LMFDB - Embedded newform 483.2.y.b.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(4,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 12]))

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

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

chi := DirichletCharacter("483.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.y (of order $33$, degree $20$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			16.2
Character	$\chi$	$=$	483.16
Dual form			483.2.y.b.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.740363 - 2.13914i) q^{2} +(-0.888835 - 0.458227i) q^{3} +(-2.45566 + 1.93116i) q^{4} +(2.48488 + 0.237277i) q^{5} +(-0.322149 + 2.24059i) q^{6} +(-2.63923 + 0.185589i) q^{7} +(2.14051 + 1.37562i) q^{8} +(0.580057 + 0.814576i) q^{9} +O(q^{10})$	\(q+(-0.740363 - 2.13914i) q^{2} +(-0.888835 - 0.458227i) q^{3} +(-2.45566 + 1.93116i) q^{4} +(2.48488 + 0.237277i) q^{5} +(-0.322149 + 2.24059i) q^{6} +(-2.63923 + 0.185589i) q^{7} +(2.14051 + 1.37562i) q^{8} +(0.580057 + 0.814576i) q^{9} +(-1.33214 - 5.49116i) q^{10} +(-1.88727 + 5.45291i) q^{11} +(3.06759 - 0.591229i) q^{12} +(0.0390196 + 0.0114572i) q^{13} +(2.35099 + 5.50828i) q^{14} +(-2.09992 - 1.34954i) q^{15} +(-0.115153 + 0.474667i) q^{16} +(-5.45057 + 2.18208i) q^{17} +(1.31304 - 1.84390i) q^{18} +(1.92779 + 0.771772i) q^{19} +(-6.56024 + 4.21601i) q^{20} +(2.43089 + 1.04441i) q^{21} +13.0618 q^{22} +(-0.891245 + 4.71229i) q^{23} +(-1.27221 - 2.20354i) q^{24} +(1.20867 + 0.232952i) q^{25} +(-0.00438015 - 0.0919507i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(6.12267 - 5.55252i) q^{28} +(0.0689247 - 0.479382i) q^{29} +(-1.33214 + 5.49116i) q^{30} +(-0.299001 + 6.27681i) q^{31} +(6.16644 - 0.588824i) q^{32} +(4.17614 - 3.98194i) q^{33} +(8.70317 + 10.0440i) q^{34} +(-6.60221 - 0.165064i) q^{35} +(-2.99750 - 0.880145i) q^{36} +(-3.77475 - 5.30090i) q^{37} +(0.223660 - 4.69520i) q^{38} +(-0.0294320 - 0.0280634i) q^{39} +(4.99250 + 3.92614i) q^{40} +(-3.09819 - 6.78410i) q^{41} +(0.434397 - 5.97324i) q^{42} +(6.13690 - 3.94394i) q^{43} +(-5.89591 - 17.0351i) q^{44} +(1.24809 + 2.16175i) q^{45} +(10.7401 - 1.58231i) q^{46} +(-1.01585 + 1.75951i) q^{47} +(0.319857 - 0.369134i) q^{48} +(6.93111 - 0.979624i) q^{49} +(-0.396537 - 2.75797i) q^{50} +(5.84455 + 0.558087i) q^{51} +(-0.117945 + 0.0472179i) q^{52} +(-1.16711 - 1.11284i) q^{53} +(-2.01200 + 1.03726i) q^{54} +(-5.98348 + 13.1020i) q^{55} +(-5.90460 - 3.23333i) q^{56} +(-1.35984 - 1.56934i) q^{57} +(-1.07649 + 0.207477i) q^{58} +(1.04007 + 4.28724i) q^{59} +(7.76287 - 0.741264i) q^{60} +(0.782586 - 0.403451i) q^{61} +(13.6483 - 4.00751i) q^{62} +(-1.68208 - 2.04220i) q^{63} +(-5.41917 - 11.8663i) q^{64} +(0.0942403 + 0.0377281i) q^{65} +(-11.6098 - 5.98525i) q^{66} +(-11.0901 - 2.13743i) q^{67} +(9.17084 - 15.8844i) q^{68} +(2.95147 - 3.78006i) q^{69} +(4.53493 + 14.2452i) q^{70} +(-7.17129 + 8.27611i) q^{71} +(0.121069 + 2.54154i) q^{72} +(7.04675 - 5.54163i) q^{73} +(-8.54467 + 11.9993i) q^{74} +(-0.967562 - 0.760899i) q^{75} +(-6.22442 + 1.82766i) q^{76} +(3.96895 - 14.7418i) q^{77} +(-0.0382410 + 0.0837361i) q^{78} +(0.612500 - 0.584018i) q^{79} +(-0.398768 + 1.15216i) q^{80} +(-0.327068 + 0.945001i) q^{81} +(-12.2183 + 11.6501i) q^{82} +(-0.777518 + 1.70253i) q^{83} +(-7.98636 + 2.12970i) q^{84} +(-14.0618 + 4.12891i) q^{85} +(-12.9802 - 10.2077i) q^{86} +(-0.280928 + 0.394508i) q^{87} +(-11.5408 + 9.07582i) q^{88} +(0.765817 + 16.0765i) q^{89} +(3.70025 - 4.27032i) q^{90} +(-0.105108 - 0.0229966i) q^{91} +(-6.91157 - 13.2929i) q^{92} +(3.14196 - 5.44204i) q^{93} +(4.51592 + 0.870373i) q^{94} +(4.60720 + 2.37518i) q^{95} +(-5.75077 - 2.30226i) q^{96} +(7.04181 + 15.4194i) q^{97} +(-7.22709 - 14.1013i) q^{98} +(-5.53653 + 1.62567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) $ 320 * q + 2 * q^2 + 16 * q^3 + 18 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9	\( 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 2 q^{11} + 18 q^{12} + 18 q^{14} - 18 q^{15} - 8 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{19} - 162 q^{20} - 4 q^{21} + 144 q^{22} - 26 q^{23} + 6 q^{24} - 8 q^{25} - 14 q^{26} - 32 q^{27} + 86 q^{28} - 74 q^{29} - 56 q^{31} - 28 q^{32} + 13 q^{33} + 40 q^{34} - 32 q^{35} - 14 q^{36} + 2 q^{37} - 39 q^{38} - 52 q^{40} + 60 q^{41} - 61 q^{42} + 16 q^{43} - 75 q^{44} - 2 q^{45} - 4 q^{46} - 40 q^{47} - 28 q^{48} - 100 q^{49} + 146 q^{50} - 18 q^{51} - 18 q^{52} + 34 q^{53} + 2 q^{54} + 36 q^{55} - 102 q^{56} + 28 q^{57} - 17 q^{58} - 102 q^{59} - 18 q^{60} - 18 q^{61} - 88 q^{62} + 2 q^{63} - 252 q^{64} - 78 q^{65} + 16 q^{66} + 12 q^{67} + 34 q^{68} + 8 q^{69} + 264 q^{70} + 160 q^{71} + 6 q^{72} - 8 q^{73} + 70 q^{74} + 14 q^{75} - 40 q^{76} - 90 q^{77} - 16 q^{78} + 26 q^{79} - 103 q^{80} + 16 q^{81} - 30 q^{82} - 80 q^{83} - 52 q^{84} - 128 q^{85} + 90 q^{86} + 4 q^{87} - 293 q^{88} - 36 q^{89} + 16 q^{91} - 174 q^{92} + 32 q^{93} + 57 q^{94} - 85 q^{95} - 50 q^{96} - 8 q^{97} - 193 q^{98} - 26 q^{99}+O(q^{100}) \) 320 * q + 2 * q^2 + 16 * q^3 + 18 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9 + 2 * q^11 + 18 * q^12 + 18 * q^14 - 18 * q^15 - 8 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^19 - 162 * q^20 - 4 * q^21 + 144 * q^22 - 26 * q^23 + 6 * q^24 - 8 * q^25 - 14 * q^26 - 32 * q^27 + 86 * q^28 - 74 * q^29 - 56 * q^31 - 28 * q^32 + 13 * q^33 + 40 * q^34 - 32 * q^35 - 14 * q^36 + 2 * q^37 - 39 * q^38 - 52 * q^40 + 60 * q^41 - 61 * q^42 + 16 * q^43 - 75 * q^44 - 2 * q^45 - 4 * q^46 - 40 * q^47 - 28 * q^48 - 100 * q^49 + 146 * q^50 - 18 * q^51 - 18 * q^52 + 34 * q^53 + 2 * q^54 + 36 * q^55 - 102 * q^56 + 28 * q^57 - 17 * q^58 - 102 * q^59 - 18 * q^60 - 18 * q^61 - 88 * q^62 + 2 * q^63 - 252 * q^64 - 78 * q^65 + 16 * q^66 + 12 * q^67 + 34 * q^68 + 8 * q^69 + 264 * q^70 + 160 * q^71 + 6 * q^72 - 8 * q^73 + 70 * q^74 + 14 * q^75 - 40 * q^76 - 90 * q^77 - 16 * q^78 + 26 * q^79 - 103 * q^80 + 16 * q^81 - 30 * q^82 - 80 * q^83 - 52 * q^84 - 128 * q^85 + 90 * q^86 + 4 * q^87 - 293 * q^88 - 36 * q^89 + 16 * q^91 - 174 * q^92 + 32 * q^93 + 57 * q^94 - 85 * q^95 - 50 * q^96 - 8 * q^97 - 193 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.740363	−	2.13914i	−0.523515	−	1.51260i	−0.828360	−	0.560196i	$-0.810726\pi$
$2$	−0.740363	−	2.13914i	−0.523515	−	1.51260i	0.304845	−	0.952402i	$-0.401395\pi$
$3$	−0.888835	−	0.458227i	−0.513169	−	0.264557i
$3$	−0.888835	−	0.458227i	−0.513169	−	0.264557i
$4$	−2.45566	+	1.93116i	−1.22783	+	0.965578i
$5$	2.48488	+	0.237277i	1.11127	+	0.106113i	0.634506	−	0.772918i	$-0.281203\pi$
$5$	2.48488	+	0.237277i	1.11127	+	0.106113i	0.476764	+	0.879031i	$0.341810\pi$
$6$	−0.322149	+	2.24059i	−0.131517	+	0.914719i
$7$	−2.63923	+	0.185589i	−0.997537	+	0.0701460i
$7$	−2.63923	+	0.185589i	−0.997537	+	0.0701460i
$8$	2.14051	+	1.37562i	0.756784	+	0.486355i
$9$	0.580057	+	0.814576i	0.193352	+	0.271525i
$10$	−1.33214	−	5.49116i	−0.421260	−	1.73646i
$11$	−1.88727	+	5.45291i	−0.569033	+	1.64411i	0.181584	+	0.983375i	$0.441878\pi$
$11$	−1.88727	+	5.45291i	−0.569033	+	1.64411i	−0.750617	+	0.660738i	$0.770244\pi$
$12$	3.06759	−	0.591229i	0.885537	−	0.170673i
$13$	0.0390196	+	0.0114572i	0.0108221	+	0.00317765i	0.287139	−	0.957889i	$-0.407296\pi$
$13$	0.0390196	+	0.0114572i	0.0108221	+	0.00317765i	−0.276317	+	0.961067i	$0.589114\pi$
$14$	2.35099	+	5.50828i	0.628328	+	1.47215i
$15$	−2.09992	−	1.34954i	−0.542197	−	0.348449i
$16$	−0.115153	+	0.474667i	−0.0287882	+	0.118667i
$17$	−5.45057	+	2.18208i	−1.32196	+	0.529232i	−0.921961	−	0.387284i	$-0.873413\pi$
$17$	−5.45057	+	2.18208i	−1.32196	+	0.529232i	−0.399998	+	0.916516i	$0.630989\pi$
$18$	1.31304	−	1.84390i	0.309486	−	0.434612i
$19$	1.92779	+	0.771772i	0.442266	+	0.177057i	0.582098	−	0.813119i	$-0.302232\pi$
$19$	1.92779	+	0.771772i	0.442266	+	0.177057i	−0.139832	+	0.990175i	$0.544656\pi$
$20$	−6.56024	+	4.21601i	−1.46691	+	0.942729i
$21$	2.43089	+	1.04441i	0.530463	+	0.227909i
$22$	13.0618			2.78478
$23$	−0.891245	+	4.71229i	−0.185837	+	0.982581i
$23$	−0.891245	+	4.71229i	−0.185837	+	0.982581i
$24$	−1.27221	−	2.20354i	−0.259689	−	0.449795i
$25$	1.20867	+	0.232952i	0.241734	+	0.0465903i
$26$	−0.00438015	−	0.0919507i	−0.000859018	−	0.0180330i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	6.12267	−	5.55252i	1.15708	−	1.04933i
$29$	0.0689247	−	0.479382i	0.0127990	−	0.0890189i	−0.982421	−	0.186680i	$-0.940227\pi$
$29$	0.0689247	−	0.479382i	0.0127990	−	0.0890189i	0.995220	+	0.0976614i	$0.0311362\pi$
$30$	−1.33214	+	5.49116i	−0.243215	+	1.00254i
$31$	−0.299001	+	6.27681i	−0.0537022	+	1.12735i	0.797775	+	0.602956i	$0.206010\pi$
$31$	−0.299001	+	6.27681i	−0.0537022	+	1.12735i	−0.851477	+	0.524392i	$0.824293\pi$
$32$	6.16644	−	0.588824i	1.09008	−	0.104090i
$33$	4.17614	−	3.98194i	0.726972	−	0.693167i
$34$	8.70317	+	10.0440i	1.49258	+	1.72253i
$35$	−6.60221	−	0.165064i	−1.11598	−	0.0279010i
$36$	−2.99750	−	0.880145i	−0.499583	−	0.146691i
$37$	−3.77475	−	5.30090i	−0.620566	−	0.871463i	0.377956	−	0.925824i	$-0.376627\pi$
$37$	−3.77475	−	5.30090i	−0.620566	−	0.871463i	−0.998521	+	0.0543610i	$0.982688\pi$
$38$	0.223660	−	4.69520i	0.0362825	−	0.761663i
$39$	−0.0294320	−	0.0280634i	−0.00471289	−	0.00449373i
$40$	4.99250	+	3.92614i	0.789383	+	0.620777i
$41$	−3.09819	−	6.78410i	−0.483856	−	1.05950i	−0.981385	−	0.192050i	$-0.938486\pi$
$41$	−3.09819	−	6.78410i	−0.483856	−	1.05950i	0.497529	−	0.867447i	$-0.334241\pi$
$42$	0.434397	−	5.97324i	0.0670289	−	0.921691i
$43$	6.13690	−	3.94394i	0.935868	−	0.601446i	0.0186478	−	0.999826i	$-0.494064\pi$
$43$	6.13690	−	3.94394i	0.935868	−	0.601446i	0.917220	+	0.398380i	$0.130428\pi$
$44$	−5.89591	−	17.0351i	−0.888842	−	2.56814i
$45$	1.24809	+	2.16175i	0.186054	+	0.322255i
$46$	10.7401	−	1.58231i	1.58354	−	0.233299i
$47$	−1.01585	+	1.75951i	−0.148177	+	0.256650i	−0.930554	−	0.366155i	$-0.880674\pi$
$47$	−1.01585	+	1.75951i	−0.148177	+	0.256650i	0.782377	+	0.622806i	$0.214007\pi$
$48$	0.319857	−	0.369134i	0.0461673	−	0.0532800i
