LMFDB - Embedded newform 507.2.q.a.490.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			490.12
Character	$\chi$	$=$	507.490
Dual form			507.2.q.a.328.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.388806 + 1.90450i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(-1.63599 + 0.697029i) q^{4} +(0.449945 - 0.110901i) q^{5} +(-0.0782682 - 1.94220i) q^{6} +(-0.611025 + 1.28771i) q^{7} +(0.244816 + 0.354677i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})$	\(q+(0.388806 + 1.90450i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(-1.63599 + 0.697029i) q^{4} +(0.449945 - 0.110901i) q^{5} +(-0.0782682 - 1.94220i) q^{6} +(-0.611025 + 1.28771i) q^{7} +(0.244816 + 0.354677i) q^{8} +(0.948536 + 0.316668i) q^{9} +(0.386153 + 0.813800i) q^{10} +(-1.54294 + 0.515109i) q^{11} +(1.72661 - 0.425572i) q^{12} +(-3.60499 - 0.0637555i) q^{13} +(-2.69001 - 0.663028i) q^{14} +(-0.461908 + 0.0372891i) q^{15} +(-3.04402 + 3.16916i) q^{16} +(-1.78576 + 3.76341i) q^{17} +(-0.234297 + 1.92961i) q^{18} +(3.89104 + 6.73948i) q^{19} +(-0.658802 + 0.495058i) q^{20} +(0.809676 - 1.17302i) q^{21} +(-1.58093 - 2.73825i) q^{22} +(2.56052 - 4.43495i) q^{23} +(-0.184751 - 0.389355i) q^{24} +(-4.23713 + 2.22382i) q^{25} +(-1.28022 - 6.89048i) q^{26} +(-0.885456 - 0.464723i) q^{27} +(0.102059 - 2.53258i) q^{28} +(0.00751256 + 0.0367990i) q^{29} +(-0.250610 - 0.865205i) q^{30} +(-5.26530 - 2.76344i) q^{31} +(-6.49070 - 4.10447i) q^{32} +(1.60559 - 0.260933i) q^{33} +(-7.86173 - 1.93774i) q^{34} +(-0.132119 + 0.647161i) q^{35} +(-1.77252 + 0.143093i) q^{36} +(-0.540038 + 0.341500i) q^{37} +(-11.3225 + 10.0308i) q^{38} +(3.54808 + 0.641211i) q^{39} +(0.149488 + 0.132435i) q^{40} +(3.53531 + 0.574544i) q^{41} +(2.54882 + 1.08595i) q^{42} +(3.67875 + 2.32630i) q^{43} +(2.16518 - 1.91818i) q^{44} +(0.461908 + 0.0372891i) q^{45} +(9.44191 + 3.15217i) q^{46} +(-1.26336 - 10.4047i) q^{47} +(3.51297 - 2.63982i) q^{48} +(3.14228 + 3.84859i) q^{49} +(-5.88268 - 7.20497i) q^{50} +(2.36633 - 3.42822i) q^{51} +(5.94215 - 2.40848i) q^{52} +(-3.52870 - 5.11220i) q^{53} +(0.540794 - 1.86704i) q^{54} +(-0.637111 + 0.402885i) q^{55} +(-0.606309 + 0.0985348i) q^{56} +(-2.75957 - 7.27638i) q^{57} +(-0.0671627 + 0.0286153i) q^{58} +(9.45680 + 9.84557i) q^{59} +(0.729683 - 0.382967i) q^{60} +(-2.00848 - 0.162141i) q^{61} +(3.21579 - 11.1022i) q^{62} +(-0.987356 + 1.02795i) q^{63} +(2.17687 - 5.73994i) q^{64} +(-1.62912 + 0.371112i) q^{65} +(1.12121 + 2.95639i) q^{66} +(11.3340 + 4.82897i) q^{67} +(0.298275 - 7.40161i) q^{68} +(-3.23878 + 3.96678i) q^{69} -1.28389 q^{70} +(1.27318 - 1.55937i) q^{71} +(0.119902 + 0.413949i) q^{72} +(10.1755 + 9.01469i) q^{73} +(-0.860356 - 0.895725i) q^{74} +(4.53898 - 1.51534i) q^{75} +(-11.0633 - 8.31353i) q^{76} +(0.279465 - 2.30160i) q^{77} +(0.158330 + 7.00661i) q^{78} +(0.751631 + 6.19024i) q^{79} +(-1.01818 + 1.76353i) q^{80} +(0.799443 + 0.600742i) q^{81} +(0.280333 + 6.95639i) q^{82} +(4.80930 - 12.6811i) q^{83} +(-0.506991 + 2.48341i) q^{84} +(-0.386126 + 1.89137i) q^{85} +(-3.00011 + 7.91065i) q^{86} +(-0.00151231 - 0.0375275i) q^{87} +(-0.560433 - 0.421138i) q^{88} +(-8.90467 + 15.4233i) q^{89} +(0.108576 + 0.894201i) q^{90} +(2.28484 - 4.60322i) q^{91} +(-1.09769 + 9.04028i) q^{92} +(4.75383 + 3.57227i) q^{93} +(19.3245 - 6.45147i) q^{94} +(2.49817 + 2.60087i) q^{95} +(5.74824 + 5.09250i) q^{96} +(-2.36677 - 8.17104i) q^{97} +(-6.10790 + 7.48082i) q^{98} -1.62665 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) $ 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21} + 22 q^{22} + 46 q^{23} + 3 q^{24} + 28 q^{25} + 34 q^{26} + 30 q^{27} - 2 q^{28} + 36 q^{29} + q^{30} - 34 q^{31} - 190 q^{32} + 15 q^{33} - 51 q^{34} - 80 q^{35} + 15 q^{36} + q^{37} - 53 q^{38} + 5 q^{39} - 45 q^{40} + 9 q^{41} + 130 q^{42} + 78 q^{43} + 35 q^{44} - q^{45} - 318 q^{46} - 12 q^{47} - 15 q^{48} - 71 q^{49} + 48 q^{50} - 14 q^{51} - 63 q^{52} - 26 q^{53} - q^{54} - 61 q^{55} - 4 q^{56} - 38 q^{57} - 27 q^{58} + 208 q^{59} - 180 q^{60} - 3 q^{61} - 61 q^{62} + 2 q^{63} + 140 q^{64} + 45 q^{65} - 60 q^{66} - 80 q^{67} - 140 q^{68} + 6 q^{69} - 100 q^{70} + 84 q^{71} - 3 q^{72} + 134 q^{73} - 151 q^{74} - 12 q^{75} + 32 q^{76} + 82 q^{77} - 63 q^{78} + 4 q^{79} - 155 q^{80} + 15 q^{81} - 56 q^{82} + 106 q^{83} + 2 q^{84} - 19 q^{85} + q^{86} - 49 q^{87} + 8 q^{88} - 14 q^{89} + 2 q^{90} - 368 q^{91} + 36 q^{92} - 4 q^{93} - 59 q^{94} + 104 q^{95} + 75 q^{96} - 28 q^{97} + 101 q^{98} + 30 q^{99}+O(q^{100}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9 - q^10 - 2 * q^11 + 30 * q^12 - 19 * q^13 + q^15 + 15 * q^16 - 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 22 * q^22 + 46 * q^23 + 3 * q^24 + 28 * q^25 + 34 * q^26 + 30 * q^27 - 2 * q^28 + 36 * q^29 + q^30 - 34 * q^31 - 190 * q^32 + 15 * q^33 - 51 * q^34 - 80 * q^35 + 15 * q^36 + q^37 - 53 * q^38 + 5 * q^39 - 45 * q^40 + 9 * q^41 + 130 * q^42 + 78 * q^43 + 35 * q^44 - q^45 - 318 * q^46 - 12 * q^47 - 15 * q^48 - 71 * q^49 + 48 * q^50 - 14 * q^51 - 63 * q^52 - 26 * q^53 - q^54 - 61 * q^55 - 4 * q^56 - 38 * q^57 - 27 * q^58 + 208 * q^59 - 180 * q^60 - 3 * q^61 - 61 * q^62 + 2 * q^63 + 140 * q^64 + 45 * q^65 - 60 * q^66 - 80 * q^67 - 140 * q^68 + 6 * q^69 - 100 * q^70 + 84 * q^71 - 3 * q^72 + 134 * q^73 - 151 * q^74 - 12 * q^75 + 32 * q^76 + 82 * q^77 - 63 * q^78 + 4 * q^79 - 155 * q^80 + 15 * q^81 - 56 * q^82 + 106 * q^83 + 2 * q^84 - 19 * q^85 + q^86 - 49 * q^87 + 8 * q^88 - 14 * q^89 + 2 * q^90 - 368 * q^91 + 36 * q^92 - 4 * q^93 - 59 * q^94 + 104 * q^95 + 75 * q^96 - 28 * q^97 + 101 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{17}{39}\right)$

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 $

$2$	0.388806	+	1.90450i	0.274927	+	1.34668i	0.849222	+	0.528035i	$0.177071\pi$
$2$	0.388806	+	1.90450i	0.274927	+	1.34668i	−0.574295	+	0.818649i	$0.694724\pi$
$3$	−0.987050	−	0.160411i	−0.569874	−	0.0926135i
$3$	−0.987050	−	0.160411i	−0.569874	−	0.0926135i
$4$	−1.63599	+	0.697029i	−0.817993	+	0.348514i
$5$	0.449945	−	0.110901i	0.201221	−	0.0495966i	−0.137417	−	0.990513i	$-0.543880\pi$
$5$	0.449945	−	0.110901i	0.201221	−	0.0495966i	0.338638	+	0.940917i	$0.390034\pi$
$6$	−0.0782682	−	1.94220i	−0.0319529	−	0.792902i
$7$	−0.611025	+	1.28771i	−0.230946	+	0.486708i	−0.985531	−	0.169494i	$-0.945787\pi$
$7$	−0.611025	+	1.28771i	−0.230946	+	0.486708i	0.754585	+	0.656202i	$0.227838\pi$
$8$	0.244816	+	0.354677i	0.0865554	+	0.125397i
$9$	0.948536	+	0.316668i	0.316179	+	0.105556i
$10$	0.386153	+	0.813800i	0.122112	+	0.257346i
$11$	−1.54294	+	0.515109i	−0.465214	+	0.155311i	−0.539606	−	0.841918i	$-0.681427\pi$
$11$	−1.54294	+	0.515109i	−0.465214	+	0.155311i	0.0743918	+	0.997229i	$0.476298\pi$
$12$	1.72661	−	0.425572i	0.498430	−	0.122852i
$13$	−3.60499	−	0.0637555i	−0.999844	−	0.0176826i
$13$	−3.60499	−	0.0637555i	−0.999844	−	0.0176826i
$14$	−2.69001	−	0.663028i	−0.718935	−	0.177202i
$15$	−0.461908	+	0.0372891i	−0.119264	+	0.00962799i
$16$	−3.04402	+	3.16916i	−0.761005	+	0.792290i
$17$	−1.78576	+	3.76341i	−0.433111	+	0.912761i	0.563149	+	0.826355i	$0.309590\pi$
$17$	−1.78576	+	3.76341i	−0.433111	+	0.912761i	−0.996260	+	0.0864061i	$0.972462\pi$
$18$	−0.234297	+	1.92961i	−0.0552243	+	0.454813i
$19$	3.89104	+	6.73948i	0.892666	+	1.54614i	0.836667	+	0.547713i	$0.184501\pi$
$19$	3.89104	+	6.73948i	0.892666	+	1.54614i	0.0559997	+	0.998431i	$0.482165\pi$
$20$	−0.658802	+	0.495058i	−0.147313	+	0.110698i
$21$	0.809676	−	1.17302i	0.176686	−	0.255973i
$22$	−1.58093	−	2.73825i	−0.337055	−	0.583797i
$23$	2.56052	−	4.43495i	0.533906	−	0.924751i	−0.465310	−	0.885148i	$-0.654057\pi$
$23$	2.56052	−	4.43495i	0.533906	−	0.924751i	0.999215	−	0.0396037i	$-0.0126095\pi$
$24$	−0.184751	−	0.389355i	−0.0377122	−	0.0794768i
$25$	−4.23713	+	2.22382i	−0.847426	+	0.444763i
$26$	−1.28022	−	6.89048i	−0.251072	−	1.35133i
$27$	−0.885456	−	0.464723i	−0.170406	−	0.0894360i
$28$	0.102059	−	2.53258i	0.0192874	−	0.478612i
$29$	0.00751256	+	0.0367990i	0.00139505	+	0.00683340i	0.980482	−	0.196608i	$-0.0629926\pi$
$29$	0.00751256	+	0.0367990i	0.00139505	+	0.00683340i	−0.979087	+	0.203441i	$0.934787\pi$
$30$	−0.250610	−	0.865205i	−0.0457548	−	0.157964i
$31$	−5.26530	−	2.76344i	−0.945675	−	0.496329i	−0.0799229	−	0.996801i	$-0.525467\pi$
$31$	−5.26530	−	2.76344i	−0.945675	−	0.496329i	−0.865753	+	0.500472i	$0.833160\pi$
$32$	−6.49070	−	4.10447i	−1.14740	−	0.725575i
$33$	1.60559	−	0.260933i	0.279497	−	0.0454227i
$34$	−7.86173	−	1.93774i	−1.34827	−	0.332320i
$35$	−0.132119	+	0.647161i	−0.0223322	+	0.109390i
$36$	−1.77252	+	0.143093i	−0.295420	+	0.0238488i
$37$	−0.540038	+	0.341500i	−0.0887818	+	0.0561422i	−0.578119	−	0.815952i	$-0.696213\pi$
$37$	−0.540038	+	0.341500i	−0.0887818	+	0.0561422i	0.489337	+	0.872095i	$0.337239\pi$
$38$	−11.3225	+	10.0308i	−1.83675	+	1.62722i
$39$	3.54808	+	0.641211i	0.568147	+	0.102676i
$40$	0.149488	+	0.132435i	0.0236361	+	0.0209397i
$41$	3.53531	+	0.574544i	0.552123	+	0.0897287i	0.430071	−	0.902795i	$-0.358488\pi$
$41$	3.53531	+	0.574544i	0.552123	+	0.0897287i	0.122052	+	0.992524i	$0.461053\pi$
$42$	2.54882	+	1.08595i	0.393291	+	0.167566i
$43$	3.67875	+	2.32630i	0.561003	+	0.354757i	0.784675	−	0.619908i	$-0.212830\pi$
$43$	3.67875	+	2.32630i	0.561003	+	0.354757i	−0.223671	+	0.974665i	$0.571804\pi$
$44$	2.16518	−	1.91818i	0.326413	−	0.289177i
$45$	0.461908	+	0.0372891i	0.0688572	+	0.00555873i
$46$	9.44191	+	3.15217i	1.39213	+	0.464762i
$47$	−1.26336	−	10.4047i	−0.184280	−	1.51768i	−0.732166	−	0.681126i	$-0.761490\pi$
$47$	−1.26336	−	10.4047i	−0.184280	−	1.51768i	0.547886	−	0.836553i	$-0.315433\pi$
$48$	3.51297	−	2.63982i	0.507053	−	0.381026i
$49$	3.14228	+	3.84859i	0.448897	+	0.549798i
$50$	−5.88268	−	7.20497i	−0.831936	−	1.01894i
$51$	2.36633	−	3.42822i	0.331352	−	0.480047i
$52$	5.94215	−	2.40848i	0.824028	−	0.333996i
$53$	−3.52870	−	5.11220i	−0.484704	−	0.702215i	0.501977	−	0.864881i	$-0.332606\pi$
