LMFDB - Embedded newform 76.2.d.a.75.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(75,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("76.75");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.d (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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.14453810176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 6x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 6x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.1
Root			$-1.06789 - 0.927153i$ of defining polynomial
Character	$\chi$	$=$	76.75
Dual form			76.2.d.a.75.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06789 - 0.927153i) q^{2} +1.19935 q^{3} +(0.280776 + 1.98019i) q^{4} +1.56155 q^{5} +(-1.28078 - 1.11198i) q^{6} -0.868210i q^{7} +(1.53610 - 2.37495i) q^{8} -1.56155 q^{9} +O(q^{10})$	\(q+(-1.06789 - 0.927153i) q^{2} +1.19935 q^{3} +(0.280776 + 1.98019i) q^{4} +1.56155 q^{5} +(-1.28078 - 1.11198i) q^{6} -0.868210i q^{7} +(1.53610 - 2.37495i) q^{8} -1.56155 q^{9} +(-1.66757 - 1.44780i) q^{10} -3.09218i q^{11} +(0.336750 + 2.37495i) q^{12} +4.74990i q^{13} +(-0.804963 + 0.927153i) q^{14} +1.87285 q^{15} +(-3.84233 + 1.11198i) q^{16} -1.00000 q^{17} +(1.66757 + 1.44780i) q^{18} +(-3.07221 + 3.09218i) q^{19} +(0.438447 + 3.09218i) q^{20} -1.04129i q^{21} +(-2.86692 + 3.30210i) q^{22} +3.96039i q^{23} +(1.84233 - 2.84840i) q^{24} -2.56155 q^{25} +(4.40388 - 5.07237i) q^{26} -5.47091 q^{27} +(1.71922 - 0.243773i) q^{28} -8.45851i q^{29} +(-2.00000 - 1.73642i) q^{30} +4.27156 q^{31} +(5.13416 + 2.37495i) q^{32} -3.70861i q^{33} +(1.06789 + 0.927153i) q^{34} -1.35576i q^{35} +(-0.438447 - 3.09218i) q^{36} +3.70861i q^{37} +(6.14770 - 0.453700i) q^{38} +5.69681i q^{39} +(2.39871 - 3.70861i) q^{40} -3.70861i q^{41} +(-0.965435 + 1.11198i) q^{42} -11.0129i q^{43} +(6.12311 - 0.868210i) q^{44} -2.43845 q^{45} +(3.67188 - 4.22926i) q^{46} +9.27653i q^{47} +(-4.60831 + 1.33366i) q^{48} +6.24621 q^{49} +(2.73546 + 2.37495i) q^{50} -1.19935 q^{51} +(-9.40572 + 1.33366i) q^{52} +1.04129i q^{53} +(5.84233 + 5.07237i) q^{54} -4.82860i q^{55} +(-2.06196 - 1.33366i) q^{56} +(-3.68466 + 3.70861i) q^{57} +(-7.84233 + 9.03276i) q^{58} -11.6153 q^{59} +(0.525853 + 3.70861i) q^{60} -0.684658 q^{61} +(-4.56155 - 3.96039i) q^{62} +1.35576i q^{63} +(-3.28078 - 7.29634i) q^{64} +7.41722i q^{65} +(-3.43845 + 3.96039i) q^{66} +9.74247 q^{67} +(-0.280776 - 1.98019i) q^{68} +4.74990i q^{69} +(-1.25699 + 1.44780i) q^{70} +10.9418 q^{71} +(-2.39871 + 3.70861i) q^{72} +8.12311 q^{73} +(3.43845 - 3.96039i) q^{74} -3.07221 q^{75} +(-6.98571 - 5.21535i) q^{76} -2.68466 q^{77} +(5.28181 - 6.08356i) q^{78} +8.01726 q^{79} +(-6.00000 + 1.73642i) q^{80} -1.87689 q^{81} +(-3.43845 + 3.96039i) q^{82} -9.65719i q^{83} +(2.06196 - 0.292370i) q^{84} -1.56155 q^{85} +(-10.2107 + 11.7606i) q^{86} -10.1447i q^{87} +(-7.34376 - 4.74990i) q^{88} -5.79119i q^{89} +(2.60399 + 2.26081i) q^{90} +4.12391 q^{91} +(-7.84233 + 1.11198i) q^{92} +5.12311 q^{93} +(8.60076 - 9.90631i) q^{94} +(-4.79741 + 4.82860i) q^{95} +(6.15767 + 2.84840i) q^{96} +16.9170i q^{97} +(-6.67026 - 5.79119i) q^{98} +4.82860i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q - 6 * q^4 - 4 * q^5 - 2 * q^6 + 4 * q^9	$ 8 q - 6 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{9} - 6 q^{16} - 8 q^{17} + 20 q^{20} - 10 q^{24} - 4 q^{25} - 6 q^{26} + 22 q^{28} - 16 q^{30} - 20 q^{36} + 18 q^{38} + 50 q^{42} + 16 q^{44} - 36 q^{45} - 16 q^{49} + 22 q^{54} + 20 q^{57} - 38 q^{58} + 44 q^{61} - 20 q^{62} - 18 q^{64} - 44 q^{66} + 6 q^{68} + 32 q^{73} + 44 q^{74} - 16 q^{76} + 28 q^{77} - 48 q^{80} - 48 q^{81} - 44 q^{82} + 4 q^{85} - 38 q^{92} + 8 q^{93} + 74 q^{96}+O(q^{100}) $ 8 * q - 6 * q^4 - 4 * q^5 - 2 * q^6 + 4 * q^9 - 6 * q^16 - 8 * q^17 + 20 * q^20 - 10 * q^24 - 4 * q^25 - 6 * q^26 + 22 * q^28 - 16 * q^30 - 20 * q^36 + 18 * q^38 + 50 * q^42 + 16 * q^44 - 36 * q^45 - 16 * q^49 + 22 * q^54 + 20 * q^57 - 38 * q^58 + 44 * q^61 - 20 * q^62 - 18 * q^64 - 44 * q^66 + 6 * q^68 + 32 * q^73 + 44 * q^74 - 16 * q^76 + 28 * q^77 - 48 * q^80 - 48 * q^81 - 44 * q^82 + 4 * q^85 - 38 * q^92 + 8 * q^93 + 74 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.06789	−	0.927153i	−0.755112	−	0.655596i
$2$	−1.06789	−	0.927153i	−0.755112	−	0.655596i
$3$	1.19935			0.692447			0.346223	−	0.938152i	$-0.387464\pi$
$3$	1.19935			0.692447			0.346223	+	0.938152i	$0.387464\pi$
$4$	0.280776	+	1.98019i	0.140388	+	0.990097i
$5$	1.56155			0.698348			0.349174	−	0.937058i	$-0.386462\pi$
$5$	1.56155			0.698348			0.349174	+	0.937058i	$0.386462\pi$
$6$	−1.28078	−	1.11198i	−0.522875	−	0.453965i
$7$		−	0.868210i		−	0.328153i	−0.986448	−	0.164076i	$-0.947536\pi$
$7$		−	0.868210i		−	0.328153i	0.986448	−	0.164076i	$-0.0524643\pi$
$8$	1.53610	−	2.37495i	0.543094	−	0.839672i
$9$	−1.56155			−0.520518
$10$	−1.66757	−	1.44780i	−0.527331	−	0.457834i
$11$		−	3.09218i		−	0.932326i	−0.884699	−	0.466163i	$-0.845636\pi$
$11$		−	3.09218i		−	0.932326i	0.884699	−	0.466163i	$-0.154364\pi$
$12$	0.336750	+	2.37495i	0.0972113	+	0.685589i
$13$			4.74990i			1.31739i	0.752412	+	0.658693i	$0.228890\pi$
$13$			4.74990i			1.31739i	−0.752412	+	0.658693i	$0.771110\pi$
$14$	−0.804963	+	0.927153i	−0.215135	+	0.247792i
$15$	1.87285			0.483569
$16$	−3.84233	+	1.11198i	−0.960582	+	0.277996i
$17$	−1.00000			−0.242536			−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000			−0.242536			−0.121268	+	0.992620i	$0.538696\pi$
$18$	1.66757	+	1.44780i	0.393049	+	0.341249i
$19$	−3.07221	+	3.09218i	−0.704812	+	0.709394i
$19$	−3.07221	+	3.09218i	−0.704812	+	0.709394i
$20$	0.438447	+	3.09218i	0.0980398	+	0.691432i
$21$		−	1.04129i		−	0.227228i
$22$	−2.86692	+	3.30210i	−0.611229	+	0.704011i
$23$			3.96039i			0.825798i	0.910777	+	0.412899i	$0.135484\pi$
$23$			3.96039i			0.825798i	−0.910777	+	0.412899i	$0.864516\pi$
$24$	1.84233	−	2.84840i	0.376064	−	0.581428i
$25$	−2.56155			−0.512311
$26$	4.40388	−	5.07237i	0.863672	−	0.994773i
$27$	−5.47091			−1.05288
$28$	1.71922	−	0.243773i	0.324903	−	0.0460687i
$29$		−	8.45851i		−	1.57071i	−0.619048	−	0.785353i	$-0.712481\pi$
$29$		−	8.45851i		−	1.57071i	0.619048	−	0.785353i	$-0.287519\pi$
$30$	−2.00000	−	1.73642i	−0.365148	−	0.317025i
$31$	4.27156			0.767195			0.383597	−	0.923500i	$-0.374685\pi$
$31$	4.27156			0.767195			0.383597	+	0.923500i	$0.374685\pi$
$32$	5.13416	+	2.37495i	0.907600	+	0.419836i
$33$		−	3.70861i		−	0.645586i
$34$	1.06789	+	0.927153i	0.183142	+	0.159005i
$35$		−	1.35576i		−	0.229165i
$36$	−0.438447	−	3.09218i	−0.0730745	−	0.515363i
$37$			3.70861i			0.609692i	0.952402	+	0.304846i	$0.0986050\pi$
$37$			3.70861i			0.609692i	−0.952402	+	0.304846i	$0.901395\pi$
$38$	6.14770	−	0.453700i	0.997288	−	0.0735998i
$39$			5.69681i			0.912219i
$40$	2.39871	−	3.70861i	0.379269	−	0.586383i
$41$		−	3.70861i		−	0.579188i	−0.957150	−	0.289594i	$-0.906480\pi$
$41$		−	3.70861i		−	0.579188i	0.957150	−	0.289594i	$-0.0935202\pi$
$42$	−0.965435	+	1.11198i	−0.148970	+	0.171583i
$43$		−	11.0129i		−	1.67946i	−0.543005	−	0.839729i	$-0.682714\pi$
$43$		−	11.0129i		−	1.67946i	0.543005	−	0.839729i	$-0.317286\pi$
$44$	6.12311	−	0.868210i	0.923093	−	0.130888i
$45$	−2.43845			−0.363502
$46$	3.67188	−	4.22926i	0.541389	−	0.623570i
$47$			9.27653i			1.35312i	0.736387	+	0.676560i	$0.236530\pi$
$47$			9.27653i			1.35312i	−0.736387	+	0.676560i	$0.763470\pi$
$48$	−4.60831	+	1.33366i	−0.665152	+	0.192497i
$49$	6.24621			0.892316
$50$	2.73546	+	2.37495i	0.386852	+	0.335869i
$51$	−1.19935			−0.167943
$52$	−9.40572	+	1.33366i	−1.30434	+	0.184945i
$53$			1.04129i			0.143032i	0.997439	+	0.0715161i	$0.0227837\pi$
$53$			1.04129i			0.143032i	−0.997439	+	0.0715161i	$0.977216\pi$
$54$	5.84233	+	5.07237i	0.795040	+	0.690262i
$55$		−	4.82860i		−	0.651088i
$56$	−2.06196	−	1.33366i	−0.275540	−	0.178218i
$57$	−3.68466	+	3.70861i	−0.488045	+	0.491217i
$58$	−7.84233	+	9.03276i	−1.02975	+	1.18606i
$59$	−11.6153			−1.51219			−0.756093	−	0.654464i	$-0.772894\pi$
$59$	−11.6153			−1.51219			−0.756093	+	0.654464i	$0.772894\pi$
