LMFDB - Embedded newform 275.2.z.b.124.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(49,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.z (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 56x^{12} - 141x^{10} + 551x^{8} - 1245x^{6} + 1400x^{4} + 125x^{2} + 625 $ x^16 - 11x^14 + 56x^12 - 141x^10 + 551x^8 - 1245x^6 + 1400x^4 + 125*x^2 + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.3
Root			$-1.39494 + 0.453245i$ of defining polynomial
Character	$\chi$	$=$	275.124
Dual form			275.2.z.b.224.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0549637 + 0.0756511i) q^{2} +(-1.39494 + 0.453245i) q^{3} +(0.615332 - 1.89380i) q^{4} +(-0.110960 - 0.0806171i) q^{6} +(-4.30308 - 1.39815i) q^{7} +(0.354955 - 0.115332i) q^{8} +(-0.686611 + 0.498852i) q^{9} +(-2.39815 + 2.29104i) q^{11} +2.92064i q^{12} +(0.671579 + 0.924349i) q^{13} +(-0.130741 - 0.402380i) q^{14} +(-3.19369 - 2.32035i) q^{16} +(-1.98273 + 2.72899i) q^{17} +(-0.0754774 - 0.0245241i) q^{18} +(-1.88030 - 5.78696i) q^{19} +6.63626 q^{21} +(-0.305131 - 0.0554990i) q^{22} -5.45258i q^{23} +(-0.442869 + 0.321763i) q^{24} +(-0.0330155 + 0.101611i) q^{26} +(3.31805 - 4.56691i) q^{27} +(-5.29564 + 7.28883i) q^{28} +(-1.02619 + 3.15830i) q^{29} +(-1.44887 + 1.05267i) q^{31} -1.11558i q^{32} +(2.30689 - 4.28282i) q^{33} -0.315430 q^{34} +(0.522231 + 1.60726i) q^{36} +(-1.41594 - 0.460067i) q^{37} +(0.334441 - 0.460319i) q^{38} +(-1.35577 - 0.985026i) q^{39} +(-0.539933 - 1.66174i) q^{41} +(0.364754 + 0.502041i) q^{42} -0.263041i q^{43} +(2.86310 + 5.95137i) q^{44} +(0.412494 - 0.299694i) q^{46} +(6.58580 - 2.13986i) q^{47} +(5.50670 + 1.78924i) q^{48} +(10.8985 + 7.91824i) q^{49} +(1.52890 - 4.70546i) q^{51} +(2.16377 - 0.703052i) q^{52} +(0.846269 + 1.16479i) q^{53} +0.527864 q^{54} -1.68865 q^{56} +(5.24582 + 7.22025i) q^{57} +(-0.295332 + 0.0959593i) q^{58} +(2.18416 - 6.72216i) q^{59} +(-2.02452 - 1.47090i) q^{61} +(-0.159271 - 0.0517503i) q^{62} +(3.65201 - 1.18661i) q^{63} +(-6.30297 + 4.57938i) q^{64} +(0.450796 - 0.0608810i) q^{66} +0.516598i q^{67} +(3.94812 + 5.43413i) q^{68} +(2.47136 + 7.60605i) q^{69} +(8.68098 + 6.30710i) q^{71} +(-0.186183 + 0.256258i) q^{72} +(-5.40317 - 1.75560i) q^{73} +(-0.0430208 - 0.132404i) q^{74} -12.1163 q^{76} +(13.5227 - 6.50552i) q^{77} -0.156706i q^{78} +(-9.14460 + 6.64394i) q^{79} +(-1.77179 + 5.45300i) q^{81} +(0.0960360 - 0.132182i) q^{82} +(2.63380 - 3.62511i) q^{83} +(4.08350 - 12.5677i) q^{84} +(0.0198994 - 0.0144577i) q^{86} -4.87077i q^{87} +(-0.587008 + 1.08980i) q^{88} -13.2676 q^{89} +(-1.59747 - 4.91652i) q^{91} +(-10.3261 - 3.35515i) q^{92} +(1.54398 - 2.12511i) q^{93} +(0.523863 + 0.380608i) q^{94} +(0.505633 + 1.55618i) q^{96} +(-1.97293 - 2.71551i) q^{97} +1.25970i q^{98} +(0.503711 - 2.76938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} + 26 q^{6} + 10 q^{9} - 10 q^{11} - 32 q^{14} - 40 q^{16} + 2 q^{19} - 24 q^{21} - 50 q^{24} - 28 q^{26} - 38 q^{29} + 12 q^{31} + 40 q^{34} + 42 q^{36} - 18 q^{39} - 8 q^{41} + 56 q^{44}+ \cdots - 8 q^{99}+O(q^{100}) $ 16 * q + 12 * q^4 + 26 * q^6 + 10 * q^9 - 10 * q^11 - 32 * q^14 - 40 * q^16 + 2 * q^19 - 24 * q^21 - 50 * q^24 - 28 * q^26 - 38 * q^29 + 12 * q^31 + 40 * q^34 + 42 * q^36 - 18 * q^39 - 8 * q^41 + 56 * q^44 - 82 * q^46 + 30 * q^49 + 26 * q^51 + 80 * q^54 + 60 * q^56 + 38 * q^59 - 4 * q^61 - 12 * q^64 + 26 * q^66 + 42 * q^69 + 80 * q^71 - 96 * q^74 + 32 * q^76 - 34 * q^79 + 8 * q^84 - 62 * q^86 - 24 * q^91 - 66 * q^94 + 46 * q^96 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0549637	+	0.0756511i	0.0388652	+	0.0534934i	0.828007	−	0.560717i	$-0.189475\pi$
$2$	0.0549637	+	0.0756511i	0.0388652	+	0.0534934i	−0.789142	+	0.614211i	$0.789475\pi$
$3$	−1.39494	+	0.453245i	−0.805372	+	0.261681i	−0.682636	−	0.730758i	$-0.739167\pi$
$3$	−1.39494	+	0.453245i	−0.805372	+	0.261681i	−0.122735	+	0.992439i	$0.539167\pi$
$4$	0.615332	−	1.89380i	0.307666	−	0.946898i
$5$		0			0
$5$		0			0
$6$	−0.110960	−	0.0806171i	−0.0452992	−	0.0329118i
$7$	−4.30308	−	1.39815i	−1.62641	−	0.528453i	−0.652968	−	0.757385i	$-0.726477\pi$
$7$	−4.30308	−	1.39815i	−1.62641	−	0.528453i	−0.973442	+	0.228932i	$0.926477\pi$
$8$	0.354955	−	0.115332i	0.125496	−	0.0407760i
$9$	−0.686611	+	0.498852i	−0.228870	+	0.166284i
$10$		0			0
$11$	−2.39815	+	2.29104i	−0.723071	+	0.690774i
$11$	−2.39815	+	2.29104i	−0.723071	+	0.690774i
$12$			2.92064i			0.843116i
$13$	0.671579	+	0.924349i	0.186262	+	0.256368i	0.891929	−	0.452176i	$-0.149352\pi$
$13$	0.671579	+	0.924349i	0.186262	+	0.256368i	−0.705666	+	0.708544i	$0.749352\pi$
$14$	−0.130741	−	0.402380i	−0.0349421	−	0.107541i
$15$		0			0
$16$	−3.19369	−	2.32035i	−0.798421	−	0.580087i
$17$	−1.98273	+	2.72899i	−0.480883	+	0.661878i	−0.978674	−	0.205418i	$-0.934144\pi$
$17$	−1.98273	+	2.72899i	−0.480883	+	0.661878i	0.497792	+	0.867297i	$0.334144\pi$
$18$	−0.0754774	−	0.0245241i	−0.0177902	−	0.00578038i
$19$	−1.88030	−	5.78696i	−0.431369	−	1.32762i	−0.896762	−	0.442514i	$-0.854087\pi$
$19$	−1.88030	−	5.78696i	−0.431369	−	1.32762i	0.465392	−	0.885105i	$-0.345913\pi$
$20$		0			0
$21$	6.63626			1.44815
$22$	−0.305131	−	0.0554990i	−0.0650542	−	0.0118324i
$23$		−	5.45258i		−	1.13694i	−0.822703	−	0.568471i	$-0.807535\pi$
$23$		−	5.45258i		−	1.13694i	0.822703	−	0.568471i	$-0.192465\pi$
$24$	−0.442869	+	0.321763i	−0.0904003	+	0.0656797i
$25$		0			0
$26$	−0.0330155	+	0.101611i	−0.00647488	+	0.0199276i
$27$	3.31805	−	4.56691i	0.638559	−	0.878902i
$28$	−5.29564	+	7.28883i	−1.00078	+	1.37746i
$29$	−1.02619	+	3.15830i	−0.190559	+	0.586482i	−1.00000		0.000720503i	$-0.999771\pi$
$29$	−1.02619	+	3.15830i	−0.190559	+	0.586482i	0.809440	+	0.587202i	$0.199771\pi$
$30$		0			0
$31$	−1.44887	+	1.05267i	−0.260225	+	0.189065i	−0.710246	−	0.703953i	$-0.751416\pi$
$31$	−1.44887	+	1.05267i	−0.260225	+	0.189065i	0.450021	+	0.893018i	$0.351416\pi$
$32$		−	1.11558i		−	0.197209i
$33$	2.30689	−	4.28282i	0.401578	−	0.745544i
$34$	−0.315430			−0.0540957
$35$		0			0
$36$	0.522231	+	1.60726i	0.0870385	+	0.267877i
$37$	−1.41594	−	0.460067i	−0.232779	−	0.0756345i	0.190305	−	0.981725i	$-0.439052\pi$
$37$	−1.41594	−	0.460067i	−0.232779	−	0.0756345i	−0.423084	+	0.906091i	$0.639052\pi$
$38$	0.334441	−	0.460319i	0.0542536	−	0.0746736i
$39$	−1.35577	−	0.985026i	−0.217097	−	0.157730i
$40$		0			0
$41$	−0.539933	−	1.66174i	−0.0843234	−	0.259521i	0.900001	−	0.435888i	$-0.143566\pi$
$41$	−0.539933	−	1.66174i	−0.0843234	−	0.259521i	−0.984325	+	0.176367i	$0.943566\pi$
$42$	0.364754	+	0.502041i	0.0562827	+	0.0774665i
$43$		−	0.263041i		−	0.0401134i	−0.999799	−	0.0200567i	$-0.993615\pi$
$43$		−	0.263041i		−	0.0401134i	0.999799	−	0.0200567i	$-0.00638468\pi$
$44$	2.86310	+	5.95137i	0.431628	+	0.897202i
$45$		0			0
$46$	0.412494	−	0.299694i	0.0608189	−	0.0441875i
$47$	6.58580	−	2.13986i	0.960638	−	0.312130i	0.213607	−	0.976920i	$-0.431479\pi$
$47$	6.58580	−	2.13986i	0.960638	−	0.312130i	0.747031	+	0.664790i	$0.231479\pi$
$48$	5.50670	+	1.78924i	0.794824	+	0.258254i
$49$	10.8985	+	7.91824i	1.55693	+	1.13118i
$50$		0			0
$51$	1.52890	−	4.70546i	0.214088	−	0.658896i
$52$	2.16377	−	0.703052i	0.300061	−	0.0974958i
$53$	0.846269	+	1.16479i	0.116244	+	0.159996i	0.863174	−	0.504907i	$-0.168473\pi$
$53$	0.846269	+	1.16479i	0.116244	+	0.159996i	−0.746930	+	0.664903i	$0.768473\pi$
$54$	0.527864			0.0718332
$55$		0			0
$56$	−1.68865			−0.225656
$57$	5.24582	+	7.22025i	0.694826	+	0.956345i
$58$	−0.295332	+	0.0959593i	−0.0387790	+	0.0126001i
$59$	2.18416	−	6.72216i	0.284354	−	0.875150i	−0.702238	−	0.711942i	$-0.747816\pi$
$59$	2.18416	−	6.72216i	0.284354	−	0.875150i	0.986592	−	0.163208i	$-0.0521842\pi$
$60$		0			0
$61$	−2.02452	−	1.47090i	−0.259214	−	0.188330i	0.450587	−	0.892733i	$-0.351215\pi$
$61$	−2.02452	−	1.47090i	−0.259214	−	0.188330i	−0.709800	+	0.704403i	$0.751215\pi$
$62$	−0.159271	−	0.0517503i	−0.0202274	−	0.00657229i
$63$	3.65201	−	1.18661i	0.460110	−	0.149499i
$64$	−6.30297	+	4.57938i	−0.787872	+	0.572422i
$65$		0			0
$66$	0.450796	−	0.0608810i	0.0554891	−	0.00749394i
$67$			0.516598i			0.0631124i	0.999502	+	0.0315562i	$0.0100463\pi$
$67$			0.516598i			0.0631124i	−0.999502	+	0.0315562i	$0.989954\pi$
$68$	3.94812	+	5.43413i	0.478780	+	0.658984i
$69$	2.47136	+	7.60605i	0.297516	+	0.915661i
$70$		0			0
$71$	8.68098	+	6.30710i	1.03024	+	0.748515i	0.968357	−	0.249568i	$-0.0802887\pi$
