LMFDB - Embedded newform 425.2.q.a.84.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(84,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7, 5]))

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

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

chi := DirichletCharacter("425.84");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.q (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			84.8
Character	$\chi$	$=$	425.84
Dual form			425.2.q.a.339.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.27397 + 1.75347i) q^{2} +(0.347412 + 1.06922i) q^{3} +(-0.833625 - 2.56564i) q^{4} +(2.16832 + 0.546269i) q^{5} +(-2.31745 - 0.752985i) q^{6} +2.57428 q^{7} +(1.43812 + 0.467275i) q^{8} +(1.40451 - 1.02043i) q^{9} +(-3.72024 + 3.10615i) q^{10} +(1.51857 - 2.09014i) q^{11} +(2.45363 - 1.78267i) q^{12} +(1.80492 + 2.48426i) q^{13} +(-3.27956 + 4.51393i) q^{14} +(0.169215 + 2.50820i) q^{15} +(1.71343 - 1.24488i) q^{16} +(4.12067 - 0.141819i) q^{17} +3.76276i q^{18} +(0.831872 - 2.56024i) q^{19} +(-0.406037 - 6.01849i) q^{20} +(0.894336 + 2.75248i) q^{21} +(1.73038 + 5.32555i) q^{22} +(-4.46069 - 3.24088i) q^{23} +1.70002i q^{24} +(4.40318 + 2.36897i) q^{25} -6.65551 q^{26} +(4.30762 + 3.12967i) q^{27} +(-2.14599 - 6.60466i) q^{28} +(-7.26390 + 2.36018i) q^{29} +(-4.61363 - 2.89866i) q^{30} +(-5.00591 - 1.62652i) q^{31} +7.61467i q^{32} +(2.76240 + 0.897557i) q^{33} +(-5.00094 + 7.40614i) q^{34} +(5.58185 + 1.40625i) q^{35} +(-3.78889 - 2.75279i) q^{36} +(-0.672839 + 0.488846i) q^{37} +(3.42952 + 4.72034i) q^{38} +(-2.02918 + 2.79293i) q^{39} +(2.86305 + 1.79880i) q^{40} +(-4.01713 - 5.52911i) q^{41} +(-5.96576 - 1.93839i) q^{42} -9.25232i q^{43} +(-6.62845 - 2.15371i) q^{44} +(3.60284 - 1.44538i) q^{45} +(11.3656 - 3.69290i) q^{46} +(-8.37265 + 2.72044i) q^{47} +(1.92633 + 1.39956i) q^{48} -0.373079 q^{49} +(-9.76344 + 4.70286i) q^{50} +(1.58320 + 4.35665i) q^{51} +(4.86908 - 6.70172i) q^{52} +(-12.7937 + 4.15692i) q^{53} +(-10.9756 + 3.56618i) q^{54} +(4.43452 - 3.70253i) q^{55} +(3.70214 + 1.20290i) q^{56} +3.02647 q^{57} +(5.11548 - 15.7438i) q^{58} +(-4.88543 + 3.54947i) q^{59} +(6.29405 - 2.52504i) q^{60} +(-6.99628 + 9.62955i) q^{61} +(9.22944 - 6.70558i) q^{62} +(3.61559 - 2.62688i) q^{63} +(-9.92525 - 7.21111i) q^{64} +(2.55657 + 6.37264i) q^{65} +(-5.09305 + 3.70032i) q^{66} +(13.1306 + 4.26637i) q^{67} +(-3.79895 - 10.4539i) q^{68} +(1.91553 - 5.89540i) q^{69} +(-9.57694 + 7.99610i) q^{70} +(-0.636317 + 0.206752i) q^{71} +(2.49668 - 0.811219i) q^{72} +(-6.34682 - 4.61124i) q^{73} -1.80258i q^{74} +(-1.00324 + 5.53100i) q^{75} -7.26211 q^{76} +(3.90923 - 5.38060i) q^{77} +(-2.31220 - 7.11623i) q^{78} +(4.25088 - 1.38120i) q^{79} +(4.39531 - 1.76330i) q^{80} +(-0.240381 + 0.739818i) q^{81} +14.8128 q^{82} +(6.25556 + 2.03256i) q^{83} +(6.31633 - 4.58908i) q^{84} +(9.01237 + 1.94348i) q^{85} +(16.2237 + 11.7872i) q^{86} +(-5.04713 - 6.94678i) q^{87} +(3.16057 - 2.29629i) q^{88} +(9.87913 + 7.17761i) q^{89} +(-2.05548 + 8.15886i) q^{90} +(4.64638 + 6.39519i) q^{91} +(-4.59637 + 14.1462i) q^{92} -5.91751i q^{93} +(5.89631 - 18.1470i) q^{94} +(3.20234 - 5.09698i) q^{95} +(-8.14180 + 2.64543i) q^{96} +(2.29897 + 7.07549i) q^{97} +(0.475293 - 0.654184i) q^{98} -4.48521i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) $ 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−1.27397	+	1.75347i	−0.900834	+	1.23989i	0.0693670	+	0.997591i	$0.477902\pi$
$2$	−1.27397	+	1.75347i	−0.900834	+	1.23989i	−0.970201	+	0.242301i	$0.922098\pi$
$3$	0.347412	+	1.06922i	0.200578	+	0.617317i	0.999866	+	0.0163683i	$0.00521043\pi$
$3$	0.347412	+	1.06922i	0.200578	+	0.617317i	−0.799288	+	0.600949i	$0.794790\pi$
$4$	−0.833625	−	2.56564i	−0.416813	−	1.28282i
$5$	2.16832	+	0.546269i	0.969700	+	0.244299i
$5$	2.16832	+	0.546269i	0.969700	+	0.244299i
$6$	−2.31745	−	0.752985i	−0.946094	−	0.307405i
$7$	2.57428			0.972987			0.486493	−	0.873684i	$-0.338276\pi$
$7$	2.57428			0.972987			0.486493	+	0.873684i	$0.338276\pi$
$8$	1.43812	+	0.467275i	0.508454	+	0.165207i
$9$	1.40451	−	1.02043i	0.468168	−	0.340144i
$10$	−3.72024	+	3.10615i	−1.17644	+	0.982251i
$11$	1.51857	−	2.09014i	0.457867	−	0.630200i	−0.516198	−	0.856469i	$-0.672653\pi$
$11$	1.51857	−	2.09014i	0.457867	−	0.630200i	0.974065	+	0.226270i	$0.0726531\pi$
$12$	2.45363	−	1.78267i	0.708302	−	0.514611i
$13$	1.80492	+	2.48426i	0.500595	+	0.689010i	0.982298	−	0.187324i	$-0.0599815\pi$
$13$	1.80492	+	2.48426i	0.500595	+	0.689010i	−0.481703	+	0.876335i	$0.659981\pi$
$14$	−3.27956	+	4.51393i	−0.876500	+	1.20640i
$15$	0.169215	+	2.50820i	0.0436912	+	0.647613i
$16$	1.71343	−	1.24488i	0.428359	−	0.311221i
$17$	4.12067	−	0.141819i	0.999408	−	0.0343960i
$17$	4.12067	−	0.141819i	0.999408	−	0.0343960i
$18$			3.76276i			0.886892i
$19$	0.831872	−	2.56024i	0.190844	−	0.587359i	−0.809155	−	0.587595i	$-0.800075\pi$
$19$	0.831872	−	2.56024i	0.190844	−	0.587359i	1.00000		0.000235666i	$7.50149e-5\pi$
$20$	−0.406037	−	6.01849i	−0.0907926	−	1.34578i
$21$	0.894336	+	2.75248i	0.195160	+	0.600641i
$22$	1.73038	+	5.32555i	0.368917	+	1.13541i
$23$	−4.46069	−	3.24088i	−0.930117	−	0.675770i	0.0159041	−	0.999874i	$-0.494937\pi$
$23$	−4.46069	−	3.24088i	−0.930117	−	0.675770i	−0.946022	+	0.324104i	$0.894937\pi$
$24$			1.70002i			0.347014i
$25$	4.40318	+	2.36897i	0.880636	+	0.473793i
$26$	−6.65551			−1.30525
$27$	4.30762	+	3.12967i	0.829003	+	0.602306i
$28$	−2.14599	−	6.60466i	−0.405553	−	1.24816i
$29$	−7.26390	+	2.36018i	−1.34887	+	0.438275i	−0.892312	−	0.451418i	$-0.850918\pi$
$29$	−7.26390	+	2.36018i	−1.34887	+	0.438275i	−0.456559	+	0.889693i	$0.650918\pi$
$30$	−4.61363	−	2.89866i	−0.842329	−	0.529220i
$31$	−5.00591	−	1.62652i	−0.899088	−	0.292131i	−0.177227	−	0.984170i	$-0.556713\pi$
$31$	−5.00591	−	1.62652i	−0.899088	−	0.292131i	−0.721860	+	0.692039i	$0.756713\pi$
$32$			7.61467i			1.34610i
$33$	2.76240	+	0.897557i	0.480871	+	0.156245i
$34$	−5.00094	+	7.40614i	−0.857654	+	1.27014i
$35$	5.58185	+	1.40625i	0.943505	+	0.237699i
$36$	−3.78889	−	2.75279i	−0.631482	−	0.458798i
$37$	−0.672839	+	0.488846i	−0.110614	+	0.0803658i	−0.641717	−	0.766941i	$-0.721778\pi$
$37$	−0.672839	+	0.488846i	−0.110614	+	0.0803658i	0.531103	+	0.847307i	$0.321778\pi$
$38$	3.42952	+	4.72034i	0.556342	+	0.765740i
$39$	−2.02918	+	2.79293i	−0.324929	+	0.447227i
$40$	2.86305	+	1.79880i	0.452688	+	0.284416i
$41$	−4.01713	−	5.52911i	−0.627371	−	0.863501i	0.370493	−	0.928835i	$-0.379189\pi$
$41$	−4.01713	−	5.52911i	−0.627371	−	0.863501i	−0.997863	+	0.0653338i	$0.979189\pi$
$42$	−5.96576	−	1.93839i	−0.920537	−	0.299101i
$43$		−	9.25232i		−	1.41097i	−0.708727	−	0.705483i	$-0.750730\pi$
$43$		−	9.25232i		−	1.41097i	0.708727	−	0.705483i	$-0.249270\pi$
$44$	−6.62845	−	2.15371i	−0.999276	−	0.324684i
$45$	3.60284	−	1.44538i	0.537080	−	0.215465i
$46$	11.3656	−	3.69290i	1.67576	−	0.544488i
$47$	−8.37265	+	2.72044i	−1.22128	+	0.396817i	−0.847547	−	0.530721i	$-0.821921\pi$
$47$	−8.37265	+	2.72044i	−1.22128	+	0.396817i	−0.373730	+	0.927538i	$0.621921\pi$
$48$	1.92633	+	1.39956i	0.278041	+	0.202009i