$49$	6.93111	−	0.979624i	0.990159	−	0.139946i
$50$	−0.396537	−	2.75797i	−0.0560788	−	0.390036i
$51$	5.84455	+	0.558087i	0.818401	+	0.0781478i
$52$	−0.117945	+	0.0472179i	−0.0163560	+	0.00654794i
$53$	−1.16711	−	1.11284i	−0.160315	−	0.152860i	0.605676	−	0.795711i	$-0.292903\pi$
$53$	−1.16711	−	1.11284i	−0.160315	−	0.152860i	−0.765991	+	0.642852i	$0.777751\pi$
$54$	−2.01200	+	1.03726i	−0.273798	+	0.141153i
$55$	−5.98348	+	13.1020i	−0.806812	+	1.76667i
$56$	−5.90460	−	3.23333i	−0.789036	−	0.432072i
$57$	−1.35984	−	1.56934i	−0.180116	−	0.207865i
$58$	−1.07649	+	0.207477i	−0.141350	+	0.0272431i
$59$	1.04007	+	4.28724i	0.135406	+	0.558151i	0.998581	+	0.0532468i	$0.0169570\pi$
$59$	1.04007	+	4.28724i	0.135406	+	0.558151i	−0.863175	+	0.504904i	$0.831528\pi$
$60$	7.76287	−	0.741264i	1.00218	−	0.0956967i
$61$	0.782586	−	0.403451i	0.100200	−	0.0516566i	−0.407398	−	0.913251i	$-0.633564\pi$
$61$	0.782586	−	0.403451i	0.100200	−	0.0516566i	0.507598	+	0.861594i	$0.330534\pi$
$62$	13.6483	−	4.00751i	1.73334	−	0.508954i
$63$	−1.68208	−	2.04220i	−0.211922	−	0.257294i
$64$	−5.41917	−	11.8663i	−0.677397	−	1.48329i
$65$	0.0942403	+	0.0377281i	0.0116891	+	0.00467960i
$66$	−11.6098	−	5.98525i	−1.42906	−	0.736734i
$67$	−11.0901	−	2.13743i	−1.35487	−	0.261129i	−0.540433	−	0.841387i	$-0.681740\pi$
$67$	−11.0901	−	2.13743i	−1.35487	−	0.261129i	−0.814433	+	0.580258i	$0.802952\pi$
$68$	9.17084	−	15.8844i	1.11213	−	1.92626i
$69$	2.95147	−	3.78006i	0.355315	−	0.455066i
$70$	4.53493	+	14.2452i	0.542028	+	1.70263i
$71$	−7.17129	+	8.27611i	−0.851075	+	0.982193i	−0.999978	−	0.00665850i	$-0.997881\pi$
$71$	−7.17129	+	8.27611i	−0.851075	+	0.982193i	0.148902	+	0.988852i	$0.452426\pi$
$72$	0.121069	+	2.54154i	0.0142681	+	0.299524i
$73$	7.04675	−	5.54163i	0.824760	−	0.648598i	−0.113881	−	0.993494i	$-0.536328\pi$
$73$	7.04675	−	5.54163i	0.824760	−	0.648598i	0.938641	+	0.344896i	$0.112086\pi$
$74$	−8.54467	+	11.9993i	−0.993297	+	1.39489i
$75$	−0.967562	−	0.760899i	−0.111724	−	0.0878611i
$76$	−6.22442	+	1.82766i	−0.713991	+	0.209647i
$77$	3.96895	−	14.7418i	0.452303	−	1.67998i
$78$	−0.0382410	+	0.0837361i	−0.00432994	+	0.00948125i
$79$	0.612500	−	0.584018i	0.0689116	−	0.0657071i	−0.654841	−	0.755767i	$-0.727264\pi$
$79$	0.612500	−	0.584018i	0.0689116	−	0.0657071i	0.723752	+	0.690060i	$0.242416\pi$
$80$	−0.398768	+	1.15216i	−0.0445836	+	0.128816i
$81$	−0.327068	+	0.945001i	−0.0363409	+	0.105000i
$82$	−12.2183	+	11.6501i	−1.34929	+	1.28654i
$83$	−0.777518	+	1.70253i	−0.0853437	+	0.186877i	−0.947492	−	0.319779i	$-0.896391\pi$
$83$	−0.777518	+	1.70253i	−0.0853437	+	0.186877i	0.862148	+	0.506656i	$0.169119\pi$
$84$	−7.98636	+	2.12970i	−0.871383	+	0.232370i
$85$	−14.0618	+	4.12891i	−1.52521	+	0.447843i
$86$	−12.9802	−	10.2077i	−1.39969	−	1.10073i
$87$	−0.280928	+	0.394508i	−0.0301187	+	0.0422957i
$88$	−11.5408	+	9.07582i	−1.23026	+	0.967486i
$89$	0.765817	+	16.0765i	0.0811764	+	1.70410i	0.561879	+	0.827220i	$0.310079\pi$
$89$	0.765817	+	16.0765i	0.0811764	+	1.70410i	−0.480702	+	0.876884i	$0.659618\pi$
$90$	3.70025	−	4.27032i	0.390041	−	0.450131i
$91$	−0.105108	−	0.0229966i	−0.0110183	−	0.00241070i
$92$	−6.91157	−	13.2929i	−0.720581	−	1.38588i
$93$	3.14196	−	5.44204i	0.325806	−	0.564313i
$94$	4.51592	+	0.870373i	0.465782	+	0.0897721i
$95$	4.60720	+	2.37518i	0.472689	+	0.243688i
$96$	−5.75077	−	2.30226i	−0.586935	−	0.234973i
$97$	7.04181	+	15.4194i	0.714987	+	1.56560i	0.820799	+	0.571218i	$0.193529\pi$
$97$	7.04181	+	15.4194i	0.714987	+	1.56560i	−0.105811	+	0.994386i	$0.533744\pi$
$98$	−7.22709	−	14.1013i	−0.730046	−	1.42445i
$99$	−5.53653	+	1.62567i	−0.556442	+	0.163386i
$100$	−3.41795	+	1.76207i	−0.341795	+	0.176207i
$101$	−7.88766	+	0.753180i	−0.784851	+	0.0749442i	−0.479784	−	0.877387i	$-0.659285\pi$
$101$	−7.88766	+	0.753180i	−0.784851	+	0.0749442i	−0.305067	+	0.952331i	$0.598679\pi$
$102$	−3.13326	−	12.9155i	−0.310239	−	1.27882i
$103$	6.40870	−	1.23518i	0.631468	−	0.121706i	0.136533	−	0.990636i	$-0.456404\pi$
$103$	6.40870	−	1.23518i	0.631468	−	0.121706i	0.494935	+	0.868930i	$0.335192\pi$
$104$	0.0677610	+	0.0782003i	0.00664451	+	0.00766817i
$105$	5.79264	+	3.17202i	0.565304	+	0.309558i
$106$	−1.51642	+	3.32051i	−0.147288	+	0.322516i
$107$	−16.9949	+	8.76148i	−1.64296	+	0.847004i	−0.646500	+	0.762914i	$0.723768\pi$
$107$	−16.9949	+	8.76148i	−1.64296	+	0.847004i	−0.996458	+	0.0840900i	$0.973202\pi$
$108$	2.26098	+	2.15584i	0.217563	+	0.207446i
$109$	13.2722	−	5.31338i	1.27125	−	0.508930i	0.364734	−	0.931112i	$-0.381160\pi$
$109$	13.2722	−	5.31338i	1.27125	−	0.508930i	0.906511	+	0.422182i	$0.138736\pi$
$110$	32.4569	+	3.09926i	3.09464	+	0.295503i
$111$	0.926122	+	6.44132i	0.0879036	+	0.611383i
$112$	0.215823	−	1.27413i	0.0203933	−	0.120394i
$113$	−2.79001	+	3.21985i	−0.262462	+	0.302898i	−0.871650	−	0.490128i	$-0.836950\pi$
$113$	−2.79001	+	3.21985i	−0.262462	+	0.302898i	0.609188	+	0.793026i	$0.291495\pi$
$114$	−2.35026	+	4.07078i	−0.220122	+	0.381263i
$115$	−3.33275	+	11.4980i	−0.310781	+	1.07219i
$116$	0.756505	+	1.31031i	0.0702397	+	0.121659i
$117$	0.0133008	+	0.0384302i	0.00122966	+	0.00355288i
$118$	8.40096	−	5.39897i	0.773371	−	0.497015i
$119$	13.9804	−	6.77059i	1.28158	−	0.620659i
$120$	−2.63844	−	5.77739i	−0.240856	−	0.527401i
$121$	−17.5258	−	13.7825i	−1.59326	−	1.25295i
$122$	−1.44244	−	1.37536i	−0.130592	−	0.124519i
$123$	−0.354869	+	7.44962i	−0.0319975	+	0.671709i
$124$	−11.3873	−	15.9912i	−1.02261	−	1.43605i
$125$	−9.02722	−	2.65063i	−0.807419	−	0.237080i
$126$	−3.12321	+	5.11018i	−0.278237	+	0.455251i
$127$	0.370631	+	0.427731i	0.0328882	+	0.0379550i	0.771955	−	0.635677i	$-0.219279\pi$
$127$	0.370631	+	0.427731i	0.0328882	+	0.0379550i	−0.739067	+	0.673632i	$0.764733\pi$
$128$	−12.4052	+	11.8284i	−1.09648	+	1.04549i
$129$	−7.26191	+	0.693429i	−0.639376	+	0.0610530i
$130$	0.0109336	−	0.229525i	0.000958944	−	0.0201307i
$131$	−3.80245	+	15.6739i	−0.332222	+	1.36944i	0.523511	+	0.852019i	$0.324622\pi$
$131$	−3.80245	+	15.6739i	−0.332222	+	1.36944i	−0.855733	+	0.517418i	$0.826893\pi$
$132$	−2.56545	+	17.8431i	−0.223294	+	1.55304i
$133$	−5.23113	−	1.67911i	−0.453596	−	0.145597i
$134$	3.63840	+	25.3056i	0.314310	+	2.18607i
$135$	−0.118773	−	2.49335i	−0.0102224	−	0.214594i
$136$	−14.6687	−	2.82716i	−1.25783	−	0.242427i
$137$	2.67780	+	4.63809i	0.228780	+	0.396259i	0.957447	−	0.288610i	$-0.0931930\pi$
$137$	2.67780	+	4.63809i	0.228780	+	0.396259i	−0.728667	+	0.684869i	$0.759860\pi$
$138$	−10.2712	−	3.51498i	−0.874344	−	0.299215i
$139$	−5.37665			−0.456041			−0.228021	−	0.973656i	$-0.573225\pi$
$139$	−5.37665			−0.456041			−0.228021	+	0.973656i	$0.573225\pi$
$140$	16.5316	−	12.3446i	1.39717	−	1.04330i
$141$	1.70918	−	1.09842i	0.143939	−	0.0925038i
$142$	23.0131	+	9.21305i	1.93122	+	0.773142i
$143$	−0.136115	+	0.191147i	−0.0113825	+	0.0159845i
$144$	−0.453447	+	0.181533i	−0.0377873	+	0.0151277i
$145$	0.285016	−	1.17485i	0.0236693	−	0.0975660i
$146$	−17.0715	−	10.9712i	−1.41284	−	0.907979i
$147$	−6.60951	−	2.30530i	−0.545143	−	0.190138i
$148$	19.5064	+	5.72760i	1.60342	+	0.470805i
$149$	23.4527	−	4.52014i	1.92132	−	0.370304i	0.921484	−	0.388415i	$-0.126977\pi$
$149$	23.4527	−	4.52014i	1.92132	−	0.370304i	0.999836	+	0.0181110i	$0.00576522\pi$
$150$	−0.911321	+	2.63309i	−0.0744091	+	0.214991i
$151$	0.269099	+	1.10924i	0.0218990	+	0.0902689i	0.981712	−	0.190370i	$-0.0609688\pi$
$151$	0.269099	+	1.10924i	0.0218990	+	0.0902689i	−0.959813	+	0.280639i	$0.909454\pi$
$152$	3.06479	+	4.30390i	0.248587	+	0.349092i
$153$	−4.93911	−	3.17418i	−0.399304	−	0.256617i
$154$	−34.4731	+	2.42412i	−2.77792	+	0.195341i
$155$	−2.23232	+	15.5261i	−0.179304	+	1.24709i
$156$	0.126470	+	0.0120764i	0.0101257	+	0.000966886i
$157$	−0.800132	+	0.629231i	−0.0638575	+	0.0502181i	−0.649578	−	0.760295i	$-0.725054\pi$
$157$	−0.800132	+	0.629231i	−0.0638575	+	0.0502181i	0.585720	+	0.810513i	$0.300812\pi$
$158$	−1.70277	−	0.877837i	−0.135465	−	0.0698369i
$159$	0.527437	+	1.52393i	0.0418284	+	0.120855i
$160$	15.4626			1.22242
$161$	1.47766	−	12.6022i	0.116456	−	0.993196i
$162$	2.26364			0.177848
$163$	−7.98249	−	23.0639i	−0.625237	−	1.80650i	−0.590400	−	0.807111i	$-0.701030\pi$
$163$	−7.98249	−	23.0639i	−0.625237	−	1.80650i	−0.0348369	−	0.999393i	$-0.511091\pi$
$164$	20.7093	+	10.6764i	1.61712	+	0.833684i
$165$	11.3220	−	8.90373i	0.881417	−	0.693154i
$166$	4.21758	+	0.402730i	0.327348	+	0.0312579i
$167$	2.05908	−	14.3212i	0.159336	−	1.10821i	−0.740524	−	0.672030i	$-0.765422\pi$
$167$	2.05908	−	14.3212i	0.159336	−	1.10821i	0.899860	−	0.436179i	$-0.143668\pi$
$168$	3.76662	+	5.57955i	0.290601	+	0.430471i
$169$	−10.9349	−	7.02744i	−0.841147	−	0.540572i
$170$	19.2431	+	27.0231i	1.47588	+	2.07258i
$171$	0.489563	+	2.01801i	0.0374378	+	0.154321i
$172$	−7.45379	+	21.5363i	−0.568346	+	1.64213i
$173$	12.1125	−	2.33449i	0.920896	−	0.177488i	0.293294	−	0.956022i	$-0.405249\pi$
$173$	12.1125	−	2.33449i	0.920896	−	0.177488i	0.627602	+	0.778534i	$0.284036\pi$
$174$	1.05190	+	0.308865i	0.0797440	+	0.0234150i
$175$	−3.23319	−	0.390499i	−0.244406	−	0.0295189i
$176$	−2.37099	−	1.52374i	−0.178720	−	0.114856i
$177$	1.04007	−	4.28724i	0.0781767	−	0.322249i
$178$	33.8228	−	13.5406i	2.53513	−	1.01491i
$179$	2.55891	−	3.59349i	0.191262	−	0.268590i	−0.707798	−	0.706414i	$-0.750311\pi$
$179$	2.55891	−	3.59349i	0.191262	−	0.268590i	0.899060	+	0.437825i	$0.144251\pi$
$180$	−7.23958	−	2.89829i	−0.539606	−	0.216026i
$181$	−7.13216	+	4.58356i	−0.530129	+	0.340693i	−0.778167	−	0.628057i	$-0.783850\pi$
$181$	−7.13216	+	4.58356i	−0.530129	+	0.340693i	0.248038	+	0.968750i	$0.420214\pi$
$182$	0.0286253	+	0.241867i	0.00212185	+	0.0179283i
$183$	−0.880463			−0.0650857
$184$	−8.39004	+	8.86068i	−0.618522	+	0.653218i
$185$	−8.12202	−	14.0677i	−0.597143	−	1.03428i
$186$	−13.9675	−	2.69201i	−1.02414	−	0.197388i
$187$	−1.61198	−	33.8396i	−0.117880	−	2.47460i
$188$	−0.903291	−	6.28253i	−0.0658793	−	0.458200i
$189$	0.559302	+	2.58596i	0.0406832	+	0.188101i
$190$	1.66983	−	11.6139i	0.121142	−	0.842563i
$191$	1.43339	−	5.90851i	0.103716	−	0.427525i	−0.896152	−	0.443747i	$-0.853649\pi$
