LMFDB - Embedded newform 507.2.p.b.493.8

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:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			493.8
Character	$\chi$	$=$	507.493
Dual form			507.2.p.b.181.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.279864 - 0.193176i) q^{2} +(-0.885456 + 0.464723i) q^{3} +(-0.668203 - 1.76191i) q^{4} +(2.32134 - 2.62025i) q^{5} +(0.337580 + 0.0409897i) q^{6} +(0.713484 - 2.89472i) q^{7} +(-0.316115 + 1.28253i) q^{8} +(0.568065 - 0.822984i) q^{9} +O(q^{10})$	\(q+(-0.279864 - 0.193176i) q^{2} +(-0.885456 + 0.464723i) q^{3} +(-0.668203 - 1.76191i) q^{4} +(2.32134 - 2.62025i) q^{5} +(0.337580 + 0.0409897i) q^{6} +(0.713484 - 2.89472i) q^{7} +(-0.316115 + 1.28253i) q^{8} +(0.568065 - 0.822984i) q^{9} +(-1.15583 + 0.284886i) q^{10} +(1.95520 - 1.34958i) q^{11} +(1.41046 + 1.24956i) q^{12} +(-1.48998 + 3.28328i) q^{13} +(-0.758869 + 0.672299i) q^{14} +(-0.837754 + 3.39890i) q^{15} +(-2.48470 + 2.20126i) q^{16} +(-0.847839 - 0.208974i) q^{17} +(-0.317961 + 0.120587i) q^{18} -1.22693i q^{19} +(-6.16777 - 2.33913i) q^{20} +(0.713484 + 2.89472i) q^{21} -0.807895 q^{22} -7.94211 q^{23} +(-0.316115 - 1.28253i) q^{24} +(-0.874416 - 7.20147i) q^{25} +(1.05124 - 0.631043i) q^{26} +(-0.120537 + 0.992709i) q^{27} +(-5.57698 + 0.677168i) q^{28} +(2.54788 - 3.69125i) q^{29} +(0.891043 - 0.789395i) q^{30} +(9.65204 + 1.17197i) q^{31} +(3.74317 - 0.454504i) q^{32} +(-1.10406 + 2.10362i) q^{33} +(0.196911 + 0.222266i) q^{34} +(-5.92866 - 8.58915i) q^{35} +(-1.82960 - 0.450957i) q^{36} +(2.67093 + 0.324309i) q^{37} +(-0.237014 + 0.343374i) q^{38} +(-0.206504 - 3.59963i) q^{39} +(2.62674 + 3.80550i) q^{40} +(1.53456 + 2.92386i) q^{41} +(0.359512 - 0.947955i) q^{42} +(-0.483804 - 3.98448i) q^{43} +(-3.68430 - 2.54309i) q^{44} +(-0.837754 - 3.39890i) q^{45} +(2.22271 + 1.53422i) q^{46} +(-7.35065 - 2.78773i) q^{47} +(1.17712 - 3.10381i) q^{48} +(-1.67215 - 0.877613i) q^{49} +(-1.14643 + 2.18434i) q^{50} +(0.847839 - 0.208974i) q^{51} +(6.78045 + 0.431310i) q^{52} +(-5.25317 - 1.29479i) q^{53} +(0.225501 - 0.254538i) q^{54} +(1.00245 - 8.25595i) q^{55} +(3.48702 + 1.83013i) q^{56} +(0.570184 + 1.08639i) q^{57} +(-1.42612 + 0.540856i) q^{58} +(-4.76532 + 5.37893i) q^{59} +(6.54834 - 0.795112i) q^{60} +(-3.10187 + 0.764543i) q^{61} +(-2.47486 - 2.19253i) q^{62} +(-1.97700 - 2.23157i) q^{63} +(4.74322 + 2.48943i) q^{64} +(5.14428 + 11.5258i) q^{65} +(0.715356 - 0.375448i) q^{66} +(0.740752 + 0.280930i) q^{67} +(0.198337 + 1.63345i) q^{68} +(7.03239 - 3.69088i) q^{69} +3.54906i q^{70} +(-2.16876 - 4.13222i) q^{71} +(0.875928 + 0.988718i) q^{72} +(7.38841 - 5.09985i) q^{73} +(-0.684846 - 0.606721i) q^{74} +(4.12095 + 5.97022i) q^{75} +(-2.16174 + 0.819840i) q^{76} +(-2.51164 - 6.62266i) q^{77} +(-0.637569 + 1.04730i) q^{78} +(-5.73631 + 15.1254i) q^{79} +11.6204i q^{80} +(-0.354605 - 0.935016i) q^{81} +(0.135352 - 1.11472i) q^{82} +(4.07169 - 7.75796i) q^{83} +(4.62347 - 3.19135i) q^{84} +(-2.51569 + 1.73645i) q^{85} +(-0.634307 + 1.20857i) q^{86} +(-0.540631 + 4.45250i) q^{87} +(1.11280 + 2.93423i) q^{88} -8.25170i q^{89} +(-0.422129 + 1.11306i) q^{90} +(8.44111 + 6.65565i) q^{91} +(5.30694 + 13.9933i) q^{92} +(-9.09110 + 3.44780i) q^{93} +(1.51866 + 2.20015i) q^{94} +(-3.21487 - 2.84813i) q^{95} +(-3.10320 + 2.14198i) q^{96} +(11.4850 + 12.9639i) q^{97} +(0.298441 + 0.568632i) q^{98} -2.37574i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * 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 $

$2$	−0.279864	−	0.193176i	−0.197893	−	0.136596i	0.464997	−	0.885312i	$-0.346055\pi$
$2$	−0.279864	−	0.193176i	−0.197893	−	0.136596i	−0.662891	+	0.748716i	$0.730671\pi$
$3$	−0.885456	+	0.464723i	−0.511218	+	0.268308i
$3$	−0.885456	+	0.464723i	−0.511218	+	0.268308i
$4$	−0.668203	−	1.76191i	−0.334102	−	0.880953i
$5$	2.32134	−	2.62025i	1.03814	−	1.17181i	0.0532548	−	0.998581i	$-0.483040\pi$
$5$	2.32134	−	2.62025i	1.03814	−	1.17181i	0.984881	−	0.173232i	$-0.0554211\pi$
$6$	0.337580	+	0.0409897i	0.137817	+	0.0167340i
$7$	0.713484	−	2.89472i	0.269672	−	1.09410i	−0.667326	−	0.744766i	$-0.732561\pi$
$7$	0.713484	−	2.89472i	0.269672	−	1.09410i	0.936998	−	0.349336i	$-0.113593\pi$
$8$	−0.316115	+	1.28253i	−0.111764	+	0.453443i
$9$	0.568065	−	0.822984i	0.189355	−	0.274328i
$10$	−1.15583	+	0.284886i	−0.365505	+	0.0900890i
$11$	1.95520	−	1.34958i	0.589515	−	0.406913i	−0.235623	−	0.971845i	$-0.575713\pi$
$11$	1.95520	−	1.34958i	0.589515	−	0.406913i	0.825138	+	0.564932i	$0.191098\pi$
$12$	1.41046	+	1.24956i	0.407166	+	0.360717i
$13$	−1.48998	+	3.28328i	−0.413247	+	0.910619i
$13$	−1.48998	+	3.28328i	−0.413247	+	0.910619i
$14$	−0.758869	+	0.672299i	−0.202816	+	0.179679i
$15$	−0.837754	+	3.39890i	−0.216307	+	0.877592i
$16$	−2.48470	+	2.20126i	−0.621176	+	0.550314i
$17$	−0.847839	−	0.208974i	−0.205631	−	0.0506835i	0.135155	−	0.990825i	$-0.456847\pi$
$17$	−0.847839	−	0.208974i	−0.205631	−	0.0506835i	−0.340786	+	0.940141i	$0.610693\pi$
$18$	−0.317961	+	0.120587i	−0.0749442	+	0.0284226i
$19$		−	1.22693i		−	0.281478i	−0.990047	−	0.140739i	$-0.955052\pi$
$19$		−	1.22693i		−	0.281478i	0.990047	−	0.140739i	$-0.0449478\pi$
$20$	−6.16777	−	2.33913i	−1.37916	−	0.523045i
$21$	0.713484	+	2.89472i	0.155695	+	0.631680i
$22$	−0.807895			−0.172244
$23$	−7.94211			−1.65604			−0.828022	−	0.560695i	$-0.810534\pi$
$23$	−7.94211			−1.65604			−0.828022	+	0.560695i	$0.810534\pi$
$24$	−0.316115	−	1.28253i	−0.0645268	−	0.261795i
$25$	−0.874416	−	7.20147i	−0.174883	−	1.44029i
$26$	1.05124	−	0.631043i	0.206166	−	0.123758i
$27$	−0.120537	+	0.992709i	−0.0231973	+	0.191047i
$28$	−5.57698	+	0.677168i	−1.05395	+	0.127973i
$29$	2.54788	−	3.69125i	0.473130	−	0.685447i	−0.511662	−	0.859187i	$-0.670970\pi$
$29$	2.54788	−	3.69125i	0.473130	−	0.685447i	0.984792	+	0.173740i	$0.0555852\pi$
$30$	0.891043	−	0.789395i	0.162681	−	0.144123i
$31$	9.65204	+	1.17197i	1.73356	+	0.210492i	0.925535	−	0.378661i	$-0.123615\pi$
$31$	9.65204	+	1.17197i	1.73356	+	0.210492i	0.808022	+	0.589153i	$0.200538\pi$
$32$	3.74317	−	0.454504i	0.661706	−	0.0803456i
$33$	−1.10406	+	2.10362i	−0.192193	+	0.366193i
$34$	0.196911	+	0.222266i	0.0337699	+	0.0381183i
$35$	−5.92866	−	8.58915i	−1.00213	−	1.45183i
$36$	−1.82960	−	0.450957i	−0.304934	−	0.0751595i
$37$	2.67093	+	0.324309i	0.439097	+	0.0533161i	0.337101	−	0.941469i	$-0.390554\pi$
$37$	2.67093	+	0.324309i	0.439097	+	0.0533161i	0.101997	+	0.994785i	$0.467477\pi$
$38$	−0.237014	+	0.343374i	−0.0384487	+	0.0557026i
$39$	−0.206504	−	3.59963i	−0.0330671	−	0.576403i
$40$	2.62674	+	3.80550i	0.415325	+	0.601702i
$41$	1.53456	+	2.92386i	0.239658	+	0.456630i	0.975343	−	0.220694i	$-0.0708321\pi$
$41$	1.53456	+	2.92386i	0.239658	+	0.456630i	−0.735685	+	0.677323i	$0.763140\pi$
$42$	0.359512	−	0.947955i	0.0554739	−	0.146273i
$43$	−0.483804	−	3.98448i	−0.0737794	−	0.607628i	−0.981965	−	0.189061i	$-0.939456\pi$
$43$	−0.483804	−	3.98448i	−0.0737794	−	0.607628i	0.908186	−	0.418567i	$-0.137467\pi$
$44$	−3.68430	−	2.54309i	−0.555429	−	0.383385i
$45$	−0.837754	−	3.39890i	−0.124885	−	0.506678i
$46$	2.22271	+	1.53422i	0.327720	+	0.226209i
$47$	−7.35065	−	2.78773i	−1.07220	−	0.406633i	−0.245572	−	0.969378i	$-0.578976\pi$
$47$	−7.35065	−	2.78773i	−1.07220	−	0.406633i	−0.826630	+	0.562745i	$0.809745\pi$
$48$	1.17712	−	3.10381i	0.169903	−	0.447997i
$49$	−1.67215	−	0.877613i	−0.238879	−	0.125373i
$50$	−1.14643	+	2.18434i	−0.162130	+	0.308913i
$51$	0.847839	−	0.208974i	0.118721	−	0.0292621i
$52$	6.78045	+	0.431310i	0.940279	+	0.0598119i
$53$	−5.25317	−	1.29479i	−0.721578	−	0.177853i	−0.138609	−	0.990347i	$-0.544263\pi$
$53$	−5.25317	−	1.29479i	−0.721578	−	0.177853i	−0.582969	+	0.812494i	$0.698109\pi$
$54$	0.225501	−	0.254538i	0.0306868	−	0.0346383i
$55$	1.00245	−	8.25595i	0.135171	−	1.11323i
$56$	3.48702	+	1.83013i	0.465973	+	0.244562i
$57$	0.570184	+	1.08639i	0.0755227	+	0.143897i
$58$	−1.42612	+	0.540856i	−0.187259	+	0.0710178i
$59$	−4.76532	+	5.37893i	−0.620391	+	0.700277i	−0.971763	−	0.235959i	$-0.924177\pi$
$59$	−4.76532	+	5.37893i	−0.620391	+	0.700277i	0.351372	+	0.936236i	$0.385715\pi$
$60$	6.54834	−	0.795112i	0.845387	−	0.102649i
$61$	−3.10187	+	0.764543i	−0.397154	+	0.0978897i	−0.432834	−	0.901474i	$-0.642486\pi$
$61$	−3.10187	+	0.764543i	−0.397154	+	0.0978897i	0.0356801	+	0.999363i	$0.488640\pi$
$62$	−2.47486	−	2.19253i	−0.314307	−	0.278452i
$63$	−1.97700	−	2.23157i	−0.249079	−	0.281152i
$64$	4.74322	+	2.48943i	0.592902	+	0.311179i
$65$	5.14428	+	11.5258i	0.638069	+	1.42959i
$66$	0.715356	−	0.375448i	0.0880542	−	0.0462144i
$67$	0.740752	+	0.280930i	0.0904973	+	0.0343211i	0.399438	−	0.916760i	$-0.369205\pi$
$67$	0.740752	+	0.280930i	0.0904973	+	0.0343211i	−0.308941	+	0.951081i	$0.599974\pi$
$68$	0.198337	+	1.63345i	0.0240519	+	0.198085i
$69$	7.03239	−	3.69088i	0.846600	−	0.444330i
$70$			3.54906i			0.424194i
$71$	−2.16876	−	4.13222i	−0.257384	−	0.490405i	0.722136	−	0.691751i	$-0.243161\pi$
$71$	−2.16876	−	4.13222i	−0.257384	−	0.490405i	−0.979520	+	0.201347i	$0.935468\pi$
$72$	0.875928	+	0.988718i	0.103229	+	0.116522i
$73$	7.38841	−	5.09985i	0.864748	−	0.596892i	−0.0509765	−	0.998700i	$-0.516233\pi$
$73$	7.38841	−	5.09985i	0.864748	−	0.596892i	0.915724	+	0.401808i	$0.131618\pi$
