LMFDB - Embedded newform 507.2.m.a.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

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("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$15$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			79.3
Character	$\chi$	$=$	507.79
Dual form			507.2.m.a.430.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85232 - 0.972175i) q^{2} +(0.970942 + 0.239316i) q^{3} +(1.34985 + 1.95560i) q^{4} +(0.359355 + 0.947542i) q^{5} +(-1.56584 - 1.38722i) q^{6} +(-0.194000 - 1.59773i) q^{7} +(-0.0948689 - 0.781316i) q^{8} +(0.885456 + 0.464723i) q^{9} +O(q^{10})$	\(q+(-1.85232 - 0.972175i) q^{2} +(0.970942 + 0.239316i) q^{3} +(1.34985 + 1.95560i) q^{4} +(0.359355 + 0.947542i) q^{5} +(-1.56584 - 1.38722i) q^{6} +(-0.194000 - 1.59773i) q^{7} +(-0.0948689 - 0.781316i) q^{8} +(0.885456 + 0.464723i) q^{9} +(0.255534 - 2.10451i) q^{10} +(-0.353059 + 0.185300i) q^{11} +(0.842623 + 2.22181i) q^{12} +(0.887475 - 3.49462i) q^{13} +(-1.19392 + 3.14812i) q^{14} +(0.122151 + 1.00601i) q^{15} +(1.10140 - 2.90415i) q^{16} +(0.362671 + 2.98687i) q^{17} +(-1.18836 - 1.72164i) q^{18} -0.528951 q^{19} +(-1.36794 + 1.98180i) q^{20} +(0.194000 - 1.59773i) q^{21} +0.834124 q^{22} +6.25297 q^{23} +(0.0948689 - 0.781316i) q^{24} +(2.97385 - 2.63460i) q^{25} +(-5.04128 + 5.61040i) q^{26} +(0.748511 + 0.663123i) q^{27} +(2.86265 - 2.53609i) q^{28} +(3.72926 + 1.95727i) q^{29} +(0.751752 - 1.98221i) q^{30} +(1.94268 + 1.72106i) q^{31} +(-6.04173 + 5.35250i) q^{32} +(-0.387145 + 0.0954227i) q^{33} +(2.23197 - 5.88522i) q^{34} +(1.44420 - 0.757976i) q^{35} +(0.286423 + 2.35891i) q^{36} +(5.22824 + 4.63182i) q^{37} +(0.979789 + 0.514233i) q^{38} +(1.69800 - 3.18069i) q^{39} +(0.706238 - 0.370662i) q^{40} +(-3.80508 - 0.937867i) q^{41} +(-1.91263 + 2.77092i) q^{42} +(0.952912 - 0.844206i) q^{43} +(-0.838950 - 0.440315i) q^{44} +(-0.122151 + 1.00601i) q^{45} +(-11.5825 - 6.07898i) q^{46} +(5.06156 - 7.33293i) q^{47} +(1.76440 - 2.55618i) q^{48} +(4.28148 - 1.05529i) q^{49} +(-8.06984 + 1.98904i) q^{50} +(-0.362671 + 2.98687i) q^{51} +(8.03204 - 2.98168i) q^{52} +(0.205458 + 1.69210i) q^{53} +(-0.741814 - 1.95600i) q^{54} +(-0.302453 - 0.267950i) q^{55} +(-1.22993 + 0.303150i) q^{56} +(-0.513581 - 0.126586i) q^{57} +(-5.00499 - 7.25098i) q^{58} +(-2.91253 - 7.67971i) q^{59} +(-1.80246 + 1.59684i) q^{60} +(0.933288 - 7.68631i) q^{61} +(-1.92530 - 5.07659i) q^{62} +(0.570725 - 1.50488i) q^{63} +(10.3633 - 2.55433i) q^{64} +(3.63022 - 0.414892i) q^{65} +(0.809886 + 0.199619i) q^{66} +(0.964759 - 1.39770i) q^{67} +(-5.35156 + 4.74107i) q^{68} +(6.07127 + 1.49643i) q^{69} -3.41202 q^{70} +(-9.35088 - 2.30478i) q^{71} +(0.279093 - 0.735909i) q^{72} +(5.82370 - 3.05652i) q^{73} +(-5.18146 - 13.6624i) q^{74} +(3.51794 - 1.84636i) q^{75} +(-0.714006 - 1.03442i) q^{76} +(0.364553 + 0.528146i) q^{77} +(-6.23744 + 4.24091i) q^{78} +(-3.51722 + 5.09557i) q^{79} +3.14760 q^{80} +(0.568065 + 0.822984i) q^{81} +(6.13647 + 5.43644i) q^{82} +(-6.39089 + 1.57521i) q^{83} +(3.38639 - 1.77732i) q^{84} +(-2.69985 + 1.41699i) q^{85} +(-2.58582 + 0.637347i) q^{86} +(3.15249 + 2.79286i) q^{87} +(0.178272 + 0.258272i) q^{88} +3.62834 q^{89} +(1.20428 - 1.74470i) q^{90} +(-5.75564 - 0.739991i) q^{91} +(8.44060 + 12.2283i) q^{92} +(1.47435 + 2.13597i) q^{93} +(-16.5045 + 8.66225i) q^{94} +(-0.190081 - 0.501204i) q^{95} +(-7.14710 + 3.75109i) q^{96} +(-0.483297 + 1.27435i) q^{97} +(-8.95662 - 2.20761i) q^{98} -0.398731 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) $ 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{2}{13}\right)$

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 $

$2$	−1.85232	−	0.972175i	−1.30979	−	0.687432i	−0.342122	−	0.939655i	$-0.611146\pi$
$2$	−1.85232	−	0.972175i	−1.30979	−	0.687432i	−0.967669	+	0.252224i	$0.918838\pi$
$3$	0.970942	+	0.239316i	0.560574	+	0.138169i
$3$	0.970942	+	0.239316i	0.560574	+	0.138169i
$4$	1.34985	+	1.95560i	0.674927	+	0.977800i
$5$	0.359355	+	0.947542i	0.160709	+	0.423754i	0.991048	−	0.133504i	$-0.0426228\pi$
$5$	0.359355	+	0.947542i	0.160709	+	0.423754i	−0.830340	+	0.557258i	$0.811854\pi$
$6$	−1.56584	−	1.38722i	−0.639253	−	0.566328i
$7$	−0.194000	−	1.59773i	−0.0733250	−	0.603886i	−0.982338	−	0.187117i	$-0.940086\pi$
$7$	−0.194000	−	1.59773i	−0.0733250	−	0.603886i	0.909013	−	0.416769i	$-0.136837\pi$
$8$	−0.0948689	−	0.781316i	−0.0335412	−	0.276237i
$9$	0.885456	+	0.464723i	0.295152	+	0.154908i
$10$	0.255534	−	2.10451i	0.0808070	−	0.665505i
$11$	−0.353059	+	0.185300i	−0.106451	+	0.0558700i	−0.517108	−	0.855920i	$-0.672992\pi$
$11$	−0.353059	+	0.185300i	−0.106451	+	0.0558700i	0.410657	+	0.911790i	$0.365299\pi$
$12$	0.842623	+	2.22181i	0.243244	+	0.641383i
$13$	0.887475	−	3.49462i	0.246141	−	0.969234i
$13$	0.887475	−	3.49462i	0.246141	−	0.969234i
$14$	−1.19392	+	3.14812i	−0.319090	+	0.841370i
$15$	0.122151	+	1.00601i	0.0315394	+	0.259750i
$16$	1.10140	−	2.90415i	0.275350	−	0.726037i
$17$	0.362671	+	2.98687i	0.0879607	+	0.724421i	0.968250	+	0.249984i	$0.0804253\pi$
$17$	0.362671	+	2.98687i	0.0879607	+	0.724421i	−0.880289	+	0.474437i	$0.842652\pi$
$18$	−1.18836	−	1.72164i	−0.280099	−	0.405794i
$19$	−0.528951			−0.121350			−0.0606748	−	0.998158i	$-0.519325\pi$
$19$	−0.528951			−0.121350			−0.0606748	+	0.998158i	$0.519325\pi$
$20$	−1.36794	+	1.98180i	−0.305880	+	0.443144i
$21$	0.194000	−	1.59773i	0.0423342	−	0.348654i
$22$	0.834124			0.177836
$23$	6.25297			1.30384			0.651918	−	0.758290i	$-0.273965\pi$
$23$	6.25297			1.30384			0.651918	+	0.758290i	$0.273965\pi$
$24$	0.0948689	−	0.781316i	0.0193650	−	0.159485i
$25$	2.97385	−	2.63460i	0.594771	−	0.526921i
$26$	−5.04128	+	5.61040i	−0.988676	+	1.10029i
$27$	0.748511	+	0.663123i	0.144051	+	0.127618i
$28$	2.86265	−	2.53609i	0.540990	−	0.479276i
$29$	3.72926	+	1.95727i	0.692506	+	0.363455i	0.773971	−	0.633221i	$-0.218268\pi$
$29$	3.72926	+	1.95727i	0.692506	+	0.363455i	−0.0814652	+	0.996676i	$0.525960\pi$
$30$	0.751752	−	1.98221i	0.137250	−	0.361900i
$31$	1.94268	+	1.72106i	0.348915	+	0.309112i	0.819317	−	0.573340i	$-0.194353\pi$
$31$	1.94268	+	1.72106i	0.348915	+	0.309112i	−0.470402	+	0.882452i	$0.655891\pi$
$32$	−6.04173	+	5.35250i	−1.06804	+	0.946198i
$33$	−0.387145	+	0.0954227i	−0.0673933	+	0.0166110i
$34$	2.23197	−	5.88522i	0.382780	−	1.00931i
$35$	1.44420	−	0.757976i	0.244115	−	0.128121i
$36$	0.286423	+	2.35891i	0.0477372	+	0.393151i
$37$	5.22824	+	4.63182i	0.859517	+	0.761466i	0.972690	−	0.232109i	$-0.0745628\pi$
$37$	5.22824	+	4.63182i	0.859517	+	0.761466i	−0.113172	+	0.993575i	$0.536101\pi$
$38$	0.979789	+	0.514233i	0.158943	+	0.0834196i
$39$	1.69800	−	3.18069i	0.271898	−	0.509318i
$40$	0.706238	−	0.370662i	0.111666	−	0.0586069i
$41$	−3.80508	−	0.937867i	−0.594253	−	0.146470i	−0.0692920	−	0.997596i	$-0.522074\pi$
$41$	−3.80508	−	0.937867i	−0.594253	−	0.146470i	−0.524961	+	0.851126i	$0.675920\pi$
$42$	−1.91263	+	2.77092i	−0.295124	+	0.427562i
$43$	0.952912	−	0.844206i	0.145318	−	0.128740i	−0.587332	−	0.809346i	$-0.699822\pi$
$43$	0.952912	−	0.844206i	0.145318	−	0.128740i	0.732650	+	0.680606i	$0.238283\pi$
$44$	−0.838950	−	0.440315i	−0.126477	−	0.0663800i
$45$	−0.122151	+	1.00601i	−0.0182093	+	0.149967i
$46$	−11.5825	−	6.07898i	−1.70775	−	0.896297i
$47$	5.06156	−	7.33293i	0.738304	−	1.06962i	−0.256373	−	0.966578i	$-0.582528\pi$
$47$	5.06156	−	7.33293i	0.738304	−	1.06962i	0.994677	−	0.103040i	$-0.0328569\pi$
$48$	1.76440	−	2.55618i	0.254670	−	0.368953i
$49$	4.28148	−	1.05529i	0.611640	−	0.150756i
$50$	−8.06984	+	1.98904i	−1.14125	+	0.281292i
$51$	−0.362671	+	2.98687i	−0.0507841	+	0.418245i
$52$	8.03204	−	2.98168i	1.11384	−	0.413485i
$53$	0.205458	+	1.69210i	0.0282218	+	0.232427i	0.999994	−	0.00349419i	$-0.00111224\pi$
$53$	0.205458	+	1.69210i	0.0282218	+	0.232427i	−0.971772	+	0.235922i	$0.924189\pi$
$54$	−0.741814	−	1.95600i	−0.100948	−	0.266178i
$55$	−0.302453	−	0.267950i	−0.0407828	−	0.0361304i
$56$	−1.22993	+	0.303150i	−0.164356	+	0.0405101i
$57$	−0.513581	−	0.126586i	−0.0680254	−	0.0167668i
$58$	−5.00499	−	7.25098i	−0.657188	−	0.952101i
$59$	−2.91253	−	7.67971i	−0.379179	−	0.999813i	−0.979747	−	0.200239i	$-0.935828\pi$
$59$	−2.91253	−	7.67971i	−0.379179	−	0.999813i	0.600568	−	0.799574i	$-0.294941\pi$
$60$	−1.80246	+	1.59684i	−0.232697	+	0.206151i
$61$	0.933288	−	7.68631i	0.119495	−	0.984132i	−0.802425	−	0.596753i	$-0.796457\pi$
$61$	0.933288	−	7.68631i	0.119495	−	0.984132i	0.921920	−	0.387379i	$-0.126620\pi$
$62$	−1.92530	−	5.07659i	−0.244513	−	0.644728i
$63$	0.570725	−	1.50488i	0.0719045	−	0.189597i
$64$	10.3633	−	2.55433i	1.29542	−	0.319292i
$65$	3.63022	−	0.414892i	0.450274	−	0.0514610i
$66$	0.809886	+	0.199619i	0.0996901	+	0.0245714i
$67$	0.964759	−	1.39770i	0.117864	−	0.170756i	−0.759611	−	0.650377i	$-0.774611\pi$
$67$	0.964759	−	1.39770i	0.117864	−	0.170756i	0.877475	+	0.479622i	$0.159226\pi$
$68$	−5.35156	+	4.74107i	−0.648972	+	0.574939i
$69$	6.07127	+	1.49643i	0.730895	+	0.180150i
$70$	−3.41202			−0.407814
$71$	−9.35088	−	2.30478i	−1.10975	−	0.273528i	−0.358486	−	0.933535i	$-0.616707\pi$
$71$	−9.35088	−	2.30478i	−1.10975	−	0.273528i	−0.751259	+	0.660007i	$0.770553\pi$
$72$	0.279093	−	0.735909i	0.0328915	−	0.0867277i
