LMFDB - Embedded newform 507.2.t.a.10.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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, 1]))

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, 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:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			10.6
Character	$\chi$	$=$	507.10
Dual form			507.2.t.a.355.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.561687 - 0.114669i) q^{2} +(0.987050 - 0.160411i) q^{3} +(-1.53762 - 0.655117i) q^{4} +(-0.327138 + 1.32725i) q^{5} +(-0.572808 - 0.0230834i) q^{6} +(-1.99021 + 0.944367i) q^{7} +(1.73212 + 1.19560i) q^{8} +(0.948536 - 0.316668i) q^{9} +O(q^{10})$	\(q+(-0.561687 - 0.114669i) q^{2} +(0.987050 - 0.160411i) q^{3} +(-1.53762 - 0.655117i) q^{4} +(-0.327138 + 1.32725i) q^{5} +(-0.572808 - 0.0230834i) q^{6} +(-1.99021 + 0.944367i) q^{7} +(1.73212 + 1.19560i) q^{8} +(0.948536 - 0.316668i) q^{9} +(0.335944 - 0.707987i) q^{10} +(1.44363 - 4.32420i) q^{11} +(-1.62279 - 0.399982i) q^{12} +(3.59621 - 0.259354i) q^{13} +(1.22617 - 0.302223i) q^{14} +(-0.109996 + 1.36254i) q^{15} +(1.47977 + 1.54060i) q^{16} +(-0.143906 - 0.303276i) q^{17} +(-0.569093 + 0.0691004i) q^{18} +(5.27265 + 3.04417i) q^{19} +(1.37252 - 1.82649i) q^{20} +(-1.81295 + 1.25139i) q^{21} +(-1.30672 + 2.26330i) q^{22} +(3.71633 + 6.43688i) q^{23} +(1.90148 + 0.902264i) q^{24} +(2.77270 + 1.45523i) q^{25} +(-2.04969 - 0.266699i) q^{26} +(0.885456 - 0.464723i) q^{27} +(3.67885 - 0.148253i) q^{28} +(0.102045 - 0.499849i) q^{29} +(0.218025 - 0.752708i) q^{30} +(-0.845261 - 1.61051i) q^{31} +(-2.90428 - 4.59274i) q^{32} +(0.731284 - 4.49977i) q^{33} +(0.0460539 + 0.186848i) q^{34} +(-0.602338 - 2.95045i) q^{35} +(-1.66594 - 0.134488i) q^{36} +(4.68420 - 7.40747i) q^{37} +(-2.61251 - 2.31448i) q^{38} +(3.50804 - 0.832868i) q^{39} +(-2.15350 + 1.90784i) q^{40} +(1.32728 + 8.16708i) q^{41} +(1.16181 - 0.495000i) q^{42} +(7.45466 - 4.71404i) q^{43} +(-5.05260 + 5.70321i) q^{44} +(0.109996 + 1.36254i) q^{45} +(-1.34930 - 4.04166i) q^{46} +(-11.7958 - 1.43227i) q^{47} +(1.70774 + 1.28328i) q^{48} +(-1.35801 + 1.66325i) q^{49} +(-1.39052 - 1.13533i) q^{50} +(-0.190692 - 0.276265i) q^{51} +(-5.69950 - 1.95715i) q^{52} +(1.22183 - 1.77013i) q^{53} +(-0.550639 + 0.159494i) q^{54} +(5.26703 + 3.33067i) q^{55} +(-4.57638 - 0.743734i) q^{56} +(5.69269 + 2.15895i) q^{57} +(-0.114635 + 0.269057i) q^{58} +(-4.36326 - 4.19097i) q^{59} +(1.06175 - 2.02300i) q^{60} +(10.4607 - 0.844478i) q^{61} +(0.290096 + 1.00153i) q^{62} +(-1.58874 + 1.52600i) q^{63} +(-0.410336 - 1.08197i) q^{64} +(-0.832229 + 4.85792i) q^{65} +(-0.926738 + 2.44361i) q^{66} +(-1.24635 - 2.92530i) q^{67} +(0.0225913 + 0.560598i) q^{68} +(4.70076 + 5.75738i) q^{69} +1.72630i q^{70} +(-5.16792 + 4.21947i) q^{71} +(2.02159 + 0.585561i) q^{72} +(-4.09749 - 4.62511i) q^{73} +(-3.48046 + 3.62355i) q^{74} +(2.97023 + 0.991610i) q^{75} +(-6.11303 - 8.13496i) q^{76} +(1.21050 + 9.96938i) q^{77} +(-2.06592 + 0.0655474i) q^{78} +(-1.76592 + 14.5437i) q^{79} +(-2.52885 + 1.46003i) q^{80} +(0.799443 - 0.600742i) q^{81} +(0.190997 - 4.73954i) q^{82} +(-1.36782 + 0.518744i) q^{83} +(3.60743 - 0.736462i) q^{84} +(0.449601 - 0.0917867i) q^{85} +(-4.72774 + 1.79300i) q^{86} +(0.0205420 - 0.509745i) q^{87} +(7.67055 - 5.76405i) q^{88} +(11.4022 - 6.58305i) q^{89} +(0.0944583 - 0.777934i) q^{90} +(-6.91230 + 3.91231i) q^{91} +(-1.49739 - 12.3321i) q^{92} +(-1.09266 - 1.45407i) q^{93} +(6.46131 + 2.15710i) q^{94} +(-5.76526 + 6.00227i) q^{95} +(-3.60339 - 4.06739i) q^{96} +(-0.142154 - 0.0411754i) q^{97} +(0.953498 - 0.778507i) q^{98} -4.55881i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9}+O(q^{10}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31} + 65 q^{32} - 13 q^{33} + 65 q^{34} - 82 q^{35} - 12 q^{36} - 73 q^{38} + 24 q^{40} - 132 q^{42} - 72 q^{43} + 39 q^{44} + 8 q^{48} + 68 q^{49} + 52 q^{50} - 8 q^{51} - 65 q^{52} + 37 q^{53} - 53 q^{55} + 14 q^{56} - 26 q^{57} + 26 q^{58} - 208 q^{59} + 78 q^{60} - 12 q^{61} - 49 q^{62} + 14 q^{64} + 52 q^{65} + 64 q^{66} - 26 q^{67} - 33 q^{68} + 4 q^{69} - 78 q^{71} + 52 q^{73} + 205 q^{74} - 8 q^{75} - 26 q^{76} - 114 q^{77} - 65 q^{78} + 28 q^{79} - 468 q^{80} + 14 q^{81} - 45 q^{82} - 78 q^{83} + 13 q^{85} + 13 q^{86} + 46 q^{87} + 26 q^{88} - 8 q^{90} - 260 q^{91} + 8 q^{92} - 25 q^{94} - 90 q^{95} - 65 q^{96} - 26 q^{97} + 104 q^{98}+O(q^{100}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{78}\right)$

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 $

$2$	−0.561687	−	0.114669i	−0.397173	−	0.0810834i	−0.00271227	−	0.999996i	$-0.500863\pi$
$2$	−0.561687	−	0.114669i	−0.397173	−	0.0810834i	−0.394460	+	0.918913i	$0.629068\pi$
$3$	0.987050	−	0.160411i	0.569874	−	0.0926135i
$3$	0.987050	−	0.160411i	0.569874	−	0.0926135i
$4$	−1.53762	−	0.655117i	−0.768808	−	0.327558i
$5$	−0.327138	+	1.32725i	−0.146301	+	0.593565i	0.851322	+	0.524644i	$0.175802\pi$
$5$	−0.327138	+	1.32725i	−0.146301	+	0.593565i	−0.997622	+	0.0689205i	$0.978045\pi$
$6$	−0.572808	−	0.0230834i	−0.233848	−	0.00942374i
$7$	−1.99021	+	0.944367i	−0.752229	+	0.356937i	−0.765892	−	0.642969i	$-0.777702\pi$
$7$	−1.99021	+	0.944367i	−0.752229	+	0.356937i	0.0136626	+	0.999907i	$0.495651\pi$
$8$	1.73212	+	1.19560i	0.612399	+	0.422708i
$9$	0.948536	−	0.316668i	0.316179	−	0.105556i
$10$	0.335944	−	0.707987i	0.106235	−	0.223885i
$11$	1.44363	−	4.32420i	0.435270	−	1.30379i	−0.471387	−	0.881927i	$-0.656246\pi$
$11$	1.44363	−	4.32420i	0.435270	−	1.30379i	0.906657	−	0.421868i	$-0.138625\pi$
$12$	−1.62279	−	0.399982i	−0.468460	−	0.115465i
$13$	3.59621	−	0.259354i	0.997410	−	0.0719319i
$13$	3.59621	−	0.259354i	0.997410	−	0.0719319i
$14$	1.22617	−	0.302223i	0.327707	−	0.0807724i
$15$	−0.109996	+	1.36254i	−0.0284007	+	0.351806i
$16$	1.47977	+	1.54060i	0.369942	+	0.385150i
$17$	−0.143906	−	0.303276i	−0.0349024	−	0.0735553i	0.885250	−	0.465115i	$-0.153987\pi$
$17$	−0.143906	−	0.303276i	−0.0349024	−	0.0735553i	−0.920153	+	0.391560i	$0.871936\pi$
$18$	−0.569093	+	0.0691004i	−0.134136	+	0.0162871i
$19$	5.27265	+	3.04417i	1.20963	+	0.698380i	0.962678	−	0.270648i	$-0.0872379\pi$
$19$	5.27265	+	3.04417i	1.20963	+	0.698380i	0.246951	+	0.969028i	$0.420571\pi$
$20$	1.37252	−	1.82649i	0.306904	−	0.408415i
$21$	−1.81295	+	1.25139i	−0.395618	+	0.273076i
$22$	−1.30672	+	2.26330i	−0.278594	+	0.482538i
$23$	3.71633	+	6.43688i	0.774909	+	1.34218i	0.934845	+	0.355055i	$0.115538\pi$
$23$	3.71633	+	6.43688i	0.774909	+	1.34218i	−0.159936	+	0.987127i	$0.551129\pi$
$24$	1.90148	+	0.902264i	0.388138	+	0.184174i
$25$	2.77270	+	1.45523i	0.554541	+	0.291045i
$26$	−2.04969	−	0.266699i	−0.401976	−	0.0523040i
$27$	0.885456	−	0.464723i	0.170406	−	0.0894360i
$28$	3.67885	−	0.148253i	0.695237	−	0.0280171i
$29$	0.102045	−	0.499849i	0.0189493	−	0.0928196i	−0.969216	−	0.246211i	$-0.920814\pi$
$29$	0.102045	−	0.499849i	0.0189493	−	0.0928196i	0.988166	+	0.153391i	$0.0490195\pi$
$30$	0.218025	−	0.752708i	0.0398056	−	0.137425i
$31$	−0.845261	−	1.61051i	−0.151813	−	0.289256i	0.797658	−	0.603110i	$-0.206072\pi$
$31$	−0.845261	−	1.61051i	−0.151813	−	0.289256i	−0.949471	+	0.313854i	$0.898380\pi$
$32$	−2.90428	−	4.59274i	−0.513408	−	0.811890i
$33$	0.731284	−	4.49977i	0.127300	−	0.783310i
$34$	0.0460539	+	0.186848i	0.00789818	+	0.0320442i
$35$	−0.602338	−	2.95045i	−0.101814	−	0.498717i
$36$	−1.66594	−	0.134488i	−0.277656	−	0.0224147i
$37$	4.68420	−	7.40747i	0.770078	−	1.21778i	−0.201134	−	0.979564i	$-0.564463\pi$
$37$	4.68420	−	7.40747i	0.770078	−	1.21778i	0.971212	−	0.238217i	$-0.0765629\pi$
$38$	−2.61251	−	2.31448i	−0.423805	−	0.375458i
$39$	3.50804	−	0.832868i	0.561736	−	0.133366i
$40$	−2.15350	+	1.90784i	−0.340499	+	0.301656i
$41$	1.32728	+	8.16708i	0.207286	+	1.27548i	0.857005	+	0.515309i	$0.172323\pi$
$41$	1.32728	+	8.16708i	0.207286	+	1.27548i	−0.649719	+	0.760175i	$0.725113\pi$
$42$	1.16181	−	0.495000i	0.179271	−	0.0763801i
$43$	7.45466	−	4.71404i	1.13682	−	0.718885i	0.172869	−	0.984945i	$-0.444696\pi$
$43$	7.45466	−	4.71404i	1.13682	−	0.718885i	0.963956	+	0.266060i	$0.0857221\pi$
$44$	−5.05260	+	5.70321i	−0.761708	+	0.859791i
$45$	0.109996	+	1.36254i	0.0163972	+	0.203115i
$46$	−1.34930	−	4.04166i	−0.198944	−	0.595910i
$47$	−11.7958	−	1.43227i	−1.72059	−	0.208918i	−0.800153	−	0.599797i	$-0.795248\pi$
$47$	−11.7958	−	1.43227i	−1.72059	−	0.208918i	−0.920442	+	0.390879i	$0.872171\pi$
$48$	1.70774	+	1.28328i	0.246490	+	0.185226i
$49$	−1.35801	+	1.66325i	−0.194001	+	0.237608i
$50$	−1.39052	−	1.13533i	−0.196650	−	0.160559i
$51$	−0.190692	−	0.276265i	−0.0267022	−	0.0386848i
$52$	−5.69950	−	1.95715i	−0.790378	−	0.271408i
$53$	1.22183	−	1.77013i	0.167831	−	0.243146i	−0.730039	−	0.683405i	$-0.760498\pi$
$53$	1.22183	−	1.77013i	0.167831	−	0.243146i	0.897870	+	0.440260i	$0.145114\pi$
$54$	−0.550639	+	0.159494i	−0.0749324	+	0.0217044i
$55$	5.26703	+	3.33067i	0.710206	+	0.449107i
$56$	−4.57638	−	0.743734i	−0.611544	−	0.0993856i
$57$	5.69269	+	2.15895i	0.754016	+	0.285960i
$58$	−0.114635	+	0.269057i	−0.0150523	+	0.0353289i
$59$	−4.36326	−	4.19097i	−0.568049	−	0.545618i	0.352719	−	0.935729i	$-0.385257\pi$
$59$	−4.36326	−	4.19097i	−0.568049	−	0.545618i	−0.920768	+	0.390111i	$0.872437\pi$
$60$	1.06175	−	2.02300i	0.137072	−	0.261169i
$61$	10.4607	−	0.844478i	1.33936	−	0.108124i	0.610081	−	0.792339i	$-0.291137\pi$
$61$	10.4607	−	0.844478i	1.33936	−	0.108124i	0.729280	+	0.684215i	$0.239855\pi$
$62$	0.290096	+	1.00153i	0.0368423	+	0.127194i
$63$	−1.58874	+	1.52600i	−0.200162	+	0.192258i
$64$	−0.410336	−	1.08197i	−0.0512920	−	0.135246i
$65$	−0.832229	+	4.85792i	−0.103225	+	0.602551i
