LMFDB - Embedded newform 145.2.l.a.109.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [145,2,Mod(4,145)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("145.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(145, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	145.l (of order $14$, degree $6$, 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:	$1.15783082931$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			109.7
Character	$\chi$	$=$	145.109
Dual form			145.2.l.a.4.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.117010 + 0.512653i) q^{2} +(-1.21246 - 0.583890i) q^{3} +(1.55282 - 0.747797i) q^{4} +(0.653828 + 2.13834i) q^{5} +(0.157463 - 0.689892i) q^{6} +(1.17080 - 2.43120i) q^{7} +(1.22076 + 1.53079i) q^{8} +(-0.741336 - 0.929606i) q^{9} +(-1.01972 + 0.585394i) q^{10} +(1.26349 + 1.00760i) q^{11} -2.31936 q^{12} +(5.54889 + 4.42509i) q^{13} +(1.38336 + 0.315742i) q^{14} +(0.455817 - 2.97442i) q^{15} +(1.50724 - 1.89002i) q^{16} -4.54440 q^{17} +(0.389822 - 0.488821i) q^{18} +(-2.00931 - 4.17237i) q^{19} +(2.61432 + 2.83152i) q^{20} +(-2.83910 + 2.26411i) q^{21} +(-0.368710 + 0.765633i) q^{22} +(-5.45091 - 1.24413i) q^{23} +(-0.586314 - 2.56881i) q^{24} +(-4.14502 + 2.79622i) q^{25} +(-1.61926 + 3.36243i) q^{26} +(1.25441 + 5.49594i) q^{27} -4.65072i q^{28} +(-5.19519 - 1.41774i) q^{29} +(1.57818 - 0.114360i) q^{30} +(-4.05556 + 0.925654i) q^{31} +(4.67339 + 2.25059i) q^{32} +(-0.943607 - 1.95942i) q^{33} +(-0.531738 - 2.32970i) q^{34} +(5.96424 + 0.913994i) q^{35} +(-1.84632 - 0.889139i) q^{36} +(-5.57566 - 6.99165i) q^{37} +(1.90387 - 1.51828i) q^{38} +(-4.14404 - 8.60520i) q^{39} +(-2.47518 + 3.61128i) q^{40} +7.62027i q^{41} +(-1.49291 - 1.19055i) q^{42} +(-0.402428 + 1.76315i) q^{43} +(2.71546 + 0.619785i) q^{44} +(1.50311 - 2.19303i) q^{45} -2.94000i q^{46} +(5.11496 - 6.41396i) q^{47} +(-2.93104 + 1.41151i) q^{48} +(-0.175511 - 0.220083i) q^{49} +(-1.91850 - 1.79777i) q^{50} +(5.50990 + 2.65343i) q^{51} +(11.9255 + 2.72191i) q^{52} +(1.88311 - 0.429807i) q^{53} +(-2.67073 + 1.28616i) q^{54} +(-1.32849 + 3.36058i) q^{55} +(5.15092 - 1.17566i) q^{56} +6.23204i q^{57} +(0.118921 - 2.82922i) q^{58} +9.95363 q^{59} +(-1.51646 - 4.95959i) q^{60} +(-2.85489 + 5.92824i) q^{61} +(-0.949079 - 1.97078i) q^{62} +(-3.12802 + 0.713949i) q^{63} +(0.468919 - 2.05447i) q^{64} +(-5.83435 + 14.7587i) q^{65} +(0.894092 - 0.713014i) q^{66} +(-7.92421 + 6.31934i) q^{67} +(-7.05661 + 3.39829i) q^{68} +(5.88258 + 4.69120i) q^{69} +(0.229312 + 3.16453i) q^{70} +(2.10551 - 2.64023i) q^{71} +(0.518035 - 2.26966i) q^{72} +(-0.165258 + 0.724041i) q^{73} +(2.93189 - 3.67647i) q^{74} +(6.65836 - 0.970065i) q^{75} +(-6.24016 - 4.97636i) q^{76} +(3.92898 - 1.89210i) q^{77} +(3.92659 - 3.13135i) q^{78} +(2.66395 - 2.12443i) q^{79} +(5.02699 + 1.98725i) q^{80} +(0.894360 - 3.91845i) q^{81} +(-3.90655 + 0.891645i) q^{82} +(-3.78387 - 7.85730i) q^{83} +(-2.71551 + 5.63882i) q^{84} +(-2.97125 - 9.71748i) q^{85} -0.950973 q^{86} +(5.47116 + 4.75238i) q^{87} +3.16419i q^{88} +(-8.21241 + 1.87443i) q^{89} +(1.30014 + 0.513968i) q^{90} +(17.2549 - 8.30954i) q^{91} +(-9.39462 + 2.14426i) q^{92} +(5.45768 + 1.24568i) q^{93} +(3.88664 + 1.87171i) q^{94} +(7.60821 - 7.02459i) q^{95} +(-4.35221 - 5.45750i) q^{96} +(9.03868 - 4.35280i) q^{97} +(0.0922900 - 0.115728i) q^{98} -1.92153i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 18 q^{4} - 9 q^{5} + 4 q^{6} - 14 q^{9} - 7 q^{10} - 14 q^{11} - 14 q^{14} + 7 q^{15} - 2 q^{16} - 14 q^{19} + 46 q^{20} - 14 q^{21} - 12 q^{24} - 9 q^{25} - 56 q^{26} - 12 q^{29} + 14 q^{30} - 28 q^{31}+ \cdots + 90 q^{96}+O(q^{100}) $ 72 * q - 18 * q^4 - 9 * q^5 + 4 * q^6 - 14 * q^9 - 7 * q^10 - 14 * q^11 - 14 * q^14 + 7 * q^15 - 2 * q^16 - 14 * q^19 + 46 * q^20 - 14 * q^21 - 12 * q^24 - 9 * q^25 - 56 * q^26 - 12 * q^29 + 14 * q^30 - 28 * q^31 + 4 * q^34 - 25 * q^35 - 50 * q^36 + 56 * q^40 - 70 * q^44 + 59 * q^45 - 28 * q^49 + 14 * q^50 - 64 * q^51 + 14 * q^54 + 49 * q^55 + 98 * q^56 + 100 * q^59 + 14 * q^60 - 70 * q^61 - 18 * q^64 + 27 * q^65 + 70 * q^66 - 70 * q^69 - 20 * q^71 - 54 * q^74 + 98 * q^76 - 14 * q^79 + 2 * q^80 + 160 * q^81 + 98 * q^84 - 112 * q^85 - 88 * q^86 - 14 * q^89 - 56 * q^90 + 56 * q^91 + 6 * q^94 - 119 * q^95 + 90 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/145\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$e\left(\frac{13}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.117010	+	0.512653i	0.0827384	+	0.362500i	0.999301	−	0.0373914i	$-0.0119048\pi$
$2$	0.117010	+	0.512653i	0.0827384	+	0.362500i	−0.916562	+	0.399892i	$0.869048\pi$
$3$	−1.21246	−	0.583890i	−0.700014	−	0.337109i	0.0497983	−	0.998759i	$-0.484142\pi$
$3$	−1.21246	−	0.583890i	−0.700014	−	0.337109i	−0.749813	+	0.661650i	$0.769856\pi$
$4$	1.55282	−	0.747797i	0.776408	−	0.373898i
$5$	0.653828	+	2.13834i	0.292401	+	0.956296i
$5$	0.653828	+	2.13834i	0.292401	+	0.956296i
$6$	0.157463	−	0.689892i	0.0642842	−	0.281647i
$7$	1.17080	−	2.43120i	0.442522	−	0.918906i	−0.553754	−	0.832680i	$-0.686805\pi$
$7$	1.17080	−	2.43120i	0.442522	−	0.918906i	0.996276	−	0.0862256i	$-0.0274806\pi$
$8$	1.22076	+	1.53079i	0.431605	+	0.541215i
$9$	−0.741336	−	0.929606i	−0.247112	−	0.309869i
$10$	−1.01972	+	0.585394i	−0.322465	+	0.185118i
$11$	1.26349	+	1.00760i	0.380958	+	0.303804i	0.795182	−	0.606371i	$-0.207375\pi$
$11$	1.26349	+	1.00760i	0.380958	+	0.303804i	−0.414224	+	0.910175i	$0.635947\pi$
$12$	−2.31936			−0.669541
$13$	5.54889	+	4.42509i	1.53899	+	1.22730i	0.879825	+	0.475298i	$0.157660\pi$
$13$	5.54889	+	4.42509i	1.53899	+	1.22730i	0.659161	+	0.752002i	$0.270912\pi$
$14$	1.38336	+	0.315742i	0.369717	+	0.0843856i
$15$	0.455817	−	2.97442i	0.117691	−	0.767992i
$16$	1.50724	−	1.89002i	0.376811	−	0.472505i
$17$	−4.54440			−1.10218			−0.551089	−	0.834446i	$-0.685788\pi$
$17$	−4.54440			−1.10218			−0.551089	+	0.834446i	$0.685788\pi$
$18$	0.389822	−	0.488821i	0.0918819	−	0.115216i
$19$	−2.00931	−	4.17237i	−0.460966	−	0.957206i	−0.993820	−	0.110999i	$-0.964595\pi$
$19$	−2.00931	−	4.17237i	−0.460966	−	0.957206i	0.532854	−	0.846207i	$-0.321119\pi$
$20$	2.61432	+	2.83152i	0.584580	+	0.633148i
$21$	−2.83910	+	2.26411i	−0.619543	+	0.494069i
$22$	−0.368710	+	0.765633i	−0.0786092	+	0.163234i
$23$	−5.45091	−	1.24413i	−1.13659	−	0.259420i	−0.387491	−	0.921874i	$-0.626658\pi$
$23$	−5.45091	−	1.24413i	−1.13659	−	0.259420i	−0.749103	+	0.662454i	$0.769515\pi$
$24$	−0.586314	−	2.56881i	−0.119681	−	0.524356i
$25$	−4.14502	+	2.79622i	−0.829004	+	0.559243i
$26$	−1.61926	+	3.36243i	−0.317564	+	0.659428i
$27$	1.25441	+	5.49594i	0.241412	+	1.05769i
$28$		−	4.65072i		−	0.878904i
$29$	−5.19519	−	1.41774i	−0.964723	−	0.263268i
$29$	−5.19519	−	1.41774i	−0.964723	−	0.263268i
$30$	1.57818	−	0.114360i	0.288135	−	0.0208792i
$31$	−4.05556	+	0.925654i	−0.728400	+	0.166252i	−0.570611	−	0.821220i	$-0.693294\pi$
$31$	−4.05556	+	0.925654i	−0.728400	+	0.166252i	−0.157789	+	0.987473i	$0.550436\pi$
$32$	4.67339	+	2.25059i	0.826147	+	0.397851i
$33$	−0.943607	−	1.95942i	−0.164261	−	0.341091i
$34$	−0.531738	−	2.32970i	−0.0911924	−	0.399540i
$35$	5.96424	+	0.913994i	1.00814	+	0.154493i
$36$	−1.84632	−	0.889139i	−0.307719	−	0.148190i
$37$	−5.57566	−	6.99165i	−0.916633	−	1.14942i	−0.988381	−	0.151998i	$-0.951429\pi$
$37$	−5.57566	−	6.99165i	−0.916633	−	1.14942i	0.0717482	−	0.997423i	$-0.477142\pi$
$38$	1.90387	−	1.51828i	0.308848	−	0.246298i
$39$	−4.14404	−	8.60520i	−0.663578	−	1.37793i
$40$	−2.47518	+	3.61128i	−0.391360	+	0.570994i
$41$			7.62027i			1.19009i	0.803694	+	0.595043i	$0.202865\pi$
$41$			7.62027i			1.19009i	−0.803694	+	0.595043i	$0.797135\pi$
$42$	−1.49291	−	1.19055i	−0.230360	−	0.183706i
$43$	−0.402428	+	1.76315i	−0.0613697	+	0.268878i	−0.996299	−	0.0859560i	$-0.972606\pi$
$43$	−0.402428	+	1.76315i	−0.0613697	+	0.268878i	0.934929	+	0.354834i	$0.115463\pi$
$44$	2.71546	+	0.619785i	0.409370	+	0.0934361i
$45$	1.50311	−	2.19303i	0.224071	−	0.326918i
$46$		−	2.94000i		−	0.433480i
$47$	5.11496	−	6.41396i	0.746094	−	0.935573i	−0.253400	−	0.967361i	$-0.581549\pi$
$47$	5.11496	−	6.41396i	0.746094	−	0.935573i	0.999495	+	0.0317890i	$0.0101204\pi$
$48$	−2.93104	+	1.41151i	−0.423059	+	0.203734i
$49$	−0.175511	−	0.220083i	−0.0250729	−	0.0314405i
$50$	−1.91850	−	1.79777i	−0.271316	−	0.254243i
$51$	5.50990	+	2.65343i	0.771541	+	0.371554i
$52$	11.9255	+	2.72191i	1.65377	+	0.377461i
$53$	1.88311	−	0.429807i	0.258665	−	0.0590385i	−0.0912219	−	0.995831i	$-0.529077\pi$
$53$	1.88311	−	0.429807i	0.258665	−	0.0590385i	0.349887	+	0.936792i	$0.386220\pi$
$54$	−2.67073	+	1.28616i	−0.363440	+	0.175024i
$55$	−1.32849	+	3.36058i	−0.179134	+	0.453141i
$56$	5.15092	−	1.17566i	0.688320	−	0.157105i
$57$			6.23204i			0.825454i
$58$	0.118921	−	2.82922i	0.0156151	−	0.371495i
$59$	9.95363			1.29585			0.647926	−	0.761703i	$-0.275636\pi$
$59$	9.95363			1.29585			0.647926	+	0.761703i	$0.275636\pi$
$60$	−1.51646	−	4.95959i	−0.195774	−	0.640280i
$61$	−2.85489	+	5.92824i	−0.365531	+	0.759033i	−0.999902	−	0.0139955i	$-0.995545\pi$
$61$	−2.85489	+	5.92824i	−0.365531	+	0.759033i	0.634371	+	0.773029i	$0.281259\pi$
$62$	−0.949079	−	1.97078i	−0.120533	−	0.250290i
$63$	−3.12802	+	0.713949i	−0.394093	+	0.0899491i
$64$	0.468919	−	2.05447i	0.0586149	−	0.256808i
$65$	−5.83435	+	14.7587i	−0.723662	+	1.83059i
