LMFDB - Embedded newform 370.2.o.c.201.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (of order $9$, degree $6$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			201.4
Character	$\chi$	$=$	370.201
Dual form			370.2.o.c.81.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939693 + 0.342020i) q^{2} +(2.24358 - 0.816598i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.173648 - 0.984808i) q^{5} +2.38757 q^{6} +(-0.475008 + 2.69391i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.06871 - 1.73585i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.92933 - 5.07374i) q^{11} +(2.24358 + 0.816598i) q^{12} +(3.89606 + 3.26919i) q^{13} +(-1.36773 + 2.36898i) q^{14} +(-0.414598 - 2.35130i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.15996 + 0.973322i) q^{17} +(2.53764 - 0.923626i) q^{18} +(-6.25798 + 2.27772i) q^{19} +(0.766044 - 0.642788i) q^{20} +(1.13412 + 6.43190i) q^{21} +(-1.01734 - 5.76965i) q^{22} +(3.10642 - 5.38047i) q^{23} +(1.82899 + 1.53470i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(2.54298 + 4.40456i) q^{26} +(-0.357535 + 0.619269i) q^{27} +(-2.09549 + 1.75832i) q^{28} +(-4.30376 - 7.45432i) q^{29} +(0.414598 - 2.35130i) q^{30} +1.23811 q^{31} +(-0.173648 + 0.984808i) q^{32} +(-10.7154 - 8.99129i) q^{33} +(-1.42290 + 0.517894i) q^{34} +(2.57050 + 0.935584i) q^{35} +2.70050 q^{36} +(-4.86051 + 3.65724i) q^{37} -6.65960 q^{38} +(11.4108 + 4.15318i) q^{39} +(0.939693 - 0.342020i) q^{40} +(1.39076 + 1.16699i) q^{41} +(-1.13412 + 6.43190i) q^{42} +1.26019 q^{43} +(1.01734 - 5.76965i) q^{44} +(-1.35025 - 2.33870i) q^{45} +(4.75931 - 3.99353i) q^{46} +(-1.93843 + 3.35745i) q^{47} +(1.19379 + 2.06770i) q^{48} +(-0.453652 - 0.165116i) q^{49} +(-0.766044 - 0.642788i) q^{50} +(-1.80766 + 3.13095i) q^{51} +(0.883166 + 5.00868i) q^{52} +(0.432828 + 2.45469i) q^{53} +(-0.547776 + 0.459638i) q^{54} +(-5.50533 + 2.00378i) q^{55} +(-2.57050 + 0.935584i) q^{56} +(-12.1803 + 10.2205i) q^{57} +(-1.49468 - 8.47674i) q^{58} +(1.82451 + 10.3473i) q^{59} +(1.19379 - 2.06770i) q^{60} +(4.75102 + 3.98658i) q^{61} +(1.16344 + 0.423458i) q^{62} +(3.69357 + 6.39744i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(3.89606 - 3.26919i) q^{65} +(-6.99398 - 12.1139i) q^{66} +(1.89864 - 10.7677i) q^{67} -1.51422 q^{68} +(2.57583 - 14.6082i) q^{69} +(2.09549 + 1.75832i) q^{70} +(-9.53550 + 3.47064i) q^{71} +(2.53764 + 0.923626i) q^{72} +2.06593 q^{73} +(-5.81824 + 1.77429i) q^{74} -2.38757 q^{75} +(-6.25798 - 2.27772i) q^{76} +(15.0596 - 5.48126i) q^{77} +(9.30214 + 7.80542i) q^{78} +(2.80831 - 15.9267i) q^{79} +1.00000 q^{80} +(-1.70328 + 9.65977i) q^{81} +(0.907757 + 1.57228i) q^{82} +(0.660889 - 0.554552i) q^{83} +(-3.26556 + 5.65612i) q^{84} +(0.757110 + 1.31135i) q^{85} +(1.18419 + 0.431010i) q^{86} +(-15.7430 - 13.2100i) q^{87} +(2.92933 - 5.07374i) q^{88} +(-0.0179864 - 0.102006i) q^{89} +(-0.468937 - 2.65948i) q^{90} +(-10.6575 + 8.94274i) q^{91} +(5.83815 - 2.12491i) q^{92} +(2.77780 - 1.01104i) q^{93} +(-2.96984 + 2.49199i) q^{94} +(1.15643 + 6.55843i) q^{95} +(0.414598 + 2.35130i) q^{96} +(-1.62338 + 2.81178i) q^{97} +(-0.369821 - 0.310316i) q^{98} +(-14.8672 - 5.41121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{6} - 3 q^{7} + 12 q^{8} + 12 q^{9} + 12 q^{10} - 15 q^{11} + 3 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 36 q^{21} + 9 q^{22} + 21 q^{23} - 6 q^{26} - 12 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{31}+ \cdots + 63 q^{99}+O(q^{100}) $ 24 * q - 6 * q^6 - 3 * q^7 + 12 * q^8 + 12 * q^9 + 12 * q^10 - 15 * q^11 + 3 * q^14 - 6 * q^17 + 6 * q^18 - 6 * q^19 + 36 * q^21 + 9 * q^22 + 21 * q^23 - 6 * q^26 - 12 * q^27 - 3 * q^28 + 12 * q^29 + 30 * q^31 - 39 * q^33 - 21 * q^34 + 6 * q^35 + 54 * q^36 - 12 * q^37 - 36 * q^38 - 18 * q^39 + 27 * q^41 - 36 * q^42 - 24 * q^43 - 9 * q^44 - 27 * q^45 + 3 * q^46 - 6 * q^47 - 3 * q^48 - 27 * q^49 - 6 * q^51 - 9 * q^52 + 6 * q^53 + 9 * q^54 + 9 * q^55 - 6 * q^56 - 27 * q^57 + 27 * q^58 + 51 * q^59 - 3 * q^60 - 3 * q^62 - 27 * q^63 - 12 * q^64 + 15 * q^66 - 18 * q^69 + 3 * q^70 - 66 * q^71 + 6 * q^72 + 42 * q^73 - 42 * q^74 + 6 * q^75 - 6 * q^76 + 69 * q^77 + 36 * q^78 - 30 * q^79 + 24 * q^80 - 90 * q^81 + 24 * q^82 + 57 * q^83 + 6 * q^84 - 6 * q^86 + 6 * q^87 + 15 * q^88 - 57 * q^89 + 6 * q^90 + 3 * q^91 + 15 * q^92 - 72 * q^93 + 3 * q^94 - 15 * q^95 - 3 * q^97 - 72 * q^98 + 63 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	2.24358	−	0.816598i	1.29533	−	0.471463i	0.399860	−	0.916576i	$-0.369059\pi$
$3$	2.24358	−	0.816598i	1.29533	−	0.471463i	0.895474	+	0.445113i	$0.146837\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$6$	2.38757			0.974722
$7$	−0.475008	+	2.69391i	−0.179536	+	1.01820i	0.753240	+	0.657746i	$0.228490\pi$
$7$	−0.475008	+	2.69391i	−0.179536	+	1.01820i	−0.932776	+	0.360455i	$0.882621\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.06871	−	1.73585i	0.689568	−	0.578617i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−2.92933	−	5.07374i	−0.883225	−	1.52979i	−0.847734	−	0.530421i	$-0.822034\pi$
$11$	−2.92933	−	5.07374i	−0.883225	−	1.52979i	−0.0354909	−	0.999370i	$-0.511299\pi$
$12$	2.24358	+	0.816598i	0.647667	+	0.235732i
$13$	3.89606	+	3.26919i	1.08057	+	0.906709i	0.995968	−	0.0897054i	$-0.0285926\pi$
$13$	3.89606	+	3.26919i	1.08057	+	0.906709i	0.0846055	+	0.996415i	$0.473037\pi$
$14$	−1.36773	+	2.36898i	−0.365542	+	0.633137i
$15$	−0.414598	−	2.35130i	−0.107049	−	0.607103i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−1.15996	+	0.973322i	−0.281332	+	0.236065i	−0.772524	−	0.634986i	$-0.781006\pi$
$17$	−1.15996	+	0.973322i	−0.281332	+	0.236065i	0.491192	+	0.871051i	$0.336561\pi$
$18$	2.53764	−	0.923626i	0.598128	−	0.217701i
$19$	−6.25798	+	2.27772i	−1.43568	+	0.522544i	−0.938553	−	0.345134i	$-0.887833\pi$
$19$	−6.25798	+	2.27772i	−1.43568	+	0.522544i	−0.497126	+	0.867679i	$0.665611\pi$
$20$	0.766044	−	0.642788i	0.171293	−	0.143732i
$21$	1.13412	+	6.43190i	0.247485	+	1.40356i
$22$	−1.01734	−	5.76965i	−0.216899	−	1.23009i
$23$	3.10642	−	5.38047i	0.647733	−	1.12191i	−0.335930	−	0.941887i	$-0.609051\pi$
$23$	3.10642	−	5.38047i	0.647733	−	1.12191i	0.983663	−	0.180019i	$-0.0576159\pi$
$24$	1.82899	+	1.53470i	0.373340	+	0.313270i
$25$	−0.939693	−	0.342020i	−0.187939	−	0.0684040i
$26$	2.54298	+	4.40456i	0.498718	+	0.863806i
$27$	−0.357535	+	0.619269i	−0.0688077	+	0.119178i
$28$	−2.09549	+	1.75832i	−0.396010	+	0.332292i
$29$	−4.30376	−	7.45432i	−0.799187	−	1.38423i	−0.920146	−	0.391575i	$-0.871930\pi$
$29$	−4.30376	−	7.45432i	−0.799187	−	1.38423i	0.120959	−	0.992658i	$-0.461403\pi$
$30$	0.414598	−	2.35130i	0.0756948	−	0.429287i
$31$	1.23811			0.222371			0.111186	−	0.993800i	$-0.464535\pi$
$31$	1.23811			0.222371			0.111186	+	0.993800i	$0.464535\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−10.7154	−	8.99129i	−1.86531	−	1.56518i
$34$	−1.42290	+	0.517894i	−0.244026	+	0.0888181i
$35$	2.57050	+	0.935584i	0.434493	+	0.158143i
$36$	2.70050			0.450084
$37$	−4.86051	+	3.65724i	−0.799064	+	0.601247i
$37$	−4.86051	+	3.65724i	−0.799064	+	0.601247i
$38$	−6.65960			−1.08033
$39$	11.4108	+	4.15318i	1.82718	+	0.665041i
$40$	0.939693	−	0.342020i	0.148578	−	0.0540781i
$41$	1.39076	+	1.16699i	0.217201	+	0.182253i	0.744896	−	0.667181i	$-0.232499\pi$
$41$	1.39076	+	1.16699i	0.217201	+	0.182253i	−0.527695	+	0.849434i	$0.676944\pi$
$42$	−1.13412	+	6.43190i	−0.174998	+	0.992463i
$43$	1.26019			0.192177			0.0960885	−	0.995373i	$-0.469367\pi$
$43$	1.26019			0.192177			0.0960885	+	0.995373i	$0.469367\pi$
$44$	1.01734	−	5.76965i	0.153370	−	0.869807i
$45$	−1.35025	−	2.33870i	−0.201284	−	0.348633i
$46$	4.75931	−	3.99353i	0.701721	−	0.588814i
$47$	−1.93843	+	3.35745i	−0.282748	+	0.489735i	−0.972061	−	0.234730i	$-0.924579\pi$
$47$	−1.93843	+	3.35745i	−0.282748	+	0.489735i	0.689312	+	0.724464i	$0.257913\pi$
$48$	1.19379	+	2.06770i	0.172308	+	0.298447i
$49$	−0.453652	−	0.165116i	−0.0648074	−	0.0235880i
$50$	−0.766044	−	0.642788i	−0.108335	−	0.0909039i
$51$	−1.80766	+	3.13095i	−0.253122	+	0.438421i
$52$	0.883166	+	5.00868i	0.122473	+	0.694579i
$53$	0.432828	+	2.45469i	0.0594535	+	0.337178i	0.999997	−	0.00249601i	$-0.000794505\pi$
$53$	0.432828	+	2.45469i	0.0594535	+	0.337178i	−0.940543	+	0.339674i	$0.889683\pi$
$54$	−0.547776	+	0.459638i	−0.0745428	+	0.0625489i
$55$	−5.50533	+	2.00378i	−0.742339	+	0.270189i
$56$	−2.57050	+	0.935584i	−0.343497	+	0.125023i
$57$	−12.1803	+	10.2205i	−1.61332	+	1.35374i
$58$	−1.49468	−	8.47674i	−0.196261	−	1.11305i
$59$	1.82451	+	10.3473i	0.237531	+	1.34711i	0.837217	+	0.546871i	$0.184181\pi$
$59$	1.82451	+	10.3473i	0.237531	+	1.34711i	−0.599686	+	0.800235i	$0.704708\pi$
$60$	1.19379	−	2.06770i	0.154117	−	0.266939i
$61$	4.75102	+	3.98658i	0.608306	+	0.510430i	0.894103	−	0.447861i	$-0.147814\pi$
$61$	4.75102	+	3.98658i	0.608306	+	0.510430i	−0.285797	+	0.958290i	$0.592258\pi$
$62$	1.16344	+	0.423458i	0.147757	+	0.0537793i
$63$	3.69357	+	6.39744i	0.465345	+	0.806002i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	3.89606	−	3.26919i	0.483247	−	0.405493i
$66$	−6.99398	−	12.1139i	−0.860900	−	1.49112i
$67$	1.89864	−	10.7677i	0.231956	−	1.31549i	−0.616974	−	0.786984i	$-0.711641\pi$
$67$	1.89864	−	10.7677i	0.231956	−	1.31549i	0.848930	−	0.528506i	$-0.177247\pi$
