LMFDB - Embedded newform 538.2.e.a.103.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,2,Mod(9,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(134))

chi = DirichletCharacter(H, H._module([109]))

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

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

chi := DirichletCharacter("538.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	538.e (of order $134$, degree $66$, 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:	$4.29595162874$
Analytic rank:	$0$
Dimension:	$1452$
Relative dimension:	$22$ over $\Q(\zeta_{134})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{134}]$

Embedding invariants

Embedding label			103.7
Character	$\chi$	$=$	538.103
Dual form			538.2.e.a.491.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366380 - 0.930465i) q^{2} +(0.0596016 + 1.27018i) q^{3} +(-0.731531 + 0.681808i) q^{4} +(-2.72289 - 1.54381i) q^{5} +(1.16002 - 0.520825i) q^{6} +(0.380715 + 0.338511i) q^{7} +(0.902417 + 0.430864i) q^{8} +(1.37702 - 0.129515i) q^{9} +O(q^{10})$	\(q+(-0.366380 - 0.930465i) q^{2} +(0.0596016 + 1.27018i) q^{3} +(-0.731531 + 0.681808i) q^{4} +(-2.72289 - 1.54381i) q^{5} +(1.16002 - 0.520825i) q^{6} +(0.380715 + 0.338511i) q^{7} +(0.902417 + 0.430864i) q^{8} +(1.37702 - 0.129515i) q^{9} +(-0.438854 + 3.09917i) q^{10} +(-0.0463257 + 0.393379i) q^{11} +(-0.909618 - 0.888538i) q^{12} +(-1.38322 - 0.195868i) q^{13} +(0.175487 - 0.478266i) q^{14} +(1.79863 - 3.55057i) q^{15} +(0.0702762 - 0.997528i) q^{16} +(-2.80548 + 0.330384i) q^{17} +(-0.625021 - 1.23382i) q^{18} +(-7.06479 + 2.97496i) q^{19} +(3.04446 - 0.727137i) q^{20} +(-0.407279 + 0.503752i) q^{21} +(0.382999 - 0.101022i) q^{22} +(-6.02483 + 0.282708i) q^{23} +(-0.493488 + 1.17191i) q^{24} +(2.46338 + 4.11674i) q^{25} +(0.324534 + 1.35880i) q^{26} +(0.781423 + 5.51839i) q^{27} +(-0.509305 + 0.0119427i) q^{28} +(-4.62241 - 2.76596i) q^{29} +(-3.96266 - 0.372707i) q^{30} +(-0.742739 + 3.10978i) q^{31} +(-0.953913 + 0.300085i) q^{32} +(-0.502423 - 0.0353959i) q^{33} +(1.33528 + 2.48936i) q^{34} +(-0.514045 - 1.50948i) q^{35} +(-0.919028 + 1.03361i) q^{36} +(-1.72697 - 2.60106i) q^{37} +(5.35650 + 5.48357i) q^{38} +(0.166346 - 1.76861i) q^{39} +(-1.79201 - 2.56636i) q^{40} +(0.255528 + 0.100617i) q^{41} +(0.617942 + 0.194394i) q^{42} +(-3.23110 + 5.39973i) q^{43} +(-0.234320 - 0.319354i) q^{44} +(-3.94941 - 1.77321i) q^{45} +(2.47043 + 5.50232i) q^{46} +(-8.22082 - 5.18471i) q^{47} +(1.27123 + 0.0298090i) q^{48} +(-0.788333 - 6.69421i) q^{49} +(2.92795 - 3.80038i) q^{50} +(-0.586857 - 3.54377i) q^{51} +(1.14541 - 0.799804i) q^{52} +(2.97091 - 9.44397i) q^{53} +(4.84837 - 2.74891i) q^{54} +(0.733444 - 0.999609i) q^{55} +(0.197711 + 0.469515i) q^{56} +(-4.19981 - 8.79623i) q^{57} +(-0.880075 + 5.31439i) q^{58} +(3.00666 + 3.22594i) q^{59} +(1.10505 + 3.82367i) q^{60} +(-2.71365 + 12.6693i) q^{61} +(3.16567 - 0.448270i) q^{62} +(0.568094 + 0.416828i) q^{63} +(0.628713 + 0.777638i) q^{64} +(3.46396 + 2.66876i) q^{65} +(0.151143 + 0.480455i) q^{66} +(7.13520 + 6.65021i) q^{67} +(1.82704 - 2.15449i) q^{68} +(-0.718179 - 7.63576i) q^{69} +(-1.21618 + 1.03135i) q^{70} +(13.5129 - 4.95820i) q^{71} +(1.29845 + 0.476431i) q^{72} +(2.04061 + 1.73047i) q^{73} +(-1.78747 + 2.55986i) q^{74} +(-5.08217 + 3.37430i) q^{75} +(3.13976 - 6.99311i) q^{76} +(-0.150800 + 0.134084i) q^{77} +(-1.70657 + 0.493203i) q^{78} +(0.230582 + 0.874191i) q^{79} +(-1.73135 + 2.60766i) q^{80} +(-2.88624 + 0.547775i) q^{81} -0.274623i q^{82} +(1.71926 + 9.05883i) q^{83} +(-0.0455247 - 0.646196i) q^{84} +(8.14907 + 3.43155i) q^{85} +(6.20807 + 1.02807i) q^{86} +(3.23776 - 6.03614i) q^{87} +(-0.211298 + 0.335032i) q^{88} +(9.36590 - 3.18950i) q^{89} +(-0.202920 + 4.32446i) q^{90} +(-0.460308 - 0.542805i) q^{91} +(4.21460 - 4.31459i) q^{92} +(-3.99425 - 0.758062i) q^{93} +(-1.81225 + 9.54877i) q^{94} +(23.8294 + 2.80624i) q^{95} +(-0.438016 - 1.19375i) q^{96} +(0.967228 + 4.51573i) q^{97} +(-5.93990 + 3.18614i) q^{98} +(-0.0128428 + 0.547690i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) $ 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9	$ 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + 2 q^{11} - 10 q^{13} + 12 q^{14} - 22 q^{16} + 2 q^{20} + 12 q^{21} - 4 q^{23} - 2 q^{24} - 24 q^{25} - 8 q^{30} - 12 q^{34} - 20 q^{36} - 396 q^{37} - 2 q^{38} + 24 q^{41} + 14 q^{43} - 2 q^{44} - 42 q^{45} - 402 q^{47} + 22 q^{49} + 12 q^{51} + 10 q^{52} - 10 q^{53} - 8 q^{54} - 4 q^{55} - 12 q^{56} + 16 q^{57} - 18 q^{58} - 268 q^{60} - 2 q^{61} + 4 q^{62} + 22 q^{64} + 16 q^{65} + 40 q^{66} + 6 q^{67} - 106 q^{73} + 40 q^{78} + 40 q^{79} - 2 q^{80} - 14 q^{81} - 402 q^{83} - 12 q^{84} - 100 q^{87} + 4 q^{92} - 340 q^{93} + 2 q^{96} - 64 q^{97} + 18 q^{99}+O(q^{100}) $ 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9 + 2 * q^11 - 10 * q^13 + 12 * q^14 - 22 * q^16 + 2 * q^20 + 12 * q^21 - 4 * q^23 - 2 * q^24 - 24 * q^25 - 8 * q^30 - 12 * q^34 - 20 * q^36 - 396 * q^37 - 2 * q^38 + 24 * q^41 + 14 * q^43 - 2 * q^44 - 42 * q^45 - 402 * q^47 + 22 * q^49 + 12 * q^51 + 10 * q^52 - 10 * q^53 - 8 * q^54 - 4 * q^55 - 12 * q^56 + 16 * q^57 - 18 * q^58 - 268 * q^60 - 2 * q^61 + 4 * q^62 + 22 * q^64 + 16 * q^65 + 40 * q^66 + 6 * q^67 - 106 * q^73 + 40 * q^78 + 40 * q^79 - 2 * q^80 - 14 * q^81 - 402 * q^83 - 12 * q^84 - 100 * q^87 + 4 * q^92 - 340 * q^93 + 2 * q^96 - 64 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{51}{134}\right)$