$71$	8.68098	+	6.30710i	1.03024	+	0.748515i	0.0618853	+	0.998083i	$0.480289\pi$
$72$	−0.186183	+	0.256258i	−0.0219418	+	0.0302003i
$73$	−5.40317	−	1.75560i	−0.632393	−	0.205477i	−0.0247584	−	0.999693i	$-0.507882\pi$
$73$	−5.40317	−	1.75560i	−0.632393	−	0.205477i	−0.607635	+	0.794216i	$0.707882\pi$
$74$	−0.0430208	−	0.132404i	−0.00500106	−	0.0153917i
$75$		0			0
$76$	−12.1163			−1.38984
$77$	13.5227	−	6.50552i	1.54105	−	0.741373i
$78$		−	0.156706i		−	0.0177435i
$79$	−9.14460	+	6.64394i	−1.02885	+	0.747502i	−0.968078	−	0.250650i	$-0.919356\pi$
$79$	−9.14460	+	6.64394i	−1.02885	+	0.747502i	−0.0607700	+	0.998152i	$0.519356\pi$
$80$		0			0
$81$	−1.77179	+	5.45300i	−0.196865	+	0.605888i
$82$	0.0960360	−	0.132182i	0.0106054	−	0.0145971i
$83$	2.63380	−	3.62511i	0.289097	−	0.397907i	−0.639624	−	0.768688i	$-0.720910\pi$
$83$	2.63380	−	3.62511i	0.289097	−	0.397907i	0.928720	+	0.370781i	$0.120910\pi$
$84$	4.08350	−	12.5677i	0.445547	−	1.37125i
$85$		0			0
$86$	0.0198994	−	0.0144577i	0.00214580	−	0.00155902i
$87$		−	4.87077i		−	0.522202i
$88$	−0.587008	+	1.08980i	−0.0625752	+	0.116173i
$89$	−13.2676			−1.40637			−0.703183	−	0.711009i	$-0.748238\pi$
$89$	−13.2676			−1.40637			−0.703183	+	0.711009i	$0.748238\pi$
$90$		0			0
$91$	−1.59747	−	4.91652i	−0.167461	−	0.515391i
$92$	−10.3261	−	3.35515i	−1.07657	−	0.349798i
$93$	1.54398	−	2.12511i	0.160103	−	0.220363i
$94$	0.523863	+	0.380608i	0.0540323	+	0.0392568i
$95$		0			0
$96$	0.505633	+	1.55618i	0.0516060	+	0.158827i
$97$	−1.97293	−	2.71551i	−0.200321	−	0.275718i	0.697024	−	0.717048i	$-0.254507\pi$
$97$	−1.97293	−	2.71551i	−0.200321	−	0.275718i	−0.897345	+	0.441330i	$0.854507\pi$
$98$			1.25970i			0.127249i
$99$	0.503711	−	2.76938i	0.0506248	−	0.278333i
$100$		0			0
$101$	7.55216	−	5.48696i	0.751468	−	0.545973i	−0.144814	−	0.989459i	$-0.546258\pi$
$101$	7.55216	−	5.48696i	0.751468	−	0.545973i	0.896282	+	0.443486i	$0.146258\pi$
$102$	0.440007	−	0.142967i	0.0435672	−	0.0141558i
$103$	−13.2349	−	4.30027i	−1.30407	−	0.423718i	−0.427075	−	0.904216i	$-0.640456\pi$
$103$	−13.2349	−	4.30027i	−1.30407	−	0.423718i	−0.876996	+	0.480498i	$0.840456\pi$
$104$	0.344987	+	0.250648i	0.0338288	+	0.0245781i
$105$		0			0
$106$	−0.0416035	+	0.128042i	−0.00404089	+	0.0124366i
$107$	−15.9666	+	5.18787i	−1.54355	+	0.501531i	−0.952354	−	0.304996i	$-0.901345\pi$
$107$	−15.9666	+	5.18787i	−1.54355	+	0.501531i	−0.591198	+	0.806526i	$0.701345\pi$
$108$	−6.60709	−	9.09388i	−0.635768	−	0.875059i
$109$	3.65293			0.349888			0.174944	−	0.984578i	$-0.444026\pi$
$109$	3.65293			0.349888			0.174944	+	0.984578i	$0.444026\pi$
$110$		0			0
$111$	2.18368			0.207266
$112$	10.4985	+	14.4499i	0.992012	+	1.36539i
$113$	11.3198	−	3.67802i	1.06488	−	0.345999i	0.276386	−	0.961047i	$-0.410863\pi$
$113$	11.3198	−	3.67802i	1.06488	−	0.345999i	0.788490	+	0.615047i	$0.210863\pi$
$114$	−0.257890	+	0.793704i	−0.0241536	+	0.0743372i
$115$		0			0
$116$	5.34973	+	3.88681i	0.496710	+	0.360881i
$117$	−0.922227	−	0.299650i	−0.0852599	−	0.0277026i
$118$	0.628588	−	0.204241i	0.0578662	−	0.0188019i
$119$	12.3474	−	8.97091i	1.13188	−	0.822362i
$120$		0			0
$121$	0.502293	−	10.9885i	0.0456630	−	0.998957i
$122$		−	0.234004i		−	0.0211857i
$123$	1.50635	+	2.07332i	0.135823	+	0.186945i
$124$	1.10200	+	3.39161i	0.0989626	+	0.304576i
$125$		0			0
$126$	0.290497	+	0.211058i	0.0258795	+	0.0188026i
$127$	−11.6162	+	15.9883i	−1.03077	+	1.41873i	−0.126404	+	0.991979i	$0.540344\pi$
$127$	−11.6162	+	15.9883i	−1.03077	+	1.41873i	−0.904367	+	0.426756i	$0.859656\pi$
$128$	−2.81484	−	0.914596i	−0.248799	−	0.0808397i
$129$	0.119222	+	0.366928i	0.0104969	+	0.0323062i
$130$		0			0
$131$	−1.93479			−0.169043			−0.0845215	−	0.996422i	$-0.526936\pi$
$131$	−1.93479			−0.169043			−0.0845215	+	0.996422i	$0.526936\pi$
$132$	−6.69129	−	7.00414i	−0.582402	−	0.609632i
$133$			27.5307i			2.38721i
$134$	−0.0390812	+	0.0283941i	−0.00337610	+	0.00245288i
$135$		0			0
$136$	−0.389040	+	1.19734i	−0.0333599	+	0.102671i
$137$	7.36808	−	10.1413i	0.629498	−	0.866429i	−0.368503	−	0.929626i	$-0.620130\pi$
$137$	7.36808	−	10.1413i	0.629498	−	0.866429i	0.998001	+	0.0631970i	$0.0201296\pi$
$138$	−0.439571	+	0.605018i	−0.0374188	+	0.0515025i
$139$	3.47491	−	10.6947i	0.294738	−	0.907111i	−0.688571	−	0.725169i	$-0.741762\pi$
$139$	3.47491	−	10.6947i	0.294738	−	0.907111i	0.983309	−	0.181942i	$-0.0582383\pi$
$140$		0			0
$141$	−8.21695	+	5.96996i	−0.691992	+	0.502762i
$142$			1.00339i			0.0842024i
$143$	−3.72827	−	0.678120i	−0.311773	−	0.0567072i
$144$	3.35033			0.279194
$145$		0			0
$146$	−0.164166	−	0.505250i	−0.0135864	−	0.0418148i
$147$	−18.7917	−	6.10581i	−1.54992	−	0.503599i
$148$	−1.74255	+	2.39841i	−0.143236	+	0.197148i
$149$	−14.0232	−	10.1885i	−1.14883	−	0.834672i	−0.160503	−	0.987035i	$-0.551312\pi$
$149$	−14.0232	−	10.1885i	−1.14883	−	0.834672i	−0.988325	+	0.152363i	$0.951312\pi$
$150$		0			0
$151$	−0.00166997	−	0.00513965i	−0.000135901	−	0.000418259i	0.950989	−	0.309226i	$-0.100070\pi$
$151$	−0.00166997	−	0.00513965i	−0.000135901	−	0.000418259i	−0.951124	+	0.308808i	$0.900070\pi$
$152$	−1.33484	−	1.83725i	−0.108270	−	0.149021i
$153$		−	2.86285i		−	0.231447i
$154$	1.23541	+	0.665437i	0.0995519	+	0.0536225i
$155$		0			0
$156$	−2.69969	+	1.96144i	−0.216148	+	0.157041i
$157$	0.527682	−	0.171454i	0.0421136	−	0.0136835i	−0.287884	−	0.957665i	$-0.592952\pi$
$157$	0.527682	−	0.171454i	0.0421136	−	0.0136835i	0.329998	+	0.943982i	$0.392952\pi$
$158$	−1.00524	−	0.326623i	−0.0799728	−	0.0259847i
$159$	−1.70843	−	1.24125i	−0.135488	−	0.0984375i
$160$		0			0
$161$	−7.62356	+	23.4629i	−0.600820	+	1.84914i
$162$	−0.509909	+	0.165679i	−0.0400622	+	0.0130170i
$163$	4.68129	+	6.44324i	0.366667	+	0.504673i	0.951991	−	0.306126i	$-0.0990328\pi$
$163$	4.68129	+	6.44324i	0.366667	+	0.504673i	−0.585324	+	0.810799i	$0.699033\pi$
$164$	−3.47924			−0.271683
$165$		0			0
$166$	0.419007			0.0325212
$167$	2.01400	+	2.77204i	0.155848	+	0.214507i	0.879800	−	0.475344i	$-0.157676\pi$
$167$	2.01400	+	2.77204i	0.155848	+	0.214507i	−0.723952	+	0.689850i	$0.757676\pi$
$168$	2.35558	−	0.765373i	0.181737	−	0.0590498i
$169$	3.61382	−	11.1222i	0.277986	−	0.855553i
$170$		0			0
$171$	4.17787	+	3.03540i	0.319489	+	0.232123i
$172$	−0.498147	−	0.161858i	−0.0379834	−	0.0123415i
$173$	−19.5603	+	6.35552i	−1.48714	+	0.483201i	−0.936237	−	0.351368i	$-0.885717\pi$
$173$	−19.5603	+	6.35552i	−1.48714	+	0.483201i	−0.550903	+	0.834569i	$0.685717\pi$
$174$	0.368479	−	0.267716i	0.0279343	−	0.0202955i
$175$		0			0
$176$	12.9750	−	1.75230i	0.978024	−	0.132084i
$177$			10.3670i			0.779231i
$178$	−0.729238	−	1.00371i	−0.0546587	−	0.0752313i
$179$	0.792419	+	2.43882i	0.0592282	+	0.182286i	0.976293	−	0.216452i	$-0.0694484\pi$
$179$	0.792419	+	2.43882i	0.0592282	+	0.182286i	−0.917065	+	0.398738i	$0.869448\pi$
$180$		0			0
$181$	−10.8545	−	7.88624i	−0.806807	−	0.586179i	0.106096	−	0.994356i	$-0.466165\pi$
$181$	−10.8545	−	7.88624i	−0.806807	−	0.586179i	−0.912903	+	0.408177i	$0.866165\pi$
$182$	0.284137	−	0.391081i	0.0210616	−	0.0289888i
$183$	3.49078	+	1.13422i	0.258046	+	0.0838442i
$184$	−0.628857	−	1.93542i	−0.0463599	−	0.142681i
$185$		0			0
$186$	0.245630			0.0180104
$187$	−1.49733	−	11.0871i	−0.109496	−	0.810766i
$188$		−	13.7889i		−	1.00566i
$189$	−20.6631	+	15.0126i	−1.50302	+	1.09201i
$190$		0			0
$191$	5.62097	−	17.2996i	0.406719	−	1.25175i	−0.512733	−	0.858548i	$-0.671367\pi$
$191$	5.62097	−	17.2996i	0.406719	−	1.25175i	0.919452	−	0.393203i	$-0.128633\pi$
$192$	6.71672	−	9.24477i	0.484738	−	0.667184i
$193$	9.22156	−	12.6924i	0.663782	−	0.913618i	−0.335817	−	0.941927i	$-0.609012\pi$
$193$	9.22156	−	12.6924i	0.663782	−	0.913618i	0.999599	+	0.0283094i	$0.00901235\pi$
$194$	0.0969914	−	0.298509i	0.00696358	−	0.0214317i
$195$		0			0
$196$	21.7018	−	15.7672i	1.55013	−	1.12623i
$197$			21.8486i			1.55665i	0.627862	+	0.778325i	$0.283930\pi$
$197$			21.8486i			1.55665i	−0.627862	+	0.778325i	$0.716070\pi$
$198$	0.237192	−	0.114109i	0.0168565	−	0.00810937i
$199$	4.55200			0.322683			0.161341	−	0.986899i	$-0.448418\pi$
$199$	4.55200			0.322683			0.161341	+	0.986899i	$0.448418\pi$
$200$		0			0
$201$	−0.234145	−	0.720625i	−0.0165153	−	0.0508290i
$202$	0.830190	+	0.269745i	0.0584119	+	0.0189792i
$203$	8.83159	−	12.1556i	0.619856	−	0.853158i
$204$	−7.97040	−	5.79084i	−0.558040	−	0.405440i
$205$		0			0
$206$	−0.402118	−	1.23759i	−0.0280169	−	0.0862271i