$73$	5.82370	−	3.05652i	0.681613	−	0.357738i	−0.0881149	−	0.996110i	$-0.528084\pi$
$73$	5.82370	−	3.05652i	0.681613	−	0.357738i	0.769728	+	0.638372i	$0.220392\pi$
$74$	−5.18146	−	13.6624i	−0.602333	−	1.58822i
$75$	3.51794	−	1.84636i	0.406217	−	0.213199i
$76$	−0.714006	−	1.03442i	−0.0819021	−	0.118656i
$77$	0.364553	+	0.528146i	0.0415446	+	0.0601878i
$78$	−6.23744	+	4.24091i	−0.706251	+	0.480189i
$79$	−3.51722	+	5.09557i	−0.395718	+	0.573296i	−0.969309	−	0.245845i	$-0.920934\pi$
$79$	−3.51722	+	5.09557i	−0.395718	+	0.573296i	0.573591	+	0.819142i	$0.305550\pi$
$80$	3.14760			0.351912
$81$	0.568065	+	0.822984i	0.0631183	+	0.0914427i
$82$	6.13647	+	5.43644i	0.677660	+	0.600354i
$83$	−6.39089	+	1.57521i	−0.701491	+	0.172902i	−0.573901	−	0.818925i	$-0.694570\pi$
$83$	−6.39089	+	1.57521i	−0.701491	+	0.172902i	−0.127590	+	0.991827i	$0.540724\pi$
$84$	3.38639	−	1.77732i	0.369486	−	0.193921i
$85$	−2.69985	+	1.41699i	−0.292840	+	0.153694i
$86$	−2.58582	+	0.637347i	−0.278836	+	0.0687269i
$87$	3.15249	+	2.79286i	0.337982	+	0.299426i
$88$	0.178272	+	0.258272i	0.0190039	+	0.0275318i
$89$	3.62834			0.384603			0.192302	−	0.981336i	$-0.438405\pi$
$89$	3.62834			0.384603			0.192302	+	0.981336i	$0.438405\pi$
$90$	1.20428	−	1.74470i	0.126942	−	0.183908i
$91$	−5.75564	−	0.739991i	−0.603355	−	0.0775721i
$92$	8.44060	+	12.2283i	0.879993	+	1.27489i
$93$	1.47435	+	2.13597i	0.152883	+	0.221489i
$94$	−16.5045	+	8.66225i	−1.70231	+	0.893443i
$95$	−0.190081	−	0.501204i	−0.0195019	−	0.0514224i
$96$	−7.14710	+	3.75109i	−0.729448	+	0.382844i
$97$	−0.483297	+	1.27435i	−0.0490714	+	0.129391i	−0.957311	−	0.289060i	$-0.906657\pi$
$97$	−0.483297	+	1.27435i	−0.0490714	+	0.129391i	0.908240	+	0.418450i	$0.137427\pi$
$98$	−8.95662	−	2.20761i	−0.904756	−	0.223002i
$99$	−0.398731			−0.0400740
$100$	9.16650	+	2.25934i	0.916650	+	0.225934i
$101$	7.48615	−	6.63215i	0.744900	−	0.659924i	−0.202752	−	0.979230i	$-0.564988\pi$
$101$	7.48615	−	6.63215i	0.744900	−	0.659924i	0.947652	+	0.319306i	$0.103450\pi$
$102$	3.57554	−	5.18006i	0.354031	−	0.512903i
$103$	3.49723	+	0.861989i	0.344592	+	0.0849343i	0.407814	−	0.913065i	$-0.366291\pi$
$103$	3.49723	+	0.861989i	0.344592	+	0.0849343i	−0.0632216	+	0.998000i	$0.520137\pi$
$104$	−2.81460	−	0.361867i	−0.275994	−	0.0354840i
$105$	1.58363	−	0.390331i	0.154547	−	0.0380924i
$106$	1.26444	−	3.33405i	0.122813	−	0.323832i
$107$	7.03367	+	18.5463i	0.679971	+	1.79294i	0.605693	+	0.795699i	$0.292896\pi$
$107$	7.03367	+	18.5463i	0.679971	+	1.79294i	0.0742783	+	0.997238i	$0.476335\pi$
$108$	−0.286423	+	2.35891i	−0.0275611	+	0.226986i
$109$	−11.9441	+	10.5816i	−1.14404	+	1.01353i	−0.144329	+	0.989530i	$0.546102\pi$
$109$	−11.9441	+	10.5816i	−1.14404	+	1.01353i	−0.999712	+	0.0240022i	$0.992359\pi$
$110$	0.299747	+	0.790368i	0.0285798	+	0.0753586i
$111$	3.96785	+	5.74842i	0.376612	+	0.545616i
$112$	−4.85372	−	1.19633i	−0.458634	−	0.113043i
$113$	−9.01417	+	2.22179i	−0.847981	+	0.209009i	−0.639283	−	0.768971i	$-0.720769\pi$
$113$	−9.01417	+	2.22179i	−0.847981	+	0.209009i	−0.208698	+	0.977980i	$0.566923\pi$
$114$	0.828254	+	0.733769i	0.0775731	+	0.0687238i
$115$	2.24704	+	5.92496i	0.209538	+	0.552505i
$116$	1.20632	+	9.93496i	0.112004	+	0.922438i
$117$	2.40985	−	2.68190i	0.222791	−	0.247942i
$118$	−2.07107	+	17.0568i	−0.190657	+	1.57021i
$119$	4.70185	−	1.15890i	0.431018	−	0.106236i
$120$	0.774422	−	0.190878i	0.0706947	−	0.0174247i
$121$	−6.15840	+	8.92198i	−0.559854	+	0.811089i
$122$	−9.20119	+	13.3302i	−0.833037	+	1.20686i
$123$	−3.47006	−	1.82123i	−0.312885	−	0.164215i
$124$	−0.743380	+	6.12229i	−0.0667575	+	0.549798i
$125$	8.05166	+	4.22584i	0.720162	+	0.377970i
$126$	−2.52017	+	2.23268i	−0.224515	+	0.198903i
$127$	−9.10323	+	13.1883i	−0.807781	+	1.17027i	0.174830	+	0.984599i	$0.444062\pi$
$127$	−9.10323	+	13.1883i	−0.807781	+	1.17027i	−0.982611	+	0.185675i	$0.940553\pi$
$128$	−6.00530	−	1.48017i	−0.530799	−	0.130830i
$129$	1.12725	−	0.591628i	0.0992491	−	0.0520900i
$130$	−7.12770	−	2.76070i	−0.625140	−	0.242129i
$131$	−7.66330	−	4.02201i	−0.669546	−	0.351405i	0.0954554	−	0.995434i	$-0.469569\pi$
$131$	−7.66330	−	4.02201i	−0.669546	−	0.351405i	−0.765001	+	0.644029i	$0.777262\pi$
$132$	−0.709198	−	0.628294i	−0.0617277	−	0.0546860i
$133$	0.102616	+	0.845122i	0.00889797	+	0.0732813i
$134$	−3.14585	+	1.65107i	−0.271760	+	0.142631i
$135$	−0.359355	+	0.947542i	−0.0309284	+	0.0815515i
$136$	2.29928	−	0.566721i	0.197162	−	0.0485960i
$137$	3.71615	−	3.29222i	0.317492	−	0.281273i	−0.489292	−	0.872120i	$-0.662745\pi$
$137$	3.71615	−	3.29222i	0.317492	−	0.281273i	0.806784	+	0.590847i	$0.201206\pi$
$138$	−9.79117	−	8.67422i	−0.833480	−	0.738399i
$139$	1.26447	−	3.33414i	0.107251	−	0.282798i	−0.870637	−	0.491926i	$-0.836293\pi$
$139$	1.26447	−	3.33414i	0.107251	−	0.282798i	0.977888	+	0.209128i	$0.0670625\pi$
$140$	3.43176	+	1.80113i	0.290037	+	0.152223i
$141$	6.66936	−	5.90854i	0.561662	−	0.497589i
$142$	15.0802	+	13.3599i	1.26550	+	1.12114i
$143$	0.334222	+	1.39826i	0.0279490	+	0.116928i
$144$	2.32487	−	2.05965i	0.193739	−	0.171638i
$145$	−0.514463	+	4.23698i	−0.0427238	+	0.351862i
$146$	−13.7589			−1.13869
$147$	4.40962			0.363699
$148$	−2.00062	+	16.4766i	−0.164450	+	1.35437i
$149$	−9.78243	+	14.1723i	−0.801408	+	1.16104i	0.182648	+	0.983178i	$0.441533\pi$
$149$	−9.78243	+	14.1723i	−0.801408	+	1.16104i	−0.984056	+	0.177861i	$0.943082\pi$
$150$	−8.31135			−0.678619
$151$	−6.15210	−	8.91285i	−0.500651	−	0.725318i	0.488445	−	0.872595i	$-0.337564\pi$
$151$	−6.15210	−	8.91285i	−0.500651	−	0.725318i	−0.989095	+	0.147277i	$0.952949\pi$
$152$	0.0501810	+	0.413278i	0.00407022	+	0.0335213i
$153$	−1.06694	+	2.81328i	−0.0862567	+	0.227440i
$154$	−0.161820	−	1.33271i	−0.0130398	−	0.107393i
$155$	−0.932668	+	2.45924i	−0.0749137	+	0.197531i
$156$	8.51221	−	0.972846i	0.681522	−	0.0778900i
$157$	6.65212	+	17.5402i	0.530897	+	1.39986i	0.885410	+	0.464810i	$0.153877\pi$
$157$	6.65212	+	17.5402i	0.530897	+	1.39986i	−0.354513	+	0.935051i	$0.615353\pi$
$158$	11.4688	−	6.01930i	0.912410	−	0.478870i
$159$	−0.205458	+	1.69210i	−0.0162939	+	0.134192i
$160$	−7.24285	−	3.80134i	−0.572598	−	0.300522i
$161$	−1.21308	−	9.99057i	−0.0956037	−	0.787367i
$162$	−0.252156	−	2.07669i	−0.0198112	−	0.163160i
$163$	−8.52876	−	7.55582i	−0.668024	−	0.591817i	0.259427	−	0.965763i	$-0.416466\pi$
$163$	−8.52876	−	7.55582i	−0.668024	−	0.591817i	−0.927451	+	0.373945i	$0.878005\pi$
$164$	−3.30220	−	8.70719i	−0.257859	−	0.679917i
$165$	−0.229540	−	0.332546i	−0.0178696	−	0.0258886i
$166$	13.3694	+	3.29526i	1.03767	+	0.255761i
$167$	−0.413905	−	0.217234i	−0.0320289	−	0.0168101i	0.448633	−	0.893716i	$-0.351911\pi$
$167$	−0.413905	−	0.217234i	−0.0320289	−	0.0168101i	−0.480662	+	0.876906i	$0.659603\pi$
$168$	−1.26674			−0.0977309
$169$	−11.4248	−	6.20278i	−0.878829	−	0.477137i
$170$	6.37857			0.489214
$171$	−0.468363	−	0.245816i	−0.0358166	−	0.0187980i
$172$	2.93722	+	0.723960i	0.223961	+	0.0552014i
$173$	−6.81890	−	9.87888i	−0.518431	−	0.751077i	0.473091	−	0.881014i	$-0.343138\pi$
$173$	−6.81890	−	9.87888i	−0.518431	−	0.751077i	−0.991522	+	0.129936i	$0.958523\pi$
$174$	−3.12428	−	8.23805i	−0.236851	−	0.624525i
$175$	−4.78632	−	4.24031i	−0.361812	−	0.320537i
$176$	0.149279	+	1.22943i	0.0112523	+	0.0926714i
$177$	−0.990022	−	8.15356i	−0.0744146	−	0.612859i
$178$	−6.72086	−	3.52738i	−0.503750	−	0.264388i
$179$	2.84356	−	23.4188i	0.212538	−	1.75041i	−0.362230	−	0.932089i	$-0.617984\pi$
$179$	2.84356	−	23.4188i	0.212538	−	1.75041i	0.574768	−	0.818317i	$-0.305092\pi$
$180$	−2.13224	+	1.11908i	−0.158927	+	0.0834116i
$181$	4.30535	+	11.3523i	0.320014	+	0.843808i	0.994424	+	0.105451i	$0.0336287\pi$
$181$	4.30535	+	11.3523i	0.320014	+	0.843808i	−0.674410	+	0.738357i	$0.735602\pi$
$182$	9.94191	+	6.96619i	0.736944	+	0.516368i
$183$	2.74562	−	7.23961i	0.202962	−	0.535168i
$184$	−0.593213	−	4.88555i	−0.0437322	−	0.360167i
$185$	−2.51005	+	6.61845i	−0.184542	+	0.486598i
$186$	−0.654444	−	5.38983i	−0.0479862	−	0.395202i
$187$	−0.681510	−	0.987337i	−0.0498369	−	0.0722013i
$188$	21.1726			1.54417
$189$	0.914281	−	1.32456i	0.0665042	−	0.0963479i
$190$	−0.135165	+	1.11318i	−0.00980590	+	0.0807589i
$191$	−2.09879			−0.151863			−0.0759315	−	0.997113i	$-0.524193\pi$
$191$	−2.09879			−0.151863			−0.0759315	+	0.997113i	$0.524193\pi$
$192$	10.6735			0.770293
$193$	1.63426	−	13.4593i	0.117636	−	0.968823i	−0.807678	−	0.589623i	$-0.799276\pi$
$193$	1.63426	−	13.4593i	0.117636	−	0.968823i	0.925315	−	0.379200i	$-0.123801\pi$
$194$	2.13412	−	1.89066i	0.153221	−	0.135742i
$195$	3.62402	+	0.465933i	0.259522	+	0.0333662i
$196$	7.84310	+	6.94838i	0.560221	+	0.496313i
$197$	−10.3400	+	9.16047i	−0.736697	+	0.652657i	−0.945619	−	0.325276i	$-0.894543\pi$
$197$	−10.3400	+	9.16047i	−0.736697	+	0.652657i	0.208922	+	0.977932i	$0.433004\pi$
$198$	0.738580	+	0.387637i	0.0524886	+	0.0275481i
$199$	1.84095	−	4.85417i	0.130501	−	0.344103i	−0.853800	−	0.520601i	$-0.825708\pi$
$199$	1.84095	−	4.85417i	0.130501	−	0.344103i	0.984301	+	0.176498i	$0.0564770\pi$
$200$	−2.34058	−	2.07358i	−0.165504	−	0.146624i
$201$	1.27122	−	1.12620i	0.0896646	−	0.0794359i
$202$	−20.3144	+	5.00705i	−1.42932	+	0.352295i
$203$	2.40371	−	6.33806i	0.168707	−	0.444845i
$204$	−6.33067	+	3.32259i	−0.443235	+	0.232628i
