LMFDB - Embedded newform 195.2.o.a.86.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(86,195)] 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("195.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.o (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			86.12
Character	$\chi$	$=$	195.86
Dual form			195.2.o.a.161.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.455718 - 0.455718i) q^{2} +(-0.446465 + 1.67352i) q^{3} +1.58464i q^{4} +(0.707107 - 0.707107i) q^{5} +(0.559191 + 0.966114i) q^{6} +(-2.89711 + 2.89711i) q^{7} +(1.63358 + 1.63358i) q^{8} +(-2.60134 - 1.49434i) q^{9} -0.644482i q^{10} +(-2.45902 - 2.45902i) q^{11} +(-2.65193 - 0.707488i) q^{12} +(3.43422 + 1.09825i) q^{13} +2.64053i q^{14} +(0.867659 + 1.49906i) q^{15} -1.68038 q^{16} +6.48865 q^{17} +(-1.86647 + 0.504480i) q^{18} +(3.48002 + 3.48002i) q^{19} +(1.12051 + 1.12051i) q^{20} +(-3.55491 - 6.14183i) q^{21} -2.24123 q^{22} +2.39321 q^{23} +(-3.46318 + 2.00450i) q^{24} -1.00000i q^{25} +(2.06553 - 1.06454i) q^{26} +(3.66221 - 3.68622i) q^{27} +(-4.59088 - 4.59088i) q^{28} +0.0728607i q^{29} +(1.07855 + 0.287739i) q^{30} +(-3.16484 - 3.16484i) q^{31} +(-4.03295 + 4.03295i) q^{32} +(5.21308 - 3.01735i) q^{33} +(2.95699 - 2.95699i) q^{34} +4.09713i q^{35} +(2.36799 - 4.12219i) q^{36} +(6.34157 - 6.34157i) q^{37} +3.17182 q^{38} +(-3.37121 + 5.25690i) q^{39} +2.31024 q^{40} +(2.12973 - 2.12973i) q^{41} +(-4.41897 - 1.17890i) q^{42} +3.53474i q^{43} +(3.89666 - 3.89666i) q^{44} +(-2.89608 + 0.782769i) q^{45} +(1.09063 - 1.09063i) q^{46} +(-8.05214 - 8.05214i) q^{47} +(0.750230 - 2.81215i) q^{48} -9.78648i q^{49} +(-0.455718 - 0.455718i) q^{50} +(-2.89695 + 10.8589i) q^{51} +(-1.74034 + 5.44201i) q^{52} +9.32683i q^{53} +(-0.0109441 - 3.34881i) q^{54} -3.47757 q^{55} -9.46535 q^{56} +(-7.37760 + 4.27018i) q^{57} +(0.0332039 + 0.0332039i) q^{58} +(-3.31055 - 3.31055i) q^{59} +(-2.37547 + 1.37493i) q^{60} -1.29568 q^{61} -2.88455 q^{62} +(11.8656 - 3.20711i) q^{63} +0.315013i q^{64} +(3.20494 - 1.65178i) q^{65} +(1.00063 - 3.75075i) q^{66} +(0.922676 + 0.922676i) q^{67} +10.2822i q^{68} +(-1.06849 + 4.00509i) q^{69} +(1.86713 + 1.86713i) q^{70} +(2.96569 - 2.96569i) q^{71} +(-1.80838 - 6.69063i) q^{72} +(-5.91079 + 5.91079i) q^{73} -5.77993i q^{74} +(1.67352 + 0.446465i) q^{75} +(-5.51460 + 5.51460i) q^{76} +14.2481 q^{77} +(0.859343 + 3.93198i) q^{78} +9.54897 q^{79} +(-1.18821 + 1.18821i) q^{80} +(4.53392 + 7.77455i) q^{81} -1.94111i q^{82} +(2.62525 - 2.62525i) q^{83} +(9.73260 - 5.63327i) q^{84} +(4.58817 - 4.58817i) q^{85} +(1.61084 + 1.61084i) q^{86} +(-0.121934 - 0.0325297i) q^{87} -8.03402i q^{88} +(-7.03107 - 7.03107i) q^{89} +(-0.963073 + 1.67652i) q^{90} +(-13.1311 + 6.76754i) q^{91} +3.79239i q^{92} +(6.70942 - 3.88344i) q^{93} -7.33901 q^{94} +4.92150 q^{95} +(-4.94865 - 8.54979i) q^{96} +(6.77490 + 6.77490i) q^{97} +(-4.45987 - 4.45987i) q^{98} +(2.72214 + 10.0713i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{6} - 16 q^{7} + 4 q^{15} - 64 q^{16} + 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} - 24 q^{27} + 32 q^{28} + 32 q^{31} - 4 q^{33} - 16 q^{34} + 32 q^{37} - 8 q^{39} + 8 q^{42} - 8 q^{45} - 40 q^{46}+ \cdots - 20 q^{99}+O(q^{100}) $ 40 * q + 12 * q^6 - 16 * q^7 + 4 * q^15 - 64 * q^16 + 4 * q^18 - 16 * q^19 - 12 * q^21 + 8 * q^24 - 24 * q^27 + 32 * q^28 + 32 * q^31 - 4 * q^33 - 16 * q^34 + 32 * q^37 - 8 * q^39 + 8 * q^42 - 8 * q^45 - 40 * q^46 + 8 * q^48 - 32 * q^54 + 8 * q^55 - 36 * q^57 + 24 * q^58 + 16 * q^60 + 8 * q^61 + 8 * q^63 - 48 * q^66 - 32 * q^67 + 132 * q^72 - 64 * q^73 + 16 * q^76 - 12 * q^78 + 40 * q^79 + 72 * q^81 + 124 * q^84 - 24 * q^85 + 16 * q^87 + 8 * q^91 - 108 * q^93 - 32 * q^94 - 76 * q^96 + 24 * q^97 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.455718	−	0.455718i	0.322241	−	0.322241i	−0.527385	−	0.849626i	$-0.676828\pi$
$2$	0.455718	−	0.455718i	0.322241	−	0.322241i	0.849626	+	0.527385i	$0.176828\pi$
$3$	−0.446465	+	1.67352i	−0.257767	+	0.966207i
$3$	−0.446465	+	1.67352i	−0.257767	+	0.966207i
$4$			1.58464i			0.792321i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	0.559191	+	0.966114i	0.228289	+	0.394415i
$7$	−2.89711	+	2.89711i	−1.09500	+	1.09500i	−0.100019	+	0.994986i	$0.531890\pi$
$7$	−2.89711	+	2.89711i	−1.09500	+	1.09500i	−0.994986	+	0.100019i	$0.968110\pi$
$8$	1.63358	+	1.63358i	0.577559	+	0.577559i
$9$	−2.60134	−	1.49434i	−0.867113	−	0.498112i
$10$		−	0.644482i		−	0.203803i
$11$	−2.45902	−	2.45902i	−0.741421	−	0.741421i	0.231430	−	0.972851i	$-0.425659\pi$
$11$	−2.45902	−	2.45902i	−0.741421	−	0.741421i	−0.972851	+	0.231430i	$0.925659\pi$
$12$	−2.65193	−	0.707488i	−0.765547	−	0.204234i
$13$	3.43422	+	1.09825i	0.952480	+	0.304601i
$13$	3.43422	+	1.09825i	0.952480	+	0.304601i
$14$			2.64053i			0.705711i
$15$	0.867659	+	1.49906i	0.224029	+	0.387055i
$16$	−1.68038			−0.420095
$17$	6.48865			1.57373			0.786864	−	0.617126i	$-0.211703\pi$
$17$	6.48865			1.57373			0.786864	+	0.617126i	$0.211703\pi$
$18$	−1.86647	+	0.504480i	−0.439931	+	0.118907i
$19$	3.48002	+	3.48002i	0.798372	+	0.798372i	0.982839	−	0.184466i	$-0.0590557\pi$
$19$	3.48002	+	3.48002i	0.798372	+	0.798372i	−0.184466	+	0.982839i	$0.559056\pi$
$20$	1.12051	+	1.12051i	0.250554	+	0.250554i
$21$	−3.55491	−	6.14183i	−0.775745	−	1.34026i
$22$	−2.24123			−0.477833
$23$	2.39321			0.499020			0.249510	−	0.968372i	$-0.419730\pi$
$23$	2.39321			0.499020			0.249510	+	0.968372i	$0.419730\pi$
$24$	−3.46318	+	2.00450i	−0.706918	+	0.409167i
$25$		−	1.00000i		−	0.200000i
$26$	2.06553	−	1.06454i	0.405083	−	0.208773i
$27$	3.66221	−	3.68622i	0.704792	−	0.709414i
$28$	−4.59088	−	4.59088i	−0.867595	−	0.867595i
$29$			0.0728607i			0.0135299i	0.999977	+	0.00676494i	$0.00215336\pi$
$29$			0.0728607i			0.0135299i	−0.999977	+	0.00676494i	$0.997847\pi$
$30$	1.07855	+	0.287739i	0.196916	+	0.0525336i
$31$	−3.16484	−	3.16484i	−0.568423	−	0.568423i	0.363264	−	0.931686i	$-0.381662\pi$
$31$	−3.16484	−	3.16484i	−0.568423	−	0.568423i	−0.931686	+	0.363264i	$0.881662\pi$
$32$	−4.03295	+	4.03295i	−0.712931	+	0.712931i
$33$	5.21308	−	3.01735i	0.907480	−	0.525253i
$34$	2.95699	−	2.95699i	0.507120	−	0.507120i
$35$			4.09713i			0.692541i
$36$	2.36799	−	4.12219i	0.394665	−	0.687032i
$37$	6.34157	−	6.34157i	1.04255	−	1.04255i	0.0434947	−	0.999054i	$-0.486151\pi$
$37$	6.34157	−	6.34157i	1.04255	−	1.04255i	0.999054	−	0.0434947i	$-0.0138492\pi$
$38$	3.17182			0.514537
$39$	−3.37121	+	5.25690i	−0.539825	+	0.841777i
$40$	2.31024			0.365281
$41$	2.12973	−	2.12973i	0.332607	−	0.332607i	−0.520968	−	0.853576i	$-0.674429\pi$
$41$	2.12973	−	2.12973i	0.332607	−	0.332607i	0.853576	+	0.520968i	$0.174429\pi$
$42$	−4.41897	−	1.17890i	−0.681863	−	0.181909i
$43$			3.53474i			0.539043i	0.962994	+	0.269522i	$0.0868655\pi$
$43$			3.53474i			0.539043i	−0.962994	+	0.269522i	$0.913134\pi$
$44$	3.89666	−	3.89666i	0.587444	−	0.587444i
$45$	−2.89608	+	0.782769i	−0.431722	+	0.116688i
$46$	1.09063	−	1.09063i	0.160805	−	0.160805i
$47$	−8.05214	−	8.05214i	−1.17453	−	1.17453i	−0.981119	−	0.193407i	$-0.938046\pi$
$47$	−8.05214	−	8.05214i	−1.17453	−	1.17453i	−0.193407	−	0.981119i	$-0.561954\pi$
$48$	0.750230	−	2.81215i	0.108286	−	0.405899i
$49$		−	9.78648i		−	1.39807i
$50$	−0.455718	−	0.455718i	−0.0644482	−	0.0644482i
$51$	−2.89695	+	10.8589i	−0.405655	+	1.52055i
$52$	−1.74034	+	5.44201i	−0.241342	+	0.754670i
$53$			9.32683i			1.28114i	0.767901	+	0.640569i	$0.221301\pi$
$53$			9.32683i			1.28114i	−0.767901	+	0.640569i	$0.778699\pi$
$54$	−0.0109441	−	3.34881i	−0.00148931	−	0.455715i
$55$	−3.47757			−0.468916
$56$	−9.46535			−1.26486
$57$	−7.37760	+	4.27018i	−0.977187	+	0.565599i
$58$	0.0332039	+	0.0332039i	0.00435988	+	0.00435988i
$59$	−3.31055	−	3.31055i	−0.430996	−	0.430996i	0.457971	−	0.888967i	$-0.348576\pi$
$59$	−3.31055	−	3.31055i	−0.430996	−	0.430996i	−0.888967	+	0.457971i	$0.848576\pi$
$60$	−2.37547	+	1.37493i	−0.306672	+	0.177503i
$61$	−1.29568			−0.165895			−0.0829473	−	0.996554i	$-0.526433\pi$
$61$	−1.29568			−0.165895			−0.0829473	+	0.996554i	$0.526433\pi$
$62$	−2.88455			−0.366338
$63$	11.8656	−	3.20711i	1.49493	−	0.404057i
$64$			0.315013i			0.0393766i
$65$	3.20494	−	1.65178i	0.397524	−	0.204877i
$66$	1.00063	−	3.75075i	0.123169	−	0.461685i
$67$	0.922676	+	0.922676i	0.112723	+	0.112723i	0.761218	−	0.648496i	$-0.224601\pi$
$67$	0.922676	+	0.922676i	0.112723	+	0.112723i	−0.648496	+	0.761218i	$0.724601\pi$
$68$			10.2822i			1.24690i
$69$	−1.06849	+	4.00509i	−0.128631	+	0.482156i
$70$	1.86713	+	1.86713i	0.223165	+	0.223165i
$71$	2.96569	−	2.96569i	0.351963	−	0.351963i	−0.508877	−	0.860839i	$-0.669939\pi$
