LMFDB - Embedded newform 135.2.q.a.113.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			113.9
Character	$\chi$	$=$	135.113
Dual form			135.2.q.a.92.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0152086 - 0.00133058i) q^{2} +(0.259886 - 1.71244i) q^{3} +(-1.96939 - 0.347256i) q^{4} +(-1.79388 - 1.33492i) q^{5} +(-0.00623106 + 0.0256981i) q^{6} +(0.211408 + 0.148030i) q^{7} +(0.0589827 + 0.0158044i) q^{8} +(-2.86492 - 0.890079i) q^{9} +O(q^{10})$	\(q+(-0.0152086 - 0.00133058i) q^{2} +(0.259886 - 1.71244i) q^{3} +(-1.96939 - 0.347256i) q^{4} +(-1.79388 - 1.33492i) q^{5} +(-0.00623106 + 0.0256981i) q^{6} +(0.211408 + 0.148030i) q^{7} +(0.0589827 + 0.0158044i) q^{8} +(-2.86492 - 0.890079i) q^{9} +(0.0255062 + 0.0226891i) q^{10} +(1.49616 - 4.11066i) q^{11} +(-1.10647 + 3.28221i) q^{12} +(0.187451 + 2.14258i) q^{13} +(-0.00301826 - 0.00253263i) q^{14} +(-2.75217 + 2.72499i) q^{15} +(3.75746 + 1.36760i) q^{16} +(1.70216 - 0.456091i) q^{17} +(0.0423872 + 0.0173489i) q^{18} +(4.91894 - 2.83995i) q^{19} +(3.06928 + 3.25190i) q^{20} +(0.308434 - 0.323554i) q^{21} +(-0.0282241 + 0.0605267i) q^{22} +(-3.32360 - 4.74660i) q^{23} +(0.0423928 - 0.0968971i) q^{24} +(1.43600 + 4.78935i) q^{25} -0.0328351i q^{26} +(-2.26876 + 4.67469i) q^{27} +(-0.364940 - 0.364940i) q^{28} +(3.59567 - 3.01712i) q^{29} +(0.0454826 - 0.0377814i) q^{30} +(-0.912568 + 5.17543i) q^{31} +(-0.166010 - 0.0774120i) q^{32} +(-6.65044 - 3.63039i) q^{33} +(-0.0264943 + 0.00467167i) q^{34} +(-0.181634 - 0.547759i) q^{35} +(5.33305 + 2.74777i) q^{36} +(-0.837479 - 3.12552i) q^{37} +(-0.0785891 + 0.0366467i) q^{38} +(3.71775 + 0.235826i) q^{39} +(-0.0847103 - 0.107088i) q^{40} +(0.241984 - 0.288386i) q^{41} +(-0.00512138 + 0.00451041i) q^{42} +(3.84888 + 8.25395i) q^{43} +(-4.37396 + 7.57592i) q^{44} +(3.95114 + 5.42112i) q^{45} +(0.0442317 + 0.0766116i) q^{46} +(-2.29910 + 3.28345i) q^{47} +(3.31845 - 6.07901i) q^{48} +(-2.37136 - 6.51526i) q^{49} +(-0.0154670 - 0.0747502i) q^{50} +(-0.338664 - 3.03338i) q^{51} +(0.374859 - 4.28465i) q^{52} +(-8.15900 + 8.15900i) q^{53} +(0.0407248 - 0.0680769i) q^{54} +(-8.17131 + 5.37678i) q^{55} +(0.0101299 + 0.0120724i) q^{56} +(-3.58489 - 9.16146i) q^{57} +(-0.0586997 + 0.0411020i) q^{58} +(10.6146 - 3.86341i) q^{59} +(6.36635 - 4.41085i) q^{60} +(-2.10712 - 11.9501i) q^{61} +(0.0207652 - 0.0774969i) q^{62} +(-0.473909 - 0.612263i) q^{63} +(-6.92336 - 3.99720i) q^{64} +(2.52389 - 4.09375i) q^{65} +(0.0963135 + 0.0640622i) q^{66} +(1.82940 - 0.160052i) q^{67} +(-3.51058 + 0.307136i) q^{68} +(-8.99203 + 4.45790i) q^{69} +(0.00203356 + 0.00857235i) q^{70} +(4.44360 + 2.56551i) q^{71} +(-0.154913 - 0.0977775i) q^{72} +(3.71651 - 13.8702i) q^{73} +(0.00857816 + 0.0486492i) q^{74} +(8.57469 - 1.21438i) q^{75} +(-10.6735 + 3.88483i) q^{76} +(0.924799 - 0.647552i) q^{77} +(-0.0562282 - 0.00853337i) q^{78} +(1.98949 + 2.37099i) q^{79} +(-4.91479 - 7.46920i) q^{80} +(7.41552 + 5.10001i) q^{81} +(-0.00406398 + 0.00406398i) q^{82} +(-0.432904 + 4.94812i) q^{83} +(-0.719782 + 0.530096i) q^{84} +(-3.66230 - 1.45406i) q^{85} +(-0.0475536 - 0.130653i) q^{86} +(-4.23219 - 6.94148i) q^{87} +(0.153214 - 0.218812i) q^{88} +(-1.44584 - 2.50426i) q^{89} +(-0.0528781 - 0.0877051i) q^{90} +(-0.277536 + 0.480707i) q^{91} +(4.89717 + 10.5020i) q^{92} +(8.62546 + 2.90774i) q^{93} +(0.0393351 - 0.0468777i) q^{94} +(-12.6151 - 1.47184i) q^{95} +(-0.175707 + 0.264165i) q^{96} +(-4.27105 + 1.99162i) q^{97} +(0.0273961 + 0.102243i) q^{98} +(-7.94518 + 10.4450i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.0152086	−	0.00133058i	−0.0107541	−	0.000940864i	0.0817774	−	0.996651i	$-0.473940\pi$
$2$	−0.0152086	−	0.00133058i	−0.0107541	−	0.000940864i	−0.0925315	+	0.995710i	$0.529496\pi$
$3$	0.259886	−	1.71244i	0.150045	−	0.988679i
$3$	0.259886	−	1.71244i	0.150045	−	0.988679i
$4$	−1.96939	−	0.347256i	−0.984693	−	0.173628i
$5$	−1.79388	−	1.33492i	−0.802247	−	0.596992i
$5$	−1.79388	−	1.33492i	−0.802247	−	0.596992i
$6$	−0.00623106	+	0.0256981i	−0.00254382	+	0.0104912i
$7$	0.211408	+	0.148030i	0.0799048	+	0.0559499i	0.612846	−	0.790202i	$-0.290025\pi$
$7$	0.211408	+	0.148030i	0.0799048	+	0.0559499i	−0.532941	+	0.846152i	$0.678913\pi$
$8$	0.0589827	+	0.0158044i	0.0208535	+	0.00558769i
$9$	−2.86492	−	0.890079i	−0.954973	−	0.296693i
$10$	0.0255062	+	0.0226891i	0.00806578	+	0.00717494i
$11$	1.49616	−	4.11066i	0.451108	−	1.23941i	−0.480836	−	0.876810i	$-0.659667\pi$
$11$	1.49616	−	4.11066i	0.451108	−	1.23941i	0.931945	−	0.362600i	$-0.118111\pi$
$12$	−1.10647	+	3.28221i	−0.319411	+	0.947493i
$13$	0.187451	+	2.14258i	0.0519896	+	0.594244i	0.976848	+	0.213933i	$0.0686274\pi$
$13$	0.187451	+	2.14258i	0.0519896	+	0.594244i	−0.924859	+	0.380311i	$0.875817\pi$
$14$	−0.00301826	−	0.00253263i	−0.000806665	−	0.000676873i
$15$	−2.75217	+	2.72499i	−0.710607	+	0.703589i
$16$	3.75746	+	1.36760i	0.939364	+	0.341901i
$17$	1.70216	−	0.456091i	0.412833	−	0.110618i	−0.0464236	−	0.998922i	$-0.514782\pi$
$17$	1.70216	−	0.456091i	0.412833	−	0.110618i	0.459257	+	0.888303i	$0.348116\pi$
$18$	0.0423872	+	0.0173489i	0.00999075	+	0.00408918i
$19$	4.91894	−	2.83995i	1.12848	−	0.651529i	0.184929	−	0.982752i	$-0.440794\pi$
$19$	4.91894	−	2.83995i	1.12848	−	0.651529i	0.943553	+	0.331222i	$0.107461\pi$
$20$	3.06928	+	3.25190i	0.686312	+	0.727147i
$21$	0.308434	−	0.323554i	0.0673059	−	0.0706052i
$22$	−0.0282241	+	0.0605267i	−0.00601740	+	0.0129043i
$23$	−3.32360	−	4.74660i	−0.693019	−	0.989734i	−0.999286	−	0.0377879i	$-0.987969\pi$
$23$	−3.32360	−	4.74660i	−0.693019	−	0.989734i	0.306267	−	0.951946i	$-0.400920\pi$
$24$	0.0423928	−	0.0968971i	0.00865340	−	0.0197790i
$25$	1.43600	+	4.78935i	0.287200	+	0.957871i
$26$		−	0.0328351i		−	0.00643949i
$27$	−2.26876	+	4.67469i	−0.436623	+	0.899644i
$28$	−0.364940	−	0.364940i	−0.0689672	−	0.0689672i
$29$	3.59567	−	3.01712i	0.667699	−	0.560266i	−0.244685	−	0.969603i	$-0.578684\pi$
$29$	3.59567	−	3.01712i	0.667699	−	0.560266i	0.912383	+	0.409337i	$0.134240\pi$
$30$	0.0454826	−	0.0377814i	0.00830394	−	0.00689790i
$31$	−0.912568	+	5.17543i	−0.163902	+	0.929534i	0.786287	+	0.617861i	$0.212001\pi$
$31$	−0.912568	+	5.17543i	−0.163902	+	0.929534i	−0.950189	+	0.311673i	$0.899111\pi$
$32$	−0.166010	−	0.0774120i	−0.0293468	−	0.0136846i
$33$	−6.65044	−	3.63039i	−1.15769	−	0.631969i
$34$	−0.0264943	+	0.00467167i	−0.00454374	+	0.000801184i
$35$	−0.181634	−	0.547759i	−0.0307017	−	0.0925882i
$36$	5.33305	+	2.74777i	0.888841	+	0.457962i
$37$	−0.837479	−	3.12552i	−0.137681	−	0.513832i	−0.999972	−	0.00741968i	$-0.997638\pi$
$37$	−0.837479	−	3.12552i	−0.137681	−	0.513832i	0.862292	−	0.506412i	$-0.169028\pi$
$38$	−0.0785891	+	0.0366467i	−0.0127488	+	0.00594488i
$39$	3.71775	+	0.235826i	0.595317	+	0.0377624i
$40$	−0.0847103	−	0.107088i	−0.0133939	−	0.0169321i
$41$	0.241984	−	0.288386i	0.0377916	−	0.0450383i	−0.746818	−	0.665029i	$-0.768419\pi$
$41$	0.241984	−	0.288386i	0.0377916	−	0.0450383i	0.784609	+	0.619991i	$0.212864\pi$
$42$	−0.00512138	+	0.00451041i	−0.000790246	+	0.000695972i
$43$	3.84888	+	8.25395i	0.586948	+	1.25872i	0.945627	+	0.325254i	$0.105450\pi$
$43$	3.84888	+	8.25395i	0.586948	+	1.25872i	−0.358678	+	0.933461i	$0.616772\pi$
$44$	−4.37396	+	7.57592i	−0.659400	+	1.14211i
$45$	3.95114	+	5.42112i	0.589001	+	0.808133i
$46$	0.0442317	+	0.0766116i	0.00652161	+	0.0112958i
$47$	−2.29910	+	3.28345i	−0.335358	+	0.478941i	−0.951046	−	0.309049i	$-0.899989\pi$
$47$	−2.29910	+	3.28345i	−0.335358	+	0.478941i	0.615688	+	0.787990i	$0.288878\pi$
$48$	3.31845	−	6.07901i	0.478977	−	0.877429i
$49$	−2.37136	−	6.51526i	−0.338766	−	0.930751i
$50$	−0.0154670	−	0.0747502i	−0.00218736	−	0.0105713i
$51$	−0.338664	−	3.03338i	−0.0474224	−	0.424757i
$52$	0.374859	−	4.28465i	0.0519835	−	0.594174i
$53$	−8.15900	+	8.15900i	−1.12072	+	1.12072i	−0.129092	+	0.991633i	$0.541206\pi$
$53$	−8.15900	+	8.15900i	−1.12072	+	1.12072i	−0.991633	+	0.129092i	$0.958794\pi$
$54$	0.0407248	−	0.0680769i	0.00554195	−	0.00926409i
$55$	−8.17131	+	5.37678i	−1.10182	+	0.725005i
$56$	0.0101299	+	0.0120724i	0.00135367	+	0.00161324i
$57$	−3.58489	−	9.16146i	−0.474830	−	1.21347i
$58$	−0.0586997	+	0.0411020i	−0.00770765	+	0.00539696i
$59$	10.6146	−	3.86341i	1.38191	−	0.502973i	0.459152	−	0.888358i	$-0.348153\pi$
$59$	10.6146	−	3.86341i	1.38191	−	0.502973i	0.922756	+	0.385385i	$0.125931\pi$
$60$	6.36635	−	4.41085i	0.821893	−	0.569438i
$61$	−2.10712	−	11.9501i	−0.269790	−	1.53005i	−0.755040	−	0.655678i	$-0.772383\pi$
$61$	−2.10712	−	11.9501i	−0.269790	−	1.53005i	0.485251	−	0.874375i	$-0.338728\pi$
$62$	0.0207652	−	0.0774969i	0.00263719	−	0.00984212i
$63$	−0.473909	−	0.612263i	−0.0597070	−	0.0771379i
$64$	−6.92336	−	3.99720i	−0.865420	−	0.499650i
$65$	2.52389	−	4.09375i	0.313050	−	0.507768i
$66$	0.0963135	+	0.0640622i	0.0118554	+	0.00788551i
$67$	1.82940	−	0.160052i	0.223497	−	0.0195534i	0.0251426	−	0.999684i	$-0.491996\pi$
$67$	1.82940	−	0.160052i	0.223497	−	0.0195534i	0.198354	+	0.980130i	$0.436440\pi$
$68$	−3.51058	+	0.307136i	−0.425721	+	0.0372457i
$69$	−8.99203	+	4.45790i	−1.08251	+	0.536669i
$70$	0.00203356	+	0.00857235i	0.000243057	+	0.00102459i
$71$	4.44360	+	2.56551i	0.527358	+	0.304471i	0.739940	−	0.672673i	$-0.234854\pi$
$71$	4.44360	+	2.56551i	0.527358	+	0.304471i	−0.212582	+	0.977143i	$0.568187\pi$
$72$	−0.154913	−	0.0977775i	−0.0182567	−	0.0115232i
$73$	3.71651	−	13.8702i	0.434984	−	1.62338i	−0.306120	−	0.951993i	$-0.599031\pi$
$73$	3.71651	−	13.8702i	0.434984	−	1.62338i	0.741104	−	0.671390i	$-0.234303\pi$
$74$	0.00857816	+	0.0486492i	0.000997191	+	0.00565535i
$75$	8.57469	−	1.21438i	0.990120	−	0.140225i
$76$	−10.6735	+	3.88483i	−1.22433	+	0.445620i