$68$	−1.51422			−0.183626
$69$	2.57583	−	14.6082i	0.310093	−	1.75862i
$70$	2.09549	+	1.75832i	0.250459	+	0.210160i
$71$	−9.53550	+	3.47064i	−1.13166	+	0.411889i	−0.838893	−	0.544296i	$-0.816797\pi$
$71$	−9.53550	+	3.47064i	−1.13166	+	0.411889i	−0.292762	+	0.956185i	$0.594574\pi$
$72$	2.53764	+	0.923626i	0.299064	+	0.108850i
$73$	2.06593			0.241799			0.120900	−	0.992665i	$-0.461422\pi$
$73$	2.06593			0.241799			0.120900	+	0.992665i	$0.461422\pi$
$74$	−5.81824	+	1.77429i	−0.676357	+	0.206257i
$75$	−2.38757			−0.275693
$76$	−6.25798	−	2.27772i	−0.717839	−	0.261272i
$77$	15.0596	−	5.48126i	1.71621	−	0.624648i
$78$	9.30214	+	7.80542i	1.05326	+	0.883790i
$79$	2.80831	−	15.9267i	0.315960	−	1.79190i	−0.250826	−	0.968032i	$-0.580702\pi$
$79$	2.80831	−	15.9267i	0.315960	−	1.79190i	0.566786	−	0.823865i	$-0.308187\pi$
$80$	1.00000			0.111803
$81$	−1.70328	+	9.65977i	−0.189253	+	1.07331i
$82$	0.907757	+	1.57228i	0.100245	+	0.173629i
$83$	0.660889	−	0.554552i	0.0725420	−	0.0608700i	−0.605796	−	0.795620i	$-0.707145\pi$
$83$	0.660889	−	0.554552i	0.0725420	−	0.0608700i	0.678338	+	0.734750i	$0.262701\pi$
$84$	−3.26556	+	5.65612i	−0.356302	+	0.617133i
$85$	0.757110	+	1.31135i	0.0821201	+	0.142236i
$86$	1.18419	+	0.431010i	0.127694	+	0.0464770i
$87$	−15.7430	−	13.2100i	−1.68783	−	1.41626i
$88$	2.92933	−	5.07374i	0.312267	−	0.540863i
$89$	−0.0179864	−	0.102006i	−0.00190656	−	0.0108126i	0.983840	−	0.179052i	$-0.0573030\pi$
$89$	−0.0179864	−	0.102006i	−0.00190656	−	0.0108126i	−0.985746	+	0.168239i	$0.946192\pi$
$90$	−0.468937	−	2.65948i	−0.0494303	−	0.280333i
$91$	−10.6575	+	8.94274i	−1.11721	+	0.937454i
$92$	5.83815	−	2.12491i	0.608670	−	0.221538i
$93$	2.77780	−	1.01104i	0.288045	−	0.104840i
$94$	−2.96984	+	2.49199i	−0.306316	+	0.257029i
$95$	1.15643	+	6.55843i	0.118647	+	0.672881i
$96$	0.414598	+	2.35130i	0.0423147	+	0.239979i
$97$	−1.62338	+	2.81178i	−0.164830	+	0.285493i	−0.936595	−	0.350414i	$-0.886041\pi$
$97$	−1.62338	+	2.81178i	−0.164830	+	0.285493i	0.771765	+	0.635908i	$0.219374\pi$
$98$	−0.369821	−	0.310316i	−0.0373575	−	0.0313467i
$99$	−14.8672	−	5.41121i	−1.49421	−	0.543847i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.27347	−	5.66981i	0.325722	−	0.564167i	−0.655936	−	0.754816i	$-0.727726\pi$
$101$	3.27347	−	5.66981i	0.325722	−	0.564167i	0.981658	+	0.190649i	$0.0610593\pi$
$102$	−2.76949	+	2.32388i	−0.274220	+	0.230098i
$103$	−6.38584	−	11.0606i	−0.629215	−	1.08983i	−0.987709	−	0.156301i	$-0.950043\pi$
$103$	−6.38584	−	11.0606i	−0.629215	−	1.08983i	0.358494	−	0.933532i	$-0.383290\pi$
$104$	−0.883166	+	5.00868i	−0.0866016	+	0.491142i
$105$	6.53112			0.637372
$106$	−0.432828	+	2.45469i	−0.0420400	+	0.238421i
$107$	13.3100	+	11.1684i	1.28672	+	1.07969i	0.992280	+	0.124019i	$0.0395785\pi$
$107$	13.3100	+	11.1684i	1.28672	+	1.07969i	0.294443	+	0.955669i	$0.404866\pi$
$108$	−0.671946	+	0.244569i	−0.0646581	+	0.0235336i
$109$	15.4274	+	5.61513i	1.47768	+	0.537832i	0.950174	−	0.311719i	$-0.100905\pi$
$109$	15.4274	+	5.61513i	1.47768	+	0.537832i	0.527507	+	0.849551i	$0.323127\pi$
$110$	−5.85865			−0.558601
$111$	−7.91848	+	12.1744i	−0.751589	+	1.15554i
$112$	−2.73546			−0.258477
$113$	−13.0114	−	4.73575i	−1.22401	−	0.445502i	−0.352466	−	0.935825i	$-0.614657\pi$
$113$	−13.0114	−	4.73575i	−1.22401	−	0.445502i	−0.871541	+	0.490322i	$0.836879\pi$
$114$	−14.9414	+	5.43822i	−1.39939	+	0.509336i
$115$	−4.75931	−	3.99353i	−0.443808	−	0.372399i
$116$	1.49468	−	8.47674i	0.138777	−	0.787046i
$117$	13.7346			1.26977
$118$	−1.82451	+	10.3473i	−0.167960	+	0.952548i
$119$	−2.07105	−	3.58716i	−0.189853	−	0.328834i
$120$	1.82899	−	1.53470i	0.166963	−	0.140098i
$121$	−11.6619	+	20.1990i	−1.06017	+	1.83627i
$122$	3.10101	+	5.37111i	0.280752	+	0.486277i
$123$	4.07326	+	1.48255i	0.367273	+	0.133677i
$124$	0.948447	+	0.795842i	0.0851731	+	0.0714687i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$	1.28276	+	7.27490i	0.114278	+	0.648100i
$127$	−1.64911	−	9.35257i	−0.146335	−	0.829907i	−0.966286	−	0.257472i	$-0.917110\pi$
$127$	−1.64911	−	9.35257i	−0.146335	−	0.829907i	0.819951	−	0.572434i	$-0.194001\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	2.82734	−	1.02907i	0.248933	−	0.0906043i
$130$	4.77923	−	1.73950i	0.419166	−	0.152564i
$131$	14.8390	−	12.4514i	1.29649	−	1.08788i	0.305748	−	0.952112i	$-0.401093\pi$
$131$	14.8390	−	12.4514i	1.29649	−	1.08788i	0.990740	−	0.135770i	$-0.0433509\pi$
$132$	−2.42898	−	13.7755i	−0.211416	−	1.19900i
$133$	−3.16337	−	17.9403i	−0.274299	−	1.55563i
$134$	5.46693	−	9.46900i	0.472271	−	0.817997i
$135$	0.547776	+	0.459638i	0.0471450	+	0.0395594i
$136$	−1.42290	−	0.517894i	−0.122013	−	0.0444090i
$137$	−1.40803	−	2.43878i	−0.120296	−	0.208359i	0.799588	−	0.600549i	$-0.205051\pi$
$137$	−1.40803	−	2.43878i	−0.120296	−	0.208359i	−0.919885	+	0.392189i	$0.871718\pi$
$138$	7.41680	−	12.8463i	0.631360	−	1.09355i
$139$	−12.4751	+	10.4678i	−1.05812	+	0.887869i	−0.993924	−	0.110068i	$-0.964893\pi$
$139$	−12.4751	+	10.4678i	−1.05812	+	0.887869i	−0.0641972	+	0.997937i	$0.520449\pi$
$140$	1.36773	+	2.36898i	0.115594	+	0.200216i
$141$	−1.60733	+	9.11564i	−0.135362	+	0.767675i
$142$	−10.1475			−0.851556
$143$	5.17416	−	29.3441i	0.432685	−	2.45388i
$144$	2.06871	+	1.73585i	0.172392	+	0.144654i
$145$	−8.08841	+	2.94394i	−0.671706	+	0.244481i
$146$	1.94134	+	0.706590i	0.160667	+	0.0584778i
$147$	−1.15264			−0.0950681
$148$	−6.07420	−	0.322669i	−0.499296	−	0.0265232i
$149$	0.804648			0.0659193			0.0329597	−	0.999457i	$-0.489507\pi$
$149$	0.804648			0.0659193			0.0329597	+	0.999457i	$0.489507\pi$
$150$	−2.24358	−	0.816598i	−0.183188	−	0.0666749i
$151$	1.62878	−	0.592827i	0.132548	−	0.0482436i	−0.274894	−	0.961474i	$-0.588643\pi$
$151$	1.62878	−	0.592827i	0.132548	−	0.0482436i	0.407442	+	0.913231i	$0.366421\pi$
$152$	−5.10155	−	4.28071i	−0.413790	−	0.347211i
$153$	−0.710075	+	4.02703i	−0.0574061	+	0.325566i
$154$	16.0261			1.29142
$155$	0.214996	−	1.21930i	0.0172689	−	0.0979365i
$156$	6.07154	+	10.5162i	0.486112	+	0.841971i
$157$	9.39534	−	7.88362i	0.749830	−	0.629182i	−0.185628	−	0.982620i	$-0.559432\pi$
$157$	9.39534	−	7.88362i	0.749830	−	0.629182i	0.935458	+	0.353438i	$0.114988\pi$
$158$	8.08621	−	14.0057i	0.643305	−	1.11424i
$159$	2.97558	+	5.15386i	0.235979	+	0.408727i
$160$	0.939693	+	0.342020i	0.0742892	+	0.0270391i
$161$	13.0189	+	10.9242i	1.02603	+	0.860945i
$162$	−4.90440	+	8.49466i	−0.385326	+	0.667404i
$163$	−1.14531	−	6.49540i	−0.0897079	−	0.508759i	−0.996241	−	0.0866241i	$-0.972392\pi$
$163$	−1.14531	−	6.49540i	−0.0897079	−	0.508759i	0.906533	−	0.422135i	$-0.138719\pi$
$164$	0.315261	+	1.78793i	0.0246177	+	0.139614i
$165$	−10.7154	+	8.99129i	−0.834193	+	0.699971i
$166$	0.810701	−	0.295071i	0.0629226	−	0.0229019i
$167$	5.03558	−	1.83280i	0.389665	−	0.141826i	−0.139755	−	0.990186i	$-0.544632\pi$
$167$	5.03558	−	1.83280i	0.389665	−	0.141826i	0.529420	+	0.848360i	$0.322409\pi$
$168$	−5.00313	+	4.19812i	−0.386000	+	0.323892i
$169$	2.23431	+	12.6714i	0.171870	+	0.974724i
$170$	0.262942	+	1.49122i	0.0201667	+	0.114371i
$171$	−8.99214	+	15.5748i	−0.687646	+	1.19104i
$172$	0.965361	+	0.810034i	0.0736081	+	0.0617645i
$173$	12.7992	+	4.65854i	0.973107	+	0.354182i	0.779157	−	0.626829i	$-0.215648\pi$
$173$	12.7992	+	4.65854i	0.973107	+	0.354182i	0.193951	+	0.981011i	$0.437870\pi$
$174$	−10.2755	−	17.7977i	−0.778986	−	1.34924i
$175$	1.36773	−	2.36898i	0.103391	−	0.179078i
$176$	4.48799	−	3.76587i	0.338295	−	0.283863i
$177$	12.5430	+	21.7252i	0.942793	+	1.63297i
$178$	0.0179864	−	0.102006i	0.00134814	−	0.00764568i
$179$	−0.657445			−0.0491398			−0.0245699	−	0.999698i	$-0.507822\pi$
$179$	−0.657445			−0.0491398			−0.0245699	+	0.999698i	$0.507822\pi$
$180$	0.468937	−	2.65948i	0.0349525	−	0.198226i
$181$	6.78776	+	5.69561i	0.504530	+	0.423351i	0.859200	−	0.511641i	$-0.170962\pi$
$181$	6.78776	+	5.69561i	0.504530	+	0.423351i	−0.354669	+	0.934992i	$0.615407\pi$
$182$	−13.0734	+	4.75833i	−0.969066	+	0.352711i
$183$	13.9148	+	5.06456i	1.02861	+	0.374383i
$184$	6.21283			0.458016
$185$	2.75766	+	5.42174i	0.202747	+	0.398615i
$186$	2.95608			0.216750
$187$	8.33629	+	3.03416i	0.609610	+	0.221880i
$188$	−3.64305	+	1.32596i	−0.265697	+	0.0967056i
$189$	−1.49842	−	1.25732i	−0.108994	−	0.0914569i
$190$	−1.15643	+	6.55843i	−0.0838961	+	0.475798i
$191$	−19.7740			−1.43080			−0.715399	−	0.698716i	$-0.753755\pi$
$191$	−19.7740			−1.43080			−0.715399	+	0.698716i	$0.753755\pi$
$192$	−0.414598	+	2.35130i	−0.0299210	+	0.169690i
$193$	4.29106	+	7.43233i	0.308877	+	0.534991i	0.978117	−	0.208056i	$-0.0667135\pi$
$193$	4.29106	+	7.43233i	0.308877	+	0.534991i	−0.669240	+	0.743046i	$0.733380\pi$
$194$	−2.48717	+	2.08698i	−0.178568	+	0.149837i
$195$	6.07154	−	10.5162i	0.434792	−	0.753082i
$196$	−0.241383	−	0.418088i	−0.0172417	−	0.0298634i
$197$	24.7208	+	8.99763i	1.76128	+	0.641054i	0.999973	−	0.00733449i	$-0.00233466\pi$
$197$	24.7208	+	8.99763i	1.76128	+	0.641054i	0.761309	+	0.648389i	$0.224557\pi$
$198$	−12.1198	−	10.1697i	−0.861319	−	0.722732i
$199$	9.23243	−	15.9910i	0.654470	−	1.13357i	−0.327557	−	0.944831i	$-0.606225\pi$
$199$	9.23243	−	15.9910i	0.654470	−	1.13357i	0.982026	−	0.188743i	$-0.0604414\pi$
$200$	−0.173648	−	0.984808i	−0.0122788	−	0.0696364i
$201$	−4.53315	−	25.7088i	−0.319744	−	1.81336i