$60$	0.525853	+	3.70861i	0.0678873	+	0.478780i
$61$	−0.684658			−0.0876615			−0.0438308	−	0.999039i	$-0.513956\pi$
$61$	−0.684658			−0.0876615			−0.0438308	+	0.999039i	$0.513956\pi$
$62$	−4.56155	−	3.96039i	−0.579318	−	0.502970i
$63$			1.35576i			0.170809i
$64$	−3.28078	−	7.29634i	−0.410097	−	0.912042i
$65$			7.41722i			0.919993i
$66$	−3.43845	+	3.96039i	−0.423244	+	0.487490i
$67$	9.74247			1.19023			0.595116	−	0.803640i	$-0.297106\pi$
$67$	9.74247			1.19023			0.595116	+	0.803640i	$0.297106\pi$
$68$	−0.280776	−	1.98019i	−0.0340491	−	0.240134i
$69$			4.74990i			0.571821i
$70$	−1.25699	+	1.44780i	−0.150239	+	0.173045i
$71$	10.9418			1.29856			0.649278	−	0.760551i	$-0.275071\pi$
$71$	10.9418			1.29856			0.649278	+	0.760551i	$0.275071\pi$
$72$	−2.39871	+	3.70861i	−0.282690	+	0.437064i
$73$	8.12311			0.950738			0.475369	−	0.879787i	$-0.342315\pi$
$73$	8.12311			0.950738			0.475369	+	0.879787i	$0.342315\pi$
$74$	3.43845	−	3.96039i	0.399711	−	0.460386i
$75$	−3.07221			−0.354748
$76$	−6.98571	−	5.21535i	−0.801316	−	0.598242i
$77$	−2.68466			−0.305945
$78$	5.28181	−	6.08356i	0.598047	−	0.688828i
$79$	8.01726			0.902013			0.451006	−	0.892521i	$-0.351065\pi$
$79$	8.01726			0.902013			0.451006	+	0.892521i	$0.351065\pi$
$80$	−6.00000	+	1.73642i	−0.670820	+	0.194138i
$81$	−1.87689			−0.208544
$82$	−3.43845	+	3.96039i	−0.379713	+	0.437351i
$83$		−	9.65719i		−	1.06001i	−0.847993	−	0.530007i	$-0.822189\pi$
$83$		−	9.65719i		−	1.06001i	0.847993	−	0.530007i	$-0.177811\pi$
$84$	2.06196	−	0.292370i	0.224978	−	0.0319002i
$85$	−1.56155			−0.169374
$86$	−10.2107	+	11.7606i	−1.10105	+	1.26818i
$87$		−	10.1447i		−	1.08763i
$88$	−7.34376	−	4.74990i	−0.782848	−	0.506341i
$89$		−	5.79119i		−	0.613865i	−0.951731	−	0.306932i	$-0.900697\pi$
$89$		−	5.79119i		−	0.613865i	0.951731	−	0.306932i	$-0.0993026\pi$
$90$	2.60399	+	2.26081i	0.274485	+	0.238311i
$91$	4.12391			0.432303
$92$	−7.84233	+	1.11198i	−0.817619	+	0.115932i
$93$	5.12311			0.531241
$94$	8.60076	−	9.90631i	0.887100	−	1.02176i
$95$	−4.79741	+	4.82860i	−0.492204	+	0.495404i
$96$	6.15767	+	2.84840i	0.628465	+	0.290714i
$97$			16.9170i			1.71766i	0.512258	+	0.858832i	$0.328809\pi$
$97$			16.9170i			1.71766i	−0.512258	+	0.858832i	$0.671191\pi$
$98$	−6.67026	−	5.79119i	−0.673798	−	0.584999i
$99$			4.82860i			0.485292i
$100$	−0.719224	−	5.07237i	−0.0719224	−	0.507237i
$101$	8.24621			0.820529			0.410264	−	0.911967i	$-0.365436\pi$
$101$	8.24621			0.820529			0.410264	+	0.911967i	$0.365436\pi$
$102$	1.28078	+	1.11198i	0.126816	+	0.110103i
$103$	−3.74571			−0.369075			−0.184538	−	0.982825i	$-0.559079\pi$
$103$	−3.74571			−0.369075			−0.184538	+	0.982825i	$0.559079\pi$
$104$	11.2808	+	7.29634i	1.10617	+	0.715465i
$105$		−	1.62603i		−	0.158684i
$106$	0.965435	−	1.11198i	0.0937713	−	0.108005i
$107$	−7.86962			−0.760785			−0.380392	−	0.924825i	$-0.624211\pi$
$107$	−7.86962			−0.760785			−0.380392	+	0.924825i	$0.624211\pi$
$108$	−1.53610	−	10.8335i	−0.147812	−	1.04245i
$109$		−	15.8757i		−	1.52062i	−0.649561	−	0.760310i	$-0.725047\pi$
$109$		−	15.8757i		−	1.52062i	0.649561	−	0.760310i	$-0.274953\pi$
$110$	−4.47685	+	5.15641i	−0.426850	+	0.491644i
$111$			4.44793i			0.422179i
$112$	0.965435	+	3.33595i	0.0912250	+	0.315218i
$113$			3.70861i			0.348877i	0.984668	+	0.174438i	$0.0558110\pi$
$113$			3.70861i			0.348877i	−0.984668	+	0.174438i	$0.944189\pi$
$114$	7.37326	−	0.544146i	0.690569	−	0.0509639i
$115$			6.18435i			0.576694i
$116$	16.7495	−	2.37495i	1.55515	−	0.220509i
$117$		−	7.41722i		−	0.685722i
$118$	12.4039	+	10.7692i	1.14187	+	0.991383i
$119$			0.868210i			0.0795887i
$120$	2.87689	−	4.44793i	0.262623	−	0.406039i
$121$	1.43845			0.130768
$122$	0.731140	+	0.634783i	0.0661943	+	0.0574705i
$123$		−	4.44793i		−	0.401057i
$124$	1.19935	+	8.45851i	0.107705	+	0.759597i
$125$	−11.8078			−1.05612
$126$	1.25699	−	1.44780i	0.111982	−	0.128980i
$127$	−1.87285			−0.166189			−0.0830944	−	0.996542i	$-0.526480\pi$
$127$	−1.87285			−0.166189			−0.0830944	+	0.996542i	$0.526480\pi$
$128$	−3.26131	+	10.8335i	−0.288262	+	0.957552i
$129$		−	13.2084i		−	1.16294i
$130$	6.87689	−	7.92077i	0.603144	−	0.694698i
$131$			4.82860i			0.421876i	0.977499	+	0.210938i	$0.0676519\pi$
$131$			4.82860i			0.421876i	−0.977499	+	0.210938i	$0.932348\pi$
$132$	7.34376	−	1.04129i	0.639193	−	0.0906327i
$133$	2.68466	+	2.66732i	0.232789	+	0.231286i
$134$	−10.4039	−	9.03276i	−0.898759	−	0.780311i
$135$	−8.54312			−0.735274
$136$	−1.53610	+	2.37495i	−0.131720	+	0.203650i
$137$	−3.87689			−0.331225			−0.165613	−	0.986191i	$-0.552960\pi$
$137$	−3.87689			−0.331225			−0.165613	+	0.986191i	$0.552960\pi$
$138$	4.40388	−	5.07237i	0.374883	−	0.431789i
$139$			0.380664i			0.0322875i	0.999870	+	0.0161438i	$0.00513894\pi$
$139$			0.380664i			0.0322875i	−0.999870	+	0.0161438i	$0.994861\pi$
$140$	2.68466	−	0.380664i	0.226895	−	0.0321720i
$141$			11.1258i			0.936964i
$142$	−11.6847	−	10.1447i	−0.980555	−	0.851328i
$143$	14.6875			1.22823
$144$	6.00000	−	1.73642i	0.500000	−	0.144702i
$145$		−	13.2084i		−	1.09690i
$146$	−8.67458	−	7.53136i	−0.717913	−	0.623300i
$147$	7.49141			0.617881
$148$	−7.34376	+	1.04129i	−0.603654	+	0.0855935i
$149$	−17.8078			−1.45887			−0.729434	−	0.684051i	$-0.760217\pi$
$149$	−17.8078			−1.45887			−0.729434	+	0.684051i	$0.760217\pi$
$150$	3.28078	+	2.84840i	0.267874	+	0.232571i
$151$	−24.2824			−1.97607			−0.988035	−	0.154231i	$-0.950710\pi$
$151$	−24.2824			−1.97607			−0.988035	+	0.154231i	$0.950710\pi$
$152$	2.62454	+	12.0462i	0.212878	+	0.977079i
$153$	1.56155			0.126244
$154$	2.86692	+	2.48909i	0.231023	+	0.200576i
$155$	6.67026			0.535769
$156$	−11.2808	+	1.59953i	−0.903185	+	0.128065i
$157$	6.00000			0.478852			0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000			0.478852			0.239426	+	0.970915i	$0.423041\pi$
$158$	−8.56155	−	7.43323i	−0.681121	−	0.591356i
$159$			1.24887i			0.0990422i
$160$	8.01726	+	3.70861i	0.633820	+	0.293191i
$161$	3.43845			0.270988
$162$	2.00432	+	1.74017i	0.157474	+	0.136720i
$163$			10.6323i			0.832785i	0.909185	+	0.416392i	$0.136706\pi$
$163$			10.6323i			0.832785i	−0.909185	+	0.416392i	$0.863294\pi$
$164$	7.34376	−	1.04129i	0.573452	−	0.0813111i
$165$		−	5.79119i		−	0.450844i
$166$	−8.95369	+	10.3128i	−0.694941	+	0.800430i
$167$	−0.525853			−0.0406917			−0.0203459	−	0.999793i	$-0.506477\pi$
$167$	−0.525853			−0.0406917			−0.0203459	+	0.999793i	$0.506477\pi$
$168$	−2.47301	−	1.59953i	−0.190797	−	0.123406i
$169$	−9.56155			−0.735504
$170$	1.66757	+	1.44780i	0.127896	+	0.111041i
$171$	4.79741	−	4.82860i	0.366867	−	0.369252i
$172$	21.8078	−	3.09218i	1.66283	−	0.235776i
$173$			16.9170i			1.28618i	0.765792	+	0.643089i	$0.222347\pi$
$173$			16.9170i			1.28618i	−0.765792	+	0.643089i	$0.777653\pi$
$174$	−9.40572	+	10.8335i	−0.713046	+	0.821283i
$175$			2.22397i			0.168116i
$176$	3.43845	+	11.8812i	0.259183	+	0.895576i
$177$	−13.9309			−1.04711
$178$	−5.36932	+	6.18435i	−0.402447	+	0.463537i
$179$	−9.06897			−0.677847			−0.338923	−	0.940814i	$-0.610063\pi$
$179$	−9.06897			−0.677847			−0.338923	+	0.940814i	$0.610063\pi$
$180$	−0.684658	−	4.82860i	−0.0510314	−	0.359902i
$181$			2.08258i			0.154797i	0.997000	+	0.0773985i	$0.0246614\pi$
$181$			2.08258i			0.154797i	−0.997000	+	0.0773985i	$0.975339\pi$
$182$	−4.40388	−	3.82349i	−0.326437	−	0.283416i
$183$	−0.821147			−0.0607009
$184$	9.40572	+	6.08356i	0.693399	+	0.448486i
$185$			5.79119i			0.425777i
$186$	−5.47091	−	4.74990i	−0.401147	−	0.348280i
$187$			3.09218i			0.226122i
$188$	−18.3693	+	2.60463i	−1.33972	+	0.189962i
$189$			4.74990i			0.345504i
$190$	9.59995	−	0.708476i	0.696454	−	0.0513982i
$191$		−	8.78898i		−	0.635948i	−0.948099	−	0.317974i	$-0.896997\pi$
$191$		−	8.78898i		−	0.635948i	0.948099	−	0.317974i	$-0.103003\pi$
$192$	−3.93481	−	8.75088i	−0.283970	−	0.631540i
$193$		−	3.70861i		−	0.266952i	−0.991052	−	0.133476i	$-0.957386\pi$
$193$		−	3.70861i		−	0.266952i	0.991052	−	0.133476i	$-0.0426138\pi$
$194$	15.6847	−	18.0655i	1.12609	−	1.29703i
$195$			8.89586i			0.637046i
$196$	1.75379	+	12.3687i	0.125271	+	0.883479i