$66$	−0.926738	+	2.44361i	−0.114074	+	0.300787i
$67$	−1.24635	−	2.92530i	−0.152266	−	0.357382i	0.826326	−	0.563193i	$-0.190427\pi$
$67$	−1.24635	−	2.92530i	−0.152266	−	0.357382i	−0.978592	+	0.205811i	$0.934017\pi$
$68$	0.0225913	+	0.560598i	0.00273960	+	0.0679825i
$69$	4.70076	+	5.75738i	0.565905	+	0.693107i
$70$			1.72630i			0.206332i
$71$	−5.16792	+	4.21947i	−0.613319	+	0.500760i	−0.887432	−	0.460938i	$-0.847513\pi$
$71$	−5.16792	+	4.21947i	−0.613319	+	0.500760i	0.274113	+	0.961697i	$0.411616\pi$
$72$	2.02159	+	0.585561i	0.238247	+	0.0690090i
$73$	−4.09749	−	4.62511i	−0.479575	−	0.541329i	0.458073	−	0.888915i	$-0.348540\pi$
$73$	−4.09749	−	4.62511i	−0.479575	−	0.541329i	−0.937648	+	0.347586i	$0.887001\pi$
$74$	−3.48046	+	3.62355i	−0.404596	+	0.421229i
$75$	2.97023	+	0.991610i	0.342973	+	0.114501i
$76$	−6.11303	−	8.13496i	−0.701213	−	0.933144i
$77$	1.21050	+	9.96938i	0.137949	+	1.13612i
$78$	−2.06592	+	0.0655474i	−0.233920	+	0.00742178i
$79$	−1.76592	+	14.5437i	−0.198682	+	1.63629i	0.462894	+	0.886414i	$0.346811\pi$
$79$	−1.76592	+	14.5437i	−0.198682	+	1.63629i	−0.661576	+	0.749878i	$0.730112\pi$
$80$	−2.52885	+	1.46003i	−0.282734	+	0.163237i
$81$	0.799443	−	0.600742i	0.0888270	−	0.0667491i
$82$	0.190997	−	4.73954i	0.0210921	−	0.523395i
$83$	−1.36782	+	0.518744i	−0.150137	+	0.0569396i	−0.428529	−	0.903528i	$-0.640968\pi$
$83$	−1.36782	+	0.518744i	−0.150137	+	0.0569396i	0.278391	+	0.960468i	$0.410199\pi$
$84$	3.60743	−	0.736462i	0.393603	−	0.0803546i
$85$	0.449601	−	0.0917867i	0.0487661	−	0.00995567i
$86$	−4.72774	+	1.79300i	−0.509805	+	0.193344i
$87$	0.0205420	−	0.509745i	0.00220234	−	0.0546504i
$88$	7.67055	−	5.76405i	0.817684	−	0.614449i
$89$	11.4022	−	6.58305i	1.20863	−	0.697802i	0.246168	−	0.969227i	$-0.420828\pi$
$89$	11.4022	−	6.58305i	1.20863	−	0.697802i	0.962459	+	0.271425i	$0.0874950\pi$
$90$	0.0944583	−	0.777934i	0.00995678	−	0.0820015i
$91$	−6.91230	+	3.91231i	−0.724605	+	0.410122i
$92$	−1.49739	−	12.3321i	−0.156113	−	1.28571i
$93$	−1.09266	−	1.45407i	−0.113303	−	0.150780i
$94$	6.46131	+	2.15710i	0.666433	+	0.222488i
$95$	−5.76526	+	6.00227i	−0.591503	+	0.615820i
$96$	−3.60339	−	4.06739i	−0.367770	−	0.415126i
$97$	−0.142154	−	0.0411754i	−0.0144335	−	0.00418073i	0.270993	−	0.962581i	$-0.412648\pi$
$97$	−0.142154	−	0.0411754i	−0.0144335	−	0.00418073i	−0.285426	+	0.958401i	$0.592135\pi$
$98$	0.953498	−	0.778507i	0.0963178	−	0.0786411i
$99$		−	4.55881i		−	0.458178i
$100$	−3.31001	−	4.05403i	−0.331001	−	0.405403i
$101$	−0.0512694	−	1.27224i	−0.00510150	−	0.126592i	−0.999733	−	0.0231111i	$-0.992643\pi$
$101$	−0.0512694	−	1.27224i	−0.00510150	−	0.126592i	0.994631	−	0.103481i	$-0.0329982\pi$
$102$	0.0754300	+	0.177041i	0.00746869	+	0.0175296i
$103$	−3.18547	+	8.39940i	−0.313874	+	0.827617i	0.681525	+	0.731795i	$0.261317\pi$
$103$	−3.18547	+	8.39940i	−0.313874	+	0.827617i	−0.995398	+	0.0958221i	$0.969452\pi$
$104$	6.53917	+	3.85039i	0.641218	+	0.377562i
$105$	−1.06782	−	2.81562i	−0.104209	−	0.274776i
$106$	−0.889265	+	0.854151i	−0.0863730	+	0.0829624i
$107$	−3.29860	−	11.3881i	−0.318888	−	1.10093i	−0.946581	−	0.322467i	$-0.895488\pi$
$107$	−3.29860	−	11.3881i	−0.318888	−	1.10093i	0.627693	−	0.778461i	$-0.283999\pi$
$108$	−1.66594	+	0.134488i	−0.160305	+	0.0129412i
$109$	−4.42055	+	8.42265i	−0.423412	+	0.806744i	−0.999947	−	0.0103287i	$-0.996712\pi$
$109$	−4.42055	+	8.42265i	−0.423412	+	0.806744i	0.576535	+	0.817073i	$0.304405\pi$
$110$	−2.57650	−	2.47476i	−0.245659	−	0.235959i
$111$	3.43530	−	8.06294i	0.326064	−	0.765301i
$112$	−4.39995	−	1.66868i	−0.415756	−	0.157675i
$113$	−6.94093	−	1.12801i	−0.652948	−	0.106114i	−0.175091	−	0.984552i	$-0.556022\pi$
$113$	−6.94093	−	1.12801i	−0.652948	−	0.106114i	−0.477857	+	0.878438i	$0.658586\pi$
$114$	−2.94995	−	1.86543i	−0.276288	−	0.174714i
$115$	−9.75911	+	2.82676i	−0.910042	+	0.263597i
$116$	−0.484365	+	0.701724i	−0.0449722	+	0.0651534i
$117$	3.32901	−	1.38481i	0.307767	−	0.128026i
$118$	1.97021	+	2.85435i	0.181373	+	0.262764i
$119$	0.572808	+	0.467683i	0.0525092	+	0.0428725i
$120$	−1.81958	+	2.22858i	−0.166104	+	0.203440i
$121$	−7.82074	−	5.87690i	−0.710976	−	0.534264i
$122$	−5.97250	−	0.725193i	−0.540725	−	0.0656559i
$123$	2.62018	+	7.84841i	0.236254	+	0.707667i
$124$	0.244614	+	3.03009i	0.0219670	+	0.272110i
$125$	−7.37086	+	8.31998i	−0.659270	+	0.744162i
$126$	1.06736	−	0.674957i	0.0950879	−	0.0601299i
$127$	16.8429	−	7.17611i	1.49457	−	0.636777i	0.518666	−	0.854977i	$-0.326429\pi$
$127$	16.8429	−	7.17611i	1.49457	−	0.636777i	0.975904	+	0.218200i	$0.0700185\pi$
$128$	1.84975	+	11.3820i	0.163497	+	1.00604i
$129$	6.60194	−	5.84881i	0.581268	−	0.514959i
$130$	1.02451	−	2.63320i	0.0898551	−	0.230947i
$131$	−10.0186	−	8.87567i	−0.875326	−	0.775471i	0.100289	−	0.994958i	$-0.468023\pi$
$131$	−10.0186	−	8.87567i	−0.875326	−	0.775471i	−0.975615	+	0.219487i	$0.929562\pi$
$132$	−4.07231	+	6.43985i	−0.354449	+	0.560517i
$133$	−13.3685	−	1.07922i	−1.15920	−	0.0935800i
$134$	0.364618	+	1.78602i	0.0314982	+	0.154289i
$135$	0.327138	+	1.32725i	0.0281556	+	0.114232i
$136$	0.113333	−	0.697367i	0.00971824	−	0.0597987i
$137$	6.29118	+	9.94871i	0.537492	+	0.849975i	0.999315	−	0.0369964i	$-0.0117790\pi$
$137$	6.29118	+	9.94871i	0.537492	+	0.849975i	−0.461824	+	0.886972i	$0.652805\pi$
$138$	−1.98016	−	3.77288i	−0.168562	−	0.321169i
$139$	−1.66848	+	5.76026i	−0.141519	+	0.488579i	−0.999693	−	0.0247794i	$-0.992112\pi$
$139$	−1.66848	+	5.76026i	−0.141519	+	0.488579i	0.858174	+	0.513358i	$0.171599\pi$
$140$	−1.00672	+	4.93126i	−0.0850837	+	0.416767i
$141$	−11.8728	+	0.478458i	−0.999870	+	0.0402934i
$142$	3.38660	−	1.77742i	0.284197	−	0.149158i
$143$	4.07010	−	15.9251i	0.340359	−	1.33173i
$144$	1.89147	+	0.992722i	0.157623	+	0.0827268i
$145$	0.630042	+	0.298959i	0.0523221	+	0.0248272i
$146$	1.77115	+	3.06772i	0.146581	+	0.253887i
$147$	−1.07361	+	1.85956i	−0.0885502	+	0.153374i
$148$	−12.0553	+	8.32114i	−0.990936	+	0.683994i
$149$	−3.10101	+	4.12669i	−0.254045	+	0.338072i	−0.908390	−	0.418124i	$-0.862688\pi$
$149$	−3.10101	+	4.12669i	−0.254045	+	0.338072i	0.654345	+	0.756196i	$0.272944\pi$
$150$	−1.55463	−	0.897569i	−0.126935	−	0.0732862i
$151$	−18.4041	+	2.23467i	−1.49771	+	0.181855i	−0.827982	−	0.560755i	$-0.810511\pi$
$151$	−18.4041	+	2.23467i	−1.49771	+	0.181855i	−0.669725	+	0.742609i	$0.733588\pi$
$152$	5.49329	+	11.5769i	0.445565	+	0.939007i
$153$	−0.232538	−	0.242098i	−0.0187996	−	0.0195725i
$154$	0.463258	−	5.73848i	0.0373304	−	0.462420i
$155$	2.41407	−	0.595015i	0.193903	−	0.0477927i
$156$	−5.93964	−	1.01754i	−0.475552	−	0.0814686i
$157$	4.80252	+	1.18371i	0.383283	+	0.0944707i	0.426249	−	0.904606i	$-0.359835\pi$
$157$	4.80252	+	1.18371i	0.383283	+	0.0944707i	−0.0429664	+	0.999077i	$0.513681\pi$
$158$	2.65961	−	7.96650i	0.211587	−	0.633781i
$159$	0.922059	−	1.94320i	0.0731241	−	0.154106i
$160$	7.04582	−	2.35224i	0.557021	−	0.185961i
$161$	−13.4751	−	9.30117i	−1.06198	−	0.733035i
$162$	−0.517923	+	0.245758i	−0.0406919	+	0.0193085i
$163$	22.0904	+	0.890211i	1.73025	+	0.0697267i	0.885272	−	0.465074i	$-0.153972\pi$
$163$	22.0904	+	0.890211i	1.73025	+	0.0697267i	0.844978	+	0.534801i	$0.179613\pi$
$164$	3.30954	−	13.4274i	0.258432	−	1.04850i
$165$	5.73310	+	2.44264i	0.446321	+	0.190160i
$166$	0.827769	−	0.134526i	0.0642473	−	0.0104412i
$167$	−13.0647	−	2.66718i	−1.01098	−	0.206393i	−0.334139	−	0.942524i	$-0.608445\pi$
$167$	−13.0647	−	2.66718i	−1.01098	−	0.206393i	−0.676839	+	0.736131i	$0.736651\pi$
$168$	−4.63642			−0.357708
$169$	12.8655	−	1.86538i	0.989652	−	0.143491i
$170$	−0.263060			−0.0201758
$171$	5.96529	+	1.21782i	0.456177	+	0.0931293i
$172$	−14.5506	+	2.36471i	−1.10948	+	0.180307i
$173$	−16.4736	−	7.01874i	−1.25246	−	0.533625i	−0.339093	−	0.940753i	$-0.610120\pi$
$173$	−16.4736	−	7.01874i	−1.25246	−	0.533625i	−0.913371	+	0.407128i	$0.866530\pi$
$174$	−0.0699903	+	0.283962i	−0.00530595	+	0.0215271i
$175$	−6.89254	−	0.277760i	−0.521027	−	0.0209967i
$176$	8.79810	−	4.17475i	0.663182	−	0.314684i
$177$	−4.97904	−	3.43678i	−0.374248	−	0.258324i
$178$	−7.15932	+	2.39013i	−0.536614	+	0.179148i
$179$	7.38133	−	15.5558i	0.551706	−	1.16270i	−0.415708	−	0.909498i	$-0.636466\pi$
$179$	7.38133	−	15.5558i	0.551706	−	1.16270i	0.967414	−	0.253198i	$-0.0814825\pi$
$180$	0.723492	−	2.16712i	0.0539259	−	0.161528i
$181$	4.90988	+	1.21018i	0.364948	+	0.0899517i	0.417526	−	0.908665i	$-0.362897\pi$
$181$	4.90988	+	1.21018i	0.364948	+	0.0899517i	−0.0525773	+	0.998617i	$0.516744\pi$
$182$	4.33117	−	1.40487i	0.321048	−	0.104136i
$183$	10.1898	−	2.51156i	0.753253	−	0.185660i
$184$	−1.25878	+	15.5927i	−0.0927981	+	1.14951i
$185$	8.29919	+	8.64037i	0.610169	+	0.635253i
$186$	0.446996	+	0.942024i	0.0327753	+	0.0690726i
$187$	−1.51917	+	0.184461i	−0.111093	+	0.0134891i
$188$	17.1991	+	9.92991i	1.25437	+	0.724213i
$189$	−1.32338	+	1.76109i	−0.0962614	+	0.128101i
$190$	3.92655	−	2.71030i	0.284862	−	0.196626i
$191$	−5.69678	+	9.86712i	−0.412205	+	0.713960i	−0.995131	−	0.0985658i	$-0.968575\pi$
$191$	−5.69678	+	9.86712i	−0.412205	+	0.713960i	0.582926	+	0.812525i	$0.301908\pi$
$192$	−0.578582	−	1.00213i	−0.0417556	−	0.0723228i
$193$	−10.2616	−	4.86919i	−0.738647	−	0.350492i	0.0219134	−	0.999760i	$-0.493024\pi$
$193$	−10.2616	−	4.86919i	−0.738647	−	0.350492i	−0.760560	+	0.649268i	$0.775075\pi$
$194$	0.0751245	+	0.0394284i	0.00539362	+	0.00283079i
$195$	−0.0421870	+	4.92851i	−0.00302107	+	0.352938i
$196$	3.17772	−	1.66779i	0.226980	−	0.119128i
$197$	−6.24884	+	0.251820i	−0.445211	+	0.0179414i	−0.261860	−	0.965106i	$-0.584336\pi$
$197$	−6.24884	+	0.251820i	−0.445211	+	0.0179414i	−0.183352	+	0.983047i	$0.558695\pi$
$198$	−0.522755	+	2.56062i	−0.0371506	+	0.181976i
