LMFDB - Embedded newform 363.2.f.i.215.4

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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			215.4
Character	$\chi$	$=$	363.215
Dual form			363.2.f.i.233.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.465371 - 1.43226i) q^{2} +(1.73106 - 0.0585784i) q^{3} +(-0.216775 + 0.157497i) q^{4} +(-2.76692 - 0.899027i) q^{5} +(-0.889484 - 2.45207i) q^{6} +(-1.66251 - 2.28825i) q^{7} +(-2.11025 - 1.53319i) q^{8} +(2.99314 - 0.202805i) q^{9} +O(q^{10})$	\(q+(-0.465371 - 1.43226i) q^{2} +(1.73106 - 0.0585784i) q^{3} +(-0.216775 + 0.157497i) q^{4} +(-2.76692 - 0.899027i) q^{5} +(-0.889484 - 2.45207i) q^{6} +(-1.66251 - 2.28825i) q^{7} +(-2.11025 - 1.53319i) q^{8} +(2.99314 - 0.202805i) q^{9} +4.38134i q^{10} +(-0.366025 + 0.285334i) q^{12} +(-0.852694 + 0.277057i) q^{13} +(-2.50369 + 3.44603i) q^{14} +(-4.84237 - 1.39419i) q^{15} +(-1.37948 + 4.24561i) q^{16} +(-0.806046 + 2.48075i) q^{17} +(-1.68339 - 4.19258i) q^{18} +(1.43977 - 1.98168i) q^{19} +(0.741394 - 0.240894i) q^{20} +(-3.01194 - 3.86370i) q^{21} +(-3.74279 - 2.53043i) q^{24} +(2.80252 + 2.03615i) q^{25} +(0.793638 + 1.09235i) q^{26} +(5.16942 - 0.526402i) q^{27} +(0.720782 + 0.234196i) q^{28} +(6.98368 - 5.07394i) q^{29} +(0.256652 + 7.58436i) q^{30} +(-3.15078 - 9.69712i) q^{31} +1.50597 q^{32} +3.92820 q^{34} +(2.54283 + 7.82603i) q^{35} +(-0.616897 + 0.515372i) q^{36} +(2.86060 - 2.07835i) q^{37} +(-3.50832 - 1.13992i) q^{38} +(-1.45983 + 0.529552i) q^{39} +(4.46053 + 6.13939i) q^{40} +(3.65507 + 2.65556i) q^{41} +(-4.13217 + 6.11195i) q^{42} +4.24264i q^{43} +(-8.46410 - 2.12976i) q^{45} +(1.25184 - 1.72302i) q^{47} +(-2.13927 + 7.43022i) q^{48} +(-0.309017 + 0.951057i) q^{49} +(1.61209 - 4.96151i) q^{50} +(-1.24999 + 4.34155i) q^{51} +(0.141208 - 0.194356i) q^{52} +(-6.27524 + 2.03895i) q^{53} +(-3.15964 - 7.15900i) q^{54} +7.37772i q^{56} +(2.37625 - 3.51474i) q^{57} +(-10.5172 - 7.64121i) q^{58} +(-0.335431 - 0.461681i) q^{59} +(1.26929 - 0.460431i) q^{60} +(9.67880 + 3.14483i) q^{61} +(-12.4225 + 9.02551i) q^{62} +(-5.44018 - 6.51187i) q^{63} +(2.05813 + 6.33428i) q^{64} +2.60842 q^{65} +2.00000 q^{67} +(-0.215979 - 0.664716i) q^{68} +(10.0256 - 7.28401i) q^{70} +(9.04216 + 2.93797i) q^{71} +(-6.62722 - 4.16108i) q^{72} +(1.88524 + 2.59481i) q^{73} +(-4.30798 - 3.12993i) q^{74} +(4.97060 + 3.36053i) q^{75} +0.656339i q^{76} +(1.43782 + 1.84443i) q^{78} +(6.98881 - 2.27080i) q^{79} +(7.63384 - 10.5071i) q^{80} +(8.91774 - 1.21405i) q^{81} +(2.10250 - 6.47084i) q^{82} +(-1.95277 + 6.01000i) q^{83} +(1.26144 + 0.363185i) q^{84} +(4.46053 - 6.13939i) q^{85} +(6.07658 - 1.97440i) q^{86} +(11.7919 - 9.19239i) q^{87} -12.4168i q^{89} +(0.888560 + 13.1140i) q^{90} +(2.05158 + 1.49056i) q^{91} +(-6.02224 - 16.6017i) q^{93} +(-3.05038 - 0.991130i) q^{94} +(-5.76532 + 4.18875i) q^{95} +(2.60693 - 0.0882174i) q^{96} +(1.77130 + 5.45150i) q^{97} +1.50597 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} - 16 q^{4} + 8 q^{9}+O(q^{10}) $ 32 * q + 4 * q^3 - 16 * q^4 + 8 * q^9	$ 32 q + 4 q^{3} - 16 q^{4} + 8 q^{9} + 16 q^{12} - 4 q^{15} + 8 q^{16} + 4 q^{27} + 40 q^{31} - 96 q^{34} + 40 q^{36} + 56 q^{37} - 64 q^{42} - 160 q^{45} - 28 q^{48} + 8 q^{49} - 104 q^{58} + 28 q^{60} + 16 q^{64} + 64 q^{67} + 16 q^{70} - 24 q^{75} + 240 q^{78} + 8 q^{81} - 96 q^{82} + 48 q^{91} - 56 q^{93} - 32 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 - 16 * q^4 + 8 * q^9 + 16 * q^12 - 4 * q^15 + 8 * q^16 + 4 * q^27 + 40 * q^31 - 96 * q^34 + 40 * q^36 + 56 * q^37 - 64 * q^42 - 160 * q^45 - 28 * q^48 + 8 * q^49 - 104 * q^58 + 28 * q^60 + 16 * q^64 + 64 * q^67 + 16 * q^70 - 24 * q^75 + 240 * q^78 + 8 * q^81 - 96 * q^82 + 48 * q^91 - 56 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.465371	−	1.43226i	−0.329067	−	1.01276i	−0.969571	−	0.244809i	$-0.921275\pi$
$2$	−0.465371	−	1.43226i	−0.329067	−	1.01276i	0.640505	−	0.767954i	$-0.278725\pi$
$3$	1.73106	−	0.0585784i	0.999428	−	0.0338203i
$3$	1.73106	−	0.0585784i	0.999428	−	0.0338203i
$4$	−0.216775	+	0.157497i	−0.108388	+	0.0787483i
$5$	−2.76692	−	0.899027i	−1.23740	−	0.402057i	−0.384013	−	0.923328i	$-0.625458\pi$
$5$	−2.76692	−	0.899027i	−1.23740	−	0.402057i	−0.853392	+	0.521270i	$0.825458\pi$
$6$	−0.889484	−	2.45207i	−0.363130	−	1.00105i
$7$	−1.66251	−	2.28825i	−0.628369	−	0.864876i	0.369560	−	0.929207i	$-0.379509\pi$
$7$	−1.66251	−	2.28825i	−0.628369	−	0.864876i	−0.997929	+	0.0643314i	$0.979509\pi$
$8$	−2.11025	−	1.53319i	−0.746088	−	0.542065i
$9$	2.99314	−	0.202805i	0.997712	−	0.0676018i
$10$			4.38134i			1.38550i
$11$		0			0
$11$		0			0
$12$	−0.366025	+	0.285334i	−0.105662	+	0.0823689i
$13$	−0.852694	+	0.277057i	−0.236495	+	0.0768418i	−0.424867	−	0.905256i	$-0.639679\pi$
$13$	−0.852694	+	0.277057i	−0.236495	+	0.0768418i	0.188372	+	0.982098i	$0.439679\pi$
$14$	−2.50369	+	3.44603i	−0.669139	+	0.920991i
$15$	−4.84237	−	1.39419i	−1.25029	−	0.359978i
$16$	−1.37948	+	4.24561i	−0.344871	+	1.06140i
$17$	−0.806046	+	2.48075i	−0.195495	+	0.601671i	0.804476	+	0.593986i	$0.202446\pi$
$17$	−0.806046	+	2.48075i	−0.195495	+	0.601671i	−0.999970	+	0.00768550i	$0.997554\pi$
$18$	−1.68339	−	4.19258i	−0.396779	−	0.988201i
$19$	1.43977	−	1.98168i	0.330307	−	0.454628i	−0.611272	−	0.791420i	$-0.709342\pi$
$19$	1.43977	−	1.98168i	0.330307	−	0.454628i	0.941579	+	0.336792i	$0.109342\pi$
$20$	0.741394	−	0.240894i	0.165781	−	0.0538654i
$21$	−3.01194	−	3.86370i	−0.657260	−	0.843129i
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−3.74279	−	2.53043i	−0.763994	−	0.516522i
$25$	2.80252	+	2.03615i	0.560503	+	0.407230i
$26$	0.793638	+	1.09235i	0.155645	+	0.214227i
$27$	5.16942	−	0.526402i	0.994855	−	0.101306i
$28$	0.720782	+	0.234196i	0.136215	+	0.0442589i
$29$	6.98368	−	5.07394i	1.29684	−	0.942207i	0.296917	−	0.954903i	$-0.404041\pi$
$29$	6.98368	−	5.07394i	1.29684	−	0.942207i	0.999919	+	0.0126960i	$0.00404139\pi$
$30$	0.256652	+	7.58436i	0.0468580	+	1.38471i
$31$	−3.15078	−	9.69712i	−0.565898	−	1.74165i	−0.665270	−	0.746603i	$-0.731683\pi$
$31$	−3.15078	−	9.69712i	−0.565898	−	1.74165i	0.0993719	−	0.995050i	$-0.468317\pi$
$32$	1.50597			0.266221
$33$		0			0
$34$	3.92820			0.673681
$35$	2.54283	+	7.82603i	0.429817	+	1.32284i
$36$	−0.616897	+	0.515372i	−0.102816	+	0.0858954i
$37$	2.86060	−	2.07835i	0.470280	−	0.341678i	−0.327270	−	0.944931i	$-0.606129\pi$
$37$	2.86060	−	2.07835i	0.470280	−	0.341678i	0.797550	+	0.603252i	$0.206129\pi$
$38$	−3.50832	−	1.13992i	−0.569124	−	0.184920i
$39$	−1.45983	+	0.529552i	−0.233761	+	0.0847962i
$40$	4.46053	+	6.13939i	0.705272	+	0.970723i
$41$	3.65507	+	2.65556i	0.570826	+	0.414729i	0.835405	−	0.549635i	$-0.185233\pi$
$41$	3.65507	+	2.65556i	0.570826	+	0.414729i	−0.264579	+	0.964364i	$0.585233\pi$
$42$	−4.13217	+	6.11195i	−0.637608	+	0.943094i
$43$			4.24264i			0.646997i	0.946229	+	0.323498i	$0.104859\pi$
$43$			4.24264i			0.646997i	−0.946229	+	0.323498i	$0.895141\pi$
$44$		0			0
$45$	−8.46410	−	2.12976i	−1.26175	−	0.317487i
$46$		0			0
$47$	1.25184	−	1.72302i	0.182600	−	0.251328i	−0.707898	−	0.706315i	$-0.750356\pi$
$47$	1.25184	−	1.72302i	0.182600	−	0.251328i	0.890498	+	0.454987i	$0.150356\pi$
$48$	−2.13927	+	7.43022i	−0.308777	+	1.07246i
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$	1.61209	−	4.96151i	0.227984	−	0.701663i
$51$	−1.24999	+	4.34155i	−0.175034	+	0.607939i
$52$	0.141208	−	0.194356i	0.0195820	−	0.0269523i
$53$	−6.27524	+	2.03895i	−0.861970	+	0.280071i	−0.706451	−	0.707762i	$-0.749705\pi$
$53$	−6.27524	+	2.03895i	−0.861970	+	0.280071i	−0.155519	+	0.987833i	$0.549705\pi$
$54$	−3.15964	−	7.15900i	−0.429973	−	0.974217i
$55$		0			0
$56$			7.37772i			0.985890i
$57$	2.37625	−	3.51474i	0.314742	−	0.465539i
$58$	−10.5172	−	7.64121i	−1.38098	−	1.00334i
$59$	−0.335431	−	0.461681i	−0.0436694	−	0.0601057i	0.786624	−	0.617432i	$-0.211827\pi$
$59$	−0.335431	−	0.461681i	−0.0436694	−	0.0601057i	−0.830293	+	0.557327i	$0.811827\pi$
$60$	1.26929	−	0.460431i	0.163864	−	0.0594414i
$61$	9.67880	+	3.14483i	1.23924	+	0.402655i	0.854055	−	0.520183i	$-0.174136\pi$
$61$	9.67880	+	3.14483i	1.23924	+	0.402655i	0.385189	+	0.922838i	$0.374136\pi$
$62$	−12.4225	+	9.02551i	−1.57766	+	1.14624i
$63$	−5.44018	−	6.51187i	−0.685399	−	0.820418i
$64$	2.05813	+	6.33428i	0.257266	+	0.791785i
$65$	2.60842			0.323535
$66$		0			0
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$	−0.215979	−	0.664716i	−0.0261913	−	0.0806086i
$69$		0			0
$70$	10.0256	−	7.28401i	1.19829	−	0.870606i
$71$	9.04216	+	2.93797i	1.07311	+	0.348673i	0.791697	−	0.610914i	$-0.209198\pi$
$71$	9.04216	+	2.93797i	1.07311	+	0.348673i	0.281410	+	0.959588i	$0.409198\pi$
$72$	−6.62722	−	4.16108i	−0.781026	−	0.490388i