$66$	0.894092	−	0.713014i	0.110055	−	0.0877660i
$67$	−7.92421	+	6.31934i	−0.968096	+	0.772031i	−0.973672	−	0.227954i	$-0.926797\pi$
$67$	−7.92421	+	6.31934i	−0.968096	+	0.772031i	0.00557600	+	0.999984i	$0.498225\pi$
$68$	−7.05661	+	3.39829i	−0.855740	+	0.412103i
$69$	5.88258	+	4.69120i	0.708179	+	0.564754i
$70$	0.229312	+	3.16453i	0.0274080	+	0.378234i
$71$	2.10551	−	2.64023i	0.249879	−	0.313338i	−0.641034	−	0.767512i	$-0.721494\pi$
$71$	2.10551	−	2.64023i	0.249879	−	0.313338i	0.890913	+	0.454175i	$0.150066\pi$
$72$	0.518035	−	2.26966i	0.0610510	−	0.267482i
$73$	−0.165258	+	0.724041i	−0.0193419	+	0.0847426i	−0.983678	−	0.179939i	$-0.942410\pi$
$73$	−0.165258	+	0.724041i	−0.0193419	+	0.0847426i	0.964336	+	0.264682i	$0.0852670\pi$
$74$	2.93189	−	3.67647i	0.340825	−	0.427381i
$75$	6.65836	−	0.970065i	0.768841	−	0.112013i
$76$	−6.24016	−	4.97636i	−0.715796	−	0.570828i
$77$	3.92898	−	1.89210i	0.447749	−	0.215625i
$78$	3.92659	−	3.13135i	0.444598	−	0.354555i
$79$	2.66395	−	2.12443i	0.299717	−	0.239017i	−0.462070	−	0.886843i	$-0.652893\pi$
$79$	2.66395	−	2.12443i	0.299717	−	0.239017i	0.761788	+	0.647827i	$0.224322\pi$
$80$	5.02699	+	1.98725i	0.562035	+	0.222181i
$81$	0.894360	−	3.91845i	0.0993734	−	0.435383i
$82$	−3.90655	+	0.891645i	−0.431407	+	0.0984657i
$83$	−3.78387	−	7.85730i	−0.415334	−	0.862450i	−0.998736	−	0.0502666i	$-0.983993\pi$
$83$	−3.78387	−	7.85730i	−0.415334	−	0.862450i	0.583402	−	0.812184i	$-0.301721\pi$
$84$	−2.71551	+	5.63882i	−0.296287	+	0.615246i
$85$	−2.97125	−	9.71748i	−0.322278	−	1.05401i
$86$	−0.950973			−0.102546
$87$	5.47116	+	4.75238i	0.586570	+	0.509508i
$88$			3.16419i			0.337303i
$89$	−8.21241	+	1.87443i	−0.870513	+	0.198689i	−0.634370	−	0.773029i	$-0.718741\pi$
$89$	−8.21241	+	1.87443i	−0.870513	+	0.198689i	−0.236143	+	0.971718i	$0.575883\pi$
$90$	1.30014	+	0.513968i	0.137047	+	0.0541770i
$91$	17.2549	−	8.30954i	1.80881	−	0.871076i
$92$	−9.39462	+	2.14426i	−0.979457	+	0.223555i
$93$	5.45768	+	1.24568i	0.565935	+	0.129171i
$94$	3.88664	+	1.87171i	0.400876	+	0.193052i
$95$	7.60821	−	7.02459i	0.780586	−	0.720708i
$96$	−4.35221	−	5.45750i	−0.444195	−	0.557004i
$97$	9.03868	−	4.35280i	0.917739	−	0.441960i	0.0854759	−	0.996340i	$-0.472759\pi$
$97$	9.03868	−	4.35280i	0.917739	−	0.441960i	0.832264	+	0.554380i	$0.187045\pi$
$98$	0.0922900	−	0.115728i	0.00932269	−	0.0116903i
$99$		−	1.92153i		−	0.193121i
$100$	−4.34545	+	7.44164i	−0.434545	+	0.744164i
$101$	2.10492	+	0.480435i	0.209448	+	0.0478050i	0.325957	−	0.945385i	$-0.394313\pi$
$101$	2.10492	+	0.480435i	0.209448	+	0.0478050i	−0.116510	+	0.993190i	$0.537171\pi$
$102$	−0.715576	+	3.13514i	−0.0708526	+	0.310426i
$103$	5.68676	+	4.53504i	0.560333	+	0.446850i	0.862249	−	0.506484i	$-0.169055\pi$
$103$	5.68676	+	4.53504i	0.560333	+	0.446850i	−0.301917	+	0.953334i	$0.597626\pi$
$104$			13.8962i			1.36263i
$105$	−6.69773	−	4.59064i	−0.653631	−	0.448001i
$106$	0.440684	+	0.915089i	0.0428030	+	0.0888813i
$107$	1.37648	−	1.09771i	0.133070	−	0.106120i	−0.554693	−	0.832055i	$-0.687164\pi$
$107$	1.37648	−	1.09771i	0.133070	−	0.106120i	0.687763	+	0.725935i	$0.258593\pi$
$108$	6.05772	+	7.59614i	0.582904	+	0.730939i
$109$	1.50498	+	0.724759i	0.144151	+	0.0694193i	0.504569	−	0.863372i	$-0.331652\pi$
$109$	1.50498	+	0.724759i	0.144151	+	0.0694193i	−0.360418	+	0.932791i	$0.617366\pi$
$110$	−1.87826	−	0.287835i	−0.179085	−	0.0274440i
$111$	2.67791	+	11.7327i	0.254176	+	1.11362i
$112$	−2.83033	−	5.87724i	−0.267441	−	0.555347i
$113$	−3.43172	−	1.65263i	−0.322829	−	0.155466i	0.265449	−	0.964125i	$-0.414480\pi$
$113$	−3.43172	−	1.65263i	−0.322829	−	0.155466i	−0.588278	+	0.808659i	$0.700194\pi$
$114$	−3.19488	+	0.729209i	−0.299228	+	0.0682967i
$115$	−0.903570	−	12.4694i	−0.0842583	−	1.16277i
$116$	−9.12736	+	1.68346i	−0.847454	+	0.156305i
$117$		−	8.43877i		−	0.780164i
$118$	1.16467	+	5.10276i	0.107217	+	0.469747i
$119$	−5.32059	+	11.0483i	−0.487738	+	1.01280i
$120$	5.10965	−	2.93330i	0.466445	−	0.267773i
$121$	−1.86658	−	8.17801i	−0.169689	−	0.743455i
$122$	−3.37318	−	0.769906i	−0.305393	−	0.0697040i
$123$	4.44940	−	9.23928i	0.401189	−	0.833077i
$124$	−5.60533	+	4.47010i	−0.503374	+	0.401427i
$125$	−8.68939	−	7.03523i	−0.777203	−	0.629250i
$126$	−0.732016	−	1.52005i	−0.0652132	−	0.135417i
$127$	−4.97363	+	6.23673i	−0.441338	+	0.553421i	−0.951895	−	0.306423i	$-0.900868\pi$
$127$	−4.97363	+	6.23673i	−0.441338	+	0.553421i	0.510557	+	0.859844i	$0.329439\pi$
$128$	11.4822			1.01490
$129$	1.51742	−	1.90278i	0.133601	−	0.167530i
$130$	−8.24876	−	1.26409i	−0.723464	−	0.110868i
$131$	0.739072	+	0.168688i	0.0645730	+	0.0147384i	0.254685	−	0.967024i	$-0.418028\pi$
$131$	0.739072	+	0.168688i	0.0645730	+	0.0147384i	−0.190112	+	0.981762i	$0.560885\pi$
$132$	−2.93050	−	2.33699i	−0.255067	−	0.203409i
$133$	−12.4963			−1.08357
$134$	−4.16684	−	3.32294i	−0.359960	−	0.287059i
$135$	−10.9320	+	6.27576i	−0.940879	+	0.540131i
$136$	−5.54763	−	6.95651i	−0.475705	−	0.596516i
$137$	2.81876	+	3.53462i	0.240823	+	0.301983i	0.887524	−	0.460761i	$-0.152423\pi$
$137$	2.81876	+	3.53462i	0.240823	+	0.301983i	−0.646701	+	0.762743i	$0.723852\pi$
$138$	−1.71664	+	3.56464i	−0.146130	+	0.303442i
$139$	0.526979	−	2.30884i	0.0446978	−	0.195834i	−0.947649	−	0.319313i	$-0.896548\pi$
$139$	0.526979	−	2.30884i	0.0446978	−	0.195834i	0.992347	+	0.123479i	$0.0394051\pi$
$140$	9.94484	−	3.04077i	0.840492	−	0.256992i
$141$	−9.94674	+	4.79010i	−0.837667	+	0.403399i
$142$	1.59989	+	0.770465i	0.134260	+	0.0646560i
$143$	2.55225	+	11.1822i	0.213430	+	0.935099i
$144$	−2.87435			−0.239529
$145$	−0.365146	−	12.0361i	−0.0303238	−	0.999540i
$146$	−0.390519			−0.0323195
$147$	0.0842952	+	0.369321i	0.00695255	+	0.0304611i
$148$	−13.8863	−	6.68729i	−1.14145	−	0.549692i
$149$	2.94263	−	1.41709i	0.241069	−	0.116093i	−0.309449	−	0.950916i	$-0.600144\pi$
$149$	2.94263	−	1.41709i	0.241069	−	0.116093i	0.550518	+	0.834823i	$0.314430\pi$
$150$	1.27640	+	3.29992i	0.104218	+	0.269437i
$151$	2.23792	−	9.80496i	0.182119	−	0.797917i	−0.798500	−	0.601995i	$-0.794373\pi$
$151$	2.23792	−	9.80496i	0.182119	−	0.797917i	0.980619	−	0.195922i	$-0.0627700\pi$
$152$	3.93412	−	8.16929i	0.319099	−	0.662617i
$153$	3.36893	+	4.22450i	0.272362	+	0.341531i
$154$	1.42972	+	1.79281i	0.115210	+	0.144469i
$155$	−4.63100	−	8.06695i	−0.371971	−	0.647953i
$156$	−12.8699	−	10.2634i	−1.03041	−	0.821728i
$157$	4.24697			0.338945			0.169473	−	0.985535i	$-0.445794\pi$
$157$	4.24697			0.338945			0.169473	+	0.985535i	$0.445794\pi$
$158$	1.40080	+	1.11710i	0.111442	+	0.0888718i
$159$	−2.53415	−	0.578404i	−0.200971	−	0.0458704i
$160$	−1.75693	+	11.4648i	−0.138898	+	0.906373i
$161$	−9.40668	+	11.7956i	−0.741350	+	0.929624i
$162$	2.11345			0.166049
$163$	−6.13350	+	7.69117i	−0.480413	+	0.602419i	−0.961686	−	0.274152i	$-0.911603\pi$
$163$	−6.13350	+	7.69117i	−0.480413	+	0.602419i	0.481274	+	0.876570i	$0.340174\pi$
$164$	5.69841	+	11.8329i	0.444971	+	0.923992i
$165$	3.57296	−	3.29888i	0.278154	−	0.256817i
$166$	3.58532	−	2.85919i	0.278275	−	0.221917i
$167$	−0.154299	+	0.320405i	−0.0119400	+	0.0247937i	−0.906854	−	0.421446i	$-0.861523\pi$
$167$	−0.154299	+	0.320405i	−0.0119400	+	0.0247937i	0.894914	+	0.446239i	$0.147237\pi$
$168$	−6.93174	−	1.58213i	−0.534796	−	0.122064i
$169$	8.31597	+	36.4347i	0.639690	+	2.80267i
$170$	4.63403	−	2.66026i	0.355414	−	0.204033i
$171$	−2.38909	+	4.96099i	−0.182698	+	0.379376i
$172$	0.693583	+	3.03879i	0.0528852	+	0.231705i
$173$		−	2.46714i		−	0.187573i	−0.995592	−	0.0937866i	$-0.970103\pi$
$173$		−	2.46714i		−	0.187573i	0.995592	−	0.0937866i	$-0.0298971\pi$
$174$	−1.79614	+	3.36088i	−0.136165	+	0.254788i
$175$	1.94515	+	13.3512i	0.147040	+	1.00925i
$176$	3.80878	−	0.869330i	0.287098	−	0.0655282i
$177$	−12.0684	−	5.81183i	−0.907116	−	0.436844i
$178$	−1.92186	−	3.99079i	−0.144050	−	0.299122i
$179$	−3.97186	−	17.4018i	−0.296870	−	1.30067i	−0.874759	−	0.484559i	$-0.838980\pi$
$179$	−3.97186	−	17.4018i	−0.296870	−	1.30067i	0.577888	−	0.816116i	$-0.303877\pi$
$180$	0.694111	−	4.52940i	0.0517360	−	0.337601i
$181$	17.3573	+	8.35883i	1.29016	+	0.621307i	0.947980	−	0.318329i	$-0.103122\pi$
$181$	17.3573	+	8.35883i	1.29016	+	0.621307i	0.342177	+	0.939636i	$0.388836\pi$
$182$	6.27890	+	7.87349i	0.465423	+	0.583622i
$183$	6.92288	−	5.52082i	0.511754	−	0.408110i
$184$	−4.74976	−	9.86298i	−0.350157	−	0.727109i
$185$	11.3050	−	16.4940i	0.831163	−	1.21266i
$186$			2.94365i			0.215839i
$187$	−5.74182	−	4.57895i	−0.419883	−	0.334846i
$188$	3.14626	−	13.7847i	0.229464	−	1.00535i
$189$	14.8304	+	3.38494i	1.07875	+	0.246218i
$190$	4.49141	+	3.07843i	0.325841	+	0.223332i
$191$			13.1761i			0.953388i	0.879069	+	0.476694i	$0.158165\pi$
$191$			13.1761i			0.953388i	−0.879069	+	0.476694i	$0.841835\pi$
$192$	−1.76813	+	2.21716i	−0.127604	+	0.160010i
$193$	19.6423	−	9.45924i	1.41388	−	0.680891i	0.437959	−	0.898995i	$-0.355701\pi$
$193$	19.6423	−	9.45924i	1.41388	−	0.680891i	0.975926	+	0.218104i	$0.0699871\pi$
$194$	3.28909	+	4.12439i	0.236143	+	0.296114i
$195$	15.6914	−	14.4877i	1.12368	−	1.03749i
$196$	−0.437113	−	0.210503i	−0.0312224	−	0.0150359i
$197$	1.30769	+	0.298472i	0.0931691	+	0.0212652i	0.268851	−	0.963182i	$-0.413356\pi$
$197$	1.30769	+	0.298472i	0.0931691	+	0.0212652i	−0.175682	+	0.984447i	$0.556213\pi$
$198$	0.985076	−	0.224837i	0.0700063	−	0.0159785i
