LMFDB - Embedded newform 363.2.f.h.161.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(161,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("363.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.f (of order $10$, degree $4$, not 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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.26873856000000000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2x^{14} - 8x^{10} - 16x^{8} - 32x^{6} + 128x^{2} + 256 $ x^16 + 2x^14 - 8x^10 - 16x^8 - 32x^6 + 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.4
Root			$-1.05097 + 0.946294i$ of defining polynomial
Character	$\chi$	$=$	363.161
Dual form			363.2.f.h.239.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.98168 + 1.43977i) q^{2} +(0.360114 + 1.69420i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-1.01807 - 1.40126i) q^{5} +(-1.72564 + 3.87585i) q^{6} +(1.34500 - 0.437016i) q^{7} +(-1.51387 + 4.65921i) q^{8} +(-2.74064 + 1.22021i) q^{9} +O(q^{10})$	\(q+(1.98168 + 1.43977i) q^{2} +(0.360114 + 1.69420i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-1.01807 - 1.40126i) q^{5} +(-1.72564 + 3.87585i) q^{6} +(1.34500 - 0.437016i) q^{7} +(-1.51387 + 4.65921i) q^{8} +(-2.74064 + 1.22021i) q^{9} -4.24264i q^{10} +(-6.00000 + 3.46410i) q^{12} +(-1.66251 + 2.28825i) q^{13} +(3.29456 + 1.07047i) q^{14} +(2.00739 - 2.22943i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(1.98168 - 1.43977i) q^{17} +(-7.18789 - 1.52783i) q^{18} +(2.68999 + 0.874032i) q^{19} +(4.07230 - 5.60503i) q^{20} +(1.22474 + 2.12132i) q^{21} -8.66025i q^{23} +(-8.43880 - 0.886953i) q^{24} +(0.618034 - 1.90211i) q^{25} +(-6.58911 + 2.14093i) q^{26} +(-3.05422 - 4.20378i) q^{27} +(3.32502 + 4.57649i) q^{28} +(1.51387 + 4.65921i) q^{29} +(7.18789 - 1.52783i) q^{30} +(-2.42705 - 1.76336i) q^{31} +6.00000 q^{34} +(-1.98168 - 1.43977i) q^{35} +(-8.02957 - 8.91774i) q^{36} +(0.927051 + 2.85317i) q^{37} +(4.07230 + 5.60503i) q^{38} +(-4.47544 - 1.99259i) q^{39} +(8.06998 - 2.62210i) q^{40} +(3.02774 - 9.31841i) q^{41} +(-0.627171 + 5.96713i) q^{42} +9.89949i q^{43} +(4.50000 + 2.59808i) q^{45} +(12.4688 - 17.1618i) q^{46} +(-6.58911 - 2.14093i) q^{47} +(-5.14866 - 4.63587i) q^{48} +(-4.04508 + 2.93893i) q^{49} +(3.96336 - 2.87955i) q^{50} +(3.15290 + 2.83888i) q^{51} +(-10.7600 - 3.49613i) q^{52} +(2.03615 - 2.80252i) q^{53} -12.7279i q^{54} +6.92820i q^{56} +(-0.512083 + 4.87214i) q^{57} +(-3.70820 + 11.4127i) q^{58} +(-1.64728 + 0.535233i) q^{59} +(10.9625 + 4.88084i) q^{60} +(1.66251 + 2.28825i) q^{61} +(-2.27080 - 6.98881i) q^{62} +(-3.15290 + 2.83888i) q^{63} +(6.47214 + 4.70228i) q^{64} +4.89898 q^{65} -3.00000 q^{67} +(7.92672 + 5.75910i) q^{68} +(14.6722 - 3.11868i) q^{69} +(-1.85410 - 5.70634i) q^{70} +(-1.01807 - 1.40126i) q^{71} +(-1.53625 - 14.6164i) q^{72} +(-5.37999 + 1.74806i) q^{73} +(-2.27080 + 6.98881i) q^{74} +(3.44512 + 0.362097i) q^{75} +11.3137i q^{76} +(-6.00000 - 10.3923i) q^{78} +(-5.81878 + 8.00886i) q^{79} +(6.58911 + 2.14093i) q^{80} +(6.02218 - 6.68830i) q^{81} +(19.4164 - 14.1068i) q^{82} +(-1.98168 + 1.43977i) q^{83} +(-6.55611 + 7.28130i) q^{84} +(-4.03499 - 1.31105i) q^{85} +(-14.2530 + 19.6176i) q^{86} +(-7.34847 + 4.24264i) q^{87} +8.66025i q^{89} +(5.17691 + 11.6275i) q^{90} +(-1.23607 + 3.80423i) q^{91} +(32.9456 - 10.7047i) q^{92} +(2.11347 - 4.74692i) q^{93} +(-9.97505 - 13.7295i) q^{94} +(-1.51387 - 4.65921i) q^{95} +(-10.5172 - 7.64121i) q^{97} -12.2474 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{3} - 16 q^{4} - 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^3 - 16 * q^4 - 6 * q^9	$ 16 q + 6 q^{3} - 16 q^{4} - 6 q^{9} - 96 q^{12} + 6 q^{15} - 16 q^{16} - 8 q^{25} - 12 q^{31} + 96 q^{34} - 24 q^{36} - 12 q^{37} + 12 q^{42} + 72 q^{45} + 24 q^{48} - 20 q^{49} + 48 q^{58} + 24 q^{60} + 32 q^{64} - 48 q^{67} - 30 q^{69} + 24 q^{70} + 12 q^{75} - 96 q^{78} + 18 q^{81} + 96 q^{82} + 16 q^{91} + 18 q^{93} - 52 q^{97}+O(q^{100}) $ 16 * q + 6 * q^3 - 16 * q^4 - 6 * q^9 - 96 * q^12 + 6 * q^15 - 16 * q^16 - 8 * q^25 - 12 * q^31 + 96 * q^34 - 24 * q^36 - 12 * q^37 + 12 * q^42 + 72 * q^45 + 24 * q^48 - 20 * q^49 + 48 * q^58 + 24 * q^60 + 32 * q^64 - 48 * q^67 - 30 * q^69 + 24 * q^70 + 12 * q^75 - 96 * q^78 + 18 * q^81 + 96 * q^82 + 16 * q^91 + 18 * q^93 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	1.98168	+	1.43977i	1.40126	+	1.01807i	0.994522	+	0.104528i	$0.0333333\pi$
$2$	1.98168	+	1.43977i	1.40126	+	1.01807i	0.406737	+	0.913545i	$0.366667\pi$
$3$	0.360114	+	1.69420i	0.207912	+	0.978148i
$3$	0.360114	+	1.69420i	0.207912	+	0.978148i
$4$	1.23607	+	3.80423i	0.618034	+	1.90211i
$5$	−1.01807	−	1.40126i	−0.455296	−	0.626662i	0.518229	−	0.855242i	$-0.326592\pi$
$5$	−1.01807	−	1.40126i	−0.455296	−	0.626662i	−0.973525	+	0.228580i	$0.926592\pi$
$6$	−1.72564	+	3.87585i	−0.704489	+	1.58231i
$7$	1.34500	−	0.437016i	0.508361	−	0.165177i	−0.0435957	−	0.999049i	$-0.513881\pi$
$7$	1.34500	−	0.437016i	0.508361	−	0.165177i	0.551957	+	0.833873i	$0.313881\pi$
$8$	−1.51387	+	4.65921i	−0.535233	+	1.64728i
$9$	−2.74064	+	1.22021i	−0.913545	+	0.406737i
$10$		−	4.24264i		−	1.34164i
$11$		0			0
$11$		0			0
$12$	−6.00000	+	3.46410i	−1.73205	+	1.00000i
$13$	−1.66251	+	2.28825i	−0.461097	+	0.634645i	−0.974736	−	0.223361i	$-0.928297\pi$
$13$	−1.66251	+	2.28825i	−0.461097	+	0.634645i	0.513639	+	0.858006i	$0.328297\pi$
$14$	3.29456	+	1.07047i	0.880507	+	0.286094i
$15$	2.00739	−	2.22943i	0.518306	−	0.575638i
$16$	−3.23607	+	2.35114i	−0.809017	+	0.587785i
$17$	1.98168	−	1.43977i	0.480628	−	0.349196i	−0.320941	−	0.947099i	$-0.603999\pi$
$17$	1.98168	−	1.43977i	0.480628	−	0.349196i	0.801569	+	0.597903i	$0.203999\pi$
$18$	−7.18789	−	1.52783i	−1.69420	−	0.360114i
$19$	2.68999	+	0.874032i	0.617127	+	0.200517i	0.600864	−	0.799351i	$-0.294823\pi$
$19$	2.68999	+	0.874032i	0.617127	+	0.200517i	0.0162627	+	0.999868i	$0.494823\pi$
$20$	4.07230	−	5.60503i	0.910593	−	1.25332i
$21$	1.22474	+	2.12132i	0.267261	+	0.462910i
$22$		0			0
$23$		−	8.66025i		−	1.80579i	−0.429863	−	0.902894i	$-0.641438\pi$
$23$		−	8.66025i		−	1.80579i	0.429863	−	0.902894i	$-0.358562\pi$
$24$	−8.43880	−	0.886953i	−1.72256	−	0.181049i
$25$	0.618034	−	1.90211i	0.123607	−	0.380423i
$26$	−6.58911	+	2.14093i	−1.29223	+	0.419871i
$27$	−3.05422	−	4.20378i	−0.587785	−	0.809017i
$28$	3.32502	+	4.57649i	0.628369	+	0.864876i
$29$	1.51387	+	4.65921i	0.281118	+	0.865193i	0.987535	+	0.157397i	$0.0503103\pi$
$29$	1.51387	+	4.65921i	0.281118	+	0.865193i	−0.706417	+	0.707796i	$0.749690\pi$
$30$	7.18789	−	1.52783i	1.31232	−	0.278943i
$31$	−2.42705	−	1.76336i	−0.435911	−	0.316708i	0.348097	−	0.937459i	$-0.386828\pi$
$31$	−2.42705	−	1.76336i	−0.435911	−	0.316708i	−0.784008	+	0.620750i	$0.786828\pi$
$32$		0			0
$33$		0			0
$34$	6.00000			1.02899
$35$	−1.98168	−	1.43977i	−0.334965	−	0.243366i
$36$	−8.02957	−	8.91774i	−1.33826	−	1.48629i
$37$	0.927051	+	2.85317i	0.152406	+	0.469058i	0.997889	−	0.0649448i	$-0.0206871\pi$
$37$	0.927051	+	2.85317i	0.152406	+	0.469058i	−0.845483	+	0.534003i	$0.820687\pi$
$38$	4.07230	+	5.60503i	0.660614	+	0.909257i
$39$	−4.47544	−	1.99259i	−0.716644	−	0.319070i
$40$	8.06998	−	2.62210i	1.27598	−	0.414590i
$41$	3.02774	−	9.31841i	0.472853	−	1.45529i	−0.375979	−	0.926628i	$-0.622693\pi$
$41$	3.02774	−	9.31841i	0.472853	−	1.45529i	0.848832	−	0.528663i	$-0.177307\pi$
$42$	−0.627171	+	5.96713i	−0.0967746	+	0.920748i
$43$			9.89949i			1.50966i	0.655921	+	0.754829i	$0.272280\pi$
$43$			9.89949i			1.50966i	−0.655921	+	0.754829i	$0.727720\pi$
$44$		0			0
$45$	4.50000	+	2.59808i	0.670820	+	0.387298i
$46$	12.4688	−	17.1618i	1.83843	−	2.53038i
$47$	−6.58911	−	2.14093i	−0.961121	−	0.312287i	−0.213895	−	0.976857i	$-0.568615\pi$
$47$	−6.58911	−	2.14093i	−0.961121	−	0.312287i	−0.747226	+	0.664570i	$0.768615\pi$
$48$	−5.14866	−	4.63587i	−0.743145	−	0.669131i
$49$	−4.04508	+	2.93893i	−0.577869	+	0.419847i
$50$	3.96336	−	2.87955i	0.560503	−	0.407230i
$51$	3.15290	+	2.83888i	0.441494	+	0.397523i
$52$	−10.7600	−	3.49613i	−1.49214	−	0.484826i
$53$	2.03615	−	2.80252i	0.279686	−	0.384955i	−0.645944	−	0.763385i	$-0.723536\pi$
$53$	2.03615	−	2.80252i	0.279686	−	0.384955i	0.925630	+	0.378430i	$0.123536\pi$
$54$		−	12.7279i		−	1.73205i
$55$		0			0
$56$			6.92820i			0.925820i
$57$	−0.512083	+	4.87214i	−0.0678270	+	0.645331i
$58$	−3.70820	+	11.4127i	−0.486911	+	1.49856i
$59$	−1.64728	+	0.535233i	−0.214457	+	0.0696814i	−0.414275	−	0.910152i	$-0.635965\pi$
$59$	−1.64728	+	0.535233i	−0.214457	+	0.0696814i	0.199818	+	0.979833i	$0.435965\pi$
$60$	10.9625	+	4.88084i	1.41526	+	0.630114i
$61$	1.66251	+	2.28825i	0.212862	+	0.292980i	0.902075	−	0.431579i	$-0.142043\pi$
$61$	1.66251	+	2.28825i	0.212862	+	0.292980i	−0.689213	+	0.724559i	$0.742043\pi$
$62$	−2.27080	−	6.98881i	−0.288392	−	0.887580i
