LMFDB - Embedded newform 403.2.l.c.25.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(25,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("403.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.l (of order $6$, degree $2$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.14
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.768888i q^{2} +(-0.723761 - 1.25359i) q^{3} +1.40881 q^{4} +(0.354729 + 0.204803i) q^{5} +(-0.963871 + 0.556491i) q^{6} +(-0.855619 + 0.493992i) q^{7} -2.62099i q^{8} +(0.452340 - 0.783476i) q^{9} +O(q^{10})$	\(q-0.768888i q^{2} +(-0.723761 - 1.25359i) q^{3} +1.40881 q^{4} +(0.354729 + 0.204803i) q^{5} +(-0.963871 + 0.556491i) q^{6} +(-0.855619 + 0.493992i) q^{7} -2.62099i q^{8} +(0.452340 - 0.783476i) q^{9} +(0.157470 - 0.272747i) q^{10} +(1.18713 + 0.685387i) q^{11} +(-1.01964 - 1.76607i) q^{12} +(-0.850558 - 3.50379i) q^{13} +(0.379824 + 0.657875i) q^{14} -0.592913i q^{15} +0.802369 q^{16} +(-0.514354 - 0.890888i) q^{17} +(-0.602406 - 0.347799i) q^{18} +(0.266857 - 0.154070i) q^{19} +(0.499746 + 0.288528i) q^{20} +(1.23853 + 0.715064i) q^{21} +(0.526986 - 0.912767i) q^{22} +4.43618 q^{23} +(-3.28565 + 1.89697i) q^{24} +(-2.41611 - 4.18483i) q^{25} +(-2.69402 + 0.653984i) q^{26} -5.65211 q^{27} +(-1.20540 + 0.695941i) q^{28} +3.23233 q^{29} -0.455884 q^{30} +(-2.67082 + 4.88536i) q^{31} -5.85892i q^{32} -1.98423i q^{33} +(-0.684993 + 0.395481i) q^{34} -0.404683 q^{35} +(0.637262 - 1.10377i) q^{36} +(-6.52893 + 3.76948i) q^{37} +(-0.118463 - 0.205183i) q^{38} +(-3.77672 + 3.60216i) q^{39} +(0.536787 - 0.929742i) q^{40} +(1.40110 + 0.808925i) q^{41} +(0.549804 - 0.952289i) q^{42} +(3.77694 + 6.54184i) q^{43} +(1.67243 + 0.965581i) q^{44} +(0.320916 - 0.185281i) q^{45} -3.41093i q^{46} -9.98933i q^{47} +(-0.580723 - 1.00584i) q^{48} +(-3.01194 + 5.21684i) q^{49} +(-3.21767 + 1.85772i) q^{50} +(-0.744539 + 1.28958i) q^{51} +(-1.19827 - 4.93618i) q^{52} +(-1.20902 + 2.09409i) q^{53} +4.34584i q^{54} +(0.280738 + 0.486253i) q^{55} +(1.29475 + 2.24257i) q^{56} +(-0.386282 - 0.223020i) q^{57} -2.48530i q^{58} +(11.1451 - 6.43461i) q^{59} -0.835302i q^{60} -2.55141 q^{61} +(3.75629 + 2.05356i) q^{62} +0.893809i q^{63} -2.90012 q^{64} +(0.415869 - 1.41709i) q^{65} -1.52565 q^{66} +(7.90391 + 4.56333i) q^{67} +(-0.724628 - 1.25509i) q^{68} +(-3.21074 - 5.56116i) q^{69} +0.311156i q^{70} +(8.21061 + 4.74040i) q^{71} +(-2.05349 - 1.18558i) q^{72} +(3.28711 + 1.89782i) q^{73} +(2.89831 + 5.02002i) q^{74} +(-3.49737 + 6.05763i) q^{75} +(0.375951 - 0.217056i) q^{76} -1.35430 q^{77} +(2.76966 + 2.90388i) q^{78} +(7.10174 + 12.3006i) q^{79} +(0.284623 + 0.164327i) q^{80} +(2.73376 + 4.73500i) q^{81} +(0.621973 - 1.07729i) q^{82} +(6.42313 + 3.70839i) q^{83} +(1.74485 + 1.00739i) q^{84} -0.421365i q^{85} +(5.02995 - 2.90404i) q^{86} +(-2.33943 - 4.05202i) q^{87} +(1.79640 - 3.11145i) q^{88} +10.6730i q^{89} +(-0.142460 - 0.246749i) q^{90} +(2.45860 + 2.57774i) q^{91} +6.24974 q^{92} +(8.05727 - 0.187717i) q^{93} -7.68068 q^{94} +0.126216 q^{95} +(-7.34469 + 4.24046i) q^{96} -11.8188i q^{97} +(4.01117 + 2.31585i) q^{98} +(1.07397 - 0.620056i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		−	0.768888i		−	0.543686i	−0.962342	−	0.271843i	$-0.912367\pi$
$2$		−	0.768888i		−	0.543686i	0.962342	−	0.271843i	$-0.0876332\pi$
$3$	−0.723761	−	1.25359i	−0.417864	−	0.723761i	0.577861	−	0.816135i	$-0.303888\pi$
$3$	−0.723761	−	1.25359i	−0.417864	−	0.723761i	−0.995724	+	0.0923744i	$0.970554\pi$
$4$	1.40881			0.704405
$5$	0.354729	+	0.204803i	0.158639	+	0.0915906i	0.577218	−	0.816590i	$-0.304138\pi$
$5$	0.354729	+	0.204803i	0.158639	+	0.0915906i	−0.418579	+	0.908181i	$0.637472\pi$
$6$	−0.963871	+	0.556491i	−0.393499	+	0.227187i
$7$	−0.855619	+	0.493992i	−0.323393	+	0.186711i	−0.652904	−	0.757441i	$-0.726450\pi$
$7$	−0.855619	+	0.493992i	−0.323393	+	0.186711i	0.329511	+	0.944152i	$0.393116\pi$
$8$		−	2.62099i		−	0.926662i
$9$	0.452340	−	0.783476i	0.150780	−	0.261159i
$10$	0.157470	−	0.272747i	0.0497965	−	0.0862501i
$11$	1.18713	+	0.685387i	0.357932	+	0.206652i	0.668173	−	0.744006i	$-0.267077\pi$
$11$	1.18713	+	0.685387i	0.357932	+	0.206652i	−0.310241	+	0.950658i	$0.600410\pi$
$12$	−1.01964	−	1.76607i	−0.294345	−	0.509821i
$13$	−0.850558	−	3.50379i	−0.235902	−	0.971777i
$13$	−0.850558	−	3.50379i	−0.235902	−	0.971777i
$14$	0.379824	+	0.657875i	0.101512	+	0.175825i
$15$		−	0.592913i		−	0.153089i
$16$	0.802369			0.200592
$17$	−0.514354	−	0.890888i	−0.124749	−	0.216072i	0.796886	−	0.604130i	$-0.206479\pi$
$17$	−0.514354	−	0.890888i	−0.124749	−	0.216072i	−0.921635	+	0.388058i	$0.873146\pi$
$18$	−0.602406	−	0.347799i	−0.141988	−	0.0819770i
$19$	0.266857	−	0.154070i	0.0612212	−	0.0353461i	−0.469077	−	0.883157i	$-0.655413\pi$
$19$	0.266857	−	0.154070i	0.0612212	−	0.0353461i	0.530298	+	0.847811i	$0.322080\pi$
$20$	0.499746	+	0.288528i	0.111747	+	0.0645169i
$21$	1.23853	+	0.715064i	0.270269	+	0.156040i
$22$	0.526986	−	0.912767i	0.112354	−	0.194603i
$23$	4.43618			0.925008			0.462504	−	0.886617i	$-0.346951\pi$
$23$	4.43618			0.925008			0.462504	+	0.886617i	$0.346951\pi$
$24$	−3.28565	+	1.89697i	−0.670681	+	0.387218i
$25$	−2.41611	−	4.18483i	−0.483222	−	0.836966i
$26$	−2.69402	+	0.653984i	−0.528342	+	0.128257i
$27$	−5.65211			−1.08775
$28$	−1.20540	+	0.695941i	−0.227800	+	0.131520i
$29$	3.23233			0.600229			0.300114	−	0.953903i	$-0.402975\pi$
$29$	3.23233			0.600229			0.300114	+	0.953903i	$0.402975\pi$
$30$	−0.455884			−0.0832326
$31$	−2.67082	+	4.88536i	−0.479693	+	0.877436i
$31$	−2.67082	+	4.88536i	−0.479693	+	0.877436i
$32$		−	5.85892i		−	1.03572i
$33$		−	1.98423i		−	0.345409i
$34$	−0.684993	+	0.395481i	−0.117475	+	0.0678244i
$35$	−0.404683			−0.0684040
$36$	0.637262	−	1.10377i	0.106210	−	0.183962i
$37$	−6.52893	+	3.76948i	−1.07335	+	0.619699i	−0.929095	−	0.369842i	$-0.879412\pi$
$37$	−6.52893	+	3.76948i	−1.07335	+	0.619699i	−0.144255	+	0.989541i	$0.546078\pi$
$38$	−0.118463	−	0.205183i	−0.0192172	−	0.0332851i
$39$	−3.77672	+	3.60216i	−0.604759	+	0.576807i
$40$	0.536787	−	0.929742i	0.0848734	−	0.147005i
$41$	1.40110	+	0.808925i	0.218815	+	0.126333i	0.605401	−	0.795920i	$-0.293013\pi$
$41$	1.40110	+	0.808925i	0.218815	+	0.126333i	−0.386586	+	0.922253i	$0.626346\pi$
$42$	0.549804	−	0.952289i	0.0848366	−	0.146941i
$43$	3.77694	+	6.54184i	0.575977	+	0.997622i	0.995935	+	0.0900781i	$0.0287117\pi$
$43$	3.77694	+	6.54184i	0.575977	+	0.997622i	−0.419957	+	0.907544i	$0.637955\pi$
$44$	1.67243	+	0.965581i	0.252129	+	0.145567i
$45$	0.320916	−	0.185281i	0.0478393	−	0.0276201i
$46$		−	3.41093i		−	0.502914i
$47$		−	9.98933i		−	1.45709i	−0.684996	−	0.728546i	$-0.740196\pi$
$47$		−	9.98933i		−	1.45709i	0.684996	−	0.728546i	$-0.259804\pi$
$48$	−0.580723	−	1.00584i	−0.0838202	−	0.145181i
$49$	−3.01194	+	5.21684i	−0.430278	+	0.745263i
$50$	−3.21767	+	1.85772i	−0.455047	+	0.262721i
$51$	−0.744539	+	1.28958i	−0.104256	+	0.180577i
$52$	−1.19827	−	4.93618i	−0.166171	−	0.684525i
$53$	−1.20902	+	2.09409i	−0.166072	+	0.287645i	−0.937035	−	0.349234i	$-0.886442\pi$
$53$	−1.20902	+	2.09409i	−0.166072	+	0.287645i	0.770963	+	0.636879i	$0.219775\pi$
$54$			4.34584i			0.591394i
$55$	0.280738	+	0.486253i	0.0378547	+	0.0655663i
$56$	1.29475	+	2.24257i	0.173018	+	0.299676i
$57$	−0.386282	−	0.223020i	−0.0511643	−	0.0295397i
$58$		−	2.48530i		−	0.326336i
$59$	11.1451	−	6.43461i	1.45096	−	0.837715i	0.452428	−	0.891801i	$-0.350558\pi$
$59$	11.1451	−	6.43461i	1.45096	−	0.837715i	0.998536	+	0.0540858i	$0.0172245\pi$
$60$		−	0.835302i		−	0.107837i
$61$	−2.55141			−0.326674			−0.163337	−	0.986570i	$-0.552226\pi$
$61$	−2.55141			−0.326674			−0.163337	+	0.986570i	$0.552226\pi$
$62$	3.75629	+	2.05356i	0.477050	+	0.260803i
$63$			0.893809i			0.112609i
$64$	−2.90012			−0.362515
$65$	0.415869	−	1.41709i	0.0515822	−	0.175769i
$66$	−1.52565			−0.187794
$67$	7.90391	+	4.56333i	0.965617	+	0.557499i	0.897897	−	0.440205i	$-0.145094\pi$
$67$	7.90391	+	4.56333i	0.965617	+	0.557499i	0.0677195	+	0.997704i	$0.478428\pi$
$68$	−0.724628	−	1.25509i	−0.0878740	−	0.152202i
$69$	−3.21074	−	5.56116i	−0.386527	−	0.669485i
$70$			0.311156i			0.0371903i
$71$	8.21061	+	4.74040i	0.974420	+	0.562582i	0.900581	−	0.434689i	$-0.143142\pi$
$71$	8.21061	+	4.74040i	0.974420	+	0.562582i	0.0738391	+	0.997270i	$0.476475\pi$
$72$	−2.05349	−	1.18558i	−0.242006	−	0.139722i
$73$	3.28711	+	1.89782i	0.384728	+	0.222123i	0.679873	−	0.733330i	$-0.262035\pi$
$73$	3.28711	+	1.89782i	0.384728	+	0.222123i	−0.295146	+	0.955452i	$0.595368\pi$