$53$	−3.52870	−	5.11220i	−0.484704	−	0.702215i	−0.986681	+	0.162666i	$0.947991\pi$
$54$	0.540794	−	1.86704i	0.0735927	−	0.254072i
$55$	−0.637111	+	0.402885i	−0.0859081	+	0.0543250i
$56$	−0.606309	+	0.0985348i	−0.0810215	+	0.0131673i
$57$	−2.75957	−	7.27638i	−0.365513	−	0.963779i
$58$	−0.0671627	+	0.0286153i	−0.00881889	+	0.00375738i
$59$	9.45680	+	9.84557i	1.23117	+	1.28178i	0.946327	+	0.323211i	$0.104762\pi$
$59$	9.45680	+	9.84557i	1.23117	+	1.28178i	0.284844	+	0.958574i	$0.408058\pi$
$60$	0.729683	−	0.382967i	0.0942017	−	0.0494409i
$61$	−2.00848	−	0.162141i	−0.257160	−	0.0207601i	−0.0487855	−	0.998809i	$-0.515535\pi$
$61$	−2.00848	−	0.162141i	−0.257160	−	0.0207601i	−0.208374	+	0.978049i	$0.566817\pi$
$62$	3.21579	−	11.1022i	0.408406	−	1.40998i
$63$	−0.987356	+	1.02795i	−0.124395	+	0.129509i
$64$	2.17687	−	5.73994i	0.272109	−	0.717493i
$65$	−1.62912	+	0.371112i	−0.202067	+	0.0460308i
$66$	1.12121	+	2.95639i	0.138011	+	0.363906i
$67$	11.3340	+	4.82897i	1.38467	+	0.589952i	0.950456	−	0.310858i	$-0.100616\pi$
$67$	11.3340	+	4.82897i	1.38467	+	0.589952i	0.434213	+	0.900810i	$0.357027\pi$
$68$	0.298275	−	7.40161i	0.0361711	−	0.897577i
$69$	−3.23878	+	3.96678i	−0.389903	+	0.477545i
$70$	−1.28389			−0.153454
$71$	1.27318	−	1.55937i	0.151099	−	0.185063i	−0.693509	−	0.720448i	$-0.743936\pi$
$71$	1.27318	−	1.55937i	0.151099	−	0.185063i	0.844608	+	0.535385i	$0.179834\pi$
$72$	0.119902	+	0.413949i	0.0141306	+	0.0487844i
$73$	10.1755	+	9.01469i	1.19095	+	1.05509i	0.997256	+	0.0740281i	$0.0235854\pi$
$73$	10.1755	+	9.01469i	1.19095	+	1.05509i	0.193694	+	0.981062i	$0.437953\pi$
$74$	−0.860356	−	0.895725i	−0.100014	−	0.104126i
$75$	4.53898	−	1.51534i	0.524117	−	0.174976i
$76$	−11.0633	−	8.31353i	−1.26905	−	0.953628i
$77$	0.279465	−	2.30160i	0.0318480	−	0.262292i
$78$	0.158330	+	7.00661i	0.0179273	+	0.793343i
$79$	0.751631	+	6.19024i	0.0845651	+	0.696456i	0.971911	+	0.235351i	$0.0756239\pi$
$79$	0.751631	+	6.19024i	0.0845651	+	0.696456i	−0.887345	+	0.461105i	$0.847453\pi$
$80$	−1.01818	+	1.76353i	−0.113836	+	0.197169i
$81$	0.799443	+	0.600742i	0.0888270	+	0.0667491i
$82$	0.280333	+	6.95639i	0.0309576	+	0.768204i
$83$	4.80930	−	12.6811i	0.527889	−	1.39193i	−0.360466	−	0.932772i	$-0.617382\pi$
$83$	4.80930	−	12.6811i	0.527889	−	1.39193i	0.888355	−	0.459157i	$-0.151848\pi$
$84$	−0.506991	+	2.48341i	−0.0553173	+	0.270962i
$85$	−0.386126	+	1.89137i	−0.0418812	+	0.205148i
$86$	−3.00011	+	7.91065i	−0.323510	+	0.853027i
$87$	−0.00151231	−	0.0375275i	−0.000162136	−	0.00402337i
$88$	−0.560433	−	0.421138i	−0.0597424	−	0.0448935i
$89$	−8.90467	+	15.4233i	−0.943893	+	1.63487i	−0.185940	+	0.982561i	$0.559533\pi$
$89$	−8.90467	+	15.4233i	−0.943893	+	1.63487i	−0.757953	+	0.652310i	$0.773800\pi$
$90$	0.108576	+	0.894201i	0.0114449	+	0.0942571i
$91$	2.28484	−	4.60322i	0.239516	−	0.482548i
$92$	−1.09769	+	9.04028i	−0.114442	+	0.942514i
$93$	4.75383	+	3.57227i	0.492949	+	0.370427i
$94$	19.3245	−	6.45147i	1.99317	−	0.665418i
$95$	2.49817	+	2.60087i	0.256307	+	0.266844i
$96$	5.74824	+	5.09250i	0.586678	+	0.519751i
$97$	−2.36677	−	8.17104i	−0.240309	−	0.829643i	−0.986479	−	0.163888i	$-0.947597\pi$
$97$	−2.36677	−	8.17104i	−0.240309	−	0.829643i	0.746170	−	0.665756i	$-0.231891\pi$
$98$	−6.10790	+	7.48082i	−0.616991	+	0.755676i
$99$	−1.62665			−0.163485
$100$	5.38182	−	6.59153i	0.538182	−	0.659153i
$101$	−0.256302	+	6.36008i	−0.0255030	+	0.632851i	0.935011	+	0.354619i	$0.115389\pi$
$101$	−0.256302	+	6.36008i	−0.0255030	+	0.632851i	−0.960514	+	0.278232i	$0.910252\pi$
$102$	7.44908	+	3.17376i	0.737569	+	0.314249i
$103$	3.03815	+	8.01095i	0.299358	+	0.789342i	0.997317	+	0.0732044i	$0.0233225\pi$
$103$	3.03815	+	8.01095i	0.299358	+	0.789342i	−0.697959	+	0.716138i	$0.745908\pi$
$104$	−0.859945	−	1.29421i	−0.0843246	−	0.126908i
$105$	0.234220	−	0.617587i	0.0228575	−	0.0602704i
$106$	8.36421	−	8.70806i	0.812404	−	0.845802i
$107$	5.09558	−	17.5920i	0.492608	−	1.70068i	−0.200367	−	0.979721i	$-0.564214\pi$
$107$	5.09558	−	17.5920i	0.492608	−	1.70068i	0.692976	−	0.720961i	$-0.256299\pi$
$108$	1.77252	+	0.143093i	0.170561	+	0.0137691i
$109$	0.467042	−	0.245122i	0.0447345	−	0.0234785i	−0.442208	−	0.896913i	$-0.645805\pi$
$109$	0.467042	−	0.245122i	0.0447345	−	0.0234785i	0.486942	+	0.873434i	$0.338112\pi$
$110$	−1.01501	−	1.05673i	−0.0967771	−	0.100756i
$111$	0.587826	−	0.250449i	0.0557939	−	0.0237716i
$112$	−2.22098	−	5.85625i	−0.209863	−	0.553363i
$113$	−2.49301	+	0.405153i	−0.234522	+	0.0381136i	−0.276536	−	0.961003i	$-0.589187\pi$
$113$	−2.49301	+	0.405153i	−0.234522	+	0.0381136i	0.0420142	+	0.999117i	$0.486623\pi$
$114$	12.7849	−	8.08469i	1.19742	−	0.757200i
$115$	0.660250	−	2.27945i	0.0615687	−	0.212560i
$116$	−0.0379404	−	0.0549661i	−0.00352268	−	0.00510348i
$117$	−3.39927	−	1.20206i	−0.314263	−	0.111130i
$118$	−15.0740	+	21.8385i	−1.38768	+	2.01040i
$119$	−3.75503	−	4.59908i	−0.344223	−	0.421597i
$120$	−0.126308	−	0.154699i	−0.0115303	−	0.0141220i
$121$	−6.67854	+	5.01860i	−0.607140	+	0.456236i
$122$	−0.472112	−	3.88819i	−0.0427430	−	0.352020i
$123$	−3.39737	−	1.13421i	−0.306330	−	0.102268i
$124$	10.5402	+	0.850889i	0.946534	+	0.0764121i
$125$	−3.39419	+	3.00699i	−0.303585	+	0.268953i
$126$	−2.34161	−	1.48075i	−0.208607	−	0.131915i
$127$	10.9008	+	4.64439i	0.967288	+	0.412123i	0.817075	−	0.576531i	$-0.195594\pi$
$127$	10.9008	+	4.64439i	0.967288	+	0.412123i	0.150212	+	0.988654i	$0.452004\pi$
$128$	−3.38216	−	0.549654i	−0.298943	−	0.0485830i
$129$	−3.25794	−	2.88629i	−0.286846	−	0.254123i
$130$	−1.34019	−	2.95836i	−0.117543	−	0.259465i
$131$	0.604260	−	0.535328i	0.0527945	−	0.0467718i	−0.636313	−	0.771431i	$-0.719541\pi$
$131$	0.604260	−	0.535328i	0.0527945	−	0.0467718i	0.689107	+	0.724659i	$0.258003\pi$
$132$	−2.44484	+	1.54602i	−0.212796	+	0.134564i
$133$	−11.0560	+	0.892534i	−0.958678	+	0.0773925i
$134$	−4.79003	+	23.4631i	−0.413796	+	2.02691i
$135$	−0.449945	−	0.110901i	−0.0387251	−	0.00954487i
$136$	−1.77198	+	0.287974i	−0.151946	+	0.0246936i
$137$	13.1674	+	8.32657i	1.12497	+	0.711387i	0.961403	−	0.275145i	$-0.0887259\pi$
$137$	13.1674	+	8.32657i	1.12497	+	0.711387i	0.163566	+	0.986532i	$0.447700\pi$
$138$	−8.81399	−	4.62594i	−0.750297	−	0.393786i
$139$	−0.777756	−	2.68513i	−0.0659684	−	0.227749i	0.920760	−	0.390130i	$-0.127570\pi$
$139$	−0.777756	−	2.68513i	−0.0659684	−	0.227749i	−0.986728	+	0.162381i	$0.948083\pi$
$140$	−0.234945	−	1.15084i	−0.0198565	−	0.0972635i
$141$	−0.422031	+	10.4726i	−0.0355415	+	0.881952i
$142$	3.46483	+	1.81848i	0.290762	+	0.152604i
$143$	5.59512	−	1.75859i	0.467887	−	0.147061i
$144$	−3.89093	+	2.04212i	−0.324245	+	0.170177i
$145$	0.00746130	+	0.0157244i	0.000619627	+	0.00130584i
$146$	−13.2122	+	22.8842i	−1.09345	+	1.89391i
$147$	−2.48423	−	4.30281i	−0.204896	−	0.354890i
$148$	0.645460	−	0.935111i	0.0530565	−	0.0768656i
$149$	16.8882	−	12.6906i	1.38353	−	1.03966i	0.390652	−	0.920539i	$-0.372250\pi$
$149$	16.8882	−	12.6906i	1.38353	−	1.03966i	0.992880	−	0.119118i	$-0.0380067\pi$
$150$	4.65074	+	8.05532i	0.379731	+	0.657714i
$151$	2.74762	−	22.6287i	0.223598	−	1.84150i	−0.259270	−	0.965805i	$-0.583482\pi$
$151$	2.74762	−	22.6287i	0.223598	−	1.84150i	0.482868	−	0.875693i	$-0.339595\pi$
$152$	−1.43775	+	3.02999i	−0.116617	+	0.245765i
$153$	−2.88561	+	3.00424i	−0.233288	+	0.242878i
$154$	4.49205	−	0.362636i	0.361980	−	0.0292221i
$155$	−2.67556	−	0.659467i	−0.214906	−	0.0529697i
$156$	−6.25155	+	1.42410i	−0.500524	+	0.114019i
$157$	−8.16254	+	2.01188i	−0.651441	+	0.160566i	−0.551168	−	0.834394i	$-0.685818\pi$
$157$	−8.16254	+	2.01188i	−0.651441	+	0.160566i	−0.100273	+	0.994960i	$0.531972\pi$
$158$	−11.4971	+	3.83828i	−0.914657	+	0.305357i
$159$	2.66295	+	5.61205i	0.211186	+	0.445064i
$160$	−3.37565	−	1.12696i	−0.266868	−	0.0890938i
$161$	4.14638	+	6.00707i	0.326781	+	0.473424i
$162$	−0.833285	+	1.75611i	−0.0654690	+	0.137973i
$163$	−0.463948	−	11.5127i	−0.0363392	−	0.901747i	−0.909849	−	0.414940i	$-0.863802\pi$
$163$	−0.463948	−	11.5127i	−0.0363392	−	0.901747i	0.873509	−	0.486807i	$-0.161839\pi$
$164$	−6.18420	+	1.52427i	−0.482905	+	0.119025i
$165$	0.693488	−	0.295468i	0.0539880	−	0.0230021i
$166$	26.0210	+	4.22882i	2.01962	+	0.328220i
$167$	−1.06232	−	5.20360i	−0.0822049	−	0.402666i	−0.999984	−	0.00557607i	$-0.998225\pi$
$167$	−1.06232	−	5.20360i	−0.0822049	−	0.402666i	0.917780	−	0.397090i	$-0.129980\pi$
$168$	0.614264			0.0473915
$169$	12.9919	+	0.459676i	0.999375	+	0.0353597i
$170$	−3.75224			−0.287784
$171$	1.55662	+	7.62481i	0.119037	+	0.583084i
$172$	−7.63987	−	1.24160i	−0.582535	−	0.0946711i
$173$	7.49920	−	3.19511i	0.570153	−	0.242920i	−0.0875965	−	0.996156i	$-0.527919\pi$
$173$	7.49920	−	3.19511i	0.570153	−	0.242920i	0.657750	+	0.753236i	$0.271508\pi$
$174$	0.0708831	−	0.0174711i	0.00537364	−	0.00132448i
$175$	−0.274635	−	6.81500i	−0.0207605	−	0.515165i
$176$	3.06428	−	6.45782i	0.230978	−	0.486777i
$177$	−7.75500	−	11.2351i	−0.582901	−	0.844478i
$178$	−32.8359	−	10.9622i	−2.46116	−	0.821655i
$179$	0.754654	+	1.59040i	0.0564055	+	0.118872i	0.929696	−	0.368328i	$-0.120070\pi$
$179$	0.754654	+	1.59040i	0.0564055	+	0.118872i	−0.873290	+	0.487200i	$0.838018\pi$
$180$	−0.781666	+	0.260959i	−0.0582620	+	0.0194507i
$181$	−2.99308	+	0.737729i	−0.222474	+	0.0548350i	−0.348977	−	0.937131i	$-0.613471\pi$
$181$	−2.99308	+	0.737729i	−0.222474	+	0.0548350i	0.126503	+	0.991966i	$0.459625\pi$
$182$	9.65518	+	2.56171i	0.715690	+	0.189887i
$183$	1.95646	+	0.482225i	0.144626	+	0.0356471i
$184$	2.19983	−	0.177589i	0.162174	−	0.0130920i
$185$	−0.205115	+	0.213547i	−0.0150803	+	0.0157003i
$186$	−4.95506	+	10.4426i	−0.363323	+	0.765687i
$187$	0.816754	−	6.72658i	0.0597270	−	0.491896i
$188$	9.31920	+	16.1413i	0.679672	+	1.17723i
$189$	1.13946	−	0.856252i	0.0828838	−	0.0622832i
$190$	−3.98205	+	5.76900i	−0.288889	+	0.418527i
$191$	10.4337	+	18.0716i	0.754954	+	1.30762i	0.945397	+	0.325920i	$0.105674\pi$
$191$	10.4337	+	18.0716i	0.754954	+	1.30762i	−0.190444	+	0.981698i	$0.560993\pi$
$192$	−3.06943	+	5.31642i	−0.221517	+	0.383679i
