LMFDB - Embedded newform 804.2.e.a.535.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(535,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("804.535");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.e (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			535.30
Character	$\chi$	$=$	804.535
Dual form			804.2.e.a.535.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34335 + 0.442044i) q^{2} -1.00000 q^{3} +(1.60919 + 1.18764i) q^{4} -2.27075i q^{5} +(-1.34335 - 0.442044i) q^{6} -4.97497 q^{7} +(1.63672 + 2.30676i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.34335 + 0.442044i) q^{2} -1.00000 q^{3} +(1.60919 + 1.18764i) q^{4} -2.27075i q^{5} +(-1.34335 - 0.442044i) q^{6} -4.97497 q^{7} +(1.63672 + 2.30676i) q^{8} +1.00000 q^{9} +(1.00377 - 3.05042i) q^{10} -2.26020 q^{11} +(-1.60919 - 1.18764i) q^{12} -6.26095i q^{13} +(-6.68314 - 2.19916i) q^{14} +2.27075i q^{15} +(1.17901 + 3.82230i) q^{16} -0.801988 q^{17} +(1.34335 + 0.442044i) q^{18} -2.05056i q^{19} +(2.69684 - 3.65408i) q^{20} +4.97497 q^{21} +(-3.03625 - 0.999109i) q^{22} -7.41079i q^{23} +(-1.63672 - 2.30676i) q^{24} -0.156305 q^{25} +(2.76762 - 8.41067i) q^{26} -1.00000 q^{27} +(-8.00569 - 5.90849i) q^{28} -6.30284 q^{29} +(-1.00377 + 3.05042i) q^{30} +2.55441 q^{31} +(-0.105802 + 5.65586i) q^{32} +2.26020 q^{33} +(-1.07735 - 0.354514i) q^{34} +11.2969i q^{35} +(1.60919 + 1.18764i) q^{36} -10.5854 q^{37} +(0.906438 - 2.75462i) q^{38} +6.26095i q^{39} +(5.23807 - 3.71659i) q^{40} -0.0427625i q^{41} +(6.68314 + 2.19916i) q^{42} +0.122241 q^{43} +(-3.63710 - 2.68431i) q^{44} -2.27075i q^{45} +(3.27590 - 9.95531i) q^{46} +4.63996i q^{47} +(-1.17901 - 3.82230i) q^{48} +17.7503 q^{49} +(-0.209973 - 0.0690940i) q^{50} +0.801988 q^{51} +(7.43578 - 10.0751i) q^{52} -6.54272i q^{53} +(-1.34335 - 0.442044i) q^{54} +5.13235i q^{55} +(-8.14265 - 11.4761i) q^{56} +2.05056i q^{57} +(-8.46694 - 2.78614i) q^{58} +4.77379i q^{59} +(-2.69684 + 3.65408i) q^{60} +10.5577i q^{61} +(3.43147 + 1.12916i) q^{62} -4.97497 q^{63} +(-2.64227 + 7.55105i) q^{64} -14.2171 q^{65} +(3.03625 + 0.999109i) q^{66} +(-2.57302 - 7.77043i) q^{67} +(-1.29055 - 0.952476i) q^{68} +7.41079i q^{69} +(-4.99374 + 15.1757i) q^{70} -4.26791i q^{71} +(1.63672 + 2.30676i) q^{72} +12.0198 q^{73} +(-14.2199 - 4.67921i) q^{74} +0.156305 q^{75} +(2.43533 - 3.29975i) q^{76} +11.2444 q^{77} +(-2.76762 + 8.41067i) q^{78} +1.63399 q^{79} +(8.67948 - 2.67723i) q^{80} +1.00000 q^{81} +(0.0189029 - 0.0574452i) q^{82} -5.62827i q^{83} +(8.00569 + 5.90849i) q^{84} +1.82111i q^{85} +(0.164212 + 0.0540358i) q^{86} +6.30284 q^{87} +(-3.69932 - 5.21374i) q^{88} +11.1834 q^{89} +(1.00377 - 3.05042i) q^{90} +31.1481i q^{91} +(8.80138 - 11.9254i) q^{92} -2.55441 q^{93} +(-2.05107 + 6.23311i) q^{94} -4.65631 q^{95} +(0.105802 - 5.65586i) q^{96} +14.5826i q^{97} +(23.8450 + 7.84644i) q^{98} -2.26020 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9	$ 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9} - 6 q^{10} - 2 q^{12} - 4 q^{14} + 2 q^{16} + 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} - 34 q^{27} + 8 q^{28} - 16 q^{29} + 6 q^{30} + 4 q^{31} + 2 q^{36} + 12 q^{37} - 26 q^{38} - 18 q^{40} + 4 q^{42} + 4 q^{43} - 26 q^{44} + 4 q^{46} - 2 q^{48} + 46 q^{49} + 18 q^{50} - 32 q^{52} + 14 q^{56} - 4 q^{58} - 12 q^{60} - 2 q^{62} - 4 q^{63} + 26 q^{64} + 8 q^{66} + 18 q^{67} - 34 q^{68} - 56 q^{70} + 6 q^{72} + 12 q^{73} - 22 q^{74} + 34 q^{75} - 32 q^{76} - 8 q^{77} - 10 q^{78} + 12 q^{79} + 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} + 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} - 32 q^{94} + 40 q^{95} + 40 q^{98}+O(q^{100}) $ 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9 - 6 * q^10 - 2 * q^12 - 4 * q^14 + 2 * q^16 + 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 - 34 * q^27 + 8 * q^28 - 16 * q^29 + 6 * q^30 + 4 * q^31 + 2 * q^36 + 12 * q^37 - 26 * q^38 - 18 * q^40 + 4 * q^42 + 4 * q^43 - 26 * q^44 + 4 * q^46 - 2 * q^48 + 46 * q^49 + 18 * q^50 - 32 * q^52 + 14 * q^56 - 4 * q^58 - 12 * q^60 - 2 * q^62 - 4 * q^63 + 26 * q^64 + 8 * q^66 + 18 * q^67 - 34 * q^68 - 56 * q^70 + 6 * q^72 + 12 * q^73 - 22 * q^74 + 34 * q^75 - 32 * q^76 - 8 * q^77 - 10 * q^78 + 12 * q^79 + 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 + 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 - 32 * q^94 + 40 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.34335	+	0.442044i	0.949894	+	0.312573i
$2$	1.34335	+	0.442044i	0.949894	+	0.312573i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.60919	+	1.18764i	0.804597	+	0.593822i
$5$		−	2.27075i		−	1.01551i	−0.861501	−	0.507755i	$-0.830475\pi$
$5$		−	2.27075i		−	1.01551i	0.861501	−	0.507755i	$-0.169525\pi$
$6$	−1.34335	−	0.442044i	−0.548421	−	0.180464i
$7$	−4.97497			−1.88036			−0.940181	−	0.340674i	$-0.889345\pi$
$7$	−4.97497			−1.88036			−0.940181	+	0.340674i	$0.889345\pi$
$8$	1.63672	+	2.30676i	0.578669	+	0.815562i
$9$	1.00000			0.333333
$10$	1.00377	−	3.05042i	0.317421	−	0.964627i
$11$	−2.26020			−0.681476			−0.340738	−	0.940158i	$-0.610677\pi$
$11$	−2.26020			−0.681476			−0.340738	+	0.940158i	$0.610677\pi$
$12$	−1.60919	−	1.18764i	−0.464534	−	0.342843i
$13$		−	6.26095i		−	1.73648i	−0.496148	−	0.868238i	$-0.665253\pi$
$13$		−	6.26095i		−	1.73648i	0.496148	−	0.868238i	$-0.334747\pi$
$14$	−6.68314	−	2.19916i	−1.78614	−	0.587750i
$15$			2.27075i			0.586305i
$16$	1.17901	+	3.82230i	0.294752	+	0.955574i
$17$	−0.801988			−0.194511			−0.0972553	−	0.995259i	$-0.531006\pi$
$17$	−0.801988			−0.194511			−0.0972553	+	0.995259i	$0.531006\pi$
$18$	1.34335	+	0.442044i	0.316631	+	0.104191i
$19$		−	2.05056i		−	0.470431i	−0.971943	−	0.235215i	$-0.924420\pi$
$19$		−	2.05056i		−	0.470431i	0.971943	−	0.235215i	$-0.0755795\pi$
$20$	2.69684	−	3.65408i	0.603032	−	0.817076i
$21$	4.97497			1.08563
$22$	−3.03625	−	0.999109i	−0.647330	−	0.213011i
$23$		−	7.41079i		−	1.54526i	−0.634858	−	0.772629i	$-0.718941\pi$
$23$		−	7.41079i		−	1.54526i	0.634858	−	0.772629i	$-0.281059\pi$
$24$	−1.63672	−	2.30676i	−0.334095	−	0.470865i
$25$	−0.156305			−0.0312611
$26$	2.76762	−	8.41067i	0.542775	−	1.64947i
$27$	−1.00000			−0.192450
$28$	−8.00569	−	5.90849i	−1.51293	−	1.11660i
$29$	−6.30284			−1.17041			−0.585204	−	0.810886i	$-0.698986\pi$
$29$	−6.30284			−1.17041			−0.585204	+	0.810886i	$0.698986\pi$
$30$	−1.00377	+	3.05042i	−0.183263	+	0.556928i
$31$	2.55441			0.458785			0.229392	−	0.973334i	$-0.426326\pi$
$31$	2.55441			0.458785			0.229392	+	0.973334i	$0.426326\pi$
$32$	−0.105802	+	5.65586i	−0.0187033	+	0.999825i
$33$	2.26020			0.393450
$34$	−1.07735	−	0.354514i	−0.184764	−	0.0607987i
$35$			11.2969i			1.90953i
$36$	1.60919	+	1.18764i	0.268199	+	0.197941i
$37$	−10.5854			−1.74023			−0.870114	−	0.492850i	$-0.835955\pi$
$37$	−10.5854			−1.74023			−0.870114	+	0.492850i	$0.835955\pi$
$38$	0.906438	−	2.75462i	0.147044	−	0.446859i
$39$			6.26095i			1.00256i
$40$	5.23807	−	3.71659i	0.828212	−	0.587644i
$41$		−	0.0427625i		−	0.00667839i	−0.999994	−	0.00333919i	$-0.998937\pi$
$41$		−	0.0427625i		−	0.00667839i	0.999994	−	0.00333919i	$-0.00106290\pi$
$42$	6.68314	+	2.19916i	1.03123	+	0.339338i
$43$	0.122241			0.0186415			0.00932077	−	0.999957i	$-0.497033\pi$
$43$	0.122241			0.0186415			0.00932077	+	0.999957i	$0.497033\pi$
$44$	−3.63710	−	2.68431i	−0.548313	−	0.404675i
$45$		−	2.27075i		−	0.338503i
$46$	3.27590	−	9.95531i	0.483005	−	1.46783i
$47$			4.63996i			0.676808i	0.941001	+	0.338404i	$0.109887\pi$
$47$			4.63996i			0.676808i	−0.941001	+	0.338404i	$0.890113\pi$
$48$	−1.17901	−	3.82230i	−0.170175	−	0.551701i
$49$	17.7503			2.53576
$50$	−0.209973	−	0.0690940i	−0.0296947	−	0.00977136i
$51$	0.801988			0.112301
$52$	7.43578	−	10.0751i	1.03116	−	1.39716i
$53$		−	6.54272i		−	0.898711i	−0.893353	−	0.449356i	$-0.851654\pi$
$53$		−	6.54272i		−	0.898711i	0.893353	−	0.449356i	$-0.148346\pi$
$54$	−1.34335	−	0.442044i	−0.182807	−	0.0601546i
$55$			5.13235i			0.692046i
$56$	−8.14265	−	11.4761i	−1.08811	−	1.53355i
$57$			2.05056i			0.271603i