$74$	2.89831	+	5.02002i	0.336922	+	0.583565i
$75$	−3.49737	+	6.05763i	−0.403842	+	0.699475i
$76$	0.375951	−	0.217056i	0.0431246	−	0.0248980i
$77$	−1.35430			−0.154337
$78$	2.76966	+	2.90388i	0.313602	+	0.328799i
$79$	7.10174	+	12.3006i	0.799008	+	1.38392i	0.920262	+	0.391302i	$0.127975\pi$
$79$	7.10174	+	12.3006i	0.799008	+	1.38392i	−0.121254	+	0.992622i	$0.538692\pi$
$80$	0.284623	+	0.164327i	0.0318219	+	0.0183724i
$81$	2.73376	+	4.73500i	0.303751	+	0.526112i
$82$	0.621973	−	1.07729i	0.0686855	−	0.118967i
$83$	6.42313	+	3.70839i	0.705030	+	0.407049i	0.809218	−	0.587509i	$-0.199891\pi$
$83$	6.42313	+	3.70839i	0.705030	+	0.407049i	−0.104188	+	0.994558i	$0.533224\pi$
$84$	1.74485	+	1.00739i	0.190379	+	0.109915i
$85$		−	0.421365i		−	0.0457034i
$86$	5.02995	−	2.90404i	0.542393	−	0.313151i
$87$	−2.33943	−	4.05202i	−0.250814	−	0.434422i
$88$	1.79640	−	3.11145i	0.191496	−	0.331682i
$89$			10.6730i			1.13133i	0.824634	+	0.565667i	$0.191381\pi$
$89$			10.6730i			1.13133i	−0.824634	+	0.565667i	$0.808619\pi$
$90$	−0.142460	−	0.246749i	−0.0150166	−	0.0260096i
$91$	2.45860	+	2.57774i	0.257731	+	0.270221i
$92$	6.24974			0.651581
$93$	8.05727	−	0.187717i	0.835500	−	0.0194653i
$94$	−7.68068			−0.792201
$95$	0.126216			0.0129495
$96$	−7.34469	+	4.24046i	−0.749614	+	0.432790i
$97$		−	11.8188i		−	1.20002i	−0.799993	−	0.600009i	$-0.795164\pi$
$97$		−	11.8188i		−	1.20002i	0.799993	−	0.600009i	$-0.204836\pi$
$98$	4.01117	+	2.31585i	0.405189	+	0.233936i
$99$	1.07397	−	0.620056i	0.107938	−	0.0623180i
$100$	−3.40384	−	5.89563i	−0.340384	−	0.589563i
$101$	−5.34222			−0.531571			−0.265785	−	0.964032i	$-0.585631\pi$
$101$	−5.34222			−0.531571			−0.265785	+	0.964032i	$0.585631\pi$
$102$	0.991543	+	0.572467i	0.0981774	+	0.0566827i
$103$	−5.64200	+	9.77223i	−0.555923	+	0.962886i	0.441908	+	0.897060i	$0.354302\pi$
$103$	−5.64200	+	9.77223i	−0.555923	+	0.962886i	−0.997831	+	0.0658261i	$0.979032\pi$
$104$	−9.18342	+	2.22931i	−0.900508	+	0.218602i
$105$	0.292894	+	0.507307i	0.0285835	+	0.0495081i
$106$	1.61012	+	0.929604i	0.156389	+	0.0902911i
$107$	9.85254	+	17.0651i	0.952481	+	1.64975i	0.740030	+	0.672574i	$0.234811\pi$
$107$	9.85254	+	17.0651i	0.952481	+	1.64975i	0.212451	+	0.977172i	$0.431855\pi$
$108$	−7.96275			−0.766216
$109$			5.61187i			0.537520i	0.963207	+	0.268760i	$0.0866139\pi$
$109$			5.61187i			0.537520i	−0.963207	+	0.268760i	$0.913386\pi$
$110$	0.373874	−	0.215856i	0.0356475	−	0.0205811i
$111$	9.45077	+	5.45640i	0.897027	+	0.517899i
$112$	−0.686522	+	0.396364i	−0.0648702	+	0.0374528i
$113$	−0.435958	+	0.755101i	−0.0410115	+	0.0710339i	−0.885803	−	0.464062i	$-0.846391\pi$
$113$	−0.435958	+	0.755101i	−0.0410115	+	0.0710339i	0.844791	+	0.535096i	$0.179725\pi$
$114$	−0.171477	+	0.297007i	−0.0160603	+	0.0278173i
$115$	1.57364	+	0.908542i	0.146743	+	0.0847220i
$116$	4.55374			0.422804
$117$	−3.12988	−	0.918514i	−0.289357	−	0.0849166i
$118$	−4.94750	−	8.56932i	−0.455454	−	0.788869i
$119$	0.880182	+	0.508174i	0.0806862	+	0.0465842i
$120$	−1.55402			−0.141862
$121$	−4.56049	−	7.89900i	−0.414590	−	0.718091i
$122$			1.96175i			0.177608i
$123$		−	2.34187i		−	0.211160i
$124$	−3.76268	+	6.88254i	−0.337899	+	0.618071i
$125$		−	4.02733i		−	0.360216i
$126$	0.687239			0.0612242
$127$	−3.23465	−	5.60258i	−0.287029	−	0.497149i	0.686070	−	0.727535i	$-0.259334\pi$
$127$	−3.23465	−	5.60258i	−0.287029	−	0.497149i	−0.973099	+	0.230387i	$0.926001\pi$
$128$		−	9.48798i		−	0.838627i
$129$	5.46720	−	9.46946i	0.481360	−	0.833740i
$130$	−1.08959	−	0.319757i	−0.0955630	−	0.0280445i
$131$	−0.377185	−	0.653304i	−0.0329548	−	0.0570794i	0.849078	−	0.528268i	$-0.177158\pi$
$131$	−0.377185	−	0.653304i	−0.0329548	−	0.0570794i	−0.882032	+	0.471189i	$0.843825\pi$
$132$		−	2.79540i		−	0.243308i
$133$	−0.152219	+	0.263650i	−0.0131990	+	0.0228614i
$134$	3.50869	−	6.07723i	0.303104	−	0.524992i
$135$	−2.00497	−	1.15757i	−0.172560	−	0.0996275i
$136$	−2.33501	+	1.34812i	−0.200226	+	0.115600i
$137$	−8.71296	−	5.03043i	−0.744399	−	0.429779i	0.0792677	−	0.996853i	$-0.474742\pi$
$137$	−8.71296	−	5.03043i	−0.744399	−	0.429779i	−0.823666	+	0.567075i	$0.808075\pi$
$138$	−4.27591	+	2.46870i	−0.363990	+	0.210149i
$139$	−7.76904			−0.658961			−0.329481	−	0.944162i	$-0.606874\pi$
$139$	−7.76904			−0.658961			−0.329481	+	0.944162i	$0.606874\pi$
$140$	−0.570122			−0.0481841
$141$	−12.5225	+	7.22988i	−1.05459	+	0.608866i
$142$	3.64484	−	6.31304i	0.305868	−	0.529779i
$143$	1.39173	−	4.74240i	0.116383	−	0.396579i
$144$	0.362944	−	0.628637i	0.0302453	−	0.0523864i
$145$	1.14660	+	0.661990i	0.0952200	+	0.0549753i
$146$	1.45921	−	2.52742i	0.120765	−	0.209171i
$147$	8.71971			0.719190
$148$	−9.19803	+	5.31048i	−0.756073	+	0.436519i
$149$	14.9225	−	8.61552i	1.22250	−	0.705811i	0.257051	−	0.966398i	$-0.417249\pi$
$149$	14.9225	−	8.61552i	1.22250	−	0.705811i	0.965450	+	0.260587i	$0.0839160\pi$
$150$	4.65764	+	2.68909i	0.380295	+	0.219563i
$151$			2.25736i			0.183701i	0.995773	+	0.0918505i	$0.0292782\pi$
$151$			2.25736i			0.183701i	−0.995773	+	0.0918505i	$0.970722\pi$
$152$	−0.403817	−	0.699431i	−0.0327539	−	0.0567314i
$153$	−0.930653			−0.0752388
$154$			1.04131i			0.0839109i
$155$	−1.94795	+	1.18599i	−0.156463	+	0.0952606i
$156$	−5.32068	+	5.07476i	−0.425996	+	0.406306i
$157$	12.3767			0.987766			0.493883	−	0.869528i	$-0.335577\pi$
$157$	12.3767			0.987766			0.493883	+	0.869528i	$0.335577\pi$
$158$	9.45777	−	5.46045i	0.752420	−	0.434410i
$159$	3.50017			0.277582
$160$	1.19992	−	2.07833i	0.0948622	−	0.164306i
$161$	−3.79568	+	2.19144i	−0.299142	+	0.172709i
$162$	3.64069	−	2.10195i	0.286040	−	0.165145i
$163$		−	21.3428i		−	1.67169i	−0.548963	−	0.835847i	$-0.684977\pi$
$163$		−	21.3428i		−	1.67169i	0.548963	−	0.835847i	$-0.315023\pi$
$164$	1.97388	+	1.13962i	0.154134	+	0.0889896i
$165$	0.406375	−	0.703862i	0.0316362	−	0.0547956i
$166$	2.85134	−	4.93867i	0.221307	−	0.383315i
$167$	−15.0313	+	8.67830i	−1.16315	+	0.671547i	−0.952058	−	0.305918i	$-0.901037\pi$
$167$	−15.0313	+	8.67830i	−1.16315	+	0.671547i	−0.211096	+	0.977465i	$0.567703\pi$
$168$	1.87418	−	3.24617i	0.144596	−	0.250448i
$169$	−11.5531	+	5.96035i	−0.888700	+	0.458489i
$170$	−0.323982			−0.0248483
$171$		−	0.278768i		−	0.0213180i
$172$	5.32099	+	9.21622i	0.405721	+	0.702730i
$173$	−7.26576	+	12.5847i	−0.552406	+	0.956795i	0.445694	+	0.895185i	$0.352957\pi$
$173$	−7.26576	+	12.5847i	−0.552406	+	0.956795i	−0.998100	+	0.0616099i	$0.980377\pi$
$174$	−3.11555	+	1.79876i	−0.236189	+	0.136364i
$175$	4.13454	+	2.38708i	0.312542	+	0.180446i
$176$	0.952512	+	0.549933i	0.0717983	+	0.0414528i
$177$	−16.1327	−	9.31424i	−1.21261	−	0.700101i
$178$	8.20633			0.615091
$179$	−1.29839	−	2.24888i	−0.0970465	−	0.168089i	0.813414	−	0.581685i	$-0.197606\pi$
$179$	−1.29839	−	2.24888i	−0.0970465	−	0.168089i	−0.910461	+	0.413595i	$0.864273\pi$
$180$	0.452110	−	0.261026i	0.0336983	−	0.0194557i
$181$	−1.86623	+	3.23241i	−0.138716	+	0.240263i	−0.927011	−	0.375035i	$-0.877631\pi$
$181$	−1.86623	+	3.23241i	−0.138716	+	0.240263i	0.788295	+	0.615298i	$0.210964\pi$
$182$	1.98199	−	1.89039i	0.146915	−	0.140125i
$183$	1.84661	+	3.19842i	0.136505	+	0.236434i
$184$		−	11.6272i		−	0.857169i
$185$	−3.08800			−0.227034
$186$	−0.144333	−	6.19514i	−0.0105830	−	0.454250i
$187$		−	1.41013i		−	0.103119i
$188$		−	14.0731i		−	1.02638i
$189$	4.83605	−	2.79210i	0.351771	−	0.203095i
$190$		−	0.0970459i		−	0.00704045i
$191$	3.17274	−	5.49534i	0.229571	−	0.397629i	−0.728110	−	0.685460i	$-0.759601\pi$
$191$	3.17274	−	5.49534i	0.229571	−	0.397629i	0.957681	+	0.287832i	$0.0929343\pi$
$192$	2.09899	+	3.63556i	0.151482	+	0.262374i
$193$	−19.7858	+	11.4233i	−1.42421	+	0.822270i	−0.996656	−	0.0817172i	$-0.973960\pi$
$193$	−19.7858	+	11.4233i	−1.42421	+	0.822270i	−0.427559	+	0.903988i	$0.640626\pi$
$194$	−9.08735			−0.652434
$195$	−2.07744	+	0.504307i	−0.148769	+	0.0361141i
$196$	−4.24326	+	7.34954i	−0.303090	+	0.524967i
$197$	−3.13938	−	1.81252i	−0.223672	−	0.129137i	0.383978	−	0.923342i	$-0.374554\pi$
$197$	−3.13938	−	1.81252i	−0.223672	−	0.129137i	−0.607649	+	0.794206i	$0.707887\pi$
$198$	−0.476754	−	0.825762i	−0.0338814	−	0.0586844i
$199$	−1.56206	+	2.70556i	−0.110731	+	0.191792i	−0.916065	−	0.401029i	$-0.868653\pi$
$199$	−1.56206	+	2.70556i	−0.110731	+	0.191792i	0.805334	+	0.592821i	$0.201986\pi$
$200$	−10.9684	+	6.33262i	−0.775584	+	0.447784i
$201$		−	13.2110i		−	0.931834i
$202$			4.10757i			0.289008i
$203$	−2.76564	+	1.59674i	−0.194110	+	0.112069i
$204$	−1.04891	+	1.81677i	−0.0734387	+	0.127200i
$205$	0.331340	+	0.573898i	0.0231418	+	0.0400828i