$73$	1.88524	+	2.59481i	0.220651	+	0.303700i	0.904964	−	0.425489i	$-0.139898\pi$
$73$	1.88524	+	2.59481i	0.220651	+	0.303700i	−0.684313	+	0.729188i	$0.739898\pi$
$74$	−4.30798	−	3.12993i	−0.500793	−	0.363847i
$75$	4.97060	+	3.36053i	0.573955	+	0.388040i
$76$			0.656339i			0.0752872i
$77$		0			0
$78$	1.43782	+	1.84443i	0.162801	+	0.208841i
$79$	6.98881	−	2.27080i	0.786303	−	0.255485i	0.111774	−	0.993734i	$-0.464347\pi$
$79$	6.98881	−	2.27080i	0.786303	−	0.255485i	0.674529	+	0.738249i	$0.264347\pi$
$80$	7.63384	−	10.5071i	0.853490	−	1.17473i
$81$	8.91774	−	1.21405i	0.990860	−	0.134894i
$82$	2.10250	−	6.47084i	0.232183	−	0.714585i
$83$	−1.95277	+	6.01000i	−0.214344	+	0.659683i	0.784856	+	0.619679i	$0.212737\pi$
$83$	−1.95277	+	6.01000i	−0.214344	+	0.659683i	−0.999200	+	0.0400041i	$0.987263\pi$
$84$	1.26144	+	0.363185i	0.137634	+	0.0396268i
$85$	4.46053	−	6.13939i	0.483812	−	0.665911i
$86$	6.07658	−	1.97440i	0.655255	−	0.212905i
$87$	11.7919	−	9.19239i	1.26423	−	0.985527i
$88$		0			0
$89$		−	12.4168i		−	1.31618i	−0.752940	−	0.658089i	$-0.771365\pi$
$89$		−	12.4168i		−	1.31618i	0.752940	−	0.658089i	$-0.228635\pi$
$90$	0.888560	+	13.1140i	0.0936624	+	1.38233i
$91$	2.05158	+	1.49056i	0.215065	+	0.156254i
$92$		0			0
$93$	−6.02224	−	16.6017i	−0.624477	−	1.72152i
$94$	−3.05038	−	0.991130i	−0.314623	−	0.102227i
$95$	−5.76532	+	4.18875i	−0.591510	+	0.429757i
$96$	2.60693	−	0.0882174i	0.266068	−	0.00900365i
$97$	1.77130	+	5.45150i	0.179848	+	0.553516i	0.999822	−	0.0188854i	$-0.00601177\pi$
$97$	1.77130	+	5.45150i	0.179848	+	0.553516i	−0.819973	+	0.572402i	$0.806012\pi$
$98$	1.50597			0.152126
$99$		0			0
$100$	−0.928203			−0.0928203
$101$	−4.74499	−	14.6036i	−0.472144	−	1.45311i	−0.849771	−	0.527152i	$-0.823260\pi$
$101$	−4.74499	−	14.6036i	−0.472144	−	1.45311i	0.377627	−	0.925958i	$-0.376740\pi$
$102$	6.79996	−	0.230108i	0.673296	−	0.0227841i
$103$	−7.49793	+	5.44756i	−0.738793	+	0.536764i	−0.892333	−	0.451378i	$-0.850933\pi$
$103$	−7.49793	+	5.44756i	−0.738793	+	0.536764i	0.153540	+	0.988142i	$0.450933\pi$
$104$	2.22418	+	0.722681i	0.218099	+	0.0708647i
$105$	4.86023	+	13.3984i	0.474310	+	1.30755i
$106$	5.84062	+	8.03893i	0.567291	+	0.780810i
$107$	6.65722	+	4.83676i	0.643578	+	0.467587i	0.861078	−	0.508474i	$-0.169790\pi$
$107$	6.65722	+	4.83676i	0.643578	+	0.467587i	−0.217500	+	0.976060i	$0.569790\pi$
$108$	−1.03770	+	0.928277i	−0.0998524	+	0.0893235i
$109$			6.45189i			0.617979i	0.951065	+	0.308990i	$0.0999909\pi$
$109$			6.45189i			0.617979i	−0.951065	+	0.308990i	$0.900009\pi$
$110$		0			0
$111$	4.83013	−	3.76532i	0.458455	−	0.357388i
$112$	12.0084	−	3.90177i	1.13469	−	0.368682i
$113$	−6.04657	+	8.32239i	−0.568813	+	0.782904i	−0.992413	−	0.122945i	$-0.960766\pi$
$113$	−6.04657	+	8.32239i	−0.568813	+	0.782904i	0.423600	+	0.905849i	$0.360766\pi$
$114$	−6.13988	−	1.76776i	−0.575052	−	0.165566i
$115$		0			0
$116$	−0.714762	+	2.19981i	−0.0663640	+	0.204247i
$117$	−2.49604	+	1.00220i	−0.230759	+	0.0926535i
$118$	−0.505149	+	0.695278i	−0.0465027	+	0.0640055i
$119$	7.01663	−	2.27984i	0.643213	−	0.208993i
$120$	8.08108	+	10.3664i	0.737698	+	0.946315i
$121$		0			0
$122$		−	15.3261i		−	1.38756i
$123$	6.48270	+	4.38283i	0.584526	+	0.395187i
$124$	2.21028	+	1.60586i	0.198489	+	0.144210i
$125$	2.62646	+	3.61502i	0.234918	+	0.323337i
$126$	−6.79501	+	10.8222i	−0.605348	+	0.964119i
$127$	−0.263824	−	0.0857218i	−0.0234106	−	0.00760658i	0.297288	−	0.954788i	$-0.403918\pi$
$127$	−0.263824	−	0.0857218i	−0.0234106	−	0.00760658i	−0.320699	+	0.947181i	$0.603918\pi$
$128$	10.5513	−	7.66595i	0.932610	−	0.677581i
$129$	0.248527	+	7.34427i	0.0218816	+	0.646627i
$130$	−1.21388	−	3.73594i	−0.106464	−	0.327664i
$131$	−17.5600			−1.53422			−0.767112	−	0.641513i	$-0.778307\pi$
$131$	−17.5600			−1.53422			−0.767112	+	0.641513i	$0.778307\pi$
$132$		0			0
$133$	−6.92820			−0.600751
$134$	−0.930741	−	2.86453i	−0.0804038	−	0.247457i
$135$	−14.7766	−	3.19094i	−1.27177	−	0.274632i
$136$	5.50443	−	3.99920i	0.472001	−	0.342929i
$137$	17.6870	+	5.74686i	1.51110	+	0.490987i	0.943233	−	0.332132i	$-0.107768\pi$
$137$	17.6870	+	5.74686i	1.51110	+	0.490987i	0.567870	+	0.823119i	$0.307768\pi$
$138$		0			0
$139$	−11.3551	−	15.6290i	−0.963130	−	1.32564i	−0.945442	−	0.325792i	$-0.894369\pi$
$139$	−11.3551	−	15.6290i	−0.963130	−	1.32564i	−0.0176887	−	0.999844i	$-0.505631\pi$
$140$	−1.78380	−	1.29600i	−0.150758	−	0.109532i
$141$	2.06609	−	3.05597i	0.173996	−	0.257360i
$142$		−	14.3180i		−	1.20154i
$143$		0			0
$144$	−3.26795	+	12.9875i	−0.272329	+	1.08229i
$145$	−23.8849	+	7.76067i	−1.98353	+	0.644489i
$146$	2.83912	−	3.90771i	0.234967	−	0.323405i
$147$	−0.479216	+	1.66444i	−0.0395250	+	0.137280i
$148$	−0.292775	+	0.901070i	−0.0240660	+	0.0740675i
$149$	4.62029	−	14.2198i	0.378509	−	1.16493i	−0.562571	−	0.826749i	$-0.690188\pi$
$149$	4.62029	−	14.2198i	0.378509	−	1.16493i	0.941080	−	0.338183i	$-0.109812\pi$
$150$	2.49999	−	8.68310i	0.204123	−	0.708972i
$151$	−4.70511	+	6.47603i	−0.382896	+	0.527011i	−0.956349	−	0.292227i	$-0.905604\pi$
$151$	−4.70511	+	6.47603i	−0.382896	+	0.527011i	0.573453	+	0.819239i	$0.305604\pi$
$152$	−6.07658	+	1.97440i	−0.492876	+	0.160145i
$153$	−1.90949	+	7.58871i	−0.154374	+	0.613511i
$154$		0			0
$155$			29.6638i			2.38265i
$156$	0.233054	−	0.344713i	0.0186592	−	0.0275991i
$157$	3.66962	+	2.66613i	0.292867	+	0.212781i	0.724510	−	0.689264i	$-0.242066\pi$
$157$	3.66962	+	2.66613i	0.292867	+	0.212781i	−0.431643	+	0.902045i	$0.642066\pi$
$158$	−6.50477	−	8.95305i	−0.517492	−	0.712267i
$159$	−10.7434	+	3.89713i	−0.852005	+	0.309063i
$160$	−4.16690	−	1.35391i	−0.329423	−	0.107036i
$161$		0			0
$162$	−5.88889	−	12.2076i	−0.462675	−	0.959117i
$163$	−2.59336	−	7.98156i	−0.203128	−	0.625164i	−0.999785	−	0.0207322i	$-0.993400\pi$
$163$	−2.59336	−	7.98156i	−0.203128	−	0.625164i	0.796657	−	0.604432i	$-0.206600\pi$
$164$	−1.21057			−0.0945297
$165$		0			0
$166$	9.51666			0.738636
$167$	3.81425	+	11.7391i	0.295155	+	0.908395i	0.983169	+	0.182697i	$0.0584829\pi$
$167$	3.81425	+	11.7391i	0.295155	+	0.908395i	−0.688014	+	0.725698i	$0.741517\pi$
$168$	0.432175	+	12.7713i	0.0333430	+	0.985326i
$169$	−9.86689	+	7.16872i	−0.758992	+	0.551440i
$170$	−10.8690	−	3.53156i	−0.833616	−	0.270858i
$171$	3.90755	−	6.22343i	0.298817	−	0.475918i
$172$	−0.668201	−	0.919700i	−0.0509499	−	0.0701265i
$173$	−1.54481	−	1.12237i	−0.117450	−	0.0853324i	0.527510	−	0.849549i	$-0.323126\pi$
$173$	−1.54481	−	1.12237i	−0.117450	−	0.0853324i	−0.644960	+	0.764217i	$0.723126\pi$
$174$	−18.6535	−	12.6113i	−1.41412	−	0.956061i
$175$		−	9.79796i		−	0.740656i
$176$		0			0
$177$	−0.607695	−	0.779548i	−0.0456772	−	0.0585944i
$178$	−17.7841	+	5.77841i	−1.33298	+	0.433110i
$179$	−4.09096	+	5.63073i	−0.305773	+	0.420860i	−0.934057	−	0.357124i	$-0.883758\pi$
$179$	−4.09096	+	5.63073i	−0.305773	+	0.420860i	0.628284	+	0.777984i	$0.283758\pi$
$180$	2.17024	−	0.871386i	0.161760	−	0.0649493i
$181$	−4.59088	+	14.1293i	−0.341238	+	1.05022i	0.622330	+	0.782755i	$0.286186\pi$
$181$	−4.59088	+	14.1293i	−0.341238	+	1.05022i	−0.963567	+	0.267466i	$0.913814\pi$
$182$	1.18013	−	3.63208i	0.0874773	−	0.269227i
$183$	16.9388	+	4.87693i	1.25215	+	0.360513i
$184$		0			0
$185$	−9.78355	+	3.17887i	−0.719301	+	0.233715i
$186$	−20.9755	+	16.3514i	−1.53800	+	1.19894i
$187$		0			0
$188$			0.570669i			0.0416203i
$189$	−9.79874	−	10.9538i	−0.712753	−	0.796768i
$190$	8.68241	+	6.30814i	0.629888	+	0.457641i
$191$	−3.42010	−	4.70737i	−0.247470	−	0.340613i	0.667153	−	0.744920i	$-0.267513\pi$
$191$	−3.42010	−	4.70737i	−0.247470	−	0.340613i	−0.914623	+	0.404307i	$0.867513\pi$
$192$	3.93380	+	10.8445i	0.283898	+	0.782631i
$193$	−22.9003	−	7.44076i	−1.64840	−	0.535597i	−0.670007	−	0.742355i	$-0.733709\pi$
$193$	−22.9003	−	7.44076i	−1.64840	−	0.535597i	−0.978392	+	0.206757i	$0.933709\pi$
$194$	6.98368	−	5.07394i	0.501399	−	0.364288i
$195$	4.51533	−	0.152797i	0.323349	−	0.0109420i
$196$	−0.0828009	−	0.254835i	−0.00591435	−	0.0182025i
$197$	3.71087			0.264388			0.132194	−	0.991224i	$-0.457798\pi$
$197$	3.71087			0.264388			0.132194	+	0.991224i	$0.457798\pi$
$198$		0			0
$199$	−9.66025			−0.684797			−0.342399	−	0.939555i	$-0.611239\pi$
$199$	−9.66025			−0.684797			−0.342399	+	0.939555i	$0.611239\pi$
$200$	−2.79222	−	8.59358i	−0.197440	−	0.607658i
$201$	3.46212	−	0.117157i	0.244199	−	0.00826360i
$202$	−18.7080	+	13.5922i	−1.31629	+	0.956341i
$203$	−23.2208	−	7.54491i	−1.62978	−	0.529549i
$204$	−0.412811	−	1.13801i	−0.0289026	−	0.0796767i
$205$	−7.72586	−	10.6337i	−0.539598	−	0.742693i
$206$	11.2917	+	8.20387i	0.786728	+	0.571591i
$207$		0			0
$208$		−	4.00240i		−	0.277517i
$209$		0			0
$210$	16.9282	−	13.1963i	1.16816	−	0.910635i
