LMFDB - Embedded newform 363.3.h.m.251.2

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			251.2
Root			$-0.144291 - 1.72603i$ of defining polynomial
Character	$\chi$	$=$	363.251
Dual form			363.3.h.m.269.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.753510 - 0.244830i) q^{2} +(-1.91055 - 2.31296i) q^{3} +(-2.72823 - 1.98218i) q^{4} +(2.40079 - 0.780063i) q^{5} +(0.873334 + 2.21060i) q^{6} +(3.83843 + 2.78878i) q^{7} +(3.43323 + 4.72544i) q^{8} +(-1.69960 + 8.83806i) q^{9} +O(q^{10})$	\(q+(-0.753510 - 0.244830i) q^{2} +(-1.91055 - 2.31296i) q^{3} +(-2.72823 - 1.98218i) q^{4} +(2.40079 - 0.780063i) q^{5} +(0.873334 + 2.21060i) q^{6} +(3.83843 + 2.78878i) q^{7} +(3.43323 + 4.72544i) q^{8} +(-1.69960 + 8.83806i) q^{9} -2.00000 q^{10} +(0.627719 + 10.0974i) q^{12} +(-4.16837 + 12.8289i) q^{13} +(-2.20952 - 3.04114i) q^{14} +(-6.39108 - 4.06259i) q^{15} +(2.73833 + 8.42770i) q^{16} +(21.5549 - 7.00360i) q^{17} +(3.44449 - 6.24345i) q^{18} +(-6.66119 + 4.83964i) q^{19} +(-8.09613 - 2.63059i) q^{20} +(-0.883156 - 14.2063i) q^{21} +30.2372i q^{23} +(4.37041 - 16.9691i) q^{24} +(-15.0701 + 10.9491i) q^{25} +(6.28181 - 8.64617i) q^{26} +(23.6893 - 12.9544i) q^{27} +(-4.94427 - 15.2169i) q^{28} +(31.5381 - 43.4085i) q^{29} +(3.82110 + 4.62593i) q^{30} +(7.99161 - 24.5957i) q^{31} -30.3846i q^{32} -17.9565 q^{34} +(11.3907 + 3.70106i) q^{35} +(22.1555 - 20.7434i) q^{36} +(34.4690 + 25.0432i) q^{37} +(6.20416 - 2.01586i) q^{38} +(37.6367 - 14.8690i) q^{39} +(11.9286 + 8.66664i) q^{40} +(18.1520 + 24.9840i) q^{41} +(-2.81265 + 10.9208i) q^{42} +35.4891 q^{43} +(2.81386 + 22.5441i) q^{45} +(7.40297 - 22.7840i) q^{46} +(-18.3899 - 25.3115i) q^{47} +(14.2613 - 22.4352i) q^{48} +(-8.18559 - 25.1927i) q^{49} +(14.0362 - 4.56063i) q^{50} +(-57.3807 - 36.4749i) q^{51} +(36.8015 - 26.7378i) q^{52} +(-9.42707 - 3.06304i) q^{53} +(-21.0217 + 3.96143i) q^{54} +27.7128i q^{56} +(23.9205 + 6.16073i) q^{57} +(-34.3920 + 24.9873i) q^{58} +(-36.1628 + 49.7739i) q^{59} +(9.38359 + 23.7519i) q^{60} +(15.8976 + 48.9277i) q^{61} +(-12.0435 + 16.5765i) q^{62} +(-31.1713 + 29.1845i) q^{63} +(3.51423 - 10.8157i) q^{64} +34.0511i q^{65} +34.3288 q^{67} +(-72.6891 - 23.6181i) q^{68} +(69.9374 - 57.7696i) q^{69} +(-7.67686 - 5.57757i) q^{70} +(13.7915 - 4.48112i) q^{71} +(-47.5988 + 22.3117i) q^{72} +(71.3826 + 51.8625i) q^{73} +(-19.8414 - 27.3093i) q^{74} +(54.1171 + 13.9379i) q^{75} +27.7663 q^{76} +(-32.0000 + 1.98933i) q^{78} +(-28.9485 + 89.0943i) q^{79} +(13.1483 + 18.0970i) q^{80} +(-75.2227 - 30.0424i) q^{81} +(-7.56083 - 23.2699i) q^{82} +(-32.4890 + 10.5563i) q^{83} +(-25.7499 + 40.5086i) q^{84} +(46.2854 - 33.6283i) q^{85} +(-26.7414 - 8.68881i) q^{86} +(-160.658 + 9.98755i) q^{87} -143.482i q^{89} +(3.39921 - 17.6761i) q^{90} +(-51.7771 + 37.6183i) q^{91} +(59.9354 - 82.4940i) q^{92} +(-72.1572 + 28.5069i) q^{93} +(7.65993 + 23.5748i) q^{94} +(-12.2169 + 16.8151i) q^{95} +(-70.2785 + 58.0513i) 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	0.114517	−	0.993421i	$-0.463468\pi$
$2$	−0.753510	−	0.244830i	−0.376755	−	0.122415i	−0.491272	+	0.871006i	$0.663468\pi$
$3$	−1.91055	−	2.31296i	−0.636850	−	0.770988i
$3$	−1.91055	−	2.31296i	−0.636850	−	0.770988i
$4$	−2.72823	−	1.98218i	−0.682058	−	0.495544i
$5$	2.40079	−	0.780063i	0.480158	−	0.156013i	−0.0589304	−	0.998262i	$-0.518769\pi$
$5$	2.40079	−	0.780063i	0.480158	−	0.156013i	0.539088	+	0.842249i	$0.318769\pi$
$6$	0.873334	+	2.21060i	0.145556	+	0.368433i
$7$	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
$9$	−1.69960	+	8.83806i	−0.188845	+	0.982007i
$10$	−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
$15$	−6.39108	−	4.06259i	−0.426072	−	0.270839i
$16$	2.73833	+	8.42770i	0.171145	+	0.526731i
$17$	21.5549	−	7.00360i	1.26793	−	0.411977i	0.403619	−	0.914927i	$-0.367752\pi$
$17$	21.5549	−	7.00360i	1.26793	−	0.411977i	0.864315	+	0.502951i	$0.167752\pi$
$18$	3.44449	−	6.24345i	0.191361	−	0.346858i
$19$	−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	$0.228314\pi$
$23$			30.2372i			1.31466i	−0.753603	+	0.657329i	$0.771686\pi$
$24$	4.37041	−	16.9691i	0.182100	−	0.707047i
$25$	−15.0701	+	10.9491i	−0.602806	+	0.437964i
$26$	6.28181	−	8.64617i	0.241608	−	0.332545i
$27$	23.6893	−	12.9544i	0.877381	−	0.479794i
$28$	−4.94427	−	15.2169i	−0.176581	−	0.543461i
$29$	31.5381	−	43.4085i	1.08752	−	1.49685i	0.236562	−	0.971616i	$-0.423979\pi$
$29$	31.5381	−	43.4085i	1.08752	−	1.49685i	0.850960	−	0.525230i	$-0.176021\pi$
$30$	3.82110	+	4.62593i	0.127370	+	0.154198i
$31$	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
$36$	22.1555	−	20.7434i	0.615431	−	0.576205i
$37$	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
$39$	37.6367	−	14.8690i	0.965044	−	0.381256i
$40$	11.9286	+	8.66664i	0.298215	+	0.216666i
$41$	18.1520	+	24.9840i	0.442731	+	0.609367i	0.970816	−	0.239825i	$-0.0770899\pi$
$41$	18.1520	+	24.9840i	0.442731	+	0.609367i	−0.528085	+	0.849191i	$0.677090\pi$
$42$	−2.81265	+	10.9208i	−0.0669680	+	0.260019i
$43$	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	0.567253	−	0.823543i	$-0.308006\pi$
$47$	−18.3899	−	25.3115i	−0.391274	−	0.538542i	−0.958527	+	0.285001i	$0.908006\pi$
$48$	14.2613	−	22.4352i	0.297110	−	0.467400i
$49$	−8.18559	−	25.1927i	−0.167053	−	0.514136i
$50$	14.0362	−	4.56063i	0.280723	−	0.0912125i
$51$	−57.3807	−	36.4749i	−1.12511	−	0.715195i
$52$	36.8015	−	26.7378i	0.707721	−	0.514189i
$53$	−9.42707	−	3.06304i	−0.177869	−	0.0577932i	0.218728	−	0.975786i	$-0.429809\pi$
$53$	−9.42707	−	3.06304i	−0.177869	−	0.0577932i	−0.396598	+	0.917993i	$0.629809\pi$
$54$	−21.0217	+	3.96143i	−0.389292	+	0.0733599i
$55$		0			0
$56$			27.7128i			0.494872i
$57$	23.9205	+	6.16073i	0.419657	+	0.108083i
$58$	−34.3920	+	24.9873i	−0.592966	+	0.430815i
$59$	−36.1628	+	49.7739i	−0.612929	+	0.843625i	−0.996814	−	0.0797561i	$-0.974586\pi$
$59$	−36.1628	+	49.7739i	−0.612929	+	0.843625i	0.383885	+	0.923381i	$0.374586\pi$
$60$	9.38359	+	23.7519i	0.156393	+	0.395866i
