LMFDB - Embedded newform 76.2.d.a.75.7

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			75.7
Root			$1.06789 - 0.927153i$ of defining polynomial
Character	$\chi$	$=$	76.75
Dual form			76.2.d.a.75.8

$q$-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} +(0.413858 - 6.15051i) 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} +(-5.26050 - 6.95177i) 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	$-0.612536\pi$
$3$	−1.19935			−0.692447			−0.346223	+	0.938152i	$0.612536\pi$
$4$	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	$0.0524643\pi$
$7$			0.868210i			0.328153i	−0.986448	+	0.164076i	$0.947536\pi$
$8$	−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	$0.154364\pi$
$11$			3.09218i			0.932326i	−0.884699	+	0.466163i	$0.845636\pi$
$12$	−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	$-0.864516\pi$
$23$		−	3.96039i		−	0.825798i	0.910777	−	0.412899i	$-0.135484\pi$
$24$	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	$-0.625315\pi$
$31$	−4.27156			−0.767195			−0.383597	+	0.923500i	$0.625315\pi$
$32$	−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	$0.901395\pi$
$38$	0.413858	−	6.15051i	0.0671366	−	0.997744i
$39$		−	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	$0.317286\pi$
$43$			11.0129i			1.67946i	−0.543005	+	0.839729i	$0.682714\pi$
$44$	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	$-0.763470\pi$
$47$		−	9.27653i		−	1.35312i	0.736387	−	0.676560i	$-0.236530\pi$
$48$	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	$-0.227106\pi$
$59$	11.6153			1.51219			0.756093	+	0.654464i	$0.227106\pi$
$60$	−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	$-0.702894\pi$
$67$	−9.74247			−1.19023			−0.595116	+	0.803640i	$0.702894\pi$
$68$	−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	$-0.724929\pi$
$71$	−10.9418			−1.29856			−0.649278	+	0.760551i	$0.724929\pi$
$72$	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
$76$	−5.26050	−	6.95177i	−0.603421	−	0.797423i
$77$	−2.68466			−0.305945
$78$	−5.28181	−	6.08356i	−0.598047	−	0.688828i
$79$	−8.01726			−0.902013			−0.451006	−	0.892521i	$-0.648935\pi$
$79$	−8.01726			−0.902013			−0.451006	+	0.892521i	$0.648935\pi$
$80$	−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	$0.177811\pi$
$83$			9.65719i			1.06001i	−0.847993	+	0.530007i	$0.822189\pi$
$84$	−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	$-0.440921\pi$
$103$	3.74571			0.369075			0.184538	+	0.982825i	$0.440921\pi$
$104$	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	$-0.375789\pi$
$107$	7.86962			0.760785			0.380392	+	0.924825i	$0.375789\pi$
$108$	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	$0.944189\pi$
$114$	−0.496361	+	7.37663i	−0.0464885	+	0.690884i
$115$		−	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	$-0.473520\pi$
$127$	1.87285			0.166189			0.0830944	+	0.996542i	$0.473520\pi$
$128$	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	$-0.932348\pi$
$131$		−	4.82860i		−	0.421876i	0.977499	−	0.210938i	$-0.0676519\pi$
$132$	−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	$-0.994861\pi$
$139$		−	0.380664i		−	0.0322875i	0.999870	−	0.0161438i	$-0.00513894\pi$
$140$	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	$-0.0492900\pi$
$151$	24.2824			1.97607			0.988035	+	0.154231i	$0.0492900\pi$
$152$	−12.0630	−	2.54643i	−0.978437	−	0.206543i
$153$	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	$-0.863294\pi$
$163$		−	10.6323i		−	0.832785i	0.909185	−	0.416392i	$-0.136706\pi$
$164$	−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	$-0.493523\pi$
$167$	0.525853			0.0406917			0.0203459	+	0.999793i	$0.493523\pi$
$168$	−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	$-0.389937\pi$
$179$	9.06897			0.677847			0.338923	+	0.940814i	$0.389937\pi$
$180$	−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
$190$	0.646260	−	9.60434i	0.0468847	−	0.696772i
$191$			8.78898i			0.635948i	0.948099	+	0.317974i	$0.103003\pi$
$191$			8.78898i			0.635948i	−0.948099	+	0.317974i	$0.896997\pi$
$192$	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	$0.155447\pi$
$199$			13.2369i			0.938340i	−0.883108	+	0.469170i	$0.844553\pi$
