LMFDB - Embedded newform 525.2.bb.a.41.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(41,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 2, 5]))

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

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

chi := DirichletCharacter("525.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bb (of order $10$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.7
Character	$\chi$	$=$	525.41
Dual form			525.2.bb.a.461.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41289 + 1.94468i) q^{2} +(-1.73181 + 0.0287273i) q^{3} +(-1.16748 - 3.59315i) q^{4} +(-0.433145 - 2.19371i) q^{5} +(2.39100 - 3.40841i) q^{6} +(-0.449509 - 2.60729i) q^{7} +(4.06484 + 1.32074i) q^{8} +(2.99835 - 0.0995005i) q^{9} +O(q^{10})$	\(q+(-1.41289 + 1.94468i) q^{2} +(-1.73181 + 0.0287273i) q^{3} +(-1.16748 - 3.59315i) q^{4} +(-0.433145 - 2.19371i) q^{5} +(2.39100 - 3.40841i) q^{6} +(-0.449509 - 2.60729i) q^{7} +(4.06484 + 1.32074i) q^{8} +(2.99835 - 0.0995005i) q^{9} +(4.87807 + 2.25716i) q^{10} +(-1.04911 + 1.44397i) q^{11} +(2.12508 + 6.18912i) q^{12} +(-2.91883 - 4.01743i) q^{13} +(5.70545 + 2.80967i) q^{14} +(0.813145 + 3.78666i) q^{15} +(-2.19859 + 1.59737i) q^{16} +(-2.04945 + 6.30755i) q^{17} +(-4.04285 + 5.97142i) q^{18} +(0.698794 + 0.227052i) q^{19} +(-7.37665 + 4.11748i) q^{20} +(0.853366 + 4.50242i) q^{21} +(-1.32579 - 4.08036i) q^{22} +(0.767204 - 1.05597i) q^{23} +(-7.07747 - 2.17051i) q^{24} +(-4.62477 + 1.90039i) q^{25} +11.9366 q^{26} +(-5.18972 + 0.258451i) q^{27} +(-8.84356 + 4.65912i) q^{28} +(-3.56540 + 1.15847i) q^{29} +(-8.51274 - 3.76884i) q^{30} +(4.73903 + 1.53980i) q^{31} +2.01558i q^{32} +(1.77538 - 2.53083i) q^{33} +(-9.37053 - 12.8974i) q^{34} +(-5.52494 + 2.11543i) q^{35} +(-3.85804 - 10.6573i) q^{36} +(-7.98232 + 5.79949i) q^{37} +(-1.42887 + 1.03813i) q^{38} +(5.17028 + 6.87359i) q^{39} +(1.13668 - 9.48916i) q^{40} +(5.40604 - 3.92772i) q^{41} +(-9.96149 - 4.70191i) q^{42} +11.8562 q^{43} +(6.41322 + 2.08378i) q^{44} +(-1.51700 - 6.53443i) q^{45} +(0.969539 + 2.98393i) q^{46} +(-0.593047 - 1.82521i) q^{47} +(3.76165 - 2.82950i) q^{48} +(-6.59588 + 2.34400i) q^{49} +(2.83865 - 11.6788i) q^{50} +(3.36806 - 10.9824i) q^{51} +(-11.0275 + 15.1781i) q^{52} +(-2.10884 + 0.685203i) q^{53} +(6.82992 - 10.4575i) q^{54} +(3.62208 + 1.67599i) q^{55} +(1.61638 - 11.1919i) q^{56} +(-1.21670 - 0.373137i) q^{57} +(2.78468 - 8.57037i) q^{58} +(-4.38634 + 3.18686i) q^{59} +(12.6567 - 7.34261i) q^{60} +(-2.33319 + 3.21136i) q^{61} +(-9.69017 + 7.04032i) q^{62} +(-1.60721 - 7.77283i) q^{63} +(-8.31684 - 6.04254i) q^{64} +(-7.54882 + 8.14322i) q^{65} +(2.41324 + 7.02834i) q^{66} +(1.39499 - 4.29335i) q^{67} +25.0566 q^{68} +(-1.29832 + 1.85077i) q^{69} +(3.69232 - 13.7331i) q^{70} +(-0.169770 + 0.0551616i) q^{71} +(12.3192 + 3.55560i) q^{72} +(-5.73841 + 7.89825i) q^{73} -23.7171i q^{74} +(7.95464 - 3.42398i) q^{75} -2.77595i q^{76} +(4.23644 + 2.08625i) q^{77} +(-20.6720 + 0.342907i) q^{78} +(2.85977 + 8.80148i) q^{79} +(4.45647 + 4.13118i) q^{80} +(8.98020 - 0.596675i) q^{81} +16.0625i q^{82} +(-4.62581 + 14.2368i) q^{83} +(15.1816 - 8.32277i) q^{84} +(14.7247 + 1.76382i) q^{85} +(-16.7515 + 23.0564i) q^{86} +(6.14133 - 2.10868i) q^{87} +(-6.17157 + 4.48391i) q^{88} +(-5.25402 - 3.81727i) q^{89} +(14.8507 + 6.28238i) q^{90} +(-9.16255 + 9.41611i) q^{91} +(-4.68993 - 1.52385i) q^{92} +(-8.25134 - 2.53051i) q^{93} +(4.38737 + 1.42554i) q^{94} +(0.195408 - 1.63130i) q^{95} +(-0.0579022 - 3.49061i) q^{96} +(-0.120899 + 0.0392824i) q^{97} +(4.76095 - 16.1387i) q^{98} +(-3.00192 + 4.43392i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) $ 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9	$ 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9} + 8 q^{15} - 92 q^{16} - 16 q^{18} + 12 q^{21} - 48 q^{22} - 32 q^{25} - 36 q^{28} - 14 q^{30} - 8 q^{36} - 4 q^{37} - 26 q^{39} - 11 q^{42} - 20 q^{49} + 20 q^{51} - 168 q^{57} + 32 q^{58} + 76 q^{60} + 29 q^{63} + 68 q^{64} - 44 q^{67} + 30 q^{70} - 114 q^{72} - 124 q^{78} - 68 q^{79} - 2 q^{81} + 102 q^{84} + 72 q^{85} - 156 q^{88} + 70 q^{91} - 32 q^{93} - 36 q^{99}+O(q^{100}) $ 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9 + 8 * q^15 - 92 * q^16 - 16 * q^18 + 12 * q^21 - 48 * q^22 - 32 * q^25 - 36 * q^28 - 14 * q^30 - 8 * q^36 - 4 * q^37 - 26 * q^39 - 11 * q^42 - 20 * q^49 + 20 * q^51 - 168 * q^57 + 32 * q^58 + 76 * q^60 + 29 * q^63 + 68 * q^64 - 44 * q^67 + 30 * q^70 - 114 * q^72 - 124 * q^78 - 68 * q^79 - 2 * q^81 + 102 * q^84 + 72 * q^85 - 156 * q^88 + 70 * q^91 - 32 * q^93 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$	$-1$

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 $

$2$	−1.41289	+	1.94468i	−0.999067	+	1.37510i	−0.0731709	+	0.997319i	$0.523312\pi$
$2$	−1.41289	+	1.94468i	−0.999067	+	1.37510i	−0.925896	+	0.377778i	$0.876688\pi$
$3$	−1.73181	+	0.0287273i	−0.999862	+	0.0165857i
$3$	−1.73181	+	0.0287273i	−0.999862	+	0.0165857i
$4$	−1.16748	−	3.59315i	−0.583742	−	1.79657i
$5$	−0.433145	−	2.19371i	−0.193708	−	0.981059i
$5$	−0.433145	−	2.19371i	−0.193708	−	0.981059i
$6$	2.39100	−	3.40841i	0.976123	−	1.39148i
$7$	−0.449509	−	2.60729i	−0.169899	−	0.985462i
$7$	−0.449509	−	2.60729i	−0.169899	−	0.985462i
$8$	4.06484	+	1.32074i	1.43714	+	0.466954i
$9$	2.99835	−	0.0995005i	0.999450	−	0.0331668i
$10$	4.87807	+	2.25716i	1.54258	+	0.713776i
$11$	−1.04911	+	1.44397i	−0.316318	+	0.435374i	−0.937339	−	0.348420i	$-0.886718\pi$
$11$	−1.04911	+	1.44397i	−0.316318	+	0.435374i	0.621021	+	0.783794i	$0.286718\pi$
$12$	2.12508	+	6.18912i	0.613459	+	1.78664i
$13$	−2.91883	−	4.01743i	−0.809539	−	1.11423i	−0.991394	−	0.130910i	$-0.958210\pi$
$13$	−2.91883	−	4.01743i	−0.809539	−	1.11423i	0.181855	−	0.983325i	$-0.441790\pi$
$14$	5.70545	+	2.80967i	1.52485	+	0.750915i
$15$	0.813145	+	3.78666i	0.209953	+	0.977711i
$16$	−2.19859	+	1.59737i	−0.549646	+	0.399341i
$17$	−2.04945	+	6.30755i	−0.497064	+	1.52981i	0.316651	+	0.948542i	$0.397442\pi$
$17$	−2.04945	+	6.30755i	−0.497064	+	1.52981i	−0.813715	+	0.581264i	$0.802558\pi$
$18$	−4.04285	+	5.97142i	−0.952910	+	1.40748i
$19$	0.698794	+	0.227052i	0.160314	+	0.0520893i	0.388075	−	0.921628i	$-0.373140\pi$
$19$	0.698794	+	0.227052i	0.160314	+	0.0520893i	−0.227760	+	0.973717i	$0.573140\pi$
$20$	−7.37665	+	4.11748i	−1.64947	+	0.920696i
$21$	0.853366	+	4.50242i	0.186220	+	0.982508i
$22$	−1.32579	−	4.08036i	−0.282659	−	0.869936i
$23$	0.767204	−	1.05597i	0.159973	−	0.220184i	−0.721505	−	0.692409i	$-0.756549\pi$
$23$	0.767204	−	1.05597i	0.159973	−	0.220184i	0.881478	+	0.472226i	$0.156549\pi$
$24$	−7.07747	−	2.17051i	−1.44468	−	0.443054i
$25$	−4.62477	+	1.90039i	−0.924954	+	0.380079i
$26$	11.9366			2.34097
$27$	−5.18972	+	0.258451i	−0.998762	+	0.0497389i
$28$	−8.84356	+	4.65912i	−1.67128	+	0.880490i
$29$	−3.56540	+	1.15847i	−0.662079	+	0.215122i	−0.620732	−	0.784022i	$-0.713165\pi$
$29$	−3.56540	+	1.15847i	−0.662079	+	0.215122i	−0.0413462	+	0.999145i	$0.513165\pi$
$30$	−8.51274	−	3.76884i	−1.55421	−	0.688093i
$31$	4.73903	+	1.53980i	0.851154	+	0.276557i	0.701929	−	0.712246i	$-0.252322\pi$
$31$	4.73903	+	1.53980i	0.851154	+	0.276557i	0.149225	+	0.988803i	$0.452322\pi$
$32$			2.01558i			0.356308i
$33$	1.77538	−	2.53083i	0.309053	−	0.440561i
$34$	−9.37053	−	12.8974i	−1.60703	−	2.21189i
$35$	−5.52494	+	2.11543i	−0.933885	+	0.357573i
$36$	−3.85804	−	10.6573i	−0.643007	−	1.77622i
$37$	−7.98232	+	5.79949i	−1.31229	+	0.953431i	−0.312291	+	0.949986i	$0.601096\pi$
$37$	−7.98232	+	5.79949i	−1.31229	+	0.953431i	−0.999994	+	0.00344450i	$0.998904\pi$
$38$	−1.42887	+	1.03813i	−0.231793	+	0.168407i
$39$	5.17028	+	6.87359i	0.827908	+	1.10065i
$40$	1.13668	−	9.48916i	0.179724	−	1.50037i
$41$	5.40604	−	3.92772i	0.844281	−	0.613406i	−0.0792822	−	0.996852i	$-0.525263\pi$
$41$	5.40604	−	3.92772i	0.844281	−	0.613406i	0.923563	+	0.383446i	$0.125263\pi$
$42$	−9.96149	−	4.70191i	−1.53709	−	0.725521i
$43$	11.8562			1.80805			0.904023	−	0.427483i	$-0.140600\pi$
$43$	11.8562			1.80805			0.904023	+	0.427483i	$0.140600\pi$
$44$	6.41322	+	2.08378i	0.966830	+	0.314142i
$45$	−1.51700	−	6.53443i	−0.226140	−	0.974095i
$46$	0.969539	+	2.98393i	0.142951	+	0.439957i
$47$	−0.593047	−	1.82521i	−0.0865048	−	0.266235i	0.898442	−	0.439092i	$-0.144700\pi$
$47$	−0.593047	−	1.82521i	−0.0865048	−	0.266235i	−0.984947	+	0.172858i	$0.944700\pi$
$48$	3.76165	−	2.82950i	0.542947	−	0.408403i
$49$	−6.59588	+	2.34400i	−0.942269	+	0.334857i
$50$	2.83865	−	11.6788i	0.401446	−	1.65163i
$51$	3.36806	−	10.9824i	0.471623	−	1.53784i
$52$	−11.0275	+	15.1781i	−1.52924	+	2.10482i
$53$	−2.10884	+	0.685203i	−0.289671	+	0.0941199i	−0.450248	−	0.892903i	$-0.648665\pi$
$53$	−2.10884	+	0.685203i	−0.289671	+	0.0941199i	0.160577	+	0.987023i	$0.448665\pi$
$54$	6.82992	−	10.4575i	0.929435	−	1.42309i
$55$	3.62208	+	1.67599i	0.488401	+	0.225991i
$56$	1.61638	−	11.1919i	0.215998	−	1.49558i
$57$	−1.21670	−	0.373137i	−0.161156	−	0.0494232i
$58$	2.78468	−	8.57037i	0.365647	−	1.12534i
$59$	−4.38634	+	3.18686i	−0.571053	+	0.414894i	−0.835487	−	0.549510i	$-0.814815\pi$
$59$	−4.38634	+	3.18686i	−0.571053	+	0.414894i	0.264435	+	0.964404i	$0.414815\pi$
$60$	12.6567	−	7.34261i	1.63397	−	0.947927i
$61$	−2.33319	+	3.21136i	−0.298734	+	0.411172i	−0.931827	−	0.362904i	$-0.881785\pi$