$202$	5.01524	−	4.20829i	0.352871	−	0.296094i
$203$	22.1256	−	8.05305i	1.55291	−	0.565213i
$204$	−3.39728	+	1.23651i	−0.237857	+	0.0865730i
$205$	1.39076	−	1.16699i	0.0971352	−	0.0815061i
$206$	−2.21778	−	12.5776i	−0.154520	−	0.876326i
$207$	−2.91343	−	16.5229i	−0.202497	−	1.14842i
$208$	−2.54298	+	4.40456i	−0.176324	+	0.305401i
$209$	29.8882	+	25.0792i	2.06741	+	1.73476i
$210$	6.13725	+	2.23377i	0.423510	+	0.154145i
$211$	9.17959	+	15.8995i	0.631949	+	1.09457i	0.987153	+	0.159779i	$0.0510782\pi$
$211$	9.17959	+	15.8995i	0.631949	+	1.09457i	−0.355204	+	0.934789i	$0.615588\pi$
$212$	−1.24628	+	2.15862i	−0.0855948	+	0.148254i
$213$	−18.5596	+	15.5733i	−1.27168	+	1.06707i
$214$	8.68746	+	15.0471i	0.593863	+	1.02860i
$215$	0.218829	−	1.24104i	0.0149240	−	0.0846385i
$216$	−0.715071			−0.0486544
$217$	−0.588113	+	3.33535i	−0.0399237	+	0.226418i
$218$	12.5766	+	10.5530i	0.851793	+	0.714739i
$219$	4.63509	−	1.68704i	0.313211	−	0.113999i
$220$	−5.50533	−	2.00378i	−0.371170	−	0.135095i
$221$	−7.70125			−0.518042
$222$	−11.6048	+	8.73193i	−0.778865	+	0.586049i
$223$	15.7788			1.05663			0.528313	−	0.849049i	$-0.322825\pi$
$223$	15.7788			1.05663			0.528313	+	0.849049i	$0.322825\pi$
$224$	−2.57050	−	0.935584i	−0.171748	−	0.0625113i
$225$	−2.53764	+	0.923626i	−0.169176	+	0.0615751i
$226$	−10.6070	−	8.90030i	−0.705565	−	0.592039i
$227$	0.527943	−	2.99411i	0.0350408	−	0.198726i	−0.962262	−	0.272125i	$-0.912274\pi$
$227$	0.527943	−	2.99411i	0.0350408	−	0.198726i	0.997303	+	0.0733990i	$0.0233846\pi$
$228$	−15.9003			−1.05302
$229$	−2.15256	+	12.2078i	−0.142245	+	0.806712i	0.827293	+	0.561771i	$0.189880\pi$
$229$	−2.15256	+	12.2078i	−0.142245	+	0.806712i	−0.969538	+	0.244941i	$0.921231\pi$
$230$	−3.10642	−	5.38047i	−0.204831	−	0.354778i
$231$	29.3116	−	24.5954i	1.92856	−	1.61826i
$232$	4.30376	−	7.45432i	0.282555	−	0.489400i
$233$	0.0279008	+	0.0483255i	0.00182784	+	0.00316591i	0.866938	−	0.498416i	$-0.166085\pi$
$233$	0.0279008	+	0.0483255i	0.00182784	+	0.00316591i	−0.865110	+	0.501582i	$0.832752\pi$
$234$	12.9063	+	4.69752i	0.843713	+	0.307086i
$235$	2.96984	+	2.49199i	0.193731	+	0.162560i
$236$	−5.25347	+	9.09928i	−0.341972	+	0.592313i
$237$	−6.70505	−	38.0262i	−0.435540	−	2.47007i
$238$	−0.719267	−	4.07917i	−0.0466232	−	0.264413i
$239$	−16.4210	+	13.7788i	−1.06219	+	0.891280i	−0.994322	−	0.106415i	$-0.966063\pi$
$239$	−16.4210	+	13.7788i	−1.06219	+	0.891280i	−0.0678639	+	0.997695i	$0.521618\pi$
$240$	2.24358	−	0.816598i	0.144823	−	0.0527112i
$241$	10.9016	−	3.96787i	0.702237	−	0.255593i	0.0338712	−	0.999426i	$-0.489216\pi$
$241$	10.9016	−	3.96787i	0.702237	−	0.255593i	0.668366	+	0.743833i	$0.266994\pi$
$242$	−17.8671	+	14.9923i	−1.14854	+	0.963739i
$243$	3.69419	+	20.9508i	0.236982	+	1.34399i
$244$	1.07697	+	6.10780i	0.0689459	+	0.391012i
$245$	−0.241383	+	0.418088i	−0.0154214	+	0.0267107i
$246$	3.32055	+	2.78627i	0.211711	+	0.177646i
$247$	−31.8278	−	11.5844i	−2.02515	−	0.737095i
$248$	0.619055	+	1.07223i	0.0393100	+	0.0680870i
$249$	1.02991	−	1.78386i	0.0652682	−	0.113048i
$250$	−0.766044	+	0.642788i	−0.0484489	+	0.0406535i
$251$	−8.31133	−	14.3956i	−0.524607	−	0.908645i	−0.999589	−	0.0286503i	$-0.990879\pi$
$251$	−8.31133	−	14.3956i	−0.524607	−	0.908645i	0.474983	−	0.879995i	$-0.342454\pi$
$252$	−1.28276	+	7.27490i	−0.0808064	+	0.458276i
$253$	−36.3988			−2.28838
$254$	1.64911	−	9.35257i	0.103474	−	0.586833i
$255$	2.76949	+	2.32388i	0.173432	+	0.145527i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−13.3985	−	4.87667i	−0.835777	−	0.304198i	−0.111550	−	0.993759i	$-0.535581\pi$
$257$	−13.3985	−	4.87667i	−0.835777	−	0.304198i	−0.724228	+	0.689561i	$0.757804\pi$
$258$	3.00879			0.187319
$259$	−7.54348	−	14.8310i	−0.468729	−	0.921553i
$260$	5.08595			0.315417
$261$	−21.8428	−	7.95012i	−1.35203	−	0.492100i
$262$	18.2027	−	6.62525i	1.12457	−	0.409309i
$263$	3.25932	+	2.73490i	0.200978	+	0.168641i	0.737722	−	0.675104i	$-0.235901\pi$
$263$	3.25932	+	2.73490i	0.200978	+	0.168641i	−0.536744	+	0.843745i	$0.680346\pi$
$264$	2.42898	−	13.7755i	0.149494	−	0.847821i
$265$	2.49256			0.153117
$266$	3.16337	−	17.9403i	0.193958	−	1.09999i
$267$	−0.123652	−	0.214172i	−0.00756738	−	0.0131071i
$268$	8.37582	−	7.02815i	0.511635	−	0.429312i
$269$	−0.621527	+	1.07652i	−0.0378952	+	0.0656363i	−0.884351	−	0.466823i	$-0.845399\pi$
$269$	−0.621527	+	1.07652i	−0.0378952	+	0.0656363i	0.846456	+	0.532459i	$0.178732\pi$
$270$	0.357535	+	0.619269i	0.0217589	+	0.0376875i
$271$	−1.42374	−	0.518199i	−0.0864861	−	0.0314784i	0.298415	−	0.954436i	$-0.403542\pi$
$271$	−1.42374	−	0.518199i	−0.0864861	−	0.0314784i	−0.384901	+	0.922958i	$0.625764\pi$
$272$	−1.15996	−	0.973322i	−0.0703329	−	0.0590163i
$273$	−16.6085	+	28.7667i	−1.00519	+	1.74104i
$274$	−0.489005	−	2.77328i	−0.0295419	−	0.167540i
$275$	1.01734	+	5.76965i	0.0613482	+	0.347923i
$276$	11.3632	−	9.53485i	0.683984	−	0.573930i
$277$	12.8735	−	4.68556i	0.773492	−	0.281528i	0.0750359	−	0.997181i	$-0.476093\pi$
$277$	12.8735	−	4.68556i	0.773492	−	0.281528i	0.698456	+	0.715653i	$0.253871\pi$
$278$	−15.3029	+	5.56981i	−0.917809	+	0.334055i
$279$	2.56128	−	2.14917i	0.153340	−	0.128668i
$280$	0.475008	+	2.69391i	0.0283872	+	0.160992i
$281$	−1.59474	−	9.04424i	−0.0951345	−	0.539534i	−0.994706	−	0.102761i	$-0.967232\pi$
$281$	−1.59474	−	9.04424i	−0.0951345	−	0.539534i	0.899572	−	0.436773i	$-0.143879\pi$
$282$	−4.62813	+	8.01616i	−0.275601	+	0.477355i
$283$	0.269706	+	0.226310i	0.0160323	+	0.0134527i	0.650769	−	0.759276i	$-0.274447\pi$
$283$	0.269706	+	0.226310i	0.0160323	+	0.0134527i	−0.634736	+	0.772729i	$0.718891\pi$
$284$	−9.53550	−	3.47064i	−0.565828	−	0.205944i
$285$	7.95014	+	13.7701i	0.470926	+	0.815667i
$286$	14.8984	−	25.8048i	0.880962	−	1.52587i
$287$	−3.80439	+	3.19226i	−0.224566	+	0.188433i
$288$	1.35025	+	2.33870i	0.0795643	+	0.137809i
$289$	−2.55387	+	14.4837i	−0.150227	+	0.851982i
$290$	−8.60751			−0.505450
$291$	−1.34610	+	7.63413i	−0.0789099	+	0.447521i
$292$	1.58260	+	1.32796i	0.0926144	+	0.0777127i
$293$	8.97267	−	3.26578i	0.524189	−	0.190789i	−0.0663529	−	0.997796i	$-0.521136\pi$
$293$	8.97267	−	3.26578i	0.524189	−	0.190789i	0.590542	+	0.807007i	$0.298914\pi$
$294$	−1.08313	−	0.394226i	−0.0631693	−	0.0229917i
$295$	10.5069			0.611738
$296$	−5.59752	−	2.38071i	−0.325349	−	0.138376i
$297$	4.18935			0.243091
$298$	0.756122	+	0.275206i	0.0438010	+	0.0159422i
$299$	29.6926	−	10.8072i	1.71717	−	0.624997i
$300$	−1.82899	−	1.53470i	−0.105597	−	0.0886061i
$301$	−0.598600	+	3.39483i	−0.0345027	+	0.195675i
$302$	1.73331			0.0997407
$303$	2.71434	−	15.3938i	0.155935	−	0.884351i
$304$	−3.32980	−	5.76738i	−0.190977	−	0.330782i
$305$	4.75102	−	3.98658i	0.272043	−	0.228271i
$306$	−2.04458	+	3.54131i	−0.116881	+	0.202443i
$307$	−6.77068	−	11.7272i	−0.386423	−	0.669305i	0.605542	−	0.795813i	$-0.292956\pi$
$307$	−6.77068	−	11.7272i	−0.386423	−	0.669305i	−0.991966	+	0.126509i	$0.959623\pi$
$308$	15.0596	+	5.48126i	0.858103	+	0.312324i
$309$	−23.3592	−	19.6007i	−1.32886	−	1.11505i
$310$	0.619055	−	1.07223i	0.0351600	−	0.0608988i
$311$	−3.33296	−	18.9022i	−0.188995	−	1.07184i	−0.920714	−	0.390237i	$-0.872393\pi$
$311$	−3.33296	−	18.9022i	−0.188995	−	1.07184i	0.731719	−	0.681606i	$-0.238718\pi$
$312$	2.10862	+	11.9586i	0.119377	+	0.677022i
$313$	−9.63808	+	8.08731i	−0.544776	+	0.457122i	−0.873168	−	0.487420i	$-0.837938\pi$
$313$	−9.63808	+	8.08731i	−0.544776	+	0.457122i	0.328391	+	0.944542i	$0.393494\pi$
$314$	11.5251	−	4.19479i	0.650398	−	0.236726i
$315$	6.94163	−	2.52655i	0.391117	−	0.142355i
$316$	12.3888	−	10.3954i	0.696924	−	0.584789i
$317$	−0.867978	−	4.92255i	−0.0487505	−	0.276478i	0.950682	−	0.310168i	$-0.100385\pi$
$317$	−0.867978	−	4.92255i	−0.0487505	−	0.276478i	−0.999432	+	0.0336900i	$0.989274\pi$
$318$	1.03341	+	5.86075i	0.0579507	+	0.328655i
$319$	−25.2142	+	43.6723i	−1.41172	+	2.44518i
$320$	0.766044	+	0.642788i	0.0428232	+	0.0359329i
$321$	38.9821	+	14.1883i	2.17577	+	0.791915i
$322$	8.49749	+	14.7181i	0.473547	+	0.820207i
$323$	5.04205	−	8.73309i	0.280547	−	0.485922i
$324$	−7.51397	+	6.30497i	−0.417443	+	0.350276i
$325$	−2.54298	−	4.40456i	−0.141059	−	0.244321i
$326$	1.14531	−	6.49540i	0.0634330	−	0.359747i
$327$	39.1981			2.16766
$328$	−0.315261	+	1.78793i	−0.0174074	+	0.0987221i
$329$	−8.12389	−	6.81675i	−0.447885	−	0.375820i
$330$	−13.1444	+	4.78416i	−0.723575	+	0.263360i
$331$	−31.2014	−	11.3564i	−1.71498	−	0.624203i	−0.717597	−	0.696459i	$-0.754758\pi$
$331$	−31.2014	−	11.3564i	−1.71498	−	0.624203i	−0.997386	+	0.0722557i	$0.976980\pi$
$332$	0.862730			0.0473484
$333$	−3.70655	+	16.0029i	−0.203118	+	0.876952i
$334$	5.35876			0.293218
$335$	−10.2745	−	3.73960i	−0.561354	−	0.204316i
$336$	−6.13725	+	2.23377i	−0.334814	+	0.121862i
$337$	−9.34228	−	7.83911i	−0.508907	−	0.427023i	0.351838	−	0.936061i	$-0.385557\pi$
$337$	−9.34228	−	7.83911i	−0.508907	−	0.427023i	−0.860744	+	0.509038i	$0.830001\pi$
$338$	−2.23431	+	12.6714i	−0.121531	+	0.689234i
$339$	−33.0593			−1.79554
$340$	−0.262942	+	1.49122i	−0.0142600	+	0.0808725i
$341$	−3.62683	−	6.28185i	−0.196404	−	0.340181i
$342$	−13.7768	+	11.5601i	−0.744962	+	0.625097i
$343$	−8.91383	+	15.4392i	−0.481302	+	0.833639i
$344$	0.630094	+	1.09136i	0.0339724	+	0.0588419i
$345$	−13.9390	−	5.07339i	−0.750451	−	0.273142i
