LMFDB - Embedded newform 441.3.r.g.50.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,3,Mod(50,441)] 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("441.50"); 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([5, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22,6,11] 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			50.10
Character	$\chi$	$=$	441.50
Dual form			441.3.r.g.344.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.79169 - 1.61178i) q^{2} +(2.80334 - 1.06831i) q^{3} +(3.19568 - 5.53509i) q^{4} +(4.79167 + 2.76647i) q^{5} +(6.10417 - 7.50076i) q^{6} -7.70873i q^{8} +(6.71743 - 5.98966i) q^{9} +17.8358 q^{10} +(-15.3189 + 8.84435i) q^{11} +(3.04541 - 18.9307i) q^{12} +(2.03775 - 3.52949i) q^{13} +(16.3881 + 2.63638i) q^{15} +(0.357941 + 0.619972i) q^{16} -16.5523i q^{17} +(9.09895 - 27.5483i) q^{18} +7.84192 q^{19} +(30.6253 - 17.6815i) q^{20} +(-28.5103 + 49.3813i) q^{22} +(-8.71877 - 5.03378i) q^{23} +(-8.23530 - 21.6102i) q^{24} +(2.80674 + 4.86141i) q^{25} -13.1376i q^{26} +(12.4324 - 23.9674i) q^{27} +(-39.9040 + 23.0386i) q^{29} +(49.9998 - 19.0541i) q^{30} +(-14.8117 + 25.6547i) q^{31} +(28.7023 + 16.5713i) q^{32} +(-33.4955 + 41.1590i) q^{33} +(-26.6788 - 46.2090i) q^{34} +(-11.6865 - 56.3227i) q^{36} -31.1896 q^{37} +(21.8922 - 12.6395i) q^{38} +(1.94193 - 12.0713i) q^{39} +(21.3260 - 36.9377i) q^{40} +(27.8184 + 16.0609i) q^{41} +(3.35243 + 5.80658i) q^{43} +113.055i q^{44} +(48.7580 - 10.1169i) q^{45} -32.4535 q^{46} +(14.2377 - 8.22012i) q^{47} +(1.66575 + 1.35560i) q^{48} +(15.6711 + 9.04769i) q^{50} +(-17.6830 - 46.4019i) q^{51} +(-13.0240 - 22.5583i) q^{52} -37.6313i q^{53} +(-3.92265 - 86.9478i) q^{54} -97.8706 q^{55} +(21.9836 - 8.37759i) q^{57} +(-74.2663 + 128.633i) q^{58} +(-82.3206 - 47.5278i) q^{59} +(66.9639 - 82.2847i) q^{60} +(36.8839 + 63.8848i) q^{61} +95.4932i q^{62} +103.974 q^{64} +(19.5285 - 11.2748i) q^{65} +(-27.1696 + 168.890i) q^{66} +(6.09545 - 10.5576i) q^{67} +(-91.6187 - 52.8961i) q^{68} +(-29.8193 - 4.79707i) q^{69} +20.0140i q^{71} +(-46.1727 - 51.7829i) q^{72} +22.9864 q^{73} +(-87.0715 + 50.2708i) q^{74} +(13.0617 + 10.6297i) q^{75} +(25.0603 - 43.4057i) q^{76} +(-14.0351 - 36.8293i) q^{78} +(-69.4400 - 120.274i) q^{79} +3.96094i q^{80} +(9.24784 - 80.4704i) q^{81} +103.547 q^{82} +(13.6928 - 7.90552i) q^{83} +(45.7916 - 79.3134i) q^{85} +(18.7179 + 10.8068i) q^{86} +(-87.2521 + 107.215i) q^{87} +(68.1787 + 118.089i) q^{88} +54.2068i q^{89} +(119.811 - 106.830i) q^{90} +(-55.7249 + 32.1728i) q^{92} +(-14.1152 + 87.7423i) q^{93} +(26.4981 - 45.8960i) q^{94} +(37.5759 + 21.6944i) q^{95} +(98.1657 + 15.7921i) q^{96} +(86.1189 + 149.162i) q^{97} +(-49.9287 + 151.166i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 6 q^{2} + 11 q^{3} + 12 q^{4} - 12 q^{5} - 8 q^{6} + 17 q^{9} - 50 q^{10} - 24 q^{11} - 20 q^{12} - 18 q^{13} + 53 q^{15} + 12 q^{16} + 16 q^{18} - 6 q^{19} - 39 q^{20} - 59 q^{22} - 81 q^{23} - 141 q^{24}+ \cdots - 103 q^{99}+O(q^{100}) $ 22 * q + 6 * q^2 + 11 * q^3 + 12 * q^4 - 12 * q^5 - 8 * q^6 + 17 * q^9 - 50 * q^10 - 24 * q^11 - 20 * q^12 - 18 * q^13 + 53 * q^15 + 12 * q^16 + 16 * q^18 - 6 * q^19 - 39 * q^20 - 59 * q^22 - 81 * q^23 - 141 * q^24 + 57 * q^25 - 97 * q^27 - 63 * q^29 + 58 * q^30 - 29 * q^31 - 246 * q^32 - 73 * q^33 - 99 * q^34 + 76 * q^36 + 40 * q^37 + 48 * q^38 - 124 * q^39 - 105 * q^40 - 51 * q^41 + 65 * q^43 + 143 * q^45 - 150 * q^46 - 261 * q^47 - 113 * q^48 + 63 * q^50 - 63 * q^51 - 46 * q^52 + 52 * q^54 - 100 * q^55 + 224 * q^57 + 40 * q^58 + 102 * q^59 + 379 * q^60 + 78 * q^61 + 106 * q^64 + 225 * q^65 + 340 * q^66 - 132 * q^67 - 27 * q^68 - 297 * q^69 + 288 * q^72 - 2 * q^73 - 342 * q^74 + 541 * q^75 + 233 * q^76 - 440 * q^78 + 140 * q^79 + 65 * q^81 + 314 * q^82 + 255 * q^83 + 102 * q^85 - 504 * q^86 - 568 * q^87 + 408 * q^88 + 418 * q^90 - 1239 * q^92 - 174 * q^93 + 261 * q^94 - 642 * q^95 - 142 * q^96 + 178 * q^97 - 103 * q^99

Character values

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

$n$	$199$	$344$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.79169	−	1.61178i	1.39584	−	0.805891i	0.401890	−	0.915688i	$-0.368353\pi$
$2$	2.79169	−	1.61178i	1.39584	−	0.805891i	0.993954	+	0.109797i	$0.0350200\pi$
$3$	2.80334	−	1.06831i	0.934447	−	0.356103i
$3$	2.80334	−	1.06831i	0.934447	−	0.356103i
$4$	3.19568	−	5.53509i	0.798921	−	1.38377i
$5$	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
$9$	6.71743	−	5.98966i	0.746382	−	0.665518i
$10$	17.8358			1.78358
$11$	−15.3189	+	8.84435i	−1.39262	+	0.804032i	−0.993605	−	0.112911i	$-0.963982\pi$
$11$	−15.3189	+	8.84435i	−1.39262	+	0.804032i	−0.399018	+	0.916943i	$0.630649\pi$
$12$	3.04541	−	18.9307i	0.253784	−	1.57756i
$13$	2.03775	−	3.52949i	0.156750	−	0.271499i	−0.776945	−	0.629569i	$-0.783232\pi$
$13$	2.03775	−	3.52949i	0.156750	−	0.271499i	0.933695	+	0.358070i	$0.116565\pi$
$14$		0			0
$15$	16.3881	+	2.63638i	1.09254	+	0.175759i
$16$	0.357941	+	0.619972i	0.0223713	+	0.0387483i
$17$		−	16.5523i		−	0.973667i	−0.873495	−	0.486834i	$-0.838152\pi$
$17$		−	16.5523i		−	0.973667i	0.873495	−	0.486834i	$-0.161848\pi$
$18$	9.09895	−	27.5483i	0.505497	−	1.53046i
$19$	7.84192			0.412732			0.206366	−	0.978475i	$-0.433836\pi$
$19$	7.84192			0.412732			0.206366	+	0.978475i	$0.433836\pi$
$20$	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	0.298340	−	0.954460i	$-0.403567\pi$
$23$	−8.71877	−	5.03378i	−0.379077	−	0.218860i	−0.677417	+	0.735600i	$0.736901\pi$
$24$	−8.23530	−	21.6102i	−0.343138	−	0.900425i
$25$	2.80674	+	4.86141i	0.112269	+	0.194456i
$26$		−	13.1376i		−	0.505294i
$27$	12.4324	−	23.9674i	0.460461	−	0.887680i
$28$		0			0
$29$	−39.9040	+	23.0386i	−1.37600	+	0.794434i	−0.991675	−	0.128764i	$-0.958899\pi$
$29$	−39.9040	+	23.0386i	−1.37600	+	0.794434i	−0.384324	+	0.923198i	$0.625566\pi$
$30$	49.9998	−	19.0541i	1.66666	−	0.635138i
$31$	−14.8117	+	25.6547i	−0.477798	+	0.827570i	−0.999676	−	0.0254498i	$-0.991898\pi$
$31$	−14.8117	+	25.6547i	−0.477798	+	0.827570i	0.521878	+	0.853020i	$0.325232\pi$
$32$	28.7023	+	16.5713i	0.896948	+	0.517853i
$33$	−33.4955	+	41.1590i	−1.01501	+	1.24724i
$34$	−26.6788	−	46.2090i	−0.784670	−	1.35909i
$35$		0			0
$36$	−11.6865	−	56.3227i	−0.324626	−	1.56452i
$37$	−31.1896			−0.842961			−0.421481	−	0.906837i	$-0.638489\pi$
$37$	−31.1896			−0.842961			−0.421481	+	0.906837i	$0.638489\pi$
$38$	21.8922	−	12.6395i	0.576110	−	0.332617i
$39$	1.94193	−	12.0713i	0.0497930	−	0.309520i
$40$	21.3260	−	36.9377i	0.533150	−	0.923442i
$41$	27.8184	+	16.0609i	0.678497	+	0.391730i	0.799288	−	0.600948i	$-0.205210\pi$
$41$	27.8184	+	16.0609i	0.678497	+	0.391730i	−0.120792	+	0.992678i	$0.538543\pi$
$42$		0			0
$43$	3.35243	+	5.80658i	0.0779635	+	0.135037i	0.902371	−	0.430960i	$-0.141825\pi$
$43$	3.35243	+	5.80658i	0.0779635	+	0.135037i	−0.824408	+	0.565997i	$0.808492\pi$
$44$			113.055i			2.56943i
$45$	48.7580	−	10.1169i	1.08351	−	0.224820i
$46$	−32.4535			−0.705510
$47$	14.2377	−	8.22012i	0.302929	−	0.174896i	−0.340829	−	0.940125i	$-0.610708\pi$
$47$	14.2377	−	8.22012i	0.302929	−	0.174896i	0.643758	+	0.765229i	$0.277374\pi$
$48$	1.66575	+	1.35560i	0.0347032	+	0.0282417i
$49$		0			0
$50$	15.6711	+	9.04769i	0.313421	+	0.180954i
$51$	−17.6830	−	46.4019i	−0.346726	−	0.909840i
$52$	−13.0240	−	22.5583i	−0.250462	−	0.433813i
$53$		−	37.6313i		−	0.710025i	−0.934862	−	0.355013i	$-0.884477\pi$
$53$		−	37.6313i		−	0.710025i	0.934862	−	0.355013i	$-0.115523\pi$
$54$	−3.92265	−	86.9478i	−0.0726417	−	1.61014i