$74$	−0.684846	−	0.606721i	−0.0796118	−	0.0705299i
$75$	4.12095	+	5.97022i	0.475846	+	0.689382i
$76$	−2.16174	+	0.819840i	−0.247969	+	0.0940421i
$77$	−2.51164	−	6.62266i	−0.286228	−	0.754722i
$78$	−0.637569	+	1.04730i	−0.0721905	+	0.118583i
$79$	−5.73631	+	15.1254i	−0.645386	+	1.70174i	0.0649592	+	0.997888i	$0.479308\pi$
$79$	−5.73631	+	15.1254i	−0.645386	+	1.70174i	−0.710345	+	0.703854i	$0.751461\pi$
$80$			11.6204i			1.29920i
$81$	−0.354605	−	0.935016i	−0.0394005	−	0.103891i
$82$	0.135352	−	1.11472i	0.0149471	−	0.123100i
$83$	4.07169	−	7.75796i	0.446926	−	0.851546i	−0.552907	−	0.833243i	$-0.686481\pi$
$83$	4.07169	−	7.75796i	0.446926	−	0.851546i	0.999832	−	0.0183029i	$-0.00582633\pi$
$84$	4.62347	−	3.19135i	0.504462	−	0.348205i
$85$	−2.51569	+	1.73645i	−0.272865	+	0.188345i
$86$	−0.634307	+	1.20857i	−0.0683991	+	0.130324i
$87$	−0.540631	+	4.45250i	−0.0579617	+	0.477358i
$88$	1.11280	+	2.93423i	0.118625	+	0.312789i
$89$		−	8.25170i		−	0.874678i	−0.899297	−	0.437339i	$-0.855921\pi$
$89$		−	8.25170i		−	0.874678i	0.899297	−	0.437339i	$-0.144079\pi$
$90$	−0.422129	+	1.11306i	−0.0444963	+	0.117327i
$91$	8.44111	+	6.65565i	0.884869	+	0.697702i
$92$	5.30694	+	13.9933i	0.553287	+	1.45890i
$93$	−9.09110	+	3.44780i	−0.942703	+	0.357520i
$94$	1.51866	+	2.20015i	0.156637	+	0.226929i
$95$	−3.21487	−	2.84813i	−0.329839	−	0.292212i
$96$	−3.10320	+	2.14198i	−0.316719	+	0.218615i
$97$	11.4850	+	12.9639i	1.16613	+	1.31629i	0.939597	+	0.342281i	$0.111200\pi$
$97$	11.4850	+	12.9639i	1.16613	+	1.31629i	0.226530	+	0.974004i	$0.427262\pi$
$98$	0.298441	+	0.568632i	0.0301471	+	0.0574405i
$99$		−	2.37574i		−	0.238771i
$100$	−12.1040	+	6.35268i	−1.21040	+	0.635268i
$101$	0.854908	+	7.04080i	0.0850666	+	0.700586i	0.971385	+	0.237510i	$0.0763313\pi$
$101$	0.854908	+	7.04080i	0.0850666	+	0.700586i	−0.886319	+	0.463076i	$0.846746\pi$
$102$	−0.277648	−	0.105298i	−0.0274912	−	0.0104261i
$103$	2.17357	−	1.14078i	0.214168	−	0.112404i	−0.354228	−	0.935159i	$-0.615256\pi$
$103$	2.17357	−	1.14078i	0.214168	−	0.112404i	0.568396	+	0.822755i	$0.307564\pi$
$104$	−3.73991	−	2.94885i	−0.366728	−	0.289158i
$105$	9.24114	+	4.85013i	0.901843	+	0.473324i
$106$	1.22005	+	1.37715i	0.118502	+	0.133761i
$107$	−9.70583	−	8.59862i	−0.938298	−	0.831260i	0.0475553	−	0.998869i	$-0.484857\pi$
$107$	−9.70583	−	8.59862i	−0.938298	−	0.831260i	−0.985854	+	0.167609i	$0.946395\pi$
$108$	1.82960	−	0.450957i	0.176054	−	0.0433933i
$109$	19.3090	−	2.34454i	1.84947	−	0.224566i	0.880898	−	0.473307i	$-0.156940\pi$
$109$	19.3090	−	2.34454i	1.84947	−	0.224566i	0.968570	+	0.248741i	$0.0800168\pi$
$110$	−1.87540	+	2.11689i	−0.178812	+	0.201838i
$111$	−2.51570	+	0.954080i	−0.238780	+	0.0905572i
$112$	4.59922	+	8.76308i	0.434585	+	0.828033i
$113$	12.0613	+	6.33024i	1.13463	+	0.595499i	0.924123	−	0.382094i	$-0.124797\pi$
$113$	12.0613	+	6.33024i	1.13463	+	0.595499i	0.210505	+	0.977593i	$0.432489\pi$
$114$	0.0502916	−	0.414188i	0.00471024	−	0.0387923i
$115$	−18.4364	+	20.8103i	−1.71920	+	1.94057i
$116$	−8.20613	−	2.02263i	−0.761920	−	0.187796i
$117$	1.85568	+	3.09135i	0.171558	+	0.285795i
$118$	2.37272	−	0.584822i	0.218426	−	0.0538373i
$119$	−1.20984	+	2.30516i	−0.110906	+	0.211313i
$120$	−4.09437	−	2.14889i	−0.373763	−	0.196166i
$121$	−1.89921	+	5.00779i	−0.172655	+	0.455254i
$122$	1.01579	+	0.385239i	0.0919655	+	0.0348779i
$123$	−2.71757	−	1.87580i	−0.245035	−	0.169135i
$124$	−4.38462	−	17.7891i	−0.393750	−	1.59751i
$125$	−6.49471	−	4.48297i	−0.580904	−	0.400969i
$126$	0.122205	+	1.00645i	0.0108869	+	0.0896613i
$127$	6.43575	−	16.9697i	0.571081	−	1.50582i	−0.268883	−	0.963173i	$-0.586654\pi$
$127$	6.43575	−	16.9697i	0.571081	−	1.50582i	0.839963	−	0.542643i	$-0.182576\pi$
$128$	−4.35119	−	8.29050i	−0.384594	−	0.732783i
$129$	2.28007	+	3.30325i	0.200749	+	0.290835i
$130$	0.786803	−	4.21939i	0.0690072	−	0.370065i
$131$	8.40698	−	12.1796i	0.734521	−	1.06414i	−0.260597	−	0.965448i	$-0.583919\pi$
$131$	8.40698	−	12.1796i	0.734521	−	1.06414i	0.995118	−	0.0986903i	$-0.0314653\pi$
$132$	4.44412	+	0.539613i	0.386811	+	0.0469673i
$133$	−3.55163	−	0.875397i	−0.307965	−	0.0759066i
$134$	−0.153041	−	0.221718i	−0.0132207	−	0.0191535i
$135$	2.32134	+	2.62025i	0.199789	+	0.225516i
$136$	0.536030	−	1.02132i	0.0459642	−	0.0875774i
$137$	8.21709	−	0.997736i	0.702034	−	0.0852423i	0.238267	−	0.971200i	$-0.423421\pi$
$137$	8.21709	−	0.997736i	0.702034	−	0.0852423i	0.463767	+	0.885957i	$0.346498\pi$
$138$	−2.68110	−	0.325544i	−0.228230	−	0.0277122i
$139$	1.06758	−	0.945795i	0.0905511	−	0.0802213i	−0.616633	−	0.787251i	$-0.711504\pi$
$139$	1.06758	−	0.945795i	0.0905511	−	0.0802213i	0.707184	+	0.707030i	$0.249965\pi$
$140$	−11.1717	+	16.1850i	−0.944183	+	1.36789i
$141$	7.80420	−	0.947602i	0.657232	−	0.0798025i
$142$	−0.191290	+	1.57541i	−0.0160527	+	0.132206i
$143$	1.51783	+	8.43032i	0.126927	+	0.704979i
$144$	0.400125	+	3.29533i	0.0333438	+	0.274611i
$145$	−3.75749	−	15.2447i	−0.312043	−	1.26601i
$146$	−3.05291			−0.252661
$147$	1.88846			0.155758
$148$	−1.21332	−	4.92263i	−0.0997342	−	0.404637i
$149$	8.38955	+	3.18174i	0.687299	+	0.260658i	0.673436	−	0.739246i	$-0.264818\pi$
$149$	8.38955	+	3.18174i	0.687299	+	0.260658i	0.0138631	+	0.999904i	$0.495587\pi$
$150$		−	2.46692i		−	0.201423i
$151$	7.90918	−	2.99956i	0.643640	−	0.244100i	−0.0111190	−	0.999938i	$-0.503539\pi$
$151$	7.90918	−	2.99956i	0.643640	−	0.244100i	0.654759	+	0.755838i	$0.272770\pi$
$152$	1.57358	+	0.387852i	0.127634	+	0.0314590i
$153$	−0.653609	+	0.579047i	−0.0528412	+	0.0468132i
$154$	−0.576421	+	2.33863i	−0.0464493	+	0.188452i
$155$	25.4765	−	22.5702i	2.04632	−	1.81289i
$156$	−6.20423	+	2.76913i	−0.496736	+	0.221708i
$157$	4.57166	+	4.05014i	0.364858	+	0.323236i	0.825555	−	0.564321i	$-0.190862\pi$
$157$	4.57166	+	4.05014i	0.364858	+	0.323236i	−0.460697	+	0.887558i	$0.652400\pi$
$158$	4.52725	−	3.12494i	0.360169	−	0.248607i
$159$	5.25317	−	1.29479i	0.416604	−	0.102684i
$160$	7.49827	−	10.8631i	0.592791	−	0.858805i
$161$	−5.66657	+	22.9902i	−0.446588	+	1.81188i
$162$	−0.0813816	+	0.330178i	−0.00639394	+	0.0259412i
$163$	−14.7282	−	1.78833i	−1.15360	−	0.140073i	−0.478699	−	0.877979i	$-0.658892\pi$
$163$	−14.7282	−	1.78833i	−1.15360	−	0.140073i	−0.674903	+	0.737906i	$0.735815\pi$
$164$	4.12617	−	4.65748i	0.322200	−	0.363688i
$165$	2.94910	+	7.77614i	0.229587	+	0.605372i
$166$	−2.63817	+	1.38462i	−0.204762	+	0.107467i
$167$	−16.3406	−	11.2791i	−1.26448	−	0.872805i	−0.268576	−	0.963259i	$-0.586553\pi$
$167$	−16.3406	−	11.2791i	−1.26448	−	0.872805i	−0.995901	+	0.0904534i	$0.971168\pi$
$168$	−3.93811			−0.303832
$169$	−8.55990	−	9.78407i	−0.658454	−	0.752621i
$170$	1.03949			0.0797253
$171$	−1.00975	−	0.696977i	−0.0772172	−	0.0532992i
$172$	−6.69701	+	3.51486i	−0.510642	+	0.268006i
$173$	8.22692	+	21.6926i	0.625481	+	1.64926i	0.753469	+	0.657483i	$0.228379\pi$
$173$	8.22692	+	21.6926i	0.625481	+	1.64926i	−0.127988	+	0.991776i	$0.540852\pi$
$174$	1.01142	−	1.14165i	0.0766754	−	0.0865486i
$175$	−21.4701	−	2.60694i	−1.62299	−	0.197066i
$176$	−1.88733	+	7.65719i	−0.142263	+	0.577182i
$177$	1.71976	−	6.97736i	0.129265	−	0.524450i
$178$	−1.59403	+	2.30935i	−0.119478	+	0.173093i
$179$	1.91578	−	0.472198i	0.143192	−	0.0352937i	−0.167068	−	0.985945i	$-0.553430\pi$
$179$	1.91578	−	0.472198i	0.143192	−	0.0352937i	0.310260	+	0.950652i	$0.399584\pi$
$180$	−5.42876	+	3.74720i	−0.404636	+	0.279300i
$181$	1.42377	+	1.26135i	0.105828	+	0.0937552i	0.714378	−	0.699761i	$-0.246710\pi$
$181$	1.42377	+	1.26135i	0.105828	+	0.0937552i	−0.608550	+	0.793516i	$0.708248\pi$
$182$	−1.07665	−	3.49329i	−0.0798064	−	0.258940i
$183$	2.39127	−	2.11848i	0.176768	−	0.156603i
$184$	2.51062	−	10.1860i	0.185086	−	0.750922i
$185$	7.04990	−	6.24567i	0.518319	−	0.459191i
$186$	3.21030	+	0.791268i	0.235391	+	0.0580185i
$187$	−1.93972	+	0.735639i	−0.141846	+	0.0537952i
$188$			14.8139i			1.08042i
$189$	2.78761	+	1.05720i	0.202769	+	0.0769002i
$190$	0.349536	+	1.41812i	0.0253580	+	0.102882i
$191$	22.7287			1.64459			0.822295	−	0.569061i	$-0.192693\pi$
$191$	22.7287			1.64459			0.822295	+	0.569061i	$0.192693\pi$
$192$	−5.35681			−0.386594
$193$	3.55554	+	14.4254i	0.255933	+	1.03836i	0.948442	+	0.316952i	$0.102659\pi$
$193$	3.55554	+	14.4254i	0.255933	+	1.03836i	−0.692509	+	0.721410i	$0.743495\pi$
$194$	−0.709925	−	5.84676i	−0.0509696	−	0.419773i
$195$	−9.91132	−	7.81489i	−0.709764	−	0.559636i
$196$	−0.428935	+	3.53260i	−0.0306382	+	0.252329i
$197$	2.84727	−	0.345721i	0.202860	−	0.0246316i	−0.0184760	−	0.999829i	$-0.505881\pi$
$197$	2.84727	−	0.345721i	0.202860	−	0.0246316i	0.221336	+	0.975198i	$0.428958\pi$
$198$	−0.458937	+	0.664885i	−0.0326152	+	0.0472513i
$199$	11.9740	−	10.6080i	0.848814	−	0.751984i	−0.121818	−	0.992552i	$-0.538872\pi$
$199$	11.9740	−	10.6080i	0.848814	−	0.751984i	0.970632	+	0.240569i	$0.0773339\pi$
$200$	9.51252	+	1.15503i	0.672637	+	0.0816729i
$201$	−0.786458	+	0.0954933i	−0.0554725	+	0.00673558i
$202$	1.12086	−	2.13561i	0.0788631	−	0.150261i
$203$	−8.86725	−	10.0091i	−0.622359	−	0.702498i
$204$	−0.934720	−	1.35418i	−0.0654435	−	0.0948113i
$205$	11.2235	+	2.76634i	0.783882	+	0.193210i
$206$	−0.828673	−	0.100619i	−0.0577364	−	0.00701046i
$207$	−4.51163	+	6.53623i	−0.313580	+	0.454299i