$346$	10.4340	+	8.75519i	0.560937	+	0.470682i
$347$	−10.6942	+	18.5229i	−0.574094	+	0.994360i	0.422045	+	0.906575i	$0.361312\pi$
$347$	−10.6942	+	18.5229i	−0.574094	+	0.994360i	−0.996139	+	0.0877853i	$0.972021\pi$
$348$	−3.56865	−	20.2388i	−0.191300	−	1.08492i
$349$	2.38005	+	13.4979i	0.127401	+	0.722528i	0.979853	+	0.199722i	$0.0640039\pi$
$349$	2.38005	+	13.4979i	0.127401	+	0.722528i	−0.852451	+	0.522807i	$0.824885\pi$
$350$	2.09549	−	1.75832i	0.112009	−	0.0939863i
$351$	−3.41749	+	1.24386i	−0.182412	+	0.0663925i
$352$	5.50533	−	2.00378i	0.293435	−	0.106802i
$353$	−8.33948	+	6.99765i	−0.443866	+	0.372448i	−0.837154	−	0.546968i	$-0.815782\pi$
$353$	−8.33948	+	6.99765i	−0.443866	+	0.372448i	0.393288	+	0.919415i	$0.371338\pi$
$354$	4.35615	+	24.7050i	0.231527	+	1.31305i
$355$	1.76209	+	9.99330i	0.0935219	+	0.530389i
$356$	0.0517898	−	0.0897026i	0.00274486	−	0.00475423i
$357$	−7.57584	−	6.35688i	−0.400956	−	0.336442i
$358$	−0.617796	−	0.224859i	−0.0326516	−	0.0118842i
$359$	−9.33692	−	16.1720i	−0.492784	−	0.853527i	0.507182	−	0.861839i	$-0.330687\pi$
$359$	−9.33692	−	16.1720i	−0.492784	−	0.853527i	−0.999965	+	0.00831257i	$0.997354\pi$
$360$	1.35025	−	2.33870i	0.0711645	−	0.123261i
$361$	19.4195	−	16.2949i	1.02208	−	0.857624i
$362$	4.43040	+	7.67367i	0.232856	+	0.403319i
$363$	−9.67000	+	54.8413i	−0.507543	+	2.87842i
$364$	−13.9124			−0.729210
$365$	0.358745	−	2.03455i	0.0187776	−	0.106493i
$366$	11.3434	+	9.51825i	0.592930	+	0.497527i
$367$	−24.2864	+	8.83954i	−1.26774	+	0.461420i	−0.886360	−	0.462997i	$-0.846774\pi$
$367$	−24.2864	+	8.83954i	−1.26774	+	0.461420i	−0.381382	+	0.924417i	$0.624552\pi$
$368$	5.83815	+	2.12491i	0.304335	+	0.110769i
$369$	4.90280			0.255230
$370$	0.737006	+	6.03795i	0.0383151	+	0.313898i
$371$	−6.81830			−0.353989
$372$	2.77780	+	1.01104i	0.144022	+	0.0524199i
$373$	−18.1066	+	6.59025i	−0.937523	+	0.341230i	−0.765187	−	0.643808i	$-0.777354\pi$
$373$	−18.1066	+	6.59025i	−0.937523	+	0.341230i	−0.172336	+	0.985038i	$0.555131\pi$
$374$	6.79580	+	5.70236i	0.351403	+	0.294862i
$375$	−0.414598	+	2.35130i	−0.0214097	+	0.121421i
$376$	−3.87685			−0.199933
$377$	7.60186	−	43.1123i	0.391516	−	2.22040i
$378$	−0.978025	−	1.69399i	−0.0503042	−	0.0871294i
$379$	−17.1475	+	14.3885i	−0.880809	+	0.739087i	−0.966345	−	0.257248i	$-0.917184\pi$
$379$	−17.1475	+	14.3885i	−0.880809	+	0.739087i	0.0855360	+	0.996335i	$0.472740\pi$
$380$	−3.32980	+	5.76738i	−0.170815	+	0.295861i
$381$	−11.3372	−	19.6366i	−0.580823	−	1.00601i
$382$	−18.5815	−	6.76311i	−0.950712	−	0.346031i
$383$	−18.9267	−	15.8814i	−0.967110	−	0.811502i	0.0149851	−	0.999888i	$-0.495230\pi$
$383$	−18.9267	−	15.8814i	−0.967110	−	0.811502i	−0.982095	+	0.188386i	$0.939674\pi$
$384$	−1.19379	+	2.06770i	−0.0609202	+	0.105517i
$385$	−2.78291	−	15.7827i	−0.141830	−	0.804359i
$386$	1.49027	+	8.45173i	0.0758527	+	0.430182i
$387$	2.60696	−	2.18750i	0.132519	−	0.111197i
$388$	−3.05096	+	1.11046i	−0.154889	+	0.0563751i
$389$	25.7830	−	9.38425i	1.30725	−	0.475800i	0.407899	−	0.913027i	$-0.366262\pi$
$389$	25.7830	−	9.38425i	1.30725	−	0.475800i	0.899351	+	0.437227i	$0.144039\pi$
$390$	9.30214	−	7.80542i	0.471032	−	0.395243i
$391$	1.63361	+	9.26468i	0.0826153	+	0.468535i
$392$	−0.0838315	−	0.475432i	−0.00423413	−	0.0240129i
$393$	23.1247	−	40.0532i	1.16649	−	2.02042i
$394$	20.1526	+	16.9100i	1.01527	+	0.851914i
$395$	−15.1971	−	5.53130i	−0.764650	−	0.278310i
$396$	−7.91066	−	13.7017i	−0.397525	−	0.688534i
$397$	−15.4879	+	26.8258i	−0.777314	+	1.34635i	0.156171	+	0.987730i	$0.450085\pi$
$397$	−15.4879	+	26.8258i	−0.777314	+	1.34635i	−0.933485	+	0.358617i	$0.883248\pi$
$398$	14.1449	−	11.8690i	0.709020	−	0.594938i
$399$	−21.7473	−	37.6675i	−1.08873	−	1.88573i
$400$	0.173648	−	0.984808i	0.00868241	−	0.0492404i
$401$	−0.377257			−0.0188393			−0.00941966	−	0.999956i	$-0.502998\pi$
$401$	−0.377257			−0.0188393			−0.00941966	+	0.999956i	$0.502998\pi$
$402$	4.53315	−	25.7088i	0.226093	−	1.28224i
$403$	4.82376	+	4.04761i	0.240288	+	0.201626i
$404$	6.15211	−	2.23918i	0.306079	−	0.111404i
$405$	9.21725	+	3.35480i	0.458009	+	0.166702i
$406$	23.5455			1.16855
$407$	32.7939	+	13.9477i	1.62553	+	0.691364i
$408$	−3.61531			−0.178985
$409$	13.1305	+	4.77911i	0.649261	+	0.236312i	0.645593	−	0.763682i	$-0.276610\pi$
$409$	13.1305	+	4.77911i	0.649261	+	0.236312i	0.00366789	+	0.999993i	$0.498832\pi$
$410$	1.70603	−	0.620943i	0.0842546	−	0.0306662i
$411$	−5.15055	−	4.32182i	−0.254058	−	0.213180i
$412$	2.21778	−	12.5776i	0.109262	−	0.619656i
$413$	−28.7414			−1.41427
$414$	2.91343	−	16.5229i	0.143187	−	0.812055i
$415$	−0.431365	−	0.747146i	−0.0211749	−	0.0366759i
$416$	−3.89606	+	3.26919i	−0.191020	+	0.160285i
$417$	−19.4409	+	33.6726i	−0.952023	+	1.64895i
$418$	19.5082	+	33.7891i	0.954175	+	1.65268i
$419$	−7.00802	−	2.55071i	−0.342364	−	0.124610i	0.165115	−	0.986274i	$-0.447200\pi$
$419$	−7.00802	−	2.55071i	−0.342364	−	0.124610i	−0.507479	+	0.861664i	$0.669423\pi$
$420$	5.00313	+	4.19812i	0.244128	+	0.204847i
$421$	12.4175	−	21.5078i	0.605194	−	1.04823i	−0.386827	−	0.922152i	$-0.626429\pi$
$421$	12.4175	−	21.5078i	0.605194	−	1.04823i	0.992021	−	0.126074i	$-0.0402376\pi$
$422$	3.18804	+	18.0803i	0.155191	+	0.880134i
$423$	1.81800	+	10.3104i	0.0883942	+	0.501308i
$424$	−1.90941	+	1.60219i	−0.0927291	+	0.0778090i
$425$	1.42290	−	0.517894i	0.0690209	−	0.0251215i
$426$	−22.7667	+	8.28640i	−1.10305	+	0.401477i
$427$	−12.9963	+	10.9052i	−0.628933	+	0.527737i
$428$	3.01712	+	17.1110i	0.145838	+	0.827089i
$429$	−12.3537	−	70.0613i	−0.596442	−	3.38259i
$430$	0.630094	−	1.09136i	0.0303858	−	0.0526298i
$431$	9.19639	+	7.71669i	0.442975	+	0.371700i	0.836821	−	0.547476i	$-0.184411\pi$
$431$	9.19639	+	7.71669i	0.442975	+	0.371700i	−0.393847	+	0.919176i	$0.628856\pi$
$432$	−0.671946	−	0.244569i	−0.0323290	−	0.0117668i
$433$	−2.28322	−	3.95465i	−0.109724	−	0.190048i	0.805934	−	0.592005i	$-0.201663\pi$
$433$	−2.28322	−	3.95465i	−0.109724	−	0.190048i	−0.915659	+	0.401957i	$0.868330\pi$
$434$	−1.69340	+	2.93306i	−0.0812859	+	0.140791i
$435$	−15.7430	+	13.2100i	−0.754820	+	0.633369i
$436$	8.20877	+	14.2180i	0.393129	+	0.680919i
$437$	−7.18469	+	40.7464i	−0.343690	+	1.94917i
$438$	4.93256			0.235687
$439$	−0.351997	+	1.99627i	−0.0167999	+	0.0952769i	−0.992055	−	0.125806i	$-0.959848\pi$
$439$	−0.351997	+	1.99627i	−0.0167999	+	0.0952769i	0.975255	+	0.221083i	$0.0709593\pi$
$440$	−4.48799	−	3.76587i	−0.213956	−	0.179531i
$441$	−1.22509	+	0.445896i	−0.0583376	+	0.0212331i
$442$	−7.23681	−	2.63398i	−0.344220	−	0.125286i
$443$	−4.75222			−0.225785			−0.112892	−	0.993607i	$-0.536012\pi$
$443$	−4.75222			−0.225785			−0.112892	+	0.993607i	$0.536012\pi$
$444$	−13.8915	+	4.23624i	−0.659260	+	0.201043i
$445$	−0.103580			−0.00491015
$446$	14.8272	+	5.39667i	0.702090	+	0.255540i
$447$	1.80530	−	0.657074i	0.0853876	−	0.0310785i
$448$	−2.09549	−	1.75832i	−0.0990025	−	0.0830729i
$449$	−3.30294	+	18.7319i	−0.155876	+	0.884014i	0.802105	+	0.597182i	$0.203713\pi$
$449$	−3.30294	+	18.7319i	−0.155876	+	0.884014i	−0.957981	+	0.286832i	$0.907398\pi$
$450$	−2.70050			−0.127303
$451$	1.84700	−	10.4749i	0.0869720	−	0.493243i
$452$	−6.92321	−	11.9913i	−0.325640	−	0.564026i
$453$	3.17020	−	2.66011i	0.148949	−	0.124983i
$454$	1.52015	−	2.63298i	0.0713442	−	0.123572i
$455$	6.95622	+	12.0485i	0.326113	+	0.564844i
$456$	−14.9414	−	5.43822i	−0.699694	−	0.254668i
$457$	−12.5068	−	10.4945i	−0.585044	−	0.490910i	0.301555	−	0.953449i	$-0.402494\pi$
$457$	−12.5068	−	10.4945i	−0.585044	−	0.490910i	−0.886599	+	0.462538i	$0.846939\pi$
$458$	−6.19805	+	10.7353i	−0.289616	+	0.501629i
$459$	−0.188022	−	1.06632i	−0.00877611	−	0.0497718i
$460$	−1.07885	−	6.11845i	−0.0503015	−	0.285274i
$461$	−19.2773	+	16.1756i	−0.897835	+	0.753373i	−0.969766	−	0.244037i	$-0.921528\pi$
$461$	−19.2773	+	16.1756i	−0.897835	+	0.753373i	0.0719313	+	0.997410i	$0.477084\pi$
$462$	35.9560	−	13.0869i	1.67282	−	0.608858i
$463$	8.26430	−	3.00796i	0.384075	−	0.139792i	−0.142765	−	0.989757i	$-0.545599\pi$
$463$	8.26430	−	3.00796i	0.384075	−	0.139792i	0.526839	+	0.849965i	$0.323377\pi$
$464$	6.59374	−	5.53280i	0.306106	−	0.256854i
$465$	−0.513317	−	2.91117i	−0.0238045	−	0.135002i
$466$	0.00968983	+	0.0549538i	0.000448873	+	0.00254568i
$467$	8.99555	−	15.5807i	0.416264	−	0.720991i	−0.579296	−	0.815117i	$-0.696672\pi$
$467$	8.99555	−	15.5807i	0.416264	−	0.720991i	0.995560	+	0.0941263i	$0.0300058\pi$
$468$	10.5213	+	8.82845i	0.486349	+	0.408095i
$469$	28.1054	+	10.2295i	1.29779	+	0.472356i
$470$	1.93843	+	3.35745i	0.0894129	+	0.154868i
$471$	14.6415	−	25.3598i	0.674644	−	1.16852i
$472$	−8.04878	+	6.75373i	−0.370475	+	0.310866i
$473$	−3.69150	−	6.39387i	−0.169736	−	0.293991i
$474$	6.70505	−	38.0262i	0.307973	−	1.74660i
$475$	6.65960			0.305564
$476$	0.719267	−	4.07917i	0.0329676	−	0.186968i
$477$	5.15637	+	4.32671i	0.236094	+	0.198106i
$478$	−20.1433	+	7.33157i	−0.921334	+	0.335338i
$479$	−9.34282	−	3.40051i	−0.426884	−	0.155373i	0.119638	−	0.992818i	$-0.461827\pi$
$479$	−9.34282	−	3.40051i	−0.426884	−	0.155373i	−0.546523	+	0.837444i	$0.684049\pi$
$480$	2.38757			0.108977
$481$	−30.8931	−	1.64108i	−1.40860	−	0.0748268i
$482$	11.6013			0.528424
$483$	38.1297	+	13.8781i	1.73496	+	0.631474i
$484$	−21.9172	+	7.97722i	−0.996237	+	0.362601i
