LMFDB - Embedded newform 975.2.bn.d.218.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(218,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.218"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,2,0,0,-12,12,0,0,0,0,12,24,0,0,16,0,0,0,0,0,-20,0,0,0,0, 32,36,0,0,0,0,-30,0,0,-4,84,0,0,0,0,48,-8,0,0,0,0,28,0,0,-16,-28,0,0,0, 0,0,-84,0,0,-32,0,-90,0,0,0,-36,0,0,0,0,-90,0,0,0,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(76)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			218.22
Character	$\chi$	$=$	975.218
Dual form			975.2.bn.d.407.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.12039 + 0.568157i) q^{2} +(1.41092 + 1.00464i) q^{3} +(2.44121 + 1.40943i) q^{4} +(2.42092 + 2.93185i) q^{6} +(3.37093 - 0.903238i) q^{7} +(1.27107 + 1.27107i) q^{8} +(0.981406 + 2.83493i) q^{9} +(0.662995 + 1.14834i) q^{11} +(2.02839 + 4.44113i) q^{12} +(-3.14579 - 1.76182i) q^{13} +7.66087 q^{14} +(-0.845867 - 1.46508i) q^{16} +(-4.63881 + 1.24296i) q^{17} +(0.470279 + 6.56876i) q^{18} +(2.69447 - 4.66695i) q^{19} +(5.66355 + 2.11216i) q^{21} +(0.753371 + 2.81162i) q^{22} +(-2.13883 - 0.573097i) q^{23} +(0.516417 + 3.07034i) q^{24} +(-5.66931 - 5.52306i) q^{26} +(-1.46339 + 4.98583i) q^{27} +(9.50219 + 2.54610i) q^{28} +(-2.06922 - 3.58399i) q^{29} +9.82014i q^{31} +(-1.89166 - 7.05976i) q^{32} +(-0.218232 + 2.28629i) q^{33} -10.5423 q^{34} +(-1.59983 + 8.30389i) q^{36} +(0.871294 - 3.25171i) q^{37} +(8.36489 - 8.36489i) q^{38} +(-2.66847 - 5.64617i) q^{39} +(0.983308 + 1.70314i) q^{41} +(10.8089 + 7.69640i) q^{42} +(-6.59808 + 1.76795i) q^{43} +3.73779i q^{44} +(-4.20954 - 2.43038i) q^{46} +(-3.61835 + 3.61835i) q^{47} +(0.278426 - 2.91691i) q^{48} +(4.48514 - 2.58950i) q^{49} +(-7.79372 - 2.90659i) q^{51} +(-5.19635 - 8.73475i) q^{52} +(2.43489 - 2.43489i) q^{53} +(-5.93570 + 9.74047i) q^{54} +(5.43276 + 3.13661i) q^{56} +(8.49028 - 3.87775i) q^{57} +(-2.35128 - 8.77510i) q^{58} +(5.33897 + 3.08246i) q^{59} +(3.34455 - 5.79293i) q^{61} +(-5.57939 + 20.8226i) q^{62} +(5.86887 + 8.66991i) q^{63} -12.6608i q^{64} +(-1.76171 + 4.72384i) q^{66} +(0.132637 - 0.495007i) q^{67} +(-13.0762 - 3.50375i) q^{68} +(-2.44197 - 2.95734i) q^{69} +(-7.13214 + 12.3532i) q^{71} +(-2.35596 + 4.85083i) q^{72} +(5.00425 - 5.00425i) q^{73} +(3.69497 - 6.39988i) q^{74} +(13.1555 - 7.59533i) q^{76} +(3.27213 + 3.27213i) q^{77} +(-2.45028 - 13.4882i) q^{78} -0.914386i q^{79} +(-7.07368 + 5.56444i) q^{81} +(1.11735 + 4.17000i) q^{82} +(-2.26406 - 2.26406i) q^{83} +(10.8489 + 13.1386i) q^{84} -14.9950 q^{86} +(0.681105 - 7.13554i) q^{87} +(-0.616909 + 2.30233i) q^{88} +(3.65216 - 2.10858i) q^{89} +(-12.1956 - 3.09759i) q^{91} +(-4.41358 - 4.41358i) q^{92} +(-9.86569 + 13.8555i) q^{93} +(-9.72811 + 5.61653i) q^{94} +(4.42352 - 11.8612i) q^{96} +(5.46692 - 1.46486i) q^{97} +(10.9815 - 2.94249i) q^{98} +(-2.60480 + 3.00654i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) $ 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.12039	+	0.568157i	1.49934	+	0.401748i	0.912880	−	0.408228i	$-0.133853\pi$
$2$	2.12039	+	0.568157i	1.49934	+	0.401748i	0.586463	+	0.809976i	$0.300520\pi$
$3$	1.41092	+	1.00464i	0.814597	+	0.580028i
$3$	1.41092	+	1.00464i	0.814597	+	0.580028i
$4$	2.44121	+	1.40943i	1.22060	+	0.704716i
$5$		0			0
$5$		0			0
$6$	2.42092	+	2.93185i	0.988335	+	1.19692i
$7$	3.37093	−	0.903238i	1.27409	−	0.341392i	0.442494	−	0.896771i	$-0.354094\pi$
$7$	3.37093	−	0.903238i	1.27409	−	0.341392i	0.831597	+	0.555380i	$0.187427\pi$
$8$	1.27107	+	1.27107i	0.449391	+	0.449391i
$9$	0.981406	+	2.83493i	0.327135	+	0.944977i
$10$		0			0
$11$	0.662995	+	1.14834i	0.199901	+	0.346238i	0.948496	−	0.316789i	$-0.102605\pi$
$11$	0.662995	+	1.14834i	0.199901	+	0.346238i	−0.748595	+	0.663027i	$0.769271\pi$
$12$	2.02839	+	4.44113i	0.585545	+	1.28204i
$13$	−3.14579	−	1.76182i	−0.872484	−	0.488642i
$13$	−3.14579	−	1.76182i	−0.872484	−	0.488642i
$14$	7.66087			2.04745
$15$		0			0
$16$	−0.845867	−	1.46508i	−0.211467	−	0.366271i
$17$	−4.63881	+	1.24296i	−1.12508	+	0.301463i	−0.772936	−	0.634484i	$-0.781213\pi$
$17$	−4.63881	+	1.24296i	−1.12508	+	0.301463i	−0.352140	+	0.935947i	$0.614546\pi$
$18$	0.470279	+	6.56876i	0.110846	+	1.54827i
$19$	2.69447	−	4.66695i	0.618153	−	1.07067i	−0.371670	−	0.928365i	$-0.621215\pi$
$19$	2.69447	−	4.66695i	0.618153	−	1.07067i	0.989823	−	0.142307i	$-0.0454521\pi$
$20$		0			0
$21$	5.66355	+	2.11216i	1.23589	+	0.460912i
$22$	0.753371	+	2.81162i	0.160619	+	0.599439i
$23$	−2.13883	−	0.573097i	−0.445976	−	0.119499i	0.0288398	−	0.999584i	$-0.490819\pi$
$23$	−2.13883	−	0.573097i	−0.445976	−	0.119499i	−0.474816	+	0.880085i	$0.657485\pi$
$24$	0.516417	+	3.07034i	0.105413	+	0.626731i
$25$		0			0
$26$	−5.66931	−	5.52306i	−1.11184	−	1.08316i
$27$	−1.46339	+	4.98583i	−0.281630	+	0.959523i
$28$	9.50219	+	2.54610i	1.79575	+	0.481168i
$29$	−2.06922	−	3.58399i	−0.384244	−	0.665530i	0.607420	−	0.794381i	$-0.292204\pi$
$29$	−2.06922	−	3.58399i	−0.384244	−	0.665530i	−0.991664	+	0.128851i	$0.958871\pi$
$30$		0			0
$31$			9.82014i			1.76375i	0.471483	+	0.881875i	$0.343719\pi$
$31$			9.82014i			1.76375i	−0.471483	+	0.881875i	$0.656281\pi$
$32$	−1.89166	−	7.05976i	−0.334401	−	1.24800i
$33$	−0.218232	+	2.28629i	−0.0379893	+	0.397992i
$34$	−10.5423			−1.80799
$35$		0			0
$36$	−1.59983	+	8.30389i	−0.266638	+	1.38398i
$37$	0.871294	−	3.25171i	0.143240	−	0.534579i	−0.856588	−	0.516002i	$-0.827420\pi$
$37$	0.871294	−	3.25171i	0.143240	−	0.534579i	0.999827	−	0.0185768i	$-0.00591353\pi$
$38$	8.36489	−	8.36489i	1.35696	−	1.35696i
$39$	−2.66847	−	5.64617i	−0.427297	−	0.904111i
$40$		0			0
$41$	0.983308	+	1.70314i	0.153567	+	0.265986i	0.932536	−	0.361076i	$-0.117591\pi$
$41$	0.983308	+	1.70314i	0.153567	+	0.265986i	−0.778969	+	0.627062i	$0.784257\pi$
$42$	10.8089	+	7.69640i	1.66785	+	1.18758i
$43$	−6.59808	+	1.76795i	−1.00620	+	0.269610i	−0.724040	−	0.689758i	$-0.757717\pi$
$43$	−6.59808	+	1.76795i	−1.00620	+	0.269610i	−0.282158	+	0.959368i	$0.591050\pi$
$44$			3.73779i			0.563493i
$45$		0			0
$46$	−4.20954	−	2.43038i	−0.620663	−	0.358340i
$47$	−3.61835	+	3.61835i	−0.527791	+	0.527791i	−0.919913	−	0.392122i	$-0.871741\pi$
$47$	−3.61835	+	3.61835i	−0.527791	+	0.527791i	0.392122	+	0.919913i	$0.371741\pi$
$48$	0.278426	−	2.91691i	0.0401873	−	0.421020i
$49$	4.48514	−	2.58950i	0.640735	−	0.369929i
$50$		0			0
$51$	−7.79372	−	2.90659i	−1.09134	−	0.407004i
$52$	−5.19635	−	8.73475i	−0.720604	−	1.21129i
$53$	2.43489	−	2.43489i	0.334457	−	0.334457i	−0.519819	−	0.854276i	$-0.674001\pi$
$53$	2.43489	−	2.43489i	0.334457	−	0.334457i	0.854276	+	0.519819i	$0.174001\pi$
$54$	−5.93570	+	9.74047i	−0.807746	+	1.32551i
$55$		0			0
$56$	5.43276	+	3.13661i	0.725983	+	0.419147i
$57$	8.49028	−	3.87775i	1.12457	−	0.513620i
$58$	−2.35128	−	8.77510i	−0.308738	−	1.15223i
$59$	5.33897	+	3.08246i	0.695075	+	0.401302i	0.805510	−	0.592582i	$-0.201891\pi$
$59$	5.33897	+	3.08246i	0.695075	+	0.401302i	−0.110435	+	0.993883i	$0.535225\pi$
$60$		0			0
$61$	3.34455	−	5.79293i	0.428226	−	0.741709i	−0.568490	−	0.822690i	$-0.692472\pi$
$61$	3.34455	−	5.79293i	0.428226	−	0.741709i	0.996716	+	0.0809813i	$0.0258054\pi$
$62$	−5.57939	+	20.8226i	−0.708583	+	2.64447i
$63$	5.86887	+	8.66991i	0.739408	+	1.09231i
$64$		−	12.6608i		−	1.58259i
$65$		0			0
$66$	−1.76171	+	4.72384i	−0.216852	+	0.581465i
$67$	0.132637	−	0.495007i	0.0162041	−	0.0604747i	−0.957350	−	0.288930i	$-0.906701\pi$
$67$	0.132637	−	0.495007i	0.0162041	−	0.0604747i	0.973555	+	0.228455i	$0.0733673\pi$
$68$	−13.0762	−	3.50375i	−1.58572	−	0.424892i
$69$	−2.44197	−	2.95734i	−0.293978	−	0.356022i
$70$		0			0
$71$	−7.13214	+	12.3532i	−0.846430	+	1.46606i	0.0379444	+	0.999280i	$0.487919\pi$
$71$	−7.13214	+	12.3532i	−0.846430	+	1.46606i	−0.884374	+	0.466779i	$0.845414\pi$
$72$	−2.35596	+	4.85083i	−0.277653	+	0.571676i
$73$	5.00425	−	5.00425i	0.585703	−	0.585703i	−0.350762	−	0.936465i	$-0.614077\pi$
$73$	5.00425	−	5.00425i	0.585703	−	0.585703i	0.936465	+	0.350762i	$0.114077\pi$
$74$	3.69497	−	6.39988i	0.429532	−	0.743971i
$75$		0			0
$76$	13.1555	−	7.59533i	1.50904	−	0.871245i
$77$	3.27213	+	3.27213i	0.372894	+	0.372894i
