LMFDB - Embedded newform 285.2.bf.c.224.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(14,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 7]))

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

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

chi := DirichletCharacter("285.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.bf (of order $18$, 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:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			224.20
Character	$\chi$	$=$	285.224
Dual form			285.2.bf.c.14.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.266954 - 0.733451i) q^{2} +(1.16679 + 1.28008i) q^{3} +(1.06540 + 0.893980i) q^{4} +(-1.49957 - 1.65870i) q^{5} +(1.25036 - 0.514056i) q^{6} +(2.52789 + 1.45948i) q^{7} +(2.29201 - 1.32329i) q^{8} +(-0.277222 + 2.98716i) q^{9} +O(q^{10})$	\(q+(0.266954 - 0.733451i) q^{2} +(1.16679 + 1.28008i) q^{3} +(1.06540 + 0.893980i) q^{4} +(-1.49957 - 1.65870i) q^{5} +(1.25036 - 0.514056i) q^{6} +(2.52789 + 1.45948i) q^{7} +(2.29201 - 1.32329i) q^{8} +(-0.277222 + 2.98716i) q^{9} +(-1.61689 + 0.657068i) q^{10} +(-3.52126 + 2.03300i) q^{11} +(0.0987298 + 2.40689i) q^{12} +(0.641785 - 3.63974i) q^{13} +(1.74529 - 1.46447i) q^{14} +(0.373587 - 3.85492i) q^{15} +(0.124307 + 0.704980i) q^{16} +(0.993740 + 0.361692i) q^{17} +(2.11693 + 1.00076i) q^{18} +(-1.64736 - 4.03562i) q^{19} +(-0.114810 - 3.10777i) q^{20} +(1.08126 + 4.93881i) q^{21} +(0.551091 + 3.12539i) q^{22} +(1.88849 + 1.58463i) q^{23} +(4.36820 + 1.38996i) q^{24} +(-0.502553 + 4.97468i) q^{25} +(-2.49825 - 1.44236i) q^{26} +(-4.14728 + 3.13051i) q^{27} +(1.38848 + 3.81482i) q^{28} +(3.47358 - 1.26428i) q^{29} +(-2.72767 - 1.30310i) q^{30} +(-7.63449 - 4.40778i) q^{31} +(5.76300 + 1.01617i) q^{32} +(-6.71097 - 2.13543i) q^{33} +(0.530566 - 0.632304i) q^{34} +(-1.36993 - 6.38161i) q^{35} +(-2.96582 + 2.93470i) q^{36} +6.63764 q^{37} +(-3.39970 + 0.130930i) q^{38} +(5.40800 - 3.42526i) q^{39} +(-5.63198 - 1.81737i) q^{40} +(-0.771734 - 4.37672i) q^{41} +(3.91102 + 0.525390i) q^{42} +(-6.90512 - 8.22920i) q^{43} +(-5.56903 - 0.981970i) q^{44} +(5.37052 - 4.01965i) q^{45} +(1.66639 - 0.962090i) q^{46} +(-10.8688 + 3.95592i) q^{47} +(-0.757393 + 0.981683i) q^{48} +(0.760167 + 1.31665i) q^{49} +(3.51452 + 1.69661i) q^{50} +(0.696486 + 1.69409i) q^{51} +(3.93762 - 3.30405i) q^{52} +(-0.566815 + 0.675504i) q^{53} +(1.18894 + 3.87753i) q^{54} +(8.65253 + 2.79207i) q^{55} +7.72527 q^{56} +(3.24381 - 6.81745i) q^{57} -2.88521i q^{58} +(-6.30821 - 2.29600i) q^{59} +(3.84424 - 3.77307i) q^{60} +(5.24334 + 4.39968i) q^{61} +(-5.27095 + 4.42285i) q^{62} +(-5.06050 + 7.14663i) q^{63} +(1.56792 - 2.71571i) q^{64} +(-6.99964 + 4.39354i) q^{65} +(-3.35775 + 4.35210i) q^{66} +(-3.61261 + 1.31488i) q^{67} +(0.735389 + 1.27373i) q^{68} +(0.175004 + 4.26635i) q^{69} +(-5.04631 - 0.698822i) q^{70} +(1.20512 - 1.01122i) q^{71} +(3.31749 + 7.21345i) q^{72} +(-4.16722 + 0.734794i) q^{73} +(1.77194 - 4.86838i) q^{74} +(-6.95437 + 5.16108i) q^{75} +(1.85266 - 5.77227i) q^{76} -11.8685 q^{77} +(-1.06857 - 4.88089i) q^{78} +(-10.4655 + 1.84536i) q^{79} +(0.982940 - 1.26336i) q^{80} +(-8.84630 - 1.65622i) q^{81} +(-3.41613 - 0.602355i) q^{82} +(7.48538 - 12.9651i) q^{83} +(-3.26323 + 6.22845i) q^{84} +(-0.890250 - 2.19070i) q^{85} +(-7.87907 + 2.86775i) q^{86} +(5.67131 + 2.97133i) q^{87} +(-5.38051 + 9.31931i) q^{88} +(-2.14511 + 12.1655i) q^{89} +(-1.51453 - 5.01207i) q^{90} +(6.93450 - 8.26422i) q^{91} +(0.595376 + 3.37654i) q^{92} +(-3.26550 - 14.9157i) q^{93} +9.02778i q^{94} +(-4.22353 + 8.78418i) q^{95} +(5.42340 + 8.56277i) q^{96} +(10.3221 + 3.75693i) q^{97} +(1.16863 - 0.206060i) q^{98} +(-5.09674 - 11.0822i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{4} - 30 q^{6} - 12 q^{9}+O(q^{10}) $ 192 * q - 12 * q^4 - 30 * q^6 - 12 * q^9	$ 192 q - 12 q^{4} - 30 q^{6} - 12 q^{9} + 18 q^{10} + 15 q^{15} - 36 q^{16} - 48 q^{19} - 30 q^{21} - 156 q^{24} - 12 q^{25} - 24 q^{30} - 36 q^{31} + 24 q^{34} - 6 q^{36} - 6 q^{40} - 30 q^{45} + 36 q^{46} + 60 q^{49} + 24 q^{51} - 6 q^{54} - 90 q^{55} + 90 q^{60} + 12 q^{61} - 60 q^{64} + 108 q^{66} + 90 q^{69} - 18 q^{70} - 132 q^{76} - 120 q^{79} + 36 q^{81} + 198 q^{84} - 66 q^{85} - 114 q^{90} - 72 q^{91} + 144 q^{96} + 78 q^{99}+O(q^{100}) $ 192 * q - 12 * q^4 - 30 * q^6 - 12 * q^9 + 18 * q^10 + 15 * q^15 - 36 * q^16 - 48 * q^19 - 30 * q^21 - 156 * q^24 - 12 * q^25 - 24 * q^30 - 36 * q^31 + 24 * q^34 - 6 * q^36 - 6 * q^40 - 30 * q^45 + 36 * q^46 + 60 * q^49 + 24 * q^51 - 6 * q^54 - 90 * q^55 + 90 * q^60 + 12 * q^61 - 60 * q^64 + 108 * q^66 + 90 * q^69 - 18 * q^70 - 132 * q^76 - 120 * q^79 + 36 * q^81 + 198 * q^84 - 66 * q^85 - 114 * q^90 - 72 * q^91 + 144 * q^96 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	0.266954	−	0.733451i	0.188765	−	0.518628i	−0.808822	−	0.588054i	$-0.799894\pi$
$2$	0.266954	−	0.733451i	0.188765	−	0.518628i	0.997587	+	0.0694256i	$0.0221166\pi$
$3$	1.16679	+	1.28008i	0.673644	+	0.739056i
$3$	1.16679	+	1.28008i	0.673644	+	0.739056i
$4$	1.06540	+	0.893980i	0.532702	+	0.446990i
$5$	−1.49957	−	1.65870i	−0.670630	−	0.741792i
$5$	−1.49957	−	1.65870i	−0.670630	−	0.741792i
$6$	1.25036	−	0.514056i	0.510456	−	0.209863i
$7$	2.52789	+	1.45948i	0.955454	+	0.551632i	0.894771	−	0.446525i	$-0.147339\pi$
$7$	2.52789	+	1.45948i	0.955454	+	0.551632i	0.0606833	+	0.998157i	$0.480672\pi$
$8$	2.29201	−	1.32329i	0.810347	−	0.467854i
$9$	−0.277222	+	2.98716i	−0.0924074	+	0.995721i
$10$	−1.61689	+	0.657068i	−0.511306	+	0.207783i
$11$	−3.52126	+	2.03300i	−1.06170	+	0.612973i	−0.925902	−	0.377763i	$-0.876693\pi$
$11$	−3.52126	+	2.03300i	−1.06170	+	0.612973i	−0.135799	+	0.990736i	$0.543360\pi$
$12$	0.0987298	+	2.40689i	0.0285008	+	0.694808i
$13$	0.641785	−	3.63974i	0.177999	−	1.00948i	−0.756626	−	0.653848i	$-0.773153\pi$
$13$	0.641785	−	3.63974i	0.177999	−	1.00948i	0.934625	−	0.355635i	$-0.115735\pi$
$14$	1.74529	−	1.46447i	0.466448	−	0.391396i
$15$	0.373587	−	3.85492i	0.0964598	−	0.995337i
$16$	0.124307	+	0.704980i	0.0310767	+	0.176245i
$17$	0.993740	+	0.361692i	0.241017	+	0.0877231i	0.459705	−	0.888072i	$-0.347955\pi$
$17$	0.993740	+	0.361692i	0.241017	+	0.0877231i	−0.218687	+	0.975795i	$0.570177\pi$
$18$	2.11693	+	1.00076i	0.498966	+	0.235883i
$19$	−1.64736	−	4.03562i	−0.377930	−	0.925834i
$19$	−1.64736	−	4.03562i	−0.377930	−	0.925834i
$20$	−0.114810	−	3.10777i	−0.0256723	−	0.694919i
$21$	1.08126	+	4.93881i	0.235949	+	1.07774i
$22$	0.551091	+	3.12539i	0.117493	+	0.666336i
$23$	1.88849	+	1.58463i	0.393777	+	0.330418i	0.818083	−	0.575101i	$-0.195037\pi$
$23$	1.88849	+	1.58463i	0.393777	+	0.330418i	−0.424305	+	0.905519i	$0.639482\pi$
$24$	4.36820	+	1.38996i	0.891656	+	0.283725i
$25$	−0.502553	+	4.97468i	−0.100511	+	0.994936i
$26$	−2.49825	−	1.44236i	−0.489946	−	0.282871i
$27$	−4.14728	+	3.13051i	−0.798143	+	0.602467i
$28$	1.38848	+	3.81482i	0.262398	+	0.720934i
$29$	3.47358	−	1.26428i	0.645028	−	0.234771i	0.00126888	−	0.999999i	$-0.499596\pi$
$29$	3.47358	−	1.26428i	0.645028	−	0.234771i	0.643759	+	0.765228i	$0.277374\pi$
$30$	−2.72767	−	1.30310i	−0.498001	−	0.237912i
$31$	−7.63449	−	4.40778i	−1.37120	−	0.791660i	−0.380117	−	0.924938i	$-0.624116\pi$
$31$	−7.63449	−	4.40778i	−1.37120	−	0.791660i	−0.991079	+	0.133278i	$0.957450\pi$
$32$	5.76300	+	1.01617i	1.01876	+	0.179636i
$33$	−6.71097	−	2.13543i	−1.16823	−	0.371731i
$34$	0.530566	−	0.632304i	0.0909913	−	0.108439i
$35$	−1.36993	−	6.38161i	−0.231560	−	1.07869i
$36$	−2.96582	+	2.93470i	−0.494303	+	0.489117i
$37$	6.63764			1.09122			0.545610	−	0.838039i	$-0.316298\pi$
$37$	6.63764			1.09122			0.545610	+	0.838039i	$0.316298\pi$
$38$	−3.39970	+	0.130930i	−0.551504	+	0.0212397i
$39$	5.40800	−	3.42526i	0.865973	−	0.548481i
$40$	−5.63198	−	1.81737i	−0.890494	−	0.287352i
$41$	−0.771734	−	4.37672i	−0.120525	−	0.683529i	−0.983866	−	0.178908i	$-0.942743\pi$
$41$	−0.771734	−	4.37672i	−0.120525	−	0.683529i	0.863341	−	0.504621i	$-0.168368\pi$
$42$	3.91102	+	0.525390i	0.603484	+	0.0810694i
$43$	−6.90512	−	8.22920i	−1.05302	−	1.25494i	−0.965947	−	0.258740i	$-0.916693\pi$
$43$	−6.90512	−	8.22920i	−1.05302	−	1.25494i	−0.0870739	−	0.996202i	$-0.527752\pi$
$44$	−5.56903	−	0.981970i	−0.839563	−	0.148038i
$45$	5.37052	−	4.01965i	0.800589	−	0.599214i
$46$	1.66639	−	0.962090i	0.245696	−	0.141852i
$47$	−10.8688	+	3.95592i	−1.58538	+	0.577030i	−0.976364	−	0.216131i	$-0.930656\pi$
$47$	−10.8688	+	3.95592i	−1.58538	+	0.577030i	−0.609012	+	0.793161i	$0.708434\pi$
$48$	−0.757393	+	0.981683i	−0.109320	+	0.141694i
$49$	0.760167	+	1.31665i	0.108595	+	0.188093i
$50$	3.51452	+	1.69661i	0.497029	+	0.239937i
$51$	0.696486	+	1.69409i	0.0975276	+	0.237219i
$52$	3.93762	−	3.30405i	0.546049	−	0.458190i
$53$	−0.566815	+	0.675504i	−0.0778581	+	0.0927877i	−0.803567	−	0.595214i	$-0.797067\pi$
$53$	−0.566815	+	0.675504i	−0.0778581	+	0.0927877i	0.725709	+	0.688002i	$0.241512\pi$
$54$	1.18894	+	3.87753i	0.161795	+	0.527664i
$55$	8.65253	+	2.79207i	1.16671	+	0.376483i
$56$	7.72527			1.03233
$57$	3.24381	−	6.81745i	0.429653	−	0.902994i
$58$		−	2.88521i		−	0.378846i
$59$	−6.30821	−	2.29600i	−0.821259	−	0.298914i	−0.102993	−	0.994682i	$-0.532842\pi$
$59$	−6.30821	−	2.29600i	−0.821259	−	0.298914i	−0.718266	+	0.695768i	$0.755064\pi$
$60$	3.84424	−	3.77307i	0.496290	−	0.487101i
$61$	5.24334	+	4.39968i	0.671341	+	0.563322i	0.913462	−	0.406924i	$-0.133399\pi$
$61$	5.24334	+	4.39968i	0.671341	+	0.563322i	−0.242121	+	0.970246i	$0.577843\pi$
$62$	−5.27095	+	4.42285i	−0.669411	+	0.561703i
