LMFDB - Embedded newform 403.2.i.a.216.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(216,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("403.216");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.i (of order $4$, 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 $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			216.15
Character	$\chi$	$=$	403.216
Dual form			403.2.i.a.278.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.459282 - 0.459282i) q^{2} -0.325710i q^{3} -1.57812i q^{4} +(-0.464951 - 0.464951i) q^{5} +(-0.149593 + 0.149593i) q^{6} +(2.03738 - 2.03738i) q^{7} +(-1.64337 + 1.64337i) q^{8} +2.89391 q^{9} +O(q^{10})$	\(q+(-0.459282 - 0.459282i) q^{2} -0.325710i q^{3} -1.57812i q^{4} +(-0.464951 - 0.464951i) q^{5} +(-0.149593 + 0.149593i) q^{6} +(2.03738 - 2.03738i) q^{7} +(-1.64337 + 1.64337i) q^{8} +2.89391 q^{9} +0.427088i q^{10} +(2.38794 + 2.38794i) q^{11} -0.514009 q^{12} +(2.76830 - 2.31009i) q^{13} -1.87146 q^{14} +(-0.151439 + 0.151439i) q^{15} -1.64670 q^{16} -7.78833 q^{17} +(-1.32912 - 1.32912i) q^{18} +(-5.44541 - 5.44541i) q^{19} +(-0.733748 + 0.733748i) q^{20} +(-0.663594 - 0.663594i) q^{21} -2.19348i q^{22} +5.34650 q^{23} +(0.535261 + 0.535261i) q^{24} -4.56764i q^{25} +(-2.33242 - 0.210452i) q^{26} -1.91971i q^{27} +(-3.21522 - 3.21522i) q^{28} +0.875257i q^{29} +0.139107 q^{30} +(-3.90491 + 3.96884i) q^{31} +(4.04303 + 4.04303i) q^{32} +(0.777777 - 0.777777i) q^{33} +(3.57705 + 3.57705i) q^{34} -1.89456 q^{35} -4.56694i q^{36} +(3.16262 + 3.16262i) q^{37} +5.00196i q^{38} +(-0.752417 - 0.901664i) q^{39} +1.52817 q^{40} +(2.74764 + 2.74764i) q^{41} +0.609554i q^{42} -2.68610 q^{43} +(3.76846 - 3.76846i) q^{44} +(-1.34553 - 1.34553i) q^{45} +(-2.45556 - 2.45556i) q^{46} +(4.11103 - 4.11103i) q^{47} +0.536346i q^{48} -1.30181i q^{49} +(-2.09784 + 2.09784i) q^{50} +2.53674i q^{51} +(-3.64559 - 4.36871i) q^{52} -10.8423i q^{53} +(-0.881687 + 0.881687i) q^{54} -2.22055i q^{55} +6.69632i q^{56} +(-1.77362 + 1.77362i) q^{57} +(0.401990 - 0.401990i) q^{58} +(-3.51223 + 3.51223i) q^{59} +(0.238989 + 0.238989i) q^{60} +9.92428i q^{61} +(3.61627 - 0.0293647i) q^{62} +(5.89599 - 5.89599i) q^{63} -0.420393i q^{64} +(-2.36120 - 0.213049i) q^{65} -0.714438 q^{66} +(5.11275 + 5.11275i) q^{67} +12.2909i q^{68} -1.74141i q^{69} +(0.870139 + 0.870139i) q^{70} +(3.48425 + 3.48425i) q^{71} +(-4.75576 + 4.75576i) q^{72} +(5.88914 + 5.88914i) q^{73} -2.90508i q^{74} -1.48773 q^{75} +(-8.59350 + 8.59350i) q^{76} +9.73029 q^{77} +(-0.0685462 + 0.759690i) q^{78} -13.1227i q^{79} +(0.765635 + 0.765635i) q^{80} +8.05647 q^{81} -2.52389i q^{82} +(-3.25726 + 3.25726i) q^{83} +(-1.04723 + 1.04723i) q^{84} +(3.62120 + 3.62120i) q^{85} +(1.23368 + 1.23368i) q^{86} +0.285080 q^{87} -7.84854 q^{88} +(-6.17262 - 6.17262i) q^{89} +1.23596i q^{90} +(0.933564 - 10.3466i) q^{91} -8.43742i q^{92} +(1.29269 + 1.27187i) q^{93} -3.77625 q^{94} +5.06370i q^{95} +(1.31686 - 1.31686i) q^{96} +(9.90572 + 9.90572i) q^{97} +(-0.597900 + 0.597900i) q^{98} +(6.91050 + 6.91050i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9}+O(q^{10}) $ 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9	$ 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9} - 48 q^{14} - 40 q^{16} + 4 q^{18} - 24 q^{19} - 16 q^{20} + 44 q^{28} + 24 q^{31} + 28 q^{32} - 40 q^{35} - 24 q^{39} + 24 q^{40} + 20 q^{41} - 24 q^{45} - 36 q^{47} + 80 q^{50} + 28 q^{59} - 76 q^{63} + 152 q^{66} - 32 q^{67} - 48 q^{70} + 20 q^{71} - 32 q^{72} + 72 q^{76} + 84 q^{78} - 20 q^{80} + 52 q^{81} - 112 q^{87} - 8 q^{93} - 16 q^{94} - 4 q^{97} - 92 q^{98}+O(q^{100}) $ 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9 - 48 * q^14 - 40 * q^16 + 4 * q^18 - 24 * q^19 - 16 * q^20 + 44 * q^28 + 24 * q^31 + 28 * q^32 - 40 * q^35 - 24 * q^39 + 24 * q^40 + 20 * q^41 - 24 * q^45 - 36 * q^47 + 80 * q^50 + 28 * q^59 - 76 * q^63 + 152 * q^66 - 32 * q^67 - 48 * q^70 + 20 * q^71 - 32 * q^72 + 72 * q^76 + 84 * q^78 - 20 * q^80 + 52 * q^81 - 112 * q^87 - 8 * q^93 - 16 * q^94 - 4 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.459282	−	0.459282i	−0.324762	−	0.324762i	0.525829	−	0.850590i	$-0.323755\pi$
$2$	−0.459282	−	0.459282i	−0.324762	−	0.324762i	−0.850590	+	0.525829i	$0.823755\pi$
$3$		−	0.325710i		−	0.188049i	−0.995570	−	0.0940243i	$-0.970027\pi$
$3$		−	0.325710i		−	0.188049i	0.995570	−	0.0940243i	$-0.0299731\pi$
$4$		−	1.57812i		−	0.789060i
$5$	−0.464951	−	0.464951i	−0.207933	−	0.207933i	0.595456	−	0.803388i	$-0.296972\pi$
$5$	−0.464951	−	0.464951i	−0.207933	−	0.207933i	−0.803388	+	0.595456i	$0.796972\pi$
$6$	−0.149593	+	0.149593i	−0.0610710	+	0.0610710i
$7$	2.03738	−	2.03738i	0.770056	−	0.770056i	−0.208060	−	0.978116i	$-0.566715\pi$
$7$	2.03738	−	2.03738i	0.770056	−	0.770056i	0.978116	+	0.208060i	$0.0667149\pi$
$8$	−1.64337	+	1.64337i	−0.581018	+	0.581018i
$9$	2.89391			0.964638
$10$			0.427088i			0.135057i
$11$	2.38794	+	2.38794i	0.719992	+	0.719992i	0.968603	−	0.248611i	$-0.0799741\pi$
$11$	2.38794	+	2.38794i	0.719992	+	0.719992i	−0.248611	+	0.968603i	$0.579974\pi$
$12$	−0.514009			−0.148382
$13$	2.76830	−	2.31009i	0.767789	−	0.640702i
$13$	2.76830	−	2.31009i	0.767789	−	0.640702i
$14$	−1.87146			−0.500170
$15$	−0.151439	+	0.151439i	−0.0391014	+	0.0391014i
$16$	−1.64670			−0.411675
$17$	−7.78833			−1.88895			−0.944474	−	0.328585i	$-0.893428\pi$
$17$	−7.78833			−1.88895			−0.944474	+	0.328585i	$0.893428\pi$
$18$	−1.32912	−	1.32912i	−0.313277	−	0.313277i
$19$	−5.44541	−	5.44541i	−1.24926	−	1.24926i	−0.956046	−	0.293215i	$-0.905275\pi$
$19$	−5.44541	−	5.44541i	−1.24926	−	1.24926i	−0.293215	−	0.956046i	$-0.594725\pi$
$20$	−0.733748	+	0.733748i	−0.164071	+	0.164071i
$21$	−0.663594	−	0.663594i	−0.144808	−	0.144808i
$22$		−	2.19348i		−	0.467652i
$23$	5.34650			1.11482			0.557412	−	0.830236i	$-0.311795\pi$
$23$	5.34650			1.11482			0.557412	+	0.830236i	$0.311795\pi$
$24$	0.535261	+	0.535261i	0.109260	+	0.109260i
$25$		−	4.56764i		−	0.913528i
$26$	−2.33242	−	0.210452i	−0.457424	−	0.0412730i
$27$		−	1.91971i		−	0.369447i
$28$	−3.21522	−	3.21522i	−0.607620	−	0.607620i
$29$			0.875257i			0.162531i	0.996692	+	0.0812656i	$0.0258962\pi$
$29$			0.875257i			0.162531i	−0.996692	+	0.0812656i	$0.974104\pi$
$30$	0.139107			0.0253973
$31$	−3.90491	+	3.96884i	−0.701342	+	0.712825i
$31$	−3.90491	+	3.96884i	−0.701342	+	0.712825i
$32$	4.04303	+	4.04303i	0.714714	+	0.714714i
$33$	0.777777	−	0.777777i	0.135394	−	0.135394i
$34$	3.57705	+	3.57705i	0.613458	+	0.613458i
$35$	−1.89456			−0.320239
$36$		−	4.56694i		−	0.761157i
$37$	3.16262	+	3.16262i	0.519932	+	0.519932i	0.917551	−	0.397619i	$-0.130163\pi$
$37$	3.16262	+	3.16262i	0.519932	+	0.519932i	−0.397619	+	0.917551i	$0.630163\pi$
$38$			5.00196i			0.811425i
$39$	−0.752417	−	0.901664i	−0.120483	−	0.144382i
$40$	1.52817			0.241625
$41$	2.74764	+	2.74764i	0.429110	+	0.429110i	0.888325	−	0.459215i	$-0.151869\pi$
$41$	2.74764	+	2.74764i	0.429110	+	0.429110i	−0.459215	+	0.888325i	$0.651869\pi$
$42$			0.609554i			0.0940562i
$43$	−2.68610			−0.409626			−0.204813	−	0.978801i	$-0.565659\pi$
$43$	−2.68610			−0.409626			−0.204813	+	0.978801i	$0.565659\pi$
$44$	3.76846	−	3.76846i	0.568117	−	0.568117i
$45$	−1.34553	−	1.34553i	−0.200580	−	0.200580i
$46$	−2.45556	−	2.45556i	−0.362052	−	0.362052i
$47$	4.11103	−	4.11103i	0.599655	−	0.599655i	−0.340565	−	0.940221i	$-0.610619\pi$
$47$	4.11103	−	4.11103i	0.599655	−	0.599655i	0.940221	+	0.340565i	$0.110619\pi$
$48$			0.536346i			0.0774149i
$49$		−	1.30181i		−	0.185973i
$50$	−2.09784	+	2.09784i	−0.296679	+	0.296679i
$51$			2.53674i			0.355214i
$52$	−3.64559	−	4.36871i	−0.505552	−	0.605832i
$53$		−	10.8423i		−	1.48931i	−0.667451	−	0.744654i	$-0.732615\pi$
$53$		−	10.8423i		−	1.48931i	0.667451	−	0.744654i	$-0.267385\pi$
$54$	−0.881687	+	0.881687i	−0.119982	+	0.119982i
$55$		−	2.22055i		−	0.299420i
$56$			6.69632i			0.894833i
$57$	−1.77362	+	1.77362i	−0.234922	+	0.234922i
$58$	0.401990	−	0.401990i	0.0527839	−	0.0527839i
$59$	−3.51223	+	3.51223i	−0.457254	+	0.457254i	−0.897753	−	0.440499i	$-0.854801\pi$
$59$	−3.51223	+	3.51223i	−0.457254	+	0.457254i	0.440499	+	0.897753i	$0.354801\pi$
$60$	0.238989	+	0.238989i	0.0308534	+	0.0308534i
$61$			9.92428i			1.27067i	0.772235	+	0.635337i	$0.219139\pi$
$61$			9.92428i			1.27067i	−0.772235	+	0.635337i	$0.780861\pi$