$199$	1.17486	−	4.05607i	0.0832833	−	0.287527i	−0.908057	−	0.418847i	$-0.862434\pi$
$199$	1.17486	−	4.05607i	0.0832833	−	0.287527i	0.991340	+	0.131320i	$0.0419215\pi$
$200$	3.06280	+	5.83568i	0.216573	+	0.412645i
$201$	−1.69946	−	2.68749i	−0.119871	−	0.189561i
$202$	−0.117089	+	0.720479i	−0.00823837	+	0.0506927i
$203$	0.268950	+	1.09117i	0.0188766	+	0.0765853i
$204$	0.112225	+	0.549714i	0.00785732	+	0.0384877i
$205$	−11.2740	−	0.910129i	−0.787408	−	0.0635661i
$206$	2.75239	−	4.35256i	0.191768	−	0.303257i
$207$	5.56343	+	4.92877i	0.386685	+	0.342573i
$208$	5.72112	+	5.15655i	0.396688	+	0.357542i
$209$	20.7753	−	18.4053i	1.43706	−	1.27312i
$210$	0.276918	+	1.70394i	0.0191091	+	0.117583i
$211$	10.0005	−	4.26080i	0.688460	−	0.293326i	−0.0192638	−	0.999814i	$-0.506132\pi$
$211$	10.0005	−	4.26080i	0.688460	−	0.293326i	0.707724	+	0.706489i	$0.249722\pi$
$212$	−3.03834	+	1.92133i	−0.208674	+	0.131958i
$213$	−4.42414	+	4.99383i	−0.303137	+	0.342171i
$214$	0.546917	+	6.77479i	0.0373865	+	0.463115i
$215$	3.81801	+	11.4363i	0.260386	+	0.779952i
$216$	2.08934	+	0.253692i	0.142162	+	0.0172616i
$217$	3.20316	+	2.40702i	0.217445	+	0.163399i
$218$	3.44878	−	4.22399i	0.233581	−	0.286085i
$219$	−4.78635	−	3.90794i	−0.323432	−	0.264074i
$220$	−5.91669	−	8.57180i	−0.398903	−	0.577911i
$221$	−0.596174	−	1.05332i	−0.0401030	−	0.0708542i
$222$	−2.85413	+	4.13493i	−0.191557	+	0.277518i
$223$	−23.1519	+	6.70603i	−1.55037	+	0.449069i	−0.939467	−	0.342640i	$-0.888679\pi$
$223$	−23.1519	+	6.70603i	−1.55037	+	0.449069i	−0.610898	+	0.791709i	$0.709192\pi$
$224$	10.1174	+	6.39783i	0.675994	+	0.427473i
$225$	3.09083	+	0.502310i	0.206056	+	0.0334873i
$226$	3.76928	+	1.42950i	0.250729	+	0.0950889i
$227$	7.44128	−	17.4653i	0.493895	−	1.15922i	−0.467487	−	0.884000i	$-0.654841\pi$
$227$	7.44128	−	17.4653i	0.493895	−	1.15922i	0.961383	−	0.275215i	$-0.0887491\pi$
$228$	−7.33881	−	7.04902i	−0.486024	−	0.466833i
$229$	3.33894	−	6.36183i	0.220644	−	0.420401i	−0.749822	−	0.661639i	$-0.769861\pi$
$229$	3.33894	−	6.36183i	0.220644	−	0.420401i	0.970466	+	0.241238i	$0.0775534\pi$
$230$	5.80571	−	0.468685i	0.382817	−	0.0309042i
$231$	2.79403	+	9.64610i	0.183833	+	0.634667i
$232$	0.774373	−	0.743796i	0.0508401	−	0.0488326i
$233$	10.1539	+	26.7735i	0.665201	+	1.75399i	0.656844	+	0.754027i	$0.271891\pi$
$233$	10.1539	+	26.7735i	0.665201	+	1.75399i	0.00835778	+	0.999965i	$0.497340\pi$
$234$	−2.02866	+	0.396096i	−0.132617	+	0.0258936i
$235$	5.75984	−	15.1874i	0.375730	−	0.990719i
$236$	3.96345	+	9.30255i	0.257998	+	0.605545i
$237$	0.589916	+	14.6386i	0.0383192	+	0.950880i
$238$	−0.268110	−	0.328375i	−0.0173790	−	0.0212854i
$239$		−	4.73435i		−	0.306239i	−0.988208	−	0.153120i	$-0.951068\pi$
$239$		−	4.73435i		−	0.306239i	0.988208	−	0.153120i	$-0.0489320\pi$
$240$	−2.26190	+	1.84678i	−0.146005	+	0.119209i
$241$	−7.84731	−	2.27300i	−0.505489	−	0.146417i	0.0156682	−	0.999877i	$-0.495012\pi$
$241$	−7.84731	−	2.27300i	−0.505489	−	0.146417i	−0.521158	+	0.853460i	$0.674500\pi$
$242$	3.71891	+	4.19778i	0.239060	+	0.269843i
$243$	0.692724	−	0.721202i	0.0444383	−	0.0462652i
$244$	−16.6378	−	5.55452i	−1.06513	−	0.355592i
$245$	−1.76330	−	2.34653i	−0.112653	−	0.149914i
$246$	−0.571752	−	4.70880i	−0.0364536	−	0.300222i
$247$	19.7511	+	9.57999i	1.25673	+	0.609560i
$248$	0.461428	−	3.80020i	0.0293007	−	0.241313i
$249$	−1.26689	+	0.731440i	−0.0802860	+	0.0463531i
$250$	5.09416	−	3.82802i	0.322183	−	0.242105i
$251$	0.231034	−	5.73304i	0.0145827	−	0.361866i	−0.975379	−	0.220533i	$-0.929220\pi$
$251$	0.231034	−	5.73304i	0.0145827	−	0.361866i	0.989962	−	0.141333i	$-0.0451388\pi$
$252$	3.44258	−	1.30560i	0.216862	−	0.0822449i
$253$	33.1993	−	6.77769i	2.08722	−	0.426110i
$254$	−10.2833	+	2.09936i	−0.645234	+	0.131726i
$255$	0.429055	−	0.162719i	0.0268685	−	0.0101899i
$256$	0.172993	−	4.29278i	0.0108121	−	0.268299i
$257$	4.43851	−	3.33533i	0.276867	−	0.208052i	−0.453234	−	0.891392i	$-0.649730\pi$
$257$	4.43851	−	3.33533i	0.276867	−	0.208052i	0.730100	+	0.683340i	$0.239473\pi$
$258$	−4.37890	+	2.52816i	−0.272618	+	0.157396i
$259$	−2.32718	+	19.1660i	−0.144604	+	1.19092i
$260$	4.46215	−	6.92441i	0.276731	−	0.429433i
$261$	−0.0614928	−	0.506439i	−0.00380631	−	0.0313478i
$262$	4.60953	+	6.13417i	0.284778	+	0.378970i
$263$	17.5468	+	5.85798i	1.08198	+	0.361218i	0.801104	−	0.598525i	$-0.204246\pi$
$263$	17.5468	+	5.85798i	1.08198	+	0.361218i	0.280877	+	0.959744i	$0.409375\pi$
$264$	6.64660	−	6.91985i	0.409070	−	0.425887i
$265$	1.94969	+	2.20075i	0.119769	+	0.135191i
$266$	7.38516	+	2.13914i	0.452813	+	0.131159i
$267$	10.1985	−	8.32684i	0.624139	−	0.509594i
$268$			5.31449i			0.324634i
$269$	7.11336	+	8.71228i	0.433709	+	0.531197i	0.944502	−	0.328507i	$-0.106545\pi$
$269$	7.11336	+	8.71228i	0.433709	+	0.531197i	−0.510793	+	0.859704i	$0.670648\pi$
$270$	−0.0315543	−	0.783012i	−0.00192033	−	0.0476526i
$271$	6.23982	+	14.6454i	0.379042	+	0.889644i	0.994813	+	0.101719i	$0.0324343\pi$
$271$	6.23982	+	14.6454i	0.379042	+	0.889644i	−0.615771	+	0.787925i	$0.711155\pi$
$272$	0.254280	−	0.670481i	0.0154180	−	0.0406539i
$273$	−6.19520	+	4.97046i	−0.374951	+	0.300826i
$274$	−2.39286	−	6.30946i	−0.144558	−	0.381169i
$275$	10.2954	−	9.88891i	0.620839	−	0.596324i
$276$	−3.45620	−	11.9322i	−0.208039	−	0.718233i
$277$	25.6651	−	2.07190i	1.54207	−	0.124489i	0.720039	−	0.693934i	$-0.244124\pi$
$277$	25.6651	−	2.07190i	1.54207	−	0.124489i	0.822029	+	0.569445i	$0.192842\pi$
$278$	1.59769	−	3.04414i	0.0958230	−	0.182575i
$279$	−1.31176	−	1.25996i	−0.0785329	−	0.0754319i
$280$	2.48423	−	5.83070i	0.148461	−	0.348451i
$281$	22.3461	+	8.47477i	1.33306	+	0.505563i	0.915219	−	0.402958i	$-0.132018\pi$
$281$	22.3461	+	8.47477i	1.33306	+	0.505563i	0.417840	+	0.908520i	$0.362787\pi$
$282$	6.72366	+	1.09270i	0.400388	+	0.0650694i
$283$	−20.9709	−	13.2612i	−1.24659	−	0.788297i	−0.262324	−	0.964980i	$-0.584489\pi$
$283$	−20.9709	−	13.2612i	−1.24659	−	0.788297i	−0.984268	+	0.176683i	$0.943463\pi$
$284$	10.7105	−	3.10234i	0.635552	−	0.184090i
$285$	−4.72777	+	6.84936i	−0.280049	+	0.405721i
$286$	−4.11224	+	8.47823i	−0.243162	+	0.501328i
$287$	−10.3543	−	15.0008i	−0.611194	−	0.885468i
$288$	−4.20919	−	3.43669i	−0.248029	−	0.202509i
$289$	10.6803	−	13.0810i	0.628253	−	0.769470i
$290$	−0.319605	−	0.240168i	−0.0187679	−	0.0141031i
$291$	−0.146918	−	0.0178391i	−0.00861249	−	0.00104575i
$292$	3.27038	+	9.79598i	0.191385	+	0.573267i
$293$	−1.70218	−	21.0853i	−0.0994424	−	1.23181i	−0.833420	−	0.552641i	$-0.813620\pi$
$293$	−1.70218	−	21.0853i	−0.0994424	−	1.23181i	0.733977	−	0.679174i	$-0.237662\pi$
$294$	0.816269	−	0.921377i	0.0476058	−	0.0537358i
$295$	6.98986	−	4.42012i	0.406966	−	0.257349i
$296$	16.9700	−	7.23024i	0.986361	−	0.420249i
$297$	−0.731284	−	4.49977i	−0.0424334	−	0.261103i
$298$	2.21500	−	1.96232i	0.128312	−	0.113674i
$299$	15.0342	+	22.1845i	0.869448	+	1.28296i
$300$	−3.91746	−	3.47056i	−0.226174	−	0.200373i
$301$	−10.3846	+	16.4219i	−0.598556	+	0.946541i
$302$	10.5936	+	0.855205i	0.609594	+	0.0492115i
$303$	−0.254687	−	1.24754i	−0.0146314	−	0.0716692i
$304$	3.11245	+	12.6277i	0.178511	+	0.724250i
$305$	−2.30127	+	14.1603i	−0.131770	+	0.810816i
$306$	0.102853	+	0.162648i	0.00587969	+	0.00929799i
$307$	−11.0452	−	21.0450i	−0.630386	−	1.20110i	−0.965864	−	0.259051i	$-0.916590\pi$
$307$	−11.0452	−	21.0450i	−0.630386	−	1.20110i	0.335478	−	0.942048i	$-0.391102\pi$
$308$	4.66982	−	16.1221i	0.266088	−	0.918642i
$309$	−1.79686	+	8.80161i	−0.102220	+	0.500706i
$310$	−1.42418	+	0.0573925i	−0.0808880	+	0.00325968i
$311$	−1.11114	+	0.583169i	−0.0630067	+	0.0330685i	−0.495932	−	0.868361i	$-0.665174\pi$
$311$	−1.11114	+	0.583169i	−0.0630067	+	0.0330685i	0.432926	+	0.901430i	$0.357481\pi$
$312$	7.07214	+	2.75158i	0.400381	+	0.155777i
$313$	−20.2243	−	10.6145i	−1.14314	−	0.599969i	−0.216640	−	0.976252i	$-0.569510\pi$
$313$	−20.2243	−	10.6145i	−1.14314	−	0.599969i	−0.926505	+	0.376283i	$0.877202\pi$
$314$	−2.56178	−	1.21558i	−0.144569	−	0.0685991i
$315$	−1.50565	−	2.60787i	−0.0848339	−	0.146937i
$316$	12.2431	−	21.2057i	0.688729	−	1.19291i
$317$	−11.8217	+	8.15995i	−0.663974	+	0.458308i	−0.851781	−	0.523898i	$-0.824477\pi$
$317$	−11.8217	+	8.15995i	−0.663974	+	0.458308i	0.187807	+	0.982206i	$0.439862\pi$
$318$	−0.740734	+	0.985738i	−0.0415383	+	0.0552774i
$319$	−2.01413	−	1.16286i	−0.112770	−	0.0651076i
$320$	1.57028	−	0.190666i	0.0877813	−	0.0106586i
$321$	−5.08266	−	10.7115i	−0.283686	−	0.597856i
$322$	6.50221	+	6.76952i	0.362354	+	0.377251i
$323$	0.164455	−	2.03715i	0.00915054	−	0.113350i
$324$	−1.62279	+	0.399982i	−0.0901551	+	0.0222212i
$325$	10.3486	+	4.51419i	0.574040	+	0.250402i
$326$	−12.3058	−	3.03310i	−0.681554	−	0.167988i
$327$	−3.01222	+	9.02269i	−0.166576	+	0.498956i
$328$	−7.46554	+	15.7333i	−0.412216	+	0.868726i
$329$	24.8287	−	8.28905i	1.36885	−	0.456990i
$330$	−2.94011	−	2.02941i	−0.161848	−	0.111715i
$331$	−29.6236	+	14.0566i	−1.62826	+	0.772620i	−0.999986	−	0.00537057i	$-0.998290\pi$
$331$	−29.6236	+	14.0566i	−1.62826	+	0.772620i	−0.628276	+	0.777990i	$0.716239\pi$
$332$	2.44301	+	0.0984501i	0.134078	+	0.00540315i
$333$	2.09743	−	8.50959i	0.114938	−	0.466323i
$334$	7.03243	+	2.99624i	0.384798	+	0.163947i
$335$	4.29033	−	0.697247i	0.234406	−	0.0380947i
$336$	−4.61064	−	0.941269i	−0.251531	−	0.0513505i
$337$	−18.3957			−1.00208			−0.501039	−	0.865425i	$-0.667049\pi$
$337$	−18.3957			−1.00208			−0.501039	+	0.865425i	$0.667049\pi$
$338$	−7.44027	−	0.427511i	−0.404697	−	0.0232535i
$339$	−7.03199			−0.381925
$340$	−0.751445	−	0.153408i	−0.0407528	−	0.00831974i
$341$	−8.18441	+	1.33010i	−0.443211	+	0.0720287i
$342$	−3.21098	−	1.36807i	−0.173630	−	0.0739768i
