LMFDB - Embedded newform 770.2.bd.a.263.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(263,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 8, 6]))

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

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

chi := DirichletCharacter("770.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			263.2
Character	$\chi$	$=$	770.263
Dual form			770.2.bd.a.527.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-2.93076 + 0.785295i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.860133 - 2.06402i) q^{5} -3.03415i q^{6} +(-0.604940 + 2.57566i) q^{7} +(0.707107 - 0.707107i) q^{8} +(5.37460 - 3.10303i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-2.93076 + 0.785295i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.860133 - 2.06402i) q^{5} -3.03415i q^{6} +(-0.604940 + 2.57566i) q^{7} +(0.707107 - 0.707107i) q^{8} +(5.37460 - 3.10303i) q^{9} +(1.77107 + 1.36503i) q^{10} +(0.981809 + 3.16797i) q^{11} +(2.93076 + 0.785295i) q^{12} +(-1.57020 + 1.57020i) q^{13} +(-2.33133 - 1.25096i) q^{14} +(-0.899981 + 6.72460i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-5.75068 + 1.54089i) q^{17} +(1.60624 + 5.99458i) q^{18} +(0.0868117 + 0.150362i) q^{19} +(-1.77691 + 1.35743i) q^{20} +(-0.249721 - 8.02371i) q^{21} +(-3.31414 + 0.128423i) q^{22} +(0.910995 - 3.39988i) q^{23} +(-1.51707 + 2.62765i) q^{24} +(-3.52034 - 3.55066i) q^{25} +(-1.11030 - 1.92310i) q^{26} +(-6.87847 + 6.87847i) q^{27} +(1.81173 - 1.92812i) q^{28} +6.62678 q^{29} +(-6.26254 - 2.60977i) q^{30} +(-1.64358 + 2.84676i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-5.36524 - 8.51356i) q^{33} -5.95354i q^{34} +(4.79589 + 3.46402i) q^{35} -6.20605 q^{36} +(-11.1973 - 3.00030i) q^{37} +(-0.167707 + 0.0449370i) q^{38} +(3.36882 - 5.83496i) q^{39} +(-0.851275 - 2.06769i) q^{40} -4.78788i q^{41} +(7.81495 + 1.83548i) q^{42} +(3.69185 - 3.69185i) q^{43} +(0.733715 - 3.23445i) q^{44} +(-1.78183 - 13.7623i) q^{45} +(3.04825 + 1.75991i) q^{46} +(1.43298 + 0.383965i) q^{47} +(-2.14547 - 2.14547i) q^{48} +(-6.26809 - 3.11625i) q^{49} +(4.34081 - 2.48141i) q^{50} +(15.6438 - 9.03197i) q^{51} +(2.14494 - 0.574734i) q^{52} +(6.50511 - 1.74304i) q^{53} +(-4.86381 - 8.42437i) q^{54} +(7.38324 + 0.698406i) q^{55} +(1.39351 + 2.24903i) q^{56} +(-0.372503 - 0.372503i) q^{57} +(-1.71514 + 6.40098i) q^{58} +(-12.2623 - 7.07963i) q^{59} +(4.14171 - 5.37369i) q^{60} +(-2.80684 + 1.62053i) q^{61} +(-2.32437 - 2.32437i) q^{62} +(4.74104 + 15.7203i) q^{63} -1.00000i q^{64} +(1.89034 + 4.59151i) q^{65} +(9.61210 - 2.97895i) q^{66} +(0.436089 + 1.62751i) q^{67} +(5.75068 + 1.54089i) q^{68} +10.6796i q^{69} +(-4.58726 + 3.73592i) q^{70} -10.7182 q^{71} +(1.60624 - 5.99458i) q^{72} +(-2.05631 - 7.67425i) q^{73} +(5.79614 - 10.0392i) q^{74} +(13.1056 + 7.64163i) q^{75} -0.173623i q^{76} +(-8.75357 + 0.612377i) q^{77} +(4.76423 + 4.76423i) q^{78} +(-4.40422 - 7.62834i) q^{79} +(2.21756 - 0.287112i) q^{80} +(5.44846 - 9.43700i) q^{81} +(4.62473 + 1.23919i) q^{82} +(-2.26431 + 2.26431i) q^{83} +(-3.79559 + 7.07360i) q^{84} +(-1.76593 + 13.1949i) q^{85} +(2.61053 + 4.52158i) q^{86} +(-19.4215 + 5.20398i) q^{87} +(2.93434 + 1.54585i) q^{88} +(0.191972 - 0.110835i) q^{89} +(13.7545 + 1.84082i) q^{90} +(-3.09444 - 4.99420i) q^{91} +(-2.48888 + 2.48888i) q^{92} +(2.58139 - 9.63388i) q^{93} +(-0.741764 + 1.28477i) q^{94} +(0.385020 - 0.0498493i) q^{95} +(2.62765 - 1.51707i) q^{96} +(7.97257 - 7.97257i) q^{97} +(4.63236 - 5.24797i) q^{98} +(15.1071 + 13.9800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{5}+O(q^{10}) $ 192 * q + 8 * q^5	$ 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) $ 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−2.93076	+	0.785295i	−1.69208	+	0.453390i	−0.970924	−	0.239387i	$-0.923054\pi$
$3$	−2.93076	+	0.785295i	−1.69208	+	0.453390i	−0.721152	+	0.692777i	$0.756387\pi$
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.860133	−	2.06402i	0.384663	−	0.923057i
$5$	0.860133	−	2.06402i	0.384663	−	0.923057i
$6$		−	3.03415i		−	1.23869i
$7$	−0.604940	+	2.57566i	−0.228646	+	0.973510i
$7$	−0.604940	+	2.57566i	−0.228646	+	0.973510i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	5.37460	−	3.10303i	1.79153	−	1.03434i
$10$	1.77107	+	1.36503i	0.560061	+	0.431661i
$11$	0.981809	+	3.16797i	0.296027	+	0.955180i
$11$	0.981809	+	3.16797i	0.296027	+	0.955180i
$12$	2.93076	+	0.785295i	0.846038	+	0.226695i
$13$	−1.57020	+	1.57020i	−0.435496	+	0.435496i	−0.890493	−	0.454997i	$-0.849640\pi$
$13$	−1.57020	+	1.57020i	−0.435496	+	0.435496i	0.454997	+	0.890493i	$0.349640\pi$
$14$	−2.33133	−	1.25096i	−0.623074	−	0.334333i
$15$	−0.899981	+	6.72460i	−0.232374	+	1.73629i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−5.75068	+	1.54089i	−1.39475	+	0.373721i	−0.876455	−	0.481484i	$-0.840098\pi$
$17$	−5.75068	+	1.54089i	−1.39475	+	0.373721i	−0.518290	+	0.855205i	$0.673431\pi$
$18$	1.60624	+	5.99458i	0.378595	+	1.41294i
$19$	0.0868117	+	0.150362i	0.0199160	+	0.0344955i	0.875812	−	0.482653i	$-0.160327\pi$
$19$	0.0868117	+	0.150362i	0.0199160	+	0.0344955i	−0.855896	+	0.517149i	$0.826993\pi$
$20$	−1.77691	+	1.35743i	−0.397328	+	0.303530i
$21$	−0.249721	−	8.02371i	−0.0544937	−	1.75092i
$22$	−3.31414	+	0.128423i	−0.706576	+	0.0273799i
$23$	0.910995	−	3.39988i	0.189956	−	0.708924i	−0.803560	−	0.595224i	$-0.797063\pi$
$23$	0.910995	−	3.39988i	0.189956	−	0.708924i	0.993515	−	0.113700i	$-0.0362701\pi$
$24$	−1.51707	+	2.62765i	−0.309671	+	0.536367i
$25$	−3.52034	−	3.55066i	−0.704068	−	0.710132i
$26$	−1.11030	−	1.92310i	−0.217748	−	0.377151i
$27$	−6.87847	+	6.87847i	−1.32376	+	1.32376i
$28$	1.81173	−	1.92812i	0.342384	−	0.364381i
$29$	6.62678			1.23056			0.615281	−	0.788308i	$-0.289043\pi$
$29$	6.62678			1.23056			0.615281	+	0.788308i	$0.289043\pi$
$30$	−6.26254	−	2.60977i	−1.14338	−	0.476477i
$31$	−1.64358	+	2.84676i	−0.295196	+	0.511294i	−0.975030	−	0.222071i	$-0.928718\pi$
$31$	−1.64358	+	2.84676i	−0.295196	+	0.511294i	0.679835	+	0.733365i	$0.262052\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−5.36524	−	8.51356i	−0.933969	−	1.48202i
$34$		−	5.95354i		−	1.02102i
$35$	4.79589	+	3.46402i	0.810653	+	0.585527i
$36$	−6.20605			−1.03434
$37$	−11.1973	−	3.00030i	−1.84082	−	0.493246i	−0.841897	−	0.539638i	$-0.818561\pi$
$37$	−11.1973	−	3.00030i	−1.84082	−	0.493246i	−0.998923	+	0.0463914i	$0.985228\pi$
$38$	−0.167707	+	0.0449370i	−0.0272057	+	0.00728975i
$39$	3.36882	−	5.83496i	0.539443	−	0.934342i
$40$	−0.851275	−	2.06769i	−0.134598	−	0.326930i
$41$		−	4.78788i		−	0.747741i	−0.927481	−	0.373870i	$-0.878031\pi$
$41$		−	4.78788i		−	0.747741i	0.927481	−	0.373870i	$-0.121969\pi$
$42$	7.81495	+	1.83548i	1.20587	+	0.283220i
$43$	3.69185	−	3.69185i	0.563002	−	0.563002i	−0.367157	−	0.930159i	$-0.619669\pi$
$43$	3.69185	−	3.69185i	0.563002	−	0.563002i	0.930159	+	0.367157i	$0.119669\pi$
$44$	0.733715	−	3.23445i	0.110612	−	0.487612i
$45$	−1.78183	−	13.7623i	−0.265620	−	2.05156i
$46$	3.04825	+	1.75991i	0.449440	+	0.259484i
$47$	1.43298	+	0.383965i	0.209021	+	0.0560071i	0.361810	−	0.932252i	$-0.382159\pi$
$47$	1.43298	+	0.383965i	0.209021	+	0.0560071i	−0.152789	+	0.988259i	$0.548825\pi$
$48$	−2.14547	−	2.14547i	−0.309671	−	0.309671i
$49$	−6.26809	−	3.11625i	−0.895442	−	0.445178i
$50$	4.34081	−	2.48141i	0.613883	−	0.350924i
$51$	15.6438	−	9.03197i	2.19057	−	1.26473i
$52$	2.14494	−	0.574734i	0.297449	−	0.0797013i
$53$	6.50511	−	1.74304i	0.893545	−	0.239425i	0.217303	−	0.976104i	$-0.430274\pi$
$53$	6.50511	−	1.74304i	0.893545	−	0.239425i	0.676242	+	0.736680i	$0.263607\pi$
$54$	−4.86381	−	8.42437i	−0.661881	−	1.14641i
$55$	7.38324	+	0.698406i	0.995556	+	0.0941730i
$56$	1.39351	+	2.24903i	0.186216	+	0.300539i
$57$	−0.372503	−	0.372503i	−0.0493392	−	0.0493392i
$58$	−1.71514	+	6.40098i	−0.225208	+	0.840489i
$59$	−12.2623	−	7.07963i	−1.59641	−	0.921689i	−0.992171	−	0.124889i	$-0.960143\pi$
$59$	−12.2623	−	7.07963i	−1.59641	−	0.921689i	−0.604242	−	0.796801i	$-0.706524\pi$
$60$	4.14171	−	5.37369i	0.534692	−	0.693740i
$61$	−2.80684	+	1.62053i	−0.359379	+	0.207487i	−0.668808	−	0.743435i	$-0.733195\pi$
$61$	−2.80684	+	1.62053i	−0.359379	+	0.207487i	0.309429	+	0.950922i	$0.399862\pi$
$62$	−2.32437	−	2.32437i	−0.295196	−	0.295196i
$63$	4.74104	+	15.7203i	0.597315	+	1.98057i
$64$		−	1.00000i		−	0.125000i
$65$	1.89034	+	4.59151i	0.234468	+	0.569507i
$66$	9.61210	−	2.97895i	1.18317	−	0.366684i
$67$	0.436089	+	1.62751i	0.0532767	+	0.198831i	0.987435	−	0.158029i	$-0.0505139\pi$
$67$	0.436089	+	1.62751i	0.0532767	+	0.198831i	−0.934158	+	0.356860i	$0.883847\pi$
$68$	5.75068	+	1.54089i	0.697373	+	0.186860i
$69$			10.6796i			1.28568i
$70$	−4.58726	+	3.73592i	−0.548282	+	0.446528i
$71$	−10.7182			−1.27202			−0.636008	−	0.771682i	$-0.719416\pi$
$71$	−10.7182			−1.27202			−0.636008	+	0.771682i	$0.719416\pi$
$72$	1.60624	−	5.99458i	0.189298	−	0.706469i
$73$	−2.05631	−	7.67425i	−0.240673	−	0.898203i	−0.975509	−	0.219958i	$-0.929408\pi$
$73$	−2.05631	−	7.67425i	−0.240673	−	0.898203i	0.734837	−	0.678244i	$-0.237259\pi$
$74$	5.79614	−	10.0392i	0.673787	−	1.16703i
