LMFDB - Embedded newform 363.3.h.m.251.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

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, 8]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("363.245");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (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:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.343361479062744140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 3 x^{14} - 8 x^{13} + 8 x^{12} + 7 x^{11} + 6 x^{10} + 56 x^{9} - 137 x^{8} + \cdots + 6561 $ x^16 - x^15 + 3x^14 - 8x^13 + 8x^12 + 7x^11 + 6x^10 + 56x^9 - 137x^8 + 168x^7 + 54x^6 + 189x^5 + 648x^4 - 1944x^3 + 2187x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			251.3
Root			$-0.897801 - 1.48120i$ of defining polynomial
Character	$\chi$	$=$	363.251
Dual form			363.3.h.m.269.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.753510 + 0.244830i) q^{2} +(1.60937 + 2.53179i) q^{3} +(-2.72823 - 1.98218i) q^{4} +(-2.40079 + 0.780063i) q^{5} +(0.592816 + 2.30175i) q^{6} +(3.83843 + 2.78878i) q^{7} +(-3.43323 - 4.72544i) q^{8} +(-3.81987 + 8.14914i) q^{9} +O(q^{10})$	\(q+(0.753510 + 0.244830i) q^{2} +(1.60937 + 2.53179i) q^{3} +(-2.72823 - 1.98218i) q^{4} +(-2.40079 + 0.780063i) q^{5} +(0.592816 + 2.30175i) q^{6} +(3.83843 + 2.78878i) q^{7} +(-3.43323 - 4.72544i) q^{8} +(-3.81987 + 8.14914i) q^{9} -2.00000 q^{10} +(0.627719 - 10.0974i) q^{12} +(-4.16837 + 12.8289i) q^{13} +(2.20952 + 3.04114i) q^{14} +(-5.83870 - 4.82287i) q^{15} +(2.73833 + 8.42770i) q^{16} +(-21.5549 + 7.00360i) q^{17} +(-4.87347 + 5.20524i) q^{18} +(-6.66119 + 4.83964i) q^{19} +(8.09613 + 2.63059i) q^{20} +(-0.883156 + 14.2063i) q^{21} -30.2372i q^{23} +(6.43846 - 16.2972i) q^{24} +(-15.0701 + 10.9491i) q^{25} +(-6.28181 + 8.64617i) q^{26} +(-26.7795 + 3.44386i) q^{27} +(-4.94427 - 15.2169i) q^{28} +(-31.5381 + 43.4085i) q^{29} +(-3.21873 - 5.06357i) q^{30} +(7.99161 - 24.5957i) q^{31} +30.3846i q^{32} -17.9565 q^{34} +(-11.3907 - 3.70106i) q^{35} +(26.5746 - 14.6611i) q^{36} +(34.4690 + 25.0432i) q^{37} +(-6.20416 + 2.01586i) q^{38} +(-39.1885 + 10.0930i) q^{39} +(11.9286 + 8.66664i) q^{40} +(-18.1520 - 24.9840i) q^{41} +(-4.14359 + 10.4883i) q^{42} +35.4891 q^{43} +(2.81386 - 22.5441i) q^{45} +(7.40297 - 22.7840i) q^{46} +(18.3899 + 25.3115i) q^{47} +(-16.9302 + 20.4961i) q^{48} +(-8.18559 - 25.1927i) q^{49} +(-14.0362 + 4.56063i) q^{50} +(-52.4213 - 43.3009i) q^{51} +(36.8015 - 26.7378i) q^{52} +(9.42707 + 3.06304i) q^{53} +(-21.0217 - 3.96143i) q^{54} -27.7128i q^{56} +(-22.9732 - 9.07595i) q^{57} +(-34.3920 + 24.9873i) q^{58} +(36.1628 - 49.7739i) q^{59} +(6.36955 + 24.7313i) q^{60} +(15.8976 + 48.9277i) q^{61} +(12.0435 - 16.5765i) q^{62} +(-37.3885 + 20.6271i) q^{63} +(3.51423 - 10.8157i) q^{64} -34.0511i q^{65} +34.3288 q^{67} +(72.6891 + 23.6181i) q^{68} +(76.5540 - 48.6627i) q^{69} +(-7.67686 - 5.57757i) q^{70} +(-13.7915 + 4.48112i) q^{71} +(51.6228 - 9.92732i) q^{72} +(71.3826 + 51.8625i) q^{73} +(19.8414 + 27.3093i) q^{74} +(-51.9742 - 20.5332i) q^{75} +27.7663 q^{76} +(-32.0000 - 1.98933i) q^{78} +(-28.9485 + 89.0943i) q^{79} +(-13.1483 - 18.0970i) q^{80} +(-51.8171 - 62.2574i) q^{81} +(-7.56083 - 23.2699i) q^{82} +(32.4890 - 10.5563i) q^{83} +(30.5688 - 37.0074i) q^{84} +(46.2854 - 33.6283i) q^{85} +(26.7414 + 8.68881i) q^{86} +(-160.658 - 9.98755i) q^{87} +143.482i q^{89} +(7.63975 - 16.2983i) q^{90} +(-51.7771 + 37.6183i) q^{91} +(-59.9354 + 82.4940i) q^{92} +(75.1324 - 19.3504i) q^{93} +(7.65993 + 23.5748i) q^{94} +(12.2169 - 16.8151i) q^{95} +(-76.9274 + 48.9000i) q^{96} +(-12.4488 + 38.3136i) q^{97} -20.9870i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} + 7 q^{9}+O(q^{10}) $ 16 * q + 5 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 + 7 * q^9	$ 16 q + 5 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} + 7 q^{9} - 32 q^{10} + 56 q^{12} + 8 q^{13} - 13 q^{15} + 22 q^{16} - 38 q^{18} + 36 q^{19} - 152 q^{21} - 24 q^{24} - 86 q^{25} + 20 q^{27} + 64 q^{28} - 10 q^{30} - 46 q^{31} + 448 q^{34} + 86 q^{36} + 90 q^{37} + 56 q^{39} + 36 q^{40} + 68 q^{42} + 384 q^{43} + 68 q^{45} + 88 q^{46} - 110 q^{48} + 60 q^{49} - 214 q^{51} + 136 q^{52} - 704 q^{54} - 144 q^{57} - 216 q^{58} - 56 q^{60} + 24 q^{61} - 158 q^{63} - 34 q^{64} - 232 q^{67} + 253 q^{69} + 8 q^{70} - 72 q^{72} + 284 q^{73} + 124 q^{75} + 720 q^{76} - 512 q^{78} + 76 q^{79} - 113 q^{81} - 40 q^{82} - 80 q^{84} + 68 q^{85} - 1008 q^{87} - 14 q^{90} - 256 q^{91} - 25 q^{93} - 260 q^{94} - 272 q^{96} - 218 q^{97}+O(q^{100}) $ 16 * q + 5 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 + 7 * q^9 - 32 * q^10 + 56 * q^12 + 8 * q^13 - 13 * q^15 + 22 * q^16 - 38 * q^18 + 36 * q^19 - 152 * q^21 - 24 * q^24 - 86 * q^25 + 20 * q^27 + 64 * q^28 - 10 * q^30 - 46 * q^31 + 448 * q^34 + 86 * q^36 + 90 * q^37 + 56 * q^39 + 36 * q^40 + 68 * q^42 + 384 * q^43 + 68 * q^45 + 88 * q^46 - 110 * q^48 + 60 * q^49 - 214 * q^51 + 136 * q^52 - 704 * q^54 - 144 * q^57 - 216 * q^58 - 56 * q^60 + 24 * q^61 - 158 * q^63 - 34 * q^64 - 232 * q^67 + 253 * q^69 + 8 * q^70 - 72 * q^72 + 284 * q^73 + 124 * q^75 + 720 * q^76 - 512 * q^78 + 76 * q^79 - 113 * q^81 - 40 * q^82 - 80 * q^84 + 68 * q^85 - 1008 * q^87 - 14 * q^90 - 256 * q^91 - 25 * q^93 - 260 * q^94 - 272 * q^96 - 218 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.753510	+	0.244830i	0.376755	+	0.122415i	0.491272	−	0.871006i	$-0.336532\pi$
$2$	0.753510	+	0.244830i	0.376755	+	0.122415i	−0.114517	+	0.993421i	$0.536532\pi$
$3$	1.60937	+	2.53179i	0.536456	+	0.843928i
$3$	1.60937	+	2.53179i	0.536456	+	0.843928i
$4$	−2.72823	−	1.98218i	−0.682058	−	0.495544i
$5$	−2.40079	+	0.780063i	−0.480158	+	0.156013i	−0.539088	−	0.842249i	$-0.681231\pi$
$5$	−2.40079	+	0.780063i	−0.480158	+	0.156013i	0.0589304	+	0.998262i	$0.481231\pi$
$6$	0.592816	+	2.30175i	0.0988027	+	0.383624i
$7$	3.83843	+	2.78878i	0.548347	+	0.398398i	0.827176	−	0.561943i	$-0.189946\pi$
$7$	3.83843	+	2.78878i	0.548347	+	0.398398i	−0.278828	+	0.960341i	$0.589946\pi$
$8$	−3.43323	−	4.72544i	−0.429154	−	0.590680i
$9$	−3.81987	+	8.14914i	−0.424430	+	0.905461i
$10$	−2.00000			−0.200000
$11$		0			0
$11$		0			0
$12$	0.627719	−	10.0974i	0.0523099	−	0.841446i
$13$	−4.16837	+	12.8289i	−0.320644	+	0.986840i	0.652725	+	0.757595i	$0.273626\pi$
$13$	−4.16837	+	12.8289i	−0.320644	+	0.986840i	−0.973369	+	0.229245i	$0.926374\pi$
$14$	2.20952	+	3.04114i	0.157823	+	0.217224i
$15$	−5.83870	−	4.82287i	−0.389247	−	0.321525i
$16$	2.73833	+	8.42770i	0.171145	+	0.526731i
$17$	−21.5549	+	7.00360i	−1.26793	+	0.411977i	−0.864315	−	0.502951i	$-0.832248\pi$
$17$	−21.5549	+	7.00360i	−1.26793	+	0.411977i	−0.403619	+	0.914927i	$0.632248\pi$
$18$	−4.87347	+	5.20524i	−0.270748	+	0.289180i
$19$	−6.66119	+	4.83964i	−0.350589	+	0.254718i	−0.749116	−	0.662439i	$-0.769522\pi$
$19$	−6.66119	+	4.83964i	−0.350589	+	0.254718i	0.398527	+	0.917157i	$0.369522\pi$
$20$	8.09613	+	2.63059i	0.404807	+	0.131530i
$21$	−0.883156	+	14.2063i	−0.0420550	+	0.676489i
$22$		0			0
$23$		−	30.2372i		−	1.31466i	−0.753603	−	0.657329i	$-0.771686\pi$
$23$		−	30.2372i		−	1.31466i	0.753603	−	0.657329i	$-0.228314\pi$
$24$	6.43846	−	16.2972i	0.268269	−	0.679049i
$25$	−15.0701	+	10.9491i	−0.602806	+	0.437964i
$26$	−6.28181	+	8.64617i	−0.241608	+	0.332545i
$27$	−26.7795	+	3.44386i	−0.991832	+	0.127551i
$28$	−4.94427	−	15.2169i	−0.176581	−	0.543461i
$29$	−31.5381	+	43.4085i	−1.08752	+	1.49685i	−0.236562	+	0.971616i	$0.576021\pi$
$29$	−31.5381	+	43.4085i	−1.08752	+	1.49685i	−0.850960	+	0.525230i	$0.823979\pi$
$30$	−3.21873	−	5.06357i	−0.107291	−	0.168786i
$31$	7.99161	−	24.5957i	0.257794	−	0.793408i	−0.735472	−	0.677555i	$-0.763040\pi$
$31$	7.99161	−	24.5957i	0.257794	−	0.793408i	0.993266	−	0.115854i	$-0.0369603\pi$
$32$			30.3846i			0.949520i
$33$		0			0
$34$	−17.9565			−0.528132
$35$	−11.3907	−	3.70106i	−0.325448	−	0.105745i
$36$	26.5746	−	14.6611i	0.738182	−	0.407253i
$37$	34.4690	+	25.0432i	0.931593	+	0.676842i	0.946382	−	0.323048i	$-0.104708\pi$
$37$	34.4690	+	25.0432i	0.931593	+	0.676842i	−0.0147891	+	0.999891i	$0.504708\pi$
$38$	−6.20416	+	2.01586i	−0.163267	+	0.0530488i
$39$	−39.1885	+	10.0930i	−1.00483	+	0.258796i
$40$	11.9286	+	8.66664i	0.298215	+	0.216666i
$41$	−18.1520	−	24.9840i	−0.442731	−	0.609367i	0.528085	−	0.849191i	$-0.322910\pi$
$41$	−18.1520	−	24.9840i	−0.442731	−	0.609367i	−0.970816	+	0.239825i	$0.922910\pi$
$42$	−4.14359	+	10.4883i	−0.0986569	+	0.249722i
$43$	35.4891			0.825328			0.412664	−	0.910883i	$-0.364598\pi$
$43$	35.4891			0.825328			0.412664	+	0.910883i	$0.364598\pi$
$44$		0			0
$45$	2.81386	−	22.5441i	0.0625302	−	0.500980i
$46$	7.40297	−	22.7840i	0.160934	−	0.495304i
$47$	18.3899	+	25.3115i	0.391274	+	0.538542i	0.958527	−	0.285001i	$-0.0919940\pi$
$47$	18.3899	+	25.3115i	0.391274	+	0.538542i	−0.567253	+	0.823543i	$0.691994\pi$
$48$	−16.9302	+	20.4961i	−0.352712	+	0.427002i
$49$	−8.18559	−	25.1927i	−0.167053	−	0.514136i
$50$	−14.0362	+	4.56063i	−0.280723	+	0.0912125i
$51$	−52.4213	−	43.3009i	−1.02787	−	0.849038i
$52$	36.8015	−	26.7378i	0.707721	−	0.514189i
$53$	9.42707	+	3.06304i	0.177869	+	0.0577932i	0.396598	−	0.917993i	$-0.370191\pi$