$485$	2.48717	+	2.08698i	0.112937	+	0.0947650i
$486$	−3.69419	+	20.9508i	−0.167572	+	0.950347i
$487$	16.7156			0.757454			0.378727	−	0.925508i	$-0.376362\pi$
$487$	16.7156			0.757454			0.378727	+	0.925508i	$0.376362\pi$
$488$	−1.07697	+	6.10780i	−0.0487521	+	0.276487i
$489$	−7.87373	−	13.6377i	−0.356063	−	0.616718i
$490$	−0.369821	+	0.310316i	−0.0167068	+	0.0140187i
$491$	4.09169	−	7.08701i	0.184655	−	0.319832i	−0.758805	−	0.651318i	$-0.774216\pi$
$491$	4.09169	−	7.08701i	0.184655	−	0.319832i	0.943460	+	0.331485i	$0.107550\pi$
$492$	2.16734	+	3.75394i	0.0977111	+	0.169241i
$493$	12.2476	+	4.45778i	0.551606	+	0.200768i
$494$	−25.9462	−	21.7715i	−1.16738	−	0.979545i
$495$	−7.91066	+	13.7017i	−0.355558	+	0.615844i
$496$	0.214996	+	1.21930i	0.00965358	+	0.0547482i
$497$	−4.82013	−	27.3363i	−0.216212	−	1.22620i
$498$	1.57792	−	1.32403i	0.0707083	−	0.0593313i
$499$	23.6781	−	8.61811i	1.05998	−	0.385800i	0.247556	−	0.968873i	$-0.420372\pi$
$499$	23.6781	−	8.61811i	1.05998	−	0.385800i	0.812419	+	0.583074i	$0.198150\pi$
$500$	−0.939693	+	0.342020i	−0.0420243	+	0.0152956i
$501$	9.80109	−	8.22409i	0.437881	−	0.367425i
$502$	−2.88650	−	16.3701i	−0.128831	−	0.730635i
$503$	0.147752	+	0.837941i	0.00658792	+	0.0373620i	0.987925	−	0.154936i	$-0.0495171\pi$
$503$	0.147752	+	0.837941i	0.00658792	+	0.0373620i	−0.981337	+	0.192298i	$0.938406\pi$
$504$	−3.69357	+	6.39744i	−0.164524	+	0.284965i
$505$	−5.01524	−	4.20829i	−0.223175	−	0.187266i
$506$	−34.2037	−	12.4491i	−1.52054	−	0.553432i
$507$	15.3603	+	26.6049i	0.682176	+	1.18156i
$508$	4.74843	−	8.22451i	0.210677	−	0.364904i
$509$	10.1381	−	8.50685i	0.449362	−	0.377060i	−0.389837	−	0.920884i	$-0.627469\pi$
$509$	10.1381	−	8.50685i	0.449362	−	0.377060i	0.839199	+	0.543824i	$0.183024\pi$
$510$	1.80766	+	3.13095i	0.0800443	+	0.138641i
$511$	−0.981335	+	5.56543i	−0.0434117	+	0.246200i
$512$	−1.00000			−0.0441942
$513$	0.826927	−	4.68974i	0.0365097	−	0.207057i
$514$	−10.9226	−	9.16513i	−0.481774	−	0.404257i
$515$	−12.0015	+	4.36817i	−0.528847	+	0.192485i
$516$	2.82734	+	1.02907i	0.124467	+	0.0453022i
$517$	22.7131			0.998922
$518$	−2.01605	−	16.5166i	−0.0885804	−	0.725697i
$519$	32.5203			1.42748
$520$	4.77923	+	1.73950i	0.209583	+	0.0762820i
$521$	−38.5542	+	14.0326i	−1.68909	+	0.614779i	−0.994511	−	0.104635i	$-0.966632\pi$
$521$	−38.5542	+	14.0326i	−1.68909	+	0.614779i	−0.694581	+	0.719415i	$0.744410\pi$
$522$	−17.8064	−	14.9413i	−0.779365	−	0.653965i
$523$	−4.89719	+	27.7733i	−0.214139	+	1.21444i	0.668255	+	0.743932i	$0.267041\pi$
$523$	−4.89719	+	27.7733i	−0.214139	+	1.21444i	−0.882394	+	0.470511i	$0.844070\pi$
$524$	19.3709			0.846223
$525$	1.13412	−	6.43190i	0.0494969	−	0.280711i
$526$	2.12737	+	3.68471i	0.0927578	+	0.160661i
$527$	−1.43616	+	1.20508i	−0.0625600	+	0.0524941i
$528$	6.99398	−	12.1139i	0.304374	−	0.527191i
$529$	−7.79965	−	13.5094i	−0.339115	−	0.587365i
$530$	2.34224	+	0.852505i	0.101740	+	0.0370304i
$531$	21.7358	+	18.2385i	0.943252	+	0.791482i
$532$	9.10855	−	15.7765i	0.394906	−	0.683997i
$533$	1.60340	+	9.09334i	0.0694510	+	0.393876i
$534$	−0.0429439	−	0.243547i	−0.00185836	−	0.0105393i
$535$	13.3100	−	11.1684i	0.575440	−	0.482851i
$536$	10.2745	−	3.73960i	0.443789	−	0.161526i
$537$	−1.47503	+	0.536868i	−0.0636524	+	0.0231676i
$538$	−0.952234	+	0.799019i	−0.0410537	+	0.0344482i
$539$	0.491140	+	2.78539i	0.0211549	+	0.119975i
$540$	0.124171	+	0.704207i	0.00534346	+	0.0303042i
$541$	10.7969	−	18.7008i	0.464196	−	0.804011i	−0.534969	−	0.844872i	$-0.679677\pi$
$541$	10.7969	−	18.7008i	0.464196	−	0.804011i	0.999165	+	0.0408608i	$0.0130100\pi$
$542$	−1.16064	−	0.973896i	−0.0498539	−	0.0418324i
$543$	19.8799	+	7.23570i	0.853130	+	0.310514i
$544$	−0.757110	−	1.31135i	−0.0324608	−	0.0562238i
$545$	8.20877	−	14.2180i	0.351625	−	0.609033i
$546$	−25.4457	+	21.3514i	−1.08897	+	0.913758i
$547$	−16.0418	−	27.7852i	−0.685899	−	1.18801i	−0.973153	−	0.230157i	$-0.926076\pi$
$547$	−16.0418	−	27.7852i	−0.685899	−	1.18801i	0.287255	−	0.957854i	$-0.407257\pi$
$548$	0.489005	−	2.77328i	0.0208892	−	0.118469i
$549$	16.7486			0.714812
$550$	−1.01734	+	5.76965i	−0.0433797	+	0.246019i
$551$	43.9117	+	36.8463i	1.87070	+	1.56970i
$552$	13.9390	−	5.07339i	0.593284	−	0.215938i
$553$	41.5712	+	15.1307i	1.76779	+	0.643421i
$554$	13.6997			0.582043
$555$	10.6144	+	9.91224i	0.450557	+	0.420751i
$556$	−16.2850			−0.690640
$557$	10.3654	+	3.77269i	0.439196	+	0.159854i	0.552148	−	0.833746i	$-0.313808\pi$
$557$	10.3654	+	3.77269i	0.439196	+	0.159854i	−0.112952	+	0.993600i	$0.536031\pi$
$558$	3.14188	−	1.14355i	0.133006	−	0.0484104i
$559$	4.90978	+	4.11979i	0.207661	+	0.174249i
$560$	−0.475008	+	2.69391i	−0.0200728	+	0.113838i
$561$	21.1809			0.894256
$562$	1.59474	−	9.04424i	0.0672702	−	0.381508i
$563$	−1.31189	−	2.27226i	−0.0552896	−	0.0957644i	0.837056	−	0.547117i	$-0.184275\pi$
$563$	−1.31189	−	2.27226i	−0.0552896	−	0.0957644i	−0.892345	+	0.451353i	$0.850942\pi$
$564$	−7.09071	+	5.94981i	−0.298573	+	0.250532i
$565$	−6.92321	+	11.9913i	−0.291262	+	0.504480i
$566$	0.176038	+	0.304907i	0.00739942	+	0.0128162i
$567$	−25.2135	−	9.17695i	−1.05887	−	0.385396i
$568$	−7.77341	−	6.52266i	−0.326165	−	0.273685i
$569$	−16.6879	+	28.9043i	−0.699594	+	1.21173i	0.269013	+	0.963137i	$0.413303\pi$
$569$	−16.6879	+	28.9043i	−0.699594	+	1.21173i	−0.968607	+	0.248596i	$0.920031\pi$
$570$	2.76106	+	15.6587i	0.115648	+	0.655872i
$571$	2.96886	+	16.8373i	0.124243	+	0.704617i	0.981755	+	0.190153i	$0.0608983\pi$
$571$	2.96886	+	16.8373i	0.124243	+	0.704617i	−0.857511	+	0.514465i	$0.827991\pi$
$572$	22.8257	−	19.1530i	0.954390	−	0.800828i
$573$	−44.3647	+	16.1474i	−1.85336	+	0.674568i
$574$	−4.66677	+	1.69857i	−0.194787	+	0.0708968i
$575$	−4.75931	+	3.99353i	−0.198477	+	0.166542i
$576$	0.468937	+	2.65948i	0.0195391	+	0.110812i
$577$	−6.93400	−	39.3247i	−0.288666	−	1.63711i	−0.691888	−	0.722005i	$-0.743221\pi$
$577$	−6.93400	−	39.3247i	−0.288666	−	1.63711i	0.403221	−	0.915102i	$-0.367890\pi$
$578$	−7.35357	+	12.7368i	−0.305868	+	0.529779i
$579$	15.6966	+	13.1710i	0.652327	+	0.547368i
$580$	−8.08841	−	2.94394i	−0.335853	−	0.122241i
$581$	1.17998	+	2.04379i	0.0489539	+	0.0847907i
$582$	−3.87595	+	6.71334i	−0.160663	+	0.278277i
$583$	11.1866	−	9.38665i	0.463300	−	0.388755i
$584$	1.03297	+	1.78915i	0.0427444	+	0.0740355i
$585$	2.38499	−	13.5260i	0.0986073	−	0.559230i
$586$	9.54851			0.394445
$587$	−7.18940	+	40.7731i	−0.296738	+	1.68289i	0.363314	+	0.931667i	$0.381645\pi$
$587$	−7.18940	+	40.7731i	−0.296738	+	1.68289i	−0.660053	+	0.751219i	$0.729466\pi$
$588$	−0.882973	−	0.740903i	−0.0364132	−	0.0305543i
$589$	−7.74806	+	2.82007i	−0.319253	+	0.116199i
$590$	9.87330	+	3.59359i	0.406477	+	0.147946i
$591$	62.8106			2.58368
$592$	−4.44570	−	4.15160i	−0.182717	−	0.170630i
$593$	−30.9038			−1.26907			−0.634533	−	0.772896i	$-0.718808\pi$
$593$	−30.9038			−1.26907			−0.634533	+	0.772896i	$0.718808\pi$
$594$	3.93670	+	1.43284i	0.161525	+	0.0587902i
$595$	−3.89230	+	1.41668i	−0.159569	+	0.0580782i
$596$	0.616396	+	0.517218i	0.0252486	+	0.0211861i
$597$	7.65549	−	43.4164i	0.313318	−	1.77692i
$598$	31.5982			1.29214
$599$	−5.97686	+	33.8965i	−0.244208	+	1.38497i	0.578117	+	0.815954i	$0.303788\pi$
$599$	−5.97686	+	33.8965i	−0.244208	+	1.38497i	−0.822325	+	0.569018i	$0.807323\pi$
$600$	−1.19379	−	2.06770i	−0.0487361	−	0.0844134i
$601$	−23.3173	+	19.5655i	−0.951132	+	0.798095i	−0.979488	−	0.201503i	$-0.935417\pi$
$601$	−23.3173	+	19.5655i	−0.951132	+	0.798095i	0.0283554	+	0.999598i	$0.490973\pi$
$602$	−1.72360	+	2.98536i	−0.0702487	+	0.121674i
$603$	−14.7635	−	25.5711i	−0.601214	−	1.04133i
$604$	1.62878	+	0.592827i	0.0662740	+	0.0241218i
$605$	17.8671	+	14.9923i	0.726400	+	0.609522i
$606$	7.81564	−	13.5371i	0.317489	−	0.549906i
$607$	−1.30474	−	7.39956i	−0.0529578	−	0.300339i	0.946812	−	0.321787i	$-0.104283\pi$
$607$	−1.30474	−	7.39956i	−0.0529578	−	0.300339i	−0.999770	+	0.0214480i	$0.993172\pi$
$608$	−1.15643	−	6.55843i	−0.0468993	−	0.265979i
$609$	43.0645	−	36.1354i	1.74506	−	1.46428i
$610$	5.82799	−	2.12122i	0.235969	−	0.0858855i
$611$	−18.5284	+	6.74377i	−0.749577	+	0.272824i
$612$	−3.13248	+	2.62846i	−0.126623	+	0.106249i
$613$	3.76733	+	21.3656i	0.152161	+	0.862949i	0.961335	+	0.275380i	$0.0888038\pi$
$613$	3.76733	+	21.3656i	0.152161	+	0.862949i	−0.809174	+	0.587569i	$0.800085\pi$
$614$	−2.35143	−	13.3356i	−0.0948961	−	0.538183i
$615$	2.16734	−	3.75394i	0.0873954	−	0.151373i
$616$	12.2767	+	10.3014i	0.494644	+	0.415055i
$617$	−7.89167	−	2.87233i	−0.317707	−	0.115636i	0.178244	−	0.983986i	$-0.442958\pi$
$617$	−7.89167	−	2.87233i	−0.317707	−	0.115636i	−0.495951	+	0.868350i	$0.665180\pi$
$618$	−15.2467	−	26.4080i	−0.613310	−	1.06228i
$619$	2.01018	−	3.48174i	0.0807960	−	0.139943i	−0.822796	−	0.568337i	$-0.807587\pi$
$619$	2.01018	−	3.48174i	0.0807960	−	0.139943i	0.903592	+	0.428394i	$0.140920\pi$
$620$	0.948447	−	0.795842i	0.0380906	−	0.0319618i
$621$	2.22131	+	3.84742i	0.0891380	+	0.154392i
$622$	3.33296	−	18.9022i	0.133640	−	0.757908i
$623$	0.283339			0.0113517
$624$	−2.10862	+	11.9586i	−0.0844125	+	0.478727i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	−11.8229	+	4.30317i	−0.472536	+	0.171989i
$627$	87.5364	+	31.8606i	3.49587	+	1.27239i
$628$	12.2647			0.489417
$629$	2.07833	−	8.97310i	0.0828684	−	0.357781i