$343$	4.82232	−	19.5649i	0.260381	−	1.05641i
$344$	18.5485	+	0.747479i	1.00007	+	0.0403014i
$345$	−9.17929	+	4.35563i	−0.494196	+	0.234499i
$346$	8.44817	+	5.83135i	0.454176	+	0.313495i
$347$	−34.4624	+	11.5053i	−1.85004	+	0.617635i	−0.854946	+	0.518718i	$0.826410\pi$
$347$	−34.4624	+	11.5053i	−1.85004	+	0.617635i	−0.995096	+	0.0989167i	$0.968462\pi$
$348$	−0.365528	+	0.770335i	−0.0195944	+	0.0412943i
$349$	2.54644	−	7.62753i	0.136308	−	0.408292i	−0.858154	−	0.513393i	$-0.828388\pi$
$349$	2.54644	−	7.62753i	0.136308	−	0.408292i	0.994462	+	0.105101i	$0.0335165\pi$
$350$	3.83960	+	0.946376i	0.205235	+	0.0505859i
$351$	3.06376	−	1.90089i	0.163531	−	0.101462i
$352$	−24.0526	+	5.92844i	−1.28201	+	0.315987i
$353$	−0.335068	+	4.15056i	−0.0178339	+	0.220912i	0.981701	+	0.190427i	$0.0609872\pi$
$353$	−0.335068	+	4.15056i	−0.0178339	+	0.220912i	−0.999535	+	0.0304850i	$0.990295\pi$
$354$	2.40257	+	2.50134i	0.127695	+	0.132945i
$355$	−3.90968	−	8.23948i	−0.207504	−	0.437306i
$356$	−21.8448	+	2.65244i	−1.15777	+	0.140579i
$357$	0.640412	+	0.369742i	0.0338942	+	0.0195688i
$358$	−5.92977	+	7.89109i	−0.313398	+	0.417057i
$359$	−23.5061	+	16.2251i	−1.24060	+	0.856326i	−0.993629	−	0.112696i	$-0.964051\pi$
$359$	−23.5061	+	16.2251i	−1.24060	+	0.856326i	−0.246973	+	0.969022i	$0.579436\pi$
$360$	−1.43853	+	2.49160i	−0.0758170	+	0.131319i
$361$	9.03392	+	15.6472i	0.475469	+	0.823537i
$362$	−2.61904	−	1.24275i	−0.137654	−	0.0653176i
$363$	−8.66218	−	4.54626i	−0.454647	−	0.238617i
$364$	13.1915	−	1.48727i	0.691421	−	0.0779543i
$365$	7.47913	−	3.92535i	0.391476	−	0.205462i
$366$	−6.01149	+	0.242255i	−0.314225	+	0.0126628i
$367$	1.15672	−	5.66597i	0.0603801	−	0.295761i	−0.938376	−	0.345615i	$-0.887670\pi$
$367$	1.15672	−	5.66597i	0.0603801	−	0.295761i	0.998757	+	0.0498537i	$0.0158755\pi$
$368$	−4.41736	+	15.2505i	−0.230271	+	0.794986i
$369$	3.84523	+	7.32646i	0.200174	+	0.381401i
$370$	−3.67076	−	5.80485i	−0.190834	−	0.301780i
$371$	−0.760051	+	4.67678i	−0.0394599	+	0.242806i
$372$	0.727507	+	2.95161i	0.0377195	+	0.153034i
$373$	6.01900	+	29.4830i	0.311652	+	1.52657i	0.770141	+	0.637873i	$0.220186\pi$
$373$	6.01900	+	29.4830i	0.311652	+	1.52657i	−0.458489	+	0.888700i	$0.651609\pi$
$374$	0.874452	+	0.0705931i	0.0452168	+	0.00365028i
$375$	−5.94079	+	9.39461i	−0.306781	+	0.485136i
$376$	−18.7194	−	16.5839i	−0.965379	−	0.855251i
$377$	0.237337	−	1.82403i	0.0122235	−	0.0939422i
$378$	0.945266	−	0.837433i	0.0486192	−	0.0430729i
$379$	−3.18633	−	19.6063i	−0.163671	−	1.00711i	−0.930777	−	0.365587i	$-0.880868\pi$
$379$	−3.18633	−	19.6063i	−0.163671	−	1.00711i	0.767106	−	0.641520i	$-0.221696\pi$
$380$	12.7969	−	5.45227i	0.656469	−	0.279695i
$381$	15.4737	−	9.78498i	0.792742	−	0.501300i
$382$	4.33126	−	4.88899i	0.221607	−	0.250142i
$383$	−1.03700	−	12.8456i	−0.0529883	−	0.656378i	−0.967673	−	0.252209i	$-0.918843\pi$
$383$	−1.03700	−	12.8456i	−0.0529883	−	0.656378i	0.914684	−	0.404169i	$-0.132439\pi$
$384$	3.65160	+	10.9379i	0.186345	+	0.558172i
$385$	−13.6279	−	1.65472i	−0.694541	−	0.0843325i
$386$	5.20546	+	3.91165i	0.264951	+	0.199098i
$387$	5.57823	−	6.83209i	0.283557	−	0.347295i
$388$	0.191603	+	0.156439i	0.00972719	+	0.00794201i
$389$	15.1447	+	21.9409i	0.767867	+	1.11245i	0.990496	+	0.137544i	$0.0439208\pi$
$389$	15.1447	+	21.9409i	0.767867	+	1.11245i	−0.222629	+	0.974903i	$0.571464\pi$
$390$	0.588844	−	2.76344i	0.0298173	−	0.139932i
$391$	1.41735	−	2.05338i	0.0716784	−	0.103844i
$392$	−4.34082	+	1.25733i	−0.219245	+	0.0635050i
$393$	−11.3126	−	7.15365i	−0.570644	−	0.360854i
$394$	3.53877	+	0.575106i	0.178280	+	0.0289734i
$395$	−18.7254	−	7.10161i	−0.942178	−	0.357321i
$396$	−2.98655	+	7.00970i	−0.150080	+	0.352250i
$397$	−12.7114	−	12.2095i	−0.637969	−	0.612778i	0.302299	−	0.953213i	$-0.402246\pi$
$397$	−12.7114	−	12.2095i	−0.637969	−	0.612778i	−0.940268	+	0.340435i	$0.889426\pi$
$398$	−1.12501	+	2.14352i	−0.0563915	+	0.107445i
$399$	−13.3685	+	1.07922i	−0.669262	+	0.0540285i
$400$	1.86103	+	6.42503i	0.0930517	+	0.321252i
$401$	−14.1784	+	13.6185i	−0.708035	+	0.680076i	−0.957541	−	0.288297i	$-0.906911\pi$
$401$	−14.1784	+	13.6185i	−0.708035	+	0.680076i	0.249507	+	0.968373i	$0.419732\pi$
$402$	0.646394	+	1.70440i	0.0322392	+	0.0850078i
$403$	−3.45743	−	5.57251i	−0.172227	−	0.277587i
$404$	−0.754632	+	1.98980i	−0.0375443	+	0.0989963i
$405$	0.535808	+	1.25759i	0.0266245	+	0.0624900i
$406$	−0.0259417	−	0.643738i	−0.00128747	−	0.0319482i
$407$	−25.2691	−	30.9490i	−1.25254	−	1.53409i
$408$		−	0.706516i		−	0.0349778i
$409$	6.36709	−	5.19857i	0.314832	−	0.257053i	−0.461832	−	0.886968i	$-0.652808\pi$
$409$	6.36709	−	5.19857i	0.314832	−	0.257053i	0.776664	+	0.629915i	$0.216910\pi$
$410$	6.22808	+	1.80398i	0.307583	+	0.0890924i
$411$	7.80560	+	8.81070i	0.385022	+	0.434600i
$412$	10.4006	−	10.8282i	0.512402	−	0.533467i
$413$	12.6416	+	4.22040i	0.622054	+	0.207672i
$414$	−2.55973	−	3.40638i	−0.125804	−	0.167414i
$415$	−0.241039	−	1.98514i	−0.0118322	−	0.0974465i
$416$	−11.6355	−	15.7632i	−0.570479	−	0.772857i
$417$	−0.722863	+	5.95331i	−0.0353987	+	0.291535i
$418$	−13.7798	+	7.95575i	−0.673990	+	0.389128i
$419$	−18.3513	+	13.7901i	−0.896519	+	0.673690i	−0.945679	−	0.325101i	$-0.894602\pi$
$419$	−18.3513	+	13.7901i	−0.896519	+	0.673690i	0.0491607	+	0.998791i	$0.484345\pi$
$420$	−0.202657	+	5.02889i	−0.00988866	+	0.245385i
$421$	4.59468	−	1.74253i	0.223931	−	0.0849258i	−0.240088	−	0.970751i	$-0.577176\pi$
$421$	4.59468	−	1.74253i	0.223931	−	0.0849258i	0.464019	+	0.885825i	$0.346407\pi$
$422$	−6.10571	+	1.24649i	−0.297221	+	0.0606782i
$423$	−11.6423	+	2.37679i	−0.566068	+	0.115564i
$424$	4.23272	−	1.60526i	0.205559	−	0.0779583i
$425$	0.0423261	−	1.05031i	0.00205312	−	0.0509476i
$426$	3.05762	−	2.29765i	0.148142	−	0.111322i
$427$	−20.0216	+	11.5595i	−0.968913	+	0.559402i
$428$	−2.38855	+	19.6715i	−0.115455	+	0.950856i
$429$	1.46282	−	16.3718i	0.0706255	−	0.790438i
$430$	−0.833132	−	6.86146i	−0.0401772	−	0.330889i
$431$	−11.2588	−	14.9827i	−0.542316	−	0.721692i	0.442213	−	0.896910i	$-0.354193\pi$
$431$	−11.2588	−	14.9827i	−0.542316	−	0.721692i	−0.984530	+	0.175218i	$0.943937\pi$
$432$	2.02622	+	0.676453i	0.0974867	+	0.0325458i
$433$	−21.9432	+	22.8453i	−1.05452	+	1.09787i	−0.0594988	+	0.998228i	$0.518950\pi$
$433$	−21.9432	+	22.8453i	−1.05452	+	1.09787i	−0.995023	+	0.0996452i	$0.968229\pi$
$434$	−1.52316	−	1.71930i	−0.0731142	−	0.0825288i
$435$	0.669840	+	0.194021i	0.0321163	+	0.00930261i
$436$	12.3149	−	10.0548i	0.589778	−	0.481539i
$437$			45.2526i			2.16472i
$438$	2.24031	+	2.74388i	0.107046	+	0.131108i
$439$	−1.02375	−	25.4041i	−0.0488609	−	1.21247i	−0.818695	−	0.574228i	$-0.805302\pi$
$439$	−1.02375	−	25.4041i	−0.0488609	−	1.21247i	0.769835	−	0.638244i	$-0.220339\pi$
$440$	5.14101	+	12.0664i	0.245088	+	0.575242i
$441$	−0.761418	+	2.00769i	−0.0362580	+	0.0956045i
$442$	0.214079	+	0.660001i	0.0101827	+	0.0313930i
$443$	−9.22302	−	24.3191i	−0.438199	−	1.15544i	−0.954285	−	0.298899i	$-0.903381\pi$
$443$	−9.22302	−	24.3191i	−0.438199	−	1.15544i	0.516086	−	0.856537i	$-0.327389\pi$
$444$	−10.5643	+	10.1472i	−0.501361	+	0.481564i
$445$	5.00727	+	17.2871i	0.237367	+	0.819488i
$446$	13.7731	−	1.11188i	0.652175	−	0.0526490i
$447$	−2.39888	+	4.57069i	−0.113463	+	0.216186i
$448$	1.83843	+	1.76584i	0.0868577	+	0.0834279i
$449$	2.70929	−	6.35894i	0.127859	−	0.300097i	−0.843731	−	0.536766i	$-0.819646\pi$
$449$	2.70929	−	6.35894i	0.127859	−	0.300097i	0.971590	+	0.236670i	$0.0760559\pi$
$450$	−1.67848	−	0.636564i	−0.0791244	−	0.0300079i
$451$	37.2321	+	6.05081i	1.75319	+	0.284922i
$452$	9.93350	+	6.28157i	0.467233	+	0.295460i
$453$	−17.8073	+	5.15796i	−0.836662	+	0.242342i
$454$	−6.18241	+	8.95677i	−0.290155	+	0.420362i
$455$	−2.93135	−	10.4542i	−0.137424	−	0.490101i
$456$	7.27921	+	10.5458i	0.340880	+	0.493850i
$457$	−1.79938	−	1.46915i	−0.0841713	−	0.0687238i	0.589426	−	0.807823i	$-0.299354\pi$
$457$	−1.79938	−	1.46915i	−0.0841713	−	0.0687238i	−0.673597	+	0.739099i	$0.735252\pi$
$458$	−2.60495	+	3.19048i	−0.121721	+	0.149081i
$459$	−0.268362	−	0.201661i	−0.0125261	−	0.00941274i
$460$	16.8576	+	2.04689i	0.785990	+	0.0954365i
$461$	−4.90744	−	14.6996i	−0.228562	−	0.684628i	−0.998896	−	0.0469862i	$-0.985038\pi$
$461$	−4.90744	−	14.6996i	−0.228562	−	0.684628i	0.770333	−	0.637642i	$-0.220090\pi$
$462$	−0.463258	−	5.73848i	−0.0215527	−	0.266978i
$463$	3.12083	−	3.52269i	0.145037	−	0.163713i	−0.671503	−	0.741002i	$-0.734351\pi$
$463$	3.12083	−	3.52269i	0.145037	−	0.163713i	0.816540	+	0.577289i	$0.195889\pi$
$464$	0.921071	−	0.582450i	0.0427596	−	0.0270396i
$465$	2.28736	−	0.974553i	0.106074	−	0.0451938i
$466$	−2.63319	−	16.2027i	−0.121980	−	0.750574i
$467$	10.6988	−	9.47829i	0.495081	−	0.438603i	−0.378270	−	0.925695i	$-0.623481\pi$
$467$	10.6988	−	9.47829i	0.495081	−	0.438603i	0.873351	+	0.487092i	$0.161942\pi$
$468$	−6.02595	−	0.0515809i	−0.278550	−	0.00238433i
$469$	5.24306	+	4.64494i	0.242102	+	0.214484i
$470$	−4.97676	+	7.87011i	−0.229561	+	0.363021i
$471$	4.93021	+	0.398008i	0.227172	+	0.0183392i
$472$	−2.54699	−	12.4760i	−0.117235	−	0.574255i
$473$	−9.62268	−	39.0407i	−0.442451	−	1.79509i
$474$	1.34725	−	8.28997i	0.0618813	−	0.380771i
$475$	10.1896	+	16.1135i	0.467529	+	0.739338i
$476$	−0.574372	−	1.09437i	−0.0263263	−	0.0501605i
$477$	0.598408	−	2.06594i	0.0273992	−	0.0945931i
$478$	−0.542884	+	2.65922i	−0.0248309	+	0.121630i
$479$	16.4760	−	0.663958i	0.752805	−	0.0303370i	0.339103	−	0.940749i	$-0.389876\pi$
$479$	16.4760	−	0.663958i	0.752805	−	0.0303370i	0.413702	+	0.910412i	$0.364235\pi$
$480$	6.57726	−	3.45201i	0.300209	−	0.157562i
$481$	14.9242	−	27.8537i	0.680486	−	1.27002i