$199$	−8.40136	+	4.04588i	−0.595557	+	0.286805i	−0.707279	−	0.706934i	$-0.750078\pi$
$199$	−8.40136	+	4.04588i	−0.595557	+	0.286805i	0.111722	+	0.993739i	$0.464363\pi$
$200$	−9.34050	−	2.93163i	−0.660473	−	0.207298i
$201$	13.2976	−	3.03509i	0.937940	−	0.214079i
$202$			1.13531i			0.0798801i
$203$	−9.52935	+	10.9706i	−0.668829	+	0.769988i
$204$	10.5401			0.737954
$205$	−16.2947	+	4.98234i	−1.13807	+	0.347982i
$206$	−1.65949	+	3.44598i	−0.115622	+	0.240092i
$207$	2.88440	+	5.98952i	0.200480	+	0.416301i
$208$	16.7270	−	3.81784i	1.15981	−	0.264719i
$209$	1.66534	−	7.29634i	0.115194	−	0.504699i
$210$	1.56971	−	3.97076i	0.108320	−	0.274008i
$211$	22.3864	−	17.8526i	1.54115	−	1.22902i	0.665146	−	0.746713i	$-0.268369\pi$
$211$	22.3864	−	17.8526i	1.54115	−	1.22902i	0.876000	−	0.482310i	$-0.160202\pi$
$212$	2.60271	−	2.07559i	0.178755	−	0.142552i
$213$	−4.09446	+	1.97179i	−0.280548	+	0.135105i
$214$	0.723806	+	0.577216i	0.0494783	+	0.0394577i
$215$	−4.03334	+	0.292269i	−0.275072	+	0.0199326i
$216$	−6.88178	+	8.62948i	−0.468246	+	0.587161i
$217$	−2.49781	+	10.9436i	−0.169562	+	0.742901i
$218$	−0.195453	+	0.856335i	−0.0132377	+	0.0579983i
$219$	0.623129	−	0.781379i	0.0421071	−	0.0528007i
$220$	0.450127	+	6.21181i	0.0303476	+	0.418800i
$221$	−25.2164	−	20.1094i	−1.69624	−	1.35270i
$222$	−5.70145	+	2.74567i	−0.382656	+	0.184278i
$223$	−10.4724	+	8.35143i	−0.701282	+	0.559253i	−0.907910	−	0.419166i	$-0.862322\pi$
$223$	−10.4724	+	8.35143i	−0.701282	+	0.559253i	0.206628	+	0.978420i	$0.433751\pi$
$224$	10.9432	−	8.72694i	0.731176	−	0.583094i
$225$	5.67223	+	1.78030i	0.378149	+	0.118687i
$226$	0.445680	−	1.95265i	0.0296462	−	0.129889i
$227$	−19.9394	+	4.55103i	−1.32342	+	0.302063i	−0.825129	−	0.564945i	$-0.808897\pi$
$227$	−19.9394	+	4.55103i	−1.32342	+	0.302063i	−0.498295	+	0.867008i	$0.666040\pi$
$228$	4.66030	+	9.67722i	0.308636	+	0.640889i
$229$	−1.01567	+	2.10907i	−0.0671176	+	0.139371i	−0.931829	−	0.362898i	$-0.881787\pi$
$229$	−1.01567	+	2.10907i	−0.0671176	+	0.139371i	0.864711	+	0.502270i	$0.167501\pi$
$230$	6.28673	−	1.92225i	0.414535	−	0.126750i
$231$	−5.86852			−0.386120
$232$	−4.17184	−	9.68346i	−0.273894	−	0.635750i
$233$			0.607445i			0.0397951i	0.999802	+	0.0198975i	$0.00633400\pi$
$233$			0.607445i			0.0397951i	−0.999802	+	0.0198975i	$0.993666\pi$
$234$	4.32616	−	0.987418i	0.282810	−	0.0645495i
$235$	17.0596	+	6.74392i	1.11284	+	0.439925i
$236$	15.4562	−	7.44329i	1.00611	−	0.484517i
$237$	−4.47036	+	1.02033i	−0.290381	+	0.0662776i
$238$	−6.28652	−	1.43486i	−0.407494	−	0.0930079i
$239$	2.46990	+	1.18944i	0.159765	+	0.0769387i	0.512057	−	0.858951i	$-0.328884\pi$
$239$	2.46990	+	1.18944i	0.159765	+	0.0769387i	−0.352293	+	0.935890i	$0.614598\pi$
$240$	−4.93469	−	5.34468i	−0.318533	−	0.344997i
$241$	8.07240	+	10.1225i	0.519989	+	0.652045i	0.970607	−	0.240672i	$-0.0773677\pi$
$241$	8.07240	+	10.1225i	0.519989	+	0.652045i	−0.450618	+	0.892717i	$0.648796\pi$
$242$	3.97407	−	1.91381i	0.255463	−	0.123024i
$243$	7.17203	−	8.99345i	0.460086	−	0.576930i
$244$			11.3403i			0.725991i
$245$	0.355860	−	0.519198i	0.0227351	−	0.0331704i
$246$	5.25717	+	1.19991i	0.335185	+	0.0765037i
$247$	7.31369	−	32.0434i	0.465359	−	2.03887i
$248$	−6.36785	−	5.07819i	−0.404359	−	0.322466i
$249$			11.7360i			0.743741i
$250$	2.58989	−	5.27783i	0.163799	−	0.333800i
$251$	1.89798	+	3.94120i	0.119800	+	0.248766i	0.952242	−	0.305346i	$-0.0987721\pi$
$251$	1.89798	+	3.94120i	0.119800	+	0.248766i	−0.832442	+	0.554112i	$0.813058\pi$
$252$	−4.32334	+	3.44775i	−0.272345	+	0.217188i
$253$	−5.63360	−	7.06431i	−0.354181	−	0.444129i
$254$	−3.77924	−	1.81999i	−0.237131	−	0.114196i
$255$	−2.07141	+	13.5169i	−0.129717	+	0.846464i
$256$	0.405697	+	1.77747i	0.0253560	+	0.111092i
$257$	9.09051	+	18.8766i	0.567050	+	1.17749i	0.965524	+	0.260312i	$0.0838255\pi$
$257$	9.09051	+	18.8766i	0.567050	+	1.17749i	−0.398474	+	0.917180i	$0.630460\pi$
$258$	1.15302	+	0.555264i	0.0717837	+	0.0345692i
$259$	−23.5261	+	5.36968i	−1.46184	+	0.333655i
$260$	1.97683	+	27.2804i	0.122598	+	1.69186i
$261$	2.53344	+	5.88051i	0.156816	+	0.363994i
$262$			0.398626i			0.0246272i
$263$	−6.06381	−	26.5673i	−0.373910	−	1.63821i	−0.715683	−	0.698426i	$-0.753884\pi$
$263$	−6.06381	−	26.5673i	−0.373910	−	1.63821i	0.341772	−	0.939783i	$-0.388973\pi$
$264$	1.84754	−	3.83645i	0.113708	−	0.236117i
$265$	2.15030	+	3.74571i	0.132092	+	0.230097i
$266$	−1.46219	−	6.40629i	−0.0896528	−	0.392795i
$267$	11.0517	+	2.52247i	0.676352	+	0.154373i
$268$	−7.57925	+	15.7385i	−0.462976	+	0.961380i
$269$	4.02532	−	3.21008i	0.245428	−	0.195722i	−0.493048	−	0.870002i	$-0.664117\pi$
$269$	4.02532	−	3.21008i	0.245428	−	0.195722i	0.738476	+	0.674280i	$0.235546\pi$
$270$	−4.49644	−	4.87001i	−0.273645	−	0.296380i
$271$	−2.72456	−	5.65762i	−0.165506	−	0.343676i	0.801677	−	0.597757i	$-0.203941\pi$
$271$	−2.72456	−	5.65762i	−0.165506	−	0.343676i	−0.967183	+	0.254081i	$0.918227\pi$
$272$	−6.84951	+	8.58901i	−0.415312	+	0.520785i
$273$	−25.7728			−1.55984
$274$	−1.48221	+	1.85863i	−0.0895435	+	0.112284i
$275$	−8.05468	−	0.643532i	−0.485716	−	0.0388064i
$276$	12.6426	+	2.88560i	0.760996	+	0.173692i
$277$	6.37734	+	5.08576i	0.383177	+	0.305574i	0.796068	−	0.605207i	$-0.206910\pi$
$277$	6.37734	+	5.08576i	0.383177	+	0.305574i	−0.412891	+	0.910780i	$0.635481\pi$
$278$	1.24530			0.0746880
$279$	3.86703	+	3.08385i	0.231513	+	0.184625i
$280$	5.88178	+	10.2457i	0.351504	+	0.612301i
$281$	−8.47335	−	10.6252i	−0.505478	−	0.633849i	0.461978	−	0.886892i	$-0.347140\pi$
$281$	−8.47335	−	10.6252i	−0.505478	−	0.633849i	−0.967455	+	0.253043i	$0.918569\pi$
$282$	−3.61952	−	4.53874i	−0.215540	−	0.270278i
$283$	1.68505	−	3.49903i	0.100166	−	0.207996i	−0.844864	−	0.534981i	$-0.820319\pi$
$283$	1.68505	−	3.49903i	0.100166	−	0.207996i	0.945029	+	0.326986i	$0.106033\pi$
$284$	1.29512	−	5.67429i	0.0768512	−	0.336707i
$285$	−13.3262	+	4.07468i	−0.789379	+	0.241363i
$286$	−5.43393	+	2.61684i	−0.321315	+	0.154737i
$287$	18.5264	+	8.92183i	1.09358	+	0.526639i
$288$	−1.37240	−	6.01286i	−0.0808692	−	0.354311i
$289$	3.65154			0.214797
$290$	6.12759	−	1.59553i	0.359825	−	0.0936927i
$291$	−13.5006			−0.791420
$292$	0.284821	+	1.24788i	0.0166679	+	0.0730267i
$293$	16.4646	+	7.92896i	0.961875	+	0.463215i	0.847834	−	0.530262i	$-0.177906\pi$
$293$	16.4646	+	7.92896i	0.961875	+	0.463215i	0.114041	+	0.993476i	$0.463621\pi$
$294$	−0.179470	+	0.0864284i	−0.0104669	+	0.00504060i
$295$	6.50796	+	21.2843i	0.378908	+	1.23922i
$296$	3.89618	−	17.0703i	0.226461	−	0.992191i
$297$	−3.95278	+	8.20804i	−0.229364	+	0.476279i
$298$	1.07079	+	1.34273i	0.0620294	+	0.0777824i
$299$	−24.7411	−	31.0244i	−1.43081	−	1.79418i
$300$	9.61379	−	6.48543i	0.555052	−	0.374436i
$301$	3.81541	+	3.04269i	0.219916	+	0.175377i
$302$	5.28840			0.304313
$303$	−2.27161	−	1.81155i	−0.130501	−	0.104071i
$304$	−10.9144	−	2.49113i	−0.625982	−	0.142876i
$305$	−14.5432	−	2.22869i	−0.832742	−	0.127614i
$306$	−1.77151	+	2.22140i	−0.101270	+	0.126989i
$307$	22.4442			1.28096			0.640480	−	0.767975i	$-0.278735\pi$
$307$	22.4442			1.28096			0.640480	+	0.767975i	$0.278735\pi$
$308$	4.68608	−	5.87616i	0.267014	−	0.334825i
$309$	−4.24700	−	8.81899i	−0.241604	−	0.501695i
$310$	3.59368	−	3.31801i	0.204107	−	0.188450i
$311$	−18.7354	+	14.9410i	−1.06239	+	0.847226i	−0.988678	−	0.150054i	$-0.952055\pi$
$311$	−18.7354	+	14.9410i	−1.06239	+	0.847226i	−0.0737097	+	0.997280i	$0.523484\pi$
$312$	8.11383	−	16.8486i	0.459355	−	0.953861i
$313$	9.13235	+	2.08440i	0.516191	+	0.117817i	0.472677	−	0.881236i	$-0.343288\pi$
$313$	9.13235	+	2.08440i	0.516191	+	0.117817i	0.0435138	+	0.999053i	$0.486145\pi$
$314$	0.496937	+	2.17722i	0.0280438	+	0.122868i
$315$	−3.57185	−	6.22197i	−0.201251	−	0.350568i
$316$	2.54798	−	5.29093i	0.143335	−	0.297638i
$317$	−3.40053	−	14.8987i	−0.190993	−	0.836794i	−0.976081	−	0.217409i	$-0.930239\pi$
$317$	−3.40053	−	14.8987i	−0.190993	−	0.836794i	0.785088	−	0.619385i	$-0.212618\pi$
$318$		−	1.36682i		−	0.0766475i
$319$	−5.13558	−	7.02600i	−0.287537	−	0.393380i
$320$	4.69975	−	0.340559i	0.262724	−	0.0190378i
$321$	−2.30987	+	0.527214i	−0.128925	+	0.0294262i
$322$	−7.14772	−	3.44216i	−0.398327	−	0.191824i
$323$	9.13108	+	18.9609i	0.508067	+	1.05501i
$324$	−1.54143	−	6.75343i	−0.0856348	−	0.375190i
$325$	−35.3738	−	2.82620i	−1.96218	−	0.156769i
$326$	−4.66058	−	2.24442i	−0.258126	−	0.124307i
$327$	−1.40155	−	1.75748i	−0.0775057	−	0.0971891i
$328$	−11.6650	+	9.30254i	−0.644093	+	0.513647i
$329$	−9.60499	−	19.9450i	−0.529540	−	1.09960i
$330$	2.10925	+	1.44569i	0.116110	+	0.0795824i
$331$			0.916209i			0.0503594i	0.999683	+	0.0251797i	$0.00801580\pi$
$331$			0.916209i			0.0503594i	−0.999683	+	0.0251797i	$0.991984\pi$
$332$	−11.7513	−	9.37137i	−0.644938	−	0.514321i
$333$	−2.36605	+	10.3663i	−0.129659	+	0.568072i
$334$	−0.182311	−	0.0416113i	−0.00997561	−	0.00227687i
$335$	−18.6940	−	12.8129i	−1.02136	−	0.700044i
$336$			8.77853i			0.478908i
$337$	−2.20288	+	2.76233i	−0.119999	+	0.150474i	−0.838202	−	0.545359i	$-0.816393\pi$
$337$	−2.20288	+	2.76233i	−0.119999	+	0.150474i	0.718204	+	0.695833i	$0.244965\pi$
$338$	−17.7053	+	8.52642i	−0.963041	+	0.463776i
$339$	3.19587	+	4.00749i	0.173576	+	0.217657i
$340$	−11.8805	−	12.8676i	−0.644311	−	0.697841i
$341$	−6.05687	−	2.91683i	−0.327998	−	0.157955i
$342$	−2.82281	−	0.644289i	−0.152640	−	0.0348391i
$343$	17.6748	−	4.03417i	0.954351	−	0.217824i
