LMFDB - Embedded newform 425.2.q.a.84.7

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			84.7
Character	$\chi$	$=$	425.84
Dual form			425.2.q.a.339.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-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} +(3.25033 + 2.53680i) 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} +(-8.58904 + 2.46755i) 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} +(-5.66197 - 7.27614i) 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	$-0.994790\pi$
$3$	−0.347412	−	1.06922i	−0.200578	−	0.617317i	0.799288	−	0.600949i	$-0.205210\pi$
$4$	−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	$-0.661724\pi$
$7$	−2.57428			−0.972987			−0.486493	+	0.873684i	$0.661724\pi$
$8$	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	−0.974065	−	0.226270i	$-0.927347\pi$
$11$	−1.51857	+	2.09014i	−0.457867	+	0.630200i	0.516198	+	0.856469i	$0.327347\pi$
$12$	−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
$17$	3.25033	+	2.53680i	0.788321	+	0.615264i
$17$	3.25033	+	2.53680i	0.788321	+	0.615264i
$18$			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	0.946022	−	0.324104i	$-0.105063\pi$
$23$	4.46069	+	3.24088i	0.930117	+	0.675770i	−0.0159041	+	0.999874i	$0.505063\pi$
$24$		−	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	0.456559	−	0.889693i	$-0.349082\pi$
$29$	7.26390	−	2.36018i	1.34887	−	0.438275i	0.892312	+	0.451418i	$0.149082\pi$
$30$	−4.61363	−	2.89866i	−0.842329	−	0.529220i
$31$	5.00591	+	1.62652i	0.899088	+	0.292131i	0.721860	−	0.692039i	$-0.243287\pi$
$31$	5.00591	+	1.62652i	0.899088	+	0.292131i	0.177227	+	0.984170i	$0.443287\pi$
$32$			7.61467i			1.34610i
$33$	2.76240	+	0.897557i	0.480871	+	0.156245i
$34$	−8.58904	+	2.46755i	−1.47301	+	0.423181i
$35$	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	−0.531103	−	0.847307i	$-0.678222\pi$
$37$	0.672839	−	0.488846i	0.110614	−	0.0803658i	0.641717	+	0.766941i	$0.278222\pi$
$38$	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	0.997863	−	0.0653338i	$-0.0208112\pi$
$41$	4.01713	+	5.52911i	0.627371	+	0.863501i	−0.370493	+	0.928835i	$0.620811\pi$
$42$	−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	$-0.524219\pi$
$61$	6.99628	−	9.62955i	0.895782	−	1.23294i	0.971794	−	0.235831i	$-0.0757811\pi$
$62$	−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	−0.271015	−	0.962575i	$-0.587359\pi$
$71$	0.636317	−	0.206752i	0.0755170	−	0.0245369i	0.346532	+	0.938038i	$0.387359\pi$
$72$	2.49668	−	0.811219i	0.294236	−	0.0956031i
$73$	6.34682	+	4.61124i	0.742839	+	0.539704i	0.893599	−	0.448866i	$-0.148172\pi$
$73$	6.34682	+	4.61124i	0.742839	+	0.539704i	−0.150760	+	0.988570i	$0.548172\pi$
$74$			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	−0.538220	−	0.842804i	$-0.680903\pi$
$79$	−4.25088	+	1.38120i	−0.478262	+	0.155397i	0.0599586	+	0.998201i	$0.480903\pi$
$80$	−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
$85$	−5.66197	−	7.27614i	−0.614126	−	0.789208i
$86$	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	$-0.976719\pi$
$97$	−2.29897	−	7.07549i	−0.233425	−	0.718407i	0.763902	−	0.645332i	$-0.223281\pi$
$98$	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	$0.448867\pi$
$102$	5.62230	+	8.32635i	0.556691	+	0.824432i
$103$	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	$-0.412936\pi$
$107$	5.58835			0.540246			0.270123	+	0.962826i	$0.412936\pi$
$108$	−4.43865	+	13.6608i	−0.427109	+	1.31451i
$109$	6.39558	+	8.80276i	0.612585	+	0.843151i	0.996787	−	0.0800980i	$-0.0255233\pi$
$109$	6.39558	+	8.80276i	0.612585	+	0.843151i	−0.384202	+	0.923249i	$0.625523\pi$
$110$	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	0.213822	−	0.976873i	$-0.431409\pi$
$113$	12.8514	−	9.33708i	1.20896	−	0.878359i	0.995136	+	0.0985138i	$0.0314088\pi$
$114$	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
$119$	−8.36726	−	6.53044i	−0.767026	−	0.598644i
$120$	−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	0.452970	−	0.891526i	$-0.350365\pi$