$58$	−8.46694	−	2.78614i	−1.11176	−	0.365838i
$59$			4.77379i			0.621495i	0.950492	+	0.310748i	$0.100579\pi$
$59$			4.77379i			0.621495i	−0.950492	+	0.310748i	$0.899421\pi$
$60$	−2.69684	+	3.65408i	−0.348161	+	0.471739i
$61$			10.5577i			1.35177i	0.737007	+	0.675885i	$0.236238\pi$
$61$			10.5577i			1.35177i	−0.737007	+	0.675885i	$0.763762\pi$
$62$	3.43147	+	1.12916i	0.435797	+	0.143404i
$63$	−4.97497			−0.626788
$64$	−2.64227	+	7.55105i	−0.330284	+	0.943882i
$65$	−14.2171			−1.76341
$66$	3.03625	+	0.999109i	0.373736	+	0.122982i
$67$	−2.57302	−	7.77043i	−0.314345	−	0.949309i
$67$	−2.57302	−	7.77043i	−0.314345	−	0.949309i
$68$	−1.29055	−	0.952476i	−0.156503	−	0.115505i
$69$			7.41079i			0.892155i
$70$	−4.99374	+	15.1757i	−0.596866	+	1.81385i
$71$		−	4.26791i		−	0.506508i	−0.967400	−	0.253254i	$-0.918499\pi$
$71$		−	4.26791i		−	0.506508i	0.967400	−	0.253254i	$-0.0815008\pi$
$72$	1.63672	+	2.30676i	0.192890	+	0.271854i
$73$	12.0198			1.40681			0.703405	−	0.710789i	$-0.251662\pi$
$73$	12.0198			1.40681			0.703405	+	0.710789i	$0.251662\pi$
$74$	−14.2199	−	4.67921i	−1.65303	−	0.543948i
$75$	0.156305			0.0180486
$76$	2.43533	−	3.29975i	0.279352	−	0.378507i
$77$	11.2444			1.28142
$78$	−2.76762	+	8.41067i	−0.313371	+	0.952321i
$79$	1.63399			0.183838			0.0919192	−	0.995766i	$-0.470700\pi$
$79$	1.63399			0.183838			0.0919192	+	0.995766i	$0.470700\pi$
$80$	8.67948	−	2.67723i	0.970395	−	0.299323i
$81$	1.00000			0.111111
$82$	0.0189029	−	0.0574452i	0.00208748	−	0.00634376i
$83$		−	5.62827i		−	0.617783i	−0.951097	−	0.308892i	$-0.900042\pi$
$83$		−	5.62827i		−	0.617783i	0.951097	−	0.308892i	$-0.0999580\pi$
$84$	8.00569	+	5.90849i	0.873493	+	0.644669i
$85$			1.82111i			0.197528i
$86$	0.164212	+	0.0540358i	0.0177075	+	0.00582684i
$87$	6.30284			0.675736
$88$	−3.69932	−	5.21374i	−0.394349	−	0.555786i
$89$	11.1834			1.18544			0.592719	−	0.805409i	$-0.298055\pi$
$89$	11.1834			1.18544			0.592719	+	0.805409i	$0.298055\pi$
$90$	1.00377	−	3.05042i	0.105807	−	0.321542i
$91$			31.1481i			3.26520i
$92$	8.80138	−	11.9254i	0.917607	−	1.24331i
$93$	−2.55441			−0.264880
$94$	−2.05107	+	6.23311i	−0.211552	+	0.642896i
$95$	−4.65631			−0.477727
$96$	0.105802	−	5.65586i	0.0107983	−	0.577249i
$97$			14.5826i			1.48063i	0.672258	+	0.740317i	$0.265325\pi$
$97$			14.5826i			1.48063i	−0.672258	+	0.740317i	$0.734675\pi$
$98$	23.8450	+	7.84644i	2.40871	+	0.792610i
$99$	−2.26020			−0.227159
$100$	−0.251526	−	0.185635i	−0.0251526	−	0.0185635i
$101$		−	12.0397i		−	1.19799i	−0.800752	−	0.598996i	$-0.795566\pi$
$101$		−	12.0397i		−	1.19799i	0.800752	−	0.598996i	$-0.204434\pi$
$102$	1.07735	+	0.354514i	0.106674	+	0.0351021i
$103$			0.784321i			0.0772814i	0.999253	+	0.0386407i	$0.0123028\pi$
$103$			0.784321i			0.0772814i	−0.999253	+	0.0386407i	$0.987697\pi$
$104$	14.4425	−	10.2475i	1.41620	−	1.00485i
$105$		−	11.2969i		−	1.10247i
$106$	2.89217	−	8.78917i	0.280912	−	0.853680i
$107$			8.08673i			0.781774i	0.920439	+	0.390887i	$0.127832\pi$
$107$			8.08673i			0.781774i	−0.920439	+	0.390887i	$0.872168\pi$
$108$	−1.60919	−	1.18764i	−0.154845	−	0.114281i
$109$		−	0.577666i		−	0.0553303i	−0.999617	−	0.0276652i	$-0.991193\pi$
$109$		−	0.577666i		−	0.0553303i	0.999617	−	0.0276652i	$-0.00880722\pi$
$110$	−2.26873	+	6.89456i	−0.216315	+	0.657370i
$111$	10.5854			1.00472
$112$	−5.86553	−	19.0158i	−0.554240	−	1.79683i
$113$		−	3.80706i		−	0.358138i	−0.983837	−	0.179069i	$-0.942691\pi$
$113$		−	3.80706i		−	0.358138i	0.983837	−	0.179069i	$-0.0573086\pi$
$114$	−0.906438	+	2.75462i	−0.0848957	+	0.257994i
$115$	−16.8281			−1.56922
$116$	−10.1425	−	7.48553i	−0.941707	−	0.695014i
$117$		−	6.26095i		−	0.578825i
$118$	−2.11023	+	6.41289i	−0.194262	+	0.590354i
$119$	3.98987			0.365751
$120$	−5.23807	+	3.71659i	−0.478168	+	0.339277i
$121$	−5.89150			−0.535590
$122$	−4.66695	+	14.1827i	−0.422526	+	1.28404i
$123$			0.0427625i			0.00385577i
$124$	4.11053	+	3.03372i	0.369137	+	0.272436i
$125$		−	10.9988i		−	0.983764i
$126$	−6.68314	−	2.19916i	−0.595382	−	0.195917i
$127$		−	2.71383i		−	0.240814i	−0.992725	−	0.120407i	$-0.961580\pi$
$127$		−	2.71383i		−	0.240814i	0.992725	−	0.120407i	$-0.0384199\pi$
$128$	−6.88740	+	8.97573i	−0.608766	+	0.793350i
$129$	−0.122241			−0.0107627
$130$	−19.0985	−	6.28457i	−1.67505	−	0.551193i
$131$		−	15.8408i		−	1.38402i	−0.721889	−	0.692009i	$-0.756726\pi$
$131$		−	15.8408i		−	1.38402i	0.721889	−	0.692009i	$-0.243274\pi$
$132$	3.63710	+	2.68431i	0.316569	+	0.233639i
$133$			10.2015i			0.884580i
$134$	−0.0216033	−	11.5758i	−0.00186624	−	0.999998i
$135$			2.27075i			0.195435i
$136$	−1.31263	−	1.84999i	−0.112557	−	0.158636i
$137$			6.43436i			0.549724i	0.961484	+	0.274862i	$0.0886322\pi$
$137$			6.43436i			0.549724i	−0.961484	+	0.274862i	$0.911368\pi$
$138$	−3.27590	+	9.95531i	−0.278863	+	0.847452i
$139$	9.48021			0.804101			0.402051	−	0.915617i	$-0.368298\pi$
$139$	9.48021			0.804101			0.402051	+	0.915617i	$0.368298\pi$
$140$	−13.4167	+	18.1789i	−1.13392	+	1.53640i
$141$		−	4.63996i		−	0.390756i
$142$	1.88661	−	5.73331i	0.158320	−	0.481129i
$143$			14.1510i			1.18337i
$144$	1.17901	+	3.82230i	0.0982506	+	0.318525i
$145$			14.3122i			1.18856i
$146$	16.1468	+	5.31328i	1.33632	+	0.439730i
$147$	−17.7503			−1.46402
$148$	−17.0339	−	12.5717i	−1.40018	−	1.03339i
$149$	−2.55864			−0.209612			−0.104806	−	0.994493i	$-0.533422\pi$
$149$	−2.55864			−0.209612			−0.104806	+	0.994493i	$0.533422\pi$
$150$	0.209973	+	0.0690940i	0.0171443	+	0.00564150i
$151$			9.72333i			0.791274i	0.918407	+	0.395637i	$0.129476\pi$
$151$			9.72333i			0.791274i	−0.918407	+	0.395637i	$0.870524\pi$
$152$	4.73015	−	3.35620i	0.383666	−	0.272224i
$153$	−0.801988			−0.0648369
$154$	15.1052	+	4.97054i	1.21721	+	0.400537i
$155$		−	5.80042i		−	0.465901i
$156$	−7.43578	+	10.0751i	−0.595339	+	0.806652i
$157$	−1.07000			−0.0853952			−0.0426976	−	0.999088i	$-0.513595\pi$
$157$	−1.07000			−0.0853952			−0.0426976	+	0.999088i	$0.513595\pi$
$158$	2.19503	+	0.722297i	0.174627	+	0.0574629i
$159$			6.54272i			0.518871i
$160$	12.8431	+	0.240249i	1.01533	+	0.0189934i
$161$			36.8685i			2.90564i
$162$	1.34335	+	0.442044i	0.105544	+	0.0347303i
$163$			12.5690i			0.984480i	0.870460	+	0.492240i	$0.163822\pi$
$163$			12.5690i			0.984480i	−0.870460	+	0.492240i	$0.836178\pi$
$164$	0.0507866	−	0.0688132i	0.00396577	−	0.00537341i
$165$		−	5.13235i		−	0.399553i
$166$	2.48795	−	7.56076i	0.193102	−	0.586828i
$167$		−	18.3858i		−	1.42273i	−0.702821	−	0.711367i	$-0.748077\pi$
$167$		−	18.3858i		−	1.42273i	0.702821	−	0.711367i	$-0.251923\pi$
$168$	8.14265	+	11.4761i	0.628219	+	0.885397i
$169$	−26.1995			−2.01535
$170$	−0.805013	+	2.44640i	−0.0617417	+	0.187630i
$171$		−	2.05056i		−	0.156810i
$172$	0.196709	+	0.145178i	0.0149989	+	0.0110698i
$173$	7.50460			0.570564			0.285282	−	0.958444i	$-0.407913\pi$
$173$	7.50460			0.570564			0.285282	+	0.958444i	$0.407913\pi$
$174$	8.46694	+	2.78614i	0.641877	+	0.211216i
$175$	0.777615			0.0587822
$176$	−2.66479	−	8.63915i	−0.200866	−	0.651201i
$177$		−	4.77379i		−	0.358820i
$178$	15.0232	+	4.94356i	1.12604	+	0.370535i
$179$	16.1813			1.20945			0.604725	−	0.796434i	$-0.293283\pi$
$179$	16.1813			1.20945			0.604725	+	0.796434i	$0.293283\pi$
$180$	2.69684	−	3.65408i	0.201011	−	0.272359i
$181$	−7.75811			−0.576655			−0.288328	−	0.957532i	$-0.593099\pi$
$181$	−7.75811			−0.576655			−0.288328	+	0.957532i	$0.593099\pi$
$182$	−13.7688	+	41.8428i	−1.02061	+	3.10160i
$183$		−	10.5577i		−	0.780445i
$184$	17.0949	−	12.1294i	1.26025	−	0.894193i
$185$			24.0368i			1.76722i
$186$	−3.43147	−	1.12916i	−0.251608	−	0.0827941i
$187$	1.81265			0.132554
$188$	−5.51062	+	7.46660i	−0.401903	+	0.544558i
$189$	4.97497			0.361876
$190$	−6.25506	−	2.05830i	−0.453790	−	0.149324i
$191$	−22.1612			−1.60353			−0.801763	−	0.597643i	$-0.796104\pi$
$191$	−22.1612			−1.60353			−0.801763	+	0.597643i	$0.796104\pi$
$192$	2.64227	−	7.55105i	0.190690	−	0.544950i
$193$	−2.08597			−0.150151			−0.0750756	−	0.997178i	$-0.523920\pi$
$193$	−2.08597			−0.150151			−0.0750756	+	0.997178i	$0.523920\pi$