$193$	−0.604635	−	1.27424i	−0.0435226	−	0.0917218i	0.880524	−	0.474001i	$-0.157191\pi$
$193$	−0.604635	−	1.27424i	−0.0435226	−	0.0917218i	−0.924047	+	0.382279i	$0.875139\pi$
$194$	14.6415	−	7.68446i	1.05120	−	0.551712i
$195$	1.66755	−	0.104977i	0.119416	−	0.00751759i
$196$	−7.82330	−	4.10598i	−0.558807	−	0.293284i
$197$	0.787256	−	19.5355i	0.0560896	−	1.39185i	−0.688940	−	0.724819i	$-0.741924\pi$
$197$	0.787256	−	19.5355i	0.0560896	−	1.39185i	0.745029	−	0.667032i	$-0.232435\pi$
$198$	−0.632453	−	3.09796i	−0.0449465	−	0.220162i
$199$	6.59806	+	22.7791i	0.467724	+	1.61477i	0.754173	+	0.656675i	$0.228038\pi$
$199$	6.59806	+	22.7791i	0.467724	+	1.61477i	−0.286449	+	0.958095i	$0.592475\pi$
$200$	−1.82605	−	0.958386i	−0.129121	−	0.0677681i
$201$	−10.4126	−	6.58454i	−0.734449	−	0.464437i
$202$	−12.2124	+	1.98471i	−0.859262	+	0.139644i
$203$	−0.0519767	−	0.0128111i	−0.00364805	−	0.000899164i
$204$	−1.48171	+	7.25792i	−0.103741	+	0.508156i
$205$	1.65441	−	0.133558i	0.115549	−	0.00932810i
$206$	−14.0756	+	8.90086i	−0.980693	+	0.620152i
$207$	3.83315	−	3.39588i	0.266423	−	0.236030i
$208$	11.1757	−	11.2307i	0.774896	−	0.778709i
$209$	−9.47521	−	8.39430i	−0.655414	−	0.580646i
$210$	1.26726	+	0.205950i	0.0874493	+	0.0142119i
$211$	−22.3920	−	9.54035i	−1.54153	−	0.656785i	−0.556765	−	0.830670i	$-0.687958\pi$
$211$	−22.3920	−	9.54035i	−1.54153	−	0.656785i	−0.984766	+	0.173885i	$0.944368\pi$
$212$	9.33626	+	5.90389i	0.641217	+	0.405481i
$213$	−1.50683	+	1.33494i	−0.103247	+	0.0914685i
$214$	35.4851	+	2.86465i	2.42571	+	0.195824i
$215$	1.91322	+	0.638727i	0.130481	+	0.0435608i
$216$	−0.0519470	−	0.427822i	−0.00353455	−	0.0291096i
$217$	6.77574	−	5.09164i	0.459967	−	0.345643i
$218$	0.648424	+	0.794175i	0.0439168	+	0.0537883i
$219$	−8.59766	−	10.5302i	−0.580976	−	0.711566i
$220$	0.761483	−	1.10320i	0.0513392	−	0.0743776i
$221$	6.67758	−	13.4532i	0.449183	−	0.904960i
$222$	0.705530	+	1.02214i	0.0473521	+	0.0686013i
$223$	−0.947118	+	3.26983i	−0.0634237	+	0.218964i	−0.985970	−	0.166922i	$-0.946617\pi$
$223$	−0.947118	+	3.26983i	−0.0634237	+	0.218964i	0.922546	+	0.385886i	$0.126104\pi$
$224$	9.25134	−	5.85020i	0.618131	−	0.390883i
$225$	−4.72328	+	0.767608i	−0.314886	+	0.0511739i
$226$	−1.74091	−	4.59040i	−0.115804	−	0.305349i
$227$	−15.9936	+	6.81425i	−1.06154	+	0.452278i	−0.850922	−	0.525292i	$-0.823956\pi$
$227$	−15.9936	+	6.81425i	−1.06154	+	0.452278i	−0.210613	+	0.977570i	$0.567546\pi$
$228$	9.58645	+	9.98055i	0.634878	+	0.660978i
$229$	−1.90148	+	0.997975i	−0.125654	+	0.0659480i	−0.526379	−	0.850250i	$-0.676451\pi$
$229$	−1.90148	+	0.997975i	−0.125654	+	0.0659480i	0.400725	+	0.916198i	$0.368758\pi$
$230$	4.59792	+	0.371182i	0.303178	+	0.0244750i
$231$	−0.645049	+	2.22697i	−0.0424411	+	0.146524i
$232$	−0.0112125	+	0.0116735i	−0.000736140	+	0.000766403i
$233$	−0.695305	+	1.83337i	−0.0455510	+	0.120108i	−0.955861	−	0.293819i	$-0.905074\pi$
$233$	−0.695305	+	1.83337i	−0.0455510	+	0.120108i	0.910310	+	0.413927i	$0.135843\pi$
$234$	0.967661	−	6.94128i	0.0632580	−	0.453766i
$235$	−1.72234	−	4.54142i	−0.112353	−	0.296250i
$236$	−22.3338	−	9.51556i	−1.45381	−	0.619410i
$237$	0.251086	−	6.23064i	0.0163098	−	0.404724i
$238$	7.29896	−	8.93960i	0.473121	−	0.579468i
$239$	14.1309			0.914053			0.457027	−	0.889453i	$-0.348914\pi$
$239$	14.1309			0.914053			0.457027	+	0.889453i	$0.348914\pi$
$240$	1.28788	−	1.57737i	0.0831324	−	0.101819i
$241$	0.981131	+	3.38726i	0.0632002	+	0.218193i	0.985903	−	0.167321i	$-0.0535116\pi$
$241$	0.981131	+	3.38726i	0.0632002	+	0.218193i	−0.922702	+	0.385513i	$0.874024\pi$
$242$	−12.1546	−	10.7680i	−0.781326	−	0.692194i
$243$	−0.692724	−	0.721202i	−0.0444383	−	0.0462652i
$244$	3.39886	−	1.13471i	0.217590	−	0.0726422i
$245$	1.84066	+	1.38317i	0.117596	+	0.0883675i
$246$	0.839180	−	6.91127i	0.0535042	−	0.440647i
$247$	−13.5975	−	24.5438i	−0.865187	−	1.56169i
$248$	−0.308899	−	2.54401i	−0.0196151	−	0.161545i
$249$	−6.78121	+	11.7454i	−0.429742	+	0.744334i
$250$	−7.04649	−	5.29509i	−0.445659	−	0.334891i
$251$	−0.0356589	−	0.884866i	−0.00225077	−	0.0558522i	0.997673	−	0.0681763i	$-0.0217180\pi$
$251$	−0.0356589	−	0.884866i	−0.00225077	−	0.0558522i	−0.999924	+	0.0123241i	$0.996077\pi$
$252$	0.898793	−	2.36992i	0.0566186	−	0.149291i
$253$	−1.66625	+	8.16181i	−0.104756	+	0.513129i
$254$	−4.60694	+	22.5663i	−0.289065	+	1.41593i
$255$	0.684523	−	1.80494i	0.0428665	−	0.113030i
$256$	−0.762563	−	18.9228i	−0.0476602	−	1.18268i
$257$	0.786420	+	0.590956i	0.0490555	+	0.0368628i	0.624987	−	0.780635i	$-0.285104\pi$
$257$	0.786420	+	0.590956i	0.0490555	+	0.0368628i	−0.575932	+	0.817498i	$0.695361\pi$
$258$	4.23022	−	7.32695i	0.263362	−	0.456156i
$259$	−0.109775	−	0.904077i	−0.00682108	−	0.0561766i
$260$	2.40654	−	1.74267i	0.149247	−	0.108076i
$261$	−0.00452712	+	0.0372842i	−0.000280221	+	0.00230783i
$262$	1.25447	+	0.942674i	0.0775015	+	0.0582386i
$263$	12.0919	−	4.03686i	0.745617	−	0.248923i	0.0816248	−	0.996663i	$-0.473989\pi$
$263$	12.0919	−	4.03686i	0.745617	−	0.248923i	0.663992	+	0.747740i	$0.268861\pi$
$264$	0.485620	+	0.505584i	0.0298879	+	0.0311166i
$265$	−2.15467	−	1.90887i	−0.132360	−	0.117261i
$266$	−5.99848	−	20.7091i	−0.367790	−	1.26976i
$267$	11.2634	−	13.7952i	0.689311	−	0.844253i
$268$	−21.9082			−1.33826
$269$	3.54078	−	4.33667i	0.215885	−	0.264412i	−0.655297	−	0.755372i	$-0.727456\pi$
$269$	3.54078	−	4.33667i	0.215885	−	0.264412i	0.871182	+	0.490960i	$0.163354\pi$
$270$	0.0362703	−	0.900038i	0.00220734	−	0.0547746i
$271$	−19.0463	−	8.11485i	−1.15698	−	0.492942i	−0.273711	−	0.961812i	$-0.588251\pi$
$271$	−19.0463	−	8.11485i	−1.15698	−	0.492942i	−0.883267	+	0.468870i	$0.844661\pi$
$272$	−6.49096	−	17.1153i	−0.393572	−	1.03776i
$273$	−2.99366	+	4.17709i	−0.181184	+	0.252809i
$274$	−10.7384	+	28.3148i	−0.648729	+	1.71056i
$275$	5.39213	−	5.61380i	0.325157	−	0.338525i
$276$	2.53364	−	8.74713i	0.152507	−	0.526515i
$277$	−0.394498	−	0.0318472i	−0.0237031	−	0.00191351i	0.0686093	−	0.997644i	$-0.478144\pi$
$277$	−0.394498	−	0.0318472i	−0.0237031	−	0.00191351i	−0.0923124	+	0.995730i	$0.529426\pi$
$278$	4.81142	−	2.52523i	0.288570	−	0.151453i
$279$	−4.11923	−	4.28858i	−0.246612	−	0.256750i
$280$	−0.261878	+	0.111576i	−0.0156502	+	0.00666793i
$281$	4.47194	+	11.7915i	0.266773	+	0.703424i	0.999732	+	0.0231504i	$0.00736966\pi$
$281$	4.47194	+	11.7915i	0.266773	+	0.703424i	−0.732959	+	0.680273i	$0.761861\pi$
$282$	−20.1091	+	3.26805i	−1.19748	+	0.194610i
$283$	4.19598	−	2.65338i	0.249425	−	0.157727i	−0.403903	−	0.914802i	$-0.632347\pi$
$283$	4.19598	−	2.65338i	0.249425	−	0.157727i	0.653328	+	0.757075i	$0.273372\pi$
$284$	−0.995986	+	3.43854i	−0.0591009	+	0.204040i
$285$	−2.04861	−	2.96793i	−0.121349	−	0.175805i
$286$	5.52465	+	9.97215i	0.326679	+	0.589665i
$287$	−2.90001	+	4.20139i	−0.171182	+	0.248000i
$288$	−4.85691	−	5.94864i	−0.286196	−	0.350527i
$289$	−0.222748	−	0.272817i	−0.0131028	−	0.0160480i
$290$	−0.0270460	+	0.0203238i	−0.00158820	+	0.00119345i
$291$	1.02539	+	8.44488i	0.0601097	+	0.495048i
$292$	−22.9305	−	7.65531i	−1.34190	−	0.447993i
$293$	−12.7185	−	1.02675i	−0.743025	−	0.0599832i	−0.296844	−	0.954926i	$-0.595934\pi$
$293$	−12.7185	−	1.02675i	−0.743025	−	0.0599832i	−0.446181	+	0.894943i	$0.647216\pi$
$294$	7.22881	−	6.40417i	0.421593	−	0.373499i
$295$	5.34693	+	3.38119i	0.311310	+	0.196861i
$296$	−0.253332	−	0.107935i	−0.0147246	−	0.00627357i
$297$	1.60559	+	0.260933i	0.0931657	+	0.0151409i
$298$	30.7355	+	27.2293i	1.78046	+	1.57735i
$299$	−9.51340	+	15.8247i	−0.550174	+	0.915166i
$300$	−6.36948	+	5.64287i	−0.367742	+	0.325791i
$301$	−5.24340	+	3.31573i	−0.302225	+	0.191115i
$302$	44.1646	−	3.56534i	2.54139	−	0.205162i
$303$	1.27321	−	6.23660i	0.0731441	−	0.358283i
$304$	−33.2029	−	8.18378i	−1.90432	−	0.469372i
$305$	−0.921687	+	0.149789i	−0.0527756	+	0.00857688i
$306$	−6.84351	−	4.32758i	−0.391218	−	0.247391i
$307$	11.1894	+	5.87264i	0.638612	+	0.335169i	0.752761	−	0.658294i	$-0.228722\pi$
$307$	11.1894	+	5.87264i	0.638612	+	0.335169i	−0.114149	+	0.993464i	$0.536414\pi$
$308$	1.14708	+	3.96018i	0.0653610	+	0.225652i
$309$	−1.71376	−	8.39456i	−0.0974925	−	0.477550i
$310$	0.215679	−	5.35201i	0.0122497	−	0.303974i
$311$	−13.8444	−	7.26608i	−0.785042	−	0.412022i	0.0240450	−	0.999711i	$-0.492345\pi$
$311$	−13.8444	−	7.26608i	−0.785042	−	0.412022i	−0.809087	+	0.587689i	$0.800038\pi$
$312$	0.641203	+	1.41540i	0.0363009	+	0.0801312i
$313$	−14.9859	+	7.86522i	−0.847055	+	0.444569i	−0.831642	−	0.555312i	$-0.812599\pi$
$313$	−14.9859	+	7.86522i	−0.847055	+	0.444569i	−0.0154132	+	0.999881i	$0.504906\pi$
$314$	−7.00528	−	14.7633i	−0.395331	−	0.833142i
$315$	−0.330255	+	0.572018i	−0.0186078	+	0.0322296i
$316$	−5.54443	−	9.60323i	−0.311899	−	0.540224i
$317$	−1.54067	+	2.23204i	−0.0865326	+	0.125364i	−0.863860	−	0.503733i	$-0.831960\pi$
$317$	−1.54067	+	2.23204i	−0.0865326	+	0.125364i	0.777327	+	0.629097i	$0.216575\pi$
$318$	−9.65276	+	7.25358i	−0.541300	+	0.406761i
$319$	−0.0305469	−	0.0529088i	−0.00171030	−	0.00296232i
$320$	0.342905	−	2.82407i	0.0191690	−	0.157871i
$321$	−7.85155	+	16.5468i	−0.438231	+	0.923552i
$322$	−9.82832	+	10.2324i	−0.547711	+	0.570228i
$323$	−32.3119	+	2.60849i	−1.79788	+	0.145140i
$324$	−1.72661	−	0.425572i	−0.0959229	−	0.0236429i
$325$	15.4166	−	7.74669i	0.855158	−	0.429709i
$326$	21.7456	−	5.35981i	1.20438	−	0.296853i
$327$	−0.500314	+	0.167029i	−0.0276674	+	0.00923674i
$328$	0.661723	+	1.39455i	0.0365375	+	0.0770012i
$329$	14.1701	+	4.73069i	0.781225	+	0.260811i
$330$	0.832350	+	1.20587i	0.0458194	+	0.0663808i
$331$	3.71479	−	7.82875i	0.204183	−	0.430307i	−0.775366	−	0.631512i	$-0.782435\pi$
$331$	3.71479	−	7.82875i	0.204183	−	0.430307i	0.979549	+	0.201205i	$0.0644858\pi$
$332$	0.971128	+	24.0983i	0.0532976	+	1.32257i
$333$	−0.620388	+	0.152912i	−0.0339971	+	0.00837952i
$334$	9.49721	−	4.04638i	0.519664	−	0.221408i
$335$	5.63522	+	0.915812i	0.307885	+	0.0500361i
$336$	1.25281	+	6.13668i	0.0683465	+	0.334783i
