LMFDB - Embedded newform 261.2.x.a.2.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(2,261)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(84))

chi = DirichletCharacter(H, H._module([14, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("261.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			2.15
Character	$\chi$	$=$	261.2
Dual form			261.2.x.a.131.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0309399 - 0.0228347i) q^{2} +(-1.45710 - 0.936412i) q^{3} +(-0.589074 - 1.90973i) q^{4} +(0.319150 - 0.813182i) q^{5} +(0.0236998 + 0.0622449i) q^{6} +(-1.11047 - 0.342536i) q^{7} +(-0.0507833 + 0.145130i) q^{8} +(1.24626 + 2.72889i) q^{9} +O(q^{10})$	\(q+(-0.0309399 - 0.0228347i) q^{2} +(-1.45710 - 0.936412i) q^{3} +(-0.589074 - 1.90973i) q^{4} +(0.319150 - 0.813182i) q^{5} +(0.0236998 + 0.0622449i) q^{6} +(-1.11047 - 0.342536i) q^{7} +(-0.0507833 + 0.145130i) q^{8} +(1.24626 + 2.72889i) q^{9} +(-0.0284432 + 0.0178721i) q^{10} +(0.898758 + 0.170054i) q^{11} +(-0.929958 + 3.33428i) q^{12} +(-6.85876 + 0.513993i) q^{13} +(0.0265362 + 0.0359553i) q^{14} +(-1.22651 + 0.886028i) q^{15} +(-3.29763 + 2.24828i) q^{16} +(-3.86016 - 3.86016i) q^{17} +(0.0237540 - 0.112890i) q^{18} +(0.803604 + 1.27893i) q^{19} +(-1.74096 - 0.130467i) q^{20} +(1.29731 + 1.53897i) q^{21} +(-0.0239243 - 0.0257843i) q^{22} +(0.918226 - 6.09203i) q^{23} +(0.209898 - 0.163915i) q^{24} +(3.10585 + 2.88181i) q^{25} +(0.223946 + 0.140715i) q^{26} +(0.739436 - 5.14327i) q^{27} +2.32249i q^{28} +(4.53784 + 2.89966i) q^{29} +(0.0581802 + 0.000593254i) q^{30} +(-1.76941 - 4.05553i) q^{31} +(0.460669 + 0.0172370i) q^{32} +(-1.15034 - 1.08939i) q^{33} +(0.0312874 + 0.207579i) q^{34} +(-0.632952 + 0.793696i) q^{35} +(4.47730 - 3.98755i) q^{36} +(-5.03442 - 1.76162i) q^{37} +(0.00434050 - 0.0579200i) q^{38} +(10.4752 + 5.67369i) q^{39} +(0.101810 + 0.0876144i) q^{40} +(-4.03392 - 1.08089i) q^{41} +(-0.00499687 - 0.0772393i) q^{42} +(3.72276 + 1.62422i) q^{43} +(-0.204677 - 1.81656i) q^{44} +(2.61683 - 0.142514i) q^{45} +(-0.167519 + 0.167519i) q^{46} +(0.943565 - 4.98686i) q^{47} +(6.91028 - 0.188030i) q^{48} +(-4.66785 - 3.18249i) q^{49} +(-0.0302895 - 0.160084i) q^{50} +(2.00993 + 9.23933i) q^{51} +(5.02191 + 12.7956i) q^{52} +(6.56205 - 5.23306i) q^{53} +(-0.140323 + 0.142247i) q^{54} +(0.425124 - 0.676581i) q^{55} +(0.106106 - 0.143768i) q^{56} +(0.0266752 - 2.61603i) q^{57} +(-0.0741874 - 0.193335i) q^{58} +(12.1030 - 6.98770i) q^{59} +(2.41458 + 1.82036i) q^{60} +(-7.66279 + 4.04990i) q^{61} +(-0.0378614 + 0.165882i) q^{62} +(-0.449202 - 3.45725i) q^{63} +(6.22692 + 4.96581i) q^{64} +(-1.77101 + 5.74146i) q^{65} +(0.0107153 + 0.0599733i) q^{66} +(4.14812 - 6.08418i) q^{67} +(-5.09795 + 9.64580i) q^{68} +(-7.04259 + 8.01684i) q^{69} +(0.0377073 - 0.0101036i) q^{70} +(-6.35694 - 3.06134i) q^{71} +(-0.459333 + 0.0422888i) q^{72} +(3.04500 - 0.343089i) q^{73} +(0.115538 + 0.169464i) q^{74} +(-1.82697 - 7.10743i) q^{75} +(1.96903 - 2.28805i) q^{76} +(-0.939797 - 0.496697i) q^{77} +(-0.194544 - 0.414741i) q^{78} +(-6.44400 - 7.48807i) q^{79} +(0.775825 + 3.39911i) q^{80} +(-5.89365 + 6.80183i) q^{81} +(0.100127 + 0.125556i) q^{82} +(7.61539 - 8.20744i) q^{83} +(2.17480 - 3.38409i) q^{84} +(-4.37098 + 1.90704i) q^{85} +(-0.0780932 - 0.135261i) q^{86} +(-3.89679 - 8.47437i) q^{87} +(-0.0703218 + 0.121801i) q^{88} +(-1.81215 + 16.0833i) q^{89} +(-0.0842186 - 0.0553450i) q^{90} +(7.79253 + 1.77859i) q^{91} +(-12.1750 + 1.83509i) q^{92} +(-1.21945 + 7.56621i) q^{93} +(-0.143067 + 0.132747i) q^{94} +(1.29647 - 0.245306i) q^{95} +(-0.655099 - 0.456492i) q^{96} +(-0.308116 - 8.23458i) q^{97} +(0.0717517 + 0.205055i) q^{98} +(0.656031 + 2.66454i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.0309399	−	0.0228347i	−0.0218778	−	0.0161466i	0.582826	−	0.812597i	$-0.301947\pi$
$2$	−0.0309399	−	0.0228347i	−0.0218778	−	0.0161466i	−0.604704	+	0.796450i	$0.706709\pi$
$3$	−1.45710	−	0.936412i	−0.841255	−	0.540638i
$3$	−1.45710	−	0.936412i	−0.841255	−	0.540638i
$4$	−0.589074	−	1.90973i	−0.294537	−	0.954866i
$5$	0.319150	−	0.813182i	0.142728	−	0.363666i	−0.841578	−	0.540136i	$-0.818373\pi$
$5$	0.319150	−	0.813182i	0.142728	−	0.363666i	0.984306	+	0.176470i	$0.0564680\pi$
$6$	0.0236998	+	0.0622449i	0.00967539	+	0.0254114i
$7$	−1.11047	−	0.342536i	−0.419720	−	0.129466i	0.0776993	−	0.996977i	$-0.475243\pi$
$7$	−1.11047	−	0.342536i	−0.419720	−	0.129466i	−0.497419	+	0.867511i	$0.665719\pi$
$8$	−0.0507833	+	0.145130i	−0.0179546	+	0.0513113i
$9$	1.24626	+	2.72889i	0.415421	+	0.909629i
$10$	−0.0284432	+	0.0178721i	−0.00899454	+	0.00565164i
$11$	0.898758	+	0.170054i	0.270986	+	0.0512733i	0.319628	−	0.947543i	$-0.396442\pi$
$11$	0.898758	+	0.170054i	0.270986	+	0.0512733i	−0.0486427	+	0.998816i	$0.515490\pi$
$12$	−0.929958	+	3.33428i	−0.268456	+	0.962524i
$13$	−6.85876	+	0.513993i	−1.90228	+	0.142556i	−0.973589	−	0.228306i	$-0.926681\pi$
$13$	−6.85876	+	0.513993i	−1.90228	+	0.142556i	−0.928688	+	0.370862i	$0.879062\pi$
$14$	0.0265362	+	0.0359553i	0.00709211	+	0.00960947i
$15$	−1.22651	+	0.886028i	−0.316683	+	0.228772i
$16$	−3.29763	+	2.24828i	−0.824407	+	0.562071i
$17$	−3.86016	−	3.86016i	−0.936227	−	0.936227i	0.0618581	−	0.998085i	$-0.480297\pi$
$17$	−3.86016	−	3.86016i	−0.936227	−	0.936227i	−0.998085	+	0.0618581i	$0.980297\pi$
$18$	0.0237540	−	0.112890i	0.00559887	−	0.0266083i
$19$	0.803604	+	1.27893i	0.184359	+	0.293406i	0.926098	−	0.377283i	$-0.123141\pi$
$19$	0.803604	+	1.27893i	0.184359	+	0.293406i	−0.741739	+	0.670689i	$0.765999\pi$
$20$	−1.74096	−	0.130467i	−0.389291	−	0.0291733i
$21$	1.29731	+	1.53897i	0.283097	+	0.335831i
$22$	−0.0239243	−	0.0257843i	−0.00510069	−	0.00549723i
$23$	0.918226	−	6.09203i	0.191463	−	1.27028i	−0.662151	−	0.749370i	$-0.730356\pi$
$23$	0.918226	−	6.09203i	0.191463	−	1.27028i	0.853614	−	0.520905i	$-0.174406\pi$
$24$	0.209898	−	0.163915i	0.0428452	−	0.0334590i
$25$	3.10585	+	2.88181i	0.621170	+	0.576362i
$26$	0.223946	+	0.140715i	0.0439195	+	0.0275964i
$27$	0.739436	−	5.14327i	0.142304	−	0.989823i
$28$			2.32249i			0.438909i
$29$	4.53784	+	2.89966i	0.842655	+	0.538454i
$29$	4.53784	+	2.89966i	0.842655	+	0.538454i
$30$	0.0581802		0.000593254i	0.0106222		0.000108313i
$31$	−1.76941	−	4.05553i	−0.317796	−	0.728395i	0.682200	−	0.731165i	$-0.261023\pi$
$31$	−1.76941	−	4.05553i	−0.317796	−	0.728395i	−0.999996	+	0.00276972i	$0.999118\pi$
$32$	0.460669	+	0.0172370i	0.0814356	+	0.00304710i
$33$	−1.15034	−	1.08939i	−0.200248	−	0.189639i
$34$	0.0312874	+	0.207579i	0.00536575	+	0.0355994i
$35$	−0.632952	+	0.793696i	−0.106988	+	0.134159i
$36$	4.47730	−	3.98755i	0.746217	−	0.664592i
$37$	−5.03442	−	1.76162i	−0.827653	−	0.289608i	−0.116983	−	0.993134i	$-0.537322\pi$
$37$	−5.03442	−	1.76162i	−0.827653	−	0.289608i	−0.710670	+	0.703526i	$0.751608\pi$
$38$	0.00434050	−	0.0579200i	0.000704122	−	0.00939586i
$39$	10.4752	+	5.67369i	1.67737	+	0.908517i
$40$	0.101810	+	0.0876144i	0.0160975	+	0.0138530i
$41$	−4.03392	−	1.08089i	−0.629993	−	0.168806i	−0.0703265	−	0.997524i	$-0.522404\pi$
$41$	−4.03392	−	1.08089i	−0.629993	−	0.168806i	−0.559667	+	0.828718i	$0.689071\pi$
$42$	−0.00499687	−	0.0772393i	−0.000771033	−	0.0119183i
$43$	3.72276	+	1.62422i	0.567716	+	0.247692i	0.664089	−	0.747653i	$-0.268820\pi$
$43$	3.72276	+	1.62422i	0.567716	+	0.247692i	−0.0963734	+	0.995345i	$0.530724\pi$
$44$	−0.204677	−	1.81656i	−0.0308563	−	0.273857i
$45$	2.61683	−	0.142514i	0.390093	−	0.0212447i
$46$	−0.167519	+	0.167519i	−0.0246994	+	0.0246994i
$47$	0.943565	−	4.98686i	0.137633	−	0.727408i	−0.843957	−	0.536410i	$-0.819780\pi$
$47$	0.943565	−	4.98686i	0.137633	−	0.727408i	0.981590	−	0.190998i	$-0.0611724\pi$
$48$	6.91028	−	0.188030i	0.997413	−	0.0271398i
$49$	−4.66785	−	3.18249i	−0.666836	−	0.454641i
$50$	−0.0302895	−	0.160084i	−0.00428359	−	0.0226393i
$51$	2.00993	+	9.23933i	0.281446	+	1.29377i
$52$	5.02191	+	12.7956i	0.696413	+	1.77443i
$53$	6.56205	−	5.23306i	0.901366	−	0.718816i	−0.0587925	−	0.998270i	$-0.518725\pi$
$53$	6.56205	−	5.23306i	0.901366	−	0.718816i	0.960159	+	0.279455i	$0.0901536\pi$
$54$	−0.140323	+	0.142247i	−0.0190955	+	0.0193574i
$55$	0.425124	−	0.676581i	0.0573237	−	0.0912301i
$56$	0.106106	−	0.143768i	0.0141790	−	0.0192118i
$57$	0.0266752	−	2.61603i	0.00353322	−	0.346501i
$58$	−0.0741874	−	0.193335i	−0.00974128	−	0.0253862i
$59$	12.1030	−	6.98770i	1.57568	−	0.909721i	0.580231	−	0.814452i	$-0.302962\pi$
$59$	12.1030	−	6.98770i	1.57568	−	0.909721i	0.995452	−	0.0952691i	$-0.0303712\pi$
$60$	2.41458	+	1.82036i	0.311721	+	0.235008i
$61$	−7.66279	+	4.04990i	−0.981120	+	0.518537i	−0.879301	−	0.476266i	$-0.841990\pi$
$61$	−7.66279	+	4.04990i	−0.981120	+	0.518537i	−0.101819	+	0.994803i	$0.532466\pi$
$62$	−0.0378614	+	0.165882i	−0.00480841	+	0.0210670i
$63$	−0.449202	−	3.45725i	−0.0565941	−	0.435572i
$64$	6.22692	+	4.96581i	0.778365	+	0.620726i
$65$	−1.77101	+	5.74146i	−0.219666	+	0.712140i
$66$	0.0107153	+	0.0599733i	0.00131897	+	0.00738220i
$67$	4.14812	−	6.08418i	0.506774	−	0.743301i	−0.484547	−	0.874765i	$-0.661016\pi$
$67$	4.14812	−	6.08418i	0.506774	−	0.743301i	0.991321	+	0.131464i	$0.0419679\pi$
$68$	−5.09795	+	9.64580i	−0.618218	+	1.16973i
$69$	−7.04259	+	8.01684i	−0.847829	+	0.965114i
$70$	0.0377073	−	0.0101036i	0.00450688	−	0.00120761i
$71$	−6.35694	−	3.06134i	−0.754431	−	0.363315i	0.0168098	−	0.999859i	$-0.494649\pi$
$71$	−6.35694	−	3.06134i	−0.754431	−	0.363315i	−0.771240	+	0.636544i	$0.780363\pi$
$72$	−0.459333	+	0.0422888i	−0.0541329	+	0.00498378i
$73$	3.04500	−	0.343089i	0.356390	−	0.0401555i	0.0680456	−	0.997682i	$-0.478324\pi$
$73$	3.04500	−	0.343089i	0.356390	−	0.0401555i	0.288345	+	0.957527i	$0.406895\pi$