$62$	3.61627	−	0.0293647i	0.459267	−	0.00372933i
$63$	5.89599	−	5.89599i	0.742825	−	0.742825i
$64$		−	0.420393i		−	0.0525491i
$65$	−2.36120	−	0.213049i	−0.292871	−	0.0264255i
$66$	−0.714438			−0.0879413
$67$	5.11275	+	5.11275i	0.624622	+	0.624622i	0.946710	−	0.322088i	$-0.104385\pi$
$67$	5.11275	+	5.11275i	0.624622	+	0.624622i	−0.322088	+	0.946710i	$0.604385\pi$
$68$			12.2909i			1.49049i
$69$		−	1.74141i		−	0.209641i
$70$	0.870139	+	0.870139i	0.104002	+	0.104002i
$71$	3.48425	+	3.48425i	0.413505	+	0.413505i	0.882957	−	0.469453i	$-0.155549\pi$
$71$	3.48425	+	3.48425i	0.413505	+	0.413505i	−0.469453	+	0.882957i	$0.655549\pi$
$72$	−4.75576	+	4.75576i	−0.560472	+	0.560472i
$73$	5.88914	+	5.88914i	0.689272	+	0.689272i	0.962071	−	0.272799i	$-0.0879493\pi$
$73$	5.88914	+	5.88914i	0.689272	+	0.689272i	−0.272799	+	0.962071i	$0.587949\pi$
$74$		−	2.90508i		−	0.337708i
$75$	−1.48773			−0.171788
$76$	−8.59350	+	8.59350i	−0.985742	+	0.985742i
$77$	9.73029			1.10887
$78$	−0.0685462	+	0.759690i	−0.00776133	+	0.0860180i
$79$		−	13.1227i		−	1.47642i	−0.674572	−	0.738209i	$-0.735672\pi$
$79$		−	13.1227i		−	1.47642i	0.674572	−	0.738209i	$-0.264328\pi$
$80$	0.765635	+	0.765635i	0.0856005	+	0.0856005i
$81$	8.05647			0.895164
$82$		−	2.52389i		−	0.278717i
$83$	−3.25726	+	3.25726i	−0.357531	+	0.357531i	−0.862902	−	0.505371i	$-0.831356\pi$
$83$	−3.25726	+	3.25726i	−0.357531	+	0.357531i	0.505371	+	0.862902i	$0.331356\pi$
$84$	−1.04723	+	1.04723i	−0.114262	+	0.114262i
$85$	3.62120	+	3.62120i	0.392774	+	0.392774i
$86$	1.23368	+	1.23368i	0.133031	+	0.133031i
$87$	0.285080			0.0305638
$88$	−7.84854			−0.836657
$89$	−6.17262	−	6.17262i	−0.654296	−	0.654296i	0.299728	−	0.954025i	$-0.403104\pi$
$89$	−6.17262	−	6.17262i	−0.654296	−	0.654296i	−0.954025	+	0.299728i	$0.903104\pi$
$90$			1.23596i			0.130281i
$91$	0.933564	−	10.3466i	0.0978641	−	1.08462i
$92$		−	8.43742i		−	0.879662i
$93$	1.29269	+	1.27187i	0.134046	+	0.131886i
$94$	−3.77625			−0.389490
$95$			5.06370i			0.519524i
$96$	1.31686	−	1.31686i	0.134401	−	0.134401i
$97$	9.90572	+	9.90572i	1.00577	+	1.00577i	0.999983	+	0.00579059i	$0.00184321\pi$
$97$	9.90572	+	9.90572i	1.00577	+	1.00577i	0.00579059	+	0.999983i	$0.498157\pi$
$98$	−0.597900	+	0.597900i	−0.0603970	+	0.0603970i
$99$	6.91050	+	6.91050i	0.694532	+	0.694532i
$100$	−7.20828			−0.720828
$101$			11.1891i			1.11336i	0.830728	+	0.556678i	$0.187924\pi$
$101$			11.1891i			1.11336i	−0.830728	+	0.556678i	$0.812076\pi$
$102$	1.16508	−	1.16508i	0.115360	−	0.115360i
$103$		−	6.39694i		−	0.630309i	−0.949040	−	0.315154i	$-0.897944\pi$
$103$		−	6.39694i		−	0.630309i	0.949040	−	0.315154i	$-0.102056\pi$
$104$	−0.753021	+	8.34566i	−0.0738398	+	0.818359i
$105$			0.617077i			0.0602206i
$106$	−4.97969	+	4.97969i	−0.483670	+	0.483670i
$107$	11.6894			1.13006			0.565030	−	0.825071i	$-0.308865\pi$
$107$	11.6894			1.13006			0.565030	+	0.825071i	$0.308865\pi$
$108$	−3.02952			−0.291516
$109$	6.24617	+	6.24617i	0.598275	+	0.598275i	0.939853	−	0.341578i	$-0.110961\pi$
$109$	6.24617	+	6.24617i	0.598275	+	0.598275i	−0.341578	+	0.939853i	$0.610961\pi$
$110$	−1.01986	+	1.01986i	−0.0972400	+	0.0972400i
$111$	1.03010	−	1.03010i	0.0977725	−	0.0977725i
$112$	−3.35495	+	3.35495i	−0.317013	+	0.317013i
$113$	7.70219			0.724561			0.362281	−	0.932069i	$-0.381998\pi$
$113$	7.70219			0.724561			0.362281	+	0.932069i	$0.381998\pi$
$114$	1.62919			0.152587
$115$	−2.48586	−	2.48586i	−0.231808	−	0.231808i
$116$	1.38126			0.128247
$117$	8.01123	−	6.68519i	0.740639	−	0.618046i
$118$	3.22621			0.296997
$119$	−15.8678	+	15.8678i	−1.45460	+	1.45460i
$120$		−	0.497740i		−	0.0454373i
$121$			0.404553i			0.0367775i
$122$	4.55805	−	4.55805i	0.412666	−	0.412666i
$123$	0.894934	−	0.894934i	0.0806935	−	0.0806935i
$124$	6.26331	+	6.16241i	0.562461	+	0.553401i
$125$	−4.44849	+	4.44849i	−0.397885	+	0.397885i
$126$	−5.41585			−0.482482
$127$	−16.2554			−1.44243			−0.721215	−	0.692711i	$-0.756416\pi$
$127$	−16.2554			−1.44243			−0.721215	+	0.692711i	$0.756416\pi$
$128$	7.89299	−	7.89299i	0.697648	−	0.697648i
$129$			0.874889i			0.0770296i
$130$	0.986609	+	1.18231i	0.0865314	+	0.103695i
$131$	−3.89217			−0.340060			−0.170030	−	0.985439i	$-0.554387\pi$
$131$	−3.89217			−0.340060			−0.170030	+	0.985439i	$0.554387\pi$
$132$	−1.22742	−	1.22742i	−0.106834	−	0.106834i
$133$	−22.1887			−1.92400
$134$		−	4.69639i		−	0.405707i
$135$	−0.892569	+	0.892569i	−0.0768201	+	0.0768201i
$136$	12.7991	−	12.7991i	1.09751	−	1.09751i
$137$	5.96336	+	5.96336i	0.509484	+	0.509484i	0.914368	−	0.404884i	$-0.132688\pi$
$137$	5.96336	+	5.96336i	0.509484	+	0.509484i	−0.404884	+	0.914368i	$0.632688\pi$
$138$	−0.799798	+	0.799798i	−0.0680834	+	0.0680834i
$139$		−	5.51661i		−	0.467913i	−0.972247	−	0.233957i	$-0.924833\pi$
$139$		−	5.51661i		−	0.467913i	0.972247	−	0.233957i	$-0.0751673\pi$
$140$			2.98984i			0.252688i
$141$	−1.33900	−	1.33900i	−0.112764	−	0.112764i
$142$		−	3.20051i		−	0.268581i
$143$	12.1269	+	1.09420i	1.01410	+	0.0915016i
$144$	−4.76540			−0.397117
$145$	0.406952	−	0.406952i	0.0337955	−	0.0337955i
$146$		−	5.40956i		−	0.447699i
$147$	−0.424013			−0.0349720
$148$	4.99100	−	4.99100i	0.410258	−	0.410258i
$149$	1.34729	+	1.34729i	0.110374	+	0.110374i	0.760137	−	0.649763i	$-0.225132\pi$
$149$	1.34729	+	1.34729i	0.110374	+	0.110374i	−0.649763	+	0.760137i	$0.725132\pi$
$150$	0.683286	+	0.683286i	0.0557901	+	0.0557901i
$151$	8.86728	+	8.86728i	0.721609	+	0.721609i	0.968933	−	0.247324i	$-0.0795511\pi$
$151$	8.86728	+	8.86728i	0.721609	+	0.721609i	−0.247324	+	0.968933i	$0.579551\pi$
$152$	17.8976			1.45169
$153$	−22.5388			−1.82215
$154$	−4.46895	−	4.46895i	−0.360118	−	0.360118i
$155$	3.66091	−	0.0297272i	0.294051	−	0.00238775i
$156$	−1.42293	+	1.18740i	−0.113926	+	0.0950684i
$157$	7.25386			0.578921			0.289461	−	0.957190i	$-0.406524\pi$
$157$	7.25386			0.578921			0.289461	+	0.957190i	$0.406524\pi$
$158$	−6.02702	+	6.02702i	−0.479484	+	0.479484i
$159$	−3.53145			−0.280062
$160$		−	3.75963i		−	0.297225i
$161$	10.8928	−	10.8928i	0.858476	−	0.858476i
$162$	−3.70020	−	3.70020i	−0.290715	−	0.290715i
$163$	6.76164	−	6.76164i	0.529613	−	0.529613i	−0.390844	−	0.920457i	$-0.627817\pi$
$163$	6.76164	−	6.76164i	0.529613	−	0.529613i	0.920457	+	0.390844i	$0.127817\pi$
$164$	4.33611	−	4.33611i	0.338593	−	0.338593i
$165$	−0.723256			−0.0563054
$166$	2.99201			0.232225
$167$	10.9564	+	10.9564i	0.847829	+	0.847829i	0.989862	−	0.142033i	$-0.0453639\pi$
$167$	10.9564	+	10.9564i	0.847829	+	0.847829i	−0.142033	+	0.989862i	$0.545364\pi$
$168$	2.18106			0.168272
$169$	2.32701	−	12.7900i	0.179001	−	0.983849i
$170$		−	3.32630i		−	0.255116i
$171$	−15.7585	−	15.7585i	−1.20509	−	1.20509i
$172$			4.23898i			0.323219i
$173$			9.30588i			0.707513i	0.935338	+	0.353756i	$0.115096\pi$
$173$			9.30588i			0.707513i	−0.935338	+	0.353756i	$0.884904\pi$
$174$	−0.130932	−	0.130932i	−0.00992594	−	0.00992594i
$175$	−9.30601	−	9.30601i	−0.703468	−	0.703468i
$176$	−3.93222	−	3.93222i	−0.296403	−	0.296403i
$177$	1.14397	+	1.14397i	0.0859859	+	0.0859859i
$178$			5.66995i			0.424981i
$179$	−7.98090			−0.596521			−0.298260	−	0.954485i	$-0.596406\pi$
$179$	−7.98090			−0.596521			−0.298260	+	0.954485i	$0.596406\pi$
$180$	−2.12340	+	2.12340i	−0.158269	+	0.158269i
$181$	−5.12095			−0.380637			−0.190319	−	0.981722i	$-0.560952\pi$
$181$	−5.12095			−0.380637			−0.190319	+	0.981722i	$0.560952\pi$
$182$	−5.18078	+	4.32324i	−0.384025	+	0.320460i
$183$	3.23244			0.238949
$184$	−8.78627	+	8.78627i	−0.647732	+	0.647732i
$185$		−	2.94093i		−	0.216222i
$186$	−0.00956439	−	1.17786i	−0.000701295	−	0.0863646i
$187$	−18.5981	−	18.5981i	−1.36003	−	1.36003i
$188$	−6.48769	−	6.48769i	−0.473164	−	0.473164i
$189$	−3.91116	−	3.91116i	−0.284495	−	0.284495i
$190$	2.32567	−	2.32567i	0.168722	−	0.168722i
$191$	−16.1362			−1.16758			−0.583788	−	0.811906i	$-0.698430\pi$
$191$	−16.1362			−1.16758			−0.583788	+	0.811906i	$0.698430\pi$
$192$	−0.136926			−0.00988178
$193$	−2.80934	+	2.80934i	−0.202220	+	0.202220i	−0.800951	−	0.598730i	$-0.795672\pi$
$193$	−2.80934	+	2.80934i	−0.202220	+	0.202220i	0.598730	+	0.800951i	$0.295672\pi$
$194$		−	9.09905i		−	0.653274i
$195$	−0.0693922	+	0.769067i	−0.00496928	+	0.0550740i
$196$	−2.05442			−0.146744
$197$	0.200033	−	0.200033i	0.0142517	−	0.0142517i	−0.699945	−	0.714197i	$-0.746792\pi$