$191$	1.43339	−	5.90851i	0.103716	−	0.427525i	0.999868	+	0.0162222i	$0.00516393\pi$
$192$	−0.620716	+	13.0304i	−0.0447963	+	0.940390i
$193$	−7.40721	+	0.707302i	−0.533182	+	0.0509127i	−0.358175	−	0.933654i	$-0.616601\pi$
$193$	−7.40721	+	0.707302i	−0.533182	+	0.0509127i	−0.175007	+	0.984567i	$0.555995\pi$
$194$	27.7707	−	26.4793i	1.99382	−	1.90111i
$195$	−0.0664761	−	0.0767175i	−0.00476045	−	0.00549385i
$196$	−15.1287	+	15.7907i	−1.08062	+	1.12791i
$197$	−19.2997	−	5.66690i	−1.37505	−	0.403750i	−0.491004	−	0.871158i	$-0.663370\pi$
$197$	−19.2997	−	5.66690i	−1.37505	−	0.403750i	−0.884042	+	0.467408i	$0.845188\pi$
$198$	7.57657	+	10.6398i	0.538444	+	0.756138i
$199$	0.0220856	−	0.463634i	0.00156561	−	0.0328662i	−0.997949	−	0.0640086i	$-0.979612\pi$
$199$	0.0220856	−	0.463634i	0.00156561	−	0.0328662i	0.999515	+	0.0311424i	$0.00991454\pi$
$200$	2.26671	+	2.16130i	0.160281	+	0.152827i
$201$	8.87780	+	6.98158i	0.626192	+	0.492443i
$202$	7.45088	+	16.3152i	0.524242	+	1.14793i
$203$	−0.0929405	+	1.27799i	−0.00652315	+	0.0896975i
$204$	−15.4300	+	9.91626i	−1.08032	+	0.694277i
$205$	−6.08892	−	17.5928i	−0.425268	−	1.22873i
$206$	−7.38697	−	12.7946i	−0.514675	−	0.891443i
$207$	−4.35549	+	2.00741i	−0.302728	+	0.139525i
$208$	−0.00993156	+	0.0172020i	−0.000688630	+	0.00119274i
$209$	−7.84666	+	9.05553i	−0.542765	+	0.626384i
$210$	2.49674	−	14.7397i	0.172291	−	1.01714i
$211$	0.0234410	+	0.163036i	0.00161374	+	0.0112238i	0.990612	−	0.136701i	$-0.0436498\pi$
$211$	0.0234410	+	0.163036i	0.00161374	+	0.0112238i	−0.988999	+	0.147924i	$0.952741\pi$
$212$	5.01509	+	0.478883i	0.344438	+	0.0328898i
$213$	10.1664	−	4.07002i	0.696592	−	0.278873i
$214$	31.3244	+	29.8677i	2.14129	+	2.04172i
$215$	16.1852	−	8.34407i	1.10382	−	0.569061i
$216$	1.05699	−	2.31449i	0.0719193	−	0.157481i
$217$	−0.375771	−	16.6215i	−0.0255090	−	1.12834i
$218$	−21.1923	−	24.4572i	−1.43532	−	1.65645i
$219$	−8.80272	+	1.69659i	−0.594833	+	0.114645i
$220$	−10.6086	−	43.7291i	−0.715230	−	2.94822i
$221$	−0.237680	+	0.0226956i	−0.0159881	+	0.00152667i
$222$	13.0932	−	6.75002i	0.878758	−	0.453031i
$223$	7.64726	−	2.24544i	0.512099	−	0.150366i	−0.0154664	−	0.999880i	$-0.504923\pi$
$223$	7.64726	−	2.24544i	0.512099	−	0.150366i	0.527565	+	0.849515i	$0.323105\pi$
$224$	−16.1654	+	2.69847i	−1.08010	+	0.180299i
$225$	0.511339	+	1.11968i	0.0340893	+	0.0746451i
$226$	8.95331	+	3.58436i	0.595565	+	0.238428i
$227$	22.4610	+	11.5795i	1.49079	+	0.768556i	0.994999	−	0.0998856i	$-0.0318477\pi$
$227$	22.4610	+	11.5795i	1.49079	+	0.768556i	0.495792	+	0.868442i	$0.334878\pi$
$228$	6.36997	+	1.22771i	0.421862	+	0.0813072i
$229$	−11.4054	+	19.7548i	−0.753692	+	1.30543i	0.192330	+	0.981330i	$0.438396\pi$
$229$	−11.4054	+	19.7548i	−0.753692	+	1.30543i	−0.946022	+	0.324103i	$0.894938\pi$
$230$	27.0632	−	1.38347i	1.78450	−	0.0912231i
$231$	−10.2828	+	11.2843i	−0.676559	+	0.742453i
$232$	0.806981	−	0.931306i	0.0529809	−	0.0611432i
$233$	0.0663213	+	1.39225i	0.00434485	+	0.0912096i	0.999998	−	0.00192749i	$-0.000613538\pi$
$233$	0.0663213	+	1.39225i	0.00434485	+	0.0912096i	−0.995653	+	0.0931371i	$0.970311\pi$
$234$	0.0723601	−	0.0569046i	0.00473033	−	0.00371997i
$235$	−2.94176	+	4.13112i	−0.191899	+	0.269484i
$236$	−10.8334	−	8.51948i	−0.705194	−	0.554571i
$237$	−0.812024	+	0.238432i	−0.0527466	+	0.0154878i
$238$	−24.8338	−	24.8932i	−1.60973	−	1.61359i
$239$	−0.861143	+	1.88564i	−0.0557027	+	0.121972i	−0.935437	−	0.353494i	$-0.884993\pi$
$239$	−0.861143	+	1.88564i	−0.0557027	+	0.121972i	0.879734	+	0.475466i	$0.157721\pi$
$240$	0.882392	−	0.841359i	0.0569581	−	0.0543095i
$241$	−1.18729	+	3.43046i	−0.0764804	+	0.220975i	−0.976760	−	0.214337i	$-0.931241\pi$
$241$	−1.18729	+	3.43046i	−0.0764804	+	0.220975i	0.900279	+	0.435313i	$0.143362\pi$
$242$	−16.5071	+	47.6941i	−1.06112	+	3.06589i
$243$	0.723734	−	0.690079i	0.0464276	−	0.0442686i
$244$	−1.14264	+	2.50204i	−0.0731502	+	0.160177i
$245$	17.4554	−	0.789652i	1.11518	−	0.0504490i
$246$	16.1985	−	4.75630i	1.03278	−	0.303251i
$247$	0.0663793	+	0.0522013i	0.00422362	+	0.00332149i
$248$	−9.27452	+	13.0242i	−0.588933	+	0.827040i
$249$	1.47123	−	1.15699i	0.0932353	−	0.0733211i
$250$	1.01335	+	21.2729i	0.0640900	+	1.34542i
$251$	20.1969	−	23.3085i	1.27482	−	1.47122i	0.464099	−	0.885784i	$-0.346378\pi$
$251$	20.1969	−	23.3085i	1.27482	−	1.47122i	0.810719	−	0.585435i	$-0.199076\pi$
$252$	8.07445	+	1.76661i	0.508642	+	0.111286i
$253$	−24.0137	−	13.7532i	−1.50973	−	0.864659i
$254$	0.640574	−	1.10951i	0.0401932	−	0.0696167i
$255$	14.3906	+	2.77355i	0.901172	+	0.173687i
$256$	11.2968	+	5.82390i	0.706049	+	0.363994i
$257$	−7.60983	−	3.04652i	−0.474688	−	0.190037i	0.121967	−	0.992534i	$-0.461080\pi$
$257$	−7.60983	−	3.04652i	−0.474688	−	0.190037i	−0.596655	+	0.802498i	$0.703504\pi$
$258$	6.85979	+	15.0208i	0.427072	+	0.935157i
$259$	10.9462	+	13.2898i	0.680167	+	0.825786i
$260$	−0.304282	+	0.0893451i	−0.0188707	+	0.00554095i
$261$	0.430473	−	0.221924i	0.0266456	−	0.0137368i
$262$	36.3439	−	3.47042i	2.24533	−	0.214403i
$263$	0.0395370	+	0.162974i	0.00243795	+	0.0100494i	0.973018	−	0.230731i	$-0.0741118\pi$
$263$	0.0395370	+	0.162974i	0.00243795	+	0.0100494i	−0.970580	+	0.240780i	$0.922597\pi$
$264$	14.4167	−	2.77859i	0.887286	−	0.171010i
$265$	−2.63607	−	3.04219i	−0.161932	−	0.186880i
$266$	0.281086	+	12.4333i	0.0172345	+	0.762332i
$267$	6.68598	−	14.6403i	0.409176	−	0.895969i
$268$	31.3612	−	16.1678i	1.91569	−	0.987606i
$269$	20.2914	+	19.3478i	1.23719	+	1.17966i	0.976800	+	0.214154i	$0.0686995\pi$
$269$	20.2914	+	19.3478i	1.23719	+	1.17966i	0.260390	+	0.965504i	$0.416149\pi$
$270$	−5.24569	+	2.10006i	−0.319242	+	0.127805i
$271$	−2.63319	−	0.251439i	−0.159955	−	0.0152739i	0.0147712	−	0.999891i	$-0.495298\pi$
$271$	−2.63319	−	0.251439i	−0.159955	−	0.0152739i	−0.174726	+	0.984617i	$0.555904\pi$
$272$	−0.408111	−	2.83848i	−0.0247454	−	0.172108i
$273$	0.0828862	+	0.0686035i	0.00501650	+	0.00415207i
$274$	7.93897	−	9.16206i	0.479611	−	0.553500i
$275$	−3.55134	+	6.15111i	−0.214154	+	0.370926i
$276$	0.0520707	+	14.9823i	0.00313429	+	0.901829i
$277$	7.02022	+	12.1594i	0.421804	+	0.730587i	0.996116	−	0.0880502i	$-0.0280636\pi$
$277$	7.02022	+	12.1594i	0.421804	+	0.730587i	−0.574312	+	0.818637i	$0.694730\pi$
$278$	3.98067	+	11.5014i	0.238745	+	0.689807i
$279$	−5.28637	+	3.39735i	−0.316487	+	0.203394i
$280$	−13.9050	−	9.43546i	−0.830983	−	0.563876i
$281$	10.9753	+	24.0326i	0.654734	+	1.43367i	0.887349	+	0.461099i	$0.152545\pi$
$281$	10.9753	+	24.0326i	0.654734	+	1.43367i	−0.232615	+	0.972569i	$0.574728\pi$
$282$	−3.61509	−	2.84294i	−0.215275	−	0.169294i
$283$	−4.86919	−	4.64276i	−0.289443	−	0.275983i	0.531420	−	0.847109i	$-0.321659\pi$
$283$	−4.86919	−	4.64276i	−0.289443	−	0.275983i	−0.820863	+	0.571125i	$0.806507\pi$
$284$	1.62782	−	34.1722i	0.0965936	−	2.02775i
$285$	−3.00668	−	4.22229i	−0.178100	−	0.250107i
$286$	0.509665	+	0.149651i	0.0301371	+	0.00884906i
$287$	9.43591	+	17.3298i	0.556984	+	1.02295i
$288$	4.05653	+	4.68148i	0.239033	+	0.275859i
$289$	12.6438	−	12.0558i	0.743753	−	0.709167i
$290$	−2.72418	+	0.260128i	−0.159969	+	0.0152752i
$291$	0.806574	−	16.9321i	0.0472822	−	0.992575i
$292$	−6.60271	+	27.2168i	−0.386395	+	1.59274i
$293$	−2.31626	+	16.1100i	−0.135318	+	0.941154i	0.803148	+	0.595780i	$0.203157\pi$
$293$	−2.31626	+	16.1100i	−0.135318	+	0.941154i	−0.938465	+	0.345374i	$0.887752\pi$
$294$	−0.0379095	+	15.8454i	−0.00221093	+	0.924123i
$295$	1.56719	+	10.9000i	0.0912453	+	0.634625i
$296$	−0.787862	−	16.5393i	−0.0457935	−	0.961325i
$297$	5.66599	+	1.09203i	0.328774	+	0.0633660i
$298$	−27.0327	−	46.8220i	−1.56596	−	2.71233i
$299$	−0.0887656	+	0.173660i	−0.00513345	+	0.0100430i
$300$	3.84542			0.222016
$301$	−15.4648	+	11.5479i	−0.891374	+	0.665612i
$302$	2.17359	−	1.39688i	0.125076	−	0.0803815i
$303$	7.35596	+	2.94488i	0.422589	+	0.169179i
$304$	−0.588325	+	0.826187i	−0.0337428	+	0.0473851i
$305$	2.04036	−	0.816837i	0.116831	−	0.0467719i
$306$	−3.13326	+	12.9155i	−0.179117	+	0.738329i
$307$	24.4495	+	15.7127i	1.39540	+	0.896772i	0.999766	−	0.0216341i	$-0.00688689\pi$
$307$	24.4495	+	15.7127i	1.39540	+	0.896772i	0.395639	+	0.918406i	$0.370523\pi$
$308$	18.7222	+	43.8655i	1.06680	+	2.49947i
$309$	−6.26227	−	1.83877i	−0.356248	−	0.104604i
$310$	34.8653	−	6.71973i	1.98022	−	0.381655i
$311$	3.67824	−	10.6276i	0.208574	−	0.602635i	−0.791388	−	0.611314i	$-0.790641\pi$
$311$	3.67824	−	10.6276i	0.208574	−	0.602635i	0.999962	+	0.00867878i	$0.00276257\pi$
$312$	−0.0243949	−	0.100557i	−0.00138109	−	0.00569293i
$313$	11.6457	+	16.3542i	0.658257	+	0.924392i	0.999881	−	0.0154446i	$-0.00491637\pi$
$313$	11.6457	+	16.3542i	0.658257	+	0.924392i	−0.341624	+	0.939837i	$0.610977\pi$
$314$	1.93840	+	1.24573i	0.109390	+	0.0703008i
$315$	−3.69520	−	5.47375i	−0.208201	−	0.308411i
$316$	−0.376266	+	2.61698i	−0.0211666	+	0.147217i
$317$	17.1700	+	1.63953i	0.964362	+	0.0920854i	0.565342	−	0.824857i	$-0.308744\pi$
$317$	17.1700	+	1.63953i	0.964362	+	0.0920854i	0.399020	+	0.916942i	$0.369350\pi$
$318$	2.86940	−	2.25652i	0.160908	−	0.126539i
$319$	2.48394	+	1.28056i	0.139074	+	0.0716977i
$320$	−10.6504	−	30.7722i	−0.595374	−	1.72022i
$321$	19.1204			1.06720
$322$	−28.0519	+	6.16932i	−1.56327	+	0.343803i
$323$	−12.1916			−0.678361
$324$	−1.02177	−	2.95222i	−0.0567653	−	0.164012i
$325$	0.0444927	+	0.0229376i	0.00246801	+	0.00127235i
$326$	−43.4269	+	34.1513i	−2.40519	+	1.89147i
$327$	−14.2315	−	1.35895i	−0.787005	−	0.0751499i
$328$	2.70064	−	18.7833i	0.149118	−	1.03714i
$329$	2.35453	−	4.83228i	0.129809	−	0.266412i
$330$	−27.4287	−	17.6273i	−1.50990	−	0.970353i
$331$	−2.42950	−	3.41175i	−0.133537	−	0.187527i	0.742393	−	0.669965i	$-0.233691\pi$
$331$	−2.42950	−	3.41175i	−0.133537	−	0.187527i	−0.875930	+	0.482438i	$0.839751\pi$
$332$	−1.37852	−	5.68234i	−0.0756562	−	0.311859i
$333$	2.12841	−	6.14965i	0.116636	−	0.336999i
$334$	−32.1595	+	6.19824i	−1.75969	+	0.339153i
$335$	−27.0502	−	7.94267i	−1.47791	−	0.433954i
$336$	−0.775670	+	1.03359i	−0.0423162	+	0.0563872i
