LMFDB - Embedded newform 507.2.p.a.493.7

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			493.7
Character	$\chi$	$=$	507.493
Dual form			507.2.p.a.181.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.203838 - 0.140699i) q^{2} +(0.885456 - 0.464723i) q^{3} +(-0.687456 - 1.81267i) q^{4} +(2.06415 - 2.32994i) q^{5} +(-0.245875 - 0.0298547i) q^{6} +(-0.296263 + 1.20198i) q^{7} +(-0.233460 + 0.947184i) q^{8} +(0.568065 - 0.822984i) q^{9} +O(q^{10})$	\(q+(-0.203838 - 0.140699i) q^{2} +(0.885456 - 0.464723i) q^{3} +(-0.687456 - 1.81267i) q^{4} +(2.06415 - 2.32994i) q^{5} +(-0.245875 - 0.0298547i) q^{6} +(-0.296263 + 1.20198i) q^{7} +(-0.233460 + 0.947184i) q^{8} +(0.568065 - 0.822984i) q^{9} +(-0.748572 + 0.184507i) q^{10} +(1.56001 - 1.07679i) q^{11} +(-1.45110 - 1.28557i) q^{12} +(3.56361 + 0.548367i) q^{13} +(0.229508 - 0.203326i) q^{14} +(0.744935 - 3.02232i) q^{15} +(-2.72135 + 2.41091i) q^{16} +(0.475961 + 0.117314i) q^{17} +(-0.231586 + 0.0878290i) q^{18} -3.70373i q^{19} +(-5.64244 - 2.13990i) q^{20} +(0.296263 + 1.20198i) q^{21} -0.469492 q^{22} -2.66460 q^{23} +(0.233460 + 0.947184i) q^{24} +(-0.565240 - 4.65517i) q^{25} +(-0.649243 - 0.613174i) q^{26} +(0.120537 - 0.992709i) q^{27} +(2.38247 - 0.289285i) q^{28} +(-2.93357 + 4.25002i) q^{29} +(-0.577084 + 0.511251i) q^{30} +(-6.12858 - 0.744144i) q^{31} +(2.83076 - 0.343717i) q^{32} +(0.880905 - 1.67842i) q^{33} +(-0.0805128 - 0.0908802i) q^{34} +(2.18903 + 3.17135i) q^{35} +(-1.88232 - 0.463950i) q^{36} +(-8.87128 - 1.07717i) q^{37} +(-0.521112 + 0.754960i) q^{38} +(3.41026 - 1.17054i) q^{39} +(1.72499 + 2.49908i) q^{40} +(4.60849 + 8.78074i) q^{41} +(0.108729 - 0.286694i) q^{42} +(-1.17390 - 9.66790i) q^{43} +(-3.02431 - 2.08753i) q^{44} +(-0.744935 - 3.02232i) q^{45} +(0.543146 + 0.374907i) q^{46} +(0.298082 + 0.113048i) q^{47} +(-1.28923 + 3.39943i) q^{48} +(4.84120 + 2.54086i) q^{49} +(-0.539760 + 1.02843i) q^{50} +(0.475961 - 0.117314i) q^{51} +(-1.45581 - 6.83663i) q^{52} +(9.72457 + 2.39689i) q^{53} +(-0.164243 + 0.185392i) q^{54} +(0.711216 - 5.85739i) q^{55} +(-1.06933 - 0.561230i) q^{56} +(-1.72121 - 3.27949i) q^{57} +(1.19595 - 0.453563i) q^{58} +(3.02362 - 3.41296i) q^{59} +(-5.99059 + 0.727390i) q^{60} +(1.53451 - 0.378223i) q^{61} +(1.14454 + 1.01397i) q^{62} +(0.820918 + 0.926625i) q^{63} +(5.81311 + 3.05095i) q^{64} +(8.63349 - 7.17109i) q^{65} +(-0.415714 + 0.218184i) q^{66} +(9.43253 + 3.57729i) q^{67} +(-0.114551 - 0.943409i) q^{68} +(-2.35939 + 1.23830i) q^{69} -0.954435i q^{70} +(5.50678 + 10.4923i) q^{71} +(0.646897 + 0.730195i) q^{72} +(-9.37720 + 6.47262i) q^{73} +(1.65674 + 1.46775i) q^{74} +(-2.66386 - 3.85927i) q^{75} +(-6.71366 + 2.54615i) q^{76} +(0.832119 + 2.19412i) q^{77} +(-0.859832 - 0.241220i) q^{78} +(3.28357 - 8.65806i) q^{79} +11.3171i q^{80} +(-0.354605 - 0.935016i) q^{81} +(0.296058 - 2.43826i) q^{82} +(2.36264 - 4.50164i) q^{83} +(1.97514 - 1.36334i) q^{84} +(1.25579 - 0.866809i) q^{85} +(-1.12098 + 2.13585i) q^{86} +(-0.622470 + 5.12650i) q^{87} +(0.655723 + 1.72900i) q^{88} +16.3822i q^{89} +(-0.273392 + 0.720875i) q^{90} +(-1.71489 + 4.12094i) q^{91} +(1.83180 + 4.83005i) q^{92} +(-5.77241 + 2.18919i) q^{93} +(-0.0448547 - 0.0649832i) q^{94} +(-8.62949 - 7.64506i) q^{95} +(2.34678 - 1.61987i) q^{96} +(-5.49509 - 6.20268i) q^{97} +(-0.629322 - 1.19907i) q^{98} -1.89555i 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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{26}\right)$

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 $

$2$	−0.203838	−	0.140699i	−0.144135	−	0.0994892i	0.493815	−	0.869567i	$-0.335602\pi$
$2$	−0.203838	−	0.140699i	−0.144135	−	0.0994892i	−0.637950	+	0.770078i	$0.720217\pi$
$3$	0.885456	−	0.464723i	0.511218	−	0.268308i
$3$	0.885456	−	0.464723i	0.511218	−	0.268308i
$4$	−0.687456	−	1.81267i	−0.343728	−	0.906336i
$5$	2.06415	−	2.32994i	0.923116	−	1.04198i	−0.0758768	−	0.997117i	$-0.524176\pi$
$5$	2.06415	−	2.32994i	0.923116	−	1.04198i	0.998993	−	0.0448656i	$-0.0142860\pi$
$6$	−0.245875	−	0.0298547i	−0.100378	−	0.0121881i
$7$	−0.296263	+	1.20198i	−0.111977	+	0.454308i	−0.999985	−	0.00552045i	$-0.998243\pi$
$7$	−0.296263	+	1.20198i	−0.111977	+	0.454308i	0.888008	+	0.459828i	$0.152089\pi$
$8$	−0.233460	+	0.947184i	−0.0825405	+	0.334880i
$9$	0.568065	−	0.822984i	0.189355	−	0.274328i
$10$	−0.748572	+	0.184507i	−0.236719	+	0.0583461i
$11$	1.56001	−	1.07679i	0.470359	−	0.324666i	−0.309197	−	0.950998i	$-0.600060\pi$
$11$	1.56001	−	1.07679i	0.470359	−	0.324666i	0.779556	+	0.626333i	$0.215445\pi$
$12$	−1.45110	−	1.28557i	−0.418897	−	0.371111i
$13$	3.56361	+	0.548367i	0.988367	+	0.152090i
$13$	3.56361	+	0.548367i	0.988367	+	0.152090i
$14$	0.229508	−	0.203326i	0.0613385	−	0.0543411i
$15$	0.744935	−	3.02232i	0.192341	−	0.780360i
$16$	−2.72135	+	2.41091i	−0.680338	+	0.602727i
$17$	0.475961	+	0.117314i	0.115437	+	0.0284528i	0.296611	−	0.954998i	$-0.404143\pi$
$17$	0.475961	+	0.117314i	0.115437	+	0.0284528i	−0.181174	+	0.983451i	$0.557990\pi$
$18$	−0.231586	+	0.0878290i	−0.0545853	+	0.0207015i
$19$		−	3.70373i		−	0.849695i	−0.905265	−	0.424847i	$-0.860328\pi$
$19$		−	3.70373i		−	0.849695i	0.905265	−	0.424847i	$-0.139672\pi$
$20$	−5.64244	−	2.13990i	−1.26169	−	0.478495i
$21$	0.296263	+	1.20198i	0.0646498	+	0.262295i
$22$	−0.469492			−0.100096
$23$	−2.66460			−0.555608			−0.277804	−	0.960638i	$-0.589607\pi$
$23$	−2.66460			−0.555608			−0.277804	+	0.960638i	$0.589607\pi$
$24$	0.233460	+	0.947184i	0.0476548	+	0.193343i
$25$	−0.565240	−	4.65517i	−0.113048	−	0.931033i
$26$	−0.649243	−	0.613174i	−0.127327	−	0.120253i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	2.38247	−	0.289285i	0.450245	−	0.0546696i
$29$	−2.93357	+	4.25002i	−0.544751	+	0.789208i	−0.994587	−	0.103903i	$-0.966867\pi$
$29$	−2.93357	+	4.25002i	−0.544751	+	0.789208i	0.449836	+	0.893111i	$0.351482\pi$
$30$	−0.577084	+	0.511251i	−0.105361	+	0.0933413i
$31$	−6.12858	−	0.744144i	−1.10073	−	0.133652i	−0.450047	−	0.893005i	$-0.648593\pi$
$31$	−6.12858	−	0.744144i	−1.10073	−	0.133652i	−0.650679	+	0.759353i	$0.725516\pi$
$32$	2.83076	−	0.343717i	0.500413	−	0.0607611i
$33$	0.880905	−	1.67842i	0.153346	−	0.292176i
$34$	−0.0805128	−	0.0908802i	−0.0138078	−	0.0155858i
$35$	2.18903	+	3.17135i	0.370013	+	0.536056i
$36$	−1.88232	−	0.463950i	−0.313720	−	0.0773250i
$37$	−8.87128	−	1.07717i	−1.45843	−	0.177085i	−0.647427	−	0.762128i	$-0.724155\pi$
$37$	−8.87128	−	1.07717i	−1.45843	−	0.177085i	−0.811003	+	0.585042i	$0.801078\pi$
$38$	−0.521112	+	0.754960i	−0.0845355	+	0.122471i
$39$	3.41026	−	1.17054i	0.546078	−	0.187436i
$40$	1.72499	+	2.49908i	0.272745	+	0.395139i
$41$	4.60849	+	8.78074i	0.719725	+	1.37132i	0.920132	+	0.391609i	$0.128081\pi$
$41$	4.60849	+	8.78074i	0.719725	+	1.37132i	−0.200407	+	0.979713i	$0.564226\pi$
$42$	0.108729	−	0.286694i	0.0167772	−	0.0442378i
$43$	−1.17390	−	9.66790i	−0.179017	−	1.47434i	−0.754377	−	0.656441i	$-0.772061\pi$
$43$	−1.17390	−	9.66790i	−0.179017	−	1.47434i	0.575360	−	0.817900i	$-0.304862\pi$
$44$	−3.02431	−	2.08753i	−0.455932	−	0.314707i
$45$	−0.744935	−	3.02232i	−0.111048	−	0.450541i
$46$	0.543146	+	0.374907i	0.0800825	+	0.0552770i
$47$	0.298082	+	0.113048i	0.0434797	+	0.0164897i	0.376249	−	0.926519i	$-0.377214\pi$
$47$	0.298082	+	0.113048i	0.0434797	+	0.0164897i	−0.332769	+	0.943008i	$0.607983\pi$
$48$	−1.28923	+	3.39943i	−0.186085	+	0.490665i
$49$	4.84120	+	2.54086i	0.691599	+	0.362979i
$50$	−0.539760	+	1.02843i	−0.0763336	+	0.145442i
$51$	0.475961	−	0.117314i	0.0666478	−	0.0164272i
$52$	−1.45581	−	6.83663i	−0.201885	−	0.948070i
$53$	9.72457	+	2.39689i	1.33577	+	0.329238i	0.841588	−	0.540119i	$-0.181621\pi$
$53$	9.72457	+	2.39689i	1.33577	+	0.329238i	0.494183	+	0.869358i	$0.335467\pi$
$54$	−0.164243	+	0.185392i	−0.0223506	+	0.0252287i
$55$	0.711216	−	5.85739i	0.0959003	−	0.789810i
$56$	−1.06933	−	0.561230i	−0.142896	−	0.0749975i
$57$	−1.72121	−	3.27949i	−0.227980	−	0.434380i
$58$	1.19595	−	0.453563i	0.157035	−	0.0595557i
$59$	3.02362	−	3.41296i	0.393641	−	0.444329i	−0.517960	−	0.855405i	$-0.673308\pi$
$59$	3.02362	−	3.41296i	0.393641	−	0.444329i	0.911601	+	0.411076i	$0.134847\pi$
$60$	−5.99059	+	0.727390i	−0.773382	+	0.0939056i
$61$	1.53451	−	0.378223i	0.196474	−	0.0484265i	−0.139851	−	0.990173i	$-0.544662\pi$
$61$	1.53451	−	0.378223i	0.196474	−	0.0484265i	0.336325	+	0.941746i	$0.390816\pi$
$62$	1.14454	+	1.01397i	0.145356	+	0.128774i
$63$	0.820918	+	0.926625i	0.103426	+	0.116744i
$64$	5.81311	+	3.05095i	0.726638	+	0.381369i
$65$	8.63349	−	7.17109i	1.07085	−	0.889465i
$66$	−0.415714	+	0.218184i	−0.0511709	+	0.0268566i
$67$	9.43253	+	3.57729i	1.15237	+	0.437035i	0.855459	−	0.517871i	$-0.173275\pi$
$67$	9.43253	+	3.57729i	1.15237	+	0.437035i	0.296908	+	0.954906i	$0.404045\pi$
$68$	−0.114551	−	0.943409i	−0.0138913	−	0.114405i
$69$	−2.35939	+	1.23830i	−0.284037	+	0.149074i
$70$		−	0.954435i		−	0.114077i
$71$	5.50678	+	10.4923i	0.653534	+	1.24521i	0.956369	+	0.292162i	$0.0943747\pi$
$71$	5.50678	+	10.4923i	0.653534	+	1.24521i	−0.302835	+	0.953043i	$0.597933\pi$
$72$	0.646897	+	0.730195i	0.0762375	+	0.0860543i
$73$	−9.37720	+	6.47262i	−1.09752	+	0.757562i	−0.972106	−	0.234542i	$-0.924641\pi$
$73$	−9.37720	+	6.47262i	−1.09752	+	0.757562i	−0.125413	+	0.992105i	$0.540026\pi$