$63$	−5.06050	+	7.14663i	−0.637563	+	0.900391i
$64$	1.56792	−	2.71571i	0.195989	−	0.339464i
$65$	−6.99964	+	4.39354i	−0.868198	+	0.544952i
$66$	−3.35775	+	4.35210i	−0.413311	+	0.535707i
$67$	−3.61261	+	1.31488i	−0.441350	+	0.160638i	−0.553131	−	0.833095i	$-0.686567\pi$
$67$	−3.61261	+	1.31488i	−0.441350	+	0.160638i	0.111780	+	0.993733i	$0.464345\pi$
$68$	0.735389	+	1.27373i	0.0891790	+	0.154463i
$69$	0.175004	+	4.26635i	0.0210680	+	0.513608i
$70$	−5.04631	−	0.698822i	−0.603149	−	0.0835253i
$71$	1.20512	−	1.01122i	0.143022	−	0.120009i	−0.568470	−	0.822704i	$-0.692464\pi$
$71$	1.20512	−	1.01122i	0.143022	−	0.120009i	0.711492	+	0.702695i	$0.248020\pi$
$72$	3.31749	+	7.21345i	0.390970	+	0.850113i
$73$	−4.16722	+	0.734794i	−0.487736	+	0.0860011i	−0.412108	−	0.911135i	$-0.635207\pi$
$73$	−4.16722	+	0.734794i	−0.487736	+	0.0860011i	−0.0756284	+	0.997136i	$0.524096\pi$
$74$	1.77194	−	4.86838i	0.205984	−	0.565938i
$75$	−6.95437	+	5.16108i	−0.803022	+	0.595950i
$76$	1.85266	−	5.77227i	0.212515	−	0.662124i
$77$	−11.8685			−1.35254
$78$	−1.06857	−	4.88089i	−0.120992	−	0.552652i
$79$	−10.4655	+	1.84536i	−1.17747	+	0.207619i	−0.727935	−	0.685646i	$-0.759520\pi$
$79$	−10.4655	+	1.84536i	−1.17747	+	0.207619i	−0.449530	+	0.893265i	$0.648409\pi$
$80$	0.982940	−	1.26336i	0.109896	−	0.141248i
$81$	−8.84630	−	1.65622i	−0.982922	−	0.184024i
$82$	−3.41613	−	0.602355i	−0.377248	−	0.0665190i
$83$	7.48538	−	12.9651i	0.821627	−	1.42310i	−0.0828429	−	0.996563i	$-0.526400\pi$
$83$	7.48538	−	12.9651i	0.821627	−	1.42310i	0.904470	−	0.426537i	$-0.140267\pi$
$84$	−3.26323	+	6.22845i	−0.356047	+	0.679580i
$85$	−0.890250	−	2.19070i	−0.0965611	−	0.237614i
$86$	−7.87907	+	2.86775i	−0.849621	+	0.309237i
$87$	5.67131	+	2.97133i	0.608028	+	0.318560i
$88$	−5.38051	+	9.31931i	−0.573564	+	0.993442i
$89$	−2.14511	+	12.1655i	−0.227381	+	1.28954i	0.630698	+	0.776028i	$0.282769\pi$
$89$	−2.14511	+	12.1655i	−0.227381	+	1.28954i	−0.858080	+	0.513516i	$0.828343\pi$
$90$	−1.51453	−	5.01207i	−0.159646	−	0.528319i
$91$	6.93450	−	8.26422i	0.726933	−	0.866325i
$92$	0.595376	+	3.37654i	0.0620722	+	0.352029i
$93$	−3.26550	−	14.9157i	−0.338617	−	1.54669i
$94$			9.02778i			0.931144i
$95$	−4.22353	+	8.78418i	−0.433325	+	0.901238i
$96$	5.42340	+	8.56277i	0.553524	+	0.873934i
$97$	10.3221	+	3.75693i	1.04805	+	0.381459i	0.807926	−	0.589283i	$-0.200590\pi$
$97$	10.3221	+	3.75693i	1.04805	+	0.381459i	0.240123	+	0.970742i	$0.422812\pi$
$98$	1.16863	−	0.206060i	0.118049	−	0.0208152i
$99$	−5.09674	−	11.0822i	−0.512241	−	1.11380i
$100$	−4.98268	+	4.85077i	−0.498268	+	0.485077i
$101$	3.14180	+	0.553985i	0.312621	+	0.0551235i	0.327757	−	0.944762i	$-0.393707\pi$
$101$	3.14180	+	0.553985i	0.312621	+	0.0551235i	−0.0151363	+	0.999885i	$0.504818\pi$
$102$	1.42846	−	0.0585949i	0.141438	−	0.00580176i
$103$	4.42546	+	7.66512i	0.436053	+	0.755267i	0.997381	−	0.0723270i	$-0.0230425\pi$
$103$	4.42546	+	7.66512i	0.436053	+	0.755267i	−0.561328	+	0.827594i	$0.689709\pi$
$104$	−3.34547	−	9.19159i	−0.328050	−	0.901310i
$105$	6.57057	−	9.19960i	0.641222	−	0.897789i
$106$	0.344135	+	0.596060i	0.0334254	+	0.0578945i
$107$	12.0467	+	6.95516i	1.16460	+	0.672381i	0.952402	−	0.304846i	$-0.0986050\pi$
$107$	12.0467	+	6.95516i	1.16460	+	0.672381i	0.212196	+	0.977227i	$0.431938\pi$
$108$	−7.21714	−	0.372321i	−0.694469	−	0.0358266i
$109$	6.80889	+	8.11451i	0.652173	+	0.777229i	0.986240	−	0.165320i	$-0.0528657\pi$
$109$	6.80889	+	8.11451i	0.652173	+	0.777229i	−0.334067	+	0.942549i	$0.608421\pi$
$110$	4.35768	−	5.60085i	0.415488	−	0.534020i
$111$	7.74470	+	8.49672i	0.735094	+	0.806473i
$112$	−0.714669	+	1.96354i	−0.0675299	+	0.185537i
$113$		−	8.24716i		−	0.775827i	−0.921696	−	0.387914i	$-0.873196\pi$
$113$		−	8.24716i		−	0.775827i	0.921696	−	0.387914i	$-0.126804\pi$
$114$	−4.13432	−	4.19912i	−0.387214	−	0.393284i
$115$	−0.203508	−	5.50870i	−0.0189772	−	0.513689i
$116$	4.83101	+	1.75834i	0.448548	+	0.163258i
$117$	10.6946	+	2.92614i	0.988716	+	0.270521i
$118$	−3.36801	+	4.01383i	−0.310050	+	0.369503i
$119$	1.98419	+	2.36466i	0.181890	+	0.216768i
$120$	−4.24492	−	9.32988i	−0.387507	−	0.851697i
$121$	2.76620	−	4.79119i	0.251472	−	0.435563i
$122$	4.62668	−	2.67122i	0.418880	−	0.241841i
$123$	4.70212	−	6.09458i	0.423976	−	0.549530i
$124$	−4.19335	−	11.5211i	−0.376574	−	1.03463i
$125$	9.00510	−	6.62632i	0.805441	−	0.592676i
$126$	3.89078	+	5.61945i	0.346619	+	0.500620i
$127$	−1.68535	+	9.55809i	−0.149551	+	0.848143i	0.814050	+	0.580795i	$0.197258\pi$
$127$	−1.68535	+	9.55809i	−0.149551	+	0.848143i	−0.963600	+	0.267348i	$0.913853\pi$
$128$	5.94979	+	7.09068i	0.525892	+	0.626734i
$129$	2.47726	−	18.4408i	0.218111	−	1.62363i
$130$	1.35386	+	6.30676i	0.118742	+	0.553140i
$131$	3.89493	−	10.7012i	0.340301	−	0.934970i	−0.645006	−	0.764178i	$-0.723145\pi$
$131$	3.89493	−	10.7012i	0.340301	−	0.934970i	0.985307	−	0.170792i	$-0.0546327\pi$
$132$	−5.24086	−	8.27457i	−0.456158	−	0.720208i
$133$	1.72556	−	12.6059i	0.149625	−	1.09307i
$134$			3.00068i			0.259220i
$135$	11.4117	+	2.18464i	0.982165	+	0.188024i
$136$	2.75628	−	0.486007i	0.236349	−	0.0416748i
$137$	5.68108	+	4.76700i	0.485368	+	0.407272i	0.852363	−	0.522951i	$-0.175169\pi$
$137$	5.68108	+	4.76700i	0.485368	+	0.407272i	−0.366995	+	0.930223i	$0.619613\pi$
$138$	3.17587	+	1.01056i	0.270348	+	0.0860248i
$139$	−1.07671	+	6.10632i	−0.0913252	+	0.517931i	0.904486	+	0.426502i	$0.140254\pi$
$139$	−1.07671	+	6.10632i	−0.0913252	+	0.517931i	−0.995812	+	0.0914286i	$0.970857\pi$
$140$	4.24550	−	8.02368i	0.358811	−	0.678125i
$141$	−17.7455	−	9.29725i	−1.49444	−	0.782969i
$142$	−0.419966	−	1.15385i	−0.0352428	−	0.0968287i
$143$	5.13971	+	14.1212i	0.429805	+	1.18088i
$144$	−2.14035	+	0.175889i	−0.178363	+	0.0146574i
$145$	−7.30595	−	3.86574i	−0.606726	−	0.321032i
$146$	−0.573523	+	3.25261i	−0.0474651	+	0.269188i
$147$	−0.798466	+	2.50932i	−0.0658564	+	0.206965i
$148$	7.07176	+	5.93391i	0.581295	+	0.487764i
$149$	−5.07686	+	0.895187i	−0.415912	+	0.0733365i	−0.377689	−	0.925933i	$-0.623281\pi$
$149$	−5.07686	+	0.895187i	−0.415912	+	0.0733365i	−0.0382236	+	0.999269i	$0.512170\pi$
$150$	1.92890	+	6.47846i	0.157494	+	0.528964i
$151$		−	19.6743i		−	1.60107i	−0.599286	−	0.800535i	$-0.704549\pi$
$151$		−	19.6743i		−	1.60107i	0.599286	−	0.800535i	$-0.295451\pi$
$152$	−9.11605	−	7.06973i	−0.739410	−	0.573431i
$153$	−1.35592	+	2.86819i	−0.109620	+	0.231880i
$154$	−3.16835	+	8.70497i	−0.255313	+	0.701466i
$155$	4.13732	+	19.2731i	0.332318	+	1.54805i
$156$	8.82382	+	1.18535i	0.706471	+	0.0949042i
$157$	7.74092	+	9.22526i	0.617792	+	0.736256i	0.980689	−	0.195573i	$-0.0626567\pi$
$157$	7.74092	+	9.22526i	0.617792	+	0.736256i	−0.362897	+	0.931829i	$0.618212\pi$
$158$	−1.44034	+	8.16858i	−0.114587	+	0.649858i
$159$	−1.52605	+	0.0625983i	−0.121024	+	0.00496437i
$160$	−6.95653	−	11.0829i	−0.549962	−	0.876180i
$161$	2.46116	+	6.76199i	0.193967	+	0.532920i
$162$	−3.57631	+	6.04619i	−0.280981	+	0.475033i
$163$	−0.938621	+	0.541913i	−0.0735184	+	0.0424459i	−0.536309	−	0.844022i	$-0.680182\pi$
$163$	−0.938621	+	0.541913i	−0.0735184	+	0.0424459i	0.462790	+	0.886468i	$0.346848\pi$
$164$	3.09049	−	5.35289i	0.241327	−	0.417990i
$165$	6.52157	+	14.3337i	0.507703	+	1.11588i
$166$	−7.51098	−	8.95123i	−0.582965	−	0.694750i
$167$	−1.39303	+	1.66014i	−0.107796	+	0.128466i	−0.817245	−	0.576291i	$-0.804499\pi$
$167$	−1.39303	+	1.66014i	−0.107796	+	0.128466i	0.709449	+	0.704757i	$0.248944\pi$
$168$	9.01374	+	9.88899i	0.695425	+	0.762952i
$169$	−0.619848	−	0.225606i	−0.0476806	−	0.0173543i
$170$	−1.84442	+	0.0681384i	−0.141461	+	0.00522598i
$171$	12.5117	−	3.80216i	0.956796	−	0.290759i
$172$		−	14.9405i		−	1.13920i
$173$	5.92723	−	16.2849i	0.450639	−	1.23812i	−0.481636	−	0.876371i	$-0.659957\pi$
$173$	5.92723	−	16.2849i	0.450639	−	1.23812i	0.932275	−	0.361749i	$-0.117820\pi$
$174$	3.69330	−	3.36642i	0.279989	−	0.255207i
$175$	−8.53085	+	11.8420i	−0.644872	+	0.895171i
$176$	−1.87094	−	2.22970i	−0.141028	−	0.168070i
$177$	−4.42126	−	10.7540i	−0.332322	−	0.808318i
$178$	8.35018	+	4.82098i	0.625872	+	0.361347i
$179$	7.80304	+	13.5153i	0.583226	+	1.01018i	0.995094	+	0.0989342i	$0.0315433\pi$
$179$	7.80304	+	13.5153i	0.583226	+	1.01018i	−0.411867	+	0.911244i	$0.635123\pi$
$180$	9.31525	+	0.518587i	0.694318	+	0.0386532i
$181$	1.63083	+	4.48068i	0.121219	+	0.333046i	0.985430	−	0.170084i	$-0.0544039\pi$
$181$	1.63083	+	4.48068i	0.121219	+	0.333046i	−0.864211	+	0.503130i	$0.832182\pi$
$182$	−4.21020	−	7.29228i	−0.312081	−	0.540540i
$183$	0.485895	+	11.8454i	0.0359184	+	0.875637i
$184$	6.42536	+	1.13296i	0.473684	+	0.0835233i
$185$	−9.95363	−	11.0098i	−0.731805	−	0.809459i
$186$	−11.8117	−	1.58673i	−0.866074	−	0.116345i
$187$	−4.23454	+	0.746664i	−0.309660	+	0.0546014i
$188$	−15.1162	−	5.50183i	−1.10246	−	0.401262i
$189$	−15.0528	+	1.86074i	−1.09493	+	0.135349i
$190$	5.31527	+	5.44273i	0.385610	+	0.394857i
$191$			12.7088i			0.919580i	0.888028	+	0.459790i	$0.152075\pi$
$191$			12.7088i			0.919580i	−0.888028	+	0.459790i	$0.847925\pi$
$192$	5.30575	−	1.16159i	0.382910	−	0.0838305i
$193$	0.681796	+	3.86666i	0.0490768	+	0.278328i	0.999464	−	0.0327415i	$-0.0104238\pi$
$193$	0.681796	+	3.86666i	0.0490768	+	0.278328i	−0.950387	+	0.311070i	$0.899313\pi$
$194$	5.51105	−	6.56782i	0.395671	−	0.471542i
$195$	−13.7912	−	3.83380i	−0.987606	−	0.274544i
$196$	−0.367172	+	2.08234i	−0.0262266	+	0.148738i
$197$	8.13901	−	14.0972i	0.579881	−	1.00438i	−0.415612	−	0.909542i	$-0.636433\pi$
$197$	8.13901	−	14.0972i	0.579881	−	1.00438i	0.995492	−	0.0948407i	$-0.0302342\pi$
$198$	−9.48883	+	0.779770i	−0.674342	+	0.0554159i