$53$	9.42707	+	3.06304i	0.177869	+	0.0577932i	−0.218728	+	0.975786i	$0.570191\pi$
$54$	−21.0217	−	3.96143i	−0.389292	−	0.0733599i
$55$		0			0
$56$		−	27.7128i		−	0.494872i
$57$	−22.9732	−	9.07595i	−0.403039	−	0.159227i
$58$	−34.3920	+	24.9873i	−0.592966	+	0.430815i
$59$	36.1628	−	49.7739i	0.612929	−	0.843625i	−0.383885	−	0.923381i	$-0.625414\pi$
$59$	36.1628	−	49.7739i	0.612929	−	0.843625i	0.996814	+	0.0797561i	$0.0254142\pi$
$60$	6.36955	+	24.7313i	0.106159	+	0.412188i
$61$	15.8976	+	48.9277i	0.260616	+	0.802093i	0.992671	+	0.120848i	$0.0385614\pi$
$61$	15.8976	+	48.9277i	0.260616	+	0.802093i	−0.732055	+	0.681245i	$0.761439\pi$
$62$	12.0435	−	16.5765i	0.194250	−	0.267363i
$63$	−37.3885	+	20.6271i	−0.593469	+	0.327415i
$64$	3.51423	−	10.8157i	0.0549098	−	0.168995i
$65$		−	34.0511i		−	0.523863i
$66$		0			0
$67$	34.3288			0.512370			0.256185	−	0.966628i	$-0.417534\pi$
$67$	34.3288			0.512370			0.256185	+	0.966628i	$0.417534\pi$
$68$	72.6891	+	23.6181i	1.06896	+	0.347325i
$69$	76.5540	−	48.6627i	1.10948	−	0.705256i
$70$	−7.67686	−	5.57757i	−0.109669	−	0.0796795i
$71$	−13.7915	+	4.48112i	−0.194246	+	0.0631144i	−0.404525	−	0.914527i	$-0.632563\pi$
$71$	−13.7915	+	4.48112i	−0.194246	+	0.0631144i	0.210278	+	0.977642i	$0.432563\pi$
$72$	51.6228	−	9.92732i	0.716983	−	0.137879i
$73$	71.3826	+	51.8625i	0.977843	+	0.710445i	0.957226	−	0.289343i	$-0.0934367\pi$
$73$	71.3826	+	51.8625i	0.977843	+	0.710445i	0.0206176	+	0.999787i	$0.493437\pi$
$74$	19.8414	+	27.3093i	0.268127	+	0.369045i
$75$	−51.9742	−	20.5332i	−0.692989	−	0.273777i
$76$	27.7663			0.365346
$77$		0			0
$78$	−32.0000	−	1.98933i	−0.410256	−	0.0255043i
$79$	−28.9485	+	89.0943i	−0.366437	+	1.12778i	0.582640	+	0.812731i	$0.302020\pi$
$79$	−28.9485	+	89.0943i	−0.366437	+	1.12778i	−0.949076	+	0.315046i	$0.897980\pi$
$80$	−13.1483	−	18.0970i	−0.164353	−	0.226213i
$81$	−51.8171	−	62.2574i	−0.639718	−	0.768610i
$82$	−7.56083	−	23.2699i	−0.0922053	−	0.283779i
$83$	32.4890	−	10.5563i	0.391433	−	0.127184i	−0.106686	−	0.994293i	$-0.534024\pi$
$83$	32.4890	−	10.5563i	0.391433	−	0.127184i	0.498120	+	0.867108i	$0.334024\pi$
$84$	30.5688	−	37.0074i	0.363914	−	0.440565i
$85$	46.2854	−	33.6283i	0.544534	−	0.395627i
$86$	26.7414	+	8.68881i	0.310947	+	0.101033i
$87$	−160.658	−	9.98755i	−1.84664	−	0.114799i
$88$		0			0
$89$			143.482i			1.61216i	0.591805	+	0.806081i	$0.298416\pi$
$89$			143.482i			1.61216i	−0.591805	+	0.806081i	$0.701584\pi$
$90$	7.63975	−	16.2983i	0.0848861	−	0.181092i
$91$	−51.7771	+	37.6183i	−0.568979	+	0.413387i
$92$	−59.9354	+	82.4940i	−0.651472	+	0.896674i
$93$	75.1324	−	19.3504i	0.807875	−	0.208069i
$94$	7.65993	+	23.5748i	0.0814886	+	0.250796i
$95$	12.2169	−	16.8151i	0.128599	−	0.177001i
$96$	−76.9274	+	48.9000i	−0.801327	+	0.509375i
$97$	−12.4488	+	38.3136i	−0.128339	+	0.394985i	−0.994495	−	0.104788i	$-0.966583\pi$
$97$	−12.4488	+	38.3136i	−0.128339	+	0.394985i	0.866156	+	0.499774i	$0.166583\pi$
$98$		−	20.9870i		−	0.214153i
$99$		0			0
$100$	62.8179			0.628179
$101$	−88.2159	−	28.6631i	−0.873425	−	0.283793i	−0.162200	−	0.986758i	$-0.551859\pi$
$101$	−88.2159	−	28.6631i	−0.873425	−	0.283793i	−0.711224	+	0.702965i	$0.751859\pi$
$102$	−28.8986	−	45.4620i	−0.283320	−	0.445706i
$103$	15.8374	+	11.5066i	0.153761	+	0.111714i	0.662006	−	0.749499i	$-0.269705\pi$
$103$	15.8374	+	11.5066i	0.153761	+	0.111714i	−0.508245	+	0.861213i	$0.669705\pi$
$104$	74.9332	−	24.3473i	0.720512	−	0.234109i
$105$	−8.96151	−	34.7951i	−0.0853478	−	0.331382i
$106$	6.35346	+	4.61606i	0.0599383	+	0.0435477i
$107$	49.6256	+	68.3037i	0.463790	+	0.638353i	0.975289	−	0.220931i	$-0.0709096\pi$
$107$	49.6256	+	68.3037i	0.463790	+	0.638353i	−0.511499	+	0.859284i	$0.670910\pi$
$108$	79.8870	+	43.6860i	0.739694	+	0.404500i
$109$	167.723			1.53874			0.769371	−	0.638803i	$-0.220570\pi$
$109$	167.723			1.53874			0.769371	+	0.638803i	$0.220570\pi$
$110$		0			0
$111$	−7.93070	+	127.572i	−0.0714478	+	1.14929i
$112$	−12.9922	+	39.9857i	−0.116001	+	0.357016i
$113$	−72.5958	−	99.9196i	−0.642441	−	0.884244i	0.356302	−	0.934371i	$-0.384037\pi$
$113$	−72.5958	−	99.9196i	−0.642441	−	0.884244i	−0.998743	+	0.0501267i	$0.984037\pi$
$114$	−15.0885	−	12.4634i	−0.132355	−	0.109328i
$115$	23.5869	+	72.5930i	0.205103	+	0.631243i
$116$	172.087	−	55.9144i	1.48351	−	0.482021i
$117$	−88.6221	−	82.9735i	−0.757454	−	0.709175i
$118$	39.4352	−	28.6513i	0.334196	−	0.242808i
$119$	−102.268	−	33.2290i	−0.859399	−	0.279236i
$120$	−2.74456	+	44.1485i	−0.0228714	+	0.367904i
$121$		0			0
$122$			40.7597i			0.334096i
$123$	34.0410	−	86.1654i	0.276756	−	0.700531i
$124$	−70.5559	+	51.2619i	−0.569000	+	0.413402i
$125$	64.7334	−	89.0979i	0.517867	−	0.712783i
$126$	−33.2228	+	6.38891i	−0.263673	+	0.0507056i
$127$	−39.8161	−	122.541i	−0.313513	−	0.964894i	−0.976362	−	0.216141i	$-0.930653\pi$
$127$	−39.8161	−	122.541i	−0.313513	−	0.964894i	0.662849	−	0.748753i	$-0.269347\pi$
$128$	76.7346	−	105.616i	0.599489	−	0.825125i
$129$	57.1150	+	89.8508i	0.442752	+	0.696518i
$130$	8.33674	−	25.6578i	0.0641288	−	0.197368i
$131$		−	125.997i		−	0.961811i	−0.876772	−	0.480906i	$-0.840308\pi$
$131$		−	125.997i		−	0.961811i	0.876772	−	0.480906i	$-0.159692\pi$
$132$		0			0
$133$	−39.0652			−0.293724
$134$	25.8671	+	8.40472i	0.193038	+	0.0627218i
$135$	61.6054	−	29.1577i	0.456336	−	0.215983i
$136$	107.098	+	77.8112i	0.787485	+	0.572141i
$137$	56.4118	−	18.3293i	0.411765	−	0.133791i	−0.0958068	−	0.995400i	$-0.530543\pi$
$137$	56.4118	−	18.3293i	0.411765	−	0.133791i	0.507572	+	0.861609i	$0.330543\pi$
$138$	69.5983	−	17.9251i	0.504335	−	0.129892i
$139$	105.928	+	76.9615i	0.762075	+	0.553680i	0.899546	−	0.436826i	$-0.143897\pi$
$139$	105.928	+	76.9615i	0.762075	+	0.553680i	−0.137471	+	0.990506i	$0.543897\pi$
$140$	23.7403	+	32.6757i	0.169574	+	0.233398i
$141$	−34.4872	+	87.2947i	−0.244590	+	0.619111i
$142$	−11.4891			−0.0809093
$143$		0			0
$144$	−79.1386	−	9.87774i	−0.549574	−	0.0685954i
$145$	41.8550	−	128.816i	0.288655	−	0.888389i
$146$	41.0900	+	56.5555i	0.281438	+	0.387366i
$147$	50.6088	−	61.2684i	0.344277	−	0.416792i
$148$	−44.3993	−	136.647i	−0.299996	−	0.923292i
$149$	−70.6927	+	22.9695i	−0.474448	+	0.154157i	−0.536474	−	0.843917i	$-0.680244\pi$
$149$	−70.6927	+	22.9695i	−0.474448	+	0.154157i	0.0620259	+	0.998075i	$0.480244\pi$
$150$	−34.1359	−	28.1968i	−0.227573	−	0.187979i
$151$	5.04316	−	3.66407i	0.0333984	−	0.0242654i	−0.570961	−	0.820977i	$-0.693429\pi$
$151$	5.04316	−	3.66407i	0.0333984	−	0.0242654i	0.604359	+	0.796712i	$0.293429\pi$
$152$	45.7388	+	14.8615i	0.300913	+	0.0977727i
$153$	25.2635	−	202.407i	0.165121	−	1.32292i
$154$		0			0
$155$			65.2829i			0.421180i
$156$	126.922	+	50.1424i	0.813600	+	0.321426i
$157$	−79.9278	+	58.0709i	−0.509094	+	0.369879i	−0.812480	−	0.582989i	$-0.801883\pi$
$157$	−79.9278	+	58.0709i	−0.509094	+	0.369879i	0.303386	+	0.952868i	$0.401883\pi$
$158$	−43.6260	+	60.0460i	−0.276114	+	0.380038i
$159$	7.41665	+	28.7969i	0.0466456	+	0.181112i
$160$	−23.7019	−	72.9470i	−0.148137	−	0.455919i
$161$	84.3249	−	116.063i	0.523757	−	0.720890i
$162$	−23.8022	−	59.5980i	−0.146927	−	0.367889i
$163$	64.2352	−	197.696i	0.394081	−	1.21286i	−0.535594	−	0.844476i	$-0.679912\pi$
$163$	64.2352	−	197.696i	0.394081	−	1.21286i	0.929675	−	0.368381i	$-0.120088\pi$
$164$			104.143i			0.635016i
$165$		0			0
$166$	27.0652			0.163044
$167$	−60.0719	−	19.5185i	−0.359712	−	0.116878i	0.123585	−	0.992334i	$-0.460561\pi$
$167$	−60.0719	−	19.5185i	−0.359712	−	0.116878i	−0.483297	+	0.875456i	$0.660561\pi$
$168$	70.1629	−	44.6001i	0.417636	−	0.265477i
$169$	−10.4820	−	7.61564i	−0.0620238	−	0.0450630i
$170$	43.1098	−	14.0072i	0.253587	−	0.0823953i
$171$	−13.9940	−	72.7698i	−0.0818363	−	0.425555i
$172$	−96.8226	−	70.3457i	−0.562922	−	0.408987i
$173$	−113.654	−	156.431i	−0.656957	−	0.904223i	0.342419	−	0.939547i	$-0.388754\pi$
$173$	−113.654	−	156.431i	−0.656957	−	0.904223i	−0.999376	+	0.0353239i	$0.988754\pi$
$174$	−118.612	−	46.8595i	−0.681677	−	0.269308i
$175$	−88.3804			−0.505031
$176$		0			0
$177$	184.216	+	11.4521i	1.04077	+	0.0647011i
$178$	−35.1288	+	108.115i	−0.197353	+	0.607390i
$179$	18.2285	+	25.0894i	0.101835	+	0.140164i	0.856893	−	0.515494i	$-0.172391\pi$
$179$	18.2285	+	25.0894i	0.101835	+	0.140164i	−0.755058	+	0.655658i	$0.772391\pi$
$180$	−52.3633	+	55.9280i	−0.290907	+	0.310711i
$181$	31.5626	+	97.1396i	0.174379	+	0.536683i	0.999605	−	0.0281203i	$-0.00895215\pi$
$181$	31.5626	+	97.1396i	0.174379	+	0.536683i	−0.825226	+	0.564803i	$0.808952\pi$
$182$	−48.2246	+	15.6691i	−0.264970	+	0.0860941i
$183$	−98.2894	+	118.992i	−0.537101	+	0.650229i
$184$	−142.884	+	103.811i	−0.776542	+	0.564191i
$185$	−102.288	−	33.2354i	−0.552908	−	0.179651i
$186$	61.3505	+	3.81396i	0.329842	+	0.0205052i
$187$		0			0
$188$		−	105.508i		−	0.561211i
$189$	−112.395	−	61.4631i	−0.594684	−	0.325202i
$190$	13.3224	−	9.67928i	0.0701178	−	0.0509436i
$191$	40.8438	−	56.2167i	0.213842	−	0.294328i	−0.688599	−	0.725143i	$-0.741774\pi$
$191$	40.8438	−	56.2167i	0.213842	−	0.294328i	0.902440	+	0.430815i	$0.141774\pi$
$192$	33.0387	−	8.50913i	0.172076	−	0.0443184i
$193$	83.8998	+	258.217i	0.434714	+	1.33791i	0.893380	+	0.449303i	$0.148327\pi$
