LMFDB - Embedded newform 403.2.bl.b.16.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(16,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("403.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bl (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$35$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.7
Character	$\chi$	$=$	403.16
Dual form			403.2.bl.b.126.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58921 - 0.707561i) q^{2} +(0.119963 - 1.14138i) q^{3} +(0.686679 + 0.762634i) q^{4} -0.807451 q^{5} +(-0.998239 + 1.72900i) q^{6} +(0.398118 + 0.442154i) q^{7} +(0.523470 + 1.61107i) q^{8} +(1.64610 + 0.349889i) q^{9} +O(q^{10})$	\(q+(-1.58921 - 0.707561i) q^{2} +(0.119963 - 1.14138i) q^{3} +(0.686679 + 0.762634i) q^{4} -0.807451 q^{5} +(-0.998239 + 1.72900i) q^{6} +(0.398118 + 0.442154i) q^{7} +(0.523470 + 1.61107i) q^{8} +(1.64610 + 0.349889i) q^{9} +(1.28321 + 0.571321i) q^{10} +(4.46112 - 0.948240i) q^{11} +(0.952828 - 0.692270i) q^{12} +(0.623037 - 3.55131i) q^{13} +(-0.319840 - 0.984368i) q^{14} +(-0.0968645 + 0.921604i) q^{15} +(0.522570 - 4.97193i) q^{16} +(0.144258 + 0.0306631i) q^{17} +(-2.36842 - 1.72076i) q^{18} +(-0.223375 - 2.12527i) q^{19} +(-0.554459 - 0.615789i) q^{20} +(0.552424 - 0.401359i) q^{21} +(-7.76058 - 1.64956i) q^{22} +(-0.136417 + 0.151507i) q^{23} +(1.90164 - 0.404205i) q^{24} -4.34802 q^{25} +(-3.50291 + 5.20294i) q^{26} +(1.66077 - 5.11131i) q^{27} +(-0.0638231 + 0.607236i) q^{28} +(1.14618 + 0.510313i) q^{29} +(0.806029 - 1.39608i) q^{30} +(-2.75646 + 4.83755i) q^{31} +(-2.65443 + 4.59761i) q^{32} +(-0.547127 - 5.20556i) q^{33} +(-0.207561 - 0.150802i) q^{34} +(-0.321460 - 0.357018i) q^{35} +(0.863503 + 1.49563i) q^{36} +(0.460601 + 0.797785i) q^{37} +(-1.14877 + 3.53555i) q^{38} +(-3.97864 - 1.13715i) q^{39} +(-0.422676 - 1.30086i) q^{40} +(0.558896 + 0.248837i) q^{41} +(-1.16190 + 0.246970i) q^{42} +(-1.24772 - 11.8713i) q^{43} +(3.78651 + 2.75106i) q^{44} +(-1.32914 - 0.282518i) q^{45} +(0.323996 - 0.144252i) q^{46} +(4.59558 + 3.33888i) q^{47} +(-5.61214 - 1.19290i) q^{48} +(0.694696 - 6.60959i) q^{49} +(6.90991 + 3.07649i) q^{50} +(0.0523038 - 0.160974i) q^{51} +(3.13618 - 1.96346i) q^{52} +(-0.974979 - 3.00068i) q^{53} +(-6.25587 + 6.94785i) q^{54} +(-3.60213 + 0.765657i) q^{55} +(-0.503941 + 0.872851i) q^{56} -2.45253 q^{57} +(-1.46044 - 1.62199i) q^{58} +(0.769130 - 0.342439i) q^{59} +(-0.769361 + 0.558974i) q^{60} +(5.61070 - 9.71802i) q^{61} +(7.80345 - 5.73752i) q^{62} +(0.500635 + 0.867126i) q^{63} +(-0.617524 + 0.448657i) q^{64} +(-0.503072 + 2.86751i) q^{65} +(-2.81376 + 8.65985i) q^{66} +(-4.34113 - 7.51905i) q^{67} +(0.0756744 + 0.131072i) q^{68} +(0.156561 + 0.173878i) q^{69} +(0.258255 + 0.794828i) q^{70} +(9.50414 + 2.02017i) q^{71} +(0.297985 + 2.83514i) q^{72} +(-0.844951 + 2.60049i) q^{73} +(-0.167510 - 1.59375i) q^{74} +(-0.521604 + 4.96273i) q^{75} +(1.46742 - 1.62973i) q^{76} +(2.19532 + 1.59499i) q^{77} +(5.51828 + 4.62229i) q^{78} +(1.76714 + 5.43871i) q^{79} +(-0.421950 + 4.01458i) q^{80} +(-1.02256 - 0.455272i) q^{81} +(-0.712136 - 0.790907i) q^{82} +(-3.56898 + 2.59302i) q^{83} +(0.685428 + 0.145692i) q^{84} +(-0.116481 - 0.0247589i) q^{85} +(-6.41676 + 19.7487i) q^{86} +(0.719958 - 1.24700i) q^{87} +(3.86294 + 6.69081i) q^{88} +(16.3876 - 3.48329i) q^{89} +(1.91238 + 1.38943i) q^{90} +(1.81827 - 1.13836i) q^{91} -0.209219 q^{92} +(5.19079 + 3.72648i) q^{93} +(-4.94087 - 8.55784i) q^{94} +(0.180365 + 1.71605i) q^{95} +(4.92916 + 3.58125i) q^{96} +(6.27142 + 6.96512i) q^{97} +(-5.78071 + 10.0125i) q^{98} +7.67521 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q + q^{2} + 39 q^{4} - 8 q^{5} - 2 q^{7} + 12 q^{8} + 29 q^{9}+O(q^{10}) $ 280 * q + q^2 + 39 * q^4 - 8 * q^5 - 2 * q^7 + 12 * q^8 + 29 * q^9	\( 280 q + q^{2} + 39 q^{4} - 8 q^{5} - 2 q^{7} + 12 q^{8} + 29 q^{9} - 21 q^{10} - q^{11} - 16 q^{12} - 54 q^{14} - 27 q^{15} + 31 q^{16} + 2 q^{17} - 10 q^{18} + 5 q^{19} - 3 q^{20} + 68 q^{21} - 39 q^{22} - 7 q^{23} + 48 q^{24} + 200 q^{25} + 6 q^{26} - 78 q^{27} + 30 q^{28} - 16 q^{29} - 66 q^{30} - 62 q^{31} - 56 q^{32} - 20 q^{33} - 126 q^{34} - 37 q^{35} - 140 q^{36} - 36 q^{37} + 4 q^{38} + 28 q^{39} - 158 q^{40} - 4 q^{41} + 16 q^{42} - 16 q^{43} + 42 q^{44} - 46 q^{45} - 29 q^{46} + 8 q^{47} - 36 q^{48} + 43 q^{49} - 5 q^{50} - 134 q^{51} - q^{52} + 8 q^{53} + 44 q^{54} - 55 q^{55} - 42 q^{56} + 140 q^{57} + 38 q^{58} - 23 q^{59} + 38 q^{60} + 40 q^{61} + 19 q^{62} - 146 q^{63} - 68 q^{64} + 2 q^{65} + 6 q^{66} + 46 q^{67} + 86 q^{68} - 32 q^{69} - 4 q^{70} + 60 q^{71} + 73 q^{72} - 12 q^{73} - 44 q^{74} + 16 q^{75} - 70 q^{76} + 10 q^{77} - 142 q^{78} + 134 q^{79} - 72 q^{80} - 18 q^{81} + 28 q^{82} - 88 q^{83} + 81 q^{84} - 69 q^{85} + 188 q^{86} - 28 q^{87} + 42 q^{88} + 12 q^{89} + 22 q^{90} + 67 q^{91} - 324 q^{92} - 25 q^{93} - 62 q^{94} + 16 q^{95} + 276 q^{96} + 16 q^{97} + 76 q^{98} - 60 q^{99}+O(q^{100}) \) 280 * q + q^2 + 39 * q^4 - 8 * q^5 - 2 * q^7 + 12 * q^8 + 29 * q^9 - 21 * q^10 - q^11 - 16 * q^12 - 54 * q^14 - 27 * q^15 + 31 * q^16 + 2 * q^17 - 10 * q^18 + 5 * q^19 - 3 * q^20 + 68 * q^21 - 39 * q^22 - 7 * q^23 + 48 * q^24 + 200 * q^25 + 6 * q^26 - 78 * q^27 + 30 * q^28 - 16 * q^29 - 66 * q^30 - 62 * q^31 - 56 * q^32 - 20 * q^33 - 126 * q^34 - 37 * q^35 - 140 * q^36 - 36 * q^37 + 4 * q^38 + 28 * q^39 - 158 * q^40 - 4 * q^41 + 16 * q^42 - 16 * q^43 + 42 * q^44 - 46 * q^45 - 29 * q^46 + 8 * q^47 - 36 * q^48 + 43 * q^49 - 5 * q^50 - 134 * q^51 - q^52 + 8 * q^53 + 44 * q^54 - 55 * q^55 - 42 * q^56 + 140 * q^57 + 38 * q^58 - 23 * q^59 + 38 * q^60 + 40 * q^61 + 19 * q^62 - 146 * q^63 - 68 * q^64 + 2 * q^65 + 6 * q^66 + 46 * q^67 + 86 * q^68 - 32 * q^69 - 4 * q^70 + 60 * q^71 + 73 * q^72 - 12 * q^73 - 44 * q^74 + 16 * q^75 - 70 * q^76 + 10 * q^77 - 142 * q^78 + 134 * q^79 - 72 * q^80 - 18 * q^81 + 28 * q^82 - 88 * q^83 + 81 * q^84 - 69 * q^85 + 188 * q^86 - 28 * q^87 + 42 * q^88 + 12 * q^89 + 22 * q^90 + 67 * q^91 - 324 * q^92 - 25 * q^93 - 62 * q^94 + 16 * q^95 + 276 * q^96 + 16 * q^97 + 76 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.58921	−	0.707561i	−1.12374	−	0.500321i	−0.241161	−	0.970485i	$-0.577528\pi$
$2$	−1.58921	−	0.707561i	−1.12374	−	0.500321i	−0.882579	+	0.470164i	$0.844195\pi$
$3$	0.119963	−	1.14138i	0.0692609	−	0.658973i	−0.903726	−	0.428112i	$-0.859179\pi$
$3$	0.119963	−	1.14138i	0.0692609	−	0.658973i	0.972987	−	0.230861i	$-0.0741544\pi$
$4$	0.686679	+	0.762634i	0.343339	+	0.381317i
$5$	−0.807451			−0.361103			−0.180551	−	0.983566i	$-0.557788\pi$
$5$	−0.807451			−0.361103			−0.180551	+	0.983566i	$0.557788\pi$
$6$	−0.998239	+	1.72900i	−0.407530	+	0.705862i
$7$	0.398118	+	0.442154i	0.150474	+	0.167119i	0.813669	−	0.581328i	$-0.197467\pi$
$7$	0.398118	+	0.442154i	0.150474	+	0.167119i	−0.663195	+	0.748447i	$0.730800\pi$
$8$	0.523470	+	1.61107i	0.185074	+	0.569601i
$9$	1.64610	+	0.349889i	0.548699	+	0.116630i
$10$	1.28321	+	0.571321i	0.405786	+	0.180667i
$11$	4.46112	−	0.948240i	1.34508	−	0.285905i	0.521569	−	0.853209i	$-0.325347\pi$
$11$	4.46112	−	0.948240i	1.34508	−	0.285905i	0.823508	+	0.567304i	$0.192014\pi$
$12$	0.952828	−	0.692270i	0.275058	−	0.199841i
$13$	0.623037	−	3.55131i	0.172799	−	0.984957i
$13$	0.623037	−	3.55131i	0.172799	−	0.984957i
$14$	−0.319840	−	0.984368i	−0.0854810	−	0.263083i
$15$	−0.0968645	+	0.921604i	−0.0250103	+	0.237957i
$16$	0.522570	−	4.97193i	0.130643	−	1.24298i
$17$	0.144258	+	0.0306631i	0.0349878	+	0.00743688i	0.225372	−	0.974273i	$-0.427640\pi$
$17$	0.144258	+	0.0306631i	0.0349878	+	0.00743688i	−0.190385	+	0.981710i	$0.560973\pi$
$18$	−2.36842	−	1.72076i	−0.558243	−	0.405587i
$19$	−0.223375	−	2.12527i	−0.0512458	−	0.487571i	−0.989803	−	0.142446i	$-0.954503\pi$
$19$	−0.223375	−	2.12527i	−0.0512458	−	0.487571i	0.938557	−	0.345125i	$-0.112163\pi$
$20$	−0.554459	−	0.615789i	−0.123981	−	0.137695i
$21$	0.552424	−	0.401359i	0.120549	−	0.0875838i
$22$	−7.76058	−	1.64956i	−1.65456	−	0.351688i
$23$	−0.136417	+	0.151507i	−0.0284450	+	0.0315913i	−0.757199	−	0.653184i	$-0.773433\pi$
$23$	−0.136417	+	0.151507i	−0.0284450	+	0.0315913i	0.728754	+	0.684775i	$0.240100\pi$
$24$	1.90164	−	0.404205i	0.388170	−	0.0825081i
$25$	−4.34802			−0.869605
$26$	−3.50291	+	5.20294i	−0.686977	+	1.02038i
$27$	1.66077	−	5.11131i	0.319615	−	0.983673i
$28$	−0.0638231	+	0.607236i	−0.0120614	+	0.114757i
$29$	1.14618	+	0.510313i	0.212841	+	0.0947627i	0.510388	−	0.859944i	$-0.329502\pi$
$29$	1.14618	+	0.510313i	0.212841	+	0.0947627i	−0.297547	+	0.954707i	$0.596169\pi$
$30$	0.806029	−	1.39608i	0.147160	−	0.254889i
$31$	−2.75646	+	4.83755i	−0.495075	+	0.868850i
$31$	−2.75646	+	4.83755i	−0.495075	+	0.868850i
$32$	−2.65443	+	4.59761i	−0.469242	+	0.812750i
$33$	−0.547127	−	5.20556i	−0.0952425	−	0.906172i
$34$	−0.207561	−	0.150802i	−0.0355963	−	0.0258623i
$35$	−0.321460	−	0.357018i	−0.0543367	−	0.0603470i
$36$	0.863503	+	1.49563i	0.143917	+	0.249272i
$37$	0.460601	+	0.797785i	0.0757224	+	0.131155i	0.901400	−	0.432987i	$-0.142540\pi$
$37$	0.460601	+	0.797785i	0.0757224	+	0.131155i	−0.825678	+	0.564142i	$0.809207\pi$
$38$	−1.14877	+	3.53555i	−0.186355	+	0.573543i
$39$	−3.97864	−	1.13715i	−0.637092	−	0.182089i
$40$	−0.422676	−	1.30086i	−0.0668309	−	0.205684i
$41$	0.558896	+	0.248837i	0.0872850	+	0.0388618i	0.449915	−	0.893072i	$-0.351454\pi$
$41$	0.558896	+	0.248837i	0.0872850	+	0.0388618i	−0.362630	+	0.931933i	$0.618121\pi$
$42$	−1.16190	+	0.246970i	−0.179285	+	0.0381083i
$43$	−1.24772	−	11.8713i	−0.190275	−	1.81035i	−0.507123	−	0.861874i	$-0.669291\pi$
$43$	−1.24772	−	11.8713i	−0.190275	−	1.81035i	0.316847	−	0.948477i	$-0.397376\pi$
$44$	3.78651	+	2.75106i	0.570839	+	0.414738i
$45$	−1.32914	−	0.282518i	−0.198137	−	0.0421153i
$46$	0.323996	−	0.144252i	0.0477705	−	0.0212688i
$47$	4.59558	+	3.33888i	0.670334	+	0.487026i	0.870137	−	0.492810i	$-0.164030\pi$
$47$	4.59558	+	3.33888i	0.670334	+	0.487026i	−0.199803	+	0.979836i	$0.564030\pi$
