LMFDB - Embedded newform 430.2.l.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(7,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("430.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.l (of order $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.1
Character	$\chi$	$=$	430.7
Dual form			430.2.l.a.123.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.695712 + 2.59643i) q^{3} -1.00000i q^{4} +(-0.0995241 - 2.23385i) q^{5} +(-1.34401 - 2.32790i) q^{6} +(0.420775 + 1.57036i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.65937 - 2.11274i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.695712 + 2.59643i) q^{3} -1.00000i q^{4} +(-0.0995241 - 2.23385i) q^{5} +(-1.34401 - 2.32790i) q^{6} +(0.420775 + 1.57036i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.65937 - 2.11274i) q^{9} +(1.64995 + 1.50920i) q^{10} -5.50736 q^{11} +(2.59643 + 0.695712i) q^{12} +(-1.36060 - 5.07782i) q^{13} +(-1.40794 - 0.812876i) q^{14} +(5.86929 + 1.29571i) q^{15} -1.00000 q^{16} +(-5.17320 + 1.38615i) q^{17} +(4.08150 - 1.09363i) q^{18} +(-2.89319 - 5.01116i) q^{19} +(-2.23385 + 0.0995241i) q^{20} -4.37006 q^{21} +(3.89429 - 3.89429i) q^{22} +(6.52040 + 1.74714i) q^{23} +(-2.32790 + 1.34401i) q^{24} +(-4.98019 + 0.444644i) q^{25} +(4.55264 + 2.62847i) q^{26} +(2.32929 - 2.32929i) q^{27} +(1.57036 - 0.420775i) q^{28} +(-0.946967 + 1.64019i) q^{29} +(-5.06642 + 3.23401i) q^{30} +(0.0569001 + 0.0985539i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.83153 - 14.2995i) q^{33} +(2.67784 - 4.63816i) q^{34} +(3.46606 - 1.09624i) q^{35} +(-2.11274 + 3.65937i) q^{36} +(4.26916 + 1.14392i) q^{37} +(5.58922 + 1.49763i) q^{38} +14.1308 q^{39} +(1.50920 - 1.64995i) q^{40} -5.59971 q^{41} +(3.09010 - 3.09010i) q^{42} +(2.67007 - 5.98922i) q^{43} +5.50736i q^{44} +(-4.35535 + 8.38476i) q^{45} +(-5.84603 + 3.37521i) q^{46} +(1.09259 + 1.09259i) q^{47} +(0.695712 - 2.59643i) q^{48} +(3.77321 - 2.17847i) q^{49} +(3.20711 - 3.83594i) q^{50} -14.3962i q^{51} +(-5.07782 + 1.36060i) q^{52} +(-5.15279 - 1.38068i) q^{53} +3.29411i q^{54} +(0.548115 + 12.3026i) q^{55} +(-0.812876 + 1.40794i) q^{56} +(15.0240 - 4.02566i) q^{57} +(-0.490186 - 1.82940i) q^{58} +8.68403i q^{59} +(1.29571 - 5.86929i) q^{60} +(-4.24348 - 2.44998i) q^{61} +(-0.109923 - 0.0294537i) q^{62} +(1.77798 - 6.63550i) q^{63} +1.00000i q^{64} +(-11.2077 + 3.54474i) q^{65} +(7.40195 + 12.8206i) q^{66} +(-3.37100 + 12.5808i) q^{67} +(1.38615 + 5.17320i) q^{68} +(-9.07264 + 15.7143i) q^{69} +(-1.67572 + 3.22603i) q^{70} +(-4.81888 - 2.78218i) q^{71} +(-1.09363 - 4.08150i) q^{72} +(-3.61389 + 0.968338i) q^{73} +(-3.82763 + 2.20988i) q^{74} +(2.31029 - 13.2401i) q^{75} +(-5.01116 + 2.89319i) q^{76} +(-2.31736 - 8.64851i) q^{77} +(-9.99198 + 9.99198i) q^{78} +(-6.69555 - 3.86567i) q^{79} +(0.0995241 + 2.23385i) q^{80} +(-1.91089 - 3.30976i) q^{81} +(3.95960 - 3.95960i) q^{82} +(-16.9711 - 4.54738i) q^{83} +4.37006i q^{84} +(3.61132 + 11.4182i) q^{85} +(2.34699 + 6.12304i) q^{86} +(-3.59984 - 3.59984i) q^{87} +(-3.89429 - 3.89429i) q^{88} +(1.64655 + 2.85190i) q^{89} +(-2.84922 - 9.00862i) q^{90} +(7.40147 - 4.27324i) q^{91} +(1.74714 - 6.52040i) q^{92} +(-0.295475 + 0.0791722i) q^{93} -1.54516 q^{94} +(-10.9062 + 6.96170i) q^{95} +(1.34401 + 2.32790i) q^{96} +(-3.42212 - 3.42212i) q^{97} +(-1.12766 + 4.20847i) q^{98} +(20.1535 + 11.6356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) $ 88 * q + 4 * q^6 + 12 * q^7	$ 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) $ 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.695712	+	2.59643i	−0.401669	+	1.49905i	0.408447	+	0.912782i	$0.366070\pi$
$3$	−0.695712	+	2.59643i	−0.401669	+	1.49905i	−0.810117	+	0.586269i	$0.800596\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−0.0995241	−	2.23385i	−0.0445085	−	0.999009i
$5$	−0.0995241	−	2.23385i	−0.0445085	−	0.999009i
$6$	−1.34401	−	2.32790i	−0.548691	−	0.950360i
$7$	0.420775	+	1.57036i	0.159038	+	0.593538i	0.998726	+	0.0504686i	$0.0160715\pi$
$7$	0.420775	+	1.57036i	0.159038	+	0.593538i	−0.839687	+	0.543070i	$0.817262\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−3.65937	−	2.11274i	−1.21979	−	0.704246i
$10$	1.64995	+	1.50920i	0.521759	+	0.477250i
$11$	−5.50736			−1.66053			−0.830265	−	0.557369i	$-0.811811\pi$
$11$	−5.50736			−1.66053			−0.830265	+	0.557369i	$0.811811\pi$
$12$	2.59643	+	0.695712i	0.749525	+	0.200835i
$13$	−1.36060	−	5.07782i	−0.377362	−	1.40833i	−0.849863	−	0.527003i	$-0.823316\pi$
$13$	−1.36060	−	5.07782i	−0.377362	−	1.40833i	0.472502	−	0.881330i	$-0.343351\pi$
$14$	−1.40794	−	0.812876i	−0.376288	−	0.217250i
$15$	5.86929	+	1.29571i	1.51544	+	0.334551i
$16$	−1.00000			−0.250000
$17$	−5.17320	+	1.38615i	−1.25468	+	0.336192i	−0.824145	−	0.566380i	$-0.808344\pi$
$17$	−5.17320	+	1.38615i	−1.25468	+	0.336192i	−0.430540	+	0.902571i	$0.641677\pi$
$18$	4.08150	−	1.09363i	0.962018	−	0.257772i
$19$	−2.89319	−	5.01116i	−0.663744	−	1.14964i	−0.979624	−	0.200839i	$-0.935633\pi$
$19$	−2.89319	−	5.01116i	−0.663744	−	1.14964i	0.315880	−	0.948799i	$-0.397700\pi$
$20$	−2.23385	+	0.0995241i	−0.499505	+	0.0222543i
$21$	−4.37006			−0.953625
$22$	3.89429	−	3.89429i	0.830265	−	0.830265i
$23$	6.52040	+	1.74714i	1.35960	+	0.364303i	0.863669	−	0.504060i	$-0.168161\pi$
$23$	6.52040	+	1.74714i	1.35960	+	0.364303i	0.495929	+	0.868363i	$0.334828\pi$
$24$	−2.32790	+	1.34401i	−0.475180	+	0.274345i
$25$	−4.98019	+	0.444644i	−0.996038	+	0.0889289i
$26$	4.55264	+	2.62847i	0.892847	+	0.515486i
$27$	2.32929	−	2.32929i	0.448271	−	0.448271i
$28$	1.57036	−	0.420775i	0.296769	−	0.0795191i
$29$	−0.946967	+	1.64019i	−0.175847	+	0.304576i	−0.940454	−	0.339920i	$-0.889600\pi$
$29$	−0.946967	+	1.64019i	−0.175847	+	0.304576i	0.764607	+	0.644497i	$0.222933\pi$
$30$	−5.06642	+	3.23401i	−0.924997	+	0.590446i
$31$	0.0569001	+	0.0985539i	0.0102196	+	0.0177008i	0.871090	−	0.491123i	$-0.163414\pi$
$31$	0.0569001	+	0.0985539i	0.0102196	+	0.0177008i	−0.860870	+	0.508824i	$0.830080\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	3.83153	−	14.2995i	0.666984	−	2.48922i
$34$	2.67784	−	4.63816i	0.459247	−	0.795438i
$35$	3.46606	−	1.09624i	0.585872	−	0.185298i
$36$	−2.11274	+	3.65937i	−0.352123	+	0.609895i
$37$	4.26916	+	1.14392i	0.701846	+	0.188059i	0.592057	−	0.805896i	$-0.298316\pi$
$37$	4.26916	+	1.14392i	0.701846	+	0.188059i	0.109789	+	0.993955i	$0.464983\pi$
$38$	5.58922	+	1.49763i	0.906691	+	0.242947i
$39$	14.1308			2.26274
$40$	1.50920	−	1.64995i	0.238625	−	0.260879i
$41$	−5.59971			−0.874528			−0.437264	−	0.899333i	$-0.644053\pi$
$41$	−5.59971			−0.874528			−0.437264	+	0.899333i	$0.644053\pi$
$42$	3.09010	−	3.09010i	0.476813	−	0.476813i
$43$	2.67007	−	5.98922i	0.407182	−	0.913347i
$43$	2.67007	−	5.98922i	0.407182	−	0.913347i
$44$			5.50736i			0.830265i
$45$	−4.35535	+	8.38476i	−0.649257	+	1.24993i
$46$	−5.84603	+	3.37521i	−0.861951	+	0.497647i
$47$	1.09259	+	1.09259i	0.159371	+	0.159371i	0.782288	−	0.622917i	$-0.214052\pi$
$47$	1.09259	+	1.09259i	0.159371	+	0.159371i	−0.622917	+	0.782288i	$0.714052\pi$
$48$	0.695712	−	2.59643i	0.100417	−	0.374763i
$49$	3.77321	−	2.17847i	0.539031	−	0.311209i
$50$	3.20711	−	3.83594i	0.453555	−	0.542483i
$51$		−	14.3962i		−	2.01587i
$52$	−5.07782	+	1.36060i	−0.704166	+	0.188681i
$53$	−5.15279	−	1.38068i	−0.707790	−	0.189652i	−0.113072	−	0.993587i	$-0.536069\pi$
$53$	−5.15279	−	1.38068i	−0.707790	−	0.189652i	−0.594717	+	0.803935i	$0.702736\pi$
$54$			3.29411i			0.448271i
$55$	0.548115	+	12.3026i	0.0739078	+	1.65888i
$56$	−0.812876	+	1.40794i	−0.108625	+	0.188144i
$57$	15.0240	−	4.02566i	1.98997	−	0.533211i
$58$	−0.490186	−	1.82940i	−0.0643646	−	0.240212i
$59$			8.68403i			1.13056i	0.824897	+	0.565282i	$0.191233\pi$
$59$			8.68403i			1.13056i	−0.824897	+	0.565282i	$0.808767\pi$
$60$	1.29571	−	5.86929i	0.167275	−	0.757722i
$61$	−4.24348	−	2.44998i	−0.543322	−	0.313687i	0.203102	−	0.979158i	$-0.434898\pi$
$61$	−4.24348	−	2.44998i	−0.543322	−	0.313687i	−0.746424	+	0.665470i	$0.768231\pi$
$62$	−0.109923	−	0.0294537i	−0.0139602	−	0.00374062i
$63$	1.77798	−	6.63550i	0.224004	−	0.835994i
$64$			1.00000i			0.125000i
$65$	−11.2077	+	3.54474i	−1.39014	+	0.439670i
$66$	7.40195	+	12.8206i	0.911118	+	1.57810i
$67$	−3.37100	+	12.5808i	−0.411834	+	1.53698i	0.379261	+	0.925290i	$0.376178\pi$
$67$	−3.37100	+	12.5808i	−0.411834	+	1.53698i	−0.791094	+	0.611694i	$0.790488\pi$
$68$	1.38615	+	5.17320i	0.168096	+	0.627342i
$69$	−9.07264	+	15.7143i	−1.09222	+	1.89178i
$70$	−1.67572	+	3.22603i	−0.200287	+	0.385585i
$71$	−4.81888	−	2.78218i	−0.571896	−	0.330185i	0.186010	−	0.982548i	$-0.440444\pi$
$71$	−4.81888	−	2.78218i	−0.571896	−	0.330185i	−0.757906	+	0.652363i	$0.773778\pi$
$72$	−1.09363	−	4.08150i	−0.128886	−	0.481009i
$73$	−3.61389	+	0.968338i	−0.422973	+	0.113335i	−0.464026	−	0.885822i	$-0.653596\pi$
$73$	−3.61389	+	0.968338i	−0.422973	+	0.113335i	0.0410526	+	0.999157i	$0.486929\pi$
$74$	−3.82763	+	2.20988i	−0.444953	+	0.256893i
$75$	2.31029	−	13.2401i	0.266769	−	1.52883i
