LMFDB - Embedded newform 441.3.j.f.263.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,3,Mod(263,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.263"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [22,0,19] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.2
Character	$\chi$	$=$	441.263
Dual form			441.3.j.f.275.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.22356i q^{2} +(2.32685 - 1.89361i) q^{3} -6.39137 q^{4} +(4.79167 + 2.76647i) q^{5} +(-6.10417 - 7.50076i) q^{6} +7.70873i q^{8} +(1.82848 - 8.81230i) q^{9} +(8.91790 - 15.4463i) q^{10} +(15.3189 - 8.84435i) q^{11} +(-14.8718 + 12.1028i) q^{12} +(-2.03775 - 3.52949i) q^{13} +(16.3881 - 2.63638i) q^{15} -0.715882 q^{16} +(14.3348 + 8.27617i) q^{17} +(-28.4070 - 5.89424i) q^{18} +(3.92096 + 6.79130i) q^{19} +(-30.6253 - 17.6815i) q^{20} +(-28.5103 - 49.3813i) q^{22} +(8.71877 + 5.03378i) q^{23} +(14.5973 + 17.9371i) q^{24} +(2.80674 + 4.86141i) q^{25} +(-11.3775 + 6.56882i) q^{26} +(-12.4324 - 23.9674i) q^{27} +(-39.9040 - 23.0386i) q^{29} +(-8.49854 - 52.8282i) q^{30} -29.6235 q^{31} +33.1426i q^{32} +(18.8970 - 49.5874i) q^{33} +(26.6788 - 46.2090i) q^{34} +(-11.6865 + 56.3227i) q^{36} +(15.5948 + 27.0110i) q^{37} +(21.8922 - 12.6395i) q^{38} +(-11.4250 - 4.35389i) q^{39} +(-21.3260 + 36.9377i) q^{40} +(-27.8184 + 16.0609i) q^{41} +(3.35243 - 5.80658i) q^{43} +(-97.9085 + 56.5275i) q^{44} +(33.1405 - 37.1672i) q^{45} +(16.2267 - 28.1055i) q^{46} +16.4402i q^{47} +(-1.66575 + 1.35560i) q^{48} +(15.6711 - 9.04769i) q^{50} +(49.0267 - 7.88699i) q^{51} +(13.0240 + 22.5583i) q^{52} +(-32.5897 - 18.8157i) q^{53} +(-77.2603 + 40.0768i) q^{54} +97.8706 q^{55} +(21.9836 + 8.37759i) q^{57} +(-74.2663 + 128.633i) q^{58} +95.0557i q^{59} +(-104.743 + 16.8501i) q^{60} +73.7679 q^{61} +95.4932i q^{62} +103.974 q^{64} -22.5495i q^{65} +(-159.848 - 60.9156i) q^{66} -12.1909 q^{67} +(-91.6187 - 52.8961i) q^{68} +(29.8193 - 4.79707i) q^{69} -20.0140i q^{71} +(67.9317 + 14.0953i) q^{72} +(11.4932 - 19.9068i) q^{73} +(87.0715 - 50.2708i) q^{74} +(15.7365 + 5.99692i) q^{75} +(-25.0603 - 43.4057i) q^{76} +(-14.0351 + 36.8293i) q^{78} +138.880 q^{79} +(-3.43027 - 1.98047i) q^{80} +(-74.3133 - 32.2263i) q^{81} +(51.7735 + 89.6743i) q^{82} +(-13.6928 - 7.90552i) q^{83} +(45.7916 + 79.3134i) q^{85} +(-18.7179 - 10.8068i) q^{86} +(-136.477 + 21.9552i) q^{87} +(68.1787 + 118.089i) q^{88} +(46.9444 - 27.1034i) q^{89} +(-119.811 - 106.830i) q^{90} +(-55.7249 - 32.1728i) q^{92} +(-68.9294 + 56.0953i) q^{93} +52.9962 q^{94} +43.3889i q^{95} +(62.7592 + 77.1180i) q^{96} +(-86.1189 + 149.162i) q^{97} +(-49.9287 - 151.166i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 19 q^{3} - 24 q^{4} - 12 q^{5} + 8 q^{6} - 37 q^{9} - 25 q^{10} + 24 q^{11} - 40 q^{12} + 18 q^{13} + 53 q^{15} - 24 q^{16} + 6 q^{17} + 40 q^{18} - 3 q^{19} + 39 q^{20} - 59 q^{22} + 81 q^{23} - 126 q^{24}+ \cdots - 103 q^{99}+O(q^{100}) $ 22 * q + 19 * q^3 - 24 * q^4 - 12 * q^5 + 8 * q^6 - 37 * q^9 - 25 * q^10 + 24 * q^11 - 40 * q^12 + 18 * q^13 + 53 * q^15 - 24 * q^16 + 6 * q^17 + 40 * q^18 - 3 * q^19 + 39 * q^20 - 59 * q^22 + 81 * q^23 - 126 * q^24 + 57 * q^25 - 3 * q^26 + 97 * q^27 - 63 * q^29 - 38 * q^30 - 58 * q^31 + 4 * q^33 + 99 * q^34 + 76 * q^36 - 20 * q^37 + 48 * q^38 - 76 * q^39 + 105 * q^40 + 51 * q^41 + 65 * q^43 - 54 * q^44 + 214 * q^45 + 75 * q^46 + 113 * q^48 + 63 * q^50 + 141 * q^51 + 46 * q^52 + 63 * q^53 - 433 * q^54 + 100 * q^55 + 224 * q^57 + 40 * q^58 - 482 * q^60 + 156 * q^61 + 106 * q^64 - 61 * q^66 + 264 * q^67 - 27 * q^68 + 297 * q^69 - 222 * q^72 - q^73 + 342 * q^74 + 296 * q^75 - 233 * q^76 - 440 * q^78 - 280 * q^79 + 96 * q^80 - 169 * q^81 + 157 * q^82 - 255 * q^83 + 102 * q^85 + 504 * q^86 - 704 * q^87 + 408 * q^88 - 720 * q^89 - 418 * q^90 - 1239 * q^92 - 36 * q^93 + 522 * q^94 + 397 * q^96 - 178 * q^97 - 103 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	3.22356i		−	1.61178i	−0.592064	−	0.805891i	$-0.701687\pi$
$2$		−	3.22356i		−	1.61178i	0.592064	−	0.805891i	$-0.298313\pi$
$3$	2.32685	−	1.89361i	0.775617	−	0.631203i
$3$	2.32685	−	1.89361i	0.775617	−	0.631203i
$4$	−6.39137			−1.59784
$5$	4.79167	+	2.76647i	0.958334	+	0.553294i	0.895660	−	0.444740i	$-0.146704\pi$
$5$	4.79167	+	2.76647i	0.958334	+	0.553294i	0.0626741	+	0.998034i	$0.480037\pi$
$6$	−6.10417	−	7.50076i	−1.01736	−	1.25013i
$7$		0			0
$7$		0			0
$8$			7.70873i			0.963591i
$9$	1.82848	−	8.81230i	0.203165	−	0.979145i
$10$	8.91790	−	15.4463i	0.891790	−	1.54463i
$11$	15.3189	−	8.84435i	1.39262	−	0.804032i	0.399018	−	0.916943i	$-0.369351\pi$
$11$	15.3189	−	8.84435i	1.39262	−	0.804032i	0.993605	+	0.112911i	$0.0360176\pi$
$12$	−14.8718	+	12.1028i	−1.23931	+	1.00856i
$13$	−2.03775	−	3.52949i	−0.156750	−	0.271499i	0.776945	−	0.629569i	$-0.216768\pi$
$13$	−2.03775	−	3.52949i	−0.156750	−	0.271499i	−0.933695	+	0.358070i	$0.883435\pi$
$14$		0			0
$15$	16.3881	−	2.63638i	1.09254	−	0.175759i
$16$	−0.715882			−0.0447426
$17$	14.3348	+	8.27617i	0.843221	+	0.486834i	0.858358	−	0.513052i	$-0.171485\pi$
$17$	14.3348	+	8.27617i	0.843221	+	0.486834i	−0.0151370	+	0.999885i	$0.504818\pi$
$18$	−28.4070	−	5.89424i	−1.57817	−	0.327458i
$19$	3.92096	+	6.79130i	0.206366	+	0.357437i	0.950567	−	0.310519i	$-0.100503\pi$
$19$	3.92096	+	6.79130i	0.206366	+	0.357437i	−0.744201	+	0.667956i	$0.767170\pi$
$20$	−30.6253	−	17.6815i	−1.53127	−	0.884077i
$21$		0			0
$22$	−28.5103	−	49.3813i	−1.29592	−	2.24461i
$23$	8.71877	+	5.03378i	0.379077	+	0.218860i	0.677417	−	0.735600i	$-0.263099\pi$
$23$	8.71877	+	5.03378i	0.379077	+	0.218860i	−0.298340	+	0.954460i	$0.596433\pi$
$24$	14.5973	+	17.9371i	0.608222	+	0.747378i
$25$	2.80674	+	4.86141i	0.112269	+	0.194456i
$26$	−11.3775	+	6.56882i	−0.437597	+	0.252647i
$27$	−12.4324	−	23.9674i	−0.460461	−	0.887680i
$28$		0			0
$29$	−39.9040	−	23.0386i	−1.37600	−	0.794434i	−0.384324	−	0.923198i	$-0.625566\pi$
$29$	−39.9040	−	23.0386i	−1.37600	−	0.794434i	−0.991675	+	0.128764i	$0.958899\pi$
$30$	−8.49854	−	52.8282i	−0.283285	−	1.76094i
$31$	−29.6235			−0.955596			−0.477798	−	0.878470i	$-0.658565\pi$
$31$	−29.6235			−0.955596			−0.477798	+	0.878470i	$0.658565\pi$
$32$			33.1426i			1.03571i
$33$	18.8970	−	49.5874i	0.572636	−	1.50265i
$34$	26.6788	−	46.2090i	0.784670	−	1.35909i
$35$		0			0
$36$	−11.6865	+	56.3227i	−0.324626	+	1.56452i
$37$	15.5948	+	27.0110i	0.421481	+	0.730026i	0.996085	−	0.0884059i	$-0.0281772\pi$
$37$	15.5948	+	27.0110i	0.421481	+	0.730026i	−0.574604	+	0.818432i	$0.694844\pi$
$38$	21.8922	−	12.6395i	0.576110	−	0.332617i
$39$	−11.4250	−	4.35389i	−0.292949	−	0.111638i
$40$	−21.3260	+	36.9377i	−0.533150	+	0.923442i
$41$	−27.8184	+	16.0609i	−0.678497	+	0.391730i	−0.799288	−	0.600948i	$-0.794790\pi$
$41$	−27.8184	+	16.0609i	−0.678497	+	0.391730i	0.120792	+	0.992678i	$0.461457\pi$
$42$		0			0
$43$	3.35243	−	5.80658i	0.0779635	−	0.135037i	−0.824408	−	0.565997i	$-0.808492\pi$
$43$	3.35243	−	5.80658i	0.0779635	−	0.135037i	0.902371	+	0.430960i	$0.141825\pi$
$44$	−97.9085	+	56.5275i	−2.22519	+	1.28472i
$45$	33.1405	−	37.1672i	0.736455	−	0.825937i
$46$	16.2267	−	28.1055i	0.352755	−	0.610990i
$47$			16.4402i			0.349792i	0.984587	+	0.174896i	$0.0559590\pi$
$47$			16.4402i			0.349792i	−0.984587	+	0.174896i	$0.944041\pi$
$48$	−1.66575	+	1.35560i	−0.0347032	+	0.0282417i
$49$		0			0
$50$	15.6711	−	9.04769i	0.313421	−	0.180954i
$51$	49.0267	−	7.88699i	0.961308	−	0.154647i
$52$	13.0240	+	22.5583i	0.250462	+	0.433813i
$53$	−32.5897	−	18.8157i	−0.614900	−	0.355013i	0.159981	−	0.987120i	$-0.448857\pi$
$53$	−32.5897	−	18.8157i	−0.614900	−	0.355013i	−0.774881	+	0.632108i	$0.782190\pi$
$54$	−77.2603	+	40.0768i	−1.43075	+	0.742163i
$55$	97.8706			1.77946
$56$		0			0
$57$	21.9836	+	8.37759i	0.385676	+	0.146975i
$58$	−74.2663	+	128.633i	−1.28045	+	2.21781i
$59$			95.0557i			1.61111i	0.592519	+	0.805557i	$0.298134\pi$
$59$			95.0557i			1.61111i	−0.592519	+	0.805557i	$0.701866\pi$
$60$	−104.743	+	16.8501i	−1.74571	+	0.280835i
$61$	73.7679			1.20931			0.604655	−	0.796488i	$-0.293311\pi$
$61$	73.7679			1.20931			0.604655	+	0.796488i	$0.293311\pi$
$62$			95.4932i			1.54021i
$63$		0			0
$64$	103.974			1.62459
$65$		−	22.5495i		−	0.346916i
$66$	−159.848	−	60.9156i	−2.42194	−	0.922964i
$67$	−12.1909			−0.181954			−0.0909769	−	0.995853i	$-0.528999\pi$