$74$	1.65674	+	1.46775i	0.192593	+	0.170622i
$75$	−2.66386	−	3.85927i	−0.307596	−	0.445630i
$76$	−6.71366	+	2.54615i	−0.770109	+	0.292064i
$77$	0.832119	+	2.19412i	0.0948287	+	0.250043i
$78$	−0.859832	−	0.241220i	−0.0973568	−	0.0273128i
$79$	3.28357	−	8.65806i	0.369430	−	0.974108i	−0.613429	−	0.789750i	$-0.710210\pi$
$79$	3.28357	−	8.65806i	0.369430	−	0.974108i	0.982859	−	0.184358i	$-0.0590205\pi$
$80$			11.3171i			1.26529i
$81$	−0.354605	−	0.935016i	−0.0394005	−	0.103891i
$82$	0.296058	−	2.43826i	0.0326941	−	0.269260i
$83$	2.36264	−	4.50164i	0.259334	−	0.494119i	−0.720624	−	0.693326i	$-0.756144\pi$
$83$	2.36264	−	4.50164i	0.259334	−	0.494119i	0.979957	+	0.199208i	$0.0638368\pi$
$84$	1.97514	−	1.36334i	0.215505	−	0.148752i
$85$	1.25579	−	0.866809i	0.136209	−	0.0940186i
$86$	−1.12098	+	2.13585i	−0.120878	+	0.230314i
$87$	−0.622470	+	5.12650i	−0.0667358	+	0.549619i
$88$	0.655723	+	1.72900i	0.0699003	+	0.184312i
$89$			16.3822i			1.73651i	0.496117	+	0.868256i	$0.334759\pi$
$89$			16.3822i			1.73651i	−0.496117	+	0.868256i	$0.665241\pi$
$90$	−0.273392	+	0.720875i	−0.0288180	+	0.0759869i
$91$	−1.71489	+	4.12094i	−0.179770	+	0.431992i
$92$	1.83180	+	4.83005i	0.190978	+	0.503568i
$93$	−5.77241	+	2.18919i	−0.598571	+	0.227008i
$94$	−0.0448547	−	0.0649832i	−0.00462640	−	0.00670250i
$95$	−8.62949	−	7.64506i	−0.885367	−	0.784367i
$96$	2.34678	−	1.61987i	0.239517	−	0.165327i
$97$	−5.49509	−	6.20268i	−0.557942	−	0.629787i	0.400080	−	0.916480i	$-0.368982\pi$
$97$	−5.49509	−	6.20268i	−0.557942	−	0.629787i	−0.958022	+	0.286694i	$0.907444\pi$
$98$	−0.629322	−	1.19907i	−0.0635712	−	0.121125i
$99$		−	1.89555i		−	0.190510i
$100$	−8.04972	+	4.22482i	−0.804972	+	0.422482i
$101$	0.938888	+	7.73244i	0.0934228	+	0.769406i	0.961848	+	0.273586i	$0.0882097\pi$
$101$	0.938888	+	7.73244i	0.0934228	+	0.769406i	−0.868425	+	0.495821i	$0.834867\pi$
$102$	−0.113525	−	0.0430542i	−0.0112406	−	0.00426300i
$103$	−3.28051	+	1.72174i	−0.323238	+	0.169648i	−0.618535	−	0.785757i	$-0.712274\pi$
$103$	−3.28051	+	1.72174i	−0.323238	+	0.169648i	0.295297	+	0.955405i	$0.404581\pi$
$104$	−1.35136	+	3.24737i	−0.132512	+	0.318431i
$105$	3.41209	+	1.79080i	0.332986	+	0.174764i
$106$	−1.64499	−	1.85681i	−0.159776	−	0.180350i
$107$	−4.57705	−	4.05491i	−0.442480	−	0.392003i	0.412254	−	0.911069i	$-0.364741\pi$
$107$	−4.57705	−	4.05491i	−0.442480	−	0.392003i	−0.854734	+	0.519066i	$0.826280\pi$
$108$	−1.88232	+	0.463950i	−0.181126	+	0.0446436i
$109$	6.31408	−	0.766668i	0.604779	−	0.0734335i	0.187581	−	0.982249i	$-0.439935\pi$
$109$	6.31408	−	0.766668i	0.604779	−	0.0734335i	0.417198	+	0.908816i	$0.363012\pi$
$110$	−0.969102	+	1.09389i	−0.0924002	+	0.104298i
$111$	−8.35571	+	3.16890i	−0.793089	+	0.300779i
$112$	−2.09164	−	3.98528i	−0.197641	−	0.376574i
$113$	2.40089	+	1.26008i	0.225857	+	0.118539i	0.573856	−	0.818956i	$-0.305447\pi$
$113$	2.40089	+	1.26008i	0.225857	+	0.118539i	−0.348000	+	0.937495i	$0.613139\pi$
$114$	−0.110574	+	0.910657i	−0.0103562	+	0.0852908i
$115$	−5.50014	+	6.20837i	−0.512891	+	0.578934i
$116$	9.72060	+	2.39591i	0.902535	+	0.222455i
$117$	2.47566	−	2.62128i	0.228875	−	0.242338i
$118$	−1.09653	+	0.270270i	−0.100944	+	0.0248803i
$119$	−0.282019	+	0.537342i	−0.0258526	+	0.0492580i
$120$	2.68878	+	1.41118i	0.245451	+	0.128823i
$121$	−2.62652	+	6.92557i	−0.238775	+	0.629597i
$122$	−0.366007	−	0.138808i	−0.0331367	−	0.0125671i
$123$	8.16123	+	5.63329i	0.735873	+	0.507937i
$124$	2.86424	+	11.6207i	0.257216	+	1.04357i
$125$	0.795791	+	0.549295i	0.0711777	+	0.0491304i
$126$	−0.0369588	−	0.304383i	−0.00329255	−	0.0271166i
$127$	−1.73957	+	4.58687i	−0.154362	+	0.407019i	−0.989781	−	0.142594i	$-0.954456\pi$
$127$	−1.73957	+	4.58687i	−0.154362	+	0.407019i	0.835419	+	0.549613i	$0.185225\pi$
$128$	−3.40603	−	6.48965i	−0.301053	−	0.573609i
$129$	−5.53233	−	8.01497i	−0.487095	−	0.705678i
$130$	−2.76880	+	0.247016i	−0.242839	+	0.0216648i
$131$	0.600064	−	0.869343i	0.0524278	−	0.0759548i	−0.795893	−	0.605437i	$-0.792998\pi$
$131$	0.600064	−	0.869343i	0.0524278	−	0.0759548i	0.848321	+	0.529482i	$0.177614\pi$
$132$	−3.64802	−	0.442950i	−0.317519	−	0.0385538i
$133$	4.45183	+	1.09728i	0.386023	+	0.0951461i
$134$	−1.41938	−	2.05633i	−0.122616	−	0.177640i
$135$	−2.06415	−	2.32994i	−0.177654	−	0.200530i
$136$	−0.222235	+	0.423434i	−0.0190565	+	0.0363092i
$137$	−9.37944	+	1.13887i	−0.801340	+	0.0973003i	−0.510952	−	0.859609i	$-0.670707\pi$
$137$	−9.37944	+	1.13887i	−0.801340	+	0.0973003i	−0.290387	+	0.956909i	$0.593784\pi$
$138$	0.655160	+	0.0795508i	0.0557709	+	0.00677181i
$139$	14.8009	−	13.1124i	1.25540	−	1.11218i	0.266459	−	0.963846i	$-0.414146\pi$
$139$	14.8009	−	13.1124i	1.25540	−	1.11218i	0.988937	−	0.148337i	$-0.0473920\pi$
$140$	4.24377	−	6.14816i	0.358664	−	0.519614i
$141$	0.316474	−	0.0384269i	0.0266519	−	0.00323613i
$142$	0.353766	−	2.91352i	0.0296873	−	0.244497i
$143$	6.14972	−	2.98181i	0.514266	−	0.249352i
$144$	0.438234	+	3.60918i	0.0365195	+	0.300765i
$145$	3.84696	+	15.6077i	0.319473	+	1.29615i
$146$	2.82212			0.233560
$147$	5.46746			0.450949
$148$	4.14606	+	16.8212i	0.340804	+	1.38270i
$149$	2.86471	+	1.08644i	0.234686	+	0.0890047i	0.469144	−	0.883121i	$-0.344562\pi$
$149$	2.86471	+	1.08644i	0.234686	+	0.0890047i	−0.234458	+	0.972126i	$0.575332\pi$
$150$			1.16147i			0.0948333i
$151$	−4.40980	+	1.67241i	−0.358864	+	0.136099i	−0.527446	−	0.849588i	$-0.676850\pi$
$151$	−4.40980	+	1.67241i	−0.358864	+	0.136099i	0.168582	+	0.985688i	$0.446081\pi$
$152$	3.50812	+	0.864673i	0.284546	+	0.0701342i
$153$	0.366924	−	0.325066i	0.0296640	−	0.0262800i
$154$	0.139093	−	0.564322i	0.0112084	−	0.0454744i
$155$	−14.3841	+	12.7432i	−1.15536	+	1.02356i
$156$	−4.46620	−	5.37699i	−0.357582	−	0.430503i
$157$	−2.46612	−	2.18480i	−0.196818	−	0.174366i	0.558957	−	0.829196i	$-0.311201\pi$
$157$	−2.46612	−	2.18480i	−0.196818	−	0.174366i	−0.755776	+	0.654831i	$0.772740\pi$
$158$	−1.88749	+	1.30284i	−0.150161	+	0.103649i
$159$	9.72457	−	2.39689i	0.771208	−	0.190086i
$160$	5.04228	−	7.30500i	0.398627	−	0.577511i
$161$	0.789422	−	3.20281i	0.0622152	−	0.252417i
$162$	−0.0592740	+	0.240484i	−0.00465701	+	0.0188942i
$163$	−1.70867	−	0.207471i	−0.133834	−	0.0162504i	0.0533457	−	0.998576i	$-0.483011\pi$
$163$	−1.70867	−	0.207471i	−0.133834	−	0.0162504i	−0.187179	+	0.982326i	$0.559935\pi$
$164$	12.7485	−	14.3901i	0.995489	−	1.12367i
$165$	−2.09231	−	5.51698i	−0.162886	−	0.429496i
$166$	−1.11497	+	0.585182i	−0.0865385	+	0.0454189i
$167$	15.8462	+	10.9379i	1.22622	+	0.846397i	0.992056	−	0.125801i	$-0.0401501\pi$
$167$	15.8462	+	10.9379i	1.22622	+	0.846397i	0.234162	+	0.972198i	$0.424765\pi$
$168$	−1.20767			−0.0931734
$169$	12.3986	+	3.90833i	0.953737	+	0.300641i
$170$	−0.377936			−0.0289864
$171$	−3.04811	−	2.10396i	−0.233095	−	0.160894i
$172$	−16.7177	+	8.77415i	−1.27472	+	0.669023i
$173$	−5.35613	−	14.1229i	−0.407219	−	1.07375i	−0.969130	−	0.246550i	$-0.920703\pi$
$173$	−5.35613	−	14.1229i	−0.407219	−	1.07375i	0.561911	−	0.827198i	$-0.310066\pi$
$174$	0.848177	−	0.957394i	0.0643001	−	0.0725798i
$175$	5.76290	+	0.699743i	0.435634	+	0.0528956i
$176$	−1.64927	+	6.69136i	−0.124319	+	0.504380i
$177$	1.09120	−	4.42717i	0.0820196	−	0.332766i
$178$	2.30496	−	3.33931i	0.172764	−	0.250292i
$179$	2.65659	−	0.654792i	0.198563	−	0.0489414i	−0.138780	−	0.990323i	$-0.544318\pi$
$179$	2.65659	−	0.654792i	0.198563	−	0.0489414i	0.337343	+	0.941382i	$0.390472\pi$
$180$	−4.96637	+	3.42804i	−0.370171	+	0.255511i
$181$	−8.19217	−	7.25763i	−0.608919	−	0.539455i	0.301328	−	0.953520i	$-0.402570\pi$
$181$	−8.19217	−	7.25763i	−0.608919	−	0.539455i	−0.910247	+	0.414065i	$0.864108\pi$
$182$	0.929372	−	0.598719i	0.0688896	−	0.0443800i
$183$	1.18297	−	1.04802i	0.0874479	−	0.0774721i
$184$	0.622077	−	2.52387i	0.0458601	−	0.186062i
$185$	−20.8214	+	18.4462i	−1.53082	+	1.35619i
$186$	1.48465	+	0.365934i	0.108860	+	0.0268316i
$187$	0.868824	−	0.329501i	0.0635347	−	0.0240955i
$188$		−	0.618040i		−	0.0450752i
$189$	1.15751	+	0.438986i	0.0841965	+	0.0319315i
$190$	0.683363	+	2.77251i	0.0495764	+	0.201139i
$191$	−17.0089			−1.23072			−0.615362	−	0.788245i	$-0.710990\pi$
$191$	−17.0089			−1.23072			−0.615362	+	0.788245i	$0.710990\pi$
$192$	6.56510			0.473795
$193$	3.53278	+	14.3331i	0.254295	+	1.03172i	0.949716	+	0.313113i	$0.101372\pi$
$193$	3.53278	+	14.3331i	0.254295	+	1.03172i	−0.695421	+	0.718603i	$0.744782\pi$
$194$	0.247397	+	2.03749i	0.0177620	+	0.146284i
$195$	4.31200	−	10.3619i	0.308789	−	0.742029i
$196$	1.27763	−	10.5222i	0.0912593	−	0.751588i
$197$	12.3338	−	1.49760i	0.878747	−	0.106699i	0.331286	−	0.943530i	$-0.392517\pi$
$197$	12.3338	−	1.49760i	0.878747	−	0.106699i	0.547461	+	0.836831i	$0.315594\pi$
$198$	−0.266702	+	0.386384i	−0.0189537	+	0.0274591i
$199$	−5.38107	+	4.76721i	−0.381454	+	0.337939i	−0.831961	−	0.554834i	$-0.812782\pi$
$199$	−5.38107	+	4.76721i	−0.381454	+	0.337939i	0.450507	+	0.892773i	$0.351243\pi$
$200$	4.54126	+	0.551409i	0.321116	+	0.0389905i
$201$	10.0145	−	1.21598i	0.706371	−	0.0857689i
$202$	0.896566	−	1.70826i	0.0630821	−	0.120193i
$203$	−4.23935	−	4.78523i	−0.297544	−	0.335858i
$204$	−0.539854	−	0.782113i	−0.0377973	−	0.0547589i
$205$	29.9713	+	7.38725i	2.09328	+	0.515948i
$206$	0.910939	+	0.110608i	0.0634681	+	0.00770642i
$207$	−1.51367	+	2.19292i	−0.105207	+	0.152419i