$131$	3.38105	+	1.09857i	0.295404	+	0.0959826i	−0.157566	+	0.987509i	$0.550365\pi$
$132$		−	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
$136$	3.48900	+	5.16703i	0.299179	+	0.443070i
$137$	−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	$0.425271\pi$
$139$	−9.01016	+	12.4014i	−0.764232	+	1.05188i	−0.996850	+	0.0793071i	$0.974729\pi$
$140$	−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
$153$	7.15374	+	0.246206i	0.578346	+	0.0199046i
$154$	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	0.237237	−	0.971452i	$-0.423758\pi$
$163$	15.7604	−	11.4506i	1.23445	−	0.896883i	0.997216	+	0.0745691i	$0.0237581\pi$
$164$	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	−0.990561	−	0.137076i	$-0.956230\pi$
$167$	−1.40354	+	4.31966i	−0.108609	+	0.334265i	0.881951	+	0.471340i	$0.156230\pi$
$168$			4.37632i			0.337640i
$169$	1.10341	−	3.39593i	0.0848773	−	0.261226i
$170$	19.9717	−	0.658505i	1.53176	−	0.0505050i
$171$	−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	0.595795	−	0.803136i	$-0.296837\pi$
$173$	0.211474	+	0.153645i	0.0160781	+	0.0116814i	−0.579717	+	0.814818i	$0.696837\pi$
$174$	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	−0.277961	−	0.960592i	$-0.589659\pi$
$181$	−14.3612	−	4.66623i	−1.06746	−	0.346838i	−0.789497	+	0.613754i	$0.789659\pi$
$182$	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
$187$	−10.2381	+	2.94132i	−0.748686	+	0.215090i
$188$	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	$-0.434613\pi$
$193$	5.66751			0.407956			0.203978	+	0.978975i	$0.434613\pi$
$194$	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	0.991656	−	0.128910i	$-0.0411477\pi$
$197$	1.59471	+	4.90801i	0.113618	+	0.349681i	−0.878038	+	0.478591i	$0.841148\pi$
$198$	−7.86469	−	5.71403i	−0.558919	−	0.406078i
$199$			24.1701i			1.71337i	0.515837	+	0.856686i	$0.327481\pi$
$199$			24.1701i			1.71337i	−0.515837	+	0.856686i	$0.672519\pi$
$200$	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
$204$	−12.4974	−	0.430114i	−0.874991	−	0.0301140i
$205$	−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	−0.846081	−	0.533054i	$-0.821044\pi$
$211$	−1.12813	+	1.55274i	−0.0776637	+	0.106895i	0.768418	+	0.639949i	$0.221044\pi$
$212$	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
$221$	−0.435485	+	12.6534i	−0.0292939	+	0.851160i
$222$	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	0.172045	−	0.985089i	$-0.444962\pi$
$227$	−10.7223	−	7.79022i	−0.711665	−	0.517055i	−0.883710	+	0.468034i	$0.844962\pi$
$228$	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	$-0.696234\pi$
$233$	5.63500	−	17.3427i	0.369161	−	1.13616i	0.947334	−	0.320247i	$-0.103766\pi$
$234$	−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
$238$	22.1106	−	6.35217i	1.43322	−	0.411750i
$239$	−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	0.788143	−	0.615492i	$-0.211043\pi$
$241$	−0.632980	−	0.871222i	−0.0407738	−	0.0561203i	−0.828917	+	0.559371i	$0.811043\pi$
$242$	−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
$255$	−5.81279	+	8.58173i	−0.364011	+	0.537409i
$256$	−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	0.573373	−	0.819294i	$-0.305635\pi$
$269$	9.11370	+	2.96122i	0.555672	+	0.180549i	−0.0177007	+	0.999843i	$0.505635\pi$
$270$	−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	$-0.201206\pi$
$272$	8.72725	+	0.300360i	0.529167	+	0.0182120i
$273$	−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	0.866384	−	0.499378i	$-0.166438\pi$
$277$	10.9709	+	7.97079i	0.659175	+	0.478918i	−0.207210	+	0.978297i	$0.566438\pi$
$278$	−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	$-0.612636\pi$
$283$	8.16214	−	25.1205i	0.485189	−	1.49326i	0.831708	−	0.555214i	$-0.187364\pi$
$284$	−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
$289$	4.12929	+	16.4909i	0.242899	+	0.970051i
$290$	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
$306$	−9.54538	+	12.2302i	−0.545673	+	0.699155i
