LMFDB - Embedded newform 966.2.y.d.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			151.1
Character	$\chi$	$=$	966.151
Dual form			966.2.y.d.499.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-4.06127 + 0.387805i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-0.441487 - 2.60866i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})$	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-4.06127 + 0.387805i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-0.441487 - 2.60866i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(0.961837 - 3.96475i) q^{10} +(-0.312235 - 0.902145i) q^{11} +(0.981929 + 0.189251i) q^{12} +(-1.52758 + 0.448539i) q^{13} +(2.60958 + 0.436002i) q^{14} +(3.43210 - 2.20568i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-2.07884 - 0.832244i) q^{17} +(0.580057 + 0.814576i) q^{18} +(-3.26162 + 1.30576i) q^{19} +(3.43210 + 2.20568i) q^{20} +(1.58777 + 2.11637i) q^{21} +0.954650 q^{22} +(4.68392 + 1.03001i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(11.4339 - 2.20371i) q^{25} +(0.0757539 - 1.59027i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(-1.26553 + 2.32345i) q^{28} +(1.00567 + 6.99456i) q^{29} +(0.961837 + 3.96475i) q^{30} +(-0.413086 - 8.67173i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(0.690913 + 0.658784i) q^{33} +(1.46639 - 1.69231i) q^{34} +(2.80465 + 10.4233i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(2.17727 - 3.05755i) q^{37} +(-0.167169 - 3.50930i) q^{38} +(1.15224 - 1.09866i) q^{39} +(-3.20690 + 2.52193i) q^{40} +(-2.95986 + 6.48118i) q^{41} +(-2.51927 + 0.808244i) q^{42} +(2.27287 + 1.46068i) q^{43} +(-0.312235 + 0.902145i) q^{44} +(-2.03987 + 3.53317i) q^{45} +(-2.50532 + 4.08942i) q^{46} +(5.17428 + 8.96212i) q^{47} +(-0.654861 - 0.755750i) q^{48} +(-6.61018 + 2.30338i) q^{49} +(-1.65716 + 11.5258i) q^{50} +(2.22911 - 0.212854i) q^{51} +(1.47803 + 0.591714i) q^{52} +(-5.29567 + 5.04941i) q^{53} +(-0.888835 - 0.458227i) q^{54} +(1.61793 + 3.54277i) q^{55} +(-1.78175 - 1.95586i) q^{56} +(2.30071 - 2.65516i) q^{57} +(-6.93878 - 1.33734i) q^{58} +(0.359373 - 1.48136i) q^{59} +(-4.06127 - 0.387805i) q^{60} +(12.2315 + 6.30577i) q^{61} +(8.32990 + 2.44588i) q^{62} +(-2.38104 - 1.15354i) q^{63} +(0.415415 - 0.909632i) q^{64} +(6.02999 - 2.41404i) q^{65} +(-0.848527 + 0.437446i) q^{66} +(-4.64146 + 0.894569i) q^{67} +(1.11962 + 1.93924i) q^{68} +(-4.63521 + 1.23079i) q^{69} +(-10.7673 - 0.758718i) q^{70} +(1.32294 + 1.52675i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(0.310122 + 0.243882i) q^{73} +(2.17727 + 3.05755i) q^{74} +(-9.15307 + 7.19805i) q^{75} +(3.37097 + 0.989806i) q^{76} +(-2.21554 + 1.21280i) q^{77} +(0.661371 + 1.44820i) q^{78} +(-1.45807 - 1.39027i) q^{79} +(-1.33435 - 3.85536i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-5.15665 - 4.91685i) q^{82} +(-4.32329 - 9.46668i) q^{83} +(0.0601825 - 2.64507i) q^{84} +(8.76551 + 2.57378i) q^{85} +(-2.12373 + 1.67012i) q^{86} +(-4.09896 - 5.75619i) q^{87} +(-0.750406 - 0.590125i) q^{88} +(0.370248 - 7.77245i) q^{89} +(-2.67167 - 3.08327i) q^{90} +(1.84449 + 3.78692i) q^{91} +(-3.04510 - 3.70505i) q^{92} +(4.34078 + 7.51846i) q^{93} +(-10.1615 + 1.95848i) q^{94} +(12.7400 - 6.56790i) q^{95} +(0.928368 - 0.371662i) q^{96} +(1.10283 - 2.41485i) q^{97} +(-0.0147157 - 6.99998i) q^{98} +(-0.915980 - 0.268956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{11}\right)$

Coefficient data

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

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

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

$2$	−0.327068	+	0.945001i	−0.231272	+	0.668216i
$2$	−0.327068	+	0.945001i	−0.231272	+	0.668216i
$3$	−0.888835	+	0.458227i	−0.513169	+	0.264557i
$3$	−0.888835	+	0.458227i	−0.513169	+	0.264557i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−4.06127	+	0.387805i	−1.81626	+	0.173432i	−0.947065	−	0.321043i	$-0.895967\pi$
$5$	−4.06127	+	0.387805i	−1.81626	+	0.173432i	−0.869192	+	0.494474i	$0.835361\pi$
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	−0.441487	−	2.60866i	−0.166866	−	0.985980i
$7$	−0.441487	−	2.60866i	−0.166866	−	0.985980i
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$	0.580057	−	0.814576i	0.193352	−	0.271525i
$10$	0.961837	−	3.96475i	0.304160	−	1.25376i
$11$	−0.312235	−	0.902145i	−0.0941425	−	0.272007i	0.888092	−	0.459666i	$-0.152031\pi$
$11$	−0.312235	−	0.902145i	−0.0941425	−	0.272007i	−0.982234	+	0.187660i	$0.939910\pi$
$12$	0.981929	+	0.189251i	0.283458	+	0.0546321i
$13$	−1.52758	+	0.448539i	−0.423675	+	0.124402i	−0.486618	−	0.873615i	$-0.661770\pi$
$13$	−1.52758	+	0.448539i	−0.423675	+	0.124402i	0.0629427	+	0.998017i	$0.479951\pi$
$14$	2.60958	+	0.436002i	0.697439	+	0.116526i
$15$	3.43210	−	2.20568i	0.886165	−	0.569504i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−2.07884	−	0.832244i	−0.504194	−	0.201849i	0.105600	−	0.994409i	$-0.466324\pi$
$17$	−2.07884	−	0.832244i	−0.504194	−	0.201849i	−0.609794	+	0.792560i	$0.708748\pi$
$18$	0.580057	+	0.814576i	0.136721	+	0.191997i
$19$	−3.26162	+	1.30576i	−0.748267	+	0.299561i	−0.714279	−	0.699861i	$-0.753245\pi$
$19$	−3.26162	+	1.30576i	−0.748267	+	0.299561i	−0.0339881	+	0.999422i	$0.510821\pi$
$20$	3.43210	+	2.20568i	0.767441	+	0.493205i
$21$	1.58777	+	2.11637i	0.346479	+	0.461829i
$22$	0.954650			0.203532
$23$	4.68392	+	1.03001i	0.976664	+	0.214772i
$23$	4.68392	+	1.03001i	0.976664	+	0.214772i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	11.4339	−	2.20371i	2.28678	−	0.440741i
$26$	0.0757539	−	1.59027i	0.0148566	−	0.311878i
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$	−1.26553	+	2.32345i	−0.239163	+	0.439091i
$29$	1.00567	+	6.99456i	0.186747	+	1.29886i	0.840360	+	0.542028i	$0.182343\pi$
$29$	1.00567	+	6.99456i	0.186747	+	1.29886i	−0.653613	+	0.756829i	$0.726748\pi$
$30$	0.961837	+	3.96475i	0.175607	+	0.723860i
$31$	−0.413086	−	8.67173i	−0.0741924	−	1.55749i	−0.662630	−	0.748947i	$-0.730560\pi$
$31$	−0.413086	−	8.67173i	−0.0741924	−	1.55749i	0.588438	−	0.808542i	$-0.299743\pi$
$32$	−0.995472	−	0.0950560i	−0.175976	−	0.0168037i
$33$	0.690913	+	0.658784i	0.120272	+	0.114680i
$34$	1.46639	−	1.69231i	0.251485	−	0.290229i
$35$	2.80465	+	10.4233i	0.474072	+	1.76185i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	2.17727	−	3.05755i	0.357942	−	0.502659i	−0.595863	−	0.803086i	$-0.703190\pi$
$37$	2.17727	−	3.05755i	0.357942	−	0.502659i	0.953805	+	0.300427i	$0.0971293\pi$
$38$	−0.167169	−	3.50930i	−0.0271183	−	0.569284i
$39$	1.15224	−	1.09866i	0.184506	−	0.175926i
$40$	−3.20690	+	2.52193i	−0.507055	+	0.398753i
$41$	−2.95986	+	6.48118i	−0.462252	+	1.01219i	0.524716	+	0.851277i	$0.324171\pi$
$41$	−2.95986	+	6.48118i	−0.462252	+	1.01219i	−0.986968	+	0.160914i	$0.948556\pi$
$42$	−2.51927	+	0.808244i	−0.388732	+	0.124715i
$43$	2.27287	+	1.46068i	0.346609	+	0.222752i	0.702349	−	0.711833i	$-0.252135\pi$
$43$	2.27287	+	1.46068i	0.346609	+	0.222752i	−0.355740	+	0.934585i	$0.615771\pi$
$44$	−0.312235	+	0.902145i	−0.0470713	+	0.136003i
$45$	−2.03987	+	3.53317i	−0.304086	+	0.526693i
$46$	−2.50532	+	4.08942i	−0.369389	+	0.602952i
$47$	5.17428	+	8.96212i	0.754746	+	1.30726i	0.945500	+	0.325621i	$0.105573\pi$
$47$	5.17428	+	8.96212i	0.754746	+	1.30726i	−0.190754	+	0.981638i	$0.561093\pi$
$48$	−0.654861	−	0.755750i	−0.0945210	−	0.109083i
$49$	−6.61018	+	2.30338i	−0.944311	+	0.329054i
$50$	−1.65716	+	11.5258i	−0.234358	+	1.63000i
$51$	2.22911	−	0.212854i	0.312137	−	0.0298055i
$52$	1.47803	+	0.591714i	0.204966	+	0.0820560i
$53$	−5.29567	+	5.04941i	−0.727416	+	0.693590i	−0.960317	−	0.278910i	$-0.910027\pi$
$53$	−5.29567	+	5.04941i	−0.727416	+	0.693590i	0.232901	+	0.972500i	$0.425178\pi$
$54$	−0.888835	−	0.458227i	−0.120955	−	0.0623567i
$55$	1.61793	+	3.54277i	0.218162	+	0.477707i
$56$	−1.78175	−	1.95586i	−0.238096	−	0.261362i
$57$	2.30071	−	2.65516i	0.304737	−	0.351685i
$58$	−6.93878	−	1.33734i	−0.911107	−	0.175601i
$59$	0.359373	−	1.48136i	0.0467864	−	0.192856i	−0.943623	−	0.331024i	$-0.892606\pi$
$59$	0.359373	−	1.48136i	0.0467864	−	0.192856i	0.990409	+	0.138167i	$0.0441212\pi$
$60$	−4.06127	−	0.387805i	−0.524308	−	0.0500654i
$61$	12.2315	+	6.30577i	1.56608	+	0.807371i	0.999858	−	0.0168804i	$-0.00537346\pi$
$61$	12.2315	+	6.30577i	1.56608	+	0.807371i	0.566224	+	0.824251i	$0.308404\pi$
$62$	8.32990	+	2.44588i	1.05790	+	0.310627i
$63$	−2.38104	−	1.15354i	−0.299982	−	0.145333i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	6.02999	−	2.41404i	0.747928	−	0.299425i
$66$	−0.848527	+	0.437446i	−0.104446	+	0.0538459i
$67$	−4.64146	+	0.894569i	−0.567045	+	0.109289i	−0.464713	−	0.885461i	$-0.653843\pi$
$67$	−4.64146	+	0.894569i	−0.567045	+	0.109289i	−0.102332	+	0.994750i	$0.532630\pi$
$68$	1.11962	+	1.93924i	0.135774	+	0.235168i
$69$	−4.63521	+	1.23079i	−0.558014	+	0.148169i
$70$	−10.7673	−	0.758718i	−1.28694	−	0.0906841i
$71$	1.32294	+	1.52675i	0.157004	+	0.181192i	0.828802	−	0.559543i	$-0.189023\pi$
$71$	1.32294	+	1.52675i	0.157004	+	0.181192i	−0.671798	+	0.740734i	$0.734478\pi$
$72$	0.0475819	−	0.998867i	0.00560758	−	0.117718i
$73$	0.310122	+	0.243882i	0.0362970	+	0.0285443i	0.636143	−	0.771571i	$-0.280529\pi$
$73$	0.310122	+	0.243882i	0.0362970	+	0.0285443i	−0.599846	+	0.800116i	$0.704771\pi$
$74$	2.17727	+	3.05755i	0.253103	+	0.355433i
$75$	−9.15307	+	7.19805i	−1.05691	+	0.831160i