$205$	−0.478706	−	3.94250i	−0.0334343	−	0.275356i
$206$	−5.63999	−	4.99660i	−0.392957	−	0.348130i
$207$	5.53673	+	2.90590i	0.384830	+	0.201974i
$208$	−9.17144	−	6.42633i	−0.635925	−	0.445586i
$209$	0.186751	−	0.0980145i	0.0129178	−	0.00677980i
$210$	−3.31287	−	0.816550i	−0.228610	−	0.0563473i
$211$	−0.699188	+	1.01295i	−0.0481341	+	0.0697343i	−0.846312	−	0.532688i	$-0.821182\pi$
$211$	−0.699188	+	1.01295i	−0.0481341	+	0.0697343i	0.798178	+	0.602422i	$0.205797\pi$
$212$	−3.03173	+	2.68588i	−0.208220	+	0.184467i
$213$	−8.52759	−	4.47562i	−0.584301	−	0.306665i
$214$	5.00158	−	41.1917i	0.341901	−	2.81581i
$215$	1.14235	+	0.599554i	0.0779080	+	0.0408893i
$216$	0.447098	−	0.647733i	0.0304212	−	0.0440727i
$217$	2.37292	−	3.43777i	0.161084	−	0.233371i
$218$	32.4116	−	7.98874i	2.19519	−	0.541065i
$219$	6.38595	−	1.57400i	0.431522	−	0.106361i
$220$	0.115736	−	0.953171i	0.00780291	−	0.0642627i
$221$	10.7598	+	1.38337i	0.723784	+	0.0930555i
$222$	−1.76127	−	14.5054i	−0.118209	−	0.973538i
$223$	6.30505	+	16.6251i	0.422218	+	1.11330i	0.962373	+	0.271731i	$0.0875961\pi$
$223$	6.30505	+	16.6251i	0.422218	+	1.11330i	−0.540156	+	0.841565i	$0.681635\pi$
$224$	9.72396	+	8.61467i	0.649709	+	0.575592i
$225$	3.85758	−	0.950808i	0.257172	−	0.0633872i
$226$	18.8571	+	4.64787i	1.25436	+	0.309171i
$227$	5.67571	+	8.22268i	0.376710	+	0.545759i	0.964782	−	0.263050i	$-0.0847283\pi$
$227$	5.67571	+	8.22268i	0.376710	+	0.545759i	−0.588072	+	0.808808i	$0.700113\pi$
$228$	−0.445706	−	1.17523i	−0.0295176	−	0.0778316i
$229$	−5.92426	+	5.24843i	−0.391486	+	0.346826i	−0.835789	−	0.549050i	$-0.814990\pi$
$229$	−5.92426	+	5.24843i	−0.391486	+	0.346826i	0.444304	+	0.895876i	$0.353451\pi$
$230$	1.59785	−	13.1595i	0.105359	−	0.867709i
$231$	0.227566	+	0.600042i	0.0149727	+	0.0394799i
$232$	1.17545	−	3.09941i	0.0771722	−	0.203486i
$233$	−2.63219	+	0.648777i	−0.172441	+	0.0425028i	−0.324591	−	0.945855i	$-0.605227\pi$
$233$	−2.63219	+	0.648777i	−0.172441	+	0.0425028i	0.152150	+	0.988357i	$0.451380\pi$
$234$	−7.07111	+	2.62496i	−0.462253	+	0.171599i
$235$	8.76716	+	2.16091i	0.571906	+	0.140962i
$236$	11.0869	−	16.0622i	0.721699	−	1.04556i
$237$	−4.63446	+	4.10578i	−0.301041	+	0.266699i
$238$	−9.83601	−	2.42436i	−0.637574	−	0.157148i
$239$	−14.0192			−0.906824			−0.453412	−	0.891301i	$-0.649793\pi$
$239$	−14.0192			−0.906824			−0.453412	+	0.891301i	$0.649793\pi$
$240$	3.05613	+	0.753270i	0.197273	+	0.0486233i
$241$	1.56504	−	4.12668i	0.100813	−	0.265823i	−0.875115	−	0.483915i	$-0.839214\pi$
$241$	1.56504	−	4.12668i	0.100813	−	0.265823i	0.975928	+	0.218093i	$0.0699835\pi$
$242$	20.0811	−	10.5394i	1.29086	−	0.677496i
$243$	0.354605	+	0.935016i	0.0227479	+	0.0599813i
$244$	16.2912	−	8.55026i	1.04293	−	0.547374i
$245$	2.53851	+	3.67766i	0.162179	+	0.234957i
$246$	4.65713	+	6.74702i	0.296928	+	0.430174i
$247$	−0.469431	+	1.84848i	−0.0298692	+	0.117616i
$248$	1.16039	−	1.68112i	0.0736851	−	0.106751i
$249$	−6.58215			−0.417127
$250$	−10.8060	−	15.6552i	−0.683434	−	0.990125i
$251$	−14.4295	−	12.7834i	−0.910780	−	0.806881i	0.0708869	−	0.997484i	$-0.477417\pi$
$251$	−14.4295	−	12.7834i	−0.910780	−	0.806881i	−0.981667	+	0.190604i	$0.938956\pi$
$252$	3.71333	−	0.915254i	0.233918	−	0.0576556i
$253$	−2.20767	+	1.15867i	−0.138795	+	0.0728452i
$254$	29.6835	−	15.5791i	1.86251	−	0.977519i
$255$	−2.96051	+	0.729700i	−0.185394	+	0.0456956i
$256$	−6.29367	−	5.57570i	−0.393354	−	0.348481i
$257$	6.16624	+	8.93334i	0.384639	+	0.557246i	0.966704	−	0.255896i	$-0.0823705\pi$
$257$	6.16624	+	8.93334i	0.384639	+	0.557246i	−0.582065	+	0.813142i	$0.697755\pi$
$258$	−2.66321			−0.165804
$259$	6.38612	−	9.25189i	0.396814	−	0.574885i
$260$	5.71163	+	6.53922i	0.354220	+	0.405545i
$261$	2.39251	+	3.46614i	0.148092	+	0.214549i
$262$	10.2848	+	14.9001i	0.635398	+	0.920533i
$263$	−1.24067	+	0.651155i	−0.0765032	+	0.0401520i	−0.502541	−	0.864553i	$-0.667601\pi$
$263$	−1.24067	+	0.651155i	−0.0765032	+	0.0401520i	0.426038	+	0.904705i	$0.359909\pi$
$264$	0.111283	+	0.293430i	0.00684901	+	0.0180594i
$265$	−1.52950	+	0.802744i	−0.0939565	+	0.0493122i
$266$	0.631527	−	1.66520i	0.0387214	−	0.102100i
$267$	3.52291	+	0.868319i	0.215598	+	0.0531402i
$268$	4.03562			0.246514
$269$	−21.0981	−	5.20023i	−1.28638	−	0.317063i	−0.463913	−	0.885881i	$-0.653555\pi$
$269$	−21.0981	−	5.20023i	−1.28638	−	0.317063i	−0.822464	+	0.568818i	$0.807401\pi$
$270$	1.58682	−	1.40580i	0.0965708	−	0.0855543i
$271$	−1.86725	+	2.70518i	−0.113427	+	0.164328i	−0.875586	−	0.483063i	$-0.839524\pi$
$271$	−1.86725	+	2.70518i	−0.113427	+	0.164328i	0.762158	+	0.647391i	$0.224140\pi$
$272$	9.07375	+	2.23648i	0.550177	+	0.135606i
$273$	−5.41130	−	2.09590i	−0.327507	−	0.126850i
$274$	−10.0841	+	2.48551i	−0.609204	+	0.150155i
$275$	−0.561755	+	1.48123i	−0.0338751	+	0.0893213i
$276$	5.26890	+	13.8929i	0.317151	+	0.836257i
$277$	−0.572308	+	4.71338i	−0.0343866	+	0.283199i	0.965365	+	0.260904i	$0.0840206\pi$
$277$	−0.572308	+	4.71338i	−0.0343866	+	0.283199i	−0.999751	+	0.0222956i	$0.992903\pi$
$278$	−5.58357	+	4.94662i	−0.334881	+	0.296678i
$279$	0.920339	+	2.42673i	0.0550992	+	0.145285i
$280$	−0.729229	−	1.05647i	−0.0435798	−	0.0631362i
$281$	14.8141	+	3.65134i	0.883734	+	0.217821i	0.654964	−	0.755660i	$-0.272684\pi$
$281$	14.8141	+	3.65134i	0.883734	+	0.217821i	0.228770	+	0.973481i	$0.426530\pi$
$282$	−18.0980	+	4.46075i	−1.07772	+	0.265634i
$283$	−24.0389	−	21.2966i	−1.42896	−	1.26595i	−0.912153	−	0.409849i	$-0.865581\pi$
$283$	−24.0389	−	21.2966i	−1.42896	−	1.26595i	−0.516809	−	0.856101i	$-0.672880\pi$
$284$	−8.11508	−	21.3977i	−0.481541	−	1.26972i
$285$	−0.0646121	−	0.532129i	−0.00382729	−	0.0315206i
$286$	0.740264	−	2.91495i	0.0437727	−	0.172365i
$287$	−0.760276	+	6.26144i	−0.0448777	+	0.369601i
$288$	−7.83712	+	1.93168i	−0.461806	+	0.113825i
$289$	7.71618	−	1.90187i	0.453893	−	0.111875i
$290$	5.07204	−	7.34812i	0.297841	−	0.431497i
$291$	−0.774226	+	1.12166i	−0.0453859	+	0.0657528i
$292$	13.8385	+	7.26299i	0.809835	+	0.425034i
$293$	−1.40798	+	11.5958i	−0.0822552	+	0.677433i	0.892008	+	0.452019i	$0.149296\pi$
$293$	−1.40798	+	11.5958i	−0.0822552	+	0.677433i	−0.974263	+	0.225413i	$0.927627\pi$
$294$	−8.16804	−	4.28692i	−0.476370	−	0.250018i
$295$	6.23022	−	5.51949i	0.362737	−	0.321357i
$296$	3.12291	−	4.52432i	0.181516	−	0.262971i
$297$	−0.387145	−	0.0954227i	−0.0224644	−	0.00553699i
$298$	31.8982	−	16.7415i	1.84781	−	0.969807i
$299$	5.54936	−	21.8518i	0.320928	−	1.26372i
$300$	8.35944	+	4.38737i	0.482632	+	0.253305i
$301$	−1.53368	−	1.35872i	−0.0883998	−	0.0783154i
$302$	2.73083	+	22.4904i	0.157142	+	1.29418i
$303$	8.85580	−	4.64788i	0.508752	−	0.267014i
$304$	−0.582586	+	1.53615i	−0.0334136	+	0.0881044i
$305$	7.61849	−	1.87779i	0.436234	−	0.107522i
$306$	4.71131	−	4.17386i	0.269328	−	0.238604i
$307$	13.5283	+	11.9851i	0.772103	+	0.684024i	0.954171	−	0.299262i	$-0.0967405\pi$
$307$	13.5283	+	11.9851i	0.772103	+	0.684024i	−0.182068	+	0.983286i	$0.558279\pi$
$308$	−0.540749	+	1.42584i	−0.0308120	+	0.0812447i
$309$	3.18932	+	1.67388i	0.181434	+	0.0952238i
$310$	4.11842	−	3.64860i	0.233911	−	0.207227i
$311$	−16.3352	−	14.4717i	−0.926284	−	0.820616i	0.0577989	−	0.998328i	$-0.481592\pi$
$311$	−16.3352	−	14.4717i	−0.926284	−	0.820616i	−0.984082	+	0.177713i	$0.943130\pi$
$312$	−2.64621	−	1.02493i	−0.149812	−	0.0580252i
$313$	−0.438317	+	0.388315i	−0.0247752	+	0.0219489i	−0.675419	−	0.737434i	$-0.736037\pi$
$313$	−0.438317	+	0.388315i	−0.0247752	+	0.0219489i	0.650644	+	0.759383i	$0.274499\pi$
$314$	4.73026	−	38.9572i	0.266944	−	2.19848i
$315$	1.63103			0.0918980
$316$	−14.7126			−0.827649
$317$	1.52462	−	12.5564i	0.0856312	−	0.705236i	−0.885156	−	0.465294i	$-0.845948\pi$
$317$	1.52462	−	12.5564i	0.0856312	−	0.705236i	0.970787	−	0.239942i	$-0.0771284\pi$
$318$	2.02559	−	2.93457i	0.113589	−	0.164563i
$319$	−1.67933			−0.0940244
$320$	6.14446	+	8.90179i	0.343486	+	0.497625i
$321$	2.39087	+	19.6906i	0.133446	+	1.09902i
$322$	−7.46558	+	19.6851i	−0.416040	+	1.09701i
$323$	−0.191835	−	1.57991i	−0.0106740	−	0.0879083i
$324$	−0.842623	+	2.22181i	−0.0468124	+	0.123434i
$325$	−6.56773	−	12.7306i	−0.364312	−	0.706169i
$326$	8.45245	+	22.2873i	0.468138	+	1.23438i
$327$	−14.1294	+	7.41568i	−0.781358	+	0.410088i
$328$	−0.371787	+	3.06194i	−0.0205285	+	0.169067i
$329$	−12.6980	−	6.66442i	−0.700063	−	0.367421i
$330$	0.101889	+	0.839135i	0.00560883	+	0.0461929i
$331$	−1.65523	−	13.6321i	−0.0909798	−	0.749286i	−0.964790	−	0.263020i	$-0.915282\pi$
$331$	−1.65523	−	13.6321i	−0.0909798	−	0.749286i	0.873811	−	0.486266i	$-0.161642\pi$
$332$	−11.7072	−	10.3717i	−0.642518	−	0.569222i
$333$	2.47686	+	6.53095i	0.135731	+	0.357894i
$334$	0.555497	+	0.804776i	0.0303954	+	0.0440354i
$335$	1.67107	+	0.411881i	0.0913001	+	0.0225035i
$336$	−4.42638	−	2.32314i	−0.241479	−	0.126738i
$337$	12.1371			0.661152			0.330576	−	0.943779i	$-0.392757\pi$
$337$	12.1371			0.661152			0.330576	+	0.943779i	$0.392757\pi$
$338$	15.1322	+	22.5964i	0.823084	+	1.22908i
$339$	−9.28394			−0.504234
$340$	−6.41548	−	3.36710i	−0.347928	−	0.182607i
$341$	−1.00479	−	0.247659i	−0.0544126	−	0.0134115i
$342$	0.628584	+	0.910661i	0.0339899	+	0.0492429i
$343$	−6.51175	−	17.1701i	−0.351601	−	0.927097i
$344$	−0.749993	−	0.664436i	−0.0404369	−	0.0358240i