$61$	−2.33319	+	3.21136i	−0.298734	+	0.411172i	0.633092	+	0.774076i	$0.281785\pi$
$62$	−9.69017	+	7.04032i	−1.23065	+	0.894122i
$63$	−1.60721	−	7.77283i	−0.202490	−	0.979284i
$64$	−8.31684	−	6.04254i	−1.03960	−	0.755317i
$65$	−7.54882	+	8.14322i	−0.936316	+	1.01004i
$66$	2.41324	+	7.02834i	0.297049	+	0.865128i
$67$	1.39499	−	4.29335i	0.170426	−	0.524517i	−0.828969	−	0.559294i	$-0.811072\pi$
$67$	1.39499	−	4.29335i	0.170426	−	0.524517i	0.999395	+	0.0347775i	$0.0110723\pi$
$68$	25.0566			3.03856
$69$	−1.29832	+	1.85077i	−0.156299	+	0.222807i
$70$	3.69232	−	13.7331i	0.441317	−	1.64142i
$71$	−0.169770	+	0.0551616i	−0.0201480	+	0.00654648i	−0.319074	−	0.947730i	$-0.603372\pi$
$71$	−0.169770	+	0.0551616i	−0.0201480	+	0.00654648i	0.298926	+	0.954276i	$0.403372\pi$
$72$	12.3192	+	3.55560i	1.45183	+	0.419032i
$73$	−5.73841	+	7.89825i	−0.671630	+	0.924420i	−0.999796	−	0.0202002i	$-0.993570\pi$
$73$	−5.73841	+	7.89825i	−0.671630	+	0.924420i	0.328165	+	0.944620i	$0.393570\pi$
$74$		−	23.7171i		−	2.75706i
$75$	7.95464	−	3.42398i	0.918523	−	0.395367i
$76$		−	2.77595i		−	0.318423i
$77$	4.23644	+	2.08625i	0.482787	+	0.237750i
$78$	−20.6720	+	0.342907i	−2.34064	+	0.0388266i
$79$	2.85977	+	8.80148i	0.321750	+	0.990244i	0.972886	+	0.231284i	$0.0742925\pi$
$79$	2.85977	+	8.80148i	0.321750	+	0.990244i	−0.651137	+	0.758961i	$0.725708\pi$
$80$	4.45647	+	4.13118i	0.498249	+	0.461880i
$81$	8.98020	−	0.596675i	0.997800	−	0.0662972i
$82$			16.0625i			1.77380i
$83$	−4.62581	+	14.2368i	−0.507749	+	1.56269i	0.288351	+	0.957525i	$0.406893\pi$
$83$	−4.62581	+	14.2368i	−0.507749	+	1.56269i	−0.796100	+	0.605166i	$0.793107\pi$
$84$	15.1816	−	8.32277i	1.65644	−	0.908088i
$85$	14.7247	+	1.76382i	1.59712	+	0.191313i
$86$	−16.7515	+	23.0564i	−1.80636	+	2.48624i
$87$	6.14133	−	2.10868i	0.658420	−	0.226074i
$88$	−6.17157	+	4.48391i	−0.657892	+	0.477986i
$89$	−5.25402	−	3.81727i	−0.556925	−	0.404629i	0.273408	−	0.961898i	$-0.411849\pi$
$89$	−5.25402	−	3.81727i	−0.556925	−	0.404629i	−0.830332	+	0.557269i	$0.811849\pi$
$90$	14.8507	+	6.28238i	1.56540	+	0.662221i
$91$	−9.16255	+	9.41611i	−0.960496	+	0.987076i
$92$	−4.68993	−	1.52385i	−0.488960	−	0.158873i
$93$	−8.25134	−	2.53051i	−0.855624	−	0.262402i
$94$	4.38737	+	1.42554i	0.452523	+	0.147034i
$95$	0.195408	−	1.63130i	0.0200485	−	0.167368i
$96$	−0.0579022	−	3.49061i	−0.00590962	−	0.356259i
$97$	−0.120899	+	0.0392824i	−0.0122754	+	0.00398852i	−0.315148	−	0.949042i	$-0.602054\pi$
$97$	−0.120899	+	0.0392824i	−0.0122754	+	0.00398852i	0.302873	+	0.953031i	$0.402054\pi$
$98$	4.76095	−	16.1387i	0.480929	−	1.63026i
$99$	−3.00192	+	4.43392i	−0.301704	+	0.445626i
$100$	12.2277	+	14.3988i	1.22277	+	1.43988i
$101$	−18.6977			−1.86049			−0.930245	−	0.366938i	$-0.880406\pi$
$101$	−18.6977			−1.86049			−0.930245	+	0.366938i	$0.880406\pi$
$102$	16.5985	+	22.0667i	1.64350	+	2.18493i
$103$	−0.639238	+	0.207701i	−0.0629860	+	0.0204654i	−0.340341	−	0.940302i	$-0.610542\pi$
$103$	−0.639238	+	0.207701i	−0.0629860	+	0.0204654i	0.277355	+	0.960768i	$0.410542\pi$
$104$	−6.55858	−	20.1852i	−0.643122	−	1.97932i
$105$	9.50739	−	3.82224i	0.927826	−	0.373013i
$106$	1.64706	−	5.06914i	0.159977	−	0.492358i
$107$		−	7.45395i		−	0.720600i	−0.932836	−	0.360300i	$-0.882674\pi$
$107$		−	7.45395i		−	0.720600i	0.932836	−	0.360300i	$-0.117326\pi$
$108$	6.98757	+	18.3457i	0.672379	+	1.76531i
$109$	−4.96048	+	3.60400i	−0.475128	+	0.345201i	−0.799436	−	0.600751i	$-0.794868\pi$
$109$	−4.96048	+	3.60400i	−0.475128	+	0.345201i	0.324309	+	0.945951i	$0.394868\pi$
$110$	−8.37689	+	4.67579i	−0.798705	+	0.445820i
$111$	13.6573	−	10.2729i	1.29629	−	0.975065i
$112$	5.15307	+	5.01431i	0.486920	+	0.473808i
$113$	−0.797482	−	1.09764i	−0.0750208	−	0.103257i	0.769858	−	0.638216i	$-0.220327\pi$
$113$	−0.797482	−	1.09764i	−0.0750208	−	0.103257i	−0.844878	+	0.534959i	$0.820327\pi$
$114$	2.44471	−	1.83890i	0.228968	−	0.172228i
$115$	−2.64880	−	1.22564i	−0.247002	−	0.114292i
$116$	8.32510	+	11.4585i	0.772966	+	1.06390i
$117$	−9.15142	−	11.7552i	−0.846049	−	1.08677i
$118$		−	13.0327i		−	1.19976i
$119$	17.3668	+	2.50819i	1.59202	+	0.229926i
$120$	−1.69591	+	16.4661i	−0.154815	+	1.50314i
$121$	2.41476	+	7.43185i	0.219523	+	0.675623i
$122$	−2.94852	−	9.07462i	−0.266947	−	0.821578i
$123$	−9.24941	+	6.95737i	−0.833991	+	0.627325i
$124$		−	18.8257i		−	1.69060i
$125$	6.17212	+	9.32228i	0.552051	+	0.833810i
$126$	17.3865	+	7.85667i	1.54891	+	0.699928i
$127$	3.88272	+	2.82096i	0.344536	+	0.250320i	0.746573	−	0.665303i	$-0.231698\pi$
$127$	3.88272	+	2.82096i	0.344536	+	0.250320i	−0.402037	+	0.915623i	$0.631698\pi$
$128$	19.6678	−	6.39044i	1.73840	−	0.564841i
$129$	−20.5326	+	0.340595i	−1.80780	+	0.0299877i
$130$	−5.17029	−	26.1856i	−0.453464	−	2.29663i
$131$	−1.76276	+	5.42522i	−0.154013	+	0.474004i	−0.998060	−	0.0622665i	$-0.980167\pi$
$131$	−1.76276	+	5.42522i	−0.154013	+	0.474004i	0.844046	+	0.536270i	$0.180167\pi$
$132$	−11.1664	−	3.42449i	−0.971907	−	0.298063i
$133$	0.277875	−	1.92402i	0.0240948	−	0.166834i
$134$	6.37823	+	8.77887i	0.550995	+	0.758379i
$135$	2.81487	+	11.2728i	0.242265	+	0.970210i
$136$	−16.6613	+	22.9324i	−1.42870	+	1.96643i
$137$	12.3607	+	17.0130i	1.05604	+	1.45352i	0.883450	+	0.468525i	$0.155214\pi$
$137$	12.3607	+	17.0130i	1.05604	+	1.45352i	0.172592	+	0.984993i	$0.444786\pi$
$138$	−1.76478	−	5.13976i	−0.150228	−	0.437526i
$139$	−8.08950	+	11.1342i	−0.686143	+	0.944395i	−0.999987	−	0.00507992i	$-0.998383\pi$
$139$	−8.08950	+	11.1342i	−0.686143	+	0.944395i	0.313844	+	0.949474i	$0.398383\pi$
$140$	14.0513	+	17.3822i	1.18755	+	1.46906i
$141$	1.07948	+	3.14389i	0.0909086	+	0.264763i
$142$	0.132595	−	0.408086i	0.0111271	−	0.0342458i
$143$	8.86324			0.741181
$144$	−6.43319	+	5.00822i	−0.536099	+	0.417352i
$145$	4.08569	+	7.31969i	0.339298	+	0.607867i
$146$	−7.25181	−	22.3188i	−0.600164	−	1.84712i
$147$	11.3555	−	4.24885i	0.936586	−	0.350439i
$148$	30.1577	+	21.9108i	2.47894	+	1.80106i
$149$		−	8.86182i		−	0.725989i	−0.931791	−	0.362994i	$-0.881754\pi$
$149$		−	8.86182i		−	0.725989i	0.931791	−	0.362994i	$-0.118246\pi$
$150$	−4.58051	+	20.3070i	−0.373997	+	1.65806i
$151$	9.24761			0.752560			0.376280	−	0.926506i	$-0.377203\pi$
$151$	9.24761			0.752560			0.376280	+	0.926506i	$0.377203\pi$
$152$	2.54060	+	1.84586i	0.206070	+	0.149719i
$153$	−5.51736	+	19.1162i	−0.446052	+	1.54545i
$154$	−10.0427	+	5.29088i	−0.809265	+	0.426351i
$155$	1.32520	−	11.0630i	0.106443	−	0.888604i
$156$	18.6616	−	26.6024i	1.49412	−	2.12990i
$157$		−	13.4929i		−	1.07685i	−0.842674	−	0.538424i	$-0.819020\pi$
$157$		−	13.4929i		−	1.07685i	0.842674	−	0.538424i	$-0.180980\pi$
$158$	−21.1566	−	6.87421i	−1.68313	−	0.546883i
$159$	3.63243	−	1.24722i	0.288070	−	0.0989113i
$160$	4.42162	−	0.873040i	0.349559	−	0.0690199i
$161$	−3.09807	−	1.52565i	−0.244162	−	0.120238i
$162$	−11.5277	+	18.3067i	−0.905704	+	1.43831i
$163$	13.3550	−	9.70294i	1.04604	−	0.759993i	0.0745851	−	0.997215i	$-0.476237\pi$
$163$	13.3550	−	9.70294i	1.04604	−	0.759993i	0.971456	+	0.237222i	$0.0762368\pi$
$164$	−20.4243	−	14.8391i	−1.59487	−	1.15874i
$165$	−6.32091	−	2.79846i	−0.492082	−	0.217859i
$166$	−21.1502	−	29.1108i	−1.64158	−	2.25944i
$167$	2.94397	−	9.06062i	0.227811	−	0.701132i	−0.770183	−	0.637823i	$-0.779835\pi$
$167$	2.94397	−	9.06062i	0.227811	−	0.701132i	0.997994	−	0.0633081i	$-0.0201651\pi$
$168$	−2.47775	+	19.4287i	−0.191163	+	1.49895i
$169$	−3.60294	+	11.0887i	−0.277149	+	0.852977i
$170$	−24.2345	+	26.1427i	−1.85870	+	2.00506i
$171$	2.11782	+	0.611251i	0.161954	+	0.0467435i
$172$	−13.8419	−	42.6009i	−1.05543	−	3.24829i
$173$	0.215652	+	0.156680i	0.0163957	+	0.0119122i	0.595953	−	0.803019i	$-0.296774\pi$
$173$	0.215652	+	0.156680i	0.0163957	+	0.0119122i	−0.579557	+	0.814932i	$0.696774\pi$
$174$	−4.57634	+	14.9223i	−0.346932	+	1.13125i
$175$	7.03375	+	11.2039i	0.531701	+	0.846932i
$176$		−	4.85051i		−	0.365621i
$177$	7.50476	−	5.64505i	0.564093	−	0.424308i
$178$	14.8467	−	4.82400i	1.11281	−	0.361574i
$179$	−17.3449	+	5.63570i	−1.29642	+	0.421232i	−0.874334	−	0.485324i	$-0.838702\pi$
$179$	−17.3449	+	5.63570i	−1.29642	+	0.421232i	−0.422085	+	0.906556i	$0.638702\pi$
$180$	−21.7081	+	13.0796i	−1.61802	+	0.974898i
$181$	19.0380	+	6.18581i	1.41508	+	0.459787i	0.914036	−	0.405634i	$-0.132949\pi$
$181$	19.0380	+	6.18581i	1.41508	+	0.459787i	0.501045	+	0.865421i	$0.332949\pi$
$182$	−5.36562	−	31.1222i	−0.397727	−	2.30693i
$183$	3.94839	−	5.62850i	0.291874	−	0.416071i
$184$	4.51322	−	3.27904i	0.332719	−	0.241734i
$185$	16.1799	+	14.9989i	1.18957	+	1.10274i
$186$	16.5793	−	12.4709i	1.21565	−	0.914410i
$187$	−6.95784	−	9.57665i	−0.508808	−	0.700314i
$188$	−5.86588	+	4.26181i	−0.427813	+	0.310825i
$189$	3.00668	+	13.4149i	0.218704	+	0.975791i
$190$	2.89627	+	2.68486i	0.210118	+	0.194780i
$191$	−12.0923	−	16.6436i	−0.874969	−	1.20429i	−0.977789	−	0.209591i	$-0.932787\pi$
$191$	−12.0923	−	16.6436i	−0.874969	−	1.20429i	0.102820	−	0.994700i	$-0.467213\pi$
$192$	14.5768	+	10.2256i	1.05199	+	0.737971i
$193$	−14.9548			−1.07647			−0.538236	−	0.842794i	$-0.680909\pi$
$193$	−14.9548			−1.07647			−0.538236	+	0.842794i	$0.680909\pi$
$194$	0.0944253	−	0.290611i	0.00677934	−	0.0208647i
$195$	12.8392	−	14.3194i	0.919435	−	1.02543i
$196$	16.1229	+	20.9634i	1.15164	+	1.49738i
$197$	8.90550	−	2.89357i	0.634490	−	0.206158i	0.0259271	−	0.999664i	$-0.491746\pi$
$197$	8.90550	−	2.89357i	0.634490	−	0.206158i	0.608563	+	0.793505i	$0.291746\pi$
