LMFDB - Embedded newform 770.2.bv.a.367.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			367.43
Character	$\chi$	$=$	770.367
Dual form			770.2.bv.a.663.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.777146 - 0.629320i) q^{2} +(0.0939735 - 1.79312i) q^{3} +(0.207912 - 0.978148i) q^{4} +(-2.21031 - 0.338427i) q^{5} +(-1.05542 - 1.45266i) q^{6} +(-2.36727 + 1.18155i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.222884 - 0.0234260i) q^{9} +O(q^{10})$	\(q+(0.777146 - 0.629320i) q^{2} +(0.0939735 - 1.79312i) q^{3} +(0.207912 - 0.978148i) q^{4} +(-2.21031 - 0.338427i) q^{5} +(-1.05542 - 1.45266i) q^{6} +(-2.36727 + 1.18155i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.222884 - 0.0234260i) q^{9} +(-1.93071 + 1.12799i) q^{10} +(-3.02220 + 1.36613i) q^{11} +(-1.73440 - 0.464731i) q^{12} +(-0.129996 - 0.820762i) q^{13} +(-1.09614 + 2.40800i) q^{14} +(-0.814552 + 3.93155i) q^{15} +(-0.913545 - 0.406737i) q^{16} +(0.237530 + 0.192348i) q^{17} +(-0.187956 + 0.122060i) q^{18} +(-7.23869 + 1.53863i) q^{19} +(-0.790581 + 2.09165i) q^{20} +(1.89620 + 4.35583i) q^{21} +(-1.48896 + 2.96361i) q^{22} +(2.23485 + 0.598826i) q^{23} +(-1.64034 + 0.730329i) q^{24} +(4.77093 + 1.49606i) q^{25} +(-0.617548 - 0.556043i) q^{26} +(0.779721 - 4.92297i) q^{27} +(0.663546 + 2.56119i) q^{28} +(-1.03617 + 0.336673i) q^{29} +(1.84118 + 3.56800i) q^{30} +(-1.15676 - 2.59813i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(2.16562 + 5.54755i) q^{33} +0.305644 q^{34} +(5.63226 - 1.81044i) q^{35} +(-0.0692543 + 0.213143i) q^{36} +(-6.67625 + 0.349887i) q^{37} +(-4.65723 + 5.75120i) q^{38} +(-1.48394 + 0.155969i) q^{39} +(0.701918 + 2.12304i) q^{40} +(-2.48856 - 0.808583i) q^{41} +(4.21483 + 2.19180i) q^{42} +(-1.41752 + 1.41752i) q^{43} +(0.707921 + 3.24019i) q^{44} +(0.484714 + 0.127209i) q^{45} +(2.11366 - 0.941061i) q^{46} +(-2.54148 + 3.91354i) q^{47} +(-0.815177 + 1.59987i) q^{48} +(4.20789 - 5.59408i) q^{49} +(4.64921 - 1.83979i) q^{50} +(0.367224 - 0.407844i) q^{51} +(-0.829854 - 0.0434908i) q^{52} +(2.13947 - 5.57351i) q^{53} +(-2.49217 - 4.31656i) q^{54} +(7.14233 - 1.99676i) q^{55} +(2.12748 + 1.57284i) q^{56} +(2.07871 + 13.1244i) q^{57} +(-0.593382 + 0.913728i) q^{58} +(-2.79197 - 0.593451i) q^{59} +(3.67628 + 1.61417i) q^{60} +(2.49687 - 5.60807i) q^{61} +(-2.53403 - 1.29115i) q^{62} +(0.555304 - 0.207892i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(0.00956282 + 1.85813i) q^{65} +(5.17419 + 2.94839i) q^{66} +(14.6897 - 3.93608i) q^{67} +(0.237530 - 0.192348i) q^{68} +(1.28378 - 3.95108i) q^{69} +(3.23774 - 4.95147i) q^{70} +(-9.66390 + 7.02124i) q^{71} +(0.0803144 + 0.209226i) q^{72} +(-7.43643 - 11.4511i) q^{73} +(-4.96823 + 4.47341i) q^{74} +(3.13095 - 8.41427i) q^{75} +7.40041i q^{76} +(5.54021 - 6.80486i) q^{77} +(-1.05508 + 1.05508i) q^{78} +(-5.63261 - 0.592011i) q^{79} +(1.88157 + 1.20818i) q^{80} +(-9.41184 - 2.00055i) q^{81} +(-2.44283 + 0.937716i) q^{82} +(-4.58045 - 0.725472i) q^{83} +(4.65488 - 0.949135i) q^{84} +(-0.459919 - 0.505535i) q^{85} +(-0.209546 + 1.99369i) q^{86} +(0.506322 + 1.88962i) q^{87} +(2.58928 + 2.07259i) q^{88} +(0.908036 + 1.57276i) q^{89} +(0.456749 - 0.206181i) q^{90} +(1.27751 + 1.78937i) q^{91} +(1.05039 - 2.06151i) q^{92} +(-4.76746 + 1.83006i) q^{93} +(0.487768 + 4.64080i) q^{94} +(16.5205 - 0.951079i) q^{95} +(0.373322 + 1.75634i) q^{96} +(11.9252 - 1.88876i) q^{97} +(-0.250323 - 6.99552i) q^{98} +(0.705603 - 0.233689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.777146	−	0.629320i	0.549525	−	0.444997i
$2$	0.777146	−	0.629320i	0.549525	−	0.444997i
$3$	0.0939735	−	1.79312i	0.0542556	−	1.03526i	−0.826875	−	0.562386i	$-0.809884\pi$
$3$	0.0939735	−	1.79312i	0.0542556	−	1.03526i	0.881131	−	0.472873i	$-0.156783\pi$
$4$	0.207912	−	0.978148i	0.103956	−	0.489074i
$5$	−2.21031	−	0.338427i	−0.988480	−	0.151349i
$5$	−2.21031	−	0.338427i	−0.988480	−	0.151349i
$6$	−1.05542	−	1.45266i	−0.430872	−	0.593044i
$7$	−2.36727	+	1.18155i	−0.894742	+	0.446583i
$7$	−2.36727	+	1.18155i	−0.894742	+	0.446583i
$8$	−0.453990	−	0.891007i	−0.160510	−	0.315018i
$9$	−0.222884	−	0.0234260i	−0.0742946	−	0.00780868i
$10$	−1.93071	+	1.12799i	−0.610545	+	0.356700i
$11$	−3.02220	+	1.36613i	−0.911228	+	0.411902i
$11$	−3.02220	+	1.36613i	−0.911228	+	0.411902i
$12$	−1.73440	−	0.464731i	−0.500678	−	0.134156i
$13$	−0.129996	−	0.820762i	−0.0360544	−	0.227638i	0.963081	−	0.269212i	$-0.0867631\pi$
$13$	−0.129996	−	0.820762i	−0.0360544	−	0.227638i	−0.999135	+	0.0415730i	$0.986763\pi$
$14$	−1.09614	+	2.40800i	−0.292955	+	0.643566i
$15$	−0.814552	+	3.93155i	−0.210316	+	1.01512i
$16$	−0.913545	−	0.406737i	−0.228386	−	0.101684i
$17$	0.237530	+	0.192348i	0.0576094	+	0.0466512i	0.657693	−	0.753286i	$-0.271533\pi$
$17$	0.237530	+	0.192348i	0.0576094	+	0.0466512i	−0.600083	+	0.799938i	$0.704866\pi$
$18$	−0.187956	+	0.122060i	−0.0443016	+	0.0287698i
$19$	−7.23869	+	1.53863i	−1.66067	+	0.352986i	−0.940232	−	0.340534i	$-0.889392\pi$
$19$	−7.23869	+	1.53863i	−1.66067	+	0.352986i	−0.720438	+	0.693520i	$0.756059\pi$
$20$	−0.790581	+	2.09165i	−0.176779	+	0.467706i
$21$	1.89620	+	4.35583i	0.413784	+	0.950519i
$22$	−1.48896	+	2.96361i	−0.317448	+	0.631844i
$23$	2.23485	+	0.598826i	0.465998	+	0.124864i	0.484176	−	0.874971i	$-0.339120\pi$
$23$	2.23485	+	0.598826i	0.465998	+	0.124864i	−0.0181772	+	0.999835i	$0.505786\pi$
$24$	−1.64034	+	0.730329i	−0.334834	+	0.149078i
$25$	4.77093	+	1.49606i	0.954187	+	0.299212i
$26$	−0.617548	−	0.556043i	−0.121111	−	0.109049i
$27$	0.779721	−	4.92297i	0.150057	−	0.947426i
$28$	0.663546	+	2.56119i	0.125399	+	0.484020i
$29$	−1.03617	+	0.336673i	−0.192412	+	0.0625186i	−0.403638	−	0.914919i	$-0.632255\pi$
$29$	−1.03617	+	0.336673i	−0.192412	+	0.0625186i	0.211226	+	0.977437i	$0.432255\pi$
$30$	1.84118	+	3.56800i	0.336151	+	0.651425i
$31$	−1.15676	−	2.59813i	−0.207761	−	0.466638i	0.779368	−	0.626566i	$-0.215540\pi$
$31$	−1.15676	−	2.59813i	−0.207761	−	0.466638i	−0.987129	+	0.159929i	$0.948874\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	2.16562	+	5.54755i	0.376986	+	0.965705i
$34$	0.305644			0.0524175
$35$	5.63226	−	1.81044i	0.952025	−	0.306020i
$36$	−0.0692543	+	0.213143i	−0.0115424	+	0.0355238i
$37$	−6.67625	+	0.349887i	−1.09757	+	0.0575211i	−0.592509	−	0.805564i	$-0.701863\pi$
$37$	−6.67625	+	0.349887i	−1.09757	+	0.0575211i	−0.505059	+	0.863085i	$0.668529\pi$
$38$	−4.65723	+	5.75120i	−0.755502	+	0.932968i
$39$	−1.48394	+	0.155969i	−0.237621	+	0.0249750i
$40$	0.701918	+	2.12304i	0.110983	+	0.335683i
$41$	−2.48856	−	0.808583i	−0.388648	−	0.126279i	0.108174	−	0.994132i	$-0.465500\pi$
$41$	−2.48856	−	0.808583i	−0.388648	−	0.126279i	−0.496822	+	0.867853i	$0.665500\pi$
$42$	4.21483	+	2.19180i	0.650363	+	0.338201i
$43$	−1.41752	+	1.41752i	−0.216170	+	0.216170i	−0.806882	−	0.590712i	$-0.798847\pi$
$43$	−1.41752	+	1.41752i	−0.216170	+	0.216170i	0.590712	+	0.806882i	$0.298847\pi$
$44$	0.707921	+	3.24019i	0.106723	+	0.488477i
$45$	0.484714	+	0.127209i	0.0722569	+	0.0189632i
$46$	2.11366	−	0.941061i	0.311642	−	0.138752i
$47$	−2.54148	+	3.91354i	−0.370713	+	0.570849i	−0.973964	−	0.226703i	$-0.927205\pi$
$47$	−2.54148	+	3.91354i	−0.370713	+	0.570849i	0.603250	+	0.797552i	$0.293872\pi$
$48$	−0.815177	+	1.59987i	−0.117661	+	0.230922i
$49$	4.20789	−	5.59408i	0.601127	−	0.799154i
$50$	4.64921	−	1.83979i	0.657498	−	0.260186i
$51$	0.367224	−	0.407844i	0.0514217	−	0.0571096i
$52$	−0.829854	−	0.0434908i	−0.115080	−	0.00603109i
$53$	2.13947	−	5.57351i	0.293879	−	0.765581i	−0.704556	−	0.709649i	$-0.748854\pi$
$53$	2.13947	−	5.57351i	0.293879	−	0.765581i	0.998435	−	0.0559321i	$-0.0178130\pi$
$54$	−2.49217	−	4.31656i	−0.339141	−	0.587409i
$55$	7.14233	−	1.99676i	0.963072	−	0.269244i
$56$	2.12748	+	1.57284i	0.284297	+	0.210179i
$57$	2.07871	+	13.1244i	0.275331	+	1.73837i
$58$	−0.593382	+	0.913728i	−0.0779149	+	0.119978i
$59$	−2.79197	−	0.593451i	−0.363483	−	0.0772607i	0.0225498	−	0.999746i	$-0.492822\pi$
$59$	−2.79197	−	0.593451i	−0.363483	−	0.0772607i	−0.386033	+	0.922485i	$0.626155\pi$
$60$	3.67628	+	1.61417i	0.474606	+	0.208388i
$61$	2.49687	−	5.60807i	0.319692	−	0.718039i	−0.680196	−	0.733030i	$-0.738105\pi$
$61$	2.49687	−	5.60807i	0.319692	−	0.718039i	0.999888	+	0.0149910i	$0.00477195\pi$
$62$	−2.53403	−	1.29115i	−0.321822	−	0.163976i
$63$	0.555304	−	0.207892i	0.0699617	−	0.0261920i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	0.00956282	+	1.85813i	0.00118612	+	0.230473i
$66$	5.17419	+	2.94839i	0.636899	+	0.362921i
$67$	14.6897	−	3.93608i	1.79463	−	0.480869i	0.801510	−	0.597981i	$-0.204030\pi$
$67$	14.6897	−	3.93608i	1.79463	−	0.480869i	0.993119	+	0.117112i	$0.0373637\pi$
$68$	0.237530	−	0.192348i	0.0288047	−	0.0233256i
$69$	1.28378	−	3.95108i	0.154549	−	0.475654i
$70$	3.23774	−	4.95147i	0.386984	−	0.591814i
$71$	−9.66390	+	7.02124i	−1.14689	+	0.833268i	−0.988065	−	0.154038i	$-0.950772\pi$
$71$	−9.66390	+	7.02124i	−1.14689	+	0.833268i	−0.158830	+	0.987306i	$0.550772\pi$
$72$	0.0803144	+	0.209226i	0.00946514	+	0.0246575i
$73$	−7.43643	−	11.4511i	−0.870368	−	1.34025i	−0.939467	−	0.342639i	$-0.888679\pi$
$73$	−7.43643	−	11.4511i	−0.870368	−	1.34025i	0.0690994	−	0.997610i	$-0.477987\pi$
$74$	−4.96823	+	4.47341i	−0.577545	+	0.520023i
$75$	3.13095	−	8.41427i	0.361531	−	0.971596i
$76$			7.40041i			0.848885i
$77$	5.54021	−	6.80486i	0.631365	−	0.775486i
$78$	−1.05508	+	1.05508i	−0.119465	+	0.119465i
$79$	−5.63261	−	0.592011i	−0.633718	−	0.0666065i	−0.217778	−	0.975998i	$-0.569881\pi$
