LMFDB - Embedded newform 195.2.bf.a.17.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(17,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.bf (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	195.17
Dual form			195.2.bf.a.23.3

$q$-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} +(2.19791 - 0.411355i) q^{5} +(2.42092 - 2.93185i) q^{6} +(-3.37093 - 0.903238i) q^{7} +(-1.27107 + 1.27107i) q^{8} +(0.981406 - 2.83493i) q^{9} +(-4.42671 + 2.12099i) q^{10} +(0.662995 - 1.14834i) q^{11} +(-2.02839 + 4.44113i) q^{12} +(3.14579 - 1.76182i) q^{13} +7.66087 q^{14} +(-2.68781 + 2.78849i) q^{15} +(-0.845867 + 1.46508i) q^{16} +(4.63881 + 1.24296i) q^{17} +(-0.470279 + 6.56876i) q^{18} +(2.69447 + 4.66695i) q^{19} +(4.78577 - 4.10200i) q^{20} +(5.66355 - 2.11216i) q^{21} +(-0.753371 + 2.81162i) q^{22} +(2.13883 - 0.573097i) q^{23} +(0.516417 - 3.07034i) q^{24} +(4.66157 - 1.80824i) q^{25} +(-5.66931 + 5.52306i) q^{26} +(1.46339 + 4.98583i) q^{27} +(-9.50219 + 2.54610i) q^{28} +(-2.06922 + 3.58399i) q^{29} +(4.11491 - 7.43979i) q^{30} -9.82014i q^{31} +(1.89166 - 7.05976i) q^{32} +(0.218232 + 2.28629i) q^{33} -10.5423 q^{34} +(-7.78053 - 0.598582i) q^{35} +(-1.59983 - 8.30389i) q^{36} +(-0.871294 - 3.25171i) q^{37} +(-8.36489 - 8.36489i) q^{38} +(-2.66847 + 5.64617i) q^{39} +(-2.27083 + 3.31655i) q^{40} +(0.983308 - 1.70314i) q^{41} +(-10.8089 + 7.69640i) q^{42} +(6.59808 + 1.76795i) q^{43} -3.73779i q^{44} +(0.990875 - 6.63462i) q^{45} +(-4.20954 + 2.43038i) q^{46} +(3.61835 + 3.61835i) q^{47} +(-0.278426 - 2.91691i) q^{48} +(4.48514 + 2.58950i) q^{49} +(-8.85700 + 6.48268i) q^{50} +(-7.79372 + 2.90659i) q^{51} +(5.19635 - 8.73475i) q^{52} +(-2.43489 - 2.43489i) q^{53} +(-5.93570 - 9.74047i) q^{54} +(0.984825 - 2.79667i) q^{55} +(5.43276 - 3.13661i) q^{56} +(-8.49028 - 3.87775i) q^{57} +(2.35128 - 8.77510i) q^{58} +(5.33897 - 3.08246i) q^{59} +(-2.63132 + 10.5956i) q^{60} +(3.34455 + 5.79293i) q^{61} +(5.57939 + 20.8226i) q^{62} +(-5.86887 + 8.66991i) q^{63} +12.6608i q^{64} +(6.18941 - 5.16636i) q^{65} +(-1.76171 - 4.72384i) q^{66} +(-0.132637 - 0.495007i) q^{67} +(13.0762 - 3.50375i) q^{68} +(-2.44197 + 2.95734i) q^{69} +(16.8379 - 3.15134i) q^{70} +(-7.13214 - 12.3532i) q^{71} +(2.35596 + 4.85083i) q^{72} +(-5.00425 - 5.00425i) q^{73} +(3.69497 + 6.39988i) q^{74} +(-4.76050 + 7.23448i) q^{75} +(13.1555 + 7.59533i) q^{76} +(-3.27213 + 3.27213i) q^{77} +(2.45028 - 13.4882i) q^{78} +0.914386i q^{79} +(-1.25646 + 3.56807i) q^{80} +(-7.07368 - 5.56444i) q^{81} +(-1.11735 + 4.17000i) q^{82} +(2.26406 - 2.26406i) q^{83} +(10.8489 - 13.1386i) q^{84} +(10.7070 + 0.823721i) q^{85} -14.9950 q^{86} +(-0.681105 - 7.13554i) q^{87} +(0.616909 + 2.30233i) q^{88} +(3.65216 + 2.10858i) q^{89} +(1.66846 + 14.6310i) q^{90} +(-12.1956 + 3.09759i) q^{91} +(4.41358 - 4.41358i) q^{92} +(9.86569 + 13.8555i) q^{93} +(-9.72811 - 5.61653i) q^{94} +(7.84196 + 9.14914i) q^{95} +(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} + 4 q^{10} - 12 q^{12} - 24 q^{13} - 6 q^{15} + 16 q^{16} + 20 q^{22} - 16 q^{25} - 32 q^{27} - 36 q^{28} + 30 q^{33} - 4 q^{36} - 84 q^{37} - 152 q^{40} - 48 q^{42}+ \cdots - 48 q^{97}+O(q^{100}) $ 96 * q - 2 * q^3 - 12 * q^6 - 12 * q^7 + 4 * q^10 - 12 * q^12 - 24 * q^13 - 6 * q^15 + 16 * q^16 + 20 * q^22 - 16 * q^25 - 32 * q^27 - 36 * q^28 + 30 * q^33 - 4 * q^36 - 84 * q^37 - 152 * q^40 - 48 * q^42 + 8 * q^43 + 54 * q^45 - 28 * q^48 - 16 * q^51 + 28 * q^52 - 40 * q^55 + 84 * q^58 - 32 * q^61 + 90 * q^63 + 36 * q^67 + 90 * q^72 - 20 * q^75 + 72 * q^76 + 60 * q^78 + 32 * q^81 - 68 * q^82 + 84 * q^85 - 26 * q^87 - 108 * q^88 - 20 * q^90 - 80 * q^91 + 48 * q^93 - 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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	$-0.866147\pi$
$2$	−2.12039	+	0.568157i	−1.49934	+	0.401748i	−0.586463	+	0.809976i	$0.699480\pi$
$3$	−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
$5$	2.19791	−	0.411355i	0.982933	−	0.183964i
$5$	2.19791	−	0.411355i	0.982933	−	0.183964i
$6$	2.42092	−	2.93185i	0.988335	−	1.19692i
$7$	−3.37093	−	0.903238i	−1.27409	−	0.341392i	−0.442494	−	0.896771i	$-0.645906\pi$
$7$	−3.37093	−	0.903238i	−1.27409	−	0.341392i	−0.831597	+	0.555380i	$0.812573\pi$
$8$	−1.27107	+	1.27107i	−0.449391	+	0.449391i
$9$	0.981406	−	2.83493i	0.327135	−	0.944977i
$10$	−4.42671	+	2.12099i	−1.39985	+	0.670716i
$11$	0.662995	−	1.14834i	0.199901	−	0.346238i	−0.748595	−	0.663027i	$-0.769271\pi$
$11$	0.662995	−	1.14834i	0.199901	−	0.346238i	0.948496	+	0.316789i	$0.102605\pi$
$12$	−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
$15$	−2.68781	+	2.78849i	−0.693990	+	0.719985i
$16$	−0.845867	+	1.46508i	−0.211467	+	0.366271i
$17$	4.63881	+	1.24296i	1.12508	+	0.301463i	0.772936	−	0.634484i	$-0.218787\pi$
$17$	4.63881	+	1.24296i	1.12508	+	0.301463i	0.352140	+	0.935947i	$0.385454\pi$
$18$	−0.470279	+	6.56876i	−0.110846	+	1.54827i
$19$	2.69447	+	4.66695i	0.618153	+	1.07067i	0.989823	+	0.142307i	$0.0454521\pi$
$19$	2.69447	+	4.66695i	0.618153	+	1.07067i	−0.371670	+	0.928365i	$0.621215\pi$
$20$	4.78577	−	4.10200i	1.07013	−	0.917235i
$21$	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	$-0.509181\pi$
$23$	2.13883	−	0.573097i	0.445976	−	0.119499i	0.474816	+	0.880085i	$0.342515\pi$
$24$	0.516417	−	3.07034i	0.105413	−	0.626731i
$25$	4.66157	−	1.80824i	0.932315	−	0.361648i
$26$	−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	−0.991664	−	0.128851i	$-0.958871\pi$
$29$	−2.06922	+	3.58399i	−0.384244	+	0.665530i	0.607420	+	0.794381i	$0.292204\pi$
$30$	4.11491	−	7.43979i	0.751277	−	1.35831i
$31$		−	9.82014i		−	1.76375i	−0.471483	−	0.881875i	$-0.656281\pi$
$31$		−	9.82014i		−	1.76375i	0.471483	−	0.881875i	$-0.343719\pi$
$32$	1.89166	−	7.05976i	0.334401	−	1.24800i
$33$	0.218232	+	2.28629i	0.0379893	+	0.397992i
$34$	−10.5423			−1.80799
$35$	−7.78053	−	0.598582i	−1.31515	−	0.101179i
$36$	−1.59983	−	8.30389i	−0.266638	−	1.38398i
$37$	−0.871294	−	3.25171i	−0.143240	−	0.534579i	−0.999827	−	0.0185768i	$-0.994086\pi$
$37$	−0.871294	−	3.25171i	−0.143240	−	0.534579i	0.856588	−	0.516002i	$-0.172580\pi$
$38$	−8.36489	−	8.36489i	−1.35696	−	1.35696i
$39$	−2.66847	+	5.64617i	−0.427297	+	0.904111i
$40$	−2.27083	+	3.31655i	−0.359050	+	0.524393i
$41$	0.983308	−	1.70314i	0.153567	−	0.265986i	−0.778969	−	0.627062i	$-0.784257\pi$
$41$	0.983308	−	1.70314i	0.153567	−	0.265986i	0.932536	+	0.361076i	$0.117591\pi$
$42$	−10.8089	+	7.69640i	−1.66785	+	1.18758i
$43$	6.59808	+	1.76795i	1.00620	+	0.269610i	0.724040	−	0.689758i	$-0.242283\pi$
$43$	6.59808	+	1.76795i	1.00620	+	0.269610i	0.282158	+	0.959368i	$0.408950\pi$
$44$		−	3.73779i		−	0.563493i
$45$	0.990875	−	6.63462i	0.147711	−	0.989031i
$46$	−4.20954	+	2.43038i	−0.620663	+	0.358340i
$47$	3.61835	+	3.61835i	0.527791	+	0.527791i	0.919913	−	0.392122i	$-0.128259\pi$
$47$	3.61835	+	3.61835i	0.527791	+	0.527791i	−0.392122	+	0.919913i	$0.628259\pi$
$48$	−0.278426	−	2.91691i	−0.0401873	−	0.421020i
$49$	4.48514	+	2.58950i	0.640735	+	0.369929i
$50$	−8.85700	+	6.48268i	−1.25257	+	0.916790i
$51$	−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	$-0.325999\pi$
$53$	−2.43489	−	2.43489i	−0.334457	−	0.334457i	−0.854276	+	0.519819i	$0.825999\pi$
$54$	−5.93570	−	9.74047i	−0.807746	−	1.32551i