$197$	0.200033	−	0.200033i	0.0142517	−	0.0142517i	0.714197	+	0.699945i	$0.246792\pi$
$198$		−	6.34775i		−	0.451115i
$199$	19.8643			1.40814			0.704071	−	0.710129i	$-0.251364\pi$
$199$	19.8643			1.40814			0.704071	+	0.710129i	$0.251364\pi$
$200$	7.50631	+	7.50631i	0.530776	+	0.530776i
$201$	1.66527	−	1.66527i	0.117459	−	0.117459i
$202$	5.13895	−	5.13895i	0.361576	−	0.361576i
$203$	1.78323	+	1.78323i	0.125158	+	0.125158i
$204$	4.00327			0.280285
$205$		−	2.55504i		−	0.178452i
$206$	−2.93800	+	2.93800i	−0.204700	+	0.204700i
$207$	15.4723			1.07540
$208$	−4.55856	+	3.80401i	−0.316079	+	0.263761i
$209$		−	26.0066i		−	1.79892i
$210$	0.283413	−	0.283413i	0.0195573	−	0.0195573i
$211$	−10.1826			−0.701001			−0.350501	−	0.936563i	$-0.613989\pi$
$211$	−10.1826			−0.701001			−0.350501	+	0.936563i	$0.613989\pi$
$212$	−17.1105			−1.17515
$213$	1.13485	−	1.13485i	0.0777590	−	0.0777590i
$214$	−5.36875	−	5.36875i	−0.367000	−	0.367000i
$215$	1.24890	+	1.24890i	0.0851746	+	0.0851746i
$216$	3.15478	+	3.15478i	0.214656	+	0.214656i
$217$	0.130262	+	16.0418i	0.00884276	+	1.08899i
$218$		−	5.73752i		−	0.388594i
$219$	1.91815	−	1.91815i	0.129617	−	0.129617i
$220$	−3.50430			−0.236260
$221$	−21.5605	+	17.9917i	−1.45031	+	1.21025i
$222$	−0.946212			−0.0635056
$223$	3.73161	−	3.73161i	0.249887	−	0.249887i	−0.571037	−	0.820924i	$-0.693459\pi$
$223$	3.73161	−	3.73161i	0.249887	−	0.249887i	0.820924	+	0.571037i	$0.193459\pi$
$224$	16.4744			1.10074
$225$		−	13.2184i		−	0.881224i
$226$	−3.53748	−	3.53748i	−0.235310	−	0.235310i
$227$	−12.6618	−	12.6618i	−0.840390	−	0.840390i	0.148519	−	0.988910i	$-0.452549\pi$
$227$	−12.6618	−	12.6618i	−0.840390	−	0.840390i	−0.988910	+	0.148519i	$0.952549\pi$
$228$	2.79899	+	2.79899i	0.185367	+	0.185367i
$229$	−2.89955	−	2.89955i	−0.191607	−	0.191607i	0.604783	−	0.796390i	$-0.293260\pi$
$229$	−2.89955	−	2.89955i	−0.191607	−	0.191607i	−0.796390	+	0.604783i	$0.793260\pi$
$230$			2.28343i			0.150565i
$231$		−	3.16925i		−	0.208521i
$232$	−1.43837	−	1.43837i	−0.0944336	−	0.0944336i
$233$			15.2203i			0.997117i	0.866856	+	0.498559i	$0.166137\pi$
$233$			15.2203i			0.997117i	−0.866856	+	0.498559i	$0.833863\pi$
$234$	−6.74981	−	0.609029i	−0.441249	−	0.0398135i
$235$	−3.82286			−0.249376
$236$	5.54272	+	5.54272i	0.360800	+	0.360800i
$237$	−4.27419			−0.277638
$238$	14.5756			0.944795
$239$	−0.0313922	+	0.0313922i	−0.00203059	+	0.00203059i	−0.708121	−	0.706091i	$-0.750457\pi$
$239$	−0.0313922	+	0.0313922i	−0.00203059	+	0.00203059i	0.706091	+	0.708121i	$0.250457\pi$
$240$	0.249375	−	0.249375i	0.0160971	−	0.0160971i
$241$	15.8732	+	15.8732i	1.02248	+	1.02248i	0.999741	+	0.0227415i	$0.00723947\pi$
$241$	15.8732	+	15.8732i	1.02248	+	1.02248i	0.0227415	+	0.999741i	$0.492761\pi$
$242$	0.185804	−	0.185804i	0.0119439	−	0.0119439i
$243$		−	8.38319i		−	0.537782i
$244$	15.6617			1.00264
$245$	−0.605280	+	0.605280i	−0.0386699	+	0.0386699i
$246$	−0.822055			−0.0524123
$247$	−27.6539	−	2.49519i	−1.75957	−	0.158765i
$248$	−0.105071	−	12.9395i	−0.00667199	−	0.821657i
$249$	1.06092	+	1.06092i	0.0672332	+	0.0672332i
$250$	4.08622			0.258435
$251$	−17.1216			−1.08071			−0.540354	−	0.841438i	$-0.681710\pi$
$251$	−17.1216			−1.08071			−0.540354	+	0.841438i	$0.681710\pi$
$252$	−9.30458	−	9.30458i	−0.586133	−	0.586133i
$253$	12.7672	+	12.7672i	0.802664	+	0.802664i
$254$	7.46580	+	7.46580i	0.468446	+	0.468446i
$255$	1.17946	−	1.17946i	0.0738606	−	0.0738606i
$256$	−8.09101			−0.505688
$257$		−	6.21633i		−	0.387764i	−0.981025	−	0.193882i	$-0.937892\pi$
$257$		−	6.21633i		−	0.387764i	0.981025	−	0.193882i	$-0.0621079\pi$
$258$	0.401821	−	0.401821i	0.0250163	−	0.0250163i
$259$	12.8869			0.800754
$260$	−0.336217	+	3.72626i	−0.0208513	+	0.231093i
$261$			2.53292i			0.156784i
$262$	1.78760	+	1.78760i	0.110439	+	0.110439i
$263$		−	11.1155i		−	0.685414i	−0.939442	−	0.342707i	$-0.888656\pi$
$263$		−	11.1155i		−	0.685414i	0.939442	−	0.342707i	$-0.111344\pi$
$264$			2.55635i			0.157332i
$265$	−5.04115	+	5.04115i	−0.309675	+	0.309675i
$266$	10.1909	+	10.1909i	0.624843	+	0.624843i
$267$	−2.01048	+	2.01048i	−0.123040	+	0.123040i
$268$	8.06853	−	8.06853i	0.492864	−	0.492864i
$269$			32.2497i			1.96630i	0.182804	+	0.983149i	$0.441483\pi$
$269$			32.2497i			1.96630i	−0.182804	+	0.983149i	$0.558517\pi$
$270$	0.819883			0.0498965
$271$	−15.4548	−	15.4548i	−0.938811	−	0.938811i	0.0594217	−	0.998233i	$-0.481074\pi$
$271$	−15.4548	−	15.4548i	−0.938811	−	0.938811i	−0.998233	+	0.0594217i	$0.981074\pi$
$272$	12.8250			0.777632
$273$	−3.36999	−	0.304071i	−0.203961	−	0.0184032i
$274$		−	5.47773i		−	0.330922i
$275$	10.9073	−	10.9073i	0.657733	−	0.657733i
$276$	−2.74815			−0.165419
$277$	−28.7890			−1.72977			−0.864883	−	0.501973i	$-0.832608\pi$
$277$	−28.7890			−1.72977			−0.864883	+	0.501973i	$0.832608\pi$
$278$	−2.53368	+	2.53368i	−0.151960	+	0.151960i
$279$	−11.3005	+	11.4855i	−0.676541	+	0.687618i
$280$	3.11346	−	3.11346i	0.186065	−	0.186065i
$281$	−13.6968	+	13.6968i	−0.817084	+	0.817084i	−0.985684	−	0.168601i	$-0.946075\pi$
$281$	−13.6968	+	13.6968i	−0.817084	+	0.817084i	0.168601	+	0.985684i	$0.446075\pi$
$282$			1.22996i			0.0732431i
$283$		−	24.0983i		−	1.43249i	−0.697847	−	0.716247i	$-0.745859\pi$
$283$		−	24.0983i		−	1.43249i	0.697847	−	0.716247i	$-0.254141\pi$
$284$	5.49856	−	5.49856i	0.326280	−	0.326280i
$285$	1.64930			0.0976958
$286$	−5.06713	−	6.07222i	−0.299626	−	0.359058i
$287$	11.1960			0.660877
$288$	11.7002	+	11.7002i	0.689440	+	0.689440i
$289$	43.6582			2.56813
$290$	−0.373812			−0.0219510
$291$	3.22639	−	3.22639i	0.189134	−	0.189134i
$292$	9.29377	−	9.29377i	0.543877	−	0.543877i
$293$	−8.40718	+	8.40718i	−0.491153	+	0.491153i	−0.908669	−	0.417517i	$-0.862901\pi$
$293$	−8.40718	+	8.40718i	−0.491153	+	0.491153i	0.417517	+	0.908669i	$0.362901\pi$
$294$	0.194742	+	0.194742i	0.0113576	+	0.0113576i
$295$	3.26603			0.190156
$296$	−10.3947			−0.604180
$297$	4.58415	−	4.58415i	0.265999	−	0.265999i
$298$		−	1.23757i		−	0.0716907i
$299$	14.8007	−	12.3509i	0.855949	−	0.714270i
$300$			2.34781i			0.135551i
$301$	−5.47260	+	5.47260i	−0.315435	+	0.315435i
$302$		−	8.14518i		−	0.468702i
$303$	3.64440			0.209365
$304$	8.96694	+	8.96694i	0.514289	+	0.514289i
$305$	4.61431	−	4.61431i	0.264214	−	0.264214i
$306$	10.3517	+	10.3517i	0.591765	+	0.591765i
$307$	1.80186	−	1.80186i	0.102837	−	0.102837i	−0.653816	−	0.756653i	$-0.726833\pi$
$307$	1.80186	−	1.80186i	0.102837	−	0.102837i	0.756653	+	0.653816i	$0.226833\pi$
$308$		−	15.3556i		−	0.874964i
$309$	−2.08354			−0.118529
$310$	−1.69504	−	1.66774i	−0.0962721	−	0.0947212i
$311$			19.9037i			1.12864i	0.825557	+	0.564319i	$0.190861\pi$
$311$			19.9037i			1.12864i	−0.825557	+	0.564319i	$0.809139\pi$
$312$	2.71826	+	0.245266i	0.153891	+	0.0138855i
$313$		−	13.6456i		−	0.771298i	−0.922646	−	0.385649i	$-0.873978\pi$
$313$		−	13.6456i		−	0.771298i	0.922646	−	0.385649i	$-0.126022\pi$
$314$	−3.33157	−	3.33157i	−0.188012	−	0.188012i
$315$	−5.48270			−0.308915
$316$	−20.7092			−1.16498
$317$	12.7390	+	12.7390i	0.715496	+	0.715496i	0.967679	−	0.252183i	$-0.0811486\pi$
$317$	12.7390	+	12.7390i	0.715496	+	0.715496i	−0.252183	+	0.967679i	$0.581149\pi$
$318$	1.62193	+	1.62193i	0.0909535	+	0.0909535i
$319$	−2.09007	+	2.09007i	−0.117021	+	0.117021i
$320$	−0.195462	+	0.195462i	−0.0109267	+	0.0109267i
$321$		−	3.80736i		−	0.212506i
$322$	−10.0058			−0.557601
$323$	42.4106	+	42.4106i	2.35979	+	2.35979i
$324$		−	12.7141i		−	0.706337i
$325$	−10.5516	−	12.6446i	−0.585300	−	0.701397i
$326$	−6.21101			−0.343996
$327$	2.03444	−	2.03444i	0.112505	−	0.112505i
$328$	−9.03078			−0.498641
$329$		−	16.7514i		−	0.923537i
$330$	0.332179	+	0.332179i	0.0182859	+	0.0182859i
$331$	−6.99107	+	6.99107i	−0.384264	+	0.384264i	−0.872636	−	0.488372i	$-0.837591\pi$
$331$	−6.99107	+	6.99107i	−0.384264	+	0.384264i	0.488372	+	0.872636i	$0.337591\pi$
$332$	5.14035	+	5.14035i	0.282113	+	0.282113i
$333$	9.15236	+	9.15236i	0.501546	+	0.501546i
$334$		−	10.0641i		−	0.550685i
$335$		−	4.75436i		−	0.259758i
$336$	1.09274	+	1.09274i	0.0596138	+	0.0596138i
$337$	30.5774			1.66566			0.832829	−	0.553530i	$-0.186720\pi$
$337$	30.5774			1.66566			0.832829	+	0.553530i	$0.186720\pi$
$338$	−6.94300	+	4.80548i	−0.377649	+	0.261384i
$339$		−	2.50868i		−	0.136253i
$340$	5.71468	−	5.71468i	0.309922	−	0.309922i