$71$	2.96569	−	2.96569i	0.351963	−	0.351963i	0.860839	+	0.508877i	$0.169939\pi$
$72$	−1.80838	−	6.69063i	−0.213120	−	0.788498i
$73$	−5.91079	+	5.91079i	−0.691805	+	0.691805i	−0.962629	−	0.270824i	$-0.912704\pi$
$73$	−5.91079	+	5.91079i	−0.691805	+	0.691805i	0.270824	+	0.962629i	$0.412704\pi$
$74$		−	5.77993i		−	0.671904i
$75$	1.67352	+	0.446465i	0.193241	+	0.0515533i
$76$	−5.51460	+	5.51460i	−0.632568	+	0.632568i
$77$	14.2481			1.62372
$78$	0.859343	+	3.93198i	0.0973014	+	0.445209i
$79$	9.54897			1.07434			0.537171	−	0.843473i	$-0.319493\pi$
$79$	9.54897			1.07434			0.537171	+	0.843473i	$0.319493\pi$
$80$	−1.18821	+	1.18821i	−0.132846	+	0.132846i
$81$	4.53392	+	7.77455i	0.503769	+	0.863838i
$82$		−	1.94111i		−	0.214360i
$83$	2.62525	−	2.62525i	0.288158	−	0.288158i	−0.548193	−	0.836352i	$-0.684684\pi$
$83$	2.62525	−	2.62525i	0.288158	−	0.288158i	0.836352	+	0.548193i	$0.184684\pi$
$84$	9.73260	−	5.63327i	1.06191	−	0.614640i
$85$	4.58817	−	4.58817i	0.497657	−	0.497657i
$86$	1.61084	+	1.61084i	0.173702	+	0.173702i
$87$	−0.121934	−	0.0325297i	−0.0130727	−	0.00348755i
$88$		−	8.03402i		−	0.856429i
$89$	−7.03107	−	7.03107i	−0.745292	−	0.745292i	0.228299	−	0.973591i	$-0.426683\pi$
$89$	−7.03107	−	7.03107i	−0.745292	−	0.745292i	−0.973591	+	0.228299i	$0.926683\pi$
$90$	−0.963073	+	1.67652i	−0.101517	+	0.176720i
$91$	−13.1311	+	6.76754i	−1.37651	+	0.709431i
$92$			3.79239i			0.395384i
$93$	6.70942	−	3.88344i	0.695735	−	0.402694i
$94$	−7.33901			−0.756961
$95$	4.92150			0.504935
$96$	−4.94865	−	8.54979i	−0.505069	−	0.872609i
$97$	6.77490	+	6.77490i	0.687887	+	0.687887i	0.961765	−	0.273878i	$-0.0883063\pi$
$97$	6.77490	+	6.77490i	0.687887	+	0.687887i	−0.273878	+	0.961765i	$0.588306\pi$
$98$	−4.45987	−	4.45987i	−0.450515	−	0.450515i
$99$	2.72214	+	10.0713i	0.273585	+	1.01221i
$100$	1.58464			0.158464
$101$	−3.16651			−0.315080			−0.157540	−	0.987513i	$-0.550356\pi$
$101$	−3.16651			−0.315080			−0.157540	+	0.987513i	$0.550356\pi$
$102$	3.62839	+	6.26878i	0.359264	+	0.620702i
$103$			13.7432i			1.35416i	0.735910	+	0.677080i	$0.236755\pi$
$103$			13.7432i			1.35416i	−0.735910	+	0.677080i	$0.763245\pi$
$104$	3.81599	+	7.40417i	0.374189	+	0.726039i
$105$	−6.85663	−	1.82923i	−0.669139	−	0.178514i
$106$	4.25040	+	4.25040i	0.412835	+	0.412835i
$107$		−	9.01108i		−	0.871134i	−0.900156	−	0.435567i	$-0.856548\pi$
$107$		−	9.01108i		−	0.871134i	0.900156	−	0.435567i	$-0.143452\pi$
$108$	5.84135	+	5.80329i	0.562084	+	0.558422i
$109$	−5.87504	−	5.87504i	−0.562727	−	0.562727i	0.367354	−	0.930081i	$-0.380264\pi$
$109$	−5.87504	−	5.87504i	−0.562727	−	0.562727i	−0.930081	+	0.367354i	$0.880264\pi$
$110$	−1.58479	+	1.58479i	−0.151104	+	0.151104i
$111$	7.78146	+	13.4440i	0.738584	+	1.27605i
$112$	4.86824	−	4.86824i	0.460006	−	0.460006i
$113$			0.651432i			0.0612816i	0.999530	+	0.0306408i	$0.00975479\pi$
$113$			0.651432i			0.0612816i	−0.999530	+	0.0306408i	$0.990245\pi$
$114$	−1.41611	+	5.30810i	−0.132630	+	0.497149i
$115$	1.69226	−	1.69226i	0.157804	−	0.157804i
$116$	−0.115458			−0.0107200
$117$	−7.29240	−	7.98880i	−0.674182	−	0.738565i
$118$	−3.01735			−0.277769
$119$	−18.7983	+	18.7983i	−1.72324	+	1.72324i
$120$	−1.03144	+	3.86623i	−0.0941572	+	0.352937i
$121$			1.09351i			0.0994103i
$122$	−0.590464	+	0.590464i	−0.0534581	+	0.0534581i
$123$	2.61329	+	4.51499i	0.235633	+	0.407103i
$124$	5.01515	−	5.01515i	0.450374	−	0.450374i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	3.94583	−	6.86890i	0.351523	−	0.611931i
$127$			3.65542i			0.324366i	0.986761	+	0.162183i	$0.0518534\pi$
$127$			3.65542i			0.324366i	−0.986761	+	0.162183i	$0.948147\pi$
$128$	−7.92234	−	7.92234i	−0.700242	−	0.700242i
$129$	−5.91546	−	1.57814i	−0.520827	−	0.138947i
$130$	0.707804	−	2.21329i	0.0620786	−	0.194118i
$131$		−	10.5741i		−	0.923863i	−0.886916	−	0.461932i	$-0.847157\pi$
$131$		−	10.5741i		−	0.923863i	0.886916	−	0.461932i	$-0.152843\pi$
$132$	4.78142	+	8.26086i	0.416169	+	0.719016i
$133$	−20.1640			−1.74844
$134$	0.840960			0.0726479
$135$	−0.0169813	−	5.19612i	−0.00146152	−	0.447211i
$136$	10.5998	+	10.5998i	0.908922	+	0.908922i
$137$	−4.62847	−	4.62847i	−0.395437	−	0.395437i	0.481183	−	0.876620i	$-0.340207\pi$
$137$	−4.62847	−	4.62847i	−0.395437	−	0.395437i	−0.876620	+	0.481183i	$0.840207\pi$
$138$	1.33826	+	2.31212i	0.113921	+	0.196821i
$139$	8.02113			0.680343			0.340172	−	0.940363i	$-0.389515\pi$
$139$	8.02113			0.680343			0.340172	+	0.940363i	$0.389515\pi$
$140$	−6.49249			−0.548715
$141$	17.0704	−	9.88042i	1.43759	−	0.832082i
$142$		−	2.70304i		−	0.226834i
$143$	−5.74417	−	11.1454i	−0.480351	−	0.932026i
$144$	4.37123	+	2.51105i	0.364270	+	0.209254i
$145$	0.0515203	+	0.0515203i	0.00427853	+	0.00427853i
$146$			5.38730i			0.445856i
$147$	16.3779	+	4.36932i	1.35082	+	0.360375i
$148$	10.0491	+	10.0491i	0.826033	+	0.826033i
$149$	−1.16217	+	1.16217i	−0.0952087	+	0.0952087i	−0.753107	−	0.657898i	$-0.771446\pi$
$149$	−1.16217	+	1.16217i	−0.0952087	+	0.0952087i	0.657898	+	0.753107i	$0.271446\pi$
$150$	0.966114	−	0.559191i	0.0788829	−	0.0456577i
$151$	5.51342	−	5.51342i	0.448675	−	0.448675i	−0.446239	−	0.894914i	$-0.647237\pi$
$151$	5.51342	−	5.51342i	0.448675	−	0.448675i	0.894914	+	0.446239i	$0.147237\pi$
$152$			11.3698i			0.922215i
$153$	−16.8792	−	9.69622i	−1.36460	−	0.783893i
$154$	6.49310	−	6.49310i	0.523229	−	0.523229i
$155$	−4.47577			−0.359502
$156$	−8.33031	−	5.34216i	−0.666958	−	0.427715i
$157$	−20.7693			−1.65757			−0.828785	−	0.559567i	$-0.810968\pi$
$157$	−20.7693			−1.65757			−0.828785	+	0.559567i	$0.810968\pi$
$158$	4.35163	−	4.35163i	0.346197	−	0.346197i
$159$	−15.6086	−	4.16410i	−1.23784	−	0.330235i
$160$			5.70345i			0.450897i
$161$	−6.93340	+	6.93340i	−0.546429	+	0.546429i
$162$	5.60918	+	1.47681i	0.440699	+	0.116029i
$163$	−1.79004	+	1.79004i	−0.140207	+	0.140207i	−0.773726	−	0.633520i	$-0.781610\pi$
$163$	−1.79004	+	1.79004i	−0.140207	+	0.140207i	0.633520	+	0.773726i	$0.281610\pi$
$164$	3.37486	+	3.37486i	0.263532	+	0.263532i
$165$	1.55261	−	5.81979i	0.120871	−	0.453070i
$166$		−	2.39274i		−	0.185713i
$167$	7.06139	+	7.06139i	0.546427	+	0.546427i	0.925405	−	0.378979i	$-0.123725\pi$
$167$	7.06139	+	7.06139i	0.546427	+	0.546427i	−0.378979	+	0.925405i	$0.623725\pi$
$168$	4.22595	−	15.8404i	0.326039	−	1.22212i
$169$	10.5877	+	7.54328i	0.814437	+	0.580252i
$170$		−	4.18182i		−	0.320731i
$171$	−3.85239	−	14.2530i	−0.294600	−	1.08996i
$172$	−5.60130			−0.427095
$173$	−22.6054			−1.71866			−0.859329	−	0.511423i	$-0.829119\pi$
$173$	−22.6054			−1.71866			−0.859329	+	0.511423i	$0.829119\pi$
$174$	−0.0703917	+	0.0407430i	−0.00533638	+	0.00308872i
$175$	2.89711	+	2.89711i	0.219001	+	0.219001i
$176$	4.13208	+	4.13208i	0.311467	+	0.311467i
$177$	7.01831	−	4.06222i	0.527528	−	0.305335i
$178$	−6.40836			−0.480327
$179$	14.3368			1.07158			0.535790	−	0.844351i	$-0.320014\pi$
$179$	14.3368			1.07158			0.535790	+	0.844351i	$0.320014\pi$
$180$	−1.24041	−	4.58925i	−0.0924546	−	0.342063i
$181$		−	14.9736i		−	1.11298i	−0.830856	−	0.556488i	$-0.812148\pi$
$181$		−	14.9736i		−	1.11298i	0.830856	−	0.556488i	$-0.187852\pi$
$182$	−2.89997	+	9.06814i	−0.214960	+	0.672175i
$183$	0.578475	−	2.16834i	0.0427621	−	0.160289i
$184$	3.90952	+	3.90952i	0.288214	+	0.288214i
$185$		−	8.96834i		−	0.659365i
$186$	1.28785	−	4.82735i	0.0944298	−	0.353959i
$187$	−15.9557	−	15.9557i	−1.16680	−	1.16680i
$188$	12.7598	−	12.7598i	0.930602	−	0.930602i
$189$	0.0695745	+	21.2892i	0.00506080	+	1.54856i
$190$	2.24281	−	2.24281i	0.162711	−	0.162711i
$191$			13.0774i			0.946247i	0.880996	+	0.473124i	$0.156874\pi$
$191$			13.0774i			0.946247i	−0.880996	+	0.473124i	$0.843126\pi$
$192$	−0.527180	−	0.140642i	−0.0380459	−	0.0101500i
$193$	8.44842	−	8.44842i	0.608130	−	0.608130i	−0.334327	−	0.942457i	$-0.608509\pi$
$193$	8.44842	−	8.44842i	0.608130	−	0.608130i	0.942457	+	0.334327i	$0.108509\pi$
$194$	6.17488			0.443331
$195$	1.33339	+	6.10099i	0.0954857	+	0.436901i
$196$	15.5081			1.10772
$197$	−6.31663	+	6.31663i	−0.450041	+	0.450041i	−0.895368	−	0.445327i	$-0.853088\pi$
$197$	−6.31663	+	6.31663i	−0.450041	+	0.450041i	0.445327	+	0.895368i	$0.353088\pi$
$198$	5.83021	+	3.34916i	0.414335	+	0.238014i
$199$		−	21.9442i		−	1.55558i	−0.628523	−	0.777791i	$-0.716340\pi$
$199$		−	21.9442i		−	1.55558i	0.628523	−	0.777791i	$-0.283660\pi$
$200$	1.63358	−	1.63358i	0.115512	−	0.115512i
$201$	−1.95606	+	1.13217i	−0.137970	+	0.0798575i
$202$	−1.44304	+	1.44304i	−0.101532	+	0.101532i
$203$	−0.211085	−	0.211085i	−0.0148153	−	0.0148153i
$204$	−17.2075	−	4.59064i	−1.20476	−	0.321409i
$205$		−	3.01189i		−	0.210359i
$206$	6.26302	+	6.26302i	0.436366	+	0.436366i