$482$	4.14709	+	2.17656i	0.188895	+	0.0991395i
$483$	−14.7926	−	7.01917i	−0.673086	−	0.319383i
$484$	8.17523	+	14.1599i	0.371601	+	0.643633i
$485$	0.101154	−	0.175204i	0.00459317	−	0.00795560i
$486$	−0.471794	+	0.325656i	−0.0214010	+	0.0147721i
$487$	−19.9296	+	26.5214i	−0.903095	+	1.20180i	0.0757358	+	0.997128i	$0.475869\pi$
$487$	−19.9296	+	26.5214i	−0.903095	+	1.20180i	−0.978830	+	0.204673i	$0.934387\pi$
$488$	19.1290	+	11.0441i	0.865928	+	0.499944i
$489$	21.9471	−	2.66486i	0.992482	−	0.120509i
$490$	0.721349	+	1.52021i	0.0325872	+	0.0686761i
$491$	−6.89969	−	7.18334i	−0.311379	−	0.324179i	0.547062	−	0.837092i	$-0.315746\pi$
$491$	−6.89969	−	7.18334i	−0.311379	−	0.324179i	−0.858441	+	0.512912i	$0.828567\pi$
$492$	1.11279	−	13.7844i	0.0501684	−	0.621447i
$493$	−0.166277	+	0.0409836i	−0.00748875	+	0.00184581i
$494$	−9.99540	−	7.64580i	−0.449714	−	0.344001i
$495$	6.05068	+	1.49136i	0.271958	+	0.0670316i
$496$	1.23037	−	3.68539i	0.0552450	−	0.165479i
$497$	6.30052	−	13.2781i	0.282617	−	0.595602i
$498$	0.795470	−	0.265567i	0.0356459	−	0.0119003i
$499$	−4.70080	−	3.24472i	−0.210437	−	0.145254i	0.458185	−	0.888857i	$-0.348500\pi$
$499$	−4.70080	−	3.24472i	−0.210437	−	0.145254i	−0.668621	+	0.743603i	$0.733115\pi$
$500$	16.7841	−	7.96416i	0.750608	−	0.356168i
$501$	−13.3234	−	0.536914i	−0.595244	−	0.0239875i
$502$	−0.787172	+	3.19368i	−0.0351332	+	0.142541i
$503$	1.75102	+	0.746039i	0.0780741	+	0.0332642i	0.430651	−	0.902519i	$-0.358284\pi$
$503$	1.75102	+	0.746039i	0.0780741	+	0.0332642i	−0.352577	+	0.935783i	$0.614694\pi$
$504$	−4.57638	+	0.743734i	−0.203848	+	0.0331285i
$505$	1.70535	+	0.348150i	0.0758871	+	0.0154925i
$506$	−19.4248			−0.863539
$507$	12.3996	−	3.90500i	0.550687	−	0.173427i
$508$	−30.5992			−1.35762
$509$	35.5455	+	7.25666i	1.57553	+	0.321646i	0.906701	−	0.421774i	$-0.138592\pi$
$509$	35.5455	+	7.25666i	1.57553	+	0.321646i	0.668825	+	0.743420i	$0.266798\pi$
$510$	−0.259654	+	0.0421978i	−0.0114977	+	0.00186855i
$511$	12.5227	+	5.33542i	0.553971	+	0.236025i
$512$	4.92984	−	20.0011i	0.217870	−	0.883934i
$513$	6.08340	+	0.245153i	0.268589	+	0.0108238i
$514$	−2.87551	+	1.36445i	−0.126833	+	0.0601832i
$515$	−10.1060	−	6.97568i	−0.445324	−	0.307385i
$516$	−13.9829	+	4.66818i	−0.615563	+	0.205505i
$517$	−23.2222	+	48.9397i	−1.02131	+	2.15237i
$518$	3.50490	−	10.4985i	0.153996	−	0.461276i
$519$	−17.3861	−	4.28530i	−0.763167	−	0.188104i
$520$	−7.24965	+	7.41951i	−0.317918	+	0.325367i
$521$	−7.33436	+	1.80776i	−0.321324	+	0.0791993i	−0.396679	−	0.917958i	$-0.629837\pi$
$521$	−7.33436	+	1.80776i	−0.321324	+	0.0791993i	0.0753546	+	0.997157i	$0.475991\pi$
$522$	−0.0235333	+	0.291512i	−0.00103002	+	0.0127591i
$523$	−15.8439	−	16.4953i	−0.692807	−	0.721289i	0.278151	−	0.960537i	$-0.410278\pi$
$523$	−15.8439	−	16.4953i	−0.692807	−	0.721289i	−0.970958	+	0.239249i	$0.923099\pi$
$524$	9.59010	+	20.2107i	0.418945	+	0.882909i
$525$	−6.84784	+	0.831478i	−0.298864	+	0.0362887i
$526$	−9.18407	−	5.30243i	−0.400444	−	0.231197i
$527$	−0.366791	+	0.488110i	−0.0159777	+	0.0212624i
$528$	8.01449	−	5.53200i	0.348786	−	0.240750i
$529$	−16.1223	+	27.9246i	−0.700969	+	1.21411i
$530$	−0.842760	−	1.45970i	−0.0366071	−	0.0634054i
$531$	−5.46586	−	2.59358i	−0.237198	−	0.112552i
$532$	19.8486	+	10.4174i	0.860547	+	0.451650i
$533$	6.89134	+	29.0263i	0.298497	+	1.25727i
$534$	−6.68321	+	3.50762i	−0.289211	+	0.151790i
$535$	16.1939	−	0.652593i	0.700125	−	0.0282141i
$536$	1.33864	−	6.55712i	0.0578206	−	0.283224i
$537$	4.79041	−	16.5384i	0.206722	−	0.713686i
$538$	−2.99645	−	5.70926i	−0.129186	−	0.246144i
$539$	5.23178	+	8.27340i	0.225349	+	0.356361i
$540$	0.366492	−	2.25512i	0.0157713	−	0.0970447i
$541$	−1.85913	−	7.54280i	−0.0799304	−	0.324290i	0.917342	−	0.398100i	$-0.130330\pi$
$541$	−1.85913	−	7.54280i	−0.0799304	−	0.324290i	−0.997272	+	0.0738098i	$0.976484\pi$
$542$	−1.82545	−	8.94164i	−0.0784098	−	0.384076i
$543$	5.04042	+	0.406905i	0.216305	+	0.0174620i
$544$	−0.974927	+	1.54172i	−0.0417996	+	0.0661008i
$545$	−9.73285	−	8.62255i	−0.416909	−	0.369349i
$546$	4.04972	−	2.08144i	0.173312	−	0.0890776i
$547$	−2.27160	+	2.01246i	−0.0971267	+	0.0860467i	−0.710289	−	0.703910i	$-0.751436\pi$
$547$	−2.27160	+	2.01246i	−0.0971267	+	0.0860467i	0.613162	+	0.789957i	$0.289897\pi$
$548$	−3.15585	−	19.4187i	−0.134811	−	0.829528i
$549$	9.65498	−	4.11360i	0.412064	−	0.175564i
$550$	−6.91677	+	4.37390i	−0.294932	+	0.186504i
$551$	2.05967	−	2.32489i	0.0877449	−	0.0990436i
$552$	1.25878	+	15.5927i	0.0535770	+	0.663671i
$553$	−10.2200	−	30.6127i	−0.434599	−	1.30178i
$554$	−14.6534	−	1.77924i	−0.622561	−	0.0755926i
$555$	9.57773	+	7.19720i	0.406552	+	0.305504i
$556$	6.33913	−	7.76402i	0.268839	−	0.329268i
$557$	−23.5683	−	19.2430i	−0.998623	−	0.815350i	−0.0157949	−	0.999875i	$-0.505028\pi$
$557$	−23.5683	−	19.2430i	−0.998623	−	0.815350i	−0.982828	+	0.184525i	$0.940925\pi$
$558$	0.592319	+	0.858122i	0.0250749	+	0.0363272i
$559$	25.5859	−	18.8861i	1.08217	−	0.798796i
$560$	3.65415	−	5.29394i	0.154416	−	0.223710i
$561$	−1.46991	+	0.425765i	−0.0620597	+	0.0179758i
$562$	−11.5797	−	7.32258i	−0.488462	−	0.308885i
$563$	−4.73820	−	0.770032i	−0.199691	−	0.0324530i	0.0597429	−	0.998214i	$-0.480972\pi$
$563$	−4.73820	−	0.770032i	−0.199691	−	0.0324530i	−0.259434	+	0.965761i	$0.583536\pi$
$564$	18.5693	+	7.04239i	0.781907	+	0.296538i
$565$	3.76780	−	8.84334i	0.158512	−	0.372042i
$566$	10.2584	+	9.85336i	0.431194	+	0.414168i
$567$	−1.02374	+	1.95057i	−0.0429930	+	0.0819163i
$568$	−13.9963	+	1.12990i	−0.587271	+	0.0474094i
$569$	−3.05329	−	10.5412i	−0.128000	−	0.441909i	0.870759	−	0.491711i	$-0.163628\pi$
$569$	−3.05329	−	10.5412i	−0.128000	−	0.441909i	−0.998759	+	0.0498017i	$0.984141\pi$
$570$	3.44094	−	3.30506i	0.144125	−	0.138434i
$571$	1.08446	+	2.85950i	0.0453834	+	0.119666i	0.955792	−	0.294045i	$-0.0950016\pi$
$571$	1.08446	+	2.85950i	0.0453834	+	0.119666i	−0.910408	+	0.413711i	$0.864232\pi$
$572$	−16.6911	+	21.8203i	−0.697889	+	0.912355i
$573$	−4.04021	+	10.6532i	−0.168782	+	0.445043i
$574$	4.09574	+	9.61306i	0.170953	+	0.401241i
$575$	0.937172	+	23.2557i	0.0390828	+	0.969829i
$576$	−0.731844	−	0.896346i	−0.0304935	−	0.0373477i
$577$			16.3566i			0.680935i	0.940256	+	0.340467i	$0.110585\pi$
$577$			16.3566i			0.680935i	−0.940256	+	0.340467i	$0.889415\pi$
$578$	−7.49898	+	6.12272i	−0.311916	+	0.254672i
$579$	−10.9098	−	3.16006i	−0.453396	−	0.131328i
$580$	−0.772910	−	0.872435i	−0.0320933	−	0.0362259i
$581$	2.23236	−	2.32413i	0.0926139	−	0.0964213i
$582$	0.0804764	+	0.0268670i	0.00333585	+	0.00111367i
$583$	−5.89050	−	7.83884i	−0.243960	−	0.324651i
$584$	−1.56759	−	12.9102i	−0.0648672	−	0.534229i
$585$	0.748948	+	4.87145i	0.0309652	+	0.201410i
$586$	−1.46174	+	12.0385i	−0.0603839	+	0.497306i
$587$	4.83213	−	2.78983i	0.199443	−	0.115149i	−0.396952	−	0.917839i	$-0.629932\pi$
$587$	4.83213	−	2.78983i	0.199443	−	0.115149i	0.596396	+	0.802690i	$0.296599\pi$
$588$	2.86903	−	2.15594i	0.118317	−	0.0889094i
$589$	0.445895	−	11.0648i	0.0183728	−	0.455916i
$590$	−4.43297	+	1.68120i	−0.182502	+	0.0692140i
$591$	−6.12752	+	1.25094i	−0.252053	+	0.0514569i
$592$	18.3435	−	3.74485i	0.753913	−	0.153912i
$593$	−9.60667	+	3.64333i	−0.394498	+	0.149614i	−0.543874	−	0.839167i	$-0.683043\pi$
$593$	−9.60667	+	3.64333i	−0.394498	+	0.149614i	0.149375	+	0.988781i	$0.452274\pi$
$594$	−0.105233	+	2.61132i	−0.00431775	+	0.107144i
$595$	−0.808121	+	0.607263i	−0.0331297	+	0.0248954i
$596$	7.47163	−	4.31375i	0.306050	−	0.176698i
$597$	0.509002	−	4.19201i	0.0208320	−	0.171567i
$598$	−5.90061	−	14.1847i	−0.241294	−	0.580056i
$599$	3.23529	+	26.6450i	0.132190	+	1.08869i	0.896253	+	0.443544i	$0.146279\pi$
$599$	3.23529	+	26.6450i	0.132190	+	1.08869i	−0.764062	+	0.645143i	$0.776798\pi$
$600$	3.95925	+	5.26880i	0.161636	+	0.215098i
$601$	21.7952	+	7.27631i	0.889045	+	0.296807i	0.724264	−	0.689523i	$-0.242180\pi$
$601$	21.7952	+	7.27631i	0.889045	+	0.296807i	0.164782	+	0.986330i	$0.447308\pi$
$602$	7.71596	−	8.03316i	0.314479	−	0.327407i
$603$	−2.10856	−	2.38007i	−0.0858671	−	0.0969239i
$604$	29.7625	+	8.62080i	1.21102	+	0.350775i
$605$	10.3586	−	8.45752i	0.421136	−	0.343847i
$606$			0.729931i			0.0296514i
$607$	0.815813	+	0.999190i	0.0331128	+	0.0405559i	0.790896	−	0.611951i	$-0.209615\pi$
$607$	0.815813	+	0.999190i	0.0331128	+	0.0405559i	−0.757783	+	0.652507i	$0.773717\pi$
$608$	−1.33215	−	33.0571i	−0.0540260	−	1.34064i
$609$	0.440503	+	1.03390i	0.0178501	+	0.0418957i
$610$	2.91634	−	7.68977i	0.118079	−	0.311350i
$611$	−42.7917	−	2.09145i	−1.73117	−	0.0846112i
$612$	0.198952	+	0.524594i	0.00804216	+	0.0212054i
$613$	0.975410	−	0.936894i	0.0393964	−	0.0378408i	−0.672768	−	0.739854i	$-0.734895\pi$
$613$	0.975410	−	0.936894i	0.0393964	−	0.0378408i	0.712164	+	0.702013i	$0.247715\pi$
$614$	3.79076	+	13.0872i	0.152983	+	0.528158i
$615$	−11.2740	+	0.910129i	−0.454610	+	0.0366999i
$616$	−9.82265	+	18.7155i	−0.395766	+	0.754068i
$617$	3.07873	+	2.95716i	0.123945	+	0.119051i	0.752135	−	0.659010i	$-0.229024\pi$
$617$	3.07873	+	2.95716i	0.123945	+	0.119051i	−0.628190	+	0.778060i	$0.716204\pi$
$618$	2.01855	−	4.73771i	0.0811979	−	0.190579i
$619$	−11.2222	−	4.25601i	−0.451057	−	0.171063i	0.118607	−	0.992941i	$-0.462157\pi$
$619$	−11.2222	−	4.25601i	−0.451057	−	0.171063i	−0.569664	+	0.821878i	$0.692927\pi$
$620$	−4.10171	−	0.666593i	−0.164729	−	0.0267710i
$621$	6.28202	+	3.97251i	0.252089	+	0.159411i
$622$	0.690982	−	0.200145i	0.0277059	−	0.00802510i
$623$	−16.4759	+	23.8695i	−0.660094	+	0.956311i
$624$	6.47420	+	4.17204i	0.259175	+	0.167015i
$625$	0.262732	+	0.380632i	0.0105093	+	0.0152253i
$626$	10.1426	+	8.28115i	0.405378	+	0.330981i
$627$	17.5539	−	21.4996i	0.701034	−	0.858611i