$78$	−2.45028	−	13.4882i	−0.277440	−	1.52724i
$79$		−	0.914386i		−	0.102876i	−0.998676	−	0.0514382i	$-0.983619\pi$
$79$		−	0.914386i		−	0.102876i	0.998676	−	0.0514382i	$-0.0163805\pi$
$80$		0			0
$81$	−7.07368	+	5.56444i	−0.785965	+	0.618271i
$82$	1.11735	+	4.17000i	0.123390	+	0.460499i
$83$	−2.26406	−	2.26406i	−0.248513	−	0.248513i	0.571847	−	0.820360i	$-0.306227\pi$
$83$	−2.26406	−	2.26406i	−0.248513	−	0.248513i	−0.820360	+	0.571847i	$0.806227\pi$
$84$	10.8489	+	13.1386i	1.18372	+	1.43354i
$85$		0			0
$86$	−14.9950			−1.61695
$87$	0.681105	−	7.13554i	0.0730221	−	0.765011i
$88$	−0.616909	+	2.30233i	−0.0657627	+	0.245430i
$89$	3.65216	−	2.10858i	0.387128	−	0.223509i	−0.293787	−	0.955871i	$-0.594916\pi$
$89$	3.65216	−	2.10858i	0.387128	−	0.223509i	0.680915	+	0.732362i	$0.261582\pi$
$90$		0			0
$91$	−12.1956	−	3.09759i	−1.27844	−	0.324716i
$92$	−4.41358	−	4.41358i	−0.460148	−	0.460148i
$93$	−9.86569	+	13.8555i	−1.02302	+	1.43674i
$94$	−9.72811	+	5.61653i	−1.00338	+	0.579301i
$95$		0			0
$96$	4.42352	−	11.8612i	0.451474	−	1.21058i
$97$	5.46692	−	1.46486i	0.555081	−	0.148734i	0.0296356	−	0.999561i	$-0.490565\pi$
$97$	5.46692	−	1.46486i	0.555081	−	0.148734i	0.525446	+	0.850827i	$0.323899\pi$
$98$	10.9815	−	2.94249i	1.10930	−	0.297236i
$99$	−2.60480	+	3.00654i	−0.261792	+	0.302168i
$100$		0			0
$101$	3.23649	−	1.86859i	0.322043	−	0.185932i	−0.330260	−	0.943890i	$-0.607136\pi$
$101$	3.23649	−	1.86859i	0.322043	−	0.185932i	0.652303	+	0.757958i	$0.273803\pi$
$102$	−14.8743	−	10.5912i	−1.47278	−	1.04868i
$103$	−1.44650	−	1.44650i	−0.142528	−	0.142528i	0.632242	−	0.774771i	$-0.282135\pi$
$103$	−1.44650	−	1.44650i	−0.142528	−	0.142528i	−0.774771	+	0.632242i	$0.782135\pi$
$104$	−1.75911	−	6.23791i	−0.172495	−	0.611678i
$105$		0			0
$106$	6.54631	−	3.77951i	0.635834	−	0.367099i
$107$	1.02751	−	3.83471i	0.0993328	−	0.370715i	−0.898308	−	0.439366i	$-0.855203\pi$
$107$	1.02751	−	3.83471i	0.0993328	−	0.370715i	0.997641	+	0.0686514i	$0.0218696\pi$
$108$	−10.5996	+	10.1089i	−1.01995	+	0.972729i
$109$	−4.56958			−0.437686			−0.218843	−	0.975760i	$-0.570228\pi$
$109$	−4.56958			−0.437686			−0.218843	+	0.975760i	$0.570228\pi$
$110$		0			0
$111$	4.49612	−	3.71258i	0.426753	−	0.352383i
$112$	−4.17467	−	4.17467i	−0.394470	−	0.394470i
$113$	2.81333	+	10.4995i	0.264656	+	0.987709i	0.962461	+	0.271421i	$0.0874935\pi$
$113$	2.81333	+	10.4995i	0.264656	+	0.987709i	−0.697805	+	0.716288i	$0.745840\pi$
$114$	20.2059	−	3.39853i	1.89246	−	0.318301i
$115$		0			0
$116$		−	11.6657i		−	1.08313i
$117$	1.90736	−	10.6472i	0.176335	−	0.984330i
$118$	9.56939	+	9.56939i	0.880934	+	0.880934i
$119$	−14.5144	+	8.37989i	−1.33053	+	0.768183i
$120$		0			0
$121$	4.62087	−	8.00359i	0.420080	−	0.727599i
$122$	10.3831	−	10.3831i	0.940038	−	0.940038i
$123$	−0.323666	+	3.39087i	−0.0291840	+	0.305744i
$124$	−13.8408	+	23.9730i	−1.24294	+	2.15284i
$125$		0			0
$126$	7.51843	+	21.7181i	0.669795	+	1.93480i
$127$	1.60168	+	0.429168i	0.142126	+	0.0380825i	0.329181	−	0.944267i	$-0.393228\pi$
$127$	1.60168	+	0.429168i	0.142126	+	0.0380825i	−0.187055	+	0.982349i	$0.559894\pi$
$128$	3.40999	−	12.7262i	0.301403	−	1.12485i
$129$	−11.0855	−	4.13424i	−0.976027	−	0.363999i
$130$		0			0
$131$		−	6.69098i		−	0.584593i	−0.956328	−	0.292297i	$-0.905581\pi$
$131$		−	6.69098i		−	0.584593i	0.956328	−	0.292297i	$-0.0944195\pi$
$132$	−3.75512	+	5.27373i	−0.326841	+	0.459019i
$133$	4.86749	−	18.1657i	0.422065	−	1.57517i
$134$	0.562483	−	0.974250i	0.0485912	−	0.0841624i
$135$		0			0
$136$	−7.47614	−	4.31635i	−0.641073	−	0.370124i
$137$	0.749428	+	2.79690i	0.0640279	+	0.238955i	0.990522	−	0.137354i	$-0.0438597\pi$
$137$	0.749428	+	2.79690i	0.0640279	+	0.238955i	−0.926494	+	0.376309i	$0.877193\pi$
$138$	−3.49769	−	7.65814i	−0.297743	−	0.651904i
$139$	2.10674	+	1.21633i	0.178692	+	0.103168i	0.586678	−	0.809820i	$-0.300435\pi$
$139$	2.10674	+	1.21633i	0.178692	+	0.103168i	−0.407986	+	0.912988i	$0.633769\pi$
$140$		0			0
$141$	−8.74035	+	1.47008i	−0.736070	+	0.123803i
$142$	−22.1415	+	22.1415i	−1.85807	+	1.85807i
$143$	−0.0624653	−	4.78052i	−0.00522361	−	0.399767i
$144$	3.32327	−	3.83582i	0.276940	−	0.319651i
$145$		0			0
$146$	13.4542	−	7.76776i	1.11347	−	0.642865i
$147$	8.92970	+	0.852361i	0.736509	+	0.0703016i
$148$	6.71008	−	6.71008i	0.551565	−	0.551565i
$149$	−18.8773	−	10.8988i	−1.54649	−	0.892867i	−0.998406	−	0.0564450i	$-0.982023\pi$
$149$	−18.8773	−	10.8988i	−1.54649	−	0.892867i	−0.548086	−	0.836422i	$-0.684643\pi$
$150$		0			0
$151$		−	23.8695i		−	1.94248i	−0.238112	−	0.971238i	$-0.576529\pi$
$151$		−	23.8695i		−	1.94248i	0.238112	−	0.971238i	$-0.423471\pi$
$152$	9.35687	−	2.50717i	0.758943	−	0.203358i
$153$	−8.07627	−	11.9308i	−0.652928	−	0.964552i
$154$	5.07912	+	8.79730i	0.409287	+	0.708906i
$155$		0			0
$156$	1.44362	−	17.5445i	0.115582	−	1.40468i
$157$	15.8944	−	15.8944i	1.26852	−	1.26852i	0.321660	−	0.946855i	$-0.395759\pi$
$157$	15.8944	−	15.8944i	1.26852	−	1.26852i	0.946855	−	0.321660i	$-0.104241\pi$
$158$	0.519515	−	1.93886i	0.0413304	−	0.154247i
$159$	5.88161	−	0.989258i	0.466442	−	0.0784533i
$160$		0			0
$161$	−7.72748			−0.609010
$162$	−18.1605	+	7.77983i	−1.42682	+	0.611241i
$163$	4.27873	+	15.9685i	0.335136	+	1.25075i	0.903721	+	0.428121i	$0.140824\pi$
$163$	4.27873	+	15.9685i	0.335136	+	1.25075i	−0.568585	+	0.822625i	$0.692509\pi$
$164$			5.54362i			0.432884i
$165$		0			0
$166$	−3.51436	−	6.08705i	−0.272767	−	0.472447i
$167$	11.3555	+	3.04269i	0.878713	+	0.235450i	0.669852	−	0.742495i	$-0.266358\pi$
$167$	11.3555	+	3.04269i	0.878713	+	0.235450i	0.208861	+	0.977945i	$0.433024\pi$
$168$	4.51405	+	9.88347i	0.348267	+	0.762526i
$169$	6.79195	+	11.0846i	0.522458	+	0.852665i
$170$		0			0
$171$	15.8749	+	3.05845i	1.21398	+	0.233886i
$172$	−18.5991	−	4.98361i	−1.41817	−	0.379997i
$173$	4.58535	+	17.1128i	0.348618	+	1.30106i	0.888329	+	0.459208i	$0.151867\pi$
$173$	4.58535	+	17.1128i	0.348618	+	1.30106i	−0.539711	+	0.841850i	$0.681467\pi$
$174$	5.49832	−	14.7432i	0.416827	−	1.11768i
$175$		0			0
$176$	1.12161	−	1.94269i	0.0845446	−	0.146436i
$177$	4.43613	+	9.71284i	0.333440	+	0.730062i
$178$	8.94201	−	2.39600i	0.670232	−	0.179588i
$179$	8.88040	+	15.3813i	0.663752	+	1.14965i	0.979622	+	0.200850i	$0.0643703\pi$
$179$	8.88040	+	15.3813i	0.663752	+	1.14965i	−0.315870	+	0.948802i	$0.602296\pi$
$180$		0			0
$181$	−10.5369			−0.783204			−0.391602	−	0.920135i	$-0.628079\pi$
$181$	−10.5369			−0.783204			−0.391602	+	0.920135i	$0.628079\pi$
$182$	−24.0995	−	13.4971i	−1.78637	−	1.00047i
$183$	10.5387	−	4.81332i	0.779043	−	0.355811i
$184$	−1.99015	−	3.44704i	−0.146716	−	0.254119i
$185$		0			0
$186$	−28.7912	+	23.7738i	−2.11107	+	1.74318i
$187$	−4.50285	−	4.50285i	−0.329281	−	0.329281i
$188$	−13.9330	+	3.73333i	−1.01617	+	0.272281i
$189$	−0.429598	+	18.1287i	−0.0312487	+	1.31867i
$190$		0			0
$191$	12.5492	+	7.24527i	0.908026	+	0.524249i	0.879796	−	0.475352i	$-0.157679\pi$
$191$	12.5492	+	7.24527i	0.908026	+	0.524249i	0.0282306	+	0.999601i	$0.491013\pi$
$192$	12.7195	−	17.8634i	0.917949	−	1.28918i
$193$	5.86194	+	1.57070i	0.421951	+	0.113062i	0.463546	−	0.886073i	$-0.346577\pi$
$193$	5.86194	+	1.57070i	0.421951	+	0.113062i	−0.0415943	+	0.999135i	$0.513244\pi$
$194$	12.4243			0.892011
$195$		0			0
$196$	14.5989			1.04278
$197$	−19.1589	−	5.13360i	−1.36501	−	0.365754i	−0.499358	−	0.866396i	$-0.666431\pi$
$197$	−19.1589	−	5.13360i	−1.36501	−	0.365754i	−0.865654	+	0.500642i	$0.833097\pi$
$198$	−7.23139	+	4.89510i	−0.513912	+	0.347879i
$199$	−21.3830	−	12.3455i	−1.51580	−	0.875146i	−0.999828	−	0.0185397i	$-0.994098\pi$
$199$	−21.3830	−	12.3455i	−1.51580	−	0.875146i	−0.515970	−	0.856607i	$-0.672568\pi$
$200$		0			0
$201$	0.684443	−	0.565165i	0.0482769	−	0.0398636i
$202$	7.92429	−	2.12331i	0.557551	−	0.149395i
$203$	−10.2124	−	10.2124i	−0.716768	−	0.716768i
$204$	−14.9295	−	18.0803i	−1.04527	−	1.26588i
$205$		0			0
$206$	−2.24531	−	3.88900i	−0.156438	−	0.270959i
$207$	−0.474368	−	6.62587i	−0.0329708	−	0.460530i
$208$	0.0796948	+	6.09911i	0.00552584	+	0.422897i
$209$	7.14567			0.494277
$210$		0			0
$211$	8.05125	+	13.9452i	0.554271	+	0.960025i	0.997960	+	0.0638442i	$0.0203361\pi$