$337$	28.7262	+	18.4612i	1.56482	+	1.00565i	0.981057	+	0.193719i	$0.0620550\pi$
$337$	28.7262	+	18.4612i	1.56482	+	1.00565i	0.583759	+	0.811927i	$0.301581\pi$
$338$	−6.93686	+	28.5941i	−0.377315	+	1.55531i
$339$	3.95528	−	1.58346i	0.214821	−	0.0860015i
$340$	26.5574	−	37.2947i	1.44028	−	2.02259i
$341$	−33.6625	−	13.4765i	−1.82293	−	0.729791i
$342$	3.95434	−	2.54130i	0.213826	−	0.137418i
$343$	−18.1110	+	3.87179i	−0.977903	+	0.209057i
$344$	18.5615			1.00077
$345$	8.23095	−	8.69266i	0.443140	−	0.467997i
$346$	−13.9614	−	24.1819i	−0.750572	−	1.30003i
$347$	−26.7867	−	5.16272i	−1.43799	−	0.277149i	−0.590101	−	0.807329i	$-0.700912\pi$
$347$	−26.7867	−	5.16272i	−1.43799	−	0.277149i	−0.847885	+	0.530180i	$0.822124\pi$
$348$	−0.0719919	−	1.51130i	−0.00385917	−	0.0810140i
$349$	−1.22571	−	8.52502i	−0.0656109	−	0.456334i	−0.995970	−	0.0896846i	$-0.971414\pi$
$349$	−1.22571	−	8.52502i	−0.0656109	−	0.456334i	0.930359	−	0.366649i	$-0.119495\pi$
$350$	1.55840	+	7.20535i	0.0833001	+	0.385142i
$351$	0.00578750	−	0.0402529i	0.000308914	−	0.00214854i
$352$	−8.42694	+	34.7363i	−0.449157	+	1.85145i
$353$	0.144770	−	3.03909i	0.00770532	−	0.161755i	−0.991735	−	0.128303i	$-0.959047\pi$
$353$	0.144770	−	3.03909i	0.00770532	−	0.161755i	0.999440	−	0.0334516i	$-0.0106500\pi$
$354$	−9.94102	+	0.949253i	−0.528359	+	0.0504522i
$355$	−19.7835	+	18.8635i	−1.05000	+	1.00117i
$356$	−32.9268	−	37.9995i	−1.74512	−	2.01397i
$357$	−15.5287	−	0.388239i	−0.821867	−	0.0205478i
$358$	−9.58149	−	2.81338i	−0.506397	−	0.148692i
$359$	−14.5313	−	20.4064i	−0.766935	−	1.07701i	−0.994652	−	0.103282i	$-0.967065\pi$
$359$	−14.5313	−	20.4064i	−0.766935	−	1.07701i	0.227717	−	0.973727i	$-0.426874\pi$
$360$	−0.302209	+	6.34415i	−0.0159278	+	0.334366i
$361$	−10.6302	−	10.1359i	−0.559484	−	0.533467i
$362$	15.0852	+	11.8632i	0.792863	+	0.623514i
$363$	9.26208	+	20.2811i	0.486133	+	1.06448i
$364$	0.302520	−	0.146508i	0.0158564	−	0.00767912i
$365$	18.8252	−	12.0982i	0.985357	−	0.633250i
$366$	0.651862	+	1.88343i	0.0340733	+	0.0984485i
$367$	4.52145	+	7.83138i	0.236018	+	0.408795i	0.959568	−	0.281477i	$-0.0908244\pi$
$367$	4.52145	+	7.83138i	0.236018	+	0.408795i	−0.723550	+	0.690272i	$0.757491\pi$
$368$	−2.13414	−	0.965678i	−0.111250	−	0.0503394i
$369$	3.72903	−	6.45887i	0.194126	−	0.336236i
$370$	−24.0796	+	27.7893i	−1.25184	+	1.44470i
$371$	3.28680	+	2.72043i	0.170642	+	0.141238i
$372$	2.79382	+	19.4314i	0.144853	+	1.00747i
$373$	31.1854	+	2.97785i	1.61472	+	0.154187i	0.862968	−	0.505258i	$-0.168603\pi$
$373$	31.1854	+	2.97785i	1.61472	+	0.154187i	0.751753	+	0.659445i	$0.229209\pi$
$374$	−71.1942	+	28.5018i	−3.68136	+	1.47380i
$375$	6.80912	+	6.49248i	0.351622	+	0.335270i
$376$	−4.59485	+	2.36881i	−0.236961	+	0.122162i
$377$	0.00818178	−	0.0179156i	0.000421383	−	0.000922700i
$378$	5.11763	−	3.11097i	0.263223	−	0.160011i
$379$	−6.84635	−	7.90111i	−0.351673	−	0.405853i	0.552159	−	0.833739i	$-0.313804\pi$
$379$	−6.84635	−	7.90111i	−0.351673	−	0.405853i	−0.903833	+	0.427886i	$0.859259\pi$
$380$	−15.9006	+	3.06459i	−0.815683	+	0.157210i
$381$	−0.133432	−	0.550016i	−0.00683595	−	0.0281782i
$382$	−13.7004	+	1.30822i	−0.700971	+	0.0669346i
$383$	−17.2809	+	8.90892i	−0.883013	+	0.455225i	−0.839205	−	0.543815i	$-0.816979\pi$
$383$	−17.2809	+	8.90892i	−0.883013	+	0.455225i	−0.0438077	+	0.999040i	$0.513949\pi$
$384$	16.4463	−	4.82906i	0.839271	−	0.246432i
$385$	13.3602	−	35.6897i	0.680900	−	1.81892i
$386$	6.99703	+	15.3214i	0.356140	+	0.779837i
$387$	6.77239	+	2.71126i	0.344260	+	0.137821i
$388$	−47.0696	−	24.2661i	−2.38960	−	1.23192i
$389$	11.7236	+	2.25955i	0.594412	+	0.114564i	0.477580	−	0.878588i	$-0.341514\pi$
$389$	11.7236	+	2.25955i	0.594412	+	0.114564i	0.116832	+	0.993152i	$0.462726\pi$
$390$	−0.114893	+	0.199000i	−0.00581783	+	0.0100768i
$391$	−5.42480	−	27.6295i	−0.274344	−	1.39728i
$392$	16.1837	+	7.43769i	0.817400	+	0.375660i
$393$	10.5620	−	12.1892i	0.532780	−	0.614861i
$394$	2.16649	+	45.4802i	0.109146	+	2.29126i
$395$	1.66056	−	1.30588i	0.0835519	−	0.0657059i
$396$	10.4564	−	14.6840i	0.525456	−	0.737899i
$397$	11.7185	+	9.21552i	0.588134	+	0.462514i	0.867339	−	0.497718i	$-0.165829\pi$
$397$	11.7185	+	9.21552i	0.588134	+	0.462514i	−0.279205	+	0.960231i	$0.590071\pi$
$398$	−1.00813	+	0.296013i	−0.0505329	+	0.0148378i
$399$	3.88020	+	3.88949i	0.194253	+	0.194718i
$400$	−0.249756	+	0.546889i	−0.0124878	+	0.0273445i
$401$	2.23988	−	2.13572i	0.111854	−	0.106653i	−0.632089	−	0.774896i	$-0.717802\pi$
$401$	2.23988	−	2.13572i	0.111854	−	0.106653i	0.743943	+	0.668244i	$0.232954\pi$
$402$	8.36177	−	24.1597i	0.417047	−	1.20498i
$403$	−0.0835814	+	0.241493i	−0.00416349	+	0.0120296i
$404$	17.9149	−	17.0819i	0.891302	−	0.849854i
$405$	−1.03695	+	2.27060i	−0.0515265	+	0.112827i
$406$	2.80261	−	0.747365i	0.139091	−	0.0370911i
$407$	36.0293	−	10.5792i	1.78591	−	0.524389i
$408$	11.7426	+	9.23448i	0.581345	+	0.457175i
$409$	−4.98306	+	6.99773i	−0.246397	+	0.346015i	−0.919190	−	0.393815i	$-0.871155\pi$
$409$	−4.98306	+	6.99773i	−0.246397	+	0.346015i	0.672793	+	0.739831i	$0.265094\pi$
$410$	−33.1253	+	26.0501i	−1.63594	+	1.28652i
$411$	−0.254830	−	5.34954i	−0.0125698	−	0.263873i
$412$	−13.3523	+	15.4094i	−0.657821	+	0.759166i
$413$	−3.54066	−	11.1220i	−0.174224	−	0.547278i
$414$	7.51877	+	7.83078i	0.369527	+	0.384862i
$415$	−2.33601	+	4.04608i	−0.114670	+	0.198614i
$416$	0.247358	+	0.0476744i	0.0121277	+	0.00233743i
$417$	4.77895	+	2.46372i	0.234026	+	0.120649i
$418$	25.1804	+	10.0807i	1.23161	+	0.493064i
$419$	8.10984	+	17.7581i	0.396191	+	0.867538i	0.997642	+	0.0686285i	$0.0218623\pi$
$419$	8.10984	+	17.7581i	0.396191	+	0.867538i	−0.601451	+	0.798910i	$0.705410\pi$
$420$	−20.3504	+	3.39707i	−0.993000	+	0.165760i
$421$	−1.68238	+	0.493992i	−0.0819943	+	0.0240757i	−0.322472	−	0.946579i	$-0.604514\pi$
$421$	−1.68238	+	0.493992i	−0.0819943	+	0.0240757i	0.240478	+	0.970655i	$0.422696\pi$
$422$	0.331401	−	0.170849i	0.0161323	−	0.00831680i
$423$	−2.02250	+	0.193126i	−0.0983375	+	0.00939009i
$424$	−0.967365	−	3.98753i	−0.0469794	−	0.193652i
$425$	−7.09625	+	1.36769i	−0.344219	+	0.0663427i
$426$	−16.2332	−	18.7341i	−0.786500	−	0.907670i
$427$	−1.99055	+	1.21004i	−0.0963296	+	0.0585580i
$428$	24.8140	−	54.3350i	1.19943	−	2.62638i
$429$	0.208573	−	0.107527i	0.0100700	−	0.00519144i
$430$	−29.8321	−	28.4448i	−1.43863	−	1.37173i
$431$	23.5876	−	9.44306i	1.13618	−	0.454856i	0.274133	−	0.961692i	$-0.411609\pi$
$431$	23.5876	−	9.44306i	1.13618	−	0.454856i	0.862043	+	0.506836i	$0.169185\pi$
$432$	0.486223	+	0.0464287i	0.0233934	+	0.00223380i
$433$	−4.06352	−	28.2624i	−0.195280	−	1.35820i	−0.817756	−	0.575565i	$-0.804782\pi$
$433$	−4.06352	−	28.2624i	−0.195280	−	1.35820i	0.622476	−	0.782639i	$-0.286127\pi$
$434$	−35.2774	+	13.1097i	−1.69337	+	0.629287i
$435$	−0.791679	+	0.913647i	−0.0379581	+	0.0438060i
$436$	−22.3311	+	38.6786i	−1.06946	+	1.85237i
$437$	−5.35495	+	8.39648i	−0.256162	+	0.401658i
$438$	10.1464	+	17.5741i	0.484816	+	0.839725i
$439$	−4.95939	−	14.3292i	−0.236699	−	0.683896i	−0.999314	−	0.0370431i	$-0.988206\pi$
$439$	−4.95939	−	14.3292i	−0.236699	−	0.683896i	0.762615	−	0.646853i	$-0.223915\pi$
$440$	−30.8311	+	19.8139i	−1.46981	+	0.944592i
$441$	4.81842	+	5.07768i	0.229449	+	0.241794i
$442$	0.224518	+	0.491626i	0.0106792	+	0.0233843i
$443$	−11.5268	−	9.06479i	−0.547656	−	0.430681i	0.305611	−	0.952157i	$-0.401139\pi$
$443$	−11.5268	−	9.06479i	−0.547656	−	0.430681i	−0.853266	+	0.521475i	$0.825382\pi$
$444$	−14.7134	−	14.0292i	−0.698269	−	0.665798i
$445$	−1.91162	+	40.1298i	−0.0906193	+	1.90233i
$446$	−10.4650	−	14.6961i	−0.495534	−	0.695881i
$447$	−22.9168	−	6.72899i	−1.08393	−	0.318270i
$448$	16.5047	+	30.3123i	0.779775	+	1.43212i
$449$	−21.7805	−	25.1360i	−1.02789	−	1.18624i	−0.982306	−	0.187282i	$-0.940032\pi$
$449$	−21.7805	−	25.1360i	−1.02789	−	1.18624i	−0.0455789	−	0.998961i	$-0.514513\pi$
$450$	2.01657	−	1.92279i	0.0950618	−	0.0906413i
$451$	42.8402	−	4.09074i	2.01726	−	0.192625i
$452$	0.633310	−	13.2948i	0.0297884	−	0.625335i
$453$	0.269099	−	1.10924i	0.0126434	−	0.0521167i
$454$	8.14076	−	56.6202i	0.382065	−	2.65732i
$455$	−0.255724	−	0.0820834i	−0.0119885	−	0.00384813i
$456$	−0.751935	−	5.22982i	−0.0352126	−	0.244909i
$457$	−0.419696	−	8.81051i	−0.0196326	−	0.412138i	−0.987196	−	0.159511i	$-0.949008\pi$
$457$	−0.419696	−	8.81051i	−0.0196326	−	0.412138i	0.967564	−	0.252627i	$-0.0812947\pi$
$458$	50.7024	+	9.77208i	2.36917	+	0.456619i
$459$	2.93557	+	5.08455i	0.137021	+	0.237327i
$460$	−14.0203	−	34.6713i	−0.653699	−	1.61656i
$461$	10.7464			0.500511			0.250255	−	0.968180i	$-0.419485\pi$
$461$	10.7464			0.500511			0.250255	+	0.968180i	$0.419485\pi$
$462$	31.7517	+	13.6418i	1.47722	+	0.634676i
$463$	22.9664	−	14.7596i	1.06734	−	0.685937i	0.115740	−	0.993280i	$-0.463076\pi$
$463$	22.9664	−	14.7596i	1.06734	−	0.685937i	0.951599	+	0.307342i	$0.0994397\pi$
$464$	0.219610	+	0.0879184i	0.0101951	+	0.00408151i
$465$	9.09866	−	12.7773i	0.421940	−	0.592532i
$466$	2.92912	−	1.17264i	0.135689	−	0.0543217i
$467$	1.76226	−	7.26412i	0.0815475	−	0.336144i	−0.916394	−	0.400278i	$-0.868914\pi$
$467$	1.76226	−	7.26412i	0.0815475	−	0.336144i	0.997941	+	0.0641345i	$0.0204287\pi$
$468$	−0.106877	−	0.0686858i	−0.00494040	−	0.00317500i
$469$	29.6659	+	3.58300i	1.36985	+	0.165447i
$470$	11.0150	+	3.23429i	0.508084	+	0.149187i
$471$	0.999516	−	0.192641i	0.0460553	−	0.00887643i
$472$	−3.67133	+	10.6076i	−0.168987	+	0.488255i
$473$	9.92398	+	40.9072i	0.456305	+	1.88092i
$474$	1.11123	+	1.56050i	0.0510405	+	0.0716764i
$475$	2.15028	+	1.38190i	0.0986614	+	0.0634058i
$476$	−21.2560	+	43.6246i	−0.974269	+	1.99953i
$477$	0.229500	−	1.59621i	0.0105081	−	0.0730853i
$478$	4.67120	+	0.446046i	0.213656	+	0.0204017i
$479$	−18.6541	+	14.6697i	−0.852326	+	0.670277i	−0.945588	−	0.325365i	$-0.894513\pi$
$479$	−18.6541	+	14.6697i	−0.852326	+	0.670277i	0.0932626	+	0.995642i	$0.470270\pi$
$480$	−13.7437	−	7.08536i	−0.627310	−	0.323401i
$481$	−0.0865559	−	0.250087i	−0.00394661	−	0.0114030i
$482$	8.21726			0.374286