$337$	−31.7564			−1.72988			−0.864941	−	0.501874i	$-0.832644\pi$
$337$	−31.7564			−1.72988			−0.864941	+	0.501874i	$0.832644\pi$
$338$	4.17587	+	24.9217i	0.227137	+	1.35556i
$339$	2.52571			0.137178
$340$	−0.686642	−	3.36340i	−0.0372384	−	0.182406i
$341$	9.54751	+	1.55162i	0.517027	+	0.0840250i
$342$	−13.9162	+	5.92915i	−0.752503	+	0.320612i
$343$	−16.5632	+	4.08247i	−0.894329	+	0.220432i
$344$	0.0755309	+	1.87428i	0.00407235	+	0.101054i
$345$	−1.01735	+	2.14402i	−0.0547723	+	0.115430i
$346$	9.00082	+	13.0399i	0.483887	+	0.701031i
$347$	26.2686	+	8.76976i	1.41017	+	0.470785i	0.916910	−	0.399094i	$-0.130675\pi$
$347$	26.2686	+	8.76976i	1.41017	+	0.470785i	0.493265	+	0.869879i	$0.335803\pi$
$348$	0.0286319	+	0.0603404i	0.00153483	+	0.00323459i
$349$	−2.58689	+	0.863630i	−0.138473	+	0.0462290i	−0.385060	−	0.922892i	$-0.625819\pi$
$349$	−2.58689	+	0.863630i	−0.138473	+	0.0462290i	0.246587	+	0.969121i	$0.420691\pi$
$350$	12.8724	−	3.17275i	0.688057	−	0.169591i
$351$	3.16243	+	1.73177i	0.168798	+	0.0924353i
$352$	12.1290	+	2.98953i	0.646478	+	0.159343i
$353$	−18.3542	+	1.48171i	−0.976896	+	0.0788632i	−0.558591	−	0.829443i	$-0.688658\pi$
$353$	−18.3542	+	1.48171i	−0.976896	+	0.0788632i	−0.418305	+	0.908307i	$0.637376\pi$
$354$	18.3820	−	19.1376i	0.976990	−	1.01715i
$355$	0.399926	−	0.842826i	0.0212259	−	0.0447326i
$356$	3.81741	−	31.4392i	0.202322	−	1.66627i
$357$	2.96866	+	5.14187i	0.157118	+	0.272137i
$358$	−2.73550	+	2.05559i	−0.144576	+	0.108642i
$359$	−0.138613	+	0.200816i	−0.00731574	+	0.0105987i	−0.826625	−	0.562754i	$-0.809742\pi$
$359$	−0.138613	+	0.200816i	−0.00731574	+	0.0105987i	0.819309	+	0.573352i	$0.194357\pi$
$360$	0.0998568	+	0.172957i	0.00526291	+	0.00911563i
$361$	−20.7804	+	35.9927i	−1.09371	+	1.89435i
$362$	−2.56873	−	5.41349i	−0.135010	−	0.284527i
$363$	7.39710	−	3.88230i	0.388247	−	0.203768i
$364$	−0.529388	+	9.12340i	−0.0277475	+	0.478196i
$365$	5.57815	+	2.92764i	0.291974	+	0.153240i
$366$	−0.157712	+	3.91357i	−0.00824371	+	0.204566i
$367$	5.15860	+	25.2685i	0.269277	+	1.31901i	0.859239	+	0.511574i	$0.170937\pi$
$367$	5.15860	+	25.2685i	0.269277	+	1.31901i	−0.589962	+	0.807431i	$0.700857\pi$
$368$	6.26080	+	21.6148i	0.326367	+	1.12675i
$369$	3.17143	+	1.66450i	0.165098	+	0.0866502i
$370$	−0.486450	−	0.307612i	−0.0252893	−	0.0159920i
$371$	8.73916	−	1.42025i	0.453714	−	0.0737358i
$372$	−10.2672	−	2.53063i	−0.532328	−	0.131207i
$373$	−4.28548	+	20.9917i	−0.221894	+	1.08691i	0.704313	+	0.709890i	$0.251255\pi$
$373$	−4.28548	+	20.9917i	−0.221894	+	1.08691i	−0.926206	+	0.377017i	$0.876950\pi$
$374$	13.1283	−	1.05983i	0.678849	−	0.0548024i
$375$	3.83259	−	2.42358i	0.197914	−	0.125153i
$376$	3.38101	−	2.99531i	0.174362	−	0.154472i
$377$	−0.0247366	−	0.133139i	−0.00127400	−	0.00685700i
$378$	2.07376	+	1.83719i	0.106663	+	0.0944950i
$379$	−3.00037	−	0.487607i	−0.154118	−	0.0250467i	0.0828625	−	0.996561i	$-0.473594\pi$
$379$	−3.00037	−	0.487607i	−0.154118	−	0.0250467i	−0.236981	+	0.971514i	$0.576158\pi$
$380$	−5.89986	−	2.51369i	−0.302656	−	0.128950i
$381$	−10.0146	−	6.33285i	−0.513064	−	0.324442i
$382$	−30.3607	+	26.8973i	−1.55339	+	1.37618i
$383$	−17.2992	−	1.39653i	−0.883946	−	0.0713595i	−0.369849	−	0.929092i	$-0.620591\pi$
$383$	−17.2992	−	1.39653i	−0.883946	−	0.0713595i	−0.514097	+	0.857732i	$0.671873\pi$
$384$	3.25019	+	1.08507i	0.165861	+	0.0553724i
$385$	−0.129507	−	1.06659i	−0.00660029	−	0.0543583i
$386$	2.19170	−	1.64696i	0.111555	−	0.0838280i
$387$	2.75276	+	3.37152i	0.139931	+	0.171384i
$388$	9.56745	+	11.7180i	0.485714	+	0.594891i
$389$	10.2116	−	14.7940i	0.517748	−	0.750088i	−0.473686	−	0.880694i	$-0.657077\pi$
$389$	10.2116	−	14.7940i	0.517748	−	0.750088i	0.991434	+	0.130606i	$0.0416923\pi$
$390$	0.848283	+	3.13503i	0.0429545	+	0.158748i
$391$	12.1181	+	17.5561i	0.612837	+	0.887848i
$392$	−0.595727	+	2.05669i	−0.0300888	+	0.103878i
$393$	−0.682308	+	0.431465i	−0.0344179	+	0.0217646i
$394$	37.5115	−	6.09622i	1.88980	−	0.307123i
$395$	1.02470	+	2.70191i	0.0515582	+	0.135948i
$396$	2.66118	−	1.13382i	0.133729	−	0.0569768i
$397$	−6.68269	−	6.95742i	−0.335395	−	0.349183i	0.532053	−	0.846711i	$-0.321421\pi$
$397$	−6.68269	−	6.95742i	−0.335395	−	0.349183i	−0.867448	+	0.497528i	$0.834241\pi$
$398$	−40.8175	+	21.4227i	−2.04600	+	1.07382i
$399$	11.0560	+	0.892534i	0.553493	+	0.0446826i
$400$	5.85027	−	20.1975i	0.292514	−	1.00987i
$401$	1.41025	−	1.46823i	0.0704248	−	0.0733199i	−0.685058	−	0.728489i	$-0.740223\pi$
$401$	1.41025	−	1.46823i	0.0704248	−	0.0733199i	0.755482	+	0.655169i	$0.227403\pi$
$402$	8.49175	−	22.3909i	0.423530	−	1.11676i
$403$	18.8052	+	10.2979i	0.936751	+	0.512973i
$404$	−4.01385	−	10.5836i	−0.199696	−	0.526556i
$405$	0.426328	+	0.181641i	0.0211844	+	0.00902584i
$406$	0.00418987	−	0.103971i	0.000207940	−	0.00515998i
$407$	0.657337	−	0.805092i	0.0325830	−	0.0399069i
$408$	1.79522			0.0888769
$409$	−6.68926	+	8.19286i	−0.330763	+	0.405111i	−0.913034	−	0.407884i	$-0.866267\pi$
$409$	−6.68926	+	8.19286i	−0.330763	+	0.405111i	0.582271	+	0.812995i	$0.302164\pi$
$410$	0.897607	+	3.09890i	0.0443297	+	0.153044i
$411$	−11.6612	−	10.3310i	−0.575206	−	0.509588i
$412$	−10.5542	−	10.9881i	−0.519970	−	0.541346i
$413$	−18.4566	+	6.16171i	−0.908189	+	0.303198i
$414$	7.95780	+	5.97990i	0.391105	+	0.293896i
$415$	0.757569	−	6.23914i	0.0371876	−	0.306268i
$416$	23.1372	+	15.2104i	1.13439	+	0.745750i
$417$	0.336960	+	2.77511i	0.0165010	+	0.135898i
$418$	12.3029	−	21.3093i	0.601756	−	1.04227i
$419$	−23.4499	−	17.6214i	−1.14560	−	0.860863i	−0.153730	−	0.988113i	$-0.549129\pi$
$419$	−23.4499	−	17.6214i	−1.14560	−	0.860863i	−0.991871	+	0.127250i	$0.959385\pi$
$420$	0.0472954	+	1.17362i	0.00230778	+	0.0572669i
$421$	−5.31340	+	14.0103i	−0.258959	+	0.682819i	0.740977	+	0.671530i	$0.234363\pi$
$421$	−5.31340	+	14.0103i	−0.258959	+	0.682819i	−0.999936	+	0.0112888i	$0.996407\pi$
$422$	9.46343	−	46.3549i	0.460673	−	2.25652i
$423$	2.09649	−	10.2693i	0.101935	−	0.499310i
$424$	0.949299	−	2.50310i	0.0461020	−	0.121561i
$425$	−0.802638	−	19.9173i	−0.0389337	−	0.966129i
$426$	−3.12826	−	2.35073i	−0.151565	−	0.113893i
$427$	1.43602	−	2.48727i	0.0694940	−	0.120367i
$428$	3.92582	+	32.3320i	0.189762	+	1.56283i
$429$	−5.80476	+	0.838297i	−0.280257	+	0.0404734i
$430$	−0.472583	+	3.89207i	−0.0227900	+	0.187692i
$431$	19.1602	+	14.3979i	0.922914	+	0.693525i	0.952015	−	0.306052i	$-0.0990081\pi$
$431$	19.1602	+	14.3979i	0.922914	+	0.693525i	−0.0291011	+	0.999576i	$0.509264\pi$
$432$	4.16813	−	1.39153i	0.200539	−	0.0669498i
$433$	10.8947	+	11.3426i	0.523567	+	0.545091i	0.929505	−	0.368810i	$-0.120235\pi$
$433$	10.8947	+	11.3426i	0.523567	+	0.545091i	−0.405938	+	0.913901i	$0.633055\pi$
$434$	12.3315	+	10.9247i	0.591929	+	0.524404i
$435$	−0.00484231	−	0.0167176i	−0.000232171	−	0.000801548i
$436$	−0.593216	+	0.726558i	−0.0284099	+	0.0347958i
$437$	39.8524			1.90640
$438$	16.7120	−	20.4684i	0.798529	−	0.978020i
$439$	−0.960250	+	23.8284i	−0.0458303	+	1.13727i	0.798690	+	0.601743i	$0.205527\pi$
$439$	−0.960250	+	23.8284i	−0.0458303	+	1.13727i	−0.844520	+	0.535523i	$0.820114\pi$
$440$	−0.298869	−	0.127336i	−0.0142480	−	0.00607051i
$441$	1.76184	+	4.64559i	0.0838971	+	0.221218i
$442$	28.2179	+	7.48676i	1.34219	+	0.356109i
$443$	5.11760	−	13.4940i	0.243144	−	0.641119i	−0.756777	−	0.653673i	$-0.773227\pi$
$443$	5.11760	−	13.4940i	0.243144	−	0.641119i	0.999921	+	0.0125544i	$0.00399630\pi$
$444$	−0.787104	+	0.819462i	−0.0373543	+	0.0388900i
$445$	−2.29614	+	7.92719i	−0.108847	+	0.375785i
$446$	−6.59563	−	0.532454i	−0.312312	−	0.0252124i
$447$	−18.7052	+	9.81724i	−0.884725	+	0.464339i
$448$	6.06125	+	6.31043i	0.286367	+	0.298140i
$449$	−0.840405	+	0.358063i	−0.0396612	+	0.0168980i	−0.411706	−	0.911317i	$-0.635067\pi$
$449$	−0.840405	+	0.358063i	−0.0396612	+	0.0168980i	0.372045	+	0.928215i	$0.378657\pi$
$450$	−3.29835	−	8.69704i	−0.155486	−	0.409982i
$451$	−5.75073	+	0.934584i	−0.270791	+	0.0440079i
$452$	3.79612	−	2.40052i	0.178554	−	0.112911i
$453$	−6.34194	+	21.8949i	−0.297970	+	1.02871i
$454$	−19.1962	−	27.8104i	−0.900920	−	1.30521i
$455$	0.517547	−	2.32459i	0.0242630	−	0.108978i
$456$	1.90518	−	2.76013i	0.0892181	−	0.129255i
$457$	−23.8193	−	29.1734i	−1.11422	−	1.36467i	−0.923756	−	0.382981i	$-0.874898\pi$
$457$	−23.8193	−	29.1734i	−1.11422	−	1.36467i	−0.190466	−	0.981694i	$-0.561000\pi$
$458$	−2.63995	−	3.23335i	−0.123357	−	0.151085i
$459$	3.33016	−	2.50245i	0.155438	−	0.116804i
$460$	0.508680	+	4.18936i	0.0237173	+	0.195330i
$461$	−1.73695	−	0.579881i	−0.0808980	−	0.0270077i	0.275931	−	0.961177i	$-0.411014\pi$
$461$	−1.73695	−	0.579881i	−0.0808980	−	0.0270077i	−0.356829	+	0.934170i	$0.616142\pi$
$462$	−4.49205	−	0.362636i	−0.208989	−	0.0168714i
$463$	1.26730	−	1.12273i	0.0588966	−	0.0521778i	−0.633161	−	0.774020i	$-0.718243\pi$
$463$	1.26730	−	1.12273i	0.0588966	−	0.0521778i	0.692058	+	0.721842i	$0.256704\pi$
$464$	−0.139490	−	0.0882083i	−0.00647567	−	0.00409497i
$465$	2.53513	+	1.08012i	0.117564	+	0.0500893i
$466$	−3.76199	−	0.611383i	−0.174271	−	0.0283218i
$467$	−1.70095	−	1.50691i	−0.0787105	−	0.0697314i	0.622850	−	0.782341i	$-0.285975\pi$
$467$	−1.70095	−	1.50691i	−0.0787105	−	0.0697314i	−0.701561	+	0.712610i	$0.747513\pi$
$468$	6.39903	−	0.402839i	0.295795	−	0.0186212i
$469$	−13.1437	+	11.6443i	−0.606918	+	0.537683i
$470$	7.97948	−	5.04592i	0.368066	−	0.232751i
$471$	8.37956	−	0.676468i	0.386110	−	0.0311700i
$472$	−1.17682	+	5.76446i	−0.0541677	+	0.265331i
$473$	−6.87438	−	1.69438i	−0.316084	−	0.0779078i
$474$	11.9639	−	1.94432i	0.549519	−	0.0893056i
$475$	−31.4742	−	19.9031i	−1.44414	−	0.913216i
$476$	9.34887	+	4.90667i	0.428505	+	0.224897i
$477$	−1.72823	−	5.96654i	−0.0791302	−	0.273189i
$478$	5.49419	+	26.9123i	0.251298	+	1.23094i
$479$	−1.49594	+	37.1214i	−0.0683513	+	1.69612i	0.494193	+	0.869352i	$0.335464\pi$
$479$	−1.49594	+	37.1214i	−0.0683513	+	1.69612i	−0.562544	+	0.826767i	$0.690177\pi$
$480$	3.15116	+	1.65386i	0.143830	+	0.0754878i
$481$	1.96860	−	1.19667i	0.0897606	−	0.0545635i