$211$	25.0980	−	8.15483i	1.72782	−	0.561402i	0.734685	−	0.678408i	$-0.237330\pi$
$211$	25.0980	−	8.15483i	1.72782	−	0.561402i	0.993131	+	0.117006i	$0.0373298\pi$
$212$	1.03919	−	1.43032i	0.0713719	−	0.0982349i
$213$	15.8246	+	4.55614i	1.08428	+	0.312181i
$214$	3.82943	−	11.7858i	0.261775	−	0.805659i
$215$	3.81425	−	11.7391i	0.260130	−	0.800597i
$216$	−11.7159	−	6.81486i	−0.797164	−	0.463693i
$217$	−16.9512	+	23.3313i	−1.15072	+	1.58383i
$218$	9.24081	−	3.00252i	0.625867	−	0.203356i
$219$	3.41547	+	4.38134i	0.230796	+	0.296064i
$220$		0			0
$221$		−	2.33864i		−	0.157314i
$222$	−7.64073	−	5.16575i	−0.512812	−	0.346702i
$223$	0.750932	+	0.545584i	0.0502861	+	0.0365350i	0.612644	−	0.790359i	$-0.290106\pi$
$223$	0.750932	+	0.545584i	0.0502861	+	0.0365350i	−0.562358	+	0.826894i	$0.690106\pi$
$224$	−2.50369	−	3.44603i	−0.167285	−	0.230248i
$225$	8.80126	+	5.52610i	0.586751	+	0.368407i
$226$	14.7337	+	4.78728i	0.980074	+	0.318445i
$227$	9.98583	−	7.25513i	0.662783	−	0.481540i	−0.204819	−	0.978800i	$-0.565660\pi$
$227$	9.98583	−	7.25513i	0.662783	−	0.481540i	0.867602	+	0.497260i	$0.165660\pi$
$228$	0.0384473	+	1.13616i	0.00254623	+	0.0752442i
$229$	3.85162	+	11.8541i	0.254522	+	0.783339i	0.993923	+	0.110074i	$0.0351087\pi$
$229$	3.85162	+	11.8541i	0.254522	+	0.783339i	−0.739401	+	0.673265i	$0.764891\pi$
$230$		0			0
$231$		0			0
$232$	−22.5167			−1.47829
$233$	2.66753	+	8.20981i	0.174756	+	0.537842i	0.999622	−	0.0274850i	$-0.00874984\pi$
$233$	2.66753	+	8.20981i	0.174756	+	0.537842i	−0.824867	+	0.565327i	$0.808750\pi$
$234$	2.59700	+	3.10859i	0.169771	+	0.203215i
$235$	−5.01279	+	3.64201i	−0.326999	+	0.237578i
$236$	0.145426	+	0.0472519i	0.00946644	+	0.00307583i
$237$	11.9650	−	4.34029i	0.777212	−	0.281932i
$238$	−6.53067	−	8.98869i	−0.423320	−	0.582650i
$239$	−7.54912	−	5.48476i	−0.488312	−	0.354779i	0.316223	−	0.948685i	$-0.397585\pi$
$239$	−7.54912	−	5.48476i	−0.488312	−	0.354779i	−0.804535	+	0.593905i	$0.797585\pi$
$240$	12.5992	−	18.6356i	0.813272	−	1.20292i
$241$			20.7327i			1.33551i	0.744380	+	0.667756i	$0.232745\pi$
$241$			20.7327i			1.33551i	−0.744380	+	0.667756i	$0.767255\pi$
$242$		0			0
$243$	15.3660	−	2.62398i	0.985731	−	0.168328i
$244$	−2.59343	+	0.842656i	−0.166027	+	0.0539455i
$245$	1.71005	−	2.35368i	0.109251	−	0.150371i
$246$	3.26051	−	11.3246i	0.207883	−	0.722029i
$247$	−0.678648	+	2.08867i	−0.0431814	+	0.132899i
$248$	−8.21856	+	25.2941i	−0.521879	+	1.60618i
$249$	−3.02830	+	10.5181i	−0.191911	+	0.666555i
$250$	3.95538	−	5.44411i	0.250160	−	0.344316i
$251$	19.1698	−	6.22864i	1.20999	−	0.393148i	0.366561	−	0.930394i	$-0.380535\pi$
$251$	19.1698	−	6.22864i	1.20999	−	0.393148i	0.843426	+	0.537246i	$0.180535\pi$
$252$	2.20489	+	0.554803i	0.138895	+	0.0349493i
$253$		0			0
$254$			0.417759i			0.0262125i
$255$	7.36181	−	10.8889i	0.461014	−	0.681892i
$256$	−5.11340	−	3.71510i	−0.319587	−	0.232194i
$257$	−2.29103	−	3.15334i	−0.142911	−	0.196700i	0.731561	−	0.681776i	$-0.238792\pi$
$257$	−2.29103	−	3.15334i	−0.142911	−	0.196700i	−0.874472	+	0.485076i	$0.838792\pi$
$258$	10.4033	−	3.77376i	0.647679	−	0.234944i
$259$	−9.51155	−	3.09049i	−0.591019	−	0.192034i
$260$	−0.565441	+	0.410817i	−0.0350672	+	0.0254778i
$261$	19.8741	−	16.6033i	1.23018	−	1.02772i
$262$	8.17191	+	25.1506i	0.504862	+	1.55381i
$263$	30.4148			1.87546			0.937729	−	0.347367i	$-0.112924\pi$
$263$	30.4148			1.87546			0.937729	+	0.347367i	$0.112924\pi$
$264$		0			0
$265$	19.1962			1.17921
$266$	3.22418	+	9.92301i	0.197687	+	0.608419i
$267$	−0.727356	−	21.4942i	−0.0445135	−	1.31543i
$268$	−0.433551	+	0.314993i	−0.0264833	+	0.0192413i
$269$	−7.75802	−	2.52074i	−0.473015	−	0.153692i	0.0628020	−	0.998026i	$-0.479996\pi$
$269$	−7.75802	−	2.52074i	−0.473015	−	0.153692i	−0.535817	+	0.844334i	$0.679996\pi$
$270$	2.30634	+	22.6490i	0.140360	+	1.37837i
$271$	0.385786	+	0.530989i	0.0234348	+	0.0322553i	0.820574	−	0.571541i	$-0.193654\pi$
$271$	0.385786	+	0.530989i	0.0234348	+	0.0322553i	−0.797139	+	0.603796i	$0.793654\pi$
$272$	−9.42039	−	6.84432i	−0.571195	−	0.414998i
$273$	3.63873	+	2.46008i	0.220226	+	0.148891i
$274$		−	28.0069i		−	1.69196i
$275$		0			0
$276$		0			0
$277$	−22.2761	+	7.23794i	−1.33844	+	0.434885i	−0.888788	−	0.458318i	$-0.848452\pi$
$277$	−22.2761	+	7.23794i	−1.33844	+	0.434885i	−0.449652	+	0.893204i	$0.648452\pi$
$278$	−17.1005	+	23.5368i	−1.02562	+	1.41165i
$279$	−11.3974	−	28.3858i	−0.682342	−	1.69941i
$280$	6.63277	−	20.4136i	0.396384	−	1.21994i
$281$	−8.21856	+	25.2941i	−0.490278	+	1.50892i	0.333909	+	0.942605i	$0.391632\pi$
$281$	−8.21856	+	25.2941i	−0.490278	+	1.50892i	−0.824188	+	0.566317i	$0.808368\pi$
$282$	−5.33846	−	1.53702i	−0.317901	−	0.0915282i
$283$	12.6319	−	17.3863i	0.750886	−	1.03351i	−0.247032	−	0.969007i	$-0.579455\pi$
$283$	12.6319	−	17.3863i	0.750886	−	1.03351i	0.997918	−	0.0644987i	$-0.0205448\pi$
$284$	−2.42284	+	0.787228i	−0.143769	+	0.0467134i
$285$	−9.73475	+	7.58871i	−0.576637	+	0.449516i
$286$		0			0
$287$		−	12.7786i		−	0.754296i
$288$	4.50758	−	0.305419i	0.265612	−	0.0179970i
$289$	8.24886	+	5.99315i	0.485227	+	0.352538i
$290$	22.2307	+	30.5979i	1.30543	+	1.79677i
$291$	3.38557	+	9.33312i	0.198466	+	0.547117i
$292$	−0.817348	−	0.265573i	−0.0478317	−	0.0155415i
$293$	−21.4290	+	15.5691i	−1.25190	+	0.909556i	−0.998330	−	0.0577625i	$-0.981603\pi$
$293$	−21.4290	+	15.5691i	−1.25190	+	0.909556i	−0.253566	+	0.967318i	$0.581603\pi$
$294$	2.60693	−	0.0882174i	0.152039	−	0.00514494i
$295$	0.513047	+	1.57900i	0.0298707	+	0.0919327i
$296$	−9.22310			−0.536082
$297$		0			0
$298$	−22.5167			−1.30436
$299$		0			0
$300$	−1.60678	+	0.0543727i	−0.0927672	+	0.00313921i
$301$	9.70820	−	7.05342i	0.559572	−	0.406553i
$302$	11.4650	+	3.72520i	0.659736	+	0.214361i
$303$	−9.06932	−	25.0017i	−0.521019	−	1.43631i
$304$	6.42730	+	8.84642i	0.368631	+	0.507377i
$305$	−23.9532	−	17.4030i	−1.37156	−	0.996494i
$306$	11.7577	−	0.796661i	0.672140	−	0.0455421i
$307$		−	22.7017i		−	1.29566i	−0.761786	−	0.647829i	$-0.775677\pi$
$307$		−	22.7017i		−	1.29566i	0.761786	−	0.647829i	$-0.224323\pi$
$308$		0			0
$309$	−12.6603	+	9.86928i	−0.720217	+	0.561444i
$310$	42.4864	−	13.8047i	2.41306	−	0.784052i
$311$	12.7640	−	17.5681i	0.723780	−	0.996197i	−0.275610	−	0.961270i	$-0.588880\pi$
$311$	12.7640	−	17.5681i	0.723780	−	0.996197i	0.999390	−	0.0349279i	$-0.0111202\pi$
$312$	3.89253	+	1.12071i	0.220371	+	0.0634480i
$313$	4.13845	−	12.7368i	0.233919	−	0.719929i	−0.763344	−	0.645992i	$-0.776444\pi$
$313$	4.13845	−	12.7368i	0.233919	−	0.719929i	0.997263	−	0.0739364i	$-0.0235562\pi$
$314$	2.11087	−	6.49660i	0.119124	−	0.366624i
$315$	9.19821	+	22.9087i	0.518260	+	1.29076i
$316$	−1.15736	+	1.59297i	−0.0651065	+	0.0896114i
$317$	−21.7381	+	7.06312i	−1.22093	+	0.396704i	−0.847421	−	0.530922i	$-0.821846\pi$
$317$	−21.7381	+	7.06312i	−1.22093	+	0.396704i	−0.373510	+	0.927626i	$0.621846\pi$
$318$	10.5814	+	13.5737i	0.593374	+	0.761177i
$319$		0			0
$320$		−	19.3768i		−	1.08319i
$321$	11.8074	+	7.98274i	0.659024	+	0.445553i
$322$		0			0
$323$	3.75553	+	5.16905i	0.208963	+	0.287614i
$324$	−1.74194	+	1.66769i	−0.0967744	+	0.0926494i
$325$	−2.95382	−	0.959754i	−0.163848	−	0.0532376i
$326$	−10.2248	+	7.42876i	−0.566300	+	0.411441i
$327$	0.377942	+	11.1686i	0.0209002	+	0.617626i
$328$	−3.64164	−	11.2078i	−0.201076	−	0.618849i
$329$	−6.02388			−0.332108
$330$		0			0
$331$	20.3923			1.12086			0.560431	−	0.828201i	$-0.310635\pi$
$331$	20.3923			1.12086			0.560431	+	0.828201i	$0.310635\pi$
$332$	−0.523242	−	1.61037i	−0.0287166	−	0.0883807i
$333$	8.14067	−	6.80093i	0.446106	−	0.372689i
$334$	15.0384	−	10.9260i	0.822863	−	0.597845i
$335$	−5.53384	−	1.79805i	−0.302346	−	0.0982382i
$336$	20.5587	−	7.45763i	1.12157	−	0.406847i
$337$	10.8281	+	14.9037i	0.589847	+	0.811854i	0.994732	−	0.102513i	$-0.0326884\pi$
$337$	10.8281	+	14.9037i	0.589847	+	0.811854i	−0.404885	+	0.914368i	$0.632688\pi$
$338$	14.8593	+	10.7959i	0.808237	+	0.587219i
$339$	−9.97946	+	14.7607i	−0.542010	+	0.801694i
$340$			2.03339i			0.110276i
$341$		0			0
$342$	−10.7321	−	2.70043i	−0.580323	−	0.146023i
$343$	−16.1400	+	5.24419i	−0.871476	+	0.283160i
$344$	6.50477	−	8.95305i	0.350714	−	0.482716i
$345$		0			0
$346$	−0.888623	+	2.73490i	−0.0477727	+	0.147029i
$347$	3.47357	−	10.6906i	0.186471	−	0.573899i	−0.813499	−	0.581566i	$-0.802440\pi$
$347$	3.47357	−	10.6906i	0.186471	−	0.573899i	0.999971	+	0.00766635i	$0.00244030\pi$
$348$	−1.10843	+	3.84988i	−0.0594183	+	0.206375i
$349$	−10.5020	+	14.4548i	−0.562161	+	0.773749i	−0.991599	−	0.129348i	$-0.958712\pi$
$349$	−10.5020	+	14.4548i	−0.562161	+	0.773749i	0.429438	+	0.903096i	$0.358712\pi$
$350$	−14.0333	+	4.55968i	−0.750109	+	0.243725i