$63$	−3.15290	+	2.83888i	−0.397228	+	0.357665i
$64$	6.47214	+	4.70228i	0.809017	+	0.587785i
$65$	4.89898			0.607644
$66$		0			0
$67$	−3.00000			−0.366508			−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000			−0.366508			−0.183254	+	0.983066i	$0.558663\pi$
$68$	7.92672	+	5.75910i	0.961255	+	0.698393i
$69$	14.6722	−	3.11868i	1.76633	−	0.375444i
$70$	−1.85410	−	5.70634i	−0.221608	−	0.682038i
$71$	−1.01807	−	1.40126i	−0.120823	−	0.166299i	0.744321	−	0.667822i	$-0.232773\pi$
$71$	−1.01807	−	1.40126i	−0.120823	−	0.166299i	−0.865144	+	0.501523i	$0.832773\pi$
$72$	−1.53625	−	14.6164i	−0.181049	−	1.72256i
$73$	−5.37999	+	1.74806i	−0.629680	+	0.204595i	−0.606433	−	0.795134i	$-0.707400\pi$
$73$	−5.37999	+	1.74806i	−0.629680	+	0.204595i	−0.0232466	+	0.999730i	$0.507400\pi$
$74$	−2.27080	+	6.98881i	−0.263975	+	0.812433i
$75$	3.44512	+	0.362097i	0.397809	+	0.0418114i
$76$			11.3137i			1.29777i
$77$		0			0
$78$	−6.00000	−	10.3923i	−0.679366	−	1.17670i
$79$	−5.81878	+	8.00886i	−0.654664	+	0.901067i	−0.999290	−	0.0376728i	$-0.988006\pi$
$79$	−5.81878	+	8.00886i	−0.654664	+	0.901067i	0.344627	+	0.938740i	$0.388006\pi$
$80$	6.58911	+	2.14093i	0.736685	+	0.239364i
$81$	6.02218	−	6.68830i	0.669131	−	0.743145i
$82$	19.4164	−	14.1068i	2.14418	−	1.55784i
$83$	−1.98168	+	1.43977i	−0.217518	+	0.158036i	−0.691208	−	0.722655i	$-0.742921\pi$
$83$	−1.98168	+	1.43977i	−0.217518	+	0.158036i	0.473691	+	0.880691i	$0.342921\pi$
$84$	−6.55611	+	7.28130i	−0.715331	+	0.794455i
$85$	−4.03499	−	1.31105i	−0.437656	−	0.142203i
$86$	−14.2530	+	19.6176i	−1.53694	+	2.11542i
$87$	−7.34847	+	4.24264i	−0.787839	+	0.454859i
$88$		0			0
$89$			8.66025i			0.917985i	0.888440	+	0.458993i	$0.151790\pi$
$89$			8.66025i			0.917985i	−0.888440	+	0.458993i	$0.848210\pi$
$90$	5.17691	+	11.6275i	0.545694	+	1.22565i
$91$	−1.23607	+	3.80423i	−0.129575	+	0.398791i
$92$	32.9456	−	10.7047i	3.43481	−	1.11604i
$93$	2.11347	−	4.74692i	0.219156	−	0.492233i
$94$	−9.97505	−	13.7295i	−1.02885	−	1.41609i
$95$	−1.51387	−	4.65921i	−0.155320	−	0.478024i
$96$		0			0
$97$	−10.5172	−	7.64121i	−1.06786	−	0.775847i	−0.0923353	−	0.995728i	$-0.529433\pi$
$97$	−10.5172	−	7.64121i	−1.06786	−	0.775847i	−0.975527	+	0.219881i	$0.929433\pi$
$98$	−12.2474			−1.23718
$99$		0			0
$100$	8.00000			0.800000
$101$	−9.90839	−	7.19887i	−0.985922	−	0.716314i	−0.0268978	−	0.999638i	$-0.508563\pi$
$101$	−9.90839	−	7.19887i	−0.985922	−	0.716314i	−0.959024	+	0.283324i	$0.908563\pi$
$102$	2.16068	+	10.1652i	0.213939	+	1.00651i
$103$	−0.618034	−	1.90211i	−0.0608967	−	0.187421i	0.915980	−	0.401224i	$-0.131415\pi$
$103$	−0.618034	−	1.90211i	−0.0608967	−	0.187421i	−0.976877	+	0.213803i	$0.931415\pi$
$104$	−8.14459	−	11.2101i	−0.798643	−	1.09924i
$105$	1.72564	−	3.87585i	0.168405	−	0.378244i
$106$	8.06998	−	2.62210i	0.783826	−	0.254680i
$107$	0.756934	−	2.32960i	0.0731756	−	0.225211i	−0.907779	−	0.419449i	$-0.862223\pi$
$107$	0.756934	−	2.32960i	0.0731756	−	0.225211i	0.980954	+	0.194238i	$0.0622233\pi$
$108$	12.2169	−	16.8151i	1.17557	−	1.61803i
$109$		−	18.3848i		−	1.76094i	−0.474100	−	0.880471i	$-0.657226\pi$
$109$		−	18.3848i		−	1.76094i	0.474100	−	0.880471i	$-0.342774\pi$
$110$		0			0
$111$	−4.50000	+	2.59808i	−0.427121	+	0.246598i
$112$	−3.32502	+	4.57649i	−0.314184	+	0.432438i
$113$	1.64728	+	0.535233i	0.154963	+	0.0503505i	0.385471	−	0.922720i	$-0.374039\pi$
$113$	1.64728	+	0.535233i	0.154963	+	0.0503505i	−0.230508	+	0.973070i	$0.574039\pi$
$114$	−8.02957	+	8.91774i	−0.752038	+	0.835223i
$115$	−12.1353	+	8.81678i	−1.13162	+	0.822169i
$116$	−15.8534	+	11.5182i	−1.47195	+	1.06944i
$117$	1.76419	−	8.29986i	0.163099	−	0.767322i
$118$	−4.03499	−	1.31105i	−0.371451	−	0.120692i
$119$	2.03615	−	2.80252i	0.186653	−	0.256906i
$120$	7.34847	+	12.7279i	0.670820	+	1.16190i
$121$		0			0
$122$			6.92820i			0.627250i
$123$	16.8776	+	1.77391i	1.52180	+	0.159948i
$124$	3.70820	−	11.4127i	0.333007	−	1.02489i
$125$	−11.5309	+	3.74663i	−1.03136	+	0.335109i
$126$	−10.3354	+	1.08629i	−0.920748	+	0.0967746i
$127$	1.66251	+	2.28825i	0.147524	+	0.203049i	0.876383	−	0.481614i	$-0.159949\pi$
$127$	1.66251	+	2.28825i	0.147524	+	0.203049i	−0.728860	+	0.684663i	$0.759949\pi$
$128$	6.05547	+	18.6368i	0.535233	+	1.64728i
$129$	−16.7717	+	3.56494i	−1.47667	+	0.313876i
$130$	9.70820	+	7.05342i	0.851466	+	0.618626i
$131$	−12.2474			−1.07006			−0.535032	−	0.844832i	$-0.679701\pi$
$131$	−12.2474			−1.07006			−0.535032	+	0.844832i	$0.679701\pi$
$132$		0			0
$133$	4.00000			0.346844
$134$	−5.94504	−	4.31932i	−0.513573	−	0.373133i
$135$	−2.78115	+	8.55951i	−0.239364	+	0.736685i
$136$	3.70820	+	11.4127i	0.317976	+	0.978629i
$137$	9.16267	+	12.6113i	0.782819	+	1.07746i	0.994965	+	0.100220i	$0.0319548\pi$
$137$	9.16267	+	12.6113i	0.782819	+	1.07746i	−0.212146	+	0.977238i	$0.568045\pi$
$138$	33.5658	+	14.9445i	2.85731	+	1.27216i
$139$	14.7950	−	4.80718i	1.25489	−	0.407739i	0.395221	−	0.918586i	$-0.370668\pi$
$139$	14.7950	−	4.80718i	1.25489	−	0.407739i	0.859672	+	0.510847i	$0.170668\pi$
$140$	3.02774	−	9.31841i	0.255890	−	0.787550i
$141$	1.25434	−	11.9343i	0.105635	−	1.00505i
$142$		−	4.24264i		−	0.356034i
$143$		0			0
$144$	6.00000	−	10.3923i	0.500000	−	0.866025i
$145$	4.98752	−	6.86474i	0.414191	−	0.570085i
$146$	−13.1782	−	4.28187i	−1.09064	−	0.354370i
$147$	−6.43582	−	5.79484i	−0.530818	−	0.477950i
$148$	−9.70820	+	7.05342i	−0.798009	+	0.579788i
$149$	1.98168	−	1.43977i	0.162345	−	0.117951i	−0.503646	−	0.863910i	$-0.668009\pi$
$149$	1.98168	−	1.43977i	0.162345	−	0.117951i	0.665992	+	0.745959i	$0.268009\pi$
$150$	6.30579	+	5.67776i	0.514866	+	0.463587i
$151$	9.41498	+	3.05911i	0.766180	+	0.248947i	0.665929	−	0.746015i	$-0.268035\pi$
$151$	9.41498	+	3.05911i	0.766180	+	0.248947i	0.100251	+	0.994962i	$0.468035\pi$
$152$	−8.14459	+	11.2101i	−0.660614	+	0.909257i
$153$	−3.67423	+	6.36396i	−0.297044	+	0.514496i
$154$		0			0
$155$			5.19615i			0.417365i
$156$	2.04833	−	19.4886i	0.163998	−	1.56033i
$157$	4.63525	−	14.2658i	0.369934	−	1.13854i	−0.576900	−	0.816815i	$-0.695738\pi$
$157$	4.63525	−	14.2658i	0.369934	−	1.13854i	0.946834	−	0.321724i	$-0.104262\pi$
$158$	−23.0619	+	7.49326i	−1.83471	+	0.596132i
$159$	5.48127	+	2.44042i	0.434693	+	0.193538i
$160$		0			0
$161$	−3.78467	−	11.6480i	−0.298274	−	0.917992i
$162$	21.5637	−	4.58350i	1.69420	−	0.360114i
$163$	8.09017	+	5.87785i	0.633671	+	0.460389i	0.857670	−	0.514200i	$-0.171911\pi$
$163$	8.09017	+	5.87785i	0.633671	+	0.460389i	−0.223999	+	0.974589i	$0.571911\pi$
$164$	39.1918			3.06037
$165$		0			0
$166$	−6.00000			−0.465690
$167$	−15.8534	−	11.5182i	−1.22678	−	0.891304i	−0.230131	−	0.973160i	$-0.573915\pi$
$167$	−15.8534	−	11.5182i	−1.22678	−	0.891304i	−0.996644	+	0.0818552i	$0.973915\pi$
$168$	−11.7378	+	2.49494i	−0.905589	+	0.192489i
$169$	1.54508	+	4.75528i	0.118853	+	0.365791i
$170$	−6.10844	−	8.40755i	−0.468496	−	0.644830i
$171$	−8.43880	+	0.886953i	−0.645331	+	0.0678270i
$172$	−37.6599	+	12.2364i	−2.87154	+	0.933020i
$173$	−0.756934	+	2.32960i	−0.0575486	+	0.177116i	−0.975699	−	0.219116i	$-0.929683\pi$
$173$	−0.756934	+	2.32960i	−0.0575486	+	0.177116i	0.918150	+	0.396233i	$0.129683\pi$
$174$	−20.6707	−	2.17258i	−1.56705	−	0.164703i
$175$		−	2.82843i		−	0.213809i
$176$		0			0
$177$	−1.50000	−	2.59808i	−0.112747	−	0.195283i
$178$	−12.4688	+	17.1618i	−0.934577	+	1.28633i
$179$	−14.8255	−	4.81710i	−1.10811	−	0.360047i	−0.302892	−	0.953025i	$-0.597952\pi$
$179$	−14.8255	−	4.81710i	−1.10811	−	0.360047i	−0.805219	+	0.592978i	$0.797952\pi$
$180$	−4.32136	+	20.3304i	−0.322095	+	1.51534i
$181$	4.04508	−	2.93893i	0.300669	−	0.218449i	−0.427213	−	0.904151i	$-0.640505\pi$
$181$	4.04508	−	2.93893i	0.300669	−	0.218449i	0.727882	+	0.685702i	$0.240505\pi$
$182$	−7.92672	+	5.75910i	−0.587567	+	0.426893i
$183$	−3.27806	+	3.64065i	−0.242321	+	0.269125i
$184$	40.3499	+	13.1105i	2.97463	+	0.966517i
$185$	3.05422	−	4.20378i	0.224551	−	0.309068i
$186$	11.0227	−	6.36396i	0.808224	−	0.466628i
$187$		0			0
$188$		−	27.7128i		−	2.02116i
$189$	−5.94504	−	4.31932i	−0.432438	−	0.314184i
$190$	3.70820	−	11.4127i	0.269021	−	0.827963i
$191$	4.94183	−	1.60570i	0.357579	−	0.116184i	−0.124718	−	0.992192i	$-0.539803\pi$
$191$	4.94183	−	1.60570i	0.357579	−	0.116184i	0.482297	+	0.876008i	$0.339803\pi$
$192$	−5.63591	+	12.6585i	−0.406737	+	0.913545i
$193$	8.31254	+	11.4412i	0.598350	+	0.823558i	0.995556	−	0.0941717i	$-0.0300203\pi$
$193$	8.31254	+	11.4412i	0.598350	+	0.823558i	−0.397206	+	0.917729i	$0.630020\pi$
$194$	−9.84014	−	30.2848i	−0.706481	−	2.17432i
$195$	1.76419	+	8.29986i	0.126336	+	0.594365i
$196$	−16.1803	−	11.7557i	−1.15574	−	0.839693i
$197$	7.34847			0.523557			0.261778	−	0.965128i	$-0.415691\pi$
$197$	7.34847			0.523557			0.261778	+	0.965128i	$0.415691\pi$
$198$		0			0
$199$	−18.0000			−1.27599			−0.637993	−	0.770042i	$-0.720235\pi$