$76$	−5.01116	+	2.89319i	−0.574819	+	0.331872i
$77$	−2.31736	−	8.64851i	−0.264088	−	0.985589i
$78$	−9.99198	+	9.99198i	−1.13137	+	1.13137i
$79$	−6.69555	−	3.86567i	−0.753308	−	0.434922i	0.0735801	−	0.997289i	$-0.476558\pi$
$79$	−6.69555	−	3.86567i	−0.753308	−	0.434922i	−0.826888	+	0.562367i	$0.809891\pi$
$80$	0.0995241	+	2.23385i	0.0111271	+	0.249752i
$81$	−1.91089	−	3.30976i	−0.212321	−	0.367751i
$82$	3.95960	−	3.95960i	0.437264	−	0.437264i
$83$	−16.9711	−	4.54738i	−1.86282	−	0.499140i	−0.862836	−	0.505484i	$-0.831314\pi$
$83$	−16.9711	−	4.54738i	−1.86282	−	0.499140i	−0.999980	+	0.00634376i	$0.997981\pi$
$84$			4.37006i			0.476813i
$85$	3.61132	+	11.4182i	0.391703	+	1.23848i
$86$	2.34699	+	6.12304i	0.253082	+	0.660265i
$87$	−3.59984	−	3.59984i	−0.385943	−	0.385943i
$88$	−3.89429	−	3.89429i	−0.415133	−	0.415133i
$89$	1.64655	+	2.85190i	0.174533	+	0.302301i	0.940000	−	0.341175i	$-0.110825\pi$
$89$	1.64655	+	2.85190i	0.174533	+	0.302301i	−0.765466	+	0.643476i	$0.777492\pi$
$90$	−2.84922	−	9.00862i	−0.300334	−	0.949591i
$91$	7.40147	−	4.27324i	0.775885	−	0.447957i
$92$	1.74714	−	6.52040i	0.182152	−	0.679799i
$93$	−0.295475	+	0.0791722i	−0.0306393	+	0.00820977i
$94$	−1.54516			−0.159371
$95$	−10.9062	+	6.96170i	−1.11896	+	0.714255i
$96$	1.34401	+	2.32790i	0.137173	+	0.237590i
$97$	−3.42212	−	3.42212i	−0.347464	−	0.347464i	0.511700	−	0.859164i	$-0.329016\pi$
$97$	−3.42212	−	3.42212i	−0.347464	−	0.347464i	−0.859164	+	0.511700i	$0.829016\pi$
$98$	−1.12766	+	4.20847i	−0.113911	+	0.425120i
$99$	20.1535	+	11.6356i	2.02550	+	1.16942i
$100$	0.444644	+	4.98019i	0.0444644	+	0.498019i
$101$	1.14192	−	1.97787i	0.113626	−	0.196805i	−0.803604	−	0.595165i	$-0.797087\pi$
$101$	1.14192	−	1.97787i	0.113626	−	0.196805i	0.917230	+	0.398359i	$0.130420\pi$
$102$	10.1797	+	10.1797i	1.00794	+	1.00794i
$103$	3.00874	+	11.2288i	0.296460	+	1.10640i	0.940051	+	0.341034i	$0.110777\pi$
$103$	3.00874	+	11.2288i	0.296460	+	1.10640i	−0.643591	+	0.765370i	$0.722556\pi$
$104$	2.62847	−	4.55264i	0.257743	−	0.446424i
$105$	0.434926	+	9.76207i	0.0424445	+	0.952680i
$106$	4.61986	−	2.66728i	0.448721	−	0.259069i
$107$	0.681039	+	0.681039i	0.0658385	+	0.0658385i	0.739259	−	0.673421i	$-0.235176\pi$
$107$	0.681039	+	0.681039i	0.0658385	+	0.0658385i	−0.673421	+	0.739259i	$0.735176\pi$
$108$	−2.32929	−	2.32929i	−0.224136	−	0.224136i
$109$	1.44672	−	0.835265i	0.138571	−	0.0800039i	−0.429112	−	0.903251i	$-0.641173\pi$
$109$	1.44672	−	0.835265i	0.138571	−	0.0800039i	0.567683	+	0.823247i	$0.307840\pi$
$110$	−9.08684	−	8.31169i	−0.866396	−	0.792489i
$111$	−5.94021	+	10.2888i	−0.563820	+	0.976565i
$112$	−0.420775	−	1.57036i	−0.0397595	−	0.148385i
$113$	3.63075	+	3.63075i	0.341552	+	0.341552i	0.856951	−	0.515398i	$-0.172356\pi$
$113$	3.63075	+	3.63075i	0.341552	+	0.341552i	−0.515398	+	0.856951i	$0.672356\pi$
$114$	−7.77697	+	13.4701i	−0.728380	+	1.26159i
$115$	3.25391	−	14.7395i	0.303428	−	1.37447i
$116$	1.64019	+	0.946967i	0.152288	+	0.0879237i
$117$	−5.74917	+	21.4562i	−0.531511	+	1.98363i
$118$	−6.14054	−	6.14054i	−0.565282	−	0.565282i
$119$	−4.35351	−	7.54050i	−0.399086	−	0.691236i
$120$	3.23401	+	5.06642i	0.295223	+	0.462498i
$121$	19.3310			1.75736
$122$	4.73299	−	1.26820i	0.428505	−	0.114817i
$123$	3.89579	−	14.5393i	0.351271	−	1.31096i
$124$	0.0985539	−	0.0569001i	0.00885040	−	0.00510978i
$125$	1.48892	+	11.0808i	0.133173	+	0.991093i
$126$	3.43479	+	5.94922i	0.305995	+	0.529999i
$127$	13.8684	+	13.8684i	1.23062	+	1.23062i	0.963725	+	0.266898i	$0.0859987\pi$
$127$	13.8684	+	13.8684i	1.23062	+	1.23062i	0.266898	+	0.963725i	$0.414001\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	13.6930	+	11.0994i	1.20560	+	0.977250i
$130$	5.41852	−	10.4315i	0.475235	−	0.914906i
$131$		−	0.252302i		−	0.0220437i	−0.999939	−	0.0110219i	$-0.996492\pi$
$131$		−	0.252302i		−	0.0220437i	0.999939	−	0.0110219i	$-0.00350844\pi$
$132$	−14.2995	−	3.83153i	−1.24461	−	0.333492i
$133$	6.65191	−	6.65191i	0.576794	−	0.576794i
$134$	−6.51228	−	11.2796i	−0.562575	−	0.974409i
$135$	−5.43510	−	4.97146i	−0.467779	−	0.427875i
$136$	−4.63816	−	2.67784i	−0.397719	−	0.229623i
$137$	−13.5898	+	13.5898i	−1.16106	+	1.16106i	−0.176811	+	0.984245i	$0.556578\pi$
$137$	−13.5898	+	13.5898i	−1.16106	+	1.16106i	−0.984245	+	0.176811i	$0.943422\pi$
$138$	−4.69635	−	17.5270i	−0.399780	−	1.49200i
$139$	10.5280	−	6.07834i	0.892973	−	0.515558i	0.0180592	−	0.999837i	$-0.494251\pi$
$139$	10.5280	−	6.07834i	0.892973	−	0.515558i	0.874914	+	0.484279i	$0.160918\pi$
$140$	−1.09624	−	3.46606i	−0.0926490	−	0.292936i
$141$	−3.59698	+	2.07672i	−0.302920	+	0.174891i
$142$	5.37477	−	1.44016i	0.451040	−	0.120856i
$143$	7.49329	+	27.9653i	0.626620	+	2.33858i
$144$	3.65937	+	2.11274i	0.304947	+	0.176061i
$145$	3.75820	+	1.95214i	0.312101	+	0.162117i
$146$	1.87068	−	3.24012i	0.154819	−	0.268154i
$147$	3.03117	+	11.3125i	0.250007	+	0.933038i
$148$	1.14392	−	4.26916i	0.0940295	−	0.350923i
$149$	−9.25636	−	16.0325i	−0.758311	−	1.31343i	−0.943711	−	0.330770i	$-0.892692\pi$
$149$	−9.25636	−	16.0325i	−0.758311	−	1.31343i	0.185400	−	0.982663i	$-0.440642\pi$
$150$	7.72852	+	10.9958i	0.631031	+	0.897800i
$151$		−	19.7009i		−	1.60323i	−0.597839	−	0.801616i	$-0.703974\pi$
$151$		−	19.7009i		−	1.60323i	0.597839	−	0.801616i	$-0.296026\pi$
$152$	1.49763	−	5.58922i	0.121474	−	0.453346i
$153$	21.8592	+	5.85716i	1.76721	+	0.473523i
$154$	7.75404	+	4.47680i	0.624838	+	0.360750i
$155$	0.214492	−	0.136915i	0.0172284	−	0.0109973i
$156$		−	14.1308i		−	1.13137i
$157$	−3.29800	−	12.3083i	−0.263209	−	0.982310i	−0.963337	−	0.268293i	$-0.913541\pi$
$157$	−3.29800	−	12.3083i	−0.263209	−	0.982310i	0.700128	−	0.714017i	$-0.253126\pi$
$158$	7.46791	−	2.00102i	0.594115	−	0.159193i
$159$	7.16971	−	12.4183i	0.568595	−	0.984835i
$160$	−1.64995	−	1.50920i	−0.130440	−	0.119313i
$161$			10.9745i			0.864912i
$162$	3.69156	+	0.989150i	0.290036	+	0.0777150i
$163$	−3.15262	+	0.844743i	−0.246933	+	0.0661654i	−0.380162	−	0.924920i	$-0.624132\pi$
$163$	−3.15262	+	0.844743i	−0.246933	+	0.0661654i	0.133230	+	0.991085i	$0.457465\pi$
$164$			5.59971i			0.437264i
$165$	−32.3242	−	7.13594i	−2.51644	−	0.555532i
$166$	15.2158	−	8.78487i	1.18098	−	0.681838i
$167$	2.74301	−	10.2371i	0.212261	−	0.792168i	−0.774852	−	0.632142i	$-0.782176\pi$
$167$	2.74301	−	10.2371i	0.212261	−	0.792168i	0.987113	−	0.160025i	$-0.0511576\pi$
$168$	−3.09010	−	3.09010i	−0.238406	−	0.238406i
$169$	−12.6747	+	7.31772i	−0.974974	+	0.562901i
$170$	−10.6275	−	5.52030i	−0.815090	−	0.423388i
$171$			24.4502i			1.86976i
$172$	−5.98922	−	2.67007i	−0.456673	−	0.203591i
$173$	−1.62006	+	1.62006i	−0.123171	+	0.123171i	−0.766005	−	0.642834i	$-0.777758\pi$
$173$	−1.62006	+	1.62006i	−0.123171	+	0.123171i	0.642834	+	0.766005i	$0.277758\pi$
$174$	5.09094			0.385943
$175$	−2.79379	−	7.63357i	−0.211191	−	0.577044i
$176$	5.50736			0.415133
$177$	−22.5475	−	6.04159i	−1.69477	−	0.454113i
$178$	−3.18088	−	0.852314i	−0.238417	−	0.0638837i
$179$	−6.25125	+	10.8275i	−0.467241	+	0.809284i	−0.999300	−	0.0374229i	$-0.988085\pi$
$179$	−6.25125	+	10.8275i	−0.467241	+	0.809284i	0.532059	+	0.846707i	$0.321418\pi$
$180$	8.38476	+	4.35535i	0.624963	+	0.324628i
$181$	5.04499	−	8.73818i	0.374991	−	0.649504i	−0.615334	−	0.788266i	$-0.710979\pi$
$181$	5.04499	−	8.73818i	0.374991	−	0.649504i	0.990326	+	0.138762i	$0.0443124\pi$
$182$	−2.21199	+	8.25527i	−0.163964	+	0.611921i
$183$	9.31344	−	9.31344i	0.688469	−	0.688469i
$184$	3.37521	+	5.84603i	0.248824	+	0.430975i
$185$	2.13046	−	9.65052i	0.156635	−	0.709521i
$186$	0.152949	−	0.264915i	0.0112148	−	0.0194245i
$187$	28.4906	−	7.63405i	2.08344	−	0.558257i
$188$	1.09259	−	1.09259i	0.0796857	−	0.0796857i
$189$	4.63791	+	2.67770i	0.337359	+	0.194774i
$190$	2.78921	−	12.6345i	0.202351	−	0.916606i
$191$	−10.2379	+	5.91087i	−0.740790	+	0.427695i	−0.822356	−	0.568973i	$-0.807341\pi$
$191$	−10.2379	+	5.91087i	−0.740790	+	0.427695i	0.0815665	+	0.996668i	$0.474008\pi$
$192$	−2.59643	−	0.695712i	−0.187381	−	0.0502087i
$193$	−18.5441	+	18.5441i	−1.33484	+	1.33484i	−0.433850	+	0.900985i	$0.642845\pi$
$193$	−18.5441	+	18.5441i	−1.33484	+	1.33484i	−0.900985	+	0.433850i	$0.857155\pi$
$194$	4.83961			0.347464
$195$	−1.40635	−	31.5661i	−0.100711	−	2.26049i
$196$	−2.17847	−	3.77321i	−0.155605	−	0.269515i
$197$	20.0231	−	5.36518i	1.42659	−	0.382253i	0.538773	−	0.842451i	$-0.318888\pi$
$197$	20.0231	−	5.36518i	1.42659	−	0.382253i	0.887816	+	0.460198i	$0.152222\pi$
$198$	−22.4783	+	6.02303i	−1.59746	+	0.428038i
$199$	−23.2011			−1.64468			−0.822340	−	0.568996i	$-0.807332\pi$
$199$	−23.2011			−1.64468			−0.822340	+	0.568996i	$0.807332\pi$
$200$	−3.83594	−	3.20711i	−0.271242	−	0.226777i
$201$	−30.3198	−	17.5052i	−2.13860	−	1.23472i
$202$	0.591103	+	2.20603i	0.0415899	+	0.155216i
$203$	−2.97415	−	0.796921i	−0.208744	−	0.0559329i
$204$	−14.3962			−1.00794
$205$	0.557307	+	12.5089i	0.0389240	+	0.873662i
$206$	−10.0674	−	5.81244i	−0.701432	−	0.404972i
$207$	−20.1693	−	20.1693i	−1.40186	−	1.40186i
$208$	1.36060	+	5.07782i	0.0943404	+	0.352083i