$207$	2.72003	+	3.74380i	0.189055	+	0.260212i
$208$		−	4.51038i		−	0.312738i
$209$	17.7674	+	9.57019i	1.22900	+	0.661984i
$210$		0			0
$211$	−15.3393	+	11.1447i	−1.05600	+	0.767230i	−0.973345	−	0.229348i	$-0.926341\pi$
$211$	−15.3393	+	11.1447i	−1.05600	+	0.767230i	−0.0826575	+	0.996578i	$0.526341\pi$
$212$	2.72661	−	0.885929i	0.187264	−	0.0608459i
$213$	−14.9681	−	4.86345i	−1.02560	−	0.333238i
$214$	−1.27005	−	0.922748i	−0.0868191	−	0.0630778i
$215$		0			0
$216$	0.651050	−	2.00372i	0.0442983	−	0.136336i
$217$	7.70641	−	2.50396i	0.523145	−	0.169980i
$218$	0.200779	+	0.276348i	0.0135985	+	0.0187167i
$219$	8.33284			0.563081
$220$		0			0
$221$	−3.85410			−0.259255
$222$	0.120023	+	0.165198i	0.00805543	+	0.0110873i
$223$	−4.64070	+	1.50785i	−0.310764	+	0.100973i	−0.460247	−	0.887791i	$-0.652239\pi$
$223$	−4.64070	+	1.50785i	−0.310764	+	0.100973i	0.149483	+	0.988764i	$0.452239\pi$
$224$	−1.55976	+	4.80045i	−0.104216	+	0.320743i
$225$		0			0
$226$	0.900424	+	0.654197i	0.0598953	+	0.0435165i
$227$	−15.5240	−	5.04404i	−1.03036	−	0.334785i	−0.255428	−	0.966828i	$-0.582216\pi$
$227$	−15.5240	−	5.04404i	−1.03036	−	0.334785i	−0.774933	+	0.632043i	$0.782216\pi$
$228$	16.9016	−	5.49166i	1.11934	−	0.363694i
$229$	−3.90890	+	2.83998i	−0.258307	+	0.187671i	−0.709401	−	0.704806i	$-0.751034\pi$
$229$	−3.90890	+	2.83998i	−0.258307	+	0.187671i	0.451093	+	0.892477i	$0.351034\pi$
$230$		0			0
$231$	−15.9148	+	15.2039i	−1.04712	+	1.00035i
$232$			1.23941i			0.0813711i
$233$	4.94900	+	6.81172i	0.324220	+	0.446251i	0.939750	−	0.341863i	$-0.111058\pi$
$233$	4.94900	+	6.81172i	0.324220	+	0.446251i	−0.615530	+	0.788114i	$0.711058\pi$
$234$	−0.0280202	−	0.0862373i	−0.00183174	−	0.00563751i
$235$		0			0
$236$	−11.3864	−	8.27272i	−0.741193	−	0.538508i
$237$	9.74488	−	13.4127i	0.632998	−	0.871247i
$238$	1.35732	+	0.441019i	0.0879819	+	0.0285870i
$239$	7.01245	+	21.5821i	0.453598	+	1.39603i	0.872773	+	0.488126i	$0.162319\pi$
$239$	7.01245	+	21.5821i	0.453598	+	1.39603i	−0.419175	+	0.907905i	$0.637681\pi$
$240$		0			0
$241$	11.6065			0.747638			0.373819	−	0.927502i	$-0.378048\pi$
$241$	11.6065			0.747638			0.373819	+	0.927502i	$0.378048\pi$
$242$	0.858902	−	0.565971i	0.0552123	−	0.0363820i
$243$			8.52534i			0.546901i
$244$	−4.03135	+	2.92894i	−0.258080	+	0.187506i
$245$		0			0
$246$	−0.0740540	+	0.227915i	−0.00472151	+	0.0145313i
$247$	4.08640	−	5.62445i	0.260011	−	0.357875i
$248$	−0.392879	+	0.540751i	−0.0249478	+	0.0343377i
$249$	−2.03094	+	6.25058i	−0.128705	+	0.396114i
$250$		0			0
$251$	−2.68032	+	1.94736i	−0.169180	+	0.122917i	−0.669153	−	0.743124i	$-0.733343\pi$
$251$	−2.68032	+	1.94736i	−0.169180	+	0.122917i	0.499973	+	0.866041i	$0.333343\pi$
$252$		−	7.64633i		−	0.481674i
$253$	12.4921	+	13.0761i	0.785370	+	0.822090i
$254$	−1.84800			−0.115954
$255$		0			0
$256$	4.72952	+	14.5560i	0.295595	+	0.909748i
$257$	25.5326	+	8.29606i	1.59268	+	0.517494i	0.965284	−	0.261204i	$-0.0841197\pi$
$257$	25.5326	+	8.29606i	1.59268	+	0.517494i	0.627399	+	0.778698i	$0.284120\pi$
$258$	−0.0212056	+	0.0291870i	−0.00132020	+	0.00181711i
$259$	5.44965	+	3.95940i	0.338625	+	0.246025i
$260$		0			0
$261$	−0.870929	−	2.68044i	−0.0539091	−	0.165915i
$262$	−0.106343	−	0.146369i	−0.00656990	−	0.00904269i
$263$			12.1682i			0.750324i	0.926959	+	0.375162i	$0.122413\pi$
$263$			12.1682i			0.750324i	−0.926959	+	0.375162i	$0.877587\pi$
$264$	0.324897	−	1.78627i	0.0199960	−	0.109937i
$265$		0			0
$266$	−2.08273	+	1.51319i	−0.127700	+	0.0927795i
$267$	18.5076	−	6.01349i	1.13265	−	0.368019i
$268$	0.978331	+	0.317879i	0.0597611	+	0.0194176i
$269$	−1.69369	−	1.23053i	−0.103266	−	0.0750270i	0.534954	−	0.844881i	$-0.320329\pi$
$269$	−1.69369	−	1.23053i	−0.103266	−	0.0750270i	−0.638220	+	0.769854i	$0.720329\pi$
$270$		0			0
$271$	4.67938	−	14.4017i	0.284252	−	0.874838i	−0.702370	−	0.711812i	$-0.747875\pi$
$271$	4.67938	−	14.4017i	0.284252	−	0.874838i	0.986622	−	0.163026i	$-0.0521254\pi$
$272$	12.6644	−	4.11492i	0.767894	−	0.249504i
$273$	4.45677	+	6.13422i	0.269736	+	0.371260i
$274$	1.17218			0.0708138
$275$		0			0
$276$	15.9250			0.958574
$277$	4.86137	+	6.69110i	0.292091	+	0.402029i	0.929692	−	0.368338i	$-0.120073\pi$
$277$	4.86137	+	6.69110i	0.292091	+	0.402029i	−0.637601	+	0.770367i	$0.720073\pi$
$278$	1.00006	−	0.324939i	0.0599795	−	0.0194885i
$279$	0.469687	−	1.44555i	0.0281194	−	0.0865426i
$280$		0			0
$281$	−1.97985	−	1.43844i	−0.118108	−	0.0858104i	0.527163	−	0.849764i	$-0.323256\pi$
$281$	−1.97985	−	1.43844i	−0.118108	−	0.0858104i	−0.645271	+	0.763954i	$0.723256\pi$
$282$	−0.903268	−	0.293490i	−0.0537888	−	0.0174771i
$283$	−24.8176	+	8.06372i	−1.47525	+	0.479339i	−0.932691	−	0.360677i	$-0.882546\pi$
$283$	−24.8176	+	8.06372i	−1.47525	+	0.479339i	−0.542562	+	0.840016i	$0.682546\pi$
$284$	17.2860	−	12.5590i	1.02574	−	0.745242i
$285$		0			0
$286$	−0.153619	−	0.319320i	−0.00908369	−	0.0188818i
$287$			7.90553i			0.466648i
$288$	0.556512	+	0.765973i	0.0327928	+	0.0451354i
$289$	1.73710	+	5.34624i	0.102182	+	0.314485i
$290$		0			0
$291$	3.98292	+	2.89376i	0.233483	+	0.169635i
$292$	−6.64949	+	9.15223i	−0.389132	+	0.535594i
$293$	12.7945	+	4.15719i	0.747463	+	0.242866i	0.657889	−	0.753115i	$-0.271449\pi$
$293$	12.7945	+	4.15719i	0.747463	+	0.242866i	0.0895739	+	0.995980i	$0.471449\pi$
$294$	−0.570953	−	1.75721i	−0.0332987	−	0.102483i
$295$		0			0
$296$	−0.555655			−0.0322968
$297$	2.50575	+	18.5539i	0.145399	+	1.07661i
$298$		−	1.62087i		−	0.0938944i
$299$	5.04009	−	3.66184i	0.291476	−	0.211770i
$300$		0			0
$301$	−0.367773	+	1.13189i	−0.0211981	+	0.0652409i
$302$	0.000297032	0	0.000408830i	1.70923e−5	0	2.35255e-5i
$303$	−8.04791	+	11.0770i	−0.462340	+	0.636357i
$304$	−7.42268	+	22.8447i	−0.425720	+	1.31023i
$305$		0			0
$306$	0.216577	−	0.157353i	0.0123809	−	0.00899526i
$307$		−	27.1844i		−	1.55150i	−0.631042	−	0.775748i	$-0.717373\pi$
$307$		−	27.1844i		−	1.55150i	0.631042	−	0.775748i	$-0.282627\pi$
$308$	−3.99921	−	29.6123i	−0.227876	−	1.68731i
$309$	20.4110			1.16114
$310$		0			0
$311$	−4.07872	−	12.5530i	−0.231283	−	0.711817i	−0.997593	−	0.0693450i	$-0.977909\pi$
$311$	−4.07872	−	12.5530i	−0.231283	−	0.711817i	0.766310	−	0.642472i	$-0.222091\pi$
$312$	−0.594843	−	0.193276i	−0.0336764	−	0.0109421i
$313$	9.50561	−	13.0833i	0.537289	−	0.739515i	−0.450931	−	0.892559i	$-0.648908\pi$
$313$	9.50561	−	13.0833i	0.537289	−	0.739515i	0.988219	+	0.153044i	$0.0489078\pi$
$314$	0.0419741	+	0.0304959i	0.00236873	+	0.00172099i
$315$		0			0
$316$	6.95531	+	21.4062i	0.391267	+	1.20420i
$317$	−3.16296	−	4.35344i	−0.177650	−	0.244514i	0.710901	−	0.703292i	$-0.248287\pi$
$317$	−3.16296	−	4.35344i	−0.177650	−	0.244514i	−0.888551	+	0.458778i	$0.848287\pi$
$318$		−	0.197469i		−	0.0110735i
$319$	−4.77481	−	9.92514i	−0.267338	−	0.555701i
$320$		0			0
$321$	19.9212	−	14.4736i	1.11189	−	0.807837i
$322$	−2.19401	+	0.712878i	−0.122268	+	0.0397271i
$323$	19.5207	+	6.34266i	1.08616	+	0.352915i
$324$	9.23663	+	6.71080i	0.513146	+	0.372822i
$325$		0			0
$326$	−0.230137	+	0.708289i	−0.0127461	+	0.0392285i
$327$	−5.09564	+	1.65567i	−0.281790	+	0.0915590i
$328$	−0.383304	−	0.527573i	−0.0211644	−	0.0291304i
$329$	−31.3311			−1.72734
$330$		0			0
$331$	−18.5702			−1.02071			−0.510356	−	0.859963i	$-0.670486\pi$
$331$	−18.5702			−1.02071			−0.510356	+	0.859963i	$0.670486\pi$
$332$	−5.24456	−	7.21852i	−0.287833	−	0.396168i
$333$	1.20170	−	0.390457i	0.0658530	−	0.0213969i
$334$	−0.0990106	+	0.304723i	−0.00541762	+	0.0166737i
$335$		0			0
$336$	−21.1941	−	15.3984i	−1.15623	−	0.840054i
$337$	−8.56535	−	2.78305i	−0.466585	−	0.151603i	0.0662836	−	0.997801i	$-0.478886\pi$
$337$	−8.56535	−	2.78305i	−0.466585	−	0.151603i	−0.532868	+	0.846198i	$0.678886\pi$
$338$	1.04003	−	0.337928i	0.0565704	−	0.0183808i
$339$	−14.1234	+	10.2613i	−0.767080	+	0.557316i
$340$		0			0
$341$	1.06292	−	5.84388i	0.0575604	−	0.316464i
$342$			0.482897i			0.0261121i
$343$	−17.2101	−	23.6877i	−0.929260	−	1.27902i
$344$	−0.0303371	−	0.0933679i	−0.00163567	−	0.00503406i
$345$		0			0
$346$	−1.55591	−	1.13043i	−0.0836461	−	0.0607725i
$347$	−6.03712	+	8.30939i	−0.324090	+	0.446071i	−0.939710	−	0.341971i	$-0.888905\pi$
$347$	−6.03712	+	8.30939i	−0.324090	+	0.446071i	0.615621	+	0.788043i	$0.288905\pi$
$348$	−9.22425	−	2.99714i	−0.494472	−	0.160664i
$349$	−5.33402	−	16.4164i	−0.285524	−	0.878752i	−0.986241	−	0.165313i	$-0.947137\pi$