$630$	7.38713			0.294310
$631$	−15.4659	−	5.62912i	−0.615687	−	0.224092i	0.0153028	−	0.999883i	$-0.495129\pi$
$631$	−15.4659	−	5.62912i	−0.615687	−	0.224092i	−0.630990	+	0.775791i	$0.717351\pi$
$632$	15.1971	−	5.53130i	0.604509	−	0.220023i
$633$	33.5787	+	28.1759i	1.33463	+	1.11989i
$634$	0.867978	−	4.92255i	0.0344718	−	0.195499i
$635$	−9.49685			−0.376871
$636$	−1.03341	+	5.86075i	−0.0409773	+	0.232394i
$637$	−1.22766	−	2.12637i	−0.0486418	−	0.0842500i
$638$	−38.6304	+	32.4148i	−1.52939	+	1.28331i
$639$	−13.7016	+	23.7319i	−0.542028	+	0.938820i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−20.0010	−	7.27978i	−0.789993	−	0.287534i	−0.0846601	−	0.996410i	$-0.526980\pi$
$641$	−20.0010	−	7.27978i	−0.789993	−	0.287534i	−0.705333	+	0.708876i	$0.749203\pi$
$642$	31.7785	+	26.6653i	1.25420	+	1.05240i
$643$	−7.86362	+	13.6202i	−0.310111	+	0.537128i	−0.978386	−	0.206786i	$-0.933700\pi$
$643$	−7.86362	+	13.6202i	−0.310111	+	0.537128i	0.668275	+	0.743914i	$0.267033\pi$
$644$	2.95115	+	16.7368i	0.116292	+	0.659522i
$645$	−0.522471	−	2.96308i	−0.0205723	−	0.116671i
$646$	7.72487	−	6.48194i	0.303931	−	0.255028i
$647$	38.1726	−	13.8937i	1.50072	−	0.546217i	0.544472	−	0.838779i	$-0.316730\pi$
$647$	38.1726	−	13.8937i	1.50072	−	0.546217i	0.956247	+	0.292562i	$0.0945077\pi$
$648$	−9.21725	+	3.35480i	−0.362088	+	0.131789i
$649$	47.1550	−	39.5678i	1.85100	−	1.55317i
$650$	−0.883166	−	5.00868i	−0.0346406	−	0.196457i
$651$	1.40416	+	7.96340i	0.0550334	+	0.312110i
$652$	3.29780	−	5.71195i	0.129152	−	0.223697i
$653$	−17.6525	−	14.8122i	−0.690797	−	0.579647i	0.228342	−	0.973581i	$-0.426670\pi$
$653$	−17.6525	−	14.8122i	−0.690797	−	0.579647i	−0.919139	+	0.393934i	$0.871114\pi$
$654$	36.8341	+	13.4065i	1.44033	+	0.524237i
$655$	−9.68546	−	16.7757i	−0.378442	−	0.655481i
$656$	−0.907757	+	1.57228i	−0.0354420	+	0.0613873i
$657$	4.27381	−	3.58615i	0.166737	−	0.139909i
$658$	−5.30249	−	9.18419i	−0.206713	−	0.358037i
$659$	−5.68200	+	32.2242i	−0.221339	+	1.25528i	0.648222	+	0.761451i	$0.275513\pi$
$659$	−5.68200	+	32.2242i	−0.221339	+	1.25528i	−0.869561	+	0.493825i	$0.835598\pi$
$660$	−13.9880			−0.544481
$661$	1.32718	−	7.52682i	0.0516214	−	0.292759i	−0.948058	−	0.318099i	$-0.896956\pi$
$661$	1.32718	−	7.52682i	0.0516214	−	0.292759i	0.999679	+	0.0253396i	$0.00806670\pi$
$662$	−25.4356	−	21.3430i	−0.988583	−	0.829519i
$663$	−17.2784	+	6.28883i	−0.671038	+	0.244238i
$664$	0.810701	+	0.295071i	0.0314613	+	0.0114510i
$665$	−18.2171			−0.706429
$666$	−8.95632	+	13.7701i	−0.347050	+	0.533579i
$667$	−53.4770			−2.07064
$668$	5.03558	+	1.83280i	0.194833	+	0.0709132i
$669$	35.4011	−	12.8849i	1.36868	−	0.498161i
$670$	−8.37582	−	7.02815i	−0.323586	−	0.271521i
$671$	6.30959	−	35.7835i	0.243579	−	1.38141i
$672$	−6.53112			−0.251943
$673$	3.30640	−	18.7515i	0.127452	−	0.722818i	−0.852369	−	0.522941i	$-0.824835\pi$
$673$	3.30640	−	18.7515i	0.127452	−	0.722818i	0.979821	−	0.199877i	$-0.0640543\pi$
$674$	−6.09774	−	10.5616i	−0.234876	−	0.406818i
$675$	0.547776	−	0.459638i	0.0210839	−	0.0176915i
$676$	−6.43345	+	11.1431i	−0.247440	+	0.428579i
$677$	1.23332	+	2.13617i	0.0474003	+	0.0820998i	0.888752	−	0.458388i	$-0.151573\pi$
$677$	1.23332	+	2.13617i	0.0474003	+	0.0820998i	−0.841352	+	0.540488i	$0.818240\pi$
$678$	−31.0656	−	11.3070i	−1.19307	−	0.434241i
$679$	−6.80356	−	5.70887i	−0.261097	−	0.219086i
$680$	−0.757110	+	1.31135i	−0.0290339	+	0.0502881i
$681$	−1.26050	−	7.14866i	−0.0483025	−	0.273937i
$682$	−1.25958	−	7.14346i	−0.0482320	−	0.273537i
$683$	15.2281	−	12.7779i	0.582687	−	0.488933i	−0.303141	−	0.952946i	$-0.598035\pi$
$683$	15.2281	−	12.7779i	0.582687	−	0.488933i	0.885828	+	0.464013i	$0.153591\pi$
$684$	−16.8997	+	6.15098i	−0.646176	+	0.235189i
$685$	−2.64624	+	0.963151i	−0.101107	+	0.0368001i
$686$	−13.6568	+	11.4594i	−0.521418	+	0.437522i
$687$	5.13939	+	29.1469i	0.196080	+	1.11203i
$688$	0.218829	+	1.24104i	0.00834280	+	0.0473143i
$689$	−6.33851	+	10.9786i	−0.241478	+	0.418252i
$690$	−11.3632	−	9.53485i	−0.432589	−	0.362985i
$691$	25.4373	+	9.25842i	0.967681	+	0.352207i	0.777039	−	0.629453i	$-0.216721\pi$
$691$	25.4373	+	9.25842i	0.967681	+	0.352207i	0.190642	+	0.981660i	$0.438943\pi$
$692$	6.81033	+	11.7958i	0.258890	+	0.448410i
$693$	21.6393	−	37.4804i	0.822010	−	1.42376i
$694$	−16.3844	+	13.7482i	−0.621945	+	0.521874i
$695$	8.14252	+	14.1033i	0.308863	+	0.534967i
$696$	3.56865	−	20.2388i	0.135269	−	0.767151i
$697$	−2.74909			−0.104129
$698$	−2.38005	+	13.4979i	−0.0900863	+	0.510905i
$699$	0.102060	+	0.0856387i	0.00386027	+	0.00323915i
$700$	2.57050	−	0.935584i	0.0971556	−	0.0353618i
$701$	−0.636906	−	0.231815i	−0.0240556	−	0.00875553i	0.329964	−	0.943993i	$-0.392963\pi$
$701$	−0.636906	−	0.231815i	−0.0240556	−	0.00875553i	−0.354020	+	0.935238i	$0.615186\pi$
$702$	−3.63681			−0.137263
$703$	22.0868	−	33.9578i	0.833021	−	1.28074i
$704$	5.85865			0.220806
$705$	8.69804	+	3.16583i	0.327587	+	0.119232i
$706$	−10.2299	+	3.72337i	−0.385007	+	0.140131i
$707$	13.7190	+	11.5116i	0.515957	+	0.432939i
$708$	−4.35615	+	24.7050i	−0.163714	+	0.928470i
$709$	−31.8495			−1.19613			−0.598066	−	0.801447i	$-0.704064\pi$
$709$	−31.8495			−1.19613			−0.598066	+	0.801447i	$0.704064\pi$
$710$	−1.76209	+	9.99330i	−0.0661300	+	0.375042i
$711$	−21.8368	−	37.8225i	−0.818946	−	1.41846i
$712$	0.0793466	−	0.0665797i	0.00297364	−	0.00249518i
$713$	3.84608	−	6.66161i	0.144037	−	0.249479i
$714$	−4.94478	−	8.56461i	−0.185054	−	0.320522i
$715$	−27.9999	−	10.1911i	−1.04714	−	0.381126i
$716$	−0.503632	−	0.422598i	−0.0188216	−	0.0157932i
$717$	−25.5901	+	44.3234i	−0.955680	+	1.65529i
$718$	−3.24268	−	18.3901i	−0.121016	−	0.686314i
$719$	−7.25686	−	41.1557i	−0.270635	−	1.53485i	−0.752493	−	0.658600i	$-0.771149\pi$
$719$	−7.25686	−	41.1557i	−0.270635	−	1.53485i	0.481858	−	0.876249i	$-0.339962\pi$
$720$	2.06871	−	1.73585i	0.0770961	−	0.0646913i
$721$	32.8295	−	11.9490i	1.22264	−	0.445003i
$722$	23.8215	−	8.67031i	0.886544	−	0.322676i
$723$	21.2186	−	17.8045i	0.789128	−	0.662157i
$724$	1.53866	+	8.72618i	0.0571839	+	0.324306i
$725$	1.49468	+	8.47674i	0.0555110	+	0.314818i
$726$	−27.8437	+	48.2266i	−1.03338	+	1.78986i
$727$	−29.6405	−	24.8713i	−1.09930	−	0.922426i	−0.101927	−	0.994792i	$-0.532501\pi$
$727$	−29.6405	−	24.8713i	−1.09930	−	0.922426i	−0.997378	+	0.0723656i	$0.976945\pi$
$728$	−13.0734	−	4.75833i	−0.484533	−	0.176356i
$729$	10.6834	+	18.5042i	0.395682	+	0.685341i
$730$	1.03297	−	1.78915i	0.0382318	−	0.0662194i
$731$	−1.46177	+	1.22657i	−0.0540655	+	0.0453663i
$732$	7.40389	+	12.8239i	0.273656	+	0.473985i
$733$	1.36455	−	7.73873i	0.0504007	−	0.285837i	−0.949182	−	0.314728i	$-0.898087\pi$
$733$	1.36455	−	7.73873i	0.0504007	−	0.285837i	0.999583	+	0.0288916i	$0.00919776\pi$
$734$	−25.8451			−0.953960
$735$	−0.200154	+	1.13513i	−0.00738278	+	0.0418699i
$736$	4.75931	+	3.99353i	0.175430	+	0.147204i
$737$	−60.1945	+	21.9090i	−2.21729	+	0.807029i
$738$	4.60713	+	1.67686i	0.169591	+	0.0617260i
$739$	−12.6309			−0.464637			−0.232318	−	0.972640i	$-0.574631\pi$
$739$	−12.6309			−0.464637			−0.232318	+	0.972640i	$0.574631\pi$
$740$	−1.37254	+	5.92589i	−0.0504556	+	0.217840i
$741$	−80.8681			−2.97076
$742$	−6.40711	−	2.33200i	−0.235212	−	0.0856103i
$743$	−0.959051	+	0.349066i	−0.0351842	+	0.0128060i	−0.359552	−	0.933125i	$-0.617071\pi$
$743$	−0.959051	+	0.349066i	−0.0351842	+	0.0128060i	0.324368	+	0.945931i	$0.394848\pi$
$744$	2.26449	+	1.90013i	0.0830201	+	0.0696621i
$745$	0.139726	−	0.792424i	0.00511915	−	0.0290322i
$746$	−19.2686			−0.705474
$747$	0.404566	−	2.29441i	0.0148023	−	0.0839480i
$748$	4.43565	+	7.68277i	0.162183	+	0.280910i
$749$	−36.4089	+	30.5507i	−1.33035	+	1.11630i
$750$	−1.19379	+	2.06770i	−0.0435909	+	0.0755017i
$751$	1.23175	+	2.13346i	0.0449473	+	0.0778510i	0.887624	−	0.460569i	$-0.152355\pi$
$751$	1.23175	+	2.13346i	0.0449473	+	0.0778510i	−0.842677	+	0.538420i	$0.819021\pi$
$752$	−3.64305	−	1.32596i	−0.132848	−	0.0483528i
$753$	−30.4026	−	25.5108i	−1.10793	−	0.929667i
$754$	21.8887	−	37.9123i	0.797139	−	1.38069i
$755$	−0.300986	−	1.70698i	−0.0109540	−	0.0621232i
$756$	−0.339665	−	1.92633i	−0.0123535	−	0.0700601i
$757$	−3.00211	+	2.51907i	−0.109114	+	0.0915571i	−0.695712	−	0.718321i	$-0.744911\pi$
$757$	−3.00211	+	2.51907i	−0.109114	+	0.0915571i	0.586599	+	0.809878i	$0.300467\pi$
$758$	−21.0346	+	7.65595i	−0.764010	+	0.278077i
$759$	−81.6639	+	29.7232i	−2.96421	+	1.07888i
$760$	−5.10155	+	4.28071i	−0.185053	+	0.155278i
$761$	0.564493	+	3.20140i	0.0204629	+	0.116051i	0.993328	−	0.115321i	$-0.0367897\pi$
$761$	0.564493	+	3.20140i	0.0204629	+	0.116051i	−0.972865	+	0.231372i	$0.925679\pi$
$762$	−3.93737	−	22.3299i	−0.142636	−	0.808929i
$763$	−22.4548	+	38.8929i	−0.812918	+	1.40802i
$764$	−15.1478	−	12.7105i	−0.548027	−	0.459849i
$765$	3.84255	+	1.39857i	0.138928	+	0.0505656i
$766$	−12.3535	−	21.3970i	−0.446351	−	0.773103i
$767$	−26.7189	+	46.2785i	−0.964763	+	1.67102i
$768$	−1.82899	+	1.53470i	−0.0659979	+	0.0553788i
$769$	5.73064	+	9.92576i	0.206652	+	0.357932i	0.950658	−	0.310241i	$-0.100410\pi$
$769$	5.73064	+	9.92576i	0.206652	+	0.357932i	−0.744006	+	0.668173i	$0.767076\pi$
$770$	2.78291	−	15.7827i	0.100289	−	0.568768i
$771$	−34.0430			−1.22603
$772$	−1.49027	+	8.45173i	−0.0536359	+	0.304184i