$208$	−11.0199	+	7.09922i	−0.764092	+	0.492243i
$209$	−3.98816	−	5.77784i	−0.275867	−	0.399662i
$210$	−0.443548	−	0.845110i	−0.0306077	−	0.0583182i
$211$	8.75388	−	23.0821i	0.602642	−	1.58904i	−0.191625	−	0.981468i	$-0.561376\pi$
$211$	8.75388	−	23.0821i	0.602642	−	1.58904i	0.794267	−	0.607568i	$-0.207855\pi$
$212$	−2.34043	−	19.2752i	−0.160742	−	1.32383i
$213$	9.75202	+	6.73133i	0.668197	+	0.461223i
$214$	0.362453	+	1.47053i	0.0247768	+	0.100523i
$215$	−24.9488	−	17.2209i	−1.70149	−	1.17446i
$216$	0.912137	+	0.345928i	0.0620631	+	0.0235374i
$217$	2.71012	−	7.14600i	0.183975	−	0.485102i
$218$	−1.39492	−	0.732108i	−0.0944756	−	0.0495846i
$219$	−5.29513	+	10.0890i	−0.357811	+	0.681753i
$220$	−11.1065	+	2.73750i	−0.748798	+	0.184562i
$221$	1.63181	+	0.679061i	0.109767	+	0.0456786i
$222$	2.14907	+	0.529698i	0.144236	+	0.0355510i
$223$	−4.63997	+	5.23744i	−0.310715	+	0.350725i	−0.883036	−	0.469304i	$-0.844505\pi$
$223$	−4.63997	+	5.23744i	−0.310715	+	0.350725i	0.572321	+	0.820030i	$0.306043\pi$
$224$	−0.425507	+	3.50436i	−0.0284304	+	0.234145i
$225$	−4.15222	−	2.17925i	−0.276815	−	0.145284i
$226$	−0.312099	−	0.594655i	−0.0207605	−	0.0395559i
$227$	−13.8142	+	5.23904i	−0.916881	+	0.347727i	−0.767497	−	0.641052i	$-0.778498\pi$
$227$	−13.8142	+	5.23904i	−0.916881	+	0.347727i	−0.149384	+	0.988779i	$0.547729\pi$
$228$	−4.76139	+	5.37450i	−0.315331	+	0.355935i
$229$	−20.0649	+	2.43632i	−1.32593	+	0.160997i	−0.752680	−	0.658386i	$-0.771239\pi$
$229$	−20.0649	+	2.43632i	−1.32593	+	0.160997i	−0.573247	+	0.819383i	$0.694316\pi$
$230$	1.99465	−	0.491636i	0.131523	−	0.0324175i
$231$	1.75646	+	1.55609i	0.115567	+	0.102383i
$232$	−3.34067	−	3.77084i	−0.219326	−	0.247568i
$233$	−5.44175	−	2.85605i	−0.356501	−	0.187106i	0.276959	−	0.960882i	$-0.410673\pi$
$233$	−5.44175	−	2.85605i	−0.356501	−	0.187106i	−0.633460	+	0.773776i	$0.718366\pi$
$234$	−0.873444	+	0.185994i	−0.0570988	+	0.0121588i
$235$	0.878681	−	0.461167i	0.0573188	−	0.0300832i
$236$	−8.26518	−	3.13457i	−0.538018	−	0.204043i
$237$	−1.11614	−	9.19228i	−0.0725014	−	0.597103i
$238$	0.133089	−	0.0698507i	0.00862691	−	0.00452775i
$239$			1.08987i			0.0704980i	0.999379	+	0.0352490i	$0.0112224\pi$
$239$			1.08987i			0.0704980i	−0.999379	+	0.0352490i	$0.988778\pi$
$240$	5.25930	+	10.0208i	0.339487	+	0.646838i
$241$	9.20132	+	10.3861i	0.592709	+	0.669030i	0.965957	−	0.258701i	$-0.0832945\pi$
$241$	9.20132	+	10.3861i	0.592709	+	0.669030i	−0.373248	+	0.927731i	$0.621756\pi$
$242$	1.50980	−	1.04214i	0.0970539	−	0.0669915i
$243$	−0.748511	−	0.663123i	−0.0480170	−	0.0425393i
$244$	−1.74050	−	2.52156i	−0.111424	−	0.161426i
$245$	15.9130	−	6.03501i	1.01664	−	0.385563i
$246$	−0.870968	−	2.29655i	−0.0555309	−	0.146423i
$247$	2.03101	−	13.1987i	0.129230	−	0.839810i
$248$	2.13562	−	5.63116i	0.135612	−	0.357579i
$249$		−	5.08397i		−	0.322184i
$250$	−0.0849270	−	0.223934i	−0.00537125	−	0.0141628i
$251$	−3.28284	+	27.0366i	−0.207211	+	1.70654i	0.403745	+	0.914872i	$0.367708\pi$
$251$	−3.28284	+	27.0366i	−0.207211	+	1.70654i	−0.610956	+	0.791665i	$0.709215\pi$
$252$	1.11532	−	2.12507i	0.0702587	−	0.133867i
$253$	−4.15679	+	2.86923i	−0.261335	+	0.180387i
$254$	0.999959	−	0.690222i	0.0627430	−	0.0433084i
$255$	0.709120	−	1.35112i	0.0444068	−	0.0846101i
$256$	1.36386	−	11.2324i	0.0852413	−	0.702025i
$257$	−4.64532	−	12.2487i	−0.289767	−	0.764053i	−0.998295	−	0.0583705i	$-0.981410\pi$
$257$	−4.64532	−	12.2487i	−0.289767	−	0.764053i	0.708528	−	0.705683i	$-0.249360\pi$
$258$			2.41215i			0.150174i
$259$	3.92297	−	10.3440i	0.243761	−	0.642746i
$260$	−18.9340	−	10.7199i	−1.17424	−	0.664818i
$261$	1.83123	+	4.82857i	0.113351	+	0.298881i
$262$	−0.244631	+	0.0927764i	−0.0151134	+	0.00573174i
$263$	−8.38204	−	12.1435i	−0.516859	−	0.748799i	0.474460	−	0.880277i	$-0.342643\pi$
$263$	−8.38204	−	12.1435i	−0.516859	−	0.748799i	−0.991319	+	0.131478i	$0.958028\pi$
$264$	1.38412	+	1.22622i	0.0851867	+	0.0754688i
$265$	25.6576	−	17.7102i	1.57613	−	1.08793i
$266$	−0.753065	−	0.850035i	−0.0461734	−	0.0521190i
$267$	7.61319	+	14.5057i	0.465920	+	0.887736i
$268$		−	19.5573i		−	1.19465i
$269$	27.6755	−	14.5252i	1.68740	−	0.885618i	0.702677	−	0.711509i	$-0.251988\pi$
$269$	27.6755	−	14.5252i	1.68740	−	0.885618i	0.984726	−	0.174109i	$-0.0557045\pi$
$270$	0.0929308	+	0.765354i	0.00565559	+	0.0465780i
$271$	−12.9270	−	4.90257i	−0.785261	−	0.297810i	−0.0708045	−	0.997490i	$-0.522557\pi$
$271$	−12.9270	−	4.90257i	−0.785261	−	0.297810i	−0.714456	+	0.699680i	$0.753326\pi$
$272$	−1.57809	+	0.828245i	−0.0956857	+	0.0502197i
$273$	0.396635	+	4.44586i	0.0240054	+	0.269076i
$274$	2.07212	+	1.08753i	0.125181	+	0.0657003i
$275$	−5.89443	−	6.65344i	−0.355448	−	0.401217i
$276$	3.86661	+	3.42552i	0.232743	+	0.206192i
$277$	28.6976	−	7.07333i	1.72427	−	0.424995i	0.752061	−	0.659094i	$-0.229060\pi$
$277$	28.6976	−	7.07333i	1.72427	−	0.424995i	0.972213	+	0.234099i	$0.0752139\pi$
$278$	−4.86189	+	0.590340i	−0.291597	+	0.0354062i
$279$	−4.09385	+	4.62100i	−0.245092	+	0.276652i
$280$	−3.51490	+	1.33303i	−0.210056	+	0.0796636i
$281$	−13.9448	−	26.5696i	−0.831878	−	1.58501i	−0.810865	−	0.585233i	$-0.801003\pi$
$281$	−13.9448	−	26.5696i	−0.831878	−	1.58501i	−0.0210131	−	0.999779i	$-0.506689\pi$
$282$	−0.0699160	−	0.0366948i	−0.00416344	−	0.00218514i
$283$	−0.378916	+	3.12066i	−0.0225242	+	0.185504i	−0.999628	−	0.0272575i	$-0.991323\pi$
$283$	−0.378916	+	3.12066i	−0.0225242	+	0.185504i	0.977104	+	0.212761i	$0.0682457\pi$
$284$	15.2334	−	17.1950i	0.903937	−	1.02033i
$285$	−11.1939	−	2.75904i	−0.663068	−	0.163432i
$286$	−1.67308	−	0.257454i	−0.0989315	−	0.0152236i
$287$	−11.9196	+	2.93793i	−0.703594	+	0.173420i
$288$	1.32518	−	2.52492i	0.0780871	−	0.148783i
$289$	−14.8400	−	7.78862i	−0.872940	−	0.458154i
$290$	1.41184	−	3.72271i	0.0829060	−	0.218605i
$291$	−7.74819	−	2.93850i	−0.454207	−	0.172258i
$292$	18.1792	+	12.5482i	1.06385	+	0.734326i
$293$	−0.273035	−	1.10775i	−0.0159509	−	0.0647152i	0.962427	−	0.271540i	$-0.0875330\pi$
$293$	−0.273035	−	1.10775i	−0.0159509	−	0.0647152i	−0.978378	+	0.206825i	$0.933687\pi$
$294$	−1.11447	−	0.769266i	−0.0649975	−	0.0448645i
$295$	−1.71080	−	14.0897i	−0.0996067	−	0.820335i
$296$	3.09136	−	8.15126i	0.179682	−	0.473782i
$297$	−0.880905	−	1.67842i	−0.0511153	−	0.0973921i
$298$	−0.431075	−	0.624519i	−0.0249715	−	0.0361774i
$299$	−9.49559	−	1.46118i	−0.549144	−	0.0845022i
$300$	−5.16430	+	7.48178i	−0.298161	+	0.431961i
$301$	11.9685	+	1.45323i	0.689850	+	0.0837630i
$302$	1.13419	+	0.279553i	0.0652653	+	0.0160864i
$303$	4.42479	+	6.41041i	0.254197	+	0.368268i
$304$	8.92936	+	10.0792i	0.512134	+	0.578079i
$305$	2.28622	−	4.35604i	0.130909	−	0.249426i
$306$	−0.120529	+	0.0146349i	−0.00689021	+	0.000836622i
$307$	−11.1434	−	1.35306i	−0.635989	−	0.0772230i	−0.203809	−	0.979011i	$-0.565332\pi$
$307$	−11.1434	−	1.35306i	−0.635989	−	0.0772230i	−0.432179	+	0.901788i	$0.642255\pi$
$308$	3.40517	−	3.01672i	0.194028	−	0.171893i
$309$	−2.10461	+	3.04906i	−0.119727	+	0.173455i
$310$	4.72499	−	0.573717i	0.268361	−	0.0325849i
$311$	−2.29259	+	18.8812i	−0.130001	+	1.07065i	0.771000	+	0.636836i	$0.219757\pi$
$311$	−2.29259	+	18.8812i	−0.130001	+	1.07065i	−0.901000	+	0.433818i	$0.857166\pi$
$312$	0.312555	+	3.50341i	0.0176949	+	0.198342i
$313$	−2.38167	−	19.6148i	−0.134620	−	1.10870i	−0.890821	−	0.454355i	$-0.849870\pi$
$313$	−2.38167	−	19.6148i	−0.134620	−	1.10870i	0.756201	−	0.654340i	$-0.227053\pi$
$314$	0.195291	+	0.792325i	0.0110209	+	0.0447135i
$315$	3.85348			0.217119
$316$	−17.9515			−1.00985
$317$	2.45458	+	9.95862i	0.137863	+	0.559332i	0.998724	+	0.0504926i	$0.0160791\pi$
$317$	2.45458	+	9.95862i	0.137863	+	0.559332i	−0.860861	+	0.508839i	$0.830075\pi$
$318$	−2.31947	−	0.879660i	−0.130070	−	0.0493289i
$319$			9.78890i			0.548073i
$320$	19.1077	−	7.24659i	1.06815	−	0.405096i
$321$	−5.93718	−	1.46338i	−0.331381	−	0.0816782i
$322$	−0.611546	+	0.541783i	−0.0340801	+	0.0301924i
$323$	0.434499	−	1.76283i	0.0241762	−	0.0980866i
$324$	−1.45110	+	1.28557i	−0.0806169	+	0.0714203i
$325$	0.538448	−	16.8991i	0.0298677	−	0.937396i
$326$	0.319101	+	0.282699i	0.0176734	+	0.0156573i
$327$	5.23455	−	3.61315i	0.289471	−	0.199808i
$328$	−9.39287	+	2.31514i	−0.518635	+	0.127832i
$329$	−0.224192	+	0.324798i	−0.0123601	+	0.0179067i
$330$	−0.349741	+	1.41896i	−0.0192526	+	0.0781109i
$331$	−4.96749	+	20.1539i	−0.273038	+	1.10776i	0.660943	+	0.750436i	$0.270157\pi$
$331$	−4.96749	+	20.1539i	−0.273038	+	1.10776i	−0.933981	+	0.357323i	$0.883690\pi$
$332$	−9.78421	−	1.18802i	−0.536978	−	0.0652009i
$333$	−5.92595	+	6.68902i	−0.324740	+	0.366556i
$334$	−1.69111	−	4.45909i	−0.0925335	−	0.243991i
$335$	27.8050	−	14.5932i	1.51915	−	0.797312i
$336$	−3.70411	−	2.55676i	−0.202076	−	0.139483i
$337$	−16.4029			−0.893525			−0.446762	−	0.894653i	$-0.647423\pi$
$337$	−16.4029			−0.893525			−0.446762	+	0.894653i	$0.647423\pi$
$338$	−1.97740	−	2.54113i	−0.107556	−	0.138219i
$339$	2.71147			0.147267
$340$	−2.43454	−	1.68044i	−0.132031	−	0.0911348i
$341$	−10.3619	+	5.43835i	−0.561129	+	0.294503i
$342$	0.325295	+	0.857733i	0.0175899	+	0.0463809i
$343$	−10.2348	+	11.5527i	−0.552625	+	0.623785i
$344$	9.43134	+	1.14517i	0.508504	+	0.0617435i
$345$	−1.98496	+	8.05328i	−0.106866	+	0.433574i
$346$	−0.895304	+	3.63239i	−0.0481318	+	0.195278i