$75$	13.1056	+	7.64163i	1.51330	+	0.882380i
$76$		−	0.173623i		−	0.0199160i
$77$	−8.75357	+	0.612377i	−0.997562	+	0.0697869i
$78$	4.76423	+	4.76423i	0.539443	+	0.539443i
$79$	−4.40422	−	7.62834i	−0.495514	−	0.858255i	0.504473	−	0.863428i	$-0.331687\pi$
$79$	−4.40422	−	7.62834i	−0.495514	−	0.858255i	−0.999987	+	0.00517260i	$0.998354\pi$
$80$	2.21756	−	0.287112i	0.247931	−	0.0321001i
$81$	5.44846	−	9.43700i	0.605384	−	1.04856i
$82$	4.62473	+	1.23919i	0.510716	+	0.136846i
$83$	−2.26431	+	2.26431i	−0.248540	+	0.248540i	−0.820371	−	0.571831i	$-0.806233\pi$
$83$	−2.26431	+	2.26431i	−0.248540	+	0.248540i	0.571831	+	0.820371i	$0.306233\pi$
$84$	−3.79559	+	7.07360i	−0.414133	+	0.771793i
$85$	−1.76593	+	13.1949i	−0.191542	+	1.43119i
$86$	2.61053	+	4.52158i	0.281501	+	0.487574i
$87$	−19.4215	+	5.20398i	−2.08220	+	0.557925i
$88$	2.93434	+	1.54585i	0.312802	+	0.164788i
$89$	0.191972	−	0.110835i	0.0203490	−	0.0117485i	−0.489791	−	0.871840i	$-0.662927\pi$
$89$	0.191972	−	0.110835i	0.0203490	−	0.0117485i	0.510140	+	0.860091i	$0.329594\pi$
$90$	13.7545	+	1.84082i	1.44985	+	0.194040i
$91$	−3.09444	−	4.99420i	−0.324385	−	0.523534i
$92$	−2.48888	+	2.48888i	−0.259484	+	0.259484i
$93$	2.58139	−	9.63388i	0.267678	−	0.998987i
$94$	−0.741764	+	1.28477i	−0.0765071	+	0.132514i
$95$	0.385020	−	0.0498493i	0.0395022	−	0.00511443i
$96$	2.62765	−	1.51707i	0.268183	−	0.154836i
$97$	7.97257	−	7.97257i	0.809492	−	0.809492i	−0.175065	−	0.984557i	$-0.556014\pi$
$97$	7.97257	−	7.97257i	0.809492	−	0.809492i	0.984557	+	0.175065i	$0.0560136\pi$
$98$	4.63236	−	5.24797i	0.467939	−	0.530125i
$99$	15.1071	+	13.9800i	1.51832	+	1.40504i
$100$	1.27338	+	4.83513i	0.127338	+	0.483513i
$101$	−10.4760	−	6.04831i	−1.04240	−	0.601829i	−0.121887	−	0.992544i	$-0.538895\pi$
$101$	−10.4760	−	6.04831i	−1.04240	−	0.601829i	−0.920512	+	0.390715i	$0.872228\pi$
$102$	4.67529	+	17.4484i	0.462923	+	1.72765i
$103$	1.11781	−	4.17171i	0.110141	−	0.411050i	−0.888737	−	0.458418i	$-0.848416\pi$
$103$	1.11781	−	4.17171i	0.110141	−	0.411050i	0.998878	+	0.0473672i	$0.0150831\pi$
$104$			2.22060i			0.217748i
$105$	−16.7759	−	6.38603i	−1.63716	−	0.623213i
$106$			6.73458i			0.654120i
$107$	−3.81701	+	14.2453i	−0.369004	+	1.37714i	0.492907	+	0.870082i	$0.335934\pi$
$107$	−3.81701	+	14.2453i	−0.369004	+	1.37714i	−0.861911	+	0.507060i	$0.830732\pi$
$108$	9.39617	−	2.51770i	0.904147	−	0.242265i
$109$	6.68805	−	11.5840i	0.640599	−	1.10955i	−0.344701	−	0.938713i	$-0.612020\pi$
$109$	6.68805	−	11.5840i	0.640599	−	1.10955i	0.985299	−	0.170837i	$-0.0546471\pi$
$110$	−2.58553	+	6.95090i	−0.246521	+	0.662742i
$111$	35.1727			3.33844
$112$	−2.53306	+	0.763939i	−0.239352	+	0.0721854i
$113$	−12.3054	−	12.3054i	−1.15759	−	1.15759i	−0.984991	−	0.172603i	$-0.944782\pi$
$113$	−12.3054	−	12.3054i	−1.15759	−	1.15759i	−0.172603	−	0.984991i	$-0.555218\pi$
$114$	0.456221	−	0.263399i	0.0427290	−	0.0246696i
$115$	−6.23384	−	4.80466i	−0.581308	−	0.448037i
$116$	−5.73896	−	3.31339i	−0.532849	−	0.307641i
$117$	−3.56683	+	13.3116i	−0.329754	+	1.23066i
$118$	10.0121	−	10.0121i	0.921689	−	0.921689i
$119$	−0.489999	−	15.7440i	−0.0449181	−	1.44325i
$120$	4.11863	+	5.39140i	0.375978	+	0.492165i
$121$	−9.07210	+	6.22069i	−0.824736	+	0.565517i
$122$	−0.838847	−	3.13062i	−0.0759457	−	0.283433i
$123$	3.75990	+	14.0321i	0.339018	+	1.26523i
$124$	2.84676	−	1.64358i	0.255647	−	0.147598i
$125$	−10.3566	+	4.21201i	−0.926322	+	0.376734i
$126$	−16.4117	+	0.510781i	−1.46207	+	0.0455040i
$127$	−1.77750	−	1.77750i	−0.157728	−	0.157728i	0.623831	−	0.781559i	$-0.285575\pi$
$127$	−1.77750	−	1.77750i	−0.157728	−	0.157728i	−0.781559	+	0.623831i	$0.785575\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−7.92074	+	13.7191i	−0.697382	+	1.20790i
$130$	−4.92432	+	0.637562i	−0.431891	+	0.0559179i
$131$	−8.44934	+	4.87823i	−0.738223	+	0.426213i	−0.821423	−	0.570320i	$-0.806819\pi$
$131$	−8.44934	+	4.87823i	−0.738223	+	0.426213i	0.0832002	+	0.996533i	$0.473486\pi$
$132$	0.389655	+	10.0556i	0.0339151	+	0.875226i
$133$	−0.439799	+	0.132638i	−0.0381354	+	0.0115011i
$134$	−1.68492			−0.145555
$135$	8.28089	+	20.1137i	0.712706	+	1.73111i
$136$	−2.97677	+	5.15592i	−0.255256	+	0.442117i
$137$	0.818642	+	3.05521i	0.0699413	+	0.261024i	0.992039	−	0.125933i	$-0.0401926\pi$
$137$	0.818642	+	3.05521i	0.0699413	+	0.261024i	−0.922097	+	0.386958i	$0.873526\pi$
$138$	−10.3157	−	2.76409i	−0.878134	−	0.235295i
$139$	−13.6178			−1.15505			−0.577524	−	0.816373i	$-0.695981\pi$
$139$	−13.6178			−1.15505			−0.577524	+	0.816373i	$0.695981\pi$
$140$	−2.42135	−	5.39788i	−0.204642	−	0.456204i
$141$	−4.50124			−0.379073
$142$	2.77407	−	10.3530i	0.232795	−	0.868803i
$143$	−6.51600	−	3.43272i	−0.544895	−	0.287059i
$144$	5.37460	+	3.10303i	0.447883	+	0.258585i
$145$	5.69991	−	13.6778i	0.473352	−	1.13588i
$146$	7.94496			0.657530
$147$	20.8175	+	4.21067i	1.71700	+	0.347290i
$148$	8.19697	+	8.19697i	0.673787	+	0.673787i
$149$	10.1456	+	17.5727i	0.831161	+	1.43961i	0.897118	+	0.441791i	$0.145657\pi$
$149$	10.1456	+	17.5727i	0.831161	+	1.43961i	−0.0659563	+	0.997823i	$0.521010\pi$
$150$	−10.7732	+	10.6812i	−0.879630	+	0.872119i
$151$	−5.57438	−	3.21837i	−0.453637	−	0.261907i	0.255728	−	0.966749i	$-0.417685\pi$
$151$	−5.57438	−	3.21837i	−0.453637	−	0.261907i	−0.709365	+	0.704841i	$0.751018\pi$
$152$	0.167707	+	0.0449370i	0.0136029	+	0.00364487i
$153$	−26.1262	+	26.1262i	−2.11218	+	2.11218i
$154$	1.67408	−	8.61379i	0.134901	−	0.694119i
$155$	4.46208	+	5.84098i	0.358403	+	0.469159i
$156$	−5.83496	+	3.36882i	−0.467171	+	0.269721i
$157$	2.05496	+	7.66923i	0.164004	+	0.612071i	0.998165	+	0.0605504i	$0.0192856\pi$
$157$	2.05496	+	7.66923i	0.164004	+	0.612071i	−0.834161	+	0.551521i	$0.814048\pi$
$158$	8.50830	−	2.27979i	0.676884	−	0.181371i
$159$	−17.6961	+	10.2169i	−1.40339	+	0.810249i
$160$	−0.296618	+	2.21631i	−0.0234497	+	0.175214i
$161$	8.20585	+	4.40314i	0.646712	+	0.347016i
$162$	7.70528	+	7.70528i	0.605384	+	0.605384i
$163$	−1.75132	+	6.53602i	−0.137174	+	0.511941i	0.862805	+	0.505536i	$0.168705\pi$
$163$	−1.75132	+	6.53602i	−0.137174	+	0.511941i	−0.999979	+	0.00640458i	$0.997961\pi$
$164$	−2.39394	+	4.14642i	−0.186935	+	0.323781i
$165$	−22.1870	+	3.75116i	−1.72725	+	0.292027i
$166$	−1.60111	−	2.77320i	−0.124270	−	0.215242i
$167$	5.38564	+	5.38564i	0.416753	+	0.416753i	0.884083	−	0.467330i	$-0.154784\pi$
$167$	5.38564	+	5.38564i	0.416753	+	0.416753i	−0.467330	+	0.884083i	$0.654784\pi$
$168$	−5.85020	−	5.49704i	−0.451353	−	0.424106i
$169$			8.06892i			0.620686i
$170$	−12.2882	−	5.12084i	−0.942464	−	0.392751i
$171$	0.933156	+	0.538758i	0.0713602	+	0.0411998i
$172$	−5.04316	+	1.35131i	−0.384538	+	0.103037i
$173$	13.9833	+	3.74680i	1.06313	+	0.284864i	0.747666	−	0.664075i	$-0.231174\pi$
$173$	13.9833	+	3.74680i	1.06313	+	0.284864i	0.315461	+	0.948939i	$0.397841\pi$
$174$		−	20.1066i		−	1.52428i
$175$	11.2749	−	6.91928i	0.852303	−	0.523049i
$176$	−2.25264	+	2.43426i	−0.169799	+	0.183489i
$177$	41.4974	+	11.1192i	3.11914	+	0.835770i
$178$	0.0573725	+	0.214117i	0.00430025	+	0.0160488i
$179$	21.0192	+	12.1354i	1.57105	+	0.907046i	0.996041	+	0.0888993i	$0.0283349\pi$
$179$	21.0192	+	12.1354i	1.57105	+	0.907046i	0.575009	+	0.818147i	$0.304998\pi$
$180$	−5.33803	+	12.8094i	−0.397873	+	0.954756i
$181$	7.62742			0.566942			0.283471	−	0.958981i	$-0.408514\pi$
$181$	7.62742			0.566942			0.283471	+	0.958981i	$0.408514\pi$
$182$	5.62492	−	1.69640i	0.416947	−	0.125746i
$183$	6.95358	−	6.95358i	0.514023	−	0.514023i
$184$	−1.75991	−	3.04825i	−0.129742	−	0.224720i
$185$	−15.8238	+	20.5307i	−1.16339	+	1.50945i
$186$	8.63750	+	4.98687i	0.633333	+	0.365655i
$187$	−10.5276	−	16.7051i	−0.769852	−	1.22160i
$188$	−1.04901	−	1.04901i	−0.0765071	−	0.0765071i
$189$	−13.5556	−	21.8777i	−0.986023	−	1.59137i
$190$	−0.0514997	+	0.384803i	−0.00373618	+	0.0279165i
$191$	−6.84090	−	11.8488i	−0.494990	−	0.857348i	0.504993	−	0.863123i	$-0.331495\pi$
$191$	−6.84090	−	11.8488i	−0.494990	−	0.857348i	−0.999983	+	0.00577514i	$0.998162\pi$
$192$	0.785295	+	2.93076i	0.0566738	+	0.211509i
$193$	−3.52203	−	13.1444i	−0.253521	−	0.946153i	−0.968907	−	0.247424i	$-0.920416\pi$
$193$	−3.52203	−	13.1444i	−0.253521	−	0.946153i	0.715386	−	0.698729i	$-0.246251\pi$
$194$	5.63746	+	9.76436i	0.404746	+	0.701040i
$195$	−9.14584	−	11.9721i	−0.654947	−	0.857343i
$196$	3.87021	+	5.83280i	0.276443	+	0.416628i
$197$	12.6533	+	12.6533i	0.901511	+	0.901511i	0.995567	−	0.0940555i	$-0.0299831\pi$
$197$	12.6533	+	12.6533i	0.901511	+	0.901511i	−0.0940555	+	0.995567i	$0.529983\pi$
$198$	−17.4137	+	10.9741i	−1.23753	+	0.779894i
$199$	−12.6332	−	7.29381i	−0.895547	−	0.517044i	−0.0197941	−	0.999804i	$-0.506301\pi$
$199$	−12.6332	−	7.29381i	−0.895547	−	0.517044i	−0.875753	+	0.482760i	$0.839634\pi$
$200$	−4.99995	−	0.0214386i	−0.353550	−	0.00151594i
$201$	−2.55614	−	4.42737i	−0.180297	−	0.312283i
$202$	8.55360	−	8.55360i	0.601829	−	0.601829i
$203$	−4.00881	+	17.0684i	−0.281363	+	1.19796i
$204$	−18.0639			−1.26473
$205$	−9.88226	−	4.11821i	−0.690207	−	0.287628i
$206$	3.74025	+	2.15943i	0.260595	+	0.150455i
$207$	−5.65368	−	21.0998i	−0.392958	−	1.46654i
$208$	−2.14494	−	0.574734i	−0.148725	−	0.0398507i