$48$	−5.61214	−	1.19290i	−0.810043	−	0.172180i
$49$	0.694696	−	6.60959i	0.0992423	−	0.944228i
$50$	6.90991	+	3.07649i	0.977210	+	0.435082i
$51$	0.0523038	−	0.160974i	0.00732399	−	0.0225409i
$52$	3.13618	−	1.96346i	0.434910	−	0.272283i
$53$	−0.974979	−	3.00068i	−0.133924	−	0.412175i	0.861497	−	0.507762i	$-0.169527\pi$
$53$	−0.974979	−	3.00068i	−0.133924	−	0.412175i	−0.995421	+	0.0955874i	$0.969527\pi$
$54$	−6.25587	+	6.94785i	−0.851316	+	0.945483i
$55$	−3.60213	+	0.765657i	−0.485711	+	0.103241i
$56$	−0.503941	+	0.872851i	−0.0673419	+	0.116640i
$57$	−2.45253			−0.324846
$58$	−1.46044	−	1.62199i	−0.191766	−	0.212977i
$59$	0.769130	−	0.342439i	0.100132	−	0.0445817i	−0.356059	−	0.934463i	$-0.615880\pi$
$59$	0.769130	−	0.342439i	0.100132	−	0.0445817i	0.456191	+	0.889882i	$0.349213\pi$
$60$	−0.769361	+	0.558974i	−0.0993241	+	0.0721632i
$61$	5.61070	−	9.71802i	0.718377	−	1.24426i	−0.243266	−	0.969960i	$-0.578219\pi$
$61$	5.61070	−	9.71802i	0.718377	−	1.24426i	0.961643	−	0.274305i	$-0.0884479\pi$
$62$	7.80345	−	5.73752i	0.991040	−	0.728665i
$63$	0.500635	+	0.867126i	0.0630741	+	0.109248i
$64$	−0.617524	+	0.448657i	−0.0771905	+	0.0560822i
$65$	−0.503072	+	2.86751i	−0.0623984	+	0.355671i
$66$	−2.81376	+	8.65985i	−0.346349	+	1.06595i
$67$	−4.34113	−	7.51905i	−0.530353	−	0.918598i	−0.999373	−	0.0354107i	$-0.988726\pi$
$67$	−4.34113	−	7.51905i	−0.530353	−	0.918598i	0.469020	−	0.883188i	$-0.344607\pi$
$68$	0.0756744	+	0.131072i	0.00917687	+	0.0158948i
$69$	0.156561	+	0.173878i	0.0188477	+	0.0209325i
$70$	0.258255	+	0.794828i	0.0308674	+	0.0950002i
$71$	9.50414	+	2.02017i	1.12793	+	0.239750i	0.733841	−	0.679321i	$-0.237726\pi$
$71$	9.50414	+	2.02017i	1.12793	+	0.239750i	0.394092	+	0.919071i	$0.371059\pi$
$72$	0.297985	+	2.83514i	0.0351179	+	0.334124i
$73$	−0.844951	+	2.60049i	−0.0988940	+	0.304364i	−0.988249	−	0.152853i	$-0.951154\pi$
$73$	−0.844951	+	2.60049i	−0.0988940	+	0.304364i	0.889355	+	0.457217i	$0.151154\pi$
$74$	−0.167510	−	1.59375i	−0.0194726	−	0.185270i
$75$	−0.521604	+	4.96273i	−0.0602296	+	0.573046i
$76$	1.46742	−	1.62973i	0.168325	−	0.186943i
$77$	2.19532	+	1.59499i	0.250180	+	0.181766i
$78$	5.51828	+	4.62229i	0.624823	+	0.523372i
$79$	1.76714	+	5.43871i	0.198819	+	0.611902i	0.999911	+	0.0133606i	$0.00425295\pi$
$79$	1.76714	+	5.43871i	0.198819	+	0.611902i	−0.801092	+	0.598542i	$0.795747\pi$
$80$	−0.421950	+	4.01458i	−0.0471754	+	0.448844i
$81$	−1.02256	−	0.455272i	−0.113617	−	0.0505858i
$82$	−0.712136	−	0.790907i	−0.0786422	−	0.0873410i
$83$	−3.56898	+	2.59302i	−0.391747	+	0.284621i	−0.766171	−	0.642637i	$-0.777840\pi$
$83$	−3.56898	+	2.59302i	−0.391747	+	0.284621i	0.374424	+	0.927258i	$0.377840\pi$
$84$	0.685428	+	0.145692i	0.0747863	+	0.0158963i
$85$	−0.116481	−	0.0247589i	−0.0126342	−	0.00268548i
$86$	−6.41676	+	19.7487i	−0.691937	+	2.12956i
$87$	0.719958	−	1.24700i	0.0771876	−	0.133693i
$88$	3.86294	+	6.69081i	0.411791	+	0.713243i
$89$	16.3876	−	3.48329i	1.73708	−	0.369228i	0.772913	−	0.634512i	$-0.218799\pi$
$89$	16.3876	−	3.48329i	1.73708	−	0.369228i	0.964170	+	0.265284i	$0.0854656\pi$
$90$	1.91238	+	1.38943i	0.201583	+	0.146459i
$91$	1.81827	−	1.13836i	0.190607	−	0.119333i
$92$	−0.209219			−0.0218126
$93$	5.19079	+	3.72648i	0.538260	+	0.386418i
$94$	−4.94087	−	8.55784i	−0.509612	−	0.882673i
$95$	0.180365	+	1.71605i	0.0185050	+	0.176063i
$96$	4.92916	+	3.58125i	0.503081	+	0.365509i
$97$	6.27142	+	6.96512i	0.636766	+	0.707201i	0.972012	−	0.234930i	$-0.0754861\pi$
$97$	6.27142	+	6.96512i	0.636766	+	0.707201i	−0.335246	+	0.942131i	$0.608819\pi$
$98$	−5.78071	+	10.0125i	−0.583940	+	1.01141i
$99$	7.67521			0.771388
$100$	−2.98570	−	3.31595i	−0.298570	−	0.331595i
$101$	0.808625	−	0.898069i	0.0804612	−	0.0893612i	−0.701570	−	0.712601i	$-0.747517\pi$
$101$	0.808625	−	0.898069i	0.0804612	−	0.0893612i	0.782031	+	0.623240i	$0.214184\pi$
$102$	−0.197021	+	0.218814i	−0.0195080	+	0.0216658i
$103$	−5.31493	+	3.86152i	−0.523695	+	0.380487i	−0.817994	−	0.575227i	$-0.804914\pi$
$103$	−5.31493	+	3.86152i	−0.523695	+	0.380487i	0.294299	+	0.955713i	$0.404914\pi$
$104$	6.04757	−	0.855246i	0.593013	−	0.0838637i
$105$	−0.446055	+	0.324078i	−0.0435305	+	0.0316267i
$106$	−0.573717	+	5.45856i	−0.0557244	+	0.530182i
$107$	−12.3173	+	13.6798i	−1.19076	+	1.32248i	−0.256223	+	0.966618i	$0.582478\pi$
$107$	−12.3173	+	13.6798i	−1.19076	+	1.32248i	−0.934540	+	0.355859i	$0.884188\pi$
$108$	5.03848	−	2.24327i	0.484828	−	0.215859i
$109$	5.35931	+	3.89377i	0.513329	+	0.372955i	0.814085	−	0.580746i	$-0.197239\pi$
$109$	5.35931	+	3.89377i	0.513329	+	0.372955i	−0.300756	+	0.953701i	$0.597239\pi$
$110$	6.26629	+	1.33194i	0.597467	+	0.126996i
$111$	0.965827	−	0.430014i	0.0916722	−	0.0408151i
$112$	2.40640	−	1.74835i	0.227384	−	0.165204i
$113$	−11.3824	−	12.6415i	−1.07077	−	1.18921i	−0.981153	−	0.193232i	$-0.938103\pi$
$113$	−11.3824	−	12.6415i	−1.07077	−	1.18921i	−0.0896152	−	0.995976i	$-0.528564\pi$
$114$	3.89758	+	1.73532i	0.365042	+	0.162527i
$115$	0.110150	−	0.122334i	0.0102716	−	0.0114077i
$116$	0.397877	+	1.22454i	0.0369419	+	0.113696i
$117$	2.26814	−	5.62781i	0.209690	−	0.520291i
$118$	−1.46460			−0.134828
$119$	0.0438740	+	0.0759919i	0.00402192	+	0.00696617i
$120$	−1.53548	+	0.326376i	−0.140169	+	0.0297939i
$121$	8.95341	−	3.98631i	0.813946	−	0.362392i
$122$	−15.7927	+	11.4740i	−1.42980	+	1.03881i
$123$	0.351063	−	0.608059i	0.0316543	−	0.0548268i
$124$	−5.58209	+	1.21968i	−0.501286	+	0.109530i
$125$	7.54807			0.675120
$126$	−0.182069	−	1.73227i	−0.0162200	−	0.154323i
$127$	−0.838647	+	7.97919i	−0.0744179	+	0.708039i	0.892169	+	0.451701i	$0.149183\pi$
$127$	−0.838647	+	7.97919i	−0.0744179	+	0.708039i	−0.966587	+	0.256338i	$0.917484\pi$
$128$	11.6845	−	2.48362i	1.03278	−	0.219523i
$129$	−13.6992			−1.20615
$130$	2.82842	−	4.20112i	0.248069	−	0.368462i
$131$	−4.93572	+	15.1906i	−0.431236	+	1.32721i	0.465659	+	0.884964i	$0.345817\pi$
$131$	−4.93572	+	15.1906i	−0.431236	+	1.32721i	−0.896895	+	0.442243i	$0.854183\pi$
$132$	3.59424	−	3.99181i	0.312838	−	0.347442i
$133$	0.850770	−	0.944875i	0.0737711	−	0.0819311i
$134$	1.57877	+	15.0209i	0.136385	+	1.29761i
$135$	−1.34099	+	4.12713i	−0.115414	+	0.355207i
$136$	0.0261144	+	0.248462i	0.00223929	+	0.0213054i
$137$	−12.0314	+	5.35672i	−1.02791	+	0.457656i	−0.850218	−	0.526430i	$-0.823530\pi$
$137$	−12.0314	+	5.35672i	−1.02791	+	0.457656i	−0.177693	+	0.984086i	$0.556863\pi$
$138$	−0.125778	−	0.387106i	−0.0107070	−	0.0329526i
$139$	10.1340	−	4.51193i	0.859550	−	0.382697i	0.0708595	−	0.997486i	$-0.477426\pi$
$139$	10.1340	−	4.51193i	0.859550	−	0.382697i	0.788691	+	0.614790i	$0.210759\pi$
$140$	0.0515340	−	0.490313i	0.00435542	−	0.0414390i
$141$	4.36222	−	4.84474i	0.367365	−	0.408000i
$142$	−13.6747	−	9.93522i	−1.14755	−	0.833745i
$143$	−0.588054	−	16.4336i	−0.0491756	−	1.37425i
$144$	2.59982	−	8.00143i	0.216652	−	0.666786i
$145$	−0.925485	−	0.412052i	−0.0768573	−	0.0342191i
$146$	3.18281	−	3.53487i	0.263411	−	0.292548i
$147$	−7.46069	−	1.58582i	−0.615347	−	0.130796i
$148$	−0.292133	+	0.899092i	−0.0240132	+	0.0739049i
$149$	−7.73724	+	13.4013i	−0.633859	+	1.09788i	0.352896	+	0.935662i	$0.385197\pi$
$149$	−7.73724	+	13.4013i	−0.633859	+	1.09788i	−0.986756	+	0.162214i	$0.948137\pi$
$150$	4.34037	−	7.51774i	0.354390	−	0.613821i
$151$	−1.03939	+	3.19891i	−0.0845842	+	0.260323i	−0.984400	−	0.175948i	$-0.943701\pi$
$151$	−1.03939	+	3.19891i	−0.0845842	+	0.260323i	0.899815	+	0.436271i	$0.143701\pi$
$152$	3.30704	−	1.47239i	0.268237	−	0.119427i
$153$	0.226735	+	0.100949i	0.0183304	+	0.00816122i
$154$	−2.36026	−	4.08809i	−0.190195	−	0.329428i
$155$	2.22571	−	3.90609i	0.178773	−	0.313744i
$156$	−1.86482	−	3.81510i	−0.149305	−	0.305452i
$157$	0.0386908	−	0.0281105i	0.00308787	−	0.00224347i	−0.586240	−	0.810137i	$-0.699393\pi$
$157$	0.0386908	−	0.0281105i	0.00308787	−	0.00224347i	0.589328	+	0.807894i	$0.299393\pi$
$158$	1.03986	−	9.89360i	0.0827268	−	0.787093i
$159$	−3.54186	+	0.752845i	−0.280888	+	0.0597045i
$160$	2.14332	−	3.71234i	0.169444	−	0.293486i
$161$	−0.121299			−0.00955974
$162$	1.30292	+	1.44704i	0.102367	+	0.113690i
$163$	−20.9787	−	4.45915i	−1.64318	−	0.349268i	−0.708760	−	0.705450i	$-0.750745\pi$
$163$	−20.9787	−	4.45915i	−1.64318	−	0.349268i	−0.934417	+	0.356182i	$0.884078\pi$
$164$	0.194011	+	0.597104i	0.0151497	+	0.0466260i
$165$	0.441778	+	4.20323i	0.0343923	+	0.327221i
$166$	7.50657	−	1.59557i	0.582623	−	0.123840i
$167$	7.26615	+	3.23510i	0.562272	+	0.250340i	0.668134	−	0.744041i	$-0.267093\pi$
$167$	7.26615	+	3.23510i	0.562272	+	0.250340i	−0.105862	+	0.994381i	$0.533760\pi$
$168$	0.935796	+	0.679896i	0.0721982	+	0.0524551i
$169$	−12.2236	−	4.42520i	−0.940281	−	0.340400i
$170$	0.167595	+	0.121765i	0.0128539	+	0.00933893i
$171$	0.375912	−	3.57656i	0.0287467	−	0.273507i
$172$	8.19665	−	9.10330i	0.624988	−	0.694120i
$173$	13.7248	−	6.11068i	1.04348	−	0.464587i	0.187861	−	0.982196i	$-0.439844\pi$
$173$	13.7248	−	6.11068i	1.04348	−	0.464587i	0.855617	+	0.517609i	$0.173178\pi$
$174$	−2.02650	+	1.47234i	−0.153628	+	0.111617i
$175$	−1.73102	−	1.92250i	−0.130853	−	0.145327i
$176$	−2.38333	−	22.6759i	−0.179650	−	1.70926i
$177$	−0.298584	−	0.918946i	−0.0224429	−	0.0690722i
$178$	−28.5080	−	6.05956i	−2.13676	−	0.454183i
$179$	−6.61098	+	1.40521i	−0.494128	+	0.105030i	−0.448234	−	0.893916i	$-0.647947\pi$
$179$	−6.61098	+	1.40521i	−0.494128	+	0.105030i	−0.0458937	+	0.998946i	$0.514614\pi$
$180$	−0.697236	−	1.20765i	−0.0519689	−	0.0900128i
$181$	22.3718			1.66288			0.831440	−	0.555615i	$-0.187517\pi$
$181$	22.3718			1.66288			0.831440	+	0.555615i	$0.187517\pi$
$182$	−3.69507	+	0.522556i	−0.273897	+	0.0387344i
$183$	−10.4188	−	7.56972i	−0.770182	−	0.559570i
$184$	−0.315499	−	0.140469i	−0.0232589	−	0.0103555i
$185$	−0.371913	−	0.644172i	−0.0273436	−	0.0473604i
$186$	−5.61253	−	9.59496i	−0.411531	−	0.703537i
$187$	0.672629			0.0491875
$188$	0.609341	+	5.79749i	0.0444407	+	0.422825i
$189$	2.92117	−	1.30059i	0.212484	−	0.0946039i
$190$	0.927576	−	2.85479i	0.0672934	−	0.207108i