$49$	−0.373079			−0.0532971
$50$	−9.76344	+	4.70286i	−1.38076	+	0.665085i
$51$	1.58320	+	4.35665i	0.221693	+	0.610053i
$52$	4.86908	−	6.70172i	0.675220	−	0.929361i
$53$	−12.7937	+	4.15692i	−1.75735	+	0.570996i	−0.996920	−	0.0784284i	$-0.975010\pi$
$53$	−12.7937	+	4.15692i	−1.75735	+	0.570996i	−0.760426	+	0.649425i	$0.775010\pi$
$54$	−10.9756	+	3.56618i	−1.49359	+	0.485296i
$55$	4.43452	−	3.70253i	0.597951	−	0.499248i
$56$	3.70214	+	1.20290i	0.494719	+	0.160744i
$57$	3.02647			0.400866
$58$	5.11548	−	15.7438i	0.671696	−	2.06727i
$59$	−4.88543	+	3.54947i	−0.636029	+	0.462102i	−0.858484	−	0.512841i	$-0.828593\pi$
$59$	−4.88543	+	3.54947i	−0.636029	+	0.462102i	0.222455	+	0.974943i	$0.428593\pi$
$60$	6.29405	−	2.52504i	0.812559	−	0.325981i
$61$	−6.99628	+	9.62955i	−0.895782	+	1.23294i	0.0760125	+	0.997107i	$0.475781\pi$
$61$	−6.99628	+	9.62955i	−0.895782	+	1.23294i	−0.971794	+	0.235831i	$0.924219\pi$
$62$	9.22944	−	6.70558i	1.17214	−	0.851610i
$63$	3.61559	−	2.62688i	0.455522	−	0.330956i
$64$	−9.92525	−	7.21111i	−1.24066	−	0.901389i
$65$	2.55657	+	6.37264i	0.317103	+	0.790428i
$66$	−5.09305	+	3.70032i	−0.626912	+	0.455478i
$67$	13.1306	+	4.26637i	1.60415	+	0.521221i	0.968130	−	0.250450i	$-0.0805785\pi$
$67$	13.1306	+	4.26637i	1.60415	+	0.521221i	0.636022	+	0.771671i	$0.280579\pi$
$68$	−3.79895	−	10.4539i	−0.460690	−	1.26772i
$69$	1.91553	−	5.89540i	0.230603	−	0.709722i
$70$	−9.57694	+	7.99610i	−1.14466	+	0.955717i
$71$	−0.636317	+	0.206752i	−0.0755170	+	0.0245369i	−0.346532	−	0.938038i	$-0.612641\pi$
$71$	−0.636317	+	0.206752i	−0.0755170	+	0.0245369i	0.271015	+	0.962575i	$0.412641\pi$
$72$	2.49668	−	0.811219i	0.294236	−	0.0956031i
$73$	−6.34682	−	4.61124i	−0.742839	−	0.539704i	0.150760	−	0.988570i	$-0.451828\pi$
$73$	−6.34682	−	4.61124i	−0.742839	−	0.539704i	−0.893599	+	0.448866i	$0.851828\pi$
$74$		−	1.80258i		−	0.209546i
$75$	−1.00324	+	5.53100i	−0.115844	+	0.638664i
$76$	−7.26211			−0.833021
$77$	3.90923	−	5.38060i	0.445498	−	0.613176i
$78$	−2.31220	−	7.11623i	−0.261805	−	0.805754i
$79$	4.25088	−	1.38120i	0.478262	−	0.155397i	−0.0599586	−	0.998201i	$-0.519097\pi$
$79$	4.25088	−	1.38120i	0.478262	−	0.155397i	0.538220	+	0.842804i	$0.319097\pi$
$80$	4.39531	−	1.76330i	0.491410	−	0.197143i
$81$	−0.240381	+	0.739818i	−0.0267091	+	0.0822020i
$82$	14.8128			1.63581
$83$	6.25556	+	2.03256i	0.686637	+	0.223102i	0.631499	−	0.775377i	$-0.282440\pi$
$83$	6.25556	+	2.03256i	0.686637	+	0.223102i	0.0551383	+	0.998479i	$0.482440\pi$
$84$	6.31633	−	4.58908i	0.689168	−	0.500710i
$85$	9.01237	+	1.94348i	0.977529	+	0.210800i
$86$	16.2237	+	11.7872i	1.74944	+	1.27105i
$87$	−5.04713	−	6.94678i	−0.541109	−	0.744773i
$88$	3.16057	−	2.29629i	0.336917	−	0.244785i
$89$	9.87913	+	7.17761i	1.04719	+	0.760825i	0.971675	−	0.236320i	$-0.0759413\pi$
$89$	9.87913	+	7.17761i	1.04719	+	0.760825i	0.0755106	+	0.997145i	$0.475941\pi$
$90$	−2.05548	+	8.15886i	−0.216667	+	0.860019i
$91$	4.64638	+	6.39519i	0.487073	+	0.670398i
$92$	−4.59637	+	14.1462i	−0.479205	+	1.47484i
$93$		−	5.91751i		−	0.613617i
$94$	5.89631	−	18.1470i	0.608158	−	1.87172i
$95$	3.20234	−	5.09698i	0.328553	−	0.522939i
$96$	−8.14180	+	2.64543i	−0.830969	+	0.269998i
$97$	2.29897	+	7.07549i	0.233425	+	0.718407i	0.997326	+	0.0730747i	$0.0232811\pi$
$97$	2.29897	+	7.07549i	0.233425	+	0.718407i	−0.763902	+	0.645332i	$0.776719\pi$
$98$	0.475293	−	0.654184i	0.0480118	−	0.0660826i
$99$		−	4.48521i		−	0.450780i
$100$	2.40730	−	13.2718i	0.240730	−	1.32718i
$101$	3.21496			0.319900			0.159950	−	0.987125i	$-0.448867\pi$
$101$	3.21496			0.319900			0.159950	+	0.987125i	$0.448867\pi$
$102$	−9.65622	−	2.77414i	−0.956108	−	0.274681i
$103$	7.85909	−	2.55357i	0.774379	−	0.251611i	0.104941	−	0.994478i	$-0.466535\pi$
$103$	7.85909	−	2.55357i	0.774379	−	0.251611i	0.669439	+	0.742867i	$0.266535\pi$
$104$	1.43487	+	4.41608i	0.140701	+	0.433032i
$105$	0.435607	+	6.45680i	0.0425109	+	0.630119i
$106$	9.00974	−	27.7291i	0.875104	−	2.69329i
$107$	−5.58835			−0.540246			−0.270123	−	0.962826i	$-0.587064\pi$
$107$	−5.58835			−0.540246			−0.270123	+	0.962826i	$0.587064\pi$
$108$	4.43865	−	13.6608i	0.427109	−	1.31451i
$109$	−6.39558	−	8.80276i	−0.612585	−	0.843151i	0.384202	−	0.923249i	$-0.374477\pi$
$109$	−6.39558	−	8.80276i	−0.612585	−	0.843151i	−0.996787	+	0.0800980i	$0.974477\pi$
$110$	0.842820	+	12.4927i	0.0803597	+	1.19113i
$111$	−0.756438	−	0.549585i	−0.0717980	−	0.0521643i
$112$	4.41086	−	3.20468i	0.416787	−	0.302814i
$113$	−12.8514	+	9.33708i	−1.20896	+	0.878359i	−0.995136	−	0.0985138i	$-0.968591\pi$
$113$	−12.8514	+	9.33708i	−1.20896	+	0.878359i	−0.213822	+	0.976873i	$0.568591\pi$
$114$	−3.85564	+	5.30683i	−0.361114	+	0.497030i
$115$	−7.90178	−	9.46398i	−0.736845	−	0.882521i
$116$	12.1107	+	16.6690i	1.12445	+	1.54768i
$117$	5.07005	+	1.64736i	0.468726	+	0.152298i
$118$		−	13.0884i		−	1.20488i
$119$	10.6078	−	0.365081i	0.972411	−	0.0334669i
$120$	−0.928665	+	3.68617i	−0.0847751	+	0.336500i
$121$	1.33658	+	4.11357i	0.121507	+	0.373961i
$122$	−7.97209	−	24.5356i	−0.721759	−	2.22134i
$123$	4.51626	−	6.21609i	0.407217	−	0.560486i
$124$			14.1992i			1.27513i
$125$	8.25339	+	7.54198i	0.738206	+	0.674575i
$126$			9.68641i			0.862934i
$127$	−1.40153	+	1.92904i	−0.124366	+	0.171175i	−0.866660	−	0.498899i	$-0.833738\pi$
$127$	−1.40153	+	1.92904i	−0.124366	+	0.171175i	0.742294	+	0.670074i	$0.233738\pi$
$128$	10.8050	−	3.51076i	0.955037	−	0.310310i
$129$	9.89281	−	3.21437i	0.871013	−	0.283009i
$130$	−14.4312	−	3.63569i	−1.26570	−	0.318871i
$131$	−3.38105	−	1.09857i	−0.295404	−	0.0959826i	0.157566	−	0.987509i	$-0.449635\pi$
$131$	−3.38105	−	1.09857i	−0.295404	−	0.0959826i	−0.452970	+	0.891526i	$0.649635\pi$
$132$		−	7.83552i		−	0.681995i
$133$	2.14147	−	6.59077i	0.185689	−	0.571492i
$134$	−24.2089	+	17.5888i	−2.09133	+	1.51944i
$135$	7.63064	+	9.13923i	0.656741	+	0.786580i
$136$	5.99230	+	1.72153i	0.513836	+	0.147620i
$137$	−0.481197	−	0.662311i	−0.0411114	−	0.0565850i	0.787966	−	0.615718i	$-0.211134\pi$
$137$	−0.481197	−	0.662311i	−0.0411114	−	0.0565850i	−0.829078	+	0.559133i	$0.811134\pi$
$138$	7.89708	+	10.8694i	0.672244	+	0.925265i
$139$	9.01016	−	12.4014i	0.764232	−	1.05188i	−0.232618	−	0.972568i	$-0.574729\pi$
$139$	9.01016	−	12.4014i	0.764232	−	1.05188i	0.996850	−	0.0793071i	$-0.0252708\pi$
$140$	−1.04525	−	15.4933i	−0.0883399	−	1.30942i
$141$	−5.81752	−	8.00713i	−0.489924	−	0.674322i
$142$	0.448116	−	1.37916i	0.0376051	−	0.115737i
$143$	7.93335			0.663420
$144$	1.13621	−	3.49689i	0.0946840	−	0.291407i
$145$	−17.0397	+	1.14958i	−1.41507	+	0.0954676i
$146$	16.1713	−	5.25439i	1.33835	−	0.434856i
$147$	−0.129612	−	0.398906i	−0.0106902	−	0.0329012i
$148$	1.81510	+	1.31874i	0.149200	+	0.108400i
$149$	4.04408			0.331304			0.165652	−	0.986184i	$-0.447027\pi$
$149$	4.04408			0.331304			0.165652	+	0.986184i	$0.447027\pi$
$150$	−8.42035	−	8.80548i	−0.687519	−	0.718965i
$151$	−14.2865			−1.16262			−0.581308	−	0.813684i	$-0.697459\pi$
$151$	−14.2865			−1.16262			−0.581308	+	0.813684i	$0.697459\pi$
$152$	2.39267	−	3.29323i	0.194071	−	0.267116i
$153$	5.64278	−	4.40405i	0.456192	−	0.356046i