$209$	−0.391111	+	0.422644i	−0.0270537	+	0.0292349i
$210$	10.5104	−	14.5514i	0.725283	−	1.00414i
$211$			3.56375i			0.245338i	0.992448	+	0.122669i	$0.0391454\pi$
$211$			3.56375i			0.245338i	−0.992448	+	0.122669i	$0.960855\pi$
$212$	−6.50511	−	1.74304i	−0.446772	−	0.119712i
$213$	31.4125	−	8.41695i	2.15235	−	0.576720i
$214$	−12.7720	−	7.37389i	−0.873073	−	0.504069i
$215$	−4.44456	−	10.7955i	−0.303117	−	0.736249i
$216$			9.72763i			0.661881i
$217$	−6.33804	−	5.95543i	−0.430254	−	0.404281i
$218$	9.45833	+	9.45833i	0.640599	+	0.640599i
$219$	12.0531	+	20.8766i	0.814473	+	1.41071i
$220$	−6.04487	−	4.29646i	−0.407545	−	0.289667i
$221$	6.61023	−	11.4493i	0.444652	−	0.770160i
$222$	−9.10335	+	33.9742i	−0.610977	+	2.28020i
$223$	−12.9561	−	12.9561i	−0.867603	−	0.867603i	0.124604	−	0.992207i	$-0.460234\pi$
$223$	−12.9561	−	12.9561i	−0.867603	−	0.867603i	−0.992207	+	0.124604i	$0.960234\pi$
$224$	−0.0823037	−	2.64447i	−0.00549915	−	0.176691i
$225$	−29.9382	−	8.15966i	−1.99588	−	0.543977i
$226$	15.0710	−	8.70123i	1.00251	−	0.578797i
$227$	20.7994	−	5.57318i	1.38050	−	0.369905i	0.509199	−	0.860649i	$-0.329942\pi$
$227$	20.7994	−	5.57318i	1.38050	−	0.369905i	0.871304	+	0.490744i	$0.163275\pi$
$228$	0.136346	+	0.508849i	0.00902971	+	0.0336993i
$229$	−3.96454	+	2.28893i	−0.261984	+	0.151257i	−0.625239	−	0.780433i	$-0.714999\pi$
$229$	−3.96454	+	2.28893i	−0.261984	+	0.151257i	0.363255	+	0.931690i	$0.381665\pi$
$230$	6.25438	−	4.77789i	0.412402	−	0.315045i
$231$	25.1737	−	8.66887i	1.65631	−	0.570370i
$232$	4.68584	−	4.68584i	0.307641	−	0.307641i
$233$	−24.8878	−	6.66867i	−1.63046	−	0.436879i	−0.676407	−	0.736528i	$-0.736464\pi$
$233$	−24.8878	−	6.66867i	−1.63046	−	0.436879i	−0.954050	+	0.299649i	$0.903130\pi$
$234$	−11.9348	−	6.89059i	−0.780205	−	0.450452i
$235$	2.02506	−	2.62743i	0.132101	−	0.171395i
$236$	7.07963	+	12.2623i	0.460845	+	0.798207i
$237$	18.8982	+	18.8982i	1.22757	+	1.22757i
$238$	15.3343	+	3.60154i	0.993977	+	0.233453i
$239$	−1.13070			−0.0731389			−0.0365695	−	0.999331i	$-0.511643\pi$
$239$	−1.13070			−0.0731389			−0.0365695	+	0.999331i	$0.511643\pi$
$240$	−6.27367	+	2.58289i	−0.404964	+	0.166725i
$241$	19.2028	+	11.0867i	1.23696	+	0.714160i	0.968472	−	0.249122i	$-0.0801422\pi$
$241$	19.2028	+	11.0867i	1.23696	+	0.714160i	0.268490	+	0.963283i	$0.413475\pi$
$242$	−3.66069	−	10.3730i	−0.235318	−	0.666802i
$243$	−1.00420	+	3.74774i	−0.0644197	+	0.240418i
$244$	3.24106			0.207487
$245$	−11.8234	+	10.2571i	−0.755368	+	0.655301i
$246$	−14.5271			−0.926215
$247$	−0.372411	−	0.0997873i	−0.0236960	−	0.00634931i
$248$	0.850780	+	3.17515i	0.0540246	+	0.201622i
$249$	4.85800	−	8.41431i	0.307863	−	0.533235i
$250$	−1.38801	−	11.0938i	−0.0877852	−	0.701636i
$251$	7.78989			0.491693			0.245847	−	0.969309i	$-0.420934\pi$
$251$	7.78989			0.491693			0.245847	+	0.969309i	$0.420934\pi$
$252$	3.75429	−	15.9847i	0.236498	−	1.00694i
$253$	11.6651	−	0.452026i	0.733382	−	0.0284186i
$254$	2.17699	−	1.25688i	0.136596	−	0.0788639i
$255$	−5.18637	−	40.0578i	−0.324783	−	2.50852i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.79149	−	1.01593i	−0.236507	−	0.0633718i	0.138619	−	0.990346i	$-0.455734\pi$
$257$	−3.79149	−	1.01593i	−0.236507	−	0.0633718i	−0.375126	+	0.926974i	$0.622400\pi$
$258$	−11.2016	−	11.2016i	−0.697382	−	0.697382i
$259$	14.5014	−	27.0254i	0.901076	−	1.67928i
$260$	0.658670	−	4.92154i	0.0408490	−	0.305221i
$261$	35.6163	−	20.5631i	2.20459	−	1.27282i
$262$	−2.52516	−	9.42402i	−0.156005	−	0.582218i
$263$	7.67621	+	28.6480i	0.473336	+	1.76651i	0.627655	+	0.778492i	$0.284015\pi$
$263$	7.67621	+	28.6480i	0.473336	+	1.76651i	−0.154319	+	0.988021i	$0.549318\pi$
$264$	−9.81380	−	2.22620i	−0.603997	−	0.137013i
$265$	1.99760	−	14.9259i	0.122711	−	0.916891i
$266$	−0.0142898	−	0.459142i	−0.000876166	−	0.0281518i
$267$	−0.475586	+	0.475586i	−0.0291054	+	0.0291054i
$268$	0.436089	−	1.62751i	0.0266384	−	0.0994157i
$269$	1.31311	+	0.758122i	0.0800615	+	0.0462235i	0.539496	−	0.841988i	$-0.318615\pi$
$269$	1.31311	+	0.758122i	0.0800615	+	0.0462235i	−0.459435	+	0.888211i	$0.651948\pi$
$270$	−21.5716	+	2.79292i	−1.31281	+	0.169972i
$271$	−9.20142	+	5.31244i	−0.558947	+	0.322708i	−0.752723	−	0.658338i	$-0.771260\pi$
$271$	−9.20142	+	5.31244i	−0.558947	+	0.322708i	0.193776	+	0.981046i	$0.437927\pi$
$272$	−4.20979	−	4.20979i	−0.255256	−	0.255256i
$273$	12.9910	+	12.2067i	0.786250	+	0.738786i
$274$	−3.16299			−0.191083
$275$	7.79209	−	14.6384i	0.469881	−	0.882730i
$276$	5.33982	−	9.24884i	0.321419	−	0.556715i
$277$	11.9243	−	3.19511i	0.716461	−	0.191975i	0.117869	−	0.993029i	$-0.462394\pi$
$277$	11.9243	−	3.19511i	0.716461	−	0.191975i	0.598592	+	0.801054i	$0.295727\pi$
$278$	3.52455	−	13.1538i	0.211389	−	0.788913i
$279$			20.4003i			1.22133i
$280$	5.84064	−	0.941772i	0.349045	−	0.0562817i
$281$			14.5160i			0.865950i	0.901406	+	0.432975i	$0.142536\pi$
$281$			14.5160i			0.865950i	−0.901406	+	0.432975i	$0.857464\pi$
$282$	1.16501	−	4.34787i	0.0693752	−	0.258912i
$283$	−1.82776	−	6.82129i	−0.108649	−	0.405484i	0.890085	−	0.455795i	$-0.150645\pi$
$283$	−1.82776	−	6.82129i	−0.108649	−	0.405484i	−0.998734	+	0.0503119i	$0.983978\pi$
$284$	9.28223	+	5.35910i	0.550799	+	0.318004i
$285$	−1.08926	+	0.448451i	−0.0645219	+	0.0265639i
$286$	5.00222	−	5.40552i	0.295787	−	0.319635i
$287$	12.3320	+	2.89638i	0.727933	+	0.170968i
$288$	−4.38834	+	4.38834i	−0.258585	+	0.258585i
$289$	15.9736	−	9.22234i	0.939622	−	0.542491i
$290$	11.7365	+	9.04577i	0.689190	+	0.531186i
$291$	−17.1049	+	29.6265i	−1.00271	+	1.73674i
$292$	−2.05631	+	7.67425i	−0.120336	+	0.449101i
$293$	−22.8571	+	22.8571i	−1.33533	+	1.33533i	−0.434800	+	0.900527i	$0.643181\pi$
$293$	−22.8571	+	22.8571i	−1.33533	+	1.33533i	−0.900527	+	0.434800i	$0.856819\pi$
$294$	−9.45515	+	19.0183i	−0.551435	+	1.10917i
$295$	−25.1597	+	19.2201i	−1.46485	+	1.11904i
$296$	−10.0392	+	5.79614i	−0.583517	+	0.336894i
$297$	−28.5442	−	15.0375i	−1.65630	−	0.872562i
$298$	−19.5998	+	5.25176i	−1.13539	+	0.304226i
$299$	3.90806	+	6.76895i	0.226009	+	0.391458i
$300$	−7.52897	−	13.1706i	−0.434685	−	0.760408i
$301$	7.27562	+	11.7423i	0.419360	+	0.676816i
$302$	4.55147	−	4.55147i	0.261907	−	0.261907i
$303$	35.4523	+	9.49942i	2.03668	+	0.545727i
$304$	−0.0868117	+	0.150362i	−0.00497899	+	0.00862387i
$305$	0.930546	+	7.18723i	0.0532829	+	0.411540i
$306$	−18.4740	−	31.9979i	−1.05609	−	1.82920i
$307$	−11.0798	−	11.0798i	−0.632358	−	0.632358i	0.316301	−	0.948659i	$-0.397559\pi$
$307$	−11.0798	−	11.0798i	−0.632358	−	0.632358i	−0.948659	+	0.316301i	$0.897559\pi$
$308$	7.88700	+	3.84645i	0.449404	+	0.219172i
$309$			13.1041i			0.745465i
$310$	−6.79682	+	2.79828i	−0.386033	+	0.158932i
$311$	2.71169	−	4.69678i	0.153766	−	0.266330i	−0.778843	−	0.627219i	$-0.784193\pi$
$311$	2.71169	−	4.69678i	0.153766	−	0.266330i	0.932609	+	0.360889i	$0.117527\pi$
$312$	−1.74383	−	6.50806i	−0.0987249	−	0.368446i
$313$	7.45027	−	27.8048i	0.421114	−	1.57162i	−0.351152	−	0.936319i	$-0.614210\pi$
$313$	7.45027	−	27.8048i	0.421114	−	1.57162i	0.772266	−	0.635300i	$-0.219124\pi$
$314$	−7.93977			−0.448067
$315$	36.5249	+	3.73596i	2.05795	+	0.210497i
$316$			8.80844i			0.495514i
$317$	−11.0514	−	2.96122i	−0.620709	−	0.166319i	−0.0652590	−	0.997868i	$-0.520787\pi$
$317$	−11.0514	−	2.96122i	−0.620709	−	0.166319i	−0.555450	+	0.831550i	$0.687454\pi$
$318$	−5.28863	−	19.7374i	−0.296572	−	1.10682i
$319$	6.50623	+	20.9935i	0.364279	+	1.17541i
$320$	−2.06402	−	0.860133i	−0.115382	−	0.0480829i
$321$		−	44.7469i		−	2.49753i
$322$	−6.37694	+	6.78663i	−0.355373	+	0.378204i
$323$	−0.730918	−	0.730918i	−0.0406694	−	0.0406694i
$324$	−9.43700	+	5.44846i	−0.524278	+	0.302692i
$325$	11.1029	+	0.0476065i	0.615879	+	0.00264074i
$326$	−5.86004	−	3.38329i	−0.324558	−	0.187383i
$327$	−10.5042	+	39.2021i	−0.580883	+	2.16788i
$328$	−3.38554	−	3.38554i	−0.186935	−	0.186935i
$329$	−1.85583	+	3.45859i	−0.102315	+	0.190678i
$330$	2.11907	−	22.4018i	0.116651	−	1.23318i
$331$	−1.64939	−	2.85683i	−0.0906586	−	0.157025i	0.817130	−	0.576454i	$-0.195564\pi$
$331$	−1.64939	−	2.85683i	−0.0906586	−	0.157025i	−0.907788	+	0.419428i	$0.862231\pi$
$332$	3.09311	−	0.828795i	0.169756	−	0.0454860i
$333$	−69.4909	+	18.6200i	−3.80808	+	1.02037i
$334$	−6.59603	+	3.80822i	−0.360919	+	0.208377i
$335$	3.73430	+	0.499776i	0.204026	+	0.0273057i
$336$	6.82388	−	4.22812i	0.372273	−	0.230663i
$337$	−11.5468	−	11.5468i	−0.628993	−	0.628993i	0.318821	−	0.947815i	$-0.396713\pi$
$337$	−11.5468	−	11.5468i	−0.628993	−	0.628993i	−0.947815	+	0.318821i	$0.896713\pi$
$338$	−7.79398	−	2.08839i	−0.423937	−	0.113593i
$339$	45.7275	+	26.4008i	2.48358	+	1.43390i
$340$	8.12678	−	10.5441i	0.440736	−	0.571836i
$341$	−10.6322	−	2.41184i	−0.575764	−	0.130608i
$342$	−0.761918	+	0.761918i	−0.0411998	+	0.0411998i
$343$	11.8182	−	14.2594i	0.638124	−	0.769933i
$344$		−	5.22107i		−	0.281501i
$345$	22.0430	+	9.18591i	1.18675	+	0.494553i
$346$	−7.23827	+	12.5370i	−0.389132	+	0.673996i
$347$	−28.9808	+	7.76538i	−1.55577	+	0.416868i	−0.931322	−	0.364198i	$-0.881343\pi$
$347$	−28.9808	+	7.76538i	−1.55577	+	0.416868i	−0.624449	+	0.781065i	$0.714677\pi$
$348$	19.4215	+	5.20398i	1.04110	+	0.278962i