$207$	−6.22556	−	3.57627i	−0.432706	−	0.248568i
$208$	−5.77079	−	1.84548i	−0.400132	−	0.127961i
$209$		−	17.1149i		−	1.18386i
$210$	−3.95830	+	2.29108i	−0.273148	+	0.158099i
$211$	0.438580			0.0301931			0.0150966	−	0.999886i	$-0.495194\pi$
$211$	0.438580			0.0301931			0.0150966	+	0.999886i	$0.495194\pi$
$212$	−14.7797			−1.01507
$213$	3.63907	+	6.28722i	0.249345	+	0.430793i
$214$	−4.10651	−	4.10651i	−0.280715	−	0.280715i
$215$	2.49944	+	2.49944i	0.170460	+	0.170460i
$216$	12.0043	−	0.0392308i	0.816788	−	0.00266932i
$217$	18.3378			1.24485
$218$	−5.35472			−0.362667
$219$	−7.25286	−	12.5308i	−0.490103	−	0.846752i
$220$		−	5.51071i		−	0.371532i
$221$	22.2834	+	7.12618i	1.49895	+	0.479359i
$222$	9.67283	+	2.58054i	0.649198	+	0.173194i
$223$	−1.59677	−	1.59677i	−0.106927	−	0.106927i	0.651619	−	0.758546i	$-0.274090\pi$
$223$	−1.59677	−	1.59677i	−0.106927	−	0.106927i	−0.758546	+	0.651619i	$0.774090\pi$
$224$		−	23.3678i		−	1.56133i
$225$	−1.49434	+	2.60134i	−0.0996224	+	0.173423i
$226$	0.296869	+	0.296869i	0.0197474	+	0.0197474i
$227$	13.0961	−	13.0961i	0.869216	−	0.869216i	−0.123169	−	0.992386i	$-0.539306\pi$
$227$	13.0961	−	13.0961i	0.869216	−	0.869216i	0.992386	+	0.123169i	$0.0393058\pi$
$228$	−6.76671	−	11.6909i	−0.448137	−	0.774246i
$229$	−2.58892	+	2.58892i	−0.171080	+	0.171080i	−0.787454	−	0.616373i	$-0.788601\pi$
$229$	−2.58892	+	2.58892i	−0.171080	+	0.171080i	0.616373	+	0.787454i	$0.288601\pi$
$230$		−	1.54238i		−	0.101702i
$231$	−6.36126	+	23.8444i	−0.418540	+	1.56885i
$232$	−0.119024	+	0.119024i	−0.00781431	+	0.00781431i
$233$	6.66598			0.436703			0.218351	−	0.975870i	$-0.429932\pi$
$233$	6.66598			0.436703			0.218351	+	0.975870i	$0.429932\pi$
$234$	−6.96391	−	0.317363i	−0.455245	−	0.0207467i
$235$	−11.3874			−0.742835
$236$	5.24603	−	5.24603i	0.341488	−	0.341488i
$237$	−4.26328	+	15.9804i	−0.276930	+	1.03804i
$238$			17.1335i			1.11060i
$239$	−1.15681	+	1.15681i	−0.0748278	+	0.0748278i	−0.743530	−	0.668702i	$-0.766850\pi$
$239$	−1.15681	+	1.15681i	−0.0748278	+	0.0748278i	0.668702	+	0.743530i	$0.266850\pi$
$240$	−1.45800	−	2.51898i	−0.0941132	−	0.162600i
$241$	3.93884	−	3.93884i	0.253723	−	0.253723i	−0.568772	−	0.822495i	$-0.692581\pi$
$241$	3.93884	−	3.93884i	0.253723	−	0.253723i	0.822495	+	0.568772i	$0.192581\pi$
$242$	0.498333	+	0.498333i	0.0320341	+	0.0320341i
$243$	−15.0351	+	4.11654i	−0.964502	+	0.264076i
$244$		−	2.05319i		−	0.131442i
$245$	−6.92009	−	6.92009i	−0.442108	−	0.442108i
$246$	3.24848	+	0.866637i	0.207116	+	0.0552547i
$247$	8.12921	+	15.7731i	0.517249	+	1.00362i
$248$		−	10.3401i		−	0.656596i
$249$	3.22132	+	5.56549i	0.204143	+	0.352698i
$250$	−0.644482			−0.0407606
$251$	−17.0218			−1.07441			−0.537205	−	0.843452i	$-0.680520\pi$
$251$	−17.0218			−1.07441			−0.537205	+	0.843452i	$0.680520\pi$
$252$	5.08212	+	18.8028i	0.320143	+	1.18446i
$253$	−5.88495	−	5.88495i	−0.369984	−	0.369984i
$254$	1.66584	+	1.66584i	0.104524	+	0.104524i
$255$	5.62994	+	9.72685i	0.352560	+	0.609119i
$256$	−7.85072			−0.490670
$257$	15.7772			0.984152			0.492076	−	0.870552i	$-0.336238\pi$
$257$	15.7772			0.984152			0.492076	+	0.870552i	$0.336238\pi$
$258$	−3.41496	+	1.97659i	−0.212606	+	0.123057i
$259$			36.7445i			2.28319i
$260$	2.61747	+	5.07869i	0.162329	+	0.314967i
$261$	0.108878	−	0.189535i	0.00673940	−	0.0117319i
$262$	−4.81880	−	4.81880i	−0.297707	−	0.297707i
$263$			5.23074i			0.322541i	0.986910	+	0.161271i	$0.0515592\pi$
$263$			5.23074i			0.322541i	−0.986910	+	0.161271i	$0.948441\pi$
$264$	13.4451	+	3.58691i	0.827488	+	0.220759i
$265$	6.59506	+	6.59506i	0.405131	+	0.405131i
$266$	−9.18910	+	9.18910i	−0.563420	+	0.563420i
$267$	14.9058	−	8.62751i	0.912217	−	0.527995i
$268$	−1.46211	+	1.46211i	−0.0893127	+	0.0893127i
$269$			24.7143i			1.50686i	0.657529	+	0.753429i	$0.271602\pi$
$269$			24.7143i			1.50686i	−0.657529	+	0.753429i	$0.728398\pi$
$270$	−2.37570	−	2.36023i	−0.144581	−	0.143639i
$271$	−13.3905	+	13.3905i	−0.813413	+	0.813413i	−0.985144	−	0.171730i	$-0.945064\pi$
$271$	−13.3905	+	13.3905i	−0.813413	+	0.813413i	0.171730	+	0.985144i	$0.445064\pi$
$272$	−10.9034			−0.661115
$273$	−5.46305	−	24.9966i	−0.330639	−	1.51286i
$274$	−4.21855			−0.254852
$275$	−2.45902	+	2.45902i	−0.148284	+	0.148284i
$276$	−6.34664	−	1.69317i	−0.382023	−	0.101917i
$277$			5.07891i			0.305162i	0.988291	+	0.152581i	$0.0487585\pi$
$277$			5.07891i			0.305162i	−0.988291	+	0.152581i	$0.951241\pi$
$278$	3.65537	−	3.65537i	0.219234	−	0.219234i
$279$	3.50349	+	12.9622i	0.209748	+	0.776025i
$280$	−6.69301	+	6.69301i	−0.399984	+	0.399984i
$281$	−1.89588	−	1.89588i	−0.113098	−	0.113098i	0.648293	−	0.761391i	$-0.275483\pi$
$281$	−1.89588	−	1.89588i	−0.113098	−	0.113098i	−0.761391	+	0.648293i	$0.775483\pi$
$282$	3.27661	−	12.2820i	0.195119	−	0.731381i
$283$		−	12.6318i		−	0.750881i	−0.926847	−	0.375440i	$-0.877491\pi$
$283$		−	12.6318i		−	0.750881i	0.926847	−	0.375440i	$-0.122509\pi$
$284$	4.69956	+	4.69956i	0.278868	+	0.278868i
$285$	−2.19728	+	8.23623i	−0.130155	+	0.487872i
$286$	−7.69688	−	2.46144i	−0.455126	−	0.145548i
$287$			12.3401i			0.728413i
$288$	16.5176	−	4.46448i	0.973311	−	0.263072i
$289$	25.1026			1.47662
$290$	0.0469574			0.00275743
$291$	−14.3627	+	8.31317i	−0.841956	+	0.487327i
$292$	−9.36649	−	9.36649i	−0.548132	−	0.548132i
$293$	−19.7059	−	19.7059i	−1.15123	−	1.15123i	−0.986306	−	0.164928i	$-0.947261\pi$
$293$	−19.7059	−	19.7059i	−1.15123	−	1.15123i	−0.164928	−	0.986306i	$-0.552739\pi$
$294$	9.45486	−	5.47251i	0.551419	−	0.319163i
$295$	−4.68182			−0.272586
$296$	20.7190			1.20427
$297$	−18.0699	+	0.0590536i	−1.04852	+	0.00342664i
$298$			1.05924i			0.0613603i
$299$	8.21882	+	2.62836i	0.475306	+	0.152002i
$300$	−0.707488	+	2.65193i	−0.0408468	+	0.153109i
$301$	−10.2405	−	10.2405i	−0.590254	−	0.590254i
$302$		−	5.02512i		−	0.289163i
$303$	1.41374	−	5.29922i	0.0812171	−	0.304432i
$304$	−5.84776	−	5.84776i	−0.335392	−	0.335392i
$305$	−0.916183	+	0.916183i	−0.0524605	+	0.0524605i
$306$	−12.1109	+	3.27340i	−0.692333	+	0.187128i
$307$	8.41607	−	8.41607i	0.480330	−	0.480330i	−0.424907	−	0.905237i	$-0.639693\pi$
$307$	8.41607	−	8.41607i	0.480330	−	0.480330i	0.905237	+	0.424907i	$0.139693\pi$
$308$			22.5781i			1.28651i
$309$	−22.9995	−	6.13586i	−1.30840	−	0.349057i
$310$	−2.03969	+	2.03969i	−0.115846	+	0.115846i
$311$	24.9831			1.41666			0.708330	−	0.705881i	$-0.249449\pi$
$311$	24.9831			1.41666			0.708330	+	0.705881i	$0.249449\pi$
$312$	−14.0947	+	3.08044i	−0.797957	+	0.174395i
$313$	−8.22919			−0.465141			−0.232571	−	0.972579i	$-0.574714\pi$
$313$	−8.22919			−0.465141			−0.232571	+	0.972579i	$0.574714\pi$
$314$	−9.46493	+	9.46493i	−0.534137	+	0.534137i
$315$	6.12249	−	10.6580i	0.344963	−	0.600512i
$316$			15.1317i			0.851225i
$317$	5.60105	−	5.60105i	0.314586	−	0.314586i	−0.532097	−	0.846683i	$-0.678596\pi$
$317$	5.60105	−	5.60105i	0.314586	−	0.314586i	0.846683	+	0.532097i	$0.178596\pi$
$318$	−9.01078	+	5.21547i	−0.505300	+	0.292469i
$319$	0.179165	−	0.179165i	0.0100313	−	0.0100313i
$320$	0.222747	+	0.222747i	0.0124520	+	0.0124520i
$321$	15.0802	+	4.02313i	0.841696	+	0.224549i
$322$			6.31935i			0.352163i
$323$	22.5807	+	22.5807i	1.25642	+	1.25642i
$324$	−12.3199	+	7.18464i	−0.684438	+	0.399147i
$325$	1.09825	−	3.43422i	0.0609201	−	0.190496i
$326$			1.63150i			0.0903607i
$327$	12.4550	−	7.20900i	0.688763	−	0.398658i
$328$	6.95818			0.384201
$329$	46.6559			2.57222
$330$	−1.94463	−	3.35973i	−0.107048	−	0.184947i
$331$	0.890691	+	0.890691i	0.0489568	+	0.0489568i	0.731161	−	0.682205i	$-0.238979\pi$
$331$	0.890691	+	0.890691i	0.0489568	+	0.0489568i	−0.682205	+	0.731161i	$0.738979\pi$
$332$	4.16008	+	4.16008i	0.228314	+	0.228314i
$333$	−25.9730	+	7.02014i	−1.42331	+	0.384701i
$334$	6.43600			0.352162
$335$	1.30486			0.0712922
$336$	5.97360	+	10.3206i	0.325887	+	0.563035i
$337$			0.362018i			0.0197204i	0.999951	+	0.00986020i	$0.00313865\pi$
$337$			0.362018i			0.0197204i	−0.999951	+	0.00986020i	$0.996861\pi$
$338$	8.26260	−	1.38739i	0.449426	−	0.0754639i
$339$	−1.09018	−	0.290842i	−0.0592107	−	0.0157964i
$340$	7.27061	+	7.27061i	0.394304	+	0.394304i
$341$			15.5648i			0.842881i
$342$	−8.25097	−	4.73976i	−0.446161	−	0.256297i
$343$	8.07273	+	8.07273i	0.435887	+	0.435887i
$344$	−5.77430	+	5.77430i	−0.311329	+	0.311329i
$345$	2.07649	+	3.58756i	0.111795	+	0.193148i
$346$	−10.3017	+	10.3017i	−0.553822	+	0.553822i
$347$		−	5.96761i		−	0.320358i	−0.987088	−	0.160179i	$-0.948793\pi$
$347$		−	5.96761i		−	0.320358i	0.987088	−	0.160179i	$-0.0512071\pi$
$348$	0.0515480	−	0.193221i	0.00276326	−	0.0103578i
$349$	−13.7435	+	13.7435i	−0.735673	+	0.735673i	−0.971737	−	0.236064i	$-0.924142\pi$