$211$	8.05125	+	13.9452i	0.554271	+	0.960025i	−0.443689	+	0.896181i	$0.646331\pi$
$212$	9.37587	−	2.51226i	0.643937	−	0.172542i
$213$	−22.4734	+	10.2642i	−1.53985	+	0.703294i
$214$	4.35743	−	7.54729i	0.297868	−	0.515922i
$215$		0			0
$216$	−8.19740	+	4.47726i	−0.557763	+	0.304639i
$217$	8.86992	+	33.1030i	0.602130	+	2.24718i
$218$	−9.68930	−	2.59624i	−0.656242	−	0.175840i
$219$	12.0881	−	2.03315i	0.816835	−	0.137388i
$220$		0			0
$221$	16.7826	+	4.26266i	1.12892	+	0.286738i
$222$	11.6429	−	5.31763i	0.781419	−	0.356896i
$223$	14.5938	+	3.91041i	0.977276	+	0.261860i	0.711897	−	0.702284i	$-0.247836\pi$
$223$	14.5938	+	3.91041i	0.977276	+	0.261860i	0.265379	+	0.964144i	$0.414503\pi$
$224$	−12.7533	−	22.0893i	−0.852115	−	1.47591i
$225$		0			0
$226$			23.8614i			1.58724i
$227$	2.09464	+	7.81731i	0.139026	+	0.518853i	0.999949	+	0.0101170i	$0.00322039\pi$
$227$	2.09464	+	7.81731i	0.139026	+	0.518853i	−0.860923	+	0.508736i	$0.830113\pi$
$228$	26.1920	+	2.50008i	1.73461	+	0.165572i
$229$	19.8970			1.31483			0.657416	−	0.753528i	$-0.271650\pi$
$229$	19.8970			1.31483			0.657416	+	0.753528i	$0.271650\pi$
$230$		0			0
$231$	1.32942	+	7.90404i	0.0874694	+	0.520048i
$232$	1.92538	−	7.18561i	0.126407	−	0.471759i
$233$	−7.71282	+	7.71282i	−0.505284	+	0.505284i	−0.913075	−	0.407791i	$-0.866299\pi$
$233$	−7.71282	+	7.71282i	−0.505284	+	0.505284i	0.407791	+	0.913075i	$0.366299\pi$
$234$	10.0936	−	21.4925i	0.659840	−	1.40501i
$235$		0			0
$236$	8.68903	+	15.0498i	0.565608	+	0.979661i
$237$	0.918626	−	1.29013i	0.0596712	−	0.0838028i
$238$	−35.5373	+	9.52219i	−2.30354	+	0.617232i
$239$		−	22.0067i		−	1.42349i	−0.702436	−	0.711747i	$-0.747904\pi$
$239$		−	22.0067i		−	1.42349i	0.702436	−	0.711747i	$-0.252096\pi$
$240$		0			0
$241$	13.0273	+	7.52130i	0.839160	+	0.484489i	0.856979	−	0.515352i	$-0.172339\pi$
$241$	13.0273	+	7.52130i	0.839160	+	0.484489i	−0.0178185	+	0.999841i	$0.505672\pi$
$242$	14.3454	−	14.3454i	0.922155	−	0.922155i
$243$	−15.5707	+	0.744511i	−0.998859	+	0.0477604i
$244$	16.3295	−	9.42784i	1.04539	−	0.603555i
$245$		0			0
$246$	−2.61285	+	7.00607i	−0.166589	+	0.446691i
$247$	−16.6986	+	9.93406i	−1.06250	+	0.632089i
$248$	−12.4821	+	12.4821i	−0.792613	+	0.792613i
$249$	−0.919856	−	5.46899i	−0.0582935	−	0.346583i
$250$		0			0
$251$	2.22630	+	1.28535i	0.140523	+	0.0811307i	0.568613	−	0.822605i	$-0.307480\pi$
$251$	2.22630	+	1.28535i	0.140523	+	0.0811307i	−0.428090	+	0.903736i	$0.640814\pi$
$252$	2.10748	+	29.4368i	0.132759	+	1.85435i
$253$	−0.759921	−	2.83606i	−0.0477758	−	0.178302i
$254$	3.15235	+	1.82001i	0.197796	+	0.114197i
$255$		0			0
$256$	1.80025	−	3.11813i	0.112516	−	0.194883i
$257$	−1.15416	+	4.30737i	−0.0719943	+	0.268686i	−0.992535	−	0.121960i	$-0.961082\pi$
$257$	−1.15416	+	4.30737i	−0.0719943	+	0.268686i	0.920541	+	0.390647i	$0.127749\pi$
$258$	−21.1568	−	15.0645i	−1.31716	−	0.937877i
$259$		−	11.7483i		−	0.730003i
$260$		0			0
$261$	8.12962	−	9.38344i	0.503211	−	0.580820i
$262$	3.80153	−	14.1875i	0.234859	−	0.876506i
$263$	9.59599	+	2.57124i	0.591714	+	0.158549i	0.542237	−	0.840226i	$-0.317578\pi$
$263$	9.59599	+	2.57124i	0.591714	+	0.158549i	0.0494778	+	0.998775i	$0.484244\pi$
$264$	−3.18342	+	2.62865i	−0.195926	+	0.161782i
$265$		0			0
$266$	20.6420	−	35.7529i	1.26564	−	2.19215i
$267$	7.27127	+	0.694060i	0.444994	+	0.0424758i
$268$	1.02147	−	1.02147i	0.0623963	−	0.0623963i
$269$	−13.3419	+	23.1088i	−0.813467	+	1.40897i	0.0969562	+	0.995289i	$0.469089\pi$
$269$	−13.3419	+	23.1088i	−0.813467	+	1.40897i	−0.910423	+	0.413678i	$0.864244\pi$
$270$		0			0
$271$	3.65623	−	2.11093i	0.222100	−	0.128230i	−0.384822	−	0.922991i	$-0.625737\pi$
$271$	3.65623	−	2.11093i	0.222100	−	0.128230i	0.606922	+	0.794761i	$0.292404\pi$
$272$	5.74486	+	5.74486i	0.348333	+	0.348333i
$273$	−14.0950	−	16.6226i	−0.853071	−	1.00605i
$274$			6.35632i			0.383999i
$275$		0			0
$276$	−1.79317	−	10.6613i	−0.107936	−	0.641733i
$277$	−4.94873	−	18.4689i	−0.297340	−	1.10969i	−0.939341	−	0.342985i	$-0.888562\pi$
$277$	−4.94873	−	18.4689i	−0.297340	−	1.10969i	0.642000	−	0.766704i	$-0.278105\pi$
$278$	3.77606	+	3.77606i	0.226473	+	0.226473i
$279$	−27.8394	+	9.63755i	−1.66670	+	0.576985i
$280$		0			0
$281$	−32.4638			−1.93663			−0.968314	−	0.249735i	$-0.919656\pi$
$281$	−32.4638			−1.93663			−0.968314	+	0.249735i	$0.919656\pi$
$282$	−19.3682	−	1.84874i	−1.15336	−	0.110091i
$283$	−2.41604	+	9.01678i	−0.143619	+	0.535992i	0.856194	+	0.516654i	$0.172823\pi$
$283$	−2.41604	+	9.01678i	−0.143619	+	0.535992i	−0.999813	+	0.0193382i	$0.993844\pi$
$284$	−34.8221	+	20.1045i	−2.06631	+	1.19298i
$285$		0			0
$286$	2.58364	−	10.1721i	0.152774	−	0.601487i
$287$	4.85300	+	4.85300i	0.286464	+	0.286464i
$288$	18.1575	−	12.2912i	1.06994	−	0.724267i
$289$	5.25112	−	3.03174i	0.308890	−	0.178337i
$290$		0			0
$291$	9.18504	+	3.42547i	0.538437	+	0.200805i
$292$	19.2695	−	5.16326i	1.12766	−	0.302157i
$293$	12.6866	−	3.39935i	0.741157	−	0.198592i	0.131564	−	0.991308i	$-0.458000\pi$
$293$	12.6866	−	3.39935i	0.741157	−	0.198592i	0.609592	+	0.792715i	$0.291333\pi$
$294$	18.4502	+	6.88081i	1.07604	+	0.401297i
$295$		0			0
$296$	5.24063	−	3.02568i	0.304605	−	0.175864i
$297$	−6.69565	+	1.62511i	−0.388521	+	0.0942983i
$298$	−33.8351	−	33.8351i	−1.96001	−	1.96001i
$299$	5.71860	+	5.57108i	0.330715	+	0.322184i
$300$		0			0
$301$	−20.6448	+	11.9193i	−1.18995	+	0.687015i
$302$	13.5617	−	50.6128i	0.780385	−	2.91244i
$303$	6.44370	+	0.615066i	0.370181	+	0.0353346i
$304$	−9.11664			−0.522875
$305$		0			0
$306$	−10.3463	−	29.8867i	−0.591457	−	1.70851i
$307$	−6.16399	−	6.16399i	−0.351798	−	0.351798i	0.508980	−	0.860778i	$-0.330023\pi$
$307$	−6.16399	−	6.16399i	−0.351798	−	0.351798i	−0.860778	+	0.508980i	$0.830023\pi$
$308$	3.37611	+	12.5998i	0.192372	+	0.717941i
$309$	−0.587693	−	3.49412i	−0.0334327	−	0.198773i
$310$		0			0
$311$			7.33730i			0.416060i	0.978122	+	0.208030i	$0.0667052\pi$
$311$			7.33730i			0.416060i	−0.978122	+	0.208030i	$0.933295\pi$
$312$	3.78487	−	10.5685i	0.214276	−	0.598323i
$313$	3.28923	+	3.28923i	0.185918	+	0.185918i	0.793929	−	0.608011i	$-0.208032\pi$
$313$	3.28923	+	3.28923i	0.185918	+	0.185918i	−0.608011	+	0.793929i	$0.708032\pi$
$314$	42.7330	−	24.6719i	2.41156	−	1.39232i
$315$		0			0
$316$	1.28876	−	2.23221i	0.0724987	−	0.125571i
$317$	−7.57102	+	7.57102i	−0.425231	+	0.425231i	−0.887000	−	0.461769i	$-0.847215\pi$
$317$	−7.57102	+	7.57102i	−0.425231	+	0.425231i	0.461769	+	0.887000i	$0.347215\pi$
$318$	13.0334	+	1.24407i	0.730876	+	0.0697638i
$319$	2.74376	−	4.75233i	0.153621	−	0.266080i
$320$		0			0
$321$	5.30222	−	4.37820i	0.295941	−	0.244367i
$322$	−16.3853	−	4.39042i	−0.913116	−	0.244669i
$323$	−6.69825	+	24.9982i	−0.372701	+	1.39094i
$324$	−25.1110	+	3.61408i	−1.39506	+	0.200782i
$325$		0			0
$326$			36.2904i			2.00994i
$327$	−6.44732	−	4.59077i	−0.356538	−	0.253870i
$328$	−0.914956	+	3.41466i	−0.0505200	+	0.188543i
$329$	−8.92897	+	15.4654i	−0.492270	+	0.852637i
$330$		0			0
$331$	−9.04584	−	5.22262i	−0.497204	−	0.287061i	0.230354	−	0.973107i	$-0.426012\pi$
$331$	−9.04584	−	5.22262i	−0.497204	−	0.287061i	−0.727558	+	0.686046i	$0.759345\pi$
$332$	−2.33601	−	8.71810i	−0.128205	−	0.478468i
$333$	10.0735	−	0.721193i	0.552024	−	0.0395212i
$334$	22.3493	+	12.9034i	1.22290	+	0.706042i
$335$		0			0
$336$	−1.69611	−	10.0842i	−0.0925303	−	0.550137i
$337$	−11.9670	+	11.9670i	−0.651883	+	0.651883i	−0.953446	−	0.301563i	$-0.902492\pi$
$337$	−11.9670	+	11.9670i	−0.651883	+	0.651883i	0.301563	+	0.953446i	$0.402492\pi$
$338$	8.10377	+	27.3627i	0.440787	+	1.48833i
$339$	−6.57879	+	17.6403i	−0.357311	+	0.958092i
$340$		0			0
$341$	−11.2769	+	6.51071i	−0.610677	+	0.352575i
$342$	31.9232	+	15.5045i	1.72621	+	0.838389i
$343$	−4.49367	+	4.49367i	−0.242635	+	0.242635i
$344$	−10.6338	−	6.13943i	−0.573336	−	0.331016i
$345$		0			0
$346$			38.8909i			2.09079i
$347$	17.4398	−	4.67299i	0.936219	−	0.250859i	0.241715	−	0.970347i	$-0.422290\pi$
$347$	17.4398	−	4.67299i	0.936219	−	0.250859i	0.694505	+	0.719488i	$0.255624\pi$
$348$	11.7198	−	16.4594i	0.628246	−	0.882315i
$349$	−1.81560	−	3.14471i	−0.0971869	−	0.168333i	0.813332	−	0.581799i	$-0.197651\pi$
$349$	−1.81560	−	3.14471i	−0.0971869	−	0.168333i	−0.910519	+	0.413467i	$0.864318\pi$