$154$	4.45447	+	13.7095i	0.358952	+	1.10474i
$155$	−9.96587	−	6.26137i	−0.800478	−	0.502926i
$156$	8.85722	+	2.87788i	0.709145	+	0.230415i
$157$			12.3920i			0.988988i	0.869181	+	0.494494i	$0.164647\pi$
$157$			12.3920i			0.988988i	−0.869181	+	0.494494i	$0.835353\pi$
$158$	−2.99362	+	9.21341i	−0.238159	+	0.732979i
$159$	−8.88935	−	12.2351i	−0.704971	−	0.970310i
$160$	−4.15966	+	16.5110i	−0.328850	+	1.30531i
$161$	−11.4831	−	8.34293i	−0.904992	−	0.657515i
$162$	−0.991011	−	1.36401i	−0.0778612	−	0.107167i
$163$	−15.7604	+	11.4506i	−1.23445	+	0.896883i	−0.997216	−	0.0745691i	$-0.976242\pi$
$163$	−15.7604	+	11.4506i	−1.23445	+	0.896883i	−0.237237	+	0.971452i	$0.576242\pi$
$164$	−10.8369	+	14.9157i	−0.846219	+	1.16472i
$165$	5.49944	+	3.45520i	0.428131	+	0.268987i
$166$	−11.5334	+	8.37954i	−0.895169	+	0.650378i
$167$	1.40354	−	4.31966i	0.108609	−	0.334265i	−0.881951	−	0.471340i	$-0.843770\pi$
$167$	1.40354	−	4.31966i	0.108609	−	0.334265i	0.990561	+	0.137076i	$0.0437703\pi$
$168$			4.37632i			0.337640i
$169$	1.10341	−	3.39593i	0.0848773	−	0.261226i
$170$	−14.8894	+	13.3270i	−1.14196	+	1.02213i
$171$	−1.44418	−	4.44474i	−0.110439	−	0.339898i
$172$	−23.7381	+	7.71297i	−1.81001	+	0.588108i
$173$	−0.211474	−	0.153645i	−0.0160781	−	0.0116814i	0.579717	−	0.814818i	$-0.303163\pi$
$173$	−0.211474	−	0.153645i	−0.0160781	−	0.0116814i	−0.595795	+	0.803136i	$0.703163\pi$
$174$	18.6109			1.41089
$175$	11.3350	+	6.09838i	0.856847	+	0.460994i
$176$		−	5.47176i		−	0.412449i
$177$	−5.49244	−	3.99049i	−0.412837	−	0.299944i
$178$	−25.1715	+	8.17871i	−1.88668	+	0.613020i
$179$	−1.47297	−	4.53334i	−0.110095	−	0.338838i	0.880797	−	0.473493i	$-0.157007\pi$
$179$	−1.47297	−	4.53334i	−0.110095	−	0.338838i	−0.990892	+	0.134655i	$0.957007\pi$
$180$	−6.71174	−	8.03867i	−0.500264	−	0.599167i
$181$	14.3612	+	4.66623i	1.06746	+	0.346838i	0.789497	−	0.613754i	$-0.210341\pi$
$181$	14.3612	+	4.66623i	1.06746	+	0.346838i	0.277961	+	0.960592i	$0.410341\pi$
$182$	−17.1331			−1.26999
$183$	−12.7267	−	4.13517i	−0.940788	−	0.305681i
$184$	−4.90064	−	6.74516i	−0.361280	−	0.497260i
$185$	−1.72597	+	0.692421i	−0.126896	+	0.0509078i
$186$	10.3762	+	7.53874i	0.760819	+	0.552767i
$187$	5.96111	−	8.82811i	0.435920	−	0.645576i
$188$	13.9593	+	19.2133i	1.01809	+	1.40128i
$189$	11.0890	+	8.05665i	0.806608	+	0.586035i
$190$	4.85772	+	12.1086i	0.352416	+	0.878451i
$191$	−0.0171787	+	0.0124811i	−0.00124301	+	0.000903100i	−0.588407	−	0.808565i	$-0.700245\pi$
$191$	−0.0171787	+	0.0124811i	−0.00124301	+	0.000903100i	0.587164	+	0.809468i	$0.300245\pi$
$192$	4.26215	−	13.1175i	0.307594	−	0.946677i
$193$	−5.66751			−0.407956			−0.203978	−	0.978975i	$-0.565387\pi$
$193$	−5.66751			−0.407956			−0.203978	+	0.978975i	$0.565387\pi$
$194$	−15.3355	−	4.98280i	−1.10102	−	0.357744i
$195$	−5.92560	+	4.94747i	−0.424341	+	0.354296i
$196$	0.311009	+	0.957186i	0.0222149	+	0.0683704i
$197$	−1.59471	−	4.90801i	−0.113618	−	0.349681i	0.878038	−	0.478591i	$-0.158852\pi$
$197$	−1.59471	−	4.90801i	−0.113618	−	0.349681i	−0.991656	+	0.128910i	$0.958852\pi$
$198$	7.86469	+	5.71403i	0.558919	+	0.406078i
$199$		−	24.1701i		−	1.71337i	−0.515837	−	0.856686i	$-0.672519\pi$
$199$		−	24.1701i		−	1.71337i	0.515837	−	0.856686i	$-0.327481\pi$
$200$	5.22537	+	5.46436i	0.369489	+	0.386389i
$201$			15.5217i			1.09482i
$202$	−4.09576	+	5.63733i	−0.288177	+	0.396641i
$203$	−18.6993	+	6.07577i	−1.31243	+	0.426436i
$204$	9.85777	−	7.69374i	0.690182	−	0.538669i
$205$	−5.69003	−	14.1833i	−0.397409	−	0.990603i
$206$	−5.53464	+	17.0339i	−0.385617	+	1.18681i
$207$	−9.57216			−0.665311
$208$	6.18523	+	2.00970i	0.428869	+	0.139348i
$209$	−4.08799	−	5.62663i	−0.282772	−	0.389202i
$210$	−11.8768	−	7.46196i	−0.819575	−	0.514924i
$211$	1.12813	−	1.55274i	0.0776637	−	0.106895i	−0.768418	−	0.639949i	$-0.778956\pi$
$211$	1.12813	−	1.55274i	0.0776637	−	0.106895i	0.846081	+	0.533054i	$0.178956\pi$
$212$	21.3303	+	29.3586i	1.46497	+	2.01636i
$213$	−0.442129	−	0.608538i	−0.0302941	−	0.0416963i
$214$	7.11940	−	9.79901i	0.486672	−	0.669846i
$215$	5.05425	−	20.0619i	0.344697	−	1.36821i
$216$	4.73248	+	6.51370i	0.322005	+	0.443201i
$217$	−12.8866	−	4.18711i	−0.874800	−	0.284240i
$218$	23.5832			1.59725
$219$	2.72548	−	8.38817i	0.184171	−	0.566820i
$220$	−13.1961	−	8.29084i	−0.889678	−	0.558968i
$221$	7.78980	+	9.98084i	0.523998	+	0.671384i
$222$	1.92736	−	0.626238i	0.129356	−	0.0420303i
$223$	−4.85250	+	6.67890i	−0.324948	+	0.447252i	−0.939970	−	0.341258i	$-0.889147\pi$
$223$	−4.85250	+	6.67890i	−0.324948	+	0.447252i	0.615022	+	0.788510i	$0.289147\pi$
$224$			19.6023i			1.30973i
$225$	8.60166	−	1.16593i	0.573444	−	0.0777284i
$226$		−	34.4297i		−	2.29023i
$227$	10.7223	+	7.79022i	0.711665	+	0.517055i	0.883710	−	0.468034i	$-0.155038\pi$
$227$	10.7223	+	7.79022i	0.711665	+	0.517055i	−0.172045	+	0.985089i	$0.555038\pi$
$228$	−2.52294	−	7.76482i	−0.167086	−	0.514238i
$229$	7.33988	+	22.5898i	0.485033	+	1.49278i	0.831933	+	0.554876i	$0.187234\pi$
$229$	7.33988	+	22.5898i	0.485033	+	1.49278i	−0.346900	+	0.937902i	$0.612766\pi$
$230$	26.6615	−	1.79871i	1.75801	−	0.118604i
$231$	7.11118	+	2.31056i	0.467881	+	0.152024i
$232$	−11.5492			−0.758245
$233$	−5.63500	+	17.3427i	−0.369161	+	1.13616i	0.578173	+	0.815914i	$0.303766\pi$
$233$	−5.63500	+	17.3427i	−0.369161	+	1.13616i	−0.947334	+	0.320247i	$0.896234\pi$
$234$	−9.34769	+	6.79150i	−0.611078	+	0.443974i
$235$	−19.6406	+	1.32505i	−1.28121	+	0.0864369i
$236$	13.1793	+	9.57530i	0.857897	+	0.623299i
$237$	2.95362	+	4.06530i	0.191858	+	0.264070i
$238$	−12.8738	+	19.0655i	−0.834486	+	1.23583i
$239$	−10.5218	−	7.64456i	−0.680601	−	0.494485i	0.192956	−	0.981207i	$-0.438192\pi$
$239$	−10.5218	−	7.64456i	−0.680601	−	0.494485i	−0.873557	+	0.486722i	$0.838192\pi$
$240$	3.41235	+	4.08698i	0.220266	+	0.263813i
$241$	0.632980	+	0.871222i	0.0407738	+	0.0561203i	0.828917	−	0.559371i	$-0.188957\pi$
$241$	0.632980	+	0.871222i	0.0407738	+	0.0561203i	−0.788143	+	0.615492i	$0.788957\pi$
$242$	−8.91580	−	2.89692i	−0.573130	−	0.186221i
$243$	15.0990			0.968602
$244$	30.5382	+	9.92246i	1.95501	+	0.635220i
$245$	−0.808954	−	0.203802i	−0.0516822	−	0.0130204i
$246$	5.14616	+	15.8383i	0.328107	+	1.00981i
$247$	7.86177	−	2.55444i	0.500232	−	0.162535i
$248$	−6.43909	−	4.67827i	−0.408883	−	0.297071i
$249$			7.39474i			0.468622i
$250$	−23.7392	+	4.86382i	−1.50140	+	0.307615i
$251$	11.1641			0.704670			0.352335	−	0.935874i	$-0.385388\pi$
$251$	11.1641			0.704670			0.352335	+	0.935874i	$0.385388\pi$
$252$	−9.75366	−	7.08645i	−0.614423	−	0.446405i
$253$	−13.5478	+	4.40193i	−0.851740	+	0.276747i
$254$	−1.59701	−	4.91509i	−0.100205	−	0.308400i
$255$	1.05299	+	10.3114i	0.0659406	+	0.645727i
$256$	−0.0270410	+	0.0832235i	−0.00169006	+	0.00520147i
$257$			12.9832i			0.809870i	0.914346	+	0.404935i	$0.132706\pi$
$257$			12.9832i			0.809870i	−0.914346	+	0.404935i	$0.867294\pi$
$258$	−6.96685	+	21.4418i	−0.433737	+	1.33491i
$259$	−1.73208	+	1.25843i	−0.107626	+	0.0781948i
$260$	14.2186	−	11.8716i	0.881803	−	0.736246i
$261$	−7.79377	+	10.7272i	−0.482422	+	0.663997i