$341$	−18.8021	+	0.152676i	−1.01819	+	0.00826786i
$342$			14.4752i			0.782731i
$343$	11.6094	+	11.6094i	0.626846	+	0.626846i
$344$	4.41425	−	4.41425i	0.238000	−	0.238000i
$345$	−0.809670	+	0.809670i	−0.0435912	+	0.0435912i
$346$	4.27403	−	4.27403i	0.229773	−	0.229773i
$347$		−	7.18851i		−	0.385899i	−0.981209	−	0.192950i	$-0.938195\pi$
$347$		−	7.18851i		−	0.385899i	0.981209	−	0.192950i	$-0.0618054\pi$
$348$		−	0.449890i		−	0.0241166i
$349$	−21.5985	+	21.5985i	−1.15614	+	1.15614i	−0.170846	+	0.985298i	$0.554650\pi$
$349$	−21.5985	+	21.5985i	−1.15614	+	1.15614i	−0.985298	+	0.170846i	$0.945350\pi$
$350$			8.54817i			0.456919i
$351$	−4.43468	−	5.31433i	−0.236706	−	0.283658i
$352$			19.3091i			1.02918i
$353$	−20.3138	+	20.3138i	−1.08120	+	1.08120i	−0.0847985	+	0.996398i	$0.527025\pi$
$353$	−20.3138	+	20.3138i	−1.08120	+	1.08120i	−0.996398	+	0.0847985i	$0.972975\pi$
$354$		−	1.05081i		−	0.0558499i
$355$		−	3.24001i		−	0.171962i
$356$	−9.74113	+	9.74113i	−0.516279	+	0.516279i
$357$	5.16829	+	5.16829i	0.273535	+	0.273535i
$358$	3.66549	+	3.66549i	0.193727	+	0.193727i
$359$	−4.06486	+	4.06486i	−0.214535	+	0.214535i	−0.806191	−	0.591656i	$-0.798474\pi$
$359$	−4.06486	+	4.06486i	−0.214535	+	0.214535i	0.591656	+	0.806191i	$0.298474\pi$
$360$	4.42240			0.233081
$361$			40.3049i			2.12131i
$362$	2.35196	+	2.35196i	0.123616	+	0.123616i
$363$	0.131767			0.00691596
$364$	−16.3282	−	1.47328i	−0.855828	−	0.0772206i
$365$		−	5.47633i		−	0.286644i
$366$	−1.48460	−	1.48460i	−0.0776013	−	0.0776013i
$367$		−	14.6523i		−	0.764846i	−0.923987	−	0.382423i	$-0.875090\pi$
$367$		−	14.6523i		−	0.764846i	0.923987	−	0.382423i	$-0.124910\pi$
$368$	−8.80408			−0.458944
$369$	7.95144	+	7.95144i	0.413936	+	0.413936i
$370$	−1.35072	+	1.35072i	−0.0702205	+	0.0702205i
$371$	−22.0899	−	22.0899i	−1.14685	−	1.14685i
$372$	2.00716	−	2.04002i	0.104066	−	0.105770i
$373$	7.41803			0.384091			0.192046	−	0.981386i	$-0.438488\pi$
$373$	7.41803			0.384091			0.192046	+	0.981386i	$0.438488\pi$
$374$			17.0836i			0.883370i
$375$	1.44892	+	1.44892i	0.0748217	+	0.0748217i
$376$			13.5119i			0.696821i
$377$	2.02192	+	2.42298i	0.104134	+	0.124790i
$378$			3.59266i			0.184786i
$379$	13.7969	+	13.7969i	0.708698	+	0.708698i	0.966261	−	0.257563i	$-0.0829195\pi$
$379$	13.7969	+	13.7969i	0.708698	+	0.708698i	−0.257563	+	0.966261i	$0.582920\pi$
$380$	7.99112			0.409936
$381$			5.29453i			0.271247i
$382$	7.41108	+	7.41108i	0.379184	+	0.379184i
$383$	20.3158	−	20.3158i	1.03809	−	1.03809i	0.0388443	−	0.999245i	$-0.487632\pi$
$383$	20.3158	−	20.3158i	1.03809	−	1.03809i	0.999245	−	0.0388443i	$-0.0123676\pi$
$384$	−2.57082	−	2.57082i	−0.131192	−	0.131192i
$385$	−4.52411	−	4.52411i	−0.230570	−	0.230570i
$386$	2.58056			0.131347
$387$	−7.77334			−0.395141
$388$	15.6324	−	15.6324i	0.793615	−	0.793615i
$389$	−9.83932			−0.498873			−0.249437	−	0.968391i	$-0.580245\pi$
$389$	−9.83932			−0.498873			−0.249437	+	0.968391i	$0.580245\pi$
$390$	0.385090	−	0.321348i	0.0194998	−	0.0162721i
$391$	−41.6404			−2.10584
$392$	2.13936	+	2.13936i	0.108054	+	0.108054i
$393$			1.26772i			0.0639479i
$394$	−0.183743			−0.00925684
$395$	−6.10141	+	6.10141i	−0.306995	+	0.306995i
$396$	10.9056	−	10.9056i	0.548027	−	0.548027i
$397$	−3.18603	+	3.18603i	−0.159902	+	0.159902i	−0.782523	−	0.622621i	$-0.786068\pi$
$397$	−3.18603	+	3.18603i	−0.159902	+	0.159902i	0.622621	+	0.782523i	$0.286068\pi$
$398$	−9.12332	−	9.12332i	−0.457311	−	0.457311i
$399$			7.22707i			0.361806i
$400$			7.52153i			0.376076i
$401$	12.3617	+	12.3617i	0.617312	+	0.617312i	0.944841	−	0.327529i	$-0.106216\pi$
$401$	12.3617	+	12.3617i	0.617312	+	0.617312i	−0.327529	+	0.944841i	$0.606216\pi$
$402$	−1.52966			−0.0762926
$403$	−1.64160	+	20.0076i	−0.0817740	+	0.996651i
$404$	17.6577			0.878504
$405$	−3.74587	−	3.74587i	−0.186134	−	0.186134i
$406$		−	1.63801i		−	0.0812932i
$407$			15.1043i			0.748694i
$408$	−4.16879	−	4.16879i	−0.206386	−	0.206386i
$409$	21.3388	−	21.3388i	1.05514	−	1.05514i	0.0567464	−	0.998389i	$-0.481927\pi$
$409$	21.3388	−	21.3388i	1.05514	−	1.05514i	0.998389	−	0.0567464i	$-0.0180727\pi$
$410$	−1.17349	+	1.17349i	−0.0579543	+	0.0579543i
$411$	1.94232	−	1.94232i	0.0958078	−	0.0958078i
$412$	−10.0951			−0.497351
$413$			14.3115i			0.704222i
$414$	−7.10616	−	7.10616i	−0.349249	−	0.349249i
$415$	3.02894			0.148685
$416$	20.5321	+	1.85259i	1.00667	+	0.0908309i
$417$	−1.79681			−0.0879904
$418$	−11.9444	+	11.9444i	−0.584220	+	0.584220i
$419$	−20.1286			−0.983345			−0.491673	−	0.870780i	$-0.663614\pi$
$419$	−20.1286			−0.983345			−0.491673	+	0.870780i	$0.663614\pi$
$420$	0.973822			0.0475176
$421$	−15.9725	−	15.9725i	−0.778453	−	0.778453i	0.201114	−	0.979568i	$-0.435544\pi$
$421$	−15.9725	−	15.9725i	−0.778453	−	0.778453i	−0.979568	+	0.201114i	$0.935544\pi$
$422$	4.67670	+	4.67670i	0.227658	+	0.227658i
$423$	11.8970	−	11.8970i	0.578450	−	0.578450i
$424$	17.8179	+	17.8179i	0.865315	+	0.865315i
$425$			35.5743i			1.72561i
$426$	−1.04244			−0.0505063
$427$	20.2195	+	20.2195i	0.978491	+	0.978491i
$428$		−	18.4473i		−	0.891684i
$429$	0.356392	−	3.94985i	0.0172068	−	0.190701i
$430$		−	1.14720i		−	0.0553229i
$431$	−24.4283	−	24.4283i	−1.17667	−	1.17667i	−0.980588	−	0.196082i	$-0.937178\pi$
$431$	−24.4283	−	24.4283i	−1.17667	−	1.17667i	−0.196082	−	0.980588i	$-0.562822\pi$
$432$			3.16118i			0.152092i
$433$	7.23782			0.347827			0.173914	−	0.984761i	$-0.444359\pi$
$433$	7.23782			0.347827			0.173914	+	0.984761i	$0.444359\pi$
$434$	7.30789	−	7.42754i	0.350790	−	0.356533i
$435$	−0.132548	−	0.132548i	−0.00635520	−	0.00635520i
$436$	9.85721	−	9.85721i	0.472075	−	0.472075i
$437$	−29.1139	−	29.1139i	−1.39271	−	1.39271i
$438$	−1.76195			−0.0841891
$439$		−	14.6807i		−	0.700674i	−0.936624	−	0.350337i	$-0.886067\pi$
$439$		−	14.6807i		−	0.700674i	0.936624	−	0.350337i	$-0.113933\pi$
$440$	3.64919	+	3.64919i	0.173968	+	0.173968i
$441$		−	3.76733i		−	0.179397i
$442$	18.1656	+	1.63907i	0.864051	+	0.0779626i
$443$	23.2313			1.10375			0.551875	−	0.833927i	$-0.313912\pi$
$443$	23.2313			1.10375			0.551875	+	0.833927i	$0.313912\pi$
$444$	−1.62562	−	1.62562i	−0.0771484	−	0.0771484i
$445$			5.73993i			0.272099i
$446$	−3.42772			−0.162307
$447$	0.438825	−	0.438825i	0.0207557	−	0.0207557i
$448$	−0.856498	−	0.856498i	−0.0404657	−	0.0404657i
$449$	−7.20941	−	7.20941i	−0.340233	−	0.340233i	0.516222	−	0.856455i	$-0.327338\pi$
$449$	−7.20941	−	7.20941i	−0.340233	−	0.340233i	−0.856455	+	0.516222i	$0.827338\pi$
$450$	−6.07096	+	6.07096i	−0.286188	+	0.286188i
$451$			13.1224i			0.617911i
$452$		−	12.1550i		−	0.571722i
$453$	2.88816	−	2.88816i	0.135698	−	0.135698i
$454$			11.6306i			0.545853i
$455$	−5.24472	+	4.37660i	−0.245876	+	0.205178i
$456$		−	5.82942i		−	0.272988i
$457$	14.9112	−	14.9112i	0.697515	−	0.697515i	−0.266359	−	0.963874i	$-0.585821\pi$
$457$	14.9112	−	14.9112i	0.697515	−	0.697515i	0.963874	+	0.266359i	$0.0858206\pi$
$458$			2.66342i			0.124453i
$459$			14.9513i			0.697867i
$460$	−3.92299	+	3.92299i	−0.182910	+	0.182910i
$461$	1.95552	−	1.95552i	0.0910777	−	0.0910777i	−0.660100	−	0.751178i	$-0.729486\pi$
$461$	1.95552	−	1.95552i	0.0910777	−	0.0910777i	0.751178	+	0.660100i	$0.229486\pi$
$462$	−1.45558	+	1.45558i	−0.0677197	+	0.0677197i
$463$	−7.85383	−	7.85383i	−0.364998	−	0.364998i	0.500651	−	0.865649i	$-0.333094\pi$
$463$	−7.85383	−	7.85383i	−0.364998	−	0.364998i	−0.865649	+	0.500651i	$0.833094\pi$
$464$		−	1.44129i		−	0.0669100i
$465$	−0.00968243	−	1.19239i	−0.000449012	−	0.0552959i
$466$	6.99043	−	6.99043i	0.323826	−	0.323826i
$467$		−	37.2287i		−	1.72274i	−0.507980	−	0.861369i	$-0.669608\pi$
$467$		−	37.2287i		−	1.72274i	0.507980	−	0.861369i	$-0.330392\pi$
$468$	−10.5500	−	12.6427i	−0.487675	−	0.584408i
$469$	20.8332			0.961988
$470$	1.75577	+	1.75577i	0.0809877	+	0.0809877i
$471$		−	2.36265i		−	0.108865i
$472$		−	11.5438i		−	0.531345i
$473$	−6.41425	−	6.41425i	−0.294928	−	0.294928i
$474$	1.96306	+	1.96306i	0.0901663	+	0.0901663i
$475$	−24.8727	+	24.8727i	−1.14124	+	1.14124i
$476$	25.0412	+	25.0412i	1.14776	+	1.14776i
$477$		−	31.3767i		−	1.43664i
$478$	0.0288358			0.00131892
$479$	−21.9052	+	21.9052i	−1.00087	+	1.00087i	−0.000874478		1.00000i	$0.500278\pi$
$479$	−21.9052	+	21.9052i	−1.00087	+	1.00087i	−1.00000		0.000874478i	$0.999722\pi$
$480$	−1.22455			−0.0558927
$481$	16.0610	+	1.44917i	0.732320	+	0.0660766i
