LMFDB - Embedded newform 507.2.p.a.25.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, 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:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.7
Character	$\chi$	$=$	507.25
Dual form			507.2.p.a.142.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.239472 - 0.0908198i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-1.44792 - 1.28275i) q^{4} +(-3.85869 - 0.468530i) q^{5} +(-0.0612925 - 0.248673i) q^{6} +(0.285060 + 0.543137i) q^{7} +(0.468284 + 0.892241i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})$	\(q+(-0.239472 - 0.0908198i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-1.44792 - 1.28275i) q^{4} +(-3.85869 - 0.468530i) q^{5} +(-0.0612925 - 0.248673i) q^{6} +(0.285060 + 0.543137i) q^{7} +(0.468284 + 0.892241i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(0.881497 + 0.462645i) q^{10} +(5.04551 - 1.91351i) q^{11} +(0.233167 - 1.92030i) q^{12} +(0.554679 + 3.56263i) q^{13} +(-0.0189364 - 0.155955i) q^{14} +(-1.80639 - 3.44179i) q^{15} +(0.435226 + 3.58441i) q^{16} +(3.94351 - 2.06971i) q^{17} +(0.169836 - 0.191705i) q^{18} +4.79835i q^{19} +(4.98608 + 5.62812i) q^{20} +(-0.285060 + 0.543137i) q^{21} -1.38204 q^{22} +2.06303 q^{23} +(-0.468284 + 0.892241i) q^{24} +(9.81524 + 2.41924i) q^{25} +(0.190727 - 0.903527i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(0.283963 - 1.15208i) q^{28} +(1.54888 - 4.08406i) q^{29} +(0.119998 + 0.988270i) q^{30} +(2.00372 + 8.12939i) q^{31} +(0.703609 - 2.85466i) q^{32} +(4.44096 + 3.06538i) q^{33} +(-1.13233 + 0.137490i) q^{34} +(-0.845484 - 2.22936i) q^{35} +(1.71283 - 0.898963i) q^{36} +(-0.662742 - 2.68885i) q^{37} +(0.435786 - 1.14907i) q^{38} +(-2.61689 + 2.48030i) q^{39} +(-1.38892 - 3.66228i) q^{40} +(0.587063 - 0.405220i) q^{41} +(0.117592 - 0.104177i) q^{42} +(-7.24817 - 1.78651i) q^{43} +(-9.76006 - 3.70150i) q^{44} +(1.80639 - 3.44179i) q^{45} +(-0.494040 - 0.187364i) q^{46} +(5.89159 + 6.65023i) q^{47} +(-2.70267 + 2.39436i) q^{48} +(3.76271 - 5.45123i) q^{49} +(-2.13076 - 1.47076i) q^{50} +(3.94351 + 2.06971i) q^{51} +(3.76682 - 5.86993i) q^{52} +(-9.45949 + 4.96472i) q^{53} +(0.254248 + 0.0308713i) q^{54} +(-20.3656 + 5.01967i) q^{55} +(-0.351120 + 0.508685i) q^{56} +(-3.94897 + 2.72577i) q^{57} +(-0.741827 + 0.837349i) q^{58} +(-2.75543 - 0.334570i) q^{59} +(-1.79944 + 7.30060i) q^{60} +(6.41645 + 3.36761i) q^{61} +(0.258476 - 2.12874i) q^{62} +(-0.608926 + 0.0739370i) q^{63} +(3.67450 - 5.32344i) q^{64} +(-0.471135 - 14.0070i) q^{65} +(-0.785091 - 1.13740i) q^{66} +(4.89247 + 5.52246i) q^{67} +(-8.36481 - 2.06174i) q^{68} +(1.17194 + 1.69784i) q^{69} +0.610656i q^{70} +(-5.61311 + 3.87445i) q^{71} +(-1.00032 + 0.121460i) q^{72} +(5.74886 - 2.18026i) q^{73} +(-0.0854927 + 0.704095i) q^{74} +(3.58470 + 9.45207i) q^{75} +(6.15507 - 6.94764i) q^{76} +(2.47757 + 2.19494i) q^{77} +(0.851933 - 0.356296i) q^{78} +(6.34747 - 5.62337i) q^{79} -14.0350i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-0.177387 + 0.0437221i) q^{82} +(8.63771 + 5.96218i) q^{83} +(1.10945 - 0.420760i) q^{84} +(-16.1865 + 6.13872i) q^{85} +(1.57348 + 1.08610i) q^{86} +(4.24098 - 1.04531i) q^{87} +(4.07004 + 3.60574i) q^{88} -5.00506i q^{89} +(-0.745164 + 0.660158i) q^{90} +(-1.77688 + 1.31683i) q^{91} +(-2.98711 - 2.64635i) q^{92} +(-5.55212 + 6.26705i) q^{93} +(-0.806900 - 2.12762i) q^{94} +(2.24817 - 18.5153i) q^{95} +(2.74903 - 1.04257i) q^{96} +(-8.09549 + 0.982970i) q^{97} +(-1.39615 + 0.963690i) q^{98} +5.39617i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9}+O(q^{10}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31} + 130 q^{32} + 13 q^{33} - 65 q^{34} - 35 q^{35} + 12 q^{36} + 61 q^{38} + 12 q^{40} - 63 q^{42} + 72 q^{43} - 39 q^{44} - 8 q^{48} - 68 q^{49} - 52 q^{50} - 4 q^{51} + 65 q^{52} - q^{53} + 53 q^{55} - 14 q^{56} - 13 q^{57} - 26 q^{58} - 104 q^{59} + 117 q^{60} + 12 q^{61} + 49 q^{62} - 32 q^{64} - 52 q^{65} - 46 q^{66} + 26 q^{67} - 84 q^{68} - 4 q^{69} - 39 q^{71} - 52 q^{73} + 29 q^{74} + 8 q^{75} - 130 q^{76} + 60 q^{77} + 65 q^{78} + 14 q^{79} - 14 q^{81} + 45 q^{82} + 78 q^{83} - 13 q^{85} - 13 q^{86} - 46 q^{87} - 26 q^{88} - 4 q^{90} - 208 q^{91} + 82 q^{92} - 39 q^{93} + 25 q^{94} - 66 q^{95} + 65 q^{96} + 26 q^{97} - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * 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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

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 $

$2$	−0.239472	−	0.0908198i	−0.169332	−	0.0642193i	0.268482	−	0.963285i	$-0.413478\pi$
$2$	−0.239472	−	0.0908198i	−0.169332	−	0.0642193i	−0.437814	+	0.899065i	$0.644247\pi$
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$4$	−1.44792	−	1.28275i	−0.723961	−	0.641374i
$5$	−3.85869	−	0.468530i	−1.72566	−	0.209533i	−0.803221	−	0.595681i	$-0.796882\pi$
$5$	−3.85869	−	0.468530i	−1.72566	−	0.209533i	−0.922437	+	0.386148i	$0.873805\pi$
$6$	−0.0612925	−	0.248673i	−0.0250225	−	0.101520i
$7$	0.285060	+	0.543137i	0.107743	+	0.205287i	0.933358	−	0.358947i	$-0.116864\pi$
$7$	0.285060	+	0.543137i	0.107743	+	0.205287i	−0.825615	+	0.564234i	$0.809172\pi$
$8$	0.468284	+	0.892241i	0.165563	+	0.315455i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	0.881497	+	0.462645i	0.278754	+	0.146301i
$11$	5.04551	−	1.91351i	1.52128	−	0.576945i	0.554416	−	0.832240i	$-0.312942\pi$
$11$	5.04551	−	1.91351i	1.52128	−	0.576945i	0.966863	+	0.255295i	$0.0821726\pi$
$12$	0.233167	−	1.92030i	0.0673094	−	0.554343i
$13$	0.554679	+	3.56263i	0.153840	+	0.988096i
$13$	0.554679	+	3.56263i	0.153840	+	0.988096i
$14$	−0.0189364	−	0.155955i	−0.00506097	−	0.0416809i
$15$	−1.80639	−	3.44179i	−0.466408	−	0.888667i
$16$	0.435226	+	3.58441i	0.108806	+	0.896101i
$17$	3.94351	−	2.06971i	0.956441	−	0.501979i	0.0871042	−	0.996199i	$-0.472239\pi$
$17$	3.94351	−	2.06971i	0.956441	−	0.501979i	0.869337	+	0.494220i	$0.164546\pi$
$18$	0.169836	−	0.191705i	0.0400307	−	0.0451854i
$19$			4.79835i			1.10082i	0.834895	+	0.550409i	$0.185528\pi$
$19$			4.79835i			1.10082i	−0.834895	+	0.550409i	$0.814472\pi$
$20$	4.98608	+	5.62812i	1.11492	+	1.25849i
$21$	−0.285060	+	0.543137i	−0.0622053	+	0.118522i
$22$	−1.38204			−0.294653
$23$	2.06303			0.430172			0.215086	−	0.976595i	$-0.430997\pi$
$23$	2.06303			0.430172			0.215086	+	0.976595i	$0.430997\pi$
$24$	−0.468284	+	0.892241i	−0.0955881	+	0.182128i
$25$	9.81524	+	2.41924i	1.96305	+	0.483848i
$26$	0.190727	−	0.903527i	0.0374047	−	0.177196i
$27$	−0.970942	+	0.239316i	−0.186858	+	0.0460563i
$28$	0.283963	−	1.15208i	0.0536639	−	0.217723i
$29$	1.54888	−	4.08406i	0.287619	−	0.758390i	−0.710864	−	0.703330i	$-0.751696\pi$
$29$	1.54888	−	4.08406i	0.287619	−	0.758390i	0.998483	−	0.0550603i	$-0.0175351\pi$
$30$	0.119998	+	0.988270i	0.0219085	+	0.180433i
$31$	2.00372	+	8.12939i	0.359878	+	1.46008i	0.820070	+	0.572263i	$0.193934\pi$
$31$	2.00372	+	8.12939i	0.359878	+	1.46008i	−0.460192	+	0.887819i	$0.652220\pi$
$32$	0.703609	−	2.85466i	0.124382	−	0.504637i
$33$	4.44096	+	3.06538i	0.773073	+	0.533614i
$34$	−1.13233	+	0.137490i	−0.194193	+	0.0235793i
$35$	−0.845484	−	2.22936i	−0.142913	−	0.376830i
$36$	1.71283	−	0.898963i	0.285472	−	0.149827i
$37$	−0.662742	−	2.68885i	−0.108954	−	0.442044i	0.890974	−	0.454055i	$-0.150023\pi$
$37$	−0.662742	−	2.68885i	−0.108954	−	0.442044i	−0.999928	+	0.0120105i	$0.996177\pi$
$38$	0.435786	−	1.14907i	0.0706937	−	0.186404i
$39$	−2.61689	+	2.48030i	−0.419038	+	0.397165i
$40$	−1.38892	−	3.66228i	−0.219608	−	0.579058i
$41$	0.587063	−	0.405220i	0.0916838	−	0.0632848i	−0.521341	−	0.853349i	$-0.674568\pi$
$41$	0.587063	−	0.405220i	0.0916838	−	0.0632848i	0.613025	+	0.790064i	$0.289953\pi$
$42$	0.117592	−	0.104177i	0.0181448	−	0.0160749i
$43$	−7.24817	−	1.78651i	−1.10534	−	0.272441i	−0.355904	−	0.934522i	$-0.615827\pi$
$43$	−7.24817	−	1.78651i	−1.10534	−	0.272441i	−0.749432	+	0.662082i	$0.769673\pi$
$44$	−9.76006	−	3.70150i	−1.47138	−	0.558023i
$45$	1.80639	−	3.44179i	0.269281	−	0.513072i
$46$	−0.494040	−	0.187364i	−0.0728422	−	0.0276254i
$47$	5.89159	+	6.65023i	0.859377	+	0.970036i	0.999799	−	0.0200555i	$-0.00638430\pi$
$47$	5.89159	+	6.65023i	0.859377	+	0.970036i	−0.140422	+	0.990092i	$0.544846\pi$
$48$	−2.70267	+	2.39436i	−0.390097	+	0.345596i
$49$	3.76271	−	5.45123i	0.537531	−	0.778748i
$50$	−2.13076	−	1.47076i	−0.301335	−	0.207997i
$51$	3.94351	+	2.06971i	0.552201	+	0.289818i
$52$	3.76682	−	5.86993i	0.522364	−	0.814012i
$53$	−9.45949	+	4.96472i	−1.29936	+	0.681957i	−0.965436	−	0.260642i	$-0.916066\pi$
$53$	−9.45949	+	4.96472i	−1.29936	+	0.681957i	−0.333926	+	0.942599i	$0.608373\pi$
$54$	0.254248	+	0.0308713i	0.0345988	+	0.00420106i
$55$	−20.3656	+	5.01967i	−2.74610	+	0.676852i
$56$	−0.351120	+	0.508685i	−0.0469204	+	0.0679759i
$57$	−3.94897	+	2.72577i	−0.523053	+	0.361038i
$58$	−0.741827	+	0.837349i	−0.0974066	+	0.109949i
$59$	−2.75543	−	0.334570i	−0.358726	−	0.0435573i	−0.0608103	−	0.998149i	$-0.519368\pi$
$59$	−2.75543	−	0.334570i	−0.358726	−	0.0435573i	−0.297916	+	0.954592i	$0.596292\pi$
$60$	−1.79944	+	7.30060i	−0.232306	+	0.942503i
$61$	6.41645	+	3.36761i	0.821542	+	0.431179i	0.822461	−	0.568821i	$-0.192600\pi$
$61$	6.41645	+	3.36761i	0.821542	+	0.431179i	−0.000919072		1.00000i	$0.500293\pi$
$62$	0.258476	−	2.12874i	0.0328265	−	0.270350i
$63$	−0.608926	+	0.0739370i	−0.0767175	+	0.00931519i
$64$	3.67450	−	5.32344i	0.459313	−	0.665430i
$65$	−0.471135	−	14.0070i	−0.0584371	−	1.73735i