$55$	−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
$59$	−82.3206	−	47.5278i	−1.39527	−	0.805557i	−0.401373	−	0.915915i	$-0.631467\pi$
$59$	−82.3206	−	47.5278i	−1.39527	−	0.805557i	−0.993892	+	0.110358i	$0.964800\pi$
$60$	66.9639	−	82.2847i	1.11606	−	1.37141i
$61$	36.8839	+	63.8848i	0.604655	+	1.04729i	0.992106	+	0.125402i	$0.0400222\pi$
$61$	36.8839	+	63.8848i	0.604655	+	1.04729i	−0.387451	+	0.921890i	$0.626644\pi$
$62$			95.4932i			1.54021i
$63$		0			0
$64$	103.974			1.62459
$65$	19.5285	−	11.2748i	0.300438	−	0.173458i
$66$	−27.1696	+	168.890i	−0.411661	+	2.55895i
$67$	6.09545	−	10.5576i	0.0909769	−	0.157577i	−0.816946	−	0.576715i	$-0.804334\pi$
$67$	6.09545	−	10.5576i	0.0909769	−	0.157577i	0.907922	+	0.419138i	$0.137668\pi$
$68$	−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	$0.0450136\pi$
$71$			20.0140i			0.281887i	−0.990018	+	0.140944i	$0.954986\pi$
$72$	−46.1727	−	51.7829i	−0.641288	−	0.719207i
$73$	22.9864			0.314883			0.157441	−	0.987528i	$-0.449675\pi$
$73$	22.9864			0.314883			0.157441	+	0.987528i	$0.449675\pi$
$74$	−87.0715	+	50.2708i	−1.17664	+	0.679335i
$75$	13.0617	+	10.6297i	0.174156	+	0.141730i
$76$	25.0603	−	43.4057i	0.329741	−	0.571128i
$77$		0			0
$78$	−14.0351	−	36.8293i	−0.179937	−	0.472170i
$79$	−69.4400	−	120.274i	−0.878988	−	1.52245i	−0.852453	−	0.522804i	$-0.824886\pi$
$79$	−69.4400	−	120.274i	−0.878988	−	1.52245i	−0.0265350	−	0.999648i	$-0.508447\pi$
$80$			3.96094i			0.0495117i
$81$	9.24784	−	80.4704i	0.114171	−	0.993461i
$82$	103.547			1.26277
$83$	13.6928	−	7.90552i	0.164973	−	0.0952472i	−0.415240	−	0.909712i	$-0.636303\pi$
$83$	13.6928	−	7.90552i	0.164973	−	0.0952472i	0.580213	+	0.814465i	$0.302969\pi$
$84$		0			0
$85$	45.7916	−	79.3134i	0.538725	−	0.933099i
$86$	18.7179	+	10.8068i	0.217650	+	0.125660i
$87$	−87.2521	+	107.215i	−1.00290	+	1.23235i
$88$	68.1787	+	118.089i	0.774758	+	1.34192i
$89$			54.2068i			0.609065i	0.952502	+	0.304532i	$0.0985002\pi$
$89$			54.2068i			0.609065i	−0.952502	+	0.304532i	$0.901500\pi$
$90$	119.811	−	106.830i	1.33123	−	1.18701i
$91$		0			0
$92$	−55.7249	+	32.1728i	−0.605705	+	0.349704i
$93$	−14.1152	+	87.7423i	−0.151777	+	0.943466i
$94$	26.4981	−	45.8960i	0.281894	−	0.488256i
$95$	37.5759	+	21.6944i	0.395536	+	0.228363i
$96$	98.1657	+	15.7921i	1.02256	+	0.164501i
$97$	86.1189	+	149.162i	0.887823	+	1.53776i	0.842443	+	0.538785i	$0.181117\pi$
$97$	86.1189	+	149.162i	0.887823	+	1.53776i	0.0453802	+	0.998970i	$0.485550\pi$
$98$		0			0
$99$	−49.9287	+	151.166i	−0.504331	+	1.52693i
$100$	35.8778			0.358778
$101$	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	$0.306011\pi$
$102$	−124.155	−	101.038i	−1.21721	−	0.990572i
$103$	13.7999	−	23.9021i	0.133979	−	0.232059i	−0.791228	−	0.611521i	$-0.790558\pi$
$103$	13.7999	−	23.9021i	0.133979	−	0.232059i	0.925207	+	0.379463i	$0.123891\pi$
$104$	−27.2079	−	15.7085i	−0.261614	−	0.151043i
$105$		0			0
$106$	−60.6535	−	105.055i	−0.572203	−	0.991085i
$107$			122.501i			1.14487i	0.819950	+	0.572436i	$0.194001\pi$
$107$			122.501i			1.14487i	−0.819950	+	0.572436i	$0.805999\pi$
$108$	−92.9313	−	145.407i	−0.860475	−	1.34636i
$109$	34.1451			0.313257			0.156629	−	0.987658i	$-0.449937\pi$
$109$	34.1451			0.313257			0.156629	+	0.987658i	$0.449937\pi$
$110$	−273.224	+	157.746i	−2.48386	+	1.43405i
$111$	−87.4350	+	33.3201i	−0.787702	+	0.300181i
$112$		0			0
$113$	67.4250	+	38.9278i	0.596681	+	0.344494i	0.767735	−	0.640768i	$-0.221384\pi$
$113$	67.4250	+	38.9278i	0.596681	+	0.344494i	−0.171054	+	0.985262i	$0.554717\pi$
$114$	47.8684	−	58.8203i	0.419898	−	0.515968i
$115$	−27.8516	−	48.2405i	−0.242188	−	0.419482i
$116$			294.496i			2.53876i
$117$	−7.45199	−	35.9145i	−0.0636922	−	0.306962i
$118$	−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
$122$	205.937	+	118.898i	1.68801	+	0.974572i
$123$	95.1424	+	15.3057i	0.773515	+	0.124436i
$124$	94.6673	+	163.968i	0.763446	+	1.32233i
$125$		−	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	$0.482353\pi$
$128$	175.453	−	101.298i	1.37073	−	0.791390i
$129$	15.6012	+	12.6964i	0.120940	+	0.0984217i
$130$	36.3449	−	62.9512i	0.279576	−	0.484240i
$131$	−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
$135$	125.877	−	80.4497i	0.932424	−	0.595924i
$136$	−127.598			−0.938217
$137$	−32.1175	+	18.5430i	−0.234434	+	0.135351i	−0.612616	−	0.790381i	$-0.709883\pi$
$137$	−32.1175	+	18.5430i	−0.234434	+	0.135351i	0.378182	+	0.925731i	$0.376549\pi$
$138$	−90.9781	+	34.6703i	−0.659262	+	0.251234i
$139$	70.5358	−	122.172i	0.507451	−	0.878932i	−0.492511	−	0.870306i	$-0.663921\pi$
$139$	70.5358	−	122.172i	0.507451	−	0.878932i	0.999963	−	0.00862568i	$-0.00274567\pi$
$140$		0			0
$141$	31.1314	−	38.2540i	0.220790	−	0.271305i
$142$	32.2582	+	55.8728i	0.227170	+	0.393471i
$143$			72.0903i			0.504128i
$144$	6.11787	+	2.02067i	0.0424852	+	0.0140325i
$145$	−254.942			−1.75822
$146$	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	0.124472	−	0.992223i	$-0.460276\pi$
$149$	−100.215	−	57.8590i	−0.672582	−	0.388315i	−0.797054	+	0.603908i	$0.793610\pi$
$150$	53.5970	+	8.62223i	0.357314	+	0.0574815i
$151$	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	$0.667499\pi$
$152$		−	60.4512i		−	0.397705i
$153$	−99.1430	−	111.189i	−0.647993	−	0.726727i
$154$		0			0
$155$	−141.946	+	81.9525i	−0.915780	+	0.528726i
$156$	−60.6099	−	49.3248i	−0.388525	−	0.316185i
$157$	137.028	−	237.339i	0.872788	−	1.51171i	0.0136883	−	0.999906i	$-0.495643\pi$
$157$	137.028	−	237.339i	0.872788	−	1.51171i	0.859100	−	0.511808i	$-0.171024\pi$
$158$	−387.710	−	223.844i	−2.45386	−	1.41674i
$159$	−40.2019	−	105.493i	−0.252842	−	0.663481i
$160$	91.6881	+	158.808i	0.573051	+	0.992553i
$161$		0			0
$162$	−103.884	−	239.554i	−0.641257	−	1.47873i
$163$	222.652			1.36596			0.682981	−	0.730436i	$-0.260683\pi$
$163$	222.652			1.36596			0.682981	+	0.730436i	$0.260683\pi$
$164$	177.797	−	102.651i	1.08413	−	0.625923i
$165$	−274.364	+	104.556i	−1.66281	+	0.633672i
$166$	25.4839	−	44.1395i	0.153518	−	0.265900i
$167$	62.7878	+	36.2506i	0.375975	+	0.217069i	0.676066	−	0.736841i	$-0.263684\pi$
$167$	62.7878	+	36.2506i	0.375975	+	0.217069i	−0.300091	+	0.953911i	$0.597017\pi$
$168$		0			0
$169$	76.1951	+	131.974i	0.450859	+	0.780910i
$170$		−	295.224i		−	1.73661i
$171$	52.6776	−	46.9704i	0.308056	−	0.274681i
$172$	42.8533			0.249147
$173$	182.881	−	105.587i	1.05712	−	0.610328i	0.132485	−	0.991185i	$-0.457704\pi$
$173$	182.881	−	105.587i	1.05712	−	0.610328i	0.924634	+	0.380857i	$0.124371\pi$
$174$	−70.7740	+	439.942i	−0.406747	+	2.52840i
$175$		0			0
$176$	−10.9665	−	6.33151i	−0.0623096	−	0.0359745i
$177$	−281.547	−	45.2929i	−1.59066	−	0.255892i
$178$	87.3695	+	151.328i	0.490840	+	0.850160i
$179$			80.3634i			0.448957i	0.974479	+	0.224479i	$0.0720679\pi$
$179$			80.3634i			0.448957i	−0.974479	+	0.224479i	$0.927932\pi$
$180$	99.8171	−	302.210i	0.554540	−	1.67894i
$181$	122.944			0.679250			0.339625	−	0.940561i	$-0.389700\pi$
$181$	122.944			0.679250			0.339625	+	0.940561i	$0.389700\pi$
$182$		0			0
$183$	171.647	+	139.688i	0.937961	+	0.763320i
$184$	−38.8041	+	67.2107i	−0.210892	+	0.365275i
$185$	−149.450	−	86.2850i	−0.807838	−	0.466406i
$186$	102.016	+	267.700i	0.548474	+	1.43925i
$187$	146.395	+	253.563i	0.782859	+	1.35595i
$188$		−	105.076i		−	0.558913i
$189$		0			0
$190$	139.867			0.736141
$191$	−307.863	+	177.745i	−1.61185	+	0.930602i	−0.622909	+	0.782294i	$0.714049\pi$
$191$	−307.863	+	177.745i	−1.61185	+	0.930602i	−0.988941	+	0.148308i	$0.952617\pi$
$192$	291.474	−	111.076i	1.51809	−	0.578522i