$349$	−8.29717			−0.444137			−0.222069	−	0.975031i	$-0.571281\pi$
$349$	−8.29717			−0.444137			−0.222069	+	0.975031i	$0.571281\pi$
$350$	3.76535	+	12.6816i	0.201267	+	0.677858i
$351$		−	21.6012i		−	1.15299i
$352$	−1.76829	−	2.80592i	−0.0942500	−	0.149556i
$353$	24.4459	−	6.55027i	1.30113	−	0.348636i	0.459250	−	0.888307i	$-0.348118\pi$
$353$	24.4459	−	6.55027i	1.30113	−	0.348636i	0.841876	+	0.539671i	$0.181452\pi$
$354$	−21.4806	+	37.2056i	−1.14168	+	1.97745i
$355$	−9.21908	+	22.1226i	−0.489298	+	1.17414i
$356$	−0.221670			−0.0117485
$357$	13.7997	+	45.7570i	0.730359	+	2.42172i
$358$	−17.1621	+	17.1621i	−0.907046	+	0.907046i
$359$	−9.78988	−	16.9566i	−0.516690	−	0.894933i	−0.999812	−	0.0193804i	$-0.993831\pi$
$359$	−9.78988	−	16.9566i	−0.516690	−	0.894933i	0.483122	−	0.875553i	$-0.339503\pi$
$360$	−10.9913	−	8.47146i	−0.579295	−	0.446485i
$361$	9.48493	−	16.4284i	0.499207	−	0.864651i
$362$	−1.97412	+	7.36753i	−0.103758	+	0.387229i
$363$	21.7031	−	25.3556i	1.13912	−	1.33083i
$364$	0.182764	+	5.87232i	0.00957942	+	0.307793i
$365$	−17.6085	−	2.35662i	−0.921670	−	0.123351i
$366$	4.91692	+	8.51636i	0.257012	+	0.445157i
$367$	−0.955476	−	3.56588i	−0.0498754	−	0.186138i	0.936494	−	0.350684i	$-0.114051\pi$
$367$	−0.955476	−	3.56588i	−0.0498754	−	0.186138i	−0.986369	+	0.164546i	$0.947384\pi$
$368$	3.39988	−	0.910995i	0.177231	−	0.0474889i
$369$	−14.8569	−	25.7329i	−0.773419	−	1.33960i
$370$	−15.7356	−	20.5984i	−0.818057	−	1.07086i
$371$	0.554281	+	17.8094i	0.0287768	+	0.924618i
$372$	−7.05249	+	7.05249i	−0.365655	+	0.365655i
$373$	8.98030	+	2.40626i	0.464982	+	0.124592i	0.483701	−	0.875233i	$-0.339292\pi$
$373$	8.98030	+	2.40626i	0.464982	+	0.124592i	−0.0187190	+	0.999825i	$0.505959\pi$
$374$	18.8607	−	5.84525i	0.975262	−	0.302250i
$375$	27.0450	−	20.4774i	1.39660	−	1.05745i
$376$	1.28477	−	0.741764i	0.0662571	−	0.0382535i
$377$	−10.4054	+	10.4054i	−0.535905	+	0.535905i
$378$	24.6407	−	7.43131i	1.26738	−	0.382225i
$379$			1.64295i			0.0843928i	0.999109	+	0.0421964i	$0.0134355\pi$
$379$			1.64295i			0.0843928i	−0.999109	+	0.0421964i	$0.986564\pi$
$380$	−0.358362	−	0.149339i	−0.0183836	−	0.00766094i
$381$	6.60530	+	3.81357i	0.338400	+	0.195375i
$382$	13.2156	−	3.54111i	0.676169	−	0.181179i
$383$	−4.30896	+	16.0813i	−0.220178	+	0.821714i	0.764102	+	0.645096i	$0.223183\pi$
$383$	−4.30896	+	16.0813i	−0.220178	+	0.821714i	−0.984279	+	0.176619i	$0.943484\pi$
$384$	−3.03415			−0.154836
$385$	−6.26528	+	18.5943i	−0.319308	+	0.947651i
$386$	13.6081			0.692632
$387$	8.38631	−	31.2981i	0.426300	−	1.59097i
$388$	−10.8907	+	2.91816i	−0.552893	+	0.148147i
$389$	−10.4826	−	6.05215i	−0.531491	−	0.306856i	0.210133	−	0.977673i	$-0.432610\pi$
$389$	−10.4826	−	6.05215i	−0.531491	−	0.306856i	−0.741623	+	0.670817i	$0.765944\pi$
$390$	13.9313	−	5.73558i	0.705440	−	0.290433i
$391$			20.9554i			1.05976i
$392$	−6.63573	+	2.22869i	−0.335155	+	0.112566i
$393$	20.9322	−	20.9322i	1.05589	−	1.05589i
$394$	−15.4971	+	8.94725i	−0.780732	+	0.450756i
$395$	−19.5332	+	2.52901i	−0.982824	+	0.127248i
$396$	−6.09316	−	19.6606i	−0.306193	−	0.987982i
$397$	−4.16274	−	1.11540i	−0.208922	−	0.0559805i	0.152840	−	0.988251i	$-0.451158\pi$
$397$	−4.16274	−	1.11540i	−0.208922	−	0.0559805i	−0.361762	+	0.932270i	$0.617825\pi$
$398$	10.3150	−	10.3150i	0.517044	−	0.517044i
$399$	1.18478	−	0.734101i	0.0593134	−	0.0367510i
$400$	1.31479	−	4.82404i	0.0657396	−	0.241202i
$401$	14.5822	+	25.2571i	0.728201	+	1.26128i	0.957643	+	0.287958i	$0.0929765\pi$
$401$	14.5822	+	25.2571i	0.728201	+	1.26128i	−0.229442	+	0.973322i	$0.573690\pi$
$402$	4.93809	−	1.32316i	0.246290	−	0.0659931i
$403$	−1.88924	−	7.05076i	−0.0941100	−	0.351223i
$404$	6.04831	+	10.4760i	0.300915	+	0.521200i
$405$	−14.7917	−	19.3628i	−0.735008	−	0.962145i
$406$	−15.4492	−	8.28982i	−0.766732	−	0.411417i
$407$	−1.48872	−	38.4184i	−0.0737930	−	1.90433i
$408$	4.67529	−	17.4484i	0.231461	−	0.863825i
$409$	7.10664	−	12.3091i	0.351401	−	0.608644i	−0.635095	−	0.772434i	$-0.719039\pi$
$409$	7.10664	−	12.3091i	0.351401	−	0.608644i	0.986495	+	0.163791i	$0.0523722\pi$
$410$	6.53560	−	8.47966i	0.322770	−	0.418781i
$411$	−4.79849	−	8.31123i	−0.236692	−	0.409963i
$412$	−3.05390	+	3.05390i	−0.150455	+	0.150455i
$413$	25.6527	−	27.3008i	1.26229	−	1.34338i
$414$	21.8441			1.07358
$415$	2.72597	+	6.62119i	0.133813	+	0.325021i
$416$	1.11030	−	1.92310i	0.0544370	−	0.0942877i
$417$	39.9106	−	10.6940i	1.95443	−	0.523688i
$418$	−0.307016	−	0.487172i	−0.0150166	−	0.0238284i
$419$			18.0151i			0.880097i	0.897974	+	0.440048i	$0.145039\pi$
$419$			18.0151i			0.880097i	−0.897974	+	0.440048i	$0.854961\pi$
$420$	11.3353	+	13.9184i	0.553107	+	0.679149i
$421$	−10.5777			−0.515527			−0.257763	−	0.966208i	$-0.582985\pi$
$421$	−10.5777			−0.515527			−0.257763	+	0.966208i	$0.582985\pi$
$422$	−3.44231	−	0.922365i	−0.167569	−	0.0449000i
$423$	8.89313	−	2.38291i	0.432399	−	0.115861i
$424$	3.36729	−	5.83232i	0.163530	−	0.283242i
$425$	25.7155	+	14.9943i	1.24739	+	0.727328i
$426$			32.5206i			1.57563i
$427$	−2.47597	−	8.20979i	−0.119821	−	0.397300i
$428$	10.4283	−	10.4283i	0.504069	−	0.504069i
$429$	21.7925	+	4.94350i	1.05215	+	0.238675i
$430$	11.5780	−	1.49903i	0.558342	−	0.0722897i
$431$	−16.2778	−	9.39799i	−0.784074	−	0.452685i	0.0537982	−	0.998552i	$-0.482867\pi$
$431$	−16.2778	−	9.39799i	−0.784074	−	0.452685i	−0.837872	+	0.545867i	$0.816201\pi$
$432$	−9.39617	−	2.51770i	−0.452073	−	0.121133i
$433$	−0.462481	−	0.462481i	−0.0222254	−	0.0222254i	0.695907	−	0.718132i	$-0.255003\pi$
$433$	−0.462481	−	0.462481i	−0.0222254	−	0.0222254i	−0.718132	+	0.695907i	$0.755003\pi$
$434$	7.39291	−	4.58070i	0.354871	−	0.219881i
$435$	−5.96398	+	44.5625i	−0.285951	+	2.13661i
$436$	−11.5840	+	6.68805i	−0.554775	+	0.320299i
$437$	0.590299	−	0.158170i	0.0282378	−	0.00756630i
$438$	−23.2848	+	6.23914i	−1.11259	+	0.298118i
$439$	14.4458	+	25.0209i	0.689461	+	1.19418i	0.972012	+	0.234929i	$0.0754859\pi$
$439$	14.4458	+	25.0209i	0.689461	+	1.19418i	−0.282551	+	0.959252i	$0.591181\pi$
$440$	5.71459	−	4.72689i	0.272432	−	0.225346i
$441$	−43.3583	+	2.70149i	−2.06468	+	0.128642i
$442$	9.34828	+	9.34828i	0.444652	+	0.444652i
$443$	5.06677	−	18.9094i	0.240730	−	0.898415i	−0.734752	−	0.678335i	$-0.762702\pi$
$443$	5.06677	−	18.9094i	0.240730	−	0.898415i	0.975482	−	0.220079i	$-0.0706317\pi$
$444$	−30.4604	−	17.5863i	−1.44559	−	0.834610i
$445$	−0.0636442	−	0.491567i	−0.00301703	−	0.0233025i
$446$	15.8679	−	9.16133i	0.751366	−	0.433801i
$447$	−43.5342	−	43.5342i	−2.05910	−	2.05910i
$448$	2.57566	+	0.604940i	0.121689	+	0.0285807i
$449$		−	31.8378i		−	1.50252i	−0.660008	−	0.751259i	$-0.729447\pi$
$449$		−	31.8378i		−	1.50252i	0.660008	−	0.751259i	$-0.270553\pi$
$450$	15.6302	−	26.8062i	0.736815	−	1.26366i
$451$	15.1679	−	4.70078i	0.714227	−	0.221351i
$452$	4.50409	+	16.8095i	0.211854	+	0.790652i
$453$	18.8646	+	5.05474i	0.886334	+	0.237493i
$454$			21.5331i			1.01060i
$455$	−12.9697	+	2.09130i	−0.608031	+	0.0980418i
$456$	−0.526799			−0.0246696
$457$	−3.05364	+	11.3964i	−0.142843	+	0.533099i	0.856999	+	0.515319i	$0.172327\pi$
$457$	−3.05364	+	11.3964i	−0.142843	+	0.533099i	−0.999842	+	0.0177800i	$0.994340\pi$
$458$	−1.18484	−	4.42187i	−0.0553638	−	0.206620i
$459$	28.9569	−	50.1549i	1.35159	−	2.34103i
$460$	2.99633	+	7.27788i	0.139705	+	0.339333i
$461$			25.8772i			1.20522i	0.798035	+	0.602611i	$0.205873\pi$
$461$			25.8772i			1.20522i	−0.798035	+	0.602611i	$0.794127\pi$
$462$	1.85804	+	26.5596i	0.0864440	+	1.23567i
$463$	−9.58794	−	9.58794i	−0.445589	−	0.445589i	0.448296	−	0.893885i	$-0.352031\pi$
$463$	−9.58794	−	9.58794i	−0.445589	−	0.445589i	−0.893885	+	0.448296i	$0.852031\pi$
$464$	3.31339	+	5.73896i	0.153820	+	0.266424i
$465$	−17.6642	−	13.6145i	−0.819156	−	0.631356i
$466$	12.8829	−	22.3138i	0.596788	−	1.03367i
$467$	−3.42025	−	0.916452i	−0.158270	−	0.0424084i	0.178814	−	0.983883i	$-0.442774\pi$
$467$	−3.42025	−	0.916452i	−0.158270	−	0.0424084i	−0.337084	+	0.941475i	$0.609441\pi$
$468$	9.74476	−	9.74476i	0.450452	−	0.450452i
$469$	−4.45572	+	0.138675i	−0.205746	+	0.00640341i
$470$	2.01378	+	2.63609i	0.0928887	+	0.121594i
$471$	−12.0452	−	20.8629i	−0.555014	−	0.961313i
$472$	−13.6768	+	3.66469i	−0.629526	+	0.168681i
$473$	15.3204	+	8.07099i	0.704432	+	0.371105i
$474$	−23.1455	+	13.3631i	−1.06311	+	0.613786i
$475$	0.228278	−	0.837565i	0.0104741	−	0.0384301i
$476$	−7.44764	+	13.8797i	−0.341362	+	0.636174i
$477$	29.5536	−	29.5536i	1.35317	−	1.35317i
$478$	0.292647	−	1.09217i	0.0133853	−	0.0499548i
$479$	−15.8513	+	27.4553i	−0.724266	+	1.25447i	0.235010	+	0.971993i	$0.424488\pi$
$479$	−15.8513	+	27.4553i	−0.724266	+	1.25447i	−0.959275	+	0.282472i	$0.908845\pi$
$480$	−0.871140	−	6.72840i	−0.0397619	−	0.307108i
$481$	22.2931	−	12.8709i	1.01648	−	0.586863i
$482$	−15.6790	+	15.6790i	−0.714160	+	0.714160i
$483$	−27.5072	−	6.46054i	−1.25162	−	0.293965i
$484$	10.9670	−	0.851225i	0.498501	−	0.0386920i
$485$	−9.59806	−	23.3130i	−0.435825	−	1.05859i
$486$	−3.36013	−	1.93997i	−0.152419	−	0.0879989i
$487$	−1.53288	−	5.72078i	−0.0694614	−	0.259233i	0.922459	−	0.386095i	$-0.126176\pi$