$74$	0.115538	+	0.169464i	0.0134311	+	0.0196997i
$75$	−1.82697	−	7.10743i	−0.210960	−	0.820696i
$76$	1.96903	−	2.28805i	0.225863	−	0.262458i
$77$	−0.939797	−	0.496697i	−0.107100	−	0.0566039i
$78$	−0.194544	−	0.414741i	−0.0220278	−	0.0469602i
$79$	−6.44400	−	7.48807i	−0.725007	−	0.842473i	0.267640	−	0.963519i	$-0.413756\pi$
$79$	−6.44400	−	7.48807i	−0.725007	−	0.842473i	−0.992647	+	0.121046i	$0.961375\pi$
$80$	0.775825	+	3.39911i	0.0867398	+	0.380032i
$81$	−5.89365	+	6.80183i	−0.654850	+	0.755759i
$82$	0.100127	+	0.125556i	0.0110572	+	0.0138653i
$83$	7.61539	−	8.20744i	0.835897	−	0.900883i	−0.160383	−	0.987055i	$-0.551273\pi$
$83$	7.61539	−	8.20744i	0.835897	−	0.900883i	0.996280	+	0.0861717i	$0.0274634\pi$
$84$	2.17480	−	3.38409i	0.237291	−	0.369234i
$85$	−4.37098	+	1.90704i	−0.474100	+	0.206848i
$86$	−0.0780932	−	0.135261i	−0.00842101	−	0.0145856i
$87$	−3.89679	−	8.47437i	−0.417780	−	0.908548i
$88$	−0.0703218	+	0.121801i	−0.00749633	+	0.0129840i
$89$	−1.81215	+	16.0833i	−0.192088	+	1.70482i	0.414698	+	0.909959i	$0.363887\pi$
$89$	−1.81215	+	16.0833i	−0.192088	+	1.70482i	−0.606786	+	0.794865i	$0.707541\pi$
$90$	−0.0842186	−	0.0553450i	−0.00887742	−	0.00583388i
$91$	7.79253	+	1.77859i	0.816879	+	0.186447i
$92$	−12.1750	+	1.83509i	−1.26934	+	0.191322i
$93$	−1.21945	+	7.56621i	−0.126451	+	0.784579i
$94$	−0.143067	+	0.132747i	−0.0147562	+	0.0136918i
$95$	1.29647	−	0.245306i	0.133015	−	0.0251678i
$96$	−0.655099	−	0.456492i	−0.0668608	−	0.0465906i
$97$	−0.308116	−	8.23458i	−0.0312844	−	0.836094i	−0.923298	−	0.384085i	$-0.874517\pi$
$97$	−0.308116	−	8.23458i	−0.0312844	−	0.836094i	0.892013	−	0.452009i	$-0.149293\pi$
$98$	0.0717517	+	0.205055i	0.00724802	+	0.0207137i
$99$	0.656031	+	2.66454i	0.0659336	+	0.267796i
$100$	3.67391	−	7.62895i	0.367391	−	0.762895i
$101$	4.09040	−	9.37529i	0.407010	−	0.932877i	−0.585495	−	0.810676i	$-0.699100\pi$
$101$	4.09040	−	9.37529i	0.407010	−	0.932877i	0.992505	−	0.122201i	$-0.0389952\pi$
$102$	0.148790	−	0.331760i	0.0147324	−	0.0328491i
$103$	−0.0414519	−	0.553137i	−0.00408438	−	0.0545022i	0.994789	−	0.101953i	$-0.0325092\pi$
$103$	−0.0414519	−	0.553137i	−0.00408438	−	0.0545022i	−0.998874	+	0.0474511i	$0.984890\pi$
$104$	0.273714	−	1.02152i	0.0268399	−	0.100168i
$105$	1.66550	−	0.563789i	0.162536	−	0.0550202i
$106$	−0.322524	+	0.0120680i	−0.0313263	+	0.00117215i
$107$	3.09220	+	6.42102i	0.298934	+	0.620743i	0.995289	−	0.0969548i	$-0.0309102\pi$
$107$	3.09220	+	6.42102i	0.298934	+	0.620743i	−0.696355	+	0.717698i	$0.745196\pi$
$108$	−10.2579	+	1.61764i	−0.987063	+	0.155658i
$109$	4.57673	−	1.04461i	0.438371	−	0.100055i	0.00236139	−	0.999997i	$-0.499248\pi$
$109$	4.57673	−	1.04461i	0.438371	−	0.100055i	0.436010	+	0.899942i	$0.356391\pi$
$110$	−0.0286028	+	0.0112258i	−0.00272717	+	0.00107034i
$111$	5.68603	+	7.28114i	0.539694	+	0.691095i
$112$	4.43204	−	1.36710i	0.418789	−	0.129179i
$113$	−0.184426	+	4.92889i	−0.0173493	+	0.463671i	0.963361	+	0.268206i	$0.0864309\pi$
$113$	−0.184426	+	4.92889i	−0.0173493	+	0.463671i	−0.980711	+	0.195464i	$0.937379\pi$
$114$	−0.0605615	+	0.0803305i	−0.00567210	+	0.00752364i
$115$	−4.66087	−	2.69096i	−0.434629	−	0.250933i
$116$	2.86445	−	10.3742i	0.265958	−	0.963218i
$117$	−9.95045	−	18.0762i	−0.919920	−	1.67115i
$118$	−0.534029	−	0.0601706i	−0.0491614	−	0.00553915i
$119$	2.96436	+	5.60885i	0.271743	+	0.514163i
$120$	−0.0663035	−	0.222998i	−0.00605265	−	0.0203569i
$121$	−9.46076	−	3.71308i	−0.860069	−	0.337552i
$122$	0.329564	+	0.0496738i	0.0298373	+	0.00449726i
$123$	4.86566	+	5.35237i	0.438722	+	0.482607i
$124$	−6.70267	+	5.76811i	−0.601918	+	0.517992i
$125$	7.26996	−	3.50103i	0.650245	−	0.313141i
$126$	−0.0650469	+	0.117224i	−0.00579484	+	0.0104432i
$127$	−4.73071	+	1.65535i	−0.419783	+	0.146888i	−0.531901	−	0.846807i	$-0.678522\pi$
$127$	−4.73071	+	1.65535i	−0.419783	+	0.146888i	0.112118	+	0.993695i	$0.464236\pi$
$128$	−0.317895	−	1.18640i	−0.0280982	−	0.104864i
$129$	−3.90348	−	5.85269i	−0.343682	−	0.515301i
$130$	0.185899	−	0.137200i	0.0163044	−	0.0120332i
$131$	−10.3464	+	7.63601i	−0.903971	+	0.667161i	−0.943256	−	0.332067i	$-0.892254\pi$
$131$	−10.3464	+	7.63601i	−0.903971	+	0.667161i	0.0392847	+	0.999228i	$0.487492\pi$
$132$	−1.40282	+	2.83857i	−0.122099	+	0.247066i
$133$	−0.454302	−	1.69548i	−0.0393930	−	0.147017i
$134$	−0.267273	+	0.0935228i	−0.0230889	+	0.00807914i
$135$	−3.94642	−	2.24277i	−0.339654	−	0.193027i
$136$	0.756258	−	0.364195i	0.0648486	−	0.0312294i
$137$	−12.2119	+	10.5092i	−1.04333	+	0.897858i	−0.994890	−	0.100968i	$-0.967806\pi$
$137$	−12.2119	+	10.5092i	−1.04333	+	0.897858i	−0.0484399	+	0.998826i	$0.515425\pi$
$138$	0.400959	−	0.0872248i	0.0341319	−	0.00742507i
$139$	14.1246	+	2.12894i	1.19803	+	0.180574i	0.717599	−	0.696456i	$-0.245241\pi$
$139$	14.1246	+	2.12894i	1.19803	+	0.180574i	0.480434	+	0.877031i	$0.340479\pi$
$140$	1.88860	+	0.741222i	0.159616	+	0.0626447i
$141$	−6.04462	+	6.38277i	−0.509049	+	0.537526i
$142$	0.126778	+	0.239876i	0.0106390	+	0.0201300i
$143$	−6.25177	−	0.704405i	−0.522799	−	0.0589053i
$144$	−10.2450	−	6.19690i	−0.853752	−	0.516408i
$145$	3.80620	−	2.76466i	0.316088	−	0.229592i
$146$	−0.102046	−	0.0589165i	−0.00844541	−	0.00487596i
$147$	3.82139	+	9.00823i	0.315183	+	0.742986i
$148$	−0.398574	+	10.6521i	−0.0327626	+	0.875598i
$149$	7.29158	−	2.24915i	0.597349	−	0.184258i	0.0186873	−	0.999825i	$-0.494051\pi$
$149$	7.29158	−	2.24915i	0.597349	−	0.184258i	0.578662	+	0.815568i	$0.303575\pi$
$150$	−0.105770	+	0.261621i	−0.00863607	+	0.0213613i
$151$	−7.28415	+	2.85882i	−0.592776	+	0.232647i	−0.642716	−	0.766105i	$-0.722192\pi$
$151$	−7.28415	+	2.85882i	−0.592776	+	0.232647i	0.0499397	+	0.998752i	$0.484097\pi$
$152$	−0.226421	+	0.0516791i	−0.0183651	+	0.00419173i
$153$	5.72317	−	15.3447i	0.462691	−	1.24055i
$154$	0.0177353	+	0.0368277i	0.00142915	+	0.00296766i
$155$	−3.86259	+	0.144528i	−0.310251	+	0.0116088i
$156$	4.66456	−	23.3470i	0.373464	−	1.86926i
$157$	−1.08278	+	4.04099i	−0.0864153	+	0.322506i	−0.995578	−	0.0939339i	$-0.970056\pi$
$157$	−1.08278	+	4.04099i	−0.0864153	+	0.322506i	0.909163	+	0.416440i	$0.136722\pi$
$158$	0.0283891	+	0.378827i	0.00225852	+	0.0301378i
$159$	−14.4618	+	1.48029i	−1.14690	+	0.117395i
$160$	0.161040	−	0.369107i	0.0127313	−	0.0291804i
$161$	−3.10640	+	6.45051i	−0.244819	+	0.508371i
$162$	0.337667	−	0.0758682i	0.0265296	−	0.00596077i
$163$	0.371895	+	1.06282i	0.0291291	+	0.0832461i	0.957530	−	0.288335i	$-0.0931016\pi$
$163$	0.371895	+	1.06282i	0.0291291	+	0.0832461i	−0.928401	+	0.371581i	$0.878816\pi$
$164$	0.312077	+	8.34044i	0.0243691	+	0.651279i
$165$	−1.25301	+	0.587753i	−0.0975463	+	0.0457565i
$166$	−0.423034	+	0.0800423i	−0.0328338	+	0.00621248i
$167$	−9.68646	+	8.98773i	−0.749561	+	0.695491i	−0.959339	−	0.282258i	$-0.908917\pi$
$167$	−9.68646	+	8.98773i	−0.749561	+	0.695491i	0.209777	+	0.977749i	$0.432726\pi$
$168$	−0.289233	+	0.110125i	−0.0223148	+	0.00849636i
$169$	33.9236	−	5.11316i	2.60951	−	0.393320i
$170$	0.178785	+	0.0408064i	0.0137121	+	0.00312971i
$171$	−2.48855	+	3.78683i	−0.190304	+	0.289586i
$172$	0.908850	−	8.06627i	0.0692992	−	0.615047i
$173$	−1.63135	+	2.82558i	−0.124029	+	0.214825i	−0.921353	−	0.388727i	$-0.872915\pi$
$173$	−1.63135	+	2.82558i	−0.124029	+	0.214825i	0.797324	+	0.603552i	$0.206248\pi$
$174$	−0.0729433	+	0.351178i	−0.00552982	+	0.0266228i
$175$	−2.46184	−	4.26404i	−0.186098	−	0.322331i
$176$	−3.34610	+	1.45989i	−0.252222	+	0.110043i
$177$	−24.1787	−	1.15169i	−1.81738	−	0.0865662i
$178$	0.423324	−	0.456235i	0.0317295	−	0.0341963i
$179$	−0.604177	−	0.757614i	−0.0451583	−	0.0566267i	0.758739	−	0.651394i	$-0.225816\pi$
$179$	−0.604177	−	0.757614i	−0.0451583	−	0.0566267i	−0.803898	+	0.594767i	$0.797244\pi$
$180$	−1.81367	−	4.91349i	−0.135183	−	0.366230i
$181$	−1.87570	−	8.21799i	−0.139420	−	0.610839i	−0.995563	−	0.0940994i	$-0.970003\pi$
$181$	−1.87570	−	8.21799i	−0.139420	−	0.610839i	0.856143	−	0.516739i	$-0.172854\pi$
$182$	−0.200486	−	0.232969i	−0.0148610	−	0.0172688i
$183$	14.9578	+	1.27443i	1.10571	+	0.0942085i
$184$	0.837507	+	0.442635i	0.0617418	+	0.0326315i
$185$	−3.03925	+	3.53167i	−0.223450	+	0.259654i
$186$	0.210502	−	0.206252i	0.0154347	−	0.0151231i
$187$	−2.81291	−	4.12579i	−0.205701	−	0.301707i
$188$	−10.0794	+	1.13568i	−0.735115	+	0.0828276i
$189$	−2.58288	+	5.45818i	−0.187877	+	0.397024i
$190$	−0.0457142	−	0.0220148i	−0.00331645	−	0.00159712i
$191$	10.2915	−	2.75761i	0.744669	−	0.199533i	0.133517	−	0.991047i	$-0.457373\pi$
$191$	10.2915	−	2.75761i	0.744669	−	0.199533i	0.611152	+	0.791513i	$0.290706\pi$
$192$	−4.42319	−	13.0666i	−0.319216	−	0.943003i
$193$	−1.36659	+	2.58571i	−0.0983693	+	0.186124i	−0.928389	−	0.371611i	$-0.878806\pi$
$193$	−1.36659	+	2.58571i	−0.0983693	+	0.186124i	0.830019	+	0.557735i	$0.188329\pi$
$194$	−0.178501	+	0.261813i	−0.0128156	+	0.0187971i
$195$	7.95690	−	6.70747i	0.569805	−	0.480332i
$196$	−3.32799	+	10.7891i	−0.237713	+	0.770648i
$197$	9.39330	+	7.49091i	0.669245	+	0.533705i	0.898120	−	0.439751i	$-0.144933\pi$
$197$	9.39330	+	7.49091i	0.669245	+	0.533705i	−0.228875	+	0.973456i	$0.573505\pi$
$198$	0.0405464	−	0.0974209i	0.00288151	−	0.00692340i
$199$	−0.858057	+	3.75939i	−0.0608260	+	0.266496i	−0.996192	−	0.0871846i	$-0.972213\pi$
$199$	−0.858057	+	3.75939i	−0.0608260	+	0.266496i	0.935366	+	0.353681i	$0.115070\pi$
$200$	−0.575963	+	0.304405i	−0.0407267	+	0.0215247i
$201$	−11.7415	+	4.98089i	−0.828183	+	0.351325i
$202$	−0.340638	+	0.196668i	−0.0239672	+	0.0138375i
$203$	−4.04591	−	4.77437i	−0.283967	−	0.335095i
$204$	16.4607	−	9.28108i	1.15248	−	0.649806i
$205$	−2.16639	+	2.93535i	−0.151307	+	0.205014i