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 $

$2$	−0.366380	−	0.930465i	−0.259070	−	0.657938i
$2$	−0.366380	−	0.930465i	−0.259070	−	0.657938i
$3$	0.0596016	+	1.27018i	0.0344110	+	0.733338i	0.946376	+	0.323069i	$0.104714\pi$
$3$	0.0596016	+	1.27018i	0.0344110	+	0.733338i	−0.911965	+	0.410269i	$0.865435\pi$
$4$	−0.731531	+	0.681808i	−0.365766	+	0.340904i
$5$	−2.72289	−	1.54381i	−1.21771	−	0.690415i	−0.256585	−	0.966522i	$-0.582597\pi$
$5$	−2.72289	−	1.54381i	−1.21771	−	0.690415i	−0.961127	+	0.276107i	$0.910956\pi$
$6$	1.16002	−	0.520825i	0.473576	−	0.212626i
$7$	0.380715	+	0.338511i	0.143897	+	0.127945i	0.733333	−	0.679869i	$-0.237964\pi$
$7$	0.380715	+	0.338511i	0.143897	+	0.127945i	−0.589436	+	0.807815i	$0.700650\pi$
$8$	0.902417	+	0.430864i	0.319053	+	0.152333i
$9$	1.37702	−	0.129515i	0.459006	−	0.0431717i
$10$	−0.438854	+	3.09917i	−0.138778	+	0.980045i
$11$	−0.0463257	+	0.393379i	−0.0139677	+	0.118608i	−0.998349	−	0.0574425i	$-0.981705\pi$
$11$	−0.0463257	+	0.393379i	−0.0139677	+	0.118608i	0.984381	+	0.176051i	$0.0563323\pi$
$12$	−0.909618	−	0.888538i	−0.262584	−	0.256499i
$13$	−1.38322	−	0.195868i	−0.383635	−	0.0543241i	−0.0542690	−	0.998526i	$-0.517283\pi$
$13$	−1.38322	−	0.195868i	−0.383635	−	0.0543241i	−0.329366	+	0.944202i	$0.606835\pi$
$14$	0.175487	−	0.478266i	0.0469008	−	0.127822i
$15$	1.79863	−	3.55057i	0.464404	−	0.916752i
$16$	0.0702762	−	0.997528i	0.0175690	−	0.249382i
$17$	−2.80548	+	0.330384i	−0.680430	+	0.0801298i	−0.450094	−	0.892981i	$-0.648609\pi$
$17$	−2.80548	+	0.330384i	−0.680430	+	0.0801298i	−0.230336	+	0.973111i	$0.573983\pi$
$18$	−0.625021	−	1.23382i	−0.147319	−	0.290813i
$19$	−7.06479	+	2.97496i	−1.62077	+	0.682503i	−0.995218	−	0.0976762i	$-0.968859\pi$
$19$	−7.06479	+	2.97496i	−1.62077	+	0.682503i	−0.625556	+	0.780180i	$0.715128\pi$
$20$	3.04446	−	0.727137i	0.680762	−	0.162593i
$21$	−0.407279	+	0.503752i	−0.0888755	+	0.109928i
$22$	0.382999	−	0.101022i	0.0816556	−	0.0215379i
$23$	−6.02483	+	0.282708i	−1.25626	+	0.0589487i	−0.664577	−	0.747219i	$-0.731388\pi$
$23$	−6.02483	+	0.282708i	−1.25626	+	0.0589487i	−0.591686	+	0.806168i	$0.701538\pi$
$24$	−0.493488	+	1.17191i	−0.100733	+	0.239215i
$25$	2.46338	+	4.11674i	0.492676	+	0.823348i
$26$	0.324534	+	1.35880i	0.0636464	+	0.266482i
$27$	0.781423	+	5.51839i	0.150385	+	1.06201i
$28$	−0.509305	+	0.0119427i	−0.0962495	+	0.00225696i
$29$	−4.62241	−	2.76596i	−0.858360	−	0.513627i	0.0154577	−	0.999881i	$-0.495079\pi$
$29$	−4.62241	−	2.76596i	−0.858360	−	0.513627i	−0.873818	+	0.486254i	$0.838363\pi$
$30$	−3.96266	−	0.372707i	−0.723479	−	0.0680467i
$31$	−0.742739	+	3.10978i	−0.133400	+	0.558534i	0.864989	+	0.501791i	$0.167325\pi$
$31$	−0.742739	+	3.10978i	−0.133400	+	0.558534i	−0.998389	+	0.0567429i	$0.981928\pi$
$32$	−0.953913	+	0.300085i	−0.168630	+	0.0530480i
$33$	−0.502423	−	0.0353959i	−0.0874606	−	0.00616163i
$34$	1.33528	+	2.48936i	0.228999	+	0.426922i
$35$	−0.514045	−	1.50948i	−0.0868895	−	0.255149i
$36$	−0.919028	+	1.03361i	−0.153171	+	0.172268i
$37$	−1.72697	−	2.60106i	−0.283912	−	0.427612i	0.663235	−	0.748411i	$-0.269183\pi$
$37$	−1.72697	−	2.60106i	−0.283912	−	0.427612i	−0.947147	+	0.320799i	$0.896049\pi$
$38$	5.35650	+	5.48357i	0.868939	+	0.889553i
$39$	0.166346	−	1.76861i	0.0266366	−	0.283204i
$40$	−1.79201	−	2.56636i	−0.283341	−	0.405777i
$41$	0.255528	+	0.100617i	0.0399067	+	0.0157137i	0.386249	−	0.922394i	$-0.373771\pi$
$41$	0.255528	+	0.100617i	0.0399067	+	0.0157137i	−0.346342	+	0.938108i	$0.612576\pi$
$42$	0.617942	+	0.194394i	0.0953505	+	0.0299957i
$43$	−3.23110	+	5.39973i	−0.492738	+	0.823451i	−0.999248	−	0.0387835i	$-0.987652\pi$
$43$	−3.23110	+	5.39973i	−0.492738	+	0.823451i	0.506510	+	0.862234i	$0.330935\pi$
$44$	−0.234320	−	0.319354i	−0.0353251	−	0.0481445i
$45$	−3.94941	−	1.77321i	−0.588744	−	0.264334i
$46$	2.47043	+	5.50232i	0.364245	+	0.811272i
$47$	−8.22082	−	5.18471i	−1.19913	−	0.756268i	−0.223290	−	0.974752i	$-0.571680\pi$
$47$	−8.22082	−	5.18471i	−1.19913	−	0.756268i	−0.975840	+	0.218485i	$0.929889\pi$
$48$	1.27123	+	0.0298090i	0.183486	+	0.00430256i
$49$	−0.788333	−	6.69421i	−0.112619	−	0.956315i
$50$	2.92795	−	3.80038i	0.414075	−	0.537455i
$51$	−0.586857	−	3.54377i	−0.0821765	−	0.496227i
$52$	1.14541	−	0.799804i	0.158840	−	0.110913i
$53$	2.97091	−	9.44397i	0.408086	−	1.29723i	−0.495420	−	0.868654i	$-0.664986\pi$
$53$	2.97091	−	9.44397i	0.408086	−	1.29723i	0.903506	−	0.428576i	$-0.140984\pi$
$54$	4.84837	−	2.74891i	0.659779	−	0.374080i
$55$	0.733444	−	0.999609i	0.0988976	−	0.134787i
$56$	0.197711	+	0.469515i	0.0264203	+	0.0627415i
$57$	−4.19981	−	8.79623i	−0.556278	−	1.16509i
$58$	−0.880075	+	5.31439i	−0.115560	+	0.697813i
$59$	3.00666	+	3.22594i	0.391434	+	0.419981i	0.896461	−	0.443122i	$-0.146129\pi$
$59$	3.00666	+	3.22594i	0.391434	+	0.419981i	−0.505027	+	0.863104i	$0.668517\pi$
$60$	1.10505	+	3.82367i	0.142661	+	0.493634i
$61$	−2.71365	+	12.6693i	−0.347447	+	1.62214i	0.372447	+	0.928054i	$0.378519\pi$
$61$	−2.71365	+	12.6693i	−0.347447	+	1.62214i	−0.719893	+	0.694085i	$0.755809\pi$
$62$	3.16567	−	0.448270i	0.402041	−	0.0569304i
$63$	0.568094	+	0.416828i	0.0715731	+	0.0525154i
$64$	0.628713	+	0.777638i	0.0785891	+	0.0972047i
$65$	3.46396	+	2.66876i	0.429651	+	0.331019i
$66$	0.151143	+	0.480455i	0.0186044	+	0.0591400i
$67$	7.13520	+	6.65021i	0.871704	+	0.812453i	0.983430	−	0.181286i	$-0.0580261\pi$