$482$		−	14.5806i		−	0.664127i
$483$	−3.54791	−	3.54791i	−0.161435	−	0.161435i
$484$	0.638433			0.0290197
$485$		−	9.21136i		−	0.418266i
$486$	−3.85025	+	3.85025i	−0.174651	+	0.174651i
$487$	−13.8581	+	13.8581i	−0.627970	+	0.627970i	−0.947557	−	0.319587i	$-0.896456\pi$
$487$	−13.8581	+	13.8581i	−0.627970	+	0.627970i	0.319587	+	0.947557i	$0.396456\pi$
$488$	−16.3092	−	16.3092i	−0.738285	−	0.738285i
$489$	−2.20233	−	2.20233i	−0.0995929	−	0.0995929i
$490$	0.555989			0.0251170
$491$	−32.6082			−1.47159			−0.735793	−	0.677207i	$-0.763190\pi$
$491$	−32.6082			−1.47159			−0.735793	+	0.677207i	$0.763190\pi$
$492$	−1.41231	−	1.41231i	−0.0636720	−	0.0636720i
$493$		−	6.81680i		−	0.307013i
$494$	11.5550	+	13.8469i	0.519882	+	0.623003i
$495$		−	6.42609i		−	0.288831i
$496$	6.43020	−	6.53549i	0.288725	−	0.293452i
$497$	14.1975			0.636844
$498$		−	0.974526i		−	0.0436696i
$499$	−18.2950	+	18.2950i	−0.818996	+	0.818996i	−0.985963	−	0.166967i	$-0.946603\pi$
$499$	−18.2950	+	18.2950i	−0.818996	+	0.818996i	0.166967	+	0.985963i	$0.446603\pi$
$500$	7.02024	+	7.02024i	0.313955	+	0.313955i
$501$	3.56859	−	3.56859i	0.159433	−	0.159433i
$502$	7.86367	+	7.86367i	0.350973	+	0.350973i
$503$	−25.6811			−1.14506			−0.572532	−	0.819882i	$-0.694039\pi$
$503$	−25.6811			−1.14506			−0.572532	+	0.819882i	$0.694039\pi$
$504$			19.3786i			0.863190i
$505$	5.20238	−	5.20238i	0.231503	−	0.231503i
$506$		−	11.7275i		−	0.521349i
$507$	−4.16584	−	0.757931i	−0.185011	−	0.0336609i
$508$			25.6529i			1.13816i
$509$	−3.57902	+	3.57902i	−0.158637	+	0.158637i	−0.781963	−	0.623325i	$-0.785781\pi$
$509$	−3.57902	+	3.57902i	−0.158637	+	0.158637i	0.623325	+	0.781963i	$0.285781\pi$
$510$	−1.08341			−0.0479742
$511$	23.9968			1.06156
$512$	−12.0699	−	12.0699i	−0.533420	−	0.533420i
$513$	−10.4536	+	10.4536i	−0.461537	+	0.461537i
$514$	−2.85505	+	2.85505i	−0.125931	+	0.125931i
$515$	−2.97426	+	2.97426i	−0.131062	+	0.131062i
$516$	1.38068			0.0607810
$517$	19.6338			0.863494
$518$	−5.91874	−	5.91874i	−0.260054	−	0.260054i
$519$	3.03102			0.133047
$520$	4.23044	−	3.53021i	0.185517	−	0.154810i
$521$	−8.58286			−0.376022			−0.188011	−	0.982167i	$-0.560204\pi$
$521$	−8.58286			−0.376022			−0.188011	+	0.982167i	$0.560204\pi$
$522$	1.16333	−	1.16333i	0.0509174	−	0.0509174i
$523$			16.8123i			0.735151i	0.929994	+	0.367575i	$0.119812\pi$
$523$			16.8123i			0.735151i	−0.929994	+	0.367575i	$0.880188\pi$
$524$			6.14231i			0.268328i
$525$	−3.03106	+	3.03106i	−0.132286	+	0.132286i
$526$	−5.10518	+	5.10518i	−0.222596	+	0.222596i
$527$	30.4127	−	30.9107i	1.32480	−	1.34649i
$528$	−1.28076	+	1.28076i	−0.0557381	+	0.0557381i
$529$	5.58510			0.242830
$530$	4.63062			0.201141
$531$	−10.1641	+	10.1641i	−0.441084	+	0.441084i
$532$			35.0164i			1.51815i
$533$	13.9536	+	1.25902i	0.604398	+	0.0545343i
$534$	1.84676			0.0799171
$535$	−5.43501	−	5.43501i	−0.234976	−	0.234976i
$536$	−16.8043			−0.725833
$537$			2.59946i			0.112175i
$538$	14.8117	−	14.8117i	0.638579	−	0.638579i
$539$	3.10866	−	3.10866i	0.133899	−	0.133899i
$540$	1.40858	+	1.40858i	0.0606157	+	0.0606157i
$541$	−3.36679	+	3.36679i	−0.144750	+	0.144750i	−0.775768	−	0.631018i	$-0.782637\pi$
$541$	−3.36679	+	3.36679i	−0.144750	+	0.144750i	0.631018	+	0.775768i	$0.282637\pi$
$542$			14.1962i			0.609780i
$543$			1.66794i			0.0715783i
$544$	−31.4885	−	31.4885i	−1.35006	−	1.35006i
$545$		−	5.80833i		−	0.248802i
$546$	1.40812	+	1.68743i	0.0602620	+	0.0722154i
$547$	2.72065			0.116326			0.0581632	−	0.998307i	$-0.481476\pi$
$547$	2.72065			0.116326			0.0581632	+	0.998307i	$0.481476\pi$
$548$	9.41089	−	9.41089i	0.402013	−	0.402013i
$549$			28.7200i			1.22574i
$550$	−10.0190			−0.427213
$551$	4.76613	−	4.76613i	0.203044	−	0.203044i
$552$	2.86177	+	2.86177i	0.121805	+	0.121805i
$553$	−26.7359	−	26.7359i	−1.13692	−	1.13692i
$554$	13.2223	+	13.2223i	0.561762	+	0.561762i
$555$	−0.957890			−0.0406602
$556$	−8.70587			−0.369211
$557$	−28.3046	−	28.3046i	−1.19931	−	1.19931i	−0.974375	−	0.224931i	$-0.927784\pi$
$557$	−28.3046	−	28.3046i	−1.19931	−	1.19931i	−0.224931	−	0.974375i	$-0.572216\pi$
$558$	10.4652	−	0.0849790i	0.443027	−	0.00359745i
$559$	−7.43594	+	6.20512i	−0.314507	+	0.262448i
$560$	3.11977			0.131834
$561$	−6.05759	+	6.05759i	−0.255751	+	0.255751i
$562$	12.5814			0.530715
$563$		−	22.0524i		−	0.929396i	−0.885469	−	0.464698i	$-0.846163\pi$
$563$		−	22.0524i		−	0.929396i	0.885469	−	0.464698i	$-0.153837\pi$
$564$	−2.11311	+	2.11311i	−0.0889778	+	0.0889778i
$565$	−3.58114	−	3.58114i	−0.150660	−	0.150660i
$566$	−11.0679	+	11.0679i	−0.465219	+	0.465219i
$567$	16.4141	−	16.4141i	0.689326	−	0.689326i
$568$	−11.4518			−0.480507
$569$	34.4003			1.44214			0.721068	−	0.692865i	$-0.243652\pi$
$569$	34.4003			1.44214			0.721068	+	0.692865i	$0.243652\pi$
$570$	−0.757492	−	0.757492i	−0.0317279	−	0.0317279i
$571$	20.9110			0.875099			0.437550	−	0.899194i	$-0.355846\pi$
$571$	20.9110			0.875099			0.437550	+	0.899194i	$0.355846\pi$
$572$	1.72678	−	19.1377i	0.0722002	−	0.800188i
$573$			5.25572i			0.219561i
$574$	−5.14211	−	5.14211i	−0.214628	−	0.214628i
$575$		−	24.4209i		−	1.01842i
$576$		−	1.21658i		−	0.0506908i
$577$	12.9207	+	12.9207i	0.537898	+	0.537898i	0.922911	−	0.385013i	$-0.125803\pi$
$577$	12.9207	+	12.9207i	0.537898	+	0.537898i	−0.385013	+	0.922911i	$0.625803\pi$
$578$	−20.0514	−	20.0514i	−0.834029	−	0.834029i
$579$	0.915028	+	0.915028i	0.0380273	+	0.0380273i
$580$	−0.642219	−	0.642219i	−0.0266667	−	0.0266667i
$581$			13.2725i			0.550638i
$582$	−2.96365			−0.122847
$583$	25.8909	−	25.8909i	1.07229	−	1.07229i
$584$	−19.3561			−0.800959
$585$	−6.83312	−	0.616546i	−0.282515	−	0.0254910i
$586$	7.72254			0.319015
$587$	−2.18345	+	2.18345i	−0.0901204	+	0.0901204i	−0.750730	−	0.660609i	$-0.770298\pi$
$587$	−2.18345	+	2.18345i	−0.0901204	+	0.0901204i	0.660609	+	0.750730i	$0.270298\pi$
$588$			0.669143i			0.0275950i
$589$	42.8758	−	0.348158i	1.76666	−	0.0143456i
$590$	−1.50003	−	1.50003i	−0.0617553	−	0.0617553i
$591$	−0.0651526	−	0.0651526i	−0.00268002	−	0.00268002i
$592$	−5.20789	−	5.20789i	−0.214043	−	0.214043i
$593$	28.5934	−	28.5934i	1.17419	−	1.17419i	0.192992	−	0.981200i	$-0.438181\pi$
$593$	28.5934	−	28.5934i	1.17419	−	1.17419i	0.981200	−	0.192992i	$-0.0618191\pi$
$594$	−4.21084			−0.172773
$595$	14.7555			0.604916
$596$	2.12618	−	2.12618i	0.0870919	−	0.0870919i
$597$		−	6.47000i		−	0.264799i
$598$	−12.4703	−	1.12518i	−0.509947	−	0.0460121i
$599$	−41.4844			−1.69501			−0.847503	−	0.530791i	$-0.821895\pi$
$599$	−41.4844			−1.69501			−0.847503	+	0.530791i	$0.821895\pi$
$600$	2.44488	−	2.44488i	0.0998118	−	0.0998118i
$601$			3.65139i			0.148943i	0.997223	+	0.0744717i	$0.0237270\pi$
$601$			3.65139i			0.148943i	−0.997223	+	0.0744717i	$0.976273\pi$
$602$	5.02694			0.204883
$603$	14.7959	+	14.7959i	0.602534	+	0.602534i
$604$	13.9936	−	13.9936i	0.569393	−	0.569393i
$605$	0.188097	−	0.188097i	0.00764725	−	0.00764725i
$606$	−1.67381	−	1.67381i	−0.0679938	−	0.0679938i
$607$	17.8698			0.725311			0.362655	−	0.931923i	$-0.381870\pi$
$607$	17.8698			0.725311			0.362655	+	0.931923i	$0.381870\pi$
$608$		−	44.0319i		−	1.78573i
$609$	0.580815	−	0.580815i	0.0235358	−	0.0235358i
$610$	−4.23854			−0.171614
$611$	1.88375	−	20.8774i	0.0762084	−	0.844610i
$612$			35.5689i			1.43779i
$613$	−20.7359	+	20.7359i	−0.837514	+	0.837514i	−0.988531	−	0.151018i	$-0.951745\pi$
$613$	−20.7359	+	20.7359i	−0.837514	+	0.837514i	0.151018	+	0.988531i	$0.451745\pi$
$614$	−1.65512			−0.0667953
$615$	−0.832202			−0.0335576
$616$	−15.9904	+	15.9904i	−0.644273	+	0.644273i
$617$	−4.20333	−	4.20333i	−0.169220	−	0.169220i	0.617417	−	0.786636i	$-0.288179\pi$
$617$	−4.20333	−	4.20333i	−0.169220	−	0.169220i	−0.786636	+	0.617417i	$0.788179\pi$
$618$	0.956935	+	0.956935i	0.0384936	+	0.0384936i
$619$	−11.9430	−	11.9430i	−0.480029	−	0.480029i	0.425112	−	0.905141i	$-0.360235\pi$
$619$	−11.9430	−	11.9430i	−0.480029	−	0.480029i	−0.905141	+	0.425112i	$0.860235\pi$
$620$	−0.0469130	−	5.77735i	−0.00188407	−	0.232024i
$621$		−	10.2637i		−	0.411868i
$622$	9.14144	−	9.14144i	0.366538	−	0.366538i
$623$	−25.1519			−1.00769
$624$	1.23900	+	1.48477i	0.0495999	+	0.0594383i
$625$	−18.7015			−0.748062
$626$	−6.26721	+	6.26721i	−0.250488	+	0.250488i
$627$	−8.47062			−0.338284
$628$		−	11.4475i		−	0.456803i
$629$	−24.6316	−	24.6316i	−0.982125	−	0.982125i