$193$	19.8296	−	34.3459i	0.102744	−	0.177958i	−0.810070	−	0.586333i	$-0.800571\pi$
$193$	19.8296	−	34.3459i	0.102744	−	0.177958i	0.912814	+	0.408375i	$0.133904\pi$
$194$	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	$-0.892425\pi$
$197$		−	130.634i		−	0.663119i	0.943434	−	0.331559i	$-0.107575\pi$
$198$	104.261	+	502.483i	0.526573	+	2.53779i
$199$	−217.042			−1.09066			−0.545331	−	0.838221i	$-0.683596\pi$
$199$	−217.042			−1.09066			−0.545331	+	0.838221i	$0.683596\pi$
$200$	37.4753	−	21.6364i	0.187376	−	0.108182i
$201$	5.80882	−	36.1085i	0.0288996	−	0.179644i
$202$	27.9122	−	48.3454i	0.138179	−	0.239333i
$203$		0			0
$204$	−313.348	−	50.4087i	−1.53602	−	0.247101i
$205$	88.8643	+	153.917i	0.433484	+	0.750817i
$206$		−	88.9695i		−	0.431891i
$207$	−88.7184	+	18.4084i	−0.428592	+	0.0889295i
$208$	2.91758			0.0140268
$209$	−120.129	+	69.3566i	−0.574781	+	0.331850i
$210$		0			0
$211$	54.6113	−	94.5895i	0.258821	−	0.448292i	−0.707105	−	0.707108i	$-0.749999\pi$
$211$	54.6113	−	94.5895i	0.258821	−	0.448292i	0.965926	+	0.258817i	$0.0833326\pi$
$212$	−208.293	−	120.258i	−0.982513	−	0.567254i
$213$	21.3811	+	56.1060i	0.100381	+	0.263409i
$214$	197.445	+	341.985i	0.922642	+	1.59806i
$215$			37.0976i			0.172547i
$216$	−184.758	−	95.8384i	−0.855361	−	0.443696i
$217$		0			0
$218$	95.3224	−	55.0344i	0.437259	−	0.252451i
$219$	64.4388	−	24.5566i	0.294241	−	0.112131i
$220$	−312.763	+	541.722i	−1.42165	+	2.46237i
$221$	−58.4213	−	33.7295i	−0.264350	−	0.152622i
$222$	−190.386	+	233.945i	−0.857597	+	1.05381i
$223$	−93.3685	−	161.719i	−0.418693	−	0.725197i	0.577115	−	0.816663i	$-0.304178\pi$
$223$	−93.3685	−	161.719i	−0.418693	−	0.725197i	−0.995808	+	0.0914653i	$0.970845\pi$
$224$		0			0
$225$	47.9723	+	15.8448i	0.213210	+	0.0704213i
$226$	250.973			1.11050
$227$	−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	$0.480535\pi$
$228$	23.8818	−	148.453i	0.104745	−	0.651110i
$229$	39.6366	−	68.6525i	0.173085	−	0.299793i	−0.766412	−	0.642350i	$-0.777960\pi$
$229$	39.6366	−	68.6525i	0.173085	−	0.299793i	0.939497	+	0.342557i	$0.111293\pi$
$230$	−155.506	−	89.7816i	−0.676114	−	0.390355i
$231$		0			0
$232$	177.598	+	307.609i	0.765509	+	1.32590i
$233$		−	326.122i		−	1.39967i	−0.714306	−	0.699833i	$-0.753258\pi$
$233$		−	326.122i		−	1.39967i	0.714306	−	0.699833i	$-0.246742\pi$
$234$	−78.6900	−	88.2512i	−0.336282	−	0.377142i
$235$	90.9629			0.387076
$236$	−526.142	+	303.768i	−2.22941	+	1.28715i
$237$	−323.154	−	262.985i	−1.36352	−	1.10964i
$238$		0			0
$239$	−210.918	−	121.774i	−0.882503	−	0.509514i	−0.0110203	−	0.999939i	$-0.503508\pi$
$239$	−210.918	−	121.774i	−0.882503	−	0.509514i	−0.871483	+	0.490426i	$0.836841\pi$
$240$	4.23150	+	11.1039i	0.0176313	+	0.0462661i
$241$	−14.1702	−	24.5436i	−0.0587976	−	0.101840i	0.835128	−	0.550055i	$-0.185393\pi$
$241$	−14.1702	−	24.5436i	−0.0587976	−	0.101840i	−0.893926	+	0.448215i	$0.852060\pi$
$242$		−	618.569i		−	2.55607i
$243$	−60.0423	−	235.465i	−0.247088	−	0.968993i
$244$	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
$248$	197.765	+	114.180i	0.797440	+	0.460402i
$249$	29.9399	−	36.7899i	0.120241	−	0.147751i
$250$	−172.887	−	299.449i	−0.691549	−	1.19780i
$251$			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
$254$	39.2909	−	22.6846i	0.154688	−	0.0893094i
$255$	43.6383	−	271.262i	0.171131	−	1.06377i
$256$	118.593	−	205.409i	0.463253	−	0.802378i
$257$	−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
$261$	−130.059	+	393.772i	−0.498311	+	1.50870i
$262$	−71.7884			−0.274001
$263$	42.7543	−	24.6842i	0.162564	−	0.0938563i	−0.416511	−	0.909131i	$-0.636747\pi$
$263$	42.7543	−	24.6842i	0.162564	−	0.0938563i	0.579075	+	0.815274i	$0.303414\pi$
$264$	317.284	+	258.208i	1.20183	+	0.978059i
$265$	104.106	−	180.317i	0.392853	−	0.680441i
$266$		0			0
$267$	57.9095	+	151.960i	0.216890	+	0.569139i
$268$	−38.9583	−	67.4777i	−0.145367	−	0.251783i
$269$		−	187.108i		−	0.695568i	−0.937575	−	0.347784i	$-0.886934\pi$
$269$		−	187.108i		−	0.695568i	0.937575	−	0.347784i	$-0.113066\pi$
$270$	221.743	−	427.477i	0.821269	−	1.58325i
$271$	−216.293			−0.798128			−0.399064	−	0.916923i	$-0.630665\pi$
$271$	−216.293			−0.798128			−0.399064	+	0.916923i	$0.630665\pi$
$272$	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
$276$	−121.845	+	149.723i	−0.441469	+	0.542473i
$277$	−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	$0.878371\pi$
$278$		−	454.753i		−	1.63580i
$279$	54.1661	+	261.051i	0.194144	+	0.935666i
$280$		0			0
$281$	−385.051	+	222.309i	−1.37029	+	0.791135i	−0.990964	−	0.134129i	$-0.957176\pi$
$281$	−385.051	+	222.309i	−1.37029	+	0.791135i	−0.379323	+	0.925264i	$0.623843\pi$
$282$	25.2520	−	156.970i	0.0895462	−	0.556632i
$283$	64.2122	−	111.219i	0.226898	−	0.392999i	−0.729989	−	0.683459i	$-0.760475\pi$
$283$	64.2122	−	111.219i	0.226898	−	0.392999i	0.956887	+	0.290460i	$0.0938082\pi$
$284$	110.779	+	63.9584i	0.390068	+	0.225206i
$285$	128.514	+	20.6743i	0.450927	+	0.0725413i
$286$	116.194	+	201.254i	0.406272	+	0.703684i
$287$		0			0
$288$	292.063	−	60.6008i	1.01411	−	0.210419i
$289$	15.0199			0.0519719
$290$	−711.720	+	410.912i	−2.45421	+	1.41694i
$291$	400.772	+	326.151i	1.37722	+	1.12079i
$292$	73.4574	−	127.232i	0.251566	−	0.435726i
$293$	−42.6510	−	24.6246i	−0.145567	−	0.0840429i	0.425448	−	0.904983i	$-0.360117\pi$
$293$	−42.6510	−	24.6246i	−0.145567	−	0.0840429i	−0.571014	+	0.820940i	$0.693450\pi$
$294$		0			0
$295$	−262.969	−	455.475i	−0.891420	−	1.54398i
$296$			240.432i			0.812270i
$297$	21.5248	+	477.109i	0.0724741	+	1.60643i
$298$	−373.024			−1.25176
$299$	−35.5334	+	20.5152i	−0.118841	+	0.0686127i
$300$	100.578	−	38.3285i	0.335259	−	0.127762i
$301$		0			0
$302$	419.635	+	242.276i	1.38952	+	0.802239i
$303$	32.7928	−	40.2955i	0.108227	−	0.132988i
$304$	2.80694	+	4.86177i	0.00923337	+	0.0159927i
$305$			408.153i			1.33821i
$306$	−455.989	−	150.609i	−1.49016	−	0.492186i
$307$	−387.296			−1.26155			−0.630776	−	0.775965i	$-0.717263\pi$
$307$	−387.296			−1.26155			−0.630776	+	0.775965i	$0.717263\pi$
$308$		0			0
$309$	13.1509	−	81.7481i	0.0425596	−	0.264557i
$310$	−264.179	+	457.572i	−0.852191	+	1.47604i
$311$	87.5525	+	50.5485i	0.281519	+	0.162535i	0.634111	−	0.773242i	$-0.281366\pi$
$311$	87.5525	+	50.5485i	0.281519	+	0.162535i	−0.352592	+	0.935777i	$0.614700\pi$
$312$	−93.0544	−	14.9698i	−0.298251	−	0.0479801i
$313$	−182.396	−	315.918i	−0.582733	−	1.00932i	−0.995154	−	0.0983303i	$-0.968650\pi$
$313$	−182.396	−	315.918i	−0.582733	−	1.00932i	0.412420	−	0.910994i	$-0.364684\pi$
$314$		−	883.436i		−	2.81349i
$315$		0			0
$316$	−887.634			−2.80897
$317$	−28.7096	+	16.5755i	−0.0905665	+	0.0522886i	−0.544599	−	0.838696i	$-0.683318\pi$
$317$	−28.7096	+	16.5755i	−0.0905665	+	0.0522886i	0.454033	+	0.890985i	$0.349985\pi$
$318$	−282.264	−	229.708i	−0.887621	−	0.722353i
$319$	407.522	−	705.849i	1.27750	−	2.21269i
$320$	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
$324$	−415.857	−	308.345i	−1.28351	−	0.951683i
$325$	22.8777			0.0703929
$326$	621.575	−	358.866i	1.90667	−	1.10082i
$327$	95.7202	−	36.4775i	0.292722	−	0.111552i
$328$	123.809	−	214.444i	0.377468	−	0.653794i
$329$		0			0
$330$	−597.419	+	734.103i	−1.81036	+	2.22456i
$331$	45.2538	+	78.3820i	0.136719	+	0.236804i	0.926253	−	0.376903i	$-0.123011\pi$
$331$	45.2538	+	78.3820i	0.136719	+	0.236804i	−0.789534	+	0.613707i	$0.789678\pi$
$332$		−	101.054i		−	0.304380i
$333$	−209.514	+	186.815i	−0.629171	+	0.561006i
$334$	233.712			0.699737
$335$	58.4148	−	33.7258i	0.174373	−	0.100674i
$336$		0			0
$337$	216.839	−	375.576i	0.643438	−	1.11447i	−0.341221	−	0.939983i	$-0.610841\pi$