$206$	−0.0113482	+	0.0180605i	−0.000790666	+	0.00125834i
$207$	17.7688	−	5.08654i	1.23502	−	0.353539i
$208$	21.4620	−	17.1154i	1.48812	−	1.18674i
$209$	0.504758	+	1.28610i	0.0349149	+	0.0889616i
$210$	−0.0644043	−	0.0205876i	−0.00444432	−	0.00142068i
$211$	0.754508	+	3.98767i	0.0519425	+	0.274522i	0.998903	−	0.0468274i	$-0.0149111\pi$
$211$	0.754508	+	3.98767i	0.0519425	+	0.274522i	−0.946961	+	0.321350i	$0.895863\pi$
$212$	−13.8593	−	9.44909i	−0.951859	−	0.648966i
$213$	6.39601	+	10.4134i	0.438247	+	0.713514i
$214$	0.0509496	−	0.269275i	0.00348284	−	0.0184073i
$215$	2.50891	−	2.50891i	0.171106	−	0.171106i
$216$	0.708893	+	0.368506i	0.0482341	+	0.0250737i
$217$	0.575719	+	5.10965i	0.0390824	+	0.346866i
$218$	−0.165457	−	0.0721881i	−0.0112062	−	0.00488920i
$219$	−4.75813	−	2.35146i	−0.321525	−	0.158897i
$220$	−1.54252	−	0.413316i	−0.103997	−	0.0278658i
$221$	28.4600	+	24.4918i	1.91443	+	1.64750i
$222$	−0.00966277	−	0.355116i	−0.000648522	−	0.0238339i
$223$	−1.80086	+	24.0308i	−0.120594	+	1.60922i	0.528785	+	0.848756i	$0.322648\pi$
$223$	−1.80086	+	24.0308i	−0.120594	+	1.60922i	−0.649379	+	0.760465i	$0.724971\pi$
$224$	−0.505657	−	0.176937i	−0.0337856	−	0.0118221i
$225$	−3.99342	+	12.0670i	−0.266228	+	0.804468i
$226$	0.118256	−	0.148288i	0.00786625	−	0.00986397i
$227$	−1.95602	−	12.9773i	−0.129826	−	0.861337i	−0.955031	−	0.296505i	$-0.904179\pi$
$227$	−1.95602	−	12.9773i	−0.129826	−	0.861337i	0.825206	−	0.564832i	$-0.191059\pi$
$228$	−5.01163	+	1.49009i	−0.331903	+	0.0986838i
$229$	20.5094	+	0.767406i	1.35530	+	0.0507116i	0.705129	−	0.709079i	$-0.250889\pi$
$229$	20.5094	+	0.767406i	1.35530	+	0.0507116i	0.650168	+	0.759791i	$0.274699\pi$
$230$	0.0827598	+	0.189688i	0.00545702	+	0.0125076i
$231$	0.904262	+	1.60377i	0.0594961	+	0.105521i
$232$	−0.651275	+	0.511323i	−0.0427583	+	0.0335700i
$233$			1.84424i			0.120820i	0.998174	+	0.0604101i	$0.0192408\pi$
$233$			1.84424i			0.120820i	−0.998174	+	0.0604101i	$0.980759\pi$
$234$	−0.104899	+	0.786492i	−0.00685743	+	0.0514146i
$235$	−3.75408	−	2.35885i	−0.244889	−	0.153874i
$236$	−20.4742	−	18.9973i	−1.33276	−	1.23662i
$237$	2.37762	+	16.9451i	0.154443	+	1.10070i
$238$	0.0363592	−	0.241228i	0.00235682	−	0.0156365i
$239$	4.88931	+	5.26942i	0.316263	+	0.340851i	0.871097	−	0.491110i	$-0.163409\pi$
$239$	4.88931	+	5.26942i	0.316263	+	0.340851i	−0.554834	+	0.831961i	$0.687218\pi$
$240$	2.05252	−	5.67932i	0.132489	−	0.366599i
$241$	−8.29693	−	0.621769i	−0.534453	−	0.0400517i	−0.195229	−	0.980758i	$-0.562545\pi$
$241$	−8.29693	−	0.621769i	−0.534453	−	0.0400517i	−0.339223	+	0.940706i	$0.610164\pi$
$242$	0.207928	+	0.330916i	0.0133661	+	0.0212721i
$243$	14.9569	−	4.39204i	0.959488	−	0.281749i
$244$	12.2482	+	12.2482i	0.784110	+	0.784110i
$245$	−4.07769	+	2.78012i	−0.260514	+	0.177615i
$246$	−0.0283234	−	0.276708i	−0.00180583	−	0.0176422i
$247$	−6.16909	−	8.35881i	−0.392530	−	0.531859i
$248$	0.678437	−	0.0508418i	0.0430808	−	0.00322846i
$249$	−18.7819	+	4.82789i	−1.19025	+	0.305955i
$250$	−0.304877	−	0.0576858i	−0.0192821	−	0.00364837i
$251$	24.4641	−	15.3718i	1.54416	−	0.970261i	0.553663	−	0.832741i	$-0.313230\pi$
$251$	24.4641	−	15.3718i	1.54416	−	0.970261i	0.990499	−	0.137520i	$-0.0439131\pi$
$252$	−6.33780	+	2.89443i	−0.399244	+	0.182332i
$253$	1.86124	−	5.31911i	0.117015	−	0.334410i
$254$	0.184167	+	0.0568080i	0.0115557	+	0.00356445i
$255$	8.15473	+	1.31430i	0.510669	+	0.0823046i
$256$	5.80229	−	14.7840i	0.362643	−	0.923999i
$257$	−4.40693	−	14.2869i	−0.274897	−	0.891194i	−0.982767	−	0.184851i	$-0.940820\pi$
$257$	−4.40693	−	14.2869i	−0.274897	−	0.891194i	0.707870	−	0.706343i	$-0.249656\pi$
$258$	−0.0128711	+	0.270216i	−0.000801317	+	0.0168229i
$259$	4.98717	+	3.68070i	0.309888	+	0.228707i
$260$	12.0079			0.744699
$261$	−2.25750	+	15.9970i	−0.139736	+	0.990189i
$262$	0.494483			0.0305493
$263$	−5.73784	−	4.23472i	−0.353810	−	0.261124i	0.402384	−	0.915471i	$-0.368182\pi$
$263$	−5.73784	−	4.23472i	−0.353810	−	0.261124i	−0.756194	+	0.654347i	$0.772944\pi$
$264$	0.216522	−	0.111626i	0.0133260	−	0.00687008i
$265$	−2.16115	−	7.00627i	−0.132758	−	0.430392i
$266$	−0.0246597	+	0.0628318i	−0.00151198	+	0.00385246i
$267$	17.7011	−	21.7380i	1.08329	−	1.33034i
$268$	−14.0627	−	4.33777i	−0.859017	−	0.264972i
$269$	−6.01865	+	17.2003i	−0.366963	+	1.04872i	0.601351	+	0.798985i	$0.294629\pi$
$269$	−6.01865	+	17.2003i	−0.366963	+	1.04872i	−0.968314	+	0.249736i	$0.919656\pi$
$270$	0.0708889	+	0.159506i	0.00431416	+	0.00970725i
$271$	6.34621	−	3.98759i	0.385505	−	0.242229i	−0.325311	−	0.945607i	$-0.605469\pi$
$271$	6.34621	−	3.98759i	0.385505	−	0.242229i	0.710816	+	0.703378i	$0.248326\pi$
$272$	21.4081	+	4.05063i	1.29806	+	0.245606i
$273$	−9.68898	−	9.88861i	−0.586404	−	0.598486i
$274$	0.617807	−	0.0462982i	0.0373231	−	0.00279698i
$275$	2.30135	+	3.11821i	0.138776	+	0.188035i
$276$	19.4586	+	8.72696i	1.17127	+	0.525301i
$277$	17.7293	−	12.0876i	1.06525	−	0.726274i	0.101973	−	0.994787i	$-0.467485\pi$
$277$	17.7293	−	12.0876i	1.06525	−	0.726274i	0.963276	+	0.268513i	$0.0865321\pi$
$278$	−0.388400	−	0.388400i	−0.0232947	−	0.0232947i
$279$	8.86194	−	9.88279i	0.530551	−	0.591667i
$280$	−0.0830460	−	0.132167i	−0.00496295	−	0.00789848i
$281$	29.4384	+	2.20610i	1.75615	+	0.131605i	0.913494	−	0.406852i	$-0.133373\pi$
$281$	29.4384	+	2.20610i	1.75615	+	0.131605i	0.842653	+	0.538457i	$0.180992\pi$
$282$	0.332769	−	0.0594553i	0.0198161	−	0.00354051i
$283$	5.53447	+	5.96475i	0.328990	+	0.354567i	0.875787	−	0.482698i	$-0.160343\pi$
$283$	5.53447	+	5.96475i	0.328990	+	0.354567i	−0.546796	+	0.837266i	$0.684153\pi$
$284$	−2.10163	+	13.9434i	−0.124709	+	0.827390i
$285$	−2.11879	−	0.856598i	−0.125506	−	0.0507405i
$286$	0.177344	+	0.164551i	0.0104866	+	0.00973013i
$287$	4.10932	+	2.58206i	0.242566	+	0.152414i
$288$	0.527078	+	1.27860i	0.0310583	+	0.0753420i
$289$			12.8017i			0.753041i
$290$	−0.180894	−	0.00137520i	−0.0106224	−	8.07545e-5i
$291$	−7.26200	+	12.2871i	−0.425706	+	0.720283i
$292$	−2.44894	−	5.61303i	−0.143313	−	0.328478i
$293$	−21.5377	−	0.805885i	−1.25825	−	0.0470803i	−0.600073	−	0.799945i	$-0.704862\pi$
$293$	−21.5377	−	0.805885i	−1.25825	−	0.0470803i	−0.658175	+	0.752865i	$0.728671\pi$
$294$	0.0874665	−	0.365974i	0.00510115	−	0.0213440i
$295$	−1.81958	−	12.0721i	−0.105940	−	0.702865i
$296$	0.511328	−	0.641185i	0.0297203	−	0.0372681i
$297$	1.53921	−	4.49681i	0.0893139	−	0.260931i
$298$	−0.276959	−	0.0969123i	−0.0160438	−	0.00561398i
$299$	−3.16663	+	42.2557i	−0.183131	+	2.44371i
$300$	−12.4971	+	7.67582i	−0.721519	+	0.443164i
$301$	−3.57767	−	3.07884i	−0.206214	−	0.177461i
$302$	0.290651	+	0.0778798i	0.0167251	+	0.00448148i
$303$	−14.7392	+	9.83041i	−0.846748	+	0.564743i
$304$	−5.52538	−	2.41070i	−0.316902	−	0.138263i
$305$	0.847725	+	7.52377i	0.0485406	+	0.430810i
$306$	−0.527466	+	0.344078i	−0.0301532	+	0.0196696i
$307$	−7.91078	+	7.91078i	−0.451492	+	0.451492i	−0.895850	−	0.444357i	$-0.853432\pi$
$307$	−7.91078	+	7.91078i	−0.451492	+	0.451492i	0.444357	+	0.895850i	$0.353432\pi$
$308$	−0.394949	+	2.08735i	−0.0225043	+	0.118938i
$309$	−0.457565	+	0.844791i	−0.0260300	+	0.0480585i
$310$	0.122809	+	0.0837294i	0.00697506	+	0.00475551i
$311$	−6.06188	−	32.0378i	−0.343737	−	1.81670i	−0.546489	−	0.837466i	$-0.684036\pi$
$311$	−6.06188	−	32.0378i	−0.343737	−	1.81670i	0.202752	−	0.979230i	$-0.435011\pi$
$312$	−1.35539	+	1.23214i	−0.0767337	+	0.0697561i
$313$	−3.60228	−	9.17847i	−0.203613	−	0.518798i	0.792195	−	0.610268i	$-0.208938\pi$
$313$	−3.60228	−	9.17847i	−0.203613	−	0.518798i	−0.995808	+	0.0914707i	$0.970843\pi$
$314$	0.125776	−	0.100303i	0.00709794	−	0.00566042i
$315$	−2.95473	−	0.738099i	−0.166480	−	0.0415871i
$316$	−10.5042	+	16.7174i	−0.590908	+	0.940424i
$317$	16.1774	−	21.9196i	0.908613	−	1.23113i	−0.0638238	−	0.997961i	$-0.520330\pi$
$317$	16.1774	−	21.9196i	0.908613	−	1.23113i	0.972437	−	0.233166i	$-0.0749085\pi$
$318$	0.481250	+	0.284431i	0.0269871	+	0.0159501i
$319$	3.58532	+	3.37777i	0.200739	+	0.189119i
$320$	6.02543	−	3.47878i	0.336832	−	0.194470i
$321$	1.50708	−	12.2516i	0.0841173	−	0.683819i
$322$	0.243407	−	0.128644i	0.0135645	−	0.00716907i
$323$	1.83483	−	8.03891i	0.102093	−	0.447297i
$324$	16.4615	+	7.24852i	0.914526	+	0.402695i
$325$	−22.7835	−	18.1692i	−1.26380	−	1.00785i
$326$	0.0127627	−	0.0413755i	0.000706858	−	0.00229158i
$327$	−7.64693	−	2.76361i	−0.422876	−	0.152828i
$328$	0.361725	−	0.530553i	0.0199729	−	0.0292949i
$329$	−2.75598	+	5.21457i	−0.151942	+	0.287489i
$330$	0.0521890	+	0.0104270i	0.00287291	+	0.000573986i
$331$	−25.2830	+	6.77456i	−1.38968	+	0.372363i	−0.874627	−	0.484796i	$-0.838894\pi$
$331$	−25.2830	+	6.77456i	−1.38968	+	0.372363i	−0.515052	+	0.857159i	$0.672227\pi$
$332$	−20.1600	−	9.70856i	−1.10643	−	0.532827i
$333$	−1.46695	−	15.9338i	−0.0803886	−	0.873167i
$334$	0.504930	−	0.0568920i	0.0276285	−	0.00311299i
$335$	−3.62367	−	5.31495i	−0.197982	−	0.290387i
$336$	−7.73809	−	2.15822i	−0.422148	−	0.117740i
$337$	−12.9813	+	15.0846i	−0.707138	+	0.821709i	−0.990530	−	0.137295i	$-0.956159\pi$
$337$	−12.9813	+	15.0846i	−0.707138	+	0.821709i	0.283393	+	0.959004i	$0.408540\pi$
$338$	−1.16635	−	0.616434i	−0.0634410	−	0.0335296i
$339$	4.88420	−	7.00917i	0.265273	−	0.380686i
$340$	6.21677	+	7.22402i	0.337152	+	0.391778i
$341$	−0.900612	−	3.94584i	−0.0487709	−	0.213679i
$342$	0.163466	−	0.0603388i	0.00883925	−	0.00326275i
$343$	9.16532	+	11.4930i	0.494881	+	0.620561i
$344$	−0.424778	+	0.457802i	−0.0229025	+	0.0246830i
$345$	4.27150	+	8.28548i	0.229970	+	0.446075i
$346$	0.114995	−	0.0501718i	0.00618217	−	0.00269725i
$347$	−3.84281	−	6.65595i	−0.206293	−	0.357310i	0.744251	−	0.667900i	$-0.232807\pi$