$67$	7.13520	+	6.65021i	0.871704	+	0.812453i	−0.111726	+	0.993739i	$0.535638\pi$
$68$	1.82704	−	2.15449i	0.221561	−	0.261270i
$69$	−0.718179	−	7.63576i	−0.0864586	−	0.919237i
$70$	−1.21618	+	1.03135i	−0.145362	+	0.123269i
$71$	13.5129	−	4.95820i	1.60369	−	0.588430i	0.622693	−	0.782467i	$-0.286039\pi$
$71$	13.5129	−	4.95820i	1.60369	−	0.588430i	0.980994	+	0.194037i	$0.0621581\pi$
$72$	1.29845	+	0.476431i	0.153024	+	0.0561479i
$73$	2.04061	+	1.73047i	0.238836	+	0.202537i	0.758210	−	0.652010i	$-0.226074\pi$
$73$	2.04061	+	1.73047i	0.238836	+	0.202537i	−0.519375	+	0.854547i	$0.673835\pi$
$74$	−1.78747	+	2.55986i	−0.207789	+	0.297578i
$75$	−5.08217	+	3.37430i	−0.586839	+	0.389630i
$76$	3.13976	−	6.99311i	0.360155	−	0.802164i
$77$	−0.150800	+	0.134084i	−0.0171853	+	0.0152802i
$78$	−1.70657	+	0.493203i	−0.193231	+	0.0558442i
$79$	0.230582	+	0.874191i	0.0259425	+	0.0983542i	0.978650	−	0.205536i	$-0.0658936\pi$
$79$	0.230582	+	0.874191i	0.0259425	+	0.0983542i	−0.952707	+	0.303890i	$0.901715\pi$
$80$	−1.73135	+	2.60766i	−0.193571	+	0.291545i
$81$	−2.88624	+	0.547775i	−0.320693	+	0.0608639i
$82$		−	0.274623i		−	0.0303271i
$83$	1.71926	+	9.05883i	0.188713	+	0.994336i	0.941739	+	0.336345i	$0.109191\pi$
$83$	1.71926	+	9.05883i	0.188713	+	0.994336i	−0.753026	+	0.657991i	$0.771406\pi$
$84$	−0.0455247	−	0.646196i	−0.00496716	−	0.0705057i
$85$	8.14907	+	3.43155i	0.883890	+	0.372204i
$86$	6.20807	+	1.02807i	0.669433	+	0.110860i
$87$	3.23776	−	6.03614i	0.347125	−	0.647142i
$88$	−0.211298	+	0.335032i	−0.0225244	+	0.0357145i
$89$	9.36590	−	3.18950i	0.992783	−	0.338086i	0.221905	−	0.975068i	$-0.428773\pi$
$89$	9.36590	−	3.18950i	0.992783	−	0.338086i	0.770879	+	0.636982i	$0.219817\pi$
$90$	−0.202920	+	4.32446i	−0.0213897	+	0.455838i
$91$	−0.460308	−	0.542805i	−0.0482533	−	0.0569014i
$92$	4.21460	−	4.31459i	0.439402	−	0.449827i
$93$	−3.99425	−	0.758062i	−0.414184	−	0.0786074i
$94$	−1.81225	+	9.54877i	−0.186919	+	0.984880i
$95$	23.8294	+	2.80624i	2.44485	+	0.287914i
$96$	−0.438016	−	1.19375i	−0.0447048	−	0.121837i
$97$	0.967228	+	4.51573i	0.0982072	+	0.458503i	0.999671	+	0.0256490i	$0.00816522\pi$
$97$	0.967228	+	4.51573i	0.0982072	+	0.458503i	−0.901464	+	0.432854i	$0.857506\pi$
$98$	−5.93990	+	3.18614i	−0.600020	+	0.321849i
$99$	−0.0128428	+	0.547690i	−0.00129075	+	0.0550449i
$100$	−4.60887	−	1.33197i	−0.460887	−	0.133197i
$101$	−11.4028	+	5.44434i	−1.13462	+	0.541732i	−0.902387	−	0.430927i	$-0.858187\pi$
$101$	−11.4028	+	5.44434i	−1.13462	+	0.541732i	−0.232238	+	0.972659i	$0.574605\pi$
$102$	−3.08234	+	1.84442i	−0.305197	+	0.182625i
$103$	−4.30870	+	2.71741i	−0.424549	+	0.267754i	−0.728651	−	0.684885i	$-0.759852\pi$
$103$	−4.30870	+	2.71741i	−0.424549	+	0.267754i	0.304102	+	0.952639i	$0.401643\pi$
$104$	−1.16385	−	0.772733i	−0.114124	−	0.0757727i
$105$	1.88667	−	0.742896i	0.184120	−	0.0724992i
$106$	−9.87577	+	0.695752i	−0.959220	+	0.0675774i
$107$	−10.1718	−	16.1284i	−0.983349	−	1.55919i	−0.819798	−	0.572653i	$-0.805914\pi$
$107$	−10.1718	−	16.1284i	−0.983349	−	1.55919i	−0.163551	−	0.986535i	$-0.552295\pi$
$108$	−4.33411	−	3.50409i	−0.417050	−	0.337181i
$109$	−5.83927	−	1.25072i	−0.559300	−	0.119797i	−0.0789578	−	0.996878i	$-0.525159\pi$
$109$	−5.83927	−	1.25072i	−0.559300	−	0.119797i	−0.480342	+	0.877081i	$0.659488\pi$
$110$	−1.19882	−	0.316208i	−0.114303	−	0.0301492i
$111$	3.20088	−	2.34859i	0.303814	−	0.222918i
$112$	0.364430	−	0.355984i	0.0344354	−	0.0336374i
$113$	−8.45205	−	10.9705i	−0.795102	−	1.03202i	−0.998598	−	0.0529406i	$-0.983141\pi$
$113$	−8.45205	−	10.9705i	−0.795102	−	1.03202i	0.203495	−	0.979076i	$-0.434770\pi$
$114$	−6.64586	+	7.13054i	−0.622442	+	0.667836i
$115$	16.8414	+	8.53144i	1.57047	+	0.795561i
$116$	5.26729	−	1.12821i	0.489056	−	0.104751i
$117$	−1.93008	−	0.0905669i	−0.178436	−	0.00837291i
$118$	1.90004	−	3.97952i	0.174913	−	0.366344i
$119$	−1.17993	−	0.823906i	−0.108164	−	0.0755274i
$120$	3.15292	−	2.42913i	0.287821	−	0.221748i
$121$	10.5465	+	2.51891i	0.958770	+	0.228992i
$122$	12.7826	−	2.11683i	1.15728	−	0.191648i
$123$	−0.112571	+	0.330562i	−0.0101502	+	0.0298058i
$124$	−1.57694	−	2.78131i	−0.141613	−	0.249769i
$125$	0.0148605	+	0.633736i	0.00132916	+	0.0566831i
$126$	0.179706	−	0.681309i	0.0160095	−	0.0606958i
$127$	−1.40214	−	1.57695i	−0.124420	−	0.139932i	0.681821	−	0.731519i	$-0.261188\pi$
$127$	−1.40214	−	1.57695i	−0.124420	−	0.139932i	−0.806241	+	0.591587i	$0.798502\pi$
$128$	0.493217	−	0.869906i	0.0435946	−	0.0768896i
$129$	−7.05119	−	3.78224i	−0.620823	−	0.333007i
$130$	1.21406	−	4.20087i	0.106480	−	0.368441i
$131$	6.88570	−	3.48813i	0.601607	−	0.304759i	−0.124631	−	0.992203i	$-0.539775\pi$
$131$	6.88570	−	3.48813i	0.601607	−	0.304759i	0.726238	+	0.687444i	$0.241267\pi$
$132$	0.391671	−	0.316663i	0.0340906	−	0.0275619i
$133$	−3.69673	−	1.25890i	−0.320547	−	0.109160i
$134$	3.57359	−	9.07556i	0.308712	−	0.784009i
$135$	6.39164	−	16.2323i	0.550104	−	1.39706i
$136$	−2.67407	−	0.910637i	−0.229299	−	0.0780865i
$137$	−1.12001	+	0.905514i	−0.0956885	+	0.0773633i	−0.675366	−	0.737483i	$-0.736014\pi$
$137$	−1.12001	+	0.905514i	−0.0956885	+	0.0773633i	0.579678	+	0.814846i	$0.303179\pi$
$138$	−6.84168	+	3.46583i	−0.582402	+	0.295031i
$139$	1.26676	−	4.38322i	0.107445	−	0.371780i	−0.888806	−	0.458283i	$-0.848465\pi$
$139$	1.26676	−	4.38322i	0.107445	−	0.371780i	0.996252	+	0.0865027i	$0.0275691\pi$
$140$	1.40522	+	0.753753i	0.118762	+	0.0637038i