$337$	216.839	−	375.576i	0.643438	−	1.11447i	0.984660	−	0.174485i	$-0.0558261\pi$
$338$	425.426	+	245.620i	1.25866	+	0.726686i
$339$	230.602	+	37.0973i	0.680242	+	0.109431i
$340$	−292.671	−	506.921i	−0.860797	−	1.49094i
$341$		−	524.000i		−	1.53666i
$342$	71.3532	−	216.032i	0.208635	−	0.631671i
$343$		0			0
$344$	44.7614	−	25.8430i	0.130120	−	0.0751250i
$345$	−129.613	−	105.480i	−0.375691	−	0.305740i
$346$	340.365	−	589.530i	0.983715	−	1.70384i
$347$	10.1281	+	5.84745i	0.0291876	+	0.0168514i	0.514523	−	0.857477i	$-0.327969\pi$
$347$	10.1281	+	5.84745i	0.0291876	+	0.0168514i	−0.485335	+	0.874328i	$0.661302\pi$
$348$	314.613	+	825.573i	0.904059	+	2.37234i
$349$	91.7075	+	158.842i	0.262772	+	0.455135i	0.966978	−	0.254862i	$-0.0820299\pi$
$349$	91.7075	+	158.842i	0.262772	+	0.455135i	−0.704205	+	0.709996i	$0.748697\pi$
$350$		0			0
$351$	−59.2583	−	92.7196i	−0.168827	−	0.264159i
$352$	−586.250			−1.66548
$353$	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	$0.302589\pi$
$354$	−858.994	+	327.349i	−2.42654	+	0.924715i
$355$	−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
$359$			445.910i			1.24209i	0.783775	+	0.621044i	$0.213291\pi$
$359$			445.910i			1.24209i	−0.783775	+	0.621044i	$0.786709\pi$
$360$	−77.9885	−	375.862i	−0.216635	−	1.04406i
$361$	−299.504			−0.829652
$362$	343.222	−	198.159i	0.948127	−	0.547401i
$363$	91.4332	−	568.362i	0.251882	−	1.56574i
$364$		0			0
$365$	110.143	+	63.5913i	0.301763	+	0.174223i
$366$	704.331	+	113.307i	1.92440	+	0.309581i
$367$	−63.3424	−	109.712i	−0.172595	−	0.298943i	0.766731	−	0.641968i	$-0.221882\pi$
$367$	−63.3424	−	109.712i	−0.172595	−	0.298943i	−0.939326	+	0.343025i	$0.888549\pi$
$368$		−	7.20719i		−	0.0195848i
$369$	283.068	−	58.7344i	0.767121	−	0.159172i
$370$	−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	$-0.139815\pi$
$374$	817.377	+	471.913i	2.18550	+	1.26180i
$375$	−114.592	−	300.699i	−0.305578	−	0.801864i
$376$	−63.3667	−	109.754i	−0.168528	−	0.291900i
$377$			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	$0.317662\pi$
$380$	240.161	−	138.657i	0.632003	−	0.364887i
$381$	39.4548	−	15.0356i	0.103556	−	0.0394636i
$382$	−572.973	+	992.418i	−1.49993	+	2.59795i
$383$	−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
$387$	57.2992	+	18.9254i	0.148060	+	0.0489028i
$388$	1100.83			2.83720
$389$	−149.180	+	86.1293i	−0.383497	+	0.221412i	−0.679339	−	0.733825i	$-0.737733\pi$
$389$	−149.180	+	86.1293i	−0.383497	+	0.221412i	0.295842	+	0.955237i	$0.404400\pi$
$390$	34.6358	−	215.301i	0.0888098	−	0.552055i
$391$	−83.3209	+	144.316i	−0.213097	+	0.369095i
$392$		0			0
$393$	−65.9615	−	10.6113i	−0.167841	−	0.0270008i
$394$	−210.554	−	364.691i	−0.534402	−	0.925611i
$395$		−	768.416i		−	1.94536i
$396$	677.161	+	759.439i	1.71000	+	1.91778i
$397$	371.042			0.934616			0.467308	−	0.884095i	$-0.345224\pi$
$397$	371.042			0.934616			0.467308	+	0.884095i	$0.345224\pi$
$398$	−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	0.787168	−	0.616739i	$-0.211547\pi$
$401$	259.303	+	149.708i	0.646640	+	0.373338i	−0.140528	+	0.990077i	$0.544880\pi$
$402$	−41.9826	−	110.166i	−0.104434	−	0.274045i
$403$	60.3652	+	104.556i	0.149790	+	0.259443i
$404$		−	110.683i		−	0.273968i
$405$	266.932	−	360.004i	0.659090	−	0.888898i
$406$		0			0
$407$	477.788	−	275.851i	1.17393	−	0.677767i
$408$	−357.699	+	136.314i	−0.876714	+	0.334102i
$409$	187.201	−	324.241i	0.457703	−	0.792766i	−0.541136	−	0.840935i	$-0.682005\pi$
$409$	187.201	−	324.241i	0.457703	−	0.792766i	0.998839	+	0.0481696i	$0.0153388\pi$
$410$	496.163	+	286.460i	1.21015	+	0.698682i
$411$	−70.2265	+	86.2938i	−0.170867	+	0.209961i
$412$	−88.2000	−	152.767i	−0.214078	−	0.370793i
$413$		0			0
$414$	−218.004	+	194.385i	−0.526580	+	0.469530i
$415$	87.4816			0.210799
$416$	116.976	−	67.5364i	0.281193	−	0.162347i
$417$	67.2189	−	417.842i	0.161196	−	1.00202i
$418$	−223.576	+	387.244i	−0.534870	+	0.926422i
$419$	350.317	+	202.256i	0.836080	+	0.482711i	0.855930	−	0.517092i	$-0.172986\pi$
$419$	350.317	+	202.256i	0.836080	+	0.482711i	−0.0198501	+	0.999803i	$0.506319\pi$
$420$		0			0
$421$	−231.002	−	400.107i	−0.548698	−	0.950372i	−0.998364	−	0.0571757i	$-0.981790\pi$
$421$	−231.002	−	400.107i	−0.548698	−	0.950372i	0.449666	−	0.893197i	$-0.351543\pi$
$422$		−	352.086i		−	0.834327i
$423$	46.4048	−	140.497i	0.109704	−	0.332144i
$424$	−290.090			−0.684174
$425$	80.4677	−	46.4580i	0.189336	−	0.109313i
$426$	150.120	+	122.169i	0.352395	+	0.286781i
$427$		0			0
$428$	678.055	+	391.475i	1.58424	+	0.914662i
$429$	77.0147	+	202.094i	0.179521	+	0.471081i
$430$	59.7933	+	103.565i	0.139054	+	0.240849i
$431$			228.122i			0.529285i	0.964347	+	0.264643i	$0.0852540\pi$
$431$			228.122i			0.529285i	−0.964347	+	0.264643i	$0.914746\pi$
$432$	19.3092	−	0.871134i	0.0446972	−	0.00201651i
$433$	777.626			1.79590			0.897951	−	0.440095i	$-0.145055\pi$
$433$	777.626			1.79590			0.897951	+	0.440095i	$0.145055\pi$
$434$		0			0
$435$	−714.690	+	272.357i	−1.64297	+	0.626108i
$436$	109.117	−	188.996i	0.250268	−	0.433477i
$437$	−68.3719	−	39.4745i	−0.156457	−	0.0903307i
$438$	140.313	−	172.416i	0.320350	−	0.393643i
$439$	−34.4006	−	59.5836i	−0.0783612	−	0.135726i	0.824182	−	0.566325i	$-0.191635\pi$
$439$	−34.4006	−	59.5836i	−0.0783612	−	0.135726i	−0.902543	+	0.430600i	$0.858302\pi$
$440$			754.458i			1.71468i
$441$		0			0
$442$	−217.459			−0.491988
$443$	180.419	−	104.165i	0.407267	−	0.235136i	−0.282348	−	0.959312i	$-0.591113\pi$
$443$	180.419	−	104.165i	0.407267	−	0.235136i	0.689615	+	0.724176i	$0.257780\pi$
$444$	−94.9850	+	590.441i	−0.213930	+	1.32982i
$445$	−149.961	+	259.741i	−0.336992	+	0.583687i
$446$	−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	$0.0931461\pi$
$449$			259.045i			0.576937i	−0.957489	+	0.288469i	$0.906854\pi$
$450$	159.462	−	33.0871i	0.354360	−	0.0735270i
$451$	−568.194			−1.25985
$452$	430.938	−	248.802i	0.953402	−	0.550447i
$453$	349.763	+	284.639i	0.772103	+	0.628343i
$454$	−326.463	+	565.450i	−0.719081	+	1.24548i
$455$		0			0
$456$	−64.5806	−	169.465i	−0.141624	−	0.371635i
$457$	−79.7186	−	138.077i	−0.174439	−	0.302137i	0.765528	−	0.643403i	$-0.222478\pi$
$457$	−79.7186	−	138.077i	−0.174439	−	0.302137i	−0.939967	+	0.341265i	$0.889144\pi$
$458$		−	255.542i		−	0.557952i
$459$	−396.716	−	205.786i	−0.864305	−	0.448336i
$460$	−356.020			−0.773957
$461$	−176.910	+	102.139i	−0.383752	+	0.221559i	−0.679449	−	0.733722i	$-0.737781\pi$
$461$	−176.910	+	102.139i	−0.383752	+	0.221559i	0.295697	+	0.955282i	$0.404448\pi$
$462$		0			0
$463$	−381.105	+	660.092i	−0.823120	+	1.42569i	0.0802276	+	0.996777i	$0.474435\pi$
$463$	−381.105	+	660.092i	−0.823120	+	1.42569i	−0.903348	+	0.428909i	$0.858898\pi$
$464$	−28.5666	−	16.4929i	−0.0615659	−	0.0355451i
$465$	−310.372	+	381.383i	−0.667467	+	0.820178i
$466$	−525.638	−	910.432i	−1.12798	−	1.95372i
$467$			533.524i			1.14245i	0.820793	+	0.571225i	$0.193532\pi$
$467$			533.524i			1.14245i	−0.820793	+	0.571225i	$0.806468\pi$
$468$	−222.604	−	73.5241i	−0.475650	−	0.157103i
$469$		0			0
$470$	253.940	−	146.612i	0.540298	−	0.311941i
$471$	130.584	−	811.730i	0.277249	−	1.72342i
$472$	−366.379	+	634.588i	−0.776227	+	1.34447i
$473$	−102.711	−	59.3001i	−0.217148	−	0.125370i
$474$	−1326.02	−	213.318i	−2.79751	−	0.450039i
$475$	22.0102	+	38.1228i	0.0463372	+	0.0802584i
$476$		0			0
$477$	−225.399	−	252.786i	−0.472535	−	0.529950i
$478$	−785.091			−1.64245
$479$	−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	$0.550696\pi$
$480$	426.689	+	347.243i	0.888936	+	0.723423i