$482$	−6.06956	+	3.18555i	−0.276461	+	0.145098i
$483$	−3.12909	−	6.59441i	−0.142378	−	0.300056i
$484$	7.42790	−	12.8655i	0.337632	−	0.584795i
$485$	−1.97110	−	3.41404i	−0.0895028	−	0.155023i
$486$	1.10419	−	1.59970i	0.0500872	−	0.0725639i
$487$	28.3933	−	21.3362i	1.28662	−	0.966836i	0.286664	−	0.958031i	$-0.407454\pi$
$487$	28.3933	−	21.3362i	1.28662	−	0.966836i	0.999961	−	0.00880446i	$-0.00280258\pi$
$488$	−0.434200	−	0.752056i	−0.0196553	−	0.0340440i
$489$	−1.38883	+	11.4381i	−0.0628052	+	0.517248i
$490$	−1.91858	+	4.04333i	−0.0866727	+	0.182659i
$491$	0.0892875	−	0.0929582i	0.00402949	−	0.00419514i	−0.719185	−	0.694819i	$-0.755484\pi$
$491$	0.0892875	−	0.0929582i	0.00402949	−	0.00419514i	0.723214	+	0.690624i	$0.242664\pi$
$492$	6.34862	−	0.512514i	0.286218	−	0.0231059i
$493$	−0.151905	−	0.0374413i	−0.00684147	−	0.00168627i
$494$	41.4569	−	35.4392i	1.86523	−	1.59448i
$495$	−0.731904	+	0.180398i	−0.0328966	+	0.00810829i
$496$	24.7855	−	8.27460i	1.11290	−	0.371541i
$497$	1.23006	+	2.59230i	0.0551758	+	0.116281i
$498$	−25.0057	−	8.34812i	−1.12053	−	0.374088i
$499$	−17.4090	−	25.2212i	−0.779332	−	1.12906i	−0.988506	−	0.151179i	$-0.951693\pi$
$499$	−17.4090	−	25.2212i	−0.779332	−	1.12906i	0.209174	−	0.977878i	$-0.432922\pi$
$500$	3.45689	−	7.28524i	0.154597	−	0.325806i
$501$	0.213849	+	5.30662i	0.00955409	+	0.237082i
$502$	1.67136	−	0.411953i	0.0745965	−	0.0183864i
$503$	10.0137	−	4.26644i	0.446489	−	0.190231i	−0.157007	−	0.987598i	$-0.550184\pi$
$503$	10.0137	−	4.26644i	0.446489	−	0.190231i	0.603495	+	0.797367i	$0.293774\pi$
$504$	−0.606309	−	0.0985348i	−0.0270072	−	0.00438909i
$505$	0.590020	+	2.89011i	0.0262555	+	0.128608i
$506$	−16.1920			−0.719822
$507$	−12.7499	−	2.53777i	−0.566243	−	0.112706i
$508$	−21.0708			−0.934865
$509$	0.487007	+	2.38552i	0.0215862	+	0.105736i	0.989156	−	0.146866i	$-0.0469187\pi$
$509$	0.487007	+	2.38552i	0.0215862	+	0.105736i	−0.967570	+	0.252602i	$0.918714\pi$
$510$	3.70365	+	0.601902i	0.164000	+	0.0266527i
$511$	−17.8258	+	7.59485i	−0.788566	+	0.335977i
$512$	29.0880	−	7.16956i	1.28552	−	0.316853i
$513$	−0.313353	−	7.77577i	−0.0138349	−	0.343309i
$514$	−0.819710	+	1.72750i	−0.0361559	+	0.0761969i
$515$	2.25543	+	3.26755i	0.0993859	+	0.143985i
$516$	7.34177	+	2.45104i	0.323203	+	0.107901i
$517$	7.30883	+	15.4030i	0.321442	+	0.677424i
$518$	1.67913	−	0.560577i	0.0737769	−	0.0246303i
$519$	−7.91462	+	1.95078i	−0.347413	+	0.0856296i
$520$	−0.530458	−	0.486956i	−0.0232621	−	0.0213544i
$521$	28.7886	+	7.09576i	1.26125	+	0.310871i	0.812593	−	0.582831i	$-0.198055\pi$
$521$	28.7886	+	7.09576i	1.26125	+	0.310871i	0.448660	+	0.893702i	$0.351901\pi$
$522$	−0.0727678	+	0.00587442i	−0.00318496	+	0.000257117i
$523$	27.9967	−	29.1477i	1.22421	−	1.27454i	0.274438	−	0.961605i	$-0.411508\pi$
$523$	27.9967	−	29.1477i	1.22421	−	1.27454i	0.949774	−	0.312935i	$-0.101312\pi$
$524$	−0.615423	+	1.29698i	−0.0268849	+	0.0566587i
$525$	−0.822124	+	6.77080i	−0.0358804	+	0.295502i
$526$	12.3896	+	21.4594i	0.540212	+	0.935674i
$527$	19.8025	−	14.8806i	0.862612	−	0.648211i
$528$	−4.06050	+	5.88265i	−0.176711	+	0.256010i
$529$	−1.61253	−	2.79299i	−0.0701102	−	0.121434i
$530$	2.79769	−	4.84575i	0.121524	−	0.210486i
$531$	5.85234	+	12.3336i	0.253970	+	0.535231i
$532$	17.4654	−	9.16653i	0.757220	−	0.397420i
$533$	−12.7081	−	2.29662i	−0.550450	−	0.0994777i
$534$	30.6522	+	16.0875i	1.32645	+	0.696176i
$535$	0.341754	−	8.48053i	0.0147753	−	0.366645i
$536$	1.06202	+	5.20212i	0.0458723	+	0.224697i
$537$	−0.489763	−	1.69086i	−0.0211348	−	0.0729660i
$538$	9.63587	+	5.05729i	0.415432	+	0.218035i
$539$	−6.83078	−	4.31953i	−0.294223	−	0.186055i
$540$	0.813405	−	0.132191i	0.0350034	−	0.00568860i
$541$	18.7541	+	4.62248i	0.806304	+	0.198736i	0.620863	−	0.783919i	$-0.286782\pi$
$541$	18.7541	+	4.62248i	0.806304	+	0.198736i	0.185441	+	0.982655i	$0.440629\pi$
$542$	8.04942	−	39.4287i	0.345752	−	1.69361i
$543$	3.07266	−	0.248051i	0.131861	−	0.0106449i
$544$	27.0376	−	17.0976i	1.15923	−	0.733052i
$545$	0.182958	−	0.162087i	0.00783708	−	0.00694305i
$546$	−9.11922	−	4.07734i	−0.390267	−	0.174494i
$547$	19.1241	+	16.9425i	0.817687	+	0.724407i	0.964307	−	0.264786i	$-0.0853012\pi$
$547$	19.1241	+	16.9425i	0.817687	+	0.724407i	−0.146621	+	0.989193i	$0.546840\pi$
$548$	−27.3456	−	4.44409i	−1.16815	−	0.189842i
$549$	−1.85377	−	0.789818i	−0.0791171	−	0.0337086i
$550$	12.7880	+	8.08662i	0.545281	+	0.344815i
$551$	−0.218774	+	0.193817i	−0.00932010	+	0.00825689i
$552$	−2.19983	−	0.177589i	−0.0936310	−	0.00755868i
$553$	−8.43049	−	2.81451i	−0.358501	−	0.119685i
$554$	−0.0927304	−	0.763703i	−0.00393974	−	0.0324466i
$555$	0.236714	−	0.177879i	0.0100479	−	0.00755054i
$556$	3.14401	+	3.85071i	0.133336	+	0.163306i
$557$	2.88511	+	3.53361i	0.122246	+	0.149724i	0.832102	−	0.554623i	$-0.187137\pi$
$557$	2.88511	+	3.53361i	0.122246	+	0.149724i	−0.709856	+	0.704347i	$0.751240\pi$
$558$	6.56600	−	9.51250i	0.277961	−	0.402696i
$559$	−13.1135	−	8.62081i	−0.554643	−	0.364622i
$560$	−1.64879	−	2.38868i	−0.0696739	−	0.100940i
$561$	−1.88520	+	6.50845i	−0.0795930	+	0.274787i
$562$	−20.7182	+	13.1014i	−0.873946	+	0.552650i
$563$	−14.3855	+	2.33787i	−0.606275	+	0.0985293i	−0.455797	−	0.890084i	$-0.650646\pi$
$563$	−14.3855	+	2.33787i	−0.606275	+	0.0985293i	−0.150479	+	0.988613i	$0.548081\pi$
$564$	−6.60926	−	17.4272i	−0.278300	−	0.733817i
$565$	−1.07678	+	0.458774i	−0.0453006	+	0.0193008i
$566$	6.68477	+	6.95958i	0.280982	+	0.292533i
$567$	−1.26206	+	0.662381i	−0.0530016	+	0.0278174i
$568$	0.864766	+	0.0698111i	0.0362848	+	0.00292921i
$569$	1.34673	−	4.64947i	0.0564580	−	0.194916i	−0.927332	−	0.374240i	$-0.877904\pi$
$569$	1.34673	−	4.64947i	0.0564580	−	0.194916i	0.983790	+	0.179324i	$0.0573910\pi$
$570$	4.85590	−	5.05553i	0.203391	−	0.211753i
$571$	1.05652	−	2.78582i	0.0442140	−	0.116583i	−0.911090	−	0.412206i	$-0.864758\pi$
$571$	1.05652	−	2.78582i	0.0442140	−	0.116583i	0.955304	+	0.295624i	$0.0955275\pi$
$572$	−7.92775	+	6.77699i	−0.331476	+	0.283360i
$573$	−7.39966	−	19.5113i	−0.309125	−	0.815096i
$574$	−9.12909	−	3.88954i	−0.381041	−	0.162346i
$575$	−0.986736	+	24.4856i	−0.0411497	+	1.02112i
$576$	3.88250	−	4.75520i	0.161771	−	0.198133i
$577$	−29.6424			−1.23403			−0.617014	−	0.786952i	$-0.711658\pi$
$577$	−29.6424			−1.23403			−0.617014	+	0.786952i	$0.711658\pi$
$578$	0.432973	−	0.530296i	0.0180093	−	0.0220574i
$579$	0.392402	+	1.35473i	0.0163077	+	0.0563006i
$580$	−0.0231669	−	0.0205241i	−0.000961953	−	0.000852216i
$581$	13.3909	+	13.9414i	0.555550	+	0.578388i
$582$	−15.6846	+	5.23628i	−0.650147	+	0.217051i
$583$	8.07791	+	6.07016i	0.334553	+	0.251400i
$584$	−0.706184	+	5.81595i	−0.0292221	+	0.240666i
$585$	−1.66279	−	0.163876i	−0.0687481	−	0.00677543i
$586$	−2.98961	−	24.6217i	−0.123500	−	1.01711i
$587$	−3.28992	+	5.69832i	−0.135790	+	0.235195i	−0.925899	−	0.377771i	$-0.876690\pi$
$587$	−3.28992	+	5.69832i	−0.135790	+	0.235195i	0.790109	+	0.612966i	$0.210024\pi$
$588$	7.06334	+	5.30776i	0.291287	+	0.218888i
$589$	−1.86333	−	46.2381i	−0.0767772	−	1.90521i
$590$	−4.36056	+	11.4978i	−0.179521	+	0.473359i
$591$	−3.91078	+	19.1563i	−0.160868	+	0.787984i
$592$	0.561621	−	2.75100i	0.0230825	−	0.113065i
$593$	−10.4989	+	27.6833i	−0.431138	+	1.13682i	0.526836	+	0.849967i	$0.323378\pi$
$593$	−10.4989	+	27.6833i	−0.431138	+	1.13682i	−0.957975	+	0.286852i	$0.907391\pi$
$594$	0.127315	+	3.15929i	0.00522380	+	0.129627i
$595$	−2.19960	−	1.65289i	−0.0901749	−	0.0677620i
$596$	−18.7831	+	32.5332i	−0.769384	+	1.33261i
$597$	−2.85858	−	23.5426i	−0.116994	−	0.963533i
$598$	−33.8370	−	11.9655i	−1.38370	−	0.489306i
$599$	4.52891	−	37.2990i	0.185046	−	1.52399i	−0.543740	−	0.839254i	$-0.682992\pi$
$599$	4.52891	−	37.2990i	0.185046	−	1.52399i	0.728787	−	0.684741i	$-0.240085\pi$
$600$	1.64867	+	1.23889i	0.0673066	+	0.0505777i
$601$	34.4215	−	11.4916i	1.40408	−	0.468751i	0.489093	−	0.872231i	$-0.337328\pi$
$601$	34.4215	−	11.4916i	1.40408	−	0.468751i	0.914988	+	0.403480i	$0.132200\pi$
$602$	−8.35346	−	8.69688i	−0.340462	−	0.354458i
$603$	9.22154	+	8.16957i	0.375530	+	0.332691i
$604$	11.2778	+	38.9354i	0.458886	+	1.58426i
$605$	−2.44841	+	2.99875i	−0.0995419	+	0.121917i
$606$	12.3726			0.502604
$607$	7.87002	−	9.63902i	0.319434	−	0.391236i	−0.589780	−	0.807564i	$-0.700786\pi$
$607$	7.87002	−	9.63902i	0.319434	−	0.391236i	0.909215	+	0.416328i	$0.136683\pi$
$608$	2.40642	−	59.7146i	0.0975931	−	2.42175i
$609$	0.0492486	+	0.0209829i	0.00199565	+	0.000850269i
$610$	−0.643630	−	1.69711i	−0.0260598	−	0.0687141i
$611$	3.89103	+	37.5893i	0.157414	+	1.52070i
$612$	2.62678	−	6.92625i	0.106181	−	0.279977i
$613$	−3.78324	+	3.93877i	−0.152804	+	0.159085i	−0.793204	−	0.608956i	$-0.791589\pi$
$613$	−3.78324	+	3.93877i	−0.152804	+	0.159085i	0.640401	+	0.768041i	$0.278768\pi$
$614$	−6.83394	+	23.5935i	−0.275795	+	0.952156i
$615$	−1.65441	−	0.133558i	−0.0667124	−	0.00538558i
$616$	0.884742	−	0.464349i	0.0356473	−	0.0187091i
$617$	−7.24059	−	7.53825i	−0.291495	−	0.303479i	0.559311	−	0.828958i	$-0.311066\pi$
$617$	−7.24059	−	7.53825i	−0.291495	−	0.303479i	−0.850807	+	0.525479i	$0.823886\pi$
$618$	15.3211	−	6.52771i	0.616305	−	0.262583i
$619$	2.57447	+	6.78831i	0.103477	+	0.272845i	0.976749	−	0.214388i	$-0.0687756\pi$
$619$	2.57447	+	6.78831i	0.103477	+	0.272845i	−0.873272	+	0.487233i	$0.838006\pi$
$620$	4.83685	−	0.786065i	0.194253	−	0.0315691i
$621$	−4.32825	+	2.73702i	−0.173687	+	0.109833i
$622$	8.45547	−	29.1917i	0.339033	−	1.17048i
$623$	−14.4198	−	20.8907i	−0.577717	−	0.836967i
$624$	−12.8325	+	9.29256i	−0.513712	+	0.372000i
$625$	12.3979	−	17.9615i	0.495918	−	0.718461i
$626$	−20.8059	−	25.4826i	−0.831572	−	1.01849i
$627$	8.00597	+	9.80553i	0.319728	+	0.391595i
$628$	11.9515	−	8.98094i	0.476915	−	0.358378i
$629$	−0.320824	−	2.64222i	−0.0127921	−	0.105352i
$630$	−1.21781	−	0.406566i	−0.0485188	−	0.0161980i
$631$	1.39408	+	0.112542i	0.0554974	+	0.00448021i	0.108184	−	0.994131i	$-0.465496\pi$
$631$	1.39408	+	0.112542i	0.0554974	+	0.00448021i	−0.0526867	+	0.998611i	$0.516778\pi$