$347$	−3.84281	−	6.65595i	−0.206293	−	0.357310i	−0.950544	+	0.310590i	$0.899473\pi$
$348$	−13.8883	+	12.4339i	−0.744490	+	0.666525i
$349$	5.50269	−	9.53094i	0.294552	−	0.510180i	−0.680328	−	0.732907i	$-0.738163\pi$
$349$	5.50269	−	9.53094i	0.294552	−	0.510180i	0.974881	+	0.222728i	$0.0714961\pi$
$350$	−0.0211988	+	0.188144i	−0.00113312	+	0.0100567i
$351$	−2.42801	+	35.6565i	−0.129597	+	1.90320i
$352$	0.411099	+	0.0938306i	0.0219116	+	0.00500119i
$353$	−19.6742	+	2.96540i	−1.04715	+	0.157832i	−0.650010	−	0.759926i	$-0.725235\pi$
$353$	−19.6742	+	2.96540i	−1.04715	+	0.157832i	−0.397140	+	0.917758i	$0.629997\pi$
$354$	0.721788	+	0.587746i	0.0383626	+	0.0312383i
$355$	−4.51825	+	4.19232i	−0.239804	+	0.222505i
$356$	31.7823	−	6.01353i	1.68446	−	0.318716i
$357$	0.932830	−	10.9485i	0.0493706	−	0.579456i
$358$	0.00139330	+	0.0372367i	7.36381e−5	+	0.00196802i
$359$	−8.02846	−	22.9440i	−0.423726	−	1.21094i	−0.935964	−	0.352095i	$-0.885469\pi$
$359$	−8.02846	−	22.9440i	−0.423726	−	1.21094i	0.512238	−	0.858843i	$-0.328816\pi$
$360$	−0.112208	+	0.387018i	−0.00591388	+	0.0203976i
$361$	7.25391	−	15.0629i	0.381785	−	0.792784i
$362$	−0.129621	+	0.297095i	−0.00681274	+	0.0156150i
$363$	10.3083	+	14.2695i	0.541044	+	0.748954i
$364$	−1.19374	−	15.9294i	−0.0625691	−	0.834926i
$365$	0.692819	−	2.58563i	0.0362638	−	0.135338i
$366$	−0.433692	−	0.380988i	−0.0226694	−	0.0199145i
$367$	17.4316	−	0.652243i	0.909921	−	0.0340468i	0.421669	−	0.906750i	$-0.361444\pi$
$367$	17.4316	−	0.652243i	0.909921	−	0.0340468i	0.488252	+	0.872703i	$0.337635\pi$
$368$	10.6686	+	22.1537i	0.556141	+	1.15484i
$369$	−2.07772	−	12.3552i	−0.108162	−	0.643186i
$370$	0.174679	−	0.0398693i	0.00908112	−	0.00207271i
$371$	−9.07949	+	3.56344i	−0.471383	+	0.185004i
$372$	15.1678	−	2.12824i	0.786413	−	0.110344i
$373$	−15.8326	+	4.88370i	−0.819780	+	0.252869i	−0.676151	−	0.736763i	$-0.736353\pi$
$373$	−15.8326	+	4.88370i	−0.819780	+	0.252869i	−0.143629	+	0.989632i	$0.545877\pi$
$374$	−0.00717977	+	0.191883i	−0.000371257	+	0.00992206i
$375$	−13.8714	−	1.70634i	−0.716318	−	0.0881151i
$376$	0.675826	+	0.390189i	0.0348531	+	0.0201224i
$377$	−32.6143	−	17.5557i	−1.67972	−	0.904162i
$378$	0.204550	−	0.109896i	0.0105209	−	0.00565246i
$379$	−24.8255	−	2.79717i	−1.27520	−	0.143681i	−0.551723	−	0.834027i	$-0.686030\pi$
$379$	−24.8255	−	2.79717i	−1.27520	−	0.143681i	−0.723479	+	0.690346i	$0.757458\pi$
$380$	−1.23219	−	2.33141i	−0.0632098	−	0.119599i
$381$	8.44319	+	2.01789i	0.432558	+	0.103380i
$382$	−0.381388	−	0.149684i	−0.0195135	−	0.00765849i
$383$	26.4141	+	3.98129i	1.34970	+	0.203434i	0.783787	−	0.621030i	$-0.213286\pi$
$383$	26.4141	+	3.98129i	1.34970	+	0.203434i	0.565913	+	0.824465i	$0.308524\pi$
$384$	−0.647755	+	2.02638i	−0.0330556	+	0.103408i
$385$	−0.703842	+	0.605705i	−0.0358711	+	0.0308696i
$386$	0.101326	−	0.0487961i	0.00515736	−	0.00248366i
$387$	0.207219	+	12.1832i	0.0105335	+	0.619307i
$388$	−15.5443	+	5.43920i	−0.789144	+	0.276133i
$389$	0.296724	+	1.10739i	0.0150445	+	0.0561468i	0.973040	−	0.230636i	$-0.0740808\pi$
$389$	0.296724	+	1.10739i	0.0150445	+	0.0561468i	−0.957996	+	0.286783i	$0.907414\pi$
$390$	−0.399349	+	0.0258352i	−0.0202218	+	0.00130822i
$391$	−27.0607	+	19.9717i	−1.36852	+	1.01001i
$392$	0.698924	−	0.515829i	0.0353010	−	0.0260533i
$393$	22.2262	−	1.43789i	1.12116	−	0.0725318i
$394$	−0.119575	−	0.446261i	−0.00602412	−	0.0224823i
$395$	−8.14576	+	2.85033i	−0.409858	+	0.143415i
$396$	4.70211	−	2.82246i	0.236290	−	0.141834i
$397$	−33.6365	+	16.1985i	−1.68817	+	0.812979i	−0.692356	+	0.721556i	$0.743427\pi$
$397$	−33.6365	+	16.1985i	−1.68817	+	0.812979i	−0.995812	+	0.0914228i	$0.970859\pi$
$398$	0.112393	−	0.0967218i	0.00563374	−	0.00484823i
$399$	−0.925705	+	2.89589i	−0.0463432	+	0.144976i
$400$	−16.7211	−	2.52029i	−0.836053	−	0.126015i
$401$	−15.9294	−	6.25181i	−0.795474	−	0.312201i	−0.0674240	−	0.997724i	$-0.521478\pi$
$401$	−15.9294	−	6.25181i	−0.795474	−	0.312201i	−0.728050	+	0.685524i	$0.759573\pi$
$402$	0.477018	+	0.114006i	0.0237915	+	0.00568609i
$403$	14.2205	+	26.9065i	0.708373	+	1.34031i
$404$	−20.3139	−	2.28882i	−1.01065	−	0.113873i
$405$	3.65016	+	6.96341i	0.181378	+	0.346015i
$406$	0.0161589	+	0.240106i	0.000801951	+	0.0119162i
$407$	−4.22515	−	2.43939i	−0.209433	−	0.120916i
$408$	−1.44298	−	0.177502i	−0.0714380	−	0.00878767i
$409$	−0.695938	+	18.5993i	−0.0344119	+	0.919678i	0.870009	+	0.493036i	$0.164113\pi$
$409$	−0.695938	+	18.5993i	−0.0344119	+	0.919678i	−0.904421	+	0.426642i	$0.859697\pi$
$410$	0.134055	−	0.0413506i	0.00662053	−	0.00204216i
$411$	27.6348	−	3.87752i	1.36312	−	0.191264i
$412$	−1.03193	+	0.405001i	−0.0508393	+	0.0199530i
$413$	−15.8337	+	3.61393i	−0.779123	+	0.177830i
$414$	−0.665915	−	0.248368i	−0.0327279	−	0.0122066i
$415$	−4.24368	−	8.81210i	−0.208314	−	0.432569i
$416$	−3.16848	+	0.118556i	−0.155347	+	0.00581269i
$417$	−18.5874	−	16.3285i	−0.910227	−	0.799611i
$418$	0.0137506	−	0.0513179i	0.000672563	−	0.00251004i
$419$	−2.06442	−	27.5478i	−0.100854	−	1.34580i	−0.786377	−	0.617747i	$-0.788046\pi$
$419$	−2.06442	−	27.5478i	−0.100854	−	1.34580i	0.685523	−	0.728051i	$-0.259573\pi$
$420$	−2.05779	−	2.84854i	−0.100410	−	0.138995i
$421$	6.46543	−	14.8189i	0.315106	−	0.722231i	−0.684873	−	0.728662i	$-0.740142\pi$
$421$	6.46543	−	14.8189i	0.315106	−	0.722231i	0.999979	+	0.00643159i	$0.00204725\pi$
$422$	0.0677128	−	0.140607i	0.00329621	−	0.00684464i
$423$	14.7845	−	3.64006i	0.718847	−	0.176986i
$424$	0.426233	+	1.21810i	0.0206997	+	0.0591563i
$425$	−0.864840	−	23.1133i	−0.0419509	−	1.12116i
$426$	0.0398948	−	0.468240i	0.00193291	−	0.0226863i
$427$	9.89656	−	1.87253i	0.478928	−	0.0906181i
$428$	10.4409	−	9.68773i	0.504679	−	0.468274i
$429$	8.44982	+	6.88062i	0.407961	+	0.332200i
$430$	−0.134916	+	0.0203352i	−0.00650621	+	0.000980653i
$431$	9.90484	+	2.26071i	0.477099	+	0.108895i	0.454307	−	0.890845i	$-0.349887\pi$
$431$	9.90484	+	2.26071i	0.477099	+	0.108895i	0.0227927	+	0.999740i	$0.492744\pi$
$432$	9.12515	+	18.6230i	0.439034	+	0.896002i
$433$	−3.05887	+	27.1482i	−0.147000	+	1.30466i	0.676119	+	0.736792i	$0.263660\pi$
$433$	−3.05887	+	27.1482i	−0.147000	+	1.30466i	−0.823119	+	0.567868i	$0.807768\pi$
$434$	0.0988645	−	0.171238i	0.00474565	−	0.00821971i
$435$	−8.13487	+	0.464200i	−0.390037	+	0.0222567i
$436$	−4.69096	−	8.12498i	−0.224656	−	0.389116i
$437$	8.52916	−	3.72123i	0.408005	−	0.178011i
$438$	0.0935213	+	0.181404i	0.00446862	+	0.00866784i
$439$	16.9141	−	18.2291i	0.807268	−	0.870028i	−0.186389	−	0.982476i	$-0.559679\pi$
$439$	16.9141	−	18.2291i	0.807268	−	0.870028i	0.993658	+	0.112448i	$0.0358691\pi$
$440$	0.0766031	+	0.0960573i	0.00365191	+	0.00457935i
$441$	2.86727	−	16.7043i	0.136537	−	0.795441i
$442$	−0.321287	−	1.40765i	−0.0152821	−	0.0669551i
$443$	11.6779	+	13.5699i	0.554832	+	0.644726i	0.963421	−	0.267992i	$-0.0863601\pi$
$443$	11.6779	+	13.5699i	0.554832	+	0.644726i	−0.408589	+	0.912718i	$0.633979\pi$
$444$	10.5555	−	15.1479i	0.500943	−	0.718889i
$445$	12.5003	+	6.60659i	0.592570	+	0.313182i
$446$	0.604454	−	0.702388i	0.0286217	−	0.0332590i
$447$	−12.7307	−	3.55069i	−0.602140	−	0.167942i
$448$	−5.21387	−	7.64734i	−0.246332	−	0.361303i
$449$	9.43602	−	1.06318i	0.445313	−	0.0501748i	0.113539	−	0.993534i	$-0.463781\pi$
$449$	9.43602	−	1.06318i	0.445313	−	0.0501748i	0.331774	+	0.943359i	$0.392353\pi$
$450$	0.399103	−	0.282164i	0.0188139	−	0.0133013i
$451$	−3.44171	−	1.65744i	−0.162064	−	0.0780459i
$452$	9.52150	−	2.55128i	0.447854	−	0.120002i
$453$	13.2908	+	2.65539i	0.624454	+	0.124761i
$454$	−0.235815	+	0.446183i	−0.0110673	+	0.0209404i
$455$	3.93331	−	5.76910i	0.184396	−	0.270460i
$456$	0.378310	+	0.136722i	0.0177160	+	0.00640258i
$457$	5.00490	−	16.2255i	0.234120	−	0.758997i	−0.759924	−	0.650012i	$-0.774764\pi$
$457$	5.00490	−	16.2255i	0.234120	−	0.758997i	0.994043	−	0.108985i	$-0.0347600\pi$
$458$	−0.617034	−	0.492068i	−0.0288321	−	0.0229928i
$459$	−22.7082	+	16.9995i	−1.05993	+	0.793469i
$460$	−2.39341	+	10.4862i	−0.111593	+	0.488921i
$461$	−1.18589	+	0.626763i	−0.0552326	+	0.0291913i	−0.494657	−	0.869088i	$-0.664706\pi$
$461$	−1.18589	+	0.626763i	−0.0552326	+	0.0291913i	0.439424	+	0.898280i	$0.355182\pi$
$462$	0.00864389	−	0.0702691i	0.000402150	−	0.00326922i
$463$	2.75959	−	1.59325i	0.128249	−	0.0740447i	−0.434503	−	0.900670i	$-0.643076\pi$
$463$	2.75959	−	1.59325i	0.128249	−	0.0740447i	0.562752	+	0.826626i	$0.309743\pi$
$464$	−21.4834	+	0.640346i	−0.997340	+	0.0297273i
$465$	5.76351	+	3.40639i	0.267277	+	0.157968i
$466$	0.0421126	−	0.0570606i	0.00195083	−	0.00264328i
$467$	0.690634	−	1.09914i	0.0319587	−	0.0508620i	−0.830363	−	0.557223i	$-0.811867\pi$
$467$	0.690634	−	1.09914i	0.0319587	−	0.0508620i	0.862322	+	0.506361i	$0.169010\pi$
$468$	−28.6592	+	29.6509i	−1.32477	+	1.37062i
$469$	−6.69043	+	5.33544i	−0.308935	+	0.246368i
$470$	0.0622874	+	0.158706i	0.00287310	+	0.00732055i
$471$	5.36175	−	4.87419i	0.247056	−	0.224591i
$472$	0.399494	+	2.11138i	0.0183882	+	0.0971840i
$473$	3.06965	+	2.09286i	0.141143	+	0.0962296i
$474$	0.313372	−	0.578571i	0.0143937	−	0.0265747i
$475$	−1.18975	+	6.28800i	−0.0545896	+	0.288513i
$476$	8.96517	−	8.96517i	0.410918	−	0.410918i
$477$	22.4585	+	11.3853i	1.02830	+	0.521298i
$478$	−0.0309492	−	0.274681i	−0.00141558	−	0.0125636i
$479$	−27.4089	−	11.9584i	−1.25234	−	0.546393i	−0.334149	−	0.942520i	$-0.608449\pi$
$479$	−27.4089	−	11.9584i	−1.25234	−	0.546393i	−0.918195	+	0.396128i	$0.870354\pi$
$480$	−0.580286	+	0.387025i	−0.0264863	+	0.0176652i
$481$	35.4353	+	9.49486i	1.61571	+	0.432928i
$482$	0.242508	+	0.208695i	0.0110460	+	0.00950581i
$483$	10.5667	−	6.49015i	0.480800	−	0.295312i
$484$	−1.51789	+	20.2548i	−0.0689949	+	0.920673i