$66$	−0.785091	−	1.13740i	−0.0966380	−	0.140004i
$67$	4.89247	+	5.52246i	0.597711	+	0.674676i	0.967041	−	0.254622i	$-0.0819511\pi$
$67$	4.89247	+	5.52246i	0.597711	+	0.674676i	−0.369330	+	0.929298i	$0.620413\pi$
$68$	−8.36481	−	2.06174i	−1.01438	−	0.250023i
$69$	1.17194	+	1.69784i	0.141085	+	0.204396i
$70$			0.610656i			0.0729873i
$71$	−5.61311	+	3.87445i	−0.666153	+	0.459813i	−0.852539	−	0.522664i	$-0.824938\pi$
$71$	−5.61311	+	3.87445i	−0.666153	+	0.459813i	0.186385	+	0.982477i	$0.440323\pi$
$72$	−1.00032	+	0.121460i	−0.117888	+	0.0143142i
$73$	5.74886	−	2.18026i	0.672853	−	0.255180i	0.00557093	−	0.999984i	$-0.498227\pi$
$73$	5.74886	−	2.18026i	0.672853	−	0.255180i	0.667282	+	0.744805i	$0.267457\pi$
$74$	−0.0854927	+	0.704095i	−0.00993832	+	0.0818494i
$75$	3.58470	+	9.45207i	0.413925	+	1.09143i
$76$	6.15507	−	6.94764i	0.706035	−	0.796949i
$77$	2.47757	+	2.19494i	0.282346	+	0.250137i
$78$	0.851933	−	0.356296i	0.0964625	−	0.0403426i
$79$	6.34747	−	5.62337i	0.714146	−	0.632679i	−0.225731	−	0.974190i	$-0.572477\pi$
$79$	6.34747	−	5.62337i	0.714146	−	0.632679i	0.939878	+	0.341511i	$0.110939\pi$
$80$		−	14.0350i		−	1.56916i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	−0.177387	+	0.0437221i	−0.0195892	+	0.00482829i
$83$	8.63771	+	5.96218i	0.948112	+	0.654435i	0.938412	−	0.345518i	$-0.112297\pi$
$83$	8.63771	+	5.96218i	0.948112	+	0.654435i	0.00970012	+	0.999953i	$0.496912\pi$
$84$	1.10945	−	0.420760i	0.121051	−	0.0459087i
$85$	−16.1865	+	6.13872i	−1.75567	+	0.665838i
$86$	1.57348	+	1.08610i	0.169673	+	0.117117i
$87$	4.24098	−	1.04531i	0.454680	−	0.112069i
$88$	4.07004	+	3.60574i	0.433868	+	0.384374i
$89$		−	5.00506i		−	0.530536i	−0.964175	−	0.265268i	$-0.914540\pi$
$89$		−	5.00506i		−	0.530536i	0.964175	−	0.265268i	$-0.0854604\pi$
$90$	−0.745164	+	0.660158i	−0.0785472	+	0.0695867i
$91$	−1.77688	+	1.31683i	−0.186268	+	0.138041i
$92$	−2.98711	−	2.64635i	−0.311428	−	0.275901i
$93$	−5.55212	+	6.26705i	−0.575728	+	0.649863i
$94$	−0.806900	−	2.12762i	−0.0832254	−	0.219447i
$95$	2.24817	−	18.5153i	0.230657	−	1.89963i
$96$	2.74903	−	1.04257i	0.280572	−	0.106407i
$97$	−8.09549	+	0.982970i	−0.821972	+	0.0998055i	−0.520708	−	0.853735i	$-0.674332\pi$
$97$	−8.09549	+	0.982970i	−0.821972	+	0.0998055i	−0.301265	+	0.953541i	$0.597409\pi$
$98$	−1.39615	+	0.963690i	−0.141032	+	0.0973474i
$99$			5.39617i			0.542336i
$100$	−11.1084	−	16.0934i	−1.11084	−	1.60934i
$101$	10.7511	+	2.64992i	1.06978	+	0.263677i	0.734616	−	0.678483i	$-0.237362\pi$
$101$	10.7511	+	2.64992i	1.06978	+	0.263677i	0.335163	+	0.942160i	$0.391209\pi$
$102$	−0.756390	−	0.853787i	−0.0748937	−	0.0845375i
$103$	7.52556	+	10.9027i	0.741515	+	1.07427i	0.994287	+	0.106744i	$0.0340426\pi$
$103$	7.52556	+	10.9027i	0.741515	+	1.07427i	−0.252771	+	0.967526i	$0.581342\pi$
$104$	−2.91898	+	2.16323i	−0.286229	+	0.212122i
$105$	1.35444	−	1.96224i	0.132179	−	0.191495i
$106$	2.71618	−	0.329804i	0.263819	−	0.0320334i
$107$	0.352066	−	2.89953i	0.0340355	−	0.280308i	−0.965748	−	0.259483i	$-0.916448\pi$
$107$	0.352066	−	2.89953i	0.0340355	−	0.280308i	0.999783	−	0.0208246i	$-0.00662917\pi$
$108$	1.71283	+	0.898963i	0.164817	+	0.0865027i
$109$	−2.43609	+	9.88360i	−0.233335	+	0.946677i	0.731082	+	0.682290i	$0.239016\pi$
$109$	−2.43609	+	9.88360i	−0.233335	+	0.946677i	−0.964417	+	0.264387i	$0.914830\pi$
$110$	5.33288	+	0.647529i	0.508470	+	0.0617394i
$111$	1.83640	−	2.07287i	0.174303	−	0.196748i
$112$	−1.82276	+	1.25816i	−0.172235	+	0.118885i
$113$	6.55685	−	9.49924i	0.616817	−	0.893614i	−0.382726	−	0.923862i	$-0.625015\pi$
$113$	6.55685	−	9.49924i	0.616817	−	0.893614i	0.999542	+	0.0302486i	$0.00962989\pi$
$114$	1.19322	−	0.294103i	0.111755	−	0.0275453i
$115$	−7.96061	−	0.966593i	−0.742330	−	0.0901352i
$116$	−7.48147	+	3.92658i	−0.694637	+	0.364574i
$117$	−3.52781	−	0.744692i	−0.326146	−	0.0688468i
$118$	0.629463	+	0.330368i	0.0579468	+	0.0304128i
$119$	2.24828	+	1.55187i	0.206099	+	0.142260i
$120$	2.22500	−	3.22347i	0.203114	−	0.294262i
$121$	13.5620	−	12.0149i	1.23291	−	1.09227i
$122$	−1.23072	−	1.38919i	−0.111424	−	0.125771i
$123$	0.666980	+	0.252952i	0.0601395	+	0.0228079i
$124$	7.52674	−	14.3410i	0.675921	−	1.28786i
$125$	−18.5683	−	7.04203i	−1.66080	−	0.629858i
$126$	0.152536	+	0.0375967i	0.0135890	+	0.00334938i
$127$	−13.9697	+	12.3760i	−1.23961	+	1.09820i	−0.248020	+	0.968755i	$0.579780\pi$
$127$	−13.9697	+	12.3760i	−1.23961	+	1.09820i	−0.991587	+	0.129441i	$0.958682\pi$
$128$	−6.20271	+	4.28142i	−0.548247	+	0.378428i
$129$	−2.64716	−	6.97998i	−0.233069	−	0.614553i
$130$	−1.15929	+	3.39707i	−0.101676	+	0.297942i
$131$	3.22888	−	8.51385i	0.282108	−	0.743859i	−0.716806	−	0.697273i	$-0.754397\pi$
$131$	3.22888	−	8.51385i	0.282108	−	0.743859i	0.998914	−	0.0465858i	$-0.0148341\pi$
$132$	−2.49807	−	10.1351i	−0.217429	−	0.882144i
$133$	−2.60616	+	1.36782i	−0.225983	+	0.118605i
$134$	−0.670063	−	1.76681i	−0.0578846	−	0.152629i
$135$	3.85869	−	0.468530i	0.332103	−	0.0403246i
$136$	3.69336	+	2.54934i	0.316703	+	0.218604i
$137$	−4.11232	+	16.6844i	−0.351340	+	1.42544i	0.483692	+	0.875238i	$0.339296\pi$
$137$	−4.11232	+	16.6844i	−0.351340	+	1.42544i	−0.835031	+	0.550202i	$0.814551\pi$
$138$	−0.126448	−	0.513022i	−0.0107640	−	0.0436713i
$139$	0.469016	+	3.86270i	0.0397814	+	0.327630i	0.998990	+	0.0449306i	$0.0143067\pi$
$139$	0.469016	+	3.86270i	0.0397814	+	0.327630i	−0.959209	+	0.282699i	$0.908770\pi$
$140$	−1.63551	+	4.31248i	−0.138226	+	0.364471i
$141$	−2.12623	+	8.62645i	−0.179061	+	0.726478i
$142$	1.69606	−	0.418041i	0.142330	−	0.0350813i
$143$	9.61577	+	16.9139i	0.804111	+	1.41441i
$144$	−3.50581	−	0.864105i	−0.292151	−	0.0720087i
$145$	−7.89014	+	15.0334i	−0.655240	+	1.24846i
$146$	−1.57470			−0.130323
$147$	6.62374			0.546317
$148$	−2.48952	+	4.74338i	−0.204637	+	0.389903i
$149$	−8.80721	−	9.94129i	−0.721515	−	0.814422i	0.267293	−	0.963615i	$-0.413871\pi$
$149$	−8.80721	−	9.94129i	−0.721515	−	0.814422i	−0.988808	+	0.149193i	$0.952332\pi$
$150$		−	2.58907i		−	0.211397i
$151$	−1.10315	+	1.24520i	−0.0897734	+	0.101333i	−0.791681	−	0.610935i	$-0.790794\pi$
$151$	−1.10315	+	1.24520i	−0.0897734	+	0.101333i	0.701907	+	0.712268i	$0.252332\pi$
$152$	−4.28128	+	2.24699i	−0.347258	+	0.182255i
$153$	0.536828	+	4.42117i	0.0433999	+	0.357431i
$154$	−0.393966	−	0.750640i	−0.0317467	−	0.0604883i
$155$	−3.92285	−	32.3076i	−0.315091	−	2.59501i
$156$	6.97065	−	0.234464i	0.558099	−	0.0187721i
$157$	0.298844	−	2.46120i	0.0238503	−	0.196425i	−0.975913	−	0.218158i	$-0.929995\pi$
$157$	0.298844	−	2.46120i	0.0238503	−	0.196425i	0.999764	+	0.0217327i	$0.00691829\pi$
$158$	−2.03076	+	0.770165i	−0.161558	+	0.0612710i
$159$	−9.45949	−	4.96472i	−0.750187	−	0.393728i
$160$	−4.05250	+	10.6856i	−0.320378	+	0.844768i
$161$	0.588090	+	1.12051i	0.0463480	+	0.0883086i
$162$	0.119023	+	0.226779i	0.00935132	+	0.0178174i
$163$	−2.58756	−	10.4981i	−0.202673	−	0.822277i	−0.980935	−	0.194337i	$-0.937744\pi$
$163$	−2.58756	−	10.4981i	−0.202673	−	0.822277i	0.778262	−	0.627940i	$-0.216102\pi$
$164$	−1.36982	−	0.166326i	−0.106965	−	0.0129879i
$165$	−15.7001	−	13.9091i	−1.22225	−	1.08282i
$166$	−1.52701	−	2.21225i	−0.118519	−	0.171704i
$167$	−18.5084	−	7.01929i	−1.43222	−	0.543169i	−0.488105	−	0.872785i	$-0.662312\pi$
$167$	−18.5084	−	7.01929i	−1.43222	−	0.543169i	−0.944115	+	0.329616i	$0.893081\pi$
$168$	−0.618099			−0.0476873
$169$	−12.3847	+	3.95223i	−0.952666	+	0.304018i
$170$	4.43373			0.340052
$171$	−4.48654	−	1.70152i	−0.343094	−	0.130118i
$172$	8.20315	+	11.8843i	0.625484	+	0.906170i
$173$	−14.0304	−	12.4299i	−1.06671	−	0.945026i	−0.0681005	−	0.997678i	$-0.521694\pi$
$173$	−14.0304	−	12.4299i	−1.06671	−	0.945026i	−0.998613	+	0.0526529i	$0.983232\pi$
$174$	−1.11053	−	0.134843i	−0.0841891	−	0.0102224i
$175$	1.48396	+	6.02065i	0.112177	+	0.455119i
$176$	9.05473	+	17.2523i	0.682526	+	1.30044i
$177$	−1.28992	−	2.45773i	−0.0969561	−	0.184734i
$178$	−0.454559	+	1.19857i	−0.0340706	+	0.0898369i
$179$	1.91008	+	1.00249i	0.142766	+	0.0749296i	0.534594	−	0.845109i	$-0.320465\pi$
$179$	1.91008	+	1.00249i	0.142766	+	0.0749296i	−0.391827	+	0.920039i	$0.628157\pi$
$180$	−7.03047	+	2.66630i	−0.524020	+	0.198735i
$181$	1.24144	−	10.2242i	0.0922754	−	0.759957i	−0.870970	−	0.491335i	$-0.836509\pi$
$181$	1.24144	−	10.2242i	0.0922754	−	0.759957i	0.963246	−	0.268621i	$-0.0865680\pi$
$182$	0.545108	−	0.153969i	0.0404061	−	0.0114129i
$183$	0.873468	+	7.19366i	0.0645686	+	0.531770i
$184$	0.966086	+	1.84072i	0.0712208	+	0.135700i
$185$	1.29751	+	10.6860i	0.0953948	+	0.785647i
$186$	1.89875	−	0.996541i	0.139223	−	0.0730700i
$187$	15.9366	−	17.9887i	1.16540	−	1.31546i
$188$		−	17.1865i		−	1.25345i
$189$	−0.406758	−	0.459135i	−0.0295873	−	0.0333972i
$190$	−2.21993	+	4.22973i	−0.161051	+	0.306857i
$191$	20.7032			1.49803			0.749015	−	0.662553i	$-0.230527\pi$
$191$	20.7032			1.49803			0.749015	+	0.662553i	$0.230527\pi$
$192$	6.46846			0.466821
$193$	4.84992	−	9.24075i	0.349105	−	0.665163i	−0.646070	−	0.763278i	$-0.723589\pi$
$193$	4.84992	−	9.24075i	0.349105	−	0.665163i	0.995175	+	0.0981144i	$0.0312811\pi$
$194$	2.02792	+	0.499837i	0.145596	+	0.0358862i
$195$	11.2599	−	8.34460i	0.806336	−	0.597569i
$196$	−12.4407	+	3.06635i	−0.888620	+	0.219025i
$197$	−5.24340	+	21.2733i	−0.373577	+	1.51566i	0.420189	+	0.907437i	$0.361964\pi$
$197$	−5.24340	+	21.2733i	−0.373577	+	1.51566i	−0.793766	+	0.608223i	$0.791882\pi$
$198$	0.490080	−	1.29223i	0.0348285	−	0.0918351i
$199$	−1.93156	−	15.9078i	−0.136925	−	1.12768i	−0.885504	−	0.464632i	$-0.846187\pi$