$76$	3.37097	+	0.989806i	0.386677	+	0.113539i
$77$	−2.21554	+	1.21280i	−0.252484	+	0.138211i
$78$	0.661371	+	1.44820i	0.0748855	+	0.163976i
$79$	−1.45807	−	1.39027i	−0.164046	−	0.156418i	0.603610	−	0.797280i	$-0.293728\pi$
$79$	−1.45807	−	1.39027i	−0.164046	−	0.156418i	−0.767656	+	0.640862i	$0.778577\pi$
$80$	−1.33435	−	3.85536i	−0.149185	−	0.431043i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	−5.15665	−	4.91685i	−0.569457	−	0.542976i
$83$	−4.32329	−	9.46668i	−0.474542	−	1.03910i	−0.983928	−	0.178565i	$-0.942855\pi$
$83$	−4.32329	−	9.46668i	−0.474542	−	1.03910i	0.509386	−	0.860538i	$-0.329873\pi$
$84$	0.0601825	−	2.64507i	0.00656645	−	0.288600i
$85$	8.76551	+	2.57378i	0.950753	+	0.279166i
$86$	−2.12373	+	1.67012i	−0.229008	+	0.180094i
$87$	−4.09896	−	5.75619i	−0.439455	−	0.617128i
$88$	−0.750406	−	0.590125i	−0.0799935	−	0.0629076i
$89$	0.370248	−	7.77245i	0.0392462	−	0.823878i	−0.890345	−	0.455286i	$-0.849537\pi$
$89$	0.370248	−	7.77245i	0.0392462	−	0.823878i	0.929591	−	0.368592i	$-0.120160\pi$
$90$	−2.67167	−	3.08327i	−0.281618	−	0.325005i
$91$	1.84449	+	3.78692i	0.193355	+	0.396977i
$92$	−3.04510	−	3.70505i	−0.317473	−	0.386278i
$93$	4.34078	+	7.51846i	0.450118	+	0.779628i
$94$	−10.1615	+	1.95848i	−1.04808	+	0.202002i
$95$	12.7400	−	6.56790i	1.30709	−	0.673853i
$96$	0.928368	−	0.371662i	0.0947512	−	0.0379326i
$97$	1.10283	−	2.41485i	0.111975	−	0.245191i	−0.845345	−	0.534220i	$-0.820605\pi$
$97$	1.10283	−	2.41485i	0.111975	−	0.245191i	0.957320	+	0.289029i	$0.0933325\pi$
$98$	−0.0147157	−	6.99998i	−0.00148651	−	0.707105i
$99$	−0.915980	−	0.268956i	−0.0920594	−	0.0270311i
$100$	−10.3499	−	5.33575i	−1.03499	−	0.533575i
$101$	5.20039	+	0.496577i	0.517458	+	0.0494113i	0.350519	−	0.936556i	$-0.386005\pi$
$101$	5.20039	+	0.496577i	0.517458	+	0.0494113i	0.166940	+	0.985967i	$0.446611\pi$
$102$	−0.527922	+	2.17613i	−0.0522721	+	0.215469i
$103$	17.8924	+	3.44847i	1.76299	+	0.339788i	0.964872	−	0.262719i	$-0.0846193\pi$
$103$	17.8924	+	3.44847i	1.76299	+	0.339788i	0.798114	+	0.602507i	$0.205831\pi$
$104$	−1.04259	+	1.20321i	−0.102234	+	0.117984i
$105$	−7.26909	−	7.97940i	−0.709390	−	0.778709i
$106$	−3.03965	−	6.65591i	−0.295237	−	0.646480i
$107$	5.87077	+	3.02659i	0.567549	+	0.292592i	0.718020	−	0.696023i	$-0.245049\pi$
$107$	5.87077	+	3.02659i	0.567549	+	0.292592i	−0.150471	+	0.988614i	$0.548079\pi$
$108$	0.723734	−	0.690079i	0.0696413	−	0.0664029i
$109$	3.54220	+	1.41808i	0.339281	+	0.135828i	0.535045	−	0.844823i	$-0.320294\pi$
$109$	3.54220	+	1.41808i	0.339281	+	0.135828i	−0.195764	+	0.980651i	$0.562719\pi$
$110$	−3.87710	+	0.370218i	−0.369667	+	0.0352989i
$111$	−0.534186	+	3.71535i	−0.0507027	+	0.352645i
$112$	2.43104	−	1.04406i	0.229712	−	0.0986541i
$113$	2.32757	+	2.68615i	0.218959	+	0.252692i	0.854593	−	0.519298i	$-0.173807\pi$
$113$	2.32757	+	2.68615i	0.218959	+	0.252692i	−0.635634	+	0.771991i	$0.719261\pi$
$114$	1.75664	+	3.04259i	0.164525	+	0.284965i
$115$	−19.4221	−	2.36671i	−1.81112	−	0.220697i
$116$	3.53324	−	6.11976i	0.328053	−	0.568205i
$117$	−0.520716	+	1.50451i	−0.0481402	+	0.139092i
$118$	1.28234	+	0.824112i	0.118049	+	0.0758656i
$119$	−1.25326	+	5.79042i	−0.114886	+	0.530807i
$120$	1.69479	−	3.71107i	0.154712	−	0.338773i
$121$	7.93021	−	6.23639i	0.720928	−	0.566944i
$122$	−9.95948	+	9.49635i	−0.901689	+	0.859759i
$123$	−0.339024	−	7.11699i	−0.0305688	−	0.641717i
$124$	−5.03580	+	7.07180i	−0.452228	+	0.635066i
$125$	−26.0092	+	7.63699i	−2.32633	+	0.683073i
$126$	1.86886	−	1.87279i	0.166491	−	0.166842i
$127$	6.87771	−	7.93730i	0.610298	−	0.704321i	−0.363537	−	0.931580i	$-0.618431\pi$
$127$	6.87771	−	7.93730i	0.610298	−	0.704321i	0.973834	+	0.227259i	$0.0729763\pi$
$128$	0.723734	+	0.690079i	0.0639697	+	0.0609949i
$129$	−2.68953	−	0.256819i	−0.236800	−	0.0226116i
$130$	0.309057	+	6.48790i	0.0271061	+	0.569027i
$131$	2.47554	+	10.2043i	0.216289	+	0.891555i	0.971684	+	0.236285i	$0.0759299\pi$
$131$	2.47554	+	10.2043i	0.216289	+	0.891555i	−0.755395	+	0.655270i	$0.772555\pi$
$132$	−0.135861	−	0.944933i	−0.0118252	−	0.0822459i
$133$	4.84623	+	7.93197i	0.420221	+	0.687789i
$134$	0.672706	−	4.67877i	0.0581129	−	0.404184i
$135$	0.194122	−	4.07513i	0.0167074	−	0.350731i
$136$	−2.19878	+	0.423780i	−0.188544	+	0.0363389i
$137$	10.5820	−	18.3286i	0.904082	−	1.56592i	0.0819379	−	0.996637i	$-0.473889\pi$
$137$	10.5820	−	18.3286i	0.904082	−	1.56592i	0.822144	−	0.569279i	$-0.192778\pi$
$138$	0.352935	−	4.78283i	0.0300438	−	0.407141i
$139$	19.6049			1.66286			0.831432	−	0.555627i	$-0.187522\pi$
$139$	19.6049			1.66286			0.831432	+	0.555627i	$0.187522\pi$
$140$	4.23863	−	9.92695i	0.358229	−	0.838981i
$141$	−8.70576	−	5.59485i	−0.733157	−	0.471172i
$142$	−1.87547	+	0.750825i	−0.157386	+	0.0630078i
$143$	0.881613	+	1.23805i	0.0737242	+	0.103531i
$144$	0.928368	+	0.371662i	0.0773640	+	0.0309719i
$145$	−6.79681	−	28.0168i	−0.564444	−	2.32667i
$146$	−0.331900	+	0.213299i	−0.0274682	+	0.0176528i
$147$	4.81989	−	5.07628i	0.397538	−	0.418685i
$148$	−3.60151	+	1.05750i	−0.296042	+	0.0869258i
$149$	2.02973	+	0.391199i	0.166282	+	0.0320482i	0.271713	−	0.962378i	$-0.412410\pi$
$149$	2.02973	+	0.391199i	0.166282	+	0.0320482i	−0.105431	+	0.994427i	$0.533622\pi$
$150$	−3.80849	−	11.0039i	−0.310962	−	0.898466i
$151$	−4.47887	+	18.4622i	−0.364485	+	1.50243i	0.434275	+	0.900780i	$0.357005\pi$
$151$	−4.47887	+	18.4622i	−0.364485	+	1.50243i	−0.798761	+	0.601649i	$0.794511\pi$
$152$	−2.03790	+	2.86184i	−0.165296	+	0.232126i
$153$	−1.88377	+	1.21063i	−0.152294	+	0.0978735i
$154$	−0.421466	−	2.49035i	−0.0339627	−	0.200678i
$155$	5.04059	+	35.0581i	0.404870	+	2.81593i
$156$	−1.58486	+	0.151336i	−0.126891	+	0.0121166i
$157$	−12.5910	−	9.90169i	−1.00487	−	0.790241i	−0.0270418	−	0.999634i	$-0.508609\pi$
$157$	−12.5910	−	9.90169i	−1.00487	−	0.790241i	−0.977832	+	0.209393i	$0.932851\pi$
$158$	1.79070	−	0.923168i	0.142460	−	0.0734433i
$159$	2.39321	−	6.91471i	0.189794	−	0.548372i
$160$	4.07975			0.322532
$161$	0.619052	−	12.6735i	0.0487882	−	0.998809i
$162$	1.00000			0.0785674
$163$	−0.937563	+	2.70891i	−0.0734356	+	0.212178i	−0.975745	−	0.218911i	$-0.929749\pi$
$163$	−0.937563	+	2.70891i	−0.0734356	+	0.212178i	0.902309	+	0.431089i	$0.141871\pi$
$164$	6.33301	−	3.26489i	0.494525	−	0.254945i
$165$	−3.06147	−	2.40756i	−0.238335	−	0.187429i
$166$	10.3600	−	0.989263i	0.804094	−	0.0767817i
$167$	−0.318947	−	2.21832i	−0.0246808	−	0.171659i	0.973753	−	0.227608i	$-0.0730906\pi$
$167$	−0.318947	−	2.21832i	−0.0246808	−	0.171659i	−0.998434	+	0.0559493i	$0.982181\pi$
$168$	2.47991	+	0.921989i	0.191329	+	0.0711330i
$169$	−8.80397	+	5.65797i	−0.677229	+	0.435228i
$170$	−5.29915	+	7.44161i	−0.406426	+	0.570745i
$171$	−0.828288	+	3.41425i	−0.0633408	+	0.261094i
$172$	−0.883660	−	2.55317i	−0.0673784	−	0.194677i
$173$	0.131914	+	0.0254243i	0.0100292	+	0.00193297i	0.194263	−	0.980949i	$-0.437768\pi$
$173$	0.131914	+	0.0254243i	0.0100292	+	0.00193297i	−0.184234	+	0.982882i	$0.558980\pi$
$174$	6.78024	−	1.99086i	0.514009	−	0.150927i
$175$	−10.7966	−	28.8542i	−0.816149	−	2.18118i
$176$	0.803103	−	0.516123i	0.0605361	−	0.0389042i
$177$	0.359373	+	1.48136i	0.0270121	+	0.111346i
$178$	7.22388	+	2.89200i	0.541453	+	0.216765i
$179$	7.81150	+	10.9697i	0.583859	+	0.819915i	0.995825	−	0.0912839i	$-0.0290971\pi$
$179$	7.81150	+	10.9697i	0.583859	+	0.819915i	−0.411966	+	0.911199i	$0.635158\pi$
$180$	3.78751	−	1.51629i	0.282304	−	0.113018i
$181$	−8.59437	−	5.52327i	−0.638815	−	0.410541i	0.180749	−	0.983529i	$-0.442148\pi$
$181$	−8.59437	−	5.52327i	−0.638815	−	0.410541i	−0.819564	+	0.572988i	$0.805784\pi$
$182$	−4.18191	+	0.504468i	−0.309984	+	0.0373937i
$183$	−13.7612			−1.01726
$184$	4.49723	−	1.66582i	0.331540	−	0.122806i
$185$	−7.65677	+	13.2619i	−0.562937	+	0.975036i
$186$	−8.52468	+	1.64300i	−0.625060	+	0.120470i
$187$	−0.101716	+	2.13528i	−0.00743819	+	0.156147i
$188$	1.47275	−	10.2432i	0.107412	−	0.747064i
$189$	2.64493	−	0.0657430i	0.192391	−	0.00478210i
$190$	2.03984	+	14.1874i	0.147986	+	1.02926i
$191$	−0.519927	−	2.14317i	−0.0376206	−	0.155074i	0.949903	−	0.312544i	$-0.101181\pi$
$191$	−0.519927	−	2.14317i	−0.0376206	−	0.155074i	−0.987524	+	0.157470i	$0.949666\pi$
$192$	0.0475819	+	0.998867i	0.00343393	+	0.0720870i
$193$	8.75019	+	0.835542i	0.629853	+	0.0601436i	0.405100	−	0.914272i	$-0.367237\pi$
$193$	8.75019	+	0.835542i	0.629853	+	0.0601436i	0.224752	+	0.974416i	$0.427843\pi$
$194$	1.92134	+	1.83199i	0.137944	+	0.131529i
$195$	−4.25349	+	4.90879i	−0.304599	+	0.351526i
$196$	6.61980	+	2.27556i	0.472843	+	0.162540i
$197$	−12.2847	+	3.60711i	−0.875247	+	0.256996i	−0.688345	−	0.725383i	$-0.741663\pi$
$197$	−12.2847	+	3.60711i	−0.875247	+	0.256996i	−0.186901	+	0.982379i	$0.559845\pi$
$198$	0.553751	−	0.777635i	0.0393534	−	0.0552641i
$199$	1.30361	+	27.3662i	0.0924106	+	1.93994i	0.284734	+	0.958607i	$0.408095\pi$
$199$	1.30361	+	27.3662i	0.0924106	+	1.93994i	−0.192323	+	0.981332i	$0.561602\pi$
$200$	8.42741	−	8.03552i	0.595908	−	0.568197i
$201$	3.71558	−	2.92197i	0.262077	−	0.206100i
$202$	−2.17015	+	4.75196i	−0.152691	+	0.334347i
$203$	17.8024	−	5.71144i	1.24948	−	0.400865i
$204$	−1.88377	−	1.21063i	−0.131891	−	0.0847609i
$205$	9.50736	−	27.4697i	0.664023	−	1.91857i
$206$	−9.11082	+	15.7804i	−0.634781	+	1.09947i
$207$	3.55596	−	3.21794i	0.247156	−	0.223662i
$208$	−0.796037	−	1.37878i	−0.0551952	−	0.0956009i
$209$	2.19637	+	2.53475i	0.151926	+	0.175332i