$206$	7.51375	+	4.33807i	0.523508	+	0.302247i
$207$	2.00666	−	3.47564i	0.139473	−	0.241574i
$208$	−0.682461	−	2.81133i	−0.0473202	−	0.194931i
$209$	0.422391			0.0292174
$210$	0.390063	−	0.225203i	0.0269169	−	0.0155405i
$211$	3.26901	+	5.66210i	0.225048	+	0.389795i	0.956334	−	0.292276i	$-0.0944127\pi$
$211$	3.26901	+	5.66210i	0.225048	+	0.389795i	−0.731286	+	0.682071i	$0.761079\pi$
$212$	−1.70328	+	2.95018i	−0.116982	+	0.202619i
$213$		−	13.7237i		−	0.940329i
$214$	13.1212	−	7.57550i	0.896944	−	0.517851i
$215$			3.09411i			0.211016i
$216$			14.8142i			1.00798i
$217$	−0.128123	−	5.49937i	−0.00869756	−	0.373321i
$218$	4.31491			0.292242
$219$		−	5.49426i		−	0.371268i
$220$	0.395507	+	0.685038i	0.0266651	+	0.0461853i
$221$	−2.68400	+	2.55994i	−0.180545	+	0.172200i
$222$	4.19536	−	7.26659i	0.281574	−	0.487701i
$223$	3.87804	−	2.23898i	0.259692	−	0.149934i	−0.364502	−	0.931203i	$-0.618761\pi$
$223$	3.87804	−	2.23898i	0.259692	−	0.149934i	0.624194	+	0.781269i	$0.285427\pi$
$224$	2.89426	+	5.01300i	0.193381	+	0.334945i
$225$	−4.37162			−0.291441
$226$	0.580588	+	0.335203i	0.0386202	+	0.0222974i
$227$	7.48328	+	4.32047i	0.496683	+	0.286760i	0.727343	−	0.686275i	$-0.240755\pi$
$227$	7.48328	+	4.32047i	0.496683	+	0.286760i	−0.230660	+	0.973034i	$0.574088\pi$
$228$	−0.544198	−	0.314193i	−0.0360404	−	0.0208079i
$229$	−8.33620	+	4.81291i	−0.550872	+	0.318046i	−0.749474	−	0.662034i	$-0.769693\pi$
$229$	−8.33620	+	4.81291i	−0.550872	+	0.318046i	0.198602	+	0.980080i	$0.436360\pi$
$230$	0.698567	−	1.20995i	0.0460622	−	0.0797820i
$231$	0.980191	+	1.69774i	0.0644918	+	0.111703i
$232$		−	8.47192i		−	0.556209i
$233$	20.2755			1.32829			0.664147	−	0.747602i	$-0.268795\pi$
$233$	20.2755			1.32829			0.664147	+	0.747602i	$0.268795\pi$
$234$	−0.706235	+	2.40653i	−0.0461680	+	0.157320i
$235$	2.04584	−	3.54350i	0.133456	−	0.231152i
$236$	15.7013	−	9.06515i	1.02207	−	0.590091i
$237$	10.2799	−	17.8054i	0.667753	−	1.15658i
$238$	0.390729	−	0.676762i	0.0253272	−	0.0438680i
$239$	−6.52519	−	3.76732i	−0.422079	−	0.243688i	0.273887	−	0.961762i	$-0.411690\pi$
$239$	−6.52519	−	3.76732i	−0.422079	−	0.243688i	−0.695966	+	0.718074i	$0.745024\pi$
$240$		−	0.475735i		−	0.0307086i
$241$	−11.1593	+	6.44284i	−0.718835	+	0.415020i	−0.814324	−	0.580411i	$-0.802892\pi$
$241$	−11.1593	+	6.44284i	−0.718835	+	0.415020i	0.0954885	+	0.995431i	$0.469559\pi$
$242$	−6.07345	+	3.50651i	−0.390416	+	0.225407i
$243$	−4.52099	+	7.83059i	−0.290022	+	0.502333i
$244$	−3.59445			−0.230111
$245$	−2.13685	+	1.23371i	−0.136518	+	0.0788188i
$246$	−1.80064			−0.114805
$247$	−0.766807	−	0.803966i	−0.0487908	−	0.0511552i
$248$	12.8045	+	7.00020i	0.813086	+	0.444513i
$249$		−	10.7360i		−	0.680364i
$250$	−3.09657			−0.195844
$251$	−7.60170	−	13.1665i	−0.479815	−	0.831064i	0.519917	−	0.854217i	$-0.325963\pi$
$251$	−7.60170	−	13.1665i	−0.479815	−	0.831064i	−0.999732	+	0.0231530i	$0.992630\pi$
$252$			1.25921i			0.0793226i
$253$	5.26630	+	3.04050i	0.331090	+	0.191155i
$254$	−4.30776	+	2.48709i	−0.270293	+	0.156054i
$255$	−0.528219	+	0.304967i	−0.0330783	+	0.0190978i
$256$	−13.0954			−0.818465
$257$	13.1268	−	22.7362i	0.818825	−	1.41825i	−0.0877232	−	0.996145i	$-0.527959\pi$
$257$	13.1268	−	22.7362i	0.818825	−	1.41825i	0.906548	−	0.422102i	$-0.138708\pi$
$258$	−7.28096	−	4.20366i	−0.453293	−	0.261709i
$259$	3.72418	−	6.45047i	0.231409	−	0.400813i
$260$	0.585880	−	1.99641i	0.0363347	−	0.123812i
$261$	1.46211	−	2.53245i	0.0905025	−	0.156755i
$262$	−0.502318	+	0.290013i	−0.0310333	+	0.0179171i
$263$	−29.7632			−1.83528			−0.917639	−	0.397416i	$-0.869907\pi$
$263$	−29.7632			−1.83528			−0.917639	+	0.397416i	$0.869907\pi$
$264$	−5.20064			−0.320078
$265$	−0.857750	+	0.495222i	−0.0526912	+	0.0304213i
$266$	0.202718	+	0.117039i	0.0124294	+	0.00717613i
$267$	13.3796	−	7.72469i	0.818815	−	0.472743i
$268$	11.1351	+	6.42886i	0.680185	+	0.392705i
$269$	0.700445	−	1.21321i	0.0427069	−	0.0739705i	−0.843882	−	0.536529i	$-0.819735\pi$
$269$	0.700445	−	1.21321i	0.0427069	−	0.0739705i	0.886589	+	0.462559i	$0.153068\pi$
$270$	−0.890040	+	1.54159i	−0.0541661	+	0.0938185i
$271$			12.0091i			0.729503i	0.931105	+	0.364751i	$0.118846\pi$
$271$			12.0091i			0.729503i	−0.931105	+	0.364751i	$0.881154\pi$
$272$	−0.412702	−	0.714821i	−0.0250237	−	0.0433424i
$273$	1.45200	−	4.94774i	0.0878788	−	0.299451i
$274$	−3.86784	+	6.69930i	−0.233665	+	0.404719i
$275$		−	6.62389i		−	0.399435i
$276$	−4.52332	−	7.83462i	−0.272272	−	0.471589i
$277$	11.4159			0.685915			0.342957	−	0.939351i	$-0.388571\pi$
$277$	11.4159			0.685915			0.342957	+	0.939351i	$0.388571\pi$
$278$			5.97352i			0.358268i
$279$	2.61944	+	4.30237i	0.156822	+	0.257576i
$280$			1.06067i			0.0633873i
$281$			3.08535i			0.184057i	0.995756	+	0.0920284i	$0.0293351\pi$
$281$			3.08535i			0.184057i	−0.995756	+	0.0920284i	$0.970665\pi$
$282$	5.55897	+	9.62842i	0.331032	+	0.573364i
$283$	−22.2452			−1.32234			−0.661170	−	0.750236i	$-0.729940\pi$
$283$	−22.2452			−1.32234			−0.661170	+	0.750236i	$0.729940\pi$
$284$	11.5672	+	6.67832i	0.686387	+	0.396285i
$285$	−0.0913501	−	0.158223i	−0.00541111	−	0.00937232i
$286$	−3.64638	−	1.07009i	−0.215615	−	0.0632757i
$287$	−1.59841			−0.0943511
$288$	−4.59033	−	2.65023i	−0.270488	−	0.156166i
$289$	7.97088	−	13.8060i	0.468875	−	0.812116i
$290$	0.508996	−	0.881608i	0.0298893	−	0.0517698i
$291$	−14.8160	+	8.55400i	−0.868527	+	0.501444i
$292$	4.63092	+	2.67366i	0.271004	+	0.156464i
$293$	−19.0010	+	10.9703i	−1.11005	+	0.640889i	−0.938843	−	0.344345i	$-0.888101\pi$
$293$	−19.0010	+	10.9703i	−1.11005	+	0.640889i	−0.171210	+	0.985235i	$0.554768\pi$
$294$		−	6.70448i		−	0.391013i
$295$	5.27130			0.306907
$296$	9.87978	+	17.1123i	0.574251	+	0.994632i
$297$	−6.70976	−	3.87388i	−0.389340	−	0.224785i
$298$	−6.62438	−	11.4738i	−0.383740	−	0.664657i
$299$	−3.77323	−	15.5435i	−0.218211	−	0.898901i
$300$	−4.92714	+	8.53405i	−0.284468	+	0.492714i
$301$	−6.46323	−	3.73155i	−0.372535	−	0.215083i
$302$	1.73565			0.0998757
$303$	3.86649	+	6.69696i	0.222124	+	0.384730i
$304$	0.214118	−	0.123621i	0.0122805	−	0.00709015i
$305$	−0.905057	−	0.522535i	−0.0518234	−	0.0299203i
$306$			0.715568i			0.0409063i
$307$	−16.5909	+	9.57878i	−0.946895	+	0.546690i	−0.892115	−	0.451809i	$-0.850779\pi$
$307$	−16.5909	+	9.57878i	−0.946895	+	0.546690i	−0.0547797	+	0.998498i	$0.517446\pi$
$308$	−1.90796			−0.108716
$309$	16.3338			0.929199
$310$	0.911890	+	1.49776i	0.0517919	+	0.0850669i
$311$	−14.8758			−0.843530			−0.421765	−	0.906705i	$-0.638589\pi$
$311$	−14.8758			−0.843530			−0.421765	+	0.906705i	$0.638589\pi$
$312$	9.44124	+	9.89876i	0.534505	+	0.560407i
$313$	−11.1105	−	19.2439i	−0.628000	−	1.08773i	−0.987952	−	0.154758i	$-0.950540\pi$
$313$	−11.1105	−	19.2439i	−0.628000	−	1.08773i	0.359952	−	0.932971i	$-0.382793\pi$
$314$		−	9.51628i		−	0.537035i
$315$	−0.183055	+	0.317060i	−0.0103140	+	0.0178643i
$316$	10.0050	+	17.3292i	0.562826	+	0.974843i
$317$	12.6650	−	7.31214i	0.711337	−	0.410691i	−0.100219	−	0.994965i	$-0.531954\pi$
$317$	12.6650	−	7.31214i	0.711337	−	0.410691i	0.811556	+	0.584275i	$0.198621\pi$
$318$		−	2.69124i		−	0.150917i
$319$	3.83718	+	2.21540i	0.214841	+	0.124038i
$320$	−1.02876	−	0.593952i	−0.0575092	−	0.0332029i
$321$	14.2618	−	24.7021i	0.796014	−	1.37874i
$322$	1.68497	+	2.91845i	0.0938997	+	0.162639i
$323$	−0.274518	−	0.158493i	−0.0152746	−	0.00881880i
$324$	3.85134	+	6.67072i	0.213964	+	0.370596i
$325$	−12.6077	+	12.0250i	−0.699351	+	0.667026i
$326$	−16.4102			−0.908877
$327$	7.03499	−	4.06166i	0.389036	−	0.224610i
$328$	2.12019	−	3.67228i	0.117068	−	0.202767i
$329$	4.93464	+	8.54705i	0.272056	+	0.471214i
$330$	−0.541191	−	0.312457i	−0.0297916	−	0.0172002i
$331$	20.5644	+	11.8728i	1.13032	+	0.652590i	0.944015	−	0.329902i	$-0.107016\pi$
$331$	20.5644	+	11.8728i	1.13032	+	0.652590i	0.186305	+	0.982492i	$0.440349\pi$
$332$	9.04897	+	5.22442i	0.496627	+	0.286728i
$333$			6.82035i			0.373753i
$334$	6.67265	+	11.5574i	0.365111	+	0.632391i
$335$	1.86916	+	3.23749i	0.102123	+	0.176883i
$336$	0.993755	+	0.573745i	0.0542138	+	0.0313004i
$337$	−0.0890634			−0.00485159			−0.00242580	−	0.999997i	$-0.500772\pi$
$337$	−0.0890634			−0.00485159			−0.00242580	+	0.999997i	$0.500772\pi$
$338$	4.58285	+	8.88305i	0.249274	+	0.483174i
$339$	1.26212			0.0685488
$340$		−	0.593623i		−	0.0321937i
$341$	−6.51896	+	3.96899i	−0.353021	+	0.214933i
$342$	−0.214342			−0.0115903
$343$		−	12.8674i		−	0.694774i
$344$	17.1461	−	9.89933i	0.924458	−	0.533736i
$345$		−	2.63027i		−	0.141609i
$346$	9.67621	+	5.58656i	0.520196	+	0.300335i