$77$	0.924799	−	0.647552i	0.105391	−	0.0737953i
$78$	−0.0562282	−	0.00853337i	−0.00636659	−	0.000966214i
$79$	1.98949	+	2.37099i	0.223835	+	0.266757i	0.866261	−	0.499591i	$-0.166516\pi$
$79$	1.98949	+	2.37099i	0.223835	+	0.266757i	−0.642426	+	0.766348i	$0.722072\pi$
$80$	−4.91479	−	7.46920i	−0.549490	−	0.835082i
$81$	7.41552	+	5.10001i	0.823946	+	0.566668i
$82$	−0.00406398	+	0.00406398i	−0.000448791	+	0.000448791i
$83$	−0.432904	+	4.94812i	−0.0475174	+	0.543127i	0.934707	+	0.355418i	$0.115662\pi$
$83$	−0.432904	+	4.94812i	−0.0475174	+	0.543127i	−0.982225	+	0.187708i	$0.939894\pi$
$84$	−0.719782	+	0.530096i	−0.0785347	+	0.0578383i
$85$	−3.66230	−	1.45406i	−0.397233	−	0.157715i
$86$	−0.0475536	−	0.130653i	−0.00512784	−	0.0140886i
$87$	−4.23219	−	6.94148i	−0.453738	−	0.744205i
$88$	0.153214	−	0.218812i	0.0163326	−	0.0233254i
$89$	−1.44584	−	2.50426i	−0.153259	−	0.265452i	0.779165	−	0.626819i	$-0.215643\pi$
$89$	−1.44584	−	2.50426i	−0.153259	−	0.265452i	−0.932424	+	0.361367i	$0.882310\pi$
$90$	−0.0528781	−	0.0877051i	−0.00557384	−	0.00924493i
$91$	−0.277536	+	0.480707i	−0.0290937	+	0.0503917i
$92$	4.89717	+	10.5020i	0.510565	+	1.09491i
$93$	8.62546	+	2.90774i	0.894418	+	0.301519i
$94$	0.0393351	−	0.0468777i	0.00405710	−	0.00483507i
$95$	−12.6151	−	1.47184i	−1.29428	−	0.151008i
$96$	−0.175707	+	0.264165i	−0.0179331	+	0.0269612i
$97$	−4.27105	+	1.99162i	−0.433659	+	0.202219i	−0.627175	−	0.778879i	$-0.715789\pi$
$97$	−4.27105	+	1.99162i	−0.433659	+	0.202219i	0.193516	+	0.981097i	$0.438011\pi$
$98$	0.0273961	+	0.102243i	0.00276742	+	0.0103282i
$99$	−7.94518	+	10.4450i	−0.798521	+	1.04976i
$100$	−1.16491	−	9.93074i	−0.116491	−	0.993074i
$101$	2.84523	−	0.501690i	0.283110	−	0.0499200i	−0.0302897	−	0.999541i	$-0.509643\pi$
$101$	2.84523	−	0.501690i	0.283110	−	0.0499200i	0.313400	+	0.949621i	$0.398532\pi$
$102$	0.00111446	+	0.0465841i	0.000110348	+	0.00461251i
$103$	9.15274	+	4.26799i	0.901846	+	0.420538i	0.817520	−	0.575900i	$-0.195348\pi$
$103$	9.15274	+	4.26799i	0.901846	+	0.420538i	0.0843263	+	0.996438i	$0.473126\pi$
$104$	−0.0228057	+	0.129337i	−0.00223628	+	0.0126826i
$105$	−0.985210	+	0.168682i	−0.0961467	+	0.0164617i
$106$	0.134943	−	0.113231i	0.0131069	−	0.0109980i
$107$	10.6261	+	10.6261i	1.02727	+	1.02727i	0.999618	+	0.0276498i	$0.00880233\pi$
$107$	10.6261	+	10.6261i	1.02727	+	1.02727i	0.0276498	+	0.999618i	$0.491198\pi$
$108$	6.09138	−	8.41843i	0.586143	−	0.810064i
$109$			12.0030i			1.14968i	0.818265	+	0.574841i	$0.194936\pi$
$109$			12.0030i			1.14968i	−0.818265	+	0.574841i	$0.805064\pi$
$110$	0.131429	−	0.0709009i	0.0125312	−	0.00676013i
$111$	−5.56991	+	0.621858i	−0.528673	+	0.0590241i
$112$	0.591912	+	0.845337i	0.0559304	+	0.0798769i
$113$	−3.92562	+	8.41851i	−0.369291	+	0.791947i	0.630584	+	0.776121i	$0.282816\pi$
$113$	−3.92562	+	8.41851i	−0.369291	+	0.791947i	−0.999875	+	0.0158260i	$0.994962\pi$
$114$	0.0423312	+	0.144103i	0.00396468	+	0.0134965i
$115$	−0.374165	+	12.9515i	−0.0348911	+	1.20774i
$116$	−8.12897	+	4.69326i	−0.754756	+	0.435759i
$117$	1.37003	−	6.30515i	0.126659	−	0.582912i
$118$	−0.166575	+	0.0446336i	−0.0153344	+	0.00410885i
$119$	0.427365	+	0.155548i	0.0391765	+	0.0142591i
$120$	−0.205397	+	0.117231i	−0.0187501	+	0.0107017i
$121$	−6.23254	−	5.22972i	−0.566595	−	0.475429i
$122$	0.0161459	+	0.184548i	0.00146178	+	0.0167082i
$123$	−0.430956	−	0.489332i	−0.0388580	−	0.0441216i
$124$	3.59440	−	9.87552i	0.322786	−	0.886848i
$125$	3.81737	−	10.5085i	0.341436	−	0.939905i
$126$	0.00639285	+	0.00994226i	0.000569520	+	0.000885727i
$127$	18.7735	+	5.03035i	1.66588	+	0.446371i	0.963996	−	0.265918i	$-0.0856752\pi$
$127$	18.7735	+	5.03035i	1.66588	+	0.446371i	0.701885	+	0.712290i	$0.252342\pi$
$128$	0.400068	+	0.280131i	0.0353614	+	0.0247603i
$129$	15.1347	−	4.44590i	1.33253	−	0.391440i
$130$	−0.0438320	+	0.0589021i	−0.00384433	+	0.00516606i
$131$	−4.49710	−	0.792959i	−0.392913	−	0.0692812i	−0.0262986	−	0.999654i	$-0.508372\pi$
$131$	−4.49710	−	0.792959i	−0.392913	−	0.0692812i	−0.366614	+	0.930373i	$0.619483\pi$
$132$	11.8366	+	9.45903i	1.03024	+	0.823303i
$133$	1.46030	+	0.127760i	0.126624	+	0.0110782i
$134$	−0.0280356			−0.00242191
$135$	10.3102	−	5.35722i	0.887361	−	0.461076i
$136$	0.107606			0.00922713
$137$	−6.96948	−	0.609750i	−0.595443	−	0.0520945i	−0.214549	−	0.976713i	$-0.568828\pi$
$137$	−6.96948	−	0.609750i	−0.595443	−	0.0520945i	−0.380894	+	0.924619i	$0.624384\pi$
$138$	0.142688	−	0.0558340i	0.0121464	−	0.00475291i
$139$	−8.03836	−	1.41738i	−0.681805	−	0.120221i	−0.177990	−	0.984032i	$-0.556959\pi$
$139$	−8.03836	−	1.41738i	−0.681805	−	0.120221i	−0.503815	+	0.863812i	$0.668071\pi$
$140$	0.167494	+	1.14182i	0.0141558	+	0.0965017i
$141$	5.02522	+	4.79040i	0.423200	+	0.403424i
$142$	−0.0641675	−	0.0449306i	−0.00538482	−	0.00377049i
$143$	9.08786	+	2.43508i	0.759965	+	0.203632i
$144$	−9.54753	−	7.26250i	−0.795628	−	0.605209i
$145$	−10.4778	+	0.612441i	−0.870133	+	0.0508605i
$146$	−0.0749784	+	0.206002i	−0.00620526	+	0.0170488i
$147$	−11.7733	+	2.36759i	−0.971045	+	0.195276i
$148$	0.563966	+	6.44617i	0.0463578	+	0.529872i
$149$	14.7726	+	12.3956i	1.21021	+	1.01549i	0.999278	+	0.0379911i	$0.0120959\pi$
$149$	14.7726	+	12.3956i	1.21021	+	1.01549i	0.210937	+	0.977500i	$0.432349\pi$
$150$	−0.132025	+	0.00705980i	−0.0107798	+	0.000576430i
$151$	−14.1147	−	5.13734i	−1.14864	−	0.418070i	−0.303613	−	0.952795i	$-0.598193\pi$
$151$	−14.1147	−	5.13734i	−1.14864	−	0.418070i	−0.845026	+	0.534725i	$0.820415\pi$
$152$	0.335016	−	0.0897672i	0.0271734	−	0.00728108i
$153$	−5.28249	−	0.208389i	−0.427064	−	0.0168473i
$154$	−0.0149266	+	0.00861785i	−0.00120282	+	0.000694446i
$155$	8.54579	−	8.06589i	0.686415	−	0.647868i
$156$	−7.23980	−	1.75544i	−0.579648	−	0.140548i
$157$	0.987420	−	2.11753i	0.0788047	−	0.168997i	−0.862958	−	0.505276i	$-0.831391\pi$
$157$	0.987420	−	2.11753i	0.0788047	−	0.168997i	0.941762	+	0.336279i	$0.109168\pi$
$158$	−0.0271027	−	0.0387066i	−0.00215617	−	0.00307933i
$159$	11.8514	+	16.0922i	0.939878	+	1.27620i
$160$	0.194464	+	0.360478i	0.0153737	+	0.0284983i
$161$		−	1.49546i		−	0.117859i
$162$	−0.105994	−	0.0874311i	−0.00832767	−	0.00686924i
$163$	10.7302	+	10.7302i	0.840451	+	0.840451i	0.988917	−	0.148467i	$-0.0474338\pi$
$163$	10.7302	+	10.7302i	0.840451	+	0.840451i	−0.148467	+	0.988917i	$0.547434\pi$
$164$	−0.576705	+	0.483913i	−0.0450331	+	0.0377872i
$165$	7.08382	+	15.3902i	0.551475	+	1.19813i
$166$	0.0131678	−	0.0746781i	0.00102202	−	0.00579615i
$167$	−17.5852	−	8.20013i	−1.36079	−	0.634545i	−0.401208	−	0.915987i	$-0.631410\pi$
$167$	−17.5852	−	8.20013i	−1.36079	−	0.634545i	−0.959578	+	0.281442i	$0.909187\pi$
$168$	0.0233058	−	0.0142095i	0.00179808	−	0.00109628i
$169$	8.24701	−	1.45417i	0.634385	−	0.111859i
$170$	0.0537639	+	0.0269873i	0.00412350	+	0.00206983i
$171$	−16.6201	+	3.75798i	−1.27097	+	0.287380i
$172$	−4.71370	−	17.5918i	−0.359416	−	1.34136i
$173$	−5.26921	+	2.45707i	−0.400610	+	0.186808i	−0.612472	−	0.790492i	$-0.709825\pi$
$173$	−5.26921	+	2.45707i	−0.400610	+	0.186808i	0.211862	+	0.977300i	$0.432047\pi$
$174$	0.0551296	+	0.111202i	0.00417936	+	0.00843018i
$175$	−0.405384	+	1.22508i	−0.0306441	+	0.0926073i
$176$	11.2435	−	13.3995i	0.847510	−	1.01002i
$177$	−3.85728	−	19.1810i	−0.289931	−	1.44173i
$178$	0.0186571	+	0.0400103i	0.00139841	+	0.00299890i
$179$	−4.77974	+	8.27875i	−0.357254	+	0.618783i	−0.987501	−	0.157612i	$-0.949620\pi$
$179$	−4.77974	+	8.27875i	−0.357254	+	0.618783i	0.630247	+	0.776395i	$0.282954\pi$
$180$	−5.89880	−	12.0483i	−0.439670	−	0.898029i
$181$	6.93879	+	12.0183i	0.515756	+	0.893315i	0.999833	+	0.0182899i	$0.00582219\pi$
$181$	6.93879	+	12.0183i	0.515756	+	0.893315i	−0.484077	+	0.875026i	$0.660844\pi$
$182$	0.00486056	−	0.00694161i	0.000360289	−	0.000514546i
$183$	−21.0115	+	0.502668i	−1.55321	+	0.0371583i
$184$	−0.121018	−	0.332494i	−0.00892157	−	0.0245118i
$185$	−2.66996	+	6.72476i	−0.196300	+	0.494414i
$186$	−0.127312	−	0.0556997i	−0.00933500	−	0.00408410i
$187$	0.671857	−	7.67937i	0.0491311	−	0.561571i
$188$	5.66801	−	5.66801i	0.413382	−	0.413382i
$189$	−1.17163	+	0.652424i	−0.0852234	+	0.0474569i
$190$	0.189900	+	0.0391701i	0.0137768	+	0.00284170i
$191$	−7.63489	−	9.09890i	−0.552441	−	0.658374i	0.415488	−	0.909599i	$-0.363611\pi$
$191$	−7.63489	−	9.09890i	−0.552441	−	0.658374i	−0.967929	+	0.251225i	$0.919167\pi$
$192$	−8.64426	+	10.8170i	−0.623846	+	0.780652i
$193$	9.91741	−	6.94425i	0.713871	−	0.499858i	−0.159325	−	0.987226i	$-0.550932\pi$
$193$	9.91741	−	6.94425i	0.713871	−	0.499858i	0.873197	+	0.487368i	$0.162043\pi$
$194$	0.0676068	−	0.0246069i	0.00485389	−	0.00176667i
$195$	−6.35439	−	5.38593i	−0.455047	−	0.385695i
$196$	2.40766	+	13.6545i	0.171976	+	0.975323i
$197$	1.53862	−	5.74222i	0.109622	−	0.409116i	−0.889206	−	0.457507i	$-0.848743\pi$
$197$	1.53862	−	5.74222i	0.109622	−	0.409116i	0.998828	+	0.0483907i	$0.0154092\pi$
$198$	0.134733	−	0.148283i	0.00957508	−	0.0105380i
$199$	−4.84519	−	2.79737i	−0.343466	−	0.198300i	0.318337	−	0.947977i	$-0.396876\pi$
$199$	−4.84519	−	2.79737i	−0.343466	−	0.198300i	−0.661804	+	0.749677i	$0.730209\pi$
$200$	0.00900656	+	0.305184i	0.000636860	+	0.0215798i
$201$	0.201356	−	3.17433i	0.0142025	−	0.223900i
$202$	−0.0439395	+	0.00384421i	−0.00309157	+	0.000270478i
$203$	1.20678	−	0.105579i	0.0846992	−	0.00741022i
$204$	−0.386398	+	6.09149i	−0.0270533	+	0.426490i
$205$	−0.819062	+	0.194300i	−0.0572057	+	0.0135705i
$206$	−0.133522	−	0.0770888i	−0.00930290	−	0.00537103i
$207$	5.29700	+	16.5569i	0.368167	+	1.15078i
$208$	−2.22585	+	8.30699i	−0.154335	+	0.575986i
$209$	−4.31456	−	24.4691i	−0.298444	−	1.69256i
$210$	0.0152082	−	0.00125452i	0.00104946	−	8.65703e-5i