$194$	−6.44614	+	19.5895i	−0.462806	+	1.40645i
$195$	14.2171			1.01810
$196$	28.5637	+	21.0811i	2.04027	+	1.50579i
$197$		−	10.2001i		−	0.726730i	−0.931647	−	0.363365i	$-0.881628\pi$
$197$		−	10.2001i		−	0.726730i	0.931647	−	0.363365i	$-0.118372\pi$
$198$	−3.03625	−	0.999109i	−0.215777	−	0.0710036i
$199$		−	9.92139i		−	0.703309i	−0.936130	−	0.351655i	$-0.885619\pi$
$199$		−	9.92139i		−	0.703309i	0.936130	−	0.351655i	$-0.114381\pi$
$200$	−0.255829	−	0.360559i	−0.0180898	−	0.0254954i
$201$	2.57302	+	7.77043i	0.181487	+	0.548084i
$202$	5.32207	−	16.1735i	0.374460	−	1.13797i
$203$	31.3565			2.20079
$204$	1.29055	+	0.952476i	0.0903568	+	0.0666866i
$205$	−0.0971030			−0.00678197
$206$	−0.346705	+	1.05362i	−0.0241561	+	0.0734091i
$207$		−	7.41079i		−	0.515086i
$208$	23.9312	−	7.38171i	1.65933	−	0.511830i
$209$			4.63468i			0.320587i
$210$	4.99374	−	15.1757i	0.344601	−	1.04723i
$211$		−	4.80215i		−	0.330594i	−0.986244	−	0.165297i	$-0.947142\pi$
$211$		−	4.80215i		−	0.330594i	0.986244	−	0.165297i	$-0.0528582\pi$
$212$	7.77041	−	10.5285i	0.533674	−	0.723100i
$213$			4.26791i			0.292432i
$214$	−3.57469	+	10.8633i	−0.244361	+	0.742602i
$215$		−	0.277578i		−	0.0189307i
$216$	−1.63672	−	2.30676i	−0.111365	−	0.156955i
$217$	−12.7081			−0.862682
$218$	0.255354	−	0.776009i	0.0172947	−	0.0525579i
$219$	−12.0198			−0.812222
$220$	−6.09540	+	8.25894i	−0.410952	+	0.556818i
$221$			5.02121i			0.337763i
$222$	14.2199	+	4.67921i	0.954378	+	0.314048i
$223$			20.5061i			1.37319i	0.727042	+	0.686593i	$0.240895\pi$
$223$			20.5061i			1.37319i	−0.727042	+	0.686593i	$0.759105\pi$
$224$	0.526360	−	28.1378i	0.0351689	−	1.88003i
$225$	−0.156305			−0.0104204
$226$	1.68289	−	5.11423i	0.111944	−	0.340193i
$227$		−	17.8100i		−	1.18209i	−0.806637	−	0.591047i	$-0.798715\pi$
$227$		−	17.8100i		−	1.18209i	0.806637	−	0.591047i	$-0.201285\pi$
$228$	−2.43533	+	3.29975i	−0.161284	+	0.218531i
$229$			15.6488i			1.03410i	0.855956	+	0.517049i	$0.172970\pi$
$229$			15.6488i			1.03410i	−0.855956	+	0.517049i	$0.827030\pi$
$230$	−22.6060	−	7.43875i	−1.49060	−	0.490497i
$231$	−11.2444			−0.739829
$232$	−10.3160	−	14.5391i	−0.677279	−	0.954541i
$233$		−	21.3398i		−	1.39802i	−0.715114	−	0.699008i	$-0.753625\pi$
$233$		−	21.3398i		−	1.39802i	0.715114	−	0.699008i	$-0.246375\pi$
$234$	2.76762	−	8.41067i	0.180925	−	0.549823i
$235$	10.5362			0.687306
$236$	−5.66956	+	7.68196i	−0.369057	+	0.500053i
$237$	−1.63399			−0.106139
$238$	5.35980	+	1.76370i	0.347424	+	0.114324i
$239$	14.7710			0.955455			0.477727	−	0.878508i	$-0.341461\pi$
$239$	14.7710			0.955455			0.477727	+	0.878508i	$0.341461\pi$
$240$	−8.67948	+	2.67723i	−0.560258	+	0.172814i
$241$	12.6074			0.812116			0.406058	−	0.913847i	$-0.366903\pi$
$241$	12.6074			0.812116			0.406058	+	0.913847i	$0.366903\pi$
$242$	−7.91436	−	2.60430i	−0.508754	−	0.167411i
$243$	−1.00000			−0.0641500
$244$	−12.5387	+	16.9893i	−0.802710	+	1.08763i
$245$		−	40.3066i		−	2.57509i
$246$	−0.0189029	+	0.0574452i	−0.00120521	+	0.00366257i
$247$	−12.8385			−0.816892
$248$	4.18086	+	5.89240i	0.265485	+	0.374168i
$249$			5.62827i			0.356677i
$250$	4.86197	−	14.7753i	0.307498	−	0.934472i
$251$	−10.5634			−0.666758			−0.333379	−	0.942793i	$-0.608189\pi$
$251$	−10.5634			−0.666758			−0.333379	+	0.942793i	$0.608189\pi$
$252$	−8.00569	−	5.90849i	−0.504311	−	0.372200i
$253$			16.7499i			1.05306i
$254$	1.19963	−	3.64563i	0.0752718	−	0.228747i
$255$		−	1.82111i		−	0.114043i
$256$	−13.2199	+	9.01303i	−0.826243	+	0.563314i
$257$	−28.7622			−1.79414			−0.897069	−	0.441891i	$-0.854308\pi$
$257$	−28.7622			−1.79414			−0.897069	+	0.441891i	$0.854308\pi$
$258$	−0.164212	−	0.0540358i	−0.0102234	−	0.00336412i
$259$	52.6620			3.27226
$260$	−22.8780	−	16.8848i	−1.41883	−	1.04715i
$261$	−6.30284			−0.390136
$262$	7.00234	−	21.2798i	0.432606	−	1.31467i
$263$		−	27.1396i		−	1.67350i	−0.547584	−	0.836751i	$-0.684452\pi$
$263$		−	27.1396i		−	1.67350i	0.547584	−	0.836751i	$-0.315548\pi$
$264$	3.69932	+	5.21374i	0.227678	+	0.320883i
$265$	−14.8569			−0.912650
$266$	−4.50951	+	13.7042i	−0.276496	+	0.840257i
$267$	−11.1834			−0.684413
$268$	5.08800	−	15.5600i	0.310799	−	0.950476i
$269$	−26.0364			−1.58747			−0.793734	−	0.608265i	$-0.791866\pi$
$269$	−26.0364			−1.58747			−0.793734	+	0.608265i	$0.791866\pi$
$270$	−1.00377	+	3.05042i	−0.0610876	+	0.185643i
$271$	22.5243			1.36825			0.684127	−	0.729363i	$-0.260183\pi$
$271$	22.5243			1.36825			0.684127	+	0.729363i	$0.260183\pi$
$272$	−0.945550	−	3.06543i	−0.0573324	−	0.185869i
$273$		−	31.1481i		−	1.88517i
$274$	−2.84427	+	8.64361i	−0.171829	+	0.522180i
$275$	0.353282			0.0213037
$276$	−8.80138	+	11.9254i	−0.529781	+	0.717825i
$277$	26.8832			1.61525			0.807627	−	0.589693i	$-0.200751\pi$
$277$	26.8832			1.61525			0.807627	+	0.589693i	$0.200751\pi$
$278$	12.7353	+	4.19068i	0.763811	+	0.251340i
$279$	2.55441			0.152928
$280$	−26.0593	+	18.4899i	−1.55734	+	1.10498i
$281$		−	9.50374i		−	0.566946i	−0.958980	−	0.283473i	$-0.908513\pi$
$281$		−	9.50374i		−	0.566946i	0.958980	−	0.283473i	$-0.0914866\pi$
$282$	2.05107	−	6.23311i	0.122139	−	0.371176i
$283$		−	30.5183i		−	1.81413i	−0.420995	−	0.907063i	$-0.638319\pi$
$283$		−	30.5183i		−	1.81413i	0.420995	−	0.907063i	$-0.361681\pi$
$284$	5.06875	−	6.86789i	0.300775	−	0.407534i
$285$	4.65631			0.275816
$286$	−6.25537	+	19.0098i	−0.369888	+	1.12407i
$287$			0.212742i			0.0125578i
$288$	−0.105802	+	5.65586i	−0.00623442	+	0.333275i
$289$	−16.3568			−0.962166
$290$	−6.32662	+	19.2263i	−0.371512	+	1.12901i
$291$		−	14.5826i		−	0.854844i
$292$	19.3422	+	14.2752i	1.13191	+	0.835394i
$293$	27.4962			1.60634			0.803172	−	0.595748i	$-0.203144\pi$
$293$	27.4962			1.60634			0.803172	+	0.595748i	$0.203144\pi$
$294$	−23.8450	−	7.84644i	−1.39067	−	0.457614i
$295$	10.8401			0.631135
$296$	−17.3254	−	24.4180i	−1.00702	−	1.41926i
$297$	2.26020			0.131150
$298$	−3.43715	−	1.13103i	−0.199109	−	0.0655188i
$299$	−46.3986			−2.68330
$300$	0.251526	+	0.185635i	0.0145218	+	0.0107177i
$301$	−0.608144			−0.0350529
$302$	−4.29814	+	13.0619i	−0.247330	+	0.751626i
$303$			12.0397i			0.691661i
$304$	7.83784	−	2.41762i	0.449531	−	0.138660i
$305$	23.9738			1.37274
$306$	−1.07735	−	0.354514i	−0.0615882	−	0.0202662i
$307$		−	30.1875i		−	1.72289i	−0.507849	−	0.861446i	$-0.669559\pi$
$307$		−	30.1875i		−	1.72289i	0.507849	−	0.861446i	$-0.330441\pi$
$308$	18.0945	+	13.3544i	1.03103	+	0.760936i
$309$		−	0.784321i		−	0.0446184i
$310$	2.56404	−	7.79201i	0.145628	−	0.442556i
$311$	3.78543			0.214652			0.107326	−	0.994224i	$-0.465771\pi$
$311$	3.78543			0.214652			0.107326	+	0.994224i	$0.465771\pi$
$312$	−14.4425	+	10.2475i	−0.817646	+	0.580148i
$313$			2.73274i			0.154463i	0.997013	+	0.0772317i	$0.0246081\pi$
$313$			2.73274i			0.154463i	−0.997013	+	0.0772317i	$0.975392\pi$
$314$	−1.43739	−	0.472987i	−0.0811164	−	0.0266922i
$315$			11.2969i			0.636509i
$316$	2.62941	+	1.94060i	0.147916	+	0.109167i
$317$	22.7802			1.27946			0.639731	−	0.768599i	$-0.279046\pi$
$317$	22.7802			1.27946			0.639731	+	0.768599i	$0.279046\pi$
$318$	−2.89217	+	8.78917i	−0.162185	+	0.492872i
$319$	14.2457			0.797605
$320$	17.1466	+	5.99994i	0.958521	+	0.335407i
$321$		−	8.08673i		−	0.451357i
$322$	−16.2975	+	49.5274i	−0.908225	+	2.76005i
$323$			1.64452i			0.0915038i
$324$	1.60919	+	1.18764i	0.0893996	+	0.0659802i
$325$			0.978621i			0.0542842i
$326$	−5.55606	+	16.8846i	−0.307721	+	0.935151i
$327$			0.577666i			0.0319450i
$328$	0.0986429	−	0.0699904i	0.00544664	−	0.00386458i
$329$		−	23.0837i		−	1.27265i
$330$	2.26873	−	6.89456i	0.124889	−	0.379533i
$331$	30.0443			1.65138			0.825692	−	0.564121i	$-0.190785\pi$
$331$	30.0443			1.65138			0.825692	+	0.564121i	$0.190785\pi$
$332$	6.68438	−	9.05698i	0.366853	−	0.497066i
$333$	−10.5854			−0.580076
$334$	8.12733	−	24.6986i	0.444707	−	1.35145i
$335$	−17.6447	+	5.84269i	−0.964033	+	0.319220i
$336$	5.86553	+	19.0158i	0.319991	+	1.03740i
$337$		−	4.09206i		−	0.222909i	−0.993770	−	0.111454i	$-0.964449\pi$
$337$		−	4.09206i		−	0.222909i	0.993770	−	0.111454i	$-0.0355509\pi$
$338$	−35.1952	−	11.5814i	−1.91437	−	0.629943i