$79$	−5.63261	−	0.592011i	−0.633718	−	0.0666065i	−0.415940	+	0.909392i	$0.636547\pi$
$80$	1.88157	+	1.20818i	0.210366	+	0.135079i
$81$	−9.41184	−	2.00055i	−1.04576	−	0.222283i
$82$	−2.44283	+	0.937716i	−0.269766	+	0.103553i
$83$	−4.58045	−	0.725472i	−0.502770	−	0.0796309i	−0.100102	−	0.994977i	$-0.531917\pi$
$83$	−4.58045	−	0.725472i	−0.502770	−	0.0796309i	−0.402668	+	0.915346i	$0.631917\pi$
$84$	4.65488	−	0.949135i	0.507889	−	0.103559i
$85$	−0.459919	−	0.505535i	−0.0498852	−	0.0548330i
$86$	−0.209546	+	1.99369i	−0.0225959	+	0.214986i
$87$	0.506322	+	1.88962i	0.0542834	+	0.202589i
$88$	2.58928	+	2.07259i	0.276018	+	0.220939i
$89$	0.908036	+	1.57276i	0.0962516	+	0.166713i	0.910130	−	0.414322i	$-0.135981\pi$
$89$	0.908036	+	1.57276i	0.0962516	+	0.166713i	−0.813879	+	0.581035i	$0.802648\pi$
$90$	0.456749	−	0.206181i	0.0481455	−	0.0217334i
$91$	1.27751	+	1.78937i	0.133919	+	0.187576i
$92$	1.05039	−	2.06151i	0.109511	−	0.214927i
$93$	−4.76746	+	1.83006i	−0.494363	+	0.189768i
$94$	0.487768	+	4.64080i	0.0503094	+	0.478662i
$95$	16.5205	−	0.951079i	1.69496	−	0.0975787i
$96$	0.373322	+	1.75634i	0.0381020	+	0.179256i
$97$	11.9252	−	1.88876i	1.21082	−	0.191775i	0.481807	−	0.876278i	$-0.339981\pi$
$97$	11.9252	−	1.88876i	1.21082	−	0.191775i	0.729010	+	0.684503i	$0.239981\pi$
$98$	−0.250323	−	6.99552i	−0.0252865	−	0.706655i
$99$	0.705603	−	0.233689i	0.0709157	−	0.0234866i
$100$	2.45530	−	4.35563i	0.245530	−	0.435563i
$101$	−4.49227	−	10.0898i	−0.446998	−	1.00397i	−0.986765	−	0.162159i	$-0.948154\pi$
$101$	−4.49227	−	10.0898i	−0.446998	−	1.00397i	0.539767	−	0.841815i	$-0.318512\pi$
$102$	0.0287224	−	0.548056i	0.00284394	−	0.0542656i
$103$	−14.0353	+	0.735557i	−1.38293	+	0.0724765i	−0.729228	−	0.684271i	$-0.760120\pi$
$103$	−14.0353	+	0.735557i	−1.38293	+	0.0724765i	−0.653707	+	0.756748i	$0.726787\pi$
$104$	−0.672288	+	0.488445i	−0.0659232	+	0.0478960i
$105$	−2.71705	−	10.2694i	−0.265157	−	1.00220i
$106$	−1.84484	−	5.67785i	−0.179187	−	0.551481i
$107$	12.3840	+	8.04228i	1.19721	+	0.777477i	0.980068	−	0.198664i	$-0.0636601\pi$
$107$	12.3840	+	8.04228i	1.19721	+	0.777477i	0.217141	+	0.976140i	$0.430327\pi$
$108$	−4.65328	−	1.78623i	−0.447762	−	0.171880i
$109$	−15.5164	−	8.95842i	−1.48621	−	0.858061i	−0.486329	−	0.873776i	$-0.661664\pi$
$109$	−15.5164	−	8.95842i	−1.48621	−	0.858061i	−0.999877	+	0.0157152i	$0.994998\pi$
$110$	4.29403	−	6.04659i	0.409420	−	0.576520i
$111$			12.0042i			1.13939i
$112$	2.64318	−	0.116545i	0.249757	−	0.0110124i
$113$	2.94229	+	5.77456i	0.276787	+	0.543225i	0.986992	−	0.160770i	$-0.0513977\pi$
$113$	2.94229	+	5.77456i	0.276787	+	0.543225i	−0.710205	+	0.703995i	$0.751398\pi$
$114$	9.87493	+	8.89143i	0.924872	+	0.832759i
$115$	−4.73705	−	2.07993i	−0.441732	−	0.193954i
$116$	0.113883	+	1.08353i	0.0105738	+	0.100603i
$117$	0.00974679	+	0.185980i	0.000901091	+	0.0171938i
$118$	−2.54324	+	1.29584i	−0.234124	+	0.119292i
$119$	−0.789564	−	0.174685i	−0.0723792	−	0.0160134i
$120$	3.87283	−	1.05911i	0.353540	−	0.0966835i
$121$	7.26740	−	8.25741i	0.660673	−	0.750674i
$122$	−1.58884	−	5.92962i	−0.143847	−	0.536843i
$123$	−1.68374	+	4.38631i	−0.151818	+	0.395500i
$124$	−2.78186	+	0.591302i	−0.249818	+	0.0531005i
$125$	−10.0389	−	4.92137i	−0.897909	−	0.440180i
$126$	0.300721	−	0.511027i	0.0267904	−	0.0455259i
$127$	−5.99086	−	0.948858i	−0.531603	−	0.0841976i	−0.115138	−	0.993350i	$-0.536731\pi$
$127$	−5.99086	−	0.948858i	−0.531603	−	0.0841976i	−0.416465	+	0.909152i	$0.636731\pi$
$128$	0.0523360	+	0.998630i	0.00462589	+	0.0882672i
$129$	2.40858	+	2.67499i	0.212063	+	0.235520i
$130$	1.17679	+	1.43802i	0.103212	+	0.126123i
$131$	−18.6884	+	10.7897i	−1.63281	+	0.942704i	−0.649590	+	0.760285i	$0.725059\pi$
$131$	−18.6884	+	10.7897i	−1.63281	+	0.942704i	−0.983221	+	0.182419i	$0.941607\pi$
$132$	5.87658	−	0.964896i	0.511491	−	0.0839834i
$133$	15.3179	−	12.1952i	1.32823	−	1.05746i
$134$	8.93896	−	12.3034i	0.772208	−	1.06285i
$135$	−3.38949	+	10.6174i	−0.291721	+	0.913800i
$136$	0.0635469	−	0.298965i	0.00544910	−	0.0256360i
$137$	3.77246	−	4.65859i	0.322303	−	0.398011i	−0.590083	−	0.807343i	$-0.700905\pi$
$137$	3.77246	−	4.65859i	0.322303	−	0.398011i	0.912385	+	0.409332i	$0.134238\pi$
$138$	−1.48881	−	3.87848i	−0.126736	−	0.330158i
$139$	−5.24545	−	16.1438i	−0.444913	−	1.36930i	−0.882579	−	0.470165i	$-0.844195\pi$
$139$	−5.24545	−	16.1438i	−0.444913	−	1.36930i	0.437665	−	0.899138i	$-0.355805\pi$
$140$	−0.599865	−	5.88559i	−0.0506979	−	0.497423i
$141$	6.77862	+	4.92495i	0.570863	+	0.414756i
$142$	−3.09166	+	11.5382i	−0.259446	+	0.968266i
$143$	1.51414	+	2.30292i	0.126619	+	0.192580i
$144$	0.194086	+	0.112056i	0.0161739	+	0.00933798i
$145$	2.40420	−	0.393482i	0.199658	−	0.0326769i
$146$	−12.9856	−	4.21927i	−1.07470	−	0.349190i
$147$	−9.63542	−	8.07094i	−0.794716	−	0.665680i
$148$	−1.04583	+	6.60310i	−0.0859666	+	0.542771i
$149$	−9.33153	+	20.9589i	−0.764468	+	1.71702i	−0.0699484	+	0.997551i	$0.522283\pi$
$149$	−9.33153	+	20.9589i	−0.764468	+	1.71702i	−0.694520	+	0.719473i	$0.744383\pi$
$150$	−2.86206	−	8.50949i	−0.233686	−	0.694797i
$151$	−1.46876	−	1.63123i	−0.119526	−	0.132747i	0.680412	−	0.732830i	$-0.261801\pi$
$151$	−1.46876	−	1.63123i	−0.119526	−	0.132747i	−0.799938	+	0.600083i	$0.795134\pi$
$152$	4.65723	+	5.75120i	0.377751	+	0.466484i
$153$	−0.0484356	−	0.0484356i	−0.00391579	−	0.00391579i
$154$	0.0231145	−	8.77493i	0.00186262	−	0.707104i
$155$	1.67752	+	6.13415i	0.134742	+	0.492707i
$156$	−0.155969	+	1.48394i	−0.0124875	+	0.118810i
$157$	15.8037	+	0.828238i	1.26127	+	0.0661006i	0.671217	−	0.741261i	$-0.265772\pi$
$157$	15.8037	+	0.828238i	1.26127	+	0.0661006i	0.590057	+	0.807361i	$0.299105\pi$
$158$	−4.74992	+	3.08464i	−0.377884	+	0.245401i
$159$	−9.79292	−	4.36009i	−0.776629	−	0.345778i
$160$	2.22259	−	0.245174i	0.175711	−	0.0193827i
$161$	−5.99802	+	1.22300i	−0.472710	+	0.0963861i
$162$	−8.57336	+	4.36835i	−0.673587	+	0.343210i
$163$	2.16365	+	2.67189i	0.169470	+	0.209278i	0.854804	−	0.518951i	$-0.173677\pi$
$163$	2.16365	+	2.67189i	0.169470	+	0.209278i	−0.685334	+	0.728229i	$0.740344\pi$
$164$	−1.30831	+	2.26607i	−0.102162	+	0.176950i
$165$	−2.90925	−	12.9947i	−0.226485	−	1.01164i
$166$	−4.01623	+	2.31877i	−0.311720	+	0.179972i
$167$	20.2529	−	3.20774i	1.56722	−	0.248223i	0.688382	−	0.725349i	$-0.258321\pi$
$167$	20.2529	−	3.20774i	1.56722	−	0.248223i	0.878835	+	0.477126i	$0.158321\pi$
$168$	3.02021	−	3.66703i	0.233014	−	0.282917i
$169$	11.7070	−	3.80383i	0.900537	−	0.292602i
$170$	−0.675567	−	0.103438i	−0.0518136	−	0.00793335i
$171$	1.64943	−	0.173362i	0.126135	−	0.0132573i
$172$	1.09183	+	1.68126i	0.0832509	+	0.128195i
$173$	−8.21627	−	5.33571i	−0.624671	−	0.405666i	0.193125	−	0.981174i	$-0.438138\pi$
$173$	−8.21627	−	5.33571i	−0.624671	−	0.405666i	−0.817796	+	0.575508i	$0.804804\pi$
$174$	1.58266	+	1.14987i	0.119981	+	0.0871716i
$175$	−13.0617	+	2.09552i	−0.987374	+	0.158407i
$176$	3.31657	−	0.0187778i	0.249996	−	0.00141543i
$177$	−1.32650	+	4.95056i	−0.0997058	+	0.372107i
$178$	1.69545	+	0.650822i	0.127079	+	0.0487812i
$179$	9.50178	−	8.55545i	0.710197	−	0.639464i	−0.232700	−	0.972549i	$-0.574756\pi$
$179$	9.50178	−	8.55545i	0.710197	−	0.639464i	0.942897	+	0.333084i	$0.108089\pi$
$180$	0.225207	−	0.447674i	0.0167859	−	0.0333676i
$181$	7.08946	+	9.75780i	0.526955	+	0.725292i	0.986663	−	0.162779i	$-0.0520457\pi$
$181$	7.08946	+	9.75780i	0.526955	+	0.725292i	−0.459707	+	0.888070i	$0.652046\pi$
$182$	2.11889	+	0.586638i	0.157063	+	0.0434845i
$183$	−9.82130	−	5.00420i	−0.726011	−	0.369921i
$184$	−0.481042	−	2.26313i	−0.0354629	−	0.166840i
$185$	14.8750	+	1.48607i	1.09363	+	0.109258i
$186$	−2.55332	+	4.42248i	−0.187219	+	0.324272i
$187$	−0.980634	−	0.256818i	−0.0717111	−	0.0187804i
$188$	3.29962	+	3.29962i	0.240649	+	0.240649i
$189$	3.97092	+	12.5752i	0.288842	+	0.914715i
$190$	12.2403	−	11.1358i	0.888003	−	0.807875i
$191$	6.44974	−	7.16316i	0.466687	−	0.518308i	−0.463150	−	0.886280i	$-0.653281\pi$
$191$	6.44974	−	7.16316i	0.466687	−	0.518308i	0.929837	+	0.367972i	$0.119948\pi$
$192$	1.39543	+	1.13000i	0.100706	+	0.0815504i
$193$	7.69431	+	6.23073i	0.553848	+	0.448497i	0.864935	−	0.501884i	$-0.167360\pi$
$193$	7.69431	+	6.23073i	0.553848	+	0.448497i	−0.311087	+	0.950382i	$0.600693\pi$
$194$	8.07896	−	8.97259i	0.580035	−	0.644194i
$195$	3.33275	+	0.157468i	0.238663	+	0.0112765i
$196$	−4.59696	−	5.27901i	−0.328354	−	0.377072i
$197$	−11.3172	−	11.3172i	−0.806320	−	0.806320i	0.177755	−	0.984075i	$-0.443117\pi$
$197$	−11.3172	−	11.3172i	−0.806320	−	0.806320i	−0.984075	+	0.177755i	$0.943117\pi$
$198$	0.401291	−	0.625661i	0.0285185	−	0.0444638i
$199$	4.89332	−	8.47548i	0.346878	−	0.600811i	−0.638815	−	0.769360i	$-0.720575\pi$
$199$	4.89332	−	8.47548i	0.346878	−	0.600811i	0.985693	+	0.168550i	$0.0539084\pi$
$200$	−0.832961	−	4.93013i	−0.0588992	−	0.348613i
$201$	−5.67743	−	26.7102i	−0.400455	−	1.88399i
$202$	−9.84087	−	5.01418i	−0.692401	−	0.352796i
$203$	2.05510	−	2.02128i	0.144240	−	0.141866i
$204$	−0.322581	−	0.443995i	−0.0225852	−	0.0310859i
$205$	5.22684	+	2.62942i	0.365059	+	0.183646i
$206$	−10.4445	+	9.40431i	−0.727706	+	0.655229i
$207$	−0.484084	−	0.185822i	−0.0336461	−	0.0129155i
$208$	−0.215077	+	0.802678i	−0.0149129	+	0.0556557i
$209$	19.7748	−	14.5390i	1.36785	−	1.00568i
$210$	−8.57432	−	6.27096i	−0.591684	−	0.432737i
$211$	−19.1874	−	13.9405i	−1.32092	−	0.959702i	−0.999920	−	0.0126216i	$-0.995982\pi$