$210$	9.91802	−	4.25949i	0.684409	−	0.293933i
$211$	−1.46586	+	10.1953i	−0.100914	+	0.701873i	0.875064	+	0.484007i	$0.160819\pi$
$211$	−1.46586	+	10.1953i	−0.100914	+	0.701873i	−0.975979	+	0.217867i	$0.930090\pi$
$212$	7.28402	−	0.695539i	0.500268	−	0.0477698i
$213$	−1.87547	−	0.750825i	−0.128505	−	0.0514457i
$214$	−4.78027	+	4.55798i	−0.326773	+	0.311577i
$215$	−9.79720	−	5.05081i	−0.668163	−	0.344462i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	−22.4392	+	4.90606i	−1.52327	+	0.333045i
$218$	−2.49863	+	2.88357i	−0.169229	+	0.195300i
$219$	−0.387401	−	0.0746653i	−0.0261781	−	0.00504542i
$220$	0.918218	−	3.78494i	0.0619062	−	0.255181i
$221$	3.54890	+	0.338879i	0.238725	+	0.0227955i
$222$	−3.33629	−	1.71998i	−0.223917	−	0.115437i
$223$	22.7366	+	6.67606i	1.52255	+	0.447062i	0.932761	−	0.360494i	$-0.117392\pi$
$223$	22.7366	+	6.67606i	1.52255	+	0.447062i	0.589791	+	0.807556i	$0.299210\pi$
$224$	0.191520	+	2.63881i	0.0127964	+	0.176313i
$225$	4.83723	−	10.5921i	0.322482	−	0.706138i
$226$	−3.29969	+	1.32100i	−0.219492	+	0.0878714i
$227$	15.6130	−	8.04907i	1.03627	−	0.534236i	0.145820	−	0.989311i	$-0.453418\pi$
$227$	15.6130	−	8.04907i	1.03627	−	0.534236i	0.890453	+	0.455075i	$0.150388\pi$
$228$	−3.44979	+	0.664893i	−0.228468	+	0.0440336i
$229$	13.7580	+	23.8296i	0.909156	+	1.57470i	0.815239	+	0.579125i	$0.196606\pi$
$229$	13.7580	+	23.8296i	0.909156	+	1.57470i	0.0939170	+	0.995580i	$0.470061\pi$
$230$	8.58889	−	17.5798i	0.566335	−	1.15918i
$231$	1.41351	−	2.09320i	0.0930023	−	0.137722i
$232$	4.62756	+	5.34049i	0.303814	+	0.350621i
$233$	1.02752	−	21.5703i	0.0673151	−	1.41312i	−0.672395	−	0.740193i	$-0.734734\pi$
$233$	1.02752	−	21.5703i	0.0673151	−	1.41312i	0.739710	−	0.672926i	$-0.234963\pi$
$234$	−1.25145	−	0.984155i	−0.0818101	−	0.0643362i
$235$	−24.4897	−	34.3910i	−1.59753	−	2.24342i
$236$	−1.19820	+	0.942275i	−0.0779962	+	0.0613369i
$237$	1.93305	+	0.567593i	0.125565	+	0.0368692i
$238$	−5.06205	−	3.07819i	−0.328124	−	0.199529i
$239$	0.235453	+	0.515570i	0.0152302	+	0.0333494i	0.917094	−	0.398670i	$-0.130528\pi$
$239$	0.235453	+	0.515570i	0.0152302	+	0.0333494i	−0.901864	+	0.432020i	$0.857801\pi$
$240$	2.95265	+	2.81535i	0.190593	+	0.181730i
$241$	−8.63656	−	24.9537i	−0.556330	−	1.60741i	−0.775242	−	0.631665i	$-0.782372\pi$
$241$	−8.63656	−	24.9537i	−0.556330	−	1.60741i	0.218912	−	0.975745i	$-0.429749\pi$
$242$	3.29967	+	9.53378i	0.212111	+	0.612854i
$243$	0.723734	+	0.690079i	0.0464276	+	0.0442686i
$244$	−5.71663	−	12.5177i	−0.365970	−	0.801362i
$245$	25.9525	−	11.9181i	1.65804	−	0.761420i
$246$	6.83645	+	2.00736i	0.435876	+	0.127985i
$247$	4.39671	−	3.45761i	0.279756	−	0.220003i
$248$	−5.03580	−	7.07180i	−0.319774	−	0.449059i
$249$	8.18057	+	6.43327i	0.518423	+	0.407692i
$250$	1.28981	−	27.0765i	0.0815750	−	1.71247i
$251$	−16.7088	−	19.2830i	−1.05465	−	1.21713i	−0.975438	−	0.220275i	$-0.929305\pi$
$251$	−16.7088	−	19.2830i	−1.05465	−	1.21713i	−0.0792137	−	0.996858i	$-0.525241\pi$
$252$	1.15855	+	2.37861i	0.0729816	+	0.149838i
$253$	−0.533267	−	4.54718i	−0.0335262	−	0.285879i
$254$	5.25127	+	9.09547i	0.329494	+	0.570701i
$255$	−8.97047	+	1.72892i	−0.561753	+	0.108269i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−10.3962	+	4.16199i	−0.648494	+	0.259618i	−0.672504	−	0.740094i	$-0.734781\pi$
$257$	−10.3962	+	4.16199i	−0.648494	+	0.259618i	0.0240093	+	0.999712i	$0.492357\pi$
$258$	1.12235	−	2.45761i	0.0698746	−	0.153004i
$259$	−8.93735	−	4.32989i	−0.555340	−	0.269046i
$260$	−6.23215	−	1.82993i	−0.386502	−	0.113487i
$261$	6.28094	+	3.23805i	0.388781	+	0.200430i
$262$	−10.4528	−	0.998117i	−0.645773	−	0.0616639i
$263$	1.86471	−	7.68644i	0.114983	−	0.473966i	−0.884982	−	0.465625i	$-0.845830\pi$
$263$	1.86471	−	7.68644i	0.114983	−	0.473966i	0.999965	−	0.00834154i	$-0.00265523\pi$
$264$	0.937398	+	0.180669i	0.0576929	+	0.0111194i
$265$	19.5490	−	22.5607i	1.20088	−	1.38589i
$266$	−9.08076	+	1.98540i	−0.556777	+	0.121733i
$267$	3.23246	+	7.07809i	0.197823	+	0.433172i
$268$	4.20142	+	2.16598i	0.256643	+	0.132309i
$269$	−2.07024	+	1.97397i	−0.126225	+	0.120355i	−0.750563	−	0.660799i	$-0.770217\pi$
$269$	−2.07024	+	1.97397i	−0.126225	+	0.120355i	0.624338	+	0.781155i	$0.285369\pi$
$270$	3.78751	+	1.51629i	0.230500	+	0.0922784i
$271$	−24.3223	+	2.32250i	−1.47748	+	0.141082i	−0.802453	−	0.596715i	$-0.796472\pi$
$271$	−24.3223	+	2.32250i	−1.47748	+	0.141082i	−0.675023	+	0.737797i	$0.735866\pi$
$272$	0.318678	−	2.21645i	0.0193227	−	0.134392i
$273$	−3.37472	−	2.52075i	−0.204247	−	0.152563i
$274$	13.8595	+	15.9947i	0.837282	+	0.966275i
$275$	−5.55814	−	9.62697i	−0.335168	−	0.580528i
$276$	4.40434	+	1.89783i	0.265110	+	0.114236i
$277$	2.92838	−	5.07210i	0.175949	−	0.304753i	−0.764540	−	0.644576i	$-0.777034\pi$
$277$	2.92838	−	5.07210i	0.175949	−	0.304753i	0.940489	+	0.339823i	$0.110367\pi$
$278$	−6.41212	+	18.5266i	−0.384574	+	1.11115i
$279$	−7.30340	−	4.69361i	−0.437243	−	0.280999i
$280$	7.99466	+	7.25230i	0.477772	+	0.433408i
$281$	2.99516	−	6.55848i	0.178676	−	0.391246i	−0.799010	−	0.601318i	$-0.794643\pi$
$281$	2.99516	−	6.55848i	0.178676	−	0.391246i	0.977686	+	0.210072i	$0.0673698\pi$
$282$	8.13452	−	6.39706i	0.484403	−	0.380939i
$283$	−0.506883	+	0.483312i	−0.0301311	+	0.0287299i	−0.704995	−	0.709212i	$-0.749051\pi$
$283$	−0.506883	+	0.483312i	−0.0301311	+	0.0287299i	0.674864	+	0.737942i	$0.264202\pi$
$284$	−0.0961240	−	2.01789i	−0.00570391	−	0.119740i
$285$	−8.31413	+	11.6756i	−0.492487	+	0.691601i
$286$	−1.45831	+	0.428198i	−0.0862315	+	0.0253199i
$287$	18.2139	+	4.85989i	1.07513	+	0.286870i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	−8.67451	−	8.27113i	−0.510265	−	0.486537i
$290$	28.6989	+	2.74042i	1.68526	+	0.160923i
$291$	0.126318	+	2.65175i	0.00740491	+	0.155448i
$292$	−0.0930140	−	0.383409i	−0.00544323	−	0.0224373i
$293$	0.451375	+	3.13938i	0.0263696	+	0.183405i	0.998749	−	0.0500005i	$-0.0159223\pi$
$293$	0.451375	+	3.13938i	0.0263696	+	0.183405i	−0.972380	+	0.233405i	$0.925013\pi$
$294$	3.22066	+	6.21509i	0.187833	+	0.362471i
$295$	−0.885036	+	6.15556i	−0.0515288	+	0.358390i
$296$	0.178601	−	3.74930i	0.0103810	−	0.217924i
$297$	0.937398	−	0.180669i	0.0543934	−	0.0104835i
$298$	−1.03354	+	1.79015i	−0.0598715	+	0.103701i
$299$	−7.61707	+	0.527493i	−0.440507	+	0.0305057i
$300$	11.6443			0.672286
$301$	2.80698	−	6.57400i	0.161792	−	0.378919i
$302$	−15.9819	−	10.2709i	−0.919653	−	0.591025i
$303$	−4.84984	+	1.94158i	−0.278616	+	0.111541i
$304$	−2.03790	−	2.86184i	−0.116882	−	0.164138i
$305$	−52.1208	−	20.8660i	−2.98443	−	1.19479i
$306$	−0.527922	−	2.17613i	−0.0301793	−	0.124401i
$307$	15.0566	−	9.67629i	0.859326	−	0.552255i	−0.0351445	−	0.999382i	$-0.511189\pi$
$307$	15.0566	−	9.67629i	0.859326	−	0.552255i	0.894471	+	0.447127i	$0.147553\pi$
$308$	2.49123	+	0.416230i	0.141951	+	0.0237169i
$309$	−17.4835	+	5.13363i	−0.994604	+	0.292042i
$310$	−34.7785	−	6.70301i	−1.97529	−	0.380706i
$311$	11.2718	+	32.5678i	0.639167	+	1.84675i	0.520589	+	0.853808i	$0.325713\pi$
$311$	11.2718	+	32.5678i	0.639167	+	1.84675i	0.118579	+	0.992945i	$0.462166\pi$
$312$	0.375346	−	1.54720i	0.0212498	−	0.0875927i
$313$	−14.4478	+	20.2891i	−0.816637	+	1.14681i	0.170252	+	0.985401i	$0.445542\pi$
$313$	−14.4478	+	20.2891i	−0.816637	+	1.14681i	−0.986888	+	0.161405i	$0.948397\pi$
$314$	13.4752	−	8.66000i	0.760451	−	0.488712i
$315$	10.1174	+	3.76148i	0.570050	+	0.211936i
$316$	0.286715	+	1.99415i	0.0161290	+	0.112180i
$317$	−1.23665	+	0.118086i	−0.0694573	+	0.00663236i	−0.129727	−	0.991550i	$-0.541410\pi$
$317$	−1.23665	+	0.118086i	−0.0694573	+	0.00663236i	0.0602695	+	0.998182i	$0.480804\pi$
$318$	5.75167	+	4.52316i	0.322538	+	0.253646i
$319$	5.99610	−	3.09121i	0.335717	−	0.173074i
$320$	−1.33435	+	3.85536i	−0.0745927	+	0.215521i
$321$	−6.60501			−0.368656
$322$	11.7740	+	4.73009i	0.656137	+	0.263598i
$323$	7.86711			0.437738
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	−16.4778	+	8.49490i	−0.914024	+	0.471212i
$326$	−2.25328	−	1.77200i	−0.124797	−	0.0981417i
$327$	−3.79824	+	0.362688i	−0.210043	+	0.0200567i
$328$	1.01400	+	7.05254i	0.0559889	+	0.389411i
$329$	21.0947	−	17.4546i	1.16299	−	0.962302i
$330$	3.27646	−	2.10565i	0.180363	−	0.115912i
$331$	−3.15615	+	4.43220i	−0.173478	+	0.243616i	−0.892156	−	0.451727i	$-0.850808\pi$
$331$	−3.15615	+	4.43220i	−0.173478	+	0.243616i	0.718678	+	0.695343i	$0.244747\pi$
$332$	−2.45358	+	10.1138i	−0.134658	+	0.555066i
$333$	−1.22767	−	3.54711i	−0.0672757	−	0.194380i
$334$	2.20064	+	0.424138i	0.120413	+	0.0232078i
$335$	18.5033	−	5.43307i	1.01095	−	0.296840i
$336$	−1.68238	+	2.04196i	−0.0917813	+	0.111398i
$337$	12.0672	−	7.75511i	0.657341	−	0.422448i	−0.169001	−	0.985616i	$-0.554054\pi$
$337$	12.0672	−	7.75511i	0.657341	−	0.422448i	0.826342	+	0.563168i	$0.190418\pi$
$338$	−2.46729	−	10.1703i	−0.134203	−	0.553191i
$339$	−3.29969	−	1.32100i	−0.179215	−	0.0717467i
$340$	−5.29915	−	7.44161i	−0.287386	−	0.403578i
$341$	−7.69418	+	3.08029i	−0.416663	+	0.166807i
$342$	−2.95556	−	1.89942i	−0.159818	−	0.102709i
$343$	8.92703	+	16.2268i	0.482014	+	0.876163i
$344$	2.70176			0.145669
$345$	18.3476	−	6.79611i	0.987799	−	0.365891i
$346$	−0.0671708	+	0.116343i	−0.00361112	+	0.00625465i
$347$	19.5090	−	3.76004i	1.04730	−	0.201850i	0.363554	−	0.931573i	$-0.381563\pi$
$347$	19.5090	−	3.76004i	1.04730	−	0.201850i	0.683742	+	0.729724i	$0.260351\pi$