$208$	−3.52518	−	11.4378i	−0.244427	−	0.793070i
$209$	−1.65584	−	2.39890i	−0.114537	−	0.165935i
$210$	−1.64933	−	3.14254i	−0.113815	−	0.216856i
$211$	−0.266923	+	0.703819i	−0.0183758	+	0.0484529i	−0.943890	−	0.330259i	$-0.892864\pi$
$211$	−0.266923	+	0.703819i	−0.0183758	+	0.0484529i	0.925514	+	0.378712i	$0.123633\pi$
$212$	1.22889	+	10.1208i	0.0844002	+	0.695098i
$213$	3.84068	+	2.65103i	0.263159	+	0.181646i
$214$	1.05526	+	4.28137i	0.0721364	+	0.292669i
$215$	−11.5634	−	7.98166i	−0.788619	−	0.544345i
$216$	−1.23508	−	0.468403i	−0.0840363	−	0.0318708i
$217$	10.2791	−	27.1038i	0.697791	−	1.83992i
$218$	−5.85680	−	3.07388i	−0.396672	−	0.208190i
$219$	−4.17209	+	7.94926i	−0.281924	+	0.537161i
$220$	−15.2161	+	3.75042i	−1.02587	+	0.252853i
$221$	1.94938	−	2.47233i	0.131130	−	0.166307i
$222$	0.888358	+	0.218961i	0.0596227	+	0.0146957i
$223$	−4.47928	+	5.05607i	−0.299955	+	0.338579i	−0.879093	−	0.476650i	$-0.841851\pi$
$223$	−4.47928	+	5.05607i	−0.299955	+	0.338579i	0.579138	+	0.815230i	$0.303389\pi$
$224$	1.35504	−	11.1597i	0.0905371	−	0.745640i
$225$	−6.42342	−	3.37127i	−0.428228	−	0.224751i
$226$	−2.15266	−	4.10155i	−0.143193	−	0.272831i
$227$	−25.3272	+	9.60533i	−1.68102	+	0.637528i	−0.995863	−	0.0908648i	$-0.971037\pi$
$227$	−25.3272	+	9.60533i	−1.68102	+	0.637528i	−0.685160	+	0.728393i	$0.740268\pi$
$228$	1.53313	−	1.73054i	0.101534	−	0.114608i
$229$	7.02455	−	0.852935i	0.464195	−	0.0563635i	0.114902	−	0.993377i	$-0.463345\pi$
$229$	7.02455	−	0.852935i	0.464195	−	0.0563635i	0.349294	+	0.937013i	$0.386422\pi$
$230$	9.17972	−	2.26260i	0.605293	−	0.149191i
$231$	5.30165	+	4.69685i	0.348823	+	0.309030i
$232$	3.92871	+	4.43460i	0.257932	+	0.291146i
$233$	−4.70327	−	2.46847i	−0.308121	−	0.161715i	0.303574	−	0.952808i	$-0.401820\pi$
$233$	−4.70327	−	2.46847i	−0.308121	−	0.161715i	−0.611696	+	0.791093i	$0.709512\pi$
$234$	0.0778361	−	1.22363i	0.00508830	−	0.0799912i
$235$	−24.3679	+	12.7893i	−1.58959	+	0.834281i
$236$	12.6614	+	4.80182i	0.824185	+	0.312572i
$237$	−1.94988	−	16.0587i	−0.126658	−	1.04312i
$238$	0.783891	−	0.411418i	0.0508121	−	0.0266683i
$239$			1.90582i			0.123277i	0.998099	+	0.0616386i	$0.0196326\pi$
$239$			1.90582i			0.123277i	−0.998099	+	0.0616386i	$0.980367\pi$
$240$	−5.40028	−	10.2894i	−0.348586	−	0.664176i
$241$	−0.993168	−	1.12106i	−0.0639756	−	0.0722135i	0.715652	−	0.698457i	$-0.246130\pi$
$241$	−0.993168	−	1.12106i	−0.0639756	−	0.0722135i	−0.779627	+	0.626244i	$0.784591\pi$
$242$	1.49890	−	1.03462i	0.0963532	−	0.0665078i
$243$	0.748511	+	0.663123i	0.0480170	+	0.0425393i
$244$	3.41973	+	4.95434i	0.218926	+	0.317169i
$245$	−6.18121	+	2.34422i	−0.394903	+	0.149767i
$246$	0.398189	+	1.04994i	0.0253876	+	0.0669416i
$247$	4.02837	+	1.82811i	0.256319	+	0.116320i
$248$	−4.55424	+	12.0086i	−0.289195	+	0.762544i
$249$			8.76154i			0.555240i
$250$	0.951630	+	2.50924i	0.0601864	+	0.158698i
$251$	0.386298	−	3.18145i	0.0243829	−	0.200811i	−0.975427	−	0.220324i	$-0.929288\pi$
$251$	0.386298	−	3.18145i	0.0243829	−	0.200811i	0.999810	+	0.0195128i	$0.00621151\pi$
$252$	−2.61079	+	4.97444i	−0.164464	+	0.313360i
$253$	−15.5284	+	10.7185i	−0.976263	+	0.673866i
$254$	−5.07927	+	3.50597i	−0.318702	+	0.219984i
$255$	1.42056	−	2.70665i	0.0889590	−	0.169497i
$256$	0.907599	−	7.47475i	0.0567249	−	0.467172i
$257$	4.16754	+	10.9889i	0.259964	+	0.685469i	0.999918	+	0.0128115i	$0.00407815\pi$
$257$	4.16754	+	10.9889i	0.259964	+	0.685469i	−0.739954	+	0.672658i	$0.765153\pi$
$258$		−	1.36491i		−	0.0849758i
$259$	2.84445	−	7.50019i	0.176745	−	0.466039i
$260$	16.8699	−	16.7653i	1.04623	−	1.03974i
$261$	−1.59047	−	4.19373i	−0.0984478	−	0.259586i
$262$	−4.70562	+	1.78461i	−0.290714	+	0.110253i
$263$	8.75043	+	12.6772i	0.539575	+	0.781709i	0.994035	−	0.109058i	$-0.0347833\pi$
$263$	8.75043	+	12.6772i	0.539575	+	0.781709i	−0.454461	+	0.890767i	$0.650168\pi$
$264$	−2.34894	−	2.08098i	−0.144567	−	0.128076i
$265$	−15.5871	+	10.7590i	−0.957507	+	0.660919i
$266$	0.824865	+	0.931081i	0.0505757	+	0.0570882i
$267$	3.83475	+	7.30651i	0.234683	+	0.447151i
$268$		−	1.49285i		−	0.0911906i
$269$	18.4351	−	9.67547i	1.12401	−	0.589924i	0.202886	−	0.979202i	$-0.434968\pi$
$269$	18.4351	−	9.67547i	1.12401	−	0.589924i	0.921120	+	0.389278i	$0.127276\pi$
$270$	−0.143489	−	1.18174i	−0.00873248	−	0.0719185i
$271$	−14.8917	−	5.64767i	−0.904605	−	0.343071i	−0.141948	−	0.989874i	$-0.545336\pi$
$271$	−14.8917	−	5.64767i	−0.904605	−	0.343071i	−0.762657	+	0.646803i	$0.776106\pi$
$272$	2.56663	−	1.34707i	0.155625	−	0.0816783i
$273$	−10.5673	−	1.97051i	−0.639560	−	0.119261i
$274$	−2.49240	−	1.30811i	−0.150572	−	0.0790261i
$275$	−11.4286	−	12.9002i	−0.689170	−	0.777912i
$276$	−11.2021	−	9.92415i	−0.674284	−	0.597364i
$277$	−15.9278	+	3.92586i	−0.957011	+	0.235882i	−0.686741	−	0.726903i	$-0.740959\pi$
$277$	−15.9278	+	3.92586i	−0.957011	+	0.235882i	−0.270270	+	0.962785i	$0.587113\pi$
$278$	−0.481482	+	0.0584625i	−0.0288774	+	0.00350635i
$279$	6.44749	−	7.27772i	0.386001	−	0.435705i
$280$	12.8900	−	4.88853i	0.770324	−	0.292145i
$281$	−11.4091	−	21.7383i	−0.680613	−	1.29680i	−0.943307	−	0.331920i	$-0.892303\pi$
$281$	−11.4091	−	21.7383i	−0.680613	−	1.29680i	0.262695	−	0.964879i	$-0.415389\pi$
$282$	−2.36717	−	1.24238i	−0.140963	−	0.0739829i
$283$	−2.57025	+	21.1679i	−0.152786	+	1.25830i	0.691487	+	0.722389i	$0.256956\pi$
$283$	−2.57025	+	21.1679i	−0.152786	+	1.25830i	−0.844273	+	0.535914i	$0.819967\pi$
$284$	−5.83142	+	6.58231i	−0.346031	+	0.390588i
$285$	4.17022	+	1.02787i	0.247023	+	0.0608856i
$286$	1.20375	−	2.65255i	0.0711792	−	0.156848i
$287$	9.55863	−	2.35599i	0.564228	−	0.139070i
$288$	1.75232	−	3.33876i	0.103256	−	0.196738i
$289$	−14.3776	−	7.54594i	−0.845741	−	0.443879i
$290$	−1.89333	+	4.99231i	−0.111180	+	0.293158i
$291$	−16.1941	−	6.14162i	−0.949316	−	0.360028i
$292$	−13.9224	−	9.60995i	−0.814748	−	0.562380i
$293$	−1.68174	−	6.82309i	−0.0982483	−	0.398609i	0.901142	−	0.433524i	$-0.142730\pi$
$293$	−1.68174	−	6.82309i	−0.0982483	−	0.398609i	−0.999390	+	0.0349151i	$0.988884\pi$
$294$	−0.528513	−	0.364806i	−0.0308235	−	0.0212759i
$295$	3.03223	+	24.9727i	0.176543	+	1.45397i
$296$	−1.26026	+	3.32303i	−0.0732510	+	0.193147i
$297$	1.10406	+	2.10362i	0.0640643	+	0.122064i
$298$	−1.73330	−	2.51111i	−0.100407	−	0.145465i
$299$	11.8336	−	26.0762i	0.684355	−	1.50803i
$300$	7.76534	−	11.2500i	0.448332	−	0.649521i
$301$	−11.8791	−	1.44239i	−0.684703	−	0.0831380i
$302$	−2.79293	−	0.688396i	−0.160715	−	0.0396128i
$303$	−4.02901	−	5.83703i	−0.231460	−	0.335328i
$304$	2.70079	+	3.04856i	0.154901	+	0.174847i
$305$	−5.19721	+	9.90245i	−0.297591	+	0.567013i
$306$	0.294779	−	0.0357927i	0.0168514	−	0.00204613i
$307$	25.8136	+	3.13434i	1.47326	+	0.178886i	0.817432	−	0.576024i	$-0.195397\pi$
$307$	25.8136	+	3.13434i	1.47326	+	0.178886i	0.655828	+	0.754911i	$0.272320\pi$
$308$	−9.99022	+	8.85056i	−0.569245	+	0.504307i
$309$	−1.39445	+	2.02021i	−0.0793276	+	0.114926i
$310$	−11.4900	+	1.39514i	−0.652587	+	0.0792384i
$311$	1.01767	−	8.38124i	0.0577066	−	0.475256i	−0.934995	−	0.354661i	$-0.884596\pi$
$311$	1.01767	−	8.38124i	0.0577066	−	0.475256i	0.992702	−	0.120596i	$-0.0384805\pi$
$312$	4.68192	+	0.873052i	0.265061	+	0.0494268i
$313$	−2.19035	−	18.0392i	−0.123806	−	1.01963i	−0.913700	−	0.406390i	$-0.866787\pi$
$313$	−2.19035	−	18.0392i	−0.123806	−	1.01963i	0.789894	−	0.613244i	$-0.210136\pi$
$314$	−0.497053	−	2.01662i	−0.0280503	−	0.113805i
$315$	−10.4366			−0.588035
$316$	30.4826			1.71478
$317$	−4.99435	−	20.2629i	−0.280511	−	1.13808i	−0.926972	−	0.375130i	$-0.877598\pi$
$317$	−4.99435	−	20.2629i	−0.280511	−	1.13808i	0.646461	−	0.762947i	$-0.276248\pi$
$318$	−1.72029	−	0.652421i	−0.0964693	−	0.0365860i
$319$		−	10.6557i		−	0.596604i
$320$	17.5336	−	6.64961i	0.980157	−	0.371724i
$321$	12.5901	+	3.10317i	0.702709	+	0.173202i
$322$	6.02702	−	5.33947i	0.335873	−	0.297557i
$323$	−0.256396	+	1.04024i	−0.0142663	+	0.0578806i
$324$	−1.41046	+	1.24956i	−0.0783591	+	0.0694201i
$325$	24.9473	+	7.85910i	1.38383	+	0.435945i
$326$	3.77643	+	3.34562i	0.209157	+	0.185297i
$327$	−16.0077	+	11.0493i	−0.885229	+	0.611029i
$328$	−4.23503	+	1.04384i	−0.233841	+	0.0576365i
$329$	−13.3143	+	19.2891i	−0.734040	+	1.06344i
$330$	0.676817	−	2.74596i	0.0372576	−	0.151160i
$331$	−8.08585	+	32.8056i	−0.444439	+	1.80316i	0.138173	+	0.990408i	$0.455877\pi$
$331$	−8.08585	+	32.8056i	−0.444439	+	1.80316i	−0.582612	+	0.812750i	$0.697969\pi$
$332$	−16.3895	−	1.99005i	−0.899491	−	0.109218i
$333$	1.78416	−	2.01390i	0.0977714	−	0.110361i
$334$	2.39429	+	6.31324i	0.131010	+	0.345445i
$335$	2.45565	−	1.28882i	0.134166	−	0.0704160i
$336$	−8.14481	−	5.62196i	−0.444336	−	0.306703i
$337$	−29.5544			−1.60993			−0.804967	−	0.593320i	$-0.797817\pi$
$337$	−29.5544			−1.60993			−0.804967	+	0.593320i	$0.797817\pi$
$338$	0.505559	+	4.39177i	0.0274988	+	0.238881i
$339$	−13.6215			−0.739820
$340$	4.74046	+	3.27210i	0.257088	+	0.177455i
$341$	20.4533	−	10.7347i	1.10761	−	0.581318i
$342$	0.147952	+	0.390117i	0.00800032	+	0.0210951i
$343$	10.1055	−	11.4068i	0.545647	−	0.615908i
$344$	5.26316	+	0.639063i	0.283771	+	0.0344560i
$345$	6.65353	−	26.9944i	0.358214	−	1.45333i
$346$	1.88807	−	7.66022i	0.101504	−	0.411816i
$347$	−5.41528	+	7.84539i	−0.290708	+	0.421163i	−0.940940	−	0.338572i	$-0.890056\pi$