$198$	−4.38118	−	12.1024i	−0.311357	−	0.860083i
$199$			11.0049i			0.780120i	0.920790	+	0.390060i	$0.127546\pi$
$199$			11.0049i			0.780120i	−0.920790	+	0.390060i	$0.872454\pi$
$200$	−21.3089	+	1.61664i	−1.50676	+	0.114314i
$201$	−2.29253	+	7.47536i	−0.161703	+	0.527271i
$202$	26.4179	−	36.3611i	1.85875	−	2.55836i
$203$	4.62314	+	8.77528i	0.324481	+	0.615904i
$204$	−43.3934	+	0.719809i	−3.03815	+	0.0503967i
$205$	−10.9579	−	10.1580i	−0.765332	−	0.709468i
$206$	0.499263	−	1.53657i	0.0347853	−	0.107058i
$207$	2.19528	−	3.24249i	0.152582	−	0.225369i
$208$	12.8346	+	4.17022i	0.889920	+	0.289153i
$209$	−1.06097	+	0.770838i	−0.0733887	+	0.0533200i
$210$	−5.99989	+	23.8893i	−0.414032	+	1.64852i
$211$	−8.64654	−	6.28208i	−0.595252	−	0.432476i	0.248938	−	0.968519i	$-0.419918\pi$
$211$	−8.64654	−	6.28208i	−0.595252	−	0.432476i	−0.844190	+	0.536043i	$0.819918\pi$
$212$	4.92407	+	6.77740i	0.338186	+	0.465474i
$213$	0.292425	−	0.100407i	0.0200366	−	0.00687975i
$214$	14.4956	+	10.5316i	0.990896	+	0.719928i
$215$	−5.13543	−	26.0090i	−0.350234	−	1.77380i
$216$	−21.4367	−	5.80374i	−1.45858	−	0.394894i
$217$	1.88447	−	13.0482i	0.127926	−	0.885766i
$218$		−	14.7386i		−	0.998226i
$219$	9.71096	−	13.8431i	0.656206	−	0.935432i
$220$	1.79337	−	14.9714i	0.120909	−	1.00937i
$221$	31.3222	−	10.1772i	2.10696	−	0.684591i
$222$	0.681329	+	41.0736i	0.0457278	+	2.75668i
$223$	2.77842	−	3.82416i	0.186056	−	0.256085i	−0.705792	−	0.708419i	$-0.749409\pi$
$223$	2.77842	−	3.82416i	0.186056	−	0.256085i	0.891848	+	0.452334i	$0.149409\pi$
$224$	5.25520	−	0.906023i	0.351128	−	0.0605362i
$225$	−13.6776	+	6.15821i	−0.911839	+	0.410547i
$226$	3.26132			0.216940
$227$	−12.8965	−	9.36984i	−0.855969	−	0.621898i	0.0708162	−	0.997489i	$-0.477440\pi$
$227$	−12.8965	−	9.36984i	−0.855969	−	0.621898i	−0.926785	+	0.375591i	$0.877440\pi$
$228$	0.0797454	+	4.80742i	0.00528127	+	0.318379i
$229$	−6.76483	+	2.19803i	−0.447032	+	0.145250i	−0.523878	−	0.851793i	$-0.675515\pi$
$229$	−6.76483	+	2.19803i	−0.447032	+	0.145250i	0.0768455	+	0.997043i	$0.475515\pi$
$230$	6.12595	−	3.41937i	0.403933	−	0.225466i
$231$	−7.39664	−	3.49129i	−0.486663	−	0.229710i
$232$	−16.0228			−1.05195
$233$	6.83448	+	2.22066i	0.447742	+	0.145480i	0.524205	−	0.851592i	$-0.324363\pi$
$233$	6.83448	+	2.22066i	0.447742	+	0.145480i	−0.0764628	+	0.997072i	$0.524363\pi$
$234$	35.7902	−	1.18770i	2.33968	−	0.0776424i
$235$	−3.74712	+	2.09156i	−0.244435	+	0.136438i
$236$	16.5718	+	12.0401i	1.07873	+	0.783747i
$237$	−5.20544	−	15.1604i	−0.338129	−	0.984771i
$238$	−29.4151	+	30.2292i	−1.90670	+	1.95947i
$239$	10.2228	−	14.0705i	0.661261	−	0.910147i	−0.338262	−	0.941052i	$-0.609839\pi$
$239$	10.2228	−	14.0705i	0.661261	−	0.910147i	0.999522	+	0.0309049i	$0.00983890\pi$
$240$	−7.83645	−	7.02641i	−0.505841	−	0.453553i
$241$	−13.3809	−	18.4173i	−0.861941	−	1.18636i	−0.981103	−	0.193485i	$-0.938021\pi$
$241$	−13.3809	−	18.4173i	−0.861941	−	1.18636i	0.119162	−	0.992875i	$-0.461979\pi$
$242$	−17.8644	−	5.80449i	−1.14837	−	0.373127i
$243$	−15.5349	+	1.29131i	−0.996563	+	0.0828373i
$244$	14.2628	+	4.63428i	0.913085	+	0.296679i
$245$	7.99904	+	13.4542i	0.511040	+	0.859557i
$246$	−0.461431	−	27.8172i	−0.0294198	−	1.77356i
$247$	−1.12750	−	3.47008i	−0.0717410	−	0.220796i
$248$	17.2297	+	12.5181i	1.09409	+	0.794900i
$249$	7.60206	−	24.7883i	0.481761	−	1.57090i
$250$	−26.8494	−	1.16859i	−1.69811	−	0.0739084i
$251$	−7.04607			−0.444744			−0.222372	−	0.974962i	$-0.571380\pi$
$251$	−7.04607			−0.444744			−0.222372	+	0.974962i	$0.571380\pi$
$252$	−26.0525	+	14.8496i	−1.64115	+	0.935437i
$253$	0.719906	+	2.21564i	0.0452601	+	0.139296i
$254$	−10.9718	+	3.56494i	−0.688429	+	0.223684i
$255$	−25.5511	−	2.63161i	−1.60007	−	0.164798i
$256$	−9.00758	+	27.7225i	−0.562974	+	1.73266i
$257$	−20.2983			−1.26617			−0.633086	−	0.774081i	$-0.718212\pi$
$257$	−20.2983			−1.26617			−0.633086	+	0.774081i	$0.718212\pi$
$258$	28.3481	−	40.4107i	1.76488	−	2.51586i
$259$	18.7091	+	18.2053i	1.16252	+	1.13122i
$260$	38.0729	+	17.6169i	2.36118	+	1.09256i
$261$	−10.5751	+	3.82826i	−0.654579	+	0.236963i
$262$	−8.05973	−	11.0933i	−0.497932	−	0.685344i
$263$	8.46323	+	11.6486i	0.521865	+	0.718286i	0.985864	−	0.167550i	$-0.0535856\pi$
$263$	8.46323	+	11.6486i	0.521865	+	0.718286i	−0.463998	+	0.885836i	$0.653586\pi$
$264$	10.5592	−	7.94258i	0.649874	−	0.488832i
$265$	2.41657	+	4.32940i	0.148449	+	0.265953i
$266$	3.34899	+	3.25881i	0.205340	+	0.199811i
$267$	9.20863	+	6.45986i	0.563559	+	0.395337i
$268$	−17.0553			−1.04182
$269$	0.319195	−	0.982382i	0.0194617	−	0.0598969i	−0.940854	−	0.338812i	$-0.889975\pi$
$269$	0.319195	−	0.982382i	0.0194617	−	0.0598969i	0.960316	+	0.278915i	$0.0899749\pi$
$270$	−25.8992	−	10.4533i	−1.57617	−	0.636166i
$271$	7.30121	−	2.37231i	0.443517	−	0.144107i	−0.0787407	−	0.996895i	$-0.525090\pi$
$271$	7.30121	−	2.37231i	0.443517	−	0.144107i	0.522258	+	0.852788i	$0.325090\pi$
$272$	−5.56958	−	17.1414i	−0.337705	−	1.03935i
$273$	15.5973	−	16.5702i	0.943993	−	1.00287i
$274$	−50.5492			−3.05379
$275$	2.10777	−	8.67176i	0.127103	−	0.522927i
$276$	8.16586	+	2.50430i	0.491527	+	0.150741i
$277$	8.11002	+	5.89228i	0.487284	+	0.354033i	0.804139	−	0.594441i	$-0.202627\pi$
$277$	8.11002	+	5.89228i	0.487284	+	0.354033i	−0.316855	+	0.948474i	$0.602627\pi$
$278$	−10.2230	−	31.4630i	−0.613132	−	1.88703i
$279$	14.3625	+	4.14533i	0.859859	+	0.248175i
$280$	−25.2519	+	1.30183i	−1.50909	+	0.0777992i
$281$	−16.9570	−	5.50966i	−1.01157	−	0.328679i	−0.244091	−	0.969752i	$-0.578489\pi$
$281$	−16.9570	−	5.50966i	−1.01157	−	0.328679i	−0.767480	+	0.641073i	$0.778489\pi$
$282$	−7.63905	−	2.34274i	−0.454899	−	0.139508i
$283$	−1.09705	−	0.356452i	−0.0652126	−	0.0211889i	0.276229	−	0.961092i	$-0.410915\pi$
$283$	−1.09705	−	0.356452i	−0.0652126	−	0.0211889i	−0.341442	+	0.939903i	$0.610915\pi$
$284$	0.396407	+	0.545608i	0.0235224	+	0.0323759i
$285$	−0.291547	+	2.83072i	−0.0172698	+	0.167677i
$286$	−12.5228	+	17.2362i	−0.740489	+	1.01920i
$287$	−12.6707	−	12.3295i	−0.747930	−	0.727790i
$288$	0.200552	+	6.04342i	0.0118176	+	0.356112i
$289$	−21.8317	−	15.8616i	−1.28422	−	0.933038i
$290$	−20.0071	−	2.39659i	−1.17486	−	0.140732i
$291$	0.208245	−	0.0715028i	0.0122076	−	0.00419157i
$292$	35.0791	+	11.3979i	2.05285	+	0.667010i
$293$	0.0590960			0.00345243			0.00172621	−	0.999999i	$-0.499451\pi$
$293$	0.0590960			0.00345243			0.00172621	+	0.999999i	$0.499451\pi$
$294$	−7.78146	+	28.0860i	−0.453824	+	1.63801i
$295$	8.89098	+	8.24200i	0.517653	+	0.479868i
$296$	−40.1065	+	13.0314i	−2.33114	+	0.757434i
$297$	5.07138	−	7.76496i	0.294271	−	0.450569i
$298$	17.2334	+	12.5208i	0.998305	+	0.725311i
$299$	−6.48161			−0.374841
$300$	−21.5898	−	24.5847i	−1.24649	−	1.41940i
$301$	−5.32945	−	30.9124i	−0.307184	−	1.78176i
$302$	−13.0659	+	17.9837i	−0.751857	+	1.03484i
$303$	32.3809	−	0.537134i	1.86023	−	0.0308575i
$304$	−1.89904	+	0.617037i	−0.108918	+	0.0353895i
$305$	8.05542	+	3.72737i	0.461252	+	0.213428i
$306$	−29.3794	−	37.7386i	−1.67951	−	2.15737i
$307$			12.5035i			0.713613i	0.934178	+	0.356806i	$0.116134\pi$
$307$			12.5035i			0.713613i	−0.934178	+	0.356806i	$0.883866\pi$
$308$	2.55021	−	17.6578i	0.145312	−	1.00615i
$309$	1.10107	−	0.378063i	0.0626379	−	0.0215072i
$310$	19.6417	+	18.2080i	1.11557	+	1.03414i
$311$	18.0610	+	13.1221i	1.02414	+	0.744084i	0.967128	−	0.254290i	$-0.0818416\pi$
$311$	18.0610	+	13.1221i	1.02414	+	0.744084i	0.0570152	+	0.998373i	$0.481842\pi$
$312$	11.9381	+	34.7686i	0.675862	+	1.96839i
$313$	8.83894	+	12.1658i	0.499606	+	0.687649i	0.982124	−	0.188237i	$-0.0602775\pi$
$313$	8.83894	+	12.1658i	0.499606	+	0.687649i	−0.482517	+	0.875886i	$0.660277\pi$
$314$	26.2394	+	19.0640i	1.48077	+	1.07584i
$315$	−16.3552	+	6.89253i	−0.921512	+	0.388350i
$316$	28.2863	−	20.5512i	1.59123	−	1.15609i
$317$	−25.1125	−	8.15954i	−1.41046	−	0.458285i	−0.497900	−	0.867234i	$-0.665895\pi$
$317$	−25.1125	−	8.15954i	−1.41046	−	0.458285i	−0.912557	+	0.408949i	$0.865895\pi$
$318$	−2.70678	+	8.82611i	−0.151789	+	0.494944i
$319$	2.06769	−	6.36371i	0.115769	−	0.356299i
$320$	−9.65321	+	20.8621i	−0.539631	+	1.16623i
$321$	0.214132	+	12.9088i	0.0119517	+	0.720501i
$322$	7.34415	−	3.86917i	0.409274	−	0.215620i
$323$	−2.86428	+	3.94235i	−0.159373	+	0.219358i
$324$	−12.6282	−	31.5706i	−0.701565	−	1.75392i
$325$	21.1336	+	13.0328i	1.17228	+	0.722928i
$326$			39.6804i			2.19769i
$327$	8.48709	−	6.38395i	0.469337	−	0.353033i
$328$	27.1622	−	8.82552i	1.49978	−	0.487308i
$329$	−4.49227	+	2.36669i	−0.247667	+	0.130480i
$330$	14.3729	−	8.33824i	0.791201	−	0.459005i
$331$	−4.73326	+	14.5675i	−0.260164	+	0.800702i	0.732605	+	0.680655i	$0.238305\pi$
$331$	−4.73326	+	14.5675i	−0.260164	+	0.800702i	−0.992768	+	0.120047i	$0.961695\pi$
$332$	56.5554			3.10388
$333$	−23.3567	+	18.1832i	−1.27994	+	0.996431i
$334$	13.4605	+	18.5268i	0.736526	+	1.01374i
$335$	−10.0226	−	1.20058i	−0.547595	−	0.0655945i
$336$	−9.06821	−	8.53581i	−0.494711	−	0.465667i
$337$	−11.6110	+	8.43590i	−0.632492	+	0.459533i	−0.857263	−	0.514879i	$-0.827837\pi$
$337$	−11.6110	+	8.43590i	−0.632492	+	0.459533i	0.224770	+	0.974412i	$0.427837\pi$
$338$	−16.4734	−	22.6737i	−0.896036	−	1.23329i
$339$	1.41262	+	1.87800i	0.0767231	+	0.101999i
$340$	−10.8532	−	54.9671i	−0.588595	−	2.98101i
$341$	−7.19519	+	5.22761i	−0.389641	+	0.283091i
$342$	−4.18094	+	3.25485i	−0.226080	+	0.176002i
