0140872i
$929$	−20.7324	+	14.1351i	−0.680208	+	0.463758i	−0.853486	−	0.521115i	$-0.825516\pi$
$929$	−20.7324	+	14.1351i	−0.680208	+	0.463758i	0.173279	+	0.984873i	$0.444564\pi$
$930$	−0.108564	−	0.160577i	−0.00355995	−	0.00526552i
$931$	−3.73804	−	52.6262i	−0.122509	−	1.72476i
$932$			5.77048i			0.189018i
$933$	23.3859	+	9.28375i	0.765620	+	0.303936i
$934$	9.28184	+	10.0034i	0.303711	+	0.327323i
$935$	2.63924	+	1.03583i	0.0863125	+	0.0338751i
$936$	1.92200	−	2.37190i	0.0628226	−	0.0775280i
$937$	−24.4206	−	5.57384i	−0.797786	−	0.182089i	−0.195850	−	0.980634i	$-0.562747\pi$
$937$	−24.4206	−	5.57384i	−0.797786	−	0.182089i	−0.601936	+	0.798544i	$0.705604\pi$
$938$	−13.9602	+	10.2612i	−0.455816	+	0.335040i
$939$	11.9557	+	11.1804i	0.390161	+	0.364860i
$940$	0.162061	−	2.16256i	0.00528585	−	0.0705348i
$941$	−40.0372	+	12.3498i	−1.30517	+	0.402593i	−0.867902	−	0.496736i	$-0.834532\pi$
$941$	−40.0372	+	12.3498i	−1.30517	+	0.402593i	−0.437273	+	0.899329i	$0.644056\pi$
$942$	−29.0871	+	23.0111i	−0.947710	+	0.749742i
$943$	−17.6992	+	6.94642i	−0.576365	+	0.226207i
$944$	−10.7948	−	5.19852i	−0.351342	−	0.169198i
$945$	−2.68616	−	27.1687i	−0.0873808	−	0.883799i
$946$	0.672839	−	0.324022i	0.0218759	−	0.0105349i
$947$	18.9998	−	20.4769i	0.617411	−	0.665411i	−0.344496	−	0.938788i	$-0.611950\pi$
$947$	18.9998	−	20.4769i	0.617411	−	0.665411i	0.961907	+	0.273377i	$0.0881407\pi$
$948$	−5.96753	−	12.5164i	−0.193816	−	0.406514i
$949$	7.59724	+	13.1588i	0.246617	+	0.427153i
$950$	−3.98073	+	6.89482i	−0.129152	+	0.223698i
$951$	4.31600	−	54.7267i	0.139956	−	1.77463i
$952$	6.72915	+	2.95149i	0.218093	+	0.0956582i
$953$	−17.5756	+	14.0161i	−0.569330	+	0.454025i	−0.865358	−	0.501154i	$-0.832909\pi$
$953$	−17.5756	+	14.0161i	−0.569330	+	0.454025i	0.296029	+	0.955179i	$0.404338\pi$
$954$	8.08691	−	34.1986i	0.261824	−	1.10722i
$955$	−24.6890	+	36.2121i	−0.798917	+	1.17180i
$956$	0.906002	−	1.32886i	0.0293022	−	0.0429784i
$957$	0.380491	+	0.413295i	0.0122995	+	0.0133599i
$958$	−22.8605	+	18.2306i	−0.738590	+	0.589006i
$959$	8.06388	−	42.1696i	0.260396	−	1.36173i
$960$	3.42898	+	0.270426i	0.110670	+	0.00872795i
$961$	−15.4984	+	26.8440i	−0.499949	+	0.865937i
$962$	−3.70535	−	6.41786i	−0.119465	−	0.206920i
$963$	−30.1605	−	17.7285i	−0.971910	−	0.571291i
$964$	−1.22481	+	1.32004i	−0.0394486	+	0.0425155i
$965$	34.4774	−	16.6034i	1.10987	−	0.534484i
$966$	−12.8402	+	0.405287i	−0.413127	+	0.0130399i
$967$	−37.9532	−	18.2773i	−1.22049	−	0.587758i	−0.291043	−	0.956710i	$-0.594002\pi$