$199$	−18.0000			−1.27599			−0.637993	+	0.770042i	$0.720235\pi$
$200$	7.92672	+	5.75910i	0.560503	+	0.407230i
$201$	−1.08034	−	5.08260i	−0.0762014	−	0.358499i
$202$	−9.27051	−	28.5317i	−0.652271	−	2.00748i
$203$	4.07230	+	5.60503i	0.285819	+	0.393396i
$204$	−6.90255	+	15.5034i	−0.483275	+	1.08545i
$205$	−16.1400	+	5.24419i	−1.12726	+	0.366270i
$206$	1.51387	−	4.65921i	0.105476	−	0.324622i
$207$	10.5673	+	23.7346i	0.734480	+	1.64967i
$208$		−	11.3137i		−	0.784465i
$209$		0			0
$210$	9.00000	−	5.19615i	0.621059	−	0.358569i
$211$	−3.32502	+	4.57649i	−0.228904	+	0.315059i	−0.907984	−	0.419005i	$-0.862379\pi$
$211$	−3.32502	+	4.57649i	−0.228904	+	0.315059i	0.679080	+	0.734064i	$0.262379\pi$
$212$	13.1782	+	4.28187i	0.905084	+	0.294080i
$213$	2.00739	−	2.22943i	0.137544	−	0.152758i
$214$	4.85410	−	3.52671i	0.331820	−	0.241081i
$215$	13.8718	−	10.0784i	0.946046	−	0.687342i
$216$	24.2099	−	7.86629i	1.64728	−	0.535233i
$217$	−4.03499	−	1.31105i	−0.273913	−	0.0889997i
$218$	26.4699	−	36.4327i	1.79277	−	2.46754i
$219$	−4.89898	−	8.48528i	−0.331042	−	0.573382i
$220$		0			0
$221$			6.92820i			0.466041i
$222$	−12.6582	−	1.33043i	−0.849563	−	0.0892926i
$223$	−3.39919	+	10.4616i	−0.227626	+	0.700562i	0.770388	+	0.637575i	$0.220063\pi$
$223$	−3.39919	+	10.4616i	−0.227626	+	0.700562i	−0.998014	+	0.0629866i	$0.979937\pi$
$224$		0			0
$225$	0.627171	+	5.96713i	0.0418114	+	0.397809i
$226$	2.49376	+	3.43237i	0.165883	+	0.228318i
$227$	6.81241	+	20.9664i	0.452155	+	1.39159i	0.874443	+	0.485129i	$0.161227\pi$
$227$	6.81241	+	20.9664i	0.452155	+	1.39159i	−0.422287	+	0.906462i	$0.638773\pi$
$228$	−19.1677	+	4.07422i	−1.26941	+	0.269822i
$229$	7.28115	+	5.29007i	0.481152	+	0.349577i	0.801772	−	0.597631i	$-0.203891\pi$
$229$	7.28115	+	5.29007i	0.481152	+	0.349577i	−0.320619	+	0.947208i	$0.603891\pi$
$230$	−36.7423			−2.42272
$231$		0			0
$232$	−24.0000			−1.57568
$233$	19.8168	+	14.3977i	1.29824	+	0.943227i	0.999937	−	0.0112436i	$-0.00357902\pi$
$233$	19.8168	+	14.3977i	1.29824	+	0.943227i	0.298304	+	0.954471i	$0.403579\pi$
$234$	15.4460	−	13.9076i	1.00973	−	0.909169i
$235$	3.70820	+	11.4127i	0.241897	+	0.744481i
$236$	−4.07230	−	5.60503i	−0.265084	−	0.364857i
$237$	−15.6640	−	6.97408i	−1.01749	−	0.453015i
$238$	8.06998	−	2.62210i	0.523099	−	0.169965i
$239$	−6.81241	+	20.9664i	−0.440658	+	1.35621i	0.446518	+	0.894775i	$0.352664\pi$
$239$	−6.81241	+	20.9664i	−0.440658	+	1.35621i	−0.887176	+	0.461431i	$0.847336\pi$
$240$	−1.25434	+	11.9343i	−0.0809674	+	0.770353i
$241$			2.82843i			0.182195i	0.995842	+	0.0910975i	$0.0290375\pi$
$241$			2.82843i			0.182195i	−0.995842	+	0.0910975i	$0.970963\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	−6.65003	+	9.15298i	−0.425725	+	0.585960i
$245$	8.23639	+	2.67617i	0.526204	+	0.170974i
$246$	30.8920	+	27.8152i	1.96960	+	1.77343i
$247$	−6.47214	+	4.70228i	−0.411812	+	0.299199i
$248$	11.8901	−	8.63864i	0.755020	−	0.548554i
$249$	−3.15290	−	2.83888i	−0.199807	−	0.179907i
$250$	−28.2449	−	9.17734i	−1.78637	−	0.580426i
$251$	−9.16267	+	12.6113i	−0.578342	+	0.796020i	−0.993512	−	0.113724i	$-0.963722\pi$
$251$	−9.16267	+	12.6113i	−0.578342	+	0.796020i	0.415170	+	0.909744i	$0.363722\pi$
$252$	−14.6969	−	8.48528i	−0.925820	−	0.534522i
$253$		0			0
$254$			6.92820i			0.434714i
$255$	0.768124	−	7.30821i	0.0481018	−	0.457658i
$256$	−9.88854	+	30.4338i	−0.618034	+	1.90211i
$257$	−9.88367	+	3.21140i	−0.616526	+	0.200322i	−0.600597	−	0.799552i	$-0.705071\pi$
$257$	−9.88367	+	3.21140i	−0.616526	+	0.200322i	−0.0159289	+	0.999873i	$0.505071\pi$
$258$	−38.3689	−	17.0829i	−2.38874	−	1.06354i
$259$	2.49376	+	3.43237i	0.154955	+	0.213277i
$260$	6.05547	+	18.6368i	0.375544	+	1.15581i
$261$	−9.83417	−	10.9220i	−0.608720	−	0.676052i
$262$	−24.2705	−	17.6336i	−1.49944	−	1.08940i
$263$	12.2474			0.755210			0.377605	−	0.925967i	$-0.376748\pi$
$263$	12.2474			0.755210			0.377605	+	0.925967i	$0.376748\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$	7.92672	+	5.75910i	0.486018	+	0.353113i
$267$	−14.6722	+	3.11868i	−0.897925	+	0.190860i
$268$	−3.70820	−	11.4127i	−0.226515	−	0.697140i
$269$	−10.1807	−	14.0126i	−0.620731	−	0.854362i	0.376675	−	0.926345i	$-0.377067\pi$
$269$	−10.1807	−	14.0126i	−0.620731	−	0.854362i	−0.997406	+	0.0719830i	$0.977067\pi$
$270$	−17.8351	+	12.9580i	−1.08541	+	0.788597i
$271$	5.37999	−	1.74806i	0.326811	−	0.106187i	−0.141016	−	0.990007i	$-0.545037\pi$
$271$	5.37999	−	1.74806i	0.326811	−	0.106187i	0.467827	+	0.883820i	$0.345037\pi$
$272$	−3.02774	+	9.31841i	−0.183583	+	0.565012i
$273$	−6.89025	−	0.724194i	−0.417017	−	0.0438302i
$274$			38.1838i			2.30677i
$275$		0			0
$276$	30.0000	+	51.9615i	1.80579	+	3.12772i
$277$	10.8063	−	14.8736i	0.649288	−	0.893668i	−0.349780	−	0.936832i	$-0.613744\pi$
$277$	10.8063	−	14.8736i	0.649288	−	0.893668i	0.999068	+	0.0431639i	$0.0137438\pi$
$278$	36.2401	+	11.7751i	2.17354	+	0.706225i
$279$	8.80333	+	1.87121i	0.527041	+	0.112026i
$280$	9.70820	−	7.05342i	0.580176	−	0.421523i
$281$	−17.8351	+	12.9580i	−1.06395	+	0.773007i	−0.974816	−	0.223012i	$-0.928411\pi$
$281$	−17.8351	+	12.9580i	−1.06395	+	0.773007i	−0.0891377	+	0.996019i	$0.528411\pi$
$282$	19.6683	−	21.8439i	1.17123	−	1.30079i
$283$	18.8300	+	6.11822i	1.11932	+	0.363691i	0.809510	−	0.587106i	$-0.199733\pi$
$283$	18.8300	+	6.11822i	1.11932	+	0.363691i	0.309815	+	0.950797i	$0.399733\pi$
$284$	4.07230	−	5.60503i	0.241646	−	0.332598i
$285$	7.34847	−	4.24264i	0.435286	−	0.251312i
$286$		0			0
$287$		−	13.8564i		−	0.817918i
$288$		0			0
$289$	−3.39919	+	10.4616i	−0.199952	+	0.615390i
$290$	19.7673	−	6.42280i	1.16078	−	0.377160i
$291$	9.15835	−	20.5700i	0.536872	−	1.20583i
$292$	−13.3001	−	18.3060i	−0.778327	−	1.07128i
$293$	1.51387	+	4.65921i	0.0884411	+	0.272194i	0.985489	−	0.169740i	$-0.0542927\pi$
$293$	1.51387	+	4.65921i	0.0884411	+	0.272194i	−0.897048	+	0.441934i	$0.854293\pi$
$294$	−4.41047	−	20.7496i	−0.257224	−	1.21014i
$295$	2.42705	+	1.76336i	0.141308	+	0.102667i
$296$	−14.6969			−0.854242
$297$		0			0
$298$	6.00000			0.347571
$299$	19.8168	+	14.3977i	1.14603	+	0.832643i
$300$	2.88091	+	13.5536i	0.166329	+	0.782518i
$301$	4.32624	+	13.3148i	0.249360	+	0.767452i
$302$	14.2530	+	19.6176i	0.820170	+	1.12887i
$303$	8.62819	−	19.3792i	0.495676	−	1.11331i
$304$	−10.7600	+	3.49613i	−0.617127	+	0.200517i
$305$	1.51387	−	4.65921i	0.0866838	−	0.266785i
$306$	−16.4438	+	7.32126i	−0.940031	+	0.418529i
$307$			2.82843i			0.161427i	0.996737	+	0.0807134i	$0.0257199\pi$
$307$			2.82843i			0.161427i	−0.996737	+	0.0807134i	$0.974280\pi$
$308$		0			0
$309$	3.00000	−	1.73205i	0.170664	−	0.0985329i
$310$	−7.48128	+	10.2971i	−0.424908	+	0.584836i
$311$	16.4728	+	5.35233i	0.934086	+	0.303503i	0.736232	−	0.676729i	$-0.236603\pi$
$311$	16.4728	+	5.35233i	0.934086	+	0.303503i	0.197853	+	0.980232i	$0.436603\pi$
$312$	16.0591	−	17.8355i	0.909169	−	1.00973i
$313$	26.6976	−	19.3969i	1.50904	−	1.09638i	0.542432	−	0.840099i	$-0.317503\pi$
$313$	26.6976	−	19.3969i	1.50904	−	1.09638i	0.966603	−	0.256279i	$-0.0824966\pi$
$314$	29.7252	−	21.5966i	1.67749	−	1.21877i
$315$	7.18789	+	1.52783i	0.404992	+	0.0860836i
$316$	−37.6599	−	12.2364i	−2.11854	−	0.688354i
$317$	1.01807	−	1.40126i	0.0571807	−	0.0787025i	−0.779469	−	0.626441i	$-0.784511\pi$
$317$	1.01807	−	1.40126i	0.0571807	−	0.0787025i	0.836650	+	0.547738i	$0.184511\pi$
$318$	7.34847	+	12.7279i	0.412082	+	0.713746i
$319$		0			0
$320$		−	13.8564i		−	0.774597i
$321$	4.21940	+	0.443477i	0.235504	+	0.0247525i
$322$	9.27051	−	28.5317i	0.516625	−	1.59001i
$323$	6.58911	−	2.14093i	0.366628	−	0.119125i
$324$	32.8876	+	14.6425i	1.82709	+	0.813473i
$325$	3.32502	+	4.57649i	0.184439	+	0.253858i
$326$	7.56934	+	23.2960i	0.419227	+	1.29025i
$327$	31.1475	−	6.62061i	1.72246	−	0.366120i
$328$	38.8328	+	28.2137i	2.14418	+	1.55784i
$329$	−9.79796			−0.540179
$330$		0			0
$331$	5.00000			0.274825			0.137412	−	0.990514i	$-0.456121\pi$
$331$	5.00000			0.274825			0.137412	+	0.990514i	$0.456121\pi$
$332$	−7.92672	−	5.75910i	−0.435035	−	0.316071i
$333$	−6.02218	−	6.68830i	−0.330013	−	0.366517i
$334$	−14.8328	−	45.6507i	−0.811616	−	2.49790i
$335$	3.05422	+	4.20378i	0.166870	+	0.229677i
$336$	−8.95088	−	3.98519i	−0.488311	−	0.217410i
$337$	−22.8649	+	7.42927i	−1.24553	+	0.404698i	−0.856318	−	0.516449i	$-0.827254\pi$
$337$	−22.8649	+	7.42927i	−1.24553	+	0.404698i	−0.389215	+	0.921147i	$0.627254\pi$
$338$	−3.78467	+	11.6480i	−0.205859	+	0.633569i
$339$	−0.313585	+	2.98357i	−0.0170316	+	0.162045i
$340$		−	16.9706i		−	0.920358i
$341$		0			0
$342$	−18.0000	−	10.3923i	−0.973329	−	0.561951i
$343$	−9.97505	+	13.7295i	−0.538602	+	0.741322i
$344$	−46.1238	−	14.9865i	−2.48683	−	0.808019i
$345$	−19.3075	−	17.3845i	−1.03948	−	0.935951i
$346$	−4.85410	+	3.52671i	−0.260958	+	0.189597i