$347$	6.69253	+	11.5918i	0.359274	+	0.622281i	0.987840	−	0.155476i	$-0.0496910\pi$
$347$	6.69253	+	11.5918i	0.359274	+	0.622281i	−0.628566	+	0.777757i	$0.716358\pi$
$348$	−3.29582	−	5.70853i	−0.176675	−	0.306009i
$349$		−	6.57832i		−	0.352130i	−0.984379	−	0.176065i	$-0.943663\pi$
$349$		−	6.57832i		−	0.352130i	0.984379	−	0.176065i	$-0.0563368\pi$
$350$	1.83540	−	3.17900i	0.0981061	−	0.169925i
$351$	4.80745	+	19.8038i	0.256602	+	1.05705i
$352$	4.01563	−	6.95527i	0.214034	−	0.370717i
$353$	10.3118	−	5.95351i	0.548841	−	0.316873i	−0.199813	−	0.979834i	$-0.564034\pi$
$353$	10.3118	−	5.95351i	0.548841	−	0.316873i	0.748654	+	0.662961i	$0.230700\pi$
$354$	−7.16161	+	12.4043i	−0.380635	+	0.659280i
$355$	1.94169	+	3.36311i	0.103054	+	0.178495i
$356$			15.0362i			0.796918i
$357$		−	1.47118i		−	0.0778633i
$358$	−1.72914	+	0.998320i	−0.0913879	+	0.0527628i
$359$	5.29131	+	3.05494i	0.279265	+	0.161234i	0.633091	−	0.774078i	$-0.281786\pi$
$359$	5.29131	+	3.05494i	0.279265	+	0.161234i	−0.353826	+	0.935311i	$0.615119\pi$
$360$	−0.485621	−	0.841119i	−0.0255944	−	0.0443309i
$361$	−9.45252	+	16.3723i	−0.497501	+	0.861698i
$362$	2.48536	+	1.43492i	0.130628	+	0.0754180i
$363$	−6.60141	+	11.4340i	−0.346484	+	0.600128i
$364$	3.46370	+	3.63155i	0.181547	+	0.190345i
$365$	0.777356	+	1.34642i	0.0406887	+	0.0704748i
$366$	2.45923	−	1.41984i	0.128546	−	0.0742160i
$367$	3.39668	−	5.88322i	0.177305	−	0.307102i	−0.763651	−	0.645629i	$-0.776595\pi$
$367$	3.39668	−	5.88322i	0.177305	−	0.307102i	0.940957	+	0.338527i	$0.109929\pi$
$368$	3.55946			0.185549
$369$	1.26755	−	0.731819i	0.0659859	−	0.0380970i
$370$			2.37433i			0.123435i
$371$		−	2.38899i		−	0.124030i
$372$	11.3512	−	0.264457i	0.588531	−	0.0137115i
$373$	−15.9272			−0.824677			−0.412338	−	0.911031i	$-0.635288\pi$
$373$	−15.9272			−0.824677			−0.412338	+	0.911031i	$0.635288\pi$
$374$	−1.08423			−0.0560642
$375$	−5.04863	+	2.91483i	−0.260710	+	0.150521i
$376$	−26.1820			−1.35023
$377$	−2.74928	−	11.3254i	−0.141595	−	0.583288i
$378$	−2.14681	−	3.71838i	−0.110420	−	0.191253i
$379$	12.9183	−	7.45839i	0.663569	−	0.383112i	−0.130067	−	0.991505i	$-0.541519\pi$
$379$	12.9183	−	7.45839i	0.663569	−	0.383112i	0.793635	+	0.608394i	$0.208186\pi$
$380$	0.177814			0.00912168
$381$	−4.68223	+	8.10986i	−0.239878	+	0.415481i
$382$	−4.22530	−	2.43948i	−0.216185	−	0.124815i
$383$	10.0296	+	5.79062i	0.512491	+	0.295887i	0.733857	−	0.679304i	$-0.237718\pi$
$383$	10.0296	+	5.79062i	0.512491	+	0.295887i	−0.221366	+	0.975191i	$0.571052\pi$
$384$	−11.8940	+	6.86703i	−0.606965	+	0.350431i
$385$	−0.480410	−	0.277365i	−0.0244839	−	0.0141358i
$386$	8.78328	+	15.2131i	0.447057	+	0.774326i
$387$	6.83384			0.347384
$388$		−	16.6505i		−	0.845300i
$389$	6.35730	+	11.0112i	0.322328	+	0.558288i	0.980968	−	0.194170i	$-0.0622014\pi$
$389$	6.35730	+	11.0112i	0.322328	+	0.558288i	−0.658640	+	0.752458i	$0.728868\pi$
$390$	0.387755	+	1.59732i	0.0196348	+	0.0808835i
$391$	−2.28177	−	3.95214i	−0.115394	−	0.199868i
$392$	13.6733	+	7.89429i	0.690607	+	0.398722i
$393$	−0.545984	+	0.945672i	−0.0275412	+	0.0477028i
$394$	−1.39363	+	2.41383i	−0.0702099	+	0.121607i
$395$			5.81782i			0.292727i
$396$	1.51302	−	0.873542i	0.0760321	−	0.0438971i
$397$	32.7281	−	18.8956i	1.64258	−	0.948342i	0.662663	−	0.748918i	$-0.269426\pi$
$397$	32.7281	−	18.8956i	1.64258	−	0.948342i	0.979913	−	0.199424i	$-0.0639071\pi$
$398$	2.08028	+	1.20105i	0.104275	+	0.0602031i
$399$	0.440680			0.0220616
$400$	−1.93861	−	3.35778i	−0.0969307	−	0.167889i
$401$			11.9218i			0.595347i	0.954668	+	0.297673i	$0.0962106\pi$
$401$			11.9218i			0.595347i	−0.954668	+	0.297673i	$0.903789\pi$
$402$	−10.1578			−0.506625
$403$	19.3890	+	5.20272i	0.965833	+	0.259166i
$404$	−7.52618			−0.374441
$405$			2.23952i			0.111283i
$406$	1.22772	+	2.12647i	0.0609306	+	0.105535i
$407$	−10.3342			−0.512248
$408$	3.37998	+	1.95143i	0.167334	+	0.0966103i
$409$	14.5460	−	8.39813i	0.719253	−	0.415261i	−0.0952249	−	0.995456i	$-0.530357\pi$
$409$	14.5460	−	8.39813i	0.719253	−	0.415261i	0.814478	+	0.580195i	$0.197024\pi$
$410$	0.441264	−	0.254764i	0.0217925	−	0.0125819i
$411$			14.5633i			0.718356i
$412$	−7.94851	+	13.7672i	−0.391595	+	0.678262i
$413$	−6.35729	+	11.0111i	−0.312822	+	0.541823i
$414$	−2.67238	−	1.54290i	−0.131340	−	0.0758294i
$415$	1.51898	+	2.63095i	0.0745637	+	0.129148i
$416$	−20.5284	+	4.98335i	−1.00649	+	0.244329i
$417$	5.62293	+	9.73919i	0.275356	+	0.476930i
$418$		−	0.324771i		−	0.0158851i
$419$	8.09045			0.395244			0.197622	−	0.980278i	$-0.436678\pi$
$419$	8.09045			0.395244			0.197622	+	0.980278i	$0.436678\pi$
$420$	0.412632	+	0.714700i	0.0201344	+	0.0348738i
$421$	−10.4090	−	6.00965i	−0.507305	−	0.292892i	0.224420	−	0.974492i	$-0.427951\pi$
$421$	−10.4090	−	6.00965i	−0.507305	−	0.292892i	−0.731725	+	0.681600i	$0.761284\pi$
$422$	4.35352	−	2.51351i	0.211926	−	0.122356i
$423$	−7.82640	−	4.51857i	−0.380533	−	0.219701i
$424$	5.48860	+	3.16884i	0.266550	+	0.153893i
$425$	−2.48548	+	4.30497i	−0.120563	+	0.208822i
$426$	−10.5520			−0.511244
$427$	2.18303	−	1.26037i	0.105644	−	0.0609938i
$428$	13.8804	+	24.0415i	0.670933	+	1.16209i
$429$	−6.95231	+	1.68770i	−0.335661	+	0.0814828i
$430$	2.37902			0.114727
$431$	−15.2654	+	8.81348i	−0.735309	+	0.424531i	−0.820361	−	0.571846i	$-0.806228\pi$
$431$	−15.2654	+	8.81348i	−0.735309	+	0.424531i	0.0850525	+	0.996376i	$0.472894\pi$
$432$	−4.53508			−0.218194
$433$	26.4596			1.27157			0.635783	−	0.771867i	$-0.280677\pi$
$433$	26.4596			1.27157			0.635783	+	0.771867i	$0.280677\pi$
$434$	−4.22840	+	0.0985123i	−0.202970	+	0.00472874i
$435$		−	1.91649i		−	0.0918887i
$436$			7.90607i			0.378632i
$437$	1.18383	−	0.683483i	0.0566301	−	0.0326954i
$438$	−4.22447			−0.201853
$439$	4.38412	−	7.59352i	0.209243	−	0.362419i	−0.742234	−	0.670141i	$-0.766233\pi$
$439$	4.38412	−	7.59352i	0.209243	−	0.362419i	0.951476	+	0.307722i	$0.0995668\pi$
$440$	1.27447	−	0.735813i	0.0607578	−	0.0350785i
$441$	2.72485	+	4.71957i	0.129755	+	0.224742i
$442$	1.96831	+	2.06369i	0.0936229	+	0.0981599i
$443$	−4.33949	+	7.51622i	−0.206175	+	0.357106i	−0.950507	−	0.310704i	$-0.899435\pi$
$443$	−4.33949	+	7.51622i	−0.206175	+	0.357106i	0.744331	+	0.667811i	$0.232768\pi$
$444$	13.3143	+	7.68704i	0.631871	+	0.364811i
$445$	−2.18586	+	3.78601i	−0.103619	+	0.179474i
$446$	−1.72153	−	2.98178i	−0.0815168	−	0.141191i
$447$	−21.6007	−	12.4712i	−1.02168	−	0.589866i
$448$	2.48140	−	1.43263i	0.117235	−	0.0676856i
$449$		−	22.5287i		−	1.06320i	−0.846997	−	0.531598i	$-0.821592\pi$
$449$		−	22.5287i		−	1.06320i	0.846997	−	0.531598i	$-0.178408\pi$
$450$			3.36129i			0.158453i
$451$	1.10885	+	1.92059i	0.0522139	+	0.0904371i
$452$	−0.614182	+	1.06379i	−0.0288887	+	0.0500367i
$453$	2.82980	−	1.63379i	0.132956	−	0.0767619i
$454$	3.32196	−	5.75381i	0.155907	−	0.270039i
$455$	0.344206	+	1.41793i	0.0161366	+	0.0664734i
$456$	−0.584534	+	1.01244i	−0.0273733	+	0.0474120i
$457$		−	31.8776i		−	1.49117i	−0.666410	−	0.745585i	$-0.732170\pi$
$457$		−	31.8776i		−	1.49117i	0.666410	−	0.745585i	$-0.267830\pi$
$458$	3.70059	+	6.40961i	0.172917	+	0.299501i
$459$	2.90719	+	5.03540i	0.135696	+	0.235032i
$460$	2.21696	+	1.27996i	0.103366	+	0.0596786i
$461$			7.24046i			0.337222i	0.985683	+	0.168611i	$0.0539282\pi$
$461$			7.24046i			0.337222i	−0.985683	+	0.168611i	$0.946072\pi$
$462$	1.30537	−	0.753657i	0.0607314	−	0.0350633i
$463$			12.0837i			0.561576i	0.959770	+	0.280788i	$0.0905958\pi$
$463$			12.0837i			0.561576i	−0.959770	+	0.280788i	$0.909404\pi$
$464$	2.59352			0.120401
$465$	2.89659	+	1.58356i	0.134326	+	0.0734360i
$466$		−	15.5896i		−	0.722175i
$467$	10.6866			0.494518			0.247259	−	0.968949i	$-0.420470\pi$
$467$	10.6866			0.494518			0.247259	+	0.968949i	$0.420470\pi$
$468$	−4.40941	−	1.29401i	−0.203825	−	0.0598157i
$469$	−9.01698			−0.416365
$470$	−2.72456	−	1.57302i	−0.125674	−	0.0725582i
$471$	−8.95775	−	15.5153i	−0.412751	−	0.714906i
$472$	−16.8651	−	29.2112i	−0.776278	−	1.34455i
$473$			10.3547i			0.476107i
$474$	−13.6903	−	7.90412i	−0.628818	−	0.363048i
$475$	−1.28951	−	0.744501i	−0.0591669	−	0.0341601i
$476$	1.24001	+	0.715920i	0.0568358	+	0.0328142i
$477$	1.09378	+	1.89448i	0.0500807	+	0.0867424i
$478$	−2.89665	+	5.01714i	−0.132490	+	0.229479i
$479$	−32.0732	+	18.5175i	−1.46546	+	0.846086i	−0.999255	−	0.0385892i	$-0.987714\pi$
$479$	−32.0732	+	18.5175i	−1.46546	+	0.846086i	−0.466208	+	0.884675i	$0.654380\pi$
$480$	−3.47383			−0.158558
$481$	18.7607	+	19.6698i	0.855414	+	0.896868i
$482$	4.95382	+	8.58028i	0.225641	+	0.390821i
$483$	5.49433	+	3.17215i	0.250001	+	0.144338i