$350$		0			0
$351$	13.3877	−	13.1061i	0.714581	−	0.699553i
$352$	6.85286	−	6.85286i	0.365259	−	0.365259i
$353$	−2.30221	+	8.59197i	−0.122534	+	0.457304i	−0.999740	−	0.0228108i	$-0.992738\pi$
$353$	−2.30221	+	8.59197i	−0.122534	+	0.457304i	0.877205	+	0.480115i	$0.159405\pi$
$354$	3.88790	+	23.1155i	0.206640	+	1.22857i
$355$		0			0
$356$	11.8876			0.630040
$357$	−28.8974	−	2.75833i	−1.52941	−	0.145986i
$358$	10.0909	+	37.6598i	0.533322	+	1.99038i
$359$			19.1514i			1.01077i	0.862893	+	0.505387i	$0.168650\pi$
$359$			19.1514i			1.01077i	−0.862893	+	0.505387i	$0.831350\pi$
$360$		0			0
$361$	−5.02030	−	8.69541i	−0.264226	−	0.457653i
$362$	−22.3424	−	5.98663i	−1.17429	−	0.314650i
$363$	14.5604	−	6.65014i	0.764223	−	0.349042i
$364$	−25.4061	−	24.7507i	−1.33164	−	1.29729i
$365$		0			0
$366$	25.0809	−	4.21848i	1.31100	−	0.220504i
$367$	12.2124	+	3.27232i	0.637484	+	0.170813i	0.563064	−	0.826413i	$-0.309623\pi$
$367$	12.2124	+	3.27232i	0.637484	+	0.170813i	0.0744208	+	0.997227i	$0.476289\pi$
$368$	0.969527	+	3.61832i	0.0505401	+	0.188618i
$369$	−3.86326	+	4.45908i	−0.201113	+	0.232131i
$370$		0			0
$371$	6.00855	−	10.4071i	0.311948	−	0.540310i
$372$	−43.6125	+	19.9191i	−2.26120	+	1.03276i
$373$	4.83305	−	1.29501i	0.250246	−	0.0670531i	−0.131516	−	0.991314i	$-0.541984\pi$
$373$	4.83305	−	1.29501i	0.250246	−	0.0670531i	0.381761	+	0.924261i	$0.375318\pi$
$374$	−6.98948	−	12.1061i	−0.361418	−	0.625994i
$375$		0			0
$376$	−9.19835			−0.474369
$377$	0.194955	+	14.9201i	0.0100407	+	0.768422i
$378$	−11.2108	+	38.1958i	−0.576624	+	1.96458i
$379$	9.29282	+	16.0956i	0.477340	+	0.826777i	0.999663	−	0.0259707i	$-0.00826766\pi$
$379$	9.29282	+	16.0956i	0.477340	+	0.826777i	−0.522323	+	0.852748i	$0.674934\pi$
$380$		0			0
$381$	1.82868	+	2.21463i	0.0936863	+	0.113459i
$382$	22.4927	+	22.4927i	1.15083	+	1.15083i
$383$	−2.40884	+	0.645446i	−0.123086	+	0.0329807i	−0.319836	−	0.947473i	$-0.603628\pi$
$383$	−2.40884	+	0.645446i	−0.123086	+	0.0329807i	0.196750	+	0.980454i	$0.436961\pi$
$384$	17.5965	−	14.5299i	0.897967	−	0.741478i
$385$		0			0
$386$	11.5372	+	6.66100i	0.587228	+	0.339036i
$387$	−11.4874	−	16.9700i	−0.583938	−	0.862635i
$388$	15.4105	+	4.12923i	0.782349	+	0.209630i
$389$	23.0324			1.16779			0.583893	−	0.811830i	$-0.301529\pi$
$389$	23.0324			1.16779			0.583893	+	0.811830i	$0.301529\pi$
$390$		0			0
$391$	10.6339			0.537782
$392$	8.99236	+	2.40950i	0.454183	+	0.121698i
$393$	6.72201	−	9.44045i	0.339080	−	0.476208i
$394$	−37.7076	−	21.7705i	−1.89968	−	1.09678i
$395$		0			0
$396$	−10.5964	+	3.66829i	−0.532488	+	0.184338i
$397$	−2.72459	+	0.730050i	−0.136743	+	0.0366402i	−0.326541	−	0.945183i	$-0.605883\pi$
$397$	−2.72459	+	0.730050i	−0.136743	+	0.0366402i	0.189798	+	0.981823i	$0.439217\pi$
$398$	−38.3261	−	38.3261i	−1.92111	−	1.92111i
$399$	25.1176	−	20.7404i	1.25745	−	1.03832i
$400$		0			0
$401$	−15.8342	−	27.4256i	−0.790723	−	1.36957i	−0.925520	−	0.378698i	$-0.876372\pi$
$401$	−15.8342	−	27.4256i	−0.790723	−	1.36957i	0.134798	−	0.990873i	$-0.456962\pi$
$402$	1.77239	−	0.809499i	0.0883987	−	0.0403742i
$403$	17.3014	−	30.8921i	0.861843	−	1.53884i
$404$	10.5346			0.524116
$405$		0			0
$406$	−15.8520	−	27.4565i	−0.786722	−	1.36264i
$407$	4.31174	−	1.15533i	0.213725	−	0.0572675i
$408$	−6.21188	−	13.6008i	−0.307534	−	0.673342i
$409$	0.754968	−	1.30764i	0.0373308	−	0.0646588i	−0.846756	−	0.531981i	$-0.821448\pi$
$409$	0.754968	−	1.30764i	0.0373308	−	0.0646588i	0.884087	+	0.467322i	$0.154781\pi$
$410$		0			0
$411$	−1.75249	+	4.69912i	−0.0864439	+	0.231790i
$412$	−1.49247	−	5.56996i	−0.0735286	−	0.274412i
$413$	20.7815	+	5.56838i	1.02259	+	0.274002i
$414$	2.75869	−	14.3190i	0.135582	−	0.703738i
$415$		0			0
$416$	−6.48731	+	25.5413i	−0.318067	+	1.25226i
$417$	1.75048	+	3.83266i	0.0857216	+	0.187686i
$418$	15.1516	+	4.05987i	0.741090	+	0.198575i
$419$	−1.10455	−	1.91314i	−0.0539608	−	0.0934628i	0.837783	−	0.546003i	$-0.183851\pi$
$419$	−1.10455	−	1.91314i	−0.0539608	−	0.0934628i	−0.891744	+	0.452540i	$0.850518\pi$
$420$		0			0
$421$		−	2.54783i		−	0.124173i	−0.998071	−	0.0620867i	$-0.980224\pi$
$421$		−	2.54783i		−	0.124173i	0.998071	−	0.0620867i	$-0.0197755\pi$
$422$	9.14875	+	34.1436i	0.445354	+	1.66208i
$423$	−13.8089	−	6.70671i	−0.671409	−	0.326091i
$424$	6.18982			0.300604
$425$		0			0
$426$	−53.4842	+	8.99577i	−2.59132	+	0.435846i
$427$	6.04185	−	22.5485i	0.292386	−	1.09120i
$428$	7.91311	−	7.91311i	0.382495	−	0.382495i
$429$	4.71456	−	6.80770i	0.227621	−	0.328679i
$430$		0			0
$431$	−5.28016	−	9.14551i	−0.254336	−	0.440524i	0.710379	−	0.703820i	$-0.248524\pi$
$431$	−5.28016	−	9.14551i	−0.254336	−	0.440524i	−0.964715	+	0.263296i	$0.915190\pi$
$432$	8.54249	−	2.07336i	0.411001	−	0.0997544i
$433$	−18.7630	+	5.02752i	−0.901691	+	0.241607i	−0.679742	−	0.733451i	$-0.737908\pi$
$433$	−18.7630	+	5.02752i	−0.901691	+	0.241607i	−0.221949	+	0.975058i	$0.571242\pi$
$434$			75.2309i			3.61120i
$435$		0			0
$436$	−11.1553	−	6.44051i	−0.534242	−	0.308445i
$437$	−8.43761	+	8.43761i	−0.403626	+	0.403626i
$438$	26.7866	+	2.55684i	1.27991	+	0.122171i
$439$	−27.0226	+	15.6015i	−1.28972	+	0.744619i	−0.978604	−	0.205753i	$-0.934036\pi$
$439$	−27.0226	+	15.6015i	−1.28972	+	0.744619i	−0.311115	+	0.950372i	$0.600702\pi$
$440$		0			0
$441$	11.7428	+	10.1737i	0.559181	+	0.484463i
$442$	33.1638	+	18.5737i	1.57744	+	0.883459i
$443$	−3.19916	+	3.19916i	−0.151997	+	0.151997i	−0.779009	−	0.627012i	$-0.784278\pi$
$443$	−3.19916	+	3.19916i	−0.151997	+	0.151997i	0.627012	+	0.779009i	$0.284278\pi$
$444$	16.2086	−	2.72621i	0.769226	−	0.129380i
$445$		0			0
$446$	28.7229	+	16.5832i	1.36007	+	0.785237i
$447$	−15.6851	−	34.3423i	−0.741879	−	1.62433i
$448$	−11.4357	−	42.6785i	−0.540285	−	2.01637i
$449$	−18.1137	−	10.4579i	−0.854838	−	0.493541i	0.00744231	−	0.999972i	$-0.497631\pi$
$449$	−18.1137	−	10.4579i	−0.854838	−	0.493541i	−0.862280	+	0.506431i	$0.830964\pi$
$450$		0			0
$451$	−1.30386	+	2.25835i	−0.0613962	+	0.106341i
$452$	−7.93039	+	29.5966i	−0.373014	+	1.39211i
$453$	23.9802	−	33.6781i	1.12669	−	1.58233i
$454$			17.7658i			0.833792i
$455$		0			0
$456$	15.7206	+	5.86285i	0.736185	+	0.274553i
$457$	2.77860	−	10.3699i	0.129977	−	0.485082i	−0.869991	−	0.493068i	$-0.835875\pi$
$457$	2.77860	−	10.3699i	0.129977	−	0.485082i	0.999968	+	0.00798609i	$0.00254208\pi$
$458$	42.1895	+	11.3046i	1.97138	+	0.528231i
$459$	0.591179	−	24.9472i	0.0275939	−	1.16444i
$460$		0			0
$461$	−14.1969	+	24.5898i	−0.661216	+	1.14526i	0.319080	+	0.947728i	$0.396626\pi$
$461$	−14.1969	+	24.5898i	−0.661216	+	1.14526i	−0.980296	+	0.197532i	$0.936707\pi$
$462$	−1.67185	+	17.5150i	−0.0777813	+	0.814871i
$463$	−27.9464	+	27.9464i	−1.29878	+	1.29878i	−0.369580	+	0.929199i	$0.620498\pi$
$463$	−27.9464	+	27.9464i	−1.29878	+	1.29878i	−0.929199	+	0.369580i	$0.879502\pi$
$464$	−3.50056	+	6.06315i	−0.162510	+	0.281475i
$465$		0			0
$466$	−20.7363	+	11.9721i	−0.960591	+	0.554597i
$467$	6.29228	+	6.29228i	0.291172	+	0.291172i	0.837543	−	0.546371i	$-0.183991\pi$
$467$	6.29228	+	6.29228i	0.291172	+	0.291172i	−0.546371	+	0.837543i	$0.683991\pi$
$468$	19.6627	−	23.3036i	0.908909	−	1.07721i
$469$		−	1.78844i		−	0.0825823i
$470$		0			0
$471$	38.3940	−	6.45768i	1.76910	−	0.297554i
$472$	2.86819	+	10.7042i	0.132019	+	0.492702i
$473$	−6.40471	−	6.40471i	−0.294489	−	0.294489i
$474$	2.68084	−	2.21365i	0.123135	−	0.101676i
$475$		0			0
$476$	−47.2435			−2.16540
$477$	9.29235	+	4.51312i	0.425467	+	0.206642i
$478$	12.5033	−	46.6628i	0.571885	−	2.13431i
$479$	−0.457393	+	0.264076i	−0.0208988	+	0.0120659i	−0.510413	−	0.859929i	$-0.670507\pi$
$479$	−0.457393	+	0.264076i	−0.0208988	+	0.0120659i	0.489514	+	0.871995i	$0.337174\pi$
$480$		0			0
$481$	−8.46986	+	8.69413i	−0.386192	+	0.396418i
$482$	23.3496	+	23.3496i	1.06355	+	1.06355i
$483$	−10.9029	−	7.76331i	−0.496098	−	0.353243i
$484$	22.5610	−	13.0256i	1.02550	−	0.592074i
$485$		0			0
$486$	−33.4389	−	7.26793i	−1.51682	−	0.329680i
$487$	−4.72696	+	1.26659i	−0.214199	+	0.0573945i	−0.364323	−	0.931273i	$-0.618700\pi$
$487$	−4.72696	+	1.26659i	−0.214199	+	0.0573945i	0.150124	+	0.988667i	$0.452033\pi$
$488$	11.6144	−	3.11206i	0.525758	−	0.140876i