$141$	6.09553	−	10.7509i	0.513336	−	0.905391i
$142$	−9.56429	−	10.7567i	−0.802617	−	0.902683i
$143$	0.141129	−	0.535055i	0.0118018	−	0.0447436i
$144$	−0.0324233	−	1.38272i	−0.00270194	−	0.115226i
$145$	8.31617	+	14.6676i	0.690620	+	1.21807i
$146$	0.862507	−	2.53273i	0.0713815	−	0.209610i
$147$	8.45585	−	1.40031i	0.697427	−	0.115496i
$148$	3.03676	+	0.725297i	0.249620	+	0.0596191i
$149$	−12.7897	+	9.85362i	−1.04777	+	0.807240i	−0.981673	−	0.190573i	$-0.938965\pi$
$149$	−12.7897	+	9.85362i	−1.04777	+	0.807240i	−0.0660978	+	0.997813i	$0.521055\pi$
$150$	5.00167	+	3.49251i	0.408385	+	0.285162i
$151$	4.52343	−	9.47405i	0.368112	−	0.770987i	−0.631880	−	0.775066i	$-0.717716\pi$
$151$	4.52343	−	9.47405i	0.368112	−	0.770987i	0.999992	+	0.00407921i	$0.00129845\pi$
$152$	−7.65719	−	0.359305i	−0.621080	−	0.0291435i
$153$	−3.82041	+	0.818297i	−0.308862	+	0.0661554i
$154$	0.180010	+	0.0911889i	0.0145056	+	0.00734821i
$155$	6.82332	−	7.32094i	0.548062	−	0.588032i
$156$	1.08416	+	1.40721i	0.0868024	+	0.112667i
$157$	7.62690	−	7.45016i	0.608693	−	0.594587i	−0.328026	−	0.944669i	$-0.606383\pi$
$157$	7.62690	−	7.45016i	0.608693	−	0.594587i	0.936719	+	0.350081i	$0.113846\pi$
$158$	0.728924	−	0.534834i	0.0579901	−	0.0425491i
$159$	12.1726	+	3.21071i	0.965350	+	0.254626i
$160$	3.06067	+	0.655567i	0.241967	+	0.0518272i
$161$	−2.38944	−	1.93184i	−0.188314	−	0.152251i
$162$	1.56715	+	2.48485i	0.123127	+	0.195228i
$163$	−12.9523	+	0.912493i	−1.01450	+	0.0714720i	−0.567762	−	0.823192i	$-0.692191\pi$
$163$	−12.9523	+	0.912493i	−1.01450	+	0.0714720i	−0.446739	+	0.894664i	$0.647415\pi$
$164$	−0.255528	+	0.100617i	−0.0199533	+	0.00785683i
$165$	1.31340	+	0.872026i	0.102248	+	0.0678872i
$166$	7.79902	−	4.91869i	0.605322	−	0.381764i
$167$	13.2552	−	7.93165i	1.02572	−	0.613770i	0.101182	−	0.994868i	$-0.467738\pi$
$167$	13.2552	−	7.93165i	1.02572	−	0.613770i	0.924534	+	0.381098i	$0.124454\pi$
$168$	−0.584583	+	0.279112i	−0.0451016	+	0.0215340i
$169$	−10.6140	−	3.06746i	−0.816460	−	0.235959i
$170$	0.207282	−	8.83967i	0.0158978	−	0.677972i
$171$	−9.34304	+	5.01158i	−0.714480	+	0.383245i
$172$	−1.31793	−	6.15306i	−0.100491	−	0.469166i
$173$	2.58976	+	7.05805i	0.196896	+	0.536613i	0.998089	−	0.0617925i	$-0.0196817\pi$
$173$	2.58976	+	7.05805i	0.196896	+	0.536613i	−0.801193	+	0.598406i	$0.795801\pi$
$174$	−6.80267	−	0.801106i	−0.515709	−	0.0607317i
$175$	−0.455718	+	2.40119i	−0.0344490	+	0.181513i
$176$	0.389151	+	0.0738564i	0.0293334	+	0.00556713i
$177$	−3.91831	+	4.01127i	−0.294518	+	0.301505i
$178$	−6.39920	−	7.54608i	−0.479640	−	0.565602i
$179$	−0.329864	+	7.02978i	−0.0246552	+	0.525430i	0.951407	+	0.307937i	$0.0996387\pi$
$179$	−0.329864	+	7.02978i	−0.0246552	+	0.525430i	−0.976062	+	0.217493i	$0.930212\pi$
$180$	4.09810	−	1.39559i	0.305455	−	0.104021i
$181$	9.60967	−	15.2370i	0.714281	−	1.13256i	−0.271159	−	0.962535i	$-0.587407\pi$
$181$	9.60967	−	15.2370i	0.714281	−	1.13256i	0.985440	−	0.170023i	$-0.0543841\pi$
$182$	−0.336413	+	0.627173i	−0.0249366	+	0.0464892i
$183$	−16.2540	−	2.69170i	−1.20153	−	0.198976i
$184$	−5.55872	−	2.34076i	−0.409794	−	0.172563i
$185$	0.686787	+	9.74853i	0.0504936	+	0.716726i
$186$	0.758062	+	3.99425i	0.0555838	+	0.292872i
$187$		−	1.11892i		−	0.0818238i
$188$	9.54877	−	1.81225i	0.696415	−	0.132172i
$189$	−1.57054	+	2.36545i	−0.114240	+	0.172061i
$190$	−6.11952	−	23.2006i	−0.443956	−	1.68315i
$191$	0.0853392	−	0.0246632i	0.00617493	−	0.00178457i	−0.274551	−	0.961573i	$-0.588529\pi$
$191$	0.0853392	−	0.0246632i	0.00617493	−	0.00178457i	0.280726	+	0.959788i	$0.409425\pi$
$192$	−0.950266	+	0.844926i	−0.0685795	+	0.0609773i
$193$	−1.98984	+	4.43191i	−0.143232	+	0.319016i	−0.969832	−	0.243773i	$-0.921615\pi$
$193$	−1.98984	+	4.43191i	−0.143232	+	0.319016i	0.826601	+	0.562789i	$0.190272\pi$
$194$	3.84736	−	2.55445i	0.276224	−	0.183399i
$195$	−3.18334	+	4.55891i	−0.227964	+	0.326470i
$196$	5.14085	+	4.35953i	0.367204	+	0.311395i
$197$	−8.45413	−	3.10202i	−0.602332	−	0.221010i	0.0250948	−	0.999685i	$-0.492011\pi$
$197$	−8.45413	−	3.10202i	−0.602332	−	0.221010i	−0.627427	+	0.778676i	$0.715892\pi$
$198$	0.514312	−	0.188713i	0.0365506	−	0.0134113i
$199$	3.24054	−	2.74804i	0.229716	−	0.194803i	−0.524536	−	0.851388i	$-0.675761\pi$
$199$	3.24054	−	2.74804i	0.229716	−	0.194803i	0.754252	+	0.656585i	$0.228000\pi$
$200$	0.449243	+	4.77640i	0.0317663	+	0.337742i
$201$	−8.02168	+	9.45934i	−0.565806	+	0.667211i
$202$	9.24354	+	8.61524i	0.650374	+	0.606166i
$203$	−0.823510	−	2.61778i	−0.0577991	−	0.183732i
$204$	2.84548	+	2.19226i	0.199223	+	0.153489i
$205$	−0.540439	−	0.668455i	−0.0377459	−	0.0466869i
$206$	4.10708	+	3.01349i	0.286154	+	0.209960i
$207$	−8.25969	+	1.16960i	−0.574088	+	0.0812929i
$208$	−0.292591	+	1.36603i	−0.0202876	+	0.0947173i
$209$	−0.843007	−	2.91696i	−0.0583120	−	0.201770i
$210$	−1.38248	−	1.48330i	−0.0954001	−	0.102357i
$211$	−0.597300	+	3.60683i	−0.0411198	+	0.248304i	−0.999281	−	0.0379263i	$-0.987925\pi$
$211$	−0.597300	+	3.60683i	−0.0411198	+	0.248304i	0.958161	+	0.286231i	$0.0924024\pi$
$212$	4.26566	+	8.93415i	0.292967	+	0.613600i
$213$	7.10318	+	16.8683i	0.486702	+	1.15580i
$214$	−11.2801	+	15.3737i	−0.771094	+	1.05092i
$215$	17.1341	−	9.71463i	1.16854	−	0.662532i
$216$	−1.67250	+	5.31657i	−0.113799	+	0.361747i
$217$	−1.33547	+	0.932516i	−0.0906575	+	0.0633033i
$218$	0.975642	+	5.89147i	0.0660788	+	0.399021i
$219$	−2.07639	+	2.69508i	−0.140309	+	0.182117i