$339$			3.80706i			0.206771i
$340$	−2.16283	+	2.93052i	−0.117296	+	0.158930i
$341$	−5.77347			−0.312651
$342$	0.906438	−	2.75462i	0.0490146	−	0.148953i
$343$	−53.4827			−2.88779
$344$	0.200074	+	0.281980i	0.0107873	+	0.0152033i
$345$	16.8281			0.905992
$346$	10.0813	+	3.31737i	0.541976	+	0.178343i
$347$	−23.6605			−1.27016			−0.635082	−	0.772445i	$-0.719034\pi$
$347$	−23.6605			−1.27016			−0.635082	+	0.772445i	$0.719034\pi$
$348$	10.1425	+	7.48553i	0.543695	+	0.401266i
$349$	−15.4316			−0.826036			−0.413018	−	0.910723i	$-0.635525\pi$
$349$	−15.4316			−0.826036			−0.413018	+	0.910723i	$0.635525\pi$
$350$	1.04461	+	0.343741i	0.0558368	+	0.0183737i
$351$			6.26095i			0.334185i
$352$	0.239133	−	12.7834i	0.0127458	−	0.681357i
$353$		−	26.5179i		−	1.41141i	−0.708508	−	0.705703i	$-0.750631\pi$
$353$		−	26.5179i		−	1.41141i	0.708508	−	0.705703i	$-0.249369\pi$
$354$	2.11023	−	6.41289i	0.112157	−	0.340841i
$355$	−9.69136			−0.514364
$356$	17.9962	+	13.2819i	0.953799	+	0.703938i
$357$	−3.98987			−0.211166
$358$	21.7373	+	7.15287i	1.14885	+	0.378041i
$359$			5.34011i			0.281840i	0.990021	+	0.140920i	$0.0450061\pi$
$359$			5.34011i			0.281840i	−0.990021	+	0.140920i	$0.954994\pi$
$360$	5.23807	−	3.71659i	0.276071	−	0.195881i
$361$	14.7952			0.778695
$362$	−10.4219	−	3.42943i	−0.547761	−	0.180247i
$363$	5.89150			0.309223
$364$	−36.9928	+	50.1233i	−1.93895	+	2.62717i
$365$		−	27.2939i		−	1.42863i
$366$	4.66695	−	14.1827i	0.243946	−	0.741340i
$367$	1.83574			0.0958246			0.0479123	−	0.998852i	$-0.484743\pi$
$367$	1.83574			0.0958246			0.0479123	+	0.998852i	$0.484743\pi$
$368$	28.3262	−	8.73738i	1.47661	−	0.455467i
$369$		−	0.0427625i		−	0.00222613i
$370$	−10.6253	+	32.2899i	−0.552384	+	1.67867i
$371$			32.5498i			1.68990i
$372$	−4.11053	−	3.03372i	−0.213121	−	0.157291i
$373$		−	7.22623i		−	0.374160i	−0.982345	−	0.187080i	$-0.940098\pi$
$373$		−	7.22623i		−	0.374160i	0.982345	−	0.187080i	$-0.0599024\pi$
$374$	2.43503	+	0.801273i	0.125913	+	0.0414329i
$375$			10.9988i			0.567977i
$376$	−10.7033	+	7.59434i	−0.551980	+	0.391648i
$377$			39.4618i			2.03239i
$378$	6.68314	+	2.19916i	0.343744	+	0.113113i
$379$	−5.69650			−0.292610			−0.146305	−	0.989240i	$-0.546738\pi$
$379$	−5.69650			−0.292610			−0.146305	+	0.989240i	$0.546738\pi$
$380$	−7.49290	−	5.53003i	−0.384378	−	0.283685i
$381$			2.71383i			0.139034i
$382$	−29.7703	−	9.79622i	−1.52318	−	0.501218i
$383$	−5.56592			−0.284405			−0.142203	−	0.989838i	$-0.545418\pi$
$383$	−5.56592			−0.284405			−0.142203	+	0.989838i	$0.545418\pi$
$384$	6.88740	−	8.97573i	0.351471	−	0.458041i
$385$		−	25.5333i		−	1.30130i
$386$	−2.80219	−	0.922090i	−0.142628	−	0.0469331i
$387$	0.122241			0.00621385
$388$	−17.3189	+	23.4662i	−0.879232	+	1.19131i
$389$	10.8987			0.552584			0.276292	−	0.961074i	$-0.410894\pi$
$389$	10.8987			0.552584			0.276292	+	0.961074i	$0.410894\pi$
$390$	19.0985	+	6.28457i	0.967092	+	0.318232i
$391$			5.94337i			0.300569i
$392$	29.0524	+	40.9458i	1.46737	+	2.06807i
$393$			15.8408i			0.799063i
$394$	4.50892	−	13.7024i	0.227156	−	0.690316i
$395$		−	3.71039i		−	0.186690i
$396$	−3.63710	−	2.68431i	−0.182771	−	0.134892i
$397$	24.9955			1.25449			0.627244	−	0.778823i	$-0.284183\pi$
$397$	24.9955			1.25449			0.627244	+	0.778823i	$0.284183\pi$
$398$	4.38570	−	13.3279i	0.219835	−	0.668069i
$399$		−	10.2015i		−	0.510713i
$400$	−0.184285	−	0.597446i	−0.00921426	−	0.0298723i
$401$			34.5434i			1.72502i	0.506043	+	0.862508i	$0.331108\pi$
$401$			34.5434i			1.72502i	−0.506043	+	0.862508i	$0.668892\pi$
$402$	0.0216033	+	11.5758i	0.00107747	+	0.577349i
$403$		−	15.9930i		−	0.796669i
$404$	14.2988	−	19.3742i	0.711394	−	0.963901i
$405$		−	2.27075i		−	0.112834i
$406$	42.1228	+	13.8610i	2.09052	+	0.687907i
$407$	23.9251			1.18592
$408$	1.31263	+	1.84999i	0.0649850	+	0.0915883i
$409$			24.7341i			1.22302i	0.791236	+	0.611511i	$0.209438\pi$
$409$			24.7341i			1.22302i	−0.791236	+	0.611511i	$0.790562\pi$
$410$	−0.130444	−	0.0429238i	−0.00644215	−	0.00211986i
$411$		−	6.43436i		−	0.317383i
$412$	−0.931493	+	1.26212i	−0.0458914	+	0.0621804i
$413$		−	23.7495i		−	1.16864i
$414$	3.27590	−	9.95531i	0.161002	−	0.489277i
$415$	−12.7804			−0.627365
$416$	35.4111	+	0.662419i	1.73617	+	0.0324778i
$417$	−9.48021			−0.464248
$418$	−2.04873	+	6.22600i	−0.100207	+	0.304524i
$419$		−	20.1239i		−	0.983115i	−0.870845	−	0.491558i	$-0.836428\pi$
$419$		−	20.1239i		−	0.983115i	0.870845	−	0.491558i	$-0.163572\pi$
$420$	13.4167	−	18.1789i	0.654668	−	0.887041i
$421$	−28.3976			−1.38401			−0.692007	−	0.721891i	$-0.743273\pi$
$421$	−28.3976			−1.38401			−0.692007	+	0.721891i	$0.743273\pi$
$422$	2.12276	−	6.45098i	0.103334	−	0.314029i
$423$			4.63996i			0.225603i
$424$	15.0925	−	10.7086i	0.732955	−	0.520056i
$425$	0.125355			0.00608062
$426$	−1.88661	+	5.73331i	−0.0914064	+	0.277780i
$427$		−	52.5241i		−	2.54182i
$428$	−9.60415	+	13.0131i	−0.464234	+	0.629013i
$429$		−	14.1510i		−	0.683217i
$430$	0.122702	−	0.372885i	0.00591721	−	0.0179821i
$431$			21.5989i			1.04038i	0.854050	+	0.520190i	$0.174139\pi$
$431$			21.5989i			1.04038i	−0.854050	+	0.520190i	$0.825861\pi$
$432$	−1.17901	−	3.82230i	−0.0567250	−	0.183900i
$433$		−	24.8260i		−	1.19306i	−0.802591	−	0.596530i	$-0.796546\pi$
$433$		−	24.8260i		−	1.19306i	0.802591	−	0.596530i	$-0.203454\pi$
$434$	−17.0715	−	5.61755i	−0.819456	−	0.269651i
$435$		−	14.3122i		−	0.686216i
$436$	0.686061	−	0.929576i	0.0328563	−	0.0445186i
$437$	−15.1963			−0.726936
$438$	−16.1468	−	5.31328i	−0.771525	−	0.253878i
$439$		−	30.2045i		−	1.44158i	−0.693153	−	0.720790i	$-0.743779\pi$
$439$		−	30.2045i		−	1.44158i	0.693153	−	0.720790i	$-0.256221\pi$
$440$	−11.8391	+	8.40024i	−0.564407	+	0.400466i
$441$	17.7503			0.845255
$442$	−2.21960	+	6.74526i	−0.105575	+	0.320839i
$443$	−8.19067			−0.389150			−0.194575	−	0.980888i	$-0.562333\pi$
$443$	−8.19067			−0.389150			−0.194575	+	0.980888i	$0.562333\pi$
$444$	17.0339	+	12.5717i	0.808395	+	0.596625i
$445$		−	25.3947i		−	1.20382i
$446$	−9.06459	+	27.5469i	−0.429221	+	1.30438i
$447$	2.55864			0.121019
$448$	13.1452	−	37.5663i	0.621054	−	1.77484i
$449$	−19.9290			−0.940507			−0.470253	−	0.882532i	$-0.655837\pi$
$449$	−19.9290			−0.940507			−0.470253	+	0.882532i	$0.655837\pi$
$450$	−0.209973	−	0.0690940i	−0.00989824	−	0.00325712i
$451$			0.0966519i			0.00455116i
$452$	4.52143	−	6.12630i	0.212670	−	0.288157i
$453$		−	9.72333i		−	0.456842i
$454$	7.87283	−	23.9252i	0.369490	−	1.12286i
$455$	70.7295			3.31585
$456$	−4.73015	+	3.35620i	−0.221509	+	0.157168i
$457$	10.7034			0.500684			0.250342	−	0.968157i	$-0.419457\pi$
$457$	10.7034			0.500684			0.250342	+	0.968157i	$0.419457\pi$
$458$	−6.91744	+	21.0218i	−0.323231	+	0.982284i
$459$	0.801988			0.0374336
$460$	−27.0796	−	19.9857i	−1.26259	−	0.931839i
$461$	−5.20155			−0.242260			−0.121130	−	0.992637i	$-0.538652\pi$
$461$	−5.20155			−0.242260			−0.121130	+	0.992637i	$0.538652\pi$
$462$	−15.1052	−	4.97054i	−0.702759	−	0.231250i
$463$	13.5838			0.631295			0.315647	−	0.948877i	$-0.397778\pi$
$463$	13.5838			0.631295			0.315647	+	0.948877i	$0.397778\pi$
$464$	−7.43110	−	24.0913i	−0.344980	−	1.11841i
$465$			5.80042i			0.268988i
$466$	9.43313	−	28.6669i	0.436981	−	1.32797i
$467$			20.1652i			0.933133i	0.884486	+	0.466567i	$0.154509\pi$
$467$			20.1652i			0.933133i	−0.884486	+	0.466567i	$0.845491\pi$
$468$	7.43578	−	10.0751i	0.343719	−	0.465721i
$469$	12.8007	+	38.6577i	0.591082	+	1.78504i
$470$	14.1538	+	4.65747i	0.652868	+	0.214833i
$471$	1.07000			0.0493029
$472$	−11.0120	+	7.81338i	−0.506868	+	0.359640i
$473$	−0.276289			−0.0127038
$474$	−2.19503	−	0.722297i	−0.100821	−	0.0331762i
$475$			0.320514i			0.0147062i
$476$	6.42047	+	4.73854i	0.294282	+	0.217191i
$477$		−	6.54272i		−	0.299570i
$478$	19.8426	+	6.52942i	0.907581	+	0.298649i
$479$		−	1.14279i		−	0.0522153i	−0.999659	−	0.0261076i	$-0.991689\pi$
$479$		−	1.14279i		−	0.0522153i	0.999659	−	0.0261076i	$-0.00831126\pi$
$480$	−12.8431	−	0.240249i	−0.586203	−	0.0109658i
$481$			66.2747i			3.02186i
$482$	16.9362	+	5.57305i	0.771424	+	0.253845i