$349$	−13.7435	+	13.7435i	−0.735673	+	0.735673i	0.236064	+	0.971737i	$0.424142\pi$
$350$	2.64053			0.141142
$351$	16.6252	−	8.63725i	0.887388	−	0.461022i
$352$	19.8342			1.05716
$353$	13.8222	−	13.8222i	0.735682	−	0.735682i	−0.236057	−	0.971739i	$-0.575855\pi$
$353$	13.8222	−	13.8222i	0.735682	−	0.735682i	0.971739	+	0.236057i	$0.0758554\pi$
$354$	1.34714	−	5.04959i	0.0715997	−	0.268383i
$355$		−	4.19412i		−	0.222601i
$356$	11.1417	−	11.1417i	0.590511	−	0.590511i
$357$	−23.0666	−	39.8522i	−1.22081	−	2.10920i
$358$	6.53352	−	6.53352i	0.345307	−	0.345307i
$359$	−1.19127	−	1.19127i	−0.0628729	−	0.0628729i	0.674971	−	0.737844i	$-0.264156\pi$
$359$	−1.19127	−	1.19127i	−0.0628729	−	0.0628729i	−0.737844	+	0.674971i	$0.764156\pi$
$360$	−6.00971	−	3.45227i	−0.316740	−	0.181951i
$361$			5.22115i			0.274797i
$362$	−6.82372	−	6.82372i	−0.358647	−	0.358647i
$363$	−1.83002	−	0.488215i	−0.0960509	−	0.0256247i
$364$	−10.7241	−	20.8080i	−0.562097	−	1.09064i
$365$			8.35911i			0.437536i
$366$	−0.724531	−	1.25177i	−0.0378719	−	0.0654313i
$367$	23.7852			1.24158			0.620790	−	0.783977i	$-0.286812\pi$
$367$	23.7852			1.24158			0.620790	+	0.783977i	$0.286812\pi$
$368$	−4.02151			−0.209636
$369$	−8.72267	+	2.35761i	−0.454084	+	0.122732i
$370$	−4.08703	−	4.08703i	−0.212475	−	0.212475i
$371$	−27.0208	−	27.0208i	−1.40285	−	1.40285i
$372$	6.15386	+	10.6320i	0.319063	+	0.551246i
$373$	27.0932			1.40283			0.701416	−	0.712752i	$-0.252552\pi$
$373$	27.0932			1.40283			0.701416	+	0.712752i	$0.252552\pi$
$374$	−14.5426			−0.751979
$375$	1.49906	−	0.867659i	0.0774109	−	0.0448057i
$376$		−	26.3077i		−	1.35672i
$377$	−0.0800195	+	0.250219i	−0.00412121	+	0.0128869i
$378$	9.73357	+	9.67016i	0.500641	+	0.497379i
$379$	−9.55318	−	9.55318i	−0.490714	−	0.490714i	0.417817	−	0.908531i	$-0.362795\pi$
$379$	−9.55318	−	9.55318i	−0.490714	−	0.490714i	−0.908531	+	0.417817i	$0.862795\pi$
$380$			7.79882i			0.400071i
$381$	−6.11741	−	1.63201i	−0.313404	−	0.0836107i
$382$	5.95960	+	5.95960i	0.304920	+	0.304920i
$383$	−19.9744	+	19.9744i	−1.02064	+	1.02064i	−0.0208607	+	0.999782i	$0.506641\pi$
$383$	−19.9744	+	19.9744i	−1.02064	+	1.02064i	−0.999782	+	0.0208607i	$0.993359\pi$
$384$	16.7952	−	9.72115i	0.857079	−	0.496080i
$385$	10.0749	−	10.0749i	0.513465	−	0.513465i
$386$		−	7.70018i		−	0.391929i
$387$	5.28209	−	9.19506i	0.268504	−	0.467411i
$388$	−10.7358	+	10.7358i	−0.545028	+	0.545028i
$389$	−35.1328			−1.78130			−0.890651	−	0.454688i	$-0.849751\pi$
$389$	−35.1328			−1.78130			−0.890651	+	0.454688i	$0.849751\pi$
$390$	3.38798	+	2.17268i	0.171557	+	0.110018i
$391$	15.5287			0.785322
$392$	15.9870	−	15.9870i	0.807468	−	0.807468i
$393$	17.6960	+	4.72096i	0.892643	+	0.238141i
$394$			5.75720i			0.290044i
$395$	6.75214	−	6.75214i	0.339737	−	0.339737i
$396$	−15.9595	+	4.31361i	−0.801993	+	0.216767i
$397$	−13.0793	+	13.0793i	−0.656433	+	0.656433i	−0.954534	−	0.298101i	$-0.903647\pi$
$397$	−13.0793	+	13.0793i	−0.656433	+	0.656433i	0.298101	+	0.954534i	$0.403647\pi$
$398$	−10.0004	−	10.0004i	−0.501272	−	0.501272i
$399$	9.00253	−	33.7449i	0.450690	−	1.68936i
$400$			1.68038i			0.0840190i
$401$	−1.57949	−	1.57949i	−0.0788759	−	0.0788759i	0.666568	−	0.745444i	$-0.267763\pi$
$401$	−1.57949	−	1.57949i	−0.0788759	−	0.0788759i	−0.745444	+	0.666568i	$0.767763\pi$
$402$	−0.375459	+	1.40736i	−0.0187262	+	0.0701929i
$403$	−7.39296	−	14.3446i	−0.368270	−	0.714553i
$404$		−	5.01779i		−	0.249644i
$405$	8.70340	+	2.29147i	0.432475	+	0.113864i
$406$	−0.192391			−0.00954818
$407$	−31.1881			−1.54593
$408$	−22.4713	+	13.0065i	−1.11250	+	0.643917i
$409$	−9.54482	−	9.54482i	−0.471961	−	0.471961i	0.430588	−	0.902549i	$-0.358306\pi$
$409$	−9.54482	−	9.54482i	−0.471961	−	0.471961i	−0.902549	+	0.430588i	$0.858306\pi$
$410$	−1.37257	−	1.37257i	−0.0677864	−	0.0677864i
$411$	9.81229	−	5.67939i	0.484005	−	0.280144i
$412$	−21.7781			−1.07293
$413$	19.1820			0.943885
$414$	−4.46687	+	1.20733i	−0.219534	+	0.0593370i
$415$		−	3.71266i		−	0.182247i
$416$	−18.2792	+	9.42082i	−0.896212	+	0.461894i
$417$	−3.58115	+	13.4235i	−0.175370	+	0.657353i
$418$	−7.79955	−	7.79955i	−0.381488	−	0.381488i
$419$		−	36.4123i		−	1.77886i	−0.457074	−	0.889428i	$-0.651103\pi$
$419$		−	36.4123i		−	1.77886i	0.457074	−	0.889428i	$-0.348897\pi$
$420$	2.89867	−	10.8653i	0.141441	−	0.530173i
$421$	−4.66950	−	4.66950i	−0.227578	−	0.227578i	0.584102	−	0.811680i	$-0.301447\pi$
$421$	−4.66950	−	4.66950i	−0.227578	−	0.227578i	−0.811680	+	0.584102i	$0.801447\pi$
$422$	0.199869	−	0.199869i	0.00972946	−	0.00972946i
$423$	8.91374	+	32.9790i	0.433401	+	1.60349i
$424$	−15.2362	+	15.2362i	−0.739933	+	0.739933i
$425$		−	6.48865i		−	0.314746i
$426$	4.52359	+	1.20681i	0.219168	+	0.0584702i
$427$	3.75372	−	3.75372i	0.181655	−	0.181655i
$428$	14.2794			0.690218
$429$	21.2166	−	4.63694i	1.02435	−	0.223874i
$430$	2.27808			0.109859
$431$	−3.48824	+	3.48824i	−0.168023	+	0.168023i	−0.786110	−	0.618087i	$-0.787908\pi$
$431$	−3.48824	+	3.48824i	−0.168023	+	0.168023i	0.618087	+	0.786110i	$0.287908\pi$
$432$	−6.15390	+	6.19425i	−0.296080	+	0.298021i
$433$		−	0.0657330i		−	0.00315893i	−0.999999	−	0.00157946i	$-0.999497\pi$
$433$		−	0.0657330i		−	0.00315893i	0.999999	−	0.00157946i	$-0.000502759\pi$
$434$	8.35686	−	8.35686i	0.401142	−	0.401142i
$435$	−0.109222	+	0.0632182i	−0.00523680	+	0.00303108i
$436$	9.30984	−	9.30984i	0.445860	−	0.445860i
$437$	8.32845	+	8.32845i	0.398404	+	0.398404i
$438$	−9.01575	−	2.40524i	−0.430789	−	0.114927i
$439$			9.56530i			0.456527i	0.973599	+	0.228264i	$0.0733048\pi$
$439$			9.56530i			0.456527i	−0.973599	+	0.228264i	$0.926695\pi$
$440$	−5.68091	−	5.68091i	−0.270827	−	0.270827i
$441$	−14.6243	+	25.4579i	−0.696395	+	1.21228i
$442$	13.4025	−	6.90742i	0.637491	−	0.328553i
$443$			35.0176i			1.66374i	0.554973	+	0.831868i	$0.312728\pi$
$443$			35.0176i			1.66374i	−0.554973	+	0.831868i	$0.687272\pi$
$444$	−21.3040	+	12.3308i	−1.01104	+	0.585196i
$445$	−9.94343			−0.471364
$446$	−1.45535			−0.0689128
$447$	−1.42605	−	2.46378i	−0.0674497	−	0.116533i
$448$	−0.912626	−	0.912626i	−0.0431175	−	0.0431175i
$449$	23.2242	+	23.2242i	1.09602	+	1.09602i	0.994871	+	0.101149i	$0.0322517\pi$
$449$	23.2242	+	23.2242i	1.09602	+	1.09602i	0.101149	+	0.994871i	$0.467748\pi$
$450$	0.504480	+	1.86647i	0.0237814	+	0.0879863i
$451$	−10.4741			−0.493204
$452$	−1.03229			−0.0485547
$453$	6.76526	+	11.6884i	0.317860	+	0.549167i
$454$		−	11.9362i		−	0.560194i
$455$	−4.49969	+	14.0704i	−0.210949	+	0.659632i
$456$	−19.0276	−	5.07623i	−0.891051	−	0.237716i
$457$	5.85273	+	5.85273i	0.273779	+	0.273779i	0.830620	−	0.556840i	$-0.187986\pi$
$457$	5.85273	+	5.85273i	0.273779	+	0.273779i	−0.556840	+	0.830620i	$0.687986\pi$
$458$			2.35963i			0.110258i
$459$	23.7628	−	23.9186i	1.10915	−	1.11643i
$460$	2.68163	+	2.68163i	0.125031	+	0.125031i
$461$	24.2884	−	24.2884i	1.13122	−	1.13122i	0.141250	−	0.989974i	$-0.454888\pi$
$461$	24.2884	−	24.2884i	1.13122	−	1.13122i	0.989974	−	0.141250i	$-0.0451123\pi$
$462$	7.96739	+	13.7653i	0.370676	+	0.640418i
$463$	11.4811	−	11.4811i	0.533570	−	0.533570i	−0.388063	−	0.921633i	$-0.626856\pi$
$463$	11.4811	−	11.4811i	0.533570	−	0.533570i	0.921633	+	0.388063i	$0.126856\pi$
$464$		−	0.122434i		−	0.00568383i
$465$	1.99827	−	7.49028i	0.0926677	−	0.347354i
$466$	3.03780	−	3.03780i	0.140724	−	0.140724i
$467$	−21.9057			−1.01367			−0.506837	−	0.862042i	$-0.669185\pi$
$467$	−21.9057			−1.01367			−0.506837	+	0.862042i	$0.669185\pi$
$468$	12.6594	−	11.5558i	0.585181	−	0.534169i
$469$	−5.34619			−0.246864
$470$	−5.18946	+	5.18946i	−0.239372	+	0.239372i
$471$	9.27276	−	34.7578i	0.427266	−	1.60156i
$472$		−	10.8161i		−	0.497852i
$473$	8.69198	−	8.69198i	0.399658	−	0.399658i
$474$	5.33969	+	9.22539i	0.245260	+	0.423736i
$475$	3.48002	−	3.48002i	0.159674	−	0.159674i
$476$	−29.7886	−	29.7886i	−1.36536	−	1.36536i
$477$	13.9374	−	24.2622i	0.638150	−	1.11089i
$478$			1.05436i			0.0482251i
$479$	−19.9645	−	19.9645i	−0.912201	−	0.912201i	0.0842446	−	0.996445i	$-0.473152\pi$
$479$	−19.9645	−	19.9645i	−0.912201	−	0.912201i	−0.996445	+	0.0842446i	$0.973152\pi$
$480$	−9.54484	−	2.54639i	−0.435660	−	0.116226i
$481$	28.7430	−	14.8137i	1.31057	−	0.675446i
$482$		−	3.59000i		−	0.163520i
$483$	−8.50767	−	14.6987i	−0.387112	−	0.668814i
$484$	−1.73283			−0.0787649
$485$	9.58116			0.435058
$486$	−4.97578	+	8.72774i	−0.225706	+	0.395898i
$487$	12.2103	+	12.2103i	0.553302	+	0.553302i	0.927392	−	0.374091i	$-0.122045\pi$
$487$	12.2103	+	12.2103i	0.553302	+	0.553302i	−0.374091	+	0.927392i	$0.622045\pi$
$488$	−2.11660	−	2.11660i	−0.0958140	−	0.0958140i
$489$	−2.19648	−	3.79486i	−0.0993281	−	0.171609i
$490$	−6.30721			−0.284931