$220$	0.145004	+	1.23131i	0.00977615	+	0.0830151i
$221$	3.94530	+	0.0925135i	0.265390	+	0.00622313i
$222$	−3.35802	−	2.11784i	−0.225376	−	0.142140i
$223$	0.747633	+	1.66518i	0.0500652	+	0.111509i	0.935597	−	0.353070i	$-0.114862\pi$
$223$	0.747633	+	1.66518i	0.0500652	+	0.111509i	−0.885532	+	0.464579i	$0.846206\pi$
$224$	−0.464751	−	0.208664i	−0.0310525	−	0.0139419i
$225$	3.92530	+	5.34978i	0.261687	+	0.356652i
$226$	−7.11099	+	11.8837i	−0.473016	+	0.790493i
$227$	−15.6485	−	4.92275i	−1.03863	−	0.326734i	−0.267596	−	0.963531i	$-0.586229\pi$
$227$	−15.6485	−	4.92275i	−1.03863	−	0.326734i	−0.771032	+	0.636797i	$0.780259\pi$
$228$	9.06963	+	3.57126i	0.600651	+	0.236512i
$229$	1.89956	+	2.72039i	0.125527	+	0.179768i	0.877720	−	0.479174i	$-0.159064\pi$
$229$	1.89956	+	2.72039i	0.125527	+	0.179768i	−0.752193	+	0.658942i	$0.771004\pi$
$230$	1.76786	−	18.7961i	0.116569	−	1.23938i
$231$	−0.179298	−	0.183552i	−0.0117969	−	0.0120768i
$232$	−2.97959	−	4.48768i	−0.195619	−	0.294631i
$233$	−10.9461	+	12.3108i	−0.717106	+	0.806510i	−0.987729	−	0.156175i	$-0.950084\pi$
$233$	−10.9461	+	12.3108i	−0.717106	+	0.806510i	0.270623	+	0.962685i	$0.412770\pi$
$234$	0.622874	+	1.82906i	0.0407186	+	0.119569i
$235$	14.3802	+	26.8088i	0.938058	+	1.74881i
$236$	−4.39894	−	0.309907i	−0.286346	−	0.0201732i
$237$	−1.09664	+	0.344983i	−0.0712341	+	0.0224090i
$238$	−0.334314	+	1.39974i	−0.0216704	+	0.0907320i
$239$	4.34036	+	0.408232i	0.280755	+	0.0264063i	0.233083	−	0.972457i	$-0.425119\pi$
$239$	4.34036	+	0.408232i	0.280755	+	0.0264063i	0.0476713	+	0.998863i	$0.484820\pi$
$240$	−3.41539	−	2.04370i	−0.220462	−	0.131921i
$241$	−6.53172	+	0.153162i	−0.420745	+	0.00986606i	−0.233290	−	0.972407i	$-0.574949\pi$
$241$	−6.53172	+	0.153162i	−0.420745	+	0.00986606i	−0.187455	+	0.982273i	$0.560024\pi$
$242$	−1.52026	−	10.7360i	−0.0977258	−	0.690136i
$243$	3.01642	+	12.6295i	0.193504	+	0.810183i
$244$	−6.65291	−	11.1182i	−0.425909	−	0.711768i
$245$	−8.18807	+	19.4446i	−0.523117	+	1.24227i
$246$	0.348821	−	0.0163680i	0.0222400	−	0.00104359i
$247$	10.3548	−	2.73125i	0.658863	−	0.173785i
$248$	−2.01015	+	2.48630i	−0.127645	+	0.157880i
$249$	−11.4039	+	2.72369i	−0.722690	+	0.172607i
$250$	0.584225	−	0.246016i	0.0369496	−	0.0155594i
$251$	8.01496	+	15.8218i	0.505900	+	0.998665i	0.992174	+	0.124859i	$0.0398479\pi$
$251$	8.01496	+	15.8218i	0.505900	+	0.998665i	−0.486275	+	0.873806i	$0.661645\pi$
$252$	−0.699775	+	0.0824080i	−0.0440817	+	0.00519121i
$253$	0.167893	−	2.38314i	0.0105553	−	0.149827i
$254$	−0.953583	+	1.88241i	−0.0598331	+	0.118113i
$255$	−3.87298	+	10.5553i	−0.242535	+	0.660998i
$256$	−0.990123	−	0.140205i	−0.0618827	−	0.00876280i
$257$	−12.9585	−	12.6582i	−0.808327	−	0.789595i	0.172390	−	0.985029i	$-0.444851\pi$
$257$	−12.9585	−	12.6582i	−0.808327	−	0.789595i	−0.980717	+	0.195434i	$0.937389\pi$
$258$	−0.935822	+	7.94662i	−0.0582618	+	0.494735i
$259$	0.223006	−	1.57486i	0.0138569	−	0.0978572i
$260$	−4.35357	+	0.409474i	−0.269997	+	0.0253945i
$261$	−6.72338	−	3.21011i	−0.416167	−	0.198701i
$262$	−5.76837	−	5.12893i	−0.356371	−	0.316866i
$263$	29.1025	−	13.0664i	1.79454	−	0.805710i	0.823294	−	0.567614i	$-0.192134\pi$
$263$	29.1025	−	13.0664i	1.79454	−	0.805710i	0.971242	−	0.238096i	$-0.0765231\pi$
$264$	−0.438144	−	0.248418i	−0.0269659	−	0.0152890i
$265$	−22.6692	+	21.1283i	−1.39256	+	1.29790i
$266$	0.183046	+	3.90091i	0.0112233	+	0.239180i
$267$	4.60946	+	11.7063i	0.282094	+	0.716412i
$268$	−9.75379			−0.595808
$269$	−12.5017	−	10.6163i	−0.762244	−	0.647290i
$269$	−12.5017	−	10.6163i	−0.762244	−	0.647290i
$270$	−17.4454			−1.06169
$271$	2.83407	+	7.19744i	0.172157	+	0.437214i	0.990499	−	0.137518i	$-0.0439125\pi$
$271$	2.83407	+	7.19744i	0.172157	+	0.437214i	−0.818342	+	0.574731i	$0.805107\pi$
$272$	0.132408	+	2.82176i	0.00802842	+	0.171095i
$273$	0.662024	−	0.617025i	0.0400675	−	0.0373440i
$274$	1.25290	+	0.710364i	0.0756903	+	0.0429146i
$275$	−1.73356	+	0.778332i	−0.104537	+	0.0469352i
$276$	5.73149	+	5.09613i	0.344995	+	0.306751i
$277$	−2.44777	−	1.16870i	−0.147072	−	0.0702205i	0.355895	−	0.934526i	$-0.384176\pi$
$277$	−2.44777	−	1.16870i	−0.147072	−	0.0702205i	−0.502967	+	0.864306i	$0.667758\pi$
$278$	−4.54255	+	0.427249i	−0.272444	+	0.0256247i
$279$	−0.620001	+	4.37842i	−0.0371185	+	0.262129i
$280$	0.186498	−	1.58367i	0.0111454	−	0.0946421i
$281$	16.1157	+	15.7422i	0.961380	+	0.939101i	0.998185	−	0.0602219i	$-0.0191808\pi$
$281$	16.1157	+	15.7422i	0.961380	+	0.939101i	−0.0368054	+	0.999322i	$0.511718\pi$
$282$	−12.2366	−	1.73275i	−0.728682	−	0.103184i
$283$	−1.97084	+	5.37126i	−0.117154	+	0.319288i	−0.983702	−	0.179806i	$-0.942453\pi$
$283$	−1.97084	+	5.37126i	−0.117154	+	0.319288i	0.866548	+	0.499094i	$0.166334\pi$
$284$	−6.50458	+	12.8403i	−0.385976	+	0.761930i
$285$	−2.14415	+	30.4349i	−0.127008	+	1.80281i
$286$	−0.549557	+	0.0647178i	−0.0324960	+	0.00382684i
$287$	0.0632233	+	0.124805i	0.00373195	+	0.00736702i
$288$	−1.27469	+	0.536768i	−0.0751118	+	0.0316294i
$289$	−8.77335	+	2.09542i	−0.516079	+	0.123260i
$290$	10.6008	−	13.1118i	0.622499	−	0.769952i
$291$	−5.67814	+	1.49770i	−0.332858	+	0.0877966i
$292$	−2.67262	+	0.125410i	−0.156403	+	0.00733905i
$293$	−6.25580	+	14.8560i	−0.365468	+	0.867894i	0.630331	+	0.776327i	$0.282919\pi$
$293$	−6.25580	+	14.8560i	−0.365468	+	0.867894i	−0.995799	+	0.0915679i	$0.970812\pi$
$294$	−4.40099	−	7.35483i	−0.256671	−	0.428942i
$295$	−3.20656	−	13.4256i	−0.186693	−	0.781668i