$489$	−10.0055	+	26.8288i	−0.452466	+	1.21324i
$490$		0			0
$491$	15.6499	−	9.03548i	0.706271	−	0.407766i	−0.103408	−	0.994639i	$-0.532975\pi$
$491$	15.6499	−	9.03548i	0.706271	−	0.407766i	0.809679	+	0.586874i	$0.199641\pi$
$492$	−5.56933	+	7.82163i	−0.251085	+	0.352626i
$493$	14.0535	+	14.0535i	0.632936	+	0.632936i
$494$	−41.0516	+	11.5767i	−1.84700	+	0.520860i
$495$		0			0
$496$	14.3873	−	8.30653i	0.646010	−	0.372974i
$497$	−12.8840	+	48.0839i	−0.577928	+	2.15686i
$498$	1.15679	−	12.1190i	0.0518369	−	0.543066i
$499$	−17.8261			−0.798005			−0.399002	−	0.916950i	$-0.630643\pi$
$499$	−17.8261			−0.798005			−0.399002	+	0.916950i	$0.630643\pi$
$500$		0			0
$501$	12.9649	+	15.7011i	0.579229	+	0.701475i
$502$	3.99034	+	3.99034i	0.178097	+	0.178097i
$503$	−6.40876	−	23.9178i	−0.285753	−	1.06644i	−0.948288	−	0.317412i	$-0.897186\pi$
$503$	−6.40876	−	23.9178i	−0.285753	−	1.06644i	0.662535	−	0.749031i	$-0.269481\pi$
$504$	−3.56032	+	18.4798i	−0.158589	+	0.823156i
$505$		0			0
$506$		−	6.44532i		−	0.286530i
$507$	−1.55314	+	22.4630i	−0.0689775	+	0.997618i
$508$	3.30514	+	3.30514i	0.146642	+	0.146642i
$509$	32.8417	−	18.9612i	1.45568	−	0.840440i	0.456890	−	0.889523i	$-0.348963\pi$
$509$	32.8417	−	18.9612i	1.45568	−	0.840440i	0.998795	+	0.0490835i	$0.0156300\pi$
$510$		0			0
$511$	12.3489	−	21.3890i	0.546285	−	0.946193i
$512$	−13.0437	+	13.0437i	−0.576454	+	0.576454i
$513$	19.3256	+	20.2637i	0.853245	+	0.894665i
$514$	−4.89453	+	8.47757i	−0.215888	+	0.373930i
$515$		0			0
$516$	−21.2352	−	25.7168i	−0.934826	−	1.13212i
$517$	−6.55405	−	1.75615i	−0.288247	−	0.0772355i
$518$	6.67487	−	24.9110i	0.293277	−	1.09452i
$519$	−10.7225	+	28.7514i	−0.470667	+	1.26205i
$520$		0			0
$521$			4.36775i			0.191355i	0.995412	+	0.0956773i	$0.0305017\pi$
$521$			4.36775i			0.191355i	−0.995412	+	0.0956773i	$0.969498\pi$
$522$	22.5693	−	15.2777i	0.987829	−	0.668685i
$523$	5.72006	−	21.3475i	0.250121	−	0.933463i	−0.720619	−	0.693331i	$-0.756143\pi$
$523$	5.72006	−	21.3475i	0.250121	−	0.933463i	0.970740	−	0.240132i	$-0.0771908\pi$
$524$	9.43048	−	16.3341i	0.411972	−	0.713557i
$525$		0			0
$526$	18.8864	+	10.9041i	0.823486	+	0.475440i
$527$	−12.2061	−	45.5537i	−0.531705	−	1.98435i
$528$	3.53420	−	1.61417i	0.153806	−	0.0702477i
$529$	−15.6724	−	9.04849i	−0.681411	−	0.393413i
$530$		0			0
$531$	−3.49886	+	18.1608i	−0.151837	+	0.788110i
$532$	37.4859	−	37.4859i	1.62522	−	1.62522i
$533$	−0.0926441	−	7.09013i	−0.00401286	−	0.307108i
$534$	15.0236	+	5.60290i	0.650135	+	0.242461i
$535$		0			0
$536$	0.797778	−	0.460598i	0.0344588	−	0.0198948i
$537$	−2.92308	+	30.6234i	−0.126140	+	1.32150i
$538$	−41.4194	+	41.4194i	−1.78572	+	1.78572i
$539$	5.94726	+	3.43365i	0.256167	+	0.147898i
$540$		0			0
$541$		−	3.55250i		−	0.152734i	−0.997080	−	0.0763670i	$-0.975668\pi$
$541$		−	3.55250i		−	0.152734i	0.997080	−	0.0763670i	$-0.0243321\pi$
$542$	8.95198	−	2.39868i	0.384521	−	0.103032i
$543$	−14.8668	−	10.5858i	−0.637995	−	0.454280i
$544$	17.5501	+	30.3976i	0.752453	+	1.30329i
$545$		0			0
$546$	−20.4428	−	43.2546i	−0.874870	−	1.85113i
$547$	−15.5692	+	15.5692i	−0.665690	+	0.665690i	−0.956715	−	0.291026i	$-0.906003\pi$
$547$	−15.5692	+	15.5692i	−0.665690	+	0.665690i	0.291026	+	0.956715i	$0.406003\pi$
$548$	−2.11253	+	7.88409i	−0.0902430	+	0.336791i
$549$	19.7049	+	3.79636i	0.840986	+	0.162024i
$550$		0			0
$551$	−22.3017			−0.950086
$552$	0.655079	−	6.86289i	0.0278820	−	0.292104i
$553$	−0.825907	−	3.08233i	−0.0351212	−	0.131074i
$554$		−	41.9730i		−	1.78326i
$555$		0			0
$556$	3.42867	+	5.93863i	0.145408	+	0.251854i
$557$	0.786720	+	0.210801i	0.0333344	+	0.00893192i	0.275448	−	0.961316i	$-0.411174\pi$
$557$	0.786720	+	0.210801i	0.0333344	+	0.00893192i	−0.242113	+	0.970248i	$0.577841\pi$
$558$	−64.5062	+	4.61821i	−2.73076	+	0.195504i
$559$	23.8710	+	6.06307i	1.00963	+	0.256440i
$560$		0			0
$561$	−1.82944	−	10.8769i	−0.0772391	−	0.459224i
$562$	−68.8360	−	18.4445i	−2.90367	−	0.778036i
$563$	1.32972	+	4.96257i	0.0560408	+	0.209147i	0.988269	−	0.152724i	$-0.0488046\pi$
$563$	1.32972	+	4.96257i	0.0560408	+	0.209147i	−0.932228	+	0.361871i	$0.882138\pi$
$564$	−23.4090	−	8.73015i	−0.985696	−	0.367605i
$565$		0			0
$566$	−10.2459	+	17.7464i	−0.430667	+	0.745938i
$567$	−18.8189	+	25.1466i	−0.790318	+	1.05606i
$568$	−24.7673	+	6.63637i	−1.03921	+	0.278456i
$569$	−16.4127	−	28.4277i	−0.688058	−	1.19175i	−0.972465	−	0.233048i	$-0.925130\pi$
$569$	−16.4127	−	28.4277i	−0.688058	−	1.19175i	0.284407	−	0.958704i	$-0.408203\pi$
$570$		0			0
$571$	1.13239			0.0473889			0.0236944	−	0.999719i	$-0.492457\pi$
$571$	1.13239			0.0473889			0.0236944	+	0.999719i	$0.492457\pi$
$572$	6.58533	−	11.7583i	0.275346	−	0.491638i
$573$	10.4270	+	22.8299i	0.435596	+	0.953732i
$574$	7.53300	+	13.0475i	0.314421	+	0.544594i
$575$		0			0
$576$	35.8924	−	12.4253i	1.49552	−	0.517723i
$577$	20.5537	+	20.5537i	0.855660	+	0.855660i	0.990823	−	0.135163i	$-0.0431558\pi$
$577$	20.5537	+	20.5537i	0.855660	+	0.855660i	−0.135163	+	0.990823i	$0.543156\pi$
$578$	12.8569	−	3.44501i	0.534778	−	0.143293i
$579$	6.69275	+	8.10526i	0.278141	+	0.336843i
$580$		0			0
$581$	−9.67699	−	5.58701i	−0.401469	−	0.231788i
$582$	17.5297	+	12.4819i	0.726629	+	0.517391i
$583$	4.41040	+	1.18176i	0.182660	+	0.0489436i
$584$	12.7215			0.526419
$585$		0			0
$586$	28.8318			1.19103
$587$	41.5931	+	11.1448i	1.71673	+	0.459997i	0.977059	−	0.212969i	$-0.0683134\pi$
$587$	41.5931	+	11.1448i	1.71673	+	0.459997i	0.739673	+	0.672966i	$0.234980\pi$
$588$	20.5979	+	14.6666i	0.849444	+	0.604840i
$589$	45.8301	+	26.4600i	1.88840	+	1.09027i
$590$		0			0
$591$	−21.8743	−	26.4908i	−0.899787	−	1.08969i
$592$	−5.50103	+	1.47400i	−0.226091	+	0.0605809i
$593$	19.3903	+	19.3903i	0.796265	+	0.796265i	0.982504	−	0.186239i	$-0.0596299\pi$
$593$	19.3903	+	19.3903i	0.796265	+	0.796265i	−0.186239	+	0.982504i	$0.559630\pi$
$594$	−15.1207	−	0.358319i	−0.620411	−	0.0147020i
$595$		0			0
$596$	−30.7223	−	53.2126i	−1.25844	−	2.17967i
$597$	−17.7670	−	38.9006i	−0.727155	−	1.59210i
$598$	8.96042	+	15.0619i	0.366419	+	0.615928i
$599$	39.3261			1.60682			0.803410	−	0.595426i	$-0.203017\pi$
$599$	39.3261			1.60682			0.803410	+	0.595426i	$0.203017\pi$
$600$		0			0
$601$	3.77677	+	6.54156i	0.154058	+	0.266836i	0.932715	−	0.360613i	$-0.117433\pi$
$601$	3.77677	+	6.54156i	0.154058	+	0.266836i	−0.778658	+	0.627449i	$0.784099\pi$
$602$	−50.5471	+	13.5440i	−2.06014	+	0.552014i
$603$	1.53348	−	0.109787i	0.0624482	−	0.00447087i
$604$	33.6425	−	58.2705i	1.36889	−	2.37099i
$605$		0			0
$606$	13.3137	+	4.96522i	0.540833	+	0.201698i
$607$	5.94776	+	22.1974i	0.241412	+	0.900963i	0.975153	+	0.221533i	$0.0711061\pi$
$607$	5.94776	+	22.1974i	0.241412	+	0.900963i	−0.733741	+	0.679430i	$0.762227\pi$
$608$	−38.0446	−	10.1940i	−1.54291	−	0.413422i
$609$	−4.14914	−	24.6686i	−0.168132	−	0.999622i
$610$		0			0
$611$	17.7575	−	5.00766i	0.718390	−	0.202588i
$612$	−2.90014	−	40.5086i	−0.117231	−	1.63746i
$613$	−26.9913	−	7.23231i	−1.09017	−	0.292110i	−0.331414	−	0.943485i	$-0.607526\pi$
$613$	−26.9913	−	7.23231i	−1.09017	−	0.292110i	−0.758756	+	0.651375i	$0.774192\pi$
$614$	−9.56797	−	16.5722i	−0.386132	−	0.668800i
$615$		0			0
$616$			8.31822i			0.335151i
$617$	−4.94472	−	18.4539i	−0.199067	−	0.742928i	−0.991176	−	0.132549i	$-0.957684\pi$
$617$	−4.94472	−	18.4539i	−0.199067	−	0.742928i	0.792110	−	0.610379i	$-0.208983\pi$
$618$	0.739068	−	7.74280i	0.0297297	−	0.311461i
$619$	16.6072			0.667500			0.333750	−	0.942662i	$-0.391686\pi$
$619$	16.6072			0.667500			0.333750	+	0.942662i	$0.391686\pi$
$620$		0			0
$621$	5.98730	−	9.82516i	0.240262	−	0.394270i
$622$	−4.16874	+	15.5579i	−0.167151	+	0.623817i
$623$	10.4066	−	10.4066i	0.416933	−	0.416933i
$624$	−6.01495	+	8.68544i	−0.240791	+	0.347696i
$625$		0			0
$626$	5.10566	+	8.84326i	0.204063	+	0.353448i
$627$	10.0820	+	7.17881i	0.402636	+	0.286694i
$628$	61.2038	−	16.3995i	2.44230	−	0.654412i
$629$			16.1671i			0.644623i
$630$		0			0
$631$	20.1472	+	11.6320i	0.802047	+	0.463062i	0.844186	−	0.536050i	$-0.180084\pi$
$631$	20.1472	+	11.6320i	0.802047	+	0.463062i	−0.0421393	+	0.999112i	$0.513417\pi$
$632$	1.16225	−	1.16225i	0.0462317	−	0.0462317i