$55$	0.984825	−	2.79667i	0.132794	−	0.377103i
$56$	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	−0.110435	−	0.993883i	$-0.535225\pi$
$59$	5.33897	−	3.08246i	0.695075	−	0.401302i	0.805510	+	0.592582i	$0.201891\pi$
$60$	−2.63132	+	10.5956i	−0.339702	+	1.36788i
$61$	3.34455	+	5.79293i	0.428226	+	0.741709i	0.996716	−	0.0809813i	$-0.0258054\pi$
$61$	3.34455	+	5.79293i	0.428226	+	0.741709i	−0.568490	+	0.822690i	$0.692472\pi$
$62$	5.57939	+	20.8226i	0.708583	+	2.64447i
$63$	−5.86887	+	8.66991i	−0.739408	+	1.09231i
$64$			12.6608i			1.58259i
$65$	6.18941	−	5.16636i	0.767701	−	0.640808i
$66$	−1.76171	−	4.72384i	−0.216852	−	0.581465i
$67$	−0.132637	−	0.495007i	−0.0162041	−	0.0604747i	0.957350	−	0.288930i	$-0.0932993\pi$
$67$	−0.132637	−	0.495007i	−0.0162041	−	0.0604747i	−0.973555	+	0.228455i	$0.926633\pi$
$68$	13.0762	−	3.50375i	1.58572	−	0.424892i
$69$	−2.44197	+	2.95734i	−0.293978	+	0.356022i
$70$	16.8379	−	3.15134i	2.01251	−	0.376657i
$71$	−7.13214	−	12.3532i	−0.846430	−	1.46606i	−0.884374	−	0.466779i	$-0.845414\pi$
$71$	−7.13214	−	12.3532i	−0.846430	−	1.46606i	0.0379444	−	0.999280i	$-0.487919\pi$
$72$	2.35596	+	4.85083i	0.277653	+	0.571676i
$73$	−5.00425	−	5.00425i	−0.585703	−	0.585703i	0.350762	−	0.936465i	$-0.385923\pi$
$73$	−5.00425	−	5.00425i	−0.585703	−	0.585703i	−0.936465	+	0.350762i	$0.885923\pi$
$74$	3.69497	+	6.39988i	0.429532	+	0.743971i
$75$	−4.76050	+	7.23448i	−0.549695	+	0.835366i
$76$	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	$0.0163805\pi$
$79$			0.914386i			0.102876i	−0.998676	+	0.0514382i	$0.983619\pi$
$80$	−1.25646	+	3.56807i	−0.140477	+	0.398922i
$81$	−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	$-0.693773\pi$
$83$	2.26406	−	2.26406i	0.248513	−	0.248513i	0.820360	+	0.571847i	$0.193773\pi$
$84$	10.8489	−	13.1386i	1.18372	−	1.43354i
$85$	10.7070	+	0.823721i	1.16133	+	0.0893451i
$86$	−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	0.680915	−	0.732362i	$-0.261582\pi$
$89$	3.65216	+	2.10858i	0.387128	+	0.223509i	−0.293787	+	0.955871i	$0.594916\pi$
$90$	1.66846	+	14.6310i	0.175872	+	1.54224i
$91$	−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
$95$	7.84196	+	9.14914i	0.804568	+	0.938682i
$96$	4.42352	+	11.8612i	0.451474	+	1.21058i
$97$	−5.46692	−	1.46486i	−0.555081	−	0.148734i	−0.0296356	−	0.999561i	$-0.509435\pi$
$97$	−5.46692	−	1.46486i	−0.555081	−	0.148734i	−0.525446	+	0.850827i	$0.676101\pi$
$98$	−10.9815	−	2.94249i	−1.10930	−	0.297236i
$99$	−2.60480	−	3.00654i	−0.261792	−	0.302168i
$100$	8.83128	−	10.9845i	0.883128	−	1.09845i
$101$	3.23649	+	1.86859i	0.322043	+	0.185932i	0.652303	−	0.757958i	$-0.273803\pi$
$101$	3.23649	+	1.86859i	0.322043	+	0.185932i	−0.330260	+	0.943890i	$0.607136\pi$
$102$	14.8743	−	10.5912i	1.47278	−	1.04868i
$103$	1.44650	−	1.44650i	0.142528	−	0.142528i	−0.632242	−	0.774771i	$-0.717865\pi$
$103$	1.44650	−	1.44650i	0.142528	−	0.142528i	0.774771	+	0.632242i	$0.217865\pi$
$104$	−1.75911	+	6.23791i	−0.172495	+	0.611678i
$105$	11.5791	−	6.97206i	1.13000	−	0.680404i
$106$	6.54631	+	3.77951i	0.635834	+	0.367099i
$107$	−1.02751	−	3.83471i	−0.0993328	−	0.370715i	0.898308	−	0.439366i	$-0.144797\pi$
$107$	−1.02751	−	3.83471i	−0.0993328	−	0.370715i	−0.997641	+	0.0686514i	$0.978130\pi$
$108$	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	$0.570228\pi$
$110$	−0.499265	+	6.48958i	−0.0476030	+	0.618757i
$111$	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	0.697805	+	0.716288i	$0.254160\pi$
$113$	−2.81333	+	10.4995i	−0.264656	+	0.987709i	−0.962461	+	0.271421i	$0.912506\pi$
$114$	20.2059	+	3.39853i	1.89246	+	0.318301i
$115$	4.46519	−	2.13943i	0.416381	−	0.199503i
$116$			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
$120$	−0.127967	−	6.96076i	−0.0116817	−	0.635427i
$121$	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
$125$	9.50187	−	5.89190i	0.849873	−	0.526987i
$126$	7.51843	−	21.7181i	0.669795	−	1.93480i
$127$	−1.60168	+	0.429168i	−0.142126	+	0.0380825i	−0.329181	−	0.944267i	$-0.606772\pi$
$127$	−1.60168	+	0.429168i	−0.142126	+	0.0380825i	0.187055	+	0.982349i	$0.440106\pi$
$128$	−3.40999	−	12.7262i	−0.301403	−	1.12485i
$129$	−11.0855	+	4.13424i	−0.976027	+	0.363999i
$130$	−10.1887	+	14.4713i	−0.893605	+	1.26921i
$131$			6.69098i			0.584593i	0.956328	+	0.292297i	$0.0944195\pi$
$131$			6.69098i			0.584593i	−0.956328	+	0.292297i	$0.905581\pi$
$132$	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
$135$	5.26734	+	10.3564i	0.453340	+	0.891337i
$136$	−7.47614	+	4.31635i	−0.641073	+	0.370124i
$137$	−0.749428	+	2.79690i	−0.0640279	+	0.238955i	−0.990522	−	0.137354i	$-0.956140\pi$
$137$	−0.749428	+	2.79690i	−0.0640279	+	0.238955i	0.926494	+	0.376309i	$0.122807\pi$
$138$	3.49769	−	7.65814i	0.297743	−	0.651904i
$139$	2.10674	−	1.21633i	0.178692	−	0.103168i	−0.407986	−	0.912988i	$-0.633769\pi$
$139$	2.10674	−	1.21633i	0.178692	−	0.103168i	0.586678	+	0.809820i	$0.300435\pi$
$140$	−19.8376	+	9.50487i	−1.67658	+	0.803308i
$141$	−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
$145$	−3.07365	+	8.72845i	−0.255253	+	0.724858i
$146$	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	−0.548086	+	0.836422i	$0.684643\pi$
$149$	−18.8773	+	10.8988i	−1.54649	+	0.892867i	−0.998406	+	0.0564450i	$0.982023\pi$
$150$	5.98380	−	18.0446i	0.488575	−	1.47334i
$151$			23.8695i			1.94248i	0.238112	+	0.971238i	$0.423471\pi$
$151$			23.8695i			1.94248i	−0.238112	+	0.971238i	$0.576529\pi$
$152$	−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
$155$	−4.03957	−	21.5837i	−0.324466	−	1.73365i
$156$	1.44362	+	17.5445i	0.115582	+	1.40468i
$157$	−15.8944	−	15.8944i	−1.26852	−	1.26852i	−0.946855	−	0.321660i	$-0.895759\pi$
$157$	−15.8944	−	15.8944i	−1.26852	−	1.26852i	−0.321660	−	0.946855i	$-0.604241\pi$
$158$	−0.519515	−	1.93886i	−0.0413304	−	0.154247i
$159$	5.88161	+	0.989258i	0.466442	+	0.0784533i
$160$	1.25362	−	16.2948i	0.0991070	−	1.28822i
$161$	−7.72748			−0.609010
$162$	18.1605	+	7.77983i	1.42682	+	0.611241i
$163$	−4.27873	+	15.9685i	−0.335136	+	1.25075i	0.568585	+	0.822625i	$0.307491\pi$
$163$	−4.27873	+	15.9685i	−0.335136	+	1.25075i	−0.903721	+	0.428121i	$0.859176\pi$
$164$		−	5.54362i		−	0.432884i
$165$	1.42013	+	4.93528i	0.110557	+	0.384211i
$166$	−3.51436	+	6.08705i	−0.272767	+	0.472447i
$167$	−11.3555	+	3.04269i	−0.878713	+	0.235450i	−0.669852	−	0.742495i	$-0.733642\pi$
$167$	−11.3555	+	3.04269i	−0.878713	+	0.235450i	−0.208861	+	0.977945i	$0.566976\pi$
$168$	−4.51405	+	9.88347i	−0.348267	+	0.762526i
$169$	6.79195	−	11.0846i	0.522458	−	0.852665i
$170$	−23.1709	+	4.33662i	−1.77713	+	0.332604i
$171$	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	0.539711	+	0.841850i	$0.318533\pi$
$173$	−4.58535	+	17.1128i	−0.348618	+	1.30106i	−0.888329	+	0.459208i	$0.848133\pi$
$174$	5.49832	+	14.7432i	0.416827	+	1.11768i
$175$	−17.3471	+	1.88493i	−1.31132	+	0.142488i
$176$	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	−0.315870	−	0.948802i	$-0.602296\pi$
$179$	8.88040	−	15.3813i	0.663752	−	1.14965i	0.979622	−	0.200850i	$-0.0643703\pi$
$180$	−6.93211	−	17.5931i	−0.516689	−	1.31131i
$181$	−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
$185$	−3.25263	−	6.78855i	−0.239138	−	0.499104i
$186$	−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
$190$	−21.8262	−	14.9443i	−1.58344	−	1.08417i