$484$	−6.42487	−	11.1282i	−0.292039	−	0.505827i
$485$	2.42052	−	4.19247i	0.109910	−	0.190370i
$486$	6.02085	+	3.47614i	0.273111	+	0.157681i
$487$	−26.0934	−	15.0650i	−1.18240	−	0.682661i	−0.225834	−	0.974166i	$-0.572511\pi$
$487$	−26.0934	−	15.0650i	−1.18240	−	0.682661i	−0.956569	+	0.291505i	$0.905844\pi$
$488$			6.68723i			0.302716i
$489$	−26.7551	+	15.4471i	−1.20991	+	0.698540i
$490$	0.948584	+	1.64300i	0.0428527	+	0.0742230i
$491$	−0.301927	+	0.522953i	−0.0136258	+	0.0236005i	−0.872758	−	0.488153i	$-0.837671\pi$
$491$	−0.301927	+	0.522953i	−0.0136258	+	0.0236005i	0.859132	+	0.511754i	$0.171004\pi$
$492$		−	3.29926i		−	0.148742i
$493$	−1.66256	−	2.87964i	−0.0748781	−	0.129693i
$494$	−0.618160	+	0.589589i	−0.0278124	+	0.0265269i
$495$	0.507957			0.0228310
$496$	−2.14298	+	3.91986i	−0.0962228	+	0.176007i
$497$	−9.36687			−0.420161
$498$	−8.25476			−0.369904
$499$	31.7952	−	18.3570i	1.42335	−	0.821770i	0.426765	−	0.904363i	$-0.359653\pi$
$499$	31.7952	−	18.3570i	1.42335	−	0.821770i	0.996583	+	0.0825924i	$0.0263200\pi$
$500$		−	5.67375i		−	0.253738i
$501$	21.7581	+	12.5620i	0.972079	+	0.561230i
$502$	−10.1236	+	5.84486i	−0.451838	+	0.260869i
$503$	−11.2292	−	19.4496i	−0.500686	−	0.867213i	−1.00000		0.000792110i	$-0.999748\pi$
$503$	−11.2292	−	19.4496i	−0.500686	−	0.867213i	0.499314	−	0.866421i	$-0.333585\pi$
$504$	2.34267			0.104351
$505$	−1.89504	−	1.09410i	−0.0843281	−	0.0486869i
$506$	2.33781	−	4.04920i	0.103928	−	0.180009i
$507$	15.8335	+	10.1690i	0.703192	+	0.451621i
$508$	−4.55701	−	7.89297i	−0.202185	−	0.350194i
$509$	−16.6693	−	9.62404i	−0.738855	−	0.426578i	0.0827980	−	0.996566i	$-0.473614\pi$
$509$	−16.6693	−	9.62404i	−0.738855	−	0.426578i	−0.821653	+	0.569988i	$0.806948\pi$
$510$	0.234486	+	0.406141i	0.0103832	+	0.0179842i
$511$	−3.75002			−0.165891
$512$		−	8.90703i		−	0.393639i
$513$	−1.50831	+	0.870821i	−0.0665934	+	0.0384477i
$514$	−17.4816	−	10.0930i	−0.771081	−	0.445184i
$515$	−4.00276	+	2.31099i	−0.176383	+	0.101835i
$516$	7.70225	−	13.3407i	0.339072	−	0.587291i
$517$	6.84655	−	11.8586i	0.301111	−	0.521540i
$518$	−4.95969	−	2.86348i	−0.217916	−	0.125814i
$519$	21.0347			0.923321
$520$	−3.71419	−	1.08999i	−0.162878	−	0.0477992i
$521$	−12.2705	−	21.2532i	−0.537582	−	0.931120i	−0.999034	−	0.0439543i	$-0.986004\pi$
$521$	−12.2705	−	21.2532i	−0.537582	−	0.931120i	0.461451	−	0.887166i	$-0.347329\pi$
$522$	−1.94717	−	1.12420i	−0.0852255	−	0.0492050i
$523$	6.53866			0.285916			0.142958	−	0.989729i	$-0.454339\pi$
$523$	6.53866			0.285916			0.142958	+	0.989729i	$0.454339\pi$
$524$	−0.531382	−	0.920381i	−0.0232135	−	0.0402070i
$525$		−	6.91070i		−	0.301607i
$526$			22.8846i			0.997815i
$527$	5.72605	−	0.133404i	0.249431	−	0.00581118i
$528$		−	1.59208i		−	0.0692864i
$529$	−3.32029			−0.144360
$530$	0.380771	+	0.659514i	0.0165396	+	0.0286475i
$531$		−	11.6425i		−	0.505243i
$532$	−0.214447	+	0.371434i	−0.00929747	+	0.0161037i
$533$	1.64259	−	5.59720i	0.0711484	−	0.242442i
$534$	−5.93942	−	10.2874i	−0.257024	−	0.445179i
$535$			8.07131i			0.348953i
$536$	11.9605	−	20.7161i	0.516613	−	0.894800i
$537$	−1.87945	+	3.25531i	−0.0811044	+	0.140477i
$538$	−0.932821	−	0.538564i	−0.0402168	−	0.0232192i
$539$	−7.15111	+	4.12870i	−0.308020	+	0.177835i
$540$	−2.82462	−	1.63079i	−0.121552	−	0.0701782i
$541$	8.02611	−	4.63387i	0.345069	−	0.199226i	−0.317442	−	0.948278i	$-0.602824\pi$
$541$	8.02611	−	4.63387i	0.345069	−	0.199226i	0.662511	+	0.749052i	$0.269491\pi$
$542$	9.23368			0.396621
$543$	5.40282			0.231857
$544$	−5.21964	+	3.01356i	−0.223790	+	0.129205i
$545$	−1.14933	+	1.99069i	−0.0492318	+	0.0852719i
$546$	−3.80426	−	1.11642i	−0.162807	−	0.0477785i
$547$	0.907659	−	1.57211i	0.0388087	−	0.0672186i	−0.845969	−	0.533233i	$-0.820977\pi$
$547$	0.907659	−	1.57211i	0.0388087	−	0.0672186i	0.884777	+	0.466014i	$0.154310\pi$
$548$	−12.2749	−	7.08693i	−0.524358	−	0.302738i
$549$	−1.15410	+	1.99897i	−0.0492560	+	0.0853138i
$550$	−5.09303			−0.217167
$551$	0.862571	−	0.498005i	0.0367467	−	0.0212157i
$552$	−14.5758	+	8.41532i	−0.620386	+	0.358180i
$553$	−12.1528	−	7.01640i	−0.516788	−	0.298368i
$554$		−	8.77755i		−	0.372922i
$555$	2.23497	+	3.87109i	0.0948693	+	0.164318i
$556$	−10.9451			−0.464176
$557$			21.3312i			0.903833i	0.892060	+	0.451917i	$0.149260\pi$
$557$			21.3312i			0.903833i	−0.892060	+	0.451917i	$0.850740\pi$
$558$	3.30804	−	2.01406i	0.140041	−	0.0852619i
$559$	19.7088	−	18.7978i	0.833592	−	0.795063i
$560$	−0.324705			−0.0137213
$561$	−1.76772	+	1.02059i	−0.0746333	+	0.0430896i
$562$	2.37229			0.100069
$563$	7.06219	−	12.2321i	0.297636	−	0.515520i	−0.677959	−	0.735100i	$-0.737135\pi$
$563$	7.06219	−	12.2321i	0.297636	−	0.515520i	0.975595	+	0.219580i	$0.0704685\pi$
$564$	−17.6419	+	10.1855i	−0.742857	+	0.428889i
$565$	−0.309293	+	0.178571i	−0.0130121	+	0.00751252i
$566$			17.1041i			0.718938i
$567$	−4.67811	−	2.70091i	−0.196462	−	0.113427i
$568$	12.4246	−	21.5200i	0.521323	−	0.902958i
$569$	21.1174	−	36.5764i	0.885288	−	1.53336i	0.0399054	−	0.999203i	$-0.487294\pi$
$569$	21.1174	−	36.5764i	0.885288	−	1.53336i	0.845383	−	0.534161i	$-0.179372\pi$
$570$	−0.121656	+	0.0702380i	−0.00509560	+	0.00294195i
$571$	−12.6496	+	21.9097i	−0.529368	+	0.916893i	0.470045	+	0.882643i	$0.344238\pi$
$571$	−12.6496	+	21.9097i	−0.529368	+	0.916893i	−0.999413	+	0.0342505i	$0.989096\pi$
$572$	1.96069	−	6.68114i	0.0819806	−	0.279353i
$573$	−9.18521			−0.383718
$574$			1.22900i			0.0512974i
$575$	−10.7183	−	18.5647i	−0.446985	−	0.774200i
$576$	−1.31184	+	2.27217i	−0.0546600	+	0.0946739i
$577$	9.75219	−	5.63043i	0.405989	−	0.234398i	−0.283076	−	0.959098i	$-0.591355\pi$
$577$	9.75219	−	5.63043i	0.405989	−	0.234398i	0.689065	+	0.724700i	$0.258022\pi$
$578$	−10.6152	−	6.12872i	−0.441536	−	0.254921i
$579$	28.6404	+	16.5355i	1.19025	+	0.687194i
$580$	1.61534	+	0.932619i	0.0670735	+	0.0387249i
$581$	−7.32766			−0.304003
$582$	6.57707	+	11.3918i	0.272628	+	0.472206i
$583$	−2.87052	+	1.65730i	−0.118885	+	0.0686382i
$584$	4.97417	−	8.61551i	0.205832	−	0.356512i
$585$	−0.922144	−	0.966831i	−0.0381259	−	0.0399735i
$586$	8.43491	+	14.6097i	0.348443	+	0.603521i
$587$			1.88917i			0.0779744i	0.999240	+	0.0389872i	$0.0124132\pi$
$587$			1.88917i			0.0779744i	−0.999240	+	0.0389872i	$0.987587\pi$
$588$	12.2844			0.506601
$589$	0.0399600	+	1.71519i	0.00164652	+	0.0706730i
$590$		−	4.05304i		−	0.166861i
$591$			5.24733i			0.215846i
$592$	−5.23861	+	3.02451i	−0.215306	+	0.124307i
$593$		−	40.8014i		−	1.67551i	−0.546045	−	0.837756i	$-0.683867\pi$
$593$		−	40.8014i		−	1.67551i	0.546045	−	0.837756i	$-0.316133\pi$
$594$	−2.97858	+	5.15906i	−0.122213	+	0.211679i
$595$	0.208151	+	0.360527i	0.00853334	+	0.0147802i
$596$	21.0230	−	12.1376i	0.861136	−	0.497177i
$597$	4.52223			0.185082
$598$	−11.9512	+	2.90119i	−0.488720	+	0.118639i
$599$	18.2936	−	31.6854i	0.747455	−	1.29463i	−0.201584	−	0.979471i	$-0.564609\pi$
$599$	18.2936	−	31.6854i	0.747455	−	1.29463i	0.949039	−	0.315158i	$-0.102058\pi$
$600$	15.8770	+	9.16660i	0.648177	+	0.374225i
$601$	−1.36499	−	2.36424i	−0.0556792	−	0.0964393i	0.836842	−	0.547444i	$-0.184399\pi$
$601$	−1.36499	−	2.36424i	−0.0556792	−	0.0964393i	−0.892522	+	0.451005i	$0.851066\pi$
$602$	−2.86915	+	4.96951i	−0.116938	+	0.202542i
$603$	7.15051	−	4.12835i	0.291191	−	0.168119i
$604$			3.18019i			0.129400i
$605$		−	3.73600i		−	0.151890i
$606$	5.14921	−	2.97290i	0.209172	−	0.120766i
$607$	−8.24022	+	14.2725i	−0.334460	+	0.579302i	−0.983381	−	0.181554i	$-0.941887\pi$
$607$	−8.24022	+	14.2725i	−0.334460	+	0.579302i	0.648921	+	0.760856i	$0.275221\pi$
$608$	−0.902685	−	1.56350i	−0.0366087	−	0.0634081i
$609$	4.00333	+	2.31132i	0.162223	+	0.0936595i
$610$	−0.401771	+	0.695888i	−0.0162672	+	0.0281757i
$611$	−35.0005	+	8.49650i	−1.41597	+	0.343732i
$612$	−1.31111			−0.0529986
$613$	−10.5290	+	6.07891i	−0.425262	+	0.245525i	−0.697326	−	0.716754i	$-0.745627\pi$
$613$	−10.5290	+	6.07891i	−0.425262	+	0.245525i	0.272064	+	0.962279i	$0.412294\pi$
$614$	7.36501	+	12.7566i	0.297228	+	0.514813i
$615$	0.479622	−	0.830730i	0.0193402	−	0.0334983i
$616$			3.54962i			0.143018i
$617$	−18.7421	+	10.8208i	−0.754529	+	0.435627i	−0.827328	−	0.561719i	$-0.810140\pi$
$617$	−18.7421	+	10.8208i	−0.754529	+	0.435627i	0.0727991	+	0.997347i	$0.476807\pi$
$618$		−	12.5589i		−	0.505193i
$619$		−	14.6930i		−	0.590560i	−0.955411	−	0.295280i	$-0.904587\pi$
$619$		−	14.6930i		−	0.590560i	0.955411	−	0.295280i	$-0.0954129\pi$
$620$	−2.74429	+	1.67083i	−0.110213	+	0.0671021i
$621$	−25.0738			−1.00618
$622$			11.4378i			0.458616i
$623$	−5.27236	−	9.13200i	−0.211233	−	0.365866i