$351$	−4.26209	+	1.88108i	−0.227494	+	0.100405i
$352$		0			0
$353$			12.4168i			0.660880i	0.943827	+	0.330440i	$0.107197\pi$
$353$			12.4168i			0.660880i	−0.943827	+	0.330440i	$0.892803\pi$
$354$	−0.833715	+	1.23316i	−0.0443114	+	0.0655416i
$355$	−22.3776	−	16.2583i	−1.18768	−	0.862900i
$356$	1.95560	+	2.69166i	0.103647	+	0.142658i
$357$	12.0127	−	4.35757i	0.635777	−	0.230627i
$358$	9.96850	+	3.23896i	0.526852	+	0.171185i
$359$	7.78810	−	5.65839i	0.411040	−	0.298638i	−0.362982	−	0.931796i	$-0.618242\pi$
$359$	7.78810	−	5.65839i	0.411040	−	0.298638i	0.774023	+	0.633158i	$0.218242\pi$
$360$	14.5961	+	17.4714i	0.769281	+	0.920825i
$361$	4.01722	+	12.3637i	0.211433	+	0.650723i
$362$	22.3733			1.17592
$363$		0			0
$364$	−0.679492			−0.0356151
$365$	−2.88351	−	8.87452i	−0.150930	−	0.464514i
$366$	−0.897779	−	26.5304i	−0.0469277	−	1.38677i
$367$	−3.11990	+	2.26674i	−0.162857	+	0.118323i	−0.666229	−	0.745747i	$-0.732093\pi$
$367$	−3.11990	+	2.26674i	−0.162857	+	0.118323i	0.503372	+	0.864070i	$0.332093\pi$
$368$		0			0
$369$	11.4787	+	7.20720i	0.597556	+	0.375192i
$370$	9.10596	+	12.5333i	0.473396	+	0.651574i
$371$	15.0982	+	10.9695i	0.783862	+	0.569509i
$372$	3.92019	+	2.65036i	0.203252	+	0.137415i
$373$		−	24.3190i		−	1.25919i	−0.776923	−	0.629596i	$-0.783220\pi$
$373$		−	24.3190i		−	1.25919i	0.776923	−	0.629596i	$-0.216780\pi$
$374$		0			0
$375$	4.75833	+	6.10396i	0.245719	+	0.315207i
$376$	−5.28342	+	1.71669i	−0.272472	+	0.0885314i
$377$	−4.54917	+	6.26140i	−0.234294	+	0.322478i
$378$	−11.1286	+	19.1319i	−0.572395	+	0.984040i
$379$	0.181843	−	0.559656i	0.00934066	−	0.0287476i	−0.946278	−	0.323356i	$-0.895189\pi$
$379$	0.181843	−	0.559656i	0.00934066	−	0.0287476i	0.955618	+	0.294608i	$0.0951890\pi$
$380$	0.590066	−	1.81604i	0.0302698	−	0.0931608i
$381$	−0.461717	−	0.132935i	−0.0236545	−	0.00681047i
$382$	−5.15058	+	7.08916i	−0.263526	+	0.362713i
$383$	−26.7292	+	8.68483i	−1.36580	+	0.443774i	−0.897974	−	0.440048i	$-0.854961\pi$
$383$	−26.7292	+	8.68483i	−1.36580	+	0.443774i	−0.467822	+	0.883823i	$0.654961\pi$
$384$	17.8158	−	13.8883i	0.909160	−	0.708734i
$385$		0			0
$386$			36.2620i			1.84569i
$387$	0.860431	+	12.6988i	0.0437381	+	0.645517i
$388$	−1.24257	−	0.902778i	−0.0630818	−	0.0458316i
$389$	9.22112	+	12.6918i	0.467529	+	0.643499i	0.976049	−	0.217552i	$-0.0698071\pi$
$389$	9.22112	+	12.6918i	0.467529	+	0.643499i	−0.508520	+	0.861050i	$0.669807\pi$
$390$	−2.32015	−	6.39603i	−0.117485	−	0.323876i
$391$		0			0
$392$	2.11025	−	1.53319i	0.106584	−	0.0774378i
$393$	−30.3974	+	1.02864i	−1.53335	+	0.0518879i
$394$	−1.72693	−	5.31494i	−0.0870014	−	0.267763i
$395$	−21.3790			−1.07569
$396$		0			0
$397$	−10.8038			−0.542230			−0.271115	−	0.962547i	$-0.587392\pi$
$397$	−10.8038			−0.542230			−0.271115	+	0.962547i	$0.587392\pi$
$398$	4.49560	+	13.8360i	0.225344	+	0.693538i
$399$	−11.9931	+	0.405843i	−0.600408	+	0.0203176i
$400$	−12.5107	+	9.08957i	−0.625536	+	0.454479i
$401$	−2.76692	−	0.899027i	−0.138173	−	0.0448953i	0.239114	−	0.970992i	$-0.423143\pi$
$401$	−2.76692	−	0.899027i	−0.138173	−	0.0448953i	−0.377287	+	0.926096i	$0.623143\pi$
$402$	−1.77897	−	4.90415i	−0.0887269	−	0.244597i
$403$	5.37331	+	7.39573i	0.267664	+	0.368407i
$404$	3.32861	+	2.41838i	0.165605	+	0.120319i
$405$	−25.7661	−	4.65811i	−1.28033	−	0.231463i
$406$			36.7696i			1.82484i
$407$		0			0
$408$	9.29423	−	7.24530i	0.460133	−	0.358696i
$409$	3.34956	−	1.08834i	0.165625	−	0.0538148i	−0.225031	−	0.974352i	$-0.572248\pi$
$409$	3.34956	−	1.08834i	0.165625	−	0.0538148i	0.390656	+	0.920537i	$0.372248\pi$
$410$	−11.6349	+	16.0141i	−0.574608	+	0.790880i
$411$	30.9539	+	8.91208i	1.52684	+	0.439600i
$412$	0.767394	−	2.36180i	0.0378068	−	0.116357i
$413$	−0.498783	+	1.53510i	−0.0245435	+	0.0755371i
$414$		0			0
$415$	10.8063	−	14.8736i	0.530460	−	0.730116i
$416$	−1.28413	+	0.417240i	−0.0629598	+	0.0204569i
$417$	−20.5719	−	26.3896i	−1.00741	−	1.29230i
$418$		0			0
$419$		−	14.3377i		−	0.700442i	−0.936667	−	0.350221i	$-0.886107\pi$
$419$		−	14.3377i		−	0.700442i	0.936667	−	0.350221i	$-0.113893\pi$
$420$	−3.16378	−	2.13897i	−0.154377	−	0.104371i
$421$	7.12246	+	5.17477i	0.347128	+	0.252203i	0.747663	−	0.664078i	$-0.231176\pi$
$421$	7.12246	+	5.17477i	0.347128	+	0.252203i	−0.400535	+	0.916281i	$0.631176\pi$
$422$	−23.3597	−	32.1519i	−1.13713	−	1.56513i
$423$	3.39750	−	5.41110i	0.165192	−	0.263097i
$424$	16.3684	+	5.31843i	0.794922	+	0.258286i
$425$	−7.31014	+	5.31113i	−0.354594	+	0.257627i
$426$	−0.838726	−	24.7853i	−0.0406364	−	1.20085i
$427$	−8.89493	−	27.3758i	−0.430456	−	1.32481i
$428$	−2.20489			−0.106578
$429$		0			0
$430$	−18.5885			−0.896415
$431$	−2.45155	−	7.54509i	−0.118087	−	0.363434i	0.874491	−	0.485041i	$-0.161195\pi$
$431$	−2.45155	−	7.54509i	−0.118087	−	0.363434i	−0.992578	+	0.121607i	$0.961195\pi$
$432$	−4.89623	+	22.6735i	−0.235570	+	1.09088i
$433$	20.2679	−	14.7255i	0.974015	−	0.707664i	0.0176522	−	0.999844i	$-0.494381\pi$
$433$	20.2679	−	14.7255i	0.974015	−	0.707664i	0.956363	+	0.292181i	$0.0943808\pi$
$434$	41.3052	+	13.4209i	1.98271	+	0.644222i
$435$	−40.8916	+	14.8333i	−1.96060	+	0.711204i
$436$	−1.01615	−	1.39861i	−0.0486648	−	0.0669814i
$437$		0			0
$438$	4.68578	−	6.93080i	0.223895	−	0.331166i
$439$			11.2122i			0.535128i	0.963540	+	0.267564i	$0.0862186\pi$
$439$			11.2122i			0.535128i	−0.963540	+	0.267564i	$0.913781\pi$
$440$		0			0
$441$	−0.732051	+	2.90931i	−0.0348596	+	0.138539i
$442$	−3.34956	+	1.08834i	−0.159322	+	0.0517669i
$443$	18.1068	−	24.9219i	0.860280	−	1.18407i	−0.121222	−	0.992625i	$-0.538681\pi$
$443$	18.1068	−	24.9219i	0.860280	−	1.18407i	0.981503	−	0.191449i	$-0.0613186\pi$
$444$	−0.454029	+	1.57696i	−0.0215472	+	0.0748390i
$445$	−11.1630	+	34.3563i	−0.529179	+	1.62864i
$446$	0.431959	−	1.32943i	0.0204538	−	0.0629504i
$447$	7.16503	−	24.8860i	0.338894	−	1.17707i
$448$	11.0727	−	15.2403i	0.523137	−	0.720036i
$449$	34.6326	−	11.2528i	1.63441	−	0.531053i	0.659134	−	0.752026i	$-0.270923\pi$
$449$	34.6326	−	11.2528i	1.63441	−	0.531053i	0.975280	+	0.220972i	$0.0709231\pi$
$450$	3.81899	−	15.1774i	0.180029	−	0.715470i
$451$		0			0
$452$		−	2.75640i		−	0.129650i
$453$	−7.76547	+	11.4860i	−0.364854	+	0.539660i
$454$	−15.0384	−	10.9260i	−0.705786	−	0.512784i
$455$	−4.33652	−	5.96870i	−0.203299	−	0.279817i
$456$	−10.4033	+	3.77376i	−0.487178	+	0.176723i
$457$	−8.10533	−	2.63358i	−0.379151	−	0.123194i	0.113240	−	0.993568i	$-0.463877\pi$
$457$	−8.10533	−	2.63358i	−0.379151	−	0.123194i	−0.492391	+	0.870374i	$0.663877\pi$
$458$	15.1857	−	11.0331i	0.709582	−	0.515541i
$459$	−2.86092	+	13.2484i	−0.133536	+	0.618380i
$460$		0			0
$461$	−13.8491			−0.645019			−0.322509	−	0.946566i	$-0.604526\pi$
$461$	−13.8491			−0.645019			−0.322509	+	0.946566i	$0.604526\pi$
$462$		0			0
$463$	−4.73205			−0.219917			−0.109959	−	0.993936i	$-0.535072\pi$
$463$	−4.73205			−0.219917			−0.109959	+	0.993936i	$0.535072\pi$
$464$	11.9081	+	36.6494i	0.552820	+	1.70141i
$465$	1.73766	+	51.3498i	0.0805820	+	2.38129i
$466$	10.5172	−	7.64121i	0.487201	−	0.353972i
$467$	−4.59379	−	1.49261i	−0.212575	−	0.0690699i	0.200793	−	0.979634i	$-0.435648\pi$
$467$	−4.59379	−	1.49261i	−0.212575	−	0.0690699i	−0.413369	+	0.910564i	$0.635648\pi$
$468$	0.383237	−	0.610370i	0.0177151	−	0.0282144i
$469$	−3.32502	−	4.57649i	−0.153535	−	0.211323i
$470$	7.54912	+	5.48476i	0.348215	+	0.252993i
$471$	6.50851	+	4.40028i	0.299896	+	0.202754i
$472$			1.48854i			0.0685157i
$473$		0			0
$474$	−11.7846	−	15.1172i	−0.541285	−	0.694358i
$475$	8.06998	−	2.62210i	0.370276	−	0.120310i
$476$	−1.16197	+	1.59931i	−0.0532586	+	0.0733042i
$477$	−18.3691	+	7.37550i	−0.841065	+	0.337701i
$478$	−4.34248	+	13.3648i	−0.198620	+	0.611291i
$479$	0.340675	−	1.04849i	0.0155658	−	0.0479067i	−0.942972	−	0.332872i	$-0.891982\pi$
$479$	0.340675	−	1.04849i	0.0155658	−	0.0479067i	0.958538	+	0.284966i	$0.0919822\pi$
$480$	−7.29247	−	2.09961i	−0.332854	−	0.0958335i
$481$	−1.86340	+	2.56475i	−0.0849636	+	0.116942i
$482$	29.6947	−	9.64840i	1.35256	−	0.439473i
$483$		0			0
$484$		0			0
$485$		−	16.6763i		−	0.757233i
$486$	−10.9091	−	20.7871i	−0.494848	−	0.942921i
$487$	23.6046	+	17.1498i	1.06963	+	0.777130i	0.975845	−	0.218463i	$-0.0701043\pi$
$487$	23.6046	+	17.1498i	1.06963	+	0.777130i	0.0937822	+	0.995593i	$0.470104\pi$
$488$	−15.6031	−	21.4758i	−0.706320	−	0.972166i
$489$	−4.95682	−	13.6646i	−0.224155	−	0.617936i
$490$	−4.16690	−	1.35391i	−0.188242	−	0.0611634i
$491$	−6.41824	+	4.66312i	−0.289651	+	0.210444i	−0.723116	−	0.690727i	$-0.757291\pi$
$491$	−6.41824	+	4.66312i	−0.289651	+	0.210444i	0.433465	+	0.901170i	$0.357291\pi$
$492$	−2.09557	+	0.0709133i	−0.0944757	+	0.00319702i
$493$	6.95803	+	21.4146i	0.313374	+	0.964466i