$191$	12.5492	−	7.24527i	0.908026	−	0.524249i	0.0282306	−	0.999601i	$-0.491013\pi$
$191$	12.5492	−	7.24527i	0.908026	−	0.524249i	0.879796	+	0.475352i	$0.157679\pi$
$192$	−12.7195	−	17.8634i	−0.917949	−	1.28918i
$193$	−5.86194	+	1.57070i	−0.421951	+	0.113062i	−0.463546	−	0.886073i	$-0.653423\pi$
$193$	−5.86194	+	1.57070i	−0.421951	+	0.113062i	0.0415943	+	0.999135i	$0.486756\pi$
$194$	12.4243			0.892011
$195$	−3.54245	+	13.5074i	−0.253680	+	0.967288i
$196$	14.5989			1.04278
$197$	19.1589	−	5.13360i	1.36501	−	0.365754i	0.499358	−	0.866396i	$-0.333569\pi$
$197$	19.1589	−	5.13360i	1.36501	−	0.365754i	0.865654	+	0.500642i	$0.166903\pi$
$198$	7.23139	+	4.89510i	0.513912	+	0.347879i
$199$	−21.3830	+	12.3455i	−1.51580	+	0.875146i	−0.515970	+	0.856607i	$0.672568\pi$
$199$	−21.3830	+	12.3455i	−1.51580	+	0.875146i	−0.999828	+	0.0185397i	$0.994098\pi$
$200$	−3.62679	+	8.22358i	−0.256453	+	0.581495i
$201$	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
$205$	1.46062	−	4.14783i	0.102014	−	0.289697i
$206$	−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
$210$	−20.5910	+	21.3622i	−1.42091	+	1.47414i
$211$	8.05125	−	13.9452i	0.554271	−	0.960025i	−0.443689	−	0.896181i	$-0.646331\pi$
$211$	8.05125	−	13.9452i	0.554271	−	0.960025i	0.997960	−	0.0638442i	$-0.0203361\pi$
$212$	−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
$215$	15.2292	+	1.17163i	1.03862	+	0.0799048i
$216$	−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
$220$	−1.53756	−	8.21530i	−0.103662	−	0.553876i
$221$	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	$-0.752164\pi$
$223$	−14.5938	+	3.91041i	−0.977276	+	0.261860i	−0.265379	+	0.964144i	$0.585497\pi$
$224$	−12.7533	+	22.0893i	−0.852115	+	1.47591i
$225$	−0.551335	−	14.9899i	−0.0367557	−	0.999324i
$226$		−	23.8614i		−	1.58724i
$227$	−2.09464	+	7.81731i	−0.139026	+	0.518853i	0.860923	+	0.508736i	$0.169887\pi$
$227$	−2.09464	+	7.81731i	−0.139026	+	0.518853i	−0.999949	+	0.0101170i	$0.996780\pi$
$228$	−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	$0.271650\pi$
$230$	−8.25243	+	7.07336i	−0.544149	+	0.466404i
$231$	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	$-0.133701\pi$
$233$	7.71282	+	7.71282i	0.505284	+	0.505284i	−0.407791	+	0.913075i	$0.633701\pi$
$234$	10.0936	+	21.4925i	0.659840	+	1.40501i
$235$	9.44122	+	6.46437i	0.615877	+	0.421689i
$236$	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	$0.252096\pi$
$239$			22.0067i			1.42349i	−0.702436	+	0.711747i	$0.747904\pi$
$240$	−1.81184	−	6.29656i	−0.116954	−	0.406441i
$241$	13.0273	−	7.52130i	0.839160	−	0.484489i	−0.0178185	−	0.999841i	$-0.505672\pi$
$241$	13.0273	−	7.52130i	0.839160	−	0.484489i	0.856979	+	0.515352i	$0.172339\pi$
$242$	−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
$245$	10.9231	+	3.84649i	0.697853	+	0.245743i
$246$	−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
$250$	−16.8002	+	17.8917i	−1.06254	+	1.13157i
$251$	2.22630	−	1.28535i	0.140523	−	0.0811307i	−0.428090	−	0.903736i	$-0.640814\pi$
$251$	2.22630	−	1.28535i	0.140523	−	0.0811307i	0.568613	+	0.822605i	$0.307480\pi$
$252$	−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
$255$	−15.9342	+	9.59440i	−0.997840	+	0.600825i
$256$	1.80025	+	3.11813i	0.112516	+	0.194883i
$257$	1.15416	+	4.30737i	0.0719943	+	0.268686i	0.992535	−	0.121960i	$-0.0389181\pi$
$257$	1.15416	+	4.30737i	0.0719943	+	0.268686i	−0.920541	+	0.390647i	$0.872251\pi$
$258$	21.1568	−	15.0645i	1.31716	−	0.937877i
$259$			11.7483i			0.730003i
$260$	7.82799	−	21.3357i	0.485472	−	1.32318i
$261$	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	$-0.682422\pi$
$263$	−9.59599	+	2.57124i	−0.591714	+	0.158549i	−0.0494778	+	0.998775i	$0.515756\pi$
$264$	−3.18342	−	2.62865i	−0.195926	−	0.161782i
$265$	−6.35325	−	4.35005i	−0.390277	−	0.267221i
$266$	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	−0.910423	−	0.413678i	$-0.864244\pi$
$269$	−13.3419	−	23.1088i	−0.813467	−	1.40897i	0.0969562	−	0.995289i	$-0.469089\pi$
$270$	−17.0529	−	18.9670i	−1.03781	−	1.15429i
$271$	3.65623	+	2.11093i	0.222100	+	0.128230i	0.606922	−	0.794761i	$-0.292404\pi$
$271$	3.65623	+	2.11093i	0.222100	+	0.128230i	−0.384822	+	0.922991i	$0.625737\pi$
$272$	−5.74486	+	5.74486i	−0.348333	+	0.348333i
$273$	14.0950	−	16.6226i	0.853071	−	1.00605i
$274$		−	6.35632i		−	0.383999i
$275$	1.01413	−	6.55193i	0.0611541	−	0.395096i
$276$	−1.79317	+	10.6613i	−0.107936	+	0.641733i
$277$	4.94873	−	18.4689i	0.297340	−	1.10969i	−0.642000	−	0.766704i	$-0.721895\pi$
$277$	4.94873	−	18.4689i	0.297340	−	1.10969i	0.939341	−	0.342985i	$-0.111438\pi$
$278$	−3.77606	+	3.77606i	−0.226473	+	0.226473i
$279$	−27.8394	−	9.63755i	−1.66670	−	0.576985i
$280$	10.6504	−	9.12876i	0.636485	−	0.545548i
$281$	−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	0.999813	+	0.0193382i	$0.00615593\pi$
$283$	2.41604	+	9.01678i	0.143619	+	0.535992i	−0.856194	+	0.516654i	$0.827177\pi$
$284$	−34.8221	−	20.1045i	−2.06631	−	1.19298i
$285$	−20.2560	−	5.03040i	−1.19986	−	0.297975i
$286$	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
$290$	1.55821	−	20.2540i	0.0915013	−	1.18936i
$291$	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	$-0.542000\pi$
$293$	−12.6866	−	3.39935i	−0.741157	−	0.198592i	−0.609592	+	0.792715i	$0.708667\pi$
$294$	18.4502	−	6.88081i	1.07604	−	0.401297i
$295$	10.4666	−	8.97116i	0.609387	−	0.522321i
$296$	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
$300$	−1.42486	+	24.3705i	−0.0822642	+	1.40703i
$301$	−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
$305$	9.73396	+	11.3565i	0.557365	+	0.650272i
$306$	−10.3463	+	29.8867i	−0.591457	+	1.70851i
$307$	6.16399	−	6.16399i	0.351798	−	0.351798i	−0.508980	−	0.860778i	$-0.669977\pi$
$307$	6.16399	−	6.16399i	0.351798	−	0.351798i	0.860778	+	0.508980i	$0.169977\pi$
$308$	−3.37611	+	12.5998i	−0.192372	+	0.717941i
$309$	−0.587693	+	3.49412i	−0.0334327	+	0.198773i
$310$	20.8284	+	43.4709i	1.18298	+	2.46898i
$311$		−	7.33730i		−	0.416060i	−0.978122	−	0.208030i	$-0.933295\pi$
$311$		−	7.33730i		−	0.416060i	0.978122	−	0.208030i	$-0.0667052\pi$
$312$	−3.78487	−	10.5685i	−0.214276	−	0.598323i
$313$	−3.28923	+	3.28923i	−0.185918	+	0.185918i	−0.793929	−	0.608011i	$-0.791968\pi$
$313$	−3.28923	+	3.28923i	−0.185918	+	0.185918i	0.608011	+	0.793929i	$0.291968\pi$
$314$	42.7330	+	24.6719i	2.41156	+	1.39232i
$315$	−9.33281	+	21.4698i	−0.525844	+	1.20969i
$316$	1.28876	+	2.23221i	0.0724987	+	0.125571i
$317$	7.57102	+	7.57102i	0.425231	+	0.425231i	0.887000	−	0.461769i	$-0.152785\pi$
$317$	7.57102	+	7.57102i	0.425231	+	0.425231i	−0.461769	+	0.887000i	$0.652785\pi$
$318$	−13.0334	+	1.24407i	−0.730876	+	0.0697638i
$319$	2.74376	+	4.75233i	0.153621	+	0.266080i
$320$	5.20807	+	27.8271i	0.291140	+	1.55558i
$321$	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
$325$	11.4785	−	13.9012i	0.636714	−	0.771100i
$326$		−	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
$330$	−5.81525	−	9.65787i	−0.320119	−	0.531648i
$331$	−9.04584	+	5.22262i	−0.497204	+	0.287061i	−0.727558	−	0.686046i	$-0.759345\pi$
$331$	−9.04584	+	5.22262i	−0.497204	+	0.287061i	0.230354	+	0.973107i	$0.426012\pi$
$332$	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
$335$	−0.495146	−	1.03342i	−0.0270527	−	0.0564616i
$336$	−1.69611	+	10.0842i	−0.0925303	+	0.550137i