$347$	−5.41528	+	7.84539i	−0.290708	+	0.421163i	0.650233	+	0.759735i	$0.274671\pi$
$348$	8.20613	−	2.02263i	0.439895	−	0.108424i
$349$	20.8913	−	14.4202i	1.11828	−	0.771896i	0.142319	−	0.989821i	$-0.454544\pi$
$349$	20.8913	−	14.4202i	1.11828	−	0.771896i	0.975966	+	0.217925i	$0.0699288\pi$
$350$	5.50511	+	4.87710i	0.294260	+	0.260692i
$351$	−3.07975	−	1.87488i	−0.164385	−	0.100073i
$352$	6.70526	−	5.94035i	0.357392	−	0.316621i
$353$	−3.01083	+	12.2154i	−0.160251	+	0.650162i	0.834779	+	0.550585i	$0.185595\pi$
$353$	−3.01083	+	12.2154i	−0.160251	+	0.650162i	−0.995030	+	0.0995772i	$0.968251\pi$
$354$	−1.82916	+	1.62049i	−0.0972186	+	0.0861282i
$355$	−15.8619	−	3.90961i	−0.841862	−	0.207500i
$356$	−14.5387	+	5.51381i	−0.770551	+	0.292231i
$357$		−	2.60336i		−	0.137784i
$358$	−0.627375	−	0.237932i	−0.0331578	−	0.0125751i
$359$	0.0195289	+	0.0792320i	0.00103070	+	0.00418171i	0.971455	−	0.237224i	$-0.0762376\pi$
$359$	0.0195289	+	0.0792320i	0.00103070	+	0.00418171i	−0.970424	+	0.241406i	$0.922391\pi$
$360$	4.62402			0.243707
$361$	17.4946			0.920770
$362$	−0.154799	−	0.628043i	−0.00813604	−	0.0330092i
$363$	−0.645575	−	5.31679i	−0.0338839	−	0.279059i
$364$	6.08627	−	19.3198i	0.319007	−	1.01263i
$365$	3.78812	−	31.1980i	0.198279	−	1.63298i
$366$	−1.07847	+	0.130950i	−0.0563725	+	0.00684486i
$367$	10.2801	−	14.8933i	0.536617	−	0.777425i	−0.457091	−	0.889420i	$-0.651109\pi$
$367$	10.2801	−	14.8933i	0.536617	−	0.777425i	0.993709	+	0.111995i	$0.0357241\pi$
$368$	19.7338	−	17.4826i	1.02869	−	0.911344i
$369$	3.27802	+	0.398023i	0.170647	+	0.0207203i
$370$	−3.17953	+	0.386064i	−0.165296	+	0.0200705i
$371$	−7.49611	+	14.2826i	−0.389179	+	0.741518i
$372$	12.1494	+	13.7138i	0.629917	+	0.711029i
$373$	17.0883	+	24.7566i	0.884798	+	1.28185i	0.958652	+	0.284582i	$0.0918546\pi$
$373$	17.0883	+	24.7566i	0.884798	+	1.28185i	−0.0738543	+	0.997269i	$0.523530\pi$
$374$	0.684965	+	0.168829i	0.0354187	+	0.00872992i
$375$	7.83412	+	0.951235i	0.404552	+	0.0491215i
$376$	5.89901	−	8.54619i	0.304218	−	0.440736i
$377$	8.32311	+	13.8653i	0.428662	+	0.714100i
$378$	−0.575926	−	0.834372i	−0.0296224	−	0.0429155i
$379$	0.325751	+	0.620667i	0.0167327	+	0.0318815i	0.893679	−	0.448707i	$-0.148115\pi$
$379$	0.325751	+	0.620667i	0.0167327	+	0.0318815i	−0.876946	+	0.480589i	$0.840423\pi$
$380$	−2.86995	+	7.56744i	−0.147225	+	0.388201i
$381$	2.18763	+	18.0168i	0.112076	+	0.923026i
$382$	−6.36093	−	4.39063i	−0.325454	−	0.224644i
$383$	6.33514	+	25.7027i	0.323710	+	1.31334i	0.877054	+	0.480392i	$0.159506\pi$
$383$	6.33514	+	25.7027i	0.323710	+	1.31334i	−0.553344	+	0.832953i	$0.686648\pi$
$384$	7.70557	+	5.31877i	0.393223	+	0.271422i
$385$	−23.1834	−	8.79231i	−1.18154	−	0.448098i
$386$	1.79157	−	4.72398i	0.0911885	−	0.240444i
$387$	−3.55400	−	1.86528i	−0.180660	−	0.0948176i
$388$	15.1669	−	28.8981i	0.769981	−	1.46708i
$389$	9.98124	−	2.46015i	0.506069	−	0.124735i	0.0219883	−	0.999758i	$-0.493000\pi$
$389$	9.98124	−	2.46015i	0.506069	−	0.124735i	0.484081	+	0.875023i	$0.339154\pi$
$390$	1.26417	+	4.10173i	0.0640137	+	0.207699i
$391$	6.73363	+	1.65969i	0.340534	+	0.0839342i
$392$	1.65416	−	1.86716i	0.0835477	−	0.0943058i
$393$	−1.78386	+	14.6914i	−0.0899840	+	0.741085i
$394$	−0.863632	−	0.453269i	−0.0435092	−	0.0228354i
$395$	26.3165	+	50.1419i	1.32413	+	2.52291i
$396$	−4.18584	+	1.58748i	−0.210346	+	0.0797739i
$397$	−10.2892	+	11.6141i	−0.516398	+	0.582893i	−0.947639	−	0.319344i	$-0.896537\pi$
$397$	−10.2892	+	11.6141i	−0.516398	+	0.582893i	0.431241	+	0.902237i	$0.358076\pi$
$398$	−5.40030	+	0.655716i	−0.270693	+	0.0328681i
$399$	3.55163	−	0.875397i	0.177804	−	0.0438247i
$400$	18.0249	+	15.9687i	0.901246	+	0.798435i
$401$	−12.2078	−	13.7797i	−0.609627	−	0.688127i	0.359933	−	0.932978i	$-0.382799\pi$
$401$	−12.2078	−	13.7797i	−0.609627	−	0.688127i	−0.969561	+	0.244851i	$0.921261\pi$
$402$	0.238548	+	0.125200i	0.0118977	+	0.00624439i
$403$	−18.2293	+	29.9442i	−0.908065	+	1.49162i
$404$	11.8340	−	6.21095i	0.588763	−	0.309007i
$405$	−3.27314	−	1.24134i	−0.162644	−	0.0616826i
$406$	0.548112	+	4.51411i	0.0272023	+	0.224031i
$407$	5.65987	−	2.97053i	0.280549	−	0.147244i
$408$			1.15344i			0.0571038i
$409$	−6.79179	−	12.9407i	−0.335832	−	0.639875i	0.657718	−	0.753264i	$-0.271522\pi$
$409$	−6.79179	−	12.9407i	−0.335832	−	0.639875i	−0.993551	+	0.113389i	$0.963829\pi$
$410$	−2.60665	−	2.94231i	−0.128734	−	0.145310i
$411$	−6.81221	+	4.70213i	−0.336021	+	0.231939i
$412$	−3.46232	−	3.06735i	−0.170576	−	0.151118i
$413$	12.1705	+	17.6320i	0.598872	+	0.867616i
$414$	2.52528	−	0.957714i	0.124111	−	0.0470691i
$415$	−10.8760	−	28.6777i	−0.533883	−	1.40773i
$416$	−4.08500	+	12.9671i	−0.200284	+	0.635765i
$417$	−0.505764	+	1.33359i	−0.0247674	+	0.0653062i
$418$			0.991233i			0.0484828i
$419$	14.2555	+	37.5887i	0.696427	+	1.83633i	0.524940	+	0.851140i	$0.324088\pi$
$419$	14.2555	+	37.5887i	0.696427	+	1.83633i	0.171487	+	0.985186i	$0.445143\pi$
$420$	2.37051	−	19.5229i	0.115669	−	0.952620i
$421$	−15.5394	+	29.6078i	−0.757342	+	1.44300i	0.134625	+	0.990897i	$0.457017\pi$
$421$	−15.5394	+	29.6078i	−0.757342	+	1.44300i	−0.891968	+	0.452099i	$0.850675\pi$
$422$	0.210663	−	0.145410i	0.0102549	−	0.00707846i
$423$	−6.46991	+	4.46585i	−0.314578	+	0.217137i
$424$	3.32122	−	6.32805i	0.161293	−	0.307317i
$425$	−0.763552	+	6.28841i	−0.0370377	+	0.305033i
$426$	−0.562752	−	1.48385i	−0.0272654	−	0.0718930i
$427$			9.52454i			0.460925i
$428$	−8.66449	+	22.8464i	−0.418814	+	1.10432i
$429$	−5.26174	−	6.75931i	−0.254039	−	0.326342i
$430$	1.69432	+	4.46755i	0.0817073	+	0.215444i
$431$	−12.3134	+	4.66986i	−0.593116	+	0.224939i	−0.632854	−	0.774271i	$-0.718117\pi$
$431$	−12.3134	+	4.66986i	−0.593116	+	0.224939i	0.0397385	+	0.999210i	$0.487348\pi$
$432$	−1.88571	−	2.73192i	−0.0907261	−	0.131440i
$433$	−9.01892	−	7.99006i	−0.433422	−	0.383978i	0.418011	−	0.908442i	$-0.362727\pi$
$433$	−9.01892	−	7.99006i	−0.433422	−	0.383978i	−0.851433	+	0.524464i	$0.824266\pi$
$434$	−8.11254	+	5.59968i	−0.389414	+	0.268793i
$435$	10.4117	+	11.7524i	0.499202	+	0.563482i
$436$	−17.0332	−	32.4540i	−0.815742	−	1.55427i
$437$			9.74443i			0.466139i
$438$	2.70322	−	1.41876i	0.129165	−	0.0677910i
$439$	−1.25866	−	10.3660i	−0.0600727	−	0.494743i	−0.991430	−	0.130637i	$-0.958298\pi$
$439$	−1.25866	−	10.3660i	−0.0600727	−	0.494743i	0.931357	−	0.364106i	$-0.118625\pi$
$440$	10.2716	+	3.89551i	0.489680	+	0.185711i
$441$	−1.67215	+	0.877613i	−0.0796263	+	0.0417911i
$442$	−1.02316	+	0.315341i	−0.0486666	+	0.0149992i
$443$	8.98341	+	4.71486i	0.426815	+	0.224010i	0.664431	−	0.747349i	$-0.268674\pi$
$443$	8.98341	+	4.71486i	0.426815	+	0.224010i	−0.237617	+	0.971359i	$0.576366\pi$
$444$	3.36200	+	3.79491i	0.159553	+	0.180099i
$445$	−21.6215	−	19.1550i	−1.02496	−	0.908035i
$446$	2.23030	−	0.549719i	0.105608	−	0.0260300i
$447$	−8.90721	+	1.08153i	−0.421296	+	0.0511546i
$448$	10.5904	−	11.9541i	0.500350	−	0.564779i
$449$	−32.3068	+	12.2524i	−1.52465	+	0.578225i	−0.967652	−	0.252287i	$-0.918817\pi$
$449$	−32.3068	+	12.2524i	−1.52465	+	0.578225i	−0.557001	+	0.830512i	$0.688048\pi$
$450$	1.14643	+	2.18434i	0.0540434	+	0.102971i
$451$	6.94634	+	3.64572i	0.327090	+	0.171670i
$452$	3.09392	−	25.4807i	0.145526	−	1.19851i
$453$	−5.60927	+	6.33156i	−0.263546	+	0.297482i
$454$	8.94367	+	2.20442i	0.419747	+	0.103458i
$455$	37.0342	−	6.66779i	1.73619	−	0.312591i
$456$	−1.57358	+	0.387852i	−0.0736896	+	0.0181628i
$457$	−3.03601	+	5.78463i	−0.142018	+	0.270594i	−0.946068	−	0.323969i	$-0.894983\pi$
$457$	−3.03601	+	5.78463i	−0.142018	+	0.270594i	0.804049	+	0.594563i	$0.202675\pi$
$458$	−2.13068	−	1.11827i	−0.0995603	−	0.0522533i
$459$	0.309646	−	0.816468i	0.0144530	−	0.0381095i
$460$	48.9851	+	18.5776i	2.28394	+	0.866185i
$461$	−20.6587	−	14.2597i	−0.962172	−	0.664139i	−0.0201875	−	0.999796i	$-0.506426\pi$
$461$	−20.6587	−	14.2597i	−0.962172	−	0.664139i	−0.941984	+	0.335657i	$0.891042\pi$
$462$	−0.576421	−	2.33863i	−0.0268175	−	0.108803i
$463$	−7.93053	−	5.47405i	−0.368563	−	0.254401i	0.369359	−	0.929287i	$-0.379577\pi$
$463$	−7.93053	−	5.47405i	−0.368563	−	0.254401i	−0.737922	+	0.674886i	$0.764193\pi$
$464$	1.79464	+	14.7802i	0.0833141	+	0.686153i
$465$	−12.0694	+	31.8245i	−0.559707	+	1.47583i
$466$	0.839426	+	1.59939i	0.0388856	+	0.0740904i
$467$	−6.16018	−	8.92456i	−0.285059	−	0.412979i	0.654129	−	0.756383i	$-0.273035\pi$
$467$	−6.16018	−	8.92456i	−0.285059	−	0.412979i	−0.939188	+	0.343404i	$0.888420\pi$
$468$	4.20670	−	5.33519i	0.194455	−	0.246619i
$469$	1.34173	−	1.94383i	0.0619553	−	0.0897578i
$470$	9.29028	+	1.12804i	0.428529	+	0.0520328i
$471$	−5.93020	−	1.46166i	−0.273249	−	0.0673499i
$472$	−5.39225	−	7.81203i	−0.248199	−	0.359578i
$473$	−6.32330	−	7.13753i	−0.290746	−	0.328184i
$474$	−2.55645	+	4.87091i	−0.117422	+	0.223728i
$475$	−8.83571	+	1.07285i	−0.405410	+	0.0492257i
$476$	4.86989	+	0.591312i	0.223211	+	0.0271027i
$477$	−4.04973	+	3.58775i	−0.185425	+	0.164272i
$478$	0.368158	−	0.533369i	0.0168392	−	0.0243957i
$479$	9.50278	−	1.15385i	0.434193	−	0.0527206i	0.0994777	−	0.995040i	$-0.468283\pi$
$479$	9.50278	−	1.15385i	0.434193	−	0.0527206i	0.334716	+	0.942319i	$0.391360\pi$
$480$	−1.59105	+	13.1034i	−0.0726210	+	0.598087i
$481$	−5.04443	+	8.28619i	−0.230006	+	0.377818i