$191$	−6.61265	+	11.4534i	−0.478474	+	0.828742i	−0.999695	−	0.0246798i	$-0.992143\pi$
$191$	−6.61265	+	11.4534i	−0.478474	+	0.828742i	0.521221	+	0.853422i	$0.325477\pi$
$192$	0.438006	+	0.758649i	0.0316104	+	0.0547508i
$193$	7.53154	−	1.60088i	0.542132	−	0.115234i	0.0712973	−	0.997455i	$-0.477286\pi$
$193$	7.53154	−	1.60088i	0.542132	−	0.115234i	0.470835	+	0.882221i	$0.343953\pi$
$194$	−5.03835	−	15.5064i	−0.361732	−	1.11330i
$195$	3.21255	+	0.918190i	0.230056	+	0.0657529i
$196$	5.51774	−	4.00887i	0.394124	−	0.286348i
$197$	3.02397	−	0.642764i	0.215449	−	0.0457950i	−0.0989227	−	0.995095i	$-0.531540\pi$
$197$	3.02397	−	0.642764i	0.215449	−	0.0457950i	0.314371	+	0.949300i	$0.398206\pi$
$198$	−12.1975	−	5.43068i	−0.866839	−	0.385942i
$199$	−4.36110	+	1.94169i	−0.309150	+	0.137643i	−0.555447	−	0.831552i	$-0.687453\pi$
$199$	−4.36110	+	1.94169i	−0.309150	+	0.137643i	0.246297	+	0.969194i	$0.420786\pi$
$200$	−2.27606	−	7.00499i	−0.160942	−	0.495327i
$201$	−9.10283	+	4.05284i	−0.642064	+	0.285865i
$202$	−1.92051	+	0.855067i	−0.135127	+	0.0601623i
$203$	0.230678	+	0.709954i	0.0161904	+	0.0498290i
$204$	0.158680	−	0.0706491i	0.0111099	−	0.00494643i
$205$	−0.451281	−	0.200923i	−0.0315188	−	0.0140331i
$206$	11.1788	−	2.37612i	0.778863	−	0.165552i
$207$	−0.277566	+	0.201664i	−0.0192922	+	0.0140166i
$208$	−17.3313	−	4.95351i	−1.20171	−	0.343464i
$209$	−3.01177	−	9.26928i	−0.208329	−	0.641170i
$210$	0.938178	−	0.199416i	0.0647405	−	0.0137610i
$211$	7.49767	+	12.9863i	0.516161	+	0.894017i	0.999824	+	0.0187624i	$0.00597261\pi$
$211$	7.49767	+	12.9863i	0.516161	+	0.894017i	−0.483663	+	0.875254i	$0.660694\pi$
$212$	1.61892	−	2.80405i	0.111188	−	0.192583i
$213$	3.44592	−	10.6054i	0.236110	−	0.726673i
$214$	29.2541	−	13.0248i	1.99977	−	0.890355i
$215$	1.00747	+	9.58546i	0.0687090	+	0.653723i
$216$	9.10407			0.619453
$217$	−3.23634	+	0.707134i	−0.219697	+	0.0480034i
$218$	−5.76198	−	9.98005i	−0.390251	−	0.675934i
$219$	2.86677	+	1.27637i	0.193719	+	0.0862490i
$220$	−3.05742	−	2.22135i	−0.206131	−	0.149763i
$221$	0.198772	−	0.493202i	0.0133709	−	0.0331764i
$222$	−1.83916			−0.123436
$223$	−8.56954	−	14.8429i	−0.573859	−	0.993953i	−0.996165	−	0.0874992i	$-0.972112\pi$
$223$	−8.56954	−	14.8429i	−0.573859	−	0.993953i	0.422306	−	0.906453i	$-0.361221\pi$
$224$	−3.08963	+	0.656721i	−0.206435	+	0.0438790i
$225$	−7.15727	−	1.52132i	−0.477151	−	0.101422i
$226$	9.14443	+	28.1437i	0.608279	+	1.87209i
$227$	1.50156	+	14.2864i	0.0996623	+	0.948223i	0.924069	+	0.382226i	$0.124842\pi$
$227$	1.50156	+	14.2864i	0.0996623	+	0.948223i	−0.824407	+	0.565998i	$0.808491\pi$
$228$	−1.68410	−	1.87038i	−0.111532	−	0.123869i
$229$	−6.70630	+	4.87241i	−0.443165	+	0.321978i	−0.786891	−	0.617092i	$-0.788311\pi$
$229$	−6.70630	+	4.87241i	−0.443165	+	0.321978i	0.343726	+	0.939070i	$0.388311\pi$
$230$	−0.261610	+	0.116476i	−0.0172501	+	0.00768023i
$231$	2.08384	−	2.31434i	0.137107	−	0.152272i
$232$	−0.222161	+	2.11372i	−0.0145856	+	0.138772i
$233$	3.46919	+	2.52051i	0.227274	+	0.165124i	0.695595	−	0.718434i	$-0.255141\pi$
$233$	3.46919	+	2.52051i	0.227274	+	0.165124i	−0.468321	+	0.883559i	$0.655141\pi$
$234$	−7.58657	+	7.33891i	−0.495950	+	0.479760i
$235$	−3.71070	−	2.69598i	−0.242060	−	0.175867i
$236$	0.789301	+	0.351419i	0.0513791	+	0.0228755i
$237$	6.41960	−	1.36453i	0.416998	−	0.0886356i
$238$	−0.0159559	−	0.151811i	−0.00103427	−	0.00984042i
$239$	−5.81488	−	17.8964i	−0.376133	−	1.15762i	−0.942711	−	0.333611i	$-0.891733\pi$
$239$	−5.81488	−	17.8964i	−0.376133	−	1.15762i	0.566578	−	0.824008i	$-0.308267\pi$
$240$	4.53153	+	0.963206i	0.292509	+	0.0621747i
$241$	16.3303	+	18.1367i	1.05193	+	1.16829i	0.985357	+	0.170505i	$0.0545397\pi$
$241$	16.3303	+	18.1367i	1.05193	+	1.16829i	0.0665726	+	0.997782i	$0.478794\pi$
$242$	−17.0494			−1.09598
$243$	7.41923	−	12.8505i	0.475944	−	0.824358i
$244$	11.2640	−	2.39425i	0.721106	−	0.153276i
$245$	−0.560933	+	5.33692i	−0.0358367	+	0.340963i
$246$	−0.988151	+	0.717934i	−0.0630022	+	0.0457738i
$247$	−7.68669	−	0.530849i	−0.489092	−	0.0337771i
$248$	−9.23658	−	1.90855i	−0.586523	−	0.121193i
$249$	2.53146	+	4.38461i	0.160425	+	0.277864i
$250$	−11.9954	−	5.34072i	−0.758659	−	0.337777i
$251$	4.85530	−	2.16172i	0.306464	−	0.136446i	−0.247742	−	0.968826i	$-0.579689\pi$
$251$	4.85530	−	2.16172i	0.306464	−	0.136446i	0.554206	+	0.832380i	$0.313022\pi$
$252$	−0.317524	+	0.977238i	−0.0200021	+	0.0615602i
$253$	−0.464909	+	0.805245i	−0.0292286	+	0.0506253i
$254$	6.97855	−	12.0872i	0.437873	−	0.758418i
$255$	−0.0422327	+	0.129979i	−0.00264471	+	0.00813959i
$256$	−18.8332	−	4.00312i	−1.17708	−	0.250195i
$257$	20.7579	−	23.0540i	1.29484	−	1.43807i	0.459660	−	0.888095i	$-0.347971\pi$
$257$	20.7579	−	23.0540i	1.29484	−	1.43807i	0.835182	−	0.549973i	$-0.185362\pi$
$258$	21.7709	+	9.69305i	1.35540	+	0.603463i
$259$	−0.169371	+	0.521269i	−0.0105242	+	0.0323901i
$260$	−2.53231	+	1.58540i	−0.157047	+	0.0983222i
$261$	1.70817	+	1.24106i	0.105733	+	0.0768197i
$262$	18.5922	−	20.6487i	1.14863	−	1.27568i
$263$	−2.61590	+	24.8886i	−0.161303	+	1.53470i	0.552000	+	0.833844i	$0.313865\pi$
$263$	−2.61590	+	24.8886i	−0.161303	+	1.53470i	−0.713303	+	0.700855i	$0.752802\pi$
$264$	8.10014	−	3.60641i	0.498529	−	0.221959i
$265$	0.787247	+	2.42290i	0.0483602	+	0.148837i
$266$	−2.02061	+	0.899632i	−0.123891	+	0.0551600i
$267$	−2.00983	−	19.1223i	−0.123000	−	1.17026i
$268$	2.75333	−	8.47386i	0.168186	−	0.517624i
$269$	0.618142	+	5.88123i	0.0376888	+	0.358585i	0.997071	+	0.0764767i	$0.0243671\pi$
$269$	0.618142	+	5.88123i	0.0376888	+	0.358585i	−0.959383	+	0.282108i	$0.908966\pi$
$270$	5.05131	−	5.61004i	0.307413	−	0.341416i
$271$	−11.1431	+	12.3757i	−0.676897	+	0.751770i	−0.979521	−	0.201340i	$-0.935470\pi$
$271$	−11.1431	+	12.3757i	−0.676897	+	0.751770i	0.302625	+	0.953110i	$0.402137\pi$
$272$	0.227840	−	0.701218i	0.0138148	−	0.0425176i
$273$	−1.08117	−	2.21189i	−0.0654355	−	0.133870i
$274$	22.9106			1.38408
$275$	−19.3970	+	4.12297i	−1.16969	+	0.248624i
$276$	−0.0250986	+	0.238797i	−0.00151076	+	0.0143739i
$277$	2.44659	+	23.2778i	0.147001	+	1.39862i	0.780633	+	0.624990i	$0.214897\pi$
$277$	2.44659	+	23.2778i	0.147001	+	1.39862i	−0.633632	+	0.773635i	$0.718436\pi$
$278$	−19.2974			−1.15738
$279$	−6.23001	+	6.99863i	−0.372981	+	0.418997i
$280$	0.406907	−	0.704784i	0.0243174	−	0.0421189i
$281$	−18.4709	+	13.4199i	−1.10188	+	0.800562i	−0.981366	−	0.192150i	$-0.938454\pi$
$281$	−18.4709	+	13.4199i	−1.10188	+	0.800562i	−0.120513	+	0.992712i	$0.538454\pi$
$282$	−10.3604	+	4.61276i	−0.616954	+	0.274686i
$283$	−6.26790	+	1.33228i	−0.372588	+	0.0791960i	−0.390400	−	0.920645i	$-0.627663\pi$
$283$	−6.26790	+	1.33228i	−0.372588	+	0.0791960i	0.0178121	+	0.999841i	$0.494330\pi$
$284$	4.98564	+	8.63539i	0.295843	+	0.512416i
$285$	1.98030			0.117303
$286$	−10.6932	+	26.5325i	−0.632305	+	1.56890i
$287$	0.112482	+	0.346185i	0.00663962	+	0.0204346i
$288$	−5.97810	+	6.63936i	−0.352263	+	0.391228i
$289$	−15.5104	−	6.90568i	−0.912377	−	0.406216i
$290$	1.17924	+	1.30967i	0.0692471	+	0.0769067i
$291$	8.70215	−	6.32248i	0.510129	−	0.370631i
$292$	−2.56343	+	1.14131i	−0.150014	+	0.0667903i
$293$	11.8191	+	2.51223i	0.690479	+	0.146766i	0.539770	−	0.841812i	$-0.318511\pi$
$293$	11.8191	+	2.51223i	0.690479	+	0.146766i	0.150709	+	0.988578i	$0.451844\pi$
$294$	10.7345	+	7.79909i	0.626050	+	0.454852i
$295$	−0.621035	+	0.276502i	−0.0361580	+	0.0160986i
$296$	−1.04418	+	1.15968i	−0.0606917	+	0.0674049i
$297$	2.56212	−	24.3770i	0.148670	−	1.41450i
$298$	21.7783	−	15.8229i	1.26158	−	0.916594i
$299$	0.453055	+	0.578855i	0.0262008	+	0.0334760i
$300$	−4.14292	+	3.01001i	−0.239191	+	0.173783i
$301$	4.75219	−	5.27784i	0.273912	−	0.304210i
$302$	3.91523	−	4.34830i	0.225296	−	0.250217i
$303$	−0.928028	−	1.03068i	−0.0533138	−	0.0592110i
$304$	−10.6834			−0.612737
$305$	−4.53036	+	7.84682i	−0.259408	+	0.449308i
$306$	−0.288901	−	0.320857i	−0.0165154	−	0.0183422i
$307$	1.05088	+	0.763512i	0.0599771	+	0.0435759i	0.617370	−	0.786673i	$-0.288198\pi$
$307$	1.05088	+	0.763512i	0.0599771	+	0.0435759i	−0.557393	+	0.830249i	$0.688198\pi$
$308$	0.291083	+	2.76947i	0.0165860	+	0.157805i
$309$	3.76985	+	6.52957i	0.214459	+	0.371454i
$310$	−6.30090	+	4.63276i	−0.357867	+	0.263123i
$311$	−5.26260			−0.298415			−0.149207	−	0.988806i	$-0.547672\pi$
$311$	−5.26260			−0.298415			−0.149207	+	0.988806i	$0.547672\pi$
$312$	−0.250669	−	7.00514i	−0.0141914	−	0.396588i
$313$	9.95647	+	7.23380i	0.562773	+	0.408878i	0.832473	−	0.554066i	$-0.186925\pi$
$313$	9.95647	+	7.23380i	0.562773	+	0.408878i	−0.269700	+	0.962944i	$0.586925\pi$
$314$	−0.0813777	+	0.0172974i	−0.00459241	+	0.000976147i
$315$	−0.404238	−	0.700161i	−0.0227762	−	0.0394496i
$316$	−2.93428	+	5.08233i	−0.165066	+	0.285903i
$317$	−5.59445	+	17.2179i	−0.314215	+	0.967055i	0.661861	+	0.749627i	$0.269767\pi$
$317$	−5.59445	+	17.2179i	−0.314215	+	0.967055i	−0.976076	+	0.217429i	$0.930233\pi$
$318$	6.16144	+	1.30965i	0.345516	+	0.0734417i
$319$	5.59715	+	1.18971i	0.313380	+	0.0666110i
$320$	0.498620	−	0.362269i	0.0278737	−	0.0202514i
$321$	14.1362	+	15.6998i	0.789003	+	0.876277i
$322$	0.192770	+	0.0858268i	0.0107427	+	0.00478294i
$323$	0.0329436	−	0.313438i	0.00183303	−	0.0174402i
$324$	−0.354963	−	1.09246i	−0.0197201	−	0.0606924i
$325$	−2.70898	+	15.4412i	−0.150267	+	0.856523i
$326$	30.1844	+	21.9302i	1.67176	+	1.21460i
$327$	5.08717	−	5.64988i	0.281321	−	0.312439i
$328$	−0.108329	+	1.03068i	−0.00598147	+	0.0569099i
$329$	0.353279	+	3.36122i	0.0194769	+	0.185310i
$330$	2.27197	−	6.99240i	0.125068	−	0.384919i
$331$	1.76546	+	16.7972i	0.0970384	+	0.923259i	0.929412	+	0.369044i	$0.120315\pi$
$331$	1.76546	+	16.7972i	0.0970384	+	0.923259i	−0.832374	+	0.554215i	$0.813019\pi$
$332$	−4.42827	−	0.941257i	−0.243033	−	0.0516582i
$333$	0.479058	+	1.47439i	0.0262522	+	0.0807961i
$334$	−9.25840	−	10.2825i	−0.506597	−	0.562633i
$335$	3.50524	+	6.07126i	0.191512	+	0.331708i
$336$	−1.70685	−	2.95635i	−0.0931162	−	0.161282i