$632$	−2.01152	+	1.78205i	−0.0800141	+	0.0708863i
$633$	20.5717	+	13.0087i	0.817651	+	0.517051i
$634$	−4.84995	−	2.06637i	−0.192616	−	0.0820660i
$635$	5.41982	+	0.880806i	0.215079	+	0.0349537i
$636$	−8.26830	−	7.32508i	−0.327860	−	0.290458i
$637$	−11.0825	−	14.0745i	−0.439104	−	0.557650i
$638$	0.0888879	−	0.0787478i	0.00351911	−	0.00311766i
$639$	1.70146	−	1.07594i	0.0673088	−	0.0425635i
$640$	−1.58274	+	0.127772i	−0.0625634	+	0.00505064i
$641$	4.85561	−	23.7844i	0.191785	−	0.939426i	−0.763968	−	0.645255i	$-0.776751\pi$
$641$	4.85561	−	23.7844i	0.191785	−	0.939426i	0.955753	−	0.294171i	$-0.0950436\pi$
$642$	−34.5661	−	8.51977i	−1.36421	−	0.336248i
$643$	46.8160	−	7.60834i	1.84624	−	0.300043i	0.866329	−	0.499473i	$-0.166473\pi$
$643$	46.8160	−	7.60834i	1.84624	−	0.300043i	0.979912	+	0.199430i	$0.0639089\pi$
$644$	−10.9705	−	6.93734i	−0.432299	−	0.273370i
$645$	−1.78599	−	0.937358i	−0.0703232	−	0.0369085i
$646$	−17.5309	−	60.5238i	−0.689745	−	2.38128i
$647$	8.68137	+	42.5242i	0.341300	+	1.67180i	0.681789	+	0.731549i	$0.261202\pi$
$647$	8.68137	+	42.5242i	0.341300	+	1.67180i	−0.340489	+	0.940248i	$0.610593\pi$
$648$	−0.0173532	+	0.430615i	−0.000681698	+	0.0169162i
$649$	−19.6628	−	10.3198i	−0.771833	−	0.405089i
$650$	20.7476	+	26.3489i	0.813789	+	1.03349i
$651$	−7.50475	+	3.93880i	−0.294134	+	0.154374i
$652$	8.78372	+	18.5113i	0.343997	+	0.724958i
$653$	−8.39741	+	14.5447i	−0.328616	+	0.569180i	−0.982237	−	0.187642i	$-0.939916\pi$
$653$	−8.39741	+	14.5447i	−0.328616	+	0.569180i	0.653622	+	0.756822i	$0.273249\pi$
$654$	−0.512632	−	0.887905i	−0.0200455	−	0.0347198i
$655$	0.212515	−	0.307881i	0.00830365	−	0.0120299i
$656$	−12.5824	+	9.45505i	−0.491260	+	0.369158i
$657$	6.79715	+	11.7730i	0.265182	+	0.459309i
$658$	−3.50015	+	28.8263i	−0.136450	+	1.12377i
$659$	−9.08806	+	19.1527i	−0.354021	+	0.746083i	−0.999849	−	0.0174002i	$-0.994461\pi$
$659$	−9.08806	+	19.1527i	−0.354021	+	0.746083i	0.645828	+	0.763483i	$0.276512\pi$
$660$	−0.928588	+	0.966762i	−0.0361452	+	0.0376312i
$661$	−16.1566	+	1.30430i	−0.628420	+	0.0507313i	−0.390574	−	0.920572i	$-0.627723\pi$
$661$	−16.1566	+	1.30430i	−0.628420	+	0.0507313i	−0.237846	+	0.971303i	$0.576441\pi$
$662$	16.3542	+	4.03094i	0.635623	+	0.156667i
$663$	−8.74915	+	12.2078i	−0.339789	+	0.474113i
$664$	5.67508	−	1.39878i	0.220236	−	0.0542832i
$665$	−4.87561	+	1.62772i	−0.189068	+	0.0631202i
$666$	−0.532431	−	1.12208i	−0.0206313	−	0.0434795i
$667$	0.182438	+	0.0609067i	0.00706402	+	0.00235832i
$668$	5.36500	+	7.77254i	0.207578	+	0.300729i
$669$	1.45937	−	3.07556i	0.0564225	−	0.118908i
$670$	0.446845	+	11.0883i	0.0172631	+	0.428380i
$671$	3.18248	−	0.784412i	0.122858	−	0.0302819i
$672$	−10.0700	+	4.29042i	−0.388458	+	0.165506i
$673$	6.76730	+	1.09979i	0.260860	+	0.0423939i	0.289435	−	0.957198i	$-0.406533\pi$
$673$	6.76730	+	1.09979i	0.260860	+	0.0423939i	−0.0285744	+	0.999592i	$0.509097\pi$
$674$	−12.3471	−	60.4800i	−0.475592	−	2.32960i
$675$	4.78525			0.184184
$676$	−21.5749	+	8.30368i	−0.829805	+	0.319372i
$677$	25.6168			0.984533			0.492266	−	0.870445i	$-0.336169\pi$
$677$	25.6168			0.984533			0.492266	+	0.870445i	$0.336169\pi$
$678$	0.982013	+	4.81022i	0.0377140	+	0.184735i
$679$	11.9681	+	1.94500i	0.459292	+	0.0746423i
$680$	−0.765355	+	0.326087i	−0.0293500	+	0.0125049i
$681$	16.8796	−	4.16045i	0.646828	−	0.159429i
$682$	0.757070	+	18.7865i	0.0289897	+	0.719372i
$683$	−21.1503	+	44.5732i	−0.809292	+	1.70555i	−0.106316	+	0.994332i	$0.533906\pi$
$683$	−21.1503	+	44.5732i	−0.809292	+	1.70555i	−0.702975	+	0.711214i	$0.748146\pi$
$684$	−7.86132	−	11.3891i	−0.300585	−	0.435472i
$685$	6.84804	+	2.28621i	0.261650	+	0.0873517i
$686$	−14.2149	−	29.9573i	−0.542729	−	1.14378i
$687$	2.03695	−	0.680032i	0.0777143	−	0.0259448i
$688$	−18.5706	+	4.57724i	−0.707997	+	0.174506i
$689$	12.3950	+	18.6544i	0.472211	+	0.710676i
$690$	−4.47883	−	1.10393i	−0.170506	−	0.0420260i
$691$	49.8426	−	4.02371i	1.89610	−	0.153069i	0.923205	−	0.384308i	$-0.125560\pi$
$691$	49.8426	−	4.02371i	1.89610	−	0.153069i	0.972897	+	0.231238i	$0.0742778\pi$
$692$	−10.0415	+	10.4543i	−0.381721	+	0.397413i
$693$	0.993926	−	2.09466i	0.0377561	−	0.0795694i
$694$	−6.48859	+	53.4383i	−0.246303	+	2.02849i
$695$	−0.647731	−	1.12190i	−0.0245699	−	0.0425562i
$696$	0.0129399	−	0.00972371i	0.000490486	−	0.000368576i
$697$	−8.47547	+	12.2788i	−0.321031	+	0.465094i
$698$	−2.65058	−	4.59094i	−0.100326	−	0.173770i
$699$	0.980394	−	1.69809i	0.0370819	−	0.0642278i
$700$	5.19955	+	10.9578i	0.196524	+	0.414166i
$701$	−22.7892	+	11.9607i	−0.860738	+	0.451750i	−0.836507	−	0.547956i	$-0.815406\pi$
$701$	−22.7892	+	11.9607i	−0.860738	+	0.451750i	−0.0242310	+	0.999706i	$0.507714\pi$
$702$	−2.06859	+	6.69617i	−0.0780739	+	0.252731i
$703$	−4.40284	−	2.31079i	−0.166056	−	0.0871531i
$704$	−0.402088	+	9.97771i	−0.0151543	+	0.376049i
$705$	0.971536	+	4.75890i	0.0365901	+	0.179230i
$706$	−9.95814	−	34.3795i	−0.374779	−	1.29389i
$707$	−8.03332	−	4.21621i	−0.302124	−	0.158567i
$708$	20.5182	+	12.9749i	0.771122	+	0.487628i
$709$	19.6533	−	3.19398i	0.738096	−	0.119952i	0.220271	−	0.975439i	$-0.429306\pi$
$709$	19.6533	−	3.19398i	0.738096	−	0.119952i	0.517825	+	0.855486i	$0.326742\pi$
$710$	1.76065	+	0.433962i	0.0660762	+	0.0162863i
$711$	−1.24730	+	6.10968i	−0.0467774	+	0.229131i
$712$	−7.65030	+	0.617596i	−0.286707	+	0.0231454i
$713$	−25.7376	+	16.2755i	−0.963882	+	0.609522i
$714$	−8.63845	+	7.65300i	−0.323286	+	0.286406i
$715$	2.32246	−	1.41178i	0.0868552	−	0.0527974i
$716$	−2.34316	−	2.07586i	−0.0875679	−	0.0775784i
$717$	−13.9479	−	2.26676i	−0.520895	−	0.0846536i
$718$	−0.436348	−	0.185911i	−0.0162844	−	0.00693812i
$719$	2.39026	+	1.51151i	0.0891415	+	0.0563697i	0.578293	−	0.815829i	$-0.303719\pi$
$719$	2.39026	+	1.51151i	0.0891415	+	0.0563697i	−0.489151	+	0.872199i	$0.662693\pi$
$720$	−1.52423	+	1.35035i	−0.0568048	+	0.0503246i
$721$	−12.1722	−	0.982638i	−0.453315	−	0.0365953i
$722$	−76.6277	−	25.5821i	−2.85179	−	0.952066i
$723$	−0.425072	−	3.50078i	−0.0158086	−	0.130195i
$724$	4.38243	−	3.29318i	0.162872	−	0.122390i
$725$	−0.113666	−	0.139215i	−0.00422144	−	0.00517033i
$726$	10.2699	+	12.5783i	0.381151	+	0.466825i
$727$	−25.6510	+	37.1619i	−0.951344	+	1.37826i	−0.0257805	+	0.999668i	$0.508207\pi$
$727$	−25.6510	+	37.1619i	−0.951344	+	1.37826i	−0.925564	+	0.378592i	$0.876408\pi$
$728$	2.19202	−	0.316561i	0.0812416	−	0.0117325i
$729$	0.568065	+	0.822984i	0.0210394	+	0.0304809i
$730$	−3.40686	+	11.7619i	−0.126094	+	0.435326i
$731$	−15.3242	+	9.69042i	−0.566785	+	0.358413i
$732$	−3.53687	+	0.574797i	−0.130726	+	0.0212451i
$733$	−18.0534	−	47.6028i	−0.666816	−	1.75825i	−0.651833	−	0.758362i	$-0.726000\pi$
$733$	−18.0534	−	47.6028i	−0.666816	−	1.75825i	−0.0149832	−	0.999888i	$-0.504769\pi$
$734$	−46.1181	+	19.6491i	−1.70225	+	0.725262i
$735$	−1.59495	−	1.66052i	−0.0588307	−	0.0612493i
$736$	−34.8227	+	18.2764i	−1.28358	+	0.673676i
$737$	−19.9751	−	1.61256i	−0.735793	−	0.0593994i
$738$	−1.93696	+	6.68716i	−0.0713004	+	0.246158i
$739$	24.2863	−	25.2847i	0.893387	−	0.930114i	−0.104537	−	0.994521i	$-0.533336\pi$
$739$	24.2863	−	25.2847i	0.893387	−	0.930114i	0.997924	+	0.0644068i	$0.0205155\pi$
$740$	0.186716	−	0.492331i	0.00686383	−	0.0180984i
$741$	9.48429	+	26.4072i	0.348414	+	0.970092i
$742$	6.10270	+	16.0915i	0.224037	+	0.590738i
$743$	−32.9140	−	14.0233i	−1.20750	−	0.514466i	−0.307997	−	0.951387i	$-0.599659\pi$
$743$	−32.9140	−	14.0233i	−1.20750	−	0.514466i	−0.899500	+	0.436921i	$0.856069\pi$
$744$	−0.103189	+	2.56062i	−0.00378311	+	0.0938769i
$745$	6.19133	−	7.58300i	0.226833	−	0.277820i
$746$	−41.6448			−1.52473
$747$	8.57749	−	10.5055i	0.313834	−	0.384377i
$748$	3.35242	+	11.5739i	0.122577	+	0.423183i
$749$	19.5398	+	17.3108i	0.713970	+	0.632522i
$750$	6.10585	+	6.35686i	0.222954	+	0.232120i
$751$	−25.6427	+	8.56078i	−0.935715	+	0.312387i	−0.743324	−	0.668931i	$-0.766752\pi$
$751$	−25.6427	+	8.56078i	−0.935715	+	0.312387i	−0.192390	+	0.981319i	$0.561624\pi$
$752$	36.8198	+	27.6683i	1.34268	+	1.00896i
$753$	−0.106745	+	0.879127i	−0.00389002	+	0.0320372i
$754$	0.243945	−	0.0988759i	0.00888395	−	0.00360085i
$755$	−1.27328	−	10.4864i	−0.0463393	−	0.381639i
$756$	−1.26732	+	2.19506i	−0.0460918	+	0.0798334i
$757$	−3.14698	−	2.36480i	−0.114379	−	0.0859502i	0.542014	−	0.840370i	$-0.317662\pi$
$757$	−3.14698	−	2.36480i	−0.114379	−	0.0859502i	−0.656393	+	0.754419i	$0.727919\pi$
$758$	−0.237914	−	5.90378i	−0.00864143	−	0.214435i
$759$	2.95391	−	7.78883i	0.107220	−	0.282717i
$760$	−0.310877	+	1.52278i	−0.0112767	+	0.0552370i
$761$	5.41086	−	26.5041i	0.196143	−	0.960774i	−0.755871	−	0.654721i	$-0.772786\pi$
$761$	5.41086	−	26.5041i	0.196143	−	0.960774i	0.952014	−	0.306053i	$-0.0990086\pi$
$762$	8.16717	−	21.5351i	0.295865	−	0.780133i
$763$	0.0302719	+	0.751189i	0.00109592	+	0.0271949i
$764$	−29.6658	−	22.2924i	−1.07327	−	0.806510i
$765$	−0.965191	+	1.67176i	−0.0348966	+	0.0604426i
$766$	−4.06633	−	33.4892i	−0.146922	−	1.21001i
$767$	−33.4639	−	36.0961i	−1.20831	−	1.30335i
$768$	−2.28274	+	18.8001i	−0.0823714	+	0.678390i
$769$	14.6517	+	11.0101i	0.528355	+	0.397033i	0.831172	−	0.556016i	$-0.187671\pi$
$769$	14.6517	+	11.0101i	0.528355	+	0.397033i	−0.302817	+	0.953049i	$0.597927\pi$
$770$	1.98096	−	0.661341i	0.0713888	−	0.0238331i
$771$	−0.681440	−	0.709454i	−0.0245414	−	0.0255504i
$772$	1.87736	+	1.66319i	0.0675675	+	0.0598596i
$773$	−6.80213	−	23.4837i	−0.244656	−	0.844649i	−0.985020	−	0.172443i	$-0.944834\pi$
$773$	−6.80213	−	23.4837i	−0.244656	−	0.844649i	0.740364	−	0.672206i	$-0.234653\pi$
$774$	−5.35076	+	6.55350i	−0.192329	+	0.235561i
$775$	28.4551			1.02214
$776$	2.31866	−	2.83984i	0.0832349	−	0.101944i
$777$	−0.0366709	+	0.909979i	−0.00131556	+	0.0326453i
$778$	32.1456	+	13.6959i	1.15247	+	0.491023i
$779$	9.88392	+	26.0618i	0.354128	+	0.933759i
$780$	−2.65492	+	1.33407i	−0.0950612	+	0.0477674i
$781$	−1.16120	+	3.06183i	−0.0415510	+	0.109561i
$782$	−28.7239	+	29.9048i	−1.02716	+	1.06939i