$209$	15.9338	+	27.5982i	1.10217	+	1.90901i
$210$	−7.21036	−	6.59528i	−0.497562	−	0.455118i
$211$		−	1.14913i		−	0.0791095i	−0.999217	−	0.0395548i	$-0.987406\pi$
$211$		−	1.14913i		−	0.0791095i	0.999217	−	0.0395548i	$-0.0125940\pi$
$212$	−1.38068	+	5.15279i	−0.0948258	+	0.353895i
$213$	10.5763	−	10.5763i	0.724677	−	0.724677i
$214$	−0.963134			−0.0658385
$215$	−13.6448	−	5.36847i	−0.930565	−	0.366127i
$216$	3.29411			0.224136
$217$	−0.130822	+	0.130822i	−0.00888081	+	0.00888081i
$218$	−0.432365	+	1.61361i	−0.0292835	+	0.109287i
$219$		−	10.0569i		−	0.679582i
$220$	12.3026	−	0.548115i	0.829442	−	0.0369539i
$221$	14.0773	+	24.3826i	0.946940	+	1.64015i
$222$	−3.07488	−	11.4756i	−0.206373	−	0.770193i
$223$	0.0928113	+	0.0928113i	0.00621511	+	0.00621511i	0.710208	−	0.703992i	$-0.248601\pi$
$223$	0.0928113	+	0.0928113i	0.00621511	+	0.00621511i	−0.703992	+	0.710208i	$0.748601\pi$
$224$	1.40794	+	0.812876i	0.0940721	+	0.0543125i
$225$	19.1638	+	8.89472i	1.27758	+	0.592981i
$226$	−5.13466			−0.341552
$227$	−1.26722	−	0.339551i	−0.0841084	−	0.0225368i	0.216519	−	0.976278i	$-0.430530\pi$
$227$	−1.26722	−	0.339551i	−0.0841084	−	0.0225368i	−0.300628	+	0.953742i	$0.597196\pi$
$228$	−4.02566	−	15.0240i	−0.266606	−	0.994986i
$229$	22.4124	+	12.9398i	1.48105	+	0.855086i	0.999769	−	0.0214797i	$-0.00683774\pi$
$229$	22.4124	+	12.9398i	1.48105	+	0.855086i	0.481283	+	0.876565i	$0.340171\pi$
$230$	8.12154	+	12.7233i	0.535518	+	0.838947i
$231$	24.0675			1.58352
$232$	−1.82940	+	0.490186i	−0.120106	+	0.0321823i
$233$	21.1574	−	5.66910i	1.38606	−	0.371395i	0.512744	−	0.858541i	$-0.328629\pi$
$233$	21.1574	−	5.66910i	1.38606	−	0.371395i	0.873320	+	0.487146i	$0.161962\pi$
$234$	−11.1065	−	19.2371i	−0.726057	−	1.25757i
$235$	2.33196	−	2.54943i	0.152120	−	0.166307i
$236$	8.68403			0.565282
$237$	14.6951	−	14.6951i	0.954552	−	0.954552i
$238$	8.41033	+	2.25354i	0.545161	+	0.146075i
$239$	−0.232452	+	0.134206i	−0.0150361	+	0.00868108i	−0.507499	−	0.861652i	$-0.669430\pi$
$239$	−0.232452	+	0.134206i	−0.0150361	+	0.00868108i	0.492463	+	0.870333i	$0.336097\pi$
$240$	−5.86929	−	1.29571i	−0.378861	−	0.0836377i
$241$	9.99192	+	5.76884i	0.643636	+	0.371604i	0.786014	−	0.618209i	$-0.212141\pi$
$241$	9.99192	+	5.76884i	0.643636	+	0.371604i	−0.142378	+	0.989812i	$0.545475\pi$
$242$	−13.6691	+	13.6691i	−0.878681	+	0.878681i
$243$	19.4686	−	5.21659i	1.24891	−	0.334645i
$244$	−2.44998	+	4.24348i	−0.156844	+	0.271661i
$245$	−5.24190	−	8.21199i	−0.334893	−	0.524645i
$246$	7.52608	+	13.0356i	0.479846	+	0.831117i
$247$	−21.5093	+	21.5093i	−1.36860	+	1.36860i
$248$	−0.0294537	+	0.109923i	−0.00187031	+	0.00698009i
$249$	23.6139	−	40.9005i	1.49647	−	2.59197i
$250$	−8.88810	−	6.78245i	−0.562133	−	0.428960i
$251$	1.24945	−	2.16410i	0.0788643	−	0.136597i	−0.823896	−	0.566741i	$-0.808204\pi$
$251$	1.24945	−	2.16410i	0.0788643	−	0.136597i	0.902760	+	0.430144i	$0.141537\pi$
$252$	−6.63550	−	1.77798i	−0.417997	−	0.112002i
$253$	−35.9102	−	9.62210i	−2.25765	−	0.604937i
$254$	−19.6129			−1.23062
$255$	−32.1590	+	1.43277i	−2.01388	+	0.0897237i
$256$	1.00000			0.0625000
$257$	5.67017	−	5.67017i	0.353696	−	0.353696i	−0.507787	−	0.861483i	$-0.669536\pi$
$257$	5.67017	−	5.67017i	0.353696	−	0.353696i	0.861483	+	0.507787i	$0.169536\pi$
$258$	−17.5309	+	1.83393i	−1.09143	+	0.114175i
$259$			7.18543i			0.446481i
$260$	3.54474	+	11.2077i	0.219835	+	0.695071i
$261$	6.93060	−	4.00138i	0.428994	−	0.247680i
$262$	0.178404	+	0.178404i	0.0110219	+	0.0110219i
$263$	1.11304	−	4.15393i	0.0686332	−	0.256143i	−0.923081	−	0.384605i	$-0.874338\pi$
$263$	1.11304	−	4.15393i	0.0686332	−	0.256143i	0.991714	+	0.128463i	$0.0410043\pi$
$264$	12.8206	−	7.40195i	0.789051	−	0.455559i
$265$	−2.57142	+	11.6480i	−0.157961	+	0.715529i
$266$			9.40722i			0.576794i
$267$	−8.55029	+	2.29104i	−0.523269	+	0.140210i
$268$	12.5808	+	3.37100i	0.768492	+	0.205917i
$269$		−	22.7867i		−	1.38933i	−0.719332	−	0.694666i	$-0.755552\pi$
$269$		−	22.7867i		−	1.38933i	0.719332	−	0.694666i	$-0.244448\pi$
$270$	7.35855	−	0.327843i	0.447827	−	0.0199519i
$271$	−9.29651	+	16.1020i	−0.564723	+	0.978129i	0.432353	+	0.901705i	$0.357684\pi$
$271$	−9.29651	+	16.1020i	−0.564723	+	0.978129i	−0.997075	+	0.0764239i	$0.975650\pi$
$272$	5.17320	−	1.38615i	0.313671	−	0.0840480i
$273$	5.94589	+	22.1904i	0.359862	+	1.34302i
$274$		−	19.2189i		−	1.16106i
$275$	27.4277	−	2.44882i	1.65395	−	0.147669i
$276$	15.7143	+	9.07264i	0.945889	+	0.546109i
$277$	10.5248	+	2.82010i	0.632372	+	0.169444i	0.560746	−	0.827988i	$-0.310514\pi$
$277$	10.5248	+	2.82010i	0.632372	+	0.169444i	0.0716263	+	0.997432i	$0.477181\pi$
$278$	−3.14638	+	11.7425i	−0.188707	+	0.704266i
$279$		−	0.480860i		−	0.0287883i
$280$	3.22603	+	1.67572i	0.192792	+	0.100143i
$281$	−1.15780	−	2.00537i	−0.0690687	−	0.119631i	0.829423	−	0.558621i	$-0.188669\pi$
$281$	−1.15780	−	2.00537i	−0.0690687	−	0.119631i	−0.898492	+	0.438991i	$0.855336\pi$
$282$	1.07499	−	4.01191i	0.0640146	−	0.238906i
$283$	−7.89235	−	29.4546i	−0.469151	−	1.75090i	−0.642745	−	0.766080i	$-0.722205\pi$
$283$	−7.89235	−	29.4546i	−0.469151	−	1.75090i	0.173594	−	0.984817i	$-0.444462\pi$
$284$	−2.78218	+	4.81888i	−0.165092	+	0.285948i
$285$	−10.4880	−	33.1607i	−0.621254	−	1.96427i
$286$	−25.0730	−	14.4759i	−1.48260	−	0.855979i
$287$	−2.35622	−	8.79354i	−0.139083	−	0.519066i
$288$	−4.08150	+	1.09363i	−0.240504	+	0.0644430i
$289$	10.1181	−	5.84170i	0.595184	−	0.343630i
$290$	−4.03782	+	1.27707i	−0.237109	+	0.0749923i
$291$	11.2661	−	6.50450i	0.660432	−	0.381301i
$292$	0.968338	+	3.61389i	0.0566677	+	0.211487i
$293$	−18.8046	+	18.8046i	−1.09858	+	1.09858i	−0.104002	+	0.994577i	$0.533165\pi$
$293$	−18.8046	+	18.8046i	−1.09858	+	1.09858i	−0.994577	+	0.104002i	$0.966835\pi$
$294$	−10.1425	−	5.85577i	−0.591522	−	0.341515i
$295$	19.3988	−	0.864271i	1.12944	−	0.0503198i
$296$	2.20988	+	3.82763i	0.128447	+	0.222476i
$297$	−12.8282	+	12.8282i	−0.744368	+	0.744368i
$298$	17.8819	+	4.79145i	1.03587	+	0.277561i
$299$		−	35.4866i		−	2.05224i
$300$	−13.2401	−	2.31029i	−0.764416	−	0.133385i
$301$	10.5287	+	1.67285i	0.606864	+	0.0964213i
$302$	13.9306	+	13.9306i	0.801616	+	0.801616i
$303$	4.34095	+	4.34095i	0.249381	+	0.249381i
$304$	2.89319	+	5.01116i	0.165936	+	0.287410i
$305$	−5.05055	+	9.72314i	−0.289194	+	0.556746i
$306$	−19.5984	+	11.3152i	−1.12037	+	0.646845i
$307$	−4.55692	+	17.0067i	−0.260077	+	0.970621i	0.705118	+	0.709090i	$0.250894\pi$
$307$	−4.55692	+	17.0067i	−0.260077	+	0.970621i	−0.965195	+	0.261531i	$0.915773\pi$
$308$	−8.64851	+	2.31736i	−0.492794	+	0.132044i
$309$	−31.2480			−1.77763
$310$	−0.0548552	+	0.248482i	−0.00311557	+	0.0141128i
$311$	−3.48834	−	6.04198i	−0.197806	−	0.342609i	0.750011	−	0.661425i	$-0.230048\pi$
$311$	−3.48834	−	6.04198i	−0.197806	−	0.342609i	−0.947817	+	0.318816i	$0.896715\pi$
$312$	9.99198	+	9.99198i	0.565684	+	0.565684i
$313$	3.30492	−	12.3341i	0.186805	−	0.697165i	−0.807432	−	0.589960i	$-0.799143\pi$
$313$	3.30492	−	12.3341i	0.186805	−	0.697165i	0.994237	−	0.107205i	$-0.0341900\pi$
$314$	11.0353	+	6.37125i	0.622759	+	0.359550i
$315$	−14.9997	−	3.31134i	−0.845136	−	0.186573i
$316$	−3.86567	+	6.69555i	−0.217461	+	0.376654i
$317$	−4.55505	−	4.55505i	−0.255837	−	0.255837i	0.567522	−	0.823359i	$-0.307902\pi$
$317$	−4.55505	−	4.55505i	−0.255837	−	0.255837i	−0.823359	+	0.567522i	$0.807902\pi$
$318$	3.71131	+	13.8508i	0.208120	+	0.776715i
$319$	5.21528	−	9.03314i	0.292000	−	0.505758i
$320$	2.23385	−	0.0995241i	0.124876	−	0.00556357i
$321$	−2.24208	+	1.29446i	−0.125141	+	0.0722500i
$322$	−7.76014	−	7.76014i	−0.432456	−	0.432456i
$323$	21.9133	+	21.9133i	1.21929	+	1.21929i
$324$	−3.30976	+	1.91089i	−0.183876	+	0.106161i
$325$	9.03385	+	24.6835i	0.501108	+	1.36919i
$326$	1.63192	−	2.82657i	0.0903836	−	0.156549i
$327$	1.16221	+	4.33742i	0.0642703	+	0.239860i
$328$	−3.95960	−	3.95960i	−0.218632	−	0.218632i
$329$	−1.25602	+	2.17550i	−0.0692469	+	0.119939i
$330$	27.9026	−	17.8108i	1.53599	−	0.980454i
$331$	−9.07443	−	5.23913i	−0.498776	−	0.287968i	0.229432	−	0.973325i	$-0.426313\pi$
$331$	−9.07443	−	5.23913i	−0.498776	−	0.287968i	−0.728208	+	0.685356i	$0.759646\pi$
$332$	−4.54738	+	16.9711i	−0.249570	+	0.931408i
$333$	−13.2056	−	13.2056i	−0.723665	−	0.723665i
$334$	5.29909	+	9.17830i	0.289954	+	0.502214i
$335$	28.4390	+	6.27823i	1.55379	+	0.343017i
$336$	4.37006			0.238406
$337$	1.61105	−	0.431678i	0.0877592	−	0.0235150i	−0.214672	−	0.976686i	$-0.568868\pi$
$337$	1.61105	−	0.431678i	0.0877592	−	0.0235150i	0.302431	+	0.953171i	$0.402202\pi$
$338$	3.78793	−	14.1367i	0.206036	−	0.768938i
$339$	−11.9530	+	6.90104i	−0.649195	+	0.374813i
$340$	11.4182	−	3.61132i	0.619239	−	0.195851i
$341$	−0.313369	−	0.542772i	−0.0169699	−	0.0293927i
$342$	−17.2889	−	17.2889i	−0.934878	−	0.934878i
$343$	13.0557	+	13.0557i	0.704942	+	0.704942i
$344$	6.12304	−	2.34699i	0.330132	−	0.126541i
$345$	36.0063	+	18.7030i	1.93852	+	1.00694i
$346$		−	2.29111i		−	0.123171i
$347$	22.4885	+	6.02578i	1.20725	+	0.323481i	0.805681	−	0.592349i	$-0.201799\pi$
$347$	22.4885	+	6.02578i	1.20725	+	0.323481i	0.401566	+	0.915830i	$0.368466\pi$