$624$	−3.03032	+	2.89026i	−0.121310	+	0.115703i
$625$	−11.2558	+	19.4955i	−0.450230	+	0.779821i
$626$	−14.7964	+	8.54270i	−0.591383	+	0.341435i
$627$	−0.305710	−	0.529505i	−0.0122089	−	0.0211464i
$628$	17.4364			0.695788
$629$	6.71637	+	3.87770i	0.267799	+	0.154614i
$630$	0.243784	+	0.140748i	0.00971257	+	0.00560755i
$631$	−10.1198	−	5.84267i	−0.402863	−	0.232593i	0.284856	−	0.958570i	$-0.408054\pi$
$631$	−10.1198	−	5.84267i	−0.402863	−	0.232593i	−0.687718	+	0.725978i	$0.741388\pi$
$632$	32.2398	−	18.6136i	1.28243	−	0.740410i
$633$	4.73197	−	8.19601i	0.188079	−	0.325762i
$634$	−5.62222	−	9.73797i	−0.223287	−	0.386744i
$635$		−	2.64986i		−	0.105157i
$636$	4.93108			0.195530
$637$	20.8406	+	6.11600i	0.825733	+	0.242325i
$638$	1.70339	−	2.95036i	0.0674380	−	0.116806i
$639$	7.42798	−	4.28854i	0.293846	−	0.169652i
$640$	1.94316	−	3.36566i	0.0768103	−	0.133039i
$641$	11.0342	−	19.1118i	0.435825	−	0.754871i	−0.561538	−	0.827451i	$-0.689790\pi$
$641$	11.0342	−	19.1118i	0.435825	−	0.754871i	0.997363	+	0.0725803i	$0.0231234\pi$
$642$	−18.9932	−	10.9657i	−0.749600	−	0.432782i
$643$			32.5200i			1.28246i	0.767347	+	0.641232i	$0.221576\pi$
$643$			32.5200i			1.28246i	−0.767347	+	0.641232i	$0.778424\pi$
$644$	−5.34740	+	3.08732i	−0.210717	+	0.121657i
$645$	3.87874	−	2.23939i	0.152725	−	0.0881760i
$646$	−0.121864	+	0.211074i	−0.00479466	+	0.00830459i
$647$	−37.5850			−1.47762			−0.738810	−	0.673914i	$-0.764612\pi$
$647$	−37.5850			−1.47762			−0.738810	+	0.673914i	$0.764612\pi$
$648$	12.4104	−	7.16516i	0.487527	−	0.281474i
$649$	17.6408			0.692462
$650$	9.24587	+	9.69393i	0.362653	+	0.380227i
$651$	−6.80122	+	4.14084i	−0.266561	+	0.162292i
$652$		−	30.0679i		−	1.17755i
$653$	8.78391			0.343741			0.171870	−	0.985120i	$-0.445019\pi$
$653$	8.78391			0.343741			0.171870	+	0.985120i	$0.445019\pi$
$654$	−3.12296	−	5.40913i	−0.122117	−	0.211514i
$655$		−	0.308994i		−	0.0120734i
$656$	1.12420	+	0.649057i	0.0438926	+	0.0253414i
$657$	2.97379	−	1.71692i	0.116019	−	0.0669833i
$658$	6.57173	−	3.79419i	0.256193	−	0.147913i
$659$	8.22232			0.320296			0.160148	−	0.987093i	$-0.448803\pi$
$659$	8.22232			0.320296			0.160148	+	0.987093i	$0.448803\pi$
$660$	0.572505	−	0.991608i	0.0222847	−	0.0385983i
$661$	9.75493	+	5.63201i	0.379423	+	0.219060i	0.677567	−	0.735461i	$-0.263034\pi$
$661$	9.75493	+	5.63201i	0.379423	+	0.219060i	−0.298144	+	0.954521i	$0.596368\pi$
$662$	9.12889	−	15.8117i	0.354804	−	0.614539i
$663$	5.15169	+	1.51185i	0.200075	+	0.0587153i
$664$	9.71968	−	16.8350i	0.377197	−	0.653324i
$665$	−0.107993	+	0.0623496i	−0.00418778	+	0.00241781i
$666$	5.24409			0.203204
$667$	14.3392			0.555216
$668$	−21.1762	+	12.2261i	−0.819332	+	0.473042i
$669$	−5.61354	−	3.24098i	−0.217032	−	0.125304i
$670$	2.48926	−	1.43718i	0.0961687	−	0.0555230i
$671$	−3.02884	−	1.74870i	−0.116927	−	0.0675079i
$672$	4.18950	−	7.25643i	0.161614	−	0.279923i
$673$	−2.96767	+	5.14015i	−0.114395	+	0.198138i	−0.917538	−	0.397649i	$-0.869826\pi$
$673$	−2.96767	+	5.14015i	−0.114395	+	0.198138i	0.803143	+	0.595787i	$0.203160\pi$
$674$			0.0684798i			0.00263774i
$675$	13.6561	+	23.6531i	0.525625	+	0.910409i
$676$	−16.2761	+	8.39701i	−0.626005	+	0.322962i
$677$	0.854614	−	1.48023i	0.0328455	−	0.0568900i	−0.849135	−	0.528175i	$-0.822876\pi$
$677$	0.854614	−	1.48023i	0.0328455	−	0.0568900i	0.881981	+	0.471285i	$0.156210\pi$
$678$		−	0.970427i		−	0.0372690i
$679$	5.83840	+	10.1124i	0.224057	+	0.388078i
$680$	−1.10439			−0.0423516
$681$		−	12.5080i		−	0.479306i
$682$	3.05171	+	5.01235i	0.116856	+	0.191933i
$683$			20.1006i			0.769128i	0.923098	+	0.384564i	$0.125648\pi$
$683$			20.1006i			0.769128i	−0.923098	+	0.384564i	$0.874352\pi$
$684$		−	0.392732i		−	0.0150165i
$685$	−2.06049	−	3.56888i	−0.0787274	−	0.136360i
$686$	−9.89358			−0.377739
$687$	12.0668	+	6.96679i	0.460379	+	0.265800i
$688$	3.03050	+	5.24897i	0.115537	+	0.200115i
$689$	8.36560	+	2.45502i	0.318704	+	0.0935288i
$690$	−2.02238			−0.0769908
$691$	−12.2320	−	7.06214i	−0.465327	−	0.268657i	0.248955	−	0.968515i	$-0.419913\pi$
$691$	−12.2320	−	7.06214i	−0.465327	−	0.268657i	−0.714281	+	0.699859i	$0.753246\pi$
$692$	−10.2361	+	17.7294i	−0.389118	+	0.673972i
$693$	−0.612605	+	1.06106i	−0.0232709	+	0.0403065i
$694$	8.91281	−	5.14581i	0.338326	−	0.195332i
$695$	−2.75590	−	1.59112i	−0.104537	−	0.0603546i
$696$	−10.6203	+	6.13165i	−0.402562	+	0.232419i
$697$		−	1.66430i		−	0.0630397i
$698$	−5.05800			−0.191448
$699$	−14.6746	−	25.4172i	−0.555046	−	0.961367i
$700$	5.82479	+	3.36294i	0.220156	+	0.127107i
$701$	−6.15837	−	10.6666i	−0.232599	−	0.402872i	0.725974	−	0.687723i	$-0.241389\pi$
$701$	−6.15837	−	10.6666i	−0.232599	−	0.402872i	−0.958572	+	0.284850i	$0.908056\pi$
$702$	15.2269	−	3.69639i	0.574703	−	0.139511i
$703$	−1.16153	+	2.01183i	−0.0438079	+	0.0758774i
$704$	−3.44280	−	1.98770i	−0.129756	−	0.0749144i
$705$	−5.92280			−0.223066
$706$	−4.57759	−	7.92861i	−0.172280	−	0.298397i
$707$	4.57090	−	2.63901i	0.171906	−	0.0992503i
$708$	−22.7280	−	13.1220i	−0.854169	−	0.493155i
$709$		−	33.6428i		−	1.26348i	−0.775180	−	0.631740i	$-0.782341\pi$
$709$		−	33.6428i		−	1.26348i	0.775180	−	0.631740i	$-0.217659\pi$
$710$	2.58586	−	1.49294i	0.0970454	−	0.0560292i
$711$	12.8496			0.481898
$712$	27.9738			1.04836
$713$	−11.8482	+	21.6723i	−0.443720	+	0.811635i
$714$	−1.13118			−0.0423332
$715$	1.46494	−	1.39723i	0.0547858	−	0.0522536i
$716$	−1.82919	−	3.16825i	−0.0683601	−	0.118403i
$717$			10.9065i			0.407313i
$718$	2.34891	−	4.06843i	0.0876605	−	0.151832i
$719$	−4.51085	−	7.81302i	−0.168226	−	0.291377i	0.769570	−	0.638562i	$-0.220471\pi$
$719$	−4.51085	−	7.81302i	−0.168226	−	0.291377i	−0.937796	+	0.347186i	$0.887137\pi$
$720$	0.257493	−	0.148664i	0.00959620	−	0.00554037i
$721$		−	11.1484i		−	0.415188i
$722$	12.5884	+	7.26794i	0.468493	+	0.270485i
$723$	16.1534	+	9.32615i	0.600750	+	0.346843i
$724$	−2.62917	+	4.55385i	−0.0977123	+	0.169243i
$725$	−7.80967	−	13.5267i	−0.290044	−	0.502371i
$726$	8.79145	+	5.07575i	0.326281	+	0.188379i
$727$	11.9416	+	20.6835i	0.442890	+	0.767109i	0.997903	−	0.0647335i	$-0.0206197\pi$
$727$	11.9416	+	20.6835i	0.442890	+	0.767109i	−0.555012	+	0.831842i	$0.687286\pi$
$728$	6.75625	−	6.44397i	0.250403	−	0.238829i
$729$	29.4910			1.09226
$730$	1.03525	−	0.597700i	0.0383162	−	0.0221219i
$731$	3.88537	−	6.72965i	0.143705	−	0.248905i
$732$	2.60152	+	4.50597i	0.0961550	+	0.166545i
$733$	42.3885	+	24.4730i	1.56566	+	0.903932i	0.996666	+	0.0815877i	$0.0259991\pi$
$733$	42.3885	+	24.4730i	1.56566	+	0.903932i	0.568990	+	0.822344i	$0.307334\pi$
$734$	−4.52354	−	2.61167i	−0.166967	−	0.0963984i
$735$	3.09313	+	1.78582i	0.114092	+	0.0658710i
$736$		−	25.9912i		−	0.958050i
$737$	6.25529	+	10.8345i	0.230417	+	0.399093i
$738$	−0.562687	−	0.974603i	−0.0207128	−	0.0358756i
$739$	−39.2840	−	22.6806i	−1.44509	−	0.834321i	−0.446903	−	0.894582i	$-0.647473\pi$
$739$	−39.2840	−	22.6806i	−1.44509	−	0.834321i	−0.998183	+	0.0602614i	$0.980807\pi$
$740$	−4.35040			−0.159924
$741$	−0.452860	+	1.54314i	−0.0166362	+	0.0566887i
$742$	−1.83687			−0.0674335
$743$			51.5272i			1.89035i	0.326564	+	0.945175i	$0.394109\pi$
$743$			51.5272i			1.89035i	−0.326564	+	0.945175i	$0.605891\pi$
$744$	−0.492004	−	21.1181i	−0.0180377	−	0.774226i
$745$	7.05793			0.258583
$746$			12.2462i			0.448365i
$747$	5.81088	−	3.35491i	0.212609	−	0.122750i
$748$		−	1.98660i		−	0.0726374i
$749$	−16.8600	−	9.73415i	−0.616052	−	0.355678i
$750$	2.24118	+	3.88183i	0.0818362	+	0.141744i
$751$	12.8428	+	22.2445i	0.468642	+	0.811712i	0.999358	−	0.0358383i	$-0.0114101\pi$
$751$	12.8428	+	22.2445i	0.468642	+	0.811712i	−0.530716	+	0.847550i	$0.678077\pi$
$752$		−	8.01513i		−	0.292282i
$753$	−11.0036	+	19.0588i	−0.400994	+	0.694542i
$754$	−8.70798	+	2.11389i	−0.317126	+	0.0769834i
$755$	−0.462312	+	0.800749i	−0.0168253	+	0.0291422i
$756$	6.81308	−	3.93353i	0.247789	−	0.143061i
$757$	−20.4731	+	35.4605i	−0.744109	+	1.28883i	0.206501	+	0.978446i	$0.433792\pi$
$757$	−20.4731	+	35.4605i	−0.744109	+	1.28883i	−0.950610	+	0.310388i	$0.899541\pi$
$758$	−5.73467	−	9.93274i	−0.208292	−	0.360773i
$759$		−	8.80239i		−	0.319506i
$760$		−	0.330811i		−	0.0119998i
$761$	−12.2274	+	7.05950i	−0.443244	+	0.255907i	−0.704973	−	0.709235i	$-0.749041\pi$
$761$	−12.2274	+	7.05950i	−0.443244	+	0.255907i	0.261729	+	0.965141i	$0.415707\pi$
$762$	6.23557	+	3.60011i	0.225891	+	0.130418i
$763$	−2.77222	−	4.80163i	−0.100361	−	0.173830i
$764$	4.46978	−	7.74189i	0.161711	−	0.280092i
$765$	−0.330129	−	0.190600i	−0.0119358	−	0.00689116i