$344$	−3.19028	+	1.53636i	−0.172008	+	0.0828349i
$345$	−6.18520	+	15.6462i	−0.333000	+	0.842363i
$346$	1.26479	−	0.288679i	0.0679953	−	0.0155195i
$347$			2.57627i			0.138301i	0.997606	+	0.0691506i	$0.0220289\pi$
$347$			2.57627i			0.138301i	−0.997606	+	0.0691506i	$0.977971\pi$
$348$	12.0495	+	3.28825i	0.645922	+	0.176269i
$349$	5.60433			0.299993			0.149996	−	0.988687i	$-0.452074\pi$
$349$	5.60433			0.299993			0.149996	+	0.988687i	$0.452074\pi$
$350$	−6.61692	+	2.55940i	−0.353689	+	0.136806i
$351$	−17.3594	+	36.0473i	−0.926579	+	1.92406i
$352$	3.63711	+	7.55253i	0.193858	+	0.402551i
$353$	21.9151	−	5.00197i	1.16642	−	0.266228i	0.404896	−	0.914363i	$-0.367308\pi$
$353$	21.9151	−	5.00197i	1.16642	−	0.266228i	0.761526	+	0.648134i	$0.224451\pi$
$354$	1.56733	−	6.86694i	0.0833028	−	0.364974i
$355$	7.02236	+	2.77605i	0.372708	+	0.147338i
$356$	−11.3507	+	9.05185i	−0.601584	+	0.479747i
$357$	12.9020	−	10.2890i	0.682847	−	0.544552i
$358$	8.45636	−	4.07237i	0.446932	−	0.215231i
$359$	11.0654	+	8.82433i	0.584007	+	0.465730i	0.870375	−	0.492390i	$-0.163876\pi$
$359$	11.0654	+	8.82433i	0.584007	+	0.465730i	−0.286368	+	0.958120i	$0.592448\pi$
$360$	5.19201	−	0.376230i	0.273643	−	0.0198290i
$361$	−1.52502	+	1.91232i	−0.0802642	+	0.100648i
$362$	−2.25421	+	9.87633i	−0.118479	+	0.519088i
$363$	−2.51191	+	11.0054i	−0.131841	+	0.577633i
$364$	20.5799	−	25.8064i	1.07868	−	1.35262i
$365$	−1.65630	+	0.120021i	−0.0866946	+	0.00628216i
$366$	3.64031	+	2.90305i	0.190282	+	0.151745i
$367$	−17.0857	+	8.22802i	−0.891864	+	0.429499i	−0.822943	−	0.568123i	$-0.807670\pi$
$367$	−17.0857	+	8.22802i	−0.891864	+	0.429499i	−0.0689202	+	0.997622i	$0.521955\pi$
$368$	−10.5673	+	8.42713i	−0.550858	+	0.439294i
$369$	7.08385	−	5.64918i	0.368771	−	0.294085i
$370$	9.77850	+	3.86560i	0.508360	+	0.200963i
$371$	1.15980	−	5.08142i	0.0602139	−	0.263814i
$372$	9.40629	−	2.14693i	0.487694	−	0.111313i
$373$	5.13035	+	10.6533i	0.265640	+	0.551606i	0.990536	−	0.137251i	$-0.0438268\pi$
$373$	5.13035	+	10.6533i	0.265640	+	0.551606i	−0.724897	+	0.688858i	$0.758113\pi$
$374$	1.67556	−	3.47934i	0.0866413	−	0.179912i
$375$	6.42775	+	13.6036i	0.331927	+	0.702486i
$376$	16.0626			0.828364
$377$	−22.5539	−	30.8561i	−1.16159	−	1.58917i
$378$			7.99891i			0.411419i
$379$	−25.3552	+	5.78715i	−1.30241	+	0.297266i	−0.816805	−	0.576914i	$-0.804257\pi$
$379$	−25.3552	+	5.78715i	−1.30241	+	0.297266i	−0.485602	+	0.874180i	$0.661400\pi$
$380$	6.56118	−	16.5973i	0.336581	−	0.851423i
$381$	9.67190	−	4.65774i	0.495506	−	0.238623i
$382$	−6.75476	+	1.54173i	−0.345604	+	0.0788818i
$383$	−9.73190	−	2.22124i	−0.497277	−	0.113500i	−0.0334758	−	0.999440i	$-0.510658\pi$
$383$	−9.73190	−	2.22124i	−0.497277	−	0.113500i	−0.463801	+	0.885939i	$0.653515\pi$
$384$	−13.9218	−	6.70437i	−0.710442	−	0.342131i
$385$	6.61483	+	7.16441i	0.337123	+	0.365132i
$386$	7.14765	+	8.96287i	0.363806	+	0.456198i
$387$	1.93737	−	0.932989i	0.0984822	−	0.0474265i
$388$	10.7804	−	13.5182i	0.547292	−	0.686283i
$389$		−	3.16804i		−	0.160626i	−0.996770	−	0.0803130i	$-0.974408\pi$
$389$		−	3.16804i		−	0.160626i	0.996770	−	0.0803130i	$-0.0255920\pi$
$390$	9.26320	+	6.34902i	0.469061	+	0.321495i
$391$	24.7711	+	5.65384i	1.25273	+	0.285927i
$392$	0.122644	−	0.537339i	0.00619446	−	0.0271397i
$393$	−0.797600	−	0.636065i	−0.0402336	−	0.0320852i
$394$			0.705316i			0.0355333i
$395$	6.28451	+	4.30742i	0.316208	+	0.216730i
$396$	−1.43691	−	2.98377i	−0.0722075	−	0.149940i
$397$	−12.7152	+	10.1401i	−0.638159	+	0.508915i	−0.888282	−	0.459299i	$-0.848101\pi$
$397$	−12.7152	+	10.1401i	−0.638159	+	0.508915i	0.250123	+	0.968214i	$0.419529\pi$
$398$	−3.05717	−	3.83358i	−0.153242	−	0.192160i
$399$	15.1513	+	7.29649i	0.758515	+	0.365282i
$400$	−0.962639	+	12.0487i	−0.0481320	+	0.602437i
$401$	−2.37443	−	10.4030i	−0.118573	−	0.519503i	−0.998975	−	0.0452741i	$-0.985584\pi$
$401$	−2.37443	−	10.4030i	−0.118573	−	0.519503i	0.880401	−	0.474229i	$-0.157273\pi$
$402$	3.11189	+	6.46192i	0.155207	+	0.322291i
$403$	−26.6000	−	12.8099i	−1.32504	−	0.638105i
$404$	3.62782	−	0.828027i	0.180491	−	0.0411959i
$405$	8.96374	−	0.649541i	0.445412	−	0.0322760i
$406$	−6.73916	−	3.60158i	−0.334459	−	0.178743i
$407$		−	14.4520i		−	0.716357i
$408$	2.66445	+	11.6737i	0.131910	+	0.577934i
$409$	11.0453	−	22.9359i	0.546156	−	1.13410i	−0.427062	−	0.904222i	$-0.640451\pi$
$409$	11.0453	−	22.9359i	0.546156	−	1.13410i	0.973218	−	0.229883i	$-0.0738343\pi$
$410$	−4.46086	−	7.77057i	−0.220306	−	0.383761i
$411$	−1.35381	−	5.93143i	−0.0667785	−	0.292576i
$412$	12.2218	+	2.78954i	0.602123	+	0.137431i
$413$	11.6537	−	24.1992i	0.573443	−	1.19077i
$414$	−2.73304	+	2.17953i	−0.134322	+	0.107118i
$415$	14.3276	−	13.2285i	0.703314	−	0.649363i
$416$	15.9731	+	33.1685i	0.783145	+	1.62622i
$417$	−1.98705	+	2.49169i	−0.0973064	+	0.122018i
$418$	3.93535			0.192484
$419$	15.8180	−	19.8351i	0.772758	−	0.969008i	−0.227230	−	0.973841i	$-0.572967\pi$
$419$	15.8180	−	19.8351i	0.772758	−	0.969008i	0.999988	+	0.00483306i	$0.00153842\pi$
$420$	−13.8332	−	2.11988i	−0.674991	−	0.103440i
$421$	26.7043	+	6.09509i	1.30149	+	0.297057i	0.816440	−	0.577430i	$-0.195944\pi$
$421$	26.7043	+	6.09509i	1.30149	+	0.297057i	0.485050	+	0.874487i	$0.338801\pi$
$422$	11.7716	+	9.38755i	0.573033	+	0.456979i
$423$	−9.75437			−0.474274
$424$	2.95677	+	2.35795i	0.143593	+	0.114512i
$425$	18.8366	−	12.7071i	0.913710	−	0.616385i
$426$	−1.48993	−	1.86832i	−0.0721875	−	0.0905203i
$427$	11.0702	+	13.8816i	0.535725	+	0.671778i
$428$	1.31656	−	2.73387i	0.0636384	−	0.132147i
$429$	3.43465	−	15.0482i	0.165826	−	0.726532i
$430$	−0.621773	−	2.03351i	−0.0299845	−	0.0980644i
$431$	−14.6942	+	7.07635i	−0.707795	+	0.340856i	−0.752908	−	0.658126i	$-0.771349\pi$
$431$	−14.6942	+	7.07635i	−0.707795	+	0.340856i	0.0451131	+	0.998982i	$0.485635\pi$
$432$	12.2781	+	5.91284i	0.590733	+	0.284482i
$433$	−3.14733	−	13.7894i	−0.151251	−	0.662675i	−0.992523	−	0.122062i	$-0.961049\pi$
$433$	−3.14733	−	13.7894i	−0.151251	−	0.662675i	0.841271	−	0.540613i	$-0.181808\pi$
$434$	−5.90255			−0.283331
$435$	−6.58501	+	14.8065i	−0.315727	+	0.709915i
$436$	2.87893			0.137876
$437$	5.76156	+	25.2430i	0.275613	+	1.20754i
$438$	0.473488	+	0.228020i	0.0226241	+	0.0108952i
$439$	−15.2502	+	7.34409i	−0.727850	+	0.350514i	−0.760838	−	0.648942i	$-0.775212\pi$
$439$	−15.2502	+	7.34409i	−0.727850	+	0.350514i	0.0329881	+	0.999456i	$0.489498\pi$
$440$	−6.76611	+	2.06883i	−0.322562	+	0.0986277i
$441$	−0.0744785	+	0.326312i	−0.00354660	+	0.0155386i
$442$	7.35857	−	15.2802i	0.350012	−	0.726807i
$443$	6.43313	+	8.06689i	0.305647	+	0.383270i	0.910806	−	0.412836i	$-0.135462\pi$
$443$	6.43313	+	8.06689i	0.305647	+	0.383270i	−0.605158	+	0.796105i	$0.706890\pi$
$444$	12.9320	+	16.2162i	0.613723	+	0.769585i
$445$	−9.37767	−	16.3354i	−0.444544	−	0.774372i
$446$	−5.50676	−	4.39149i	−0.260752	−	0.207943i
$447$	−4.39525			−0.207888
$448$	−4.44580	−	3.54541i	−0.210044	−	0.167505i
$449$	25.0490	+	5.71726i	1.18213	+	0.269814i	0.768029	−	0.640415i	$-0.221238\pi$
$449$	25.0490	+	5.71726i	1.18213	+	0.269814i	0.414104	+	0.910229i	$0.364095\pi$
$450$	−0.248970	+	3.11620i	−0.0117366	+	0.146899i
$451$	−7.67821	+	9.62816i	−0.361553	+	0.453373i
$452$	−6.56465			−0.308775
$453$	−8.43841	+	10.5814i	−0.396471	+	0.497159i
$454$	−4.66620	−	9.68947i	−0.218996	−	0.454749i
$455$	29.0504	+	31.4639i	1.36190	+	1.47505i
$456$	−9.53994	+	7.60784i	−0.446748	+	0.356270i
$457$	−13.2173	+	27.4460i	−0.618280	+	1.28387i	0.323049	+	0.946382i	$0.395292\pi$
$457$	−13.2173	+	27.4460i	−0.618280	+	1.28387i	−0.941329	+	0.337489i	$0.890422\pi$
$458$	−1.20006	−	0.273907i	−0.0560753	−	0.0127988i
$459$	−5.70055	−	24.9757i	−0.266079	−	1.16577i
$460$	−10.7276	−	18.6869i	−0.500178	−	0.871283i
$461$	−2.04923	+	4.25527i	−0.0954421	+	0.198188i	−0.943224	−	0.332158i	$-0.892223\pi$
$461$	−2.04923	+	4.25527i	−0.0954421	+	0.198188i	0.847782	+	0.530345i	$0.177938\pi$
$462$	−0.686673	−	3.00851i	−0.0319469	−	0.139969i
$463$			15.9670i			0.742049i	0.928623	+	0.371024i	$0.120993\pi$
$463$			15.9670i			0.742049i	−0.928623	+	0.371024i	$0.879007\pi$
$464$	−10.5100	+	7.68215i	−0.487913	+	0.356635i
$465$	0.904692	+	12.4849i	0.0419541	+	0.578971i
$466$	−0.311409	+	0.0710770i	−0.0144257	+	0.00329258i
$467$	−19.7293	−	9.50115i	−0.912965	−	0.439661i	−0.0824110	−	0.996598i	$-0.526262\pi$
$467$	−19.7293	−	9.50115i	−0.912965	−	0.439661i	−0.830554	+	0.556937i	$0.811976\pi$
$468$	−6.31048	−	13.1039i	−0.291702	−	0.605726i
$469$	6.08589	+	26.6640i	0.281020	+	1.23123i
$470$	−1.46116	+	9.53474i	−0.0673982	+	0.439805i
$471$	−5.14928	−	2.47976i	−0.237266	−	0.114261i
$472$	12.1510	+	15.2369i	0.559296	+	0.701335i
$473$	−2.28502	+	1.82225i	−0.105065	+	0.0837869i
$474$	−1.04615	−	2.17236i	−0.0480513	−	0.0997796i
$475$	19.9954	+	11.6761i	0.917454	+	0.535735i
$476$			21.1347i			0.968709i
$477$	−1.79557	−	1.43192i	−0.0822134	−	0.0655630i
$478$	−0.320769	+	1.40538i	−0.0146716	+	0.0642806i
$479$	−20.1242	−	4.59321i	−0.919496	−	0.209869i	−0.263523	−	0.964653i	$-0.584884\pi$
$479$	−20.1242	−	4.59321i	−0.919496	−	0.209869i	−0.655973	+	0.754784i	$0.727742\pi$
$480$	8.82441	−	12.8748i	0.402777	−	0.587651i
$481$		−	63.4687i		−	2.89393i
$482$	−4.24476	+	5.32277i	−0.193344	+	0.242445i
$483$	18.2926	−	8.80923i	0.832340	−	0.400834i
$484$	−9.01394	−	11.3031i	−0.409724	−	0.513778i