$197$	10.4924			0.747554			0.373777	−	0.927519i	$-0.378063\pi$
$197$	10.4924			0.747554			0.373777	+	0.927519i	$0.378063\pi$
$198$	4.47685	−	5.15641i	0.318156	−	0.366450i
$199$		−	13.2369i		−	0.938340i	−0.883108	−	0.469170i	$-0.844553\pi$
$199$		−	13.2369i		−	0.938340i	0.883108	−	0.469170i	$-0.155447\pi$
$200$	−3.93481	+	6.08356i	−0.278233	+	0.430173i
$201$	11.6847			0.824172
$202$	−8.80604	−	7.64550i	−0.619591	−	0.537935i
$203$	−7.34376			−0.515431
$204$	−0.336750	−	2.37495i	−0.0235772	−	0.166280i
$205$		−	5.79119i		−	0.404474i
$206$	4.00000	+	3.47284i	0.278693	+	0.241964i
$207$		−	6.18435i		−	0.429842i
$208$	−5.28181	−	18.2507i	−0.366228	−	1.26546i
$209$	9.56155	+	9.49980i	0.661386	+	0.657115i
$210$	−1.50758	+	1.73642i	−0.104033	+	0.119824i
$211$	2.02050			0.139097			0.0695485	−	0.997579i	$-0.477844\pi$
$211$	2.02050			0.139097			0.0695485	+	0.997579i	$0.477844\pi$
$212$	−2.06196	+	0.292370i	−0.141616	+	0.0200800i
$213$	13.1231			0.899180
$214$	8.40388	+	7.29634i	0.574478	+	0.498767i
$215$		−	17.1973i		−	1.17285i
$216$	−8.40388	+	12.9931i	−0.571812	+	0.884071i
$217$		−	3.70861i		−	0.251757i
$218$	−14.7192	+	16.9535i	−0.996912	+	1.14824i
$219$	9.74247			0.658335
$220$	9.56155	−	1.35576i	0.644640	−	0.0914050i
$221$		−	4.74990i		−	0.319513i
$222$	4.12391	−	4.74990i	0.276779	−	0.318792i
$223$	16.2651			1.08919			0.544595	−	0.838699i	$-0.316683\pi$
$223$	16.2651			1.08919			0.544595	+	0.838699i	$0.316683\pi$
$224$	2.06196	−	4.45753i	0.137770	−	0.297831i
$225$	4.00000			0.266667
$226$	3.43845	−	3.96039i	0.228722	−	0.263441i
$227$	17.4644			1.15916			0.579578	−	0.814917i	$-0.303217\pi$
$227$	17.4644			1.15916			0.579578	+	0.814917i	$0.303217\pi$
$228$	−8.37833	−	6.25504i	−0.554868	−	0.414250i
$229$	−2.43845			−0.161137			−0.0805686	−	0.996749i	$-0.525674\pi$
$229$	−2.43845			−0.161137			−0.0805686	+	0.996749i	$0.525674\pi$
$230$	5.73384	−	6.60421i	0.378078	−	0.435468i
$231$	−3.21985			−0.211851
$232$	−20.0885	−	12.9931i	−1.31888	−	0.853042i
$233$	−9.80776			−0.642528			−0.321264	−	0.946990i	$-0.604108\pi$
$233$	−9.80776			−0.642528			−0.321264	+	0.946990i	$0.604108\pi$
$234$	−6.87689	+	7.92077i	−0.449557	+	0.517797i
$235$			14.4858i			0.944949i
$236$	−3.26131	−	23.0006i	−0.212293	−	1.49721i
$237$	9.61553			0.624596
$238$	0.804963	−	0.927153i	0.0521780	−	0.0600984i
$239$			19.4213i			1.25626i	0.778110	+	0.628129i	$0.216179\pi$
$239$			19.4213i			1.25626i	−0.778110	+	0.628129i	$0.783821\pi$
$240$	−7.19612	+	2.08258i	−0.464507	+	0.134430i
$241$			15.2910i			0.984979i	0.870318	+	0.492490i	$0.163913\pi$
$241$			15.2910i			0.984979i	−0.870318	+	0.492490i	$0.836087\pi$
$242$	−1.53610	−	1.33366i	−0.0987444	−	0.0857309i
$243$	14.1617			0.908472
$244$	−0.192236	−	1.35576i	−0.0123066	−	0.0867934i
$245$	9.75379			0.623147
$246$	−4.12391	+	4.74990i	−0.262931	+	0.302843i
$247$	−14.6875	−	14.5927i	−0.934545	−	0.928509i
$248$	6.56155	−	10.1447i	0.416659	−	0.644192i
$249$		−	11.5824i		−	0.734004i
$250$	12.6094	+	10.9476i	0.797488	+	0.692387i
$251$		−	22.4066i		−	1.41429i	−0.707069	−	0.707145i	$-0.749983\pi$
$251$		−	22.4066i		−	1.41429i	0.707069	−	0.707145i	$-0.250017\pi$
$252$	−2.68466	+	0.380664i	−0.169118	+	0.0239796i
$253$	12.2462			0.769913
$254$	2.00000	+	1.73642i	0.125491	+	0.108953i
$255$	−1.87285			−0.117283
$256$	13.5270	−	8.54521i	0.845437	−	0.534076i
$257$		−	18.9996i		−	1.18516i	−0.805511	−	0.592581i	$-0.798109\pi$
$257$		−	18.9996i		−	1.18516i	0.805511	−	0.592581i	$-0.201891\pi$
$258$	−12.2462	+	14.1051i	−0.762416	+	0.878147i
$259$	3.21985			0.200072
$260$	−14.6875	+	2.08258i	−0.910882	+	0.129156i
$261$			13.2084i			0.817580i
$262$	4.47685	−	5.15641i	0.276580	−	0.318564i
$263$		−	6.56502i		−	0.404816i	−0.979301	−	0.202408i	$-0.935123\pi$
$263$		−	6.56502i		−	0.404816i	0.979301	−	0.202408i	$-0.0648768\pi$
$264$	−8.80776	−	5.69681i	−0.542080	−	0.350614i
$265$			1.62603i			0.0998862i
$266$	−0.393906	−	5.33749i	−0.0241520	−	0.327263i
$267$		−	6.94568i		−	0.425069i
$268$	2.73546	+	19.2920i	0.167095	+	1.17844i
$269$		−	3.70861i		−	0.226118i	−0.993588	−	0.113059i	$-0.963935\pi$
$269$		−	3.70861i		−	0.226118i	0.993588	−	0.113059i	$-0.0360649\pi$
$270$	9.12311	+	7.92077i	0.555215	+	0.482043i
$271$			15.3540i			0.932689i	0.884603	+	0.466345i	$0.154429\pi$
$271$			15.3540i			0.932689i	−0.884603	+	0.466345i	$0.845571\pi$
$272$	3.84233	−	1.11198i	0.232975	−	0.0674239i
$273$	4.94602			0.299347
$274$	4.14010	+	3.59447i	0.250112	+	0.217150i
$275$			7.92077i			0.477641i
$276$	−9.40572	+	1.33366i	−0.566158	+	0.0802769i
$277$	−24.0540			−1.44526			−0.722632	−	0.691233i	$-0.757068\pi$
$277$	−24.0540			−1.44526			−0.722632	+	0.691233i	$0.757068\pi$
$278$	0.352934	−	0.406507i	0.0211676	−	0.0243807i
$279$	−6.67026			−0.399338
$280$	−3.21985	−	2.08258i	−0.192423	−	0.124458i
$281$			11.5824i			0.690947i	0.938429	+	0.345473i	$0.112282\pi$
$281$			11.5824i			0.690947i	−0.938429	+	0.345473i	$0.887718\pi$
$282$	10.3153	−	11.8812i	0.614270	−	0.707513i
$283$			4.82860i			0.287030i	0.989648	+	0.143515i	$0.0458406\pi$
$283$			4.82860i			0.287030i	−0.989648	+	0.143515i	$0.954159\pi$
$284$	3.07221	+	21.6669i	0.182302	+	1.28570i
$285$	−5.75379	+	5.79119i	−0.340825	+	0.343041i
$286$	−15.6847	−	13.6176i	−0.927453	−	0.805224i
$287$	−3.21985			−0.190062
$288$	−8.01726	−	3.70861i	−0.472422	−	0.218532i
$289$	−16.0000			−0.941176
$290$	−12.2462	+	14.1051i	−0.719122	+	0.828281i
$291$			20.2895i			1.18939i
$292$	2.28078	+	16.0853i	0.133472	+	0.941322i
$293$		−	4.74990i		−	0.277492i	−0.990328	−	0.138746i	$-0.955693\pi$
$293$		−	4.74990i		−	0.277492i	0.990328	−	0.138746i	$-0.0443072\pi$
$294$	−8.00000	−	6.94568i	−0.466569	−	0.405080i
$295$	−18.1379			−1.05603
$296$	8.80776	+	5.69681i	0.511941	+	0.331120i
$297$			16.9170i			0.981625i
$298$	19.0167	+	16.5105i	1.10161	+	0.956428i
$299$	−18.8114			−1.08789
$300$	−0.862603	−	6.08356i	−0.0498024	−	0.351235i
$301$	−9.56155			−0.551119
$302$	25.9309	+	22.5134i	1.49215	+	1.29550i
$303$	9.89012			0.568172
$304$	8.36598	−	15.2974i	0.479822	−	0.877366i
$305$	−1.06913			−0.0612182
$306$	−1.66757	−	1.44780i	−0.0953284	−	0.0827651i
$307$	8.01726			0.457569			0.228785	−	0.973477i	$-0.426525\pi$
$307$	8.01726			0.457569			0.228785	+	0.973477i	$0.426525\pi$
$308$	−0.753789	−	5.31614i	−0.0429511	−	0.302915i
$309$	−4.49242			−0.255565
$310$	−7.12311	−	6.18435i	−0.404565	−	0.351248i
$311$		−	0.868210i		−	0.0492317i	−0.999697	−	0.0246158i	$-0.992164\pi$
$311$		−	0.868210i		−	0.0492317i	0.999697	−	0.0246158i	$-0.00783626\pi$
$312$	13.5296	+	8.75088i	0.765965	+	0.495421i
$313$	−4.56155			−0.257834			−0.128917	−	0.991655i	$-0.541150\pi$
$313$	−4.56155			−0.257834			−0.128917	+	0.991655i	$0.541150\pi$
$314$	−6.40734	−	5.56292i	−0.361587	−	0.313933i
$315$			2.11708i			0.119284i
$316$	2.25106	+	15.8757i	0.126632	+	0.893080i
$317$			4.74990i			0.266781i	0.991064	+	0.133390i	$0.0425864\pi$
$317$			4.74990i			0.266781i	−0.991064	+	0.133390i	$0.957414\pi$
$318$	1.15790	−	1.33366i	0.0649316	−	0.0747879i
$319$	−26.1552			−1.46441
$320$	−5.12311	−	11.3936i	−0.286390	−	0.636922i
$321$	−9.43845			−0.526803
$322$	−3.67188	−	3.18796i	−0.204626	−	0.177658i
$323$	3.07221	−	3.09218i	0.170942	−	0.172053i
$324$	−0.526988	−	3.71661i	−0.0292771	−	0.206479i
$325$		−	12.1671i		−	0.674910i
$326$	9.85775	−	11.3541i	0.545970	−	0.628846i
$327$		−	19.0406i		−	1.05295i
$328$	−8.80776	−	5.69681i	−0.486327	−	0.314554i
$329$	8.05398			0.444030
$330$	−5.36932	+	6.18435i	−0.295571	+	0.340437i
$331$	−2.25106			−0.123729			−0.0618647	−	0.998085i	$-0.519705\pi$
$331$	−2.25106			−0.123729			−0.0618647	+	0.998085i	$0.519705\pi$
$332$	19.1231	−	2.71151i	1.04952	−	0.148814i
$333$		−	5.79119i		−	0.317355i
$334$	0.561553	+	0.487546i	0.0307268	+	0.0266773i
$335$	15.2134			0.831196
$336$	1.15790	+	4.00098i	0.0631685	+	0.218271i
$337$		−	26.4168i		−	1.43902i	−0.694484	−	0.719508i	$-0.744367\pi$
$337$		−	26.4168i		−	1.43902i	0.694484	−	0.719508i	$-0.255633\pi$
$338$	10.2107	+	8.86502i	0.555388	+	0.482193i
$339$			4.44793i			0.241579i
$340$	−0.438447	−	3.09218i	−0.0237781	−	0.167697i
$341$		−	13.2084i		−	0.715276i