$61$	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
$63$	−31.1713	+	29.1845i	−0.494782	+	0.463246i
$64$	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
$69$	69.9374	−	57.7696i	1.01359	−	0.837240i
$70$	−7.67686	−	5.57757i	−0.109669	−	0.0796795i
$71$	13.7915	−	4.48112i	0.194246	−	0.0631144i	−0.210278	−	0.977642i	$-0.567437\pi$
$71$	13.7915	−	4.48112i	0.194246	−	0.0631144i	0.404525	+	0.914527i	$0.367437\pi$
$72$	−47.5988	+	22.3117i	−0.661095	+	0.309885i
$73$	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
$75$	54.1171	+	13.9379i	0.721562	+	0.185839i
$76$	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
$81$	−75.2227	−	30.0424i	−0.928675	−	0.370894i
$82$	−7.56083	−	23.2699i	−0.0922053	−	0.283779i
$83$	−32.4890	+	10.5563i	−0.391433	+	0.127184i	−0.498120	−	0.867108i	$-0.665976\pi$
$83$	−32.4890	+	10.5563i	−0.391433	+	0.127184i	0.106686	+	0.994293i	$0.465976\pi$
$84$	−25.7499	+	40.5086i	−0.306546	+	0.482245i
$85$	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	$-0.701584\pi$
$89$		−	143.482i		−	1.61216i	0.591805	−	0.806081i	$-0.298416\pi$
$90$	3.39921	−	17.6761i	0.0377690	−	0.196401i
$91$	−51.7771	+	37.6183i	−0.568979	+	0.413387i
$92$	59.9354	−	82.4940i	0.651472	−	0.896674i
$93$	−72.1572	+	28.5069i	−0.775884	+	0.306526i
$94$	7.65993	+	23.5748i	0.0814886	+	0.250796i
$95$	−12.2169	+	16.8151i	−0.128599	+	0.177001i
$96$	−70.2785	+	58.0513i	−0.732068	+	0.604701i
$97$	−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	0.711224	−	0.702965i	$-0.248141\pi$
$101$	88.2159	+	28.6631i	0.873425	+	0.283793i	0.162200	+	0.986758i	$0.448141\pi$
$102$	34.3068	+	41.5327i	0.336341	+	0.407184i
$103$	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
$105$	−13.2021	−	33.4173i	−0.125734	−	0.318260i
$106$	6.35346	+	4.61606i	0.0599383	+	0.0435477i
$107$	−49.6256	−	68.3037i	−0.463790	−	0.638353i	0.511499	−	0.859284i	$-0.329090\pi$
$107$	−49.6256	−	68.3037i	−0.463790	−	0.638353i	−0.975289	+	0.220931i	$0.929090\pi$
$108$	−90.3079	−	11.6137i	−0.836184	−	0.107534i
$109$	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	0.998743	−	0.0501267i	$-0.0159625\pi$
$113$	72.5958	+	99.9196i	0.642441	+	0.884244i	−0.356302	+	0.934371i	$0.615963\pi$
$114$	−16.5160	−	10.4986i	−0.144877	−	0.0920931i
$115$	23.5869	+	72.5930i	0.205103	+	0.631243i
$116$	−172.087	+	55.9144i	−1.48351	+	0.482021i
$117$	−106.298	−	58.6444i	−0.908532	−	0.501234i
$118$	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
$123$	23.1069	−	89.7181i	0.187861	−	0.729415i
$124$	−70.5559	+	51.2619i	−0.569000	+	0.413402i
$125$	−64.7334	+	89.0979i	−0.517867	+	0.712783i
$126$	30.6331	−	14.3591i	0.243120	−	0.113961i
$127$	−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
$129$	−67.8037	−	82.0851i	−0.525610	−	0.636318i
$130$	8.33674	−	25.6578i	0.0641288	−	0.197368i
$131$			125.997i			0.961811i	0.876772	+	0.480906i	$0.159692\pi$
$131$			125.997i			0.961811i	−0.876772	+	0.480906i	$0.840308\pi$
$132$		0			0
$133$	−39.0652			−0.293724
$134$	−25.8671	−	8.40472i	−0.193038	−	0.0627218i
$135$	46.7677	−	49.5800i	0.346427	−	0.367259i
$136$	107.098	+	77.8112i	0.787485	+	0.572141i
$137$	−56.4118	+	18.3293i	−0.411765	+	0.133791i	−0.507572	−	0.861609i	$-0.669457\pi$
$137$	−56.4118	+	18.3293i	−0.411765	+	0.133791i	0.0958068	+	0.995400i	$0.469457\pi$
$138$	−66.8423	+	26.4071i	−0.484364	+	0.191356i
$139$	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
$141$	−23.4098	+	90.8940i	−0.166027	+	0.644638i
$142$	−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
$147$	−42.6307	+	67.0648i	−0.290005	+	0.456223i
$148$	−44.3993	−	136.647i	−0.299996	−	0.923292i
$149$	70.6927	−	22.9695i	0.474448	−	0.154157i	−0.0620259	−	0.998075i	$-0.519756\pi$
$149$	70.6927	−	22.9695i	0.474448	−	0.154157i	0.536474	+	0.843917i	$0.319756\pi$
$150$	−37.3654	−	23.7518i	−0.249102	−	0.158346i
$151$	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
$156$	−132.155	−	34.0365i	−0.847145	−	0.218183i
$157$	−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
$159$	10.9262	+	27.6565i	0.0687181	+	0.173941i
$160$	−23.7019	−	72.9470i	−0.148137	−	0.455919i
$161$	−84.3249	+	116.063i	−0.523757	+	0.720890i
$162$	49.3257	+	41.0540i	0.304480	+	0.253420i
$163$	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	0.483297	−	0.875456i	$-0.339439\pi$
$167$	60.0719	+	19.5185i	0.359712	+	0.116878i	−0.123585	+	0.992334i	$0.539439\pi$
$168$	64.0987	−	52.9467i	0.381540	−	0.315159i
$169$	−10.4820	−	7.61564i	−0.0620238	−	0.0450630i
$170$	−43.1098	+	14.0072i	−0.253587	+	0.0823953i
$171$	−31.4517	−	67.0975i	−0.183928	−	0.392383i
$172$	−96.8226	−	70.3457i	−0.562922	−	0.408987i
$173$	113.654	+	156.431i	0.656957	+	0.904223i	0.999376	−	0.0353239i	$-0.0112463\pi$
$173$	113.654	+	156.431i	0.656957	+	0.904223i	−0.342419	+	0.939547i	$0.611246\pi$
$174$	123.502	+	31.8081i	0.709783	+	0.182805i
$175$	−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	0.755058	−	0.655658i	$-0.227609\pi$
$179$	−18.2285	−	25.0894i	−0.101835	−	0.140164i	−0.856893	+	0.515494i	$0.827609\pi$
$180$	37.0096	−	67.0832i	0.205609	−	0.372684i
$181$	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
$183$	82.7949	−	130.249i	0.452431	−	0.711745i
$184$	−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
$189$	127.057	+	16.3396i	0.672258	+	0.0864531i
$190$	13.3224	−	9.67928i	0.0701178	−	0.0509436i
$191$	−40.8438	+	56.2167i	−0.213842	+	0.294328i	−0.902440	−	0.430815i	$-0.858226\pi$
$191$	−40.8438	+	56.2167i	−0.213842	+	0.294328i	0.688599	+	0.725143i	$0.258226\pi$
$192$	−31.7304	+	12.5356i	−0.165262	+	0.0652896i
$193$	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
$195$	78.7590	−	65.0563i	0.403892	−	0.333622i
$196$	−27.6041	+	84.9567i	−0.140837	+	0.433453i
$197$		−	106.612i		−	0.541178i	−0.962695	−	0.270589i	$-0.912782\pi$
$197$		−	106.612i		−	0.541178i	0.962695	−	0.270589i	$-0.0872185\pi$
$198$		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
$201$	−65.5868	−	79.4012i	−0.326303	−	0.395031i