$347$	7.92672	−	5.75910i	0.425528	−	0.309164i	−0.354330	−	0.935120i	$-0.615291\pi$
$347$	7.92672	−	5.75910i	0.425528	−	0.309164i	0.779858	+	0.625956i	$0.215291\pi$
$348$	−25.2232	−	22.7110i	−1.35210	−	1.21744i
$349$	9.41498	+	3.05911i	0.503972	+	0.163751i	0.549959	−	0.835192i	$-0.314643\pi$
$349$	9.41498	+	3.05911i	0.503972	+	0.163751i	−0.0459869	+	0.998942i	$0.514643\pi$
$350$	4.07230	−	5.60503i	0.217673	−	0.299602i
$351$	14.6969			0.784465
$352$		0			0
$353$		−	25.9808i		−	1.38282i	−0.722464	−	0.691408i	$-0.756991\pi$
$353$		−	25.9808i		−	1.38282i	0.722464	−	0.691408i	$-0.243009\pi$
$354$	0.768124	−	7.30821i	0.0408253	−	0.388427i
$355$	−0.927051	+	2.85317i	−0.0492028	+	0.151431i
$356$	−32.9456	+	10.7047i	−1.74611	+	0.567346i
$357$	5.48127	+	2.44042i	0.290100	+	0.129161i
$358$	−22.4439	−	30.8913i	−1.18619	−	1.63266i
$359$	−7.56934	−	23.2960i	−0.399494	−	1.22952i	−0.925406	−	0.378978i	$-0.876276\pi$
$359$	−7.56934	−	23.2960i	−0.399494	−	1.22952i	0.525911	−	0.850539i	$-0.323724\pi$
$360$	−18.9174	+	17.0333i	−0.997033	+	0.897733i
$361$	−8.89919	−	6.46564i	−0.468378	−	0.340297i
$362$	12.2474			0.643712
$363$		0			0
$364$	−16.0000			−0.838628
$365$	7.92672	+	5.75910i	0.414903	+	0.301445i
$366$	−11.7378	+	2.49494i	−0.613543	+	0.130413i
$367$	−2.16312	−	6.65740i	−0.112914	−	0.347513i	0.878592	−	0.477573i	$-0.158483\pi$
$367$	−2.16312	−	6.65740i	−0.112914	−	0.347513i	−0.991506	+	0.130059i	$0.958483\pi$
$368$	20.3615	+	28.0252i	1.06142	+	1.46091i
$369$	3.07250	+	29.2329i	0.159948	+	1.52180i
$370$	12.1050	−	3.93314i	0.629308	−	0.204474i
$371$	1.51387	−	4.65921i	0.0785961	−	0.241894i
$372$	20.6707	+	2.17258i	1.07173	+	0.112643i
$373$		−	32.5269i		−	1.68418i	−0.539337	−	0.842090i	$-0.681325\pi$
$373$		−	32.5269i		−	1.68418i	0.539337	−	0.842090i	$-0.318675\pi$
$374$		0			0
$375$	−10.5000	−	18.1865i	−0.542218	−	0.939149i
$376$	19.9501	−	27.4589i	1.02885	−	1.41609i
$377$	−13.1782	−	4.28187i	−0.678713	−	0.220527i
$378$	−5.56231	−	17.1190i	−0.286094	−	0.880507i
$379$	−13.7533	+	9.99235i	−0.706459	+	0.513273i	−0.882029	−	0.471194i	$-0.843823\pi$
$379$	−13.7533	+	9.99235i	−0.706459	+	0.513273i	0.175570	+	0.984467i	$0.443823\pi$
$380$	15.8534	−	11.5182i	0.813264	−	0.590871i
$381$	−3.27806	+	3.64065i	−0.167940	+	0.186516i
$382$	12.1050	+	3.93314i	0.619344	+	0.201237i
$383$	−13.2350	+	18.2164i	−0.676275	+	0.930813i	−0.999882	−	0.0153791i	$-0.995104\pi$
$383$	−13.2350	+	18.2164i	−0.676275	+	0.930813i	0.323607	+	0.946192i	$0.395104\pi$
$384$	−29.3939	+	16.9706i	−1.50000	+	0.866025i
$385$		0			0
$386$			34.6410i			1.76318i
$387$	−12.0795	−	27.1309i	−0.614034	−	1.37914i
$388$	16.0689	−	49.4549i	0.815774	−	2.51069i
$389$	21.4146	−	6.95803i	1.08576	−	0.352786i	0.289156	−	0.957282i	$-0.406625\pi$
$389$	21.4146	−	6.95803i	1.08576	−	0.352786i	0.796608	+	0.604496i	$0.206625\pi$
$390$	−8.45386	+	18.9877i	−0.428078	+	0.961479i
$391$	−12.4688	−	17.1618i	−0.630575	−	0.867912i
$392$	−7.56934	−	23.2960i	−0.382309	−	1.17663i
$393$	−4.41047	−	20.7496i	−0.222479	−	1.04668i
$394$	14.5623	+	10.5801i	0.733638	+	0.533019i
$395$	17.1464			0.862730
$396$		0			0
$397$	32.0000			1.60603			0.803017	−	0.595956i	$-0.203227\pi$
$397$	32.0000			1.60603			0.803017	+	0.595956i	$0.203227\pi$
$398$	−35.6702	−	25.9159i	−1.78799	−	1.29905i
$399$	1.44045	+	6.77681i	0.0721129	+	0.339265i
$400$	2.47214	+	7.60845i	0.123607	+	0.380423i
$401$	−6.10844	−	8.40755i	−0.305041	−	0.419853i	0.628786	−	0.777579i	$-0.283552\pi$
$401$	−6.10844	−	8.40755i	−0.305041	−	0.419853i	−0.933827	+	0.357726i	$0.883552\pi$
$402$	5.17691	−	11.6275i	0.258201	−	0.579929i
$403$	8.06998	−	2.62210i	0.401994	−	0.130616i
$404$	15.1387	−	46.5921i	0.753177	−	2.31804i
$405$	−15.5031	−	1.62944i	−0.770353	−	0.0809674i
$406$			16.9706i			0.842235i
$407$		0			0
$408$	−18.0000	+	10.3923i	−0.891133	+	0.514496i
$409$	10.8063	−	14.8736i	0.534337	−	0.735452i	−0.453446	−	0.891284i	$-0.649806\pi$
$409$	10.8063	−	14.8736i	0.534337	−	0.735452i	0.987784	+	0.155831i	$0.0498057\pi$
$410$	−39.5347	−	12.8456i	−1.95248	−	0.634399i
$411$	−18.0665	+	20.0649i	−0.891156	+	0.989729i
$412$	6.47214	−	4.70228i	0.318859	−	0.231665i
$413$	−1.98168	+	1.43977i	−0.0975120	+	0.0708466i
$414$	−13.2314	+	62.2489i	−0.650289	+	3.05937i
$415$	4.03499	+	1.31105i	0.198070	+	0.0643568i
$416$		0			0
$417$	13.4722	+	23.3345i	0.659736	+	1.14270i
$418$		0			0
$419$			6.92820i			0.338465i	0.985576	+	0.169232i	$0.0541289\pi$
$419$			6.92820i			0.338465i	−0.985576	+	0.169232i	$0.945871\pi$
$420$	16.8776	+	1.77391i	0.823542	+	0.0865578i
$421$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$421$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$422$	−13.1782	+	4.28187i	−0.641506	+	0.208438i
$423$	20.6707	−	2.17258i	1.00505	−	0.105635i
$424$	9.97505	+	13.7295i	0.484431	+	0.666762i
$425$	−1.51387	−	4.65921i	−0.0734334	−	0.226005i
$426$	7.18789	−	1.52783i	0.348254	−	0.0740237i
$427$	3.23607	+	2.35114i	0.156604	+	0.113780i
$428$	9.79796			0.473602
$429$		0			0
$430$	42.0000			2.02542
$431$	5.94504	+	4.31932i	0.286362	+	0.208054i	0.721688	−	0.692219i	$-0.243367\pi$
$431$	5.94504	+	4.31932i	0.286362	+	0.208054i	−0.435325	+	0.900273i	$0.643367\pi$
$432$	19.7673	+	6.42280i	0.951057	+	0.309017i
$433$	1.54508	+	4.75528i	0.0742520	+	0.228524i	0.981294	−	0.192517i	$-0.0616649\pi$
$433$	1.54508	+	4.75528i	0.0742520	+	0.228524i	−0.907042	+	0.421041i	$0.861665\pi$
$434$	−6.10844	−	8.40755i	−0.293215	−	0.403575i
$435$	13.4263	+	5.97778i	0.643743	+	0.286613i
$436$	69.9398	−	22.7248i	3.34951	−	1.08832i
$437$	7.56934	−	23.2960i	0.362091	−	1.11440i
$438$	2.50868	−	23.8685i	0.119870	−	1.14048i
$439$			5.65685i			0.269987i	0.990846	+	0.134993i	$0.0431013\pi$
$439$			5.65685i			0.269987i	−0.990846	+	0.134993i	$0.956899\pi$
$440$		0			0
$441$	7.50000	−	12.9904i	0.357143	−	0.618590i
$442$	−9.97505	+	13.7295i	−0.474465	+	0.653044i
$443$	24.7092	+	8.02850i	1.17397	+	0.381445i	0.830123	−	0.557581i	$-0.188270\pi$
$443$	24.7092	+	8.02850i	1.17397	+	0.381445i	0.343846	+	0.939026i	$0.388270\pi$
$444$	−15.4460	−	13.9076i	−0.733034	−	0.660026i
$445$	12.1353	−	8.81678i	0.575266	−	0.417955i
$446$	−21.7985	+	15.8375i	−1.03219	+	0.749928i
$447$	3.15290	+	2.83888i	0.149127	+	0.134274i
$448$	10.7600	+	3.49613i	0.508361	+	0.165177i
$449$	7.12652	−	9.80881i	0.336321	−	0.462906i	−0.607041	−	0.794670i	$-0.707644\pi$
$449$	7.12652	−	9.80881i	0.336321	−	0.462906i	0.943362	+	0.331764i	$0.107644\pi$
$450$	−7.34847	+	12.7279i	−0.346410	+	0.600000i
$451$		0			0
$452$			6.92820i			0.325875i
$453$	−1.79229	+	17.0525i	−0.0842091	+	0.801196i
$454$	−16.6869	+	51.3571i	−0.783156	+	2.41031i
$455$	6.58911	−	2.14093i	0.308902	−	0.100368i
$456$	−21.9251	−	9.76168i	−1.02674	−	0.457133i
$457$	18.2876	+	25.1707i	0.855457	+	1.17744i	0.982634	+	0.185556i	$0.0594085\pi$
$457$	18.2876	+	25.1707i	0.855457	+	1.17744i	−0.127177	+	0.991880i	$0.540591\pi$
$458$	6.81241	+	20.9664i	0.318323	+	0.979697i
$459$	−12.1050	−	3.93314i	−0.565012	−	0.183583i
$460$	−48.5410	−	35.2671i	−2.26324	−	1.64434i
$461$	−4.89898			−0.228168			−0.114084	−	0.993471i	$-0.536393\pi$
$461$	−4.89898			−0.228168			−0.114084	+	0.993471i	$0.536393\pi$
$462$		0			0
$463$	19.0000			0.883005			0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000			0.883005			0.441502	+	0.897260i	$0.354446\pi$
$464$	−15.8534	−	11.5182i	−0.735977	−	0.534719i
$465$	−8.80333	+	1.87121i	−0.408245	+	0.0867751i
$466$	18.5410	+	57.0634i	0.858896	+	2.64341i
$467$	−15.2711	−	21.0189i	−0.706663	−	0.972638i	−0.999862	−	0.0165865i	$-0.994720\pi$
$467$	−15.2711	−	21.0189i	−0.706663	−	0.972638i	0.293200	−	0.956051i	$-0.405280\pi$
$468$	33.7552	−	3.54781i	1.56033	−	0.163998i
$469$	−4.03499	+	1.31105i	−0.186319	+	0.0605386i
$470$	−9.08321	+	27.9552i	−0.418977	+	1.28948i
$471$	25.8384	+	2.71573i	1.19057	+	0.125134i
$472$		−	8.48528i		−	0.390567i
$473$		0			0
$474$	−21.0000	−	36.3731i	−0.964562	−	1.67067i
$475$	3.32502	−	4.57649i	0.152562	−	0.209984i
$476$	13.1782	+	4.28187i	0.604023	+	0.196259i
$477$	−2.16068	+	10.1652i	−0.0989308	+	0.465433i
$478$	−43.6869	+	31.7404i	−1.99819	+	1.45177i
$479$	−23.7801	+	17.2773i	−1.08654	+	0.789419i	−0.978812	−	0.204761i	$-0.934358\pi$
$479$	−23.7801	+	17.2773i	−1.08654	+	0.789419i	−0.107731	+	0.994180i	$0.534358\pi$
$480$		0			0
$481$	−8.06998	−	2.62210i	−0.367960	−	0.119557i
$482$	−4.07230	+	5.60503i	−0.185488	+	0.255302i
$483$	18.3712	−	10.6066i	0.835917	−	0.482617i
$484$		0			0
$485$			22.5167i			1.02243i
$486$	15.5307	+	34.8826i	0.704489	+	1.58231i
$487$	8.34346	−	25.6785i	0.378078	−	1.16361i	−0.563300	−	0.826252i	$-0.690469\pi$
$487$	8.34346	−	25.6785i	0.378078	−	1.16361i	0.941378	−	0.337353i	$-0.109531\pi$
$488$	−13.1782	+	4.28187i	−0.596550	+	0.193831i
$489$	−7.04489	+	15.8231i	−0.318581	+	0.715544i
$490$	12.4688	+	17.1618i	0.563283	+	0.775293i
$491$	7.56934	+	23.2960i	0.341600	+	1.05134i	0.963379	+	0.268143i	$0.0864100\pi$