$485$	15.2175	+	16.4818i	0.690992	+	0.748401i
$486$	5.44972	+	2.62444i	0.247204	+	0.119047i
$487$	−25.6817	−	5.86168i	−1.16375	−	0.265618i	−0.403332	−	0.915054i	$-0.632148\pi$
$487$	−25.6817	−	5.86168i	−1.16375	−	0.265618i	−0.760417	+	0.649436i	$0.775005\pi$
$488$	−12.5600	+	2.86674i	−0.568565	+	0.129771i
$489$	11.9274	−	5.74395i	0.539377	−	0.259750i
$490$	0.307808	+	0.121681i	0.0139053	+	0.00549701i
$491$	31.8360	−	7.26636i	1.43674	−	0.327926i	0.567931	−	0.823076i	$-0.307744\pi$
$491$	31.8360	−	7.26636i	1.43674	−	0.327926i	0.868808	+	0.495150i	$0.164887\pi$
$492$		−	17.6741i		−	0.796812i
$493$	23.6090	+	6.44277i	1.06330	+	0.290168i
$494$	17.2829			0.777594
$495$	4.10888	−	1.25635i	0.184680	−	0.0564686i
$496$	−4.36320	+	9.06028i	−0.195913	+	0.406818i
$497$	−3.95378	−	8.21011i	−0.177351	−	0.368274i
$498$	−6.01651	+	1.37323i	−0.269606	+	0.0615359i
$499$	−3.46290	+	15.1720i	−0.155021	+	0.679191i	0.836360	+	0.548180i	$0.184679\pi$
$499$	−3.46290	+	15.1720i	−0.155021	+	0.679191i	−0.991381	+	0.131010i	$0.958178\pi$
$500$	−18.7539	−	4.42651i	−0.838702	−	0.197960i
$501$	0.374162	−	0.298385i	0.0167163	−	0.0133308i
$502$	−1.79839	+	1.43417i	−0.0802659	+	0.0640099i
$503$	−11.3963	+	5.48816i	−0.508135	+	0.244705i	−0.670343	−	0.742052i	$-0.733853\pi$
$503$	−11.3963	+	5.48816i	−0.508135	+	0.244705i	0.162208	+	0.986757i	$0.448139\pi$
$504$	−4.91147	−	3.91677i	−0.218774	−	0.174467i
$505$	0.348922	+	4.81517i	0.0155268	+	0.214272i
$506$	2.96235	−	3.71467i	0.131693	−	0.165137i
$507$	11.1911	−	49.0312i	0.497012	−	2.17755i
$508$	−3.05932	+	13.4038i	−0.135735	+	0.594696i
$509$	−10.5319	+	13.2066i	−0.466819	+	0.585373i	−0.958389	−	0.285465i	$-0.907852\pi$
$509$	−10.5319	+	13.2066i	−0.466819	+	0.585373i	0.491570	+	0.870838i	$0.336423\pi$
$510$	−7.17188	+	0.519697i	−0.317576	+	0.0230126i
$511$	1.56680	+	1.24948i	0.0693112	+	0.0552739i
$512$	19.8265	−	9.54796i	0.876217	−	0.421964i
$513$	20.4106	−	16.2769i	0.901149	−	0.718642i
$514$	−8.61348	+	6.86902i	−0.379924	+	0.302980i
$515$	−5.97930	+	15.1254i	−0.263480	+	0.666503i
$516$	0.933375	−	4.08938i	0.0410896	−	0.180025i
$517$	12.9255	−	2.95015i	0.568461	−	0.129747i
$518$	−5.50556	−	11.4324i	−0.241900	−	0.502311i
$519$	−1.44054	+	2.99131i	−0.0632326	+	0.131304i
$520$	−29.7148	+	9.08570i	−1.30308	+	0.398434i
$521$	−8.58149			−0.375962			−0.187981	−	0.982173i	$-0.560194\pi$
$521$	−8.58149			−0.375962			−0.187981	+	0.982173i	$0.560194\pi$
$522$	−2.71822	+	1.98685i	−0.118973	+	0.0869622i
$523$		−	27.0088i		−	1.18101i	−0.807033	−	0.590506i	$-0.798928\pi$
$523$		−	27.0088i		−	1.18101i	0.807033	−	0.590506i	$-0.201072\pi$
$524$	1.27379	−	0.290734i	0.0556457	−	0.0127008i
$525$	5.43720	−	17.3235i	0.237299	−	0.756061i
$526$	12.9103	−	6.21726i	0.562914	−	0.271085i
$527$	18.4301	−	4.20654i	0.802826	−	0.183240i
$528$	−5.12559	−	1.16988i	−0.223063	−	0.0509126i
$529$	7.44227	+	3.58401i	0.323577	+	0.155826i
$530$	−1.66864	+	1.54064i	−0.0724812	+	0.0669213i
$531$	−7.37899	−	9.25296i	−0.320221	−	0.401544i
$532$	−19.4045	+	9.34472i	−0.841293	+	0.405145i
$533$	−33.7204	+	42.2840i	−1.46059	+	1.83153i
$534$			5.96083i			0.257950i
$535$	3.24726	+	2.22568i	0.140391	+	0.0962246i
$536$	−19.3472	−	4.41586i	−0.835670	−	0.190736i
$537$	−5.34505	+	23.4182i	−0.230656	+	1.01057i
$538$	2.11666	+	1.68798i	0.0912557	+	0.0727740i
$539$		−	0.454919i		−	0.0195948i
$540$	−12.2824	+	17.9200i	−0.528552	+	0.771156i
$541$	−10.0741	−	20.9192i	−0.433121	−	0.899385i	−0.997279	−	0.0737185i	$-0.976513\pi$
$541$	−10.0741	−	20.9192i	−0.433121	−	0.899385i	0.564158	−	0.825667i	$-0.309201\pi$
$542$	2.58159	−	2.05875i	0.110889	−	0.0884310i
$543$	−16.1644	−	20.2695i	−0.693680	−	0.869848i
$544$	−21.2378	−	10.2276i	−0.910561	−	0.438503i
$545$	−0.565787	+	3.69203i	−0.0242357	+	0.158149i
$546$	−3.01567	−	13.2125i	−0.129059	−	0.565443i
$547$	−9.47543	−	19.6759i	−0.405140	−	0.841282i	−0.999317	−	0.0369478i	$-0.988236\pi$
$547$	−9.47543	−	19.6759i	−0.405140	−	0.841282i	0.594177	−	0.804334i	$-0.297478\pi$
$548$	7.02019	+	3.38075i	0.299888	+	0.144418i
$549$	7.62736	−	1.74090i	0.325528	−	0.0742996i
$550$	−0.612567	−	4.20456i	−0.0261200	−	0.179283i
$551$	4.52340	+	24.5249i	0.192703	+	1.04480i
$552$			14.7318i			0.627028i
$553$	−2.04594	−	8.96386i	−0.0870024	−	0.381182i
$554$	−1.86102	+	3.86445i	−0.0790671	+	0.164185i
$555$	−23.3376	+	13.3974i	−0.990626	+	0.568689i
$556$	−0.908246	−	3.97928i	−0.0385182	−	0.168759i
$557$	6.68918	+	1.52676i	0.283430	+	0.0646910i	0.361872	−	0.932228i	$-0.382138\pi$
$557$	6.68918	+	1.52676i	0.283430	+	0.0646910i	−0.0784427	+	0.996919i	$0.524995\pi$
$558$	−1.12847	+	2.34328i	−0.0477718	+	0.0991991i
$559$	−10.0351	+	8.00276i	−0.424441	+	0.338481i
$560$	10.7170	−	9.89492i	0.452876	−	0.418137i
$561$	4.28813	+	8.90439i	0.181045	+	0.375943i
$562$	4.45560	−	5.58714i	0.187948	−	0.235679i
$563$	32.1242			1.35387			0.676936	−	0.736042i	$-0.263307\pi$
$563$	32.1242			1.35387			0.676936	+	0.736042i	$0.263307\pi$
$564$	−11.8634	+	14.8763i	−0.499541	+	0.626405i
$565$	1.29013	−	8.41872i	0.0542763	−	0.354178i
$566$	1.99096	+	0.454423i	0.0836861	+	0.0191008i
$567$	−8.47940	−	6.76210i	−0.356101	−	0.283981i
$568$	6.61197			0.277432
$569$	10.8212	+	8.62959i	0.453647	+	0.361771i	0.823497	−	0.567320i	$-0.192020\pi$
$569$	10.8212	+	8.62959i	0.453647	+	0.361771i	−0.369851	+	0.929091i	$0.620591\pi$
$570$	−3.64820	−	6.35496i	−0.152806	−	0.266180i
$571$	−25.9802	−	32.5782i	−1.08724	−	1.36335i	−0.926473	−	0.376362i	$-0.877175\pi$
$571$	−25.9802	−	32.5782i	−1.08724	−	1.36335i	−0.160766	−	0.986993i	$-0.551396\pi$
$572$	12.3252	+	15.4553i	0.515341	+	0.646217i
$573$	7.69339	−	15.9755i	0.321396	−	0.667386i
$574$	−2.40604	+	10.5415i	−0.100426	+	0.439995i
$575$	26.0730	−	10.0850i	1.08732	−	0.420572i
$576$	−2.25747	+	1.08714i	−0.0940614	+	0.0452976i
$577$	7.28857	+	3.50999i	0.303427	+	0.146123i	0.579402	−	0.815042i	$-0.303286\pi$
$577$	7.28857	+	3.50999i	0.303427	+	0.146123i	−0.275975	+	0.961165i	$0.589001\pi$
$578$	0.427266	+	1.87197i	0.0177719	+	0.0778638i
$579$	−29.3387			−1.21927
$580$	−9.56753	−	18.4167i	−0.397270	−	0.764713i
$581$	−23.5328			−0.976305
$582$	−1.57970	−	6.92113i	−0.0654808	−	0.286890i
$583$	2.81237	+	1.35437i	0.116476	+	0.0560921i
$584$	−1.31009	+	0.630908i	−0.0542121	+	0.0261071i
$585$	18.0450	−	5.51750i	0.746068	−	0.228121i
$586$	−2.13828	+	9.36841i	−0.0883315	+	0.387006i
$587$	−8.48384	+	17.6169i	−0.350166	+	0.727127i	−0.999441	−	0.0334267i	$-0.989358\pi$
$587$	−8.48384	+	17.6169i	−0.350166	+	0.727127i	0.649275	+	0.760553i	$0.275072\pi$
$588$	0.407072	+	0.510452i	0.0167874	+	0.0210507i
$589$	12.0110	+	15.0613i	0.494906	+	0.620592i
$590$	−10.1500	+	5.82679i	−0.417867	+	0.239885i
$591$	−1.41125	−	1.12543i	−0.0580510	−	0.0462942i
$592$	−21.6182			−0.888504
$593$	−17.4116	−	13.8852i	−0.715007	−	0.570199i	0.196985	−	0.980406i	$-0.436885\pi$
$593$	−17.4116	−	13.8852i	−0.715007	−	0.570199i	−0.911992	+	0.410208i	$0.865456\pi$
$594$	−4.67039	−	1.06599i	−0.191628	−	0.0437379i
$595$	−27.1039	−	4.15355i	−1.11115	−	0.170279i
$596$	3.50966	−	4.40098i	0.143761	−	0.180271i
$597$	12.5487			0.513583
$598$	13.0098	−	16.3137i	0.532009	−	0.667119i
$599$	0.462196	+	0.959760i	0.0188848	+	0.0392147i	0.910198	−	0.414174i	$-0.135929\pi$
$599$	0.462196	+	0.959760i	0.0188848	+	0.0392147i	−0.891313	+	0.453388i	$0.850215\pi$
$600$	9.61323	+	9.00831i	0.392459	+	0.367763i
$601$	−34.6801	+	27.6564i	−1.41463	+	1.12813i	−0.441663	+	0.897181i	$0.645611\pi$
$601$	−34.6801	+	27.6564i	−1.41463	+	1.12813i	−0.972966	+	0.230948i	$0.925817\pi$
$602$	−1.11340	+	2.31200i	−0.0453789	+	0.0942302i
$603$	11.7490	+	2.68163i	0.478457	+	0.109205i
$604$	−3.85704	−	16.8988i	−0.156941	−	0.687603i
$605$	16.2670	−	9.33839i	0.661346	−	0.379659i
$606$	0.662896	−	1.37652i	0.0269283	−	0.0559172i
$607$	6.51943	+	28.5635i	0.264616	+	1.15936i	0.916181	+	0.400764i	$0.131255\pi$
$607$	6.51943	+	28.5635i	0.264616	+	1.15936i	−0.651566	+	0.758592i	$0.725887\pi$
$608$		−	24.0212i		−	0.974189i
$609$	17.9596	−	7.73737i	0.727760	−	0.313534i
$610$	−0.559155	−	7.71640i	−0.0226395	−	0.312428i
$611$	56.7648	−	12.9562i	2.29646	−	0.524151i
$612$	8.39039	+	4.04060i	0.339161	+	0.163332i
$613$	2.69606	+	5.59842i	0.108893	+	0.226118i	0.948293	−	0.317395i	$-0.102808\pi$
$613$	2.69606	+	5.59842i	0.108893	+	0.226118i	−0.839401	+	0.543513i	$0.817094\pi$
$614$	2.62619	+	11.5061i	0.105985	+	0.464349i
$615$	22.6659	+	3.47345i	0.913976	+	0.140063i
$616$	7.69276	+	3.70464i	0.309950	+	0.149264i
$617$	−25.5907	−	32.0897i	−1.03024	−	1.29188i	−0.955598	−	0.294674i	$-0.904789\pi$
$617$	−25.5907	−	32.0897i	−1.03024	−	1.29188i	−0.0746458	−	0.997210i	$-0.523783\pi$
$618$	4.02414	−	3.20915i	0.161875	−	0.129091i
$619$	12.9238	+	26.8366i	0.519453	+	1.07866i	0.981440	+	0.191769i	$0.0614225\pi$
$619$	12.9238	+	26.8366i	0.519453	+	1.07866i	−0.461987	+	0.886887i	$0.652863\pi$
$620$	−13.2235	−	9.06344i	−0.531070	−	0.363997i
$621$		−	31.5185i		−	1.26480i
$622$	−9.85177	−	7.85652i	−0.395020	−	0.315018i
$623$	−5.05800	+	22.1606i	−0.202645	+	0.887844i
$624$	−22.5101	−	5.13778i	−0.901124	−	0.205676i
$625$	9.36236	−	23.1807i	0.374494	−	0.927229i
$626$			4.92562i			0.196868i
$627$	−6.27943	+	7.87415i	−0.250776	+	0.314463i
$628$	6.59476	−	3.17587i	0.263160	−	0.126731i
$629$	25.3380	+	31.7729i	1.01029	+	1.26687i
$630$	2.77177	−	2.55915i	0.110430	−	0.101959i