$193$	83.8998	+	258.217i	0.434714	+	1.33791i	−0.458666	+	0.888609i	$0.651673\pi$
$194$	−18.7606	+	25.8218i	−0.0967043	+	0.133102i
$195$	86.2101	−	54.8007i	0.442103	−	0.281029i
$196$	−27.6041	+	84.9567i	−0.140837	+	0.433453i
$197$			106.612i			0.541178i	0.962695	+	0.270589i	$0.0872185\pi$
$197$			106.612i			0.541178i	−0.962695	+	0.270589i	$0.912782\pi$
$198$		0			0
$199$	−289.272			−1.45363			−0.726813	−	0.686835i	$-0.758999\pi$
$199$	−289.272			−1.45363			−0.726813	+	0.686835i	$0.758999\pi$
$200$	103.479	+	33.6222i	0.517393	+	0.168111i
$201$	55.2476	+	86.9131i	0.274864	+	0.432404i
$202$	−59.4540	−	43.1958i	−0.294326	−	0.213841i
$203$	−242.114	+	78.6676i	−1.19268	+	0.387525i
$204$	57.1874	+	222.043i	0.280331	+	1.08845i
$205$	63.0681	+	45.8217i	0.307649	+	0.223520i
$206$	9.11649	+	12.5478i	0.0442548	+	0.0609115i
$207$	246.407	+	115.502i	1.19037	+	0.557981i
$208$	−119.533			−0.574676
$209$		0			0
$210$	1.76631	−	28.4125i	0.00841101	−	0.135298i
$211$	−57.8517	+	178.049i	−0.274179	+	0.843835i	0.715257	+	0.698861i	$0.246310\pi$
$211$	−57.8517	+	178.049i	−0.274179	+	0.843835i	−0.989436	+	0.144973i	$0.953690\pi$
$212$	−19.6477	−	27.0428i	−0.0926780	−	0.127560i
$213$	−33.5408	−	27.7053i	−0.157468	−	0.130072i
$214$	20.6705	+	63.6174i	0.0965913	+	0.297277i
$215$	−85.2019	+	27.6838i	−0.396288	+	0.128762i
$216$	108.214	+	114.721i	0.500990	+	0.531116i
$217$	99.2672	−	72.1219i	0.457453	−	0.332359i
$218$	126.381	+	41.0636i	0.579728	+	0.188365i
$219$	−16.4239	+	264.191i	−0.0749949	+	1.20635i
$220$		0			0
$221$		−	305.719i		−	1.38335i
$222$	−37.2092	+	94.1848i	−0.167609	+	0.424256i
$223$	184.238	−	133.857i	0.826180	−	0.600255i	−0.0922959	−	0.995732i	$-0.529421\pi$
$223$	184.238	−	133.857i	0.826180	−	0.600255i	0.918476	+	0.395477i	$0.129421\pi$
$224$	−84.7362	+	116.629i	−0.378286	+	0.520667i
$225$	−31.6597	−	164.633i	−0.140710	−	0.731702i
$226$	−30.2383	−	93.0640i	−0.133798	−	0.411788i
$227$	−250.596	+	344.915i	−1.10395	+	1.51945i	−0.273896	+	0.961759i	$0.588312\pi$
$227$	−250.596	+	344.915i	−1.10395	+	1.51945i	−0.830049	+	0.557691i	$0.811688\pi$
$228$	44.6862	+	70.2983i	0.195992	+	0.308326i
$229$	−31.3913	+	96.6123i	−0.137080	+	0.421888i	−0.995908	−	0.0903761i	$-0.971193\pi$
$229$	−31.3913	+	96.6123i	−0.137080	+	0.421888i	0.858828	+	0.512264i	$0.171193\pi$
$230$			60.4743i			0.262932i
$231$		0			0
$232$	313.402			1.35087
$233$	−164.728	−	53.5233i	−0.706986	−	0.229714i	−0.0666145	−	0.997779i	$-0.521220\pi$
$233$	−164.728	−	53.5233i	−0.706986	−	0.229714i	−0.640372	+	0.768065i	$0.721220\pi$
$234$	−46.4632	−	84.2187i	−0.198561	−	0.359909i
$235$	−63.8947	−	46.4223i	−0.271893	−	0.197541i
$236$	−197.321	+	64.1135i	−0.836107	+	0.271668i
$237$	−272.156	+	70.0941i	−1.14834	+	0.295756i
$238$	−68.9248	−	50.0768i	−0.289600	−	0.210407i
$239$	94.8081	+	130.492i	0.396687	+	0.545992i	0.959909	−	0.280313i	$-0.0904384\pi$
$239$	94.8081	+	130.492i	0.396687	+	0.545992i	−0.563222	+	0.826306i	$0.690438\pi$
$240$	24.6574	−	62.4134i	0.102739	−	0.260056i
$241$	−56.7011			−0.235274			−0.117637	−	0.993057i	$-0.537532\pi$
$241$	−56.7011			−0.235274			−0.117637	+	0.993057i	$0.537532\pi$
$242$		0			0
$243$	74.2296	−	231.385i	0.305472	−	0.952201i
$244$	53.6111	−	164.998i	0.219718	−	0.676221i
$245$	39.3037	+	54.0969i	0.160423	+	0.220804i
$246$	46.7461	−	56.5922i	0.190025	−	0.230049i
$247$	−34.3210	−	105.629i	−0.138952	−	0.427649i
$248$	−143.662	+	46.6787i	−0.579284	+	0.188221i
$249$	79.0130	+	65.2661i	0.317321	+	0.262113i
$250$	70.5911	−	51.2875i	0.282365	−	0.205150i
$251$	−64.1886	−	20.8561i	−0.255731	−	0.0830922i	0.178346	−	0.983968i	$-0.442925\pi$
$251$	−64.1886	−	20.8561i	−0.255731	−	0.0830922i	−0.434077	+	0.900876i	$0.642925\pi$
$252$	142.891	+	17.8351i	0.567029	+	0.0707741i
$253$		0			0
$254$		−	102.084i		−	0.401907i
$255$	159.630	+	63.0644i	0.626000	+	0.247312i
$256$	46.8767	−	34.0580i	0.183112	−	0.133039i
$257$	−86.2117	+	118.660i	−0.335454	+	0.461713i	−0.943107	−	0.332490i	$-0.892111\pi$
$257$	−86.2117	+	118.660i	−0.335454	+	0.461713i	0.607653	+	0.794203i	$0.292111\pi$
$258$	21.0385	+	81.6870i	0.0815447	+	0.316616i
$259$	62.4668	+	192.253i	0.241184	+	0.742289i
$260$	−67.4953	+	92.8994i	−0.259597	+	0.357305i
$261$	−233.271	−	422.824i	−0.893757	−	1.62002i
$262$	30.8479	−	94.9402i	0.117740	−	0.362367i
$263$			146.192i			0.555863i	0.960601	+	0.277932i	$0.0896488\pi$
$263$			146.192i			0.555863i	−0.960601	+	0.277932i	$0.910351\pi$
$264$		0			0
$265$	−25.0217			−0.0944217
$266$	−29.4360	−	9.56435i	−0.110662	−	0.0359562i
$267$	−363.267	+	230.916i	−1.36055	+	0.864854i
$268$	−93.6569	−	68.0457i	−0.349466	−	0.253902i
$269$	54.2199	−	17.6171i	0.201561	−	0.0654912i	−0.206497	−	0.978447i	$-0.566206\pi$
$269$	54.2199	−	17.6171i	0.201561	−	0.0654912i	0.408058	+	0.912956i	$0.366206\pi$
$270$	53.5589	−	6.88773i	0.198366	−	0.0255101i
$271$	−103.862	−	75.4601i	−0.383254	−	0.278451i	0.379431	−	0.925220i	$-0.376120\pi$
$271$	−103.862	−	75.4601i	−0.383254	−	0.278451i	−0.762686	+	0.646769i	$0.776120\pi$
$272$	−118.049	−	162.480i	−0.434002	−	0.597352i
$273$	−178.570	−	70.5469i	−0.654101	−	0.258413i
$274$	46.9944			0.171513
$275$		0			0
$276$	−305.315	−	18.9804i	−1.10621	−	0.0687697i
$277$	73.0137	−	224.713i	0.263587	−	0.811238i	−0.728428	−	0.685122i	$-0.759749\pi$
$277$	73.0137	−	224.713i	0.263587	−	0.811238i	0.992015	−	0.126116i	$-0.0402512\pi$
$278$	60.9756	+	83.9257i	0.219337	+	0.301891i
$279$	169.907	+	159.077i	0.608984	+	0.570169i
$280$	21.6177	+	66.5326i	0.0772062	+	0.237616i
$281$	−193.994	+	63.0324i	−0.690370	+	0.224315i	−0.633130	−	0.774046i	$-0.718230\pi$
$281$	−193.994	+	63.0324i	−0.690370	+	0.224315i	−0.0572400	+	0.998360i	$0.518230\pi$
$282$	−47.3588	+	57.3339i	−0.167939	+	0.203312i
$283$	−387.691	+	281.674i	−1.36993	+	0.995313i	−0.372189	+	0.928157i	$0.621393\pi$
$283$	−387.691	+	281.674i	−1.36993	+	0.995313i	−0.997742	+	0.0671565i	$0.978607\pi$
$284$	46.5087	+	15.1116i	0.163763	+	0.0532099i
$285$	62.2337	+	3.86886i	0.218364	+	0.0135750i
$286$		0			0
$287$		−	146.521i		−	0.510528i
$288$	−247.609	−	116.065i	−0.859753	−	0.403005i
$289$	181.756	−	132.054i	0.628914	−	0.456933i
$290$	63.0763	−	86.8171i	0.217504	−	0.299369i
$291$	−117.037	+	30.1428i	−0.402187	+	0.103584i
$292$	−91.9476	−	282.986i	−0.314889	−	0.969129i
$293$	−5.49977	+	7.56978i	−0.0187705	+	0.0258354i	−0.818299	−	0.574793i	$-0.805083\pi$
$293$	−5.49977	+	7.56978i	−0.0187705	+	0.0258354i	0.799529	+	0.600628i	$0.205083\pi$
$294$	53.1346	−	33.7758i	0.180730	−	0.114884i
$295$	−47.9925	+	147.706i	−0.162686	+	0.500698i
$296$		−	248.860i		−	0.840743i
$297$		0			0
$298$	−58.8913			−0.197622
$299$	387.910	+	126.040i	1.29736	+	0.421537i
$300$	101.097	+	159.041i	0.336990	+	0.530138i
$301$	136.223	+	98.9715i	0.452567	+	0.328809i
$302$	4.69714	−	1.52619i	0.0155535	−	0.00505362i
$303$	−69.4030	−	269.473i	−0.229053	−	0.889350i
$304$	−59.0275	−	42.8860i	−0.194170	−	0.141072i
$305$	−76.3334	−	105.064i	−0.250273	−	0.344472i
$306$	68.5916	−	146.330i	0.224155	−	0.478203i
$307$	72.5271			0.236245			0.118122	−	0.992999i	$-0.462313\pi$
$307$	72.5271			0.236245			0.118122	+	0.992999i	$0.462313\pi$
$308$		0			0
$309$	−3.64391	+	58.6152i	−0.0117926	+	0.189693i
$310$	−15.9832	+	49.1913i	−0.0515588	+	0.158682i
$311$	223.738	+	307.949i	0.719416	+	0.990191i	0.999543	+	0.0302281i	$0.00962338\pi$
$311$	223.738	+	307.949i	0.719416	+	0.990191i	−0.280127	+	0.959963i	$0.590377\pi$
$312$	182.237	+	150.531i	0.584094	+	0.482472i
$313$	16.4090	+	50.5017i	0.0524249	+	0.161347i	0.973841	−	0.227230i	$-0.0729668\pi$
$313$	16.4090	+	50.5017i	0.0524249	+	0.161347i	−0.921416	+	0.388577i	$0.872967\pi$
$314$	−74.4439	+	24.1883i	−0.237082	+	0.0770327i
$315$	73.6715	−	78.6868i	0.233878	−	0.249799i
$316$	255.579	−	185.689i	0.808794	−	0.587623i
$317$	69.6617	+	22.6345i	0.219753	+	0.0714021i	0.416824	−	0.908987i	$-0.363143\pi$
$317$	69.6617	+	22.6345i	0.219753	+	0.0714021i	−0.197071	+	0.980389i	$0.563143\pi$
$318$	−1.46182	+	23.5145i	−0.00459692	+	0.0739451i
$319$		0			0
$320$			28.7075i			0.0897109i
$321$	−93.0646	+	235.567i	−0.289921	+	0.733854i
$322$	91.9554	−	66.8095i	0.285576	−	0.207483i
$323$	109.686	−	150.970i	0.339586	−	0.467400i
$324$	17.9639	+	272.563i	0.0554443	+	0.841245i
$325$	−77.6472	−	238.974i	−0.238914	−	0.735303i
$326$	96.8037	−	133.239i	0.296944	−	0.408708i
$327$	269.928	+	424.638i	0.825467	+	1.29859i
$328$	−55.7406	+	171.552i	−0.169941	+	0.523024i
$329$			148.442i			0.451191i
$330$		0			0
$331$	−167.351			−0.505591			−0.252795	−	0.967520i	$-0.581350\pi$
$331$	−167.351			−0.505591			−0.252795	+	0.967520i	$0.581350\pi$
$332$	−109.562	−	35.5988i	−0.330006	−	0.107225i
$333$	−335.747	+	185.231i	−1.00825	+	0.556249i
$334$	−40.4860	−	29.4148i	−0.121216	−	0.0880684i
$335$	−82.4161	+	26.7786i	−0.246018	+	0.0799362i
$336$	−122.144	+	31.4584i	−0.363525	+	0.0936262i
$337$	−347.288	−	252.320i	−1.03053	−	0.748723i	−0.0621140	−	0.998069i	$-0.519784\pi$
$337$	−347.288	−	252.320i	−1.03053	−	0.748723i	−0.968414	+	0.249346i	$0.919784\pi$
$338$	−6.03377	−	8.30478i	−0.0178514	−	0.0245703i
$339$	136.142	−	344.604i	0.401598	−	1.01653i
$340$	−192.935			−0.567455
$341$		0			0