$262$	6.23368	−	4.52903i	0.385118	−	0.279805i
$263$	0.923345	+	1.27088i	0.0569359	+	0.0783655i	0.836536	−	0.547913i	$-0.184577\pi$
$263$	0.923345	+	1.27088i	0.0569359	+	0.0783655i	−0.779600	+	0.626278i	$0.784577\pi$
$264$	3.55326	+	2.58160i	0.218688	+	0.158886i
$265$	−30.0115	+	2.02472i	−1.84359	+	0.124378i
$266$	8.82856	+	12.1515i	0.541314	+	0.745054i
$267$	−4.24235	+	13.0566i	−0.259627	+	0.799051i
$268$		−	37.2448i		−	2.27509i
$269$	−9.11370	−	2.96122i	−0.555672	−	0.180549i	0.0177007	−	0.999843i	$-0.494365\pi$
$269$	−9.11370	−	2.96122i	−0.555672	−	0.180549i	−0.573373	+	0.819294i	$0.694365\pi$
$270$	−25.7466	+	1.73699i	−1.56689	+	0.105710i
$271$	−3.18061	−	9.78892i	−0.193209	−	0.594635i	−0.999993	−	0.00378867i	$-0.998794\pi$
$271$	−3.18061	−	9.78892i	−0.193209	−	0.594635i	0.806784	−	0.590846i	$-0.201206\pi$
$272$	6.88394	−	5.37274i	0.417400	−	0.325770i
$273$	−5.22369	+	7.18979i	−0.316152	+	0.435146i
$274$	1.77438			0.107194
$275$	11.6380	−	5.60580i	0.701798	−	0.338043i
$276$	−16.7223			−1.00656
$277$	−10.9709	−	7.97079i	−0.659175	−	0.478918i	0.207210	−	0.978297i	$-0.433562\pi$
$277$	−10.9709	−	7.97079i	−0.659175	−	0.478918i	−0.866384	+	0.499378i	$0.833562\pi$
$278$	10.2669	+	31.5981i	0.615765	+	1.89513i
$279$	−8.69058	+	2.82374i	−0.520291	+	0.169053i
$280$	7.37029	+	4.63062i	0.440459	+	0.276733i
$281$	4.24717	−	13.0714i	0.253365	−	0.779777i	−0.740783	−	0.671745i	$-0.765545\pi$
$281$	4.24717	−	13.0714i	0.253365	−	0.779777i	0.994147	−	0.108032i	$-0.0344549\pi$
$282$	21.4516			1.27743
$283$	−8.16214	+	25.1205i	−0.485189	+	1.49326i	0.346519	+	0.938043i	$0.387364\pi$
$283$	−8.16214	+	25.1205i	−0.485189	+	1.49326i	−0.831708	+	0.555214i	$0.812636\pi$
$284$	1.06090	+	1.46020i	0.0629529	+	0.0866472i
$285$	6.56234	+	1.65327i	0.388720	+	0.0979311i
$286$	−10.1069	+	13.9109i	−0.597632	+	0.822569i
$287$	−10.3412	−	14.2335i	−0.610423	−	0.840175i
$288$	7.77026	+	10.6948i	0.457867	+	0.630200i
$289$	16.9598	−	1.16877i	0.997634	−	0.0687514i
$290$	19.6924	−	31.3432i	1.15637	−	1.84054i
$291$	−6.76660	+	4.91622i	−0.396665	+	0.288194i
$292$	−6.53988	+	20.1277i	−0.382717	+	1.17788i
$293$		−	23.6598i		−	1.38222i	−0.722748	−	0.691111i	$-0.757121\pi$
$293$		−	23.6598i		−	1.38222i	0.722748	−	0.691111i	$-0.242879\pi$
$294$	0.864592	+	0.280923i	0.0504241	+	0.0163838i
$295$	−12.5321	+	5.02762i	−0.729648	+	0.292719i
$296$	−1.19605	+	0.388621i	−0.0695191	+	0.0225881i
$297$	13.0829	−	4.25089i	0.759146	−	0.246661i
$298$	−5.15205	+	7.09119i	−0.298450	+	0.410781i
$299$		−	16.9311i		−	0.979148i
$300$	15.0268	−	2.03684i	0.867575	−	0.117597i
$301$		−	23.8181i		−	1.37285i
$302$	18.2006	−	25.0509i	1.04732	−	1.44152i
$303$	1.11691	+	3.43751i	0.0641651	+	0.197480i
$304$	−1.76184	−	5.42238i	−0.101048	−	0.310995i
$305$	−20.4305	+	17.0581i	−1.16984	+	0.976741i
$306$	0.533629	+	15.5051i	0.0305056	+	0.886367i
$307$		−	9.70187i		−	0.553715i	−0.960911	−	0.276857i	$-0.910707\pi$
$307$		−	9.70187i		−	0.553715i	0.960911	−	0.276857i	$-0.0892930\pi$
$308$	−17.0635	−	5.54426i	−0.972282	−	0.315914i
$309$	5.46069	+	7.51599i	0.310648	+	0.427570i
$310$	23.6754	−	9.49806i	1.34467	−	0.539453i
$311$	12.9640	−	17.8434i	0.735119	−	1.01180i	−0.263766	−	0.964587i	$-0.584965\pi$
$311$	12.9640	−	17.8434i	0.735119	−	1.01180i	0.998885	−	0.0472173i	$-0.0150353\pi$
$312$	−4.22328	+	3.06840i	−0.239096	+	0.173714i
$313$	21.7666	−	15.8144i	1.23032	−	0.893881i	0.233407	−	0.972379i	$-0.425012\pi$
$313$	21.7666	−	15.8144i	1.23032	−	0.893881i	0.996914	+	0.0784981i	$0.0250125\pi$
$314$	−21.7290	−	15.7870i	−1.22624	−	0.890914i
$315$	9.27472	−	3.72082i	0.522571	−	0.209644i
$316$	−7.08729	−	9.75481i	−0.398691	−	0.548751i
$317$	9.12850	−	28.0946i	0.512707	−	1.57795i	−0.274707	−	0.961528i	$-0.588581\pi$
$317$	9.12850	−	28.0946i	0.512707	−	1.57795i	0.787415	−	0.616423i	$-0.211419\pi$
$318$	32.7788			1.83814
$319$	−6.09765	+	18.7666i	−0.341403	+	1.05073i
$320$	−17.5819	−	21.0578i	−0.982856	−	1.17717i
$321$	−1.94146	−	5.97520i	−0.108362	−	0.333503i
$322$	29.2582	−	9.50656i	1.63050	−	0.529780i
$323$	3.06478	−	10.6679i	0.170529	−	0.593576i
$324$	2.09849			0.116583
$325$	2.06227	+	15.2145i	0.114394	+	0.843946i
$326$		−	42.2233i		−	2.33853i
$327$	7.19022	−	9.89649i	0.397620	−	0.547277i
$328$	−3.19352	−	9.82865i	−0.176333	−	0.542697i
$329$	−21.5536	+	7.00317i	−1.18829	+	0.386097i
$330$	−13.0647	+	5.24129i	−0.719189	+	0.288523i
$331$	6.14516	−	18.9129i	0.337769	−	1.03955i	−0.627573	−	0.778557i	$-0.715952\pi$
$331$	6.14516	−	18.9129i	0.337769	−	1.03955i	0.965342	−	0.260988i	$-0.0840482\pi$
$332$		−	17.7439i		−	0.973822i
$333$	−0.446171	+	1.37317i	−0.0244500	+	0.0752494i
$334$	5.78632	+	7.96419i	0.316613	+	0.435781i
$335$	26.1406	+	16.4237i	1.42821	+	0.897320i
$336$	4.95891	+	3.60286i	0.270531	+	0.196552i
$337$	8.97422	−	6.52015i	0.488857	−	0.355175i	−0.315888	−	0.948797i	$-0.602302\pi$
$337$	8.97422	−	6.52015i	0.488857	−	0.355175i	0.804744	+	0.593621i	$0.202302\pi$
$338$	4.54897	+	6.26111i	0.247431	+	0.340560i
$339$	−14.4482	−	10.4972i	−0.784717	−	0.570130i
$340$	−2.52667	−	24.7426i	−0.137028	−	1.34186i
$341$	−11.0015	+	7.99304i	−0.595764	+	0.432848i
$342$	9.63357	+	3.13014i	0.520924	+	0.169258i
$343$	−18.9804			−1.02484
$344$	4.32338	−	13.3060i	0.233101	−	0.717411i
$345$	7.37394	−	11.7367i	0.397000	−	0.631882i
$346$	0.538824	−	0.175075i	0.0289674	−	0.00941207i
$347$	8.79096	+	27.0558i	0.471924	+	1.45243i	0.850062	+	0.526683i	$0.176564\pi$
$347$	8.79096	+	27.0558i	0.471924	+	1.45243i	−0.378138	+	0.925749i	$0.623436\pi$
$348$	−13.6155	+	18.7401i	−0.729867	+	1.00458i
$349$	16.0514			0.859209			0.429605	−	0.903017i	$-0.358653\pi$
$349$	16.0514			0.859209			0.429605	+	0.903017i	$0.358653\pi$
$350$	−25.1338	+	12.1065i	−1.34346	+	0.647119i
$351$			16.3501i			0.872703i
$352$	15.9157	+	11.5634i	0.848310	+	0.616333i
$353$	15.3988	−	5.00337i	0.819595	−	0.266303i	0.130939	−	0.991390i	$-0.458201\pi$
$353$	15.3988	−	5.00337i	0.819595	−	0.266303i	0.688656	+	0.725088i	$0.258201\pi$
$354$	13.9944	−	4.54706i	0.743795	−	0.241674i
$355$	−1.49268	+	0.100703i	−0.0792231	+	0.00534478i
$356$	10.1796	−	31.3297i	0.539519	−	1.66047i
$357$	4.07561	+	11.2152i	0.215704	+	0.593573i
$358$	9.82562	+	3.19254i	0.519300	+	0.168731i
$359$	−0.369630	+	0.268552i	−0.0195083	+	0.0141736i	−0.597497	−	0.801871i	$-0.703838\pi$
$359$	−0.369630	+	0.268552i	−0.0195083	+	0.0141736i	0.577988	+	0.816045i	$0.303838\pi$
$360$	5.85673	−	0.395123i	0.308677	−	0.0208248i
$361$	9.50851	+	6.90834i	0.500448	+	0.363597i
$362$	−26.4778	+	19.2373i	−1.39164	+	1.01109i
$363$	−3.93399	+	2.85821i	−0.206481	+	0.150017i
$364$	12.5344	−	17.2521i	0.656980	−	0.904256i
$365$	−11.2429	−	13.4657i	−0.588482	−	0.704826i
$366$	23.4644	−	17.0479i	1.22650	−	0.891108i
$367$	0.615917	−	1.89560i	0.0321506	−	0.0989494i	−0.933693	−	0.358073i	$-0.883434\pi$
$367$	0.615917	−	1.89560i	0.0321506	−	0.0989494i	0.965844	+	0.259124i	$0.0834338\pi$
$368$	−11.6776			−0.608738
$369$	−11.2842	−	3.66645i	−0.587430	−	0.190868i
$370$	0.984693	−	3.90856i	0.0511917	−	0.203196i
$371$	−32.9345	+	10.7011i	−1.70987	+	0.555572i
$372$	−15.1822	+	4.93299i	−0.787159	+	0.255763i