$202$	−59.4540	−	43.1958i	−0.294326	−	0.213841i
$203$	242.114	−	78.6676i	1.19268	−	0.387525i
$204$	84.2482	+	213.251i	0.412982	+	1.04535i
$205$	63.0681	+	45.8217i	0.307649	+	0.223520i
$206$	−9.11649	−	12.5478i	−0.0442548	−	0.0609115i
$207$	−267.238	−	51.3912i	−1.29100	−	0.248267i
$208$	−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
$213$	−36.7140	−	23.3378i	−0.172366	−	0.109567i
$214$	20.6705	+	63.6174i	0.0965913	+	0.297277i
$215$	85.2019	−	27.6838i	0.396288	−	0.128762i
$216$	142.546	+	67.4667i	0.659936	+	0.312346i
$217$	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
$222$	−25.2575	+	98.0681i	−0.113773	+	0.441748i
$223$	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
$225$	−71.1555	−	151.800i	−0.316247	−	0.674667i
$226$	−30.2383	−	93.0640i	−0.133798	−	0.411788i
$227$	250.596	−	344.915i	1.10395	−	1.51945i	0.273896	−	0.961759i	$-0.411688\pi$
$227$	250.596	−	344.915i	1.10395	−	1.51945i	0.830049	−	0.557691i	$-0.188312\pi$
$228$	−53.0489	−	64.2225i	−0.232671	−	0.281678i
$229$	−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	0.640372	−	0.768065i	$-0.278780\pi$
$233$	164.728	+	53.5233i	0.706986	+	0.229714i	0.0666145	+	0.997779i	$0.478780\pi$
$234$	65.7388	+	70.2141i	0.280935	+	0.300060i
$235$	−63.8947	−	46.4223i	−0.271893	−	0.197541i
$236$	197.321	−	64.1135i	0.836107	−	0.271668i
$237$	261.379	−	103.262i	1.10287	−	0.435706i
$238$	−68.9248	−	50.0768i	−0.289600	−	0.210407i
$239$	−94.8081	−	130.492i	−0.396687	−	0.545992i	0.563222	−	0.826306i	$-0.309562\pi$
$239$	−94.8081	−	130.492i	−0.396687	−	0.545992i	−0.959909	+	0.280313i	$0.909562\pi$
$240$	16.7374	−	64.9868i	0.0697391	−	0.270778i
$241$	−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
$246$	−39.3770	+	61.9461i	−0.160069	+	0.251814i
$247$	−34.3210	−	105.629i	−0.138952	−	0.427649i
$248$	143.662	−	46.6787i	0.579284	−	0.188221i
$249$	86.4881	+	54.9775i	0.347342	+	0.220793i
$250$	70.5911	−	51.2875i	0.282365	−	0.205150i
$251$	64.1886	+	20.8561i	0.255731	+	0.0830922i	0.434077	−	0.900876i	$-0.357075\pi$
$251$	64.1886	+	20.8561i	0.255731	+	0.0830922i	−0.178346	+	0.983968i	$0.557075\pi$
$252$	142.891	−	17.8351i	0.567029	−	0.0707741i
$253$		0			0
$254$			102.084i			0.401907i
$255$	−166.212	−	42.8079i	−0.651811	−	0.167874i
$256$	46.8767	−	34.0580i	0.183112	−	0.133039i
$257$	86.2117	−	118.660i	0.335454	−	0.461713i	−0.607653	−	0.794203i	$-0.707889\pi$
$257$	86.2117	−	118.660i	0.335454	−	0.461713i	0.943107	+	0.332490i	$0.107889\pi$
$258$	30.9939	+	78.4523i	0.120131	+	0.304079i
$259$	62.4668	+	192.253i	0.241184	+	0.742289i
$260$	67.4953	−	92.8994i	0.259597	−	0.357305i
$261$	330.045	+	352.513i	1.26454	+	1.35063i
$262$	30.8479	−	94.9402i	0.117740	−	0.362367i
$263$		−	146.192i		−	0.555863i	−0.960601	−	0.277932i	$-0.910351\pi$
$263$		−	146.192i		−	0.555863i	0.960601	−	0.277932i	$-0.0896488\pi$
$264$		0			0
$265$	−25.0217			−0.0944217
$266$	29.4360	+	9.56435i	0.110662	+	0.0359562i
$267$	−331.870	+	274.130i	−1.24296	+	1.02671i
$268$	−93.6569	−	68.0457i	−0.349466	−	0.253902i
$269$	−54.2199	+	17.6171i	−0.201561	+	0.0654912i	−0.408058	−	0.912956i	$-0.633794\pi$
$269$	−54.2199	+	17.6171i	−0.201561	+	0.0654912i	0.206497	+	0.978447i	$0.433794\pi$
$270$	−47.3786	+	25.9089i	−0.175476	+	0.0959587i
$271$	−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
$273$	185.932	+	47.8870i	0.681071	+	0.175410i
$274$	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
$279$	203.795	+	112.433i	0.730449	+	0.402987i
$280$	21.6177	+	66.5326i	0.0772062	+	0.237616i
$281$	193.994	−	63.0324i	0.690370	−	0.224315i	0.0572400	−	0.998360i	$-0.481770\pi$
$281$	193.994	−	63.0324i	0.690370	−	0.224315i	0.633130	+	0.774046i	$0.281770\pi$
$282$	39.8931	−	62.7581i	0.141465	−	0.222546i
$283$	−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
$288$	268.541	+	51.6418i	0.932435	+	0.179312i
$289$	181.756	−	132.054i	0.628914	−	0.456933i
$290$	−63.0763	+	86.8171i	−0.217504	+	0.299369i
$291$	112.402	−	44.4063i	0.386261	−	0.152599i
$292$	−91.9476	−	282.986i	−0.314889	−	0.969129i
$293$	5.49977	−	7.56978i	0.0187705	−	0.0258354i	−0.799529	−	0.600628i	$-0.794917\pi$
$293$	5.49977	−	7.56978i	0.0187705	−	0.0258354i	0.818299	+	0.574793i	$0.194917\pi$
$294$	48.5421	−	40.0967i	0.165109	−	0.136383i
$295$	−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
$300$	−120.017	−	145.296i	−0.400056	−	0.484319i
$301$	136.223	+	98.9715i	0.452567	+	0.328809i
$302$	−4.69714	+	1.52619i	−0.0155535	+	0.00505362i
$303$	−102.244	−	258.802i	−0.337439	−	0.854133i
$304$	−59.0275	−	42.8860i	−0.194170	−	0.141072i
$305$	76.3334	+	105.064i	0.250273	+	0.344472i
$306$	30.5189	−	158.701i	0.0997351	−	0.518630i
$307$	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	$-0.990377\pi$
$311$	−223.738	−	307.949i	−0.719416	−	0.990191i	0.280127	−	0.959963i	$-0.409623\pi$
$312$	199.478	+	126.801i	0.639353	+	0.406414i
$313$	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
$315$	−52.0699	+	94.3813i	−0.165301	+	0.299623i
$316$	255.579	−	185.689i	0.808794	−	0.587623i
$317$	−69.6617	−	22.6345i	−0.219753	−	0.0714021i	0.197071	−	0.980389i	$-0.436857\pi$
$317$	−69.6617	−	22.6345i	−0.219753	−	0.0714021i	−0.416824	+	0.908987i	$0.636857\pi$
$318$	−1.46182	−	23.5145i	−0.00459692	−	0.0739451i
$319$		0			0
$320$		−	28.7075i		−	0.0897109i
$321$	−63.1720	+	245.280i	−0.196797	+	0.764111i
$322$	91.9554	−	66.8095i	0.285576	−	0.207483i
$323$	−109.686	+	150.970i	−0.339586	+	0.467400i
$324$	145.676	+	231.067i	0.449616	+	0.713171i
$325$	−77.6472	−	238.974i	−0.238914	−	0.735303i
$326$	−96.8037	+	133.239i	−0.296944	+	0.408708i
$327$	−320.443	−	387.937i	−0.979947	−	1.18635i
$328$	−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
$333$	−279.917	+	262.075i	−0.840590	+	0.787013i
$334$	−40.4860	−	29.4148i	−0.121216	−	0.0880684i
$335$	82.4161	−	26.7786i	0.246018	−	0.0799362i
$336$	117.308	−	46.3443i	0.349130	−	0.137930i
$337$	−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
$339$	92.4125	−	358.813i	0.272603	−	1.05844i