$199$	−5.32078	+	1.93661i	−0.377180	+	0.137282i	−0.523652	−	0.851933i	$-0.675431\pi$
$199$	−5.32078	+	1.93661i	−0.377180	+	0.137282i	0.146471	+	0.989215i	$0.453208\pi$
$200$	5.43109	+	12.0670i	0.384036	+	0.853268i
$201$	−5.89830	−	3.09025i	−0.416034	−	0.217970i
$202$	1.24504	−	2.15647i	0.0876006	−	0.151729i
$203$	10.6260	+	1.87366i	0.745802	+	0.131505i
$204$	−0.772439	+	2.42753i	−0.0540816	+	0.169961i
$205$	−6.10238	+	7.84329i	−0.426209	+	0.547799i
$206$	6.80338	−	1.19962i	0.474014	−	0.0835815i
$207$	−5.25708	+	5.20193i	−0.365393	+	0.361559i
$208$	2.64572			0.183448
$209$	14.0052	+	10.8614i	0.968760	+	0.751298i
$210$	−4.99341	−	7.27506i	−0.344578	−	0.502027i
$211$	−2.89458	+	7.95278i	−0.199271	+	0.547492i	−0.998571	−	0.0534397i	$-0.982982\pi$
$211$	−2.89458	+	7.95278i	−0.199271	+	0.547492i	0.799300	+	0.600932i	$0.205204\pi$
$212$	−1.20777	+	0.212963i	−0.0829503	+	0.0146264i
$213$	2.70056	+	0.362782i	0.185039	+	0.0248574i
$214$	8.31719	−	6.97895i	0.568551	−	0.477071i
$215$	−3.29501	+	23.7938i	−0.224718	+	1.62272i
$216$	−5.36301	+	12.6632i	−0.364906	+	0.861622i
$217$	−12.8661	−	22.2848i	−0.873410	−	1.51279i
$218$	7.76926	−	2.82778i	0.526200	−	0.191521i
$219$	−5.80285	−	4.47704i	−0.392120	−	0.302530i
$220$	6.72238	+	10.7099i	0.453223	+	0.722059i
$221$	1.95423	−	3.38483i	0.131456	−	0.227688i
$222$	8.29941	−	3.41212i	0.557020	−	0.229006i
$223$	12.2623	−	10.2893i	0.821147	−	0.689024i	−0.132093	−	0.991237i	$-0.542170\pi$
$223$	12.2623	−	10.2893i	0.821147	−	0.689024i	0.953240	+	0.302213i	$0.0977254\pi$
$224$	13.0852	+	10.9798i	0.874290	+	0.733617i
$225$	−14.7209	−	2.88030i	−0.981391	−	0.192020i
$226$	−6.04889	−	2.20161i	−0.402366	−	0.146449i
$227$			1.13816i			0.0755425i	0.999286	+	0.0377712i	$0.0120258\pi$
$227$			1.13816i			0.0755425i	−0.999286	+	0.0377712i	$0.987974\pi$
$228$	9.55063	−	4.36344i	0.632506	−	0.288976i
$229$	−6.50320			−0.429744			−0.214872	−	0.976642i	$-0.568933\pi$
$229$	−6.50320			−0.429744			−0.214872	+	0.976642i	$0.568933\pi$
$230$	−4.09469	−	1.32131i	−0.269996	−	0.0871245i
$231$	−13.8480	−	15.1927i	−0.911132	−	0.999604i
$232$	6.28847	−	7.49430i	0.412858	−	0.492025i
$233$	−4.21124	+	3.53365i	−0.275887	+	0.231497i	−0.770224	−	0.637774i	$-0.779856\pi$
$233$	−4.21124	+	3.53365i	−0.275887	+	0.231497i	0.494337	+	0.869271i	$0.335411\pi$
$234$	5.00114	−	7.06282i	0.326935	−	0.461711i
$235$	22.8602	+	12.0958i	1.49124	+	0.789046i
$236$	−4.66821	−	8.08558i	−0.303875	−	0.526326i
$237$	−14.5733	−	11.2436i	−0.946634	−	0.730352i
$238$	2.26405	−	0.824047i	0.146757	−	0.0534150i
$239$	−9.48533	+	5.47636i	−0.613555	+	0.354236i	−0.774356	−	0.632751i	$-0.781926\pi$
$239$	−9.48533	+	5.47636i	−0.613555	+	0.354236i	0.160800	+	0.986987i	$0.448592\pi$
$240$	2.76408	−	0.215822i	0.178421	−	0.0139313i
$241$	7.91913	+	1.39636i	0.510116	+	0.0899472i	0.422781	−	0.906232i	$-0.361054\pi$
$241$	7.91913	+	1.39636i	0.510116	+	0.0899472i	0.0873349	+	0.996179i	$0.472165\pi$
$242$	−2.77566	−	3.30790i	−0.178426	−	0.212640i
$243$	−8.20164	−	13.2564i	−0.526135	−	0.850401i
$244$	1.65304	+	9.37488i	0.105825	+	0.600165i
$245$	1.04399	−	3.23530i	0.0666983	−	0.206696i
$246$	−3.21482	−	5.07574i	−0.204970	−	0.323618i
$247$	−15.7459	+	3.40596i	−1.00189	+	0.216716i
$248$	−23.3311			−1.48153
$249$	25.3302	−	5.54554i	1.60523	−	0.351434i
$250$	−2.45613	−	8.37372i	−0.155339	−	0.529601i
$251$	−17.4632	+	20.8118i	−1.10227	+	1.31363i	−0.156901	+	0.987614i	$0.550150\pi$
$251$	−17.4632	+	20.8118i	−1.10227	+	1.31363i	−0.945365	+	0.326015i	$0.894294\pi$
$252$	−11.7804	+	3.09007i	−0.742096	+	0.194656i
$253$	−9.87143	−	1.74060i	−0.620611	−	0.109431i
$254$	6.56048	+	3.78769i	0.411641	+	0.237661i
$255$	1.76554	−	3.69567i	0.110563	−	0.231432i
$256$	12.6824	−	4.61602i	0.792651	−	0.288501i
$257$	3.21705	+	8.83878i	0.200674	+	0.551348i	0.998683	−	0.0512972i	$-0.0163356\pi$
$257$	3.21705	+	8.83878i	0.200674	+	0.551348i	−0.798009	+	0.602645i	$0.794113\pi$
$258$	−12.8641	−	6.73981i	−0.800886	−	0.419602i
$259$	16.7792	+	9.68750i	1.04261	+	0.601952i
$260$	−11.3852	−	1.57664i	−0.706079	−	0.0977792i
$261$	2.81366	+	10.7266i	0.174161	+	0.663963i
$262$	−6.80905	−	5.71347i	−0.420665	−	0.352979i
$263$	5.31491	+	30.1423i	0.327731	+	1.85866i	0.489743	+	0.871867i	$0.337091\pi$
$263$	5.31491	+	30.1423i	0.327731	+	1.85866i	−0.162012	+	0.986789i	$0.551798\pi$
$264$	−18.2074	+	3.98615i	−1.12059	+	0.245330i
$265$	1.97044	−	0.0727938i	0.121043	−	0.00447169i
$266$	−8.78516	−	4.63081i	−0.538653	−	0.283933i
$267$	−18.0758	+	11.4487i	−1.10622	+	0.700646i
$268$	−5.02436	−	1.82872i	−0.306912	−	0.111707i
$269$	−0.00466095	−	0.0264336i	−0.000284183	−	0.00161168i	0.984665	−	0.174454i	$-0.0558160\pi$
$269$	−0.00466095	−	0.0264336i	−0.000284183	−	0.00161168i	−0.984950	+	0.172842i	$0.944705\pi$
$270$	4.64873	−	7.78674i	0.282913	−	0.473886i
$271$	8.36891	−	7.02235i	0.508375	−	0.426577i	−0.352182	−	0.935932i	$-0.614560\pi$
$271$	8.36891	−	7.02235i	0.508375	−	0.426577i	0.860557	+	0.509354i	$0.170116\pi$
$272$	−0.131457	+	0.745527i	−0.00797072	+	0.0452042i
$273$	18.6700	−	0.765836i	1.12996	−	0.0463505i
$274$	5.01295	−	2.89423i	0.302843	−	0.174847i
$275$	−8.34391	−	18.5388i	−0.503157	−	1.11793i
$276$	−3.62758	+	4.70183i	−0.218355	+	0.283017i
$277$	−17.6454	+	10.1876i	−1.06021	+	0.612111i	−0.925490	−	0.378773i	$-0.876346\pi$
$277$	−17.6454	+	10.1876i	−1.06021	+	0.612111i	−0.134718	+	0.990884i	$0.543013\pi$
$278$	4.19125	+	2.41982i	0.251375	+	0.145131i
$279$	15.2832	−	21.5836i	0.914982	−	1.29217i
$280$	−11.5846	−	12.8139i	−0.692313	−	0.765776i
$281$	1.86505	+	1.56496i	0.111259	+	0.0933578i	0.696720	−	0.717343i	$-0.254642\pi$
$281$	1.86505	+	1.56496i	0.111259	+	0.0933578i	−0.585461	+	0.810701i	$0.699086\pi$
$282$	−11.5563	+	10.5335i	−0.688168	+	0.627260i
$283$	2.08132	−	5.71838i	0.123722	−	0.339922i	−0.862334	−	0.506340i	$-0.830998\pi$
$283$	2.08132	−	5.71838i	0.123722	−	0.339922i	0.986055	+	0.166418i	$0.0532201\pi$
$284$	2.18795			0.129831
$285$	−16.1724	+	4.84278i	−0.957972	+	0.286862i
$286$	11.7293			0.693569
$287$	4.43688	−	12.1902i	0.261901	−	0.719566i
$288$	−4.63311	+	16.9333i	−0.273008	+	0.997806i
$289$	−12.1661	−	10.2085i	−0.715650	−	0.600502i
$290$	−4.78568	+	4.32658i	−0.281025	+	0.254066i
$291$	7.23448	+	17.5967i	0.424093	+	1.03154i
$292$	−5.09666	−	2.94256i	−0.298260	−	0.172200i
$293$	−15.9878	+	9.23053i	−0.934015	+	0.539254i	−0.888079	−	0.459691i	$-0.847960\pi$
$293$	−15.9878	+	9.23053i	−0.934015	+	0.539254i	−0.0459356	+	0.998944i	$0.514627\pi$
$294$	1.62731	+	1.25551i	0.0949067	+	0.0732228i
$295$	5.65126	+	13.9064i	0.329029	+	0.809664i
$296$	15.2135	−	8.78352i	0.884267	−	0.510532i
$297$	8.23931	−	19.4548i	0.478093	−	1.12888i
$298$	−0.698713	+	3.96260i	−0.0404753	+	0.229547i
$299$	6.97966	−	5.85663i	0.403644	−	0.338698i
$300$	−12.0231	−	0.718439i	−0.694155	−	0.0414791i
$301$	−5.44506	−	30.8804i	−0.313848	−	1.77992i
$302$	−14.4301	−	5.25213i	−0.830360	−	0.302226i
$303$	2.95667	+	4.66815i	0.169856	+	0.268178i
$304$	2.64025	−	1.66301i	0.151429	−	0.0953801i
$305$	−0.565034	−	15.2948i	−0.0323537	−	0.875776i
$306$	1.74171	+	1.76018i	0.0995670	+	0.100623i
$307$	−0.413188	−	2.34330i	−0.0235819	−	0.133739i	0.970744	−	0.240117i	$-0.0771858\pi$
$307$	−0.413188	−	2.34330i	−0.0235819	−	0.133739i	−0.994326	+	0.106378i	$0.966075\pi$
$308$	−12.6448	−	10.6102i	−0.720502	−	0.604573i
$309$	−4.64842	+	14.6085i	−0.264440	+	0.831049i
$310$	15.2403	+	2.11051i	0.865594	+	0.119869i
$311$	−8.28694	−	4.78447i	−0.469909	−	0.271302i	0.246293	−	0.969196i	$-0.420788\pi$
$311$	−8.28694	−	4.78447i	−0.469909	−	0.271302i	−0.716202	+	0.697893i	$0.754121\pi$
$312$	7.86255	−	15.0071i	0.445129	−	0.849609i
$313$	−3.31414	−	9.10552i	−0.187326	−	0.514675i	0.810107	−	0.586283i	$-0.199409\pi$
$313$	−3.31414	−	9.10552i	−0.187326	−	0.514675i	−0.997433	+	0.0716080i	$0.977187\pi$
$314$	8.83275	−	3.21486i	0.498461	−	0.181425i
$315$	19.4427	−	2.32308i	1.09547	−	0.130891i
$316$	−12.7997	−	7.38993i	−0.720041	−	0.415716i
$317$	8.91172	+	1.57138i	0.500532	+	0.0882573i	0.418213	−	0.908349i	$-0.362656\pi$
$317$	8.91172	+	1.57138i	0.500532	+	0.0882573i	0.0823184	+	0.996606i	$0.473768\pi$
$318$	−0.361474	+	1.13600i	−0.0202704	+	0.0637035i
$319$	−9.66111	+	11.5137i	−0.540918	+	0.644641i
$320$	−6.85575	+	1.47171i	−0.383248	+	0.0822711i
$321$	5.15273	+	23.5360i	0.287597	+	1.31365i
$322$	5.61661			0.313001
$323$	−0.177395	−	4.60619i	−0.00987051	−	0.256295i
$324$	−7.94425	−	9.67295i	−0.441347	−	0.537386i
$325$	17.7840	+	5.02184i	0.986481	+	0.278562i
$326$	0.146898	+	0.833098i	0.00813591	+	0.0461410i
$327$	−2.44274	+	18.1838i	−0.135084	+	1.00557i
$328$	−7.56050	−	9.01025i	−0.417459	−	0.497508i
$329$	−33.2488	−	5.86265i	−1.83306	−	0.323219i
$330$	12.2540	−	0.956806i	0.674562	−	0.0526705i
$331$	7.18129	−	4.14612i	0.394719	−	0.227891i	−0.289484	−	0.957183i	$-0.593484\pi$
$331$	7.18129	−	4.14612i	0.394719	−	0.227891i	0.684203	+	0.729292i	$0.260150\pi$
$332$	19.5654	−	7.12124i	1.07379	−	0.390829i
$333$	−1.84010	+	19.8277i	−0.100837	+	1.08655i
$334$	0.845759	+	1.46490i	0.0462779	+	0.0801557i
$335$	7.59837	+	4.02046i	0.415143	+	0.219661i
$336$	−3.34736	+	1.37619i	−0.182613	+	0.0750774i
$337$	4.84264	−	4.06346i	0.263796	−	0.221351i	−0.501290	−	0.865279i	$-0.667141\pi$
$337$	4.84264	−	4.06346i	0.263796	−	0.221351i	0.765086	+	0.643929i	$0.222697\pi$
$338$	−0.330942	+	0.394402i	−0.0180009	+	0.0214526i
$339$	10.5570	−	9.62267i	0.573380	−	0.522632i
$340$	1.00996	−	3.12984i	0.0547730	−	0.169739i
$341$	35.8441			1.94107
$342$	0.551362	−	10.1917i	0.0298143	−	0.551107i
$343$		−	15.9949i		−	0.863645i