$485$	−6.79454	−	2.37751i	−0.308524	−	0.107957i
$486$	−0.563057	−	0.205648i	−0.0255408	−	0.00932837i
$487$	3.60548	−	4.52113i	0.163380	−	0.204872i	−0.693402	−	0.720551i	$-0.743889\pi$
$487$	3.60548	−	4.52113i	0.163380	−	0.204872i	0.856782	+	0.515679i	$0.172460\pi$
$488$	−0.198622	−	1.31777i	−0.00899119	−	0.0596526i
$489$	0.453346	−	1.89687i	0.0205010	−	0.0857795i
$490$	0.189646	+	0.00709606i	0.00856735	+	0.000320568i
$491$	6.73504	+	15.4369i	0.303948	+	0.696656i	0.999768	−	0.0215603i	$-0.00686339\pi$
$491$	6.73504	+	15.4369i	0.303948	+	0.696656i	−0.695819	+	0.718217i	$0.744959\pi$
$492$	7.35536	−	12.4451i	0.331605	−	0.561067i
$493$	−6.32363	−	28.7099i	−0.284802	−	1.29303i
$494$			0.399490i			0.0179739i
$495$	2.37613	+	0.316917i	0.106799	+	0.0142443i
$496$	14.9528	+	9.39550i	0.671403	+	0.421870i
$497$	6.01060	+	5.57702i	0.269612	+	0.250164i
$498$	0.691354	+	0.279504i	0.0309803	+	0.0125249i
$499$	0.775199	−	5.14311i	0.0347027	−	0.230237i	−0.964756	−	0.263147i	$-0.915239\pi$
$499$	0.775199	−	5.14311i	0.0347027	−	0.230237i	0.999458	+	0.0329102i	$0.0104775\pi$
$500$	−10.9686	−	11.8213i	−0.490529	−	0.528665i
$501$	22.5303	−	4.02546i	1.00658	−	0.179845i
$502$	−1.10793	−	0.0830277i	−0.0494493	−	0.00370571i
$503$	−18.4397	−	29.3467i	−0.822188	−	1.30850i	−0.948584	−	0.316524i	$-0.897484\pi$
$503$	−18.4397	−	29.3467i	−0.822188	−	1.30850i	0.126397	−	0.991980i	$-0.459659\pi$
$504$	0.524563	+	0.110377i	0.0233659	+	0.00491660i
$505$	−6.31837	−	6.31837i	−0.281164	−	0.281164i
$506$	−0.179047	+	0.122072i	−0.00795960	+	0.00542676i
$507$	−54.2180	−	24.3161i	−2.40790	−	1.07992i
$508$	5.94801	+	8.05927i	0.263900	+	0.357572i
$509$	7.12541	−	0.533975i	0.315828	−	0.0236680i	0.0841269	−	0.996455i	$-0.473190\pi$
$509$	7.12541	−	0.533975i	0.315828	−	0.0236680i	0.231701	+	0.972787i	$0.425571\pi$
$510$	−0.222295	−	0.226875i	−0.00984338	−	0.0100462i
$511$	−3.49891	−	0.662030i	−0.154783	−	0.0292865i
$512$	−2.59709	+	1.63186i	−0.114776	+	0.0721187i
$513$	7.17209	−	3.18747i	0.316655	−	0.140730i
$514$	−0.189887	+	0.542667i	−0.00837557	+	0.0239360i
$515$	−0.463030	−	0.142826i	−0.0204036	−	0.00629366i
$516$	−8.87763	+	10.9023i	−0.390816	+	0.479946i
$517$	1.69607	−	4.32152i	0.0745932	−	0.190060i
$518$	−0.0702549	−	0.227761i	−0.00308682	−	0.0100072i
$519$	5.02294	−	2.58953i	0.220483	−	0.113668i
$520$	−0.743321	−	0.548596i	−0.0325968	−	0.0240575i
$521$	32.9514			1.44363			0.721813	−	0.692088i	$-0.243309\pi$
$521$	32.9514			1.44363			0.721813	+	0.692088i	$0.243309\pi$
$522$	0.435133	−	0.443396i	0.0190453	−	0.0194069i
$523$	−38.4515			−1.68137			−0.840684	−	0.541526i	$-0.817847\pi$
$523$	−38.4515			−1.68137			−0.840684	+	0.541526i	$0.817847\pi$
$524$	20.6775	+	15.2607i	0.903303	+	0.666668i
$525$	−0.405753	+	8.51842i	−0.0177085	+	0.371774i
$526$	0.0808297	+	0.262044i	0.00352434	+	0.0114256i
$527$	−8.82480	+	22.4852i	−0.384415	+	0.979472i
$528$	6.24265	+	1.00613i	0.271676	+	0.0437862i
$529$	−14.2915	−	4.40834i	−0.621369	−	0.191667i
$530$	−0.0931202	+	0.266122i	−0.00404488	+	0.0115596i
$531$	34.1522	+	24.3193i	1.48208	+	1.05537i
$532$	−2.97029	+	1.86636i	−0.128779	+	0.0809169i
$533$	28.2233	+	5.34013i	1.22249	+	0.231307i
$534$	−1.04405	+	0.268373i	−0.0451804	+	0.0116136i
$535$	6.20833	−	0.465250i	0.268409	−	0.0201145i
$536$	0.672343	+	0.910993i	0.0290408	+	0.0393489i
$537$	0.170906	+	1.66968i	0.00737512	+	0.0720518i
$538$	0.578980	−	0.394742i	0.0249616	−	0.0170185i
$539$	−3.65407	−	3.65407i	−0.157392	−	0.157392i
$540$	−1.95836	+	8.85777i	−0.0842743	+	0.381178i
$541$	1.03832	+	1.65248i	0.0446410	+	0.0710457i	0.868299	−	0.496041i	$-0.165213\pi$
$541$	1.03832	+	1.65248i	0.0446410	+	0.0710457i	−0.823658	+	0.567087i	$0.808071\pi$
$542$	−0.287407	−	0.0215381i	−0.0123452	−	0.000925143i
$543$	−4.96235	+	13.7308i	−0.212955	+	0.589247i
$544$	−1.71172	−	1.84480i	−0.0733894	−	0.0790950i
$545$	0.611208	−	4.05510i	0.0261813	−	0.173701i
$546$	0.0739727	+	0.527197i	0.00316574	+	0.0225620i
$547$	12.3590	+	11.4674i	0.528431	+	0.490312i	0.898671	−	0.438624i	$-0.144534\pi$
$547$	12.3590	+	11.4674i	0.528431	+	0.490312i	−0.370240	+	0.928936i	$0.620725\pi$
$548$	27.2634	+	17.1307i	1.16463	+	0.731788i
$549$	−20.6016	−	15.8636i	−0.879254	−	0.677044i
$550$		−	0.149028i		−	0.00635456i
$551$	−0.0618348	+	8.13375i	−0.00263425	+	0.346509i
$552$	−0.805840	−	1.42921i	−0.0342988	−	0.0608314i
$553$	4.59096	+	10.5226i	0.195228	+	0.447466i
$554$	−0.824559	−	0.0308528i	−0.0350321	−	0.00131081i
$555$	7.73559	−	2.30000i	0.328357	−	0.0976296i
$556$	−4.25473	−	28.2283i	−0.180441	−	1.19715i
$557$	−16.3433	+	20.4938i	−0.692488	+	0.868352i	−0.996437	−	0.0843359i	$-0.973123\pi$
$557$	−16.3433	+	20.4938i	−0.692488	+	0.868352i	0.303950	+	0.952688i	$0.401695\pi$
$558$	−0.499858	+	0.103413i	−0.0211607	+	0.00437782i
$559$	−26.3684	−	9.22669i	−1.11526	−	0.390247i
$560$	0.302784	−	4.04037i	0.0127949	−	0.170737i
$561$	0.235251	+	8.64572i	0.00993232	+	0.365023i
$562$	−0.860445	−	0.740473i	−0.0362957	−	0.0312350i
$563$	−17.9523	−	4.81031i	−0.756600	−	0.202730i	−0.140156	−	0.990129i	$-0.544761\pi$
$563$	−17.9523	−	4.81031i	−0.756600	−	0.202730i	−0.616444	+	0.787399i	$0.711427\pi$
$564$	15.7501	+	7.78368i	0.663200	+	0.327752i
$565$	3.94922	+	1.72303i	0.166145	+	0.0724883i
$566$	−0.0350330	−	0.310927i	−0.00147255	−	0.0130692i
$567$	8.87461	−	5.53446i	0.372699	−	0.232426i
$568$	0.767120	−	0.767120i	0.0321876	−	0.0321876i
$569$	2.41159	−	12.7456i	0.101099	−	0.534323i	−0.894999	−	0.446069i	$-0.852824\pi$
$569$	2.41159	−	12.7456i	0.101099	−	0.534323i	0.996098	−	0.0882539i	$-0.0281287\pi$
$570$	0.0459951	+	0.0748850i	0.00192652	+	0.00313659i
$571$	31.7700	+	21.6604i	1.32953	+	0.906460i	0.999299	−	0.0374397i	$-0.0119202\pi$
$571$	31.7700	+	21.6604i	1.32953	+	0.906460i	0.330233	+	0.943899i	$0.392873\pi$
$572$	2.33753	+	12.3542i	0.0977371	+	0.516553i
$573$	−17.5780	−	5.61901i	−0.734332	−	0.234738i
$574$	−0.0681815	−	0.173724i	−0.00284584	−	0.00725109i
$575$	20.4079	−	16.2748i	0.851070	−	0.678706i
$576$	−5.79073	+	23.1813i	−0.241281	+	0.965886i
$577$	8.93673	−	14.2227i	0.372041	−	0.592100i	−0.607262	−	0.794502i	$-0.707732\pi$
$577$	8.93673	−	14.2227i	0.372041	−	0.592100i	0.979302	+	0.202402i	$0.0648749\pi$
$578$	0.292323	−	0.396083i	0.0121590	−	0.0164749i
$579$	4.41255	−	2.48795i	0.183379	−	0.103395i
$580$	−7.52190	−	5.64024i	−0.312330	−	0.234198i
$581$	−11.2680	+	6.50560i	−0.467476	+	0.269898i
$582$	0.505258	−	0.214336i	0.0209436	−	0.00888452i
$583$	6.78759	−	3.58735i	0.281113	−	0.148573i
$584$	−0.104842	+	0.459345i	−0.00433841	+	0.0190078i
$585$	−17.8749	+	2.32250i	−0.739037	+	0.0960235i
$586$	0.647973	+	0.516741i	0.0267675	+	0.0213464i
$587$	−4.32852	+	14.0327i	−0.178657	+	0.579192i	0.821305	+	0.570489i	$0.193246\pi$
$587$	−4.32852	+	14.0327i	−0.178657	+	0.579192i	−0.999962	+	0.00870285i	$0.997230\pi$
$588$	14.9522	−	12.6044i	0.616619	−	0.519795i
$589$	3.76483	−	5.52199i	0.155127	−	0.227530i
$590$	−0.219365	+	0.415059i	−0.00903112	+	0.0170877i
$591$	−6.67238	−	19.7110i	−0.274465	−	0.810802i
$592$	20.5622	−	5.50964i	0.845103	−	0.226445i
$593$	26.8540	+	12.9322i	1.10276	+	0.531063i	0.894526	−	0.447016i	$-0.147513\pi$
$593$	26.8540	+	12.9322i	1.10276	+	0.531063i	0.208237	+	0.978078i	$0.433228\pi$
$594$	−0.150306	+	0.103984i	−0.00616714	+	0.00426650i
$595$	5.50709	−	0.620500i	0.225769	−	0.0254380i
$596$	−8.59056	−	12.6000i	−0.351883	−	0.516118i
$597$	4.77061	−	4.67431i	0.195248	−	0.191307i
$598$	1.06287	−	1.23508i	0.0434640	−	0.0505061i
$599$	25.6925	+	13.5789i	1.04977	+	0.554817i	0.900894	−	0.434040i	$-0.142912\pi$
$599$	25.6925	+	13.5789i	1.04977	+	0.554817i	0.148871	+	0.988857i	$0.452436\pi$
$600$	1.12428	+	0.0957907i	0.0458986	+	0.00391064i
$601$	−27.5013	−	31.9571i	−1.12180	−	1.30356i	−0.947819	−	0.318809i	$-0.896717\pi$
$601$	−27.5013	−	31.9571i	−1.12180	−	1.30356i	−0.173983	−	0.984749i	$-0.555664\pi$
$602$	0.0403886	+	0.176954i	0.00164612	+	0.00721210i
$603$	21.7727	+	3.73727i	0.886653	+	0.152193i
$604$	9.75049	+	12.2267i	0.396742	+	0.497499i
$605$	−6.03881	+	6.50829i	−0.245513	+	0.264600i
$606$	0.680505	+	0.0324141i	0.0276436	+	0.00131673i
$607$	11.2139	−	4.89258i	0.455159	−	0.198584i	−0.159790	−	0.987151i	$-0.551082\pi$
$607$	11.2139	−	4.89258i	0.455159	−	0.198584i	0.614948	+	0.788567i	$0.289177\pi$
$608$	0.348151	+	0.603015i	0.0141194	+	0.0244555i
$609$	1.42451	+	10.7454i	0.0577240	+	0.435424i
$610$	0.145574	−	0.252142i	0.00589413	−	0.0102089i
$611$	−3.90847	+	34.6886i	−0.158120	+	1.40335i
$612$	−32.6757	−	1.89053i	−1.32084	−	0.0764201i
$613$	21.4171	+	4.88832i	0.865030	+	0.197437i	0.631939	−	0.775018i	$-0.282259\pi$
$613$	21.4171	+	4.88832i	0.865030	+	0.197437i	0.233090	+	0.972455i	$0.425116\pi$
$614$	0.425399	−	0.0641186i	0.0171677	−	0.00258762i
$615$	5.90533	−	2.24846i	0.238126	−	0.0906665i
$616$	0.119812	−	0.111169i	0.00482735	−	0.00447913i
$617$	−3.99808	+	0.756477i	−0.160957	+	0.0304546i	−0.265765	−	0.964038i	$-0.585625\pi$
$617$	−3.99808	+	0.756477i	−0.160957	+	0.0304546i	0.104809	+	0.994492i	$0.466577\pi$
$618$	0.0334475	−	0.0156894i	0.00134546	−	0.000631120i
$619$	−0.777441	−	20.7775i	−0.0312480	−	0.835120i	−0.923504	−	0.383590i	$-0.874688\pi$
$619$	−0.777441	−	20.7775i	−0.0312480	−	0.835120i	0.892256	−	0.451531i	$-0.149122\pi$
$620$	2.55137	+	7.29138i	0.102465	+	0.292829i
$621$	−30.6540	−	9.22735i	−1.23010	−	0.370281i
$622$	−0.544019	+	1.12967i	−0.0218132	+	0.0452955i
$623$	7.52144	−	17.2393i	0.301340	−	0.690679i
$624$	−47.2993	+	4.84149i	−1.89349	+	0.193815i
$625$	1.05635	+	14.0960i	0.0422540	+	0.563840i
$626$	−0.0981332	+	0.366238i	−0.00392219	+	0.0146378i
$627$	0.468841	−	2.34664i	0.0187237	−	0.0937157i
$628$	8.35505	−	0.312624i	0.333403	−	0.0124751i