$487$	−1.53288	−	5.72078i	−0.0694614	−	0.259233i	−0.991920	+	0.126861i	$0.959510\pi$
$488$	−0.838847	+	3.13062i	−0.0379728	+	0.141717i
$489$		−	20.5308i		−	0.928436i
$490$	−6.84746	−	14.0752i	−0.309337	−	0.635854i
$491$			24.5502i			1.10793i	0.832538	+	0.553967i	$0.186887\pi$
$491$			24.5502i			1.10793i	−0.832538	+	0.553967i	$0.813113\pi$
$492$	3.75990	−	14.0321i	0.169509	−	0.632617i
$493$	−38.1085	+	10.2111i	−1.71632	+	0.459887i
$494$	0.192774	−	0.333895i	0.00867332	−	0.0150226i
$495$	41.8491	−	19.1567i	1.88098	−	0.861031i
$496$	−3.28716			−0.147598
$497$	6.48387	−	27.6065i	0.290841	−	1.23832i
$498$	6.87025	+	6.87025i	0.307863	+	0.307863i
$499$	−16.3553	+	9.44273i	−0.732164	+	0.422715i	−0.819213	−	0.573489i	$-0.805589\pi$
$499$	−16.3553	+	9.44273i	−0.732164	+	0.422715i	0.0870496	+	0.996204i	$0.472256\pi$
$500$	11.0751	+	1.53059i	0.495292	+	0.0684500i
$501$	−20.0133	−	11.5547i	−0.894130	−	0.516226i
$502$	−2.01617	+	7.52445i	−0.0899861	+	0.335833i
$503$	−2.64950	+	2.64950i	−0.118136	+	0.118136i	−0.763703	−	0.645568i	$-0.776621\pi$
$503$	−2.64950	+	2.64950i	−0.118136	+	0.118136i	0.645568	+	0.763703i	$0.276621\pi$
$504$	14.4684	+	7.76351i	0.644472	+	0.345814i
$505$	−21.4946	+	16.4203i	−0.956495	+	0.730692i
$506$	−2.58254	+	11.3847i	−0.114808	+	0.506110i
$507$	−6.33649	−	23.6481i	−0.281413	−	1.05025i
$508$	0.650611	+	2.42811i	0.0288662	+	0.107730i
$509$	−4.80854	+	2.77621i	−0.213135	+	0.123053i	−0.602767	−	0.797917i	$-0.705935\pi$
$509$	−4.80854	+	2.77621i	−0.213135	+	0.123053i	0.389633	+	0.920970i	$0.372602\pi$
$510$	40.0352	+	5.35808i	1.77279	+	0.237260i
$511$	21.0102	−	0.653900i	0.929438	−	0.0289268i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−1.63139	−	0.437131i	−0.0720278	−	0.0192998i
$514$	1.96262	−	3.39936i	0.0865676	−	0.149939i
$515$	−7.64901	−	5.89539i	−0.337056	−	0.259782i
$516$	13.7191	−	7.92074i	0.603951	−	0.348691i
$517$	0.190520	+	4.91661i	0.00837904	+	0.216232i
$518$	22.3513	+	21.0020i	0.982060	+	0.922776i
$519$	−43.9239			−1.92805
$520$	4.58336	+	1.91001i	0.200994	+	0.0837597i
$521$	−13.9099	+	24.0926i	−0.609403	+	1.05552i	0.381935	+	0.924189i	$0.375258\pi$
$521$	−13.9099	+	24.0926i	−0.609403	+	1.05552i	−0.991339	+	0.131329i	$0.958076\pi$
$522$	10.6442	+	39.7248i	0.465885	+	1.73871i
$523$	−27.4535	−	7.35614i	−1.20046	−	0.321662i	−0.397447	−	0.917625i	$-0.630104\pi$
$523$	−27.4535	−	7.35614i	−1.20046	−	0.321662i	−0.803011	+	0.595964i	$0.796770\pi$
$524$	9.75646			0.426213
$525$	−27.6104	+	29.1329i	−1.20502	+	1.27146i
$526$	−29.6586			−1.29318
$527$	5.06516	−	18.9034i	0.220642	−	0.823446i
$528$	4.69034	−	8.90322i	0.204121	−	0.387463i
$529$	9.18931	+	5.30545i	0.399535	+	0.230672i
$530$	13.9003	+	5.79264i	0.603790	+	0.251616i
$531$	−87.8731			−3.81337
$532$	0.447196	+	0.105032i	0.0193884	+	0.00455370i
$533$	7.51794	+	7.51794i	0.325638	+	0.325638i
$534$	−0.336290	−	0.582472i	−0.0145527	−	0.0252060i
$535$	26.1193	+	20.1312i	1.12924	+	0.870347i
$536$	1.45918	+	0.842459i	0.0630271	+	0.0363887i
$537$	−71.1322	−	19.0598i	−3.06958	−	0.822492i
$538$	−1.07215	+	1.07215i	−0.0462235	+	0.0462235i
$539$	3.71811	−	22.9167i	0.160150	−	0.987093i
$540$	2.88539	−	21.5594i	0.124167	−	0.927770i
$541$	−8.08058	+	4.66532i	−0.347411	+	0.200578i	−0.663544	−	0.748137i	$-0.730949\pi$
$541$	−8.08058	+	4.66532i	−0.347411	+	0.200578i	0.316133	+	0.948715i	$0.397615\pi$
$542$	−2.74992	−	10.2629i	−0.118119	−	0.440827i
$543$	−22.3542	+	5.98978i	−0.959309	+	0.257046i
$544$	5.15592	−	2.97677i	0.221058	−	0.127628i
$545$	−18.1571	−	23.7681i	−0.777763	−	1.01811i
$546$	−15.1531	+	9.38898i	−0.648494	+	0.401811i
$547$	3.74412	+	3.74412i	0.160087	+	0.160087i	0.782605	−	0.622518i	$-0.213890\pi$
$547$	3.74412	+	3.74412i	0.160087	+	0.160087i	−0.622518	+	0.782605i	$0.713890\pi$
$548$	0.818642	−	3.05521i	0.0349707	−	0.130512i
$549$	−10.0571	+	17.4194i	−0.429226	+	0.743441i
$550$	12.1229	+	11.3153i	0.516922	+	0.482485i
$551$	0.575282	+	0.996417i	0.0245078	+	0.0424488i
$552$	7.55164	+	7.55164i	0.321419	+	0.321419i
$553$	22.3123	−	6.72911i	0.948817	−	0.286151i
$554$			12.3449i			0.524486i
$555$	30.2532	−	72.5970i	1.28418	−	3.08157i
$556$	11.7934	+	6.80891i	0.500151	+	0.288762i
$557$	15.6638	−	4.19710i	0.663696	−	0.177837i	0.0887824	−	0.996051i	$-0.471702\pi$
$557$	15.6638	−	4.19710i	0.663696	−	0.177837i	0.574913	+	0.818214i	$0.305036\pi$
$558$	−19.7052	−	5.27998i	−0.834186	−	0.223519i
$559$			11.5939i			0.490370i
$560$	−0.601986	+	5.88537i	−0.0254386	+	0.248702i
$561$	43.9723	+	40.6915i	1.85651	+	1.71800i
$562$	−14.0213	−	3.75701i	−0.591455	−	0.158480i
$563$	11.4072	+	42.5721i	0.480755	+	1.79420i	0.598460	+	0.801153i	$0.295780\pi$
$563$	11.4072	+	42.5721i	0.480755	+	1.79420i	−0.117705	+	0.993049i	$0.537554\pi$
$564$	3.89819	+	2.25062i	0.164143	+	0.0947682i
$565$	−35.9828	+	14.8143i	−1.51381	+	0.623242i
$566$	7.06192			0.296835
$567$	21.0106	+	19.7422i	0.882361	+	0.829095i
$568$	−7.57891	+	7.57891i	−0.318004	+	0.318004i
$569$	−9.08697	−	15.7391i	−0.380946	−	0.659817i	0.610252	−	0.792207i	$-0.291068\pi$
$569$	−9.08697	−	15.7391i	−0.380946	−	0.659817i	−0.991198	+	0.132390i	$0.957735\pi$
$570$	−0.151250	−	1.16821i	−0.00633518	−	0.0489308i
$571$	−34.8710	−	20.1328i	−1.45931	−	0.842531i	−0.460330	−	0.887748i	$-0.652269\pi$
$571$	−34.8710	−	20.1328i	−1.45931	−	0.842531i	−0.998977	+	0.0452164i	$0.985602\pi$
$572$	3.92666	+	6.23082i	0.164182	+	0.260524i
$573$	29.3538	+	29.3538i	1.22627	+	1.22627i
$574$	−5.98943	+	11.1621i	−0.249994	+	0.465898i
$575$	−15.2788	+	8.73411i	−0.637171	+	0.364237i
$576$	−3.10303	−	5.37460i	−0.129293	−	0.223942i
$577$	3.73411	+	13.9359i	0.155453	+	0.580159i	0.999066	+	0.0432071i	$0.0137575\pi$
$577$	3.73411	+	13.9359i	0.155453	+	0.580159i	−0.843613	+	0.536952i	$0.819576\pi$
$578$	4.77384	+	17.8162i	0.198565	+	0.741056i
$579$	20.6444	+	35.7572i	0.857953	+	1.48602i
$580$	−11.7752	+	8.99536i	−0.488937	+	0.373512i
$581$	−4.46233	−	7.20188i	−0.185129	−	0.298784i
$582$	−24.1899	−	24.1899i	−1.00271	−	1.00271i
$583$	11.9087	+	18.8967i	0.493207	+	0.782620i
$584$	−6.88054	−	3.97248i	−0.284719	−	0.164382i
$585$	24.4074	+	18.8117i	1.00912	+	0.777770i
$586$	−16.1624	−	27.9941i	−0.667663	−	1.15643i
$587$	28.7754	−	28.7754i	1.18769	−	1.18769i	0.209984	−	0.977705i	$-0.432659\pi$
$587$	28.7754	−	28.7754i	1.18769	−	1.18769i	0.977705	−	0.209984i	$-0.0673413\pi$
$588$	−15.9231	−	14.0553i	−0.656658	−	0.579630i
$589$	−0.570728			−0.0235164
$590$	−12.0534	−	29.2769i	−0.496232	−	1.20531i
$591$	−47.0204	−	27.1473i	−1.93416	−	1.11669i
$592$	−3.00030	−	11.1973i	−0.123312	−	0.460205i
$593$	−6.60744	−	1.77046i	−0.271335	−	0.0727041i	0.120586	−	0.992703i	$-0.461523\pi$
$593$	−6.60744	−	1.77046i	−0.271335	−	0.0727041i	−0.391921	+	0.919999i	$0.628189\pi$
$594$	21.9128	−	23.6796i	0.899095	−	0.971584i
$595$	−32.9173	−	12.5305i	−1.34948	−	0.513702i
$596$		−	20.2912i		−	0.831161i
$597$	42.7528	+	11.4556i	1.74976	+	0.468846i
$598$	−7.54978	+	2.02296i	−0.308734	+	0.0827249i
$599$	−38.7397	−	22.3664i	−1.58286	−	0.913865i	−0.994439	−	0.105310i	$-0.966417\pi$
$599$	−38.7397	−	22.3664i	−1.58286	−	0.913865i	−0.588421	−	0.808555i	$-0.700250\pi$
$600$	14.6705	−	3.86361i	0.598921	−	0.157731i
$601$		−	41.4937i		−	1.69256i	−0.532735	−	0.846282i	$-0.678836\pi$
$601$		−	41.4937i		−	1.69256i	0.532735	−	0.846282i	$-0.321164\pi$
$602$	−13.2253	+	3.98857i	−0.539022	+	0.162562i
$603$	7.39399	+	7.39399i	0.301107	+	0.301107i
$604$	3.21837	+	5.57438i	0.130954	+	0.226818i
$605$	5.03640	+	24.0756i	0.204759	+	0.978812i
$606$	−18.3515	+	31.7857i	−0.745477	+	1.29120i
$607$	−6.40193	+	23.8923i	−0.259847	+	0.969760i	0.705483	+	0.708727i	$0.250730\pi$
$607$	−6.40193	+	23.8923i	−0.259847	+	0.969760i	−0.965330	+	0.261034i	$0.915937\pi$
$608$	−0.122770	−	0.122770i	−0.00497899	−	0.00497899i
$609$	−1.65485	−	53.1714i	−0.0670579	−	2.15461i
$610$	−7.18318	−	0.961354i	−0.290838	−	0.0389241i
$611$	−2.85297	+	1.64716i	−0.115419	+	0.0666371i
$612$	35.6890	−	9.56285i	1.44264	−	0.386555i
$613$	−1.50058	−	5.60024i	−0.0606078	−	0.226192i	0.928978	−	0.370135i	$-0.120688\pi$
$613$	−1.50058	−	5.60024i	−0.0606078	−	0.226192i	−0.989586	+	0.143943i	$0.954022\pi$
$614$	13.5699	−	7.83461i	0.547638	−	0.316179i
$615$	32.1966	+	4.30900i	1.29829	+	0.173756i
$616$	−5.75669	+	6.62273i	−0.231944	+	0.266837i
$617$	−12.1840	+	12.1840i	−0.490511	+	0.490511i	−0.908467	−	0.417956i	$-0.862746\pi$
$617$	−12.1840	+	12.1840i	−0.490511	+	0.490511i	0.417956	+	0.908467i	$0.362746\pi$
$618$	−12.6576	−	3.39159i	−0.509162	−	0.136430i
$619$	−2.75556	−	1.59092i	−0.110755	−	0.0639445i	0.443599	−	0.896225i	$-0.353701\pi$
$619$	−2.75556	−	1.59092i	−0.110755	−	0.0639445i	−0.554354	+	0.832281i	$0.687035\pi$
$620$	−0.943783	−	7.28947i	−0.0379032	−	0.292752i
$621$	17.1197	+	29.6522i	0.686991	+	1.18990i
$622$	3.83491	+	3.83491i	0.153766	+	0.153766i
$623$	0.169343	+	0.561505i	0.00678457	+	0.0224962i
$624$	6.73764			0.269721
$625$	−0.214384	+	24.9991i	−0.00857535	+	0.999963i
$626$	24.9291	+	14.3928i	0.996366	+	0.575252i
$627$	0.814353	−	1.54581i	0.0325221	−	0.0617336i
$628$	2.05496	−	7.66923i	0.0820020	−	0.306036i
$629$	69.0151			2.75181
$630$	−13.0620	+	34.3134i	−0.520403	+	1.36708i