$344$	−26.7162	−	9.72391i	−1.44044	−	0.524278i
$345$	6.81415	−	6.68798i	0.366861	−	0.360069i
$346$	−10.3619	−	8.69466i	−0.557059	−	0.467428i
$347$	14.9716	−	12.5627i	0.803719	−	0.674400i	−0.145381	−	0.989376i	$-0.546441\pi$
$347$	14.9716	−	12.5627i	0.803719	−	0.674400i	0.949100	+	0.314976i	$0.101996\pi$
$348$	3.38593	+	8.23570i	0.181505	+	0.441480i
$349$	−7.89425	+	13.6732i	−0.422569	+	0.731912i	−0.996190	−	0.0872095i	$-0.972205\pi$
$349$	−7.89425	+	13.6732i	−0.422569	+	0.731912i	0.573621	+	0.819121i	$0.305538\pi$
$350$	6.40818	+	9.41823i	0.342531	+	0.503426i
$351$	8.73261	+	17.1041i	0.466112	+	0.912951i
$352$	−22.3589	+	8.13798i	−1.19173	+	0.433756i
$353$	−8.47212	−	14.6741i	−0.450926	−	0.781026i	0.547518	−	0.836794i	$-0.315573\pi$
$353$	−8.47212	−	14.6741i	−0.450926	−	0.781026i	−0.998444	+	0.0557677i	$0.982239\pi$
$354$	−9.06778	+	0.371958i	−0.481947	+	0.0197693i
$355$	−3.48448	−	0.482537i	−0.184937	−	0.0256104i
$356$	−13.1612	+	11.0435i	−0.697540	+	0.585305i
$357$	−0.711841	+	5.29898i	−0.0376746	+	0.280452i
$358$	11.9958	−	2.11519i	0.633999	−	0.111791i
$359$	0.875766	−	2.40615i	0.0462212	−	0.126992i	−0.914434	−	0.404734i	$-0.867364\pi$
$359$	0.875766	−	2.40615i	0.0462212	−	0.126992i	0.960656	+	0.277743i	$0.0895862\pi$
$360$	6.99010	−	16.3198i	0.368411	−	0.860130i
$361$	−13.5724	+	13.2962i	−0.714338	+	0.699801i
$362$	3.72171			0.195609
$363$	9.36068	−	2.04934i	0.491308	−	0.107562i
$364$	14.7761	−	2.60542i	0.774477	−	0.136561i
$365$	7.46786	+	5.81028i	0.390886	+	0.304124i
$366$	8.81773	+	2.80580i	0.460910	+	0.146661i
$367$	−11.5238	−	2.03196i	−0.601537	−	0.106067i	−0.135417	−	0.990789i	$-0.543237\pi$
$367$	−11.5238	−	2.03196i	−0.601537	−	0.106067i	−0.466120	+	0.884721i	$0.654349\pi$
$368$	−0.882380	+	1.52833i	−0.0459972	+	0.0796696i
$369$	13.2879	−	1.09197i	0.691742	−	0.0568457i
$370$	−10.7323	+	4.36138i	−0.557947	+	0.226737i
$371$	−2.41874	+	0.880348i	−0.125574	+	0.0457054i
$372$	9.85527	−	18.8105i	0.510972	−	0.975281i
$373$	−10.2697	+	17.7877i	−0.531746	+	0.921011i	0.467567	+	0.883958i	$0.345131\pi$
$373$	−10.2697	+	17.7877i	−0.531746	+	0.921011i	−0.999313	+	0.0370538i	$0.988203\pi$
$374$	−0.582787	+	3.30515i	−0.0301352	+	0.170905i
$375$	18.9893	+	3.79578i	0.980601	+	0.196013i
$376$	−19.6765	+	23.4496i	−1.01474	+	1.20932i
$377$	−2.37236	−	13.4543i	−0.122183	−	0.692934i
$378$	−2.65365	+	11.5372i	−0.136489	+	0.593410i
$379$			9.40373i			0.483037i	0.970396	+	0.241519i	$0.0776455\pi$
$379$			9.40373i			0.483037i	−0.970396	+	0.241519i	$0.922355\pi$
$380$	−12.3526	+	5.58294i	−0.633677	+	0.286399i
$381$	−14.2016	+	8.99486i	−0.727569	+	0.460820i
$382$	9.32131	+	3.39268i	0.476920	+	0.173585i
$383$	10.2850	−	1.81352i	0.525538	−	0.0926665i	0.0954163	−	0.995437i	$-0.469582\pi$
$383$	10.2850	−	1.81352i	0.525538	−	0.0926665i	0.430122	+	0.902771i	$0.358471\pi$
$384$	−2.13453	+	15.8895i	−0.108927	+	0.810859i
$385$	17.7977	+	19.6863i	0.907055	+	1.00330i
$386$	3.01801	+	0.532157i	0.153613	+	0.0270861i
$387$	26.4962	−	18.3454i	1.34688	−	0.932549i
$388$	7.63857	+	13.2304i	0.387790	+	0.671671i
$389$	−0.231373	−	0.635692i	−0.0117311	−	0.0322309i	0.933689	−	0.358085i	$-0.116570\pi$
$389$	−0.231373	−	0.635692i	−0.0117311	−	0.0322309i	−0.945420	+	0.325854i	$0.894348\pi$
$390$	−6.49351	+	9.09170i	−0.328812	+	0.460376i
$391$	1.30352	+	2.25776i	0.0659218	+	0.114180i
$392$	3.48462	+	2.01185i	0.176000	+	0.101614i
$393$	18.2430	−	7.50020i	0.920237	−	0.378335i
$394$	−8.16685	−	9.73287i	−0.411440	−	0.490335i
$395$	18.7547	+	14.5919i	0.943654	+	0.734199i
$396$	4.47716	−	16.3634i	0.224986	−	0.822291i
$397$	1.99566	−	5.48302i	0.100159	−	0.275185i	−0.879485	−	0.475926i	$-0.842113\pi$
$397$	1.99566	−	5.48302i	0.100159	−	0.275185i	0.979644	+	0.200742i	$0.0643351\pi$
$398$			4.41952i			0.221530i
$399$	18.1500	−	12.4995i	0.908634	−	0.625759i
$400$	−3.56952	+	0.264097i	−0.178476	+	0.0132049i
$401$	−31.3720	−	11.4185i	−1.56664	−	0.570212i	−0.594397	−	0.804172i	$-0.702609\pi$
$401$	−31.3720	−	11.4185i	−1.56664	−	0.570212i	−0.972246	+	0.233960i	$0.924832\pi$
$402$	−3.84112	+	3.50116i	−0.191578	+	0.174622i
$403$	−20.9429	+	24.9588i	−1.04324	+	1.24328i
$404$	2.85204	+	3.39893i	0.141894	+	0.169103i
$405$	10.5185	+	17.1569i	0.522669	+	0.852536i
$406$	4.21090	−	7.29350i	0.208984	−	0.361970i
$407$	−23.3729	+	13.4943i	−1.15855	+	0.668889i
$408$	3.83812	+	2.96120i	0.190015	+	0.146601i
$409$	1.33443	+	3.66632i	0.0659833	+	0.181288i	0.968302	−	0.249781i	$-0.0803588\pi$
$409$	1.33443	+	3.66632i	0.0659833	+	0.181288i	−0.902319	+	0.431069i	$0.858137\pi$
$410$	4.12361	+	6.56960i	0.203651	+	0.324449i
$411$	0.526460	+	12.8343i	0.0259684	+	0.633070i
$412$	−2.13756	+	12.1227i	−0.105310	+	0.597243i
$413$	−12.5955	−	15.0108i	−0.619785	−	0.738631i
$414$	2.41196	+	5.24449i	0.118541	+	0.257753i
$415$	−32.7300	+	7.02609i	−1.60665	+	0.344897i
$416$	7.39722	−	20.3237i	0.362678	−	0.996451i
$417$	−9.07288	+	5.74649i	−0.444301	+	0.281407i
$418$	11.7050	−	7.37263i	0.572512	−	0.360607i
$419$		−	38.8111i		−	1.89604i	−0.318204	−	0.948022i	$-0.603080\pi$
$419$		−	38.8111i		−	1.89604i	0.318204	−	0.948022i	$-0.396920\pi$
$420$	15.2246	−	3.92732i	0.742883	−	0.191634i
$421$	−1.36304	+	0.240341i	−0.0664305	+	0.0117135i	−0.206765	−	0.978391i	$-0.566293\pi$
$421$	−1.36304	+	0.240341i	−0.0664305	+	0.0117135i	0.140334	+	0.990104i	$0.455182\pi$
$422$	5.06026	+	4.24606i	0.246329	+	0.206695i
$423$	−8.80390	−	33.5635i	−0.428060	−	1.63192i
$424$	−0.405256	+	2.29832i	−0.0196810	+	0.111616i
$425$	−2.29871	+	4.76177i	−0.111504	+	0.230980i
$426$	0.987009	−	1.88388i	0.0478207	−	0.0912744i
$427$	6.83336	+	18.7745i	0.330689	+	0.908561i
$428$	6.61682	+	18.1796i	0.319836	+	0.878742i
$429$	−12.0794	+	23.0557i	−0.583200	+	1.11314i
$430$	16.5720	+	8.76859i	0.799171	+	0.422859i
$431$	−0.402293	+	2.28152i	−0.0193778	+	0.109897i	−0.992962	−	0.118429i	$-0.962214\pi$
$431$	−0.402293	+	2.28152i	−0.0193778	+	0.109897i	0.973585	+	0.228326i	$0.0733252\pi$
$432$	−2.72248	−	2.53460i	−0.130986	−	0.121946i
$433$	28.1105	+	23.5875i	1.35090	+	1.13354i	0.978678	+	0.205399i	$0.0658493\pi$
$433$	28.1105	+	23.5875i	1.35090	+	1.13354i	0.372224	+	0.928143i	$0.378595\pi$
$434$	−19.7795	+	3.48765i	−0.949445	+	0.167413i
$435$	−3.57602	−	13.8627i	−0.171457	−	0.664666i
$436$			14.7322i			0.705546i
$437$	3.28395	−	10.2317i	0.157093	−	0.489447i
$438$	−4.83279	+	3.06094i	−0.230919	+	0.146257i
$439$	11.5149	−	31.6370i	0.549577	−	1.50995i	−0.284706	−	0.958615i	$-0.591896\pi$
$439$	11.5149	−	31.6370i	0.549577	−	1.50995i	0.834283	−	0.551336i	$-0.185882\pi$
$440$	23.5264	−	5.05037i	1.12158	−	0.240767i
$441$	−4.14378	+	1.90574i	−0.197323	+	0.0907495i
$442$	−1.96092	−	2.33693i	−0.0932712	−	0.111156i
$443$	4.99550	−	28.3309i	0.237343	−	1.34604i	−0.600279	−	0.799791i	$-0.704944\pi$
$443$	4.99550	−	28.3309i	0.237343	−	1.34604i	0.837622	−	0.546250i	$-0.183945\pi$
$444$	0.655333	+	15.9760i	0.0311007	+	0.758189i
$445$	23.3957	−	14.6850i	1.10906	−	0.696137i
$446$	−4.27323	−	11.7406i	−0.202343	−	0.555934i
$447$	−7.06952	−	5.45430i	−0.334377	−	0.257980i
$448$	7.92705	−	4.57668i	0.374518	−	0.216228i
$449$	18.3868	−	31.8469i	0.867727	−	1.50295i	0.00341265	−	0.999994i	$-0.498914\pi$
$449$	18.3868	−	31.8469i	0.867727	−	1.50295i	0.864314	−	0.502953i	$-0.167753\pi$
$450$	−6.04236	+	10.0281i	−0.284839	+	0.472730i
$451$	11.6154	+	13.8427i	0.546946	+	0.651825i
$452$	7.37279	−	8.78655i	0.346787	−	0.413285i
$453$	25.1847	−	22.9557i	1.18328	−	1.07855i
$454$	0.834786	+	0.303837i	0.0391784	+	0.0142598i
$455$	−24.1066	+	0.890570i	−1.13014	+	0.0417506i
$456$	−1.58664	−	19.9182i	−0.0743011	−	0.932754i
$457$		−	20.2428i		−	0.946920i	−0.880815	−	0.473460i	$-0.843005\pi$
$457$		−	20.2428i		−	0.946920i	0.880815	−	0.473460i	$-0.156995\pi$
$458$	−1.73606	+	4.76978i	−0.0811207	+	0.222877i
$459$	−5.25359	+	1.61088i	−0.245217	+	0.0751894i
$460$	4.70785	−	6.05092i	0.219505	−	0.282126i
$461$	23.5298	+	28.0418i	1.09589	+	1.30604i	0.948437	+	0.316967i	$0.102664\pi$
$461$	23.5298	+	28.0418i	1.09589	+	1.30604i	0.147457	+	0.989069i	$0.452891\pi$
$462$	−14.8399	+	6.10108i	−0.690413	+	0.283848i
$463$	−19.5226	−	11.2714i	−0.907293	−	0.523826i	−0.0277341	−	0.999615i	$-0.508829\pi$
$463$	−19.5226	−	11.2714i	−0.907293	−	0.523826i	−0.879559	+	0.475789i	$0.842162\pi$
$464$	1.32308	+	2.29165i	0.0614226	+	0.106387i
$465$	−19.8438	+	27.7837i	−0.920234	+	1.28844i
$466$	1.46755	+	4.03206i	0.0679829	+	0.186781i
$467$	15.3391	+	26.5681i	0.709809	+	1.22942i	0.964928	+	0.262515i	$0.0845519\pi$
$467$	15.3391	+	26.5681i	0.709809	+	1.22942i	−0.255119	+	0.966910i	$0.582115\pi$
$468$	8.77815	+	12.6783i	0.405770	+	0.586053i
$469$	−11.0513	−	1.94865i	−0.510304	−	0.0899803i
$470$	14.9743	−	13.5378i	0.690715	−	0.624453i
$471$	−2.77711	+	20.6729i	−0.127962	+	0.952558i
$472$	−17.4967	+	3.08515i	−0.805353	+	0.142005i
$473$	41.0447	+	14.9391i	1.88724	+	0.686899i
$474$	−12.1370	+	7.68723i	−0.557472	+	0.353086i
$475$	20.9038	−	6.16696i	0.959132	−	0.282960i
$476$			4.29314i			0.196776i
$477$	−1.86071	−	1.88044i	−0.0851960	−	0.0860992i
$478$	1.48449	+	8.41896i	0.0678990	+	0.385074i
$479$	−11.7463	+	13.9987i	−0.536703	+	0.639618i	−0.964445	−	0.264283i	$-0.914865\pi$
$479$	−11.7463	+	13.9987i	−0.536703	+	0.639618i	0.427742	+	0.903901i	$0.359309\pi$
$480$	6.07025	−	21.8363i	0.277068	−	0.996686i
$481$	4.25994	−	24.1593i	0.194236	−	1.10157i
$482$	3.13820	−	5.43553i	0.142941	−	0.247582i
$483$	−5.78426	+	11.0403i	−0.263193	+	0.502351i
$484$	7.23035	−	2.63163i	0.328652	−	0.119620i
$485$	−9.24713	−	22.7550i	−0.419891	−	1.03325i
$486$	−11.9124	+	2.47663i	−0.540358	+	0.112342i