$349$	−5.33402	−	16.4164i	−0.285524	−	0.878752i	0.700718	−	0.713439i	$-0.252863\pi$
$350$		0			0
$351$	6.44975			0.344262
$352$	2.55585	+	2.67534i	0.136227	+	0.142596i
$353$		−	22.8096i		−	1.21403i	−0.794689	−	0.607017i	$-0.792366\pi$
$353$		−	22.8096i		−	1.21403i	0.794689	−	0.607017i	$-0.207634\pi$
$354$	−0.784275	+	0.569809i	−0.0416837	+	0.0302850i
$355$		0			0
$356$	−8.16399	+	25.1262i	−0.432691	+	1.33169i
$357$	−13.1579	+	18.1103i	−0.696391	+	0.958500i
$358$	−0.140945	+	0.193994i	−0.00744916	+	0.0102529i
$359$	4.96736	−	15.2879i	0.262167	−	0.806867i	−0.730166	−	0.683270i	$-0.760557\pi$
$359$	4.96736	−	15.2879i	0.262167	−	0.806867i	0.992333	−	0.123597i	$-0.0394429\pi$
$360$		0			0
$361$	−14.5820	+	10.5945i	−0.767475	+	0.557603i
$362$		−	1.25461i		−	0.0659408i
$363$	4.27982	+	15.5560i	0.224632	+	0.816481i
$364$	−10.2939			−0.539545
$365$		0			0
$366$	0.106061	+	0.326422i	0.00554390	+	0.0170624i
$367$	−20.9208	−	6.79759i	−1.09206	−	0.354832i	−0.293017	−	0.956107i	$-0.594659\pi$
$367$	−20.9208	−	6.79759i	−1.09206	−	0.354832i	−0.799042	+	0.601276i	$0.794659\pi$
$368$	−12.6519	+	17.4138i	−0.659525	+	0.907759i
$369$	1.19969	+	0.871625i	0.0624533	+	0.0453750i
$370$		0			0
$371$	−2.01301	−	6.19539i	−0.104510	−	0.321649i
$372$	−3.07446	−	4.23163i	−0.159403	−	0.219400i
$373$		−	20.2604i		−	1.04905i	−0.851396	−	0.524523i	$-0.824244\pi$
$373$		−	20.2604i		−	1.04905i	0.851396	−	0.524523i	$-0.175756\pi$
$374$	0.756449	−	0.722661i	0.0391151	−	0.0373679i
$375$		0			0
$376$	2.09087	−	1.51911i	0.107828	−	0.0783419i
$377$	−3.60854	+	1.17249i	−0.185849	+	0.0603861i
$378$	−2.27144	−	0.738036i	−0.116830	−	0.0379605i
$379$	−3.01578	−	2.19109i	−0.154910	−	0.112549i	0.507630	−	0.861575i	$-0.330522\pi$
$379$	−3.01578	−	2.19109i	−0.154910	−	0.112549i	−0.662540	+	0.749026i	$0.730522\pi$
$380$		0			0
$381$	8.95733	−	27.5678i	0.458898	−	1.41234i
$382$	1.61768	−	0.525616i	0.0827677	−	0.0268928i
$383$	6.46411	+	8.89708i	0.330301	+	0.454620i	0.941577	−	0.336797i	$-0.109344\pi$
$383$	6.46411	+	8.89708i	0.330301	+	0.454620i	−0.611277	+	0.791417i	$0.709344\pi$
$384$	4.34108			0.221530
$385$		0			0
$386$	1.46704			0.0746706
$387$	0.131219	+	0.180607i	0.00667023	+	0.00918078i
$388$	−6.35663	+	2.06539i	−0.322709	+	0.104854i
$389$	−2.89926	+	8.92300i	−0.146998	+	0.452414i	−0.997263	−	0.0739418i	$-0.976442\pi$
$389$	−2.89926	+	8.92300i	−0.146998	+	0.452414i	0.850264	+	0.526356i	$0.176442\pi$
$390$		0			0
$391$	14.8801	+	10.8110i	0.752517	+	0.546736i
$392$	4.78171	+	1.55367i	0.241513	+	0.0784723i
$393$	2.69892	−	0.876932i	0.136143	−	0.0442354i
$394$	−1.65287	+	1.20088i	−0.0832705	+	0.0604996i
$395$		0			0
$396$	−4.93469	−	2.65801i	−0.247977	−	0.133570i
$397$		−	22.3136i		−	1.11989i	−0.828530	−	0.559945i	$-0.810822\pi$
$397$		−	22.3136i		−	1.11989i	0.828530	−	0.559945i	$-0.189178\pi$
$398$	0.250195	+	0.344364i	0.0125411	+	0.0172614i
$399$	−12.4781	−	38.4038i	−0.624688	−	1.92259i
$400$		0			0
$401$	19.9683	+	14.5078i	0.997171	+	0.724487i	0.961480	−	0.274876i	$-0.0886368\pi$
$401$	19.9683	+	14.5078i	0.997171	+	0.724487i	0.0356909	+	0.999363i	$0.488637\pi$
$402$	0.0416466	−	0.0573216i	0.00207714	−	0.00285894i
$403$	−1.94606	−	0.632315i	−0.0969404	−	0.0314978i
$404$	−5.74411	−	17.6786i	−0.285780	−	0.879541i
$405$		0			0
$406$	1.40500			0.0697292
$407$	4.44967	−	2.14066i	0.220562	−	0.106109i
$408$		−	1.84656i		−	0.0914182i
$409$	23.8705	−	17.3429i	1.18032	−	0.857553i	0.188113	−	0.982147i	$-0.439763\pi$
$409$	23.8705	−	17.3429i	1.18032	−	0.857553i	0.992208	+	0.124594i	$0.0397630\pi$
$410$		0			0
$411$	−5.68158	+	17.4861i	−0.280252	+	0.862526i
$412$	−16.2877	+	22.4181i	−0.802437	+	1.10446i
$413$	−18.7972	+	25.8722i	−0.924951	+	1.27309i
$414$	−0.133720	+	0.411547i	−0.00657196	+	0.0202264i
$415$		0			0
$416$	1.03119	−	0.749203i	0.0505582	−	0.0367327i
$417$			16.4935i			0.807689i
$418$	0.252566	+	1.87013i	0.0123534	+	0.0914713i
$419$	−9.03564			−0.441420			−0.220710	−	0.975339i	$-0.570837\pi$
$419$	−9.03564			−0.441420			−0.220710	+	0.975339i	$0.570837\pi$
$420$		0			0
$421$	4.39426	+	13.5242i	0.214163	+	0.659127i	0.999212	+	0.0396928i	$0.0126379\pi$
$421$	4.39426	+	13.5242i	0.214163	+	0.659127i	−0.785049	+	0.619434i	$0.787362\pi$
$422$	−1.68621	−	0.547884i	−0.0820835	−	0.0266706i
$423$	−3.45441	+	4.75459i	−0.167959	+	0.231176i
$424$	0.434725	+	0.315846i	0.0211121	+	0.0153388i
$425$		0			0
$426$	−0.454780	−	1.39967i	−0.0220342	−	0.0678142i
$427$	6.65514	+	9.16001i	0.322065	+	0.443284i
$428$			33.4298i			1.61589i
$429$	5.50808	−	0.743880i	0.265933	−	0.0359149i
$430$		0			0
$431$	1.40086	−	1.01778i	0.0674769	−	0.0490248i	−0.553535	−	0.832826i	$-0.686722\pi$
$431$	1.40086	−	1.01778i	0.0674769	−	0.0490248i	0.621012	+	0.783801i	$0.286722\pi$
$432$	−21.1936	+	6.88623i	−1.01968	+	0.331314i
$433$	17.5447	+	5.70062i	0.843145	+	0.273955i	0.698572	−	0.715540i	$-0.253819\pi$
$433$	17.5447	+	5.70062i	0.843145	+	0.273955i	0.144573	+	0.989494i	$0.453819\pi$
$434$	0.613000	+	0.445371i	0.0294250	+	0.0213785i
$435$		0			0
$436$	2.24777	−	6.91791i	0.107649	−	0.331308i
$437$	−31.5539	+	10.2525i	−1.50943	+	0.490442i
$438$	0.458004	+	0.630389i	0.0218843	+	0.0301211i
$439$	17.1704			0.819499			0.409750	−	0.912198i	$-0.365616\pi$
$439$	17.1704			0.819499			0.409750	+	0.912198i	$0.365616\pi$
$440$		0			0
$441$	−11.4331			−0.544432
$442$	−0.211836	−	0.291567i	−0.0100760	−	0.0138684i
$443$	−34.8079	+	11.3098i	−1.65377	+	0.537344i	−0.979553	−	0.201185i	$-0.935521\pi$
$443$	−34.8079	+	11.3098i	−1.65377	+	0.537344i	−0.674221	+	0.738529i	$0.735521\pi$
$444$	1.34369	−	4.13545i	0.0637686	−	0.196260i
$445$		0			0
$446$	−0.369141	−	0.268196i	−0.0174793	−	0.0126995i
$447$	24.1795	+	7.85640i	1.14365	+	0.371595i
$448$	33.5249	−	10.8929i	1.58390	−	0.514641i
$449$	−13.4320	+	9.75895i	−0.633897	+	0.460553i	−0.857748	−	0.514070i	$-0.828137\pi$
$449$	−13.4320	+	9.75895i	−0.633897	+	0.460553i	0.223851	+	0.974623i	$0.428137\pi$
$450$		0			0
$451$	5.10196	+	2.74811i	0.240242	+	0.129404i
$452$		−	23.7006i		−	1.11478i
$453$	0.00465904	+	0.00641262i	0.000218901	+	0.000301291i
$454$	−0.471667	−	1.45164i	−0.0221365	−	0.0681290i
$455$		0			0
$456$	2.69476	+	1.95785i	0.126193	+	0.0916849i
$457$	18.6124	−	25.6178i	0.870651	−	1.19835i	−0.108272	−	0.994121i	$-0.534532\pi$
$457$	18.6124	−	25.6178i	0.870651	−	1.19835i	0.978923	−	0.204227i	$-0.0654682\pi$
$458$	−0.429696	−	0.139617i	−0.0200784	−	0.00652385i
$459$	5.88426	+	18.1099i	0.274654	+	0.845297i
$460$		0			0
$461$	−25.4351			−1.18463			−0.592315	−	0.805706i	$-0.701786\pi$
$461$	−25.4351			−1.18463			−0.592315	+	0.805706i	$0.701786\pi$
$462$	−2.02493	−	0.368306i	−0.0942083	−	0.0171352i
$463$		−	16.3319i		−	0.759007i	−0.925190	−	0.379503i	$-0.876095\pi$
$463$		−	16.3319i		−	0.759007i	0.925190	−	0.379503i	$-0.123905\pi$
$464$	10.6057	−	7.70549i	0.492357	−	0.357718i
$465$		0			0
$466$	−0.243298	+	0.748795i	−0.0112706	+	0.0346873i
$467$	−5.01329	+	6.90020i	−0.231987	+	0.319303i	−0.909101	−	0.416575i	$-0.863230\pi$
$467$	−5.01329	+	6.90020i	−0.231987	+	0.319303i	0.677114	+	0.735878i	$0.263230\pi$
$468$	−1.13495	+	1.56213i	−0.0524631	+	0.0722093i
$469$	0.722284	−	2.22296i	0.0333520	−	0.102647i
$470$		0			0
$471$	−0.658376	+	0.478338i	−0.0303364	+	0.0220407i
$472$		−	2.63797i		−	0.121422i
$473$	0.602638	+	0.630814i	0.0277093	+	0.0290049i
$474$	1.55030			0.0712076
$475$		0			0
$476$	−9.39133	−	28.9036i	−0.430451	−	1.32479i
$477$	−1.16211	−	0.377594i	−0.0532096	−	0.0172888i
$478$	−1.24728	+	1.71673i	−0.0570493	+	0.0785216i
$479$	24.2283	+	17.6029i	1.10702	+	0.804296i	0.982192	−	0.187882i	$-0.0601623\pi$
$479$	24.2283	+	17.6029i	1.10702	+	0.804296i	0.124827	+	0.992178i	$0.460162\pi$
$480$		0			0
$481$	−0.525653	−	1.61779i	−0.0239677	−	0.0737650i
$482$	0.637934	+	0.878041i	0.0290571	+	0.0399937i
$483$		−	36.1848i		−	1.64646i
$484$	−20.5010	−	7.71283i	−0.931862	−	0.350583i
$485$		0			0
$486$	−0.644951	+	0.468585i	−0.0292556	+	0.0212554i
$487$	−18.6436	+	6.05768i	−0.844823	+	0.274500i	−0.699276	−	0.714852i	$-0.746494\pi$
$487$	−18.6436	+	6.05768i	−0.844823	+	0.274500i	−0.145547	+	0.989351i	$0.546494\pi$
$488$	−0.888257	−	0.288612i	−0.0402095	−	0.0130649i
$489$	−9.45050	−	6.86619i	−0.427367	−	0.310500i
$490$		0			0
$491$	−4.87911	+	15.0163i	−0.220191	+	0.677678i	0.778553	+	0.627579i	$0.215954\pi$
$491$	−4.87911	+	15.0163i	−0.220191	+	0.677678i	−0.998744	+	0.0500997i	$0.984046\pi$