$491$	−23.7653			−1.07251			−0.536257	−	0.844054i	$-0.680162\pi$
$491$	−23.7653			−1.07251			−0.536257	+	0.844054i	$0.680162\pi$
$492$	−7.15464	+	4.14113i	−0.322556	+	0.186697i
$493$			0.472767i			0.0212924i
$494$	10.8927	+	3.48346i	0.490086	+	0.156728i
$495$	9.04634	+	5.19666i	0.406603	+	0.233573i
$496$	5.31814	+	5.31814i	0.238791	+	0.238791i
$497$			17.1839i			0.770802i
$498$	4.00430	+	1.06828i	0.179437	+	0.0478706i
$499$	13.6731	+	13.6731i	0.612092	+	0.612092i	0.943491	−	0.331399i	$-0.107520\pi$
$499$	13.6731	+	13.6731i	0.612092	+	0.612092i	−0.331399	+	0.943491i	$0.607520\pi$
$500$	1.12051	−	1.12051i	0.0501108	−	0.0501108i
$501$	−14.9700	+	8.66471i	−0.668812	+	0.387111i
$502$	−7.75715	+	7.75715i	−0.346219	+	0.346219i
$503$			17.6986i			0.789140i	0.918866	+	0.394570i	$0.129106\pi$
$503$			17.6986i			0.789140i	−0.918866	+	0.394570i	$0.870894\pi$
$504$	24.6226	+	14.1444i	1.09678	+	0.630042i
$505$	−2.23906	+	2.23906i	−0.0996370	+	0.0996370i
$506$	−5.36375			−0.238448
$507$	−17.3509	+	14.3509i	−0.770578	+	0.637345i
$508$	−5.79253			−0.257002
$509$	−23.6849	+	23.6849i	−1.04982	+	1.04982i	−0.0511241	+	0.998692i	$0.516280\pi$
$509$	−23.6849	+	23.6849i	−1.04982	+	1.04982i	−0.998692	+	0.0511241i	$0.983720\pi$
$510$	6.99836	+	1.86704i	0.309892	+	0.0826737i
$511$		−	34.2484i		−	1.51506i
$512$	12.2670	−	12.2670i	0.542128	−	0.542128i
$513$	25.5727	−	0.0835734i	1.12906	−	0.00368985i
$514$	7.18993	−	7.18993i	0.317134	−	0.317134i
$515$	9.71792	+	9.71792i	0.428223	+	0.428223i
$516$	2.50079	−	9.37389i	0.110091	−	0.412663i
$517$			39.6007i			1.74164i
$518$	16.7451	+	16.7451i	0.735737	+	0.735737i
$519$	10.0925	−	37.8306i	0.443013	−	1.66058i
$520$	7.93386	+	2.53723i	0.347923	+	0.111265i
$521$			12.3852i			0.542605i	0.962494	+	0.271302i	$0.0874544\pi$
$521$			12.3852i			0.542605i	−0.962494	+	0.271302i	$0.912546\pi$
$522$	−0.0367568	−	0.135992i	−0.00160880	−	0.00595222i
$523$	41.8255			1.82890			0.914450	−	0.404699i	$-0.132624\pi$
$523$	41.8255			1.82890			0.914450	+	0.404699i	$0.132624\pi$
$524$	16.7562			0.731997
$525$	−6.14183	+	3.55491i	−0.268051	+	0.155149i
$526$	2.38374	+	2.38374i	0.103936	+	0.103936i
$527$	−20.5356	−	20.5356i	−0.894543	−	0.894543i
$528$	−8.75994	+	5.07029i	−0.381228	+	0.220656i
$529$	−17.2725			−0.750979
$530$	6.01097			0.261100
$531$	3.66478	+	13.5589i	0.159038	+	0.588407i
$532$		−	31.9528i		−	1.38533i
$533$	9.65292	−	4.97496i	0.418114	−	0.215490i
$534$	2.86111	−	10.7245i	0.123812	−	0.464095i
$535$	−6.37180	−	6.37180i	−0.275477	−	0.275477i
$536$			3.01454i			0.130208i
$537$	−6.40087	+	23.9929i	−0.276218	+	1.03537i
$538$	11.2627	+	11.2627i	0.485571	+	0.485571i
$539$	−24.0651	+	24.0651i	−1.03656	+	1.03656i
$540$	8.23400	−	0.0269093i	0.354335	−	0.00115799i
$541$	−22.6303	+	22.6303i	−0.972954	+	0.972954i	−0.999644	−	0.0266894i	$-0.991504\pi$
$541$	−22.6303	+	22.6303i	−0.972954	+	0.972954i	0.0266894	+	0.999644i	$0.491504\pi$
$542$			12.2046i			0.524230i
$543$	25.0586	+	6.68517i	1.07537	+	0.286888i
$544$	−26.1684	+	26.1684i	−1.12196	+	1.12196i
$545$	−8.30856			−0.355900
$546$	−13.8810	−	8.90176i	−0.594051	−	0.380960i
$547$	−38.6695			−1.65339			−0.826694	−	0.562652i	$-0.809781\pi$
$547$	−38.6695			−1.65339			−0.826694	+	0.562652i	$0.809781\pi$
$548$	7.33448	−	7.33448i	0.313313	−	0.313313i
$549$	3.37050	+	1.93618i	0.143849	+	0.0826341i
$550$			2.24123i			0.0955665i
$551$	−0.253557	+	0.253557i	−0.0108019	+	0.0108019i
$552$	−8.28812	+	4.79720i	−0.352766	+	0.204182i
$553$	−27.6644	+	27.6644i	−1.17641	+	1.17641i
$554$	2.31455	+	2.31455i	0.0983358	+	0.0983358i
$555$	15.0087	+	4.00405i	0.637084	+	0.169962i
$556$			12.7106i			0.539051i
$557$	−7.82191	−	7.82191i	−0.331425	−	0.331425i	0.521702	−	0.853128i	$-0.325297\pi$
$557$	−7.82191	−	7.82191i	−0.331425	−	0.331425i	−0.853128	+	0.521702i	$0.825297\pi$
$558$	7.50369	+	4.31049i	0.317657	+	0.182477i
$559$	−3.88204	+	12.1391i	−0.164193	+	0.513428i
$560$		−	6.88473i		−	0.290933i
$561$	33.8258	−	19.5785i	1.42813	−	0.826605i
$562$	−1.72797			−0.0728899
$563$	−37.4306			−1.57751			−0.788755	−	0.614708i	$-0.789274\pi$
$563$	−37.4306			−1.57751			−0.788755	+	0.614708i	$0.789274\pi$
$564$	15.6569	+	27.0505i	0.659276	+	1.13903i
$565$	0.460632	+	0.460632i	0.0193789	+	0.0193789i
$566$	−5.75652	−	5.75652i	−0.241965	−	0.241965i
$567$	−35.6590	−	9.38845i	−1.49754	−	0.394278i
$568$	9.68942			0.406559
$569$	2.32113			0.0973066			0.0486533	−	0.998816i	$-0.484507\pi$
$569$	2.32113			0.0973066			0.0486533	+	0.998816i	$0.484507\pi$
$570$	2.75206	+	4.75473i	0.115271	+	0.199154i
$571$			12.7963i			0.535507i	0.963487	+	0.267753i	$0.0862812\pi$
$571$			12.7963i			0.535507i	−0.963487	+	0.267753i	$0.913719\pi$
$572$	17.6615	−	9.10246i	0.738464	−	0.380593i
$573$	−21.8853	−	5.83860i	−0.914271	−	0.243911i
$574$	5.62360	+	5.62360i	0.234725	+	0.234725i
$575$		−	2.39321i		−	0.0998039i
$576$	0.470735	−	0.819454i	0.0196139	−	0.0341439i
$577$	−0.396526	−	0.396526i	−0.0165076	−	0.0165076i	0.698805	−	0.715312i	$-0.253716\pi$
$577$	−0.396526	−	0.396526i	−0.0165076	−	0.0165076i	−0.715312	+	0.698805i	$0.753716\pi$
$578$	11.4397	−	11.4397i	0.475828	−	0.475828i
$579$	10.3667	+	17.9105i	0.430824	+	0.744336i
$580$	−0.0816412	+	0.0816412i	−0.00338997	+	0.00338997i
$581$			15.2113i			0.631069i
$582$	−2.75687	+	10.3338i	−0.114276	+	0.428349i
$583$	22.9348	−	22.9348i	0.949863	−	0.949863i
$584$	−19.3115			−0.799117
$585$	−10.8054	−	0.492431i	−0.446750	−	0.0203595i
$586$	−17.9607			−0.741949
$587$	−4.38510	+	4.38510i	−0.180992	+	0.180992i	−0.791788	−	0.610796i	$-0.790850\pi$
$587$	−4.38510	+	4.38510i	−0.180992	+	0.180992i	0.610796	+	0.791788i	$0.290850\pi$
$588$	−6.92381	+	25.9531i	−0.285533	+	1.07029i
$589$		−	22.0275i		−	0.907626i
$590$	−2.13359	+	2.13359i	−0.0878384	+	0.0878384i
$591$	−7.75086	−	13.3912i	−0.318828	−	0.550839i
$592$	−10.6562	+	10.6562i	−0.437969	+	0.437969i
$593$	−4.95766	−	4.95766i	−0.203587	−	0.203587i	0.597948	−	0.801535i	$-0.295983\pi$
$593$	−4.95766	−	4.95766i	−0.203587	−	0.203587i	−0.801535	+	0.597948i	$0.795983\pi$
$594$	−8.20786	+	8.26168i	−0.336773	+	0.338981i
$595$			26.5848i			1.08987i
$596$	−1.84162	−	1.84162i	−0.0754359	−	0.0754359i
$597$	36.7240	+	9.79731i	1.50302	+	0.400977i
$598$	4.94325	−	2.54767i	0.202144	−	0.104182i
$599$		−	5.16408i		−	0.210998i	−0.994419	−	0.105499i	$-0.966356\pi$
$599$		−	5.16408i		−	0.210998i	0.994419	−	0.105499i	$-0.0336441\pi$
$600$	2.00450	+	3.46318i	0.0818333	+	0.141384i
$601$	28.3815			1.15770			0.578852	−	0.815432i	$-0.303501\pi$
$601$	28.3815			1.15770			0.578852	+	0.815432i	$0.303501\pi$
$602$	−9.33358			−0.380408
$603$	−1.02140	−	3.77898i	−0.0415948	−	0.153892i
$604$	8.73679	+	8.73679i	0.355495	+	0.355495i
$605$	0.773230	+	0.773230i	0.0314363	+	0.0314363i
$606$	−1.77068	−	3.05921i	−0.0719291	−	0.124272i
$607$	−35.8341			−1.45446			−0.727230	−	0.686394i	$-0.759192\pi$
$607$	−35.8341			−1.45446			−0.727230	+	0.686394i	$0.759192\pi$
$608$	−28.0695			−1.13837
$609$	0.447498	−	0.259013i	0.0181335	−	0.0104957i
$610$			0.835042i			0.0338099i
$611$	−18.8095	−	36.4961i	−0.760951	−	1.47647i
$612$	15.3651	−	26.7475i	0.621095	−	1.08120i
$613$	5.88345	+	5.88345i	0.237630	+	0.237630i	0.815868	−	0.578238i	$-0.196259\pi$
$613$	5.88345	+	5.88345i	0.237630	+	0.237630i	−0.578238	+	0.815868i	$0.696259\pi$
$614$		−	7.67070i		−	0.309564i
$615$	5.04046	+	1.34470i	0.203251	+	0.0542236i
$616$	23.2754	+	23.2754i	0.937794	+	0.937794i
$617$	−30.1305	+	30.1305i	−1.21301	+	1.21301i	−0.242977	+	0.970032i	$0.578124\pi$
$617$	−30.1305	+	30.1305i	−1.21301	+	1.21301i	−0.970032	+	0.242977i	$0.921876\pi$
$618$	−13.2775	+	7.68508i	−0.534100	+	0.309139i
$619$	−8.02687	+	8.02687i	−0.322627	+	0.322627i	−0.849774	−	0.527147i	$-0.823262\pi$
$619$	−8.02687	+	8.02687i	−0.322627	+	0.322627i	0.527147	+	0.849774i	$0.323262\pi$
$620$		−	7.09249i		−	0.284841i
$621$	8.76445	−	8.82192i	0.351705	−	0.354012i
$622$	11.3852	−	11.3852i	0.456506	−	0.456506i
$623$	40.7395			1.63219
$624$	5.66490	−	8.83358i	0.226778	−	0.353626i
$625$	−1.00000			−0.0400000
$626$	−3.75019	+	3.75019i	−0.149888	+	0.149888i
$627$	28.6421	+	7.64119i	1.14385	+	0.305160i
$628$		−	32.9119i		−	1.31333i
$629$	41.1483	−	41.1483i	1.64069	−	1.64069i
$630$	−2.06692	−	7.64717i	−0.0823481	−	0.304671i
$631$	−14.4365	+	14.4365i	−0.574709	+	0.574709i	−0.933441	−	0.358732i	$-0.883209\pi$
$631$	−14.4365	+	14.4365i	−0.574709	+	0.574709i	0.358732	+	0.933441i	$0.383209\pi$
$632$	15.5990	+	15.5990i	0.620497	+	0.620497i
$633$	−0.195811	+	0.733973i	−0.00778278	+	0.0291728i
$634$		−	5.10500i		−	0.202745i
$635$	2.58477	+	2.58477i	0.102573	+	0.102573i
$636$	6.59861	−	24.7341i	0.261652	−	0.980771i