$483$	−7.08808	+	10.5242i	−0.322519	+	0.478869i
$484$	69.6536			3.16607
$485$	13.8394	+	39.9862i	0.628413	+	1.81568i
$486$	−2.01200	−	1.03726i	−0.0912661	−	0.0470510i
$487$	−13.0117	+	10.2325i	−0.589617	+	0.463680i	−0.867845	−	0.496835i	$-0.834495\pi$
$487$	−13.0117	+	10.2325i	−0.589617	+	0.463680i	0.278228	+	0.960515i	$0.410253\pi$
$488$	2.23013	+	0.212951i	0.100953	+	0.00963986i
$489$	−3.47337	+	24.1578i	−0.157071	+	1.09245i
$490$	−14.6125	−	36.7549i	−0.660126	−	1.66042i
$491$	4.82396	+	3.10017i	0.217702	+	0.139909i	0.644947	−	0.764227i	$-0.276879\pi$
$491$	4.82396	+	3.10017i	0.217702	+	0.139909i	−0.427245	+	0.904136i	$0.640516\pi$
$492$	−13.5149	−	18.9791i	−0.609300	−	0.855643i
$493$	0.670370	+	2.76330i	0.0301920	+	0.124453i
$494$	0.0625209	−	0.180642i	0.00281295	−	0.00812748i
$495$	−14.1433	+	2.72590i	−0.635695	+	0.122520i
$496$	−2.94496	−	0.864718i	−0.132233	−	0.0388270i
$497$	17.3908	−	23.1735i	0.780082	−	1.03947i
$498$	−3.56420	−	2.29057i	−0.159715	−	0.102643i
$499$	−3.87740	+	15.9829i	−0.173576	+	0.715491i	0.816780	+	0.576949i	$0.195757\pi$
$499$	−3.87740	+	15.9829i	−0.173576	+	0.715491i	−0.990356	+	0.138542i	$0.955758\pi$
$500$	27.2866	−	10.9239i	1.22029	−	0.488532i
$501$	−8.39255	+	11.7857i	−0.374951	+	0.526545i
$502$	−64.8131	−	25.9472i	−2.89275	−	1.15808i
$503$	−23.6342	+	15.1888i	−1.05380	+	0.677235i	−0.948362	−	0.317191i	$-0.897260\pi$
$503$	−23.6342	+	15.1888i	−1.05380	+	0.677235i	−0.105437	+	0.994426i	$0.533624\pi$
$504$	−0.791211	−	6.68526i	−0.0352433	−	0.297785i
$505$	−19.7786			−0.880135
$506$	−11.6412	+	61.5509i	−0.517516	+	2.73627i
$507$	6.49917	+	11.2569i	0.288638	+	0.499936i
$508$	−1.73616	−	0.334618i	−0.0770298	−	0.0148463i
$509$	0.630694	+	13.2399i	0.0279550	+	0.586848i	0.968775	+	0.247941i	$0.0797541\pi$
$509$	0.630694	+	13.2399i	0.0279550	+	0.586848i	−0.940820	+	0.338907i	$0.889943\pi$
$510$	−4.72122	−	32.8368i	−0.209059	−	1.45404i
$511$	−17.5696	+	15.9334i	−0.777232	+	0.704854i
$512$	−0.784322	+	5.45508i	−0.0346625	+	0.241083i
$513$	0.489563	−	2.01801i	0.0216147	−	0.0890971i
$514$	−0.882884	+	18.5340i	−0.0389423	+	0.817500i
$515$	16.2179	−	1.54862i	0.714647	−	0.0682405i
$516$	16.4937	−	15.7267i	0.726095	−	0.692330i
$517$	−7.67724	−	8.86001i	−0.337645	−	0.389663i
$518$	20.3244	−	33.2548i	0.893005	−	1.46113i
$519$	−11.8357	−	3.47529i	−0.519531	−	0.152548i
$520$	0.149823	+	0.210396i	0.00657015	+	0.00922649i
$521$	1.36452	−	28.6448i	0.0597807	−	1.25495i	−0.747291	−	0.664497i	$-0.768646\pi$
$521$	1.36452	−	28.6448i	0.0597807	−	1.25495i	0.807071	−	0.590454i	$-0.201051\pi$
$522$	−0.793433	−	0.756536i	−0.0347276	−	0.0331127i
$523$	27.1460	+	21.3479i	1.18701	+	0.933477i	0.998816	−	0.0486549i	$-0.0154935\pi$
$523$	27.1460	+	21.3479i	1.18701	+	0.933477i	0.188196	+	0.982131i	$0.439736\pi$
$524$	−20.9312	−	45.8330i	−0.914386	−	2.00223i
$525$	2.69484	+	1.82862i	0.117612	+	0.0798076i
$526$	0.319351	−	0.205235i	0.0139244	−	0.00894866i
$527$	−12.0668	−	34.8646i	−0.525637	−	1.51873i
$528$	1.40920	+	2.44080i	0.0613275	+	0.106222i
$529$	−21.4114	−	8.39961i	−0.930929	−	0.365201i
$530$	−4.55601	+	7.89124i	−0.197900	+	0.342773i
$531$	−2.88898	+	3.33406i	−0.125371	+	0.144686i
$532$	16.0885	−	5.97880i	0.697526	−	0.259214i
$533$	−0.0431635	−	0.300209i	−0.00186962	−	0.0130035i
$534$	−36.2676	−	3.46313i	−1.56945	−	0.149864i
$535$	−44.3091	+	17.7387i	−1.91565	+	0.766910i
$536$	−20.7981	−	19.8309i	−0.898339	−	0.856564i
$537$	−3.92108	+	2.02146i	−0.169207	+	0.0872324i
$538$	26.3647	−	57.7305i	1.13666	−	2.48894i
$539$	−7.73908	+	39.6435i	−0.333346	+	1.70757i
$540$	5.10672	+	5.89347i	0.219758	+	0.253614i
$541$	−16.2134	+	3.12487i	−0.697068	+	0.134349i	−0.525462	−	0.850817i	$-0.676108\pi$
$541$	−16.2134	+	3.12487i	−0.697068	+	0.134349i	−0.171606	+	0.985166i	$0.554895\pi$
$542$	1.41165	+	5.81892i	0.0606357	+	0.249944i
$543$	8.43962	−	0.805886i	0.362179	−	0.0345839i
$544$	−32.3258	+	16.6651i	−1.38596	+	0.714510i
$545$	34.2405	−	10.0539i	1.46670	−	0.430663i
$546$	0.0853865	−	0.228096i	0.00365420	−	0.00976162i
$547$	−0.251189	−	0.550028i	−0.0107401	−	0.0235175i	0.904186	−	0.427139i	$-0.140479\pi$
$547$	−0.251189	−	0.550028i	−0.0107401	−	0.0235175i	−0.914926	+	0.403622i	$0.867751\pi$
$548$	−15.5327	−	6.21834i	−0.663523	−	0.265634i
$549$	0.782586	+	0.403451i	0.0334000	+	0.0172189i
$550$	15.7873	+	3.04276i	0.673175	+	0.129744i
$551$	0.502846	−	0.870954i	0.0214220	−	0.0371039i
$552$	11.5176	−	4.03115i	0.490220	−	0.171577i
$553$	−1.50814	+	1.65503i	−0.0641328	+	0.0703791i
$554$	20.8131	−	24.0196i	0.884263	−	1.02049i
$555$	0.772922	+	16.2256i	0.0328087	+	0.688740i
$556$	13.2032	−	10.3831i	0.559942	−	0.440343i
$557$	23.5507	−	33.0724i	0.997876	−	1.40132i	0.0834760	−	0.996510i	$-0.473398\pi$
$557$	23.5507	−	33.0724i	0.997876	−	1.40132i	0.914400	−	0.404811i	$-0.132663\pi$
$558$	11.1812	+	8.79301i	0.473339	+	0.372238i
$559$	0.284646	−	0.0835795i	0.0120392	−	0.00353504i
$560$	0.838613	−	3.11484i	0.0354379	−	0.131626i
$561$	−14.0734	+	30.8165i	−0.594181	+	1.30107i
$562$	43.2834	−	41.2706i	1.82580	−	1.74090i
$563$	−7.87799	+	22.7619i	−0.332017	+	0.959302i	0.648216	+	0.761457i	$0.275515\pi$
$563$	−7.87799	+	22.7619i	−0.332017	+	0.959302i	−0.980233	+	0.197845i	$0.936606\pi$
$564$	−2.07594	+	5.99804i	−0.0874130	+	0.252563i
$565$	−7.69683	+	7.33891i	−0.323808	+	0.308750i
$566$	−6.32654	+	13.8532i	−0.265924	+	0.582293i
$567$	0.687827	−	2.55478i	0.0288860	−	0.107291i
$568$	−26.7350	+	7.85010i	−1.12178	+	0.329383i
$569$	−5.61359	−	4.41458i	−0.235334	−	0.185069i	0.493527	−	0.869731i	$-0.335707\pi$
$569$	−5.61359	−	4.41458i	−0.235334	−	0.185069i	−0.728861	+	0.684662i	$0.759950\pi$
$570$	−6.80602	+	9.55771i	−0.285073	+	0.400329i
$571$	34.4213	−	27.0692i	1.44049	−	1.13281i	0.472646	−	0.881253i	$-0.343299\pi$
$571$	34.4213	−	27.0692i	1.44049	−	1.13281i	0.967842	−	0.251559i	$-0.0809434\pi$
$572$	−0.0348815	−	0.732254i	−0.00145847	−	0.0306171i
$573$	−3.98149	+	4.59488i	−0.166329	+	0.191954i
$574$	30.0849	−	33.0151i	1.25572	−	1.37802i
$575$	−2.17495	+	5.48798i	−0.0907019	+	0.228864i
$576$	6.52260	−	11.2975i	0.271775	−	0.470728i
$577$	−13.9427	−	2.68723i	−0.580442	−	0.111871i	−0.109425	−	0.993995i	$-0.534901\pi$
$577$	−13.9427	−	2.68723i	−0.580442	−	0.111871i	−0.471017	+	0.882124i	$0.656113\pi$
$578$	−35.1501	−	18.1211i	−1.46205	−	0.753739i
$579$	6.90789	+	2.76550i	0.287082	+	0.114930i
$580$	1.56892	+	3.43545i	0.0651457	+	0.142649i
$581$	1.73608	−	4.63766i	0.0720248	−	0.192403i
$582$	−36.8172	+	10.8105i	−1.52612	+	0.448109i
$583$	8.27084	−	4.26391i	0.342543	−	0.176593i
$584$	22.7068	−	2.16824i	0.939614	−	0.0897223i
$585$	0.0239323	+	0.0986503i	0.000989479	+	0.00407869i
$586$	36.1763	−	6.97241i	1.49443	−	0.288028i
$587$	−9.35029	−	10.7908i	−0.385928	−	0.445384i	0.529231	−	0.848478i	$-0.322480\pi$
$587$	−9.35029	−	10.7908i	−0.385928	−	0.445384i	−0.915159	+	0.403093i	$0.867935\pi$
$588$	20.6826	−	7.10296i	0.852937	−	0.292921i
$589$	−5.42068	+	11.8696i	−0.223355	+	0.489079i
$590$	22.1564	−	11.4224i	0.912165	−	0.470254i
$591$	14.5575	+	13.8806i	0.598816	+	0.570970i
$592$	2.95083	−	1.18134i	0.121279	−	0.0485526i
$593$	31.4721	+	3.00522i	1.29240	+	0.123409i	0.718507	−	0.695519i	$-0.244826\pi$
$593$	31.4721	+	3.00522i	1.29240	+	0.123409i	0.573895	+	0.818929i	$0.305432\pi$
$594$	−1.85888	−	12.9288i	−0.0762710	−	0.530476i
$595$	36.3460	−	13.5069i	1.49004	−	0.553727i
$596$	−48.8629	+	56.3908i	−2.00150	+	2.30986i
$597$	−0.232080	+	0.401974i	−0.00949840	+	0.0164517i
$598$	0.437202	+	0.0613101i	0.0178785	+	0.00250715i
$599$	9.49438	+	16.4447i	0.387930	+	0.671914i	0.992171	−	0.124888i	$-0.0398570\pi$
$599$	9.49438	+	16.4447i	0.387930	+	0.671914i	−0.604241	+	0.796801i	$0.706524\pi$
$600$	−1.02437	−	2.95971i	−0.0418195	−	0.120830i
$601$	1.16615	−	0.749439i	0.0475682	−	0.0305703i	−0.516641	−	0.856202i	$-0.672818\pi$
$601$	1.16615	−	0.749439i	0.0475682	−	0.0305703i	0.564209	+	0.825632i	$0.309181\pi$
$602$	36.1521	+	24.5316i	1.47345	+	0.999833i
$603$	−4.69176	−	10.2735i	−0.191063	−	0.418370i
$604$	−2.80294	−	2.20425i	−0.114050	−	0.0896898i
$605$	−40.2792	−	38.4062i	−1.63758	−	1.56143i
$606$	0.853429	−	17.9157i	0.0346682	−	0.727775i
$607$	2.67970	+	3.76311i	0.108766	+	0.152740i	0.865371	−	0.501132i	$-0.167083\pi$
$607$	2.67970	+	3.76311i	0.108766	+	0.152740i	−0.756605	+	0.653872i	$0.773144\pi$
$608$	12.3421	+	3.62396i	0.500537	+	0.146971i
$609$	0.668219	−	1.09334i	0.0270776	−	0.0443042i
$610$	−3.25793	−	3.75985i	−0.131910	−	0.152232i
$611$	−0.0597971	+	0.0570164i	−0.00241913	+	0.00230664i
$612$	18.2586	−	1.74349i	0.738062	−	0.0704763i
$613$	1.25504	−	26.3465i	0.0506905	−	1.06412i	−0.820022	−	0.572332i	$-0.806039\pi$
$613$	1.25504	−	26.3465i	0.0506905	−	1.06412i	0.870713	−	0.491792i	$-0.163658\pi$
$614$	15.5102	−	63.9339i	0.625940	−	2.58016i
$615$	−2.64943	+	18.4272i	−0.106835	+	0.743056i
$616$	28.7746	−	26.0951i	1.15936	−	1.05140i
$617$	−0.501419	−	3.48744i	−0.0201864	−	0.140399i	0.977236	−	0.212156i	$-0.0680485\pi$
$617$	−0.501419	−	3.48744i	−0.0201864	−	0.140399i	−0.997422	+	0.0717569i	$0.977139\pi$
$618$	0.702973	+	14.7572i	0.0282777	+	0.593622i
$619$	−7.93717	−	1.52977i	−0.319022	−	0.0614865i	0.0272265	−	0.999629i	$-0.491332\pi$
$619$	−7.93717	−	1.52977i	−0.319022	−	0.0614865i	−0.346248	+	0.938143i	$0.612545\pi$
$620$	−24.5016	−	42.4380i	−0.984007	−	1.70435i
$621$	4.79116	+	0.211545i	0.192263	+	0.00848899i
$622$	−25.4571			−1.02074
$623$	−5.00478	−	42.2875i	−0.200512	−	1.69421i
$624$	0.0167099	−	0.0107388i	0.000668932	−	0.000429896i
$625$	−27.5163	−	11.0159i	−1.10065	−	0.440634i
$626$	26.3617	−	37.0199i	1.05363	−	1.47961i
$627$	11.1239	−	4.45333i	0.444245	−	0.177849i
$628$	0.749714	−	3.09036i	0.0299168	−	0.123319i
$629$	32.1416	+	20.6561i	1.28157	+	0.823614i
$630$	−8.97331	+	11.9571i	−0.357505	+	0.476382i
$631$	18.4605	+	5.42050i	0.734903	+	0.215787i	0.627705	−	0.778451i	$-0.283994\pi$
$631$	18.4605	+	5.42050i	0.734903	+	0.215787i	0.107197	+	0.994238i	$0.465812\pi$
$632$	2.11445	−	0.407526i	0.0841082	−	0.0162105i
$633$	0.0538721	−	0.155653i	0.00214122	−	0.00618666i