$492$	4.85335	−	1.57695i	0.218806	−	0.0710944i
$493$	−6.58432	−	9.06253i	−0.296543	−	0.408156i
$494$	0.650099			0.0292494
$495$		0			0
$496$	7.06980			0.317443
$497$	−28.5366	−	39.2773i	−1.28004	−	1.76183i
$498$	−0.584491	+	0.189913i	−0.0261917	+	0.00851019i
$499$	−3.46350	+	10.6596i	−0.155048	+	0.477188i	−0.998166	−	0.0605408i	$-0.980717\pi$
$499$	−3.46350	+	10.6596i	−0.155048	+	0.477188i	0.843118	+	0.537729i	$0.180717\pi$
$500$		0			0
$501$	−4.06584	−	2.95400i	−0.181648	−	0.131975i
$502$	−0.294640	−	0.0957345i	−0.0131504	−	0.00427284i
$503$	0.326125	−	0.105965i	0.0145412	−	0.00472473i	−0.301737	−	0.953391i	$-0.597567\pi$
$503$	0.326125	−	0.105965i	0.0145412	−	0.00472473i	0.316279	+	0.948666i	$0.397567\pi$
$504$	1.15945	−	0.842387i	0.0516459	−	0.0375229i
$505$		0			0
$506$	−0.302613	+	1.66375i	−0.0134528	+	0.0739628i
$507$			17.1528i			0.761782i
$508$	23.1308	+	31.8368i	1.02626	+	1.41253i
$509$	6.04518	+	18.6052i	0.267948	+	0.824659i	0.991000	+	0.133865i	$0.0427389\pi$
$509$	6.04518	+	18.6052i	0.267948	+	0.824659i	−0.723052	+	0.690794i	$0.757261\pi$
$510$		0			0
$511$	20.7957	+	15.1089i	0.919946	+	0.668380i
$512$	−4.32055	+	5.94673i	−0.190943	+	0.262811i
$513$	−32.6674	−	10.6143i	−1.44230	−	0.468632i
$514$	0.775763	+	2.38755i	0.0342175	+	0.105311i
$515$		0			0
$516$	0.768249			0.0338203
$517$	−10.8913	+	20.2200i	−0.478998	+	0.889275i
$518$			0.629896i			0.0276760i
$519$	24.4049	−	17.7312i	1.07126	−	0.778313i
$520$		0			0
$521$	12.9869	−	39.9695i	0.568966	−	1.75110i	−0.0868981	−	0.996217i	$-0.527695\pi$
$521$	12.9869	−	39.9695i	0.568966	−	1.75110i	0.655864	−	0.754879i	$-0.272305\pi$
$522$	0.154909	−	0.213214i	0.00678018	−	0.00933212i
$523$	17.6398	−	24.2790i	0.771333	−	1.06165i	−0.224853	−	0.974393i	$-0.572190\pi$
$523$	17.6398	−	24.2790i	0.771333	−	1.06165i	0.996186	−	0.0872555i	$-0.0278097\pi$
$524$	−1.19054	+	3.66409i	−0.0520088	+	0.160067i
$525$		0			0
$526$	−0.920538	+	0.668810i	−0.0401374	+	0.0291615i
$527$		−	6.04112i		−	0.263155i
$528$	−17.3051	+	8.32519i	−0.753109	+	0.362308i
$529$	−6.73067			−0.292638
$530$		0			0
$531$	1.85369	+	5.70508i	0.0804434	+	0.247579i
$532$	52.1375	+	16.9405i	2.26045	+	0.734464i
$533$	1.17342	−	1.61508i	0.0508266	−	0.0699568i
$534$	1.47217	+	1.06960i	0.0637072	+	0.0462860i
$535$		0			0
$536$	0.0595802	+	0.183369i	0.00257347	+	0.00792033i
$537$	−2.21076	−	3.04285i	−0.0954014	−	0.131309i
$538$		−	0.195764i		−	0.00843998i
$539$	−44.2773	+	5.97976i	−1.90716	+	0.257567i
$540$		0			0
$541$	8.35196	−	6.06806i	0.359079	−	0.260886i	−0.393589	−	0.919287i	$-0.628767\pi$
$541$	8.35196	−	6.06806i	0.359079	−	0.260886i	0.752668	+	0.658400i	$0.228767\pi$
$542$	1.34670	−	0.437568i	0.0578456	−	0.0187952i
$543$	18.7158	+	6.08113i	0.803171	+	0.260966i
$544$	3.04442	+	2.21190i	0.130529	+	0.0948346i
$545$		0			0
$546$	−0.219100	+	0.674320i	−0.00937660	+	0.0288582i
$547$	39.7702	−	12.9221i	1.70045	−	0.552510i	0.711752	−	0.702431i	$-0.247902\pi$
$547$	39.7702	−	12.9221i	1.70045	−	0.552510i	0.988698	+	0.149921i	$0.0479020\pi$
$548$	−14.6717	−	20.1939i	−0.626746	−	0.862641i
$549$	2.12382			0.0906426
$550$		0			0
$551$	20.2065			0.860826
$552$	1.75444	+	2.41478i	0.0746740	+	0.102780i
$553$	48.6392	−	15.8038i	2.06835	−	0.672047i
$554$	−0.238990	+	0.735536i	−0.0101537	+	0.0312499i
$555$		0			0
$556$	−18.1153	−	13.1616i	−0.768261	−	0.558174i
$557$	36.5993	+	11.8918i	1.55076	+	0.503874i	0.954321	−	0.298782i	$-0.0965804\pi$
$557$	36.5993	+	11.8918i	1.55076	+	0.503874i	0.596442	+	0.802656i	$0.296580\pi$
$558$	0.135173	−	0.0439203i	0.00572233	−	0.00185930i
$559$	0.243142	−	0.176653i	0.0102838	−	0.00747163i
$560$		0			0
$561$	7.11385	+	14.7872i	0.300347	+	0.624315i
$562$		−	0.228840i		−	0.00965303i
$563$	−18.0370	−	24.8258i	−0.760170	−	1.04628i	−0.997200	−	0.0747817i	$-0.976174\pi$
$563$	−18.0370	−	24.8258i	−0.760170	−	1.04628i	0.237030	−	0.971502i	$-0.423826\pi$
$564$	6.24975	+	19.2347i	0.263162	+	0.809929i
$565$		0			0
$566$	−1.97410	−	1.43427i	−0.0829775	−	0.0602867i
$567$	15.2483	−	20.9874i	0.640367	−	0.881389i
$568$	3.80877	+	1.23754i	0.159812	+	0.0519262i
$569$	−4.03220	−	12.4098i	−0.169039	−	0.520247i	0.830273	−	0.557357i	$-0.188185\pi$
$569$	−4.03220	−	12.4098i	−0.169039	−	0.520247i	−0.999311	+	0.0371104i	$0.988185\pi$
$570$		0			0
$571$	16.1300			0.675018			0.337509	−	0.941322i	$-0.390416\pi$
$571$	16.1300			0.675018			0.337509	+	0.941322i	$0.390416\pi$
$572$	−3.57834	+	6.64331i	−0.149618	+	0.277771i
$573$			26.6796i			1.11456i
$574$	−0.598062	+	0.434517i	−0.0249626	+	0.0181364i
$575$		0			0
$576$	2.04326	−	6.28850i	0.0851358	−	0.262021i
$577$	8.56487	−	11.7885i	0.356560	−	0.490763i	−0.592626	−	0.805478i	$-0.701909\pi$
$577$	8.56487	−	11.7885i	0.356560	−	0.490763i	0.949186	+	0.314715i	$0.101909\pi$
$578$	−0.308972	+	0.425263i	−0.0128515	+	0.0176886i
$579$	−7.11080	+	21.8848i	−0.295515	+	0.909501i
$580$		0			0
$581$	−16.4019	+	11.9167i	−0.680465	+	0.494387i
$582$			0.460364i			0.0190827i
$583$	−4.69806	−	0.854511i	−0.194574	−	0.0353902i
$584$	−2.12036			−0.0877411
$585$		0			0
$586$	0.388738	+	1.19641i	0.0160586	+	0.0494234i
$587$	26.5099	+	8.61360i	1.09418	+	0.355521i	0.799861	−	0.600185i	$-0.204906\pi$
$587$	26.5099	+	8.61360i	1.09418	+	0.355521i	0.294321	+	0.955707i	$0.404906\pi$
$588$	−23.1263	+	31.8307i	−0.953713	+	1.31267i
$589$	8.81605	+	6.40524i	0.363259	+	0.263923i
$590$		0			0
$591$	−9.90278	−	30.4776i	−0.407346	−	1.25368i
$592$	3.45455	+	4.75478i	0.141981	+	0.195420i
$593$			15.1037i			0.620236i	0.950698	+	0.310118i	$0.100369\pi$
$593$			15.1037i			0.620236i	−0.950698	+	0.310118i	$0.899631\pi$
$594$	−1.26590	+	1.20936i	−0.0519405	+	0.0496205i
$595$		0			0
$596$	−27.9238	+	20.2878i	−1.14380	+	0.831023i
$597$	−6.34979	+	2.06317i	−0.259880	+	0.0844400i
$598$	0.554044	+	0.180020i	0.0226566	+	0.00736156i
$599$	−20.9339	−	15.2093i	−0.855334	−	0.621437i	0.0712774	−	0.997457i	$-0.477292\pi$
$599$	−20.9339	−	15.2093i	−0.855334	−	0.621437i	−0.926612	+	0.376020i	$0.877292\pi$
$600$		0			0
$601$	−14.5321	+	44.7252i	−0.592776	+	1.82438i	−0.0272781	+	0.999628i	$0.508684\pi$
$601$	−14.5321	+	44.7252i	−0.592776	+	1.82438i	−0.565498	+	0.824750i	$0.691316\pi$
$602$	−0.105843	+	0.0343904i	−0.00431383	+	0.00140165i
$603$	−0.257706	−	0.354702i	−0.0104946	−	0.0144446i
$604$	−0.0107610			−0.000437861
$605$		0			0
$606$	−1.28033			−0.0520098
$607$	−20.7041	−	28.4967i	−0.840353	−	1.15665i	−0.985907	−	0.167297i	$-0.946496\pi$
$607$	−20.7041	−	28.4967i	−0.840353	−	1.15665i	0.145553	−	0.989350i	$-0.453504\pi$
$608$	−6.45584	+	2.09763i	−0.261819	+	0.0850701i
$609$	−6.81009	+	20.9593i	−0.275959	+	0.849314i
$610$		0			0
$611$	6.40086	+	4.65049i	0.258951	+	0.188139i
$612$	−5.42165	−	1.76160i	−0.219157	−	0.0712085i
$613$	22.2658	−	7.23461i	0.899309	−	0.292203i	0.177357	−	0.984147i	$-0.443245\pi$
$613$	22.2658	−	7.23461i	0.899309	−	0.292203i	0.721952	+	0.691943i	$0.243245\pi$
$614$	2.05653	−	1.49416i	0.0829948	−	0.0602993i
$615$		0			0
$616$	4.04965	−	3.86876i	0.163165	−	0.155877i
$617$		−	22.8910i		−	0.921557i	−0.887515	−	0.460778i	$-0.847570\pi$
$617$		−	22.8910i		−	0.921557i	0.887515	−	0.460778i	$-0.152430\pi$
$618$	1.12187	+	1.54411i	0.0451280	+	0.0621134i
$619$	−0.657441	−	2.02339i	−0.0264248	−	0.0813271i	0.936974	−	0.349398i	$-0.113614\pi$
$619$	−0.657441	−	2.02339i	−0.0264248	−	0.0813271i	−0.963399	+	0.268071i	$0.913614\pi$
$620$		0			0
$621$	−24.9014	−	18.0920i	−0.999260	−	0.726005i
$622$	0.725468	−	0.998521i	0.0290886	−	0.0400370i
$623$	57.0916	+	18.5502i	2.28733	+	0.743198i
$624$	2.04431	+	6.29173i	0.0818377	+	0.251871i
$625$		0			0
$626$	1.51223			0.0604410
$627$	−29.1221	−	5.29691i	−1.16303	−	0.211538i
$628$		−	1.10482i		−	0.0440873i
$629$	4.06294	−	2.95190i	0.162000	−	0.117700i
$630$		0			0
$631$	4.77702	−	14.7022i	0.190170	−	0.585284i	−0.809829	−	0.586666i	$-0.800440\pi$
$631$	4.77702	−	14.7022i	0.190170	−	0.585284i	0.999999	+	0.00138227i	$0.000439991\pi$
$632$	−2.47966	+	3.41296i	−0.0986357	+	0.135760i
$633$	16.3462	−	22.4987i	0.649705	−	0.894242i
$634$	0.155494	−	0.478563i	0.00617547	−	0.0190062i
$635$		0			0
$636$	−3.40193	+	2.47164i	−0.134895	+	0.0980071i
$637$			15.3918i			0.609844i
$638$	0.488406	−	0.906743i	0.0193362	−	0.0358983i
$639$	−9.10676			−0.360258
$640$		0			0
$641$	4.38201	+	13.4864i	0.173079	+	0.532682i	0.999541	−	0.0303108i	$-0.00964970\pi$