$337$	11.9670	+	11.9670i	0.651883	+	0.651883i	0.953446	−	0.301563i	$-0.0975084\pi$
$337$	11.9670	+	11.9670i	0.651883	+	0.651883i	−0.301563	+	0.953446i	$0.597508\pi$
$338$	−8.10377	+	27.3627i	−0.440787	+	1.48833i
$339$	−6.57879	−	17.6403i	−0.357311	−	0.958092i
$340$	27.2989	−	13.0798i	1.48049	−	0.709354i
$341$	−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
$345$	−4.15069	+	7.50447i	−0.223466	+	0.404027i
$346$		−	38.8909i		−	2.09079i
$347$	−17.4398	−	4.67299i	−0.936219	−	0.250859i	−0.241715	−	0.970347i	$-0.577710\pi$
$347$	−17.4398	−	4.67299i	−0.936219	−	0.250859i	−0.694505	+	0.719488i	$0.744376\pi$
$348$	−11.7198	−	16.4594i	−0.628246	−	0.882315i
$349$	−1.81560	+	3.14471i	−0.0971869	+	0.168333i	−0.910519	−	0.413467i	$-0.864318\pi$
$349$	−1.81560	+	3.14471i	−0.0971869	+	0.168333i	0.813332	+	0.581799i	$0.197651\pi$
$350$	35.7117	−	13.8527i	1.90887	−	0.740457i
$351$	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	$-0.00726153\pi$
$353$	2.30221	+	8.59197i	0.122534	+	0.457304i	−0.877205	+	0.480115i	$0.840595\pi$
$354$	3.88790	−	23.1155i	0.206640	−	1.22857i
$355$	−20.7573	−	24.2174i	−1.10168	−	1.28533i
$356$	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	$-0.831350\pi$
$359$		−	19.1514i		−	1.01077i	0.862893	−	0.505387i	$-0.168650\pi$
$360$	7.17359	+	9.69253i	0.378081	+	0.510841i
$361$	−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
$365$	−13.0574	−	8.94034i	−0.683454	−	0.467959i
$366$	25.0809	+	4.21848i	1.31100	+	0.220504i
$367$	−12.2124	+	3.27232i	−0.637484	+	0.170813i	−0.563064	−	0.826413i	$-0.690377\pi$
$367$	−12.2124	+	3.27232i	−0.637484	+	0.170813i	−0.0744208	+	0.997227i	$0.523711\pi$
$368$	−0.969527	+	3.61832i	−0.0505401	+	0.188618i
$369$	−3.86326	−	4.45908i	−0.201113	−	0.232131i
$370$	10.7538	+	12.5464i	0.559064	+	0.652255i
$371$	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	$-0.458016\pi$
$373$	−4.83305	−	1.29501i	−0.250246	−	0.0670531i	−0.381761	+	0.924261i	$0.624682\pi$
$374$	−6.98948	+	12.1061i	−0.361418	+	0.625994i
$375$	−7.48718	+	17.8590i	−0.386636	+	0.922232i
$376$	−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	−0.522323	−	0.852748i	$-0.674934\pi$
$379$	9.29282	−	16.0956i	0.477340	−	0.826777i	0.999663	+	0.0259707i	$0.00826766\pi$
$380$	32.0389	+	11.2822i	1.64356	+	0.578767i
$381$	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	$-0.396372\pi$
$383$	2.40884	+	0.645446i	0.123086	+	0.0329807i	−0.196750	+	0.980454i	$0.563039\pi$
$384$	17.5965	+	14.5299i	0.897967	+	0.741478i
$385$	−5.84583	+	8.53785i	−0.297931	+	0.435129i
$386$	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	$0.301529\pi$
$390$	−0.162960	−	30.6537i	−0.00825179	−	1.55221i
$391$	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
$395$	0.376137	+	2.00973i	0.0189255	+	0.101121i
$396$	−10.5964	−	3.66829i	−0.532488	−	0.184338i
$397$	2.72459	+	0.730050i	0.136743	+	0.0366402i	0.326541	−	0.945183i	$-0.394117\pi$
$397$	2.72459	+	0.730050i	0.136743	+	0.0366402i	−0.189798	+	0.981823i	$0.560783\pi$
$398$	38.3261	−	38.3261i	1.92111	−	1.92111i
$399$	25.1176	+	20.7404i	1.25745	+	1.03832i
$400$	−1.29385	+	8.35913i	−0.0646924	+	0.417956i
$401$	−15.8342	+	27.4256i	−0.790723	+	1.36957i	0.134798	+	0.990873i	$0.456962\pi$
$401$	−15.8342	+	27.4256i	−0.790723	+	1.36957i	−0.925520	+	0.378698i	$0.876372\pi$
$402$	−1.77239	−	0.809499i	−0.0883987	−	0.0403742i
$403$	−17.3014	−	30.8921i	−0.861843	−	1.53884i
$404$	10.5346			0.524116
$405$	−17.8362	−	9.32032i	−0.886290	−	0.463130i
$406$	−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	0.884087	−	0.467322i	$-0.154781\pi$
$409$	0.754968	+	1.30764i	0.0373308	+	0.0646588i	−0.846756	+	0.531981i	$0.821448\pi$
$410$	−0.740474	+	9.62489i	−0.0365694	+	0.475339i
$411$	−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
$415$	4.04486	−	5.90753i	0.198555	−	0.289989i
$416$	−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	−0.891744	−	0.452540i	$-0.850518\pi$
$419$	−1.10455	+	1.91314i	−0.0539608	+	0.0934628i	0.837783	+	0.546003i	$0.183851\pi$
$420$	18.4403	−	33.3402i	0.899795	−	1.62684i
$421$			2.54783i			0.124173i	0.998071	+	0.0620867i	$0.0197755\pi$
$421$			2.54783i			0.124173i	−0.998071	+	0.0620867i	$0.980224\pi$
$422$	−9.14875	+	34.1436i	−0.445354	+	1.66208i
$423$	13.8089	−	6.70671i	0.671409	−	0.326091i
$424$	6.18982			0.300604
$425$	23.8717	−	2.59390i	1.15795	−	0.125823i
$426$	−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
$430$	−32.9576	+	6.16827i	−1.58936	+	0.297460i
$431$	−5.28016	+	9.14551i	−0.254336	+	0.440524i	−0.964715	−	0.263296i	$-0.915190\pi$
$431$	−5.28016	+	9.14551i	−0.254336	+	0.440524i	0.710379	+	0.703820i	$0.248524\pi$
$432$	−8.54249	−	2.07336i	−0.411001	−	0.0997544i
$433$	18.7630	+	5.02752i	0.901691	+	0.241607i	0.679742	−	0.733451i	$-0.262092\pi$
$433$	18.7630	+	5.02752i	0.901691	+	0.241607i	0.221949	+	0.975058i	$0.428758\pi$
$434$		−	75.2309i		−	3.61120i
$435$	−4.43224	−	15.4031i	−0.212510	−	0.738521i
$436$	−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	−0.311115	−	0.950372i	$-0.600702\pi$
$439$	−27.0226	−	15.6015i	−1.28972	−	0.744619i	−0.978604	+	0.205753i	$0.934036\pi$
$440$	2.30298	+	4.80654i	0.109790	+	0.229143i
$441$	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	$-0.215722\pi$
$443$	3.19916	+	3.19916i	0.151997	+	0.151997i	−0.627012	+	0.779009i	$0.715722\pi$
$444$	16.2086	+	2.72621i	0.769226	+	0.129380i
$445$	8.89447	+	3.13211i	0.421638	+	0.148476i
$446$	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	−0.862280	−	0.506431i	$-0.830964\pi$
$449$	−18.1137	+	10.4579i	−0.854838	+	0.493541i	0.00744231	+	0.999972i	$0.497631\pi$
$450$	9.68565	+	31.4711i	0.456586	+	1.48356i
$451$	−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
$455$	−25.5305	+	11.8249i	−1.19689	+	0.554361i
$456$	15.7206	−	5.86285i	0.736185	−	0.274553i
$457$	−2.77860	−	10.3699i	−0.129977	−	0.485082i	0.869991	−	0.493068i	$-0.164125\pi$
$457$	−2.77860	−	10.3699i	−0.129977	−	0.485082i	−0.999968	+	0.00798609i	$0.997458\pi$
$458$	−42.1895	+	11.3046i	−1.97138	+	0.528231i
$459$	0.591179	+	24.9472i	0.0275939	+	1.16444i
$460$	7.88508	−	11.5162i	0.367644	−	0.536945i
$461$	−14.1969	−	24.5898i	−0.661216	−	1.14526i	−0.980296	−	0.197532i	$-0.936707\pi$
$461$	−14.1969	−	24.5898i	−0.661216	−	1.14526i	0.319080	−	0.947728i	$-0.396626\pi$
$462$	1.67185	+	17.5150i	0.0777813	+	0.814871i
$463$	27.9464	+	27.9464i	1.29878	+	1.29878i	0.929199	+	0.369580i	$0.120498\pi$
$463$	27.9464	+	27.9464i	1.29878	+	1.29878i	0.369580	+	0.929199i	$0.379502\pi$
$464$	−3.50056	−	6.06315i	−0.162510	−	0.281475i
$465$	27.3834	+	26.3947i	1.26987	+	1.22402i
$466$	−20.7363	−	11.9721i	−0.960591	−	0.554597i
$467$	−6.29228	+	6.29228i	−0.291172	+	0.291172i	−0.837543	−	0.546371i	$-0.816009\pi$
$467$	−6.29228	+	6.29228i	−0.291172	+	0.291172i	0.546371	+	0.837543i	$0.316009\pi$
$468$	−19.6627	−	23.3036i	−0.908909	−	1.07721i
$469$			1.78844i			0.0825823i
$470$	−23.6919	−	8.34289i	−1.09282	−	0.384829i
$471$	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
$475$	20.9994	+	16.8831i	0.963519	+	0.774650i
$476$	−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	0.489514	−	0.871995i	$-0.337174\pi$
$479$	−0.457393	−	0.264076i	−0.0208988	−	0.0120659i	−0.510413	+	0.859929i	$0.670507\pi$
$480$	14.6016	+	24.2502i	0.666471	+	1.10686i
$481$	−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