$348$	−0.336237	+	7.05848i	−0.0180242	+	0.378374i
$349$	−1.03681	+	7.21114i	−0.0554989	+	0.386004i	0.943073	+	0.332585i	$0.107921\pi$
$349$	−1.03681	+	7.21114i	−0.0554989	+	0.386004i	−0.998572	+	0.0534186i	$0.982988\pi$
$350$	30.7985	−	0.765534i	1.64625	−	0.0409195i
$351$	−0.226576	−	1.57587i	−0.0120937	−	0.0841136i
$352$	0.225067	+	0.927740i	0.0119961	+	0.0494487i
$353$	0.341018	+	7.15885i	0.0181506	+	0.381027i	0.989606	+	0.143805i	$0.0459339\pi$
$353$	0.341018	+	7.15885i	0.0181506	+	0.381027i	−0.971455	+	0.237222i	$0.923763\pi$
$354$	−1.51742	−	0.144896i	−0.0806501	−	0.00770115i
$355$	−5.96489	−	5.68751i	−0.316583	−	0.301862i
$356$	−5.09565	+	5.88069i	−0.270069	+	0.311676i
$357$	−1.53939	−	5.72100i	−0.0814729	−	0.302788i
$358$	−12.9213	+	3.79403i	−0.682911	+	0.200521i
$359$	−14.5667	+	20.4560i	−0.768799	+	1.07963i	0.225629	+	0.974213i	$0.427556\pi$
$359$	−14.5667	+	20.4560i	−0.768799	+	1.07963i	−0.994428	+	0.105414i	$0.966383\pi$
$360$	0.194122	+	4.07513i	0.0102311	+	0.214778i
$361$	−4.81778	+	4.59375i	−0.253568	+	0.241776i
$362$	8.03044	−	6.31521i	0.422070	−	0.331920i
$363$	−4.19097	+	9.17695i	−0.219969	+	0.481665i
$364$	0.891047	−	4.11691i	0.0467036	−	0.215785i
$365$	−1.35407	−	0.870207i	−0.0708752	−	0.0455487i
$366$	4.50086	−	13.0044i	0.235264	−	0.679750i
$367$	−10.3442	+	17.9168i	−0.539965	+	0.935247i	0.458940	+	0.888467i	$0.348229\pi$
$367$	−10.3442	+	17.9168i	−0.539965	+	0.935247i	−0.998905	+	0.0467801i	$0.985104\pi$
$368$	0.103300	+	4.79472i	0.00538488	+	0.249942i
$369$	3.56253	+	6.17048i	0.185458	+	0.321223i
$370$	−10.0282	−	11.5732i	−0.521343	−	0.601662i
$371$	15.5102	+	11.5853i	0.805247	+	0.601481i
$372$	1.23552	−	8.59320i	0.0640585	−	0.445537i
$373$	16.3773	−	1.56385i	0.847986	−	0.0809728i	0.337990	−	0.941150i	$-0.390253\pi$
$373$	16.3773	−	1.56385i	0.847986	−	0.0809728i	0.509996	+	0.860177i	$0.329647\pi$
$374$	−1.98457	−	0.794502i	−0.102620	−	0.0410827i
$375$	19.6184	−	18.7061i	1.01309	−	0.965981i
$376$	9.19817	+	4.74198i	0.474359	+	0.244549i
$377$	−4.67357	−	10.2337i	−0.240701	−	0.527062i
$378$	−0.802946	+	2.52097i	−0.0412991	+	0.129665i
$379$	−11.0862	+	12.7942i	−0.569460	+	0.657192i	−0.965305	−	0.261126i	$-0.915906\pi$
$379$	−11.0862	+	12.7942i	−0.569460	+	0.657192i	0.395845	+	0.918317i	$0.370452\pi$
$380$	−14.0743	−	2.71260i	−0.721996	−	0.139153i
$381$	−2.47607	+	10.2065i	−0.126853	+	0.522895i
$382$	2.19535	+	0.209630i	0.112324	+	0.0107256i
$383$	16.1438	+	8.32270i	0.824909	+	0.425270i	0.818358	−	0.574708i	$-0.194885\pi$
$383$	16.1438	+	8.32270i	0.824909	+	0.425270i	0.00655078	+	0.999979i	$0.497915\pi$
$384$	−0.959493	−	0.281733i	−0.0489639	−	0.0143771i
$385$	8.52758	−	5.78471i	0.434606	−	0.294816i
$386$	−3.65149	+	7.99566i	−0.185856	+	0.406968i
$387$	2.50823	−	1.00414i	0.127500	−	0.0510435i
$388$	−2.35964	+	1.21648i	−0.119793	+	0.0617574i
$389$	−11.9364	+	2.30055i	−0.605198	+	0.116642i	−0.482640	−	0.875819i	$-0.660322\pi$
$389$	−11.9364	+	2.30055i	−0.605198	+	0.116642i	−0.122558	+	0.992461i	$0.539110\pi$
$390$	−3.24763	−	5.62506i	−0.164450	−	0.284836i
$391$	−8.87992	−	6.03939i	−0.449077	−	0.305425i
$392$	−4.31554	+	5.51146i	−0.217967	+	0.278371i
$393$	−6.87623	−	7.93559i	−0.346860	−	0.400298i
$394$	0.609206	−	12.7888i	0.0306913	−	0.644290i
$395$	6.46079	+	5.08082i	0.325078	+	0.255644i
$396$	0.553751	+	0.777635i	0.0278271	+	0.0390776i
$397$	−11.6175	+	9.13614i	−0.583068	+	0.458530i	−0.865606	−	0.500727i	$-0.833066\pi$
$397$	−11.6175	+	9.13614i	−0.583068	+	0.458530i	0.282538	+	0.959256i	$0.408824\pi$
$398$	−26.2874	−	7.71869i	−1.31767	−	0.386903i
$399$	−7.94214	−	4.82954i	−0.397604	−	0.241780i
$400$	4.83723	+	10.5921i	0.241862	+	0.529603i
$401$	−10.0587	−	9.59096i	−0.502308	−	0.478949i	0.396041	−	0.918233i	$-0.370384\pi$
$401$	−10.0587	−	9.59096i	−0.502308	−	0.478949i	−0.898348	+	0.439283i	$0.855232\pi$
$402$	1.54601	+	4.46691i	0.0771081	+	0.222789i
$403$	4.52063	+	13.0615i	0.225189	+	0.650640i
$404$	−3.78082	−	3.60501i	−0.188103	−	0.179356i
$405$	1.69479	+	3.71107i	0.0842147	+	0.184405i
$406$	−0.425279	+	18.6913i	−0.0211062	+	0.927635i
$407$	−3.43818	−	1.00954i	−0.170424	−	0.0500411i
$408$	1.76017	−	1.38421i	0.0871412	−	0.0685286i
$409$	−7.46204	−	10.4790i	−0.368974	−	0.518151i	0.587791	−	0.809013i	$-0.299998\pi$
$409$	−7.46204	−	10.4790i	−0.368974	−	0.518151i	−0.956765	+	0.290861i	$0.906058\pi$
$410$	22.8493	+	17.9689i	1.12845	+	0.887422i
$411$	−1.00702	+	21.1401i	−0.0496729	+	1.04276i
$412$	−11.9326	−	13.7710i	−0.587879	−	0.678448i
$413$	−4.02301	−	0.283481i	−0.197959	−	0.0139492i
$414$	1.87792	+	4.41287i	0.0922946	+	0.216881i
$415$	21.2293	+	36.7702i	1.04210	+	1.80498i
$416$	1.56330	−	0.301302i	0.0766472	−	0.0147725i
$417$	−17.4255	+	8.98347i	−0.853331	+	0.439922i
$418$	−3.11370	+	1.24654i	−0.152296	+	0.0609702i
$419$	−11.8176	+	25.8770i	−0.577329	+	1.26417i	0.365474	+	0.930822i	$0.380907\pi$
$419$	−11.8176	+	25.8770i	−0.577329	+	1.26417i	−0.942802	+	0.333352i	$0.891820\pi$
$420$	0.781351	+	10.7657i	0.0381260	+	0.525311i
$421$	21.3257	+	6.26180i	1.03935	+	0.305181i	0.756508	−	0.653984i	$-0.226904\pi$
$421$	21.3257	+	6.26180i	1.03935	+	0.305181i	0.282845	+	0.959166i	$0.408722\pi$
$422$	−9.15513	−	4.71980i	−0.445665	−	0.229756i
$423$	10.3017	+	0.983693i	0.500886	+	0.0478288i
$424$	−1.72508	+	7.11089i	−0.0837775	+	0.345335i
$425$	−25.6033	−	4.93464i	−1.24194	−	0.239365i
$426$	1.32294	−	1.52675i	0.0640965	−	0.0739713i
$427$	11.0495	−	34.6917i	0.534725	−	1.67885i
$428$	−2.74382	−	6.00813i	−0.132628	−	0.290414i
$429$	−1.35092	−	0.696446i	−0.0652229	−	0.0336247i
$430$	7.97737	−	7.60640i	0.384703	−	0.366813i
$431$	−28.1199	−	11.2575i	−1.35449	−	0.542256i	−0.423035	−	0.906113i	$-0.639035\pi$
$431$	−28.1199	−	11.2575i	−1.35449	−	0.542256i	−0.931455	+	0.363858i	$0.881459\pi$
$432$	−0.995472	+	0.0950560i	−0.0478947	+	0.00457339i
$433$	−3.33568	+	23.2002i	−0.160303	+	1.11493i	0.737761	+	0.675062i	$0.235883\pi$
$433$	−3.33568	+	23.2002i	−0.160303	+	1.11493i	−0.898063	+	0.439866i	$0.855026\pi$
$434$	2.70292	−	22.8097i	0.129744	−	1.09490i
$435$	18.8793	+	21.7879i	0.905193	+	1.04465i
$436$	−1.90776	−	3.30433i	−0.0913650	−	0.158249i
$437$	−16.6221	+	2.75655i	−0.795143	+	0.131864i
$438$	0.197265	−	0.341673i	0.00942569	−	0.0163258i
$439$	3.51330	−	10.1510i	0.167681	−	0.484481i	−0.829585	−	0.558380i	$-0.811423\pi$
$439$	3.51330	−	10.1510i	0.167681	−	0.484481i	0.997266	+	0.0738990i	$0.0235443\pi$
$440$	3.27646	+	2.10565i	0.156199	+	0.100383i
$441$	−1.95800	+	6.72058i	−0.0932383	+	0.320028i
$442$	−1.48097	+	3.24288i	−0.0704427	+	0.154248i
$443$	3.70802	−	2.91602i	0.176173	−	0.138544i	−0.526179	−	0.850374i	$-0.676376\pi$
$443$	3.70802	−	2.91602i	0.176173	−	0.138544i	0.702352	+	0.711830i	$0.252133\pi$
$444$	2.71657	−	2.59025i	0.128923	−	0.122928i
$445$	1.51052	+	31.7096i	0.0716054	+	1.50318i
$446$	−13.7453	+	19.3025i	−0.650858	+	0.914002i
$447$	−1.98335	+	0.582365i	−0.0938094	+	0.0275449i
$448$	−2.55632	−	0.682084i	−0.120775	−	0.0322254i
$449$	−21.7674	+	25.1209i	−1.02727	+	1.18553i	−0.0448163	+	0.998995i	$0.514270\pi$
$449$	−21.7674	+	25.1209i	−1.02727	+	1.18553i	−0.982449	+	0.186532i	$0.940275\pi$
$450$	8.42741	+	8.03552i	0.397272	+	0.378798i
$451$	6.77114	+	0.646565i	0.318840	+	0.0304456i
$452$	−0.169120	−	3.55027i	−0.00795474	−	0.166990i
$453$	−4.47887	−	18.4622i	−0.210436	−	0.867428i
$454$	2.49986	+	17.3869i	0.117324	+	0.816008i
$455$	−8.95957	−	14.6644i	−0.420031	−	0.687478i
$456$	0.499992	−	3.47752i	0.0234143	−	0.162850i
$457$	−0.294107	+	6.17407i	−0.0137578	+	0.288811i	0.981495	+	0.191487i	$0.0613311\pi$
$457$	−0.294107	+	6.17407i	−0.0137578	+	0.288811i	−0.995253	+	0.0973234i	$0.968972\pi$
$458$	−27.0188	+	5.20745i	−1.26251	+	0.243328i
$459$	1.11962	−	1.93924i	0.0522595	−	0.0905162i
$460$	13.8038	+	13.8663i	0.643606	+	0.646520i
$461$	−34.0798			−1.58725			−0.793627	−	0.608404i	$-0.791810\pi$
$461$	−34.0798			−1.58725			−0.793627	+	0.608404i	$0.791810\pi$
$462$	1.51576	+	2.02039i	0.0705195	+	0.0939970i
$463$	2.96037	+	1.90252i	0.137580	+	0.0884175i	0.607620	−	0.794228i	$-0.292124\pi$
$463$	2.96037	+	1.90252i	0.137580	+	0.0884175i	−0.470040	+	0.882645i	$0.655761\pi$
$464$	−6.56030	+	2.62635i	−0.304554	+	0.121925i
$465$	−20.5448	−	28.8511i	−0.952742	−	1.33794i
$466$	20.0479	+	8.02597i	0.928701	+	0.371796i
$467$	−8.55423	−	35.2610i	−0.395843	−	1.63169i	−0.725954	−	0.687743i	$-0.758601\pi$
$467$	−8.55423	−	35.2610i	−0.395843	−	1.63169i	0.330111	−	0.943942i	$-0.392914\pi$
$468$	1.33934	−	0.860740i	0.0619109	−	0.0397877i
$469$	4.38277	+	11.7130i	0.202378	+	0.540858i
$470$	40.5093	−	11.8946i	1.86856	−	0.548657i
$471$	15.7286	+	3.03143i	0.724734	+	0.139681i
$472$	−0.498558	−	1.44049i	−0.0229480	−	0.0663038i
$473$	0.608078	−	2.50653i	0.0279595	−	0.115251i
$474$	−1.16861	+	1.64109i	−0.0536762	+	0.0753777i
$475$	−34.4156	+	22.1175i	−1.57909	+	1.01482i
$476$	4.56452	−	3.77686i	0.209215	−	0.173112i
$477$	1.04134	+	7.24267i	0.0476796	+	0.331619i
$478$	−0.564223	+	0.0538767i	−0.0258069	+	0.00246426i
$479$	24.0137	+	18.8846i	1.09721	+	0.862858i	0.991314	−	0.131519i	$-0.0419853\pi$
$479$	24.0137	+	18.8846i	1.09721	+	0.862858i	0.105900	+	0.994377i	$0.466228\pi$
$480$	−3.62622	+	1.86945i	−0.165514	+	0.0853283i
$481$	−1.95454	+	5.64726i	−0.0891192	+	0.257493i
$482$	26.4060			1.20276
$483$	5.25708	+	11.5483i	0.239206	+	0.525466i
$484$	−10.0886			−0.458575
$485$	−3.54239	+	10.2351i	−0.160851	+	0.464750i