$345$	0.763810	+	6.29054i	0.0411221	+	0.338671i
$346$	3.02681	+	24.9281i	0.162723	+	1.34014i
$347$	−20.5781	−	10.8002i	−1.10469	−	0.579787i	−0.189126	−	0.981953i	$-0.560565\pi$
$347$	−20.5781	−	10.8002i	−1.10469	−	0.579787i	−0.915567	+	0.402165i	$0.868258\pi$
$348$	−1.20632	+	9.93496i	−0.0646657	+	0.532570i
$349$	−16.7484	+	8.79022i	−0.896520	+	0.470530i	−0.849032	−	0.528342i	$-0.822814\pi$
$349$	−16.7484	+	8.79022i	−0.896520	+	0.470530i	−0.0474880	+	0.998872i	$0.515122\pi$
$350$	4.74349	+	12.5076i	0.253550	+	0.668557i
$351$	2.98165	−	2.02726i	0.159149	−	0.108207i
$352$	1.14127	−	3.00928i	0.0608299	−	0.160395i
$353$	2.59501	+	21.3719i	0.138119	+	1.13751i	0.882687	+	0.469962i	$0.155732\pi$
$353$	2.59501	+	21.3719i	0.138119	+	1.13751i	−0.744568	+	0.667547i	$0.767344\pi$
$354$	−6.09285	+	16.0655i	−0.323831	+	0.853873i
$355$	−1.17641	−	9.68859i	−0.0624373	−	0.514217i
$356$	4.89773	+	7.09558i	0.259579	+	0.376065i
$357$	4.84257			0.256296
$358$	−28.0344	+	40.6148i	−1.48166	+	2.14656i
$359$	0.384004	−	3.16255i	0.0202669	−	0.166913i	−0.979061	−	0.203567i	$-0.934747\pi$
$359$	0.384004	−	3.16255i	0.0202669	−	0.166913i	0.999328	+	0.0366534i	$0.0116697\pi$
$360$	0.797598			0.0420371
$361$	−18.7202			−0.985274
$362$	3.06149	−	25.2137i	0.160908	−	1.32520i
$363$	−8.11461	+	7.18892i	−0.425907	+	0.377321i
$364$	−6.32214	−	12.2546i	−0.331370	−	0.642316i
$365$	4.98896	+	4.41983i	0.261134	+	0.231345i
$366$	−12.1240	+	10.7409i	−0.633729	+	0.561435i
$367$	15.2308	+	7.99374i	0.795041	+	0.417270i	0.812778	−	0.582573i	$-0.197954\pi$
$367$	15.2308	+	7.99374i	0.795041	+	0.417270i	−0.0177376	+	0.999843i	$0.505646\pi$
$368$	6.88702	−	18.1596i	0.359011	−	0.946633i
$369$	−2.93338	−	2.59875i	−0.152706	−	0.135285i
$370$	11.0837	−	9.81931i	0.576215	−	0.510482i
$371$	2.66366	−	0.656533i	0.138290	−	0.0340855i
$372$	−2.18694	+	5.76648i	−0.113387	+	0.298978i
$373$	−6.80613	+	3.57213i	−0.352408	+	0.184958i	−0.631633	−	0.775268i	$-0.717615\pi$
$373$	−6.80613	+	3.57213i	−0.352408	+	0.184958i	0.279225	+	0.960226i	$0.409923\pi$
$374$	0.302513	+	2.49142i	0.0156426	+	0.128828i
$375$	6.80639	+	6.02993i	0.351480	+	0.311384i
$376$	−6.20952	−	3.25901i	−0.320232	−	0.168070i
$377$	10.1495	−	11.2953i	0.522727	−	0.581739i
$378$	−2.98125	+	1.56468i	−0.153339	+	0.0804786i
$379$	16.0360	+	3.95253i	0.823716	+	0.203028i	0.628577	−	0.777748i	$-0.283638\pi$
$379$	16.0360	+	3.95253i	0.823716	+	0.203028i	0.195140	+	0.980775i	$0.437484\pi$
$380$	0.723571	−	1.04827i	0.0371184	−	0.0537753i
$381$	−11.9949	+	10.6265i	−0.614516	+	0.544414i
$382$	3.88764	+	2.04039i	0.198909	+	0.104395i
$383$	−0.613634	+	5.05373i	−0.0313552	+	0.258234i	0.968599	+	0.248630i	$0.0799802\pi$
$383$	−0.613634	+	5.05373i	−0.0313552	+	0.258234i	−0.999954	+	0.00960397i	$0.996943\pi$
$384$	−5.47657	−	2.87433i	−0.279475	−	0.146680i
$385$	−0.369436	+	0.535221i	−0.0188282	+	0.0272774i
$386$	−16.1120	+	23.3422i	−0.820079	+	1.18809i
$387$	1.23608	−	0.304667i	0.0628337	−	0.0154871i
$388$	−3.14450	+	0.775050i	−0.159638	+	0.0393472i
$389$	−0.369639	+	3.04425i	−0.0187414	+	0.154349i	−0.999075	−	0.0429971i	$-0.986309\pi$
$389$	−0.369639	+	3.04425i	−0.0187414	+	0.154349i	0.980334	+	0.197347i	$0.0632324\pi$
$390$	−6.25990	−	4.38625i	−0.316982	−	0.222106i
$391$	2.26777	+	18.6768i	0.114686	+	0.944526i
$392$	−1.23070	−	3.24508i	−0.0621595	−	0.163901i
$393$	−6.47809	−	5.73908i	−0.326776	−	0.289499i
$394$	28.0587	−	6.91585i	1.41358	−	0.348415i
$395$	−6.09220	−	1.50159i	−0.306532	−	0.0755533i
$396$	−0.538229	−	0.779759i	−0.0270470	−	0.0391844i
$397$	3.15640	+	8.32275i	0.158415	+	0.417707i	0.990600	−	0.136792i	$-0.0436792\pi$
$397$	3.15640	+	8.32275i	0.158415	+	0.417707i	−0.832185	+	0.554499i	$0.812910\pi$
$398$	−8.12913	+	7.20179i	−0.407477	+	0.360993i
$399$	−0.102616	+	0.845122i	−0.00513724	+	0.0423090i
$400$	−4.37589	−	11.5383i	−0.218794	−	0.576913i
$401$	−9.68107	+	25.5269i	−0.483449	+	1.27475i	0.442386	+	0.896825i	$0.354132\pi$
$401$	−9.68107	+	25.5269i	−0.483449	+	1.27475i	−0.925836	+	0.377927i	$0.876637\pi$
$402$	−3.44957	+	0.850242i	−0.172049	+	0.0424062i
$403$	7.73855	−	5.26153i	0.385484	−	0.262095i
$404$	23.0750	+	5.68749i	1.14803	+	0.282963i
$405$	−0.575675	+	0.834009i	−0.0286055	+	0.0414422i
$406$	−10.6142	+	9.40332i	−0.526772	+	0.466679i
$407$	−2.70415	−	0.666514i	−0.134040	−	0.0330379i
$408$	2.36809			0.117238
$409$	25.3730	+	6.25389i	1.25462	+	0.309235i	0.809970	−	0.586472i	$-0.199483\pi$
$409$	25.3730	+	6.25389i	1.25462	+	0.309235i	0.444646	+	0.895707i	$0.353330\pi$
$410$	−2.94608	+	7.76818i	−0.145497	+	0.383643i
$411$	4.39604	−	2.30722i	0.216841	−	0.113807i
$412$	3.03504	+	8.00273i	0.149526	+	0.394266i
$413$	−11.7051	+	6.14330i	−0.575969	+	0.302292i
$414$	−7.43078	−	10.7653i	−0.365203	−	0.529088i
$415$	−3.78918	−	5.48958i	−0.186004	−	0.269473i
$416$	13.3431	+	25.8638i	0.654199	+	1.26808i
$417$	2.02564	−	2.93464i	0.0991960	−	0.143710i
$418$	−0.441211			−0.0215803
$419$	−13.5156	−	19.5807i	−0.660279	−	0.956579i	−0.999872	−	0.0160068i	$-0.994905\pi$
$419$	−13.5156	−	19.5807i	−0.660279	−	0.956579i	0.339593	−	0.940573i	$-0.389711\pi$
$420$	2.90100	+	2.57006i	0.141554	+	0.125406i
$421$	8.03916	−	1.98147i	0.391805	−	0.0965712i	−0.0384916	−	0.999259i	$-0.512255\pi$
$421$	8.03916	−	1.98147i	0.391805	−	0.0965712i	0.430296	+	0.902688i	$0.358409\pi$
$422$	2.27989	−	1.19658i	0.110983	−	0.0582485i
$423$	7.88957	−	4.14076i	0.383604	−	0.201331i
$424$	1.30257	−	0.321055i	0.0632584	−	0.0155918i
$425$	8.94774	+	7.92700i	0.434029	+	0.384516i
$426$	11.4448	+	16.5806i	0.554501	+	0.803333i
$427$	−12.4617			−0.603065
$428$	−26.7747	+	38.7898i	−1.29420	+	1.87498i
$429$	−0.0101152	+	1.43761i	−0.000488366	+	0.0694085i
$430$	−1.53314	−	2.22114i	−0.0739346	−	0.107113i
$431$	−16.0057	−	23.1883i	−0.770968	−	1.11694i	−0.989979	−	0.141218i	$-0.954898\pi$
$431$	−16.0057	−	23.1883i	−0.770968	−	1.11694i	0.219010	−	0.975723i	$-0.429717\pi$
$432$	2.75022	−	1.44342i	0.132320	−	0.0694468i
$433$	8.57329	+	22.6059i	0.412006	+	1.08637i	0.967058	+	0.254555i	$0.0819289\pi$
$433$	8.57329	+	22.6059i	0.412006	+	1.08637i	−0.555053	+	0.831815i	$0.687302\pi$
$434$	−7.73752	+	4.06097i	−0.371413	+	0.194933i
$435$	−1.51349	+	3.99075i	−0.0725663	+	0.191342i
$436$	−36.8162	−	9.07437i	−1.76318	−	0.434584i
$437$	−3.30752			−0.158220
$438$	−13.3591	−	3.29271i	−0.638320	−	0.157332i
$439$	−12.1468	+	10.7611i	−0.579735	+	0.513601i	−0.901247	−	0.433305i	$-0.857347\pi$
$439$	−12.1468	+	10.7611i	−0.579735	+	0.513601i	0.321512	+	0.946905i	$0.395809\pi$
$440$	−0.180660	+	0.261732i	−0.00861264	+	0.0124776i
$441$	4.28148	+	1.05529i	0.203880	+	0.0502519i
$442$	−18.5858	−	13.0229i	−0.884037	−	0.619435i
$443$	4.09457	−	1.00922i	0.194539	−	0.0479495i	−0.140842	−	0.990032i	$-0.544981\pi$
$443$	4.09457	−	1.00922i	0.194539	−	0.0479495i	0.335381	+	0.942083i	$0.391135\pi$
$444$	−5.88560	+	15.5191i	−0.279318	+	0.736502i
$445$	1.30386	+	3.43801i	0.0618091	+	0.162977i
$446$	4.48346	−	36.9246i	0.212298	−	1.74843i
$447$	−12.8898	+	11.4194i	−0.609668	+	0.540118i
$448$	−6.09163	−	16.0623i	−0.287802	−	0.758872i
$449$	17.5836	+	25.4743i	0.829823	+	1.20221i	0.977030	+	0.213100i	$0.0683561\pi$
$449$	17.5836	+	25.4743i	0.829823	+	1.20221i	−0.147208	+	0.989106i	$0.547029\pi$
$450$	−8.06984	−	1.98904i	−0.380416	−	0.0937641i
$451$	1.51720	−	0.373957i	0.0714424	−	0.0176090i
$452$	−16.5127	−	14.6290i	−0.776694	−	0.688091i
$453$	−3.84034	−	10.1262i	−0.180435	−	0.475768i
$454$	−2.51937	−	20.7489i	−0.118240	−	0.973792i
$455$	−1.36715	−	5.71963i	−0.0640929	−	0.268140i
$456$	−0.0501810	+	0.413278i	−0.00234994	+	0.0193535i
$457$	−21.6672	+	5.34049i	−1.01355	+	0.249818i	−0.710907	−	0.703286i	$-0.751715\pi$
$457$	−21.6672	+	5.34049i	−1.01355	+	0.249818i	−0.302644	+	0.953104i	$0.597869\pi$
$458$	16.0760	−	3.96239i	0.751184	−	0.185150i
$459$	−1.70919	+	2.47620i	−0.0797784	+	0.115579i
$460$	−8.55367	+	12.3921i	−0.398817	+	0.577786i
$461$	1.50948	+	0.792238i	0.0703037	+	0.0368982i	0.499509	−	0.866309i	$-0.333514\pi$
$461$	1.50948	+	0.792238i	0.0703037	+	0.0368982i	−0.429205	+	0.903207i	$0.641206\pi$
$462$	0.161820	−	1.33271i	0.00752854	−	0.0620031i
$463$	30.0968	+	15.7960i	1.39872	+	0.734104i	0.984386	−	0.176022i	$-0.0563230\pi$
$463$	30.0968	+	15.7960i	1.39872	+	0.734104i	0.414332	+	0.910126i	$0.364015\pi$
$464$	9.79159	−	8.67459i	0.454563	−	0.402708i
$465$	−1.49410	+	2.16458i	−0.0692873	+	0.100380i
$466$	5.50640	+	1.35721i	0.255079	+	0.0628714i
$467$	−7.44331	+	3.90655i	−0.344435	+	0.180773i	−0.628066	−	0.778160i	$-0.716153\pi$
$467$	−7.44331	+	3.90655i	−0.344435	+	0.180773i	0.283631	+	0.958934i	$0.408461\pi$
$468$	8.49768	+	1.09253i	0.392805	+	0.0505022i
$469$	−2.42030	−	1.27027i	−0.111759	−	0.0586558i
$470$	−14.1388	−	12.5259i	−0.652176	−	0.577778i
$471$	2.26118	+	18.6225i	0.104190	+	0.858078i
$472$	−5.72397	+	3.00417i	−0.263467	+	0.138278i
$473$	−0.180003	+	0.474629i	−0.00827655	+	0.0218235i
$474$	12.5761	−	3.09972i	0.577638	−	0.142375i
$475$	−1.57302	+	1.39358i	−0.0721752	+	0.0639417i
$476$	8.61316	+	7.63059i	0.394783	+	0.349748i
$477$	−0.604433	+	1.59376i	−0.0276751	+	0.0729732i
$478$	25.9680	+	13.6291i	1.18775	+	0.623380i
$479$	21.6688	−	19.1968i	0.990071	−	0.877126i	−0.00235162	−	0.999997i	$-0.500749\pi$
$479$	21.6688	−	19.1968i	0.990071	−	0.877126i	0.992423	+	0.122871i	$0.0392101\pi$