$967$	−37.9532	−	18.2773i	−1.22049	−	0.587758i	−0.929448	+	0.368952i	$0.879717\pi$
$968$	9.99361	−	3.92220i	0.321207	−	0.126064i
$969$	−22.4943	−	28.4338i	−0.722620	−	0.913426i
$970$	−22.8218	+	7.03960i	−0.732765	+	0.226028i
$971$	−3.50572	+	46.7806i	−0.112504	+	1.50126i	0.600230	+	0.799827i	$0.295076\pi$
$971$	−3.50572	+	46.7806i	−0.112504	+	1.50126i	−0.712734	+	0.701434i	$0.752544\pi$
$972$	−15.5646	+	0.861443i	−0.499236	+	0.0276308i
$973$	30.8699	+	8.33595i	0.989645	+	0.267238i
$974$	−6.72900	−	1.53585i	−0.215611	−	0.0492119i
$975$	1.78125	−	0.541841i	0.0570458	−	0.0173528i
$976$	4.24886	+	1.66755i	0.136003	+	0.0533771i
$977$	−1.35108	−	1.45611i	−0.0432247	−	0.0465852i	0.711069	−	0.703122i	$-0.248211\pi$
$977$	−1.35108	−	1.45611i	−0.0432247	−	0.0465852i	−0.754294	+	0.656537i	$0.772021\pi$
$978$	2.35503	−	5.93236i	0.0753057	−	0.189696i
$979$			6.56505i			0.209820i
$980$	−13.8581	−	1.09273i	−0.442680	−	0.0349060i
$981$	9.26907	−	23.0858i	0.295939	−	0.737073i
$982$	33.8552	−	23.0821i	1.08036	−	0.736580i
$983$	37.6603	−	34.9437i	1.20118	−	1.11453i	0.210602	−	0.977572i	$-0.432458\pi$
$983$	37.6603	−	34.9437i	1.20118	−	1.11453i	0.990577	−	0.136959i	$-0.0437328\pi$
$984$	2.56935	+	11.4631i	0.0819079	+	0.365429i
$985$	−1.65006	+	5.34937i	−0.0525754	+	0.170445i
$986$	−0.389914	+	1.70832i	−0.0124174	+	0.0544042i
$987$	4.96946	+	0.589366i	0.158180	+	0.0187597i
$988$	1.70669	+	7.47750i	0.0542971	+	0.237891i
$989$	−4.06111	−	0.304338i	−0.129136	−	0.00967739i
$990$	−0.252695	+	3.05216i	−0.00803119	+	0.0970041i
$991$	2.42492	+	32.3583i	0.0770301	+	1.02790i	0.893075	+	0.449907i	$0.148543\pi$
$991$	2.42492	+	32.3583i	0.0770301	+	1.02790i	−0.816045	+	0.577988i	$0.803838\pi$
$992$	0.0205880	+	0.0524573i	0.000653669	+	0.00166552i
$993$	4.35041	+	29.6476i	0.138056	+	0.940838i
$994$	15.3371	+	15.3969i	0.486464	+	0.488359i
$995$	−18.0155	−	37.4096i	−0.571131	−	1.18596i
$996$	−4.11181	+	26.5760i	−0.130288	+	0.842093i
$997$	−5.76851	+	38.2715i	−0.182690	+	1.21207i	0.690004	+	0.723805i	$0.257609\pi$
$997$	−5.76851	+	38.2715i	−0.182690	+	1.21207i	−0.872695	+	0.488266i	$0.837629\pi$
$998$	33.0271	−	19.0682i	1.04545	−	0.603593i
$999$	−11.5761	+	36.0261i	−0.366252	+	1.13982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.p.a.257.18	yes	216
3.2	odd	2	inner	294.2.p.a.257.6	yes	216
49.45	odd	42	inner	294.2.p.a.143.6	✓	216
147.143	even	42	inner	294.2.p.a.143.18	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.p.a.143.6	✓	216	49.45	odd	42	inner