$342$	7.27163	−	58.2589i	0.0212621	−	0.170348i
$343$	110.678	−	340.633i	0.322678	−	0.993100i
$344$	−121.842	−	167.702i	−0.354193	−	0.487505i
$345$	−145.830	+	176.546i	−0.422695	+	0.511727i
$346$	−47.3401	−	145.698i	−0.136821	−	0.421092i
$347$	490.113	−	159.247i	1.41243	−	0.458926i	0.499241	−	0.866463i	$-0.333612\pi$
$347$	490.113	−	159.247i	1.41243	−	0.458926i	0.913189	+	0.407537i	$0.133612\pi$
$348$	418.514	+	345.700i	1.20263	+	0.993391i
$349$	−226.538	+	164.589i	−0.649106	+	0.471603i	−0.862966	−	0.505261i	$-0.831396\pi$
$349$	−226.538	+	164.589i	−0.649106	+	0.471603i	0.213861	+	0.976864i	$0.431396\pi$
$350$	−66.5955	−	21.6382i	−0.190273	−	0.0618234i
$351$	67.4456	−	357.907i	0.192153	−	1.01968i
$352$		0			0
$353$			373.911i			1.05924i	0.848236	+	0.529619i	$0.177665\pi$
$353$			373.911i			1.05924i	−0.848236	+	0.529619i	$0.822335\pi$
$354$	136.005	+	53.7309i	0.384194	+	0.151782i
$355$	29.6149	−	21.5164i	0.0834221	−	0.0606097i
$356$	284.408	−	391.454i	0.798898	−	1.09959i
$357$	−80.4587	−	312.400i	−0.225375	−	0.875069i
$358$	7.59272	+	23.3680i	0.0212087	+	0.0652737i
$359$	63.9874	−	88.0711i	0.178238	−	0.245324i	−0.710545	−	0.703652i	$-0.751552\pi$
$359$	63.9874	−	88.0711i	0.178238	−	0.245324i	0.888783	+	0.458328i	$0.151552\pi$
$360$	−116.191	+	64.1024i	−0.322754	+	0.178062i
$361$	−90.6058	+	278.856i	−0.250985	+	0.772454i
$362$			80.9231i			0.223544i
$363$		0			0
$364$	215.826			0.592929
$365$	−211.830	−	68.8279i	−0.580357	−	0.188569i
$366$	−103.195	+	65.5973i	−0.281953	+	0.179228i
$367$	−386.681	−	280.941i	−1.05363	−	0.765506i	−0.0807290	−	0.996736i	$-0.525725\pi$
$367$	−386.681	−	280.941i	−1.05363	−	0.765506i	−0.972899	+	0.231231i	$0.925725\pi$
$368$	254.830	−	82.7992i	0.692472	−	0.224998i
$369$	272.937	−	52.4871i	0.739666	−	0.142241i
$370$	−68.9379	−	50.0863i	−0.186319	−	0.135368i
$371$	27.6430	+	38.0473i	0.0745094	+	0.102553i
$372$	−243.335	−	96.1333i	−0.654125	−	0.258423i
$373$	−207.081			−0.555178			−0.277589	−	0.960700i	$-0.589535\pi$
$373$	−207.081			−0.555178			−0.277589	+	0.960700i	$0.589535\pi$
$374$		0			0
$375$	329.757	+	20.4999i	0.879351	+	0.0546663i
$376$	56.4712	−	173.800i	0.150189	−	0.462235i
$377$	−425.422	−	585.543i	−1.12844	−	1.55317i
$378$	−69.6430	−	73.8308i	−0.184241	−	0.195320i
$379$	95.9825	+	295.404i	0.253252	+	0.779430i	0.994169	+	0.107833i	$0.0343912\pi$
$379$	95.9825	+	295.404i	0.253252	+	0.779430i	−0.740917	+	0.671597i	$0.765609\pi$
$380$	−66.6610	+	21.6595i	−0.175424	+	0.0569986i
$381$	246.170	−	298.020i	0.646115	−	0.782205i
$382$	44.5397	−	32.3600i	0.116596	−	0.0847121i
$383$	342.256	+	111.206i	0.893619	+	0.290354i	0.719601	−	0.694388i	$-0.244325\pi$
$383$	342.256	+	111.206i	0.893619	+	0.290354i	0.174018	+	0.984742i	$0.444325\pi$
$384$	390.891	+	24.3004i	1.01795	+	0.0632823i
$385$		0			0
$386$			215.110i			0.557280i
$387$	−135.564	+	289.206i	−0.350295	+	0.747302i
$388$	109.908	−	79.8526i	0.283267	−	0.205806i
$389$	−367.096	+	505.264i	−0.943691	+	1.29888i	0.0105826	+	0.999944i	$0.496631\pi$
$389$	−367.096	+	505.264i	−0.943691	+	1.29888i	−0.954273	+	0.298935i	$0.903369\pi$
$390$	78.3770	−	20.1861i	0.200967	−	0.0517591i
$391$	211.769	+	651.758i	0.541609	+	1.66690i
$392$	−90.9433	+	125.173i	−0.231998	+	0.319318i
$393$	318.998	−	202.776i	0.811700	−	0.515969i
$394$	−26.1019	+	80.3332i	−0.0662484	+	0.203891i
$395$		−	236.478i		−	0.598679i
$396$		0			0
$397$	−78.7284			−0.198308			−0.0991541	−	0.995072i	$-0.531614\pi$
$397$	−78.7284			−0.198308			−0.0991541	+	0.995072i	$0.531614\pi$
$398$	−217.969	−	70.8224i	−0.547661	−	0.177946i
$399$	−62.8703	−	98.9048i	−0.157570	−	0.247882i
$400$	−133.543	−	97.0244i	−0.333857	−	0.242561i
$401$	751.433	−	244.155i	1.87390	−	0.608867i	0.883922	−	0.467635i	$-0.154894\pi$
$401$	751.433	−	244.155i	1.87390	−	0.608867i	0.989977	−	0.141232i	$-0.0451064\pi$
$402$	20.3507	+	79.0162i	0.0506235	+	0.196558i
$403$	282.224	+	205.048i	0.700307	+	0.508803i
$404$	183.858	+	253.059i	0.455095	+	0.626384i
$405$	172.967	+	109.046i	0.427078	+	0.269250i
$406$	−201.696			−0.496787
$407$		0			0
$408$	−24.6414	+	396.376i	−0.0603955	+	0.971510i
$409$	−156.887	+	482.847i	−0.383586	+	1.18056i	0.553915	+	0.832573i	$0.313133\pi$
$409$	−156.887	+	482.847i	−0.383586	+	1.18056i	−0.937501	+	0.347982i	$0.886867\pi$
$410$	36.3039	+	49.9681i	0.0885462	+	0.121873i
$411$	137.193	+	113.324i	0.333804	+	0.275728i
$412$	−20.4001	−	62.7851i	−0.0495149	−	0.152391i
$413$	277.617	−	90.2033i	0.672196	−	0.218410i
$414$	157.392	+	147.360i	0.380173	+	0.355942i
$415$	−69.7645	+	50.6869i	−0.168107	+	0.122137i
$416$	−389.802	−	126.654i	−0.937024	−	0.304458i
$417$	−24.3723	+	392.047i	−0.0584467	+	0.940162i
$418$		0			0
$419$			334.392i			0.798073i	0.916935	+	0.399036i	$0.130655\pi$
$419$			334.392i			0.798073i	−0.916935	+	0.399036i	$0.869345\pi$
$420$	−44.5210	+	112.693i	−0.106002	+	0.268316i
$421$	358.649	−	260.574i	0.851899	−	0.618941i	−0.0737700	−	0.997275i	$-0.523503\pi$
$421$	358.649	−	260.574i	0.851899	−	0.618941i	0.925669	+	0.378334i	$0.123503\pi$
$422$	−87.1836	+	119.998i	−0.206596	+	0.284355i
$423$	−276.514	+	53.1750i	−0.653697	+	0.125709i
$424$	−17.8911	−	55.0631i	−0.0421960	−	0.129866i
$425$	248.152	−	341.552i	0.583887	−	0.803651i
$426$	−18.4902	−	29.0880i	−0.0434043	−	0.0682817i
$427$	−75.4270	+	232.141i	−0.176644	+	0.543655i
$428$		−	284.715i		−	0.665222i
$429$		0			0
$430$	−70.9783			−0.165066
$431$	756.378	+	245.762i	1.75494	+	0.570214i	0.996656	−	0.0817130i	$-0.0260391\pi$
$431$	756.378	+	245.762i	1.75494	+	0.570214i	0.758282	+	0.651927i	$0.226039\pi$
$432$	−102.355	−	216.259i	−0.236932	−	0.500599i
$433$	15.0656	+	10.9458i	0.0347936	+	0.0252791i	0.605046	−	0.796190i	$-0.293155\pi$
$433$	15.0656	+	10.9458i	0.0347936	+	0.0252791i	−0.570253	+	0.821469i	$0.693155\pi$
$434$	92.4564	−	30.0409i	0.213033	−	0.0692187i
$435$	393.496	−	101.345i	0.904588	−	0.232977i
$436$	−457.587	−	332.456i	−1.04951	−	0.762515i
$437$	146.337	+	201.416i	0.334867	+	0.460905i
$438$	−77.0575	+	195.049i	−0.175930	+	0.445318i
$439$	−254.891			−0.580618			−0.290309	−	0.956933i	$-0.593758\pi$
$439$	−254.891			−0.580618			−0.290309	+	0.956933i	$0.593758\pi$
$440$		0			0
$441$	236.567	+	29.5272i	0.536432	+	0.0669551i
$442$	74.8493	−	230.363i	0.169342	−	0.521182i
$443$	36.1793	+	49.7965i	0.0816689	+	0.112408i	0.847897	−	0.530161i	$-0.177869\pi$
$443$	36.1793	+	49.7965i	0.0816689	+	0.112408i	−0.766228	+	0.642569i	$0.777869\pi$
$444$	274.506	−	332.325i	0.618258	−	0.748480i
$445$	−111.925	−	344.471i	−0.251518	−	0.774092i
$446$	171.597	−	55.7554i	0.384748	−	0.125012i
$447$	−171.924	−	142.012i	−0.384618	−	0.317701i
$448$	43.6517	−	31.7148i	0.0974369	−	0.0707920i
$449$	130.706	+	42.4691i	0.291105	+	0.0945859i	0.450929	−	0.892560i	$-0.351093\pi$
$449$	130.706	+	42.4691i	0.291105	+	0.0945859i	−0.159824	+	0.987146i	$0.551093\pi$
$450$	16.4512	−	131.804i	0.0365582	−	0.292897i
$451$		0			0
$452$			416.502i			0.921464i
$453$	17.3929	+	6.87136i	0.0383950	+	0.0151686i
$454$	−273.272	+	198.544i	−0.601920	+	0.437321i
$455$	94.9612	−	130.703i	0.208706	−	0.287259i
$456$	35.9846	+	139.718i	0.0789136	+	0.306400i
$457$	−95.0513	−	292.538i	−0.207990	−	0.640126i	−0.999577	−	0.0290707i	$-0.990745\pi$
$457$	−95.0513	−	292.538i	−0.207990	−	0.640126i	0.791588	−	0.611056i	$-0.209255\pi$
$458$	−47.3072	+	65.1128i	−0.103291	+	0.142168i
$459$	553.109	−	261.785i	1.20503	−	0.570337i
$460$	79.5416	−	244.804i	0.172917	−	0.532183i
$461$		−	528.162i		−	1.14569i	−0.819664	−	0.572844i	$-0.805840\pi$
$461$		−	528.162i		−	1.14569i	0.819664	−	0.572844i	$-0.194160\pi$
$462$		0			0
$463$	−45.9484			−0.0992406			−0.0496203	−	0.998768i	$-0.515801\pi$
$463$	−45.9484			−0.0992406			−0.0496203	+	0.998768i	$0.515801\pi$
$464$	−452.196	−	146.927i	−0.974560	−	0.316654i
$465$	−165.282	+	105.064i	−0.355446	+	0.225945i
$466$	−111.020	−	80.6607i	−0.238240	−	0.173092i
$467$	−341.492	+	110.958i	−0.731247	+	0.237597i	−0.650893	−	0.759170i	$-0.725605\pi$
$467$	−341.492	+	110.958i	−0.731247	+	0.237597i	−0.0803544	+	0.996766i	$0.525605\pi$
$468$	77.3135	+	402.036i	0.165200	+	0.859051i
$469$	131.769	+	95.7356i	0.280957	+	0.204127i
$470$	−36.7797	−	50.6230i	−0.0782548	−	0.107708i
$471$	−275.656	−	108.903i	−0.585257	−	0.231216i
$472$	−359.359			−0.761353
$473$		0			0
$474$	−222.234	−	13.8155i	−0.468847	−	0.0291467i
$475$	47.3954	−	145.868i	0.0997798	−	0.307091i
$476$	213.146	+	293.371i	0.447786	+	0.616325i
$477$	−60.9714	+	65.1221i	−0.127823	+	0.136524i
$478$	39.4904	+	121.539i	0.0826159	+	0.254266i
$479$	549.141	−	178.427i	1.14643	−	0.372498i	0.326633	−	0.945151i	$-0.394086\pi$
$479$	549.141	−	178.427i	1.14643	−	0.372498i	0.819798	+	0.572653i	$0.194086\pi$
$480$	146.541	−	177.407i	0.305294	−	0.369597i
$481$	−464.956	+	337.810i	−0.966645	+	0.702308i
$482$	−42.7248	−	13.8821i	−0.0886407	−	0.0288011i
$483$	429.557	+	26.7041i	0.889352	+	0.0552880i
$484$		0			0
$485$		−	101.694i		−	0.209678i
$486$	112.583	−	156.177i	0.231652	−	0.321352i
$487$	490.992	−	356.726i	1.00820	−	0.732498i	0.0443668	−	0.999015i	$-0.485873\pi$
$487$	490.992	−	356.726i	1.00820	−	0.732498i	0.963830	+	0.266517i	$0.0858730\pi$
$488$	176.625	−	243.103i	0.361936	−	0.498162i