$633$	−2.65015	+	27.7641i	−0.105334	+	1.10353i
$634$	−20.3551	+	11.7520i	−0.808402	+	0.466731i
$635$		0			0
$636$	15.7525	+	5.87475i	0.624629	+	0.232949i
$637$	−18.6716	+	0.243974i	−0.739794	+	0.00966662i
$638$	8.51792	−	8.51792i	0.337228	−	0.337228i
$639$	−42.0201	−	8.09560i	−1.66229	−	0.320257i
$640$		0			0
$641$	15.4235	+	8.90479i	0.609193	+	0.351718i	0.772650	−	0.634833i	$-0.218931\pi$
$641$	15.4235	+	8.90479i	0.609193	+	0.351718i	−0.163456	+	0.986551i	$0.552264\pi$
$642$	13.7303	−	6.27101i	0.541892	−	0.247497i
$643$	−4.91502	−	18.3431i	−0.193829	−	0.723381i	−0.992567	−	0.121701i	$-0.961165\pi$
$643$	−4.91502	−	18.3431i	−0.193829	−	0.723381i	0.798737	−	0.601680i	$-0.205502\pi$
$644$	−18.8644	−	10.8914i	−0.743361	−	0.429179i
$645$		0			0
$646$	−28.4058	+	49.2003i	−1.11761	+	1.93576i
$647$	4.34268	−	16.2071i	0.170728	−	0.637167i	−0.826512	−	0.562920i	$-0.809678\pi$
$647$	4.34268	−	16.2071i	0.170728	−	0.637167i	0.997240	−	0.0742469i	$-0.0236553\pi$
$648$	−16.0639	−	1.91835i	−0.631051	−	0.0753599i
$649$			8.17462i			0.320882i
$650$		0			0
$651$	−20.7417	+	55.6168i	−0.812933	+	2.17980i
$652$	−12.0612	+	45.0129i	−0.472352	+	1.76284i
$653$	−23.6534	−	6.33792i	−0.925630	−	0.248022i	−0.235640	−	0.971840i	$-0.575719\pi$
$653$	−23.6534	−	6.33792i	−0.925630	−	0.248022i	−0.689990	+	0.723818i	$0.742385\pi$
$654$	−11.0626	−	13.3973i	−0.432581	−	0.523877i
$655$		0			0
$656$	1.66350	−	2.88126i	0.0649486	−	0.112494i
$657$	19.0979	+	9.27550i	0.745080	+	0.361872i
$658$	−27.7197	+	27.7197i	−1.08063	+	1.08063i
$659$	7.16295	−	12.4066i	0.279029	−	0.483292i	−0.692115	−	0.721787i	$-0.743321\pi$
$659$	7.16295	−	12.4066i	0.279029	−	0.483292i	0.971144	+	0.238495i	$0.0766542\pi$
$660$		0			0
$661$	−21.7429	+	12.5533i	−0.845700	+	0.488265i	−0.859198	−	0.511644i	$-0.829037\pi$
$661$	−21.7429	+	12.5533i	−0.845700	+	0.488265i	0.0134974	+	0.999909i	$0.495704\pi$
$662$	−16.2135	−	16.2135i	−0.630154	−	0.630154i
$663$	19.3965	+	22.8747i	0.753297	+	0.888380i
$664$		−	5.75557i		−	0.223359i
$665$		0			0
$666$	21.7695	+	4.19411i	0.843550	+	0.162518i
$667$	2.37172	+	8.85139i	0.0918335	+	0.342727i
$668$	23.4326	+	23.4326i	0.906634	+	0.906634i
$669$	16.6622	+	20.1788i	0.644199	+	0.780158i
$670$		0			0
$671$	8.86969			0.342410
$672$	4.19788	−	43.9788i	0.161937	−	1.69652i
$673$	−5.86395	+	21.8845i	−0.226038	+	0.843587i	0.755947	+	0.654632i	$0.227177\pi$
$673$	−5.86395	+	21.8845i	−0.226038	+	0.843587i	−0.981986	+	0.188955i	$0.939490\pi$
$674$	−32.1738	+	18.5756i	−1.23929	+	0.715504i
$675$		0			0
$676$	0.957496	+	36.6327i	0.0368268	+	1.40895i
$677$	−5.82836	−	5.82836i	−0.224002	−	0.224002i	0.586179	−	0.810181i	$-0.300631\pi$
$677$	−5.82836	−	5.82836i	−0.224002	−	0.224002i	−0.810181	+	0.586179i	$0.800631\pi$
$678$	−23.9721	+	33.6666i	−0.920643	+	1.29296i
$679$	17.1055	−	9.87585i	0.656448	−	0.379000i
$680$		0			0
$681$	−4.89818	+	13.1340i	−0.187699	+	0.503295i
$682$	−27.6105	+	7.39821i	−1.05726	+	0.283292i
$683$	−0.379453	+	0.101674i	−0.0145194	+	0.00389045i	−0.266071	−	0.963953i	$-0.585726\pi$
$683$	−0.379453	+	0.101674i	−0.0145194	+	0.00389045i	0.251552	+	0.967844i	$0.419059\pi$
$684$	34.4432	+	29.8409i	1.31697	+	1.14099i
$685$		0			0
$686$	−12.0814	+	6.97523i	−0.461272	+	0.266315i
$687$	28.0731	+	19.9893i	1.07106	+	0.762639i
$688$	8.17129	+	8.17129i	0.311528	+	0.311528i
$689$	−11.9495	+	3.36979i	−0.455239	+	0.128379i
$690$		0			0
$691$	17.3238	−	10.0019i	0.659029	−	0.380491i	−0.132878	−	0.991132i	$-0.542422\pi$
$691$	17.3238	−	10.0019i	0.659029	−	0.380491i	0.791907	+	0.610642i	$0.209088\pi$
$692$	−12.9255	+	48.2385i	−0.491353	+	1.83375i
$693$	−6.06499	+	12.4876i	−0.230390	+	0.474364i
$694$	39.6343			1.50450
$695$		0			0
$696$	9.93550	−	8.20404i	0.376604	−	0.310973i
$697$	−6.67832	−	6.67832i	−0.252959	−	0.252959i
$698$	−2.06309	−	7.69957i	−0.0780892	−	0.291433i
$699$	−18.6308	+	3.13361i	−0.704681	+	0.118524i
$700$		0			0
$701$		−	30.5041i		−	1.15212i	−0.817406	−	0.576062i	$-0.804589\pi$
$701$		−	30.5041i		−	1.15212i	0.817406	−	0.576062i	$-0.195411\pi$
$702$	35.8334	−	20.1838i	1.35245	−	0.761788i
$703$	−12.8279	−	12.8279i	−0.483814	−	0.483814i
$704$	14.5389	−	8.39402i	0.547954	−	0.316362i
$705$		0			0
$706$	−9.76318	+	16.9103i	−0.367442	+	0.636428i
$707$	9.22221	−	9.22221i	0.346837	−	0.346837i
$708$	−2.86009	+	29.9635i	−0.107489	+	1.12610i
$709$	−4.57699	+	7.92757i	−0.171892	+	0.297726i	−0.939081	−	0.343695i	$-0.888321\pi$
$709$	−4.57699	+	7.92757i	−0.171892	+	0.297726i	0.767189	+	0.641421i	$0.221655\pi$
$710$		0			0
$711$	2.59222	−	0.897384i	0.0972159	−	0.0336545i
$712$	7.32229	+	1.96200i	0.274415	+	0.0735291i
$713$	5.62790	−	21.0036i	0.210766	−	0.786591i
$714$	−59.7067	−	22.2670i	−2.23447	−	0.833322i
$715$		0			0
$716$			50.0653i			1.87103i
$717$	22.1087	−	31.0497i	0.825666	−	1.15957i
$718$	−10.8810	+	40.6085i	−0.406076	+	1.51550i
$719$	−11.4775	+	19.8796i	−0.428038	+	0.741383i	−0.996699	−	0.0811891i	$-0.974128\pi$
$719$	−11.4775	+	19.8796i	−0.428038	+	0.741383i	0.568661	+	0.822572i	$0.307462\pi$
$720$		0			0
$721$	−6.18260	−	3.56952i	−0.230252	−	0.132936i
$722$	−5.70464	−	21.2900i	−0.212305	−	0.792332i
$723$	10.8243	+	23.6997i	0.402560	+	0.881400i
$724$	−25.7228	−	14.8511i	−0.955981	−	0.551936i
$725$		0			0
$726$	34.6521	−	5.82831i	1.28606	−	0.216309i
$727$	26.3876	−	26.3876i	0.978663	−	0.978663i	−0.0211144	−	0.999777i	$-0.506721\pi$
$727$	26.3876	−	26.3876i	0.978663	−	0.978663i	0.999777	+	0.0211144i	$0.00672141\pi$
$728$	−11.5642	−	19.4387i	−0.428596	−	0.720445i
$729$	−22.7170	−	14.5924i	−0.841369	−	0.540460i
$730$		0			0
$731$	28.4097	−	16.4024i	1.05077	−	0.606663i
$732$	32.5112	+	3.10327i	1.20165	+	0.114700i
$733$	29.9702	−	29.9702i	1.10697	−	1.10697i	0.113427	−	0.993546i	$-0.463817\pi$
$733$	29.9702	−	29.9702i	1.10697	−	1.10697i	0.993546	−	0.113427i	$-0.0361829\pi$
$734$	24.0360	+	13.8772i	0.887184	+	0.512216i
$735$		0			0
$736$			16.1837i			0.596540i
$737$	0.656374	−	0.175875i	0.0241779	−	0.00647844i
$738$	−10.7251	+	7.26007i	−0.394796	+	0.267247i
$739$	8.61473	+	14.9212i	0.316898	+	0.548884i	0.979839	−	0.199788i	$-0.0640253\pi$
$739$	8.61473	+	14.9212i	0.316898	+	0.548884i	−0.662941	+	0.748672i	$0.730692\pi$
$740$		0			0
$741$	−33.5405	−	2.75982i	−1.23214	−	0.101384i
$742$	18.6533	−	18.6533i	0.684786	−	0.684786i
$743$	5.10822	−	19.0641i	0.187402	−	0.699395i	−0.806701	−	0.590960i	$-0.798749\pi$
$743$	5.10822	−	19.0641i	0.187402	−	0.699395i	0.994103	−	0.108435i	$-0.0345841\pi$
$744$	−30.1512	+	5.07129i	−1.10540	+	0.185922i
$745$		0			0
$746$	10.9837			0.402143
$747$	4.19650	−	8.64044i	0.153542	−	0.316137i
$748$	−4.64594	−	17.3389i	−0.169872	−	0.633972i
$749$		−	13.8546i		−	0.506236i
$750$		0			0
$751$	19.4070	+	33.6140i	0.708173	+	1.22659i	0.965534	+	0.260276i	$0.0838135\pi$
$751$	19.4070	+	33.6140i	0.708173	+	1.22659i	−0.257362	+	0.966315i	$0.582853\pi$
$752$	8.36183	+	2.24055i	0.304925	+	0.0817043i
$753$	1.84982	+	4.05015i	0.0674111	+	0.147596i
$754$	−8.06356	+	31.7471i	−0.293658	+	1.15616i
$755$		0			0
$756$	−26.5999	+	43.6503i	−0.967427	+	1.58755i
$757$	48.9488	+	13.1158i	1.77908	+	0.476702i	0.990415	−	0.138126i	$-0.0441079\pi$
$757$	48.9488	+	13.1158i	1.77908	+	0.476702i	0.788661	+	0.614828i	$0.210775\pi$
$758$	10.5596	+	39.4088i	0.383541	+	1.43139i
$759$	1.77703	−	4.76491i	0.0645020	−	0.172955i
$760$		0			0
$761$	−6.65465	+	11.5262i	−0.241231	+	0.417824i	−0.961065	−	0.276322i	$-0.910884\pi$
$761$	−6.65465	+	11.5262i	−0.241231	+	0.417824i	0.719834	+	0.694146i	$0.244218\pi$
$762$	2.61927	+	5.73486i	0.0948861	+	0.207752i
$763$	−15.4037	+	4.12742i	−0.557652	+	0.149422i
$764$	20.4234	+	35.3744i	0.738894	+	1.27980i
$765$		0			0
$766$	−5.47439			−0.197798
$767$	−11.3645	−	19.1031i	−0.410349	−	0.689773i
$768$	5.67261	−	2.59084i	0.204693	−	0.0934889i
$769$	−21.1483	−	36.6300i	−0.762629	−	1.32091i	−0.941491	−	0.337038i	$-0.890575\pi$
$769$	−21.1483	−	36.6300i	−0.762629	−	1.32091i	0.178862	−	0.983874i	$-0.442758\pi$
$770$		0			0
$771$	−5.95577	+	4.91786i	−0.214492	+	0.177112i
$772$	12.0964	+	12.0964i	0.435359	+	0.435359i
$773$	27.7237	−	7.42855i	0.997153	−	0.267186i	0.276901	−	0.960899i	$-0.410693\pi$
$773$	27.7237	−	7.42855i	0.997153	−	0.267186i	0.720252	+	0.693712i	$0.244026\pi$