$373$	6.18199	−	8.50877i	0.320091	−	0.440568i	−0.618404	−	0.785860i	$-0.712220\pi$
$373$	6.18199	−	8.50877i	0.320091	−	0.440568i	0.938495	+	0.345293i	$0.112220\pi$
$374$	7.88556	+	21.6994i	0.407753	+	1.12205i
$375$	−5.19674	+	11.4449i	−0.268359	+	0.591012i
$376$	−13.3121			−0.686520
$377$	−18.9741	−	13.7855i	−0.977215	−	0.709988i
$378$	−28.2542	+	9.18036i	−1.45324	+	0.472187i
$379$	11.3924	−	3.70162i	0.585188	−	0.190139i	−0.00143516	−	0.999999i	$-0.500457\pi$
$379$	11.3924	−	3.70162i	0.585188	−	0.190139i	0.586624	+	0.809860i	$0.300457\pi$
$380$	−15.7465	−	3.96706i	−0.807780	−	0.203506i
$381$	−2.54949	−	0.828379i	−0.130614	−	0.0424391i
$382$		−	0.0460230i		−	0.00235474i
$383$	−13.5867	−	4.41459i	−0.694248	−	0.225575i	−0.0594252	−	0.998233i	$-0.518927\pi$
$383$	−13.5867	−	4.41459i	−0.694248	−	0.225575i	−0.634823	+	0.772658i	$0.718927\pi$
$384$	7.50758	+	10.3333i	0.383120	+	0.527319i
$385$	11.4157	−	9.53134i	0.581798	−	0.485762i
$386$	7.22025	−	9.93782i	0.367501	−	0.505822i
$387$	−9.44137	−	12.9949i	−0.479932	−	0.660569i
$388$	16.2366	−	11.7966i	0.824291	−	0.598882i
$389$	3.87534	+	2.81560i	0.196487	+	0.142756i	0.681679	−	0.731651i	$-0.261250\pi$
$389$	3.87534	+	2.81560i	0.196487	+	0.142756i	−0.485192	+	0.874408i	$0.661250\pi$
$390$	−1.12621	−	16.6933i	−0.0570280	−	0.845299i
$391$	−18.8406	−	12.7220i	−0.952811	−	0.643378i
$392$	−0.536535	−	0.174331i	−0.0270991	−	0.00880503i
$393$		−	3.99676i		−	0.201610i
$394$	10.6377	+	3.45639i	0.535919	+	0.174131i
$395$	9.97175	−	0.672743i	0.501733	−	0.0338494i
$396$	−11.5074	+	3.73898i	−0.578269	+	0.187891i
$397$	8.51070	+	26.1932i	0.427140	+	1.31460i	0.900931	+	0.433963i	$0.142885\pi$
$397$	8.51070	+	26.1932i	0.427140	+	1.31460i	−0.473791	+	0.880637i	$0.657115\pi$
$398$	42.3816	+	30.7920i	2.12440	+	1.54346i
$399$	7.79099			0.390037
$400$	10.4936	−	1.42238i	0.524682	−	0.0711190i
$401$			21.1735i			1.05735i	0.848823	+	0.528677i	$0.177312\pi$
$401$			21.1735i			1.05735i	−0.848823	+	0.528677i	$0.822688\pi$
$402$	−27.2169	−	19.7742i	−1.35745	−	0.986248i
$403$	−4.99458	−	15.3717i	−0.248798	−	0.765720i
$404$	−2.68007	−	8.24840i	−0.133338	−	0.410373i
$405$	−0.925362	+	1.47285i	−0.0459816	+	0.0731863i
$406$	13.1687	−	40.5291i	0.653551	−	2.01142i
$407$			2.14867i			0.106506i
$408$	0.241094	+	7.00520i	0.0119359	+	0.346809i
$409$	−24.6673	+	17.9218i	−1.21972	+	0.886176i	−0.996077	−	0.0884952i	$-0.971794\pi$
$409$	−24.6673	+	17.9218i	−1.21972	+	0.886176i	−0.223641	+	0.974672i	$0.571794\pi$
$410$	32.1189	+	8.09179i	1.58624	+	0.399625i
$411$	0.540985	−	0.744602i	0.0266848	−	0.0367285i
$412$	−13.1031	−	18.0348i	−0.645542	−	0.888512i
$413$	−12.5765	+	9.13734i	−0.618847	+	0.449619i
$414$	12.1947	−	16.7845i	0.599335	−	0.824914i
$415$	12.4537	+	7.82444i	0.611329	+	0.384087i
$416$	−18.9168	+	13.7439i	−0.927475	+	0.673850i
$417$	16.3901	+	5.32548i	0.802629	+	0.260790i
$418$	15.0741			0.737300
$419$	26.3102	+	8.54869i	1.28534	+	0.417631i	0.870456	−	0.492246i	$-0.163824\pi$
$419$	26.3102	+	8.54869i	1.28534	+	0.417631i	0.414879	+	0.909877i	$0.363824\pi$
$420$	16.2027	−	6.50016i	0.790609	−	0.317175i
$421$	8.92430	+	27.4662i	0.434944	+	1.33862i	0.893144	+	0.449771i	$0.148494\pi$
$421$	8.92430	+	27.4662i	0.434944	+	1.33862i	−0.458200	+	0.888849i	$0.651506\pi$
$422$	1.28548	+	3.95629i	0.0625760	+	0.192589i
$423$	−8.98341	+	12.3646i	−0.436788	+	0.601187i
$424$	−20.3413			−0.987862
$425$	18.4800	+	9.13726i	0.896412	+	0.443222i
$426$	1.63031			0.0789889
$427$	−18.0104	+	24.7892i	−0.871584	+	1.19963i
$428$	4.65859	+	14.3377i	0.225181	+	0.693037i
$429$	2.75614	+	8.48254i	0.133068	+	0.409541i
$430$	28.7391	+	34.4208i	1.38592	+	1.65992i
$431$	8.68578	+	2.82218i	0.418379	+	0.135940i	0.510639	−	0.859795i	$-0.329409\pi$
$431$	8.68578	+	2.82218i	0.418379	+	0.135940i	−0.0922594	+	0.995735i	$0.529409\pi$
$432$	11.2769			0.542560
$433$	18.0900	+	5.87781i	0.869352	+	0.282470i	0.709529	−	0.704676i	$-0.248908\pi$
$433$	18.0900	+	5.87781i	0.869352	+	0.282470i	0.159823	+	0.987146i	$0.448908\pi$
$434$	23.7592	−	17.2620i	1.14048	−	0.828605i
$435$	−7.14896	−	17.8199i	−0.342766	−	0.854399i
$436$	−17.2531	+	23.7469i	−0.826276	+	1.13727i
$437$	−12.0081	+	8.72442i	−0.574427	+	0.417346i
$438$	11.2362	+	15.4654i	0.536888	+	0.738963i
$439$	20.2802	−	27.9134i	0.967923	−	1.33223i	0.0248341	−	0.999692i	$-0.492094\pi$
$439$	20.2802	−	27.9134i	0.967923	−	1.33223i	0.943089	−	0.332540i	$-0.107906\pi$
$440$	8.10749	−	3.25255i	0.386510	−	0.155059i
$441$	−0.523992	+	0.380703i	−0.0249520	+	0.0181287i
$442$	−27.4251	+	0.943874i	−1.30448	+	0.0448955i
$443$		−	21.0708i		−	1.00110i	−0.865707	−	0.500551i	$-0.833131\pi$
$443$		−	21.0708i		−	1.00110i	0.865707	−	0.500551i	$-0.166869\pi$
$444$	−0.779447	+	2.39889i	−0.0369909	+	0.113846i
$445$	17.5002	+	20.9600i	0.829588	+	0.993598i
$446$	−5.52931	−	17.0175i	−0.261820	−	0.805800i
$447$	1.40496	+	4.32403i	0.0664525	+	0.204520i
$448$	−25.5504	−	18.5634i	−1.20714	−	0.877040i
$449$		−	22.2116i		−	1.04823i	−0.851648	−	0.524115i	$-0.824396\pi$
$449$		−	22.2116i		−	1.04823i	0.851648	−	0.524115i	$-0.175604\pi$
$450$	−8.91385	+	16.5681i	−0.420203	+	0.781029i
$451$	−17.6569			−0.831431
$452$	34.6688	+	25.1884i	1.63068	+	1.18476i
$453$	−4.96329	−	15.2754i	−0.233196	−	0.717703i
$454$	−27.3199	+	8.87676i	−1.28218	+	0.416607i
$455$	6.58132	+	16.4050i	0.308537	+	0.769076i
$456$	4.35244	+	1.41419i	0.203822	+	0.0662257i
$457$		−	19.6740i		−	0.920309i	−0.887839	−	0.460154i	$-0.847794\pi$
$457$		−	19.6740i		−	0.920309i	0.887839	−	0.460154i	$-0.152206\pi$
$458$	−48.9614	−	15.9085i	−2.28782	−	0.743357i
$459$	18.1941	+	12.2854i	0.849229	+	0.573435i
$460$	−17.6940	+	28.1625i	−0.824987	+	1.31308i
$461$	−4.15487	−	3.01869i	−0.193512	−	0.140595i	0.486811	−	0.873508i	$-0.338160\pi$
$461$	−4.15487	−	3.01869i	−0.193512	−	0.140595i	−0.680322	+	0.732913i	$0.738160\pi$
$462$	−13.1110	+	9.52566i	−0.609977	+	0.443174i
$463$	23.1439	+	31.8548i	1.07559	+	1.48042i	0.864289	+	0.502996i	$0.167769\pi$
$463$	23.1439	+	31.8548i	1.07559	+	1.48042i	0.211297	+	0.977422i	$0.432231\pi$
$464$	−9.50806	+	13.0867i	−0.441401	+	0.607536i
$465$	3.23255	−	12.8310i	0.149906	−	0.595025i
$466$	−23.2312	−	31.9750i	−1.07616	−	1.48121i
$467$	−27.5743	−	8.95944i	−1.27599	−	0.414594i	−0.408823	−	0.912614i	$-0.634061\pi$
$467$	−27.5743	−	8.95944i	−1.27599	−	0.414594i	−0.867165	+	0.498020i	$0.834061\pi$
$468$		−	14.3812i		−	0.664770i
$469$	33.8017	+	10.9828i	1.56082	+	0.507141i
$470$	22.6982	−	36.1274i	1.04699	−	1.66643i
$471$	−13.2498	+	4.30513i	−0.610519	+	0.198370i
$472$	−8.68444	+	2.82174i	−0.399734	+	0.129881i
$473$	−19.3386	−	14.0503i	−0.889190	−	0.646034i
$474$	−10.8912			−0.500250
$475$	9.72800	−	9.30252i	0.446351	−	0.426829i
$476$	−9.77955	−	26.9113i	−0.448245	−	1.23348i
$477$	−13.7269	+	18.8935i	−0.628513	+	0.865073i
$478$	26.8090	−	8.71079i	1.22622	−	0.398422i
$479$	−15.5563	+	5.05454i	−0.710784	+	0.230948i	−0.642023	−	0.766685i	$-0.721905\pi$
$479$	−15.5563	+	5.05454i	−0.710784	+	0.230948i	−0.0687613	+	0.997633i	$0.521905\pi$
$480$	−19.0991	+	1.28852i	−0.871750	+	0.0588125i