$347$	6.69165	−	9.69453i	0.359227	−	0.520430i	−0.601150	−	0.799136i	$-0.705290\pi$
$347$	6.69165	−	9.69453i	0.359227	−	0.520430i	0.960376	+	0.278707i	$0.0899058\pi$
$348$	9.72060	−	2.39591i	0.521079	−	0.128434i
$349$	−10.1644	+	7.01596i	−0.544087	+	0.375556i	−0.808175	−	0.588943i	$-0.799544\pi$
$349$	−10.1644	+	7.01596i	−0.544087	+	0.375556i	0.264088	+	0.964499i	$0.414929\pi$
$350$	−1.07624	−	0.953468i	−0.0575276	−	0.0509650i
$351$	0.973914	−	3.47153i	0.0519837	−	0.185296i
$352$	4.04589	−	3.58435i	0.215647	−	0.191046i
$353$	−6.46233	+	26.2187i	−0.343955	+	1.39548i	0.503216	+	0.864161i	$0.332150\pi$
$353$	−6.46233	+	26.2187i	−0.343955	+	1.39548i	−0.847171	+	0.531320i	$0.821696\pi$
$354$	−0.845326	+	0.748893i	−0.0449286	+	0.0398032i
$355$	35.8133	+	8.82718i	1.90077	+	0.468498i
$356$	29.6956	−	11.2621i	1.57386	−	0.596888i
$357$			0.606853i			0.0321181i
$358$	−0.633642	−	0.240309i	−0.0334890	−	0.0127007i
$359$	−4.70148	−	19.0747i	−0.248135	−	1.00672i	−0.954342	−	0.298717i	$-0.903441\pi$
$359$	−4.70148	−	19.0747i	−0.248135	−	1.00672i	0.706207	−	0.708005i	$-0.250405\pi$
$360$	3.03661			0.160043
$361$	5.28236			0.278019
$362$	0.648732	+	2.63201i	0.0340966	+	0.138335i
$363$	0.892803	+	7.35289i	0.0468600	+	0.385927i
$364$	8.64883	+	0.275573i	0.453322	+	0.0144439i
$365$	−4.27512	+	35.2088i	−0.223770	+	1.84291i
$366$	−0.388590	+	0.0471834i	−0.0203119	+	0.00246632i
$367$	−15.4338	+	22.3597i	−0.805637	+	1.16717i	0.177469	+	0.984126i	$0.443209\pi$
$367$	−15.4338	+	22.3597i	−0.805637	+	1.16717i	−0.983105	+	0.183040i	$0.941406\pi$
$368$	7.25132	−	6.42411i	0.378001	−	0.334880i
$369$	9.84433	+	1.19532i	0.512475	+	0.0622258i
$370$	6.83954	−	0.830471i	0.355571	−	0.0431741i
$371$	−5.76205	+	10.9787i	−0.299151	+	0.569984i
$372$	7.93656	+	8.95852i	0.411491	+	0.464478i
$373$	−0.0304100	−	0.0440565i	−0.00157457	−	0.00228116i	0.822196	−	0.569205i	$-0.192749\pi$
$373$	−0.0304100	−	0.0440565i	−0.00157457	−	0.00228116i	−0.823770	+	0.566924i	$0.808133\pi$
$374$	−0.223460	−	0.0550778i	−0.0115548	−	0.00284801i
$375$	0.959908	+	0.116554i	0.0495694	+	0.00601882i
$376$	−0.176667	+	0.255946i	−0.00911090	+	0.0131994i
$377$	−12.7847	+	13.5367i	−0.658444	+	0.697176i
$378$	−0.174179	−	0.252342i	−0.00895882	−	0.0129791i
$379$	−4.03297	−	7.68417i	−0.207159	−	0.394709i	0.759602	−	0.650388i	$-0.225394\pi$
$379$	−4.03297	−	7.68417i	−0.207159	−	0.394709i	−0.966762	+	0.255678i	$0.917701\pi$
$380$	−7.92560	+	20.8981i	−0.406575	+	1.07205i
$381$	0.591312	+	4.86989i	0.0302938	+	0.249492i
$382$	3.46706	+	2.39314i	0.177390	+	0.122444i
$383$	2.16747	+	8.79379i	0.110753	+	0.449342i	0.999967	−	0.00814979i	$-0.00259419\pi$
$383$	2.16747	+	8.79379i	0.110753	+	0.449342i	−0.889214	+	0.457491i	$0.848748\pi$
$384$	−6.03178	−	4.16344i	−0.307808	−	0.212464i
$385$	6.82979	+	2.59020i	0.348078	+	0.132009i
$386$	1.29653	−	3.41868i	0.0659918	−	0.174006i
$387$	−8.62338	−	4.52590i	−0.438351	−	0.230064i
$388$	−7.46579	+	14.2249i	−0.379018	+	0.722159i
$389$	17.3504	−	4.27649i	0.879699	−	0.216826i	0.226499	−	0.974011i	$-0.427272\pi$
$389$	17.3504	−	4.27649i	0.879699	−	0.216826i	0.653201	+	0.757185i	$0.273426\pi$
$390$	−2.33685	+	1.50545i	−0.118331	+	0.0762312i
$391$	−1.26825	−	0.312594i	−0.0641379	−	0.0158086i
$392$	−3.53688	+	3.99231i	−0.178640	+	0.201642i
$393$	0.127327	−	1.04863i	0.00642277	−	0.0528963i
$394$	−2.72481	−	1.43009i	−0.137274	−	0.0720468i
$395$	−13.3950	−	25.5221i	−0.673976	−	1.28415i
$396$	−3.43601	+	1.30311i	−0.172666	+	0.0654835i
$397$	−15.5301	+	17.5298i	−0.779431	+	0.879796i	−0.995321	−	0.0966220i	$-0.969196\pi$
$397$	−15.5301	+	17.5298i	−0.779431	+	0.879796i	0.215890	+	0.976418i	$0.430735\pi$
$398$	1.76761	−	0.214626i	0.0886021	−	0.0107582i
$399$	4.45183	−	1.09728i	0.222870	−	0.0549326i
$400$	12.7614	+	11.3056i	0.638069	+	0.565280i
$401$	−7.07840	−	7.98987i	−0.353479	−	0.398995i	0.544696	−	0.838633i	$-0.316645\pi$
$401$	−7.07840	−	7.98987i	−0.353479	−	0.398995i	−0.898175	+	0.439639i	$0.855107\pi$
$402$	−2.21243	−	1.16117i	−0.110346	−	0.0579140i
$403$	−21.4318	−	6.01255i	−1.06759	−	0.299506i
$404$	13.3709	−	7.01761i	0.665229	−	0.349139i
$405$	−2.91049	−	1.10380i	−0.144624	−	0.0548485i
$406$	0.190861	+	1.57188i	0.00947228	+	0.0780112i
$407$	−14.9991	+	7.87215i	−0.743479	+	0.390208i
$408$			0.478210i			0.0236749i
$409$	5.37558	+	10.2423i	0.265805	+	0.506450i	0.981378	−	0.192089i	$-0.0615262\pi$
$409$	5.37558	+	10.2423i	0.265805	+	0.506450i	−0.715572	+	0.698539i	$0.753834\pi$
$410$	−5.06989	−	5.72273i	−0.250384	−	0.282625i
$411$	−7.77582	+	5.36726i	−0.383553	+	0.264748i
$412$	5.37616	+	4.76287i	0.264865	+	0.234650i
$413$	3.20654	+	4.64547i	0.157783	+	0.228589i
$414$	0.617084	−	0.234029i	0.0303280	−	0.0115019i
$415$	−5.61172	−	14.7969i	−0.275468	−	0.726350i
$416$	10.2762	+	0.327425i	0.503832	+	0.0160533i
$417$	7.01188	−	18.4888i	0.343373	−	0.905401i
$418$			1.73887i			0.0850510i
$419$	−8.78547	−	23.1654i	−0.429198	−	1.13170i	−0.958956	−	0.283554i	$-0.908486\pi$
$419$	−8.78547	−	23.1654i	−0.429198	−	1.13170i	0.529758	−	0.848149i	$-0.322283\pi$
$420$	0.900477	−	7.41610i	0.0439388	−	0.361869i
$421$	−13.4135	+	25.5572i	−0.653732	+	1.24558i	0.302549	+	0.953134i	$0.402162\pi$
$421$	−13.4135	+	25.5572i	−0.653732	+	1.24558i	−0.956281	+	0.292448i	$0.905530\pi$
$422$	−5.03200	+	3.47334i	−0.244954	+	0.169079i
$423$	0.262366	−	0.181098i	0.0127567	−	0.00880530i
$424$	−4.54059	+	8.65137i	−0.220511	+	0.420148i
$425$	0.277083	−	2.28199i	0.0134405	−	0.110693i
$426$	−1.04074	−	2.74420i	−0.0504239	−	0.132957i
$427$			1.95651i			0.0946823i
$428$	−4.20371	+	11.0843i	−0.203194	+	0.535778i
$429$	4.05959	−	5.49819i	0.195999	−	0.265455i
$430$	2.66254	+	7.02053i	0.128399	+	0.338560i
$431$	−21.6507	+	8.21103i	−1.04288	+	0.395512i	−0.815781	−	0.578361i	$-0.803693\pi$
$431$	−21.6507	+	8.21103i	−1.04288	+	0.395512i	−0.227097	+	0.973872i	$0.572923\pi$
$432$	2.06531	+	2.99211i	0.0993671	+	0.143958i
$433$	−9.99857	−	8.85796i	−0.480501	−	0.425686i	0.387786	−	0.921750i	$-0.373240\pi$
$433$	−9.99857	−	8.85796i	−0.480501	−	0.425686i	−0.868287	+	0.496063i	$0.834778\pi$
$434$	−1.55786	+	1.07531i	−0.0747796	+	0.0516167i
$435$	10.6596	+	12.0322i	0.511088	+	0.576900i
$436$	−5.73037	−	10.9183i	−0.274435	−	0.522892i
$437$			9.86897i			0.472097i
$438$	2.49886	−	1.31150i	0.119400	−	0.0626661i
$439$	2.90063	+	23.8889i	0.138440	+	1.14015i	0.881921	+	0.471397i	$0.156250\pi$
$439$	2.90063	+	23.8889i	0.138440	+	1.14015i	−0.743481	+	0.668757i	$0.766827\pi$
$440$	5.38198	+	2.04112i	0.256576	+	0.0973064i
$441$	4.84120	−	2.54086i	0.230533	−	0.120993i
$442$	−0.237080	−	0.368012i	−0.0112768	−	0.0175045i
$443$	13.8933	+	7.29178i	0.660092	+	0.346443i	0.761279	−	0.648424i	$-0.224572\pi$
$443$	13.8933	+	7.29178i	0.660092	+	0.346443i	−0.101187	+	0.994867i	$0.532264\pi$
$444$	11.4884	+	12.9677i	0.545214	+	0.615420i
$445$	38.1696	+	33.8154i	1.80941	+	1.60300i
$446$	1.68270	−	0.414749i	0.0796784	−	0.0196390i
$447$	3.04147	−	0.369301i	0.143857	−	0.0174673i
$448$	−5.38941	+	6.08338i	−0.254625	+	0.287413i
$449$	37.6994	−	14.2975i	1.77915	−	0.674741i	0.780368	−	0.625321i	$-0.215032\pi$
$449$	37.6994	−	14.2975i	1.77915	−	0.674741i	0.998778	−	0.0494202i	$-0.0157373\pi$
$450$	0.539760	+	1.02843i	0.0254445	+	0.0484805i
$451$	16.6443	+	8.73561i	0.783750	+	0.411344i
$452$	0.633614	−	5.21828i	0.0298027	−	0.245447i
$453$	−3.12747	+	3.53018i	−0.146941	+	0.165863i
$454$	3.55298	+	0.875732i	0.166750	+	0.0411001i
$455$	6.06177	+	12.5018i	0.284180	+	0.586096i
$456$	3.50812	−	0.864673i	0.164283	−	0.0404920i
$457$	−4.37781	+	8.34122i	−0.204785	+	0.390186i	−0.966089	−	0.258210i	$-0.916867\pi$
$457$	−4.37781	+	8.34122i	−0.204785	+	0.390186i	0.761304	+	0.648396i	$0.224560\pi$
$458$	4.43277	+	2.32650i	0.207130	+	0.108710i
$459$	0.173829	−	0.458350i	0.00811365	−	0.0213939i
$460$	15.0349	+	5.70197i	0.701004	+	0.265856i
$461$	−10.6709	−	7.36558i	−0.496993	−	0.343049i	0.293054	−	0.956096i	$-0.405328\pi$
$461$	−10.6709	−	7.36558i	−0.496993	−	0.343049i	−0.790047	+	0.613047i	$0.789944\pi$
$462$	−0.139093	−	0.564322i	−0.00647118	−	0.0262546i
$463$	5.19574	+	3.58636i	0.241467	+	0.166672i	0.682652	−	0.730744i	$-0.260826\pi$
$463$	5.19574	+	3.58636i	0.241467	+	0.166672i	−0.441185	+	0.897416i	$0.645442\pi$
$464$	−2.26311	−	18.6384i	−0.105062	−	0.865264i
$465$	−6.81444	+	17.9682i	−0.316012	+	0.833256i
$466$	0.707390	+	1.34782i	0.0327692	+	0.0624365i
$467$	−12.8821	−	18.6630i	−0.596113	−	0.863619i	0.402546	−	0.915400i	$-0.368126\pi$
$467$	−12.8821	−	18.6630i	−0.596113	−	0.863619i	−0.998658	+	0.0517813i	$0.983510\pi$
$468$	−6.45343	−	2.68554i	−0.298310	−	0.124139i
$469$	−7.09435	+	10.2779i	−0.327586	+	0.474591i
$470$	−0.243994	−	0.0296262i	−0.0112546	−	0.00136656i
$471$	−3.19897	−	0.788475i	−0.147401	−	0.0363310i
$472$	2.52681	+	3.66071i	0.116306	+	0.168498i
$473$	−12.2416	−	13.8179i	−0.562870	−	0.635349i
$474$	−1.06583	+	2.03077i	−0.0489553	+	0.0932765i
$475$	−17.2415	+	2.09350i	−0.791094	+	0.0960562i
$476$	1.16790	+	0.141809i	0.0535306	+	0.00649979i
$477$	7.49678	−	6.64157i	0.343254	−	0.304097i
$478$	0.153344	−	0.222157i	0.00701379	−	0.0101612i
$479$	−1.10194	+	0.133800i	−0.0503491	+	0.00611349i	−0.145672	−	0.989333i	$-0.546535\pi$
$479$	−1.10194	+	0.133800i	−0.0503491	+	0.00611349i	0.0953234	+	0.995446i	$0.469611\pi$