$631$	32.4996			1.29379			0.646893	−	0.762580i	$-0.276068\pi$
$631$	32.4996			1.29379			0.646893	+	0.762580i	$0.276068\pi$
$632$	−8.50830	−	2.27979i	−0.338442	−	0.0906853i
$633$	−2.79859	−	10.4445i	−0.111234	−	0.415131i
$634$	5.72063	−	9.90842i	0.227195	−	0.393514i
$635$	−5.19769	+	2.13991i	−0.206264	+	0.0849197i
$636$	20.4337			0.810249
$637$	14.7353	−	4.94904i	0.583835	−	0.196088i
$638$	−21.9621	+	0.851033i	−0.869486	+	0.0336927i
$639$	−57.6060	+	33.2588i	−2.27886	+	1.31570i
$640$	1.36503	−	1.77107i	0.0539576	−	0.0700077i
$641$	11.8777	−	20.5728i	0.469141	−	0.812576i	−0.530237	−	0.847849i	$-0.677897\pi$
$641$	11.8777	−	20.5728i	0.469141	−	0.812576i	0.999378	+	0.0352739i	$0.0112304\pi$
$642$	43.2222	+	11.5814i	1.70585	+	0.457080i
$643$	18.1265	+	18.1265i	0.714840	+	0.714840i	0.967544	−	0.252704i	$-0.0813198\pi$
$643$	18.1265	+	18.1265i	0.714840	+	0.714840i	−0.252704	+	0.967544i	$0.581320\pi$
$644$	−4.90491	−	7.91616i	−0.193280	−	0.311940i
$645$	21.5036	+	28.1488i	0.846705	+	1.10836i
$646$	0.895188	−	0.516837i	0.0352207	−	0.0203347i
$647$	7.24195	+	27.0273i	0.284710	+	1.06255i	0.949051	+	0.315124i	$0.102046\pi$
$647$	7.24195	+	27.0273i	0.284710	+	1.06255i	−0.664340	+	0.747430i	$0.731287\pi$
$648$	−2.82033	−	10.5256i	−0.110793	−	0.413485i
$649$	10.3889	−	45.7974i	0.407798	−	1.79771i
$650$	−2.91963	+	10.7123i	−0.114517	+	0.420170i
$651$	23.2521	+	12.4767i	0.911320	+	0.489001i
$652$	4.78470	−	4.78470i	0.187383	−	0.187383i
$653$	−2.29359	+	8.55981i	−0.0897553	+	0.334971i	−0.996172	−	0.0874130i	$-0.972140\pi$
$653$	−2.29359	+	8.55981i	−0.0897553	+	0.334971i	0.906417	+	0.422384i	$0.138807\pi$
$654$	−35.1477	−	20.2925i	−1.37438	−	0.793500i
$655$	2.80120	+	21.6355i	0.109452	+	0.845370i
$656$	4.14642	−	2.39394i	0.161891	−	0.0934676i
$657$	−34.8652	−	34.8652i	−1.36022	−	1.36022i
$658$	−2.86042	−	2.68775i	−0.111511	−	0.104779i
$659$	36.2312			1.41137			0.705685	−	0.708526i	$-0.250640\pi$
$659$	36.2312			1.41137			0.705685	+	0.708526i	$0.250640\pi$
$660$	21.0901	+	7.84488i	0.820929	+	0.305362i
$661$	−1.46096	+	2.53045i	−0.0568246	+	0.0984230i	−0.893038	−	0.449981i	$-0.851431\pi$
$661$	−1.46096	+	2.53045i	−0.0568246	+	0.0984230i	0.836214	+	0.548404i	$0.184764\pi$
$662$	3.18638	−	0.853787i	0.123842	−	0.0331834i
$663$	−10.3820	+	38.7460i	−0.403202	+	1.50477i
$664$			3.20222i			0.124270i
$665$	−0.104519	+	1.02184i	−0.00405307	+	0.0396252i
$666$		−	71.9422i		−	2.78770i
$667$	6.03696	−	22.5303i	0.233752	−	0.872375i
$668$	−1.97128	−	7.35692i	−0.0762711	−	0.284648i
$669$	48.1455	+	27.7968i	1.86141	+	1.07469i
$670$	−1.44925	+	3.47770i	−0.0559896	+	0.134355i
$671$	−7.88957	−	7.30093i	−0.304573	−	0.281849i
$672$	2.31790	+	7.68568i	0.0894150	+	0.296482i
$673$	−12.7070	+	12.7070i	−0.489819	+	0.489819i	−0.908249	−	0.418430i	$-0.862580\pi$
$673$	−12.7070	+	12.7070i	−0.489819	+	0.489819i	0.418430	+	0.908249i	$0.362580\pi$
$674$	14.1419	−	8.16481i	0.544724	−	0.314497i
$675$	48.6377	+	0.208546i	1.87207	+	0.00802695i
$676$	4.03446	−	6.98789i	0.155172	−	0.268765i
$677$	5.59473	−	20.8798i	0.215023	−	0.802476i	−0.771136	−	0.636671i	$-0.780311\pi$
$677$	5.59473	−	20.8798i	0.215023	−	0.802476i	0.986159	−	0.165805i	$-0.0530223\pi$
$678$	−37.3364	+	37.3364i	−1.43390	+	1.43390i
$679$	15.7117	+	25.3576i	0.602961	+	0.973135i
$680$	8.08149	+	10.5789i	0.309911	+	0.405682i
$681$	−56.5814	+	32.6673i	−2.16821	+	1.25181i
$682$	5.08146	−	9.64564i	0.194579	−	0.369351i
$683$	2.78893	−	0.747293i	0.106716	−	0.0285944i	−0.205066	−	0.978748i	$-0.565741\pi$
$683$	2.78893	−	0.747293i	0.106716	−	0.0285944i	0.311782	+	0.950154i	$0.399074\pi$
$684$	−0.538758	−	0.933156i	−0.0205999	−	0.0356801i
$685$	7.01016	+	0.938198i	0.267844	+	0.0358467i
$686$	10.7147	+	15.1061i	0.409089	+	0.576755i
$687$	9.82163	−	9.82163i	0.374719	−	0.374719i
$688$	5.04316	+	1.35131i	0.192269	+	0.0515183i
$689$	−7.47741	+	12.9513i	−0.284867	+	0.493404i
$690$	−14.5780	+	18.9144i	−0.554977	+	0.720058i
$691$	1.52075	+	2.63402i	0.0578522	+	0.100203i	0.893501	−	0.449061i	$-0.148241\pi$
$691$	1.52075	+	2.63402i	0.0578522	+	0.100203i	−0.835649	+	0.549264i	$0.814908\pi$
$692$	−10.2365	−	10.2365i	−0.389132	−	0.389132i
$693$	−45.1467	+	30.4538i	−1.71498	+	1.15685i
$694$		−	30.0031i		−	1.13890i
$695$	−11.7131	+	28.1074i	−0.444305	+	1.06618i
$696$	−10.0533	+	17.4128i	−0.381070	+	0.660032i
$697$	7.37759	+	27.5335i	0.279446	+	1.04291i
$698$	2.14747	−	8.01445i	0.0812828	−	0.303351i
$699$	78.1772			2.95693
$700$	−13.2240	+	0.354821i	−0.499820	+	0.0134110i
$701$		−	6.89263i		−	0.260331i	−0.991492	−	0.130166i	$-0.958449\pi$
$701$		−	6.89263i		−	0.260331i	0.991492	−	0.130166i	$-0.0415509\pi$
$702$	20.8652	+	5.59080i	0.787505	+	0.211011i
$703$	−0.520922	−	1.94411i	−0.0196470	−	0.0733234i
$704$	3.16797	−	0.981809i	0.119397	−	0.0370033i
$705$	−3.87167	+	9.29064i	−0.145815	+	0.349906i
$706$			25.3083i			0.952490i
$707$	21.9158	−	23.3237i	0.824227	−	0.877180i
$708$	−30.3782	−	30.3782i	−1.14168	−	1.14168i
$709$	−13.8771	+	8.01192i	−0.521164	+	0.300894i	−0.737411	−	0.675445i	$-0.763952\pi$
$709$	−13.8771	+	8.01192i	−0.521164	+	0.300894i	0.216247	+	0.976339i	$0.430618\pi$
$710$	−18.9827	−	14.6307i	−0.712407	−	0.549080i
$711$	−47.3418	−	27.3328i	−1.77546	−	1.02506i
$712$	0.0573725	−	0.214117i	0.00215013	−	0.00802438i
$713$	8.18136	+	8.18136i	0.306395	+	0.306395i
$714$	−47.7695	+	1.48673i	−1.78773	+	0.0556394i
$715$	−12.6898	+	10.4965i	−0.474573	+	0.392549i
$716$	−12.1354	−	21.0192i	−0.453523	−	0.785525i
$717$	3.31381	−	0.887933i	0.123757	−	0.0331605i
$718$	18.9126	−	5.06761i	0.705812	−	0.189122i
$719$	29.9863	−	17.3126i	1.11830	−	0.645650i	0.177332	−	0.984151i	$-0.443253\pi$
$719$	29.9863	−	17.3126i	1.11830	−	0.645650i	0.940966	+	0.338501i	$0.109920\pi$
$720$	11.0276	−	8.42425i	0.410973	−	0.313953i
$721$	10.0687	+	5.40272i	0.374978	+	0.201208i
$722$	13.4137	+	13.4137i	0.499207	+	0.499207i
$723$	−64.9852	−	17.4127i	−2.41683	−	0.647587i
$724$	−6.60554	−	3.81371i	−0.245493	−	0.141736i
$725$	−23.3285	−	23.5294i	−0.866400	−	0.873862i
$726$	18.8745	+	27.5261i	0.700498	+	1.02159i
$727$	−15.2561	+	15.2561i	−0.565816	+	0.565816i	−0.930954	−	0.365138i	$-0.881022\pi$
$727$	−15.2561	+	15.2561i	−0.565816	+	0.565816i	0.365138	+	0.930954i	$0.381022\pi$
$728$	−5.71953	−	1.34333i	−0.211980	−	0.0497872i
$729$			20.9184i			0.774756i
$730$	6.83373	−	16.3986i	0.252928	−	0.606938i
$731$	−15.5419	+	26.9194i	−0.574839	+	0.995650i
$732$	−9.49876	+	2.54519i	−0.351084	+	0.0940728i
$733$	−10.1203	−	2.71171i	−0.373800	−	0.100159i	0.0670277	−	0.997751i	$-0.478648\pi$
$733$	−10.1203	−	2.71171i	−0.373800	−	0.100159i	−0.440828	+	0.897592i	$0.645315\pi$
$734$	3.69167			0.136262
$735$	26.5967	−	39.3459i	0.981034	−	1.45129i
$736$			3.51981i			0.129742i
$737$	−4.72774	+	2.97942i	−0.174148	+	0.109748i
$738$	28.7013	−	7.69050i	1.05651	−	0.283091i
$739$	−13.0304	+	22.5694i	−0.479333	+	0.830228i	−0.999719	−	0.0237025i	$-0.992455\pi$
$739$	−13.0304	+	22.5694i	−0.479333	+	0.830228i	0.520386	+	0.853931i	$0.325788\pi$
$740$	23.9692	−	9.86821i	0.881125	−	0.362763i
$741$	1.16981			0.0429741
$742$	−17.3460	−	4.07402i	−0.636792	−	0.149562i
$743$	−14.8293	+	14.8293i	−0.544035	+	0.544035i	−0.924709	−	0.380674i	$-0.875692\pi$
$743$	−14.8293	+	14.8293i	−0.544035	+	0.544035i	0.380674	+	0.924709i	$0.375692\pi$
$744$	−4.98687	−	8.63750i	−0.182827	−	0.316666i
$745$	44.9970	−	5.82586i	1.64856	−	0.213443i
$746$	−4.64854	+	8.05152i	−0.170195	+	0.294787i
$747$	−5.14354	+	19.1960i	−0.188192	+	0.702344i
$748$	0.764574	+	19.7309i	0.0279556	+	0.721432i
$749$	−34.3820	−	18.4489i	−1.25629	−	0.674107i
$750$	12.7799	+	31.4234i	0.466654	+	1.14742i
$751$	3.47651	+	6.02149i	0.126860	+	0.219727i	0.922458	−	0.386097i	$-0.126177\pi$
$751$	3.47651	+	6.02149i	0.126860	+	0.219727i	−0.795599	+	0.605824i	$0.792844\pi$
$752$	0.383965	+	1.43298i	0.0140018	+	0.0522553i
$753$	−22.8303	+	6.11736i	−0.831982	+	0.222929i
$754$	−7.35772	−	12.7439i	−0.267952	−	0.464107i
$755$	−11.4375	+	8.73740i	−0.416253	+	0.317987i
$756$	0.800620	+	25.7244i	0.0291183	+	0.935589i
$757$	−30.5139	+	30.5139i	−1.10905	+	1.10905i	−0.115769	+	0.993276i	$0.536933\pi$
$757$	−30.5139	+	30.5139i	−1.10905	+	1.10905i	−0.993276	+	0.115769i	$0.963067\pi$
$758$	−1.58697	−	0.425227i	−0.0576414	−	0.0154450i
$759$	−33.8328	+	10.4854i	−1.22805	+	0.380595i
$760$	0.237001	−	0.307499i	0.00859695	−	0.0111542i
$761$	0.600352	−	0.346613i	0.0217627	−	0.0125647i	−0.489079	−	0.872239i	$-0.662667\pi$
$761$	0.600352	−	0.346613i	0.0217627	−	0.0125647i	0.510842	+	0.859675i	$0.329334\pi$
$762$	−5.39321	+	5.39321i	−0.195375	+	0.195375i
$763$	25.7907	+	24.2338i	0.933687	+	0.877323i
$764$			13.6818i			0.494990i
$765$	31.4529	+	76.3969i	1.13718	+	2.76214i
$766$	−14.4181	−	8.32428i	−0.520946	−	0.300768i
$767$	30.3707	−	8.13781i	1.09662	−	0.293839i
$768$	0.785295	−	2.93076i	0.0283369	−	0.105755i
$769$	1.97482			0.0712139			0.0356070	−	0.999366i	$-0.488664\pi$
$769$	1.97482			0.0712139			0.0356070	+	0.999366i	$0.488664\pi$
$770$	−16.3391	−	10.8643i	−0.588820	−	0.391524i
$771$	11.9098			0.428920
$772$	−3.52203	+	13.1444i	−0.126760	+	0.473076i
$773$	40.1761	−	10.7651i	1.44503	−	0.387195i	0.550740	−	0.834677i	$-0.314346\pi$