$211$	−19.1874	−	13.9405i	−1.32092	−	0.959702i	−0.320996	−	0.947080i	$-0.604018\pi$
$212$	−5.00690	−	3.25152i	−0.343875	−	0.223315i
$213$	11.6818	+	17.9884i	0.800422	+	1.23254i
$214$	14.6854	−	1.54349i	1.00387	−	0.105511i
$215$	3.61289	−	2.65343i	0.246397	−	0.180962i
$216$	−4.74038	+	1.54024i	−0.322542	+	0.104800i
$217$	5.80818	+	4.78369i	0.394285	+	0.324738i
$218$	−17.6963	+	2.80281i	−1.19854	+	0.189830i
$219$	−21.2320	+	12.2583i	−1.43473	+	0.828340i
$220$	−0.468155	−	7.40141i	−0.0315630	−	0.499003i
$221$	0.126994	−	0.219960i	0.00854254	−	0.0147961i
$222$	7.55448	+	9.32901i	0.507024	+	0.626122i
$223$	−6.79358	+	3.46150i	−0.454932	+	0.231799i	−0.666413	−	0.745583i	$-0.732171\pi$
$223$	−6.79358	+	3.46150i	−0.454932	+	0.231799i	0.211481	+	0.977382i	$0.432171\pi$
$224$	1.98080	−	1.75398i	0.132347	−	0.117193i
$225$	−1.02832	−	0.445211i	−0.0685545	−	0.0296807i
$226$	5.92063	+	2.63604i	0.393835	+	0.175347i
$227$	11.7951	−	7.65984i	0.782870	−	0.508402i	−0.0902430	−	0.995920i	$-0.528764\pi$
$227$	11.7951	−	7.65984i	0.782870	−	0.508402i	0.873113	+	0.487518i	$0.162098\pi$
$228$	13.2698	+	0.695442i	0.878816	+	0.0460568i
$229$	−0.130533	+	1.24194i	−0.00862586	+	0.0820696i	−0.997988	−	0.0634046i	$-0.979804\pi$
$229$	−0.130533	+	1.24194i	−0.00862586	+	0.0820696i	0.989362	+	0.145474i	$0.0464708\pi$
$230$	−4.99032	+	1.36472i	−0.329052	+	0.0899867i
$231$	−11.6813	−	10.5737i	−0.768573	−	0.695701i
$232$	0.770390	+	0.770390i	0.0505786	+	0.0505786i
$233$	3.49449	+	4.31534i	0.228932	+	0.282707i	0.878649	−	0.477469i	$-0.158446\pi$
$233$	3.49449	+	4.31534i	0.228932	+	0.282707i	−0.649717	+	0.760177i	$0.725112\pi$
$234$	0.124616	+	0.138400i	0.00814638	+	0.00904747i
$235$	6.94191	−	7.79003i	0.452841	−	0.508165i
$236$	−1.16097	+	2.60757i	−0.0755724	+	0.169738i
$237$	−1.59086	+	10.0443i	−0.103338	+	0.652448i
$238$	−0.723540	+	0.361133i	−0.0469001	+	0.0234088i
$239$	12.5553	+	4.07946i	0.812134	+	0.263878i	0.685501	−	0.728071i	$-0.259583\pi$
$239$	12.5553	+	4.07946i	0.812134	+	0.263878i	0.126632	+	0.991950i	$0.459583\pi$
$240$	2.34323	−	3.26034i	0.151255	−	0.210454i
$241$	20.2407	+	11.6859i	1.30382	+	0.752758i	0.981056	−	0.193723i	$-0.0620564\pi$
$241$	20.2407	+	11.6859i	1.30382	+	0.752758i	0.322759	+	0.946481i	$0.395390\pi$
$242$	0.451273	−	10.9907i	0.0290089	−	0.706511i
$243$	−0.601567	+	2.24508i	−0.0385906	+	0.144022i
$244$	−4.96639	−	3.60829i	−0.317940	−	0.230997i
$245$	−11.1939	+	10.9406i	−0.715153	+	0.698968i
$246$	1.45188	+	4.46841i	0.0925682	+	0.284896i
$247$	2.20385	+	5.74123i	0.140228	+	0.365306i
$248$	−1.78979	+	2.21021i	−0.113652	+	0.140348i
$249$	−1.73130	+	8.14513i	−0.109717	+	0.516176i
$250$	−10.8988	+	2.49308i	−0.689303	+	0.157676i
$251$	−7.82203	+	10.7661i	−0.493722	+	0.679550i	−0.981069	−	0.193658i	$-0.937965\pi$
$251$	−7.82203	+	10.7661i	−0.493722	+	0.679550i	0.487347	+	0.873208i	$0.337965\pi$
$252$	−0.0878952	−	0.586392i	−0.00553688	−	0.0369393i
$253$	−7.57224	+	1.24331i	−0.476062	+	0.0781664i
$254$	−5.25291	+	3.03277i	−0.329597	+	0.190293i
$255$	−0.949705	+	0.777182i	−0.0594728	+	0.0486691i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	0.403304	+	7.69549i	0.0251574	+	0.480032i	0.981936	+	0.189214i	$0.0605940\pi$
$257$	0.403304	+	7.69549i	0.0251574	+	0.480032i	−0.956778	+	0.290818i	$0.906073\pi$
$258$	3.55524	+	0.563095i	0.221340	+	0.0350568i
$259$	15.3910	−	8.71658i	0.956352	−	0.541622i
$260$	1.81952	+	0.376974i	0.112842	+	0.0233789i
$261$	0.238833	−	0.0507655i	0.0147834	−	0.00314231i
$262$	−7.73339	+	20.1462i	−0.477771	+	1.24463i
$263$	5.04816	+	18.8400i	0.311283	+	1.16172i	0.927401	+	0.374069i	$0.122038\pi$
$263$	5.04816	+	18.8400i	0.311283	+	1.16172i	−0.616118	+	0.787654i	$0.711296\pi$
$264$	3.95973	−	4.44812i	0.243705	−	0.273763i
$265$	−6.61512	+	11.5951i	−0.406364	+	0.712283i
$266$	4.22958	−	19.1174i	0.259332	−	1.17216i
$267$	2.90549	−	1.48042i	0.177813	−	0.0906002i
$268$	−0.795918	−	15.1870i	−0.0486184	−	0.927695i
$269$	0.437542	+	4.16293i	0.0266774	+	0.253818i	0.999730	+	0.0232353i	$0.00739670\pi$
$269$	0.437542	+	4.16293i	0.0266774	+	0.253818i	−0.973053	+	0.230583i	$0.925937\pi$
$270$	4.04762	+	10.3843i	0.246330	+	0.631971i
$271$	17.6530	+	15.8948i	1.07234	+	0.965541i	0.999494	−	0.0318021i	$-0.0101246\pi$
$271$	17.6530	+	15.8948i	1.07234	+	0.965541i	0.0728477	+	0.997343i	$0.476791\pi$
$272$	−0.138759	−	0.272331i	−0.00841352	−	0.0165125i
$273$	3.32860	−	2.12257i	0.201456	−	0.128464i
$274$		−	5.99449i		−	0.362140i
$275$	−16.4625	+	1.99630i	−0.992728	+	0.120382i
$276$	−3.59783	−	2.07721i	−0.216564	−	0.125033i
$277$	17.0910	+	6.56063i	1.02690	+	0.394190i	0.812751	−	0.582611i	$-0.197969\pi$
$277$	17.0910	+	6.56063i	1.02690	+	0.394190i	0.214149	+	0.976801i	$0.431302\pi$
$278$	−14.2361	−	9.24505i	−0.853826	−	0.554481i
$279$	0.196960	+	0.606179i	0.0117917	+	0.0362910i
$280$	−4.17010	−	4.19645i	−0.249211	−	0.250786i
$281$	−0.0831910	+	0.0604418i	−0.00496276	+	0.00360565i	−0.590264	−	0.807210i	$-0.700976\pi$
$281$	−0.0831910	+	0.0604418i	−0.00496276	+	0.00360565i	0.585301	+	0.810816i	$0.300976\pi$
$282$	8.36735	−	0.438514i	0.498268	−	0.0261131i
$283$	0.161487	−	3.08135i	0.00959940	−	0.183167i	−0.989621	−	0.143699i	$-0.954100\pi$
$283$	0.161487	−	3.08135i	0.00959940	−	0.183167i	0.999221	−	0.0394683i	$-0.0125664\pi$
$284$	4.85857	+	10.9125i	0.288303	+	0.647539i
$285$	−0.152915	−	29.7126i	−0.00905789	−	1.76002i
$286$	2.62598	+	0.836825i	0.155277	+	0.0494825i
$287$	6.84646	−	1.02623i	0.404134	−	0.0605762i
$288$	0.221352	−	0.0350588i	0.0130433	−	0.00206586i
$289$	−3.51508	−	16.5371i	−0.206769	−	0.972773i
$290$	1.62079	−	1.81881i	0.0951760	−	0.106804i
$291$	−2.26613	−	21.5607i	−0.132843	−	1.26391i
$292$	−12.7470	+	4.89311i	−0.745960	+	0.286347i
$293$	2.69622	−	5.29162i	0.157515	−	0.309140i	−0.798740	−	0.601677i	$-0.794499\pi$
$293$	2.69622	−	5.29162i	0.157515	−	0.309140i	0.956254	+	0.292537i	$0.0944995\pi$
$294$	−12.5673	−	0.208534i	−0.732942	−	0.0121620i
$295$	5.97027	+	2.25659i	0.347603	+	0.131384i
$296$	3.34270	+	5.78973i	0.194291	+	0.336521i
$297$	4.36892	+	15.9434i	0.253510	+	0.925130i
$298$	5.93794	+	22.1607i	0.343975	+	1.28373i
$299$	0.200972	−	1.91213i	0.0116225	−	0.110581i
$300$	−7.57943	−	4.81196i	−0.437599	−	0.277819i
$301$	1.68078	−	5.03052i	0.0968784	−	0.289954i
$302$	−2.16801	−	0.343379i	−0.124755	−	0.0197592i
$303$	−18.5144	+	7.10701i	−1.06362	+	0.408287i
$304$	7.23869	+	1.53863i	0.415167	+	0.0882466i
$305$	−7.41678	+	11.5506i	−0.424684	+	0.661383i
$306$	−0.0681230	−	0.00716002i	−0.00389434	−	0.000409311i
$307$	−2.62276	+	2.62276i	−0.149689	+	0.149689i	−0.777979	−	0.628290i	$-0.783755\pi$
$307$	−2.62276	+	2.62276i	−0.149689	+	0.149689i	0.628290	+	0.777979i	$0.283755\pi$
$308$	−5.50428	−	6.83395i	−0.313636	−	0.389400i
$309$			25.2360i			1.43563i
$310$	5.16402	+	3.71143i	0.293297	+	0.210795i
$311$	−10.4406	+	9.40073i	−0.592030	+	0.533066i	−0.909771	−	0.415111i	$-0.863743\pi$
$311$	−10.4406	+	9.40073i	−0.592030	+	0.533066i	0.317740	+	0.948178i	$0.397076\pi$
$312$	0.812664	+	1.25139i	0.0460081	+	0.0708462i
$313$	−5.82721	−	15.1804i	−0.329373	−	0.858047i	−0.993850	−	0.110738i	$-0.964679\pi$
$313$	−5.82721	−	15.1804i	−0.329373	−	0.858047i	0.664476	−	0.747309i	$-0.268655\pi$
$314$	12.8030	−	9.30194i	0.722517	−	0.524939i
$315$	−1.29775	+	0.271576i	−0.0731199	+	0.0153016i
$316$	−1.75016	+	5.38644i	−0.0984542	+	0.303011i
$317$	−11.5175	+	9.32671i	−0.646889	+	0.523840i	−0.895670	−	0.444720i	$-0.853303\pi$
$317$	−11.5175	+	9.32671i	−0.646889	+	0.523840i	0.248781	+	0.968560i	$0.419970\pi$
$318$	−10.3544	+	2.77446i	−0.580647	+	0.155584i
$319$	2.67158	−	2.43304i	0.149580	−	0.136224i
$320$	1.57298	−	1.58926i	0.0879323	−	0.0888421i
$321$	15.5845	−	21.4503i	0.869844	−	1.19724i
$322$	−3.89168	+	4.72513i	−0.216875	+	0.263321i
$323$	−2.01536	−	1.02688i	−0.112138	−	0.0571369i
$324$	−3.91366	+	8.79023i	−0.217426	+	0.488346i
$325$	0.607706	−	4.11028i	0.0337095	−	0.227998i
$326$	3.36294	+	0.714816i	0.186256	+	0.0395900i
$327$	−17.5217	+	26.9810i	−0.968950	+	1.49205i
$328$	0.409331	+	2.58441i	0.0226015	+	0.142700i
$329$	1.39233	−	12.2673i	0.0767615	−	0.676317i
$330$	−10.4387	−	8.26793i	−0.574634	−	0.455135i
$331$	−11.5982	−	20.0887i	−0.637497	−	1.10418i	−0.985980	−	0.166862i	$-0.946637\pi$
$331$	−11.5982	−	20.0887i	−0.637497	−	1.10418i	0.348484	−	0.937315i	$-0.386697\pi$
$332$	−1.66195	+	4.32952i	−0.0912113	+	0.237614i
$333$	1.49622	+	0.0784137i	0.0819925	+	0.00429705i
$334$	13.7208	−	15.2385i	0.750767	−	0.833811i
$335$	−33.8008	+	3.72858i	−1.84673	+	0.203714i
$336$	0.0394106	−	4.75050i	0.00215002	−	0.259161i
$337$	−3.09618	+	6.07659i	−0.168660	+	0.331013i	−0.959830	−	0.280583i	$-0.909472\pi$
$337$	−3.09618	+	6.07659i	−0.168660	+	0.331013i	0.791170	+	0.611596i	$0.209472\pi$
$338$	6.70421	−	10.3236i	0.364661	−	0.561528i
$339$	10.6310	−	4.73322i	0.577396	−	0.257073i
$340$	−0.590110	+	0.344762i	−0.0320032	+	0.0186973i
$341$	7.04534	+	6.27179i	0.381526	+	0.339636i
$342$	1.17275	−	1.17275i	0.0634150	−	0.0634150i
$343$	−3.35151	+	18.2145i	−0.180965	+	0.983490i
$344$	1.90656	+	0.619479i	0.102795	+	0.0334001i
$345$	−4.17471	+	8.29864i	−0.224759	+	0.446784i
$346$	−9.74311	+	1.02404i	−0.523793	+	0.0550529i
$347$	1.24783	−	1.54094i	0.0669868	−	0.0827218i	−0.742551	−	0.669789i	$-0.766384\pi$
$347$	1.24783	−	1.54094i	0.0669868	−	0.0827218i	0.809538	+	0.587068i	$0.199718\pi$
$348$	1.95360	−	0.102384i	0.104724	−	0.00548834i
$349$	0.414956	−	1.27710i	0.0222121	−	0.0683618i	−0.939336	−	0.342998i	$-0.888558\pi$