$641$	4.38201	+	13.4864i	0.173079	+	0.532682i	−0.826461	+	0.562993i	$0.809650\pi$
$642$	2.18989	+	0.711537i	0.0864279	+	0.0280821i
$643$	−7.28504	+	10.0270i	−0.287294	+	0.395426i	−0.928133	−	0.372249i	$-0.878587\pi$
$643$	−7.28504	+	10.0270i	−0.287294	+	0.395426i	0.640839	+	0.767675i	$0.278587\pi$
$644$	39.7429	+	28.8749i	1.56609	+	1.13783i
$645$		0			0
$646$	0.593101	+	1.82538i	0.0233352	+	0.0718185i
$647$	19.5418	+	26.8970i	0.768267	+	1.05743i	0.996481	+	0.0838181i	$0.0267115\pi$
$647$	19.5418	+	26.8970i	0.768267	+	1.05743i	−0.228214	+	0.973611i	$0.573289\pi$
$648$			2.13991i			0.0840637i
$649$	10.1628	+	21.1248i	0.398923	+	0.829220i
$650$		0			0
$651$	−9.61510	+	6.98578i	−0.376846	+	0.273794i
$652$	15.0827	−	4.90068i	0.590685	−	0.191925i
$653$	−33.1030	−	10.7558i	−1.29542	−	0.420908i	−0.421435	−	0.906858i	$-0.638474\pi$
$653$	−33.1030	−	10.7558i	−1.29542	−	0.420908i	−0.873986	+	0.485951i	$0.838474\pi$
$654$	−0.405329	−	0.294489i	−0.0158496	−	0.0115154i
$655$		0			0
$656$	−2.13145	+	6.55992i	−0.0832191	+	0.256122i
$657$	4.58566	−	1.48997i	0.178904	−	0.0581293i
$658$	−1.72207	−	2.37023i	−0.0671334	−	0.0924011i
$659$	34.4953			1.34375			0.671873	−	0.740666i	$-0.265490\pi$
$659$	34.4953			1.34375			0.671873	+	0.740666i	$0.265490\pi$
$660$		0			0
$661$	1.77827			0.0691668			0.0345834	−	0.999402i	$-0.488990\pi$
$661$	1.77827			0.0691668			0.0345834	+	0.999402i	$0.488990\pi$
$662$	−1.02069	−	1.40486i	−0.0396702	−	0.0546014i
$663$	5.37626	−	1.74685i	0.208797	−	0.0678421i
$664$	0.516788	−	1.59051i	0.0200553	−	0.0617238i
$665$		0			0
$666$	0.0955887	+	0.0694493i	0.00370399	+	0.00269110i
$667$	17.2209	+	5.59541i	0.666796	+	0.216655i
$668$	6.48896	−	2.10839i	0.251065	−	0.0815761i
$669$	5.79009	−	4.20675i	0.223858	−	0.162642i
$670$		0			0
$671$	8.22502	−	1.11081i	0.317523	−	0.0428823i
$672$		−	7.40331i		−	0.285589i
$673$	−11.3422	−	15.6111i	−0.437208	−	0.601765i	0.532381	−	0.846505i	$-0.321297\pi$
$673$	−11.3422	−	15.6111i	−0.437208	−	0.601765i	−0.969589	+	0.244740i	$0.921297\pi$
$674$	−0.260243	−	0.800945i	−0.0100242	−	0.0308513i
$675$		0			0
$676$	−18.8395	−	13.6877i	−0.724595	−	0.526449i
$677$	9.93949	−	13.6805i	0.382006	−	0.525786i	−0.574109	−	0.818779i	$-0.694651\pi$
$677$	9.93949	−	13.6805i	0.382006	−	0.525786i	0.956114	+	0.292993i	$0.0946514\pi$
$678$	−1.55255	−	0.504455i	−0.0596255	−	0.0193735i
$679$	4.69298	+	14.4435i	0.180100	+	0.554291i
$680$		0			0
$681$	23.9412			0.917430
$682$	0.500518	−	0.240791i	0.0191658	−	0.00922035i
$683$			4.14018i			0.158420i	0.996858	+	0.0792098i	$0.0252397\pi$
$683$			4.14018i			0.158420i	−0.996858	+	0.0792098i	$0.974760\pi$
$684$	8.31920	−	6.04425i	0.318093	−	0.231108i
$685$		0			0
$686$	0.846069	−	2.60393i	0.0323031	−	0.0994186i
$687$	4.16549	−	5.73331i	0.158923	−	0.218739i
$688$	−0.610348	+	0.840072i	−0.0232693	+	0.0320274i
$689$	−0.508335	+	1.56450i	−0.0193660	+	0.0596025i
$690$		0			0
$691$	37.4996	−	27.2450i	1.42655	−	1.03645i	0.435904	−	0.899993i	$-0.356429\pi$
$691$	37.4996	−	27.2450i	1.42655	−	1.03645i	0.990646	−	0.136457i	$-0.0435714\pi$
$692$			40.9539i			1.55684i
$693$	−6.03952	+	11.2126i	−0.229422	+	0.425931i
$694$	−0.960437			−0.0364577
$695$		0			0
$696$	−0.561756	−	1.72891i	−0.0212933	−	0.0655340i
$697$	5.60543	+	1.82132i	0.212321	+	0.0689872i
$698$	0.948743	−	1.30583i	0.0359105	−	0.0494265i
$699$	−9.99096	−	7.25886i	−0.377893	−	0.274555i
$700$		0			0
$701$	−14.0465	−	43.2306i	−0.530528	−	1.63280i	−0.753119	−	0.657884i	$-0.771452\pi$
$701$	−14.0465	−	43.2306i	−0.530528	−	1.63280i	0.222591	−	0.974912i	$-0.428548\pi$
$702$	0.354502	+	0.487931i	0.0133798	+	0.0184158i
$703$			9.05904i			0.341668i
$704$	4.62398	−	25.4224i	0.174273	−	0.958143i
$705$		0			0
$706$	1.72557	−	1.25370i	0.0649428	−	0.0471837i
$707$	−40.1692	+	13.0518i	−1.51072	+	0.490862i
$708$	19.6330	+	6.37915i	0.737853	+	0.239743i
$709$	−11.3458	−	8.24318i	−0.426099	−	0.309579i	0.353988	−	0.935250i	$-0.384825\pi$
$709$	−11.3458	−	8.24318i	−0.426099	−	0.309579i	−0.780087	+	0.625671i	$0.784825\pi$
$710$		0			0
$711$	2.96444	−	9.12360i	0.111175	−	0.342162i
$712$	−4.70941	+	1.53018i	−0.176493	+	0.0573460i
$713$	5.73976	+	7.90010i	0.214956	+	0.295861i
$714$	−2.09327			−0.0783388
$715$		0			0
$716$	5.10622			0.190829
$717$	−19.5640	−	26.9275i	−0.730630	−	1.00563i
$718$	1.42957	−	0.464497i	0.0533512	−	0.0173349i
$719$	−4.05999	+	12.4954i	−0.151412	+	0.465998i	−0.997780	−	0.0666007i	$-0.978785\pi$
$719$	−4.05999	+	12.4954i	−0.151412	+	0.465998i	0.846368	+	0.532599i	$0.178785\pi$
$720$		0			0
$721$	50.9383	+	37.0088i	1.89704	+	1.37828i
$722$	−1.60297	−	0.520835i	−0.0596562	−	0.0193835i
$723$	−16.1904	+	5.26057i	−0.602126	+	0.195643i
$724$	−21.6140	+	15.7035i	−0.803279	+	0.583616i
$725$		0			0
$726$	−0.941597	+	1.17879i	−0.0349459	+	0.0437491i
$727$			18.3635i			0.681063i	0.940233	+	0.340532i	$0.110607\pi$
$727$			18.3635i			0.681063i	−0.940233	+	0.340532i	$0.889393\pi$
$728$	−1.13406	−	1.56090i	−0.0420312	−	0.0578509i
$729$	−9.17943	−	28.2514i	−0.339979	−	1.04635i
$730$		0			0
$731$	0.717839	+	0.521540i	0.0265502	+	0.0192899i
$732$	4.29598	−	5.91290i	0.158784	−	0.218547i
$733$	−35.1869	−	11.4329i	−1.29966	−	0.422284i	−0.424195	−	0.905571i	$-0.639443\pi$
$733$	−35.1869	−	11.4329i	−1.29966	−	0.422284i	−0.875462	+	0.483287i	$0.839443\pi$
$734$	−0.635642	−	1.95631i	−0.0234620	−	0.0722086i
$735$		0			0
$736$	−6.08282			−0.224216
$737$	−1.18354	−	1.23888i	−0.0435964	−	0.0456348i
$738$			0.138666i			0.00510435i
$739$	7.96909	−	5.78988i	0.293148	−	0.212984i	−0.431484	−	0.902121i	$-0.642010\pi$
$739$	7.96909	−	5.78988i	0.293148	−	0.212984i	0.724632	+	0.689136i	$0.242010\pi$
$740$		0			0
$741$	−3.15105	+	9.69793i	−0.115757	+	0.356262i
$742$	0.358046	−	0.492808i	0.0131443	−	0.0180915i
$743$	16.1330	−	22.2052i	0.591862	−	0.814629i	−0.403071	−	0.915169i	$-0.632057\pi$
$743$	16.1330	−	22.2052i	0.591862	−	0.814629i	0.994933	+	0.100540i	$0.0320571\pi$
$744$	0.302951	−	0.932388i	0.0111067	−	0.0341830i
$745$		0			0
$746$	1.53272	−	1.11359i	0.0561170	−	0.0407714i
$747$			3.80291i			0.139141i
$748$	−21.9180	−	3.98658i	−0.801401	−	0.145764i
$749$	75.9591			2.77549
$750$		0			0
$751$	4.24232	+	13.0565i	0.154804	+	0.476439i	0.998141	−	0.0609469i	$-0.0194120\pi$
$751$	4.24232	+	13.0565i	0.154804	+	0.476439i	−0.843337	+	0.537385i	$0.819412\pi$
$752$	−25.9982	−	8.44732i	−0.948056	−	0.308042i
$753$	2.85626	−	3.93131i	0.104088	−	0.143265i
$754$	−0.287039	−	0.208546i	−0.0104533	−	0.00759479i
$755$		0			0
$756$	15.7162	+	48.3694i	0.571592	+	1.75918i
$757$	−13.4779	−	18.5507i	−0.489861	−	0.674236i	0.490501	−	0.871440i	$-0.336814\pi$
$757$	−13.4779	−	18.5507i	−0.489861	−	0.674236i	−0.980362	+	0.197205i	$0.936814\pi$
$758$		−	0.348578i		−	0.0126609i
$759$	−23.3524	−	12.5785i	−0.847640	−	0.456571i
$760$		0			0
$761$	16.7319	−	12.1565i	0.606533	−	0.440672i	−0.241659	−	0.970361i	$-0.577692\pi$
$761$	16.7319	−	12.1565i	0.606533	−	0.440672i	0.848192	+	0.529689i	$0.177692\pi$
$762$	2.57786	−	0.837599i	0.0933861	−	0.0303430i
$763$	−15.7189	−	5.10737i	−0.569061	−	0.184899i
$764$	−29.3031	−	21.2899i	−1.06015	−	0.770243i
$765$		0			0
$766$	−0.317783	+	0.978034i	−0.0114819	+	0.0353378i
$767$	7.68046	−	2.49553i	0.277325	−	0.0901084i
$768$	−13.1948	−	18.1611i	−0.476128	−	0.655334i
$769$	−38.4306			−1.38584			−0.692922	−	0.721013i	$-0.743677\pi$
$769$	−38.4306			−1.38584			−0.692922	+	0.721013i	$0.743677\pi$
$770$		0			0
$771$	−39.3768			−1.41812
$772$	−18.3625	−	25.2738i	−0.660880	−	0.909624i
$773$	−47.4964	+	15.4325i	−1.70833	+	0.555069i	−0.990053	−	0.140693i	$-0.955067\pi$
$773$	−47.4964	+	15.4325i	−1.70833	+	0.555069i	−0.718272	+	0.695762i	$0.755067\pi$
$774$	−0.00645085	+	0.0198537i	−0.000231871	+	0.000713626i
$775$		0			0
$776$	−1.01349	−	0.736341i	−0.0363821	−	0.0264331i
$777$	−9.39654	−	3.05312i	−0.337099	−	0.109530i
$778$	−0.834389	+	0.271109i	−0.0299143	+	0.00971975i
$779$	−8.60121	+	6.24914i	−0.308170	+	0.223899i
$780$		0			0
$781$	−35.2681	+	4.76305i	−1.26199	+	0.170435i
$782$			1.71991i			0.0615037i
$783$	11.0187	+	15.1659i	0.393776	+	0.541986i
$784$	−16.4334	−	50.5767i	−0.586906	−	1.80631i
$785$		0			0
$786$	0.214684	+	0.155977i	0.00765751	+	0.00556351i
$787$	9.14241	−	12.5834i	0.325892	−	0.448551i	−0.614363	−	0.789024i	$-0.710587\pi$
$787$	9.14241	−	12.5834i	0.325892	−	0.448551i	0.940255	+	0.340472i	$0.110587\pi$
$788$	41.3769	+	13.4442i	1.47399	+	0.478928i