$348$	−3.59984	+	3.59984i	−0.192972	+	0.192972i
$349$	−6.46570	−	11.1989i	−0.346101	−	0.599465i	0.639452	−	0.768831i	$-0.279161\pi$
$349$	−6.46570	−	11.1989i	−0.346101	−	0.599465i	−0.985553	+	0.169366i	$0.945828\pi$
$350$	7.37326	+	3.42224i	0.394117	+	0.182927i
$351$	−14.9969	−	8.65847i	−0.800476	−	0.462155i
$352$	−3.89429	+	3.89429i	−0.207566	+	0.207566i
$353$	−3.85035	−	14.3697i	−0.204933	−	0.764822i	−0.989470	−	0.144739i	$-0.953766\pi$
$353$	−3.85035	−	14.3697i	−0.204933	−	0.764822i	0.784536	−	0.620083i	$-0.212901\pi$
$354$	20.2155	−	11.6714i	1.07444	−	0.620330i
$355$	−5.73539	+	11.0416i	−0.304403	+	0.586026i
$356$	2.85190	−	1.64655i	0.151150	−	0.0872667i
$357$	22.6072	−	6.05758i	1.19650	−	0.320601i
$358$	−3.23589	−	12.0765i	−0.171022	−	0.638262i
$359$	7.93887	+	4.58351i	0.418997	+	0.241908i	0.694648	−	0.719350i	$-0.255560\pi$
$359$	7.93887	+	4.58351i	0.418997	+	0.241908i	−0.275651	+	0.961258i	$0.588893\pi$
$360$	−9.00862	+	2.84922i	−0.474796	+	0.150167i
$361$	−7.24113	+	12.5420i	−0.381112	+	0.660106i
$362$	2.61148	+	9.74617i	0.137256	+	0.512248i
$363$	−13.4488	+	50.1916i	−0.705878	+	2.63437i
$364$	−4.27324	−	7.40147i	−0.223979	−	0.387942i
$365$	2.52279	+	7.97651i	0.132049	+	0.417510i
$366$			13.1712i			0.688469i
$367$	−1.46309	+	5.46031i	−0.0763725	+	0.285026i	−0.993541	−	0.113473i	$-0.963802\pi$
$367$	−1.46309	+	5.46031i	−0.0763725	+	0.285026i	0.917169	+	0.398500i	$0.130469\pi$
$368$	−6.52040	−	1.74714i	−0.339900	−	0.0910758i
$369$	20.4914	+	11.8307i	1.06674	+	0.615883i
$370$	5.31749	+	8.33041i	0.276443	+	0.433078i
$371$		−	8.67266i		−	0.450262i
$372$	0.0791722	+	0.295475i	0.00410489	+	0.0153196i
$373$	4.72949	−	1.26726i	0.244884	−	0.0656164i	−0.134289	−	0.990942i	$-0.542875\pi$
$373$	4.72949	−	1.26726i	0.244884	−	0.0656164i	0.379173	+	0.925326i	$0.376208\pi$
$374$	−14.7478	+	25.5440i	−0.762593	+	1.32085i
$375$	−29.8063	−	3.84314i	−1.53919	−	0.198459i
$376$			1.54516i			0.0796857i
$377$	9.61704	+	2.57688i	0.495303	+	0.132716i
$378$	−5.17292	+	1.38608i	−0.266066	+	0.0712923i
$379$		−	11.9758i		−	0.615156i	−0.951523	−	0.307578i	$-0.900481\pi$
$379$		−	11.9758i		−	0.615156i	0.951523	−	0.307578i	$-0.0995185\pi$
$380$	6.96170	+	10.9062i	0.357127	+	0.559478i
$381$	−45.6568	+	26.3600i	−2.33907	+	1.35046i
$382$	3.05969	−	11.4189i	0.156547	−	0.584243i
$383$	0.478787	+	0.478787i	0.0244649	+	0.0244649i	0.719233	−	0.694769i	$-0.244493\pi$
$383$	0.478787	+	0.478787i	0.0244649	+	0.0244649i	−0.694769	+	0.719233i	$0.744493\pi$
$384$	2.32790	−	1.34401i	0.118795	−	0.0685863i
$385$	−19.0888	+	6.03737i	−0.972858	+	0.307693i
$386$		−	26.2253i		−	1.33484i
$387$	−22.4244	+	16.2756i	−1.13990	+	0.827335i
$388$	−3.42212	+	3.42212i	−0.173732	+	0.173732i
$389$	−6.39659			−0.324320			−0.162160	−	0.986764i	$-0.551846\pi$
$389$	−6.39659			−0.324320			−0.162160	+	0.986764i	$0.551846\pi$
$390$	23.3150	+	21.3262i	1.18060	+	1.07989i
$391$	−36.1531			−1.82834
$392$	4.20847	+	1.12766i	0.212560	+	0.0569553i
$393$	0.655085	+	0.175529i	0.0330447	+	0.00885429i
$394$	−10.3647	+	17.9522i	−0.522168	+	0.904421i
$395$	−7.96898	+	15.3416i	−0.400963	+	0.771919i
$396$	11.6356	−	20.1535i	0.584711	−	1.01275i
$397$	1.37823	−	5.14362i	0.0691713	−	0.258151i	−0.922677	−	0.385573i	$-0.874004\pi$
$397$	1.37823	−	5.14362i	0.0691713	−	0.258151i	0.991849	+	0.127422i	$0.0406704\pi$
$398$	16.4056	−	16.4056i	0.822340	−	0.822340i
$399$	12.6434	+	21.8991i	0.632963	+	1.09632i
$400$	4.98019	−	0.444644i	0.249009	−	0.0222322i
$401$	−1.45496	+	2.52007i	−0.0726573	+	0.125846i	−0.900065	−	0.435755i	$-0.856481\pi$
$401$	−1.45496	+	2.52007i	−0.0726573	+	0.125846i	0.827408	+	0.561602i	$0.189815\pi$
$402$	33.8174	−	9.06134i	1.68666	−	0.451939i
$403$	0.423020	−	0.423020i	0.0210722	−	0.0210722i
$404$	−1.97787	−	1.14192i	−0.0984027	−	0.0568128i
$405$	−7.20333	+	4.59805i	−0.357937	+	0.228479i
$406$	2.66655	−	1.53953i	0.132339	−	0.0764057i
$407$	−23.5118	−	6.29997i	−1.16544	−	0.312278i
$408$	10.1797	−	10.1797i	0.503969	−	0.503969i
$409$	−3.31176			−0.163756			−0.0818780	−	0.996642i	$-0.526092\pi$
$409$	−3.31176			−0.163756			−0.0818780	+	0.996642i	$0.526092\pi$
$410$	−9.23922	−	8.45107i	−0.456293	−	0.417369i
$411$	−25.8304	−	44.7396i	−1.27412	−	2.20684i
$412$	11.2288	−	3.00874i	0.553202	−	0.148230i
$413$	−13.6370	+	3.65403i	−0.671034	+	0.179803i
$414$	28.5237			1.40186
$415$	−8.46915	+	38.3634i	−0.415734	+	1.88319i
$416$	−4.55264	−	2.62847i	−0.223212	−	0.128871i
$417$	8.45755	+	31.5640i	0.414168	+	1.54570i
$418$	−30.7818	−	8.24797i	−1.50559	−	0.403421i
$419$	3.67672			0.179619			0.0898097	−	0.995959i	$-0.471374\pi$
$419$	3.67672			0.179619			0.0898097	+	0.995959i	$0.471374\pi$
$420$	9.76207	−	0.434926i	0.476340	−	0.0212222i
$421$	−16.4637	−	9.50529i	−0.802389	−	0.463260i	0.0419167	−	0.999121i	$-0.486654\pi$
$421$	−16.4637	−	9.50529i	−0.802389	−	0.463260i	−0.844306	+	0.535861i	$0.819987\pi$
$422$	0.812559	+	0.812559i	0.0395548	+	0.0395548i
$423$	−1.68984	−	6.30657i	−0.0821629	−	0.306636i
$424$	−2.66728	−	4.61986i	−0.129534	−	0.224360i
$425$	25.1472	−	9.20355i	1.21982	−	0.446438i
$426$			14.9572i			0.724677i
$427$	2.06178	−	7.69466i	0.0997765	−	0.372371i
$428$	0.681039	−	0.681039i	0.0329193	−	0.0329193i
$429$	−77.8233			−3.75734
$430$	13.4444	−	5.85222i	0.648346	−	0.282219i
$431$	26.5403			1.27840			0.639201	−	0.769040i	$-0.279265\pi$
$431$	26.5403			1.27840			0.639201	+	0.769040i	$0.279265\pi$
$432$	−2.32929	+	2.32929i	−0.112068	+	0.112068i
$433$	7.22026	−	26.9464i	0.346984	−	1.29496i	−0.543294	−	0.839543i	$-0.682823\pi$
$433$	7.22026	−	26.9464i	0.346984	−	1.29496i	0.890278	−	0.455418i	$-0.150510\pi$
$434$		−	0.185011i		−	0.00888081i
$435$	−7.68323	+	8.39978i	−0.368383	+	0.402738i
$436$	−0.835265	−	1.44672i	−0.0400020	−	0.0692854i
$437$	−10.1096	−	37.7296i	−0.483608	−	1.80485i
$438$	7.11130	+	7.11130i	0.339791	+	0.339791i
$439$	14.4424	+	8.33831i	0.689297	+	0.397966i	0.803349	−	0.595509i	$-0.203050\pi$
$439$	14.4424	+	8.33831i	0.689297	+	0.397966i	−0.114052	+	0.993475i	$0.536383\pi$
$440$	−8.31169	+	9.08684i	−0.396244	+	0.433198i
$441$	−18.4101			−0.876672
$442$	−27.1952	−	7.28693i	−1.29354	−	0.346604i
$443$	−1.02956	−	3.84239i	−0.0489161	−	0.182557i	0.937145	−	0.348940i	$-0.113458\pi$
$443$	−1.02956	−	3.84239i	−0.0489161	−	0.182557i	−0.986061	+	0.166382i	$0.946791\pi$
$444$	10.2888	+	5.94021i	0.488283	+	0.281910i
$445$	6.20685	−	3.96197i	0.294233	−	0.187815i
$446$	−0.131255			−0.00621511
$447$	48.0670	−	12.8795i	2.27349	−	0.609181i
$448$	−1.57036	+	0.420775i	−0.0741923	+	0.0198798i
$449$	−8.54671	−	14.8033i	−0.403344	−	0.698612i	0.590783	−	0.806830i	$-0.298819\pi$
$449$	−8.54671	−	14.8033i	−0.403344	−	0.698612i	−0.994127	+	0.108218i	$0.965486\pi$
$450$	−19.8403	+	7.26132i	−0.935283	+	0.342302i
$451$	30.8396			1.45218
$452$	3.63075	−	3.63075i	0.170776	−	0.170776i
$453$	51.1519	+	13.7061i	2.40333	+	0.643970i
$454$	1.13616	−	0.655962i	0.0533226	−	0.0307858i
$455$	−10.2824	−	16.1085i	−0.482047	−	0.755178i
$456$	13.4701	+	7.77697i	0.630796	+	0.364190i
$457$	−7.08324	+	7.08324i	−0.331340	+	0.331340i	−0.853095	−	0.521755i	$-0.825277\pi$
$457$	−7.08324	+	7.08324i	−0.331340	+	0.331340i	0.521755	+	0.853095i	$0.325277\pi$
$458$	−24.9978	+	6.69813i	−1.16807	+	0.312983i
$459$	−8.82111	+	15.2786i	−0.411734	+	0.713145i
$460$	−14.7395	−	3.25391i	−0.687233	−	0.151714i
$461$	−12.6075	−	21.8368i	−0.587190	−	1.01704i	−0.994599	−	0.103796i	$-0.966901\pi$
$461$	−12.6075	−	21.8368i	−0.587190	−	1.01704i	0.407409	−	0.913246i	$-0.366432\pi$
$462$	−17.0183	+	17.0183i	−0.791762	+	0.791762i
$463$	−10.8695	+	40.5655i	−0.505149	+	1.88524i	−0.0416725	+	0.999131i	$0.513269\pi$
$463$	−10.8695	+	40.5655i	−0.505149	+	1.88524i	−0.463476	+	0.886109i	$0.653398\pi$
$464$	0.946967	−	1.64019i	0.0439618	−	0.0761441i
$465$	0.206266	+	0.652167i	0.00956535	+	0.0302435i
$466$	−10.9519	+	18.9692i	−0.507335	+	0.878730i
$467$	−29.8215	−	7.99064i	−1.37997	−	0.369763i	−0.508862	−	0.860848i	$-0.669934\pi$
$467$	−29.8215	−	7.99064i	−1.37997	−	0.369763i	−0.871111	+	0.491086i	$0.836600\pi$
$468$	21.4562	+	5.74917i	0.991813	+	0.265755i
$469$	−21.1747			−0.977756
$470$	0.153781	+	3.45166i	0.00709339	+	0.159213i
$471$	34.2521			1.57826
$472$	−6.14054	+	6.14054i	−0.282641	+	0.282641i
$473$	−14.7050	+	32.9847i	−0.676138	+	1.51664i
$474$			20.7821i			0.954552i
$475$	16.6368	+	23.6701i	0.763350	+	1.08606i
$476$	−7.54050	+	4.35351i	−0.345618	+	0.199543i
$477$	15.9389	+	15.9389i	0.729793	+	0.729793i
$478$	0.0694703	−	0.259267i	0.00317750	−	0.0118586i
$479$	−9.90824	+	5.72052i	−0.452719	+	0.261377i	−0.708978	−	0.705231i	$-0.750843\pi$
$479$	−9.90824	+	5.72052i	−0.452719	+	0.261377i	0.256259	+	0.966608i	$0.417510\pi$
$480$	5.06642	−	3.23401i	0.231249	−	0.147612i
$481$		−	23.2344i		−	1.05940i
$482$	−11.1445	+	2.98617i	−0.507620	+	0.136016i
$483$	−28.4945	−	7.63509i	−1.29655	−	0.347409i
$484$		−	19.3310i		−	0.878681i
$485$	−7.30393	+	7.98510i	−0.331655	+	0.362585i
$486$	−10.0777	+	17.4551i	−0.457133	+	0.791778i