$491$	7.56934	+	23.2960i	0.341600	+	1.05134i	−0.621780	+	0.783192i	$0.713590\pi$
$492$	14.1135	+	66.3989i	0.636286	+	2.99349i
$493$	9.70820	+	7.05342i	0.437236	+	0.317670i
$494$	−19.5959			−0.881662
$495$		0			0
$496$	12.0000			0.538816
$497$	−1.98168	−	1.43977i	−0.0888904	−	0.0645827i
$498$	−2.16068	−	10.1652i	−0.0968225	−	0.455514i
$499$	1.85410	+	5.70634i	0.0830010	+	0.255451i	0.983941	−	0.178492i	$-0.0571219\pi$
$499$	1.85410	+	5.70634i	0.0830010	+	0.255451i	−0.900940	+	0.433943i	$0.857122\pi$
$500$	−28.5061	−	39.2352i	−1.27483	−	1.75465i
$501$	13.8051	−	31.0068i	0.616766	−	1.38528i
$502$	−36.3149	+	11.7994i	−1.62081	+	0.526634i
$503$	−6.81241	+	20.9664i	−0.303750	+	0.934847i	0.676390	+	0.736543i	$0.263543\pi$
$503$	−6.81241	+	20.9664i	−0.303750	+	0.934847i	−0.980141	+	0.198304i	$0.936457\pi$
$504$	−8.45386	−	18.9877i	−0.376565	−	0.845779i
$505$			21.2132i			0.943975i
$506$		0			0
$507$	−7.50000	+	4.33013i	−0.333087	+	0.192308i
$508$	−6.65003	+	9.15298i	−0.295047	+	0.406098i
$509$	28.0037	+	9.09896i	1.24124	+	0.403304i	0.854775	−	0.518998i	$-0.173695\pi$
$509$	28.0037	+	9.09896i	1.24124	+	0.403304i	0.386468	+	0.922303i	$0.373695\pi$
$510$	12.0444	−	13.3766i	0.533333	−	0.592326i
$511$	−6.47214	+	4.70228i	−0.286310	+	0.208017i
$512$	−31.7069	+	23.0364i	−1.40126	+	1.01807i
$513$	−4.54160	−	13.9776i	−0.200517	−	0.617127i
$514$	−24.2099	−	7.86629i	−1.06785	−	0.346967i
$515$	−2.03615	+	2.80252i	−0.0897234	+	0.123494i
$516$	−34.2929	−	59.3970i	−1.50966	−	2.61481i
$517$		0			0
$518$			10.3923i			0.456612i
$519$	−4.21940	−	0.443477i	−0.185211	−	0.0194665i
$520$	−7.41641	+	22.8254i	−0.325231	+	1.00096i
$521$	37.8874	−	12.3104i	1.65988	−	0.539327i	0.679031	−	0.734110i	$-0.262400\pi$
$521$	37.8874	−	12.3104i	1.65988	−	0.539327i	0.980846	+	0.194783i	$0.0624003\pi$
$522$	−3.76302	−	35.8028i	−0.164703	−	1.56705i
$523$	−16.6251	−	22.8825i	−0.726964	−	1.00058i	−0.999264	−	0.0383675i	$-0.987784\pi$
$523$	−16.6251	−	22.8825i	−0.726964	−	1.00058i	0.272300	−	0.962212i	$-0.412216\pi$
$524$	−15.1387	−	46.5921i	−0.661336	−	2.03538i
$525$	4.79193	−	1.01856i	0.209137	−	0.0444534i
$526$	24.2705	+	17.6336i	1.05824	+	0.768860i
$527$	−7.34847			−0.320104
$528$		0			0
$529$	−52.0000			−2.26087
$530$	−11.8901	−	8.63864i	−0.516472	−	0.375239i
$531$	3.86149	−	3.47690i	0.167575	−	0.150885i
$532$	4.94427	+	15.2169i	0.214361	+	0.659736i
$533$	16.2892	+	22.4201i	0.705563	+	0.971124i
$534$	−33.5658	−	14.9445i	−1.45253	−	0.646710i
$535$	−4.03499	+	1.31105i	−0.174448	+	0.0566816i
$536$	4.54160	−	13.9776i	0.196167	−	0.603741i
$537$	2.82227	−	26.8521i	0.121790	−	1.15875i
$538$		−	42.4264i		−	1.82913i
$539$		0			0
$540$	−36.0000			−1.54919
$541$	−8.31254	+	11.4412i	−0.357384	+	0.491897i	−0.949418	−	0.314016i	$-0.898325\pi$
$541$	−8.31254	+	11.4412i	−0.357384	+	0.491897i	0.592034	+	0.805913i	$0.298325\pi$
$542$	13.1782	+	4.28187i	0.566053	+	0.183922i
$543$	6.43582	+	5.79484i	0.276188	+	0.248680i
$544$		0			0
$545$	−25.7618	+	18.7171i	−1.10352	+	0.801751i
$546$	−12.6116	−	11.3555i	−0.539726	−	0.485972i
$547$	−13.4500	−	4.37016i	−0.575079	−	0.186855i	0.00701574	−	0.999975i	$-0.497767\pi$
$547$	−13.4500	−	4.37016i	−0.575079	−	0.186855i	−0.582095	+	0.813121i	$0.697767\pi$
$548$	−36.6507	+	50.4453i	−1.56564	+	2.15492i
$549$	−7.34847	−	4.24264i	−0.313625	−	0.181071i
$550$		0			0
$551$			13.8564i			0.590303i
$552$	−7.68124	+	73.0821i	−0.326935	+	3.11058i
$553$	−4.32624	+	13.3148i	−0.183970	+	0.566203i
$554$	42.8292	−	13.9161i	1.81964	−	0.591237i
$555$	8.22191	+	3.66063i	0.349001	+	0.155385i
$556$	36.5752	+	50.3414i	1.55113	+	2.13495i
$557$	−9.84014	−	30.2848i	−0.416940	−	1.28321i	−0.910504	−	0.413500i	$-0.864306\pi$
$557$	−9.84014	−	30.2848i	−0.416940	−	1.28321i	0.493564	−	0.869710i	$-0.335694\pi$
$558$	14.7513	+	16.3829i	0.624471	+	0.693545i
$559$	−22.6525	−	16.4580i	−0.958098	−	0.696099i
$560$	9.79796			0.414039
$561$		0			0
$562$	−54.0000			−2.27785
$563$	3.96336	+	2.87955i	0.167036	+	0.121358i	0.668163	−	0.744015i	$-0.267081\pi$
$563$	3.96336	+	2.87955i	0.167036	+	0.121358i	−0.501127	+	0.865374i	$0.667081\pi$
$564$	46.9511	−	9.97976i	1.97700	−	0.420224i
$565$	−0.927051	−	2.85317i	−0.0390013	−	0.120034i
$566$	28.5061	+	39.2352i	1.19820	+	1.64918i
$567$	5.17691	−	11.6275i	0.217410	−	0.488311i
$568$	8.06998	−	2.62210i	0.338609	−	0.110021i
$569$	−9.08321	+	27.9552i	−0.380788	+	1.17194i	0.558702	+	0.829368i	$0.311299\pi$
$569$	−9.08321	+	27.9552i	−0.380788	+	1.17194i	−0.939490	+	0.342576i	$0.888701\pi$
$570$	20.6707	+	2.17258i	0.865802	+	0.0909995i
$571$			19.7990i			0.828562i	0.910149	+	0.414281i	$0.135967\pi$
$571$			19.7990i			0.828562i	−0.910149	+	0.414281i	$0.864033\pi$
$572$		0			0
$573$	4.50000	+	7.79423i	0.187990	+	0.325609i
$574$	19.9501	−	27.4589i	0.832701	−	1.14611i
$575$	−16.4728	−	5.35233i	−0.686963	−	0.223208i
$576$	−23.4755	−	4.98988i	−0.978148	−	0.207912i
$577$	−2.42705	+	1.76336i	−0.101039	+	0.0734095i	−0.637158	−	0.770733i	$-0.719890\pi$
$577$	−2.42705	+	1.76336i	−0.101039	+	0.0734095i	0.536118	+	0.844143i	$0.319890\pi$
$578$	−21.7985	+	15.8375i	−0.906697	+	0.658754i
$579$	−16.3903	+	18.2033i	−0.681157	+	0.756502i
$580$	32.2799	+	10.4884i	1.34035	+	0.435506i
$581$	−2.03615	+	2.80252i	−0.0844736	+	0.116268i
$582$	47.7650	−	27.5772i	1.97993	−	1.14311i
$583$		0			0
$584$		−	27.7128i		−	1.14676i
$585$	−13.4263	+	5.97778i	−0.555110	+	0.247151i
$586$	−3.70820	+	11.4127i	−0.153184	+	0.471453i
$587$	−26.3565	+	8.56373i	−1.08785	+	0.353463i	−0.797414	−	0.603432i	$-0.793799\pi$
$587$	−26.3565	+	8.56373i	−1.08785	+	0.353463i	−0.290433	+	0.956895i	$0.593799\pi$
$588$	14.0898	−	31.6461i	0.581052	−	1.30506i
$589$	−4.98752	−	6.86474i	−0.205507	−	0.282857i
$590$	2.27080	+	6.98881i	0.0934874	+	0.287725i
$591$	2.64628	+	12.4498i	0.108854	+	0.512116i
$592$	−9.70820	−	7.05342i	−0.399005	−	0.289894i
$593$	−19.5959			−0.804708			−0.402354	−	0.915484i	$-0.631808\pi$
$593$	−19.5959			−0.804708			−0.402354	+	0.915484i	$0.631808\pi$
$594$		0			0
$595$	−6.00000			−0.245976
$596$	7.92672	+	5.75910i	0.324691	+	0.235902i
$597$	−6.48205	−	30.4956i	−0.265292	−	1.24810i
$598$	18.5410	+	57.0634i	0.758199	+	2.33350i
$599$	−12.2169	−	16.8151i	−0.499168	−	0.687046i	0.482878	−	0.875688i	$-0.339592\pi$
$599$	−12.2169	−	16.8151i	−0.499168	−	0.687046i	−0.982046	+	0.188641i	$0.939592\pi$
$600$	−6.90255	+	15.5034i	−0.281795	+	0.632923i
$601$	−1.34500	+	0.437016i	−0.0548636	+	0.0178263i	−0.336320	−	0.941748i	$-0.609182\pi$
$601$	−1.34500	+	0.437016i	−0.0548636	+	0.0178263i	0.281457	+	0.959574i	$0.409182\pi$
$602$	−10.5971	+	32.6144i	−0.431905	+	1.32927i
$603$	8.22191	−	3.66063i	0.334822	−	0.149072i
$604$			39.5980i			1.61122i
$605$		0			0
$606$	45.0000	−	25.9808i	1.82800	−	1.05540i
$607$	−5.81878	+	8.00886i	−0.236177	+	0.325070i	−0.910610	−	0.413266i	$-0.864388\pi$
$607$	−5.81878	+	8.00886i	−0.236177	+	0.325070i	0.674433	+	0.738336i	$0.264388\pi$
$608$		0			0
$609$	−8.02957	+	8.91774i	−0.325374	+	0.361365i
$610$	9.70820	−	7.05342i	0.393074	−	0.285585i
$611$	15.8534	−	11.5182i	0.641361	−	0.465976i
$612$	−28.7516	−	6.11133i	−1.16221	−	0.247036i
$613$	−10.7600	−	3.49613i	−0.434591	−	0.141207i	0.0835475	−	0.996504i	$-0.473375\pi$
$613$	−10.7600	−	3.49613i	−0.434591	−	0.141207i	−0.518139	+	0.855297i	$0.673375\pi$
$614$	−4.07230	+	5.60503i	−0.164344	+	0.226201i
$615$	−14.6969	−	25.4558i	−0.592638	−	1.02648i
$616$		0			0
$617$		−	10.3923i		−	0.418378i	−0.977875	−	0.209189i	$-0.932918\pi$
$617$		−	10.3923i		−	0.418378i	0.977875	−	0.209189i	$-0.0670825\pi$
$618$	8.43880	+	0.886953i	0.339458	+	0.0356785i
$619$	−7.72542	+	23.7764i	−0.310511	+	0.955655i	0.667052	+	0.745011i	$0.267556\pi$
$619$	−7.72542	+	23.7764i	−0.310511	+	0.955655i	−0.977563	+	0.210643i	$0.932444\pi$
$620$	−19.7673	+	6.42280i	−0.793875	+	0.257946i
$621$	−36.4058	+	26.4503i	−1.46091	+	1.06142i
$622$	24.9376	+	34.3237i	0.999907	+	1.37625i
$623$	3.78467	+	11.6480i	0.151630	+	0.466668i
$624$	19.1677	−	4.07422i	0.767322	−	0.163099i
$625$	8.89919	+	6.46564i	0.355967	+	0.258626i
$626$	80.8332			3.23074
$627$		0			0
$628$	60.0000			2.39426
$629$	5.94504	+	4.31932i	0.237044	+	0.172223i
$630$	12.0444	+	13.3766i	0.479858	+	0.532937i
$631$	−12.0517	−	37.0912i	−0.479769	−	1.47658i	−0.839416	−	0.543489i	$-0.817103\pi$
$631$	−12.0517	−	37.0912i	−0.479769	−	1.47658i	0.359647	−	0.933088i	$-0.382897\pi$
$632$	−28.5061	−	39.2352i	−1.13391	−	1.56069i
$633$	−8.95088	−	3.98519i	−0.355766	−	0.158397i
$634$	4.03499	−	1.31105i	0.160250	−	0.0520684i
$635$	1.51387	−	4.65921i	0.0600760	−	0.184895i
$636$	−2.50868	+	23.8685i	−0.0994758	+	0.946449i
$637$		−	14.1421i		−	0.560332i
$638$		0			0
$639$	4.50000	+	2.59808i	0.178017	+	0.102778i
$640$	19.9501	−	27.4589i	0.788597	−	1.08541i
$641$	−8.23639	−	2.67617i	−0.325318	−	0.105702i	0.141805	−	0.989895i	$-0.454709\pi$