$630$	2.51811	+	2.51811i	0.100324	+	0.100324i
$631$	9.13815	+	9.13815i	0.363784	+	0.363784i	0.865204	−	0.501420i	$-0.167189\pi$
$631$	9.13815	+	9.13815i	0.363784	+	0.363784i	−0.501420	+	0.865204i	$0.667189\pi$
$632$	21.5654	+	21.5654i	0.857826	+	0.857826i
$633$			3.31658i			0.131822i
$634$		−	11.7016i		−	0.464732i
$635$	7.55795	+	7.55795i	0.299928	+	0.299928i
$636$			5.57305i			0.220986i
$637$	−3.00730	−	3.60381i	−0.119154	−	0.142788i
$638$	1.91986			0.0760080
$639$	10.0831	+	10.0831i	0.398882	+	0.398882i
$640$	−7.33971			−0.290128
$641$	28.0149			1.10652			0.553261	−	0.833008i	$-0.313383\pi$
$641$	28.0149			1.10652			0.553261	+	0.833008i	$0.313383\pi$
$642$	−1.74865	+	1.74865i	−0.0690138	+	0.0690138i
$643$	−14.6552	+	14.6552i	−0.577945	+	0.577945i	−0.934337	−	0.356392i	$-0.884007\pi$
$643$	−14.6552	+	14.6552i	−0.577945	+	0.577945i	0.356392	+	0.934337i	$0.384007\pi$
$644$	−17.1902	−	17.1902i	−0.677389	−	0.677389i
$645$	0.406780	−	0.406780i	0.0160170	−	0.0160170i
$646$		−	38.9569i		−	1.53274i
$647$	17.7183			0.696579			0.348290	−	0.937387i	$-0.386763\pi$
$647$	17.7183			0.696579			0.348290	+	0.937387i	$0.386763\pi$
$648$	−13.2397	+	13.2397i	−0.520106	+	0.520106i
$649$	−16.7740			−0.658438
$650$	−0.961268	+	10.6536i	−0.0377040	+	0.417870i
$651$	5.22497	−	0.0424276i	0.204783	−	0.00166287i
$652$	−10.6707	−	10.6707i	−0.417896	−	0.417896i
$653$	−26.2998			−1.02919			−0.514595	−	0.857434i	$-0.672058\pi$
$653$	−26.2998			−1.02919			−0.514595	+	0.857434i	$0.672058\pi$
$654$	−1.86877			−0.0730745
$655$	1.80967	+	1.80967i	0.0707096	+	0.0707096i
$656$	−4.52454	−	4.52454i	−0.176654	−	0.176654i
$657$	17.0427	+	17.0427i	0.664898	+	0.664898i
$658$	−7.69364	+	7.69364i	−0.299929	+	0.299929i
$659$	11.5559			0.450153			0.225077	−	0.974341i	$-0.427737\pi$
$659$	11.5559			0.450153			0.225077	+	0.974341i	$0.427737\pi$
$660$			1.14138i			0.0444283i
$661$	17.3471	−	17.3471i	0.674723	−	0.674723i	−0.284078	−	0.958801i	$-0.591687\pi$
$661$	17.3471	−	17.3471i	0.674723	−	0.674723i	0.958801	+	0.284078i	$0.0916874\pi$
$662$	6.42175			0.249589
$663$	5.86008	+	7.02246i	0.227587	+	0.272730i
$664$		−	10.7058i		−	0.415464i
$665$	10.3167	+	10.3167i	0.400063	+	0.400063i
$666$		−	8.40704i		−	0.325766i
$667$			4.67957i			0.181194i
$668$	17.2904	−	17.2904i	0.668988	−	0.668988i
$669$	−1.21542	−	1.21542i	−0.0469909	−	0.0469909i
$670$	−2.18359	+	2.18359i	−0.0843596	+	0.0843596i
$671$	−23.6986	+	23.6986i	−0.914876	+	0.914876i
$672$		−	5.36586i		−	0.206993i
$673$	−27.7297			−1.06890			−0.534452	−	0.845199i	$-0.679482\pi$
$673$	−27.7297			−1.06890			−0.534452	+	0.845199i	$0.679482\pi$
$674$	−14.0437	−	14.0437i	−0.540942	−	0.540942i
$675$	−8.76852			−0.337501
$676$	−20.1842	−	3.67230i	−0.776315	−	0.141242i
$677$			25.1303i			0.965835i	0.875666	+	0.482917i	$0.160423\pi$
$677$			25.1303i			0.965835i	−0.875666	+	0.482917i	$0.839577\pi$
$678$	−1.15219	+	1.15219i	−0.0442497	+	0.0442497i
$679$	40.3634			1.54900
$680$	−11.9019			−0.456417
$681$	−4.12406	+	4.12406i	−0.158034	+	0.158034i
$682$	8.70558	+	8.56534i	0.333354	+	0.327984i
$683$	−12.6007	+	12.6007i	−0.482152	+	0.482152i	−0.905818	−	0.423666i	$-0.860743\pi$
$683$	−12.6007	+	12.6007i	−0.482152	+	0.482152i	0.423666	+	0.905818i	$0.360743\pi$
$684$	−24.8688	+	24.8688i	−0.950884	+	0.950884i
$685$		−	5.54534i		−	0.211877i
$686$		−	10.6639i		−	0.407151i
$687$	−0.944410	+	0.944410i	−0.0360315	+	0.0360315i
$688$	4.42319			0.168633
$689$	−25.0467	−	30.0148i	−0.954203	−	1.14347i
$690$	0.743734			0.0283135
$691$	25.0782	+	25.0782i	0.954020	+	0.954020i	0.998988	−	0.0449686i	$-0.0143188\pi$
$691$	25.0782	+	25.0782i	0.954020	+	0.954020i	−0.0449686	+	0.998988i	$0.514319\pi$
$692$	14.6858			0.558270
$693$	28.1586			1.06966
$694$	−3.30155	+	3.30155i	−0.125325	+	0.125325i
$695$	−2.56496	+	2.56496i	−0.0972943	+	0.0972943i
$696$	−0.468491	+	0.468491i	−0.0177581	+	0.0177581i
$697$	−21.3996	−	21.3996i	−0.810566	−	0.810566i
$698$	19.8397			0.750942
$699$	4.95741			0.187507
$700$	−14.6860	+	14.6860i	−0.555078	+	0.555078i
$701$			40.9955i			1.54838i	0.632955	+	0.774189i	$0.281842\pi$
$701$			40.9955i			1.54838i	−0.632955	+	0.774189i	$0.718158\pi$
$702$	−0.404005	+	4.47755i	−0.0152482	+	0.168994i
$703$		−	34.4435i		−	1.29906i
$704$	1.00387	−	1.00387i	0.0378349	−	0.0378349i
$705$			1.24514i			0.0468947i
$706$	18.6596			0.702263
$707$	22.7964	+	22.7964i	0.857347	+	0.857347i
$708$	1.80532	−	1.80532i	0.0678480	−	0.0678480i
$709$	−15.9682	−	15.9682i	−0.599700	−	0.599700i	0.340533	−	0.940233i	$-0.389393\pi$
$709$	−15.9682	−	15.9682i	−0.599700	−	0.599700i	−0.940233	+	0.340533i	$0.889393\pi$
$710$	−1.48808	+	1.48808i	−0.0558467	+	0.0558467i
$711$		−	37.9759i		−	1.42421i
$712$	20.2878			0.760316
$713$	−20.8776	+	21.2194i	−0.781872	+	0.794674i
$714$		−	4.74741i		−	0.177667i
$715$	−5.12967	−	6.14717i	−0.191839	−	0.229891i
$716$			12.5948i			0.470690i
$717$	0.0102248	+	0.0102248i	0.000381850	+	0.000381850i
$718$	3.73383			0.139345
$719$	9.17931			0.342331			0.171165	−	0.985242i	$-0.445247\pi$
$719$	9.17931			0.342331			0.171165	+	0.985242i	$0.445247\pi$
$720$	2.21568	+	2.21568i	0.0825735	+	0.0825735i
$721$	−13.0330	−	13.0330i	−0.485373	−	0.485373i
$722$	18.5113	−	18.5113i	0.688920	−	0.688920i
$723$	5.17006	−	5.17006i	0.192276	−	0.192276i
$724$			8.08147i			0.300345i
$725$	3.99786			0.148477
$726$	−0.0605182	−	0.0605182i	−0.00224604	−	0.00224604i
$727$		−	2.19613i		−	0.0814501i	−0.999170	−	0.0407250i	$-0.987033\pi$
$727$		−	2.19613i		−	0.0814501i	0.999170	−	0.0407250i	$-0.0129668\pi$
$728$	15.4691	+	18.5374i	0.573322	+	0.687043i
$729$	21.4389			0.794035
$730$	−2.51518	+	2.51518i	−0.0930911	+	0.0930911i
$731$	20.9202			0.773763
$732$		−	5.10117i		−	0.188545i
$733$	−28.4020	−	28.4020i	−1.04905	−	1.04905i	−0.998733	−	0.0503200i	$-0.983976\pi$
$733$	−28.4020	−	28.4020i	−1.04905	−	1.04905i	−0.0503200	−	0.998733i	$-0.516024\pi$
$734$	−6.72956	+	6.72956i	−0.248393	+	0.248393i
$735$	0.197145	+	0.197145i	0.00727182	+	0.00727182i
$736$	21.6161	+	21.6161i	0.796780	+	0.796780i
$737$			24.4179i			0.899446i
$738$		−	7.30392i		−	0.268861i
$739$	−1.45679	−	1.45679i	−0.0535889	−	0.0535889i	0.679804	−	0.733393i	$-0.262065\pi$
$739$	−1.45679	−	1.45679i	−0.0535889	−	0.0535889i	−0.733393	+	0.679804i	$0.762065\pi$
$740$	−4.64114			−0.170612
$741$	−0.812706	+	9.00714i	−0.0298555	+	0.330886i
$742$			20.2910i			0.744906i
$743$	−2.88747	+	2.88747i	−0.105931	+	0.105931i	−0.758086	−	0.652155i	$-0.773865\pi$
$743$	−2.88747	+	2.88747i	−0.105931	+	0.105931i	0.652155	+	0.758086i	$0.273865\pi$
$744$	−4.21451	+	0.0342225i	−0.154511	+	0.00125466i
$745$		−	1.25285i		−	0.0459008i
$746$	−3.40697	−	3.40697i	−0.124738	−	0.124738i
$747$	−9.42623	+	9.42623i	−0.344888	+	0.344888i
$748$	−29.3500	+	29.3500i	−1.07314	+	1.07314i
$749$	23.8158	−	23.8158i	0.870209	−	0.870209i
$750$		−	1.33092i		−	0.0485984i
$751$		−	20.7666i		−	0.757786i	−0.925441	−	0.378893i	$-0.876305\pi$
$751$		−	20.7666i		−	0.757786i	0.925441	−	0.378893i	$-0.123695\pi$
$752$	−6.76963	+	6.76963i	−0.246863	+	0.246863i
$753$			5.57668i			0.203226i
$754$	0.184199	−	2.04146i	0.00670815	−	0.0743457i
$755$		−	8.24571i		−	0.300092i
$756$	−6.17228	+	6.17228i	−0.224484	+	0.224484i
$757$		−	4.81632i		−	0.175052i	−0.996162	−	0.0875261i	$-0.972104\pi$
$757$		−	4.81632i		−	0.175052i	0.996162	−	0.0875261i	$-0.0278961\pi$
$758$		−	12.6733i		−	0.460316i
$759$	4.15839	−	4.15839i	0.150940	−	0.150940i
$760$	−8.32151	−	8.32151i	−0.301853	−	0.301853i
$761$	−26.6614	−	26.6614i	−0.966476	−	0.966476i	0.0329796	−	0.999456i	$-0.489500\pi$
$761$	−26.6614	−	26.6614i	−0.966476	−	0.966476i	−0.999456	+	0.0329796i	$0.989500\pi$
$762$	2.43168	−	2.43168i	0.0880906	−	0.0880906i
$763$	25.4516			0.921411
$764$			25.4649i			0.921287i
$765$	10.4794	+	10.4794i	0.378884	+	0.378884i
$766$	−18.6614			−0.674264
$767$	−1.60937	+	17.8365i	−0.0581110	+	0.644038i
$768$			2.63532i			0.0950940i
$769$	−11.8858	−	11.8858i	−0.428613	−	0.428613i	0.459542	−	0.888156i	$-0.348013\pi$
$769$	−11.8858	−	11.8858i	−0.428613	−	0.428613i	−0.888156	+	0.459542i	$0.848013\pi$
$770$			4.15569i			0.149761i
$771$	−2.02472			−0.0729185
$772$	4.43347	+	4.43347i	0.159564	+	0.159564i
$773$	10.2966	−	10.2966i	0.370344	−	0.370344i	−0.497259	−	0.867602i	$-0.665660\pi$
$773$	10.2966	−	10.2966i	0.370344	−	0.370344i	0.867602	+	0.497259i	$0.165660\pi$