$494$	3.30734			0.148804
$495$		0			0
$496$	45.5167			2.04376
$497$	−8.30985	−	25.5751i	−0.372748	−	1.14720i
$498$	16.4739	−	0.557471i	0.738214	−	0.0249809i
$499$	−29.2833	+	21.2756i	−1.31090	+	0.952425i	−0.310903	+	0.950442i	$0.600631\pi$
$499$	−29.2833	+	21.2756i	−1.31090	+	0.952425i	−0.999998	+	0.00198330i	$0.999369\pi$
$500$	−1.13871	−	0.369988i	−0.0509245	−	0.0165464i
$501$	7.29035	+	20.0976i	0.325709	+	0.897893i
$502$	−17.8421	−	24.5576i	−0.796333	−	1.09606i
$503$	6.65722	+	4.83676i	0.296831	+	0.215660i	0.726225	−	0.687457i	$-0.241273\pi$
$503$	6.65722	+	4.83676i	0.296831	+	0.215660i	−0.429394	+	0.903117i	$0.641273\pi$
$504$	1.49624	+	22.0825i	0.0666479	+	0.983634i
$505$			44.6728i			1.98791i
$506$		0			0
$507$	−16.6603	+	12.9875i	−0.739908	+	0.576794i
$508$	0.0706915	−	0.0229691i	0.00313643	−	0.00101909i
$509$	4.33652	−	5.96870i	0.192213	−	0.264558i	−0.702023	−	0.712154i	$-0.747720\pi$
$509$	4.33652	−	5.96870i	0.192213	−	0.264558i	0.894236	+	0.447596i	$0.147720\pi$
$510$	−19.0218	−	5.47665i	−0.842300	−	0.242510i
$511$	2.80334	−	8.62779i	0.124012	−	0.381671i
$512$	5.11908	−	15.7549i	0.226233	−	0.696275i
$513$	6.39964	−	11.0020i	0.282551	−	0.485751i
$514$	−3.45023	+	4.74884i	−0.152183	+	0.209462i
$515$	25.6437	−	8.33214i	1.13000	−	0.367158i
$516$	−1.21057	−	1.55291i	−0.0532924	−	0.0683632i
$517$		0			0
$518$			15.0613i			0.661754i
$519$	−2.73991	−	1.85240i	−0.120269	−	0.0813114i
$520$	−5.50443	−	3.99920i	−0.241385	−	0.175377i
$521$	−3.42010	−	4.70737i	−0.149837	−	0.206234i	0.727500	−	0.686108i	$-0.240682\pi$
$521$	−3.42010	−	4.70737i	−0.149837	−	0.206234i	−0.877337	+	0.479874i	$0.840682\pi$
$522$	−33.0292	−	20.7382i	−1.44565	−	0.907688i
$523$	26.2499	+	8.52909i	1.14783	+	0.372951i	0.820324	−	0.571899i	$-0.193793\pi$
$523$	26.2499	+	8.52909i	1.14783	+	0.372951i	0.327502	+	0.944850i	$0.393793\pi$
$524$	3.80658	−	2.76564i	0.166291	−	0.120818i
$525$	−0.573949	−	16.9609i	−0.0250492	−	0.740232i
$526$	−14.1542	−	43.5620i	−0.617151	−	1.89940i
$527$	26.5958			1.15853
$528$		0			0
$529$	23.0000			1.00000
$530$	−8.93333	−	27.4940i	−0.388039	−	1.19426i
$531$	−1.09762	−	1.31385i	−0.0476327	−	0.0570161i
$532$	1.50186	−	1.09117i	0.0651141	−	0.0473081i
$533$	−3.85240	−	1.25172i	−0.166866	−	0.0542180i
$534$	−30.4469	+	11.0445i	−1.31757	+	0.477944i
$535$	−14.0716	−	19.3679i	−0.608370	−	0.837349i
$536$	−4.22051	−	3.06638i	−0.182298	−	0.132447i
$537$	−6.75186	+	9.98677i	−0.291364	+	0.430961i
$538$			12.2846i			0.529627i
$539$		0			0
$540$	3.70577	−	1.63555i	0.159471	−	0.0703829i
$541$	0.360391	−	0.117098i	0.0154944	−	0.00503444i	−0.301260	−	0.953542i	$-0.597407\pi$
$541$	0.360391	−	0.117098i	0.0154944	−	0.00503444i	0.316754	+	0.948508i	$0.397407\pi$
$542$	0.580983	−	0.799654i	0.0249554	−	0.0343481i
$543$	−7.11942	+	24.7276i	−0.305524	+	1.06116i
$544$	−1.21388	+	3.73594i	−0.0520447	+	0.160177i
$545$	5.80043	−	17.8519i	0.248463	−	0.764691i
$546$	1.83012	−	6.35647i	0.0783219	−	0.272032i
$547$	0.890935	−	1.22627i	0.0380936	−	0.0524314i	−0.789545	−	0.613692i	$-0.789684\pi$
$547$	0.890935	−	1.22627i	0.0380936	−	0.0524314i	0.827639	+	0.561261i	$0.189684\pi$
$548$	−4.73922	+	1.53987i	−0.202449	+	0.0657798i
$549$	29.6078	+	7.45001i	1.26363	+	0.317958i
$550$		0			0
$551$		−	21.1447i		−	0.900796i
$552$		0			0
$553$	−16.8151	−	12.2169i	−0.715051	−	0.519515i
$554$	20.7333	+	28.5369i	0.880872	+	1.21242i
$555$	−16.7497	+	6.07592i	−0.710985	+	0.257908i
$556$	4.92303	+	1.59959i	0.208783	+	0.0678377i
$557$	26.3899	−	19.1734i	1.11818	−	0.812403i	0.134245	−	0.990948i	$-0.457139\pi$
$557$	26.3899	−	19.1734i	1.11818	−	0.812403i	0.983932	+	0.178546i	$0.0571392\pi$
$558$	−35.3520	+	29.5339i	−1.49657	+	1.25027i
$559$	−1.17545	−	3.61767i	−0.0497164	−	0.153011i
$560$	−36.7341			−1.55230
$561$		0			0
$562$	40.0526			1.68952
$563$	−12.4648	−	38.3626i	−0.525328	−	1.61679i	−0.763667	−	0.645610i	$-0.776603\pi$
$563$	−12.4648	−	38.3626i	−0.525328	−	1.61679i	0.238340	−	0.971182i	$-0.423397\pi$
$564$	0.0334289	+	0.987862i	0.00140761	+	0.0415965i
$565$	24.2124	−	17.5914i	1.01862	−	0.740074i
$566$	−30.7802	−	10.0011i	−1.29379	−	0.420377i
$567$	−17.6039	−	18.3876i	−0.739292	−	0.772207i
$568$	−14.5768	−	20.0632i	−0.611628	−	0.841834i
$569$	−13.5534	−	9.84714i	−0.568189	−	0.412814i	0.266258	−	0.963902i	$-0.414213\pi$
$569$	−13.5534	−	9.84714i	−0.568189	−	0.412814i	−0.834447	+	0.551088i	$0.814213\pi$
$570$	15.3993	+	10.4112i	0.645006	+	0.436076i
$571$			21.6665i			0.906714i	0.891329	+	0.453357i	$0.149774\pi$
$571$			21.6665i			0.906714i	−0.891329	+	0.453357i	$0.850226\pi$
$572$		0			0
$573$	−6.19615	−	7.94839i	−0.258848	−	0.332049i
$574$	−18.3023	+	5.94678i	−0.763924	+	0.248214i
$575$		0			0
$576$	7.44490	+	18.5420i	0.310204	+	0.772582i
$577$	4.69587	−	14.4524i	0.195492	−	0.601661i	−0.804479	−	0.593981i	$-0.797555\pi$
$577$	4.69587	−	14.4524i	0.195492	−	0.601661i	0.999971	−	0.00768006i	$-0.00244466\pi$
$578$	4.74499	−	14.6036i	0.197366	−	0.607429i
$579$	−40.0777	−	11.5389i	−1.66557	−	0.479542i
$580$	3.95538	−	5.44411i	0.164238	−	0.226055i
$581$	16.9988	−	5.52326i	0.705231	−	0.229143i
$582$	11.7919	−	9.19239i	0.488792	−	0.381037i
$583$		0			0
$584$		−	8.36615i		−	0.346194i
$585$	7.80735	−	0.529001i	0.322794	−	0.0218715i
$586$	32.2715	+	23.4466i	1.33312	+	0.968570i
$587$	−14.9323	−	20.5525i	−0.616320	−	0.848292i	0.380758	−	0.924675i	$-0.375663\pi$
$587$	−14.9323	−	20.5525i	−0.616320	−	0.848292i	−0.997079	+	0.0763827i	$0.975663\pi$
$588$	−0.158261	−	0.436284i	−0.00652658	−	0.0179920i
$589$	−23.7530	−	7.71781i	−0.978725	−	0.318007i
$590$	2.02278	−	1.46964i	0.0832766	−	0.0605040i
$591$	6.42373	−	0.217377i	0.264237	−	0.00894168i
$592$	4.87771	+	15.0121i	0.200473	+	0.616992i
$593$	−16.5657			−0.680271			−0.340136	−	0.940376i	$-0.610473\pi$
$593$	−16.5657			−0.680271			−0.340136	+	0.940376i	$0.610473\pi$
$594$		0			0
$595$	−21.4641			−0.879942
$596$	1.23800	+	3.81019i	0.0507106	+	0.156071i
$597$	−16.7225	+	0.565882i	−0.684406	+	0.0231600i
$598$		0			0
$599$	22.6781	+	7.36856i	0.926602	+	0.301071i	0.733172	−	0.680043i	$-0.238039\pi$
$599$	22.6781	+	7.36856i	0.926602	+	0.301071i	0.193430	+	0.981114i	$0.438039\pi$
$600$	−5.33691	−	14.7124i	−0.217878	−	0.600633i
$601$	22.9708	+	31.6167i	0.937000	+	1.28967i	0.957065	+	0.289872i	$0.0936127\pi$
$601$	22.9708	+	31.6167i	0.937000	+	1.28967i	−0.0200650	+	0.999799i	$0.506387\pi$
$602$	−14.6203	−	10.6223i	−0.595878	−	0.432931i
$603$	5.98627	−	0.405611i	0.243780	−	0.0165178i
$604$		−	2.14488i		−	0.0872740i
$605$		0			0
$606$	−31.5885	+	24.6247i	−1.28319	+	1.00031i
$607$	14.2673	−	4.63573i	0.579093	−	0.188159i	−0.00480144	−	0.999988i	$-0.501528\pi$
$607$	14.2673	−	4.63573i	0.579093	−	0.188159i	0.583894	+	0.811830i	$0.301528\pi$
$608$	2.16826	−	2.98435i	0.0879345	−	0.121031i
$609$	−40.6386	−	11.7005i	−1.64676	−	0.474126i
$610$	−13.7786	+	42.4061i	−0.557879	+	1.71697i
$611$	−0.590066	+	1.81604i	−0.0238715	+	0.0734690i
$612$	−0.781264	−	1.94578i	−0.0315807	−	0.0786537i
$613$	13.3816	−	18.4182i	0.540477	−	0.743903i	−0.448205	−	0.893931i	$-0.647936\pi$
$613$	13.3816	−	18.4182i	0.540477	−	0.743903i	0.988682	+	0.150028i	$0.0479364\pi$
$614$	−32.5149	+	10.5647i	−1.31219	+	0.426358i
$615$	−13.9968	−	17.9551i	−0.564407	−	0.724018i
$616$		0			0
$617$			32.0024i			1.28837i	0.764870	+	0.644185i	$0.222803\pi$
$617$			32.0024i			1.28837i	−0.764870	+	0.644185i	$0.777197\pi$
$618$	20.0271	+	13.5400i	0.805609	+	0.544657i
$619$	22.5363	+	16.3736i	0.905811	+	0.658110i	0.939952	−	0.341307i	$-0.110870\pi$
$619$	22.5363	+	16.3736i	0.905811	+	0.658110i	−0.0341412	+	0.999417i	$0.510870\pi$
$620$	−4.67195	−	6.43038i	−0.187630	−	0.258250i
$621$		0			0
$622$	−31.1022	−	10.1057i	−1.24708	−	0.405202i
$623$	−28.4127	+	20.6430i	−1.13833	+	0.827045i
$624$	−0.234454	−	6.92840i	−0.00938569	−	0.277358i
$625$	−9.36955	−	28.8365i	−0.374782	−	1.15346i
$626$	−20.1684			−0.806092
$627$		0			0
$628$	−1.21539			−0.0484994
$629$	2.85010	+	8.77169i	0.113641	+	0.349750i
$630$	28.5307	−	23.8353i	1.13669	−	0.949621i
$631$	5.92242	−	4.30289i	0.235768	−	0.171295i	−0.463628	−	0.886030i	$-0.653453\pi$
$631$	5.92242	−	4.30289i	0.235768	−	0.171295i	0.699396	+	0.714735i	$0.253453\pi$
$632$	−18.2297	−	5.92320i	−0.725140	−	0.235612i
$633$	42.9684	−	15.5867i	1.70784	−	0.619516i
$634$	20.2325	+	27.8477i	0.803536	+	1.10597i
$635$	0.652915	+	0.474371i	0.0259101	+	0.0188248i
$636$	1.71511	−	2.53685i	0.0680087	−	0.100593i
$637$		−	0.896575i		−	0.0355236i
$638$		0			0
$639$	27.6603	+	6.95996i	1.09422	+	0.275332i
$640$	−36.0864	+	11.7252i	−1.42644	+	0.463479i
$641$	−23.7281	+	32.6589i	−0.937202	+	1.28995i	0.0197810	+	0.999804i	$0.493703\pi$
$641$	−23.7281	+	32.6589i	−0.937202	+	1.28995i	−0.956983	+	0.290144i	$0.906297\pi$