$485$	−12.6183	−	0.970770i	−0.572969	−	0.0440804i
$486$	−33.4389	+	7.26793i	−1.51682	+	0.329680i
$487$	4.72696	+	1.26659i	0.214199	+	0.0573945i	0.364323	−	0.931273i	$-0.381300\pi$
$487$	4.72696	+	1.26659i	0.214199	+	0.0573945i	−0.150124	+	0.988667i	$0.547967\pi$
$488$	−11.6144	−	3.11206i	−0.525758	−	0.140876i
$489$	−10.0055	−	26.8288i	−0.452466	−	1.21324i
$490$	−25.3467	−	1.95001i	−1.14505	−	0.0880923i
$491$	15.6499	+	9.03548i	0.706271	+	0.407766i	0.809679	−	0.586874i	$-0.199641\pi$
$491$	15.6499	+	9.03548i	0.706271	+	0.407766i	−0.103408	+	0.994639i	$0.532975\pi$
$492$	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
$495$	−6.96186	−	5.53658i	−0.312912	−	0.248851i
$496$	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	$0.630643\pi$
$500$	14.8918	−	27.7756i	0.665982	−	1.24216i
$501$	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	−0.662535	−	0.749031i	$-0.730519\pi$
$503$	6.40876	−	23.9178i	0.285753	−	1.06644i	0.948288	−	0.317412i	$-0.102814\pi$
$504$	−3.56032	−	18.4798i	−0.158589	−	0.823156i
$505$	7.88216	+	2.77564i	0.350752	+	0.123514i
$506$			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	0.998795	−	0.0490835i	$-0.0156300\pi$
$509$	32.8417	+	18.9612i	1.45568	+	0.840440i	0.456890	+	0.889523i	$0.348963\pi$
$510$	28.3357	−	29.3970i	1.25472	−	1.30172i
$511$	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
$515$	2.58425	−	3.77430i	0.113876	−	0.166316i
$516$	−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
$520$	−1.30036	+	14.4340i	−0.0570247	+	0.632971i
$521$		−	4.36775i		−	0.191355i	−0.995412	−	0.0956773i	$-0.969498\pi$
$521$		−	4.36775i		−	0.191355i	0.995412	−	0.0956773i	$-0.0305017\pi$
$522$	−22.5693	−	15.2777i	−0.987829	−	0.668685i
$523$	−5.72006	−	21.3475i	−0.250121	−	0.933463i	−0.970740	−	0.240132i	$-0.922809\pi$
$523$	−5.72006	−	21.3475i	−0.250121	−	0.933463i	0.720619	−	0.693331i	$-0.243857\pi$
$524$	9.43048	+	16.3341i	0.411972	+	0.713557i
$525$	22.5817	−	20.0871i	0.985548	−	0.876671i
$526$	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
$530$	15.9429	+	5.61416i	0.692515	+	0.243863i
$531$	−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
$535$	−3.83579	−	8.00565i	−0.165836	−	0.346114i
$536$	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
$540$	27.4553	+	17.8582i	1.18149	+	0.768494i
$541$			3.55250i			0.152734i	0.997080	+	0.0763670i	$0.0243321\pi$
$541$			3.55250i			0.152734i	−0.997080	+	0.0763670i	$0.975668\pi$
$542$	−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
$545$	−10.0435	+	1.87972i	−0.430216	+	0.0805183i
$546$	−20.4428	+	43.2546i	−0.874870	+	1.85113i
$547$	15.5692	+	15.5692i	0.665690	+	0.665690i	0.956715	−	0.291026i	$-0.0939965\pi$
$547$	15.5692	+	15.5692i	0.665690	+	0.665690i	−0.291026	+	0.956715i	$0.593997\pi$
$548$	2.11253	+	7.88409i	0.0902430	+	0.336791i
$549$	19.7049	−	3.79636i	0.840986	−	0.162024i
$550$	1.57218	+	14.4688i	0.0670381	+	0.616954i
$551$	−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
$555$	11.4092	+	6.31040i	0.484295	+	0.267862i
$556$	3.42867	−	5.93863i	0.145408	−	0.251854i
$557$	−0.786720	+	0.210801i	−0.0333344	+	0.00893192i	−0.275448	−	0.961316i	$-0.588826\pi$
$557$	−0.786720	+	0.210801i	−0.0333344	+	0.00893192i	0.242113	+	0.970248i	$0.422159\pi$
$558$	64.5062	+	4.61821i	2.73076	+	0.195504i
$559$	23.8710	−	6.06307i	1.00963	−	0.256440i
$560$	7.45827	−	10.8928i	0.315169	−	0.460305i
$561$	−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	$-0.951195\pi$
$563$	−1.32972	+	4.96257i	−0.0560408	+	0.209147i	0.932228	+	0.361871i	$0.117862\pi$
$564$	−23.4090	+	8.73015i	−0.985696	+	0.367605i
$565$	−1.86441	+	24.2342i	−0.0784365	+	1.01954i
$566$	−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	0.284407	+	0.958704i	$0.408203\pi$
$569$	−16.4127	+	28.4277i	−0.688058	+	1.19175i	−0.972465	+	0.233048i	$0.925130\pi$
$570$	45.8086	−	0.842148i	1.91871	−	0.0352737i
$571$	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
$575$	8.93400	−	6.53904i	0.372574	−	0.272697i
$576$	35.8924	+	12.4253i	1.49552	+	0.517723i
$577$	−20.5537	+	20.5537i	−0.855660	+	0.855660i	−0.990823	−	0.135163i	$-0.956844\pi$
$577$	−20.5537	+	20.5537i	−0.855660	+	0.855660i	0.135163	+	0.990823i	$0.456844\pi$
$578$	−12.8569	−	3.44501i	−0.534778	−	0.143293i
$579$	6.69275	−	8.10526i	0.278141	−	0.336843i
$580$	4.79874	+	25.6401i	0.199257	+	1.06465i
$581$	−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
$585$	−8.57195	−	22.6168i	−0.354407	−	0.935091i
$586$	28.8318			1.19103
$587$	−41.5931	+	11.1448i	−1.71673	+	0.459997i	−0.977059	−	0.212969i	$-0.931687\pi$
$587$	−41.5931	+	11.1448i	−1.71673	+	0.459997i	−0.739673	+	0.672966i	$0.765020\pi$
$588$	−20.5979	+	14.6666i	−0.849444	+	0.604840i
$589$	45.8301	−	26.4600i	1.88840	−	1.09027i
$590$	−17.0962	+	24.9690i	−0.703840	+	1.02796i
$591$	−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	$-0.940370\pi$
$593$	−19.3903	+	19.3903i	−0.796265	+	0.796265i	0.186239	+	0.982504i	$0.440370\pi$
$594$	−15.1207	+	0.358319i	−0.620411	+	0.0147020i
$595$	−35.3484	−	12.4476i	−1.44914	−	0.510303i
$596$	−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	$0.203017\pi$
$600$	−3.14460	−	15.2464i	−0.128378	−	0.622433i
$601$	3.77677	−	6.54156i	0.154058	−	0.266836i	−0.778658	−	0.627449i	$-0.784099\pi$
$601$	3.77677	−	6.54156i	0.154058	−	0.266836i	0.932715	+	0.360613i	$0.117433\pi$
$602$	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
$605$	13.4486	+	15.6903i	0.546762	+	0.637902i
$606$	13.3137	−	4.96522i	0.540833	−	0.201698i
$607$	−5.94776	+	22.1974i	−0.241412	+	0.900963i	0.733741	+	0.679430i	$0.237773\pi$
$607$	−5.94776	+	22.1974i	−0.241412	+	0.900963i	−0.975153	+	0.221533i	$0.928894\pi$
$608$	38.0446	−	10.1940i	1.54291	−	0.413422i
$609$	−4.14914	+	24.6686i	−0.168132	+	0.999622i
$610$	−27.0921	−	18.5499i	−1.09693	−	0.751062i
$611$	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	$-0.392474\pi$
$613$	26.9913	−	7.23231i	1.09017	−	0.292110i	0.758756	+	0.651375i	$0.225808\pi$
$614$	−9.56797	+	16.5722i	−0.386132	+	0.668800i
$615$	2.10624	+	7.31966i	0.0849317	+	0.295157i
$616$		−	8.31822i		−	0.335151i
$617$	4.94472	−	18.4539i	0.199067	−	0.742928i	−0.792110	−	0.610379i	$-0.791017\pi$
$617$	4.94472	−	18.4539i	0.199067	−	0.742928i	0.991176	−	0.132549i	$-0.0423161\pi$
$618$	−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	$0.391686\pi$
$620$	−40.2822	−	46.9969i	−1.61777	−	1.88744i
$621$	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
$625$	18.4605	−	16.8585i	0.738422	−	0.674339i
$626$	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
$630$	7.59096	−	50.8270i	0.302431	−	2.02499i
$631$	20.1472	−	11.6320i	0.802047	−	0.463062i	−0.0421393	−	0.999112i	$-0.513417\pi$
$631$	20.1472	−	11.6320i	0.802047	−	0.463062i	0.844186	+	0.536050i	$0.180084\pi$
$632$	−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
$635$	−3.34379	+	1.60213i	−0.132694	+	0.0635785i
$636$	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
$640$	−12.7298	−	26.5684i	−0.503191	−	1.05021i
$641$	15.4235	−	8.90479i	0.609193	−	0.351718i	−0.163456	−	0.986551i	$-0.552264\pi$
$641$	15.4235	−	8.90479i	0.609193	−	0.351718i	0.772650	+	0.634833i	$0.218931\pi$
$642$	−13.7303	−	6.27101i	−0.541892	−	0.247497i
$643$	4.91502	−	18.3431i	0.193829	−	0.723381i	−0.798737	−	0.601680i	$-0.794498\pi$