$199$	−1.93156	−	15.9078i	−0.136925	−	1.12768i	0.748579	−	0.663046i	$-0.230736\pi$
$200$	2.43778	+	9.89045i	0.172377	+	0.699361i
$201$	−1.76566	+	7.16354i	−0.124540	+	0.505277i
$202$	−2.33394	−	1.61100i	−0.164215	−	0.113350i
$203$	2.65973	−	0.322949i	0.186676	−	0.0226666i
$204$	−3.05498	−	8.05531i	−0.213891	−	0.563984i
$205$	−2.45515	+	1.28856i	−0.171475	+	0.0899971i
$206$	−0.811985	−	3.29435i	−0.0565737	−	0.229528i
$207$	−0.731562	+	1.92897i	−0.0508471	+	0.134073i
$208$	−12.5285	+	3.53874i	−0.868695	+	0.245368i
$209$	9.18169	+	24.2101i	0.635111	+	1.67465i
$210$	−0.502560	+	0.346892i	−0.0346799	+	0.0239378i
$211$	−0.173072	+	0.153328i	−0.0119148	+	0.0105556i	−0.669059	−	0.743209i	$-0.733303\pi$
$211$	−0.173072	+	0.153328i	−0.0119148	+	0.0105556i	0.657144	+	0.753765i	$0.271764\pi$
$212$	20.0651	+	4.94560i	1.37808	+	0.339665i
$213$	−6.37722	−	2.41856i	−0.436960	−	0.165717i
$214$	−0.347645	+	0.662382i	−0.0237645	+	0.0452795i
$215$	27.1314	+	10.2896i	1.85035	+	0.701744i
$216$	−0.668204	−	0.754246i	−0.0454655	−	0.0513200i
$217$	−3.84420	+	3.40566i	−0.260961	+	0.231191i
$218$	1.48100	−	2.14560i	0.100306	−	0.145318i
$219$	5.06004	+	3.49269i	0.341926	+	0.236014i
$220$	35.9268	+	18.8558i	2.42218	+	1.27126i
$221$	9.56100	+	12.9012i	0.643142	+	0.867831i
$222$	−0.628025	+	0.329613i	−0.0421502	+	0.0221222i
$223$	23.9754	+	2.91115i	1.60551	+	0.194945i	0.873667	−	0.486524i	$-0.161735\pi$
$223$	23.9754	+	2.91115i	1.60551	+	0.194945i	0.731847	+	0.681469i	$0.238658\pi$
$224$	1.75104	−	0.431593i	0.116996	−	0.0288370i
$225$	−5.74256	+	8.31954i	−0.382837	+	0.554636i
$226$	−2.43290	+	1.67931i	−0.161834	+	0.111706i
$227$	−0.591698	+	0.667889i	−0.0392724	+	0.0443293i	−0.767819	−	0.640667i	$-0.778658\pi$
$227$	−0.591698	+	0.667889i	−0.0392724	+	0.0443293i	0.728546	+	0.684997i	$0.240196\pi$
$228$	9.21428	+	1.11882i	0.610230	+	0.0740954i
$229$	−0.497452	+	2.01824i	−0.0328725	+	0.133369i	−0.985085	−	0.172066i	$-0.944956\pi$
$229$	−0.497452	+	2.01824i	−0.0328725	+	0.133369i	0.952213	+	0.305435i	$0.0988019\pi$
$230$	1.81856	+	0.954453i	0.119912	+	0.0629348i
$231$	−0.398977	+	3.28587i	−0.0262508	+	0.216194i
$232$	4.36928	−	0.530526i	0.286857	−	0.0348308i
$233$	−2.22508	+	3.22358i	−0.145770	+	0.211184i	−0.889067	−	0.457778i	$-0.848646\pi$
$233$	−2.22508	+	3.22358i	−0.145770	+	0.211184i	0.743297	+	0.668962i	$0.233261\pi$
$234$	0.777179	+	0.498728i	0.0508058	+	0.0326029i
$235$	−19.6180	−	28.4216i	−1.27974	−	1.85402i
$236$	3.56048	+	4.01895i	0.231768	+	0.261612i
$237$	8.23372	+	2.02943i	0.534837	+	0.131826i
$238$	−0.397459	−	0.575819i	−0.0257634	−	0.0373248i
$239$			17.6523i			1.14183i	0.821008	+	0.570917i	$0.193412\pi$
$239$			17.6523i			1.14183i	−0.821008	+	0.570917i	$0.806588\pi$
$240$	11.5506	−	7.97280i	0.745588	−	0.514642i
$241$	26.4205	−	3.20803i	1.70189	−	0.206647i	0.788872	−	0.614557i	$-0.210665\pi$
$241$	26.4205	−	3.20803i	1.70189	−	0.206647i	0.913022	+	0.407910i	$0.133742\pi$
$242$	−4.33893	+	1.64554i	−0.278917	+	0.105779i
$243$	0.120537	−	0.992709i	0.00773243	−	0.0636823i
$244$	−4.97073	−	13.1067i	−0.318218	−	0.839072i
$245$	−17.0732	+	19.2717i	−1.09077	+	1.23122i
$246$	−0.136750	−	0.121150i	−0.00871886	−	0.00772424i
$247$	−17.0948	+	2.66154i	−1.08771	+	0.169350i
$248$	−6.31507	+	5.59466i	−0.401007	+	0.355261i
$249$			10.4956i			0.665132i
$250$	3.80704	+	3.37274i	0.240778	+	0.213311i
$251$	18.3691	−	4.52758i	1.15945	−	0.285778i	0.387749	−	0.921765i	$-0.373253\pi$
$251$	18.3691	−	4.52758i	1.15945	−	0.285778i	0.771700	+	0.635987i	$0.219407\pi$
$252$	0.976521	+	0.674043i	0.0615150	+	0.0424607i
$253$	10.4091	−	3.94764i	0.654412	−	0.248186i
$254$	4.46934	−	1.69500i	0.280431	−	0.106354i
$255$	−14.2470	−	9.83402i	−0.892184	−	0.615830i
$256$	−10.6868	+	2.63406i	−0.667924	+	0.164628i
$257$	3.08923	+	2.73682i	0.192701	+	0.170718i	0.753956	−	0.656925i	$-0.228143\pi$
$257$	3.08923	+	2.73682i	0.192701	+	0.170718i	−0.561256	+	0.827643i	$0.689682\pi$
$258$			1.91193i			0.119031i
$259$	1.27149	−	1.12645i	0.0790068	−	0.0699939i
$260$	−17.2852	+	20.8853i	−1.07198	+	1.29525i
$261$	3.26942	+	2.89645i	0.202372	+	0.179286i
$262$	−1.54645	+	1.74558i	−0.0955402	+	0.107843i
$263$	−7.94518	−	20.9497i	−0.489921	−	1.29182i	−0.921022	−	0.389512i	$-0.872644\pi$
$263$	−7.94518	−	20.9497i	−0.489921	−	1.29182i	0.431101	−	0.902304i	$-0.358125\pi$
$264$	−0.655421	+	5.39788i	−0.0403384	+	0.332216i
$265$	38.8273	−	14.7253i	2.38515	−	0.904566i
$266$	0.748329	−	0.0908636i	0.0458830	−	0.00557121i
$267$	4.11909	−	2.84320i	0.252084	−	0.174001i
$268$		−	14.2719i		−	0.871796i
$269$	−12.0487	−	17.4555i	−0.734621	−	1.06428i	−0.995107	−	0.0988044i	$-0.968498\pi$
$269$	−12.0487	−	17.4555i	−0.734621	−	1.06428i	0.260486	−	0.965478i	$-0.416117\pi$
$270$	−0.966600	−	0.238246i	−0.0588254	−	0.0144992i
$271$	−11.5832	−	13.0747i	−0.703627	−	0.794231i	0.282668	−	0.959218i	$-0.408780\pi$
$271$	−11.5832	−	13.0747i	−0.703627	−	0.794231i	−0.986296	+	0.164986i	$0.947242\pi$
$272$	9.13500	+	13.2343i	0.553891	+	0.802449i
$273$	−2.09311	−	0.714298i	−0.126681	−	0.0432313i
$274$	2.50006	−	3.62196i	0.151034	−	0.218811i
$275$	54.1522	−	6.57526i	3.26550	−	0.396503i
$276$	0.481031	−	3.96165i	0.0289547	−	0.238463i
$277$	19.7988	+	10.3912i	1.18959	+	0.624346i	0.939057	−	0.343761i	$-0.111701\pi$
$277$	19.7988	+	10.3912i	1.18959	+	0.624346i	0.250535	+	0.968108i	$0.419393\pi$
$278$	0.238493	−	0.967604i	0.0143039	−	0.0580330i
$279$	−8.31164	−	1.00922i	−0.497605	−	0.0604202i
$280$	1.59320	−	1.79835i	0.0952117	−	0.107472i
$281$	−11.8123	+	8.15347i	−0.704666	+	0.486396i	−0.865706	−	0.500552i	$-0.833130\pi$
$281$	−11.8123	+	8.15347i	−0.704666	+	0.486396i	0.161041	+	0.986948i	$0.448515\pi$
$282$	1.29263	−	1.87269i	0.0769747	−	0.111517i
$283$	−20.4409	+	5.03822i	−1.21508	+	0.299491i	−0.794219	−	0.607632i	$-0.792119\pi$
$283$	−20.4409	+	5.03822i	−1.21508	+	0.299491i	−0.420865	+	0.907123i	$0.638273\pi$
$284$	13.0973	+	1.59030i	0.777181	+	0.0943669i
$285$	16.5149	−	8.66770i	0.978260	−	0.513431i
$286$	−0.766591	−	4.92371i	−0.0453295	−	0.291145i
$287$	0.387439	+	0.203344i	0.0228698	+	0.0120030i
$288$	2.41965	+	1.67016i	0.142579	+	0.0984152i
$289$	1.61044	−	2.33312i	0.0947316	−	0.137242i
$290$	3.25480	−	2.88350i	0.191128	−	0.169325i
$291$	−5.40773	−	6.10407i	−0.317007	−	0.357827i
$292$	−11.1206	−	4.21750i	−0.650785	−	0.246810i
$293$	3.86952	−	7.37276i	0.226060	−	0.430721i	−0.745837	−	0.666129i	$-0.767950\pi$
$293$	3.86952	−	7.37276i	0.226060	−	0.430721i	0.971897	+	0.235407i	$0.0756424\pi$
$294$	−1.58620	−	0.601567i	−0.0925092	−	0.0350841i
$295$	10.4756	+	2.58200i	0.609912	+	0.150330i
$296$	2.08875	−	1.85047i	0.121406	−	0.107557i
$297$	−4.44096	+	3.06538i	−0.257691	+	0.177871i
$298$	1.20622	+	3.18053i	0.0698742	+	0.184243i
$299$	1.14432	+	7.34983i	0.0661778	+	0.425052i
$300$	6.93426	−	18.2841i	0.400349	−	1.05563i
$301$	−1.09584	−	4.44602i	−0.0631634	−	0.256264i
$302$	0.377264	−	0.198003i	0.0217091	−	0.0113938i
$303$	3.92651	+	10.3533i	0.225572	+	0.594784i
$304$	−17.1992	+	2.08837i	−0.986444	+	0.119776i
$305$	−23.1813	−	16.0009i	−1.32735	−	0.916207i
$306$	0.272975	−	1.10750i	0.0156049	−	0.0633117i
$307$	3.82878	+	15.5340i	0.218520	+	0.886570i	0.973104	+	0.230367i	$0.0739926\pi$
$307$	3.82878	+	15.5340i	0.218520	+	0.886570i	−0.754584	+	0.656204i	$0.772161\pi$
$308$	−0.771783	−	6.35621i	−0.0439764	−	0.362178i
$309$	−4.69770	+	12.3868i	−0.267243	+	0.704662i
$310$	−1.99476	+	8.09304i	−0.113295	+	0.459654i
$311$	−26.7297	+	6.58828i	−1.51570	+	0.373587i	−0.907451	−	0.420157i	$-0.861975\pi$
$311$	−26.7297	+	6.58828i	−1.51570	+	0.373587i	−0.608252	+	0.793744i	$0.708129\pi$
$312$	−3.43847	−	1.17342i	−0.194665	−	0.0664316i
$313$	7.26801	+	1.79140i	0.410812	+	0.101256i	0.439305	−	0.898338i	$-0.355225\pi$
$313$	7.26801	+	1.79140i	0.410812	+	0.101256i	−0.0284929	+	0.999594i	$0.509071\pi$
$314$	−0.295091	+	0.562248i	−0.0166529	+	0.0317295i
$315$	2.38430			0.134340
$316$	−16.4040			−0.922798
$317$	1.68648	−	3.21332i	0.0947223	−	0.180478i	−0.833485	−	0.552543i	$-0.813658\pi$
$317$	1.68648	−	3.21332i	0.0947223	−	0.180478i	0.928207	+	0.372064i	$0.121350\pi$
$318$	1.81439	+	2.04802i	0.101746	+	0.114847i
$319$		−	23.5699i		−	1.31966i
$320$	−16.6730	+	18.8199i	−0.932046	+	1.05206i
$321$	2.58626	−	1.35737i	0.144351	−	0.0757613i
$322$	−0.0390665	−	0.321742i	−0.00217709	−	0.0179300i
$323$	9.93121	+	18.9223i	0.552587	+	1.05287i
$324$	0.233167	+	1.92030i	0.0129537	+	0.106683i
$325$	−3.17455	+	36.3100i	−0.176092	+	2.01412i
$326$	−0.333791	+	2.74901i	−0.0184869	+	0.152254i
$327$	−9.51790	+	3.60966i	−0.526341	+	0.199615i
$328$	0.636466	+	0.334043i	0.0351430	+	0.0184445i
$329$	−1.93253	+	5.09566i	−0.106544	+	0.280933i
$330$	2.49651	+	4.75671i	0.137429	+	0.261848i
$331$	−9.85446	−	18.7761i	−0.541650	−	1.03203i	−0.990382	−	0.138361i	$-0.955816\pi$
$331$	−9.85446	−	18.7761i	−0.541650	−	1.03203i	0.448732	−	0.893666i	$-0.351876\pi$
$332$	−4.85877	−	19.7128i	−0.266659	−	1.08188i
$333$	2.74913	+	0.333805i	0.150651	+	0.0182924i
$334$	3.79475	+	3.36185i	0.207639	+	0.183952i
$335$	−16.2911	−	23.6017i	−0.890078	−	1.28950i
$336$	−2.07089	−	0.785385i	−0.112976	−	0.0428463i
$337$	−20.3615			−1.10916			−0.554581	−	0.832130i	$-0.687121\pi$
$337$	−20.3615			−1.10916			−0.554581	+	0.832130i	$0.687121\pi$
$338$	3.32472	+	0.178323i	0.180841	+	0.00969952i
$339$	11.5424			0.626899
$340$	31.3112	+	11.8748i	1.69809	+	0.644000i
$341$	25.6654	+	37.1828i	1.38986	+	2.01356i
$342$	0.919869	+	0.814933i	0.0497408	+	0.0440665i