$67$	−12.1909			−0.181954			−0.0909769	+	0.995853i	$0.528999\pi$
$68$	−91.6187	−	52.8961i	−1.34733	−	0.777883i
$69$	29.8193	−	4.79707i	0.432164	−	0.0695228i
$70$		0			0
$71$		−	20.0140i		−	0.281887i	−0.990018	−	0.140944i	$-0.954986\pi$
$71$		−	20.0140i		−	0.281887i	0.990018	−	0.140944i	$-0.0450136\pi$
$72$	67.9317	+	14.0953i	0.943495	+	0.195768i
$73$	11.4932	−	19.9068i	0.157441	−	0.272696i	−0.776504	−	0.630112i	$-0.783009\pi$
$73$	11.4932	−	19.9068i	0.157441	−	0.272696i	0.933945	+	0.357416i	$0.116342\pi$
$74$	87.0715	−	50.2708i	1.17664	−	0.679335i
$75$	15.7365	+	5.99692i	0.209820	+	0.0799589i
$76$	−25.0603	−	43.4057i	−0.329741	−	0.571128i
$77$		0			0
$78$	−14.0351	+	36.8293i	−0.179937	+	0.472170i
$79$	138.880			1.75798			0.878988	−	0.476844i	$-0.158219\pi$
$79$	138.880			1.75798			0.878988	+	0.476844i	$0.158219\pi$
$80$	−3.43027	−	1.98047i	−0.0428784	−	0.0247559i
$81$	−74.3133	−	32.2263i	−0.917448	−	0.397856i
$82$	51.7735	+	89.6743i	0.631384	+	1.09359i
$83$	−13.6928	−	7.90552i	−0.164973	−	0.0952472i	0.415240	−	0.909712i	$-0.363697\pi$
$83$	−13.6928	−	7.90552i	−0.164973	−	0.0952472i	−0.580213	+	0.814465i	$0.697031\pi$
$84$		0			0
$85$	45.7916	+	79.3134i	0.538725	+	0.933099i
$86$	−18.7179	−	10.8068i	−0.217650	−	0.125660i
$87$	−136.477	+	21.9552i	−1.56870	+	0.252359i
$88$	68.1787	+	118.089i	0.774758	+	1.34192i
$89$	46.9444	−	27.1034i	0.527466	−	0.304532i	−0.212518	−	0.977157i	$-0.568166\pi$
$89$	46.9444	−	27.1034i	0.527466	−	0.304532i	0.739984	+	0.672625i	$0.234833\pi$
$90$	−119.811	−	106.830i	−1.33123	−	1.18701i
$91$		0			0
$92$	−55.7249	−	32.1728i	−0.605705	−	0.349704i
$93$	−68.9294	+	56.0953i	−0.741177	+	0.603175i
$94$	52.9962			0.563789
$95$			43.3889i			0.456725i
$96$	62.7592	+	77.1180i	0.653741	+	0.803312i
$97$	−86.1189	+	149.162i	−0.887823	+	1.53776i	−0.0453802	+	0.998970i	$0.514450\pi$
$97$	−86.1189	+	149.162i	−0.887823	+	1.53776i	−0.842443	+	0.538785i	$0.818883\pi$
$98$		0			0
$99$	−49.9287	−	151.166i	−0.504331	−	1.52693i
$100$	−17.9389	−	31.0710i	−0.179389	−	0.310710i
$101$	14.9975	−	8.65880i	0.148490	−	0.0857307i	−0.423914	−	0.905702i	$-0.639344\pi$
$101$	14.9975	−	8.65880i	0.148490	−	0.0857307i	0.572404	+	0.819972i	$0.306011\pi$
$102$	−25.4242	−	158.041i	−0.249257	−	1.54942i
$103$	−13.7999	+	23.9021i	−0.133979	+	0.232059i	−0.925207	−	0.379463i	$-0.876109\pi$
$103$	−13.7999	+	23.9021i	−0.133979	+	0.232059i	0.791228	+	0.611521i	$0.209442\pi$
$104$	27.2079	−	15.7085i	0.261614	−	0.151043i
$105$		0			0
$106$	−60.6535	+	105.055i	−0.572203	+	0.991085i
$107$	−106.089	+	61.2506i	−0.991488	+	0.572436i	−0.905719	−	0.423879i	$-0.860668\pi$
$107$	−106.089	+	61.2506i	−0.991488	+	0.572436i	−0.0857691	+	0.996315i	$0.527335\pi$
$108$	79.4603	+	153.184i	0.735744	+	1.41837i
$109$	−17.0725	+	29.5705i	−0.156629	+	0.271289i	−0.933651	−	0.358184i	$-0.883396\pi$
$109$	−17.0725	+	29.5705i	−0.156629	+	0.271289i	0.777022	+	0.629473i	$0.216729\pi$
$110$		−	315.492i		−	2.86811i
$111$	87.4350	+	33.3201i	0.787702	+	0.300181i
$112$		0			0
$113$	67.4250	−	38.9278i	0.596681	−	0.344494i	−0.171054	−	0.985262i	$-0.554717\pi$
$113$	67.4250	−	38.9278i	0.596681	−	0.344494i	0.767735	+	0.640768i	$0.221384\pi$
$114$	27.0057	−	70.8654i	0.236892	−	0.621626i
$115$	27.8516	+	48.2405i	0.242188	+	0.419482i
$116$	255.041	+	147.248i	2.19863	+	1.26938i
$117$	−34.8289	+	11.5037i	−0.297683	+	0.0983218i
$118$	306.418			2.59676
$119$		0			0
$120$	20.3231	+	126.332i	0.169360	+	1.05276i
$121$	95.9449	−	166.182i	0.792933	−	1.37340i
$122$		−	237.795i		−	1.94914i
$123$	−34.3161	+	90.0486i	−0.278992	+	0.732102i
$124$	189.335			1.52689
$125$		−	107.265i		−	0.858117i
$126$		0			0
$127$	14.0742			0.110821			0.0554103	−	0.998464i	$-0.482353\pi$
$127$	14.0742			0.110821			0.0554103	+	0.998464i	$0.482353\pi$
$128$		−	202.596i		−	1.58278i
$129$	−3.19479	−	19.8593i	−0.0247658	−	0.153948i
$130$	−72.6898			−0.559152
$131$	−19.2863	−	11.1349i	−0.147223	−	0.0849995i	0.424579	−	0.905391i	$-0.360422\pi$
$131$	−19.2863	−	11.1349i	−0.147223	−	0.0849995i	−0.571802	+	0.820391i	$0.693756\pi$
$132$	−120.778	+	316.932i	−0.914982	+	2.40100i
$133$		0			0
$134$			39.2982i			0.293270i
$135$	6.73286	−	149.238i	0.0498731	−	1.10546i
$136$	−63.7988	+	110.503i	−0.469109	+	0.812520i
$137$	32.1175	−	18.5430i	0.234434	−	0.135351i	−0.378182	−	0.925731i	$-0.623451\pi$
$137$	32.1175	−	18.5430i	0.234434	−	0.135351i	0.612616	+	0.790381i	$0.290117\pi$
$138$	−15.4637	−	96.1245i	−0.112056	−	0.696554i
$139$	−70.5358	−	122.172i	−0.507451	−	0.878932i	−0.999963	−	0.00862568i	$-0.997254\pi$
$139$	−70.5358	−	122.172i	−0.507451	−	0.878932i	0.492511	−	0.870306i	$-0.336079\pi$
$140$		0			0
$141$	31.1314	+	38.2540i	0.220790	+	0.271305i
$142$	−64.5164			−0.454341
$143$	−62.4320	−	36.0451i	−0.436587	−	0.252064i
$144$	−1.30898	+	6.30857i	−0.00909014	+	0.0438095i
$145$	−127.471	−	220.787i	−0.879111	−	1.52267i
$146$	−64.1710	−	37.0491i	−0.439527	−	0.253761i
$147$		0			0
$148$	−99.6720	−	172.637i	−0.673459	−	1.16647i
$149$	100.215	+	57.8590i	0.672582	+	0.388315i	0.797054	−	0.603908i	$-0.206390\pi$
$149$	100.215	+	57.8590i	0.672582	+	0.388315i	−0.124472	+	0.992223i	$0.539724\pi$
$150$	19.3315	−	50.7275i	0.128876	−	0.338183i
$151$	75.1579	+	130.177i	0.497734	+	0.862101i	0.999997	−	0.00261420i	$-0.000832125\pi$
$151$	75.1579	+	130.177i	0.497734	+	0.862101i	−0.502262	+	0.864715i	$0.667499\pi$
$152$	−52.3523	+	30.2256i	−0.344423	+	0.198853i
$153$	99.1430	−	111.189i	0.647993	−	0.726727i
$154$		0			0
$155$	−141.946	−	81.9525i	−0.915780	−	0.528726i
$156$	73.0215	+	27.8273i	0.468086	+	0.178380i
$157$	274.056			1.74558			0.872788	−	0.488099i	$-0.162309\pi$
$157$	274.056			1.74558			0.872788	+	0.488099i	$0.162309\pi$
$158$		−	447.689i		−	2.83347i
$159$	−111.461	+	17.9309i	−0.701012	+	0.112773i
$160$	−91.6881	+	158.808i	−0.573051	+	0.992553i
$161$		0			0
$162$	−103.884	+	239.554i	−0.641257	+	1.47873i
$163$	−111.326	−	192.822i	−0.682981	−	1.18296i	−0.974067	−	0.226261i	$-0.927350\pi$
$163$	−111.326	−	192.822i	−0.682981	−	1.18296i	0.291085	−	0.956697i	$-0.405984\pi$
$164$	177.797	−	102.651i	1.08413	−	0.625923i
$165$	227.730	−	185.329i	1.38018	−	1.12320i
$166$	−25.4839	+	44.1395i	−0.153518	+	0.265900i
$167$	−62.7878	+	36.2506i	−0.375975	+	0.217069i	−0.676066	−	0.736841i	$-0.736316\pi$
$167$	−62.7878	+	36.2506i	−0.375975	+	0.217069i	0.300091	+	0.953911i	$0.402983\pi$
$168$		0			0
$169$	76.1951	−	131.974i	0.450859	−	0.780910i
$170$	255.672	−	147.612i	1.50395	−	0.868307i
$171$	67.0164	−	22.1349i	0.391909	−	0.129444i
$172$	−21.4266	+	37.1120i	−0.124573	+	0.215768i
$173$			211.173i			1.22066i	0.792149	+	0.610328i	$0.208962\pi$
$173$			211.173i			1.22066i	−0.792149	+	0.610328i	$0.791038\pi$
$174$	70.7740	+	439.942i	0.406747	+	2.52840i
$175$		0			0
$176$	−10.9665	+	6.33151i	−0.0623096	+	0.0359745i
$177$	179.998	+	221.181i	1.01694	+	1.24961i
$178$	−87.3695	−	151.328i	−0.490840	−	0.850160i
$179$	69.5967	+	40.1817i	0.388809	+	0.224479i	0.681644	−	0.731684i	$-0.261265\pi$
$179$	69.5967	+	40.1817i	0.388809	+	0.224479i	−0.292835	+	0.956163i	$0.594599\pi$
$180$	−211.813	+	237.549i	−1.17674	+	1.31972i
$181$	−122.944			−0.679250			−0.339625	−	0.940561i	$-0.610300\pi$
$181$	−122.944			−0.679250			−0.339625	+	0.940561i	$0.610300\pi$
$182$		0			0
$183$	171.647	−	139.688i	0.937961	−	0.763320i
$184$	−38.8041	+	67.2107i	−0.210892	+	0.365275i
$185$			172.570i			0.932811i
$186$	180.827	+	222.199i	0.972187	+	1.19462i
$187$	292.789			1.56572
$188$		−	105.076i		−	0.558913i
$189$		0			0
$190$	139.867			0.736141
$191$			355.490i			1.86120i	0.366032	+	0.930602i	$0.380716\pi$
$191$			355.490i			1.86120i	−0.366032	+	0.930602i	$0.619284\pi$
$192$	241.932	−	196.886i	1.26006	−	1.02545i
$193$	−39.6593			−0.205488			−0.102744	−	0.994708i	$-0.532762\pi$
$193$	−39.6593			−0.205488			−0.102744	+	0.994708i	$0.532762\pi$
$194$	480.834	+	277.610i	2.47853	+	1.43098i
$195$	−42.7000	−	52.4694i	−0.218974	−	0.269074i
$196$		0			0
$197$			130.634i			0.663119i	0.943434	+	0.331559i	$0.107575\pi$
$197$			130.634i			0.663119i	−0.943434	+	0.331559i	$0.892425\pi$
$198$	−487.294	+	160.949i	−2.46108	+	0.812871i
$199$	−108.521	+	187.964i	−0.545331	+	0.944540i	0.453255	+	0.891381i	$0.350263\pi$
$199$	−108.521	+	187.964i	−0.545331	+	0.944540i	−0.998586	+	0.0531596i	$0.983071\pi$
$200$	−37.4753	+	21.6364i	−0.187376	+	0.108182i
$201$	−28.3664	+	23.0848i	−0.141127	+	0.114850i