$211$	5.33826	−	1.94297i	0.367501	−	0.133759i	−0.151667	−	0.988432i	$-0.548464\pi$
$211$	5.33826	−	1.94297i	0.367501	−	0.133759i	0.519168	+	0.854672i	$0.326242\pi$
$212$	18.9015	−	13.2350i	1.29816	−	0.908980i
$213$	5.54813	−	6.94267i	0.380151	−	0.475704i
$214$	−0.147470	−	0.175748i	−0.0100808	−	0.0120139i
$215$	4.11390	−	19.9445i	0.280566	−	1.36020i
$216$	−0.207698	+	0.239869i	−0.0141321	+	0.0163210i
$217$	−0.959041	+	0.959041i	−0.0651039	+	0.0651039i
$218$	0.0159710	−	0.182550i	0.00108169	−	0.0123638i
$219$	−22.7860	−	9.96897i	−1.53974	−	0.673641i
$220$	17.9596	−	7.75142i	1.21083	−	0.522601i
$221$	1.29628	+	3.56150i	0.0871973	+	0.239573i
$222$	0.0855382	−	0.00204637i	0.00574095	−	0.000137344i
$223$	−7.56295	+	10.8010i	−0.506452	+	0.723289i	−0.988225	−	0.153007i	$-0.951104\pi$
$223$	−7.56295	+	10.8010i	−0.506452	+	0.723289i	0.481773	+	0.876296i	$0.339993\pi$
$224$	−0.0236367	−	0.0409400i	−0.00157929	−	0.00273542i
$225$	0.148876	−	14.9993i	0.00992508	−	0.999951i
$226$	0.0709048	−	0.122811i	0.00471652	−	0.00816925i
$227$	−6.15899	−	13.2080i	−0.408787	−	0.876646i	−0.997657	−	0.0684181i	$-0.978205\pi$
$227$	−6.15899	−	13.2080i	−0.408787	−	0.876646i	0.588870	−	0.808228i	$-0.299573\pi$
$228$	3.87866	+	19.2873i	0.256870	+	1.27733i
$229$	5.35302	−	6.37948i	0.353738	−	0.421568i	−0.559605	−	0.828759i	$-0.689047\pi$
$229$	5.35302	−	6.37948i	0.353738	−	0.421568i	0.913343	+	0.407191i	$0.133492\pi$
$230$	0.0229236	−	0.196477i	0.00151154	−	0.0129553i
$231$	−0.868552	−	1.75196i	−0.0571466	−	0.115270i
$232$	0.259766	−	0.121131i	0.0170545	−	0.00795262i
$233$	−7.15675	−	26.7094i	−0.468854	−	1.74979i	−0.643784	−	0.765207i	$-0.722637\pi$
$233$	−7.15675	−	26.7094i	−0.468854	−	1.74979i	0.174930	−	0.984581i	$-0.444030\pi$
$234$	−0.0292258	+	0.0940698i	−0.00191055	+	0.00614954i
$235$	8.50744	−	2.82101i	0.554964	−	0.184023i
$236$	−22.2459	+	3.92255i	−1.44808	+	0.255336i
$237$	4.57722	−	2.79071i	0.297322	−	0.181276i
$238$	−0.00629266	−	0.00293432i	−0.000407893	−	0.000190204i
$239$	−3.76477	+	21.3510i	−0.243522	+	1.38108i	0.580377	+	0.814348i	$0.302905\pi$
$239$	−3.76477	+	21.3510i	−0.243522	+	1.38108i	−0.823899	+	0.566736i	$0.808206\pi$
$240$	−14.0679	+	6.47515i	−0.908076	+	0.417969i
$241$	3.99926	−	3.35578i	0.257615	−	0.216165i	−0.504828	−	0.863220i	$-0.668444\pi$
$241$	3.99926	−	3.35578i	0.257615	−	0.216165i	0.762443	+	0.647055i	$0.224000\pi$
$242$	0.0878299	+	0.0878299i	0.00564592	+	0.00564592i
$243$	10.6607	−	11.3732i	0.683882	−	0.729593i
$244$			24.2661i			1.55348i
$245$	−4.44339	+	14.8531i	−0.283878	+	0.948933i
$246$	0.00590315	+	0.00801549i	0.000376371	+	0.000511049i
$247$	7.00687	+	10.0068i	0.445837	+	0.636721i
$248$	−0.135620	+	0.290838i	−0.00861188	+	0.0184682i
$249$	8.36086	+	2.02727i	0.529848	+	0.128473i
$250$	−0.0720393	+	0.154740i	−0.00455617	+	0.00978662i
$251$	12.0778	−	6.97313i	0.762345	−	0.440140i	−0.0677923	−	0.997699i	$-0.521596\pi$
$251$	12.0778	−	6.97313i	0.762345	−	0.440140i	0.830137	+	0.557560i	$0.188262\pi$
$252$	0.720698	+	1.37035i	0.0453997	+	0.0863239i
$253$	−24.4843	+	6.56054i	−1.53931	+	0.412458i
$254$	−0.278826	−	0.101484i	−0.0174951	−	0.00636770i
$255$	−3.44178	+	5.89359i	−0.215532	+	0.369071i
$256$	12.2424	+	10.2726i	0.765152	+	0.642039i
$257$	0.816897	+	9.33717i	0.0509566	+	0.582437i	0.978156	+	0.207870i	$0.0666531\pi$
$257$	0.816897	+	9.33717i	0.0509566	+	0.582437i	−0.927200	+	0.374567i	$0.877791\pi$
$258$	−0.236093	+	0.0474781i	−0.0146985	+	0.00295586i
$259$	0.285619	−	0.784731i	0.0177475	−	0.0487608i
$260$	−6.39210	+	7.18574i	−0.396421	+	0.445641i
$261$	−12.9868	+	5.44338i	−0.803861	+	0.336937i
$262$	0.0673396	+	0.0180436i	0.00416025	+	0.00111474i
$263$	8.22122	+	5.75656i	0.506942	+	0.354965i	0.798897	−	0.601467i	$-0.205417\pi$
$263$	8.22122	+	5.75656i	0.506942	+	0.354965i	−0.291955	+	0.956432i	$0.594306\pi$
$264$	−0.334885	−	0.319236i	−0.0206107	−	0.0196476i
$265$	25.5278	−	3.74468i	1.56816	−	0.230034i
$266$	−0.0220392	−	0.00388610i	−0.00135131	−	0.000238272i
$267$	−4.66416	+	1.82509i	−0.285442	+	0.111694i
$268$	−3.65837	−	0.320066i	−0.223470	−	0.0195511i
$269$	−1.84882			−0.112724			−0.0563622	−	0.998410i	$-0.517950\pi$
$269$	−1.84882			−0.112724			−0.0563622	+	0.998410i	$0.517950\pi$
$270$	−0.163932	+	0.0677574i	−0.00997660	+	0.00412359i
$271$	14.0068			0.850851			0.425426	−	0.904993i	$-0.360124\pi$
$271$	14.0068			0.850851			0.425426	+	0.904993i	$0.360124\pi$
$272$	7.01953	+	0.614129i	0.425621	+	0.0372370i
$273$	0.751055	+	0.600193i	0.0454559	+	0.0363254i
$274$	0.105185	+	0.0185469i	0.00635445	+	0.00112046i
$275$	21.8359	+	1.26271i	1.31675	+	0.0761445i
$276$	19.2568	−	5.65680i	1.15912	−	0.340499i
$277$	−14.8975	−	10.4313i	−0.895103	−	0.626758i	0.0328481	−	0.999460i	$-0.489542\pi$
$277$	−14.8975	−	10.4313i	−0.895103	−	0.626758i	−0.927951	+	0.372703i	$0.878431\pi$
$278$	0.120367	+	0.0322521i	0.00721911	+	0.00193435i
$279$	7.22097	−	14.0149i	0.432308	−	0.839051i
$280$	−0.00205625	−	0.0351789i	−0.000122885	−	0.00210234i
$281$	−8.98091	+	24.6748i	−0.535756	+	1.47198i	0.316368	+	0.948637i	$0.397537\pi$
$281$	−8.98091	+	24.6748i	−0.535756	+	1.47198i	−0.852124	+	0.523341i	$0.824686\pi$
$282$	−0.0700527	−	0.0795419i	−0.00417158	−	0.00473665i
$283$	−1.59875	−	18.2738i	−0.0950360	−	1.08627i	−0.882629	−	0.470071i	$-0.844228\pi$
$283$	−1.59875	−	18.2738i	−0.0950360	−	1.08627i	0.787593	−	0.616196i	$-0.211327\pi$
$284$	−7.86028	−	6.59556i	−0.466422	−	0.391374i
$285$	−5.79892	+	21.2201i	−0.343499	+	1.25697i
$286$	−0.134974	−	0.0491264i	−0.00798117	−	0.00290491i
$287$	0.0938472	−	0.0251463i	0.00553962	−	0.00148434i
$288$	0.406704	+	0.369541i	0.0239652	+	0.0217754i
$289$	−12.0331	+	6.94732i	−0.707830	+	0.408666i
$290$	0.160168	+	0.00462718i	0.00940538	+	0.000271718i
$291$	2.30055	+	7.83152i	0.134861	+	0.459092i
$292$	−12.1357	+	26.0252i	−0.710191	+	1.52301i
$293$	6.02781	+	8.60861i	0.352149	+	0.502920i	0.955675	−	0.294422i	$-0.0951272\pi$
$293$	6.02781	+	8.60861i	0.352149	+	0.502920i	−0.603527	+	0.797343i	$0.706238\pi$
$294$	0.182206	−	0.0203425i	0.0106265	−	0.00118640i
$295$	−24.1987	−	7.23915i	−1.40890	−	0.421480i
$296$		−	0.197587i		−	0.0114845i
$297$	15.8216	+	16.3202i	0.918064	+	0.946993i
$298$	−0.208177	−	0.208177i	−0.0120594	−	0.0120594i
$299$	9.54693	−	8.01082i	0.552113	−	0.463278i
$300$	−17.3086	−	0.586018i	−0.999311	−	0.0338338i
$301$	−0.408144	+	2.31470i	−0.0235250	+	0.133417i
$302$	0.207830	+	0.0969127i	0.0119593	+	0.00557670i
$303$	−0.119681	−	5.00267i	−0.00687551	−	0.287396i
$304$	22.3666	−	3.94384i	1.28281	−	0.226195i
$305$	−12.1724	+	24.2499i	−0.696992	+	1.38854i
$306$	0.0800623	+	0.0101981i	0.00457685	+	0.000582987i
$307$	3.31491	+	12.3714i	0.189192	+	0.706074i	0.993694	+	0.112124i	$0.0357654\pi$
$307$	3.31491	+	12.3714i	0.189192	+	0.706074i	−0.804502	+	0.593949i	$0.797568\pi$
$308$	−2.04615	+	0.954137i	−0.116590	+	0.0543670i
$309$	9.68736	−	14.5643i	0.551095	−	0.828537i
$310$	−0.140702	+	0.111300i	−0.00799135	+	0.00632143i
$311$	13.5014	−	16.0903i	0.765592	−	0.912397i	−0.232596	−	0.972573i	$-0.574722\pi$
$311$	13.5014	−	16.0903i	0.765592	−	0.912397i	0.998188	+	0.0601768i	$0.0191664\pi$
$312$	0.215556	+	0.0726664i	0.0122035	+	0.00411392i
$313$	−12.4918	−	26.7887i	−0.706078	−	1.51419i	−0.851237	−	0.524781i	$-0.824147\pi$
$313$	−12.4918	−	26.7887i	−0.706078	−	1.51419i	0.145159	−	0.989408i	$-0.453631\pi$
$314$	−0.0178349	+	0.0308909i	−0.00100648	+	0.00174327i
$315$	0.0328165	+	1.73095i	0.00184900	+	0.0975282i
$316$	−3.09474	−	5.36025i	−0.174093	−	0.301538i
$317$	−15.2311	+	21.7523i	−0.855465	+	1.22173i	0.118027	+	0.993010i	$0.462343\pi$
$317$	−15.2311	+	21.7523i	−0.855465	+	1.22173i	−0.973492	+	0.228720i	$0.926546\pi$
$318$	−0.158832	−	0.260510i	−0.00890684	−	0.0146087i
$319$	−7.02268	−	19.2947i	−0.393195	−	1.08029i
$320$	7.08374	+	16.4126i	0.395993	+	0.917492i
$321$	20.9582	−	15.4351i	1.16977	−	0.861501i
$322$	−0.00198984	+	0.0227439i	−0.000110889	+	0.00126747i
$323$	7.07752	−	7.07752i	0.393804	−	0.393804i
$324$	−12.8330	−	12.6190i	−0.712945	−	0.701054i
$325$	−9.99237	+	3.97451i	−0.554277	+	0.220466i
$326$	−0.148914	−	0.177468i	−0.00824756	−	0.00982906i
$327$	20.5545	+	3.11942i	1.13667	+	0.172504i
$328$	0.0188306	−	0.0131854i	0.00103975	−	0.000728040i
$329$	−0.972097	+	0.353814i	−0.0535934	+	0.0195064i
$330$	−0.0872572	−	0.243490i	−0.00480335	−	0.0134037i
$331$	−1.72647	−	9.79132i	−0.0948956	−	0.538179i	−0.994779	−	0.102050i	$-0.967460\pi$
$331$	−1.72647	−	9.79132i	−0.0948956	−	0.538179i	0.899884	−	0.436130i	$-0.143651\pi$
$332$	2.57082	−	9.59443i	0.141092	−	0.526563i
$333$	−0.382646	+	9.69977i	−0.0209689	+	0.531544i
$334$	0.256536	+	0.148111i	0.0140371	+	0.00810430i
$335$	−3.49537	−	2.15498i	−0.190973	−	0.117739i
$336$	1.60142	−	0.793923i	0.0873647	−	0.0433121i
$337$	−13.9748	+	1.22264i	−0.761258	+	0.0666015i	−0.461172	−	0.887311i	$-0.652571\pi$
$337$	−13.9748	+	1.22264i	−0.761258	+	0.0666015i	−0.300086	+	0.953912i	$0.597015\pi$
$338$	−0.127361	+	0.0111426i	−0.00692750	+	0.000606078i
$339$	13.3960	+	8.91025i	0.727571	+	0.483938i
$340$	6.70756	+	4.13536i	0.363768	+	0.224272i
$341$	19.9091	+	11.4945i	1.07814	+	0.622463i
$342$	0.257770	−	0.0350393i	0.0139386	−	0.00189471i
$343$	0.930702	−	3.47343i	0.0502532	−	0.187547i
$344$	0.0965688	+	0.547669i	0.00520664	+	0.0295283i
$345$	22.0815	+	4.00666i	1.18883	+	0.215711i
$346$	0.0834068	−	0.0303576i	0.00448397	−	0.00163203i
$347$	5.00149	−	3.50208i	0.268494	−	0.188001i	−0.431574	−	0.902077i	$-0.642042\pi$
$347$	5.00149	−	3.50208i	0.268494	−	0.188001i	0.700068	+	0.714076i	$0.253153\pi$
$348$	5.92434	+	15.1401i	0.317578	+	0.811595i
$349$	2.45708	+	2.92823i	0.131524	+	0.156745i	0.827787	−	0.561042i	$-0.189600\pi$
$349$	2.45708	+	2.92823i	0.131524	+	0.156745i	−0.696263	+	0.717787i	$0.745155\pi$