$487$	−6.72105	+	11.6412i	−0.304560	+	0.527513i	−0.977163	−	0.212490i	$-0.931843\pi$
$487$	−6.72105	+	11.6412i	−0.304560	+	0.527513i	0.672604	+	0.740003i	$0.265176\pi$
$488$	17.8398	+	3.14564i	0.807571	+	0.142397i
$489$	−1.78886	−	0.569216i	−0.0808951	−	0.0257408i
$490$	−2.09423	−	1.62939i	−0.0946079	−	0.0736086i
$491$	−7.46059	+	1.31550i	−0.336692	+	0.0593678i	−0.339438	−	0.940628i	$-0.610237\pi$
$491$	−7.46059	+	1.31550i	−0.336692	+	0.0593678i	0.00274640	+	0.999996i	$0.499126\pi$
$492$	10.4581	−	2.28959i	0.471487	−	0.103223i
$493$	3.90912			0.176058
$494$	−1.70532	+	12.4581i	−0.0767261	+	0.560514i
$495$	−10.7391	+	25.0725i	−0.482684	+	1.12693i
$496$	2.15837	−	5.93008i	0.0969138	−	0.266268i
$497$	4.52228	−	0.797399i	0.202852	−	0.0357682i
$498$	2.69462	−	20.0588i	0.120749	−	0.898858i
$499$	−13.0603	+	10.9589i	−0.584660	+	0.490588i	−0.886474	−	0.462779i	$-0.846852\pi$
$499$	−13.0603	+	10.9589i	−0.584660	+	0.490588i	0.301814	+	0.953367i	$0.402408\pi$
$500$	15.5179	+	0.990676i	0.693980	+	0.0443044i
$501$	−3.75048	+	0.153844i	−0.167559	+	0.00687323i
$502$	10.6026	+	18.3642i	0.473215	+	0.819633i
$503$	−30.6254	+	11.1467i	−1.36552	+	0.497009i	−0.917757	−	0.397143i	$-0.870002\pi$
$503$	−30.6254	+	11.1467i	−1.36552	+	0.497009i	−0.447764	+	0.894152i	$0.647779\pi$
$504$	−2.14162	+	23.0767i	−0.0953952	+	1.02792i
$505$	−3.79248	−	6.04204i	−0.168763	−	0.268867i
$506$	−3.91186	+	6.77555i	−0.173904	+	0.301210i
$507$	−0.434435	−	1.05669i	−0.0192940	−	0.0469293i
$508$	−10.3403	+	8.67655i	−0.458777	+	0.384960i
$509$	−13.8854	−	11.6512i	−0.615458	−	0.516431i	0.280914	−	0.959733i	$-0.409362\pi$
$509$	−13.8854	−	11.6512i	−0.615458	−	0.516431i	−0.896372	+	0.443302i	$0.853807\pi$
$510$	−2.23927	−	2.28151i	−0.0991566	−	0.101027i
$511$	−11.6067	−	4.22450i	−0.513451	−	0.186881i
$512$			7.97826i			0.352592i
$513$	19.4656	+	11.5797i	0.859427	+	0.511258i
$514$	7.34162			0.323825
$515$	6.07781	−	18.8349i	0.267820	−	0.829966i
$516$	19.1250	−	17.4323i	0.841932	−	0.767415i
$517$	30.2295	−	36.0261i	1.32949	−	1.58443i
$518$	11.5846	−	9.72063i	0.508998	−	0.427100i
$519$	27.7619	−	11.4137i	1.21861	−	0.501005i
$520$	−10.2293	+	19.3326i	−0.448584	+	0.847790i
$521$	−13.4667	−	23.3250i	−0.589986	−	1.02189i	−0.994234	−	0.107236i	$-0.965800\pi$
$521$	−13.4667	−	23.3250i	−0.589986	−	1.02189i	0.404247	−	0.914650i	$-0.367533\pi$
$522$	8.61858	+	0.799844i	0.377225	+	0.0350082i
$523$	28.1466	−	10.2445i	1.23076	−	0.447961i	0.356905	−	0.934141i	$-0.383832\pi$
$523$	28.1466	−	10.2445i	1.23076	−	0.447961i	0.873859	+	0.486180i	$0.161610\pi$
$524$	13.7163	−	7.91913i	0.599201	−	0.345949i
$525$	−25.1124	+	2.89688i	−1.09600	+	0.126430i
$526$	23.5268	+	4.14840i	1.02582	+	0.180879i
$527$	−5.99244	−	7.14152i	−0.261035	−	0.311089i
$528$	0.671214	−	4.99655i	0.0292108	−	0.217447i
$529$	−2.93857	−	16.6655i	−0.127764	−	0.724585i
$530$	0.472626	−	1.46465i	0.0205296	−	0.0636205i
$531$	8.60731	−	18.2072i	0.373525	−	0.790123i
$532$	13.1078	−	11.8878i	0.568297	−	0.515400i
$533$	−16.4254			−0.711465
$534$	3.57162	+	16.3140i	0.154559	+	0.705974i
$535$	−6.52841	−	30.4116i	−0.282248	−	1.31481i
$536$	−6.54016	+	7.79425i	−0.282492	+	0.336661i
$537$	−8.19617	+	25.7579i	−0.353691	+	1.11154i
$538$	−0.0206320	−	0.00363798i	−0.000889508	−	0.000156844i
$539$	−5.35350	−	3.09084i	−0.230592	−	0.133132i
$540$	10.2051	+	12.5294i	0.439156	+	0.539178i
$541$	13.3029	−	4.84186i	0.571936	−	0.208168i	−0.0398298	−	0.999206i	$-0.512682\pi$
$541$	13.3029	−	4.84186i	0.571936	−	0.208168i	0.611766	+	0.791039i	$0.290459\pi$
$542$	−2.91643	−	8.01283i	−0.125271	−	0.344181i
$543$	−3.83280	+	7.31559i	−0.164481	+	0.313942i
$544$	5.35938	+	3.09424i	0.229782	+	0.132664i
$545$	3.24909	−	23.4622i	0.139176	−	1.00501i
$546$	4.42232	−	13.8979i	0.189258	−	0.594777i
$547$	3.60439	+	3.02444i	0.154113	+	0.129316i	0.716584	−	0.697501i	$-0.245705\pi$
$547$	3.60439	+	3.02444i	0.154113	+	0.129316i	−0.562471	+	0.826817i	$0.690149\pi$
$548$	1.79105	+	10.1575i	0.0765099	+	0.433909i
$549$	−14.5961	+	14.4430i	−0.622948	+	0.616413i
$550$	−15.8248	+	1.17083i	−0.674771	+	0.0499242i
$551$	−10.8244	−	11.9353i	−0.461134	−	0.508462i
$552$	6.04673	+	9.54692i	0.257366	+	0.406344i
$553$	−29.1490	−	10.6094i	−1.23954	−	0.451157i
$554$	2.76157	+	15.6616i	0.117328	+	0.665399i
$555$	2.47974	−	25.5876i	0.105259	−	1.08613i
$556$	−6.60605	+	5.54314i	−0.280159	+	0.235081i
$557$	−4.32909	+	24.5515i	−0.183430	+	1.04028i	0.744527	+	0.667592i	$0.232675\pi$
$557$	−4.32909	+	24.5515i	−0.183430	+	1.04028i	−0.927957	+	0.372688i	$0.878436\pi$
$558$	−11.7506	−	16.9713i	−0.497441	−	0.718452i
$559$	−34.3838	+	19.8515i	−1.45428	+	0.839629i
$560$	4.32861	−	1.75905i	0.182917	−	0.0743335i
$561$	−5.89659	−	4.54936i	−0.248954	−	0.192074i
$562$	1.64570	−	0.950148i	0.0694199	−	0.0400796i
$563$	−39.4679	−	22.7868i	−1.66337	−	0.960348i	−0.971087	−	0.238724i	$-0.923271\pi$
$563$	−39.4679	−	22.7868i	−1.66337	−	0.960348i	−0.692285	−	0.721624i	$-0.743396\pi$
$564$	−10.5945	−	25.7694i	−0.446110	−	1.08509i
$565$	−13.6795	+	12.3672i	−0.575503	+	0.520293i
$566$	−3.63853	−	3.05309i	−0.152939	−	0.128331i
$567$	−19.9453	−	17.0977i	−0.837623	−	0.718038i
$568$	1.42401	−	3.91245i	0.0597503	−	0.164163i
$569$	13.7231			0.575300			0.287650	−	0.957736i	$-0.407126\pi$
$569$	13.7231			0.575300			0.287650	+	0.957736i	$0.407126\pi$
$570$	−0.765358	+	13.1545i	−0.0320573	+	0.550981i
$571$	−25.4522			−1.06514			−0.532570	−	0.846386i	$-0.678774\pi$
$571$	−25.4522			−1.06514			−0.532570	+	0.846386i	$0.678774\pi$
$572$	−7.14824	+	19.6396i	−0.298883	+	0.821174i
$573$	−16.2684	+	14.8285i	−0.679621	+	0.619470i
$574$	−7.75648	−	6.50846i	−0.323749	−	0.271658i
$575$	−8.83210	+	8.59827i	−0.368324	+	0.358573i
$576$	7.67761	+	5.43648i	0.319900	+	0.226520i
$577$	−2.19977	−	1.27004i	−0.0915774	−	0.0528723i	0.453512	−	0.891250i	$-0.350171\pi$
$577$	−2.19977	−	1.27004i	−0.0915774	−	0.0528723i	−0.545089	+	0.838378i	$0.683504\pi$
$578$	−10.7352	+	6.19799i	−0.446527	+	0.257803i
$579$	−4.15413	+	5.38432i	−0.172640	+	0.223765i
$580$	−4.32790	−	10.6499i	−0.179706	−	0.442215i
$581$	37.8445	−	21.8495i	1.57005	−	0.906471i
$582$	14.8376	−	0.608633i	0.615037	−	0.0252286i
$583$	0.622605	−	3.53097i	0.0257856	−	0.146238i
$584$	−8.57896	+	7.19860i	−0.355000	+	0.297880i
$585$	−11.1838	−	22.1271i	−0.462392	−	0.914841i
$586$	2.50214	+	14.1904i	0.103363	+	0.586198i
$587$	−42.2649	−	15.3832i	−1.74446	−	0.634931i	−0.744976	−	0.667092i	$-0.767539\pi$
$587$	−42.2649	−	15.3832i	−1.74446	−	0.634931i	−0.999483	+	0.0321609i	$0.989761\pi$
$588$	−3.09397	+	1.95963i	−0.127593	+	0.0808137i
$589$	−5.21137	+	38.0711i	−0.214731	+	1.56869i
$590$	11.7083	−	0.432539i	0.482024	−	0.0178074i
$591$	27.5420	−	6.02978i	1.13293	−	0.248032i
$592$	0.825104	+	4.67940i	0.0339116	+	0.192322i
$593$	17.7238	+	14.8721i	0.727831	+	0.610723i	0.929539	−	0.368723i	$-0.120205\pi$
$593$	17.7238	+	14.8721i	0.727831	+	0.610723i	−0.201708	+	0.979446i	$0.564649\pi$
$594$	−12.0696	−	11.2367i	−0.495222	−	0.461046i
$595$	0.946822	−	6.83715i	0.0388159	−	0.280296i
$596$	−6.20918	−	3.58487i	−0.254338	−	0.146842i
$597$	−8.68723	−	4.55144i	−0.355545	−	0.186278i
$598$	−2.43230	−	6.68269i	−0.0994641	−	0.273275i
$599$	2.54474	−	0.926208i	0.103975	−	0.0378438i	−0.289509	−	0.957175i	$-0.593492\pi$
$599$	2.54474	−	0.926208i	0.103975	−	0.0378438i	0.393484	+	0.919332i	$0.371270\pi$
$600$	−9.10987	+	21.0319i	−0.371909	+	0.858623i
$601$	19.4640	+	11.2375i	0.793952	+	0.458388i	0.841352	−	0.540488i	$-0.181760\pi$
$601$	19.4640	+	11.2375i	0.793952	+	0.458388i	−0.0474003	+	0.998876i	$0.515094\pi$
$602$	−24.1029	−	4.24999i	−0.982359	−	0.173216i
$603$	−2.92627	−	11.1560i	−0.119167	−	0.454306i
$604$	17.5884	−	20.9611i	0.715662	−	0.852893i
$605$	−12.0953	+	2.59647i	−0.491742	+	0.105561i
$606$	4.21315	−	0.922386i	0.171148	−	0.0374694i
$607$	5.87399			0.238418			0.119209	−	0.992869i	$-0.461964\pi$
$607$	5.87399			0.238418			0.119209	+	0.992869i	$0.461964\pi$
$608$	−5.39284	−	24.9313i	−0.218708	−	1.01110i
$609$	9.99988	+	15.7884i	0.405215	+	0.639777i
$610$	−11.3688	−	3.66858i	−0.460309	−	0.148536i
$611$	7.42310	+	42.0985i	0.300306	+	1.70312i
$612$	−4.00871	+	1.84362i	−0.162042	+	0.0745239i
$613$	−8.66968	−	10.3321i	−0.350165	−	0.417310i	0.561998	−	0.827139i	$-0.310033\pi$
$613$	−8.66968	−	10.3321i	−0.350165	−	0.417310i	−0.912163	+	0.409828i	$0.865589\pi$
$614$	−1.82900	−	0.322502i	−0.0738124	−	0.0130151i
$615$	−17.1602	+	1.33989i	−0.691967	+	0.0540295i
$616$	−27.2027	+	15.7055i	−1.09603	+	0.632792i
$617$	−13.5726	+	4.94004i	−0.546414	+	0.198879i	−0.600453	−	0.799660i	$-0.705013\pi$
$617$	−13.5726	+	4.94004i	−0.546414	+	0.198879i	0.0540383	+	0.998539i	$0.482791\pi$
$618$	9.47370	+	7.30919i	0.381088	+	0.294019i
$619$	−24.5992	−	42.6071i	−0.988725	−	1.71252i	−0.624041	−	0.781391i	$-0.714510\pi$
$619$	−24.5992	−	42.6071i	−0.988725	−	1.71252i	−0.364684	−	0.931131i	$-0.618823\pi$
$620$	−12.8218	+	24.2323i	−0.514938	+	0.973193i
$621$	−12.7928	−	0.659960i	−0.513357	−	0.0264833i
$622$	−5.72140	+	4.80083i	−0.229407	+	0.192496i
$623$	−23.1780	+	27.6224i	−0.928606	+	1.10667i
$624$	3.08699	+	3.38675i	0.123579	+	0.135578i
$625$	−24.4949	−	5.00008i	−0.979795	−	0.200003i
$626$	−7.56318			−0.302285
$627$	2.43759	+	30.6007i	0.0973479	+	1.22208i
$628$			16.7489i			0.668352i
$629$	6.59608	+	2.40078i	0.263003	+	0.0957253i
$630$	3.48645	−	14.8804i	0.138903	−	0.592850i
$631$	27.3478	+	22.9475i	1.08870	+	0.913528i	0.996614	−	0.0822236i	$-0.0262022\pi$
$631$	27.3478	+	22.9475i	1.08870	+	0.913528i	0.0920858	+	0.995751i	$0.470647\pi$