$642$	5.93859	−	20.6262i	0.234377	−	0.814052i
$643$	−4.38685	+	13.5013i	−0.173001	+	0.532441i	−0.999537	−	0.0304430i	$-0.990308\pi$
$643$	−4.38685	+	13.5013i	−0.173001	+	0.532441i	0.826536	+	0.562884i	$0.190308\pi$
$644$		0			0
$645$	5.91504	−	20.5444i	0.232904	−	0.808936i
$646$	5.65572	−	7.78444i	0.222522	−	0.306275i
$647$	−18.0843	+	5.87595i	−0.710968	+	0.231007i	−0.642103	−	0.766619i	$-0.721938\pi$
$647$	−18.0843	+	5.87595i	−0.710968	+	0.231007i	−0.0688650	+	0.997626i	$0.521938\pi$
$648$	−20.6801	−	11.1106i	−0.812390	−	0.436467i
$649$		0			0
$650$			4.67729i			0.183458i
$651$	−27.9768	+	41.3809i	−1.09650	+	1.62184i
$652$	1.81925	+	1.32176i	0.0712472	+	0.0517641i
$653$	−5.67824	−	7.81543i	−0.222207	−	0.305841i	0.683330	−	0.730110i	$-0.260531\pi$
$653$	−5.67824	−	7.81543i	−0.222207	−	0.305841i	−0.905536	+	0.424269i	$0.860531\pi$
$654$	15.8205	−	5.73886i	0.618631	−	0.224407i
$655$	48.5872	+	15.7869i	1.89846	+	0.616846i
$656$	−16.3166	+	11.8547i	−0.637056	+	0.462848i
$657$	6.16903	+	7.38429i	0.240677	+	0.288089i
$658$	2.80334	+	8.62779i	0.109286	+	0.336346i
$659$	17.5600			0.684041			0.342020	−	0.939693i	$-0.388889\pi$
$659$	17.5600			0.684041			0.342020	+	0.939693i	$0.388889\pi$
$660$		0			0
$661$	−7.19615			−0.279898			−0.139949	−	0.990159i	$-0.544694\pi$
$661$	−7.19615			−0.279898			−0.139949	+	0.990159i	$0.544694\pi$
$662$	−9.48998	−	29.2072i	−0.368839	−	1.13517i
$663$	−0.136994	−	4.04833i	−0.00532041	−	0.157224i
$664$	13.3353	−	9.68866i	0.517510	−	0.375993i
$665$	19.1698	+	6.22864i	0.743373	+	0.241536i
$666$	−13.5292	−	8.49464i	−0.524244	−	0.329161i
$667$		0			0
$668$	−2.67570	−	1.94401i	−0.103526	−	0.0752159i
$669$	1.33187	+	0.900451i	0.0514930	+	0.0348134i
$670$			8.76268i			0.338532i
$671$		0			0
$672$	−4.53590	−	5.81863i	−0.174976	−	0.224458i
$673$	29.9503	−	9.73145i	1.15450	−	0.375120i	0.331664	−	0.943398i	$-0.392390\pi$
$673$	29.9503	−	9.73145i	1.15450	−	0.375120i	0.822837	+	0.568278i	$0.192390\pi$
$674$	16.3069	−	22.4445i	0.628117	−	0.864529i
$675$	15.5592	+	9.05045i	0.598875	+	0.348352i
$676$	1.00985	−	3.10800i	0.0388405	−	0.119539i
$677$	−7.07184	+	21.7649i	−0.271793	+	0.836493i	0.718257	+	0.695778i	$0.244940\pi$
$677$	−7.07184	+	21.7649i	−0.271793	+	0.836493i	−0.990050	+	0.140715i	$0.955060\pi$
$678$	25.7854	+	7.42400i	0.990283	+	0.285117i
$679$	9.52958	−	13.1163i	0.365712	−	0.503359i
$680$	−18.8257	+	6.11684i	−0.721933	+	0.234570i
$681$	16.8611	−	13.1440i	0.646118	−	0.503680i
$682$		0			0
$683$		−	3.84177i		−	0.147001i	−0.997295	−	0.0735006i	$-0.976583\pi$
$683$		−	3.84177i		−	0.147001i	0.997295	−	0.0735006i	$-0.0234171\pi$
$684$	0.133109	+	1.96451i	0.00508955	+	0.0751150i
$685$	−43.7720	−	31.8022i	−1.67244	−	1.21510i
$686$	15.0221	+	20.6762i	0.573548	+	0.789421i
$687$	7.36178	+	20.2945i	0.280869	+	0.774283i
$688$	−18.0126	−	5.85265i	−0.686724	−	0.223130i
$689$	4.78595	−	3.47720i	0.182330	−	0.132471i
$690$		0			0
$691$	−8.83432	−	27.1892i	−0.336073	−	1.03433i	−0.966191	−	0.257828i	$-0.916993\pi$
$691$	−8.83432	−	27.1892i	−0.336073	−	1.03433i	0.630118	−	0.776500i	$-0.283007\pi$
$692$	0.511648			0.0194499
$693$		0			0
$694$	−16.9282			−0.642586
$695$	17.3679	+	53.4528i	0.658801	+	2.02758i
$696$	−38.9777	+	1.31899i	−1.47745	+	0.0499962i
$697$	−9.53395	+	6.92682i	−0.361124	+	0.262372i
$698$	25.5905	+	8.31484i	0.968613	+	0.314721i
$699$	5.09857	+	14.0554i	0.192846	+	0.531624i
$700$	1.54315	+	2.12396i	0.0583254	+	0.0802780i
$701$	32.0678	+	23.2986i	1.21118	+	0.879976i	0.995338	−	0.0964521i	$-0.0307495\pi$
$701$	32.0678	+	23.2986i	1.21118	+	0.879976i	0.215845	+	0.976428i	$0.430749\pi$
$702$	4.67766	+	5.22904i	0.176547	+	0.197357i
$703$		−	8.66115i		−	0.326661i
$704$		0			0
$705$	−8.46410	+	6.59817i	−0.318777	+	0.248502i
$706$	17.7841	−	5.77841i	0.669315	−	0.217474i
$707$	−25.5280	+	35.1363i	−0.960079	+	1.32144i
$708$	0.254510	+	0.0732770i	0.00956505	+	0.00275392i
$709$	1.44604	−	4.45046i	0.0543073	−	0.167141i	−0.920224	−	0.391392i	$-0.871994\pi$
$709$	1.44604	−	4.45046i	0.0543073	−	0.167141i	0.974531	+	0.224251i	$0.0719937\pi$
$710$	−12.8723	+	39.6168i	−0.483088	+	1.48679i
$711$	20.4579	−	8.21419i	0.767232	−	0.308056i
$712$	−19.0373	+	26.2026i	−0.713453	+	0.981984i
$713$		0			0
$714$	−11.8315	−	15.1774i	−0.442784	−	0.568000i
$715$		0			0
$716$		−	1.86492i		−	0.0696952i
$717$	−13.3893	−	9.05223i	−0.500031	−	0.338062i
$718$	−11.7287	−	8.52137i	−0.437710	−	0.318015i
$719$	25.7735	+	35.4742i	0.961191	+	1.32297i	0.946373	+	0.323076i	$0.104717\pi$
$719$	25.7735	+	35.4742i	0.961191	+	1.32297i	0.0148179	+	0.999890i	$0.495283\pi$
$720$	20.7182	−	32.9973i	0.772123	−	1.22974i
$721$	24.9307	+	8.10048i	0.928469	+	0.301678i
$722$	15.8386	−	11.5074i	0.589453	−	0.428263i
$723$	1.21449	+	35.8896i	0.0451674	+	1.33475i
$724$	−1.23012	−	3.78593i	−0.0457172	−	0.140703i
$725$	29.9032			1.11058
$726$		0			0
$727$	−15.0718			−0.558982			−0.279491	−	0.960148i	$-0.590166\pi$
$727$	−15.0718			−0.558982			−0.279491	+	0.960148i	$0.590166\pi$
$728$	−2.04405	−	6.29094i	−0.0757575	−	0.233158i
$729$	26.4458	−	5.44238i	0.979474	−	0.201570i
$730$	−11.3688	+	8.25989i	−0.420777	+	0.305712i
$731$	−10.5249	−	3.41976i	−0.389279	−	0.126484i
$732$	−4.44002	+	1.61061i	−0.164108	+	0.0595297i
$733$	−3.91169	−	5.38398i	−0.144482	−	0.198862i	0.730643	−	0.682760i	$-0.239221\pi$
$733$	−3.91169	−	5.38398i	−0.144482	−	0.198862i	−0.875124	+	0.483898i	$0.839221\pi$
$734$	4.69848	+	3.41364i	0.173424	+	0.126000i
$735$	2.82233	−	4.17454i	0.104103	−	0.153980i
$736$		0			0
$737$		0			0
$738$	4.98076	−	19.7945i	0.183344	−	0.728646i
$739$	2.78656	−	0.905408i	0.102505	−	0.0333060i	−0.257315	−	0.966327i	$-0.582838\pi$
$739$	2.78656	−	0.905408i	0.102505	−	0.0333060i	0.359821	+	0.933022i	$0.382838\pi$
$740$	1.62017	−	2.22998i	0.0595587	−	0.0819756i
$741$	−1.05243	+	3.65536i	−0.0386620	+	0.134283i
$742$	8.68496	−	26.7296i	0.318835	−	0.981273i
$743$	−7.37911	+	22.7106i	−0.270713	+	0.833169i	0.719609	+	0.694380i	$0.244321\pi$
$743$	−7.37911	+	22.7106i	−0.270713	+	0.833169i	−0.990322	+	0.138790i	$0.955679\pi$
$744$	−12.7451	+	44.2671i	−0.467259	+	1.62291i
$745$	−25.5680	+	35.1913i	−0.936738	+	1.28931i
$746$	−34.8313	+	11.3174i	−1.27526	+	0.414358i
$747$	−4.62604	+	18.3848i	−0.169258	+	0.672664i
$748$		0			0
$749$		−	23.2745i		−	0.850432i
$750$	6.52809	−	9.65579i	0.238372	−	0.352580i
$751$	−23.5621	−	17.1189i	−0.859793	−	0.624676i	0.0680355	−	0.997683i	$-0.478327\pi$
$751$	−23.5621	−	17.1189i	−0.859793	−	0.624676i	−0.927829	+	0.373007i	$0.878327\pi$
$752$	5.58836	+	7.69172i	0.203787	+	0.280488i
$753$	32.8192	−	11.9051i	1.19600	−	0.433846i
$754$	11.0850	+	3.60174i	0.403693	+	0.131168i
$755$	18.8408	−	13.6886i	0.685686	−	0.498180i
$756$	3.84930	+	0.831238i	0.139998	+	0.0302318i
$757$	3.29420	+	10.1385i	0.119730	+	0.368490i	0.992904	−	0.118918i	$-0.0379425\pi$
$757$	3.29420	+	10.1385i	0.119730	+	0.368490i	−0.873174	+	0.487408i	$0.837942\pi$
$758$	−0.886200			−0.0321882
$759$		0			0
$760$	18.5885			0.674274
$761$	12.0662	+	37.1360i	0.437400	+	1.34618i	0.890607	+	0.454774i	$0.150280\pi$
$761$	12.0662	+	37.1360i	0.437400	+	1.34618i	−0.453206	+	0.891406i	$0.649720\pi$
$762$	0.0244716	+	0.723165i	0.000886513	+	0.0261975i
$763$	14.7635	−	10.7263i	0.534475	−	0.388319i
$764$	1.48279	+	0.481787i	0.0536454	+	0.0174304i
$765$	12.1059	−	19.2807i	0.437689	−	0.697094i
$766$	24.8779	+	34.2415i	0.898876	+	1.23720i
$767$	0.413932	+	0.300739i	0.0149462	+	0.0108591i
$768$	−9.06922	−	6.13153i	−0.327257	−	0.221252i
$769$		−	29.0793i		−	1.04863i	−0.851525	−	0.524313i	$-0.824322\pi$
$769$		−	29.0793i		−	1.04863i	0.851525	−	0.524313i	$-0.175678\pi$
$770$		0			0
$771$	−4.15064	−	5.32441i	−0.149481	−	0.191754i
$772$	6.13612	−	1.99374i	0.220844	−	0.0717564i
$773$	18.9333	−	26.0595i	0.680985	−	0.937295i	−0.318960	−	0.947768i	$-0.603334\pi$
$773$	18.9333	−	26.0595i	0.680985	−	0.937295i	0.999945	+	0.0104728i	$0.00333365\pi$
$774$	17.7876	−	7.14202i	0.639363	−	0.256714i
$775$	10.9146	−	33.5918i	0.392065	−	1.20665i
$776$	4.62029	−	14.2198i	0.165859	−	0.510461i
$777$	−16.6461	−	4.79265i	−0.597175	−	0.171935i
$778$	13.8867	−	19.1135i	0.497864	−	0.685251i
$779$	10.5249	−	3.41976i	0.377095	−	0.122526i
$780$	−0.954747	+	0.744272i	−0.0341854	+	0.0266492i
$781$		0			0
$782$		0			0
$783$	33.4306	−	29.9055i	1.19471	−	1.06874i
$784$	−3.61153	−	2.62393i	−0.128983	−	0.0937119i
$785$	−7.75662	−	10.6761i	−0.276846	−	0.381045i
$786$	15.6193	+	43.0584i	0.557124	+	1.53584i
$787$	29.3261	+	9.52863i	1.04536	+	0.339659i	0.780847	−	0.624722i	$-0.214788\pi$
$787$	29.3261	+	9.52863i	1.04536	+	0.339659i	0.264516	+	0.964381i	$0.414788\pi$
$788$	−0.804425	+	0.584449i	−0.0286564	+	0.0208201i