$643$	4.91502	−	18.3431i	0.193829	−	0.723381i	0.992567	−	0.121701i	$-0.0388350\pi$
$644$	−18.8644	+	10.8914i	−0.743361	+	0.429179i
$645$	−22.6643	+	13.6468i	−0.892406	+	0.537340i
$646$	−28.4058	−	49.2003i	−1.11761	−	1.93576i
$647$	−4.34268	−	16.2071i	−0.170728	−	0.637167i	−0.997240	−	0.0742469i	$-0.976345\pi$
$647$	−4.34268	−	16.2071i	−0.170728	−	0.637167i	0.826512	−	0.562920i	$-0.190322\pi$
$648$	16.0639	−	1.91835i	0.631051	−	0.0753599i
$649$		−	8.17462i		−	0.320882i
$650$	−16.4409	+	35.9976i	−0.644864	+	1.41194i
$651$	−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	$-0.424281\pi$
$653$	23.6534	−	6.33792i	0.925630	−	0.248022i	0.689990	+	0.723818i	$0.257615\pi$
$654$	−11.0626	+	13.3973i	−0.432581	+	0.523877i
$655$	2.75237	+	14.7061i	0.107544	+	0.574616i
$656$	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	0.971144	−	0.238495i	$-0.0766542\pi$
$659$	7.16295	+	12.4066i	0.279029	+	0.483292i	−0.692115	+	0.721787i	$0.743321\pi$
$660$	10.4228	+	10.0465i	0.405706	+	0.391058i
$661$	−21.7429	−	12.5533i	−0.845700	−	0.488265i	0.0134974	−	0.999909i	$-0.495704\pi$
$661$	−21.7429	−	12.5533i	−0.845700	−	0.488265i	−0.859198	+	0.511644i	$0.829037\pi$
$662$	16.2135	−	16.2135i	0.630154	−	0.630154i
$663$	−19.3965	+	22.8747i	−0.753297	+	0.888380i
$664$			5.75557i			0.223359i
$665$	−18.1708	−	37.9242i	−0.704635	−	1.47064i
$666$	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
$670$	1.63705	+	1.90993i	0.0632447	+	0.0737870i
$671$	8.86969			0.342410
$672$	−4.19788	−	43.9788i	−0.161937	−	1.69652i
$673$	5.86395	+	21.8845i	0.226038	+	0.843587i	0.981986	+	0.188955i	$0.0605099\pi$
$673$	5.86395	+	21.8845i	0.226038	+	0.843587i	−0.755947	+	0.654632i	$0.772823\pi$
$674$	−32.1738	−	18.5756i	−1.23929	−	0.715504i
$675$	15.8373	+	20.5956i	0.609577	+	0.792727i
$676$	0.957496	−	36.6327i	0.0368268	−	1.40895i
$677$	5.82836	−	5.82836i	0.224002	−	0.224002i	−0.586179	−	0.810181i	$-0.699369\pi$
$677$	5.82836	−	5.82836i	0.224002	−	0.224002i	0.810181	+	0.586179i	$0.199369\pi$
$678$	23.9721	+	33.6666i	0.920643	+	1.29296i
$679$	17.1055	+	9.87585i	0.656448	+	0.379000i
$680$	−14.6563	+	12.5623i	−0.562043	+	0.481741i
$681$	−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	$-0.414274\pi$
$683$	0.379453	+	0.101674i	0.0145194	+	0.00389045i	−0.251552	+	0.967844i	$0.580941\pi$
$684$	34.4432	−	29.8409i	1.31697	−	1.14099i
$685$	−0.496651	+	6.45561i	−0.0189761	+	0.246656i
$686$	−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
$690$	4.53737	−	18.2707i	0.172735	−	0.695552i
$691$	17.3238	+	10.0019i	0.659029	+	0.380491i	0.791907	−	0.610642i	$-0.209088\pi$
$691$	17.3238	+	10.0019i	0.659029	+	0.380491i	−0.132878	+	0.991132i	$0.542422\pi$
$692$	12.9255	+	48.2385i	0.491353	+	1.83375i
$693$	6.06499	+	12.4876i	0.230390	+	0.474364i
$694$	39.6343			1.50450
$695$	4.13008	−	3.54000i	0.156663	−	0.134280i
$696$	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
$700$	−39.6912	+	29.0511i	−1.50019	+	1.09803i
$701$			30.5041i			1.15212i	0.817406	+	0.576062i	$0.195411\pi$
$701$			30.5041i			1.15212i	−0.817406	+	0.576062i	$0.804589\pi$
$702$	−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
$705$	−19.8152	+	0.364283i	−0.746283	+	0.0137197i
$706$	−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	0.767189	−	0.641421i	$-0.221655\pi$
$709$	−4.57699	−	7.92757i	−0.171892	−	0.297726i	−0.939081	+	0.343695i	$0.888321\pi$
$710$	57.7730	+	39.5569i	2.16818	+	1.48454i
$711$	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
$715$	−1.82920	−	10.5328i	−0.0684081	−	0.393905i
$716$		−	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	0.568661	−	0.822572i	$-0.307462\pi$
$719$	−11.4775	−	19.8796i	−0.428038	−	0.741383i	−0.996699	+	0.0811891i	$0.974128\pi$
$720$	8.88213	+	7.06372i	0.331017	+	0.263249i
$721$	−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
$725$	−3.16510	+	20.4487i	−0.117549	+	0.759444i
$726$	34.6521	+	5.82831i	1.28606	+	0.216309i
$727$	−26.3876	−	26.3876i	−0.978663	−	0.978663i	0.0211144	−	0.999777i	$-0.493279\pi$
$727$	−26.3876	−	26.3876i	−0.978663	−	0.978663i	−0.999777	+	0.0211144i	$0.993279\pi$
$728$	11.5642	−	19.4387i	0.428596	−	0.720445i
$729$	−22.7170	+	14.5924i	−0.841369	+	0.540460i
$730$	32.7663	+	11.5384i	1.21273	+	0.427054i
$731$	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	−0.993546	−	0.113427i	$-0.963817\pi$
$733$	−29.9702	−	29.9702i	−1.10697	−	1.10697i	−0.113427	−	0.993546i	$-0.536183\pi$
$734$	24.0360	−	13.8772i	0.887184	−	0.512216i
$735$	−19.2760	+	5.54669i	−0.711007	+	0.204593i
$736$		−	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	−0.662941	−	0.748672i	$-0.730692\pi$
$739$	8.61473	−	14.9212i	0.316898	−	0.548884i	0.979839	+	0.199788i	$0.0640253\pi$
$740$	−17.5083	−	11.9879i	−0.643620	−	0.440684i
$741$	−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	−0.994103	−	0.108435i	$-0.965416\pi$
$743$	−5.10822	−	19.0641i	−0.187402	−	0.699395i	0.806701	−	0.590960i	$-0.201251\pi$
$744$	−30.1512	−	5.07129i	−1.10540	−	0.185922i
$745$	−37.0073	+	31.7199i	−1.35584	+	1.16213i
$746$	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
$750$	5.72907	−	42.1219i	0.209196	−	1.53807i
$751$	19.4070	−	33.6140i	0.708173	−	1.22659i	−0.257362	−	0.966315i	$-0.582853\pi$
$751$	19.4070	−	33.6140i	0.708173	−	1.22659i	0.965534	−	0.260276i	$-0.0838135\pi$
$752$	−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
$755$	9.81885	+	52.4630i	0.357345	+	1.90932i
$756$	−26.5999	−	43.6503i	−0.967427	−	1.58755i
$757$	−48.9488	+	13.1158i	−1.77908	+	0.476702i	−0.990415	−	0.138126i	$-0.955892\pi$
$757$	−48.9488	+	13.1158i	−1.77908	+	0.476702i	−0.788661	+	0.614828i	$0.789225\pi$
$758$	−10.5596	+	39.4088i	−0.383541	+	1.43139i
$759$	1.77703	+	4.76491i	0.0645020	+	0.172955i
$760$	−21.5969	−	1.66152i	−0.783400	−	0.0602696i
$761$	−6.65465	−	11.5262i	−0.241231	−	0.417824i	0.719834	−	0.694146i	$-0.244218\pi$
$761$	−6.65465	−	11.5262i	−0.241231	−	0.417824i	−0.961065	+	0.276322i	$0.910884\pi$
$762$	−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
$765$	12.8431	−	29.5451i	0.464342	−	1.06820i
$766$	−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	0.178862	+	0.983874i	$0.442758\pi$
$769$	−21.1483	+	36.6300i	−0.762629	+	1.32091i	−0.941491	+	0.337038i	$0.890575\pi$
$770$	7.54461	−	21.4249i	0.271889	−	0.772101i
$771$	−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	$-0.589307\pi$
$773$	−27.7237	−	7.42855i	−0.997153	−	0.267186i	−0.720252	+	0.693712i	$0.755974\pi$
$774$	−14.7162	+	42.5098i	−0.528962	+	1.52798i
$775$	−17.7572	−	45.7773i	−0.637856	−	1.64437i
$776$	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
$780$	10.3900	+	37.9673i	0.372020	+	1.35945i
$781$	−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
$785$	−41.4728	−	28.3962i	−1.48023	−	1.01350i
$786$	19.6169	+	16.1983i	0.699713	+	0.577774i
$787$	−19.3070	−	5.17330i	−0.688221	−	0.184408i	−0.102272	−	0.994756i	$-0.532611\pi$
$787$	−19.3070	−	5.17330i	−0.688221	−	0.184408i	−0.585948	+	0.810348i	$0.699278\pi$
$788$	39.5353	−	39.5353i	1.40839	−	1.40839i
$789$	10.9560	−	13.2683i	0.390046	−	0.472365i
$790$	−1.93940	−	4.04772i	−0.0690008	−	0.144011i
$791$	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
$795$	13.3342	−	0.245136i	0.472914	−	0.00869408i
$796$	−34.8002	+	60.2757i	−1.23346	+	2.13641i
$797$	29.9034	+	8.01258i	1.05923	+	0.283820i	0.746062	−	0.665877i	$-0.231942\pi$