$637$	10.7480	−	33.6089i	0.425853	−	1.33163i
$638$		−	0.163298i		−	0.00646502i
$639$	−12.1465	+	3.28303i	−0.480508	+	0.129875i
$640$	−11.2039			−0.442872
$641$	13.1832			0.520706			0.260353	−	0.965513i	$-0.416161\pi$
$641$	13.1832			0.520706			0.260353	+	0.965513i	$0.416161\pi$
$642$	8.70574	−	5.03891i	0.343588	−	0.198870i
$643$	−26.1092	−	26.1092i	−1.02964	−	1.02964i	−0.999547	−	0.0300976i	$-0.990418\pi$
$643$	−26.1092	−	26.1092i	−1.02964	−	1.02964i	−0.0300976	−	0.999547i	$-0.509582\pi$
$644$	−10.9870	−	10.9870i	−0.432947	−	0.432947i
$645$	−5.29877	+	3.06695i	−0.208639	+	0.120761i
$646$	20.5808			0.809741
$647$	24.4734			0.962150			0.481075	−	0.876679i	$-0.340246\pi$
$647$	24.4734			0.962150			0.481075	+	0.876679i	$0.340246\pi$
$648$	−5.29384	+	20.1069i	−0.207962	+	0.789875i
$649$			16.2814i			0.639099i
$650$	−1.06454	−	2.06553i	−0.0417547	−	0.0810166i
$651$	−8.18718	+	30.6887i	−0.320881	+	1.20278i
$652$	−2.83657	−	2.83657i	−0.111089	−	0.111089i
$653$			27.4272i			1.07331i	0.843802	+	0.536655i	$0.180312\pi$
$653$			27.4272i			1.07331i	−0.843802	+	0.536655i	$0.819688\pi$
$654$	2.39069	−	8.96123i	0.0934835	−	0.350412i
$655$	−7.47702	−	7.47702i	−0.292151	−	0.292151i
$656$	−3.57875	+	3.57875i	−0.139727	+	0.139727i
$657$	24.2087	−	6.54325i	0.944470	−	0.255277i
$658$	21.2619	−	21.2619i	0.828875	−	0.828875i
$659$		−	28.8992i		−	1.12575i	−0.826541	−	0.562877i	$-0.809695\pi$
$659$		−	28.8992i		−	1.12575i	0.826541	−	0.562877i	$-0.190305\pi$
$660$	9.22229	+	2.46034i	0.358977	+	0.0957686i
$661$	2.27091	−	2.27091i	0.0883282	−	0.0883282i	−0.661562	−	0.749890i	$-0.730106\pi$
$661$	2.27091	−	2.27091i	0.0883282	−	0.0883282i	0.749890	+	0.661562i	$0.230106\pi$
$662$	0.811807			0.0315518
$663$	−21.8746	+	34.1102i	−0.849538	+	1.32473i
$664$	8.57713			0.332857
$665$	−14.2581	+	14.2581i	−0.552906	+	0.552906i
$666$	−8.63716	+	15.0356i	−0.334683	+	0.582616i
$667$			0.174371i			0.00675168i
$668$	−11.1898	+	11.1898i	−0.432946	+	0.432946i
$669$	3.38512	−	1.95932i	0.130876	−	0.0757517i
$670$	0.594648	−	0.594648i	0.0229733	−	0.0229733i
$671$	3.18609	+	3.18609i	0.122998	+	0.122998i
$672$	39.1064	+	10.4329i	1.50856	+	0.402458i
$673$			35.6852i			1.37556i	0.725918	+	0.687782i	$0.241415\pi$
$673$			35.6852i			1.37556i	−0.725918	+	0.687782i	$0.758585\pi$
$674$	0.164978	+	0.164978i	0.00635472	+	0.00635472i
$675$	−3.68622	−	3.66221i	−0.141883	−	0.140958i
$676$	−11.9534	+	16.7777i	−0.459746	+	0.645296i
$677$			2.22785i			0.0856231i	0.999083	+	0.0428116i	$0.0136315\pi$
$677$			2.22785i			0.0856231i	−0.999083	+	0.0428116i	$0.986368\pi$
$678$	−0.629358	+	0.364275i	−0.0241704	+	0.0139899i
$679$	−39.2552			−1.50648
$680$	14.9903			0.574853
$681$	16.0696	+	27.7635i	0.615788	+	1.06390i
$682$	7.09315	+	7.09315i	0.271611	+	0.271611i
$683$	−5.68940	−	5.68940i	−0.217699	−	0.217699i	0.589829	−	0.807528i	$-0.299195\pi$
$683$	−5.68940	−	5.68940i	−0.217699	−	0.217699i	−0.807528	+	0.589829i	$0.799195\pi$
$684$	22.5860	−	6.10467i	0.863597	−	0.233418i
$685$	−6.54565			−0.250096
$686$	7.35777			0.280921
$687$	−3.17674	−	5.48847i	−0.121200	−	0.209398i
$688$		−	5.93971i		−	0.226449i
$689$	−10.2432	+	32.0303i	−0.390236	+	1.22026i
$690$	2.58121	+	0.688620i	0.0982650	+	0.0262153i
$691$	10.3521	+	10.3521i	0.393813	+	0.393813i	0.876044	−	0.482231i	$-0.160174\pi$
$691$	10.3521	+	10.3521i	0.393813	+	0.393813i	−0.482231	+	0.876044i	$0.660174\pi$
$692$		−	35.8215i		−	1.36173i
$693$	−37.0640	−	21.2914i	−1.40795	−	0.808794i
$694$	−2.71954	−	2.71954i	−0.103232	−	0.103232i
$695$	5.67179	−	5.67179i	0.215143	−	0.215143i
$696$	−0.146049	−	0.252329i	−0.00553598	−	0.00956451i
$697$	13.8191	−	13.8191i	0.523434	−	0.523434i
$698$			12.5263i			0.474128i
$699$	−2.97613	+	11.1557i	−0.112567	+	0.421946i
$700$	−4.59088	+	4.59088i	−0.173519	+	0.173519i
$701$	12.8424			0.485052			0.242526	−	0.970145i	$-0.422024\pi$
$701$	12.8424			0.485052			0.242526	+	0.970145i	$0.422024\pi$
$702$	3.64026	−	11.5126i	0.137393	−	0.434513i
$703$	44.1377			1.66468
$704$	0.774621	−	0.774621i	0.0291946	−	0.0291946i
$705$	5.08410	−	19.0571i	0.191478	−	0.717733i
$706$		−	12.5980i		−	0.474134i
$707$	9.17373	−	9.17373i	0.345014	−	0.345014i
$708$	6.43717	+	11.1215i	0.241924	+	0.417972i
$709$	−4.43471	+	4.43471i	−0.166549	+	0.166549i	−0.785461	−	0.618912i	$-0.787574\pi$
$709$	−4.43471	+	4.43471i	−0.166549	+	0.166549i	0.618912	+	0.785461i	$0.287574\pi$
$710$	−1.91134	−	1.91134i	−0.0717311	−	0.0717311i
$711$	−24.8401	−	14.2694i	−0.931576	−	0.535143i
$712$		−	22.9717i		−	0.860900i
$713$	−7.57415	−	7.57415i	−0.283654	−	0.283654i
$714$	−28.6732	−	7.64949i	−1.07307	−	0.286275i
$715$	−11.9427	−	3.81926i	−0.446633	−	0.142832i
$716$			22.7187i			0.849036i
$717$	−1.41947	−	2.45242i	−0.0530110	−	0.0915872i
$718$	−1.08577			−0.0405204
$719$	−47.3354			−1.76531			−0.882656	−	0.470019i	$-0.844247\pi$
$719$	−47.3354			−1.76531			−0.882656	+	0.470019i	$0.844247\pi$
$720$	4.86651	−	1.31535i	0.181364	−	0.0490201i
$721$	−39.8156	−	39.8156i	−1.48281	−	1.48281i
$722$	2.37937	+	2.37937i	0.0885509	+	0.0885509i
$723$	4.83317	+	8.35028i	0.179748	+	0.310550i
$724$	23.7278			0.881835
$725$	0.0728607			0.00270598
$726$	−1.05646	+	0.611482i	−0.0392089	+	0.0226942i
$727$		−	12.6597i		−	0.469523i	−0.972053	−	0.234762i	$-0.924569\pi$
$727$		−	12.6597i		−	0.469523i	0.972053	−	0.234762i	$-0.0754310\pi$
$728$	−32.5060	−	10.3953i	−1.20475	−	0.385277i
$729$	−0.176474	−	26.9994i	−0.00653606	−	0.999979i
$730$	3.80940	+	3.80940i	0.140992	+	0.140992i
$731$			22.9357i			0.848308i
$732$	3.43605	+	0.916677i	0.127000	+	0.0338813i
$733$	−34.2421	−	34.2421i	−1.26476	−	1.26476i	−0.948758	−	0.316003i	$-0.897659\pi$
$733$	−34.2421	−	34.2421i	−1.26476	−	1.26476i	−0.316003	−	0.948758i	$-0.602341\pi$
$734$	10.8394	−	10.8394i	0.400088	−	0.400088i
$735$	14.6705	−	8.49133i	0.541129	−	0.313207i
$736$	−9.65171	+	9.65171i	−0.355767	+	0.355767i
$737$		−	4.53775i		−	0.167150i
$738$	−2.90067	+	5.04948i	−0.106775	+	0.185874i
$739$	0.527783	−	0.527783i	0.0194148	−	0.0194148i	−0.697333	−	0.716748i	$-0.745630\pi$
$739$	0.527783	−	0.527783i	0.0194148	−	0.0194148i	0.716748	+	0.697333i	$0.245630\pi$
$740$	14.2116			0.522429
$741$	−30.0260	+	6.56225i	−1.10303	+	0.241070i
$742$	−24.6277			−0.904113
$743$	15.9143	−	15.9143i	0.583840	−	0.583840i	−0.352116	−	0.935956i	$-0.614538\pi$
$743$	15.9143	−	15.9143i	0.583840	−	0.583840i	0.935956	+	0.352116i	$0.114538\pi$
$744$	17.3043	+	4.61648i	0.634408	+	0.169249i
$745$			1.64356i			0.0602152i
$746$	12.3468	−	12.3468i	0.452050	−	0.452050i
$747$	−10.7522	+	2.90616i	−0.393401	+	0.106331i
$748$	25.2841	−	25.2841i	0.924477	−	0.924477i
$749$	26.1061	+	26.1061i	0.953896	+	0.953896i
$750$	0.287739	−	1.07855i	0.0105067	−	0.0393832i
$751$		−	44.2811i		−	1.61584i	−0.589292	−	0.807920i	$-0.700593\pi$
$751$		−	44.2811i		−	1.61584i	0.589292	−	0.807920i	$-0.299407\pi$
$752$	13.5307	+	13.5307i	0.493412	+	0.493412i
$753$	7.59966	−	28.4864i	0.276947	−	1.03810i
$754$	0.0775630	+	0.150496i	0.00282468	+	0.00548073i
$755$		−	7.79715i		−	0.283767i
$756$	−33.7358	+	0.110251i	−1.22696	+	0.00400978i
$757$	22.8856			0.831790			0.415895	−	0.909413i	$-0.363468\pi$
$757$	22.8856			0.831790			0.415895	+	0.909413i	$0.363468\pi$
$758$	−8.70710			−0.316256
$759$	12.4760	−	7.22116i	0.452850	−	0.262111i
$760$	8.03969	+	8.03969i	0.291630	+	0.291630i
$761$	7.52971	+	7.52971i	0.272952	+	0.272952i	0.830287	−	0.557336i	$-0.188176\pi$
$761$	7.52971	+	7.52971i	0.272952	+	0.272952i	−0.557336	+	0.830287i	$0.688176\pi$
$762$	−3.53155	+	2.04407i	−0.127935	+	0.0740490i
$763$	34.0413			1.23238
$764$	−20.7230			−0.749732
$765$	−18.7916	+	5.07911i	−0.679413	+	0.183636i
$766$			18.2054i			0.657786i
$767$	−7.73331	−	15.0049i	−0.279234	−	0.541797i
$768$	3.50507	−	13.1383i	0.126478	−	0.474089i
$769$	36.8433	+	36.8433i	1.32860	+	1.32860i	0.906589	+	0.422015i	$0.138677\pi$
$769$	36.8433	+	36.8433i	1.32860	+	1.32860i	0.422015	+	0.906589i	$0.361323\pi$
$770$		−	9.18262i		−	0.330919i
$771$	−7.04394	+	26.4034i	−0.253681	+	0.950894i
$772$	13.3877	+	13.3877i	0.481835	+	0.481835i
$773$	−10.1075	+	10.1075i	−0.363542	+	0.363542i	−0.865115	−	0.501573i	$-0.832755\pi$
$773$	−10.1075	+	10.1075i	−0.363542	+	0.363542i	0.501573	+	0.865115i	$0.332755\pi$
$774$	−1.78321	−	6.59749i	−0.0640961	−	0.237142i
$775$	−3.16484	+	3.16484i	−0.113685	+	0.113685i
$776$			22.1347i			0.794591i
$777$	−61.4926	−	16.4051i	−2.20603	−	0.588530i
$778$	−16.0106	+	16.0106i	−0.574008	+	0.574008i
$779$	14.8230			0.531089
$780$	−9.66789	+	2.11294i	−0.346166	+	0.0756554i
$781$	−14.5854			−0.521905
$782$	7.07672	−	7.07672i	0.253063	−	0.253063i
$783$	0.268581	+	0.266831i	0.00959829	+	0.00953576i