$631$	−25.4117	−	12.2376i	−1.01162	−	0.487173i	−0.146757	−	0.989173i	$-0.546884\pi$
$631$	−25.4117	−	12.2376i	−1.01162	−	0.487173i	−0.864868	+	0.502000i	$0.832598\pi$
$632$	6.50409	+	1.48452i	0.258719	+	0.0590509i
$633$	−37.5666	+	8.57434i	−1.49314	+	0.340799i
$634$	7.23996	−	3.48658i	0.287536	−	0.138470i
$635$	−16.5882	−	6.55757i	−0.658281	−	0.260229i
$636$	−4.36760	+	0.996877i	−0.173187	+	0.0395287i
$637$		−	1.99787i		−	0.0791585i
$638$	3.00099	−	3.45488i	0.118810	−	0.136780i
$639$	−4.01527			−0.158842
$640$	7.50741	+	24.5530i	0.296756	+	0.970542i
$641$	−8.53483	+	17.7228i	−0.337106	+	0.700007i	−0.998759	−	0.0498029i	$-0.984141\pi$
$641$	−8.53483	+	17.7228i	−0.337106	+	0.700007i	0.661654	+	0.749810i	$0.269855\pi$
$642$	−0.540555	−	1.12247i	−0.0213340	−	0.0443005i
$643$	−39.4384	+	9.00156i	−1.55530	+	0.354987i	−0.911857	−	0.410509i	$-0.865351\pi$
$643$	−39.4384	+	9.00156i	−1.55530	+	0.354987i	−0.643442	+	0.765495i	$0.722494\pi$
$644$	−5.78613	+	25.3507i	−0.228005	+	0.998957i
$645$	5.06092	+	2.00066i	0.199274	+	0.0787761i
$646$	−8.65193	+	6.89968i	−0.340406	+	0.271464i
$647$	−34.2910	+	27.3462i	−1.34812	+	1.07509i	−0.358172	+	0.933656i	$0.616600\pi$
$647$	−34.2910	+	27.3462i	−1.34812	+	1.07509i	−0.989948	+	0.141434i	$0.954829\pi$
$648$	7.09011	−	3.41442i	0.278526	−	0.134131i
$649$	12.5764	+	10.0293i	0.493665	+	0.393685i
$650$	−2.69021	−	18.4652i	−0.105519	−	0.724263i
$651$	9.41837	−	11.8103i	0.369135	−	0.462881i
$652$	−3.77277	+	16.5296i	−0.147753	+	0.647348i
$653$	−0.829146	+	3.63272i	−0.0324470	+	0.142159i	−0.988557	−	0.150849i	$-0.951799\pi$
$653$	−0.829146	+	3.63272i	−0.0324470	+	0.142159i	0.956110	+	0.293008i	$0.0946564\pi$
$654$	0.736985	−	0.924150i	0.0288184	−	0.0361371i
$655$	0.122512	+	1.69068i	0.00478695	+	0.0660604i
$656$	14.4025	+	11.4856i	0.562322	+	0.448437i
$657$	0.795585	−	0.383133i	0.0310387	−	0.0149475i
$658$	9.10097	−	7.25778i	0.354793	−	0.282938i
$659$	2.19123	−	1.74745i	0.0853581	−	0.0680708i	−0.579881	−	0.814701i	$-0.696901\pi$
$659$	2.19123	−	1.74745i	0.0853581	−	0.0680708i	0.665239	+	0.746630i	$0.268330\pi$
$660$	3.08125	−	7.79440i	0.119938	−	0.303397i
$661$	9.62543	−	42.1717i	0.374386	−	1.64029i	−0.339918	−	0.940455i	$-0.610399\pi$
$661$	9.62543	−	42.1717i	0.374386	−	1.64029i	0.714304	−	0.699836i	$-0.246744\pi$
$662$	−0.469697	+	0.107205i	−0.0182553	+	0.00416665i
$663$	18.8322	+	39.1054i	0.731381	+	1.51873i
$664$	7.40864	−	15.3842i	0.287511	−	0.597023i
$665$	−8.17045	−	26.7215i	−0.316837	−	1.03621i
$666$	−5.59118			−0.216654
$667$	26.5547	+	14.1915i	1.02820	+	0.549497i
$668$			0.612914i			0.0237143i
$669$	17.5737	−	4.01107i	0.679437	−	0.155077i
$670$	4.38120	−	11.0828i	0.169260	−	0.428165i
$671$	−9.58045	+	4.61370i	−0.369849	+	0.178110i
$672$	−18.3638	+	4.19142i	−0.708400	+	0.161688i
$673$	18.0351	+	4.11639i	0.695202	+	0.158675i	0.555498	−	0.831518i	$-0.312528\pi$
$673$	18.0351	+	4.11639i	0.695202	+	0.158675i	0.139704	+	0.990193i	$0.455385\pi$
$674$	−1.67388	−	0.806096i	−0.0644753	−	0.0310497i
$675$	−20.5674	−	19.2732i	−0.791639	−	0.741824i
$676$	40.1589	+	50.3577i	1.54457	+	1.93683i
$677$	38.0908	−	18.3436i	1.46395	−	0.705001i	0.478995	−	0.877818i	$-0.341001\pi$
$677$	38.0908	−	18.3436i	1.46395	−	0.705001i	0.984954	+	0.172817i	$0.0552869\pi$
$678$	−1.68050	+	2.10729i	−0.0645394	+	0.0809298i
$679$		−	27.0711i		−	1.03889i
$680$	11.2482	−	16.4111i	0.431349	−	0.629337i
$681$	26.8330	+	6.12446i	1.02824	+	0.234690i
$682$	0.786611	−	3.44637i	0.0301209	−	0.131968i
$683$	28.9844	+	23.1143i	1.10906	+	0.884442i	0.994050	−	0.108923i	$-0.0347401\pi$
$683$	28.9844	+	23.1143i	1.10906	+	0.884442i	0.115005	+	0.993365i	$0.463311\pi$
$684$			9.49006i			0.362861i
$685$	−5.71524	+	8.33851i	−0.218368	+	0.318598i
$686$	4.13625	+	8.58902i	0.157923	+	0.327930i
$687$	2.46293	−	1.96412i	0.0939666	−	0.0749359i
$688$	2.72584	+	3.41809i	0.103922	+	0.130314i
$689$	12.3511	+	5.94797i	0.470539	+	0.226600i
$690$	−8.74480	−	1.34010i	−0.332909	−	0.0510169i
$691$	4.52909	+	19.8432i	0.172295	+	0.754872i	0.985050	+	0.172267i	$0.0551092\pi$
$691$	4.52909	+	19.8432i	0.172295	+	0.754872i	−0.812756	+	0.582605i	$0.802034\pi$
$692$	−1.84492	−	3.83101i	−0.0701333	−	0.145633i
$693$	−4.67161	−	2.24973i	−0.177460	−	0.0854601i
$694$	−1.32073	+	0.301448i	−0.0501343	+	0.0114428i
$695$	5.28166	−	0.382725i	0.200345	−	0.0145176i
$696$	−0.595890	+	14.1767i	−0.0225872	+	0.537367i
$697$		−	34.6295i		−	1.31169i
$698$	0.655761	+	2.87307i	0.0248209	+	0.108747i
$699$	0.354681	−	0.736504i	0.0134153	−	0.0278571i
$700$	13.0044	+	19.2773i	0.491521	+	0.728615i
$701$	−6.20083	−	27.1676i	−0.234202	−	1.02611i	−0.946113	−	0.323836i	$-0.895027\pi$
$701$	−6.20083	−	27.1676i	−0.234202	−	1.02611i	0.711911	−	0.702270i	$-0.247830\pi$
$702$	−20.5110	−	4.68149i	−0.774136	−	0.176692i
$703$	−17.9685	+	37.3121i	−0.677696	+	1.40725i
$704$	2.66256	−	2.12332i	0.100349	−	0.0800258i
$705$	−16.7463	−	18.1376i	−0.630703	−	0.683103i
$706$	5.12855	+	10.6496i	0.193016	+	0.400801i
$707$	3.63248	−	4.55498i	0.136613	−	0.171308i
$708$	−23.0861			−0.867627
$709$	−14.1360	+	17.7260i	−0.530889	+	0.665714i	−0.972881	−	0.231305i	$-0.925701\pi$
$709$	−14.1360	+	17.7260i	−0.530889	+	0.665714i	0.441992	+	0.897019i	$0.354272\pi$
$710$	−0.601468	+	3.92486i	−0.0225727	+	0.147297i
$711$	−3.94976	−	0.901507i	−0.148128	−	0.0338092i
$712$	−12.8948	−	10.2832i	−0.483251	−	0.385380i
$713$	23.2581			0.871023
$714$	6.78436	+	5.41034i	0.253898	+	0.202477i
$715$	−22.2426	+	12.7688i	−0.831824	+	0.477526i
$716$	−19.1806	−	24.0517i	−0.716813	−	0.898855i
$717$	−2.30016	−	2.88431i	−0.0859009	−	0.107716i
$718$	−3.22906	+	6.70522i	−0.120508	+	0.250237i
$719$	−10.2689	+	44.9909i	−0.382965	+	1.67788i	0.305173	+	0.952297i	$0.401286\pi$
$719$	−10.2689	+	44.9909i	−0.382965	+	1.67788i	−0.688138	+	0.725580i	$0.741571\pi$
$720$	−1.87933	−	6.14634i	−0.0700385	−	0.229061i
$721$	17.6836	−	8.51599i	0.658573	−	0.317152i
$722$	−1.15880	−	0.558047i	−0.0431259	−	0.0207684i
$723$	−3.87706	−	16.9865i	−0.144189	−	0.631734i
$724$	33.2034			1.23399
$725$	25.4985	−	8.65031i	0.946989	−	0.321265i
$726$	−5.93586			−0.220300
$727$	−2.17929	−	9.54809i	−0.0808253	−	0.354119i	0.918302	−	0.395880i	$-0.129560\pi$
$727$	−2.17929	−	9.54809i	−0.0808253	−	0.354119i	−0.999128	+	0.0417610i	$0.986703\pi$
$728$	33.7843	+	16.2697i	1.25213	+	0.602994i
$729$	−24.8106	+	11.9481i	−0.918910	+	0.442524i
$730$	−0.255332	−	0.835062i	−0.00945025	−	0.0309070i
$731$	1.82879	−	8.01246i	0.0676403	−	0.296352i
$732$	6.62152	−	13.7497i	0.244738	−	0.508204i
$733$	−16.6556	−	20.8855i	−0.615190	−	0.771424i	0.372469	−	0.928045i	$-0.378511\pi$
$733$	−16.6556	−	20.8855i	−0.615190	−	0.771424i	−0.987659	+	0.156621i	$0.949940\pi$
$734$	−6.21730	−	7.79625i	−0.229485	−	0.287765i
$735$	−0.734621	+	0.421725i	−0.0270969	+	0.0155555i
$736$	−22.6742	−	18.0821i	−0.835783	−	0.666514i
$737$	−16.3796			−0.603350
$738$	3.72495	+	2.97055i	0.137117	+	0.109347i
$739$	2.06709	+	0.471799i	0.0760391	+	0.0173554i	0.260371	−	0.965509i	$-0.416155\pi$
$739$	2.06709	+	0.471799i	0.0760391	+	0.0173554i	−0.184332	+	0.982864i	$0.559012\pi$
$740$	5.22047	−	34.0660i	0.191908	−	1.25229i
$741$	−27.5774	+	34.5809i	−1.01308	+	1.27036i
$742$	2.74072			0.100615
$743$	28.8186	−	36.1373i	1.05725	−	1.32575i	0.114069	−	0.993473i	$-0.463611\pi$
$743$	28.8186	−	36.1373i	1.05725	−	1.32575i	0.943182	−	0.332278i	$-0.107817\pi$
$744$	4.75566	+	9.87524i	0.174351	+	0.362044i
$745$	4.95421	+	5.36581i	0.181508	+	0.196588i
$746$	−4.86114	+	3.87663i	−0.177979	+	0.141933i
$747$	−4.49907	+	9.34241i	−0.164612	+	0.341821i
$748$	−12.3401	−	2.81655i	−0.451199	−	0.102983i
$749$	−1.05716	−	4.63170i	−0.0386276	−	0.169239i
$750$	−6.22181	+	4.88696i	−0.227188	+	0.178446i
$751$	6.91246	−	14.3539i	0.252239	−	0.523780i	−0.735947	−	0.677039i	$-0.763263\pi$
$751$	6.91246	−	14.3539i	0.252239	−	0.523780i	0.988186	+	0.153259i	$0.0489770\pi$
$752$	−4.41304	−	19.3348i	−0.160927	−	0.705067i
$753$		−	5.88677i		−	0.214526i
$754$	13.1794	−	15.1728i	0.479967	−	0.552561i
$755$	22.4296	−	1.62532i	0.816296	−	0.0591514i
$756$	25.5601	−	5.83392i	0.929612	−	0.212178i
$757$	37.3984	+	18.0101i	1.35927	+	0.654589i	0.964473	−	0.264181i	$-0.0851016\pi$
$757$	37.3984	+	18.0101i	1.35927	+	0.654589i	0.394794	+	0.918770i	$0.370816\pi$
$758$	−5.93360	−	12.3212i	−0.215518	−	0.447528i
$759$	2.70574	+	11.8546i	0.0982120	+	0.430295i
$760$	20.0410	+	3.07119i	0.726963	+	0.111404i
$761$	−7.23149	−	3.48250i	−0.262141	−	0.126241i	0.298197	−	0.954504i	$-0.403615\pi$
$761$	−7.23149	−	3.48250i	−0.262141	−	0.126241i	−0.560339	+	0.828264i	$0.689329\pi$
$762$	3.51951	+	4.41333i	0.127498	+	0.159878i
$763$	3.52406	−	2.81035i	0.127580	−	0.101741i
$764$	9.85303	+	20.4600i	0.356470	+	0.740218i
$765$	−6.83073	+	9.96602i	−0.246966	+	0.360322i
$766$		−	5.24900i		−	0.189654i
$767$	55.2316	+	44.0458i	1.99430	+	1.59040i
$768$	0.545958	−	2.39200i	0.0197006	−	0.0863138i
$769$	3.71363	+	0.847611i	0.133917	+	0.0305656i	0.288954	−	0.957343i	$-0.406693\pi$
$769$	3.71363	+	0.847611i	0.133917	+	0.0305656i	−0.155037	+	0.987909i	$0.549550\pi$
$770$	−2.89885	+	4.22942i	−0.104467	+	0.152418i
$771$		−	28.1950i		−	1.01542i
$772$	23.4273	−	29.3769i	0.843167	−	1.05730i
$773$	−38.7457	+	18.6589i	−1.39359	+	0.671116i	−0.971849	−	0.235603i	$-0.924294\pi$
$773$	−38.7457	+	18.6589i	−1.39359	+	0.671116i	−0.421736	+	0.906718i	$0.638579\pi$