$342$	−9.59995	+	0.708476i	−0.519106	+	0.0383100i
$343$		−	11.5005i		−	0.620968i
$344$	−26.1552	−	16.9170i	−1.41019	−	0.912105i
$345$			7.41722i			0.399330i
$346$	15.6847	−	18.0655i	0.843212	−	0.971208i
$347$			24.1430i			1.29606i	0.761613	+	0.648032i	$0.224408\pi$
$347$			24.1430i			1.29606i	−0.761613	+	0.648032i	$0.775592\pi$
$348$	20.0885	−	2.84840i	1.07686	−	0.152690i
$349$	−28.0540			−1.50169			−0.750847	−	0.660476i	$-0.770355\pi$
$349$	−28.0540			−1.50169			−0.750847	+	0.660476i	$0.770355\pi$
$350$	2.06196	−	2.37495i	0.110216	−	0.126946i
$351$		−	25.9863i		−	1.38705i
$352$	7.34376	−	15.8757i	0.391424	−	0.846179i
$353$	6.31534			0.336132			0.168066	−	0.985776i	$-0.446248\pi$
$353$	6.31534			0.336132			0.168066	+	0.985776i	$0.446248\pi$
$354$	14.8766	+	12.9160i	0.790684	+	0.686480i
$355$	17.0862			0.906843
$356$	11.4677	−	1.62603i	0.607786	−	0.0861794i
$357$			1.04129i			0.0551109i
$358$	9.68466	+	8.40832i	0.511850	+	0.444393i
$359$			27.3420i			1.44306i	0.692384	+	0.721529i	$0.256560\pi$
$359$			27.3420i			1.44306i	−0.692384	+	0.721529i	$0.743440\pi$
$360$	−3.74571	+	5.79119i	−0.197416	+	0.305223i
$361$	−0.123106	−	18.9996i	−0.00647924	−	0.999979i
$362$	1.93087	−	2.22397i	0.101484	−	0.116889i
$363$	1.72521			0.0905498
$364$	1.15790	+	8.16614i	0.0606903	+	0.428022i
$365$	12.6847			0.663945
$366$	0.876894	+	0.761329i	0.0458360	+	0.0397953i
$367$			14.1051i			0.736282i	0.929770	+	0.368141i	$0.120006\pi$
$367$			14.1051i			0.736282i	−0.929770	+	0.368141i	$0.879994\pi$
$368$	−4.40388	−	15.2171i	−0.229568	−	0.793247i
$369$			5.79119i			0.301477i
$370$	5.36932	−	6.18435i	0.279137	−	0.321509i
$371$	0.904059			0.0469364
$372$	1.43845	+	10.1447i	0.0745800	+	0.525980i
$373$		−	12.1671i		−	0.629990i	−0.949093	−	0.314995i	$-0.897997\pi$
$373$		−	12.1671i		−	0.629990i	0.949093	−	0.314995i	$-0.102003\pi$
$374$	2.86692	−	3.30210i	0.148245	−	0.170748i
$375$	−14.1617			−0.731306
$376$	22.0313	+	14.2497i	1.13618	+	0.734872i
$377$	40.1771			2.06922
$378$	4.40388	−	5.07237i	0.226511	−	0.260895i
$379$	−6.81791			−0.350213			−0.175106	−	0.984550i	$-0.556027\pi$
$379$	−6.81791			−0.350213			−0.175106	+	0.984550i	$0.556027\pi$
$380$	−10.9086	−	8.14404i	−0.559597	−	0.417781i
$381$	−2.24621			−0.115077
$382$	−8.14873	+	9.38566i	−0.416925	+	0.480212i
$383$	−16.2651			−0.831107			−0.415554	−	0.909569i	$-0.636412\pi$
$383$	−16.2651			−0.831107			−0.415554	+	0.909569i	$0.636412\pi$
$384$	−3.91146	+	12.9931i	−0.199606	+	0.663053i
$385$	−4.19224			−0.213656
$386$	−3.43845	+	3.96039i	−0.175012	+	0.201578i
$387$			17.1973i			0.874188i
$388$	−33.4990	+	4.74990i	−1.70065	+	0.241140i
$389$	−5.80776			−0.294465			−0.147233	−	0.989102i	$-0.547037\pi$
$389$	−5.80776			−0.294465			−0.147233	+	0.989102i	$0.547037\pi$
$390$	8.24782	−	9.49980i	0.417645	−	0.481041i
$391$		−	3.96039i		−	0.200285i
$392$	9.59482	−	14.8344i	0.484612	−	0.749252i
$393$			5.79119i			0.292127i
$394$	−11.2047	−	9.72808i	−0.564487	−	0.490093i
$395$	12.5194			0.629918
$396$	−9.56155	+	1.35576i	−0.480486	+	0.0681293i
$397$	24.9309			1.25124			0.625622	−	0.780126i	$-0.284845\pi$
$397$	24.9309			1.25124			0.625622	+	0.780126i	$0.284845\pi$
$398$	−12.2726	+	14.1356i	−0.615172	+	0.708552i
$399$	3.21985	+	3.19906i	0.161194	+	0.160153i
$400$	9.84233	−	2.84840i	0.492116	−	0.142420i
$401$		−	20.6256i		−	1.02999i	−0.857192	−	0.514997i	$-0.827793\pi$
$401$		−	20.6256i		−	1.02999i	0.857192	−	0.514997i	$-0.172207\pi$
$402$	−12.4779	−	10.8335i	−0.622342	−	0.540324i
$403$			20.2895i			1.01069i
$404$	2.31534	+	16.3291i	0.115193	+	0.812403i
$405$	−2.93087			−0.145636
$406$	7.84233	+	6.80879i	0.389208	+	0.337915i
$407$	11.4677			0.568432
$408$	−1.84233	+	2.84840i	−0.0912089	+	0.141017i
$409$			18.5431i			0.916895i	0.888722	+	0.458447i	$0.151594\pi$
$409$			18.5431i			0.916895i	−0.888722	+	0.458447i	$0.848406\pi$
$410$	−5.36932	+	6.18435i	−0.265172	+	0.305423i
$411$	−4.64976			−0.229356
$412$	−1.05171	−	7.41722i	−0.0518138	−	0.365420i
$413$			10.0845i			0.496228i
$414$	−5.73384	+	6.60421i	−0.281803	+	0.324579i
$415$		−	15.0802i		−	0.740259i
$416$	−11.2808	+	24.3868i	−0.553086	+	1.19566i
$417$			0.456551i			0.0223574i
$418$	−1.40292	−	19.0098i	−0.0686190	−	0.929798i
$419$		−	27.4489i		−	1.34097i	−0.741924	−	0.670484i	$-0.766087\pi$
$419$		−	27.4489i		−	1.34097i	0.741924	−	0.670484i	$-0.233913\pi$
$420$	3.21985	−	0.456551i	0.157113	−	0.0222774i
$421$			23.2930i			1.13523i	0.823294	+	0.567614i	$0.192134\pi$
$421$			23.2930i			1.13523i	−0.823294	+	0.567614i	$0.807866\pi$
$422$	−2.15767	−	1.87331i	−0.105034	−	0.0911914i
$423$		−	14.4858i		−	0.704323i
$424$	2.47301	+	1.59953i	0.120100	+	0.0776800i
$425$	2.56155			0.124254
$426$	−14.0140	−	12.1671i	−0.678982	−	0.589499i
$427$			0.594427i			0.0287664i
$428$	−2.20960	−	15.5834i	−0.106805	−	0.753250i
$429$	17.6155			0.850486
$430$	−15.9445	+	18.3648i	−0.768913	+	0.885630i
$431$	17.0862			0.823015			0.411507	−	0.911406i	$-0.365002\pi$
$431$	17.0862			0.823015			0.411507	+	0.911406i	$0.365002\pi$
$432$	21.0210	−	6.08356i	1.01138	−	0.292695i
$433$			28.0429i			1.34765i	0.738889	+	0.673827i	$0.235351\pi$
$433$			28.0429i			1.34765i	−0.738889	+	0.673827i	$0.764649\pi$
$434$	−3.43845	+	3.96039i	−0.165051	+	0.190105i
$435$		−	15.8415i		−	0.759544i
$436$	31.4370	−	4.45753i	1.50556	−	0.213477i
$437$	−12.2462	−	12.1671i	−0.585816	−	0.582032i
$438$	−10.4039	−	9.03276i	−0.497117	−	0.431602i
$439$	24.8082			1.18403			0.592015	−	0.805927i	$-0.298332\pi$
$439$	24.8082			1.18403			0.592015	+	0.805927i	$0.298332\pi$
$440$	−11.4677	−	7.41722i	−0.546700	−	0.353602i
$441$	−9.75379			−0.464466
$442$	−4.40388	+	5.07237i	−0.209471	+	0.241268i
$443$		−	34.7753i		−	1.65222i	−0.563507	−	0.826111i	$-0.690548\pi$
$443$		−	34.7753i		−	1.65222i	0.563507	−	0.826111i	$-0.309452\pi$
$444$	−8.80776	+	1.24887i	−0.417998	+	0.0592690i
$445$		−	9.04325i		−	0.428691i
$446$	−17.3693	−	15.0802i	−0.822461	−	0.714069i
$447$	−21.3578			−1.01019
$448$	−6.33475	+	2.84840i	−0.299289	+	0.134574i
$449$			35.9166i			1.69501i	0.530787	+	0.847505i	$0.321896\pi$
$449$			35.9166i			1.69501i	−0.530787	+	0.847505i	$0.678104\pi$
$450$	−4.27156	−	3.70861i	−0.201363	−	0.174826i
$451$	−11.4677			−0.539992
$452$	−7.34376	+	1.04129i	−0.345422	+	0.0489782i
$453$	−29.1231			−1.36832
$454$	−18.6501	−	16.1922i	−0.875292	−	0.759938i
$455$	6.43971			0.301898
$456$	3.14775	+	14.4477i	0.147407	+	0.676575i
$457$	12.1231			0.567095			0.283547	−	0.958958i	$-0.408489\pi$
$457$	12.1231			0.567095			0.283547	+	0.958958i	$0.408489\pi$
$458$	2.60399	+	2.26081i	0.121677	+	0.105641i
$459$	5.47091			0.255360
$460$	−12.2462	+	1.73642i	−0.570983	+	0.0809610i
$461$	19.3153			0.899605			0.449803	−	0.893128i	$-0.351494\pi$
$461$	19.3153			0.899605			0.449803	+	0.893128i	$0.351494\pi$
$462$	3.43845	+	2.98529i	0.159971	+	0.138888i
$463$			21.6452i			1.00594i	0.864304	+	0.502970i	$0.167759\pi$
$463$			21.6452i			1.00594i	−0.864304	+	0.502970i	$0.832241\pi$
$464$	9.40572	+	32.5004i	0.436650	+	1.50879i
$465$	8.00000			0.370991
$466$	10.4736	+	9.09329i	0.485181	+	0.421239i
$467$		−	3.09218i		−	0.143089i	−0.997437	−	0.0715444i	$-0.977207\pi$
$467$		−	3.09218i		−	0.143089i	0.997437	−	0.0715444i	$-0.0227928\pi$
$468$	14.6875	−	2.08258i	0.678931	−	0.0962673i
$469$		−	8.45851i		−	0.390578i
$470$	13.4305	−	15.4692i	0.619504	−	0.713542i
$471$	7.19612			0.331580
$472$	−17.8423	+	27.5858i	−0.821260	+	1.26974i
$473$	−34.0540			−1.56580
$474$	−10.2683	−	8.91506i	−0.471640	−	0.409482i
$475$	7.86962	−	7.92077i	0.361083	−	0.363430i
$476$	−1.71922	+	0.243773i	−0.0788005	+	0.0111733i
$477$		−	1.62603i		−	0.0744508i
$478$	18.0065	−	20.7398i	0.823597	−	0.948615i
$479$		−	8.68210i		−	0.396695i	−0.980132	−	0.198348i	$-0.936442\pi$
$479$		−	8.68210i		−	0.396695i	0.980132	−	0.198348i	$-0.0635575\pi$
$480$	9.61553	+	4.44793i	0.438887	+	0.203019i
$481$	−17.6155			−0.803199
$482$	14.1771	−	16.3291i	0.645748	−	0.743770i
$483$	4.12391			0.187644
$484$	0.403882	+	2.84840i	0.0183583	+	0.129473i
$485$			26.4168i			1.19953i
$486$	−15.1231	−	13.1300i	−0.685998	−	0.595590i