$784$			16.4450i			0.587321i
$785$	−14.6861	+	14.6861i	−0.524170	+	0.524170i
$786$	10.2158	−	5.91294i	0.364385	−	0.210907i
$787$	20.3419	−	20.3419i	0.725112	−	0.725112i	−0.244530	−	0.969642i	$-0.578634\pi$
$787$	20.3419	−	20.3419i	0.725112	−	0.725112i	0.969642	+	0.244530i	$0.0786336\pi$
$788$	−10.0096	−	10.0096i	−0.356577	−	0.356577i
$789$	−8.75375	−	2.33534i	−0.311642	−	0.0831404i
$790$		−	6.15414i		−	0.218954i
$791$	−1.88727	−	1.88727i	−0.0671036	−	0.0671036i
$792$	−12.0055	+	20.8992i	−0.426598	+	0.742621i
$793$	−4.44964	−	1.42298i	−0.158011	−	0.0505316i
$794$			11.9210i			0.423059i
$795$	−13.9814	+	8.09250i	−0.495870	+	0.287012i
$796$	34.7737			1.23252
$797$	22.8088			0.807930			0.403965	−	0.914774i	$-0.367632\pi$
$797$	22.8088			0.807930			0.403965	+	0.914774i	$0.367632\pi$
$798$	−11.2755	−	19.4808i	−0.399149	−	0.689611i
$799$	−52.2475	−	52.2475i	−1.84838	−	1.84838i
$800$	4.03295	+	4.03295i	0.142586	+	0.142586i
$801$	7.78341	+	28.7970i	0.275013	+	1.01749i
$802$	−1.43960			−0.0508341
$803$	29.0694			1.02584
$804$	−1.79409	−	3.09966i	−0.0632728	−	0.109316i
$805$			9.80531i			0.345592i
$806$	−9.90617	−	3.16797i	−0.348930	−	0.111587i
$807$	−41.3599	−	11.0341i	−1.45594	−	0.388418i
$808$	−5.17277	−	5.17277i	−0.181977	−	0.181977i
$809$		−	2.21292i		−	0.0778020i	−0.999243	−	0.0389010i	$-0.987614\pi$
$809$		−	2.21292i		−	0.0778020i	0.999243	−	0.0389010i	$-0.0123857\pi$
$810$	5.01056	−	2.92203i	0.176053	−	0.102670i
$811$	−10.2655	−	10.2655i	−0.360469	−	0.360469i	0.503517	−	0.863985i	$-0.332039\pi$
$811$	−10.2655	−	10.2655i	−0.360469	−	0.360469i	−0.863985	+	0.503517i	$0.832039\pi$
$812$	0.334495	−	0.334495i	0.0117385	−	0.0117385i
$813$	−16.4309	−	28.3876i	−0.576255	−	0.995597i
$814$	−14.2129	+	14.2129i	−0.498163	+	0.498163i
$815$			2.53150i			0.0886745i
$816$	4.86798	−	18.2470i	0.170413	−	0.638774i
$817$	−12.3010	+	12.3010i	−0.430357	+	0.430357i
$818$	−8.69948			−0.304170
$819$	44.2713	+	2.01756i	1.54696	+	0.0704991i
$820$	4.77277			0.166672
$821$	−0.236912	+	0.236912i	−0.00826830	+	0.00826830i	−0.711229	−	0.702961i	$-0.751861\pi$
$821$	−0.236912	+	0.236912i	−0.00826830	+	0.00826830i	0.702961	+	0.711229i	$0.251861\pi$
$822$	1.88344	−	7.05983i	0.0656924	−	0.246240i
$823$			9.65610i			0.336591i	0.985737	+	0.168295i	$0.0538262\pi$
$823$			9.65610i			0.336591i	−0.985737	+	0.168295i	$0.946174\pi$
$824$	−22.4507	+	22.4507i	−0.782107	+	0.782107i
$825$	−3.01735	−	5.21308i	−0.105051	−	0.181496i
$826$	8.74158	−	8.74158i	0.304159	−	0.304159i
$827$	−6.76442	−	6.76442i	−0.235222	−	0.235222i	0.579646	−	0.814868i	$-0.303191\pi$
$827$	−6.76442	−	6.76442i	−0.235222	−	0.235222i	−0.814868	+	0.579646i	$0.803191\pi$
$828$	5.66711	−	9.86529i	0.196946	−	0.342843i
$829$		−	10.8499i		−	0.376834i	−0.982089	−	0.188417i	$-0.939664\pi$
$829$		−	10.8499i		−	0.376834i	0.982089	−	0.188417i	$-0.0603356\pi$
$830$	−1.69193	−	1.69193i	−0.0587276	−	0.0587276i
$831$	−8.49966	−	2.26756i	−0.294850	−	0.0786607i
$832$	−0.345964	+	1.08182i	−0.0119941	+	0.0375054i
$833$		−	63.5010i		−	2.20018i
$834$	4.48534	+	7.74933i	0.155315	+	0.268337i
$835$	9.98631			0.345591
$836$	27.1210			0.937998
$837$	−23.2566	+	0.0760042i	−0.803867	+	0.00262709i
$838$	−16.5937	−	16.5937i	−0.573221	−	0.573221i
$839$	34.4849	+	34.4849i	1.19055	+	1.19055i	0.976912	+	0.213640i	$0.0685319\pi$
$839$	34.4849	+	34.4849i	1.19055	+	1.19055i	0.213640	+	0.976912i	$0.431468\pi$
$840$	−8.21269	−	14.1891i	−0.283365	−	0.489570i
$841$	28.9947			0.999817
$842$	−4.25595			−0.146670
$843$	4.01923	−	2.32634i	0.138430	−	0.0801235i
$844$			0.694993i			0.0239227i
$845$	12.8205	−	2.15272i	0.441039	−	0.0740557i
$846$	19.0912	+	10.9669i	0.656370	+	0.377051i
$847$	−3.16803	−	3.16803i	−0.108855	−	0.108855i
$848$		−	15.6726i		−	0.538199i
$849$	21.1395	+	5.63964i	0.725506	+	0.193552i
$850$	−2.95699	−	2.95699i	−0.101424	−	0.101424i
$851$	15.1767	−	15.1767i	0.520252	−	0.520252i
$852$	−9.96300	+	5.76662i	−0.341327	+	0.197561i
$853$	−30.7565	+	30.7565i	−1.05308	+	1.05308i	−0.0545730	+	0.998510i	$0.517380\pi$
$853$	−30.7565	+	30.7565i	−1.05308	+	1.05308i	−0.998510	+	0.0545730i	$0.982620\pi$
$854$		−	3.42128i		−	0.117074i
$855$	−12.8025	−	7.35437i	−0.437836	−	0.251514i
$856$	14.7204	−	14.7204i	0.503132	−	0.503132i
$857$	38.8679			1.32770			0.663852	−	0.747864i	$-0.268921\pi$
$857$	38.8679			1.32770			0.663852	+	0.747864i	$0.268921\pi$
$858$	7.55566	−	11.7819i	0.257946	−	0.402229i
$859$	−3.20072			−0.109207			−0.0546036	−	0.998508i	$-0.517390\pi$
$859$	−3.20072			−0.109207			−0.0546036	+	0.998508i	$0.517390\pi$
$860$	−3.96072	+	3.96072i	−0.135059	+	0.135059i
$861$	−20.6514	−	5.50942i	−0.703798	−	0.187761i
$862$			3.17930i			0.108288i
$863$	−24.0668	+	24.0668i	−0.819244	+	0.819244i	−0.985998	−	0.166755i	$-0.946671\pi$
$863$	−24.0668	+	24.0668i	−0.819244	+	0.819244i	0.166755	+	0.985998i	$0.446671\pi$
$864$	0.0968519	+	29.6358i	0.00329497	+	1.00823i
$865$	−15.9844	+	15.9844i	−0.543488	+	0.543488i
$866$	−0.0299557	−	0.0299557i	−0.00101794	−	0.00101794i
$867$	−11.2074	+	42.0097i	−0.380624	+	1.42672i
$868$			29.0589i			0.986322i
$869$	−23.4811	−	23.4811i	−0.796540	−	0.796540i
$870$	−0.0209648	+	0.0785841i	−0.000710774	+	0.00266425i
$871$	2.15534	+	4.18200i	0.0730308	+	0.141702i
$872$		−	19.1948i		−	0.650016i
$873$	−7.49983	−	27.7478i	−0.253831	−	0.939120i
$874$	7.59084			0.256764
$875$	4.09713			0.138508
$876$	19.8568	−	11.4932i	0.670899	−	0.388319i
$877$	34.6511	+	34.6511i	1.17008	+	1.17008i	0.982189	+	0.187895i	$0.0601664\pi$
$877$	34.6511	+	34.6511i	1.17008	+	1.17008i	0.187895	+	0.982189i	$0.439834\pi$
$878$	4.35908	+	4.35908i	0.147112	+	0.147112i
$879$	41.7763	−	24.1803i	1.40908	−	0.815580i
$880$	5.84364			0.196989
$881$	5.44243			0.183360			0.0916800	−	0.995789i	$-0.470776\pi$
$881$	5.44243			0.183360			0.0916800	+	0.995789i	$0.470776\pi$
$882$	4.93709	+	18.2662i	0.166240	+	0.615054i
$883$		−	2.38247i		−	0.0801763i	−0.999196	−	0.0400882i	$-0.987236\pi$
$883$		−	2.38247i		−	0.0801763i	0.999196	−	0.0400882i	$-0.0127639\pi$
$884$	−11.2925	+	35.3113i	−0.379806	+	1.18765i
$885$	2.09027	−	7.83512i	0.0702636	−	0.263375i
$886$	15.9581	+	15.9581i	0.536124	+	0.536124i
$887$			36.3502i			1.22052i	0.792201	+	0.610260i	$0.208935\pi$
$887$			36.3502i			1.22052i	−0.792201	+	0.610260i	$0.791065\pi$
$888$	−9.25031	+	34.6737i	−0.310420	+	1.16357i
$889$	−10.5901	−	10.5901i	−0.355182	−	0.355182i
$890$	−4.53140	+	4.53140i	−0.151893	+	0.151893i
$891$	7.96875	−	30.2667i	0.266963	−	1.01397i
$892$	2.53030	−	2.53030i	0.0847209	−	0.0847209i
$893$		−	56.0433i		−	1.87542i
$894$	−1.77266	−	0.472915i	−0.0592867	−	0.0158166i
$895$	10.1376	−	10.1376i	0.338864	−	0.338864i
$896$	45.9038			1.53354
$897$	−8.06802	+	12.5809i	−0.269383	+	0.420063i
$898$	21.1674			0.706365
$899$	0.230593	−	0.230593i	0.00769070	−	0.00769070i
$900$	−4.12219	−	2.36799i	−0.137406	−	0.0789330i
$901$			60.5185i			2.01616i
$902$	−4.77321	+	4.77321i	−0.158931	+	0.158931i
$903$	21.7098	−	12.5657i	0.722456	−	0.418160i
$904$	−1.06417	+	1.06417i	−0.0353938	+	0.0353938i
$905$	−10.5879	−	10.5879i	−0.351954	−	0.351954i
$906$	8.40964	+	2.24354i	0.279392	+	0.0745366i
$907$			17.6809i			0.587085i	0.955946	+	0.293542i	$0.0948342\pi$
$907$			17.6809i			0.587085i	−0.955946	+	0.293542i	$0.905166\pi$
$908$	20.7526	+	20.7526i	0.688699	+	0.688699i
$909$	8.23717	+	4.73183i	0.273210	+	0.156945i
$910$	4.36156	+	8.46273i	0.144584	+	0.280537i
$911$		−	5.92923i		−	0.196444i	−0.995165	−	0.0982220i	$-0.968684\pi$
$911$		−	5.92923i		−	0.196444i	0.995165	−	0.0982220i	$-0.0313155\pi$
$912$	12.3972	−	7.17552i	0.410511	−	0.237605i
$913$	−12.9111			−0.427293
$914$	5.33439			0.176446
$915$	−1.12421	−	1.94229i	−0.0371651	−	0.0642103i
$916$	−4.10251	−	4.10251i	−0.135551	−	0.135551i
$917$	30.6343	+	30.6343i	1.01163	+	1.01163i
$918$	−0.0710126	−	21.7292i	−0.00234377	−	0.717172i
$919$	−22.9927			−0.758459			−0.379230	−	0.925303i	$-0.623811\pi$
$919$	−22.9927			−0.758459			−0.379230	+	0.925303i	$0.623811\pi$
$920$	5.52890			0.182282
$921$	10.3270	+	17.8419i	0.340286	+	0.587912i
$922$		−	22.1373i		−	0.729054i
$923$	13.4419	−	6.92775i	0.442446	−	0.228030i
$924$	−37.7849	−	10.0803i	−1.24303	−	0.331619i
$925$	−6.34157	−	6.34157i	−0.208510	−	0.208510i
$926$		−	10.4642i		−	0.343876i
$927$	20.5370	−	35.7507i	0.674523	−	1.17421i
$928$	−0.293843	−	0.293843i	−0.00964588	−	0.00964588i
$929$	31.4998	−	31.4998i	1.03348	−	1.03348i	0.0340553	−	0.999420i	$-0.489158\pi$
$929$	31.4998	−	31.4998i	1.03348	−	1.03348i	0.999420	−	0.0340553i	$-0.0108422\pi$
$930$	−2.50281	−	4.32410i	−0.0820702	−	0.141793i
$931$	34.0572	−	34.0572i	1.11618	−	1.11618i
$932$			10.5632i			0.346009i