$350$	0.00779540	−	0.0180924i	0.000416682	−	0.000967079i
$351$	−10.4412	−	3.98472i	−0.557308	−	0.212689i
$352$	−0.566592	+	0.566592i	−0.0301995	+	0.0301995i
$353$	0.194119	−	2.21879i	0.0103319	−	0.118094i	−0.989277	−	0.146050i	$-0.953344\pi$
$353$	0.194119	−	2.21879i	0.0103319	−	0.118094i	0.999609	+	0.0279554i	$0.00889964\pi$
$354$	0.0331420	+	0.296849i	0.00176148	+	0.0157774i
$355$	−4.54654	−	10.5341i	−0.241305	−	0.559090i
$356$	1.97779	+	5.43394i	0.104823	+	0.287998i
$357$	0.377433	−	0.691413i	0.0199759	−	0.0365934i
$358$	0.0837088	−	0.119549i	0.00442415	−	0.00631834i
$359$	−5.90045	−	10.2199i	−0.311414	−	0.539385i	0.667255	−	0.744829i	$-0.267469\pi$
$359$	−5.90045	−	10.2199i	−0.311414	−	0.539385i	−0.978669	+	0.205445i	$0.934136\pi$
$360$	0.147371	+	0.382197i	0.00776715	+	0.0201436i
$361$	6.63064	−	11.4846i	0.348981	−	0.604453i
$362$	−0.0895381	−	0.192015i	−0.00470602	−	0.0100921i
$363$	−10.5753	+	9.31374i	−0.555062	+	0.488844i
$364$	0.713504	−	0.850321i	0.0373978	−	0.0445689i
$365$	−25.1825	+	19.9202i	−1.31811	+	1.04267i
$366$	0.320225	+	0.0203126i	0.0167384	+	0.00106176i
$367$	−1.92158	+	0.896047i	−0.100306	+	0.0467733i	−0.472123	−	0.881532i	$-0.656512\pi$
$367$	−1.92158	+	0.896047i	−0.100306	+	0.0467733i	0.371818	+	0.928306i	$0.378735\pi$
$368$	−5.99683	−	22.3805i	−0.312607	−	1.16666i
$369$	−0.949952	+	0.610817i	−0.0494525	+	0.0317978i
$370$	0.0495543	−	0.0987218i	0.00257621	−	0.00513230i
$371$	−2.93265	+	0.517106i	−0.152256	+	0.0268468i
$372$	−15.9771	−	8.72170i	−0.828376	−	0.452199i
$373$	3.00825	+	1.40277i	0.155762	+	0.0726328i	0.498936	−	0.866639i	$-0.333724\pi$
$373$	3.00825	+	1.40277i	0.155762	+	0.0726328i	−0.343174	+	0.939272i	$0.611502\pi$
$374$	−0.0204361	+	0.115899i	−0.00105672	+	0.00599298i
$375$	−17.0031	−	9.26802i	−0.878034	−	0.478599i
$376$	−0.187500	+	0.157331i	−0.00966957	+	0.00811373i
$377$	7.13843	+	7.13843i	0.367648	+	0.367648i
$378$	0.0186870	−	0.00836353i	0.000961153	−	0.000430173i
$379$			15.7634i			0.809713i	0.914380	+	0.404856i	$0.132678\pi$
$379$			15.7634i			0.809713i	−0.914380	+	0.404856i	$0.867322\pi$
$380$	24.3328	+	7.27928i	1.24825	+	0.373419i
$381$	13.4932	−	30.8413i	0.691276	−	1.58005i
$382$	0.104009	+	0.148541i	0.00532158	+	0.00760001i
$383$	−11.6401	+	24.9622i	−0.594781	+	1.27551i	0.346552	+	0.938031i	$0.387352\pi$
$383$	−11.6401	+	24.9622i	−0.594781	+	1.27551i	−0.941333	+	0.337480i	$0.890425\pi$
$384$	0.583680	−	0.612292i	0.0297858	−	0.0312459i
$385$	−2.52340	−	0.0729001i	−0.128605	−	0.00371533i
$386$	−0.160070	+	0.0924166i	−0.00814736	+	0.00470388i
$387$	−3.68006	−	27.0727i	−0.187068	−	1.37618i
$388$	9.10294	−	2.43913i	0.462132	−	0.123828i
$389$	−28.2091	−	10.2673i	−1.43026	−	0.520571i	−0.493252	−	0.869886i	$-0.664192\pi$
$389$	−28.2091	−	10.2673i	−1.43026	−	0.520571i	−0.937005	+	0.349315i	$0.886414\pi$
$390$	0.0894752	+	0.0903677i	0.00453075	+	0.00457595i
$391$	−7.82217	−	6.56358i	−0.395584	−	0.331934i
$392$	−0.0368997	−	0.421765i	−0.00186372	−	0.0213024i
$393$	−2.52663	+	7.49494i	−0.127452	+	0.378070i
$394$	−0.0310408	+	0.0852840i	−0.00156382	+	0.00429655i
$395$	−0.403844	−	6.90906i	−0.0203196	−	0.347633i
$396$	19.2742	−	17.8112i	0.968566	−	0.895048i
$397$	4.62074	+	1.23812i	0.231908	+	0.0621397i	0.372902	−	0.927871i	$-0.378363\pi$
$397$	4.62074	+	1.23812i	0.231908	+	0.0621397i	−0.140993	+	0.990011i	$0.545030\pi$
$398$	0.0699666	+	0.0489911i	0.00350711	+	0.00245570i
$399$	0.598293	−	2.46748i	0.0299521	−	0.123528i
$400$	−1.15422	+	19.9597i	−0.0577108	+	0.997983i
$401$	−8.47214	−	1.49387i	−0.423078	−	0.0746001i	−0.0419444	−	0.999120i	$-0.513355\pi$
$401$	−8.47214	−	1.49387i	−0.423078	−	0.0746001i	−0.381134	+	0.924520i	$0.624466\pi$
$402$	−0.00728606	+	0.0480094i	−0.000363396	+	0.00239449i
$403$	−11.2598	−	0.985106i	−0.560891	−	0.0490716i
$404$	−5.77756			−0.287444
$405$	−6.49446	−	19.0479i	−0.322712	−	0.946497i
$406$	−0.0184939			−0.000917838
$407$	−14.1009	−	1.23367i	−0.698957	−	0.0611508i
$408$	0.0279653	−	0.184269i	0.00138449	−	0.00912267i
$409$	−8.33076	−	1.46894i	−0.411930	−	0.0726343i	−0.0361568	−	0.999346i	$-0.511512\pi$
$409$	−8.33076	−	1.46894i	−0.411930	−	0.0726343i	−0.375773	+	0.926712i	$0.622623\pi$
$410$	0.0127153	−	0.00186522i	0.000627966	−	9.21164e-5i
$411$	−2.85543	+	11.7764i	−0.140848	+	0.580885i
$412$	−16.5432	−	11.5837i	−0.815024	−	0.570686i
$413$	2.81592	+	0.754524i	0.138562	+	0.0371277i
$414$	−0.0585299	−	0.258856i	−0.00287659	−	0.0127221i
$415$	7.38190	−	8.29843i	0.362363	−	0.407354i
$416$	0.134742	−	0.370201i	0.00660628	−	0.0181506i
$417$	−4.51624	+	13.3969i	−0.221161	+	0.656048i
$418$	0.0330604	+	0.377882i	0.00161704	+	0.0184828i
$419$	−6.72816	−	5.64560i	−0.328692	−	0.275806i	0.463475	−	0.886110i	$-0.346603\pi$
$419$	−6.72816	−	5.64560i	−0.328692	−	0.275806i	−0.792167	+	0.610305i	$0.791047\pi$
$420$	1.99884	+	0.00991955i	0.0975332	+	0.000484024i
$421$	0.538899	+	0.196143i	0.0262643	+	0.00955944i	0.355119	−	0.934821i	$-0.384440\pi$
$421$	0.538899	+	0.196143i	0.0262643	+	0.00955944i	−0.328855	+	0.944381i	$0.606663\pi$
$422$	−0.0837730	+	0.0224469i	−0.00407800	+	0.00109270i
$423$	9.50926	−	7.36045i	0.462356	−	0.357877i
$424$	−0.610187	+	0.352292i	−0.0296333	+	0.0171088i
$425$	4.62868	+	7.49728i	0.224524	+	0.363671i
$426$	−0.0936172	+	0.0982063i	−0.00453577	+	0.00475811i
$427$	1.32351	−	2.83827i	0.0640489	−	0.137353i
$428$	−17.2370	−	24.6170i	−0.833181	−	1.18991i
$429$	6.53175	−	14.9296i	0.315356	−	0.720807i
$430$	−0.0891046	+	0.297855i	−0.00429701	+	0.0143638i
$431$			25.0117i			1.20477i	0.798205	+	0.602386i	$0.205783\pi$
$431$			25.0117i			1.20477i	−0.798205	+	0.602386i	$0.794217\pi$
$432$	−14.9179	+	14.4622i	−0.717737	+	0.695812i
$433$	−24.9892	−	24.9892i	−1.20090	−	1.20090i	−0.973892	−	0.227011i	$-0.927105\pi$
$433$	−24.9892	−	24.9892i	−1.20090	−	1.20090i	−0.227011	−	0.973892i	$-0.572895\pi$
$434$	0.0158618	−	0.0133096i	0.000761390	−	0.000638882i
$435$	−1.67426	+	18.1018i	−0.0802747	+	0.867914i
$436$	4.16812	−	23.6386i	0.199617	−	1.13208i
$437$	−29.8287	−	13.9093i	−1.42690	−	0.665374i
$438$	0.333280	+	0.181933i	0.0159247	+	0.00869310i
$439$	4.64923	−	0.819785i	0.221896	−	0.0391262i	−0.0615948	−	0.998101i	$-0.519619\pi$
$439$	4.64923	−	0.819785i	0.221896	−	0.0391262i	0.283491	+	0.958975i	$0.408508\pi$
$440$	−0.566942	+	0.187995i	−0.0270279	+	0.00896229i
$441$	0.994657	+	20.7764i	0.0473646	+	0.989352i
$442$	−0.0149758	−	0.0558904i	−0.000712326	−	0.00265844i
$443$	26.7976	−	12.4959i	1.27319	−	0.593700i	0.335787	−	0.941938i	$-0.390998\pi$
$443$	26.7976	−	12.4959i	1.27319	−	0.593700i	0.937406	+	0.348238i	$0.113220\pi$
$444$	11.1853	+	0.709507i	0.530829	+	0.0336717i
$445$	−0.749324	+	6.42242i	−0.0355214	+	0.304452i
$446$	0.129394	−	0.154205i	0.00612697	−	0.00730184i
$447$	25.0660	−	22.0757i	1.18558	−	1.04414i
$448$	−0.871951	−	1.86990i	−0.0411958	−	0.0883447i
$449$	−3.36725	+	5.83225i	−0.158910	+	0.275241i	−0.934476	−	0.356026i	$-0.884131\pi$
$449$	−3.36725	+	5.83225i	−0.158910	+	0.275241i	0.775566	+	0.631267i	$0.217465\pi$
$450$	−0.0222220	+	0.227920i	−0.00104755	+	0.0107443i
$451$	−0.823409	−	1.42619i	−0.0387728	−	0.0671565i
$452$	10.6544	−	15.2161i	0.501142	−	0.715706i
$453$	−12.4656	+	22.8355i	−0.585685	+	1.07291i
$454$	0.0760955	+	0.209071i	0.00357134	+	0.00981217i
$455$	1.13957	−	0.491842i	0.0534238	−	0.0230579i
$456$	−0.0666553	−	0.597025i	−0.00312142	−	0.0279582i
$457$	−3.16016	+	36.1208i	−0.147826	+	1.68966i	0.453974	+	0.891015i	$0.350006\pi$
$457$	−3.16016	+	36.1208i	−0.147826	+	1.68966i	−0.601800	+	0.798647i	$0.705550\pi$
$458$	−0.0899006	+	0.0899006i	−0.00420078	+	0.00420078i
$459$	−1.72970	+	8.99181i	−0.0807355	+	0.419702i
$460$	5.23438	−	25.3767i	0.244054	−	1.18319i
$461$	16.9825	+	20.2390i	0.790956	+	0.942625i	0.999373	−	0.0354156i	$-0.0112755\pi$
$461$	16.9825	+	20.2390i	0.790956	+	0.942625i	−0.208417	+	0.978040i	$0.566831\pi$
$462$	0.0108784	+	0.0278005i	0.000506108	+	0.00129340i
$463$	−9.85172	+	6.89825i	−0.457848	+	0.320589i	−0.779647	−	0.626219i	$-0.784601\pi$
$463$	−9.85172	+	6.89825i	−0.457848	+	0.320589i	0.321799	+	0.946808i	$0.395713\pi$
$464$	17.6368	−	6.41927i	0.818767	−	0.298007i
$465$	−11.5914	−	16.7304i	−0.537540	−	0.775853i
$466$	0.0733054	+	0.415735i	0.00339581	+	0.0192586i
$467$	−2.86104	+	10.6775i	−0.132393	+	0.494098i	−0.999995	−	0.00316149i	$-0.998994\pi$
$467$	−2.86104	+	10.6775i	−0.132393	+	0.494098i	0.867602	+	0.497260i	$0.165660\pi$
$468$	−4.88762	+	11.9415i	−0.225930	+	0.551997i
$469$	0.410442	+	0.236969i	0.0189525	+	0.0109422i
$470$	−0.133140	+	0.0315839i	−0.00614129	+	0.00145686i
$471$	−3.36953	−	2.24122i	−0.155260	−	0.103270i
$472$	0.687138	−	0.0601168i	0.0316281	−	0.00276710i
$473$	39.6877	−	3.47222i	1.82484	−	0.159653i
$474$	−0.0733265	+	0.0363525i	−0.00336800	+	0.00166972i
$475$	20.6651	+	19.4804i	0.948181	+	0.893820i
$476$	−0.787631	−	0.454739i	−0.0361010	−	0.0208429i
$477$	30.6370	−	16.1127i	1.40277	−	0.737750i
$478$	0.0856663	−	0.319711i	0.00391828	−	0.0146232i
$479$	0.735877	+	4.17337i	0.0336231	+	0.190686i	0.996993	−	0.0774895i	$-0.0246904\pi$
$479$	0.735877	+	4.17337i	0.0336231	+	0.190686i	−0.963370	+	0.268175i	$0.913579\pi$
$480$	0.667836	−	0.239326i	0.0304824	−	0.0109237i
$481$	6.53967	−	2.38024i	0.298183	−	0.108530i
$482$	−0.0652884	+	0.0457155i	−0.00297381	+	0.00208228i
$483$	−2.56089	−	0.388649i	−0.116525	−	0.0176842i
$484$	10.4582	+	12.4636i	0.475374	+	0.566529i
$485$	10.3204	+	2.12876i	0.468625	+	0.0966619i
$486$	−0.177267	+	0.158786i	−0.00804100	+	0.00720270i
$487$	16.7646	−	16.7646i	0.759676	−	0.759676i	−0.216587	−	0.976263i	$-0.569493\pi$
$487$	16.7646	−	16.7646i	0.759676	−	0.759676i	0.976263	+	0.216587i	$0.0694925\pi$