$481$	−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
$485$			952.982i			1.96491i
$486$	−547.138	−	560.571i	−1.12580	−	1.15344i
$487$	156.203			0.320746			0.160373	−	0.987056i	$-0.448730\pi$
$487$	156.203			0.320746			0.160373	+	0.987056i	$0.448730\pi$
$488$	492.471	−	284.328i	1.00916	−	0.582640i
$489$	624.169	−	237.861i	1.27642	−	0.486423i
$490$		0			0
$491$	−346.903	−	200.285i	−0.706523	−	0.407911i	0.103249	−	0.994656i	$-0.467076\pi$
$491$	−346.903	−	200.285i	−0.706523	−	0.407911i	−0.809772	+	0.586744i	$0.800409\pi$
$492$	388.763	−	477.709i	0.790169	−	0.970954i
$493$	381.342	+	660.505i	0.773514	+	1.33977i
$494$		−	103.024i		−	0.208551i
$495$	−657.439	+	586.212i	−1.32816	+	1.18427i
$496$	−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	$0.127565\pi$
$500$	−593.719	−	342.784i	−1.18744	−	0.685567i
$501$	214.743	+	34.5459i	0.428628	+	0.0689539i
$502$	225.862	+	391.204i	0.449924	+	0.779291i
$503$			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
$506$	497.150	−	287.030i	0.982510	−	0.567252i
$507$	354.590	+	288.568i	0.699388	+	0.569167i
$508$	44.9768	−	77.9021i	0.0885370	−	0.153351i
$509$	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
$513$	97.4942	−	187.950i	0.190047	−	0.366374i
$514$	−356.758			−0.694081
$515$	132.249	−	76.3539i	0.256794	−	0.148260i
$516$	120.132	−	45.7805i	0.232814	−	0.0887219i
$517$	−145.403	+	251.846i	−0.281244	+	0.487129i
$518$		0			0
$519$	399.880	−	491.369i	0.770482	−	0.946762i
$520$	−86.9141	−	150.540i	−0.167142	−	0.289499i
$521$			511.236i			0.981259i	0.871368	+	0.490630i	$0.163233\pi$
$521$			511.236i			0.981259i	−0.871368	+	0.490630i	$0.836767\pi$
$522$	271.590	+	1308.91i	0.520287	+	2.50750i
$523$	−979.307			−1.87248			−0.936240	−	0.351360i	$-0.885719\pi$
$523$	−979.307			−1.87248			−0.936240	+	0.351360i	$0.885719\pi$
$524$	−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
$528$	−37.5068	−	6.03378i	−0.0710357	−	0.0114276i
$529$	−213.822	−	370.351i	−0.404200	−	0.700096i
$530$		−	671.185i		−	1.26639i
$531$	−837.659	+	173.808i	−1.57751	+	0.327322i
$532$		0			0
$533$	113.374	−	65.4564i	0.212709	−	0.122807i
$534$	406.592	+	330.887i	0.761408	+	0.619639i
$535$	−338.896	+	586.986i	−0.633451	+	1.09717i
$536$	−81.3860	−	46.9882i	−0.151840	−	0.0876646i
$537$	85.8529	+	225.286i	0.159875	+	0.419527i
$538$	−301.577	−	522.346i	−0.560552	−	0.970904i
$539$		0			0
$540$	−43.0322	−	953.833i	−0.0796893	−	1.76636i
$541$	−700.529			−1.29488			−0.647439	−	0.762117i	$-0.724160\pi$
$541$	−700.529			−1.29488			−0.647439	+	0.762117i	$0.724160\pi$
$542$	−603.822	+	348.617i	−1.11406	+	0.643204i
$543$	344.655	−	131.342i	0.634723	−	0.241883i
$544$	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	0.999038	+	0.0438616i	$0.0139660\pi$
$547$	294.015	+	509.248i	0.537504	+	0.930984i	−0.461534	+	0.887123i	$0.652701\pi$
$548$			237.031i			0.432538i
$549$	630.414	+	208.220i	1.14830	+	0.379271i
$550$	−320.084			−0.581970
$551$	−312.924	+	180.667i	−0.567920	+	0.327889i
$552$	−36.9794	+	229.869i	−0.0669916	+	0.416430i
$553$		0			0
$554$	−218.097	−	125.918i	−0.393676	−	0.227289i
$555$	−511.139	−	82.2276i	−0.920970	−	0.148158i
$556$	−450.820	−	780.843i	−0.810827	−	1.40439i
$557$			400.729i			0.719442i	0.933060	+	0.359721i	$0.117128\pi$
$557$			400.729i			0.719442i	−0.933060	+	0.359721i	$0.882872\pi$
$558$	571.972	+	641.469i	1.02504	+	1.14959i
$559$	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
$563$	78.9486	+	45.5810i	0.140228	+	0.0809609i	0.568473	−	0.822702i	$-0.307534\pi$
$563$	78.9486	+	45.5810i	0.140228	+	0.0809609i	−0.428244	+	0.903663i	$0.640868\pi$
$564$	−112.253	−	294.563i	−0.199030	−	0.522274i
$565$	215.385	+	373.058i	0.381213	+	0.660281i
$566$		−	413.984i		−	0.731421i
$567$		0			0
$568$	154.282			0.271624
$569$	−255.596	+	147.568i	−0.449202	+	0.259347i	−0.707493	−	0.706720i	$-0.750174\pi$
$569$	−255.596	+	147.568i	−0.449202	+	0.259347i	0.258291	+	0.966067i	$0.416841\pi$
$570$	392.094	−	149.421i	0.687885	−	0.262142i
$571$	−457.407	+	792.252i	−0.801062	+	1.38748i	0.117855	+	0.993031i	$0.462398\pi$
$571$	−457.407	+	792.252i	−0.801062	+	1.38748i	−0.918917	+	0.394450i	$0.870935\pi$
$572$	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
$576$	698.437	−	622.768i	1.21256	−	1.08120i
$577$	534.601			0.926519			0.463259	−	0.886223i	$-0.346680\pi$
$577$	534.601			0.926519			0.463259	+	0.886223i	$0.346680\pi$
$578$	41.9308	−	24.2088i	0.0725447	−	0.0418837i
$579$	18.8972	−	117.467i	0.0326376	−	0.202880i
$580$	−814.715	+	1411.13i	−1.40468	+	2.43298i
$581$		0			0
$582$	1644.51	+	264.555i	2.82563	+	0.454562i
$583$	332.825	+	576.469i	0.570883	+	0.988798i
$584$		−	177.196i		−	0.303418i
$585$	63.6491	−	192.706i	0.108802	−	0.329413i
$586$	−158.758			−0.270918
$587$	299.889	−	173.141i	0.510884	−	0.294959i	−0.222313	−	0.974975i	$-0.571361\pi$
$587$	299.889	−	173.141i	0.510884	−	0.294959i	0.733197	+	0.680016i	$0.238027\pi$
$588$		0			0
$589$	−116.152	+	201.182i	−0.197203	+	0.341565i
$590$	−1468.25	−	847.697i	−2.48857	−	1.43677i
$591$	−139.558	−	366.213i	−0.236139	−	0.619649i
$592$	−11.1640	−	19.3367i	−0.0188582	−	0.0326633i
$593$		−	4.10166i		−	0.00691679i	−0.999994	−	0.00345840i	$-0.998899\pi$
$593$		−	4.10166i		−	0.00691679i	0.999994	−	0.00345840i	$-0.00110084\pi$
$594$	829.087	+	1297.25i	1.39577	+	2.18392i
$595$		0			0
$596$	−640.509	+	369.798i	−1.07468	+	0.620467i
$597$	−608.441	+	231.867i	−1.01916	+	0.388388i
$598$	−66.1320	+	114.544i	−0.110589	+	0.191545i
$599$	−146.853	−	84.7858i	−0.245164	−	0.141546i	0.372384	−	0.928079i	$-0.378541\pi$
$599$	−146.853	−	84.7858i	−0.245164	−	0.141546i	−0.617548	+	0.786533i	$0.711874\pi$
$600$	81.9417	−	100.689i	0.136569	−	0.167815i
$601$	−312.975	−	542.089i	−0.520757	−	0.901978i	−0.999709	−	0.0241366i	$-0.992316\pi$
$601$	−312.975	−	542.089i	−0.520757	−	0.901978i	0.478951	−	0.877841i	$-0.341017\pi$
$602$		0			0
$603$	−22.2909	−	107.430i	−0.0369667	−	0.178159i
$604$	960.723			1.59060
$605$	919.473	−	530.858i	1.51979	−	0.877451i
$606$	26.5996	−	165.347i	0.0438938	−	0.272850i
$607$	18.8059	−	32.5727i	0.0309817	−	0.0536618i	−0.850119	−	0.526591i	$-0.823470\pi$
$607$	18.8059	−	32.5727i	0.0309817	−	0.0536618i	0.881101	+	0.472929i	$0.156803\pi$
$608$	225.081	+	129.951i	0.370200	+	0.213735i
$609$		0			0
$610$	657.855	+	1139.44i	1.07845	+	1.86793i
$611$		−	67.0022i		−	0.109660i
$612$	−932.272	+	193.439i	−1.52332	+	0.316077i
$613$	298.038			0.486195			0.243098	−	0.970002i	$-0.421836\pi$
$613$	298.038			0.486195			0.243098	+	0.970002i	$0.421836\pi$
$614$	−1081.21	+	624.238i	−1.76093	+	1.01667i
$615$	413.548	+	336.549i	0.672436	+	0.547233i
$616$		0			0
$617$	818.560	+	472.596i	1.32668	+	0.765957i	0.984784	−	0.173782i	$-0.0555987\pi$
$617$	818.560	+	472.596i	1.32668	+	0.765957i	0.341893	+	0.939739i	$0.388932\pi$
$618$	−95.0469	−	249.412i	−0.153797	−	0.403579i
$619$	596.799	+	1033.69i	0.964133	+	1.66993i	0.711926	+	0.702255i	$0.247823\pi$
$619$	596.799	+	1033.69i	0.964133	+	1.66993i	0.252208	+	0.967673i	$0.418843\pi$
$620$			1047.58i			1.68964i
$621$	−229.042	+	146.384i	−0.368828	+	0.235723i
$622$	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
$626$	−1018.38	−	587.964i	−1.62681	−	0.939239i
$627$	−262.669	+	322.765i	−0.418929	+	0.514777i
$628$	−875.795	−	1516.92i	−1.39458	−	2.41548i
$629$			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	$0.726147\pi$
$632$	−927.158	+	535.295i	−1.46702	+	0.846985i
$633$	52.0432	−	323.508i	0.0822168	−	0.511072i
$634$	−53.4322	+	92.5472i	−0.0842779	+	0.145974i
$635$	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