$200$	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	$-0.522156\pi$
$211$	−2.02050			−0.139097			−0.0695485	+	0.997579i	$0.522156\pi$
$212$	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	$-0.683317\pi$
$223$	−16.2651			−1.08919			−0.544595	+	0.838699i	$0.683317\pi$
$224$	−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	$-0.696783\pi$
$227$	−17.4644			−1.15916			−0.579578	+	0.814917i	$0.696783\pi$
$228$	6.30920	+	8.33763i	0.417837	+	0.552173i
$229$	−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	$-0.783821\pi$
$239$		−	19.4213i		−	1.25626i	0.778110	−	0.628129i	$-0.216179\pi$
$240$	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	$0.250017\pi$
$251$			22.4066i			1.41429i	−0.707069	+	0.707145i	$0.749983\pi$
$252$	−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	$0.0648768\pi$
$263$			6.56502i			0.404816i	−0.979301	+	0.202408i	$0.935123\pi$
$264$	−8.80776	+	5.69681i	−0.542080	+	0.350614i
$265$			1.62603i			0.0998862i
$266$	5.33993	+	0.359315i	0.327412	+	0.0220310i
$267$			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	$-0.845571\pi$
$271$		−	15.3540i		−	0.932689i	0.884603	−	0.466345i	$-0.154429\pi$
$272$	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	$-0.954159\pi$
$283$		−	4.82860i		−	0.287030i	0.989648	−	0.143515i	$-0.0458406\pi$
$284$	−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
$304$	−15.2429	+	8.46492i	−0.874239	+	0.485496i
$305$	−1.06913			−0.0612182
$306$	1.66757	−	1.44780i	0.0953284	−	0.0827651i
$307$	−8.01726			−0.457569			−0.228785	−	0.973477i	$-0.573475\pi$
$307$	−8.01726			−0.457569			−0.228785	+	0.973477i	$0.573475\pi$
$308$	−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	$0.00783626\pi$
$311$			0.868210i			0.0492317i	−0.999697	+	0.0246158i	$0.992164\pi$
$312$	−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	$-0.480295\pi$
$331$	2.25106			0.123729			0.0618647	+	0.998085i	$0.480295\pi$
$332$	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
$342$	−0.646260	+	9.60434i	−0.0349458	+	0.519343i
$343$			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	$-0.775592\pi$
$347$		−	24.1430i		−	1.29606i	0.761613	−	0.648032i	$-0.224408\pi$
$348$	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	$-0.743440\pi$
$359$		−	27.3420i		−	1.44306i	0.692384	−	0.721529i	$-0.256560\pi$
$360$	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	$-0.879994\pi$
$367$		−	14.1051i		−	0.736282i	0.929770	−	0.368141i	$-0.120006\pi$
$368$	−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	$-0.443973\pi$
$379$	6.81791			0.350213			0.175106	+	0.984550i	$0.443973\pi$
$380$	−8.21455	−	10.8556i	−0.421398	−	0.556878i
$381$	−2.24621			−0.115077
$382$	8.14873	+	9.38566i	0.416925	+	0.480212i
$383$	16.2651			0.831107			0.415554	−	0.909569i	$-0.363588\pi$
$383$	16.2651			0.831107			0.415554	+	0.909569i	$0.363588\pi$
$384$	−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
$418$	19.0184	+	1.27972i	0.930223	+	0.0625932i
$419$			27.4489i			1.34097i	0.741924	+	0.670484i	$0.233913\pi$
$419$			27.4489i			1.34097i	−0.741924	+	0.670484i	$0.766087\pi$
$420$	−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	$-0.634998\pi$
$431$	−17.0862			−0.823015			−0.411507	+	0.911406i	$0.634998\pi$
$432$	−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	$-0.701668\pi$
$439$	−24.8082			−1.18403			−0.592015	+	0.805927i	$0.701668\pi$
$440$	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	$0.309452\pi$
$443$			34.7753i			1.65222i	−0.563507	+	0.826111i	$0.690548\pi$
$444$	−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
$456$	14.4678	+	3.05407i	0.677516	+	0.143020i
$457$	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	$-0.832241\pi$
$463$		−	21.6452i		−	1.00594i	0.864304	−	0.502970i	$-0.167759\pi$
$464$	−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	$0.0227928\pi$
$467$			3.09218i			0.143089i	−0.997437	+	0.0715444i	$0.977207\pi$
$468$	−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	$0.0635575\pi$
$479$			8.68210i			0.396695i	−0.980132	+	0.198348i	$0.936442\pi$
$480$	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	$-0.569755\pi$