$774$	3.57016	+	3.57016i	0.128327	+	0.128327i
$775$	18.1282	+	17.8362i	0.651186	+	0.640696i
$776$	−32.5575			−1.16875
$777$		−	4.19740i		−	0.150581i
$778$	4.51903	+	4.51903i	0.162015	+	0.162015i
$779$		−	29.9241i		−	1.07214i
$780$	1.21368	+	0.109509i	0.0434567	+	0.00392106i
$781$			16.6404i			0.595440i
$782$	19.1247	+	19.1247i	0.683897	+	0.683897i
$783$	1.68024			0.0600467
$784$			2.14369i			0.0765605i
$785$	−3.37269	−	3.37269i	−0.120377	−	0.120377i
$786$	0.582240	−	0.582240i	0.0207678	−	0.0207678i
$787$	11.3405	+	11.3405i	0.404245	+	0.404245i	0.879726	−	0.475481i	$-0.157726\pi$
$787$	11.3405	+	11.3405i	0.404245	+	0.404245i	−0.475481	+	0.879726i	$0.657726\pi$
$788$	−0.315676	−	0.315676i	−0.0112455	−	0.0112455i
$789$	−3.62044			−0.128891
$790$	5.60454			0.199401
$791$	15.6923	−	15.6923i	0.557953	−	0.557953i
$792$	−22.7130			−0.807071
$793$	22.9259	+	27.4734i	0.814124	+	0.975610i
$794$	2.92658			0.103860
$795$	1.64195	+	1.64195i	0.0582340	+	0.0582340i
$796$		−	31.3482i		−	1.11111i
$797$	33.6256			1.19108			0.595540	−	0.803326i	$-0.296938\pi$
$797$	33.6256			1.19108			0.595540	+	0.803326i	$0.296938\pi$
$798$	3.31927	−	3.31927i	0.117501	−	0.117501i
$799$	−32.0181	+	32.0181i	−1.13272	+	1.13272i
$800$	18.4671	−	18.4671i	0.652912	−	0.652912i
$801$	−17.8630	−	17.8630i	−0.631159	−	0.631159i
$802$		−	11.3550i		−	0.400958i
$803$			28.1259i			0.992541i
$804$	−2.62800	−	2.62800i	−0.0926824	−	0.0926824i
$805$	−10.1293			−0.357010
$806$	9.94311	−	8.43519i	0.350231	−	0.297117i
$807$	10.5040			0.369760
$808$	−18.3878	−	18.3878i	−0.646880	−	0.646880i
$809$		−	0.195408i		−	0.00687019i	−0.999994	−	0.00343509i	$-0.998907\pi$
$809$		−	0.195408i		−	0.00687019i	0.999994	−	0.00343509i	$-0.00109343\pi$
$810$			3.44082i			0.120898i
$811$	−6.56833	−	6.56833i	−0.230645	−	0.230645i	0.582317	−	0.812962i	$-0.302146\pi$
$811$	−6.56833	−	6.56833i	−0.230645	−	0.230645i	−0.812962	+	0.582317i	$0.802146\pi$
$812$	2.81415	−	2.81415i	0.0987573	−	0.0987573i
$813$	−5.03377	+	5.03377i	−0.176542	+	0.176542i
$814$	6.93716	−	6.93716i	0.243147	−	0.243147i
$815$	−6.28767			−0.220247
$816$		−	4.17724i		−	0.146233i
$817$	14.6269	+	14.6269i	0.511730	+	0.511730i
$818$	−19.6011			−0.685335
$819$	2.70165	−	29.9421i	0.0944034	−	1.04626i
$820$	−4.03216			−0.140809
$821$	−1.47445	+	1.47445i	−0.0514588	+	0.0514588i	−0.732368	−	0.680909i	$-0.761585\pi$
$821$	−1.47445	+	1.47445i	−0.0514588	+	0.0514588i	0.680909	+	0.732368i	$0.261585\pi$
$822$	−1.78415			−0.0622294
$823$	−9.81106			−0.341992			−0.170996	−	0.985272i	$-0.554699\pi$
$823$	−9.81106			−0.341992			−0.170996	+	0.985272i	$0.554699\pi$
$824$	10.5125	+	10.5125i	0.366221	+	0.366221i
$825$	−3.55260	−	3.55260i	−0.123686	−	0.123686i
$826$	6.57301	−	6.57301i	0.228704	−	0.228704i
$827$	−28.8385	−	28.8385i	−1.00281	−	1.00281i	−0.999996	−	0.00281523i	$-0.999104\pi$
$827$	−28.8385	−	28.8385i	−1.00281	−	1.00281i	−0.00281523	−	0.999996i	$-0.500896\pi$
$828$		−	24.4172i		−	0.848555i
$829$	27.2314			0.945786			0.472893	−	0.881120i	$-0.343210\pi$
$829$	27.2314			0.945786			0.472893	+	0.881120i	$0.343210\pi$
$830$	−1.39114	−	1.39114i	−0.0482871	−	0.0482871i
$831$			9.37687i			0.325280i
$832$	−0.971143	−	1.16377i	−0.0336683	−	0.0403466i
$833$			10.1390i			0.351294i
$834$	0.825246	+	0.825246i	0.0285759	+	0.0285759i
$835$		−	10.1883i		−	0.352582i
$836$	−41.0416			−1.41945
$837$	7.61901	+	7.49627i	0.263351	+	0.259109i
$838$	9.24470	+	9.24470i	0.319353	+	0.319353i
$839$	17.3869	−	17.3869i	0.600262	−	0.600262i	−0.340120	−	0.940382i	$-0.610468\pi$
$839$	17.3869	−	17.3869i	0.600262	−	0.600262i	0.940382	+	0.340120i	$0.110468\pi$
$840$	−1.01408	−	1.01408i	−0.0349893	−	0.0349893i
$841$	28.2339			0.973584
$842$			14.6718i			0.505624i
$843$	4.46119	+	4.46119i	0.153651	+	0.153651i
$844$			16.0694i			0.553132i
$845$	−7.02869	+	4.86480i	−0.241794	+	0.167354i
$846$	−10.9281			−0.375717
$847$	0.824227	+	0.824227i	0.0283208	+	0.0283208i
$848$			17.8540i			0.613110i
$849$	−7.84904			−0.269378
$850$	16.3387	−	16.3387i	0.560411	−	0.560411i
$851$	16.9090	+	16.9090i	0.579632	+	0.579632i
$852$	−1.79094	−	1.79094i	−0.0613565	−	0.0613565i
$853$	−36.3612	+	36.3612i	−1.24499	+	1.24499i	−0.287078	+	0.957907i	$0.592684\pi$
$853$	−36.3612	+	36.3612i	−1.24499	+	1.24499i	−0.957907	+	0.287078i	$0.907316\pi$
$854$		−	18.5729i		−	0.635553i
$855$			14.6539i			0.501153i
$856$	−19.2100	+	19.2100i	−0.656585	+	0.656585i
$857$		−	9.93638i		−	0.339420i	−0.985494	−	0.169710i	$-0.945717\pi$
$857$		−	9.93638i		−	0.339420i	0.985494	−	0.169710i	$-0.0542832\pi$
$858$	−1.97778	+	1.65041i	−0.0675204	+	0.0563442i
$859$			28.6500i			0.977524i	0.872417	+	0.488762i	$0.162551\pi$
$859$			28.6500i			0.977524i	−0.872417	+	0.488762i	$0.837449\pi$
$860$	1.97092	−	1.97092i	0.0672078	−	0.0672078i
$861$		−	3.64664i		−	0.124277i
$862$			22.4390i			0.764274i
$863$	24.1815	−	24.1815i	0.823147	−	0.823147i	−0.163411	−	0.986558i	$-0.552250\pi$
$863$	24.1815	−	24.1815i	0.823147	−	0.823147i	0.986558	+	0.163411i	$0.0522496\pi$
$864$	7.76143	−	7.76143i	0.264049	−	0.264049i
$865$	4.32678	−	4.32678i	0.147115	−	0.147115i
$866$	−3.32420	−	3.32420i	−0.112961	−	0.112961i
$867$		−	14.2199i		−	0.482933i
$868$	25.3159	−	0.205569i	0.859277	−	0.00697747i
$869$	31.3362	−	31.3362i	1.06301	−	1.06301i
$870$			0.121754i			0.00412785i
$871$	25.9645	+	2.34276i	0.879775	+	0.0793813i
$872$	−20.5295			−0.695217
$873$	28.6663	+	28.6663i	0.970207	+	0.970207i
$874$			26.7430i			0.904595i
$875$			18.1265i			0.612787i
$876$	−3.02707	−	3.02707i	−0.102275	−	0.102275i
$877$	0.700034	+	0.700034i	0.0236385	+	0.0236385i	0.718827	−	0.695189i	$-0.244679\pi$
$877$	0.700034	+	0.700034i	0.0236385	+	0.0236385i	−0.695189	+	0.718827i	$0.744679\pi$
$878$	−6.74261	+	6.74261i	−0.227552	+	0.227552i
$879$	2.73830	+	2.73830i	0.0923606	+	0.0923606i
$880$			3.65658i			0.123263i
$881$	−2.76537			−0.0931676			−0.0465838	−	0.998914i	$-0.514833\pi$
$881$	−2.76537			−0.0931676			−0.0465838	+	0.998914i	$0.514833\pi$
$882$	−1.73027	+	1.73027i	−0.0582612	+	0.0582612i
$883$	−28.8209			−0.969900			−0.484950	−	0.874542i	$-0.661162\pi$
$883$	−28.8209			−0.969900			−0.484950	+	0.874542i	$0.661162\pi$
$884$	28.3931	+	34.0250i	0.954962	+	1.14438i
$885$		−	1.06378i		−	0.0357585i
$886$	−10.6697	−	10.6697i	−0.358456	−	0.358456i
$887$	−32.2691			−1.08349			−0.541746	−	0.840542i	$-0.682236\pi$
$887$	−32.2691			−1.08349			−0.541746	+	0.840542i	$0.682236\pi$
$888$			3.38566i			0.113615i
$889$	−33.1183	+	33.1183i	−1.11075	+	1.11075i
$890$	2.63625	−	2.63625i	0.0883674	−	0.0883674i
$891$	19.2384	+	19.2384i	0.644511	+	0.644511i
$892$	−5.88892	−	5.88892i	−0.197176	−	0.197176i
$893$	−44.7724			−1.49825
$894$	−0.403090			−0.0134813
$895$	3.71073	+	3.71073i	0.124036	+	0.124036i
$896$		−	32.1620i		−	1.07446i
$897$	−4.02280	−	4.82075i	−0.134317	−	0.160960i
$898$			6.62231i			0.220989i
$899$	−3.47376	−	3.41780i	−0.115856	−	0.113990i
$900$	−20.8601			−0.695338
$901$			84.4436i			2.81323i
$902$	6.02691	−	6.02691i	0.200674	−	0.200674i
$903$	1.78248	+	1.78248i	0.0593172	+	0.0593172i
$904$	−12.6575	+	12.6575i	−0.420983	+	0.420983i
$905$	2.38099	+	2.38099i	0.0791468	+	0.0791468i
$906$	−2.65296			−0.0881388
$907$			42.4257i			1.40872i	0.709842	+	0.704361i	$0.248766\pi$
$907$			42.4257i			1.40872i	−0.709842	+	0.704361i	$0.751234\pi$
$908$	−19.9818	+	19.9818i	−0.663118	+	0.663118i
$909$			32.3803i			1.07399i
$910$	4.41891	+	0.398714i	0.146485	+	0.0132172i
$911$			30.6468i			1.01537i	0.861542	+	0.507687i	$0.169499\pi$
$911$			30.6468i			1.01537i	−0.861542	+	0.507687i	$0.830501\pi$
$912$	2.92062	−	2.92062i	0.0967114	−	0.0967114i
$913$	−15.5563			−0.514839
$914$	−13.6969			−0.453053
$915$	−1.50293	−	1.50293i	−0.0496852	−	0.0496852i
$916$	−4.57583	+	4.57583i	−0.151190	+	0.151190i
$917$	−7.92982	+	7.92982i	−0.261866	+	0.261866i
$918$	6.86687	−	6.86687i	0.226641	−	0.226641i
$919$	0.260867			0.00860520			0.00430260	−	0.999991i	$-0.498630\pi$
$919$	0.260867			0.00860520			0.00430260	+	0.999991i	$0.498630\pi$
$920$	8.17037			0.269369
$921$	−0.586882	−	0.586882i	−0.0193384	−	0.0193384i
$922$	−1.79627			−0.0591571
$923$	17.6944	+	1.59655i	0.582418	+	0.0525510i
$924$	−5.00145			−0.164536
$925$	14.4457	−	14.4457i	0.474973	−	0.474973i
$926$			7.21425i			0.237075i
$927$		−	18.5122i		−	0.608020i
$928$	−3.53870	+	3.53870i	−0.116163	+	0.116163i