$632$	−21.5452	+	18.0785i	−0.857020	+	0.719125i
$633$	−13.5576	+	5.57390i	−0.538865	+	0.221543i
$634$	3.53155	−	6.11682i	0.140256	−	0.242930i
$635$	18.3813	−	11.5376i	0.729439	−	0.457855i
$636$	−1.68182	−	1.29757i	−0.0666887	−	0.0514519i
$637$	5.28013	−	1.92181i	0.209206	−	0.0761449i
$638$	5.86563	+	10.1596i	0.232223	+	0.402221i
$639$	2.68659	+	3.88023i	0.106280	+	0.153500i
$640$	2.83914	−	20.5019i	0.112227	−	0.810409i
$641$	−8.77053	+	7.35935i	−0.346415	+	0.290677i	−0.799349	−	0.600867i	$-0.794822\pi$
$641$	−8.77053	+	7.35935i	−0.346415	+	0.290677i	0.452934	+	0.891544i	$0.350377\pi$
$642$	18.6380	+	2.50375i	0.735583	+	0.0988151i
$643$	41.4700	−	7.31228i	1.63542	−	0.288368i	0.720937	−	0.693001i	$-0.243712\pi$
$643$	41.4700	−	7.31228i	1.63542	−	0.288368i	0.914479	+	0.404632i	$0.132601\pi$
$644$	−3.42295	+	9.40448i	−0.134883	+	0.370589i
$645$	−34.3026	+	23.5444i	−1.35066	+	0.927059i
$646$	−3.42577	−	1.09953i	−0.134785	−	0.0432605i
$647$	20.2577			0.796412			0.398206	−	0.917296i	$-0.369633\pi$
$647$	20.2577			0.796412			0.398206	+	0.917296i	$0.369633\pi$
$648$	−22.4674	+	7.91016i	−0.882604	+	0.310741i
$649$	26.8806	−	4.73978i	1.05516	−	0.186053i
$650$	8.43080	−	11.7031i	0.330683	−	0.459034i
$651$	13.5144	−	42.4713i	0.529669	−	1.66458i
$652$	−1.48447	−	0.261752i	−0.0581363	−	0.0102510i
$653$	−8.96797	+	15.5330i	−0.350944	+	0.607852i	−0.986415	−	0.164272i	$-0.947472\pi$
$653$	−8.96797	+	15.5330i	−0.350944	+	0.607852i	0.635471	+	0.772124i	$0.280806\pi$
$654$	12.6848	+	6.64588i	0.496017	+	0.259874i
$655$	−23.5908	+	9.58677i	−0.921769	+	0.374586i
$656$	2.98957	−	1.08811i	0.116723	−	0.0424837i
$657$	−1.03970	−	12.6519i	−0.0405626	−	0.493597i
$658$	−13.1759	+	22.8213i	−0.513649	+	0.889666i
$659$	−1.01836	+	5.77542i	−0.0396698	+	0.224978i	−0.998197	−	0.0600224i	$-0.980883\pi$
$659$	−1.01836	+	5.77542i	−0.0396698	+	0.224978i	0.958527	+	0.285001i	$0.0919939\pi$
$660$	−5.86594	+	21.1013i	−0.228331	+	0.821368i
$661$	17.5979	−	20.9724i	0.684479	−	0.815730i	−0.306197	−	0.951968i	$-0.599057\pi$
$661$	17.5979	−	20.9724i	0.684479	−	0.815730i	0.990676	+	0.136238i	$0.0435011\pi$
$662$	−1.12390	−	6.37395i	−0.0436816	−	0.247730i
$663$	6.61303	−	1.44779i	0.256829	−	0.0562276i
$664$		−	39.6213i		−	1.53761i
$665$	−23.4970	+	16.0413i	−0.911174	+	0.622055i
$666$	14.0514	+	6.64271i	0.544482	+	0.257400i
$667$	8.56324	+	3.11677i	0.331570	+	0.120682i
$668$	−2.96827	+	0.523386i	−0.114846	+	0.0202504i
$669$	27.4787	+	3.69137i	1.06239	+	0.142717i
$670$	4.97723	−	4.49975i	0.192287	−	0.173840i
$671$	−27.4077	−	4.83273i	−1.05806	−	0.186565i
$672$	1.21259	+	29.5611i	0.0467767	+	1.14035i
$673$	−11.6311	−	20.1456i	−0.448345	−	0.776556i	0.549934	−	0.835208i	$-0.314653\pi$
$673$	−11.6311	−	20.1456i	−0.448345	−	0.776556i	−0.998278	+	0.0586523i	$0.981320\pi$
$674$	−1.68758	−	4.63660i	−0.0650033	−	0.178595i
$675$	−13.4891	−	22.2046i	−0.519195	−	0.854656i
$676$	−0.458701	−	0.794493i	−0.0176423	−	0.0305574i
$677$	29.6028	+	17.0912i	1.13773	+	0.656867i	0.945867	−	0.324555i	$-0.105214\pi$
$677$	29.6028	+	17.0912i	1.13773	+	0.656867i	0.191861	+	0.981422i	$0.438548\pi$
$678$	−4.23950	−	10.3119i	−0.162817	−	0.396026i
$679$	20.6100	+	24.5620i	0.790939	+	0.942604i
$680$	−4.93939	−	3.84303i	−0.189417	−	0.147374i
$681$	−1.45694	+	1.32799i	−0.0558301	+	0.0508887i
$682$	9.56873	−	26.2899i	0.366406	−	1.00669i
$683$		−	13.7959i		−	0.527884i	−0.964539	−	0.263942i	$-0.914977\pi$
$683$		−	13.7959i		−	0.527884i	0.964539	−	0.263942i	$-0.0850227\pi$
$684$	16.7291	+	7.13440i	0.639653	+	0.272791i
$685$	−0.612206	−	16.5717i	−0.0233912	−	0.633171i
$686$	−11.7315	−	4.26991i	−0.447911	−	0.163026i
$687$	−7.58785	−	8.32464i	−0.289494	−	0.317605i
$688$	4.94307	−	5.89092i	0.188453	−	0.224589i
$689$	2.09489	+	2.49659i	0.0798089	+	0.0951126i
$690$	−3.08624	−	6.78323i	−0.117491	−	0.258233i
$691$	−14.0499	+	24.3351i	−0.534483	+	0.925753i	0.464705	+	0.885466i	$0.346160\pi$
$691$	−14.0499	+	24.3351i	−0.534483	+	0.925753i	−0.999188	+	0.0402868i	$0.987173\pi$
$692$	20.8733	−	12.0512i	0.793483	−	0.458118i
$693$	3.29022	−	35.4532i	0.124985	−	1.34676i
$694$	−5.21737	−	14.3346i	−0.198049	−	0.544134i
$695$	11.7431	−	7.37094i	0.445443	−	0.279596i
$696$	16.9306	−	0.694489i	0.641753	−	0.0263245i
$697$	0.816121	−	4.62845i	0.0309128	−	0.175315i
$698$	7.92124	+	9.44017i	0.299823	+	0.357316i
$699$	−9.43697	−	1.26772i	−0.356939	−	0.0479496i
$700$	−19.6753	+	4.99010i	−0.743657	+	0.188608i
$701$	11.2621	−	30.9424i	0.425364	−	1.16868i	−0.523232	−	0.852190i	$-0.675274\pi$
$701$	11.2621	−	30.9424i	0.425364	−	1.16868i	0.948596	−	0.316488i	$-0.102504\pi$
$702$	14.8762	−	1.83891i	0.561468	−	0.0694053i
$703$	−10.9346	−	26.7870i	−0.412405	−	1.01029i
$704$			12.7503i			0.480545i
$705$	11.1893	+	43.3763i	0.421414	+	1.63364i
$706$	−13.0244	+	2.29656i	−0.490181	+	0.0864321i
$707$	7.13362	+	5.98582i	0.268287	+	0.225120i
$708$	4.90341	−	15.4098i	0.184281	−	0.579137i
$709$	2.44988	−	13.8940i	0.0920072	−	0.521799i	−0.903616	−	0.428343i	$-0.859097\pi$
$709$	2.44988	−	13.8940i	0.0920072	−	0.521799i	0.995623	−	0.0934559i	$-0.0297914\pi$
$710$	−1.28411	+	2.42688i	−0.0481919	+	0.0910790i
$711$	−2.61110	−	31.7739i	−0.0979240	−	1.19161i
$712$	11.1819	+	30.7221i	0.419061	+	1.15136i
$713$	−7.43296	−	20.4219i	−0.278367	−	0.764806i
$714$	3.69651	+	1.93669i	0.138338	+	0.0724786i
$715$	15.7155	−	29.7011i	0.587726	−	1.11076i
$716$	−3.76898	+	21.3750i	−0.140853	+	0.798820i
$717$	−18.0775	−	5.75227i	−0.675118	−	0.214822i
$718$	−1.53100	−	1.28466i	−0.0571365	−	0.0479432i
$719$	49.0310	−	8.64549i	1.82855	−	0.322422i	0.849740	−	0.527202i	$-0.176759\pi$
$719$	49.0310	−	8.64549i	1.82855	−	0.322422i	0.978808	+	0.204779i	$0.0656477\pi$
$720$	3.50136	+	3.28643i	0.130488	+	0.122478i
$721$			25.8355i			0.962164i
$722$	6.12890	+	13.5042i	0.228094	+	0.502574i
$723$	7.45248	+	11.7664i	0.277161	+	0.437597i
$724$	−2.26814	+	6.23166i	−0.0842947	+	0.231598i
$725$	4.54373	+	17.9153i	0.168750	+	0.665359i
$726$	0.995787	−	7.41268i	0.0369571	−	0.275110i
$727$	11.8126	+	14.0777i	0.438104	+	0.522112i	0.939242	−	0.343256i	$-0.111530\pi$
$727$	11.8126	+	14.0777i	0.438104	+	0.522112i	−0.501138	+	0.865367i	$0.667085\pi$
$728$	4.95796	−	28.1180i	0.183754	−	1.04212i
$729$	7.39978	−	25.9662i	0.274066	−	0.961711i
$730$	6.25513	−	3.92623i	0.231513	−	0.145316i
$731$	−3.88546	−	10.6752i	−0.143709	−	0.394837i
$732$	−10.0719	+	13.0545i	−0.372267	+	0.482508i
$733$	−42.8437	+	24.7358i	−1.58247	+	0.913637i	−0.587968	+	0.808884i	$0.700072\pi$
$733$	−42.8437	+	24.7358i	−1.58247	+	0.913637i	−0.994498	+	0.104753i	$0.966595\pi$
$734$	−4.56667	+	7.90970i	−0.168559	+	0.291952i
$735$	5.35957	−	2.43850i	0.197691	−	0.0899456i
$736$	9.27311	+	11.0513i	0.341811	+	0.407355i
$737$	10.0478	−	11.9745i	0.370115	−	0.441086i
$738$	2.74636	−	10.0375i	0.101095	−	0.369487i
$739$	32.3891	+	11.7887i	1.19145	+	0.433654i	0.860234	−	0.509900i	$-0.170318\pi$
$739$	32.3891	+	11.7887i	1.19145	+	0.433654i	0.331220	+	0.943554i	$0.392540\pi$
$740$	−0.762068	−	20.6282i	−0.0280142	−	0.758310i
$741$	−22.7320	−	16.1820i	−0.835080	−	0.594460i
$742$			2.00904i			0.0737540i
$743$	6.72181	−	18.4680i	0.246599	−	0.677526i	−0.753206	−	0.657785i	$-0.771494\pi$
$743$	6.72181	−	18.4680i	0.246599	−	0.677526i	0.999805	−	0.0197409i	$-0.00628413\pi$
$744$	−27.2224	−	29.8657i	−0.998021	−	1.09493i
$745$	9.09797	+	7.07857i	0.333324	+	0.259339i
$746$	10.3048	+	12.2808i	0.377287	+	0.449633i
$747$	36.6536	+	25.9543i	1.34109	+	0.949617i
$748$	−5.17899	−	2.99009i	−0.189363	−	0.109329i
$749$	20.3019	+	35.1638i	0.741814	+	1.28486i
$750$	7.85328	−	12.9144i	0.286761	−	0.471567i
$751$	6.69434	+	18.3926i	0.244280	+	0.671154i	0.999870	+	0.0161092i	$0.00512793\pi$
$751$	6.69434	+	18.3926i	0.244280	+	0.671154i	−0.755590	+	0.655045i	$0.772650\pi$
$752$	−4.13991	−	7.17053i	−0.150967	−	0.261482i
$753$	−47.0166	+	1.92861i	−1.71338	+	0.0702824i
$754$	−10.5014	−	1.85168i	−0.382439	−	0.0674343i
$755$	−32.6337	+	29.5031i	−1.18766	+	1.07373i
$756$	−17.7008	−	11.4745i	−0.643771	−	0.417322i
$757$	36.3518	−	6.40980i	1.32123	−	0.232968i	0.531830	−	0.846851i	$-0.321505\pi$
$757$	36.3518	−	6.40980i	1.32123	−	0.232968i	0.789397	+	0.613883i	$0.210393\pi$
$758$	6.89717	+	2.51037i	0.250517	+	0.0911806i
$759$	−9.28973	−	14.6671i	−0.337196	−	0.532384i
$760$	1.94365	+	25.7224i	0.0705037	+	0.933048i
$761$		−	14.3418i		−	0.519888i	−0.965624	−	0.259944i	$-0.916296\pi$
$761$		−	14.3418i		−	0.519888i	0.965624	−	0.259944i	$-0.0837041\pi$
$762$	2.80611	+	12.8174i	0.101655	+	0.464325i
$763$	5.36917	+	30.4501i	0.194377	+	1.10237i
$764$	−11.3615	+	13.5401i	−0.411043	+	0.489862i
$765$	6.79077	−	2.05201i	0.245521	−	0.0741906i
$766$	1.41549	−	8.02765i	0.0511438	−	0.290051i
$767$	−12.4054	+	21.4867i	−0.447932	+	0.775841i
$768$	20.7066	+	10.8486i	0.747184	+	0.391466i
$769$	14.5431	−	5.29326i	0.524438	−	0.190880i	−0.0662150	−	0.997805i	$-0.521092\pi$
$769$	14.5431	−	5.29326i	0.524438	−	0.190880i	0.590653	+	0.806925i	$0.298870\pi$
$770$	19.1901	−	7.79841i	0.691563	−	0.281035i
$771$	−7.56076	+	14.4311i	−0.272294	+	0.519722i
$772$	−2.73033	+	4.72907i	−0.0982666	+	0.170203i
$773$	11.1722	+	1.96996i	0.401836	+	0.0708546i	0.370914	−	0.928667i	$-0.379044\pi$
$773$	11.1722	+	1.96996i	0.401836	+	0.0708546i	0.0309224	+	0.999522i	$0.490156\pi$
$774$	−6.38217	−	24.3311i	−0.229402	−	0.874562i
$775$	25.7640	−	35.7640i	0.925471	−	1.28468i
$776$	28.6298	−	5.04821i	1.02775	−	0.181220i
$777$	7.17698	+	32.7821i	0.257473	+	1.17605i
$778$	−0.528015			−0.0189303
$779$	−16.3915	+	10.3244i	−0.587285	+	0.369912i
$780$	−11.2658	−	16.4136i	−0.403381	−	0.587700i