$202$	−27.9122	−	48.3454i	−0.138179	−	0.239333i
$203$		0			0
$204$	−313.348	+	50.4087i	−1.53602	+	0.247101i
$205$	−177.729			−0.866969
$206$	77.0498	+	44.4847i	0.374028	+	0.215945i
$207$	60.3014	−	67.6282i	0.291311	−	0.326706i
$208$	1.45879	+	2.52670i	0.00701341	+	0.0121476i
$209$	120.129	+	69.3566i	0.574781	+	0.331850i
$210$		0			0
$211$	54.6113	+	94.5895i	0.258821	+	0.448292i	0.965926	−	0.258817i	$-0.0833326\pi$
$211$	54.6113	+	94.5895i	0.258821	+	0.448292i	−0.707105	+	0.707108i	$0.749999\pi$
$212$	208.293	+	120.258i	0.982513	+	0.567254i
$213$	−37.8987	−	46.5696i	−0.177928	−	0.218637i
$214$	197.445	+	341.985i	0.922642	+	1.59806i
$215$	32.1275	−	18.5488i	0.149430	−	0.0862736i
$216$	184.758	−	95.8384i	0.855361	−	0.443696i
$217$		0			0
$218$	95.3224	+	55.0344i	0.437259	+	0.252451i
$219$	−10.9528	−	68.0839i	−0.0500126	−	0.310885i
$220$	−625.527			−2.84330
$221$		−	67.4591i		−	0.305245i
$222$	107.409	−	281.852i	0.483826	−	1.26960i
$223$	93.3685	−	161.719i	0.418693	−	0.725197i	−0.577115	−	0.816663i	$-0.695822\pi$
$223$	93.3685	−	161.719i	0.418693	−	0.725197i	0.995808	+	0.0914653i	$0.0291551\pi$
$224$		0			0
$225$	47.9723	−	15.8448i	0.213210	−	0.0704213i
$226$	−125.486	−	217.349i	−0.555249	−	0.961720i
$227$	−175.411	+	101.274i	−0.772737	+	0.446140i	−0.833850	−	0.551991i	$-0.813868\pi$
$227$	−175.411	+	101.274i	−0.772737	+	0.446140i	0.0611131	+	0.998131i	$0.480535\pi$
$228$	−140.505	−	53.5442i	−0.616250	−	0.234843i
$229$	−39.6366	+	68.6525i	−0.173085	+	0.299793i	−0.939497	−	0.342557i	$-0.888707\pi$
$229$	−39.6366	+	68.6525i	−0.173085	+	0.299793i	0.766412	+	0.642350i	$0.222040\pi$
$230$	155.506	−	89.7816i	0.676114	−	0.390355i
$231$		0			0
$232$	177.598	−	307.609i	0.765509	−	1.32590i
$233$	282.430	−	163.061i	1.21215	−	0.699833i	0.248921	−	0.968524i	$-0.419924\pi$
$233$	282.430	−	163.061i	1.21215	−	0.699833i	0.963227	+	0.268690i	$0.0865909\pi$
$234$	37.0828	+	112.273i	0.158473	+	0.479800i
$235$	−45.4814	+	78.7762i	−0.193538	+	0.335218i
$236$		−	607.536i		−	2.57430i
$237$	323.154	−	262.985i	1.36352	−	1.10964i
$238$		0			0
$239$	−210.918	+	121.774i	−0.882503	+	0.509514i	−0.871483	−	0.490426i	$-0.836841\pi$
$239$	−210.918	+	121.774i	−0.882503	+	0.509514i	−0.0110203	+	0.999939i	$0.503508\pi$
$240$	−11.7320	+	1.88734i	−0.0488832	+	0.00786391i
$241$	14.1702	+	24.5436i	0.0587976	+	0.101840i	0.893926	−	0.448215i	$-0.147940\pi$
$241$	14.1702	+	24.5436i	0.0587976	+	0.101840i	−0.835128	+	0.550055i	$0.814607\pi$
$242$	−535.697	−	309.285i	−2.21362	−	1.27804i
$243$	−233.940	+	65.7345i	−0.962717	+	0.270512i
$244$	−471.478			−1.93229
$245$		0			0
$246$	290.277	+	110.620i	1.17999	+	0.449675i
$247$	15.9799	−	27.6779i	0.0646958	−	0.112056i
$248$		−	228.359i		−	0.920804i
$249$	−46.8310	+	7.53377i	−0.188076	+	0.0302561i
$250$	−345.774			−1.38310
$251$			140.132i			0.558294i	0.960248	+	0.279147i	$0.0900516\pi$
$251$			140.132i			0.558294i	−0.960248	+	0.279147i	$0.909948\pi$
$252$		0			0
$253$	178.082			0.703882
$254$		−	45.3692i		−	0.178619i
$255$	256.739	+	97.8391i	1.00682	+	0.383683i
$256$	−237.186			−0.926506
$257$	−95.8445	−	55.3359i	−0.372936	−	0.215315i	0.301804	−	0.953370i	$-0.402411\pi$
$257$	−95.8445	−	55.3359i	−0.372936	−	0.215315i	−0.674740	+	0.738055i	$0.735744\pi$
$258$	−64.0176	+	10.2986i	−0.248130	+	0.0399171i
$259$		0			0
$260$			144.122i			0.554316i
$261$	−275.987	+	309.520i	−1.05742	+	1.18590i
$262$	−35.8942	+	62.1705i	−0.137001	+	0.237292i
$263$	−42.7543	+	24.6842i	−0.162564	+	0.0938563i	−0.579075	−	0.815274i	$-0.696586\pi$
$263$	−42.7543	+	24.6842i	−0.162564	+	0.0938563i	0.416511	+	0.909131i	$0.363253\pi$
$264$	382.256	+	145.672i	1.44794	+	0.551787i
$265$	−104.106	−	180.317i	−0.392853	−	0.680441i
$266$		0			0
$267$	57.9095	−	151.960i	0.216890	−	0.569139i
$268$	77.9166			0.290734
$269$	162.040	+	93.5538i	0.602379	+	0.347784i	0.769977	−	0.638072i	$-0.220268\pi$
$269$	162.040	+	93.5538i	0.602379	+	0.347784i	−0.167598	+	0.985855i	$0.553601\pi$
$270$	−481.077	−	21.7038i	−1.78177	−	0.0803845i
$271$	−108.146	−	187.315i	−0.399064	−	0.691199i	0.594547	−	0.804061i	$-0.297332\pi$
$271$	−108.146	−	187.315i	−0.399064	−	0.691199i	−0.993611	+	0.112862i	$0.963998\pi$
$272$	−10.2620	−	5.92476i	−0.0377279	−	0.0217822i
$273$		0			0
$274$	−59.7747	−	103.533i	−0.218156	−	0.377857i
$275$	85.9920	+	49.6475i	0.312698	+	0.180536i
$276$	−190.586	+	30.6599i	−0.690530	+	0.111086i
$277$	−39.0618	−	67.6570i	−0.141017	−	0.244249i	0.786863	−	0.617128i	$-0.211704\pi$
$277$	−39.0618	−	67.6570i	−0.141017	−	0.244249i	−0.927880	+	0.372879i	$0.878371\pi$
$278$	−393.828	+	227.377i	−1.41665	+	0.817901i
$279$	−54.1661	+	261.051i	−0.194144	+	0.935666i
$280$		0			0
$281$	−385.051	−	222.309i	−1.37029	−	0.791135i	−0.379323	−	0.925264i	$-0.623843\pi$
$281$	−385.051	−	222.309i	−1.37029	−	0.791135i	−0.990964	+	0.134129i	$0.957176\pi$
$282$	123.314	−	100.354i	0.437285	−	0.355865i
$283$	128.424			0.453796			0.226898	−	0.973919i	$-0.427142\pi$
$283$	128.424			0.453796			0.226898	+	0.973919i	$0.427142\pi$
$284$			127.917i			0.450411i
$285$	82.1616	+	100.960i	0.288286	+	0.354244i
$286$	−116.194	+	201.254i	−0.406272	+	0.703684i
$287$		0			0
$288$	292.063	+	60.6008i	1.01411	+	0.210419i
$289$	−7.50994	−	13.0076i	−0.0259859	−	0.0450090i
$290$	−711.720	+	410.912i	−2.45421	+	1.41694i
$291$	82.0692	+	510.154i	0.282025	+	1.75311i
$292$	−73.4574	+	127.232i	−0.251566	+	0.435726i
$293$	42.6510	−	24.6246i	0.145567	−	0.0840429i	−0.425448	−	0.904983i	$-0.639883\pi$
$293$	42.6510	−	24.6246i	0.145567	−	0.0840429i	0.571014	+	0.820940i	$0.306550\pi$
$294$		0			0
$295$	−262.969	+	455.475i	−0.891420	+	1.54398i
$296$	−208.220	+	120.216i	−0.703446	+	0.406135i
$297$	−402.426	−	257.196i	−1.35497	−	0.865979i
$298$	186.512	−	323.049i	0.625880	−	1.08406i
$299$		−	41.0304i		−	0.137225i
$300$	−100.578	−	38.3285i	−0.335259	−	0.127762i
$301$		0			0
$302$	419.635	−	242.276i	1.38952	−	0.802239i
$303$	18.5005	−	48.5471i	0.0610579	−	0.160222i
$304$	−2.80694	−	4.86177i	−0.00923337	−	0.0159927i
$305$	353.471	+	204.077i	1.15892	+	0.669104i
$306$	−358.426	−	319.594i	−1.17133	−	1.04442i
$307$	387.296			1.26155			0.630776	−	0.775965i	$-0.282737\pi$
$307$	387.296			1.26155			0.630776	+	0.775965i	$0.282737\pi$
$308$		0			0
$309$	13.1509	+	81.7481i	0.0425596	+	0.264557i
$310$	−264.179	+	457.572i	−0.852191	+	1.47604i
$311$		−	101.097i		−	0.325070i	−0.986703	−	0.162535i	$-0.948033\pi$
$311$		−	101.097i		−	0.325070i	0.986703	−	0.162535i	$-0.0519671\pi$
$312$	33.5630	−	88.0724i	0.107574	−	0.282283i
$313$	−364.791			−1.16547			−0.582733	−	0.812663i	$-0.698017\pi$
$313$	−364.791			−1.16547			−0.582733	+	0.812663i	$0.698017\pi$
$314$		−	883.436i		−	2.81349i
$315$		0			0
$316$	−887.634			−2.80897
$317$			33.1510i			0.104577i	0.998632	+	0.0522886i	$0.0166516\pi$
$317$			33.1510i			0.104577i	−0.998632	+	0.0522886i	$0.983348\pi$
$318$	57.8013	+	359.301i	0.181765	+	1.12988i
$319$	−815.045			−2.55500
$320$	498.208	+	287.641i	1.55690	+	0.898877i
$321$	−130.869	+	343.413i	−0.407692	+	1.06982i
$322$		0			0
$323$			129.802i			0.401864i
$324$	474.964	+	205.970i	1.46594	+	0.635711i
$325$	11.4388	−	19.8127i	0.0351965	−	0.0609621i
$326$	−621.575	+	358.866i	−1.90667	+	1.10082i
$327$	16.2697	+	101.135i	0.0497545	+	0.309281i
$328$	−123.809	−	214.444i	−0.377468	−	0.653794i
$329$		0			0
$330$	−597.419	−	734.103i	−1.81036	−	2.22456i
$331$	−90.5077			−0.273437			−0.136719	−	0.990610i	$-0.543656\pi$
$331$	−90.5077			−0.273437			−0.136719	+	0.990610i	$0.543656\pi$
$332$	87.5154	+	50.5271i	0.263601	+	0.152190i
$333$	266.543	−	88.0368i	0.800431	−	0.264375i
$334$	116.856	+	202.401i	0.349869	+	0.605990i
$335$	−58.4148	−	33.7258i	−0.174373	−	0.100674i
$336$		0			0
$337$	216.839	+	375.576i	0.643438	+	1.11447i	0.984660	+	0.174485i	$0.0558261\pi$
$337$	216.839	+	375.576i	0.643438	+	1.11447i	−0.341221	+	0.939983i	$0.610841\pi$
$338$	−425.426	−	245.620i	−1.25866	−	0.726686i
$339$	83.1738	−	218.256i	0.245351	−	0.643822i
$340$	−292.671	−	506.921i	−0.860797	−	1.49094i
$341$	−453.798	+	262.000i	−1.33079	+	0.768329i
$342$	−71.3532	−	216.032i	−0.208635	−	0.631671i
$343$		0			0
$344$	44.7614	+	25.8430i	0.130120	+	0.0751250i
$345$	156.155	+	59.5083i	0.452624	+	0.172488i
$346$	680.731			1.96743
$347$			11.6949i			0.0337029i	0.999858	+	0.0168514i	$0.00536423\pi$
$347$			11.6949i			0.0337029i	−0.999858	+	0.0168514i	$0.994636\pi$