$337$	5.82027	−	17.9130i	0.317050	−	0.975781i	−0.657852	−	0.753147i	$-0.728535\pi$
$337$	5.82027	−	17.9130i	0.317050	−	0.975781i	0.974902	−	0.222633i	$-0.0714653\pi$
$338$	16.2948	+	15.6815i	0.886322	+	0.852963i
$339$	−15.7941	+	11.4751i	−0.857819	+	0.623242i
$340$	−0.0611034	−	0.105834i	−0.00331380	−	0.00573966i
$341$	−7.70973	+	24.1947i	−0.417505	+	1.31022i
$342$	−3.12804	+	5.41792i	−0.169145	+	0.292968i
$343$	6.56846	−	4.77227i	0.354663	−	0.257678i
$344$	18.4723	−	8.22441i	0.995961	−	0.443431i
$345$	−0.126415	−	0.140398i	−0.00680596	−	0.00755879i
$346$	−26.1353			−1.40504
$347$	2.09423	−	3.62731i	0.112424	−	0.194724i	−0.804323	−	0.594192i	$-0.797472\pi$
$347$	2.09423	−	3.62731i	0.112424	−	0.194724i	0.916747	+	0.399468i	$0.130805\pi$
$348$	1.44539	−	0.307227i	0.0774809	−	0.0164691i
$349$	12.7675	−	14.1797i	0.683426	−	0.759022i	−0.297220	−	0.954809i	$-0.596060\pi$
$349$	12.7675	−	14.1797i	0.683426	−	0.759022i	0.980646	+	0.195787i	$0.0627262\pi$
$350$	1.39067	+	4.28005i	0.0743347	+	0.228779i
$351$	−17.1172	−	9.08244i	−0.913646	−	0.484785i
$352$	−7.48209	+	23.0275i	−0.398797	+	1.22737i
$353$	−16.3132	−	7.26310i	−0.868263	−	0.386576i	−0.0762564	−	0.997088i	$-0.524297\pi$
$353$	−16.3132	−	7.26310i	−0.868263	−	0.386576i	−0.792006	+	0.610513i	$0.790963\pi$
$354$	−0.175699	+	1.67166i	−0.00933829	+	0.0888479i
$355$	−7.67412	−	1.63118i	−0.407300	−	0.0865743i
$356$	13.9095	+	10.1058i	0.737202	+	0.535609i
$357$	0.0919986	−	0.0409604i	0.00486908	−	0.00216785i
$358$	11.5005	+	2.44451i	0.607820	+	0.129196i
$359$	7.04152	+	5.11597i	0.371637	+	0.270010i	0.757890	−	0.652383i	$-0.226231\pi$
$359$	7.04152	+	5.11597i	0.371637	+	0.270010i	−0.386252	+	0.922393i	$0.626231\pi$
$360$	−0.240608	−	2.28923i	−0.0126812	−	0.120653i
$361$	14.1179	−	3.00085i	0.743048	−	0.157940i
$362$	−35.5534	−	15.8294i	−1.86864	−	0.831974i
$363$	−3.47580	−	10.6974i	−0.182432	−	0.561468i
$364$	2.11672	+	0.604986i	0.110946	+	0.0317099i
$365$	0.682256	−	2.09977i	0.0357109	−	0.109907i
$366$	11.2016	+	19.4018i	0.585519	+	1.01415i
$367$	14.6364	+	25.3510i	0.764014	+	1.32331i	0.940766	+	0.339056i	$0.110108\pi$
$367$	14.6364	+	25.3510i	0.764014	+	1.32331i	−0.176752	+	0.984255i	$0.556559\pi$
$368$	0.681992	+	0.757429i	0.0355513	+	0.0394837i
$369$	0.832932	+	0.605161i	0.0433607	+	0.0315034i
$370$	0.135256	+	1.28687i	0.00703162	+	0.0669014i
$371$	0.938606	−	1.62571i	0.0487300	−	0.0844028i
$372$	0.722461	+	6.51757i	0.0374579	+	0.337920i
$373$	5.39321	−	9.34132i	0.279250	−	0.483675i	−0.691949	−	0.721947i	$-0.743248\pi$
$373$	5.39321	−	9.34132i	0.279250	−	0.483675i	0.971199	+	0.238272i	$0.0765808\pi$
$374$	−1.06895	−	0.475926i	−0.0552740	−	0.0246096i
$375$	0.905491	−	8.61518i	0.0467594	−	0.444886i
$376$	−2.97354	+	9.15162i	−0.153349	+	0.471959i
$377$	2.52639	−	3.75251i	0.130116	−	0.193264i
$378$	−5.56259			−0.286109
$379$	1.01035	−	0.214756i	0.0518980	−	0.0110313i	−0.181890	−	0.983319i	$-0.558221\pi$
$379$	1.01035	−	0.214756i	0.0518980	−	0.0110313i	0.233788	+	0.972288i	$0.424888\pi$
$380$	−1.18487	+	1.31593i	−0.0607825	+	0.0675058i
$381$	9.00664	+	1.91442i	0.461424	+	0.0980788i
$382$	18.6129	−	13.5231i	0.952318	−	0.691899i
$383$	−12.9042	−	14.3315i	−0.659371	−	0.732306i	0.316995	−	0.948427i	$-0.397326\pi$
$383$	−12.9042	−	14.3315i	−0.659371	−	0.732306i	−0.976367	+	0.216121i	$0.930659\pi$
$384$	−1.43303	−	13.6344i	−0.0731290	−	0.695776i
$385$	−1.77261	−	1.28788i	−0.0903406	−	0.0656363i
$386$	−13.1019	−	2.78490i	−0.666869	−	0.141747i
$387$	2.09975	−	19.9778i	0.106736	−	1.01553i
$388$	−1.00538	+	9.56560i	−0.0510407	+	0.485620i
$389$	1.61964	+	4.98473i	0.0821188	+	0.252736i	0.983683	−	0.179909i	$-0.0575804\pi$
$389$	1.61964	+	4.98473i	0.0821188	+	0.252736i	−0.901564	+	0.432645i	$0.857580\pi$
$390$	−4.45574	−	3.73227i	−0.225625	−	0.188991i
$391$	−0.0243250	+	0.0176731i	−0.00123017	+	0.000893769i
$392$	11.0122	−	2.34071i	0.556200	−	0.118224i
$393$	16.7460	+	7.45582i	0.844726	+	0.376096i
$394$	−5.26051	−	1.11816i	−0.265020	−	0.0563318i
$395$	−1.42688	−	4.39149i	−0.0717942	−	0.220960i
$396$	5.27040	+	5.85338i	0.264848	+	0.294143i
$397$	−9.40625	+	16.2921i	−0.472086	+	0.817677i	−0.999490	−	0.0319378i	$-0.989832\pi$
$397$	−9.40625	+	16.2921i	−0.472086	+	0.817677i	0.527404	+	0.849615i	$0.323166\pi$
$398$	8.30456			0.416270
$399$	−0.976396	−	1.08440i	−0.0488809	−	0.0542878i
$400$	−2.27215	+	21.6180i	−0.113607	+	1.08090i
$401$	−23.7454	−	10.5721i	−1.18579	−	0.527946i	−0.283454	−	0.958986i	$-0.591480\pi$
$401$	−23.7454	−	10.5721i	−1.18579	−	0.527946i	−0.902333	+	0.431040i	$0.858147\pi$
$402$	17.3339			0.864538
$403$	15.4623	+	12.8030i	0.770232	+	0.637764i
$404$	1.24016			0.0617004
$405$	0.825664	+	0.367609i	0.0410276	+	0.0182667i
$406$	0.135740	−	1.29148i	0.00673668	−	0.0640952i
$407$	2.81129	+	3.12225i	0.139350	+	0.154764i
$408$	0.286721			0.0141948
$409$	2.66483	−	4.61562i	0.131767	−	0.228228i	−0.792591	−	0.609754i	$-0.791268\pi$
$409$	2.66483	−	4.61562i	0.131767	−	0.228228i	0.924358	+	0.381526i	$0.124601\pi$
$410$	0.575014	+	0.638618i	0.0283979	+	0.0315391i
$411$	4.67070	+	14.3749i	0.230389	+	0.709064i
$412$	−6.59457	−	1.40172i	−0.324891	−	0.0690578i
$413$	0.457615	+	0.203743i	0.0225178	+	0.0100256i
$414$	0.583800	−	0.124091i	0.0286922	−	0.00609872i
$415$	2.88178	−	2.09373i	0.141461	−	0.102777i
$416$	14.6737	+	12.2912i	0.719439	+	0.602626i
$417$	−3.93410	−	12.1079i	−0.192654	−	0.592927i
$418$	−1.77225	+	16.8618i	−0.0866836	+	0.824739i
$419$	1.44754	−	13.7725i	0.0707172	−	0.672829i	−0.900536	−	0.434781i	$-0.856826\pi$
$419$	1.44754	−	13.7725i	0.0707172	−	0.672829i	0.971253	−	0.238048i	$-0.0765075\pi$
$420$	−0.553449	−	0.117639i	−0.0270055	−	0.00574021i
$421$	23.3285	+	16.9492i	1.13696	+	0.826052i	0.986693	−	0.162593i	$-0.0519858\pi$
$421$	23.3285	+	16.9492i	1.13696	+	0.826052i	0.150270	+	0.988645i	$0.451986\pi$
$422$	−2.72673	−	25.9431i	−0.132735	−	1.26289i
$423$	6.39653	+	7.10407i	0.311010	+	0.345412i
$424$	4.32394	−	3.14153i	0.209989	−	0.152566i
$425$	−0.627239	−	0.133324i	−0.0304255	−	0.00646715i
$426$	−12.9803	+	14.4161i	−0.628896	+	0.698460i
$427$	6.53058	−	1.38812i	0.316037	−	0.0671758i
$428$	−18.8907			−0.913119
$429$	−18.8275	−	1.30024i	−0.908998	−	0.0627762i
$430$	5.18121	−	15.9461i	0.249860	−	0.768991i
$431$	−1.52963	+	14.5534i	−0.0736795	+	0.701014i	0.893869	+	0.448328i	$0.147980\pi$
$431$	−1.52963	+	14.5534i	−0.0736795	+	0.701014i	−0.967548	+	0.252686i	$0.918686\pi$
$432$	−24.5452	−	10.9282i	−1.18093	−	0.525785i
$433$	5.97309	−	10.3457i	0.287048	−	0.497182i	−0.686056	−	0.727549i	$-0.740659\pi$
$433$	5.97309	−	10.3457i	0.287048	−	0.497182i	0.973104	+	0.230367i	$0.0739927\pi$
$434$	5.64356	+	1.16612i	0.270900	+	0.0559758i
$435$	−0.581331	+	1.00689i	−0.0278727	+	0.0482769i
$436$	0.710606	+	6.76096i	0.0340318	+	0.323791i
$437$	0.352466	+	0.256081i	0.0168607	+	0.0122500i
$438$	−3.65279	−	4.05683i	−0.174537	−	0.193843i
$439$	−18.2608	−	31.6287i	−0.871542	−	1.50956i	−0.860401	−	0.509618i	$-0.829787\pi$
$439$	−18.2608	−	31.6287i	−0.871542	−	1.50956i	−0.0111416	−	0.999938i	$-0.503547\pi$
$440$	−3.11914	−	5.40250i	−0.148699	−	0.257554i
$441$	3.45616	−	10.6370i	0.164579	−	0.506522i
$442$	−0.664861	+	0.643157i	−0.0316242	+	0.0305919i
$443$	−0.813771	−	2.50453i	−0.0386634	−	0.118994i	0.929862	−	0.367909i	$-0.119926\pi$
$443$	−0.813771	−	2.50453i	−0.0386634	−	0.118994i	−0.968525	+	0.248915i	$0.919926\pi$
$444$	0.991156	+	0.441291i	0.0470382	+	0.0209427i
$445$	−13.2322	+	2.81259i	−0.627266	+	0.133329i
$446$	3.11654	+	29.6519i	0.147572	+	1.40406i
$447$	14.3677	+	10.4388i	0.679570	+	0.493736i
$448$	−0.444223	−	0.0944225i	−0.0209876	−	0.00446104i
$449$	21.4761	−	9.56178i	1.01352	−	0.451248i	0.168340	−	0.985729i	$-0.446159\pi$
$449$	21.4761	−	9.56178i	1.01352	−	0.451248i	0.845181	+	0.534481i	$0.179493\pi$
$450$	10.2980	+	7.48191i	0.485450	+	0.352700i
$451$	2.72926	+	0.580122i	0.128516	+	0.0273169i
$452$	1.82474	−	17.3612i	0.0858286	−	0.816604i
$453$	3.52647	+	1.57008i	0.165688	+	0.0737690i
$454$	7.72222	−	23.7666i	0.362422	−	1.11542i
$455$	−1.46816	+	0.919171i	−0.0688286	+	0.0430914i
$456$	−1.28383	−	3.95121i	−0.0601207	−	0.185032i
$457$	−1.04170	+	1.15692i	−0.0487286	+	0.0541186i	−0.767016	−	0.641628i	$-0.778259\pi$
$457$	−1.04170	+	1.15692i	−0.0487286	+	0.0541186i	0.718288	+	0.695746i	$0.244926\pi$
$458$	14.1052	−	2.99816i	0.659094	−	0.140095i
$459$	0.396308	−	0.686426i	0.0184981	−	0.0320396i
$460$	0.168934			0.00787659
$461$	−17.6818	−	19.6377i	−0.823525	−	0.914617i	0.174013	−	0.984743i	$-0.444327\pi$
$461$	−17.6818	−	19.6377i	−0.823525	−	0.914617i	−0.997538	+	0.0701261i	$0.977660\pi$
$462$	−4.94919	+	2.20352i	−0.230257	+	0.102517i
$463$	−29.1742	+	21.1963i	−1.35584	+	0.985076i	−0.357144	+	0.934049i	$0.616249\pi$
$463$	−29.1742	+	21.1963i	−1.35584	+	0.985076i	−0.998697	+	0.0510268i	$0.983751\pi$
$464$	3.13620	−	5.43205i	0.145594	−	0.252177i
$465$	−4.19131	−	3.00895i	−0.194367	−	0.139537i
$466$	−3.72985	−	6.46029i	−0.172782	−	0.299267i
$467$	6.62641	−	4.81437i	0.306634	−	0.222782i	−0.423817	−	0.905748i	$-0.639310\pi$
$467$	6.62641	−	4.81437i	0.306634	−	0.222782i	0.730451	+	0.682965i	$0.239310\pi$
$468$	5.84945	−	2.13474i	0.270391	−	0.0986782i
$469$	1.59630	−	4.91291i	0.0737104	−	0.226857i
$470$	3.98951	+	6.91003i	0.184022	+	0.318736i
$471$	−0.0274432	−	0.0475330i	−0.00126452	−	0.00219021i
$472$	0.954310	+	1.05987i	0.0439257	+	0.0487844i
$473$	−16.8230	−	51.7760i	−0.773524	−	2.38066i
$474$	−11.1676	−	2.37374i	−0.512943	−	0.109029i
$475$	0.971241	+	9.24074i	0.0445636	+	0.423994i
$476$	−0.0278267	+	0.0856419i	−0.00127544	+	0.00392539i
$477$	−0.555007	−	5.28054i	−0.0254120	−	0.241779i
$478$	−3.42171	+	32.5554i	−0.156505	+	1.48905i
$479$	−20.6628	+	22.9484i	−0.944109	+	1.04854i	0.0546388	+	0.998506i	$0.482599\pi$
$479$	−20.6628	+	22.9484i	−0.944109	+	1.04854i	−0.998748	+	0.0500329i	$0.984067\pi$
$480$	−3.98005	−	2.89168i	−0.181664	−	0.131986i
$481$	3.12015	−	1.13869i	0.142267	−	0.0519198i
$482$	−13.1195	−	40.3777i	−0.597577	−	1.83915i