$486$	−0.888835	+	0.458227i	−0.0403184	+	0.0207856i
$487$	0.526799	+	0.414279i	0.0238715	+	0.0187728i	0.630023	−	0.776576i	$-0.283045\pi$
$487$	0.526799	+	0.414279i	0.0238715	+	0.0187728i	−0.606152	+	0.795349i	$0.707288\pi$
$488$	13.6989	−	1.30809i	0.620122	−	0.0592145i
$489$	−0.407955	−	2.83739i	−0.0184484	−	0.128311i
$490$	2.77439	+	28.4232i	0.125334	+	1.28403i
$491$	−12.1926	+	7.83572i	−0.550245	+	0.353621i	−0.786034	−	0.618183i	$-0.787869\pi$
$491$	−12.1926	+	7.83572i	−0.550245	+	0.353621i	0.235789	+	0.971804i	$0.424233\pi$
$492$	−4.13294	+	5.80390i	−0.186327	+	0.261660i
$493$	3.73056	−	15.3776i	0.168016	−	0.692570i
$494$	1.82942	+	5.28577i	0.0823097	+	0.237818i
$495$	3.82435	+	0.737083i	0.171892	+	0.0331294i
$496$	8.32990	−	2.44588i	0.374024	−	0.109823i
$497$	3.39871	−	4.12513i	0.152453	−	0.185037i
$498$	−8.75505	+	5.62653i	−0.392323	+	0.252131i
$499$	4.24665	+	17.5049i	0.190106	+	0.783628i	0.984378	+	0.176066i	$0.0563372\pi$
$499$	4.24665	+	17.5049i	0.190106	+	0.783628i	−0.794272	+	0.607562i	$0.792148\pi$
$500$	25.1655	+	10.0747i	1.12543	+	0.450556i
$501$	1.29999	+	1.82558i	0.0580791	+	0.0815607i
$502$	23.6874	−	9.48300i	1.05722	−	0.423247i
$503$	35.1553	+	22.5929i	1.56750	+	1.00737i	0.980203	+	0.197996i	$0.0634432\pi$
$503$	35.1553	+	22.5929i	1.56750	+	1.00737i	0.587294	+	0.809374i	$0.300193\pi$
$504$	−2.62671	+	0.316862i	−0.117003	+	0.0141142i
$505$	−21.3128			−0.948407
$506$	4.47150	+	0.983299i	0.198782	+	0.0437130i
$507$	5.23265	−	9.06322i	0.232390	−	0.402512i
$508$	−10.3128	+	1.98762i	−0.457554	+	0.0881864i
$509$	−0.199523	+	4.18849i	−0.00884368	+	0.185652i	0.990123	+	0.140202i	$0.0447752\pi$
$509$	−0.199523	+	4.18849i	−0.00884368	+	0.185652i	−0.998967	+	0.0454499i	$0.985528\pi$
$510$	1.30013	−	9.04257i	0.0575705	−	0.400412i
$511$	0.499291	−	0.916672i	0.0220873	−	0.0405512i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	−0.828288	−	3.41425i	−0.0365698	−	0.150743i
$514$	−0.532837	−	11.1856i	−0.0235024	−	0.493377i
$515$	−74.0031	−	7.06644i	−3.26097	−	0.311384i
$516$	1.95536	+	1.86443i	0.0860798	+	0.0820769i
$517$	6.46953	−	7.46624i	0.284530	−	0.328365i
$518$	7.01487	−	7.02963i	0.308216	−	0.308864i
$519$	−0.128900	+	0.0378484i	−0.00565807	+	0.00166136i
$520$	3.76762	−	5.29088i	0.165221	−	0.232020i
$521$	−1.71803	−	36.0659i	−0.0752682	−	1.58007i	−0.648844	−	0.760921i	$-0.724747\pi$
$521$	−1.71803	−	36.0659i	−0.0752682	−	1.58007i	0.573576	−	0.819152i	$-0.305556\pi$
$522$	−5.11426	+	4.87643i	−0.223845	+	0.213436i
$523$	−15.0763	+	11.8562i	−0.659242	+	0.518434i	−0.890805	−	0.454386i	$-0.849859\pi$
$523$	−15.0763	+	11.8562i	−0.659242	+	0.518434i	0.231563	+	0.972820i	$0.425616\pi$
$524$	4.36198	−	9.55141i	0.190554	−	0.417255i
$525$	22.8182	+	20.6994i	0.995869	+	0.903395i
$526$	6.65381	+	4.27614i	0.290120	+	0.186449i
$527$	−6.35826	+	18.3710i	−0.276970	+	0.800252i
$528$	−0.477325	+	0.826751i	−0.0207729	+	0.0359797i
$529$	20.8782	+	9.64896i	0.907746	+	0.419520i
$530$	14.9261	+	25.8527i	0.648347	+	1.12297i
$531$	−0.998220	−	1.15201i	−0.0433191	−	0.0499929i
$532$	1.09382	−	9.23069i	0.0474233	−	0.400201i
$533$	1.61437	−	11.2282i	0.0699259	−	0.486346i
$534$	−7.74603	+	0.739656i	−0.335204	+	0.0320081i
$535$	−25.0165	−	10.0151i	−1.08156	−	0.432991i
$536$	−3.42101	+	3.26192i	−0.147765	+	0.140894i
$537$	−11.9698	−	6.17084i	−0.516533	−	0.266291i
$538$	−1.18830	−	2.60201i	−0.0512311	−	0.112180i
$539$	4.14191	+	5.24414i	0.178405	+	0.225881i
$540$	−2.67167	+	3.08327i	−0.114970	+	0.132683i
$541$	41.7300	+	8.04280i	1.79411	+	0.345787i	0.974024	−	0.226446i	$-0.0727108\pi$
$541$	41.7300	+	8.04280i	1.79411	+	0.345787i	0.820091	+	0.572234i	$0.193923\pi$
$542$	5.76029	−	23.7442i	0.247426	−	1.01990i
$543$	10.1699	+	0.971107i	0.436432	+	0.0416742i
$544$	1.99032	+	1.02608i	0.0853343	+	0.0439929i
$545$	−14.9358	−	4.38554i	−0.639779	−	0.187856i
$546$	3.48587	−	2.36465i	0.149182	−	0.101198i
$547$	−6.08239	+	13.3186i	−0.260064	+	0.569461i	−0.993953	−	0.109809i	$-0.964976\pi$
$547$	−6.08239	+	13.3186i	−0.260064	+	0.569461i	0.733888	+	0.679270i	$0.237703\pi$
$548$	−19.6480	+	7.86587i	−0.839321	+	0.336013i
$549$	12.2315	−	6.30577i	0.522027	−	0.269124i
$550$	10.9154	−	2.10377i	0.465434	−	0.0897050i
$551$	−12.4133	−	21.5004i	−0.528824	−	0.915949i
$552$	−3.23397	+	3.54139i	−0.137647	+	0.150731i
$553$	−2.98302	+	4.41740i	−0.126851	+	0.187847i
$554$	3.83536	+	4.42624i	0.162949	+	0.188053i
$555$	0.728648	−	15.2962i	0.0309294	−	0.649288i
$556$	−15.4105	−	12.1189i	−0.653549	−	0.513957i
$557$	−20.2263	−	28.4039i	−0.857016	−	1.20351i	−0.977529	−	0.210799i	$-0.932393\pi$
$557$	−20.2263	−	28.4039i	−0.857016	−	1.20351i	0.120513	−	0.992712i	$-0.461546\pi$
$558$	6.82417	−	5.36659i	0.288890	−	0.227186i
$559$	−4.12717	−	1.21185i	−0.174561	−	0.0512556i
$560$	−9.46822	+	5.18297i	−0.400105	+	0.219020i
$561$	−0.888031	−	1.94452i	−0.0374927	−	0.0820976i
$562$	5.21815	+	4.97549i	0.220114	+	0.209879i
$563$	0.126077	+	0.364277i	0.00531353	+	0.0153524i	0.947626	−	0.319381i	$-0.103475\pi$
$563$	0.126077	+	0.364277i	0.00531353	+	0.0153524i	−0.942313	+	0.334733i	$0.891354\pi$
$564$	3.38468	+	9.77940i	0.142521	+	0.411787i
$565$	−10.4946	−	10.0066i	−0.441511	−	0.420980i
$566$	−0.290945	−	0.637081i	−0.0122293	−	0.0267785i
$567$	−2.32079	+	1.27041i	−0.0974639	+	0.0533524i
$568$	1.93835	+	0.569150i	0.0813313	+	0.0238810i
$569$	32.2836	−	25.3881i	1.35340	−	1.06433i	0.362180	−	0.932108i	$-0.382033\pi$
$569$	32.2836	−	25.3881i	1.35340	−	1.06433i	0.991221	−	0.132218i	$-0.0422098\pi$
$570$	−8.31413	−	11.6756i	−0.348241	−	0.489036i
$571$	−1.27654	−	1.00388i	−0.0534216	−	0.0420112i	0.591091	−	0.806605i	$-0.298697\pi$
$571$	−1.27654	−	1.00388i	−0.0534216	−	0.0420112i	−0.644513	+	0.764594i	$0.722940\pi$
$572$	0.0723185	−	1.51815i	0.00302379	−	0.0634771i
$573$	1.44419	+	1.66668i	0.0603317	+	0.0696265i
$574$	−10.5498	+	15.6227i	−0.440340	+	0.652077i
$575$	55.8253	+	1.45507i	2.32808	+	0.0606804i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	3.98330	−	0.767719i	0.165827	−	0.0319606i	−0.105662	−	0.994402i	$-0.533696\pi$
$577$	3.98330	−	0.767719i	0.165827	−	0.0319606i	0.271489	+	0.962442i	$0.412484\pi$
$578$	10.6534	−	5.49220i	0.443122	−	0.228445i
$579$	−8.16035	+	3.26691i	−0.339132	+	0.135768i
$580$	−11.9762	+	26.2242i	−0.497285	+	1.08890i
$581$	−22.7866	+	15.4574i	−0.945349	+	0.641280i
$582$	−2.54722	−	0.747931i	−0.105586	−	0.0310027i
$583$	6.20880	+	3.20086i	0.257142	+	0.132566i
$584$	0.392744	+	0.0375025i	0.0162519	+	0.00155186i
$585$	1.53132	−	6.31217i	0.0633121	−	0.260976i
$586$	−3.11435	−	0.600241i	−0.128653	−	0.0247957i
$587$	19.2392	−	22.2033i	0.794088	−	0.916426i	−0.203954	−	0.978981i	$-0.565379\pi$
$587$	19.2392	−	22.2033i	0.794088	−	0.916426i	0.998042	+	0.0625542i	$0.0199246\pi$
$588$	−6.92664	+	1.01077i	−0.285650	+	0.0416834i
$589$	12.6705	+	27.7445i	0.522078	+	1.14319i
$590$	−5.52754	−	2.84965i	−0.227565	−	0.117318i
$591$	9.26618	−	8.83529i	0.381160	−	0.363435i
$592$	3.48468	+	1.39505i	0.143219	+	0.0573364i
$593$	30.8430	−	2.94515i	1.26657	−	0.120943i	0.559945	−	0.828530i	$-0.310822\pi$
$593$	30.8430	−	2.94515i	1.26657	−	0.120943i	0.706627	+	0.707587i	$0.250216\pi$
$594$	−0.135861	+	0.944933i	−0.00557444	+	0.0387711i
$595$	2.84426	−	24.0025i	0.116603	−	0.984006i
$596$	−1.35365	−	1.56220i	−0.0554478	−	0.0639902i
$597$	−13.6986	−	23.7267i	−0.560647	−	0.971069i
$598$	1.99282	−	7.37067i	0.0814924	−	0.301409i
$599$	1.17739	−	2.03930i	0.0481070	−	0.0833237i	−0.840969	−	0.541083i	$-0.818015\pi$
$599$	1.17739	−	2.03930i	0.0481070	−	0.0833237i	0.889076	+	0.457759i	$0.151348\pi$
$600$	−3.80849	+	11.0039i	−0.155481	+	0.449233i
$601$	35.5419	+	22.8414i	1.44979	+	0.931721i	0.999241	+	0.0389668i	$0.0124067\pi$
$601$	35.5419	+	22.8414i	1.44979	+	0.931721i	0.450545	+	0.892754i	$0.351230\pi$
$602$	5.29437	+	4.80274i	0.215782	+	0.195745i
$603$	−1.96362	+	4.29973i	−0.0799647	+	0.175098i
$604$	14.9332	−	11.7436i	0.607623	−	0.477840i
$605$	−29.7883	+	28.4030i	−1.21106	+	1.15475i
$606$	−0.248570	−	5.21813i	−0.0100975	−	0.211972i
$607$	23.4744	−	32.9652i	0.952798	−	1.33802i	0.0116823	−	0.999932i	$-0.496281\pi$
$607$	23.4744	−	32.9652i	0.952798	−	1.33802i	0.941115	−	0.338085i	$-0.109779\pi$
$608$	3.37097	−	0.989806i	0.136711	−	0.0401419i
$609$	−13.2063	+	13.2341i	−0.535145	+	0.536272i
$610$	36.7655	−	42.4296i	1.48859	−	1.71792i
$611$	−11.9240	−	11.3695i	−0.482393	−	0.459961i
$612$	2.22911	+	0.212854i	0.0901063	+	0.00860411i
$613$	1.69609	+	35.6054i	0.0685046	+	1.43809i	0.727586	+	0.686016i	$0.240642\pi$
$613$	1.69609	+	35.6054i	0.0685046	+	1.43809i	−0.659082	+	0.752071i	$0.729055\pi$
$614$	4.21957	+	17.3933i	0.170288	+	0.701937i
$615$	4.13687	+	28.7726i	0.166815	+	1.16022i
$616$	−1.20814	+	2.21808i	−0.0486774	+	0.0893691i
$617$	3.41537	−	23.7544i	0.137498	−	0.956317i	−0.797918	−	0.602766i	$-0.794065\pi$
$617$	3.41537	−	23.7544i	0.137498	−	0.956317i	0.935415	−	0.353551i	$-0.115026\pi$
$618$	0.867021	−	18.2010i	0.0348767	−	0.732152i
$619$	32.6761	−	6.29781i	1.31336	−	0.253130i	0.515979	−	0.856601i	$-0.327428\pi$
$619$	32.6761	−	6.29781i	1.31336	−	0.253130i	0.797385	+	0.603471i	$0.206216\pi$
$620$	17.7093	−	30.6734i	0.711223	−	1.23187i
$621$	−1.68612	+	4.48966i	−0.0676615	+	0.180164i
$622$	−34.4633			−1.38185
$623$	−20.4391	+	2.46559i	−0.818876	+	0.0987818i
$624$	1.33934	+	0.860740i	0.0536164	+	0.0344572i
$625$	48.6177	−	19.4636i	1.94471	−	0.778543i