$348$	872.273	−	140.324i	2.50653	−	0.403229i
$349$	−91.7075	+	158.842i	−0.262772	+	0.455135i	−0.966978	−	0.254862i	$-0.917970\pi$
$349$	−91.7075	+	158.842i	−0.262772	+	0.455135i	0.704205	+	0.709996i	$0.251303\pi$
$350$		0			0
$351$	−59.2583	+	92.7196i	−0.168827	+	0.264159i
$352$	293.125	+	507.707i	0.832741	+	1.44235i
$353$	58.9619	−	34.0417i	0.167031	−	0.0964353i	−0.414154	−	0.910207i	$-0.635923\pi$
$353$	58.9619	−	34.0417i	0.167031	−	0.0964353i	0.581185	+	0.813771i	$0.302589\pi$
$354$	712.990	−	580.236i	2.01410	−	1.63909i
$355$	55.3681	−	95.9004i	0.155967	−	0.270142i
$356$	−300.039	+	173.228i	−0.842807	+	0.486595i
$357$		0			0
$358$	129.528	−	224.350i	0.361811	−	0.626675i
$359$	−386.169	+	222.955i	−1.07568	+	0.621044i	−0.929728	−	0.368247i	$-0.879958\pi$
$359$	−386.169	+	222.955i	−1.07568	+	0.621044i	−0.145952	+	0.989292i	$0.546625\pi$
$360$	286.512	+	255.471i	0.795866	+	0.709642i
$361$	149.752	−	259.378i	0.414826	−	0.718500i
$362$			396.319i			1.09480i
$363$	−91.4332	−	568.362i	−0.251882	−	1.56574i
$364$		0			0
$365$	110.143	−	63.5913i	0.301763	−	0.174223i
$366$	−450.292	−	553.315i	−1.23031	−	1.51179i
$367$	63.3424	+	109.712i	0.172595	+	0.298943i	0.939326	−	0.343025i	$-0.111451\pi$
$367$	63.3424	+	109.712i	0.172595	+	0.298943i	−0.766731	+	0.641968i	$0.778118\pi$
$368$	−6.24161	−	3.60360i	−0.0169609	−	0.00979238i
$369$	90.6684	+	274.511i	0.245714	+	0.743932i
$370$	556.291			1.50349
$371$		0			0
$372$	440.553	−	358.526i	1.18428	−	0.963779i
$373$	306.165	−	530.293i	0.820817	−	1.42170i	−0.0842582	−	0.996444i	$-0.526852\pi$
$373$	306.165	−	530.293i	0.820817	−	1.42170i	0.905075	−	0.425252i	$-0.139815\pi$
$374$		−	943.825i		−	2.52360i
$375$	−203.117	−	249.589i	−0.541646	−	0.665570i
$376$	−126.733			−0.337057
$377$			187.787i			0.498110i
$378$		0			0
$379$	410.847			1.08403			0.542015	−	0.840369i	$-0.317662\pi$
$379$	410.847			1.08403			0.542015	+	0.840369i	$0.317662\pi$
$380$		−	277.314i		−	0.729775i
$381$	32.7486	−	26.6511i	0.0859544	−	0.0699504i
$382$	1145.95			2.99986
$383$	−190.627	−	110.059i	−0.497722	−	0.287360i	0.230051	−	0.973179i	$-0.426111\pi$
$383$	−190.627	−	110.059i	−0.497722	−	0.287360i	−0.727772	+	0.685819i	$0.759444\pi$
$384$	−383.638	−	471.411i	−0.999056	−	1.22763i
$385$		0			0
$386$			127.844i			0.331203i
$387$	−45.0395	−	40.1599i	−0.116381	−	0.103772i
$388$	550.417	−	953.351i	1.41860	−	2.45709i
$389$	149.180	−	86.1293i	0.383497	−	0.221412i	−0.295842	−	0.955237i	$-0.595600\pi$
$389$	149.180	−	86.1293i	0.383497	−	0.221412i	0.679339	+	0.733825i	$0.262267\pi$
$390$	−169.138	+	137.646i	−0.433688	+	0.352939i
$391$	83.3209	+	144.316i	0.213097	+	0.369095i
$392$		0			0
$393$	−65.9615	+	10.6113i	−0.167841	+	0.0270008i
$394$	421.109			1.06880
$395$	665.468	+	384.208i	1.68473	+	0.972678i
$396$	319.113	+	966.159i	0.805841	+	2.43979i
$397$	185.521	+	321.332i	0.467308	+	0.809401i	0.999302	−	0.0373470i	$-0.0118907\pi$
$397$	185.521	+	321.332i	0.467308	+	0.809401i	−0.531995	+	0.846748i	$0.678557\pi$
$398$	605.912	+	349.824i	1.52239	+	0.878954i
$399$		0			0
$400$	−2.00929	−	3.48020i	−0.00502323	−	0.00870049i
$401$	−259.303	−	149.708i	−0.646640	−	0.373338i	0.140528	−	0.990077i	$-0.455120\pi$
$401$	−259.303	−	149.708i	−0.646640	−	0.373338i	−0.787168	+	0.616739i	$0.788453\pi$
$402$	74.4154	+	91.4411i	0.185113	+	0.227465i
$403$	60.3652	+	104.556i	0.149790	+	0.259443i
$404$	−95.8544	+	55.3416i	−0.237263	+	0.136984i
$405$	−266.932	−	360.004i	−0.659090	−	0.888898i
$406$		0			0
$407$	477.788	+	275.851i	1.17393	+	0.677767i
$408$	60.7987	+	377.934i	0.149016	+	0.926308i
$409$	374.401			0.915407			0.457703	−	0.889105i	$-0.348672\pi$
$409$	374.401			0.915407			0.457703	+	0.889105i	$0.348672\pi$
$410$			572.919i			1.39736i
$411$	39.6194	−	103.965i	0.0963975	−	0.252956i
$412$	88.2000	−	152.767i	0.214078	−	0.370793i
$413$		0			0
$414$	−218.004	−	194.385i	−0.526580	−	0.469530i
$415$	−43.7408	−	75.7613i	−0.105399	−	0.182557i
$416$	116.976	−	67.5364i	0.281193	−	0.162347i
$417$	−395.471	−	150.708i	−0.948373	−	0.361410i
$418$	223.576	−	387.244i	0.534870	−	0.926422i
$419$	−350.317	+	202.256i	−0.836080	+	0.482711i	−0.855930	−	0.517092i	$-0.827014\pi$
$419$	−350.317	+	202.256i	−0.836080	+	0.482711i	0.0198501	+	0.999803i	$0.493681\pi$
$420$		0			0
$421$	−231.002	+	400.107i	−0.548698	+	0.950372i	0.449666	+	0.893197i	$0.351543\pi$
$421$	−231.002	+	400.107i	−0.548698	+	0.950372i	−0.998364	+	0.0571757i	$0.981790\pi$
$422$	304.916	−	176.043i	0.722549	−	0.417164i
$423$	144.876	+	30.0607i	0.342497	+	0.0710655i
$424$	145.045	−	251.225i	0.342087	−	0.592512i
$425$			92.9161i			0.218626i
$426$	−150.120	+	122.169i	−0.352395	+	0.286781i
$427$		0			0
$428$	678.055	−	391.475i	1.58424	−	0.914662i
$429$	−213.525	+	34.3501i	−0.497728	+	0.0800703i
$430$	−59.7933	−	103.565i	−0.139054	−	0.240849i
$431$	197.559	+	114.061i	0.458374	+	0.264643i	0.711360	−	0.702827i	$-0.248079\pi$
$431$	197.559	+	114.061i	0.458374	+	0.264643i	−0.252986	+	0.967470i	$0.581413\pi$
$432$	8.90017	+	17.1578i	0.0206022	+	0.0397171i
$433$	−777.626			−1.79590			−0.897951	−	0.440095i	$-0.854945\pi$
$433$	−777.626			−1.79590			−0.897951	+	0.440095i	$0.854945\pi$
$434$		0			0
$435$	−714.690	−	272.357i	−1.64297	−	0.626108i
$436$	109.117	−	188.996i	0.250268	−	0.433477i
$437$			78.9490i			0.180661i
$438$	−219.473	+	35.3069i	−0.501080	+	0.0806094i
$439$	−68.8012			−0.156722			−0.0783612	−	0.996925i	$-0.524969\pi$
$439$	−68.8012			−0.156722			−0.0783612	+	0.996925i	$0.524969\pi$
$440$			754.458i			1.71468i
$441$		0			0
$442$	−217.459			−0.491988
$443$		−	208.330i		−	0.470271i	−0.971963	−	0.235136i	$-0.924447\pi$
$443$		−	208.330i		−	0.470271i	0.971963	−	0.235136i	$-0.0755534\pi$
$444$	−558.829	−	212.961i	−1.25862	−	0.479642i
$445$	299.923			0.673984
$446$	−521.312	−	300.979i	−1.16886	−	0.674842i
$447$	342.747	−	55.1382i	0.766772	−	0.123352i
$448$		0			0
$449$		−	259.045i		−	0.576937i	−0.957489	−	0.288469i	$-0.906854\pi$
$449$		−	259.045i		−	0.576937i	0.957489	−	0.288469i	$-0.0931461\pi$
$450$	−51.0767	−	154.642i	−0.113504	−	0.343648i
$451$	−284.097	+	492.071i	−0.629927	+	1.09107i
$452$	−430.938	+	248.802i	−0.953402	+	0.550447i
$453$	421.386	+	160.584i	0.930212	+	0.354489i
$454$	326.463	+	565.450i	0.719081	+	1.24548i
$455$		0			0
$456$	−64.5806	+	169.465i	−0.141624	+	0.371635i
$457$	159.437			0.348878			0.174439	−	0.984668i	$-0.444189\pi$
$457$	159.437			0.348878			0.174439	+	0.984668i	$0.444189\pi$
$458$	221.306	+	127.771i	0.483201	+	0.278976i
$459$	20.1420	−	446.459i	0.0438824	−	0.972678i
$460$	−178.010	−	308.323i	−0.386979	−	0.670267i
$461$	176.910	+	102.139i	0.383752	+	0.221559i	0.679449	−	0.733722i	$-0.262219\pi$
$461$	176.910	+	102.139i	0.383752	+	0.221559i	−0.295697	+	0.955282i	$0.595552\pi$
$462$		0			0
$463$	−381.105	−	660.092i	−0.823120	−	1.42569i	−0.903348	−	0.428909i	$-0.858898\pi$
$463$	−381.105	−	660.092i	−0.823120	−	1.42569i	0.0802276	−	0.996777i	$-0.474435\pi$
$464$	28.5666	+	16.4929i	0.0615659	+	0.0355451i
$465$	−485.473	+	78.0987i	−1.04403	+	0.167954i
$466$	−525.638	−	910.432i	−1.12798	−	1.95372i
$467$	462.046	−	266.762i	0.989391	−	0.571225i	0.0842988	−	0.996441i	$-0.473135\pi$
$467$	462.046	−	266.762i	0.989391	−	0.571225i	0.905092	+	0.425215i	$0.139802\pi$
$468$	222.604	−	73.5241i	0.475650	−	0.157103i
$469$		0			0
$470$	253.940	+	146.612i	0.540298	+	0.311941i
$471$	637.687	−	518.954i	1.35390	−	1.10181i
$472$	−732.759			−1.55245
$473$		−	118.600i		−	0.250741i
$474$	−847.748	−	1041.71i	−1.78850	−	2.19769i
$475$	−22.0102	+	38.1228i	−0.0463372	+	0.0802584i
$476$		0			0
$477$	−225.399	+	252.786i	−0.472535	+	0.529950i
$478$	392.545	+	679.909i	0.821225	+	1.42240i
$479$	−523.526	+	302.258i	−1.09296	+	0.631019i	−0.934362	−	0.356325i	$-0.884030\pi$
$479$	−523.526	+	302.258i	−1.09296	+	0.631019i	−0.158595	+	0.987344i	$0.550696\pi$
$480$	87.3766	+	543.145i	0.182034	+	1.13155i
$481$	63.5565	−	110.083i	0.132134	−	0.228863i
$482$	79.1177	−	45.6787i	0.164145	−	0.0947690i
$483$		0			0
$484$	−613.220	+	1062.13i	−1.26698	+	2.19448i
$485$	−825.306	+	476.491i	−1.70166	+	0.982455i
$486$	211.899	+	754.121i	0.436007	+	1.55169i
$487$	−78.1017	+	135.276i	−0.160373	+	0.277774i	−0.935002	−	0.354641i	$-0.884603\pi$
$487$	−78.1017	+	135.276i	−0.160373	+	0.277774i	0.774629	+	0.632415i	$0.217936\pi$
$488$			568.657i			1.16528i
$489$	−624.169	−	237.861i	−1.27642	−	0.486423i