$634$	−9.20482	−	37.9428i	−0.365570	−	1.50690i
$635$	0.819482	+	1.15080i	0.0325202	+	0.0456682i
$636$	−4.23815	−	2.72369i	−0.168054	−	0.108001i
$637$	0.281673	+	0.0411865i	0.0111603	+	0.00163187i
$638$	0.900279	−	6.26158i	0.0356424	−	0.247898i
$639$	−10.9013	−	1.04095i	−0.431248	−	0.0411792i
$640$	−33.6321	+	26.4485i	−1.32942	+	1.04547i
$641$	3.35006	+	1.72707i	0.132319	+	0.0682153i	0.523115	−	0.852262i	$-0.324770\pi$
$641$	3.35006	+	1.72707i	0.132319	+	0.0682153i	−0.390796	+	0.920477i	$0.627800\pi$
$642$	−14.1560	−	40.9012i	−0.558694	−	1.61424i
$643$	10.5874			0.417527			0.208764	−	0.977966i	$-0.433056\pi$
$643$	10.5874			0.417527			0.208764	+	0.977966i	$0.433056\pi$
$644$	20.7083	+	33.8005i	0.816020	+	1.33193i
$645$	−18.2095			−0.716998
$646$	9.02624	+	26.0796i	0.355133	+	1.02609i
$647$	−5.30291	−	2.73384i	−0.208479	−	0.107478i	0.350825	−	0.936441i	$-0.385901\pi$
$647$	−5.30291	−	2.73384i	−0.208479	−	0.107478i	−0.559304	+	0.828963i	$0.688932\pi$
$648$	−2.00005	+	1.57286i	−0.0785696	+	0.0617878i
$649$	−25.3408	−	2.41975i	−0.994714	−	0.0949836i
$650$	0.0161259	−	0.112158i	0.000632510	−	0.00439921i
$651$	−7.28239	+	14.9459i	−0.285420	+	0.585777i
$652$	64.1423	+	41.2218i	2.51201	+	1.61437i
$653$	18.6847	+	26.2391i	0.731191	+	1.02681i	0.998009	+	0.0630667i	$0.0200881\pi$
$653$	18.6847	+	26.2391i	0.731191	+	1.02681i	−0.266819	+	0.963747i	$0.585973\pi$
$654$	7.62952	+	31.4493i	0.298338	+	1.22976i
$655$	−13.1677	+	38.0455i	−0.514504	+	1.48656i
$656$	3.57695	−	0.689400i	0.139656	−	0.0269166i
$657$	8.60159	+	2.52566i	0.335580	+	0.0985352i
$658$	−12.0801	−	1.45901i	−0.470932	−	0.0568783i
$659$	−19.5077	−	12.5368i	−0.759911	−	0.488365i	0.102400	−	0.994743i	$-0.467348\pi$
$659$	−19.5077	−	12.5368i	−0.759911	−	0.488365i	−0.862312	+	0.506378i	$0.830984\pi$
$660$	−10.6086	+	43.7291i	−0.412938	+	1.70215i
$661$	−41.4042	+	16.5757i	−1.61044	+	0.644722i	−0.990195	−	0.139689i	$-0.955390\pi$
$661$	−41.4042	+	16.5757i	−1.61044	+	0.644722i	−0.620242	+	0.784411i	$0.712965\pi$
$662$	−5.49949	+	7.72296i	−0.213744	+	0.300161i
$663$	0.221658	+	0.0887384i	0.00860847	+	0.00344631i
$664$	−4.00631	+	2.57470i	−0.155475	+	0.0999178i
$665$	−12.6003	−	5.41361i	−0.488618	−	0.209931i
$666$	−14.7307			−0.570805
$667$	2.19756	+	0.752040i	0.0850898	+	0.0291191i
$668$	22.6001	+	39.1445i	0.874424	+	1.51455i
$669$	−7.82608	−	1.50835i	−0.302574	−	0.0583163i
$670$	3.03653	+	63.7446i	0.117311	+	2.46267i
$671$	0.723031	+	5.02879i	0.0279123	+	0.194134i
$672$	15.6049	+	5.00893i	0.601972	+	0.193223i
$673$	−6.47838	+	45.0581i	−0.249723	+	1.73686i	0.350085	+	0.936718i	$0.386153\pi$
$673$	−6.47838	+	45.0581i	−0.249723	+	1.73686i	−0.599808	+	0.800144i	$0.704756\pi$
$674$	18.2233	−	75.1173i	0.701933	−	2.89341i
$675$	0.0585691	−	1.22952i	0.00225433	−	0.0473242i
$676$	40.4235	−	3.85998i	1.55475	−	0.148461i
$677$	−20.0027	+	19.0725i	−0.768765	+	0.733016i	−0.969088	−	0.246714i	$-0.920649\pi$
$677$	−20.0027	+	19.0725i	−0.768765	+	0.733016i	0.200323	+	0.979730i	$0.435801\pi$
$678$	−6.31557	−	7.28856i	−0.242548	−	0.279915i
$679$	−21.4467	−	39.3886i	−0.823047	−	1.51159i
$680$	−35.7791	−	10.5057i	−1.37207	−	0.402875i
$681$	−14.6581	−	20.5845i	−0.561701	−	0.788799i
$682$	−3.90549	+	81.9863i	−0.149549	+	3.13942i
$683$	−16.7976	−	16.0165i	−0.642742	−	0.612853i	0.296943	−	0.954895i	$-0.404033\pi$
$683$	−16.7976	−	16.0165i	−0.642742	−	0.612853i	−0.939685	+	0.342042i	$0.888881\pi$
$684$	−5.09929	−	4.01012i	−0.194976	−	0.153331i
$685$	5.55350	+	12.1605i	0.212188	+	0.464628i
$686$	21.6910	+	35.8754i	0.828167	+	1.36973i
$687$	19.1897	−	12.3325i	0.732133	−	0.470514i
$688$	1.16538	+	3.36714i	0.0444296	+	0.128371i
$689$	−0.0327901	−	0.0567941i	−0.00124920	−	0.00216368i
$690$	−24.6887	−	11.1714i	−0.939882	−	0.425288i
$691$	−9.35815	+	16.2088i	−0.356001	+	0.616611i	−0.987289	−	0.158937i	$-0.949193\pi$
$691$	−9.35815	+	16.2088i	−0.356001	+	0.616611i	0.631288	+	0.775548i	$0.282527\pi$
$692$	−25.2360	+	29.1239i	−0.959327	+	1.10712i
$693$	14.3105	−	5.31805i	0.543611	−	0.202016i
$694$	8.78812	+	61.1227i	0.333593	+	2.32019i
$695$	−13.3603	−	1.27575i	−0.506785	−	0.0483921i
$696$	−1.14402	+	0.457998i	−0.0433641	+	0.0173604i
$697$	31.6904	+	30.2167i	1.20036	+	1.14454i
$698$	−17.3287	+	8.93357i	−0.655901	+	0.338141i
$699$	0.579019	−	1.26788i	0.0219005	−	0.0479554i
$700$	8.69375	−	5.28486i	0.328593	−	0.199749i
$701$	−12.7942	−	14.7653i	−0.483229	−	0.557676i	0.460815	−	0.887496i	$-0.347557\pi$
$701$	−12.7942	−	14.7653i	−0.483229	−	0.557676i	−0.944044	+	0.329820i	$0.893012\pi$
$702$	−0.0903914	+	0.0174215i	−0.00341160	+	0.000657533i
$703$	−3.18586	−	13.1323i	−0.120157	−	0.495294i
$704$	74.9334	−	7.15527i	2.82416	−	0.269675i
$705$	4.50773	−	2.32389i	0.169771	−	0.0875229i
$706$	−6.60822	+	1.94035i	−0.248704	+	0.0730260i
$707$	20.6776	−	3.45168i	0.777661	−	0.129814i
$708$	5.72526	+	12.5366i	0.215168	+	0.471153i
$709$	33.2805	+	13.3235i	1.24988	+	0.500375i	0.899782	−	0.436340i	$-0.143726\pi$
$709$	33.2805	+	13.3235i	1.24988	+	0.500375i	0.350093	+	0.936715i	$0.386150\pi$
$710$	54.9986	+	28.3538i	2.06406	+	1.06410i
$711$	0.831011	+	0.160164i	0.0311654	+	0.00600663i
$712$	−20.4759	+	35.4653i	−0.767367	+	1.32912i
$713$	−29.3117	−	7.00316i	−1.09773	−	0.262270i
$714$	10.6664	+	33.5055i	0.399179	+	1.25391i
$715$	−0.383585	+	0.442680i	−0.0143453	+	0.0165553i
$716$	0.655758	+	13.7661i	0.0245068	+	0.514462i
$717$	1.62946	−	1.28143i	0.0608535	−	0.0478557i
$718$	−32.8937	+	46.1927i	−1.22758	+	1.72390i
$719$	21.7919	+	17.1374i	0.812702	+	0.639116i	0.935504	−	0.353315i	$-0.114946\pi$
$719$	21.7919	+	17.1374i	0.812702	+	0.639116i	−0.122802	+	0.992431i	$0.539188\pi$
$720$	−1.16983	+	0.343494i	−0.0435971	+	0.0128013i
$721$	−16.6848	+	4.44930i	−0.621376	+	0.165701i
$722$	−13.8118	+	30.2437i	−0.514023	+	1.12555i
$723$	2.62724	−	2.50507i	0.0977080	−	0.0931644i
$724$	8.66262	−	25.0290i	0.321944	−	0.930195i
$725$	0.194980	−	0.563357i	0.00724137	−	0.0209226i
$726$	36.5268	−	34.8282i	1.35564	−	1.29260i
$727$	−10.8519	+	23.7623i	−0.402474	+	0.881294i	0.594540	+	0.804066i	$0.297334\pi$
$727$	−10.8519	+	23.7623i	−0.402474	+	0.881294i	−0.997013	+	0.0772281i	$0.975393\pi$
$728$	−0.193350	−	0.193813i	−0.00716603	−	0.00718320i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−39.8172	−	31.3126i	−1.47370	−	1.15893i
$731$	−24.8436	+	34.8880i	−0.918874	+	1.29038i
$732$	2.16212	−	1.70031i	0.0799143	−	0.0628453i
$733$	0.0133116	+	0.279445i	0.000491676	+	0.0103216i	0.999100	−	0.0424205i	$-0.0135069\pi$
$733$	0.0133116	+	0.279445i	0.000491676	+	0.0103216i	−0.998608	+	0.0527421i	$0.983204\pi$
$734$	13.4049	−	15.4701i	0.494783	−	0.571010i
$735$	−15.8768	−	7.29666i	−0.585625	−	0.269141i
$736$	−2.72110	+	29.5829i	−0.100301	+	1.09044i
$737$	32.5851	−	56.4391i	1.20029	−	2.07896i
$738$	−16.5773	−	3.19500i	−0.610217	−	0.117610i
$739$	14.8324	+	7.64662i	0.545618	+	0.281286i	0.708918	−	0.705291i	$-0.249184\pi$
$739$	14.8324	+	7.64662i	0.545618	+	0.281286i	−0.163300	+	0.986576i	$0.552214\pi$
$740$	47.1120	+	18.8608i	1.73187	+	0.693336i
$741$	−0.0350803	−	0.0768151i	−0.00128871	−	0.00282187i
$742$	3.38595	−	9.04503i	0.124302	−	0.332053i
$743$	−11.8524	+	3.48018i	−0.434823	+	0.127675i	−0.491816	−	0.870699i	$-0.663667\pi$
$743$	−11.8524	+	3.48018i	−0.434823	+	0.127675i	0.0569935	+	0.998375i	$0.481849\pi$
$744$	14.2116	−	7.32658i	0.521022	−	0.268605i
$745$	59.3496	−	5.66720i	2.17440	−	0.207630i
$746$	−16.7185	−	68.9146i	−0.612108	−	2.52314i
$747$	−1.83784	+	0.354215i	−0.0672431	+	0.0129600i
$748$	69.3081	+	79.9858i	2.53416	+	2.92457i
$749$	43.2275	−	26.2776i	1.57950	−	0.960164i
$750$	8.84710	−	19.3724i	0.323050	−	0.707381i
$751$	−7.50223	+	3.86767i	−0.273760	+	0.141133i	−0.589641	−	0.807666i	$-0.700731\pi$
$751$	−7.50223	+	3.86767i	−0.273760	+	0.141133i	0.315880	+	0.948799i	$0.397700\pi$
$752$	−0.718201	−	0.684803i	−0.0261901	−	0.0249722i
$753$	−28.6323	+	11.4626i	−1.04342	+	0.417722i
$754$	−0.0443814	−	0.00423791i	−0.00161627	−	0.000154336i
$755$	0.405481	+	2.82018i	0.0147570	+	0.102637i
$756$	−6.36735	−	5.27015i	−0.231578	−	0.191673i
$757$	−28.9784	+	33.4429i	−1.05324	+	1.21550i	−0.0774022	+	0.997000i	$0.524663\pi$
$757$	−28.9784	+	33.4429i	−1.05324	+	1.21550i	−0.975836	+	0.218502i	$0.929883\pi$
$758$	−11.8328	+	20.4950i	−0.429786	+	0.744411i
$759$	15.0421	+	23.2281i	0.545993	+	0.843125i
$760$	6.59441	+	11.4219i	0.239204	+	0.414314i
$761$	−10.7551	−	31.0749i	−0.389873	−	1.12646i	−0.953749	−	0.300604i	$-0.902812\pi$
$761$	−10.7551	−	31.0749i	−0.389873	−	1.12646i	0.563876	−	0.825859i	$-0.309309\pi$
$762$	−1.07777	+	0.692641i	−0.0390435	+	0.0250918i
$763$	−34.0423	+	16.4864i	−1.23241	+	0.596849i
$764$	7.89034	+	17.2774i	0.285462	+	0.625076i
$765$	−11.5199	−	9.05937i	−0.416504	−	0.327542i
$766$	31.8515	+	30.3704i	1.15084	+	1.09733i
$767$	−0.00853647	+	0.179203i	−0.000308234	+	0.00647063i
$768$	−7.37232	−	10.3530i	−0.266026	−	0.373581i
$769$	9.32556	+	2.73823i	0.336288	+	0.0987431i	0.445517	−	0.895274i	$-0.353020\pi$
$769$	9.32556	+	2.73823i	0.336288	+	0.0987431i	−0.109229	+	0.994017i	$0.534838\pi$
$770$	−86.2366	−	2.15603i	−3.10775	−	0.0776980i
$771$	5.36790	+	6.19488i	0.193320	+	0.223103i
$772$	16.8237	−	16.0414i	0.605498	−	0.577342i
$773$	8.76118	−	0.836591i	0.315118	−	0.0300901i	0.0637009	−	0.997969i	$-0.479710\pi$
$773$	8.76118	−	0.836591i	0.315118	−	0.0300901i	0.251417	+	0.967879i	$0.419104\pi$
$774$	0.785725	−	16.4944i	0.0282423	−	0.592879i
$775$	−1.82359	+	7.51692i	−0.0655051	+	0.270016i
$776$	−6.13822	+	42.6922i	−0.220349	+	1.53256i
$777$	−3.63969	−	16.8283i	−0.130573	−	0.603711i
$778$	−3.84627	−	26.7514i	−0.137895	−	0.959083i
$779$	−0.736900	−	15.4694i	−0.0264022	−	0.554250i
$780$	0.311396	+	0.0600168i	0.0111498	+	0.00214894i
$781$	−31.5947	−	54.7236i	−1.13055	−	1.95816i
$782$	−55.0869	+	32.0602i	−1.96990	+	1.14647i
$783$	−0.484311			−0.0173079
$784$	−0.333143	+	3.40277i	−0.0118980	+	0.121528i
$785$	−2.13753	+	1.37371i	−0.0762918	+	0.0490298i
$786$	−33.8939	−	13.5691i	−1.20896	−	0.483993i
$787$	22.1300	−	31.0773i	0.788850	−	1.10778i	−0.202850	−	0.979210i	$-0.565020\pi$