$773$	22.4543	+	18.8414i	0.807625	+	0.677678i	0.950040	−	0.312129i	$-0.101042\pi$
$773$	22.4543	+	18.8414i	0.807625	+	0.677678i	−0.142415	+	0.989807i	$0.545487\pi$
$774$	3.19791	−	1.16394i	0.114946	−	0.0418371i
$775$	−1.16344	−	0.423458i	−0.0417921	−	0.0152111i
$776$	−3.24677			−0.116552
$777$	−29.0354	−	27.1146i	−1.04164	−	0.972730i
$778$	27.4377			0.983689
$779$	−11.3615	−	4.13523i	−0.407066	−	0.148160i
$780$	11.4108	−	4.15318i	0.408571	−	0.148708i
$781$	45.5417	+	38.2140i	1.62961	+	1.36741i
$782$	−1.63361	+	9.26468i	−0.0584179	+	0.331304i
$783$	6.15498			0.219961
$784$	0.0838315	−	0.475432i	0.00299398	−	0.0169797i
$785$	−6.13237	−	10.6216i	−0.218874	−	0.379100i
$786$	35.4292	−	29.7286i	1.26372	−	1.06038i
$787$	−6.95372	+	12.0442i	−0.247874	+	0.429330i	−0.962936	−	0.269731i	$-0.913065\pi$
$787$	−6.95372	+	12.0442i	−0.247874	+	0.429330i	0.715062	+	0.699061i	$0.246398\pi$
$788$	13.1537	+	22.7828i	0.468579	+	0.811603i
$789$	9.54587	+	3.47441i	0.339842	+	0.123692i
$790$	−12.3888	−	10.3954i	−0.440774	−	0.369853i
$791$	18.9382	−	32.8019i	0.673364	−	1.16630i
$792$	−2.74734	−	15.5810i	−0.0976226	−	0.553645i
$793$	5.47741	+	31.0640i	0.194509	+	1.10311i
$794$	−23.7288	+	19.9108i	−0.842104	+	0.706609i
$795$	5.59226	−	2.03542i	0.198337	−	0.0721888i
$796$	17.3513	−	6.31535i	0.615000	−	0.223842i
$797$	−15.5988	+	13.0889i	−0.552536	+	0.463633i	−0.875799	−	0.482676i	$-0.839665\pi$
$797$	−15.5988	+	13.0889i	−0.552536	+	0.463633i	0.323263	+	0.946309i	$0.395220\pi$
$798$	−7.55277	−	42.8339i	−0.267365	−	1.51630i
$799$	−1.01939	−	5.78122i	−0.0360633	−	0.204525i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−0.214276	−	0.179799i	−0.00757107	−	0.00635288i
$802$	−0.354506	−	0.129030i	−0.0125180	−	0.00455619i
$803$	−6.05179	−	10.4820i	−0.213563	−	0.369902i
$804$	13.0527	−	22.6079i	0.460333	−	0.797320i
$805$	13.0189	−	10.9242i	0.458856	−	0.385026i
$806$	3.14848	+	5.45333i	0.110901	+	0.192085i
$807$	−0.515367	+	2.92279i	−0.0181418	+	0.102887i
$808$	6.54693			0.230320
$809$	9.23783	−	52.3904i	0.324785	−	1.84195i	−0.186397	−	0.982474i	$-0.559681\pi$
$809$	9.23783	−	52.3904i	0.324785	−	1.84195i	0.511182	−	0.859472i	$-0.329208\pi$
$810$	7.51397	+	6.30497i	0.264014	+	0.221534i
$811$	−23.8177	+	8.66895i	−0.836354	+	0.304408i	−0.724464	−	0.689313i	$-0.757913\pi$
$811$	−23.8177	+	8.66895i	−0.836354	+	0.304408i	−0.111890	+	0.993721i	$0.535690\pi$
$812$	22.1256	+	8.05305i	0.776455	+	0.282607i
$813$	−3.61744			−0.126869
$814$	26.0458	+	24.3228i	0.912905	+	0.852513i
$815$	−6.59560			−0.231034
$816$	−3.39728	−	1.23651i	−0.118929	−	0.0432865i
$817$	−7.88623	+	2.87035i	−0.275904	+	0.100421i
$818$	10.7041	+	8.98178i	0.374259	+	0.314041i
$819$	−6.52406	+	36.9998i	−0.227969	+	1.29288i
$820$	1.81551			0.0634005
$821$	4.34504	−	24.6419i	0.151643	−	0.860009i	−0.810148	−	0.586225i	$-0.800613\pi$
$821$	4.34504	−	24.6419i	0.151643	−	0.860009i	0.961791	−	0.273784i	$-0.0882754\pi$
$822$	−3.36178	−	5.82278i	−0.117256	−	0.203093i
$823$	35.0787	−	29.4345i	1.22277	−	1.02602i	0.224092	−	0.974568i	$-0.428059\pi$
$823$	35.0787	−	29.4345i	1.22277	−	1.02602i	0.998675	−	0.0514552i	$-0.0163859\pi$
$824$	6.38584	−	11.0606i	0.222461	−	0.385314i
$825$	6.99398	+	12.1139i	0.243499	+	0.421753i
$826$	−27.0080	−	9.83013i	−0.939730	−	0.342034i
$827$	−20.3090	−	17.0413i	−0.706212	−	0.592582i	0.217321	−	0.976100i	$-0.430268\pi$
$827$	−20.3090	−	17.0413i	−0.706212	−	0.592582i	−0.923534	+	0.383518i	$0.874713\pi$
$828$	8.38889	−	14.5300i	0.291534	−	0.504952i
$829$	0.749828	+	4.25249i	0.0260426	+	0.147695i	0.995056	−	0.0993118i	$-0.0316641\pi$
$829$	0.749828	+	4.25249i	0.0260426	+	0.147695i	−0.969014	+	0.247007i	$0.920553\pi$
$830$	−0.149811	−	0.849623i	−0.00520003	−	0.0294908i
$831$	25.0565	−	21.0249i	0.869201	−	0.729346i
$832$	−4.77923	+	1.73950i	−0.165690	+	0.0603062i
$833$	0.686929	−	0.250022i	0.0238007	−	0.00866274i
$834$	−29.7851	+	24.9927i	−1.03137	+	0.865426i
$835$	−0.930538	−	5.27734i	−0.0322026	−	0.182630i
$836$	6.77511	+	38.4236i	0.234322	+	1.32891i
$837$	−0.442668	+	0.766723i	−0.0153008	+	0.0265018i
$838$	−5.71299	−	4.79377i	−0.197352	−	0.165598i
$839$	43.1432	+	15.7028i	1.48947	+	0.542122i	0.953309	−	0.301995i	$-0.0976527\pi$
$839$	43.1432	+	15.7028i	1.48947	+	0.542122i	0.536159	+	0.844117i	$0.319875\pi$
$840$	3.26556	+	5.65612i	0.112673	+	0.195155i
$841$	−22.5446	+	39.0484i	−0.777401	+	1.34650i
$842$	19.0248	−	15.9637i	0.655637	−	0.550145i
$843$	−10.9635	−	18.9893i	−0.377601	−	0.654025i
$844$	−3.18804	+	18.0803i	−0.109737	+	0.622348i
$845$	12.8669			0.442635
$846$	−1.81800	+	10.3104i	−0.0625041	+	0.354479i
$847$	−48.8748	−	41.0108i	−1.67936	−	1.40915i
$848$	−2.34224	+	0.852505i	−0.0804328	+	0.0292751i
$849$	0.789912	+	0.287504i	0.0271097	+	0.00986712i
$850$	1.51422			0.0519373
$851$	4.57890	+	37.5128i	0.156963	+	1.28592i
$852$	−24.2278			−0.830031
$853$	19.0132	+	6.92022i	0.650998	+	0.236944i	0.646345	−	0.763045i	$-0.276297\pi$
$853$	19.0132	+	6.92022i	0.650998	+	0.236944i	0.00465299	+	0.999989i	$0.498519\pi$
$854$	−15.9423	+	5.80251i	−0.545533	+	0.198558i
$855$	13.7768	+	11.5601i	0.471155	+	0.395346i
$856$	−3.01712	+	17.1110i	−0.103123	+	0.584841i
$857$	−32.9480			−1.12548			−0.562742	−	0.826633i	$-0.690253\pi$
$857$	−32.9480			−1.12548			−0.562742	+	0.826633i	$0.690253\pi$
$858$	12.3537	−	70.0613i	0.421748	−	2.39185i
$859$	23.9727	+	41.5220i	0.817939	+	1.41671i	0.907198	+	0.420703i	$0.138217\pi$
$859$	23.9727	+	41.5220i	0.817939	+	1.41671i	−0.0892598	+	0.996008i	$0.528450\pi$
$860$	0.965361	−	0.810034i	0.0329185	−	0.0276219i
$861$	−5.92867	+	10.2688i	−0.202049	+	0.349958i
$862$	6.00252	+	10.3967i	0.204447	+	0.354112i
$863$	−17.4164	−	6.33907i	−0.592863	−	0.215784i	0.0281254	−	0.999604i	$-0.491046\pi$
$863$	−17.4164	−	6.33907i	−0.592863	−	0.215784i	−0.620988	+	0.783820i	$0.713268\pi$
$864$	−0.547776	−	0.459638i	−0.0186357	−	0.0156372i
$865$	6.81033	−	11.7958i	0.231558	−	0.401070i
$866$	−0.792952	−	4.49706i	−0.0269456	−	0.152816i
$867$	6.09754	+	34.5809i	0.207083	+	1.17443i
$868$	−2.59444	+	2.17700i	−0.0880611	+	0.0738921i
$869$	−89.0346	+	32.4060i	−3.02029	+	1.09930i
$870$	−19.3117	+	7.02888i	−0.654727	+	0.238301i
$871$	42.5990	−	35.7448i	1.44341	−	1.21117i
$872$	2.85088	+	16.1681i	0.0965429	+	0.547522i
$873$	1.52253	+	8.63471i	0.0515299	+	0.292241i
$874$	−20.6875	+	35.8318i	−0.699765	+	1.21203i
$875$	−2.09549	−	1.75832i	−0.0708404	−	0.0594422i
$876$	4.63509	+	1.68704i	0.156605	+	0.0569997i
$877$	23.3054	+	40.3661i	0.786966	+	1.36307i	0.927817	+	0.373035i	$0.121683\pi$
$877$	23.3054	+	40.3661i	0.786966	+	1.36307i	−0.140851	+	0.990031i	$0.544984\pi$
$878$	−1.01353	+	1.75549i	−0.0342051	+	0.0592450i
$879$	17.4641	−	14.6541i	0.589050	−	0.494271i
$880$	−2.92933	−	5.07374i	−0.0987476	−	0.171036i
$881$	5.46797	−	31.0104i	0.184221	−	1.04477i	−0.742732	−	0.669589i	$-0.766470\pi$
$881$	5.46797	−	31.0104i	0.184221	−	1.04477i	0.926953	−	0.375178i	$-0.122419\pi$
$882$	−1.30371			−0.0438983
$883$	7.63626	−	43.3074i	0.256980	−	1.45741i	−0.533957	−	0.845512i	$-0.679296\pi$
$883$	7.63626	−	43.3074i	0.256980	−	1.45741i	0.790938	−	0.611897i	$-0.209593\pi$
$884$	−5.89950	−	4.95027i	−0.198422	−	0.166496i
$885$	23.5732	−	8.57995i	0.792405	−	0.288412i
$886$	−4.46563	−	1.62536i	−0.150026	−	0.0546049i
$887$	20.1646			0.677060			0.338530	−	0.940956i	$-0.390070\pi$
$887$	20.1646			0.677060			0.338530	+	0.940956i	$0.390070\pi$
$888$	−14.5026	−	0.770396i	−0.486675	−	0.0258528i
$889$	25.9783			0.871284
$890$	−0.0973331	−	0.0354263i	−0.00326261	−	0.00118749i
$891$	54.0007	−	19.6546i	1.80909	−	0.658455i
$892$	12.0873	+	10.1424i	0.404712	+	0.339593i
$893$	4.48330	−	25.4260i	0.150028	−	0.850850i
$894$	1.92116			0.0642531
$895$	−0.114164	+	0.647457i	−0.00381609	+	0.0216421i
$896$	−1.36773	−	2.36898i	−0.0456927	−	0.0791421i
$897$	57.7926	−	48.4938i	1.92964	−	1.61916i
$898$	−9.51045	+	16.4726i	−0.317368	+	0.549697i
$899$	−5.32852	−	9.22927i	−0.177716	−	0.307813i
$900$	−2.53764	−	0.923626i	−0.0845881	−	0.0307875i
$901$	−2.89127	−	2.42606i	−0.0963221	−	0.0808238i
$902$	5.31824	−	9.21145i	0.177078	−	0.306708i
$903$	1.42920	+	8.10541i	0.0475609	+	0.269731i
$904$	−2.40440	−	13.6361i	−0.0799693	−	0.453528i
$905$	6.78776	−	5.69561i	0.225633	−	0.189328i
$906$	3.88883	−	1.41542i	0.129198	−	0.0470241i
$907$	33.0186	−	12.0178i	1.09636	−	0.399044i	0.270390	−	0.962751i	$-0.412848\pi$
$907$	33.0186	−	12.0178i	1.09636	−	0.399044i	0.825975	+	0.563707i	$0.190625\pi$
$908$	2.32901	−	1.95427i	0.0772908	−	0.0648546i
$909$	−3.07010	−	17.4114i	−0.101829	−	0.577500i
$910$	2.41587	+	13.7011i	0.0800853	+	0.454186i
$911$	−26.1462	+	45.2865i	−0.866262	+	1.50041i	−0.000473250		1.00000i	$0.500151\pi$
$911$	−26.1462	+	45.2865i	−0.866262	+	1.50041i	−0.865789	+	0.500410i	$0.833183\pi$
$912$	−12.1803	−	10.2205i	−0.403331	−	0.338435i
$913$	−4.74961	−	1.72872i	−0.157189	−	0.0572122i
$914$	−8.16325	−	14.1392i	−0.270016	−	0.467682i
$915$	7.40389	−	12.8239i	0.244765	−	0.423945i
$916$	−9.49596	+	7.96806i	−0.313755	+	0.263272i
$917$	26.4942	+	45.8894i	0.874917	+	1.51540i
$918$	0.188022	−	1.06632i	0.00620564	−	0.0351940i
$919$	44.1853			1.45754			0.728770	−	0.684758i	$-0.240092\pi$
$919$	44.1853			1.45754			0.728770	+	0.684758i	$0.240092\pi$
$920$	1.07885	−	6.11845i	0.0355685	−	0.201719i
$921$	−24.7670	−	20.7820i	−0.816099	−	0.684789i