$480$	−6.12267	−	5.42421i	−0.279460	−	0.247580i
$481$	20.8264	−	14.1601i	0.949601	−	0.645645i
$482$	−6.91082	+	6.12245i	−0.314779	+	0.278870i
$483$	1.21308	−	9.99057i	0.0551968	−	0.454587i
$484$	−25.7608			−1.17094
$485$	−1.38118			−0.0627160
$486$	0.252156	−	2.07669i	0.0114380	−	0.0942006i
$487$	14.0513	−	20.3568i	0.636724	−	0.922455i	−0.363233	−	0.931698i	$-0.618327\pi$
$487$	14.0513	−	20.3568i	0.636724	−	0.922455i	0.999957	+	0.00924380i	$0.00294243\pi$
$488$	−6.09398			−0.275862
$489$	−6.47270	−	9.37733i	−0.292706	−	0.424057i
$490$	−1.12681	−	9.28010i	−0.0509040	−	0.419232i
$491$	−11.8521	+	31.2513i	−0.534876	+	1.41035i	0.346551	+	0.938031i	$0.387353\pi$
$491$	−11.8521	+	31.2513i	−0.534876	+	1.41035i	−0.881427	+	0.472321i	$0.843416\pi$
$492$	−1.12248	−	9.24445i	−0.0506053	−	0.416772i
$493$	−4.49359	+	11.8486i	−0.202381	+	0.533636i
$494$	2.66659	−	2.96762i	0.119975	−	0.133520i
$495$	−0.143286	−	0.377815i	−0.00644024	−	0.0169815i
$496$	7.13789	−	3.74625i	0.320501	−	0.168212i
$497$	−1.86836	+	15.3873i	−0.0838074	+	0.690216i
$498$	12.1923	+	6.39900i	0.546349	+	0.286746i
$499$	−2.31247	−	19.0449i	−0.103520	−	0.852566i	−0.948283	−	0.317425i	$-0.897182\pi$
$499$	−2.31247	−	19.0449i	−0.103520	−	0.852566i	0.844763	−	0.535141i	$-0.179741\pi$
$500$	2.60451	+	21.4501i	0.116477	+	0.959277i
$501$	−0.349890	−	0.309975i	−0.0156319	−	0.0138487i
$502$	14.3004	+	37.7070i	0.638257	+	1.68294i
$503$	−3.24858	−	4.70638i	−0.144847	−	0.209847i	0.743845	−	0.668353i	$-0.233000\pi$
$503$	−3.24858	−	4.70638i	−0.144847	−	0.209847i	−0.888691	+	0.458506i	$0.848385\pi$
$504$	−1.22993	−	0.303150i	−0.0547854	−	0.0135034i
$505$	8.97443	+	4.71015i	0.399357	+	0.209599i
$506$	5.21576			0.231869
$507$	−9.60837	−	8.75667i	−0.426723	−	0.388897i
$508$	−38.0791			−1.68949
$509$	−7.61798	−	3.99823i	−0.337661	−	0.177218i	0.287367	−	0.957821i	$-0.407220\pi$
$509$	−7.61798	−	3.99823i	−0.337661	−	0.177218i	−0.625028	+	0.780602i	$0.714912\pi$
$510$	6.19322	+	1.52649i	0.274240	+	0.0675942i
$511$	−6.01329	−	8.71175i	−0.266012	−	0.385385i
$512$	10.6238	+	28.0128i	0.469512	+	1.23800i
$513$	−0.395926	−	0.350759i	−0.0174805	−	0.0154864i
$514$	−2.73711	−	22.5421i	−0.120729	−	0.994290i
$515$	0.439976	+	3.62353i	0.0193877	+	0.159672i
$516$	2.67861	+	1.40585i	0.117919	+	0.0618889i
$517$	−0.428239	+	3.52686i	−0.0188339	+	0.155111i
$518$	−20.8236	+	10.9291i	−0.914938	+	0.480196i
$519$	−4.25658	−	11.2237i	−0.186843	−	0.492665i
$520$	−0.668557	−	2.79699i	−0.0293182	−	0.122656i
$521$	10.1273	−	26.7035i	0.443686	−	1.16990i	−0.507600	−	0.861593i	$-0.669467\pi$
$521$	10.1273	−	26.7035i	0.443686	−	1.16990i	0.951286	−	0.308311i	$-0.0997636\pi$
$522$	−1.06200	−	8.74636i	−0.0464825	−	0.382818i
$523$	9.68703	−	25.5426i	0.423584	−	1.11690i	−0.538134	−	0.842859i	$-0.680871\pi$
$523$	9.68703	−	25.5426i	0.423584	−	1.11690i	0.961718	−	0.274041i	$-0.0883602\pi$
$524$	−2.47889	−	20.4155i	−0.108291	−	0.891854i
$525$	−3.63246	−	5.26253i	−0.158534	−	0.229676i
$526$	2.93117			0.127805
$527$	−4.43603	+	6.42670i	−0.193237	+	0.279951i
$528$	−0.149279	+	1.22943i	−0.00649655	+	0.0535039i
$529$	16.0997			0.699986
$530$	3.61354			0.156962
$531$	0.990022	−	8.15356i	0.0429633	−	0.353834i
$532$	−1.51420	+	1.34147i	−0.0656490	+	0.0581600i
$533$	−6.65440	+	12.4650i	−0.288234	+	0.539918i
$534$	−5.68141	−	5.03329i	−0.245859	−	0.217812i
$535$	−15.0458	+	13.3294i	−0.650486	+	0.576281i
$536$	−1.18357	−	0.621184i	−0.0511223	−	0.0268311i
$537$	8.36542	−	22.0578i	0.360995	−	0.951865i
$538$	34.0251	+	30.1436i	1.46693	+	1.29958i
$539$	−1.31607	+	1.16594i	−0.0566872	+	0.0502205i
$540$	−2.33809	+	0.576288i	−0.100615	+	0.0247995i
$541$	15.7915	−	41.6388i	0.678931	−	1.79019i	0.0691753	−	0.997605i	$-0.477963\pi$
$541$	15.7915	−	41.6388i	0.678931	−	1.79019i	0.609756	−	0.792589i	$-0.291268\pi$
$542$	6.08866	−	3.19558i	0.261530	−	0.137262i
$543$	1.46347	+	12.0527i	0.0628034	+	0.517233i
$544$	−18.1784	−	16.1046i	−0.779391	−	0.690480i
$545$	−14.3187	−	7.51503i	−0.613345	−	0.321908i
$546$	7.98590	+	9.14302i	0.341765	+	0.391285i
$547$	−39.1940	+	20.5706i	−1.67581	+	0.879535i	−0.687667	+	0.726026i	$0.741365\pi$
$547$	−39.1940	+	20.5706i	−1.67581	+	0.879535i	−0.988147	+	0.153509i	$0.950943\pi$
$548$	11.4545	+	2.82328i	0.489313	+	0.120605i
$549$	4.39839	−	6.37217i	0.187719	−	0.271958i
$550$	2.48056	−	2.19759i	0.105772	−	0.0937054i
$551$	−1.97259	−	1.03530i	−0.0840354	−	0.0441052i
$552$	0.593213	−	4.88555i	0.0252488	−	0.207943i
$553$	8.82369	+	4.63103i	0.375221	+	0.196931i
$554$	5.64233	−	8.17433i	0.239720	−	0.347294i
$555$	−4.02101	+	5.82543i	−0.170682	+	0.247276i
$556$	8.22709	−	2.02779i	0.348906	−	0.0859977i
$557$	−16.3385	+	4.02708i	−0.692285	+	0.170633i	−0.569734	−	0.821829i	$-0.692954\pi$
$557$	−16.3385	+	4.02708i	−0.692285	+	0.170633i	−0.122551	+	0.992462i	$0.539107\pi$
$558$	0.654444	−	5.38983i	0.0277048	−	0.228170i
$559$	−2.10450	−	4.07928i	−0.0890107	−	0.172535i
$560$	−0.610633	−	5.02902i	−0.0258040	−	0.212515i
$561$	−0.425421	−	1.12174i	−0.0179613	−	0.0473600i
$562$	−23.8907	−	21.1654i	−1.00777	−	0.892807i
$563$	39.2818	−	9.68210i	1.65553	−	0.408052i	0.702684	−	0.711502i	$-0.251985\pi$
$563$	39.2818	−	9.68210i	1.65553	−	0.408052i	0.952847	+	0.303451i	$0.0981388\pi$
$564$	20.5574	+	5.06694i	0.865622	+	0.213357i
$565$	−5.34453	−	7.74289i	−0.224846	−	0.325746i
$566$	23.8238	+	62.8182i	1.00139	+	2.64044i
$567$	1.20470	−	1.06727i	0.0505928	−	0.0448213i
$568$	−0.913657	+	7.52464i	−0.0383362	+	0.315727i
$569$	−3.45454	−	9.10888i	−0.144822	−	0.381864i	0.842903	−	0.538065i	$-0.180844\pi$
$569$	−3.45454	−	9.10888i	−0.144822	−	0.381864i	−0.987725	+	0.156201i	$0.950075\pi$
$570$	−0.397640	+	1.04849i	−0.0166553	+	0.0439164i
$571$	26.5397	−	6.54146i	1.11065	−	0.273752i	0.359018	−	0.933330i	$-0.383112\pi$
$571$	26.5397	−	6.54146i	1.11065	−	0.273752i	0.751635	+	0.659579i	$0.229265\pi$
$572$	−2.28328	+	2.54105i	−0.0954688	+	0.106246i
$573$	−2.03780	−	0.502273i	−0.0851304	−	0.0209828i
$574$	7.49549	−	10.8591i	0.312856	−	0.453250i
$575$	18.5954	−	16.4741i	0.775483	−	0.687018i
$576$	10.3633	+	2.55433i	0.431806	+	0.106431i
$577$	24.0634			1.00177			0.500886	−	0.865514i	$-0.333008\pi$
$577$	24.0634			1.00177			0.500886	+	0.865514i	$0.333008\pi$
$578$	−16.1418	−	3.97860i	−0.671411	−	0.165488i
$579$	4.80779	−	12.6771i	0.199805	−	0.526843i
$580$	−8.98029	+	4.71322i	−0.372886	+	0.195706i
$581$	3.75660	+	9.90533i	0.155850	+	0.410942i
$582$	2.52457	−	1.32499i	0.104647	−	0.0549228i
$583$	−0.386084	−	0.559339i	−0.0159900	−	0.0231655i
$584$	−2.94059	−	4.26018i	−0.121683	−	0.176288i
$585$	3.40721	+	1.31968i	0.140871	+	0.0545621i
$586$	13.8812	−	20.1103i	0.573426	−	0.830751i
$587$	13.6256			0.562388			0.281194	−	0.959651i	$-0.409270\pi$
$587$	13.6256			0.562388			0.281194	+	0.959651i	$0.409270\pi$
$588$	5.95234	+	8.62345i	0.245470	+	0.355625i
$589$	−1.02758	−	0.910358i	−0.0423408	−	0.0375107i
$590$	−16.9063	+	4.16703i	−0.696021	+	0.171554i
$591$	−12.2318	+	6.41975i	−0.503150	+	0.264073i
$592$	19.2099	−	10.0821i	0.789520	−	0.414372i
$593$	35.2729	−	8.69399i	1.44848	−	0.357019i	0.564849	−	0.825195i	$-0.308935\pi$
$593$	35.2729	−	8.69399i	1.44848	−	0.357019i	0.883636	+	0.468175i	$0.155088\pi$
$594$	0.624351	+	0.553127i	0.0256174	+	0.0226951i
$595$	2.78774	+	4.03875i	0.114286	+	0.165572i
$596$	−40.9202			−1.67616
$597$	2.94913	−	4.27255i	0.120700	−	0.174864i
$598$	−31.5230	+	35.0817i	−1.28907	+	1.43460i
$599$	−17.4093	−	25.2218i	−0.711325	−	1.03053i	−0.997381	−	0.0723199i	$-0.976960\pi$
$599$	−17.4093	−	25.2218i	−0.711325	−	1.03053i	0.286056	−	0.958213i	$-0.407656\pi$
$600$	−1.77633	−	2.57346i	−0.0725184	−	0.105061i
$601$	16.5051	−	8.66256i	0.673258	−	0.353353i	−0.0932001	−	0.995647i	$-0.529710\pi$
$601$	16.5051	−	8.66256i	0.673258	−	0.353353i	0.766458	+	0.642294i	$0.222017\pi$
$602$	1.51996	+	4.00780i	0.0619488	+	0.163346i
$603$	1.50379	−	0.789252i	0.0612392	−	0.0321408i
$604$	9.12555	−	24.0621i	0.371313	−	0.979072i
$605$	−10.6670	−	2.62918i	−0.433676	−	0.106891i
$606$	−20.9224			−0.849913
$607$	−42.9405	−	10.5839i	−1.74290	−	0.429586i	−0.765924	−	0.642931i	$-0.777718\pi$
$607$	−42.9405	−	10.5839i	−1.74290	−	0.429586i	−0.976977	+	0.213345i	$0.931564\pi$
$608$	3.19578	−	2.83121i	0.129606	−	0.114821i
$609$	3.85066	−	5.57864i	0.156037	−	0.226058i
$610$	−15.9375	−	3.92823i	−0.645289	−	0.159049i
$611$	−21.1338	−	24.1960i	−0.854983	−	0.978866i
$612$	−6.94186	+	1.71101i	−0.280608	+	0.0691636i
$613$	14.0896	−	37.1512i	0.569073	−	1.50052i	−0.273463	−	0.961883i	$-0.588169\pi$
$613$	14.0896	−	37.1512i	0.569073	−	1.50052i	0.842536	−	0.538640i	$-0.181062\pi$
$614$	−13.4073	−	35.3522i	−0.541075	−	1.42670i
$615$	0.478706	−	3.94250i	0.0193033	−	0.158977i
$616$	0.378064	−	0.334935i	0.0152326	−	0.0134949i
$617$	6.08668	+	16.0493i	0.245041	+	0.646119i	0.999953	−	0.00970672i	$-0.00308979\pi$
$617$	6.08668	+	16.0493i	0.245041	+	0.646119i	−0.754912	+	0.655826i	$0.772321\pi$
$618$	−4.28034	−	6.20115i	−0.172181	−	0.249447i
$619$	−6.83753	−	1.68530i	−0.274823	−	0.0677379i	0.0994952	−	0.995038i	$-0.468277\pi$
$619$	−6.83753	−	1.68530i	−0.274823	−	0.0677379i	−0.374319	+	0.927300i	$0.622123\pi$
$620$	−6.06826	+	1.49569i	−0.243707	+	0.0600685i
$621$	4.68042	+	4.14649i	0.187819	+	0.166393i