$481$	−2.42884	−	0.789179i	−0.110746	−	0.0359835i
$482$	−2.33406			−0.106314
$483$	4.93111	−	15.1764i	0.224373	−	0.690550i
$484$	9.43972	−	6.85836i	0.429078	−	0.311744i
$485$	1.11976	+	16.5977i	0.0508459	+	0.753665i
$486$	−19.2357	+	26.4757i	−0.872549	+	1.20096i
$487$	−22.3806	+	16.2604i	−1.01416	+	0.736831i	−0.965078	−	0.261964i	$-0.915630\pi$
$487$	−22.3806	+	16.2604i	−1.01416	+	0.736831i	−0.0490827	+	0.998795i	$0.515630\pi$
$488$	−14.5612	+	10.5793i	−0.659153	+	0.478903i
$489$	−17.7187	−	12.8734i	−0.801266	−	0.582154i
$490$	1.38794	−	1.15884i	0.0627010	−	0.0523511i
$491$	4.21471	−	3.06216i	0.190207	−	0.138194i	−0.488606	−	0.872504i	$-0.662495\pi$
$491$	4.21471	−	3.06216i	0.190207	−	0.138194i	0.678813	+	0.734311i	$0.262495\pi$
$492$	−19.7131	−	6.40517i	−0.888735	−	0.288768i
$493$	−29.5974	+	10.7557i	−1.33300	+	0.484411i
$494$	−5.53653	+	17.0397i	−0.249100	+	0.766651i
$495$	2.45013	−	9.72535i	0.110125	−	0.437122i
$496$	−10.6021	+	3.44484i	−0.476049	+	0.154678i
$497$	−1.63806	+	0.532238i	−0.0734770	+	0.0238741i
$498$	−12.9665	−	9.42069i	−0.581041	−	0.422151i
$499$			5.69381i			0.254890i	0.991846	+	0.127445i	$0.0406776\pi$
$499$			5.69381i			0.254890i	−0.991846	+	0.127445i	$0.959322\pi$
$500$	12.4697	−	27.4624i	0.557664	−	1.22816i
$501$	5.10629			0.228132
$502$	−14.2227	+	19.5759i	−0.634790	+	0.873714i
$503$	−4.83362	−	14.8764i	−0.215521	−	0.663304i	−0.999116	−	0.0420330i	$-0.986617\pi$
$503$	−4.83362	−	14.8764i	−0.215521	−	0.663304i	0.783596	−	0.621271i	$-0.213383\pi$
$504$	6.42715	−	2.08831i	0.286288	−	0.0930206i
$505$	6.97104	+	1.75623i	0.310207	+	0.0781512i
$506$	9.54079	−	29.3635i	0.424140	−	1.30537i
$507$	4.01435			0.178284
$508$	6.11757	+	1.98772i	0.271423	+	0.0881908i
$509$	5.43817	−	3.95106i	0.241043	−	0.175128i	−0.460705	−	0.887553i	$-0.652403\pi$
$509$	5.43817	−	3.95106i	0.241043	−	0.175128i	0.701748	+	0.712426i	$0.252403\pi$
$510$	−19.4223	−	11.2901i	−0.860034	−	0.499934i
$511$	−16.3385	−	11.8706i	−0.722773	−	0.525125i
$512$	13.2442	+	18.2291i	0.585318	+	0.805621i
$513$	11.5961	−	8.42506i	0.511980	−	0.371975i
$514$	−22.7657	−	16.5402i	−1.00415	−	0.729558i
$515$	18.4359	−	1.24378i	0.812384	−	0.0548074i
$516$	−16.4938	−	22.7018i	−0.726099	−	0.999389i
$517$	−7.02839	+	21.6312i	−0.309108	+	0.951338i
$518$		−	4.64035i		−	0.203885i
$519$	0.0908122	−	0.279491i	0.00398621	−	0.0122683i
$520$	0.698887	+	10.3593i	0.0306482	+	0.454284i
$521$	−1.11802	+	0.363266i	−0.0489812	+	0.0159150i	−0.333405	−	0.942784i	$-0.608198\pi$
$521$	−1.11802	+	0.363266i	−0.0489812	+	0.0159150i	0.284424	+	0.958699i	$0.408198\pi$
$522$	−8.88081	−	27.3323i	−0.388702	−	1.19630i
$523$	7.25499	−	9.98563i	0.317238	−	0.436641i	−0.620383	−	0.784299i	$-0.713023\pi$
$523$	7.25499	−	9.98563i	0.317238	−	0.436641i	0.937622	+	0.347658i	$0.113023\pi$
$524$			9.59035i			0.418956i
$525$	−2.58261	+	14.2383i	−0.112714	+	0.621412i
$526$	−3.40476			−0.148455
$527$	−20.8583	−	5.99241i	−0.908604	−	0.261033i
$528$	5.85054	−	1.90095i	0.254612	−	0.0827284i
$529$	2.28704	+	7.03879i	0.0994366	+	0.306034i
$530$	34.6835	−	55.2038i	1.50656	−	2.39790i
$531$	−3.23961	+	9.97050i	−0.140587	+	0.432683i
$532$	−18.6947			−0.810518
$533$	6.48514	−	19.9592i	0.280903	−	0.864530i
$534$	−17.4897	−	24.0726i	−0.756855	−	1.04172i
$535$	−12.1173	−	3.05274i	−0.523876	−	0.131981i
$536$	16.8898	+	12.2712i	0.729528	+	0.530033i
$537$	4.33543	−	3.14988i	0.187088	−	0.135927i
$538$	16.8030	−	12.2081i	0.724430	−	0.526329i
$539$	−0.566548	+	0.779787i	−0.0244030	+	0.0335878i
$540$	17.0868	−	27.1961i	0.735301	−	1.17034i
$541$	21.7574	+	29.9464i	0.935422	+	1.28750i	0.957707	+	0.287746i	$0.0929058\pi$
$541$	21.7574	+	29.9464i	0.935422	+	1.28750i	−0.0222851	+	0.999752i	$0.507094\pi$
$542$	21.2166	+	6.89370i	0.911332	+	0.296110i
$543$			16.9764i			0.728528i
$544$	1.07990	+	31.3775i	0.0463004	+	1.34530i
$545$	−9.05896	−	22.5809i	−0.388043	−	0.967257i
$546$	−5.95226	−	18.3192i	−0.254733	−	0.783988i
$547$	0.151842	+	0.467323i	0.00649231	+	0.0199813i	0.954250	−	0.299009i	$-0.0966562\pi$
$547$	0.151842	+	0.467323i	0.00649231	+	0.0199813i	−0.947758	+	0.318991i	$0.896656\pi$
$548$	−1.29811	+	1.78670i	−0.0554525	+	0.0763238i
$549$			20.6640i			0.881917i
$550$	−4.99688	+	27.5486i	−0.213068	+	1.17467i
$551$			20.5607i			0.875914i
$552$	5.50954	−	7.58324i	0.234502	−	0.322764i
$553$	10.9430	−	3.55558i	0.465342	−	0.151199i
$554$	27.9531	−	9.08252i	1.18761	−	0.385879i
$555$	−1.33998	−	1.60489i	−0.0568788	−	0.0681238i
$556$	−39.3286	−	12.7786i	−1.66791	−	0.541935i
$557$			0.886090i			0.0375448i	0.999824	+	0.0187724i	$0.00597580\pi$
$557$			0.886090i			0.0375448i	−0.999824	+	0.0187724i	$0.994024\pi$
$558$	6.12020	−	18.8360i	0.259089	−	0.797393i
$559$	22.9852	−	16.6997i	0.972170	−	0.706323i
$560$	11.3148	−	4.53924i	0.478136	−	0.191818i
$561$	11.5102	+	3.30677i	0.485961	+	0.139612i
$562$	17.5096	+	24.0999i	0.738599	+	1.01659i
$563$	22.3950	+	30.8241i	0.943838	+	1.29908i	0.954211	+	0.299135i	$0.0966982\pi$
$563$	22.3950	+	30.8241i	0.943838	+	1.29908i	−0.0103729	+	0.999946i	$0.503302\pi$
$564$	−15.6937	+	21.6006i	−0.660826	+	0.909549i
$565$	−32.9664	+	13.2254i	−1.38691	+	0.556398i
$566$	−33.6497	−	46.3149i	−1.41440	−	1.94676i
$567$	−0.618809	+	1.90450i	−0.0259876	+	0.0799815i
$568$	−1.01171			−0.0424506
$569$	10.4963	−	32.3042i	0.440026	−	1.35426i	−0.447821	−	0.894123i	$-0.647800\pi$
$569$	10.4963	−	32.3042i	0.440026	−	1.35426i	0.887847	−	0.460138i	$-0.152200\pi$
$570$	−11.2592	+	9.40067i	−0.471596	+	0.393751i
$571$	−14.4948	+	4.70965i	−0.606588	+	0.197093i	−0.596177	−	0.802853i	$-0.703314\pi$
$571$	−14.4948	+	4.70965i	−0.606588	+	0.197093i	−0.0104118	+	0.999946i	$0.503314\pi$
$572$	−6.61344	−	20.3541i	−0.276522	−	0.851047i
$573$	−0.0193132	−	0.0140318i	−0.000806820	−	0.000586189i
$574$	38.1324			1.59162
$575$	−11.9637	−	24.8374i	−0.498920	−	1.03579i
$576$	−21.2985			−0.887438
$577$	−7.20767	+	9.92050i	−0.300059	+	0.412996i	−0.932249	−	0.361818i	$-0.882156\pi$
$577$	−7.20767	+	9.92050i	−0.300059	+	0.412996i	0.632190	+	0.774814i	$0.282156\pi$
$578$	−19.5569	+	31.2275i	−0.813458	+	1.29889i
$579$	−1.96896	−	6.05984i	−0.0818272	−	0.251838i
$580$	17.1541	+	42.7594i	0.712287	+	1.77549i
$581$	16.1036	+	5.23237i	0.668089	+	0.217075i
$582$		−	18.1282i		−	0.751437i
$583$	−10.7396	+	33.0531i	−0.444789	+	1.36892i
$584$	−6.97281	−	9.59724i	−0.288537	−	0.397137i
$585$	10.0936	+	6.34160i	0.417317	+	0.262193i
$586$	41.4869	+	30.1420i	1.71381	+	1.24515i
$587$	−23.0027	−	31.6604i	−0.949421	−	1.30677i	−0.951784	−	0.306769i	$-0.900752\pi$
$587$	−23.0027	−	31.6604i	−0.949421	−	1.30677i	0.00236271	−	0.999997i	$-0.499248\pi$
$588$	−0.915398	+	0.665076i	−0.0377504	+	0.0274273i
$589$	−8.32855	+	11.4633i	−0.343172	+	0.472335i
$590$	7.14978	−	28.3798i	0.294352	−	1.16838i
$591$	4.69375	−	3.41021i	0.193075	−	0.140277i
$592$	−0.544309	+	1.67521i	−0.0223710	+	0.0688508i
$593$			24.3459i			0.999768i	0.866092	+	0.499884i	$0.166624\pi$
$593$			24.3459i			0.999768i	−0.866092	+	0.499884i	$0.833376\pi$
$594$	−9.21341	+	28.3560i	−0.378031	+	1.16346i
$595$	23.2004	+	5.00307i	0.951123	+	0.205106i
$596$	−3.37125	−	10.3756i	−0.138092	−	0.425003i