$483$	−0.0145515	+	0.138448i	−0.000662116	+	0.00629961i
$484$	9.18821	+	4.09086i	0.417646	+	0.185948i
$485$	−5.06386	−	5.62399i	−0.229938	−	0.255372i
$486$	−20.8832	+	15.1725i	−0.947281	+	0.688240i
$487$	−38.5362	−	8.19112i	−1.74624	−	0.371175i	−0.779394	−	0.626534i	$-0.784473\pi$
$487$	−38.5362	−	8.19112i	−1.74624	−	0.371175i	−0.966846	+	0.255359i	$0.917806\pi$
$488$	18.5935	+	3.95217i	0.841687	+	0.178906i
$489$	−7.60624	+	23.4096i	−0.343966	+	1.05862i
$490$	4.66764	−	8.08458i	0.210862	−	0.365224i
$491$	−1.57621	−	2.73007i	−0.0711333	−	0.123206i	0.828265	−	0.560337i	$-0.189328\pi$
$491$	−1.57621	−	2.73007i	−0.0711333	−	0.123206i	−0.899398	+	0.437130i	$0.855995\pi$
$492$	0.704794	−	0.149809i	0.0317746	−	0.00675390i
$493$	0.149698	+	0.108762i	0.00674208	+	0.00489841i
$494$	11.8401	+	6.28243i	0.532713	+	0.282660i
$495$	−6.19735			−0.278550
$496$	22.6115	+	16.2329i	1.01529	+	0.728878i
$497$	2.89054	+	5.00656i	0.129658	+	0.224575i
$498$	−0.920632	−	8.75923i	−0.0412545	−	0.392510i
$499$	−7.28364	−	5.29187i	−0.326060	−	0.236897i	0.412697	−	0.910869i	$-0.364587\pi$
$499$	−7.28364	−	5.29187i	−0.326060	−	0.236897i	−0.738757	+	0.673972i	$0.764587\pi$
$500$	5.18310	+	5.75641i	0.231795	+	0.257435i
$501$	4.56414	−	7.90531i	0.203911	−	0.353183i
$502$	−9.24562			−0.412652
$503$	2.41702	+	2.68437i	0.107769	+	0.119690i	0.794616	−	0.607112i	$-0.207672\pi$
$503$	2.41702	+	2.68437i	0.107769	+	0.119690i	−0.686847	+	0.726802i	$0.741006\pi$
$504$	−1.13494	+	1.26047i	−0.0505541	+	0.0561460i
$505$	−0.652925	+	0.725146i	−0.0290548	+	0.0322686i
$506$	1.30860	−	0.950751i	0.0581742	−	0.0422660i
$507$	−6.51720	+	13.4209i	−0.289439	+	0.596043i
$508$	−6.66108	+	4.83956i	−0.295538	+	0.214721i
$509$	−0.286961	+	2.73025i	−0.0127193	+	0.121016i	−0.999039	−	0.0438267i	$-0.986045\pi$
$509$	−0.286961	+	2.73025i	−0.0127193	+	0.121016i	0.986320	+	0.164843i	$0.0527117\pi$
$510$	0.159085	−	0.176681i	0.00704438	−	0.00782358i
$511$	−1.48621	+	0.661702i	−0.0657460	+	0.0292720i
$512$	7.76912	+	5.64459i	0.343350	+	0.249458i
$513$	−11.2339	−	2.38784i	−0.495990	−	0.105426i
$514$	−49.3007	+	21.9501i	−2.17456	+	0.968177i
$515$	4.29154	−	3.11799i	0.189108	−	0.137395i
$516$	−9.40698	−	10.4475i	−0.414119	−	0.459926i
$517$	23.6675	+	10.5374i	1.04089	+	0.463436i
$518$	0.637995	−	0.708565i	0.0280319	−	0.0311326i
$519$	−5.32811	−	16.3982i	−0.233878	−	0.719802i
$520$	−4.88311	+	0.690568i	−0.214139	+	0.0302834i
$521$	4.27928			0.187479			0.0937394	−	0.995597i	$-0.470118\pi$
$521$	4.27928			0.187479			0.0937394	+	0.995597i	$0.470118\pi$
$522$	−1.83652	−	3.18094i	−0.0803822	−	0.139226i
$523$	−31.4643	+	6.68795i	−1.37584	+	0.292444i	−0.835725	−	0.549148i	$-0.814952\pi$
$523$	−31.4643	+	6.68795i	−1.37584	+	0.292444i	−0.540114	+	0.841592i	$0.681619\pi$
$524$	−14.9741	+	6.66690i	−0.654147	+	0.291245i
$525$	−2.40195	+	1.74512i	−0.104830	+	0.0761632i
$526$	21.7674	−	37.7023i	0.949106	−	1.64390i
$527$	−0.545976	+	0.613336i	−0.0237831	+	0.0267173i
$528$	−26.1676			−1.13880
$529$	2.39981	+	22.8327i	0.104340	+	0.992725i
$530$	0.463248	−	4.40751i	0.0201222	−	0.191450i
$531$	1.38588	−	0.294577i	0.0601420	−	0.0127836i
$532$	1.30480			0.0565702
$533$	1.23191	−	1.82978i	0.0533600	−	0.0792566i
$534$	−10.3361	+	31.8114i	−0.447288	+	1.37661i
$535$	9.94565	−	11.0458i	0.429988	−	0.477550i
$536$	9.84130	−	10.9299i	0.425079	−	0.472098i
$537$	0.810793	+	7.71418i	0.0349883	+	0.332891i
$538$	3.17897	−	9.78388i	0.137055	−	0.421813i
$539$	−3.16836	−	30.1449i	−0.136471	−	1.29843i
$540$	−4.06832	+	1.81133i	−0.175073	+	0.0779474i
$541$	3.45311	+	10.6276i	0.148461	+	0.456916i	0.997440	−	0.0715111i	$-0.0227821\pi$
$541$	3.45311	+	10.6276i	0.148461	+	0.456916i	−0.848979	+	0.528427i	$0.822782\pi$
$542$	26.4653	−	11.7831i	1.13678	−	0.506128i
$543$	2.68379	−	25.5346i	0.115173	−	1.09579i
$544$	−0.523901	+	0.581850i	−0.0224621	+	0.0249466i
$545$	−4.32738	−	3.14403i	−0.185365	−	0.134675i
$546$	0.153159	+	4.28015i	0.00655461	+	0.183173i
$547$	−1.08574	+	3.34156i	−0.0464228	+	0.142875i	−0.971581	−	0.236707i	$-0.923932\pi$
$547$	−1.08574	+	3.34156i	−0.0464228	+	0.142875i	0.925158	+	0.379581i	$0.123932\pi$
$548$	−12.3469	−	5.49720i	−0.527434	−	0.234829i
$549$	12.6360	−	14.0337i	0.539291	−	0.598943i
$550$	33.7432	+	7.17234i	1.43881	+	0.305829i
$551$	0.828526	−	2.54994i	0.0352964	−	0.108631i
$552$	−0.198176	+	0.343251i	−0.00843494	+	0.0146097i
$553$	−1.70122	+	2.94660i	−0.0723431	+	0.125302i
$554$	12.5823	−	38.7243i	0.534570	−	1.64524i
$555$	−0.779857	+	0.347215i	−0.0331031	+	0.0147385i
$556$	10.3997	+	4.63025i	0.441046	+	0.196366i
$557$	−2.30090	−	3.98527i	−0.0974921	−	0.168861i	0.813154	−	0.582049i	$-0.197749\pi$
$557$	−2.30090	−	3.98527i	−0.0974921	−	0.168861i	−0.910646	+	0.413188i	$0.864415\pi$
$558$	14.8527	−	6.71417i	0.628766	−	0.284233i
$559$	−42.9359	−	2.96519i	−1.81600	−	0.125414i
$560$	−1.94305	+	1.41171i	−0.0821089	+	0.0596556i
$561$	0.0806909	−	0.767722i	0.00340677	−	0.0324133i
$562$	38.8494	−	8.25770i	1.63876	−	0.348330i
$563$	−12.6638	+	21.9344i	−0.533717	+	0.924425i	0.465507	+	0.885044i	$0.345872\pi$
$563$	−12.6638	+	21.9344i	−0.533717	+	0.924425i	−0.999224	+	0.0393810i	$0.987461\pi$
$564$	6.69021			0.281709
$565$	9.19074	+	10.2074i	0.386657	+	0.429427i
$566$	10.9037	+	2.31765i	0.458315	+	0.0974179i
$567$	−0.205798	−	0.633380i	−0.00864269	−	0.0265995i
$568$	1.72049	+	16.3694i	0.0721901	+	0.686843i
$569$	7.48659	−	1.59132i	0.313854	−	0.0667118i	−0.0482915	−	0.998833i	$-0.515378\pi$
$569$	7.48659	−	1.59132i	0.313854	−	0.0667118i	0.362146	+	0.932122i	$0.382044\pi$
$570$	−3.14711	−	1.40118i	−0.131818	−	0.0586891i
$571$	7.94949	+	5.77564i	0.332676	+	0.241703i	0.741565	−	0.670881i	$-0.234084\pi$
$571$	7.94949	+	5.77564i	0.332676	+	0.241703i	−0.408889	+	0.912584i	$0.634084\pi$
$572$	12.1290	−	11.7331i	0.507140	−	0.490585i
$573$	12.2794	+	8.92150i	0.512979	+	0.372701i
$574$	0.0661892	−	0.629748i	0.00276268	−	0.0262852i
$575$	0.593145	−	0.658755i	0.0247359	−	0.0274720i
$576$	−1.17348	+	0.522469i	−0.0488952	+	0.0217695i
$577$	−7.44835	+	5.41154i	−0.310079	+	0.225286i	−0.731930	−	0.681379i	$-0.761380\pi$
$577$	−7.44835	+	5.41154i	−0.310079	+	0.225286i	0.421851	+	0.906665i	$0.361380\pi$
$578$	19.7631	+	21.9491i	0.822035	+	0.912963i
$579$	−0.923694	−	8.78836i	−0.0383874	−	0.365232i
$580$	−0.321266	−	0.988754i	−0.0133398	−	0.0410558i
$581$	−2.56739	−	0.545715i	−0.106513	−	0.0226401i
$582$	−18.3031	+	3.89044i	−0.758687	+	0.161264i
$583$	−7.19486	−	12.4619i	−0.297980	−	0.516117i
$584$	−4.63189			−0.191669
$585$	−1.83141	+	4.54418i	−0.0757196	+	0.187879i
$586$	−17.0055	−	12.3552i	−0.702489	−	0.510388i
$587$	11.2841	+	5.02402i	0.465746	+	0.207363i	0.626173	−	0.779684i	$-0.284620\pi$
$587$	11.2841	+	5.02402i	0.465746	+	0.207363i	−0.160427	+	0.987048i	$0.551287\pi$
$588$	−3.91370	−	6.77872i	−0.161398	−	0.279550i
$589$	10.8969	+	4.77764i	0.448997	+	0.196859i
$590$	1.18260			0.0486867
$591$	−0.370869	−	3.52859i	−0.0152555	−	0.145147i
$592$	4.20722	−	1.87318i	0.172916	−	0.0769871i
$593$	−5.83493	+	17.9581i	−0.239612	+	0.737450i	0.756864	+	0.653572i	$0.226730\pi$
$593$	−5.83493	+	17.9581i	−0.239612	+	0.737450i	−0.996476	+	0.0838775i	$0.973270\pi$
$594$	−21.3200	+	36.9272i	−0.874768	+	1.51514i
$595$	−0.0354261	−	0.0613597i	−0.00145233	−	0.00251550i
$596$	−15.5333	+	3.30170i	−0.636268	+	0.135243i
$597$	1.69302	+	5.21059i	0.0692908	+	0.213255i
$598$	−0.310423	−	1.24048i	−0.0126941	−	0.0507272i
$599$	25.1368	−	18.2630i	1.02706	−	0.746205i	0.0593438	−	0.998238i	$-0.481099\pi$
$599$	25.1368	−	18.2630i	1.02706	−	0.746205i	0.967719	+	0.252033i	$0.0810992\pi$
$600$	−8.26836	+	1.75749i	−0.337554	+	0.0717494i
$601$	31.3369	+	13.9521i	1.27826	+	0.569118i	0.929751	−	0.368188i	$-0.120022\pi$
$601$	31.3369	+	13.9521i	1.27826	+	0.569118i	0.348508	+	0.937306i	$0.386689\pi$
$602$	−11.2866	+	5.02513i	−0.460008	+	0.204809i
$603$	−4.51508	−	13.8960i	−0.183868	−	0.565889i
$604$	−3.15332	+	1.40395i	−0.128307	+	0.0571259i
$605$	−7.22943	+	3.21875i	−0.293918	+	0.130861i
$606$	0.745561	+	2.29460i	0.0302864	+	0.0932118i
$607$	21.6015	−	9.61761i	0.876778	−	0.390367i	0.0815444	−	0.996670i	$-0.474015\pi$
$607$	21.6015	−	9.61761i	0.876778	−	0.390367i	0.795234	+	0.606303i	$0.207348\pi$
$608$	10.3641	+	4.61440i	0.420320	+	0.187139i
$609$	0.837996	−	0.178122i	0.0339573	−	0.00721785i
$610$	12.7518	−	9.26472i	0.516305	−	0.375118i
$611$	14.7206	−	14.2401i	0.595533	−	0.576093i
$612$	0.0787069	+	0.242235i	0.00318154	+	0.00979176i
$613$	13.5635	−	2.88300i	0.547823	−	0.116443i	0.0743184	−	0.997235i	$-0.476322\pi$
$613$	13.5635	−	2.88300i	0.547823	−	0.116443i	0.473505	+	0.880791i	$0.342989\pi$
$614$	−1.12984	−	1.95694i	−0.0455967	−	0.0789758i
$615$	−0.283466	+	0.490978i	−0.0114305	+	0.0197981i
$616$	−1.42047	+	4.37175i	−0.0572322	+	0.176143i
$617$	−6.07590	+	2.70516i	−0.244606	+	0.108906i	−0.525378	−	0.850869i	$-0.676076\pi$
$617$	−6.07590	+	2.70516i	−0.244606	+	0.108906i	0.280772	+	0.959775i	$0.409410\pi$
$618$	−1.37100	−	13.0442i	−0.0551499	−	0.524716i
$619$	−4.76536			−0.191536			−0.0957681	−	0.995404i	$-0.530531\pi$
$619$	−4.76536			−0.191536			−0.0957681	+	0.995404i	$0.530531\pi$
$620$	4.50726	−	0.984828i	0.181016	−	0.0395516i
$621$	0.547841	+	0.948889i	0.0219841	+	0.0380776i
$622$	8.36336	+	3.72361i	0.335340	+	0.149303i
$623$	8.06435	+	5.85909i	0.323091	+	0.234740i
$624$	−7.73293	+	19.1873i	−0.309565	+	0.768105i
$625$	15.6454			0.625817
$626$	−10.7045	−	18.5408i	−0.427840	−	0.741040i
$627$	−10.9410	+	2.32559i	−0.436943	+	0.0928751i
$628$	0.0480062	+	0.0102040i	0.00191566	+	0.000407186i
$629$	0.0419830	+	0.129211i	0.00167397	+	0.00515196i
$630$	0.147012	+	1.39873i	0.00585710	+	0.0557265i
$631$	21.8236	+	24.2376i	0.868785	+	0.964884i	0.999648	−	0.0265164i	$-0.00844144\pi$
$631$	21.8236	+	24.2376i	0.868785	+	0.964884i	−0.130863	+	0.991400i	$0.541775\pi$
$632$	−7.83711	+	5.69400i	−0.311744	+	0.226495i
$633$	15.7217	−	6.99977i	0.624883	−	0.278216i
$634$	21.0735	−	23.4045i	0.836935	−	0.929510i