$307$		−	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	$0.415035\pi$
$311$	−12.9640	+	17.8434i	−0.735119	+	1.01180i	−0.998885	+	0.0472173i	$0.984965\pi$
$312$	4.22328	−	3.06840i	0.239096	−	0.173714i
$313$	−21.7666	+	15.8144i	−1.23032	+	0.893881i	−0.996914	−	0.0784981i	$-0.974988\pi$
$313$	−21.7666	+	15.8144i	−1.23032	+	0.893881i	−0.233407	+	0.972379i	$0.574988\pi$
$314$	−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	$0.411419\pi$
$317$	−9.12850	+	28.0946i	−0.512707	+	1.57795i	−0.787415	+	0.616423i	$0.788581\pi$
$318$	−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
$323$	9.19867	−	6.21133i	0.511828	−	0.345607i
$324$	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	−0.804744	−	0.593621i	$-0.797698\pi$
$337$	−8.97422	+	6.52015i	−0.488857	+	0.355175i	0.315888	+	0.948797i	$0.397698\pi$
$338$	4.54897	+	6.26111i	0.247431	+	0.340560i
$339$	−14.4482	−	10.4972i	−0.784717	−	0.570130i
$340$	−13.9480	+	20.5921i	−0.756434	+	1.11676i
$341$	−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	$-0.823436\pi$
$347$	−8.79096	−	27.0558i	−0.471924	−	1.45243i	0.378138	−	0.925749i	$-0.376564\pi$
$348$	−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	−0.965844	−	0.259124i	$-0.916566\pi$
$367$	−0.615917	+	1.89560i	−0.0321506	+	0.0989494i	0.933693	+	0.358073i	$0.116566\pi$
$368$	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	−0.586624	−	0.809860i	$-0.699543\pi$
$379$	−11.3924	+	3.70162i	−0.585188	+	0.190139i	0.00143516	+	0.999999i	$0.499543\pi$
$380$	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
$391$	6.27724	+	21.8498i	0.317454	+	1.10499i
$392$	−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	$-0.857115\pi$
$397$	−8.51070	−	26.1932i	−0.427140	−	1.31460i	0.473791	−	0.880637i	$-0.342885\pi$
$398$	−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	$-0.822688\pi$
$401$		−	21.1735i		−	1.05735i	0.848823	−	0.528677i	$-0.177312\pi$
$402$	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
$408$	4.31260	−	5.52561i	0.213505	−	0.273559i
$409$	−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	−0.414879	−	0.909877i	$-0.636176\pi$
$419$	−26.3102	−	8.54869i	−1.28534	−	0.417631i	−0.870456	+	0.492246i	$0.836176\pi$
$420$	−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
$425$	8.30220	+	18.8699i	0.402716	+	0.915325i
$426$	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	0.0922594	−	0.995735i	$-0.470591\pi$
$431$	−8.68578	−	2.82218i	−0.418379	−	0.135940i	−0.510639	+	0.859795i	$0.670591\pi$
$432$	−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	$0.507906\pi$
$439$	−20.2802	+	27.9134i	−0.967923	+	1.33223i	−0.943089	+	0.332540i	$0.892094\pi$
$440$	8.10749	−	3.25255i	0.386510	−	0.155059i
$441$	−0.523992	+	0.380703i	−0.0249520	+	0.0181287i
$442$	−21.6326	−	16.8837i	−1.02896	−	0.803075i
$443$		−	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	$0.175604\pi$
$449$			22.2116i			1.04823i	−0.851648	+	0.524115i	$0.824396\pi$
$450$	−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
$459$	−6.06185	−	21.1000i	−0.282943	−	0.984866i
$460$	−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	0.0687613	−	0.997633i	$-0.478095\pi$
$479$	15.5563	−	5.05454i	0.710784	−	0.230948i	0.642023	+	0.766685i	$0.278095\pi$
$480$	−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	0.0490827	−	0.998795i	$-0.484370\pi$
$487$	22.3806	−	16.2604i	1.01416	−	0.736831i	0.965078	+	0.261964i	$0.0843702\pi$
$488$	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	$-0.959322\pi$
$499$		−	5.69381i		−	0.254890i	0.991846	−	0.127445i	$-0.0406776\pi$
$500$	−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	$0.0133835\pi$
$503$	4.83362	+	14.8764i	0.215521	+	0.663304i	−0.783596	+	0.621271i	$0.786617\pi$
$504$	−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	$0.252403\pi$
$510$	−7.64249	−	21.1254i	−0.338415	−	0.935450i
$511$	−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	−0.284424	−	0.958699i	$-0.591802\pi$