$797$	29.9034	+	8.01258i	1.05923	+	0.283820i	0.313170	+	0.949697i	$0.398609\pi$
$798$	−65.0429	−	29.7069i	−2.30250	−	1.05161i
$799$	12.2873	+	21.2823i	0.434695	+	0.752914i
$800$	−3.94763	−	36.3302i	−0.139570	−	1.28447i
$801$	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
$805$	−16.9843	+	3.17874i	−0.598617	+	0.112036i
$806$	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	−0.899836	−	0.436228i	$-0.856314\pi$
$809$	−2.05170	+	3.55365i	−0.0721340	+	0.124940i	0.827702	+	0.561167i	$0.189648\pi$
$810$	43.1152	+	9.62894i	1.51491	+	0.338326i
$811$			8.34467i			0.293021i	0.989209	+	0.146510i	$0.0468042\pi$
$811$			8.34467i			0.293021i	−0.989209	+	0.146510i	$0.953196\pi$
$812$	10.5369	−	39.3242i	0.369772	−	1.38001i
$813$	−7.27938	+	0.694834i	−0.255299	+	0.0243689i
$814$	9.79899			0.343454
$815$	−2.83555	+	36.8572i	−0.0993249	+	1.29105i
$816$	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
$820$	−2.28040	−	12.1844i	−0.0796350	−	0.425496i
$821$	−14.5480	+	25.1979i	−0.507730	+	0.879414i	0.492230	+	0.870465i	$0.336182\pi$
$821$	−14.5480	+	25.1979i	−0.507730	+	0.879414i	−0.999960	+	0.00894856i	$0.997152\pi$
$822$	6.38580	+	8.96828i	0.222730	+	0.312805i
$823$	7.06632	+	1.89342i	0.246317	+	0.0660003i	0.379865	−	0.925042i	$-0.375970\pi$
$823$	7.06632	+	1.89342i	0.246317	+	0.0660003i	−0.133548	+	0.991042i	$0.542637\pi$
$824$			3.67721i			0.128102i
$825$	5.15146	+	10.2631i	0.179351	+	0.357315i
$826$	40.9012	−	23.6143i	1.42313	−	0.821647i
$827$	3.39420	+	3.39420i	0.118028	+	0.118028i	0.763654	−	0.645626i	$-0.223403\pi$
$827$	3.39420	+	3.39420i	0.118028	+	0.118028i	−0.645626	+	0.763654i	$0.723403\pi$
$828$	−8.18069	−	16.8437i	−0.284298	−	0.585360i
$829$	31.8232	+	18.3731i	1.10527	+	0.638125i	0.937599	−	0.347719i	$-0.113044\pi$
$829$	31.8232	+	18.3731i	1.10527	+	0.638125i	0.167666	+	0.985844i	$0.446377\pi$
$830$	−5.22029	+	14.8244i	−0.181199	+	0.514563i
$831$	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
$835$	−23.7066	+	11.3587i	−0.820401	+	0.393083i
$836$	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	−0.999895	−	0.0144808i	$-0.995390\pi$
$839$	−43.0804	+	24.8725i	−1.48730	+	0.858694i	−0.487407	+	0.873175i	$0.662057\pi$
$840$	−5.85585	+	23.5798i	−0.202046	+	0.813580i
$841$	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
$845$	10.3683	−	27.1569i	0.356681	−	0.934226i
$846$	−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
$850$	−49.1436	+	19.0630i	−1.68561	+	0.653854i
$851$	−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	$-0.303701\pi$
$853$	−6.93524	−	6.93524i	−0.237458	−	0.237458i	−0.815797	+	0.578339i	$0.803701\pi$
$854$	25.6222	+	44.3789i	0.876773	+	1.51862i
$855$	33.6333	−	13.2524i	1.15024	−	0.453222i
$856$	6.18021	+	3.56815i	0.211235	+	0.121957i
$857$	−7.66857	+	7.66857i	−0.261953	+	0.261953i	−0.825847	−	0.563894i	$-0.809303\pi$
$857$	−7.66857	+	7.66857i	−0.261953	+	0.261953i	0.563894	+	0.825847i	$0.309303\pi$
$858$	−13.8645	−	11.7564i	−0.473328	−	0.401356i
$859$		−	2.92998i		−	0.0999695i	−0.998750	−	0.0499847i	$-0.984083\pi$
$859$		−	2.92998i		−	0.0999695i	0.998750	−	0.0499847i	$-0.0159173\pi$
$860$	38.8290	−	18.6043i	1.32406	−	0.634403i
$861$	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	$-0.711586\pi$
$863$	5.00161	−	5.00161i	0.170257	−	0.170257i	0.787092	+	0.616835i	$0.211586\pi$
$864$	37.9670	−	0.899711i	1.29166	−	0.0306088i
$865$	−3.03874	+	39.4984i	−0.103320	+	1.34299i
$866$	−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
$870$	18.1495	+	30.1423i	0.615324	+	1.02192i
$871$	−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
$875$	−37.3519	+	11.2787i	−1.26273	+	0.381291i
$876$	32.3751	−	12.0740i	1.09385	−	0.407941i
$877$	−8.91238	−	2.38806i	−0.300950	−	0.0806392i	0.105184	−	0.994453i	$-0.466457\pi$
$877$	−8.91238	−	2.38806i	−0.300950	−	0.0806392i	−0.406134	+	0.913814i	$0.633123\pi$
$878$	66.1626	+	17.7282i	2.23288	+	0.598299i
$879$	21.3149	−	7.94917i	0.718933	−	0.268119i
$880$	3.26433	+	3.80846i	0.110040	+	0.128383i
$881$	−9.32780	−	5.38541i	−0.314261	−	0.181439i	0.334570	−	0.942371i	$-0.391409\pi$
$881$	−9.32780	−	5.38541i	−0.314261	−	0.181439i	−0.648832	+	0.760932i	$0.724742\pi$
$882$	−19.1191	+	28.2441i	−0.643773	+	0.951027i
$883$	3.44423	−	3.44423i	0.115907	−	0.115907i	−0.646774	−	0.762682i	$-0.723882\pi$
$883$	3.44423	−	3.44423i	0.115907	−	0.115907i	0.762682	+	0.646774i	$0.223882\pi$
$884$	34.9618	−	34.0599i	1.17589	−	1.14556i
$885$	−5.75476	+	23.1727i	−0.193444	+	0.778943i
$886$	−8.60111	−	4.96585i	−0.288960	−	0.166831i
$887$	−13.3630	−	49.8713i	−0.448685	−	1.67451i	−0.706020	−	0.708192i	$-0.749511\pi$
$887$	−13.3630	−	49.8713i	−0.448685	−	1.67451i	0.257335	−	0.966322i	$-0.417156\pi$
$888$	−10.4338	+	0.995934i	−0.350137	+	0.0334214i
$889$	5.78678			0.194082
$890$	−20.6393	−	1.58785i	−0.691831	−	0.0532248i
$891$	−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
$895$	13.1911	−	37.4596i	0.440930	−	1.25214i
$896$			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
$900$	−22.4731	−	35.8163i	−0.749104	−	1.19388i
$901$	−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
$905$	−23.1592	+	4.33442i	−0.769837	+	0.144081i
$906$	69.9819	+	57.7862i	2.32499	+	1.91982i
$907$	−43.5204	+	11.6613i	−1.44507	+	0.387206i	−0.894306	−	0.447455i	$-0.852330\pi$
$907$	−43.5204	+	11.6613i	−1.44507	+	0.387206i	−0.550765	+	0.834661i	$0.685664\pi$
$908$	5.90451	+	22.0359i	0.195948	+	0.731288i
$909$	8.47365	−	7.34140i	0.281053	−	0.243499i
$910$	47.4162	−	39.5788i	1.57183	−	1.31202i
$911$			22.6957i			0.751941i	0.926632	+	0.375971i	$0.122691\pi$
$911$			22.6957i			0.751941i	−0.926632	+	0.375971i	$0.877309\pi$
$912$	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
$915$	−25.1431	−	6.24407i	−0.831204	−	0.206423i
$916$	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	−0.957848	−	0.287274i	$-0.907251\pi$
$919$	−36.0138	+	20.7926i	−1.18799	+	0.685884i	−0.230137	+	0.973158i	$0.573918\pi$
$920$	−2.95621	+	8.39493i	−0.0974632	+	0.276773i
$921$	−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
$925$	−9.94148	−	13.5826i	−0.326874	−	0.446593i
$926$	−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	−0.441100	−	0.897458i	$-0.645411\pi$
$929$	3.52259	−	2.03377i	0.115572	−	0.0667257i	0.556672	+	0.830732i	$0.312078\pi$
$930$	−73.0598	−	40.4091i	−2.39572	−	1.32506i
$931$			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
$935$	8.04457	−	11.7491i	0.263086	−	0.384237i
$936$	15.9577	+	11.1089i	0.521592	+	0.363105i
$937$	28.3766	+	28.3766i	0.927022	+	0.927022i	0.997512	−	0.0704901i	$-0.0224563\pi$
$937$	28.3766	+	28.3766i	0.927022	+	0.927022i	−0.0704901	+	0.997512i	$0.522456\pi$
$938$	−1.01611	−	3.79218i	−0.0331772	−	0.123819i
$939$	1.33637	−	7.94534i	0.0436107	−	0.259286i
$940$	32.1591	+	2.47410i	1.04891	+	0.0806963i
$941$	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
$945$	−8.40153	−	39.6684i	−0.273302	−	1.29041i
$946$	−9.94161	+	17.2194i	−0.323230	+	0.559850i
$947$	44.1667	−	11.8344i	1.43523	−	0.384568i	0.544367	−	0.838847i	$-0.316770\pi$
$947$	44.1667	−	11.8344i	1.43523	−	0.384568i	0.890859	+	0.454279i	$0.150103\pi$
$948$	−4.06090	−	1.85473i	−0.131892	−	0.0602388i
$949$	−24.5589	−	6.92569i	−0.797215	−	0.224817i
$950$	−54.1193	−	23.8678i	−1.75586	−	0.774375i