$787$	22.1300	−	31.0773i	0.788850	−	1.10778i	0.991700	−	0.128575i	$-0.0410402\pi$
$788$	58.3372	−	23.3547i	2.07818	−	0.831977i
$789$	0.0395370	−	0.162974i	0.00140755	−	0.00580202i
$790$	−4.02287	−	2.58534i	−0.143127	−	0.0919824i
$791$	6.76593	−	9.01572i	0.240569	−	0.320562i
$792$	−14.0873	−	4.13640i	−0.500570	−	0.146981i
$793$	0.0351586	−	0.00677627i	0.00124852	−	0.000240632i
$794$	11.0373	−	31.8903i	0.391700	−	1.13174i
$795$	0.949022	+	3.91192i	0.0336583	+	0.138742i
$796$	0.841115	+	1.18118i	0.0298125	+	0.0418659i
$797$	25.0560	+	16.1025i	0.887529	+	0.570380i	0.903067	−	0.429499i	$-0.141310\pi$
$797$	25.0560	+	16.1025i	0.887529	+	0.570380i	−0.0155381	+	0.999879i	$0.504946\pi$
$798$	5.44741	−	11.1799i	0.192836	−	0.395765i
$799$	1.69759	−	11.8070i	0.0600564	−	0.417701i
$800$	7.59035	+	0.724790i	0.268359	+	0.0256252i
$801$	−12.6513	+	9.94909i	−0.447012	+	0.351534i
$802$	−6.22691	−	3.21020i	−0.219880	−	0.113356i
$803$	16.9189	+	48.8838i	0.597053	+	1.72507i
$804$	−35.2834			−1.24435
$805$	6.66202	−	30.9644i	0.234805	−	1.09135i
$806$	0.578467			0.0203756
$807$	−9.17004	−	26.4951i	−0.322801	−	0.932672i
$808$	−17.9197	−	9.23824i	−0.630412	−	0.325000i
$809$	31.6203	−	24.8665i	1.11171	−	0.874259i	0.118776	−	0.992921i	$-0.462103\pi$
$809$	31.6203	−	24.8665i	1.11171	−	0.874259i	0.992935	+	0.118662i	$0.0378604\pi$
$810$	5.62485	+	0.537108i	0.197637	+	0.0188721i
$811$	−2.29416	+	15.9562i	−0.0805587	+	0.560298i	0.909069	+	0.416645i	$0.136794\pi$
$811$	−2.29416	+	15.9562i	−0.0805587	+	0.560298i	−0.989628	+	0.143653i	$0.954115\pi$
$812$	−2.23977	−	3.31780i	−0.0786006	−	0.116432i
$813$	2.22526	+	1.43009i	0.0780433	+	0.0501554i
$814$	−49.3050	−	69.2392i	−1.72814	−	2.42683i
$815$	−14.3630	−	59.2050i	−0.503113	−	2.07386i
$816$	−0.937922	+	2.70995i	−0.0328338	+	0.0948671i
$817$	14.8745	−	2.86682i	0.520393	−	0.100297i
$818$	18.6584	+	5.47859i	0.652375	+	0.191555i
$819$	−0.0422362	−	0.0989579i	−0.00147585	−	0.00345787i
$820$	48.9267	+	31.4433i	1.70860	+	1.09805i
$821$	−5.32858	+	21.9647i	−0.185969	+	0.766573i	0.800049	+	0.599934i	$0.204807\pi$
$821$	−5.32858	+	21.9647i	−0.185969	+	0.766573i	−0.986018	+	0.166639i	$0.946709\pi$
$822$	−11.2547	+	4.50572i	−0.392554	+	0.157155i
$823$	−19.5810	+	27.4977i	−0.682551	+	0.958508i	0.317397	+	0.948293i	$0.397191\pi$
$823$	−19.5810	+	27.4977i	−0.682551	+	0.958508i	−0.999948	+	0.0102154i	$0.996748\pi$
$824$	15.4170	+	6.17204i	0.537077	+	0.215013i
$825$	5.97516	−	3.84000i	0.208028	−	0.133692i
$826$	−21.1701	+	15.8083i	−0.736603	+	0.550040i
$827$	−17.5468			−0.610162			−0.305081	−	0.952326i	$-0.598684\pi$
$827$	−17.5468			−0.610162			−0.305081	+	0.952326i	$0.598684\pi$
$828$	6.81901	−	13.3407i	0.236977	−	0.463620i
$829$	−4.50972	−	7.81106i	−0.156629	−	0.271289i	0.777022	−	0.629473i	$-0.216729\pi$
$829$	−4.50972	−	7.81106i	−0.156629	−	0.271289i	−0.933651	+	0.358184i	$0.883396\pi$
$830$	10.3846	+	2.00147i	0.360455	+	0.0694721i
$831$	−0.668071	−	14.0245i	−0.0231751	−	0.486506i
$832$	−0.0754991	−	0.525108i	−0.00261746	−	0.0182048i
$833$	−35.6409	+	20.4638i	−1.23488	+	0.709027i
$834$	1.73208	−	12.0469i	0.0599770	−	0.417149i
$835$	8.51466	−	35.0979i	0.294662	−	1.21461i
$836$	1.78113	−	37.3905i	0.0616016	−	1.29318i
$837$	6.25547	−	0.597325i	0.216221	−	0.0206466i
$838$	31.9827	−	30.4955i	1.10482	−	1.05345i
$839$	31.6081	+	36.4777i	1.09123	+	1.25935i	0.963548	+	0.267535i	$0.0862091\pi$
$839$	31.6081	+	36.4777i	1.09123	+	1.25935i	0.127685	+	0.991815i	$0.459245\pi$
$840$	8.03569	+	14.7582i	0.277258	+	0.509207i
$841$	27.6002	+	8.10416i	0.951732	+	0.279454i
$842$	2.30229	+	3.23311i	0.0793421	+	0.111420i
$843$	1.25712	−	26.3903i	0.0432976	−	0.908929i
$844$	−0.372411	−	0.355093i	−0.0128189	−	0.0122228i
$845$	−25.5044	−	20.0569i	−0.877379	−	0.689979i
$846$	1.91051	+	4.18343i	0.0656846	+	0.143829i
$847$	48.8126	+	33.1225i	1.67722	+	1.13810i
$848$	0.662622	−	0.425841i	0.0227545	−	0.0146234i
$849$	2.20047	+	6.35784i	0.0755199	+	0.218200i
$850$	8.17948	+	14.1673i	0.280554	+	0.485933i
$851$	28.3436	−	13.0633i	0.971607	−	0.447805i
$852$	−17.1055	+	29.6276i	−0.586024	+	1.01502i
$853$	−24.8208	+	28.6448i	−0.849849	+	0.980778i	−0.999969	−	0.00789006i	$-0.997488\pi$
$853$	−24.8208	+	28.6448i	−0.849849	+	0.980778i	0.150120	+	0.988668i	$0.452034\pi$
$854$	4.06218	+	3.36220i	0.139005	+	0.115052i
$855$	0.737677	+	5.13066i	0.0252280	+	0.175465i
$856$	−48.4302	−	4.62452i	−1.65531	−	0.158063i
$857$	−41.4114	+	16.5786i	−1.41459	+	0.566315i	−0.948031	−	0.318177i	$-0.896930\pi$
$857$	−41.4114	+	16.5786i	−1.41459	+	0.566315i	−0.466556	+	0.884492i	$0.654505\pi$
$858$	−0.384434	−	0.366557i	−0.0131244	−	0.0125141i
$859$	24.4122	−	12.5854i	0.832934	−	0.429407i	0.0116535	−	0.999932i	$-0.496290\pi$
$859$	24.4122	−	12.5854i	0.832934	−	0.429407i	0.821280	+	0.570525i	$0.193260\pi$
$860$	−23.6318	+	51.7465i	−0.805838	+	1.76454i
$861$	−0.445983	−	19.7271i	−0.0151991	−	0.672299i
$862$	−37.6634	−	43.4659i	−1.28282	−	1.48045i
$863$	−24.3701	+	4.69696i	−0.829568	+	0.159886i	−0.586322	−	0.810078i	$-0.699425\pi$
$863$	−24.3701	+	4.69696i	−0.829568	+	0.159886i	−0.243247	+	0.969964i	$0.578212\pi$
$864$	−1.46041	−	6.01988i	−0.0496840	−	0.204800i
$865$	30.6520	−	2.92691i	1.04220	−	0.0995179i
$866$	−57.4487	+	29.6168i	−1.95219	+	1.00642i
$867$	−16.7626	+	4.92193i	−0.569286	+	0.167158i
$868$	33.0214	+	40.0911i	1.12082	+	1.36078i
$869$	2.02864	+	4.44210i	0.0688169	+	0.150688i
$870$	2.54055	+	1.01708i	0.0861326	+	0.0344823i
$871$	−0.408240	−	0.210462i	−0.0138327	−	0.00713125i
$872$	35.7184	+	6.88416i	1.20958	+	0.233127i
$873$	−8.47563	+	14.6802i	−0.286857	+	0.496850i
$874$	21.9258	+	5.23853i	0.741652	+	0.177196i
$875$	24.3169	+	5.32028i	0.822060	+	0.179858i
$876$	18.3402	−	21.1657i	0.619657	−	0.715122i
$877$	0.537908	+	11.2921i	0.0181639	+	0.381306i	0.989586	+	0.143946i	$0.0459792\pi$
$877$	0.537908	+	11.2921i	0.0181639	+	0.381306i	−0.971422	+	0.237360i	$0.923718\pi$
$878$	−26.9804	+	21.2176i	−0.910544	+	0.716060i
$879$	9.44079	−	13.2577i	0.318430	−	0.447172i
$880$	−5.53006	−	4.34889i	−0.186418	−	0.146601i
$881$	36.3684	−	10.6787i	1.22528	−	0.359776i	0.395815	−	0.918330i	$-0.370462\pi$
$881$	36.3684	−	10.6787i	1.22528	−	0.359776i	0.829468	+	0.558555i	$0.188644\pi$
$882$	7.29448	−	14.0666i	0.245618	−	0.473646i
$883$	3.69928	−	8.10030i	0.124491	−	0.272597i	−0.837117	−	0.547024i	$-0.815761\pi$
$883$	3.69928	−	8.10030i	0.124491	−	0.272597i	0.961608	+	0.274427i	$0.0884881\pi$
$884$	0.539833	−	0.514729i	0.0181565	−	0.0173122i
$885$	3.60172	−	10.4065i	0.121070	−	0.349810i
$886$	−10.8568	+	31.3687i	−0.364741	+	1.05385i
$887$	−10.2891	+	9.81062i	−0.345474	+	0.329408i	−0.842872	−	0.538114i	$-0.819137\pi$
$887$	−10.2891	+	9.81062i	−0.345474	+	0.329408i	0.497399	+	0.867522i	$0.334289\pi$
$888$	−6.87844	+	15.0617i	−0.230825	+	0.505437i
$889$	−1.05756	−	1.06010i	−0.0354696	−	0.0355546i
$890$	87.2584	−	25.6214i	2.92491	−	0.858830i
$891$	−4.53574	−	3.56694i	−0.151953	−	0.119497i
$892$	−14.4428	+	20.2821i	−0.483581	+	0.679095i
$893$	−3.31629	+	2.60796i	−0.110975	+	0.0872720i
$894$	2.57254	+	54.0042i	0.0860385	+	1.80617i
$895$	7.21123	−	8.32221i	0.241045	−	0.278181i
$896$	30.5451	−	33.5201i	1.02044	−	1.11983i
$897$	0.158474	−	0.113681i	0.00529129	−	0.00379569i
$898$	−37.6440	+	65.2012i	−1.25620	+	2.17579i
$899$	2.98838	+	0.575963i	0.0996680	+	0.0192094i
$900$	−3.41795	−	1.76207i	−0.113932	−	0.0587358i
$901$	8.78971	+	3.51887i	0.292828	+	0.117230i
$902$	−40.4679	−	88.6123i	−1.34743	−	2.95047i
$903$	19.0372	−	3.17785i	0.633518	−	0.105752i
$904$	−10.4013	+	3.05411i	−0.345943	+	0.101578i
$905$	−18.8101	+	9.69728i	−0.625269	+	0.322349i
$906$	−2.57205	+	0.245601i	−0.0854507	+	0.00815955i
$907$	−2.87832	−	11.8646i	−0.0955731	−	0.393958i	0.903853	−	0.427844i	$-0.140727\pi$
$907$	−2.87832	−	11.8646i	−0.0955731	−	0.393958i	−0.999426	+	0.0338862i	$0.989212\pi$
$908$	−77.5185	+	14.9405i	−2.57254	+	0.495817i
$909$	−5.18881	−	5.98821i	−0.172102	−	0.198616i
$910$	0.0137409	+	0.607801i	0.000455506	+	0.0201484i
$911$	−23.1679	+	50.7306i	−0.767587	+	1.68078i	−0.0356922	+	0.999363i	$0.511364\pi$
$911$	−23.1679	+	50.7306i	−0.767587	+	1.68078i	−0.731895	+	0.681418i	$0.761364\pi$
$912$	0.901505	−	0.464758i	0.0298518	−	0.0153897i
$913$	−7.81633	−	7.45286i	−0.258683	−	0.246654i
$914$	−18.5362	+	7.42076i	−0.613122	+	0.245457i
$915$	−2.18784	−	0.208913i	−0.0723278	−	0.00690647i
$916$	−10.1417	−	70.5368i	−0.335090	−	2.33060i
$917$	7.12666	−	42.0728i	0.235343	−	1.38937i
$918$	8.70317	−	10.0440i	0.287247	−	0.331501i
$919$	4.56034	−	7.89874i	0.150432	−	0.260556i	−0.780954	−	0.624588i	$-0.785267\pi$
$919$	4.56034	−	7.89874i	0.150432	−	0.260556i	0.931386	+	0.364032i	$0.118600\pi$
$920$	−22.9507	+	20.0269i	−0.756661	+	0.660268i
$921$	−14.5316	−	25.1694i	−0.478831	−	0.829360i
$922$	−7.95625	−	22.9881i	−0.262025	−	0.757072i
$923$	−0.374642	+	0.240767i	−0.0123315	+	0.00792496i
$924$	3.45934	−	47.5682i	0.113804	−	1.56488i
$925$	−3.32757	−	7.28636i	−0.109410	−	0.239574i
$926$	−48.5763	−	38.2008i	−1.59632	−	1.25536i
$927$	4.72356	+	4.50390i	0.155142	+	0.147928i
$928$	0.142749	−	2.99666i	0.00468596	−	0.0983703i
$929$	−14.6648	−	20.5939i	−0.481137	−	0.675663i	0.500649	−	0.865650i	$-0.333095\pi$
$929$	−14.6648	−	20.5939i	−0.481137	−	0.675663i	−0.981786	+	0.189988i	$0.939155\pi$
$930$	−34.0687	−	10.0035i	−1.11716	−	0.328026i
$931$	14.1178	+	3.46073i	0.462692	+	0.113421i
$932$	−2.85152	−	3.29083i	−0.0934048	−	0.107795i
$933$	−8.13919	+	7.76070i	−0.266465	+	0.254074i
$934$	−16.8437	+	1.60838i	−0.551142	+	0.0526276i
$935$	4.02379	−	84.4698i	0.131592	−	2.76246i
$936$	−0.0243949	+	0.100557i	−0.000797372	+	0.00328681i
$937$	4.44684	−	30.9284i	0.145272	−	1.01039i	−0.778555	−	0.627577i	$-0.784047\pi$
$937$	4.44684	−	30.9284i	0.145272	−	1.01039i	0.923826	−	0.382811i	$-0.125044\pi$
$938$	−14.2990	−	66.1122i	−0.466880	−	2.15864i
$939$	−2.85724	−	19.8726i	−0.0932426	−	0.648516i
$940$	−0.753868	−	15.8256i	−0.0245885	−	0.516175i
$941$	41.7091	+	8.03877i	1.35968	+	0.262056i	0.816395	−	0.577493i	$-0.195969\pi$