$483$		−	36.8685i		−	1.67757i
$484$	−9.48056	−	6.99699i	−0.430934	−	0.318045i
$485$	33.1133			1.50360
$486$	−1.34335	−	0.442044i	−0.0609357	−	0.0200515i
$487$	1.60567			0.0727597			0.0363799	−	0.999338i	$-0.488417\pi$
$487$	1.60567			0.0727597			0.0363799	+	0.999338i	$0.488417\pi$
$488$	−24.3540	+	17.2800i	−1.10245	+	0.782228i
$489$		−	12.5690i		−	0.568390i
$490$	17.8173	−	54.1460i	0.804904	−	2.44607i
$491$			13.2070i			0.596025i	0.954562	+	0.298013i	$0.0963237\pi$
$491$			13.2070i			0.596025i	−0.954562	+	0.298013i	$0.903676\pi$
$492$	−0.0507866	+	0.0688132i	−0.00228964	+	0.00310234i
$493$	5.05480			0.227657
$494$	−17.2466	−	5.67517i	−0.775960	−	0.255338i
$495$			5.13235i			0.230682i
$496$	3.01166	+	9.76370i	0.135228	+	0.438403i
$497$			21.2327i			0.952418i
$498$	−2.48795	+	7.56076i	−0.111488	+	0.338806i
$499$	−8.99468			−0.402657			−0.201329	−	0.979524i	$-0.564526\pi$
$499$	−8.99468			−0.402657			−0.201329	+	0.979524i	$0.564526\pi$
$500$	13.0627	−	17.6992i	0.584180	−	0.791534i
$501$			18.3858i			0.821416i
$502$	−14.1904	−	4.66951i	−0.633350	−	0.208410i
$503$	−26.6513			−1.18832			−0.594162	−	0.804345i	$-0.702516\pi$
$503$	−26.6513			−1.18832			−0.594162	+	0.804345i	$0.702516\pi$
$504$	−8.14265	−	11.4761i	−0.362703	−	0.511184i
$505$	−27.3391			−1.21657
$506$	−7.40419	+	22.5010i	−0.329156	+	1.00029i
$507$	26.1995			1.16356
$508$	3.22306	−	4.36708i	0.143000	−	0.193758i
$509$	−13.3609			−0.592212			−0.296106	−	0.955155i	$-0.595688\pi$
$509$	−13.3609			−0.592212			−0.296106	+	0.955155i	$0.595688\pi$
$510$	0.805013	−	2.44640i	0.0356466	−	0.108328i
$511$	−59.7981			−2.64531
$512$	−21.7431	+	6.26390i	−0.960920	+	0.276828i
$513$			2.05056i			0.0905344i
$514$	−38.6378	−	12.7142i	−1.70424	−	0.560798i
$515$	1.78100			0.0784801
$516$	−0.196709	−	0.145178i	−0.00865963	−	0.00639112i
$517$		−	10.4872i		−	0.461229i
$518$	70.7437	+	23.2790i	3.10830	+	1.02282i
$519$	−7.50460			−0.329415
$520$	−23.2694	−	32.7953i	−1.02043	−	1.43817i
$521$			1.99406i			0.0873612i	0.999046	+	0.0436806i	$0.0139084\pi$
$521$			1.99406i			0.0873612i	−0.999046	+	0.0436806i	$0.986092\pi$
$522$	−8.46694	−	2.78614i	−0.370588	−	0.121946i
$523$			22.8614i			0.999657i	0.866124	+	0.499829i	$0.166604\pi$
$523$			22.8614i			0.999657i	−0.866124	+	0.499829i	$0.833396\pi$
$524$	18.8132	−	25.4909i	0.821860	−	1.11358i
$525$	−0.777615			−0.0339379
$526$	11.9969	−	36.4581i	0.523091	−	1.58965i
$527$	−2.04860			−0.0892386
$528$	2.66479	+	8.63915i	0.115970	+	0.375971i
$529$	−31.9199			−1.38782
$530$	−19.9580	−	6.56740i	−0.866921	−	0.285269i
$531$			4.77379i			0.207165i
$532$	−12.1157	+	16.4161i	−0.525283	+	0.711730i
$533$	−0.267734			−0.0115969
$534$	−15.0232	−	4.94356i	−0.650119	−	0.213929i
$535$	18.3629			0.793899
$536$	13.7132	−	18.6534i	0.592319	−	0.805704i
$537$	−16.1813			−0.698277
$538$	−34.9761	−	11.5093i	−1.50793	−	0.496199i
$539$	−40.1193			−1.72806
$540$	−2.69684	+	3.65408i	−0.116054	+	0.157246i
$541$		−	34.9068i		−	1.50076i	−0.661006	−	0.750381i	$-0.729870\pi$
$541$		−	34.9068i		−	1.50076i	0.661006	−	0.750381i	$-0.270130\pi$
$542$	30.2581	+	9.95674i	1.29970	+	0.427679i
$543$	7.75811			0.332932
$544$	0.0848516	−	4.53594i	0.00363798	−	0.194477i
$545$	−1.31173			−0.0561885
$546$	13.7688	−	41.8428i	0.589252	−	1.79071i
$547$	−15.7623			−0.673949			−0.336974	−	0.941514i	$-0.609404\pi$
$547$	−15.7623			−0.673949			−0.336974	+	0.941514i	$0.609404\pi$
$548$	−7.64172	+	10.3541i	−0.326438	+	0.442306i
$549$			10.5577i			0.450590i
$550$	0.474582	+	0.156166i	0.0202362	+	0.00665895i
$551$			12.9244i			0.550596i
$552$	−17.0949	+	12.1294i	−0.727608	+	0.516262i
$553$	−8.12906			−0.345683
$554$	36.1136	+	11.8836i	1.53432	+	0.504884i
$555$		−	24.0368i		−	1.02030i
$556$	15.2555	+	11.2591i	0.646977	+	0.477493i
$557$	−17.8525			−0.756434			−0.378217	−	0.925717i	$-0.623463\pi$
$557$	−17.8525			−0.756434			−0.378217	+	0.925717i	$0.623463\pi$
$558$	3.43147	+	1.12916i	0.145266	+	0.0478012i
$559$		−	0.765344i		−	0.0323706i
$560$	−43.1802	+	13.3191i	−1.82469	+	0.562837i
$561$	−1.81265			−0.0765303
$562$	4.20107	−	12.7669i	0.177212	−	0.538538i
$563$	−4.39824			−0.185364			−0.0926819	−	0.995696i	$-0.529544\pi$
$563$	−4.39824			−0.185364			−0.0926819	+	0.995696i	$0.529544\pi$
$564$	5.51062	−	7.46660i	0.232039	−	0.314401i
$565$	−8.64488			−0.363693
$566$	13.4905	−	40.9969i	0.567046	−	1.72323i
$567$	−4.97497			−0.208929
$568$	9.84504	−	6.98539i	0.413089	−	0.293100i
$569$	30.0978			1.26177			0.630883	−	0.775878i	$-0.282693\pi$
$569$	30.0978			1.26177			0.630883	+	0.775878i	$0.282693\pi$
$570$	6.25506	+	2.05830i	0.261996	+	0.0862125i
$571$			14.9871i			0.627193i	0.949556	+	0.313596i	$0.101534\pi$
$571$			14.9871i			0.627193i	−0.949556	+	0.313596i	$0.898466\pi$
$572$	−16.8063	+	22.7717i	−0.702709	+	0.952133i
$573$	22.1612			0.925796
$574$	−0.0940416	+	0.285788i	−0.00392522	+	0.0119286i
$575$			1.15835i			0.0483064i
$576$	−2.64227	+	7.55105i	−0.110095	+	0.314627i
$577$		−	8.20721i		−	0.341671i	−0.985300	−	0.170835i	$-0.945353\pi$
$577$		−	8.20721i		−	0.341671i	0.985300	−	0.170835i	$-0.0546466\pi$
$578$	−21.9730	−	7.23044i	−0.913955	−	0.300747i
$579$	2.08597			0.0866898
$580$	−16.9978	+	23.0311i	−0.705794	+	0.956313i
$581$			28.0005i			1.16166i
$582$	6.44614	−	19.5895i	0.267201	−	0.812012i
$583$			14.7878i			0.612450i
$584$	19.6731	+	27.7268i	0.814078	+	1.14734i
$585$	−14.2171			−0.587803
$586$	36.9371	+	12.1545i	1.52586	+	0.502099i
$587$	40.7038			1.68003			0.840013	−	0.542567i	$-0.182548\pi$
$587$	40.7038			1.68003			0.840013	+	0.542567i	$0.182548\pi$
$588$	−28.5637	−	21.0811i	−1.17795	−	0.869369i
$589$		−	5.23796i		−	0.215827i
$590$	14.5621	+	4.79180i	0.599511	+	0.197275i
$591$			10.2001i			0.419578i
$592$	−12.4803	−	40.4605i	−0.512935	−	1.66292i
$593$			25.6918i			1.05504i	0.849544	+	0.527518i	$0.176877\pi$
$593$			25.6918i			1.05504i	−0.849544	+	0.527518i	$0.823123\pi$
$594$	3.03625	+	0.999109i	0.124579	+	0.0409939i
$595$		−	9.05999i		−	0.371423i
$596$	−4.11734	−	3.03875i	−0.168653	−	0.124472i
$597$			9.92139i			0.406056i
$598$	−62.3297	−	20.5103i	−2.54885	−	0.838727i
$599$	11.2224			0.458534			0.229267	−	0.973364i	$-0.426367\pi$
$599$	11.2224			0.458534			0.229267	+	0.973364i	$0.426367\pi$
$600$	0.255829	+	0.360559i	0.0104442	+	0.0147198i
$601$	41.1487			1.67849			0.839246	−	0.543752i	$-0.182997\pi$
$601$	41.1487			1.67849			0.839246	+	0.543752i	$0.182997\pi$
$602$	−0.816952	−	0.268827i	−0.0332965	−	0.0109566i
$603$	−2.57302	−	7.77043i	−0.104782	−	0.316436i
$604$	−11.5478	+	15.6467i	−0.469875	+	0.636656i
$605$			13.3781i			0.543898i
$606$	−5.32207	+	16.1735i	−0.216194	+	0.657005i
$607$			30.0411i			1.21933i	0.792658	+	0.609666i	$0.208696\pi$
$607$			30.0411i			1.21933i	−0.792658	+	0.609666i	$0.791304\pi$
$608$	11.5977	+	0.216953i	0.470348	+	0.00879859i
$609$	−31.3565			−1.27063
$610$	32.2053	+	10.5975i	1.30395	+	0.429080i
$611$	29.0506			1.17526
$612$	−1.29055	−	0.952476i	−0.0521675	−	0.0385015i
$613$	14.2161			0.574183			0.287091	−	0.957903i	$-0.407312\pi$
$613$	14.2161			0.574183			0.287091	+	0.957903i	$0.407312\pi$
$614$	13.3442	−	40.5525i	0.538529	−	1.63657i
$615$	0.0971030			0.00391557
$616$	18.4040	+	25.9382i	0.741519	+	1.04508i
$617$	−15.1626			−0.610422			−0.305211	−	0.952285i	$-0.598727\pi$
$617$	−15.1626			−0.610422			−0.305211	+	0.952285i	$0.598727\pi$
$618$	0.346705	−	1.05362i	0.0139465	−	0.0423828i
$619$		−	25.2680i		−	1.01561i	−0.861473	−	0.507803i	$-0.830458\pi$
$619$		−	25.2680i		−	1.01561i	0.861473	−	0.507803i	$-0.169542\pi$
$620$	6.88883	−	9.33400i	0.276662	−	0.374862i
$621$			7.41079i			0.297385i
$622$	5.08516	+	1.67333i	0.203896	+	0.0670943i
$623$	−55.6371			−2.22905
$624$	−23.9312	+	7.38171i	−0.958015	+	0.295505i
$625$	−25.7571			−1.03028
$626$	−1.20799	+	3.67103i	−0.0482811	+	0.146724i
$627$		−	4.63468i		−	0.185091i
$628$	−1.72183	−	1.27078i	−0.0687087	−	0.0507095i
$629$	8.48936			0.338493
$630$	−4.99374	+	15.1757i	−0.198955	+	0.604616i
$631$	21.9479			0.873730			0.436865	−	0.899527i	$-0.356089\pi$
$631$	21.9479			0.873730			0.436865	+	0.899527i	$0.356089\pi$