$482$	0.0613908	+	0.505599i	0.00279628	+	0.0230294i
$483$	−5.66657	−	22.9902i	−0.257838	−	1.04609i
$484$	10.0923			0.458742
$485$	60.6294			2.75304
$486$	−0.0813816	−	0.330178i	−0.00369154	−	0.0149772i
$487$	32.1465	+	12.1915i	1.45670	+	0.552452i	0.950708	−	0.310089i	$-0.100359\pi$
$487$	32.1465	+	12.1915i	1.45670	+	0.552452i	0.505988	+	0.862540i	$0.331128\pi$
$488$		−	4.21993i		−	0.191027i
$489$	13.8723	−	5.26106i	0.627326	−	0.237913i
$490$	2.18274	+	0.537998i	0.0986063	+	0.0243043i
$491$	−20.3721	+	18.0481i	−0.919381	+	0.814501i	−0.983025	−	0.183472i	$-0.941266\pi$
$491$	−20.3721	+	18.0481i	−0.919381	+	0.814501i	0.0636439	+	0.997973i	$0.479728\pi$
$492$	−1.48910	+	6.04152i	−0.0671338	+	0.272373i
$493$	−2.93157	+	2.59714i	−0.132031	+	0.116969i
$494$	−0.774247	−	1.28980i	−0.0348350	−	0.0580311i
$495$	−6.22505	−	5.51492i	−0.279795	−	0.247877i
$496$	−26.5623	+	18.3346i	−1.19268	+	0.823248i
$497$	−13.5090	+	3.32967i	−0.605962	+	0.149356i
$498$	1.69252	−	2.45204i	0.0758435	−	0.109878i
$499$	−2.09761	+	8.51034i	−0.0939019	+	0.380975i	−0.999024	−	0.0441773i	$-0.985933\pi$
$499$	−2.09761	+	8.51034i	−0.0939019	+	0.380975i	0.905122	+	0.425152i	$0.139779\pi$
$500$	−3.55880	+	14.4386i	−0.159154	+	0.645714i
$501$	19.7106	+	2.39330i	0.880604	+	0.106925i
$502$	−0.722691	+	0.815749i	−0.0322553	+	0.0364087i
$503$	−4.69857	−	12.3891i	−0.209499	−	0.552403i	0.788541	−	0.614982i	$-0.210837\pi$
$503$	−4.69857	−	12.3891i	−0.209499	−	0.552403i	−0.998040	+	0.0625788i	$0.980068\pi$
$504$	3.48702	−	1.83013i	0.155324	−	0.0815205i
$505$	20.4332	+	14.1040i	0.909267	+	0.627621i
$506$	6.41639			0.285243
$507$	12.1263	+	4.68538i	0.538548	+	0.208085i
$508$	−34.1994			−1.51735
$509$	15.0246	+	10.3707i	0.665952	+	0.459674i	0.852469	−	0.522778i	$-0.175104\pi$
$509$	15.0246	+	10.3707i	0.665952	+	0.459674i	−0.186517	+	0.982452i	$0.559720\pi$
$510$	−0.920423	+	0.483075i	−0.0407570	+	0.0213909i
$511$	−9.49112	−	25.0260i	−0.419863	−	1.10709i
$512$	−14.1155	+	15.9331i	−0.623824	+	0.704152i
$513$	1.21799	+	0.147890i	0.0537754	+	0.00652952i
$514$	0.956449	−	3.88047i	0.0421871	−	0.171160i
$515$	2.05647	−	8.34343i	0.0906189	−	0.367655i
$516$	4.29647	−	6.22451i	0.189141	−	0.274019i
$517$	−18.1343	+	4.46969i	−0.797543	+	0.196577i
$518$	−2.24491	+	1.54955i	−0.0986359	+	0.0680834i
$519$	−17.3656	−	15.3846i	−0.762267	−	0.675310i
$520$	−16.4083	+	2.95422i	−0.719553	+	0.129551i
$521$	−14.5757	+	12.9129i	−0.638572	+	0.565725i	−0.919053	−	0.394134i	$-0.871044\pi$
$521$	−14.5757	+	12.9129i	−0.638572	+	0.565725i	0.280481	+	0.959860i	$0.409506\pi$
$522$	−0.365013	+	1.48091i	−0.0159762	+	0.0648179i
$523$	28.3406	−	25.1076i	1.23925	−	1.09788i	0.247605	−	0.968861i	$-0.420356\pi$
$523$	28.3406	−	25.1076i	1.23925	−	1.09788i	0.991642	−	0.129017i	$-0.0411820\pi$
$524$	−27.0769	−	6.67386i	−1.18286	−	0.291549i
$525$	20.2223	−	7.66933i	0.882576	−	0.334717i
$526$		−	5.23826i		−	0.228399i
$527$	−7.93846	−	3.01066i	−0.345805	−	0.131146i
$528$	−1.88733	−	7.65719i	−0.0821354	−	0.333236i
$529$	40.0771			1.74248
$530$	6.44064			0.279763
$531$	1.71976	+	6.97736i	0.0746314	+	0.302792i
$532$	0.830839	+	6.84258i	0.0360215	+	0.296663i
$533$	−11.8863	+	0.681895i	−0.514854	+	0.0295362i
$534$	0.338234	−	2.78561i	0.0146368	−	0.120545i
$535$	−45.0611	+	5.47141i	−1.94816	+	0.236550i
$536$	−0.594465	+	0.861231i	−0.0256770	+	0.0371995i
$537$	−1.47690	+	1.30842i	−0.0637329	+	0.0564624i
$538$	−7.02837	−	0.853399i	−0.303015	−	0.0367926i
$539$	−4.45380	+	0.540789i	−0.191839	+	0.0232934i
$540$	3.06551	−	5.84085i	0.131919	−	0.251350i
$541$	6.16484	+	6.95867i	0.265047	+	0.299176i	0.865935	−	0.500157i	$-0.166724\pi$
$541$	6.16484	+	6.95867i	0.265047	+	0.299176i	−0.600887	+	0.799334i	$0.705186\pi$
$542$	3.07665	+	4.45729i	0.132153	+	0.191457i
$543$	−1.84686	−	0.455210i	−0.0792564	−	0.0195349i
$544$	−3.26859	−	0.396878i	−0.140140	−	0.0170160i
$545$	38.6795	−	56.0370i	1.65685	−	2.40036i
$546$	2.57674	+	2.59282i	0.110274	+	0.110962i
$547$	8.88232	+	12.8683i	0.379781	+	0.550207i	0.965532	−	0.260283i	$-0.0838160\pi$
$547$	8.88232	+	12.8683i	0.379781	+	0.550207i	−0.585752	+	0.810491i	$0.699201\pi$
$548$	−7.24861	−	13.8111i	−0.309645	−	0.589979i
$549$	−1.13286	+	2.98710i	−0.0483492	+	0.127486i
$550$	0.706437	+	5.81803i	0.0301226	+	0.248082i
$551$	−4.52891	−	3.12608i	−0.192938	−	0.133176i
$552$	2.51062	+	10.1860i	0.106859	+	0.433545i
$553$	39.6911	+	27.3968i	1.68784	+	1.16503i
$554$	5.21600	+	1.97817i	0.221607	+	0.0840443i
$555$	−3.33987	+	8.80652i	−0.141770	+	0.373816i
$556$	−2.37976	−	1.24900i	−0.100924	−	0.0529693i
$557$	−1.57655	+	3.00386i	−0.0668004	+	0.127278i	−0.916566	−	0.399883i	$-0.869051\pi$
$557$	−1.57655	+	3.00386i	−0.0668004	+	0.127278i	0.849766	+	0.527160i	$0.176743\pi$
$558$	−3.21030	+	0.791268i	−0.135903	+	0.0334970i
$559$	13.8030	+	4.34834i	0.583807	+	0.183915i
$560$	33.6379	+	8.29099i	1.42146	+	0.350358i
$561$	1.37567	−	1.55281i	0.0580808	−	0.0655596i
$562$	−1.00631	+	8.28774i	−0.0424488	+	0.349597i
$563$	−19.7623	−	10.3721i	−0.832884	−	0.437131i	−0.00632382	−	0.999980i	$-0.502013\pi$
$563$	−19.7623	−	10.3721i	−0.832884	−	0.437131i	−0.826560	+	0.562849i	$0.809705\pi$
$564$	−6.88438	−	13.1171i	−0.289885	−	0.552329i
$565$	44.5851	−	16.9089i	1.87571	−	0.711363i
$566$	4.80846	−	5.42762i	0.202114	−	0.228140i
$567$	−2.95962	+	0.359362i	−0.124292	+	0.0150918i
$568$	5.98528	−	1.47524i	0.251137	−	0.0618997i
$569$	−7.70598	−	6.82690i	−0.323051	−	0.286198i	0.485973	−	0.873974i	$-0.338465\pi$
$569$	−7.70598	−	6.82690i	−0.323051	−	0.286198i	−0.809024	+	0.587775i	$0.800004\pi$
$570$	−0.968534	−	1.09325i	−0.0405674	−	0.0457912i
$571$	15.0413	+	7.89426i	0.629457	+	0.330365i	0.749104	−	0.662452i	$-0.230484\pi$
$571$	15.0413	+	7.89426i	0.629457	+	0.330365i	−0.119647	+	0.992816i	$0.538176\pi$
$572$	13.8392	−	8.30744i	0.578647	−	0.347352i
$573$	−20.1253	+	10.5625i	−0.840744	+	0.441257i
$574$	−3.13023	−	1.18714i	−0.130653	−	0.0495503i
$575$	6.94471	+	57.1948i	0.289614	+	2.38519i
$576$	4.74322	−	2.48943i	0.197634	−	0.103726i
$577$		−	4.58427i		−	0.190846i	−0.995437	−	0.0954229i	$-0.969580\pi$
$577$		−	4.58427i		−	0.190846i	0.995437	−	0.0954229i	$-0.0304203\pi$
$578$	2.56607	+	4.88924i	0.106734	+	0.203366i
$579$	−9.85208	−	11.1207i	−0.409438	−	0.462160i
$580$	−24.3490	+	16.8069i	−1.01104	+	0.697870i
$581$	−19.5520	−	17.3216i	−0.811155	−	0.718620i
$582$	3.34573	+	4.84713i	0.138685	+	0.200920i
$583$	−12.0184	+	4.55798i	−0.497752	+	0.188772i
$584$	4.20512	+	11.0880i	0.174009	+	0.458825i
$585$	12.4078	+	2.31372i	0.512999	+	0.0956605i
$586$	−0.847398	+	2.23441i	−0.0350057	+	0.0923024i
$587$		−	28.6139i		−	1.18102i	−0.807030	−	0.590510i	$-0.798927\pi$
$587$		−	28.6139i		−	1.18102i	0.807030	−	0.590510i	$-0.201073\pi$
$588$	−1.26188	−	3.32730i	−0.0520390	−	0.137215i
$589$	1.43793	−	11.8424i	0.0592488	−	0.487957i
$590$	3.97551	−	7.57470i	0.163669	−	0.311845i
$591$	−2.36047	+	1.62931i	−0.0970967	+	0.0670210i
$592$	−7.35034	+	5.07358i	−0.302097	+	0.208523i
$593$	−7.33996	+	13.9851i	−0.301416	+	0.574300i	−0.988310	−	0.152458i	$-0.951281\pi$
$593$	−7.33996	+	13.9851i	−0.301416	+	0.574300i	0.686894	+	0.726757i	$0.258974\pi$
$594$	0.0973810	−	0.802005i	0.00399559	−	0.0329066i
$595$	3.23164	+	8.52115i	0.132485	+	0.349333i
$596$		−	16.9077i		−	0.692564i
$597$	−5.67265	+	14.9575i	−0.232166	+	0.612172i
$598$	−8.34909	+	5.01181i	−0.341420	+	0.204948i
$599$	14.5444	+	38.3504i	0.594268	+	1.56696i	0.807445	+	0.589943i	$0.200850\pi$
$599$	14.5444	+	38.3504i	0.594268	+	1.56696i	−0.213177	+	0.977014i	$0.568381\pi$
$600$	−8.95969	+	3.39796i	−0.365778	+	0.138721i
$601$	−6.04267	−	8.75432i	−0.246486	−	0.357096i	0.680139	−	0.733083i	$-0.261919\pi$
$601$	−6.04267	−	8.75432i	−0.246486	−	0.357096i	−0.926625	+	0.375987i	$0.877304\pi$
$602$	3.04591	+	2.69844i	0.124142	+	0.109980i
$603$	0.651996	−	0.450041i	0.0265513	−	0.0183271i
$604$	−10.5699	−	11.9309i	−0.430082	−	0.485462i
$605$	8.71299	+	16.6012i	0.354233	+	0.674935i
$606$			2.41188i			0.0979759i
$607$	−40.4672	+	21.2388i	−1.64251	+	0.862058i	−0.647527	+	0.762042i	$0.724197\pi$
$607$	−40.4672	+	21.2388i	−1.64251	+	0.862058i	−0.994986	+	0.100015i	$0.968111\pi$
$608$	−0.557645	−	4.59262i	−0.0226155	−	0.186255i
$609$	12.5030	+	4.74176i	0.506647	+	0.192146i
$610$	3.36743	−	1.76736i	0.136343	−	0.0715584i
$611$	20.1053	−	19.9806i	0.813372	−	0.808328i
$612$	1.45697	+	0.764677i	0.0588946	+	0.0309103i
$613$	3.54573	+	4.00230i	0.143211	+	0.161651i	0.815739	−	0.578420i	$-0.196330\pi$
$613$	3.54573	+	4.00230i	0.143211	+	0.161651i	−0.672529	+	0.740071i	$0.734792\pi$
$614$	−6.61881	−	5.86375i	−0.267113	−	0.236642i
$615$	−11.2235	+	2.76634i	−0.452575	+	0.111550i
$616$	9.28773	−	1.12773i	0.374213	−	0.0454377i
$617$	29.5054	−	33.3047i	1.18784	−	1.34080i	0.261004	−	0.965338i	$-0.415946\pi$
$617$	29.5054	−	33.3047i	1.18784	−	1.34080i	0.926839	−	0.375460i	$-0.122515\pi$
$618$	0.780513	−	0.296010i	0.0313968	−	0.0119073i
$619$	10.8262	+	20.6275i	0.435140	+	0.829089i	0.999992	+	0.00389770i	$0.00124068\pi$
$619$	10.8262	+	20.6275i	0.435140	+	0.829089i	−0.564853	+	0.825192i	$0.691067\pi$
$620$	−56.7902	−	29.8058i	−2.28075	−	1.19703i
$621$	0.957316	−	7.88420i	0.0384158	−	0.316382i
$622$	−1.90386	+	2.14902i	−0.0763379	+	0.0861677i