$783$	0.0104493	−	0.0360751i	0.000373427	−	0.00128922i
$784$	−21.7619	−	1.75681i	−0.777212	−	0.0627431i
$785$	−3.44957	+	1.81047i	−0.123120	+	0.0646186i
$786$	−1.08701	−	1.13170i	−0.0387724	−	0.0403663i
$787$	−13.7126	+	5.84238i	−0.488800	+	0.208258i	−0.622282	−	0.782793i	$-0.713794\pi$
$787$	−13.7126	+	5.84238i	−0.488800	+	0.208258i	0.133482	+	0.991051i	$0.457384\pi$
$788$	12.3289	+	32.5086i	0.439199	+	1.15807i
$789$	−12.5828	+	2.04491i	−0.447961	+	0.0728008i
$790$	−4.74737	+	3.00206i	−0.168904	+	0.106808i
$791$	1.00157	−	3.45782i	0.0356118	−	0.122946i
$792$	−0.398230	−	0.576936i	−0.0141505	−	0.0205005i
$793$	7.23021	+	0.712569i	0.256752	+	0.0253041i
$794$	10.6521	−	15.4323i	0.378030	−	0.547671i
$795$	1.82056	+	2.22979i	0.0645687	+	0.0790824i
$796$	−26.6720	−	32.6673i	−0.945366	−	1.15786i
$797$	−41.2806	+	31.0203i	−1.46223	+	1.09880i	−0.488109	+	0.872782i	$0.662313\pi$
$797$	−41.2806	+	31.0203i	−1.46223	+	1.09880i	−0.974124	+	0.226015i	$0.927430\pi$
$798$	2.59882	+	21.4032i	0.0919972	+	0.757665i
$799$	41.4131	+	13.8257i	1.46509	+	0.489120i
$800$	36.6295	+	2.95704i	1.29505	+	0.104547i
$801$	−13.3305	+	11.8098i	−0.471009	+	0.417278i
$802$	3.34456	+	2.11497i	0.118100	+	0.0746822i
$803$	−20.3437	−	8.66764i	−0.717914	−	0.305875i
$804$	21.6245	+	3.51432i	0.762637	+	0.123941i
$805$	2.53184	+	2.24301i	0.0892355	+	0.0790558i
$806$	−12.3007	+	39.8183i	−0.433274	+	1.40254i
$807$	−4.19058	+	3.71253i	−0.147516	+	0.130687i
$808$	−2.31852	+	1.46614i	−0.0815652	+	0.0515787i
$809$	−21.3387	+	1.72264i	−0.750228	+	0.0605647i	−0.449665	−	0.893197i	$-0.648457\pi$
$809$	−21.3387	+	1.72264i	−0.750228	+	0.0605647i	−0.300563	+	0.953762i	$0.597175\pi$
$810$	−0.180177	+	0.882565i	−0.00633077	+	0.0310102i
$811$	4.88773	+	1.20472i	0.171631	+	0.0423033i	0.324195	−	0.945990i	$-0.394907\pi$
$811$	4.88773	+	1.20472i	0.171631	+	0.0423033i	−0.152563	+	0.988294i	$0.548753\pi$
$812$	0.0939629	−	0.0152705i	0.00329745	−	0.000535888i
$813$	17.4979	+	11.0650i	0.613678	+	0.388067i
$814$	1.78887	+	0.938873i	0.0627000	+	0.0329075i
$815$	−1.48553	−	5.12864i	−0.0520358	−	0.179649i
$816$	3.66142	+	17.9348i	0.128175	+	0.627845i
$817$	−1.36389	+	33.8446i	−0.0477164	+	1.18407i
$818$	−18.2041	−	9.55425i	−0.636492	−	0.334057i
$819$	3.62494	−	3.64278i	0.126666	−	0.127289i
$820$	−2.61350	+	1.37167i	−0.0912675	+	0.0479009i
$821$	5.65470	+	11.9170i	0.197350	+	0.415907i	0.977867	−	0.209228i	$-0.0670952\pi$
$821$	5.65470	+	11.9170i	0.197350	+	0.415907i	−0.780517	+	0.625135i	$0.785044\pi$
$822$	15.1413	−	26.2255i	0.528114	−	0.914721i
$823$	−23.4732	−	40.6568i	−0.818224	−	1.41721i	−0.906989	−	0.421153i	$-0.861625\pi$
$823$	−23.4732	−	40.6568i	−0.818224	−	1.41721i	0.0887653	−	0.996053i	$-0.471708\pi$
$824$	−2.09751	+	3.03877i	−0.0730702	+	0.105861i
$825$	−6.22282	+	4.67614i	−0.216651	+	0.162802i
$826$	−18.9110	−	32.7548i	−0.657998	−	1.13969i
$827$	2.78558	−	22.9413i	0.0968640	−	0.797747i	−0.860618	−	0.509252i	$-0.829922\pi$
$827$	2.78558	−	22.9413i	0.0968640	−	0.797747i	0.957481	−	0.288495i	$-0.0931548\pi$
$828$	−3.90396	+	8.22743i	−0.135672	+	0.285923i
$829$	14.6830	−	15.2866i	0.509962	−	0.530927i	−0.415588	−	0.909553i	$-0.636424\pi$
$829$	14.6830	−	15.2866i	0.509962	−	0.530927i	0.925550	+	0.378627i	$0.123604\pi$
$830$	12.1770	−	0.983028i	0.422669	−	0.0341214i
$831$	0.384281	+	0.0947167i	0.0133305	+	0.00328568i
$832$	−8.21355	+	20.5536i	−0.284754	+	0.712569i
$833$	−20.0952	+	4.95302i	−0.696257	+	0.171612i
$834$	−5.15419	+	1.72072i	−0.178475	+	0.0595837i
$835$	−1.05507	−	2.22352i	−0.0365123	−	0.0769480i
$836$	21.3524	+	7.12847i	0.738488	+	0.246543i
$837$	3.37795	+	4.89381i	0.116759	+	0.169155i
$838$	24.4425	−	51.5115i	0.844353	−	1.77944i
$839$	−2.08804	−	51.8143i	−0.0720873	−	1.78883i	−0.481469	−	0.876463i	$-0.659896\pi$
$839$	−2.08804	−	51.8143i	−0.0720873	−	1.78883i	0.409381	−	0.912363i	$-0.365745\pi$
$840$	0.276385	−	0.0681227i	0.00953618	−	0.00235046i
$841$	26.6781	−	11.3665i	0.919935	−	0.391948i
$842$	−28.7484	−	4.67207i	−0.990736	−	0.161010i
$843$	−2.52253	−	12.3562i	−0.0868806	−	0.425569i
$844$	43.2830			1.48986
$845$	5.89660	−	1.23399i	0.202849	−	0.0424505i
$846$	20.3730			0.700437
$847$	−2.38174	−	11.6665i	−0.0818374	−	0.400866i
$848$	26.9428	+	4.37863i	0.925220	+	0.150363i
$849$	−4.56727	+	1.94593i	−0.156748	+	0.0667842i
$850$	37.6203	−	9.27258i	1.29037	−	0.318047i
$851$	0.131755	+	3.26946i	0.00451650	+	0.112076i
$852$	1.53467	−	3.23425i	0.0525769	−	0.110804i
$853$	−29.2844	−	42.4258i	−1.00268	−	1.45263i	−0.888338	−	0.459189i	$-0.848140\pi$
$853$	−29.2844	−	42.4258i	−1.00268	−	1.45263i	−0.114340	−	0.993442i	$-0.536475\pi$
$854$	5.29533	+	1.76784i	0.181202	+	0.0604943i
$855$	1.54599	+	3.25811i	0.0528719	+	0.111425i
$856$	7.48695	−	2.49951i	0.255899	−	0.0854315i
$857$	4.54779	−	1.12093i	0.155349	−	0.0382902i	−0.160874	−	0.986975i	$-0.551431\pi$
$857$	4.54779	−	1.12093i	0.155349	−	0.0382902i	0.316223	+	0.948685i	$0.397585\pi$
$858$	−3.85346	−	10.7292i	−0.131555	−	0.366290i
$859$	−2.28041	−	0.562071i	−0.0778066	−	0.0191776i	0.200220	−	0.979751i	$-0.435834\pi$
$859$	−2.28041	−	0.562071i	−0.0778066	−	0.0191776i	−0.278027	+	0.960573i	$0.589680\pi$
$860$	−3.57522	+	0.288621i	−0.121914	+	0.00984190i
$861$	3.53641	−	3.68179i	0.120520	−	0.125475i
$862$	−19.9713	+	42.0886i	−0.680224	+	1.43354i
$863$	−0.179998	+	1.48241i	−0.00612719	+	0.0504619i	−0.995452	−	0.0952668i	$-0.969630\pi$
$863$	−0.179998	+	1.48241i	−0.00612719	+	0.0504619i	0.989325	+	0.145729i	$0.0465527\pi$
$864$	3.83979	+	6.65071i	0.130632	+	0.226262i
$865$	3.01988	−	2.26929i	0.102679	−	0.0771583i
$866$	−17.3660	+	25.1591i	−0.590122	+	0.854940i
$867$	0.176100	+	0.305015i	0.00598068	+	0.0103588i
$868$	−7.53600	+	13.0527i	−0.255788	+	0.443039i
$869$	−4.34837	−	9.16399i	−0.147508	−	0.310867i
$870$	0.0299559	−	0.0157221i	0.00101560	−	0.000533029i
$871$	−40.5511	−	18.1310i	−1.37402	−	0.614345i
$872$	0.201278	+	0.105639i	0.00681614	+	0.00357739i
$873$	0.342539	−	8.50001i	0.0115932	−	0.287682i
$874$	15.4949	+	75.8988i	0.524121	+	2.56732i
$875$	−1.79819	−	6.20807i	−0.0607899	−	0.209871i
$876$	21.4055	+	11.2345i	0.723225	+	0.379578i
$877$	23.8934	+	15.1093i	0.806823	+	0.510204i	0.873067	−	0.487599i	$-0.162127\pi$
$877$	23.8934	+	15.1093i	0.806823	+	0.510204i	−0.0662444	+	0.997803i	$0.521102\pi$
$878$	−45.7544	+	7.43582i	−1.54414	+	0.250947i
$879$	12.3891	+	3.05365i	0.417875	+	0.102997i
$880$	0.662573	−	3.24550i	0.0223353	−	0.109406i
$881$	23.1993	−	1.87284i	0.781604	−	0.0630976i	0.316778	−	0.948500i	$-0.397399\pi$
$881$	23.1993	−	1.87284i	0.781604	−	0.0630976i	0.464826	+	0.885402i	$0.346117\pi$
$882$	−8.16250	+	5.16165i	−0.274846	+	0.173802i
$883$	3.43837	−	3.04613i	0.115710	−	0.102510i	−0.603284	−	0.797527i	$-0.706141\pi$
$883$	3.43837	−	3.04613i	0.115710	−	0.102510i	0.718994	+	0.695016i	$0.244603\pi$
$884$	−1.54717	+	26.6637i	−0.0520370	+	0.896798i
$885$	−4.73530	−	4.19511i	−0.159176	−	0.141017i
$886$	27.6890	+	4.49991i	0.930232	+	0.151177i
$887$	−23.5131	−	10.0180i	−0.789492	−	0.336371i	−0.0406957	−	0.999172i	$-0.512957\pi$
$887$	−23.5131	−	10.0180i	−0.789492	−	0.336371i	−0.748796	+	0.662801i	$0.769368\pi$
$888$	0.232737	+	0.147174i	0.00781016	+	0.00493884i
$889$	−12.6413	+	11.1992i	−0.423975	+	0.375609i
$890$	−15.9901	−	1.29085i	−0.535989	−	0.0432695i
$891$	−1.54294	−	0.515109i	−0.0516904	−	0.0172568i
$892$	−0.729693	−	6.00956i	−0.0244319	−	0.201215i
$893$	65.2064	−	48.9994i	2.18205	−	1.63970i
$894$	−25.9696	−	31.8070i	−0.868553	−	1.06378i
$895$	0.515930	+	0.631900i	0.0172456	+	0.0211221i
$896$	2.77438	−	4.01938i	0.0926855	−	0.134278i
$897$	11.9287	−	14.0937i	0.398286	−	0.470576i
$898$	−1.00869	−	1.46133i	−0.0336603	−	0.0487653i
$899$	0.0621359	−	0.214518i	0.00207235	−	0.00715458i
$900$	7.19218	−	4.54806i	0.239739	−	0.151602i
$901$	25.5407	−	4.15077i	0.850885	−	0.138282i
$902$	−4.01583	−	10.5889i	−0.133713	−	0.352571i
$903$	5.70738	−	2.43169i	0.189930	−	0.0809215i
$904$	−0.754025	−	0.785024i	−0.0250785	−	0.0261095i
$905$	−1.26491	+	0.663875i	−0.0420469	+	0.0220679i
$906$	−44.1646	−	3.56534i	−1.46727	−	0.118450i
$907$	−6.11863	+	21.1240i	−0.203166	+	0.701410i	0.792621	+	0.609714i	$0.208716\pi$
$907$	−6.11863	+	21.1240i	−0.203166	+	0.701410i	−0.995787	+	0.0916956i	$0.970771\pi$
$908$	21.4156	−	22.2960i	0.710703	−	0.739920i
$909$	−2.25714	+	5.95160i	−0.0748648	+	0.197402i
$910$	4.62840	+	0.0818549i	0.153430	+	0.00271346i
$911$	−0.580210	−	1.52989i	−0.0192232	−	0.0506874i	0.925061	−	0.379818i	$-0.124013\pi$
$911$	−0.580210	−	1.52989i	−0.0192232	−	0.0506874i	−0.944284	+	0.329131i	$0.893244\pi$
$912$	31.4602	+	13.4039i	1.04175	+	0.443848i
$913$	−0.888321	+	22.0435i	−0.0293991	+	0.729532i
$914$	46.2996	−	56.7067i	1.53145	−	1.87569i
$915$	0.933779			0.0308698
$916$	2.41518	−	2.95806i	0.0797999	−	0.0977371i
$917$	0.320128	+	1.10521i	0.0105716	+	0.0364973i
$918$	6.06070	+	5.36931i	0.200033	+	0.177214i
$919$	−3.26478	−	3.39899i	−0.107695	−	0.112122i	0.665173	−	0.746690i	$-0.268358\pi$
$919$	−3.26478	−	3.39899i	−0.107695	−	0.112122i	−0.772868	+	0.634567i	$0.781178\pi$
$920$	0.970107	−	0.323869i	0.0319835	−	0.0106777i
$921$	−10.1024	−	7.59150i	−0.332887	−	0.250148i
$922$	0.429043	−	3.53349i	0.0141298	−	0.116369i
$923$	−4.68922	+	5.54032i	−0.154348	+	0.182362i
$924$	−0.496969	−	4.09290i	−0.0163491	−	0.134647i
$925$	1.52878	−	2.64792i	0.0502660	−	0.0870632i
$926$	2.63098	+	1.97705i	0.0864593	+	0.0649699i
$927$	0.344987	+	8.56076i	0.0113309	+	0.281172i
$928$	0.102278	−	0.269686i	0.00335746	−	0.00885288i
$929$	6.33573	−	31.0345i	0.207869	−	1.01821i	−0.733206	−	0.680007i	$-0.761977\pi$
$929$	6.33573	−	31.0345i	0.207869	−	1.01821i	0.941074	−	0.338200i	$-0.109818\pi$
$930$	−1.07141	+	5.24811i	−0.0351329	+	0.172092i
$931$	−13.7108	+	36.1523i	−0.449352	+	1.18484i
$932$	−0.140401	−	3.48401i	−0.00459899	−	0.114123i
$933$	12.4995	+	9.39278i	0.409216	+	0.307506i
$934$	2.20857	−	3.82535i	0.0722665	−	0.125169i
$935$	−0.378493	−	3.11717i	−0.0123780	−	0.101942i