$789$	52.6499	−	1.78165i	1.87439	−	0.0634285i
$790$	9.94916	+	30.6204i	0.353975	+	1.08942i
$791$	29.0961			1.03454
$792$		0			0
$793$	−9.12436			−0.324015
$794$	5.02779	+	15.4740i	0.178430	+	0.549150i
$795$	33.2297	−	1.12448i	1.17854	−	0.0398812i
$796$	2.09411	−	1.52146i	0.0742236	−	0.0539266i
$797$	−23.2208	−	7.54491i	−0.822525	−	0.267254i	−0.132631	−	0.991165i	$-0.542343\pi$
$797$	−23.2208	−	7.54491i	−0.822525	−	0.267254i	−0.689893	+	0.723911i	$0.742343\pi$
$798$	6.16253	+	16.9885i	0.218151	+	0.601385i
$799$	3.26533	+	4.49435i	0.115519	+	0.158999i
$800$	4.22051	+	3.06638i	0.149218	+	0.108413i
$801$	−2.51819	−	37.1652i	−0.0889760	−	1.31317i
$802$			4.38134i			0.154711i
$803$		0			0
$804$	−0.732051	+	0.570669i	−0.0258174	+	0.0201259i
$805$		0			0
$806$	8.09205	−	11.1378i	0.285030	−	0.392311i
$807$	−13.5773	−	3.90909i	−0.477942	−	0.137607i
$808$	−12.3769	+	38.0922i	−0.435419	+	1.34008i
$809$	2.01959	−	6.21566i	0.0710050	−	0.218531i	−0.909256	−	0.416236i	$-0.863349\pi$
$809$	2.01959	−	6.21566i	0.0710050	−	0.218531i	0.980262	+	0.197705i	$0.0633489\pi$
$810$	5.31916	+	39.0717i	0.186896	+	1.37284i
$811$	1.98861	−	2.73709i	0.0698296	−	0.0961122i	−0.772674	−	0.634803i	$-0.781081\pi$
$811$	1.98861	−	2.73709i	0.0698296	−	0.0961122i	0.842503	+	0.538691i	$0.181081\pi$
$812$	6.22201	−	2.02165i	0.218350	−	0.0709461i
$813$	0.698924	+	0.896575i	0.0245123	+	0.0314443i
$814$		0			0
$815$			24.4158i			0.855250i
$816$	−16.7082	−	11.2961i	−0.584904	−	0.395442i
$817$	8.40755	+	6.10844i	0.294143	+	0.213707i
$818$	−3.11757	−	4.29097i	−0.109003	−	0.150030i
$819$	6.44297	+	4.04539i	0.225136	+	0.141357i
$820$	3.34956	+	1.08834i	0.116972	+	0.0380064i
$821$	−18.4269	+	13.3879i	−0.643102	+	0.467241i	−0.860914	−	0.508750i	$-0.830108\pi$
$821$	−18.4269	+	13.3879i	−0.643102	+	0.467241i	0.217813	+	0.975991i	$0.430108\pi$
$822$	−1.64060	−	48.4816i	−0.0572224	−	1.69099i
$823$	17.6524	+	54.3285i	0.615324	+	1.89377i	0.396630	+	0.917979i	$0.370180\pi$
$823$	17.6524	+	54.3285i	0.615324	+	1.89377i	0.218694	+	0.975793i	$0.429820\pi$
$824$	24.1747			0.842165
$825$		0			0
$826$	2.43078			0.0845777
$827$	9.24059	+	28.4396i	0.321327	+	0.988942i	0.973071	+	0.230504i	$0.0740374\pi$
$827$	9.24059	+	28.4396i	0.321327	+	0.988942i	−0.651745	+	0.758438i	$0.725963\pi$
$828$		0			0
$829$	9.37526	−	6.81152i	0.325616	−	0.236574i	−0.412952	−	0.910753i	$-0.635502\pi$
$829$	9.37526	−	6.81152i	0.325616	−	0.236574i	0.738568	+	0.674179i	$0.235502\pi$
$830$	−26.3318	−	8.55574i	−0.913992	−	0.296974i
$831$	−38.1372	+	13.8342i	−1.32297	+	0.479903i
$832$	−3.50991	−	4.83098i	−0.121684	−	0.167484i
$833$	−2.11025	−	1.53319i	−0.0731160	−	0.0531219i
$834$	−28.2233	+	41.7454i	−0.977292	+	1.44552i
$835$		−	35.9101i		−	1.24272i
$836$		0			0
$837$	−21.3923	−	48.4699i	−0.739426	−	1.67536i
$838$	−20.5353	+	6.67234i	−0.709382	+	0.230492i
$839$	−15.6031	+	21.4758i	−0.538679	+	0.741429i	−0.988422	−	0.151730i	$-0.951516\pi$
$839$	−15.6031	+	21.4758i	−0.538679	+	0.741429i	0.449743	+	0.893158i	$0.351516\pi$
$840$	10.2859	−	35.7257i	0.354898	−	1.23265i
$841$	14.0654	−	43.2889i	0.485015	−	1.49272i
$842$	4.09705	−	12.6094i	0.141194	−	0.434550i
$843$	−12.7451	+	44.2671i	−0.438966	+	1.52464i
$844$	−4.15627	+	5.72061i	−0.143065	+	0.196912i
$845$	33.7458	−	10.9647i	1.16089	−	0.377196i
$846$	−9.33123	−	2.34795i	−0.320814	−	0.0807243i
$847$		0			0
$848$		−	29.4549i		−	1.01149i
$849$	20.8480	−	30.8366i	0.715503	−	1.05831i
$850$	11.0089	+	7.99840i	0.377601	+	0.274343i
$851$		0			0
$852$	−4.14796	+	1.50466i	−0.142107	+	0.0515490i
$853$	−33.4930	−	10.8825i	−1.14678	−	0.372611i	−0.326850	−	0.945076i	$-0.605987\pi$
$853$	−33.4930	−	10.8825i	−1.14678	−	0.372611i	−0.819929	+	0.572465i	$0.805987\pi$
$854$	−35.0699	+	25.4798i	−1.20007	+	0.871900i
$855$	−16.4069	+	13.7068i	−0.561104	+	0.468761i
$856$	−6.63277	−	20.4136i	−0.226703	−	0.697722i
$857$	−32.4035			−1.10688			−0.553441	−	0.832889i	$-0.686685\pi$
$857$	−32.4035			−1.10688			−0.553441	+	0.832889i	$0.686685\pi$
$858$		0			0
$859$	−23.1244			−0.788993			−0.394496	−	0.918897i	$-0.629081\pi$
$859$	−23.1244			−0.788993			−0.394496	+	0.918897i	$0.629081\pi$
$860$	1.02202	+	3.14547i	0.0348508	+	0.107260i
$861$	−0.748549	−	22.1205i	−0.0255105	−	0.753865i
$862$	−9.66568	+	7.02253i	−0.329214	+	0.239188i
$863$	31.3230	+	10.1774i	1.06625	+	0.346444i	0.789024	−	0.614362i	$-0.210586\pi$
$863$	31.3230	+	10.1774i	1.06625	+	0.346444i	0.277221	+	0.960806i	$0.410586\pi$
$864$	7.78500	−	0.792746i	0.264851	−	0.0269698i
$865$	3.26533	+	4.49435i	0.111025	+	0.152812i
$866$	−30.5229	−	22.1762i	−1.03721	−	0.753578i
$867$	14.6303	+	9.89129i	0.496872	+	0.335926i
$868$		−	7.72741i		−	0.262285i
$869$		0			0
$870$	40.2750	+	51.6645i	1.36545	+	1.75159i
$871$	−1.70539	+	0.554114i	−0.0577849	+	0.0187754i
$872$	9.89198	−	13.6151i	0.334985	−	0.461067i
$873$	6.40734	+	15.9579i	0.216856	+	0.540092i
$874$		0			0
$875$	3.90553	−	12.0200i	0.132031	−	0.406350i
$876$	−1.43044	−	0.411843i	−0.0483299	−	0.0139149i
$877$	27.7196	−	38.1528i	0.936026	−	1.28833i	−0.0214362	−	0.999770i	$-0.506824\pi$
$877$	27.7196	−	38.1528i	0.936026	−	1.28833i	0.957462	−	0.288559i	$-0.0931761\pi$
$878$	16.0588	−	5.21782i	0.541958	−	0.176093i
$879$	−36.1829	+	28.2063i	−1.22042	+	0.951375i
$880$		0			0
$881$			32.0024i			1.07819i	0.842245	+	0.539095i	$0.181234\pi$
$881$			32.0024i			1.07819i	−0.842245	+	0.539095i	$0.818766\pi$
$882$	4.50758	−	0.305419i	0.151778	−	0.0102840i
$883$	3.66962	+	2.66613i	0.123493	+	0.0897226i	0.647817	−	0.761796i	$-0.275682\pi$
$883$	3.66962	+	2.66613i	0.123493	+	0.0897226i	−0.524325	+	0.851519i	$0.675682\pi$
$884$	0.368328	+	0.506961i	0.0123882	+	0.0170509i
$885$	0.980610	+	2.70328i	0.0329628	+	0.0908698i
$886$	−44.1211	−	14.3358i	−1.48228	−	0.481621i
$887$	6.17926	−	4.48949i	0.207479	−	0.150742i	−0.479193	−	0.877709i	$-0.659071\pi$
$887$	6.17926	−	4.48949i	0.207479	−	0.150742i	0.686672	+	0.726967i	$0.259071\pi$
$888$	−15.9657	+	0.540275i	−0.535775	+	0.0181304i
$889$	0.242458	+	0.746208i	0.00813177	+	0.0250270i
$890$	54.4022			1.82357
$891$		0			0
$892$	−0.248711			−0.00832747
$893$	−1.61209	−	4.96151i	−0.0539466	−	0.166031i
$894$	−38.9777	+	1.31899i	−1.30361	+	0.0441136i
$895$	16.3816	−	11.9019i	0.547575	−	0.397836i
$896$	−35.0832	−	11.3992i	−1.17205	−	0.380821i
$897$		0			0
$898$	−32.2340	−	44.3663i	−1.07566	−	1.48052i
$899$	−71.2067	−	51.7347i	−2.37488	−	1.72545i
$900$	−2.77824	+	0.188245i	−0.0926080	+	0.00627482i
$901$		−	17.2108i		−	0.573375i
$902$		0			0
$903$	16.3923	−	12.7786i	0.545502	−	0.425245i
$904$	25.5196	−	8.29182i	0.848769	−	0.275782i
$905$	25.4052	−	34.9673i	0.844498	−	1.16235i
$906$	20.0648	+	5.77695i	0.666609	+	0.191926i
$907$	10.0260	−	30.8569i	0.332908	−	1.02459i	−0.634835	−	0.772648i	$-0.718932\pi$
$907$	10.0260	−	30.8569i	0.332908	−	1.02459i	0.967743	−	0.251939i	$-0.0810681\pi$
$908$	−1.02202	+	3.14547i	−0.0339171	+	0.104386i
$909$	−17.1641	−	42.7482i	−0.569297	−	1.41787i
$910$	−6.53067	+	8.98869i	−0.216490	+	0.297972i
$911$	−23.0754	+	7.49766i	−0.764523	+	0.248408i	−0.665219	−	0.746649i	$-0.731662\pi$
$911$	−23.0754	+	7.49766i	−0.764523	+	0.248408i	−0.0993041	+	0.995057i	$0.531662\pi$
$912$	11.6442	+	14.9372i	0.385580	+	0.494619i
$913$		0			0
$914$			12.8346i			0.424529i
$915$	−42.4839	−	28.7225i	−1.40447	−	0.949537i
$916$	−2.70191	−	1.96305i	−0.0892737	−	0.0648611i
$917$	29.1936	+	40.1816i	0.964059	+	1.32691i
$918$	20.3065	−	2.06781i	0.670215	−	0.0682480i
$919$	4.82646	+	1.56821i	0.159210	+	0.0517306i	0.387538	−	0.921854i	$-0.373326\pi$
$919$	4.82646	+	1.56821i	0.159210	+	0.0517306i	−0.228327	+	0.973584i	$0.573326\pi$
$920$		0			0
$921$	−1.32983	−	39.2981i	−0.0438195	−	1.29492i
$922$	6.44498	+	19.8356i	0.212254	+	0.653251i
$923$	−8.52418			−0.280577
$924$		0			0
$925$	12.2487			0.402735
$926$	2.20216	+	6.77754i	0.0723674	+	0.222724i
$927$	−21.3375	+	17.8259i	−0.700817	+	0.585480i
$928$	10.5172	−	7.64121i	0.345245	−	0.250835i
$929$	−43.6748	−	14.1908i	−1.43292	−	0.465585i	−0.513239	−	0.858246i	$-0.671555\pi$
$929$	−43.6748	−	14.1908i	−1.43292	−	0.465585i	−0.919683	+	0.392661i	$0.871555\pi$
$930$	72.7378	−	26.3855i	2.38517	−	0.865214i
$931$	1.43977	+	1.98168i	0.0471867	+	0.0649469i
$932$	−1.87127	−	1.35956i	−0.0612955	−	0.0445338i
$933$	21.0661	−	31.1592i	0.689674	−	1.02011i
$934$			7.27414i			0.238017i
$935$		0			0
$936$	6.80385	+	1.71201i	0.222391	+	0.0559587i
$937$	12.4041	−	4.03035i	0.405226	−	0.131666i	−0.0993102	−	0.995057i	$-0.531664\pi$
$937$	12.4041	−	4.03035i	0.405226	−	0.131666i	0.504536	+	0.863391i	$0.331664\pi$
$938$	−5.00738	+	6.89206i	−0.163497	+	0.225034i
$939$	6.41780	−	22.2907i	0.209437	−	0.727428i
$940$	0.513047	−	1.57900i	0.0167337	−	0.0515012i