$490$		0			0
$491$	−346.903	+	200.285i	−0.706523	+	0.407911i	−0.809772	−	0.586744i	$-0.800409\pi$
$491$	−346.903	+	200.285i	−0.706523	+	0.407911i	0.103249	+	0.994656i	$0.467076\pi$
$492$	219.327	−	575.534i	0.445786	−	1.16978i
$493$	−381.342	−	660.505i	−0.773514	−	1.33977i
$494$	−89.2216	−	51.5121i	−0.180611	−	0.104276i
$495$	178.955	−	862.465i	0.361525	−	1.74235i
$496$	21.2069			0.0427559
$497$		0			0
$498$	24.2856	+	150.963i	0.0487662	+	0.303138i
$499$	61.1444	−	105.905i	0.122534	−	0.212235i	−0.798232	−	0.602350i	$-0.794231\pi$
$499$	61.1444	−	105.905i	0.122534	−	0.212235i	0.920766	+	0.390115i	$0.127565\pi$
$500$			685.567i			1.37113i
$501$	−77.4536	+	203.245i	−0.154598	+	0.405680i
$502$	451.724			0.899848
$503$			786.814i			1.56424i	0.623126	+	0.782121i	$0.285862\pi$
$503$			786.814i			1.56424i	−0.623126	+	0.782121i	$0.714138\pi$
$504$		0			0
$505$	95.8173			0.189737
$506$		−	574.059i		−	1.13450i
$507$	−72.6121	−	451.368i	−0.143219	−	0.890271i
$508$	−89.9536			−0.177074
$509$	781.867	+	451.411i	1.53609	+	0.886859i	0.999062	+	0.0432914i	$0.0137844\pi$
$509$	781.867	+	451.411i	1.53609	+	0.886859i	0.537023	+	0.843568i	$0.319549\pi$
$510$	315.391	−	827.614i	0.618413	−	1.62277i
$511$		0			0
$512$		−	45.8004i		−	0.0894539i
$513$	114.022	−	178.407i	0.222266	−	0.347773i
$514$	−178.379	+	308.961i	−0.347040	+	0.601092i
$515$	−132.249	+	76.3539i	−0.256794	+	0.148260i
$516$	20.4191	+	126.928i	0.0395718	+	0.245984i
$517$	145.403	+	251.846i	0.281244	+	0.487129i
$518$		0			0
$519$	399.880	+	491.369i	0.770482	+	0.946762i
$520$	173.828			0.334285
$521$	−442.743	−	255.618i	−0.849795	−	0.490630i	0.0107865	−	0.999942i	$-0.496566\pi$
$521$	−442.743	−	255.618i	−0.849795	−	0.490630i	−0.860582	+	0.509312i	$0.829900\pi$
$522$	997.759	+	889.661i	1.91141	+	1.70433i
$523$	−489.654	−	848.105i	−0.936240	−	1.62162i	−0.772407	−	0.635128i	$-0.780947\pi$
$523$	−489.654	−	848.105i	−0.936240	−	1.62162i	−0.163833	−	0.986488i	$-0.552386\pi$
$524$	123.266	+	71.1675i	0.235240	+	0.135816i
$525$		0			0
$526$	79.5711	+	137.821i	0.151276	+	0.262018i
$527$	−424.645	−	245.169i	−0.805778	−	0.465216i
$528$	−13.5280	+	35.4988i	−0.0256212	+	0.0672325i
$529$	−213.822	−	370.351i	−0.404200	−	0.700096i
$530$	−581.263	+	335.592i	−1.09672	+	0.633193i
$531$	837.659	+	173.808i	1.57751	+	0.327322i
$532$		0			0
$533$	113.374	+	65.4564i	0.212709	+	0.122807i
$534$	−489.853	−	186.675i	−0.917327	−	0.349579i
$535$	−677.793			−1.26690
$536$		−	93.9764i		−	0.175329i
$537$	238.030	−	38.2922i	0.443258	−	0.0713076i
$538$	301.577	−	522.346i	0.560552	−	0.970904i
$539$		0			0
$540$	−43.0322	+	953.833i	−0.0796893	+	1.76636i
$541$	350.265	+	606.676i	0.647439	+	1.12140i	0.983732	+	0.179640i	$0.0574934\pi$
$541$	350.265	+	606.676i	0.647439	+	1.12140i	−0.336293	+	0.941757i	$0.609173\pi$
$542$	−603.822	+	348.617i	−1.11406	+	0.643204i
$543$	−286.073	+	232.808i	−0.526838	+	0.428745i
$544$	−274.294	+	475.091i	−0.504217	+	0.873329i
$545$	−163.612	+	94.4613i	−0.300205	+	0.173324i
$546$		0			0
$547$	294.015	−	509.248i	0.537504	−	0.930984i	−0.461534	−	0.887123i	$-0.652701\pi$
$547$	294.015	−	509.248i	0.537504	−	0.930984i	0.999038	−	0.0438616i	$-0.0139660\pi$
$548$	−205.275	+	118.515i	−0.374589	+	0.216269i
$549$	134.883	−	650.065i	0.245689	−	1.18409i
$550$	160.042	−	277.201i	0.290985	−	0.504001i
$551$		−	361.333i		−	0.655777i
$552$	36.9794	+	229.869i	0.0669916	+	0.416430i
$553$		0			0
$554$	−218.097	+	125.918i	−0.393676	+	0.227289i
$555$	326.780	+	401.545i	0.588794	+	0.723505i
$556$	450.820	+	780.843i	0.810827	+	1.40439i
$557$	347.042	+	200.365i	0.623055	+	0.359721i	0.778057	−	0.628193i	$-0.216205\pi$
$557$	347.042	+	200.365i	0.623055	+	0.359721i	−0.155002	+	0.987914i	$0.549539\pi$
$558$	841.514	+	174.608i	1.50809	+	0.312917i
$559$	−27.3257			−0.0488831
$560$		0			0
$561$	681.278	−	554.429i	1.21440	−	0.988287i
$562$	−716.628	+	1241.24i	−1.27514	+	2.20860i
$563$		−	91.1620i		−	0.161922i	−0.996717	−	0.0809609i	$-0.974201\pi$
$563$		−	91.1620i		−	0.161922i	0.996717	−	0.0809609i	$-0.0257989\pi$
$564$	−198.972	−	244.495i	−0.352788	−	0.433502i
$565$	430.771			0.762426
$566$		−	413.984i		−	0.731421i
$567$		0			0
$568$	154.282			0.271624
$569$			295.137i			0.518693i	0.965784	+	0.259347i	$0.0835072\pi$
$569$			295.137i			0.518693i	−0.965784	+	0.259347i	$0.916493\pi$
$570$	325.450	−	264.853i	0.570964	−	0.464655i
$571$	914.813			1.60212			0.801062	−	0.598581i	$-0.204268\pi$
$571$	914.813			1.60212			0.801062	+	0.598581i	$0.204268\pi$
$572$	399.026	+	230.378i	0.697598	+	0.402758i
$573$	673.159	+	827.173i	1.17480	+	1.44358i
$574$		0			0
$575$			56.5140i			0.0982852i
$576$	190.115	−	916.249i	0.330060	−	1.59071i
$577$	267.301	−	462.978i	0.463259	−	0.802389i	−0.535862	−	0.844306i	$-0.680013\pi$
$577$	267.301	−	462.978i	0.463259	−	0.802389i	0.999121	+	0.0419171i	$0.0133465\pi$
$578$	−41.9308	+	24.2088i	−0.0725447	+	0.0418837i
$579$	−92.2812	+	75.0992i	−0.159380	+	0.129705i
$580$	814.715	+	1411.13i	1.40468	+	2.43298i
$581$		0			0
$582$	1644.51	−	264.555i	2.82563	−	0.454562i
$583$	−665.649			−1.14177
$584$	153.456	+	88.5981i	0.262768	+	0.151709i
$585$	−198.713	−	41.2314i	−0.339681	−	0.0704811i
$586$	−79.3789	−	137.488i	−0.135459	−	0.234622i
$587$	−299.889	−	173.141i	−0.510884	−	0.294959i	0.222313	−	0.974975i	$-0.428639\pi$
$587$	−299.889	−	173.141i	−0.510884	−	0.294959i	−0.733197	+	0.680016i	$0.761973\pi$
$588$		0			0
$589$	−116.152	−	201.182i	−0.197203	−	0.341565i
$590$	1468.25	+	847.697i	2.48857	+	1.43677i
$591$	247.371	+	303.967i	0.418563	+	0.514327i
$592$	−11.1640	−	19.3367i	−0.0188582	−	0.0326633i
$593$	−3.55214	+	2.05083i	−0.00599012	+	0.00345840i	−0.502992	−	0.864291i	$-0.667768\pi$
$593$	−3.55214	+	2.05083i	−0.00599012	+	0.00345840i	0.497002	+	0.867749i	$0.334434\pi$
$594$	−829.087	+	1297.25i	−1.39577	+	2.18392i
$595$		0			0
$596$	−640.509	−	369.798i	−1.07468	−	0.620467i
$597$	103.418	+	642.859i	0.173229	+	1.07682i
$598$	−132.264			−0.221177
$599$		−	169.572i		−	0.283091i	−0.989932	−	0.141546i	$-0.954793\pi$
$599$		−	169.572i		−	0.283091i	0.989932	−	0.141546i	$-0.0452072\pi$
$600$	−46.2286	+	121.308i	−0.0770477	+	0.202180i
$601$	312.975	−	542.089i	0.520757	−	0.901978i	−0.478951	−	0.877841i	$-0.658983\pi$
$601$	312.975	−	542.089i	0.520757	−	0.901978i	0.999709	−	0.0241366i	$-0.00768366\pi$
$602$		0			0
$603$	−22.2909	+	107.430i	−0.0369667	+	0.178159i
$604$	−480.362	−	832.011i	−0.795301	−	1.37750i
$605$	919.473	−	530.858i	1.51979	−	0.877451i
$606$	−156.495	−	59.6377i	−0.258242	−	0.0984120i
$607$	−18.8059	+	32.5727i	−0.0309817	+	0.0536618i	−0.881101	−	0.472929i	$-0.843197\pi$
$607$	−18.8059	+	32.5727i	−0.0309817	+	0.0536618i	0.850119	+	0.526591i	$0.176530\pi$
$608$	−225.081	+	129.951i	−0.370200	+	0.213735i
$609$		0			0
$610$	657.855	−	1139.44i	1.07845	−	1.86793i
$611$	58.0256	−	33.5011i	0.0949682	−	0.0548299i
$612$	−633.659	+	710.652i	−1.03539	+	1.16120i
$613$	−149.019	+	258.108i	−0.243098	+	0.421057i	−0.961595	−	0.274472i	$-0.911497\pi$
$613$	−149.019	+	258.108i	−0.243098	+	0.421057i	0.718497	+	0.695530i	$0.244830\pi$
$614$		−	1248.48i		−	2.03335i
$615$	−413.548	+	336.549i	−0.672436	+	0.547233i
$616$		0			0
$617$	818.560	−	472.596i	1.32668	−	0.765957i	0.341893	−	0.939739i	$-0.388932\pi$
$617$	818.560	−	472.596i	1.32668	−	0.765957i	0.984784	+	0.173782i	$0.0555987\pi$
$618$	263.520	−	42.3929i	0.426408	−	0.0685969i
$619$	−596.799	−	1033.69i	−0.964133	−	1.66993i	−0.711926	−	0.702255i	$-0.752177\pi$
$619$	−596.799	−	1033.69i	−0.964133	−	1.66993i	−0.252208	−	0.967673i	$-0.581157\pi$
$620$	907.229	+	523.789i	1.46327	+	0.844820i
$621$	12.2509	−	271.548i	0.0197277	−	0.437276i
$622$	−325.892			−0.523943
$623$		0			0
$624$	8.17896	+	3.11687i	0.0131073	+	0.00499499i
$625$	366.913	−	635.512i	0.587061	−	1.01682i
$626$			1175.93i			1.87848i
$627$	410.857	−	66.0952i	0.655275	−	0.105415i
$628$	−1751.59			−2.78916
$629$			516.260i			0.820764i
$630$		0			0
$631$	−823.055			−1.30437			−0.652183	−	0.758062i	$-0.726147\pi$
$631$	−823.055			−1.30437			−0.652183	+	0.758062i	$0.726147\pi$
$632$			1070.59i			1.69397i
$633$	306.188	+	116.683i	0.483709	+	0.184334i
$634$	106.864			0.168556
$635$	67.4390	+	38.9359i	0.106203	+	0.0613165i
$636$	712.388	−	114.603i	1.12011	−	0.180193i
$637$		0			0
$638$			2627.35i			4.11810i
$639$	−176.369	−	36.5953i	−0.276008	−	0.0572696i