$489$	603.901	−	155.535i	1.23497	−	0.318068i
$490$	16.3712	+	50.3853i	0.0334106	+	0.102827i
$491$	451.929	−	622.027i	0.920425	−	1.26686i	−0.0430540	−	0.999073i	$-0.513709\pi$
$491$	451.929	−	622.027i	0.920425	−	1.26686i	0.963479	−	0.267784i	$-0.0862913\pi$
$492$	−263.667	+	167.604i	−0.535908	+	0.340658i
$493$	375.785	−	1156.55i	0.762241	−	2.34594i
$494$		−	87.9956i		−	0.178129i
$495$		0			0
$496$	229.168			0.462033
$497$	−65.4345	−	21.2610i	−0.131659	−	0.0427786i
$498$	43.5579	+	68.5234i	0.0874657	+	0.137597i
$499$	402.917	+	292.736i	0.807448	+	0.586645i	0.913090	−	0.407759i	$-0.133690\pi$
$499$	402.917	+	292.736i	0.807448	+	0.586645i	−0.105641	+	0.994404i	$0.533690\pi$
$500$	−353.216	+	114.767i	−0.706432	+	0.229534i
$501$	−47.2610	−	183.502i	−0.0943333	−	0.366271i
$502$	−43.2605	−	31.4306i	−0.0861763	−	0.0626108i
$503$	100.227	+	137.950i	0.199258	+	0.274255i	0.896940	−	0.442153i	$-0.145785\pi$
$503$	100.227	+	137.950i	0.199258	+	0.274255i	−0.697682	+	0.716408i	$0.745785\pi$
$504$	225.836	+	105.859i	0.448087	+	0.210039i
$505$	234.147			0.463657
$506$		0			0
$507$	2.41173	−	38.7946i	0.00475687	−	0.0765180i
$508$	−134.271	+	413.244i	−0.264313	+	0.813473i
$509$	−242.636	−	333.960i	−0.476692	−	0.656110i	0.501173	−	0.865347i	$-0.332902\pi$
$509$	−242.636	−	333.960i	−0.476692	−	0.656110i	−0.977865	+	0.209237i	$0.932902\pi$
$510$	104.843	+	86.6019i	0.205574	+	0.169808i
$511$	129.364	+	398.141i	0.253158	+	0.779141i
$512$	−452.976	+	147.181i	−0.884719	+	0.287463i
$513$	161.716	−	152.543i	0.315236	−	0.297355i
$514$	−94.0129	+	68.3044i	−0.182905	+	0.132888i
$515$	−46.9981	−	15.2706i	−0.0912585	−	0.0296517i
$516$	22.2772	−	358.346i	0.0431728	−	0.694469i
$517$		0			0
$518$			160.158i			0.309186i
$519$	213.139	−	539.501i	0.410672	−	1.03950i
$520$	−160.906	+	116.905i	−0.309435	+	0.224818i
$521$	65.4029	−	90.0193i	0.125533	−	0.172782i	−0.741624	−	0.670815i	$-0.765944\pi$
$521$	65.4029	−	90.0193i	0.125533	−	0.172782i	0.867158	+	0.498033i	$0.165944\pi$
$522$	−72.2516	−	375.714i	−0.138413	−	0.719758i
$523$	−94.5104	−	290.873i	−0.180708	−	0.556163i	0.819140	−	0.573594i	$-0.194451\pi$
$523$	−94.5104	−	290.873i	−0.180708	−	0.556163i	−0.999848	+	0.0174310i	$0.994451\pi$
$524$	−249.749	+	343.750i	−0.476620	+	0.656011i
$525$	−142.236	−	223.760i	−0.270927	−	0.426210i
$526$	−35.7922	+	110.157i	−0.0680460	+	0.209424i
$527$			586.126i			1.11219i
$528$		0			0
$529$	−385.285			−0.728328
$530$	−18.8541	−	6.12608i	−0.0355738	−	0.0115586i
$531$	267.477	+	484.826i	0.503723	+	0.913043i
$532$	106.579	+	77.4342i	0.200337	+	0.145553i
$533$	396.182	−	128.727i	0.743306	−	0.241515i
$534$	−330.260	+	85.0588i	−0.618465	+	0.159286i
$535$	−172.422	−	125.272i	−0.322284	−	0.234153i
$536$	−117.859	−	162.219i	−0.219886	−	0.302647i
$537$	−34.1846	+	86.5288i	−0.0636585	+	0.161134i
$538$	45.1684			0.0839562
$539$		0			0
$540$	−225.870	−	42.5639i	−0.418277	−	0.0788220i
$541$	96.3495	−	296.533i	0.178095	−	0.548121i	−0.821666	−	0.569969i	$-0.806955\pi$
$541$	96.3495	−	296.533i	0.178095	−	0.548121i	0.999761	+	0.0218484i	$0.00695512\pi$
$542$	−59.7861	−	82.2884i	−0.110306	−	0.151824i
$543$	−195.141	+	236.243i	−0.359375	+	0.435070i
$544$	−212.802	−	654.937i	−0.391180	−	1.20393i
$545$	−402.667	+	130.834i	−0.738838	+	0.240063i
$546$	−117.282	−	96.8770i	−0.214802	−	0.177430i
$547$	714.349	−	519.005i	1.30594	−	0.948820i	0.305944	−	0.952050i	$-0.401028\pi$
$547$	714.349	−	519.005i	1.30594	−	0.948820i	0.999995	+	0.00322943i	$0.00102796\pi$
$548$	−190.237	−	61.8116i	−0.347147	−	0.112795i
$549$	−459.446	−	57.3460i	−0.836877	−	0.104455i
$550$		0			0
$551$		−	441.786i		−	0.801789i
$552$	−492.780	−	194.681i	−0.892717	−	0.352683i
$553$	−359.582	+	261.251i	−0.650238	+	0.472426i
$554$	110.033	−	151.447i	0.198616	−	0.273371i
$555$	−80.4740	−	312.459i	−0.144998	−	0.562989i
$556$	−136.446	−	419.938i	−0.245407	−	0.755284i
$557$	−190.382	+	262.038i	−0.341798	+	0.470445i	−0.944966	−	0.327170i	$-0.893905\pi$
$557$	−190.382	+	262.038i	−0.341798	+	0.470445i	0.603167	+	0.797615i	$0.293905\pi$
$558$	89.0794	+	161.464i	0.159641	+	0.289363i
$559$	−147.932	+	455.287i	−0.264636	+	0.814467i
$560$		−	106.132i		−	0.189521i
$561$		0			0
$562$	−161.609			−0.287560
$563$	470.984	+	153.032i	0.836562	+	0.271815i	0.695807	−	0.718229i	$-0.255047\pi$
$563$	470.984	+	153.032i	0.836562	+	0.271815i	0.140755	+	0.990044i	$0.455047\pi$
$564$	267.123	−	169.801i	0.473622	−	0.301065i
$565$	252.231	+	183.256i	0.446426	+	0.324348i
$566$	−361.091	+	117.326i	−0.637970	+	0.207289i
$567$	−25.2740	−	383.478i	−0.0445750	−	0.676327i
$568$	68.5246	+	49.7860i	0.120642	+	0.0876515i
$569$	−320.018	−	440.467i	−0.562422	−	0.774108i	0.429210	−	0.903205i	$-0.358792\pi$
$569$	−320.018	−	440.467i	−0.562422	−	0.774108i	−0.991632	+	0.129097i	$0.958792\pi$
$570$	45.9465	+	18.1519i	0.0806078	+	0.0318455i
$571$	779.886			1.36582			0.682912	−	0.730500i	$-0.260713\pi$
$571$	779.886			1.36582			0.682912	+	0.730500i	$0.260713\pi$
$572$		0			0
$573$	208.061	+	12.9345i	0.363109	+	0.0225732i
$574$	35.8729	−	110.405i	0.0624963	−	0.192344i
$575$	331.070	+	455.678i	0.575773	+	0.792484i
$576$	74.7147	+	69.9525i	0.129713	+	0.121445i
$577$	350.826	+	1079.73i	0.608017	+	1.87128i	0.474546	+	0.880231i	$0.342612\pi$
$577$	350.826	+	1079.73i	0.608017	+	1.87128i	0.133471	+	0.991053i	$0.457388\pi$
$578$	169.286	−	55.0043i	0.292882	−	0.0951632i
$579$	−518.724	+	627.982i	−0.895897	+	1.08460i
$580$	−369.527	+	268.477i	−0.637116	+	0.462892i
$581$	154.146	+	50.0850i	0.265311	+	0.0862049i
$582$	−95.5680	−	5.94115i	−0.164206	−	0.0102082i
$583$		0			0
$584$		−	515.370i		−	0.882482i
$585$	277.487	+	130.071i	0.474337	+	0.222344i
$586$	−5.99744	+	4.35739i	−0.0102345	+	0.00743582i
$587$	−368.838	+	507.662i	−0.628344	+	0.864841i	−0.997927	−	0.0643568i	$-0.979500\pi$
$587$	−368.838	+	507.662i	−0.628344	+	0.864841i	0.369583	+	0.929198i	$0.379500\pi$
$588$	−259.517	+	66.8389i	−0.441356	+	0.113672i
$589$	65.8005	+	202.513i	0.111716	+	0.343825i
$590$	−72.3256	+	99.5477i	−0.122586	+	0.168725i
$591$	−269.919	+	171.578i	−0.456716	+	0.290318i
$592$	−116.669	+	359.070i	−0.197076	+	0.606538i
$593$			961.677i			1.62171i	0.585244	+	0.810857i	$0.300999\pi$
$593$			961.677i			1.62171i	−0.585244	+	0.810857i	$0.699001\pi$
$594$		0			0
$595$	271.446			0.456211
$596$	238.396	+	77.4595i	0.399993	+	0.129966i
$597$	−465.544	−	732.374i	−0.779806	−	1.22676i
$598$	261.436	+	189.944i	0.437183	+	0.317632i
$599$	−934.344	+	303.587i	−1.55984	+	0.506822i	−0.956765	−	0.290863i	$-0.906058\pi$
$599$	−934.344	+	303.587i	−1.55984	+	0.506822i	−0.603074	+	0.797685i	$0.706058\pi$
$600$	81.4108	+	316.096i	0.135685	+	0.526827i
$601$	259.888	+	188.820i	0.432426	+	0.314176i	0.782618	−	0.622502i	$-0.213884\pi$
$601$	259.888	+	188.820i	0.432426	+	0.314176i	−0.350192	+	0.936678i	$0.613884\pi$
$602$	78.4138	+	107.927i	0.130256	+	0.179281i
$603$	−131.132	+	279.750i	−0.217465	+	0.463931i
$604$	−21.0217			−0.0348042
$605$		0			0
$606$	13.6793	−	220.043i	0.0225731	−	0.363107i
$607$	−154.991	+	477.012i	−0.255339	+	0.785851i	0.738424	+	0.674337i	$0.235570\pi$
$607$	−154.991	+	477.012i	−0.255339	+	0.785851i	−0.993763	+	0.111515i	$0.964430\pi$
$608$	−147.051	−	202.398i	−0.241860	−	0.332891i
$609$	−588.820	−	486.376i	−0.966864	−	0.798647i
$610$	−31.7951	−	97.8554i	−0.0521232	−	0.160419i
$611$	−401.375	+	130.415i	−0.656915	+	0.213445i
$612$	−470.131	+	502.136i	−0.768187	+	0.820483i
$613$	299.134	−	217.334i	0.487984	−	0.354541i	−0.316425	−	0.948618i	$-0.602482\pi$
$613$	299.134	−	217.334i	0.487984	−	0.354541i	0.804408	+	0.594077i	$0.202482\pi$
$614$	54.6499	+	17.7568i	0.0890063	+	0.0289199i
$615$	−14.5109	+	233.419i	−0.0235949	+	0.379543i
$616$		0			0
$617$		−	560.582i		−	0.908560i	−0.890859	−	0.454280i	$-0.849897\pi$
$617$		−	560.582i		−	0.908560i	0.890859	−	0.454280i	$-0.150103\pi$
$618$	−17.0965	+	43.2750i	−0.0276642	+	0.0700243i
$619$	−334.456	+	242.996i	−0.540316	+	0.392563i	−0.824203	−	0.566295i	$-0.808376\pi$
$619$	−334.456	+	242.996i	−0.540316	+	0.392563i	0.283886	+	0.958858i	$0.408376\pi$
$620$	129.402	−	178.107i	0.208713	−	0.287269i
$621$	104.133	+	809.735i	0.167685	+	1.30392i
$622$	93.1937	+	286.821i	0.149829	+	0.461127i
$623$	−400.142	+	550.748i	−0.642282	+	0.884025i
$624$	−192.372	−	302.631i	−0.308288	−	0.484985i
$625$	57.9978	−	178.499i	0.0927965	−	0.285598i
$626$			42.0710i			0.0672060i
$627$		0			0
$628$	333.168			0.530523
$629$	−918.366	−	298.395i	−1.46004	−	0.474396i
$630$	74.7771	−	41.2543i	0.118694	−	0.0654830i
$631$	−886.280	−	643.920i	−1.40456	−	1.02048i	−0.994085	−	0.108606i	$-0.965361\pi$
$631$	−886.280	−	643.920i	−1.40456	−	1.02048i	−0.410479	−	0.911870i	$-0.634639\pi$
$632$	520.397	−	169.087i	0.823412	−	0.267543i
$633$	−543.887	+	140.078i	−0.859221	+	0.221293i
$634$	46.9492	+	34.1106i	0.0740523	+	0.0538022i
$635$	191.180	+	263.137i	0.301071	+	0.414389i
$636$	36.8461	−	93.2657i	0.0579342	−	0.146644i
$637$	357.315			0.560934
$638$		0			0
$639$	16.1644	−	129.506i	0.0252964	−	0.202670i
$640$	−101.836	+	313.420i	−0.159119	+	0.489718i
$641$	580.698	+	799.262i	0.905925	+	1.24690i	0.968539	+	0.248860i	$0.0800560\pi$
$641$	580.698	+	799.262i	0.905925	+	1.24690i	−0.0626148	+	0.998038i	$0.519944\pi$