$343$	8.29585	+	1.00730i	0.447934	+	0.0543890i
$344$	−1.80020	−	7.30371i	−0.0970604	−	0.393790i
$345$	−3.72665	−	7.10054i	−0.200636	−	0.382280i
$346$	2.23102	+	4.25085i	0.119940	+	0.228527i
$347$	−1.30769	+	3.44810i	−0.0702006	+	0.185104i	−0.965525	−	0.260312i	$-0.916175\pi$
$347$	−1.30769	+	3.44810i	−0.0702006	+	0.185104i	0.895324	+	0.445415i	$0.146944\pi$
$348$	−7.48147	−	3.92658i	−0.401049	−	0.210487i
$349$	−30.6468	+	11.6228i	−1.64048	+	0.622153i	−0.990465	−	0.137765i	$-0.956008\pi$
$349$	−30.6468	+	11.6228i	−1.64048	+	0.622153i	−0.650019	+	0.759918i	$0.725239\pi$
$350$	0.191428	−	1.57655i	0.0102323	−	0.0842703i
$351$	−1.39115	−	3.32636i	−0.0742543	−	0.177548i
$352$	−1.91234	−	15.7496i	−0.101928	−	0.839454i
$353$	6.42390	+	12.2397i	0.341910	+	0.651455i	0.994322	−	0.106409i	$-0.0339354\pi$
$353$	6.42390	+	12.2397i	0.341910	+	0.651455i	−0.652413	+	0.757864i	$0.726243\pi$
$354$	0.0856885	+	0.705709i	0.00455429	+	0.0375080i
$355$	23.4745	−	12.3204i	1.24590	−	0.653898i
$356$	−6.42023	+	7.24694i	−0.340272	+	0.384087i
$357$			2.73186i			0.144585i
$358$	−0.366366	−	0.413542i	−0.0193631	−	0.0218564i
$359$	6.84577	−	13.0435i	0.361306	−	0.688411i	−0.635162	−	0.772379i	$-0.719067\pi$
$359$	6.84577	−	13.0435i	0.361306	−	0.688411i	0.996468	+	0.0839675i	$0.0267592\pi$
$360$	3.91681			0.206434
$361$	−4.02418			−0.211799
$362$	−1.22585	+	2.33566i	−0.0644291	+	0.122759i
$363$	17.5922	+	4.33609i	0.923351	+	0.227586i
$364$	4.26195	+	0.372618i	0.223387	+	0.0195305i
$365$	−23.2046	+	5.71941i	−1.21458	+	0.299368i
$366$	0.444155	−	1.80201i	0.0232164	−	0.0941926i
$367$	8.90936	−	23.4920i	0.465065	−	1.22627i	−0.473384	−	0.880856i	$-0.656968\pi$
$367$	8.90936	−	23.4920i	0.465065	−	1.22627i	0.938449	−	0.345419i	$-0.112263\pi$
$368$	0.897885	+	7.39475i	0.0468055	+	0.385478i
$369$	0.170712	+	0.692607i	0.00888692	+	0.0360557i
$370$	0.659779	−	2.67683i	0.0343003	−	0.139162i
$371$	−5.39306	−	3.72256i	−0.279993	−	0.193266i
$372$	16.0781	−	1.95223i	0.833610	−	0.101219i
$373$	−0.421924	−	1.11252i	−0.0218464	−	0.0576042i	0.923649	−	0.383239i	$-0.125191\pi$
$373$	−0.421924	−	1.11252i	−0.0218464	−	0.0576042i	−0.945496	+	0.325635i	$0.894422\pi$
$374$	−5.45010	+	2.86043i	−0.281818	+	0.147910i
$375$	−4.75252	−	19.2817i	−0.245419	−	0.995704i
$376$	−3.17467	+	8.37092i	−0.163721	+	0.431697i
$377$	15.4091	+	3.25274i	0.793610	+	0.167525i
$378$	0.0557088	+	0.146892i	0.00286535	+	0.00755530i
$379$	−10.6142	+	7.32648i	−0.545217	+	0.376336i	−0.808603	−	0.588354i	$-0.799776\pi$
$379$	−10.6142	+	7.32648i	−0.545217	+	0.376336i	0.263386	+	0.964690i	$0.415161\pi$
$380$	−27.0057	+	23.9249i	−1.38536	+	1.22732i
$381$	−18.1210	−	4.46641i	−0.928365	−	0.228821i
$382$	−4.95784	−	1.88026i	−0.253665	−	0.0962025i
$383$	−3.91603	+	7.46138i	−0.200100	+	0.381259i	−0.964742	−	0.263196i	$-0.915223\pi$
$383$	−3.91603	+	7.46138i	−0.200100	+	0.381259i	0.764642	+	0.644455i	$0.222916\pi$
$384$	−7.04708	−	2.67260i	−0.359620	−	0.136386i
$385$	−8.53179	−	9.63040i	−0.434820	−	0.490811i
$386$	−2.00066	+	1.77243i	−0.101831	+	0.0902145i
$387$	4.24066	−	6.14365i	0.215565	−	0.312299i
$388$	12.9825	+	8.96120i	0.659089	+	0.454936i
$389$	−14.9086	−	7.82464i	−0.755897	−	0.396725i	0.0423133	−	0.999104i	$-0.486527\pi$
$389$	−14.9086	−	7.82464i	−0.755897	−	0.396725i	−0.798210	+	0.602379i	$0.794220\pi$
$390$	−3.45428	+	0.975680i	−0.174914	+	0.0494055i
$391$	8.13559	−	4.26989i	0.411435	−	0.215937i
$392$	6.62583	+	0.804522i	0.334655	+	0.0406345i
$393$	8.84097	−	2.17910i	0.445968	−	0.109921i
$394$	3.18769	−	4.61816i	0.160593	−	0.232660i
$395$	−27.1276	+	18.7249i	−1.36494	+	0.942149i
$396$	6.92193	−	7.81324i	0.347840	−	0.392630i
$397$	9.27643	+	1.12636i	0.465571	+	0.0565305i	0.349961	−	0.936764i	$-0.386195\pi$
$397$	9.27643	+	1.12636i	0.465571	+	0.0565305i	0.115610	+	0.993295i	$0.463118\pi$
$398$	−0.982193	+	3.98491i	−0.0492329	+	0.199746i
$399$	−2.60616	−	1.36782i	−0.130471	−	0.0684767i
$400$	−4.39969	+	36.2347i	−0.219985	+	1.81174i
$401$	25.0215	−	3.03816i	1.24951	−	0.151718i	0.531084	−	0.847319i	$-0.321785\pi$
$401$	25.0215	−	3.03816i	1.24951	−	0.151718i	0.718428	+	0.695601i	$0.244862\pi$
$402$	1.07342	−	1.55511i	0.0535372	−	0.0775620i
$403$	−27.8506	+	11.6477i	−1.38734	+	0.580213i
$404$	−12.1677	−	17.6279i	−0.605363	−	0.877020i
$405$	2.57758	+	2.90948i	0.128081	+	0.144573i
$406$	−0.666261	−	0.164219i	−0.0330660	−	0.00815003i
$407$	−8.48902	−	12.2985i	−0.420785	−	0.609612i
$408$			4.48777i			0.222178i
$409$	5.94401	−	4.10286i	0.293913	−	0.202873i	−0.411979	−	0.911194i	$-0.635162\pi$
$409$	5.94401	−	4.10286i	0.293913	−	0.202873i	0.705891	+	0.708320i	$0.250547\pi$
$410$	0.704967	−	0.0855985i	0.0348159	−	0.00422741i
$411$	−16.0670	+	6.09342i	−0.792528	+	0.300566i
$412$	3.08893	−	25.4396i	0.152180	−	1.25332i
$413$	−0.603747	−	1.59195i	−0.0297084	−	0.0783347i
$414$	0.350378	−	0.395495i	0.0172201	−	0.0194375i
$415$	−30.5368	−	27.0532i	−1.49899	−	1.32799i
$416$	10.5604	+	0.923283i	0.517764	+	0.0452677i
$417$	−2.91250	+	2.58025i	−0.142626	+	0.126356i
$418$		−	6.63154i		−	0.324359i
$419$	−19.5900	−	17.3552i	−0.957032	−	0.847856i	0.0314024	−	0.999507i	$-0.490003\pi$
$419$	−19.5900	−	17.3552i	−0.957032	−	0.847856i	−0.988434	+	0.151651i	$0.951541\pi$
$420$	−4.47817	+	1.10377i	−0.218513	+	0.0538585i
$421$	16.2847	+	11.2405i	0.793669	+	0.547830i	0.894497	−	0.447074i	$-0.147534\pi$
$421$	16.2847	+	11.2405i	0.793669	+	0.547830i	−0.100828	+	0.994904i	$0.532149\pi$
$422$	0.0553712	−	0.0209995i	0.00269543	−	0.00102224i
$423$	−8.30726	+	3.15053i	−0.403913	+	0.153184i
$424$	−8.85946	−	6.11524i	−0.430253	−	0.296982i
$425$	43.7136	−	10.7744i	2.12042	−	0.522637i
$426$	1.30751	+	1.15836i	0.0633492	+	0.0561225i
$427$			4.44499i			0.215108i
$428$	−4.22913	+	3.74668i	−0.204423	+	0.181103i
$429$	−8.45749	+	17.5218i	−0.408332	+	0.845961i
$430$	−5.56272	−	4.92814i	−0.268258	−	0.237656i
$431$	11.7821	−	13.2993i	0.567525	−	0.640603i	−0.392755	−	0.919643i	$-0.628478\pi$
$431$	11.7821	−	13.2993i	0.567525	−	0.640603i	0.960279	+	0.279040i	$0.0900163\pi$
$432$	−1.28038	−	3.37609i	−0.0616025	−	0.162432i
$433$	−2.19429	+	18.0716i	−0.105451	+	0.868466i	0.839974	+	0.542626i	$0.182570\pi$
$433$	−2.19429	+	18.0716i	−0.105451	+	0.868466i	−0.945425	+	0.325840i	$0.894353\pi$
$434$	1.22988	−	0.466432i	0.0590361	−	0.0223895i
$435$	−16.8544	+	2.04649i	−0.808105	+	0.0981217i
$436$	16.2054	−	11.1858i	0.776099	−	0.535703i
$437$			9.89916i			0.473541i
$438$	−0.894533	−	1.29596i	−0.0427425	−	0.0619231i
$439$	40.5647	+	9.99829i	1.93605	+	0.477192i	0.986566	+	0.163364i	$0.0522343\pi$
$439$	40.5647	+	9.99829i	1.93605	+	0.477192i	0.949480	+	0.313829i	$0.101612\pi$
$440$	−14.0156	−	15.8204i	−0.668169	−	0.754207i
$441$	3.76271	+	5.45123i	0.179177	+	0.259583i
$442$	−1.11791	−	3.95781i	−0.0531734	−	0.188254i
$443$	9.46616	−	13.7141i	0.449751	−	0.651577i	−0.530879	−	0.847448i	$-0.678138\pi$
$443$	9.46616	−	13.7141i	0.449751	−	0.651577i	0.980630	+	0.195871i	$0.0627534\pi$
$444$	−5.31793	+	0.645714i	−0.252378	+	0.0306442i
$445$	−2.34502	+	19.3130i	−0.111165	+	0.915523i
$446$	−5.47706	−	2.87459i	−0.259347	−	0.136116i
$447$	3.17845	−	12.8955i	0.150336	−	0.609936i
$448$	3.93881	+	0.478259i	0.186091	+	0.0225956i
$449$	11.4549	−	12.9299i	0.540588	−	0.610198i	−0.413214	−	0.910634i	$-0.635594\pi$
$449$	11.4549	−	12.9299i	0.540588	−	0.610198i	0.953802	+	0.300436i	$0.0971322\pi$
$450$	2.13076	−	1.47076i	0.100445	−	0.0693323i
$451$	2.18664	−	3.16789i	0.102965	−	0.149170i
$452$	−21.6789	+	5.34338i	−1.01969	+	0.251331i
$453$	−1.65144	−	0.200522i	−0.0775916	−	0.00942133i
$454$	0.202353	−	0.106203i	0.00949689	−	0.00498435i
$455$	7.47340	−	4.24872i	0.350358	−	0.199183i
$456$	−4.28128	−	2.24699i	−0.200490	−	0.105225i
$457$	−23.5803	−	16.2763i	−1.10304	−	0.761373i	−0.129886	−	0.991529i	$-0.541461\pi$
$457$	−23.5803	−	16.2763i	−1.10304	−	0.761373i	−0.973154	+	0.230156i	$0.926076\pi$
$458$	0.302422	−	0.438134i	0.0141313	−	0.0204727i
$459$	−3.33360	+	2.95331i	−0.155599	+	0.137849i
$460$	10.2864	+	11.6110i	0.479608	+	0.541366i
$461$	−37.7090	−	14.3011i	−1.75628	−	0.666070i	−0.999929	−	0.0119047i	$-0.996211\pi$
$461$	−37.7090	−	14.3011i	−1.75628	−	0.666070i	−0.756352	−	0.654165i	$-0.773020\pi$
$462$	0.393966	−	0.750640i	0.0183290	−	0.0349229i
$463$	16.6780	+	6.32514i	0.775094	+	0.293954i	0.710258	−	0.703942i	$-0.248578\pi$
$463$	16.6780	+	6.32514i	0.775094	+	0.293954i	0.0648359	+	0.997896i	$0.479348\pi$
$464$	15.3130	+	3.77432i	0.710889	+	0.175218i
$465$	24.3602	−	21.5812i	1.12968	−	1.00081i
$466$	0.825610	−	0.569878i	0.0382457	−	0.0263991i
$467$	4.28639	+	11.3023i	0.198350	+	0.523007i	0.996879	−	0.0789506i	$-0.0251569\pi$
$467$	4.28639	+	11.3023i	0.198350	+	0.523007i	−0.798528	+	0.601957i	$0.794388\pi$
$468$	4.15274	+	5.60354i	0.191961	+	0.259024i
$469$	−1.60480	+	4.23152i	−0.0741030	+	0.195394i
$470$	2.11672	+	8.58788i	0.0976371	+	0.396129i
$471$	2.19529	−	1.15218i	0.101154	−	0.0530895i
$472$	−0.991807	−	2.61518i	−0.0456516	−	0.120373i
$473$	−39.9892	+	4.85557i	−1.83871	+	0.223259i
$474$	−1.78743	−	1.23378i	−0.0820996	−	0.0566693i
$475$	−11.6084	+	47.0970i	−0.532628	+	2.16096i
$476$	−1.26467	−	5.13096i	−0.0579660	−	0.235177i
$477$	−1.28772	−	10.6053i	−0.0589605	−	0.485583i
$478$	1.60318	−	4.22724i	0.0733278	−	0.193349i
$479$	4.81121	−	19.5199i	0.219830	−	0.891885i	−0.752560	−	0.658524i	$-0.771181\pi$
$479$	4.81121	−	19.5199i	0.219830	−	0.891885i	0.972390	−	0.233362i	$-0.0749726\pi$
$480$	−11.0961	+	2.73495i	−0.506467	+	0.124833i