$521$	1.11802	−	0.363266i	0.0489812	−	0.0159150i	0.333405	+	0.942784i	$0.391802\pi$
$522$	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
$527$	12.1447	+	17.9857i	0.529031	+	0.783470i
$528$	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	$-0.907094\pi$
$541$	−21.7574	−	29.9464i	−0.935422	−	1.28750i	0.0222851	−	0.999752i	$-0.492906\pi$
$542$	21.2166	+	6.89370i	0.911332	+	0.296110i
$543$			16.9764i			0.728528i
$544$	−19.3169	+	24.7502i	−0.828206	+	1.06116i
$545$	−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	0.947758	−	0.318991i	$-0.103344\pi$
$547$	−0.151842	−	0.467323i	−0.00649231	−	0.0199813i	−0.954250	+	0.299009i	$0.903344\pi$
$548$	−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
$561$	6.70177	+	9.92500i	0.282949	+	0.419034i
$562$	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	0.0104118	−	0.999946i	$-0.496686\pi$
$571$	14.4948	−	4.70965i	0.606588	−	0.197093i	0.596177	+	0.802853i	$0.296686\pi$
$572$	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	$0.282156\pi$
$578$	−34.1769	−	13.7683i	−1.42157	−	0.572687i
$579$	−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
$595$	14.5755	+	18.7308i	0.597537	+	0.767889i
$596$	−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	$0.175433\pi$
$601$			25.6752i			1.04731i	−0.851929	+	0.523657i	$0.824567\pi$
$602$	−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	$-0.254956\pi$
$607$	34.2958			1.39202			0.696011	+	0.718031i	$0.254956\pi$
$608$	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
$612$	−5.33186	−	18.5591i	−0.215528	−	0.750208i
$613$	−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	$-0.641276\pi$
$617$	11.1486	−	34.3120i	0.448827	−	1.38135i	0.878232	−	0.478236i	$-0.158724\pi$
$618$	20.1358			0.809982
$619$	25.7772	+	8.37551i	1.03607	+	0.336640i	0.777188	−	0.629268i	$-0.216645\pi$
$619$	25.7772	+	8.37551i	1.03607	+	0.336640i	0.258884	+	0.965908i	$0.416645\pi$
$620$	−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
$629$	3.42705	+	0.117947i	0.136646	+	0.00470285i
$630$	−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	0.644449	−	0.764647i	$-0.277087\pi$
$641$	−7.13763	−	9.82410i	−0.281919	−	0.388029i	−0.926368	+	0.376619i	$0.877087\pi$
$642$	12.9507	+	4.20794i	0.511123	+	0.166074i
$643$	−40.5507			−1.59916			−0.799581	−	0.600558i	$-0.794945\pi$
$643$	−40.5507			−1.59916			−0.799581	+	0.600558i	$0.794945\pi$
$644$	−11.8323	+	36.4162i	−0.466260	+	1.43500i
$645$	23.2066	−	1.56563i	0.913760	−	0.0616467i
$646$	−0.827462	+	24.0427i	−0.0325561	+	0.945946i
$647$	−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	0.986894	−	0.161367i	$-0.0515904\pi$
$653$	2.39262	+	7.36374i	0.0936306	+	0.288165i	−0.893264	+	0.449533i	$0.851590\pi$
$654$	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
$663$	13.6806	−	3.93031i	0.531311	−	0.152641i
$664$	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	0.934475	−	0.356028i	$-0.115869\pi$
$673$	22.9496	+	16.6738i	0.884641	+	0.642729i	−0.0498345	+	0.998757i	$0.515869\pi$
$674$		−	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	0.265553	−	0.964096i	$-0.414446\pi$
$677$	−14.8127	−	10.7620i	−0.569297	−	0.413619i	−0.834850	+	0.550478i	$0.814446\pi$
$678$	36.8131	−	11.9613i	1.41380	−	0.459371i
$679$	5.91818	+	18.2143i	0.227119	+	0.699001i
$680$	−4.74266	−	13.1097i	−0.181873	−	0.502734i
$681$	−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	$0.326633\pi$
$683$	−10.5527	+	32.4777i	−0.403786	+	1.24273i	−0.921904	+	0.387417i	$0.873367\pi$
$684$	−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	0.807000	−	0.590551i	$-0.201090\pi$
$691$	−0.105778	−	0.145591i	−0.00402399	−	0.00553855i	−0.811024	+	0.585013i	$0.801090\pi$
$692$	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
$697$	−0.969238	+	28.1621i	−0.0367125	+	1.06671i
$698$	−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	$-0.829630\pi$
$709$	−28.7420	−	39.5599i	−1.07943	−	1.48570i	−0.219278	−	0.975662i	$-0.570370\pi$