$488$	0.0645798	−	0.738151i	0.00292339	−	0.0334145i
$489$	21.1634	−	15.5862i	0.957041	−	0.704830i
$490$	0.0873412	−	0.219984i	0.00394567	−	0.00993786i
$491$	0.697417	+	1.91614i	0.0314740	+	0.0864740i	0.954434	−	0.298421i	$-0.0964599\pi$
$491$	0.697417	+	1.91614i	0.0314740	+	0.0864740i	−0.922960	+	0.384895i	$0.874238\pi$
$492$	0.678795	+	1.11334i	0.0306024	+	0.0501930i
$493$	4.74430	−	6.77556i	0.213673	−	0.305156i
$494$	−0.0932500	−	0.161514i	−0.00419552	−	0.00726685i
$495$	28.1959	−	8.13093i	1.26731	−	0.365458i
$496$	−10.5069	+	18.1984i	−0.471772	+	0.817133i
$497$	0.559642	+	1.20016i	0.0251034	+	0.0538343i
$498$	−0.124460	−	0.0419568i	−0.00557718	−	0.00188013i
$499$	−8.77600	+	10.4588i	−0.392868	+	0.468202i	−0.925832	−	0.377937i	$-0.876634\pi$
$499$	−8.77600	+	10.4588i	−0.392868	+	0.468202i	0.532964	+	0.846138i	$0.321078\pi$
$500$	−11.1670	+	19.3696i	−0.499403	+	0.866235i
$501$	−18.6124	+	27.9826i	−0.831541	+	1.25017i
$502$	−0.192965	+	0.0899812i	−0.00861246	+	0.00401606i
$503$	11.4964	+	42.9050i	0.512597	+	1.91304i	0.390772	+	0.920487i	$0.372208\pi$
$503$	11.4964	+	42.9050i	0.512597	+	1.91304i	0.121825	+	0.992552i	$0.461125\pi$
$504$	−0.0182760	−	0.0436027i	−0.000814078	−	0.00194222i
$505$	−5.77370	−	2.89816i	−0.256926	−	0.128967i
$506$	0.381102	−	0.0671985i	0.0169420	−	0.00298734i
$507$	−0.346901	−	14.5004i	−0.0154064	−	0.643987i
$508$	−35.2255	−	16.4259i	−1.56288	−	0.728782i
$509$	−0.883595	+	5.01112i	−0.0391647	+	0.222114i	−0.998108	−	0.0614836i	$-0.980417\pi$
$509$	−0.883595	+	5.01112i	−0.0391647	+	0.222114i	0.958943	+	0.283597i	$0.0915279\pi$
$510$	0.0601867	−	0.0850540i	0.00266511	−	0.00376625i
$511$	2.83890	−	2.38212i	0.125586	−	0.105379i
$512$	−0.863214	−	0.863214i	−0.0381490	−	0.0381490i
$513$	2.11599	+	29.4377i	0.0934231	+	1.29971i
$514$		−	0.143093i		−	0.00631155i
$515$	−10.7215	−	19.8744i	−0.472445	−	0.875770i
$516$	−31.3499	+	3.50008i	−1.38010	+	0.154083i
$517$	10.0573	+	14.3634i	0.442321	+	0.631700i
$518$	−0.00538802	+	0.0115547i	−0.000236736	+	0.000507682i
$519$	2.83820	+	9.66177i	0.124583	+	0.424105i
$520$	0.213565	−	0.201572i	0.00936545	−	0.00883952i
$521$	−14.9219	+	8.61518i	−0.653742	+	0.377438i	−0.789888	−	0.613251i	$-0.789862\pi$
$521$	−14.9219	+	8.61518i	−0.653742	+	0.377438i	0.136146	+	0.990689i	$0.456528\pi$
$522$	0.204754	−	0.0655064i	0.00896184	−	0.00286714i
$523$	12.9054	−	3.45799i	0.564314	−	0.151207i	0.0346265	−	0.999400i	$-0.488976\pi$
$523$	12.9054	−	3.45799i	0.564314	−	0.151207i	0.529688	+	0.848193i	$0.322309\pi$
$524$	8.58116	+	3.12329i	0.374870	+	0.136441i
$525$	1.99252	+	1.01258i	0.0869609	+	0.0441925i
$526$	−0.117374	−	0.0984884i	−0.00511775	−	0.00429430i
$527$	0.807135	+	9.22560i	0.0351594	+	0.401873i
$528$	−20.0238	−	22.7362i	−0.871424	−	0.989465i
$529$	−3.61738	+	9.93866i	−0.157277	+	0.432116i
$530$	−0.393226	+	0.0229846i	−0.0170806	+	0.000998386i
$531$	−33.8488	+	1.62049i	−1.46891	+	0.0703233i
$532$	−2.83153	−	0.758707i	−0.122762	−	0.0328941i
$533$	0.663249	+	0.464412i	0.0287285	+	0.0201159i
$534$	0.0733640	−	0.0215511i	0.00317477	−	0.000932607i
$535$	−4.87701	−	33.2470i	−0.210851	−	1.43739i
$536$	0.110432	+	0.0194722i	0.00476995	+	0.000841071i
$537$	12.9347	+	10.3366i	0.558173	+	0.446055i
$538$	0.0281180	+	0.00246001i	0.00121225	+	0.000106058i
$539$	−30.3299			−1.30640
$540$	−22.1651	+	6.97016i	−0.953833	+	0.299948i
$541$	7.10549			0.305489			0.152745	−	0.988266i	$-0.451189\pi$
$541$	7.10549			0.305489			0.152745	+	0.988266i	$0.451189\pi$
$542$	−0.213024	−	0.0186372i	−0.00915016	−	0.000800535i
$543$	22.3840	−	8.75888i	0.960589	−	0.375879i
$544$	−0.317883	−	0.0560513i	−0.0136291	−	0.00240318i
$545$	16.0230	−	21.5320i	0.686351	−	0.922328i
$546$	−0.0106239	−	0.0101275i	−0.000454661	−	0.000433415i
$547$	8.41425	+	5.89172i	0.359767	+	0.251912i	0.739459	−	0.673201i	$-0.235081\pi$
$547$	8.41425	+	5.89172i	0.359767	+	0.251912i	−0.379692	+	0.925113i	$0.623970\pi$
$548$	13.5139	+	3.62103i	0.577283	+	0.154683i
$549$	−4.59979	+	36.1116i	−0.196314	+	1.54120i
$550$	−0.330414	−	0.0482586i	−0.0140889	−	0.00205775i
$551$	9.11839	−	25.0526i	0.388456	−	1.06728i
$552$	−0.600828	+	0.120826i	−0.0255730	+	0.00514269i
$553$	0.0696191	+	0.795750i	0.00296050	+	0.0338387i
$554$	0.212691	+	0.178469i	0.00903636	+	0.00758240i
$555$	10.8219	+	6.31983i	0.459363	+	0.268262i
$556$	15.3384	+	5.58274i	0.650495	+	0.236761i
$557$	−5.55174	+	1.48759i	−0.235235	+	0.0630310i	−0.374511	−	0.927223i	$-0.622189\pi$
$557$	−5.55174	+	1.48759i	−0.235235	+	0.0630310i	0.139276	+	0.990254i	$0.455523\pi$
$558$	−0.128469	+	0.203540i	−0.00543853	+	0.00861652i
$559$	−16.9632	+	9.79373i	−0.717468	+	0.414230i
$560$	0.0666363	−	2.30658i	0.00281590	−	0.0974710i
$561$	−12.9759	−	3.14628i	−0.547841	−	0.132836i
$562$	0.169419	−	0.363321i	0.00714652	−	0.0153258i
$563$	−14.1548	−	20.2152i	−0.596555	−	0.851969i	0.401399	−	0.915903i	$-0.368524\pi$
$563$	−14.1548	−	20.2152i	−0.596555	−	0.851969i	−0.997954	+	0.0639343i	$0.979635\pi$
$564$	−8.23311	−	11.1792i	−0.346676	−	0.470728i
$565$	18.2801	−	9.86143i	0.769049	−	0.414873i
$566$			0.280047i			0.0117713i
$567$	0.812749	+	2.17590i	0.0341322	+	0.0913792i
$568$	0.221549	+	0.221549i	0.00929600	+	0.00929600i
$569$	1.46173	−	1.22654i	0.0612790	−	0.0514192i	−0.611634	−	0.791141i	$-0.709487\pi$
$569$	1.46173	−	1.22654i	0.0612790	−	0.0514192i	0.672913	+	0.739722i	$0.265043\pi$
$570$	0.116429	−	0.315012i	0.00487666	−	0.0131944i
$571$	−7.82276	+	44.3651i	−0.327372	+	1.85662i	0.165080	+	0.986280i	$0.447212\pi$
$571$	−7.82276	+	44.3651i	−0.327372	+	1.85662i	−0.492452	+	0.870340i	$0.663899\pi$
$572$	−17.0519	−	7.95143i	−0.712976	−	0.332466i
$573$	−17.5655	+	10.7096i	−0.733811	+	0.447401i
$574$	−0.00146075		0.000257569i	−6.09704e−5		1.07507e-5i
$575$	17.9604	−	22.7340i	0.749001	−	0.948074i
$576$	16.2770	+	17.6140i	0.678210	+	0.733917i
$577$	5.87132	+	21.9121i	0.244426	+	0.912211i	0.973671	+	0.227958i	$0.0732049\pi$
$577$	5.87132	+	21.9121i	0.244426	+	0.912211i	−0.729245	+	0.684253i	$0.760128\pi$
$578$	0.192251	−	0.0896482i	0.00799660	−	0.00372888i
$579$	−9.31423	−	18.7877i	−0.387086	−	0.780791i
$580$	20.8475	+	2.43234i	0.865645	+	0.100998i
$581$	−0.823988	+	0.981990i	−0.0341848	+	0.0407398i
$582$	−0.0245678	−	0.122168i	−0.00101837	−	0.00506402i
$583$	21.3317	+	45.7460i	0.883469	+	1.89461i
$584$	0.438419	−	0.759364i	0.0181419	−	0.0314227i
$585$	−10.8745	+	9.48180i	−0.449606	+	0.392024i
$586$	−0.0802204	−	0.138946i	−0.00331387	−	0.00573980i
$587$	4.91190	−	7.01492i	0.202736	−	0.289537i	−0.704890	−	0.709316i	$-0.749004\pi$
$587$	4.91190	−	7.01492i	0.202736	−	0.289537i	0.907626	+	0.419780i	$0.137893\pi$
$588$	24.0083	−	0.574363i	0.990086	−	0.0236863i
$589$	10.2091	+	28.0493i	0.420659	+	1.15575i
$590$	0.358397	+	0.142296i	0.0147550	+	0.00585823i
$591$	−9.43335	−	4.12712i	−0.388036	−	0.169767i
$592$	1.12767	−	12.8893i	0.0463469	−	0.529748i
$593$	4.26261	−	4.26261i	0.175044	−	0.175044i	−0.614147	−	0.789192i	$-0.710500\pi$
$593$	4.26261	−	4.26261i	0.175044	−	0.175044i	0.789192	+	0.614147i	$0.210500\pi$
$594$	−0.218910	−	0.269260i	−0.00898199	−	0.0110479i
$595$	−0.558997	−	0.849530i	−0.0229166	−	0.0348273i
$596$	−24.7884	−	29.5417i	−1.01537	−	1.21007i
$597$	−6.04953	+	7.57011i	−0.247591	+	0.309824i
$598$	−0.155855	+	0.109131i	−0.00637338	+	0.00446269i
$599$	13.5981	−	4.94929i	0.555602	−	0.202223i	−0.0489318	−	0.998802i	$-0.515582\pi$
$599$	13.5981	−	4.94929i	0.555602	−	0.202223i	0.604534	+	0.796580i	$0.293359\pi$
$600$	0.524951	+	0.0638898i	0.0214310	+	0.00260829i
$601$	−2.11215	−	11.9786i	−0.0861565	−	0.488618i	−0.997101	−	0.0760891i	$-0.975757\pi$
$601$	−2.11215	−	11.9786i	−0.0861565	−	0.488618i	0.910944	−	0.412529i	$-0.135354\pi$
$602$	0.00928722	−	0.0346604i	0.000378519	−	0.00141265i
$603$	−5.38353	−	1.16977i	−0.219234	−	0.0476369i
$604$	26.0133	+	15.0188i	1.05847	+	0.611107i
$605$	4.19918	+	17.7014i	0.170721	+	0.719664i
$606$	−0.00483627	+	0.0762430i	−0.000196460	+	0.00309716i
$607$	19.3845	−	1.69592i	0.786792	−	0.0688354i	0.313324	−	0.949646i	$-0.398557\pi$
$607$	19.3845	−	1.69592i	0.786792	−	0.0688354i	0.473468	+	0.880811i	$0.343002\pi$
$608$	−1.03644	+	0.0906769i	−0.0420333	+	0.00367743i
$609$	0.132826	−	2.09398i	0.00538238	−	0.0848522i
$610$	0.217393	−	0.352611i	0.00880197	−	0.0142768i
$611$	−7.46602	−	4.31051i	−0.302043	−	0.174384i
$612$	10.3309	+	2.24478i	0.417602	+	0.0907397i
$613$	3.48768	−	13.0162i	0.140866	−	0.525720i	−0.859038	−	0.511911i	$-0.828938\pi$
$613$	3.48768	−	13.0162i	0.140866	−	0.525720i	0.999905	−	0.0138088i	$-0.00439561\pi$
$614$	−0.0339541	−	0.192563i	−0.00137027	−	0.00777121i
$615$	0.119866	+	1.45309i	0.00483346	+	0.0585943i
$616$	0.0647813	−	0.0235785i	0.00261011	−	0.000950003i
$617$	37.1967	−	26.0454i	1.49748	−	1.04855i	0.516090	−	0.856535i	$-0.327387\pi$
$617$	37.1967	−	26.0454i	1.49748	−	1.04855i	0.981392	−	0.192014i	$-0.0615018\pi$
$618$	−0.166711	+	0.208614i	−0.00670608	+	0.00839169i
$619$	−0.765342	−	0.912099i	−0.0307617	−	0.0366604i	0.750444	−	0.660934i	$-0.229840\pi$
$619$	−0.765342	−	0.912099i	−0.0307617	−	0.0366604i	−0.781206	+	0.624273i	$0.785395\pi$
$620$	−19.6309	+	12.9173i	−0.788396	+	0.518770i
$621$	29.7293	−	4.76791i	1.19300	−	0.191330i
$622$	−0.226747	+	0.226747i	−0.00909171	+	0.00909171i
$623$	0.0650434	−	0.743449i	0.00260591	−	0.0297857i
$624$	13.6468	+	5.97052i	0.546309	+	0.239012i
$625$	−20.8758	+	13.7550i	−0.835032	+	0.550201i
$626$	0.154339	+	0.424042i	0.00616861	+	0.0169481i
$627$	−43.0232	+	1.02927i	−1.71818	+	0.0411049i
$628$	−2.67993	+	3.82734i	−0.106941	+	0.152728i
$629$	−2.85104	−	4.93815i	−0.113678	−	0.196897i
$630$	0.00180409	−	0.0263691i	7.18765e−5	−	0.00105057i
$631$	10.8669	−	18.8220i	0.432605	−	0.749293i	−0.564492	−	0.825438i	$-0.690928\pi$