$487$	19.2131	−	5.14813i	0.870628	−	0.233284i	0.204269	−	0.978915i	$-0.434518\pi$
$487$	19.2131	−	5.14813i	0.870628	−	0.233284i	0.666359	+	0.745631i	$0.267852\pi$
$488$	−1.26820	−	4.73299i	−0.0574087	−	0.214252i
$489$		−	8.77327i		−	0.396741i
$490$	9.51334	+	2.10017i	0.429769	+	0.0948762i
$491$	28.7404	+	16.5933i	1.29704	+	0.748844i	0.979891	−	0.199533i	$-0.0639424\pi$
$491$	28.7404	+	16.5933i	1.29704	+	0.748844i	0.317145	+	0.948377i	$0.397276\pi$
$492$	−14.5393	−	3.89579i	−0.655481	−	0.175636i
$493$	2.62528	−	9.79769i	0.118237	−	0.441266i
$494$		−	30.4187i		−	1.36860i
$495$	23.9865	−	46.1779i	1.07811	−	2.07554i
$496$	−0.0569001	−	0.0985539i	−0.00255489	−	0.00442520i
$497$	2.34135	−	8.73803i	0.105024	−	0.391954i
$498$	12.2235	+	45.6186i	0.547747	+	2.04422i
$499$	11.9489	−	20.6961i	0.534907	−	0.926485i	−0.464261	−	0.885698i	$-0.653680\pi$
$499$	11.9489	−	20.6961i	0.534907	−	0.926485i	0.999168	−	0.0407870i	$-0.0129865\pi$
$500$	11.0808	−	1.48892i	0.495546	−	0.0665865i
$501$	24.6715	+	14.2441i	1.10224	+	0.636379i
$502$	0.646761	+	2.41374i	0.0288664	+	0.107731i
$503$	6.85430	−	1.83660i	0.305618	−	0.0818901i	−0.102751	−	0.994707i	$-0.532764\pi$
$503$	6.85430	−	1.83660i	0.305618	−	0.0818901i	0.408369	+	0.912817i	$0.366098\pi$
$504$	5.94922	−	3.43479i	0.265000	−	0.152998i
$505$	−4.53192	−	2.35404i	−0.201668	−	0.104754i
$506$	32.1962	−	18.5885i	1.43130	−	0.826359i
$507$	−10.1820	−	37.9999i	−0.452201	−	1.68764i
$508$	13.8684	−	13.8684i	0.615311	−	0.615311i
$509$	−0.0149995	−	0.00865994i	−0.000664840	−	0.000383845i	0.499668	−	0.866217i	$-0.333456\pi$
$509$	−0.0149995	−	0.00865994i	−0.000664840	−	0.000383845i	−0.500332	+	0.865833i	$0.666789\pi$
$510$	21.7267	−	23.7530i	0.962077	−	1.05180i
$511$	−3.04127	−	5.26763i	−0.134538	−	0.233026i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−18.4115	−	4.93335i	−0.812888	−	0.217813i
$514$			8.01884i			0.353696i
$515$	24.7840	−	7.83862i	1.09211	−	0.345411i
$516$	11.0994	−	13.6930i	0.488625	−	0.602800i
$517$	−6.01731	−	6.01731i	−0.264641	−	0.264641i
$518$	−5.08087	−	5.08087i	−0.223241	−	0.223241i
$519$	−3.07928	−	5.33347i	−0.135165	−	0.234113i
$520$	−10.4315	−	5.41852i	−0.457453	−	0.237618i
$521$	22.1701	−	12.7999i	0.971290	−	0.560775i	0.0716608	−	0.997429i	$-0.477170\pi$
$521$	22.1701	−	12.7999i	0.971290	−	0.560775i	0.899629	+	0.436654i	$0.143837\pi$
$522$	−2.07127	+	7.73008i	−0.0906570	+	0.338337i
$523$	−25.9884	+	6.96356i	−1.13639	+	0.304495i	−0.777499	−	0.628884i	$-0.783512\pi$
$523$	−25.9884	+	6.96356i	−1.13639	+	0.304495i	−0.358892	+	0.933379i	$0.616845\pi$
$524$	−0.252302			−0.0110219
$525$	21.7637	−	1.94312i	0.949847	−	0.0848048i
$526$	2.15023	+	3.72431i	0.0937547	+	0.162388i
$527$	−0.430967	−	0.430967i	−0.0187732	−	0.0187732i
$528$	−3.83153	+	14.2995i	−0.166746	+	0.622305i
$529$	19.5446	+	11.2841i	0.849765	+	0.490612i
$530$	−6.41809	−	10.0546i	−0.278784	−	0.436745i
$531$	18.3471	−	31.7781i	0.796196	−	1.37905i
$532$	−6.65191	−	6.65191i	−0.288397	−	0.288397i
$533$	7.61895	+	28.4343i	0.330013	+	1.23163i
$534$	4.42595	−	7.66598i	0.191530	−	0.331739i
$535$	1.45356	−	1.58912i	0.0628429	−	0.0687036i
$536$	−11.2796	+	6.51228i	−0.487204	+	0.281288i
$537$	−23.7638	−	23.7638i	−1.02548	−	1.02548i
$538$	16.1127	+	16.1127i	0.694666	+	0.694666i
$539$	−20.7804	+	11.9976i	−0.895077	+	0.516773i
$540$	−4.97146	+	5.43510i	−0.213938	+	0.233890i
$541$	12.6481	−	21.9071i	0.543782	−	0.941859i	−0.454900	−	0.890542i	$-0.650325\pi$
$541$	12.6481	−	21.9071i	0.543782	−	0.941859i	0.998682	−	0.0513162i	$-0.0163416\pi$
$542$	−4.81223	−	17.9595i	−0.206703	−	0.771426i
$543$	19.1782	+	19.1782i	0.823017	+	0.823017i
$544$	−2.67784	+	4.63816i	−0.114812	+	0.198860i
$545$	−2.00984	−	3.14863i	−0.0860922	−	0.134873i
$546$	−19.8953	−	11.4866i	−0.851441	−	0.491580i
$547$	−11.6556	+	43.4994i	−0.498358	+	1.85990i	0.0119864	+	0.999928i	$0.496185\pi$
$547$	−11.6556	+	43.4994i	−0.498358	+	1.85990i	−0.510345	+	0.859970i	$0.670482\pi$
$548$	13.5898	+	13.5898i	0.580528	+	0.580528i
$549$	10.3523	+	17.9307i	0.441826	+	0.765265i
$550$	−17.6627	+	21.1259i	−0.753141	+	0.900810i
$551$	10.9590			0.466870
$552$	−17.5270	+	4.69635i	−0.745999	+	0.199890i
$553$	3.25316	−	12.1410i	0.138339	−	0.516286i
$554$	−9.43625	+	5.44802i	−0.400908	+	0.231464i
$555$	23.5747	+	12.2456i	1.00069	+	0.519796i
$556$	−6.07834	−	10.5280i	−0.257779	−	0.446486i
$557$	17.2236	+	17.2236i	0.729786	+	0.729786i	0.970577	−	0.240791i	$-0.0774069\pi$
$557$	17.2236	+	17.2236i	0.729786	+	0.729786i	−0.240791	+	0.970577i	$0.577407\pi$
$558$	0.340020	+	0.340020i	0.0143942	+	0.0143942i
$559$	−34.0450	−	5.40923i	−1.43995	−	0.228786i
$560$	−3.46606	+	1.09624i	−0.146468	+	0.0463245i
$561$			79.2851i			3.34742i
$562$	2.23670	+	0.599323i	0.0943496	+	0.0252809i
$563$	11.8058	−	11.8058i	0.497555	−	0.497555i	−0.413121	−	0.910676i	$-0.635561\pi$
$563$	11.8058	−	11.8058i	0.497555	−	0.497555i	0.910676	+	0.413121i	$0.135561\pi$
$564$	2.07672	+	3.59698i	0.0874456	+	0.151460i
$565$	7.74921	−	8.47191i	0.326012	−	0.356416i
$566$	26.4083	+	15.2468i	1.11002	+	0.640873i
$567$	4.39344	−	4.39344i	0.184507	−	0.184507i
$568$	−1.44016	−	5.37477i	−0.0604280	−	0.225520i
$569$	−29.1015	+	16.8018i	−1.22000	+	0.704367i	−0.964918	−	0.262552i	$-0.915436\pi$
$569$	−29.1015	+	16.8018i	−1.22000	+	0.704367i	−0.255082	+	0.966919i	$0.582102\pi$
$570$	30.8642	+	16.0320i	1.29276	+	0.671507i
$571$	3.62961	−	2.09556i	0.151895	−	0.0876964i	−0.422126	−	0.906537i	$-0.638716\pi$
$571$	3.62961	−	2.09556i	0.151895	−	0.0876964i	0.574021	+	0.818841i	$0.305383\pi$
$572$	27.9653	−	7.49329i	1.16929	−	0.313310i
$573$	−8.22452	−	30.6943i	−0.343584	−	1.28227i
$574$	7.88407	+	4.55187i	0.329075	+	0.189991i
$575$	−33.2497	−	5.80181i	−1.38661	−	0.241952i
$576$	2.11274	−	3.65937i	0.0880307	−	0.152474i
$577$	−2.49648	−	9.31698i	−0.103930	−	0.387871i	0.894292	−	0.447484i	$-0.147680\pi$
$577$	−2.49648	−	9.31698i	−0.103930	−	0.387871i	−0.998222	+	0.0596133i	$0.981013\pi$
$578$	−3.02389	+	11.2853i	−0.125777	+	0.469407i
$579$	−35.2472	−	61.0499i	−1.46482	−	2.53715i
$580$	1.95214	−	3.75820i	0.0810584	−	0.156051i
$581$		−	28.5640i		−	1.18504i
$582$	−3.36698	+	12.5657i	−0.139566	+	0.520866i
$583$	28.3782	+	7.60392i	1.17531	+	0.314922i
$584$	−3.24012	−	1.87068i	−0.134077	−	0.0774095i
$585$	48.5021	+	10.7074i	2.00532	+	0.442696i
$586$		−	26.5938i		−	1.09858i
$587$	−3.93496	−	14.6855i	−0.162413	−	0.606134i	−0.998356	−	0.0573177i	$-0.981745\pi$
$587$	−3.93496	−	14.6855i	−0.162413	−	0.606134i	0.835943	−	0.548817i	$-0.184921\pi$
$588$	11.3125	−	3.03117i	0.466519	−	0.125003i
$589$	0.329246	−	0.570271i	0.0135664	−	0.0234976i
$590$	−13.1059	+	14.3282i	−0.539562	+	0.589882i
$591$			55.7213i			2.29207i
$592$	−4.26916	−	1.14392i	−0.175461	−	0.0470148i
$593$	−0.117227	+	0.0314108i	−0.00481392	+	0.00128989i	−0.261225	−	0.965278i	$-0.584127\pi$
$593$	−0.117227	+	0.0314108i	−0.00481392	+	0.00128989i	0.256411	+	0.966568i	$0.417460\pi$
$594$		−	18.1418i		−	0.744368i
$595$	−16.4111	+	10.4756i	−0.672789	+	0.429456i
$596$	−16.0325	+	9.25636i	−0.656717	+	0.379155i
$597$	16.1413	−	60.2400i	0.660618	−	2.46546i
$598$	25.0928	+	25.0928i	1.02612	+	1.02612i
$599$	−2.47430	+	1.42854i	−0.101097	+	0.0583685i	−0.549696	−	0.835365i	$-0.685257\pi$
$599$	−2.47430	+	1.42854i	−0.101097	+	0.0583685i	0.448599	+	0.893733i	$0.351923\pi$
$600$	10.9958	−	7.72852i	0.448900	−	0.315516i
$601$		−	29.3698i		−	1.19802i	−0.800742	−	0.599009i	$-0.795561\pi$
$601$		−	29.3698i		−	1.19802i	0.800742	−	0.599009i	$-0.204439\pi$
$602$	−8.62779	+	6.26203i	−0.351643	+	0.255221i
$603$	38.9156	−	38.9156i	1.58477	−	1.58477i
$604$	−19.7009			−0.801616
$605$	−1.92390	−	43.1825i	−0.0782176	−	1.75562i
$606$	−6.13904			−0.249381
$607$	−9.48773	−	2.54223i	−0.385095	−	0.103186i	0.0610772	−	0.998133i	$-0.480546\pi$
$607$	−9.48773	−	2.54223i	−0.385095	−	0.103186i	−0.446172	+	0.894947i	$0.647213\pi$
$608$	−5.58922	−	1.49763i	−0.226673	−	0.0607368i
$609$	4.13830	−	7.16775i	0.167692	−	0.290452i
$610$	−3.30402	−	10.4466i	−0.133776	−	0.422970i
$611$	4.06141	−	7.03458i	0.164307	−	0.284588i
$612$	5.85716	−	21.8592i	0.236762	−	0.883607i
$613$	−15.0473	+	15.0473i	−0.607754	+	0.607754i	−0.942359	−	0.334605i	$-0.891397\pi$
$613$	−15.0473	+	15.0473i	−0.607754	+	0.607754i	0.334605	+	0.942359i	$0.391397\pi$
$614$	−8.80329	−	15.2477i	−0.355272	−	0.615349i
$615$	−32.8663	−	7.25560i	−1.32530	−	0.292574i
$616$	4.47680	−	7.75404i	0.180375	−	0.312419i
$617$	−35.7068	+	9.56761i	−1.43750	+	0.385178i	−0.891658	−	0.452709i	$-0.850458\pi$
$617$	−35.7068	+	9.56761i	−1.43750	+	0.385178i	−0.545844	+	0.837887i	$0.683791\pi$
$618$	22.0956	−	22.0956i	0.888817	−	0.888817i
$619$	35.5580	+	20.5294i	1.42920	+	0.825148i	0.997057	−	0.0766588i	$-0.0244252\pi$
$619$	35.5580	+	20.5294i	1.42920	+	0.825148i	0.432140	+	0.901806i	$0.357759\pi$
$620$	−0.136915	−	0.214492i	−0.00549864	−	0.00861420i
$621$	19.2575	−	11.1183i	0.772776	−	0.446162i
$622$	6.73895	+	1.80570i	0.270207	+	0.0724018i
$623$	−3.78567	+	3.78567i	−0.151670	+	0.151670i
$624$	−14.1308			−0.565684
$625$	24.6046	−	4.42883i	0.984183	−	0.177153i