$640$	560.476	−	970.773i	0.875744	−	1.51683i
$641$	−617.070	+	356.265i	−0.962667	+	0.555796i	−0.896993	−	0.442045i	$-0.854253\pi$
$641$	−617.070	+	356.265i	−0.962667	+	0.555796i	−0.0656744	+	0.997841i	$0.520920\pi$
$642$	1107.01	+	421.865i	1.72432	+	0.657111i
$643$	−534.902	−	926.478i	−0.831885	−	1.44087i	−0.896542	−	0.442960i	$-0.853928\pi$
$643$	−534.902	−	926.478i	−0.831885	−	1.44087i	0.0646564	−	0.997908i	$-0.479405\pi$
$644$		0			0
$645$	39.6317	−	103.997i	0.0614445	−	0.161236i
$646$	418.425			0.647717
$647$	−973.422	−	562.006i	−1.50452	−	0.868633i	−0.999986	−	0.00523936i	$-0.998332\pi$
$647$	−973.422	−	562.006i	−1.50452	−	0.868633i	−0.504531	−	0.863394i	$-0.668334\pi$
$648$	248.424	−	572.861i	0.383370	−	0.884045i
$649$	840.705	+	1456.14i	1.29539	+	2.24367i
$650$	−63.8674	−	36.8739i	−0.0982576	−	0.0567290i
$651$		0			0
$652$	711.525	+	1232.40i	1.09130	+	1.89018i
$653$	41.9432	+	24.2159i	0.0642315	+	0.0370841i	0.531772	−	0.846888i	$-0.321526\pi$
$653$	41.9432	+	24.2159i	0.0642315	+	0.0370841i	−0.467540	+	0.883972i	$0.654860\pi$
$654$	326.015	−	52.4464i	0.498494	−	0.0801933i
$655$	−61.6090	−	106.710i	−0.0940595	−	0.162916i
$656$	19.9147	−	11.4977i	0.0303577	−	0.0175270i
$657$	−154.410	−	137.681i	−0.235023	−	0.209560i
$658$		0			0
$659$	−818.128	−	472.346i	−1.24147	−	0.716762i	−0.272076	−	0.962276i	$-0.587710\pi$
$659$	−818.128	−	472.346i	−1.24147	−	0.716762i	−0.969393	+	0.245514i	$0.921043\pi$
$660$	−1455.51	+	1184.50i	−2.20532	+	1.79470i
$661$	−281.194			−0.425407			−0.212703	−	0.977117i	$-0.568227\pi$
$661$	−281.194			−0.425407			−0.212703	+	0.977117i	$0.568227\pi$
$662$			291.757i			0.440721i
$663$	−127.741	−	156.967i	−0.192671	−	0.236753i
$664$	60.9415	−	105.554i	0.0917794	−	0.158967i
$665$		0			0
$666$	−283.792	−	859.220i	−0.426114	−	1.29012i
$667$	−231.942	−	401.736i	−0.347740	−	0.602303i
$668$	401.300	−	231.691i	0.600749	−	0.346843i
$669$	−88.9779	−	553.100i	−0.133001	−	0.826756i
$670$	−108.717	+	188.304i	−0.162265	+	0.281051i
$671$	1130.04	−	652.429i	1.68411	−	0.972323i
$672$		0			0
$673$	246.892	−	427.630i	0.366854	−	0.635409i	−0.622218	−	0.782844i	$-0.713768\pi$
$673$	246.892	−	427.630i	0.366854	−	0.635409i	0.989072	+	0.147435i	$0.0471017\pi$
$674$	1210.69	−	698.994i	1.79628	−	1.03708i
$675$	81.6205	−	127.709i	0.120919	−	0.189199i
$676$	−486.991	+	843.494i	−0.720401	+	1.24777i
$677$			705.620i			1.04227i	0.853473	+	0.521137i	$0.174492\pi$
$677$			705.620i			1.04227i	−0.853473	+	0.521137i	$0.825508\pi$
$678$	−703.562	−	268.116i	−1.03770	−	0.395452i
$679$		0			0
$680$	−611.405	+	352.995i	−0.899126	+	0.519110i
$681$	−216.383	+	567.810i	−0.317743	+	0.833788i
$682$	844.575	+	1462.85i	1.23838	+	2.14494i
$683$	−1010.24	−	583.260i	−1.47912	−	0.853968i	−0.479394	−	0.877600i	$-0.659144\pi$
$683$	−1010.24	−	583.260i	−1.47912	−	0.853968i	−0.999721	+	0.0236320i	$0.992477\pi$
$684$	−428.326	+	141.472i	−0.626208	+	0.206831i
$685$	205.195			0.299555
$686$		0			0
$687$	37.7727	+	234.800i	0.0549821	+	0.341777i
$688$	−2.39995	+	4.15683i	−0.00348829	+	0.00604190i
$689$			153.366i			0.222593i
$690$	191.829	−	503.377i	0.278013	−	0.729531i
$691$	−365.668			−0.529186			−0.264593	−	0.964360i	$-0.585238\pi$
$691$	−365.668			−0.529186			−0.264593	+	0.964360i	$0.585238\pi$
$692$		−	1349.69i		−	1.95041i
$693$		0			0
$694$	37.6993			0.0543217
$695$		−	780.541i		−	1.12308i
$696$	−169.247	−	1052.06i	−0.243171	−	1.51158i
$697$	−531.692			−0.762830
$698$	512.038	+	295.625i	0.733578	+	0.423532i
$699$	348.399	−	914.232i	0.498425	−	1.30791i
$700$		0			0
$701$		−	254.519i		−	0.363080i	−0.983384	−	0.181540i	$-0.941892\pi$
$701$		−	254.519i		−	0.363080i	0.983384	−	0.181540i	$-0.0581083\pi$
$702$	298.888	+	191.023i	0.425766	+	0.272112i
$703$	−122.293	+	211.818i	−0.173959	+	0.301305i
$704$	1592.76	−	919.581i	2.26244	−	1.30622i
$705$	43.3427	+	269.425i	0.0614790	+	0.382163i
$706$	−109.735	−	190.067i	−0.155433	−	0.269217i
$707$		0			0
$708$	−1150.44	−	1413.65i	−1.62491	−	1.99668i
$709$	−1040.99			−1.46825			−0.734124	−	0.679015i	$-0.762407\pi$
$709$	−1040.99			−1.46825			−0.734124	+	0.679015i	$0.762407\pi$
$710$	−309.141	−	178.483i	−0.435410	−	0.251384i
$711$	253.940	−	1223.85i	0.357159	−	1.72131i
$712$	208.933	+	361.882i	0.293445	+	0.508261i
$713$	−258.280	−	149.118i	−0.362244	−	0.209142i
$714$		0			0
$715$	−199.436	−	345.433i	−0.278931	−	0.483123i
$716$	−444.818	−	256.816i	−0.621255	−	0.358682i
$717$	−260.184	+	682.746i	−0.362878	+	0.952227i
$718$	718.710	+	1244.84i	1.00099	+	1.73376i
$719$	−653.543	+	377.323i	−0.908961	+	0.524789i	−0.880097	−	0.474795i	$-0.842522\pi$
$719$	−653.543	+	377.323i	−0.908961	+	0.524789i	−0.0288642	+	0.999583i	$0.509189\pi$
$720$	−23.7247	+	26.6073i	−0.0329509	+	0.0369546i
$721$		0			0
$722$	−836.123	−	482.736i	−1.15807	−	0.668609i
$723$	79.4480	+	30.2764i	0.109887	+	0.0418760i
$724$	785.782			1.08533
$725$		−	258.653i		−	0.356762i
$726$	−1832.15	+	294.741i	−2.52363	+	0.405979i
$727$	−698.773	+	1210.31i	−0.961174	+	1.66480i	−0.241612	+	0.970373i	$0.577676\pi$
$727$	−698.773	+	1210.31i	−0.961174	+	1.66480i	−0.719561	+	0.694429i	$0.755657\pi$
$728$		0			0
$729$	−419.869	+	595.946i	−0.575952	+	0.817484i
$730$	−204.991	−	355.054i	−0.280809	−	0.486376i
$731$	96.1126	−	55.4906i	0.131481	−	0.0759106i
$732$	−1097.06	+	892.795i	−1.49871	+	1.21966i
$733$	626.744	−	1085.55i	0.855039	−	1.48097i	−0.0215697	−	0.999767i	$-0.506866\pi$
$733$	626.744	−	1085.55i	0.855039	−	1.48097i	0.876609	−	0.481204i	$-0.159800\pi$
$734$	353.664	−	204.188i	0.481832	−	0.278186i
$735$		0			0
$736$	−166.833	+	288.963i	−0.226675	+	0.392613i
$737$	−186.751	+	107.821i	−0.253393	+	0.146297i
$738$	884.904	−	292.275i	1.19906	−	0.396037i
$739$	−534.999	+	926.646i	−0.723950	+	1.25392i	0.235454	+	0.971885i	$0.424342\pi$
$739$	−534.999	+	926.646i	−0.723950	+	1.25392i	−0.959405	+	0.282033i	$0.908991\pi$
$740$		−	1102.96i		−	1.49049i
$741$	−15.2284	−	94.6621i	−0.0205512	−	0.127749i
$742$		0			0
$743$	−620.266	+	358.111i	−0.834813	+	0.481980i	−0.855498	−	0.517806i	$-0.826749\pi$
$743$	−620.266	+	358.111i	−0.834813	+	0.481980i	0.0206847	+	0.999786i	$0.493415\pi$
$744$	−432.423	−	531.359i	−0.581214	−	0.714192i
$745$	320.131	+	554.483i	0.429706	+	0.744272i
$746$	−1709.43	−	986.941i	−2.29146	−	1.32298i
$747$	−94.7028	+	106.210i	−0.126777	+	0.142181i
$748$	−1871.32			−2.50177
$749$		0			0
$750$	−804.566	+	654.762i	−1.07275	+	0.873015i
$751$	60.3209	−	104.479i	0.0803208	−	0.139120i	−0.823067	−	0.567944i	$-0.807739\pi$
$751$	60.3209	−	104.479i	0.0803208	−	0.139120i	0.903388	+	0.428825i	$0.141072\pi$
$752$		−	11.7693i		−	0.0156506i
$753$	265.355	+	326.066i	0.352397	+	0.433022i
$754$	605.345			0.802845
$755$			831.689i			1.10157i
$756$		0			0
$757$	−369.403			−0.487983			−0.243992	−	0.969777i	$-0.578457\pi$
$757$	−369.403			−0.487983			−0.243992	+	0.969777i	$0.578457\pi$
$758$		−	1324.39i		−	1.74722i
$759$	414.371	−	337.218i	0.545943	−	0.444293i
$760$	−334.473			−0.440096
$761$	−992.067	−	572.770i	−1.30364	−	0.752655i	−0.322610	−	0.946532i	$-0.604560\pi$
$761$	−992.067	−	572.770i	−1.30364	−	0.752655i	−0.981026	+	0.193877i	$0.937894\pi$
$762$	−85.9115	−	105.567i	−0.112745	−	0.138540i
$763$		0			0
$764$		−	2272.07i		−	2.97391i
$765$	782.663	−	258.506i	1.02309	−	0.337916i
$766$	−354.782	+	614.500i	−0.463161	+	0.802219i
$767$	335.498	−	193.700i	0.437416	−	0.252542i
$768$	−551.896	+	449.137i	−0.718615	+	0.584814i
$769$	−319.295	−	553.035i	−0.415208	−	0.719162i	0.580242	−	0.814444i	$-0.302958\pi$
$769$	−319.295	−	553.035i	−0.415208	−	0.719162i	−0.995450	+	0.0952822i	$0.969625\pi$
$770$		0			0
$771$	−327.801	+	52.7337i	−0.425163	+	0.0683966i
$772$	253.477			0.328338
$773$	−169.438	−	97.8250i	−0.219195	−	0.126552i	0.386382	−	0.922339i	$-0.373725\pi$
$773$	−169.438	−	97.8250i	−0.219195	−	0.126552i	−0.605578	+	0.795786i	$0.707058\pi$
$774$	−129.458	+	145.188i	−0.167258	+	0.187581i
$775$	−83.1452	−	144.012i	−0.107284	−	0.185822i
$776$	−1149.85	−	663.867i	−1.48177	−	0.855499i
$777$		0			0
$778$	−277.643	−	480.892i	−0.356868	−	0.618114i
$779$	−218.149	−	125.949i	−0.280038	−	0.161680i
$780$	272.911	+	335.351i	0.349886	+	0.429937i
$781$	−177.011	−	306.591i	−0.226646	−	0.392563i
$782$	465.212	−	268.590i	0.594901	−	0.343466i
$783$	−56.0698	+	1242.82i	−0.0716090	+	1.58725i
$784$		0			0
$785$	1313.18	+	758.167i	1.67285	+	0.965818i