$710$	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
$714$	−14.4734	−	21.4344i	−0.541653	−	0.802161i
$715$	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	0.369209	−	0.929346i	$-0.379629\pi$
$719$	3.26192	+	1.05986i	0.121649	+	0.0395261i	−0.247560	+	0.968873i	$0.579629\pi$
$720$	−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
$731$	23.4713	−	30.0731i	0.868117	−	1.11229i
$732$			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	$-0.692342\pi$
$743$	−30.9734			−1.13631			−0.568153	+	0.822923i	$0.692342\pi$
$744$	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
$748$	16.0811	+	23.8153i	0.587983	+	0.870775i
$749$	−14.3860			−0.525652
$750$	−13.4478	−	23.6928i	−0.491045	−	0.865140i
$751$			19.5476i			0.713303i	0.934237	+	0.356652i	$0.116082\pi$
$751$			19.5476i			0.713303i	−0.934237	+	0.356652i	$0.883918\pi$
$752$	−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
$765$	−15.3771	−	4.44172i	−0.555959	−	0.160591i
$766$	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
$772$	−4.72458	−	14.5408i	−0.170041	−	0.523334i
$773$	1.76972	−	2.43581i	0.0636523	−	0.0876099i	−0.776004	−	0.630728i	$-0.782756\pi$
$773$	1.76972	−	2.43581i	0.0636523	−	0.0876099i	0.839656	+	0.543118i	$0.182756\pi$
$774$	34.8143			1.25137
$775$	18.1888	+	19.0207i	0.653359	+	0.683243i
$776$		−	11.2497i		−	0.403840i
$777$	1.94728	+	1.41479i	0.0698584	+	0.0507551i
$778$	−9.87414	+	3.20830i	−0.354005	+	0.115023i
$779$	17.4976	−	5.68530i	0.626915	−	0.203697i
$780$	17.6331	+	11.0786i	0.631368	+	0.396677i
$781$	−0.534154	+	1.64396i	−0.0191135	+	0.0588254i
$782$	−46.3100	−	16.8291i	−1.65604	−	0.601806i
$783$	−38.6767	−	12.5668i	−1.38219	−	0.449102i
$784$	−0.639247	+	0.464440i	−0.0228303	+	0.0165872i
$785$	6.76935	−	26.8697i	0.241609	−	0.959022i
$786$	7.00821	+	5.09176i	0.249975	+	0.181617i
$787$	−28.4615	+	20.6785i	−1.01454	+	0.737109i	−0.965157	−	0.261671i	$-0.915727\pi$
$787$	−28.4615	+	20.6785i	−1.01454	+	0.737109i	−0.0493862	+	0.998780i	$0.515727\pi$
$788$	11.2628	−	8.18289i	0.401220	−	0.291503i
$789$	1.03807	−	1.42878i	0.0369563	−	0.0508659i
$790$	−11.5241	+	18.3422i	−0.410009	+	0.652588i
$791$	−33.0831	+	24.0363i	−1.17630	+	0.854631i
$792$	−2.09583	+	6.45029i	−0.0744719	+	0.229201i
$793$	36.5501			1.29793
$794$	56.7715	+	18.4462i	2.01474	+	0.654630i
$795$	−12.5912	−	31.3856i	−0.446565	−	1.11313i
$796$	62.0117	−	20.1488i	2.19794	−	0.714156i
$797$	15.7416	−	5.11477i	0.557597	−	0.181174i	−0.0166426	−	0.999862i	$-0.505298\pi$
$797$	15.7416	−	5.11477i	0.557597	−	0.181174i	0.574240	+	0.818687i	$0.305298\pi$
$798$	−9.92550	+	13.6613i	−0.351359	+	0.483604i
$799$	−34.1151	−	12.3974i	−1.20691	−	0.438589i
$800$	−18.0389	+	33.5288i	−0.637771	+	1.18542i
$801$	21.1996			0.749050
$802$	37.1271	+	26.9744i	1.31100	+	0.952500i
$803$	−19.2762	+	6.26322i	−0.680243	+	0.221024i
$804$	−39.8230	+	12.9393i	−1.40445	+	0.456333i
$805$	20.3414	+	24.3629i	0.716940	+	0.858681i
$806$	−33.3168	−	10.8253i	−1.17354	−	0.381305i
$807$		−	10.7734i		−	0.379240i
$808$	4.62351	+	1.50227i	0.162654	+	0.0528496i
$809$	3.99745	+	5.50202i	0.140543	+	0.193441i	0.873486	−	0.486849i	$-0.161854\pi$
$809$	3.99745	+	5.50202i	0.140543	+	0.193441i	−0.732943	+	0.680290i	$0.761854\pi$
$810$	1.40371	+	3.49896i	0.0493213	+	0.122941i
$811$	9.37805	−	12.9078i	0.329308	−	0.453254i	−0.611973	−	0.790879i	$-0.709624\pi$
$811$	9.37805	−	12.9078i	0.329308	−	0.453254i	0.941281	+	0.337625i	$0.109624\pi$
$812$	31.1764	+	42.9107i	1.09408	+	1.50587i
$813$	−9.36157	+	6.80158i	−0.328325	+	0.238542i
$814$	−3.76764	−	2.73735i	−0.132056	−	0.0959440i
$815$	−40.4287	+	16.2191i	−1.41616	+	0.568132i
$816$	−2.71080	−	9.43574i	−0.0948969	−	0.330317i
$817$	−23.6881	−	7.69674i	−0.828743	−	0.269275i
$818$		−	66.0852i		−	2.31062i
$819$	−13.0517	−	4.24076i	−0.456064	−	0.148184i
$820$	−31.6458	+	26.4221i	−1.10512	+	0.922699i
$821$	−50.3271	+	16.3523i	−1.75643	+	0.570698i	−0.996820	−	0.0796832i	$-0.974609\pi$