$349$	0.414956	−	1.27710i	0.0222121	−	0.0683618i	0.961548	+	0.274636i	$0.0885575\pi$
$350$	−8.83212	+	9.84854i	−0.472096	+	0.526427i
$351$	−4.14195			−0.221081
$352$	2.56564	−	2.10178i	0.136749	−	0.112025i
$353$	18.8822	−	5.05947i	1.00500	−	0.269289i	0.281461	−	0.959573i	$-0.409181\pi$
$353$	18.8822	−	5.05947i	1.00500	−	0.269289i	0.723538	+	0.690284i	$0.242514\pi$
$354$	2.08461	+	4.68210i	0.110796	+	0.248851i
$355$	23.7364	−	12.2486i	1.25980	−	0.650087i
$356$	1.72719	−	0.561197i	0.0915407	−	0.0297434i
$357$	−0.387430	+	1.39937i	−0.0205050	+	0.0740624i
$358$	2.00016	−	12.6285i	0.105712	−	0.667437i
$359$	10.7857	+	9.71147i	0.569247	+	0.512552i	0.902732	−	0.430203i	$-0.141558\pi$
$359$	10.7857	+	9.71147i	0.569247	+	0.512552i	−0.333485	+	0.942755i	$0.608225\pi$
$360$	−0.106712	−	0.489635i	−0.00562420	−	0.0258060i
$361$	32.6739	−	14.5474i	1.71968	−	0.765651i
$362$	11.6503	+	3.12170i	0.612328	+	0.164073i
$363$	−14.1236	−	13.8073i	−0.741296	−	0.724695i
$364$	2.01587	−	0.877559i	0.105660	−	0.0459966i
$365$	12.5614	+	27.8271i	0.657496	+	1.45654i
$366$	−10.7818	+	2.29175i	−0.563575	+	0.119792i
$367$	−22.6266	+	14.6939i	−1.18110	+	0.767016i	−0.977272	−	0.211990i	$-0.932006\pi$
$367$	−22.6266	+	14.6939i	−1.18110	+	0.767016i	−0.203830	+	0.979006i	$0.565339\pi$
$368$	−1.79807	−	1.45605i	−0.0937310	−	0.0759019i
$369$	0.535718	+	0.238517i	0.0278884	+	0.0124167i
$370$	12.4952	−	8.20624i	0.649597	−	0.426622i
$371$	1.52068	+	15.7219i	0.0789497	+	0.816239i
$372$	0.798855	+	5.04377i	0.0414187	+	0.261507i
$373$	−5.61547	−	1.50466i	−0.290758	−	0.0779084i	0.110492	−	0.993877i	$-0.464757\pi$
$373$	−5.61547	−	1.50466i	−0.290758	−	0.0779084i	−0.401250	+	0.915969i	$0.631424\pi$
$374$	−0.923717	+	0.417548i	−0.0477643	+	0.0215909i
$375$	−9.76800	+	17.5385i	−0.504417	+	0.905686i
$376$	4.64080	+	0.487768i	0.239331	+	0.0251547i
$377$	0.411027	+	0.806685i	0.0211689	+	0.0415464i
$378$	10.9998	+	7.27382i	0.565771	+	0.374125i
$379$	−12.8102	−	17.6317i	−0.658015	−	0.905680i	0.341399	−	0.939918i	$-0.389099\pi$
$379$	−12.8102	−	17.6317i	−0.658015	−	0.905680i	−0.999414	+	0.0342389i	$0.989099\pi$
$380$	2.50450	−	16.3572i	0.128478	−	0.839106i
$381$	−2.26440	+	10.6532i	−0.116009	+	0.545778i
$382$	0.504466	−	9.62578i	0.0258107	−	0.492498i
$383$	−8.07385	+	6.53807i	−0.412554	+	0.334080i	−0.813024	−	0.582230i	$-0.802180\pi$
$383$	−8.07385	+	6.53807i	−0.412554	+	0.334080i	0.400470	+	0.916310i	$0.368847\pi$
$384$	1.79558			0.0916304
$385$	−14.5485	+	13.1659i	−0.741461	+	0.670995i
$386$	9.90072			0.503933
$387$	0.349149	−	0.282735i	0.0177483	−	0.0143723i
$388$	0.631894	−	12.0573i	0.0320796	−	0.612115i
$389$	−6.43045	+	30.2529i	−0.326037	+	1.53388i	0.444085	+	0.895985i	$0.353529\pi$
$389$	−6.43045	+	30.2529i	−0.326037	+	1.53388i	−0.770122	+	0.637897i	$0.779805\pi$
$390$	2.68913	−	1.97499i	0.136170	−	0.100008i
$391$	0.415661	+	0.572108i	0.0210209	+	0.0289327i
$392$	−6.89470	−	1.20960i	−0.348235	−	0.0610939i
$393$	17.5911	+	34.5244i	0.887353	+	1.74153i
$394$	−15.9173	−	1.67298i	−0.801903	−	0.0842834i
$395$	12.2495	+	3.21476i	0.616337	+	0.161752i
$396$	−0.0818794	−	0.738770i	−0.00411459	−	0.0371246i
$397$	−7.13117	−	1.91079i	−0.357903	−	0.0958998i	0.0753870	−	0.997154i	$-0.475981\pi$
$397$	−7.13117	−	1.91079i	−0.357903	−	0.0958998i	−0.433290	+	0.901255i	$0.642647\pi$
$398$	−1.53097	−	9.66615i	−0.0767405	−	0.484520i
$399$	−20.4280	−	28.6129i	−1.02268	−	1.43244i
$400$	−3.74996	−	3.30723i	−0.187498	−	0.165362i
$401$	16.7064	+	7.43816i	0.834277	+	0.371444i	0.778998	−	0.627027i	$-0.215728\pi$
$401$	16.7064	+	7.43816i	0.834277	+	0.371444i	0.0552793	+	0.998471i	$0.482395\pi$
$402$	−21.2215	−	17.1848i	−1.05843	−	0.857101i
$403$	−1.98207	+	1.28717i	−0.0987340	+	0.0641186i
$404$	−10.8033	+	2.29632i	−0.537485	+	0.114246i
$405$	20.1260	+	7.60706i	1.00007	+	0.377998i
$406$	0.325079	−	2.86415i	0.0161334	−	0.142145i
$407$	19.6990	−	10.1780i	0.976442	−	0.504506i
$408$	−0.530108	−	0.142042i	−0.0262443	−	0.00703213i
$409$	−14.4401	+	6.42914i	−0.714016	+	0.317900i	−0.731400	−	0.681949i	$-0.761133\pi$
$409$	−14.4401	+	6.42914i	−0.714016	+	0.317900i	0.0173843	+	0.999849i	$0.494466\pi$
$410$	5.71677	−	1.24592i	0.282331	−	0.0615316i
$411$	−7.99891	−	7.20225i	−0.394557	−	0.355261i
$412$	−2.19861	+	13.8815i	−0.108318	+	0.683892i
$413$	7.31052	−	1.89399i	0.359727	−	0.0931971i
$414$	−0.493145	+	0.160233i	−0.0242368	+	0.00787501i
$415$	9.87870	+	3.15367i	0.484926	+	0.154808i
$416$	0.337995	+	0.759150i	0.0165716	+	0.0372204i
$417$	−29.4408	+	7.88863i	−1.44172	+	0.386308i
$418$	6.21822	−	23.7436i	0.304143	−	1.16134i
$419$	−6.56853			−0.320894			−0.160447	−	0.987044i	$-0.551294\pi$
$419$	−6.56853			−0.320894			−0.160447	+	0.987044i	$0.551294\pi$
$420$	−10.6099	+	0.522541i	−0.517712	+	0.0254974i
$421$	−1.56572	+	4.81878i	−0.0763084	+	0.234853i	−0.981934	−	0.189226i	$-0.939402\pi$
$421$	−1.56572	+	4.81878i	−0.0763084	+	0.234853i	0.905625	+	0.424079i	$0.139402\pi$
$422$	−23.6845	+	1.24125i	−1.15294	+	0.0604231i
$423$	0.658134	−	0.812728i	0.0319996	−	0.0395162i
$424$	−5.93734	+	0.624039i	−0.288342	+	0.0303060i
$425$	0.845475	+	1.27304i	0.0410116	+	0.0617514i
$426$	20.3989	+	6.62800i	0.988329	+	0.321128i
$427$	0.715443	+	16.2260i	0.0346227	+	0.785229i
$428$	10.4413	−	10.4413i	0.504700	−	0.504700i
$429$	4.27170	−	2.49862i	0.206239	−	0.120634i
$430$	1.13788	−	4.33577i	0.0548735	−	0.209089i
$431$	−28.2335	+	12.5704i	−1.35996	+	0.605493i	−0.951603	−	0.307329i	$-0.900565\pi$
$431$	−28.2335	+	12.5704i	−1.35996	+	0.605493i	−0.408357	+	0.912822i	$0.633898\pi$
$432$	−2.71466	+	4.18021i	−0.130609	+	0.201121i
$433$	11.5374	−	22.6434i	0.554451	−	1.08817i	−0.428369	−	0.903604i	$-0.640912\pi$
$433$	11.5374	−	22.6434i	0.554451	−	1.08817i	0.982820	−	0.184568i	$-0.0590885\pi$
$434$	7.52427	+	0.0624221i	0.361177	+	0.00299636i
$435$	−0.479629	−	4.34800i	−0.0229965	−	0.208471i
$436$	−11.9887	+	13.3148i	−0.574155	+	0.637663i
$437$	−17.0988	−	0.896108i	−0.817945	−	0.0428667i
$438$	−8.78597	+	22.8882i	−0.419810	+	1.09364i
$439$	−11.0280	−	19.1010i	−0.526336	−	0.911640i	−0.999529	−	0.0306818i	$-0.990232\pi$
$439$	−11.0280	−	19.1010i	−0.526336	−	0.911640i	0.473193	−	0.880959i	$-0.343101\pi$
$440$	−5.02168	−	5.45735i	−0.239399	−	0.260169i
$441$	−1.06892	+	1.14825i	−0.0509008	+	0.0546788i
$442$	−0.0397325	−	0.250861i	−0.00188988	−	0.0119322i
$443$	6.36511	−	9.80140i	0.302415	−	0.465679i	−0.654493	−	0.756068i	$-0.727118\pi$
$443$	6.36511	−	9.80140i	0.302415	−	0.465679i	0.956909	+	0.290389i	$0.0937847\pi$
$444$	11.7419	+	2.49581i	0.557245	+	0.118446i
$445$	−1.47477	−	3.78360i	−0.0699110	−	0.179360i
$446$	−3.10121	+	6.96543i	−0.146847	+	0.329823i
$447$	36.7050	+	18.7021i	1.73609	+	0.884581i
$448$	0.435551	−	2.60965i	0.0205778	−	0.123295i
$449$	−1.89148	+	2.60340i	−0.0892646	+	0.122862i	−0.851314	−	0.524657i	$-0.824194\pi$
$449$	−1.89148	+	2.60340i	−0.0892646	+	0.122862i	0.762049	+	0.647519i	$0.224194\pi$
$450$	−1.07933	+	0.301147i	−0.0508802	+	0.0141962i
$451$	8.62556	−	0.955988i	0.406162	−	0.0450157i
$452$	6.26011	−	1.67739i	0.294451	−	0.0788978i
$453$	−3.06301	+	2.48038i	−0.143913	+	0.116538i
$454$	4.34604	−	13.3757i	0.203970	−	0.627754i
$455$	−2.21811	−	4.38739i	−0.103987	−	0.205684i
$456$	10.7502	−	7.81051i	0.503426	−	0.365761i
$457$	1.92645	+	5.01858i	0.0901156	+	0.234759i	0.971230	−	0.238145i	$-0.0765392\pi$
$457$	1.92645	+	5.01858i	0.0901156	+	0.234759i	−0.881114	+	0.472904i	$0.843206\pi$
$458$	0.680134	+	1.04731i	0.0317806	+	0.0489378i
$459$	1.13213	−	1.01937i	0.0528433	−	0.0475803i
$460$	−3.01936	+	4.20109i	−0.140778	+	0.195877i
$461$			0.181802i			0.00846736i	0.999991	+	0.00423368i	$0.00134763\pi$
$461$			0.181802i			0.00846736i	−0.999991	+	0.00423368i	$0.998652\pi$
$462$	−15.7323	−	0.866058i	−0.731935	−	0.0402927i
$463$	−15.0897	+	15.0897i	−0.701280	+	0.701280i	−0.964685	−	0.263405i	$-0.915154\pi$
$463$	−15.0897	+	15.0897i	−0.701280	+	0.701280i	0.263405	+	0.964685i	$0.415154\pi$
$464$	1.08353	+	0.113883i	0.0503015	+	0.00528690i
$465$	11.1569	−	2.43155i	0.517389	−	0.112761i
$466$	5.43147	+	1.15449i	0.251608	+	0.0534809i
$467$	−28.1337	+	10.7995i	−1.30187	+	0.499741i	−0.907825	−	0.419350i	$-0.862258\pi$
$467$	−28.1337	+	10.7995i	−1.30187	+	0.499741i	−0.394046	+	0.919091i	$0.628925\pi$
$468$	0.183942	+	0.0291336i	0.00850273	+	0.00134670i
$469$	−30.1237	+	26.6743i	−1.39098	+	1.23171i
$470$	0.492457	−	10.4227i	0.0227153	−	0.480762i
$471$	2.97026	−	28.2601i	0.136862	−	1.30216i
$472$	0.738758	+	2.75708i	0.0340041	+	0.126905i
$473$	2.34752	−	6.22054i	0.107939	−	0.286021i
$474$	5.08476	+	8.80706i	0.233551	+	0.404522i
$475$	−36.8372	−	3.48880i	−1.69021	−	0.160077i
$476$	−0.335028	+	0.735991i	−0.0153560	+	0.0337341i
$477$	−0.607419	+	1.19213i	−0.0278118	+	0.0545837i
$478$	12.3246	−	4.73096i	0.563713	−	0.216389i
$479$	0.775097	+	7.37456i	0.0354151	+	0.336952i	0.997855	+	0.0654584i	$0.0208510\pi$
$479$	0.775097	+	7.37456i	0.0354151	+	0.336952i	−0.962440	+	0.271494i	$0.912482\pi$
$480$	−0.230763	−	4.00840i	−0.0105328	−	0.182958i
$481$	1.15506	+	5.43413i	0.0526662	+	0.247775i
$482$	23.0841	−	3.65617i	1.05145	−	0.166534i
$483$	1.62934	+	10.8701i	0.0741373	+	0.494607i
$484$	−6.56599	−	8.82540i	−0.298454	−	0.401155i
$485$	−26.9975	+	0.138942i	−1.22589	+	0.00630902i
$486$	0.945369	+	2.12333i	0.0428828	+	0.0963163i
$487$	1.32952	−	25.3687i	0.0602462	−	1.14957i	−0.786507	−	0.617581i	$-0.788113\pi$
$487$	1.32952	−	25.3687i	0.0602462	−	1.14957i	0.846754	−	0.531985i	$-0.178554\pi$