$340$	−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
$345$	122.841	−	193.248i	0.356061	−	0.560139i
$346$	−47.3401	−	145.698i	−0.136821	−	0.421092i
$347$	−490.113	+	159.247i	−1.41243	+	0.458926i	−0.913189	−	0.407537i	$-0.866388\pi$
$347$	−490.113	+	159.247i	−1.41243	+	0.458926i	−0.499241	+	0.866463i	$0.666388\pi$
$348$	458.108	+	291.203i	1.31640	+	0.836791i
$349$	−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	$-0.822335\pi$
$353$		−	373.911i		−	1.05924i	0.848236	−	0.529619i	$-0.177665\pi$
$354$	−141.612	−	36.4724i	−0.400035	−	0.103029i
$355$	29.6149	−	21.5164i	0.0834221	−	0.0606097i
$356$	−284.408	+	391.454i	−0.798898	+	1.09959i
$357$	−118.531	−	300.029i	−0.332021	−	0.840417i
$358$	7.59272	+	23.3680i	0.0212087	+	0.0652737i
$359$	−63.9874	+	88.0711i	−0.178238	+	0.245324i	−0.888783	−	0.458328i	$-0.848448\pi$
$359$	−63.9874	+	88.0711i	−0.178238	+	0.245324i	0.710545	+	0.703652i	$0.248448\pi$
$360$	−96.8702	+	90.6959i	−0.269084	+	0.251933i
$361$	−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
$366$	−94.2757	+	77.8734i	−0.257584	+	0.212769i
$367$	−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
$369$	−251.662	+	117.965i	−0.682010	+	0.319689i
$370$	−68.9379	−	50.0863i	−0.186319	−	0.135368i
$371$	−27.6430	−	38.0473i	−0.0745094	−	0.102553i
$372$	253.367	+	65.2550i	0.681095	+	0.175417i
$373$	−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
$378$	−91.7381	−	43.4194i	−0.242693	−	0.114866i
$379$	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
$381$	−207.363	+	326.215i	−0.544261	+	0.856207i
$382$	44.5397	−	32.3600i	0.116596	−	0.0847121i
$383$	−342.256	−	111.206i	−0.893619	−	0.290354i	−0.174018	−	0.984742i	$-0.555675\pi$
$383$	−342.256	−	111.206i	−0.893619	−	0.290354i	−0.719601	+	0.694388i	$0.755675\pi$
$384$	390.891	−	24.3004i	1.01795	−	0.0632823i
$385$		0			0
$386$		−	215.110i		−	0.557280i
$387$	−60.3175	+	313.655i	−0.155859	+	0.810478i
$388$	109.908	−	79.8526i	0.283267	−	0.205806i
$389$	367.096	−	505.264i	0.943691	−	1.29888i	−0.0105826	−	0.999944i	$-0.503369\pi$
$389$	367.096	−	505.264i	0.943691	−	1.29888i	0.954273	−	0.298935i	$-0.0966314\pi$
$390$	−75.2734	+	29.7380i	−0.193009	+	0.0762513i
$391$	211.769	+	651.758i	0.541609	+	1.66690i
$392$	90.9433	−	125.173i	0.231998	−	0.319318i
$393$	291.427	−	240.724i	0.741545	−	0.612529i
$394$	−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
$399$	74.6361	+	90.3565i	0.187058	+	0.226457i
$400$	−133.543	−	97.0244i	−0.333857	−	0.242561i
$401$	−751.433	+	244.155i	−1.87390	+	0.608867i	−0.883922	+	0.467635i	$0.845106\pi$
$401$	−751.433	+	244.155i	−1.87390	+	0.608867i	−0.989977	+	0.141232i	$0.954894\pi$
$402$	29.9805	+	75.8872i	0.0745783	+	0.188774i
$403$	282.224	+	205.048i	0.700307	+	0.508803i
$404$	−183.858	−	253.059i	−0.455095	−	0.626384i
$405$	−204.029	−	13.4470i	−0.503775	−	0.0332025i
$406$	−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
$411$	150.173	+	95.4595i	0.365384	+	0.232262i
$412$	−20.4001	−	62.7851i	−0.0495149	−	0.152391i
$413$	−277.617	+	90.2033i	−0.672196	+	0.218410i
$414$	188.784	+	104.152i	0.456000	+	0.251574i
$415$	−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	$-0.869345\pi$
$419$		−	334.392i		−	0.798073i	0.916935	−	0.399036i	$-0.130655\pi$
$420$	−30.2207	+	117.339i	−0.0719542	+	0.279379i
$421$	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
$423$	254.960	−	119.511i	0.602742	−	0.282533i
$424$	−17.8911	−	55.0631i	−0.0421960	−	0.129866i
$425$	−248.152	+	341.552i	−0.583887	+	0.803651i
$426$	21.9505	+	26.5739i	0.0515271	+	0.0623801i
$427$	−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	−0.758282	−	0.651927i	$-0.773961\pi$
$431$	−756.378	−	245.762i	−1.75494	−	0.570214i	−0.996656	+	0.0817130i	$0.973961\pi$
$432$	174.045	+	164.173i	0.402882	+	0.380030i
$433$	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
$435$	−377.914	+	149.301i	−0.868767	+	0.343221i
$436$	−457.587	−	332.456i	−1.04951	−	0.762515i
$437$	−146.337	−	201.416i	−0.334867	−	0.460905i
$438$	−52.3064	+	203.092i	−0.119421	+	0.463679i
$439$	−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	0.766228	−	0.642569i	$-0.222131\pi$
$443$	−36.1793	−	49.7965i	−0.0816689	−	0.112408i	−0.847897	+	0.530161i	$0.822131\pi$
$444$	−231.233	+	363.765i	−0.520795	+	0.819291i
$445$	−111.925	−	344.471i	−0.251518	−	0.774092i
$446$	−171.597	+	55.7554i	−0.384748	+	0.125012i
$447$	−188.189	−	119.625i	−0.421005	−	0.267618i
$448$	43.6517	−	31.7148i	0.0974369	−	0.0707920i
$449$	−130.706	−	42.4691i	−0.291105	−	0.0945859i	0.159824	−	0.987146i	$-0.448907\pi$
$449$	−130.706	−	42.4691i	−0.291105	−	0.0945859i	−0.450929	+	0.892560i	$0.648907\pi$
$450$	16.4512	+	131.804i	0.0365582	+	0.292897i
$451$		0			0
$452$		−	416.502i		−	0.921464i
$453$	−18.1101	−	4.66426i	−0.0399781	−	0.0102964i
$454$	−273.272	+	198.544i	−0.601920	+	0.437321i
$455$	−94.9612	+	130.703i	−0.208706	+	0.287259i
$456$	53.0123	+	134.186i	0.116255	+	0.294267i
$457$	−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
$459$	419.892	−	445.142i	0.914798	−	0.969807i
$460$	79.5416	−	244.804i	0.172917	−	0.532183i
$461$			528.162i			1.14569i	0.819664	+	0.572844i	$0.194160\pi$
$461$			528.162i			1.14569i	−0.819664	+	0.572844i	$0.805840\pi$
$462$		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
$465$	−150.997	+	124.726i	−0.324725	+	0.268228i
$466$	−111.020	−	80.6607i	−0.238240	−	0.173092i
$467$	341.492	−	110.958i	0.731247	−	0.237597i	0.0803544	−	0.996766i	$-0.474395\pi$
$467$	341.492	−	110.958i	0.731247	−	0.237597i	0.650893	+	0.759170i	$0.274395\pi$
$468$	173.763	+	370.697i	0.371288	+	0.792089i
$469$	131.769	+	95.7356i	0.280957	+	0.204127i
$470$	36.7797	+	50.6230i	0.0782548	+	0.107708i
$471$	287.022	+	73.9227i	0.609388	+	0.156948i
$472$	−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
$477$	43.0936	−	78.1110i	0.0903430	−	0.163755i
$478$	39.4904	+	121.539i	0.0826159	+	0.254266i
$479$	−549.141	+	178.427i	−1.14643	+	0.372498i	−0.819798	−	0.572653i	$-0.805914\pi$
$479$	−549.141	+	178.427i	−1.14643	+	0.372498i	−0.326633	+	0.945151i	$0.605914\pi$