$597$	25.8433	−	8.39698i	1.05769	−	0.343666i
$598$	29.6881	+	21.5697i	1.21404	+	0.882050i
$599$	−23.9776			−0.979700			−0.489850	−	0.871807i	$-0.662948\pi$
$599$	−23.9776			−0.979700			−0.489850	+	0.871807i	$0.662948\pi$
$600$	−4.02728	+	7.48548i	−0.164413	+	0.305593i
$601$		−	25.6752i		−	1.04731i	−0.851929	−	0.523657i	$-0.824567\pi$
$601$		−	25.6752i		−	1.04731i	0.851929	−	0.523657i	$-0.175433\pi$
$602$	41.7643	+	30.3436i	1.70219	+	1.23671i
$603$	22.7955	−	7.40670i	0.928303	−	0.301624i
$604$	11.9096	+	36.6539i	0.484593	+	1.49142i
$605$	0.651013	+	9.64966i	0.0264674	+	0.392314i
$606$	−7.45049	−	2.42081i	−0.302656	−	0.0983388i
$607$	−34.2958			−1.39202			−0.696011	−	0.718031i	$-0.745044\pi$
$607$	−34.2958			−1.39202			−0.696011	+	0.718031i	$0.745044\pi$
$608$	19.4954	+	6.33443i	0.790642	+	0.256895i
$609$	−12.9927	−	17.8830i	−0.526492	−	0.724654i
$610$	−3.88299	−	57.5557i	−0.157218	−	2.33036i
$611$	−21.8703	−	15.8897i	−0.884776	−	0.642828i
$612$	−16.0031	−	10.8060i	−0.646889	−	0.436806i
$613$	−26.4117	−	36.3526i	−1.06676	−	1.46827i	−0.873315	−	0.487155i	$-0.838035\pi$
$613$	−26.4117	−	36.3526i	−1.06676	−	1.46827i	−0.193443	−	0.981112i	$-0.561965\pi$
$614$	17.0120	+	12.3599i	0.686547	+	0.498805i
$615$	13.1883	−	11.0114i	0.531805	−	0.444021i
$616$	8.13618	−	5.91128i	0.327816	−	0.238172i
$617$	−11.1486	+	34.3120i	−0.448827	+	1.38135i	0.429404	+	0.903112i	$0.358724\pi$
$617$	−11.1486	+	34.3120i	−0.448827	+	1.38135i	−0.878232	+	0.478236i	$0.841276\pi$
$618$	−20.1358			−0.809982
$619$	−25.7772	−	8.37551i	−1.03607	−	0.336640i	−0.258884	−	0.965908i	$-0.583355\pi$
$619$	−25.7772	−	8.37551i	−1.03607	−	0.336640i	−0.777188	+	0.629268i	$0.783355\pi$
$620$	−7.75660	+	30.7884i	−0.311513	+	1.23649i
$621$	−9.07207	−	27.9210i	−0.364050	−	1.12043i
$622$	14.7721	+	45.4639i	0.592308	+	1.82294i
$623$	25.4317	+	18.4772i	1.01890	+	0.740273i
$624$			7.31160i			0.292698i
$625$	13.7760	+	20.8620i	0.551040	+	0.834479i
$626$			58.3142i			2.33070i
$627$	4.59592	−	6.32574i	0.183543	−	0.252626i
$628$	31.7933	−	10.3303i	1.26869	−	0.412223i
$629$	−2.70322	+	2.10979i	−0.107784	+	0.0841229i
$630$	−5.29138	+	21.0032i	−0.210814	+	0.836787i
$631$	0.0992790	−	0.305549i	0.00395224	−	0.0121637i	−0.949061	−	0.315093i	$-0.897964\pi$
$631$	0.0992790	−	0.305549i	0.00395224	−	0.0121637i	0.953013	+	0.302929i	$0.0979644\pi$
$632$	6.75870			0.268847
$633$	2.05215	+	0.666785i	0.0815657	+	0.0265023i
$634$	37.6337	+	51.7983i	1.49462	+	2.05717i
$635$	−4.09274	+	3.41716i	−0.162415	+	0.135606i
$636$	−23.9805	+	33.0064i	−0.950890	+	1.30879i
$637$	−0.673380	−	0.926827i	−0.0266803	−	0.0367222i
$638$	−25.1385	−	34.6002i	−0.995244	−	1.36984i
$639$	−0.682734	+	0.939703i	−0.0270085	+	0.0371741i
$640$	25.3465	−	1.71000i	1.00191	−	0.0675936i
$641$	7.13763	+	9.82410i	0.281919	+	0.388029i	0.926368	−	0.376619i	$-0.122913\pi$
$641$	7.13763	+	9.82410i	0.281919	+	0.388029i	−0.644449	+	0.764647i	$0.722913\pi$
$642$	12.9507	+	4.20794i	0.511123	+	0.166074i
$643$	40.5507			1.59916			0.799581	−	0.600558i	$-0.205055\pi$
$643$	40.5507			1.59916			0.799581	+	0.600558i	$0.205055\pi$
$644$	−11.8323	+	36.4162i	−0.466260	+	1.43500i
$645$	23.2066	−	1.56563i	0.913760	−	0.0616467i
$646$	14.8014	+	18.9646i	0.582352	+	0.746150i
$647$	−13.9095	+	4.51946i	−0.546838	+	0.177678i	−0.569390	−	0.822067i	$-0.692821\pi$
$647$	−13.9095	+	4.51946i	−0.546838	+	0.177678i	0.0225527	+	0.999746i	$0.492821\pi$
$648$	−0.691397	+	0.951627i	−0.0271606	+	0.0373834i
$649$			15.6013i			0.612406i
$650$	−29.3054	−	15.7667i	−1.14945	−	0.618419i
$651$		−	15.2333i		−	0.597041i
$652$	42.5164	+	30.8900i	1.66507	+	1.20975i
$653$	−2.39262	−	7.36374i	−0.0936306	−	0.288165i	0.893264	−	0.449533i	$-0.148410\pi$
$653$	−2.39262	−	7.36374i	−0.0936306	−	0.288165i	−0.986894	+	0.161367i	$0.948410\pi$
$654$	8.19308	+	25.2157i	0.320375	+	0.986012i
$655$	−6.73108	−	4.22901i	−0.263005	−	0.165241i
$656$	−13.7662	−	4.47290i	−0.537479	−	0.174638i
$657$	−13.6196			−0.531351
$658$	15.1788	−	46.7154i	0.591729	−	1.82116i
$659$	33.5358	−	24.3652i	1.30637	−	0.949134i	0.306375	−	0.951911i	$-0.400884\pi$
$659$	33.5358	−	24.3652i	1.30637	−	0.949134i	0.999996	+	0.00277698i	$0.000883942\pi$
$660$	4.28030	−	16.9899i	0.166610	−	0.661330i
$661$	29.3881	+	21.3517i	1.14307	+	0.830486i	0.987543	−	0.157347i	$-0.0502941\pi$
$661$	29.3881	+	21.3517i	1.14307	+	0.830486i	0.155522	+	0.987832i	$0.450294\pi$
$662$	25.3344	+	34.8698i	0.984650	+	1.35525i
$663$	−7.96549	+	11.7965i	−0.309354	+	0.458138i
$664$	8.04652	+	5.84614i	0.312265	+	0.226874i
$665$	8.24372	−	13.1211i	0.319678	−	0.508813i
$666$	−1.83941	−	2.53173i	−0.0712757	−	0.0981027i
$667$	40.0510	+	13.0134i	1.55078	+	0.503880i
$668$	−12.2527			−0.474071
$669$	−8.82706	−	2.86809i	−0.341274	−	0.110887i
$670$	−62.1008	+	24.9135i	−2.39916	+	0.962493i
$671$	9.50271	+	29.2463i	0.366848	+	1.12904i
$672$	−20.9593	+	6.81008i	−0.808521	+	0.262704i
$673$	−22.9496	−	16.6738i	−0.884641	−	0.642729i	0.0498345	−	0.998757i	$-0.484131\pi$
$673$	−22.9496	−	16.6738i	−0.884641	−	0.642729i	−0.934475	+	0.356028i	$0.884131\pi$
$674$			24.0425i			0.926084i
$675$	11.5532	+	23.9851i	0.444682	+	0.923188i
$676$	−9.63255			−0.370483
$677$	14.8127	+	10.7620i	0.569297	+	0.413619i	0.834850	−	0.550478i	$-0.185554\pi$
$677$	14.8127	+	10.7620i	0.569297	+	0.413619i	−0.265553	+	0.964096i	$0.585554\pi$
$678$	36.8131	−	11.9613i	1.41380	−	0.459371i
$679$	5.91818	+	18.2143i	0.227119	+	0.699001i
$680$	12.0528	+	7.00623i	0.462203	+	0.268677i
$681$	−4.60443	+	14.1710i	−0.176442	+	0.543033i
$682$		−	29.4737i		−	1.12861i
$683$	10.5527	−	32.4777i	0.403786	−	1.24273i	−0.518118	−	0.855309i	$-0.673367\pi$
$683$	10.5527	−	32.4777i	0.403786	−	1.24273i	0.921904	−	0.387417i	$-0.126633\pi$
$684$	−10.1997	+	7.41049i	−0.389994	+	0.283347i
$685$	−0.681587	−	1.69896i	−0.0260421	−	0.0649140i
$686$	24.1805	−	33.2816i	0.923214	−	1.27070i
$687$	−21.6036	+	15.6960i	−0.824230	+	0.598838i
$688$	−11.5181	−	15.8532i	−0.439122	−	0.604399i
$689$	−33.4185	−	24.2799i	−1.27314	−	0.924992i
$690$	11.1857	+	27.8822i	0.425834	+	1.06146i
$691$	0.105778	+	0.145591i	0.00402399	+	0.00553855i	0.811024	−	0.585013i	$-0.198910\pi$
$691$	0.105778	+	0.145591i	0.00402399	+	0.00553855i	−0.807000	+	0.590551i	$0.798910\pi$
$692$	−0.217907	+	0.670648i	−0.00828357	+	0.0254942i
$693$		−	11.5462i		−	0.438603i
$694$	−58.6410	−	19.0536i	−2.22598	−	0.723266i
$695$	26.3114	−	21.9682i	0.998048	−	0.833302i
$696$	−4.01235	−	12.3487i	−0.152088	−	0.468078i
$697$	−17.3374	−	22.2139i	−0.656700	−	0.841411i
$698$	−20.4490	+	28.1456i	−0.774005	+	1.06533i
$699$	−20.5010			−0.775417
$700$	6.19706	−	34.1653i	0.234227	−	1.29133i
$701$	17.3697			0.656046			0.328023	−	0.944670i	$-0.393618\pi$
$701$	17.3697			0.656046			0.328023	+	0.944670i	$0.393618\pi$
$702$	−28.6694	−	20.8295i	−1.08206	−	0.786161i
$703$	0.691846	+	2.12928i	0.0260935	+	0.0803075i
$704$	−30.1444	+	9.79452i	−1.13611	+	0.369145i
$705$	−8.24017	−	20.5399i	−0.310343	−	0.773578i
$706$	−10.8444	+	33.3755i	−0.408133	+	1.25610i
$707$	8.27620			0.311258
$708$	−5.65951	+	17.4182i	−0.212697	+	0.654615i