$628$	−6.60896	−	4.96631i	−0.263726	−	0.198177i
$629$	−2.92060	−	0.354625i	−0.116452	−	0.0141398i
$630$	0.546663	+	1.63746i	0.0217796	+	0.0652378i
$631$	−1.05644	−	13.0864i	−0.0420563	−	0.520961i	−0.983148	−	0.182810i	$-0.941481\pi$
$631$	−1.05644	−	13.0864i	−0.0420563	−	0.520961i	0.941092	−	0.338151i	$-0.109801\pi$
$632$	−20.4472	+	23.0801i	−0.813347	+	0.918078i
$633$	9.18748	−	5.80981i	0.365170	−	0.230919i
$634$	7.57580	−	3.22775i	0.300874	−	0.128190i
$635$	4.01453	+	24.7024i	0.159312	+	0.980285i
$636$	−2.69079	+	2.38384i	−0.106697	+	0.0945253i
$637$	−4.45230	+	6.33362i	−0.176407	+	0.250947i
$638$	0.997966	+	0.884121i	0.0395099	+	0.0350027i
$639$	−3.56579	+	5.63884i	−0.141060	+	0.223069i
$640$	−15.7119	−	1.26840i	−0.621067	−	0.0501377i
$641$	5.87884	+	28.7965i	0.232200	+	1.13739i	0.913956	+	0.405812i	$0.133011\pi$
$641$	5.87884	+	28.7965i	0.232200	+	1.13739i	−0.681756	+	0.731579i	$0.738784\pi$
$642$	1.62659	+	6.59932i	0.0641963	+	0.260454i
$643$	−0.379401	+	2.33455i	−0.0149621	+	0.0920657i	−0.993457	−	0.114204i	$-0.963568\pi$
$643$	−0.379401	+	2.33455i	−0.0149621	+	0.0920657i	0.978495	+	0.206270i	$0.0661324\pi$
$644$	14.6261	+	23.1294i	0.576350	+	0.911425i
$645$	5.60309	+	10.6758i	0.220621	+	0.420359i
$646$	−0.325970	+	1.12538i	−0.0128251	+	0.0442775i
$647$	6.40882	−	31.3925i	0.251957	−	1.23417i	−0.635072	−	0.772453i	$-0.719030\pi$
$647$	6.40882	−	31.3925i	0.251957	−	1.23417i	0.887029	−	0.461713i	$-0.152765\pi$
$648$	2.10298	−	0.0847473i	0.0826129	−	0.00332919i
$649$	−24.4215	+	12.8174i	−0.958629	+	0.503127i
$650$	−5.29506	−	3.72223i	−0.207689	−	0.145998i
$651$	3.54779	+	1.86203i	0.139049	+	0.0729786i
$652$	−33.3833	−	15.8406i	−1.30739	−	0.620364i
$653$	3.52847	+	6.11148i	0.138080	+	0.239161i	0.926770	−	0.375630i	$-0.122574\pi$
$653$	3.52847	+	6.11148i	0.138080	+	0.239161i	−0.788690	+	0.614791i	$0.789240\pi$
$654$	2.72655	−	4.72252i	0.106616	−	0.184665i
$655$	15.0577	−	10.3936i	0.588353	−	0.406111i
$656$	−10.6182	+	14.1302i	−0.414569	+	0.551691i
$657$	−5.35125	−	3.08954i	−0.208772	−	0.120535i
$658$	−14.8965	+	1.80876i	−0.580725	+	0.0705128i
$659$	−1.49808	−	3.15714i	−0.0583570	−	0.122985i	0.872177	−	0.489191i	$-0.162708\pi$
$659$	−1.49808	−	3.15714i	−0.0583570	−	0.122985i	−0.930534	+	0.366206i	$0.880657\pi$
$660$	−7.21508	−	7.51170i	−0.280847	−	0.292392i
$661$	−3.71329	+	45.9973i	−0.144430	+	1.78909i	0.367463	+	0.930038i	$0.380226\pi$
$661$	−3.71329	+	45.9973i	−0.144430	+	1.78909i	−0.511893	+	0.859049i	$0.671056\pi$
$662$	18.2511	−	4.49848i	0.709348	−	0.174839i
$663$	−0.757418	−	0.944050i	−0.0294157	−	0.0366638i
$664$	−2.98944	−	0.736831i	−0.116013	−	0.0285946i
$665$	5.80574	−	17.3903i	0.225137	−	0.674367i
$666$	−2.15389	+	4.53922i	−0.0834614	+	0.175891i
$667$	3.59670	−	1.20075i	0.139265	−	0.0464934i
$668$	18.3412	+	12.6600i	0.709642	+	0.489830i
$669$	−21.7764	+	10.3330i	−0.841922	+	0.399497i
$670$	−2.48978	−	0.100335i	−0.0961884	−	0.00387626i
$671$	11.4497	−	46.4534i	0.442012	−	1.79331i
$672$	11.0126	+	4.69204i	0.424821	+	0.180999i
$673$	6.77406	−	1.10089i	0.261121	−	0.0424363i	−0.0284414	−	0.999595i	$-0.509054\pi$
$673$	6.77406	−	1.10089i	0.261121	−	0.0424363i	0.289562	+	0.957159i	$0.406490\pi$
$674$	10.3326	+	2.10942i	0.397998	+	0.0812519i
$675$	3.13139			0.120527
$676$	−21.0042	−	5.56014i	−0.807854	−	0.213852i
$677$	−15.3586			−0.590281			−0.295140	−	0.955454i	$-0.595366\pi$
$677$	−15.3586			−0.590281			−0.295140	+	0.955454i	$0.595366\pi$
$678$	3.94978	+	0.806353i	0.151690	+	0.0309678i
$679$	0.321801	−	0.0522978i	0.0123496	−	0.00200700i
$680$	0.888505	+	0.378557i	0.0340726	+	0.0145170i
$681$	4.54328	−	18.4328i	0.174099	−	0.706348i
$682$	4.74960	+	0.191402i	0.181871	+	0.00732917i
$683$	36.5488	−	17.3426i	1.39850	−	0.663597i	0.427796	−	0.903875i	$-0.359290\pi$
$683$	36.5488	−	17.3426i	1.39850	−	0.663597i	0.970704	+	0.240279i	$0.0772388\pi$
$684$	−8.37451	−	5.78051i	−0.320208	−	0.221023i
$685$	−15.2625	+	5.09538i	−0.583151	+	0.194684i
$686$	−4.95212	+	10.4364i	−0.189073	+	0.398463i
$687$	2.27520	−	6.81505i	0.0868042	−	0.260010i
$688$	18.2936	+	4.50897i	0.697438	+	0.171903i
$689$	3.93487	−	6.68263i	0.149907	−	0.254588i
$690$	5.65534	−	1.39392i	0.215295	−	0.0530655i
$691$	1.76278	−	21.8360i	0.0670594	−	0.830680i	−0.872571	−	0.488488i	$-0.837549\pi$
$691$	1.76278	−	21.8360i	0.0670594	−	0.830680i	0.939630	−	0.342192i	$-0.111169\pi$
$692$	20.7320	+	21.5842i	0.788111	+	0.820510i
$693$	4.30519	+	9.07299i	0.163541	+	0.344655i
$694$	20.6764	−	2.51057i	0.784866	−	0.0953000i
$695$	−7.09949	−	4.09889i	−0.269299	−	0.155480i
$696$	0.645032	−	0.858382i	0.0244499	−	0.0325369i
$697$	2.28588	−	1.57783i	0.0865838	−	0.0597645i
$698$	−2.30495	+	3.99229i	−0.0872435	+	0.151110i
$699$	14.3171	+	24.7980i	0.541524	+	0.937947i
$700$	10.4161	+	4.94250i	0.393692	+	0.186809i
$701$	24.5596	+	12.8899i	0.927602	+	0.486843i	0.859672	−	0.510847i	$-0.170668\pi$
$701$	24.5596	+	12.8899i	0.927602	+	0.486843i	0.0679303	+	0.997690i	$0.478360\pi$
$702$	−1.93885	+	0.716386i	−0.0731771	+	0.0270382i
$703$	47.2478	−	24.7975i	1.78198	−	0.935257i
$704$	−5.27101	+	0.212415i	−0.198659	+	0.00800568i
$705$	3.24901	−	15.9147i	0.122365	−	0.599383i
$706$	0.664145	−	2.29289i	0.0249954	−	0.0862942i
$707$	1.30350	+	2.48361i	0.0490230	+	0.0934056i
$708$	5.40436	+	8.54631i	0.203108	+	0.321190i
$709$	−0.425630	+	2.61901i	−0.0159849	+	0.0983590i	−0.993817	−	0.111033i	$-0.964584\pi$
$709$	−0.425630	+	2.61901i	−0.0159849	+	0.0983590i	0.977832	+	0.209392i	$0.0671483\pi$
$710$	1.25120	+	5.07633i	0.0469568	+	0.190511i
$711$	2.93048	+	14.3544i	0.109901	+	0.538333i
$712$	27.6207	+	2.22977i	1.03513	+	0.0835642i
$713$	7.22539	−	11.4260i	0.270593	−	0.427909i
$714$	−0.317313	−	0.281115i	−0.0118751	−	0.0105205i
$715$	19.8052	+	10.6118i	0.740671	+	0.396857i
$716$	−21.5405	+	19.0832i	−0.805007	+	0.713174i
$717$	−0.759443	−	4.67304i	−0.0283619	−	0.174518i
$718$	15.0636	−	6.41798i	0.562167	−	0.239517i
$719$	−14.9987	+	9.48460i	−0.559357	+	0.353716i	−0.784034	−	0.620717i	$-0.786841\pi$
$719$	−14.9987	+	9.48460i	−0.559357	+	0.353716i	0.224678	+	0.974433i	$0.427867\pi$
$720$	−1.93636	+	2.18570i	−0.0721640	+	0.0814563i
$721$	−1.59235	−	19.7248i	−0.0593023	−	0.734591i
$722$	−3.27998	−	9.82474i	−0.122068	−	0.365639i
$723$	−8.11030	−	0.984769i	−0.301625	−	0.0366239i
$724$	−6.75670	−	5.07733i	−0.251111	−	0.188697i
$725$	1.01033	−	1.23743i	0.0375229	−	0.0459572i
$726$	4.34412	+	3.54686i	0.161225	+	0.131636i
$727$	−23.4508	−	33.9743i	−0.869741	−	1.26004i	−0.964379	−	0.264525i	$-0.914785\pi$
$727$	−23.4508	−	33.9743i	−0.869741	−	1.26004i	0.0946381	−	0.995512i	$-0.469831\pi$
$728$	−16.6505	−	1.48772i	−0.617109	−	0.0551386i
$729$	0.568065	−	0.822984i	0.0210394	−	0.0304809i
$730$	−4.65105	+	1.34719i	−0.172143	+	0.0498618i
$731$	−2.50243	−	1.58244i	−0.0925557	−	0.0585287i
$732$	−17.3134	−	2.81370i	−0.639921	−	0.103997i
$733$	−12.1402	−	4.60417i	−0.448409	−	0.170059i	0.120055	−	0.992767i	$-0.461693\pi$
$733$	−12.1402	−	4.60417i	−0.448409	−	0.170059i	−0.568464	+	0.822708i	$0.692462\pi$
$734$	−1.29942	+	3.04986i	−0.0479626	+	0.112572i
$735$	−2.11688	−	2.03329i	−0.0780822	−	0.0749989i
$736$	18.7697	−	35.7626i	0.691860	−	1.31823i
$737$	−14.4488	+	1.16643i	−0.532229	+	0.0429660i
$738$	−1.31969	−	4.55611i	−0.0485786	−	0.167713i
$739$	−11.5760	+	11.1189i	−0.425829	+	0.409014i	−0.874763	−	0.484550i	$-0.838983\pi$
$739$	−11.5760	+	11.1189i	−0.425829	+	0.409014i	0.448934	+	0.893565i	$0.351804\pi$
$740$	−7.10051	−	18.7225i	−0.261020	−	0.688253i
$741$	21.0321	+	6.28763i	0.772632	+	0.230982i
$742$	0.963194	−	2.53973i	0.0353599	−	0.0932365i
$743$	−6.62629	−	15.5525i	−0.243095	−	0.570565i	0.753082	−	0.657927i	$-0.228567\pi$
$743$	−6.62629	−	15.5525i	−0.243095	−	0.570565i	−0.996177	+	0.0873620i	$0.972156\pi$
$744$	−0.154142	−	3.82501i	−0.00565114	−	0.140232i
$745$	−4.46270	−	5.46582i	−0.163501	−	0.200252i
$746$		−	17.2504i		−	0.631583i
$747$	−1.13315	+	0.925192i	−0.0414599	+	0.0338510i
$748$	2.45675	+	0.711606i	0.0898276	+	0.0260189i
$749$	17.3194	+	19.5496i	0.632838	+	0.714327i
$750$	4.41414	−	4.59560i	0.161182	−	0.167808i
$751$	−5.48993	−	1.83281i	−0.200330	−	0.0668801i	0.214732	−	0.976673i	$-0.431112\pi$
$751$	−5.48993	−	1.83281i	−0.200330	−	0.0668801i	−0.415063	+	0.909793i	$0.636240\pi$
$752$	−15.2485	−	20.2921i	−0.556055	−	0.739975i
$753$	−0.691602	−	5.69586i	−0.0252034	−	0.207569i
$754$	−0.342469	+	0.997317i	−0.0124720	+	0.0363202i
$755$	3.05473	−	25.1580i	0.111173	−	0.915592i
$756$	3.18856	−	1.84092i	0.115967	−	0.0669536i
$757$	−0.623781	+	0.468741i	−0.0226717	+	0.0170367i	−0.612018	−	0.790844i	$-0.709642\pi$
$757$	−0.623781	+	0.468741i	−0.0226717	+	0.0170367i	0.589346	+	0.807881i	$0.299385\pi$
$758$	−0.458516	+	11.3780i	−0.0166541	+	0.413266i
$759$	31.6822	−	12.0155i	1.14999	−	0.436134i
$760$	−17.1625	+	3.50374i	−0.622548	+	0.127094i
$761$	−38.7880	+	7.91862i	−1.40606	+	0.287050i	−0.842354	−	0.538924i	$-0.818831\pi$
$761$	−38.7880	+	7.91862i	−1.40606	+	0.287050i	−0.563708	+	0.825974i	$0.690626\pi$
$762$	−9.81342	+	3.72174i	−0.355503	+	0.134824i
$763$	0.843752	−	20.9375i	0.0305459	−	0.757988i
$764$	15.2236	−	11.4398i	0.550770	−	0.413877i
$765$	0.397397	−	0.229437i	0.0143679	−	0.00829532i
$766$	−0.890521	+	7.33410i	−0.0321758	+	0.264992i
$767$	−16.7782	−	13.9400i	−0.605825	−	0.503344i
$768$	−0.517857	−	4.26494i	−0.0186866	−	0.153898i
$769$	−0.141013	−	0.187654i	−0.00508506	−	0.00676699i	0.796893	−	0.604120i	$-0.206475\pi$
$769$	−0.141013	−	0.187654i	−0.00508506	−	0.00676699i	−0.801978	+	0.597353i	$0.796219\pi$
$770$	7.46485	+	2.49213i	0.269015	+	0.0898103i
$771$	3.84601	−	4.00412i	0.138511	−	0.144205i