$642$	−127.799	+	154.717i	−0.199064	+	0.240992i
$643$	−316.955	−	975.487i	−0.492931	−	1.51709i	−0.820156	−	0.572140i	$-0.806113\pi$
$643$	−316.955	−	975.487i	−0.492931	−	1.51709i	0.327225	−	0.944947i	$-0.393887\pi$
$644$	−460.116	+	149.501i	−0.714466	+	0.232144i
$645$	−207.210	−	171.159i	−0.321256	−	0.265364i
$646$	119.612	−	86.9030i	0.185157	−	0.134525i
$647$	457.467	+	148.640i	0.707059	+	0.229737i	0.640404	−	0.768039i	$-0.278767\pi$
$647$	457.467	+	148.640i	0.707059	+	0.229737i	0.0666556	+	0.997776i	$0.478767\pi$
$648$	−116.293	+	458.603i	−0.179465	+	0.707720i
$649$		0			0
$650$		−	199.079i		−	0.306276i
$651$	342.355	+	135.253i	0.525890	+	0.207762i
$652$	−567.116	+	412.034i	−0.869810	+	0.631954i
$653$	−456.234	+	627.953i	−0.698674	+	0.961643i	0.301293	+	0.953532i	$0.402582\pi$
$653$	−456.234	+	627.953i	−0.698674	+	0.961643i	−0.999967	+	0.00811121i	$0.997418\pi$
$654$	99.4288	+	386.055i	0.152032	+	0.590299i
$655$	98.2859	+	302.493i	0.150055	+	0.461821i
$656$	160.852	−	221.394i	0.245201	−	0.337490i
$657$	−695.307	+	383.599i	−1.05831	+	0.583864i
$658$	−36.3430	+	111.852i	−0.0552326	+	0.169988i
$659$			52.5987i			0.0798160i	0.999203	+	0.0399080i	$0.0127065\pi$
$659$			52.5987i			0.0798160i	−0.999203	+	0.0399080i	$0.987294\pi$
$660$		0			0
$661$	−233.530			−0.353297			−0.176649	−	0.984274i	$-0.556526\pi$
$661$	−233.530			−0.353297			−0.176649	+	0.984274i	$0.556526\pi$
$662$	−126.100	−	40.9725i	−0.190484	−	0.0618919i
$663$	774.016	−	492.015i	1.16744	−	0.742104i
$664$	−161.425	−	117.282i	−0.243110	−	0.176630i
$665$	93.7874	−	30.4734i	0.141034	−	0.0458246i
$666$	−298.339	+	57.3721i	−0.447956	+	0.0861443i
$667$	1312.55	+	953.624i	1.96784	+	1.42972i
$668$	125.201	+	172.324i	0.187427	+	0.257971i
$669$	635.404	+	251.027i	0.949781	+	0.375227i
$670$	−68.6576			−0.102474
$671$		0			0
$672$	−431.652	−	26.8344i	−0.642339	−	0.0399321i
$673$	73.0859	−	224.935i	0.108597	−	0.334228i	−0.881961	−	0.471323i	$-0.843777\pi$
$673$	73.0859	−	224.935i	0.108597	−	0.334228i	0.990558	+	0.137095i	$0.0437766\pi$
$674$	−199.909	−	275.152i	−0.296602	−	0.408237i
$675$	365.863	−	345.111i	0.542019	−	0.511275i
$676$	13.5019	+	41.5545i	0.0199732	+	0.0614711i
$677$	−281.192	+	91.3649i	−0.415350	+	0.134955i	−0.509235	−	0.860628i	$-0.670072\pi$
$677$	−281.192	+	91.3649i	−0.415350	+	0.134955i	0.0938846	+	0.995583i	$0.470072\pi$
$678$	186.954	−	226.331i	0.275743	−	0.333822i
$679$	−154.632	+	112.347i	−0.227735	+	0.165459i
$680$	−317.817	−	103.265i	−0.467378	−	0.151860i
$681$	−1276.55	−	79.3589i	−1.87452	−	0.116533i
$682$		0			0
$683$		−	905.661i		−	1.32600i	−0.748617	−	0.663002i	$-0.769282\pi$
$683$		−	905.661i		−	1.32600i	0.748617	−	0.663002i	$-0.230718\pi$
$684$	−106.064	+	226.272i	−0.155064	+	0.330807i
$685$	−121.135	+	88.0096i	−0.176839	+	0.128481i
$686$	166.795	−	229.573i	0.243141	−	0.334654i
$687$	−295.122	+	76.0088i	−0.429580	+	0.110639i
$688$	97.1808	+	299.092i	0.141251	+	0.434726i
$689$	−78.5910	+	108.171i	−0.114065	+	0.156997i
$690$	−153.108	+	97.3254i	−0.221896	+	0.141051i
$691$	−108.781	+	334.795i	−0.157426	+	0.484508i	−0.998399	−	0.0565700i	$-0.981984\pi$
$691$	−108.781	+	334.795i	−0.157426	+	0.484508i	0.840972	+	0.541078i	$0.181984\pi$
$692$			652.061i			0.942284i
$693$		0			0
$694$	408.293			0.588319
$695$	−314.347	−	102.137i	−0.452297	−	0.146960i
$696$	504.379	+	793.467i	0.724683	+	1.14004i
$697$	566.242	+	411.399i	0.812398	+	0.590242i
$698$	−210.995	+	68.5564i	−0.302285	+	0.0982183i
$699$	−129.598	−	503.194i	−0.185405	−	0.719877i
$700$	241.122	+	175.186i	0.344460	+	0.250265i
$701$	−734.941	−	1011.56i	−1.04842	−	1.44302i	−0.890173	−	0.455623i	$-0.849417\pi$
$701$	−734.941	−	1011.56i	−1.04842	−	1.44302i	−0.158244	−	0.987400i	$-0.550583\pi$
$702$	138.447	−	253.174i	0.197218	−	0.360646i
$703$	−350.804			−0.499010
$704$		0			0
$705$	14.7011	−	236.478i	0.0208526	−	0.335430i
$706$	−91.5447	+	281.746i	−0.129667	+	0.399073i
$707$	−258.676	−	356.036i	−0.365878	−	0.503588i
$708$	−479.884	−	396.393i	−0.677802	−	0.559877i
$709$	−41.6962	−	128.328i	−0.0588099	−	0.180998i	0.917336	−	0.398114i	$-0.130335\pi$
$709$	−41.6962	−	128.328i	−0.0588099	−	0.180998i	−0.976146	+	0.217116i	$0.930335\pi$
$710$	27.5830	−	8.96224i	0.0388492	−	0.0126229i
$711$	−615.463	−	576.235i	−0.865630	−	0.810457i
$712$	678.018	−	492.609i	0.952272	−	0.691866i
$713$	−743.703	−	241.644i	−1.04306	−	0.338911i
$714$	15.8584	−	255.095i	0.0222106	−	0.357276i
$715$		0			0
$716$		−	104.582i		−	0.146064i
$717$	−177.797	+	450.043i	−0.247974	+	0.627676i
$718$	69.7776	−	50.6964i	0.0971833	−	0.0706078i
$719$	65.9951	−	90.8344i	0.0917873	−	0.126334i	−0.760654	−	0.649158i	$-0.775121\pi$
$719$	65.9951	−	90.8344i	0.0917873	−	0.126334i	0.852441	+	0.522824i	$0.175121\pi$
$720$	197.700	−	38.0188i	0.274584	−	0.0528038i
$721$	28.7015	+	88.3343i	0.0398080	+	0.122516i
$722$	−136.545	+	187.938i	−0.189120	+	0.260301i
$723$	−91.2528	−	143.555i	−0.126214	−	0.198555i
$724$	106.438	−	327.582i	0.147014	−	0.452461i
$725$		−	999.487i		−	1.37860i
$726$		0			0
$727$	160.372			0.220595			0.110297	−	0.993899i	$-0.464820\pi$
$727$	160.372			0.220595			0.110297	+	0.993899i	$0.464820\pi$
$728$	355.525	+	115.517i	0.488359	+	0.158678i
$729$	705.280	−	184.450i	0.967462	−	0.253017i
$730$	−142.765	−	103.725i	−0.195569	−	0.142089i
$731$	−764.964	+	248.552i	−1.04646	+	0.340016i
$732$	504.019	−	129.811i	0.688551	−	0.177337i
$733$	−397.210	−	288.590i	−0.541896	−	0.393710i	0.282893	−	0.959152i	$-0.408706\pi$
$733$	−397.210	−	288.590i	−0.541896	−	0.393710i	−0.824789	+	0.565441i	$0.808706\pi$
$734$	−222.586	−	306.363i	−0.303250	−	0.417388i
$735$	−73.7077	+	186.570i	−0.100283	+	0.253837i
$736$	918.745			1.24829
$737$		0			0
$738$	218.511	+	27.2736i	0.296085	+	0.0369561i
$739$	−73.3479	+	225.741i	−0.0992528	+	0.305469i	−0.988339	−	0.152272i	$-0.951341\pi$
$739$	−73.3479	+	225.741i	−0.0992528	+	0.305469i	0.889086	+	0.457741i	$0.151341\pi$
$740$	213.187	+	293.427i	0.288090	+	0.396522i
$741$	212.196	−	256.890i	0.286364	−	0.346680i
$742$	11.5141	+	35.4369i	0.0155177	+	0.0477586i
$743$	−233.203	+	75.7723i	−0.313867	+	0.101982i	−0.461714	−	0.887029i	$-0.652765\pi$
$743$	−233.203	+	75.7723i	−0.313867	+	0.101982i	0.147848	+	0.989010i	$0.452765\pi$
$744$	−349.386	−	288.599i	−0.469605	−	0.387902i
$745$	151.801	−	110.290i	0.203759	−	0.148040i
$746$	−156.038	−	50.6998i	−0.209166	−	0.0679622i
$747$	−38.0789	+	305.081i	−0.0509758	+	0.408408i
$748$		0			0
$749$			400.574i			0.534812i
$750$	243.456	+	96.1812i	0.324608	+	0.128242i
$751$	−599.185	+	435.333i	−0.797849	+	0.579672i	−0.910282	−	0.413988i	$-0.864136\pi$
$751$	−599.185	+	435.333i	−0.797849	+	0.579672i	0.112433	+	0.993659i	$0.464136\pi$
$752$	−162.960	+	224.295i	−0.216702	+	0.298265i
$753$	−50.4997	−	196.077i	−0.0670647	−	0.260394i
$754$	−177.201	−	545.369i	−0.235015	−	0.723301i
$755$	−9.24935	+	12.7306i	−0.0122508	+	0.0168618i
$756$	184.810	+	390.473i	0.244458	+	0.516499i
$757$	100.343	−	308.824i	0.132554	−	0.407958i	−0.862648	−	0.505805i	$-0.831195\pi$
$757$	100.343	−	308.824i	0.132554	−	0.407958i	0.995201	+	0.0978467i	$0.0311955\pi$
$758$			246.089i			0.324656i
$759$		0			0
$760$	−121.402			−0.159740
$761$	644.390	+	209.375i	0.846767	+	0.275131i	0.700091	−	0.714053i	$-0.253143\pi$
$761$	644.390	+	209.375i	0.846767	+	0.275131i	0.146676	+	0.989185i	$0.453143\pi$
$762$	258.456	−	164.291i	0.339181	−	0.215605i
$763$	643.793	+	467.743i	0.843765	+	0.613031i
$764$	−222.863	+	72.4125i	−0.291705	+	0.0947808i
$765$	97.2376	+	505.643i	0.127108	+	0.660971i
$766$	230.667	+	167.589i	0.301132	+	0.218785i
$767$	487.805	+	671.406i	0.635991	+	0.875366i
$768$	161.669	+	63.8701i	0.210507	+	0.0831642i
$769$	632.440			0.822419			0.411209	−	0.911541i	$-0.365106\pi$
$769$	632.440			0.822419			0.411209	+	0.911541i	$0.365106\pi$
$770$		0			0
$771$	−439.168	−	27.3016i	−0.569609	−	0.0354107i
$772$	282.934	−	870.780i	0.366494	−	1.12795i
$773$	108.795	+	149.744i	0.140744	+	0.193718i	0.873570	−	0.486698i	$-0.161799\pi$
$773$	108.795	+	149.744i	0.140744	+	0.193718i	−0.732826	+	0.680416i	$0.761799\pi$
$774$	−172.955	+	184.729i	−0.223456	+	0.238668i
$775$	148.866	+	458.161i	0.192085	+	0.591176i
$776$	223.788	−	72.7132i	0.288387	−	0.0937026i
$777$	−386.211	+	467.558i	−0.497054	+	0.601748i
$778$	−400.314	+	290.845i	−0.514542	+	0.373837i
$779$	241.827	+	78.5745i	0.310433	+	0.100866i
$780$	−343.826	−	21.3745i	−0.440803	−	0.0274032i
$781$		0			0
$782$			542.953i			0.694314i
$783$	695.082	−	1271.07i	0.887716	−	1.62333i
$784$	189.901	−	137.971i	0.242221	−	0.175984i
$785$	146.591	−	201.765i	0.186740	−	0.257025i
$786$	290.014	−	74.6933i	0.368974	−	0.0950296i
$787$	287.300	+	884.219i	0.365057	+	1.12353i	0.949945	+	0.312417i	$0.101139\pi$
$787$	287.300	+	884.219i	0.365057	+	1.12353i	−0.584888	+	0.811114i	$0.698861\pi$
$788$	211.324	−	290.863i	0.268178	−	0.369115i
$789$	−370.127	+	235.277i	−0.469109	+	0.298196i
$790$	57.8970	−	178.189i	0.0732873	−	0.225555i
$791$		−	585.989i		−	0.740820i
$792$		0			0
$793$	−693.957			−0.875103
$794$	−59.3226	−	19.2751i	−0.0747136	−	0.0242759i
$795$	−40.2692	−	63.3497i	−0.0506531	−	0.0796852i
$796$	789.200	+	573.388i	0.991458	+	0.720336i