$786$	34.2063	+	212.631i	0.0435194	+	0.270523i
$787$	17.3655			0.0220654			0.0110327	−	0.999939i	$-0.496488\pi$
$787$	17.3655			0.0220654			0.0110327	+	0.999939i	$0.496488\pi$
$788$		−	834.933i		−	1.05956i
$789$	−52.7407	+	138.396i	−0.0668450	+	0.175407i
$790$	1238.52	−	2145.18i	1.56775	−	2.71542i
$791$		0			0
$792$	1165.30	−	384.887i	1.47134	−	0.485969i
$793$	−150.320	−	260.363i	−0.189559	−	0.328326i
$794$	1035.83	−	598.040i	1.30458	−	0.753198i
$795$	−583.689	−	222.435i	−0.734200	−	0.279792i
$796$	693.596	−	1201.34i	0.871352	−	1.50923i
$797$	871.920	−	503.403i	1.09400	−	0.631622i	0.159363	−	0.987220i	$-0.449056\pi$
$797$	871.920	−	503.403i	1.09400	−	0.631622i	0.934639	+	0.355598i	$0.115723\pi$
$798$		0			0
$799$	−136.062	+	235.667i	−0.170291	+	0.294952i
$800$	−161.120	+	93.0225i	−0.201400	+	0.116278i
$801$	−153.006	−	463.247i	−0.191019	−	0.578335i
$802$	−482.595	+	835.879i	−0.601739	+	1.04224i
$803$		−	406.600i		−	0.506351i
$804$	181.300	−	147.544i	0.225498	−	0.183512i
$805$		0			0
$806$	337.042	−	194.591i	0.418166	−	0.241428i
$807$	554.198	−	89.1545i	0.686738	−	0.110477i
$808$	66.7484	+	115.612i	0.0826094	+	0.143084i
$809$	364.210	+	210.277i	0.450198	+	0.259922i	0.707914	−	0.706299i	$-0.249636\pi$
$809$	364.210	+	210.277i	0.450198	+	0.259922i	−0.257716	+	0.966221i	$0.582970\pi$
$810$	−1160.49	+	860.471i	−1.43271	+	1.06231i
$811$	−1318.39			−1.62564			−0.812819	−	0.582517i	$-0.802068\pi$
$811$	−1318.39			−1.62564			−0.812819	+	0.582517i	$0.802068\pi$
$812$		0			0
$813$	−606.342	−	231.067i	−0.745808	−	0.284216i
$814$	889.224	−	1540.18i	1.09241	−	1.89212i
$815$		−	1231.92i		−	1.51156i
$816$	−35.0973	+	5.64616i	−0.0430114	+	0.00691931i
$817$	52.5790			0.0643562
$818$		−	1206.91i		−	1.47544i
$819$		0			0
$820$	1135.93			1.38528
$821$			771.778i			0.940047i	0.882654	+	0.470023i	$0.155755\pi$
$821$			771.778i			0.940047i	−0.882654	+	0.470023i	$0.844245\pi$
$822$	−335.137	−	127.716i	−0.407710	−	0.155372i
$823$	906.455			1.10140			0.550702	−	0.834702i	$-0.314360\pi$
$823$	906.455			1.10140			0.550702	+	0.834702i	$0.314360\pi$
$824$	−184.255	−	106.379i	−0.223610	−	0.129101i
$825$	294.104	−	47.3128i	0.356489	−	0.0573489i
$826$		0			0
$827$		−	509.463i		−	0.616038i	−0.951380	−	0.308019i	$-0.900334\pi$
$827$		−	509.463i		−	0.616038i	0.951380	−	0.308019i	$-0.0996660\pi$
$828$	−385.408	+	432.237i	−0.465469	+	0.522025i
$829$	−332.585	+	576.054i	−0.401188	+	0.694878i	−0.993870	−	0.110559i	$-0.964736\pi$
$829$	−332.585	+	576.054i	−0.401188	+	0.694878i	0.592682	+	0.805437i	$0.298069\pi$
$830$	−244.221	+	141.001i	−0.294243	+	0.169881i
$831$	−219.007	−	83.4600i	−0.263546	−	0.100433i
$832$	−211.873	−	366.974i	−0.254655	−	0.441075i
$833$		0			0
$834$	−485.817	+	1274.83i	−0.582514	+	1.52857i
$835$	−401.145			−0.480413
$836$	−767.790	−	443.284i	−0.918409	−	0.530244i
$837$	368.292	+	709.996i	0.440014	+	0.848263i
$838$	651.985	+	1129.27i	0.778025	+	1.34758i
$839$	−1237.78	−	714.635i	−1.47531	−	0.851770i	−0.475696	−	0.879610i	$-0.657804\pi$
$839$	−1237.78	−	714.635i	−1.47531	−	0.851770i	−0.999612	+	0.0278396i	$0.991137\pi$
$840$		0			0
$841$	641.052	+	1110.33i	0.762250	+	1.32026i
$842$	1289.77	+	744.649i	1.53179	+	0.884381i
$843$	−1316.92	+	211.855i	−1.56219	+	0.251311i
$844$	−349.041	−	604.557i	−0.413556	−	0.716299i
$845$	730.204	−	421.583i	0.864147	−	0.498915i
$846$	96.9027	−	467.018i	0.114542	−	0.552031i
$847$		0			0
$848$	23.3304	+	13.4698i	0.0275122	+	0.0158842i
$849$	298.824	−	243.186i	0.351972	−	0.286438i
$850$	299.521			0.352378
$851$			314.003i			0.368981i
$852$	242.224	+	297.643i	0.284301	+	0.349347i
$853$	−485.171	+	840.341i	−0.568782	+	0.985159i	0.427905	+	0.903824i	$0.359252\pi$
$853$	−485.171	+	840.341i	−0.568782	+	0.985159i	−0.996687	+	0.0813353i	$0.974082\pi$
$854$		0			0
$855$	382.356	+	79.3359i	0.447200	+	0.0927905i
$856$	−472.165	−	817.813i	−0.551594	−	0.955389i
$857$	1308.06	−	755.208i	1.52632	−	0.881223i	0.526812	−	0.849982i	$-0.323387\pi$
$857$	1308.06	−	755.208i	1.52632	−	0.881223i	0.999512	−	0.0312415i	$-0.00994611\pi$
$858$	110.730	+	688.313i	0.129056	+	0.802230i
$859$	−614.191	+	1063.81i	−0.715007	+	1.23843i	0.247950	+	0.968773i	$0.420243\pi$
$859$	−614.191	+	1063.81i	−0.715007	+	1.23843i	−0.962957	+	0.269655i	$0.913090\pi$
$860$	−205.339	+	118.552i	−0.238766	+	0.137852i
$861$		0			0
$862$	367.683	−	636.845i	0.426546	−	0.738800i
$863$	1292.69	−	746.335i	1.49790	−	0.864815i	0.497906	−	0.867231i	$-0.334102\pi$
$863$	1292.69	−	746.335i	1.49790	−	0.864815i	0.999997	+	0.00241587i	$0.000768995\pi$
$864$	794.341	−	412.044i	0.919376	−	0.476902i
$865$	−584.205	+	1011.87i	−0.675382	+	1.16980i
$866$			2506.73i			2.89460i
$867$	−42.1058	−	16.0459i	−0.0485650	−	0.0185073i
$868$		0			0
$869$	2127.48	−	1228.30i	2.44820	−	1.41347i
$870$	−877.961	+	2303.85i	−1.00915	+	2.64810i
$871$	24.8420	+	43.0277i	0.0285213	+	0.0494003i
$872$	−227.951	−	131.608i	−0.261412	−	0.150926i
$873$	1157.00	+	1031.65i	1.32531	+	1.18173i
$874$	254.497			0.291187
$875$		0			0
$876$	70.0031	+	435.149i	0.0799122	+	0.496746i
$877$	173.474	−	300.466i	0.197804	−	0.342607i	−0.750012	−	0.661424i	$-0.769952\pi$
$877$	173.474	−	300.466i	0.197804	−	0.342607i	0.947816	+	0.318817i	$0.103286\pi$
$878$			221.785i			0.252602i
$879$	52.6133	−	138.062i	0.0598558	−	0.157067i
$880$	−70.0638			−0.0796179
$881$		−	738.403i		−	0.838142i	−0.907953	−	0.419071i	$-0.862356\pi$
$881$		−	738.403i		−	0.838142i	0.907953	−	0.419071i	$-0.137644\pi$
$882$		0			0
$883$	872.215			0.987786			0.493893	−	0.869523i	$-0.335573\pi$
$883$	872.215			0.987786			0.493893	+	0.869523i	$0.335573\pi$
$884$			431.156i			0.487733i
$885$	250.603	+	1557.78i	0.283167	+	1.76021i
$886$	−671.566			−0.757975
$887$	−548.437	−	316.640i	−0.618306	−	0.356979i	0.157903	−	0.987455i	$-0.449527\pi$
$887$	−548.437	−	316.640i	−0.618306	−	0.356979i	−0.776209	+	0.630476i	$0.782860\pi$
$888$	−256.855	+	674.013i	−0.289252	+	0.759023i
$889$		0			0
$890$		−	966.821i		−	1.08632i
$891$	−1423.42	+	163.582i	−1.59755	+	0.183594i
$892$	−596.753	+	1033.61i	−0.669005	+	1.15875i
$893$	−111.651	+	64.4615i	−0.125029	+	0.0721853i
$894$	−177.742	−	1104.87i	−0.198816	−	1.23587i
$895$	222.323	+	385.075i	0.248406	+	0.430251i
$896$		0			0
$897$	−77.6955	−	95.4716i	−0.0866171	−	0.106434i
$898$	−835.048			−0.929897
$899$	1182.09	+	682.483i	1.31490	+	0.759158i
$900$	−306.608	+	101.270i	−0.340676	+	0.112522i
$901$	−311.443	−	539.436i	−0.345664	−	0.598708i
$902$	1586.22	+	915.805i	1.75856	+	1.01531i
$903$		0			0
$904$	300.084	+	519.761i	0.331951	+	0.574957i
$905$	−589.108	−	340.122i	−0.650948	−	0.375825i
$906$	517.652	−	1358.37i	0.571359	−	1.49930i
$907$	−560.854	−	971.427i	−0.618361	−	1.07103i	−0.989785	−	0.142570i	$-0.954464\pi$
$907$	−560.854	−	971.427i	−0.618361	−	1.07103i	0.371424	−	0.928464i	$-0.378870\pi$
$908$	1121.12	−	647.278i	1.23471	−	0.712861i
$909$	−48.8813	−	147.995i	−0.0537748	−	0.162811i
$910$		0			0
$911$	−770.852	−	445.052i	−0.846160	−	0.488531i	0.0131931	−	0.999913i	$-0.495800\pi$
$911$	−770.852	−	445.052i	−0.846160	−	0.488531i	−0.859353	+	0.511382i	$0.829134\pi$
$912$	−15.7376	−	5.99736i	−0.0172562	−	0.00657606i
$913$	−279.677			−0.306327
$914$		−	513.956i		−	0.562315i
$915$	1208.92	−	194.480i	1.32122	−	0.212547i
$916$	253.332	−	438.784i	0.276563	−	0.479021i
$917$		0			0
$918$	−1439.19	−	64.9291i	−1.56775	−	0.0707289i
$919$	567.953	+	983.724i	0.618012	+	1.07043i	0.989848	+	0.142130i	$0.0453952\pi$
$919$	567.953	+	983.724i	0.618012	+	1.07043i	−0.371836	+	0.928299i	$0.621271\pi$
$920$	−371.873	+	214.701i	−0.404210	+	0.233371i
$921$	901.182	−	733.388i	0.978482	−	0.796296i
$922$	329.251	−	570.280i	0.357105	−	0.618525i
$923$	−70.6391	+	40.7835i	−0.0765321	+	0.0441858i
$924$		0			0
$925$	−87.5408	+	151.625i	−0.0946387	+	0.163919i
$926$	−2127.85	+	1228.52i	−2.29790	+	1.32669i
$927$	185.399	+	165.313i	0.199999	+	0.178331i
$928$	763.559	−	1322.52i	0.822800	−	1.42513i
$929$		−	719.197i		−	0.774162i	−0.922046	−	0.387081i	$-0.873483\pi$
$929$		−	719.197i		−	0.774162i	0.922046	−	0.387081i	$-0.126517\pi$
$930$	251.756	+	1564.95i	0.270706	+	1.68275i
$931$		0			0
$932$	−1805.12	+	1042.18i	−1.93682	+	1.11822i
$933$	−191.438	−	235.238i	−0.205186	−	0.252130i
$934$	−859.925	−	1489.43i	−0.920691	−	1.59468i
$935$	1402.95	+	809.994i	1.50048	+	0.866303i
$936$	−88.6786	−	268.487i	−0.0947421	−	0.286845i