$622$	16.1890	+	42.6870i	0.649121	+	1.71159i
$623$	−0.703897	−	5.79711i	−0.0282010	−	0.232256i
$624$	−7.36702	−	8.43446i	−0.294917	−	0.337649i
$625$	1.28373	−	10.5724i	0.0513490	−	0.422897i
$626$	1.18942	−	0.293165i	0.0475386	−	0.0117172i
$627$	0.204781	−	0.0504739i	0.00817816	−	0.00201573i
$628$	−25.3222	+	36.6856i	−1.01047	+	1.46391i
$629$	−11.9385	+	17.2959i	−0.476018	+	0.689632i
$630$	−3.02119	−	1.58564i	−0.120367	−	0.0631736i
$631$	−1.65769	+	13.6523i	−0.0659916	+	0.543490i	0.921795	+	0.387677i	$0.126723\pi$
$631$	−1.65769	+	13.6523i	−0.0659916	+	0.543490i	−0.987787	+	0.155812i	$0.950201\pi$
$632$	4.31492	+	2.26465i	0.171638	+	0.0900828i
$633$	−0.921286	+	0.816188i	−0.0366178	+	0.0324406i
$634$	−15.0311	+	21.7763i	−0.596961	+	0.864847i
$635$	−15.7678	−	3.88641i	−0.625725	−	0.154227i
$636$	−3.58640	+	1.88229i	−0.142210	+	0.0746376i
$637$	0.111865	−	15.8987i	0.00443225	−	0.629930i
$638$	3.11066	+	1.63260i	0.123152	+	0.0646353i
$639$	−7.20871	−	6.38636i	−0.285172	−	0.252640i
$640$	−0.755510	−	6.22219i	−0.0298642	−	0.245954i
$641$	5.20690	−	2.73279i	0.205660	−	0.107939i	−0.358749	−	0.933434i	$-0.616796\pi$
$641$	5.20690	−	2.73279i	0.205660	−	0.107939i	0.564409	+	0.825495i	$0.309104\pi$
$642$	14.7141	−	38.7978i	0.580717	−	1.53123i
$643$	−9.90929	+	2.44242i	−0.390784	+	0.0963196i	−0.429812	−	0.902918i	$-0.641420\pi$
$643$	−9.90929	+	2.44242i	−0.390784	+	0.0963196i	0.0390277	+	0.999238i	$0.487574\pi$
$644$	17.9001	−	15.8581i	0.705362	−	0.624896i
$645$	0.965678	+	0.855516i	0.0380235	+	0.0336859i
$646$	−1.18060	+	3.11300i	−0.0464502	+	0.122479i
$647$	−25.8157	−	13.5491i	−1.01492	−	0.532671i	−0.126628	−	0.991950i	$-0.540415\pi$
$647$	−25.8157	−	13.5491i	−1.01492	−	0.532671i	−0.888292	+	0.459279i	$0.848108\pi$
$648$	0.589119	−	0.521914i	0.0231428	−	0.0205027i
$649$	2.45134	+	2.17170i	0.0962236	+	0.0852467i
$650$	−0.210846	+	29.9663i	−0.00827005	+	1.17537i
$651$	3.12668	−	2.76999i	0.122544	−	0.108565i
$652$	3.26359	−	26.8781i	0.127812	−	1.05263i
$653$	4.69081			0.183566			0.0917828	−	0.995779i	$-0.470743\pi$
$653$	4.69081			0.183566			0.0917828	+	0.995779i	$0.470743\pi$
$654$	33.3816			1.30532
$655$	1.05718	−	8.70663i	0.0413073	−	0.340196i
$656$	−6.91461	+	10.0175i	−0.269970	+	0.391120i
$657$	6.57707			0.256596
$658$	17.0418	+	24.6893i	0.664359	+	0.962491i
$659$	1.98518	+	16.3495i	0.0773317	+	0.636884i	0.978913	+	0.204275i	$0.0654838\pi$
$659$	1.98518	+	16.3495i	0.0773317	+	0.636884i	−0.901582	+	0.432609i	$0.857593\pi$
$660$	0.340481	−	0.897776i	0.0132532	−	0.0349459i
$661$	6.05519	+	49.8690i	0.235520	+	1.93968i	0.329616	+	0.944115i	$0.393081\pi$
$661$	6.05519	+	49.8690i	0.235520	+	1.93968i	−0.0940963	+	0.995563i	$0.529996\pi$
$662$	−10.1867	+	26.8602i	−0.395918	+	1.04395i
$663$	10.1161	+	3.91817i	0.392877	+	0.152169i
$664$	1.83703	+	4.84386i	0.0712908	+	0.187978i
$665$	−0.763913	+	0.400932i	−0.0296233	+	0.0155475i
$666$	1.76127	−	14.5054i	0.0682480	−	0.562073i
$667$	23.3189	+	12.2387i	0.902913	+	0.473885i
$668$	−0.133888	−	1.10267i	−0.00518028	−	0.0426634i
$669$	2.14320	+	17.6509i	0.0828610	+	0.682422i
$670$	−2.69494	−	2.38751i	−0.104115	−	0.0922374i
$671$	1.09477	+	2.88666i	0.0422630	+	0.111438i
$672$	7.37977	+	10.6914i	0.284681	+	0.412431i
$673$	−16.1355	−	3.97705i	−0.621978	−	0.153304i	−0.0842811	−	0.996442i	$-0.526859\pi$
$673$	−16.1355	−	3.97705i	−0.621978	−	0.153304i	−0.537697	+	0.843138i	$0.680706\pi$
$674$	−22.4819	−	11.7994i	−0.865972	−	0.454497i
$675$	3.97303			0.152922
$676$	−3.29162	−	30.7151i	−0.126601	−	1.18135i
$677$	−13.7527			−0.528561			−0.264280	−	0.964446i	$-0.585134\pi$
$677$	−13.7527			−0.528561			−0.264280	+	0.964446i	$0.585134\pi$
$678$	17.1969	+	9.02562i	0.660442	+	0.346627i
$679$	2.12983	+	0.524956i	0.0817353	+	0.0201460i
$680$	1.36325	+	1.97501i	0.0522783	+	0.0757382i
$681$	3.54297	+	9.34203i	0.135767	+	0.357988i
$682$	1.62044	+	1.43558i	0.0620497	+	0.0549712i
$683$	−0.00513211	−	0.0422668i	−0.000196375	−	0.00161729i	0.992610	−	0.121345i	$-0.0387208\pi$
$683$	−0.00513211	−	0.0422668i	−0.000196375	−	0.00161729i	−0.992807	+	0.119728i	$0.961798\pi$
$684$	−0.151504	−	1.24775i	−0.00579289	−	0.0477087i
$685$	4.45493	+	2.33813i	0.170214	+	0.0893354i
$686$	−4.63044	+	38.1351i	−0.176791	+	1.45601i
$687$	−7.00814	+	3.67816i	−0.267377	+	0.140330i
$688$	−1.40216	−	3.69720i	−0.0534570	−	0.140955i
$689$	6.09558	+	0.783696i	0.232223	+	0.0298564i
$690$	4.70068	−	12.3947i	0.178952	−	0.471857i
$691$	0.573941	+	4.72683i	0.0218337	+	0.179817i	0.999546	−	0.0301328i	$-0.00959301\pi$
$691$	0.573941	+	4.72683i	0.0218337	+	0.179817i	−0.977712	+	0.209950i	$0.932670\pi$
$692$	10.1146	−	26.6701i	0.384500	−	1.01384i
$693$	0.0773538	+	0.637066i	0.00293843	+	0.0242001i
$694$	27.6177	+	40.0111i	1.04835	+	1.51880i
$695$	3.61363			0.137073
$696$	1.88303	−	2.72804i	0.0713762	−	0.103406i
$697$	1.42129	−	11.7054i	0.0538353	−	0.443373i
$698$	39.5691			1.49771
$699$	−2.71097			−0.102538
$700$	1.83152	−	15.0839i	0.0692249	−	0.570118i
$701$	7.00165	−	6.20292i	0.264449	−	0.234281i	−0.520470	−	0.853880i	$-0.674243\pi$
$701$	7.00165	−	6.20292i	0.264449	−	0.234281i	0.784919	+	0.619599i	$0.212705\pi$
$702$	−7.49383	+	0.856457i	−0.282836	+	0.0323249i
$703$	−2.76548	−	2.45000i	−0.104302	−	0.0924036i
$704$	−3.18556	+	2.82216i	−0.120060	+	0.106364i
$705$	7.99526	+	4.19624i	0.301119	+	0.158039i
$706$	15.9704	−	42.1104i	0.601053	−	1.58485i
$707$	−12.0487	−	10.6742i	−0.453138	−	0.401446i
$708$	14.6087	−	12.9422i	0.549029	−	0.486398i
$709$	−36.3483	+	8.95905i	−1.36509	+	0.336464i	−0.852750	−	0.522319i	$-0.825067\pi$
$709$	−36.3483	+	8.95905i	−1.36509	+	0.336464i	−0.512339	+	0.858784i	$0.671221\pi$
$710$	−7.23992	+	19.0901i	−0.271709	+	0.716438i
$711$	−5.48237	+	2.87737i	−0.205605	+	0.107910i
$712$	−0.344217	−	2.83488i	−0.0129001	−	0.106242i
$713$	12.1475	+	10.7618i	0.454928	+	0.403031i
$714$	−8.97001	−	4.70782i	−0.335694	−	0.176186i
$715$	−1.20480	+	0.819161i	−0.0450571	+	0.0306349i
$716$	49.6362	−	26.0511i	1.85499	−	0.973576i
$717$	−13.6118	−	3.35501i	−0.508342	−	0.125295i
$718$	−3.78586	+	5.48476i	−0.141287	+	0.204689i
$719$	−16.6567	+	14.7566i	−0.621191	+	0.550328i	−0.913934	−	0.405864i	$-0.866971\pi$
$719$	−16.6567	+	14.7566i	−0.621191	+	0.550328i	0.292742	+	0.956191i	$0.405432\pi$
$720$	2.78706	+	1.46276i	0.103868	+	0.0545139i
$721$	0.698766	−	5.75485i	0.0260234	−	0.214322i
$722$	34.6759	+	18.1993i	1.29050	+	0.677309i
$723$	2.50714	−	3.63223i	0.0932417	−	0.135084i
$724$	−16.3889	+	23.7435i	−0.609090	+	0.882419i
$725$	16.2469	−	4.00450i	0.603394	−	0.148723i
$726$	22.0198	−	5.42739i	0.817231	−	0.201429i
$727$	−4.29250	+	35.3519i	−0.159200	+	1.31113i	0.665857	+	0.746079i	$0.268066\pi$
$727$	−4.29250	+	35.3519i	−0.159200	+	1.31113i	−0.825057	+	0.565050i	$0.808857\pi$
$728$	−0.0321351	+	4.56717i	−0.00119101	+	0.169271i
$729$	0.120537	+	0.992709i	0.00446432	+	0.0367670i
$730$	−4.94432	−	13.0371i	−0.182997	−	0.482525i
$731$	2.86712	+	2.54005i	0.106044	+	0.0939471i
$732$	17.8640	−	4.40307i	0.660272	−	0.162742i
$733$	37.8198	+	9.32174i	1.39691	+	0.344306i	0.864692	−	0.502303i	$-0.167514\pi$
$733$	37.8198	+	9.32174i	1.39691	+	0.344306i	0.532214	+	0.846610i	$0.321360\pi$
$734$	−20.4411	−	29.6140i	−0.754493	−	1.09307i
$735$	1.58462	+	4.17830i	0.0584496	+	0.154119i
$736$	−37.7788	+	33.4691i	−1.39254	+	1.23369i
$737$	−0.0816246	+	0.672239i	−0.00300668	+	0.0247622i
$738$	2.90713	+	7.66548i	0.107013	+	0.282170i
$739$	−13.7646	+	36.2944i	−0.506341	+	1.33511i	0.401525	+	0.915848i	$0.368480\pi$
$739$	−13.7646	+	36.2944i	−0.506341	+	1.33511i	−0.907865	+	0.419262i	$0.862289\pi$
$740$	−16.3312	+	4.02529i	−0.600348	+	0.147972i
$741$	−0.898161	+	1.68243i	−0.0329948	+	0.0618056i
$742$	−5.57222	−	1.37343i	−0.204563	−	0.0504202i
$743$	11.5708	−	16.7632i	0.424491	−	0.614982i	−0.551136	−	0.834415i	$-0.685806\pi$
$743$	11.5708	−	16.7632i	0.424491	−	0.614982i	0.975627	+	0.219434i	$0.0704209\pi$
$744$	1.52899	−	1.35457i	0.0560556	−	0.0496610i
$745$	−16.9442	−	4.17638i	−0.620788	−	0.153011i
$746$	16.0799			0.588727
$747$	−6.39089	−	1.57521i	−0.233830	−	0.0576340i
$748$	1.01090	−	2.66552i	0.0369621	−	0.0974611i
$749$	28.2674	−	14.8359i	1.03287	−	0.542092i
$750$	−6.74549	−	17.7864i	−0.246310	−	0.649467i
$751$	−18.8075	+	9.87093i	−0.686295	+	0.360195i	−0.771554	−	0.636164i	$-0.780520\pi$
$751$	−18.8075	+	9.87093i	−0.686295	+	0.360195i	0.0852595	+	0.996359i	$0.472828\pi$
$752$	−15.7211	−	22.7760i	−0.573291	−	0.830555i
$753$	−10.9509	−	15.8651i	−0.399073	−	0.578158i
$754$	−29.7813	+	11.0555i	−1.08457	+	0.402617i
$755$	6.23452	−	9.03226i	0.226897	−	0.328717i
$756$	3.82446			0.139094
$757$	23.5408	+	34.1048i	0.855607	+	1.23956i	0.969260	+	0.246040i	$0.0791294\pi$
$757$	23.5408	+	34.1048i	0.855607	+	1.23956i	−0.113653	+	0.993520i	$0.536255\pi$
$758$	−25.8614	−	22.9112i	−0.939329	−	0.832172i
$759$	−2.42081	+	0.596676i	−0.0878698	+	0.0216580i
$760$	−0.373565	+	0.196062i	−0.0135506	+	0.00711193i
$761$	−3.29833	+	1.73110i	−0.119564	+	0.0627522i	−0.523445	−	0.852059i	$-0.675353\pi$
$761$	−3.29833	+	1.73110i	−0.119564	+	0.0627522i	0.403881	+	0.914812i	$0.367661\pi$
$762$	32.5493	−	8.02267i	1.17914	−	0.290631i
$763$	19.2237	+	17.0307i	0.695944	+	0.616553i
$764$	−2.83306	−	4.10439i	−0.102496	−	0.148492i