$797$	858.556	−	278.962i	1.07723	−	0.350015i	0.283933	−	0.958844i	$-0.408361\pi$
$797$	858.556	−	278.962i	1.07723	−	0.350015i	0.793301	+	0.608830i	$0.208361\pi$
$798$	−23.1585	−	89.9183i	−0.0290207	−	0.112680i
$799$	−573.663	−	416.791i	−0.717976	−	0.521640i
$800$	−332.684	−	457.901i	−0.415855	−	0.572376i
$801$	−1169.26	−	548.085i	−1.45975	−	0.684251i
$802$	625.989			0.780535
$803$		0			0
$804$	21.5488	−	346.630i	0.0268020	−	0.431132i
$805$	−111.909	+	344.422i	−0.139018	+	0.427853i
$806$	162.457	+	223.602i	0.201559	+	0.277422i
$807$	131.863	+	108.921i	0.163398	+	0.134970i
$808$	167.420	+	515.266i	0.207203	+	0.637705i
$809$	−291.657	+	94.7652i	−0.360516	+	0.117139i	−0.483674	−	0.875248i	$-0.660698\pi$
$809$	−291.657	+	94.7652i	−0.360516	+	0.117139i	0.123158	+	0.992387i	$0.460698\pi$
$810$	103.634	+	124.515i	0.127944	+	0.153722i
$811$	1054.85	−	766.395i	1.30068	−	0.945000i	0.300719	−	0.953713i	$-0.402773\pi$
$811$	1054.85	−	766.395i	1.30068	−	0.945000i	0.999962	+	0.00871236i	$0.00277327\pi$
$812$	816.477	+	265.289i	1.00551	+	0.326711i
$813$	23.8968	−	384.399i	0.0293934	−	0.472816i
$814$		0			0
$815$			524.733i			0.643844i
$816$	221.381	−	560.363i	0.271300	−	0.686720i
$817$	−236.400	+	171.755i	−0.289351	+	0.210226i
$818$	−236.431	+	325.419i	−0.289036	+	0.397823i
$819$	−108.775	−	565.636i	−0.132814	−	0.690642i
$820$	−81.2379	−	250.024i	−0.0990706	−	0.304908i
$821$	801.178	−	1102.73i	0.975856	−	1.34315i	0.0368241	−	0.999322i	$-0.488276\pi$
$821$	801.178	−	1102.73i	0.975856	−	1.34315i	0.939032	−	0.343829i	$-0.111724\pi$
$822$	75.6313	+	118.980i	0.0920089	+	0.144744i
$823$	82.9097	−	255.170i	0.100741	−	0.310048i	−0.887966	−	0.459908i	$-0.847882\pi$
$823$	82.9097	−	255.170i	0.100741	−	0.310048i	0.988707	+	0.149860i	$0.0478823\pi$
$824$		−	114.343i		−	0.138766i
$825$		0			0
$826$	231.272			0.279990
$827$	−605.846	−	196.851i	−0.732583	−	0.238031i	−0.0811129	−	0.996705i	$-0.525847\pi$
$827$	−605.846	−	196.851i	−0.732583	−	0.238031i	−0.651470	+	0.758674i	$0.725847\pi$
$828$	−443.310	−	803.539i	−0.535398	−	0.970458i
$829$	−21.9994	−	15.9835i	−0.0265373	−	0.0192804i	0.574438	−	0.818548i	$-0.305221\pi$
$829$	−21.9994	−	15.9835i	−0.0265373	−	0.0192804i	−0.600975	+	0.799268i	$0.705221\pi$
$830$	−64.9779	+	21.1126i	−0.0782867	+	0.0254369i
$831$	686.431	−	176.791i	0.826030	−	0.212745i
$832$	124.105	+	90.1675i	0.149165	+	0.108374i
$833$	352.879	+	485.696i	0.423624	+	0.583068i
$834$	−114.350	+	289.444i	−0.137110	+	0.347056i
$835$	159.446			0.190953
$836$		0			0
$837$	−129.307	+	686.181i	−0.154489	+	0.819810i
$838$	−81.8693	+	251.968i	−0.0976961	+	0.300678i
$839$	−595.967	−	820.278i	−0.710330	−	0.977685i	−0.999790	−	0.0204952i	$-0.993476\pi$
$839$	−595.967	−	820.278i	−0.710330	−	0.977685i	0.289460	−	0.957190i	$-0.406524\pi$
$840$	−133.655	+	161.807i	−0.159113	+	0.192627i
$841$	−629.763	−	1938.21i	−0.748826	−	2.30465i
$842$	334.042	−	108.537i	0.396725	−	0.128904i
$843$	−471.792	−	389.709i	−0.559658	−	0.462288i
$844$	510.758	−	371.087i	0.605163	−	0.439677i
$845$	31.1058	+	10.1069i	0.0368116	+	0.0119608i
$846$	−221.375	−	27.6311i	−0.261672	−	0.0326608i
$847$		0			0
$848$			87.8361i			0.103580i
$849$	−1337.07	−	528.233i	−1.57488	−	0.622183i
$850$	270.607	−	196.607i	0.318361	−	0.231303i
$851$	757.234	−	1042.24i	0.889816	−	1.22473i
$852$	36.5903	+	142.070i	0.0429464	+	0.166749i
$853$	−398.741	−	1227.20i	−0.467457	−	1.43869i	−0.855866	−	0.517198i	$-0.826975\pi$
$853$	−398.741	−	1227.20i	−0.467457	−	1.43869i	0.388408	−	0.921487i	$-0.373025\pi$
$854$	−113.670	+	156.453i	−0.133103	+	0.183201i
$855$	90.3617	+	163.789i	0.105686	+	0.191566i
$856$	152.389	−	469.005i	0.178025	−	0.547903i
$857$			618.449i			0.721644i	0.932635	+	0.360822i	$0.117504\pi$
$857$			618.449i			0.721644i	−0.932635	+	0.360822i	$0.882496\pi$
$858$		0			0
$859$	1207.23			1.40538			0.702692	−	0.711494i	$-0.251981\pi$
$859$	1207.23			1.40538			0.702692	+	0.711494i	$0.251981\pi$
$860$	287.325	+	93.3574i	0.334098	+	0.108555i
$861$	370.961	−	235.807i	0.430849	−	0.273875i
$862$	509.768	+	370.368i	0.591379	+	0.429662i
$863$	1051.19	−	341.551i	1.21806	−	0.395772i	0.371686	−	0.928359i	$-0.378780\pi$
$863$	1051.19	−	341.551i	1.21806	−	0.395772i	0.846376	+	0.532587i	$0.178780\pi$
$864$	−104.641	−	813.684i	−0.121112	−	0.941764i
$865$	394.884	+	286.900i	0.456513	+	0.331676i
$866$	8.67224	+	11.9363i	0.0100141	+	0.0137833i
$867$	626.844	+	247.645i	0.723004	+	0.285634i
$868$	−413.783			−0.476708
$869$		0			0
$870$	321.315	+	19.9751i	0.369328	+	0.0229599i
$871$	−143.095	+	440.401i	−0.164288	+	0.505627i
$872$	−575.831	−	792.564i	−0.660357	−	0.908903i
$873$	−264.670	−	247.800i	−0.303173	−	0.283849i
$874$	60.9537	+	187.596i	0.0697411	+	0.214641i
$875$	496.950	−	161.469i	0.567943	−	0.184536i
$876$	568.482	−	688.220i	0.648952	−	0.785639i
$877$	−1077.90	+	783.140i	−1.22908	+	0.892977i	−0.996821	−	0.0796781i	$-0.974611\pi$
$877$	−1077.90	+	783.140i	−1.22908	+	0.892977i	−0.232256	+	0.972655i	$0.574611\pi$
$878$	−192.063	−	62.4051i	−0.218751	−	0.0710764i
$879$	−28.0162	−	1.74167i	−0.0318728	−	0.00198143i
$880$		0			0
$881$			1171.98i			1.33029i	0.746715	+	0.665145i	$0.231630\pi$
$881$			1171.98i			1.33029i	−0.746715	+	0.665145i	$0.768370\pi$
$882$	171.026	+	80.1677i	0.193907	+	0.0908930i
$883$	−589.122	+	428.022i	−0.667183	+	0.484737i	−0.869081	−	0.494670i	$-0.835289\pi$
$883$	−589.122	+	428.022i	−0.667183	+	0.484737i	0.201898	+	0.979407i	$0.435289\pi$
$884$	−605.990	+	834.074i	−0.685509	+	0.943522i
$885$	−451.197	+	116.206i	−0.509827	+	0.131306i
$886$	15.0698	+	46.3800i	0.0170088	+	0.0523476i
$887$	−575.896	+	792.653i	−0.649262	+	0.893633i	−0.999067	−	0.0431896i	$-0.986248\pi$
$887$	−575.896	+	792.653i	−0.649262	+	0.893633i	0.349804	+	0.936823i	$0.386248\pi$
$888$	630.060	−	400.507i	0.709527	−	0.451021i
$889$	188.910	−	581.406i	0.212497	−	0.654000i
$890$		−	286.965i		−	0.322433i
$891$		0			0
$892$	−767.973			−0.860956
$893$	−244.997	−	79.6044i	−0.274353	−	0.0891426i
$894$	−94.7777	−	149.100i	−0.106015	−	0.166779i
$895$	−63.3341	−	46.0149i	−0.0707644	−	0.0514133i
$896$	589.081	−	191.404i	0.657456	−	0.213620i
$897$	305.184	+	1184.95i	0.340228	+	1.32101i
$898$	88.0908	+	64.0017i	0.0980966	+	0.0712714i
$899$	815.621	+	1122.61i	0.907253	+	1.24873i
$900$	−239.957	+	511.912i	−0.266618	+	0.568791i
$901$	−224.652			−0.249336
$902$		0			0
$903$	−31.3424	+	504.168i	−0.0347092	+	0.558325i
$904$	−222.926	+	686.094i	−0.246599	+	0.758954i
$905$	−151.550	−	208.591i	−0.167459	−	0.230487i
$906$	11.4234	+	9.43595i	0.0126086	+	0.0104150i
$907$	340.755	+	1048.74i	0.375695	+	1.15627i	0.943009	+	0.332768i	$0.107982\pi$
$907$	340.755	+	1048.74i	0.375695	+	1.15627i	−0.567314	+	0.823501i	$0.692018\pi$
$908$	1367.37	−	444.284i	1.50591	−	0.489300i
$909$	570.553	−	609.395i	0.627671	−	0.670401i
$910$	103.554	−	75.2365i	0.113796	−	0.0826775i
$911$	−440.602	−	143.160i	−0.483647	−	0.157146i	0.0570373	−	0.998372i	$-0.481835\pi$
$911$	−440.602	−	143.160i	−0.483647	−	0.157146i	−0.540684	+	0.841226i	$0.681835\pi$
$912$	13.5812	−	218.464i	0.0148917	−	0.239544i
$913$		0			0
$914$		−	243.701i		−	0.266632i
$915$	143.151	−	362.346i	0.156449	−	0.396007i
$916$	277.145	−	201.358i	0.302560	−	0.219823i
$917$	351.379	−	483.632i	0.383183	−	0.527407i
$918$	480.866	−	61.8398i	0.523819	−	0.0673636i
$919$	60.5455	+	186.340i	0.0658819	+	0.202764i	0.978578	−	0.205874i	$-0.0660039\pi$
$919$	60.5455	+	186.340i	0.0658819	+	0.202764i	−0.912697	+	0.408638i	$0.866004\pi$
$920$	262.054	−	360.687i	0.284842	−	0.392051i
$921$	116.723	+	183.623i	0.126735	+	0.199373i
$922$	129.310	−	397.976i	0.140250	−	0.431644i
$923$		−	195.609i		−	0.211927i
$924$		0			0
$925$	−793.652			−0.858002
$926$	−34.6226	−	11.2496i	−0.0373894	−	0.0121485i
$927$	−154.266	+	85.1078i	−0.166414	+	0.0918099i
$928$	−1318.95	−	958.275i	−1.42128	−	1.03262i
$929$	−115.578	+	37.5535i	−0.124411	+	0.0404236i	−0.370561	−	0.928808i	$-0.620834\pi$
$929$	−115.578	+	37.5535i	−0.124411	+	0.0404236i	0.246150	+	0.969232i	$0.420834\pi$
$930$	−150.265	+	38.7008i	−0.161575	+	0.0416138i
$931$	176.449	+	128.198i	0.189527	+	0.137699i
$932$	343.323	+	472.544i	0.368372	+	0.507021i
$933$	−419.585	+	1062.06i	−0.449716	+	1.13833i
$934$	−284.484			−0.304586
$935$		0			0
$936$	−87.8260	+	703.645i	−0.0938312	+	0.751758i
$937$	102.105	−	314.247i	0.108970	−	0.335376i	−0.881672	−	0.471864i	$-0.843581\pi$
$937$	102.105	−	314.247i	0.108970	−	0.335376i	0.990642	+	0.136488i	$0.0435815\pi$
$938$	75.8500	+	104.399i	0.0808636	+	0.111299i
$939$	−101.451	+	122.820i	−0.108042	+	0.130799i
$940$	82.3026	+	253.301i	0.0875560	+	0.269470i
$941$	851.275	−	276.596i	0.904650	−	0.293939i	0.180495	−	0.983576i	$-0.442230\pi$
$941$	851.275	−	276.596i	0.904650	−	0.293939i	0.724155	+	0.689637i	$0.242230\pi$
$942$	−181.047	−	149.548i	−0.192194	−	0.158756i
$943$	−755.446	+	548.864i	−0.801109	+	0.582040i
$944$	518.505	+	168.472i	0.549263	+	0.178466i
$945$	317.783	+	59.8844i	0.336278	+	0.0633697i
$946$		0			0
$947$			1308.11i			1.38132i	0.723181	+	0.690659i	$0.242679\pi$
$947$			1308.11i			1.38132i	−0.723181	+	0.690659i	$0.757321\pi$
$948$	881.445	+	348.229i	0.929794	+	0.367331i