$941$	−12.4982	+	38.4655i	−0.407429	+	1.25394i	0.511421	+	0.859331i	$0.329119\pi$
$941$	−12.4982	+	38.4655i	−0.407429	+	1.25394i	−0.918850	+	0.394608i	$0.870881\pi$
$942$	3.27349	−	11.3697i	0.106656	−	0.370444i
$943$		0			0
$944$	2.42284	−	0.787228i	0.0788567	−	0.0256221i
$945$	17.2646	+	39.1175i	0.561618	+	1.27249i
$946$		0			0
$947$		−	10.4959i		−	0.341071i	−0.985351	−	0.170536i	$-0.945450\pi$
$947$		−	10.4959i		−	0.341071i	0.985351	−	0.170536i	$-0.0545498\pi$
$948$	−1.91014	+	2.82532i	−0.0620386	+	0.0917621i
$949$	−2.32645	−	1.69026i	−0.0755196	−	0.0548682i
$950$	−7.51107	−	10.3381i	−0.243691	−	0.335412i
$951$	−37.2161	+	13.5001i	−1.20682	+	0.437770i
$952$	−18.3023	−	5.94678i	−0.593181	−	0.192736i
$953$	−28.0222	+	20.3593i	−0.907728	+	0.659503i	−0.940439	−	0.339962i	$-0.889586\pi$
$953$	−28.0222	+	20.3593i	−0.907728	+	0.659503i	0.0327113	+	0.999465i	$0.489586\pi$
$954$	19.1121	+	22.8771i	0.618778	+	0.740673i
$955$	5.23110	+	16.0997i	0.169275	+	0.520973i
$956$	2.50029			0.0808653
$957$		0			0
$958$	−1.66025			−0.0536404
$959$	−16.2546	−	50.0264i	−0.524887	−	1.61544i
$960$	−1.13506	−	33.5423i	−0.0366339	−	1.08257i
$961$	−59.0271	+	42.8857i	−1.90410	+	1.38341i
$962$	4.54056	+	1.47532i	0.146394	+	0.0475662i
$963$	20.9069	+	13.1270i	0.673715	+	0.423010i
$964$	−3.26533	−	4.49435i	−0.105169	−	0.144753i
$965$	56.6739	+	41.1760i	1.82440	+	1.32550i
$966$		0			0
$967$			5.85993i			0.188443i	0.995551	+	0.0942213i	$0.0300361\pi$
$967$			5.85993i			0.188443i	−0.995551	+	0.0942213i	$0.969964\pi$
$968$		0			0
$969$	6.80385	+	8.72794i	0.218571	+	0.280382i
$970$	−23.8849	+	7.76067i	−0.766898	+	0.249180i
$971$	−10.2603	+	14.1221i	−0.329269	+	0.453200i	−0.941269	−	0.337658i	$-0.890365\pi$
$971$	−10.2603	+	14.1221i	−0.329269	+	0.453200i	0.612000	+	0.790858i	$0.290365\pi$
$972$	−2.91771	+	2.98891i	−0.0935856	+	0.0958694i
$973$	−16.8850	+	51.9667i	−0.541308	+	1.66598i
$974$	13.5781	−	41.7890i	0.435070	−	1.33901i
$975$	−5.16946	−	1.48836i	−0.165555	−	0.0476657i
$976$	−26.7035	+	36.7542i	−0.854758	+	1.17647i
$977$	−24.9023	+	8.09124i	−0.796695	+	0.258862i	−0.678952	−	0.734182i	$-0.737566\pi$
$977$	−24.9023	+	8.09124i	−0.796695	+	0.258862i	−0.117742	+	0.993044i	$0.537566\pi$
$978$	−17.2646	+	13.4586i	−0.552061	+	0.430358i
$979$		0			0
$980$			0.779548i			0.0249017i
$981$	1.30848	+	19.3114i	0.0417765	+	0.616566i
$982$	9.66568	+	7.02253i	0.308444	+	0.224098i
$983$	−34.8719	−	47.9970i	−1.11224	−	1.53087i	−0.818074	−	0.575114i	$-0.804958\pi$
$983$	−34.8719	−	47.9970i	−1.11224	−	1.53087i	−0.294167	−	0.955754i	$-0.595042\pi$
$984$	−6.96044	−	19.1881i	−0.221891	−	0.611694i
$985$	−10.2677	−	3.33617i	−0.327155	−	0.106299i
$986$	27.4333	−	19.9315i	0.873655	−	0.634747i
$987$	−10.4277	+	0.352870i	−0.331918	+	0.0112320i
$988$	−0.181843	−	0.559656i	−0.00578521	−	0.0178050i
$989$		0			0
$990$		0			0
$991$	−7.85641			−0.249567			−0.124783	−	0.992184i	$-0.539824\pi$
$991$	−7.85641			−0.249567			−0.124783	+	0.992184i	$0.539824\pi$
$992$	−4.74499	−	14.6036i	−0.150654	−	0.463664i
$993$	35.3003	−	1.19455i	1.12022	−	0.0379079i
$994$	−32.7631	+	23.8038i	−1.03918	+	0.755010i
$995$	26.7292	+	8.68483i	0.847371	+	0.275328i
$996$	−1.00010	−	2.75700i	−0.0316893	−	0.0873590i
$997$	16.8260	+	23.1590i	0.532884	+	0.733451i	0.987566	−	0.157202i	$-0.0502474\pi$
$997$	16.8260	+	23.1590i	0.532884	+	0.733451i	−0.454683	+	0.890653i	$0.650247\pi$
$998$	44.0998	+	32.0404i	1.39596	+	1.01422i
$999$	13.6936	−	12.2497i	0.433247	−	0.387563i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.f.i.215.4		32
3.2	odd	2	inner	363.2.f.i.215.5		32
11.2	odd	10	inner	363.2.f.i.233.5		32
11.3	even	5		363.2.d.e.362.4	yes	8
11.4	even	5	inner	363.2.f.i.239.5		32
11.5	even	5	inner	363.2.f.i.161.6		32
11.6	odd	10	inner	363.2.f.i.161.4		32
11.7	odd	10	inner	363.2.f.i.239.3		32
11.8	odd	10		363.2.d.e.362.6	yes	8
11.9	even	5	inner	363.2.f.i.233.3		32
11.10	odd	2	inner	363.2.f.i.215.6		32
33.2	even	10	inner	363.2.f.i.233.4		32
33.5	odd	10	inner	363.2.f.i.161.3		32
33.8	even	10		363.2.d.e.362.3	✓	8
33.14	odd	10		363.2.d.e.362.5	yes	8
33.17	even	10	inner	363.2.f.i.161.5		32
33.20	odd	10	inner	363.2.f.i.233.6		32
33.26	odd	10	inner	363.2.f.i.239.4		32
33.29	even	10	inner	363.2.f.i.239.6		32
33.32	even	2	inner	363.2.f.i.215.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.2.d.e.362.3	✓	8	33.8	even	10
363.2.d.e.362.4	yes	8	11.3	even	5
363.2.d.e.362.5	yes	8	33.14	odd	10
363.2.d.e.362.6	yes	8	11.8	odd	10
363.2.f.i.161.3		32	33.5	odd	10	inner
363.2.f.i.161.4		32	11.6	odd	10	inner
363.2.f.i.161.5		32	33.17	even	10	inner
363.2.f.i.161.6		32	11.5	even	5	inner
363.2.f.i.215.3		32	33.32	even	2	inner
363.2.f.i.215.4		32	1.1	even	1	trivial
363.2.f.i.215.5		32	3.2	odd	2	inner
363.2.f.i.215.6		32	11.10	odd	2	inner
363.2.f.i.233.3		32	11.9	even	5	inner
363.2.f.i.233.4		32	33.2	even	10	inner
363.2.f.i.233.5		32	11.2	odd	10	inner
363.2.f.i.233.6		32	33.20	odd	10	inner
363.2.f.i.239.3		32	11.7	odd	10	inner
363.2.f.i.239.4		32	33.26	odd	10	inner
363.2.f.i.239.5		32	11.4	even	5	inner
363.2.f.i.239.6		32	33.29	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)

\(f(q)\)	\(=\)	\(q+(-0.465371 - 1.43226i) q^{2} +(1.73106 - 0.0585784i) q^{3} +(-0.216775 + 0.157497i) q^{4} +(-2.76692 - 0.899027i) q^{5} +(-0.889484 - 2.45207i) q^{6} +(-1.66251 - 2.28825i) q^{7} +(-2.11025 - 1.53319i) q^{8} +(2.99314 - 0.202805i) q^{9} +O(q^{10})\)	\(q+(-0.465371 - 1.43226i) q^{2} +(1.73106 - 0.0585784i) q^{3} +(-0.216775 + 0.157497i) q^{4} +(-2.76692 - 0.899027i) q^{5} +(-0.889484 - 2.45207i) q^{6} +(-1.66251 - 2.28825i) q^{7} +(-2.11025 - 1.53319i) q^{8} +(2.99314 - 0.202805i) q^{9} +4.38134i q^{10} +(-0.366025 + 0.285334i) q^{12} +(-0.852694 + 0.277057i) q^{13} +(-2.50369 + 3.44603i) q^{14} +(-4.84237 - 1.39419i) q^{15} +(-1.37948 + 4.24561i) q^{16} +(-0.806046 + 2.48075i) q^{17} +(-1.68339 - 4.19258i) q^{18} +(1.43977 - 1.98168i) q^{19} +(0.741394 - 0.240894i) q^{20} +(-3.01194 - 3.86370i) q^{21} +(-3.74279 - 2.53043i) q^{24} +(2.80252 + 2.03615i) q^{25} +(0.793638 + 1.09235i) q^{26} +(5.16942 - 0.526402i) q^{27} +(0.720782 + 0.234196i) q^{28} +(6.98368 - 5.07394i) q^{29} +(0.256652 + 7.58436i) q^{30} +(-3.15078 - 9.69712i) q^{31} +1.50597 q^{32} +3.92820 q^{34} +(2.54283 + 7.82603i) q^{35} +(-0.616897 + 0.515372i) q^{36} +(2.86060 - 2.07835i) q^{37} +(-3.50832 - 1.13992i) q^{38} +(-1.45983 + 0.529552i) q^{39} +(4.46053 + 6.13939i) q^{40} +(3.65507 + 2.65556i) q^{41} +(-4.13217 + 6.11195i) q^{42} +4.24264i q^{43} +(-8.46410 - 2.12976i) q^{45} +(1.25184 - 1.72302i) q^{47} +(-2.13927 + 7.43022i) q^{48} +(-0.309017 + 0.951057i) q^{49} +(1.61209 - 4.96151i) q^{50} +(-1.24999 + 4.34155i) q^{51} +(0.141208 - 0.194356i) q^{52} +(-6.27524 + 2.03895i) q^{53} +(-3.15964 - 7.15900i) q^{54} +7.37772i q^{56} +(2.37625 - 3.51474i) q^{57} +(-10.5172 - 7.64121i) q^{58} +(-0.335431 - 0.461681i) q^{59} +(1.26929 - 0.460431i) q^{60} +(9.67880 + 3.14483i) q^{61} +(-12.4225 + 9.02551i) q^{62} +(-5.44018 - 6.51187i) q^{63} +(2.05813 + 6.33428i) q^{64} +2.60842 q^{65} +2.00000 q^{67} +(-0.215979 - 0.664716i) q^{68} +(10.0256 - 7.28401i) q^{70} +(9.04216 + 2.93797i) q^{71} +(-6.62722 - 4.16108i) q^{72} +(1.88524 + 2.59481i) q^{73} +(-4.30798 - 3.12993i) q^{74} +(4.97060 + 3.36053i) q^{75} +0.656339i q^{76} +(1.43782 + 1.84443i) q^{78} +(6.98881 - 2.27080i) q^{79} +(7.63384 - 10.5071i) q^{80} +(8.91774 - 1.21405i) q^{81} +(2.10250 - 6.47084i) q^{82} +(-1.95277 + 6.01000i) q^{83} +(1.26144 + 0.363185i) q^{84} +(4.46053 - 6.13939i) q^{85} +(6.07658 - 1.97440i) q^{86} +(11.7919 - 9.19239i) q^{87} -12.4168i q^{89} +(0.888560 + 13.1140i) q^{90} +(2.05158 + 1.49056i) q^{91} +(-6.02224 - 16.6017i) q^{93} +(-3.05038 - 0.991130i) q^{94} +(-5.76532 + 4.18875i) q^{95} +(2.60693 - 0.0882174i) q^{96} +(1.77130 + 5.45150i) q^{97} +1.50597 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 16 q^{4} + 8 q^{9}+O(q^{10}) \) 32 * q + 4 * q^3 - 16 * q^4 + 8 * q^9	\( 32 q + 4 q^{3} - 16 q^{4} + 8 q^{9} + 16 q^{12} - 4 q^{15} + 8 q^{16} + 4 q^{27} + 40 q^{31} - 96 q^{34} + 40 q^{36} + 56 q^{37} - 64 q^{42} - 160 q^{45} - 28 q^{48} + 8 q^{49} - 104 q^{58} + 28 q^{60} + 16 q^{64} + 64 q^{67} + 16 q^{70} - 24 q^{75} + 240 q^{78} + 8 q^{81} - 96 q^{82} + 48 q^{91} - 56 q^{93} - 32 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 - 16 * q^4 + 8 * q^9 + 16 * q^12 - 4 * q^15 + 8 * q^16 + 4 * q^27 + 40 * q^31 - 96 * q^34 + 40 * q^36 + 56 * q^37 - 64 * q^42 - 160 * q^45 - 28 * q^48 + 8 * q^49 - 104 * q^58 + 28 * q^60 + 16 * q^64 + 64 * q^67 + 16 * q^70 - 24 * q^75 + 240 * q^78 + 8 * q^81 - 96 * q^82 + 48 * q^91 - 56 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more