$936$	−0.405853	−	1.49993i	−0.0132657	−	0.0490266i
$937$	0.310168	−	2.55446i	0.0101327	−	0.0834506i	−0.986765	−	0.162155i	$-0.948155\pi$
$937$	0.310168	−	2.55446i	0.0101327	−	0.0834506i	0.996898	+	0.0787049i	$0.0250785\pi$
$938$	−27.2868	−	20.5047i	−0.890947	−	0.669503i
$939$	16.0535	−	5.35946i	0.523887	−	0.174899i
$940$	5.98322	+	6.22919i	0.195151	+	0.203174i
$941$	17.6087	+	15.6000i	0.574028	+	0.508544i	0.899449	−	0.437025i	$-0.143968\pi$
$941$	17.6087	+	15.6000i	0.574028	+	0.508544i	−0.325422	+	0.945569i	$0.605506\pi$
$942$	4.54636	+	15.6959i	0.148128	+	0.511398i
$943$	11.6003	−	14.2078i	0.377758	−	0.462670i
$944$	−59.9889			−1.95247
$945$	0.417736	−	0.511634i	0.0135890	−	0.0166435i
$946$	0.554148	−	13.7510i	0.0180169	−	0.447085i
$947$	17.8586	+	7.60886i	0.580328	+	0.247255i	0.662124	−	0.749394i	$-0.269655\pi$
$947$	17.8586	+	7.60886i	0.580328	+	0.247255i	−0.0817959	+	0.996649i	$0.526066\pi$
$948$	3.93216	+	10.3683i	0.127711	+	0.336746i
$949$	−36.1078	−	33.1466i	−1.17211	−	1.07598i
$950$	25.6680	−	67.6811i	0.832781	−	2.19586i
$951$	1.87876	−	1.95600i	0.0609230	−	0.0634276i
$952$	0.711896	−	2.45775i	0.0230727	−	0.0796561i
$953$	11.6297	+	0.938844i	0.376722	+	0.0304121i	0.267378	−	0.963592i	$-0.413843\pi$
$953$	11.6297	+	0.938844i	0.376722	+	0.0304121i	0.109344	+	0.994004i	$0.465125\pi$
$954$	10.6913	−	5.61124i	0.346144	−	0.181671i
$955$	6.69874	+	6.97413i	0.216766	+	0.225678i
$956$	−23.1180	+	9.84965i	−0.747689	+	0.318561i
$957$	0.0216642	+	0.0571237i	0.000700303	+	0.00184655i
$958$	−71.2793	+	11.5840i	−2.30293	+	0.374262i
$959$	−18.7678	+	11.8681i	−0.606045	+	0.383240i
$960$	−0.791478	+	2.73250i	−0.0255448	+	0.0881910i
$961$	2.47675	+	3.58819i	0.0798951	+	0.115748i
$962$	3.04446	+	3.28393i	0.0981575	+	0.105878i
$963$	10.4042	−	15.0730i	0.335269	−	0.485722i
$964$	−3.96613	−	4.85763i	−0.127741	−	0.156454i
$965$	−0.413367	−	0.506283i	−0.0133068	−	0.0162978i
$966$	11.3424	−	8.52329i	0.364937	−	0.274232i
$967$	−2.25151	−	18.5429i	−0.0724037	−	0.596298i	−0.983080	−	0.183177i	$-0.941362\pi$
$967$	−2.25151	−	18.5429i	−0.0724037	−	0.596298i	0.910676	−	0.413121i	$-0.135561\pi$
$968$	−3.41499	−	1.14009i	−0.109762	−	0.0366440i
$969$	32.3119	+	2.60849i	1.03801	+	0.0837967i
$970$	5.73566	−	5.08135i	0.184161	−	0.163152i
$971$	3.80211	+	2.40431i	0.122015	+	0.0771579i	0.594079	−	0.804406i	$-0.297517\pi$
$971$	3.80211	+	2.40431i	0.122015	+	0.0771579i	−0.472064	+	0.881564i	$0.656491\pi$
$972$	1.63599	+	0.697029i	0.0524743	+	0.0223572i
$973$	3.93289	+	0.639157i	0.126083	+	0.0204904i
$974$	51.6743	+	45.7794i	1.65575	+	1.46687i
$975$	−16.4596	+	5.17338i	−0.527129	+	0.165681i
$976$	6.62770	−	5.87163i	0.212148	−	0.187946i
$977$	26.9707	−	17.0553i	0.862870	−	0.545646i	−0.0281530	−	0.999604i	$-0.508963\pi$
$977$	26.9707	−	17.0553i	0.862870	−	0.545646i	0.891023	+	0.453958i	$0.149988\pi$
$978$	−22.3238	+	1.80216i	−0.713836	+	0.0576268i
$979$	5.79467	−	28.3842i	0.185198	−	0.907162i
$980$	−3.97541	−	0.979851i	−0.126990	−	0.0313002i
$981$	0.520628	−	0.0846103i	0.0166224	−	0.00270140i
$982$	0.211754	+	0.133905i	0.00675735	+	0.00427309i
$983$	27.9662	+	14.6778i	0.891984	+	0.468149i	0.847460	−	0.530859i	$-0.178131\pi$
$983$	27.9662	+	14.6778i	0.891984	+	0.468149i	0.0445237	+	0.999008i	$0.485823\pi$
$984$	−0.429452	−	1.48264i	−0.0136904	−	0.0472648i
$985$	−1.81230	−	8.87723i	−0.0577446	−	0.282852i
$986$	0.0122452	−	0.303861i	0.000389966	−	0.00967690i
$987$	−13.2278	−	6.94248i	−0.421045	−	0.220982i
$988$	39.3530	+	30.6755i	1.25199	+	0.975919i
$989$	19.7365	−	10.3585i	0.627585	−	0.329382i
$990$	−0.628137	−	1.32377i	−0.0199635	−	0.0420722i
$991$	−5.25414	+	9.10044i	−0.166903	+	0.289085i	−0.937330	−	0.348444i	$-0.886710\pi$
$991$	−5.25414	+	9.10044i	−0.166903	+	0.289085i	0.770426	+	0.637529i	$0.220043\pi$
$992$	22.8330	+	39.5479i	0.724949	+	1.25565i
$993$	−4.92250	+	7.13148i	−0.156211	+	0.226311i
$994$	−4.45878	+	3.35055i	−0.141424	+	0.106273i
$995$	5.49500	+	9.51762i	0.174203	+	0.301729i
$996$	2.90709	−	23.9420i	0.0921145	−	0.758631i
$997$	−25.8420	+	54.4610i	−0.818426	+	1.72480i	−0.139968	+	0.990156i	$0.544700\pi$
$997$	−25.8420	+	54.4610i	−0.818426	+	1.72480i	−0.678457	+	0.734640i	$0.737351\pi$
$998$	41.2651	−	42.9615i	1.30622	−	1.35992i
$999$	0.636883	−	0.0514145i	0.0201501	−	0.00162668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.a.490.12	yes	360
169.159	even	39	inner	507.2.q.a.328.12	✓	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.a.328.12	✓	360	169.159	even	39	inner
507.2.q.a.490.12	yes	360	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.388806 + 1.90450i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(-1.63599 + 0.697029i) q^{4} +(0.449945 - 0.110901i) q^{5} +(-0.0782682 - 1.94220i) q^{6} +(-0.611025 + 1.28771i) q^{7} +(0.244816 + 0.354677i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})\)	\(q+(0.388806 + 1.90450i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(-1.63599 + 0.697029i) q^{4} +(0.449945 - 0.110901i) q^{5} +(-0.0782682 - 1.94220i) q^{6} +(-0.611025 + 1.28771i) q^{7} +(0.244816 + 0.354677i) q^{8} +(0.948536 + 0.316668i) q^{9} +(0.386153 + 0.813800i) q^{10} +(-1.54294 + 0.515109i) q^{11} +(1.72661 - 0.425572i) q^{12} +(-3.60499 - 0.0637555i) q^{13} +(-2.69001 - 0.663028i) q^{14} +(-0.461908 + 0.0372891i) q^{15} +(-3.04402 + 3.16916i) q^{16} +(-1.78576 + 3.76341i) q^{17} +(-0.234297 + 1.92961i) q^{18} +(3.89104 + 6.73948i) q^{19} +(-0.658802 + 0.495058i) q^{20} +(0.809676 - 1.17302i) q^{21} +(-1.58093 - 2.73825i) q^{22} +(2.56052 - 4.43495i) q^{23} +(-0.184751 - 0.389355i) q^{24} +(-4.23713 + 2.22382i) q^{25} +(-1.28022 - 6.89048i) q^{26} +(-0.885456 - 0.464723i) q^{27} +(0.102059 - 2.53258i) q^{28} +(0.00751256 + 0.0367990i) q^{29} +(-0.250610 - 0.865205i) q^{30} +(-5.26530 - 2.76344i) q^{31} +(-6.49070 - 4.10447i) q^{32} +(1.60559 - 0.260933i) q^{33} +(-7.86173 - 1.93774i) q^{34} +(-0.132119 + 0.647161i) q^{35} +(-1.77252 + 0.143093i) q^{36} +(-0.540038 + 0.341500i) q^{37} +(-11.3225 + 10.0308i) q^{38} +(3.54808 + 0.641211i) q^{39} +(0.149488 + 0.132435i) q^{40} +(3.53531 + 0.574544i) q^{41} +(2.54882 + 1.08595i) q^{42} +(3.67875 + 2.32630i) q^{43} +(2.16518 - 1.91818i) q^{44} +(0.461908 + 0.0372891i) q^{45} +(9.44191 + 3.15217i) q^{46} +(-1.26336 - 10.4047i) q^{47} +(3.51297 - 2.63982i) q^{48} +(3.14228 + 3.84859i) q^{49} +(-5.88268 - 7.20497i) q^{50} +(2.36633 - 3.42822i) q^{51} +(5.94215 - 2.40848i) q^{52} +(-3.52870 - 5.11220i) q^{53} +(0.540794 - 1.86704i) q^{54} +(-0.637111 + 0.402885i) q^{55} +(-0.606309 + 0.0985348i) q^{56} +(-2.75957 - 7.27638i) q^{57} +(-0.0671627 + 0.0286153i) q^{58} +(9.45680 + 9.84557i) q^{59} +(0.729683 - 0.382967i) q^{60} +(-2.00848 - 0.162141i) q^{61} +(3.21579 - 11.1022i) q^{62} +(-0.987356 + 1.02795i) q^{63} +(2.17687 - 5.73994i) q^{64} +(-1.62912 + 0.371112i) q^{65} +(1.12121 + 2.95639i) q^{66} +(11.3340 + 4.82897i) q^{67} +(0.298275 - 7.40161i) q^{68} +(-3.23878 + 3.96678i) q^{69} -1.28389 q^{70} +(1.27318 - 1.55937i) q^{71} +(0.119902 + 0.413949i) q^{72} +(10.1755 + 9.01469i) q^{73} +(-0.860356 - 0.895725i) q^{74} +(4.53898 - 1.51534i) q^{75} +(-11.0633 - 8.31353i) q^{76} +(0.279465 - 2.30160i) q^{77} +(0.158330 + 7.00661i) q^{78} +(0.751631 + 6.19024i) q^{79} +(-1.01818 + 1.76353i) q^{80} +(0.799443 + 0.600742i) q^{81} +(0.280333 + 6.95639i) q^{82} +(4.80930 - 12.6811i) q^{83} +(-0.506991 + 2.48341i) q^{84} +(-0.386126 + 1.89137i) q^{85} +(-3.00011 + 7.91065i) q^{86} +(-0.00151231 - 0.0375275i) q^{87} +(-0.560433 - 0.421138i) q^{88} +(-8.90467 + 15.4233i) q^{89} +(0.108576 + 0.894201i) q^{90} +(2.28484 - 4.60322i) q^{91} +(-1.09769 + 9.04028i) q^{92} +(4.75383 + 3.57227i) q^{93} +(19.3245 - 6.45147i) q^{94} +(2.49817 + 2.60087i) q^{95} +(5.74824 + 5.09250i) q^{96} +(-2.36677 - 8.17104i) q^{97} +(-6.10790 + 7.48082i) q^{98} -1.62665 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21} + 22 q^{22} + 46 q^{23} + 3 q^{24} + 28 q^{25} + 34 q^{26} + 30 q^{27} - 2 q^{28} + 36 q^{29} + q^{30} - 34 q^{31} - 190 q^{32} + 15 q^{33} - 51 q^{34} - 80 q^{35} + 15 q^{36} + q^{37} - 53 q^{38} + 5 q^{39} - 45 q^{40} + 9 q^{41} + 130 q^{42} + 78 q^{43} + 35 q^{44} - q^{45} - 318 q^{46} - 12 q^{47} - 15 q^{48} - 71 q^{49} + 48 q^{50} - 14 q^{51} - 63 q^{52} - 26 q^{53} - q^{54} - 61 q^{55} - 4 q^{56} - 38 q^{57} - 27 q^{58} + 208 q^{59} - 180 q^{60} - 3 q^{61} - 61 q^{62} + 2 q^{63} + 140 q^{64} + 45 q^{65} - 60 q^{66} - 80 q^{67} - 140 q^{68} + 6 q^{69} - 100 q^{70} + 84 q^{71} - 3 q^{72} + 134 q^{73} - 151 q^{74} - 12 q^{75} + 32 q^{76} + 82 q^{77} - 63 q^{78} + 4 q^{79} - 155 q^{80} + 15 q^{81} - 56 q^{82} + 106 q^{83} + 2 q^{84} - 19 q^{85} + q^{86} - 49 q^{87} + 8 q^{88} - 14 q^{89} + 2 q^{90} - 368 q^{91} + 36 q^{92} - 4 q^{93} - 59 q^{94} + 104 q^{95} + 75 q^{96} - 28 q^{97} + 101 q^{98} + 30 q^{99}+O(q^{100}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9 - q^10 - 2 * q^11 + 30 * q^12 - 19 * q^13 + q^15 + 15 * q^16 - 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 22 * q^22 + 46 * q^23 + 3 * q^24 + 28 * q^25 + 34 * q^26 + 30 * q^27 - 2 * q^28 + 36 * q^29 + q^30 - 34 * q^31 - 190 * q^32 + 15 * q^33 - 51 * q^34 - 80 * q^35 + 15 * q^36 + q^37 - 53 * q^38 + 5 * q^39 - 45 * q^40 + 9 * q^41 + 130 * q^42 + 78 * q^43 + 35 * q^44 - q^45 - 318 * q^46 - 12 * q^47 - 15 * q^48 - 71 * q^49 + 48 * q^50 - 14 * q^51 - 63 * q^52 - 26 * q^53 - q^54 - 61 * q^55 - 4 * q^56 - 38 * q^57 - 27 * q^58 + 208 * q^59 - 180 * q^60 - 3 * q^61 - 61 * q^62 + 2 * q^63 + 140 * q^64 + 45 * q^65 - 60 * q^66 - 80 * q^67 - 140 * q^68 + 6 * q^69 - 100 * q^70 + 84 * q^71 - 3 * q^72 + 134 * q^73 - 151 * q^74 - 12 * q^75 + 32 * q^76 + 82 * q^77 - 63 * q^78 + 4 * q^79 - 155 * q^80 + 15 * q^81 - 56 * q^82 + 106 * q^83 + 2 * q^84 - 19 * q^85 + q^86 - 49 * q^87 + 8 * q^88 - 14 * q^89 + 2 * q^90 - 368 * q^91 + 36 * q^92 - 4 * q^93 - 59 * q^94 + 104 * q^95 + 75 * q^96 - 28 * q^97 + 101 * q^98 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more