$774$	0.704991	+	0.884031i	0.0253404	+	0.0317758i
$775$	14.2220	−	15.1771i	0.510870	−	0.545176i
$776$	17.6973	+	8.52257i	0.635296	+	0.305942i
$777$	31.6598	+	7.22613i	1.13579	+	0.259236i
$778$	1.62411	−	0.370692i	0.0582270	−	0.0132899i
$779$	31.7945	−	15.3114i	1.13916	−	0.548589i
$780$	13.5319	−	34.2307i	0.484521	−	1.22566i
$781$	5.32061	−	1.21439i	0.190386	−	0.0434544i
$782$			13.3605i			0.477772i
$783$	1.27490	−	30.3309i	0.0455612	−	1.08394i
$784$	−0.680499			−0.0243035
$785$	2.77679	+	9.08147i	0.0991077	+	0.324132i
$786$	0.232754	−	0.483318i	0.00830205	−	0.0172394i
$787$	−16.1103	−	33.4534i	−0.574270	−	1.19248i	−0.962591	−	0.270959i	$-0.912659\pi$
$787$	−16.1103	−	33.4534i	−0.574270	−	1.19248i	0.388321	−	0.921524i	$-0.373055\pi$
$788$	2.25380	−	0.514415i	0.0802883	−	0.0183253i
$789$	−8.16025	+	35.7524i	−0.290512	+	1.27282i
$790$	−1.47286	+	3.72579i	−0.0524021	+	0.132557i
$791$	−8.03572	+	6.40828i	−0.285717	+	0.227852i
$792$	2.94145	−	2.34573i	0.104520	−	0.0833517i
$793$	−42.0745	+	20.2620i	−1.49411	+	0.719525i
$794$	−6.68613	−	5.33201i	−0.237282	−	0.189226i
$795$	−0.420074	−	5.79707i	−0.0148985	−	0.205601i
$796$	−10.0203	+	12.5650i	−0.355159	+	0.445355i
$797$	−2.64320	+	11.5806i	−0.0936270	+	0.410207i	−0.999923	−	0.0124375i	$-0.996041\pi$
$797$	−2.64320	+	11.5806i	−0.0936270	+	0.410207i	0.906296	+	0.422644i	$0.138898\pi$
$798$	−1.96772	+	8.62113i	−0.0696564	+	0.305185i
$799$	−23.2444	+	29.1476i	−0.822329	+	1.03117i
$800$	−25.6644	+	3.73909i	−0.907375	+	0.132197i
$801$	7.83064	+	6.24472i	0.276682	+	0.220647i
$802$	5.05532	−	2.43452i	0.178510	−	0.0859657i
$803$	−0.938348	+	0.748307i	−0.0331136	+	0.0264072i
$804$	18.3791	−	14.6568i	0.648180	−	0.516907i
$805$	−31.3734	−	12.4024i	−1.10577	−	0.437128i
$806$	3.45456	−	15.1354i	0.121682	−	0.533123i
$807$	−6.75488	+	1.54176i	−0.237783	+	0.0542724i
$808$	1.83417	+	3.80868i	0.0645257	+	0.133989i
$809$	3.38419	−	7.02734i	0.118982	−	0.247068i	−0.832969	−	0.553320i	$-0.813361\pi$
$809$	3.38419	−	7.02734i	0.118982	−	0.247068i	0.951951	+	0.306252i	$0.0990750\pi$
$810$	1.38183	+	4.51929i	0.0485527	+	0.158792i
$811$	−32.6876			−1.14782			−0.573909	−	0.818919i	$-0.694574\pi$
$811$	−32.6876			−1.14782			−0.573909	+	0.818919i	$0.694574\pi$
$812$	−6.59352	+	24.1614i	−0.231387	+	0.847899i
$813$			8.45048i			0.296371i
$814$	7.40884	−	1.69102i	0.259680	−	0.0592702i
$815$	−20.4566	−	8.08683i	−0.716564	−	0.283269i
$816$	13.3198	−	6.41448i	0.466286	−	0.224552i
$817$	8.16512	−	1.86363i	0.285661	−	0.0652003i
$818$	13.0505	+	2.97870i	0.456302	+	0.104148i
$819$	−20.5163	−	9.88013i	−0.716898	−	0.345240i
$820$	−21.5770	+	19.9218i	−0.753500	+	0.695700i
$821$	22.5750	+	28.3081i	0.787872	+	0.987960i	0.999943	+	0.0107059i	$0.00340785\pi$
$821$	22.5750	+	28.3081i	0.787872	+	0.987960i	−0.212071	+	0.977254i	$0.568021\pi$
$822$	2.88236	−	1.38807i	0.100534	−	0.0484145i
$823$	11.5622	−	14.4986i	0.403034	−	0.505389i	−0.538352	−	0.842720i	$-0.680953\pi$
$823$	11.5622	−	14.4986i	0.403034	−	0.505389i	0.941386	+	0.337331i	$0.109524\pi$
$824$			14.2414i			0.496123i
$825$	9.39023	+	5.48331i	0.326926	+	0.190904i
$826$	13.7694	+	3.14278i	0.479099	+	0.109351i
$827$	−3.18754	+	13.9655i	−0.110842	+	0.485629i	0.888785	+	0.458323i	$0.151550\pi$
$827$	−3.18754	+	13.9655i	−0.110842	+	0.485629i	−0.999627	+	0.0273056i	$0.991307\pi$
$828$	8.95789	+	7.14368i	0.311308	+	0.248260i
$829$		−	40.7912i		−	1.41674i	−0.705843	−	0.708369i	$-0.749431\pi$
$829$		−	40.7912i		−	1.41674i	0.705843	−	0.708369i	$-0.250569\pi$
$830$	8.45812	+	5.79722i	0.293586	+	0.201224i
$831$	−4.76275	−	9.88995i	−0.165218	−	0.343079i
$832$	11.6932	−	9.32501i	0.405388	−	0.323286i
$833$	0.797590	+	1.00015i	0.0276349	+	0.0346530i
$834$	−1.50987	−	0.727117i	−0.0522827	−	0.0251780i
$835$	−0.786020	−	0.120454i	−0.0272013	−	0.00416849i
$836$	−2.87021	−	12.5752i	−0.0992683	−	0.434923i
$837$	−10.1747	−	21.1279i	−0.351688	−	0.730289i
$838$	12.0194	+	5.78823i	0.415203	+	0.199951i
$839$	−26.0600	+	5.94802i	−0.899690	+	0.205348i	−0.647262	−	0.762267i	$-0.724086\pi$
$839$	−26.0600	+	5.94802i	−0.899690	+	0.205348i	−0.252428	+	0.967616i	$0.581229\pi$
$840$	−1.14904	−	15.8569i	−0.0396456	−	0.547114i
$841$	24.9800	+	14.7309i	0.861380	+	0.507961i
$842$			14.4032i			0.496369i
$843$	4.06963	+	17.8302i	0.140165	+	0.614104i
$844$	21.4119	−	44.4623i	0.737029	−	1.53046i
$845$	−72.4726	+	41.6044i	−2.49313	+	1.43123i
$846$	−1.14136	−	5.00061i	−0.0392406	−	0.171924i
$847$	−22.0677	−	5.03682i	−0.758256	−	0.173067i
$848$	2.02595	−	4.20694i	0.0695716	−	0.144467i
$849$	−4.08610	+	3.25856i	−0.140235	+	0.111833i
$850$	8.71840	+	8.16979i	0.299039	+	0.280221i
$851$	21.6939	+	45.0478i	0.743656	+	1.54422i
$852$	−4.88344	+	6.12364i	−0.167304	+	0.209793i
$853$	11.0739			0.379165			0.189582	−	0.981865i	$-0.439287\pi$
$853$	11.0739			0.379165			0.189582	+	0.981865i	$0.439287\pi$
$854$	−5.82112	+	7.29946i	−0.199195	+	0.249782i
$855$	−12.1703	−	1.86505i	−0.416217	−	0.0637835i
$856$	3.36072	+	0.767062i	0.114867	+	0.0262176i
$857$	−38.6740	−	30.8415i	−1.32108	−	1.05352i	−0.994097	−	0.108493i	$-0.965398\pi$
$857$	−38.6740	−	30.8415i	−1.32108	−	1.05352i	−0.326980	−	0.945031i	$-0.606031\pi$
$858$	8.11637			0.277088
$859$	−6.87862	−	5.48551i	−0.234695	−	0.187163i	0.499079	−	0.866556i	$-0.333672\pi$
$859$	−6.87862	−	5.48551i	−0.234695	−	0.187163i	−0.733774	+	0.679393i	$0.762243\pi$
$860$	−6.04448	+	3.46996i	−0.206115	+	0.118325i
$861$	−17.2531	−	21.6347i	−0.587985	−	0.737310i
$862$	−5.34708	−	6.70502i	−0.182122	−	0.228374i
$863$	10.9585	−	22.7556i	0.373032	−	0.774609i	−0.626958	−	0.779053i	$-0.715700\pi$
$863$	10.9585	−	22.7556i	0.373032	−	0.774609i	0.999990	+	0.00444371i	$0.00141448\pi$
$864$	−6.50673	+	28.5078i	−0.221363	+	0.969857i
$865$	5.27559	−	1.61308i	0.179375	−	0.0548465i
$866$	6.70089	−	3.22698i	0.227706	−	0.109657i
$867$	−4.42735	−	2.13210i	−0.150361	−	0.0724099i
$868$	4.30496	+	18.8613i	0.146120	+	0.640193i
$869$	5.50646			0.186794
$870$	−8.36108	−	1.64333i	−0.283467	−	0.0557140i
$871$	−71.9343			−2.43740
$872$	0.727768	+	3.18856i	0.0246453	+	0.107978i
$873$	−10.7471	−	5.17553i	−0.363734	−	0.175165i
$874$	−12.2668	+	5.90736i	−0.414929	+	0.199819i
$875$	−27.2776	+	12.8888i	−0.922151	+	0.435720i
$876$	0.383292	−	1.67931i	0.0129502	−	0.0567387i
$877$	7.47213	−	15.5160i	0.252316	−	0.523939i	−0.735884	−	0.677107i	$-0.763233\pi$
$877$	7.47213	−	15.5160i	0.252316	−	0.523939i	0.988200	+	0.153168i	$0.0489475\pi$
$878$	−5.54938	−	6.95871i	−0.187283	−	0.234845i
$879$	−15.3331	−	19.2271i	−0.517172	−	0.648514i
$880$	4.34921	+	7.57609i	0.146612	+	0.255390i
$881$	−33.9936	−	27.1090i	−1.14527	−	0.913325i	−0.148138	−	0.988967i	$-0.547328\pi$
$881$	−33.9936	−	27.1090i	−1.14527	−	0.913325i	−0.997135	+	0.0756420i	$0.975899\pi$
$882$	−0.175999			−0.00592621
$883$	5.43334	+	4.33294i	0.182846	+	0.145815i	0.710636	−	0.703560i	$-0.248407\pi$
$883$	5.43334	+	4.33294i	0.182846	+	0.145815i	−0.527789	+	0.849375i	$0.676979\pi$
$884$	−54.1941	−	12.3694i	−1.82274	−	0.416030i
$885$	4.53704	−	29.6063i	0.152511	−	0.995204i
$886$	−3.38278	+	4.24187i	−0.113647	+	0.142508i
$887$	−50.5186			−1.69625			−0.848124	−	0.529798i	$-0.822268\pi$
$887$	−50.5186			−1.69625			−0.848124	+	0.529798i	$0.822268\pi$
$888$	−14.6912	+	18.4221i	−0.493003	+	0.618206i
$889$	9.33959	+	19.3939i	0.313240	+	0.650449i
$890$	7.27711	−	6.71889i	0.243929	−	0.225218i
$891$	5.07826	−	4.04978i	0.170128	−	0.135673i
$892$	−10.0165	+	20.7994i	−0.335377	+	0.696417i
$893$	−37.0389	−	8.45389i	−1.23946	−	0.282899i
$894$	−0.514287	−	2.25324i	−0.0172003	−	0.0753595i
$895$	34.6142	−	19.8710i	1.15702	−	0.664214i
$896$	13.4434	−	27.9156i	0.449114	−	0.932595i
$897$	11.8828	+	52.0619i	0.396755	+	1.73830i
$898$			13.5104i			0.450848i
$899$	22.3817	+	0.940773i	0.746473	+	0.0313765i
$900$	10.1392	−	1.47720i	0.337975	−	0.0492400i
$901$	−8.55759	+	1.95321i	−0.285095	+	0.0650710i
$902$	−5.83433	−	2.80967i	−0.194262	−	0.0935516i
$903$	−2.84944	−	5.91691i	−0.0948233	−	0.196903i
$904$	−1.65949	−	7.27069i	−0.0551938	−	0.241820i
$905$	−6.52537	+	42.5811i	−0.216910	+	1.41544i
$906$	−6.41198	−	3.08785i	−0.213024	−	0.102587i
$907$	22.6820	+	28.4423i	0.753142	+	0.944411i	0.999694	−	0.0247188i	$-0.00786903\pi$
$907$	22.6820	+	28.4423i	0.753142	+	0.944411i	−0.246552	+	0.969130i	$0.579298\pi$
$908$	−27.5589	+	21.9775i	−0.914576	+	0.729350i
$909$	−1.11384	−	2.31291i	−0.0369437	−	0.0767145i
$910$	−12.7309	+	18.5744i	−0.422026	+	0.615734i
$911$		−	29.2297i		−	0.968424i	−0.874951	−	0.484212i	$-0.839106\pi$
$911$		−	29.2297i		−	0.968424i	0.874951	−	0.484212i	$-0.160894\pi$
$912$	11.7787	+	9.39320i	0.390032	+	0.311040i
$913$	3.13613	−	13.7403i	0.103791	−	0.454737i
$914$	−15.6168	−	3.56444i	−0.516559	−	0.117901i
$915$	16.3318	+	11.1938i	0.539912	+	0.370057i
$916$			4.03451i			0.133304i
$917$	1.27542	−	1.59933i	0.0421181	−	0.0528145i
$918$	12.1369	−	5.84480i	0.400576	−	0.192907i
$919$	15.0357	+	18.8541i	0.495980	+	0.621940i	0.965317	−	0.261079i	$-0.0840784\pi$
$919$	15.0357	+	18.8541i	0.495980	+	0.621940i	−0.469337	+	0.883019i	$0.655507\pi$
$920$	17.9849	−	16.6053i	0.592945	−	0.547461i
$921$	−27.2128	−	13.1050i	−0.896691	−	0.431823i
$922$	−2.42126	−	0.552636i	−0.0797398	−	0.0182001i
$923$	23.3665	−	5.33326i	0.769119	−	0.175546i
$924$	−9.11273	+	4.38846i	−0.299787	+	0.144370i
$925$	42.6614	+	13.3898i	1.40270	+	0.440254i