$635$	0.677166	−	6.44280i	0.0268725	−	0.255675i
$636$	−3.00627	−	2.18418i	−0.119206	−	0.0866084i
$637$	−23.0399	−	6.58511i	−0.912875	−	0.260911i
$638$	−8.05324	−	5.85102i	−0.318831	−	0.231644i
$639$	14.9379	+	6.65078i	0.590934	+	0.263101i
$640$	−9.43468	+	2.00540i	−0.372938	+	0.0792705i
$641$	3.21010	+	30.5421i	0.126791	+	1.20634i	0.854130	+	0.520060i	$0.174091\pi$
$641$	3.21010	+	30.5421i	0.126791	+	1.20634i	−0.727338	+	0.686279i	$0.759243\pi$
$642$	−11.3567	−	34.9524i	−0.448214	−	1.37946i
$643$	21.8893	+	4.65271i	0.863230	+	0.183485i	0.618191	−	0.786028i	$-0.287866\pi$
$643$	21.8893	+	4.65271i	0.863230	+	0.183485i	0.245039	+	0.969513i	$0.421199\pi$
$644$	−0.0832938	−	0.0925071i	−0.00328223	−	0.00364529i
$645$	11.0615			0.435545
$646$	−0.274131	+	0.474808i	−0.0107855	+	0.0186811i
$647$	−25.2868	+	5.37487i	−0.994126	+	0.211308i	−0.676129	−	0.736783i	$-0.736344\pi$
$647$	−25.2868	+	5.37487i	−0.994126	+	0.211308i	−0.317998	+	0.948092i	$0.603010\pi$
$648$	0.198199	−	1.88574i	0.00778599	−	0.0740787i
$649$	3.10647	−	2.25698i	0.121939	−	0.0885942i
$650$	15.2307	−	22.6225i	0.597398	−	0.887328i
$651$	0.418863	+	3.77871i	0.0164166	+	0.148099i
$652$	−11.0049	−	19.0611i	−0.430985	−	0.746489i
$653$	−18.5331	−	8.25146i	−0.725255	−	0.322905i	0.0106923	−	0.999943i	$-0.496596\pi$
$653$	−18.5331	−	8.25146i	−0.725255	−	0.322905i	−0.735948	+	0.677038i	$0.763263\pi$
$654$	−12.0822	+	5.37935i	−0.472452	+	0.210349i
$655$	3.98535	−	12.2656i	0.155721	−	0.479258i
$656$	1.52926	−	2.64876i	0.0597076	−	0.103417i
$657$	−2.30075	+	3.98502i	−0.0897609	+	0.155470i
$658$	1.81684	−	5.59165i	0.0708277	−	0.217985i
$659$	15.7470	+	3.34713i	0.613416	+	0.130386i	0.504135	−	0.863625i	$-0.331812\pi$
$659$	15.7470	+	3.34713i	0.613416	+	0.130386i	0.109282	+	0.994011i	$0.465145\pi$
$660$	−2.90217	+	3.22319i	−0.112967	+	0.125462i
$661$	−31.3130	−	13.9414i	−1.21793	−	0.542259i	−0.305778	−	0.952103i	$-0.598916\pi$
$661$	−31.3130	−	13.9414i	−1.21793	−	0.542259i	−0.912156	+	0.409844i	$0.865583\pi$
$662$	9.07938	−	27.9434i	0.352880	−	1.08605i
$663$	−0.539083	−	0.286040i	−0.0209363	−	0.0111089i
$664$	−6.04580	−	4.39253i	−0.234622	−	0.170463i
$665$	−0.686954	+	0.762940i	−0.0266389	+	0.0295855i
$666$	0.281898	−	2.68208i	0.0109233	−	0.103928i
$667$	−0.233675	+	0.104039i	−0.00904792	+	0.00402839i
$668$	2.52232	+	7.76289i	0.0975914	+	0.300355i
$669$	−17.9693	+	8.00046i	−0.694734	+	0.309316i
$670$	−1.27477	−	12.1287i	−0.0492489	−	0.468572i
$671$	15.8150	−	48.6735i	0.610531	−	1.87902i
$672$	0.378923	+	3.60521i	0.0146173	+	0.139074i
$673$	−19.5249	+	21.6846i	−0.752631	+	0.835881i	−0.990799	−	0.135343i	$-0.956786\pi$
$673$	−19.5249	+	21.6846i	−0.752631	+	0.835881i	0.238168	+	0.971224i	$0.423453\pi$
$674$	−21.9241	+	24.3492i	−0.844486	+	0.937897i
$675$	−7.22105	+	22.2241i	−0.277938	+	0.855407i
$676$	−5.01891	−	12.3609i	−0.193035	−	0.475418i
$677$	43.3670			1.66673			0.833364	−	0.552725i	$-0.186412\pi$
$677$	43.3670			1.66673			0.833364	+	0.552725i	$0.186412\pi$
$678$	33.2195	−	7.06102i	1.27579	−	0.271177i
$679$	−0.582895	+	5.54587i	−0.0223694	+	0.212831i
$680$	−0.0210861	−	0.200621i	−0.000808615	−	0.00769345i
$681$	16.4863			0.631757
$682$	29.3716	−	32.9953i	1.12470	−	1.26345i
$683$	15.5592	−	26.9493i	0.595355	−	1.03118i	−0.398142	−	0.917324i	$-0.630345\pi$
$683$	15.5592	−	26.9493i	0.595355	−	1.03118i	0.993497	−	0.113861i	$-0.0363218\pi$
$684$	2.98574	−	2.16927i	0.114163	−	0.0829440i
$685$	9.71476	−	4.32529i	0.371182	−	0.165261i
$686$	−13.8153	+	2.93654i	−0.527471	+	0.112117i
$687$	4.75674	+	8.23891i	0.181481	+	0.314334i
$688$	−59.6750			−2.27509
$689$	−11.2638	+	1.59292i	−0.429116	+	0.0606855i
$690$	0.101560	+	0.312569i	0.00386631	+	0.0118993i
$691$	11.9277	−	13.2470i	0.453751	−	0.503941i	−0.472249	−	0.881465i	$-0.656558\pi$
$691$	11.9277	−	13.2470i	0.453751	−	0.503941i	0.926000	+	0.377524i	$0.123224\pi$
$692$	14.0848	+	6.27094i	0.535422	+	0.238385i
$693$	3.05564	+	3.39363i	0.116074	+	0.128913i
$694$	−5.89470	+	4.28275i	−0.223760	+	0.162571i
$695$	−8.18266	+	3.64316i	−0.310386	+	0.138193i
$696$	2.38589	+	0.507137i	0.0904370	+	0.0192230i
$697$	0.0729954	+	0.0530342i	0.00276490	+	0.00200882i
$698$	−30.3231	+	13.5007i	−1.14775	+	0.511010i
$699$	3.29303	−	3.65728i	0.124554	−	0.138331i
$700$	0.277504	−	2.64028i	0.0104887	−	0.0997931i
$701$	−6.73661	+	4.89444i	−0.254438	+	0.184860i	−0.707692	−	0.706522i	$-0.750263\pi$
$701$	−6.73661	+	4.89444i	−0.254438	+	0.184860i	0.453253	+	0.891382i	$0.350263\pi$
$702$	20.7763	+	26.5453i	0.784153	+	1.00189i
$703$	1.59262	−	1.15711i	0.0600670	−	0.0436412i
$704$	−2.32941	+	2.58707i	−0.0877930	+	0.0975040i
$705$	−3.52228	+	3.91189i	−0.132657	+	0.147330i
$706$	20.7860	+	23.0851i	0.782290	+	0.868821i
$707$	0.719013			0.0270413
$708$	0.495789	−	0.858731i	0.0186329	−	0.0322731i
$709$	−7.05525	−	7.83564i	−0.264965	−	0.294274i	0.595951	−	0.803021i	$-0.296775\pi$
$709$	−7.05525	−	7.83564i	−0.264965	−	0.294274i	−0.860916	+	0.508747i	$0.830109\pi$
$710$	11.0416	+	8.02220i	0.414384	+	0.301068i
$711$	1.00595	+	9.57094i	0.0377259	+	0.358938i
$712$	14.1903	+	24.5783i	0.531802	+	0.921109i
$713$	−0.356893	−	1.07755i	−0.0133658	−	0.0403545i
$714$	−0.175187			−0.00655621
$715$	0.474825	+	13.2693i	0.0177574	+	0.496245i
$716$	−5.61128	−	4.07683i	−0.209703	−	0.152358i
$717$	−21.1240	+	4.49005i	−0.788891	+	0.167684i
$718$	−7.57059	−	13.1126i	−0.282532	−	0.489360i
$719$	−16.9090	+	29.2872i	−0.630599	+	1.09223i	0.356831	+	0.934169i	$0.383857\pi$
$719$	−16.9090	+	29.2872i	−0.630599	+	1.09223i	−0.987429	+	0.158060i	$0.949476\pi$
$720$	−2.09923	+	6.46076i	−0.0782336	+	0.240778i
$721$	−3.82335	−	0.812679i	−0.142389	−	0.0302657i
$722$	−24.5596	−	5.22030i	−0.914013	−	0.194279i
$723$	22.6598	−	16.4633i	0.842727	−	0.612277i
$724$	15.3622	+	17.0615i	0.570932	+	0.634084i
$725$	−4.98362	−	2.21885i	−0.185087	−	0.0824061i
$726$	−2.04530	+	19.4597i	−0.0759083	+	0.722219i
$727$	−2.67868	−	8.24412i	−0.0993466	−	0.305757i	0.889015	−	0.457877i	$-0.151390\pi$
$727$	−2.67868	−	8.24412i	−0.0993466	−	0.305757i	−0.988362	+	0.152120i	$0.951390\pi$
$728$	2.78579	+	2.33347i	0.103248	+	0.0864842i
$729$	−16.4938	−	11.9835i	−0.610883	−	0.443833i
$730$	−2.56996	+	2.85423i	−0.0951185	+	0.105640i
$731$	0.184015	−	1.75079i	0.00680605	−	0.0647552i
$732$	−1.38146	−	13.1437i	−0.0510603	−	0.485806i
$733$	6.88901	−	21.2022i	0.254451	−	0.783121i	−0.739486	−	0.673172i	$-0.764931\pi$
$733$	6.88901	−	21.2022i	0.254451	−	0.783121i	0.993937	−	0.109949i	$-0.0350687\pi$
$734$	−5.32292	−	50.6442i	−0.196473	−	1.86931i
$735$	6.02414	+	1.28047i	0.222204	+	0.0472308i
$736$	−0.334458	−	1.02936i	−0.0123283	−	0.0379426i
$737$	−26.4961	−	29.4269i	−0.975998	−	1.08396i
$738$	−0.895515	−	1.55108i	−0.0329644	−	0.0570959i
$739$	6.57406	+	11.3866i	0.241831	+	0.418863i	0.961236	−	0.275728i	$-0.0889188\pi$
$739$	6.57406	+	11.3866i	0.241831	+	0.418863i	−0.719405	+	0.694591i	$0.755585\pi$
$740$	0.235883	−	0.725972i	0.00867122	−	0.0266873i
$741$	−1.52802	+	8.70971i	−0.0561332	+	0.319959i
$742$	−2.64193	+	1.91948i	−0.0969884	+	0.0704662i
$743$	14.8407	+	25.7049i	0.544453	+	0.943021i	0.998641	+	0.0521148i	$0.0165962\pi$
$743$	14.8407	+	25.7049i	0.544453	+	0.943021i	−0.454188	+	0.890906i	$0.650070\pi$
$744$	−3.28642	+	10.3134i	−0.120486	+	0.378109i
$745$	6.24744	−	10.8209i	0.228888	−	0.396446i
$746$	−15.1805	+	11.0293i	−0.555797	+	0.403810i
$747$	−6.78216	+	3.01961i	−0.248146	+	0.110482i
$748$	0.461880	+	0.512970i	0.0168880	+	0.0187560i
$749$	−10.9523			−0.400190
$750$	−7.53478	+	13.0506i	−0.275131	+	0.476541i
$751$	−52.5528	+	11.1704i	−1.91768	+	0.407615i	−0.917733	+	0.397197i	$0.869983\pi$
$751$	−52.5528	+	11.1704i	−1.91768	+	0.407615i	−0.999946	+	0.0104178i	$0.996684\pi$
$752$	19.0022	−	21.1041i	0.692939	−	0.769587i
$753$	−1.88487	−	5.80104i	−0.0686886	−	0.211402i
$754$	−6.67009	+	4.17593i	−0.242911	+	0.152079i
$755$	0.839254	−	2.58296i	0.0305436	−	0.0940035i
$756$	2.99778	+	1.33470i	0.109028	+	0.0485425i
$757$	1.69309	−	16.1086i	0.0615363	−	0.585479i	−0.919694	−	0.392637i	$-0.871563\pi$
$757$	1.69309	−	16.1086i	0.0615363	−	0.585479i	0.981230	−	0.192842i	$-0.0617704\pi$
$758$	−1.75760	−	0.373590i	−0.0638390	−	0.0135694i
$759$	0.863315	+	0.627235i	0.0313363	+	0.0227672i
$760$	−2.67027	+	1.18888i	−0.0968610	+	0.0431253i
$761$	−22.8357	−	4.85387i	−0.827792	−	0.175953i	−0.225515	−	0.974240i	$-0.572406\pi$
$761$	−22.8357	−	4.85387i	−0.827792	−	0.175953i	−0.602277	+	0.798287i	$0.705740\pi$
$762$	−12.9589	−	9.41516i	−0.469450	−	0.341075i
$763$	0.411990	+	3.91982i	0.0149150	+	0.141907i
$764$	−13.2755	+	2.82181i	−0.480293	+	0.102089i
$765$	−0.183077	−	0.0815111i	−0.00661916	−	0.00294704i
$766$	10.3670	+	31.9062i	0.374574	+	1.15282i
$767$	−0.736911	−	2.94477i	−0.0266083	−	0.106330i
$768$	−6.82836	+	21.0155i	−0.246397	+	0.758333i
$769$	−27.2576	−	47.2116i	−0.982935	−	1.70249i	−0.650775	−	0.759271i	$-0.725556\pi$
$769$	−27.2576	−	47.2116i	−0.982935	−	1.70249i	−0.332161	−	0.943223i	$-0.607778\pi$
$770$	1.90580	+	3.30093i	0.0686801	+	0.118957i
$771$	−23.8231	−	26.4582i	−0.857966	−	0.952868i
$772$	6.39263	+	4.64452i	0.230076	+	0.167160i
$773$	−0.878218	−	8.35568i	−0.0315873	−	0.300533i	−0.998898	−	0.0469381i	$-0.985054\pi$
$773$	−0.878218	−	8.35568i	−0.0315873	−	0.300533i	0.967310	−	0.253595i	$-0.0816130\pi$
$774$	−17.4725	+	30.2632i	−0.628035	+	1.08779i
$775$	11.9852	−	21.0338i	0.430519	−	0.755556i
$776$	−7.93842	+	13.7497i	−0.284973	+	0.493587i
$777$	0.574645	+	0.255849i	0.0206153	+	0.00917851i
$778$	0.953060	−	9.06776i	0.0341689	−	0.325095i
$779$	0.404003	−	1.24339i	0.0144749	−	0.0445491i
$780$	1.50575	+	3.08050i	0.0539145	+	0.110300i
$781$	44.3147			1.58570
$782$	0.0511623	−	0.0108749i	0.00182956	−	0.000388885i
$783$	4.51191	−	5.01098i	0.161243	−	0.179078i
$784$	−32.4994	−	6.90796i	−1.16069	−	0.246713i
$785$	−0.0312409	+	0.0226979i	−0.00111504	+	0.000810122i
$786$	−21.3375	−	23.6977i	−0.761084	−	0.845269i
$787$	1.41112	+	13.4259i	0.0503009	+	0.478582i	0.990455	+	0.137833i	$0.0440138\pi$