$481$	9.21177	−	3.85255i	0.420021	−	0.175661i
$482$	−6.61833	−	1.63127i	−0.301457	−	0.0743024i
$483$	−0.588090	+	1.12051i	−0.0267590	+	0.0509850i
$484$	−35.0489			−1.59313
$485$	31.6985			1.43936
$486$	−0.119023	+	0.226779i	−0.00539899	+	0.0102869i
$487$	−1.80492	−	2.03733i	−0.0817887	−	0.0923204i	0.706192	−	0.708021i	$-0.250412\pi$
$487$	−1.80492	−	2.03733i	−0.0817887	−	0.0923204i	−0.787980	+	0.615700i	$0.788873\pi$
$488$			7.30202i			0.330547i
$489$	7.16989	−	8.09313i	0.324234	−	0.365984i
$490$	5.83881	−	3.06444i	0.263770	−	0.138437i
$491$	0.513232	+	4.22684i	0.0231618	+	0.190755i	0.999697	−	0.0246017i	$-0.00783174\pi$
$491$	0.513232	+	4.22684i	0.0231618	+	0.190755i	−0.976536	+	0.215356i	$0.930909\pi$
$492$	−0.641261	−	1.22182i	−0.0289103	−	0.0550840i
$493$	−2.34481	−	19.3112i	−0.105605	−	0.869734i
$494$	4.33544	+	0.915177i	0.195061	+	0.0411757i
$495$	2.52827	−	20.8222i	0.113637	−	0.935886i
$496$	−28.2670	+	10.7202i	−1.26922	+	0.481353i
$497$	−3.70443	−	1.94424i	−0.166167	−	0.0872109i
$498$	0.953209	−	2.51341i	0.0427143	−	0.112628i
$499$	−5.36387	−	10.2200i	−0.240120	−	0.457510i	0.735337	−	0.677702i	$-0.237024\pi$
$499$	−5.36387	−	10.2200i	−0.240120	−	0.457510i	−0.975457	+	0.220192i	$0.929332\pi$
$500$	17.8523	+	34.0147i	0.798380	+	1.52119i
$501$	−4.73718	−	19.2195i	−0.211642	−	0.858664i
$502$	−4.81009	−	0.584051i	−0.214685	−	0.0260675i
$503$	7.17543	+	6.35688i	0.319937	+	0.283439i	0.807770	−	0.589497i	$-0.200674\pi$
$503$	7.17543	+	6.35688i	0.319937	+	0.283439i	−0.487833	+	0.872937i	$0.662213\pi$
$504$	−0.351120	−	0.508685i	−0.0156401	−	0.0226586i
$505$	−40.2438	−	15.2624i	−1.79082	−	0.679170i
$506$	−2.85121			−0.126752
$507$	−10.2879	−	7.94725i	−0.456902	−	0.352950i
$508$	36.1023			1.60178
$509$	−32.4938	−	12.3233i	−1.44026	−	0.546220i	−0.493956	−	0.869487i	$-0.664450\pi$
$509$	−32.4938	−	12.3233i	−1.44026	−	0.546220i	−0.946308	+	0.323267i	$0.895219\pi$
$510$	2.51865	+	3.64889i	0.111528	+	0.161576i
$511$	2.82295	+	2.50092i	0.124880	+	0.110634i
$512$	17.7622	+	2.15672i	0.784986	+	0.0953146i
$513$	−1.14832	−	4.65892i	−0.0506996	−	0.205696i
$514$	−0.491227	−	0.935955i	−0.0216671	−	0.0412832i
$515$	−23.9306	−	45.5959i	−1.05451	−	2.00919i
$516$	−5.12068	+	13.5021i	−0.225425	+	0.594397i
$517$	42.4514	+	22.2802i	1.86701	+	0.979882i
$518$	−0.406791	+	0.154276i	−0.0178734	+	0.00677848i
$519$	2.25939	−	18.6078i	0.0991764	−	0.816791i
$520$	12.2770	−	6.97960i	0.538380	−	0.306076i
$521$	0.785612	+	6.47010i	0.0344183	+	0.283460i	0.999748	+	0.0224282i	$0.00713972\pi$
$521$	0.785612	+	6.47010i	0.0344183	+	0.283460i	−0.965330	+	0.261032i	$0.915937\pi$
$522$	−0.519880	−	0.990548i	−0.0227545	−	0.0433551i
$523$	−1.15748	−	9.53271i	−0.0506131	−	0.416836i	−0.995890	−	0.0905680i	$-0.971132\pi$
$523$	−1.15748	−	9.53271i	−0.0506131	−	0.416836i	0.945277	−	0.326268i	$-0.105791\pi$
$524$	−15.5963	+	8.18556i	−0.681327	+	0.357588i
$525$	−4.11192	+	4.64140i	−0.179459	+	0.202567i
$526$			5.73846i			0.250209i
$527$	24.7272	+	27.9112i	1.07713	+	1.21583i
$528$	−9.05473	+	17.2523i	−0.394057	+	0.750812i
$529$	−18.7439			−0.814952
$530$	−10.6354			−0.461973
$531$	1.28992	−	2.45773i	0.0559776	−	0.106656i
$532$	5.52809	+	1.36255i	0.239673	+	0.0590741i
$533$	1.76928	+	1.86672i	0.0766361	+	0.0808567i
$534$	−1.24463	+	0.306773i	−0.0538602	+	0.0132754i
$535$	−2.71703	+	11.0234i	−0.117467	+	0.476584i
$536$	−2.63630	+	6.95135i	−0.113871	+	0.300252i
$537$	0.260019	+	2.14145i	0.0112206	+	0.0924103i
$538$	1.30002	+	5.27437i	0.0560477	+	0.227394i
$539$	8.55383	−	34.7042i	0.368440	−	1.49482i
$540$	−6.18809	−	4.27133i	−0.266293	−	0.183809i
$541$	−18.1991	+	2.20977i	−0.782440	+	0.0950054i	−0.502002	−	0.864867i	$-0.667403\pi$
$541$	−18.1991	+	2.20977i	−0.782440	+	0.0950054i	−0.280438	+	0.959872i	$0.590480\pi$
$542$	1.58641	+	4.18301i	0.0681420	+	0.179676i
$543$	9.11954	−	4.78631i	0.391357	−	0.205400i
$544$	−3.13363	−	12.7136i	−0.134353	−	0.545092i
$545$	14.0309	−	36.9963i	0.601016	−	1.58475i
$546$	0.436370	+	0.361151i	0.0186749	+	0.0154558i
$547$	−7.80991	−	20.5930i	−0.333927	−	0.880494i	−0.991850	−	0.127409i	$-0.959334\pi$
$547$	−7.80991	−	20.5930i	−0.333927	−	0.880494i	0.657923	−	0.753085i	$-0.271435\pi$
$548$	27.3561	−	18.8826i	1.16860	−	0.806624i
$549$	−5.42408	+	4.80531i	−0.231494	+	0.205086i
$550$	−13.5651	−	3.34350i	−0.578418	−	0.142567i
$551$	19.5967	+	7.43206i	0.834849	+	0.316617i
$552$	−0.966086	+	1.84072i	−0.0411194	+	0.0783464i
$553$	4.86368	+	1.84455i	0.206825	+	0.0784382i
$554$	−3.79753	−	4.28652i	−0.161341	−	0.182117i
$555$	−8.05730	+	7.13814i	−0.342013	+	0.302997i
$556$	4.27576	−	6.19451i	0.181333	−	0.262706i
$557$	3.68868	+	2.54611i	0.156294	+	0.107882i	0.643645	−	0.765324i	$-0.277421\pi$
$557$	3.68868	+	2.54611i	0.156294	+	0.107882i	−0.487351	+	0.873206i	$0.662037\pi$
$558$	1.89875	+	0.996541i	0.0803805	+	0.0421870i
$559$	2.34428	−	26.8135i	0.0991525	−	1.13409i
$560$	7.62294	−	4.00083i	0.322128	−	0.169066i
$561$	23.8574	+	2.89682i	1.00726	+	0.122304i
$562$	3.56923	−	0.879735i	0.150559	−	0.0371094i
$563$	13.6764	−	19.8137i	0.576393	−	0.835049i	−0.421012	−	0.907055i	$-0.638325\pi$
$563$	13.6764	−	19.8137i	0.576393	−	0.835049i	0.997404	+	0.0720065i	$0.0229402\pi$
$564$	14.1442	−	9.76302i	0.595577	−	0.411097i
$565$	−29.7515	+	33.5825i	−1.25166	+	1.41283i
$566$	5.35259	+	0.649922i	0.224986	+	0.0273183i
$567$	0.146796	−	0.595574i	0.00616485	−	0.0250118i
$568$	−6.08547	−	3.19390i	−0.255341	−	0.134013i
$569$	−3.81354	+	31.4073i	−0.159872	+	1.31666i	0.663079	+	0.748549i	$0.269249\pi$
$569$	−3.81354	+	31.4073i	−0.159872	+	1.31666i	−0.822951	+	0.568113i	$0.807674\pi$
$570$	−4.74207	+	0.575791i	−0.198623	+	0.0241172i
$571$	2.51783	−	3.64770i	0.105368	−	0.152652i	−0.766753	−	0.641942i	$-0.778129\pi$
$571$	2.51783	−	3.64770i	0.105368	−	0.152652i	0.872121	+	0.489291i	$0.162744\pi$
$572$	7.77338	−	36.8246i	0.325022	−	1.53972i
$573$	11.7607	+	17.0384i	0.491312	+	0.711789i
$574$	−0.0743132	−	0.0838823i	−0.00310177	−	0.00350118i
$575$	20.2492	+	4.99098i	0.844449	+	0.208138i
$576$	3.67450	+	5.32344i	0.153104	+	0.221810i
$577$		−	39.7285i		−	1.65392i	−0.562261	−	0.826960i	$-0.690068\pi$
$577$		−	39.7285i		−	1.65392i	0.562261	−	0.826960i	$-0.309932\pi$
$578$	−0.597549	+	0.412458i	−0.0248548	+	0.0171560i
$579$	10.3601	−	1.25794i	0.430549	−	0.0522781i
$580$	30.7084	−	11.6462i	1.27510	−	0.483580i
$581$	−0.776014	+	6.39105i	−0.0321945	+	0.265145i
$582$	0.740631	+	1.95288i	0.0307001	+	0.0809496i
$583$	−38.2279	+	43.1504i	−1.58324	+	1.78711i
$584$	4.63741	+	4.10839i	0.191897	+	0.170006i
$585$	13.2638	+	4.52642i	0.548391	+	0.187144i
$586$	−1.59624	+	1.41414i	−0.0659399	+	0.0584177i
$587$			36.0685i			1.48871i	0.667786	+	0.744354i	$0.267242\pi$
$587$			36.0685i			1.48871i	−0.667786	+	0.744354i	$0.732758\pi$
$588$	−9.59067	−	8.49659i	−0.395512	−	0.350393i
$589$	−39.0077	+	9.61453i	−1.60728	+	0.396160i
$590$	−2.27412	−	1.56971i	−0.0936239	−	0.0646239i
$591$	−20.4862	+	7.76938i	−0.842689	+	0.319590i
$592$	9.34949	−	3.54579i	0.384262	−	0.145731i
$593$	−7.80168	−	5.38511i	−0.320376	−	0.221140i	0.397012	−	0.917814i	$-0.370047\pi$
$593$	−7.80168	−	5.38511i	−0.320376	−	0.221140i	−0.717388	+	0.696674i	$0.754663\pi$
$594$	1.34188	−	0.330745i	0.0550582	−	0.0135706i
$595$	−7.94830	−	7.04158i	−0.325848	−	0.288676i
$596$			25.6916i			1.05237i
$597$	11.9947	−	10.6263i	0.490908	−	0.434907i
$598$	0.393477	−	1.86401i	0.0160905	−	0.0762249i
$599$	−19.1008	−	16.9218i	−0.780437	−	0.691407i	0.175662	−	0.984451i	$-0.443793\pi$
$599$	−19.1008	−	16.9218i	−0.780437	−	0.691407i	−0.956099	+	0.293044i	$0.905332\pi$
$600$	−6.75487	+	7.62467i	−0.275766	+	0.311276i
$601$	−13.3992	−	35.3309i	−0.546566	−	1.44118i	−0.869109	−	0.494621i	$-0.835307\pi$
$601$	−13.3992	−	35.3309i	−0.546566	−	1.44118i	0.322543	−	0.946555i	$-0.395462\pi$
$602$	−0.141362	+	1.16422i	−0.00576149	+	0.0474502i
$603$	−6.89849	+	2.61625i	−0.280928	+	0.106542i
$604$	3.19456	−	0.387890i	0.129985	−	0.0157830i
$605$	−57.9610	+	40.0076i	−2.35645	+	1.62654i
$606$		−	2.83594i		−	0.115202i
$607$	14.3799	+	20.8328i	0.583661	+	0.845578i	0.997912	−	0.0645840i	$-0.0205721\pi$
$607$	14.3799	+	20.8328i	0.583661	+	0.845578i	−0.414252	+	0.910162i	$0.635957\pi$
$608$	13.6976	+	3.37617i	0.555513	+	0.136922i
$609$	1.77668	+	2.00546i	0.0719947	+	0.0812652i
$610$	4.09807	+	5.93708i	0.165926	+	0.240385i
$611$	−20.4244	+	24.6783i	−0.826282	+	0.998378i
$612$	4.89396	−	7.09013i	0.197827	−	0.286602i
$613$	3.21102	−	0.389888i	0.129692	−	0.0157474i	−0.0554333	−	0.998462i	$-0.517654\pi$
$613$	3.21102	−	0.389888i	0.129692	−	0.0157474i	0.185125	+	0.982715i	$0.440731\pi$
$614$	0.493906	−	4.06768i	0.0199324	−	0.164158i
$615$	−2.45515	−	1.28856i	−0.0990012	−	0.0519599i
$616$	−0.798206	+	3.23845i	−0.0321606	+	0.130481i
$617$	−6.67647	−	0.810671i	−0.268785	−	0.0326364i	−0.0149653	−	0.999888i	$-0.504764\pi$
$617$	−6.67647	−	0.810671i	−0.268785	−	0.0326364i	−0.253819	+	0.967252i	$0.581687\pi$
$618$	2.24994	−	2.53966i	0.0905058	−	0.102160i
$619$	−17.7128	+	12.2263i	−0.711937	+	0.491415i	−0.868146	−	0.496309i	$-0.834688\pi$
$619$	−17.7128	+	12.2263i	−0.711937	+	0.491415i	0.156208	+	0.987724i	$0.450073\pi$
$620$	−35.7625	+	51.8109i	−1.43626	+	2.08078i
$621$	−2.00309	+	0.493716i	−0.0803811	+	0.0198122i
$622$	6.99937	+	0.849878i	0.280649	+	0.0340770i
$623$	2.71844	−	1.42675i	0.108912	−	0.0571614i
$624$	−10.0293	−	8.30052i	−0.401494	−	0.332287i
$625$	23.5945	+	12.3834i	0.943781	+	0.495334i
$626$	−1.57779	−	1.08907i	−0.0630613	−	0.0435281i