$821$	−50.3271	+	16.3523i	−1.75643	+	0.570698i	−0.759608	+	0.650381i	$0.774609\pi$
$822$	−0.616439	−	1.89721i	−0.0215008	−	0.0661726i
$823$	8.69757	+	6.31915i	0.303178	+	0.220272i	0.728964	−	0.684552i	$-0.240002\pi$
$823$	8.69757	+	6.31915i	0.303178	+	0.220272i	−0.425786	+	0.904824i	$0.640002\pi$
$824$	12.4956			0.435304
$825$	10.0370	+	10.4961i	0.349445	+	0.365428i
$826$			33.6932i			1.17234i
$827$	−22.0700	−	16.0348i	−0.767448	−	0.557584i	0.133737	−	0.991017i	$-0.457302\pi$
$827$	−22.0700	−	16.0348i	−0.767448	−	0.557584i	−0.901186	+	0.433433i	$0.857302\pi$
$828$	−7.97959	−	24.5587i	−0.277310	−	0.853472i
$829$	−10.6878	−	32.8936i	−0.371202	−	1.14244i	−0.946006	−	0.324150i	$-0.894922\pi$
$829$	−10.6878	−	32.8936i	−0.371202	−	1.14244i	0.574804	−	0.818291i	$-0.305078\pi$
$830$	29.5856	−	11.8691i	1.02693	−	0.411983i
$831$	4.71116	−	14.4995i	0.163428	−	0.502980i
$832$		−	37.6724i		−	1.30606i
$833$	−1.21263	−	0.946428i	−0.0420152	−	0.0327918i
$834$	−30.2187	+	21.9551i	−1.04639	+	0.760245i
$835$	5.40301	−	8.59966i	0.186979	−	0.297604i
$836$	11.0280	−	15.1788i	0.381413	−	0.524969i
$837$	−16.4731	−	22.6733i	−0.569394	−	0.783703i
$838$	48.5083	−	35.2433i	1.67569	−	1.21746i
$839$	−18.7546	+	25.8135i	−0.647482	+	0.891182i	−0.998987	−	0.0450040i	$-0.985670\pi$
$839$	−18.7546	+	25.8135i	−0.647482	+	0.891182i	0.351505	+	0.936186i	$0.385670\pi$
$840$	2.39064	−	9.48923i	0.0824851	−	0.327410i
$841$	23.7322	−	17.2425i	0.818352	−	0.594568i
$842$	−59.5305	−	19.3426i	−2.05156	−	0.666591i
$843$	−15.4518			−0.532189
$844$	4.92420	+	1.59997i	0.169498	+	0.0550732i
$845$	−4.24762	+	6.76070i	−0.146123	+	0.232575i
$846$	−10.2364	−	31.5043i	−0.351934	−	1.08314i
$847$	−3.44073	−	10.5895i	−0.118225	−	0.363859i
$848$	−16.7462	+	23.0492i	−0.575068	+	0.791514i
$849$	−29.6950			−1.01913
$850$	−43.6646	−	9.48206i	−1.49768	−	0.325232i
$851$	4.58561			0.157193
$852$	−1.19272	+	1.64163i	−0.0408618	+	0.0562414i
$853$	−6.28951	−	19.3571i	−0.215349	−	0.662776i	−0.999129	−	0.0417368i	$-0.986711\pi$
$853$	−6.28951	−	19.3571i	−0.215349	−	0.662776i	0.783780	−	0.621039i	$-0.213289\pi$
$854$	−20.5224	−	63.1614i	−0.702262	−	2.16134i
$855$	0.703423	+	10.4265i	0.0240565	+	0.356579i
$856$	8.03674	+	2.61129i	0.274690	+	0.0892522i
$857$	−23.4302			−0.800359			−0.400179	−	0.916437i	$-0.631052\pi$
$857$	−23.4302			−0.800359			−0.400179	+	0.916437i	$0.631052\pi$
$858$	−18.3851	−	5.97369i	−0.627658	−	0.203939i
$859$	−17.2923	+	12.5636i	−0.590006	+	0.428664i	−0.842317	−	0.538982i	$-0.818809\pi$
$859$	−17.2923	+	12.5636i	−0.590006	+	0.428664i	0.252312	+	0.967646i	$0.418809\pi$
$860$	55.6850	−	3.75678i	1.89884	−	0.128105i
$861$	−11.6261	+	16.0020i	−0.396217	+	0.545346i
$862$	16.0141	−	11.6349i	0.545441	−	0.396286i
$863$	0.0618065	+	0.0850693i	0.00210392	+	0.00289579i	0.810068	−	0.586336i	$-0.199430\pi$
$863$	0.0618065	+	0.0850693i	0.00210392	+	0.00289579i	−0.807964	+	0.589232i	$0.799430\pi$
$864$	23.8314	−	32.8012i	0.810762	−	1.11592i
$865$	−0.374611	−	0.448672i	−0.0127372	−	0.0152553i
$866$	−33.3528	+	24.2322i	−1.13337	+	0.823444i
$867$	16.1979	−	10.1443i	0.550109	−	0.344517i
$868$			36.5528i			1.24068i
$869$	3.56839	−	10.9824i	0.121049	−	0.372551i
$870$	−40.3543	−	10.1665i	−1.36814	−	0.344678i
$871$	13.1008	+	40.3202i	0.443905	+	1.36620i
$872$	5.08433	+	15.6480i	0.172177	+	0.529907i
$873$	−10.4490	−	7.59162i	−0.353644	−	0.256937i
$874$			32.1706i			1.08819i
$875$	21.2466	+	19.4152i	0.718264	+	0.656353i
$876$	−23.7930			−0.803892
$877$	6.97375	+	5.06672i	0.235487	+	0.171091i	0.699270	−	0.714857i	$-0.253508\pi$
$877$	6.97375	+	5.06672i	0.235487	+	0.171091i	−0.463783	+	0.885949i	$0.653508\pi$
$878$	−23.1088	−	71.1217i	−0.779885	−	2.40024i
$879$	−25.2977	+	8.21972i	−0.853270	+	0.277244i
$880$	2.98905	−	11.8645i	0.100761	−	0.399952i
$881$	−39.2567	−	12.7553i	−1.32259	−	0.429736i	−0.439207	−	0.898386i	$-0.644741\pi$
$881$	−39.2567	−	12.7553i	−1.32259	−	0.429736i	−0.883384	+	0.468650i	$0.844741\pi$
$882$		−	1.40381i		−	0.0472687i