$709$	28.7420	+	39.5599i	1.07943	+	1.48570i	0.860149	+	0.510042i	$0.170370\pi$
$709$	28.7420	+	39.5599i	1.07943	+	1.48570i	0.219278	+	0.975662i	$0.429630\pi$
$710$	1.72505	−	2.74566i	0.0647400	−	0.103043i
$711$	4.56097	−	6.27763i	0.171050	−	0.235430i
$712$	10.8535	+	14.9386i	0.406752	+	0.559847i
$713$	17.0584	+	23.4789i	0.638844	+	0.879293i
$714$	−24.8578	−	7.14142i	−0.930280	−	0.267261i
$715$	17.2020	+	4.33374i	0.643319	+	0.162073i
$716$	−10.4030	+	7.55822i	−0.388778	+	0.282464i
$717$	4.51834	−	13.9060i	0.168740	−	0.519330i
$718$		−	0.990264i		−	0.0369563i
$719$	−3.26192	−	1.05986i	−0.121649	−	0.0395261i	0.247560	−	0.968873i	$-0.420371\pi$
$719$	−3.26192	−	1.05986i	−0.121649	−	0.0395261i	−0.369209	+	0.929346i	$0.620371\pi$
$720$	4.37390	−	6.96168i	0.163006	−	0.259447i
$721$	20.2315	−	6.57361i	0.753460	−	0.244814i
$722$	−24.2272	+	7.87188i	−0.901642	+	0.292961i
$723$	−0.711627	+	0.979471i	−0.0264657	+	0.0364269i
$724$		−	40.7354i		−	1.51392i
$725$	−37.5754	−	6.81560i	−1.39552	−	0.253125i
$726$		−	10.5394i		−	0.391155i
$727$	−5.51250	+	7.58730i	−0.204447	+	0.281397i	−0.898912	−	0.438129i	$-0.855641\pi$
$727$	−5.51250	+	7.58730i	−0.204447	+	0.281397i	0.694465	+	0.719527i	$0.255641\pi$
$728$	3.69376	+	11.3682i	0.136900	+	0.421334i
$729$	5.96672	+	18.3637i	0.220990	+	0.680136i
$730$	37.9349	−	2.55927i	1.40403	−	0.0947229i
$731$	−1.31215	−	38.1257i	−0.0485316	−	1.41013i
$732$			36.0994i			1.33427i
$733$	−42.0066	−	13.6488i	−1.55155	−	0.504129i	−0.597015	−	0.802230i	$-0.703647\pi$
$733$	−42.0066	−	13.6488i	−1.55155	−	0.504129i	−0.954534	+	0.298101i	$0.903647\pi$
$734$	2.53922	+	3.49493i	0.0937242	+	0.129000i
$735$	−0.0631307	−	0.935756i	−0.00232861	−	0.0345159i
$736$	24.6782	−	33.9667i	0.909652	−	1.25203i
$737$	28.8570	−	20.9658i	1.06296	−	0.772287i
$738$	20.8047	−	15.1155i	0.765832	−	0.556410i
$739$	2.24019	+	1.62759i	0.0824066	+	0.0598719i	0.628226	−	0.778031i	$-0.283781\pi$
$739$	2.24019	+	1.62759i	0.0824066	+	0.0598719i	−0.545819	+	0.837903i	$0.683781\pi$
$740$	3.21531	+	3.85098i	0.118197	+	0.141565i
$741$	5.46255	+	7.51855i	0.200672	+	0.276201i
$742$	23.1936	−	71.3826i	0.851464	−	2.62054i
$743$	30.9734			1.13631			0.568153	−	0.822923i	$-0.307658\pi$
$743$	30.9734			1.13631			0.568153	+	0.822923i	$0.307658\pi$
$744$	2.76511	−	8.51012i	0.101374	−	0.311996i
$745$	8.76885	+	2.20916i	0.321266	+	0.0809372i
$746$	7.04422	+	21.6799i	0.257907	+	0.793757i
$747$	10.8601	−	3.52865i	0.397349	−	0.129106i
$748$	−27.6191	−	7.93470i	−1.00985	−	0.290121i
$749$	−14.3860			−0.525652
$750$	−13.4478	−	23.6928i	−0.491045	−	0.865140i
$751$		−	19.5476i		−	0.713303i	−0.934237	−	0.356652i	$-0.883918\pi$
$751$		−	19.5476i		−	0.713303i	0.934237	−	0.356652i	$-0.116082\pi$
$752$	−10.9594	+	15.0843i	−0.399647	+	0.550067i
$753$	3.87853	+	11.9369i	0.141342	+	0.435005i
$754$	48.3449	−	15.7082i	1.76062	−	0.572059i
$755$	−30.9776	−	7.80425i	−1.12739	−	0.284026i
$756$	11.4263	−	35.1666i	0.415572	−	1.27900i
$757$			22.3107i			0.810897i	0.914118	+	0.405449i	$0.132885\pi$
$757$			22.3107i			0.810897i	−0.914118	+	0.405449i	$0.867115\pi$
$758$	−8.02292	+	24.6920i	−0.291406	+	0.896854i
$759$	−9.41331	−	12.9563i	−0.341681	−	0.470284i
$760$	6.98705	−	5.83372i	0.253447	−	0.211611i
$761$	1.41730	+	1.02973i	0.0513770	+	0.0373276i	0.613177	−	0.789945i	$-0.289891\pi$
$761$	1.41730	+	1.02973i	0.0513770	+	0.0373276i	−0.561800	+	0.827273i	$0.689891\pi$
$762$	4.70051	−	3.41512i	0.170282	−	0.123717i
$763$	−16.4640	−	22.6608i	−0.596037	−	0.820375i
$764$	0.0463425	+	0.0336698i	0.00167661	+	0.00121813i
$765$	14.6411	−	6.46689i	0.529351	−	0.233811i
$766$	25.0499	−	18.1998i	0.905090	−	0.657587i
$767$	−17.6356	−	5.73017i	−0.636786	−	0.206904i
$768$	−0.0983790			−0.00354995
$769$	−4.63978	+	14.2798i	−0.167315	+	0.514942i	−0.999199	−	0.0400068i	$-0.987262\pi$
$769$	−4.63978	+	14.2798i	−0.167315	+	0.514942i	0.831885	+	0.554948i	$0.187262\pi$
$770$	2.16965	+	32.1598i	0.0781889	+	1.15896i
$771$	−13.8820	+	4.51052i	−0.499946	+	0.162442i
$772$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.q (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27397 + 1.75347i) q^{2} +(0.347412 + 1.06922i) q^{3} +(-0.833625 - 2.56564i) q^{4} +(2.16832 + 0.546269i) q^{5} +(-2.31745 - 0.752985i) q^{6} +2.57428 q^{7} +(1.43812 + 0.467275i) q^{8} +(1.40451 - 1.02043i) q^{9} +(-3.72024 + 3.10615i) q^{10} +(1.51857 - 2.09014i) q^{11} +(2.45363 - 1.78267i) q^{12} +(1.80492 + 2.48426i) q^{13} +(-3.27956 + 4.51393i) q^{14} +(0.169215 + 2.50820i) q^{15} +(1.71343 - 1.24488i) q^{16} +(4.12067 - 0.141819i) q^{17} +3.76276i q^{18} +(0.831872 - 2.56024i) q^{19} +(-0.406037 - 6.01849i) q^{20} +(0.894336 + 2.75248i) q^{21} +(1.73038 + 5.32555i) q^{22} +(-4.46069 - 3.24088i) q^{23} +1.70002i q^{24} +(4.40318 + 2.36897i) q^{25} -6.65551 q^{26} +(4.30762 + 3.12967i) q^{27} +(-2.14599 - 6.60466i) q^{28} +(-7.26390 + 2.36018i) q^{29} +(-4.61363 - 2.89866i) q^{30} +(-5.00591 - 1.62652i) q^{31} +7.61467i q^{32} +(2.76240 + 0.897557i) q^{33} +(-5.00094 + 7.40614i) q^{34} +(5.58185 + 1.40625i) q^{35} +(-3.78889 - 2.75279i) q^{36} +(-0.672839 + 0.488846i) q^{37} +(3.42952 + 4.72034i) q^{38} +(-2.02918 + 2.79293i) q^{39} +(2.86305 + 1.79880i) q^{40} +(-4.01713 - 5.52911i) q^{41} +(-5.96576 - 1.93839i) q^{42} -9.25232i q^{43} +(-6.62845 - 2.15371i) q^{44} +(3.60284 - 1.44538i) q^{45} +(11.3656 - 3.69290i) q^{46} +(-8.37265 + 2.72044i) q^{47} +(1.92633 + 1.39956i) q^{48} -0.373079 q^{49} +(-9.76344 + 4.70286i) q^{50} +(1.58320 + 4.35665i) q^{51} +(4.86908 - 6.70172i) q^{52} +(-12.7937 + 4.15692i) q^{53} +(-10.9756 + 3.56618i) q^{54} +(4.43452 - 3.70253i) q^{55} +(3.70214 + 1.20290i) q^{56} +3.02647 q^{57} +(5.11548 - 15.7438i) q^{58} +(-4.88543 + 3.54947i) q^{59} +(6.29405 - 2.52504i) q^{60} +(-6.99628 + 9.62955i) q^{61} +(9.22944 - 6.70558i) q^{62} +(3.61559 - 2.62688i) q^{63} +(-9.92525 - 7.21111i) q^{64} +(2.55657 + 6.37264i) q^{65} +(-5.09305 + 3.70032i) q^{66} +(13.1306 + 4.26637i) q^{67} +(-3.79895 - 10.4539i) q^{68} +(1.91553 - 5.89540i) q^{69} +(-9.57694 + 7.99610i) q^{70} +(-0.636317 + 0.206752i) q^{71} +(2.49668 - 0.811219i) q^{72} +(-6.34682 - 4.61124i) q^{73} -1.80258i q^{74} +(-1.00324 + 5.53100i) q^{75} -7.26211 q^{76} +(3.90923 - 5.38060i) q^{77} +(-2.31220 - 7.11623i) q^{78} +(4.25088 - 1.38120i) q^{79} +(4.39531 - 1.76330i) q^{80} +(-0.240381 + 0.739818i) q^{81} +14.8128 q^{82} +(6.25556 + 2.03256i) q^{83} +(6.31633 - 4.58908i) q^{84} +(9.01237 + 1.94348i) q^{85} +(16.2237 + 11.7872i) q^{86} +(-5.04713 - 6.94678i) q^{87} +(3.16057 - 2.29629i) q^{88} +(9.87913 + 7.17761i) q^{89} +(-2.05548 + 8.15886i) q^{90} +(4.64638 + 6.39519i) q^{91} +(-4.59637 + 14.1462i) q^{92} -5.91751i q^{93} +(5.89631 - 18.1470i) q^{94} +(3.20234 - 5.09698i) q^{95} +(-8.14180 + 2.64543i) q^{96} +(2.29897 + 7.07549i) q^{97} +(0.475293 - 0.654184i) q^{98} -4.48521i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) \) 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Introduction

L-functions

Modular forms

Varieties

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