$623$	−23.8864	−	5.88746i	−0.956986	−	0.235876i
$624$	8.43681	+	8.48945i	0.337743	+	0.339850i
$625$	8.39483	−	2.06914i	0.335793	−	0.0827656i
$626$	−2.87173	+	5.47163i	−0.114778	+	0.218690i
$627$	2.58100	+	1.35461i	0.103075	+	0.0540980i
$628$	4.08117	−	10.7612i	0.162856	−	0.429417i
$629$	−2.19674	−	0.833115i	−0.0875899	−	0.0332185i
$630$	2.92082	+	2.01610i	0.116368	+	0.0803233i
$631$	10.3432	+	41.9639i	0.411755	+	1.67055i	0.700892	+	0.713267i	$0.252785\pi$
$631$	10.3432	+	41.9639i	0.411755	+	1.67055i	−0.289138	+	0.957288i	$0.593369\pi$
$632$	−17.5855	−	12.1384i	−0.699512	−	0.482839i
$633$	−0.0907321	−	0.747246i	−0.00360628	−	0.0297004i
$634$	−2.51656	+	6.63563i	−0.0999455	+	0.263535i
$635$	−29.5253	−	56.2558i	−1.17168	−	2.23244i
$636$	−5.79148	−	8.39041i	−0.229647	−	0.332702i
$637$	5.37293	−	4.18252i	0.212883	−	0.165718i
$638$	−2.05842	+	2.98214i	−0.0814937	+	0.118064i
$639$	−4.63275	−	0.562517i	−0.183269	−	0.0222528i
$640$	−31.8238	−	7.84386i	−1.25795	−	0.310056i
$641$	−13.0679	−	18.9321i	−0.516150	−	0.747773i	0.475077	−	0.879944i	$-0.342420\pi$
$641$	−13.0679	−	18.9321i	−0.516150	−	0.747773i	−0.991227	+	0.132172i	$0.957805\pi$
$642$	−2.92404	−	3.30056i	−0.115403	−	0.130263i
$643$	−8.52337	+	16.2399i	−0.336129	+	0.640440i	−0.993589	−	0.113049i	$-0.963938\pi$
$643$	−8.52337	+	16.2399i	−0.336129	+	0.640440i	0.657460	+	0.753489i	$0.271631\pi$
$644$	44.2930	−	5.37814i	1.74539	−	0.211928i
$645$	13.9482	+	1.69361i	0.549209	+	0.0666860i
$646$	0.272706	−	0.241596i	0.0107295	−	0.00950547i
$647$	27.0525	−	39.1923i	1.06354	−	1.54081i	0.242326	−	0.970195i	$-0.422090\pi$
$647$	27.0525	−	39.1923i	1.06354	−	1.54081i	0.821218	−	0.570615i	$-0.193295\pi$
$648$	1.31128	−	0.159219i	0.0515121	−	0.00625470i
$649$	−2.05786	+	16.9480i	−0.0807783	+	0.665269i
$650$	−5.46366	−	7.01870i	−0.214302	−	0.275296i
$651$	3.49405	+	28.7761i	0.136943	+	1.12783i
$652$	6.69057	+	27.1447i	0.262023	+	1.06307i
$653$	−18.7360			−0.733195			−0.366598	−	0.930380i	$-0.619477\pi$
$653$	−18.7360			−0.733195			−0.366598	+	0.930380i	$0.619477\pi$
$654$	6.61444			0.258645
$655$	−12.3982	−	50.3015i	−0.484438	−	1.96544i
$656$	−10.2491	−	3.88696i	−0.400159	−	0.151760i
$657$		−	8.97758i		−	0.350249i
$658$	7.45237	−	2.82631i	0.290524	−	0.110181i
$659$	−13.8557	−	3.41513i	−0.539742	−	0.133034i	−0.0399852	−	0.999200i	$-0.512731\pi$
$659$	−13.8557	−	3.41513i	−0.539742	−	0.133034i	−0.499757	+	0.866166i	$0.666577\pi$
$660$	11.7302	−	10.3921i	0.456599	−	0.404511i
$661$	7.54156	−	30.5973i	0.293333	−	1.19010i	−0.620565	−	0.784155i	$-0.713097\pi$
$661$	7.54156	−	30.5973i	0.293333	−	1.19010i	0.913898	−	0.405943i	$-0.133057\pi$
$662$	8.60019	−	7.61910i	0.334256	−	0.296125i
$663$	−0.577146	+	3.09506i	−0.0224145	+	0.120202i
$664$	8.66269	+	7.67448i	0.336178	+	0.297827i
$665$	−10.5383	+	7.27407i	−0.408658	+	0.282076i
$666$	−0.888358	+	0.218961i	−0.0344232	+	0.00848455i
$667$	−20.2356	+	29.3163i	−0.783524	+	1.13513i
$668$	−8.95391	+	36.3274i	−0.346437	+	1.40555i
$669$	1.61654	−	6.55855i	0.0624990	−	0.253568i
$670$	−0.936216	−	0.113677i	−0.0361692	−	0.00439173i
$671$	−5.03297	+	5.68105i	−0.194296	+	0.219314i
$672$	3.98636	+	10.5112i	0.153777	+	0.405477i
$673$	−40.8509	+	21.4402i	−1.57469	+	0.826459i	−0.574719	+	0.818351i	$0.694889\pi$
$673$	−40.8509	+	21.4402i	−1.57469	+	0.826459i	−0.999967	+	0.00810809i	$0.997419\pi$
$674$	8.27122	+	5.70921i	0.318595	+	0.219910i
$675$	7.25436			0.279220
$676$	−11.5189	+	21.6195i	−0.443033	+	0.831519i
$677$	−8.57253			−0.329469			−0.164735	−	0.986338i	$-0.552677\pi$
$677$	−8.57253			−0.329469			−0.164735	+	0.986338i	$0.552677\pi$
$678$	3.81217	+	2.63135i	0.146405	+	0.101056i
$679$	45.7213	−	23.9964i	1.75462	−	0.920896i
$680$	−1.43181	−	3.77537i	−0.0549073	−	0.144779i
$681$	17.9623	−	20.2752i	0.688316	−	0.776948i
$682$	−7.79783	−	0.946828i	−0.298594	−	0.0362559i
$683$	−8.34050	+	33.8387i	−0.319140	+	1.29480i	0.564032	+	0.825753i	$0.309250\pi$
$683$	−8.34050	+	33.8387i	−0.319140	+	1.29480i	−0.883172	+	0.469050i	$0.844597\pi$
$684$	−0.553293	+	2.24480i	−0.0211557	+	0.0858321i
$685$	16.4604	−	23.8470i	0.628918	−	0.911145i
$686$	−5.03168	+	1.24020i	−0.192110	+	0.0473510i
$687$	−5.82355	+	4.01971i	−0.222182	+	0.153361i
$688$	9.97297	+	8.83528i	0.380216	+	0.336842i
$689$	12.0783	−	15.3184i	0.460146	−	0.583586i
$690$	−7.07676	+	6.26946i	−0.269408	+	0.238674i
$691$	5.45799	−	22.1439i	0.207632	−	0.842395i	−0.771010	−	0.636823i	$-0.780248\pi$
$691$	5.45799	−	22.1439i	0.207632	−	0.842395i	0.978642	−	0.205572i	$-0.0659055\pi$
$692$	32.7231	−	28.9901i	1.24395	−	1.10204i
$693$	−6.87712	−	1.69506i	−0.261240	−	0.0643899i
$694$	3.03108	−	1.14954i	0.115058	−	0.0436358i
$695$		−	4.99285i		−	0.189390i
$696$	−5.53956	−	2.10088i	−0.209977	−	0.0796336i
$697$	−0.690050	−	2.79964i	−0.0261375	−	0.106044i
$698$	−8.63235			−0.326739
$699$	5.31169			0.200907
$700$	9.75320	+	39.5703i	0.368636	+	1.49562i
$701$	1.63575	+	13.4716i	0.0617815	+	0.508816i	0.990447	+	0.137897i	$0.0440343\pi$
$701$	1.63575	+	13.4716i	0.0617815	+	0.508816i	−0.928665	+	0.370919i	$0.879043\pi$
$702$	0.499729	+	1.11964i	0.0188610	+	0.0422582i
$703$	0.397905	−	3.27705i	0.0150073	−	0.123596i
$704$	12.6336	−	1.53400i	0.476147	−	0.0578147i
$705$	15.6333	−	22.6487i	0.588783	−	0.852999i
$706$	3.20235	−	2.83703i	0.120522	−	0.106773i
$707$	20.9911	+	2.54878i	0.789452	+	0.0958569i
$708$	−13.4426	+	1.63223i	−0.505204	+	0.0613429i
$709$	10.7892	−	20.5571i	0.405197	−	0.772039i	−0.594283	−	0.804256i	$-0.702564\pi$
$709$	10.7892	−	20.5571i	0.405197	−	0.772039i	0.999481	+	0.0322164i	$0.0102566\pi$
$710$	3.68393	+	4.15830i	0.138255	+	0.156058i
$711$	9.18937	+	13.3131i	0.344628	+	0.499280i
$712$	10.5831	+	2.60849i	0.396617	+	0.0977572i
$713$	−76.6575	−	9.30791i	−2.87085	−	0.348584i
$714$	−0.502906	+	0.728585i	−0.0188208	+	0.0272666i
$715$	25.6130	+	15.5926i	0.957871	+	0.583129i
$716$	−2.11210	−	3.05990i	−0.0789329	−	0.114354i
$717$	−0.885678	−	1.68752i	−0.0330762	−	0.0630215i
$718$	0.00984028	−	0.0259467i	0.000367236	−	0.000968322i
$719$	−0.669496	−	5.51380i	−0.0249680	−	0.205630i	0.974886	−	0.222703i	$-0.0714882\pi$
$719$	−0.669496	−	5.51380i	−0.0249680	−	0.205630i	−0.999854	+	0.0170735i	$0.994565\pi$
$720$	9.56342	+	6.60115i	0.356408	+	0.246010i
$721$	−1.75142	−	7.10579i	−0.0652263	−	0.264634i
$722$	−4.89611	−	3.37954i	−0.182214	−	0.125774i
$723$	1.40039	+	0.531097i	0.0520810	+	0.0197517i
$724$	1.27101	−	3.35138i	0.0472367	−	0.124553i
$725$	−28.8103	−	15.1208i	−1.06999	−	0.561573i
$726$	−0.846402	+	1.61268i	−0.0314129	+	0.0598523i
$727$	−37.4635	+	9.23391i	−1.38944	+	0.342467i	−0.861907	−	0.507066i	$-0.830730\pi$
$727$	−37.4635	+	9.23391i	−1.38944	+	0.342467i	−0.527536	+	0.849533i	$0.676884\pi$
$728$	−11.2044	+	8.72203i	−0.415264	+	0.323260i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−7.08686	+	7.99941i	−0.262296	+	0.296071i
$731$	−0.422464	+	3.47930i	−0.0156254	+	0.128687i
$732$	−5.33042	−	2.79762i	−0.197018	−	0.103403i
$733$	−4.57341	−	8.71390i	−0.168923	−	0.321855i	0.786248	−	0.617911i	$-0.212021\pi$
$733$	−4.57341	−	8.71390i	−0.168923	−	0.321855i	−0.955171	+	0.296056i	$0.904329\pi$
$734$	−5.75406	+	2.18223i	−0.212386	+	0.0805475i
$735$	4.38377	−	4.94826i	0.161698	−	0.182519i
$736$	−29.7287	+	3.60972i	−1.09581	+	0.133056i
$737$	1.82746	−	0.450427i	0.0673152	−	0.0165917i
$738$	−0.840509	−	0.744626i	−0.0309396	−	0.0274101i
$739$	−30.4905	−	34.4166i	−1.12161	−	1.26604i	−0.960250	−	0.279141i	$-0.909950\pi$
$739$	−30.4905	−	34.4166i	−1.12161	−	1.26604i	−0.161360	−	0.986896i	$-0.551588\pi$
$740$	−15.7151	−	8.24790i	−0.577697	−	0.303199i
$741$	−4.41651	+	0.253366i	−0.162244	+	0.00930765i
$742$	4.85695	−	2.54913i	0.178304	−	0.0935813i
$743$	19.4836	+	7.38916i	0.714785	+	0.271082i	0.685071	−	0.728476i	$-0.259771\pi$
$743$	19.4836	+	7.38916i	0.714785	+	0.271082i	0.0297137	+	0.999558i	$0.490540\pi$
$744$	−1.54807	−	12.7495i	−0.0567550	−	0.467420i
$745$	27.8120	−	14.5969i	1.01895	−	0.534787i
$746$		−	10.2295i		−	0.374530i
$747$	−4.07169	−	7.75796i	−0.148975	−	0.283849i
$748$	2.59225	+	2.92605i	0.0947822	+	0.106987i
$749$	−31.8156	+	21.9607i	−1.16251	+	0.802426i
$750$	−2.00873	−	1.77958i	−0.0733485	−	0.0649811i
$751$	−4.74343	−	6.87205i	−0.173090	−	0.250765i	0.726832	−	0.686816i	$-0.240992\pi$
$751$	−4.74343	−	6.87205i	−0.173090	−	0.250765i	−0.899922	+	0.436051i	$0.856377\pi$
$752$	24.4007	−	9.25396i	0.889802	−	0.337457i
$753$	1.13644	+	2.99656i	0.0414143	+	0.109201i
$754$	0.349110	−	5.48822i	0.0127138	−	0.199869i
$755$	10.5003	−	27.6871i	0.382146	−	1.00764i
$756$		−	5.61794i		−	0.204323i
$757$	8.91802	+	23.5149i	0.324131	+	0.854663i	0.993716	+	0.111928i	$0.0357026\pi$
$757$	8.91802	+	23.5149i	0.324131	+	0.854663i	−0.669585	+	0.742735i	$0.733528\pi$
$758$	0.0287320	−	0.236629i	0.00104359	−	0.00859476i
$759$	8.76860	−	16.7072i	0.318280	−	0.606432i
$760$	4.66909	−	3.22284i	0.169366	−	0.116905i
$761$	−31.2671	+	21.5821i	−1.13343	+	0.782350i	−0.978637	−	0.205597i	$-0.934086\pi$
$761$	−31.2671	+	21.5821i	−1.13343	+	0.782350i	−0.154793	+	0.987947i	$0.549471\pi$
$762$	2.86816	−	5.46483i	0.103903	−	0.197970i
$763$	6.98990	−	57.5670i	0.253051	−	2.08406i
$764$	−15.1874	−	40.0458i	−0.549460	−	1.44881i
$765$			3.05679i			0.110518i
$766$	3.19216	−	8.41704i	0.115337	−	0.304120i