$789$	−5.51518	−	16.9740i	−0.196346	−	0.604290i
$790$		0			0
$791$	−53.8524			−1.91477
$792$	−0.140603	−	1.04110i	−0.00499610	−	0.0369938i
$793$		−	2.85919i		−	0.101533i
$794$	1.68805	−	1.22644i	0.0599067	−	0.0435248i
$795$		0			0
$796$	2.80099	−	8.62057i	0.0992786	−	0.305548i
$797$	−27.1009	+	37.3012i	−0.959962	+	1.32127i	−0.0130049	+	0.999915i	$0.504140\pi$
$797$	−27.1009	+	37.3012i	−0.959962	+	1.32127i	−0.946957	+	0.321359i	$0.895860\pi$
$798$	2.21944	−	3.05480i	0.0785674	−	0.108139i
$799$	−7.21821	+	22.2154i	−0.255362	+	0.785923i
$800$		0			0
$801$	9.10970	−	6.61858i	0.321875	−	0.233856i
$802$			2.30803i			0.0814994i
$803$	16.9798	−	8.16868i	0.599203	−	0.288266i
$804$	−1.50879			−0.0532111
$805$		0			0
$806$	−0.0591277	−	0.181976i	−0.00208268	−	0.00640984i
$807$	2.92033	+	0.948873i	0.102801	+	0.0334019i
$808$	2.04786	−	2.81863i	0.0720433	−	0.0991591i
$809$	−30.3700	−	22.0651i	−1.06775	−	0.775767i	−0.0922454	−	0.995736i	$-0.529404\pi$
$809$	−30.3700	−	22.0651i	−1.06775	−	0.775767i	−0.975507	+	0.219969i	$0.929404\pi$
$810$		0			0
$811$	2.22661	+	6.85281i	0.0781870	+	0.240635i	0.982509	−	0.186217i	$-0.0596227\pi$
$811$	2.22661	+	6.85281i	0.0781870	+	0.240635i	−0.904322	+	0.426852i	$0.859623\pi$
$812$	−17.5859	−	24.2050i	−0.617146	−	0.849428i
$813$			22.2104i			0.778953i
$814$	0.406514	+	0.218964i	0.0142483	+	0.00767468i
$815$		0			0
$816$	−15.8011	+	11.4802i	−0.553150	+	0.401887i
$817$	−1.52221	+	0.494596i	−0.0532554	+	0.0173037i
$818$	2.62402	+	0.852597i	0.0917469	+	0.0298104i
$819$	3.54946	+	2.57883i	0.124028	+	0.0901117i
$820$		0			0
$821$	−2.66807	+	8.21147i	−0.0931163	+	0.286582i	−0.986758	−	0.162198i	$-0.948142\pi$
$821$	−2.66807	+	8.21147i	−0.0931163	+	0.286582i	0.893642	+	0.448781i	$0.148142\pi$
$822$	−1.63512	+	0.531284i	−0.0570315	+	0.0185306i
$823$	14.7017	+	20.2352i	0.512470	+	0.705354i	0.984333	−	0.176318i	$-0.0564186\pi$
$823$	14.7017	+	20.2352i	0.512470	+	0.705354i	−0.471864	+	0.881672i	$0.656419\pi$
$824$	−5.19375			−0.180933
$825$		0			0
$826$	−2.99042			−0.104050
$827$	28.7265	+	39.5387i	0.998919	+	1.37489i	0.925986	+	0.377558i	$0.123236\pi$
$827$	28.7265	+	39.5387i	0.998919	+	1.37489i	0.0729332	+	0.997337i	$0.476764\pi$
$828$	8.76373	−	2.84751i	0.304561	−	0.0989577i
$829$	−1.63522	+	5.03270i	−0.0567937	+	0.174793i	−0.975429	−	0.220313i	$-0.929292\pi$
$829$	−1.63522	+	5.03270i	−0.0567937	+	0.174793i	0.918636	+	0.395106i	$0.129292\pi$
$830$		0			0
$831$	−9.81405	−	7.13033i	−0.340446	−	0.247348i
$832$	−8.46589	−	2.75073i	−0.293502	−	0.0953645i
$833$	−43.2177	+	14.0423i	−1.49740	+	0.486536i
$834$	−1.24775	+	0.906543i	−0.0432060	+	0.0313910i
$835$		0			0
$836$	29.0568	−	27.7590i	1.00495	−	0.960064i
$837$			10.1097i			0.349441i
$838$	−0.496633	−	0.683556i	−0.0171559	−	0.0236131i
$839$	4.09196	+	12.5938i	0.141270	+	0.434785i	0.996513	−	0.0834435i	$-0.0265918\pi$
$839$	4.09196	+	12.5938i	0.141270	+	0.434785i	−0.855242	+	0.518228i	$0.826592\pi$
$840$		0			0
$841$	14.5397	+	10.5637i	0.501369	+	0.364266i
$842$	−0.781592	+	1.07577i	−0.0269354	+	0.0370734i
$843$	3.41375	+	1.10919i	0.117576	+	0.0382026i
$844$	11.6670	+	35.9072i	0.401593	+	1.23598i
$845$		0			0
$846$	−0.549557			−0.0188942
$847$	−17.5251	+	46.5822i	−0.602168	+	1.60058i
$848$		−	5.68361i		−	0.195176i
$849$	30.9643	−	22.4969i	1.06269	−	0.772092i
$850$		0			0
$851$	−2.50855	+	7.72053i	−0.0859920	+	0.264656i
$852$	−18.4208	+	25.3540i	−0.631085	+	0.868614i
$853$	1.30421	−	1.79509i	0.0446552	−	0.0614626i	−0.786106	−	0.618092i	$-0.787906\pi$
$853$	1.30421	−	1.79509i	0.0446552	−	0.0614626i	0.830761	+	0.556630i	$0.187906\pi$
$854$	−0.327174	+	1.00694i	−0.0111956	+	0.0344567i
$855$		0			0
$856$	−5.06911	+	3.68292i	−0.173259	+	0.125880i
$857$		−	31.4625i		−	1.07474i	−0.843348	−	0.537368i	$-0.819418\pi$
$857$		−	31.4625i		−	1.07474i	0.843348	−	0.537368i	$-0.180582\pi$
$858$	0.359020	+	0.375806i	0.0122567	+	0.0128298i
$859$	−9.07676			−0.309695			−0.154848	−	0.987938i	$-0.549489\pi$
$859$	−9.07676			−0.309695			−0.154848	+	0.987938i	$0.549489\pi$
$860$		0			0
$861$	−3.58314	−	11.0278i	−0.122113	−	0.375826i
$862$	0.153993	+	0.0500352i	0.00524501	+	0.00170421i
$863$	24.9716	−	34.3704i	0.850042	−	1.16998i	−0.133811	−	0.991007i	$-0.542721\pi$
$863$	24.9716	−	34.3704i	0.850042	−	1.16998i	0.983853	−	0.178976i	$-0.0572785\pi$
$864$	−5.09477	−	3.70157i	−0.173328	−	0.125930i
$865$		0			0
$866$	0.533065	+	1.64060i	0.0181143	+	0.0557500i
$867$	−4.84632	−	6.67038i	−0.164590	−	0.226538i
$868$		−	16.1351i		−	0.547662i
$869$	6.70865	−	36.8838i	0.227575	−	1.25120i
$870$		0			0
$871$	−0.477516	+	0.346936i	−0.0161800	+	0.0117555i
$872$	1.29663	−	0.421300i	0.0439094	−	0.0142670i
$873$	2.70927	+	0.880296i	0.0916950	+	0.0297935i
$874$	−2.50993	−	1.82357i	−0.0848996	−	0.0616832i
$875$		0			0
$876$	5.12746	−	15.7807i	0.173241	−	0.533181i
$877$	−29.7777	+	9.67537i	−1.00552	+	0.326714i	−0.765070	−	0.643947i	$-0.777296\pi$
$877$	−29.7777	+	9.67537i	−1.00552	+	0.326714i	−0.240452	+	0.970661i	$0.577296\pi$
$878$	0.943750	+	1.29896i	0.0318500	+	0.0438378i
$879$	−19.7319			−0.665539
$880$		0			0
$881$	21.5189			0.724990			0.362495	−	0.931986i	$-0.381925\pi$
$881$	21.5189			0.724990			0.362495	+	0.931986i	$0.381925\pi$
$882$	−0.628405	−	0.864925i	−0.0211595	−	0.0291235i
$883$	0.620614	−	0.201650i	0.0208853	−	0.00678605i	−0.298556	−	0.954392i	$-0.596505\pi$
$883$	0.620614	−	0.201650i	0.0208853	−	0.00678605i	0.319441	+	0.947606i	$0.396505\pi$
$884$	−2.37155	+	7.29889i	−0.0797639	+	0.245488i
$885$		0			0
$886$	−2.76877	−	2.01163i	−0.0930187	−	0.0675820i
$887$	13.9294	+	4.52593i	0.467702	+	0.151966i	0.533381	−	0.845875i	$-0.320921\pi$
$887$	13.9294	+	4.52593i	0.467702	+	0.151966i	−0.0656786	+	0.997841i	$0.520921\pi$
$888$	0.775108	−	0.251848i	0.0260109	−	0.00845146i
$889$	72.3396	−	52.5578i	2.42619	−	1.76273i
$890$		0			0
$891$	−8.24400	−	17.1364i	−0.276184	−	0.574089i
$892$			9.71637i			0.325328i
$893$	−24.7665	−	34.0882i	−0.828780	−	1.14072i
$894$	0.734651	+	2.26102i	0.0245704	+	0.0756199i
$895$		0			0
$896$	10.8337	+	7.87116i	0.361929	+	0.262957i
$897$	−5.37094	+	7.39246i	−0.179330	+	0.246827i
$898$	−1.47655	−	0.479760i	−0.0492731	−	0.0160098i
$899$	−1.83782	−	5.65622i	−0.0612946	−	0.188645i
$900$		0			0
$901$	−4.85662			−0.161798
$902$	0.0725252	+	0.537016i	0.00241483	+	0.0178807i
$903$		−	1.74561i		−	0.0580903i
$904$	3.59382	−	2.61107i	0.119529	−	0.0868428i
$905$		0			0
$906$	−0.000229044	0	0.000704924i	−7.60946e−6	0	2.34195e-5i
$907$	−16.8959	+	23.2552i	−0.561018	+	0.772175i	−0.991456	−	0.130445i	$-0.958359\pi$
$907$	−16.8959	+	23.2552i	−0.561018	+	0.772175i	0.430437	+	0.902620i	$0.358359\pi$
$908$	−19.1048	+	26.2955i	−0.634014	+	0.872645i
$909$	−2.44821	+	7.53482i	−0.0812020	+	0.249914i
$910$		0			0
$911$	−13.9813	+	10.1580i	−0.463222	+	0.336550i	−0.794794	−	0.606880i	$-0.792421\pi$
$911$	−13.9813	+	10.1580i	−0.463222	+	0.336550i	0.331572	+	0.943430i	$0.392421\pi$
$912$		−	35.2313i		−	1.16663i
$913$	1.98901	+	14.7277i	0.0658266	+	0.487416i
$914$	2.96102			0.0979418
$915$		0			0
$916$	2.97308	+	9.15020i	0.0982333	+	0.302331i
$917$	8.32554	+	2.70513i	0.274933	+	0.0893313i
$918$	−1.04661	+	1.44054i	−0.0345433	+	0.0475448i
$919$	−1.77859	−	1.29222i	−0.0586701	−	0.0426263i	0.558064	−	0.829798i	$-0.311544\pi$
$919$	−1.77859	−	1.29222i	−0.0586701	−	0.0426263i	−0.616734	+	0.787172i	$0.711544\pi$
$920$		0			0
$921$	12.3212	+	37.9208i	0.405997	+	1.24953i
$922$	−1.39801	−	1.92419i	−0.0460409	−	0.0633699i
$923$			12.2600i			0.403542i
$924$	19.0003	+	39.4948i	0.625063	+	1.29928i
$925$		0			0
$926$	1.23552	−	0.897661i	0.0406019	−	0.0294990i
$927$	11.2324	−	3.64963i	0.368921	−	0.119870i
$928$	3.52335	+	1.14481i	0.115660	+	0.0375801i
$929$	19.5866	+	14.2305i	0.642616	+	0.466888i	0.860748	−	0.509031i	$-0.169996\pi$
$929$	19.5866	+	14.2305i	0.642616	+	0.466888i	−0.218132	+	0.975919i	$0.569996\pi$
$930$		0			0
$931$	25.3301	−	77.9579i	0.830159	−	2.55497i
$932$	15.9453	−	5.18094i	0.522305	−	0.169707i
$933$	11.3792	+	15.6621i	0.372538	+	0.512754i
$934$	−0.797556			−0.0260968
$935$		0			0
$936$	−0.361908			−0.0118293
$937$	−12.2393	−	16.8459i	−0.399840	−	0.550333i	0.560864	−	0.827908i	$-0.310469\pi$
$937$	−12.2393	−	16.8459i	−0.399840	−	0.550333i	−0.960704	+	0.277575i	$0.910469\pi$
$938$	0.207869	−	0.0675407i	0.00678716	−	0.00220528i
$939$	−7.32984	+	22.5589i	−0.239200	+	0.736183i