$487$	−9.59482			−0.434783			−0.217391	+	0.976085i	$0.569755\pi$
$488$	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	$0.0194878\pi$
$491$			2.71151i			0.122369i	−0.998126	+	0.0611844i	$0.980512\pi$
$492$	8.80776	+	1.24887i	0.397085	+	0.0563036i
$493$			8.45851i			0.380952i
$494$	29.2143	+	1.96578i	1.31441	+	0.0884447i
$495$		−	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	$0.0792817\pi$
$499$			11.0129i			0.493007i	−0.969142	+	0.246504i	$0.920718\pi$
$500$	−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	$-0.707664\pi$
$503$		−	35.6435i		−	1.58926i	0.607091	−	0.794632i	$-0.292336\pi$
$504$	−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	$-0.238398\pi$
$523$	33.4990			1.46481			0.732404	+	0.680871i	$0.238398\pi$
$524$	−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
$532$	6.03560	−	4.56722i	0.261676	−	0.198014i
$533$	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	$-0.363236\pi$
$547$	19.4849			0.833116			0.416558	+	0.909109i	$0.363236\pi$
$548$	−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	$-0.249139\pi$
$563$	33.6466			1.41804			0.709018	+	0.705191i	$0.249139\pi$
$564$	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	$-0.0861291\pi$
$570$	−0.775094	+	11.5190i	−0.0324651	+	0.482477i
$571$		−	17.5780i		−	0.735615i	−0.929902	−	0.367807i	$-0.880109\pi$
$571$		−	17.5780i		−	0.735615i	0.929902	−	0.367807i	$-0.119891\pi$
$572$	−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	$-0.968228\pi$
$587$		−	4.82860i		−	0.199297i	0.995023	−	0.0996487i	$-0.0317719\pi$
$588$	−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	$-0.449574\pi$
$599$	7.72197			0.315511			0.157756	+	0.987478i	$0.449574\pi$
$600$	−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	$-0.410749\pi$
$607$	13.6358			0.553461			0.276730	+	0.960948i	$0.410749\pi$
$608$	−8.42943	+	23.1721i	−0.341859	+	0.939751i
$609$	−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	$0.242926\pi$
$619$			34.3946i			1.38244i	−0.722646	+	0.691218i	$0.757074\pi$
$620$	−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	$-0.918329\pi$
$631$		−	12.7494i		−	0.507544i	0.967264	−	0.253772i	$-0.0816713\pi$
$632$	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	$0.0413210\pi$
$643$			6.56502i			0.258899i	−0.991586	+	0.129449i	$0.958679\pi$
$644$	0.965435	−	6.80879i	0.0380435	−	0.268304i
$645$		−	20.6256i		−	0.812133i
$646$	−0.413858	+	6.15051i	−0.0162830	+	0.241988i
$647$		−	36.2379i		−	1.42466i	−0.701845	−	0.712329i	$-0.747640\pi$
$647$		−	36.2379i		−	1.42466i	0.701845	−	0.712329i	$-0.252360\pi$
$648$	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	$-0.479107\pi$
$659$	3.36750			0.131179			0.0655896	+	0.997847i	$0.479107\pi$
$660$	−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	$-0.584013\pi$
$683$	−13.6358			−0.521760			−0.260880	+	0.965371i	$0.584013\pi$
$684$	8.21455	+	10.8556i	0.314091	+	0.415073i
$685$	−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	$0.146704\pi$
$691$			23.3817i			0.889480i	−0.895660	+	0.444740i	$0.853296\pi$
$692$	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	$-0.903885\pi$
$719$		−	15.9484i		−	0.594776i	0.954757	−	0.297388i	$-0.0961155\pi$
$720$	9.36932	+	2.71151i	0.349174	+	0.101052i
$721$			3.25206i			0.121113i
$722$	−17.7470	−	20.1753i	−0.660475	−	0.750848i
$723$		−	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	$0.144549\pi$
$727$			23.6554i			0.877332i	−0.898650	+	0.438666i	$0.855451\pi$
$728$	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	$0.188356\pi$
$739$			30.3273i			1.11561i	−0.829972	+	0.557804i	$0.811644\pi$
$740$	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	$-0.749137\pi$
$743$	−38.4440			−1.41037			−0.705187	+	0.709021i	$0.749137\pi$
$744$	−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	$-0.548083\pi$
$751$	−8.24782			−0.300967			−0.150484	+	0.988612i	$0.548083\pi$
$752$	−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
$760$	−18.8370	−	3.97639i	−0.683290	−	0.144239i
$761$	−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	$-0.760748\pi$
$787$	−40.9904			−1.46115			−0.730575	+	0.682833i	$0.760748\pi$