$480$	−123.440	+	194.191i	−0.257167	+	0.404564i
$481$	−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
$486$	0.717239	−	192.524i	0.00147580	−	0.396141i
$487$	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
$489$	−579.987	+	229.134i	−1.18607	+	0.468576i
$490$	16.3712	+	50.3853i	0.0334106	+	0.102827i
$491$	−451.929	+	622.027i	−0.920425	+	1.26686i	0.0430540	+	0.999073i	$0.486291\pi$
$491$	−451.929	+	622.027i	−0.920425	+	1.26686i	−0.963479	+	0.267784i	$0.913709\pi$
$492$	−240.878	+	198.970i	−0.489590	+	0.404410i
$493$	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
$498$	−51.7095	−	62.6009i	−0.103834	−	0.125705i
$499$	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
$501$	−69.6246	−	176.235i	−0.138971	−	0.351767i
$502$	−43.2605	−	31.4306i	−0.0861763	−	0.0626108i
$503$	−100.227	−	137.950i	−0.199258	−	0.274255i	0.697682	−	0.716408i	$-0.254215\pi$
$503$	−100.227	−	137.950i	−0.199258	−	0.274255i	−0.896940	+	0.442153i	$0.854215\pi$
$504$	−244.928	−	47.1008i	−0.485967	−	0.0934540i
$505$	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	0.977865	−	0.209237i	$-0.0670979\pi$
$509$	242.636	+	333.960i	0.476692	+	0.656110i	−0.501173	+	0.865347i	$0.667098\pi$
$510$	114.761	+	72.9498i	0.225022	+	0.143039i
$511$	129.364	+	398.141i	0.253158	+	0.779141i
$512$	452.976	−	147.181i	0.884719	−	0.287463i
$513$	−95.1042	+	200.940i	−0.185388	+	0.391695i
$514$	−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
$519$	144.678	−	561.745i	0.278763	−	1.08236i
$520$	−160.906	+	116.905i	−0.309435	+	0.224818i
$521$	−65.4029	+	90.0193i	−0.125533	+	0.172782i	−0.867158	−	0.498033i	$-0.834056\pi$
$521$	−65.4029	+	90.0193i	−0.125533	+	0.172782i	0.741624	+	0.670815i	$0.234056\pi$
$522$	−162.386	−	346.427i	−0.311085	−	0.663654i
$523$	−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
$525$	168.855	+	204.421i	0.321629	+	0.389373i
$526$	−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
$531$	−378.442	−	404.205i	−0.712697	−	0.761215i
$532$	106.579	+	77.4342i	0.200337	+	0.145553i
$533$	−396.182	+	128.727i	−0.743306	+	0.241515i
$534$	317.183	−	125.308i	0.593975	−	0.234659i
$535$	−172.422	−	125.272i	−0.322284	−	0.234153i
$536$	117.859	+	162.219i	0.219886	+	0.302647i
$537$	−23.2044	+	90.0964i	−0.0432112	+	0.167777i
$538$	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
$543$	164.379	−	258.593i	0.302723	−	0.476230i
$544$	−212.802	−	654.937i	−0.391180	−	1.20393i
$545$	402.667	−	130.834i	0.738838	−	0.240063i
$546$	−128.378	−	81.6052i	−0.235124	−	0.149460i
$547$	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
$552$	513.098	+	132.149i	0.929525	+	0.239400i
$553$	−359.582	+	261.251i	−0.650238	+	0.472426i
$554$	−110.033	+	151.447i	−0.198616	+	0.273371i
$555$	−118.554	−	300.086i	−0.213611	−	0.540695i
$556$	−136.446	−	419.938i	−0.245407	−	0.755284i
$557$	190.382	−	262.038i	0.341798	−	0.470445i	−0.603167	−	0.797615i	$-0.706095\pi$
$557$	190.382	−	262.038i	0.341798	−	0.470445i	0.944966	+	0.327170i	$0.106095\pi$
$558$	−126.035	−	134.615i	−0.225869	−	0.241245i
$559$	−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	−0.140755	−	0.990044i	$-0.544953\pi$
$563$	−470.984	−	153.032i	−0.836562	−	0.271815i	−0.695807	+	0.718229i	$0.744953\pi$
$564$	244.035	−	201.577i	0.432687	−	0.357407i
$565$	252.231	+	183.256i	0.446426	+	0.324348i
$566$	361.091	−	117.326i	0.637970	−	0.207289i
$567$	−204.955	−	325.096i	−0.361473	−	0.573361i
$568$	68.5246	+	49.7860i	0.120642	+	0.0876515i
$569$	320.018	+	440.467i	0.562422	+	0.774108i	0.991632	−	0.129097i	$-0.0412079\pi$
$569$	320.018	+	440.467i	0.562422	+	0.774108i	−0.429210	+	0.903205i	$0.641208\pi$
$570$	−47.8409	−	12.3215i	−0.0839314	−	0.0216166i
$571$	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
$576$	89.6169	+	49.4413i	0.155585	+	0.0858357i
$577$	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
$579$	436.952	−	687.393i	0.754666	−	1.18721i
$580$	−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
$585$	−300.946	−	57.8734i	−0.514437	−	0.0989289i
$586$	−5.99744	+	4.35739i	−0.0102345	+	0.00743582i
$587$	368.838	−	507.662i	0.628344	−	0.864841i	−0.369583	−	0.929198i	$-0.620500\pi$
$587$	368.838	−	507.662i	0.628344	−	0.864841i	0.997927	+	0.0643568i	$0.0204996\pi$
$588$	249.241	−	98.4667i	0.423879	−	0.167460i
$589$	65.8005	+	202.513i	0.111716	+	0.343825i
$590$	72.3256	−	99.5477i	0.122586	−	0.168725i
$591$	−246.590	+	203.688i	−0.417242	+	0.344649i
$592$	−116.669	+	359.070i	−0.197076	+	0.606538i
$593$		−	961.677i		−	1.62171i	−0.585244	−	0.810857i	$-0.699001\pi$
$593$		−	961.677i		−	1.62171i	0.585244	−	0.810857i	$-0.300999\pi$
$594$		0			0
$595$	271.446			0.456211
$596$	−238.396	−	77.4595i	−0.399993	−	0.129966i
$597$	552.668	+	669.075i	0.925741	+	1.12073i
$598$	261.436	+	189.944i	0.437183	+	0.317632i
$599$	934.344	−	303.587i	1.55984	−	0.506822i	0.603074	−	0.797685i	$-0.293942\pi$
$599$	934.344	−	303.587i	1.55984	−	0.506822i	0.956765	+	0.290863i	$0.0939422\pi$
$600$	119.934	+	303.579i	0.199890	+	0.505965i
$601$	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
$603$	−58.3453	+	303.400i	−0.0967584	+	0.503151i
$604$	−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
$609$	−644.526	−	409.703i	−1.05834	−	0.672747i
$610$	−31.7951	−	97.8554i	−0.0521232	−	0.160419i
$611$	401.375	−	130.415i	0.656915	−	0.213445i
$612$	332.281	−	602.289i	0.542943	−	0.984133i
$613$	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	$0.150103\pi$
$617$			560.582i			0.908560i	−0.890859	+	0.454280i	$0.849897\pi$
$618$	−11.6050	+	45.0593i	−0.0187784	+	0.0729114i
$619$	−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
$621$	391.705	+	716.297i	0.630765	+	1.15346i
$622$	93.1937	+	286.821i	0.149829	+	0.461127i
$623$	400.142	−	550.748i	0.642282	−	0.884025i
$624$	228.373	+	276.475i	0.365982	+	0.443068i
$625$	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
$630$	62.3425	−	58.3689i	0.0989564	−	0.0926491i
$631$	−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