294.2.p.a.143.18	yes	216	147.143	even	42	inner
294.2.p.a.257.6	yes	216	3.2	odd	2	inner
294.2.p.a.257.18	yes	216	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.p (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.563320 + 0.826239i) q^{2} +(1.68711 + 0.392004i) q^{3} +(-0.365341 + 0.930874i) q^{4} +(1.89764 + 0.585345i) q^{5} +(0.626493 + 1.61478i) q^{6} +(-2.33674 - 1.24082i) q^{7} +(-0.974928 + 0.222521i) q^{8} +(2.69267 + 1.32270i) q^{9} +O(q^{10})\)	\(q+(0.563320 + 0.826239i) q^{2} +(1.68711 + 0.392004i) q^{3} +(-0.365341 + 0.930874i) q^{4} +(1.89764 + 0.585345i) q^{5} +(0.626493 + 1.61478i) q^{6} +(-2.33674 - 1.24082i) q^{7} +(-0.974928 + 0.222521i) q^{8} +(2.69267 + 1.32270i) q^{9} +(0.585345 + 1.89764i) q^{10} +(0.512629 - 0.0384162i) q^{11} +(-0.981276 + 1.42727i) q^{12} +(-0.441530 + 0.916846i) q^{13} +(-0.291117 - 2.62969i) q^{14} +(2.97207 + 1.73142i) q^{15} +(-0.733052 - 0.680173i) q^{16} +(2.74625 + 0.413931i) q^{17} +(0.423963 + 2.96989i) q^{18} +(-6.52721 - 3.76849i) q^{19} +(-1.23817 + 1.55262i) q^{20} +(-3.45593 - 3.00941i) q^{21} +(0.320515 + 0.401913i) q^{22} +(-0.417819 - 2.77205i) q^{23} +(-1.73204 - 0.00675846i) q^{24} +(-0.872773 - 0.595046i) q^{25} +(-1.00626 + 0.151669i) q^{26} +(4.02431 + 3.28708i) q^{27} +(2.00876 - 1.72189i) q^{28} +(0.493279 + 0.393377i) q^{29} +(0.243658 + 3.43099i) q^{30} +(-0.0488029 + 0.0281764i) q^{31} +(0.149042 - 0.988831i) q^{32} +(0.879919 + 0.136140i) q^{33} +(1.20501 + 2.50224i) q^{34} +(-3.70799 - 3.72244i) q^{35} +(-2.21501 + 2.02329i) q^{36} +(2.66055 + 6.77896i) q^{37} +(-0.563239 - 7.51590i) q^{38} +(-1.10432 + 1.37374i) q^{39} +(-1.98032 - 0.148404i) q^{40} +(-1.50923 - 6.61236i) q^{41} +(0.539700 - 4.55068i) q^{42} +(0.323261 - 1.41630i) q^{43} +(-0.151524 + 0.491228i) q^{44} +(4.33548 + 4.08616i) q^{45} +(2.05501 - 1.90677i) q^{46} +(-0.902273 + 0.615159i) q^{47} +(-0.970107 - 1.43488i) q^{48} +(3.92072 + 5.79896i) q^{49} -1.05632i q^{50} +(4.47096 + 1.77489i) q^{51} +(-0.692159 - 0.745970i) q^{52} +(-10.9042 - 4.27958i) q^{53} +(-0.448937 + 5.17672i) q^{54} +(0.995273 + 0.227165i) q^{55} +(2.55426 + 0.689739i) q^{56} +(-9.53485 - 8.91654i) q^{57} +(-0.0471493 + 0.629163i) q^{58} +(11.4491 - 3.53157i) q^{59} +(-2.69756 + 2.13406i) q^{60} +(-4.24886 + 1.66755i) q^{61} +(-0.0507721 - 0.0244505i) q^{62} +(-4.65082 - 6.43194i) q^{63} +(0.900969 - 0.433884i) q^{64} +(-1.37454 + 1.48140i) q^{65} +(0.383192 + 0.803714i) q^{66} +(-3.27424 - 5.67115i) q^{67} +(-1.38864 + 