$949$	−962.888	+	699.579i	−1.01463	+	0.737175i
$950$	71.4258	−	98.3092i	0.0751851	−	0.103483i
$951$	54.8057	+	212.796i	0.0576295	+	0.223760i
$952$	194.090	+	597.346i	0.203876	+	0.627465i
$953$	1.19333	−	1.64248i	0.00125218	−	0.00172348i	−0.808390	−	0.588647i	$-0.799661\pi$
$953$	1.19333	−	1.64248i	0.00125218	−	0.00172348i	0.809643	+	0.586923i	$0.199661\pi$
$954$	−61.8864	+	34.1425i	−0.0648704	+	0.0357888i
$955$	−54.2047	+	166.825i	−0.0567589	+	0.174686i
$956$		−	543.939i		−	0.568974i
$957$		0			0
$958$	457.467			0.477523
$959$	267.650	+	86.9646i	0.279092	+	0.0906826i
$960$	−72.6812	+	46.2009i	−0.0757096	+	0.0481259i
$961$	236.385	+	171.744i	0.245978	+	0.178713i
$962$	−433.055	+	140.708i	−0.450161	+	0.146266i
$963$	−746.180	+	143.494i	−0.774850	+	0.149008i
$964$	154.694	+	112.392i	0.160471	+	0.116589i
$965$	−402.851	−	554.477i	−0.417462	−	0.574587i
$966$	317.137	+	125.290i	0.328300	+	0.129700i
$967$	−520.674			−0.538442			−0.269221	−	0.963078i	$-0.586766\pi$
$967$	−520.674			−0.538442			−0.269221	+	0.963078i	$0.586766\pi$
$968$		0			0
$969$	558.750	+	34.7356i	0.576625	+	0.0358469i
$970$	24.8977	−	76.6272i	0.0256677	−	0.0789971i
$971$	1065.10	+	1465.98i	1.09691	+	1.50977i	0.839418	+	0.543487i	$0.182896\pi$
$971$	1065.10	+	1465.98i	1.09691	+	1.50977i	0.257492	+	0.966280i	$0.417104\pi$
$972$	−661.162	+	484.136i	−0.680207	+	0.498082i
$973$	191.970	+	590.823i	0.197297	+	0.607218i
$974$	457.305	−	148.587i	0.469512	−	0.152554i
$975$	480.067	−	581.182i	0.492376	−	0.596084i
$976$	−368.815	+	267.960i	−0.377884	+	0.274549i
$977$	−406.470	−	132.070i	−0.416039	−	0.135179i	0.0935151	−	0.995618i	$-0.470190\pi$
$977$	−406.470	−	132.070i	−0.416039	−	0.135179i	−0.509554	+	0.860439i	$0.670190\pi$
$978$	493.125	+	30.6559i	0.504218	+	0.0313455i
$979$		0			0
$980$		−	225.496i		−	0.230098i
$981$	−640.680	+	1366.80i	−0.653089	+	1.39327i
$982$	492.824	−	358.057i	0.501857	−	0.364620i
$983$	589.855	−	811.865i	0.600056	−	0.825906i	−0.395658	−	0.918398i	$-0.629483\pi$
$983$	589.855	−	811.865i	0.600056	−	0.825906i	0.995713	+	0.0924923i	$0.0294834\pi$
$984$	−524.040	+	134.967i	−0.532561	+	0.137161i
$985$	−83.1642	−	255.953i	−0.0844306	−	0.259851i
$986$	566.315	−	779.465i	0.574356	−	0.790533i
$987$	−375.823	+	238.897i	−0.380773	+	0.242044i
$988$	−115.740	+	356.212i	−0.117146	+	0.360538i
$989$		−	1073.09i		−	1.08503i
$990$		0			0
$991$	862.380			0.870212			0.435106	−	0.900379i	$-0.356711\pi$
$991$	862.380			0.870212			0.435106	+	0.900379i	$0.356711\pi$
$992$	747.330	+	242.822i	0.753357	+	0.244780i
$993$	−269.328	−	423.696i	−0.271227	−	0.426682i
$994$	−44.1002	−	32.0407i	−0.0443664	−	0.0322341i
$995$	694.480	−	225.650i	0.697970	−	0.226784i
$996$	−86.1968	−	334.679i	−0.0865429	−	0.336023i
$997$	230.794	+	167.681i	0.231488	+	0.168186i	0.697483	−	0.716602i	$-0.254303\pi$
$997$	230.794	+	167.681i	0.231488	+	0.168186i	−0.465995	+	0.884788i	$0.654303\pi$
$998$	231.931	+	319.226i	0.232396	+	0.319865i
$999$	−1009.31	−	551.936i	−1.01032	−	0.552489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.m.251.3		16
3.2	odd	2	inner	363.3.h.m.251.2		16
11.2	odd	10		363.3.h.l.245.3		16
11.3	even	5	inner	363.3.h.m.323.3		16
11.4	even	5		33.3.b.b.23.3	yes	4
11.5	even	5	inner	363.3.h.m.269.2		16
11.6	odd	10		363.3.h.l.269.3		16
11.7	odd	10		363.3.b.h.122.2		4
11.8	odd	10		363.3.h.l.323.2		16
11.9	even	5	inner	363.3.h.m.245.2		16
11.10	odd	2		363.3.h.l.251.2		16
33.2	even	10		363.3.h.l.245.2		16
33.5	odd	10	inner	363.3.h.m.269.3		16
33.8	even	10		363.3.h.l.323.3		16
33.14	odd	10	inner	363.3.h.m.323.2		16
33.17	even	10		363.3.h.l.269.2		16
33.20	odd	10	inner	363.3.h.m.245.3		16
33.26	odd	10		33.3.b.b.23.2	✓	4
33.29	even	10		363.3.b.h.122.3		4
33.32	even	2		363.3.h.l.251.3		16
44.15	odd	10		528.3.i.d.353.2		4
132.59	even	10		528.3.i.d.353.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.b.b.23.2	✓	4	33.26	odd	10
33.3.b.b.23.3	yes	4	11.4	even	5
363.3.b.h.122.2		4	11.7	odd	10
363.3.b.h.122.3		4	33.29	even	10
363.3.h.l.245.2		16	33.2	even	10
363.3.h.l.245.3		16	11.2	odd	10
363.3.h.l.251.2		16	11.10	odd	2
363.3.h.l.251.3		16	33.32	even	2
363.3.h.l.269.2		16	33.17	even	10
363.3.h.l.269.3		16	11.6	odd	10
363.3.h.l.323.2		16	11.8	odd	10
363.3.h.l.323.3		16	33.8	even	10
363.3.h.m.245.2		16	11.9	even	5	inner
363.3.h.m.245.3		16	33.20	odd	10	inner
363.3.h.m.251.2		16	3.2	odd	2	inner
363.3.h.m.251.3		16	1.1	even	1	trivial
363.3.h.m.269.2		16	11.5	even	5	inner
363.3.h.m.269.3		16	33.5	odd	10	inner
363.3.h.m.323.2		16	33.14	odd	10	inner
363.3.h.m.323.3		16	11.3	even	5	inner
528.3.i.d.353.1		4	132.59	even	10
528.3.i.d.353.2		4	44.15	odd	10

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.753510 + 0.244830i) q^{2} +(1.60937 + 2.53179i) q^{3} +(-2.72823 - 1.98218i) q^{4} +(-2.40079 + 0.780063i) q^{5} +(0.592816 + 2.30175i) q^{6} +(3.83843 + 2.78878i) q^{7} +(-3.43323 - 4.72544i) q^{8} +(-3.81987 + 8.14914i) q^{9} +O(q^{10})\)	\(q+(0.753510 + 0.244830i) q^{2} +(1.60937 + 2.53179i) q^{3} +(-2.72823 - 1.98218i) q^{4} +(-2.40079 + 0.780063i) q^{5} +(0.592816 + 2.30175i) q^{6} +(3.83843 + 2.78878i) q^{7} +(-3.43323 - 4.72544i) q^{8} +(-3.81987 + 8.14914i) q^{9} -2.00000 q^{10} +(0.627719 - 10.0974i) q^{12} +(-4.16837 + 12.8289i) q^{13} +(2.20952 + 3.04114i) q^{14} +(-5.83870 - 4.82287i) q^{15} +(2.73833 + 8.42770i) q^{16} +(-21.5549 + 7.00360i) q^{17} +(-4.87347 + 5.20524i) q^{18} +(-6.66119 + 4.83964i) q^{19} +(8.09613 + 2.63059i) q^{20} +(-0.883156 + 14.2063i) q^{21} -30.2372i q^{23} +(6.43846 - 16.2972i) q^{24} +(-15.0701 + 10.9491i) q^{25} +(-6.28181 + 8.64617i) q^{26} +(-26.7795 + 3.44386i) q^{27} +(-4.94427 - 15.2169i) q^{28} +(-31.5381 + 43.4085i) q^{29} +(-3.21873 - 5.06357i) q^{30} +(7.99161 - 24.5957i) q^{31} +30.3846i q^{32} -17.9565 q^{34} +(-11.3907 - 3.70106i) q^{35} +(26.5746 - 14.6611i) q^{36} +(34.4690 + 25.0432i) q^{37} +(-6.20416 + 2.01586i) q^{38} +(-39.1885 + 10.0930i) q^{39} +(11.9286 + 8.66664i) q^{40} +(-18.1520 - 24.9840i) q^{41} +(-4.14359 + 10.4883i) q^{42} +35.4891 q^{43} +(2.81386 - 22.5441i) q^{45} +(7.40297 - 22.7840i) q^{46} +(18.3899 + 25.3115i) q^{47} +(-16.9302 + 20.4961i) q^{48} +(-8.18559 - 25.1927i) q^{49} +(-14.0362 + 4.56063i) q^{50} +(-52.4213 - 43.3009i) q^{51} +(36.8015 - 26.7378i) q^{52} +(9.42707 + 3.06304i) q^{53} +(-21.0217 - 3.96143i) q^{54} -27.7128i q^{56} +(-22.9732 - 9.07595i) q^{57} +(-34.3920 + 24.9873i) q^{58} +(36.1628 - 49.7739i) q^{59} +(6.36955 + 24.7313i) q^{60} +(15.8976 + 48.9277i) q^{61} +(12.0435 - 16.5765i) q^{62} +(-37.3885 + 20.6271i) q^{63} +(3.51423 - 10.8157i) q^{64} -34.0511i q^{65} +34.3288 q^{67} +(72.6891 + 23.6181i) q^{68} +(76.5540 - 48.6627i) q^{69} +(-7.67686 - 5.57757i) q^{70} +(-13.7915 + 4.48112i) q^{71} +(51.6228 - 9.92732i) q^{72} +(71.3826 + 51.8625i) q^{73} +(19.8414 + 27.3093i) q^{74} +(-51.9742 - 20.5332i) q^{75} +27.7663 q^{76} +(-32.0000 - 1.98933i) q^{78} +(-28.9485 + 89.0943i) q^{79} +(-13.1483 - 18.0970i) q^{80} +(-51.8171 - 62.2574i) q^{81} +(-7.56083 - 23.2699i) q^{82} +(32.4890 - 10.5563i) q^{83} +(30.5688 - 37.0074i) q^{84} +(46.2854 - 33.6283i) q^{85} +(26.7414 + 8.68881i) q^{86} +(-160.658 - 9.98755i) q^{87} +143.482i q^{89} +(7.63975 - 16.2983i) q^{90} +(-51.7771 + 37.6183i) q^{91} +(-59.9354 + 82.4940i) q^{92} +(75.1324 - 19.3504i) q^{93} +(7.65993 + 23.5748i) q^{94} +(12.2169 - 16.8151i) q^{95} +(-76.9274 + 48.9000i) q^{96} +(-12.4488 + 38.3136i) q^{97} -20.9870i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} + 7 q^{9}+O(q^{10}) \) 16 * q + 5 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 + 7 * q^9	\( 16 q + 5 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} + 7 q^{9} - 32 q^{10} + 56 q^{12} + 8 q^{13} - 13 q^{15} + 22 q^{16} - 38 q^{18} + 36 q^{19} - 152 q^{21} - 24 q^{24} - 86 q^{25} + 20 q^{27} + 64 q^{28} - 10 q^{30} - 46 q^{31} + 448 q^{34} + 86 q^{36} + 90 q^{37} + 56 q^{39} + 36 q^{40} + 68 q^{42} + 384 q^{43} + 68 q^{45} + 88 q^{46} - 110 q^{48} + 60 q^{49} - 214 q^{51} + 136 q^{52} - 704 q^{54} - 144 q^{57} - 216 q^{58} - 56 q^{60} + 24 q^{61} - 158 q^{63} - 34 q^{64} - 232 q^{67} + 253 q^{69} + 8 q^{70} - 72 q^{72} + 284 q^{73} + 124 q^{75} + 720 q^{76} - 512 q^{78} + 76 q^{79} - 113 q^{81} - 40 q^{82} - 80 q^{84} + 68 q^{85} - 1008 q^{87} - 14 q^{90} - 256 q^{91} - 25 q^{93} - 260 q^{94} - 272 q^{96} - 218 q^{97}+O(q^{100}) \) 16 * q + 5 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 + 7 * q^9 - 32 * q^10 + 56 * q^12 + 8 * q^13 - 13 * q^15 + 22 * q^16 - 38 * q^18 + 36 * q^19 - 152 * q^21 - 24 * q^24 - 86 * q^25 + 20 * q^27 + 64 * q^28 - 10 * q^30 - 46 * q^31 + 448 * q^34 + 86 * q^36 + 90 * q^37 + 56 * q^39 + 36 * q^40 + 68 * q^42 + 384 * q^43 + 68 * q^45 + 88 * q^46 - 110 * q^48 + 60 * q^49 - 214 * q^51 + 136 * q^52 - 704 * q^54 - 144 * q^57 - 216 * q^58 - 56 * q^60 + 24 * q^61 - 158 * q^63 - 34 * q^64 - 232 * q^67 + 253 * q^69 + 8 * q^70 - 72 * q^72 + 284 * q^73 + 124 * q^75 + 720 * q^76 - 512 * q^78 + 76 * q^79 - 113 * q^81 - 40 * q^82 - 80 * q^84 + 68 * q^85 - 1008 * q^87 - 14 * q^90 - 256 * q^91 - 25 * q^93 - 260 * q^94 - 272 * q^96 - 218 * q^97

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