$922$	−23.6471	+	8.60686i	−0.778777	+	0.283452i
$923$	−48.4971	−	17.6515i	−1.59630	−	0.581006i
$924$	38.2636			1.25878
$925$	5.81824	−	1.77429i	0.191303	−	0.0583382i
$926$	8.79469			0.289011
$927$	−32.4100	−	11.7963i	−1.06448	−	0.387440i
$928$	8.08841	−	2.94394i	0.265515	−	0.0966396i
$929$	12.9665	+	10.8802i	0.425418	+	0.356968i	0.830220	−	0.557436i	$-0.188215\pi$
$929$	12.9665	+	10.8802i	0.425418	+	0.356968i	−0.404801	+	0.914405i	$0.632659\pi$
$930$	0.513317	−	2.91117i	0.0168323	−	0.0954609i
$931$	3.21503			0.105368
$932$	−0.00968983	+	0.0549538i	−0.000317401	+	0.00180007i
$933$	−22.9133	−	39.6869i	−0.750146	−	1.29929i
$934$	13.7820	−	11.5645i	0.450960	−	0.378401i
$935$	4.43565	−	7.68277i	0.145061	−	0.251253i
$936$	6.86731	+	11.8945i	0.224465	+	0.388785i
$937$	46.3938	+	16.8860i	1.51562	+	0.551640i	0.960049	−	0.279830i	$-0.0902783\pi$
$937$	46.3938	+	16.8860i	1.51562	+	0.551640i	0.555569	+	0.831470i	$0.312500\pi$
$938$	22.9118	+	19.2252i	0.748095	+	0.627727i
$939$	−15.0198	+	26.0150i	−0.490151	+	0.848967i
$940$	0.673208	+	3.81795i	0.0219576	+	0.124528i
$941$	3.55037	+	20.1351i	0.115739	+	0.656386i	0.986382	+	0.164471i	$0.0525918\pi$
$941$	3.55037	+	20.1351i	0.115739	+	0.656386i	−0.870643	+	0.491915i	$0.836297\pi$
$942$	22.4321	−	18.8227i	0.730876	−	0.613278i
$943$	10.5993	−	3.85781i	0.345159	−	0.125628i
$944$	−9.87330	+	3.59359i	−0.321348	+	0.116961i
$945$	−1.49842	+	1.25732i	−0.0487436	+	0.0409008i
$946$	−1.28205	−	7.27084i	−0.0416829	−	0.236396i
$947$	9.48420	+	53.7876i	0.308195	+	1.74786i	0.608071	+	0.793883i	$0.291944\pi$
$947$	9.48420	+	53.7876i	0.308195	+	1.74786i	−0.299876	+	0.953978i	$0.596945\pi$
$948$	19.3064	−	33.4397i	0.627044	−	1.08607i
$949$	8.04901	+	6.75392i	0.261282	+	0.219241i
$950$	6.25798	+	2.27772i	0.203036	+	0.0738989i
$951$	−5.96712	−	10.3354i	−0.193497	−	0.335147i
$952$	2.07105	−	3.58716i	0.0671231	−	0.116261i
$953$	44.8459	−	37.6302i	1.45270	−	1.21896i	0.522123	−	0.852870i	$-0.325140\pi$
$953$	44.8459	−	37.6302i	1.45270	−	1.21896i	0.930579	−	0.366091i	$-0.119304\pi$
$954$	3.36558	+	5.82935i	0.108965	+	0.188732i
$955$	−3.43372	+	19.4736i	−0.111113	+	0.630151i
$956$	−21.4361			−0.693292
$957$	−20.9075	+	118.572i	−0.675844	+	3.83290i
$958$	−7.61634	−	6.39087i	−0.246073	−	0.206480i
$959$	7.23869	−	2.63467i	0.233749	−	0.0850778i
$960$	2.24358	+	0.816598i	0.0724114	+	0.0263556i
$961$	−29.4671			−0.950551
$962$	−28.4687	−	12.1082i	−0.917868	−	0.390383i
$963$	46.9210			1.51201
$964$	10.9016	+	3.96787i	0.351118	+	0.127797i
$965$	8.06455	−	2.93526i	0.259607	−	0.0944892i
$966$	31.0836	+	26.0822i	1.00010	+	0.839182i
$967$	0.482815	−	2.73818i	0.0155263	−	0.0880539i	−0.976060	−	0.217502i	$-0.930209\pi$
$967$	0.482815	−	2.73818i	0.0155263	−	0.0880539i	0.991586	+	0.129448i	$0.0413204\pi$
$968$	−23.3238			−0.749656
$969$	4.18085	−	23.7108i	0.134308	−	0.761699i
$970$	1.62338	+	2.81178i	0.0521237	+	0.0902810i
$971$	−1.93744	+	1.62570i	−0.0621753	+	0.0521713i	−0.673346	−	0.739328i	$-0.735143\pi$
$971$	−1.93744	+	1.62570i	−0.0621753	+	0.0521713i	0.611170	+	0.791499i	$0.290699\pi$
$972$	−10.6370	+	18.4238i	−0.341182	+	0.590944i
$973$	−22.2736	−	38.5790i	−0.714058	−	1.23678i
$974$	15.7075	+	5.71706i	0.503300	+	0.183186i
$975$	−9.30214	−	7.80542i	−0.297907	−	0.249973i
$976$	−3.10101	+	5.37111i	−0.0992609	+	0.171925i
$977$	2.41229	+	13.6808i	0.0771761	+	0.437687i	0.998772	+	0.0495372i	$0.0157746\pi$
$977$	2.41229	+	13.6808i	0.0771761	+	0.437687i	−0.921596	+	0.388150i	$0.873114\pi$
$978$	−2.73452	−	15.5082i	−0.0874403	−	0.495898i
$979$	−0.464865	+	0.390068i	−0.0148571	+	0.0124666i
$980$	−0.453652	+	0.165116i	−0.0144914	+	0.00527443i
$981$	41.6619	−	15.1637i	1.33016	−	0.484139i
$982$	6.26883	−	5.26017i	0.200046	−	0.167859i
$983$	2.37183	+	13.4513i	0.0756496	+	0.429030i	0.998985	+	0.0450366i	$0.0143405\pi$
$983$	2.37183	+	13.4513i	0.0756496	+	0.429030i	−0.923336	+	0.383994i	$0.874548\pi$
$984$	0.752708	+	4.26882i	0.0239955	+	0.136085i
$985$	13.1537	−	22.7828i	0.419110	−	0.725920i
$986$	9.98437	+	8.37788i	0.317967	+	0.266806i
$987$	−23.7932	−	8.66001i	−0.757345	−	0.275651i
$988$	−16.9352	−	29.3326i	−0.538781	−	0.933195i
$989$	3.91467	−	6.78041i	0.124479	−	0.215604i
$990$	−12.1198	+	10.1697i	−0.385193	+	0.323216i
$991$	26.9489	+	46.6769i	0.856061	+	1.48274i	0.875658	+	0.482932i	$0.160428\pi$
$991$	26.9489	+	46.6769i	0.856061	+	1.48274i	−0.0195971	+	0.999808i	$0.506238\pi$
$992$	−0.214996	+	1.21930i	−0.00682611	+	0.0387128i
$993$	−79.2765			−2.51576
$994$	4.82013	−	27.3363i	0.152885	−	0.867055i
$995$	−14.1449	−	11.8690i	−0.448424	−	0.376272i
$996$	1.93561	−	0.704503i	0.0613320	−	0.0223230i
$997$	11.7390	+	4.27265i	0.371778	+	0.135316i	0.521150	−	0.853465i	$-0.325503\pi$
$997$	11.7390	+	4.27265i	0.371778	+	0.135316i	−0.149372	+	0.988781i	$0.547725\pi$
$998$	25.1977			0.797618
$999$	−0.527011	−	4.31756i	−0.0166739	−	0.136602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.c.201.4	yes	24
37.7	even	9	inner	370.2.o.c.81.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.c.81.4	✓	24	37.7	even	9	inner
370.2.o.c.201.4	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(2.24358 - 0.816598i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.173648 - 0.984808i) q^{5} +2.38757 q^{6} +(-0.475008 + 2.69391i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.06871 - 1.73585i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.92933 - 5.07374i) q^{11} +(2.24358 + 0.816598i) q^{12} +(3.89606 + 3.26919i) q^{13} +(-1.36773 + 2.36898i) q^{14} +(-0.414598 - 2.35130i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.15996 + 0.973322i) q^{17} +(2.53764 - 0.923626i) q^{18} +(-6.25798 + 2.27772i) q^{19} +(0.766044 - 0.642788i) q^{20} +(1.13412 + 6.43190i) q^{21} +(-1.01734 - 5.76965i) q^{22} +(3.10642 - 5.38047i) q^{23} +(1.82899 + 1.53470i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(2.54298 + 4.40456i) q^{26} +(-0.357535 + 0.619269i) q^{27} +(-2.09549 + 1.75832i) q^{28} +(-4.30376 - 7.45432i) q^{29} +(0.414598 - 2.35130i) q^{30} +1.23811 q^{31} +(-0.173648 + 0.984808i) q^{32} +(-10.7154 - 8.99129i) q^{33} +(-1.42290 + 0.517894i) q^{34} +(2.57050 + 0.935584i) q^{35} +2.70050 q^{36} +(-4.86051 + 3.65724i) q^{37} -6.65960 q^{38} +(11.4108 + 4.15318i) q^{39} +(0.939693 - 0.342020i) q^{40} +(1.39076 + 1.16699i) q^{41} +(-1.13412 + 6.43190i) q^{42} +1.26019 q^{43} +(1.01734 - 5.76965i) q^{44} +(-1.35025 - 2.33870i) q^{45} +(4.75931 - 3.99353i) q^{46} +(-1.93843 + 3.35745i) q^{47} +(1.19379 + 2.06770i) q^{48} +(-0.453652 - 0.165116i) q^{49} +(-0.766044 - 0.642788i) q^{50} +(-1.80766 + 3.13095i) q^{51} +(0.883166 + 5.00868i) q^{52} +(0.432828 + 2.45469i) q^{53} +(-0.547776 + 0.459638i) q^{54} +(-5.50533 + 2.00378i) q^{55} +(-2.57050 + 0.935584i) q^{56} +(-12.1803 + 10.2205i) q^{57} +(-1.49468 - 8.47674i) q^{58} +(1.82451 + 10.3473i) q^{59} +(1.19379 - 2.06770i) q^{60} +(4.75102 + 3.98658i) q^{61} +(1.16344 + 0.423458i) q^{62} +(3.69357 + 6.39744i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(3.89606 - 3.26919i) q^{65} +(-6.99398 - 12.1139i) q^{66} +(1.89864 - 10.7677i) q^{67} -1.51422 q^{68} +(2.57583 - 14.6082i) q^{69} +(2.09549 + 1.75832i) q^{70} +(-9.53550 + 3.47064i) q^{71} +(2.53764 + 0.923626i) q^{72} +2.06593 q^{73} +(-5.81824 + 1.77429i) q^{74} -2.38757 q^{75} +(-6.25798 - 2.27772i) q^{76} +(15.0596 - 5.48126i) q^{77} +(9.30214 + 7.80542i) q^{78} +(2.80831 - 15.9267i) q^{79} +1.00000 q^{80} +(-1.70328 + 9.65977i) q^{81} +(0.907757 + 1.57228i) q^{82} +(0.660889 - 0.554552i) q^{83} +(-3.26556 + 5.65612i) q^{84} +(0.757110 + 1.31135i) q^{85} +(1.18419 + 0.431010i) q^{86} +(-15.7430 - 13.2100i) q^{87} +(2.92933 - 5.07374i) q^{88} +(-0.0179864 - 0.102006i) q^{89} +(-0.468937 - 2.65948i) q^{90} +(-10.6575 + 8.94274i) q^{91} +(5.83815 - 2.12491i) q^{92} +(2.77780 - 1.01104i) q^{93} +(-2.96984 + 2.49199i) q^{94} +(1.15643 + 6.55843i) q^{95} +(0.414598 + 2.35130i) q^{96} +(-1.62338 + 2.81178i) q^{97} +(-0.369821 - 0.310316i) q^{98} +(-14.8672 - 5.41121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{6} - 3 q^{7} + 12 q^{8} + 12 q^{9} + 12 q^{10} - 15 q^{11} + 3 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 36 q^{21} + 9 q^{22} + 21 q^{23} - 6 q^{26} - 12 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{31}+ \cdots + 63 q^{99}+O(q^{100}) \) 24 * q - 6 * q^6 - 3 * q^7 + 12 * q^8 + 12 * q^9 + 12 * q^10 - 15 * q^11 + 3 * q^14 - 6 * q^17 + 6 * q^18 - 6 * q^19 + 36 * q^21 + 9 * q^22 + 21 * q^23 - 6 * q^26 - 12 * q^27 - 3 * q^28 + 12 * q^29 + 30 * q^31 - 39 * q^33 - 21 * q^34 + 6 * q^35 + 54 * q^36 - 12 * q^37 - 36 * q^38 - 18 * q^39 + 27 * q^41 - 36 * q^42 - 24 * q^43 - 9 * q^44 - 27 * q^45 + 3 * q^46 - 6 * q^47 - 3 * q^48 - 27 * q^49 - 6 * q^51 - 9 * q^52 + 6 * q^53 + 9 * q^54 + 9 * q^55 - 6 * q^56 - 27 * q^57 + 27 * q^58 + 51 * q^59 - 3 * q^60 - 3 * q^62 - 27 * q^63 - 12 * q^64 + 15 * q^66 - 18 * q^69 + 3 * q^70 - 66 * q^71 + 6 * q^72 + 42 * q^73 - 42 * q^74 + 6 * q^75 - 6 * q^76 + 69 * q^77 + 36 * q^78 - 30 * q^79 + 24 * q^80 - 90 * q^81 + 24 * q^82 + 57 * q^83 + 6 * q^84 - 6 * q^86 + 6 * q^87 + 15 * q^88 - 57 * q^89 + 6 * q^90 + 3 * q^91 + 15 * q^92 - 72 * q^93 + 3 * q^94 - 15 * q^95 - 3 * q^97 - 72 * q^98 + 63 * q^99

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