$631$	10.8669	−	18.8220i	0.432605	−	0.749293i	0.997097	+	0.0761454i	$0.0242613\pi$
$632$	0.0798737	+	0.171290i	0.00317721	+	0.00681354i
$633$	−1.93988	−	9.64642i	−0.0771034	−	0.383411i
$634$	0.260588	−	0.310556i	0.0103493	−	0.0123338i
$635$	−26.9623	−	34.0849i	−1.06997	−	1.35262i
$636$	−17.7519	−	35.8073i	−0.703908	−	1.41985i
$637$	13.5149	−	6.30211i	0.535481	−	0.249699i
$638$	0.0811322	+	0.302790i	0.00321206	+	0.0119876i
$639$	−10.4470	−	11.3051i	−0.413279	−	0.447225i
$640$	−0.343723	−	1.03658i	−0.0135868	−	0.0409743i
$641$	11.0540	−	1.94912i	0.436606	−	0.0769855i	0.0489751	−	0.998800i	$-0.484405\pi$
$641$	11.0540	−	1.94912i	0.436606	−	0.0769855i	0.387631	+	0.921815i	$0.373293\pi$
$642$	−0.339284	+	0.206860i	−0.0133905	+	0.00816410i
$643$	21.6198	+	10.0815i	0.852602	+	0.397575i	0.799248	−	0.601001i	$-0.205231\pi$
$643$	21.6198	+	10.0815i	0.852602	+	0.397575i	0.0533535	+	0.998576i	$0.483009\pi$
$644$	−0.519308	+	2.94514i	−0.0204636	+	0.116055i
$645$	−33.0847	−	12.2281i	−1.30271	−	0.481481i
$646$	−0.117057	+	0.0982222i	−0.00460553	+	0.00386450i
$647$	−17.7336	−	17.7336i	−0.697179	−	0.697179i	0.266622	−	0.963801i	$-0.414092\pi$
$647$	−17.7336	−	17.7336i	−0.697179	−	0.697179i	−0.963801	+	0.266622i	$0.914092\pi$
$648$	0.356785	+	0.418010i	0.0140158	+	0.0164210i
$649$		−	49.4134i		−	1.93965i
$650$	0.157259	−	0.0471512i	0.00616820	−	0.00184942i
$651$	1.39306	+	1.89154i	0.0545984	+	0.0741355i
$652$	−17.4057	−	24.8579i	−0.681660	−	0.973511i
$653$	7.70684	−	16.5274i	0.301592	−	0.646766i	−0.695855	−	0.718183i	$-0.744974\pi$
$653$	7.70684	−	16.5274i	0.301592	−	0.646766i	0.997447	+	0.0714165i	$0.0227520\pi$
$654$	−0.308455	−	0.0747915i	−0.0120616	−	0.00292458i
$655$	7.00871	+	7.42571i	0.273853	+	0.290147i
$656$	1.30364	−	0.752659i	0.0508987	−	0.0293864i
$657$	−22.9931	+	36.4290i	−0.897045	+	1.42123i
$658$	0.0152550	−	0.00408758i	0.000594704	−	0.000159350i
$659$	32.1808	+	11.7129i	1.25359	+	0.456269i	0.881612	−	0.471974i	$-0.156458\pi$
$659$	32.1808	+	11.7129i	1.25359	+	0.456269i	0.371975	+	0.928243i	$0.378681\pi$
$660$	−8.60642	−	32.7692i	−0.335004	−	1.27554i
$661$	3.43935	+	2.88596i	0.133775	+	0.112251i	0.707220	−	0.706993i	$-0.249949\pi$
$661$	3.43935	+	2.88596i	0.133775	+	0.112251i	−0.573445	+	0.819244i	$0.694393\pi$
$662$	0.0132291	+	0.151210i	0.000514165	+	0.00587693i
$663$	6.43575	−	1.29422i	0.249944	−	0.0502634i
$664$	−0.103736	+	0.285012i	−0.00402573	+	0.0110606i
$665$	−2.44905	−	2.17856i	−0.0949703	−	0.0844811i
$666$	0.0187259	−	0.147011i	0.000725613	−	0.00569656i
$667$	−26.2716	−	7.03946i	−1.01724	−	0.272569i
$668$	31.7846	+	22.2558i	1.22978	+	0.861103i
$669$	16.5306	+	15.7581i	0.639110	+	0.609245i
$670$	0.0502925	+	0.0374252i	0.00194297	+	0.00144586i
$671$	−52.2754	−	9.21756i	−2.01807	−	0.355840i
$672$	−0.0762502	+	0.0298368i	−0.00294142	+	0.00115098i
$673$	15.0821	+	1.31952i	0.581374	+	0.0508636i	0.374050	−	0.927409i	$-0.377969\pi$
$673$	15.0821	+	1.31952i	0.581374	+	0.0508636i	0.207324	+	0.978272i	$0.433525\pi$
$674$	0.214165			0.00824933
$675$	−25.6467	−	4.15304i	−0.987141	−	0.159851i
$676$	−16.7465			−0.644096
$677$	−9.69800	−	0.848465i	−0.372724	−	0.0326092i	−0.100745	−	0.994912i	$-0.532123\pi$
$677$	−9.69800	−	0.848465i	−0.372724	−	0.0326092i	−0.271979	+	0.962303i	$0.587678\pi$
$678$	−0.191879	−	0.153337i	−0.00736908	−	0.00588888i
$679$	−1.19775	−	0.211196i	−0.0459656	−	0.00810497i
$680$	−0.193032	−	0.143645i	−0.00740244	−	0.00550853i
$681$	−24.2186	+	7.11435i	−0.928058	+	0.272622i
$682$	−0.287495	−	0.201306i	−0.0110088	−	0.00770842i
$683$	−22.4891	−	6.02595i	−0.860523	−	0.230577i	−0.198538	−	0.980093i	$-0.563619\pi$
$683$	−22.4891	−	6.02595i	−0.860523	−	0.230577i	−0.661985	+	0.749517i	$0.730286\pi$
$684$	34.0365	−	1.62948i	1.30142	−	0.0623045i
$685$	11.6884	+	10.3975i	0.446592	+	0.397267i
$686$	−0.0187764	+	0.0515877i	−0.000716886	+	0.00196963i
$687$	−9.53332	−	10.8247i	−0.363719	−	0.412987i
$688$	3.17388	+	36.2776i	0.121003	+	1.38307i
$689$	−19.0107	−	15.9519i	−0.724249	−	0.607717i
$690$	−0.330499	−	0.0903171i	−0.0125819	−	0.00343831i
$691$	−4.24724	−	1.54587i	−0.161573	−	0.0588077i	0.259968	−	0.965617i	$-0.416288\pi$
$691$	−4.24724	−	1.54587i	−0.161573	−	0.0588077i	−0.421540	+	0.906810i	$0.638510\pi$
$692$	11.2303	−	3.00916i	0.426913	−	0.114391i
$693$	−3.22585	+	1.03204i	−0.122540	+	0.0392039i
$694$	−0.0807256	+	0.0466069i	−0.00306430	+	0.00176918i
$695$	12.5278	+	13.2731i	0.475205	+	0.503479i
$696$	−0.139920	−	0.476314i	−0.00530365	−	0.0180546i
$697$	0.280365	−	0.601245i	0.0106196	−	0.0227738i
$698$	−0.0334725	−	0.0478038i	−0.00126695	−	0.00180940i
$699$	−47.5982	+	5.31414i	−1.80033	+	0.200999i
$700$	1.22377	−	2.27188i	0.0462543	−	0.0858691i
$701$		−	28.3612i		−	1.07119i	−0.844476	−	0.535593i	$-0.820088\pi$
$701$		−	28.3612i		−	1.07119i	0.844476	−	0.535593i	$-0.179912\pi$
$702$	0.153494	+	0.0744950i	0.00579325	+	0.00281163i
$703$	−12.9958	−	12.9958i	−0.490147	−	0.490147i
$704$	−26.7896	+	22.4791i	−1.00967	+	0.847214i
$705$	−2.61986	−	15.3016i	−0.0986697	−	0.576293i
$706$	−0.00590457	+	0.0334865i	−0.000222221	+	0.00126028i
$707$	0.675769	+	0.315116i	0.0254149	+	0.0118512i
$708$	0.935750	+	39.1142i	0.0351676	+	1.47000i
$709$	−27.9978	+	4.93677i	−1.05148	+	0.185404i	−0.672574	−	0.740030i	$-0.734811\pi$
$709$	−27.9978	+	4.93677i	−1.05148	+	0.185404i	−0.378907	+	0.925435i	$0.623700\pi$
$710$	0.0551302	+	0.166258i	0.00206900	+	0.00623956i
$711$	−3.58937	−	8.56349i	−0.134612	−	0.321156i
$712$	−0.0457011	−	0.170559i	−0.00171272	−	0.00639196i
$713$	27.5987	−	12.8695i	1.03358	−	0.481966i
$714$	−0.00666022	+	0.0100132i	−0.000249253	+	0.000374736i
$715$	−13.0519	−	16.4998i	−0.488113	−	0.617056i
$716$	12.2880	−	14.6443i	0.459224	−	0.547282i
$717$	35.5840	+	11.9958i	1.32891	+	0.447991i
$718$	0.0761394	+	0.163281i	0.00284150	+	0.00609361i
$719$	−8.97949	+	15.5529i	−0.334878	+	0.580026i	−0.983461	−	0.181118i	$-0.942029\pi$
$719$	−8.97949	+	15.5529i	−0.334878	+	0.580026i	0.648583	+	0.761144i	$0.275362\pi$
$720$	7.43229	+	25.7732i	0.276985	+	0.960510i
$721$	1.30318	+	2.25717i	0.0485328	+	0.0840612i
$722$	−0.116124	+	0.165843i	−0.00432170	+	0.00617202i
$723$	−4.70723	−	7.72062i	−0.175064	−	0.287133i
$724$	−9.49171	−	26.0783i	−0.352757	−	0.969191i
$725$	19.6134	+	12.8883i	0.728425	+	0.478660i
$726$	0.173229	−	0.127578i	0.00642914	−	0.00473486i
$727$	2.47494	−	28.2887i	0.0917905	−	1.04917i	−0.800990	−	0.598678i	$-0.795693\pi$
$727$	2.47494	−	28.2887i	0.0917905	−	1.04917i	0.892780	−	0.450492i	$-0.148751\pi$
$728$	−0.0239671	+	0.0239671i	−0.000888279	+	0.000888279i
$729$	−16.7054	−	21.2115i	−0.618720	−	0.785612i
$730$	0.409497	−	0.269452i	0.0151562	−	0.00997286i
$731$	10.3159	+	12.2941i	0.381549	+	0.454712i
$732$	41.5542	+	6.30641i	1.53589	+	0.233092i
$733$	−8.28966	+	5.80448i	−0.306185	+	0.214393i	−0.716563	−	0.697522i	$-0.754286\pi$
$733$	−8.28966	+	5.80448i	−0.306185	+	0.214393i	0.410378	+	0.911916i	$0.365397\pi$
$734$	0.0304169	−	0.0110708i	0.00112271	−	0.000408632i
$735$	24.2804	+	11.4692i	0.895596	+	0.423047i
$736$	0.184310	+	1.04527i	0.00679374	+	0.0385292i
$737$	2.07915	−	7.75949i	0.0765865	−	0.285825i
$738$	0.0152602	−	0.00802570i	0.000561736	−	0.000295430i
$739$	35.8294	+	20.6861i	1.31801	+	0.760951i	0.983408	−	0.181410i	$-0.0580660\pi$
$739$	35.8294	+	20.6861i	1.31801	+	0.760951i	0.334598	+	0.942361i	$0.391399\pi$
$740$	7.59340	−	12.3165i	0.279139	−	0.452763i
$741$	18.9571	−	9.39823i	0.696408	−	0.345252i
$742$	0.0452897	−	0.00396233i	0.00166264	−	0.000145462i
$743$	−7.70953	+	0.674496i	−0.282835	+	0.0247449i	−0.227691	−	0.973734i	$-0.573118\pi$
$743$	−7.70953	+	0.674496i	−0.282835	+	0.0247449i	−0.0551445	+	0.998478i	$0.517562\pi$
$744$	0.462798	+	0.307826i	0.0169670	+	0.0112855i
$745$	−9.95303	−	41.9564i	−0.364651	−	1.53716i
$746$	−0.0438849	−	0.0253370i	−0.00160674	−	0.000927653i
$747$	5.64445	−	13.7906i	0.206520	−	0.504573i
$748$	−3.98985	+	14.8903i	−0.145883	+	0.544444i
$749$	0.673470	+	3.81944i	0.0246080	+	0.139559i
$750$	0.246261	+	0.163578i	0.00899219	+	0.00597302i
$751$	−38.8916	+	14.1554i	−1.41918	+	0.516537i	−0.933808	−	0.357773i	$-0.883536\pi$
$751$	−38.8916	+	14.1554i	−1.41918	+	0.516537i	−0.485367	+	0.874311i	$0.661314\pi$
$752$	−13.1292	+	9.19318i	−0.478773	+	0.335241i
$753$	−8.80223	−	22.4948i	−0.320771	−	0.819755i
$754$	−0.0990675	−	0.118064i	−0.00360782	−	0.00429964i
$755$	18.4622	+	28.0577i	0.671907	+	1.02112i
$756$	2.53394	−	0.878020i	0.0921587	−	0.0319333i
$757$	−10.7021	+	10.7021i	−0.388975	+	0.388975i	−0.874322	−	0.485347i	$-0.838693\pi$
$757$	−10.7021	+	10.7021i	−0.388975	+	0.388975i	0.485347	+	0.874322i	$0.338693\pi$
$758$	0.0209745	−	0.239740i	0.000761830	−	0.00870775i
$759$	4.87143	+	43.6329i	0.176822	+	1.58377i
$760$	−0.720809	−	0.286186i	−0.0261465	−	0.0103811i
$761$	16.8761	+	46.3666i	0.611756	+	1.68079i	0.726308	+	0.687370i	$0.241235\pi$
$761$	16.8761	+	46.3666i	0.611756	+	1.68079i	−0.114551	+	0.993417i	$0.536543\pi$
$762$	−0.246249	+	0.451100i	−0.00892067	+	0.0163416i
$763$	−1.77680	+	2.53754i	−0.0643246	+	0.0918651i
$764$	11.8764	+	20.5705i	0.429673	+	0.744215i
$765$	9.19797	+	7.42551i	0.332553	+	0.268470i
$766$	0.210244	−	0.364154i	0.00759643	−	0.0131574i
$767$	10.2674	+	22.0185i	0.370733	+	0.795040i
$768$	20.7729	−	18.2947i	0.749578	−	0.660155i
$769$	−4.55804	+	5.43206i	−0.164367	+	0.195885i	−0.841941	−	0.539570i	$-0.818587\pi$
$769$	−4.55804	+	5.43206i	−0.164367	+	0.195885i	0.677574	+	0.735455i	$0.263031\pi$
$770$	0.0382805	+	0.00446631i	0.00137953	+	0.000160955i
$771$	16.2017	+	1.02771i	0.583489	+	0.0370121i
$772$	−21.9426	+	10.2320i	−0.789733	+	0.368259i
$773$	2.31145	+	8.62644i	0.0831370	+	0.310272i	0.994955	−	0.100323i	$-0.0319877\pi$