$766$	4.45234	−	7.71168i	0.160870	−	0.278634i
$767$	−32.0251	−	33.5770i	−1.15636	−	1.21240i
$768$	9.47796	+	16.4163i	0.342007	+	0.592373i
$769$	−43.9481	+	25.3735i	−1.58481	+	0.914991i	−0.590667	+	0.806915i	$0.701135\pi$
$769$	−43.9481	+	25.3735i	−1.58481	+	0.914991i	−0.994143	+	0.108075i	$0.965531\pi$
$770$	−0.213262	+	0.369381i	−0.00768545	+	0.0133116i
$771$	−38.0026			−1.36863
$772$	−27.8745	+	16.0933i	−1.00322	+	0.579212i
$773$		−	7.79622i		−	0.280410i	−0.990122	−	0.140205i	$-0.955224\pi$
$773$		−	7.79622i		−	0.280410i	0.990122	−	0.140205i	$-0.0447762\pi$
$774$		−	5.25446i		−	0.188868i
$775$	26.8974	−	0.626649i	0.966183	−	0.0225099i
$776$	−30.9771			−1.11201
$777$	−10.7817			−0.386790
$778$	8.46635	−	4.88805i	0.303533	−	0.175245i
$779$	0.498525			0.0178615
$780$	−2.92672	+	0.710472i	−0.104793	+	0.0254390i
$781$	6.49801	+	11.2549i	0.232517	+	0.402732i
$782$	−3.03876	+	1.75443i	−0.108666	+	0.0627381i
$783$	−18.2695			−0.652898
$784$	−2.41669	+	4.18583i	−0.0863104	+	0.149494i
$785$	4.39036	+	2.53478i	0.156699	+	0.0904700i
$786$	0.727116	+	0.419801i	0.0259354	+	0.0149738i
$787$	4.99588	−	2.88437i	0.178084	−	0.102817i	−0.408308	−	0.912844i	$-0.633881\pi$
$787$	4.99588	−	2.88437i	0.178084	−	0.102817i	0.586392	+	0.810027i	$0.300548\pi$
$788$	−4.42279	−	2.55350i	−0.157555	−	0.0909647i
$789$	21.5414	+	37.3109i	0.766895	+	1.32830i
$790$	4.47326			0.159151
$791$		−	0.861438i		−	0.0306292i
$792$	−1.62516	−	2.81487i	−0.0577477	−	0.100022i
$793$	2.17012	+	8.93960i	0.0770632	+	0.317454i
$794$	−14.5286	−	25.1643i	−0.515600	−	0.893046i
$795$	1.24161	+	0.716845i	0.0440355	+	0.0254239i
$796$	−2.20064	+	3.81163i	−0.0779998	+	0.135100i
$797$	−24.9479	+	43.2110i	−0.883699	+	1.53061i	−0.0365004	+	0.999334i	$0.511621\pi$
$797$	−24.9479	+	43.2110i	−0.883699	+	1.53061i	−0.847198	+	0.531277i	$0.821712\pi$
$798$		−	0.338834i		−	0.0119946i
$799$	−8.89937	+	5.13805i	−0.314837	+	0.181771i
$800$	−24.5186	+	14.1558i	−0.866863	+	0.500483i
$801$	8.36203	+	4.82782i	0.295458	+	0.170583i
$802$	9.16654			0.323682
$803$	2.60148	+	4.50589i	0.0918041	+	0.159009i
$804$		−	18.6118i		−	0.656389i
$805$	−1.79525			−0.0632742
$806$	4.00031	−	14.9079i	0.140905	−	0.525110i
$807$	−2.02782			−0.0713826
$808$			14.0019i			0.492586i
$809$	−26.2481	−	45.4631i	−0.922835	−	1.59840i	−0.795006	−	0.606601i	$-0.792532\pi$
$809$	−26.2481	−	45.4631i	−0.922835	−	1.59840i	−0.127829	−	0.991796i	$-0.540801\pi$
$810$	1.72194			0.0605029
$811$	−10.5832	−	6.11019i	−0.371625	−	0.214558i	0.302543	−	0.953136i	$-0.402164\pi$
$811$	−10.5832	−	6.11019i	−0.371625	−	0.214558i	−0.674168	+	0.738578i	$0.735498\pi$
$812$	−3.89627	+	2.24951i	−0.136732	+	0.0789423i
$813$	15.0545	−	8.69174i	0.527986	−	0.304833i
$814$			7.94585i			0.278502i
$815$	4.37105	−	7.57089i	0.153111	−	0.265197i
$816$	−0.597395	+	1.03472i	−0.0209130	+	0.0362224i
$817$	2.01581	+	1.16383i	0.0705241	+	0.0407171i
$818$	−6.45722	−	11.1842i	−0.225772	−	0.391048i
$819$	3.13172	−	0.760236i	0.109431	−	0.0265648i
$820$	0.466796	+	0.808514i	0.0163012	+	0.0282345i
$821$			36.8424i			1.28581i	0.765946	+	0.642905i	$0.222271\pi$
$821$			36.8424i			1.28581i	−0.765946	+	0.642905i	$0.777729\pi$
$822$	11.1976			0.390560
$823$	−0.923524	−	1.59959i	−0.0321920	−	0.0557582i	0.849481	−	0.527620i	$-0.176915\pi$
$823$	−0.923524	−	1.59959i	−0.0321920	−	0.0557582i	−0.881673	+	0.471862i	$0.843582\pi$
$824$	25.6130	+	14.7876i	0.892270	+	0.515152i
$825$	−8.30364	+	4.79411i	−0.289096	+	0.166909i
$826$	8.46634	+	4.88804i	0.294582	+	0.170077i
$827$	−43.6527	−	25.2029i	−1.51795	−	0.876390i	−0.999777	−	0.0211158i	$-0.993278\pi$
$827$	−43.6527	−	25.2029i	−1.51795	−	0.876390i	−0.518175	−	0.855274i	$-0.673389\pi$
$828$	2.82701	−	4.89652i	0.0982454	−	0.170166i
$829$	34.5171			1.19883			0.599414	−	0.800439i	$-0.295400\pi$
$829$	34.5171			1.19883			0.599414	+	0.800439i	$0.295400\pi$
$830$	2.02290	−	1.16792i	0.0702160	−	0.0405392i
$831$	−8.26238	−	14.3109i	−0.286619	−	0.496438i
$832$	2.46672	+	10.1614i	0.0855181	+	0.352284i
$833$	6.19683			0.214707
$834$	7.48835	−	4.32340i	0.259300	−	0.149707i
$835$	−7.10936			−0.246030
$836$	0.595068			0.0205809
$837$	15.0958	−	27.6126i	0.521786	−	0.954430i
$838$		−	6.22065i		−	0.214889i
$839$		−	11.0906i		−	0.382891i	−0.981503	−	0.191445i	$-0.938683\pi$
$839$		−	11.0906i		−	0.382891i	0.981503	−	0.191445i	$-0.0613175\pi$
$840$	1.32965	−	0.767674i	0.0458773	−	0.0264873i
$841$	−18.5520			−0.639726
$842$	−4.62075	+	8.00337i	−0.159242	+	0.275814i
$843$	3.86777	−	2.23306i	0.133213	−	0.0769106i
$844$	4.60542	+	7.97683i	0.158525	+	0.274574i
$845$	−5.31891	−	0.251799i	−0.182976	−	0.00866214i
$846$	−3.47428	+	6.01763i	−0.119448	+	0.206890i
$847$	7.80408	+	4.50569i	0.268151	+	0.154817i
$848$	−0.970083	+	1.68023i	−0.0333128	+	0.0576994i
$849$	16.1002	+	27.8864i	0.552558	+	0.957058i
$850$	3.31004	+	1.91105i	0.113533	+	0.0655486i
$851$	−28.9635	+	16.7221i	−0.992857	+	0.573226i
$852$		−	19.3340i		−	0.662373i
$853$			41.1522i			1.40903i	0.709691	+	0.704513i	$0.248834\pi$
$853$			41.1522i			1.40903i	−0.709691	+	0.704513i	$0.751166\pi$
$854$	−0.969087	−	1.67851i	−0.0331615	−	0.0574374i
$855$	0.0570925	−	0.0988871i	0.00195252	−	0.00338187i
$856$	44.7275	−	25.8235i	1.52876	−	0.882628i
$857$	−6.27040	+	10.8607i	−0.214193	+	0.370993i	−0.953023	−	0.302899i	$-0.902045\pi$
$857$	−6.27040	+	10.8607i	−0.214193	+	0.370993i	0.738830	+	0.673892i	$0.235379\pi$
$858$	1.29765	+	5.34555i	0.0443011	+	0.182494i
$859$	−24.6274	+	42.6560i	−0.840277	+	1.45540i	0.0493832	+	0.998780i	$0.484274\pi$
$859$	−24.6274	+	42.6560i	−0.840277	+	1.45540i	−0.889660	+	0.456623i	$0.849059\pi$
$860$			4.35901i			0.148641i
$861$	1.15687	+	2.00375i	0.0394259	+	0.0682877i
$862$	6.77659	+	11.7374i	0.230811	+	0.399777i
$863$	35.8742	+	20.7120i	1.22117	+	0.705043i	0.965168	−	0.261633i	$-0.0842609\pi$
$863$	35.8742	+	20.7120i	1.22117	+	0.705043i	0.256003	+	0.966676i	$0.417594\pi$
$864$			33.1153i			1.12660i
$865$	−5.15475	+	2.97610i	−0.175267	+	0.101190i
$866$		−	20.3445i		−	0.691333i
$867$	−23.0760			−0.783704
$868$	−0.180501	−	7.74757i	−0.00612660	−	0.262970i
$869$			19.4698i			0.660467i
$870$	−1.47357			−0.0499586
$871$	9.26621	−	31.5750i	0.313973	−	1.06988i
$872$	14.7087			0.498099
$873$	−9.25976	−	5.34612i	−0.313395	−	0.180939i
$874$	−0.525522	−	0.910231i	−0.0177761	−	0.0307890i
$875$	1.98947	+	3.44586i	0.0672563	+	0.116491i
$876$		−	7.74037i		−	0.261523i
$877$	11.2905	+	6.51856i	0.381253	+	0.220116i	0.678363	−	0.734727i	$-0.262690\pi$
$877$	11.2905	+	6.51856i	0.381253	+	0.220116i	−0.297111	+	0.954843i	$0.596023\pi$
$878$	−5.83857	−	3.37090i	−0.197042	−	0.113762i
$879$	27.5044	+	15.8797i	0.927702	+	0.535609i
$880$	0.225256	+	0.390154i	0.00759337	+	0.0131521i
$881$	−19.2752	+	33.3856i	−0.649397	+	1.12479i	0.333870	+	0.942619i	$0.391645\pi$
$881$	−19.2752	+	33.3856i	−0.649397	+	1.12479i	−0.983267	+	0.182170i	$0.941688\pi$
$882$	3.62883	−	2.09510i	0.122189	−	0.0705458i
$883$	35.1481			1.18283			0.591413	−	0.806369i	$-0.298570\pi$
$883$	35.1481			1.18283			0.591413	+	0.806369i	$0.298570\pi$
$884$	−3.78124	+	3.60647i	−0.127177	+	0.121299i
$885$	−3.81516	−	6.60806i	−0.128245	−	0.222127i
$886$	5.77913	+	3.33658i	0.194154	+	0.112095i
$887$	−4.41010	−	7.63852i	−0.148077	−	0.256476i	0.782440	−	0.622726i	$-0.213975\pi$
$887$	−4.41010	−	7.63852i	−0.148077	−	0.256476i	−0.930517	+	0.366250i	$0.880642\pi$
$888$	14.3012	−	24.7704i	0.479917	−	0.831241i
$889$	5.53526	+	3.19578i	0.185647	+	0.107183i
$890$	2.91102	+	1.68068i	0.0975777	+	0.0563365i
$891$			7.49472i			0.251083i
$892$	5.46342	−	3.15431i	0.182929	−	0.105614i
$893$	−1.53906	−	2.66572i	−0.0515026	−	0.0892050i
$894$	−9.58893	+	16.6085i	−0.320702	+	0.555472i
$895$		−	1.06366i		−	0.0355542i
$896$	4.68698	+	8.11809i	0.156581	+	0.271206i
$897$	−16.7542	+	15.9798i	−0.559407	+	0.533551i
$898$	−17.3221			−0.578045
$899$	−8.63297	+	15.7911i	−0.287926	+	0.526662i
$900$	−6.15878			−0.205293
$901$	2.48747			0.0828695
$902$	1.47672	−	0.852585i	0.0491694	−	0.0283880i
$903$			10.8030i			0.359501i
$904$	1.97912	+	1.14264i	0.0658244	+	0.0380037i
$905$	−1.32401	+	0.764419i	−0.0440117	+	0.0254101i
$906$	−1.25620	−	2.17580i	−0.0417344	−	0.0722861i
$907$	34.9341			1.15997			0.579984	−	0.814628i	$-0.303059\pi$
$907$	34.9341			1.15997			0.579984	+	0.814628i	$0.303059\pi$
$908$	10.5425	+	6.08673i	0.349866	+	0.201995i
$909$	−2.41650	+	4.18550i	−0.0801503	+	0.138824i
$910$	1.09023	−	0.264656i	0.0361407	−	0.00877327i
$911$	5.96626	+	10.3339i	0.197671	+	0.342376i	0.947773	−	0.318946i	$-0.103329\pi$
$911$	5.96626	+	10.3339i	0.197671	+	0.342376i	−0.750102	+	0.661322i	$0.769996\pi$