$488$	−6.13038	+	0.321280i	−0.277509	+	0.0145436i
$489$	4.99434	−	3.62860i	0.225852	−	0.164091i
$490$	−1.81419	+	15.5470i	−0.0819565	+	0.702341i
$491$	−2.04562	−	6.29576i	−0.0923173	−	0.284123i	0.894228	−	0.447612i	$-0.147725\pi$
$491$	−2.04562	−	6.29576i	−0.0923173	−	0.284123i	−0.986545	+	0.163488i	$0.947725\pi$
$492$	3.94038	+	2.55892i	0.177646	+	0.115365i
$493$	−0.310880	−	0.119336i	−0.0140013	−	0.00537461i
$494$	5.32579	+	3.07484i	0.239618	+	0.138344i
$495$	−1.63869	+	0.277730i	−0.0736535	+	0.0124830i
$496$			2.84401i			0.127700i
$497$	14.5811	−	28.0395i	0.654051	−	1.25774i
$498$	3.78042	+	7.41950i	0.169405	+	0.332476i
$499$	12.6550	+	11.3946i	0.566516	+	0.510094i	0.901875	−	0.431997i	$-0.142191\pi$
$499$	12.6550	+	11.3946i	0.566516	+	0.510094i	−0.335359	+	0.942090i	$0.608858\pi$
$500$	−6.90103	+	8.79635i	−0.308624	+	0.393385i
$501$	−3.84864	−	36.6173i	−0.171944	−	1.63594i
$502$	0.696468	+	13.2894i	0.0310849	+	0.593135i
$503$	−26.4960	+	13.5004i	−1.18140	+	0.601953i	−0.930583	−	0.366081i	$-0.880699\pi$
$503$	−26.4960	+	13.5004i	−1.18140	+	0.601953i	−0.250817	+	0.968035i	$0.580699\pi$
$504$	−0.437336	−	0.400398i	−0.0194805	−	0.0178352i
$505$	6.51464	+	23.8219i	0.289898	+	1.06006i
$506$	−5.10229	+	5.73160i	−0.226825	+	0.254801i
$507$	−5.72058	−	21.3495i	−0.254060	−	0.948164i
$508$	−2.17369	+	5.66266i	−0.0964420	+	0.251240i
$509$	8.76793	−	1.86368i	0.388632	−	0.0826062i	−0.00945199	−	0.999955i	$-0.503009\pi$
$509$	8.76793	−	1.86368i	0.388632	−	0.0826062i	0.398084	+	0.917349i	$0.369675\pi$
$510$	−0.248963	+	1.20165i	−0.0110242	+	0.0532101i
$511$	31.1340	+	18.3213i	1.37729	+	0.810485i
$512$	0.987688	+	0.156434i	0.0436501	+	0.00691349i
$513$	1.93047	+	36.8356i	0.0852323	+	1.62633i
$514$	5.15636	+	5.72671i	0.227437	+	0.252595i
$515$	31.2712	+	3.12411i	1.37797	+	0.137665i
$516$	3.11731	−	1.79978i	0.137232	−	0.0792309i
$517$	2.33449	−	15.2995i	0.102671	−	0.672871i
$518$	6.47556	−	16.4599i	0.284520	−	0.723209i
$519$	−10.3397	+	14.2313i	−0.453861	+	0.624687i
$520$	1.65127	−	0.852095i	0.0724128	−	0.0373668i
$521$	−3.65493	+	17.1951i	−0.160125	+	0.753330i	0.822653	+	0.568543i	$0.192493\pi$
$521$	−3.65493	+	17.1951i	−0.160125	+	0.753330i	−0.982779	+	0.184787i	$0.940840\pi$
$522$	0.153660	−	0.189755i	0.00672553	−	0.00830534i
$523$	4.21621	+	10.9836i	0.184362	+	0.480279i	0.994348	−	0.106170i	$-0.0338587\pi$
$523$	4.21621	+	10.9836i	0.184362	+	0.480279i	−0.809986	+	0.586449i	$0.800525\pi$
$524$	6.66842	+	20.5233i	0.291311	+	0.896564i
$525$	2.53007	+	23.6182i	0.110421	+	1.03078i
$526$	15.7795	+	11.4645i	0.688020	+	0.499876i
$527$	0.224979	−	0.839634i	0.00980025	−	0.0365750i
$528$	0.277999	−	5.94878i	0.0120983	−	0.258887i
$529$	−15.2826	−	8.82343i	−0.664462	−	0.383627i
$530$	2.15614	+	13.1741i	0.0936566	+	0.572248i
$531$	0.608382	+	0.197675i	0.0264015	+	0.00857838i
$532$	−8.74394	−	17.5187i	−0.379098	−	0.759533i
$533$	−0.340151	+	2.14763i	−0.0147336	+	0.0930242i
$534$	1.32633	−	2.97898i	0.0573959	−	0.128913i
$535$	−24.6508	−	21.9670i	−1.06575	−	0.949717i
$536$	−10.1760	−	11.3016i	−0.439538	−	0.488157i
$537$	−14.4480	−	17.8418i	−0.623478	−	0.769932i
$538$	2.95985	+	2.95985i	0.127608	+	0.127608i
$539$	−5.07487	+	22.6549i	−0.218590	+	0.975817i
$540$	9.68067	+	5.52291i	0.416590	+	0.237668i
$541$	1.69733	−	16.1490i	0.0729739	−	0.694300i	−0.895479	−	0.445104i	$-0.853167\pi$
$541$	1.69733	−	16.1490i	0.0729739	−	0.694300i	0.968453	−	0.249197i	$-0.0801665\pi$
$542$	23.7219	+	1.24321i	1.01894	+	0.0534005i
$543$	18.1631	−	11.7953i	0.779455	−	0.506184i
$544$	−0.279219	−	0.124317i	−0.0119714	−	0.00533003i
$545$	31.2643	+	25.0521i	1.33922	+	1.07311i
$546$	1.25103	−	3.74430i	0.0535392	−	0.160241i
$547$	36.4950	−	18.5951i	1.56041	−	0.795071i	0.560952	−	0.827849i	$-0.310435\pi$
$547$	36.4950	−	18.5951i	1.56041	−	0.795071i	0.999463	+	0.0327777i	$0.0104353\pi$
$548$	−3.77246	−	4.65859i	−0.161151	−	0.199005i
$549$	−0.687887	+	1.19146i	−0.0293583	+	0.0508501i
$550$	−11.5375	+	11.9116i	−0.491959	+	0.507913i
$551$	6.98252	−	4.03136i	0.297465	−	0.171742i
$552$	−4.10326	+	0.649893i	−0.174647	+	0.0276613i
$553$	14.0334	−	5.25375i	0.596760	−	0.223412i
$554$	17.4110	−	5.65716i	0.739721	−	0.240350i
$555$	4.06255	−	26.5330i	0.172446	−	1.12626i
$556$	−16.8816	+	1.77433i	−0.715941	+	0.0752485i
$557$	1.26154	+	1.94260i	0.0534532	+	0.0823107i	0.864387	−	0.502828i	$-0.167707\pi$
$557$	1.26154	+	1.94260i	0.0534532	+	0.0823107i	−0.810934	+	0.585138i	$0.801040\pi$
$558$	0.534547	+	0.347139i	0.0226292	+	0.0146956i
$559$	1.34772	+	0.979175i	0.0570024	+	0.0414147i
$560$	−5.88169	−	0.636926i	−0.248547	−	0.0269150i
$561$	−0.552660	+	1.73426i	−0.0233333	+	0.0732206i
$562$	−0.0266143	+	0.0993258i	−0.00112266	+	0.00418981i
$563$	35.6743	+	13.6941i	1.50349	+	0.577137i	0.964245	−	0.265011i	$-0.0853756\pi$
$563$	35.6743	+	13.6941i	1.50349	+	0.577137i	0.539247	+	0.842148i	$0.318709\pi$
$564$	6.22669	−	5.60653i	0.262191	−	0.236078i
$565$	−4.54909	−	13.7593i	−0.191382	−	0.578859i
$566$	−1.81366	−	2.49629i	−0.0762338	−	0.104927i
$567$	24.6441	−	6.38472i	1.03495	−	0.268133i
$568$	10.6433	+	5.42303i	0.446582	+	0.227545i
$569$	−6.49892	−	30.5750i	−0.272449	−	1.28177i	−0.875169	−	0.483818i	$-0.839250\pi$
$569$	−6.49892	−	30.5750i	−0.272449	−	1.28177i	0.602720	−	0.797953i	$-0.294084\pi$
$570$	−18.8176	−	22.9948i	−0.788181	−	0.963145i
$571$	−16.8854	+	29.2463i	−0.706631	+	1.22392i	0.259469	+	0.965751i	$0.416452\pi$
$571$	−16.8854	+	29.2463i	−0.706631	+	1.22392i	−0.966100	+	0.258169i	$0.916881\pi$
$572$	2.56740	−	1.00225i	0.107348	−	0.0419061i
$573$	−12.2383	−	12.2383i	−0.511263	−	0.511263i
$574$	4.67488	−	5.10615i	0.195126	−	0.213126i
$575$	9.76644	+	6.20043i	0.407289	+	0.258576i
$576$	0.149960	−	0.166547i	0.00624833	−	0.00693947i
$577$	4.76695	+	3.86020i	0.198451	+	0.160702i	0.723395	−	0.690434i	$-0.242581\pi$
$577$	4.76695	+	3.86020i	0.198451	+	0.160702i	−0.524944	+	0.851137i	$0.675914\pi$
$578$	−13.1389	−	10.6397i	−0.546505	−	0.442551i
$579$	11.8955	−	13.2113i	0.494360	−	0.549043i
$580$	0.114978	−	2.43347i	0.00477421	−	0.101044i
$581$	11.7003	−	3.69464i	0.485411	−	0.153280i
$582$	−15.3297	−	15.3297i	−0.635438	−	0.635438i
$583$	1.14821	+	19.7671i	0.0475538	+	0.818668i
$584$	−6.82693	+	11.8246i	−0.282500	+	0.489305i
$585$	0.0413973	−	0.414372i	0.00171157	−	0.0171322i
$586$	−1.23477	−	5.80915i	−0.0510080	−	0.239974i
$587$	−32.3934	−	16.5053i	−1.33702	−	0.681245i	−0.368370	−	0.929679i	$-0.620084\pi$
$587$	−32.3934	−	16.5053i	−1.33702	−	0.681245i	−0.968649	+	0.248434i	$0.920084\pi$
$588$	−9.89789	+	7.74682i	−0.408182	+	0.319473i
$589$	12.3710	+	17.0272i	0.509738	+	0.701595i
$590$	6.05989	−	2.00351i	0.249482	−	0.0824834i
$591$	−21.3567	+	19.2297i	−0.878497	+	0.791002i
$592$	6.24137	+	2.39584i	0.256519	+	0.0984683i
$593$	−10.9197	+	40.7528i	−0.448417	+	1.67352i	0.258336	+	0.966055i	$0.416826\pi$
$593$	−10.9197	+	40.7528i	−0.448417	+	1.67352i	−0.706753	+	0.707461i	$0.749841\pi$
$594$	13.4288	+	9.64090i	0.550990	+	0.395571i
$595$	1.68606	+	0.653319i	0.0691218	+	0.0267835i
$596$	18.5608	+	13.4852i	0.760281	+	0.552376i
$597$	−14.7377	−	9.57078i	−0.603174	−	0.391706i
$598$	−1.04715	−	1.61248i	−0.0428213	−	0.0659391i
$599$	−33.0758	+	3.47640i	−1.35144	+	0.142042i	−0.752415	−	0.658689i	$-0.771111\pi$
$599$	−33.0758	+	3.47640i	−1.35144	+	0.142042i	−0.599024	+	0.800731i	$0.704444\pi$
$600$	−8.91859	+	1.03030i	−0.364100	+	0.0420617i
$601$	−19.6352	+	6.37987i	−0.800938	+	0.260240i	−0.680755	−	0.732511i	$-0.738348\pi$
$601$	−19.6352	+	6.37987i	−0.800938	+	0.260240i	−0.120183	+	0.992752i	$0.538348\pi$
$602$	−1.85960	−	4.96719i	−0.0757915	−	0.202448i
$603$	−3.36630	+	0.533169i	−0.137086	+	0.0217123i
$604$	−1.90095	+	1.09752i	−0.0773487	+	0.0446573i
$605$	−18.8577	+	15.7919i	−0.766676	+	0.642034i
$606$	−9.91580	+	17.1747i	−0.402802	+	0.697673i
$607$	2.84840	+	3.51748i	0.115613	+	0.142770i	0.831667	−	0.555275i	$-0.187387\pi$
$607$	2.84840	+	3.51748i	0.115613	+	0.142770i	−0.716054	+	0.698045i	$0.754054\pi$
$608$	6.59381	−	3.35972i	0.267414	−	0.136254i
$609$	−3.43128	−	3.87499i	−0.139042	−	0.157022i
$610$	1.50507	+	13.6440i	0.0609387	+	0.552429i
$611$	3.54247	+	1.57721i	0.143313	+	0.0638070i
$612$	−0.0574475	+	0.0373068i	−0.00232218	+	0.00150804i
$613$	3.18100	+	0.166709i	0.128479	+	0.00673332i	0.116467	−	0.993195i	$-0.462843\pi$
$613$	3.18100	+	0.166709i	0.128479	+	0.00673332i	0.0120121	+	0.999928i	$0.496176\pi$
$614$	−0.387711	+	3.68882i	−0.0156467	+	0.148869i
$615$	5.20604	−	9.12527i	0.209928	−	0.367966i
$616$	−8.57837	−	1.84702i	−0.345633	−	0.0744186i
$617$	−1.26883	−	1.26883i	−0.0510813	−	0.0510813i	0.681105	−	0.732186i	$-0.261500\pi$
$617$	−1.26883	−	1.26883i	−0.0510813	−	0.0510813i	−0.732186	+	0.681105i	$0.761500\pi$
$618$	15.8815	+	19.6121i	0.638849	+	0.788913i
$619$	−0.590301	−	0.655595i	−0.0237262	−	0.0263506i	0.731165	−	0.682201i	$-0.238977\pi$
$619$	−0.590301	−	0.655595i	−0.0237262	−	0.0263506i	−0.754891	+	0.655850i	$0.772310\pi$
$620$	6.34888	−	0.365504i	0.254977	−	0.0146790i
$621$	4.69056	−	10.5352i	0.188226	−	0.422762i
$622$	−2.19777	+	13.8762i	−0.0881227	+	0.556385i
$623$	−4.00786	−	2.65026i	−0.160571	−	0.106180i
$624$	1.41909	+	0.461089i	0.0568089	+	0.0184583i
$625$	20.5236	+	14.2752i	0.820945	+	0.571008i
$626$	−14.0819	−	8.13021i	−0.562827	−	0.324948i
$627$	−24.2119	−	36.8249i	−0.966930	−	1.47065i
$628$	4.09592	−	15.2862i	0.163445	−	0.609985i
$629$	−1.65311	−	1.20105i	−0.0659137	−	0.0478891i
$630$	−0.837633	+	1.02775i	−0.0333721	+	0.0409467i