$626$	6.38461	+	11.0585i	0.255180	+	0.441985i
$627$	−82.7423	+	22.1707i	−3.30441	+	0.885414i
$628$	−12.3083	+	3.29800i	−0.491155	+	0.131605i
$629$	−23.6709			−0.943819
$630$	12.9478	−	8.26490i	0.515854	−	0.329281i
$631$	−21.3383	−	12.3197i	−0.849463	−	0.490438i	0.0110066	−	0.999939i	$-0.496496\pi$
$631$	−21.3383	−	12.3197i	−0.849463	−	0.490438i	−0.860470	+	0.509502i	$0.829830\pi$
$632$	−2.00102	−	7.46791i	−0.0795963	−	0.297058i
$633$	2.98364	+	0.799465i	0.118589	+	0.0317759i
$634$	6.44181			0.255837
$635$	29.5997	−	32.3602i	1.17463	−	1.28418i
$636$	−12.4183	−	7.16971i	−0.492418	−	0.284297i
$637$	−16.1957	−	16.1957i	−0.641696	−	0.641696i
$638$	2.69963	+	10.0752i	0.106879	+	0.398879i
$639$	11.7561	+	20.3621i	0.465062	+	0.805511i
$640$	−1.50920	+	1.64995i	−0.0596563	+	0.0652198i
$641$		−	1.76534i		−	0.0697267i	−0.999392	−	0.0348633i	$-0.988900\pi$
$641$		−	1.76534i		−	0.0697267i	0.999392	−	0.0348633i	$-0.0110996\pi$
$642$	0.670064	−	2.50071i	0.0264453	−	0.0986953i
$643$	−15.5740	+	15.5740i	−0.614180	+	0.614180i	−0.944033	−	0.329852i	$-0.893001\pi$
$643$	−15.5740	+	15.5740i	−0.614180	+	0.614180i	0.329852	+	0.944033i	$0.393001\pi$
$644$	10.9745			0.432456
$645$	23.4317	−	31.6928i	0.922622	−	1.24790i
$646$	−30.9901			−1.21929
$647$	−0.313691	+	0.313691i	−0.0123325	+	0.0123325i	−0.713246	−	0.700914i	$-0.752776\pi$
$647$	−0.313691	+	0.313691i	−0.0123325	+	0.0123325i	0.700914	+	0.713246i	$0.252776\pi$
$648$	0.989150	−	3.69156i	0.0388575	−	0.145018i
$649$		−	47.8261i		−	1.87734i
$650$	−23.8418	−	11.0660i	−0.935151	−	0.434043i
$651$	−0.248657	−	0.430686i	−0.00974563	−	0.0168799i
$652$	0.844743	+	3.15262i	0.0330827	+	0.123466i
$653$	−23.1250	−	23.1250i	−0.904952	−	0.904952i	0.0909069	−	0.995859i	$-0.471023\pi$
$653$	−23.1250	−	23.1250i	−0.904952	−	0.904952i	−0.995859	+	0.0909069i	$0.971023\pi$
$654$	−3.88882	−	2.24521i	−0.152065	−	0.0877948i
$655$	−0.563605	+	0.0251101i	−0.0220219	+	0.000981134i
$656$	5.59971			0.218632
$657$	15.2704	+	4.09169i	0.595755	+	0.159632i
$658$	−0.650166	−	2.42645i	−0.0253461	−	0.0945930i
$659$	30.3591	+	17.5278i	1.18262	+	0.682787i	0.956620	−	0.291340i	$-0.0941012\pi$
$659$	30.3591	+	17.5278i	1.18262	+	0.682787i	0.226002	+	0.974127i	$0.427434\pi$
$660$	−7.13594	+	32.3242i	−0.277766	+	1.25822i
$661$	19.1273			0.743965			0.371982	−	0.928240i	$-0.378678\pi$
$661$	19.1273			0.743965			0.371982	+	0.928240i	$0.378678\pi$
$662$	10.1212	−	2.71197i	0.393372	−	0.105404i
$663$	−73.1014	+	19.5875i	−2.83902	+	0.760714i
$664$	−8.78487	−	15.2158i	−0.340919	−	0.590489i
$665$	−15.5214	−	14.1974i	−0.601895	−	0.550550i
$666$	18.6756			0.723665
$667$	−9.04025	+	9.04025i	−0.350040	+	0.350040i
$668$	−10.2371	−	2.74301i	−0.396084	−	0.106130i
$669$	−0.305548	+	0.176408i	−0.0118132	+	0.00682034i
$670$	−24.5488	+	15.6701i	−0.948404	+	0.605387i
$671$	23.3704	+	13.4929i	0.902203	+	0.520887i
$672$	−3.09010	+	3.09010i	−0.119203	+	0.119203i
$673$	31.3257	−	8.39369i	1.20752	−	0.323553i	0.401729	−	0.915759i	$-0.368409\pi$
$673$	31.3257	−	8.39369i	1.20752	−	0.323553i	0.805787	+	0.592206i	$0.201743\pi$
$674$	−0.833938	+	1.44442i	−0.0321221	+	0.0556371i
$675$	−10.5646	+	12.6360i	−0.406631	+	0.486360i
$676$	7.31772	+	12.6747i	0.281451	+	0.487487i
$677$	−11.0185	+	11.0185i	−0.423475	+	0.423475i	−0.886398	−	0.462923i	$-0.846800\pi$
$677$	−11.0185	+	11.0185i	−0.423475	+	0.423475i	0.462923	+	0.886398i	$0.346800\pi$
$678$	3.57224	−	13.3318i	0.137191	−	0.512004i
$679$	3.93400	−	6.81390i	0.150973	−	0.261493i
$680$	−5.52030	+	10.6275i	−0.211694	+	0.407545i
$681$	1.76324	−	3.05402i	0.0675675	−	0.117030i
$682$	0.605383	+	0.162212i	0.0231813	+	0.00621141i
$683$	−10.4222	−	2.79261i	−0.398794	−	0.106856i	0.0538476	−	0.998549i	$-0.482851\pi$
$683$	−10.4222	−	2.79261i	−0.398794	−	0.106856i	−0.452641	+	0.891693i	$0.649518\pi$
$684$	24.4502			0.934878
$685$	31.7101	+	29.0051i	1.21158	+	1.10823i
$686$	−18.4635			−0.704942
$687$	−49.1899	+	49.1899i	−1.87671	+	1.87671i
$688$	−2.67007	+	5.98922i	−0.101796	+	0.228337i
$689$			28.0434i			1.06837i
$690$	−38.6853	+	12.2353i	−1.47273	+	0.465790i
$691$	−26.3385	+	15.2066i	−1.00197	+	0.578485i	−0.908829	−	0.417168i	$-0.863023\pi$
$691$	−26.3385	+	15.2066i	−1.00197	+	0.578485i	−0.0931364	+	0.995653i	$0.529689\pi$
$692$	1.62006	+	1.62006i	0.0615854	+	0.0615854i
$693$	−9.79195	+	36.5441i	−0.371965	+	1.38819i
$694$	−20.1627	+	11.6409i	−0.765364	+	0.441883i
$695$	−14.6259	−	22.9130i	−0.554792	−	0.869141i
$696$		−	5.09094i		−	0.192972i
$697$	28.9684	−	7.76207i	1.09726	−	0.294009i
$698$	12.4908	+	3.34689i	0.472783	+	0.126682i
$699$			58.8777i			2.22696i
$700$	−7.63357	+	2.79379i	−0.288522	+	0.105595i
$701$	15.1029	−	26.1589i	0.570427	−	0.988009i	−0.426095	−	0.904678i	$-0.640111\pi$
$701$	15.1029	−	26.1589i	0.570427	−	0.988009i	0.996522	−	0.0833301i	$-0.0265556\pi$
$702$	16.7269	−	4.48195i	0.631315	−	0.169160i
$703$	−6.61916	−	24.7030i	−0.249646	−	0.931692i
$704$		−	5.50736i		−	0.207566i
$705$	4.99706	+	7.82844i	0.188200	+	0.294836i
$706$	12.8835	+	7.43830i	0.484878	+	0.279944i
$707$	3.58645	+	0.960987i	0.134882	+	0.0361416i
$708$	−6.04159	+	22.5475i	−0.227057	+	0.847387i
$709$			28.9827i			1.08847i	0.838933	+	0.544235i	$0.183180\pi$
$709$			28.9827i			1.08847i	−0.838933	+	0.544235i	$0.816820\pi$
$710$	−3.75203	−	11.8631i	−0.140811	−	0.445214i
$711$	16.3343	+	28.2919i	0.612585	+	1.06103i
$712$	−0.852314	+	3.18088i	−0.0319418	+	0.119209i
$713$	0.198825	+	0.742024i	0.00744604	+	0.0277890i
$714$	−11.7023	+	20.2690i	−0.437949	+	0.758550i
$715$	61.7247	−	19.5221i	2.30837	−	0.730086i
$716$	10.8275	+	6.25125i	0.404642	+	0.233620i
$717$	−0.186738	−	0.696915i	−0.00697385	−	0.0260268i
$718$	−8.85465	+	2.37260i	−0.330453	+	0.0885445i
$719$	30.3625	−	17.5298i	1.13233	−	0.653751i	0.187811	−	0.982205i	$-0.439861\pi$
$719$	30.3625	−	17.5298i	1.13233	−	0.653751i	0.944520	+	0.328454i	$0.106528\pi$
$720$	4.35535	−	8.38476i	0.162314	−	0.312481i
$721$	−16.3672	+	9.44958i	−0.609545	+	0.351921i
$722$	−3.74829	−	13.9888i	−0.139497	−	0.520609i
$723$	−21.9299	+	21.9299i	−0.815582	+	0.815582i
$724$	−8.73818	−	5.04499i	−0.324752	−	0.187496i
$725$	3.98677	−	8.58954i	0.148065	−	0.319008i
$726$	−25.9811	−	45.0005i	−0.964248	−	1.67013i
$727$	−21.5475	+	21.5475i	−0.799152	+	0.799152i	−0.982962	−	0.183810i	$-0.941157\pi$
$727$	−21.5475	+	21.5475i	−0.799152	+	0.799152i	0.183810	+	0.982962i	$0.441157\pi$
$728$	8.25527	+	2.21199i	0.305960	+	0.0819819i
$729$			42.7128i			1.58195i
$730$	−7.42413	−	3.85636i	−0.274779	−	0.142730i
$731$	−5.51083	+	34.6845i	−0.203826	+	1.28285i
$732$	−9.31344	−	9.31344i	−0.344235	−	0.344235i
$733$	−21.3609	−	21.3609i	−0.788981	−	0.788981i	0.192346	−	0.981327i	$-0.438390\pi$
$733$	−21.3609	−	21.3609i	−0.788981	−	0.788981i	−0.981327	+	0.192346i	$0.938390\pi$
$734$	−2.82647	−	4.89558i	−0.104327	−	0.180699i
$735$	24.9687	−	7.89705i	0.920986	−	0.291287i
$736$	5.84603	−	3.37521i	0.215488	−	0.124412i
$737$	18.5653	−	69.2867i	0.683862	−	2.55221i
$738$	−22.8552	+	6.12403i	−0.841312	+	0.225429i
$739$	−4.06085			−0.149381			−0.0746905	−	0.997207i	$-0.523797\pi$
$739$	−4.06085			−0.149381			−0.0746905	+	0.997207i	$0.523797\pi$
$740$	−9.65052	−	2.13046i	−0.354760	−	0.0783173i
$741$	−40.8831	−	70.8116i	−1.50188	−	2.60133i
$742$	6.13250	+	6.13250i	0.225131	+	0.225131i
$743$	11.9537	−	44.6119i	0.438539	−	1.63665i	−0.293913	−	0.955832i	$-0.594958\pi$
$743$	11.9537	−	44.6119i	0.438539	−	1.63665i	0.732452	−	0.680818i	$-0.238376\pi$
$744$	−0.264915	−	0.152949i	−0.00971227	−	0.00560738i
$745$	−34.8930	+	22.2730i	−1.27838	+	0.816018i
$746$	−2.44816	+	4.24035i	−0.0896337	+	0.155250i
$747$	52.4960	+	52.4960i	1.92073	+	1.92073i
$748$	−7.63405	−	28.4906i	−0.279128	−	1.04172i
$749$	−0.782908	+	1.35604i	−0.0286069	+	0.0495485i
$750$	23.7937	−	18.3587i	0.868824	−	0.670366i
$751$	−29.2007	+	16.8591i	−1.06555	+	0.615196i	−0.926962	−	0.375154i	$-0.877590\pi$
$751$	−29.2007	+	16.8591i	−1.06555	+	0.615196i	−0.138588	+	0.990350i	$0.544256\pi$
$752$	−1.09259	−	1.09259i	−0.0398428	−	0.0398428i
$753$	4.74970	+	4.74970i	0.173089	+	0.173089i
$754$	−8.62241	+	4.97815i	−0.314010	+	0.181293i
$755$	−44.0088	+	1.96071i	−1.60164	+	0.0713576i
$756$	2.67770	−	4.63791i	0.0973870	−	0.168679i
$757$	2.82980	+	10.5610i	0.102851	+	0.383845i	0.998093	−	0.0617361i	$-0.0196637\pi$
$757$	2.82980	+	10.5610i	0.102851	+	0.383845i	−0.895242	+	0.445581i	$0.852997\pi$
$758$	8.46818	+	8.46818i	0.307578	+	0.307578i
$759$	49.9663	−	86.5441i	1.81366	−	3.14135i
$760$	−12.6345	−	2.78921i	−0.458303	−	0.101175i
$761$	−7.88754	−	4.55387i	−0.285923	−	0.165078i	0.350179	−	0.936683i	$-0.386121\pi$
$761$	−7.88754	−	4.55387i	−0.285923	−	0.165078i	−0.636102	+	0.771605i	$0.719454\pi$
$762$	13.6449	−	50.9236i	0.494304	−	1.84477i
$763$	1.92041	+	1.92041i	0.0695235	+	0.0695235i
$764$	5.91087	+	10.2379i	0.213848	+	0.370395i
$765$	10.9085	−	49.4132i	0.394398	−	1.78654i
$766$	−0.677107			−0.0244649
$767$	44.0959	−	11.8155i	1.59221	−	0.426632i
$768$	−0.695712	+	2.59643i	−0.0251043	+	0.0936907i