$627$	−14.7088	+	21.3093i	−0.587411	+	0.851012i
$628$	−3.58980	+	3.18029i	−0.143249	+	0.126907i
$629$	−8.17868	−	9.23182i	−0.326105	−	0.368097i
$630$	−0.570973	−	0.216542i	−0.0227481	−	0.00862722i
$631$	18.8529	−	35.9212i	0.750522	−	1.43000i	−0.147049	−	0.989129i	$-0.546977\pi$
$631$	18.8529	−	35.9212i	0.750522	−	1.43000i	0.897571	−	0.440871i	$-0.145330\pi$
$632$	7.98982	+	3.03014i	0.317818	+	0.120532i
$633$	−0.224503	−	0.0553350i	−0.00892318	−	0.00219937i
$634$	−0.695699	+	0.616336i	−0.0276297	+	0.0244778i
$635$	59.7031	−	41.2101i	2.36925	−	1.63537i
$636$	7.32813	+	19.3227i	0.290579	+	0.766194i
$637$	21.5078	+	10.3815i	0.852171	+	0.411329i
$638$	−2.14062	+	5.64435i	−0.0847479	+	0.223462i
$639$	−1.63224	−	6.62225i	−0.0645703	−	0.261972i
$640$	25.9403	−	13.6145i	1.02538	−	0.538161i
$641$	−11.4148	−	30.0984i	−0.450858	−	1.18882i	−0.947187	−	0.320681i	$-0.896088\pi$
$641$	−11.4148	−	30.0984i	−0.450858	−	1.18882i	0.496329	−	0.868135i	$-0.334681\pi$
$642$	−0.742614	+	0.0901697i	−0.0293086	+	0.00355871i
$643$	16.7473	+	11.5598i	0.660448	+	0.455874i	0.850553	−	0.525889i	$-0.176267\pi$
$643$	16.7473	+	11.5598i	0.660448	+	0.455874i	−0.190105	+	0.981764i	$0.560883\pi$
$644$	0.585825	−	2.37678i	0.0230847	−	0.0936584i
$645$	6.94423	+	28.1738i	0.273429	+	1.10934i
$646$	−0.659725	−	5.43332i	−0.0259565	−	0.213771i
$647$	0.729272	−	1.92293i	0.0286706	−	0.0755983i	−0.919917	−	0.392114i	$-0.871744\pi$
$647$	0.729272	−	1.92293i	0.0286706	−	0.0755983i	0.948587	+	0.316516i	$0.102513\pi$
$648$	0.241149	−	0.978382i	0.00947324	−	0.0384345i
$649$	−14.5428	+	3.58447i	−0.570853	+	0.140703i
$650$	4.05788	−	8.40692i	0.159163	−	0.329747i
$651$	−4.98656	−	1.22908i	−0.195439	−	0.0481713i
$652$	−9.71987	+	18.5197i	−0.380659	+	0.725286i
$653$	−11.9909			−0.469239			−0.234620	−	0.972087i	$-0.575384\pi$
$653$	−11.9909			−0.469239			−0.234620	+	0.972087i	$0.575384\pi$
$654$	2.60710			0.101946
$655$	−16.4482	+	31.3395i	−0.642685	+	1.22453i
$656$	1.70798	+	1.92791i	0.0666854	+	0.0752722i
$657$			6.14841i			0.239872i
$658$	0.925575	−	1.04476i	0.0360827	−	0.0407289i
$659$	11.0250	−	5.78635i	0.429472	−	0.225404i	−0.236114	−	0.971725i	$-0.575874\pi$
$659$	11.0250	−	5.78635i	0.429472	−	0.225404i	0.665586	+	0.746321i	$0.268182\pi$
$660$	4.89069	+	40.2785i	0.190370	+	1.56784i
$661$	7.21835	+	13.7534i	0.280761	+	0.534946i	0.984472	−	0.175540i	$-0.0561672\pi$
$661$	7.21835	+	13.7534i	0.280761	+	0.534946i	−0.703711	+	0.710486i	$0.748475\pi$
$662$	0.654627	+	5.39134i	0.0254428	+	0.209540i
$663$	−5.18624	+	15.1973i	−0.201417	+	0.590213i
$664$	−1.27480	+	10.4989i	−0.0494718	+	0.407437i
$665$	10.6972	−	4.05693i	0.414821	−	0.157321i
$666$	−0.628025	−	0.329613i	−0.0243355	−	0.0127722i
$667$	3.19539	−	8.42555i	0.123726	−	0.326239i
$668$	17.7947	+	33.9049i	0.688497	+	1.31182i
$669$	11.2238	+	21.3851i	0.433936	+	0.826797i
$670$	1.75776	+	7.13151i	0.0679082	+	0.275514i
$671$	38.8182	+	4.71339i	1.49856	+	0.181958i
$672$	1.34990	+	1.19591i	0.0520735	+	0.0461331i
$673$	17.8807	+	25.9047i	0.689250	+	0.998552i	0.998862	+	0.0476886i	$0.0151855\pi$
$673$	17.8807	+	25.9047i	0.689250	+	0.998552i	−0.309612	+	0.950863i	$0.600199\pi$
$674$	4.87602	+	1.84923i	0.187817	+	0.0712296i
$675$	−10.1090			−0.389095
$676$	23.0018	+	10.1639i	0.884683	+	0.390918i
$677$	−27.8530			−1.07048			−0.535238	−	0.844701i	$-0.679778\pi$
$677$	−27.8530			−1.07048			−0.535238	+	0.844701i	$0.679778\pi$
$678$	−2.76409	−	1.04828i	−0.106154	−	0.0402591i
$679$	−2.84159	−	4.11676i	−0.109050	−	0.157987i
$680$	−13.0571	−	11.5676i	−0.500717	−	0.443596i
$681$	−0.885785	−	0.107554i	−0.0339433	−	0.00412147i
$682$	−2.76922	−	11.2352i	−0.106039	−	0.430217i
$683$	8.83208	+	16.8281i	0.337950	+	0.643910i	0.993825	−	0.110960i	$-0.0353925\pi$
$683$	8.83208	+	16.8281i	0.337950	+	0.643910i	−0.655875	+	0.754870i	$0.727700\pi$
$684$	4.31354	+	8.21876i	0.164932	+	0.314252i
$685$	23.6853	−	62.4530i	0.904968	−	2.38621i
$686$	−1.89514	−	0.994648i	−0.0723569	−	0.0379758i
$687$	−1.94357	+	0.737097i	−0.0741516	+	0.0281220i
$688$	3.24900	−	26.7579i	0.123867	−	1.02014i
$689$	−22.9345	−	30.9468i	−0.873733	−	1.17898i
$690$	0.247559	+	2.03884i	0.00942443	+	0.0776171i
$691$	−18.3867	−	35.0330i	−0.699464	−	1.33272i	−0.932826	−	0.360328i	$-0.882665\pi$
$691$	−18.3867	−	35.0330i	−0.699464	−	1.33272i	0.233362	−	0.972390i	$-0.425027\pi$
$692$	4.37058	+	35.9950i	0.166145	+	1.36832i
$693$	−2.93086	+	1.53824i	−0.111334	+	0.0584328i
$694$	0.626312	−	0.706960i	0.0237745	−	0.0268358i
$695$		−	15.1247i		−	0.573712i
$696$	2.91865	+	3.29447i	0.110631	+	0.124877i
$697$	1.47640	−	2.81304i	0.0559225	−	0.106552i
$698$	8.39463			0.317741
$699$	−3.91695			−0.148153
$700$	5.57432	−	10.6210i	0.210690	−	0.401436i
$701$	8.03181	+	1.97966i	0.303357	+	0.0747709i	0.388056	−	0.921636i	$-0.373147\pi$
$701$	8.03181	+	1.97966i	0.303357	+	0.0747709i	−0.0846988	+	0.996407i	$0.526993\pi$
$702$	0.0310430	+	0.922916i	0.00117164	+	0.0348332i
$703$	12.9021	−	3.18007i	0.486610	−	0.119939i
$704$	8.35330	−	33.8907i	0.314827	−	1.27730i
$705$	12.2462	−	32.2906i	0.461219	−	1.21613i
$706$	−0.426737	−	3.51449i	−0.0160604	−	0.132270i
$707$	1.62546	+	6.59474i	0.0611316	+	0.248021i
$708$	−1.28495	+	5.21324i	−0.0482913	+	0.195926i
$709$	−13.3750	−	9.23213i	−0.502311	−	0.346720i	0.289810	−	0.957084i	$-0.406408\pi$
$709$	−13.3750	−	9.23213i	−0.502311	−	0.346720i	−0.792121	+	0.610364i	$0.791023\pi$
$710$	−6.74043	+	0.818437i	−0.252964	+	0.0307154i
$711$	3.00710	+	7.92906i	0.112775	+	0.297363i
$712$	4.46572	−	2.34379i	0.167360	−	0.0878373i
$713$	4.13373	+	16.7712i	0.154810	+	0.628087i
$714$	0.248107	−	0.654204i	0.00928517	−	0.0244830i
$715$	−29.1796	−	69.7707i	−1.09125	−	2.60928i
$716$	−1.47971	−	3.90168i	−0.0552995	−	0.145813i
$717$	−14.5276	+	10.0277i	−0.542542	+	0.374490i
$718$	−2.82398	+	2.50183i	−0.105390	+	0.0933675i
$719$	−15.4298	−	3.80309i	−0.575433	−	0.141831i	−0.0591492	−	0.998249i	$-0.518839\pi$
$719$	−15.4298	−	3.80309i	−0.575433	−	0.141831i	−0.516284	+	0.856418i	$0.672685\pi$
$720$	13.1230	+	4.97689i	0.489064	+	0.185478i
$721$	−3.77640	+	7.19533i	−0.140640	+	0.267968i
$722$	0.963679	+	0.365475i	0.0358644	+	0.0136016i
$723$	17.6487	+	19.9213i	0.656363	+	0.740880i
$724$	−14.9125	+	13.2114i	−0.554220	+	0.490996i
$725$	25.0829	−	36.3389i	0.931557	−	1.34959i
$726$	−3.81904	−	2.63609i	−0.141738	−	0.0978346i
$727$	46.4617	+	24.3850i	1.72317	+	0.904389i	0.968765	+	0.247980i	$0.0797668\pi$
$727$	46.4617	+	24.3850i	1.72317	+	0.904389i	0.754405	+	0.656409i	$0.227926\pi$
$728$	−2.00702	−	0.968754i	−0.0743850	−	0.0359044i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	6.07629	+	0.737795i	0.224893	+	0.0273070i
$731$	−32.2808	+	7.95650i	−1.19395	+	0.294282i
$732$	7.96293	−	11.5363i	0.294318	−	0.426394i
$733$	−28.6013	+	19.7421i	−1.05641	+	0.729190i	−0.963831	−	0.266515i	$-0.914128\pi$
$733$	−28.6013	+	19.7421i	−1.05641	+	0.729190i	−0.0925831	+	0.995705i	$0.529512\pi$
$734$	−4.26709	+	4.81655i	−0.157501	+	0.177782i
$735$	−25.5590	−	3.10342i	−0.942756	−	0.114471i
$736$	1.45157	−	5.88925i	0.0535056	−	0.217081i
$737$	35.2523	+	18.5018i	1.29854	+	0.681524i
$738$	0.0220216	−	0.181364i	0.000810626	−	0.00667610i
$739$	34.4941	−	4.18834i	1.26888	−	0.154071i	0.541735	−	0.840549i	$-0.317768\pi$
$739$	34.4941	−	4.18834i	1.26888	−	0.154071i	0.727150	+	0.686479i	$0.240845\pi$
$740$	11.8287	−	17.1368i	0.434831	−	0.629962i
$741$	−11.9013	−	12.5568i	−0.437206	−	0.461285i
$742$	0.953405	+	1.38125i	0.0350006	+	0.0507071i
$743$	−26.1027	−	29.4638i	−0.957613	−	1.08092i	−0.996658	−	0.0816846i	$-0.973970\pi$
$743$	−26.1027	−	29.4638i	−0.957613	−	1.08092i	0.0390448	−	0.999237i	$-0.487568\pi$
$744$	−8.19168	−	2.01907i	−0.300322	−	0.0740227i
$745$	29.3265	+	42.4868i	1.07444	+	1.55659i
$746$			0.304737i			0.0111572i
$747$	−8.63771	+	5.96218i	−0.316037	+	0.218145i
$748$	−46.1499	+	5.60361i	−1.68741	+	0.204888i
$749$	1.67520	−	0.635320i	0.0612106	−	0.0232141i
$750$	−0.613067	+	5.04906i	−0.0223861	+	0.184366i
$751$	−6.87074	−	18.1166i	−0.250717	−	0.661086i	0.749283	−	0.662251i	$-0.230399\pi$
$751$	−6.87074	−	18.1166i	−0.250717	−	0.661086i	−0.999999	+	0.00116459i	$0.999629\pi$
$752$	−21.2730	+	24.0122i	−0.775745	+	0.875635i
$753$	14.1610	+	12.5455i	0.516055	+	0.457185i
$754$	−3.39464	−	2.17839i	−0.123626	−	0.0793324i
$755$	4.84014	−	4.28799i	0.176151	−	0.156056i
$756$			1.18656i			0.0431548i
$757$	−33.2510	−	29.4578i	−1.20853	−	1.07066i	−0.995611	−	0.0935931i	$-0.970165\pi$
$757$	−33.2510	−	29.4578i	−1.20853	−	1.07066i	−0.212918	−	0.977070i	$-0.568297\pi$
$758$	3.20721	−	0.790505i	0.116491	−	0.0287124i
$759$	9.16186	+	6.32398i	0.332555	+	0.229546i
$760$	17.5729	−	6.66453i	0.637437	−	0.241748i
$761$	−17.3426	+	6.57717i	−0.628668	+	0.238422i	−0.648300	−	0.761385i	$-0.724520\pi$
$761$	−17.3426	+	6.57717i	−0.628668	+	0.238422i	0.0196320	+	0.999807i	$0.493751\pi$
$762$	3.93383	+	2.71532i	0.142508	+	0.0983658i
$763$	−6.06258	+	1.49429i	−0.219480	+	0.0540970i
$764$	−29.9766	−	26.5570i	−1.08452	−	0.960797i
$765$		−	17.3114i		−	0.625897i
$766$	1.61542	−	1.43114i	0.0583676	−	0.0517092i
$767$	−0.336431	−	10.0022i	−0.0121478	−	0.361157i
$768$	−8.23857	−	7.29874i	−0.297284	−	0.263370i
$769$	16.1168	−	18.1921i	0.581188	−	0.656025i	−0.382218	−	0.924072i	$-0.624840\pi$
$769$	16.1168	−	18.1921i	0.581188	−	0.656025i	0.963406	+	0.268047i	$0.0863782\pi$
$770$	1.16850	+	3.08107i	0.0421097	+	0.111034i
$771$	−0.497475	+	4.09707i	−0.0179161	+	0.147552i
$772$	−18.8759	+	7.15867i	−0.679357	+	0.257646i