$639$	119.877	+	134.443i	0.187601	+	0.210395i
$640$	1120.95			1.75149
$641$	617.070	−	356.265i	0.962667	−	0.555796i	0.0656744	−	0.997841i	$-0.479080\pi$
$641$	617.070	−	356.265i	0.962667	−	0.555796i	0.896993	+	0.442045i	$0.145747\pi$
$642$	918.852	+	747.769i	1.43123	+	1.16475i
$643$	534.902	−	926.478i	0.831885	−	1.44087i	−0.0646564	−	0.997908i	$-0.520595\pi$
$643$	534.902	−	926.478i	0.831885	−	1.44087i	0.896542	−	0.442960i	$-0.146072\pi$
$644$		0			0
$645$	39.6317	+	103.997i	0.0614445	+	0.161236i
$646$	−209.213	−	362.367i	−0.323859	−	0.560940i
$647$			1124.01i			1.73727i	0.495456	+	0.868633i	$0.335001\pi$
$647$			1124.01i			1.73727i	−0.495456	+	0.868633i	$0.664999\pi$
$648$	−620.324	−	71.2891i	−0.957291	−	0.110014i
$649$	1681.41			2.59077
$650$	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	0.467540	−	0.883972i	$-0.345140\pi$
$653$	−41.9432	−	24.2159i	−0.0642315	−	0.0370841i	−0.531772	+	0.846888i	$0.678474\pi$
$654$	208.427	−	256.114i	0.318696	−	0.391611i
$655$	−61.6090	−	106.710i	−0.0940595	−	0.162916i
$656$			22.9955i			0.0350541i
$657$	154.410	−	137.681i	0.235023	−	0.209560i
$658$		0			0
$659$	−818.128	+	472.346i	−1.24147	+	0.716762i	−0.969393	−	0.245514i	$-0.921043\pi$
$659$	−818.128	+	472.346i	−1.24147	+	0.716762i	−0.272076	+	0.962276i	$0.587710\pi$
$660$	−298.056	+	1852.76i	−0.451600	+	2.80721i
$661$	−140.597	+	243.521i	−0.212703	+	0.368413i	−0.952560	−	0.304352i	$-0.901560\pi$
$661$	−140.597	+	243.521i	−0.212703	+	0.368413i	0.739856	+	0.672765i	$0.234893\pi$
$662$	252.669	+	145.879i	0.381676	+	0.220361i
$663$	−199.808	−	32.1434i	−0.301370	−	0.0484818i
$664$	−60.9415	−	105.554i	−0.0917794	−	0.158967i
$665$		0			0
$666$	−283.792	+	859.220i	−0.426114	+	1.29012i
$667$	463.885			0.695480
$668$	401.300	−	231.691i	0.600749	−	0.346843i
$669$	−434.509	−	353.607i	−0.649491	−	0.528561i
$670$	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	0.989072	−	0.147435i	$-0.0471017\pi$
$673$	246.892	+	427.630i	0.366854	+	0.635409i	−0.622218	+	0.782844i	$0.713768\pi$
$674$		−	1397.99i		−	2.07417i
$675$	151.410	−	6.83085i	0.224311	−	0.0101198i
$676$	973.983			1.44080
$677$	611.085	−	352.810i	0.902636	−	0.521137i	0.0245816	−	0.999698i	$-0.492175\pi$
$677$	611.085	−	352.810i	0.902636	−	0.521137i	0.878055	+	0.478561i	$0.158841\pi$
$678$	703.562	−	268.116i	1.03770	−	0.395452i
$679$		0			0
$680$	−611.405	−	352.995i	−0.899126	−	0.519110i
$681$	−383.546	+	471.298i	−0.563210	+	0.692068i
$682$	−844.575	−	1462.85i	−1.23838	−	2.14494i
$683$		−	1166.52i		−	1.70794i	−0.520326	−	0.853968i	$-0.674190\pi$
$683$		−	1166.52i		−	1.70794i	0.520326	−	0.853968i	$-0.325810\pi$
$684$	−91.6447	−	441.678i	−0.133983	−	0.645727i
$685$	−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
$689$	−132.819	−	76.6832i	−0.192771	−	0.111296i
$690$	−531.851	−	85.5597i	−0.770799	−	0.124000i
$691$	−182.834	−	316.677i	−0.264593	−	0.458289i	0.702864	−	0.711324i	$-0.251904\pi$
$691$	−182.834	−	316.677i	−0.264593	−	0.458289i	−0.967457	+	0.253036i	$0.918571\pi$
$692$		−	1349.69i		−	1.95041i
$693$		0			0
$694$	37.6993			0.0543217
$695$	675.968	−	390.270i	0.972616	−	0.561540i
$696$	826.490	+	672.603i	1.18749	+	0.966384i
$697$	265.846	−	460.459i	0.381415	−	0.660630i
$698$	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	$0.0581083\pi$
$701$			254.519i			0.363080i	−0.983384	+	0.181540i	$0.941892\pi$
$702$	−314.875	−	163.333i	−0.448539	−	0.232668i
$703$	−244.586			−0.347917
$704$	−1592.76	+	919.581i	−2.26244	+	1.30622i
$705$	255.000	−	97.1764i	0.361702	−	0.137839i
$706$	109.735	−	190.067i	0.155433	−	0.269217i
$707$		0			0
$708$	−1150.44	+	1413.65i	−1.62491	+	1.99668i
$709$	520.494	+	901.522i	0.734124	+	1.27154i	0.955107	+	0.296263i	$0.0957403\pi$
$709$	520.494	+	901.522i	0.734124	+	1.27154i	−0.220982	+	0.975278i	$0.570926\pi$
$710$			356.966i			0.502768i
$711$	−1186.86	−	392.008i	−1.66928	−	0.551347i
$712$	417.865			0.586889
$713$	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
$717$	−721.368	−	116.047i	−1.00609	−	0.161851i
$718$	718.710	+	1244.84i	1.00099	+	1.73376i
$719$		−	754.646i		−	1.04958i	−0.851232	−	0.524789i	$-0.824144\pi$
$719$		−	754.646i		−	1.04958i	0.851232	−	0.524789i	$-0.175856\pi$
$720$	23.7247	+	26.6073i	0.0329509	+	0.0369546i
$721$		0			0
$722$	−836.123	+	482.736i	−1.15807	+	0.668609i
$723$	−65.9441	−	53.6658i	−0.0912089	−	0.0742265i
$724$	392.891	−	680.507i	0.542667	−	0.939927i
$725$	−224.000	−	129.326i	−0.308965	−	0.178381i
$726$	−660.823	−	1734.06i	−0.910225	−	2.38851i
$727$	698.773	+	1210.31i	0.961174	+	1.66480i	0.719561	+	0.694429i	$0.244343\pi$
$727$	698.773	+	1210.31i	0.961174	+	1.66480i	0.241612	+	0.970373i	$0.422324\pi$
$728$		0			0
$729$	−419.869	−	595.946i	−0.575952	−	0.817484i
$730$	409.981			0.561618
$731$	96.1126	−	55.4906i	0.131481	−	0.0759106i
$732$	1321.71	−	503.684i	1.80562	−	0.688092i
$733$	−626.744	+	1085.55i	−0.855039	+	1.48097i	0.0215697	+	0.999767i	$0.493134\pi$
$733$	−626.744	+	1085.55i	−0.855039	+	1.48097i	−0.876609	+	0.481204i	$0.840200\pi$
$734$	−353.664	−	204.188i	−0.481832	−	0.278186i
$735$		0			0
$736$	−166.833	−	288.963i	−0.226675	−	0.392613i
$737$			215.641i			0.292593i
$738$	695.570	−	620.211i	0.942506	−	0.840395i
$739$	1070.00			1.44790			0.723950	−	0.689852i	$-0.242324\pi$
$739$	1070.00			1.44790			0.723950	+	0.689852i	$0.242324\pi$
$740$	−955.191	+	551.480i	−1.29080	+	0.745243i
$741$	15.2284	−	94.6621i	0.0205512	−	0.127749i
$742$		0			0
$743$	−620.266	−	358.111i	−0.834813	−	0.481980i	0.0206847	−	0.999786i	$-0.493415\pi$
$743$	−620.266	−	358.111i	−0.834813	−	0.481980i	−0.855498	+	0.517806i	$0.826749\pi$
$744$	676.382	+	108.810i	0.909115	+	0.146251i
$745$	−320.131	−	554.483i	−0.429706	−	0.744272i
$746$		−	1973.88i		−	2.64596i
$747$	44.6288	−	135.120i	0.0597440	−	0.180883i
$748$	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	$0.141072\pi$
$752$	10.1925	+	5.88464i	0.0135538	+	0.00782531i
$753$	149.704	+	392.837i	0.198810	+	0.521696i
$754$	302.672	+	524.244i	0.401422	+	0.695284i
$755$			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	$0.578457\pi$
$758$	1146.96	−	662.196i	1.51314	−	0.873610i
$759$	499.225	−	190.247i	0.657740	−	0.250654i
$760$	167.237	−	289.662i	0.220048	−	0.381135i
$761$	−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
$765$	−167.458	−	807.059i	−0.218900	−	1.05498i
$766$	−709.563			−0.926323
$767$	−335.498	+	193.700i	−0.437416	+	0.252542i
$768$	113.016	−	702.524i	0.147156	−	0.914745i
$769$	319.295	−	553.035i	0.415208	−	0.719162i	−0.580242	−	0.814444i	$-0.697042\pi$
$769$	319.295	−	553.035i	0.415208	−	0.719162i	0.995450	+	0.0952822i	$0.0303754\pi$
$770$		0			0
$771$	−327.801	−	52.7337i	−0.425163	−	0.0683966i
$772$	−126.738	−	219.517i	−0.164169	−	0.284349i
$773$			195.650i			0.253105i	0.991960	+	0.126552i	$0.0403912\pi$
$773$			195.650i			0.253105i	−0.991960	+	0.126552i	$0.959609\pi$
$774$	190.465	−	39.5201i	0.246079	−	0.0510595i
$775$	−166.290			−0.214568
$776$	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
$780$	−153.967	−	404.024i	−0.197394	−	0.517979i
$781$	−177.011	−	306.591i	−0.226646	−	0.392563i
$782$			537.181i			0.686932i
$783$	56.0698	+	1242.82i	0.0716090	+	1.58725i
$784$		0			0
$785$	1313.18	−	758.167i	1.67285	−	0.965818i
$786$	−201.247	+	76.6921i	−0.256040	+	0.0975727i
$787$	8.68274	−	15.0389i	0.0110327	−	0.0191092i	−0.860456	−	0.509524i	$-0.829821\pi$
$787$	8.68274	−	15.0389i	0.0110327	−	0.0191092i	0.871489	+	0.490415i	$0.163155\pi$
$788$	−723.073	−	417.466i	−0.917605	−	0.529780i
$789$	93.4845	−	114.873i	0.118485	−	0.145593i