$769$	26.4403	−	15.2653i	0.953463	−	0.550482i	0.0593080	−	0.998240i	$-0.481111\pi$
$769$	26.4403	−	15.2653i	0.953463	−	0.550482i	0.894155	+	0.447758i	$0.147777\pi$
$770$	9.22879	−	17.7669i	0.332582	−	0.640275i
$771$	10.7774	+	18.6670i	0.388139	+	0.672277i
$772$	18.5441	+	18.5441i	0.667418	+	0.667418i
$773$	12.7470	+	12.7470i	0.458479	+	0.458479i	0.898156	−	0.439677i	$-0.144907\pi$
$773$	12.7470	+	12.7470i	0.458479	+	0.458479i	−0.439677	+	0.898156i	$0.644907\pi$
$774$	4.34788	−	27.3650i	0.156281	−	0.983616i
$775$	−0.327195	−	0.465517i	−0.0117532	−	0.0167219i
$776$		−	4.83961i		−	0.173732i
$777$	−18.6565	−	4.99899i	−0.669298	−	0.179338i
$778$	4.52307	−	4.52307i	0.162160	−	0.162160i
$779$	16.2011	+	28.0610i	0.580463	+	1.00539i
$780$	−31.5661	+	1.40635i	−1.13025	+	0.0503556i
$781$	26.5393	+	15.3225i	0.949651	+	0.548281i
$782$	25.5641	−	25.5641i	0.914171	−	0.914171i
$783$	1.61473	+	6.02624i	0.0577056	+	0.215360i
$784$	−3.77321	+	2.17847i	−0.134758	+	0.0778024i
$785$	−27.1667	+	8.59222i	−0.969621	+	0.306669i
$786$	−0.587333	+	0.339097i	−0.0209495	+	0.0120952i
$787$	−49.5323	+	13.2721i	−1.76564	+	0.473101i	−0.987848	−	0.155425i	$-0.950325\pi$
$787$	−49.5323	+	13.2721i	−1.76564	+	0.473101i	−0.777789	+	0.628526i	$0.783659\pi$
$788$	−5.36518	−	20.0231i	−0.191127	−	0.713294i
$789$	10.0110	+	5.77988i	0.356403	+	0.205769i
$790$	−5.21322	−	16.4831i	−0.185478	−	0.586441i
$791$	−4.17384	+	7.22930i	−0.148405	+	0.257044i
$792$	6.02303	+	22.4783i	0.214019	+	0.798730i
$793$	−6.66686	+	24.8810i	−0.236747	+	0.883552i
$794$	2.66253	+	4.61164i	0.0944897	+	0.163661i
$795$	−28.4542	−	14.7801i	−1.00917	−	0.524198i
$796$			23.2011i			0.822340i
$797$	3.10909	−	11.6033i	0.110130	−	0.411010i	−0.888747	−	0.458398i	$-0.848423\pi$
$797$	3.10909	−	11.6033i	0.110130	−	0.411010i	0.998877	+	0.0473888i	$0.0150900\pi$
$798$	−24.4252	−	6.54472i	−0.864644	−	0.231681i
$799$	−7.16671	−	4.13770i	−0.253540	−	0.146381i
$800$	−3.20711	+	3.83594i	−0.113389	+	0.135621i
$801$		−	13.9149i		−	0.491658i
$802$	−0.753143	−	2.81077i	−0.0265944	−	0.0992517i
$803$	19.9030	−	5.33298i	0.702360	−	0.188197i
$804$	−17.5052	+	30.3198i	−0.617360	+	1.06930i
$805$	24.5154	−	1.09223i	0.864055	−	0.0384960i
$806$			0.598241i			0.0210722i
$807$	59.1642	+	15.8530i	2.08268	+	0.558052i
$808$	2.20603	−	0.591103i	0.0776078	−	0.0207949i
$809$		−	9.15551i		−	0.321891i	−0.986963	−	0.160945i	$-0.948546\pi$
$809$		−	9.15551i		−	0.321891i	0.986963	−	0.160945i	$-0.0514543\pi$
$810$	1.84222	−	8.34484i	0.0647289	−	0.293208i
$811$	12.2244	−	7.05775i	0.429256	−	0.247831i	−0.269774	−	0.962924i	$-0.586949\pi$
$811$	12.2244	−	7.05775i	0.429256	−	0.247831i	0.699030	+	0.715093i	$0.253616\pi$
$812$	−0.796921	+	2.97415i	−0.0279664	+	0.104372i
$813$	−35.3401	−	35.3401i	−1.23943	−	1.23943i
$814$	21.0801	−	12.1706i	0.738857	−	0.426579i
$815$	2.20079	+	6.95842i	0.0770904	+	0.243743i
$816$			14.3962i			0.503969i
$817$	−37.7379	+	3.94781i	−1.32028	+	0.138116i
$818$	2.34177	−	2.34177i	0.0818780	−	0.0818780i
$819$	−36.1129			−1.26189
$820$	12.5089	−	0.557307i	0.436831	−	0.0194620i
$821$	−32.4301			−1.13182			−0.565908	−	0.824468i	$-0.691474\pi$
$821$	−32.4301			−1.13182			−0.565908	+	0.824468i	$0.691474\pi$
$822$	49.9006	+	13.3708i	1.74048	+	0.466361i
$823$	−16.1816	−	4.33584i	−0.564055	−	0.151138i	−0.0344861	−	0.999405i	$-0.510979\pi$
$823$	−16.1816	−	4.33584i	−0.564055	−	0.151138i	−0.529568	+	0.848267i	$0.677646\pi$
$824$	−5.81244	+	10.0674i	−0.202486	+	0.350716i
$825$	−12.7236	+	72.9178i	−0.442978	+	2.53867i
$826$	7.05904	−	12.2266i	0.245615	−	0.425418i
$827$	6.96819	−	26.0056i	0.242308	−	0.904304i	−0.732410	−	0.680864i	$-0.761605\pi$
$827$	6.96819	−	26.0056i	0.242308	−	0.904304i	0.974718	−	0.223440i	$-0.0717288\pi$
$828$	−20.1693	+	20.1693i	−0.700932	+	0.700932i
$829$	−6.31378	−	10.9358i	−0.219287	−	0.379815i	0.735304	−	0.677738i	$-0.237040\pi$
$829$	−6.31378	−	10.9358i	−0.219287	−	0.379815i	−0.954590	+	0.297923i	$0.903706\pi$
$830$	−21.1384	−	33.1156i	−0.733726	−	1.14946i
$831$	−14.6444	+	25.3649i	−0.508009	+	0.879898i
$832$	5.07782	−	1.36060i	0.176042	−	0.0471702i
$833$	−16.4999	+	16.4999i	−0.571688	+	0.571688i
$834$	−28.2995	−	16.3387i	−0.979932	−	0.565764i
$835$	−23.1411	−	5.10865i	−0.800830	−	0.176792i
$836$	27.5982	−	15.9338i	0.954505	−	0.551084i
$837$	0.362097	+	0.0970236i	0.0125159	+	0.00335363i
$838$	−2.59983	+	2.59983i	−0.0898097	+	0.0898097i
$839$	−12.9518			−0.447145			−0.223572	−	0.974687i	$-0.571772\pi$
$839$	−12.9518			−0.447145			−0.223572	+	0.974687i	$0.571772\pi$
$840$	−6.59528	+	7.21036i	−0.227559	+	0.248781i
$841$	12.7065	+	22.0083i	0.438155	+	0.758907i
$842$	18.3628	−	4.92030i	0.632824	−	0.169565i
$843$	6.01231	−	1.61099i	0.207075	−	0.0554856i
$844$	−1.14913			−0.0395548
$845$	17.6081	+	27.5850i	0.605738	+	0.948954i
$846$	5.65432	+	3.26452i	0.194400	+	0.112237i
$847$	8.13400	+	30.3565i	0.279487	+	1.04306i
$848$	5.15279	+	1.38068i	0.176947	+	0.0474129i
$849$	81.9678			2.81313
$850$	−11.2738	+	24.2896i	−0.386690	+	0.833127i
$851$	25.8381	+	14.9176i	0.885718	+	0.511369i
$852$	−10.5763	−	10.5763i	−0.362338	−	0.362338i
$853$	5.79545	+	21.6289i	0.198433	+	0.740560i	0.991352	+	0.131233i	$0.0418937\pi$
$853$	5.79545	+	21.6289i	0.198433	+	0.740560i	−0.792919	+	0.609327i	$0.791440\pi$
$854$	3.98305	+	6.89885i	0.136297	+	0.236074i
$855$	54.6182	−	2.43339i	1.86790	−	0.0832201i
$856$			0.963134i			0.0329193i
$857$	−2.08474	+	7.78034i	−0.0712132	+	0.265771i	−0.992348	−	0.123472i	$-0.960597\pi$
$857$	−2.08474	+	7.78034i	−0.0712132	+	0.265771i	0.921135	+	0.389244i	$0.127264\pi$
$858$	55.0294	−	55.0294i	1.87867	−	1.87867i
$859$	12.7190			0.433966			0.216983	−	0.976175i	$-0.430378\pi$
$859$	12.7190			0.433966			0.216983	+	0.976175i	$0.430378\pi$
$860$	−5.36847	+	13.6448i	−0.183063	+	0.465282i
$861$	24.4711			0.833972
$862$	−18.7668	+	18.7668i	−0.639201	+	0.639201i
$863$	13.8721	−	51.7712i	0.472210	−	1.76231i	−0.159593	−	0.987183i	$-0.551018\pi$
$863$	13.8721	−	51.7712i	0.472210	−	1.76231i	0.631803	−	0.775129i	$-0.282315\pi$
$864$		−	3.29411i		−	0.112068i
$865$	3.78021	+	3.45774i	0.128531	+	0.117567i
$866$	13.9485	+	24.1595i	0.473988	+	0.820972i
$867$	8.12829	+	30.3352i	0.276051	+	1.03024i
$868$	0.130822	+	0.130822i	0.00444040	+	0.00444040i
$869$	36.8748	+	21.2896i	1.25089	+	0.722202i
$870$	−0.506671	−	11.3724i	−0.0171778	−	0.385561i
$871$	68.4693			2.32000
$872$	1.61361	+	0.432365i	0.0546437	+	0.0146417i
$873$	5.29276	+	19.7529i	0.179133	+	0.668533i
$874$	33.8274	+	19.5303i	1.14423	+	0.660621i
$875$	−16.7742	+	7.00064i	−0.567072	+	0.236665i
$876$	−10.0569			−0.339791
$877$	−36.9316	+	9.89580i	−1.24709	+	0.334157i	−0.821212	−	0.570623i	$-0.806702\pi$
$877$	−36.9316	+	9.89580i	−1.24709	+	0.334157i	−0.425880	+	0.904780i	$0.640035\pi$
$878$	−16.1084	+	4.31623i	−0.543631	+	0.145666i
$879$	−35.7424	−	61.9076i	−1.20556	−	2.08809i
$880$	−0.548115	−	12.3026i	−0.0184770	−	0.414721i
$881$	−21.7353			−0.732281			−0.366141	−	0.930560i	$-0.619321\pi$
$881$	−21.7353			−0.732281			−0.366141	+	0.930560i	$0.619321\pi$
$882$	13.0179	−	13.0179i	0.438336	−	0.438336i
$883$	−28.3943	−	7.60824i	−0.955546	−	0.256038i	−0.252832	−	0.967510i	$-0.581362\pi$
$883$	−28.3943	−	7.60824i	−0.955546	−	0.256038i	−0.702714	+	0.711473i	$0.748029\pi$
$884$	24.3826	−	14.0773i	0.820074	−	0.473470i
$885$	−11.2520	+	50.9691i	−0.378231	+	1.71331i
$886$	3.44499	+	1.98897i	0.115737	+	0.0668206i
$887$	30.6691	−	30.6691i	1.02977	−	1.02977i	0.0302247	−	0.999543i	$-0.490378\pi$
$887$	30.6691	−	30.6691i	1.02977	−	1.02977i	0.999543	−	0.0302247i	$-0.00962230\pi$
$888$	−11.4756	+	3.07488i	−0.385096	+	0.103186i
$889$	−15.9428	+	27.6138i	−0.534706	+	0.926138i
$890$	−1.58737	+	7.19044i	−0.0532088	+	0.241024i
$891$	10.5240	+	18.2280i	0.352566	+	0.610662i
$892$	0.0928113	−	0.0928113i	0.00310755	−	0.00310755i
$893$	2.31408	−	8.63625i	0.0774376	−	0.289001i
$894$	−24.8813	+	43.0957i	−0.832156	+	1.44134i
$895$	24.8092	+	12.8868i	0.829279	+	0.430757i
$896$	0.812876	−	1.40794i	0.0271563	−	0.0470360i
$897$	92.1384	+	24.6884i	3.07641	+	0.824322i
$898$	16.5110	+	4.42410i	0.550978	+	0.147634i
$899$	−0.215530			−0.00718833
$900$	8.89472	−	19.1638i	0.296491	−	0.638792i
$901$	28.5702			0.951812
$902$	−21.8069	+	21.8069i	−0.726090	+	0.726090i
$903$	−11.6684	+	26.1732i	−0.388299	+	0.870991i
$904$			5.13466i			0.170776i
$905$	−20.0219	−	10.4001i	−0.665551	−	0.345711i
$906$	−45.8616	+	26.4782i	−1.52365	+	0.879679i
$907$	−0.831254	−	0.831254i	−0.0276013	−	0.0276013i	0.693171	−	0.720773i	$-0.256213\pi$
$907$	−0.831254	−	0.831254i	−0.0276013	−	0.0276013i	−0.720773	+	0.693171i	$0.756213\pi$
$908$	−0.339551	+	1.26722i	−0.0112684	+	0.0420542i
$909$	−8.35744	+	4.82517i	−0.277199	+	0.160041i
$910$	18.6612	+	4.11966i	0.618612	+	0.136566i
$911$			43.7800i			1.45049i	0.688488	+	0.725247i	$0.258275\pi$
$911$			43.7800i			1.45049i	−0.688488	+	0.725247i	$0.741725\pi$
$912$	−15.0240	+	4.02566i	−0.497493	+	0.133303i
$913$	93.4657	+	25.0441i	3.09326	+	0.828837i
$914$		−	10.0172i		−	0.331340i
$915$	−21.7318	−	19.8779i	−0.718430	−	0.657144i