$632$	2.67439	+	3.76923i	0.106382	+	0.149932i
$633$			4.80215i			0.190868i
$634$	30.6018	+	10.0698i	1.21535	+	0.399925i
$635$	−6.16243			−0.244549
$636$	−7.77041	+	10.5285i	−0.308117	+	0.417482i
$637$		−	111.134i		−	4.40329i
$638$	19.1370	+	6.29723i	0.757640	+	0.249310i
$639$		−	4.26791i		−	0.168836i
$640$	20.3816	+	15.6396i	0.805655	+	0.618208i
$641$			3.44266i			0.135977i	0.997686	+	0.0679884i	$0.0216581\pi$
$641$			3.44266i			0.135977i	−0.997686	+	0.0679884i	$0.978342\pi$
$642$	3.57469	−	10.8633i	0.141082	−	0.428741i
$643$			15.5927i			0.614917i	0.951561	+	0.307459i	$0.0994785\pi$
$643$			15.5927i			0.614917i	−0.951561	+	0.307459i	$0.900521\pi$
$644$	−43.7866	+	59.3285i	−1.72543	+	2.33787i
$645$			0.277578i			0.0109296i
$646$	−0.726953	+	2.20918i	−0.0286016	+	0.0869189i
$647$	40.7155			1.60069			0.800345	−	0.599540i	$-0.204650\pi$
$647$	40.7155			1.60069			0.800345	+	0.599540i	$0.204650\pi$
$648$	1.63672	+	2.30676i	0.0642966	+	0.0906180i
$649$		−	10.7897i		−	0.423534i
$650$	−0.432594	+	1.31463i	−0.0169677	+	0.0515642i
$651$	12.7081			0.498070
$652$	−14.9275	+	20.2259i	−0.584605	+	0.792109i
$653$			24.0731i			0.942053i	0.882119	+	0.471026i	$0.156116\pi$
$653$			24.0731i			0.942053i	−0.882119	+	0.471026i	$0.843884\pi$
$654$	−0.255354	+	0.776009i	−0.00998513	+	0.0303443i
$655$	−35.9705			−1.40548
$656$	0.163451	−	0.0504173i	0.00638169	−	0.00196847i
$657$	12.0198			0.468937
$658$	10.2040	−	31.0095i	0.397794	−	1.20888i
$659$		−	25.1795i		−	0.980854i	−0.871482	−	0.490427i	$-0.836841\pi$
$659$		−	25.1795i		−	0.980854i	0.871482	−	0.490427i	$-0.163159\pi$
$660$	6.09540	−	8.25894i	0.237263	−	0.321479i
$661$		−	2.99404i		−	0.116455i	−0.998303	−	0.0582274i	$-0.981455\pi$
$661$		−	2.99404i		−	0.116455i	0.998303	−	0.0582274i	$-0.0185448\pi$
$662$	40.3601	+	13.2809i	1.56864	+	0.516177i
$663$		−	5.02121i		−	0.195008i
$664$	12.9831	−	9.21193i	0.503841	−	0.357492i
$665$	23.1650			0.898300
$666$	−14.2199	−	4.67921i	−0.551011	−	0.181316i
$667$			46.7091i			1.80858i
$668$	21.8357	−	29.5863i	0.844850	−	1.14473i
$669$		−	20.5061i		−	0.792810i
$670$	−26.2858	+	0.0490557i	−1.01551	+	0.00189519i
$671$		−	23.8624i		−	0.921199i
$672$	−0.526360	+	28.1378i	−0.0203048	+	1.08544i
$673$			21.4314i			0.826118i	0.910704	+	0.413059i	$0.135540\pi$
$673$			21.4314i			0.826118i	−0.910704	+	0.413059i	$0.864460\pi$
$674$	1.80887	−	5.49709i	0.0696752	−	0.211740i
$675$	0.156305			0.00601620
$676$	−42.1601	−	31.1157i	−1.62154	−	1.19676i
$677$		−	29.4225i		−	1.13080i	−0.824818	−	0.565398i	$-0.808722\pi$
$677$		−	29.4225i		−	1.13080i	0.824818	−	0.565398i	$-0.191278\pi$
$678$	−1.68289	+	5.11423i	−0.0646310	+	0.196411i
$679$		−	72.5478i		−	2.78413i
$680$	−4.20087	+	2.98066i	−0.161096	+	0.114303i
$681$			17.8100i			0.682482i
$682$	−7.75581	−	2.55213i	−0.296985	−	0.0977261i
$683$	−40.3198			−1.54279			−0.771396	−	0.636355i	$-0.780441\pi$
$683$	−40.3198			−1.54279			−0.771396	+	0.636355i	$0.780441\pi$
$684$	2.43533	−	3.29975i	0.0931173	−	0.126169i
$685$	14.6108			0.558251
$686$	−71.8461	−	23.6417i	−2.74310	−	0.902645i
$687$		−	15.6488i		−	0.597037i
$688$	0.144123	+	0.467240i	0.00549463	+	0.0178134i
$689$	−40.9636			−1.56059
$690$	22.6060	+	7.43875i	0.860597	+	0.283188i
$691$			43.5969i			1.65851i	0.558874	+	0.829253i	$0.311234\pi$
$691$			43.5969i			1.65851i	−0.558874	+	0.829253i	$0.688766\pi$
$692$	12.0764	+	8.91279i	0.459074	+	0.338813i
$693$	11.2444			0.427141
$694$	−31.7844	−	10.4590i	−1.20652	−	0.397019i
$695$		−	21.5272i		−	0.816573i
$696$	10.3160	+	14.5391i	0.391027	+	0.551105i
$697$			0.0342950i			0.00129902i
$698$	−20.7301	−	6.82146i	−0.784646	−	0.258196i
$699$			21.3398i			0.807145i
$700$	1.25133	+	0.923530i	0.0472960	+	0.0349061i
$701$		−	10.9225i		−	0.412538i	−0.978495	−	0.206269i	$-0.933868\pi$
$701$		−	10.9225i		−	0.412538i	0.978495	−	0.206269i	$-0.0661322\pi$
$702$	−2.76762	+	8.41067i	−0.104457	+	0.317440i
$703$			21.7060i			0.818657i
$704$	5.97206	−	17.0669i	0.225081	−	0.643233i
$705$	−10.5362			−0.396816
$706$	11.7221	−	35.6229i	0.441167	−	1.34069i
$707$			59.8971i			2.25266i
$708$	5.66956	−	7.68196i	0.213075	−	0.288706i
$709$	−34.3717			−1.29086			−0.645428	−	0.763821i	$-0.723321\pi$
$709$	−34.3717			−1.29086			−0.645428	+	0.763821i	$0.723321\pi$
$710$	−13.0189	−	4.28401i	−0.488591	−	0.160776i
$711$	1.63399			0.0612795
$712$	18.3041	+	25.7974i	0.685976	+	0.966798i
$713$		−	18.9302i		−	0.708941i
$714$	−5.35980	−	1.76370i	−0.200585	−	0.0660048i
$715$	32.1334			1.20172
$716$	26.0389	+	19.2177i	0.973120	+	0.718198i
$717$	−14.7710			−0.551632
$718$	−2.36057	+	7.17365i	−0.0880955	+	0.267718i
$719$		−	16.3257i		−	0.608845i	−0.952537	−	0.304423i	$-0.901536\pi$
$719$		−	16.3257i		−	0.608845i	0.952537	−	0.304423i	$-0.0984635\pi$
$720$	8.67948	−	2.67723i	0.323465	−	0.0997745i
$721$		−	3.90197i		−	0.145317i
$722$	19.8752	+	6.54014i	0.739678	+	0.243399i
$723$	−12.6074			−0.468876
$724$	−12.4843	−	9.21386i	−0.463975	−	0.342430i
$725$	0.985169			0.0365883
$726$	7.91436	+	2.60430i	0.293729	+	0.0966547i
$727$	6.85732			0.254324			0.127162	−	0.991882i	$-0.459413\pi$
$727$	6.85732			0.254324			0.127162	+	0.991882i	$0.459413\pi$
$728$	−71.8511	+	50.9808i	−2.66298	+	1.88947i
$729$	1.00000			0.0370370
$730$	12.0651	−	36.6654i	0.446551	−	1.35705i
$731$	−0.0980356			−0.00362598
$732$	12.5387	−	16.9893i	0.463445	−	0.627943i
$733$		−	31.1448i		−	1.15036i	−0.818028	−	0.575179i	$-0.804932\pi$
$733$		−	31.1448i		−	1.15036i	0.818028	−	0.575179i	$-0.195068\pi$
$734$	2.46604	+	0.811477i	0.0910232	+	0.0299522i
$735$			40.3066i			1.48673i
$736$	41.9144	+	0.784074i	1.54499	+	0.0289014i
$737$	5.81555	+	17.5627i	0.214218	+	0.646931i
$738$	0.0189029	−	0.0574452i	0.000695827	−	0.00211459i
$739$	38.9784			1.43384			0.716921	−	0.697154i	$-0.245551\pi$
$739$	38.9784			1.43384			0.716921	+	0.697154i	$0.245551\pi$
$740$	−28.5471	+	38.6798i	−1.04941	+	1.42190i
$741$	12.8385			0.471633
$742$	−14.3885	+	43.7259i	−0.528217	+	1.60523i
$743$			44.4828i			1.63191i	0.578113	+	0.815957i	$0.303789\pi$
$743$			44.4828i			1.63191i	−0.578113	+	0.815957i	$0.696211\pi$
$744$	−4.18086	−	5.89240i	−0.153278	−	0.216026i
$745$			5.81002i			0.212863i
$746$	3.19432	−	9.70738i	0.116952	−	0.355412i
$747$		−	5.62827i		−	0.205928i
$748$	2.91691	+	2.15279i	0.106653	+	0.0787136i
$749$		−	40.2313i		−	1.47002i
$750$	−4.86197	+	14.7753i	−0.177534	+	0.539517i
$751$			27.2477i			0.994282i	0.867670	+	0.497141i	$0.165617\pi$
$751$			27.2477i			0.994282i	−0.867670	+	0.497141i	$0.834383\pi$
$752$	−17.7353	+	5.47055i	−0.646740	+	0.199491i
$753$	10.5634			0.384953
$754$	−17.4439	+	53.0111i	−0.635268	+	1.93055i
$755$	22.0793			0.803546
$756$	8.00569	+	5.90849i	0.291164	+	0.214890i
$757$			45.2637i			1.64514i	0.568665	+	0.822569i	$0.307460\pi$
$757$			45.2637i			1.64514i	−0.568665	+	0.822569i	$0.692540\pi$
$758$	−7.65241	−	2.51811i	−0.277948	−	0.0914617i
$759$		−	16.7499i		−	0.607982i
$760$	−7.62109	−	10.7410i	−0.276446	−	0.389616i
$761$	8.62710			0.312732			0.156366	−	0.987699i	$-0.450022\pi$
$761$	8.62710			0.312732			0.156366	+	0.987699i	$0.450022\pi$
$762$	−1.19963	+	3.64563i	−0.0434582	+	0.132067i
$763$			2.87387i			0.104041i
$764$	−35.6616	−	26.3196i	−1.29019	−	0.952208i
$765$			1.82111i			0.0658425i
$766$	−7.47699	−	2.46038i	−0.270155	−	0.0888973i
$767$	29.8885			1.07921
$768$	13.2199	−	9.01303i	0.477031	−	0.325230i
$769$			26.2086i			0.945107i	0.881302	+	0.472554i	$0.156668\pi$
$769$			26.2086i			0.945107i	−0.881302	+	0.472554i	$0.843332\pi$
$770$	11.2868	−	34.3002i	0.406750	−	1.23609i
$771$	28.7622			1.03585
$772$	−3.35672	−	2.47738i	−0.120811	−	0.0891630i
$773$	7.06059			0.253952			0.126976	−	0.991906i	$-0.459473\pi$
$773$	7.06059			0.253952			0.126976	+	0.991906i	$0.459473\pi$
$774$	0.164212	+	0.0540358i	0.00590250	+	0.00194228i
$775$	−0.399268			−0.0143421
$776$	−33.6384	+	23.8676i	−1.20755	+	0.856797i
$777$	−52.6620			−1.88924
$778$	14.6407	+	4.81769i	0.524896	+	0.172723i
$779$	−0.0876871			−0.00314172
$780$	22.8780	+	16.8848i	0.819164	+	0.604573i
$781$			9.64633i			0.345173i