$487$	9.59482			0.434783			0.217391	−	0.976085i	$-0.430245\pi$
$487$	9.59482			0.434783			0.217391	+	0.976085i	$0.430245\pi$
$488$	−1.05171	+	1.62603i	−0.0476085	+	0.0736069i
$489$			12.7519i			0.576659i
$490$	−10.4160	−	9.04325i	−0.470546	−	0.408532i
$491$		−	2.71151i		−	0.122369i	−0.998126	−	0.0611844i	$-0.980512\pi$
$491$		−	2.71151i		−	0.122369i	0.998126	−	0.0611844i	$-0.0194878\pi$
$492$	8.80776	−	1.24887i	0.397085	−	0.0563036i
$493$			8.45851i			0.380952i
$494$	2.15503	+	29.2009i	0.0969593	+	1.31381i
$495$			7.54011i			0.338903i
$496$	−16.4127	+	4.74990i	−0.736953	+	0.213277i
$497$		−	9.49980i		−	0.426124i
$498$	−10.7386	+	12.3687i	−0.481210	+	0.554255i
$499$		−	11.0129i		−	0.493007i	−0.969142	−	0.246504i	$-0.920718\pi$
$499$		−	11.0129i		−	0.493007i	0.969142	−	0.246504i	$-0.0792817\pi$
$500$	−3.31534	−	23.3817i	−0.148267	−	1.04566i
$501$	−0.630683			−0.0281768
$502$	−20.7743	+	23.9277i	−0.927202	+	1.06795i
$503$			35.6435i			1.58926i	0.607091	+	0.794632i	$0.292336\pi$
$503$			35.6435i			1.58926i	−0.607091	+	0.794632i	$0.707664\pi$
$504$	3.21985	+	2.08258i	0.143424	+	0.0927655i
$505$	12.8769			0.573014
$506$	−13.0776	−	11.3541i	−0.581370	−	0.504752i
$507$	−11.4677			−0.509297
$508$	−0.525853	−	3.70861i	−0.0233309	−	0.164543i
$509$		−	9.49980i		−	0.421071i	−0.977586	−	0.210536i	$-0.932479\pi$
$509$		−	9.49980i		−	0.421071i	0.977586	−	0.210536i	$-0.0675208\pi$
$510$	2.00000	+	1.73642i	0.0885615	+	0.0768900i
$511$		−	7.05256i		−	0.311987i
$512$	−22.3680	−	3.41624i	−0.988537	−	0.150978i
$513$	16.8078	−	16.9170i	0.742081	−	0.746905i
$514$	−17.6155	+	20.2895i	−0.776988	+	0.894930i
$515$	−5.84912			−0.257743
$516$	26.1552	−	3.70861i	1.15142	−	0.163262i
$517$	28.6847			1.26155
$518$	−3.43845	−	2.98529i	−0.151077	−	0.131166i
$519$			20.2895i			0.890609i
$520$	17.6155	+	11.3936i	0.772492	+	0.499643i
$521$		−	15.2910i		−	0.669910i	−0.942234	−	0.334955i	$-0.891279\pi$
$521$		−	15.2910i		−	0.669910i	0.942234	−	0.334955i	$-0.108721\pi$
$522$	12.2462	−	14.1051i	0.536002	−	0.617365i
$523$	−33.4990			−1.46481			−0.732404	−	0.680871i	$-0.761602\pi$
$523$	−33.4990			−1.46481			−0.732404	+	0.680871i	$0.761602\pi$
$524$	−9.56155	+	1.35576i	−0.417698	+	0.0592265i
$525$			2.66732i			0.116411i
$526$	−6.08677	+	7.01071i	−0.265396	+	0.305682i
$527$	−4.27156			−0.186072
$528$	4.12391	+	14.2497i	0.179470	+	0.620139i
$529$	7.31534			0.318058
$530$	1.50758	−	1.73642i	0.0654850	−	0.0754253i
$531$	18.1379			0.787120
$532$	−4.52802	+	6.06506i	−0.196315	+	0.262954i
$533$	17.6155			0.763013
$534$	−6.43971	+	7.41722i	−0.278673	+	0.320975i
$535$	−12.2888			−0.531292
$536$	14.9654	−	23.1379i	0.646408	−	0.999404i
$537$	−10.8769			−0.469373
$538$	−3.43845	+	3.96039i	−0.148242	+	0.170744i
$539$		−	19.3144i		−	0.831929i
$540$	−2.39871	−	16.9170i	−0.103224	−	0.727993i
$541$	−12.1922			−0.524185			−0.262093	−	0.965043i	$-0.584413\pi$
$541$	−12.1922			−0.524185			−0.262093	+	0.965043i	$0.584413\pi$
$542$	14.2355	−	16.3964i	0.611467	−	0.704285i
$543$			2.49775i			0.107189i
$544$	−5.13416	−	2.37495i	−0.220125	−	0.101825i
$545$		−	24.7908i		−	1.06192i
$546$	−5.28181	−	4.58572i	−0.226041	−	0.196251i
$547$	−19.4849			−0.833116			−0.416558	−	0.909109i	$-0.636764\pi$
$547$	−19.4849			−0.833116			−0.416558	+	0.909109i	$0.636764\pi$
$548$	−1.08854	−	7.67700i	−0.0465001	−	0.327945i
$549$	1.06913			0.0456294
$550$	7.34376	−	8.45851i	0.313139	−	0.360672i
$551$	26.1552	+	25.9863i	1.11425	+	1.10705i
$552$	11.2808	+	7.29634i	0.480142	+	0.310553i
$553$		−	6.96067i		−	0.295998i
$554$	25.6870	+	22.3017i	1.09134	+	0.947509i
$555$			6.94568i			0.294828i
$556$	−0.753789	+	0.106882i	−0.0319678	+	0.00453279i
$557$	−18.9309			−0.802127			−0.401063	−	0.916050i	$-0.631359\pi$
$557$	−18.9309			−0.802127			−0.401063	+	0.916050i	$0.631359\pi$
$558$	7.12311	+	6.18435i	0.301545	+	0.261805i
$559$	52.3104			2.21249
$560$	1.50758	+	5.20926i	0.0637068	+	0.220131i
$561$			3.70861i			0.156578i
$562$	10.7386	−	12.3687i	0.452982	−	0.521742i
$563$	−33.6466			−1.41804			−0.709018	−	0.705191i	$-0.750861\pi$
$563$	−33.6466			−1.41804			−0.709018	+	0.705191i	$0.750861\pi$
$564$	−22.0313	+	3.12387i	−0.927685	+	0.131539i
$565$			5.79119i			0.243637i
$566$	4.47685	−	5.15641i	0.188176	−	0.216740i
$567$			1.62954i			0.0684342i
$568$	16.8078	−	25.9863i	0.705238	−	1.09036i
$569$		−	12.7519i		−	0.534586i	−0.963615	−	0.267293i	$-0.913871\pi$
$569$		−	12.7519i		−	0.534586i	0.963615	−	0.267293i	$-0.0861291\pi$
$570$	11.5137	−	0.849712i	0.482257	−	0.0355905i
$571$			17.5780i			0.735615i	0.929902	+	0.367807i	$0.119891\pi$
$571$			17.5780i			0.735615i	−0.929902	+	0.367807i	$0.880109\pi$
$572$	4.12391	+	29.0841i	0.172429	+	1.21607i
$573$		−	10.5411i		−	0.440360i
$574$	3.43845	+	2.98529i	0.143518	+	0.124604i
$575$		−	10.1447i		−	0.423065i
$576$	5.12311	+	11.3936i	0.213463	+	0.474734i
$577$	27.0000			1.12402			0.562012	−	0.827129i	$-0.310027\pi$
$577$	27.0000			1.12402			0.562012	+	0.827129i	$0.310027\pi$
$578$	17.0862	+	14.8344i	0.710694	+	0.617031i
$579$		−	4.44793i		−	0.184850i
$580$	26.1552	−	3.70861i	1.08604	−	0.153992i
$581$	−8.38447			−0.347847
$582$	18.8114	−	21.6669i	0.779759	−	0.898123i
$583$	3.21985			0.133353
$584$	12.4779	−	19.2920i	0.516340	−	0.798307i
$585$		−	11.5824i		−	0.478873i
$586$	−4.40388	+	5.07237i	−0.181923	+	0.209538i
$587$			4.82860i			0.199297i	0.995023	+	0.0996487i	$0.0317719\pi$
$587$			4.82860i			0.199297i	−0.995023	+	0.0996487i	$0.968228\pi$
$588$	2.10341	+	14.8344i	0.0867432	+	0.611762i
$589$	−13.1231	+	13.2084i	−0.540728	+	0.544243i
$590$	19.3693	+	16.8166i	0.797422	+	0.692330i
$591$	12.5841			0.517641
$592$	−4.12391	−	14.2497i	−0.169492	−	0.585659i
$593$	−36.7386			−1.50867			−0.754337	−	0.656487i	$-0.772042\pi$
$593$	−36.7386			−1.50867			−0.754337	+	0.656487i	$0.772042\pi$
$594$	15.6847	−	18.0655i	0.643549	−	0.741237i
$595$			1.35576i			0.0555806i
$596$	−5.00000	−	35.2628i	−0.204808	−	1.44442i
$597$		−	15.8757i		−	0.649750i
$598$	20.0885	+	17.4411i	0.821482	+	0.713219i
$599$	−7.72197			−0.315511			−0.157756	−	0.987478i	$-0.550426\pi$
$599$	−7.72197			−0.315511			−0.157756	+	0.987478i	$0.550426\pi$
$600$	−4.71922	+	7.29634i	−0.192661	+	0.297872i
$601$		−	39.1687i		−	1.59772i	−0.601514	−	0.798862i	$-0.705436\pi$
$601$		−	39.1687i		−	1.59772i	0.601514	−	0.798862i	$-0.294564\pi$
$602$	10.2107	+	8.86502i	0.416156	+	0.361311i
$603$	−15.2134			−0.619537
$604$	−6.81791	−	48.0837i	−0.277417	−	1.95650i
$605$	2.24621			0.0913215
$606$	−10.5616	−	9.16965i	−0.429034	−	0.372491i
$607$	−13.6358			−0.553461			−0.276730	−	0.960948i	$-0.589251\pi$
$607$	−13.6358			−0.553461			−0.276730	+	0.960948i	$0.589251\pi$
$608$	−23.1170	+	8.57940i	−0.937517	+	0.347940i
$609$	−8.80776			−0.356909
$610$	1.14171	+	0.991247i	0.0462266	+	0.0401344i
$611$	−44.0626			−1.78258
$612$	0.438447	+	3.09218i	0.0177232	+	0.124994i
$613$	24.3002			0.981475			0.490738	−	0.871307i	$-0.336727\pi$
$613$	24.3002			0.981475			0.490738	+	0.871307i	$0.336727\pi$
$614$	−8.56155	−	7.43323i	−0.345516	−	0.299981i
$615$		−	6.94568i		−	0.280077i
$616$	−4.12391	+	6.37593i	−0.166157	+	0.256894i
$617$	−28.5464			−1.14923			−0.574617	−	0.818422i	$-0.694849\pi$
$617$	−28.5464			−1.14923			−0.574617	+	0.818422i	$0.694849\pi$
$618$	4.79741	+	4.16516i	0.192980	+	0.167547i
$619$		−	34.3946i		−	1.38244i	−0.722646	−	0.691218i	$-0.757074\pi$
$619$		−	34.3946i		−	1.38244i	0.722646	−	0.691218i	$-0.242926\pi$
$620$	1.87285	+	13.2084i	0.0752156	+	0.530463i
$621$		−	21.6669i		−	0.869464i
$622$	−0.804963	+	0.927153i	−0.0322761	+	0.0371754i
$623$	−5.02797			−0.201441
$624$	−6.33475	−	21.8890i	−0.253593	−	0.876262i
$625$	−5.63068			−0.225227
$626$	4.87123	+	4.22926i	0.194694	+	0.169035i
$627$	11.4677	+	11.3936i	0.457975	+	0.455017i
$628$	1.68466	+	11.8812i	0.0672252	+	0.474110i
$629$		−	3.70861i		−	0.147872i
$630$	1.96286	−	2.26081i	0.0782022	−	0.0900729i
$631$			12.7494i			0.507544i	0.967264	+	0.253772i	$0.0816713\pi$
$631$			12.7494i			0.507544i	−0.967264	+	0.253772i	$0.918329\pi$
$632$	12.3153	−	19.0406i	0.489878	−	0.757394i
$633$	2.42329			0.0963172