$929$	−9.07482	+	9.07482i	−0.297735	+	0.297735i	−0.840126	−	0.542391i	$-0.817519\pi$
$929$	−9.07482	+	9.07482i	−0.297735	+	0.297735i	0.542391	+	0.840126i	$0.317519\pi$
$930$	−0.543199	+	0.552093i	−0.0178122	+	0.0181038i
$931$	−7.08890	+	7.08890i	−0.232329	+	0.232329i
$932$	24.0195			0.786785
$933$	6.48284			0.212239
$934$	−17.0985	+	17.0985i	−0.559479	+	0.559479i
$935$			17.2944i			0.565588i
$936$	−2.17918	+	24.1516i	−0.0712287	+	0.789420i
$937$	50.6923			1.65605			0.828023	−	0.560694i	$-0.189465\pi$
$937$	50.6923			1.65605			0.828023	+	0.560694i	$0.189465\pi$
$938$	−9.56833	−	9.56833i	−0.312417	−	0.312417i
$939$	−4.44452			−0.145041
$940$			6.03292i			0.196772i
$941$	−5.16006	+	5.16006i	−0.168213	+	0.168213i	−0.786194	−	0.617980i	$-0.787951\pi$
$941$	−5.16006	+	5.16006i	−0.168213	+	0.168213i	0.617980	+	0.786194i	$0.287951\pi$
$942$	−1.08513	+	1.08513i	−0.0353553	+	0.0353553i
$943$	14.6903	+	14.6903i	0.478381	+	0.478381i
$944$	5.78359	−	5.78359i	0.188240	−	0.188240i
$945$			3.63700i			0.118312i
$946$			5.89191i			0.191562i
$947$	4.98192	+	4.98192i	0.161891	+	0.161891i	0.783404	−	0.621513i	$-0.213482\pi$
$947$	4.98192	+	4.98192i	0.161891	+	0.161891i	−0.621513	+	0.783404i	$0.713482\pi$
$948$			6.74518i			0.219073i
$949$	29.9074	+	2.69852i	0.970834	+	0.0875975i
$950$	22.8472			0.741259
$951$	4.14923	−	4.14923i	0.134548	−	0.134548i
$952$		−	52.1532i		−	1.69029i
$953$	−14.3116			−0.463598			−0.231799	−	0.972764i	$-0.574461\pi$
$953$	−14.3116			−0.463598			−0.231799	+	0.972764i	$0.574461\pi$
$954$	−14.4108	+	14.4108i	−0.466566	+	0.466566i
$955$	7.50255	+	7.50255i	0.242777	+	0.242777i
$956$	0.0495407	+	0.0495407i	0.00160226	+	0.00160226i
$957$	0.680755	+	0.680755i	0.0220057	+	0.0220057i
$958$	20.1213			0.650091
$959$	24.2992			0.784663
$960$	0.0636639	+	0.0636639i	0.00205474	+	0.00205474i
$961$	−0.503417	−	30.9959i	−0.0162393	−	0.999868i
$962$	−6.71097	−	8.04213i	−0.216370	−	0.259289i
$963$	33.8282			1.09010
$964$	25.0498	−	25.0498i	0.806800	−	0.806800i
$965$	2.61241			0.0840964
$966$			3.25898i			0.104856i
$967$	4.44966	−	4.44966i	0.143091	−	0.143091i	−0.631932	−	0.775024i	$-0.717738\pi$
$967$	4.44966	−	4.44966i	0.143091	−	0.143091i	0.775024	+	0.631932i	$0.217738\pi$
$968$	−0.664829	−	0.664829i	−0.0213684	−	0.0213684i
$969$	13.8136	−	13.8136i	0.443756	−	0.443756i
$970$	−4.23061	+	4.23061i	−0.135837	+	0.135837i
$971$	33.7364			1.08265			0.541326	−	0.840813i	$-0.317922\pi$
$971$	33.7364			1.08265			0.541326	+	0.840813i	$0.317922\pi$
$972$	−13.2297			−0.424342
$973$	−11.2394	−	11.2394i	−0.360319	−	0.360319i
$974$	12.7296			0.407881
$975$	−4.11848	+	3.43677i	−0.131897	+	0.110065i
$976$		−	16.3423i		−	0.523104i
$977$	−21.0549	−	21.0549i	−0.673605	−	0.673605i	0.284940	−	0.958545i	$-0.408026\pi$
$977$	−21.0549	−	21.0549i	−0.673605	−	0.673605i	−0.958545	+	0.284940i	$0.908026\pi$
$978$			2.02299i			0.0646879i
$979$		−	29.4797i		−	0.942177i
$980$	0.955203	+	0.955203i	0.0305128	+	0.0305128i
$981$	18.0759	+	18.0759i	0.577119	+	0.577119i
$982$	14.9764	+	14.9764i	0.477915	+	0.477915i
$983$	−29.7027	−	29.7027i	−0.947368	−	0.947368i	0.0513143	−	0.998683i	$-0.483659\pi$
$983$	−29.7027	−	29.7027i	−0.947368	−	0.947368i	−0.998683	+	0.0513143i	$0.983659\pi$
$984$			2.94141i			0.0937688i
$985$	−0.186011			−0.00592680
$986$	−3.13084	+	3.13084i	−0.0997061	+	0.0997061i
$987$	−5.45611			−0.173670
$988$	−3.93770	+	43.6411i	−0.125275	+	1.38841i
$989$	−14.3612			−0.456661
$990$	−2.95139	+	2.95139i	−0.0938014	+	0.0938014i
$991$		−	14.7721i		−	0.469250i	−0.972086	−	0.234625i	$-0.924614\pi$
$991$		−	14.7721i		−	0.469250i	0.972086	−	0.234625i	$-0.0753862\pi$
$992$	−31.8338	+	0.258496i	−1.01073	+	0.00820726i
$993$	2.27706	+	2.27706i	0.0722603	+	0.0722603i
$994$	−6.52065	−	6.52065i	−0.206822	−	0.206822i
$995$	−9.23593	−	9.23593i	−0.292799	−	0.292799i
$996$	1.67426	−	1.67426i	0.0530510	−	0.0530510i
$997$	−34.4020			−1.08952			−0.544761	−	0.838592i	$-0.683379\pi$
$997$	−34.4020			−1.08952			−0.544761	+	0.838592i	$0.683379\pi$
$998$	16.8051			0.531957
$999$	6.07131	−	6.07131i	0.192088	−	0.192088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.i.a.216.15	✓	68
13.5	odd	4	inner	403.2.i.a.278.15	yes	68
31.30	odd	2	inner	403.2.i.a.216.16	yes	68
403.278	even	4	inner	403.2.i.a.278.16	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.i.a.216.15	✓	68	1.1	even	1	trivial
403.2.i.a.216.16	yes	68	31.30	odd	2	inner
403.2.i.a.278.15	yes	68	13.5	odd	4	inner
403.2.i.a.278.16	yes	68	403.278	even	4	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.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.459282 - 0.459282i) q^{2} -0.325710i q^{3} -1.57812i q^{4} +(-0.464951 - 0.464951i) q^{5} +(-0.149593 + 0.149593i) q^{6} +(2.03738 - 2.03738i) q^{7} +(-1.64337 + 1.64337i) q^{8} +2.89391 q^{9} +O(q^{10})\)	\(q+(-0.459282 - 0.459282i) q^{2} -0.325710i q^{3} -1.57812i q^{4} +(-0.464951 - 0.464951i) q^{5} +(-0.149593 + 0.149593i) q^{6} +(2.03738 - 2.03738i) q^{7} +(-1.64337 + 1.64337i) q^{8} +2.89391 q^{9} +0.427088i q^{10} +(2.38794 + 2.38794i) q^{11} -0.514009 q^{12} +(2.76830 - 2.31009i) q^{13} -1.87146 q^{14} +(-0.151439 + 0.151439i) q^{15} -1.64670 q^{16} -7.78833 q^{17} +(-1.32912 - 1.32912i) q^{18} +(-5.44541 - 5.44541i) q^{19} +(-0.733748 + 0.733748i) q^{20} +(-0.663594 - 0.663594i) q^{21} -2.19348i q^{22} +5.34650 q^{23} +(0.535261 + 0.535261i) q^{24} -4.56764i q^{25} +(-2.33242 - 0.210452i) q^{26} -1.91971i q^{27} +(-3.21522 - 3.21522i) q^{28} +0.875257i q^{29} +0.139107 q^{30} +(-3.90491 + 3.96884i) q^{31} +(4.04303 + 4.04303i) q^{32} +(0.777777 - 0.777777i) q^{33} +(3.57705 + 3.57705i) q^{34} -1.89456 q^{35} -4.56694i q^{36} +(3.16262 + 3.16262i) q^{37} +5.00196i q^{38} +(-0.752417 - 0.901664i) q^{39} +1.52817 q^{40} +(2.74764 + 2.74764i) q^{41} +0.609554i q^{42} -2.68610 q^{43} +(3.76846 - 3.76846i) q^{44} +(-1.34553 - 1.34553i) q^{45} +(-2.45556 - 2.45556i) q^{46} +(4.11103 - 4.11103i) q^{47} +0.536346i q^{48} -1.30181i q^{49} +(-2.09784 + 2.09784i) q^{50} +2.53674i q^{51} +(-3.64559 - 4.36871i) q^{52} -10.8423i q^{53} +(-0.881687 + 0.881687i) q^{54} -2.22055i q^{55} +6.69632i q^{56} +(-1.77362 + 1.77362i) q^{57} +(0.401990 - 0.401990i) q^{58} +(-3.51223 + 3.51223i) q^{59} +(0.238989 + 0.238989i) q^{60} +9.92428i q^{61} +(3.61627 - 0.0293647i) q^{62} +(5.89599 - 5.89599i) q^{63} -0.420393i q^{64} +(-2.36120 - 0.213049i) q^{65} -0.714438 q^{66} +(5.11275 + 5.11275i) q^{67} +12.2909i q^{68} -1.74141i q^{69} +(0.870139 + 0.870139i) q^{70} +(3.48425 + 3.48425i) q^{71} +(-4.75576 + 4.75576i) q^{72} +(5.88914 + 5.88914i) q^{73} -2.90508i q^{74} -1.48773 q^{75} +(-8.59350 + 8.59350i) q^{76} +9.73029 q^{77} +(-0.0685462 + 0.759690i) q^{78} -13.1227i q^{79} +(0.765635 + 0.765635i) q^{80} +8.05647 q^{81} -2.52389i q^{82} +(-3.25726 + 3.25726i) q^{83} +(-1.04723 + 1.04723i) q^{84} +(3.62120 + 3.62120i) q^{85} +(1.23368 + 1.23368i) q^{86} +0.285080 q^{87} -7.84854 q^{88} +(-6.17262 - 6.17262i) q^{89} +1.23596i q^{90} +(0.933564 - 10.3466i) q^{91} -8.43742i q^{92} +(1.29269 + 1.27187i) q^{93} -3.77625 q^{94} +5.06370i q^{95} +(1.31686 - 1.31686i) q^{96} +(9.90572 + 9.90572i) q^{97} +(-0.597900 + 0.597900i) q^{98} +(6.91050 + 6.91050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9}+O(q^{10}) \) 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9	\( 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9} - 48 q^{14} - 40 q^{16} + 4 q^{18} - 24 q^{19} - 16 q^{20} + 44 q^{28} + 24 q^{31} + 28 q^{32} - 40 q^{35} - 24 q^{39} + 24 q^{40} + 20 q^{41} - 24 q^{45} - 36 q^{47} + 80 q^{50} + 28 q^{59} - 76 q^{63} + 152 q^{66} - 32 q^{67} - 48 q^{70} + 20 q^{71} - 32 q^{72} + 72 q^{76} + 84 q^{78} - 20 q^{80} + 52 q^{81} - 112 q^{87} - 8 q^{93} - 16 q^{94} - 4 q^{97} - 92 q^{98}+O(q^{100}) \) 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9 - 48 * q^14 - 40 * q^16 + 4 * q^18 - 24 * q^19 - 16 * q^20 + 44 * q^28 + 24 * q^31 + 28 * q^32 - 40 * q^35 - 24 * q^39 + 24 * q^40 + 20 * q^41 - 24 * q^45 - 36 * q^47 + 80 * q^50 + 28 * q^59 - 76 * q^63 + 152 * q^66 - 32 * q^67 - 48 * q^70 + 20 * q^71 - 32 * q^72 + 72 * q^76 + 84 * q^78 - 20 * q^80 + 52 * q^81 - 112 * q^87 - 8 * q^93 - 16 * q^94 - 4 * q^97 - 92 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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