$912$	−0.309940	−	0.178944i	−0.0102632	−	0.00592543i
$913$	5.08337	+	8.80465i	0.168235	+	0.291392i
$914$	−24.5103			−0.810729
$915$			1.51276i			0.0500104i
$916$	−11.7441	+	6.78048i	−0.388037	+	0.224033i
$917$	0.645453	+	0.372653i	0.0213147	+	0.0123061i
$918$	3.87166	−	2.23530i	0.127784	−	0.0737760i
$919$	−12.0193	+	20.8180i	−0.396480	+	0.686724i	−0.993289	−	0.115660i	$-0.963102\pi$
$919$	−12.0193	+	20.8180i	−0.396480	+	0.686724i	0.596809	+	0.802384i	$0.296435\pi$
$920$	2.38128	−	4.12451i	0.0785086	−	0.135981i
$921$	24.0157	+	13.8655i	0.791346	+	0.456884i
$922$	5.56711			0.183343
$923$	9.62576	−	32.8002i	0.316836	−	1.07963i
$924$	1.38090	+	2.39179i	0.0454284	+	0.0786843i
$925$	31.5492	+	18.2150i	1.03733	+	0.598904i
$926$	9.29100			0.305321
$927$	5.10421	+	8.84074i	0.167644	+	0.290368i
$928$		−	18.9380i		−	0.621669i
$929$		−	38.1768i		−	1.25254i	−0.779606	−	0.626270i	$-0.784581\pi$
$929$		−	38.1768i		−	1.25254i	0.779606	−	0.626270i	$-0.215419\pi$
$930$	1.21758	−	2.22716i	0.0399261	−	0.0730313i
$931$			1.85620i			0.0608346i
$932$	28.5644			0.935657
$933$	10.7665	+	18.6482i	0.352481	+	0.610514i
$934$		−	8.21681i		−	0.268862i
$935$	0.288798	−	0.500213i	0.00944470	−	0.0163587i
$936$	−2.40742	+	8.20340i	−0.0786890	+	0.268136i
$937$	−21.9297	−	37.9834i	−0.716413	−	1.24086i	−0.962412	−	0.271593i	$-0.912449\pi$
$937$	−21.9297	−	37.9834i	−0.716413	−	1.24086i	0.245999	−	0.969270i	$-0.420884\pi$
$938$			6.93305i			0.226372i
$939$	−16.0826	+	27.8559i	−0.524837	+	0.909044i
$940$	2.88220	−	4.99212i	0.0940071	−	0.162825i
$941$	43.9067	+	25.3495i	1.43132	+	0.826372i	0.997221	−	0.0744951i	$-0.0237345\pi$
$941$	43.9067	+	25.3495i	1.43132	+	0.826372i	0.434096	+	0.900867i	$0.357068\pi$
$942$	−11.9295	+	6.88751i	−0.388685	+	0.224407i
$943$	6.21553	+	3.58854i	0.202406	+	0.116859i
$944$	8.94246	−	5.16293i	0.291052	−	0.168039i
$945$	2.28731			0.0744064
$946$	7.96157			0.258853
$947$	3.65192	−	2.10844i	0.118672	−	0.0685151i	−0.439489	−	0.898248i	$-0.644841\pi$
$947$	3.65192	−	2.10844i	0.118672	−	0.0685151i	0.558161	+	0.829733i	$0.311507\pi$
$948$	14.4825	−	25.0844i	0.470369	−	0.814703i
$949$	3.85367	−	13.1316i	0.125095	−	0.426269i
$950$	−0.572438	+	0.991492i	−0.0185723	+	0.0321683i
$951$	−18.3329	−	10.5845i	−0.594484	−	0.343225i
$952$	1.33192	−	2.30695i	0.0431678	−	0.0747688i
$953$	−37.9051			−1.22787			−0.613933	−	0.789358i	$-0.710413\pi$
$953$	−37.9051			−1.22787			−0.613933	+	0.789358i	$0.710413\pi$
$954$	1.45664	−	0.840994i	0.0471606	−	0.0272282i
$955$	2.25092	−	1.29957i	0.0728381	−	0.0420531i
$956$	−9.19275	−	5.30744i	−0.297315	−	0.171655i
$957$		−	6.41367i		−	0.207325i
$958$	14.2379	+	24.6607i	0.460005	+	0.796752i
$959$	9.93997			0.320978
$960$			1.71952i			0.0554972i
$961$	−16.7334	−	26.0958i	−0.539789	−	0.841801i
$962$	15.1239	−	14.4249i	0.487615	−	0.465077i
$963$	17.8268			0.574461
$964$	−15.7214	+	9.07674i	−0.506351	+	0.292342i
$965$	−9.35813			−0.301249
$966$	2.43903	−	4.22453i	0.0784746	−	0.135922i
$967$	31.3971	−	18.1271i	1.00966	−	0.582930i	0.0985708	−	0.995130i	$-0.468573\pi$
$967$	31.3971	−	18.1271i	1.00966	−	0.582930i	0.911093	+	0.412200i	$0.135240\pi$
$968$	−20.7032	+	11.9530i	−0.665427	+	0.384185i
$969$			0.458845i			0.0147402i
$970$	−3.22354	−	1.86111i	−0.103502	−	0.0597568i
$971$	9.25546	−	16.0309i	0.297022	−	0.514457i	−0.678431	−	0.734664i	$-0.737340\pi$
$971$	9.25546	−	16.0309i	0.297022	−	0.514457i	0.975453	+	0.220207i	$0.0706732\pi$
$972$	−6.36922	+	11.0318i	−0.204293	+	0.353846i
$973$	6.64733	−	3.83784i	0.213104	−	0.123035i
$974$	−11.5833	+	20.0629i	−0.371153	+	0.642856i
$975$	24.1994	+	7.10171i	0.775001	+	0.227437i
$976$	−2.04717			−0.0655283
$977$			59.1948i			1.89381i	0.321513	+	0.946905i	$0.395808\pi$
$977$			59.1948i			1.89381i	−0.321513	+	0.946905i	$0.604192\pi$
$978$	11.8771	+	20.5717i	0.379786	+	0.657809i
$979$	−7.31512	+	12.6702i	−0.233792	+	0.404940i
$980$	−3.01041	+	1.73806i	−0.0961641	+	0.0555204i
$981$	4.39677	+	2.53848i	0.140378	+	0.0810473i
$982$	0.402092	+	0.232148i	0.0128313	+	0.00740815i
$983$	−39.6487	−	22.8912i	−1.26460	−	0.730116i	−0.290637	−	0.956833i	$-0.593867\pi$
$983$	−39.6487	−	22.8912i	−1.26460	−	0.730116i	−0.973961	+	0.226717i	$0.927201\pi$
$984$	−6.13804			−0.195674
$985$	−0.742419	−	1.28591i	−0.0236554	−	0.0409724i
$986$	−2.21412	+	1.27833i	−0.0705121	+	0.0407102i
$987$	7.14301	−	12.3720i	0.227364	−	0.393807i
$988$	−1.08029	−	1.13264i	−0.0343685	−	0.0360340i
$989$	16.7552	+	29.0208i	0.532784	+	0.922808i
$990$		−	0.390562i		−	0.0124129i
$991$	26.8013			0.851372			0.425686	−	0.904871i	$-0.360033\pi$
$991$	26.8013			0.851372			0.425686	+	0.904871i	$0.360033\pi$
$992$	28.6229	+	15.6481i	0.908779	+	0.496828i
$993$		−	34.3724i		−	1.09078i
$994$			7.20207i			0.228436i
$995$	−1.10821	+	0.639827i	−0.0351327	+	0.0202839i
$996$		−	15.1249i		−	0.479252i
$997$	−13.7240	+	23.7707i	−0.434644	+	0.752826i	−0.997267	−	0.0738882i	$-0.976459\pi$
$997$	−13.7240	+	23.7707i	−0.434644	+	0.752826i	0.562622	+	0.826714i	$0.309793\pi$
$998$	−14.1145	−	24.4469i	−0.446785	−	0.773855i
$999$	36.9022	−	21.3055i	1.16753	−	0.674077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.25.14	✓	68
13.12	even	2	inner	403.2.l.c.25.21	yes	68
31.5	even	3	inner	403.2.l.c.129.14	yes	68
403.129	even	6	inner	403.2.l.c.129.21	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.14	✓	68	1.1	even	1	trivial
403.2.l.c.25.21	yes	68	13.12	even	2	inner
403.2.l.c.129.14	yes	68	31.5	even	3	inner
403.2.l.c.129.21	yes	68	403.129	even	6	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.768888i q^{2} +(-0.723761 - 1.25359i) q^{3} +1.40881 q^{4} +(0.354729 + 0.204803i) q^{5} +(-0.963871 + 0.556491i) q^{6} +(-0.855619 + 0.493992i) q^{7} -2.62099i q^{8} +(0.452340 - 0.783476i) q^{9} +O(q^{10})\)	\(q-0.768888i q^{2} +(-0.723761 - 1.25359i) q^{3} +1.40881 q^{4} +(0.354729 + 0.204803i) q^{5} +(-0.963871 + 0.556491i) q^{6} +(-0.855619 + 0.493992i) q^{7} -2.62099i q^{8} +(0.452340 - 0.783476i) q^{9} +(0.157470 - 0.272747i) q^{10} +(1.18713 + 0.685387i) q^{11} +(-1.01964 - 1.76607i) q^{12} +(-0.850558 - 3.50379i) q^{13} +(0.379824 + 0.657875i) q^{14} -0.592913i q^{15} +0.802369 q^{16} +(-0.514354 - 0.890888i) q^{17} +(-0.602406 - 0.347799i) q^{18} +(0.266857 - 0.154070i) q^{19} +(0.499746 + 0.288528i) q^{20} +(1.23853 + 0.715064i) q^{21} +(0.526986 - 0.912767i) q^{22} +4.43618 q^{23} +(-3.28565 + 1.89697i) q^{24} +(-2.41611 - 4.18483i) q^{25} +(-2.69402 + 0.653984i) q^{26} -5.65211 q^{27} +(-1.20540 + 0.695941i) q^{28} +3.23233 q^{29} -0.455884 q^{30} +(-2.67082 + 4.88536i) q^{31} -5.85892i q^{32} -1.98423i q^{33} +(-0.684993 + 0.395481i) q^{34} -0.404683 q^{35} +(0.637262 - 1.10377i) q^{36} +(-6.52893 + 3.76948i) q^{37} +(-0.118463 - 0.205183i) q^{38} +(-3.77672 + 3.60216i) q^{39} +(0.536787 - 0.929742i) q^{40} +(1.40110 + 0.808925i) q^{41} +(0.549804 - 0.952289i) q^{42} +(3.77694 + 6.54184i) q^{43} +(1.67243 + 0.965581i) q^{44} +(0.320916 - 0.185281i) q^{45} -3.41093i q^{46} -9.98933i q^{47} +(-0.580723 - 1.00584i) q^{48} +(-3.01194 + 5.21684i) q^{49} +(-3.21767 + 1.85772i) q^{50} +(-0.744539 + 1.28958i) q^{51} +(-1.19827 - 4.93618i) q^{52} +(-1.20902 + 2.09409i) q^{53} +4.34584i q^{54} +(0.280738 + 0.486253i) q^{55} +(1.29475 + 2.24257i) q^{56} +(-0.386282 - 0.223020i) q^{57} -2.48530i q^{58} +(11.1451 - 6.43461i) q^{59} -0.835302i q^{60} -2.55141 q^{61} +(3.75629 + 2.05356i) q^{62} +0.893809i q^{63} -2.90012 q^{64} +(0.415869 - 1.41709i) q^{65} -1.52565 q^{66} +(7.90391 + 4.56333i) q^{67} +(-0.724628 - 1.25509i) q^{68} +(-3.21074 - 5.56116i) q^{69} +0.311156i q^{70} +(8.21061 + 4.74040i) q^{71} +(-2.05349 - 1.18558i) q^{72} +(3.28711 + 1.89782i) q^{73} +(2.89831 + 5.02002i) q^{74} +(-3.49737 + 6.05763i) q^{75} +(0.375951 - 0.217056i) q^{76} -1.35430 q^{77} +(2.76966 + 2.90388i) q^{78} +(7.10174 + 12.3006i) q^{79} +(0.284623 + 0.164327i) q^{80} +(2.73376 + 4.73500i) q^{81} +(0.621973 - 1.07729i) q^{82} +(6.42313 + 3.70839i) q^{83} +(1.74485 + 1.00739i) q^{84} -0.421365i q^{85} +(5.02995 - 2.90404i) q^{86} +(-2.33943 - 4.05202i) q^{87} +(1.79640 - 3.11145i) q^{88} +10.6730i q^{89} +(-0.142460 - 0.246749i) q^{90} +(2.45860 + 2.57774i) q^{91} +6.24974 q^{92} +(8.05727 - 0.187717i) q^{93} -7.68068 q^{94} +0.126216 q^{95} +(-7.34469 + 4.24046i) q^{96} -11.8188i q^{97} +(4.01117 + 2.31585i) q^{98} +(1.07397 - 0.620056i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Introduction

L-functions

Modular forms

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