$634$	4.40388	−	5.07237i	0.174900	−	0.201450i
$635$	−2.92456			−0.116058
$636$	−2.47301	+	0.350654i	−0.0980613	+	0.0139044i
$637$			29.6689i			1.17552i
$638$	27.9309	+	24.2499i	1.10579	+	0.960061i
$639$	−17.0862			−0.675921
$640$	−5.09271	+	16.9170i	−0.201307	+	0.668704i
$641$			48.6685i			1.92229i	0.276045	+	0.961145i	$0.410976\pi$
$641$			48.6685i			1.92229i	−0.276045	+	0.961145i	$0.589024\pi$
$642$	10.0792	+	8.75088i	0.397795	+	0.345370i
$643$		−	6.56502i		−	0.258899i	−0.991586	−	0.129449i	$-0.958679\pi$
$643$		−	6.56502i		−	0.258899i	0.991586	−	0.129449i	$-0.0413210\pi$
$644$	0.965435	+	6.80879i	0.0380435	+	0.268304i
$645$		−	20.6256i		−	0.812133i
$646$	−6.14770	+	0.453700i	−0.241878	+	0.0178506i
$647$			36.2379i			1.42466i	0.701845	+	0.712329i	$0.252360\pi$
$647$			36.2379i			1.42466i	−0.701845	+	0.712329i	$0.747640\pi$
$648$	−2.88310	+	4.45753i	−0.113259	+	0.175108i
$649$			35.9166i			1.40985i
$650$	−11.2808	+	12.9931i	−0.442468	+	0.509633i
$651$		−	4.44793i		−	0.174328i
$652$	−21.0540	+	2.98529i	−0.824537	+	0.116913i
$653$	−45.8078			−1.79260			−0.896298	−	0.443452i	$-0.853754\pi$
$653$	−45.8078			−1.79260			−0.896298	+	0.443452i	$0.853754\pi$
$654$	−17.6535	+	20.3333i	−0.690308	+	0.795093i
$655$			7.54011i			0.294616i
$656$	4.12391	+	14.2497i	0.161012	+	0.556357i
$657$	−12.6847			−0.494876
$658$	−8.60076	−	7.46726i	−0.335292	−	0.291104i
$659$	−3.36750			−0.131179			−0.0655896	−	0.997847i	$-0.520893\pi$
$659$	−3.36750			−0.131179			−0.0655896	+	0.997847i	$0.520893\pi$
$660$	11.4677	−	1.62603i	0.446379	−	0.0632931i
$661$			17.5018i			0.680740i	0.940292	+	0.340370i	$0.110552\pi$
$661$			17.5018i			0.680740i	−0.940292	+	0.340370i	$0.889448\pi$
$662$	2.40388	+	2.08707i	0.0934295	+	0.0811165i
$663$		−	5.69681i		−	0.221246i
$664$	−22.9354	−	14.8344i	−0.890064	−	0.575688i
$665$	4.19224	+	4.16516i	0.162568	+	0.161518i
$666$	−5.36932	+	6.18435i	−0.208057	+	0.239639i
$667$	33.4990			1.29709
$668$	−0.147647	−	1.04129i	−0.00571264	−	0.0402887i
$669$	19.5076			0.754207
$670$	−16.2462	−	14.1051i	−0.627646	−	0.544928i
$671$			2.11708i			0.0817291i
$672$	2.47301	−	5.34615i	0.0953985	−	0.206232i
$673$		−	31.7515i		−	1.22393i	−0.790885	−	0.611964i	$-0.790380\pi$
$673$		−	31.7515i		−	1.22393i	0.790885	−	0.611964i	$-0.209620\pi$
$674$	−24.4924	+	28.2102i	−0.943413	+	1.08662i
$675$	14.0140			0.539400
$676$	−2.68466	−	18.9337i	−0.103256	−	0.728220i
$677$			4.29335i			0.165007i	0.996591	+	0.0825034i	$0.0262915\pi$
$677$			4.29335i			0.165007i	−0.996591	+	0.0825034i	$0.973708\pi$
$678$	4.12391	−	4.74990i	0.158378	−	0.182419i
$679$	14.6875			0.563656
$680$	−2.39871	+	3.70861i	−0.0919862	+	0.142219i
$681$	20.9460			0.802653
$682$	−12.2462	+	14.1051i	−0.468932	+	0.540113i
$683$	13.6358			0.521760			0.260880	−	0.965371i	$-0.415987\pi$
$683$	13.6358			0.521760			0.260880	+	0.965371i	$0.415987\pi$
$684$	10.9086	+	8.14404i	0.417099	+	0.311395i
$685$	−6.05398			−0.231311
$686$	−10.6627	+	12.2813i	−0.407104	+	0.468901i
$687$	−2.92456			−0.111579
$688$	12.2462	+	42.3154i	0.466882	+	1.61326i
$689$	−4.94602			−0.188429
$690$	6.87689	−	7.92077i	0.261799	−	0.301539i
$691$		−	23.3817i		−	0.889480i	−0.895660	−	0.444740i	$-0.853296\pi$
$691$		−	23.3817i		−	0.889480i	0.895660	−	0.444740i	$-0.146704\pi$
$692$	−33.4990	+	4.74990i	−1.27344	+	0.180564i
$693$	4.19224			0.159250
$694$	22.3842	−	25.7820i	0.849694	−	0.978673i
$695$			0.594427i			0.0225479i
$696$	−24.0932	−	15.5834i	−0.913252	−	0.590686i
$697$			3.70861i			0.140474i
$698$	29.9585	+	26.0103i	1.13395	+	0.984505i
$699$	−11.7630			−0.444916
$700$	−4.40388	+	0.624437i	−0.166451	+	0.0236015i
$701$	29.3693			1.10926			0.554632	−	0.832096i	$-0.312859\pi$
$701$	29.3693			1.10926			0.554632	+	0.832096i	$0.312859\pi$
$702$	−24.0932	+	27.7505i	−0.909341	+	1.04737i
$703$	−11.4677	−	11.3936i	−0.432512	−	0.429718i
$704$	−22.5616	+	10.1447i	−0.850321	+	0.382344i
$705$			17.3736i			0.654327i
$706$	−6.74409	−	5.85528i	−0.253817	−	0.220367i
$707$		−	7.15944i		−	0.269259i
$708$	−3.91146	−	27.5858i	−0.147002	−	1.03674i
$709$	37.3693			1.40343			0.701717	−	0.712456i	$-0.252417\pi$
$709$	37.3693			1.40343			0.701717	+	0.712456i	$0.252417\pi$
$710$	−18.2462	−	15.8415i	−0.684768	−	0.594523i
$711$	−12.5194			−0.469513
$712$	−13.7538	−	8.89586i	−0.515445	−	0.333387i
$713$			16.9170i			0.633547i
$714$	0.965435	−	1.11198i	0.0361305	−	0.0416149i
$715$	22.9354			0.857733
$716$	−2.54635	−	17.9583i	−0.0951617	−	0.671134i
$717$			23.2930i			0.869891i
$718$	25.3502	−	29.1983i	0.946063	−	1.08967i
$719$			15.9484i			0.594776i	0.954757	+	0.297388i	$0.0961155\pi$
$719$			15.9484i			0.594776i	−0.954757	+	0.297388i	$0.903885\pi$
$720$	9.36932	−	2.71151i	0.349174	−	0.101052i
$721$			3.25206i			0.121113i
$722$	−17.4841	+	20.4036i	−0.650690	+	0.759344i
$723$			18.3393i			0.682046i
$724$	−4.12391	+	0.584739i	−0.153264	+	0.0217317i
$725$			21.6669i			0.804689i
$726$	−1.84233	−	1.59953i	−0.0683753	−	0.0593641i
$727$		−	23.6554i		−	0.877332i	−0.898650	−	0.438666i	$-0.855451\pi$
$727$		−	23.6554i		−	0.877332i	0.898650	−	0.438666i	$-0.144549\pi$
$728$	6.33475	−	9.79408i	0.234782	−	0.362993i
$729$	22.6155			0.837612
$730$	−13.5458	−	11.7606i	−0.501353	−	0.435280i
$731$			11.0129i			0.407329i
$732$	−0.230559	−	1.62603i	−0.00852170	−	0.0600998i
$733$	3.12311			0.115355			0.0576773	−	0.998335i	$-0.481631\pi$
$733$	3.12311			0.115355			0.0576773	+	0.998335i	$0.481631\pi$
$734$	13.0776	−	15.0627i	0.482703	−	0.555975i
$735$	11.6982			0.431496
$736$	−9.40572	+	20.3333i	−0.346699	+	0.749494i
$737$		−	30.1254i		−	1.10968i
$738$	5.36932	−	6.18435i	0.197647	−	0.227649i
$739$		−	30.3273i		−	1.11561i	−0.829972	−	0.557804i	$-0.811644\pi$
$739$		−	30.3273i		−	1.11561i	0.829972	−	0.557804i	$-0.188356\pi$
$740$	−11.4677	+	1.62603i	−0.421560	+	0.0597740i
$741$	−17.6155	−	17.5018i	−0.647123	−	0.642943i
$742$	−0.965435	−	0.838200i	−0.0354422	−	0.0307713i
$743$	38.4440			1.41037			0.705187	−	0.709021i	$-0.250863\pi$
$743$	38.4440			1.41037			0.705187	+	0.709021i	$0.250863\pi$
$744$	7.86962	−	12.1671i	0.288514	−	0.446068i
$745$	−27.8078			−1.01880
$746$	−11.2808	+	12.9931i	−0.413019	+	0.475713i
$747$			15.0802i			0.551756i
$748$	−6.12311	+	0.868210i	−0.223883	+	0.0317449i
$749$			6.83248i			0.249653i
$750$	15.1231	+	13.1300i	0.552218	+	0.479441i
$751$	8.24782			0.300967			0.150484	−	0.988612i	$-0.451917\pi$
$751$	8.24782			0.300967			0.150484	+	0.988612i	$0.451917\pi$
$752$	−10.3153	−	35.6435i	−0.376162	−	1.29978i
$753$		−	26.8734i		−	0.979320i
$754$	−42.9047	−	37.2503i	−1.56250	−	1.35658i
$755$	−37.9182			−1.37998
$756$	−9.40572	+	1.33366i	−0.342083	+	0.0485047i
$757$	−24.1922			−0.879282			−0.439641	−	0.898174i	$-0.644894\pi$
$757$	−24.1922			−0.879282			−0.439641	+	0.898174i	$0.644894\pi$
$758$	7.28078	+	6.32124i	0.264450	+	0.229598i
$759$	14.6875			0.533123
$760$	4.09836	+	18.8108i	0.148663	+	0.682341i
$761$	−10.6155			−0.384813			−0.192406	−	0.981315i	$-0.561629\pi$
$761$	−10.6155			−0.384813			−0.192406	+	0.981315i	$0.561629\pi$
$762$	2.39871	+	2.08258i	0.0868959	+	0.0754439i
$763$	−13.7835			−0.498995
$764$	17.4039	−	2.46774i	0.629650	−	0.0892797i
$765$	2.43845			0.0881622
$766$	17.3693	+	15.0802i	0.627579	+	0.544870i
$767$		−	55.1716i		−	1.99213i
$768$	16.2236	−	10.2487i	0.585420	−	0.369819i
$769$	54.2311			1.95562			0.977811	−	0.209489i	$-0.0671801\pi$
$769$	54.2311			1.95562			0.977811	+	0.209489i	$0.0671801\pi$
$770$	4.47685	+	3.88684i	0.161334	+	0.140072i
$771$		−	22.7872i		−	0.820662i
$772$	7.34376	−	1.04129i	0.264308	−	0.0374769i
$773$			25.8321i			0.929115i	0.885543	+	0.464558i	$0.153787\pi$
$773$			25.8321i			0.929115i	−0.885543	+	0.464558i	$0.846213\pi$
$774$	15.9445	−	18.3648i	0.573114	−	0.660110i
$775$	−10.9418			−0.393042
$776$	40.1771	+	25.9863i	1.44227	+	0.932853i
$777$	3.86174			0.138539
$778$	6.20205	+	5.38468i	0.222354	+	0.193050i
$779$	11.4677	+	11.3936i	0.410872	+	0.408219i
$780$	−17.6155	+	2.49775i	−0.630737	+	0.0894337i
$781$		−	33.8340i		−	1.21068i
$782$	−3.67188	+	4.22926i	−0.131306	+	0.151238i
$783$			46.2758i			1.65376i