$787$	1.41112	+	13.4259i	0.0503009	+	0.478582i	−0.940155	+	0.340748i	$0.889320\pi$
$788$	2.56669	+	1.86481i	0.0914344	+	0.0664310i
$789$	28.0935	+	5.97145i	1.00015	+	0.212589i
$790$	−0.839635	+	7.98859i	−0.0298729	+	0.284221i
$791$	1.05793	−	10.0656i	0.0376158	−	0.357891i
$792$	4.01774	+	12.3653i	0.142764	+	0.439383i
$793$	−31.0161	−	25.9800i	−1.10141	−	0.922578i
$794$	26.4761	−	19.2360i	0.939603	−	0.682662i
$795$	2.85988	−	0.607885i	0.101429	−	0.0215595i
$796$	−4.47547	−	1.99261i	−0.158629	−	0.0706262i
$797$	1.10178	+	0.234191i	0.0390272	+	0.00829548i	0.227384	−	0.973805i	$-0.426983\pi$
$797$	1.10178	+	0.234191i	0.0390272	+	0.00829548i	−0.188357	+	0.982101i	$0.560316\pi$
$798$	0.784419	+	2.41419i	0.0277681	+	0.0854615i
$799$	0.560570	+	0.622576i	0.0198316	+	0.0220252i
$800$	11.5415	−	19.9905i	0.408055	−	0.706771i
$801$	28.1944			0.996199
$802$	30.2559	+	33.6026i	1.06837	+	1.18655i
$803$	−1.30354	+	12.4023i	−0.0460008	+	0.437668i
$804$	−9.34156	−	4.15913i	−0.329451	−	0.146681i
$805$	0.0979433			0.00345205
$806$	−15.5139	−	31.2872i	−0.546453	−	1.10204i
$807$	6.78685			0.238908
$808$	1.87015	+	0.832643i	0.0657915	+	0.0292923i
$809$	−0.521299	+	4.95983i	−0.0183279	+	0.174378i	−0.999857	−	0.0169368i	$-0.994609\pi$
$809$	−0.521299	+	4.95983i	−0.0183279	+	0.174378i	0.981529	+	0.191315i	$0.0612753\pi$
$810$	−1.05205	−	1.16842i	−0.0369651	−	0.0410540i
$811$	12.1830			0.427802			0.213901	−	0.976855i	$-0.431383\pi$
$811$	12.1830			0.427802			0.213901	+	0.976855i	$0.431383\pi$
$812$	−0.383033	+	0.663433i	−0.0134418	+	0.0232819i
$813$	12.7885	+	14.2031i	0.448514	+	0.498125i
$814$	−2.25854	−	6.95106i	−0.0791617	−	0.243635i
$815$	16.9392	+	3.60055i	0.593356	+	0.126122i
$816$	−0.773020	−	0.344171i	−0.0270611	−	0.0120484i
$817$	−24.9510	+	5.30349i	−0.872924	+	0.185546i
$818$	−7.50081	+	5.44966i	−0.262260	+	0.190543i
$819$	3.39135	−	1.23766i	0.118503	−	0.0432474i
$820$	−0.156654	−	0.482132i	−0.00547060	−	0.0168368i
$821$	−3.44488	+	32.7758i	−0.120227	+	1.14388i	0.753493	+	0.657456i	$0.228367\pi$
$821$	−3.44488	+	32.7758i	−0.120227	+	1.14388i	−0.873720	+	0.486429i	$0.838299\pi$
$822$	2.74843	−	26.1496i	0.0958626	−	0.912072i
$823$	38.1869	+	8.11688i	1.33111	+	0.282937i	0.817917	−	0.575336i	$-0.195129\pi$
$823$	38.1869	+	8.11688i	1.33111	+	0.282937i	0.513195	+	0.858272i	$0.328462\pi$
$824$	−9.00340	−	6.54135i	−0.313648	−	0.227879i
$825$	2.37892	+	22.6339i	0.0828233	+	0.788012i
$826$	−0.583085	−	0.647581i	−0.0202881	−	0.0225322i
$827$	5.94846	−	4.32181i	0.206848	−	0.150284i	−0.479538	−	0.877521i	$-0.659196\pi$
$827$	5.94846	−	4.32181i	0.206848	−	0.150284i	0.686387	+	0.727237i	$0.259196\pi$
$828$	−0.344395	−	0.0732034i	−0.0119685	−	0.00254399i
$829$	−18.5166	+	20.5648i	−0.643108	+	0.714243i	−0.973266	−	0.229682i	$-0.926231\pi$
$829$	−18.5166	+	20.5648i	−0.643108	+	0.714243i	0.330158	+	0.943926i	$0.392898\pi$
$830$	−6.06119	+	1.28834i	−0.210387	+	0.0447191i
$831$	26.8621			0.931838
$832$	1.20858	+	2.47255i	0.0419001	+	0.0857203i
$833$	0.302886	−	0.932188i	0.0104944	−	0.0322984i
$834$	−2.31498	+	22.0256i	−0.0801613	+	0.762684i
$835$	−5.86706	−	2.61218i	−0.203038	−	0.0903983i
$836$	5.00095	−	8.66190i	0.172962	−	0.299578i
$837$	20.1484	+	22.1232i	0.696431	+	0.764689i
$838$	−12.0453	+	20.8631i	−0.416098	+	0.720703i
$839$	−4.47552	−	42.5818i	−0.154512	−	1.47009i	−0.747171	−	0.664632i	$-0.768588\pi$
$839$	−4.47552	−	42.5818i	−0.154512	−	1.47009i	0.592659	−	0.805454i	$-0.298078\pi$
$840$	−0.755609	−	0.548982i	−0.0260710	−	0.0189417i
$841$	−18.3515	−	20.3814i	−0.632809	−	0.702806i
$842$	−25.0813	−	43.4421i	−0.864359	−	1.49711i
$843$	13.1013	+	22.6921i	0.451232	+	0.781556i
$844$	−4.75534	+	14.6354i	−0.163685	+	0.503772i
$845$	9.86999	+	3.57313i	0.339538	+	0.122919i
$846$	−5.13886	−	15.8158i	−0.176678	−	0.543758i
$847$	5.32708	+	2.37177i	0.183040	+	0.0814949i
$848$	−15.4286	+	3.27946i	−0.529821	+	0.112617i
$849$	0.768716	+	7.31385i	0.0263823	+	0.251011i
$850$	0.902478	+	0.655689i	0.0309547	+	0.0224899i
$851$	−0.183704	−	0.0390474i	−0.00629728	−	0.00133853i
$852$	10.4543	−	4.65456i	0.358159	−	0.159463i
$853$	15.2809	+	11.1022i	0.523207	+	0.380132i	0.817811	−	0.575487i	$-0.195188\pi$
$853$	15.2809	+	11.1022i	0.523207	+	0.380132i	−0.294603	+	0.955620i	$0.595188\pi$
$854$	−11.3606	−	2.41478i	−0.388753	−	0.0826320i
$855$	−0.303530	+	2.88790i	−0.0103805	+	0.0987640i
$856$	−28.4869	−	12.6832i	−0.973663	−	0.433503i
$857$	−3.41404	+	10.5073i	−0.116622	+	0.358924i	−0.992282	−	0.124003i	$-0.960427\pi$
$857$	−3.41404	+	10.5073i	−0.116622	+	0.358924i	0.875660	+	0.482928i	$0.160427\pi$
$858$	29.0008	+	15.3879i	0.990069	+	0.525335i
$859$	1.62510	+	5.00154i	0.0554476	+	0.170650i	0.974945	−	0.222446i	$-0.0714040\pi$
$859$	1.62510	+	5.00154i	0.0554476	+	0.170650i	−0.919497	+	0.393096i	$0.871404\pi$
$860$	−6.61839	+	7.35046i	−0.225685	+	0.250649i
$861$	0.408620	−	0.0868549i	0.0139257	−	0.00296001i
$862$	12.7283	−	22.0461i	0.433529	−	0.750894i
$863$	31.5781			1.07493			0.537466	−	0.843286i	$-0.319382\pi$
$863$	31.5781			1.07493			0.537466	+	0.843286i	$0.319382\pi$
$864$	19.0914	+	21.2032i	0.649504	+	0.721347i
$865$	−11.0821	+	4.93407i	−0.376803	+	0.167764i
$866$	−16.8127	+	12.2151i	−0.571318	+	0.415087i
$867$	−9.74265	+	16.8748i	−0.330878	+	0.573097i
$868$	−2.76161	−	1.98257i	−0.0937352	−	0.0672928i
$869$	13.0406	+	22.5870i	0.442373	+	0.766213i
$870$	1.63629	−	1.18884i	0.0554756	−	0.0403054i
$871$	−29.4072	+	10.7320i	−0.996425	+	0.363642i
$872$	−3.46771	+	10.6725i	−0.117432	+	0.361417i
$873$	7.88635	+	13.6596i	0.266912	+	0.462306i
$874$	−0.378948	−	0.656357i	−0.0128181	−	0.0222016i
$875$	3.00502	+	3.33741i	0.101588	+	0.112825i
$876$	0.995149	+	3.06275i	0.0336230	+	0.103481i
$877$	−14.5227	−	3.08690i	−0.490397	−	0.104237i	−0.0439252	−	0.999035i	$-0.513986\pi$
$877$	−14.5227	−	3.08690i	−0.490397	−	0.104237i	−0.446472	+	0.894798i	$0.647320\pi$
$878$	6.64104	+	63.1853i	0.224124	+	2.13240i
$879$	4.28525	−	13.1887i	0.144538	−	0.444842i
$880$	1.92442	+	18.3096i	0.0648722	+	0.617218i
$881$	4.10091	−	39.0175i	0.138163	−	1.31453i	−0.677292	−	0.735714i	$-0.736847\pi$
$881$	4.10091	−	39.0175i	0.138163	−	1.31453i	0.815455	−	0.578820i	$-0.196487\pi$
$882$	−13.0189	+	14.4589i	−0.438368	+	0.486857i
$883$	23.4996	+	17.0735i	0.790826	+	0.574569i	0.908208	−	0.418518i	$-0.137450\pi$
$883$	23.4996	+	17.0735i	0.790826	+	0.574569i	−0.117383	+	0.993087i	$0.537450\pi$
$884$	0.512626	−	0.187081i	0.0172415	−	0.00629221i
$885$	0.241092	+	0.742004i	0.00810420	+	0.0249422i
$886$	−0.478856	+	4.55601i	−0.0160875	+	0.153062i
$887$	37.7740	+	16.8180i	1.26833	+	0.564695i	0.926933	−	0.375226i	$-0.122435\pi$
$887$	37.7740	+	16.8180i	1.26833	+	0.564695i	0.341392	+	0.939921i	$0.389102\pi$
$888$	1.19836	+	1.33092i	0.0402145	+	0.0446627i
$889$	−3.86191	+	2.80584i	−0.129524	+	0.0941050i
$890$	23.0188	+	4.89279i	0.771591	+	0.164007i
$891$	−4.99345	−	1.06139i	−0.167287	−	0.0355580i
$892$	5.43516	−	16.7277i	0.181983	−	0.560085i
$893$	6.06951	−	10.5127i	0.203108	−	0.351794i
$894$	−15.4472	−	26.7554i	−0.516633	−	0.894834i
$895$	5.33804	−	1.13464i	0.178431	−	0.0379267i
$896$	5.74996	+	4.17759i	0.192093	+	0.139564i
$897$	0.715040	−	0.447664i	0.0238745	−	0.0149471i
$898$	−40.8956			−1.36470
$899$	−5.62807	+	4.13806i	−0.187707	+	0.138012i
$900$	−3.75453	−	6.50304i	−0.125151	−	0.216768i
$901$	−0.0486389	−	0.462768i	−0.00162040	−	0.0154170i
$902$	−3.92689	−	2.85305i	−0.130751	−	0.0949962i
$903$	−5.45391	−	6.05718i	−0.181495	−	0.201570i
$904$	14.4080	−	24.9553i	0.479202	−	0.830002i
$905$	−18.0641			−0.600471
$906$	−4.49336	−	4.99038i	−0.149282	−	0.165794i
$907$	−5.25967	+	5.84146i	−0.174644	+	0.193962i	−0.824112	−	0.566427i	$-0.808325\pi$
$907$	−5.25967	+	5.84146i	−0.174644	+	0.193962i	0.649467	+	0.760389i	$0.274992\pi$
$908$	−9.86422	+	10.9553i	−0.327356	+	0.363565i
$909$	1.64530	−	1.19538i	0.0545711	−	0.0396482i
$910$	2.98359	−	0.421938i	0.0989049	−	0.0139871i
$911$	−35.8584	+	26.0527i	−1.18804	+	0.863164i	−0.993056	−	0.117642i	$-0.962467\pi$
$911$	−35.8584	+	26.0527i	−1.18804	+	0.863164i	−0.194987	+	0.980806i	$0.562467\pi$
$912$	−1.28162	+	12.1938i	−0.0424387	+	0.403777i
$913$	−13.4628	+	14.9520i	−0.445555	+	0.494839i
$914$	2.47407	−	1.10153i	0.0818350	−	0.0364353i
$915$	8.41269	+	6.11218i	0.278115	+	0.202062i
$916$	−8.32094	−	1.76867i	−0.274932	−	0.0584385i
$917$	−8.68158	+	3.86529i	−0.286691	+	0.127643i
$918$	−1.11550	+	0.810461i	−0.0368171	+	0.0267492i
$919$	24.6860	+	27.4166i	0.814316	+	0.904389i	0.996890	−	0.0788029i	$-0.0251098\pi$
$919$	24.6860	+	27.4166i	0.814316	+	0.904389i	−0.182575	+	0.983192i	$0.558443\pi$
$920$	0.254750	+	0.113422i	0.00839885	+	0.00373941i
$921$	0.997521	−	1.10786i	0.0328694	−	0.0365052i
$922$	14.2053	+	43.7193i	0.467826	+	1.43982i
$923$	13.0957	−	32.4935i	0.431049	−	1.06954i
$924$	3.19592			0.105138
$925$	−2.00270	−	3.46879i	−0.0658485	−	0.114053i
$926$	61.3616	−	13.0428i	2.01647	−	0.428613i
$927$	−10.1000	+	4.49680i	−0.331727	+	0.147694i
$928$	−5.38868	+	3.91510i	−0.176892	+	0.128520i
$929$	−21.5938	+	37.4015i	−0.708468	+	1.22710i	0.256957	+	0.966423i	$0.417280\pi$
$929$	−21.5938	+	37.4015i	−0.708468	+	1.22710i	−0.965425	+	0.260680i	$0.916053\pi$
$930$	4.53184	+	7.74746i	0.148605	+	0.254049i
$931$	−14.2024			−0.465464
$932$	0.459989	+	4.37651i	0.0150675	+	0.143357i
$933$	−0.631319	+	6.00660i	−0.0206685	+	0.196647i
$934$	−13.9372	+	2.96245i	−0.456039	+	0.0969342i
$935$	−0.543115			−0.0177618
$936$	10.2541	+	0.708159i	0.335167	+	0.0231469i
$937$	−6.98239	+	21.4896i	−0.228105	+	0.702034i	0.769857	+	0.638217i	$0.220328\pi$
$937$	−6.98239	+	21.4896i	−0.228105	+	0.702034i	−0.997962	+	0.0638175i	$0.979672\pi$
$938$	−6.01304	+	6.67816i	−0.196333	+	0.218050i
$939$	9.45088	−	10.4963i	0.308418	−	0.342533i
$940$	−0.492012	−	4.68118i	−0.0160477	−	0.152683i
$941$	2.67154	−	8.22215i	0.0870896	−	0.268034i	−0.898022	−	0.439951i	$-0.854996\pi$
$941$	2.67154	−	8.22215i	0.0870896	−	0.268034i	0.985112	+	0.171916i	$0.0549959\pi$