2.40519i) q^{68} +(0.381747 - 4.84053i) q^{69} +(0.986838 - 5.16061i) q^{70} +(-6.42198 + 5.12136i) q^{71} +(-2.91949 - 0.690367i) q^{72} +(8.41113 - 12.3369i) q^{73} +(-4.10230 + 6.01697i) q^{74} +(-1.23920 - 1.34604i) q^{75} +(5.89264 - 4.69923i) q^{76} +(-1.24555 - 0.546313i) q^{77} +(-1.75712 - 0.138575i) q^{78} +(-4.00283 + 6.93310i) q^{79} +(-0.992935 - 1.71981i) q^{80} +(5.50090 + 7.12321i) q^{81} +(4.61321 - 4.97186i) q^{82} +(13.9886 - 6.73658i) q^{83} +(4.06398 - 2.11757i) q^{84} +(4.96912 + 2.39300i) q^{85} +(1.35230 - 0.530739i) q^{86} +(0.678010 + 0.857036i) q^{87} +(-0.491228 + 0.151524i) q^{88} +(-0.954366 + 12.7351i) q^{89} +(-0.933882 + 5.88396i) q^{90} +(2.16939 - 1.59457i) q^{91} +(2.73307 + 0.623806i) q^{92} +(-0.0933810 + 0.0284057i) q^{93} +(-1.01654 - 0.398961i) q^{94} +(-10.1805 - 10.9719i) q^{95} +(0.639076 - 1.60984i) q^{96} +12.0264i q^{97} +(-2.58271 + 6.50612i) q^{98} +(1.43115 + 0.574615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9}+O(q^{10}) \) 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9	\( 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9} + 6 q^{10} - 12 q^{15} + 18 q^{16} - 4 q^{18} - 12 q^{19} + 10 q^{22} - 6 q^{24} + 16 q^{25} - 42 q^{27} + 2 q^{28} + 4 q^{30} + 6 q^{31} + 18 q^{33} - 10 q^{36} - 36 q^{37} + 4 q^{39} - 22 q^{40} + 20 q^{42} + 40 q^{43} - 14 q^{45} - 156 q^{46} - 134 q^{49} - 12 q^{51} + 16 q^{52} - 18 q^{54} - 322 q^{55} - 34 q^{57} - 164 q^{58} - 6 q^{60} + 56 q^{61} - 24 q^{63} + 36 q^{64} - 28 q^{69} - 4 q^{70} + 4 q^{72} - 24 q^{73} + 84 q^{75} + 16 q^{78} + 22 q^{79} - 52 q^{81} + 24 q^{82} + 42 q^{84} + 32 q^{85} - 94 q^{87} - 2 q^{88} + 42 q^{90} - 100 q^{91} - 266 q^{93} - 88 q^{94} - 6 q^{96} + 224 q^{99}+O(q^{100}) \) 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9 + 6 * q^10 - 12 * q^15 + 18 * q^16 - 4 * q^18 - 12 * q^19 + 10 * q^22 - 6 * q^24 + 16 * q^25 - 42 * q^27 + 2 * q^28 + 4 * q^30 + 6 * q^31 + 18 * q^33 - 10 * q^36 - 36 * q^37 + 4 * q^39 - 22 * q^40 + 20 * q^42 + 40 * q^43 - 14 * q^45 - 156 * q^46 - 134 * q^49 - 12 * q^51 + 16 * q^52 - 18 * q^54 - 322 * q^55 - 34 * q^57 - 164 * q^58 - 6 * q^60 + 56 * q^61 - 24 * q^63 + 36 * q^64 - 28 * q^69 - 4 * q^70 + 4 * q^72 - 24 * q^73 + 84 * q^75 + 16 * q^78 + 22 * q^79 - 52 * q^81 + 24 * q^82 + 42 * q^84 + 32 * q^85 - 94 * q^87 - 2 * q^88 + 42 * q^90 - 100 * q^91 - 266 * q^93 - 88 * q^94 - 6 * q^96 + 224 * q^99

Introduction

L-functions

Modular forms

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