$784$	−24.0000	+	6.94568i	−0.857143	+	0.248060i
$785$	9.36932			0.334405
$786$	5.36932	−	6.18435i	0.191517	−	0.220589i
$787$	40.9904			1.46115			0.730575	−	0.682833i	$-0.239252\pi$
$787$	40.9904			1.46115			0.730575	+	0.682833i	$0.239252\pi$
$788$	2.94602	+	20.7770i	0.104948	+	0.740151i
$789$		−	7.87377i		−	0.280314i
$790$	−13.3693	−	11.6074i	−0.475659	−	0.412972i
$791$	3.21985			0.114485
$792$	11.4677	+	7.41722i	0.407486	+	0.263559i
$793$		−	3.25206i		−	0.115484i
$794$	−26.6234	−	23.1147i	−0.944830	−	0.820311i
$795$			1.95018i			0.0691659i
$796$	26.2116	−	3.71661i	0.929047	−	0.131732i
$797$		−	23.2930i		−	0.825079i	−0.910940	−	0.412539i	$-0.864642\pi$
$797$		−	23.2930i		−	0.825079i	0.910940	−	0.412539i	$-0.135358\pi$
$798$	−0.472433	−	6.40153i	−0.0167239	−	0.226612i
$799$		−	9.27653i		−	0.328180i
$800$	−13.1514	−	6.08356i	−0.464973	−	0.215086i
$801$			9.04325i			0.319528i
$802$	−19.1231	+	22.0259i	−0.675260	+	0.777761i
$803$		−	25.1181i		−	0.886398i
$804$	3.28078	+	23.1379i	0.115704	+	0.816010i
$805$	5.36932			0.189244
$806$	18.8114	−	21.6669i	0.662605	−	0.763185i
$807$		−	4.44793i		−	0.156575i
$808$	12.6670	−	19.5843i	0.445624	−	0.688975i
$809$	19.6307			0.690178			0.345089	−	0.938570i	$-0.387849\pi$
$809$	19.6307			0.690178			0.345089	+	0.938570i	$0.387849\pi$
$810$	3.12985	+	2.71736i	0.109972	+	0.0954784i
$811$	−0.378206			−0.0132806			−0.00664030	−	0.999978i	$-0.502114\pi$
$811$	−0.378206			−0.0132806			−0.00664030	+	0.999978i	$0.502114\pi$
$812$	−2.06196	−	14.5421i	−0.0723605	−	0.510327i
$813$			18.4149i			0.645837i
$814$	−12.2462	−	10.6323i	−0.429229	−	0.372661i
$815$			16.6029i			0.581573i
$816$	4.60831	−	1.33366i	0.161323	−	0.0466874i
$817$	34.0540	+	33.8340i	1.19140	+	1.18370i
$818$	17.1922	−	19.8019i	0.601112	−	0.692358i
$819$	−6.43971			−0.225022
$820$	11.4677	−	1.62603i	0.400469	−	0.0567834i
$821$	33.4233			1.16648			0.583240	−	0.812300i	$-0.301785\pi$
$821$	33.4233			1.16648			0.583240	+	0.812300i	$0.301785\pi$
$822$	4.96543	+	4.31104i	0.173189	+	0.150365i
$823$		−	22.1328i		−	0.771500i	−0.922603	−	0.385750i	$-0.873943\pi$
$823$		−	22.1328i		−	0.771500i	0.922603	−	0.385750i	$-0.126057\pi$
$824$	−5.75379	+	8.89586i	−0.200443	+	0.309902i
$825$			9.49980i			0.330741i
$826$	9.34991	−	10.7692i	0.325325	−	0.374708i
$827$	−25.1864			−0.875817			−0.437909	−	0.899019i	$-0.644281\pi$
$827$	−25.1864			−0.875817			−0.437909	+	0.899019i	$0.644281\pi$
$828$	12.2462	−	1.73642i	0.425585	−	0.0603448i
$829$			8.91506i			0.309633i	0.987943	+	0.154816i	$0.0494786\pi$
$829$			8.91506i			0.309633i	−0.987943	+	0.154816i	$0.950521\pi$
$830$	−13.9817	+	16.1040i	−0.485311	+	0.558978i
$831$	−28.8492			−1.00077
$832$	34.6569	−	15.5834i	1.20151	−	0.540256i
$833$	−6.24621			−0.216418
$834$	0.423292	−	0.487546i	0.0146574	−	0.0168823i
$835$	−0.821147			−0.0284170
$836$	−16.1268	+	21.6010i	−0.557756	+	0.747088i
$837$	−23.3693			−0.807762
$838$	−25.4493	+	29.3124i	−0.879133	+	1.01258i
$839$	51.2587			1.76965			0.884823	−	0.465926i	$-0.154279\pi$
$839$	51.2587			1.76965			0.884823	+	0.465926i	$0.154279\pi$
$840$	−3.86174	−	2.49775i	−0.133243	−	0.0861805i
$841$	−42.5464			−1.46712
$842$	21.5961	−	24.8743i	0.744251	−	0.857225i
$843$			13.8914i			0.478444i
$844$	0.567309	+	4.00098i	0.0195276	+	0.137719i
$845$	−14.9309			−0.513638
$846$	−13.4305	+	15.4692i	−0.461751	+	0.531843i
$847$		−	1.24887i		−	0.0429118i
$848$	−1.15790	−	4.00098i	−0.0397623	−	0.137394i
$849$			5.79119i			0.198753i
$850$	−2.73546	−	2.37495i	−0.0938254	−	0.0814601i
$851$	−14.6875			−0.503482
$852$	3.68466	+	25.9863i	0.126234	+	0.890275i
$853$	6.63068			0.227030			0.113515	−	0.993536i	$-0.463789\pi$
$853$	6.63068			0.227030			0.113515	+	0.993536i	$0.463789\pi$
$854$	0.551125	−	0.634783i	0.0188591	−	0.0217218i
$855$	7.49141	−	7.54011i	0.256201	−	0.257866i
$856$	−12.0885	+	18.6899i	−0.413178	+	0.638809i
$857$		−	4.16516i		−	0.142279i	−0.997466	−	0.0711396i	$-0.977336\pi$
$857$		−	4.16516i		−	0.142279i	0.997466	−	0.0711396i	$-0.0226636\pi$
$858$	−18.8114	−	16.3323i	−0.642212	−	0.557575i
$859$			22.6203i			0.771795i	0.922542	+	0.385898i	$0.126108\pi$
$859$			22.6203i			0.771795i	−0.922542	+	0.385898i	$0.873892\pi$
$860$	34.0540	−	4.82860i	1.16123	−	0.164654i
$861$	−3.86174			−0.131608
$862$	−18.2462	−	15.8415i	−0.621468	−	0.539565i
$863$	−22.7048			−0.772880			−0.386440	−	0.922315i	$-0.626295\pi$
$863$	−22.7048			−0.772880			−0.386440	+	0.922315i	$0.626295\pi$
$864$	−28.0885	−	12.9931i	−0.955592	−	0.442036i
$865$			26.4168i			0.898199i
$866$	26.0000	−	29.9467i	0.883516	−	1.01763i
$867$	−19.1896			−0.651715
$868$	7.34376	−	1.04129i	0.249264	−	0.0353437i
$869$		−	24.7908i		−	0.840970i
$870$	−14.6875	+	16.9170i	−0.497954	+	0.573541i
$871$			46.2758i			1.56799i
$872$	−37.7041	−	24.3868i	−1.27682	−	0.825840i
$873$		−	26.4168i		−	0.894074i
$874$	1.79683	+	24.3472i	0.0607785	+	0.823558i
$875$			10.2516i			0.346568i
$876$	2.73546	+	19.2920i	0.0924225	+	0.651815i
$877$		−	14.2497i		−	0.481178i	−0.970627	−	0.240589i	$-0.922659\pi$
$877$		−	14.2497i		−	0.481178i	0.970627	−	0.240589i	$-0.0773406\pi$
$878$	−26.4924	−	23.0010i	−0.894076	−	0.776246i
$879$		−	5.69681i		−	0.192149i
$880$	5.36932	+	18.5531i	0.181000	+	0.625423i
$881$	35.1771			1.18515			0.592573	−	0.805517i	$-0.298112\pi$
$881$	35.1771			1.18515			0.592573	+	0.805517i	$0.298112\pi$
$882$	10.4160	+	9.04325i	0.350724	+	0.304502i
$883$		−	0.594427i		−	0.0200041i	−0.999950	−	0.0100020i	$-0.996816\pi$
$883$		−	0.594427i		−	0.0200041i	0.999950	−	0.0100020i	$-0.00318380\pi$
$884$	9.40572	−	1.33366i	0.316349	−	0.0448558i
$885$	−21.7538			−0.731246
$886$	−32.2420	+	37.1361i	−1.08319	+	1.24761i
$887$	−31.4785			−1.05694			−0.528472	−	0.848951i	$-0.677235\pi$
$887$	−31.4785			−1.05694			−0.528472	+	0.848951i	$0.677235\pi$
$888$	10.5636	+	6.83248i	0.354492	+	0.229283i
$889$			1.62603i			0.0545353i
$890$	−8.38447	+	9.65719i	−0.281048	+	0.323710i
$891$			5.80369i			0.194431i
$892$	4.56685	+	32.2080i	0.152910	+	1.07840i
$893$	−28.6847	−	28.4994i	−0.959895	−	0.953696i
$894$	22.8078	+	19.8019i	0.762806	+	0.662276i
$895$	−14.1617			−0.473373
$896$	9.40572	+	2.83150i	0.314223	+	0.0945938i
$897$	−22.5616			−0.753308
$898$	33.3002	−	38.3550i	1.11124	−	1.27992i
$899$		−	36.1310i		−	1.20504i
$900$	1.12311	+	7.92077i	0.0374369	+	0.264026i
$901$		−	1.04129i		−	0.0346904i
$902$	12.2462	+	10.6323i	0.407754	+	0.354016i
$903$	−11.4677			−0.381620
$904$	8.80776	+	5.69681i	0.292942	+	0.189473i
$905$			3.25206i			0.108102i
$906$	31.1003	+	27.0016i	1.03324	+	0.897067i
$907$	36.7188			1.21923			0.609614	−	0.792698i	$-0.291324\pi$
$907$	36.7188			1.21923			0.609614	+	0.792698i	$0.291324\pi$
$908$	4.90360	+	34.5830i	0.162732	+	1.14768i
$909$	−12.8769			−0.427100
$910$	−6.87689	−	5.97059i	−0.227967	−	0.197923i
$911$	10.6465			0.352735			0.176368	−	0.984324i	$-0.443565\pi$
$911$	10.6465			0.352735			0.176368	+	0.984324i	$0.443565\pi$
$912$	10.0338	−	18.3470i	0.332251	−	0.607529i
$913$	−29.8617			−0.988279
$914$	−12.9461	−	11.2400i	−0.428220	−	0.371785i
$915$	−1.28226			−0.0423904
$916$	−0.684658	−	4.82860i	−0.0226218	−	0.159541i
$917$	4.19224			0.138440
$918$	−5.84233	−	5.07237i	−0.192826	−	0.167413i
$919$			12.8563i			0.424089i	0.977260	+	0.212044i	$0.0680121\pi$
$919$			12.8563i			0.424089i	−0.977260	+	0.212044i	$0.931988\pi$
$920$	14.6875	+	9.49980i	0.484233	+	0.313199i
$921$	9.61553			0.316842
$922$	−20.6267	−	17.9083i	−0.679303	−	0.589777i
$923$			51.9726i			1.71070i
$924$	−0.904059	−	6.37593i	−0.0297413	−	0.209753i
$925$		−	9.49980i		−	0.312352i
$926$	20.0684	−	23.1147i	0.659490	−	0.759597i
$927$	5.84912			0.192110
$928$	20.0885	−	43.4274i	0.659439	−	1.42557i
$929$	−25.6847			−0.842686			−0.421343	−	0.906901i	$-0.638441\pi$
$929$	−25.6847			−0.842686			−0.421343	+	0.906901i	$0.638441\pi$
$930$	−8.54312	−	7.41722i	−0.280140	−	0.243220i
$931$	−19.1896	+	19.3144i	−0.628915	+	0.633003i
$932$	−2.75379	−	19.4213i	−0.0902033	−	0.636165i
$933$		−	1.04129i		−	0.0340903i
$934$	−2.86692	+	3.30210i	−0.0938084	+	0.108048i
$935$			4.82860i			0.157912i
$936$	−17.6155	−	11.3936i	−0.575782	−	0.372412i