$916$	12.9398	−	22.4124i	0.427543	−	0.740526i
$917$	0.396204	−	0.106162i	0.0130838	−	0.00350579i
$918$	−4.56614	−	17.0411i	−0.150705	−	0.562439i
$919$			41.9790i			1.38476i	0.721533	+	0.692381i	$0.243438\pi$
$919$			41.9790i			1.38476i	−0.721533	+	0.692381i	$0.756562\pi$
$920$	12.7233	−	8.12154i	0.419473	−	0.267759i
$921$	−40.9863	−	23.6635i	−1.35055	−	0.779738i
$922$	24.3558	+	6.52612i	0.802116	+	0.214926i
$923$	−7.57086	+	28.2548i	−0.249198	+	0.930019i
$924$		−	24.0675i		−	0.791762i
$925$	−21.7699	−	3.79867i	−0.715789	−	0.124900i
$926$	−20.9983	−	36.3701i	−0.690046	−	1.19519i
$927$	12.7134	−	47.4469i	0.417562	−	1.55836i
$928$	0.490186	+	1.82940i	0.0160911	+	0.0600530i
$929$	−20.7394	+	35.9217i	−0.680438	+	1.17855i	0.294410	+	0.955679i	$0.404877\pi$
$929$	−20.7394	+	35.9217i	−0.680438	+	1.17855i	−0.974847	+	0.222873i	$0.928456\pi$
$930$	−0.607004	−	0.315300i	−0.0199044	−	0.0103391i
$931$	−21.8333	−	12.6054i	−0.715557	−	0.413127i
$932$	−5.66910	−	21.1574i	−0.185697	−	0.693032i
$933$	18.1145	−	4.85376i	0.593041	−	0.158905i
$934$	26.7372	−	15.4367i	0.874868	−	0.505105i
$935$	−19.8888	−	62.8841i	−0.650435	−	2.05653i
$936$	−19.2371	+	11.1065i	−0.628784	+	0.363029i
$937$	−9.64019	−	35.9777i	−0.314931	−	1.17534i	−0.924054	−	0.382263i	$-0.875145\pi$
$937$	−9.64019	−	35.9777i	−0.314931	−	1.17534i	0.609122	−	0.793076i	$-0.291522\pi$
$938$	14.9728	−	14.9728i	0.488878	−	0.488878i
$939$	29.7254	+	17.1620i	0.970052	+	0.560060i
$940$	−2.54943	−	2.33196i	−0.0831534	−	0.0760600i
$941$	−8.10122	−	14.0317i	−0.264092	−	0.457421i	0.703233	−	0.710959i	$-0.251739\pi$
$941$	−8.10122	−	14.0317i	−0.264092	−	0.457421i	−0.967325	+	0.253538i	$0.918406\pi$
$942$	−24.2199	+	24.2199i	−0.789128	+	0.789128i
$943$	−36.5124	−	9.78346i	−1.18901	−	0.318593i
$944$		−	8.68403i		−	0.282641i
$945$	5.52000	−	10.6269i	0.179566	−	0.345693i
$946$	−12.9257	−	33.7218i	−0.420251	−	1.09639i
$947$	−23.5254	−	23.5254i	−0.764474	−	0.764474i	0.212654	−	0.977128i	$-0.431789\pi$
$947$	−23.5254	−	23.5254i	−0.764474	−	0.764474i	−0.977128	+	0.212654i	$0.931789\pi$
$948$	−14.6951	−	14.6951i	−0.477276	−	0.477276i
$949$	9.83408	+	17.0331i	0.319228	+	0.552919i
$950$	−28.5013	−	4.97325i	−0.924704	−	0.161354i
$951$	14.9959	−	8.65787i	0.486275	−	0.280751i
$952$	2.25354	−	8.41033i	0.0730377	−	0.272580i
$953$	40.8382	−	10.9426i	1.32288	−	0.354465i	0.472824	−	0.881157i	$-0.343235\pi$
$953$	40.8382	−	10.9426i	1.32288	−	0.354465i	0.850056	+	0.526692i	$0.176568\pi$
$954$	−22.5410			−0.729793
$955$	14.2229	+	22.2817i	0.460243	+	0.721020i
$956$	0.134206	+	0.232452i	0.00434054	+	0.00751804i
$957$	19.8256	+	19.8256i	0.640870	+	0.640870i
$958$	2.96116	−	11.0512i	0.0956707	−	0.357048i
$959$	−27.0591	−	15.6226i	−0.873784	−	0.504479i
$960$	−1.29571	+	5.86929i	−0.0418189	+	0.189430i
$961$	15.4935	−	26.8356i	0.499791	−	0.865664i
$962$	16.4292	+	16.4292i	0.529699	+	0.529699i
$963$	−1.05332	−	3.93103i	−0.0339426	−	0.126676i
$964$	5.76884	−	9.99192i	0.185802	−	0.321818i
$965$	43.2704	+	39.5792i	1.39292	+	1.27410i
$966$	25.5475	−	14.7499i	0.821978	−	0.474569i
$967$	−28.1345	−	28.1345i	−0.904745	−	0.904745i	0.0910975	−	0.995842i	$-0.470963\pi$
$967$	−28.1345	−	28.1345i	−0.904745	−	0.904745i	−0.995842	+	0.0910975i	$0.970963\pi$
$968$	13.6691	+	13.6691i	0.439340	+	0.439340i
$969$	−72.1417	+	41.6511i	−2.31753	+	1.33802i
$970$	−0.481658	−	10.8110i	−0.0154651	−	0.347120i
$971$	−13.5951	+	23.5474i	−0.436287	+	0.755672i	−0.997400	−	0.0720677i	$-0.977040\pi$
$971$	−13.5951	+	23.5474i	−0.436287	+	0.755672i	0.561112	+	0.827740i	$0.310374\pi$
$972$	−5.21659	−	19.4686i	−0.167322	−	0.624455i
$973$	13.9751	+	13.9751i	0.448020	+	0.448020i
$974$	−9.94542	+	17.2260i	−0.318672	+	0.551956i
$975$	−70.3740	+	6.28318i	−2.25377	+	0.201223i
$976$	4.24348	+	2.44998i	0.135831	+	0.0784218i
$977$	−8.33414	+	31.1034i	−0.266633	+	0.995087i	0.694611	+	0.719386i	$0.255577\pi$
$977$	−8.33414	+	31.1034i	−0.266633	+	0.995087i	−0.961243	+	0.275701i	$0.911090\pi$
$978$	6.20364	+	6.20364i	0.198371	+	0.198371i
$979$	−9.06811	−	15.7064i	−0.289818	−	0.501980i
$980$	−8.21199	+	5.24190i	−0.262322	+	0.167446i
$981$	−7.05879			−0.225370
$982$	−32.0558	+	8.58932i	−1.02294	+	0.274096i
$983$	−3.04108	+	11.3495i	−0.0969953	+	0.361991i	−0.997314	−	0.0732390i	$-0.976666\pi$
$983$	−3.04108	+	11.3495i	−0.0969953	+	0.361991i	0.900319	+	0.435230i	$0.143333\pi$
$984$	13.0356	−	7.52608i	0.415558	−	0.239923i
$985$	−13.9778	−	44.1947i	−0.445370	−	1.40816i
$986$	5.07166	+	8.78437i	0.161515	+	0.279751i
$987$	−4.77470	−	4.77470i	−0.151980	−	0.151980i
$988$	21.5093	+	21.5093i	0.684301	+	0.684301i
$989$	27.8739	−	34.3871i	0.886339	−	1.09345i
$990$	15.6917	+	49.6137i	0.498715	+	1.57683i
$991$		−	21.7594i		−	0.691211i	−0.938380	−	0.345605i	$-0.887674\pi$
$991$		−	21.7594i		−	0.691211i	0.938380	−	0.345605i	$-0.112326\pi$
$992$	0.109923	+	0.0294537i	0.00349005	+	0.000935155i
$993$	19.9162	−	19.9162i	0.632022	−	0.632022i
$994$	4.52314	+	7.83431i	0.143465	+	0.248489i
$995$	2.30907	+	51.8278i	0.0732023	+	1.64305i
$996$	−40.9005	−	23.6139i	−1.29598	−	0.748236i
$997$	8.56229	−	8.56229i	0.271171	−	0.271171i	−0.558401	−	0.829571i	$-0.688585\pi$
$997$	8.56229	−	8.56229i	0.271171	−	0.271171i	0.829571	+	0.558401i	$0.188585\pi$
$998$	6.18521	+	23.0835i	0.195789	+	0.730696i
$999$	12.6086	−	7.27959i	0.398919	−	0.230316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.l.a.7.1	✓	88
5.3	odd	4	inner	430.2.l.a.93.12	yes	88
43.37	odd	6	inner	430.2.l.a.37.12	yes	88
215.123	even	12	inner	430.2.l.a.123.1	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.l.a.7.1	✓	88	1.1	even	1	trivial
430.2.l.a.37.12	yes	88	43.37	odd	6	inner
430.2.l.a.93.12	yes	88	5.3	odd	4	inner
430.2.l.a.123.1	yes	88	215.123	even	12	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.695712 + 2.59643i) q^{3} -1.00000i q^{4} +(-0.0995241 - 2.23385i) q^{5} +(-1.34401 - 2.32790i) q^{6} +(0.420775 + 1.57036i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.65937 - 2.11274i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.695712 + 2.59643i) q^{3} -1.00000i q^{4} +(-0.0995241 - 2.23385i) q^{5} +(-1.34401 - 2.32790i) q^{6} +(0.420775 + 1.57036i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.65937 - 2.11274i) q^{9} +(1.64995 + 1.50920i) q^{10} -5.50736 q^{11} +(2.59643 + 0.695712i) q^{12} +(-1.36060 - 5.07782i) q^{13} +(-1.40794 - 0.812876i) q^{14} +(5.86929 + 1.29571i) q^{15} -1.00000 q^{16} +(-5.17320 + 1.38615i) q^{17} +(4.08150 - 1.09363i) q^{18} +(-2.89319 - 5.01116i) q^{19} +(-2.23385 + 0.0995241i) q^{20} -4.37006 q^{21} +(3.89429 - 3.89429i) q^{22} +(6.52040 + 1.74714i) q^{23} +(-2.32790 + 1.34401i) q^{24} +(-4.98019 + 0.444644i) q^{25} +(4.55264 + 2.62847i) q^{26} +(2.32929 - 2.32929i) q^{27} +(1.57036 - 0.420775i) q^{28} +(-0.946967 + 1.64019i) q^{29} +(-5.06642 + 3.23401i) q^{30} +(0.0569001 + 0.0985539i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.83153 - 14.2995i) q^{33} +(2.67784 - 4.63816i) q^{34} +(3.46606 - 1.09624i) q^{35} +(-2.11274 + 3.65937i) q^{36} +(4.26916 + 1.14392i) q^{37} +(5.58922 + 1.49763i) q^{38} +14.1308 q^{39} +(1.50920 - 1.64995i) q^{40} -5.59971 q^{41} +(3.09010 - 3.09010i) q^{42} +(2.67007 - 5.98922i) q^{43} +5.50736i q^{44} +(-4.35535 + 8.38476i) q^{45} +(-5.84603 + 3.37521i) q^{46} +(1.09259 + 1.09259i) q^{47} +(0.695712 - 2.59643i) q^{48} +(3.77321 - 2.17847i) q^{49} +(3.20711 - 3.83594i) q^{50} -14.3962i q^{51} +(-5.07782 + 1.36060i) q^{52} +(-5.15279 - 1.38068i) q^{53} +3.29411i q^{54} +(0.548115 + 12.3026i) q^{55} +(-0.812876 + 1.40794i) q^{56} +(15.0240 - 4.02566i) q^{57} +(-0.490186 - 1.82940i) q^{58} +8.68403i q^{59} +(1.29571 - 5.86929i) q^{60} +(-4.24348 - 2.44998i) q^{61} +(-0.109923 - 0.0294537i) q^{62} +(1.77798 - 6.63550i) q^{63} +1.00000i q^{64} +(-11.2077 + 3.54474i) q^{65} +(7.40195 + 12.8206i) q^{66} +(-3.37100 + 12.5808i) q^{67} +(1.38615 + 5.17320i) q^{68} +(-9.07264 + 15.7143i) q^{69} +(-1.67572 + 3.22603i) q^{70} +(-4.81888 - 2.78218i) q^{71} +(-1.09363 - 4.08150i) q^{72} +(-3.61389 + 0.968338i) q^{73} +(-3.82763 + 2.20988i) q^{74} +(2.31029 - 13.2401i) q^{75} +(-5.01116 + 2.89319i) q^{76} +(-2.31736 - 8.64851i) q^{77} +(-9.99198 + 9.99198i) q^{78} +(-6.69555 - 3.86567i) q^{79} +(0.0995241 + 2.23385i) q^{80} +(-1.91089 - 3.30976i) q^{81} +(3.95960 - 3.95960i) q^{82} +(-16.9711 - 4.54738i) q^{83} +4.37006i q^{84} +(3.61132 + 11.4182i) q^{85} +(2.34699 + 6.12304i) q^{86} +(-3.59984 - 3.59984i) q^{87} +(-3.89429 - 3.89429i) q^{88} +(1.64655 + 2.85190i) q^{89} +(-2.84922 - 9.00862i) q^{90} +(7.40147 - 4.27324i) q^{91} +(1.74714 - 6.52040i) q^{92} +(-0.295475 + 0.0791722i) q^{93} -1.54516 q^{94} +(-10.9062 + 6.96170i) q^{95} +(1.34401 + 2.32790i) q^{96} +(-3.42212 - 3.42212i) q^{97} +(-1.12766 + 4.20847i) q^{98} +(20.1535 + 11.6356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) \) 88 * q + 4 * q^6 + 12 * q^7	\( 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) \) 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

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