$296$	−0.437744	−	3.09133i	−0.0254433	−	0.179680i
$297$	−2.20702	+	0.0517524i	−0.128064	+	0.00300298i
$298$	13.8543	+	8.29018i	0.802560	+	0.480237i
$299$	8.38902	+	0.789027i	0.485150	+	0.0456306i
$300$	1.41715	−	5.93347i	0.0818189	−	0.342569i
$301$	−3.05800	+	0.961993i	−0.176260	+	0.0554484i
$302$	−10.4726	−	0.737796i	−0.602629	−	0.0424554i
$303$	−7.59491	−	14.1591i	−0.436316	−	0.813421i
$304$	2.47112	+	7.25639i	0.141729	+	0.416183i
$305$	26.9480	−	30.3077i	1.54304	−	1.73542i
$306$	2.16112	+	3.25495i	0.123543	+	0.186073i
$307$	6.04416	+	6.18755i	0.344958	+	0.353142i	0.865692	−	0.500577i	$-0.166879\pi$
$307$	6.04416	+	6.18755i	0.344958	+	0.353142i	−0.520734	+	0.853719i	$0.674342\pi$
$308$	0.0188959	−	0.200903i	0.00107669	−	0.0114475i
$309$	−3.70840	−	5.31085i	−0.210964	−	0.302124i
$310$	−9.31181	−	3.66662i	−0.528875	−	0.208250i
$311$	9.67869	+	3.04475i	0.548828	+	0.172652i	0.561814	−	0.827264i	$-0.310104\pi$
$311$	9.67869	+	3.04475i	0.548828	+	0.172652i	−0.0129856	+	0.999916i	$0.504134\pi$
$312$	0.912141	−	1.52435i	0.0516398	−	0.0862992i
$313$	3.72173	+	5.07234i	0.210365	+	0.286705i	0.898588	−	0.438794i	$-0.144594\pi$
$313$	3.72173	+	5.07234i	0.210365	+	0.286705i	−0.688223	+	0.725499i	$0.741609\pi$
$314$	−9.72646	−	4.36698i	−0.548896	−	0.246443i
$315$	−0.903350	−	2.01201i	−0.0508980	−	0.113364i
$316$	−0.764708	−	0.482286i	−0.0430182	−	0.0271307i
$317$	−0.612051	−	0.0143520i	−0.0343762	−	0.000806089i	0.00625100	−	0.999980i	$-0.498010\pi$
$317$	−0.612051	−	0.0143520i	−0.0343762	−	0.000806089i	−0.0406272	+	0.999174i	$0.512936\pi$
$318$	−1.47234	−	12.5025i	−0.0825648	−	0.701107i
$319$	1.30221	−	1.69022i	0.0729097	−	0.0946344i
$320$	−0.511386	−	3.08804i	−0.0285874	−	0.172626i
$321$	19.8796	−	13.8813i	1.10957	−	0.774780i
$322$	−0.922068	+	2.93108i	−0.0513849	+	0.163343i
$323$	18.8373	−	10.6803i	1.04813	−	0.594268i
$324$	1.73790	−	2.36857i	0.0965498	−	0.131587i
$325$	−2.60105	−	6.17684i	−0.144280	−	0.342630i
$326$	5.59450	+	11.7173i	0.309851	+	0.648963i
$327$	1.24060	−	7.49145i	0.0686055	−	0.414278i
$328$	0.187240	+	0.200896i	0.0103386	+	0.0110926i
$329$	−1.37471	−	4.75674i	−0.0757901	−	0.262248i
$330$	0.330188	−	1.54156i	0.0181763	−	0.0848602i
$331$	0.942350	−	0.133440i	0.0517962	−	0.00733453i	−0.114259	−	0.993451i	$-0.536449\pi$
$331$	0.942350	−	0.133440i	0.0517962	−	0.00733453i	0.166055	+	0.986116i	$0.446897\pi$
$332$	−7.43407	−	5.45461i	−0.407998	−	0.299361i
$333$	−2.71495	−	3.35804i	−0.148778	−	0.184020i
$334$	−12.2366	−	9.42748i	−0.669555	−	0.515849i
$335$	−9.16166	−	29.1232i	−0.500555	−	1.59117i
$336$	0.473884	+	0.441673i	0.0258525	+	0.0240953i
$337$	−19.1806	+	22.6182i	−1.04483	+	1.23209i	−0.0727769	+	0.997348i	$0.523186\pi$
$337$	−19.1806	+	22.6182i	−1.04483	+	1.23209i	−0.972057	+	0.234743i	$0.924575\pi$
$338$	1.03458	+	10.9998i	0.0562739	+	0.598310i
$339$	13.4307	−	11.3895i	0.729456	−	0.618591i
$340$	−8.30095	+	3.04581i	−0.450182	+	0.165182i
$341$	−1.18892	−	0.436241i	−0.0643834	−	0.0236238i
$342$	8.08620	+	6.85724i	0.437252	+	0.370797i
$343$	4.00757	−	5.73929i	0.216388	−	0.309893i
$344$	−5.24234	+	3.48064i	−0.282648	+	0.187664i
$345$	−9.83267	+	21.9000i	−0.529373	+	1.17906i
$346$	5.61843	−	4.99561i	0.302049	−	0.268566i
$347$	0.187041	−	0.0540554i	0.0100409	−	0.00290184i	−0.272616	−	0.962123i	$-0.587889\pi$
$347$	0.187041	−	0.0540554i	0.0100409	−	0.00290184i	0.282657	+	0.959221i	$0.408784\pi$
$348$	1.74696	+	6.62316i	0.0936469	+	0.355039i
$349$	15.6656	−	23.5946i	0.838559	−	1.26299i	−0.124099	−	0.992270i	$-0.539604\pi$
$349$	15.6656	−	23.5946i	0.838559	−	1.26299i	0.962658	−	0.270720i	$-0.0872617\pi$
$350$	2.40119	−	0.455718i	0.128349	−	0.0243591i
$351$		−	7.78618i		−	0.415596i
$352$	−0.0738564	−	0.389151i	−0.00393656	−	0.0207418i
$353$	0.184793	+	2.62303i	0.00983556	+	0.139610i	1.00000		0.000298997i	$-9.51736e-5\pi$
$353$	0.184793	+	2.62303i	0.00983556	+	0.139610i	−0.990164	+	0.139909i	$0.955319\pi$
$354$	5.16794	+	2.17620i	0.274673	+	0.115664i
$355$	−44.4487	−	7.36081i	−2.35909	−	0.390671i
$356$	−4.67682	+	8.71896i	−0.247871	+	0.462104i
$357$	0.976182	−	1.54782i	0.0516650	−	0.0819196i
$358$	6.66182	−	2.26864i	0.352088	−	0.119902i
$359$	−0.211849	+	4.51474i	−0.0111810	+	0.238279i	0.986180	+	0.165677i	$0.0529809\pi$
$359$	−0.211849	+	4.51474i	−0.0111810	+	0.238279i	−0.997361	+	0.0726017i	$0.976870\pi$
$360$	−2.80001	−	3.30183i	−0.147573	−	0.174022i
$361$	27.7842	−	28.4434i	1.46233	−	1.49702i
$362$	−17.6983	−	3.35893i	−0.930201	−	0.176541i
$363$	−2.57088	+	13.5460i	−0.134936	+	0.710982i
$364$	0.706818	+	0.0832374i	0.0370473	+	0.00436282i
$365$	−2.88483	−	7.86222i	−0.150999	−	0.411527i
$366$	3.45061	+	16.1100i	0.180366	+	0.842082i
$367$	−17.6894	+	9.48855i	−0.923380	+	0.495298i	−0.864312	−	0.502956i	$-0.832246\pi$
$367$	−17.6894	+	9.48855i	−0.923380	+	0.495298i	−0.0590683	+	0.998254i	$0.518813\pi$
$368$	−0.141393	+	6.02980i	−0.00737062	+	0.314325i
$369$	0.364897	+	0.105456i	0.0189958	+	0.00548983i
$370$	8.81904	−	4.21070i	0.458480	−	0.218904i
$371$	4.32796	−	2.58977i	0.224697	−	0.134454i
$372$	3.43877	−	2.16876i	0.178292	−	0.112445i
$373$	−12.7184	−	8.44433i	−0.658532	−	0.437231i	0.178830	−	0.983880i	$-0.442769\pi$
$373$	−12.7184	−	8.44433i	−0.658532	−	0.437231i	−0.837362	+	0.546649i	$0.815903\pi$
$374$	−1.04112	+	0.409951i	−0.0538350	+	0.0211981i
$375$	−0.804072	+	0.0566472i	−0.0415221	+	0.00292525i
$376$	−5.18471	−	8.22082i	−0.267381	−	0.423957i