$343$	9.07638	+	16.1437i	0.490079	+	0.871678i
$344$	48.1933	+	15.6590i	2.59841	+	0.844274i
$345$	4.62243	+	2.04649i	0.248863	+	0.110179i
$346$	−0.609387	+	0.198002i	−0.0327609	+	0.0106446i
$347$	−4.13303	+	1.34290i	−0.221873	+	0.0720908i	−0.417844	−	0.908519i	$-0.637214\pi$
$347$	−4.13303	+	1.34290i	−0.221873	+	0.0720908i	0.195971	+	0.980610i	$0.437214\pi$
$348$	−14.7467	−	19.6048i	−0.790505	−	1.05093i
$349$		−	14.5815i		−	0.780529i	−0.920703	−	0.390265i	$-0.872384\pi$
$349$		−	14.5815i		−	0.780529i	0.920703	−	0.390265i	$-0.127616\pi$
$350$	−31.7259	−	2.15146i	−1.69582	−	0.115001i
$351$	16.1862	+	20.0950i	0.863958	+	1.07259i
$352$	−2.91045	−	2.11456i	−0.155127	−	0.112707i
$353$	0.892962	+	2.74825i	0.0475276	+	0.146275i	0.972004	−	0.234965i	$-0.0754974\pi$
$353$	0.892962	+	2.74825i	0.0475276	+	0.146275i	−0.924476	+	0.381239i	$0.875497\pi$
$354$	0.374395	+	22.5702i	0.0198989	+	1.19959i
$355$	0.194544	+	0.348534i	0.0103253	+	0.0184983i
$356$	−7.58201	+	23.3350i	−0.401846	+	1.23675i
$357$	−30.1482	−	3.84482i	−1.59561	−	0.203489i
$358$	13.5469	−	41.6930i	0.715974	−	2.20354i
$359$	14.5035	+	19.9624i	0.765465	+	1.05357i	0.996740	+	0.0806842i	$0.0257105\pi$
$359$	14.5035	+	19.9624i	0.765465	+	1.05357i	−0.231274	+	0.972889i	$0.574289\pi$
$360$	2.46397	−	28.5649i	0.129863	−	1.50550i
$361$	−14.9346	−	10.8506i	−0.786030	−	0.571084i
$362$	−38.9280	+	28.2829i	−2.04601	+	1.48652i
$363$	−4.39540	−	12.8012i	−0.230699	−	0.671889i
$364$	44.5306	+	21.9292i	2.33404	+	1.14940i
$365$	19.8121	+	9.16736i	1.03701	+	0.479841i
$366$	5.36698	+	15.6308i	0.280536	+	0.817037i
$367$	−27.8651	−	9.05391i	−1.45455	−	0.472610i	−0.528146	−	0.849153i	$-0.677113\pi$
$367$	−27.8651	−	9.05391i	−1.45455	−	0.472610i	−0.926399	+	0.376543i	$0.877113\pi$
$368$			3.54713i			0.184907i
$369$	15.8184	−	12.3146i	0.823472	−	0.641071i
$370$	−52.0286	+	10.2730i	−2.70484	+	0.534066i
$371$	2.73446	+	5.19034i	0.141966	+	0.269469i
$372$	0.540811	+	32.6026i	0.0280398	+	1.69037i
$373$	12.8118	+	9.30829i	0.663368	+	0.481965i	0.867799	−	0.496916i	$-0.165534\pi$
$373$	12.8118	+	9.30829i	0.663368	+	0.481965i	−0.204431	+	0.978881i	$0.565534\pi$
$374$	28.4542			1.47133
$375$	−10.9568	−	15.9671i	−0.565804	−	0.824540i
$376$		−	8.20245i		−	0.423009i
$377$	15.0609	+	10.9424i	0.775675	+	0.563561i
$378$	−30.3359	−	13.1068i	−1.56031	−	0.674142i
$379$	−9.52316	−	29.3093i	−0.489172	−	1.50552i	−0.825846	−	0.563895i	$-0.809302\pi$
$379$	−9.52316	−	29.3093i	−0.489172	−	1.50552i	0.336674	−	0.941621i	$-0.390698\pi$
$380$	−6.08964	+	1.20239i	−0.312392	+	0.0616812i
$381$	−6.80519	−	4.77384i	−0.348640	−	0.244571i
$382$	49.4517			2.53017
$383$	0.276380	−	0.850611i	0.0141224	−	0.0434642i	−0.943747	−	0.330668i	$-0.892726\pi$
$383$	0.276380	−	0.850611i	0.0141224	−	0.0434642i	0.957869	+	0.287204i	$0.0927258\pi$
$384$	−33.8773	+	11.6320i	−1.72879	+	0.593595i
$385$	2.74164	−	10.1972i	0.139727	−	0.519696i
$386$	21.1296	−	29.0824i	1.07547	−	1.48025i
$387$	35.5489	−	1.17969i	1.80705	−	0.0599672i
$388$	0.282294	+	0.388545i	0.0143313	+	0.0197254i
$389$	−3.44812	+	4.74593i	−0.174827	+	0.240628i	−0.887434	−	0.460935i	$-0.847514\pi$
$389$	−3.44812	+	4.74593i	−0.174827	+	0.240628i	0.712607	+	0.701563i	$0.247514\pi$
$390$	9.70621	+	45.2000i	0.491493	+	2.28879i
$391$	5.08821	+	7.00332i	0.257322	+	0.354173i
$392$	−29.9070	+	0.816488i	−1.51053	+	0.0412389i
$393$	2.89692	−	9.44610i	0.146130	−	0.476493i
$394$	−6.95545	+	21.4067i	−0.350410	+	1.07845i
$395$	18.0692	−	10.0858i	0.909162	−	0.507474i
$396$	19.4364	+	5.60979i	0.976717	+	0.281903i
$397$	19.0591	−	6.19267i	0.956547	−	0.310801i	0.211174	−	0.977448i	$-0.432271\pi$
$397$	19.0591	−	6.19267i	0.956547	−	0.310801i	0.745373	+	0.666647i	$0.232271\pi$
$398$	−21.4011	−	15.5488i	−1.07274	−	0.779392i
$399$	−0.425956	+	3.34002i	−0.0213245	+	0.167210i
$400$	7.13233	−	11.5656i	0.356617	−	0.578281i
$401$			26.4256i			1.31963i	0.751427	+	0.659817i	$0.229366\pi$
$401$			26.4256i			1.31963i	−0.751427	+	0.659817i	$0.770634\pi$
$402$	−11.2981	−	15.0201i	−0.563497	−	0.749136i
$403$	−7.64638	−	23.5331i	−0.380893	−	1.17227i
$404$	21.8293	+	67.1836i	1.08605	+	3.34251i
$405$	−5.19866	−	19.4416i	−0.258324	−	0.966058i
$406$	−23.5971	−	3.40800i	−1.17111	−	0.169136i
$407$		−	17.6106i		−	0.872923i
$408$	28.1955	−	40.1932i	1.39589	−	1.98986i
$409$	11.0819	+	15.2529i	0.547963	+	0.754207i	0.989734	−	0.142921i	$-0.0456496\pi$
$409$	11.0819	+	15.2529i	0.547963	+	0.754207i	−0.441771	+	0.897128i	$0.645650\pi$
$410$	35.2365	−	6.95738i	1.74021	−	0.343600i
$411$	−21.8951	−	29.1082i	−1.08001	−	1.43580i
$412$	1.49260	+	2.05439i	0.0735351	+	0.101212i
$413$	10.2808	+	10.0039i	0.505883	+	0.492260i
$414$	3.20392	+	8.85041i	0.157464	+	0.434974i
$415$	33.2351	+	3.98112i	1.63145	+	0.195426i
$416$	8.09747	−	5.88315i	0.397011	−	0.288445i
$417$	13.6896	−	19.5148i	0.670385	−	0.955645i
$418$		−	3.15236i		−	0.154187i
$419$	−0.602943	+	1.85567i	−0.0294557	+	0.0906553i	−0.964704	−	0.263338i	$-0.915176\pi$
$419$	−0.602943	+	1.85567i	−0.0294557	+	0.0906553i	0.935248	+	0.353993i	$0.115176\pi$
$420$	−24.8336	−	29.6990i	−1.21176	−	1.44916i
$421$	−12.1508	−	37.3965i	−0.592196	−	1.82259i	−0.568215	−	0.822880i	$-0.692366\pi$
$421$	−12.1508	−	37.3965i	−0.592196	−	1.82259i	−0.0239811	−	0.999712i	$-0.507634\pi$
$422$	24.4333	−	7.93885i	1.18939	−	0.386457i
$423$	−1.95977	−	5.41362i	−0.0952874	−	0.263219i
$424$	−9.47706			−0.460247
$425$	−2.50860	−	33.0657i	−0.121685	−	1.60392i
$426$	−0.217907	+	0.710538i	−0.0105576	+	0.0344257i
$427$	9.42172	+	4.63976i	0.455949	+	0.224534i
$428$	−26.7831	+	8.70236i	−1.29461	+	0.420645i
$429$	−15.3495	+	0.254617i	−0.741079	+	0.0122930i
$430$	57.8351	+	26.7612i	2.78906	+	1.29054i
$431$	−28.9560	−	9.40836i	−1.39476	−	0.453185i	−0.487267	−	0.873253i	$-0.662006\pi$
$431$	−28.9560	−	9.40836i	−1.39476	−	0.453185i	−0.907492	+	0.420068i	$0.862006\pi$
$432$	10.9972	−	8.85811i	0.529103	−	0.426186i
$433$	−23.2930	−	7.56837i	−1.11939	−	0.363713i	−0.309857	−	0.950783i	$-0.600281\pi$
$433$	−23.2930	−	7.56837i	−1.11939	−	0.363713i	−0.809536	+	0.587071i	$0.800281\pi$
$434$	22.7120	+	22.1004i	1.09021	+	1.06085i
$435$	−7.28592	−	12.5590i	−0.349333	−	0.602156i
$436$	18.7410	+	13.6161i	0.897530	+	0.652094i
$437$	0.775876	−	0.563707i	0.0371152	−	0.0269658i
$438$	13.1999	+	38.4436i	0.630717	+	1.83691i
$439$	−13.9841	+	19.2475i	−0.667426	+	0.918632i	−0.999699	−	0.0245508i	$-0.992184\pi$
$439$	−13.9841	+	19.2475i	−0.667426	+	0.918632i	0.332273	+	0.943183i	$0.392184\pi$
$440$	12.5096	+	11.5965i	0.596372	+	0.552841i
$441$	−19.5435	+	7.68442i	−0.930644	+	0.365925i
$442$	−24.4635	+	75.2909i	−1.16361	+	3.58122i
$443$			5.93637i			0.282045i	0.990006	+	0.141023i	$0.0450390\pi$
$443$			5.93637i			0.282045i	−0.990006	+	0.141023i	$0.954961\pi$
$444$	−52.8568	−	37.0791i	−2.50847	−	1.75970i
$445$	−6.09824	+	13.1792i	−0.289084	+	0.624756i
$446$	3.51117	+	10.8063i	0.166259	+	0.511692i
$447$	0.254576	+	15.3470i	0.0120410	+	0.725889i
$448$	−12.0161	+	24.4006i	−0.567709	+	1.15282i
$449$			26.3962i			1.24571i	0.782336	+	0.622856i	$0.214028\pi$
$449$			26.3962i			1.24571i	−0.782336	+	0.622856i	$0.785972\pi$
$450$	7.34923	−	35.2995i	0.346446	−	1.66403i
$451$			11.9268i			0.561610i
$452$	−3.01293	+	4.14694i	−0.141716	+	0.195056i
$453$	−16.0151	+	0.265659i	−0.752456	+	0.0124817i
$454$	36.4427	−	11.8410i	1.71034	−	0.555724i
$455$	24.6250	+	16.0215i	1.15444	+	0.751099i
$456$	−4.45288	−	3.12369i	−0.208525	−	0.146280i
$457$	−27.3287			−1.27838			−0.639191	−	0.769048i	$-0.720731\pi$
$457$	−27.3287			−1.27838			−0.639191	+	0.769048i	$0.720731\pi$
$458$	5.28352	−	16.2610i	0.246883	−	0.759827i
$459$	9.00587	−	33.2641i	0.420358	−	1.55264i
$460$	−1.31148	+	10.9484i	−0.0611479	+	0.510473i
$461$	5.09088	+	3.69874i	0.237106	+	0.172267i	0.699993	−	0.714150i	$-0.253186\pi$
$461$	5.09088	+	3.69874i	0.237106	+	0.172267i	−0.462887	+	0.886417i	$0.653186\pi$
$462$	17.2401	−	9.45130i	0.802083	−	0.439714i
$463$	7.90268	−	5.74163i	0.367269	−	0.266836i	−0.388809	−	0.921318i	$-0.627113\pi$
$463$	7.90268	−	5.74163i	0.367269	−	0.266836i	0.756077	+	0.654482i	$0.227113\pi$
$464$	5.98834	−	8.24225i	0.278002	−	0.382637i
$465$	−1.97719	+	19.1972i	−0.0916902	+	0.890247i
$466$	−13.9749	+	10.1533i	−0.647374	+	0.470345i
$467$	11.8373	−	36.4315i	0.547766	−	1.68585i	−0.166556	−	0.986032i	$-0.553265\pi$
$467$	11.8373	−	36.4315i	0.547766	−	1.68585i	0.714322	−	0.699817i	$-0.246735\pi$
$468$	−31.5541	+	46.6064i	−1.45859	+	2.15438i
$469$	−11.8211	−	1.70725i	−0.545846	−	0.0788334i
$470$	1.22687	−	10.2421i	0.0565912	−	0.472433i
$471$	0.387614	+	23.3671i	0.0178603	+	1.07670i
$472$	−22.0388	+	7.16083i	−1.01442	+	0.329604i
$473$	−12.4384	+	17.1200i	−0.571918	+	0.787177i
$474$	36.8368	+	11.2971i	1.69197	+	0.518892i
$475$	−3.66325	+	0.277920i	−0.168081	+	0.0127519i
$476$	−11.2632	−	65.3299i	−0.516248	−	2.99439i
$477$	−6.25486	+	2.26431i	−0.286390	+	0.103676i
$478$	12.9189	+	39.7603i	0.590898	+	1.81860i
$479$	0.916503	+	2.82071i	0.0418761	+	0.128881i	0.969809	−	0.243866i	$-0.0784158\pi$
$479$	0.916503	+	2.82071i	0.0418761	+	0.128881i	−0.927933	+	0.372748i	$0.878416\pi$
$480$	−7.63233	+	1.63896i	−0.348367	+	0.0748080i
$481$	46.5981	+	15.1407i	2.12469	+	0.690354i
$482$	54.7215			2.49250
$483$	5.40910	+	2.55315i	0.246123	+	0.116172i
$484$	23.8845	−	17.3531i	1.08566	−	0.788779i
$485$	0.138541	+	0.248202i	0.00629082	+	0.0112703i