$765$	−3.04911			−0.110241
$766$	6.04976	−	8.76459i	0.218587	−	0.316677i
$767$	−29.4225	+	3.36264i	−1.06238	+	0.121418i
$768$	−4.77643	−	6.91986i	−0.172355	−	0.249699i
$769$	1.75395	+	2.54103i	0.0632490	+	0.0916320i	0.853332	−	0.521368i	$-0.174578\pi$
$769$	1.75395	+	2.54103i	0.0632490	+	0.0916320i	−0.790083	+	0.613000i	$0.789963\pi$
$770$	1.20464	−	0.632246i	0.0434124	−	0.0227846i
$771$	3.84917	+	10.1494i	0.138624	+	0.365523i
$772$	28.5270	−	14.9722i	1.02671	−	0.538859i
$773$	−17.5818	+	46.3594i	−0.632373	+	1.66743i	0.107103	+	0.994248i	$0.465842\pi$
$773$	−17.5818	+	46.3594i	−0.632373	+	1.66743i	−0.739476	+	0.673182i	$0.764927\pi$
$774$	−2.58582	−	0.637347i	−0.0929453	−	0.0229090i
$775$	10.3116			0.370402
$776$	1.04152	+	0.256712i	0.0373884	+	0.00921541i
$777$	8.41468	−	7.45475i	0.301875	−	0.267438i
$778$	3.64423	−	5.27958i	0.130652	−	0.189282i
$779$	2.01270	+	0.496086i	0.0721124	+	0.0177741i
$780$	3.98072	+	7.71608i	0.142533	+	0.276280i
$781$	3.72849	−	0.918990i	0.133416	−	0.0328841i
$782$	13.9565	−	36.8001i	0.499082	−	1.31597i
$783$	1.49348	+	3.93799i	0.0533727	+	0.140732i
$784$	1.65090	−	13.5964i	0.0589606	−	0.485584i
$785$	−14.2296	+	12.6063i	−0.507877	+	0.449939i
$786$	6.42013	+	16.9285i	0.228998	+	0.603819i
$787$	−0.402552	−	0.583198i	−0.0143494	−	0.0207888i	0.815744	−	0.578414i	$-0.196328\pi$
$787$	−0.402552	−	0.583198i	−0.0143494	−	0.0207888i	−0.830093	+	0.557625i	$0.811713\pi$
$788$	−31.8718	−	7.85568i	−1.13538	−	0.279847i
$789$	−1.36045	+	0.335322i	−0.0484334	+	0.0119378i
$790$	9.82492	+	8.70412i	0.349555	+	0.309679i
$791$	5.29857	+	13.9712i	0.188396	+	0.496758i
$792$	0.0378272	+	0.311535i	0.00134413	+	0.0110699i
$793$	−26.0325	−	10.0829i	−0.924441	−	0.358054i
$794$	2.24449	−	18.4850i	0.0796538	−	0.656008i
$795$	−1.67717	+	0.413384i	−0.0594829	+	0.0146612i
$796$	11.9778	−	2.95227i	0.424543	−	0.104640i
$797$	−27.8604	+	40.3627i	−0.986864	+	1.42972i	−0.0856607	+	0.996324i	$0.527300\pi$
$797$	−27.8604	+	40.3627i	−0.986864	+	1.42972i	−0.901204	+	0.433396i	$0.857315\pi$
$798$	1.01168	−	1.46568i	0.0358133	−	0.0518845i
$799$	23.7382	+	12.4587i	0.839795	+	0.440759i
$800$	−3.86548	+	31.8351i	−0.136665	+	1.12554i
$801$	3.21274	+	1.68617i	0.113516	+	0.0595780i
$802$	42.7491	−	37.8724i	1.50952	−	1.33732i
$803$	−1.48974	+	2.15826i	−0.0525718	+	0.0761634i
$804$	3.91835	+	0.965786i	0.138189	+	0.0340607i
$805$	9.03057	−	4.73961i	0.318286	−	0.167049i
$806$	−19.4494	+	2.22284i	−0.685077	+	0.0782962i
$807$	−19.2406	−	10.0982i	−0.677300	−	0.355475i
$808$	−5.89201	−	5.21986i	−0.207280	−	0.183634i
$809$	−4.52553	−	37.2711i	−0.159109	−	1.31038i	−0.825339	−	0.564637i	$-0.809016\pi$
$809$	−4.52553	−	37.2711i	−0.159109	−	1.31038i	0.666230	−	0.745746i	$-0.267907\pi$
$810$	1.87714	−	0.985199i	0.0659560	−	0.0346164i
$811$	9.74871	−	25.7052i	0.342323	−	0.902633i	−0.647721	−	0.761878i	$-0.724278\pi$
$811$	9.74871	−	25.7052i	0.342323	−	0.902633i	0.990044	−	0.140755i	$-0.0449530\pi$
$812$	15.6394	−	3.85476i	0.548834	−	0.135275i
$813$	−2.46038	+	2.17971i	−0.0862894	+	0.0764457i
$814$	4.36100	+	3.86351i	0.152853	+	0.135416i
$815$	4.09460	−	10.7966i	0.143428	−	0.378188i
$816$	8.27486	+	4.34298i	0.289678	+	0.152035i
$817$	−0.504044	+	0.446544i	−0.0176343	+	0.0156226i
$818$	−40.9192	−	36.2513i	−1.43071	−	1.26750i
$819$	−4.75247	−	3.33001i	−0.166065	−	0.116360i
$820$	7.06377	−	6.25795i	0.246678	−	0.218537i
$821$	−1.77956	+	14.6560i	−0.0621070	+	0.511497i	0.928146	+	0.372216i	$0.121402\pi$
$821$	−1.77956	+	14.6560i	−0.0621070	+	0.511497i	−0.990253	+	0.139280i	$0.955521\pi$
$822$	−10.3859			−0.362251
$823$	15.5370			0.541585			0.270793	−	0.962638i	$-0.412714\pi$
$823$	15.5370			0.541585			0.270793	+	0.962638i	$0.412714\pi$
$824$	0.341708	−	2.81421i	0.0119039	−	0.0980378i
$825$	−0.899912	+	1.30375i	−0.0313309	+	0.0453907i
$826$	27.6540			0.962205
$827$	−12.6446	−	18.3188i	−0.439695	−	0.637009i	0.539005	−	0.842303i	$-0.318800\pi$
$827$	−12.6446	−	18.3188i	−0.439695	−	0.637009i	−0.978700	+	0.205294i	$0.934185\pi$
$828$	1.79100	+	14.7502i	0.0622414	+	0.512604i
$829$	−17.5392	+	46.2471i	−0.609161	+	1.60623i	0.174235	+	0.984704i	$0.444255\pi$
$829$	−17.5392	+	46.2471i	−0.609161	+	1.60623i	−0.783396	+	0.621523i	$0.786514\pi$
$830$	1.68196	+	13.8522i	0.0583818	+	0.480818i
$831$	−1.68366	+	4.43945i	−0.0584056	+	0.154003i
$832$	0.270770	−	38.4829i	0.00938724	−	1.33415i
$833$	4.70478	+	12.4055i	0.163011	+	0.429825i
$834$	−6.60513	+	3.46664i	−0.228717	+	0.120040i
$835$	0.0570995	−	0.470257i	0.00197601	−	0.0162739i
$836$	0.443764	+	0.232905i	0.0153479	+	0.00805519i
$837$	0.312840	+	2.57647i	0.0108133	+	0.0890558i
$838$	5.99938	+	49.4093i	0.207245	+	1.70682i
$839$	−20.5216	−	18.1805i	−0.708484	−	0.627662i	0.229917	−	0.973210i	$-0.426155\pi$
$839$	−20.5216	−	18.1805i	−0.708484	−	0.627662i	−0.938401	+	0.345548i	$0.887693\pi$
$840$	−0.455209	−	1.20029i	−0.0157062	−	0.0414139i
$841$	−6.39740	−	9.26824i	−0.220600	−	0.319594i
$842$	−16.8175	−	4.14513i	−0.579568	−	0.142851i
$843$	13.5098	+	7.09048i	0.465302	+	0.244209i
$844$	−2.92473			−0.100673
$845$	1.77184	−	13.0545i	0.0609532	−	0.449087i
$846$	−18.6396			−0.640842
$847$	15.4497	+	8.10860i	0.530856	+	0.278615i
$848$	5.14039	+	1.26699i	0.176522	+	0.0435087i
$849$	−18.2437	−	26.4306i	−0.626123	−	0.907096i
$850$	−8.86768	−	23.3822i	−0.304159	−	0.802001i
$851$	32.6920	+	28.9626i	1.12067	+	0.992826i
$852$	−2.75846	−	22.7180i	−0.0945034	−	0.778305i
$853$	−0.388387	−	3.19866i	−0.0132981	−	0.109520i	0.984548	−	0.175113i	$-0.0560291\pi$
$853$	−0.388387	−	3.19866i	−0.0132981	−	0.109520i	−0.997846	+	0.0655932i	$0.979106\pi$
$854$	23.0832	+	12.1150i	0.789890	+	0.414566i
$855$	0.0646121	−	0.532129i	0.00220969	−	0.0181984i
$856$	13.8232	−	7.25499i	0.472468	−	0.247970i
$857$	15.8100	+	41.6874i	0.540058	+	1.42401i	0.876082	+	0.482162i	$0.160148\pi$
$857$	15.8100	+	41.6874i	0.540058	+	1.42401i	−0.336025	+	0.941853i	$0.609083\pi$
$858$	1.41635	−	2.65309i	0.0483533	−	0.0905750i
$859$	−17.6872	+	46.6374i	−0.603480	+	1.59125i	0.189421	+	0.981896i	$0.439339\pi$
$859$	−17.6872	+	46.6374i	−0.603480	+	1.59125i	−0.792901	+	0.609350i	$0.791430\pi$
$860$	0.369523	+	3.04330i	0.0126006	+	0.103776i
$861$	−2.23664	+	5.89755i	−0.0762246	+	0.200988i
$862$	7.10472	+	58.5126i	0.241988	+	1.99295i
$863$	−17.8076	−	25.7987i	−0.606177	−	0.878200i	0.392967	−	0.919552i	$-0.371449\pi$
$863$	−17.8076	−	25.7987i	−0.606177	−	0.878200i	−0.999145	+	0.0413529i	$0.986833\pi$
$864$	−8.07166			−0.274604
$865$	6.91025	−	10.0112i	0.234956	−	0.340392i
$866$	6.09638	−	50.2082i	0.207163	−	1.70614i
$867$	7.94711			0.269898
$868$	9.92598			0.336910
$869$	0.297578	−	2.45078i	0.0100946	−	0.0831369i
$870$	6.68318	−	5.92078i	0.226581	−	0.200733i
$871$	−4.02822	−	4.61189i	−0.136491	−	0.156268i
$872$	9.40069	+	8.32828i	0.318347	+	0.282031i
$873$	−1.02016	+	0.903782i	−0.0345271	+	0.0305884i
$874$	6.12659	+	3.21548i	0.207235	+	0.108765i
$875$	5.18973	−	13.6842i	0.175445	−	0.462611i
$876$	11.6982	+	10.3637i	0.395245	+	0.350157i
$877$	1.98878	−	1.76191i	0.0671565	−	0.0594955i	−0.628877	−	0.777505i	$-0.716485\pi$
$877$	1.98878	−	1.76191i	0.0671565	−	0.0594955i	0.696033	+	0.718009i	$0.254947\pi$
$878$	32.9615	−	8.12428i	1.11240	−	0.274181i
$879$	−4.14212	+	10.9219i	−0.139710	+	0.368386i
$880$	−1.11129	+	0.583249i	−0.0374615	+	0.0196613i
$881$	2.04252	+	16.8217i	0.0688142	+	0.566736i	0.985813	+	0.167846i	$0.0536813\pi$
$881$	2.04252	+	16.8217i	0.0688142	+	0.566736i	−0.916999	+	0.398890i	$0.869396\pi$
$882$	−6.90477	−	6.11709i	−0.232496	−	0.205973i
$883$	−34.0056	−	17.8475i	−1.14438	−	0.600617i	−0.217532	−	0.976053i	$-0.569801\pi$
$883$	−34.0056	−	17.8475i	−1.14438	−	0.600617i	−0.926848	+	0.375436i	$0.877493\pi$
$884$	11.8189	+	22.9093i	0.397512	+	0.770522i
$885$	7.37008	−	3.86811i	0.247742	−	0.130025i
$886$	−8.56561	−	2.11123i	−0.287767	−	0.0709283i
$887$	26.0446	−	37.7321i	0.874491	−	1.26692i	−0.0881413	−	0.996108i	$-0.528093\pi$
$887$	26.0446	−	37.7321i	0.874491	−	1.26692i	0.962632	−	0.270811i	$-0.0872919\pi$
$888$	4.11491	−	3.64549i	0.138087	−	0.122335i
$889$	22.8374	+	11.9860i	0.765942	+	0.401997i
$890$	0.927164	−	7.63589i	0.0310786	−	0.255955i
$891$	−0.353059	−	0.185300i	−0.0118279	−	0.00620778i
$892$	−24.0011	+	34.7715i	−0.803615	+	1.16424i
$893$	−2.67732	+	3.87876i	−0.0895929	+	0.129798i
$894$	34.9778	−	8.62125i	1.16983	−	0.288338i
$895$	23.2122	−	5.72129i	0.775898	−	0.191242i
$896$	−1.19989	+	9.88201i	−0.0400856	+	0.330135i
$897$	10.6176	−	19.8888i	0.354511	−	0.664066i
$898$	−7.80513	−	64.2810i	−0.260461	−	2.14509i
$899$	3.87617	+	10.2206i	0.129278	+	0.340877i
$900$	7.06656	+	6.26043i	0.235552	+	0.208681i
$901$	−4.97955	+	1.22735i	−0.165893	+	0.0408889i
$902$	−3.17391	−	0.782298i	−0.105680	−	0.0260477i
$903$	−1.16395	−	1.68627i	−0.0387338	−	0.0561156i
$904$	2.59109	+	6.83213i	0.0861782	+	0.227233i
$905$	−9.20961	+	8.15901i	−0.306138	+	0.271215i
$906$	−2.73083	+	22.4904i	−0.0907258	+	0.747194i
$907$	−16.0918	−	42.4306i	−0.534320	−	1.40889i	−0.881989	−	0.471269i	$-0.843796\pi$
$907$	−16.0918	−	42.4306i	−0.534320	−	1.40889i	0.347669	−	0.937617i	$-0.386973\pi$
$908$	−8.41891	+	22.1988i	−0.279391	+	0.736694i
$909$	9.71077	−	2.39349i	0.322086	−	0.0793871i
$910$	−3.02808	+	11.9237i	−0.100380	+	0.395268i