$773$	2.31145	+	8.62644i	0.0831370	+	0.310272i	−0.911818	+	0.410595i	$0.865321\pi$
$774$	0.0199462	+	0.416635i	0.000716950	+	0.0149756i
$775$	−26.0974	+	3.06131i	−0.937446	+	0.109966i
$776$	−0.283394	+	0.0499700i	−0.0101733	+	0.00179382i
$777$	−1.26958	−	0.693047i	−0.0455459	−	0.0248629i
$778$	0.415360	+	0.193686i	0.0148914	+	0.00694397i
$779$	0.371305	−	2.10578i	0.0133034	−	0.0754473i
$780$	10.6440	+	12.8136i	0.381115	+	0.458800i
$781$	17.1943	−	14.4277i	0.615260	−	0.516264i
$782$	0.110231	+	0.110231i	0.00394186	+	0.00394186i
$783$	5.94640	+	23.6538i	0.212507	+	0.845316i
$784$		−	27.7239i		−	0.990139i
$785$	−4.59803	+	2.48047i	−0.164111	+	0.0885317i
$786$	0.0483992	−	0.110626i	0.00172634	−	0.00394589i
$787$	0.397947	+	0.568328i	0.0141853	+	0.0202587i	0.826182	−	0.563403i	$-0.190508\pi$
$787$	0.397947	+	0.568328i	0.0141853	+	0.0202587i	−0.811997	+	0.583662i	$0.801619\pi$
$788$	−5.02416	+	10.7743i	−0.178978	+	0.383820i
$789$	11.9944	−	12.5823i	0.427010	−	0.447942i
$790$	−0.00305117	+	0.105615i	−0.000108556	+	0.00375761i
$791$	−2.07610	+	1.19864i	−0.0738175	+	0.0426186i
$792$	−0.633705	+	0.490506i	−0.0225177	+	0.0174294i
$793$	25.2090	−	6.75473i	0.895198	−	0.239868i
$794$	−0.0686278	−	0.0249785i	−0.00243551	−	0.000886453i
$795$	0.221772	−	44.6881i	0.00786544	−	1.58492i
$796$	8.57065	+	7.19163i	0.303778	+	0.254900i
$797$	3.24018	+	37.0354i	0.114773	+	1.31186i	0.807158	+	0.590335i	$0.201004\pi$
$797$	3.24018	+	37.0354i	0.114773	+	1.31186i	−0.692385	+	0.721528i	$0.743440\pi$
$798$	−0.0123824	+	0.0367309i	−0.000438332	+	0.00130026i
$799$	−2.41587	+	6.63755i	−0.0854673	+	0.234820i
$800$	0.132362	−	0.906246i	0.00467970	−	0.0320406i
$801$	1.91321	+	8.46143i	0.0676001	+	0.298970i
$802$	0.126862	+	0.0339926i	0.00447965	+	0.00120032i
$803$	−51.4551	−	36.0293i	−1.81581	−	1.27145i
$804$	−1.49885	+	6.18157i	−0.0528605	+	0.218007i
$805$	−1.99631	+	2.68268i	−0.0703608	+	0.0945519i
$806$	0.169936	+	0.0299642i	0.00598573	+	0.00105544i
$807$	−0.480482	+	3.16599i	−0.0169138	+	0.111448i
$808$	0.175748	+	0.0153759i	0.00618279	+	0.000540924i
$809$	9.19706			0.323351			0.161676	−	0.986844i	$-0.448310\pi$
$809$	9.19706			0.323351			0.161676	+	0.986844i	$0.448310\pi$
$810$	0.0734270	+	0.298334i	0.00257996	+	0.0104824i
$811$	−3.49413			−0.122695			−0.0613477	−	0.998116i	$-0.519540\pi$
$811$	−3.49413			−0.122695			−0.0613477	+	0.998116i	$0.519540\pi$
$812$	−2.41327	−	0.211134i	−0.0846893	−	0.00740935i
$813$	3.64016	−	23.9858i	0.127666	−	0.841219i
$814$	0.212814	+	0.0375249i	0.00745914	+	0.00131525i
$815$	−4.92475	−	33.5724i	−0.172506	−	1.17599i
$816$	2.87594	−	11.8609i	0.100678	−	0.415216i
$817$	42.3732	+	29.6700i	1.48245	+	1.03802i
$818$	0.124745	+	0.0334253i	0.00436160	+	0.00116869i
$819$	1.22299	−	1.13016i	0.0427346	−	0.0394908i
$820$	1.68052	−	0.0982287i	0.0586863	−	0.00343029i
$821$	−5.34053	+	14.6730i	−0.186386	+	0.512091i	−0.997329	−	0.0730336i	$-0.976732\pi$
$821$	−5.34053	+	14.6730i	−0.186386	+	0.512091i	0.810944	+	0.585124i	$0.198954\pi$
$822$	0.0590967	−	0.175303i	0.00206123	−	0.00611440i
$823$	−2.60641	−	29.7914i	−0.0908536	−	1.03846i	−0.895605	−	0.444850i	$-0.853257\pi$
$823$	−2.60641	−	29.7914i	−0.0908536	−	1.03846i	0.804752	−	0.593612i	$-0.202298\pi$
$824$	0.472400	+	0.396391i	0.0164568	+	0.0138089i
$825$	7.83716	−	37.0645i	0.272855	−	1.29042i
$826$	−0.0418223	−	0.0152221i	−0.00145519	−	0.000529644i
$827$	35.9960	−	9.64511i	1.25171	−	0.335393i	0.428710	−	0.903442i	$-0.358968\pi$
$827$	35.9960	−	9.64511i	1.25171	−	0.335393i	0.822995	+	0.568049i	$0.192301\pi$
$828$	−4.68237	−	34.4463i	−0.162724	−	1.19709i
$829$	6.82502	−	3.94043i	0.237043	−	0.136857i	−0.376774	−	0.926305i	$-0.622967\pi$
$829$	6.82502	−	3.94043i	0.237043	−	0.136857i	0.613817	+	0.789448i	$0.289633\pi$
$830$	−0.123310	+	0.116386i	−0.00428016	+	0.00403980i
$831$	−21.7347	+	22.8001i	−0.753968	+	0.790927i
$832$	7.26652	−	15.5831i	0.251921	−	0.540247i
$833$	−7.00798	−	10.0084i	−0.242812	−	0.346771i
$834$	0.0865115	−	0.197739i	0.00299565	−	0.00684714i
$835$	20.5993	+	38.1848i	0.712868	+	1.32144i
$836$			49.6874i			1.71847i
$837$	−22.1231	−	16.0078i	−0.764687	−	0.553310i
$838$	0.0948142	+	0.0948142i	0.00327530	+	0.00327530i
$839$	26.9906	−	22.6478i	0.931819	−	0.781889i	−0.0443239	−	0.999017i	$-0.514113\pi$
$839$	26.9906	−	22.6478i	0.931819	−	0.781889i	0.976143	+	0.217128i	$0.0696689\pi$
$840$	−0.0607763	−	0.00562129i	−0.00209698	−	0.000193953i
$841$	−1.21001	+	6.86229i	−0.0417244	+	0.236631i
$842$	−0.00793494	−	0.00370012i	−0.000273456	−	0.000127515i
$843$	39.9202	+	21.7919i	1.37493	+	0.750554i
$844$	−11.1878	+	1.97271i	−0.385100	+	0.0679035i
$845$	−16.7353	−	8.40045i	−0.575713	−	0.288984i
$846$	−0.154417	+	0.0992895i	−0.00530895	+	0.00341364i
$847$	−0.543456	−	2.02821i	−0.0186734	−	0.0696900i
$848$	−41.8153	+	19.4988i	−1.43594	+	0.669592i
$849$	−31.7084	−	2.01134i	−1.08823	−	0.0690290i
$850$	−0.0604201	−	0.120182i	−0.00207239	−	0.00412221i
$851$	−12.0521	+	14.3631i	−0.413141	+	0.492362i
$852$	−13.3373	+	11.7462i	−0.456928	+	0.402417i
$853$	−10.3392	−	22.1725i	−0.354007	−	0.759171i	0.645984	−	0.763351i	$-0.276447\pi$
$853$	−10.3392	−	22.1725i	−0.354007	−	0.759171i	−0.999991	+	0.00417979i	$0.998670\pi$
$854$	−0.0239053	+	0.0414051i	−0.000818021	+	0.00141685i
$855$	34.8311	+	15.4451i	1.19120	+	0.528212i
$856$	0.458819	+	0.794697i	0.0156821	+	0.0271622i
$857$	2.59518	−	3.70630i	0.0886496	−	0.126605i	−0.772378	−	0.635164i	$-0.780933\pi$
$857$	2.59518	−	3.70630i	0.0886496	−	0.126605i	0.861027	+	0.508559i	$0.169822\pi$
$858$	−0.119204	+	0.218368i	−0.00406956	+	0.00745495i
$859$	3.10612	+	8.53399i	0.105979	+	0.291176i	0.981336	−	0.192302i	$-0.0615954\pi$
$859$	3.10612	+	8.53399i	0.105979	+	0.291176i	−0.875356	+	0.483478i	$0.839373\pi$
$860$	−15.0277	+	37.8499i	−0.512440	+	1.29067i
$861$	−0.0186720	−	0.167243i	−0.000636340	−	0.00569963i
$862$	0.0332801	−	0.380394i	0.00113353	−	0.0129563i
$863$	−21.0851	+	21.0851i	−0.717746	+	0.717746i	−0.968143	−	0.250398i	$-0.919439\pi$
$863$	−21.0851	+	21.0851i	−0.717746	+	0.717746i	0.250398	+	0.968143i	$0.419439\pi$
$864$	0.738515	−	0.600418i	0.0251248	−	0.0204266i
$865$	12.7323	+	2.62626i	0.432911	+	0.0892954i
$866$	0.346801	+	0.413302i	0.0117848	+	0.0140446i
$867$	8.76965	+	22.4115i	0.297833	+	0.761136i
$868$	2.22175	−	1.55569i	0.0754113	−	0.0528035i
$869$	12.7229	−	4.63076i	0.431595	−	0.157088i
$870$	0.0495492	−	0.273076i	0.00167987	−	0.00925813i
$871$	0.685845	+	3.88962i	0.0232390	+	0.131795i
$872$	−0.189700	+	0.707971i	−0.00642406	+	0.0239749i
$873$	14.0089	−	1.90426i	0.474130	−	0.0644496i
$874$	0.435146	+	0.251232i	0.0147190	+	0.00849804i
$875$	2.36259	−	1.65649i	0.0798700	−	0.0559996i
$876$	41.4127	+	27.5453i	1.39921	+	0.930671i
$877$	−45.5933	+	3.98890i	−1.53958	+	0.134696i	−0.825110	−	0.564973i	$-0.808887\pi$
$877$	−45.5933	+	3.98890i	−1.53958	+	0.134696i	−0.714468	+	0.699668i	$0.753331\pi$
$878$	−0.0717992	+	0.00628162i	−0.00242311	+	0.000211994i
$879$	16.3083	−	8.08503i	0.550065	−	0.272701i
$880$	−38.0566	+	9.02792i	−1.28289	+	0.304331i
$881$	−33.3855	−	19.2752i	−1.12479	−	0.649396i	−0.182169	−	0.983267i	$-0.558312\pi$
$881$	−33.3855	−	19.2752i	−1.12479	−	0.649396i	−0.942619	+	0.333871i	$0.891645\pi$
$882$	0.0125173	−	0.317304i	0.000421480	−	0.0106842i
$883$	−4.85682	+	18.1259i	−0.163445	+	0.609986i	0.834788	+	0.550571i	$0.185590\pi$
$883$	−4.85682	+	18.1259i	−0.163445	+	0.609986i	−0.998233	+	0.0594144i	$0.981077\pi$
$884$	−1.31612	−	7.46412i	−0.0442661	−	0.251045i
$885$	−18.6855	+	39.5575i	−0.628107	+	1.32971i
$886$	−0.424182	+	0.154390i	−0.0142507	+	0.00518682i
$887$	30.0349	−	21.0306i	1.00847	−	0.706140i	0.0522057	−	0.998636i	$-0.483375\pi$
$887$	30.0349	−	21.0306i	1.00847	−	0.706140i	0.956267	+	0.292496i	$0.0944860\pi$
$888$	−0.338357	−	0.0513501i	−0.0113545	−	0.00172320i
$889$	3.22424	+	3.84250i	0.108137	+	0.128873i
$890$	0.0199418	−	0.0966792i	0.000668449	−	0.00324069i
$891$	32.0592	−	22.8522i	1.07402	−	0.765579i
$892$	18.6451	−	18.6451i	0.624283	−	0.624283i
$893$	−1.98428	+	22.6804i	−0.0664014	+	0.758972i
$894$	−0.410593	+	0.302389i	−0.0137323	+	0.0101134i
$895$	19.6257	−	8.47052i	0.656015	−	0.283138i
$896$	0.0431100	+	0.118444i	0.00144021	+	0.00395693i
$897$	−11.2370	−	18.4305i	−0.375191	−	0.615375i
$898$	0.0589716	−	0.0842201i	0.00196791	−	0.00281046i
$899$	12.3336	+	21.3624i	0.411349	+	0.712477i
$900$	−5.50178	+	29.4876i	−0.183393	+	0.982921i
$901$	−10.1666	+	17.6091i	−0.338700	+	0.586645i
$902$	0.0106253	+	0.0227860i	0.000353783	+	0.000758690i
$903$	3.85772	+	1.30048i	0.128377	+	0.0432773i
$904$	−0.364593	+	0.434505i	−0.0121262	+	0.0144514i
$905$	3.59611	−	30.8221i	0.119539	−	1.02456i
$906$	0.219969	−	0.330710i	0.00730799	−	0.0109871i
$907$	−17.4935	+	8.15736i	−0.580863	+	0.270861i	−0.690762	−	0.723082i	$-0.742725\pi$
$907$	−17.4935	+	8.15736i	−0.580863	+	0.270861i	0.109900	+	0.993943i	$0.464947\pi$
$908$	7.54288	+	28.1504i	0.250319	+	0.934204i
$909$	−8.59788	−	1.09518i	−0.285174	−	0.0363247i
$910$	−0.0179857	+	0.00596396i	−0.000596221	+	0.000197703i
$911$	39.2363	−	6.91842i	1.29996	−	0.229217i	0.519523	−	0.854456i	$-0.326110\pi$
$911$	39.2363	−	6.91842i	1.29996	−	0.229217i	0.780433	+	0.625239i	$0.214999\pi$
$912$	−0.940828	−	39.3265i	−0.0311539	−	1.30223i
$913$	19.6923	+	9.18269i	0.651721	+	0.303903i
$914$	0.0961236	−	0.545144i	0.00317949	−	0.0180318i
$915$	38.3630	+	27.1468i	1.26824	+	0.897446i
$916$	−12.7575	+	10.7048i	−0.421519	+	0.353696i
$917$	−0.833342	−	0.833342i	−0.0275194	−	0.0275194i
$918$	0.0382707	−	0.134452i	0.00126312	−	0.00443757i
$919$		−	43.5953i		−	1.43808i	−0.694971	−	0.719038i	$-0.744583\pi$
$919$		−	43.5953i		−	1.43808i	0.694971	−	0.719038i	$-0.255417\pi$