$626$	−14.4478	−	20.2891i	−0.577449	−	0.810914i
$627$	−3.11370	−	1.24654i	−0.124349	−	0.0497820i
$628$	3.77640	+	15.5665i	0.150695	+	0.621172i
$629$	−7.07085	+	4.54416i	−0.281933	+	0.181187i
$630$	−6.86368	+	8.33068i	−0.273456	+	0.331902i
$631$	−0.966845	+	0.283891i	−0.0384895	+	0.0113015i	−0.300921	−	0.953649i	$-0.597294\pi$
$631$	−0.966845	+	0.283891i	−0.0384895	+	0.0113015i	0.262431	+	0.964951i	$0.415476\pi$
$632$	−1.97825	−	0.381276i	−0.0786904	−	0.0151663i
$633$	−3.36885	−	9.73364i	−0.133900	−	0.386878i
$634$	0.292878	−	1.20726i	0.0116317	−	0.0479464i
$635$	−24.8541	+	34.9027i	−0.986306	+	1.38507i
$636$	−6.15558	+	3.95595i	−0.244085	+	0.156864i
$637$	9.06444	−	6.48352i	0.359146	−	0.256887i
$638$	0.960059	+	6.67736i	0.0380091	+	0.264359i
$639$	2.01103	−	0.192030i	0.0795552	−	0.00759660i
$640$	−3.20690	−	2.52193i	−0.126764	−	0.0996881i
$641$	−37.0815	+	19.1168i	−1.46463	+	0.755069i	−0.992006	−	0.126194i	$-0.959724\pi$
$641$	−37.0815	+	19.1168i	−1.46463	+	0.755069i	−0.472625	+	0.881264i	$0.656693\pi$
$642$	2.16029	−	6.24174i	0.0852598	−	0.246342i
$643$	11.5058			0.453746			0.226873	−	0.973924i	$-0.427150\pi$
$643$	11.5058			0.453746			0.226873	+	0.973924i	$0.427150\pi$
$644$	−8.32083	+	9.57935i	−0.327886	+	0.377479i
$645$	11.0225			0.434011
$646$	−2.57308	+	7.43442i	−0.101236	+	0.292503i
$647$	23.5102	−	12.1203i	0.924280	−	0.476500i	0.0707216	−	0.997496i	$-0.477470\pi$
$647$	23.5102	−	12.1203i	0.924280	−	0.476500i	0.853559	+	0.520996i	$0.174440\pi$
$648$	−0.786053	−	0.618159i	−0.0308791	−	0.0242836i
$649$	−1.44861	+	0.138325i	−0.0568628	+	0.00542974i
$650$	−2.63832	−	18.3500i	−0.103484	−	0.719744i
$651$	17.6967	−	14.6429i	0.693587	−	0.573901i
$652$	2.41151	−	1.54978i	0.0944421	−	0.0606942i
$653$	1.56849	−	2.20264i	0.0613799	−	0.0861961i	−0.782745	−	0.622342i	$-0.786181\pi$
$653$	1.56849	−	2.20264i	0.0613799	−	0.0861961i	0.844125	+	0.536146i	$0.180121\pi$
$654$	0.899542	−	3.70796i	0.0351749	−	0.144993i
$655$	−14.0111	−	40.4825i	−0.547460	−	1.58178i
$656$	−6.99630	−	1.34843i	−0.273160	−	0.0526472i
$657$	0.378549	−	0.111152i	0.0147686	−	0.00433645i
$658$	9.59519	+	25.6433i	0.374059	+	0.999682i
$659$	4.18282	−	2.68813i	0.162939	−	0.104715i	−0.456630	−	0.889657i	$-0.650944\pi$
$659$	4.18282	−	2.68813i	0.162939	−	0.104715i	0.619569	+	0.784942i	$0.287307\pi$
$660$	0.918218	+	3.78494i	0.0357416	+	0.147329i
$661$	−31.3932	−	12.5680i	−1.22105	−	0.488837i	−0.330541	−	0.943792i	$-0.607231\pi$
$661$	−31.3932	−	12.5680i	−1.22105	−	0.488837i	−0.890514	+	0.454955i	$0.849655\pi$
$662$	−3.15615	−	4.43220i	−0.122667	−	0.172262i
$663$	−3.30967	+	1.32499i	−0.128537	+	0.0514585i
$664$	−8.75505	−	5.62653i	−0.339762	−	0.218352i
$665$	−22.7579	−	30.3345i	−0.882515	−	1.17632i
$666$	3.75355			0.145447
$667$	−2.49401	+	33.7978i	−0.0965684	+	1.30866i
$668$	−1.12057	+	1.94088i	−0.0433561	+	0.0750949i
$669$	−23.2682	+	4.48458i	−0.899601	+	0.173384i
$670$	−0.917593	+	19.2627i	−0.0354497	+	0.744181i
$671$	1.86962	−	13.0035i	0.0721757	−	0.501993i
$672$	−1.37940	−	2.25771i	−0.0532116	−	0.0870930i
$673$	3.96465	+	27.5747i	0.152826	+	1.06293i	0.911454	+	0.411403i	$0.134961\pi$
$673$	3.96465	+	27.5747i	0.152826	+	1.06293i	−0.758628	+	0.651524i	$0.774130\pi$
$674$	3.38179	+	13.9399i	0.130262	+	0.536947i
$675$	0.554060	+	11.6312i	0.0213258	+	0.447683i
$676$	10.4179	+	0.994790i	0.400689	+	0.0382612i
$677$	23.5229	+	22.4291i	0.904059	+	0.862019i	0.990954	−	0.134199i	$-0.0428460\pi$
$677$	23.5229	+	22.4291i	0.904059	+	0.862019i	−0.0868950	+	0.996217i	$0.527694\pi$
$678$	2.32757	−	2.68615i	0.0893896	−	0.103161i
$679$	−6.78640	−	1.81077i	−0.260438	−	0.0694909i
$680$	8.76551	−	2.57378i	0.336142	−	0.0987001i
$681$	−10.1891	+	14.3086i	−0.390448	+	0.548307i
$682$	−0.394352	−	8.27847i	−0.0151005	−	0.316999i
$683$	−9.10416	+	8.68080i	−0.348361	+	0.332162i	−0.843976	−	0.536381i	$-0.819791\pi$
$683$	−9.10416	+	8.68080i	−0.348361	+	0.332162i	0.495615	+	0.868542i	$0.334943\pi$
$684$	2.76163	−	2.17177i	0.105593	−	0.0830396i
$685$	−35.8685	+	78.5412i	−1.37047	+	3.00090i
$686$	−18.2541	+	3.12879i	−0.696943	+	0.119458i
$687$	−23.1480	−	14.8763i	−0.883151	−	0.567566i
$688$	−0.883660	+	2.55317i	−0.0336892	+	0.0973386i
$689$	5.82472	−	10.0887i	0.221904	−	0.384349i
$690$	0.421437	+	19.5612i	0.0160438	+	0.744684i
$691$	5.81275	+	10.0680i	0.221127	+	0.383004i	0.955151	−	0.296121i	$-0.0956930\pi$
$691$	5.81275	+	10.0680i	0.221127	+	0.383004i	−0.734023	+	0.679124i	$0.762360\pi$
$692$	−0.0879750	−	0.101529i	−0.00334431	−	0.00385954i
$693$	−0.297220	+	2.50822i	−0.0112905	+	0.0952793i
$694$	−2.82751	+	19.6658i	−0.107331	+	0.746503i
$695$	−79.6207	+	7.60286i	−3.02019	+	0.288393i
$696$	−6.56030	−	2.62635i	−0.248667	−	0.0995514i
$697$	11.5470	−	11.0100i	0.437374	−	0.417035i
$698$	−6.47543	−	3.33832i	−0.245099	−	0.126357i
$699$	8.97079	+	19.6433i	0.339307	+	0.742978i
$700$	−9.34978	+	29.3550i	−0.353388	+	1.10951i
$701$	−8.99097	+	10.3761i	−0.339584	+	0.391901i	−0.899697	−	0.436515i	$-0.856212\pi$
$701$	−8.99097	+	10.3761i	−0.339584	+	0.391901i	0.560112	+	0.828417i	$0.310758\pi$
$702$	1.56330	+	0.301302i	0.0590031	+	0.0113719i
$703$	−3.10902	+	12.8156i	−0.117259	+	0.483348i
$704$	−0.950327	−	0.0907453i	−0.0358168	−	0.00342009i
$705$	37.5262	+	19.3461i	1.41332	+	0.728616i
$706$	−6.87666	−	2.01917i	−0.258806	−	0.0759924i
$707$	−1.00051	−	13.7853i	−0.0376279	−	0.518448i
$708$	0.633227	−	1.38657i	0.0237981	−	0.0521106i
$709$	24.2765	−	9.71886i	0.911725	−	0.364999i	0.132093	−	0.991237i	$-0.457830\pi$
$709$	24.2765	−	9.71886i	0.911725	−	0.364999i	0.779632	+	0.626238i	$0.215406\pi$
$710$	7.32563	−	3.77662i	0.274926	−	0.141734i
$711$	−1.97825	+	0.381276i	−0.0741900	+	0.0142990i
$712$	−3.89063	−	6.73877i	−0.145808	−	0.252546i
$713$	6.99711	−	41.0432i	0.262044	−	1.53708i
$714$	5.90984	+	0.416437i	0.221170	+	0.0155847i
$715$	−4.06059	−	4.68618i	−0.151858	−	0.175253i
$716$	0.640775	−	13.4515i	0.0239469	−	0.502707i
$717$	−0.445526	−	0.350366i	−0.0166385	−	0.0130847i
$718$	−14.5667	−	20.4560i	−0.543623	−	0.763412i
$719$	−6.71672	+	5.28209i	−0.250491	+	0.196989i	−0.735507	−	0.677517i	$-0.763056\pi$
$719$	−6.71672	+	5.28209i	−0.250491	+	0.196989i	0.485016	+	0.874505i	$0.338814\pi$
$720$	−3.91449	−	1.14940i	−0.145884	−	0.0428355i
$721$	1.09662	−	48.1975i	0.0408404	−	1.79497i
$722$	−2.76535	−	6.05528i	−0.102916	−	0.225354i
$723$	19.1109	+	18.2222i	0.710743	+	0.677692i
$724$	3.34138	+	9.65427i	0.124181	+	0.358798i
$725$	26.9126	+	77.7590i	0.999511	+	2.88790i
$726$	−7.30149	−	6.96196i	−0.270984	−	0.258383i
$727$	−10.0108	−	21.9205i	−0.371279	−	0.812988i	−0.999392	−	0.0348657i	$-0.988900\pi$
$727$	−10.0108	−	21.9205i	−0.371279	−	0.812988i	0.628113	−	0.778122i	$-0.283828\pi$
$728$	3.59905	+	2.18855i	0.133390	+	0.0811130i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	1.26522	−	0.994979i	0.0468278	−	0.0368258i
$731$	−3.50929	−	4.92811i	−0.129796	−	0.182273i
$732$	10.8171	+	8.50664i	0.399811	+	0.314414i
$733$	2.18742	−	45.9195i	0.0807941	−	1.69608i	−0.487398	−	0.873180i	$-0.662054\pi$
$733$	2.18742	−	45.9195i	0.0807941	−	1.69608i	0.568192	−	0.822896i	$-0.307643\pi$
$734$	−13.5481	−	15.6353i	−0.500069	−	0.577110i
$735$	−17.6063	+	22.4854i	−0.649418	+	0.829385i
$736$	−4.56480	−	1.47058i	−0.168261	−	0.0542063i
$737$	2.25626	+	3.90796i	0.0831104	+	0.143951i
$738$	−6.99630	+	1.34843i	−0.257537	+	0.0496363i
$739$	45.0931	−	23.2471i	1.65878	−	0.855159i	0.664623	−	0.747179i	$-0.268592\pi$
$739$	45.0931	−	23.2471i	1.65878	−	0.855159i	0.994153	−	0.107980i	$-0.0344382\pi$
$740$	14.2166	−	5.69147i	0.522613	−	0.209223i
$741$	−2.32358	+	5.08794i	−0.0853590	+	0.186910i
$742$	−16.0210	+	10.8679i	−0.588150	+	0.398974i
$743$	−0.133651	−	0.0392434i	−0.00490317	−	0.00143970i	0.279280	−	0.960210i	$-0.409904\pi$
$743$	−0.133651	−	0.0392434i	−0.00490317	−	0.00143970i	−0.284183	+	0.958770i	$0.591722\pi$
$744$	7.71648	+	3.97812i	0.282900	+	0.145845i
$745$	−8.39500	−	0.801625i	−0.307569	−	0.0293693i
$746$	−3.87866	+	15.9881i	−0.142008	+	0.585365i
$747$	−10.2191	−	1.96957i	−0.373897	−	0.0720627i
$748$	1.39989	−	1.61556i	0.0511852	−	0.0590708i
$749$	5.30347	−	16.6510i	0.193785	−	0.608415i
$750$	11.2608	+	24.6576i	0.411185	+	0.900369i
$751$	23.8751	+	12.3085i	0.871216	+	0.449143i	0.835032	−	0.550202i	$-0.185449\pi$
$751$	23.8751	+	12.3085i	0.871216	+	0.449143i	0.0361847	+	0.999345i	$0.488480\pi$
$752$	−7.48960	+	7.14132i	−0.273118	+	0.260417i
$753$	23.6874	+	9.48300i	0.863216	+	0.345580i
$754$	11.1994	−	1.06942i	0.407859	−	0.0389458i
$755$	11.0302	−	76.7168i	0.401431	−	2.79201i
$756$	−2.11970	−	1.58331i	−0.0770927	−	0.0575845i
$757$	−1.10850	−	1.27927i	−0.0402890	−	0.0464959i	0.735247	−	0.677799i	$-0.237066\pi$
$757$	−1.10850	−	1.27927i	−0.0402890	−	0.0464959i	−0.775536	+	0.631303i	$0.782521\pi$
$758$	−8.46455	−	14.6610i	−0.307446	−	0.532513i
$759$	2.55762	+	3.79734i	0.0928359	+	0.137835i
$760$	7.16665	−	12.4130i	0.259962	−	0.450267i
$761$	−17.1169	+	49.4560i	−0.620487	+	1.79278i	−0.0110561	+	0.999939i	$0.503519\pi$
$761$	−17.1169	+	49.4560i	−0.620487	+	1.79278i	−0.609431	+	0.792839i	$0.708602\pi$
$762$	−8.83531	−	5.67811i	−0.320069	−	0.205696i
$763$	2.13546	−	9.86645i	0.0773087	−	0.357190i
$764$	−0.916128	+	2.00604i	−0.0331443	+	0.0725760i
$765$	7.18104	−	5.64723i	0.259631	−	0.204176i
$766$	−13.1451	+	12.5338i	−0.474951	+	0.452865i
$767$	0.115474	+	2.42409i	0.00416951	+	0.0875287i