$629$	12.6335	+	26.2338i	0.503732	+	1.04601i
$630$	0.0745649	+	0.0903071i	0.00297074	+	0.00359792i
$631$	−24.4764	+	5.58657i	−0.974389	+	0.222398i	−0.679939	−	0.733269i	$-0.737994\pi$
$631$	−24.4764	+	5.58657i	−0.974389	+	0.222398i	−0.294450	+	0.955667i	$0.595137\pi$
$632$	1.41399	−	0.554951i	0.0562456	−	0.0220748i
$633$	2.63471	−	6.51695i	0.104720	−	0.259026i
$634$	−1.00105	+	0.308784i	−0.0397569	+	0.0122634i
$635$	−0.163710	+	4.37523i	−0.00649662	+	0.173626i
$636$	11.3461	+	26.7462i	0.449901	+	1.06056i
$637$	33.6514	+	19.4287i	1.33332	+	0.769792i
$638$	−0.0337990	−	0.186378i	−0.00133812	−	0.00737876i
$639$	0.431629	−	21.1626i	0.0170750	−	0.837181i
$640$	−1.06621	−	0.120133i	−0.0421458	−	0.00474869i
$641$	−10.8527	−	20.5343i	−0.428656	−	0.811056i	0.571297	−	0.820743i	$-0.306440\pi$
$641$	−10.8527	−	20.5343i	−0.428656	−	0.811056i	−0.999953	+	0.00968696i	$0.996916\pi$
$642$	−0.326391	+	0.344650i	−0.0128816	+	0.0136022i
$643$	33.0200	+	12.9594i	1.30218	+	0.511068i	0.912196	−	0.409754i	$-0.134385\pi$
$643$	33.0200	+	12.9594i	1.30218	+	0.511068i	0.389984	+	0.920822i	$0.372481\pi$
$644$	14.1487	+	2.13257i	0.557535	+	0.0840349i
$645$	−6.00510	+	1.30635i	−0.236451	+	0.0514375i
$646$	−0.240335	+	0.206825i	−0.00945587	+	0.00813744i
$647$	−24.0385	+	11.5764i	−0.945053	+	0.455113i	−0.841949	−	0.539557i	$-0.818592\pi$
$647$	−24.0385	+	11.5764i	−0.945053	+	0.455113i	−0.103104	+	0.994671i	$0.532877\pi$
$648$	−0.687852	−	1.20077i	−0.0270214	−	0.0471705i
$649$	12.0660	−	4.22208i	0.473632	−	0.165731i
$650$	0.290031	+	1.08241i	0.0113759	+	0.0424556i
$651$	3.94586	−	7.98437i	0.154650	−	0.312932i
$652$	1.81062	−	1.33630i	0.0709093	−	0.0523335i
$653$	20.9983	−	15.4974i	0.821727	−	0.606462i	−0.0996986	−	0.995018i	$-0.531788\pi$
$653$	20.9983	−	15.4974i	0.821727	−	0.606462i	0.921425	+	0.388556i	$0.127026\pi$
$654$	0.173489	+	0.260121i	0.00678396	+	0.0101715i
$655$	2.90740	+	10.8506i	0.113601	+	0.423966i
$656$	15.7325	−	5.50504i	0.614251	−	0.214936i
$657$	4.73113	+	7.88188i	0.184579	+	0.307501i
$658$	0.204343	−	0.0984063i	0.00796611	−	0.00383628i
$659$	−4.29309	+	3.69450i	−0.167235	+	0.143917i	−0.731924	−	0.681387i	$-0.761377\pi$
$659$	−4.29309	+	3.69450i	−0.167235	+	0.143917i	0.564689	+	0.825304i	$0.308996\pi$
$660$	1.86056	+	2.04667i	0.0724223	+	0.0796667i
$661$	28.9247	+	4.35970i	1.12504	+	0.169573i	0.685096	−	0.728453i	$-0.259760\pi$
$661$	28.9247	+	4.35970i	1.12504	+	0.169573i	0.439944	+	0.898025i	$0.354998\pi$
$662$	0.936948	+	0.367725i	0.0364155	+	0.0142920i
$663$	−18.5346	−	62.3373i	−0.719823	−	2.42098i
$664$	0.804413	+	1.52202i	0.0312173	+	0.0590659i
$665$	−1.52372	−	0.171682i	−0.0590874	−	0.00665756i
$666$	−0.318456	+	0.526488i	−0.0123399	+	0.0204010i
$667$	21.8316	−	24.9821i	0.845322	−	0.967310i
$668$	22.8702	+	13.2041i	0.884875	+	0.510883i
$669$	25.1267	−	33.3288i	0.971456	−	1.28857i
$670$	−0.00924917	+	0.247189i	−0.000357327	+	0.00954975i
$671$	−7.57570	+	2.33679i	−0.292457	+	0.0902109i
$672$	0.571105	+	0.731317i	0.0220309	+	0.0282112i
$673$	20.6754	−	8.11450i	0.796978	−	0.312791i	0.0683157	−	0.997664i	$-0.478237\pi$
$673$	20.6754	−	8.11450i	0.796978	−	0.312791i	0.728663	+	0.684873i	$0.240142\pi$
$674$	0.746092	−	0.170291i	0.0287384	−	0.00655935i
$675$	17.1185	−	13.8433i	0.658892	−	0.532830i
$676$	−29.7483	−	61.7729i	−1.14416	−	2.37588i
$677$	−11.4000	+	0.426557i	−0.438137	+	0.0163939i	−0.255550	−	0.966796i	$-0.582257\pi$
$677$	−11.4000	+	0.426557i	−0.438137	+	0.0163939i	−0.182587	+	0.983190i	$0.558447\pi$
$678$	−0.311169	+	0.105334i	−0.0119504	+	0.00404532i
$679$	−2.47848	+	9.24982i	−0.0951154	+	0.354975i
$680$	−0.0547964	−	0.731208i	−0.00210135	−	0.0280405i
$681$	−9.30203	+	20.7409i	−0.356455	+	0.794793i
$682$	−0.0622372	+	0.142649i	−0.00238318	+	0.00546232i
$683$	11.4109	−	23.6950i	0.436626	−	0.906663i	−0.560298	−	0.828291i	$-0.689314\pi$
$683$	11.4109	−	23.6950i	0.436626	−	0.906663i	0.996924	−	0.0783720i	$-0.0249722\pi$
$684$	8.69777	+	2.52174i	0.332567	+	0.0964211i
$685$	4.64843	+	13.2845i	0.177608	+	0.507573i
$686$	−0.0211362	−	0.564878i	−0.000806985	−	0.0215671i
$687$	−29.1655	−	20.3234i	−1.11273	−	0.775386i
$688$	−15.9280	+	3.01374i	−0.607249	+	0.114898i
$689$	−42.3177	+	39.2651i	−1.61218	+	1.49588i
$690$	0.0570366	−	0.353890i	0.00217135	−	0.0134724i
$691$	−29.9252	+	4.51050i	−1.13841	+	0.171587i	−0.691077	−	0.722781i	$-0.742863\pi$
$691$	−29.9252	+	4.51050i	−1.13841	+	0.171587i	−0.447331	+	0.894368i	$0.647625\pi$
$692$	6.35709	+	1.45096i	0.241660	+	0.0551574i
$693$	0.184196	−	3.18362i	0.00699701	−	0.120936i
$694$	−0.0330902	+	0.293684i	−0.00125609	+	0.0111481i
$695$	6.23909	−	10.8064i	0.236662	−	0.409911i
$696$	1.42778	−	0.135186i	0.0541198	−	0.00512420i
$697$	11.3992	+	19.7440i	0.431776	+	0.747857i
$698$	−0.387889	+	0.169234i	−0.0146818	+	0.00640561i
$699$	1.72697	−	2.68724i	0.0653200	−	0.101641i
$700$	−6.69296	+	7.21330i	−0.252970	+	0.272637i
$701$	−14.9462	−	18.7420i	−0.564512	−	0.707875i	0.414873	−	0.909879i	$-0.363826\pi$
$701$	−14.9462	−	18.7420i	−0.564512	−	0.707875i	−0.979385	+	0.202004i	$0.935255\pi$
$702$	0.889328	−	1.04777i	0.0335655	−	0.0395454i
$703$	−1.79269	−	7.85430i	−0.0676127	−	0.296231i
$704$	4.75204	+	5.52197i	0.179099	+	0.208117i
$705$	3.26121	+	6.95244i	0.122824	+	0.261844i
$706$	0.676430	+	0.357504i	0.0254578	+	0.0134548i
$707$	−7.75365	+	9.00991i	−0.291606	+	0.338852i
$708$	12.0436	+	46.8533i	0.452627	+	1.76085i
$709$	−10.5791	−	15.5166i	−0.397305	−	0.582739i	0.574506	−	0.818500i	$-0.305194\pi$
$709$	−10.5791	−	15.5166i	−0.397305	−	0.582739i	−0.971811	+	0.235761i	$0.924242\pi$
$710$	0.235525	−	0.0265372i	0.00883908	−	0.000995925i
$711$	12.4032	−	26.9171i	0.465155	−	1.00947i
$712$	−2.24214	−	1.07976i	−0.0840279	−	0.0404657i
$713$	−26.3311	+	7.05541i	−0.986109	+	0.264227i
$714$	−0.278867	+	0.317445i	−0.0104363	+	0.0118801i
$715$	−2.56806	+	4.85901i	−0.0960401	+	0.181717i
$716$	−1.09093	+	1.60011i	−0.0407701	+	0.0597988i
$717$	−2.18985	−	12.2565i	−0.0817814	−	0.457726i
$718$	−0.275520	+	0.893213i	−0.0102823	+	0.0333344i
$719$	−25.0534	−	19.9794i	−0.934335	−	0.745107i	0.0327761	−	0.999463i	$-0.489565\pi$
$719$	−25.0534	−	19.9794i	−0.934335	−	0.745107i	−0.967111	+	0.254356i	$0.918137\pi$
$720$	−8.30890	+	6.35333i	−0.309655	+	0.236774i
$721$	−0.143438	+	0.628443i	−0.00534191	+	0.0234044i
$722$	−0.568392	+	0.300404i	−0.0211534	+	0.0111799i
$723$	11.5072	+	8.67533i	0.427958	+	0.322639i
$724$	−14.5892	+	8.42310i	−0.542205	+	0.313042i
$725$	5.73758	+	22.0831i	0.213088	+	0.820146i
$726$	0.00690207	−	0.676883i	0.000256160	−	0.0251215i
$727$	−3.50894	+	4.75445i	−0.130139	+	0.176333i	−0.864822	−	0.502078i	$-0.832569\pi$
$727$	−3.50894	+	4.75445i	−0.130139	+	0.176333i	0.734683	+	0.678411i	$0.237331\pi$
$728$	−0.653858	+	1.04061i	−0.0242336	+	0.0385675i
$729$	−25.9065	−	7.60624i	−0.959499	−	0.281712i
$730$	−0.0804779	+	0.0641790i	−0.00297862	+	0.00237537i
$731$	−8.10069	−	20.6402i	−0.299615	−	0.763406i
$732$	−6.37744	−	29.3161i	−0.235717	−	1.08356i
$733$	−7.25999	−	38.3700i	−0.268154	−	1.41723i	−0.814741	−	0.579825i	$-0.803121\pi$
$733$	−7.25999	−	38.3700i	−0.268154	−	1.41723i	0.546587	−	0.837402i	$-0.315927\pi$
$734$	−0.554225	−	0.377864i	−0.0204568	−	0.0139472i
$735$	8.54492	−	0.232508i	0.315184	−	0.00857620i
$736$	0.528007	−	2.79058i	0.0194626	−	0.102862i
$737$	4.76280	−	4.76280i	0.175440	−	0.175440i
$738$	−0.217843	+	0.429712i	−0.00801890	+	0.0158179i
$739$	5.61262	+	49.8134i	0.206464	+	1.83242i	0.487975	+	0.872857i	$0.337736\pi$
$739$	5.61262	+	49.8134i	0.206464	+	1.83242i	−0.281512	+	0.959558i	$0.590836\pi$
$740$	8.53490	+	3.72374i	0.313749	+	0.136887i
$741$	1.16166	+	17.9564i	0.0426747	+	0.659645i
$742$	0.362288	+	0.0970749i	0.0133000	+	0.00356373i
$743$	−25.0819	−	21.5847i	−0.920165	−	0.791866i	0.0582961	−	0.998299i	$-0.481433\pi$
$743$	−25.0819	−	21.5847i	−0.920165	−	0.791866i	−0.978461	+	0.206434i	$0.933814\pi$
$744$	−1.03616	−	0.561215i	−0.0379874	−	0.0205751i
$745$	0.498138	−	6.64719i	0.0182504	−	0.243534i
$746$	0.601376	+	0.210431i	0.0220180	+	0.00770441i
$747$	31.8880	+	10.5529i	1.16672	+	0.386111i
$748$	−6.22214	+	7.80231i	−0.227504	+	0.285281i
$749$	−1.23438	−	8.18956i	−0.0451032	−	0.299240i
$750$	0.390217	+	0.369544i	0.0142487	+	0.0134938i
$751$	−39.6474	−	1.48350i	−1.44675	−	0.0541337i	−0.697580	−	0.716507i	$-0.745740\pi$
$751$	−39.6474	−	1.48350i	−1.44675	−	0.0541337i	−0.749174	+	0.662373i	$0.769549\pi$
$752$	8.10035	+	18.5662i	0.295389	+	0.677040i
$753$	−50.0410	−	0.510260i	−1.82359	−	0.0185949i
$754$	0.608206	+	1.28791i	0.0221496	+	0.0469029i
$755$			6.83573i			0.248778i
$756$	11.9452	+	1.71733i	0.434442	+	0.0624587i
$757$	1.11860	+	0.702864i	0.0406563	+	0.0255460i	0.552207	−	0.833707i	$-0.313786\pi$
$757$	1.11860	+	0.702864i	0.0406563	+	0.0255460i	−0.511551	+	0.859253i	$0.670929\pi$
$758$	0.704227	+	0.653427i	0.0255787	+	0.0237336i
$759$	−7.69288	+	6.00758i	−0.279234	+	0.218061i
$760$	−0.0302378	+	0.200615i	−0.00109684	+	0.00727706i
$761$	−1.37078	−	1.47735i	−0.0496908	−	0.0535539i	0.707717	−	0.706496i	$-0.249725\pi$
$761$	−1.37078	−	1.47735i	−0.0496908	−	0.0535539i	−0.757408	+	0.652942i	$0.773535\pi$
$762$	−0.215153	−	0.255231i	−0.00779419	−	0.00924604i
$763$	−5.44016	−	0.407683i	−0.196947	−	0.0147591i
$764$	−11.3288	−	18.0296i	−0.409860	−	0.652289i
$765$	−10.6515	−	9.55125i	−0.385106	−	0.345326i
$766$	−0.726339	−	0.726339i	−0.0262437	−	0.0262437i
$767$	−79.4203	+	54.1478i	−2.86770	+	1.95516i
$768$	−22.2984	+	16.1084i	−0.804624	+	0.581261i
$769$	11.3588	+	15.3906i	0.409608	+	0.554999i	0.960033	−	0.279885i	$-0.0902964\pi$
$769$	11.3588	+	15.3906i	0.409608	+	0.554999i	−0.550426	+	0.834884i	$0.685535\pi$