$633$	522.350	−	206.363i	0.825197	−	0.326008i
$634$	46.9492	+	34.1106i	0.0740523	+	0.0538022i
$635$	−191.180	−	263.137i	−0.301071	−	0.414389i
$636$	25.0110	−	97.1111i	0.0393255	−	0.152690i
$637$	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	$-0.919944\pi$
$641$	−580.698	−	799.262i	−0.905925	−	1.24690i	0.0626148	−	0.998038i	$-0.480056\pi$
$642$	107.653	−	169.354i	0.167683	−	0.263792i
$643$	−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
$645$	−226.814	−	144.178i	−0.351649	−	0.223531i
$646$	119.612	−	86.9030i	0.185157	−	0.134525i
$647$	−457.467	−	148.640i	−0.707059	−	0.229737i	−0.0666556	−	0.997776i	$-0.521233\pi$
$647$	−457.467	−	148.640i	−0.707059	−	0.229737i	−0.640404	+	0.768039i	$0.721233\pi$
$648$	−116.293	−	458.603i	−0.179465	−	0.707720i
$649$		0			0
$650$			199.079i			0.306276i
$651$	−356.470	−	91.8092i	−0.547573	−	0.141028i
$652$	−567.116	+	412.034i	−0.869810	+	0.631954i
$653$	456.234	−	627.953i	0.698674	−	0.961643i	−0.301293	−	0.953532i	$-0.597418\pi$
$653$	456.234	−	627.953i	0.698674	−	0.961643i	0.999967	−	0.00811121i	$-0.00258191\pi$
$654$	146.478	+	370.768i	0.223973	+	0.566924i
$655$	98.2859	+	302.493i	0.150055	+	0.461821i
$656$	−160.852	+	221.394i	−0.245201	+	0.337490i
$657$	−579.686	+	542.738i	−0.882322	+	0.826085i
$658$	−36.3430	+	111.852i	−0.0552326	+	0.169988i
$659$		−	52.5987i		−	0.0798160i	−0.999203	−	0.0399080i	$-0.987294\pi$
$659$		−	52.5987i		−	0.0798160i	0.999203	−	0.0399080i	$-0.0127065\pi$
$660$		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
$663$	707.118	−	584.092i	1.06654	−	0.880983i
$664$	−161.425	−	117.282i	−0.243110	−	0.176630i
$665$	−93.7874	+	30.4734i	−0.141034	+	0.0458246i
$666$	275.084	−	128.944i	0.413039	−	0.193610i
$667$	1312.55	+	953.624i	1.96784	+	1.42972i
$668$	−125.201	−	172.324i	−0.187427	−	0.257971i
$669$	−661.602	−	170.396i	−0.988942	−	0.254703i
$670$	−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
$675$	−215.162	+	454.602i	−0.318758	+	0.673484i
$676$	13.5019	+	41.5545i	0.0199732	+	0.0614711i
$677$	281.192	−	91.3649i	0.415350	−	0.134955i	−0.0938846	−	0.995583i	$-0.529928\pi$
$677$	281.192	−	91.3649i	0.415350	−	0.134955i	0.509235	+	0.860628i	$0.329928\pi$
$678$	−157.482	+	247.744i	−0.232274	+	0.365404i
$679$	−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	$0.230718\pi$
$683$			905.661i			1.32600i	−0.748617	+	0.663002i	$0.769282\pi$
$684$	−47.1917	+	245.400i	−0.0689938	+	0.358773i
$685$	−121.135	+	88.0096i	−0.176839	+	0.128481i
$686$	−166.795	+	229.573i	−0.243141	+	0.334654i
$687$	283.435	−	111.976i	0.412570	−	0.162992i
$688$	97.1808	+	299.092i	0.141251	+	0.434726i
$689$	78.5910	−	108.171i	0.114065	−	0.156997i
$690$	−139.875	+	115.539i	−0.202717	+	0.167448i
$691$	−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
$696$	−598.770	−	724.888i	−0.860302	−	1.04151i
$697$	566.242	+	411.399i	0.812398	+	0.590242i
$698$	210.995	−	68.5564i	0.302285	−	0.0982183i
$699$	−190.923	−	483.268i	−0.273137	−	0.691371i
$700$	241.122	+	175.186i	0.344460	+	0.250265i
$701$	734.941	+	1011.56i	1.04842	+	1.44302i	0.890173	+	0.455623i	$0.150583\pi$
$701$	734.941	+	1011.56i	1.04842	+	1.44302i	0.158244	+	0.987400i	$0.449417\pi$
$702$	36.8055	−	286.199i	0.0524294	−	0.407691i
$703$	−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
$708$	−525.284	−	333.905i	−0.741927	−	0.471617i
$709$	−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
$711$	−738.220	−	407.274i	−1.03828	−	0.572818i
$712$	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
$717$	−120.688	+	468.599i	−0.168324	+	0.653555i
$718$	69.7776	−	50.6964i	0.0971833	−	0.0706078i
$719$	−65.9951	+	90.8344i	−0.0917873	+	0.126334i	−0.852441	−	0.522824i	$-0.824879\pi$
$719$	−65.9951	+	90.8344i	−0.0917873	+	0.126334i	0.760654	+	0.649158i	$0.224879\pi$
$720$	−182.290	+	85.4475i	−0.253180	+	0.118677i
$721$	28.7015	+	88.3343i	0.0398080	+	0.122516i
$722$	136.545	−	187.938i	0.189120	−	0.260301i
$723$	108.330	+	131.148i	0.149834	+	0.181394i
$724$	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
$729$	393.365	−	613.763i	0.539596	−	0.841924i
$730$	−142.765	−	103.725i	−0.195569	−	0.142089i
$731$	764.964	−	248.552i	1.04646	−	0.340016i
$732$	−484.061	+	191.236i	−0.661285	+	0.261252i
$733$	−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
$735$	−50.0326	+	194.263i	−0.0680715	+	0.264303i
$736$	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
$741$	−178.745	+	281.193i	−0.241221	+	0.379478i
$742$	11.5141	+	35.4369i	0.0155177	+	0.0477586i
$743$	233.203	−	75.7723i	0.313867	−	0.101982i	−0.147848	−	0.989010i	$-0.547235\pi$
$743$	233.203	−	75.7723i	0.313867	−	0.101982i	0.461714	+	0.887029i	$0.347235\pi$
$744$	−382.440	−	243.104i	−0.514032	−	0.326752i
$745$	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
$750$	−253.494	−	65.2875i	−0.337992	−	0.0870500i
$751$	−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
$753$	−74.3960	−	188.313i	−0.0987994	−	0.250083i
$754$	−177.201	−	545.369i	−0.235015	−	0.723301i
$755$	9.24935	−	12.7306i	0.0122508	−	0.0168618i
$756$	−314.253	−	296.428i	−0.415678	−	0.392100i
$757$	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	−0.146676	−	0.989185i	$-0.546857\pi$
$761$	−644.390	−	209.375i	−0.846767	−	0.275131i	−0.700091	+	0.714053i	$0.746857\pi$
$762$	236.118	−	195.037i	0.309866	−	0.255954i
$763$	643.793	+	467.743i	0.843765	+	0.613031i
$764$	222.863	−	72.4125i	0.291705	−	0.0947808i
$765$	218.542	+	466.228i	0.285676	+	0.609449i
$766$	230.667	+	167.589i	0.301132	+	0.218785i
$767$	−487.805	−	671.406i	−0.635991	−	0.875366i
$768$	−168.335	−	43.3548i	−0.219186	−	0.0564516i
$769$	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	0.732826	−	0.680416i	$-0.238201\pi$
$773$	−108.795	−	149.744i	−0.140744	−	0.193718i	−0.873570	+	0.486698i	$0.838201\pi$
$774$	122.242	−	221.575i	0.157935	−	0.286272i
$775$	148.866	+	458.161i	0.192085	+	0.591176i
$776$	−223.788	+	72.7132i	−0.288387	+	0.0937026i
$777$	325.328	−	511.792i	0.418698	−	0.658677i