$631$	−9.11440	−	28.0512i	−0.362838	−	1.11670i	−0.951324	−	0.308194i	$-0.900275\pi$
$631$	−9.11440	−	28.0512i	−0.362838	−	1.11670i	0.588485	−	0.808508i	$-0.299725\pi$
$632$	2.02967	+	5.28746i	0.0807358	+	0.210324i
$633$	−26.8001	+	33.0953i	−1.06521	+	1.31542i
$634$	−3.08131	+	14.4964i	−0.122374	+	0.575727i
$635$	12.9205	+	4.12474i	0.512735	+	0.163685i
$636$	−6.30088	+	8.67241i	−0.249846	+	0.343884i
$637$	−5.13841	−	2.72647i	−0.203591	−	0.108027i
$638$	0.545053	−	3.57211i	0.0215788	−	0.141421i
$639$	2.31841	−	1.33853i	0.0917148	−	0.0529515i
$640$	0.222285	−	2.22499i	0.00878659	−	0.0879505i
$641$	−7.87330	−	8.74419i	−0.310977	−	0.345375i	0.567314	−	0.823502i	$-0.307983\pi$
$641$	−7.87330	−	8.74419i	−0.310977	−	0.345375i	−0.878291	+	0.478127i	$0.841316\pi$
$642$	−1.38764	−	26.4777i	−0.0547656	−	1.04499i
$643$	−40.6043	−	6.43109i	−1.60128	−	0.253617i	−0.709034	−	0.705174i	$-0.750869\pi$
$643$	−40.6043	−	6.43109i	−1.60128	−	0.253617i	−0.892242	+	0.451557i	$0.850869\pi$
$644$	−0.0507823	+	6.12123i	−0.00200110	+	0.241210i
$645$	−4.41841	−	6.72769i	−0.173975	−	0.264903i
$646$	−2.21246	+	0.470273i	−0.0870481	+	0.0185027i
$647$	16.9842	−	44.2454i	0.667718	−	1.73947i	−0.00545895	−	0.999985i	$-0.501738\pi$
$647$	16.9842	−	44.2454i	0.667718	−	1.73947i	0.673177	−	0.739481i	$-0.264929\pi$
$648$	2.49038	+	9.29424i	0.0978316	+	0.365112i
$649$	9.24862	−	2.02065i	0.363040	−	0.0793174i
$650$	−2.11441	−	3.57673i	−0.0829339	−	0.140291i
$651$	9.12355	−	9.96522i	0.357580	−	0.390568i
$652$	3.06335	−	1.56085i	0.119970	−	0.0611277i
$653$	−1.85735	−	35.4403i	−0.0726836	−	1.38689i	−0.754950	−	0.655782i	$-0.772339\pi$
$653$	−1.85735	−	35.4403i	−0.0726836	−	1.38689i	0.682266	−	0.731104i	$-0.260994\pi$
$654$	3.36280	+	31.9949i	0.131496	+	1.25110i
$655$	44.9586	−	17.5240i	1.75668	−	0.684719i
$656$	1.94453	+	1.75087i	0.0759213	+	0.0683598i
$657$	1.38920	+	2.72647i	0.0541980	+	0.106370i
$658$	−6.63800	−	10.4097i	−0.258776	−	0.405812i
$659$		−	39.0846i		−	1.52252i	−0.648446	−	0.761261i	$-0.724581\pi$
$659$		−	39.0846i		−	1.52252i	0.648446	−	0.761261i	$-0.275419\pi$
$660$	−13.3156	+	0.143923i	−0.518309	+	0.00560220i
$661$	17.6935	+	10.2153i	0.688196	+	0.397330i	0.802936	−	0.596065i	$-0.203270\pi$
$661$	17.6935	+	10.2153i	0.688196	+	0.397330i	−0.114740	+	0.993396i	$0.536603\pi$
$662$	−21.6558	−	8.31287i	−0.841675	−	0.323089i
$663$	−0.382481	−	0.248386i	−0.0148543	−	0.00964651i
$664$	1.43308	+	4.41057i	0.0556143	+	0.171163i
$665$	−37.9846	+	21.7712i	−1.47298	+	0.844250i
$666$	1.21213	−	0.880665i	0.0469691	−	0.0341251i
$667$	−2.51730	+	0.131926i	−0.0974702	+	0.00510820i
$668$	1.07317	−	20.4773i	0.0415221	−	0.792289i
$669$	5.56847	+	12.5070i	0.215290	+	0.483548i
$670$	−23.9217	+	24.1692i	−0.924175	+	0.933737i
$671$	0.115273	+	20.3598i	0.00445007	+	0.785979i
$672$	−2.95896	−	3.71663i	−0.114144	−	0.143372i
$673$	−0.812400	+	0.128672i	−0.0313157	+	0.00495992i	−0.172073	−	0.985084i	$-0.555046\pi$
$673$	−0.812400	+	0.128672i	−0.0313157	+	0.00495992i	0.140757	+	0.990044i	$0.455046\pi$
$674$	1.41794	+	6.67089i	0.0546171	+	0.256953i
$675$	11.0850	−	22.3206i	0.426664	−	0.859122i
$676$	−1.28669	−	12.2420i	−0.0494880	−	0.470847i
$677$	5.51096	−	2.11546i	0.211803	−	0.0813037i	−0.250153	−	0.968206i	$-0.580481\pi$
$677$	5.51096	−	2.11546i	0.211803	−	0.0813037i	0.461957	+	0.886903i	$0.347148\pi$
$678$	5.28311	−	10.3687i	0.202897	−	0.398207i
$679$	−25.9984	+	18.5614i	−0.997725	+	0.712319i
$680$	−0.241636	+	0.639298i	−0.00926633	+	0.0245160i
$681$	−12.6266	−	21.8699i	−0.483852	−	0.838056i
$682$	9.42222	+	0.440320i	0.360795	+	0.0168607i
$683$	−1.68279	−	6.28024i	−0.0643900	−	0.240307i	0.926229	−	0.376962i	$-0.123031\pi$
$683$	−1.68279	−	6.28024i	−0.0643900	−	0.240307i	−0.990619	+	0.136655i	$0.956365\pi$
$684$	0.173362	−	1.64943i	0.00662867	−	0.0630676i
$685$	−9.91489	+	9.02023i	−0.378828	+	0.344645i
$686$	8.85813	+	16.2645i	0.338205	+	0.620981i
$687$	2.21468	+	0.350771i	0.0844952	+	0.0133827i
$688$	1.87153	−	0.718412i	0.0713513	−	0.0273892i
$689$	−4.85265	−	1.03146i	−0.184871	−	0.0392956i
$690$	1.97814	+	9.07649i	0.0753066	+	0.345536i
$691$	9.82652	+	1.03281i	0.373819	+	0.0392899i	0.289575	−	0.957155i	$-0.406486\pi$
$691$	9.82652	+	1.03281i	0.373819	+	0.0392899i	0.0842434	+	0.996445i	$0.473153\pi$
$692$	−6.92737	+	6.92737i	−0.263339	+	0.263339i
$693$	−1.39423	+	1.38691i	−0.0529625	+	0.0526843i
$694$		−	1.98281i		−	0.0752666i
$695$	6.13055	+	37.4581i	0.232545	+	1.42087i
$696$	1.45380	−	1.30901i	0.0551061	−	0.0496177i
$697$	−0.435578	−	0.670732i	−0.0164987	−	0.0254058i
$698$	−0.481226	−	1.25364i	−0.0182147	−	0.0474508i
$699$	8.06632	−	5.86052i	0.305096	−	0.221665i
$700$	−0.665957	+	13.2120i	−0.0251708	+	0.499366i
$701$	7.34902	−	22.6180i	0.277569	−	0.854269i	−0.710959	−	0.703233i	$-0.751739\pi$
$701$	7.34902	−	22.6180i	0.277569	−	0.854269i	0.988528	−	0.151036i	$-0.0482609\pi$
$702$	−3.21890	+	2.60661i	−0.121489	+	0.0983802i
$703$	47.7889	−	12.8050i	1.80239	−	0.482950i
$704$	0.671187	−	3.24800i	0.0252963	−	0.122414i
$705$	−13.3161	−	13.1797i	−0.501513	−	0.496378i
$706$	11.4902	−	15.8149i	0.432440	−	0.595202i
$707$	22.5560	+	18.5774i	0.848305	+	0.698676i
$708$	4.56659	+	2.32679i	0.171623	+	0.0874462i
$709$	17.4151	−	39.1149i	0.654037	−	1.46899i	−0.216196	−	0.976350i	$-0.569365\pi$
$709$	17.4151	−	39.1149i	0.654037	−	1.46899i	0.870233	−	0.492641i	$-0.163968\pi$
$710$	10.7384	−	24.4567i	0.403004	−	0.917845i
$711$	1.24155	+	0.263899i	0.0465617	+	0.00989700i
$712$	0.989104	−	1.52309i	0.0370682	−	0.0570801i
$713$	−1.02936	−	6.49913i	−0.0385499	−	0.243394i
$714$	0.579561	+	1.33133i	0.0216895	+	0.0498238i
$715$	−2.56734	−	5.60259i	−0.0960132	−	0.209525i
$716$	−6.39296	−	11.0729i	−0.238916	−	0.413815i
$717$	8.49482	−	22.1298i	0.317245	−	0.826451i
$718$	14.4937	+	0.759582i	0.540899	+	0.0283473i
$719$	−31.8560	+	35.3797i	−1.18803	+	1.31944i	−0.251914	+	0.967750i	$0.581060\pi$
$719$	−31.8560	+	35.3797i	−1.18803	+	1.31944i	−0.936116	+	0.351691i	$0.885607\pi$
$720$	−0.391068	−	0.313362i	−0.0145742	−	0.0116783i
$721$	32.3561	−	18.3246i	1.20500	−	0.682443i
$722$	16.2374	−	31.8678i	0.604295	−	1.18600i
$723$	22.8564	−	35.1958i	0.850038	−	1.30894i
$724$	11.0186	−	4.90577i	0.409501	−	0.182322i
$725$	−5.44719	+	0.0560691i	−0.202304	+	0.00208235i
$726$	−19.6653	−	1.84203i	−0.729848	−	0.0683640i
$727$	25.5825	−	25.5825i	0.948802	−	0.948802i	−0.0499498	−	0.998752i	$-0.515906\pi$
$727$	25.5825	−	25.5825i	0.948802	−	0.948802i	0.998752	+	0.0499498i	$0.0159061\pi$
$728$	1.01436	−	1.95062i	0.0375947	−	0.0722948i
$729$	−23.4843	−	7.63052i	−0.869790	−	0.282612i
$730$	27.2743	+	13.7206i	1.00947	+	0.507822i
$731$	−0.609360	+	0.0640464i	−0.0225380	+	0.00236884i
$732$	−6.93681	+	8.56625i	−0.256392	+	0.316618i
$733$	−14.3807	+	0.753660i	−0.531163	+	0.0278371i	−0.316033	−	0.948748i	$-0.602351\pi$
$733$	−14.3807	+	0.753660i	−0.531163	+	0.0278371i	−0.215130	+	0.976585i	$0.569018\pi$
$734$	−8.33703	+	25.6587i	−0.307725	+	0.947081i
$735$	18.5658	+	21.1002i	0.684811	+	0.778292i
$736$	−2.31369			−0.0852836
$737$	−39.0179	+	31.9636i	−1.43724	+	1.17739i
$738$	0.566435	−	0.151776i	0.0208508	−	0.00558694i
$739$	−12.8543	−	28.8713i	−0.472854	−	1.06205i	−0.979784	−	0.200060i	$-0.935886\pi$
$739$	−12.8543	−	28.8713i	−0.472854	−	1.06205i	0.506929	−	0.861988i	$-0.330780\pi$
$740$	4.54627	−	14.2410i	0.167124	−	0.523508i
$741$	10.5018	−	3.41225i	0.385794	−	0.125352i
$742$	11.0759	+	11.2612i	0.406608	+	0.413411i
$743$	3.03268	−	19.1476i	0.111258	−	0.702457i	−0.867500	−	0.497438i	$-0.834274\pi$
$743$	3.03268	−	19.1476i	0.111258	−	0.702457i	0.978758	−	0.205019i	$-0.0657256\pi$
$744$	3.79498	+	3.41701i	0.139131	+	0.125274i
$745$	27.7186	−	43.1677i	1.01553	−	1.58154i
$746$	−5.31095	+	2.36459i	−0.194448	+	0.0865738i
$747$	1.00391	+	0.268998i	0.0367313	+	0.00984212i
$748$	−0.455092	+	0.905810i	−0.0166398	+	0.0331197i
$749$	−38.8186	−	4.40589i	−1.41840	−	0.160988i
$750$	3.44620	+	19.7772i	0.125837	+	0.722161i
$751$	−31.8493	+	6.76977i	−1.16220	+	0.247032i	−0.748343	−	0.663311i	$-0.769150\pi$
$751$	−31.8493	+	6.76977i	−1.16220	+	0.247032i	−0.413853	+	0.910344i	$0.635817\pi$
$752$	3.91354	−	2.54148i	0.142712	−	0.0926784i
$753$	18.5698	+	15.0376i	0.676723	+	0.547999i
$754$	0.827091	+	0.368245i	0.0301209	+	0.0134107i
$755$	2.69437	+	4.10258i	0.0980581	+	0.149308i
$756$	13.1260	−	1.26960i	0.477390	−	0.0461750i
$757$	−6.73109	−	42.4984i	−0.244646	−	1.54463i	−0.737999	−	0.674802i	$-0.764229\pi$
$757$	−6.73109	−	42.4984i	−0.244646	−	1.54463i	0.493353	−	0.869829i	$-0.335771\pi$
$758$	−21.0514	−	5.64070i	−0.764620	−	0.204879i
$759$	1.51782	+	13.6948i	0.0550933	+	0.497089i
$760$	−8.34755	−	14.2881i	−0.302798	−	0.518282i
$761$	22.3670	+	2.35087i	0.810803	+	0.0852189i	0.500851	−	0.865533i	$-0.333020\pi$
$761$	22.3670	+	2.35087i	0.810803	+	0.0852189i	0.309952	+	0.950752i	$0.399687\pi$
$762$	4.94448	+	9.70409i	0.179120	+	0.351542i
$763$	47.3163	+	2.87353i	1.71297	+	0.104029i
$764$	−5.66565	−	7.79810i	−0.204976	−	0.282125i
$765$	0.0906657	+	0.123450i	0.00327803	+	0.00446333i
$766$	−2.16002	+	10.1621i	−0.0780445	+	0.367171i
$767$	−0.124138	+	2.36869i	−0.00448235	+	0.0855283i
$768$	1.39543	−	1.13000i	0.0503532	−	0.0407752i
$769$	45.9046			1.65536			0.827682	−	0.561198i	$-0.189659\pi$
$769$	45.9046			1.65536			0.827682	+	0.561198i	$0.189659\pi$
$770$	−3.02077	+	19.3875i	−0.108861	+	0.698677i
$771$	13.8368			0.498322
$772$	7.69431	−	6.23073i	0.276924	−	0.224249i
$773$	1.96219	−	37.4408i	0.0705750	−	1.34665i	−0.702203	−	0.711976i	$-0.747800\pi$