$641$	−8.23639	−	2.67617i	−0.325318	−	0.105702i	−0.467123	+	0.884192i	$0.654709\pi$
$642$	7.72299	+	6.95381i	0.304802	+	0.274445i
$643$	−5.66312	+	4.11450i	−0.223332	+	0.162260i	−0.693825	−	0.720144i	$-0.744076\pi$
$643$	−5.66312	+	4.11450i	−0.223332	+	0.162260i	0.470493	+	0.882403i	$0.344076\pi$
$644$	39.6336	−	28.7955i	1.56178	−	1.13470i
$645$	22.0703	+	19.8722i	0.869016	+	0.782466i
$646$	16.1400	+	5.24419i	0.635018	+	0.206330i
$647$	17.3073	−	23.8214i	0.680418	−	0.936516i	−0.319520	−	0.947579i	$-0.603522\pi$
$647$	17.3073	−	23.8214i	0.680418	−	0.936516i	0.999939	+	0.0110637i	$0.00352177\pi$
$648$	22.0454	+	38.1838i	0.866025	+	1.50000i
$649$		0			0
$650$			13.8564i			0.543493i
$651$	0.768124	−	7.30821i	0.0301052	−	0.286431i
$652$	−12.3607	+	38.0423i	−0.484082	+	1.48985i
$653$	−1.64728	+	0.535233i	−0.0644630	+	0.0209453i	−0.341071	−	0.940038i	$-0.610790\pi$
$653$	−1.64728	+	0.535233i	−0.0644630	+	0.0209453i	0.276608	+	0.960983i	$0.410790\pi$
$654$	71.2565	+	31.7255i	2.78635	+	1.24056i
$655$	12.4688	+	17.1618i	0.487197	+	0.670569i
$656$	12.1109	+	37.2737i	0.472853	+	1.45529i
$657$	12.6116	−	11.3555i	0.492025	−	0.443021i
$658$	−19.4164	−	14.1068i	−0.756930	−	0.549942i
$659$	−36.7423			−1.43128			−0.715639	−	0.698470i	$-0.753865\pi$
$659$	−36.7423			−1.43128			−0.715639	+	0.698470i	$0.753865\pi$
$660$		0			0
$661$	15.0000			0.583432			0.291716	−	0.956505i	$-0.405774\pi$
$661$	15.0000			0.583432			0.291716	+	0.956505i	$0.405774\pi$
$662$	9.90839	+	7.19887i	0.385101	+	0.279792i
$663$	−11.7378	+	2.49494i	−0.455857	+	0.0968955i
$664$	−3.70820	−	11.4127i	−0.143906	−	0.442898i
$665$	−4.07230	−	5.60503i	−0.157917	−	0.217354i
$666$	−2.30437	−	21.9246i	−0.0892926	−	0.849563i
$667$	40.3499	−	13.1105i	1.56235	−	0.507640i
$668$	24.2219	−	74.5473i	0.937173	−	2.88432i
$669$	−18.9482	−	1.99153i	−0.732579	−	0.0769972i
$670$			12.7279i			0.491723i
$671$		0			0
$672$		0			0
$673$	19.1188	−	26.3148i	0.736977	−	1.01436i	−0.261810	−	0.965119i	$-0.584319\pi$
$673$	19.1188	−	26.3148i	0.736977	−	1.01436i	0.998787	−	0.0492424i	$-0.0156807\pi$
$674$	−56.0075	−	18.1979i	−2.15733	−	0.700958i
$675$	−9.88367	+	3.21140i	−0.380423	+	0.123607i
$676$	−16.1803	+	11.7557i	−0.622321	+	0.452143i
$677$	33.6885	−	24.4762i	1.29476	−	0.940695i	0.294866	−	0.955539i	$-0.404725\pi$
$677$	33.6885	−	24.4762i	1.29476	−	0.940695i	0.999890	+	0.0148435i	$0.00472501\pi$
$678$	−4.91709	+	5.46098i	−0.188840	+	0.209728i
$679$	−17.4850	−	5.68121i	−0.671011	−	0.218025i
$680$	12.2169	−	16.8151i	0.468496	−	0.644830i
$681$	−33.0681	+	19.0919i	−1.26717	+	0.731603i
$682$		0			0
$683$			45.0333i			1.72315i	0.507628	+	0.861576i	$0.330522\pi$
$683$			45.0333i			1.72315i	−0.507628	+	0.861576i	$0.669478\pi$
$684$	−13.8051	−	31.0068i	−0.527851	−	1.18557i
$685$	8.34346	−	25.6785i	0.318787	−	0.981126i
$686$	−39.5347	+	12.8456i	−1.50944	+	0.490447i
$687$	−6.34040	+	14.2408i	−0.241901	+	0.543319i
$688$	−23.2751	−	32.0354i	−0.887355	−	1.22134i
$689$	3.02774	+	9.31841i	0.115348	+	0.355003i
$690$	−13.2314	−	62.2489i	−0.503712	−	2.36978i
$691$	−4.04508	−	2.93893i	−0.153882	−	0.111802i	0.508180	−	0.861251i	$-0.330319\pi$
$691$	−4.04508	−	2.93893i	−0.153882	−	0.111802i	−0.662062	+	0.749449i	$0.730319\pi$
$692$	−9.79796			−0.372463
$693$		0			0
$694$	24.0000			0.911028
$695$	−21.7985	−	15.8375i	−0.826863	−	0.600751i
$696$	−8.64273	−	40.6608i	−0.327602	−	1.54124i
$697$	−7.41641	−	22.8254i	−0.280916	−	0.864572i
$698$	14.2530	+	19.6176i	0.539485	+	0.742538i
$699$	−17.2564	+	38.7585i	−0.652696	+	1.46598i
$700$	10.7600	−	3.49613i	0.406689	−	0.132141i
$701$	−8.32627	+	25.6256i	−0.314479	+	0.967867i	0.661489	+	0.749955i	$0.269925\pi$
$701$	−8.32627	+	25.6256i	−0.314479	+	0.967867i	−0.975968	+	0.217912i	$0.930075\pi$
$702$	29.1246	+	21.1603i	1.09924	+	0.798643i
$703$			8.48528i			0.320028i
$704$		0			0
$705$	−18.0000	+	10.3923i	−0.677919	+	0.391397i
$706$	37.4064	−	51.4855i	1.40781	−	1.93768i
$707$	−16.4728	−	5.35233i	−0.619523	−	0.201295i
$708$	8.02957	−	8.91774i	0.301770	−	0.335149i
$709$	−2.42705	+	1.76336i	−0.0911498	+	0.0662242i	−0.632427	−	0.774620i	$-0.717941\pi$
$709$	−2.42705	+	1.76336i	−0.0911498	+	0.0662242i	0.541277	+	0.840844i	$0.317941\pi$
$710$	−5.94504	+	4.31932i	−0.223113	+	0.162101i
$711$	6.17466	−	29.0495i	0.231568	−	1.08944i
$712$	−40.3499	−	13.1105i	−1.51218	−	0.491336i
$713$	−15.2711	+	21.0189i	−0.571908	+	0.787163i
$714$	7.34847	+	12.7279i	0.275010	+	0.476331i
$715$		0			0
$716$		−	62.3538i		−	2.33027i
$717$	−37.9746	−	3.99129i	−1.41819	−	0.149057i
$718$	18.5410	−	57.0634i	0.691945	−	2.12959i
$719$	−11.5309	+	3.74663i	−0.430032	+	0.139726i	−0.516032	−	0.856569i	$-0.672591\pi$
$719$	−11.5309	+	3.74663i	−0.430032	+	0.139726i	0.0860002	+	0.996295i	$0.472591\pi$
$720$	−20.6707	+	2.17258i	−0.770353	+	0.0809674i
$721$	−1.66251	−	2.28825i	−0.0619150	−	0.0852187i
$722$	−8.32627	−	25.6256i	−0.309872	−	0.953687i
$723$	−4.79193	+	1.01856i	−0.178214	+	0.0378805i
$724$	16.1803	+	11.7557i	0.601338	+	0.436897i
$725$	9.79796			0.363887
$726$		0			0
$727$	−3.00000			−0.111264			−0.0556319	−	0.998451i	$-0.517717\pi$
$727$	−3.00000			−0.111264			−0.0556319	+	0.998451i	$0.517717\pi$
$728$	−15.8534	−	11.5182i	−0.587567	−	0.426893i
$729$	−8.34346	+	25.6785i	−0.309017	+	0.951057i
$730$	7.41641	+	22.8254i	0.274494	+	0.844804i
$731$	14.2530	+	19.6176i	0.527168	+	0.725584i
$732$	−17.9018	−	7.97038i	−0.661668	−	0.294594i
$733$	34.9699	−	11.3624i	1.29164	−	0.419680i	0.418977	−	0.907997i	$-0.362389\pi$
$733$	34.9699	−	11.3624i	1.29164	−	0.419680i	0.872667	+	0.488316i	$0.162389\pi$
$734$	5.29854	−	16.3072i	0.195573	−	0.601911i
$735$	−1.56793	+	14.9178i	−0.0578339	+	0.550252i
$736$		0			0
$737$		0			0
$738$	−36.0000	+	62.3538i	−1.32518	+	2.29528i
$739$	−30.7564	+	42.3325i	−1.13139	+	1.55723i	−0.345994	+	0.938237i	$0.612458\pi$
$739$	−30.7564	+	42.3325i	−1.13139	+	1.55723i	−0.785398	+	0.618991i	$0.787542\pi$
$740$	19.7673	+	6.42280i	0.726662	+	0.236107i
$741$	−10.2973	−	9.27175i	−0.378281	−	0.340606i
$742$	9.70820	−	7.05342i	0.356399	−	0.258939i
$743$	−11.8901	+	8.63864i	−0.436204	+	0.316921i	−0.784125	−	0.620603i	$-0.786888\pi$
$743$	−11.8901	+	8.63864i	−0.436204	+	0.316921i	0.347921	+	0.937524i	$0.386888\pi$
$744$	18.9174	+	17.0333i	0.693545	+	0.624471i
$745$	−4.03499	−	1.31105i	−0.147831	−	0.0480331i
$746$	46.8314	−	64.4579i	1.71462	−	2.35997i
$747$	3.67423	−	6.36396i	0.134433	−	0.232845i
$748$		0			0
$749$		−	3.46410i		−	0.126576i
$750$	5.37687	−	51.1575i	0.196336	−	1.86801i
$751$	8.34346	−	25.6785i	0.304457	−	0.937023i	−0.675422	−	0.737431i	$-0.736039\pi$
$751$	8.34346	−	25.6785i	0.304457	−	0.937023i	0.979879	−	0.199591i	$-0.0639615\pi$
$752$	26.3565	−	8.56373i	0.961121	−	0.312287i
$753$	−24.6657	−	10.9819i	−0.898869	−	0.400202i
$754$	−19.9501	−	27.4589i	−0.726540	−	0.999996i
$755$	−5.29854	−	16.3072i	−0.192834	−	0.593481i
$756$	9.08321	−	27.9552i	0.330353	−	1.01672i
$757$	24.2705	+	17.6336i	0.882127	+	0.640903i	0.933813	−	0.357761i	$-0.116460\pi$
$757$	24.2705	+	17.6336i	0.882127	+	0.640903i	−0.0516866	+	0.998663i	$0.516460\pi$
$758$	−41.6413			−1.51248
$759$		0			0
$760$	24.0000			0.870572
$761$	−19.8168	−	14.3977i	−0.718358	−	0.521918i	0.167501	−	0.985872i	$-0.446430\pi$
$761$	−19.8168	−	14.3977i	−0.718358	−	0.521918i	−0.885859	+	0.463954i	$0.846430\pi$
$762$	−11.7378	+	2.49494i	−0.425215	+	0.0903822i
$763$	−8.03444	−	24.7275i	−0.290866	−	0.895194i
$764$	12.2169	+	16.8151i	0.441991	+	0.608349i
$765$	12.6582	−	1.33043i	0.457658	−	0.0481018i
$766$	−52.4549	+	17.0436i	−1.89527	+	0.615811i
$767$	1.51387	−	4.65921i	0.0546626	−	0.168234i
$768$	−55.1220	−	5.79356i	−1.98904	−	0.209057i
$769$		−	14.1421i		−	0.509978i	−0.966944	−	0.254989i	$-0.917928\pi$
$769$		−	14.1421i		−	0.509978i	0.966944	−	0.254989i	$-0.0820719\pi$
$770$		0			0
$771$	−9.00000	−	15.5885i	−0.324127	−	0.561405i
$772$	−33.2502	+	45.7649i	−1.19670	+	1.64712i
$773$	3.29456	+	1.07047i	0.118497	+	0.0385020i	0.367665	−	0.929958i	$-0.380157\pi$
$773$	3.29456	+	1.07047i	0.118497	+	0.0385020i	−0.249168	+	0.968460i	$0.580157\pi$
$774$	15.1248	−	71.1565i	0.543649	−	2.55767i
$775$	−4.85410	+	3.52671i	−0.174364	+	0.126683i
$776$	51.5236	−	37.4341i	1.84959	−	1.34381i
$777$	−4.91709	+	5.46098i	−0.176399	+	0.195911i
$778$	52.4549	+	17.0436i	1.88060	+	0.611044i
$779$	16.2892	−	22.4201i	0.583621	−	0.803285i
$780$	−29.3939	+	16.9706i	−1.05247	+	0.607644i
$781$		0			0
$782$		−	51.9615i		−	1.85814i
$783$	14.9626	−	20.5942i	0.534719	−	0.735977i
$784$	6.18034	−	19.0211i	0.220726	−	0.679326i
$785$	−24.7092	+	8.02850i	−0.881908	+	0.286549i
$786$	21.1347	−	47.4692i	0.753848	−	1.69317i
$787$	−16.6251	−	22.8825i	−0.592620	−	0.815671i	0.402388	−	0.915469i	$-0.368180\pi$
$787$	−16.6251	−	22.8825i	−0.592620	−	0.815671i	−0.995008	+	0.0997979i	$0.968180\pi$