$772$	12.5885	+	14.2095i	0.453071	+	0.511411i
$773$	−6.02806	−	1.74605i	−0.216814	−	0.0628010i	0.168033	−	0.985781i	$-0.446259\pi$
$773$	−6.02806	−	1.74605i	−0.216814	−	0.0628010i	−0.384847	+	0.922980i	$0.625746\pi$
$774$	−3.91665	+	3.19785i	−0.140781	+	0.114944i
$775$		−	5.69552i		−	0.204589i
$776$	−0.196999	−	0.241280i	−0.00707186	−	0.00866145i
$777$	0.777407	+	19.2911i	0.0278893	+	0.692066i
$778$	−5.99064	−	14.0605i	−0.214775	−	0.504095i
$779$	−17.8637	+	47.1026i	−0.640033	+	1.68763i
$780$	3.29362	−	7.55052i	0.117930	−	0.270352i
$781$	10.7853	+	28.4384i	0.385928	+	1.01761i
$782$	−1.03157	+	0.990833i	−0.0368887	+	0.0354321i
$783$	−0.141935	−	0.490017i	−0.00507235	−	0.0175118i
$784$	−4.57195	+	0.369086i	−0.163284	+	0.0131816i
$785$	−3.14217	+	5.98691i	−0.112149	+	0.213682i
$786$	5.53383	+	5.31531i	0.197385	+	0.189591i
$787$	−8.92034	+	20.9368i	−0.317976	+	0.746317i	0.681913	+	0.731433i	$0.261148\pi$
$787$	−8.92034	+	20.9368i	−0.317976	+	0.746317i	−0.999889	+	0.0148837i	$0.995262\pi$
$788$	9.77328	+	3.70652i	0.348159	+	0.132039i
$789$	18.2592	+	2.96742i	0.650046	+	0.105643i
$790$	9.70348	+	6.13611i	0.345234	+	0.218313i
$791$	14.8792	−	4.30981i	0.529043	−	0.153239i
$792$	5.45051	−	7.89643i	0.193675	−	0.280587i
$793$	37.4000	−	5.74996i	1.32811	−	0.204187i
$794$	5.73980	+	8.31554i	0.203698	+	0.295107i
$795$	2.27747	+	1.85950i	0.0807736	+	0.0659496i
$796$	−4.46368	+	5.46701i	−0.158211	+	0.193773i
$797$	−24.4880	−	18.4016i	−0.867411	−	0.651817i	0.0709479	−	0.997480i	$-0.477398\pi$
$797$	−24.4880	−	18.4016i	−0.867411	−	0.651817i	−0.938359	+	0.345663i	$0.887654\pi$
$798$	7.63267	+	0.926774i	0.270194	+	0.0328074i
$799$	1.26312	+	3.78350i	0.0446859	+	0.133851i
$800$	−1.36921	−	16.9607i	−0.0484089	−	0.599651i
$801$	8.73074	−	9.85496i	0.308485	−	0.348208i
$802$	9.52544	−	6.02352i	0.336355	−	0.212698i
$803$	−25.9152	+	11.0414i	−0.914526	+	0.389643i
$804$	0.852504	+	5.24567i	0.0300655	+	0.185000i
$805$	16.7532	−	14.8420i	0.590472	−	0.523113i
$806$	1.30300	+	3.52647i	0.0458961	+	0.124215i
$807$	8.41879	+	7.45840i	0.296355	+	0.262548i
$808$	1.43228	−	2.26497i	0.0503875	−	0.0796815i
$809$	14.4812	+	1.16905i	0.509133	+	0.0411015i	0.332365	−	0.943151i	$-0.392153\pi$
$809$	14.4812	+	1.16905i	0.509133	+	0.0411015i	0.176769	+	0.984252i	$0.443436\pi$
$810$	−0.156750	−	0.767811i	−0.00550762	−	0.0269781i
$811$	10.9804	+	44.5491i	0.385572	+	1.56433i	0.768066	+	0.640371i	$0.221219\pi$
$811$	10.9804	+	44.5491i	0.385572	+	1.56433i	−0.382494	+	0.923958i	$0.624935\pi$
$812$	0.301304	−	1.85400i	0.0105737	−	0.0650626i
$813$	8.50830	+	13.4548i	0.298399	+	0.471880i
$814$	10.6444	+	20.2813i	0.373087	+	0.710858i
$815$	−8.40813	+	29.0282i	−0.294524	+	1.01681i
$816$	0.143434	−	0.702588i	0.00502121	−	0.0245955i
$817$	53.6562	−	2.16227i	1.87719	−	0.0756482i
$818$	−4.17243	+	2.18986i	−0.145886	+	0.0765666i
$819$	−5.31766	+	5.89987i	−0.185814	+	0.206158i
$820$	16.7388	+	8.78519i	0.584544	+	0.306792i
$821$	0.285709	+	0.135571i	0.00997131	+	0.00473145i	0.433672	−	0.901071i	$-0.357218\pi$
$821$	0.285709	+	0.135571i	0.00997131	+	0.00473145i	−0.423700	+	0.905802i	$0.639269\pi$
$822$	−3.37399	−	5.84392i	−0.117681	−	0.203830i
$823$	−7.17472	+	12.4270i	−0.250095	+	0.433177i	−0.963552	−	0.267522i	$-0.913795\pi$
$823$	−7.17472	+	12.4270i	−0.250095	+	0.433177i	0.713457	+	0.700699i	$0.247129\pi$
$824$	−15.5599	+	10.7403i	−0.542057	+	0.374155i
$825$	8.57583	−	11.4124i	0.298572	−	0.397327i
$826$	−6.61669	−	3.82015i	−0.230224	−	0.132920i
$827$	−44.7153	+	5.42943i	−1.55490	+	0.188800i	−0.852404	−	0.522883i	$-0.824856\pi$
$827$	−44.7153	+	5.42943i	−1.55490	+	0.188800i	−0.702501	+	0.711683i	$0.747933\pi$
$828$	−5.32550	−	11.2233i	−0.185074	−	0.390035i
$829$	1.59578	+	1.66138i	0.0554237	+	0.0577022i	0.748337	−	0.663319i	$-0.230853\pi$
$829$	1.59578	+	1.66138i	0.0554237	+	0.0577022i	−0.692913	+	0.721021i	$0.743673\pi$
$830$	−0.0922455	+	1.14267i	−0.00320189	+	0.0396625i
$831$	25.0004	−	6.16205i	0.867255	−	0.213759i
$832$	−1.75627	−	3.78456i	−0.0608877	−	0.131206i
$833$	0.699851	+	0.172498i	0.0242484	+	0.00597670i
$834$	1.08868	−	3.26101i	0.0376981	−	0.112919i
$835$	7.81398	−	16.4676i	0.270414	−	0.569885i
$836$	−44.0021	+	14.6901i	−1.52185	+	0.508067i
$837$	−1.49688	−	1.03322i	−0.0517399	−	0.0357134i
$838$	11.8890	−	5.64139i	0.410698	−	0.194879i
$839$	0.961438	+	0.0387446i	0.0331925	+	0.00133761i	0.0568567	−	0.998382i	$-0.481892\pi$
$839$	0.961438	+	0.0387446i	0.0331925	+	0.00133761i	−0.0236641	+	0.999720i	$0.507533\pi$
$840$	1.51675	−	6.15369i	0.0523328	−	0.212323i
$841$	26.4400	+	11.2650i	0.911723	+	0.388449i
$842$	−2.78059	+	0.451889i	−0.0958254	+	0.0155731i
$843$	23.4162	+	4.78045i	0.806497	+	0.164648i
$844$	−18.1682			−0.625375
$845$	−1.73295	+	17.6859i	−0.0596153	+	0.608415i
$846$	6.81188			0.234197
$847$	21.1149	+	4.31063i	0.725516	+	0.148115i
$848$	4.53508	−	0.737023i	0.155735	−	0.0253095i
$849$	−22.8266	−	9.72550i	−0.783407	−	0.333778i
$850$	−0.144212	+	0.585093i	−0.00494645	+	0.0200685i
$851$	65.0891	+	2.62300i	2.23122	+	0.0899153i
$852$	10.0742	−	4.78025i	0.345135	−	0.163769i
$853$	34.7851	+	24.0105i	1.19102	+	0.822102i	0.987600	−	0.156989i	$-0.0501788\pi$
$853$	34.7851	+	24.0105i	1.19102	+	0.822102i	0.203420	+	0.979092i	$0.434794\pi$
$854$	12.5714	−	4.19694i	0.430184	−	0.143616i
$855$	−3.56783	+	7.51905i	−0.122017	+	0.257146i
$856$	7.90200	−	23.6694i	0.270085	−	0.809003i
$857$	1.42997	+	0.352456i	0.0488469	+	0.0120397i	0.263663	−	0.964615i	$-0.415069\pi$
$857$	1.42997	+	0.352456i	0.0488469	+	0.0120397i	−0.214816	+	0.976654i	$0.568915\pi$
$858$	−2.69899	+	9.02809i	−0.0921419	+	0.308214i
$859$	1.14265	−	0.281637i	0.0389866	−	0.00960934i	−0.219774	−	0.975551i	$-0.570532\pi$
$859$	1.14265	−	0.281637i	0.0389866	−	0.00960934i	0.258761	+	0.965941i	$0.416686\pi$
$860$	1.62151	−	20.0859i	0.0552929	−	0.684925i
$861$	−12.6265	−	13.1456i	−0.430310	−	0.448000i
$862$	4.60586	+	9.70663i	0.156876	+	0.330609i
$863$	30.3212	−	3.68167i	1.03215	−	0.125325i	0.413105	−	0.910683i	$-0.364444\pi$
$863$	30.3212	−	3.68167i	1.03215	−	0.125325i	0.619042	+	0.785358i	$0.287521\pi$
$864$	−4.70596	−	2.71699i	−0.160100	−	0.0924338i
$865$	14.7048	−	19.5685i	0.499977	−	0.665349i
$866$	14.9448	−	10.3157i	0.507847	−	0.350541i
$867$	8.44366	−	14.6248i	0.286762	−	0.496686i
$868$	−3.34835	−	5.79952i	−0.113650	−	0.196848i
$869$	60.3404	+	28.6319i	2.04691	+	0.971270i
$870$	−0.353992	−	0.185789i	−0.0120014	−	0.00629885i
$871$	−5.24083	−	10.1967i	−0.177579	−	0.345503i
$872$	−17.7271	+	9.30388i	−0.600314	+	0.315069i
$873$	−0.147877	+	0.00595925i	−0.00500488	+	0.000201690i
$874$	5.18908	−	25.4178i	0.175523	−	0.859770i
$875$	6.81246	−	23.5193i	0.230303	−	0.795098i
$876$	4.79942	+	9.14452i	0.162157	+	0.308965i
$877$	−11.1542	−	17.6390i	−0.376651	−	0.595627i	0.602657	−	0.798000i	$-0.294109\pi$
$877$	−11.1542	−	17.6390i	−0.376651	−	0.595627i	−0.979308	+	0.202374i	$0.935134\pi$
$878$	−2.33804	+	14.3865i	−0.0789051	+	0.485522i
$879$	−5.06245	−	20.5392i	−0.170752	−	0.692769i
$880$	2.66275	+	13.0430i	0.0897613	+	0.439680i
$881$	−24.5191	−	1.97938i	−0.826069	−	0.0666871i	−0.339801	−	0.940497i	$-0.610360\pi$
$881$	−24.5191	−	1.97938i	−0.826069	−	0.0666871i	−0.486267	+	0.873810i	$0.661642\pi$
$882$	0.657899	−	1.04038i	0.0221526	−	0.0350316i
$883$	−12.0291	−	10.6569i	−0.404812	−	0.358632i	0.436012	−	0.899941i	$-0.356391\pi$
$883$	−12.0291	−	10.6569i	−0.404812	−	0.358632i	−0.840824	+	0.541309i	$0.817929\pi$
$884$	0.226637	+	2.01017i	0.00762261	+	0.0676093i
$885$	6.19031	−	5.48413i	0.208085	−	0.184347i
$886$	2.39180	+	14.7173i	0.0803540	+	0.494438i
$887$	−45.1224	+	19.2249i	−1.51506	+	0.645508i	−0.979945	−	0.199269i	$-0.936143\pi$
$887$	−45.1224	+	19.2249i	−1.51506	+	0.645508i	−0.535119	+	0.844777i	$0.679733\pi$
$888$	15.5904	−	9.85878i	0.523180	−	0.330839i
$889$	−26.7441	+	30.1879i	−0.896970	+	1.01247i
$890$	−0.830220	−	10.2841i	−0.0278290	−	0.344725i
$891$	−1.44363	−	4.32420i	−0.0483634	−	0.144866i
$892$	39.9919	+	4.85590i	1.33903	+	0.162588i
$893$	−57.8351	−	43.4603i	−1.93538	−	1.45434i
$894$	1.87154	−	2.29222i	0.0625936	−	0.0766633i
$895$	18.2318	+	14.8858i	0.609421	+	0.497577i
$896$	−14.4302	−	20.9057i	−0.482079	−	0.698412i
$897$	18.3981	+	19.4856i	0.614295	+	0.650605i
$898$	−2.25095	+	3.26106i	−0.0751151	+	0.108823i
$899$	−0.891266	+	0.258158i	−0.0297254	+	0.00861007i
$900$	−4.42344	−	2.79722i	−0.147448	−	0.0932406i
$901$	−0.712666	−	0.115820i	−0.0237424	−	0.00385851i
$902$	−20.2190	−	7.66804i	−0.673218	−	0.255318i
$903$	−7.61583	+	17.8750i	−0.253439	+	0.594843i
$904$	−10.6739	−	10.2524i	−0.355009	−	0.340991i
$905$	−3.21241	+	6.12074i	−0.106784	+	0.203460i
$906$	10.5936	−	0.855205i	0.351949	−	0.0284123i
$907$	10.3923	+	35.8785i	0.345072	+	1.19133i	0.926048	+	0.377406i	$0.123184\pi$
$907$	10.3923	+	35.8785i	0.345072	+	1.19133i	−0.580976	+	0.813920i	$0.697329\pi$
$908$	−22.8837	+	21.9801i	−0.759421	+	0.729434i
$909$	−0.451508	−	1.19053i	−0.0149756	−	0.0394874i
$910$	0.447723	+	6.20813i	0.0148419	+	0.205798i
$911$	13.2948	−	35.0556i	0.440478	−	1.16144i	−0.512576	−	0.858642i	$-0.671309\pi$
$911$	13.2948	−	35.0556i	0.440478	−	1.16144i	0.953053	−	0.302802i	$-0.0979222\pi$
$912$	5.09778	+	11.9649i	0.168804	+	0.396198i
$913$	0.268533	+	6.66358i	0.00888715	+	0.220532i
$914$	0.842221	+	1.03153i	0.0278582	+	0.0341201i
$915$			14.3461i			0.474266i
$916$	−9.30175	+	7.59465i	−0.307339	+	0.250934i
$917$	28.3210	+	8.20327i	0.935240	+	0.270896i
$918$	0.127611	+	0.144043i	0.00421180	+	0.00475414i
$919$	−17.2420	+	17.9508i	−0.568761	+	0.592143i	−0.942009	−	0.335589i	$-0.891065\pi$
$919$	−17.2420	+	17.9508i	−0.568761	+	0.592143i	0.373247	+	0.927732i	$0.378244\pi$
$920$	−20.2837	−	6.77168i	−0.668733	−	0.223256i