$377$	5.85203	+	4.73131i	0.301395	+	0.243675i
$378$	2.77638	+	0.594676i	0.142802	+	0.0305868i
$379$	14.1768	+	3.73935i	0.728214	+	0.192078i	0.600376	−	0.799718i	$-0.295017\pi$
$379$	14.1768	+	3.73935i	0.728214	+	0.192078i	0.127837	+	0.991795i	$0.459197\pi$
$380$	−19.3453	+	14.1942i	−0.992392	+	0.728149i
$381$	1.91944	−	1.87496i	0.0983359	−	0.0960571i
$382$	−0.0542149	−	0.0703691i	−0.00277387	−	0.00360040i
$383$	−18.5397	+	19.8918i	−0.947337	+	1.01643i	0.0525046	+	0.998621i	$0.483280\pi$
$383$	−18.5397	+	19.8918i	−0.947337	+	1.01643i	−0.999841	+	0.0178044i	$0.994332\pi$
$384$	1.13433	+	0.574625i	0.0578862	+	0.0293237i
$385$	0.617612	−	0.132287i	0.0314764	−	0.00674196i
$386$	4.85278	+	0.227711i	0.247000	+	0.0115902i
$387$	−3.74993	+	7.85400i	−0.190620	+	0.399241i
$388$	−3.78642	−	2.64394i	−0.192226	−	0.134226i
$389$	−1.11568	+	0.859563i	−0.0565674	+	0.0435816i	−0.638205	−	0.769867i	$-0.720323\pi$
$389$	−1.11568	+	0.859563i	−0.0565674	+	0.0435816i	0.581637	+	0.813448i	$0.302412\pi$
$390$	5.40822	+	1.29169i	0.273856	+	0.0654075i
$391$	16.8092	−	2.78364i	0.850076	−	0.140775i
$392$	2.17289	−	6.38063i	0.109747	−	0.322271i
$393$	4.84095	+	8.53817i	0.244193	+	0.430694i
$394$	0.211107	+	9.00279i	0.0106354	+	0.453554i
$395$	0.721742	−	2.73630i	0.0363148	−	0.137678i
$396$	−0.364025	−	0.409409i	−0.0182929	−	0.0205736i
$397$	13.5463	−	23.8921i	0.679868	−	1.19911i	−0.290360	−	0.956917i	$-0.593775\pi$
$397$	13.5463	−	23.8921i	0.679868	−	1.19911i	0.970228	−	0.242193i	$-0.0778667\pi$
$398$	−3.74422	−	2.00839i	−0.187681	−	0.100671i
$399$	1.37870	−	4.77054i	0.0690211	−	0.238826i
$400$	4.27968	−	2.16798i	0.213984	−	0.108399i
$401$	0.478476	−	0.386844i	0.0238940	−	0.0193180i	−0.616692	−	0.787205i	$-0.711527\pi$
$401$	0.478476	−	0.386844i	0.0238940	−	0.0193180i	0.640586	+	0.767887i	$0.278692\pi$
$402$	11.7406	+	3.99818i	0.585567	+	0.199411i
$403$	1.63648	−	4.15603i	0.0815187	−	0.207026i
$404$	4.62954	−	11.7573i	0.230328	−	0.584945i
$405$	8.70457	+	2.96429i	0.432533	+	0.147297i
$406$	−2.13404	+	1.72535i	−0.105911	+	0.0856277i
$407$	1.10321	−	0.558858i	0.0546840	−	0.0277016i
$408$	0.997293	−	3.45082i	0.0493733	−	0.170841i
$409$	17.9700	+	9.63903i	0.888558	+	0.476620i	0.852498	−	0.522730i	$-0.175086\pi$
$409$	17.9700	+	9.63903i	0.888558	+	0.476620i	0.0360599	+	0.999350i	$0.488519\pi$
$410$	−0.423968	+	0.747769i	−0.0209383	+	0.0369297i
$411$	−1.21692	−	1.36864i	−0.0600261	−	0.0675098i
$412$	1.29920	−	4.92558i	0.0640069	−	0.242666i
$413$	0.0526654	+	2.24595i	0.00259149	+	0.110516i
$414$	4.11446	+	7.25683i	0.202215	+	0.356654i
$415$	9.30380	−	27.3204i	0.456705	−	1.34111i
$416$	1.37825	−	0.228241i	0.0675740	−	0.0111904i
$417$	5.64298	+	1.34776i	0.276338	+	0.0660003i
$418$	−2.40527	+	1.85310i	−0.117646	+	0.0906383i
$419$	−24.1680	−	16.8757i	−1.18068	−	0.824433i	−0.193045	−	0.981190i	$-0.561836\pi$
$419$	−24.1680	−	16.8757i	−1.18068	−	0.824433i	−0.987637	+	0.156757i	$0.949896\pi$
$420$	−0.873648	+	1.82980i	−0.0426296	+	0.0892851i
$421$	2.26669	+	0.106362i	0.110472	+	0.00518376i	0.102036	−	0.994781i	$-0.467464\pi$
$421$	2.26669	+	0.106362i	0.110472	+	0.00518376i	0.00843531	+	0.999964i	$0.497315\pi$
$422$	3.57487	−	0.765704i	0.174022	−	0.0372739i
$423$	−11.9917	−	6.07472i	−0.583058	−	0.295363i
$424$	6.75007	−	7.24234i	0.327812	−	0.351719i
$425$	−8.27108	−	10.7356i	−0.401206	−	0.520752i
$426$	13.0929	−	12.7895i	0.634352	−	0.619652i
$427$	−5.32183	+	3.90479i	−0.257541	+	0.188966i
$428$	18.4375	+	4.86317i	0.891209	+	0.235070i
$429$	0.688027	+	0.147369i	0.0332182	+	0.00711504i
$430$	−15.3167	−	12.3834i	−0.738638	−	0.597182i
$431$	10.9284	+	17.3280i	0.526402	+	0.834658i	0.998910	−	0.0466680i	$-0.0148603\pi$
$431$	10.9284	+	17.3280i	0.526402	+	0.834658i	−0.472508	+	0.881326i	$0.656651\pi$
$432$	5.55966	−	0.391680i	0.267489	−	0.0188447i
$433$	−33.8165	+	13.3156i	−1.62512	+	0.639907i	−0.991065	−	0.133382i	$-0.957416\pi$
$433$	−33.8165	+	13.3156i	−1.62512	+	0.639907i	−0.634054	+	0.773289i	$0.718610\pi$
$434$	1.35696	+	0.900952i	0.0651363	+	0.0432471i
$435$	−18.1347	+	11.4372i	−0.869494	+	0.548373i
$436$	5.12435	−	3.06632i	0.245412	−	0.146850i
$437$	41.7231	−	19.9209i	1.99589	−	0.952947i
$438$	3.26843	+	0.944582i	0.156171	+	0.0451339i
$439$	−0.800049	+	34.1187i	−0.0381843	+	1.62840i	0.561022	+	0.827801i	$0.310408\pi$
$439$	−0.800049	+	34.1187i	−0.0381843	+	1.62840i	−0.599207	+	0.800594i	$0.704517\pi$
$440$	1.09257	−	0.586050i	0.0520861	−	0.0279388i
$441$	−1.95255	−	9.11595i	−0.0929786	−	0.434093i
$442$	−1.35940	−	3.70486i	−0.0646601	−	0.176222i
$443$	−10.4947	−	1.23589i	−0.498619	−	0.0587191i	−0.136099	−	0.990695i	$-0.543457\pi$
$443$	−10.4947	−	1.23589i	−0.498619	−	0.0587191i	−0.362520	+	0.931976i	$0.618083\pi$
$444$	−0.740261	+	3.90045i	−0.0351312	+	0.185107i
$445$	−30.4263	−	5.77456i	−1.44234	−	0.273740i
$446$	1.27548	−	1.30574i	0.0603956	−	0.0618284i
$447$	−13.2781	−	15.6579i	−0.628034	−	0.740592i
$448$	−0.0238788	+	0.508885i	−0.00112817	+	0.0240425i
$449$	28.3215	−	9.64472i	1.33657	−	0.455163i	0.439977	−	0.898009i	$-0.354987\pi$
$449$	28.3215	−	9.64472i	1.33657	−	0.455163i	0.896598	+	0.442846i	$0.146031\pi$
$450$	3.53963	−	5.61241i	0.166860	−	0.264572i
$451$	−0.0514180	+	0.0958581i	−0.00242118	+	0.00451378i
$452$	13.6627	+	2.26258i	0.642640	+	0.106423i
$453$	12.3033	+	5.18090i	0.578061	+	0.243420i
$454$	1.15285	+	16.3640i	0.0541059	+	0.768000i
$455$	0.415376	+	2.18863i	0.0194731	+	0.102604i
$456$		−	9.74741i		−	0.456464i