$933$	−11.1541	+	41.8097i	−0.365168	+	1.36879i
$934$	−9.98280	+	9.98280i	−0.326647	+	0.326647i
$935$	−22.5648			−0.737946
$936$	1.13763	−	24.9631i	0.0371847	−	0.815946i
$937$	40.0311			1.30776			0.653879	−	0.756599i	$-0.273141\pi$
$937$	40.0311			1.30776			0.653879	+	0.756599i	$0.273141\pi$
$938$	−2.43635	+	2.43635i	−0.0795497	+	0.0795497i
$939$	3.67405	−	13.7717i	0.119898	−	0.449423i
$940$		−	18.0450i		−	0.588564i
$941$	−41.8084	+	41.8084i	−1.36292	+	1.36292i	−0.492738	+	0.870178i	$0.664004\pi$
$941$	−41.8084	+	41.8084i	−1.36292	+	1.36292i	−0.870178	+	0.492738i	$0.835996\pi$
$942$	−11.6140	−	20.0655i	−0.378404	−	0.653770i
$943$	5.09689	−	5.09689i	0.165978	−	0.165978i
$944$	5.56297	+	5.56297i	0.181059	+	0.181059i
$945$	15.1029	+	15.0045i	0.491299	+	0.488098i
$946$		−	7.92218i		−	0.257572i
$947$	33.2177	+	33.2177i	1.07943	+	1.07943i	0.996560	+	0.0828703i	$0.0264087\pi$
$947$	33.2177	+	33.2177i	1.07943	+	1.07943i	0.0828703	+	0.996560i	$0.473591\pi$
$948$	−25.3232	−	6.75577i	−0.822459	−	0.219417i
$949$	−26.7905	+	13.8074i	−0.869655	+	0.448206i
$950$		−	3.17182i		−	0.102907i
$951$	6.87280	+	11.8741i	0.222866	+	0.385046i
$952$	−61.4173			−1.99055
$953$	−9.16362			−0.296839			−0.148419	−	0.988925i	$-0.547419\pi$
$953$	−9.16362			−0.296839			−0.148419	+	0.988925i	$0.547419\pi$
$954$	−4.70520	−	17.4082i	−0.152336	−	0.563613i
$955$	9.24712	+	9.24712i	0.299230	+	0.299230i
$956$	−1.83313	−	1.83313i	−0.0592876	−	0.0592876i
$957$	0.219846	+	0.379828i	0.00710661	+	0.0122781i
$958$	−18.1963			−0.587897
$959$	26.8184			0.866011
$960$	−0.472221	+	0.273323i	−0.0152409	+	0.00882148i
$961$		−	10.9675i		−	0.353791i
$962$	6.34783	−	19.8495i	0.204662	−	0.639975i
$963$	−13.4656	+	23.4409i	−0.433923	+	0.755372i
$964$	6.24165	+	6.24165i	0.201030	+	0.201030i
$965$		−	11.9479i		−	0.384615i
$966$	−10.5756	−	2.82137i	−0.340263	−	0.0907760i
$967$	27.6848	+	27.6848i	0.890282	+	0.890282i	0.994549	−	0.104268i	$-0.0332498\pi$
$967$	27.6848	+	27.6848i	0.890282	+	0.890282i	−0.104268	+	0.994549i	$0.533250\pi$
$968$	−1.78635	+	1.78635i	−0.0574153	+	0.0574153i
$969$	−47.8707	+	27.7077i	−1.53783	+	0.890100i
$970$	4.36630	−	4.36630i	0.140193	−	0.140193i
$971$			22.0979i			0.709156i	0.935026	+	0.354578i	$0.115376\pi$
$971$			22.0979i			0.709156i	−0.935026	+	0.354578i	$0.884624\pi$
$972$	−6.52325	−	23.8253i	−0.209233	−	0.764195i
$973$	−23.2381	+	23.2381i	−0.744979	+	0.744979i
$974$	11.1289			0.356593
$975$	5.25690	+	3.37121i	0.168355	+	0.107965i
$976$	2.17723			0.0696915
$977$	−40.2412	+	40.2412i	−1.28743	+	1.28743i	−0.351086	+	0.936343i	$0.614188\pi$
$977$	−40.2412	+	40.2412i	−1.28743	+	1.28743i	−0.936343	+	0.351086i	$0.885812\pi$
$978$	−2.73036	−	0.728409i	−0.0873071	−	0.0232920i
$979$			34.5790i			1.10515i
$980$	10.9659	−	10.9659i	0.350292	−	0.350292i
$981$	6.50368	+	24.0622i	0.207647	+	0.768248i
$982$	−10.8303	+	10.8303i	−0.345608	+	0.345608i
$983$	−10.0169	−	10.0169i	−0.319490	−	0.319490i	0.529081	−	0.848571i	$-0.322537\pi$
$983$	−10.0169	−	10.0169i	−0.319490	−	0.319490i	−0.848571	+	0.529081i	$0.822537\pi$
$984$	−3.10658	+	11.6447i	−0.0990342	+	0.371218i
$985$			8.93307i			0.284631i
$986$	0.215448	+	0.215448i	0.00686127	+	0.00686127i
$987$	−20.8302	+	78.0795i	−0.663033	+	2.48530i
$988$	−24.9947	+	12.8819i	−0.795189	+	0.409828i
$989$			8.45939i			0.268993i
$990$	6.49079	−	1.75437i	0.206291	−	0.0557574i
$991$	−21.7567			−0.691124			−0.345562	−	0.938396i	$-0.612312\pi$
$991$	−21.7567			−0.691124			−0.345562	+	0.938396i	$0.612312\pi$
$992$	25.5273			0.810493
$993$	−1.88825	+	1.09293i	−0.0599218	+	0.0346830i
$994$	7.83099	+	7.83099i	0.248384	+	0.248384i
$995$	−15.5169	−	15.5169i	−0.491918	−	0.491918i
$996$	−8.81931	+	5.10465i	−0.279450	+	0.161747i
$997$	−27.2276			−0.862308			−0.431154	−	0.902278i	$-0.641893\pi$
$997$	−27.2276			−0.862308			−0.431154	+	0.902278i	$0.641893\pi$
$998$	12.4622			0.394482
$999$	−0.152294	−	46.6006i	−0.00481837	−	1.47438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.o.a.86.12	yes	40
3.2	odd	2	inner	195.2.o.a.86.9	✓	40
5.2	odd	4		975.2.n.q.749.12		40
5.3	odd	4		975.2.n.r.749.9		40
5.4	even	2		975.2.o.p.476.9		40
13.5	odd	4	inner	195.2.o.a.161.9	yes	40
15.2	even	4		975.2.n.q.749.9		40
15.8	even	4		975.2.n.r.749.12		40
15.14	odd	2		975.2.o.p.476.12		40
39.5	even	4	inner	195.2.o.a.161.12	yes	40
65.18	even	4		975.2.n.q.824.9		40
65.44	odd	4		975.2.o.p.551.12		40
65.57	even	4		975.2.n.r.824.12		40
195.44	even	4		975.2.o.p.551.9		40
195.83	odd	4		975.2.n.q.824.12		40
195.122	odd	4		975.2.n.r.824.9		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.9	✓	40	3.2	odd	2	inner
195.2.o.a.86.12	yes	40	1.1	even	1	trivial
195.2.o.a.161.9	yes	40	13.5	odd	4	inner
195.2.o.a.161.12	yes	40	39.5	even	4	inner
975.2.n.q.749.9		40	15.2	even	4
975.2.n.q.749.12		40	5.2	odd	4
975.2.n.q.824.9		40	65.18	even	4
975.2.n.q.824.12		40	195.83	odd	4
975.2.n.r.749.9		40	5.3	odd	4
975.2.n.r.749.12		40	15.8	even	4
975.2.n.r.824.9		40	195.122	odd	4
975.2.n.r.824.12		40	65.57	even	4
975.2.o.p.476.9		40	5.4	even	2
975.2.o.p.476.12		40	15.14	odd	2
975.2.o.p.551.9		40	195.44	even	4
975.2.o.p.551.12		40	65.44	odd	4

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.455718 - 0.455718i) q^{2} +(-0.446465 + 1.67352i) q^{3} +1.58464i q^{4} +(0.707107 - 0.707107i) q^{5} +(0.559191 + 0.966114i) q^{6} +(-2.89711 + 2.89711i) q^{7} +(1.63358 + 1.63358i) q^{8} +(-2.60134 - 1.49434i) q^{9} -0.644482i q^{10} +(-2.45902 - 2.45902i) q^{11} +(-2.65193 - 0.707488i) q^{12} +(3.43422 + 1.09825i) q^{13} +2.64053i q^{14} +(0.867659 + 1.49906i) q^{15} -1.68038 q^{16} +6.48865 q^{17} +(-1.86647 + 0.504480i) q^{18} +(3.48002 + 3.48002i) q^{19} +(1.12051 + 1.12051i) q^{20} +(-3.55491 - 6.14183i) q^{21} -2.24123 q^{22} +2.39321 q^{23} +(-3.46318 + 2.00450i) q^{24} -1.00000i q^{25} +(2.06553 - 1.06454i) q^{26} +(3.66221 - 3.68622i) q^{27} +(-4.59088 - 4.59088i) q^{28} +0.0728607i q^{29} +(1.07855 + 0.287739i) q^{30} +(-3.16484 - 3.16484i) q^{31} +(-4.03295 + 4.03295i) q^{32} +(5.21308 - 3.01735i) q^{33} +(2.95699 - 2.95699i) q^{34} +4.09713i q^{35} +(2.36799 - 4.12219i) q^{36} +(6.34157 - 6.34157i) q^{37} +3.17182 q^{38} +(-3.37121 + 5.25690i) q^{39} +2.31024 q^{40} +(2.12973 - 2.12973i) q^{41} +(-4.41897 - 1.17890i) q^{42} +3.53474i q^{43} +(3.89666 - 3.89666i) q^{44} +(-2.89608 + 0.782769i) q^{45} +(1.09063 - 1.09063i) q^{46} +(-8.05214 - 8.05214i) q^{47} +(0.750230 - 2.81215i) q^{48} -9.78648i q^{49} +(-0.455718 - 0.455718i) q^{50} +(-2.89695 + 10.8589i) q^{51} +(-1.74034 + 5.44201i) q^{52} +9.32683i q^{53} +(-0.0109441 - 3.34881i) q^{54} -3.47757 q^{55} -9.46535 q^{56} +(-7.37760 + 4.27018i) q^{57} +(0.0332039 + 0.0332039i) q^{58} +(-3.31055 - 3.31055i) q^{59} +(-2.37547 + 1.37493i) q^{60} -1.29568 q^{61} -2.88455 q^{62} +(11.8656 - 3.20711i) q^{63} +0.315013i q^{64} +(3.20494 - 1.65178i) q^{65} +(1.00063 - 3.75075i) q^{66} +(0.922676 + 0.922676i) q^{67} +10.2822i q^{68} +(-1.06849 + 4.00509i) q^{69} +(1.86713 + 1.86713i) q^{70} +(2.96569 - 2.96569i) q^{71} +(-1.80838 - 6.69063i) q^{72} +(-5.91079 + 5.91079i) q^{73} -5.77993i q^{74} +(1.67352 + 0.446465i) q^{75} +(-5.51460 + 5.51460i) q^{76} +14.2481 q^{77} +(0.859343 + 3.93198i) q^{78} +9.54897 q^{79} +(-1.18821 + 1.18821i) q^{80} +(4.53392 + 7.77455i) q^{81} -1.94111i q^{82} +(2.62525 - 2.62525i) q^{83} +(9.73260 - 5.63327i) q^{84} +(4.58817 - 4.58817i) q^{85} +(1.61084 + 1.61084i) q^{86} +(-0.121934 - 0.0325297i) q^{87} -8.03402i q^{88} +(-7.03107 - 7.03107i) q^{89} +(-0.963073 + 1.67652i) q^{90} +(-13.1311 + 6.76754i) q^{91} +3.79239i q^{92} +(6.70942 - 3.88344i) q^{93} -7.33901 q^{94} +4.92150 q^{95} +(-4.94865 - 8.54979i) q^{96} +(6.77490 + 6.77490i) q^{97} +(-4.45987 - 4.45987i) q^{98} +(2.72214 + 10.0713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{6} - 16 q^{7} + 4 q^{15} - 64 q^{16} + 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} - 24 q^{27} + 32 q^{28} + 32 q^{31} - 4 q^{33} - 16 q^{34} + 32 q^{37} - 8 q^{39} + 8 q^{42} - 8 q^{45} - 40 q^{46}+ \cdots - 20 q^{99}+O(q^{100}) \) 40 * q + 12 * q^6 - 16 * q^7 + 4 * q^15 - 64 * q^16 + 4 * q^18 - 16 * q^19 - 12 * q^21 + 8 * q^24 - 24 * q^27 + 32 * q^28 + 32 * q^31 - 4 * q^33 - 16 * q^34 + 32 * q^37 - 8 * q^39 + 8 * q^42 - 8 * q^45 - 40 * q^46 + 8 * q^48 - 32 * q^54 + 8 * q^55 - 36 * q^57 + 24 * q^58 + 16 * q^60 + 8 * q^61 + 8 * q^63 - 48 * q^66 - 32 * q^67 + 132 * q^72 - 64 * q^73 + 16 * q^76 - 12 * q^78 + 40 * q^79 + 72 * q^81 + 124 * q^84 - 24 * q^85 + 16 * q^87 + 8 * q^91 - 108 * q^93 - 32 * q^94 - 76 * q^96 + 24 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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