$770$	0.0356079	−	0.00266844i	0.00128322	−	9.61639e-5i
$771$	−6.95712	+	24.9441i	−0.250555	+	0.898341i
$772$	5.74305	+	1.08664i	0.206697	+	0.0391091i
$773$	−38.9653	+	24.4835i	−1.40148	+	0.880610i	−0.999388	−	0.0349872i	$-0.988861\pi$
$773$	−38.9653	+	24.4835i	−1.40148	+	0.880610i	−0.402096	+	0.915598i	$0.631718\pi$
$774$	0.271788	−	0.381679i	0.00976923	−	0.0137192i
$775$	6.19175	−	17.6950i	0.222414	−	0.635623i
$776$	1.21073	+	0.373462i	0.0434628	+	0.0134065i
$777$	−3.82014	−	10.0332i	−0.137047	−	0.359938i
$778$	0.0161063	−	0.0410381i	0.000577437	−	0.00147129i
$779$	−1.85930	−	6.02770i	−0.0666164	−	0.215965i
$780$	−17.4967	−	11.2443i	−0.626482	−	0.402612i
$781$	−5.19276	−	3.83243i	−0.185812	−	0.137135i
$782$	1.29330			0.0462484
$783$	18.2692	−	21.1952i	0.652887	−	0.757455i
$784$	22.5480			0.805284
$785$	2.94049	+	2.17018i	0.104951	+	0.0774571i
$786$	−0.720510	−	0.463040i	−0.0256997	−	0.0165161i
$787$	8.22738	+	26.6725i	0.293274	+	0.950772i	0.975569	+	0.219695i	$0.0705061\pi$
$787$	8.22738	+	26.6725i	0.293274	+	0.950772i	−0.682294	+	0.731078i	$0.739018\pi$
$788$	8.77228	−	22.3514i	0.312500	−	0.796236i
$789$	4.39515	+	11.5434i	0.156471	+	0.410955i
$790$	0.317115	+	0.0978171i	0.0112825	+	0.00348018i
$791$	1.89312	−	5.41023i	0.0673116	−	0.192366i
$792$	−0.420021	−	0.0401042i	−0.0149248	−	0.00142504i
$793$	50.4756	−	31.7159i	1.79244	−	1.12627i
$794$	1.41060	+	0.266899i	0.0500602	+	0.00947191i
$795$	−3.41175	+	12.2325i	−0.121002	+	0.433843i
$796$	7.68490	−	0.575903i	0.272384	−	0.0204124i
$797$	−12.2238	−	16.5626i	−0.432988	−	0.586678i	0.532725	−	0.846288i	$-0.321168\pi$
$797$	−12.2238	−	16.5626i	−0.432988	−	0.586678i	−0.965714	+	0.259610i	$0.916406\pi$
$798$	0.0947680	−	0.0684604i	0.00335475	−	0.00242347i
$799$	−22.8924	+	15.6078i	−0.809875	+	0.552163i
$800$	1.38110	+	1.38110i	0.0488291	+	0.0488291i
$801$	−46.1479	+	15.0989i	−1.63056	+	0.533492i
$802$	0.350095	+	0.557172i	0.0123623	+	0.0196744i
$803$	2.79506	+	0.209461i	0.0986356	+	0.00739171i
$804$	16.4288	+	19.4891i	0.579399	+	0.687326i
$805$	4.25403	+	4.58475i	0.149935	+	0.161591i
$806$	0.174420	−	1.15720i	0.00614370	−	0.0407608i
$807$	24.8763	−	19.4266i	0.875688	−	0.683848i
$808$	1.15291	+	1.06975i	0.0405594	+	0.0376336i
$809$	23.7229	+	14.9061i	0.834051	+	0.524069i	0.880055	−	0.474872i	$-0.157506\pi$
$809$	23.7229	+	14.9061i	0.834051	+	0.524069i	−0.0460037	+	0.998941i	$0.514649\pi$
$810$	0.0460718	−	0.298798i	0.00161880	−	0.0104987i
$811$			25.8319i			0.907082i	0.891236	+	0.453541i	$0.149839\pi$
$811$			25.8319i			0.907082i	−0.891236	+	0.453541i	$0.850161\pi$
$812$	−6.73442	+	10.5391i	−0.236332	+	0.369849i
$813$	−12.9811	−	0.132366i	−0.455266	−	0.00464228i
$814$	0.0750230	+	0.171955i	0.00262955	+	0.00602700i
$815$	0.982952	+	0.0367795i	0.0344313	+	0.00128833i
$816$	−27.4006	−	25.9490i	−0.959214	−	0.908396i
$817$	0.914359	+	6.06638i	0.0319894	+	0.212236i
$818$	0.446242	−	0.559570i	0.0156025	−	0.0195649i
$819$	4.85797	+	23.4815i	0.169751	+	0.820511i
$820$	6.88189	+	2.40808i	0.240326	+	0.0840937i
$821$	−3.51777	+	46.9414i	−0.122771	+	1.63827i	0.507329	+	0.861752i	$0.330633\pi$
$821$	−3.51777	+	46.9414i	−0.122771	+	1.63827i	−0.630100	+	0.776514i	$0.716986\pi$
$822$	−0.943559	−	0.511061i	−0.0329104	−	0.0178253i
$823$	−22.9438	−	19.7447i	−0.799771	−	0.688258i	0.154239	−	0.988034i	$-0.450707\pi$
$823$	−22.9438	−	19.7447i	−0.799771	−	0.688258i	−0.954010	+	0.299775i	$0.903088\pi$
$824$	0.0823820	+	0.0220742i	0.00286991	+	0.000768991i
$825$	−0.433351	−	6.69855i	−0.0150874	−	0.233213i
$826$	0.572414	+	0.249742i	0.0199168	+	0.00868963i
$827$	1.79003	+	15.8869i	0.0622454	+	0.552443i	0.985673	+	0.168670i	$0.0539471\pi$
$827$	1.79003	+	15.8869i	0.0622454	+	0.552443i	−0.923427	+	0.383773i	$0.874624\pi$
$828$	−20.1811	−	30.9373i	−0.701341	−	1.07515i
$829$	4.64232	−	4.64232i	0.161234	−	0.161234i	−0.621879	−	0.783113i	$-0.713630\pi$
$829$	4.64232	−	4.64232i	0.161234	−	0.161234i	0.783113	+	0.621879i	$0.213630\pi$
$830$	−0.0699224	+	0.369549i	−0.00242704	+	0.0128272i
$831$	−37.1523	+	1.01092i	−1.28880	+	0.0350684i
$832$	−45.2613	−	30.8587i	−1.56915	−	1.06983i
$833$	5.73375	+	30.3036i	0.198663	+	1.04996i
$834$	0.202234	+	0.929639i	0.00700279	+	0.0321908i
$835$	4.21722	+	10.7453i	0.145943	+	0.371856i
$836$	2.15877	−	1.72156i	0.0746627	−	0.0595415i
$837$	−22.1671	+	6.10176i	−0.766206	+	0.210908i
$838$	−0.565172	+	0.899466i	−0.0195235	+	0.0310715i
$839$	23.3849	−	31.6854i	0.807337	−	1.09390i	−0.186435	−	0.982467i	$-0.559693\pi$
$839$	23.3849	−	31.6854i	0.807337	−	1.09390i	0.993772	−	0.111435i	$-0.0355448\pi$
$840$	−0.00275667	+	0.270345i	−9.51141e−5	+	0.00932780i
$841$	12.1839	+	26.3164i	0.420136	+	0.907461i
$842$	−0.538425	+	0.310860i	−0.0185554	+	0.0107129i
$843$	−40.8288	−	30.7810i	−1.40622	−	1.06015i
$844$	7.17092	−	3.78994i	0.246833	−	0.130455i
$845$	6.66879	−	29.2179i	0.229414	−	1.00513i
$846$	−0.540551	−	0.224976i	−0.0185845	−	0.00773485i
$847$	9.23407	+	7.36392i	0.317286	+	0.253027i
$848$	−9.87378	+	32.0100i	−0.339067	+	1.09923i
$849$	−2.47881	−	13.8738i	−0.0850724	−	0.476146i
$850$	−0.501028	+	0.734873i	−0.0171851	+	0.0252059i
$851$	−15.3546	+	29.0522i	−0.526348	+	0.995898i
$852$	16.1191	−	18.3489i	0.552230	−	0.628624i
$853$	31.3884	−	8.41050i	1.07472	−	0.287970i	0.322289	−	0.946641i	$-0.395548\pi$
$853$	31.3884	−	8.41050i	1.07472	−	0.287970i	0.752431	+	0.658671i	$0.228881\pi$
$854$	−0.348957	−	0.168049i	−0.0119411	−	0.00575052i
$855$	2.28516	+	3.23221i	0.0781507	+	0.110539i
$856$	−1.08892	+	0.122691i	−0.0372184	+	0.00419350i
$857$	21.4711	+	31.4923i	0.733439	+	1.07576i	0.993901	+	0.110273i	$0.0351727\pi$
$857$	21.4711	+	31.4923i	0.733439	+	1.07576i	−0.260462	+	0.965484i	$0.583875\pi$
$858$	−0.104320	−	0.405835i	−0.00356142	−	0.0138550i
$859$	34.6425	−	40.2553i	1.18199	−	1.37349i	0.270215	−	0.962800i	$-0.412905\pi$
$859$	34.6425	−	40.2553i	1.18199	−	1.37349i	0.911773	−	0.410695i	$-0.134714\pi$
$860$	−6.26928	−	3.31341i	−0.213781	−	0.112986i
$861$	−3.56981	−	7.61033i	−0.121659	−	0.259359i
$862$	−0.254832	−	0.296120i	−0.00867961	−	0.0100859i
$863$	−2.06024	−	9.02652i	−0.0701315	−	0.307266i	0.927681	−	0.373374i	$-0.121799\pi$
$863$	−2.06024	−	9.02652i	−0.0701315	−	0.307266i	−0.997813	+	0.0661076i	$0.978942\pi$
$864$	0.429290	−	2.35660i	0.0146047	−	0.0801732i
$865$	1.77707	+	2.22837i	0.0604220	+	0.0757668i
$866$	0.714562	−	0.770115i	0.0242818	−	0.0261696i
$867$	11.9877	−	18.6533i	0.407123	−	0.633500i
$868$	9.41892	−	4.10943i	0.319699	−	0.139483i
$869$	−4.51822	−	7.82579i	−0.153270	−	0.265472i
$870$	0.262292	+	0.171395i	0.00889253	+	0.00581083i
$871$	−25.3238	+	43.8620i	−0.858063	+	1.48621i
$872$	−0.0808170	+	0.717271i	−0.00273681	+	0.0242899i
$873$	22.0872	−	11.1033i	0.747540	−	0.375789i
$874$	−0.348864	−	0.0796260i	−0.0118005	−	0.00269339i
$875$	−9.27232	+	1.39758i	−0.313462	+	0.0472467i
$876$	−1.68777	+	10.4719i	−0.0570244	+	0.353814i
$877$	19.8067	−	18.3780i	0.668826	−	0.620580i	−0.270860	−	0.962619i	$-0.587308\pi$
$877$	19.8067	−	18.3780i	0.668826	−	0.620580i	0.939686	+	0.342039i	$0.111118\pi$
$878$	−0.939578	+	0.177778i	−0.0317092	+	0.00599971i
$879$	30.6279	+	21.3425i	1.03305	+	0.719863i
$880$	0.119246	+	3.18691i	0.00401977	+	0.107431i
$881$	6.87784	+	19.6557i	0.231720	+	0.662219i	0.999762	+	0.0218189i	$0.00694571\pi$
$881$	6.87784	+	19.6557i	0.231720	+	0.662219i	−0.768042	+	0.640400i	$0.778769\pi$
$882$	−0.470150	+	0.451355i	−0.0158308	+	0.0151979i
$883$	11.0606	−	22.9676i	0.372219	−	0.772922i	−0.627766	−	0.778402i	$-0.716030\pi$
$883$	11.0606	−	22.9676i	0.372219	−	0.772922i	0.999985	+	0.00548090i	$0.00174463\pi$
$884$	30.0078	−	68.7785i	1.00927	−	2.31327i
$885$	−8.65317	+	19.2941i	−0.290873	+	0.648564i
$886$	−0.0514470	−	0.686512i	−0.00172839	−	0.0230638i
$887$	−2.93366	+	10.9486i	−0.0985026	+	0.367617i	−0.997527	−	0.0702814i	$-0.977610\pi$
$887$	−2.93366	+	10.9486i	−0.0985026	+	0.367617i	0.899025	+	0.437898i	$0.144277\pi$
$888$	−1.34547	+	0.455455i	−0.0451510	+	0.0152841i
$889$	5.82034	−	0.217782i	0.195208	−	0.00730417i
$890$	−0.235898	−	0.489847i	−0.00790732	−	0.0164197i
$891$	−6.45365	+	5.11096i	−0.216205	+	0.171224i
$892$	46.9532	−	10.7168i	1.57211	−	0.358824i
$893$	7.13609	−	2.80071i	0.238800	−	0.0937221i
$894$	0.312807	+	0.400559i	0.0104618	+	0.0133967i
$895$	−0.808901	+	0.249513i	−0.0270386	+	0.00834030i
$896$	−0.0533704	+	1.42635i	−0.00178298	+	0.0476512i
$897$	44.1829	−	58.6054i	1.47522	−	1.95678i
$898$	−0.316227	−	0.182574i	−0.0105526	−	0.00609256i
$899$	3.73037	−	23.5340i	0.124415	−	0.784904i
$900$	25.3972	+	0.517996i	0.846573	+	0.0172665i
$901$	−45.5310	−	5.13011i	−1.51686	−	0.170909i
$902$	0.0686391	+	0.129871i	0.00228543	+	0.00432425i
$903$	2.32996	+	7.83634i	0.0775361	+	0.260777i
$904$	−0.705965	−	0.277071i	−0.0234800	−	0.00921524i
$905$	−7.28135	−	1.09749i	−0.242040	−	0.0364817i
$906$	−0.350580	−	0.385648i	−0.0116472	−	0.0128123i
$907$	−12.1021	+	10.4147i	−0.401845	+	0.345815i	−0.829875	−	0.557949i	$-0.811588\pi$
$907$	−12.1021	+	10.4147i	−0.401845	+	0.345815i	0.428031	+	0.903764i	$0.359208\pi$
$908$	−23.6310	+	11.3801i	−0.784223	+	0.377662i
$909$	30.6818	−	0.521854i	1.01765	−	0.0173088i
$910$	−0.253432	+	0.0886796i	−0.00840118	+	0.00293970i
$911$	−13.5646	−	50.6239i	−0.449416	−	1.67724i	−0.704006	−	0.710194i	$-0.748607\pi$
$911$	−13.5646	−	50.6239i	−0.449416	−	1.67724i	0.254590	−	0.967049i	$-0.418059\pi$
$912$	5.79361	+	8.68665i	0.191845	+	0.287644i
$913$	8.24010	−	6.08147i	0.272707	−	0.201267i
$914$	−0.525355	+	0.387730i	−0.0173772	+	0.0128250i
$915$	5.81013	−	11.7567i	0.192077	−	0.388664i
$916$	−10.6160	−	39.6194i	−0.350762	−	1.30906i
$917$	14.1050	−	4.93556i	0.465789	−	0.162987i
$918$	1.09077	−	0.00742873i	0.0360007	−	0.000245184i