$773$	1.96219	−	37.4408i	0.0705750	−	1.34665i	0.772779	−	0.634676i	$-0.218866\pi$
$774$	0.0934087	−	0.439453i	0.00335751	−	0.0157958i
$775$	−1.63188	−	14.1261i	−0.0586188	−	0.507424i
$776$	−7.09681	−	9.76792i	−0.254761	−	0.350648i
$777$	−14.1835	−	28.4171i	−0.508831	−	1.01946i
$778$	14.0414	+	27.5577i	0.503407	+	0.987992i
$779$	19.2580	+	2.02410i	0.689991	+	0.0725210i
$780$	0.846945	−	3.22719i	0.0303255	−	0.115552i
$781$	19.6144	−	34.4217i	0.701857	−	1.23171i
$782$	0.683068	+	0.183027i	0.0244265	+	0.00654505i
$783$	0.849504	+	5.36355i	0.0303588	+	0.191678i
$784$	−6.11941	+	3.39894i	−0.218550	+	0.121391i
$785$	−34.6508	−	7.17908i	−1.23674	−	0.256232i
$786$	35.3978	+	15.7601i	1.26260	+	0.562144i
$787$	−24.2629	−	19.6477i	−0.864880	−	0.700366i	0.0904516	−	0.995901i	$-0.471169\pi$
$787$	−24.2629	−	19.6477i	−0.864880	−	0.700366i	−0.955332	+	0.295534i	$0.904502\pi$
$788$	−13.4229	+	8.71695i	−0.478172	+	0.310528i
$789$	34.2567	−	7.28149i	1.21957	−	0.259228i
$790$	11.5427	−	5.21050i	0.410672	−	0.185381i
$791$	−13.7881	−	10.1935i	−0.490248	−	0.362438i
$792$	−0.528555	−	0.522604i	−0.0187814	−	0.0185699i
$793$	−4.92747	−	1.32031i	−0.174980	−	0.0468857i
$794$	−6.74446	+	3.00283i	−0.239352	+	0.106566i
$795$	20.1698	+	12.9513i	0.715350	+	0.459337i
$796$	−7.27289	−	6.54854i	−0.257781	−	0.232107i
$797$	−5.95075	+	37.5716i	−0.210786	+	1.33085i	0.624494	+	0.781029i	$0.285305\pi$
$797$	−5.95075	+	37.5716i	−0.210786	+	1.33085i	−0.835281	+	0.549824i	$0.814695\pi$
$798$	−33.8822	−	9.38066i	−1.19942	−	0.332072i
$799$	−1.35644	+	0.440734i	−0.0479874	+	0.0155920i
$800$	−4.99558	−	0.210273i	−0.176620	−	0.00743428i
$801$	−0.165543	−	0.371815i	−0.00584917	−	0.0131374i
$802$	17.6643	−	4.73313i	0.623748	−	0.167133i
$803$	38.1180	+	24.4484i	1.34516	+	0.862766i
$804$	−27.3070			−0.963042
$805$	13.6714	−	0.673318i	0.481853	−	0.0237313i
$806$	−0.730315	+	2.24768i	−0.0257243	+	0.0791711i
$807$	7.50576	−	0.393360i	0.264215	−	0.0138469i
$808$	−6.95064	+	8.58332i	−0.244523	+	0.301960i
$809$	−48.2537	+	5.07167i	−1.69651	+	0.178310i	−0.902822	−	0.430014i	$-0.858508\pi$
$809$	−48.2537	+	5.07167i	−1.69651	+	0.178310i	−0.793688	+	0.608325i	$0.791842\pi$
$810$	20.4281	−	6.75393i	0.717772	−	0.237309i
$811$	30.6577	+	9.96128i	1.07654	+	0.349788i	0.793030	−	0.609183i	$-0.208502\pi$
$811$	30.6577	+	9.96128i	1.07654	+	0.349788i	0.283506	+	0.958970i	$0.408502\pi$
$812$	−1.54983	−	2.43044i	−0.0543885	−	0.0852917i
$813$	30.1602	−	30.1602i	1.05777	−	1.05777i
$814$	8.90374	−	20.3068i	0.312076	−	0.711752i
$815$	−3.87810	−	6.63793i	−0.135844	−	0.232517i
$816$	−0.501361	+	0.223220i	−0.0175512	+	0.00781428i
$817$	8.07995	−	12.4420i	0.282682	−	0.435292i
$818$	−7.17606	+	14.0838i	−0.250905	+	0.492429i
$819$	−0.242817	−	0.428747i	−0.00848473	−	0.0149816i
$820$	3.65868	−	4.56594i	0.127767	−	0.159450i
$821$	−5.46942	+	6.07440i	−0.190884	+	0.211998i	−0.830988	−	0.556290i	$-0.812224\pi$
$821$	−5.46942	+	6.07440i	−0.190884	+	0.211998i	0.640104	+	0.768288i	$0.278891\pi$
$822$	−10.7488	−	0.563323i	−0.374909	−	0.0196481i
$823$	18.8431	−	49.0878i	0.656828	−	1.71109i	−0.0452322	−	0.998976i	$-0.514403\pi$
$823$	18.8431	−	49.0878i	0.656828	−	1.71109i	0.702060	−	0.712118i	$-0.252264\pi$
$824$	7.02726	+	12.1716i	0.244806	+	0.424017i
$825$	2.03257	+	29.7069i	0.0707651	+	1.03426i
$826$	4.48941	−	6.07256i	0.156207	−	0.211292i
$827$	2.93037	+	18.5016i	0.101899	+	0.643365i	0.984785	+	0.173778i	$0.0555974\pi$
$827$	2.93037	+	18.5016i	0.101899	+	0.643365i	−0.882886	+	0.469588i	$0.844403\pi$
$828$	−0.282408	+	0.434871i	−0.00981437	+	0.0151128i
$829$	23.5999	+	5.01631i	0.819658	+	0.174224i	0.598611	−	0.801040i	$-0.295719\pi$
$829$	23.5999	+	5.01631i	0.819658	+	0.174224i	0.221046	+	0.975263i	$0.429053\pi$
$830$	9.66186	−	3.76600i	0.335368	−	0.130720i
$831$	13.3701	−	30.0297i	0.463804	−	1.04172i
$832$	0.740420	+	0.377263i	0.0256695	+	0.0130792i
$833$	2.07551	−	0.519382i	0.0719121	−	0.0179955i
$834$	−17.9153	+	24.6583i	−0.620356	+	0.853847i
$835$	−45.8508	+	0.235970i	−1.58673	+	0.00816607i
$836$	−10.1099	−	22.3655i	−0.349658	−	0.773528i
$837$	−13.6925	+	3.66888i	−0.473281	+	0.126815i
$838$	−5.10471	+	4.13371i	−0.176339	+	0.142797i
$839$	11.6519	−	35.8609i	0.402269	−	1.23806i	−0.520885	−	0.853627i	$-0.674398\pi$
$839$	11.6519	−	35.8609i	0.402269	−	1.23806i	0.923154	−	0.384430i	$-0.125602\pi$
$840$	−7.91663	+	7.08314i	−0.273150	+	0.244392i
$841$	−22.5012	+	16.3481i	−0.775903	+	0.563727i
$842$	1.81577	+	4.73023i	0.0625754	+	0.163015i
$843$	0.100562	+	0.154851i	0.00346353	+	0.00533336i
$844$	−17.6251	+	15.8697i	−0.606682	+	0.546259i
$845$	−27.1634	+	4.44567i	−0.934448	+	0.152936i
$846$		−	1.04579i		−	0.0359548i
$847$	−7.44733	+	28.1343i	−0.255893	+	0.966705i
$848$	−4.22146	+	4.22146i	−0.144965	+	0.144965i
$849$	−5.51006	−	0.579131i	−0.189105	−	0.0198757i
$850$	1.45821	+	0.457261i	0.0500161	+	0.0156839i
$851$	−15.1299	−	3.21597i	−0.518647	−	0.110242i
$852$	20.0240	−	7.68651i	0.686012	−	0.263335i
$853$	2.37169	+	0.375639i	0.0812051	+	0.0128616i	0.196905	−	0.980423i	$-0.436911\pi$
$853$	2.37169	+	0.375639i	0.0812051	+	0.0128616i	−0.115700	+	0.993284i	$0.536911\pi$
$854$	10.7673	+	12.1597i	0.368450	+	0.416096i
$855$	−3.70442	−	0.175029i	−0.126689	−	0.00598586i
$856$	1.54349	−	14.6854i	0.0527555	−	0.501935i
$857$	0.974378	+	3.63643i	0.0332841	+	0.124218i	0.980569	−	0.196174i	$-0.0628519\pi$
$857$	0.974378	+	3.63643i	0.0332841	+	0.124218i	−0.947285	+	0.320392i	$0.896185\pi$
$858$	1.74730	−	4.63006i	0.0596519	−	0.158068i
$859$	16.5361	+	28.6414i	0.564206	+	0.977233i	0.997123	+	0.0757991i	$0.0241508\pi$
$859$	16.5361	+	28.6414i	0.564206	+	0.977233i	−0.432918	+	0.901434i	$0.642516\pi$
$860$	−1.84429	−	4.08562i	−0.0628896	−	0.139318i
$861$	−1.19676	−	12.3730i	−0.0407855	−	0.421670i
$862$	−14.0308	+	27.5369i	−0.477890	+	0.937912i
$863$	12.8106	−	4.91753i	0.436078	−	0.167395i	−0.130418	−	0.991459i	$-0.541632\pi$
$863$	12.8106	−	4.91753i	0.436078	−	0.167395i	0.566496	+	0.824064i	$0.308299\pi$
$864$	0.521005	+	4.95703i	0.0177249	+	0.168642i
$865$	16.3547	+	14.5742i	0.556078	+	0.495537i
$866$	−5.28371	−	24.8579i	−0.179548	−	0.844707i
$867$	−29.9834	+	4.74890i	−1.01829	+	0.161281i
$868$	5.88674	−	4.68667i	0.199809	−	0.159076i
$869$	17.8316	−	5.90568i	0.604897	−	0.200336i
$870$	−3.10903	−	3.07719i	−0.105406	−	0.104326i
$871$	−5.14019	−	11.5450i	−0.174169	−	0.391189i
$872$	−0.937695	+	17.8923i	−0.0317544	+	0.605909i
$873$	−2.70217	+	0.141615i	−0.0914546	+	0.00479294i
$874$	−13.8522	+	10.0642i	−0.468557	+	0.340426i
$875$	29.5796	−	0.211302i	0.999974	−	0.00714331i
$876$	7.57605	+	23.3167i	0.255971	+	0.787798i
$877$	−19.8895	−	12.9164i	−0.671619	−	0.436155i	0.163263	−	0.986583i	$-0.447798\pi$
$877$	−19.8895	−	12.9164i	−0.671619	−	0.436155i	−0.834883	+	0.550428i	$0.814465\pi$
$878$	−20.5910	−	7.90414i	−0.694912	−	0.266752i
$879$	−9.23515	−	5.33191i	−0.311494	−	0.179841i
$880$	−7.33700	−	1.08091i	−0.247330	−	0.0364376i
$881$			1.77859i			0.0599221i	0.999551	+	0.0299610i	$0.00953832\pi$
$881$			1.77859i			0.0599221i	−0.999551	+	0.0299610i	$0.990462\pi$
$882$	−0.108084	+	1.56505i	−0.00363939	+	0.0526981i
$883$	3.08604	+	6.05669i	0.103853	+	0.203824i	0.937086	−	0.349099i	$-0.113512\pi$
$883$	3.08604	+	6.05669i	0.103853	+	0.203824i	−0.833232	+	0.552923i	$0.813512\pi$
$884$	−0.188750	−	0.169951i	−0.00634834	−	0.00571607i
$885$	4.60738	−	10.4934i	0.154875	−	0.352730i
$886$	−1.22161	−	11.6228i	−0.0410407	−	0.390476i
$887$	1.27472	+	24.3231i	0.0428009	+	0.816690i	0.932727	+	0.360584i	$0.117423\pi$
$887$	1.27472	+	24.3231i	0.0428009	+	0.816690i	−0.889926	+	0.456105i	$0.849244\pi$
$888$	10.6958	−	5.44979i	0.358928	−	0.182883i
$889$	15.3031	−	4.83229i	0.513248	−	0.162070i
$890$	−3.52721	−	2.01230i	−0.118232	−	0.0674526i
$891$	31.1775	−	6.81170i	1.04448	−	0.228200i
$892$	1.97340	+	7.36481i	0.0660742	+	0.246592i
$893$	12.3755	−	32.2393i	0.414131	−	1.07885i
$894$	40.2948	−	8.56492i	1.34766	−	0.286454i
$895$	−23.8973	+	15.6945i	−0.798798	+	0.524610i
$896$	−1.30382	−	2.30218i	−0.0435576	−	0.0769105i
$897$	−3.40978	−	0.540057i	−0.113849	−	0.0180320i
$898$	0.168416	+	3.21357i	0.00562012	+	0.107238i
$899$	2.07332	+	2.30266i	0.0691492	+	0.0767980i
$900$	−0.649281	+	0.913281i	−0.0216427	+	0.0304427i
$901$	1.58024	−	0.912353i	0.0526455	−	0.0303949i
$902$	6.10170	−	6.17118i	0.203164	−	0.205478i
$903$	−8.86237	−	3.48657i	−0.294921	−	0.116026i
$904$	3.80940	−	5.24319i	0.126699	−	0.174386i
$905$	−12.3676	−	23.9670i	−0.411112	−	0.796691i
$906$	−0.819454	+	3.85523i	−0.0272245	+	0.128081i
$907$	23.1124	−	28.5415i	0.767436	−	0.947704i	−0.232253	−	0.972655i	$-0.574610\pi$
$907$	23.1124	−	28.5415i	0.767436	−	0.947704i	0.999689	+	0.0249514i	$0.00794311\pi$
$908$	−5.04011	−	13.1299i	−0.167262	−	0.435732i
$909$	0.764890	+	2.35409i	0.0253698	+	0.0780803i
$910$	−4.48487	−	2.01374i	−0.148672	−	0.0667549i
$911$	23.5347	+	17.0989i	0.779739	+	0.566513i	0.904901	−	0.425623i	$-0.139945\pi$
$911$	23.5347	+	17.0989i	0.779739	+	0.566513i	−0.125162	+	0.992136i	$0.539945\pi$
$912$	3.43920	−	12.8353i	0.113883	−	0.425018i
$913$	14.8341	−	4.06495i	0.490938	−	0.134530i
$914$	4.65543	+	2.68781i	0.153988	+	0.0889049i
$915$	20.0146	+	14.3846i	0.661661	+	0.475541i
$916$	1.18766	+	0.385894i	0.0392414	+	0.0127503i
$917$	31.4917	−	47.6234i	1.03995	−	1.57266i
$918$	0.238317	−	1.50467i	0.00786563	−	0.0496617i
$919$	−11.6476	+	26.1609i	−0.384218	+	0.862968i	0.613116	+	0.789993i	$0.289916\pi$