$883$	37.2985	+	12.1190i	1.25519	+	0.407837i	0.859779	−	0.510666i	$-0.170601\pi$
$883$	37.2985	+	12.1190i	1.25519	+	0.407837i	0.395414	+	0.918503i	$0.370601\pi$
$884$	32.8270	−	9.43090i	1.10409	−	0.317196i
$885$	−9.72946	−	11.6530i	−0.327052	−	0.391711i
$886$	36.9470	+	26.8436i	1.24126	+	0.901827i
$887$	9.14623	−	6.64512i	0.307100	−	0.223121i	−0.423551	−	0.905872i	$-0.639217\pi$
$887$	9.14623	−	6.64512i	0.307100	−	0.223121i	0.730651	+	0.682751i	$0.239217\pi$
$888$	−0.831046	−	1.14384i	−0.0278881	−	0.0383846i
$889$	3.60793	−	4.96589i	0.121006	−	0.166551i
$890$	59.0475	−	3.98363i	1.97928	−	0.133532i
$891$	−1.18128	−	1.62590i	−0.0395745	−	0.0544696i
$892$	21.1808	+	6.88205i	0.709185	+	0.230428i
$893$			23.6990i			0.793058i
$894$	9.37195	+	3.04513i	0.313445	+	0.101844i
$895$	0.717446	+	10.6344i	0.0239816	+	0.355467i
$896$	−27.8151	+	9.03768i	−0.929238	+	0.301928i
$897$	18.1031	−	5.88205i	0.604445	−	0.196396i
$898$	−38.9474	−	28.2969i	−1.29969	−	0.944281i
$899$	40.2013			1.34079
$900$	−10.1619	−	21.0968i	−0.338730	−	0.703226i
$901$	−52.1289	−	18.9436i	−1.73667	−	0.631104i
$902$	22.4944	−	30.9609i	0.748981	−	1.03088i
$903$	25.4669	−	8.27468i	0.847484	−	0.275364i
$904$	22.8449	−	7.42276i	0.759810	−	0.246877i
$905$	28.5905	+	17.9629i	0.950382	+	0.597107i
$906$	−33.1081	−	10.7575i	−1.09994	−	0.357394i
$907$	30.8117			1.02309			0.511543	−	0.859258i	$-0.329074\pi$
$907$	30.8117			1.02309			0.511543	+	0.859258i	$0.329074\pi$
$908$	−11.0485	+	34.0037i	−0.366656	+	1.12845i
$909$	4.51542	−	3.28065i	0.149767	−	0.108812i
$910$	−37.1500	−	9.35930i	−1.23151	−	0.310258i
$911$	16.3665	−	22.5266i	0.542247	−	0.746339i	−0.446688	−	0.894690i	$-0.647397\pi$
$911$	16.3665	−	22.5266i	0.542247	−	0.746339i	0.988935	+	0.148351i	$0.0473966\pi$
$912$	−5.18566	+	3.76760i	−0.171714	+	0.124758i
$913$	−13.7478	+	9.98840i	−0.454987	+	0.330568i
$914$	34.4977	+	25.0641i	1.14108	+	0.829046i
$915$	25.3367	+	15.9186i	0.837605	+	0.526252i
$916$	51.8386	−	37.6629i	1.71279	−	1.24442i
$917$	−8.70378	−	2.82803i	−0.287424	−	0.0933898i
$918$	44.7210	+	16.2516i	1.47601	+	0.536382i
$919$	5.27433	−	16.2327i	0.173984	−	0.535468i	−0.825601	−	0.564254i	$-0.809164\pi$
$919$	5.27433	−	16.2327i	0.173984	−	0.535468i	0.999586	+	0.0287855i	$0.00916399\pi$
$920$	−6.94147	−	17.3027i	−0.228854	−	0.570453i
$921$	−10.3735	+	3.37055i	−0.341818	+	0.111063i
$922$	10.5864	−	3.43973i	0.348644	−	0.113281i
$923$	1.66213	+	1.20761i	0.0547097	+	0.0397489i
$924$			20.1708i			0.663572i
$925$	4.12069	−	0.558546i	0.135487	−	0.0183649i
$926$	−85.3411			−2.80448
$927$	8.43238	−	11.6062i	0.276956	−	0.381197i
$928$	17.9720	+	55.3122i	0.589961	+	1.81571i
$929$	22.5417	−	7.32425i	0.739570	−	0.240301i	0.0850830	−	0.996374i	$-0.472884\pi$
$929$	22.5417	−	7.32425i	0.739570	−	0.240301i	0.654487	+	0.756073i	$0.272884\pi$
$930$	−18.3807	−	22.0146i	−0.602726	−	0.721886i
$931$	−0.310354	+	0.955172i	−0.0101715	+	0.0313045i
$932$	−49.1926			−1.61136
$933$	23.5824	+	7.66238i	0.772053	+	0.250855i
$934$	50.8391	−	36.9367i	1.66350	−	1.20861i
$935$	23.8062	−	0.784937i	0.778547	−	0.0256702i
$936$	6.52159	+	4.73821i	0.213165	+	0.154873i
$937$	−20.2479	−	27.8689i	−0.661471	−	0.910437i	0.338058	−	0.941125i	$-0.390230\pi$
$937$	−20.2479	−	27.8689i	−0.661471	−	0.910437i	−0.999529	+	0.0306881i	$0.990230\pi$
$938$	62.3206	−	45.2785i	2.03484	−	1.47840i
$939$	24.4711	+	17.7793i	0.798584	+	0.580205i
$940$	−19.7725	−	49.2861i	−0.644909	−	1.60754i
$941$	−18.4228	−	25.3568i	−0.600566	−	0.826608i	0.395194	−	0.918598i	$-0.370677\pi$
$941$	−18.4228	−	25.3568i	−0.600566	−	0.826608i	−0.995760	+	0.0919897i	$0.970677\pi$
$942$	−9.33098	+	28.7178i	−0.304020	+	0.935676i
$943$			37.6826i			1.22712i
$944$	−3.95219	+	12.1636i	−0.128633	+	0.395891i
$945$	−19.6434	−	23.5270i	−0.639000	−	0.765332i
$946$	−49.2737	+	16.0100i	−1.60203	+	0.520530i
$947$	13.0215	+	40.0762i	0.423143	+	1.30230i	0.904761	+	0.425919i	$0.140049\pi$
$947$	13.0215	+	40.0762i	0.423143	+	1.30230i	−0.481618	+	0.876381i	$0.659951\pi$