$790$	−1238.52	−	2145.18i	−1.56775	−	2.71542i
$791$		0			0
$792$	1165.30	+	384.887i	1.47134	+	0.485969i
$793$	300.641			0.379118
$794$	1035.83	−	598.040i	1.30458	−	0.753198i
$795$	99.2105	−	616.707i	0.124793	−	0.775732i
$796$	−693.596	+	1201.34i	−0.871352	+	1.50923i
$797$	−871.920	−	503.403i	−1.09400	−	0.631622i	−0.159363	−	0.987220i	$-0.550944\pi$
$797$	−871.920	−	503.403i	−1.09400	−	0.631622i	−0.934639	+	0.355598i	$0.884277\pi$
$798$		0			0
$799$	−136.062	−	235.667i	−0.170291	−	0.294952i
$800$			186.045i			0.232556i
$801$	324.680	+	364.130i	0.405344	+	0.454595i
$802$	965.189			1.20348
$803$	−352.126	+	203.300i	−0.438513	+	0.253176i
$804$	−181.300	−	147.544i	−0.225498	−	0.183512i
$805$		0			0
$806$	337.042	+	194.591i	0.418166	+	0.241428i
$807$	−199.889	−	524.527i	−0.247694	−	0.649971i
$808$	−66.7484	−	115.612i	−0.0826094	−	0.143084i
$809$			420.554i			0.519844i	0.965630	+	0.259922i	$0.0836968\pi$
$809$			420.554i			0.519844i	−0.965630	+	0.259922i	$0.916303\pi$
$810$	164.943	−	1435.25i	0.203633	−	1.77192i
$811$	1318.39			1.62564			0.812819	−	0.582517i	$-0.197932\pi$
$811$	1318.39			1.62564			0.812819	+	0.582517i	$0.197932\pi$
$812$		0			0
$813$	−606.342	+	231.067i	−0.745808	+	0.284216i
$814$	889.224	−	1540.18i	1.09241	−	1.89212i
$815$	1066.87	+	615.960i	1.30905	+	0.755780i
$816$	22.4384	−	27.5721i	0.0274980	−	0.0337893i
$817$	26.2895	+	45.5347i	0.0321781	+	0.0557341i
$818$		−	1206.91i		−	1.47544i
$819$		0			0
$820$	1135.93			1.38528
$821$	−668.380	+	385.889i	−0.814104	+	0.470023i	−0.848379	−	0.529389i	$-0.822421\pi$
$821$	−668.380	+	385.889i	−0.814104	+	0.470023i	0.0342747	+	0.999412i	$0.489088\pi$
$822$	−56.9638	+	354.095i	−0.0692990	+	0.430773i
$823$	−453.227	+	785.013i	−0.550702	+	0.953843i	0.447522	+	0.894273i	$0.352306\pi$
$823$	−453.227	+	785.013i	−0.550702	+	0.953843i	−0.998224	+	0.0595705i	$0.981027\pi$
$824$	−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	$0.0996660\pi$
$827$			509.463i			0.616038i	−0.951380	+	0.308019i	$0.900334\pi$
$828$	−181.624	+	549.892i	−0.219353	+	0.664121i
$829$	−665.170			−0.802376			−0.401188	−	0.915996i	$-0.631403\pi$
$829$	−665.170			−0.802376			−0.401188	+	0.915996i	$0.631403\pi$
$830$	244.221	−	141.001i	0.294243	−	0.169881i
$831$	−181.782	−	147.935i	−0.218751	−	0.178021i
$832$	211.873	−	366.974i	0.254655	−	0.441075i
$833$		0			0
$834$	−485.817	−	1274.83i	−0.582514	−	1.52857i
$835$	200.572	+	347.402i	0.240207	+	0.416050i
$836$			886.567i			1.06049i
$837$	430.729	+	673.949i	0.514610	+	0.805195i
$838$	1303.97			1.55605
$839$	1237.78	−	714.635i	1.47531	−	0.851770i	0.475696	−	0.879610i	$-0.342196\pi$
$839$	1237.78	−	714.635i	1.47531	−	0.851770i	0.999612	+	0.0278396i	$0.00886276\pi$
$840$		0			0
$841$	641.052	−	1110.33i	0.762250	−	1.32026i
$842$	−1289.77	−	744.649i	−1.53179	−	0.884381i
$843$	−841.933	+	1034.56i	−0.998734	+	1.22724i
$844$	−349.041	−	604.557i	−0.413556	−	0.716299i
$845$			843.167i			0.997831i
$846$	−96.9027	−	467.018i	−0.114542	−	0.552031i
$847$		0			0
$848$	23.3304	−	13.4698i	0.0275122	−	0.0158842i
$849$	61.1926	−	380.382i	0.0720761	−	0.448036i
$850$	149.761	−	259.393i	0.176189	−	0.305168i
$851$	271.935	+	157.002i	0.319547	+	0.184491i
$852$	378.879	+	60.9508i	0.444694	+	0.0715385i
$853$	485.171	+	840.341i	0.568782	+	0.985159i	0.996687	+	0.0813353i	$0.0259185\pi$
$853$	485.171	+	840.341i	0.568782	+	0.985159i	−0.427905	+	0.903824i	$0.640748\pi$
$854$		0			0
$855$	382.356	−	79.3359i	0.447200	−	0.0927905i
$856$	944.329			1.10319
$857$	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	$-0.00994611\pi$
$858$	540.732	+	440.052i	0.630224	+	0.512881i
$859$	614.191	−	1063.81i	0.715007	−	1.23843i	−0.247950	−	0.968773i	$-0.579757\pi$
$859$	614.191	−	1063.81i	0.715007	−	1.23843i	0.962957	−	0.269655i	$-0.0869097\pi$
$860$	205.339	+	118.552i	0.238766	+	0.137852i
$861$		0			0
$862$	367.683	+	636.845i	0.426546	+	0.738800i
$863$		−	1492.67i		−	1.72963i	−0.502091	−	0.864815i	$-0.667436\pi$
$863$		−	1492.67i		−	1.72963i	0.502091	−	0.864815i	$-0.332564\pi$
$864$	754.011	−	481.898i	0.872698	−	0.557752i
$865$	1168.41			1.35076
$866$	2170.89	−	1253.36i	2.50680	−	1.44730i
$867$	42.1058	−	16.0459i	0.0485650	−	0.0185073i
$868$		0			0
$869$	2127.48	+	1228.30i	2.44820	+	1.41347i
$870$	−1556.21	+	1912.26i	−1.78875	+	2.19800i
$871$	−24.8420	−	43.0277i	−0.0285213	−	0.0494003i
$872$		−	263.215i		−	0.301852i
$873$	1471.93	+	486.164i	1.68606	+	0.556889i
$874$	−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	$0.103286\pi$
$878$	−192.071	−	110.892i	−0.218760	−	0.126301i
$879$	−145.872	−	23.4666i	−0.165952	−	0.0266969i
$880$	−35.0319	−	60.6770i	−0.0398090	−	0.0689512i
$881$		−	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	$0.335573\pi$
$884$	−373.392	+	215.578i	−0.422389	+	0.243866i
$885$	−1223.78	−	995.921i	−1.38280	−	1.12533i
$886$	335.783	−	581.593i	0.378987	−	0.656426i
$887$	−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
$891$	570.041	+	1314.50i	0.639777	+	1.47531i
$892$	−1193.51			−1.33801
$893$	111.651	−	64.4615i	0.125029	−	0.0721853i
$894$	−1045.71	+	398.505i	−1.16970	+	0.445755i
$895$	−222.323	+	385.075i	−0.248406	+	0.430251i
$896$		0			0
$897$	−77.6955	+	95.4716i	−0.0866171	+	0.106434i
$898$	417.524	+	723.172i	0.464949	+	0.805314i
$899$		−	1364.97i		−	1.51832i
$900$	241.006	−	214.896i	0.267785	−	0.238773i
$901$	−622.887			−0.691328
$902$	−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
$906$	1435.21	+	230.883i	1.58411	+	0.254838i
$907$	−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	$-0.378870\pi$
$908$			1294.56i			1.42572i
$909$	48.8813	−	147.995i	0.0537748	−	0.162811i
$910$		0			0
$911$	−770.852	+	445.052i	−0.846160	+	0.488531i	−0.859353	−	0.511382i	$-0.829134\pi$
$911$	−770.852	+	445.052i	−0.846160	+	0.488531i	0.0131931	+	0.999913i	$0.495800\pi$
$912$	13.0627	+	10.6305i	0.0143231	+	0.0116563i
$913$	−139.838	+	242.207i	−0.153163	+	0.265287i
$914$	−445.099	−	256.978i	−0.486979	−	0.281158i
$915$	436.034	+	1144.19i	0.476540	+	1.25048i
$916$	−253.332	−	438.784i	−0.276563	−	0.479021i
$917$		0			0
$918$	−1439.19	+	64.9291i	−1.56775	+	0.0707289i
$919$	−1135.91			−1.23602			−0.618012	−	0.786168i	$-0.712062\pi$
$919$	−1135.91			−1.23602			−0.618012	+	0.786168i	$0.712062\pi$
$920$	−371.873	+	214.701i	−0.404210	+	0.233371i
$921$	−1085.72	+	413.752i	−1.17885	+	0.449242i
$922$	−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
$926$			2457.03i			2.65338i
$927$	−50.4657	−	243.217i	−0.0544398	−	0.262370i
$928$	−1527.12			−1.64560
$929$	−622.843	+	359.598i	−0.670444	+	0.387081i	−0.796245	−	0.604974i	$-0.793183\pi$
$929$	−622.843	+	359.598i	−0.670444	+	0.387081i	0.125801	+	0.992056i	$0.459850\pi$
$930$	−251.756	+	1564.95i	−0.270706	+	1.68275i
$931$		0			0
$932$	−1805.12	−	1042.18i	−1.93682	−	1.11822i
$933$	299.441	+	48.1715i	0.320944	+	0.0516307i
$934$	859.925	+	1489.43i	0.920691	+	1.59468i
$935$			1619.99i			1.73261i
$936$	−276.855	+	57.4454i	−0.295786	+	0.0613733i
$937$	−1522.34			−1.62470			−0.812348	−	0.583172i	$-0.801811\pi$
$937$	−1522.34			−1.62470			−0.812348	+	0.583172i	$0.801811\pi$
$938$		0			0
$939$	−848.815	−	690.772i	−0.903957	−	0.735646i
$940$	290.689	−	503.488i	0.309243	−	0.535625i
$941$	886.384	+	511.754i	0.941960	+	0.543841i	0.890574	−	0.454838i	$-0.150303\pi$
$941$	886.384	+	511.754i	0.941960	+	0.543841i	0.0513858	+	0.998679i	$0.483636\pi$
$942$	−943.782	−	2476.57i	−1.00189	−	2.62906i
$943$	−161.695	−	280.063i	−0.171468	−	0.296992i
$944$		−	68.0487i		−	0.0720855i
$945$		0			0
$946$	−382.316			−0.404139