$778$	−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
$783$	184.784	−	1436.88i	0.235994	−	1.83509i
$784$	189.901	−	137.971i	0.242221	−	0.175984i
$785$	−146.591	+	201.765i	−0.186740	+	0.257025i
$786$	−278.530	+	110.038i	−0.354363	+	0.139997i
$787$	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
$789$	−338.137	+	279.307i	−0.428564	+	0.354001i
$790$	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
$795$	47.8053	+	57.8744i	0.0601324	+	0.0727980i
$796$	789.200	+	573.388i	0.991458	+	0.720336i
$797$	−858.556	+	278.962i	−1.07723	+	0.350015i	−0.793301	−	0.608830i	$-0.791639\pi$
$797$	−858.556	+	278.962i	−1.07723	+	0.350015i	−0.283933	+	0.958844i	$0.591639\pi$
$798$	−34.1170	−	86.3577i	−0.0427531	−	0.108218i
$799$	−573.663	−	416.791i	−0.717976	−	0.521640i
$800$	332.684	+	457.901i	0.415855	+	0.572376i
$801$	1268.11	+	243.863i	1.58316	+	0.304449i
$802$	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
$807$	144.338	+	91.7503i	0.178857	+	0.113693i
$808$	167.420	+	515.266i	0.207203	+	0.637705i
$809$	291.657	−	94.7652i	0.360516	−	0.117139i	−0.123158	−	0.992387i	$-0.539302\pi$
$809$	291.657	−	94.7652i	0.360516	−	0.117139i	0.483674	+	0.875248i	$0.339302\pi$
$810$	150.445	+	60.0848i	0.185735	+	0.0741788i
$811$	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
$816$	150.273	−	583.468i	0.184158	−	0.715034i
$817$	−236.400	+	171.755i	−0.289351	+	0.210226i
$818$	236.431	−	325.419i	0.289036	−	0.397823i
$819$	−244.472	−	521.545i	−0.298501	−	0.636807i
$820$	−81.2379	−	250.024i	−0.0990706	−	0.304908i
$821$	−801.178	+	1102.73i	−0.975856	+	1.34315i	−0.0368241	+	0.999322i	$0.511724\pi$
$821$	−801.178	+	1102.73i	−0.975856	+	1.34315i	−0.939032	+	0.343829i	$0.888276\pi$
$822$	−89.7852	−	108.696i	−0.109228	−	0.132234i
$823$	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	0.651470	−	0.758674i	$-0.274153\pi$
$827$	605.846	+	196.851i	0.732583	+	0.238031i	0.0811129	+	0.996705i	$0.474153\pi$
$828$	627.221	+	669.920i	0.757513	+	0.809082i
$829$	−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
$831$	−659.249	+	260.447i	−0.793320	+	0.313414i
$832$	124.105	+	90.1675i	0.149165	+	0.108374i
$833$	−352.879	−	485.696i	−0.423624	−	0.583068i
$834$	−77.6203	+	301.379i	−0.0930699	+	0.361365i
$835$	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	$0.00652429\pi$
$839$	595.967	+	820.278i	0.710330	+	0.977685i	−0.289460	+	0.957190i	$0.593476\pi$
$840$	112.586	−	177.115i	0.134031	−	0.210851i
$841$	−629.763	−	1938.21i	−0.748826	−	2.30465i
$842$	−334.042	+	108.537i	−0.396725	+	0.128904i
$843$	−516.427	−	328.274i	−0.612606	−	0.389412i
$844$	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
$849$	1392.20	+	358.563i	1.63982	+	0.422336i
$850$	270.607	−	196.607i	0.318361	−	0.231303i
$851$	−757.234	+	1042.24i	−0.889816	+	1.22473i
$852$	53.9046	+	136.444i	0.0632683	+	0.160146i
$853$	−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
$855$	−127.849	−	136.553i	−0.149531	−	0.159711i
$856$	152.389	−	469.005i	0.178025	−	0.547903i
$857$		−	618.449i		−	0.721644i	−0.932635	−	0.360822i	$-0.882496\pi$
$857$		−	618.449i		−	0.721644i	0.932635	−	0.360822i	$-0.117504\pi$
$858$		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
$861$	338.899	−	279.936i	0.393611	−	0.325129i
$862$	509.768	+	370.368i	0.591379	+	0.429662i
$863$	−1051.19	+	341.551i	−1.21806	+	0.395772i	−0.846376	−	0.532587i	$-0.821220\pi$
$863$	−1051.19	+	341.551i	−1.21806	+	0.395772i	−0.371686	+	0.928359i	$0.621220\pi$
$864$	−393.616	−	719.790i	−0.455574	−	0.833091i
$865$	394.884	+	286.900i	0.456513	+	0.331676i
$866$	−8.67224	−	11.9363i	−0.0100141	−	0.0137833i
$867$	−652.690	−	168.101i	−0.752814	−	0.193888i
$868$	−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
$873$	−317.460	−	175.142i	−0.363642	−	0.200620i
$874$	60.9537	+	187.596i	0.0697411	+	0.214641i
$875$	−496.950	+	161.469i	−0.567943	+	0.184536i
$876$	−478.865	+	753.330i	−0.546650	+	0.859965i
$877$	−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	$-0.768370\pi$
$881$		−	1171.98i		−	1.33029i	0.746715	−	0.665145i	$-0.231630\pi$
$882$	−185.484	−	35.6696i	−0.210300	−	0.0404417i
$883$	−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
$885$	433.330	−	171.194i	0.489639	−	0.193440i
$886$	15.0698	+	46.3800i	0.0170088	+	0.0523476i
$887$	575.896	−	792.653i	0.649262	−	0.893633i	−0.349804	−	0.936823i	$-0.613752\pi$
$887$	575.896	−	792.653i	0.649262	−	0.893633i	0.999067	+	0.0431896i	$0.0137520\pi$
$888$	575.604	−	475.459i	0.648203	−	0.535427i
$889$	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
$894$	112.515	+	136.213i	0.125855	+	0.152364i
$895$	−63.3341	−	46.0149i	−0.0707644	−	0.0514133i
$896$	−589.081	+	191.404i	−0.657456	+	0.213620i
$897$	449.596	+	1138.03i	0.501222	+	1.26870i
$898$	88.0908	+	64.0017i	0.0980966	+	0.0712714i
$899$	−815.621	−	1122.61i	−0.907253	−	1.24873i
$900$	−106.766	+	555.189i	−0.118628	+	0.616876i
$901$	−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
$906$	12.5042	+	7.94846i	0.0138015	+	0.00877313i
$907$	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
$909$	−403.258	+	730.942i	−0.443628	+	0.804116i
$910$	103.554	−	75.2365i	0.113796	−	0.0826775i
$911$	440.602	+	143.160i	0.483647	+	0.157146i	0.540684	−	0.841226i	$-0.318165\pi$
$911$	440.602	+	143.160i	0.483647	+	0.157146i	−0.0570373	+	0.998372i	$0.518165\pi$
$912$	13.5812	+	218.464i	0.0148917	+	0.239544i
$913$		0			0
$914$			243.701i			0.266632i
$915$	97.1703	−	377.286i	0.106197	−	0.412335i
$916$	277.145	−	201.358i	0.302560	−	0.219823i
$917$	−351.379	+	483.632i	−0.383183	+	0.527407i
$918$	−425.377	+	232.616i	−0.463373	+	0.253395i
$919$	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
$921$	−138.567	−	167.752i	−0.150452	−	0.182142i
$922$	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
$927$	−128.613	+	120.415i	−0.138741	+	0.129898i
$928$	−1318.95	−	958.275i	−1.42128	−	1.03262i
$929$	115.578	−	37.5535i	0.124411	−	0.0404236i	−0.246150	−	0.969232i	$-0.579166\pi$
$929$	115.578	−	37.5535i	0.124411	−	0.0404236i	0.370561	+	0.928808i	$0.379166\pi$