$480$	1.06991	−	8.81152i	0.0488346	−	0.402189i
$481$	−31.0231	−	8.70332i	−1.41453	−	0.396837i
$482$	−0.414256	−	3.41170i	−0.0188688	−	0.155399i
$483$	−0.789422	−	3.20281i	−0.0359199	−	0.145733i
$484$	14.3594			0.652701
$485$	−25.7946			−1.17127
$486$	0.0592740	+	0.240484i	0.00268872	+	0.0109086i
$487$	−8.15653	−	3.09336i	−0.369608	−	0.140174i	0.162806	−	0.986658i	$-0.447946\pi$
$487$	−8.15653	−	3.09336i	−0.369608	−	0.140174i	−0.532414	+	0.846484i	$0.678715\pi$
$488$			1.54176i			0.0697924i
$489$	−1.60937	+	0.610354i	−0.0727783	+	0.0276012i
$490$	−4.09279	−	1.00878i	−0.184893	−	0.0455721i
$491$	5.01672	−	4.44443i	0.226401	−	0.200574i	−0.542295	−	0.840188i	$-0.682444\pi$
$491$	5.01672	−	4.44443i	0.226401	−	0.200574i	0.768696	+	0.639614i	$0.220906\pi$
$492$	4.60082	−	18.6663i	0.207421	−	0.841541i
$493$	−1.89485	+	1.67869i	−0.0853398	+	0.0756045i
$494$	−2.27103	+	2.40462i	−0.102179	+	0.108189i
$495$	−4.41652	−	3.91270i	−0.198508	−	0.175863i
$496$	18.4721	−	12.7504i	0.829421	−	0.572508i
$497$	−14.2430	+	3.51059i	−0.638887	+	0.157471i
$498$	−0.715310	+	1.03631i	−0.0320538	+	0.0464380i
$499$	10.0084	−	40.6058i	0.448038	−	1.81776i	−0.117539	−	0.993068i	$-0.537500\pi$
$499$	10.0084	−	40.6058i	0.448038	−	1.81776i	0.565577	−	0.824695i	$-0.308653\pi$
$500$	0.448620	−	1.82012i	0.0200629	−	0.0813985i
$501$	19.1142	+	2.32088i	0.853960	+	0.103689i
$502$	4.47319	−	5.04919i	0.199648	−	0.225356i
$503$	−7.17845	−	18.9280i	−0.320071	−	0.843958i	−0.994415	−	0.105541i	$-0.966343\pi$
$503$	−7.17845	−	18.9280i	−0.320071	−	0.843958i	0.674344	−	0.738418i	$-0.264427\pi$
$504$	−1.06933	+	0.561230i	−0.0476320	+	0.0249992i
$505$	19.9542	+	13.7734i	0.887948	+	0.612906i
$506$	1.25101			0.0556141
$507$	12.7947	−	2.30126i	0.568232	−	0.102202i
$508$	9.51038			0.421955
$509$	1.05161	+	0.725877i	0.0466120	+	0.0321739i	0.591143	−	0.806567i	$-0.298677\pi$
$509$	1.05161	+	0.725877i	0.0466120	+	0.0321739i	−0.544531	+	0.838741i	$0.683292\pi$
$510$	−0.334646	+	0.175636i	−0.0148184	+	0.00777728i
$511$	−5.00187	−	13.1888i	−0.221270	−	0.583440i
$512$	−11.5787	+	13.0696i	−0.511709	+	0.577600i
$513$	−3.67673	−	0.446436i	−0.162332	−	0.0197106i
$514$	−0.776489	+	3.15034i	−0.0342495	+	0.138956i
$515$	−2.75990	+	11.1973i	−0.121616	+	0.493414i
$516$	−10.7253	+	15.5382i	−0.472154	+	0.684033i
$517$	0.586738	−	0.144618i	0.0258047	−	0.00636029i
$518$	−2.25504	+	1.55654i	−0.0990809	+	0.0683906i
$519$	−11.3059	−	10.0161i	−0.496273	−	0.439659i
$520$	4.77677	+	9.85166i	0.209475	+	0.432024i
$521$	21.2976	−	18.8680i	0.933065	−	0.826624i	−0.0520278	−	0.998646i	$-0.516568\pi$
$521$	21.2976	−	18.8680i	0.933065	−	0.826624i	0.985093	+	0.172022i	$0.0550300\pi$
$522$	0.306100	−	1.24190i	0.0133976	−	0.0543564i
$523$	3.28997	−	2.91466i	0.143860	−	0.127449i	−0.588123	−	0.808771i	$-0.700133\pi$
$523$	3.28997	−	2.91466i	0.143860	−	0.127449i	0.731984	+	0.681322i	$0.238595\pi$
$524$	−1.98835	−	0.490085i	−0.0868615	−	0.0214094i
$525$	5.42798	−	2.05856i	0.236896	−	0.0898430i
$526$			3.65464i			0.159350i
$527$	−2.82966	−	1.07315i	−0.123262	−	0.0467472i
$528$	1.64927	+	6.69136i	0.0717754	+	0.291204i
$529$	−15.8999			−0.691300
$530$	−7.72178			−0.335413
$531$	−1.09120	−	4.42717i	−0.0473540	−	0.192123i
$532$	−1.07143	−	8.82404i	−0.0464525	−	0.382571i
$533$	11.6078	+	33.8183i	0.502789	+	1.46483i
$534$	0.489086	−	4.02798i	0.0211648	−	0.174308i
$535$	−18.8954	+	2.29432i	−0.816921	+	0.0991921i
$536$	−5.59046	+	8.09918i	−0.241471	+	0.349831i
$537$	2.04800	−	1.81437i	0.0883777	−	0.0782958i
$538$	−7.68499	−	0.933126i	−0.331323	−	0.0402299i
$539$	10.2883	−	1.24922i	0.443147	−	0.0538078i
$540$	−2.80441	+	5.34336i	−0.120683	+	0.229942i
$541$	−6.57157	−	7.41776i	−0.282534	−	0.318915i	0.590062	−	0.807358i	$-0.299103\pi$
$541$	−6.57157	−	7.41776i	−0.282534	−	0.318915i	−0.872596	+	0.488443i	$0.837565\pi$
$542$	1.94523	+	2.81815i	0.0835547	+	0.121050i
$543$	−10.6266	−	2.61922i	−0.456031	−	0.112401i
$544$	1.38765	+	0.168492i	0.0594952	+	0.00722402i
$545$	11.2469	−	16.2940i	0.481765	−	0.697957i
$546$	0.544679	−	0.962040i	0.0233101	−	0.0411715i
$547$	7.53621	+	10.9181i	0.322225	+	0.466824i	0.950303	−	0.311327i	$-0.100773\pi$
$547$	7.53621	+	10.9181i	0.322225	+	0.466824i	−0.628078	+	0.778151i	$0.716158\pi$
$548$	8.51235	+	16.2189i	0.363630	+	0.692839i
$549$	0.560431	−	1.47773i	0.0239186	−	0.0630681i
$550$	0.265375	+	2.18556i	0.0113156	+	0.0931927i
$551$	15.7409	+	10.8652i	0.670586	+	0.462872i
$552$	−0.622077	−	2.52387i	−0.0264774	−	0.107423i
$553$	9.43405	+	6.51186i	0.401177	+	0.276912i
$554$	−6.84487	−	2.59592i	−0.290811	−	0.110290i
$555$	−9.86408	+	26.0094i	−0.418707	+	1.10404i
$556$	−33.9435	−	17.8149i	−1.43953	−	0.755522i
$557$	−19.4364	+	37.0330i	−0.823548	+	1.56914i	−0.00130696	+	0.999999i	$0.500416\pi$
$557$	−19.4364	+	37.0330i	−0.823548	+	1.56914i	−0.822241	+	0.569140i	$0.807276\pi$
$558$	1.48465	−	0.365934i	0.0628503	−	0.0154912i
$559$	1.11826	−	35.0963i	0.0472972	−	1.48442i
$560$	−13.6029	−	3.35283i	−0.574829	−	0.141683i
$561$	0.616178	−	0.695522i	0.0260151	−	0.0293649i
$562$	−0.895841	+	7.37792i	−0.0377888	+	0.311219i
$563$	−28.3730	−	14.8913i	−1.19578	−	0.627593i	−0.255107	−	0.966913i	$-0.582111\pi$
$563$	−28.3730	−	14.8913i	−1.19578	−	0.627593i	−0.940671	+	0.339320i	$0.889803\pi$
$564$	−0.287218	−	0.547248i	−0.0120940	−	0.0230433i
$565$	7.89172	−	2.99293i	0.332007	−	0.125914i
$566$	0.516311	−	0.582795i	0.0217022	−	0.0244967i
$567$	1.22893	−	0.149219i	0.0516103	−	0.00626662i
$568$	−11.2237	+	2.76640i	−0.470937	+	0.116076i
$569$	33.6409	+	29.8032i	1.41030	+	1.24942i	0.927572	+	0.373644i	$0.121892\pi$
$569$	33.6409	+	29.8032i	1.41030	+	1.24942i	0.482727	+	0.875771i	$0.339647\pi$
$570$	1.89354	+	2.13736i	0.0793116	+	0.0895243i
$571$	−15.4465	−	8.10696i	−0.646416	−	0.339266i	0.109449	−	0.993992i	$-0.465091\pi$
$571$	−15.4465	−	8.10696i	−0.646416	−	0.339266i	−0.755866	+	0.654727i	$0.772784\pi$
$572$	−9.63272	−	9.09757i	−0.402764	−	0.380389i
$573$	−15.0607	+	7.90445i	−0.629169	+	0.330213i
$574$	2.84304	+	1.07822i	0.118666	+	0.0450041i
$575$	1.50614	+	12.4042i	0.0628103	+	0.517289i
$576$	5.81311	−	3.05095i	0.242213	−	0.127123i
$577$			0.189734i			0.00789874i	0.999992	+	0.00394937i	$0.00125713\pi$
$577$			0.189734i			0.00789874i	−0.999992	+	0.00394937i	$0.998743\pi$
$578$	1.92910	+	3.67558i	0.0802398	+	0.152884i
$579$	9.78902	+	11.0495i	0.406818	+	0.459203i
$580$	25.6471	−	17.7029i	1.06494	−	0.735074i
$581$	4.71094	+	4.17352i	0.195443	+	0.173147i
$582$	1.16593	+	1.68914i	0.0483293	+	0.0700171i
$583$	17.7513	−	6.73219i	0.735185	−	0.278819i
$584$	−3.94156	−	10.3930i	−0.163103	−	0.430067i
$585$	−0.997315	−	11.1789i	−0.0412339	−	0.462189i
$586$	−0.100204	+	0.264216i	−0.00413939	+	0.0109147i
$587$			29.4651i			1.21615i	0.793878	+	0.608077i	$0.208059\pi$
$587$			29.4651i			1.21615i	−0.793878	+	0.608077i	$0.791941\pi$
$588$	−3.75864	−	9.91072i	−0.155004	−	0.408711i
$589$	−2.75611	+	22.6986i	−0.113564	+	0.935281i
$590$	−1.63368	+	3.11272i	−0.0672577	+	0.128149i
$591$	10.2251	−	7.05786i	0.420603	−	0.290322i
$592$	26.7388	−	18.4565i	1.09896	−	0.758556i
$593$	8.57832	−	16.3446i	0.352269	−	0.671193i	−0.643260	−	0.765648i	$-0.722419\pi$
$593$	8.57832	−	16.3446i	0.352269	−	0.671193i	0.995529	+	0.0944549i	$0.0301108\pi$
$594$	−0.0565910	+	0.466069i	−0.00232196	+	0.0191230i
$595$	0.669847	+	1.76624i	0.0274611	+	0.0724089i
$596$		−	5.93966i		−	0.243298i
$597$	−2.54927	+	6.72186i	−0.104335	+	0.275108i
$598$	1.72997	+	1.63386i	0.0707439	+	0.0668137i
$599$	15.7937	+	41.6445i	0.645313	+	1.70155i	0.710519	+	0.703678i	$0.248460\pi$
$599$	15.7937	+	41.6445i	0.645313	+	1.70155i	−0.0652061	+	0.997872i	$0.520770\pi$
$600$	4.27734	−	1.62218i	0.174622	−	0.0662252i
$601$	−5.70279	−	8.26192i	−0.232622	−	0.337011i	0.689238	−	0.724535i	$-0.257946\pi$
$601$	−5.70279	−	8.26192i	−0.232622	−	0.337011i	−0.921859	+	0.387525i	$0.873330\pi$
$602$	−2.23515	−	1.98017i	−0.0910980	−	0.0807058i
$603$	8.30233	−	5.73069i	0.338097	−	0.233372i
$604$	6.06308	+	6.84381i	0.246703	+	0.278471i
$605$	10.7147	+	20.4151i	0.435613	+	0.829991i
$606$		−	1.92925i		−	0.0783703i
$607$	−6.63896	+	3.48440i	−0.269467	+	0.141427i	−0.594045	−	0.804432i	$-0.702470\pi$
$607$	−6.63896	+	3.48440i	−0.269467	+	0.141427i	0.324578	+	0.945859i	$0.394778\pi$
$608$	−1.27304	−	10.4844i	−0.0516284	−	0.425198i
$609$	−5.97756	−	2.26699i	−0.242223	−	0.0918631i
$610$	−1.07891	+	0.566255i	−0.0436837	+	0.0229270i
$611$	1.00026	+	0.566315i	0.0404660	+	0.0229107i
$612$	−0.841483	−	0.441644i	−0.0340149	−	0.0178524i
$613$	−23.7102	−	26.7633i	−0.957645	−	1.08096i	−0.996655	−	0.0817191i	$-0.973959\pi$
$613$	−23.7102	−	26.7633i	−0.957645	−	1.08096i	0.0390102	−	0.999239i	$-0.487580\pi$
$614$	2.08108	+	1.84367i	0.0839854	+	0.0744046i
$615$	29.9713	−	7.38725i	1.20856	−	0.297883i
$616$	−2.27250	+	0.275931i	−0.0915615	+	0.0111176i
$617$	−22.0749	+	24.9174i	−0.888701	+	1.00314i	0.111256	+	0.993792i	$0.464513\pi$
$617$	−22.0749	+	24.9174i	−0.888701	+	1.00314i	−0.999956	+	0.00934390i	$0.997026\pi$
$618$	0.857998	−	0.325396i	0.0345138	−	0.0130893i
$619$	7.53400	+	14.3548i	0.302817	+	0.576969i	0.988552	−	0.150882i	$-0.0482113\pi$
$619$	7.53400	+	14.3548i	0.302817	+	0.576969i	−0.685735	+	0.727851i	$0.740519\pi$
$620$	32.9878	+	17.3133i	1.32482	+	0.695319i
$621$	−0.321182	+	2.64517i	−0.0128886	+	0.106147i