$951$	−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	−0.655567	−	0.755137i	$-0.727571\pi$
$953$	8.94444	−	33.3811i	0.289739	−	1.08132i	0.945306	−	0.326184i	$-0.105763\pi$
$954$	17.1393	−	14.8491i	0.554904	−	0.480758i
$955$	24.6015	−	21.0866i	0.796086	−	0.682346i
$956$	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
$960$	−35.3044	−	34.0297i	−1.13944	−	1.09830i
$961$	−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
$965$	−12.2379	+	5.86359i	−0.393951	+	0.188756i
$966$	−18.7076	+	22.6558i	−0.601907	+	0.728939i
$967$	24.2775	−	24.2775i	0.780713	−	0.780713i	−0.199238	−	0.979951i	$-0.563847\pi$
$967$	24.2775	−	24.2775i	0.780713	−	0.780713i	0.979951	+	0.199238i	$0.0638468\pi$
$968$	−16.0466	−	4.29967i	−0.515756	−	0.138196i
$969$	−34.5649	−	28.5412i	−1.11038	−	0.916876i
$970$	27.3074	−	5.11079i	0.876787	−	0.164097i
$971$	−46.2260	+	26.6886i	−1.48346	+	0.856478i	−0.999823	−	0.0187889i	$-0.994019\pi$
$971$	−46.2260	+	26.6886i	−1.48346	+	0.856478i	−0.483640	+	0.875267i	$0.660686\pi$
$972$	39.0606	−	20.1283i	1.25287	−	0.645615i
$973$	−8.20032	+	2.19727i	−0.262890	+	0.0704412i
$974$	−10.7426			−0.344216
$975$	−2.22963	+	31.1453i	−0.0714051	+	0.997447i
$976$	−11.3162			−0.362222
$977$	13.4430	−	3.60204i	0.430080	−	0.115240i	−0.0372838	−	0.999305i	$-0.511871\pi$
$977$	13.4430	−	3.60204i	0.430080	−	0.115240i	0.467364	+	0.884065i	$0.345204\pi$
$978$	36.4587	+	51.2029i	1.16582	+	1.63729i
$979$	4.84273	−	2.79595i	0.154774	−	0.0893590i
$980$	32.0870	−	6.00533i	1.02498	−	0.191833i
$981$	−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	0.0599577	−	0.998201i	$-0.480903\pi$
$983$	33.1763	−	33.1763i	1.05816	−	1.05816i	0.998201	−	0.0599577i	$-0.0190966\pi$
$984$	−4.72143	−	3.89863i	−0.150514	−	0.124284i
$985$	39.9976	−	19.1643i	1.27443	−	0.610624i
$986$	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
$990$	17.9075	+	7.78429i	0.569139	+	0.247401i
$991$	−14.0717	+	24.3729i	−0.447002	+	0.774231i	−0.998189	−	0.0601511i	$-0.980842\pi$
$991$	−14.0717	+	24.3729i	−0.447002	+	0.774231i	0.551187	+	0.834382i	$0.314175\pi$
$992$	−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
$995$	−41.9194	+	35.9301i	−1.32893	+	1.13906i
$996$	5.46260	+	14.6474i	0.173089	+	0.464121i
$997$	−1.87355	+	6.99220i	−0.0593361	+	0.221445i	−0.989227	−	0.146390i	$-0.953234\pi$
$997$	−1.87355	+	6.99220i	−0.0593361	+	0.221445i	0.929891	+	0.367836i	$0.119901\pi$
$998$	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	195.2.bf.a.17.3	✓	96
3.2	odd	2	inner	195.2.bf.a.17.22	yes	96
5.2	odd	4		975.2.bn.d.368.3		96
5.3	odd	4	inner	195.2.bf.a.173.22	yes	96
5.4	even	2		975.2.bn.d.407.22		96
13.10	even	6	inner	195.2.bf.a.62.3	yes	96
15.2	even	4		975.2.bn.d.368.22		96
15.8	even	4	inner	195.2.bf.a.173.3	yes	96
15.14	odd	2		975.2.bn.d.407.3		96
39.23	odd	6	inner	195.2.bf.a.62.22	yes	96
65.23	odd	12	inner	195.2.bf.a.23.22	yes	96
65.49	even	6		975.2.bn.d.257.22		96
65.62	odd	12		975.2.bn.d.218.3		96
195.23	even	12	inner	195.2.bf.a.23.3	yes	96
195.62	even	12		975.2.bn.d.218.22		96
195.179	odd	6		975.2.bn.d.257.3		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.3	✓	96	1.1	even	1	trivial
195.2.bf.a.17.22	yes	96	3.2	odd	2	inner
195.2.bf.a.23.3	yes	96	195.23	even	12	inner
195.2.bf.a.23.22	yes	96	65.23	odd	12	inner
195.2.bf.a.62.3	yes	96	13.10	even	6	inner
195.2.bf.a.62.22	yes	96	39.23	odd	6	inner
195.2.bf.a.173.3	yes	96	15.8	even	4	inner
195.2.bf.a.173.22	yes	96	5.3	odd	4	inner
975.2.bn.d.218.3		96	65.62	odd	12
975.2.bn.d.218.22		96	195.62	even	12
975.2.bn.d.257.3		96	195.179	odd	6
975.2.bn.d.257.22		96	65.49	even	6
975.2.bn.d.368.3		96	5.2	odd	4
975.2.bn.d.368.22		96	15.2	even	4
975.2.bn.d.407.3		96	15.14	odd	2
975.2.bn.d.407.22		96	5.4	even	2

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.bf (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} +(2.19791 - 0.411355i) q^{5} +(2.42092 - 2.93185i) q^{6} +(-3.37093 - 0.903238i) q^{7} +(-1.27107 + 1.27107i) q^{8} +(0.981406 - 2.83493i) q^{9} +(-4.42671 + 2.12099i) q^{10} +(0.662995 - 1.14834i) q^{11} +(-2.02839 + 4.44113i) q^{12} +(3.14579 - 1.76182i) q^{13} +7.66087 q^{14} +(-2.68781 + 2.78849i) q^{15} +(-0.845867 + 1.46508i) q^{16} +(4.63881 + 1.24296i) q^{17} +(-0.470279 + 6.56876i) q^{18} +(2.69447 + 4.66695i) q^{19} +(4.78577 - 4.10200i) q^{20} +(5.66355 - 2.11216i) q^{21} +(-0.753371 + 2.81162i) q^{22} +(2.13883 - 0.573097i) q^{23} +(0.516417 - 3.07034i) q^{24} +(4.66157 - 1.80824i) q^{25} +(-5.66931 + 5.52306i) q^{26} +(1.46339 + 4.98583i) q^{27} +(-9.50219 + 2.54610i) q^{28} +(-2.06922 + 3.58399i) q^{29} +(4.11491 - 7.43979i) q^{30} -9.82014i q^{31} +(1.89166 - 7.05976i) q^{32} +(0.218232 + 2.28629i) q^{33} -10.5423 q^{34} +(-7.78053 - 0.598582i) q^{35} +(-1.59983 - 8.30389i) q^{36} +(-0.871294 - 3.25171i) q^{37} +(-8.36489 - 8.36489i) q^{38} +(-2.66847 + 5.64617i) q^{39} +(-2.27083 + 3.31655i) q^{40} +(0.983308 - 1.70314i) q^{41} +(-10.8089 + 7.69640i) q^{42} +(6.59808 + 1.76795i) q^{43} -3.73779i q^{44} +(0.990875 - 6.63462i) q^{45} +(-4.20954 + 2.43038i) q^{46} +(3.61835 + 3.61835i) q^{47} +(-0.278426 - 2.91691i) q^{48} +(4.48514 + 2.58950i) q^{49} +(-8.85700 + 6.48268i) q^{50} +(-7.79372 + 2.90659i) q^{51} +(5.19635 - 8.73475i) q^{52} +(-2.43489 - 2.43489i) q^{53} +(-5.93570 - 9.74047i) q^{54} +(0.984825 - 2.79667i) q^{55} +(5.43276 - 3.13661i) q^{56} +(-8.49028 - 3.87775i) q^{57} +(2.35128 - 8.77510i) q^{58} +(5.33897 - 3.08246i) q^{59} +(-2.63132 + 10.5956i) q^{60} +(3.34455 + 5.79293i) q^{61} +(5.57939 + 20.8226i) q^{62} +(-5.86887 + 8.66991i) q^{63} +12.6608i q^{64} +(6.18941 - 5.16636i) q^{65} +(-1.76171 - 4.72384i) q^{66} +(-0.132637 - 0.495007i) q^{67} +(13.0762 - 3.50375i) q^{68} +(-2.44197 + 2.95734i) q^{69} +(16.8379 - 3.15134i) q^{70} +(-7.13214 - 12.3532i) q^{71} +(2.35596 + 4.85083i) q^{72} +(-5.00425 - 5.00425i) q^{73} +(3.69497 + 6.39988i) q^{74} +(-4.76050 + 7.23448i) q^{75} +(13.1555 + 7.59533i) q^{76} +(-3.27213 + 3.27213i) q^{77} +(2.45028 - 13.4882i) q^{78} +0.914386i q^{79} +(-1.25646 + 3.56807i) q^{80} +(-7.07368 - 5.56444i) q^{81} +(-1.11735 + 4.17000i) q^{82} +(2.26406 - 2.26406i) q^{83} +(10.8489 - 13.1386i) q^{84} +(10.7070 + 0.823721i) q^{85} -14.9950 q^{86} +(-0.681105 - 7.13554i) q^{87} +(0.616909 + 2.30233i) q^{88} +(3.65216 + 2.10858i) q^{89} +(1.66846 + 14.6310i) q^{90} +(-12.1956 + 3.09759i) q^{91} +(4.41358 - 4.41358i) q^{92} +(9.86569 + 13.8555i) q^{93} +(-9.72811 - 5.61653i) q^{94} +(7.84196 + 9.14914i) q^{95} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} - 12 q^{6} - 12 q^{7} + 4 q^{10} - 12 q^{12} - 24 q^{13} - 6 q^{15} + 16 q^{16} + 20 q^{22} - 16 q^{25} - 32 q^{27} - 36 q^{28} + 30 q^{33} - 4 q^{36} - 84 q^{37} - 152 q^{40} - 48 q^{42}+ \cdots - 48 q^{97}+O(q^{100}) \) 96 * q - 2 * q^3 - 12 * q^6 - 12 * q^7 + 4 * q^10 - 12 * q^12 - 24 * q^13 - 6 * q^15 + 16 * q^16 + 20 * q^22 - 16 * q^25 - 32 * q^27 - 36 * q^28 + 30 * q^33 - 4 * q^36 - 84 * q^37 - 152 * q^40 - 48 * q^42 + 8 * q^43 + 54 * q^45 - 28 * q^48 - 16 * q^51 + 28 * q^52 - 40 * q^55 + 84 * q^58 - 32 * q^61 + 90 * q^63 + 36 * q^67 + 90 * q^72 - 20 * q^75 + 72 * q^76 + 60 * q^78 + 32 * q^81 - 68 * q^82 + 84 * q^85 - 26 * q^87 - 108 * q^88 - 20 * q^90 - 80 * q^91 + 48 * q^93 - 48 * q^97

Introduction

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