$767$	−10.5603	−	23.6604i	−0.381311	−	0.854327i
$768$	2.67005	+	7.04034i	0.0963471	+	0.254046i
$769$	17.5469	−	6.65464i	0.632756	−	0.239973i	−0.0173105	−	0.999850i	$-0.505510\pi$
$769$	17.5469	−	6.65464i	0.632756	−	0.239973i	0.650066	+	0.759878i	$0.274741\pi$
$770$	4.78973	+	6.93913i	0.172610	+	0.250069i
$771$	−8.79698	−	7.79344i	−0.316815	−	0.280674i
$772$	23.0403	−	15.9036i	0.829240	−	0.572383i
$773$	15.5306	+	17.5304i	0.558597	+	0.630525i	0.958178	−	0.286172i	$-0.0923830\pi$
$773$	15.5306	+	17.5304i	0.558597	+	0.630525i	−0.399582	+	0.916698i	$0.630845\pi$
$774$	0.634307	+	1.20857i	0.0227997	+	0.0434412i
$775$		−	70.5336i		−	2.53364i
$776$	−20.2572	+	10.6318i	−0.727191	+	0.381659i
$777$	0.966880	+	7.96297i	0.0346866	+	0.285670i
$778$	−3.26863	−	1.23963i	−0.117186	−	0.0444428i
$779$	3.58738	−	1.88280i	0.128531	−	0.0674583i
$780$	−7.14633	+	22.6847i	−0.255880	+	0.812244i
$781$	−9.81711	−	5.15242i	−0.351284	−	0.184368i
$782$	−1.56389	−	1.76526i	−0.0559245	−	0.0631257i
$783$	3.35722	+	2.97424i	0.119977	+	0.106291i
$784$	6.08665	−	1.50023i	0.217380	−	0.0535795i
$785$	21.2248	−	2.57716i	0.757545	−	0.0919826i
$786$	3.33727	−	3.76700i	0.119036	−	0.134364i
$787$	−17.0815	+	6.47818i	−0.608891	+	0.230922i	−0.639727	−	0.768602i	$-0.720952\pi$
$787$	−17.0815	+	6.47818i	−0.608891	+	0.230922i	0.0308353	+	0.999524i	$0.490183\pi$
$788$	−2.51168	−	4.78561i	−0.0894750	−	0.170480i
$789$	−13.6395	−	7.15857i	−0.485579	−	0.254852i
$790$	2.32117	−	19.1166i	0.0825837	−	0.680138i
$791$	26.9298	−	30.3974i	0.957513	−	1.08081i
$792$	3.04697	+	0.751010i	0.108269	+	0.0266860i
$793$	2.11152	−	11.3235i	0.0749824	−	0.402109i
$794$	5.12312	−	1.26273i	0.181813	−	0.0448128i
$795$	8.80173	−	16.7703i	0.312165	−	0.594781i
$796$	−26.6914	−	14.0087i	−0.946053	−	0.496527i
$797$	−9.81843	+	25.8891i	−0.347786	+	0.917038i	0.640978	+	0.767559i	$0.278529\pi$
$797$	−9.81843	+	25.8891i	−0.347786	+	0.917038i	−0.988765	+	0.149479i	$0.952240\pi$
$798$	−1.16308	−	0.441097i	−0.0411725	−	0.0156147i
$799$	5.64961	+	3.89964i	0.199869	+	0.137959i
$800$	−6.54618	−	26.5589i	−0.231443	−	0.938999i
$801$	−6.79101	−	4.68750i	−0.239949	−	0.165625i
$802$	0.754601	+	6.21470i	0.0266459	+	0.219449i
$803$	7.56317	−	19.9424i	0.266899	−	0.703754i
$804$	0.693764	+	1.32186i	0.0244672	+	0.0466183i
$805$	47.0861	+	68.2159i	1.65957	+	2.40430i
$806$	10.8862	−	4.85882i	0.383450	−	0.171145i
$807$	−11.8270	+	17.1344i	−0.416331	+	0.603160i
$808$	−9.30030	−	1.12926i	−0.327183	−	0.0397272i
$809$	−32.5282	−	8.01748i	−1.14363	−	0.281880i	−0.378404	−	0.925641i	$-0.623527\pi$
$809$	−32.5282	−	8.01748i	−1.14363	−	0.281880i	−0.765227	+	0.643761i	$0.777373\pi$
$810$	0.676236	+	0.979697i	0.0237605	+	0.0344230i
$811$	3.62173	+	4.08809i	0.127176	+	0.143552i	0.808649	−	0.588291i	$-0.200199\pi$
$811$	3.62173	+	4.08809i	0.127176	+	0.143552i	−0.681473	+	0.731843i	$0.738660\pi$
$812$	−11.7099	+	22.3113i	−0.410937	+	0.782975i
$813$	15.8105	−	1.91975i	0.554500	−	0.0673284i
$814$	−2.15783	−	0.262008i	−0.0756318	−	0.00918337i
$815$	−38.8751	+	34.4403i	−1.36174	+	1.20639i
$816$	−1.64662	+	2.38555i	−0.0576434	+	0.0835108i
$817$	−4.88869	+	0.593595i	−0.171034	+	0.0207672i
$818$	−0.599052	+	4.93364i	−0.0209454	+	0.172501i
$819$	10.2726	−	3.16605i	0.358953	−	0.110631i
$820$	−2.62553	−	21.6232i	−0.0916876	−	0.755115i
$821$	2.32548	+	9.43485i	0.0811598	+	0.329278i	0.997461	−	0.0712109i	$-0.0226863\pi$
$821$	2.32548	+	9.43485i	0.0811598	+	0.329278i	−0.916301	+	0.400489i	$0.868840\pi$
$822$	2.81483			0.0981783
$823$	48.3638			1.68586			0.842928	−	0.538027i	$-0.180830\pi$
$823$	48.3638			1.68586			0.842928	+	0.538027i	$0.180830\pi$
$824$	0.775982	+	3.14828i	0.0270326	+	0.109676i
$825$	16.1145	+	6.11144i	0.561036	+	0.212773i
$826$		−	7.28562i		−	0.253499i
$827$	−30.3667	+	11.5166i	−1.05595	+	0.400470i	−0.820638	−	0.571449i	$-0.806381\pi$
$827$	−30.3667	+	11.5166i	−1.05595	+	0.400470i	−0.235315	+	0.971919i	$0.575612\pi$
$828$	14.5309	+	3.58155i	0.504984	+	0.124467i
$829$	−25.7584	+	22.8200i	−0.894626	+	0.792570i	−0.978999	−	0.203865i	$-0.934650\pi$
$829$	−25.7584	+	22.8200i	−0.894626	+	0.792570i	0.0843729	+	0.996434i	$0.473111\pi$
$830$	−2.49604	+	10.1268i	−0.0866389	+	0.351508i
$831$	12.2790	−	10.8782i	0.425952	−	0.377361i
$832$	−15.2408	+	11.8641i	−0.528380	+	0.411314i
$833$	1.23432	+	1.09351i	0.0427666	+	0.0378879i
$834$	0.399162	−	0.275522i	0.0138219	−	0.00954054i
$835$	−67.4864	+	16.6339i	−2.33546	+	0.575640i
$836$	−3.12020	+	4.52039i	−0.107914	+	0.156341i
$837$	−2.32685	+	9.44040i	−0.0804277	+	0.326308i
$838$	3.27163	−	13.2735i	0.113017	−	0.458526i
$839$	17.2464	+	2.09409i	0.595412	+	0.0722961i	0.412695	−	0.910869i	$-0.364588\pi$
$839$	17.2464	+	2.09409i	0.595412	+	0.0722961i	0.182717	+	0.983166i	$0.441511\pi$
$840$	−9.14170	+	10.3188i	−0.315419	+	0.356034i
$841$	3.14995	+	8.30575i	0.108619	+	0.286405i
$842$	10.0684	−	5.28431i	0.346981	−	0.182109i
$843$	20.2046	+	13.9462i	0.695883	+	0.480334i
$844$	1.41842			0.0488241
$845$	−45.5072	−	0.283058i	−1.56550	−	0.00973749i
$846$	2.67339			0.0919129
$847$	13.1411	+	9.07065i	0.451534	+	0.311671i
$848$	15.9027	−	8.34640i	0.546102	−	0.286617i
$849$	−7.56138	−	19.9377i	−0.259506	−	0.684261i
$850$	1.42846	−	1.61240i	0.0489958	−	0.0553048i
$851$	−21.2128	−	2.57570i	−0.727165	−	0.0882938i
$852$	2.10451	−	8.53835i	0.0720994	−	0.292519i
$853$	0.508346	−	2.06244i	0.0174054	−	0.0706166i	−0.961597	−	0.274466i	$-0.911499\pi$
$853$	0.508346	−	2.06244i	0.0174054	−	0.0706166i	0.979002	+	0.203849i	$0.0653452\pi$
$854$	1.83991	−	2.66557i	0.0629605	−	0.0912140i
$855$	−4.17022	+	1.02787i	−0.142619	+	0.0351523i
$856$	14.0962	−	9.72987i	0.481797	−	0.332560i
$857$	−16.3925	−	14.5225i	−0.559957	−	0.496079i	0.335008	−	0.942215i	$-0.391261\pi$
$857$	−16.3925	−	14.5225i	−0.559957	−	0.496079i	−0.894965	+	0.446137i	$0.852800\pi$
$858$	0.166834	+	2.90813i	0.00569560	+	0.0992818i
$859$	−9.04867	+	8.01642i	−0.308737	+	0.273517i	−0.803236	−	0.595661i	$-0.796890\pi$
$859$	−9.04867	+	8.01642i	−0.308737	+	0.273517i	0.494499	+	0.869178i	$0.335352\pi$
$860$	−6.33622	+	25.7071i	−0.216063	+	0.876603i
$861$	−7.36887	+	6.52824i	−0.251130	+	0.222482i
$862$	4.34818	+	1.07173i	0.148100	+	0.0365033i
$863$	9.99673	−	3.79126i	0.340293	−	0.129056i	−0.178538	−	0.983933i	$-0.557137\pi$
$863$	9.99673	−	3.79126i	0.340293	−	0.129056i	0.518831	+	0.854877i	$0.326368\pi$
$864$			3.77067i			0.128281i
$865$	75.9377	+	28.7994i	2.58196	+	0.979208i
$866$	0.980579	+	3.97837i	0.0333214	+	0.135190i
$867$	16.2375			0.551454
$868$	−54.6228			−1.85402
$869$	9.19727	+	37.3148i	0.311996	+	1.26582i
$870$	−0.643578	−	5.30034i	−0.0218193	−	0.179698i
$871$	−2.02608	+	2.01352i	−0.0686512	+	0.0682255i
$872$	−3.09693	+	25.5055i	−0.104875	+	0.863727i
$873$	17.1933	−	2.08765i	0.581906	−	0.0706562i
$874$	1.88239	−	2.72711i	0.0636728	−	0.0922460i
$875$	−17.6108	+	15.6018i	−0.595355	+	0.527438i
$876$	16.7937	+	2.03912i	0.567405	+	0.0688954i
$877$	5.66597	−	0.687973i	0.191326	−	0.0232312i	−0.0243127	−	0.999704i	$-0.507740\pi$
$877$	5.66597	−	0.687973i	0.191326	−	0.0232312i	0.215639	+	0.976473i	$0.430817\pi$
$878$	−1.65021	+	3.14422i	−0.0556920	+	0.106112i
$879$	4.65995	+	5.26000i	0.157176	+	0.177415i
$880$	15.6826	+	22.7202i	0.528662	+	0.765899i
$881$	−1.01624	−	0.250482i	−0.0342381	−	0.00843894i	0.222159	−	0.975010i	$-0.428689\pi$
$881$	−1.01624	−	0.250482i	−0.0342381	−	0.00843894i	−0.256398	+	0.966571i	$0.582536\pi$
$882$	0.637508	+	0.0774075i	0.0214660	+	0.00260645i
$883$	−28.1374	+	40.7641i	−0.946899	+	1.37182i	−0.0186634	+	0.999826i	$0.505941\pi$
$883$	−28.1374	+	40.7641i	−0.946899	+	1.37182i	−0.928235	+	0.371994i	$0.878674\pi$
$884$	−5.65860	−	1.78262i	−0.190319	−	0.0599559i
$885$	−14.2903	−	20.7031i	−0.480363	−	0.695926i
$886$	−1.60333	−	3.05490i	−0.0538650	−	0.102631i
$887$	−15.6573	+	41.2849i	−0.525721	+	1.38621i	0.364722	+	0.931117i	$0.381164\pi$
$887$	−15.6573	+	41.2849i	−0.525721	+	1.38621i	−0.890443	+	0.455096i	$0.849605\pi$
$888$	−0.428384	−	3.52806i	−0.0143756	−	0.118394i
$889$	−44.5307	−	30.7373i	−1.49351	−	1.03090i
$890$	2.35080	+	9.53755i	0.0787988	+	0.319699i
$891$	−1.95520	−	1.34958i	−0.0655017	−	0.0452125i
$892$	11.9014	+	4.51360i	0.398488	+	0.151127i
$893$	−3.42036	+	9.01875i	−0.114458	+	0.301801i
$894$	2.70173	+	1.41798i	0.0903593	+	0.0474242i
$895$	3.20991	−	6.11597i	0.107295	−	0.204434i
$896$	−27.1032	+	6.68033i	−0.905453	+	0.223174i
$897$	1.64008	+	28.5887i	0.0547606	+	0.954548i
$898$	11.4084	+	2.81191i	0.380702	+	0.0938347i
$899$	28.9183	−	32.6420i	0.964479	−	1.08867i
$900$	−1.64771	+	13.5702i	−0.0549238	+	0.452338i
$901$	4.18327	+	2.19555i	0.139365	+	0.0731443i
$902$	−1.23976	−	2.36217i	−0.0412796	−	0.0786517i
$903$	11.1888	−	4.24334i	0.372339	−	0.141210i
$904$	−11.9315	+	13.4679i	−0.396835	+	0.447934i
$905$	6.61010	−	0.802611i	0.219727	−	0.0266797i
$906$	2.79293	−	0.688396i	0.0927890	−	0.0228704i
$907$	16.4373	+	14.5622i	0.545791	+	0.483529i	0.890376	−	0.455227i	$-0.150442\pi$
$907$	16.4373	+	14.5622i	0.545791	+	0.483529i	−0.344585	+	0.938755i	$0.611980\pi$
$908$	33.8474	+	38.2058i	1.12326	+	1.26790i
$909$	6.28011	+	3.29606i	0.208298	+	0.109323i
$910$	−11.6526	−	5.28804i	−0.386279	−	0.175297i
$911$	−11.9193	+	6.25571i	−0.394902	+	0.207261i	−0.650473	−	0.759530i	$-0.725429\pi$