$941$	41.7091	+	8.03877i	1.35968	+	0.262056i	0.543283	+	0.839550i	$0.317181\pi$
$942$	−1.15209	−	1.99548i	−0.0375371	−	0.0650162i
$943$	34.7299	−	8.55329i	1.13096	−	0.278533i
$944$	−2.15478			−0.0701320
$945$	0.776208	+	6.55850i	0.0252500	+	0.213348i
$946$	80.1588	−	51.5149i	2.60619	−	1.67489i
$947$	−3.05353	−	1.22245i	−0.0992264	−	0.0397243i	0.321518	−	0.946903i	$-0.395807\pi$
$947$	−3.05353	−	1.22245i	−0.0992264	−	0.0397243i	−0.420745	+	0.907179i	$0.638231\pi$
$948$	1.53361	−	2.15365i	0.0498093	−	0.0699474i
$949$	0.338453	−	0.135496i	0.0109866	−	0.00439839i
$950$	1.36409	−	5.62284i	0.0442568	−	0.182429i
$951$	−14.5100	−	9.32501i	−0.470519	−	0.302384i
$952$	39.2389	+	4.73920i	1.27174	+	0.153598i
$953$	0.926729	+	0.272112i	0.0300197	+	0.00881458i	0.296708	−	0.954968i	$-0.404111\pi$
$953$	0.926729	+	0.272112i	0.0300197	+	0.00881458i	−0.266688	+	0.963783i	$0.585929\pi$
$954$	−3.58442	+	0.690840i	−0.116050	+	0.0223668i
$955$	4.96375	−	14.3418i	0.160623	−	0.464090i
$956$	−1.52679	−	6.29350i	−0.0493798	−	0.203546i
$957$	−1.62103	−	2.27642i	−0.0524005	−	0.0735861i
$958$	45.1913	+	29.0427i	1.46006	+	0.938327i
$959$	−7.92813	−	11.7440i	−0.256013	−	0.379235i
$960$	−4.63422	+	32.2317i	−0.149569	+	1.04027i
$961$	−8.44929	−	0.806809i	−0.272558	−	0.0260261i
$962$	−0.470888	+	0.370310i	−0.0151820	+	0.0119393i
$963$	−16.9949	−	8.76148i	−0.547653	−	0.282335i
$964$	−3.70916	−	10.7169i	−0.119464	−	0.345169i
$965$	−18.5738			−0.597912
$966$	27.7605	+	7.37063i	0.893179	+	0.237146i
$967$	−34.5580			−1.11131			−0.555654	−	0.831413i	$-0.687532\pi$
$967$	−34.5580			−1.11131			−0.555654	+	0.831413i	$0.687532\pi$
$968$	−18.5547	−	53.6103i	−0.596371	−	1.72310i
$969$	10.8364	+	5.58653i	0.348114	+	0.179465i
$970$	75.2898	−	59.2086i	2.41741	−	1.90107i
$971$	33.6238	+	3.21068i	1.07904	+	0.103036i	0.619404	−	0.785072i	$-0.287374\pi$
$971$	33.6238	+	3.21068i	1.07904	+	0.103036i	0.459635	+	0.888108i	$0.347980\pi$
$972$	−0.444598	+	3.09225i	−0.0142605	+	0.0991838i
$973$	14.1902	−	0.997845i	0.454918	−	0.0319894i
$974$	31.5221	+	20.2580i	1.01003	+	0.649110i
$975$	−0.0290361	−	0.0407755i	−0.000929899	−	0.00130586i
$976$	0.101388	+	0.417926i	0.00324534	+	0.0133775i
$977$	5.69002	−	16.4402i	0.182040	−	0.525970i	−0.816650	−	0.577133i	$-0.804172\pi$
$977$	5.69002	−	16.4402i	0.182040	−	0.525970i	0.998690	+	0.0511627i	$0.0162927\pi$
$978$	54.2484	−	10.4555i	1.73467	−	0.334331i
$979$	−89.1088	−	26.1647i	−2.84793	−	0.836228i
$980$	−41.3397	+	35.6482i	−1.32055	+	1.13874i
$981$	12.0268	+	7.72914i	0.383986	+	0.246773i
$982$	3.06021	−	12.6144i	0.0976554	−	0.402541i
$983$	17.2809	−	6.91823i	0.551175	−	0.220657i	−0.0793218	−	0.996849i	$-0.525275\pi$
$983$	17.2809	−	6.91823i	0.551175	−	0.220657i	0.630497	+	0.776192i	$0.282851\pi$
$984$	−11.0075	+	15.4578i	−0.350905	+	0.492777i
$985$	−46.6127	−	18.6609i	−1.48520	−	0.594586i
$986$	5.41477	−	3.47986i	0.172441	−	0.110821i
$987$	−4.30707	+	3.21620i	−0.137095	+	0.102373i
$988$	−0.263814			−0.00839305
$989$	13.1155	+	32.4339i	0.417050	+	1.03134i
$990$	16.3023	+	28.2364i	0.518120	+	0.897410i
$991$	−4.30558	−	0.829832i	−0.136771	−	0.0263605i	0.120406	−	0.992725i	$-0.461580\pi$
$991$	−4.30558	−	0.829832i	−0.136771	−	0.0263605i	−0.257177	+	0.966364i	$0.582792\pi$
$992$	1.85216	+	38.8816i	0.0588062	+	1.23449i
$993$	0.596068	+	4.14574i	0.0189156	+	0.131561i
$994$	−62.4468	−	20.0444i	−1.98069	−	0.635771i
$995$	0.164890	−	1.14683i	0.00522736	−	0.0363571i
$996$	−1.37852	+	5.68234i	−0.0436801	+	0.180052i
$997$	−1.67422	+	35.1462i	−0.0530231	+	1.11309i	0.802941	+	0.596058i	$0.203267\pi$
$997$	−1.67422	+	35.1462i	−0.0530231	+	1.11309i	−0.855964	+	0.517035i	$0.827036\pi$
$998$	37.0602	−	3.53882i	1.17312	−	0.112019i
$999$	−4.70974	+	4.49073i	−0.149010	+	0.142080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.y.b.16.2	✓	320
7.4	even	3	inner	483.2.y.b.361.15	yes	320
23.13	even	11	inner	483.2.y.b.289.15	yes	320
161.151	even	33	inner	483.2.y.b.151.2	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.y.b.16.2	✓	320	1.1	even	1	trivial
483.2.y.b.151.2	yes	320	161.151	even	33	inner
483.2.y.b.289.15	yes	320	23.13	even	11	inner
483.2.y.b.361.15	yes	320	7.4	even	3	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.740363 - 2.13914i) q^{2} +(-0.888835 - 0.458227i) q^{3} +(-2.45566 + 1.93116i) q^{4} +(2.48488 + 0.237277i) q^{5} +(-0.322149 + 2.24059i) q^{6} +(-2.63923 + 0.185589i) q^{7} +(2.14051 + 1.37562i) q^{8} +(0.580057 + 0.814576i) q^{9} +O(q^{10})\)	\(q+(-0.740363 - 2.13914i) q^{2} +(-0.888835 - 0.458227i) q^{3} +(-2.45566 + 1.93116i) q^{4} +(2.48488 + 0.237277i) q^{5} +(-0.322149 + 2.24059i) q^{6} +(-2.63923 + 0.185589i) q^{7} +(2.14051 + 1.37562i) q^{8} +(0.580057 + 0.814576i) q^{9} +(-1.33214 - 5.49116i) q^{10} +(-1.88727 + 5.45291i) q^{11} +(3.06759 - 0.591229i) q^{12} +(0.0390196 + 0.0114572i) q^{13} +(2.35099 + 5.50828i) q^{14} +(-2.09992 - 1.34954i) q^{15} +(-0.115153 + 0.474667i) q^{16} +(-5.45057 + 2.18208i) q^{17} +(1.31304 - 1.84390i) q^{18} +(1.92779 + 0.771772i) q^{19} +(-6.56024 + 4.21601i) q^{20} +(2.43089 + 1.04441i) q^{21} +13.0618 q^{22} +(-0.891245 + 4.71229i) q^{23} +(-1.27221 - 2.20354i) q^{24} +(1.20867 + 0.232952i) q^{25} +(-0.00438015 - 0.0919507i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(6.12267 - 5.55252i) q^{28} +(0.0689247 - 0.479382i) q^{29} +(-1.33214 + 5.49116i) q^{30} +(-0.299001 + 6.27681i) q^{31} +(6.16644 - 0.588824i) q^{32} +(4.17614 - 3.98194i) q^{33} +(8.70317 + 10.0440i) q^{34} +(-6.60221 - 0.165064i) q^{35} +(-2.99750 - 0.880145i) q^{36} +(-3.77475 - 5.30090i) q^{37} +(0.223660 - 4.69520i) q^{38} +(-0.0294320 - 0.0280634i) q^{39} +(4.99250 + 3.92614i) q^{40} +(-3.09819 - 6.78410i) q^{41} +(0.434397 - 5.97324i) q^{42} +(6.13690 - 3.94394i) q^{43} +(-5.89591 - 17.0351i) q^{44} +(1.24809 + 2.16175i) q^{45} +(10.7401 - 1.58231i) q^{46} +(-1.01585 + 1.75951i) q^{47} +(0.319857 - 0.369134i) q^{48} +(6.93111 - 0.979624i) q^{49} +(-0.396537 - 2.75797i) q^{50} +(5.84455 + 0.558087i) q^{51} +(-0.117945 + 0.0472179i) q^{52} +(-1.16711 - 1.11284i) q^{53} +(-2.01200 + 1.03726i) q^{54} +(-5.98348 + 13.1020i) q^{55} +(-5.90460 - 3.23333i) q^{56} +(-1.35984 - 1.56934i) q^{57} +(-1.07649 + 0.207477i) q^{58} +(1.04007 + 4.28724i) q^{59} +(7.76287 - 0.741264i) q^{60} +(0.782586 - 0.403451i) q^{61} +(13.6483 - 4.00751i) q^{62} +(-1.68208 - 2.04220i) q^{63} +(-5.41917 - 11.8663i) q^{64} +(0.0942403 + 0.0377281i) q^{65} +(-11.6098 - 5.98525i) q^{66} +(-11.0901 - 2.13743i) q^{67} +(9.17084 - 15.8844i) q^{68} +(2.95147 - 3.78006i) q^{69} +(4.53493 + 14.2452i) q^{70} +(-7.17129 + 8.27611i) q^{71} +(0.121069 + 2.54154i) q^{72} +(7.04675 - 5.54163i) q^{73} +(-8.54467 + 11.9993i) q^{74} +(-0.967562 - 0.760899i) q^{75} +(-6.22442 + 1.82766i) q^{76} +(3.96895 - 14.7418i) q^{77} +(-0.0382410 + 0.0837361i) q^{78} +(0.612500 - 0.584018i) q^{79} +(-0.398768 + 1.15216i) q^{80} +(-0.327068 + 0.945001i) q^{81} +(-12.2183 + 11.6501i) q^{82} +(-0.777518 + 1.70253i) q^{83} +(-7.98636 + 2.12970i) q^{84} +(-14.0618 + 4.12891i) q^{85} +(-12.9802 - 10.2077i) q^{86} +(-0.280928 + 0.394508i) q^{87} +(-11.5408 + 9.07582i) q^{88} +(0.765817 + 16.0765i) q^{89} +(3.70025 - 4.27032i) q^{90} +(-0.105108 - 0.0229966i) q^{91} +(-6.91157 - 13.2929i) q^{92} +(3.14196 - 5.44204i) q^{93} +(4.51592 + 0.870373i) q^{94} +(4.60720 + 2.37518i) q^{95} +(-5.75077 - 2.30226i) q^{96} +(7.04181 + 15.4194i) q^{97} +(-7.22709 - 14.1013i) q^{98} +(-5.53653 + 1.62567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) 320 * q + 2 * q^2 + 16 * q^3 + 18 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9	\( 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 2 q^{11} + 18 q^{12} + 18 q^{14} - 18 q^{15} - 8 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{19} - 162 q^{20} - 4 q^{21} + 144 q^{22} - 26 q^{23} + 6 q^{24} - 8 q^{25} - 14 q^{26} - 32 q^{27} + 86 q^{28} - 74 q^{29} - 56 q^{31} - 28 q^{32} + 13 q^{33} + 40 q^{34} - 32 q^{35} - 14 q^{36} + 2 q^{37} - 39 q^{38} - 52 q^{40} + 60 q^{41} - 61 q^{42} + 16 q^{43} - 75 q^{44} - 2 q^{45} - 4 q^{46} - 40 q^{47} - 28 q^{48} - 100 q^{49} + 146 q^{50} - 18 q^{51} - 18 q^{52} + 34 q^{53} + 2 q^{54} + 36 q^{55} - 102 q^{56} + 28 q^{57} - 17 q^{58} - 102 q^{59} - 18 q^{60} - 18 q^{61} - 88 q^{62} + 2 q^{63} - 252 q^{64} - 78 q^{65} + 16 q^{66} + 12 q^{67} + 34 q^{68} + 8 q^{69} + 264 q^{70} + 160 q^{71} + 6 q^{72} - 8 q^{73} + 70 q^{74} + 14 q^{75} - 40 q^{76} - 90 q^{77} - 16 q^{78} + 26 q^{79} - 103 q^{80} + 16 q^{81} - 30 q^{82} - 80 q^{83} - 52 q^{84} - 128 q^{85} + 90 q^{86} + 4 q^{87} - 293 q^{88} - 36 q^{89} + 16 q^{91} - 174 q^{92} + 32 q^{93} + 57 q^{94} - 85 q^{95} - 50 q^{96} - 8 q^{97} - 193 q^{98} - 26 q^{99}+O(q^{100}) \) 320 * q + 2 * q^2 + 16 * q^3 + 18 * q^4 - 2 * q^5 + 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9 + 2 * q^11 + 18 * q^12 + 18 * q^14 - 18 * q^15 - 8 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^19 - 162 * q^20 - 4 * q^21 + 144 * q^22 - 26 * q^23 + 6 * q^24 - 8 * q^25 - 14 * q^26 - 32 * q^27 + 86 * q^28 - 74 * q^29 - 56 * q^31 - 28 * q^32 + 13 * q^33 + 40 * q^34 - 32 * q^35 - 14 * q^36 + 2 * q^37 - 39 * q^38 - 52 * q^40 + 60 * q^41 - 61 * q^42 + 16 * q^43 - 75 * q^44 - 2 * q^45 - 4 * q^46 - 40 * q^47 - 28 * q^48 - 100 * q^49 + 146 * q^50 - 18 * q^51 - 18 * q^52 + 34 * q^53 + 2 * q^54 + 36 * q^55 - 102 * q^56 + 28 * q^57 - 17 * q^58 - 102 * q^59 - 18 * q^60 - 18 * q^61 - 88 * q^62 + 2 * q^63 - 252 * q^64 - 78 * q^65 + 16 * q^66 + 12 * q^67 + 34 * q^68 + 8 * q^69 + 264 * q^70 + 160 * q^71 + 6 * q^72 - 8 * q^73 + 70 * q^74 + 14 * q^75 - 40 * q^76 - 90 * q^77 - 16 * q^78 + 26 * q^79 - 103 * q^80 + 16 * q^81 - 30 * q^82 - 80 * q^83 - 52 * q^84 - 128 * q^85 + 90 * q^86 + 4 * q^87 - 293 * q^88 - 36 * q^89 + 16 * q^91 - 174 * q^92 + 32 * q^93 + 57 * q^94 - 85 * q^95 - 50 * q^96 - 8 * q^97 - 193 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

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Database

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