$926$	−8.18552	+	1.86829i	−0.268993	+	0.0613959i
$927$		−	8.64843i		−	0.284052i
$928$	−21.0884	−	18.3179i	−0.692261	−	0.601314i
$929$	−53.1898			−1.74510			−0.872550	−	0.488524i	$-0.837535\pi$
$929$	−53.1898			−1.74510			−0.872550	+	0.488524i	$0.837535\pi$
$930$	−6.29454	+	1.92464i	−0.206406	+	0.0631115i
$931$	−0.565614	+	1.17451i	−0.0185372	+	0.0384930i
$932$	0.454246	+	0.943251i	0.0148793	+	0.0308972i
$933$	31.4398	−	7.17594i	1.02929	−	0.234930i
$934$	2.56227	−	11.2260i	0.0838400	−	0.367327i
$935$	6.03720	−	15.2718i	0.197438	−	0.499442i
$936$	12.9180	−	10.3017i	0.422237	−	0.336723i
$937$	16.4397	−	13.1102i	0.537061	−	0.428292i	−0.317030	−	0.948416i	$-0.602685\pi$
$937$	16.4397	−	13.1102i	0.537061	−	0.428292i	0.854091	+	0.520123i	$0.174114\pi$
$938$	−12.9573	+	6.23990i	−0.423070	+	0.203740i
$939$	−9.85556	−	7.85955i	−0.321624	−	0.256487i
$940$	31.5334	−	2.28501i	1.02851	−	0.0745289i
$941$	1.09960	−	1.37886i	0.0358461	−	0.0449495i	−0.763585	−	0.645707i	$-0.776563\pi$
$941$	1.09960	−	1.37886i	0.0358461	−	0.0449495i	0.799431	+	0.600757i	$0.205134\pi$
$942$	0.668742	−	2.92995i	0.0217888	−	0.0954630i
$943$	9.48064	−	41.5374i	0.308732	−	1.35264i
$944$	15.0025	−	18.8126i	0.488291	−	0.612297i
$945$	2.45836	+	33.9256i	0.0799703	+	1.10360i
$946$	−1.20155	−	0.958204i	−0.0390657	−	0.0311539i
$947$	37.8242	−	18.2152i	1.22912	−	0.591913i	0.297283	−	0.954789i	$-0.403919\pi$
$947$	37.8242	−	18.2152i	1.22912	−	0.591913i	0.931837	+	0.362876i	$0.118205\pi$
$948$	−6.17865	+	4.92731i	−0.200673	+	0.160032i
$949$	−4.12095	+	3.28634i	−0.133772	+	0.106679i
$950$	−3.64612	+	11.6169i	−0.118296	+	0.376903i
$951$	−4.57619	+	20.0496i	−0.148393	+	0.650153i
$952$	−23.4078	+	5.34268i	−0.758652	+	0.173157i
$953$	−15.6667	−	32.5322i	−0.507494	−	1.05382i	−0.984575	−	0.174963i	$-0.944019\pi$
$953$	−15.6667	−	32.5322i	−0.507494	−	1.05382i	0.477081	−	0.878859i	$-0.341695\pi$
$954$	0.523978	−	1.08805i	0.0169644	−	0.0352270i
$955$	−28.1750	+	8.61489i	−0.911721	+	0.278771i
$956$	4.72477			0.152810
$957$	2.12427	+	11.5174i	0.0686680	+	0.372303i
$958$		−	10.8542i		−	0.350682i
$959$	11.8936	−	2.71463i	0.384063	−	0.0876599i
$960$	−5.89711	−	2.33122i	−0.190328	−	0.0752399i
$961$	−12.3393	+	5.94231i	−0.398043	+	0.191687i
$962$	32.5374	−	7.42646i	1.04905	−	0.239439i
$963$	−2.04087	−	0.465816i	−0.0657663	−	0.0150107i
$964$	20.1045	+	9.68182i	0.647522	+	0.311830i
$965$	33.0698	+	35.8173i	1.06455	+	1.15300i
$966$	6.65649	+	8.34697i	0.214169	+	0.268559i
$967$	−10.5738	+	5.09207i	−0.340030	+	0.163750i	−0.596104	−	0.802907i	$-0.703285\pi$
$967$	−10.5738	+	5.09207i	−0.340030	+	0.163750i	0.256074	+	0.966657i	$0.417571\pi$
$968$	10.2401	−	12.8407i	0.329131	−	0.412717i
$969$		−	28.3209i		−	0.909798i
$970$	−6.66886	+	9.72984i	−0.214124	+	0.312406i
$971$	44.4954	+	10.1558i	1.42793	+	0.325915i	0.865490	−	0.500926i	$-0.167007\pi$
$971$	44.4954	+	10.1558i	1.42793	+	0.325915i	0.562436	+	0.826841i	$0.309864\pi$
$972$	4.41158	−	19.3284i	0.141501	−	0.619958i
$973$	−4.99627	−	3.98439i	−0.160173	−	0.127734i
$974$		−	13.8517i		−	0.443836i
$975$	41.2391	+	24.0811i	1.32071	+	0.771211i
$976$	6.90149	+	14.3311i	0.220911	+	0.458727i
$977$	−17.4347	+	13.9037i	−0.557784	+	0.444818i	−0.861364	−	0.507988i	$-0.830389\pi$
$977$	−17.4347	+	13.9037i	−0.557784	+	0.444818i	0.303580	+	0.952806i	$0.401818\pi$
$978$	4.34028	+	5.44253i	0.138787	+	0.174033i
$979$	−12.2650	−	5.90652i	−0.391991	−	0.188773i
$980$	0.164330	−	1.07233i	0.00524933	−	0.0342543i
$981$	−0.441954	−	1.93633i	−0.0141105	−	0.0618222i
$982$	7.45024	+	15.4706i	0.237747	+	0.493686i
$983$	7.64378	+	3.68105i	0.243799	+	0.117407i	0.551794	−	0.833981i	$-0.313944\pi$
$983$	7.64378	+	3.68105i	0.243799	+	0.117407i	−0.307995	+	0.951388i	$0.599658\pi$
$984$	19.5750	−	4.46787i	0.624029	−	0.142431i
$985$	0.216769	+	2.99144i	0.00690684	+	0.0953152i
$986$	−0.540423	+	12.8571i	−0.0172106	+	0.409453i
$987$			29.7908i			0.948250i
$988$	−12.6051	−	55.2266i	−0.401022	−	1.75699i
$989$	4.38720	−	9.11011i	0.139505	−	0.289685i
$990$	1.12485	+	1.95942i	0.0357500	+	0.0622746i
$991$	−3.09317	−	13.5521i	−0.0982579	−	0.430496i	0.901741	−	0.432278i	$-0.142290\pi$
$991$	−3.09317	−	13.5521i	−0.0982579	−	0.430496i	−0.999998	+	0.00178185i	$0.999433\pi$
$992$	−21.0365	−	4.80144i	−0.667909	−	0.152446i
$993$	0.534966	−	1.11087i	0.0169766	−	0.0352523i
$994$	3.74631	−	2.98758i	0.118826	−	0.0947603i
$995$	−14.1445	−	15.3197i	−0.448412	−	0.485666i
$996$	8.77617	+	18.2239i	0.278083	+	0.577446i
$997$	8.36728	−	10.4922i	0.264994	−	0.332293i	−0.631477	−	0.775395i	$-0.717551\pi$
$997$	8.36728	−	10.4922i	0.264994	−	0.332293i	0.896471	+	0.443102i	$0.146122\pi$
$998$	−8.18315			−0.259033
$999$	31.4315	−	39.4139i	0.994450	−	1.24700i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.2.l.a.109.7	yes	72
5.2	odd	4		725.2.q.f.51.6		72
5.3	odd	4		725.2.q.f.51.7		72
5.4	even	2	inner	145.2.l.a.109.6	yes	72
29.4	even	14	inner	145.2.l.a.4.6	✓	72
145.4	even	14	inner	145.2.l.a.4.7	yes	72
145.33	odd	28		725.2.q.f.526.7		72
145.62	odd	28		725.2.q.f.526.6		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.l.a.4.6	✓	72	29.4	even	14	inner
145.2.l.a.4.7	yes	72	145.4	even	14	inner
145.2.l.a.109.6	yes	72	5.4	even	2	inner
145.2.l.a.109.7	yes	72	1.1	even	1	trivial
725.2.q.f.51.6		72	5.2	odd	4
725.2.q.f.51.7		72	5.3	odd	4
725.2.q.f.526.6		72	145.62	odd	28
725.2.q.f.526.7		72	145.33	odd	28

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:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.l (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.117010 + 0.512653i) q^{2} +(-1.21246 - 0.583890i) q^{3} +(1.55282 - 0.747797i) q^{4} +(0.653828 + 2.13834i) q^{5} +(0.157463 - 0.689892i) q^{6} +(1.17080 - 2.43120i) q^{7} +(1.22076 + 1.53079i) q^{8} +(-0.741336 - 0.929606i) q^{9} +(-1.01972 + 0.585394i) q^{10} +(1.26349 + 1.00760i) q^{11} -2.31936 q^{12} +(5.54889 + 4.42509i) q^{13} +(1.38336 + 0.315742i) q^{14} +(0.455817 - 2.97442i) q^{15} +(1.50724 - 1.89002i) q^{16} -4.54440 q^{17} +(0.389822 - 0.488821i) q^{18} +(-2.00931 - 4.17237i) q^{19} +(2.61432 + 2.83152i) q^{20} +(-2.83910 + 2.26411i) q^{21} +(-0.368710 + 0.765633i) q^{22} +(-5.45091 - 1.24413i) q^{23} +(-0.586314 - 2.56881i) q^{24} +(-4.14502 + 2.79622i) q^{25} +(-1.61926 + 3.36243i) q^{26} +(1.25441 + 5.49594i) q^{27} -4.65072i q^{28} +(-5.19519 - 1.41774i) q^{29} +(1.57818 - 0.114360i) q^{30} +(-4.05556 + 0.925654i) q^{31} +(4.67339 + 2.25059i) q^{32} +(-0.943607 - 1.95942i) q^{33} +(-0.531738 - 2.32970i) q^{34} +(5.96424 + 0.913994i) q^{35} +(-1.84632 - 0.889139i) q^{36} +(-5.57566 - 6.99165i) q^{37} +(1.90387 - 1.51828i) q^{38} +(-4.14404 - 8.60520i) q^{39} +(-2.47518 + 3.61128i) q^{40} +7.62027i q^{41} +(-1.49291 - 1.19055i) q^{42} +(-0.402428 + 1.76315i) q^{43} +(2.71546 + 0.619785i) q^{44} +(1.50311 - 2.19303i) q^{45} -2.94000i q^{46} +(5.11496 - 6.41396i) q^{47} +(-2.93104 + 1.41151i) q^{48} +(-0.175511 - 0.220083i) q^{49} +(-1.91850 - 1.79777i) q^{50} +(5.50990 + 2.65343i) q^{51} +(11.9255 + 2.72191i) q^{52} +(1.88311 - 0.429807i) q^{53} +(-2.67073 + 1.28616i) q^{54} +(-1.32849 + 3.36058i) q^{55} +(5.15092 - 1.17566i) q^{56} +6.23204i q^{57} +(0.118921 - 2.82922i) q^{58} +9.95363 q^{59} +(-1.51646 - 4.95959i) q^{60} +(-2.85489 + 5.92824i) q^{61} +(-0.949079 - 1.97078i) q^{62} +(-3.12802 + 0.713949i) q^{63} +(0.468919 - 2.05447i) q^{64} +(-5.83435 + 14.7587i) q^{65} +(0.894092 - 0.713014i) q^{66} +(-7.92421 + 6.31934i) q^{67} +(-7.05661 + 3.39829i) q^{68} +(5.88258 + 4.69120i) q^{69} +(0.229312 + 3.16453i) q^{70} +(2.10551 - 2.64023i) q^{71} +(0.518035 - 2.26966i) q^{72} +(-0.165258 + 0.724041i) q^{73} +(2.93189 - 3.67647i) q^{74} +(6.65836 - 0.970065i) q^{75} +(-6.24016 - 4.97636i) q^{76} +(3.92898 - 1.89210i) q^{77} +(3.92659 - 3.13135i) q^{78} +(2.66395 - 2.12443i) q^{79} +(5.02699 + 1.98725i) q^{80} +(0.894360 - 3.91845i) q^{81} +(-3.90655 + 0.891645i) q^{82} +(-3.78387 - 7.85730i) q^{83} +(-2.71551 + 5.63882i) q^{84} +(-2.97125 - 9.71748i) q^{85} -0.950973 q^{86} +(5.47116 + 4.75238i) q^{87} +3.16419i q^{88} +(-8.21241 + 1.87443i) q^{89} +(1.30014 + 0.513968i) q^{90} +(17.2549 - 8.30954i) q^{91} +(-9.39462 + 2.14426i) q^{92} +(5.45768 + 1.24568i) q^{93} +(3.88664 + 1.87171i) q^{94} +(7.60821 - 7.02459i) q^{95} +(-4.35221 - 5.45750i) q^{96} +(9.03868 - 4.35280i) q^{97} +(0.0922900 - 0.115728i) q^{98} -1.92153i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 18 q^{4} - 9 q^{5} + 4 q^{6} - 14 q^{9} - 7 q^{10} - 14 q^{11} - 14 q^{14} + 7 q^{15} - 2 q^{16} - 14 q^{19} + 46 q^{20} - 14 q^{21} - 12 q^{24} - 9 q^{25} - 56 q^{26} - 12 q^{29} + 14 q^{30} - 28 q^{31}+ \cdots + 90 q^{96}+O(q^{100}) \) 72 * q - 18 * q^4 - 9 * q^5 + 4 * q^6 - 14 * q^9 - 7 * q^10 - 14 * q^11 - 14 * q^14 + 7 * q^15 - 2 * q^16 - 14 * q^19 + 46 * q^20 - 14 * q^21 - 12 * q^24 - 9 * q^25 - 56 * q^26 - 12 * q^29 + 14 * q^30 - 28 * q^31 + 4 * q^34 - 25 * q^35 - 50 * q^36 + 56 * q^40 - 70 * q^44 + 59 * q^45 - 28 * q^49 + 14 * q^50 - 64 * q^51 + 14 * q^54 + 49 * q^55 + 98 * q^56 + 100 * q^59 + 14 * q^60 - 70 * q^61 - 18 * q^64 + 27 * q^65 + 70 * q^66 - 70 * q^69 - 20 * q^71 - 54 * q^74 + 98 * q^76 - 14 * q^79 + 2 * q^80 + 160 * q^81 + 98 * q^84 - 112 * q^85 - 88 * q^86 - 14 * q^89 - 56 * q^90 + 56 * q^91 + 6 * q^94 - 119 * q^95 + 90 * q^96

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