$911$	31.5765	+	7.78291i	1.04618	+	0.257859i	0.724704	−	0.689060i	$-0.241976\pi$
$911$	31.5765	+	7.78291i	1.04618	+	0.257859i	0.321472	+	0.946919i	$0.395822\pi$
$912$	−0.933282	+	1.35209i	−0.0309041	+	0.0447723i
$913$	1.96448	−	1.74037i	0.0650146	−	0.0575979i
$914$	45.3266	+	11.1720i	1.49927	+	0.369537i
$915$	7.84650			0.259397
$916$	−18.2607	−	4.50086i	−0.603351	−	0.148713i
$917$	−4.93941	+	13.0242i	−0.163114	+	0.430096i
$918$	5.57328	−	2.92508i	0.183946	−	0.0965421i
$919$	−1.11040	−	2.92787i	−0.0366286	−	0.0965817i	0.915454	−	0.402422i	$-0.131832\pi$
$919$	−1.11040	−	2.92787i	−0.0366286	−	0.0965817i	−0.952083	+	0.305841i	$0.901062\pi$
$920$	4.41609	−	2.31774i	0.145594	−	0.0764137i
$921$	10.2670	+	14.8743i	0.338310	+	0.490126i
$922$	−2.02586	−	2.93497i	−0.0667182	−	0.0966580i
$923$	−16.3530	+	30.6324i	−0.538266	+	1.00828i
$924$	−0.866261	+	1.25500i	−0.0284979	+	0.0412863i
$925$	27.7510			0.912448
$926$	−40.3926	−	58.5188i	−1.32738	−	1.92305i
$927$	2.69605	+	2.38850i	0.0885500	+	0.0784485i
$928$	−33.0074	+	8.13560i	−1.08352	+	0.267064i
$929$	19.9406	−	10.4656i	0.654229	−	0.343366i	−0.104733	−	0.994500i	$-0.533399\pi$
$929$	19.9406	−	10.4656i	0.654229	−	0.343366i	0.758963	+	0.651134i	$0.225707\pi$
$930$	4.87191	−	2.55698i	0.159756	−	0.0838466i
$931$	−2.26469	+	0.558197i	−0.0742224	+	0.0182942i
$932$	−4.82182	−	4.27176i	−0.157944	−	0.139926i
$933$	−12.3972	−	17.9605i	−0.405866	−	0.587999i
$934$	17.5853			0.575408
$935$	0.690640	−	1.00056i	0.0225863	−	0.0327220i
$936$	−2.32403	−	1.62843i	−0.0759635	−	0.0532268i
$937$	−27.0144	−	39.1371i	−0.882522	−	1.27855i	−0.959554	−	0.281525i	$-0.909160\pi$
$937$	−27.0144	−	39.1371i	−0.882522	−	1.27855i	0.0770321	−	0.997029i	$-0.475456\pi$
$938$	3.24826	+	4.70592i	0.106060	+	0.153654i
$939$	−0.518511	+	0.272135i	−0.0169210	+	0.00888080i
$940$	7.60850	+	20.0620i	0.248162	+	0.654349i
$941$	−16.8957	+	8.86756i	−0.550785	+	0.289074i	−0.717067	−	0.697004i	$-0.754516\pi$
$941$	−16.8957	+	8.86756i	−0.550785	+	0.289074i	0.166282	+	0.986078i	$0.446824\pi$
$942$	13.9159	−	36.6931i	0.453404	−	1.19553i
$943$	−23.7930	−	5.86446i	−0.774808	−	0.190973i
$944$	−25.5109			−0.830308
$945$	1.58363	+	0.390331i	0.0515156	+	0.0126975i
$946$	0.794847	−	0.704173i	0.0258427	−	0.0228946i
$947$	2.32201	−	3.36401i	0.0754551	−	0.109316i	−0.783439	−	0.621468i	$-0.786536\pi$
$947$	2.32201	−	3.36401i	0.0754551	−	0.109316i	0.858894	+	0.512153i	$0.171152\pi$
$948$	−14.2851	−	3.52096i	−0.463958	−	0.114355i
$949$	−5.51298	−	23.0642i	−0.178959	−	0.748696i
$950$	4.26855	−	1.05210i	0.138490	−	0.0341347i
$951$	4.48526	−	11.8266i	0.145444	−	0.383505i
$952$	−1.35153	−	3.56369i	−0.0438033	−	0.115500i
$953$	3.27647	−	26.9842i	0.106135	−	0.874103i	−0.838255	−	0.545278i	$-0.816424\pi$
$953$	3.27647	−	26.9842i	0.106135	−	0.874103i	0.944391	−	0.328825i	$-0.106653\pi$
$954$	2.66902	−	2.36454i	0.0864126	−	0.0765549i
$955$	−0.754211	−	1.98869i	−0.0244057	−	0.0643525i
$956$	−18.9238	−	27.4159i	−0.612040	−	0.886693i
$957$	−1.63053	−	0.401890i	−0.0527076	−	0.0129913i
$958$	−58.8003	+	14.4930i	−1.89975	+	0.468247i
$959$	−5.98101	−	5.29872i	−0.193137	−	0.171104i
$960$	3.83558	+	10.1136i	0.123793	+	0.326415i
$961$	−2.92469	−	24.0870i	−0.0943450	−	0.777001i
$962$	−52.3433	+	5.98223i	−1.68762	+	0.192875i
$963$	−2.39087	+	19.6906i	−0.0770449	+	0.634521i
$964$	10.1827	−	2.50981i	0.327963	−	0.0808356i
$965$	13.3406	−	3.28815i	0.429448	−	0.105849i
$966$	−11.9596	+	17.3265i	−0.384794	+	0.557470i
$967$	10.8050	−	15.6537i	0.347464	−	0.503388i	−0.609819	−	0.792541i	$-0.708758\pi$
$967$	10.8050	−	15.6537i	0.347464	−	0.503388i	0.957283	+	0.289152i	$0.0933733\pi$
$968$	7.55512	+	3.96524i	0.242831	+	0.127447i
$969$	0.191835	−	1.57991i	0.00616264	−	0.0507539i
$970$	2.55839	+	1.34275i	0.0821449	+	0.0431130i
$971$	10.2790	−	9.10642i	0.329869	−	0.292239i	−0.481889	−	0.876232i	$-0.660049\pi$
$971$	10.2790	−	9.10642i	0.329869	−	0.292239i	0.811758	+	0.583993i	$0.198511\pi$
$972$	−1.34985	+	1.95560i	−0.0432966	+	0.0627259i
$973$	−5.57236	−	1.37346i	−0.178642	−	0.0440312i
$974$	−45.8179	+	24.0471i	−1.46810	+	0.770519i
$975$	−3.33024	−	13.9325i	−0.106653	−	0.446196i
$976$	−21.2943	−	11.1761i	−0.681613	−	0.357738i
$977$	−39.6001	−	35.0826i	−1.26692	−	1.12239i	−0.986717	−	0.162450i	$-0.948060\pi$
$977$	−39.6001	−	35.0826i	−1.26692	−	1.12239i	−0.280201	−	0.959941i	$-0.590401\pi$
$978$	2.87314	+	23.6625i	0.0918729	+	0.756642i
$979$	−1.28102	+	0.672330i	−0.0409415	+	0.0214878i
$980$	−3.76542	+	9.92861i	−0.120282	+	0.317158i
$981$	−15.4935	+	3.81881i	−0.494670	+	0.121925i
$982$	52.3356	−	46.3653i	1.67010	−	1.47958i
$983$	29.9130	+	26.5006i	0.954078	+	0.845239i	0.988042	−	0.154184i	$-0.0492749\pi$
$983$	29.9130	+	26.5006i	0.954078	+	0.845239i	−0.0339646	+	0.999423i	$0.510813\pi$
$984$	−1.09375	+	2.88399i	−0.0348676	+	0.0919383i
$985$	−12.3957	−	6.50576i	−0.394959	−	0.207291i
$986$	19.8425	−	17.5790i	0.631915	−	0.559828i
$987$	−10.7341	−	9.50959i	−0.341671	−	0.302694i
$988$	−4.24856	+	1.57716i	−0.135165	+	0.0501763i
$989$	5.95853	−	5.27880i	0.189470	−	0.167856i
$990$	−0.101889	+	0.839135i	−0.00323826	+	0.0266695i
$991$	46.9514			1.49146			0.745730	−	0.666249i	$-0.232101\pi$
$991$	46.9514			1.49146			0.745730	+	0.666249i	$0.232101\pi$
$992$	−20.9491			−0.665136
$993$	1.65523	−	13.6321i	0.0525272	−	0.432601i
$994$	18.4200	−	26.6859i	0.584246	−	0.846427i
$995$	5.26109			0.166788
$996$	−8.88494	−	12.8721i	−0.281530	−	0.407867i
$997$	−1.01528	−	8.36161i	−0.0321544	−	0.264815i	−0.999916	−	0.0129478i	$-0.995878\pi$
$997$	−1.01528	−	8.36161i	−0.0321544	−	0.264815i	0.967762	−	0.251867i	$-0.0810446\pi$
$998$	−14.2315	+	37.5254i	−0.450491	+	1.18785i
$999$	0.841931	+	6.93393i	0.0266375	+	0.219380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.a.79.3	✓	180
169.92	even	13	inner	507.2.m.a.430.3	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.a.79.3	✓	180	1.1	even	1	trivial
507.2.m.a.430.3	yes	180	169.92	even	13	inner

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.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85232 - 0.972175i) q^{2} +(0.970942 + 0.239316i) q^{3} +(1.34985 + 1.95560i) q^{4} +(0.359355 + 0.947542i) q^{5} +(-1.56584 - 1.38722i) q^{6} +(-0.194000 - 1.59773i) q^{7} +(-0.0948689 - 0.781316i) q^{8} +(0.885456 + 0.464723i) q^{9} +O(q^{10})\)	\(q+(-1.85232 - 0.972175i) q^{2} +(0.970942 + 0.239316i) q^{3} +(1.34985 + 1.95560i) q^{4} +(0.359355 + 0.947542i) q^{5} +(-1.56584 - 1.38722i) q^{6} +(-0.194000 - 1.59773i) q^{7} +(-0.0948689 - 0.781316i) q^{8} +(0.885456 + 0.464723i) q^{9} +(0.255534 - 2.10451i) q^{10} +(-0.353059 + 0.185300i) q^{11} +(0.842623 + 2.22181i) q^{12} +(0.887475 - 3.49462i) q^{13} +(-1.19392 + 3.14812i) q^{14} +(0.122151 + 1.00601i) q^{15} +(1.10140 - 2.90415i) q^{16} +(0.362671 + 2.98687i) q^{17} +(-1.18836 - 1.72164i) q^{18} -0.528951 q^{19} +(-1.36794 + 1.98180i) q^{20} +(0.194000 - 1.59773i) q^{21} +0.834124 q^{22} +6.25297 q^{23} +(0.0948689 - 0.781316i) q^{24} +(2.97385 - 2.63460i) q^{25} +(-5.04128 + 5.61040i) q^{26} +(0.748511 + 0.663123i) q^{27} +(2.86265 - 2.53609i) q^{28} +(3.72926 + 1.95727i) q^{29} +(0.751752 - 1.98221i) q^{30} +(1.94268 + 1.72106i) q^{31} +(-6.04173 + 5.35250i) q^{32} +(-0.387145 + 0.0954227i) q^{33} +(2.23197 - 5.88522i) q^{34} +(1.44420 - 0.757976i) q^{35} +(0.286423 + 2.35891i) q^{36} +(5.22824 + 4.63182i) q^{37} +(0.979789 + 0.514233i) q^{38} +(1.69800 - 3.18069i) q^{39} +(0.706238 - 0.370662i) q^{40} +(-3.80508 - 0.937867i) q^{41} +(-1.91263 + 2.77092i) q^{42} +(0.952912 - 0.844206i) q^{43} +(-0.838950 - 0.440315i) q^{44} +(-0.122151 + 1.00601i) q^{45} +(-11.5825 - 6.07898i) q^{46} +(5.06156 - 7.33293i) q^{47} +(1.76440 - 2.55618i) q^{48} +(4.28148 - 1.05529i) q^{49} +(-8.06984 + 1.98904i) q^{50} +(-0.362671 + 2.98687i) q^{51} +(8.03204 - 2.98168i) q^{52} +(0.205458 + 1.69210i) q^{53} +(-0.741814 - 1.95600i) q^{54} +(-0.302453 - 0.267950i) q^{55} +(-1.22993 + 0.303150i) q^{56} +(-0.513581 - 0.126586i) q^{57} +(-5.00499 - 7.25098i) q^{58} +(-2.91253 - 7.67971i) q^{59} +(-1.80246 + 1.59684i) q^{60} +(0.933288 - 7.68631i) q^{61} +(-1.92530 - 5.07659i) q^{62} +(0.570725 - 1.50488i) q^{63} +(10.3633 - 2.55433i) q^{64} +(3.63022 - 0.414892i) q^{65} +(0.809886 + 0.199619i) q^{66} +(0.964759 - 1.39770i) q^{67} +(-5.35156 + 4.74107i) q^{68} +(6.07127 + 1.49643i) q^{69} -3.41202 q^{70} +(-9.35088 - 2.30478i) q^{71} +(0.279093 - 0.735909i) q^{72} +(5.82370 - 3.05652i) q^{73} +(-5.18146 - 13.6624i) q^{74} +(3.51794 - 1.84636i) q^{75} +(-0.714006 - 1.03442i) q^{76} +(0.364553 + 0.528146i) q^{77} +(-6.23744 + 4.24091i) q^{78} +(-3.51722 + 5.09557i) q^{79} +3.14760 q^{80} +(0.568065 + 0.822984i) q^{81} +(6.13647 + 5.43644i) q^{82} +(-6.39089 + 1.57521i) q^{83} +(3.38639 - 1.77732i) q^{84} +(-2.69985 + 1.41699i) q^{85} +(-2.58582 + 0.637347i) q^{86} +(3.15249 + 2.79286i) q^{87} +(0.178272 + 0.258272i) q^{88} +3.62834 q^{89} +(1.20428 - 1.74470i) q^{90} +(-5.75564 - 0.739991i) q^{91} +(8.44060 + 12.2283i) q^{92} +(1.47435 + 2.13597i) q^{93} +(-16.5045 + 8.66225i) q^{94} +(-0.190081 - 0.501204i) q^{95} +(-7.14710 + 3.75109i) q^{96} +(-0.483297 + 1.27435i) q^{97} +(-8.95662 - 2.20761i) q^{98} -0.398731 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more