$788$	9.08321	+	27.9552i	0.323576	+	0.995864i
$789$	4.41047	+	20.7496i	0.157017	+	0.738707i
$790$	33.9787	+	24.6870i	1.20891	+	0.878323i
$791$	2.44949			0.0870938
$792$		0			0
$793$	−8.00000			−0.284088
$794$	63.4137	+	46.0728i	2.25047	+	1.63506i
$795$	−2.16068	−	10.1652i	−0.0766315	−	0.360523i
$796$	−22.2492	−	68.4761i	−0.788603	−	2.42707i
$797$	19.3434	+	26.6239i	0.685179	+	0.943067i	0.999981	−	0.00608970i	$-0.00193842\pi$
$797$	19.3434	+	26.6239i	0.685179	+	0.943067i	−0.314803	+	0.949157i	$0.601938\pi$
$798$	−6.90255	+	15.5034i	−0.244348	+	0.548814i
$799$	−16.1400	+	5.24419i	−0.570991	+	0.185526i
$800$		0			0
$801$	−10.5673	−	23.7346i	−0.373378	−	0.838621i
$802$		−	25.4558i		−	0.898877i
$803$		0			0
$804$	18.0000	−	10.3923i	0.634811	−	0.366508i
$805$	−12.4688	+	17.1618i	−0.439468	+	0.604875i
$806$	19.7673	+	6.42280i	0.696275	+	0.226233i
$807$	20.0739	−	22.2943i	0.706635	−	0.784798i
$808$	48.5410	−	35.2671i	1.70767	−	1.24069i
$809$	39.6336	−	28.7955i	1.39344	−	1.01240i	0.397965	−	0.917401i	$-0.369717\pi$
$809$	39.6336	−	28.7955i	1.39344	−	1.01240i	0.995478	−	0.0949943i	$-0.0302833\pi$
$810$	−28.3761	−	25.5499i	−0.997033	−	0.897733i
$811$	−14.7950	−	4.80718i	−0.519522	−	0.168803i	0.0375066	−	0.999296i	$-0.488058\pi$
$811$	−14.7950	−	4.80718i	−0.519522	−	0.168803i	−0.557028	+	0.830494i	$0.688058\pi$
$812$	−16.2892	+	22.4201i	−0.571638	+	0.786793i
$813$	4.89898	+	8.48528i	0.171815	+	0.297592i
$814$		0			0
$815$		−	17.3205i		−	0.606711i
$816$	−16.8776	−	1.77391i	−0.590834	−	0.0620992i
$817$	−8.65248	+	26.6296i	−0.302712	+	0.931651i
$818$	42.8292	−	13.9161i	1.49749	−	0.486564i
$819$	−1.25434	−	11.9343i	−0.0438302	−	0.417017i
$820$	−39.9002	−	54.9179i	−1.39337	−	1.91782i
$821$	9.84014	+	30.2848i	0.343423	+	1.05695i	0.962422	+	0.271557i	$0.0875384\pi$
$821$	9.84014	+	30.2848i	0.343423	+	1.05695i	−0.618999	+	0.785392i	$0.712462\pi$
$822$	−64.6910	+	13.7505i	−2.25636	+	0.479604i
$823$	−25.0795	−	18.2213i	−0.874217	−	0.635156i	0.0574979	−	0.998346i	$-0.481688\pi$
$823$	−25.0795	−	18.2213i	−0.874217	−	0.635156i	−0.931715	+	0.363190i	$0.881688\pi$
$824$	9.79796			0.341328
$825$		0			0
$826$	−6.00000			−0.208767
$827$	3.96336	+	2.87955i	0.137819	+	0.100132i	0.654559	−	0.756011i	$-0.272854\pi$
$827$	3.96336	+	2.87955i	0.137819	+	0.100132i	−0.516739	+	0.856143i	$0.672854\pi$
$828$	−77.2299	+	69.5381i	−2.68392	+	2.41662i
$829$	9.57953	+	29.4828i	0.332711	+	1.02398i	0.967839	+	0.251571i	$0.0809473\pi$
$829$	9.57953	+	29.4828i	0.332711	+	1.02398i	−0.635128	+	0.772407i	$0.719053\pi$
$830$	6.10844	+	8.40755i	0.212027	+	0.291830i
$831$	29.0904	+	12.9519i	1.00913	+	0.449295i
$832$	−21.5200	+	6.99226i	−0.746070	+	0.242413i
$833$	−3.78467	+	11.6480i	−0.131131	+	0.403580i
$834$	−6.89888	+	65.6384i	−0.238889	+	2.27287i
$835$			33.9411i			1.17458i
$836$		0			0
$837$			15.5885i			0.538816i
$838$	−9.97505	+	13.7295i	−0.344582	+	0.474277i
$839$	44.4765	+	14.4513i	1.53550	+	0.498914i	0.950130	−	0.311853i	$-0.100950\pi$
$839$	44.4765	+	14.4513i	1.53550	+	0.498914i	0.585369	+	0.810767i	$0.300950\pi$
$840$	15.4460	+	13.9076i	0.532937	+	0.479858i
$841$	4.04508	−	2.93893i	0.139486	−	0.101342i
$842$		0			0
$843$	−28.3761	−	25.5499i	−0.977324	−	0.879986i
$844$	−21.5200	−	6.99226i	−0.740747	−	0.240683i
$845$	5.09037	−	7.00629i	0.175114	−	0.241024i
$846$	44.0908	+	25.4558i	1.51587	+	0.875190i
$847$		0			0
$848$			13.8564i			0.475831i
$849$	−3.58458	+	34.1050i	−0.123022	+	1.17048i
$850$	3.70820	−	11.4127i	0.127190	−	0.391452i
$851$	24.7092	−	8.02850i	0.847020	−	0.275213i
$852$	10.9625	+	4.88084i	0.375571	+	0.167215i
$853$	−34.0814	−	46.9090i	−1.16693	−	1.60613i	−0.681398	−	0.731913i	$-0.738628\pi$
$853$	−34.0814	−	46.9090i	−1.16693	−	1.60613i	−0.485528	−	0.874221i	$-0.661372\pi$
$854$	3.02774	+	9.31841i	0.103607	+	0.318870i
$855$	9.83417	+	10.9220i	0.336322	+	0.373523i
$856$	9.70820	+	7.05342i	0.331820	+	0.241081i
$857$	−19.5959			−0.669384			−0.334692	−	0.942328i	$-0.608632\pi$
$857$	−19.5959			−0.669384			−0.334692	+	0.942328i	$0.608632\pi$
$858$		0			0
$859$	25.0000			0.852989			0.426494	−	0.904490i	$-0.359748\pi$
$859$	25.0000			0.852989			0.426494	+	0.904490i	$0.359748\pi$
$860$	55.4870	+	40.3137i	1.89209	+	1.37468i
$861$	23.4755	−	4.98988i	0.800044	−	0.170055i
$862$	5.56231	+	17.1190i	0.189453	+	0.583076i
$863$	−12.2169	−	16.8151i	−0.415868	−	0.572393i	0.548770	−	0.835974i	$-0.315096\pi$
$863$	−12.2169	−	16.8151i	−0.415868	−	0.572393i	−0.964637	+	0.263581i	$0.915096\pi$
$864$		0			0
$865$	4.03499	−	1.31105i	0.137194	−	0.0445770i
$866$	−3.78467	+	11.6480i	−0.128608	+	0.395816i
$867$	−18.9482	−	1.99153i	−0.643514	−	0.0676361i
$868$		−	16.9706i		−	0.576018i
$869$		0			0
$870$	18.0000	+	31.1769i	0.610257	+	1.05700i
$871$	4.98752	−	6.86474i	0.168996	−	0.232603i
$872$	85.6585	+	27.8321i	2.90076	+	0.942515i
$873$	38.1478	+	8.10856i	1.29111	+	0.274433i
$874$	48.5410	−	35.2671i	1.64192	−	1.19293i
$875$	−13.8718	+	10.0784i	−0.468951	+	0.340713i
$876$	26.2245	−	29.1252i	0.886042	−	0.984050i
$877$	26.8999	+	8.74032i	0.908346	+	0.295140i	0.725678	−	0.688035i	$-0.241526\pi$
$877$	26.8999	+	8.74032i	0.908346	+	0.295140i	0.182669	+	0.983175i	$0.441526\pi$
$878$	−8.14459	+	11.2101i	−0.274867	+	0.378321i
$879$	−7.34847	+	4.24264i	−0.247858	+	0.143101i
$880$		0			0
$881$		−	1.73205i		−	0.0583543i	−0.999574	−	0.0291771i	$-0.990711\pi$
$881$		−	1.73205i		−	0.0583543i	0.999574	−	0.0291771i	$-0.00928869\pi$
$882$	33.5658	−	14.9445i	1.13022	−	0.503206i
$883$	1.85410	−	5.70634i	0.0623955	−	0.192034i	−0.915000	−	0.403455i	$-0.867809\pi$
$883$	1.85410	−	5.70634i	0.0623955	−	0.192034i	0.977395	+	0.211421i	$0.0678092\pi$
$884$	−26.3565	+	8.56373i	−0.886463	+	0.288029i
$885$	−2.11347	+	4.74692i	−0.0710434	+	0.159566i
$886$	37.4064	+	51.4855i	1.25669	+	1.72969i
$887$	6.81241	+	20.9664i	0.228738	+	0.703984i	0.997891	+	0.0649184i	$0.0206787\pi$
$887$	6.81241	+	20.9664i	0.228738	+	0.703984i	−0.769152	+	0.639065i	$0.779321\pi$
$888$	−5.29257	−	24.8996i	−0.177607	−	0.835575i
$889$	3.23607	+	2.35114i	0.108534	+	0.0788547i
$890$	36.7423			1.23161
$891$		0			0
$892$	−44.0000			−1.47323
$893$	−15.8534	−	11.5182i	−0.530515	−	0.385442i
$894$	2.16068	+	10.1652i	0.0722640	+	0.339975i
$895$	8.34346	+	25.6785i	0.278891	+	0.858338i
$896$	16.2892	+	22.4201i	0.544183	+	0.749004i
$897$	−17.2564	+	38.7585i	−0.576174	+	1.29411i
$898$	28.2449	−	9.17734i	0.942546	−	0.306252i
$899$	4.54160	−	13.9776i	0.151471	−	0.466180i
$900$	−21.9251	+	9.76168i	−0.730836	+	0.325389i
$901$		−	8.48528i		−	0.282686i
$902$		0			0
$903$	−21.0000	+	12.1244i	−0.698836	+	0.403473i
$904$	−4.98752	+	6.86474i	−0.165883	+	0.228318i
$905$	−8.23639	−	2.67617i	−0.273787	−	0.0889588i
$906$	−28.1035	+	31.2121i	−0.933676	+	1.03695i
$907$	−17.7984	+	12.9313i	−0.590985	+	0.429376i	−0.842668	−	0.538434i	$-0.819016\pi$
$907$	−17.7984	+	12.9313i	−0.590985	+	0.429376i	0.251682	+	0.967810i	$0.419016\pi$
$908$	−71.3404	+	51.8319i	−2.36752	+	1.72010i
$909$	35.9394	+	7.63916i	1.19204	+	0.253375i
$910$	16.1400	+	5.24419i	0.535035	+	0.173843i
$911$	−2.03615	+	2.80252i	−0.0674606	+	0.0928515i	−0.841414	−	0.540391i	$-0.818276\pi$
$911$	−2.03615	+	2.80252i	−0.0674606	+	0.0928515i	0.773954	+	0.633242i	$0.218276\pi$
$912$	−9.79796	−	16.9706i	−0.324443	−	0.561951i
$913$		0			0
$914$			76.2102i			2.52081i
$915$	8.43880	+	0.886953i	0.278978	+	0.0293218i
$916$	−11.1246	+	34.2380i	−0.367568	+	1.13126i
$917$	−16.4728	+	5.35233i	−0.543979	+	0.176750i
$918$	−18.3253	−	25.2227i	−0.604826	−	0.832472i
$919$	4.15627	+	5.72061i	0.137103	+	0.188706i	0.872047	−	0.489421i	$-0.162792\pi$
$919$	4.15627	+	5.72061i	0.137103	+	0.188706i	−0.734945	+	0.678127i	$0.762792\pi$
$920$	−22.7080	−	69.8881i	−0.748661	−	2.30414i
$921$	−4.79193	+	1.01856i	−0.157899	+	0.0335625i
$922$	−9.70820	−	7.05342i	−0.319723	−	0.232292i
$923$	4.89898			0.161252
$924$		0			0
$925$	6.00000			0.197279
$926$	37.6519	+	27.3557i	1.23732	+	0.898964i
$927$	4.01478	+	4.45887i	0.131863	+	0.146448i
$928$		0			0
$929$	−26.4699	−	36.4327i	−0.868450	−	1.19532i	−0.979488	−	0.201503i	$-0.935418\pi$
$929$	−26.4699	−	36.4327i	−0.868450	−	1.19532i	0.111038	−	0.993816i	$-0.464582\pi$
$930$	−20.1395	−	8.96668i	−0.660400	−	0.294029i
$931$	−13.4500	+	4.37016i	−0.440805	+	0.143226i
$932$	−30.2774	+	93.1841i	−0.991768	+	3.05235i
$933$	−3.13585	+	29.8357i	−0.102663	+	0.976776i
$934$		−	63.6396i		−	2.08235i
$935$		0			0
$936$	36.0000	+	20.7846i	1.17670	+	0.679366i
$937$	33.2502	−	45.7649i	1.08624	−	1.49507i	0.233769	−	0.972292i	$-0.424894\pi$
$937$	33.2502	−	45.7649i	1.08624	−	1.49507i	0.852466	−	0.522782i	$-0.175106\pi$
$938$	−9.88367	−	3.21140i	−0.322713	−	0.104856i
$939$	42.4764	+	38.2460i	1.38617	+	1.24811i
$940$	−38.8328	+	28.2137i	−1.26659	+	0.920229i
$941$	−5.94504	+	4.31932i	−0.193803	+	0.140806i	−0.680455	−	0.732790i	$-0.738218\pi$