$768$	0.580057	−	0.814576i	0.0209310	−	0.0293935i
$769$	−21.1009	+	6.19577i	−0.760917	+	0.223425i	−0.639096	−	0.769127i	$-0.720691\pi$
$769$	−21.1009	+	6.19577i	−0.760917	+	0.223425i	−0.121821	+	0.992552i	$0.538873\pi$
$770$	2.67746	+	9.95056i	0.0964889	+	0.358593i
$771$	7.33334	−	8.46312i	0.264104	−	0.304792i
$772$	−6.36162	−	6.06579i	−0.228960	−	0.218313i
$773$	36.5291	+	3.48811i	1.31386	+	0.125458i	0.728350	−	0.685206i	$-0.240288\pi$
$773$	36.5291	+	3.48811i	1.31386	+	0.125458i	0.585511	+	0.810664i	$0.300894\pi$
$774$	0.128555	+	2.69870i	0.00462082	+	0.0970029i
$775$	−23.8331	−	98.2415i	−0.856112	−	3.52894i
$776$	−0.377811	−	2.62773i	−0.0135626	−	0.0943302i
$777$	9.92790	−	0.246770i	0.356161	−	0.00885281i
$778$	1.72999	−	12.0323i	0.0620230	−	0.431379i
$779$	1.19109	−	25.0040i	0.0426751	−	0.895861i
$780$	6.37788	−	1.22924i	0.228365	−	0.0440137i
$781$	0.964282	−	1.67019i	0.0345047	−	0.0597640i
$782$	8.61157	−	6.41624i	0.307949	−	0.229444i
$783$	−7.06649			−0.252536
$784$	−3.79686	−	5.88081i	−0.135602	−	0.210029i
$785$	54.9755	+	35.3306i	1.96216	+	1.26100i
$786$	9.74814	−	3.90257i	0.347705	−	0.139200i
$787$	4.78604	+	6.72105i	0.170604	+	0.239579i	0.891022	−	0.453961i	$-0.149989\pi$
$787$	4.78604	+	6.72105i	0.170604	+	0.239579i	−0.720418	+	0.693540i	$0.756050\pi$
$788$	11.8862	+	4.75851i	0.423427	+	0.169515i
$789$	1.86471	+	7.68644i	0.0663855	+	0.273645i
$790$	−6.91450	+	4.44368i	−0.246007	+	0.158099i
$791$	5.97966	−	7.25772i	0.212612	−	0.258055i
$792$	−0.915980	+	0.268956i	−0.0325479	+	0.00955693i
$793$	−21.5130	−	4.14629i	−0.763949	−	0.147239i
$794$	−4.83393	−	13.9667i	−0.171550	−	0.495661i
$795$	−7.03791	+	29.0106i	−0.249609	+	1.02890i
$796$	15.8920	−	22.3171i	0.563275	−	0.791009i
$797$	−13.6875	+	8.79641i	−0.484835	+	0.311585i	−0.760125	−	0.649776i	$-0.774863\pi$
$797$	−13.6875	+	8.79641i	−0.484835	+	0.311585i	0.275290	+	0.961361i	$0.411226\pi$
$798$	7.16154	−	5.92574i	0.253516	−	0.209769i
$799$	−3.29786	−	22.9371i	−0.116670	−	0.811457i
$800$	−11.5916	+	1.10687i	−0.409825	+	0.0391336i
$801$	−6.11649	−	4.81006i	−0.216116	−	0.169955i
$802$	12.3533	−	6.36859i	0.436212	−	0.224883i
$803$	0.123186	−	0.355923i	0.00434715	−	0.0125603i
$804$	−4.72688			−0.166704
$805$	2.40069	+	51.7105i	0.0846131	+	1.82256i
$806$	−13.8217			−0.486848
$807$	0.935579	−	2.70318i	0.0329340	−	0.0951564i
$808$	4.64332	−	2.39380i	0.163351	−	0.0842135i
$809$	28.7286	+	22.5924i	1.01004	+	0.794307i	0.978720	−	0.205202i	$-0.0657853\pi$
$809$	28.7286	+	22.5924i	1.01004	+	0.794307i	0.0313237	+	0.999509i	$0.490028\pi$
$810$	−4.06127	+	0.387805i	−0.142699	+	0.0136261i
$811$	0.336197	+	2.33830i	0.0118055	+	0.0821088i	0.994872	−	0.101138i	$-0.0322484\pi$
$811$	0.336197	+	2.33830i	0.0118055	+	0.0821088i	−0.983067	+	0.183247i	$0.941339\pi$
$812$	−17.5242	−	6.51522i	−0.614980	−	0.228640i
$813$	20.5543	−	13.2095i	0.720872	−	0.463276i
$814$	2.07853	−	2.91889i	0.0728526	−	0.102307i
$815$	2.75717	−	11.3652i	0.0965795	−	0.398106i
$816$	0.732386	+	2.11609i	0.0256386	+	0.0740780i
$817$	−9.32052	−	1.79638i	−0.326084	−	0.0628475i
$818$	12.3432	−	3.62430i	0.431571	−	0.126721i
$819$	4.15464	+	0.694148i	0.145175	+	0.0242555i
$820$	−24.4539	+	15.7156i	−0.853968	+	0.548812i
$821$	−0.953961	−	3.93228i	−0.0332935	−	0.137238i	0.952739	−	0.303789i	$-0.0982519\pi$
$821$	−0.953961	−	3.93228i	−0.0332935	−	0.137238i	−0.986033	+	0.166552i	$0.946737\pi$
$822$	−19.6480	−	7.86587i	−0.685303	−	0.274354i
$823$	−11.3065	−	15.8778i	−0.394120	−	0.553464i	0.569069	−	0.822290i	$-0.307304\pi$
$823$	−11.3065	−	15.8778i	−0.394120	−	0.553464i	−0.963189	+	0.268826i	$0.913364\pi$
$824$	16.9164	−	6.77230i	0.589310	−	0.235924i
$825$	9.35160	+	6.00991i	0.325581	+	0.209238i
$826$	1.58369	−	3.70903i	0.0551035	−	0.129054i
$827$	−53.8134			−1.87128			−0.935638	−	0.352960i	$-0.885175\pi$
$827$	−53.8134			−1.87128			−0.935638	+	0.352960i	$0.885175\pi$
$828$	−4.78437	+	0.331325i	−0.166268	+	0.0115143i
$829$	−3.00485	+	5.20456i	−0.104363	+	0.180762i	−0.913478	−	0.406889i	$-0.866614\pi$
$829$	−3.00485	+	5.20456i	−0.104363	+	0.180762i	0.809115	+	0.587651i	$0.199947\pi$
$830$	−41.6913	+	8.03533i	−1.44712	+	0.278910i
$831$	−0.278676	+	5.85012i	−0.00966715	+	0.202938i
$832$	−0.226576	+	1.57587i	−0.00785510	+	0.0546334i
$833$	15.6585	+	0.712917i	0.542535	+	0.0247011i
$834$	−2.79006	−	19.4053i	−0.0966120	−	0.671951i
$835$	2.15561	+	8.88553i	0.0745979	+	0.307497i
$836$	−0.159588	−	3.35016i	−0.00551945	−	0.115868i
$837$	8.64226	+	0.825235i	0.298720	+	0.0285243i
$838$	−20.5886	−	19.6312i	−0.711222	−	0.678148i
$839$	−8.14898	+	9.40442i	−0.281334	+	0.324677i	−0.878775	−	0.477236i	$-0.841639\pi$
$839$	−8.14898	+	9.40442i	−0.281334	+	0.324677i	0.597441	+	0.801913i	$0.296184\pi$
$840$	−10.4291	−	2.78273i	−0.359839	−	0.0960134i
$841$	−20.0872	+	5.89813i	−0.692662	+	0.203384i
$842$	−12.8924	+	18.1048i	−0.444300	+	0.623933i
$843$	0.343067	+	7.20187i	0.0118159	+	0.248046i
$844$	7.45456	−	7.10791i	0.256597	−	0.244664i
$845$	33.5612	−	26.3928i	1.15454	−	0.907939i
$846$	−4.29895	+	9.41338i	−0.147801	+	0.323639i
$847$	−19.7697	−	17.9339i	−0.679294	−	0.616216i
$848$	−6.15558	−	3.95595i	−0.211383	−	0.135848i
$849$	0.229069	−	0.661852i	0.00786164	−	0.0227147i
$850$	13.0373	−	22.5812i	0.447175	−	0.774530i
$851$	13.3475	−	12.0787i	0.457546	−	0.414053i
$852$	1.01009	+	1.74953i	0.0346051	+	0.0599378i
$853$	19.9619	+	23.0373i	0.683483	+	0.788781i	0.986422	−	0.164229i	$-0.0525135\pi$
$853$	19.9619	+	23.0373i	0.683483	+	0.788781i	−0.302940	+	0.953010i	$0.597968\pi$
$854$	29.1697	+	21.7884i	0.998167	+	0.745582i
$855$	2.03984	−	14.1874i	0.0697611	−	0.485199i
$856$	6.57511	−	0.627847i	0.224733	−	0.0214594i
$857$	−19.9117	−	7.97144i	−0.680170	−	0.272299i	0.00574176	−	0.999984i	$-0.498172\pi$
$857$	−19.9117	−	7.97144i	−0.680170	−	0.272299i	−0.685912	+	0.727684i	$0.740597\pi$
$858$	1.09998	−	1.04883i	0.0375528	−	0.0358066i
$859$	15.8354	+	8.16373i	0.540298	+	0.278543i	0.706698	−	0.707515i	$-0.250184\pi$
$859$	15.8354	+	8.16373i	0.540298	+	0.278543i	−0.166400	+	0.986058i	$0.553214\pi$
$860$	4.57892	+	10.0264i	0.156140	+	0.341898i
$861$	−18.4161	+	4.02646i	−0.627619	+	0.137221i
$862$	19.8355	−	22.8914i	0.675600	−	0.779684i
$863$	47.9970	+	9.25066i	1.63384	+	0.314896i	0.921924	−	0.387372i	$-0.126617\pi$
$863$	47.9970	+	9.25066i	1.63384	+	0.314896i	0.711913	+	0.702268i	$0.247829\pi$
$864$	0.235759	−	0.971812i	0.00802068	−	0.0330617i
$865$	−0.545598	−	0.0520983i	−0.0185509	−	0.00177140i
$866$	−20.8332	−	10.7402i	−0.707940	−	0.364969i
$867$	11.5003	+	3.37678i	0.390570	+	0.114682i
$868$	20.6711	+	10.0146i	0.701624	+	0.339917i
$869$	−0.798963	+	1.74948i	−0.0271030	+	0.0593472i
$870$	−26.7644	+	10.7148i	−0.907397	+	0.363267i
$871$	6.68897	−	3.44841i	0.226647	−	0.116845i
$872$	3.74656	−	0.722091i	0.126875	−	0.0244531i
$873$	−1.32738	−	2.29909i	−0.0449249	−	0.0778123i
$874$	2.83161	−	16.6095i	0.0957807	−	0.561824i
$875$	31.4050	+	64.4774i	1.06168	+	2.17974i
$876$	0.258362	+	0.298166i	0.00872926	+	0.0100741i
$877$	−0.130503	+	2.73960i	−0.00440678	+	0.0925096i	−0.999999	−	0.00127606i	$-0.999594\pi$
$877$	−0.130503	+	2.73960i	−0.00440678	+	0.0925096i	0.995592	+	0.0937857i	$0.0298968\pi$
$878$	8.44362	+	6.64014i	0.284959	+	0.224094i
$879$	−1.83975	−	2.58356i	−0.0620531	−	0.0871414i
$880$	−3.06147	+	2.40756i	−0.103202	+	0.0811589i
$881$	33.3726	+	9.79909i	1.12435	+	0.330140i	0.790486	−	0.612480i	$-0.209828\pi$
$881$	33.3726	+	9.79909i	1.12435	+	0.330140i	0.333867	+	0.942620i	$0.391646\pi$
$882$	−5.71055	−	4.04840i	−0.192284	−	0.136317i
$883$	−19.4912	−	42.6797i	−0.655930	−	1.43629i	−0.886266	−	0.463176i	$-0.846710\pi$
$883$	−19.4912	−	42.6797i	−0.655930	−	1.43629i	0.230336	−	0.973111i	$-0.426018\pi$
$884$	−2.58014	−	2.46016i	−0.0867797	−	0.0827442i
$885$	−2.03399	−	5.87683i	−0.0683718	−	0.197547i
$886$	1.54287	+	4.45782i	0.0518336	+	0.149763i
$887$	0.0520912	+	0.0496688i	0.00174905	+	0.00166772i	0.690953	−	0.722900i	$-0.257191\pi$
$887$	0.0520912	+	0.0496688i	0.00174905	+	0.00166772i	−0.689204	+	0.724567i	$0.742040\pi$
$888$	1.55928	+	3.41435i	0.0523261	+	0.114578i
$889$	−23.7421	−	14.4374i	−0.796284	−	0.484213i
$890$	−30.4597	−	8.94377i	−1.02101	−	0.299796i
$891$	−0.750406	+	0.590125i	−0.0251395	+	0.0197699i
$892$	−13.7453	−	19.3025i	−0.460226	−	0.646297i
$893$	−28.5789	−	22.4747i	−0.956355	−	0.752086i
$894$	0.0983559	−	2.06474i	0.00328951	−	0.0690554i
$895$	−35.9788	−	41.5217i	−1.20264	−	1.38792i
$896$	1.48066	−	2.19263i	0.0494654	−	0.0732508i
$897$	6.52861	−	3.95920i	0.217984	−	0.132194i
$898$	−16.6198	−	28.7864i	−0.554611	−	0.960615i
$899$	60.2395	−	11.6102i	2.00910	−	0.387222i
$900$	−10.3499	+	5.33575i	−0.344997	+	0.177858i
$901$	15.2112	−	6.08965i	0.506759	−	0.202876i
$902$	−2.82563	+	6.18726i	−0.0940831	+	0.206013i
$903$	0.517440	+	7.12944i	0.0172193	+	0.237253i
$904$	3.41032	+	1.00136i	0.113425	+	0.0333047i
$905$	37.0461	+	19.0986i	1.23145	+	0.634858i
$906$	18.9117	+	1.80584i	0.628298	+	0.0599951i
$907$	−14.0246	+	57.8101i	−0.465679	+	1.91955i	−0.0803718	+	0.996765i	$0.525611\pi$
$907$	−14.0246	+	57.8101i	−0.465679	+	1.91955i	−0.385307	+	0.922789i	$0.625904\pi$
$908$	−17.2483	−	3.32433i	−0.572404	−	0.110322i
$909$	3.42102	−	3.94807i	0.113468	−	0.130949i
$910$	16.7883	−	3.67055i	0.556525	−	0.121678i
$911$	9.18375	+	20.1096i	0.304271	+	0.666261i	0.998572	−	0.0534242i	$-0.0170135\pi$
$911$	9.18375	+	20.1096i	0.304271	+	0.666261i	−0.694301	+	0.719685i	$0.744286\pi$