$622$	3.12388	−	3.52613i	0.125256	−	0.141385i
$623$	−19.6912	−	4.85344i	−0.788910	−	0.194449i
$624$	−6.45845	+	11.4072i	−0.258545	+	0.456655i
$625$	25.6879	−	6.33151i	1.02752	−	0.253260i
$626$	−2.27431	+	4.33334i	−0.0908998	+	0.173195i
$627$	−6.21644	−	3.26264i	−0.248261	−	0.130297i
$628$	−2.26497	+	5.97223i	−0.0903820	+	0.238318i
$629$	−4.09601	−	1.55341i	−0.163319	−	0.0619386i
$630$	−0.785485	−	0.542181i	−0.0312945	−	0.0216010i
$631$	6.42966	+	26.0861i	0.255961	+	1.03847i	0.948420	+	0.317016i	$0.102681\pi$
$631$	6.42966	+	26.0861i	0.255961	+	1.03847i	−0.692459	+	0.721457i	$0.743473\pi$
$632$	7.43419	+	5.13145i	0.295716	+	0.204118i
$633$	−2.97560	−	24.5063i	−0.118270	−	0.974038i
$634$	0.900832	−	2.37530i	0.0357766	−	0.0943352i
$635$	7.09642	+	13.5211i	0.281613	+	0.536569i
$636$	−11.0300	−	15.9797i	−0.437368	−	0.633636i
$637$	15.8588	+	11.7094i	0.628349	+	0.463942i
$638$	1.37729	−	1.99535i	0.0545274	−	0.0789966i
$639$	11.7632	+	1.42831i	0.465345	+	0.0565031i
$640$	−22.1511	−	5.45975i	−0.875598	−	0.215816i
$641$	0.826166	+	1.19691i	0.0326316	+	0.0472750i	0.838960	−	0.544193i	$-0.183164\pi$
$641$	0.826166	+	1.19691i	0.0326316	+	0.0472750i	−0.806329	+	0.591468i	$0.798549\pi$
$642$	1.00433	+	1.13365i	0.0396376	+	0.0447415i
$643$	15.2362	−	29.0301i	0.600857	−	1.14484i	−0.375123	−	0.926975i	$-0.622399\pi$
$643$	15.2362	−	29.0301i	0.600857	−	1.14484i	0.975980	−	0.217862i	$-0.0699082\pi$
$644$	−6.34834	+	0.770828i	−0.250160	+	0.0303749i
$645$	−30.0940	−	3.65407i	−1.18495	−	0.143879i
$646$	−0.336596	+	0.298198i	−0.0132432	+	0.0117324i
$647$	−3.86940	+	5.60579i	−0.152122	+	0.220386i	−0.891634	−	0.452756i	$-0.850441\pi$
$647$	−3.86940	+	5.60579i	−0.152122	+	0.220386i	0.739513	+	0.673143i	$0.235056\pi$
$648$	0.968418	−	0.117587i	0.0380431	−	0.00461926i
$649$	1.04181	−	8.58005i	0.0408945	−	0.336796i
$650$	−2.48745	+	3.36892i	−0.0975658	+	0.132140i
$651$	−0.921219	−	7.58692i	−0.0361054	−	0.297355i
$652$	0.798562	+	3.23989i	0.0312741	+	0.126884i
$653$	−36.8375			−1.44156			−0.720781	−	0.693162i	$-0.756217\pi$
$653$	−36.8375			−1.44156			−0.720781	+	0.693162i	$0.756217\pi$
$654$	−1.57536			−0.0616016
$655$	−0.786898	−	3.19257i	−0.0307466	−	0.124744i
$656$	−33.7109	−	12.7848i	−1.31619	−	0.499164i
$657$			11.3942i			0.444528i
$658$	0.0913975	−	0.0346625i	0.00356305	−	0.00135129i
$659$	−22.5178	−	5.55014i	−0.877169	−	0.216203i	−0.225076	−	0.974341i	$-0.572263\pi$
$659$	−22.5178	−	5.55014i	−0.877169	−	0.216203i	−0.652093	+	0.758139i	$0.726109\pi$
$660$	−8.56211	+	7.58536i	−0.333280	+	0.295260i
$661$	2.29271	−	9.30187i	0.0891759	−	0.361801i	−0.909353	−	0.416026i	$-0.863423\pi$
$661$	2.29271	−	9.30187i	0.0891759	−	0.361801i	0.998529	+	0.0542248i	$0.0172688\pi$
$662$	3.84820	−	3.40921i	0.149564	−	0.132503i
$663$	1.76047	−	0.157059i	0.0683709	−	0.00609967i
$664$	3.71229	+	3.28881i	0.144065	+	0.127630i
$665$	11.7458	−	8.10757i	0.455484	−	0.314398i
$666$	2.14907	−	0.529698i	0.0832748	−	0.0205254i
$667$	7.81681	−	11.3246i	0.302668	−	0.438490i
$668$	8.93317	−	36.2433i	0.345635	−	1.40230i
$669$	−1.67453	+	6.79383i	−0.0647410	+	0.262665i
$670$	−7.72096	−	0.937494i	−0.298287	−	0.0362186i
$671$	1.98658	−	2.24238i	0.0766910	−	0.0865662i
$672$	1.25179	+	3.30070i	0.0482889	+	0.127327i
$673$	−31.4381	+	16.5000i	−1.21185	+	0.636029i	−0.944798	−	0.327653i	$-0.893742\pi$
$673$	−31.4381	+	16.5000i	−1.21185	+	0.636029i	−0.267053	+	0.963682i	$0.586050\pi$
$674$	3.34354	+	2.30788i	0.128788	+	0.0888961i
$675$	−4.68936			−0.180493
$676$	−1.43896	−	25.1614i	−0.0553448	−	0.967746i
$677$	24.8516			0.955125			0.477563	−	0.878598i	$-0.341520\pi$
$677$	24.8516			0.955125			0.477563	+	0.878598i	$0.341520\pi$
$678$	−0.552700	−	0.381501i	−0.0212263	−	0.0146515i
$679$	9.08352	−	4.76740i	0.348593	−	0.182956i
$680$	0.527851	+	1.39183i	0.0202421	+	0.0533742i
$681$	−9.79717	+	11.0587i	−0.375428	+	0.423771i
$682$	2.87732	+	0.349370i	0.110178	+	0.0133781i
$683$	5.86415	−	23.7918i	0.224386	−	0.910368i	−0.745441	−	0.666572i	$-0.767761\pi$
$683$	5.86415	−	23.7918i	0.224386	−	0.910368i	0.969826	−	0.243796i	$-0.0783928\pi$
$684$	−1.71835	+	6.97161i	−0.0657027	+	0.266566i
$685$	−16.7071	+	24.2044i	−0.638344	+	0.924802i
$686$	3.71168	−	0.914846i	0.141712	−	0.0349290i
$687$	−16.6344	+	11.4819i	−0.634641	+	0.438061i
$688$	26.5030	+	23.4796i	1.01042	+	0.895151i
$689$	33.3402	+	13.8742i	1.27016	+	0.528565i
$690$	1.53770	−	1.36228i	0.0585391	−	0.0518612i
$691$	4.68451	−	19.0058i	0.178207	−	0.723015i	−0.812029	−	0.583617i	$-0.801637\pi$
$691$	4.68451	−	19.0058i	0.178207	−	0.723015i	0.990236	−	0.139398i	$-0.0445168\pi$
$692$	−21.9182	+	19.4178i	−0.833204	+	0.738154i
$693$	2.27842	+	0.561580i	0.0865500	+	0.0213327i
$694$	−2.72802	+	1.03460i	−0.103554	+	0.0392729i
$695$		−	61.5513i		−	2.33477i
$696$	−4.71042	−	1.78643i	−0.178548	−	0.0677143i
$697$	1.16336	+	4.71993i	0.0440653	+	0.178780i
$698$	3.05902			0.115786
$699$	−6.14570			−0.232452
$700$	−2.69334	−	10.9273i	−0.101799	−	0.413013i
$701$	2.39851	+	19.7535i	0.0905906	+	0.746081i	0.965247	+	0.261338i	$0.0841637\pi$
$701$	2.39851	+	19.7535i	0.0905906	+	0.746081i	−0.874657	+	0.484743i	$0.838913\pi$
$702$	−0.686961	+	0.570599i	−0.0259277	+	0.0215359i
$703$	−3.98955	+	32.8569i	−0.150469	+	1.23922i
$704$	12.3537	−	1.50001i	0.465598	−	0.0565339i
$705$	0.563718	−	0.816686i	0.0212308	−	0.0307582i
$706$	5.00621	−	4.43512i	0.188411	−	0.166918i
$707$	−9.57243	−	1.16230i	−0.360008	−	0.0437129i
$708$	−8.77516	+	1.06550i	−0.329791	+	0.0400439i
$709$	5.61772	−	10.7037i	0.210978	−	0.401985i	−0.756854	−	0.653585i	$-0.773264\pi$
$709$	5.61772	−	10.7037i	0.210978	−	0.401985i	0.967831	+	0.251600i	$0.0809567\pi$
$710$	−6.05812	−	6.83820i	−0.227357	−	0.256633i
$711$	−5.26016	−	7.62066i	−0.197272	−	0.285797i
$712$	−15.5170	−	3.82459i	−0.581523	−	0.143333i
$713$	16.3302	+	1.98285i	0.611572	+	0.0742583i
$714$	0.0853836	−	0.123700i	0.00319540	−	0.00462934i
$715$	5.74649	−	20.4834i	0.214907	−	0.766037i
$716$	−3.01321	−	4.36540i	−0.112609	−	0.163142i
$717$	0.506489	+	0.965034i	0.0189152	+	0.0360399i
$718$	−1.72545	+	4.54963i	−0.0643931	+	0.169791i
$719$	−0.724538	−	5.96710i	−0.0270207	−	0.222535i	0.972943	−	0.231045i	$-0.0742144\pi$
$719$	−0.724538	−	5.96710i	−0.0270207	−	0.222535i	−0.999964	+	0.00850942i	$0.997291\pi$
$720$	9.31377	+	6.42883i	0.347104	+	0.239588i
$721$	−1.09762	−	4.45321i	−0.0408774	−	0.165846i
$722$	−1.07674	−	0.743222i	−0.0400722	−	0.0276599i
$723$	12.9740	+	4.92041i	0.482510	+	0.182992i
$724$	−7.52395	+	19.8390i	−0.279625	+	0.737311i
$725$	21.4427	+	11.2540i	0.796362	+	0.417963i
$726$	0.852558	−	1.62441i	0.0316414	−	0.0602876i
$727$	−22.2469	+	5.48337i	−0.825092	+	0.203367i	−0.629185	−	0.777255i	$-0.716611\pi$
$727$	−22.2469	+	5.48337i	−0.825092	+	0.203367i	−0.195907	+	0.980622i	$0.562765\pi$
$728$	−3.50293	−	2.58639i	−0.129827	−	0.0958581i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	5.82528	−	6.57538i	0.215603	−	0.243366i
$731$	0.575450	−	4.73926i	0.0212838	−	0.175288i
$732$	−2.71297	−	1.42387i	−0.100274	−	0.0526279i
$733$	−17.8260	−	33.9646i	−0.658419	−	1.25451i	−0.954175	−	0.299248i	$-0.903264\pi$
$733$	−17.8260	−	33.9646i	−0.658419	−	1.25451i	0.295757	−	0.955263i	$-0.404428\pi$
$734$	6.29197	−	2.38623i	0.232241	−	0.0880774i
$735$	11.2857	−	12.7389i	0.416278	−	0.469881i
$736$	−7.54285	+	0.915868i	−0.278033	+	0.0337593i
$737$	18.5668	−	4.57630i	0.683916	−	0.168570i
$738$	−1.83847	−	1.62874i	−0.0676748	−	0.0599547i
$739$	−23.5991	−	26.6378i	−0.868105	−	0.979888i	0.131830	−	0.991272i	$-0.457915\pi$
$739$	−23.5991	−	26.6378i	−0.868105	−	0.979888i	−0.999935	+	0.0113841i	$0.996376\pi$
$740$	47.7506	+	25.0615i	1.75535	+	0.921278i
$741$	−4.33535	−	12.6307i	−0.159263	−	0.464000i
$742$	2.71921	−	1.42715i	0.0998254	−	0.0523924i
$743$	−30.2289	−	11.4643i	−1.10899	−	0.420584i	−0.268975	−	0.963147i	$-0.586685\pi$
$743$	−30.2289	−	11.4643i	−1.10899	−	0.420584i	−0.840015	+	0.542563i	$0.817454\pi$
$744$	−0.725936	−	5.97862i	−0.0266141	−	0.219187i
$745$	8.44454	−	4.43204i	0.309384	−	0.162377i
$746$			0.0132590i			0.000485448i
$747$	−2.36264	−	4.50164i	−0.0864445	−	0.164706i
$748$	−1.19456	−	1.34838i	−0.0436773	−	0.0493015i
$749$	6.22995	−	4.30022i	0.227637	−	0.157127i
$750$	−0.179266	−	0.158816i	−0.00654588	−	0.00579915i
$751$	−23.9441	−	34.6890i	−0.873733	−	1.26582i	−0.962915	−	0.269805i	$-0.913041\pi$
$751$	−23.9441	−	34.6890i	−0.873733	−	1.26582i	0.0891825	−	0.996015i	$-0.471575\pi$
$752$	−1.08373	+	0.411006i	−0.0395197	+	0.0149878i
$753$	9.65773	+	25.4654i	0.351947	+	0.928009i
$754$	4.51060	−	0.960501i	0.164266	−	0.0349794i
$755$	−5.20585	+	13.7267i	−0.189460	+	0.499566i
$756$		−	2.39997i		−	0.0872861i
$757$	−13.9067	−	36.6689i	−0.505447	−	1.33275i	−0.908618	−	0.417629i	$-0.862861\pi$
$757$	−13.9067	−	36.6689i	−0.505447	−	1.33275i	0.403171	−	0.915125i	$-0.367908\pi$
$758$	−0.259085	+	2.13376i	−0.00941040	+	0.0775016i
$759$	−2.34726	+	4.47233i	−0.0852002	+	0.162335i
$760$	9.25592	−	6.38890i	0.335747	−	0.231750i
$761$	10.2339	−	7.06398i	0.370980	−	0.256069i	−0.367958	−	0.929842i	$-0.619943\pi$
$761$	10.2339	−	7.06398i	0.370980	−	0.256069i	0.738938	+	0.673773i	$0.235328\pi$
$762$	0.564657	−	1.07586i	0.0204554	−	0.0389745i
$763$	−0.949102	+	7.81656i	−0.0343598	+	0.282978i
$764$	11.6929	+	30.8317i	0.423034	+	1.11545i