$486$	19.4380	−	32.0349i	0.881724	−	1.45313i
$487$	11.8482	−	8.60819i	0.536891	−	0.390074i	−0.286038	−	0.958218i	$-0.592338\pi$
$487$	11.8482	−	8.60819i	0.536891	−	0.390074i	0.822929	+	0.568144i	$0.192338\pi$
$488$	−13.7254	+	9.97210i	−0.621320	+	0.451416i
$489$	−22.8495	+	17.1873i	−1.03329	+	0.777238i
$490$	−37.4659	−	3.45377i	−1.69254	−	0.156025i
$491$	−11.8964	−	16.3740i	−0.536878	−	0.738950i	0.451281	−	0.892382i	$-0.350967\pi$
$491$	−11.8964	−	16.3740i	−0.536878	−	0.738950i	−0.988159	+	0.153432i	$0.950967\pi$
$492$	35.7974	+	25.1119i	1.61387	+	1.13213i
$493$		−	24.8632i		−	1.11978i
$494$	8.34125	+	2.71023i	0.375290	+	0.121939i
$495$	11.0270	+	4.66482i	0.495628	+	0.209668i
$496$	−12.8788	+	4.18457i	−0.578274	+	0.187893i
$497$	0.220135	+	0.417843i	0.00987442	+	0.0187428i
$498$	37.4645	+	49.8069i	1.67883	+	2.23190i
$499$	−23.8122			−1.06598			−0.532990	−	0.846121i	$-0.678932\pi$
$499$	−23.8122			−1.06598			−0.532990	+	0.846121i	$0.678932\pi$
$500$	26.2905	−	33.0609i	1.17575	−	1.47853i
$501$	−4.83812	+	15.7759i	−0.216151	+	0.704814i
$502$	9.95535	−	13.7024i	0.444329	−	0.611567i
$503$	7.73575	+	23.8082i	0.344920	+	1.06155i	0.961627	+	0.274362i	$0.0884665\pi$
$503$	7.73575	+	23.8082i	0.344920	+	1.06155i	−0.616707	+	0.787193i	$0.711533\pi$
$504$	3.73287	−	33.7180i	0.166275	−	1.50192i
$505$	8.09881	+	41.0174i	0.360392	+	1.82525i
$506$	−5.32587	−	1.73048i	−0.236764	−	0.0769293i
$507$	5.92106	−	19.3070i	0.262964	−	0.857456i
$508$	5.60312	−	17.2446i	0.248598	−	0.765106i
$509$	−27.8064	+	20.2025i	−1.23250	+	0.895462i	−0.997075	−	0.0764313i	$-0.975647\pi$
$509$	−27.8064	+	20.2025i	−1.23250	+	0.895462i	−0.235423	+	0.971893i	$0.575647\pi$
$510$	41.2186	−	45.9705i	1.82519	−	2.03561i
$511$	23.1725	+	11.4114i	1.02509	+	0.504808i
$512$	−16.8740	−	23.2250i	−0.745731	−	1.02641i
$513$	−3.68523	−	0.997732i	−0.162707	−	0.0440510i
$514$	28.6793	−	39.4737i	1.26499	−	1.74111i
$515$	0.732519	+	1.31234i	0.0322786	+	0.0578286i
$516$	25.1953	+	73.3791i	1.10916	+	3.23034i
$517$	3.25773	+	1.05850i	0.143275	+	0.0465528i
$518$	−61.8374	+	10.6611i	−2.71698	+	0.468421i
$519$	−0.377970	−	0.265146i	−0.0165910	−	0.0116386i
$520$	−41.4398	+	23.1308i	−1.81726	+	1.01435i
$521$	−10.4227	−	32.0779i	−0.456628	−	1.40536i	−0.869213	−	0.494438i	$-0.835374\pi$
$521$	−10.4227	−	32.0779i	−0.456628	−	1.40536i	0.412584	−	0.910919i	$-0.364626\pi$
$522$	7.49669	−	25.9740i	0.328121	−	1.13685i
$523$	−4.09017	+	5.62963i	−0.178851	+	0.246167i	−0.889025	−	0.457860i	$-0.848616\pi$
$523$	−4.09017	+	5.62963i	−0.178851	+	0.246167i	0.710174	+	0.704026i	$0.248616\pi$
$524$	21.5516			0.941486
$525$	−12.5030	−	19.2009i	−0.545675	−	0.837997i
$526$	−34.6106			−1.50909
$527$	−19.4248	+	26.7359i	−0.846156	+	1.16463i
$528$	0.139342	+	8.40017i	0.00606408	+	0.365571i
$529$	6.58093	+	20.2540i	0.286127	+	0.880610i
$530$	−11.8337	−	1.41752i	−0.514022	−	0.0615729i
$531$	−12.8347	+	9.99177i	−0.556978	+	0.433606i
$532$	−7.23769	+	1.24781i	−0.313794	+	0.0540996i
$533$	−31.5587	−	10.2540i	−1.36696	−	0.444151i
$534$	−25.5732	+	8.78076i	−1.10666	+	0.379981i
$535$	−16.3518	+	3.22864i	−0.706952	+	0.139586i
$536$	11.3408	−	15.6093i	0.489850	−	0.674221i
$537$	29.8762	−	10.2582i	1.28925	−	0.442676i
$538$	1.45943	+	2.00873i	0.0629205	+	0.0866027i
$539$	3.53512	−	11.9834i	0.152269	−	0.516161i
$540$	37.2186	−	23.2751i	1.60163	−	1.00160i
$541$	11.7899	−	8.56584i	0.506886	−	0.368274i	−0.304755	−	0.952431i	$-0.598575\pi$
$541$	11.7899	−	8.56584i	0.506886	−	0.368274i	0.811641	+	0.584157i	$0.198575\pi$
$542$	−5.70245	+	17.5503i	−0.244941	+	0.753852i
$543$	−33.1479	−	10.1658i	−1.42251	−	0.436254i
$544$	−12.7134	−	4.13083i	−0.545082	−	0.177108i
$545$	10.0548	+	9.32083i	0.430698	+	0.399260i
$546$	10.1863	+	53.7437i	0.435934	+	2.30002i
$547$	9.70650	+	29.8735i	0.415020	+	1.27730i	0.912233	+	0.409672i	$0.134357\pi$
$547$	9.70650	+	29.8735i	0.415020	+	1.27730i	−0.497213	+	0.867629i	$0.665643\pi$
$548$	46.6993	−	64.2761i	1.99489	−	2.74574i
$549$	−6.67618	+	9.86093i	−0.284933	+	0.420854i
$550$	13.8858	+	16.3512i	0.592091	+	0.697218i
$551$	−2.75452			−0.117346
$552$	−7.72185	+	5.80834i	−0.328664	+	0.247219i
$553$	21.6625	−	11.4126i	0.921183	−	0.485313i
$554$	−22.9172	+	7.44625i	−0.973659	+	0.316361i
$555$	−28.4515	−	25.5105i	−1.20770	−	1.08286i
$556$	49.4513	+	16.0677i	2.09720	+	0.681423i
$557$		−	19.7716i		−	0.837749i	−0.908044	−	0.418875i	$-0.862425\pi$
$557$		−	19.7716i		−	0.837749i	0.908044	−	0.418875i	$-0.137575\pi$
$558$	−28.3540	+	22.0735i	−1.20032	+	0.934447i
$559$	−34.6062	−	47.6313i	−1.46368	−	2.01459i
$560$	8.76794	−	13.4763i	0.370513	−	0.569478i
$561$	12.3248	+	16.3851i	0.520353	+	0.691779i
$562$	34.6730	−	25.1914i	1.46259	−	1.06264i
$563$	−7.32068	+	5.31878i	−0.308530	+	0.224160i	−0.731265	−	0.682093i	$-0.761070\pi$
$563$	−7.32068	+	5.31878i	−0.308530	+	0.224160i	0.422736	+	0.906253i	$0.361070\pi$
$564$	10.0362	−	7.54917i	0.422599	−	0.317877i
$565$	−2.06248	+	2.22488i	−0.0867693	+	0.0936016i
$566$	2.24320	−	1.62978i	0.0942886	−	0.0685047i
$567$	−5.59238	−	23.1457i	−0.234858	−	0.972030i
$568$	−0.762941			−0.0320123
$569$	2.29355	+	0.745219i	0.0961506	+	0.0312412i	0.356697	−	0.934220i	$-0.383903\pi$
$569$	2.29355	+	0.745219i	0.0961506	+	0.0312412i	−0.260547	+	0.965461i	$0.583903\pi$
$570$	−5.09293	−	4.56648i	−0.213319	−	0.191269i
$571$	−7.39374	−	22.7556i	−0.309418	−	0.952292i	−0.977991	−	0.208645i	$-0.933095\pi$
$571$	−7.39374	−	22.7556i	−0.309418	−	0.952292i	0.668573	−	0.743647i	$-0.266905\pi$
$572$	−10.3477	−	31.8469i	−0.432658	−	1.33159i
$573$	21.4197	+	28.4763i	0.894823	+	1.18961i
$574$	41.8794	−	7.22023i	1.74801	−	0.301366i
$575$	−1.54139	+	6.34159i	−0.0642805	+	0.264462i
$576$	−25.5380	−	17.2901i	−1.06408	−	0.720421i
$577$	−9.19217	+	12.6519i	−0.382675	+	0.526707i	−0.956291	−	0.292417i	$-0.905540\pi$
$577$	−9.19217	+	12.6519i	−0.382675	+	0.526707i	0.573616	+	0.819125i	$0.305540\pi$
$578$	61.6917	−	20.0448i	2.56604	−	0.833756i
$579$	25.8989	−	0.429611i	1.07632	−	0.0178540i
$580$	21.5307	−	23.2261i	0.894016	−	0.964411i
$581$	39.1987	+	5.66125i	1.62624	+	0.234868i
$582$	−0.155178	+	0.505997i	−0.00643236	+	0.0209742i
$583$	1.22298	−	3.76396i	0.0506508	−	0.155887i
$584$	−33.7573	+	24.5261i	−1.39689	+	1.01490i
$585$	−21.8237	+	25.1673i	−0.902301	+	1.04054i
$586$	−0.0834964	+	0.114923i	−0.00344921	+	0.00474743i
$587$	11.0837	−	8.05280i	0.457475	−	0.332375i	−0.335065	−	0.942195i	$-0.608758\pi$
$587$	11.0837	−	8.05280i	0.457475	−	0.332375i	0.792540	+	0.609820i	$0.208758\pi$
$588$	−28.5241	−	35.8415i	−1.17631	−	1.47808i
$589$	2.96199	+	2.15201i	0.122047	+	0.0886720i
$590$	−28.5901	+	5.64506i	−1.17704	+	0.232403i
$591$	−15.3395	+	5.26695i	−0.630984	+	0.216654i
$592$	8.28590	−	25.5014i	0.340548	−	1.04810i
$593$	27.4292			1.12638			0.563191	−	0.826327i	$-0.309574\pi$
$593$	27.4292			1.12638			0.563191	+	0.826327i	$0.309574\pi$
$594$	7.93505	+	20.8333i	0.325579	+	0.854800i
$595$	−2.02009	−	39.1843i	−0.0828158	−	1.60640i
$596$	−31.8418	+	10.3460i	−1.30429	+	0.423790i
$597$	−0.316142	−	19.0585i	−0.0129388	−	0.780012i
$598$	9.15783	−	12.6047i	0.374491	−	0.515443i
$599$		−	22.7483i		−	0.929471i	−0.885450	−	0.464735i	$-0.846149\pi$
$599$		−	22.7483i		−	0.929471i	0.885450	−	0.464735i	$-0.153851\pi$
$600$	36.8565	−	3.41187i	1.50466	−	0.139289i
$601$			5.39886i			0.220224i	0.993919	+	0.110112i	$0.0351210\pi$
$601$			5.39886i			0.220224i	−0.993919	+	0.110112i	$0.964879\pi$
$602$	67.6447	+	33.3118i	2.75699	+	1.35769i
$603$	3.75549	−	13.0118i	0.152935	−	0.529880i
$604$	−10.7964	−	33.2280i	−0.439301	−	1.35203i
$605$	15.2574	−	8.51636i	0.620303	−	0.346239i
$606$	−44.7062	+	63.7295i	−1.81607	+	2.58883i
$607$			15.2145i			0.617538i	0.951137	+	0.308769i	$0.0999170\pi$
$607$			15.2145i			0.617538i	−0.951137	+	0.308769i	$0.900083\pi$
$608$	−0.457642	+	1.40848i	−0.0185598	+	0.0571213i
$609$	−8.25851	−	15.0643i	−0.334652	−	0.610438i
$610$	−18.6300	+	10.3988i	−0.754306	+	0.421037i
$611$	−5.60166	+	7.71002i	−0.226619	+	0.311914i
$612$	75.1286	−	2.49315i	3.03689	−	0.100780i
$613$	−6.60883	+	4.80159i	−0.266928	+	0.193935i	−0.713196	−	0.700965i	$-0.752753\pi$
$613$	−6.60883	+	4.80159i	−0.266928	+	0.193935i	0.446268	+	0.894900i	$0.352753\pi$
$614$	−24.3153	−	17.6661i	−0.981287	−	0.712947i
$615$	19.2688	+	17.2770i	0.776994	+	0.696677i
$616$	14.4650	+	14.0755i	0.582812	+	0.567118i
$617$	−34.3397	−	11.1576i	−1.38246	−	0.449190i	−0.478985	−	0.877823i	$-0.658995\pi$
$617$	−34.3397	−	11.1576i	−1.38246	−	0.449190i	−0.903478	+	0.428633i	$0.858995\pi$
$618$	−0.820488	+	2.67540i	−0.0330049	+	0.107620i
$619$	5.28665	+	1.71774i	0.212488	+	0.0690417i	0.413327	−	0.910583i	$-0.364367\pi$
$619$	5.28665	+	1.71774i	0.212488	+	0.0690417i	−0.200839	+	0.979624i	$0.564367\pi$
$620$	−41.2982	+	8.15426i	−1.65858	+	0.327483i
$621$	−3.70866	+	5.67845i	−0.148823	+	0.227868i
$622$	−51.0365	+	16.5828i	−2.04638	+	0.664908i
$623$	−7.59098	+	15.4146i	−0.304126	+	0.617574i
$624$	−22.3469	−	6.85333i	−0.894594	−	0.274353i
$625$	17.7770	−	17.5778i	0.711080	−	0.703111i
$626$	−36.1470			−1.44472
$627$	1.81525	−	1.36543i	0.0724942	−	0.0545298i
$628$	−48.4819	+	15.7527i	−1.93464	+	0.628602i
$629$	−20.2213	−	62.2346i	−0.806275	−	2.48146i
$630$	9.70442	−	41.5441i	0.386633	−	1.65516i
$631$	10.8195	−	33.2991i	0.430719	−	1.32562i	−0.466691	−	0.884420i	$-0.654554\pi$
$631$	10.8195	−	33.2991i	0.430719	−	1.32562i	0.897410	−	0.441197i	$-0.145446\pi$