$773$	40.1761	−	10.7651i	1.44503	−	0.387195i	0.894293	+	0.447482i	$0.147679\pi$
$774$	28.0611	+	16.2011i	1.00864	+	0.582337i
$775$	15.8939	−	4.18579i	0.570924	−	0.150358i
$776$		−	11.2749i		−	0.404746i
$777$	−21.2774	+	90.5930i	−0.763321	+	3.25000i
$778$	8.55903	−	8.55903i	0.306856	−	0.306856i
$779$	0.719916	−	0.415644i	0.0257937	−	0.0148920i
$780$	1.93446	+	14.9411i	0.0692646	+	0.534977i
$781$	−10.5232	−	33.9550i	−0.376551	−	1.21500i
$782$	−20.2413	−	5.42365i	−0.723829	−	0.193949i
$783$	−45.5821	+	45.5821i	−1.62897	+	1.62897i
$784$	−0.435299	−	6.98645i	−0.0155464	−	0.249516i
$785$	17.5970	+	2.35508i	0.628063	+	0.0840563i
$786$	14.8013	+	25.6366i	0.527944	+	0.914426i
$787$	−0.695359	+	0.186321i	−0.0247869	+	0.00664163i	−0.271191	−	0.962526i	$-0.587418\pi$
$787$	−0.695359	+	0.186321i	−0.0247869	+	0.00664163i	0.246404	+	0.969167i	$0.420751\pi$
$788$	−4.63144	−	17.2848i	−0.164988	−	0.615744i
$789$	−44.9943	−	77.9324i	−1.60184	−	2.77447i
$790$	2.61274	−	19.5222i	0.0929571	−	0.694569i
$791$	39.1386	−	24.2505i	1.39161	−	0.862250i
$792$	20.5677	−	0.797001i	0.730842	−	0.0283202i
$793$	1.86275	−	6.95186i	0.0661481	−	0.246868i
$794$	2.15479	−	3.73221i	0.0764708	−	0.132451i
$795$	5.86676	+	45.3130i	0.208073	+	1.60708i
$796$	7.29381	+	12.6332i	0.258522	+	0.447773i
$797$	−5.38891	+	5.38891i	−0.190885	+	0.190885i	−0.796078	−	0.605194i	$-0.793096\pi$
$797$	−5.38891	+	5.38891i	−0.190885	+	0.190885i	0.605194	+	0.796078i	$0.293096\pi$
$798$	0.402442	+	1.33441i	0.0142463	+	0.0472377i
$799$	−8.83225			−0.312462
$800$	4.31937	+	2.51854i	0.152713	+	0.0890440i
$801$	0.687849	−	1.19139i	0.0243039	−	0.0420957i
$802$	−28.1707	+	7.54831i	−0.994741	+	0.266540i
$803$	22.2929	−	14.0490i	0.786699	−	0.495778i
$804$			5.11229i			0.180297i
$805$	16.1463	−	13.1497i	0.569082	−	0.463467i
$806$	7.29948			0.257113
$807$	−4.44375	−	1.19070i	−0.156427	−	0.0419146i
$808$	−11.6844	+	3.13084i	−0.411057	+	0.110142i
$809$	−27.8905	+	48.3078i	−0.980579	+	1.69841i	−0.320439	+	0.947269i	$0.603831\pi$
$809$	−27.8905	+	48.3078i	−0.980579	+	1.69841i	−0.660139	+	0.751143i	$0.729503\pi$
$810$	22.5314	−	9.27627i	0.791673	−	0.325935i
$811$			40.3966i			1.41852i	0.704948	+	0.709259i	$0.250970\pi$
$811$			40.3966i			1.41852i	−0.704948	+	0.709259i	$0.749030\pi$
$812$	12.0059	−	12.7772i	0.421325	−	0.448393i
$813$	22.7953	−	22.7953i	0.799467	−	0.799467i
$814$	37.4946	+	8.50542i	1.31419	+	0.298115i
$815$	11.9841	+	9.23661i	0.419785	+	0.323544i
$816$	15.6438	+	9.03197i	0.547643	+	0.316182i
$817$	0.875611	+	0.234619i	0.0306337	+	0.00820829i
$818$	10.0503	+	10.0503i	0.351401	+	0.351401i
$819$	−32.1285	−	17.2397i	−1.12266	−	0.602403i
$820$	6.49918	+	8.50761i	0.226961	+	0.297098i
$821$	−31.4310	+	18.1467i	−1.09695	+	0.633325i	−0.935418	−	0.353542i	$-0.884977\pi$
$821$	−31.4310	+	18.1467i	−1.09695	+	0.633325i	−0.161533	+	0.986867i	$0.551644\pi$
$822$	9.26997	−	2.48388i	0.323327	−	0.0866353i
$823$	−45.8192	+	12.2772i	−1.59716	+	0.427957i	−0.944182	−	0.329424i	$-0.893145\pi$
$823$	−45.8192	+	12.2772i	−1.59716	+	0.427957i	−0.652974	+	0.757381i	$0.726479\pi$
$824$	−2.15943	−	3.74025i	−0.0752274	−	0.130298i
$825$	−11.3413	+	49.0208i	−0.394853	+	1.70669i
$826$	19.7311	+	31.8446i	0.686533	+	1.10801i
$827$	−26.2169	−	26.2169i	−0.911651	−	0.911651i	0.0847510	−	0.996402i	$-0.472991\pi$
$827$	−26.2169	−	26.2169i	−0.911651	−	0.911651i	−0.996402	+	0.0847510i	$0.972991\pi$
$828$	−5.65368	+	21.0998i	−0.196479	+	0.733270i
$829$	35.1344	+	20.2849i	1.22027	+	0.704523i	0.964975	−	0.262341i	$-0.0844944\pi$
$829$	35.1344	+	20.2849i	1.22027	+	0.704523i	0.255294	+	0.966863i	$0.417828\pi$
$830$	−7.10111	+	0.919395i	−0.246483	+	0.0319127i
$831$	−32.4382	+	18.7282i	−1.12527	+	0.649673i
$832$	1.57020	+	1.57020i	0.0544370	+	0.0544370i
$833$	40.8476	+	8.26209i	1.41529	+	0.286264i
$834$			41.3185i			1.43074i
$835$	15.7484	−	6.48369i	0.544997	−	0.224377i
$836$	0.550034	−	0.170465i	0.0190233	−	0.00589566i
$837$	−8.27607	−	30.8867i	−0.286063	−	1.06760i
$838$	−17.4013	−	4.66266i	−0.601117	−	0.161069i
$839$		−	36.6709i		−	1.26602i	−0.774144	−	0.633009i	$-0.781819\pi$
$839$		−	36.6709i		−	1.26602i	0.774144	−	0.633009i	$-0.218181\pi$
$840$	−16.3779	+	7.34674i	−0.565093	+	0.253486i
$841$	14.9142			0.514283
$842$	2.73772	−	10.2173i	0.0943479	−	0.352111i
$843$	−11.3993	−	42.5428i	−0.392613	−	1.46525i
$844$	1.78187	−	3.08629i	0.0613346	−	0.106235i
$845$	16.6544	+	6.94035i	0.572929	+	0.238755i
$846$			9.20685i			0.316538i
$847$	−10.5343	−	27.1298i	−0.361964	−	0.932192i
$848$	4.76207	+	4.76207i	0.163530	+	0.163530i
$849$	10.7135	+	18.5562i	0.367685	+	0.636849i
$850$	−21.1390	+	20.9585i	−0.725062	+	0.718871i
$851$	−20.4013	+	35.3361i	−0.699348	+	1.21131i
$852$	−31.4125	−	8.41695i	−1.07617	−	0.288360i
$853$	27.7461	−	27.7461i	0.950009	−	0.950009i	−0.0487992	−	0.998809i	$-0.515539\pi$
$853$	27.7461	−	27.7461i	0.950009	−	0.950009i	0.998809	+	0.0487992i	$0.0155394\pi$
$854$	8.57088	−	0.266751i	0.293289	−	0.00912803i
$855$	1.91464	−	1.46265i	0.0654794	−	0.0500215i
$856$	7.37389	+	12.7720i	0.252034	+	0.436536i
$857$	10.6951	−	2.86573i	0.365337	−	0.0978916i	−0.0714805	−	0.997442i	$-0.522772\pi$
$857$	10.6951	−	2.86573i	0.365337	−	0.0978916i	0.436817	+	0.899550i	$0.356106\pi$
$858$	−10.4154	+	19.7705i	−0.355575	+	0.674954i
$859$	41.7079	−	24.0801i	1.42306	−	0.821602i	0.426497	−	0.904489i	$-0.359747\pi$
$859$	41.7079	−	24.0801i	1.42306	−	0.821602i	0.996559	+	0.0828871i	$0.0264141\pi$
$860$	−1.54866	+	11.5715i	−0.0528089	+	0.394584i
$861$	−38.4165	+	1.19564i	−1.30923	+	0.0407471i
$862$	13.2908	−	13.2908i	0.452685	−	0.452685i
$863$	3.64807	−	13.6148i	0.124182	−	0.463452i	−0.875628	−	0.482987i	$-0.839552\pi$
$863$	3.64807	−	13.6148i	0.124182	−	0.463452i	0.999809	+	0.0195349i	$0.00621853\pi$
$864$	4.86381	−	8.42437i	0.165470	−	0.286603i
$865$	19.7609	−	25.6389i	0.671892	−	0.871750i
$866$	0.566421	−	0.327023i	0.0192478	−	0.0111127i
$867$	−39.5725	+	39.5725i	−1.34395	+	1.34395i
$868$	2.51119	+	8.32658i	0.0852353	+	0.282623i
$869$	19.8423	−	21.4420i	0.673102	−	0.727371i
$870$	−41.5004	−	17.2944i	−1.40700	−	0.586334i
$871$	−3.24026	−	1.87077i	−0.109792	−	0.0633885i
$872$	−3.46199	−	12.9203i	−0.117238	−	0.437537i
$873$	18.1103	−	67.5884i	0.612940	−	2.28752i
$874$			0.611122i			0.0206715i
$875$	−4.58360	−	29.2231i	−0.154954	−	0.987922i
$876$		−	24.1062i		−	0.814473i
$877$	−7.65176	+	28.5567i	−0.258381	+	0.964293i	0.707796	+	0.706416i	$0.249689\pi$
$877$	−7.65176	+	28.5567i	−0.258381	+	0.964293i	−0.966178	+	0.257876i	$0.916977\pi$
$878$	−27.9072	+	7.47770i	−0.941821	+	0.252360i
$879$	49.0392	−	84.9383i	1.65405	−	2.86490i
$880$	3.08678	+	6.74328i	0.104055	+	0.227316i
$881$	4.28674			0.144424			0.0722120	−	0.997389i	$-0.476994\pi$
$881$	4.28674			0.144424			0.0722120	+	0.997389i	$0.476994\pi$
$882$	8.61251	−	42.5801i	0.289998	−	1.43375i
$883$	−10.7650	−	10.7650i	−0.362271	−	0.362271i	0.502377	−	0.864649i	$-0.332459\pi$
$883$	−10.7650	−	10.7650i	−0.362271	−	0.362271i	−0.864649	+	0.502377i	$0.832459\pi$
$884$	−11.4493	+	6.61023i	−0.385080	+	0.222326i
$885$	58.6435	−	76.0874i	1.97128	−	2.55765i
$886$	16.9537	+	9.78825i	0.569572	+	0.328843i
$887$	4.58259	−	17.1024i	0.153868	−	0.574244i	−0.845331	−	0.534242i	$-0.820597\pi$
$887$	4.58259	−	17.1024i	0.153868	−	0.574244i	0.999200	−	0.0400017i	$-0.0127363\pi$
$888$	24.8708	−	24.8708i	0.834610	−	0.834610i
$889$	5.65353	−	3.50297i	0.189613	−	0.117486i
$890$	0.491290	+	0.0657513i	0.0164681	+	0.00220399i
$891$	35.2455	+	7.99522i	1.18077	+	0.267850i
$892$	4.74225	+	17.6983i	0.158782	+	0.592584i
$893$	0.0666653	+	0.248798i	0.00223087	+	0.00832572i
$894$	53.3182	−	30.7833i	1.78323	−	1.02955i
$895$	43.1271	−	32.9459i	1.44158	−	1.10126i
$896$	−1.25096	+	2.33133i	−0.0417916	+	0.0778843i
$897$	−16.7692	−	16.7692i	−0.559907	−	0.559907i
$898$	30.7529	+	8.24022i	1.02624	+	0.274980i
$899$	−10.8916	+	18.8649i	−0.363257	+	0.629179i
$900$	21.8474	+	22.0356i	0.728247	+	0.734519i
$901$	−34.7230	+	20.0473i	−1.15679	+	0.667873i
$902$	0.614875	+	15.8677i	0.0204731	+	0.528336i
$903$	−30.5443	−	28.7004i	−1.01645	−	0.955090i
$904$	−17.4025			−0.578797
$905$	6.56060	−	15.7431i	0.218082	−	0.523320i
$906$	−9.76501	+	16.9135i	−0.324421	+	0.561913i
$907$	−5.26304	−	19.6419i	−0.174756	−	0.652200i	−0.996593	−	0.0824764i	$-0.973717\pi$
$907$	−5.26304	−	19.6419i	−0.174756	−	0.652200i	0.821837	−	0.569723i	$-0.192950\pi$
$908$	−20.7994	−	5.57318i	−0.690252	−	0.184952i
$909$	−75.0722			−2.48999
$910$	1.33677	−	13.0691i	0.0443136	−	0.433236i
$911$	22.8696			0.757704			0.378852	−	0.925457i	$-0.376319\pi$
$911$	22.8696			0.757704			0.378852	+	0.925457i	$0.376319\pi$
$912$	0.136346	−	0.508849i	0.00451485	−	0.0168497i
$913$	−9.39639	−	4.95015i	−0.310975	−	0.163826i
$914$	−10.2177	−	5.89919i	−0.337971	−	0.195128i
$915$	−8.37131	−	20.3333i	−0.276747	−	0.672199i
$916$	4.57786			0.151257
$917$	−7.45334	−	24.7137i	−0.246131	−	0.816119i
$918$	40.9513	+	40.9513i	1.35159	+	1.35159i
$919$	−5.54258	−	9.60002i	−0.182833	−	0.316676i	0.760011	−	0.649910i	$-0.225193\pi$
$919$	−5.54258	−	9.60002i	−0.182833	−	0.316676i	−0.942844	+	0.333234i	$0.891860\pi$
$920$	−7.80540	+	1.01058i	−0.257336	+	0.0333179i