$919$	−11.6476	+	26.1609i	−0.384218	+	0.862968i	−0.997334	+	0.0729750i	$0.976751\pi$
$920$	0.297348	+	5.16501i	0.00980329	+	0.170285i
$921$	4.45645	+	4.94939i	0.146845	+	0.163088i
$922$	0.114412	+	0.141287i	0.00376795	+	0.00465303i
$923$	7.01903	+	7.01903i	0.231034	+	0.231034i
$924$	−12.7714	+	9.22763i	−0.420147	+	0.303567i
$925$	−32.3754	−	8.31877i	−1.06450	−	0.273519i
$926$	−2.23065	+	21.2232i	−0.0733037	+	0.697438i
$927$	3.14546	+	0.164847i	0.103311	+	0.00541427i
$928$	0.913728	−	0.593382i	0.0299946	−	0.0194787i
$929$	40.1495	+	17.8757i	1.31726	+	0.586484i	0.940490	−	0.339822i	$-0.110367\pi$
$929$	40.1495	+	17.8757i	1.31726	+	0.586484i	0.376774	+	0.926305i	$0.377033\pi$
$930$	7.14032	−	8.91094i	0.234140	−	0.292201i
$931$	−21.8524	+	46.9682i	−0.716183	+	1.53932i
$932$	4.94759	−	2.52092i	0.162064	−	0.0825755i
$933$	15.8755	+	19.6046i	0.519741	+	0.641826i
$934$	−15.0676	+	26.0979i	−0.493027	+	0.853948i
$935$	2.08059	+	0.899522i	0.0680426	+	0.0294175i
$936$	0.161284	−	0.0931176i	0.00527174	−	0.00304364i
$937$	9.52394	−	1.50844i	0.311134	−	0.0492787i	0.00108491	−	0.999999i	$-0.499655\pi$
$937$	9.52394	−	1.50844i	0.311134	−	0.0492787i	0.310049	+	0.950721i	$0.399655\pi$
$938$	−6.62380	+	39.6873i	−0.216275	+	1.29584i
$939$	−27.7679	+	9.02233i	−0.906171	+	0.294433i
$940$	−6.17649	−	8.40985i	−0.201455	−	0.274299i
$941$	−41.3879	+	4.35004i	−1.34921	+	0.141807i	−0.751408	−	0.659838i	$-0.770625\pi$
$941$	−41.3879	+	4.35004i	−1.34921	+	0.141807i	−0.597800	+	0.801646i	$0.703958\pi$
$942$	−15.4764	−	23.8315i	−0.504247	−	0.776472i
$943$	−5.07736	−	3.29728i	−0.165342	−	0.107374i
$944$	2.30921	+	1.67774i	0.0751584	+	0.0546058i
$945$	−4.52114	−	29.1391i	−0.147073	−	0.947893i
$946$	−2.09035	−	6.31161i	−0.0679631	−	0.205208i
$947$	11.6807	−	43.5931i	0.379573	−	1.41659i	−0.466974	−	0.884271i	$-0.654656\pi$
$947$	11.6807	−	43.5931i	0.379573	−	1.41659i	0.846547	−	0.532315i	$-0.178678\pi$
$948$	9.49406	+	3.64443i	0.308353	+	0.118366i
$949$	−8.43192	+	7.59213i	−0.273712	+	0.246451i
$950$	−30.8235	+	20.4711i	−1.00005	+	0.664170i
$951$	15.6416	+	21.5288i	0.507212	+	0.698118i
$952$	0.202809	+	0.782812i	0.00657307	+	0.0253711i
$953$	−37.3985	−	19.0555i	−1.21146	−	0.617268i	−0.272784	−	0.962075i	$-0.587944\pi$
$953$	−37.3985	−	19.0555i	−1.21146	−	0.617268i	−0.938674	+	0.344807i	$0.887944\pi$
$954$	0.278176	+	1.30872i	0.00900629	+	0.0423713i
$955$	−16.6801	+	13.6500i	−0.539756	+	0.441705i
$956$	6.60070	−	11.4328i	0.213482	−	0.369762i
$957$	−4.11167	−	5.01911i	−0.132911	−	0.162245i
$958$	5.24332	+	5.24332i	0.169404	+	0.169404i
$959$	−3.42605	+	15.4855i	−0.110633	+	0.500052i
$960$	−2.70191	−	2.96989i	−0.0872037	−	0.0958528i
$961$	15.3309	−	17.0267i	0.494544	−	0.549247i
$962$	4.31746	+	3.49621i	0.139200	+	0.112722i
$963$	−2.57180	−	2.08260i	−0.0828751	−	0.0671109i
$964$	15.6389	−	17.3687i	0.503693	−	0.559408i
$965$	−14.8981	−	16.3758i	−0.479588	−	0.527155i
$966$	8.10701	+	7.42229i	0.260839	+	0.238808i
$967$	−16.1994	−	16.1994i	−0.520939	−	0.520939i	0.396916	−	0.917855i	$-0.370080\pi$
$967$	−16.1994	−	16.1994i	−0.520939	−	0.520939i	−0.917855	+	0.396916i	$0.870080\pi$
$968$	−10.6567	−	2.72652i	−0.342521	−	0.0876335i
$969$	−2.03070	+	3.51728i	−0.0652356	+	0.112991i
$970$	−20.8936	+	17.0981i	−0.670852	+	0.548986i
$971$	10.6668	+	50.1833i	0.342314	+	1.61046i	0.726474	+	0.687194i	$0.241158\pi$
$971$	10.6668	+	50.1833i	0.342314	+	1.61046i	−0.384160	+	0.923266i	$0.625509\pi$
$972$	2.07095	+	1.05520i	0.0664256	+	0.0338456i
$973$	31.4921	+	32.0190i	1.00959	+	1.02648i
$974$	−14.9318	−	20.5519i	−0.478446	−	0.658525i
$975$	−7.31312	−	1.47595i	−0.234207	−	0.0472682i
$976$	−4.56201	+	4.10765i	−0.146026	+	0.131483i
$977$	−14.2647	−	5.47572i	−0.456369	−	0.175184i	0.119314	−	0.992857i	$-0.461931\pi$
$977$	−14.2647	−	5.47572i	−0.456369	−	0.175184i	−0.575683	+	0.817673i	$0.695264\pi$
$978$	1.59778	−	5.96299i	0.0510913	−	0.190675i
$979$	−4.89286	−	3.51272i	−0.156377	−	0.112267i
$980$	8.37415	+	13.2240i	0.267502	+	0.422425i
$981$	3.24850	+	2.36017i	0.103717	+	0.0753546i
$982$	−5.55179	−	3.60537i	−0.177165	−	0.115052i
$983$	−31.3839	−	48.3270i	−1.00099	−	1.54139i	−0.831246	−	0.555904i	$-0.812372\pi$
$983$	−31.3839	−	48.3270i	−1.00099	−	1.54139i	−0.169746	−	0.985488i	$-0.554295\pi$
$984$	4.67263	−	0.491113i	0.148958	−	0.0156561i
$985$	21.1845	+	28.8447i	0.674996	+	0.919068i
$986$	−0.316700	+	0.102902i	−0.0100858	+	0.00327707i
$987$	−21.8659	−	3.64941i	−0.695998	−	0.116162i
$988$	6.07398	−	0.962023i	0.193239	−	0.0306060i
$989$	−4.01679	+	2.31910i	−0.127727	+	0.0737430i
$990$	−1.09872	+	1.24710i	−0.0349195	+	0.0396353i
$991$	6.68477	−	11.5784i	0.212349	−	0.367799i	−0.740100	−	0.672496i	$-0.765222\pi$
$991$	6.68477	−	11.5784i	0.212349	−	0.367799i	0.952449	+	0.304698i	$0.0985554\pi$
$992$	1.78979	+	2.21021i	0.0568259	+	0.0701742i
$993$	−37.1114	+	18.9092i	−1.17770	+	0.600066i
$994$	−6.31419	−	30.9670i	−0.200274	−	0.982212i
$995$	−13.6841	+	17.0774i	−0.433815	+	0.541390i
$996$	7.60718	+	3.38693i	0.241043	+	0.107319i
$997$	−33.5174	+	21.7664i	−1.06151	+	0.689350i	−0.952453	−	0.304686i	$-0.901448\pi$
$997$	−33.5174	+	21.7664i	−1.06151	+	0.689350i	−0.109053	+	0.994036i	$0.534782\pi$
$998$	17.0057	+	0.891229i	0.538305	+	0.0282114i
$999$	−3.48313	+	33.1398i	−0.110201	+	1.04850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.367.43	yes	768
5.3	odd	4	inner	770.2.bv.a.213.19	yes	768
7.5	odd	6	inner	770.2.bv.a.257.6	yes	768
11.3	even	5	inner	770.2.bv.a.157.19	yes	768
35.33	even	12	inner	770.2.bv.a.103.19	yes	768
55.3	odd	20	inner	770.2.bv.a.3.6	✓	768
77.47	odd	30	inner	770.2.bv.a.47.19	yes	768
385.278	even	60	inner	770.2.bv.a.663.43	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.6	✓	768	55.3	odd	20	inner
770.2.bv.a.47.19	yes	768	77.47	odd	30	inner
770.2.bv.a.103.19	yes	768	35.33	even	12	inner
770.2.bv.a.157.19	yes	768	11.3	even	5	inner
770.2.bv.a.213.19	yes	768	5.3	odd	4	inner
770.2.bv.a.257.6	yes	768	7.5	odd	6	inner
770.2.bv.a.367.43	yes	768	1.1	even	1	trivial
770.2.bv.a.663.43	yes	768	385.278	even	60	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.777146 - 0.629320i) q^{2} +(0.0939735 - 1.79312i) q^{3} +(0.207912 - 0.978148i) q^{4} +(-2.21031 - 0.338427i) q^{5} +(-1.05542 - 1.45266i) q^{6} +(-2.36727 + 1.18155i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.222884 - 0.0234260i) q^{9} +O(q^{10})\)	\(q+(0.777146 - 0.629320i) q^{2} +(0.0939735 - 1.79312i) q^{3} +(0.207912 - 0.978148i) q^{4} +(-2.21031 - 0.338427i) q^{5} +(-1.05542 - 1.45266i) q^{6} +(-2.36727 + 1.18155i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.222884 - 0.0234260i) q^{9} +(-1.93071 + 1.12799i) q^{10} +(-3.02220 + 1.36613i) q^{11} +(-1.73440 - 0.464731i) q^{12} +(-0.129996 - 0.820762i) q^{13} +(-1.09614 + 2.40800i) q^{14} +(-0.814552 + 3.93155i) q^{15} +(-0.913545 - 0.406737i) q^{16} +(0.237530 + 0.192348i) q^{17} +(-0.187956 + 0.122060i) q^{18} +(-7.23869 + 1.53863i) q^{19} +(-0.790581 + 2.09165i) q^{20} +(1.89620 + 4.35583i) q^{21} +(-1.48896 + 2.96361i) q^{22} +(2.23485 + 0.598826i) q^{23} +(-1.64034 + 0.730329i) q^{24} +(4.77093 + 1.49606i) q^{25} +(-0.617548 - 0.556043i) q^{26} +(0.779721 - 4.92297i) q^{27} +(0.663546 + 2.56119i) q^{28} +(-1.03617 + 0.336673i) q^{29} +(1.84118 + 3.56800i) q^{30} +(-1.15676 - 2.59813i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(2.16562 + 5.54755i) q^{33} +0.305644 q^{34} +(5.63226 - 1.81044i) q^{35} +(-0.0692543 + 0.213143i) q^{36} +(-6.67625 + 0.349887i) q^{37} +(-4.65723 + 5.75120i) q^{38} +(-1.48394 + 0.155969i) q^{39} +(0.701918 + 2.12304i) q^{40} +(-2.48856 - 0.808583i) q^{41} +(4.21483 + 2.19180i) q^{42} +(-1.41752 + 1.41752i) q^{43} +(0.707921 + 3.24019i) q^{44} +(0.484714 + 0.127209i) q^{45} +(2.11366 - 0.941061i) q^{46} +(-2.54148 + 3.91354i) q^{47} +(-0.815177 + 1.59987i) q^{48} +(4.20789 - 5.59408i) q^{49} +(4.64921 - 1.83979i) q^{50} +(0.367224 - 0.407844i) q^{51} +(-0.829854 - 0.0434908i) q^{52} +(2.13947 - 5.57351i) q^{53} +(-2.49217 - 4.31656i) q^{54} +(7.14233 - 1.99676i) q^{55} +(2.12748 + 1.57284i) q^{56} +(2.07871 + 13.1244i) q^{57} +(-0.593382 + 0.913728i) q^{58} +(-2.79197 - 0.593451i) q^{59} +(3.67628 + 1.61417i) q^{60} +(2.49687 - 5.60807i) q^{61} +(-2.53403 - 1.29115i) q^{62} +(0.555304 - 0.207892i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(0.00956282 + 1.85813i) q^{65} +(5.17419 + 2.94839i) q^{66} +(14.6897 - 3.93608i) q^{67} +(0.237530 - 0.192348i) q^{68} +(1.28378 - 3.95108i) q^{69} +(3.23774 - 4.95147i) q^{70} +(-9.66390 + 7.02124i) q^{71} +(0.0803144 + 0.209226i) q^{72} +(-7.43643 - 11.4511i) q^{73} +(-4.96823 + 4.47341i) q^{74} +(3.13095 - 8.41427i) q^{75} +7.40041i q^{76} +(5.54021 - 6.80486i) q^{77} +(-1.05508 + 1.05508i) q^{78} +(-5.63261 - 0.592011i) q^{79} +(1.88157 + 1.20818i) q^{80} +(-9.41184 - 2.00055i) q^{81} +(-2.44283 + 0.937716i) q^{82} +(-4.58045 - 0.725472i) q^{83} +(4.65488 - 0.949135i) q^{84} +(-0.459919 - 0.505535i) q^{85} +(-0.209546 + 1.99369i) q^{86} +(0.506322 + 1.88962i) q^{87} +(2.58928 + 2.07259i) q^{88} +(0.908036 + 1.57276i) q^{89} +(0.456749 - 0.206181i) q^{90} +(1.27751 + 1.78937i) q^{91} +(1.05039 - 2.06151i) q^{92} +(-4.76746 + 1.83006i) q^{93} +(0.487768 + 4.64080i) q^{94} +(16.5205 - 0.951079i) q^{95} +(0.373322 + 1.75634i) q^{96} +(11.9252 - 1.88876i) q^{97} +(-0.250323 - 6.99552i) q^{98} +(0.705603 - 0.233689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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