$919$	−5.54892	+	2.67222i	−0.183042	+	0.0881484i	−0.523160	−	0.852234i	$-0.675247\pi$
$919$	−5.54892	+	2.67222i	−0.183042	+	0.0881484i	0.340118	+	0.940383i	$0.389533\pi$
$920$	0.627233	−	0.539778i	0.0206793	−	0.0177960i
$921$	18.9345	−	4.11902i	0.623914	−	0.135726i
$922$	0.0510034	+	0.00768752i	0.00167971	+	0.000253175i
$923$	45.1743	+	17.7296i	1.48693	+	0.583577i
$924$	2.53010	−	2.67164i	0.0832342	−	0.0878906i
$925$	−10.5595	−	19.9796i	−0.347194	−	0.656924i
$926$	−0.121763	−	0.0137194i	−0.00400138	−	0.000450847i
$927$	1.45779	−	0.802472i	0.0478801	−	0.0263567i
$928$	2.04046	+	1.41400i	0.0669814	+	0.0464169i
$929$	17.8841	+	10.3254i	0.586757	+	0.338765i	0.763814	−	0.645436i	$-0.223324\pi$
$929$	17.8841	+	10.3254i	0.586757	+	0.338765i	−0.177057	+	0.984201i	$0.556658\pi$
$930$	−0.100539	−	0.237001i	−0.00329679	−	0.00777158i
$931$	0.319069	−	8.52731i	0.0104571	−	0.279471i
$932$	3.52201	−	1.08639i	0.115367	−	0.0355860i
$933$	−21.1678	+	52.3586i	−0.693004	+	1.71414i
$934$	−0.0464666	+	0.0182368i	−0.00152043	+	0.000596726i
$935$	−4.25276	+	0.970664i	−0.139080	+	0.0317441i
$936$	3.12872	−	0.526143i	0.102265	−	0.0171975i
$937$	−0.826636	−	1.71653i	−0.0270050	−	0.0560765i	0.887030	−	0.461712i	$-0.152765\pi$
$937$	−0.826636	−	1.71653i	−0.0270050	−	0.0560765i	−0.914035	+	0.405635i	$0.867050\pi$
$938$	0.328834	−	0.0123041i	0.0107368	−	0.000401744i
$939$	−3.34595	+	16.7471i	−0.109191	+	0.546522i
$940$	−2.29333	+	8.55883i	−0.0748002	+	0.279158i
$941$	−1.56690	−	20.9088i	−0.0510794	−	0.681607i	−0.962699	−	0.270573i	$-0.912787\pi$
$941$	−1.56690	−	20.9088i	−0.0510794	−	0.681607i	0.911620	−	0.411034i	$-0.134832\pi$
$942$	−0.277193	+	0.0283730i	−0.00903142	+	0.000924443i
$943$	−10.2888	+	23.5823i	−0.335051	+	0.767945i
$944$	−24.2010	+	50.2539i	−0.787676	+	1.63563i
$945$	3.61417	+	3.84233i	0.117569	+	0.124991i
$946$	−0.0471851	−	0.134847i	−0.00153412	−	0.00438426i
$947$	−0.984715	−	26.3171i	−0.0319989	−	0.855190i	−0.919196	−	0.393800i	$-0.871160\pi$
$947$	−0.984715	−	26.3171i	−0.0319989	−	0.855190i	0.887197	−	0.461390i	$-0.152649\pi$
$948$	30.9600	−	14.5225i	1.00553	−	0.471670i
$949$	−20.7086	+	3.91827i	−0.672229	+	0.127193i
$950$	0.180395	−	0.167382i	0.00585279	−	0.00543060i
$951$	−44.0978	+	16.7903i	−1.42997	+	0.544462i
$952$	−0.964554	+	0.145383i	−0.0312614	+	0.00471189i
$953$	54.2436	+	12.3807i	1.75712	+	0.401052i	0.975023	−	0.222103i	$-0.0712922\pi$
$953$	54.2436	+	12.3807i	1.75712	+	0.401052i	0.782098	+	0.623155i	$0.214149\pi$
$954$	−0.434883	−	0.865092i	−0.0140798	−	0.0280084i
$955$	1.04211	−	9.24897i	0.0337219	−	0.299290i
$956$	7.18302	−	12.4414i	0.232316	−	0.402382i
$957$	−2.06117	−	8.27908i	−0.0666281	−	0.267625i
$958$	0.574963	+	0.995865i	0.0185762	+	0.0321749i
$959$	17.1607	−	7.48714i	0.554148	−	0.241772i
$960$	−12.0372	−	0.573361i	−0.388499	−	0.0185051i
$961$	7.76881	−	8.37279i	0.250607	−	0.270090i
$962$	−0.879553	−	1.10292i	−0.0283579	−	0.0355597i
$963$	−13.6685	+	16.4405i	−0.440462	+	0.529789i
$964$	3.70010	+	16.2112i	0.119172	+	0.522127i
$965$	1.66651	+	1.93652i	0.0536468	+	0.0623387i
$966$	−0.475132	−	0.0404820i	−0.0152871	−	0.00130249i
$967$	−18.0449	−	9.53701i	−0.580285	−	0.306690i	0.151248	−	0.988496i	$-0.451671\pi$
$967$	−18.0449	−	9.53701i	−0.580285	−	0.306690i	−0.731533	+	0.681806i	$0.761195\pi$
$968$	1.01933	−	1.18448i	0.0327624	−	0.0380706i
$969$	−10.2013	+	9.99532i	−0.327712	+	0.321096i
$970$	0.155933	+	0.228711i	0.00500670	+	0.00734347i
$971$	28.0662	−	3.16231i	0.900688	−	0.101483i	0.350538	−	0.936549i	$-0.385999\pi$
$971$	28.0662	−	3.16231i	0.900688	−	0.101483i	0.550151	+	0.835065i	$0.314570\pi$
$972$	−17.1984	−	25.9765i	−0.551638	−	0.833197i
$973$	−14.9558	−	7.20231i	−0.479460	−	0.230896i
$974$	−0.214792	+	0.0575533i	−0.00688237	+	0.00184413i
$975$	16.1839	+	47.8091i	0.518299	+	1.53112i
$976$	16.1637	−	30.5832i	0.517387	−	0.978944i
$977$	0.108631	−	0.159332i	0.00347541	−	0.00509749i	−0.824497	−	0.565866i	$-0.808542\pi$
$977$	0.108631	−	0.159332i	0.00347541	−	0.00509749i	0.827973	+	0.560769i	$0.189494\pi$
$978$	−0.0573410	+	0.0483370i	−0.00183356	+	0.00154565i
$979$	−4.36371	+	14.1468i	−0.139465	+	0.452134i
$980$	7.71134	+	6.14959i	0.246330	+	0.196442i
$981$	8.55444	+	11.1875i	0.273122	+	0.357190i
$982$	0.144115	−	0.631408i	0.00459889	−	0.0201490i
$983$	−2.86630	+	1.51488i	−0.0914207	+	0.0483173i	−0.512354	−	0.858774i	$-0.671226\pi$
$983$	−2.86630	+	1.51488i	−0.0914207	+	0.0483173i	0.420933	+	0.907092i	$0.361703\pi$
$984$	−1.02389	+	0.434344i	−0.0326403	+	0.0138464i
$985$	9.08935	−	5.24774i	0.289611	−	0.167207i
$986$	−0.459930	+	1.03268i	−0.0146472	+	0.0328873i
$987$	8.89872	−	5.01740i	0.283249	−	0.159706i
$988$	−12.3290	+	16.7053i	−0.392239	+	0.531465i
$989$	13.3132	−	21.1878i	0.423334	−	0.673732i
$990$	−0.0662805	−	0.0640635i	−0.00210653	−	0.00203607i
$991$	8.35432	−	6.66235i	0.265384	−	0.211637i	−0.481753	−	0.876307i	$-0.660000\pi$
$991$	8.35432	−	6.66235i	0.265384	−	0.211637i	0.747136	+	0.664671i	$0.231428\pi$
$992$	−0.745208	−	1.89876i	−0.0236604	−	0.0602857i
$993$	43.1836	+	13.8041i	1.37039	+	0.438061i
$994$	−0.0586178	−	0.309803i	−0.00185924	−	0.00982634i
$995$	2.78322	+	1.89757i	0.0882340	+	0.0601569i
$996$	20.2839	+	33.0244i	0.642721	+	1.04642i
$997$	−10.2652	+	54.2527i	−0.325101	+	1.71820i	0.314297	+	0.949325i	$0.398231\pi$
$997$	−10.2652	+	54.2527i	−0.325101	+	1.71820i	−0.639398	+	0.768876i	$0.720816\pi$
$998$	−0.141426	+	0.141426i	−0.00447676	+	0.00447676i
$999$	−12.7831	+	24.5908i	−0.404440	+	0.778017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.2.15	✓	672
3.2	odd	2		783.2.be.a.89.14		672
9.4	even	3		783.2.be.a.611.14		672
9.5	odd	6	inner	261.2.x.a.176.15	yes	672
29.15	odd	28	inner	261.2.x.a.218.15	yes	672
87.44	even	28		783.2.be.a.305.14		672
261.131	even	84	inner	261.2.x.a.131.15	yes	672
261.247	odd	84		783.2.be.a.44.14		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.2.15	✓	672	1.1	even	1	trivial
261.2.x.a.131.15	yes	672	261.131	even	84	inner
261.2.x.a.176.15	yes	672	9.5	odd	6	inner
261.2.x.a.218.15	yes	672	29.15	odd	28	inner
783.2.be.a.44.14		672	261.247	odd	84
783.2.be.a.89.14		672	3.2	odd	2
783.2.be.a.305.14		672	87.44	even	28
783.2.be.a.611.14		672	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0309399 - 0.0228347i) q^{2} +(-1.45710 - 0.936412i) q^{3} +(-0.589074 - 1.90973i) q^{4} +(0.319150 - 0.813182i) q^{5} +(0.0236998 + 0.0622449i) q^{6} +(-1.11047 - 0.342536i) q^{7} +(-0.0507833 + 0.145130i) q^{8} +(1.24626 + 2.72889i) q^{9} +O(q^{10})\)	\(q+(-0.0309399 - 0.0228347i) q^{2} +(-1.45710 - 0.936412i) q^{3} +(-0.589074 - 1.90973i) q^{4} +(0.319150 - 0.813182i) q^{5} +(0.0236998 + 0.0622449i) q^{6} +(-1.11047 - 0.342536i) q^{7} +(-0.0507833 + 0.145130i) q^{8} +(1.24626 + 2.72889i) q^{9} +(-0.0284432 + 0.0178721i) q^{10} +(0.898758 + 0.170054i) q^{11} +(-0.929958 + 3.33428i) q^{12} +(-6.85876 + 0.513993i) q^{13} +(0.0265362 + 0.0359553i) q^{14} +(-1.22651 + 0.886028i) q^{15} +(-3.29763 + 2.24828i) q^{16} +(-3.86016 - 3.86016i) q^{17} +(0.0237540 - 0.112890i) q^{18} +(0.803604 + 1.27893i) q^{19} +(-1.74096 - 0.130467i) q^{20} +(1.29731 + 1.53897i) q^{21} +(-0.0239243 - 0.0257843i) q^{22} +(0.918226 - 6.09203i) q^{23} +(0.209898 - 0.163915i) q^{24} +(3.10585 + 2.88181i) q^{25} +(0.223946 + 0.140715i) q^{26} +(0.739436 - 5.14327i) q^{27} +2.32249i q^{28} +(4.53784 + 2.89966i) q^{29} +(0.0581802 + 0.000593254i) q^{30} +(-1.76941 - 4.05553i) q^{31} +(0.460669 + 0.0172370i) q^{32} +(-1.15034 - 1.08939i) q^{33} +(0.0312874 + 0.207579i) q^{34} +(-0.632952 + 0.793696i) q^{35} +(4.47730 - 3.98755i) q^{36} +(-5.03442 - 1.76162i) q^{37} +(0.00434050 - 0.0579200i) q^{38} +(10.4752 + 5.67369i) q^{39} +(0.101810 + 0.0876144i) q^{40} +(-4.03392 - 1.08089i) q^{41} +(-0.00499687 - 0.0772393i) q^{42} +(3.72276 + 1.62422i) q^{43} +(-0.204677 - 1.81656i) q^{44} +(2.61683 - 0.142514i) q^{45} +(-0.167519 + 0.167519i) q^{46} +(0.943565 - 4.98686i) q^{47} +(6.91028 - 0.188030i) q^{48} +(-4.66785 - 3.18249i) q^{49} +(-0.0302895 - 0.160084i) q^{50} +(2.00993 + 9.23933i) q^{51} +(5.02191 + 12.7956i) q^{52} +(6.56205 - 5.23306i) q^{53} +(-0.140323 + 0.142247i) q^{54} +(0.425124 - 0.676581i) q^{55} +(0.106106 - 0.143768i) q^{56} +(0.0266752 - 2.61603i) q^{57} +(-0.0741874 - 0.193335i) q^{58} +(12.1030 - 6.98770i) q^{59} +(2.41458 + 1.82036i) q^{60} +(-7.66279 + 4.04990i) q^{61} +(-0.0378614 + 0.165882i) q^{62} +(-0.449202 - 3.45725i) q^{63} +(6.22692 + 4.96581i) q^{64} +(-1.77101 + 5.74146i) q^{65} +(0.0107153 + 0.0599733i) q^{66} +(4.14812 - 6.08418i) q^{67} +(-5.09795 + 9.64580i) q^{68} +(-7.04259 + 8.01684i) q^{69} +(0.0377073 - 0.0101036i) q^{70} +(-6.35694 - 3.06134i) q^{71} +(-0.459333 + 0.0422888i) q^{72} +(3.04500 - 0.343089i) q^{73} +(0.115538 + 0.169464i) q^{74} +(-1.82697 - 7.10743i) q^{75} +(1.96903 - 2.28805i) q^{76} +(-0.939797 - 0.496697i) q^{77} +(-0.194544 - 0.414741i) q^{78} +(-6.44400 - 7.48807i) q^{79} +(0.775825 + 3.39911i) q^{80} +(-5.89365 + 6.80183i) q^{81} +(0.100127 + 0.125556i) q^{82} +(7.61539 - 8.20744i) q^{83} +(2.17480 - 3.38409i) q^{84} +(-4.37098 + 1.90704i) q^{85} +(-0.0780932 - 0.135261i) q^{86} +(-3.89679 - 8.47437i) q^{87} +(-0.0703218 + 0.121801i) q^{88} +(-1.81215 + 16.0833i) q^{89} +(-0.0842186 - 0.0553450i) q^{90} +(7.79253 + 1.77859i) q^{91} +(-12.1750 + 1.83509i) q^{92} +(-1.21945 + 7.56621i) q^{93} +(-0.143067 + 0.132747i) q^{94} +(1.29647 - 0.245306i) q^{95} +(-0.655099 - 0.456492i) q^{96} +(-0.308116 - 8.23458i) q^{97} +(0.0717517 + 0.205055i) q^{98} +(0.656031 + 2.66454i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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