$937$	1522.34			1.62470			0.812348	−	0.583172i	$-0.198189\pi$
$937$	1522.34			1.62470			0.812348	+	0.583172i	$0.198189\pi$
$938$		0			0
$939$	−848.815	+	690.772i	−0.903957	+	0.735646i
$940$	290.689	−	503.488i	0.309243	−	0.535625i
$941$		−	1023.51i		−	1.08768i	−0.839188	−	0.543841i	$-0.816970\pi$
$941$		−	1023.51i		−	1.08768i	0.839188	−	0.543841i	$-0.183030\pi$
$942$	−1672.88	−	2055.62i	−1.77588	−	2.18219i
$943$	−323.389			−0.342937
$944$		−	68.0487i		−	0.0720855i
$945$		0			0
$946$	−382.316			−0.404139
$947$			1572.43i			1.66043i	0.557441	+	0.830217i	$0.311783\pi$
$947$			1572.43i			1.66043i	−0.557441	+	0.830217i	$0.688217\pi$
$948$	−2065.39	+	1680.83i	−2.17868	+	1.77303i
$949$	−93.6812			−0.0987157
$950$	122.891	+	70.9512i	0.129359	+	0.0746855i
$951$	62.7750	+	77.1374i	0.0660095	+	0.0811119i
$952$		0			0
$953$			1342.92i			1.40915i	0.709629	+	0.704576i	$0.248863\pi$
$953$			1342.92i			1.40915i	−0.709629	+	0.704576i	$0.751137\pi$
$954$	814.872	+	726.588i	0.854163	+	0.761623i
$955$	−983.453	+	1703.39i	−1.02979	+	1.78366i
$956$	1348.06	−	778.301i	1.41010	−	0.814122i
$957$	−1896.49	+	1543.38i	−1.98170	+	1.61272i
$958$	974.348	+	1687.62i	1.01706	+	1.76161i
$959$		0			0
$960$	1703.94	−	274.115i	1.77493	−	0.285536i
$961$	−83.4501			−0.0868367
$962$	−354.860	−	204.879i	−0.368877	−	0.212971i
$963$	345.776	+	1046.89i	0.359062	+	1.08711i
$964$	−90.5672	−	156.867i	−0.0939493	−	0.162725i
$965$	−190.034	−	109.716i	−0.196927	−	0.113696i
$966$		0			0
$967$	−867.804	−	1503.08i	−0.897418	−	1.55437i	−0.830783	−	0.556597i	$-0.812107\pi$
$967$	−867.804	−	1503.08i	−0.897418	−	1.55437i	−0.0666355	−	0.997777i	$-0.521226\pi$
$968$	1281.05	+	739.614i	1.32340	+	0.764064i
$969$	245.795	+	302.030i	0.253658	+	0.311693i
$970$	1536.00	+	2660.43i	1.58350	+	2.74271i
$971$	43.8474	−	25.3153i	0.0451569	−	0.0260714i	−0.477252	−	0.878767i	$-0.658367\pi$
$971$	43.8474	−	25.3153i	0.0451569	−	0.0260714i	0.522409	+	0.852695i	$0.325034\pi$
$972$	1495.20	−	420.133i	1.53827	−	0.432236i
$973$		0			0
$974$	436.071	+	251.766i	0.447712	+	0.258486i
$975$	−10.9009	−	67.7619i	−0.0111805	−	0.0694994i
$976$	−52.8091			−0.0541077
$977$		−	585.107i		−	0.598881i	−0.954115	−	0.299440i	$-0.903200\pi$
$977$		−	585.107i		−	0.598881i	0.954115	−	0.299440i	$-0.0968000\pi$
$978$	−766.760	+	2012.05i	−0.784008	+	2.05731i
$979$	479.423	−	830.386i	0.489707	−	0.848198i
$980$		0			0
$981$	229.367	+	204.517i	0.233810	+	0.208479i
$982$	645.630	+	1118.26i	0.657464	+	1.13876i
$983$	−839.089	+	484.448i	−0.853600	+	0.492826i	−0.861864	−	0.507140i	$-0.830703\pi$
$983$	−839.089	+	484.448i	−0.853600	+	0.492826i	0.00826378	+	0.999966i	$0.497370\pi$
$984$	−694.160	−	264.533i	−0.705447	−	0.268835i
$985$	−361.397	+	625.957i	−0.366900	+	0.635489i
$986$	−2129.18	+	1229.28i	−2.15941	+	1.24674i
$987$		0			0
$988$	−102.133	+	176.900i	−0.103374	+	0.179048i
$989$	58.4582	−	33.7508i	0.0591084	−	0.0341262i
$990$	−2780.21	−	576.872i	−2.80829	−	0.582699i
$991$	−104.448	+	180.910i	−0.105397	+	0.182553i	−0.913900	−	0.405939i	$-0.866945\pi$
$991$	−104.448	+	180.910i	−0.105397	+	0.182553i	0.808503	+	0.588492i	$0.200278\pi$
$992$		−	981.799i		−	0.989717i
$993$	−210.598	+	171.386i	−0.212083	+	0.172594i
$994$		0			0
$995$	−1039.99	+	600.439i	−1.04522	+	0.603457i
$996$	299.314	−	48.1511i	0.300516	−	0.0483444i
$997$	76.0851	+	131.783i	0.0763140	+	0.132180i	0.901657	−	0.432452i	$-0.142352\pi$
$997$	76.0851	+	131.783i	0.0763140	+	0.132180i	−0.825343	+	0.564632i	$0.809018\pi$
$998$	−341.392	−	197.103i	−0.342077	−	0.197498i
$999$	453.500	−	709.578i	0.453954	−	0.710288i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.j.f.263.2		22
7.2	even	3		441.3.n.f.128.2		22
7.3	odd	6		441.3.r.g.344.10		22
7.4	even	3		441.3.r.f.344.10		22
7.5	odd	6		63.3.n.b.2.2	yes	22
7.6	odd	2		63.3.j.b.11.2	✓	22
9.5	odd	6		441.3.n.f.410.2		22
21.5	even	6		189.3.n.b.170.10		22
21.20	even	2		189.3.j.b.116.10		22
63.5	even	6		63.3.j.b.23.10	yes	22
63.13	odd	6		189.3.n.b.179.10		22
63.23	odd	6	inner	441.3.j.f.275.10		22
63.32	odd	6		441.3.r.f.50.10		22
63.40	odd	6		189.3.j.b.44.2		22
63.41	even	6		63.3.n.b.32.2	yes	22
63.59	even	6		441.3.r.g.50.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.2	✓	22	7.6	odd	2
63.3.j.b.23.10	yes	22	63.5	even	6
63.3.n.b.2.2	yes	22	7.5	odd	6
63.3.n.b.32.2	yes	22	63.41	even	6
189.3.j.b.44.2		22	63.40	odd	6
189.3.j.b.116.10		22	21.20	even	2
189.3.n.b.170.10		22	21.5	even	6
189.3.n.b.179.10		22	63.13	odd	6
441.3.j.f.263.2		22	1.1	even	1	trivial
441.3.j.f.275.10		22	63.23	odd	6	inner
441.3.n.f.128.2		22	7.2	even	3
441.3.n.f.410.2		22	9.5	odd	6
441.3.r.f.50.10		22	63.32	odd	6
441.3.r.f.344.10		22	7.4	even	3
441.3.r.g.50.10		22	63.59	even	6
441.3.r.g.344.10		22	7.3	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.22356i q^{2} +(2.32685 - 1.89361i) q^{3} -6.39137 q^{4} +(4.79167 + 2.76647i) q^{5} +(-6.10417 - 7.50076i) q^{6} +7.70873i q^{8} +(1.82848 - 8.81230i) q^{9} +(8.91790 - 15.4463i) q^{10} +(15.3189 - 8.84435i) q^{11} +(-14.8718 + 12.1028i) q^{12} +(-2.03775 - 3.52949i) q^{13} +(16.3881 - 2.63638i) q^{15} -0.715882 q^{16} +(14.3348 + 8.27617i) q^{17} +(-28.4070 - 5.89424i) q^{18} +(3.92096 + 6.79130i) q^{19} +(-30.6253 - 17.6815i) q^{20} +(-28.5103 - 49.3813i) q^{22} +(8.71877 + 5.03378i) q^{23} +(14.5973 + 17.9371i) q^{24} +(2.80674 + 4.86141i) q^{25} +(-11.3775 + 6.56882i) q^{26} +(-12.4324 - 23.9674i) q^{27} +(-39.9040 - 23.0386i) q^{29} +(-8.49854 - 52.8282i) q^{30} -29.6235 q^{31} +33.1426i q^{32} +(18.8970 - 49.5874i) q^{33} +(26.6788 - 46.2090i) q^{34} +(-11.6865 + 56.3227i) q^{36} +(15.5948 + 27.0110i) q^{37} +(21.8922 - 12.6395i) q^{38} +(-11.4250 - 4.35389i) q^{39} +(-21.3260 + 36.9377i) q^{40} +(-27.8184 + 16.0609i) q^{41} +(3.35243 - 5.80658i) q^{43} +(-97.9085 + 56.5275i) q^{44} +(33.1405 - 37.1672i) q^{45} +(16.2267 - 28.1055i) q^{46} +16.4402i q^{47} +(-1.66575 + 1.35560i) q^{48} +(15.6711 - 9.04769i) q^{50} +(49.0267 - 7.88699i) q^{51} +(13.0240 + 22.5583i) q^{52} +(-32.5897 - 18.8157i) q^{53} +(-77.2603 + 40.0768i) q^{54} +97.8706 q^{55} +(21.9836 + 8.37759i) q^{57} +(-74.2663 + 128.633i) q^{58} +95.0557i q^{59} +(-104.743 + 16.8501i) q^{60} +73.7679 q^{61} +95.4932i q^{62} +103.974 q^{64} -22.5495i q^{65} +(-159.848 - 60.9156i) q^{66} -12.1909 q^{67} +(-91.6187 - 52.8961i) q^{68} +(29.8193 - 4.79707i) q^{69} -20.0140i q^{71} +(67.9317 + 14.0953i) q^{72} +(11.4932 - 19.9068i) q^{73} +(87.0715 - 50.2708i) q^{74} +(15.7365 + 5.99692i) q^{75} +(-25.0603 - 43.4057i) q^{76} +(-14.0351 + 36.8293i) q^{78} +138.880 q^{79} +(-3.43027 - 1.98047i) q^{80} +(-74.3133 - 32.2263i) q^{81} +(51.7735 + 89.6743i) q^{82} +(-13.6928 - 7.90552i) q^{83} +(45.7916 + 79.3134i) q^{85} +(-18.7179 - 10.8068i) q^{86} +(-136.477 + 21.9552i) q^{87} +(68.1787 + 118.089i) q^{88} +(46.9444 - 27.1034i) q^{89} +(-119.811 - 106.830i) q^{90} +(-55.7249 - 32.1728i) q^{92} +(-68.9294 + 56.0953i) q^{93} +52.9962 q^{94} +43.3889i q^{95} +(62.7592 + 77.1180i) q^{96} +(-86.1189 + 149.162i) q^{97} +(-49.9287 - 151.166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 19 q^{3} - 24 q^{4} - 12 q^{5} + 8 q^{6} - 37 q^{9} - 25 q^{10} + 24 q^{11} - 40 q^{12} + 18 q^{13} + 53 q^{15} - 24 q^{16} + 6 q^{17} + 40 q^{18} - 3 q^{19} + 39 q^{20} - 59 q^{22} + 81 q^{23} - 126 q^{24}+ \cdots - 103 q^{99}+O(q^{100}) \) 22 * q + 19 * q^3 - 24 * q^4 - 12 * q^5 + 8 * q^6 - 37 * q^9 - 25 * q^10 + 24 * q^11 - 40 * q^12 + 18 * q^13 + 53 * q^15 - 24 * q^16 + 6 * q^17 + 40 * q^18 - 3 * q^19 + 39 * q^20 - 59 * q^22 + 81 * q^23 - 126 * q^24 + 57 * q^25 - 3 * q^26 + 97 * q^27 - 63 * q^29 - 38 * q^30 - 58 * q^31 + 4 * q^33 + 99 * q^34 + 76 * q^36 - 20 * q^37 + 48 * q^38 - 76 * q^39 + 105 * q^40 + 51 * q^41 + 65 * q^43 - 54 * q^44 + 214 * q^45 + 75 * q^46 + 113 * q^48 + 63 * q^50 + 141 * q^51 + 46 * q^52 + 63 * q^53 - 433 * q^54 + 100 * q^55 + 224 * q^57 + 40 * q^58 - 482 * q^60 + 156 * q^61 + 106 * q^64 - 61 * q^66 + 264 * q^67 - 27 * q^68 + 297 * q^69 - 222 * q^72 - q^73 + 342 * q^74 + 296 * q^75 - 233 * q^76 - 440 * q^78 - 280 * q^79 + 96 * q^80 - 169 * q^81 + 157 * q^82 - 255 * q^83 + 102 * q^85 + 504 * q^86 - 704 * q^87 + 408 * q^88 - 720 * q^89 - 418 * q^90 - 1239 * q^92 - 36 * q^93 + 522 * q^94 + 397 * q^96 - 178 * q^97 - 103 * q^99

Introduction

L-functions

Modular forms

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