$941$	−5.94504	+	4.31932i	−0.193803	+	0.140806i	0.486652	+	0.873596i	$0.338218\pi$
$942$	47.2934	+	42.5832i	1.54090	+	1.38744i
$943$	−80.6998	−	26.2210i	−2.62795	−	0.853872i
$944$	4.07230	−	5.60503i	0.132542	−	0.182428i
$945$			12.7279i			0.414039i
$946$		0			0
$947$		−	50.2295i		−	1.63224i	−0.577883	−	0.816119i	$-0.696121\pi$
$947$		−	50.2295i		−	1.63224i	0.577883	−	0.816119i	$-0.303879\pi$
$948$	7.16916	−	68.2100i	0.232843	−	2.21536i
$949$	4.94427	−	15.2169i	0.160498	−	0.493962i
$950$	13.1782	−	4.28187i	0.427558	−	0.138922i
$951$	2.74064	+	1.22021i	0.0888712	+	0.0395680i
$952$	9.97505	+	13.7295i	0.323293	+	0.444975i
$953$	−2.27080	−	6.98881i	−0.0735585	−	0.226390i	0.907517	−	0.420015i	$-0.137975\pi$
$953$	−2.27080	−	6.98881i	−0.0735585	−	0.226390i	−0.981075	+	0.193626i	$0.937975\pi$
$954$	−18.9174	+	17.0333i	−0.612473	+	0.551473i
$955$	−7.28115	−	5.29007i	−0.235613	−	0.171183i
$956$	−88.1816			−2.85200
$957$		0			0
$958$	−72.0000			−2.32621
$959$	17.8351	+	12.9580i	0.575926	+	0.418435i
$960$	23.4755	−	4.98988i	0.757670	−	0.161048i
$961$	−6.79837	−	20.9232i	−0.219302	−	0.674943i
$962$	−12.2169	−	16.8151i	−0.393888	−	0.542141i
$963$	0.768124	+	7.30821i	0.0247525	+	0.235504i
$964$	−10.7600	+	3.49613i	−0.346555	+	0.112603i
$965$	7.56934	−	23.2960i	0.243666	−	0.749926i
$966$	51.6769	+	5.43146i	1.66268	+	0.174754i
$967$			31.1127i			1.00052i	0.865876	+	0.500258i	$0.166762\pi$
$967$			31.1127i			1.00052i	−0.865876	+	0.500258i	$0.833238\pi$
$968$		0			0
$969$	6.00000	+	10.3923i	0.192748	+	0.333849i
$970$	−32.4189	+	44.6208i	−1.04091	+	1.43269i
$971$	−37.8874	−	12.3104i	−1.21586	−	0.395058i	−0.370290	−	0.928916i	$-0.620742\pi$
$971$	−37.8874	−	12.3104i	−1.21586	−	0.395058i	−0.845574	+	0.533858i	$0.820742\pi$
$972$	−12.9641	+	60.9912i	−0.415823	+	1.95630i
$973$	17.7984	−	12.9313i	0.570590	−	0.414558i
$974$	53.5053	−	38.8739i	1.71442	−	1.24560i
$975$	−6.55611	+	7.28130i	−0.209964	+	0.233188i
$976$	−10.7600	−	3.49613i	−0.344418	−	0.111908i
$977$	21.3796	−	29.4264i	0.683992	−	0.941435i	−0.315981	−	0.948766i	$-0.602333\pi$
$977$	21.3796	−	29.4264i	0.683992	−	0.941435i	0.999973	+	0.00733075i	$0.00233347\pi$
$978$	−36.7423	+	21.2132i	−1.17489	+	0.678323i
$979$		0			0
$980$			34.6410i			1.10657i
$981$	22.4333	+	50.3860i	0.716240	+	1.60870i
$982$	−18.5410	+	57.0634i	−0.591668	+	1.82097i
$983$	−1.64728	+	0.535233i	−0.0525400	+	0.0170713i	−0.335169	−	0.942158i	$-0.608793\pi$
$983$	−1.64728	+	0.535233i	−0.0525400	+	0.0170713i	0.282629	+	0.959229i	$0.408793\pi$
$984$	−33.8154	+	75.9507i	−1.07800	+	2.42122i
$985$	−7.48128	−	10.2971i	−0.238374	−	0.328093i
$986$	9.08321	+	27.9552i	0.289268	+	0.890276i
$987$	−3.52838	−	16.5997i	−0.112310	−	0.528375i
$988$	−25.8885	−	18.8091i	−0.823624	−	0.598398i
$989$	85.7321			2.72612
$990$		0			0
$991$	18.0000			0.571789			0.285894	−	0.958261i	$-0.407709\pi$
$991$	18.0000			0.571789			0.285894	+	0.958261i	$0.407709\pi$
$992$		0			0
$993$	1.80057	+	8.47101i	0.0571393	+	0.268819i
$994$	−1.85410	−	5.70634i	−0.0588085	−	0.180994i
$995$	18.3253	+	25.2227i	0.580952	+	0.799612i
$996$	6.90255	−	15.5034i	0.218716	−	0.491243i
$997$	−1.34500	+	0.437016i	−0.0425965	+	0.0138404i	−0.330238	−	0.943898i	$-0.607129\pi$
$997$	−1.34500	+	0.437016i	−0.0425965	+	0.0138404i	0.287641	+	0.957738i	$0.407129\pi$
$998$	−4.54160	+	13.9776i	−0.143762	+	0.442454i
$999$	9.16267	−	12.6113i	0.289894	−	0.399005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.f.h.161.4		16
3.2	odd	2	inner	363.2.f.h.161.1		16
11.2	odd	10	inner	363.2.f.h.215.4		16
11.3	even	5	inner	363.2.f.h.239.3		16
11.4	even	5	inner	363.2.f.h.233.1		16
11.5	even	5		363.2.d.c.362.2	yes	4
11.6	odd	10		363.2.d.c.362.4	yes	4
11.7	odd	10	inner	363.2.f.h.233.3		16
11.8	odd	10	inner	363.2.f.h.239.1		16
11.9	even	5	inner	363.2.f.h.215.2		16
11.10	odd	2	inner	363.2.f.h.161.2		16
33.2	even	10	inner	363.2.f.h.215.1		16
33.5	odd	10		363.2.d.c.362.3	yes	4
33.8	even	10	inner	363.2.f.h.239.4		16
33.14	odd	10	inner	363.2.f.h.239.2		16
33.17	even	10		363.2.d.c.362.1	✓	4
33.20	odd	10	inner	363.2.f.h.215.3		16
33.26	odd	10	inner	363.2.f.h.233.4		16
33.29	even	10	inner	363.2.f.h.233.2		16
33.32	even	2	inner	363.2.f.h.161.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.2.d.c.362.1	✓	4	33.17	even	10
363.2.d.c.362.2	yes	4	11.5	even	5
363.2.d.c.362.3	yes	4	33.5	odd	10
363.2.d.c.362.4	yes	4	11.6	odd	10
363.2.f.h.161.1		16	3.2	odd	2	inner
363.2.f.h.161.2		16	11.10	odd	2	inner
363.2.f.h.161.3		16	33.32	even	2	inner
363.2.f.h.161.4		16	1.1	even	1	trivial
363.2.f.h.215.1		16	33.2	even	10	inner
363.2.f.h.215.2		16	11.9	even	5	inner
363.2.f.h.215.3		16	33.20	odd	10	inner
363.2.f.h.215.4		16	11.2	odd	10	inner
363.2.f.h.233.1		16	11.4	even	5	inner
363.2.f.h.233.2		16	33.29	even	10	inner
363.2.f.h.233.3		16	11.7	odd	10	inner
363.2.f.h.233.4		16	33.26	odd	10	inner
363.2.f.h.239.1		16	11.8	odd	10	inner
363.2.f.h.239.2		16	33.14	odd	10	inner
363.2.f.h.239.3		16	11.3	even	5	inner
363.2.f.h.239.4		16	33.8	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.f (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.98168 + 1.43977i) q^{2} +(0.360114 + 1.69420i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-1.01807 - 1.40126i) q^{5} +(-1.72564 + 3.87585i) q^{6} +(1.34500 - 0.437016i) q^{7} +(-1.51387 + 4.65921i) q^{8} +(-2.74064 + 1.22021i) q^{9} +O(q^{10})\)	\(q+(1.98168 + 1.43977i) q^{2} +(0.360114 + 1.69420i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-1.01807 - 1.40126i) q^{5} +(-1.72564 + 3.87585i) q^{6} +(1.34500 - 0.437016i) q^{7} +(-1.51387 + 4.65921i) q^{8} +(-2.74064 + 1.22021i) q^{9} -4.24264i q^{10} +(-6.00000 + 3.46410i) q^{12} +(-1.66251 + 2.28825i) q^{13} +(3.29456 + 1.07047i) q^{14} +(2.00739 - 2.22943i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(1.98168 - 1.43977i) q^{17} +(-7.18789 - 1.52783i) q^{18} +(2.68999 + 0.874032i) q^{19} +(4.07230 - 5.60503i) q^{20} +(1.22474 + 2.12132i) q^{21} -8.66025i q^{23} +(-8.43880 - 0.886953i) q^{24} +(0.618034 - 1.90211i) q^{25} +(-6.58911 + 2.14093i) q^{26} +(-3.05422 - 4.20378i) q^{27} +(3.32502 + 4.57649i) q^{28} +(1.51387 + 4.65921i) q^{29} +(7.18789 - 1.52783i) q^{30} +(-2.42705 - 1.76336i) q^{31} +6.00000 q^{34} +(-1.98168 - 1.43977i) q^{35} +(-8.02957 - 8.91774i) q^{36} +(0.927051 + 2.85317i) q^{37} +(4.07230 + 5.60503i) q^{38} +(-4.47544 - 1.99259i) q^{39} +(8.06998 - 2.62210i) q^{40} +(3.02774 - 9.31841i) q^{41} +(-0.627171 + 5.96713i) q^{42} +9.89949i q^{43} +(4.50000 + 2.59808i) q^{45} +(12.4688 - 17.1618i) q^{46} +(-6.58911 - 2.14093i) q^{47} +(-5.14866 - 4.63587i) q^{48} +(-4.04508 + 2.93893i) q^{49} +(3.96336 - 2.87955i) q^{50} +(3.15290 + 2.83888i) q^{51} +(-10.7600 - 3.49613i) q^{52} +(2.03615 - 2.80252i) q^{53} -12.7279i q^{54} +6.92820i q^{56} +(-0.512083 + 4.87214i) q^{57} +(-3.70820 + 11.4127i) q^{58} +(-1.64728 + 0.535233i) q^{59} +(10.9625 + 4.88084i) q^{60} +(1.66251 + 2.28825i) q^{61} +(-2.27080 - 6.98881i) q^{62} +(-3.15290 + 2.83888i) q^{63} +(6.47214 + 4.70228i) q^{64} +4.89898 q^{65} -3.00000 q^{67} +(7.92672 + 5.75910i) q^{68} +(14.6722 - 3.11868i) q^{69} +(-1.85410 - 5.70634i) q^{70} +(-1.01807 - 1.40126i) q^{71} +(-1.53625 - 14.6164i) q^{72} +(-5.37999 + 1.74806i) q^{73} +(-2.27080 + 6.98881i) q^{74} +(3.44512 + 0.362097i) q^{75} +11.3137i q^{76} +(-6.00000 - 10.3923i) q^{78} +(-5.81878 + 8.00886i) q^{79} +(6.58911 + 2.14093i) q^{80} +(6.02218 - 6.68830i) q^{81} +(19.4164 - 14.1068i) q^{82} +(-1.98168 + 1.43977i) q^{83} +(-6.55611 + 7.28130i) q^{84} +(-4.03499 - 1.31105i) q^{85} +(-14.2530 + 19.6176i) q^{86} +(-7.34847 + 4.24264i) q^{87} +8.66025i q^{89} +(5.17691 + 11.6275i) q^{90} +(-1.23607 + 3.80423i) q^{91} +(32.9456 - 10.7047i) q^{92} +(2.11347 - 4.74692i) q^{93} +(-9.97505 - 13.7295i) q^{94} +(-1.51387 - 4.65921i) q^{95} +(-10.5172 - 7.64121i) q^{97} -12.2474 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{3} - 16 q^{4} - 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^3 - 16 * q^4 - 6 * q^9	\( 16 q + 6 q^{3} - 16 q^{4} - 6 q^{9} - 96 q^{12} + 6 q^{15} - 16 q^{16} - 8 q^{25} - 12 q^{31} + 96 q^{34} - 24 q^{36} - 12 q^{37} + 12 q^{42} + 72 q^{45} + 24 q^{48} - 20 q^{49} + 48 q^{58} + 24 q^{60} + 32 q^{64} - 48 q^{67} - 30 q^{69} + 24 q^{70} + 12 q^{75} - 96 q^{78} + 18 q^{81} + 96 q^{82} + 16 q^{91} + 18 q^{93} - 52 q^{97}+O(q^{100}) \) 16 * q + 6 * q^3 - 16 * q^4 - 6 * q^9 - 96 * q^12 + 6 * q^15 - 16 * q^16 - 8 * q^25 - 12 * q^31 + 96 * q^34 - 24 * q^36 - 12 * q^37 + 12 * q^42 + 72 * q^45 + 24 * q^48 - 20 * q^49 + 48 * q^58 + 24 * q^60 + 32 * q^64 - 48 * q^67 - 30 * q^69 + 24 * q^70 + 12 * q^75 - 96 * q^78 + 18 * q^81 + 96 * q^82 + 16 * q^91 + 18 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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