$948$	7.96787	−	10.9668i	0.258785	−	0.356186i
$949$			24.0901i			0.781997i
$950$	3.91851	+	28.9089i	0.127133	+	0.937929i
$951$	33.2108			1.07693
$952$	−8.98166	−	13.3014i	−0.291097	−	0.431101i
$953$	46.0539	−	14.9638i	1.49183	−	0.484726i	0.554208	−	0.832378i	$-0.313021\pi$
$953$	46.0539	−	14.9638i	1.49183	−	0.484726i	0.937623	+	0.347652i	$0.113021\pi$
$954$	−15.6415	−	48.1395i	−0.506412	−	1.55858i
$955$	0.0440669	−	0.0176787i	0.00142597	−	0.000572070i
$956$	−10.8419	+	33.3679i	−0.350652	+	1.07919i
$957$	22.1841			0.717112
$958$	−10.9553	+	33.7168i	−0.353949	+	1.08934i
$959$	1.23874	+	1.70497i	0.0400009	+	0.0550565i
$960$	16.4074	−	26.1147i	0.529546	−	0.842848i
$961$	−2.66598	−	1.93695i	−0.0859992	−	0.0624821i
$962$	−4.47808	+	3.25352i	−0.144379	+	0.104898i
$963$	7.84886	−	5.70253i	0.252926	−	0.183761i
$964$	−1.70757	+	2.35027i	−0.0549971	+	0.0756970i
$965$	−12.2889	−	3.09598i	−0.395595	−	0.0996632i
$966$	−20.3293	−	27.9809i	−0.654084	−	0.900270i
$967$	32.7774	+	10.6500i	1.05405	+	0.342482i	0.784257	−	0.620436i	$-0.213044\pi$
$967$	32.7774	+	10.6500i	1.05405	+	0.342482i	0.269794	+	0.962918i	$0.413044\pi$
$968$			6.54038i			0.210216i
$969$	−9.83703	−	7.67755i	−0.316011	−	0.246639i
$970$	−30.5302	−	19.1816i	−0.980267	−	0.615884i
$971$	−4.67439	−	14.3863i	−0.150008	−	0.461678i	0.847613	−	0.530615i	$-0.178039\pi$
$971$	−4.67439	−	14.3863i	−0.150008	−	0.461678i	−0.997621	+	0.0689375i	$0.978039\pi$
$972$	12.5869	+	38.7385i	0.403725	+	1.24254i
$973$	23.1947	−	31.9247i	0.743588	−	1.02346i
$974$			59.9590i			1.92121i
$975$	15.5512	−	7.49071i	0.498037	−	0.239895i
$976$		−	25.2092i		−	0.806925i
$977$	3.66167	−	5.03985i	0.117147	−	0.161239i	−0.746417	−	0.665479i	$-0.768227\pi$
$977$	3.66167	−	5.03985i	0.117147	−	0.161239i	0.863564	+	0.504240i	$0.168227\pi$
$978$	45.1462	−	14.6689i	1.44362	−	0.469059i
$979$	−30.0044	+	9.74901i	−0.958944	+	0.311580i
$980$	−0.151484	−	2.24537i	−0.00483898	−	0.0717259i
$981$	17.9652	+	5.83726i	0.573586	+	0.186369i
$982$			11.2915i			0.360326i
$983$	−5.45071	+	16.7756i	−0.173851	+	0.535057i	−0.999579	−	0.0290106i	$-0.990764\pi$
$983$	−5.45071	+	16.7756i	−0.173851	+	0.535057i	0.825728	+	0.564068i	$0.190764\pi$
$984$	9.39957	−	6.82919i	0.299647	−	0.217706i
$985$	−0.776741	−	11.5133i	−0.0247490	−	0.366843i
$986$	−56.5660	+	38.1957i	−1.80143	+	1.21640i
$987$	−14.9759	−	20.6126i	−0.476689	−	0.656106i
$988$	−13.1075	−	18.0410i	−0.417006	−	0.573960i
$989$	29.9856	−	41.2717i	0.953488	−	1.31236i
$990$	13.9317	+	16.6860i	0.442779	+	0.530317i
$991$	4.92051	+	6.77250i	0.156305	+	0.215135i	0.879986	−	0.474999i	$-0.157551\pi$
$991$	4.92051	+	6.77250i	0.156305	+	0.215135i	−0.723681	+	0.690134i	$0.757551\pi$
$992$	−12.3854	+	38.1184i	−0.393237	+	1.21026i
$993$	−22.3570			−0.709478
$994$	1.15358	−	3.55035i	0.0365893	−	0.112610i
$995$	13.2034	−	52.4084i	0.418575	−	1.66146i
$996$	−18.9722	+	6.16444i	−0.601157	+	0.195328i
$997$	12.2179	+	37.6029i	0.386946	+	1.19090i	0.935059	+	0.354493i	$0.115346\pi$
$997$	12.2179	+	37.6029i	0.386946	+	1.19090i	−0.548113	+	0.836404i	$0.684654\pi$
$998$	9.98394	+	7.25376i	0.316036	+	0.229614i
$999$	−4.42826			−0.140104

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.q.a.84.7	✓	176
17.16	even	2	inner	425.2.q.a.84.8	yes	176
25.14	even	10	inner	425.2.q.a.339.8	yes	176
425.339	even	10	inner	425.2.q.a.339.7	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.q.a.84.7	✓	176	1.1	even	1	trivial
425.2.q.a.84.8	yes	176	17.16	even	2	inner
425.2.q.a.339.7	yes	176	425.339	even	10	inner
425.2.q.a.339.8	yes	176	25.14	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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} +(3.25033 + 2.53680i) 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} +(-8.58904 + 2.46755i) 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} +(-5.66197 - 7.27614i) 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

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