$765$		−	1.52590i		−	0.0551689i
$766$	0.795464	−	2.09747i	0.0287413	−	0.0757846i
$767$	12.6465	−	10.5044i	0.456640	−	0.379292i
$768$	−4.01232	−	10.5796i	−0.144782	−	0.381759i
$769$	34.2765	−	12.9994i	1.23604	−	0.468769i	0.351923	−	0.936029i	$-0.385528\pi$
$769$	34.2765	−	12.9994i	1.23604	−	0.468769i	0.884120	+	0.467260i	$0.154759\pi$
$770$	−1.02773	−	1.48892i	−0.0370368	−	0.0536571i
$771$	−9.80549	−	8.68690i	−0.353136	−	0.312851i
$772$	23.5525	−	16.2571i	0.847673	−	0.585107i
$773$	−35.2073	−	39.7409i	−1.26632	−	1.42938i	−0.855617	−	0.517610i	$-0.826822\pi$
$773$	−35.2073	−	39.7409i	−1.26632	−	1.42938i	−0.410703	−	0.911769i	$-0.634717\pi$
$774$	1.12098	+	2.13585i	0.0402928	+	0.0767715i
$775$			28.9502i			1.03992i
$776$	7.15796	−	3.75679i	0.256956	−	0.134861i
$777$	−1.33349	−	10.9823i	−0.0478386	−	0.393987i
$778$	−4.13836	−	1.56947i	−0.148367	−	0.0562683i
$779$	32.5215	−	17.0686i	1.16520	−	0.611547i
$780$	−21.7470	−	0.692912i	−0.778667	−	0.0248102i
$781$	19.8886	+	10.4384i	0.711671	+	0.373514i
$782$	0.214534	+	0.242159i	0.00767174	+	0.00865960i
$783$	3.86543	+	3.42447i	0.138139	+	0.122381i
$784$	−19.3004	+	4.75711i	−0.689299	+	0.169897i
$785$	−10.1809	+	1.23619i	−0.363372	+	0.0441214i
$786$	−0.173495	+	0.195835i	−0.00618836	+	0.00698521i
$787$	7.40677	−	2.80902i	0.264023	−	0.100131i	−0.219041	−	0.975716i	$-0.570293\pi$
$787$	7.40677	−	2.80902i	0.264023	−	0.100131i	0.483064	+	0.875585i	$0.339524\pi$
$788$	−11.1936	−	21.3276i	−0.398756	−	0.759765i
$789$	−13.0653	−	6.85719i	−0.465137	−	0.244122i
$790$	−0.860520	+	7.08702i	−0.0306159	+	0.252145i
$791$	−2.22589	+	2.51252i	−0.0791437	+	0.0893348i
$792$	1.79543	+	0.442534i	0.0637979	+	0.0157248i
$793$	5.67580	−	0.506363i	0.201554	−	0.0179815i
$794$	5.63204	−	1.38817i	0.199873	−	0.0492644i
$795$	14.4883	−	27.6052i	0.513849	−	0.979057i
$796$	12.3406	+	6.47687i	0.437403	+	0.229567i
$797$	1.93092	−	5.09142i	0.0683968	−	0.180348i	−0.896459	−	0.443126i	$-0.853870\pi$
$797$	1.93092	−	5.09142i	0.0683968	−	0.180348i	0.964856	+	0.262778i	$0.0846388\pi$
$798$	−1.06184	−	0.402702i	−0.0375886	−	0.0142555i
$799$	0.128613	+	0.0887753i	0.00455001	+	0.00314064i
$800$	−3.20012	−	12.9834i	−0.113141	−	0.459032i
$801$	13.4823	+	9.30616i	0.476374	+	0.328817i
$802$	0.318679	+	2.62456i	0.0112530	+	0.0926764i
$803$	−7.65881	+	20.1946i	−0.270274	+	0.712653i
$804$	−9.08874	−	17.3171i	−0.320535	−	0.610728i
$805$	−5.83288	−	8.45039i	−0.205582	−	0.297837i
$806$	3.52265	+	4.24102i	0.124080	+	0.149383i
$807$	17.7552	−	25.7229i	0.625013	−	0.905488i
$808$	−7.54323	−	0.915914i	−0.265370	−	0.0322217i
$809$	36.8660	+	9.08666i	1.29614	+	0.319470i	0.826274	−	0.563268i	$-0.190456\pi$
$809$	36.8660	+	9.08666i	1.29614	+	0.319470i	0.469866	+	0.882738i	$0.344302\pi$
$810$	0.437964	+	0.634501i	0.0153885	+	0.0222941i
$811$	−19.4891	−	21.9986i	−0.684354	−	0.772476i	0.298985	−	0.954258i	$-0.403352\pi$
$811$	−19.4891	−	21.9986i	−0.684354	−	0.772476i	−0.983339	+	0.181782i	$0.941814\pi$
$812$	−5.75970	+	10.9742i	−0.202126	+	0.385118i
$813$	−13.7247	+	1.66647i	−0.481345	+	0.0584458i
$814$	4.16499	+	0.505722i	0.145983	+	0.0177255i
$815$	−4.01036	+	3.55287i	−0.140477	+	0.124451i
$816$	−1.01242	+	1.46675i	−0.0354419	+	0.0513465i
$817$	−35.8073	+	4.34780i	−1.25274	+	0.152110i
$818$	0.345337	−	2.84411i	0.0120744	−	0.0994419i
$819$	2.41730	+	3.75229i	0.0844672	+	0.131116i
$820$	−7.21326	−	59.4065i	−0.251898	−	2.07456i
$821$	3.50947	+	14.2385i	0.122481	+	0.496927i	0.999854	+	0.0171162i	$0.00544852\pi$
$821$	3.50947	+	14.2385i	0.122481	+	0.496927i	−0.877372	+	0.479811i	$0.840705\pi$
$822$	2.34017			0.0816230
$823$	−43.3656			−1.51163			−0.755815	−	0.654785i	$-0.772759\pi$
$823$	−43.3656			−1.51163			−0.755815	+	0.654785i	$0.772759\pi$
$824$	−0.864941	−	3.50920i	−0.0301316	−	0.122249i
$825$	−8.31127	−	3.15205i	−0.289361	−	0.109740i
$826$		−	1.39808i		−	0.0486454i
$827$	−21.0849	+	7.99645i	−0.733194	+	0.278064i	−0.692810	−	0.721121i	$-0.743627\pi$
$827$	−21.0849	+	7.99645i	−0.733194	+	0.278064i	−0.0403841	+	0.999184i	$0.512858\pi$
$828$	5.01563	+	1.23624i	0.174305	+	0.0429624i
$829$	2.30037	−	2.03795i	0.0798951	−	0.0707809i	−0.622230	−	0.782834i	$-0.713773\pi$
$829$	2.30037	−	2.03795i	0.0798951	−	0.0707809i	0.702125	+	0.712054i	$0.252235\pi$
$830$	−0.938027	+	3.80572i	−0.0325594	+	0.132099i
$831$	22.1233	−	19.5996i	0.767450	−	0.679902i
$832$	19.0426	+	14.0601i	0.660183	+	0.487447i
$833$	2.00614	+	1.77729i	0.0695087	+	0.0615793i
$834$	−4.03064	+	2.78215i	−0.139570	+	0.0963381i
$835$	58.1936	−	14.3434i	2.01387	−	0.496375i
$836$	−7.73166	+	11.2012i	−0.267405	+	0.387403i
$837$	−1.47744	+	5.99420i	−0.0510677	+	0.207190i
$838$	−1.46854	+	5.95809i	−0.0507298	+	0.205819i
$839$	−2.39891	−	0.291280i	−0.0828195	−	0.0100561i	0.0790220	−	0.996873i	$-0.474820\pi$
$839$	−2.39891	−	0.291280i	−0.0828195	−	0.0100561i	−0.161842	+	0.986817i	$0.551743\pi$
$840$	−2.49280	+	2.81379i	−0.0860099	+	0.0970851i
$841$	0.826759	+	2.17998i	0.0285089	+	0.0751719i
$842$	6.33004	−	3.32226i	0.218148	−	0.114493i
$843$	−24.6951	−	17.0458i	−0.850543	−	0.587087i
$844$	−47.8582			−1.64735
$845$	34.6987	−	20.8206i	1.19367	−	0.716252i
$846$	−0.0789605			−0.00271472
$847$	−7.54629	−	5.20883i	−0.259294	−	0.178977i
$848$	−32.2426	+	16.9222i	−1.10722	+	0.581112i
$849$	1.11473	+	2.93930i	0.0382574	+	0.100876i
$850$	−0.377553	+	0.426170i	−0.0129500	+	0.0146175i
$851$	23.6384	+	2.87022i	0.810315	+	0.0983900i
$852$	5.49762	−	22.3047i	0.188345	−	0.764147i
$853$	−4.96392	+	20.1394i	−0.169961	+	0.689560i	0.822684	+	0.568499i	$0.192476\pi$
$853$	−4.96392	+	20.1394i	−0.169961	+	0.689560i	−0.992645	+	0.121061i	$0.961370\pi$
$854$	0.275279	−	0.398811i	0.00941987	−	0.0136470i
$855$	−11.1939	+	2.75904i	−0.382822	+	0.0943573i
$856$	4.90930	−	3.38865i	0.167796	−	0.115822i
$857$	32.2318	+	28.5549i	1.10102	+	0.975416i	0.999811	−	0.0194498i	$-0.00619147\pi$
$857$	32.2318	+	28.5549i	1.10102	+	0.975416i	0.101206	+	0.994866i	$0.467730\pi$
$858$	−1.60109	+	0.549557i	−0.0546602	+	0.0187616i
$859$	6.36965	−	5.64302i	0.217330	−	0.192537i	−0.547433	−	0.836850i	$-0.684395\pi$
$859$	6.36965	−	5.64302i	0.217330	−	0.192537i	0.764762	+	0.644312i	$0.222856\pi$
$860$	−14.0647	+	57.0626i	−0.479601	+	1.94582i
$861$	−9.18900	+	8.14074i	−0.313160	+	0.277436i
$862$	5.56852	+	1.37252i	0.189664	+	0.0467481i
$863$	−24.7326	+	9.37984i	−0.841908	+	0.319294i	−0.737589	−	0.675250i	$-0.764036\pi$
$863$	−24.7326	+	9.37984i	−0.841908	+	0.319294i	−0.104319	+	0.994544i	$0.533266\pi$
$864$		−	2.85155i		−	0.0970118i
$865$	−43.9615	−	16.6724i	−1.49474	−	0.566879i
$866$	0.791779	+	3.21238i	0.0269058	+	0.109161i
$867$	−16.7597			−0.569189
$868$	−14.8164			−0.502903
$869$	−4.20056	−	17.0423i	−0.142494	−	0.578122i
$870$	−0.479909	−	3.95241i	−0.0162705	−	0.133999i
$871$	31.6521	+	17.9205i	1.07249	+	0.607214i
$872$	−0.747908	+	6.15958i	−0.0253274	+	0.208590i
$873$	−8.22627	+	0.998850i	−0.278417	+	0.0338060i
$874$	1.38855	−	2.01167i	0.0469686	−	0.0680457i
$875$	−0.896007	+	0.793793i	−0.0302906	+	0.0268351i
$876$	21.9283	+	2.66257i	0.740887	+	0.0899600i
$877$	4.29225	−	0.521173i	0.144939	−	0.0175988i	−0.0477456	−	0.998860i	$-0.515204\pi$
$877$	4.29225	−	0.521173i	0.144939	−	0.0175988i	0.192684	+	0.981261i	$0.438281\pi$
$878$	2.76988	−	5.27757i	0.0934790	−	0.178109i
$879$	−0.756556	−	0.853975i	−0.0255180	−	0.0288039i
$880$	12.1862	+	17.6547i	0.410795	+	0.595139i
$881$	31.4832	+	7.75990i	1.06069	+	0.261438i	0.730808	−	0.682583i	$-0.239143\pi$
$881$	31.4832	+	7.75990i	1.06069	+	0.261438i	0.329886	+	0.944021i	$0.392990\pi$
$882$	−1.34431	−	0.163229i	−0.0452654	−	0.00549622i
$883$	−23.3762	+	33.8663i	−0.786672	+	1.13969i	0.200447	+	0.979704i	$0.435760\pi$
$883$	−23.3762	+	33.8663i	−0.786672	+	1.13969i	−0.987119	+	0.159986i	$0.948855\pi$
$884$	0.109121	−	3.42475i	0.00367014	−	0.115187i
$885$	−8.06266	−	11.6808i	−0.271023	−	0.392645i
$886$	−1.80604	−	3.44112i	−0.0606750	−	0.115607i
$887$	17.6045	−	46.4193i	0.591102	−	1.55861i	−0.221112	−	0.975248i	$-0.570969\pi$
$887$	17.6045	−	46.4193i	0.591102	−	1.55861i	0.812214	−	0.583360i	$-0.198262\pi$
$888$	−1.05081	−	8.65421i	−0.0352629	−	0.290416i
$889$	−4.99798	−	3.44986i	−0.167627	−	0.115704i
$890$	−3.02263	−	12.2633i	−0.101319	−	0.411066i
$891$	−1.56001	−	1.07679i	−0.0522621	−	0.0360740i
$892$	12.6836	+	4.81024i	0.424677	+	0.161059i
$893$	0.418698	−	1.10402i	0.0140112	−	0.0369445i
$894$	−0.671926	−	0.352654i	−0.0224726	−	0.0117945i
$895$	3.95798	−	7.54130i	0.132301	−	0.252078i
$896$	8.80954	−	2.17136i	0.294306	−	0.0725399i
$897$	−9.08697	+	3.11901i	−0.303405	+	0.104141i
$898$	−9.69621	−	2.38990i	−0.323567	−	0.0797520i
$899$	21.1413	−	23.8636i	0.705101	−	0.795895i
$900$	−1.09580	+	9.02476i	−0.0365268	+	0.300825i
$901$	4.34732	+	2.28165i	0.144830	+	0.0760128i
$902$	−2.16365	−	4.12249i	−0.0720416	−	0.137264i
$903$	11.2729	−	4.27524i	0.375138	−	0.142271i
$904$	−1.75404	+	1.97990i	−0.0583386	+	0.0658506i
$905$	−33.8197	+	4.10646i	−1.12421	+	0.136503i
$906$	1.13419	−	0.279553i	0.0376809	−	0.00928751i
$907$	−18.2112	−	16.1337i	−0.604692	−	0.535710i	0.304272	−	0.952585i	$-0.401587\pi$
$907$	−18.2112	−	16.1337i	−0.604692	−	0.535710i	−0.908964	+	0.416875i	$0.863125\pi$
$908$	18.9933	+	21.4390i	0.630316	+	0.711479i
$909$	6.89702	+	3.61984i	0.228760	+	0.120062i