$781$	−2.18775	+	6.01078i	−0.0782837	+	0.215083i
$782$	2.00394	−	0.353348i	0.0716606	−	0.0126357i
$783$	−10.4481	+	16.1174i	−0.373383	+	0.575989i
$784$	−0.833716	+	0.699571i	−0.0297756	+	0.0249847i
$785$	3.69384	−	26.6738i	0.131839	−	0.952029i
$786$	−0.630987	−	15.3825i	−0.0225066	−	0.548677i
$787$	6.39069	+	11.0690i	0.227803	+	0.394567i	0.957157	−	0.289570i	$-0.0935123\pi$
$787$	6.39069	+	11.0690i	0.227803	+	0.394567i	−0.729353	+	0.684137i	$0.760179\pi$
$788$	21.2739	−	7.74308i	0.757852	−	0.275836i
$789$	−32.3833	+	41.9732i	−1.15288	+	1.49428i
$790$	15.7091	−	9.86031i	0.558905	−	0.350814i
$791$	12.0366	−	20.8479i	0.427971	−	0.741268i
$792$	−26.3467	−	18.6560i	−0.936190	−	0.662911i
$793$	19.3788	−	16.2608i	0.688162	−	0.577437i
$794$	−3.48877	−	2.92743i	−0.123812	−	0.103891i
$795$	2.39226	+	2.43739i	0.0848448	+	0.0864453i
$796$	−7.40007	−	2.69340i	−0.262288	−	0.0954652i
$797$			41.9630i			1.48641i	0.669066	+	0.743203i	$0.266694\pi$
$797$			41.9630i			1.48641i	−0.669066	+	0.743203i	$0.733306\pi$
$798$	−4.32258	−	16.6489i	−0.153018	−	0.589365i
$799$	−12.2316			−0.432722
$800$	−7.95135	+	28.1584i	−0.281123	+	0.995550i
$801$	−35.7458	−	9.78036i	−1.26302	−	0.345572i
$802$	−16.7498	+	19.9616i	−0.591455	+	0.704869i
$803$	13.1800	−	11.0594i	0.465114	−	0.390277i
$804$	−3.52145	−	8.56532i	−0.124192	−	0.302076i
$805$	7.52540	−	14.2224i	0.265236	−	0.501275i
$806$	12.7152	+	22.0234i	0.447875	+	0.775742i
$807$	0.0283988	−	0.0368087i	0.000999686	−	0.00129573i
$808$	7.93412	−	2.88778i	0.279121	−	0.101592i
$809$	−2.26615	+	1.30836i	−0.0796736	+	0.0459996i	−0.539308	−	0.842109i	$-0.681314\pi$
$809$	−2.26615	+	1.30836i	−0.0796736	+	0.0459996i	0.459634	+	0.888108i	$0.347981\pi$
$810$	15.3917	−	3.13469i	0.540811	−	0.110142i
$811$	−50.7118	−	8.94186i	−1.78073	−	0.313991i	−0.816163	−	0.577821i	$-0.803903\pi$
$811$	−50.7118	−	8.94186i	−1.78073	−	0.313991i	−0.964569	+	0.263830i	$0.915014\pi$
$812$	9.64601	+	11.4957i	0.338509	+	0.403419i
$813$	18.7539	+	2.51932i	0.657728	+	0.0883564i
$814$	3.65794	+	20.7452i	0.128211	+	0.727119i
$815$	2.30640	+	0.744249i	0.0807897	+	0.0260699i
$816$	−1.10772	+	0.701595i	−0.0387779	+	0.0245607i
$817$	−21.8347	+	41.4229i	−0.763900	+	1.44920i
$818$	3.04529			0.106476
$819$	22.7642	+	23.0055i	0.795445	+	0.803878i
$820$	−13.5132	+	2.90086i	−0.471903	+	0.101303i
$821$	2.03298	−	2.42281i	0.0709514	−	0.0845565i	−0.729401	−	0.684086i	$-0.760201\pi$
$821$	2.03298	−	2.42281i	0.0709514	−	0.0845565i	0.800353	+	0.599530i	$0.204646\pi$
$822$	9.55388	+	3.04004i	0.333230	+	0.106034i
$823$	19.1994	+	3.38538i	0.669251	+	0.118007i	0.497942	−	0.867210i	$-0.334089\pi$
$823$	19.1994	+	3.38538i	0.669251	+	0.118007i	0.171309	+	0.985217i	$0.445200\pi$
$824$	20.2864	+	11.7123i	0.706709	+	0.408019i
$825$	13.9957	−	32.3118i	0.487268	−	1.12495i
$826$	−14.3721	+	5.23101i	−0.500069	+	0.182010i
$827$	−15.5269	−	42.6599i	−0.539924	−	1.48343i	−0.846921	−	0.531719i	$-0.821546\pi$
$827$	−15.5269	−	42.6599i	−0.539924	−	1.48343i	0.306997	−	0.951711i	$-0.400676\pi$
$828$	−10.2513	+	0.842431i	−0.356259	+	0.0292765i
$829$	−10.0421	−	5.79784i	−0.348778	−	0.201367i	0.315369	−	0.948969i	$-0.397872\pi$
$829$	−10.0421	−	5.79784i	−0.348778	−	0.201367i	−0.664147	+	0.747602i	$0.731205\pi$
$830$	−3.58412	+	25.8815i	−0.124407	+	0.898359i
$831$	−33.6293	−	10.7008i	−1.16659	−	0.371208i
$832$	−8.87822	−	7.44971i	−0.307797	−	0.258272i
$833$	0.279188	+	1.58335i	0.00967328	+	0.0548599i
$834$	1.79272	+	8.18856i	0.0620769	+	0.283547i
$835$	4.84262	−	0.178901i	0.167586	−	0.00619111i
$836$	5.21132	+	24.0921i	0.180237	+	0.833244i
$837$	45.4610	−	5.61961i	1.57136	−	0.194242i
$838$	−28.4660	−	10.3608i	−0.983342	−	0.357907i
$839$	4.20270	+	23.8347i	0.145093	+	0.822864i	0.967292	+	0.253664i	$0.0816359\pi$
$839$	4.20270	+	23.8347i	0.145093	+	0.822864i	−0.822199	+	0.569200i	$0.807253\pi$
$840$	2.88606	−	29.7803i	0.0995787	−	1.02752i
$841$	−11.7479	+	9.85768i	−0.405101	+	0.339920i
$842$	−0.187591	+	1.06388i	−0.00646482	+	0.0366638i
$843$	0.172832	+	4.21339i	0.00595265	+	0.145117i
$844$	−10.1935	+	5.88523i	−0.350875	+	0.202578i
$845$	0.555296	+	1.36645i	0.0191028	+	0.0470074i
$846$	−26.9674	−	2.50270i	−0.927160	−	0.0860446i
$847$	13.9853	−	8.07442i	0.480541	−	0.277440i
$848$	−0.546676	−	0.315623i	−0.0187729	−	0.0108386i
$849$	9.74845	−	4.00786i	0.334566	−	0.137549i
$850$	2.87887	+	2.95716i	0.0987445	+	0.101430i
$851$	12.5351	+	10.5182i	0.429698	+	0.360559i
$852$	2.55287	+	2.80076i	0.0874598	+	0.0959523i
$853$	−14.4787	+	39.7798i	−0.495740	+	1.36204i	0.399615	+	0.916683i	$0.369144\pi$
$853$	−14.4787	+	39.7798i	−0.495740	+	1.36204i	−0.895355	+	0.445352i	$0.853078\pi$
$854$	15.5944			0.533628
$855$	−25.0689	−	15.0516i	−0.857339	−	0.514752i
$856$	36.8148			1.25830
$857$	−2.67834	+	7.35867i	−0.0914902	+	0.251367i	−0.976995	−	0.213263i	$-0.931591\pi$
$857$	−2.67834	+	7.35867i	−0.0914902	+	0.251367i	0.885504	+	0.464631i	$0.153813\pi$
$858$	13.6856	+	15.0145i	0.467218	+	0.512586i
$859$	9.23926	+	7.75266i	0.315239	+	0.264517i	0.786654	−	0.617395i	$-0.211812\pi$
$859$	9.23926	+	7.75266i	0.315239	+	0.264517i	−0.471414	+	0.881912i	$0.656256\pi$
$860$	−24.7817	+	22.4043i	−0.845049	+	0.763981i
$861$	20.7814	−	8.54381i	0.708227	−	0.291172i
$862$	1.56599	+	0.904122i	0.0533377	+	0.0307945i
$863$	24.8081	−	14.3230i	0.844477	−	0.487559i	−0.0143062	−	0.999898i	$-0.504554\pi$
$863$	24.8081	−	14.3230i	0.844477	−	0.487559i	0.858784	+	0.512338i	$0.171221\pi$
$864$	−27.0819	+	13.8268i	−0.921345	+	0.470397i
$865$	−35.9001	+	14.5890i	−1.22064	+	0.496040i
$866$	24.8045	−	14.3209i	0.842890	−	0.486643i
$867$	−1.12742	−	27.4847i	−0.0382890	−	0.933430i
$868$	6.21453	−	35.2444i	0.210935	−	1.19627i
$869$	33.1003	−	27.7745i	1.12285	−	0.942184i
$870$	−11.1222	−	1.07788i	−0.377080	−	0.0365434i
$871$	2.46732	+	13.9928i	0.0836018	+	0.474130i
$872$	26.3439	+	9.58839i	0.892116	+	0.324704i
$873$	−14.0841	+	29.7923i	−0.476674	+	1.00832i
$874$	−6.62777	−	5.14000i	−0.224188	−	0.173863i
$875$	32.4349	−	3.60786i	1.09650	−	0.121968i
$876$	−2.17999	−	9.95749i	−0.0736552	−	0.336432i
$877$	−0.538186	−	3.05220i	−0.0181732	−	0.103066i	0.974372	−	0.224943i	$-0.0722196\pi$
$877$	−0.538186	−	3.05220i	−0.0181732	−	0.103066i	−0.992545	+	0.121877i	$0.961108\pi$
$878$	−20.1302	−	16.8913i	−0.679362	−	0.570052i
$879$	−30.4701	−	9.69559i	−1.02773	−	0.327024i
$880$	−0.892784	+	6.44693i	−0.0300957	+	0.217326i
$881$	−14.5729	−	8.41365i	−0.490972	−	0.283463i	0.234005	−	0.972235i	$-0.424817\pi$
$881$	−14.5729	−	8.41365i	−0.490972	−	0.283463i	−0.724978	+	0.688772i	$0.758150\pi$
$882$	0.291567	+	3.54800i	0.00981756	+	0.119467i
$883$	−15.9511	−	43.8254i	−0.536799	−	1.47484i	−0.850836	−	0.525431i	$-0.823904\pi$
$883$	−15.9511	−	43.8254i	−0.536799	−	1.47484i	0.314038	−	0.949411i	$-0.398318\pi$
$884$	5.10802	−	1.85917i	0.171801	−	0.0625305i
$885$	−11.2076	+	23.4599i	−0.376738	+	0.788596i
$886$	−19.4457	−	11.2270i	−0.653292	−	0.377179i
$887$	−20.9242	−	3.68949i	−0.702565	−	0.123881i	−0.189057	−	0.981966i	$-0.560543\pi$
$887$	−20.9242	−	3.68949i	−0.702565	−	0.123881i	−0.513508	+	0.858085i	$0.671654\pi$
$888$	28.9945	+	9.22606i	0.972993	+	0.309606i
$889$	−18.2102	+	21.7021i	−0.610752	+	0.727865i
$890$	−4.52517	−	21.0798i	−0.151684	−	0.706597i
$891$	34.5172	−	12.1526i	1.15637	−	0.407126i
$892$	22.2628			0.745413
$893$	33.8694	+	37.3455i	1.13340	+	1.24972i
$894$	−5.88770	+	3.72909i	−0.196914	+	0.124719i
$895$	10.7165	−	33.2100i	0.358213	−	1.11009i
$896$	4.69172	+	26.6081i	0.156740	+	0.888914i
$897$	15.6407	+	2.10111i	0.522229	+	0.0701539i
$898$	−18.4497	−	21.9875i	−0.615674	−	0.733731i
$899$	−32.0917	−	5.65863i	−1.07032	−	0.188726i
$900$	−13.1087	−	16.2288i	−0.436958	−	0.540961i
$901$	−0.807591	+	0.466263i	−0.0269048	+	0.0155335i
$902$	13.2537	−	4.82394i	0.441299	−	0.160620i
$903$	33.1763	−	43.0010i	1.10404	−	1.43098i
$904$	−10.9134	−	18.9026i	−0.362974	−	0.628690i
$905$	4.98653	−	9.42417i	0.165758	−	0.313270i
$906$	−10.1137	−	24.5999i	−0.336005	−	0.817276i
$907$	13.2221	−	11.0947i	0.439033	−	0.368392i	−0.396314	−	0.918115i	$-0.629711\pi$
$907$	13.2221	−	11.0947i	0.439033	−	0.368392i	0.835347	+	0.549722i	$0.185267\pi$
$908$	−1.01749	+	1.21260i	−0.0337667	+	0.0402416i
$909$	−2.52582	+	9.23151i	−0.0837762	+	0.306190i
$910$	−5.78218	+	17.9188i	−0.191677	+	0.594001i
$911$	18.3184			0.606916			0.303458	−	0.952845i	$-0.401859\pi$
$911$	18.3184			0.606916			0.303458	+	0.952845i	$0.401859\pi$
$912$	5.20939	+	1.43936i	0.172500	+	0.0476621i
$913$			60.8712i			2.01454i
$914$	−14.8471	−	5.40391i	−0.491099	−	0.178745i
$915$	18.9193	−	18.5690i	0.625452	−	0.613872i
$916$	−6.92854	−	5.81373i	−0.228925	−	0.192091i
$917$	25.4642	−	21.3670i	0.840901	−	0.705600i
$918$	−0.220968	+	4.28328i	−0.00729302	+	0.141369i
$919$	13.9940	−	24.2383i	0.461619	−	0.799547i	−0.537423	−	0.843313i	$-0.680602\pi$
$919$	13.9940	−	24.2383i	0.461619	−	0.799547i	0.999042	+	0.0437659i	$0.0139356\pi$
$920$	−7.75606	−	12.3567i	−0.255710	−	0.407388i
$921$	2.51752	−	3.26305i	0.0829551	−	0.107521i
$922$	26.8486	−	9.77211i	0.884213	−	0.321827i
$923$	−2.90714	−	5.03532i	−0.0956898	−	0.165740i
$924$	−1.17178	−	28.5662i	−0.0385486	−	0.939758i
$925$	−3.33576	+	33.0201i	−0.109679	+	1.08569i
$926$	−13.4787	+	11.3099i	−0.442936	+	0.371668i
$927$	−24.1238	+	11.0946i	−0.792330	+	0.364395i
$928$	21.3030	−	3.75629i	0.699305	−	0.123306i
$929$	−1.85778	+	5.10421i	−0.0609518	+	0.167464i	−0.966431	−	0.256928i	$-0.917290\pi$
$929$	−1.85778	+	5.10421i	−0.0609518	+	0.167464i	0.905479	+	0.424392i	$0.139512\pi$
$930$	15.0806	+	21.9714i	0.494512	+	0.720471i