$947$	−1361.76	+	786.215i	−1.43798	+	0.830217i	−0.997709	−	0.0676499i	$-0.978450\pi$
$947$	−1361.76	+	786.215i	−1.43798	+	0.830217i	−0.440268	+	0.897866i	$0.645117\pi$
$948$	−2488.34	+	948.267i	−2.62483	+	1.00028i
$949$	46.8406	−	81.1303i	0.0493578	−	0.0854903i
$950$	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	$-0.751137\pi$
$953$		−	1342.92i		−	1.40915i	0.709629	−	0.704576i	$-0.248863\pi$
$954$	−1036.68	−	342.406i	−1.08667	−	0.358916i
$955$	−1966.91			−2.05959
$956$	−1348.06	+	778.301i	−1.41010	+	0.814122i
$957$	388.359	−	2414.10i	0.405809	−	2.52257i
$958$	−974.348	+	1687.62i	−1.01706	+	1.76161i
$959$		0			0
$960$	1703.94	+	274.115i	1.77493	+	0.285536i
$961$	41.7250	+	72.2699i	0.0434183	+	0.0752028i
$962$			409.757i			0.425943i
$963$	733.741	+	822.894i	0.761933	+	0.854511i
$964$	−181.134			−0.187899
$965$	190.034	−	109.716i	0.196927	−	0.113696i
$966$		0			0
$967$	−867.804	+	1503.08i	−0.897418	+	1.55437i	−0.0666355	+	0.997777i	$0.521226\pi$
$967$	−867.804	+	1503.08i	−0.897418	+	1.55437i	−0.830783	+	0.556597i	$0.812107\pi$
$968$	−1281.05	−	739.614i	−1.32340	−	0.764064i
$969$	−138.669	−	363.879i	−0.143105	−	0.375521i
$970$	1536.00	+	2660.43i	1.58350	+	2.74271i
$971$			50.6306i			0.0521427i	0.999660	+	0.0260714i	$0.00829971\pi$
$971$			50.6306i			0.0521427i	−0.999660	+	0.0260714i	$0.991700\pi$
$972$	−1495.20	−	420.133i	−1.53827	−	0.432236i
$973$		0			0
$974$	436.071	−	251.766i	0.447712	−	0.258486i
$975$	64.1340	−	24.4404i	0.0657784	−	0.0250671i
$976$	−26.4045	+	45.7340i	−0.0270538	+	0.0468586i
$977$	−506.717	−	292.553i	−0.518646	−	0.299440i	0.217734	−	0.976008i	$-0.430133\pi$
$977$	−506.717	−	292.553i	−0.518646	−	0.299440i	−0.736381	+	0.676568i	$0.763467\pi$
$978$	1359.11	−	1670.06i	1.38968	−	1.70763i
$979$	−479.423	−	830.386i	−0.489707	−	0.848198i
$980$		0			0
$981$	229.367	−	204.517i	0.233810	−	0.208479i
$982$	−1291.26			−1.31493
$983$	−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	$0.497370\pi$
$984$	117.987	−	733.427i	0.119906	−	0.745353i
$985$	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
$989$		−	67.5017i		−	0.0682525i
$990$	−890.519	+	2696.17i	−0.899514	+	2.72340i
$991$	208.897			0.210794			0.105397	−	0.994430i	$-0.466389\pi$
$991$	208.897			0.210794			0.105397	+	0.994430i	$0.466389\pi$
$992$	−850.263	+	490.900i	−0.857120	+	0.494859i
$993$	210.598	+	171.386i	0.212083	+	0.172594i
$994$		0			0
$995$	−1039.99	−	600.439i	−1.04522	−	0.603457i
$996$	−107.957	−	283.289i	−0.108391	−	0.284427i
$997$	−76.0851	−	131.783i	−0.0763140	−	0.132180i	0.825343	−	0.564632i	$-0.190982\pi$
$997$	−76.0851	−	131.783i	−0.0763140	−	0.132180i	−0.901657	+	0.432452i	$0.857648\pi$
$998$		−	394.206i		−	0.394996i
$999$	−387.762	+	747.531i	−0.388151	+	0.748280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.r.g.50.10		22
7.2	even	3		63.3.n.b.32.2	yes	22
7.3	odd	6		441.3.j.f.275.10		22
7.4	even	3		63.3.j.b.23.10	yes	22
7.5	odd	6		441.3.n.f.410.2		22
7.6	odd	2		441.3.r.f.50.10		22
9.2	odd	6	inner	441.3.r.g.344.10		22
21.2	odd	6		189.3.n.b.179.10		22
21.11	odd	6		189.3.j.b.44.2		22
63.2	odd	6		63.3.j.b.11.2	✓	22
63.11	odd	6		63.3.n.b.2.2	yes	22
63.16	even	3		189.3.j.b.116.10		22
63.20	even	6		441.3.r.f.344.10		22
63.25	even	3		189.3.n.b.170.10		22
63.38	even	6		441.3.n.f.128.2		22
63.47	even	6		441.3.j.f.263.2		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.2	✓	22	63.2	odd	6
63.3.j.b.23.10	yes	22	7.4	even	3
63.3.n.b.2.2	yes	22	63.11	odd	6
63.3.n.b.32.2	yes	22	7.2	even	3
189.3.j.b.44.2		22	21.11	odd	6
189.3.j.b.116.10		22	63.16	even	3
189.3.n.b.170.10		22	63.25	even	3
189.3.n.b.179.10		22	21.2	odd	6
441.3.j.f.263.2		22	63.47	even	6
441.3.j.f.275.10		22	7.3	odd	6
441.3.n.f.128.2		22	63.38	even	6
441.3.n.f.410.2		22	7.5	odd	6
441.3.r.f.50.10		22	7.6	odd	2
441.3.r.f.344.10		22	63.20	even	6
441.3.r.g.50.10		22	1.1	even	1	trivial
441.3.r.g.344.10		22	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.79169 - 1.61178i) q^{2} +(2.80334 - 1.06831i) q^{3} +(3.19568 - 5.53509i) q^{4} +(4.79167 + 2.76647i) q^{5} +(6.10417 - 7.50076i) q^{6} -7.70873i q^{8} +(6.71743 - 5.98966i) q^{9} +17.8358 q^{10} +(-15.3189 + 8.84435i) q^{11} +(3.04541 - 18.9307i) q^{12} +(2.03775 - 3.52949i) q^{13} +(16.3881 + 2.63638i) q^{15} +(0.357941 + 0.619972i) q^{16} -16.5523i q^{17} +(9.09895 - 27.5483i) q^{18} +7.84192 q^{19} +(30.6253 - 17.6815i) q^{20} +(-28.5103 + 49.3813i) q^{22} +(-8.71877 - 5.03378i) q^{23} +(-8.23530 - 21.6102i) q^{24} +(2.80674 + 4.86141i) q^{25} -13.1376i q^{26} +(12.4324 - 23.9674i) q^{27} +(-39.9040 + 23.0386i) q^{29} +(49.9998 - 19.0541i) q^{30} +(-14.8117 + 25.6547i) q^{31} +(28.7023 + 16.5713i) q^{32} +(-33.4955 + 41.1590i) q^{33} +(-26.6788 - 46.2090i) q^{34} +(-11.6865 - 56.3227i) q^{36} -31.1896 q^{37} +(21.8922 - 12.6395i) q^{38} +(1.94193 - 12.0713i) q^{39} +(21.3260 - 36.9377i) q^{40} +(27.8184 + 16.0609i) q^{41} +(3.35243 + 5.80658i) q^{43} +113.055i q^{44} +(48.7580 - 10.1169i) q^{45} -32.4535 q^{46} +(14.2377 - 8.22012i) q^{47} +(1.66575 + 1.35560i) q^{48} +(15.6711 + 9.04769i) q^{50} +(-17.6830 - 46.4019i) q^{51} +(-13.0240 - 22.5583i) q^{52} -37.6313i q^{53} +(-3.92265 - 86.9478i) q^{54} -97.8706 q^{55} +(21.9836 - 8.37759i) q^{57} +(-74.2663 + 128.633i) q^{58} +(-82.3206 - 47.5278i) q^{59} +(66.9639 - 82.2847i) q^{60} +(36.8839 + 63.8848i) q^{61} +95.4932i q^{62} +103.974 q^{64} +(19.5285 - 11.2748i) q^{65} +(-27.1696 + 168.890i) q^{66} +(6.09545 - 10.5576i) q^{67} +(-91.6187 - 52.8961i) q^{68} +(-29.8193 - 4.79707i) q^{69} +20.0140i q^{71} +(-46.1727 - 51.7829i) q^{72} +22.9864 q^{73} +(-87.0715 + 50.2708i) q^{74} +(13.0617 + 10.6297i) q^{75} +(25.0603 - 43.4057i) q^{76} +(-14.0351 - 36.8293i) q^{78} +(-69.4400 - 120.274i) q^{79} +3.96094i q^{80} +(9.24784 - 80.4704i) q^{81} +103.547 q^{82} +(13.6928 - 7.90552i) q^{83} +(45.7916 - 79.3134i) q^{85} +(18.7179 + 10.8068i) q^{86} +(-87.2521 + 107.215i) q^{87} +(68.1787 + 118.089i) q^{88} +54.2068i q^{89} +(119.811 - 106.830i) q^{90} +(-55.7249 + 32.1728i) q^{92} +(-14.1152 + 87.7423i) q^{93} +(26.4981 - 45.8960i) q^{94} +(37.5759 + 21.6944i) q^{95} +(98.1657 + 15.7921i) q^{96} +(86.1189 + 149.162i) q^{97} +(-49.9287 + 151.166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 6 q^{2} + 11 q^{3} + 12 q^{4} - 12 q^{5} - 8 q^{6} + 17 q^{9} - 50 q^{10} - 24 q^{11} - 20 q^{12} - 18 q^{13} + 53 q^{15} + 12 q^{16} + 16 q^{18} - 6 q^{19} - 39 q^{20} - 59 q^{22} - 81 q^{23} - 141 q^{24}+ \cdots - 103 q^{99}+O(q^{100}) \) 22 * q + 6 * q^2 + 11 * q^3 + 12 * q^4 - 12 * q^5 - 8 * q^6 + 17 * q^9 - 50 * q^10 - 24 * q^11 - 20 * q^12 - 18 * q^13 + 53 * q^15 + 12 * q^16 + 16 * q^18 - 6 * q^19 - 39 * q^20 - 59 * q^22 - 81 * q^23 - 141 * q^24 + 57 * q^25 - 97 * q^27 - 63 * q^29 + 58 * q^30 - 29 * q^31 - 246 * q^32 - 73 * q^33 - 99 * q^34 + 76 * q^36 + 40 * q^37 + 48 * q^38 - 124 * q^39 - 105 * q^40 - 51 * q^41 + 65 * q^43 + 143 * q^45 - 150 * q^46 - 261 * q^47 - 113 * q^48 + 63 * q^50 - 63 * q^51 - 46 * q^52 + 52 * q^54 - 100 * q^55 + 224 * q^57 + 40 * q^58 + 102 * q^59 + 379 * q^60 + 78 * q^61 + 106 * q^64 + 225 * q^65 + 340 * q^66 - 132 * q^67 - 27 * q^68 - 297 * q^69 + 288 * q^72 - 2 * q^73 - 342 * q^74 + 541 * q^75 + 233 * q^76 - 440 * q^78 + 140 * q^79 + 65 * q^81 + 314 * q^82 + 255 * q^83 + 102 * q^85 - 504 * q^86 - 568 * q^87 + 408 * q^88 + 418 * q^90 - 1239 * q^92 - 174 * q^93 + 261 * q^94 - 642 * q^95 - 142 * q^96 + 178 * q^97 - 103 * q^99

Introduction

L-functions

Modular forms

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