$632$			39.5536i			1.57336i
$633$	15.1546	+	10.6310i	0.602343	+	0.422544i
$634$	51.3490	−	37.3072i	2.03933	−	1.48166i
$635$	4.50661	−	9.73947i	0.178839	−	0.386499i
$636$	−8.72226	−	11.5957i	−0.345860	−	0.459801i
$637$	28.6691	+	19.6568i	1.13591	+	0.778829i
$638$	9.45395	+	13.0122i	0.374286	+	0.515160i
$639$	−0.503541	+	0.182286i	−0.0199198	+	0.00721112i
$640$	−22.5378	−	40.3775i	−0.890885	−	1.59606i
$641$	−9.76678	−	13.4428i	−0.385765	−	0.530960i	0.571336	−	0.820717i	$-0.306425\pi$
$641$	−9.76678	−	13.4428i	−0.385765	−	0.530960i	−0.957100	+	0.289757i	$0.906425\pi$
$642$	−25.4061	−	17.8224i	−1.00270	−	0.703394i
$643$			4.62484i			0.182386i	0.995833	+	0.0911929i	$0.0290680\pi$
$643$			4.62484i			0.182386i	−0.995833	+	0.0911929i	$0.970932\pi$
$644$	−1.86495	+	12.9130i	−0.0734893	+	0.508843i
$645$	9.64078	+	44.8952i	0.379605	+	1.76775i
$646$	−3.61968	−	11.1402i	−0.142415	−	0.438307i
$647$	−10.9999	−	33.8543i	−0.432451	−	1.33095i	−0.895676	−	0.444707i	$-0.853308\pi$
$647$	−10.9999	−	33.8543i	−0.432451	−	1.33095i	0.463225	−	0.886241i	$-0.346692\pi$
$648$	37.2911	+	9.43517i	1.46493	+	0.370648i
$649$		−	9.67712i		−	0.379860i
$650$	−55.2042	+	22.6843i	−2.16529	+	0.889751i
$651$	−2.88871	+	22.6511i	−0.113218	+	0.887766i
$652$	−50.4558	−	36.6583i	−1.97600	−	1.43565i
$653$	−37.3880	+	12.1481i	−1.46311	+	0.475392i	−0.929017	−	0.370037i	$-0.879345\pi$
$653$	−37.3880	+	12.1481i	−1.46311	+	0.475392i	−0.534088	+	0.845429i	$0.679345\pi$
$654$	0.423401	+	25.5245i	0.0165563	+	0.998088i
$655$	12.6649	+	1.51709i	0.494859	+	0.0592775i
$656$	−5.61163	+	17.2708i	−0.219098	+	0.674313i
$657$	−16.4199	+	24.2527i	−0.640601	+	0.946187i
$658$	1.74464	−	12.0799i	0.0680130	−	0.470924i
$659$	−8.73091	−	12.0171i	−0.340108	−	0.468119i	0.604365	−	0.796708i	$-0.293427\pi$
$659$	−8.73091	−	12.0171i	−0.340108	−	0.468119i	−0.944473	+	0.328589i	$0.893427\pi$
$660$	−2.67569	+	25.9791i	−0.104151	+	1.01124i
$661$	−20.4734	+	28.1792i	−0.796324	+	1.09605i	0.196968	+	0.980410i	$0.436891\pi$
$661$	−20.4734	+	28.1792i	−0.796324	+	1.09605i	−0.993292	+	0.115636i	$0.963109\pi$
$662$	−21.6415	−	29.7870i	−0.841122	−	1.15770i
$663$	−53.9517	+	18.5248i	−2.09531	+	0.719443i
$664$	−37.6063	+	51.7607i	−1.45941	+	2.00870i
$665$	−4.34111	+	0.223800i	−0.168341	+	0.00867859i
$666$	−2.35987	−	71.1123i	−0.0914430	−	2.75554i
$667$	−1.51209	+	4.65372i	−0.0585482	+	0.180193i
$668$	−35.9932			−1.39262
$669$	−4.70184	+	6.70255i	−0.181783	+	0.259135i
$670$	16.4957	−	17.7945i	0.637283	−	0.687463i
$671$	−2.18935	−	6.73813i	−0.0845189	−	0.260122i
$672$	−9.07500	+	1.72003i	−0.350076	+	0.0663516i
$673$	−19.2034	−	13.9521i	−0.740238	−	0.537815i	0.152547	−	0.988296i	$-0.451252\pi$
$673$	−19.2034	−	13.9521i	−0.740238	−	0.537815i	−0.892786	+	0.450481i	$0.851252\pi$
$674$		−	34.4988i		−	1.32884i
$675$	23.5101	−	11.0578i	0.904905	−	0.425614i
$676$	44.0497			1.69422
$677$	−3.99476	−	2.90236i	−0.153531	−	0.111547i	0.508368	−	0.861140i	$-0.330249\pi$
$677$	−3.99476	−	2.90236i	−0.153531	−	0.111547i	−0.661899	+	0.749593i	$0.730249\pi$
$678$	−5.64799	+	0.0936888i	−0.216910	+	0.00359810i
$679$	0.156765	+	0.297560i	0.00601610	+	0.0114193i
$680$	57.5238	+	26.6172i	2.20594	+	1.02072i
$681$	22.6034	+	15.8563i	0.866166	+	0.607616i
$682$		−	21.3784i		−	0.818621i
$683$	4.50525	+	1.46384i	0.172389	+	0.0560124i	0.393940	−	0.919136i	$-0.371112\pi$
$683$	4.50525	+	1.46384i	0.172389	+	0.0560124i	−0.221551	+	0.975149i	$0.571112\pi$
$684$	−0.276208	−	8.32326i	−0.0105611	−	0.318248i
$685$	31.9677	−	34.4849i	1.22142	−	1.31760i
$686$	−44.2183	−	5.15867i	−1.68826	−	0.196959i
$687$	11.6523	−	4.00090i	0.444562	−	0.152644i
$688$	−26.0668	+	18.9386i	−0.993786	+	0.722028i
$689$	8.90811	+	6.47212i	0.339372	+	0.246568i
$690$	−10.5108	+	6.09769i	−0.400138	+	0.232135i
$691$	9.22614	+	12.6987i	0.350979	+	0.483081i	0.947608	−	0.319436i	$-0.103494\pi$
$691$	9.22614	+	12.6987i	0.350979	+	0.483081i	−0.596629	+	0.802517i	$0.703494\pi$
$692$	0.311205	−	0.957791i	0.0118302	−	0.0364098i
$693$	12.9099	+	5.83377i	0.490406	+	0.221606i
$694$	3.22802	−	9.93481i	0.122534	−	0.377120i
$695$	27.9293	+	12.9233i	1.05942	+	0.490210i
$696$	27.7485	−	0.460292i	1.05180	−	0.0174473i
$697$	13.6949	+	42.1485i	0.518730	+	1.59649i
$698$	28.3564	+	20.6021i	1.07330	+	0.779801i
$699$	−11.8998	−	3.64943i	−0.450093	−	0.138034i
$700$	32.0453	−	38.3536i	1.21120	−	1.44963i
$701$		−	21.7629i		−	0.821974i	−0.911641	−	0.410987i	$-0.865184\pi$
$701$		−	21.7629i		−	0.821974i	0.911641	−	0.410987i	$-0.134816\pi$
$702$	−61.9478	+	3.08503i	−2.33807	+	0.116437i
$703$	−6.89478	+	2.24025i	−0.260042	+	0.0844927i
$704$	17.4505	−	5.67002i	0.657691	−	0.213697i
$705$	6.42922	−	3.72983i	0.242139	−	0.140474i
$706$	−6.60614	−	2.14646i	−0.248625	−	0.0807833i
$707$	8.40479	+	48.7502i	0.316095	+	1.83344i
$708$	−29.0452	−	20.3752i	−1.09159	−	0.765747i
$709$	−26.2519	+	19.0732i	−0.985913	+	0.716307i	−0.959022	−	0.283331i	$-0.908561\pi$
$709$	−26.2519	+	19.0732i	−0.985913	+	0.716307i	−0.0268904	+	0.999638i	$0.508561\pi$
$710$	−0.952657	−	0.114116i	−0.0357526	−	0.00428268i
$711$	9.45036	+	26.1054i	0.354416	+	0.979028i
$712$	−16.3151	−	22.4558i	−0.611433	−	0.841566i
$713$	5.26178	−	3.82290i	0.197055	−	0.143169i
$714$	50.0731	−	53.1963i	1.87394	−	1.99082i
$715$	−3.83907	−	19.4434i	−0.143573	−	0.727142i
$716$	40.4998	+	55.7432i	1.51355	+	2.08322i
$717$	−17.2998	+	24.6612i	−0.646074	+	0.920989i
$718$	−59.3123			−2.21352
$719$	1.39000	−	4.27799i	0.0518383	−	0.159542i	−0.921786	−	0.387699i	$-0.873270\pi$
$719$	1.39000	−	4.27799i	0.0518383	−	0.159542i	0.973624	+	0.228157i	$0.0732700\pi$
$720$	13.7731	+	11.9433i	0.513294	+	0.445100i
$721$	0.828879	+	1.57331i	0.0308691	+	0.0585932i
$722$	42.2019	−	13.7122i	1.57059	−	0.510316i
$723$	23.7023	+	31.5108i	0.881499	+	1.17190i
$724$		−	75.6280i		−	2.81069i
$725$	14.2876	−	12.1333i	0.530629	−	0.450620i
$726$	31.1045	+	9.53909i	1.15440	+	0.354029i
$727$	−24.6643	+	33.9476i	−0.914750	+	1.25905i	0.0507685	+	0.998710i	$0.483833\pi$
$727$	−24.6643	+	33.9476i	−0.914750	+	1.25905i	−0.965518	+	0.260335i	$0.916167\pi$
$728$	−49.6805	+	26.1735i	−1.84128	+	0.970056i
$729$	26.8664	−	2.68257i	0.995052	−	0.0993546i
$730$	−45.8199	+	25.5757i	−1.69587	+	0.946598i
$731$	−24.2986	+	74.7833i	−0.898715	+	2.76596i
$732$	−24.8337	−	7.61597i	−0.917880	−	0.281494i
$733$	−5.78024	−	1.87811i	−0.213498	−	0.0693697i	0.200315	−	0.979731i	$-0.435803\pi$
$733$	−5.78024	−	1.87811i	−0.213498	−	0.0693697i	−0.413813	+	0.910362i	$0.635803\pi$
$734$	56.9774	−	41.3965i	2.10307	−	1.52797i
$735$	−14.2393	−	23.0704i	−0.525226	−	0.850963i
$736$	2.12839	+	1.54636i	0.0784533	+	0.0569997i
$737$	4.73599	+	6.51853i	0.174452	+	0.240113i
$738$	1.59822	+	48.1609i	0.0588314	+	1.77283i
$739$	2.15873	+	1.56841i	0.0794100	+	0.0576947i	0.626782	−	0.779195i	$-0.284372\pi$
$739$	2.15873	+	1.56841i	0.0794100	+	0.0576947i	−0.547372	+	0.836889i	$0.684372\pi$
$740$	35.0035	−	75.6479i	1.28675	−	2.78087i
$741$	2.05230	+	5.97715i	0.0753932	+	0.219576i
$742$	−13.9571	−	2.01574i	−0.512380	−	0.0740002i
$743$		−	34.6247i		−	1.27026i	−0.772406	−	0.635129i	$-0.780947\pi$
$743$		−	34.6247i		−	1.27026i	0.772406	−	0.635129i	$-0.219053\pi$
$744$	−30.1982	−	21.1840i	−1.10712	−	0.776644i
$745$	−19.4403	+	3.83845i	−0.712238	+	0.140630i
$746$	−36.2033	+	11.7632i	−1.32550	+	0.430680i
$747$	−12.4532	+	43.1471i	−0.455640	+	1.57867i
$748$	−26.2871	+	36.1811i	−0.961153	+	1.32291i
$749$	−19.4346	+	3.35062i	−0.710124	+	0.122429i
$750$	46.5317	+	1.25248i	1.69910	+	0.0457340i
$751$	−25.4784			−0.929722			−0.464861	−	0.885384i	$-0.653896\pi$
$751$	−25.4784			−0.929722			−0.464861	+	0.885384i	$0.653896\pi$
$752$	4.21940	+	3.06557i	0.153866	+	0.111790i
$753$	12.2025	−	0.202414i	0.444683	−	0.00737639i
$754$	−42.5589	+	13.8282i	−1.54990	+	0.503594i
$755$	−4.00555	−	20.2866i	−0.145777	−	0.738305i
$756$	44.6915	−	26.4651i	1.62541	−	0.962528i
$757$	−29.9784			−1.08958			−0.544791	−	0.838572i	$-0.683391\pi$
$757$	−29.9784			−1.08958			−0.544791	+	0.838572i	$0.683391\pi$
$758$	70.4524	+	22.8914i	2.55895	+	0.831452i
$759$	−1.31039	−	3.81640i	−0.0475642	−	0.138526i
$760$	2.94884	−	6.37289i	0.106965	−	0.231169i
$761$	5.24687	+	3.81207i	0.190199	+	0.138188i	0.678810	−	0.734314i	$-0.262496\pi$
$761$	5.24687	+	3.81207i	0.190199	+	0.138188i	−0.488611	+	0.872502i	$0.662496\pi$
$762$	18.8986	−	6.48899i	0.684624	−	0.235071i
$763$	11.6264	+	11.3134i	0.420905	+	0.409571i
$764$	−45.6854	+	62.8806i	−1.65284	+	2.27494i
$765$	44.3252	+	3.82344i	1.60258	+	0.138237i
$766$	1.26367	+	1.73929i	0.0456583	+	0.0628432i
$767$	25.6060	+	8.31989i	0.924579	+	0.300414i
$768$	14.8031	−	48.2689i	0.534159	−	1.74175i
$769$	47.3093	+	15.3717i	1.70602	+	0.554318i	0.989662	−	0.143418i	$-0.0458094\pi$
$769$	47.3093	+	15.3717i	1.70602	+	0.554318i	0.716354	+	0.697737i	$0.245809\pi$
$770$	15.9566	+	19.7391i	0.575037	+	0.711349i
$771$	35.1528	−	0.583114i	1.26600	−	0.0210003i
$772$	17.4595	+	53.7348i	0.628381	+	1.93396i
$773$	−14.3234	−	10.4065i	−0.515175	−	0.374297i	0.299608	−	0.954062i	$-0.403144\pi$
$773$	−14.3234	−	10.4065i	−0.515175	−	0.374297i	−0.814783	+	0.579766i	$0.803144\pi$
$774$	−47.9327	+	70.7981i	−1.72291	+	2.54478i
$775$	−24.8431	+	1.88478i	−0.892392	+	0.0677032i
$776$	−0.543315			−0.0195039
$777$	−32.9236	−	30.9906i	−1.18113	−	1.11178i
$778$	−4.35750	−	13.4110i	−0.156224	−	0.480808i
$779$	4.66950	−	1.51721i	0.167302	−	0.0543598i