$920$	−0.226760	+	0.758003i	−0.00747606	+	0.0249906i
$921$	22.0468	−	2.46144i	0.726468	−	0.0811071i
$922$	−0.231352	−	0.330404i	−0.00761916	−	0.0108813i
$923$	−4.66385	+	10.0017i	−0.153513	+	0.329209i
$924$	1.10214	+	3.75189i	0.0362577	+	0.123428i
$925$	13.7666	−	8.49923i	0.452642	−	0.279453i
$926$	0.159010	−	0.0918044i	0.00522539	−	0.00301688i
$927$	−22.4230	−	20.3741i	−0.736468	−	0.669174i
$928$	−0.830480	+	0.222526i	−0.0272618	+	0.00730479i
$929$	−32.4046	−	11.7943i	−1.06316	−	0.386959i	−0.249546	−	0.968363i	$-0.580281\pi$
$929$	−32.4046	−	11.7943i	−1.06316	−	0.386959i	−0.813615	+	0.581404i	$0.802504\pi$
$930$	0.154029	+	0.269870i	0.00505080	+	0.00884938i
$931$	−30.1676	−	25.3136i	−0.988703	−	0.829620i
$932$	4.81942	+	55.0863i	0.157865	+	1.80441i
$933$	−24.0449	−	27.3019i	−0.787194	−	0.893825i
$934$	0.0577199	−	0.158584i	0.00188865	−	0.00518903i
$935$	−11.4565	+	12.8790i	−0.374669	+	0.421188i
$936$	0.180457	−	0.350242i	0.00589842	−	0.0114480i
$937$	−44.7642	−	11.9945i	−1.46238	−	0.391845i	−0.562072	−	0.827089i	$-0.689995\pi$
$937$	−44.7642	−	11.9945i	−1.46238	−	0.391845i	−0.900313	+	0.435244i	$0.856662\pi$
$938$	−0.00592696	−	0.00415010i	−0.000193522	−	0.000135506i
$939$	−49.1206	+	14.4295i	−1.60299	+	0.470888i
$940$	−17.7340	+	2.60141i	−0.578421	+	0.0848486i
$941$	8.77614	+	1.54747i	0.286094	+	0.0504461i	0.314854	−	0.949140i	$-0.398045\pi$
$941$	8.77614	+	1.54747i	0.286094	+	0.0504461i	−0.0287596	+	0.999586i	$0.509156\pi$
$942$	0.0482638	+	0.0385693i	0.00157252	+	0.00125665i
$943$	−2.17311	−	0.190123i	−0.0707662	−	0.00619124i
$944$	45.1676			1.47008
$945$	2.97269	+	0.393654i	0.0967016	+	0.0128056i
$946$	−0.608216			−0.0197748
$947$	36.6998	+	3.21081i	1.19258	+	0.104337i	0.666109	−	0.745854i	$-0.267959\pi$
$947$	36.6998	+	3.21081i	1.19258	+	0.104337i	0.526473	+	0.850192i	$0.323514\pi$
$948$	−9.98340	+	3.90651i	−0.324246	+	0.126878i
$949$	30.4146	+	5.36292i	0.987300	+	0.174088i
$950$	−0.288368	−	0.323766i	−0.00935590	−	0.0105044i
$951$	33.2912	+	31.7355i	1.07954	+	1.02910i
$952$	0.0227488	+	0.0159289i	0.000737292	+	0.000516257i
$953$	−27.9077	−	7.47785i	−0.904020	−	0.242231i	−0.223278	−	0.974755i	$-0.571676\pi$
$953$	−27.9077	−	7.47785i	−0.904020	−	0.242231i	−0.680742	+	0.732523i	$0.738342\pi$
$954$	−0.487387	+	0.204287i	−0.0157797	+	0.00661404i
$955$	1.54979	+	26.5143i	0.0501501	+	0.857981i
$956$	14.8286	−	40.7411i	0.479590	−	1.31766i
$957$	−34.8661	+	7.01153i	−1.12706	+	0.226650i
$958$	−0.00563868	−	0.0644504i	−0.000182177	−	0.00208230i
$959$	−1.38314	−	1.16060i	−0.0446641	−	0.0374776i
$960$	29.9466	−	7.86509i	0.966522	−	0.253845i
$961$	3.17820	+	1.15677i	0.102522	+	0.0373151i
$962$	−0.102627	+	0.0274987i	−0.00330881	+	0.000886594i
$963$	−20.9849	−	39.9011i	−0.676229	−	1.28580i
$964$	−9.04140	+	5.22006i	−0.291204	+	0.168127i
$965$	−27.0606	−	0.781770i	−0.871112	−	0.0251661i
$966$	0.0384305	+	0.00931830i	0.00123648	+	0.000299811i
$967$	8.87400	−	19.0304i	0.285369	−	0.611975i	−0.710407	−	0.703791i	$-0.751489\pi$
$967$	8.87400	−	19.0304i	0.285369	−	0.611975i	0.995776	+	0.0918158i	$0.0292671\pi$
$968$	−0.284960	−	0.406964i	−0.00915895	−	0.0130803i
$969$	−10.2805	−	13.9592i	−0.330257	−	0.448434i
$970$	−0.154126	−	0.0461076i	−0.00494870	−	0.00148043i
$971$		−	58.1766i		−	1.86697i	−0.358610	−	0.933487i	$-0.616749\pi$
$971$		−	58.1766i		−	1.86697i	0.358610	−	0.933487i	$-0.383251\pi$
$972$	−24.9444	+	18.6963i	−0.800091	+	0.599684i
$973$	−1.48956	−	1.48956i	−0.0477531	−	0.0477531i
$974$	−0.277273	+	0.232660i	−0.00888441	+	0.00745490i
$975$	4.20925	+	18.1443i	0.134804	+	0.581082i
$976$	8.42555	−	47.7837i	0.269695	−	1.52952i
$977$	−39.2996	−	18.3257i	−1.25731	−	0.586291i	−0.324232	−	0.945977i	$-0.605106\pi$
$977$	−39.2996	−	18.3257i	−1.25731	−	0.586291i	−0.933073	+	0.359686i	$0.882884\pi$
$978$	−0.342605	+	0.208885i	−0.0109553	+	0.00667939i
$979$	−12.4574	+	2.19657i	−0.398140	+	0.0702028i
$980$	13.9086	−	27.7086i	0.444294	−	0.885119i
$981$	10.6836	−	34.3877i	0.341103	−	1.09791i
$982$	−0.00805718	−	0.0300698i	−0.000257115	−	0.000959566i
$983$	−47.1628	+	21.9924i	−1.50426	+	0.701447i	−0.987924	−	0.154940i	$-0.950482\pi$
$983$	−47.1628	+	21.9924i	−1.50426	+	0.701447i	−0.516335	+	0.856387i	$0.672704\pi$
$984$	−0.0176854	−	0.0356731i	−0.000563788	−	0.00113722i
$985$	−10.4255	+	8.24691i	−0.332183	+	0.262768i
$986$	−0.0811698	+	0.0967344i	−0.00258497	+	0.00308065i
$987$	0.353252	+	1.75661i	0.0112441	+	0.0559135i
$988$	−10.3243	−	22.1405i	−0.328460	−	0.704384i
$989$	26.3860	−	45.7019i	0.839026	−	1.45324i
$990$	−0.439640	+	0.0861433i	−0.0139727	+	0.00273781i
$991$	−1.64852	−	2.85532i	−0.0523670	−	0.0907023i	0.838654	−	0.544665i	$-0.183343\pi$
$991$	−1.64852	−	2.85532i	−0.0523670	−	0.0907023i	−0.891021	+	0.453963i	$0.850010\pi$
$992$	0.552136	−	0.788532i	0.0175303	−	0.0250359i
$993$	−17.2158	+	0.411861i	−0.546325	+	0.0130700i
$994$	−0.00691448	−	0.0189974i	−0.000219314	−	0.000602560i
$995$	4.95743	+	11.4861i	0.157161	+	0.364133i
$996$	−15.7618	−	6.89584i	−0.499431	−	0.218503i
$997$	2.04371	−	23.3597i	0.0647248	−	0.739808i	−0.892610	−	0.450829i	$-0.851129\pi$
$997$	2.04371	−	23.3597i	0.0647248	−	0.739808i	0.957335	−	0.288979i	$-0.0933159\pi$
$998$	0.147387	−	0.147387i	0.00466546	−	0.00466546i
$999$	16.5109	+	3.17609i	0.522380	+	0.100487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.113.9	yes	192
3.2	odd	2		405.2.r.a.368.8		192
5.2	odd	4	inner	135.2.q.a.32.8	✓	192
5.3	odd	4		675.2.ba.b.32.9		192
5.4	even	2		675.2.ba.b.518.8		192
15.2	even	4		405.2.r.a.287.9		192
27.11	odd	18	inner	135.2.q.a.38.8	yes	192
27.16	even	9		405.2.r.a.278.9		192
135.38	even	36		675.2.ba.b.632.8		192
135.92	even	36	inner	135.2.q.a.92.9	yes	192
135.97	odd	36		405.2.r.a.197.8		192
135.119	odd	18		675.2.ba.b.443.9		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.8	✓	192	5.2	odd	4	inner
135.2.q.a.38.8	yes	192	27.11	odd	18	inner
135.2.q.a.92.9	yes	192	135.92	even	36	inner
135.2.q.a.113.9	yes	192	1.1	even	1	trivial
405.2.r.a.197.8		192	135.97	odd	36
405.2.r.a.278.9		192	27.16	even	9
405.2.r.a.287.9		192	15.2	even	4
405.2.r.a.368.8		192	3.2	odd	2
675.2.ba.b.32.9		192	5.3	odd	4
675.2.ba.b.443.9		192	135.119	odd	18
675.2.ba.b.518.8		192	5.4	even	2
675.2.ba.b.632.8		192	135.38	even	36

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0152086 - 0.00133058i) q^{2} +(0.259886 - 1.71244i) q^{3} +(-1.96939 - 0.347256i) q^{4} +(-1.79388 - 1.33492i) q^{5} +(-0.00623106 + 0.0256981i) q^{6} +(0.211408 + 0.148030i) q^{7} +(0.0589827 + 0.0158044i) q^{8} +(-2.86492 - 0.890079i) q^{9} +O(q^{10})\)	\(q+(-0.0152086 - 0.00133058i) q^{2} +(0.259886 - 1.71244i) q^{3} +(-1.96939 - 0.347256i) q^{4} +(-1.79388 - 1.33492i) q^{5} +(-0.00623106 + 0.0256981i) q^{6} +(0.211408 + 0.148030i) q^{7} +(0.0589827 + 0.0158044i) q^{8} +(-2.86492 - 0.890079i) q^{9} +(0.0255062 + 0.0226891i) q^{10} +(1.49616 - 4.11066i) q^{11} +(-1.10647 + 3.28221i) q^{12} +(0.187451 + 2.14258i) q^{13} +(-0.00301826 - 0.00253263i) q^{14} +(-2.75217 + 2.72499i) q^{15} +(3.75746 + 1.36760i) q^{16} +(1.70216 - 0.456091i) q^{17} +(0.0423872 + 0.0173489i) q^{18} +(4.91894 - 2.83995i) q^{19} +(3.06928 + 3.25190i) q^{20} +(0.308434 - 0.323554i) q^{21} +(-0.0282241 + 0.0605267i) q^{22} +(-3.32360 - 4.74660i) q^{23} +(0.0423928 - 0.0968971i) q^{24} +(1.43600 + 4.78935i) q^{25} -0.0328351i q^{26} +(-2.26876 + 4.67469i) q^{27} +(-0.364940 - 0.364940i) q^{28} +(3.59567 - 3.01712i) q^{29} +(0.0454826 - 0.0377814i) q^{30} +(-0.912568 + 5.17543i) q^{31} +(-0.166010 - 0.0774120i) q^{32} +(-6.65044 - 3.63039i) q^{33} +(-0.0264943 + 0.00467167i) q^{34} +(-0.181634 - 0.547759i) q^{35} +(5.33305 + 2.74777i) q^{36} +(-0.837479 - 3.12552i) q^{37} +(-0.0785891 + 0.0366467i) q^{38} +(3.71775 + 0.235826i) q^{39} +(-0.0847103 - 0.107088i) q^{40} +(0.241984 - 0.288386i) q^{41} +(-0.00512138 + 0.00451041i) q^{42} +(3.84888 + 8.25395i) q^{43} +(-4.37396 + 7.57592i) q^{44} +(3.95114 + 5.42112i) q^{45} +(0.0442317 + 0.0766116i) q^{46} +(-2.29910 + 3.28345i) q^{47} +(3.31845 - 6.07901i) q^{48} +(-2.37136 - 6.51526i) q^{49} +(-0.0154670 - 0.0747502i) q^{50} +(-0.338664 - 3.03338i) q^{51} +(0.374859 - 4.28465i) q^{52} +(-8.15900 + 8.15900i) q^{53} +(0.0407248 - 0.0680769i) q^{54} +(-8.17131 + 5.37678i) q^{55} +(0.0101299 + 0.0120724i) q^{56} +(-3.58489 - 9.16146i) q^{57} +(-0.0586997 + 0.0411020i) q^{58} +(10.6146 - 3.86341i) q^{59} +(6.36635 - 4.41085i) q^{60} +(-2.10712 - 11.9501i) q^{61} +(0.0207652 - 0.0774969i) q^{62} +(-0.473909 - 0.612263i) q^{63} +(-6.92336 - 3.99720i) q^{64} +(2.52389 - 4.09375i) q^{65} +(0.0963135 + 0.0640622i) q^{66} +(1.82940 - 0.160052i) q^{67} +(-3.51058 + 0.307136i) q^{68} +(-8.99203 + 4.45790i) q^{69} +(0.00203356 + 0.00857235i) q^{70} +(4.44360 + 2.56551i) q^{71} +(-0.154913 - 0.0977775i) q^{72} +(3.71651 - 13.8702i) q^{73} +(0.00857816 + 0.0486492i) q^{74} +(8.57469 - 1.21438i) q^{75} +(-10.6735 + 3.88483i) q^{76} +(0.924799 - 0.647552i) q^{77} +(-0.0562282 - 0.00853337i) q^{78} +(1.98949 + 2.37099i) q^{79} +(-4.91479 - 7.46920i) q^{80} +(7.41552 + 5.10001i) q^{81} +(-0.00406398 + 0.00406398i) q^{82} +(-0.432904 + 4.94812i) q^{83} +(-0.719782 + 0.530096i) q^{84} +(-3.66230 - 1.45406i) q^{85} +(-0.0475536 - 0.130653i) q^{86} +(-4.23219 - 6.94148i) q^{87} +(0.153214 - 0.218812i) q^{88} +(-1.44584 - 2.50426i) q^{89} +(-0.0528781 - 0.0877051i) q^{90} +(-0.277536 + 0.480707i) q^{91} +(4.89717 + 10.5020i) q^{92} +(8.62546 + 2.90774i) q^{93} +(0.0393351 - 0.0468777i) q^{94} +(-12.6151 - 1.47184i) q^{95} +(-0.175707 + 0.264165i) q^{96} +(-4.27105 + 1.99162i) q^{97} +(0.0273961 + 0.102243i) q^{98} +(-7.94518 + 10.4450i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more