$921$	41.1732	+	23.7713i	1.35670	+	0.783293i
$922$	−24.9955	−	6.69752i	−0.823182	−	0.220571i
$923$	16.8298	−	16.8298i	0.553958	−	0.553958i
$924$	−26.1355	−	5.07940i	−0.859796	−	0.167100i
$925$	28.7652	+	50.3198i	0.945794	+	1.65451i
$926$	11.7428	−	6.77970i	0.385892	−	0.222795i
$927$	−6.93715	−	25.8898i	−0.227846	−	0.850333i
$928$	−6.40098	+	1.71514i	−0.210122	+	0.0563021i
$929$	−49.3826	+	28.5111i	−1.62019	+	0.935418i	−0.633324	+	0.773887i	$0.718310\pi$
$929$	−49.3826	+	28.5111i	−1.62019	+	0.935418i	−0.986868	+	0.161531i	$0.948357\pi$
$930$	17.7224	−	13.5386i	0.581140	−	0.443948i
$931$	−0.0755781	−	1.21301i	−0.00247697	−	0.0397548i
$932$	18.2192	+	18.2192i	0.596788	+	0.596788i
$933$	−4.25895	+	15.8946i	−0.139432	+	0.520367i
$934$	1.77045	−	3.06651i	0.0579309	−	0.100339i
$935$	−43.5348	+	7.36045i	−1.42374	+	0.240713i
$936$	6.89059	+	11.9348i	0.225226	+	0.390103i
$937$	16.5248	+	16.5248i	0.539843	+	0.539843i	0.923483	−	0.383640i	$-0.125330\pi$
$937$	16.5248	+	16.5248i	0.539843	+	0.539843i	−0.383640	+	0.923483i	$0.625330\pi$
$938$	1.01927	−	4.33978i	0.0332805	−	0.141699i
$939$			87.3398i			2.85023i
$940$	−3.06747	+	1.26289i	−0.100050	+	0.0411909i
$941$	−29.3397	−	16.9393i	−0.956447	−	0.552205i	−0.0613692	−	0.998115i	$-0.519547\pi$
$941$	−29.3397	−	16.9393i	−0.956447	−	0.552205i	−0.895078	+	0.445910i	$0.852880\pi$
$942$	23.2696	−	6.23506i	0.758164	−	0.203149i
$943$	−16.2782	−	4.36173i	−0.530091	−	0.142037i
$944$		−	14.1593i		−	0.460845i
$945$	−56.8156	+	9.16121i	−1.84821	+	0.298014i
$946$	−11.7612	+	12.7094i	−0.382389	+	0.413219i
$947$	5.52842	+	1.48134i	0.179649	+	0.0481369i	0.347522	−	0.937672i	$-0.387023\pi$
$947$	5.52842	+	1.48134i	0.179649	+	0.0481369i	−0.167873	+	0.985809i	$0.553690\pi$
$948$	−6.91723	−	25.8154i	−0.224661	−	0.838447i
$949$	15.2789	+	8.82131i	0.495976	+	0.286352i
$950$	0.749943	+	0.437278i	0.0243314	+	0.0141872i
$951$	34.7145			1.12569
$952$	−11.4792	−	10.7862i	−0.372041	−	0.349582i
$953$	13.0527	−	13.0527i	0.422818	−	0.422818i	−0.463355	−	0.886173i	$-0.653354\pi$
$953$	13.0527	−	13.0527i	0.422818	−	0.422818i	0.886173	+	0.463355i	$0.153354\pi$
$954$	20.8976	+	36.1957i	0.676584	+	1.17188i
$955$	−30.3402	+	3.92821i	−0.981786	+	0.127114i
$956$	0.979215	+	0.565350i	0.0316701	+	0.0182847i
$957$	−35.5543	−	56.4175i	−1.14931	−	1.82372i
$958$	−22.4172	−	22.4172i	−0.724266	−	0.724266i
$959$	−8.36443	+	0.260326i	−0.270102	+	0.00840635i
$960$	6.72460	+	0.899981i	0.217036	+	0.0290468i
$961$	10.0973	+	17.4890i	0.325719	+	0.564162i
$962$	6.66248	+	24.8647i	0.214807	+	0.801670i
$963$	23.6885	+	88.4068i	0.763352	+	2.84887i
$964$	−11.0867	−	19.2028i	−0.357080	−	0.618481i
$965$	−30.1596	−	4.03639i	−0.970873	−	0.129936i
$966$	13.3598	−	24.8978i	0.429844	−	0.801072i
$967$	−9.95813	−	9.95813i	−0.320232	−	0.320232i	0.528624	−	0.848856i	$-0.322708\pi$
$967$	−9.95813	−	9.95813i	−0.320232	−	0.320232i	−0.848856	+	0.528624i	$0.822708\pi$
$968$	−2.01625	+	10.8136i	−0.0648048	+	0.347563i
$969$	2.71613	+	1.56816i	0.0872548	+	0.0503766i
$970$	25.0028	−	3.23716i	0.802791	−	0.103939i
$971$	9.06218	+	15.6962i	0.290819	+	0.503713i	0.974004	−	0.226532i	$-0.0727389\pi$
$971$	9.06218	+	15.6962i	0.290819	+	0.503713i	−0.683185	+	0.730246i	$0.739406\pi$
$972$	2.74353	−	2.74353i	0.0879989	−	0.0879989i
$973$	8.23797	−	35.0749i	0.264097	−	1.12445i
$974$	5.92259			0.189772
$975$	−32.5774	+	8.57954i	−1.04331	+	0.274765i
$976$	−2.80684	−	1.62053i	−0.0898447	−	0.0518718i
$977$	−5.99769	−	22.3837i	−0.191883	−	0.716117i	−0.993052	−	0.117678i	$-0.962455\pi$
$977$	−5.99769	−	22.3837i	−0.191883	−	0.716117i	0.801169	−	0.598438i	$-0.204212\pi$
$978$	19.8313	+	5.31377i	0.634134	+	0.169916i
$979$	0.539603	+	0.499344i	0.0172458	+	0.0159591i
$980$	15.3679	−	2.97120i	0.490909	−	0.0949114i
$981$		−	83.0127i		−	2.65039i
$982$	−23.7137	−	6.35406i	−0.756734	−	0.202766i
$983$	−13.9535	+	3.73882i	−0.445046	+	0.119250i	−0.474381	−	0.880320i	$-0.657328\pi$
$983$	−13.9535	+	3.73882i	−0.445046	+	0.119250i	0.0293342	+	0.999570i	$0.490661\pi$
$984$	12.5809	+	7.26356i	0.401063	+	0.231554i
$985$	37.0002	−	15.2331i	1.17892	−	0.485368i
$986$		−	39.4528i		−	1.25643i
$987$	2.72298	−	11.5937i	0.0866735	−	0.369031i
$988$	0.272624	+	0.272624i	0.00867332	+	0.00867332i
$989$	−9.18859	−	15.9151i	−0.292180	−	0.506071i
$990$	7.67263	+	45.3813i	0.243852	+	1.44231i
$991$	4.95833	−	8.58807i	0.157506	−	0.272809i	−0.776462	−	0.630164i	$-0.782988\pi$
$991$	4.95833	−	8.58807i	0.157506	−	0.272809i	0.933969	+	0.357354i	$0.116321\pi$
$992$	0.850780	−	3.17515i	0.0270123	−	0.100811i
$993$	7.07742	+	7.07742i	0.224595	+	0.224595i
$994$	24.9877	+	13.4080i	0.792561	+	0.425277i
$995$	−25.9208	+	19.8016i	−0.821745	+	0.627753i
$996$	−8.41431	+	4.85800i	−0.266617	+	0.153932i
$997$	8.45835	−	2.26641i	0.267878	−	0.0717778i	−0.122379	−	0.992483i	$-0.539052\pi$
$997$	8.45835	−	2.26641i	0.267878	−	0.0717778i	0.390258	+	0.920706i	$0.372386\pi$
$998$	−4.88792	−	18.2420i	−0.154724	−	0.577439i
$999$	97.6576	−	56.3827i	3.08975	−	1.78387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bd.a.263.2	✓	192
5.2	odd	4	inner	770.2.bd.a.417.23	yes	192
7.2	even	3	inner	770.2.bd.a.373.47	yes	192
11.10	odd	2	inner	770.2.bd.a.263.26	yes	192
35.2	odd	12	inner	770.2.bd.a.527.26	yes	192
55.32	even	4	inner	770.2.bd.a.417.47	yes	192
77.65	odd	6	inner	770.2.bd.a.373.23	yes	192
385.142	even	12	inner	770.2.bd.a.527.2	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bd.a.263.2	✓	192	1.1	even	1	trivial
770.2.bd.a.263.26	yes	192	11.10	odd	2	inner
770.2.bd.a.373.23	yes	192	77.65	odd	6	inner
770.2.bd.a.373.47	yes	192	7.2	even	3	inner
770.2.bd.a.417.23	yes	192	5.2	odd	4	inner
770.2.bd.a.417.47	yes	192	55.32	even	4	inner
770.2.bd.a.527.2	yes	192	385.142	even	12	inner
770.2.bd.a.527.26	yes	192	35.2	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-2.93076 + 0.785295i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.860133 - 2.06402i) q^{5} -3.03415i q^{6} +(-0.604940 + 2.57566i) q^{7} +(0.707107 - 0.707107i) q^{8} +(5.37460 - 3.10303i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-2.93076 + 0.785295i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.860133 - 2.06402i) q^{5} -3.03415i q^{6} +(-0.604940 + 2.57566i) q^{7} +(0.707107 - 0.707107i) q^{8} +(5.37460 - 3.10303i) q^{9} +(1.77107 + 1.36503i) q^{10} +(0.981809 + 3.16797i) q^{11} +(2.93076 + 0.785295i) q^{12} +(-1.57020 + 1.57020i) q^{13} +(-2.33133 - 1.25096i) q^{14} +(-0.899981 + 6.72460i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-5.75068 + 1.54089i) q^{17} +(1.60624 + 5.99458i) q^{18} +(0.0868117 + 0.150362i) q^{19} +(-1.77691 + 1.35743i) q^{20} +(-0.249721 - 8.02371i) q^{21} +(-3.31414 + 0.128423i) q^{22} +(0.910995 - 3.39988i) q^{23} +(-1.51707 + 2.62765i) q^{24} +(-3.52034 - 3.55066i) q^{25} +(-1.11030 - 1.92310i) q^{26} +(-6.87847 + 6.87847i) q^{27} +(1.81173 - 1.92812i) q^{28} +6.62678 q^{29} +(-6.26254 - 2.60977i) q^{30} +(-1.64358 + 2.84676i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-5.36524 - 8.51356i) q^{33} -5.95354i q^{34} +(4.79589 + 3.46402i) q^{35} -6.20605 q^{36} +(-11.1973 - 3.00030i) q^{37} +(-0.167707 + 0.0449370i) q^{38} +(3.36882 - 5.83496i) q^{39} +(-0.851275 - 2.06769i) q^{40} -4.78788i q^{41} +(7.81495 + 1.83548i) q^{42} +(3.69185 - 3.69185i) q^{43} +(0.733715 - 3.23445i) q^{44} +(-1.78183 - 13.7623i) q^{45} +(3.04825 + 1.75991i) q^{46} +(1.43298 + 0.383965i) q^{47} +(-2.14547 - 2.14547i) q^{48} +(-6.26809 - 3.11625i) q^{49} +(4.34081 - 2.48141i) q^{50} +(15.6438 - 9.03197i) q^{51} +(2.14494 - 0.574734i) q^{52} +(6.50511 - 1.74304i) q^{53} +(-4.86381 - 8.42437i) q^{54} +(7.38324 + 0.698406i) q^{55} +(1.39351 + 2.24903i) q^{56} +(-0.372503 - 0.372503i) q^{57} +(-1.71514 + 6.40098i) q^{58} +(-12.2623 - 7.07963i) q^{59} +(4.14171 - 5.37369i) q^{60} +(-2.80684 + 1.62053i) q^{61} +(-2.32437 - 2.32437i) q^{62} +(4.74104 + 15.7203i) q^{63} -1.00000i q^{64} +(1.89034 + 4.59151i) q^{65} +(9.61210 - 2.97895i) q^{66} +(0.436089 + 1.62751i) q^{67} +(5.75068 + 1.54089i) q^{68} +10.6796i q^{69} +(-4.58726 + 3.73592i) q^{70} -10.7182 q^{71} +(1.60624 - 5.99458i) q^{72} +(-2.05631 - 7.67425i) q^{73} +(5.79614 - 10.0392i) q^{74} +(13.1056 + 7.64163i) q^{75} -0.173623i q^{76} +(-8.75357 + 0.612377i) q^{77} +(4.76423 + 4.76423i) q^{78} +(-4.40422 - 7.62834i) q^{79} +(2.21756 - 0.287112i) q^{80} +(5.44846 - 9.43700i) q^{81} +(4.62473 + 1.23919i) q^{82} +(-2.26431 + 2.26431i) q^{83} +(-3.79559 + 7.07360i) q^{84} +(-1.76593 + 13.1949i) q^{85} +(2.61053 + 4.52158i) q^{86} +(-19.4215 + 5.20398i) q^{87} +(2.93434 + 1.54585i) q^{88} +(0.191972 - 0.110835i) q^{89} +(13.7545 + 1.84082i) q^{90} +(-3.09444 - 4.99420i) q^{91} +(-2.48888 + 2.48888i) q^{92} +(2.58139 - 9.63388i) q^{93} +(-0.741764 + 1.28477i) q^{94} +(0.385020 - 0.0498493i) q^{95} +(2.62765 - 1.51707i) q^{96} +(7.97257 - 7.97257i) q^{97} +(4.63236 - 5.24797i) q^{98} +(15.1071 + 13.9800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{5}+O(q^{10}) \) 192 * q + 8 * q^5	\( 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) \) 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more