$788$	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	$-0.135358\pi$
$798$	−6.40446	−	0.430946i	−0.226715	−	0.0152553i
$799$			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	$-0.497886\pi$
$811$	0.378206			0.0132806			0.00664030	+	0.999978i	$0.497886\pi$
$812$	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	$0.126057\pi$
$823$			22.1328i			0.771500i	−0.922603	+	0.385750i	$0.873943\pi$
$824$	−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	$-0.355719\pi$
$827$	25.1864			0.875817			0.437909	+	0.899019i	$0.355719\pi$
$828$	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
$836$	21.4961	−	16.2664i	0.743458	−	0.562585i
$837$	−23.3693			−0.807762
$838$	25.4493	+	29.3124i	0.879133	+	1.01258i
$839$	−51.2587			−1.76965			−0.884823	−	0.465926i	$-0.845721\pi$
$839$	−51.2587			−1.76965			−0.884823	+	0.465926i	$0.845721\pi$
$840$	−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	$-0.873892\pi$
$859$		−	22.6203i		−	0.771795i	0.922542	−	0.385898i	$-0.126108\pi$
$860$	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	$-0.373705\pi$
$863$	22.7048			0.772880			0.386440	+	0.922315i	$0.373705\pi$
$864$	−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
$874$	−24.3584	−	1.63904i	−0.823934	−	0.0554412i
$875$		−	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	$0.00318380\pi$
$883$			0.594427i			0.0200041i	−0.999950	+	0.0100020i	$0.996816\pi$
$884$	−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	$-0.322765\pi$
$887$	31.4785			1.05694			0.528472	+	0.848951i	$0.322765\pi$
$888$	−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	$-0.708676\pi$
$907$	−36.7188			−1.21923			−0.609614	+	0.792698i	$0.708676\pi$
$908$	−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	$-0.556435\pi$
$911$	−10.6465			−0.352735			−0.176368	+	0.984324i	$0.556435\pi$
$912$	18.2816	−	10.1524i	0.605364	−	0.336180i
$913$	−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	$-0.931988\pi$
$919$		−	12.8563i		−	0.424089i	0.977260	−	0.212044i	$-0.0680121\pi$
$920$	−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	$0.0140280\pi$
$947$			2.71151i			0.0881123i	−0.999029	+	0.0440561i	$0.985972\pi$
$948$	2.69981	−	19.0406i	0.0876859	−	0.618410i
$949$			38.5839i			1.25249i
$950$	−1.06012	+	15.7548i	−0.0343948	+	0.511155i
$951$		−	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	$0.139962\pi$
$967$			26.4738i			0.851341i	−0.904878	+	0.425670i	$0.860038\pi$
$968$	−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	$-0.601217\pi$
$971$	−19.4849			−0.625301			−0.312651	+	0.949868i	$0.601217\pi$
$972$	−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	$-0.431759\pi$
$983$	13.3405			0.425497			0.212748	+	0.977107i	$0.431759\pi$
$984$	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
$988$	33.0202	−	24.9869i	1.05051	−	0.794938i
$989$	43.6155			1.38689
$990$	−6.99083	−	8.05200i	−0.222183	−	0.255909i
$991$	54.1833			1.72119			0.860594	−	0.509292i	$-0.170093\pi$
$991$	54.1833			1.72119			0.860594	+	0.509292i	$0.170093\pi$
$992$	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.75.7	yes	8
3.2	odd	2		684.2.f.b.379.2		8
4.3	odd	2	inner	76.2.d.a.75.1	✓	8
8.3	odd	2		1216.2.h.d.1215.3		8
8.5	even	2		1216.2.h.d.1215.6		8
12.11	even	2		684.2.f.b.379.8		8
19.18	odd	2	inner	76.2.d.a.75.2	yes	8
57.56	even	2		684.2.f.b.379.7		8
76.75	even	2	inner	76.2.d.a.75.8	yes	8
152.37	odd	2		1216.2.h.d.1215.4		8
152.75	even	2		1216.2.h.d.1215.5		8
228.227	odd	2		684.2.f.b.379.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.d.a.75.1	✓	8	4.3	odd	2	inner
76.2.d.a.75.2	yes	8	19.18	odd	2	inner
76.2.d.a.75.7	yes	8	1.1	even	1	trivial
76.2.d.a.75.8	yes	8	76.75	even	2	inner
684.2.f.b.379.1		8	228.227	odd	2
684.2.f.b.379.2		8	3.2	odd	2
684.2.f.b.379.7		8	57.56	even	2
684.2.f.b.379.8		8	12.11	even	2
1216.2.h.d.1215.3		8	8.3	odd	2
1216.2.h.d.1215.4		8	152.37	odd	2
1216.2.h.d.1215.5		8	152.75	even	2
1216.2.h.d.1215.6		8	8.5	even	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} +(0.413858 - 6.15051i) 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} +(-5.26050 - 6.95177i) 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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