$774$	−14.7162	−	42.5098i	−0.528962	−	1.52798i
$775$		0			0
$776$	8.81076	+	5.08690i	0.316288	+	0.182609i
$777$	11.8028	−	16.5759i	0.423422	−	0.594658i
$778$	48.8376	+	13.0860i	1.75091	+	0.469156i
$779$	10.5980			0.379711
$780$		0			0
$781$	−18.9143			−0.676807
$782$	22.5481	+	6.04175i	0.806319	+	0.216053i
$783$	20.8972	−	5.07198i	0.746806	−	0.181258i
$784$	−7.58767	−	4.38074i	−0.270988	−	0.156455i
$785$		0			0
$786$	19.6169	−	16.1983i	0.699713	−	0.577774i
$787$	19.3070	−	5.17330i	0.688221	−	0.184408i	0.102272	−	0.994756i	$-0.467389\pi$
$787$	19.3070	−	5.17330i	0.688221	−	0.184408i	0.585948	+	0.810348i	$0.300722\pi$
$788$	−39.5353	−	39.5353i	−1.40839	−	1.40839i
$789$	10.9560	+	13.2683i	0.390046	+	0.472365i
$790$		0			0
$791$	18.9671	+	32.8519i	0.674391	+	1.16808i
$792$	−7.13240	+	0.510632i	−0.253439	+	0.0181445i
$793$	−20.7274	+	12.3308i	−0.736051	+	0.437880i
$794$	−6.19197			−0.219745
$795$		0			0
$796$	−34.8002	−	60.2757i	−1.23346	−	2.13641i
$797$	−29.9034	+	8.01258i	−1.05923	+	0.283820i	−0.746062	−	0.665877i	$-0.768058\pi$
$797$	−29.9034	+	8.01258i	−1.05923	+	0.283820i	−0.313170	+	0.949697i	$0.601391\pi$
$798$	65.0429	−	29.7069i	2.30250	−	1.05161i
$799$	12.2873	−	21.2823i	0.434695	−	0.752914i
$800$		0			0
$801$	9.56192	+	8.28425i	0.337854	+	0.292710i
$802$	−17.9926	−	67.1494i	−0.635342	−	2.37113i
$803$	9.06437	+	2.42879i	0.319875	+	0.0857102i
$804$	2.46743	−	0.415009i	0.0870195	−	0.0146362i
$805$		0			0
$806$	54.2372	−	55.6734i	1.91043	−	1.96101i
$807$	−42.0403	+	19.2010i	−1.47989	+	0.675906i
$808$	6.48892	+	1.73870i	0.228279	+	0.0611673i
$809$	−2.05170	−	3.55365i	−0.0721340	−	0.124940i	0.827702	−	0.561167i	$-0.189648\pi$
$809$	−2.05170	−	3.55365i	−0.0721340	−	0.124940i	−0.899836	+	0.436228i	$0.856314\pi$
$810$		0			0
$811$		−	8.34467i		−	0.293021i	−0.989209	−	0.146510i	$-0.953196\pi$
$811$		−	8.34467i		−	0.293021i	0.989209	−	0.146510i	$-0.0468042\pi$
$812$	−10.5369	−	39.3242i	−0.369772	−	1.38001i
$813$	7.27938	+	0.694834i	0.255299	+	0.0243689i
$814$	9.79899			0.343454
$815$		0			0
$816$	2.33405	+	13.8770i	0.0817081	+	0.485794i
$817$	−9.52737	+	35.5566i	−0.333320	+	1.24397i
$818$	2.34377	−	2.34377i	0.0819482	−	0.0819482i
$819$	−3.18735	−	37.6136i	−0.111375	−	1.31433i
$820$		0			0
$821$	−14.5480	−	25.1979i	−0.507730	−	0.879414i	−0.999960	−	0.00894856i	$-0.997152\pi$
$821$	−14.5480	−	25.1979i	−0.507730	−	0.879414i	0.492230	−	0.870465i	$-0.336182\pi$
$822$	−6.38580	+	8.96828i	−0.222730	+	0.312805i
$823$	−7.06632	+	1.89342i	−0.246317	+	0.0660003i	−0.379865	−	0.925042i	$-0.624030\pi$
$823$	−7.06632	+	1.89342i	−0.246317	+	0.0660003i	0.133548	+	0.991042i	$0.457363\pi$
$824$		−	3.67721i		−	0.128102i
$825$		0			0
$826$	40.9012	+	23.6143i	1.42313	+	0.821647i
$827$	−3.39420	+	3.39420i	−0.118028	+	0.118028i	−0.763654	−	0.645626i	$-0.776597\pi$
$827$	−3.39420	+	3.39420i	−0.118028	+	0.118028i	0.645626	+	0.763654i	$0.276597\pi$
$828$	8.18069	−	16.8437i	0.284298	−	0.585360i
$829$	31.8232	−	18.3731i	1.10527	−	0.638125i	0.167666	−	0.985844i	$-0.446377\pi$
$829$	31.8232	−	18.3731i	1.10527	−	0.638125i	0.937599	+	0.347719i	$0.113044\pi$
$830$		0			0
$831$	11.5723	−	31.0299i	0.401438	−	1.07641i
$832$	−22.3060	+	39.8280i	−0.773323	+	1.38079i
$833$	−17.5871	+	17.5871i	−0.609355	+	0.609355i
$834$	1.53416	+	9.12130i	0.0531235	+	0.315845i
$835$		0			0
$836$	17.4441	+	10.0713i	0.603316	+	0.348325i
$837$	−48.9616	−	14.3707i	−1.69236	−	0.496724i
$838$	−1.25512	−	4.68416i	−0.0433573	−	0.161811i
$839$	−43.0804	−	24.8725i	−1.48730	−	0.858694i	−0.487407	−	0.873175i	$-0.662057\pi$
$839$	−43.0804	−	24.8725i	−1.48730	−	0.858694i	−0.999895	+	0.0144808i	$0.995390\pi$
$840$		0			0
$841$	5.93669	−	10.2826i	0.204713	−	0.354574i
$842$	1.44757	−	5.40239i	0.0498864	−	0.186179i
$843$	−45.8039	−	32.6144i	−1.57757	−	1.12330i
$844$			45.3907i			1.56241i
$845$		0			0
$846$	−25.4697	−	22.0664i	−0.875667	−	0.758660i
$847$	8.34750	−	31.1533i	0.286823	−	1.07044i
$848$	−5.62690	−	1.50772i	−0.193229	−	0.0517754i
$849$	−12.4674	+	10.2947i	−0.427882	+	0.353315i
$850$		0			0
$851$	−3.72710	+	6.45552i	−0.127763	+	0.221292i
$852$	−69.3290	−	6.61762i	−2.37517	−	0.226716i
$853$	6.93524	−	6.93524i	0.237458	−	0.237458i	−0.578339	−	0.815797i	$-0.696299\pi$
$853$	6.93524	−	6.93524i	0.237458	−	0.237458i	0.815797	+	0.578339i	$0.196299\pi$
$854$	25.6222	−	44.3789i	0.876773	−	1.51862i
$855$		0			0
$856$	6.18021	−	3.56815i	0.211235	−	0.121957i
$857$	7.66857	+	7.66857i	0.261953	+	0.261953i	0.825847	−	0.563894i	$-0.190697\pi$
$857$	7.66857	+	7.66857i	0.261953	+	0.261953i	−0.563894	+	0.825847i	$0.690697\pi$
$858$	13.8645	−	11.7564i	0.473328	−	0.401356i
$859$			2.92998i			0.0999695i	0.998750	+	0.0499847i	$0.0159173\pi$
$859$			2.92998i			0.0999695i	−0.998750	+	0.0499847i	$0.984083\pi$
$860$		0			0
$861$	1.97170	+	11.7227i	0.0671955	+	0.399509i
$862$	−5.99992	−	22.3920i	−0.204358	−	0.762675i
$863$	−5.00161	−	5.00161i	−0.170257	−	0.170257i	0.616835	−	0.787092i	$-0.288414\pi$
$863$	−5.00161	−	5.00161i	−0.170257	−	0.170257i	−0.787092	+	0.616835i	$0.788414\pi$
$864$	37.9670	+	0.899711i	1.29166	+	0.0306088i
$865$		0			0
$866$	−42.6413			−1.44901
$867$	10.4547	+	0.997928i	0.355061	+	0.0338914i
$868$	−25.0031	+	93.3129i	−0.848661	+	3.16725i
$869$	1.05003	−	0.606233i	0.0356197	−	0.0205651i
$870$		0			0
$871$	−1.28936	+	1.32350i	−0.0436884	+	0.0448452i
$872$	−5.80825	−	5.80825i	−0.196692	−	0.196692i
$873$	9.51803	+	14.0607i	0.322137	+	0.475883i
$874$	−22.6849	+	13.0972i	−0.767330	+	0.443018i
$875$		0			0
$876$	32.3751	+	12.0740i	1.09385	+	0.407941i
$877$	8.91238	−	2.38806i	0.300950	−	0.0806392i	−0.105184	−	0.994453i	$-0.533543\pi$
$877$	8.91238	−	2.38806i	0.300950	−	0.0806392i	0.406134	+	0.913814i	$0.366877\pi$
$878$	−66.1626	+	17.7282i	−2.23288	+	0.598299i
$879$	21.3149	+	7.94917i	0.718933	+	0.268119i
$880$		0			0
$881$	−9.32780	+	5.38541i	−0.314261	+	0.181439i	−0.648832	−	0.760932i	$-0.724742\pi$
$881$	−9.32780	+	5.38541i	−0.314261	+	0.181439i	0.334570	+	0.942371i	$0.391409\pi$
$882$	19.1191	+	28.2441i	0.643773	+	0.951027i
$883$	−3.44423	−	3.44423i	−0.115907	−	0.115907i	0.646774	−	0.762682i	$-0.276118\pi$
$883$	−3.44423	−	3.44423i	−0.115907	−	0.115907i	−0.762682	+	0.646774i	$0.776118\pi$
$884$	34.9618	+	34.0599i	1.17589	+	1.14556i
$885$		0			0
$886$	−8.60111	+	4.96585i	−0.288960	+	0.166831i
$887$	13.3630	−	49.8713i	0.448685	−	1.67451i	−0.257335	−	0.966322i	$-0.582844\pi$
$887$	13.3630	−	49.8713i	0.448685	−	1.67451i	0.706020	−	0.708192i	$-0.250489\pi$
$888$	10.4338	+	0.995934i	0.350137	+	0.0334214i
$889$	5.78678			0.194082
$890$		0			0
$891$	−11.0797	−	4.43380i	−0.371184	−	0.148538i
$892$	30.1151	+	30.1151i	1.00833	+	1.00833i
$893$	7.13715	+	26.6362i	0.238836	+	0.891346i
$894$	−13.7467	−	81.7307i	−0.459758	−	2.73348i
$895$		0			0
$896$		−	45.9793i		−	1.53606i
$897$	2.47158	+	13.6055i	0.0825238	+	0.454274i
$898$	−32.4664	−	32.4664i	−1.08342	−	1.08342i
$899$	35.1953	−	20.3200i	1.17383	−	0.677710i
$900$		0			0
$901$	−8.26849	+	14.3214i	−0.275463	+	0.477116i
$902$	−4.04778	+	4.04778i	−0.134776	+	0.134776i
$903$	−41.1027	−	3.92335i	−1.36781	−	0.130561i
$904$	−9.76964	+	16.9215i	−0.324933	+	0.562801i
$905$		0			0
$906$	69.9819	−	57.7862i	2.32499	−	1.91982i
$907$	43.5204	+	11.6613i	1.44507	+	0.387206i	0.894306	−	0.447455i	$-0.147670\pi$
$907$	43.5204	+	11.6613i	1.44507	+	0.387206i	0.550765	+	0.834661i	$0.314336\pi$
$908$	−5.90451	+	22.0359i	−0.195948	+	0.731288i
$909$	8.47365	+	7.34140i	0.281053	+	0.243499i
$910$		0			0
$911$		−	22.6957i		−	0.751941i	−0.926632	−	0.375971i	$-0.877309\pi$
$911$		−	22.6957i		−	0.751941i	0.926632	−	0.375971i	$-0.122691\pi$
$912$	−12.8629	−	9.15892i	−0.425932	−	0.303282i
$913$	1.09886	−	4.10098i	0.0363668	−	0.135723i
$914$	11.7834	−	20.4095i	0.389761	−	0.675086i
$915$		0			0
$916$	48.5727	+	28.0435i	1.60489	+	0.926583i
$917$	−6.04354	−	22.5548i	−0.199575	−	0.744825i
$918$	15.4275	−	52.5620i	0.509183	−	1.73481i
$919$	−36.0138	−	20.7926i	−1.18799	−	0.685884i	−0.230137	−	0.973158i	$-0.573918\pi$
$919$	−36.0138	−	20.7926i	−1.18799	−	0.685884i	−0.957848	+	0.287274i	$0.907251\pi$
$920$		0			0
$921$	−2.50434	−	14.8895i	−0.0825208	−	0.490626i