$782$	−2.62723	+	7.98404i	−0.0939496	+	0.285509i
$783$	6.30284			0.225245
$784$	20.9278	+	67.8471i	0.747421	+	2.42311i
$785$			2.42970i			0.0867197i
$786$	−7.00234	+	21.2798i	−0.249765	+	0.759025i
$787$	−15.4792			−0.551774			−0.275887	−	0.961190i	$-0.588972\pi$
$787$	−15.4792			−0.551774			−0.275887	+	0.961190i	$0.588972\pi$
$788$	12.1141	−	16.4140i	0.431548	−	0.584725i
$789$			27.1396i			0.966196i
$790$	1.64016	−	4.98436i	0.0583541	−	0.177336i
$791$			18.9400i			0.673430i
$792$	−3.69932	−	5.21374i	−0.131450	−	0.185262i
$793$	66.1010			2.34732
$794$	33.5778	+	11.0491i	1.19163	+	0.392118i
$795$	14.8569			0.526919
$796$	11.7831	−	15.9654i	0.417640	−	0.565880i
$797$	29.1922			1.03404			0.517020	−	0.855973i	$-0.327041\pi$
$797$	29.1922			1.03404			0.517020	+	0.855973i	$0.327041\pi$
$798$	4.50951	−	13.7042i	0.159635	−	0.485123i
$799$		−	3.72120i		−	0.131646i
$800$	0.0165374	−	0.884043i	0.000584685	−	0.0312556i
$801$	11.1834			0.395146
$802$	−15.2697	+	46.4040i	−0.539193	+	1.63858i
$803$	−27.1671			−0.958707
$804$	−5.08800	+	15.5600i	−0.179440	+	0.548757i
$805$	83.7191			2.95071
$806$	7.06963	−	21.4843i	0.249017	−	0.756751i
$807$	26.0364			0.916526
$808$	27.7726	−	19.7056i	0.977038	−	0.693241i
$809$			4.96917i			0.174707i	0.996177	+	0.0873533i	$0.0278409\pi$
$809$			4.96917i			0.174707i	−0.996177	+	0.0873533i	$0.972159\pi$
$810$	1.00377	−	3.05042i	0.0352690	−	0.107181i
$811$	3.80197			0.133505			0.0667526	−	0.997770i	$-0.478736\pi$
$811$	3.80197			0.133505			0.0667526	+	0.997770i	$0.478736\pi$
$812$	50.4586	+	37.2403i	1.77075	+	1.30688i
$813$	−22.5243			−0.789962
$814$	32.1399	+	10.5760i	1.12650	+	0.370687i
$815$	28.5411			0.999749
$816$	0.945550	+	3.06543i	0.0331009	+	0.107312i
$817$		−	0.250662i		−	0.00876955i
$818$	−10.9336	+	33.2266i	−0.382283	+	1.16174i
$819$			31.1481i			1.08840i
$820$	−0.156258	−	0.115324i	−0.00545675	−	0.00402728i
$821$	34.4748			1.20318			0.601589	−	0.798806i	$-0.294534\pi$
$821$	34.4748			1.20318			0.601589	+	0.798806i	$0.294534\pi$
$822$	2.84427	−	8.64361i	0.0992054	−	0.301481i
$823$			54.8228i			1.91100i	0.294989	+	0.955501i	$0.404684\pi$
$823$			54.8228i			1.91100i	−0.294989	+	0.955501i	$0.595316\pi$
$824$	−1.80924	+	1.28372i	−0.0630278	+	0.0447204i
$825$	−0.353282			−0.0122997
$826$	10.4983	−	31.9040i	0.365284	−	1.11008i
$827$		−	22.6061i		−	0.786089i	−0.919519	−	0.393045i	$-0.871422\pi$
$827$		−	22.6061i		−	0.786089i	0.919519	−	0.393045i	$-0.128578\pi$
$828$	8.80138	−	11.9254i	0.305869	−	0.414436i
$829$	18.7455			0.651057			0.325529	−	0.945532i	$-0.394458\pi$
$829$	18.7455			0.651057			0.325529	+	0.945532i	$0.394458\pi$
$830$	−17.1686	−	5.64950i	−0.595930	−	0.196097i
$831$	−26.8832			−0.932568
$832$	47.2768	+	16.5431i	1.63903	+	0.573530i
$833$	−14.2356			−0.493233
$834$	−12.7353	−	4.19068i	−0.440986	−	0.145111i
$835$	−41.7495			−1.44480
$836$	−5.50434	+	7.45809i	−0.190372	+	0.257943i
$837$	−2.55441			−0.0882932
$838$	8.89564	−	27.0335i	0.307295	−	0.933855i
$839$		−	34.9859i		−	1.20785i	−0.797042	−	0.603923i	$-0.793603\pi$
$839$		−	34.9859i		−	1.20785i	0.797042	−	0.603923i	$-0.206397\pi$
$840$	26.0593	−	18.4899i	0.899130	−	0.637963i
$841$	10.7258			0.369856
$842$	−38.1480	−	12.5530i	−1.31467	−	0.432605i
$843$			9.50374i			0.327326i
$844$	5.70324	−	7.72759i	0.196314	−	0.265994i
$845$			59.4926i			2.04661i
$846$	−2.05107	+	6.23311i	−0.0705173	+	0.214299i
$847$	29.3100			1.00710
$848$	25.0082	−	7.71391i	0.858785	−	0.264897i
$849$			30.5183i			1.04739i
$850$	0.168396	+	0.0554125i	0.00577594	+	0.00190063i
$851$			78.4462i			2.68910i
$852$	−5.06875	+	6.86789i	−0.173653	+	0.235290i
$853$	−2.76952			−0.0948267			−0.0474133	−	0.998875i	$-0.515098\pi$
$853$	−2.76952			−0.0948267			−0.0474133	+	0.998875i	$0.515098\pi$
$854$	23.2180	−	70.5583i	0.794503	−	2.41446i
$855$	−4.65631			−0.159242
$856$	−18.6541	+	13.2357i	−0.637585	+	0.452388i
$857$		−	17.9165i		−	0.612018i	−0.952029	−	0.306009i	$-0.901006\pi$
$857$		−	17.9165i		−	0.612018i	0.952029	−	0.306009i	$-0.0989937\pi$
$858$	6.25537	−	19.0098i	0.213555	−	0.648984i
$859$			31.7718i			1.08404i	0.840366	+	0.542019i	$0.182340\pi$
$859$			31.7718i			1.08404i	−0.840366	+	0.542019i	$0.817660\pi$
$860$	0.329664	−	0.446677i	0.0112414	−	0.0152316i
$861$		−	0.212742i		−	0.00725024i
$862$	−9.54766	+	29.0149i	−0.325195	+	0.988251i
$863$		−	16.6456i		−	0.566622i	−0.959028	−	0.283311i	$-0.908567\pi$
$863$		−	16.6456i		−	0.566622i	0.959028	−	0.283311i	$-0.0914329\pi$
$864$	0.105802	−	5.65586i	0.00359944	−	0.192416i
$865$		−	17.0411i		−	0.579414i
$866$	10.9742	−	33.3500i	0.372918	−	1.13328i
$867$	16.3568			0.555507
$868$	−20.4498	−	15.0927i	−0.694111	−	0.512279i
$869$	−3.69315			−0.125281
$870$	6.32662	−	19.2263i	0.214492	−	0.651833i
$871$	−48.6503	+	16.1096i	−1.64845	+	0.545852i
$872$	1.33254	−	0.945479i	0.0451253	−	0.0320180i
$873$			14.5826i			0.493545i
$874$	−20.4140	−	6.71743i	−0.690512	−	0.227220i
$875$			54.7188i			1.84983i
$876$	−19.3422	−	14.2752i	−0.653511	−	0.482315i
$877$	12.9320			0.436681			0.218341	−	0.975873i	$-0.429936\pi$
$877$	12.9320			0.436681			0.218341	+	0.975873i	$0.429936\pi$
$878$	13.3517	−	40.5753i	0.450599	−	1.36935i
$879$	−27.4962			−0.927423
$880$	−19.6174	+	6.05108i	−0.661301	+	0.203982i
$881$	−10.0442			−0.338398			−0.169199	−	0.985582i	$-0.554118\pi$
$881$	−10.0442			−0.338398			−0.169199	+	0.985582i	$0.554118\pi$
$882$	23.8450	+	7.84644i	0.802902	+	0.264203i
$883$	−44.4610			−1.49623			−0.748116	−	0.663568i	$-0.769041\pi$
$883$	−44.4610			−1.49623			−0.748116	+	0.663568i	$0.769041\pi$
$884$	−5.96341	+	8.08010i	−0.200571	+	0.271763i
$885$	−10.8401			−0.364386
$886$	−11.0030	−	3.62064i	−0.369651	−	0.121638i
$887$			20.5908i			0.691370i	0.938351	+	0.345685i	$0.112353\pi$
$887$			20.5908i			0.691370i	−0.938351	+	0.345685i	$0.887647\pi$
$888$	17.3254	+	24.4180i	0.581401	+	0.819413i
$889$			13.5012i			0.452817i
$890$	11.2256	−	34.1140i	0.376282	−	1.14351i
$891$	−2.26020			−0.0757196
$892$	−24.3539	+	32.9982i	−0.815428	+	1.10486i
$893$	9.51452			0.318391
$894$	3.43715	+	1.13103i	0.114955	+	0.0378273i
$895$		−	36.7438i		−	1.22821i
$896$	34.2646	−	44.6540i	1.14470	−	1.49178i
$897$	46.3986			1.54921
$898$	−26.7716	−	8.80949i	−0.893381	−	0.293977i
$899$	−16.1000			−0.536966
$900$	−0.251526	−	0.185635i	−0.00838419	−	0.00618784i
$901$			5.24718i			0.174809i
$902$	−0.0427244	+	0.129838i	−0.00142257	+	0.00432312i
$903$	0.608144			0.0202378
$904$	8.78197	−	6.23111i	0.292084	−	0.207243i
$905$			17.6167i			0.585600i
$906$	4.29814	−	13.0619i	0.142796	−	0.433951i
$907$		−	14.2070i		−	0.471736i	−0.971785	−	0.235868i	$-0.924207\pi$
$907$		−	14.2070i		−	0.471736i	0.971785	−	0.235868i	$-0.0757932\pi$
$908$	21.1520	−	28.6598i	0.701953	−	0.951109i
$909$		−	12.0397i		−	0.399331i
$910$	95.0146	+	31.2656i	3.14970	+	1.03644i
$911$		−	11.4705i		−	0.380035i	−0.981781	−	0.190018i	$-0.939146\pi$
$911$		−	11.4705i		−	0.380035i	0.981781	−	0.190018i	$-0.0608545\pi$
$912$	−7.83784	+	2.41762i	−0.259537	+	0.0800556i
$913$			12.7210i			0.421004i
$914$	14.3784	+	4.73138i	0.475597	+	0.156500i
$915$	−23.9738			−0.792550
$916$	−18.5851	+	25.1819i	−0.614070	+	0.832033i
$917$			78.8076i			2.60246i
$918$	1.07735	+	0.354514i	0.0355579	+	0.0117007i
$919$	−11.3800			−0.375392			−0.187696	−	0.982227i	$-0.560102\pi$
$919$	−11.3800			−0.375392			−0.187696	+	0.982227i	$0.560102\pi$
$920$	−27.5429	−	38.8183i	−0.908062	−	1.27980i
$921$			30.1875i			0.994712i
$922$	−6.98751	−	2.29931i	−0.230121	−	0.0757239i
$923$	−26.7212			−0.879539
$924$	−18.0945	−	13.3544i	−0.595264	−	0.439327i
$925$	1.65456			0.0544014
$926$	18.2479	+	6.00466i	0.599663	+	0.197326i
$927$			0.784321i			0.0257605i
$928$	0.666851	−	35.6480i	0.0218905	−	1.17020i
$929$			0.611378i			0.0200586i	0.999950	+	0.0100293i	$0.00319249\pi$
$929$			0.611378i			0.0200586i	−0.999950	+	0.0100293i	$0.996808\pi$
$930$	−2.56404	+	7.79201i	−0.0840783	+	0.255510i
$931$		−	36.3981i		−	1.19290i
$932$	25.3440	−	34.3398i	0.830172	−	1.12484i
$933$	−3.78543			−0.123929
$934$	−8.91390	+	27.0889i	−0.291672	+	0.886377i
$935$		−	4.11608i		−	0.134610i