$940$		0			0
$941$	−27.6787	−	20.1098i	−0.902301	−	0.655560i	0.0367552	−	0.999324i	$-0.488298\pi$
$941$	−27.6787	−	20.1098i	−0.902301	−	0.655560i	−0.939056	+	0.343764i	$0.888298\pi$
$942$	−0.0723736	−	0.0235156i	−0.00235806	−	0.000766180i
$943$	−9.06080	+	2.94403i	−0.295060	+	0.0958709i
$944$	−22.5733	+	16.4004i	−0.734697	+	0.533789i
$945$		0			0
$946$	−0.0145986	+	0.0802621i	−0.000474640	+	0.00260955i
$947$		−	33.8128i		−	1.09877i	−0.835570	−	0.549383i	$-0.814863\pi$
$947$		−	33.8128i		−	1.09877i	0.835570	−	0.549383i	$-0.185137\pi$
$948$	−19.4045	−	26.7081i	−0.630230	−	0.867438i
$949$	−2.00587	−	6.17344i	−0.0651133	−	0.200398i
$950$		0			0
$951$	6.38533	+	4.63921i	0.207058	+	0.150437i
$952$	3.34814	−	4.60832i	0.108514	−	0.149356i
$953$	24.3453	+	7.91027i	0.788622	+	0.256239i	0.675517	−	0.737344i	$-0.263920\pi$
$953$	24.3453	+	7.91027i	0.788622	+	0.256239i	0.113105	+	0.993583i	$0.463920\pi$
$954$	−0.0353088	−	0.108669i	−0.00114316	−	0.00351830i
$955$		0			0
$956$	45.1871			1.46146
$957$	11.1591	+	11.6809i	0.360723	+	0.377589i
$958$			2.80042i			0.0904774i
$959$	−45.8845	+	33.3371i	−1.48169	+	1.07651i
$960$		0			0
$961$	−8.58840	+	26.4324i	−0.277045	+	0.852658i
$962$	0.0934959	−	0.128686i	0.00301443	−	0.00414901i
$963$	8.37488	−	11.5270i	0.269877	−	0.371454i
$964$	7.14182	−	21.9803i	0.230023	−	0.707937i
$965$		0			0
$966$	2.73742	−	1.98885i	0.0880750	−	0.0639902i
$967$		−	43.8942i		−	1.41154i	−0.708439	−	0.705772i	$-0.750600\pi$
$967$		−	43.8942i		−	1.41154i	0.708439	−	0.705772i	$-0.249400\pi$
$968$	−1.08904	−	3.95836i	−0.0350029	−	0.127227i
$969$	−30.1051			−0.967114
$970$		0			0
$971$	11.2392	+	34.5906i	0.360682	+	1.11006i	0.952641	+	0.304097i	$0.0983547\pi$
$971$	11.2392	+	34.5906i	0.360682	+	1.11006i	−0.591959	+	0.805968i	$0.701645\pi$
$972$	16.1453	+	5.24591i	0.517860	+	0.168263i
$973$	−29.9056	+	41.1616i	−0.958730	+	1.31958i
$974$	−1.48299	−	1.07746i	−0.0475182	−	0.0345240i
$975$		0			0
$976$	3.05269	+	9.39520i	0.0977141	+	0.300733i
$977$	6.08452	+	8.37462i	0.194661	+	0.267928i	0.895179	−	0.445707i	$-0.147048\pi$
$977$	6.08452	+	8.37462i	0.194661	+	0.267928i	−0.700518	+	0.713635i	$0.747048\pi$
$978$		−	1.09233i		−	0.0349289i
$979$	31.8178	−	30.3966i	1.01690	−	0.971481i
$980$		0			0
$981$	−2.50814	+	1.82227i	−0.0800789	+	0.0581807i
$982$	−1.40418	+	0.456245i	−0.0448091	+	0.0145594i
$983$	−21.0334	−	6.83416i	−0.670861	−	0.217976i	−0.0462712	−	0.998929i	$-0.514734\pi$
$983$	−21.0334	−	6.83416i	−0.670861	−	0.217976i	−0.624590	+	0.780953i	$0.714734\pi$
$984$	0.773808	+	0.562205i	0.0246681	+	0.0179224i
$985$		0			0
$986$	0.323692	−	0.996222i	0.0103085	−	0.0317262i
$987$	43.7051	−	14.2006i	1.39115	−	0.452012i
$988$	−8.13707	−	11.1997i	−0.258875	−	0.356310i
$989$	−1.43426			−0.0456067
$990$		0			0
$991$	−55.5911			−1.76591			−0.882955	−	0.469457i	$-0.844450\pi$
$991$	−55.5911			−1.76591			−0.882955	+	0.469457i	$0.844450\pi$
$992$	1.17434	+	1.61634i	0.0372853	+	0.0513189i
$993$	25.9044	−	8.41687i	0.822053	−	0.267101i
$994$	1.40289	−	4.31765i	0.0444970	−	0.136948i
$995$		0			0
$996$	10.5876	+	7.69236i	0.335482	+	0.243742i
$997$	−10.2630	−	3.33465i	−0.325032	−	0.105609i	0.141956	−	0.989873i	$-0.454661\pi$
$997$	−10.2630	−	3.33465i	−0.325032	−	0.105609i	−0.466988	+	0.884264i	$0.654661\pi$
$998$	−0.996775	+	0.323872i	−0.0315524	+	0.0102520i
$999$	−6.79924	+	4.93994i	−0.215118	+	0.156293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.z.b.124.3		16
5.2	odd	4		55.2.g.a.36.2	yes	8
5.3	odd	4		275.2.h.b.201.1		8
5.4	even	2	inner	275.2.z.b.124.2		16
11.4	even	5	inner	275.2.z.b.224.2		16
15.2	even	4		495.2.n.f.91.1		8
20.7	even	4		880.2.bo.e.641.1		8
55.2	even	20		605.2.a.i.1.3		4
55.4	even	10	inner	275.2.z.b.224.3		16
55.7	even	20		605.2.g.n.81.1		8
55.13	even	20		3025.2.a.be.1.2		4
55.17	even	20		605.2.g.g.251.2		8
55.27	odd	20		605.2.g.j.251.1		8
55.32	even	4		605.2.g.n.366.1		8
55.37	odd	20		55.2.g.a.26.2	✓	8
55.42	odd	20		605.2.a.l.1.2		4
55.47	odd	20		605.2.g.j.511.1		8
55.48	odd	20		275.2.h.b.26.1		8
55.52	even	20		605.2.g.g.511.2		8
55.53	odd	20		3025.2.a.v.1.3		4
165.2	odd	20		5445.2.a.bu.1.2		4
165.92	even	20		495.2.n.f.136.1		8
165.152	even	20		5445.2.a.bg.1.3		4
220.147	even	20		880.2.bo.e.81.1		8
220.167	odd	20		9680.2.a.cv.1.1		4
220.207	even	20		9680.2.a.cs.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.2	✓	8	55.37	odd	20
55.2.g.a.36.2	yes	8	5.2	odd	4
275.2.h.b.26.1		8	55.48	odd	20
275.2.h.b.201.1		8	5.3	odd	4
275.2.z.b.124.2		16	5.4	even	2	inner
275.2.z.b.124.3		16	1.1	even	1	trivial
275.2.z.b.224.2		16	11.4	even	5	inner
275.2.z.b.224.3		16	55.4	even	10	inner
495.2.n.f.91.1		8	15.2	even	4
495.2.n.f.136.1		8	165.92	even	20
605.2.a.i.1.3		4	55.2	even	20
605.2.a.l.1.2		4	55.42	odd	20
605.2.g.g.251.2		8	55.17	even	20
605.2.g.g.511.2		8	55.52	even	20
605.2.g.j.251.1		8	55.27	odd	20
605.2.g.j.511.1		8	55.47	odd	20
605.2.g.n.81.1		8	55.7	even	20
605.2.g.n.366.1		8	55.32	even	4
880.2.bo.e.81.1		8	220.147	even	20
880.2.bo.e.641.1		8	20.7	even	4
3025.2.a.v.1.3		4	55.53	odd	20
3025.2.a.be.1.2		4	55.13	even	20
5445.2.a.bg.1.3		4	165.152	even	20
5445.2.a.bu.1.2		4	165.2	odd	20
9680.2.a.cs.1.1		4	220.207	even	20
9680.2.a.cv.1.1		4	220.167	odd	20

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.z (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0549637 + 0.0756511i) q^{2} +(-1.39494 + 0.453245i) q^{3} +(0.615332 - 1.89380i) q^{4} +(-0.110960 - 0.0806171i) q^{6} +(-4.30308 - 1.39815i) q^{7} +(0.354955 - 0.115332i) q^{8} +(-0.686611 + 0.498852i) q^{9} +(-2.39815 + 2.29104i) q^{11} +2.92064i q^{12} +(0.671579 + 0.924349i) q^{13} +(-0.130741 - 0.402380i) q^{14} +(-3.19369 - 2.32035i) q^{16} +(-1.98273 + 2.72899i) q^{17} +(-0.0754774 - 0.0245241i) q^{18} +(-1.88030 - 5.78696i) q^{19} +6.63626 q^{21} +(-0.305131 - 0.0554990i) q^{22} -5.45258i q^{23} +(-0.442869 + 0.321763i) q^{24} +(-0.0330155 + 0.101611i) q^{26} +(3.31805 - 4.56691i) q^{27} +(-5.29564 + 7.28883i) q^{28} +(-1.02619 + 3.15830i) q^{29} +(-1.44887 + 1.05267i) q^{31} -1.11558i q^{32} +(2.30689 - 4.28282i) q^{33} -0.315430 q^{34} +(0.522231 + 1.60726i) q^{36} +(-1.41594 - 0.460067i) q^{37} +(0.334441 - 0.460319i) q^{38} +(-1.35577 - 0.985026i) q^{39} +(-0.539933 - 1.66174i) q^{41} +(0.364754 + 0.502041i) q^{42} -0.263041i q^{43} +(2.86310 + 5.95137i) q^{44} +(0.412494 - 0.299694i) q^{46} +(6.58580 - 2.13986i) q^{47} +(5.50670 + 1.78924i) q^{48} +(10.8985 + 7.91824i) q^{49} +(1.52890 - 4.70546i) q^{51} +(2.16377 - 0.703052i) q^{52} +(0.846269 + 1.16479i) q^{53} +0.527864 q^{54} -1.68865 q^{56} +(5.24582 + 7.22025i) q^{57} +(-0.295332 + 0.0959593i) q^{58} +(2.18416 - 6.72216i) q^{59} +(-2.02452 - 1.47090i) q^{61} +(-0.159271 - 0.0517503i) q^{62} +(3.65201 - 1.18661i) q^{63} +(-6.30297 + 4.57938i) q^{64} +(0.450796 - 0.0608810i) q^{66} +0.516598i q^{67} +(3.94812 + 5.43413i) q^{68} +(2.47136 + 7.60605i) q^{69} +(8.68098 + 6.30710i) q^{71} +(-0.186183 + 0.256258i) q^{72} +(-5.40317 - 1.75560i) q^{73} +(-0.0430208 - 0.132404i) q^{74} -12.1163 q^{76} +(13.5227 - 6.50552i) q^{77} -0.156706i q^{78} +(-9.14460 + 6.64394i) q^{79} +(-1.77179 + 5.45300i) q^{81} +(0.0960360 - 0.132182i) q^{82} +(2.63380 - 3.62511i) q^{83} +(4.08350 - 12.5677i) q^{84} +(0.0198994 - 0.0144577i) q^{86} -4.87077i q^{87} +(-0.587008 + 1.08980i) q^{88} -13.2676 q^{89} +(-1.59747 - 4.91652i) q^{91} +(-10.3261 - 3.35515i) q^{92} +(1.54398 - 2.12511i) q^{93} +(0.523863 + 0.380608i) q^{94} +(0.505633 + 1.55618i) q^{96} +(-1.97293 - 2.71551i) q^{97} +1.25970i q^{98} +(0.503711 - 2.76938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} + 26 q^{6} + 10 q^{9} - 10 q^{11} - 32 q^{14} - 40 q^{16} + 2 q^{19} - 24 q^{21} - 50 q^{24} - 28 q^{26} - 38 q^{29} + 12 q^{31} + 40 q^{34} + 42 q^{36} - 18 q^{39} - 8 q^{41} + 56 q^{44}+ \cdots - 8 q^{99}+O(q^{100}) \) 16 * q + 12 * q^4 + 26 * q^6 + 10 * q^9 - 10 * q^11 - 32 * q^14 - 40 * q^16 + 2 * q^19 - 24 * q^21 - 50 * q^24 - 28 * q^26 - 38 * q^29 + 12 * q^31 + 40 * q^34 + 42 * q^36 - 18 * q^39 - 8 * q^41 + 56 * q^44 - 82 * q^46 + 30 * q^49 + 26 * q^51 + 80 * q^54 + 60 * q^56 + 38 * q^59 - 4 * q^61 - 12 * q^64 + 26 * q^66 + 42 * q^69 + 80 * q^71 - 96 * q^74 + 32 * q^76 - 34 * q^79 + 8 * q^84 - 62 * q^86 - 24 * q^91 - 66 * q^94 + 46 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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