$922$	−44.0739	+	44.0739i	−1.45150	+	1.45150i
$923$	44.2004	−	26.2950i	1.45487	−	0.865512i
$924$	−7.89482	+	21.1691i	−0.259720	+	0.696413i
$925$		0			0
$926$	−75.1352	+	43.3793i	−2.46910	+	1.42553i
$927$	2.68113	−	5.52035i	0.0880599	−	0.181312i
$928$	−21.3879	+	21.3879i	−0.702091	+	0.702091i
$929$	3.52259	+	2.03377i	0.115572	+	0.0667257i	0.556672	−	0.830732i	$-0.312078\pi$
$929$	3.52259	+	2.03377i	0.115572	+	0.0667257i	−0.441100	+	0.897458i	$0.645411\pi$
$930$		0			0
$931$		−	27.9093i		−	0.914690i
$932$	−29.6993	+	7.95791i	−0.972833	+	0.260670i
$933$	−7.37133	+	10.3524i	−0.241326	+	0.338921i
$934$	9.76709	+	16.9171i	0.319589	+	0.553544i
$935$		0			0
$936$	15.9577	−	11.1089i	0.521592	−	0.363105i
$937$	−28.3766	+	28.3766i	−0.927022	+	0.927022i	−0.997512	−	0.0704901i	$-0.977544\pi$
$937$	−28.3766	+	28.3766i	−0.927022	+	0.927022i	0.0704901	+	0.997512i	$0.477544\pi$
$938$	1.01611	−	3.79218i	0.0331772	−	0.123819i
$939$	1.33637	+	7.94534i	0.0436107	+	0.259286i
$940$		0			0
$941$	9.20788			0.300168			0.150084	−	0.988673i	$-0.452046\pi$
$941$	9.20788			0.300168			0.150084	+	0.988673i	$0.452046\pi$
$942$	85.0793	+	8.12102i	2.77203	+	0.264597i
$943$	−1.12706	−	4.20625i	−0.0367022	−	0.136974i
$944$		−	10.4294i		−	0.339448i
$945$		0			0
$946$	−9.94161	−	17.2194i	−0.323230	−	0.559850i
$947$	−44.1667	−	11.8344i	−1.43523	−	0.384568i	−0.544367	−	0.838847i	$-0.683230\pi$
$947$	−44.1667	−	11.8344i	−1.43523	−	0.384568i	−0.890859	+	0.454279i	$0.849897\pi$
$948$	4.06090	−	1.85473i	0.131892	−	0.0602388i
$949$	−24.5589	+	6.92569i	−0.797215	+	0.224817i
$950$		0			0
$951$	−18.2883	+	3.07599i	−0.593037	+	0.0997459i
$952$	−29.1002	−	7.79738i	−0.943143	−	0.252714i
$953$	−8.94444	−	33.3811i	−0.289739	−	1.08132i	−0.945306	−	0.326184i	$-0.894237\pi$
$953$	−8.94444	−	33.3811i	−0.289739	−	1.08132i	0.655567	−	0.755137i	$-0.272429\pi$
$954$	17.1393	+	14.8491i	0.554904	+	0.480758i
$955$		0			0
$956$	31.0169	−	53.7229i	1.00316	−	1.73752i
$957$	8.64561	−	3.94869i	0.279473	−	0.127643i
$958$	−1.11989	+	0.300073i	−0.0361820	+	0.00969493i
$959$	5.05253	+	8.75125i	0.163155	+	0.282592i
$960$		0			0
$961$	−65.4352			−2.11081
$962$	−22.8990	+	13.6228i	−0.738295	+	0.439215i
$963$	11.8795	−	0.850494i	0.382813	−	0.0274068i
$964$	21.2015	+	36.7221i	0.682855	+	1.18274i
$965$		0			0
$966$	−18.7076	−	22.6558i	−0.601907	−	0.728939i
$967$	−24.2775	−	24.2775i	−0.780713	−	0.780713i	0.199238	−	0.979951i	$-0.436153\pi$
$967$	−24.2775	−	24.2775i	−0.780713	−	0.780713i	−0.979951	+	0.199238i	$0.936153\pi$
$968$	16.0466	−	4.29967i	0.515756	−	0.138196i
$969$	−34.5649	+	28.5412i	−1.11038	+	0.916876i
$970$		0			0
$971$	−46.2260	−	26.6886i	−1.48346	−	0.856478i	−0.483640	−	0.875267i	$-0.660686\pi$
$971$	−46.2260	−	26.6886i	−1.48346	−	0.856478i	−0.999823	+	0.0187889i	$0.994019\pi$
$972$	−39.0606	−	20.1283i	−1.25287	−	0.645615i
$973$	8.20032	+	2.19727i	0.262890	+	0.0704412i
$974$	−10.7426			−0.344216
$975$		0			0
$976$	−11.3162			−0.362222
$977$	−13.4430	−	3.60204i	−0.430080	−	0.115240i	0.0372838	−	0.999305i	$-0.488129\pi$
$977$	−13.4430	−	3.60204i	−0.430080	−	0.115240i	−0.467364	+	0.884065i	$0.654796\pi$
$978$	−36.4587	+	51.2029i	−1.16582	+	1.63729i
$979$	4.84273	+	2.79595i	0.154774	+	0.0893590i
$980$		0			0
$981$	−4.48461	−	12.9544i	−0.143183	−	0.413604i
$982$	38.3175	−	10.2671i	1.22276	−	0.327638i
$983$	−33.1763	−	33.1763i	−1.05816	−	1.05816i	−0.998201	−	0.0599577i	$-0.980903\pi$
$983$	−33.1763	−	33.1763i	−1.05816	−	1.05816i	−0.0599577	−	0.998201i	$-0.519097\pi$
$984$	−4.72143	+	3.89863i	−0.150514	+	0.124284i
$985$		0			0
$986$	21.8143	+	37.7834i	0.694708	+	1.20327i
$987$	−28.1352	+	12.8502i	−0.895555	+	0.409025i
$988$	−54.7661	+	0.715608i	−1.74234	+	0.0227665i
$989$	15.1254			0.480959
$990$		0			0
$991$	−14.0717	−	24.3729i	−0.447002	−	0.774231i	0.551187	−	0.834382i	$-0.314175\pi$
$991$	−14.0717	−	24.3729i	−0.447002	−	0.774231i	−0.998189	+	0.0601511i	$0.980842\pi$
$992$	69.3279	−	18.5764i	2.20116	−	0.589800i
$993$	−7.51614	−	16.4565i	−0.238518	−	0.522231i
$994$	−54.6384	+	94.6365i	−1.73303	+	3.00169i
$995$		0			0
$996$	5.46260	−	14.6474i	0.173089	−	0.464121i
$997$	1.87355	+	6.99220i	0.0593361	+	0.221445i	0.989227	−	0.146390i	$-0.0467656\pi$
$997$	1.87355	+	6.99220i	0.0593361	+	0.221445i	−0.929891	+	0.367836i	$0.880099\pi$
$998$	−37.7983	−	10.1280i	−1.19648	−	0.320597i
$999$	14.9374	+	9.10265i	0.472600	+	0.287995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.218.22		96
3.2	odd	2	inner	975.2.bn.d.218.3		96
5.2	odd	4	inner	975.2.bn.d.257.3		96
5.3	odd	4		195.2.bf.a.62.22	yes	96
5.4	even	2		195.2.bf.a.23.3	yes	96
13.4	even	6	inner	975.2.bn.d.368.22		96
15.2	even	4	inner	975.2.bn.d.257.22		96
15.8	even	4		195.2.bf.a.62.3	yes	96
15.14	odd	2		195.2.bf.a.23.22	yes	96
39.17	odd	6	inner	975.2.bn.d.368.3		96
65.4	even	6		195.2.bf.a.173.3	yes	96
65.17	odd	12	inner	975.2.bn.d.407.3		96
65.43	odd	12		195.2.bf.a.17.22	yes	96
195.17	even	12	inner	975.2.bn.d.407.22		96
195.134	odd	6		195.2.bf.a.173.22	yes	96
195.173	even	12		195.2.bf.a.17.3	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.3	✓	96	195.173	even	12
195.2.bf.a.17.22	yes	96	65.43	odd	12
195.2.bf.a.23.3	yes	96	5.4	even	2
195.2.bf.a.23.22	yes	96	15.14	odd	2
195.2.bf.a.62.3	yes	96	15.8	even	4
195.2.bf.a.62.22	yes	96	5.3	odd	4
195.2.bf.a.173.3	yes	96	65.4	even	6
195.2.bf.a.173.22	yes	96	195.134	odd	6
975.2.bn.d.218.3		96	3.2	odd	2	inner
975.2.bn.d.218.22		96	1.1	even	1	trivial
975.2.bn.d.257.3		96	5.2	odd	4	inner
975.2.bn.d.257.22		96	15.2	even	4	inner
975.2.bn.d.368.3		96	39.17	odd	6	inner
975.2.bn.d.368.22		96	13.4	even	6	inner
975.2.bn.d.407.3		96	65.17	odd	12	inner
975.2.bn.d.407.22		96	195.17	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.12039 + 0.568157i) q^{2} +(1.41092 + 1.00464i) q^{3} +(2.44121 + 1.40943i) q^{4} +(2.42092 + 2.93185i) q^{6} +(3.37093 - 0.903238i) q^{7} +(1.27107 + 1.27107i) q^{8} +(0.981406 + 2.83493i) q^{9} +(0.662995 + 1.14834i) q^{11} +(2.02839 + 4.44113i) q^{12} +(-3.14579 - 1.76182i) q^{13} +7.66087 q^{14} +(-0.845867 - 1.46508i) q^{16} +(-4.63881 + 1.24296i) q^{17} +(0.470279 + 6.56876i) q^{18} +(2.69447 - 4.66695i) q^{19} +(5.66355 + 2.11216i) q^{21} +(0.753371 + 2.81162i) q^{22} +(-2.13883 - 0.573097i) q^{23} +(0.516417 + 3.07034i) q^{24} +(-5.66931 - 5.52306i) q^{26} +(-1.46339 + 4.98583i) q^{27} +(9.50219 + 2.54610i) q^{28} +(-2.06922 - 3.58399i) q^{29} +9.82014i q^{31} +(-1.89166 - 7.05976i) q^{32} +(-0.218232 + 2.28629i) q^{33} -10.5423 q^{34} +(-1.59983 + 8.30389i) q^{36} +(0.871294 - 3.25171i) q^{37} +(8.36489 - 8.36489i) q^{38} +(-2.66847 - 5.64617i) q^{39} +(0.983308 + 1.70314i) q^{41} +(10.8089 + 7.69640i) q^{42} +(-6.59808 + 1.76795i) q^{43} +3.73779i q^{44} +(-4.20954 - 2.43038i) q^{46} +(-3.61835 + 3.61835i) q^{47} +(0.278426 - 2.91691i) q^{48} +(4.48514 - 2.58950i) q^{49} +(-7.79372 - 2.90659i) q^{51} +(-5.19635 - 8.73475i) q^{52} +(2.43489 - 2.43489i) q^{53} +(-5.93570 + 9.74047i) q^{54} +(5.43276 + 3.13661i) q^{56} +(8.49028 - 3.87775i) q^{57} +(-2.35128 - 8.77510i) q^{58} +(5.33897 + 3.08246i) q^{59} +(3.34455 - 5.79293i) q^{61} +(-5.57939 + 20.8226i) q^{62} +(5.86887 + 8.66991i) q^{63} -12.6608i q^{64} +(-1.76171 + 4.72384i) q^{66} +(0.132637 - 0.495007i) q^{67} +(-13.0762 - 3.50375i) q^{68} +(-2.44197 - 2.95734i) q^{69} +(-7.13214 + 12.3532i) q^{71} +(-2.35596 + 4.85083i) q^{72} +(5.00425 - 5.00425i) q^{73} +(3.69497 - 6.39988i) q^{74} +(13.1555 - 7.59533i) q^{76} +(3.27213 + 3.27213i) q^{77} +(-2.45028 - 13.4882i) q^{78} -0.914386i q^{79} +(-7.07368 + 5.56444i) q^{81} +(1.11735 + 4.17000i) q^{82} +(-2.26406 - 2.26406i) q^{83} +(10.8489 + 13.1386i) q^{84} -14.9950 q^{86} +(0.681105 - 7.13554i) q^{87} +(-0.616909 + 2.30233i) q^{88} +(3.65216 - 2.10858i) q^{89} +(-12.1956 - 3.09759i) q^{91} +(-4.41358 - 4.41358i) q^{92} +(-9.86569 + 13.8555i) q^{93} +(-9.72811 + 5.61653i) q^{94} +(4.42352 - 11.8612i) q^{96} +(5.46692 - 1.46486i) q^{97} +(10.9815 - 2.94249i) q^{98} +(-2.60480 + 3.00654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) \) 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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