$910$	0.523381	−	3.40123i	0.0173499	−	0.112750i
$911$	−40.3772	+	21.1916i	−1.33776	+	0.702109i	−0.973392	−	0.229147i	$-0.926406\pi$
$911$	−40.3772	+	21.1916i	−1.33776	+	0.702109i	−0.364366	+	0.931256i	$0.618714\pi$
$912$	12.5906	+	4.77497i	0.416915	+	0.158115i
$913$	−1.16160	−	9.56665i	−0.0384434	−	0.316610i
$914$	2.06596	−	1.08430i	0.0683360	−	0.0358655i
$915$		−	4.91954i		−	0.162635i
$916$	18.2100	+	34.6963i	0.601675	+	1.14640i
$917$	0.867160	+	0.978821i	0.0286361	+	0.0323235i
$918$	−0.0999223	+	0.0689714i	−0.00329793	+	0.00227639i
$919$	35.9635	+	31.8609i	1.18633	+	1.05099i	0.997619	+	0.0689592i	$0.0219678\pi$
$919$	35.9635	+	31.8609i	1.18633	+	1.05099i	0.188706	+	0.982034i	$0.439571\pi$
$920$	−4.59641	−	6.65905i	−0.151539	−	0.219542i
$921$	−10.4958	+	3.98053i	−0.345849	+	0.131163i
$922$	1.13880	+	3.00277i	0.0375043	+	0.0988908i
$923$	13.8704	+	40.4101i	0.456549	+	1.33012i
$924$	1.61319	−	4.25363i	0.0530701	−	0.139934i
$925$			41.9062i			1.37787i
$926$	−0.554491	−	1.46207i	−0.0182217	−	0.0480467i
$927$	−0.446574	+	3.67787i	−0.0146674	+	0.120797i
$928$	−6.84345	+	13.0391i	−0.224647	+	0.428030i
$929$	46.4663	−	32.0734i	1.52451	−	1.05229i	0.548090	−	0.836420i	$-0.315355\pi$
$929$	46.4663	−	32.0734i	1.52451	−	1.05229i	0.976421	−	0.215874i	$-0.0692602\pi$
$930$	3.91715	−	2.70381i	0.128448	−	0.0886615i
$931$	9.41065	−	17.9305i	0.308422	−	0.587648i
$932$	−1.43612	+	11.8275i	−0.0470417	+	0.387423i
$933$	6.74454	+	17.7839i	0.220806	+	0.582218i
$934$			5.61671i			0.183784i
$935$	1.02566	−	2.70445i	0.0335428	−	0.0884450i
$936$	1.90487	+	2.95687i	0.0622626	+	0.0966482i
$937$	−12.5344	−	33.0506i	−0.409482	−	1.07972i	−0.968160	−	0.250331i	$-0.919460\pi$
$937$	−12.5344	−	33.0506i	−0.409482	−	1.07972i	0.558678	−	0.829385i	$-0.311309\pi$
$938$	2.89219	−	1.09686i	0.0944334	−	0.0358139i
$939$	−11.2243	−	16.2612i	−0.366292	−	0.530666i
$940$	−1.44000	−	1.27573i	−0.0469676	−	0.0416097i
$941$	−17.1740	+	11.8544i	−0.559857	+	0.386442i	−0.814123	−	0.580693i	$-0.802782\pi$
$941$	−17.1740	+	11.8544i	−0.559857	+	0.386442i	0.254265	+	0.967134i	$0.418166\pi$
$942$	0.541133	+	0.610813i	0.0176311	+	0.0199014i
$943$	−12.2798	−	23.3972i	−0.399885	−	0.761917i
$944$			16.5775i			0.539552i
$945$	3.41209	−	1.79080i	0.110995	−	0.0582548i
$946$	0.551134	+	4.53900i	0.0179189	+	0.147576i
$947$	−12.5264	−	4.75063i	−0.407053	−	0.154375i	0.142576	−	0.989784i	$-0.454462\pi$
$947$	−12.5264	−	4.75063i	−0.407053	−	0.154375i	−0.549629	+	0.835409i	$0.685231\pi$
$948$	−15.8953	+	8.34250i	−0.516255	+	0.270952i
$949$	−36.9660	+	17.9237i	−1.19997	+	0.581828i
$950$	3.80902	+	1.99913i	0.123581	+	0.0648603i
$951$	6.80143	+	7.67722i	0.220551	+	0.248951i
$952$	−0.443121	−	0.392571i	−0.0143616	−	0.0127233i
$953$	−23.0067	+	5.67064i	−0.745259	+	0.183690i	−0.593620	−	0.804746i	$-0.702302\pi$
$953$	−23.0067	+	5.67064i	−0.745259	+	0.183690i	−0.151640	+	0.988436i	$0.548455\pi$
$954$	−2.46259	+	0.299013i	−0.0797293	+	0.00968089i
$955$	−35.1090	+	39.6299i	−1.13610	+	1.28239i
$956$	1.97558	−	0.749240i	0.0638949	−	0.0242321i
$957$	4.54913	+	8.66764i	0.147053	+	0.280185i
$958$	0.243443	+	0.127769i	0.00786529	+	0.00412802i
$959$	1.40987	−	11.6113i	0.0455272	−	0.374950i
$960$	13.5514	−	15.2963i	0.437368	−	0.493686i
$961$	6.90656	+	1.70231i	0.222792	+	0.0549133i
$962$	5.09912	+	6.13898i	0.164402	+	0.197929i
$963$	−5.93718	+	1.46338i	−0.191323	+	0.0471569i
$964$	12.5012	−	23.8190i	0.402636	−	0.767158i
$965$	40.6874	+	21.3544i	1.30977	+	0.687422i
$966$	−0.289718	+	0.763924i	−0.00932153	+	0.0245789i
$967$	52.9524	+	20.0822i	1.70283	+	0.645800i	0.997979	−	0.0635516i	$-0.0202428\pi$
$967$	52.9524	+	20.0822i	1.70283	+	0.645800i	0.704855	+	0.709351i	$0.251012\pi$
$968$	−5.94660	−	4.10464i	−0.191131	−	0.131928i
$969$	−0.434499	−	1.76283i	−0.0139581	−	0.0566303i
$970$	5.25791	+	3.62927i	0.168821	+	0.116529i
$971$	−0.565599	−	4.65813i	−0.0181509	−	0.149486i	0.980816	−	0.194938i	$-0.0624505\pi$
$971$	−0.565599	−	4.65813i	−0.0181509	−	0.149486i	−0.998967	+	0.0454514i	$0.985527\pi$
$972$	−0.687456	+	1.81267i	−0.0220502	+	0.0581415i
$973$	11.3760	+	21.6752i	0.364698	+	0.694874i
$974$	1.22738	+	1.77816i	0.0393276	+	0.0569759i
$975$	−7.37665	−	15.2137i	−0.236242	−	0.487228i
$976$	−3.26408	+	4.72884i	−0.104481	+	0.151367i
$977$	−17.9055	−	2.17412i	−0.572847	−	0.0695562i	−0.171013	−	0.985269i	$-0.554704\pi$
$977$	−17.9055	−	2.17412i	−0.572847	−	0.0695562i	−0.401834	+	0.915713i	$0.631627\pi$
$978$	0.413927	+	0.102024i	0.0132359	+	0.00326236i
$979$	17.6403	+	25.5563i	0.563785	+	0.816784i
$980$	−21.8790	−	24.6963i	−0.698899	−	0.788894i
$981$	2.95585	−	5.63190i	0.0943730	−	0.179813i
$982$	−1.64792	+	0.200094i	−0.0525873	+	0.00638526i
$983$	18.3987	+	2.23401i	0.586827	+	0.0712537i	0.408565	−	0.912729i	$-0.366029\pi$
$983$	18.3987	+	2.23401i	0.586827	+	0.0712537i	0.178262	+	0.983983i	$0.442952\pi$
$984$	−7.24108	+	6.41504i	−0.230837	+	0.204504i
$985$	21.9695	−	31.8283i	0.700007	−	1.01414i
$986$	0.622432	−	0.0755770i	0.0198223	−	0.00240686i
$987$	−0.0475709	+	0.391782i	−0.00151420	+	0.0124705i
$988$	−25.3211	+	5.39195i	−0.805570	+	0.171541i
$989$	3.12796	+	25.7611i	0.0994635	+	0.819155i
$990$	0.349741	+	1.41896i	0.0111155	+	0.0450974i
$991$	39.4609			1.25352			0.626758	−	0.779214i	$-0.284381\pi$
$991$	39.4609			1.25352			0.626758	+	0.779214i	$0.284381\pi$
$992$	−17.6043			−0.558938
$993$	4.96749	+	20.1539i	0.157639	+	0.639565i
$994$	3.39720	+	1.28839i	0.107753	+	0.0408652i
$995$			22.3778i			0.709425i
$996$	−9.21558	+	3.49501i	−0.292007	+	0.110744i
$997$	−22.6787	−	5.58980i	−0.718241	−	0.177031i	−0.136776	−	0.990602i	$-0.543674\pi$
$997$	−22.6787	−	5.58980i	−0.718241	−	0.177031i	−0.581465	+	0.813571i	$0.697520\pi$
$998$	−7.75328	+	6.86881i	−0.245426	+	0.217428i
$999$	−2.13863	+	8.67676i	−0.0676632	+	0.274521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.a.493.7	yes	168
169.12	even	26	inner	507.2.p.a.181.7	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.a.181.7	✓	168	169.12	even	26	inner
507.2.p.a.493.7	yes	168	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.203838 - 0.140699i) q^{2} +(0.885456 - 0.464723i) q^{3} +(-0.687456 - 1.81267i) q^{4} +(2.06415 - 2.32994i) q^{5} +(-0.245875 - 0.0298547i) q^{6} +(-0.296263 + 1.20198i) q^{7} +(-0.233460 + 0.947184i) q^{8} +(0.568065 - 0.822984i) q^{9} +O(q^{10})\)	\(q+(-0.203838 - 0.140699i) q^{2} +(0.885456 - 0.464723i) q^{3} +(-0.687456 - 1.81267i) q^{4} +(2.06415 - 2.32994i) q^{5} +(-0.245875 - 0.0298547i) q^{6} +(-0.296263 + 1.20198i) q^{7} +(-0.233460 + 0.947184i) q^{8} +(0.568065 - 0.822984i) q^{9} +(-0.748572 + 0.184507i) q^{10} +(1.56001 - 1.07679i) q^{11} +(-1.45110 - 1.28557i) q^{12} +(3.56361 + 0.548367i) q^{13} +(0.229508 - 0.203326i) q^{14} +(0.744935 - 3.02232i) q^{15} +(-2.72135 + 2.41091i) q^{16} +(0.475961 + 0.117314i) q^{17} +(-0.231586 + 0.0878290i) q^{18} -3.70373i q^{19} +(-5.64244 - 2.13990i) q^{20} +(0.296263 + 1.20198i) q^{21} -0.469492 q^{22} -2.66460 q^{23} +(0.233460 + 0.947184i) q^{24} +(-0.565240 - 4.65517i) q^{25} +(-0.649243 - 0.613174i) q^{26} +(0.120537 - 0.992709i) q^{27} +(2.38247 - 0.289285i) q^{28} +(-2.93357 + 4.25002i) q^{29} +(-0.577084 + 0.511251i) q^{30} +(-6.12858 - 0.744144i) q^{31} +(2.83076 - 0.343717i) q^{32} +(0.880905 - 1.67842i) q^{33} +(-0.0805128 - 0.0908802i) q^{34} +(2.18903 + 3.17135i) q^{35} +(-1.88232 - 0.463950i) q^{36} +(-8.87128 - 1.07717i) q^{37} +(-0.521112 + 0.754960i) q^{38} +(3.41026 - 1.17054i) q^{39} +(1.72499 + 2.49908i) q^{40} +(4.60849 + 8.78074i) q^{41} +(0.108729 - 0.286694i) q^{42} +(-1.17390 - 9.66790i) q^{43} +(-3.02431 - 2.08753i) q^{44} +(-0.744935 - 3.02232i) q^{45} +(0.543146 + 0.374907i) q^{46} +(0.298082 + 0.113048i) q^{47} +(-1.28923 + 3.39943i) q^{48} +(4.84120 + 2.54086i) q^{49} +(-0.539760 + 1.02843i) q^{50} +(0.475961 - 0.117314i) q^{51} +(-1.45581 - 6.83663i) q^{52} +(9.72457 + 2.39689i) q^{53} +(-0.164243 + 0.185392i) q^{54} +(0.711216 - 5.85739i) q^{55} +(-1.06933 - 0.561230i) q^{56} +(-1.72121 - 3.27949i) q^{57} +(1.19595 - 0.453563i) q^{58} +(3.02362 - 3.41296i) q^{59} +(-5.99059 + 0.727390i) q^{60} +(1.53451 - 0.378223i) q^{61} +(1.14454 + 1.01397i) q^{62} +(0.820918 + 0.926625i) q^{63} +(5.81311 + 3.05095i) q^{64} +(8.63349 - 7.17109i) q^{65} +(-0.415714 + 0.218184i) q^{66} +(9.43253 + 3.57729i) q^{67} +(-0.114551 - 0.943409i) q^{68} +(-2.35939 + 1.23830i) q^{69} -0.954435i q^{70} +(5.50678 + 10.4923i) q^{71} +(0.646897 + 0.730195i) q^{72} +(-9.37720 + 6.47262i) q^{73} +(1.65674 + 1.46775i) q^{74} +(-2.66386 - 3.85927i) q^{75} +(-6.71366 + 2.54615i) q^{76} +(0.832119 + 2.19412i) q^{77} +(-0.859832 - 0.241220i) q^{78} +(3.28357 - 8.65806i) q^{79} +11.3171i q^{80} +(-0.354605 - 0.935016i) q^{81} +(0.296058 - 2.43826i) q^{82} +(2.36264 - 4.50164i) q^{83} +(1.97514 - 1.36334i) q^{84} +(1.25579 - 0.866809i) q^{85} +(-1.12098 + 2.13585i) q^{86} +(-0.622470 + 5.12650i) q^{87} +(0.655723 + 1.72900i) q^{88} +16.3822i q^{89} +(-0.273392 + 0.720875i) q^{90} +(-1.71489 + 4.12094i) q^{91} +(1.83180 + 4.83005i) q^{92} +(-5.77241 + 2.18919i) q^{93} +(-0.0448547 - 0.0649832i) q^{94} +(-8.62949 - 7.64506i) q^{95} +(2.34678 - 1.61987i) q^{96} +(-5.49509 - 6.20268i) q^{97} +(-0.629322 - 1.19907i) q^{98} -1.89555i 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more