$930$	144.314	−	57.0138i	0.155177	−	0.0613052i
$931$	176.449	+	128.198i	0.189527	+	0.137699i
$932$	−343.323	−	472.544i	−0.368372	−	0.507021i
$933$	−284.813	+	1105.85i	−0.305266	+	1.18526i
$934$	−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
$939$	85.4584	−	134.439i	0.0910101	−	0.143173i
$940$	82.3026	+	253.301i	0.0875560	+	0.269470i
$941$	−851.275	+	276.596i	−0.904650	+	0.293939i	−0.724155	−	0.689637i	$-0.757770\pi$
$941$	−851.275	+	276.596i	−0.904650	+	0.293939i	−0.180495	+	0.983576i	$0.557770\pi$
$942$	−198.175	−	125.973i	−0.210377	−	0.133729i
$943$	−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	$-0.757321\pi$
$947$		−	1308.11i		−	1.38132i	0.723181	−	0.690659i	$-0.242679\pi$
$948$	−917.788	−	236.377i	−0.968131	−	0.249343i
$949$	−962.888	+	699.579i	−1.01463	+	0.737175i
$950$	−71.4258	+	98.3092i	−0.0751851	+	0.103483i
$951$	80.7394	+	204.369i	0.0848995	+	0.214899i
$952$	194.090	+	597.346i	0.203876	+	0.627465i
$953$	−1.19333	+	1.64248i	−0.00125218	+	0.00172348i	−0.809643	−	0.586923i	$-0.800339\pi$
$953$	−1.19333	+	1.64248i	−0.00125218	+	0.00172348i	0.808390	+	0.588647i	$0.200339\pi$
$954$	−51.5954	+	48.3068i	−0.0540832	+	0.0506361i
$955$	−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
$960$	−66.3994	+	54.8471i	−0.0691660	+	0.0571323i
$961$	236.385	+	171.744i	0.245978	+	0.178713i
$962$	433.055	−	140.708i	0.450161	−	0.146266i
$963$	688.016	−	322.505i	0.714451	−	0.334896i
$964$	154.694	+	112.392i	0.160471	+	0.116589i
$965$	402.851	+	554.477i	0.417462	+	0.574587i
$966$	−330.213	−	85.0467i	−0.341836	−	0.0880400i
$967$	−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	$-0.817104\pi$
$971$	−1065.10	−	1465.98i	−1.09691	−	1.50977i	−0.257492	−	0.966280i	$-0.582896\pi$
$972$	256.130	−	778.408i	0.263508	−	0.800831i
$973$	191.970	+	590.823i	0.197297	+	0.607218i
$974$	−457.305	+	148.587i	−0.469512	+	0.152554i
$975$	−404.388	+	636.166i	−0.414757	+	0.652478i
$976$	−368.815	+	267.960i	−0.377884	+	0.274549i
$977$	406.470	+	132.070i	0.416039	+	0.135179i	0.509554	−	0.860439i	$-0.329810\pi$
$977$	406.470	+	132.070i	0.416039	+	0.135179i	−0.0935151	+	0.995618i	$0.529810\pi$
$978$	493.125	−	30.6559i	0.504218	−	0.0313455i
$979$		0			0
$980$			225.496i			0.230098i
$981$	−285.062	+	1482.34i	−0.290583	+	1.51105i
$982$	492.824	−	358.057i	0.501857	−	0.364620i
$983$	−589.855	+	811.865i	−0.600056	+	0.825906i	−0.995713	−	0.0924923i	$-0.970517\pi$
$983$	−589.855	+	811.865i	−0.600056	+	0.825906i	0.395658	+	0.918398i	$0.370517\pi$
$984$	503.289	−	198.832i	0.511472	−	0.202065i
$985$	−83.1642	−	255.953i	−0.0844306	−	0.259851i
$986$	−566.315	+	779.465i	−0.574356	+	0.790533i
$987$	−343.341	+	283.605i	−0.347863	+	0.287341i
$988$	−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
$993$	319.731	+	387.076i	0.321985	+	0.389804i
$994$	−44.1002	−	32.0407i	−0.0443664	−	0.0322341i
$995$	−694.480	+	225.650i	−0.697970	+	0.226784i
$996$	−126.985	−	321.426i	−0.127495	−	0.322717i
$997$	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
$999$	1140.97	+	146.729i	1.14211	+	0.146876i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.753510 - 0.244830i) q^{2} +(-1.91055 - 2.31296i) q^{3} +(-2.72823 - 1.98218i) q^{4} +(2.40079 - 0.780063i) q^{5} +(0.873334 + 2.21060i) q^{6} +(3.83843 + 2.78878i) q^{7} +(3.43323 + 4.72544i) q^{8} +(-1.69960 + 8.83806i) q^{9} +O(q^{10})\)	\(q+(-0.753510 - 0.244830i) q^{2} +(-1.91055 - 2.31296i) q^{3} +(-2.72823 - 1.98218i) q^{4} +(2.40079 - 0.780063i) q^{5} +(0.873334 + 2.21060i) q^{6} +(3.83843 + 2.78878i) q^{7} +(3.43323 + 4.72544i) q^{8} +(-1.69960 + 8.83806i) q^{9} -2.00000 q^{10} +(0.627719 + 10.0974i) q^{12} +(-4.16837 + 12.8289i) q^{13} +(-2.20952 - 3.04114i) q^{14} +(-6.39108 - 4.06259i) q^{15} +(2.73833 + 8.42770i) q^{16} +(21.5549 - 7.00360i) q^{17} +(3.44449 - 6.24345i) q^{18} +(-6.66119 + 4.83964i) q^{19} +(-8.09613 - 2.63059i) q^{20} +(-0.883156 - 14.2063i) q^{21} +30.2372i q^{23} +(4.37041 - 16.9691i) q^{24} +(-15.0701 + 10.9491i) q^{25} +(6.28181 - 8.64617i) q^{26} +(23.6893 - 12.9544i) q^{27} +(-4.94427 - 15.2169i) q^{28} +(31.5381 - 43.4085i) q^{29} +(3.82110 + 4.62593i) q^{30} +(7.99161 - 24.5957i) q^{31} -30.3846i q^{32} -17.9565 q^{34} +(11.3907 + 3.70106i) q^{35} +(22.1555 - 20.7434i) q^{36} +(34.4690 + 25.0432i) q^{37} +(6.20416 - 2.01586i) q^{38} +(37.6367 - 14.8690i) q^{39} +(11.9286 + 8.66664i) q^{40} +(18.1520 + 24.9840i) q^{41} +(-2.81265 + 10.9208i) q^{42} +35.4891 q^{43} +(2.81386 + 22.5441i) q^{45} +(7.40297 - 22.7840i) q^{46} +(-18.3899 - 25.3115i) q^{47} +(14.2613 - 22.4352i) q^{48} +(-8.18559 - 25.1927i) q^{49} +(14.0362 - 4.56063i) q^{50} +(-57.3807 - 36.4749i) q^{51} +(36.8015 - 26.7378i) q^{52} +(-9.42707 - 3.06304i) q^{53} +(-21.0217 + 3.96143i) q^{54} +27.7128i q^{56} +(23.9205 + 6.16073i) q^{57} +(-34.3920 + 24.9873i) q^{58} +(-36.1628 + 49.7739i) q^{59} +(9.38359 + 23.7519i) q^{60} +(15.8976 + 48.9277i) q^{61} +(-12.0435 + 16.5765i) q^{62} +(-31.1713 + 29.1845i) q^{63} +(3.51423 - 10.8157i) q^{64} +34.0511i q^{65} +34.3288 q^{67} +(-72.6891 - 23.6181i) q^{68} +(69.9374 - 57.7696i) q^{69} +(-7.67686 - 5.57757i) q^{70} +(13.7915 - 4.48112i) q^{71} +(-47.5988 + 22.3117i) q^{72} +(71.3826 + 51.8625i) q^{73} +(-19.8414 - 27.3093i) q^{74} +(54.1171 + 13.9379i) q^{75} +27.7663 q^{76} +(-32.0000 + 1.98933i) q^{78} +(-28.9485 + 89.0943i) q^{79} +(13.1483 + 18.0970i) q^{80} +(-75.2227 - 30.0424i) q^{81} +(-7.56083 - 23.2699i) q^{82} +(-32.4890 + 10.5563i) q^{83} +(-25.7499 + 40.5086i) q^{84} +(46.2854 - 33.6283i) q^{85} +(-26.7414 - 8.68881i) q^{86} +(-160.658 + 9.98755i) q^{87} -143.482i q^{89} +(3.39921 - 17.6761i) q^{90} +(-51.7771 + 37.6183i) q^{91} +(59.9354 - 82.4940i) q^{92} +(-72.1572 + 28.5069i) q^{93} +(7.65993 + 23.5748i) q^{94} +(-12.2169 + 16.8151i) q^{95} +(-70.2785 + 58.0513i) 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

Introduction

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