$911$	−11.9193	+	6.25571i	−0.394902	+	0.207261i	0.255570	+	0.966791i	$0.417737\pi$
$912$	−3.80817	−	1.44425i	−0.126101	−	0.0478238i
$913$	−2.50899	−	20.6634i	−0.0830355	−	0.683859i
$914$	1.96712	−	1.03242i	0.0650665	−	0.0341495i
$915$		−	11.1835i		−	0.369714i
$916$	−6.19662	−	11.8067i	−0.204742	−	0.390103i
$917$	−29.2583	−	33.0258i	−0.966195	−	1.09061i
$918$	−0.244381	+	0.168684i	−0.00806576	+	0.00556739i
$919$	−1.35693	−	1.20214i	−0.0447611	−	0.0396549i	0.640446	−	0.768004i	$-0.278750\pi$
$919$	−1.35693	−	1.20214i	−0.0447611	−	0.0396549i	−0.685207	+	0.728349i	$0.740288\pi$
$920$	−20.8619	−	30.2237i	−0.687796	−	0.996445i
$921$	−24.3134	+	9.22086i	−0.801154	+	0.303838i
$922$	3.02699	+	7.98153i	0.0996888	+	0.262858i
$923$	16.7987	−	0.963707i	0.552935	−	0.0317208i
$924$	4.73284	−	12.4795i	0.155699	−	0.410544i
$925$		−	19.5182i		−	0.641753i
$926$	1.16201	+	3.06398i	0.0381861	+	0.100689i
$927$	0.295886	−	2.43684i	0.00971819	−	0.0800365i
$928$	7.85948	−	14.9750i	0.258000	−	0.491578i
$929$	−32.0824	+	22.1449i	−1.05259	+	0.726551i	−0.963020	−	0.269429i	$-0.913165\pi$
$929$	−32.0824	+	22.1449i	−1.05259	+	0.726551i	−0.0895709	+	0.995980i	$0.528550\pi$
$930$	9.52552	−	6.57499i	0.312354	−	0.215603i
$931$	−1.07677	+	2.05162i	−0.0352898	+	0.0672391i
$932$	−1.20647	+	9.93616i	−0.0395192	+	0.325470i
$933$	2.99386	+	7.89415i	0.0980145	+	0.258443i
$934$			3.68766i			0.120664i
$935$	−2.57519	+	6.79023i	−0.0842179	+	0.222064i
$936$	−4.55136	+	1.40275i	−0.148766	+	0.0458502i
$937$	−7.53148	−	19.8589i	−0.246043	−	0.648762i	0.753924	−	0.656962i	$-0.228159\pi$
$937$	−7.53148	−	19.8589i	−0.246043	−	0.648762i	−0.999966	+	0.00820061i	$0.997390\pi$
$938$	−0.751003	+	0.284818i	−0.0245211	+	0.00929963i
$939$	10.3227	+	14.9550i	0.336868	+	0.488037i
$940$	38.8163	+	34.3882i	1.26605	+	1.12162i
$941$	−36.4622	+	25.1681i	−1.18863	+	0.820455i	−0.987269	−	0.159061i	$-0.949153\pi$
$941$	−36.4622	+	25.1681i	−1.18863	+	0.820455i	−0.201366	+	0.979516i	$0.564538\pi$
$942$	1.37729	+	1.55464i	0.0448745	+	0.0506529i
$943$	−12.1876	−	23.2216i	−0.396884	−	0.756199i
$944$		−	23.8547i		−	0.776405i
$945$	9.24114	−	4.85013i	0.300614	−	0.157775i
$946$	0.390863	+	3.21904i	0.0127080	+	0.104660i
$947$	14.4325	+	5.47353i	0.468993	+	0.177866i	0.577769	−	0.816201i	$-0.303924\pi$
$947$	14.4325	+	5.47353i	0.468993	+	0.177866i	−0.108775	+	0.994066i	$0.534693\pi$
$948$	−26.9910	+	14.1660i	−0.876627	+	0.460089i
$949$	5.73565	+	31.8569i	0.186187	+	1.03412i
$950$	2.68004	+	1.40660i	0.0869521	+	0.0456360i
$951$	13.8389	+	15.6209i	0.448758	+	0.506543i
$952$	−2.57399	−	2.28035i	−0.0834234	−	0.0739066i
$953$	−23.2519	+	5.73107i	−0.753202	+	0.185648i	−0.597182	−	0.802106i	$-0.703713\pi$
$953$	−23.2519	+	5.73107i	−0.753202	+	0.185648i	−0.156021	+	0.987754i	$0.549867\pi$
$954$	1.82644	−	0.221770i	0.0591332	−	0.00718007i
$955$	52.7611	−	59.5549i	1.70731	−	1.92715i
$956$	3.35787	−	1.27347i	0.108601	−	0.0411871i
$957$	4.95194	+	9.43514i	0.160074	+	0.304995i
$958$	−2.88238	−	1.51279i	−0.0931254	−	0.0488760i
$959$	2.97460	−	24.4981i	0.0960549	−	0.791084i
$960$	−12.4350	+	14.0362i	−0.401337	+	0.453016i
$961$	61.6891	+	15.2050i	1.98997	+	0.490484i
$962$	3.01245	−	1.34454i	0.0971251	−	0.0433497i
$963$	−12.5901	+	3.10317i	−0.405709	+	0.0999983i
$964$	−1.31156	+	2.49896i	−0.0422424	+	0.0804862i
$965$	46.0518	+	24.1698i	1.48246	+	0.778054i
$966$	−2.85528	+	7.52876i	−0.0918672	+	0.242234i
$967$	−37.3635	−	14.1701i	−1.20153	−	0.455680i	−0.329042	−	0.944315i	$-0.606726\pi$
$967$	−37.3635	−	14.1701i	−1.20153	−	0.455680i	−0.872488	+	0.488635i	$0.837495\pi$
$968$	−5.82228	−	4.01883i	−0.187135	−	0.129170i
$969$	−0.256396	−	1.04024i	−0.00823664	−	0.0334174i
$970$	−16.9680	−	11.7121i	−0.544809	−	0.376054i
$971$	−2.33860	−	19.2601i	−0.0750492	−	0.618086i	−0.980903	−	0.194496i	$-0.937693\pi$
$971$	−2.33860	−	19.2601i	−0.0750492	−	0.618086i	0.905854	−	0.423590i	$-0.139230\pi$
$972$	0.668203	−	1.76191i	0.0214326	−	0.0565132i
$973$	−1.97611	−	3.76516i	−0.0633511	−	0.120706i
$974$	−6.64152	−	9.62190i	−0.212808	−	0.308305i
$975$	−25.7421	+	4.63471i	−0.824406	+	0.148429i
$976$	6.02428	−	8.72767i	0.192832	−	0.279366i
$977$	26.3545	+	3.20001i	0.843154	+	0.102377i	0.530704	−	0.847557i	$-0.321927\pi$
$977$	26.3545	+	3.20001i	0.843154	+	0.102377i	0.312449	+	0.949934i	$0.398850\pi$
$978$	−4.89865	−	1.20741i	−0.156642	−	0.0386087i
$979$	−11.1363	−	16.1337i	−0.355918	−	0.515636i
$980$	8.26060	+	9.32429i	0.263875	+	0.297854i
$981$	9.03925	−	17.2229i	0.288601	−	0.549883i
$982$	9.18788	−	1.11561i	0.293197	−	0.0356006i
$983$	52.3555	+	6.35710i	1.66988	+	0.202760i	0.900141	−	0.435599i	$-0.143463\pi$
$983$	52.3555	+	6.35710i	1.66988	+	0.202760i	0.769739	+	0.638359i	$0.220386\pi$
$984$	3.26484	−	2.89240i	0.104079	−	0.0922062i
$985$	5.70361	−	8.26311i	0.181732	−	0.263285i
$986$	1.32214	−	0.160537i	0.0421057	−	0.00511255i
$987$	2.82514	−	23.2671i	0.0899250	−	0.740599i
$988$	0.529188	−	8.31915i	0.0168357	−	0.264668i
$989$	3.84242	+	31.6452i	0.122182	+	1.00626i
$990$	0.676817	+	2.74596i	0.0215107	+	0.0872722i
$991$	−7.35589			−0.233668			−0.116834	−	0.993151i	$-0.537274\pi$
$991$	−7.35589			−0.233668			−0.116834	+	0.993151i	$0.537274\pi$
$992$	36.6619			1.16402
$993$	−8.08585	−	32.8056i	−0.256597	−	1.04105i
$994$	4.42389	+	1.67776i	0.140317	+	0.0532153i
$995$		−	55.9998i		−	1.77531i
$996$	15.4370	−	5.85449i	0.489140	−	0.185506i
$997$	33.4105	+	8.23494i	1.05812	+	0.260803i	0.729727	−	0.683738i	$-0.239647\pi$
$997$	33.4105	+	8.23494i	1.05812	+	0.260803i	0.328392	+	0.944541i	$0.393493\pi$
$998$	2.23104	−	1.97653i	0.0706222	−	0.0625659i
$999$	−0.643889	+	2.61236i	−0.0203717	+	0.0826514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.b.493.8	yes	192
169.12	even	26	inner	507.2.p.b.181.8	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.b.181.8	✓	192	169.12	even	26	inner
507.2.p.b.493.8	yes	192	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)

\(f(q)\)	\(=\)	\(q+(-0.279864 - 0.193176i) q^{2} +(-0.885456 + 0.464723i) q^{3} +(-0.668203 - 1.76191i) q^{4} +(2.32134 - 2.62025i) q^{5} +(0.337580 + 0.0409897i) q^{6} +(0.713484 - 2.89472i) q^{7} +(-0.316115 + 1.28253i) q^{8} +(0.568065 - 0.822984i) q^{9} +O(q^{10})\)	\(q+(-0.279864 - 0.193176i) q^{2} +(-0.885456 + 0.464723i) q^{3} +(-0.668203 - 1.76191i) q^{4} +(2.32134 - 2.62025i) q^{5} +(0.337580 + 0.0409897i) q^{6} +(0.713484 - 2.89472i) q^{7} +(-0.316115 + 1.28253i) q^{8} +(0.568065 - 0.822984i) q^{9} +(-1.15583 + 0.284886i) q^{10} +(1.95520 - 1.34958i) q^{11} +(1.41046 + 1.24956i) q^{12} +(-1.48998 + 3.28328i) q^{13} +(-0.758869 + 0.672299i) q^{14} +(-0.837754 + 3.39890i) q^{15} +(-2.48470 + 2.20126i) q^{16} +(-0.847839 - 0.208974i) q^{17} +(-0.317961 + 0.120587i) q^{18} -1.22693i q^{19} +(-6.16777 - 2.33913i) q^{20} +(0.713484 + 2.89472i) q^{21} -0.807895 q^{22} -7.94211 q^{23} +(-0.316115 - 1.28253i) q^{24} +(-0.874416 - 7.20147i) q^{25} +(1.05124 - 0.631043i) q^{26} +(-0.120537 + 0.992709i) q^{27} +(-5.57698 + 0.677168i) q^{28} +(2.54788 - 3.69125i) q^{29} +(0.891043 - 0.789395i) q^{30} +(9.65204 + 1.17197i) q^{31} +(3.74317 - 0.454504i) q^{32} +(-1.10406 + 2.10362i) q^{33} +(0.196911 + 0.222266i) q^{34} +(-5.92866 - 8.58915i) q^{35} +(-1.82960 - 0.450957i) q^{36} +(2.67093 + 0.324309i) q^{37} +(-0.237014 + 0.343374i) q^{38} +(-0.206504 - 3.59963i) q^{39} +(2.62674 + 3.80550i) q^{40} +(1.53456 + 2.92386i) q^{41} +(0.359512 - 0.947955i) q^{42} +(-0.483804 - 3.98448i) q^{43} +(-3.68430 - 2.54309i) q^{44} +(-0.837754 - 3.39890i) q^{45} +(2.22271 + 1.53422i) q^{46} +(-7.35065 - 2.78773i) q^{47} +(1.17712 - 3.10381i) q^{48} +(-1.67215 - 0.877613i) q^{49} +(-1.14643 + 2.18434i) q^{50} +(0.847839 - 0.208974i) q^{51} +(6.78045 + 0.431310i) q^{52} +(-5.25317 - 1.29479i) q^{53} +(0.225501 - 0.254538i) q^{54} +(1.00245 - 8.25595i) q^{55} +(3.48702 + 1.83013i) q^{56} +(0.570184 + 1.08639i) q^{57} +(-1.42612 + 0.540856i) q^{58} +(-4.76532 + 5.37893i) q^{59} +(6.54834 - 0.795112i) q^{60} +(-3.10187 + 0.764543i) q^{61} +(-2.47486 - 2.19253i) q^{62} +(-1.97700 - 2.23157i) q^{63} +(4.74322 + 2.48943i) q^{64} +(5.14428 + 11.5258i) q^{65} +(0.715356 - 0.375448i) q^{66} +(0.740752 + 0.280930i) q^{67} +(0.198337 + 1.63345i) q^{68} +(7.03239 - 3.69088i) q^{69} +3.54906i q^{70} +(-2.16876 - 4.13222i) q^{71} +(0.875928 + 0.988718i) q^{72} +(7.38841 - 5.09985i) q^{73} +(-0.684846 - 0.606721i) q^{74} +(4.12095 + 5.97022i) q^{75} +(-2.16174 + 0.819840i) q^{76} +(-2.51164 - 6.62266i) q^{77} +(-0.637569 + 1.04730i) q^{78} +(-5.73631 + 15.1254i) q^{79} +11.6204i q^{80} +(-0.354605 - 0.935016i) q^{81} +(0.135352 - 1.11472i) q^{82} +(4.07169 - 7.75796i) q^{83} +(4.62347 - 3.19135i) q^{84} +(-2.51569 + 1.73645i) q^{85} +(-0.634307 + 1.20857i) q^{86} +(-0.540631 + 4.45250i) q^{87} +(1.11280 + 2.93423i) q^{88} -8.25170i q^{89} +(-0.422129 + 1.11306i) q^{90} +(8.44111 + 6.65565i) q^{91} +(5.30694 + 13.9933i) q^{92} +(-9.09110 + 3.44780i) q^{93} +(1.51866 + 2.20015i) q^{94} +(-3.21487 - 2.84813i) q^{95} +(-3.10320 + 2.14198i) q^{96} +(11.4850 + 12.9639i) q^{97} +(0.298441 + 0.568632i) q^{98} -2.37574i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Introduction

L-functions

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