$780$	−66.4412	−	29.4155i	−2.37898	−	1.05324i
$781$	0.0984551	−	0.303014i	0.00352300	−	0.0108427i
$782$	−20.8083			−0.744105
$783$	18.2040	−	6.93361i	0.650559	−	0.247787i
$784$	10.7574	−	15.6895i	0.384192	−	0.560340i
$785$	−29.5995	+	5.84437i	−1.05645	+	0.208595i
$786$	14.2766	+	18.9799i	0.509230	+	0.676992i
$787$	−4.81396	−	6.62584i	−0.171599	−	0.236186i	0.714552	−	0.699582i	$-0.246631\pi$
$787$	−4.81396	−	6.62584i	−0.171599	−	0.236186i	−0.886151	+	0.463397i	$0.846631\pi$
$788$	−20.7940	−	28.6205i	−0.740757	−	1.01956i
$789$	−14.9914	−	19.9301i	−0.533707	−	0.709532i
$790$	−5.91616	+	49.3892i	−0.210488	+	1.75719i
$791$	−2.50339	+	2.57266i	−0.0890101	+	0.0914733i
$792$	−18.0584	+	14.0584i	−0.641677	+	0.499544i
$793$	19.7116			0.699980
$794$	−14.8857	+	45.8134i	−0.528273	+	1.62586i
$795$	−4.30942	−	7.42828i	−0.152840	−	0.263454i
$796$	39.5424	−	12.8481i	1.40154	−	0.455389i
$797$	−0.0273596	−	0.0842042i	−0.000969127	−	0.00298266i	0.950571	−	0.310508i	$-0.100499\pi$
$797$	−0.0273596	−	0.0842042i	−0.000969127	−	0.00298266i	−0.951540	+	0.307525i	$0.900499\pi$
$798$	−5.89345	−	5.54744i	−0.208626	−	0.196377i
$799$	12.7280			0.450286
$800$	−3.83040	−	9.32161i	−0.135425	−	0.329569i
$801$	−16.1332	−	10.9227i	−0.570038	−	0.385935i
$802$	−51.3894	−	37.3366i	−1.81462	−	1.31840i
$803$	−5.38464	−	16.5722i	−0.190020	−	0.584821i
$804$	29.5365	−	0.489952i	1.04167	−	0.0172793i
$805$	−2.00494	+	7.45711i	−0.0706647	+	0.262829i
$806$	56.5680	+	18.3801i	1.99252	+	0.647410i
$807$	−0.524565	+	1.71047i	−0.0184656	+	0.0602114i
$808$	−76.0031	−	24.6949i	−2.67378	−	0.868763i
$809$	24.4428	+	33.6426i	0.859362	+	1.18281i	0.981721	+	0.190325i	$0.0609541\pi$
$809$	24.4428	+	33.6426i	0.859362	+	1.18281i	−0.122359	+	0.992486i	$0.539046\pi$
$810$	45.1528	+	17.3591i	1.58651	+	0.609937i
$811$	−8.41911	+	11.5879i	−0.295635	+	0.406907i	−0.930834	−	0.365442i	$-0.880918\pi$
$811$	−8.41911	+	11.5879i	−0.295635	+	0.406907i	0.635199	+	0.772348i	$0.280918\pi$
$812$	26.1334	−	26.8566i	0.917103	−	0.942483i
$813$	−12.5762	+	4.31813i	−0.441066	+	0.151444i
$814$	34.2469	+	24.8818i	1.20035	+	0.872108i
$815$	−27.0701	−	25.0942i	−0.948225	−	0.879011i
$816$	10.1379	+	29.5257i	0.354897	+	1.03361i
$817$	8.28501	+	2.69196i	0.289856	+	0.0941799i
$818$	−45.3195			−1.58456
$819$	−26.5356	+	29.1445i	−0.927230	+	1.01839i
$820$	−23.7061	+	51.2326i	−0.827854	+	1.78912i
$821$	35.4726	−	11.5258i	1.23800	−	0.402252i	0.384396	−	0.923169i	$-0.374410\pi$
$821$	35.4726	−	11.5258i	1.23800	−	0.402252i	0.853607	+	0.520917i	$0.174410\pi$
$822$	87.5417	−	1.45214i	3.05337	−	0.0506492i
$823$	−17.4998	−	12.7144i	−0.610006	−	0.443195i	0.239411	−	0.970918i	$-0.423046\pi$
$823$	−17.4998	−	12.7144i	−0.610006	−	0.443195i	−0.849416	+	0.527723i	$0.823046\pi$
$824$	−2.87272			−0.100076
$825$	−3.40114	+	15.0784i	−0.118413	+	0.524963i
$826$	−33.9801	+	5.85833i	−1.18232	+	0.203837i
$827$	−14.1781	+	19.5145i	−0.493021	+	0.678585i	−0.980942	−	0.194303i	$-0.937756\pi$
$827$	−14.1781	+	19.5145i	−0.493021	+	0.678585i	0.487921	+	0.872888i	$0.337756\pi$
$828$	−14.2137	−	4.10239i	−0.493960	−	0.142568i
$829$	−17.0400	+	5.53662i	−0.591822	+	0.192295i	−0.589590	−	0.807703i	$-0.700711\pi$
$829$	−17.0400	+	5.53662i	−0.591822	+	0.192295i	−0.00223229	+	0.999998i	$0.500711\pi$
$830$	−54.6997	+	59.0068i	−1.89865	+	2.04816i
$831$	−14.2143	−	9.97134i	−0.493089	−	0.345902i
$832$			51.0495i			1.76982i
$833$	−1.26697	−	46.4078i	−0.0438980	−	1.60793i
$834$	18.6081	+	54.1944i	0.644345	+	1.87660i
$835$	−21.1516	−	2.53368i	−0.731981	−	0.0876815i
$836$	4.00840	+	2.91227i	0.138633	+	0.100723i
$837$	−24.9922	−	6.76634i	−0.863856	−	0.233879i
$838$	−2.75679	−	3.79439i	−0.0952317	−	0.131075i
$839$	36.7931	+	26.7317i	1.27024	+	0.922882i	0.999212	−	0.0396906i	$-0.0126372\pi$
$839$	36.7931	+	26.7317i	1.27024	+	0.922882i	0.271025	+	0.962572i	$0.412637\pi$
$840$	43.6942	−	2.97994i	1.50759	−	0.102818i
$841$	−12.0914	+	8.78495i	−0.416946	+	0.302929i
$842$	89.8921	+	29.2077i	3.09789	+	1.00656i
$843$	29.5246	+	9.05458i	1.01688	+	0.311856i
$844$	−12.4777	+	38.4025i	−0.429501	+	1.32187i
$845$	25.8860	+	3.10080i	0.890507	+	0.106671i
$846$	13.2967	+	3.83773i	0.457150	+	0.131944i
$847$	18.2915	−	9.63665i	0.628504	−	0.331119i
$848$	3.54194	−	4.87506i	0.121631	−	0.167410i
$849$	1.91012	+	0.585793i	0.0655551	+	0.0201044i
$850$	67.8467	+	41.8399i	2.32712	+	1.43510i
$851$			12.8784i			0.441467i
$852$	−0.702177	−	0.933503i	−0.0240562	−	0.0319813i
$853$	26.7822	−	8.70208i	0.917007	−	0.297954i	0.187768	−	0.982213i	$-0.439875\pi$
$853$	26.7822	−	8.70208i	0.917007	−	0.297954i	0.729238	+	0.684260i	$0.239875\pi$
$854$	−22.3347	+	11.7668i	−0.764279	+	0.402651i
$855$	0.423587	−	4.91065i	0.0144864	−	0.167941i
$856$	9.84476	−	30.2991i	0.336487	−	1.03560i
$857$	17.5316			0.598867			0.299434	−	0.954117i	$-0.403202\pi$
$857$	17.5316			0.598867			0.299434	+	0.954117i	$0.403202\pi$
$858$	21.1920	−	30.2096i	0.723484	−	1.03134i
$859$	−26.0137	−	35.8048i	−0.887577	−	1.22164i	−0.974264	−	0.225409i	$-0.927628\pi$
$859$	−26.0137	−	35.8048i	−0.887577	−	1.22164i	0.0866871	−	0.996236i	$-0.472372\pi$
$860$	−87.4587	+	48.8175i	−2.98232	+	1.66466i
$861$	22.2975	+	20.9885i	0.759898	+	0.715285i
$862$	59.2080	−	43.0171i	2.01663	−	1.46517i
$863$	−6.69244	−	9.21135i	−0.227813	−	0.313558i	0.679774	−	0.733422i	$-0.262078\pi$
$863$	−6.69244	−	9.21135i	−0.227813	−	0.313558i	−0.907587	+	0.419864i	$0.862078\pi$
$864$	−0.520929	−	10.4603i	−0.0177224	−	0.355867i
$865$	0.250304	−	0.540945i	0.00851058	−	0.0183927i
$866$	47.6287	−	34.6043i	1.61849	−	1.17590i
$867$	38.2640	+	26.8422i	1.29951	+	0.911610i
$868$	−49.0840	+	8.46233i	−1.66602	+	0.287230i
$869$	−15.7093	−	5.10427i	−0.532902	−	0.173150i
$870$	34.7174	+	3.57569i	1.17703	+	0.121227i
$871$	−21.3200	+	6.92729i	−0.722401	+	0.234722i
$872$	−24.9235	+	8.09814i	−0.844016	+	0.274237i
$873$	−0.358588	+	0.129812i	−0.0121364	+	0.00439346i
$874$			2.30529i			0.0779776i
$875$	21.5314	−	20.2829i	0.727895	−	0.685688i
$876$	−61.0778	−	18.7313i	−2.06363	−	0.632871i
$877$	21.8960	+	15.9084i	0.739377	+	0.537189i	0.892516	−	0.451016i	$-0.148938\pi$
$877$	21.8960	+	15.9084i	0.739377	+	0.537189i	−0.153139	+	0.988205i	$0.548938\pi$
$878$	−17.6722	−	54.3893i	−0.596407	−	1.83555i
$879$	−0.102343	+	0.00169767i	−0.00345195	+	5.72609e-5i
$880$	−10.6406	+	2.10097i	−0.358696	+	0.0708238i
$881$	8.73622	−	26.8873i	0.294331	−	0.905857i	−0.689114	−	0.724652i	$-0.742000\pi$
$881$	8.73622	−	26.8873i	0.294331	−	0.905857i	0.983445	−	0.181205i	$-0.0579997\pi$
$882$	12.6692	−	48.8632i	0.426594	−	1.64531i
$883$	−1.86013	+	5.72488i	−0.0625983	+	0.192658i	−0.977465	−	0.211099i	$-0.932296\pi$
$883$	−1.86013	+	5.72488i	−0.0625983	+	0.192658i	0.914866	+	0.403757i	$0.132296\pi$
$884$	−73.1362	−	100.663i	−2.45984	−	3.38568i
$885$	−15.6343	−	14.0182i	−0.525541	−	0.471216i
$886$	−11.5443	−	8.38745i	−0.387840	−	0.281782i
$887$	1.68328	−	1.22297i	0.0565188	−	0.0410633i	−0.559167	−	0.829055i	$-0.688879\pi$
$887$	1.68328	−	1.22297i	0.0565188	−	0.0410633i	0.615686	+	0.787992i	$0.288879\pi$
$888$	69.0825	−	23.7201i	2.31826	−	0.795993i
$889$	5.60974	−	11.3914i	0.188145	−	0.382056i
$890$	−17.0133	−	30.4800i	−0.570286	−	1.02169i
$891$	−8.55962	+	13.5931i	−0.286758	+	0.455387i
$892$	−16.9845	−	5.51861i	−0.568684	−	0.184777i
$893$		−	1.41010i		−	0.0471872i
$894$	−30.2047	−	21.1886i	−1.01020	−	0.708654i
$895$	19.8760	+	35.6087i	0.664381	+	1.19027i
$896$	−25.5025	−	48.4069i	−0.851980	−	1.61716i
$897$	11.2249	−	0.186199i	0.374789	−	0.00621700i
$898$	−51.3322	−	37.2950i	−1.71298	−	1.24455i
$899$	−18.6804			−0.623025
$900$	38.0957	+	41.9560i	1.26986	+	1.39853i
$901$		−	14.7059i		−	0.489924i
$902$	−23.1938	−	16.8513i	−0.772268	−	0.561086i
$903$	10.1176	+	53.3814i	0.336694	+	1.77642i
$904$	−1.79193	−	5.51499i	−0.0595987	−	0.183426i
$905$	5.32370	−	44.4432i	0.176966	−	1.47734i
$906$	22.1110	−	31.5197i	0.734590	−	1.04717i
$907$	0.511242			0.0169755			0.00848775	−	0.999964i	$-0.497298\pi$
$907$	0.511242			0.0169755			0.00848775	+	0.999964i	$0.497298\pi$
$908$	−18.6108	+	57.2781i	−0.617620	+	1.90084i
$909$	−56.0622	+	1.86043i	−1.85947	+	0.0617066i
$910$	−65.9492	+	25.2511i	−2.18619	+	0.837065i
$911$	−30.4264	+	41.8783i	−1.00807	+	1.38749i	−0.0878320	+	0.996135i	$0.527994\pi$
$911$	−30.4264	+	41.8783i	−1.00807	+	1.38749i	−0.920239	+	0.391356i	$0.872006\pi$
$912$	3.27106	−	1.12315i	0.108316	−	0.0371911i
$913$	−15.7046	−	21.6155i	−0.519745	−	0.715368i
$914$	38.6126	−	53.1456i	1.27719	−	1.75790i
$915$	−14.0575	−	6.22369i	−0.464728	−	0.205749i
$916$	15.7957	+	21.7409i	0.521903	+	0.718338i
$917$	14.9375	+	2.15734i	0.493279	+	0.0712415i
$918$	51.9638	+	64.5122i	1.71506	+	2.12922i
$919$	−5.72791	+	17.6287i	−0.188946	+	0.581516i	−0.999994	−	0.00346334i	$-0.998898\pi$
$919$	−5.72791	+	17.6287i	−0.188946	+	0.581516i	0.811048	+	0.584980i	$0.198898\pi$
$920$	−9.14817	−	8.48041i	−0.301606	−	0.279591i
$921$	−0.359192	−	21.6537i	−0.0118358	−	0.713514i
$922$	−14.3857	+	4.67421i	−0.473769	+	0.153937i
$923$	0.717138	+	0.521031i	0.0236049	+	0.0171500i
$924$	−3.90923	+	30.6532i	−0.128604	+	1.00842i
$925$	25.8951	−	41.9909i	0.851425	−	1.38065i
$926$			23.4805i			0.771618i
$927$	−1.89599	+	0.686364i	−0.0622725	+	0.0225432i
$928$	−2.33499	−	7.18637i	−0.0766499	−	0.235904i
$929$	9.32968	+	28.7138i	0.306097	+	0.942069i	0.979266	+	0.202580i	$0.0649327\pi$