$773$	36.2897	−	4.40637i	1.30525	−	0.158486i	0.561798	−	0.827274i	$-0.310110\pi$
$773$	36.2897	−	4.40637i	1.30525	−	0.158486i	0.743453	+	0.668788i	$0.233187\pi$
$774$	−1.57348	+	1.08610i	−0.0565577	+	0.0390390i
$775$			84.6394i			3.04034i
$776$	−4.66803	−	6.76282i	−0.167573	−	0.242771i
$777$	1.64934	+	0.406525i	0.0591696	+	0.0145840i
$778$	2.85957	+	3.22778i	0.102520	+	0.115722i
$779$	1.94439	+	2.81693i	0.0696650	+	0.100927i
$780$	−27.0074	−	2.36124i	−0.967021	−	0.0845458i
$781$	−20.9072	+	30.2893i	−0.748119	+	1.08384i
$782$	−2.33604	+	0.283646i	−0.0835366	+	0.0101432i
$783$	−0.526492	+	4.33605i	−0.0188153	+	0.154958i
$784$	21.1771	+	11.1146i	0.756323	+	0.396949i
$785$	−2.30629	+	9.35699i	−0.0823150	+	0.333965i
$786$	−2.31507	−	0.281101i	−0.0825759	−	0.0100265i
$787$	−10.7565	+	12.1416i	−0.383428	+	0.432801i	−0.908261	−	0.418404i	$-0.862589\pi$
$787$	−10.7565	+	12.1416i	−0.383428	+	0.432801i	0.524833	+	0.851206i	$0.324128\pi$
$788$	34.8803	−	24.0761i	1.24256	−	0.857677i
$789$	12.7279	−	18.4396i	0.453126	−	0.656466i
$790$	8.19690	−	2.02035i	0.291633	−	0.0718810i
$791$	7.02849	+	0.853414i	0.249904	+	0.0303439i
$792$	−4.81469	+	2.52694i	−0.171082	+	0.0897910i
$793$	−8.43849	+	24.7274i	−0.299660	+	0.878095i
$794$	−2.11915	−	1.11222i	−0.0752059	−	0.0394711i
$795$	34.1751	+	23.5894i	1.21207	+	0.836629i
$796$	−17.6090	+	25.5110i	−0.624135	+	0.904215i
$797$	−37.0575	+	32.8301i	−1.31264	+	1.16290i	−0.337500	+	0.941326i	$0.609581\pi$
$797$	−37.0575	+	32.8301i	−1.31264	+	1.16290i	−0.975143	+	0.221575i	$0.928880\pi$
$798$	0.499879	+	0.564246i	0.0176955	+	0.0199741i
$799$	36.9976	+	14.0313i	1.30888	+	0.496393i
$800$	13.8122	−	26.3169i	0.488335	−	0.930444i
$801$	4.67981	+	1.77482i	0.165353	+	0.0627102i
$802$	−6.26787	−	1.54489i	−0.221326	−	0.0545520i
$803$	24.8340	−	22.0010i	0.876373	−	0.776399i
$804$	11.7456	−	8.10737i	0.414234	−	0.285925i
$805$	−1.74426	−	4.59924i	−0.0614771	−	0.162102i
$806$	7.72729	−	0.259914i	0.272182	−	0.00915506i
$807$	7.52118	−	19.8317i	0.264758	−	0.698110i
$808$	2.67022	+	10.8335i	0.0939382	+	0.381122i
$809$	26.5912	−	13.9561i	0.934896	−	0.490671i	0.0727609	−	0.997349i	$-0.476819\pi$
$809$	26.5912	−	13.9561i	0.934896	−	0.490671i	0.862135	+	0.506678i	$0.169127\pi$
$810$	−0.353019	−	0.930835i	−0.0124038	−	0.0327062i
$811$	−36.2866	+	4.40599i	−1.27419	+	0.154715i	−0.729536	−	0.683943i	$-0.760264\pi$
$811$	−36.2866	+	4.40599i	−1.27419	+	0.154715i	−0.544659	+	0.838658i	$0.683341\pi$
$812$	−4.26534	−	2.94415i	−0.149684	−	0.103320i
$813$	4.18027	−	16.9600i	0.146609	−	0.594814i
$814$	0.915939	+	3.71611i	0.0321037	+	0.130250i
$815$	5.06589	+	41.7214i	0.177450	+	1.46144i
$816$	−5.70237	+	15.0359i	−0.199623	+	0.526362i
$817$	8.57232	−	34.7793i	0.299908	−	1.21677i
$818$	−1.79605	+	0.442686i	−0.0627973	+	0.0154781i
$819$	−0.601169	−	2.12837i	−0.0210065	−	0.0743712i
$820$	5.20777	+	1.28360i	0.181863	+	0.0448252i
$821$	3.26885	−	6.22828i	0.114084	−	0.217368i	−0.821719	−	0.569893i	$-0.806985\pi$
$821$	3.26885	−	6.22828i	0.114084	−	0.217368i	0.935802	+	0.352525i	$0.114677\pi$
$822$	4.40101			0.153503
$823$	25.8385			0.900673			0.450336	−	0.892859i	$-0.351304\pi$
$823$	25.8385			0.900673			0.450336	+	0.892859i	$0.351304\pi$
$824$	−6.20369	+	11.8201i	−0.216116	+	0.411774i
$825$	36.1733	+	40.8312i	1.25939	+	1.42156i
$826$			0.436060i			0.0151725i
$827$	1.23994	−	1.39960i	0.0431168	−	0.0486688i	−0.726557	−	0.687107i	$-0.758881\pi$
$827$	1.23994	−	1.39960i	0.0431168	−	0.0486688i	0.769673	+	0.638438i	$0.220419\pi$
$828$	3.53363	−	1.85459i	0.122802	−	0.0644515i
$829$	2.35068	+	19.3596i	0.0816426	+	0.672387i	0.974869	+	0.222780i	$0.0715131\pi$
$829$	2.35068	+	19.3596i	0.0816426	+	0.672387i	−0.893226	+	0.449608i	$0.851564\pi$
$830$	4.85574	+	9.25184i	0.168545	+	0.321136i
$831$	2.69519	+	22.1969i	0.0934953	+	0.770003i
$832$	21.0036	+	10.1381i	0.728169	+	0.351475i
$833$	3.55581	−	29.2847i	0.123201	−	1.01466i
$834$	0.931802	−	0.353386i	0.0322657	−	0.0122368i
$835$	68.1292	+	35.7570i	2.35771	+	1.23742i
$836$	17.7611	−	46.8322i	0.614281	−	1.61973i
$837$	−3.89098	−	7.41365i	−0.134492	−	0.256253i
$838$	3.11505	+	5.93524i	0.107608	+	0.205030i
$839$	−6.77028	−	27.4681i	−0.233736	−	0.948304i	−0.964162	−	0.265313i	$-0.914525\pi$
$839$	−6.77028	−	27.4681i	−0.233736	−	0.948304i	0.730426	−	0.682991i	$-0.239321\pi$
$840$	2.38505	+	0.289597i	0.0822920	+	0.00999206i
$841$	7.42632	+	6.57914i	0.256080	+	0.226867i
$842$	−2.87888	−	4.17077i	−0.0992126	−	0.143734i
$843$	−13.4204	−	5.08967i	−0.462222	−	0.175298i
$844$	0.447276			0.0153959
$845$	49.6403	−	9.44785i	1.70768	−	0.325016i
$846$	2.27549			0.0782330
$847$	10.3918	+	3.94107i	0.357065	+	0.135417i
$848$	−21.9126	−	31.7459i	−0.752482	−	1.09016i
$849$	−15.7581	−	13.9605i	−0.540817	−	0.479122i
$850$	−11.4467	−	1.38988i	−0.392620	−	0.0476726i
$851$	−1.36726	−	5.54719i	−0.0468691	−	0.190155i
$852$	6.13132	+	11.6823i	0.210055	+	0.400227i
$853$	18.9193	+	36.0477i	0.647784	+	1.23425i	0.958864	+	0.283866i	$0.0916171\pi$
$853$	18.9193	+	36.0477i	0.647784	+	1.23425i	−0.311080	+	0.950384i	$0.600691\pi$
$854$	0.403693	−	1.06445i	0.0138141	−	0.0364248i
$855$	16.5149	+	8.66770i	0.564799	+	0.296429i
$856$	2.75194	−	1.04367i	0.0940595	−	0.0356721i
$857$	0.377257	−	3.10699i	0.0128869	−	0.106133i	−0.984846	−	0.173431i	$-0.944515\pi$
$857$	0.377257	−	3.10699i	0.0128869	−	0.106133i	0.997733	+	0.0672979i	$0.0214378\pi$
$858$	3.61666	−	3.42788i	0.123471	−	0.117026i
$859$	3.02833	+	24.9405i	0.103325	+	0.850960i	0.948567	+	0.316576i	$0.102533\pi$
$859$	3.02833	+	24.9405i	0.103325	+	0.850960i	−0.845242	+	0.534384i	$0.820544\pi$
$860$	−26.0852	−	49.7013i	−0.889499	−	1.69480i
$861$	0.0527418	+	0.434368i	0.00179744	+	0.0148032i
$862$	−4.02933	+	2.11475i	−0.137239	+	0.0720288i
$863$	14.5088	−	16.3771i	0.493887	−	0.557483i	−0.447730	−	0.894169i	$-0.647767\pi$
$863$	14.5088	−	16.3771i	0.493887	−	0.557483i	0.941617	+	0.336686i	$0.109306\pi$
$864$			2.94009i			0.100024i
$865$	48.3153	+	54.5367i	1.64277	+	1.85430i
$866$	2.16673	−	4.12836i	0.0736286	−	0.140287i
$867$	2.83495			0.0962801
$868$	9.93471			0.337206
$869$	21.2659	−	40.5187i	0.721395	−	1.37450i
$870$	4.22201	+	1.04063i	0.143140	+	0.0352808i
$871$	−16.9607	+	20.4933i	−0.574693	+	0.694388i
$872$	−9.95933	+	2.45475i	−0.337265	+	0.0831285i
$873$	1.95161	−	7.91798i	0.0660519	−	0.267983i
$874$	0.899041	−	2.37058i	0.0304105	−	0.0801859i
$875$	−1.46830	−	12.0925i	−0.0496376	−	0.408802i
$876$	−2.84630	−	11.5479i	−0.0961677	−	0.390168i
$877$	7.28213	−	29.5447i	0.245900	−	0.997655i	−0.710056	−	0.704145i	$-0.751330\pi$
$877$	7.28213	−	29.5447i	0.245900	−	0.997655i	0.955956	−	0.293510i	$-0.0948234\pi$
$878$	−8.80607	−	6.07839i	−0.297190	−	0.205136i
$879$	8.26581	−	1.00365i	0.278799	−	0.0338523i
$880$	−26.8561	−	70.8138i	−0.905320	−	2.38713i
$881$	−51.3964	+	26.9749i	−1.73159	+	0.908807i	−0.768403	+	0.639967i	$0.778948\pi$
$881$	−51.3964	+	26.9749i	−1.73159	+	0.908807i	−0.963185	+	0.268840i	$0.913360\pi$
$882$	−0.405986	−	1.64715i	−0.0136702	−	0.0554624i
$883$	4.00934	−	10.5717i	0.134925	−	0.355768i	−0.850477	−	0.526012i	$-0.823687\pi$
$883$	4.00934	−	10.5717i	0.134925	−	0.355768i	0.985402	+	0.170245i	$0.0544558\pi$
$884$	2.70544	−	30.9443i	0.0909936	−	1.04077i
$885$	3.82587	+	10.0880i	0.128605	+	0.339104i
$886$	−3.51240	+	2.42443i	−0.118001	+	0.0814504i
$887$	−34.6296	+	30.6791i	−1.16275	+	1.03010i	−0.163698	+	0.986510i	$0.552342\pi$
$887$	−34.6296	+	30.6791i	−1.16275	+	1.03010i	−0.999049	+	0.0435942i	$0.986119\pi$
$888$	2.70945	+	0.667821i	0.0909233	+	0.0224106i
$889$	−10.7041	−	4.05953i	−0.359004	−	0.136152i
$890$	2.31557	−	4.41195i	0.0776180	−	0.147889i
$891$	−5.04551	−	1.91351i	−0.169031	−	0.0641050i
$892$	−30.9803	−	34.9696i	−1.03730	−	1.17087i
$893$	−31.9102	+	28.2699i	−1.06783	+	0.946017i
$894$	−1.93232	+	2.79944i	−0.0646264	+	0.0936274i
$895$	−6.90072	−	4.76323i	−0.230666	−	0.159217i
$896$	−4.09355	−	2.14846i	−0.136756	−	0.0717750i
$897$	−5.39874	+	5.11694i	−0.180259	+	0.170850i
$898$	−3.91741	+	2.05602i	−0.130726	+	0.0686101i
$899$	36.3044	+	4.40815i	1.21082	+	0.147020i
$900$	18.9867	−	4.67979i	0.632888	−	0.155993i
$901$	−27.0280	+	39.1569i	−0.900434	+	1.30450i
$902$	−0.811347	+	0.560033i	−0.0270149	+	0.0186470i
$903$	3.03649	−	3.42749i	0.101048	−	0.114060i
$904$	11.5461	+	1.40195i	0.384017	+	0.0466281i
$905$	−9.58065	+	38.8702i	−0.318472	+	1.29209i
$906$	0.377264	+	0.198003i	0.0125338	+	0.00657822i
$907$	2.11782	−	17.4418i	0.0703209	−	0.579145i	−0.914376	−	0.404867i	$-0.867318\pi$
$907$	2.11782	−	17.4418i	0.0703209	−	0.579145i	0.984696	−	0.174278i	$-0.0557591\pi$
$908$	1.71347	−	0.208052i	0.0568634	−	0.00690446i
$909$	−6.29013	+	9.11282i	−0.208630	+	0.302253i
$910$	−2.17554	+	0.338718i	−0.0721185	+	0.0112284i
$911$	26.2949	+	38.0947i	0.871189	+	1.26213i	0.963852	+	0.266437i	$0.0858464\pi$
$911$	26.2949	+	38.0947i	0.871189	+	1.26213i	−0.0926638	+	0.995697i	$0.529538\pi$
$912$	−11.4890	−	12.9684i	−0.380438	−	0.429426i
$913$	54.9904	+	13.5539i	1.81992	+	0.448569i
$914$	4.16861	+	6.03928i	0.137885	+	0.199762i
$915$		−	28.1673i		−	0.931183i
$916$	3.30917	−	2.28415i	0.109338	−	0.0754705i
$917$	5.54462	−	0.673238i	0.183099	−	0.0222323i
$918$	1.06652	−	0.404479i	0.0352006	−	0.0133498i
$919$	−4.92231	+	40.5389i	−0.162372	+	1.33726i	0.652577	+	0.757722i	$0.273688\pi$
$919$	−4.92231	+	40.5389i	−0.162372	+	1.33726i	−0.814949	+	0.579533i	$0.803235\pi$
$920$	−2.86539	−	7.55542i	−0.0944692	−	0.249095i