$936$	14.4425	−	10.2475i	0.472068	−	0.334948i
$937$		−	15.4345i		−	0.504223i	−0.967698	−	0.252111i	$-0.918875\pi$
$937$		−	15.4345i		−	0.504223i	0.967698	−	0.252111i	$-0.0811249\pi$
$938$	0.107476	+	57.5894i	0.00350921	+	1.88036i
$939$		−	2.73274i		−	0.0891795i
$940$	16.9548	+	12.5132i	0.553004	+	0.408137i
$941$			54.1333i			1.76470i	0.470597	+	0.882348i	$0.344039\pi$
$941$			54.1333i			1.76470i	−0.470597	+	0.882348i	$0.655961\pi$
$942$	1.43739	+	0.472987i	0.0468326	+	0.0154107i
$943$	−0.316904			−0.0103198
$944$	−18.2469	+	5.62834i	−0.593885	+	0.183187i
$945$		−	11.2969i		−	0.367489i
$946$	−0.371153	−	0.122132i	−0.0120672	−	0.00397085i
$947$			34.7940i			1.13065i	0.824868	+	0.565326i	$0.191250\pi$
$947$			34.7940i			1.13065i	−0.824868	+	0.565326i	$0.808750\pi$
$948$	−2.62941	−	1.94060i	−0.0853992	−	0.0630277i
$949$		−	75.2554i		−	2.44289i
$950$	−0.141681	+	0.430563i	−0.00459675	+	0.0139693i
$951$	−22.7802			−0.738698
$952$	6.53031	+	9.20366i	0.211649	+	0.298292i
$953$	−11.3366			−0.367230			−0.183615	−	0.982998i	$-0.558780\pi$
$953$	−11.3366			−0.367230			−0.183615	+	0.982998i	$0.558780\pi$
$954$	2.89217	−	8.78917i	0.0936375	−	0.284560i
$955$			50.3225i			1.62840i
$956$	23.7693	+	17.5426i	0.768756	+	0.567370i
$957$	−14.2457			−0.460498
$958$	0.505162	−	1.53517i	0.0163211	−	0.0495989i
$959$		−	32.0108i		−	1.03368i
$960$	−17.1466	−	5.99994i	−0.553403	−	0.193647i
$961$	−24.4750			−0.789516
$962$	−29.2963	+	89.0303i	−0.944552	+	2.87045i
$963$			8.08673i			0.260591i
$964$	20.2878	+	14.9731i	0.653426	+	0.482252i
$965$			4.73671i			0.152480i
$966$	16.2975	−	49.5274i	0.524364	−	1.59352i
$967$		−	40.2988i		−	1.29592i	−0.761674	−	0.647961i	$-0.775622\pi$
$967$		−	40.2988i		−	1.29592i	0.761674	−	0.647961i	$-0.224378\pi$
$968$	−9.64275	−	13.5903i	−0.309930	−	0.436807i
$969$		−	1.64452i		−	0.0528297i
$970$	44.4829	+	14.6376i	1.42826	+	0.469984i
$971$		−	18.4758i		−	0.592918i	−0.955046	−	0.296459i	$-0.904194\pi$
$971$		−	18.4758i		−	0.592918i	0.955046	−	0.296459i	$-0.0958057\pi$
$972$	−1.60919	−	1.18764i	−0.0516149	−	0.0380937i
$973$	−47.1638			−1.51200
$974$	2.15698	+	0.709776i	0.0691140	+	0.0227427i
$975$		−	0.978621i		−	0.0313410i
$976$	−40.3545	+	12.4476i	−1.29172	+	0.398437i
$977$	−51.1524			−1.63651			−0.818255	−	0.574856i	$-0.805058\pi$
$977$	−51.1524			−1.63651			−0.818255	+	0.574856i	$0.805058\pi$
$978$	5.55606	−	16.8846i	0.177663	−	0.539910i
$979$	−25.2767			−0.807847
$980$	47.8699	−	64.8611i	1.52915	−	2.07191i
$981$		−	0.577666i		−	0.0184434i
$982$	−5.83810	+	17.7417i	−0.186301	+	0.566161i
$983$	43.9724			1.40250			0.701251	−	0.712915i	$-0.252625\pi$
$983$	43.9724			1.40250			0.701251	+	0.712915i	$0.252625\pi$
$984$	−0.0986429	+	0.0699904i	−0.00314462	+	0.00223121i
$985$	−23.1620			−0.738002
$986$	6.79038	+	2.23445i	0.216250	+	0.0711593i
$987$			23.0837i			0.734762i
$988$	−20.6596	−	15.2475i	−0.657268	−	0.485088i
$989$		−	0.905901i		−	0.0288060i
$990$	−2.26873	+	6.89456i	−0.0721049	+	0.219123i
$991$	6.25879			0.198817			0.0994086	−	0.995047i	$-0.468305\pi$
$991$	6.25879			0.198817			0.0994086	+	0.995047i	$0.468305\pi$
$992$	−0.270260	+	14.4474i	−0.00858078	+	0.458705i
$993$	−30.0443			−0.953427
$994$	−9.38581	+	28.5231i	−0.297700	+	0.904696i
$995$	−22.5290			−0.714218
$996$	−6.68438	+	9.05698i	−0.211803	+	0.286981i
$997$	−27.5442			−0.872335			−0.436168	−	0.899865i	$-0.643665\pi$
$997$	−27.5442			−0.872335			−0.436168	+	0.899865i	$0.643665\pi$
$998$	−12.0830	−	3.97605i	−0.382482	−	0.125860i
$999$	10.5854			0.334907

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.e.a.535.30	yes	34
4.3	odd	2		804.2.e.b.535.6	yes	34
67.66	odd	2		804.2.e.b.535.5	yes	34
268.267	even	2	inner	804.2.e.a.535.29	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.e.a.535.29	✓	34	268.267	even	2	inner
804.2.e.a.535.30	yes	34	1.1	even	1	trivial
804.2.e.b.535.5	yes	34	67.66	odd	2
804.2.e.b.535.6	yes	34	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34335 + 0.442044i) q^{2} -1.00000 q^{3} +(1.60919 + 1.18764i) q^{4} -2.27075i q^{5} +(-1.34335 - 0.442044i) q^{6} -4.97497 q^{7} +(1.63672 + 2.30676i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.34335 + 0.442044i) q^{2} -1.00000 q^{3} +(1.60919 + 1.18764i) q^{4} -2.27075i q^{5} +(-1.34335 - 0.442044i) q^{6} -4.97497 q^{7} +(1.63672 + 2.30676i) q^{8} +1.00000 q^{9} +(1.00377 - 3.05042i) q^{10} -2.26020 q^{11} +(-1.60919 - 1.18764i) q^{12} -6.26095i q^{13} +(-6.68314 - 2.19916i) q^{14} +2.27075i q^{15} +(1.17901 + 3.82230i) q^{16} -0.801988 q^{17} +(1.34335 + 0.442044i) q^{18} -2.05056i q^{19} +(2.69684 - 3.65408i) q^{20} +4.97497 q^{21} +(-3.03625 - 0.999109i) q^{22} -7.41079i q^{23} +(-1.63672 - 2.30676i) q^{24} -0.156305 q^{25} +(2.76762 - 8.41067i) q^{26} -1.00000 q^{27} +(-8.00569 - 5.90849i) q^{28} -6.30284 q^{29} +(-1.00377 + 3.05042i) q^{30} +2.55441 q^{31} +(-0.105802 + 5.65586i) q^{32} +2.26020 q^{33} +(-1.07735 - 0.354514i) q^{34} +11.2969i q^{35} +(1.60919 + 1.18764i) q^{36} -10.5854 q^{37} +(0.906438 - 2.75462i) q^{38} +6.26095i q^{39} +(5.23807 - 3.71659i) q^{40} -0.0427625i q^{41} +(6.68314 + 2.19916i) q^{42} +0.122241 q^{43} +(-3.63710 - 2.68431i) q^{44} -2.27075i q^{45} +(3.27590 - 9.95531i) q^{46} +4.63996i q^{47} +(-1.17901 - 3.82230i) q^{48} +17.7503 q^{49} +(-0.209973 - 0.0690940i) q^{50} +0.801988 q^{51} +(7.43578 - 10.0751i) q^{52} -6.54272i q^{53} +(-1.34335 - 0.442044i) q^{54} +5.13235i q^{55} +(-8.14265 - 11.4761i) q^{56} +2.05056i q^{57} +(-8.46694 - 2.78614i) q^{58} +4.77379i q^{59} +(-2.69684 + 3.65408i) q^{60} +10.5577i q^{61} +(3.43147 + 1.12916i) q^{62} -4.97497 q^{63} +(-2.64227 + 7.55105i) q^{64} -14.2171 q^{65} +(3.03625 + 0.999109i) q^{66} +(-2.57302 - 7.77043i) q^{67} +(-1.29055 - 0.952476i) q^{68} +7.41079i q^{69} +(-4.99374 + 15.1757i) q^{70} -4.26791i q^{71} +(1.63672 + 2.30676i) q^{72} +12.0198 q^{73} +(-14.2199 - 4.67921i) q^{74} +0.156305 q^{75} +(2.43533 - 3.29975i) q^{76} +11.2444 q^{77} +(-2.76762 + 8.41067i) q^{78} +1.63399 q^{79} +(8.67948 - 2.67723i) q^{80} +1.00000 q^{81} +(0.0189029 - 0.0574452i) q^{82} -5.62827i q^{83} +(8.00569 + 5.90849i) q^{84} +1.82111i q^{85} +(0.164212 + 0.0540358i) q^{86} +6.30284 q^{87} +(-3.69932 - 5.21374i) q^{88} +11.1834 q^{89} +(1.00377 - 3.05042i) q^{90} +31.1481i q^{91} +(8.80138 - 11.9254i) q^{92} -2.55441 q^{93} +(-2.05107 + 6.23311i) q^{94} -4.65631 q^{95} +(0.105802 - 5.65586i) q^{96} +14.5826i q^{97} +(23.8450 + 7.84644i) q^{98} -2.26020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9	\( 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9} - 6 q^{10} - 2 q^{12} - 4 q^{14} + 2 q^{16} + 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} - 34 q^{27} + 8 q^{28} - 16 q^{29} + 6 q^{30} + 4 q^{31} + 2 q^{36} + 12 q^{37} - 26 q^{38} - 18 q^{40} + 4 q^{42} + 4 q^{43} - 26 q^{44} + 4 q^{46} - 2 q^{48} + 46 q^{49} + 18 q^{50} - 32 q^{52} + 14 q^{56} - 4 q^{58} - 12 q^{60} - 2 q^{62} - 4 q^{63} + 26 q^{64} + 8 q^{66} + 18 q^{67} - 34 q^{68} - 56 q^{70} + 6 q^{72} + 12 q^{73} - 22 q^{74} + 34 q^{75} - 32 q^{76} - 8 q^{77} - 10 q^{78} + 12 q^{79} + 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} + 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} - 32 q^{94} + 40 q^{95} + 40 q^{98}+O(q^{100}) \) 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9 - 6 * q^10 - 2 * q^12 - 4 * q^14 + 2 * q^16 + 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 - 34 * q^27 + 8 * q^28 - 16 * q^29 + 6 * q^30 + 4 * q^31 + 2 * q^36 + 12 * q^37 - 26 * q^38 - 18 * q^40 + 4 * q^42 + 4 * q^43 - 26 * q^44 + 4 * q^46 - 2 * q^48 + 46 * q^49 + 18 * q^50 - 32 * q^52 + 14 * q^56 - 4 * q^58 - 12 * q^60 - 2 * q^62 - 4 * q^63 + 26 * q^64 + 8 * q^66 + 18 * q^67 - 34 * q^68 - 56 * q^70 + 6 * q^72 + 12 * q^73 - 22 * q^74 + 34 * q^75 - 32 * q^76 - 8 * q^77 - 10 * q^78 + 12 * q^79 + 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 + 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 - 32 * q^94 + 40 * q^95 + 40 * q^98

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