$931$	4.06122	−	5.23674i	0.133101	−	0.171627i
$932$	−7.64568			−0.250442
$933$	−3.54457	−	16.1904i	−0.116044	−	0.530050i
$934$	23.5812	−	4.15801i	0.771601	−	0.136054i
$935$	7.58850	+	5.90414i	0.248170	+	0.193086i
$936$	28.3842	−	7.44534i	0.927767	−	0.243359i
$937$	27.5222	+	4.85291i	0.899112	+	0.158538i	0.604056	−	0.796942i	$-0.293550\pi$
$937$	27.5222	+	4.85291i	0.899112	+	0.158538i	0.295056	+	0.955480i	$0.404662\pi$
$938$	−4.37944	+	7.58541i	−0.142994	+	0.247673i
$939$	7.78893	−	14.8666i	0.254182	−	0.485152i
$940$	13.5419	+	33.3235i	0.441689	+	1.08689i
$941$	27.7887	−	10.1143i	0.905885	−	0.329715i	0.153276	−	0.988183i	$-0.451018\pi$
$941$	27.7887	−	10.1143i	0.905885	−	0.329715i	0.752609	+	0.658468i	$0.228795\pi$
$942$	14.4212	+	7.55560i	0.469868	+	0.246175i
$943$	5.47808	−	9.48831i	0.178391	−	0.308982i
$944$	0.834479	−	4.73257i	0.0271600	−	0.154032i
$945$	25.6592	+	22.1777i	0.834694	+	0.721441i
$946$	21.9141	−	26.1162i	0.712490	−	0.849112i
$947$	−3.23248	−	18.3323i	−0.105041	−	0.595719i	−0.991204	−	0.132344i	$-0.957750\pi$
$947$	−3.23248	−	18.3323i	−0.105041	−	0.595719i	0.886162	−	0.463375i	$-0.153362\pi$
$948$	−5.47483	−	25.0072i	−0.177814	−	0.812195i
$949$			15.6392i			0.507670i
$950$	1.05719	−	16.9782i	0.0342999	−	0.550846i
$951$	8.38657	+	13.2412i	0.271953	+	0.429375i
$952$	7.67691	+	2.79417i	0.248810	+	0.0905595i
$953$	−47.1436	+	8.31268i	−1.52713	+	0.269274i	−0.873231	−	0.487307i	$-0.837979\pi$
$953$	−47.1436	+	8.31268i	−1.52713	+	0.269274i	−0.653900	+	0.756581i	$0.726868\pi$
$954$	−1.87593	+	0.862748i	−0.0607355	+	0.0279325i
$955$	21.0801	−	19.0579i	0.682137	−	0.616698i
$956$	−15.0015	−	2.64516i	−0.485182	−	0.0855507i
$957$	−26.0109	+	1.06696i	−0.840813	+	0.0344899i
$958$	7.13164	+	12.3524i	0.230413	+	0.399087i
$959$	7.40385	+	20.3419i	0.239083	+	0.656874i
$960$	−9.88310	−	7.05875i	−0.318976	−	0.227820i
$961$	23.3570	+	40.4555i	0.753452	+	1.30502i
$962$	−16.5824	−	9.57388i	−0.534640	−	0.308674i
$963$	−24.1158	+	34.0573i	−0.777122	+	1.09748i
$964$	7.18876	+	8.56723i	0.231534	+	0.275932i
$965$	5.39121	−	6.92924i	0.173549	−	0.223060i
$966$	6.55338	+	7.18972i	0.210851	+	0.231325i
$967$	−17.1545	+	47.1315i	−0.551650	+	1.51565i	0.279806	+	0.960056i	$0.409730\pi$
$967$	−17.1545	+	47.1315i	−0.551650	+	1.51565i	−0.831457	+	0.555590i	$0.812493\pi$
$968$		−	14.6419i		−	0.470610i
$969$	5.68932	−	5.60152i	0.182767	−	0.179947i
$970$	−19.1583	+	0.707762i	−0.615135	+	0.0227249i
$971$	−49.3398	−	17.9582i	−1.58339	−	0.576307i	−0.607452	−	0.794356i	$-0.707808\pi$
$971$	−49.3398	−	17.9582i	−1.58339	−	0.576307i	−0.975938	+	0.218049i	$0.930031\pi$
$972$	3.11293	−	21.4556i	0.0998474	−	0.688187i
$973$	−11.6339	+	13.8647i	−0.372964	+	0.444482i
$974$	6.74403	+	8.03722i	0.216093	+	0.257529i
$975$	14.3218	+	28.6244i	0.458664	+	0.916716i
$976$	−2.44990	+	4.24336i	−0.0784195	+	0.135827i
$977$	12.9693	−	7.48783i	0.414925	−	0.239557i	−0.277979	−	0.960587i	$-0.589664\pi$
$977$	12.9693	−	7.48783i	0.414925	−	0.239557i	0.692904	+	0.721030i	$0.256331\pi$
$978$	−0.895036	+	1.16009i	−0.0286201	+	0.0370955i
$979$	−17.1791	−	47.1991i	−0.549045	−	1.50849i
$980$	4.00457	−	2.51359i	0.127921	−	0.0802937i
$981$	−26.1270	+	18.0897i	−0.834169	+	0.577561i
$982$	−1.02678	+	5.82315i	−0.0327658	+	0.185824i
$983$	23.3561	+	27.8347i	0.744942	+	0.887788i	0.996797	−	0.0799773i	$-0.0254848\pi$
$983$	23.3561	+	27.8347i	0.744942	+	0.887788i	−0.251854	+	0.967765i	$0.581040\pi$
$984$	2.71238	−	20.1911i	0.0864676	−	0.643668i
$985$	−35.5880	+	7.63962i	−1.13393	+	0.243418i
$986$	1.04356	−	2.86714i	0.0332336	−	0.0913085i
$987$	−31.2895	−	49.4016i	−0.995956	−	1.57247i
$988$	−19.8206	−	10.4478i	−0.630576	−	0.332388i
$989$		−	26.4828i		−	0.842105i
$990$	15.5226	+	14.5698i	0.493341	+	0.463058i
$991$	−6.19111	+	1.09166i	−0.196667	+	0.0346777i	−0.271114	−	0.962547i	$-0.587392\pi$
$991$	−6.19111	+	1.09166i	−0.196667	+	0.0346777i	0.0744469	+	0.997225i	$0.476281\pi$
$992$	−39.5185	−	33.1600i	−1.25472	−	1.05283i
$993$	13.6864	+	4.35501i	0.434325	+	0.138202i
$994$	0.622388	−	3.52974i	0.0197409	−	0.111956i
$995$	11.1912	+	5.92148i	0.354783	+	0.187724i
$996$	31.9445	+	16.7364i	1.01220	+	0.530314i
$997$	−12.2420	−	33.6347i	−0.387709	−	1.06522i	−0.968030	−	0.250834i	$-0.919295\pi$
$997$	−12.2420	−	33.6347i	−0.387709	−	1.06522i	0.580321	−	0.814388i	$-0.302927\pi$
$998$	4.55131	+	12.5046i	0.144069	+	0.395827i
$999$	−27.5281	+	20.7792i	−0.870951	+	0.657425i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.bf.c.224.20	yes	192
3.2	odd	2	inner	285.2.bf.c.224.14	yes	192
5.4	even	2	inner	285.2.bf.c.224.13	yes	192
15.14	odd	2	inner	285.2.bf.c.224.19	yes	192
19.14	odd	18	inner	285.2.bf.c.14.19	yes	192
57.14	even	18	inner	285.2.bf.c.14.13	✓	192
95.14	odd	18	inner	285.2.bf.c.14.14	yes	192
285.14	even	18	inner	285.2.bf.c.14.20	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.bf.c.14.13	✓	192	57.14	even	18	inner
285.2.bf.c.14.14	yes	192	95.14	odd	18	inner
285.2.bf.c.14.19	yes	192	19.14	odd	18	inner
285.2.bf.c.14.20	yes	192	285.14	even	18	inner
285.2.bf.c.224.13	yes	192	5.4	even	2	inner
285.2.bf.c.224.14	yes	192	3.2	odd	2	inner
285.2.bf.c.224.19	yes	192	15.14	odd	2	inner
285.2.bf.c.224.20	yes	192	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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.266954 - 0.733451i) q^{2} +(1.16679 + 1.28008i) q^{3} +(1.06540 + 0.893980i) q^{4} +(-1.49957 - 1.65870i) q^{5} +(1.25036 - 0.514056i) q^{6} +(2.52789 + 1.45948i) q^{7} +(2.29201 - 1.32329i) q^{8} +(-0.277222 + 2.98716i) q^{9} +O(q^{10})\)	\(q+(0.266954 - 0.733451i) q^{2} +(1.16679 + 1.28008i) q^{3} +(1.06540 + 0.893980i) q^{4} +(-1.49957 - 1.65870i) q^{5} +(1.25036 - 0.514056i) q^{6} +(2.52789 + 1.45948i) q^{7} +(2.29201 - 1.32329i) q^{8} +(-0.277222 + 2.98716i) q^{9} +(-1.61689 + 0.657068i) q^{10} +(-3.52126 + 2.03300i) q^{11} +(0.0987298 + 2.40689i) q^{12} +(0.641785 - 3.63974i) q^{13} +(1.74529 - 1.46447i) q^{14} +(0.373587 - 3.85492i) q^{15} +(0.124307 + 0.704980i) q^{16} +(0.993740 + 0.361692i) q^{17} +(2.11693 + 1.00076i) q^{18} +(-1.64736 - 4.03562i) q^{19} +(-0.114810 - 3.10777i) q^{20} +(1.08126 + 4.93881i) q^{21} +(0.551091 + 3.12539i) q^{22} +(1.88849 + 1.58463i) q^{23} +(4.36820 + 1.38996i) q^{24} +(-0.502553 + 4.97468i) q^{25} +(-2.49825 - 1.44236i) q^{26} +(-4.14728 + 3.13051i) q^{27} +(1.38848 + 3.81482i) q^{28} +(3.47358 - 1.26428i) q^{29} +(-2.72767 - 1.30310i) q^{30} +(-7.63449 - 4.40778i) q^{31} +(5.76300 + 1.01617i) q^{32} +(-6.71097 - 2.13543i) q^{33} +(0.530566 - 0.632304i) q^{34} +(-1.36993 - 6.38161i) q^{35} +(-2.96582 + 2.93470i) q^{36} +6.63764 q^{37} +(-3.39970 + 0.130930i) q^{38} +(5.40800 - 3.42526i) q^{39} +(-5.63198 - 1.81737i) q^{40} +(-0.771734 - 4.37672i) q^{41} +(3.91102 + 0.525390i) q^{42} +(-6.90512 - 8.22920i) q^{43} +(-5.56903 - 0.981970i) q^{44} +(5.37052 - 4.01965i) q^{45} +(1.66639 - 0.962090i) q^{46} +(-10.8688 + 3.95592i) q^{47} +(-0.757393 + 0.981683i) q^{48} +(0.760167 + 1.31665i) q^{49} +(3.51452 + 1.69661i) q^{50} +(0.696486 + 1.69409i) q^{51} +(3.93762 - 3.30405i) q^{52} +(-0.566815 + 0.675504i) q^{53} +(1.18894 + 3.87753i) q^{54} +(8.65253 + 2.79207i) q^{55} +7.72527 q^{56} +(3.24381 - 6.81745i) q^{57} -2.88521i q^{58} +(-6.30821 - 2.29600i) q^{59} +(3.84424 - 3.77307i) q^{60} +(5.24334 + 4.39968i) q^{61} +(-5.27095 + 4.42285i) q^{62} +(-5.06050 + 7.14663i) q^{63} +(1.56792 - 2.71571i) q^{64} +(-6.99964 + 4.39354i) q^{65} +(-3.35775 + 4.35210i) q^{66} +(-3.61261 + 1.31488i) q^{67} +(0.735389 + 1.27373i) q^{68} +(0.175004 + 4.26635i) q^{69} +(-5.04631 - 0.698822i) q^{70} +(1.20512 - 1.01122i) q^{71} +(3.31749 + 7.21345i) q^{72} +(-4.16722 + 0.734794i) q^{73} +(1.77194 - 4.86838i) q^{74} +(-6.95437 + 5.16108i) q^{75} +(1.85266 - 5.77227i) q^{76} -11.8685 q^{77} +(-1.06857 - 4.88089i) q^{78} +(-10.4655 + 1.84536i) q^{79} +(0.982940 - 1.26336i) q^{80} +(-8.84630 - 1.65622i) q^{81} +(-3.41613 - 0.602355i) q^{82} +(7.48538 - 12.9651i) q^{83} +(-3.26323 + 6.22845i) q^{84} +(-0.890250 - 2.19070i) q^{85} +(-7.87907 + 2.86775i) q^{86} +(5.67131 + 2.97133i) q^{87} +(-5.38051 + 9.31931i) q^{88} +(-2.14511 + 12.1655i) q^{89} +(-1.51453 - 5.01207i) q^{90} +(6.93450 - 8.26422i) q^{91} +(0.595376 + 3.37654i) q^{92} +(-3.26550 - 14.9157i) q^{93} +9.02778i q^{94} +(-4.22353 + 8.78418i) q^{95} +(5.42340 + 8.56277i) q^{96} +(10.3221 + 3.75693i) q^{97} +(1.16863 - 0.206060i) q^{98} +(-5.09674 - 11.0822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{4} - 30 q^{6} - 12 q^{9}+O(q^{10}) \) 192 * q - 12 * q^4 - 30 * q^6 - 12 * q^9	\( 192 q - 12 q^{4} - 30 q^{6} - 12 q^{9} + 18 q^{10} + 15 q^{15} - 36 q^{16} - 48 q^{19} - 30 q^{21} - 156 q^{24} - 12 q^{25} - 24 q^{30} - 36 q^{31} + 24 q^{34} - 6 q^{36} - 6 q^{40} - 30 q^{45} + 36 q^{46} + 60 q^{49} + 24 q^{51} - 6 q^{54} - 90 q^{55} + 90 q^{60} + 12 q^{61} - 60 q^{64} + 108 q^{66} + 90 q^{69} - 18 q^{70} - 132 q^{76} - 120 q^{79} + 36 q^{81} + 198 q^{84} - 66 q^{85} - 114 q^{90} - 72 q^{91} + 144 q^{96} + 78 q^{99}+O(q^{100}) \) 192 * q - 12 * q^4 - 30 * q^6 - 12 * q^9 + 18 * q^10 + 15 * q^15 - 36 * q^16 - 48 * q^19 - 30 * q^21 - 156 * q^24 - 12 * q^25 - 24 * q^30 - 36 * q^31 + 24 * q^34 - 6 * q^36 - 6 * q^40 - 30 * q^45 + 36 * q^46 + 60 * q^49 + 24 * q^51 - 6 * q^54 - 90 * q^55 + 90 * q^60 + 12 * q^61 - 60 * q^64 + 108 * q^66 + 90 * q^69 - 18 * q^70 - 132 * q^76 - 120 * q^79 + 36 * q^81 + 198 * q^84 - 66 * q^85 - 114 * q^90 - 72 * q^91 + 144 * q^96 + 78 * q^99

Introduction

L-functions

Modular forms

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