$921$	−14.2781	−	19.0007i	−0.470478	−	0.626093i
$922$	1.07086	+	8.81930i	0.0352668	+	0.290448i
$923$	−17.4906	+	16.5144i	−0.575710	+	0.543580i
$924$	2.02318	−	16.6624i	0.0665578	−	0.548153i
$925$	23.7675	−	13.7221i	0.781469	−	0.451181i
$926$	−2.15687	+	1.62078i	−0.0708792	+	0.0532623i
$927$	−0.361715	+	8.97587i	−0.0118803	+	0.294806i
$928$	−2.59204	+	0.983033i	−0.0850880	+	0.0322696i
$929$	14.9848	−	3.05917i	0.491636	−	0.100368i	0.0521899	−	0.998637i	$-0.483380\pi$
$929$	14.9848	−	3.05917i	0.491636	−	0.100368i	0.439446	+	0.898269i	$0.355175\pi$
$930$	−1.39653	+	0.285104i	−0.0457941	+	0.00934893i
$931$	−12.2235	+	4.63577i	−0.400610	+	0.151931i
$932$	1.92705	−	47.8194i	0.0631228	−	1.56638i
$933$	−1.00320	+	0.753856i	−0.0328433	+	0.0246801i
$934$	−7.09624	+	4.09701i	−0.232196	+	0.134058i
$935$	0.252153	−	2.07667i	0.00824629	−	0.0679143i
$936$	7.42194	+	1.58149i	0.242594	+	0.0516927i
$937$	1.52680	+	12.5744i	0.0498785	+	0.410787i	0.996168	+	0.0874648i	$0.0278765\pi$
$937$	1.52680	+	12.5744i	0.0498785	+	0.410787i	−0.946289	+	0.323322i	$0.895200\pi$
$938$	−2.41232	−	3.21022i	−0.0787652	−	0.104817i
$939$	−21.6651	−	7.23287i	−0.707013	−	0.236036i
$940$	−18.8060	+	19.5791i	−0.613383	+	0.638599i
$941$	13.9296	+	15.7232i	0.454091	+	0.512562i	0.930315	−	0.366761i	$-0.119533\pi$
$941$	13.9296	+	15.7232i	0.454091	+	0.512562i	−0.476224	+	0.879324i	$0.657995\pi$
$942$	−2.72360	−	0.788899i	−0.0887395	−	0.0257037i
$943$	−47.6379	+	38.8951i	−1.55130	+	1.26660i
$944$		−	12.9237i		−	0.420631i
$945$	−1.90449	−	2.33257i	−0.0619529	−	0.0758786i
$946$	0.928162	+	23.0321i	0.0301771	+	0.748838i
$947$	3.76884	+	8.84578i	0.122471	+	0.287449i	0.969919	−	0.243429i	$-0.0782723\pi$
$947$	3.76884	+	8.84578i	0.122471	+	0.287449i	−0.847448	+	0.530878i	$0.821862\pi$
$948$	8.68294	−	22.8950i	0.282009	−	0.743596i
$949$	−15.9350	−	15.5702i	−0.517272	−	0.505430i
$950$	−3.87562	−	10.2192i	−0.125742	−	0.331553i
$951$	−10.3597	+	9.95062i	−0.335936	+	0.322671i
$952$	0.433013	+	1.49494i	0.0140340	+	0.0484511i
$953$	−49.2251	+	3.97386i	−1.59456	+	0.128726i	−0.845572	−	0.533862i	$-0.820740\pi$
$953$	−49.2251	+	3.97386i	−1.59456	+	0.128726i	−0.748985	+	0.662587i	$0.769458\pi$
$954$	−0.573018	+	1.09179i	−0.0185521	+	0.0353482i
$955$	−11.2325	−	10.7890i	−0.363475	−	0.349123i
$956$	−3.10155	+	7.27961i	−0.100311	+	0.235439i
$957$	−2.17458	−	0.824710i	−0.0702943	−	0.0266591i
$958$	−9.33046	−	1.51635i	−0.301454	−	0.0489910i
$959$	−21.9160	−	13.8588i	−0.707705	−	0.447525i
$960$	1.51936	−	0.440088i	0.0490371	−	0.0142038i
$961$	15.7307	−	22.7899i	0.507443	−	0.735158i
$962$	−11.5767	+	13.9337i	−0.373248	+	0.449241i
$963$	−6.73508	−	9.75745i	−0.217035	−	0.314429i
$964$	10.5771	+	8.63590i	0.340664	+	0.278144i
$965$	9.81960	−	12.0268i	0.316104	−	0.387157i
$966$	7.50392	+	5.63883i	0.241435	+	0.181426i
$967$	−38.4636	−	4.67032i	−1.23690	−	0.150187i	−0.524165	−	0.851617i	$-0.675623\pi$
$967$	−38.4636	−	4.67032i	−1.23690	−	0.150187i	−0.712739	+	0.701429i	$0.752546\pi$
$968$	−6.52007	−	19.5300i	−0.209563	−	0.627718i
$969$	−0.164455	−	2.03715i	−0.00528307	−	0.0654426i
$970$	−0.0769074	+	0.0868105i	−0.00246935	+	0.00278732i
$971$	−47.1095	+	29.7903i	−1.51182	+	0.956015i	−0.516822	+	0.856093i	$0.672885\pi$
$971$	−47.1095	+	29.7903i	−1.51182	+	0.956015i	−0.994995	+	0.0999226i	$0.968140\pi$
$972$	−1.53762	+	0.655117i	−0.0493190	+	0.0210129i
$973$	−2.11917	−	13.0398i	−0.0679376	−	0.418037i
$974$	14.2354	−	12.6114i	0.456131	−	0.404096i
$975$	10.9388	+	2.79570i	0.350321	+	0.0895339i
$976$	16.7805	+	14.8662i	0.537130	+	0.475856i
$977$	1.43470	−	2.26879i	0.0459000	−	0.0725850i	−0.821461	−	0.570265i	$-0.806840\pi$
$977$	1.43470	−	2.26879i	0.0459000	−	0.0725850i	0.867361	+	0.497680i	$0.165815\pi$
$978$	−12.6330	−	1.01984i	−0.403958	−	0.0326109i
$979$	−12.0059	−	58.8087i	−0.383710	−	1.87953i
$980$	1.17403	+	4.76323i	0.0375030	+	0.152156i
$981$	−1.52587	+	9.38904i	−0.0487172	+	0.299769i
$982$	3.05176	+	4.82597i	0.0973855	+	0.154003i
$983$	11.7369	+	22.3629i	0.374350	+	0.713265i	0.997635	−	0.0687299i	$-0.0218947\pi$
$983$	11.7369	+	22.3629i	0.374350	+	0.713265i	−0.623285	+	0.781995i	$0.714202\pi$
$984$	−4.84507	+	16.7271i	−0.154455	+	0.533241i
$985$	1.71000	−	8.37616i	0.0544853	−	0.266886i
$986$	0.0980953	−	0.00395311i	0.00312399	−	0.000125893i
$987$	23.1775	−	12.1645i	0.737750	−	0.387201i
$988$	−24.0936	−	27.6696i	−0.766519	−	0.880288i
$989$	58.0477	+	30.4658i	1.84581	+	0.968756i
$990$	−3.22758	−	1.53150i	−0.102579	−	0.0486744i
$991$	23.7513	+	41.1385i	0.754485	+	1.30681i	0.945630	+	0.325245i	$0.105447\pi$
$991$	23.7513	+	41.1385i	0.754485	+	1.30681i	−0.191144	+	0.981562i	$0.561220\pi$
$992$	−4.94179	+	8.55943i	−0.156902	+	0.271762i
$993$	−26.9852	+	18.6265i	−0.856349	+	0.591095i
$994$	−5.06150	+	6.73564i	−0.160541	+	0.213641i
$995$	4.99908	+	2.88622i	0.158482	+	0.0914994i
$996$	2.42717	−	0.294712i	0.0769078	−	0.00933830i
$997$	−23.8092	−	50.1767i	−0.754044	−	1.58911i	−0.807025	−	0.590518i	$-0.798924\pi$
$997$	−23.8092	−	50.1767i	−0.754044	−	1.58911i	0.0529810	−	0.998596i	$-0.483128\pi$
$998$	2.26831	+	2.36156i	0.0718020	+	0.0747538i
$999$	0.705230	−	8.73585i	0.0223125	−	0.276390i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.a.10.6	✓	336
169.17	even	78	inner	507.2.t.a.355.6	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.a.10.6	✓	336	1.1	even	1	trivial
507.2.t.a.355.6	yes	336	169.17	even	78	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.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.561687 - 0.114669i) q^{2} +(0.987050 - 0.160411i) q^{3} +(-1.53762 - 0.655117i) q^{4} +(-0.327138 + 1.32725i) q^{5} +(-0.572808 - 0.0230834i) q^{6} +(-1.99021 + 0.944367i) q^{7} +(1.73212 + 1.19560i) q^{8} +(0.948536 - 0.316668i) q^{9} +O(q^{10})\)	\(q+(-0.561687 - 0.114669i) q^{2} +(0.987050 - 0.160411i) q^{3} +(-1.53762 - 0.655117i) q^{4} +(-0.327138 + 1.32725i) q^{5} +(-0.572808 - 0.0230834i) q^{6} +(-1.99021 + 0.944367i) q^{7} +(1.73212 + 1.19560i) q^{8} +(0.948536 - 0.316668i) q^{9} +(0.335944 - 0.707987i) q^{10} +(1.44363 - 4.32420i) q^{11} +(-1.62279 - 0.399982i) q^{12} +(3.59621 - 0.259354i) q^{13} +(1.22617 - 0.302223i) q^{14} +(-0.109996 + 1.36254i) q^{15} +(1.47977 + 1.54060i) q^{16} +(-0.143906 - 0.303276i) q^{17} +(-0.569093 + 0.0691004i) q^{18} +(5.27265 + 3.04417i) q^{19} +(1.37252 - 1.82649i) q^{20} +(-1.81295 + 1.25139i) q^{21} +(-1.30672 + 2.26330i) q^{22} +(3.71633 + 6.43688i) q^{23} +(1.90148 + 0.902264i) q^{24} +(2.77270 + 1.45523i) q^{25} +(-2.04969 - 0.266699i) q^{26} +(0.885456 - 0.464723i) q^{27} +(3.67885 - 0.148253i) q^{28} +(0.102045 - 0.499849i) q^{29} +(0.218025 - 0.752708i) q^{30} +(-0.845261 - 1.61051i) q^{31} +(-2.90428 - 4.59274i) q^{32} +(0.731284 - 4.49977i) q^{33} +(0.0460539 + 0.186848i) q^{34} +(-0.602338 - 2.95045i) q^{35} +(-1.66594 - 0.134488i) q^{36} +(4.68420 - 7.40747i) q^{37} +(-2.61251 - 2.31448i) q^{38} +(3.50804 - 0.832868i) q^{39} +(-2.15350 + 1.90784i) q^{40} +(1.32728 + 8.16708i) q^{41} +(1.16181 - 0.495000i) q^{42} +(7.45466 - 4.71404i) q^{43} +(-5.05260 + 5.70321i) q^{44} +(0.109996 + 1.36254i) q^{45} +(-1.34930 - 4.04166i) q^{46} +(-11.7958 - 1.43227i) q^{47} +(1.70774 + 1.28328i) q^{48} +(-1.35801 + 1.66325i) q^{49} +(-1.39052 - 1.13533i) q^{50} +(-0.190692 - 0.276265i) q^{51} +(-5.69950 - 1.95715i) q^{52} +(1.22183 - 1.77013i) q^{53} +(-0.550639 + 0.159494i) q^{54} +(5.26703 + 3.33067i) q^{55} +(-4.57638 - 0.743734i) q^{56} +(5.69269 + 2.15895i) q^{57} +(-0.114635 + 0.269057i) q^{58} +(-4.36326 - 4.19097i) q^{59} +(1.06175 - 2.02300i) q^{60} +(10.4607 - 0.844478i) q^{61} +(0.290096 + 1.00153i) q^{62} +(-1.58874 + 1.52600i) q^{63} +(-0.410336 - 1.08197i) q^{64} +(-0.832229 + 4.85792i) q^{65} +(-0.926738 + 2.44361i) q^{66} +(-1.24635 - 2.92530i) q^{67} +(0.0225913 + 0.560598i) q^{68} +(4.70076 + 5.75738i) q^{69} +1.72630i q^{70} +(-5.16792 + 4.21947i) q^{71} +(2.02159 + 0.585561i) q^{72} +(-4.09749 - 4.62511i) q^{73} +(-3.48046 + 3.62355i) q^{74} +(2.97023 + 0.991610i) q^{75} +(-6.11303 - 8.13496i) q^{76} +(1.21050 + 9.96938i) q^{77} +(-2.06592 + 0.0655474i) q^{78} +(-1.76592 + 14.5437i) q^{79} +(-2.52885 + 1.46003i) q^{80} +(0.799443 - 0.600742i) q^{81} +(0.190997 - 4.73954i) q^{82} +(-1.36782 + 0.518744i) q^{83} +(3.60743 - 0.736462i) q^{84} +(0.449601 - 0.0917867i) q^{85} +(-4.72774 + 1.79300i) q^{86} +(0.0205420 - 0.509745i) q^{87} +(7.67055 - 5.76405i) q^{88} +(11.4022 - 6.58305i) q^{89} +(0.0944583 - 0.777934i) q^{90} +(-6.91230 + 3.91231i) q^{91} +(-1.49739 - 12.3321i) q^{92} +(-1.09266 - 1.45407i) q^{93} +(6.46131 + 2.15710i) q^{94} +(-5.76526 + 6.00227i) q^{95} +(-3.60339 - 4.06739i) q^{96} +(-0.142154 - 0.0411754i) q^{97} +(0.953498 - 0.778507i) q^{98} -4.55881i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9}+O(q^{10}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31} + 65 q^{32} - 13 q^{33} + 65 q^{34} - 82 q^{35} - 12 q^{36} - 73 q^{38} + 24 q^{40} - 132 q^{42} - 72 q^{43} + 39 q^{44} + 8 q^{48} + 68 q^{49} + 52 q^{50} - 8 q^{51} - 65 q^{52} + 37 q^{53} - 53 q^{55} + 14 q^{56} - 26 q^{57} + 26 q^{58} - 208 q^{59} + 78 q^{60} - 12 q^{61} - 49 q^{62} + 14 q^{64} + 52 q^{65} + 64 q^{66} - 26 q^{67} - 33 q^{68} + 4 q^{69} - 78 q^{71} + 52 q^{73} + 205 q^{74} - 8 q^{75} - 26 q^{76} - 114 q^{77} - 65 q^{78} + 28 q^{79} - 468 q^{80} + 14 q^{81} - 45 q^{82} - 78 q^{83} + 13 q^{85} + 13 q^{86} + 46 q^{87} + 26 q^{88} - 8 q^{90} - 260 q^{91} + 8 q^{92} - 25 q^{94} - 90 q^{95} - 65 q^{96} - 26 q^{97} + 104 q^{98}+O(q^{100}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

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