$929$	9.32968	+	28.7138i	0.306097	+	0.942069i	−0.673169	+	0.739489i	$0.735067\pi$
$930$	−34.5388	−	30.9686i	−1.13257	−	1.01550i
$931$	−5.14137	+	0.140364i	−0.168502	+	0.00460025i
$932$		−	27.1499i		−	0.889324i
$933$	−31.6552	−	22.2061i	−1.03634	−	0.726995i
$934$	54.1228	+	74.4937i	1.77095	+	2.43751i
$935$	−17.9947	+	19.4116i	−0.588489	+	0.634827i
$936$	−21.6734	−	59.8698i	−0.708416	−	1.95691i
$937$	−20.2460	−	27.8663i	−0.661409	−	0.910352i	0.338118	−	0.941104i	$-0.390210\pi$
$937$	−20.2460	−	27.8663i	−0.661409	−	0.910352i	−0.999527	+	0.0307519i	$0.990210\pi$
$938$	20.0220	−	20.5760i	0.653740	−	0.671832i
$939$	−15.6569	−	20.8149i	−0.510943	−	0.679268i
$940$	11.8900	+	11.0221i	0.387808	+	0.359501i
$941$	18.3903	−	13.3613i	0.599505	−	0.435566i	−0.246198	−	0.969220i	$-0.579181\pi$
$941$	18.3903	−	13.3613i	0.599505	−	0.435566i	0.845703	+	0.533653i	$0.179181\pi$
$942$	−45.9893	−	32.2615i	−1.49841	−	1.05114i
$943$		−	8.72194i		−	0.284026i
$944$	4.55316	−	14.0132i	0.148193	−	0.456090i
$945$	28.1262	−	12.4064i	0.914944	−	0.403580i
$946$	−15.7188	−	48.3774i	−0.511061	−	1.57289i
$947$	30.0600	−	9.76708i	0.976818	−	0.317387i	0.223253	−	0.974761i	$-0.428332\pi$
$947$	30.0600	−	9.76708i	0.976818	−	0.317387i	0.753565	+	0.657373i	$0.228332\pi$
$948$	−48.3961	+	36.4034i	−1.57183	+	1.18233i
$949$	48.4801			1.57373
$950$	4.63532	−	7.51653i	0.150390	−	0.243868i
$951$	43.7245	+	13.4094i	1.41786	+	0.434829i
$952$	67.2806	+	33.1326i	2.18058	+	1.07383i
$953$	47.0302	−	15.2811i	1.52346	−	0.495002i	0.576703	−	0.816954i	$-0.304339\pi$
$953$	47.0302	−	15.2811i	1.52346	−	0.495002i	0.946756	+	0.321952i	$0.104339\pi$
$954$	4.43409	−	15.3629i	0.143559	−	0.497393i
$955$	−31.2737	+	33.7362i	−1.01199	+	1.09168i
$956$	−62.4925	−	20.3050i	−2.02115	−	0.656712i
$957$	−3.39805	+	11.0801i	−0.109843	+	0.358170i
$958$	−6.78030	−	2.20305i	−0.219062	−	0.0711774i
$959$	38.8015	−	39.8753i	1.25297	−	1.28764i
$960$	16.1182	−	36.4065i	0.520214	−	1.17501i
$961$	−4.99215	−	3.62701i	−0.161037	−	0.117000i
$962$	−95.2820	+	69.2264i	−3.07201	+	2.23195i
$963$	−0.741672	−	22.3495i	−0.0239000	−	0.720204i
$964$	−50.5539	+	69.5815i	−1.62823	+	2.24107i
$965$	6.47760	+	32.8066i	0.208521	+	1.05608i
$966$	−12.6075	+	6.91166i	−0.405641	+	0.222379i
$967$	−1.22625	+	3.77402i	−0.0394337	+	0.121364i	−0.968835	−	0.247705i	$-0.920324\pi$
$967$	−1.22625	+	3.77402i	−0.0394337	+	0.121364i	0.929402	+	0.369069i	$0.120324\pi$
$968$			33.3985i			1.07347i
$969$	4.84715	−	6.90969i	0.155713	−	0.221971i
$970$	−0.678418	−	0.0812654i	−0.0217827	−	0.00260928i
$971$	13.5351	+	41.6567i	0.434362	+	1.33683i	0.893739	+	0.448587i	$0.148073\pi$
$971$	13.5351	+	41.6567i	0.434362	+	1.33683i	−0.459378	+	0.888241i	$0.651927\pi$
$972$	22.7766	+	54.3115i	0.730559	+	1.74204i
$973$	32.6665	+	16.0867i	1.04724	+	0.515716i
$974$			35.2034i			1.12799i
$975$	−36.9739	−	21.9632i	−1.18411	−	0.703385i
$976$		−	10.7874i		−	0.345296i
$977$	26.5916	−	36.6002i	0.850741	−	1.17094i	−0.132958	−	0.991122i	$-0.542448\pi$
$977$	26.5916	−	36.6002i	0.850741	−	1.17094i	0.983699	−	0.179823i	$-0.0575524\pi$
$978$	−1.13991	−	68.7190i	−0.0364503	−	2.19739i
$979$	11.0241	−	3.58193i	0.352330	−	0.114479i
$980$	39.0041	−	44.4493i	1.24594	−	1.41988i
$981$	−14.5147	+	11.2996i	−0.463417	+	0.360769i
$982$	48.6507			1.55251
$983$	−10.7945	+	33.2221i	−0.344292	+	1.05962i	0.617670	+	0.786437i	$0.288077\pi$
$983$	−10.7945	+	33.2221i	−0.344292	+	1.05962i	−0.961962	+	0.273183i	$0.911923\pi$
$984$	−46.7862	+	16.0644i	−1.49149	+	0.512116i
$985$	−10.2050	−	18.2828i	−0.325160	−	0.582538i
$986$	48.3510	+	35.1290i	1.53981	+	1.11874i
$987$	7.71178	−	4.22772i	0.245469	−	0.134570i
$988$	−11.1522	+	8.10253i	−0.354798	+	0.257776i
$989$	9.09608	−	12.5197i	0.289239	−	0.398103i
$990$	−24.6516	+	14.8532i	−0.783480	+	0.472065i
$991$	16.2871	−	11.8333i	0.517377	−	0.375896i	−0.298238	−	0.954492i	$-0.596399\pi$
$991$	16.2871	−	11.8333i	0.517377	−	0.375896i	0.815615	+	0.578595i	$0.196399\pi$
$992$	−3.10360	+	9.55190i	−0.0985394	+	0.303273i
$993$	7.77864	−	25.3641i	0.246848	−	0.804906i
$994$	−1.12360	−	0.162275i	−0.0356384	−	0.00514706i
$995$	24.1417	−	4.76674i	0.765344	−	0.151116i
$996$	−97.9434	+	1.62468i	−3.10346	+	0.0514801i
$997$	−14.3376	+	4.65858i	−0.454078	+	0.147539i	−0.527122	−	0.849790i	$-0.676729\pi$
$997$	−14.3376	+	4.65858i	−0.454078	+	0.147539i	0.0730437	+	0.997329i	$0.476729\pi$
$998$	33.6441	−	46.3071i	1.06499	−	1.46583i
$999$	39.9271	−	32.1608i	1.26324	−	1.01752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bb.a.41.7	✓	304
3.2	odd	2	inner	525.2.bb.a.41.69	yes	304
7.6	odd	2	inner	525.2.bb.a.41.8	yes	304
21.20	even	2	inner	525.2.bb.a.41.70	yes	304
25.11	even	5	inner	525.2.bb.a.461.70	yes	304
75.11	odd	10	inner	525.2.bb.a.461.8	yes	304
175.111	odd	10	inner	525.2.bb.a.461.69	yes	304
525.461	even	10	inner	525.2.bb.a.461.7	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bb.a.41.7	✓	304	1.1	even	1	trivial
525.2.bb.a.41.8	yes	304	7.6	odd	2	inner
525.2.bb.a.41.69	yes	304	3.2	odd	2	inner
525.2.bb.a.41.70	yes	304	21.20	even	2	inner
525.2.bb.a.461.7	yes	304	525.461	even	10	inner
525.2.bb.a.461.8	yes	304	75.11	odd	10	inner
525.2.bb.a.461.69	yes	304	175.111	odd	10	inner
525.2.bb.a.461.70	yes	304	25.11	even	5	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41289 + 1.94468i) q^{2} +(-1.73181 + 0.0287273i) q^{3} +(-1.16748 - 3.59315i) q^{4} +(-0.433145 - 2.19371i) q^{5} +(2.39100 - 3.40841i) q^{6} +(-0.449509 - 2.60729i) q^{7} +(4.06484 + 1.32074i) q^{8} +(2.99835 - 0.0995005i) q^{9} +O(q^{10})\)	\(q+(-1.41289 + 1.94468i) q^{2} +(-1.73181 + 0.0287273i) q^{3} +(-1.16748 - 3.59315i) q^{4} +(-0.433145 - 2.19371i) q^{5} +(2.39100 - 3.40841i) q^{6} +(-0.449509 - 2.60729i) q^{7} +(4.06484 + 1.32074i) q^{8} +(2.99835 - 0.0995005i) q^{9} +(4.87807 + 2.25716i) q^{10} +(-1.04911 + 1.44397i) q^{11} +(2.12508 + 6.18912i) q^{12} +(-2.91883 - 4.01743i) q^{13} +(5.70545 + 2.80967i) q^{14} +(0.813145 + 3.78666i) q^{15} +(-2.19859 + 1.59737i) q^{16} +(-2.04945 + 6.30755i) q^{17} +(-4.04285 + 5.97142i) q^{18} +(0.698794 + 0.227052i) q^{19} +(-7.37665 + 4.11748i) q^{20} +(0.853366 + 4.50242i) q^{21} +(-1.32579 - 4.08036i) q^{22} +(0.767204 - 1.05597i) q^{23} +(-7.07747 - 2.17051i) q^{24} +(-4.62477 + 1.90039i) q^{25} +11.9366 q^{26} +(-5.18972 + 0.258451i) q^{27} +(-8.84356 + 4.65912i) q^{28} +(-3.56540 + 1.15847i) q^{29} +(-8.51274 - 3.76884i) q^{30} +(4.73903 + 1.53980i) q^{31} +2.01558i q^{32} +(1.77538 - 2.53083i) q^{33} +(-9.37053 - 12.8974i) q^{34} +(-5.52494 + 2.11543i) q^{35} +(-3.85804 - 10.6573i) q^{36} +(-7.98232 + 5.79949i) q^{37} +(-1.42887 + 1.03813i) q^{38} +(5.17028 + 6.87359i) q^{39} +(1.13668 - 9.48916i) q^{40} +(5.40604 - 3.92772i) q^{41} +(-9.96149 - 4.70191i) q^{42} +11.8562 q^{43} +(6.41322 + 2.08378i) q^{44} +(-1.51700 - 6.53443i) q^{45} +(0.969539 + 2.98393i) q^{46} +(-0.593047 - 1.82521i) q^{47} +(3.76165 - 2.82950i) q^{48} +(-6.59588 + 2.34400i) q^{49} +(2.83865 - 11.6788i) q^{50} +(3.36806 - 10.9824i) q^{51} +(-11.0275 + 15.1781i) q^{52} +(-2.10884 + 0.685203i) q^{53} +(6.82992 - 10.4575i) q^{54} +(3.62208 + 1.67599i) q^{55} +(1.61638 - 11.1919i) q^{56} +(-1.21670 - 0.373137i) q^{57} +(2.78468 - 8.57037i) q^{58} +(-4.38634 + 3.18686i) q^{59} +(12.6567 - 7.34261i) q^{60} +(-2.33319 + 3.21136i) q^{61} +(-9.69017 + 7.04032i) q^{62} +(-1.60721 - 7.77283i) q^{63} +(-8.31684 - 6.04254i) q^{64} +(-7.54882 + 8.14322i) q^{65} +(2.41324 + 7.02834i) q^{66} +(1.39499 - 4.29335i) q^{67} +25.0566 q^{68} +(-1.29832 + 1.85077i) q^{69} +(3.69232 - 13.7331i) q^{70} +(-0.169770 + 0.0551616i) q^{71} +(12.3192 + 3.55560i) q^{72} +(-5.73841 + 7.89825i) q^{73} -23.7171i q^{74} +(7.95464 - 3.42398i) q^{75} -2.77595i q^{76} +(4.23644 + 2.08625i) q^{77} +(-20.6720 + 0.342907i) q^{78} +(2.85977 + 8.80148i) q^{79} +(4.45647 + 4.13118i) q^{80} +(8.98020 - 0.596675i) q^{81} +16.0625i q^{82} +(-4.62581 + 14.2368i) q^{83} +(15.1816 - 8.32277i) q^{84} +(14.7247 + 1.76382i) q^{85} +(-16.7515 + 23.0564i) q^{86} +(6.14133 - 2.10868i) q^{87} +(-6.17157 + 4.48391i) q^{88} +(-5.25402 - 3.81727i) q^{89} +(14.8507 + 6.28238i) q^{90} +(-9.16255 + 9.41611i) q^{91} +(-4.68993 - 1.52385i) q^{92} +(-8.25134 - 2.53051i) q^{93} +(4.38737 + 1.42554i) q^{94} +(0.195408 - 1.63130i) q^{95} +(-0.0579022 - 3.49061i) q^{96} +(-0.120899 + 0.0392824i) q^{97} +(4.76095 - 16.1387i) q^{98} +(-3.00192 + 4.43392i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9	\( 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9} + 8 q^{15} - 92 q^{16} - 16 q^{18} + 12 q^{21} - 48 q^{22} - 32 q^{25} - 36 q^{28} - 14 q^{30} - 8 q^{36} - 4 q^{37} - 26 q^{39} - 11 q^{42} - 20 q^{49} + 20 q^{51} - 168 q^{57} + 32 q^{58} + 76 q^{60} + 29 q^{63} + 68 q^{64} - 44 q^{67} + 30 q^{70} - 114 q^{72} - 124 q^{78} - 68 q^{79} - 2 q^{81} + 102 q^{84} + 72 q^{85} - 156 q^{88} + 70 q^{91} - 32 q^{93} - 36 q^{99}+O(q^{100}) \) 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9 + 8 * q^15 - 92 * q^16 - 16 * q^18 + 12 * q^21 - 48 * q^22 - 32 * q^25 - 36 * q^28 - 14 * q^30 - 8 * q^36 - 4 * q^37 - 26 * q^39 - 11 * q^42 - 20 * q^49 + 20 * q^51 - 168 * q^57 + 32 * q^58 + 76 * q^60 + 29 * q^63 + 68 * q^64 - 44 * q^67 + 30 * q^70 - 114 * q^72 - 124 * q^78 - 68 * q^79 - 2 * q^81 + 102 * q^84 + 72 * q^85 - 156 * q^88 + 70 * q^91 - 32 * q^93 - 36 * q^99

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