$921$	−10.6092	+	11.9753i	−0.349585	+	0.394600i
$922$	7.73142	+	6.84944i	0.254621	+	0.225574i
$923$	−16.9167	−	17.8484i	−0.556820	−	0.587486i
$924$	4.79263	−	4.24590i	0.157666	−	0.139680i
$925$		−	27.9951i		−	0.920472i
$926$	−3.41948	−	3.02939i	−0.112371	−	0.0995520i
$927$	−12.8628	+	3.17038i	−0.422468	+	0.104129i
$928$	−10.5688	−	7.29510i	−0.346937	−	0.239473i
$929$	29.8704	−	11.3283i	0.980015	−	0.371671i	0.187998	−	0.982169i	$-0.439800\pi$
$929$	29.8704	−	11.3283i	0.980015	−	0.371671i	0.792017	+	0.610499i	$0.209031\pi$
$930$	−7.79360	+	2.95572i	−0.255562	+	0.0969219i
$931$	26.1569	+	18.0548i	0.857259	+	0.591723i
$932$	7.35679	−	1.81329i	0.240980	−	0.0593961i
$933$	−20.6063	−	18.2556i	−0.674619	−	0.597660i
$934$		−	3.09587i		−	0.101300i
$935$	−69.9226	+	61.9460i	−2.28671	+	2.02585i
$936$	−0.987572	−	3.49638i	−0.0322798	−	0.114283i
$937$	24.7778	+	21.9512i	0.809455	+	0.717114i	0.962552	−	0.271097i	$-0.0873864\pi$
$937$	24.7778	+	21.9512i	0.809455	+	0.717114i	−0.153097	+	0.988211i	$0.548925\pi$
$938$	0.768612	−	0.867584i	0.0250961	−	0.0283276i
$939$	2.65441	+	6.99909i	0.0866232	+	0.228407i
$940$	−8.05236	+	66.3172i	−0.262639	+	2.16303i
$941$	−3.44092	+	1.30497i	−0.112171	+	0.0425408i	−0.410052	−	0.912062i	$-0.634489\pi$
$941$	−3.44092	+	1.30497i	−0.112171	+	0.0425408i	0.297881	+	0.954603i	$0.403720\pi$
$942$	−0.630352	+	0.0765386i	−0.0205380	+	0.00249376i
$943$	1.21113	−	0.835984i	0.0394399	−	0.0272234i
$944$		−	10.0222i		−	0.326195i
$945$	1.35444	+	1.96224i	0.0440598	+	0.0638316i
$946$	10.0173	+	2.46904i	0.325690	+	0.0802755i
$947$	2.10870	+	2.38023i	0.0685235	+	0.0773470i	0.781773	−	0.623563i	$-0.214316\pi$
$947$	2.10870	+	2.38023i	0.0685235	+	0.0773470i	−0.713249	+	0.700910i	$0.752777\pi$
$948$	−9.31854	−	13.5002i	−0.302652	−	0.438467i
$949$	10.9562	+	19.2717i	0.355654	+	0.625586i
$950$	7.05722	−	10.2242i	0.228967	−	0.331715i
$951$	3.60254	−	0.437428i	0.116821	−	0.0141846i
$952$	−0.331812	+	2.73272i	−0.0107541	+	0.0885680i
$953$	22.9504	+	12.0453i	0.743438	+	0.390186i	0.793508	−	0.608559i	$-0.208252\pi$
$953$	22.9504	+	12.0453i	0.743438	+	0.390186i	−0.0500706	+	0.998746i	$0.515945\pi$
$954$	−0.654799	+	2.65662i	−0.0211999	+	0.0860114i
$955$	−79.8871	−	9.70005i	−2.58509	−	0.313886i
$956$	22.6435	−	25.5592i	0.732342	−	0.826643i
$957$	19.3977	−	13.3893i	0.627038	−	0.432813i
$958$	−2.92494	+	4.23751i	−0.0945006	+	0.136908i
$959$	−10.2342	+	2.52249i	−0.330478	+	0.0814556i
$960$	−24.9598	−	3.03066i	−0.805573	−	0.0978143i
$961$	−34.6230	+	18.1716i	−1.11687	+	0.586180i
$962$	−2.55585	+	0.0859681i	−0.0824040	+	0.00277172i
$963$	2.58626	+	1.35737i	0.0833411	+	0.0437408i
$964$	−42.3699	−	29.2459i	−1.36464	−	0.941946i
$965$	−23.0439	+	33.3848i	−0.741809	+	1.07470i
$966$	0.242596	−	0.214921i	0.00780539	−	0.00691497i
$967$	−11.0300	−	12.4503i	−0.354702	−	0.400376i	0.543893	−	0.839155i	$-0.316950\pi$
$967$	−11.0300	−	12.4503i	−0.354702	−	0.400376i	−0.898595	+	0.438778i	$0.855411\pi$
$968$	17.0711	+	6.47421i	0.548686	+	0.208089i
$969$	−9.93121	+	18.9223i	−0.319036	+	0.607873i
$970$	−7.59091	−	2.87885i	−0.243730	−	0.0924344i
$971$	−53.7908	−	13.2582i	−1.72623	−	0.425477i	−0.753505	−	0.657442i	$-0.771638\pi$
$971$	−53.7908	−	13.2582i	−1.72623	−	0.425477i	−0.972724	+	0.231965i	$0.925485\pi$
$972$	−1.44792	+	1.28275i	−0.0464421	+	0.0411442i
$973$	−1.96428	+	1.35584i	−0.0629718	+	0.0434663i
$974$	0.247198	+	0.651807i	0.00792073	+	0.0208853i
$975$	−31.6859	+	18.0138i	−1.01476	+	0.576904i
$976$	−9.27829	+	24.4648i	−0.296991	+	0.783100i
$977$	−6.87458	−	27.8913i	−0.219937	−	0.892320i	−0.972331	−	0.233607i	$-0.924947\pi$
$977$	−6.87458	−	27.8913i	−0.219937	−	0.892320i	0.752394	−	0.658713i	$-0.228899\pi$
$978$	−2.45201	+	1.28691i	−0.0784065	+	0.0411509i
$979$	−9.57724	−	25.2531i	−0.306090	−	0.807093i
$980$	49.4414	−	6.00327i	1.57935	−	0.191767i
$981$	−8.37747	−	5.78255i	−0.267472	−	0.184623i
$982$	0.260977	−	1.05882i	0.00832810	−	0.0337884i
$983$	−7.38688	−	29.9697i	−0.235605	−	0.955886i	−0.962964	−	0.269629i	$-0.913099\pi$
$983$	−7.38688	−	29.9697i	−0.235605	−	0.955886i	0.727359	−	0.686257i	$-0.240747\pi$
$984$	0.0866418	+	0.713560i	0.00276204	+	0.0227475i
$985$	30.1998	−	79.6303i	0.962246	−	2.53723i
$986$	−1.19233	+	4.83746i	−0.0379714	+	0.154056i
$987$	−5.29145	+	1.30423i	−0.168429	+	0.0415140i
$988$	28.1660	+	18.0745i	0.896079	+	0.575028i
$989$	−14.9532	−	3.68564i	−0.475485	−	0.117197i
$990$	−2.49651	+	4.75671i	−0.0793444	+	0.151178i
$991$	17.2582			0.548223			0.274112	−	0.961698i	$-0.411616\pi$
$991$	17.2582			0.548223			0.274112	+	0.961698i	$0.411616\pi$
$992$	24.6165			0.781573
$993$	9.85446	−	18.7761i	0.312722	−	0.595842i
$994$	0.710534	+	0.802027i	0.0225368	+	0.0254387i
$995$			62.2884i			1.97468i
$996$	13.4632	−	15.1968i	0.426598	−	0.481530i
$997$	7.58607	−	3.98148i	0.240253	−	0.126095i	−0.340300	−	0.940317i	$-0.610529\pi$
$997$	7.58607	−	3.98148i	0.240253	−	0.126095i	0.580553	+	0.814222i	$0.302836\pi$
$998$	0.356319	+	2.93455i	0.0112791	+	0.0928917i
$999$	1.28697	+	2.45211i	0.0407179	+	0.0775814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.a.25.7	✓	168
169.142	even	26	inner	507.2.p.a.142.7	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.a.25.7	✓	168	1.1	even	1	trivial
507.2.p.a.142.7	yes	168	169.142	even	26	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.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.239472 - 0.0908198i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-1.44792 - 1.28275i) q^{4} +(-3.85869 - 0.468530i) q^{5} +(-0.0612925 - 0.248673i) q^{6} +(0.285060 + 0.543137i) q^{7} +(0.468284 + 0.892241i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})\)	\(q+(-0.239472 - 0.0908198i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-1.44792 - 1.28275i) q^{4} +(-3.85869 - 0.468530i) q^{5} +(-0.0612925 - 0.248673i) q^{6} +(0.285060 + 0.543137i) q^{7} +(0.468284 + 0.892241i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(0.881497 + 0.462645i) q^{10} +(5.04551 - 1.91351i) q^{11} +(0.233167 - 1.92030i) q^{12} +(0.554679 + 3.56263i) q^{13} +(-0.0189364 - 0.155955i) q^{14} +(-1.80639 - 3.44179i) q^{15} +(0.435226 + 3.58441i) q^{16} +(3.94351 - 2.06971i) q^{17} +(0.169836 - 0.191705i) q^{18} +4.79835i q^{19} +(4.98608 + 5.62812i) q^{20} +(-0.285060 + 0.543137i) q^{21} -1.38204 q^{22} +2.06303 q^{23} +(-0.468284 + 0.892241i) q^{24} +(9.81524 + 2.41924i) q^{25} +(0.190727 - 0.903527i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(0.283963 - 1.15208i) q^{28} +(1.54888 - 4.08406i) q^{29} +(0.119998 + 0.988270i) q^{30} +(2.00372 + 8.12939i) q^{31} +(0.703609 - 2.85466i) q^{32} +(4.44096 + 3.06538i) q^{33} +(-1.13233 + 0.137490i) q^{34} +(-0.845484 - 2.22936i) q^{35} +(1.71283 - 0.898963i) q^{36} +(-0.662742 - 2.68885i) q^{37} +(0.435786 - 1.14907i) q^{38} +(-2.61689 + 2.48030i) q^{39} +(-1.38892 - 3.66228i) q^{40} +(0.587063 - 0.405220i) q^{41} +(0.117592 - 0.104177i) q^{42} +(-7.24817 - 1.78651i) q^{43} +(-9.76006 - 3.70150i) q^{44} +(1.80639 - 3.44179i) q^{45} +(-0.494040 - 0.187364i) q^{46} +(5.89159 + 6.65023i) q^{47} +(-2.70267 + 2.39436i) q^{48} +(3.76271 - 5.45123i) q^{49} +(-2.13076 - 1.47076i) q^{50} +(3.94351 + 2.06971i) q^{51} +(3.76682 - 5.86993i) q^{52} +(-9.45949 + 4.96472i) q^{53} +(0.254248 + 0.0308713i) q^{54} +(-20.3656 + 5.01967i) q^{55} +(-0.351120 + 0.508685i) q^{56} +(-3.94897 + 2.72577i) q^{57} +(-0.741827 + 0.837349i) q^{58} +(-2.75543 - 0.334570i) q^{59} +(-1.79944 + 7.30060i) q^{60} +(6.41645 + 3.36761i) q^{61} +(0.258476 - 2.12874i) q^{62} +(-0.608926 + 0.0739370i) q^{63} +(3.67450 - 5.32344i) q^{64} +(-0.471135 - 14.0070i) q^{65} +(-0.785091 - 1.13740i) q^{66} +(4.89247 + 5.52246i) q^{67} +(-8.36481 - 2.06174i) q^{68} +(1.17194 + 1.69784i) q^{69} +0.610656i q^{70} +(-5.61311 + 3.87445i) q^{71} +(-1.00032 + 0.121460i) q^{72} +(5.74886 - 2.18026i) q^{73} +(-0.0854927 + 0.704095i) q^{74} +(3.58470 + 9.45207i) q^{75} +(6.15507 - 6.94764i) q^{76} +(2.47757 + 2.19494i) q^{77} +(0.851933 - 0.356296i) q^{78} +(6.34747 - 5.62337i) q^{79} -14.0350i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-0.177387 + 0.0437221i) q^{82} +(8.63771 + 5.96218i) q^{83} +(1.10945 - 0.420760i) q^{84} +(-16.1865 + 6.13872i) q^{85} +(1.57348 + 1.08610i) q^{86} +(4.24098 - 1.04531i) q^{87} +(4.07004 + 3.60574i) q^{88} -5.00506i q^{89} +(-0.745164 + 0.660158i) q^{90} +(-1.77688 + 1.31683i) q^{91} +(-2.98711 - 2.64635i) q^{92} +(-5.55212 + 6.26705i) q^{93} +(-0.806900 - 2.12762i) q^{94} +(2.24817 - 18.5153i) q^{95} +(2.74903 - 1.04257i) q^{96} +(-8.09549 + 0.982970i) q^{97} +(-1.39615 + 0.963690i) q^{98} +5.39617i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9}+O(q^{10}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31} + 130 q^{32} + 13 q^{33} - 65 q^{34} - 35 q^{35} + 12 q^{36} + 61 q^{38} + 12 q^{40} - 63 q^{42} + 72 q^{43} - 39 q^{44} - 8 q^{48} - 68 q^{49} - 52 q^{50} - 4 q^{51} + 65 q^{52} - q^{53} + 53 q^{55} - 14 q^{56} - 13 q^{57} - 26 q^{58} - 104 q^{59} + 117 q^{60} + 12 q^{61} + 49 q^{62} - 32 q^{64} - 52 q^{65} - 46 q^{66} + 26 q^{67} - 84 q^{68} - 4 q^{69} - 39 q^{71} - 52 q^{73} + 29 q^{74} + 8 q^{75} - 130 q^{76} + 60 q^{77} + 65 q^{78} + 14 q^{79} - 14 q^{81} + 45 q^{82} + 78 q^{83} - 13 q^{85} - 13 q^{86} - 46 q^{87} - 26 q^{88} - 4 q^{90} - 208 q^{91} + 82 q^{92} - 39 q^{93} + 25 q^{94} - 66 q^{95} + 65 q^{96} + 26 q^{97} - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

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