$912$	3.12273	+	1.60988i	0.103404	+	0.0533084i
$913$	−7.19043	+	6.85606i	−0.237969	+	0.226903i
$914$	−5.73831	−	2.29727i	−0.189806	−	0.0759870i
$915$	55.8882	−	5.33668i	1.84761	−	0.176425i
$916$	3.91594	−	27.2360i	0.129386	−	0.899902i
$917$	25.5266	−	10.9629i	0.842963	−	0.362027i
$918$	1.46639	+	1.69231i	0.0483982	+	0.0558545i
$919$	−11.2047	−	19.4071i	−0.369609	−	0.640181i	0.619896	−	0.784684i	$-0.287175\pi$
$919$	−11.2047	−	19.4071i	−0.369609	−	0.640181i	−0.989504	+	0.144503i	$0.953842\pi$
$920$	−17.6185	+	8.50939i	−0.580863	+	0.280546i
$921$	−8.94891	+	15.5000i	−0.294877	+	0.510741i
$922$	11.1464	−	32.2054i	0.367088	−	1.06063i
$923$	−2.70570	−	1.73885i	−0.0890593	−	0.0572349i
$924$	−2.40502	+	0.771590i	−0.0791195	+	0.0253835i
$925$	18.1568	−	39.7579i	0.596992	−	1.30723i
$926$	−2.76612	+	2.17530i	−0.0909005	+	0.0714849i
$927$	13.1876	−	12.5744i	0.433138	−	0.412997i
$928$	−0.336237	−	7.05848i	−0.0110375	−	0.231706i
$929$	12.5585	−	17.6360i	0.412031	−	0.578617i	−0.555453	−	0.831548i	$-0.687455\pi$
$929$	12.5585	−	17.6360i	0.412031	−	0.578617i	0.967484	+	0.252931i	$0.0813946\pi$
$930$	33.9839	−	9.97857i	1.11438	−	0.327210i
$931$	18.5522	−	16.1440i	0.608025	−	0.529099i
$932$	−14.1416	+	16.3202i	−0.463222	+	0.534587i
$933$	−24.9423	−	23.7824i	−0.816573	−	0.778600i
$934$	36.1195	+	3.44899i	1.18187	+	0.112855i
$935$	−0.414974	−	8.71138i	−0.0135711	−	0.284893i
$936$	0.375346	+	1.54720i	0.0122686	+	0.0505717i
$937$	−7.20582	−	50.1176i	−0.235404	−	1.63727i	−0.674104	−	0.738636i	$-0.735470\pi$
$937$	−7.20582	−	50.1176i	−0.235404	−	1.63727i	0.438701	−	0.898633i	$-0.355439\pi$
$938$	−12.5023	+	0.310759i	−0.408215	+	0.0101467i
$939$	3.54471	−	24.6540i	0.115677	−	0.804553i
$940$	−2.00889	+	42.1717i	−0.0655226	+	1.37549i
$941$	38.4056	−	7.40208i	1.25199	−	0.241301i	0.480187	−	0.877166i	$-0.340569\pi$
$941$	38.4056	−	7.40208i	1.25199	−	0.241301i	0.771800	+	0.635865i	$0.219357\pi$
$942$	−8.00902	+	13.8720i	−0.260948	+	0.451975i
$943$	−20.5394	+	27.3086i	−0.668855	+	0.889292i
$944$	1.52432			0.0496125
$945$	−10.7163	+	1.29272i	−0.348602	+	0.0420521i
$946$	2.16979	+	1.39444i	0.0705460	+	0.0453372i
$947$	13.7925	−	5.52170i	0.448198	−	0.179431i	−0.136573	−	0.990630i	$-0.543609\pi$
$947$	13.7925	−	5.52170i	0.448198	−	0.179431i	0.584771	+	0.811199i	$0.301185\pi$
$948$	−1.16861	−	1.64109i	−0.0379548	−	0.0533001i
$949$	−0.583128	−	0.233449i	−0.0189291	−	0.00757808i
$950$	−9.64487	−	39.7567i	−0.312921	−	1.28988i
$951$	1.04507	−	0.671625i	0.0338887	−	0.0217789i
$952$	2.07623	+	5.54877i	0.0672910	+	0.179837i
$953$	−7.88684	+	2.31579i	−0.255480	+	0.0750156i	−0.406965	−	0.913444i	$-0.633413\pi$
$953$	−7.88684	+	2.31579i	−0.255480	+	0.0750156i	0.151485	+	0.988460i	$0.451595\pi$
$954$	−7.18492	−	1.38478i	−0.232620	−	0.0448339i
$955$	2.94269	+	8.50236i	0.0952234	+	0.275130i
$956$	0.133626	−	0.550812i	0.00432176	−	0.0178145i
$957$	−3.91308	+	5.49515i	−0.126492	+	0.177633i
$958$	−25.7000	+	16.5164i	−0.830331	+	0.533621i
$959$	−52.4848	−	19.5130i	−1.69482	−	0.630108i
$960$	−0.580609	−	4.03822i	−0.0187391	−	0.130333i
$961$	−44.1687	+	4.21760i	−1.42480	+	0.136052i
$962$	−4.69740	−	3.69408i	−0.151450	−	0.119102i
$963$	5.87077	−	3.02659i	0.189183	−	0.0975306i
$964$	−8.63656	+	24.9537i	−0.278165	+	0.803705i
$965$	−35.8610			−1.15440
$966$	−12.6326	+	1.19087i	−0.406446	+	0.0383156i
$967$	54.8358			1.76340			0.881700	−	0.471811i	$-0.156400\pi$
$967$	54.8358			1.76340			0.881700	+	0.471811i	$0.156400\pi$
$968$	3.29967	−	9.53378i	0.106055	−	0.306427i
$969$	−6.99256	+	3.60492i	−0.224633	+	0.115807i
$970$	−8.51353	−	6.69512i	−0.273353	−	0.214967i
$971$	−28.4855	+	2.72004i	−0.914143	+	0.0872901i	−0.541515	−	0.840691i	$-0.682149\pi$
$971$	−28.4855	+	2.72004i	−0.914143	+	0.0872901i	−0.372628	+	0.927981i	$0.621543\pi$
$972$	−0.142315	−	0.989821i	−0.00456475	−	0.0317485i
$973$	−8.65530	−	51.1424i	−0.277476	−	1.63955i
$974$	−0.563793	+	0.362328i	−0.0180651	+	0.0116097i
$975$	10.7535	−	15.1011i	0.344387	−	0.483623i
$976$	−3.24434	+	13.3733i	−0.103849	+	0.428070i
$977$	−7.75880	−	22.4176i	−0.248226	−	0.717202i	−0.998431	−	0.0559966i	$-0.982166\pi$
$977$	−7.75880	−	22.4176i	−0.248226	−	0.717202i	0.750205	−	0.661205i	$-0.229955\pi$
$978$	2.81477	+	0.542502i	0.0900063	+	0.0173473i
$979$	−7.12748	+	2.09282i	−0.227795	+	0.0668868i
$980$	−27.7673	−	6.67450i	−0.886994	−	0.213209i
$981$	3.20981	−	2.06282i	0.102482	−	0.0658609i
$982$	−3.41695	−	14.0848i	−0.109039	−	0.449466i
$983$	−14.1789	−	5.67636i	−0.452235	−	0.181048i	0.134352	−	0.990934i	$-0.457105\pi$
$983$	−14.1789	−	5.67636i	−0.452235	−	0.181048i	−0.586587	+	0.809886i	$0.699529\pi$
$984$	−4.13294	−	5.80390i	−0.131753	−	0.185022i
$985$	48.4926	−	19.4135i	1.54510	−	0.618566i
$986$	13.3117	+	8.55489i	0.423930	+	0.272443i
$987$	−10.7516	+	25.1804i	−0.342226	+	0.801501i
$988$	−5.59340			−0.177950
$989$	9.14140	+	9.18279i	0.290680	+	0.291996i
$990$	−1.94737	+	3.37294i	−0.0618913	+	0.107199i
$991$	−35.0475	+	6.75486i	−1.11332	+	0.214575i	−0.712563	−	0.701608i	$-0.752466\pi$
$991$	−35.0475	+	6.75486i	−1.11332	+	0.214575i	−0.400759	+	0.916184i	$0.631254\pi$
$992$	−0.413086	+	8.67173i	−0.0131155	+	0.275328i
$993$	0.774351	−	5.38573i	0.0245733	−	0.170911i
$994$	2.78664	+	4.56098i	0.0883869	+	0.144665i
$995$	−15.9071	−	110.636i	−0.504288	−	3.50740i
$996$	−2.45358	−	10.1138i	−0.0777446	−	0.320468i
$997$	−2.86350	−	60.1123i	−0.0906881	−	1.90378i	−0.348072	−	0.937468i	$-0.613164\pi$
$997$	−2.86350	−	60.1123i	−0.0906881	−	1.90378i	0.257384	−	0.966309i	$-0.417139\pi$
$998$	−17.9311	−	1.71221i	−0.567599	−	0.0541992i
$999$	2.71657	+	2.59025i	0.0859486	+	0.0819518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.d.151.1	✓	160
7.2	even	3	inner	966.2.y.d.289.8	yes	160
23.16	even	11	inner	966.2.y.d.361.8	yes	160
161.16	even	33	inner	966.2.y.d.499.1	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.d.151.1	✓	160	1.1	even	1	trivial
966.2.y.d.289.8	yes	160	7.2	even	3	inner
966.2.y.d.361.8	yes	160	23.16	even	11	inner
966.2.y.d.499.1	yes	160	161.16	even	33	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-4.06127 + 0.387805i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-0.441487 - 2.60866i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})\)	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-4.06127 + 0.387805i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-0.441487 - 2.60866i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(0.961837 - 3.96475i) q^{10} +(-0.312235 - 0.902145i) q^{11} +(0.981929 + 0.189251i) q^{12} +(-1.52758 + 0.448539i) q^{13} +(2.60958 + 0.436002i) q^{14} +(3.43210 - 2.20568i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-2.07884 - 0.832244i) q^{17} +(0.580057 + 0.814576i) q^{18} +(-3.26162 + 1.30576i) q^{19} +(3.43210 + 2.20568i) q^{20} +(1.58777 + 2.11637i) q^{21} +0.954650 q^{22} +(4.68392 + 1.03001i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(11.4339 - 2.20371i) q^{25} +(0.0757539 - 1.59027i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(-1.26553 + 2.32345i) q^{28} +(1.00567 + 6.99456i) q^{29} +(0.961837 + 3.96475i) q^{30} +(-0.413086 - 8.67173i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(0.690913 + 0.658784i) q^{33} +(1.46639 - 1.69231i) q^{34} +(2.80465 + 10.4233i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(2.17727 - 3.05755i) q^{37} +(-0.167169 - 3.50930i) q^{38} +(1.15224 - 1.09866i) q^{39} +(-3.20690 + 2.52193i) q^{40} +(-2.95986 + 6.48118i) q^{41} +(-2.51927 + 0.808244i) q^{42} +(2.27287 + 1.46068i) q^{43} +(-0.312235 + 0.902145i) q^{44} +(-2.03987 + 3.53317i) q^{45} +(-2.50532 + 4.08942i) q^{46} +(5.17428 + 8.96212i) q^{47} +(-0.654861 - 0.755750i) q^{48} +(-6.61018 + 2.30338i) q^{49} +(-1.65716 + 11.5258i) q^{50} +(2.22911 - 0.212854i) q^{51} +(1.47803 + 0.591714i) q^{52} +(-5.29567 + 5.04941i) q^{53} +(-0.888835 - 0.458227i) q^{54} +(1.61793 + 3.54277i) q^{55} +(-1.78175 - 1.95586i) q^{56} +(2.30071 - 2.65516i) q^{57} +(-6.93878 - 1.33734i) q^{58} +(0.359373 - 1.48136i) q^{59} +(-4.06127 - 0.387805i) q^{60} +(12.2315 + 6.30577i) q^{61} +(8.32990 + 2.44588i) q^{62} +(-2.38104 - 1.15354i) q^{63} +(0.415415 - 0.909632i) q^{64} +(6.02999 - 2.41404i) q^{65} +(-0.848527 + 0.437446i) q^{66} +(-4.64146 + 0.894569i) q^{67} +(1.11962 + 1.93924i) q^{68} +(-4.63521 + 1.23079i) q^{69} +(-10.7673 - 0.758718i) q^{70} +(1.32294 + 1.52675i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(0.310122 + 0.243882i) q^{73} +(2.17727 + 3.05755i) q^{74} +(-9.15307 + 7.19805i) q^{75} +(3.37097 + 0.989806i) q^{76} +(-2.21554 + 1.21280i) q^{77} +(0.661371 + 1.44820i) q^{78} +(-1.45807 - 1.39027i) q^{79} +(-1.33435 - 3.85536i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-5.15665 - 4.91685i) q^{82} +(-4.32329 - 9.46668i) q^{83} +(0.0601825 - 2.64507i) q^{84} +(8.76551 + 2.57378i) q^{85} +(-2.12373 + 1.67012i) q^{86} +(-4.09896 - 5.75619i) q^{87} +(-0.750406 - 0.590125i) q^{88} +(0.370248 - 7.77245i) q^{89} +(-2.67167 - 3.08327i) q^{90} +(1.84449 + 3.78692i) q^{91} +(-3.04510 - 3.70505i) q^{92} +(4.34078 + 7.51846i) q^{93} +(-10.1615 + 1.95848i) q^{94} +(12.7400 - 6.56790i) q^{95} +(0.928368 - 0.371662i) q^{96} +(1.10283 - 2.41485i) q^{97} +(-0.0147157 - 6.99998i) q^{98} +(-0.915980 - 0.268956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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