$942$	0.00998044	+	0.0949576i	0.000325180	+	0.00309389i
$943$	−0.113944	+	0.0507309i	−0.00371051	+	0.00165203i
$944$	−1.30066	−	4.00301i	−0.0423327	−	0.130287i
$945$	−2.35870	+	1.05016i	−0.0767285	+	0.0341617i
$946$	−9.89936	+	94.1861i	−0.321856	+	3.06225i
$947$	−24.3700	+	27.0656i	−0.791919	+	0.879515i	−0.995023	−	0.0996418i	$-0.968230\pi$
$947$	−24.3700	+	27.0656i	−0.791919	+	0.879515i	0.203104	+	0.979157i	$0.434897\pi$
$948$	5.44884	+	3.95881i	0.176970	+	0.128576i
$949$	8.70872	+	4.62089i	0.282697	+	0.150000i
$950$	4.99489	−	15.3727i	0.162055	−	0.498755i
$951$	18.9810	+	8.45088i	0.615501	+	0.274039i
$952$	−0.0994619	+	0.110464i	−0.00322358	+	0.00358015i
$953$	53.0698	+	11.2803i	1.71910	+	0.365406i	0.958781	−	0.284147i	$-0.0917102\pi$
$953$	53.0698	+	11.2803i	1.71910	+	0.365406i	0.760317	+	0.649552i	$0.225044\pi$
$954$	−2.85428	+	8.78458i	−0.0924108	+	0.284411i
$955$	5.33939	−	9.24809i	0.172778	−	0.299261i
$956$	9.65542	−	16.7237i	0.312278	−	0.540882i
$957$	2.02936	−	6.24573i	0.0655999	−	0.201896i
$958$	49.0749	−	21.8496i	1.58554	−	0.705927i
$959$	−7.15841	−	3.18713i	−0.231157	−	0.102918i
$960$	−0.353668	−	0.612571i	−0.0114146	−	0.0197707i
$961$	−15.8039	−	26.6690i	−0.509802	−	0.860292i
$962$	−5.76427	−	0.398085i	−0.185847	−	0.0128348i
$963$	−25.0620	+	18.2086i	−0.807610	+	0.586763i
$964$	−2.61795	+	24.9081i	−0.0843185	+	0.802237i
$965$	−6.08135	+	1.29263i	−0.195765	+	0.0416112i
$966$	0.121086	−	0.209727i	0.00389587	−	0.00674785i
$967$	−7.27172			−0.233843			−0.116921	−	0.993141i	$-0.537303\pi$
$967$	−7.27172			−0.233843			−0.116921	+	0.993141i	$0.537303\pi$
$968$	11.1091	+	12.3379i	0.357059	+	0.396555i
$969$	−0.353798	−	0.0752021i	−0.0113656	−	0.00241584i
$970$	4.06822	+	12.5207i	0.130623	+	0.402015i
$971$	−5.05142	−	48.0610i	−0.162108	−	1.54235i	−0.709036	−	0.705173i	$-0.750870\pi$
$971$	−5.05142	−	48.0610i	−0.162108	−	1.54235i	0.546928	−	0.837180i	$-0.315797\pi$
$972$	14.8948	−	3.16600i	0.477752	−	0.101549i
$973$	6.02947	+	2.68449i	0.193296	+	0.0860609i
$974$	55.4463	+	40.2841i	1.77661	+	1.29079i
$975$	17.2992	+	4.94434i	0.554018	+	0.158346i
$976$	−45.3853	−	32.9743i	−1.45275	−	1.05548i
$977$	1.90703	−	18.1442i	0.0610114	−	0.580484i	−0.920722	−	0.390220i	$-0.872399\pi$
$977$	1.90703	−	18.1442i	0.0610114	−	0.580484i	0.981733	−	0.190264i	$-0.0609345\pi$
$978$	28.6516	−	31.8208i	0.916178	−	1.01752i
$979$	69.8041	−	31.0788i	2.23095	−	0.993282i
$980$	−4.45530	+	3.23696i	−0.142319	+	0.103401i
$981$	7.45956	+	8.28468i	0.238165	+	0.264510i
$982$	0.573230	+	5.45392i	0.0182925	+	0.174041i
$983$	12.4208	+	38.2274i	0.396163	+	1.21926i	0.928052	+	0.372450i	$0.121482\pi$
$983$	12.4208	+	38.2274i	0.396163	+	1.21926i	−0.531889	+	0.846814i	$0.678518\pi$
$984$	1.16340	+	0.247288i	0.0370878	+	0.00788326i
$985$	−2.44170	+	0.519000i	−0.0777991	+	0.0165367i
$986$	−0.160946	−	0.278767i	−0.00512557	−	0.00887774i
$987$	3.87880			0.123464
$988$	−4.87344	−	6.22665i	−0.155045	−	0.198096i
$989$	1.96879	+	1.43041i	0.0626038	+	0.0454843i
$990$	9.84888	+	4.38500i	0.313018	+	0.139365i
$991$	−15.6777	−	27.1545i	−0.498018	−	0.862592i	0.501980	−	0.864879i	$-0.332605\pi$
$991$	−15.6777	−	27.1545i	−0.498018	−	0.862592i	−0.999997	+	0.00228728i	$0.999272\pi$
$992$	−14.9244	−	25.5141i	−0.473849	−	0.810073i
$993$	19.3837			0.615124
$994$	−1.05122	−	10.0017i	−0.0333427	−	0.317235i
$995$	3.52137	−	1.56782i	0.111635	−	0.0497031i
$996$	−1.60556	+	4.94140i	−0.0508740	+	0.156574i
$997$	17.0750	−	29.5747i	0.540769	−	0.936640i	−0.458091	−	0.888905i	$-0.651467\pi$
$997$	17.0750	−	29.5747i	0.540769	−	0.936640i	0.998860	−	0.0477344i	$-0.0152001\pi$
$998$	7.83090	+	13.5635i	0.247883	+	0.429345i
$999$	4.84268	−	1.02934i	0.153216	−	0.0325670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bl.b.16.7	✓	280
13.9	even	3	inner	403.2.bl.b.295.29	yes	280
31.2	even	5	inner	403.2.bl.b.250.29	yes	280
403.126	even	15	inner	403.2.bl.b.126.7	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bl.b.16.7	✓	280	1.1	even	1	trivial
403.2.bl.b.126.7	yes	280	403.126	even	15	inner
403.2.bl.b.250.29	yes	280	31.2	even	5	inner
403.2.bl.b.295.29	yes	280	13.9	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bl (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58921 - 0.707561i) q^{2} +(0.119963 - 1.14138i) q^{3} +(0.686679 + 0.762634i) q^{4} -0.807451 q^{5} +(-0.998239 + 1.72900i) q^{6} +(0.398118 + 0.442154i) q^{7} +(0.523470 + 1.61107i) q^{8} +(1.64610 + 0.349889i) q^{9} +O(q^{10})\)	\(q+(-1.58921 - 0.707561i) q^{2} +(0.119963 - 1.14138i) q^{3} +(0.686679 + 0.762634i) q^{4} -0.807451 q^{5} +(-0.998239 + 1.72900i) q^{6} +(0.398118 + 0.442154i) q^{7} +(0.523470 + 1.61107i) q^{8} +(1.64610 + 0.349889i) q^{9} +(1.28321 + 0.571321i) q^{10} +(4.46112 - 0.948240i) q^{11} +(0.952828 - 0.692270i) q^{12} +(0.623037 - 3.55131i) q^{13} +(-0.319840 - 0.984368i) q^{14} +(-0.0968645 + 0.921604i) q^{15} +(0.522570 - 4.97193i) q^{16} +(0.144258 + 0.0306631i) q^{17} +(-2.36842 - 1.72076i) q^{18} +(-0.223375 - 2.12527i) q^{19} +(-0.554459 - 0.615789i) q^{20} +(0.552424 - 0.401359i) q^{21} +(-7.76058 - 1.64956i) q^{22} +(-0.136417 + 0.151507i) q^{23} +(1.90164 - 0.404205i) q^{24} -4.34802 q^{25} +(-3.50291 + 5.20294i) q^{26} +(1.66077 - 5.11131i) q^{27} +(-0.0638231 + 0.607236i) q^{28} +(1.14618 + 0.510313i) q^{29} +(0.806029 - 1.39608i) q^{30} +(-2.75646 + 4.83755i) q^{31} +(-2.65443 + 4.59761i) q^{32} +(-0.547127 - 5.20556i) q^{33} +(-0.207561 - 0.150802i) q^{34} +(-0.321460 - 0.357018i) q^{35} +(0.863503 + 1.49563i) q^{36} +(0.460601 + 0.797785i) q^{37} +(-1.14877 + 3.53555i) q^{38} +(-3.97864 - 1.13715i) q^{39} +(-0.422676 - 1.30086i) q^{40} +(0.558896 + 0.248837i) q^{41} +(-1.16190 + 0.246970i) q^{42} +(-1.24772 - 11.8713i) q^{43} +(3.78651 + 2.75106i) q^{44} +(-1.32914 - 0.282518i) q^{45} +(0.323996 - 0.144252i) q^{46} +(4.59558 + 3.33888i) q^{47} +(-5.61214 - 1.19290i) q^{48} +(0.694696 - 6.60959i) q^{49} +(6.90991 + 3.07649i) q^{50} +(0.0523038 - 0.160974i) q^{51} +(3.13618 - 1.96346i) q^{52} +(-0.974979 - 3.00068i) q^{53} +(-6.25587 + 6.94785i) q^{54} +(-3.60213 + 0.765657i) q^{55} +(-0.503941 + 0.872851i) q^{56} -2.45253 q^{57} +(-1.46044 - 1.62199i) q^{58} +(0.769130 - 0.342439i) q^{59} +(-0.769361 + 0.558974i) q^{60} +(5.61070 - 9.71802i) q^{61} +(7.80345 - 5.73752i) q^{62} +(0.500635 + 0.867126i) q^{63} +(-0.617524 + 0.448657i) q^{64} +(-0.503072 + 2.86751i) q^{65} +(-2.81376 + 8.65985i) q^{66} +(-4.34113 - 7.51905i) q^{67} +(0.0756744 + 0.131072i) q^{68} +(0.156561 + 0.173878i) q^{69} +(0.258255 + 0.794828i) q^{70} +(9.50414 + 2.02017i) q^{71} +(0.297985 + 2.83514i) q^{72} +(-0.844951 + 2.60049i) q^{73} +(-0.167510 - 1.59375i) q^{74} +(-0.521604 + 4.96273i) q^{75} +(1.46742 - 1.62973i) q^{76} +(2.19532 + 1.59499i) q^{77} +(5.51828 + 4.62229i) q^{78} +(1.76714 + 5.43871i) q^{79} +(-0.421950 + 4.01458i) q^{80} +(-1.02256 - 0.455272i) q^{81} +(-0.712136 - 0.790907i) q^{82} +(-3.56898 + 2.59302i) q^{83} +(0.685428 + 0.145692i) q^{84} +(-0.116481 - 0.0247589i) q^{85} +(-6.41676 + 19.7487i) q^{86} +(0.719958 - 1.24700i) q^{87} +(3.86294 + 6.69081i) q^{88} +(16.3876 - 3.48329i) q^{89} +(1.91238 + 1.38943i) q^{90} +(1.81827 - 1.13836i) q^{91} -0.209219 q^{92} +(5.19079 + 3.72648i) q^{93} +(-4.94087 - 8.55784i) q^{94} +(0.180365 + 1.71605i) q^{95} +(4.92916 + 3.58125i) q^{96} +(6.27142 + 6.96512i) q^{97} +(-5.78071 + 10.0125i) q^{98} +7.67521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q + q^{2} + 39 q^{4} - 8 q^{5} - 2 q^{7} + 12 q^{8} + 29 q^{9}+O(q^{10}) \) 280 * q + q^2 + 39 * q^4 - 8 * q^5 - 2 * q^7 + 12 * q^8 + 29 * q^9	\( 280 q + q^{2} + 39 q^{4} - 8 q^{5} - 2 q^{7} + 12 q^{8} + 29 q^{9} - 21 q^{10} - q^{11} - 16 q^{12} - 54 q^{14} - 27 q^{15} + 31 q^{16} + 2 q^{17} - 10 q^{18} + 5 q^{19} - 3 q^{20} + 68 q^{21} - 39 q^{22} - 7 q^{23} + 48 q^{24} + 200 q^{25} + 6 q^{26} - 78 q^{27} + 30 q^{28} - 16 q^{29} - 66 q^{30} - 62 q^{31} - 56 q^{32} - 20 q^{33} - 126 q^{34} - 37 q^{35} - 140 q^{36} - 36 q^{37} + 4 q^{38} + 28 q^{39} - 158 q^{40} - 4 q^{41} + 16 q^{42} - 16 q^{43} + 42 q^{44} - 46 q^{45} - 29 q^{46} + 8 q^{47} - 36 q^{48} + 43 q^{49} - 5 q^{50} - 134 q^{51} - q^{52} + 8 q^{53} + 44 q^{54} - 55 q^{55} - 42 q^{56} + 140 q^{57} + 38 q^{58} - 23 q^{59} + 38 q^{60} + 40 q^{61} + 19 q^{62} - 146 q^{63} - 68 q^{64} + 2 q^{65} + 6 q^{66} + 46 q^{67} + 86 q^{68} - 32 q^{69} - 4 q^{70} + 60 q^{71} + 73 q^{72} - 12 q^{73} - 44 q^{74} + 16 q^{75} - 70 q^{76} + 10 q^{77} - 142 q^{78} + 134 q^{79} - 72 q^{80} - 18 q^{81} + 28 q^{82} - 88 q^{83} + 81 q^{84} - 69 q^{85} + 188 q^{86} - 28 q^{87} + 42 q^{88} + 12 q^{89} + 22 q^{90} + 67 q^{91} - 324 q^{92} - 25 q^{93} - 62 q^{94} + 16 q^{95} + 276 q^{96} + 16 q^{97} + 76 q^{98} - 60 q^{99}+O(q^{100}) \) 280 * q + q^2 + 39 * q^4 - 8 * q^5 - 2 * q^7 + 12 * q^8 + 29 * q^9 - 21 * q^10 - q^11 - 16 * q^12 - 54 * q^14 - 27 * q^15 + 31 * q^16 + 2 * q^17 - 10 * q^18 + 5 * q^19 - 3 * q^20 + 68 * q^21 - 39 * q^22 - 7 * q^23 + 48 * q^24 + 200 * q^25 + 6 * q^26 - 78 * q^27 + 30 * q^28 - 16 * q^29 - 66 * q^30 - 62 * q^31 - 56 * q^32 - 20 * q^33 - 126 * q^34 - 37 * q^35 - 140 * q^36 - 36 * q^37 + 4 * q^38 + 28 * q^39 - 158 * q^40 - 4 * q^41 + 16 * q^42 - 16 * q^43 + 42 * q^44 - 46 * q^45 - 29 * q^46 + 8 * q^47 - 36 * q^48 + 43 * q^49 - 5 * q^50 - 134 * q^51 - q^52 + 8 * q^53 + 44 * q^54 - 55 * q^55 - 42 * q^56 + 140 * q^57 + 38 * q^58 - 23 * q^59 + 38 * q^60 + 40 * q^61 + 19 * q^62 - 146 * q^63 - 68 * q^64 + 2 * q^65 + 6 * q^66 + 46 * q^67 + 86 * q^68 - 32 * q^69 - 4 * q^70 + 60 * q^71 + 73 * q^72 - 12 * q^73 - 44 * q^74 + 16 * q^75 - 70 * q^76 + 10 * q^77 - 142 * q^78 + 134 * q^79 - 72 * q^80 - 18 * q^81 + 28 * q^82 - 88 * q^83 + 81 * q^84 - 69 * q^85 + 188 * q^86 - 28 * q^87 + 42 * q^88 + 12 * q^89 + 22 * q^90 + 67 * q^91 - 324 * q^92 - 25 * q^93 - 62 * q^94 + 16 * q^95 + 276 * q^96 + 16 * q^97 + 76 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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