$937$	−22.1231			−0.722730			−0.361365	−	0.932424i	$-0.617689\pi$
$937$	−22.1231			−0.722730			−0.361365	+	0.932424i	$0.617689\pi$
$938$	−7.84233	+	9.03276i	−0.256061	+	0.294930i
$939$	−5.47091			−0.178536
$940$	−28.6847	+	4.06727i	−0.935590	+	0.132660i
$941$		−	24.9190i		−	0.812336i	−0.913799	−	0.406168i	$-0.866865\pi$
$941$		−	24.9190i		−	0.812336i	0.913799	−	0.406168i	$-0.133135\pi$
$942$	−7.68466	−	6.67190i	−0.250380	−	0.217382i
$943$	14.6875			0.478292
$944$	44.6299	−	12.9160i	1.45258	−	0.420381i
$945$			7.41722i			0.241282i
$946$	36.3659	+	31.5732i	1.18236	+	1.02653i
$947$		−	2.71151i		−	0.0881123i	−0.999029	−	0.0440561i	$-0.985972\pi$
$947$		−	2.71151i		−	0.0881123i	0.999029	−	0.0440561i	$-0.0140280\pi$
$948$	2.69981	+	19.0406i	0.0876859	+	0.618410i
$949$			38.5839i			1.25249i
$950$	−15.7476	+	1.16218i	−0.510921	+	0.0377059i
$951$			5.69681i			0.184732i
$952$	2.06196	+	1.33366i	0.0668284	+	0.0432242i
$953$		−	24.7908i		−	0.803053i	−0.915848	−	0.401526i	$-0.868480\pi$
$953$		−	24.7908i		−	0.803053i	0.915848	−	0.401526i	$-0.131520\pi$
$954$	−1.50758	+	1.73642i	−0.0488096	+	0.0562187i
$955$		−	13.7245i		−	0.444113i
$956$	−38.4579	+	5.45303i	−1.24382	+	0.176364i
$957$	−31.3693			−1.01403
$958$	−8.04963	+	9.27153i	−0.260072	+	0.299549i
$959$			3.36596i			0.108692i
$960$	−6.14441	−	13.6650i	−0.198310	−	0.441035i
$961$	−12.7538			−0.411413
$962$	18.8114	+	16.3323i	0.606505	+	0.526574i
$963$	12.2888			0.396002
$964$	−30.2791	+	4.29335i	−0.975225	+	0.138279i
$965$		−	5.79119i		−	0.186425i
$966$	−4.40388	−	3.82349i	−0.141693	−	0.123019i
$967$		−	26.4738i		−	0.851341i	−0.904878	−	0.425670i	$-0.860038\pi$
$967$		−	26.4738i		−	0.851341i	0.904878	−	0.425670i	$-0.139962\pi$
$968$	2.20960	−	3.41624i	0.0710193	−	0.109802i
$969$	3.68466	−	3.70861i	0.118368	−	0.119138i
$970$	24.4924	−	28.2102i	0.786404	−	0.905777i
$971$	19.4849			0.625301			0.312651	−	0.949868i	$-0.398783\pi$
$971$	19.4849			0.625301			0.312651	+	0.949868i	$0.398783\pi$
$972$	3.97626	+	28.0429i	0.127539	+	0.899475i
$973$	0.330497			0.0105952
$974$	−10.2462	−	8.89586i	−0.328310	−	0.285042i
$975$		−	14.5927i		−	0.467339i
$976$	2.63068	−	0.761329i	0.0842061	−	0.0243695i
$977$			26.8734i			0.859755i	0.902887	+	0.429878i	$0.141443\pi$
$977$			26.8734i			0.859755i	−0.902887	+	0.429878i	$0.858557\pi$
$978$	11.8229	−	13.6176i	0.378055	−	0.435442i
$979$	−17.9074			−0.572322
$980$	2.73863	+	19.3144i	0.0874824	+	0.616975i
$981$			24.7908i			0.791509i
$982$	−2.51398	+	2.89560i	−0.0802245	+	0.0924022i
$983$	−13.3405			−0.425497			−0.212748	−	0.977107i	$-0.568241\pi$
$983$	−13.3405			−0.425497			−0.212748	+	0.977107i	$0.568241\pi$
$984$	−10.5636	−	6.83248i	−0.336756	−	0.217812i
$985$	16.3845			0.522053
$986$	7.84233	−	9.03276i	0.249751	−	0.287662i
$987$	9.65956			0.307467
$988$	24.7724	−	33.1814i	0.788115	−	1.05564i
$989$	43.6155			1.38689
$990$	6.99083	−	8.05200i	0.222183	−	0.255909i
$991$	−54.1833			−1.72119			−0.860594	−	0.509292i	$-0.829907\pi$
$991$	−54.1833			−1.72119			−0.860594	+	0.509292i	$0.829907\pi$
$992$	21.9309	+	10.1447i	0.696306	+	0.322096i
$993$	−2.69981			−0.0856760
$994$	−8.80776	+	10.1447i	−0.279365	+	0.321772i
$995$		−	20.6701i		−	0.655288i
$996$	22.9354	−	3.25206i	0.726734	−	0.103045i
$997$	−28.5464			−0.904073			−0.452037	−	0.891999i	$-0.649302\pi$
$997$	−28.5464			−0.904073			−0.452037	+	0.891999i	$0.649302\pi$
$998$	−10.2107	+	11.7606i	−0.323214	+	0.372276i
$999$		−	20.2895i		−	0.641931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.d.a.75.1	✓	8
3.2	odd	2		684.2.f.b.379.8		8
4.3	odd	2	inner	76.2.d.a.75.7	yes	8
8.3	odd	2		1216.2.h.d.1215.6		8
8.5	even	2		1216.2.h.d.1215.3		8
12.11	even	2		684.2.f.b.379.2		8
19.18	odd	2	inner	76.2.d.a.75.8	yes	8
57.56	even	2		684.2.f.b.379.1		8
76.75	even	2	inner	76.2.d.a.75.2	yes	8
152.37	odd	2		1216.2.h.d.1215.5		8
152.75	even	2		1216.2.h.d.1215.4		8
228.227	odd	2		684.2.f.b.379.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.d.a.75.1	✓	8	1.1	even	1	trivial
76.2.d.a.75.2	yes	8	76.75	even	2	inner
76.2.d.a.75.7	yes	8	4.3	odd	2	inner
76.2.d.a.75.8	yes	8	19.18	odd	2	inner
684.2.f.b.379.1		8	57.56	even	2
684.2.f.b.379.2		8	12.11	even	2
684.2.f.b.379.7		8	228.227	odd	2
684.2.f.b.379.8		8	3.2	odd	2
1216.2.h.d.1215.3		8	8.5	even	2
1216.2.h.d.1215.4		8	152.75	even	2
1216.2.h.d.1215.5		8	152.37	odd	2
1216.2.h.d.1215.6		8	8.3	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06789 - 0.927153i) q^{2} +1.19935 q^{3} +(0.280776 + 1.98019i) q^{4} +1.56155 q^{5} +(-1.28078 - 1.11198i) q^{6} -0.868210i q^{7} +(1.53610 - 2.37495i) q^{8} -1.56155 q^{9} +O(q^{10})\)	\(q+(-1.06789 - 0.927153i) q^{2} +1.19935 q^{3} +(0.280776 + 1.98019i) q^{4} +1.56155 q^{5} +(-1.28078 - 1.11198i) q^{6} -0.868210i q^{7} +(1.53610 - 2.37495i) q^{8} -1.56155 q^{9} +(-1.66757 - 1.44780i) q^{10} -3.09218i q^{11} +(0.336750 + 2.37495i) q^{12} +4.74990i q^{13} +(-0.804963 + 0.927153i) q^{14} +1.87285 q^{15} +(-3.84233 + 1.11198i) q^{16} -1.00000 q^{17} +(1.66757 + 1.44780i) q^{18} +(-3.07221 + 3.09218i) q^{19} +(0.438447 + 3.09218i) q^{20} -1.04129i q^{21} +(-2.86692 + 3.30210i) q^{22} +3.96039i q^{23} +(1.84233 - 2.84840i) q^{24} -2.56155 q^{25} +(4.40388 - 5.07237i) q^{26} -5.47091 q^{27} +(1.71922 - 0.243773i) q^{28} -8.45851i q^{29} +(-2.00000 - 1.73642i) q^{30} +4.27156 q^{31} +(5.13416 + 2.37495i) q^{32} -3.70861i q^{33} +(1.06789 + 0.927153i) q^{34} -1.35576i q^{35} +(-0.438447 - 3.09218i) q^{36} +3.70861i q^{37} +(6.14770 - 0.453700i) q^{38} +5.69681i q^{39} +(2.39871 - 3.70861i) q^{40} -3.70861i q^{41} +(-0.965435 + 1.11198i) q^{42} -11.0129i q^{43} +(6.12311 - 0.868210i) q^{44} -2.43845 q^{45} +(3.67188 - 4.22926i) q^{46} +9.27653i q^{47} +(-4.60831 + 1.33366i) q^{48} +6.24621 q^{49} +(2.73546 + 2.37495i) q^{50} -1.19935 q^{51} +(-9.40572 + 1.33366i) q^{52} +1.04129i q^{53} +(5.84233 + 5.07237i) q^{54} -4.82860i q^{55} +(-2.06196 - 1.33366i) q^{56} +(-3.68466 + 3.70861i) q^{57} +(-7.84233 + 9.03276i) q^{58} -11.6153 q^{59} +(0.525853 + 3.70861i) q^{60} -0.684658 q^{61} +(-4.56155 - 3.96039i) q^{62} +1.35576i q^{63} +(-3.28078 - 7.29634i) q^{64} +7.41722i q^{65} +(-3.43845 + 3.96039i) q^{66} +9.74247 q^{67} +(-0.280776 - 1.98019i) q^{68} +4.74990i q^{69} +(-1.25699 + 1.44780i) q^{70} +10.9418 q^{71} +(-2.39871 + 3.70861i) q^{72} +8.12311 q^{73} +(3.43845 - 3.96039i) q^{74} -3.07221 q^{75} +(-6.98571 - 5.21535i) q^{76} -2.68466 q^{77} +(5.28181 - 6.08356i) q^{78} +8.01726 q^{79} +(-6.00000 + 1.73642i) q^{80} -1.87689 q^{81} +(-3.43845 + 3.96039i) q^{82} -9.65719i q^{83} +(2.06196 - 0.292370i) q^{84} -1.56155 q^{85} +(-10.2107 + 11.7606i) q^{86} -10.1447i q^{87} +(-7.34376 - 4.74990i) q^{88} -5.79119i q^{89} +(2.60399 + 2.26081i) q^{90} +4.12391 q^{91} +(-7.84233 + 1.11198i) q^{92} +5.12311 q^{93} +(8.60076 - 9.90631i) q^{94} +(-4.79741 + 4.82860i) q^{95} +(6.15767 + 2.84840i) q^{96} +16.9170i q^{97} +(-6.67026 - 5.79119i) q^{98} +4.82860i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q - 6 * q^4 - 4 * q^5 - 2 * q^6 + 4 * q^9	\( 8 q - 6 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{9} - 6 q^{16} - 8 q^{17} + 20 q^{20} - 10 q^{24} - 4 q^{25} - 6 q^{26} + 22 q^{28} - 16 q^{30} - 20 q^{36} + 18 q^{38} + 50 q^{42} + 16 q^{44} - 36 q^{45} - 16 q^{49} + 22 q^{54} + 20 q^{57} - 38 q^{58} + 44 q^{61} - 20 q^{62} - 18 q^{64} - 44 q^{66} + 6 q^{68} + 32 q^{73} + 44 q^{74} - 16 q^{76} + 28 q^{77} - 48 q^{80} - 48 q^{81} - 44 q^{82} + 4 q^{85} - 38 q^{92} + 8 q^{93} + 74 q^{96}+O(q^{100}) \) 8 * q - 6 * q^4 - 4 * q^5 - 2 * q^6 + 4 * q^9 - 6 * q^16 - 8 * q^17 + 20 * q^20 - 10 * q^24 - 4 * q^25 - 6 * q^26 + 22 * q^28 - 16 * q^30 - 20 * q^36 + 18 * q^38 + 50 * q^42 + 16 * q^44 - 36 * q^45 - 16 * q^49 + 22 * q^54 + 20 * q^57 - 38 * q^58 + 44 * q^61 - 20 * q^62 - 18 * q^64 - 44 * q^66 + 6 * q^68 + 32 * q^73 + 44 * q^74 - 16 * q^76 + 28 * q^77 - 48 * q^80 - 48 * q^81 - 44 * q^82 + 4 * q^85 - 38 * q^92 + 8 * q^93 + 74 * q^96

Introduction

L-functions

Modular forms

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