$457$	−4.53717	+	0.861102i	−0.212240	+	0.0402807i	−0.291489	−	0.956574i	$-0.594151\pi$
$457$	−4.53717	+	0.861102i	−0.212240	+	0.0402807i	0.0792492	+	0.996855i	$0.474748\pi$
$458$	1.83527	−	2.76417i	0.0857563	−	0.129161i
$459$	−4.01545	−	15.2236i	−0.187425	−	0.710575i
$460$	−18.1368	+	5.24157i	−0.845633	+	0.244390i
$461$	−19.3927	+	17.2429i	−0.903206	+	0.803083i	−0.981024	−	0.193885i	$-0.937891\pi$
$461$	−19.3927	+	17.2429i	−0.903206	+	0.803083i	0.0778184	+	0.996968i	$0.475205\pi$
$462$	−0.105097	+	0.234080i	−0.00488956	+	0.0108904i
$463$	−26.8313	+	17.8146i	−1.24696	+	0.827914i	−0.990348	−	0.138602i	$-0.955739\pi$
$463$	−26.8313	+	17.8146i	−1.24696	+	0.827914i	−0.256608	+	0.966516i	$0.582605\pi$
$464$	−3.08397	+	4.41660i	−0.143170	+	0.205035i
$465$	9.70558	+	8.23049i	0.450085	+	0.381680i
$466$	15.4653	+	5.67456i	0.716414	+	0.262869i
$467$	−26.0355	+	9.55303i	−1.20478	+	0.442061i	−0.866592	−	0.499017i	$-0.833694\pi$
$467$	−26.0355	+	9.55303i	−1.20478	+	0.442061i	−0.338187	+	0.941079i	$0.609814\pi$
$468$	1.47367	−	1.24969i	0.0681202	−	0.0577671i
$469$	0.465306	+	4.94718i	0.0214858	+	0.228440i
$470$	19.6761	−	23.2024i	0.907589	−	1.07025i
$471$	9.91760	+	9.24348i	0.456979	+	0.425917i
$472$	1.32333	+	4.20660i	0.0609110	+	0.193625i
$473$	−1.97446	−	1.52119i	−0.0907857	−	0.0699445i
$474$	0.722780	+	0.893986i	0.0331984	+	0.0410622i
$475$	−29.6504	−	21.7554i	−1.36045	−	0.998208i
$476$	1.42490	−	0.201771i	0.0653102	−	0.00924815i
$477$	2.86786	−	13.3893i	0.131310	−	0.613054i
$478$	−1.21038	−	4.18812i	−0.0553613	−	0.191560i
$479$	2.33454	+	2.50479i	0.106668	+	0.114447i	0.782624	−	0.622495i	$-0.213881\pi$
$479$	2.33454	+	2.50479i	0.106668	+	0.114447i	−0.675956	+	0.736942i	$0.736269\pi$
$480$	−0.650266	+	3.92667i	−0.0296805	+	0.179227i
$481$	1.87931	+	3.93609i	0.0856891	+	0.179470i
$482$	2.53560	+	6.02142i	0.115494	+	0.274268i
$483$	2.31137	−	3.15016i	0.105171	−	0.143337i
$484$	−9.43249	+	5.34800i	−0.428749	+	0.243091i
$485$	4.33780	−	13.7891i	0.196969	−	0.626129i
$486$	10.6462	−	7.43387i	0.482920	−	0.337207i
$487$	−2.55400	−	15.4225i	−0.115733	−	0.698859i	−0.980475	−	0.196643i	$-0.936996\pi$
$487$	−2.55400	−	15.4225i	−0.115733	−	0.698859i	0.864742	−	0.502216i	$-0.167482\pi$
$488$	−7.90759	+	10.2638i	−0.357960	+	0.464620i
$489$	−1.93101	−	16.3973i	−0.0873231	−	0.741512i
$490$	21.0925	+	0.494598i	0.952861	+	0.0223437i
$491$	21.1344	+	13.3290i	0.953782	+	0.601531i	0.917468	−	0.397809i	$-0.130229\pi$
$491$	21.1344	+	13.3290i	0.953782	+	0.601531i	0.0363137	+	0.999340i	$0.488438\pi$
$492$	−0.143031	−	0.318569i	−0.00644832	−	0.0143622i
$493$	13.8819	+	6.23270i	0.625210	+	0.280707i
$494$	−6.33514	−	8.63414i	−0.285031	−	0.388468i
$495$	0.880502	−	1.47147i	0.0395756	−	0.0661378i
$496$	3.04990	+	0.959446i	0.136944	+	0.0430804i
$497$	6.82297	+	2.68661i	0.306052	+	0.120511i
$498$	6.71244	+	9.61299i	0.300792	+	0.430768i
$499$	−0.522010	+	5.55007i	−0.0233684	+	0.248455i	0.976141	+	0.217137i	$0.0696719\pi$
$499$	−0.522010	+	5.55007i	−0.0233684	+	0.248455i	−0.999509	+	0.0313179i	$0.990030\pi$
$500$	−0.442957	−	0.453466i	−0.0198097	−	0.0202796i
$501$	10.8646	+	16.3637i	0.485396	+	0.731076i
$502$	11.7851	−	13.2544i	0.525997	−	0.591575i
$503$	−13.7591	−	40.4034i	−0.613489	−	1.80150i	−0.597834	−	0.801620i	$-0.703972\pi$
$503$	−13.7591	−	40.4034i	−0.613489	−	1.80150i	−0.0156551	−	0.999877i	$-0.504983\pi$
$504$	0.333061	+	0.620924i	0.0148357	+	0.0276581i
$505$	39.4537	+	2.77953i	1.75567	+	0.123687i
$506$	−2.27894	+	0.716916i	−0.101311	+	0.0318708i
$507$	3.26361	−	13.6645i	0.144942	−	0.606861i
$508$	2.10089	+	0.197599i	0.0932119	+	0.00876702i
$509$	−25.8154	−	15.4475i	−1.14425	−	0.684697i	−0.189432	−	0.981894i	$-0.560665\pi$
$509$	−25.8154	−	15.4475i	−1.14425	−	0.684697i	−0.954816	+	0.297197i	$0.903948\pi$
$510$	11.2403	−	0.263574i	0.497729	−	0.0116713i
$511$	0.191107	+	1.34959i	0.00845405	+	0.0597023i
$512$	0.232305	+	0.972643i	0.0102665	+	0.0429851i
$513$	−21.9376	−	36.6615i	−0.968568	−	1.61865i
$514$	−7.03026	+	16.6951i	−0.310092	+	0.736390i
$515$	15.9273	−	0.747369i	0.701840	−	0.0329330i
$516$	7.73693	−	2.04073i	0.340599	−	0.0898383i
$517$	2.42039	−	2.99372i	0.106449	−	0.131664i
$518$	−1.54706	+	0.369499i	−0.0679739	+	0.0162348i
$519$	−8.81062	+	3.71013i	−0.386743	+	0.162856i
$520$	1.97606	+	3.90083i	0.0866562	+	0.171063i
$521$	17.6966	−	2.08401i	0.775300	−	0.0913021i	0.279972	−	0.960008i	$-0.409675\pi$
$521$	17.6966	−	2.08401i	0.775300	−	0.0913021i	0.495328	+	0.868706i	$0.335048\pi$
$522$	−0.523586	+	7.43199i	−0.0229168	+	0.325289i
$523$	19.8718	−	39.2277i	0.868933	−	1.71531i	0.189074	−	0.981963i	$-0.439451\pi$
$523$	19.8718	−	39.2277i	0.868933	−	1.71531i	0.679859	−	0.733343i	$-0.262041\pi$
$524$	−2.65887	+	7.24640i	−0.116153	+	0.316561i
$525$	−3.07710	−	0.435728i	−0.134296	−	0.0190167i
$526$	−22.8204	−	22.2916i	−0.995018	−	0.971959i
$527$	1.05632	−	8.96983i	0.0460140	−	0.390732i
$528$	−0.0706167	+	0.498693i	−0.00307320	+	0.0217028i
$529$	13.3197	−	1.25278i	0.579118	−	0.0544688i
$530$	27.9647	+	13.3519i	1.21471	+	0.579970i
$531$	4.55804	+	4.05277i	0.197802	+	0.175875i
$532$	3.56260	−	1.59954i	0.154458	−	0.0693486i
$533$	−0.333742	−	0.189224i	−0.0144560	−	0.00819621i
$534$	9.20346	−	8.57788i	0.398272	−	0.371201i
$535$	2.79756	+	59.6192i	0.120949	+	2.57756i
$536$	3.57359	+	9.07556i	0.154356	+	0.392005i
$537$	−8.94873			−0.386166
$538$	−5.29776	+	15.5220i	−0.228403	+	0.669203i
$539$	2.66988			0.115000
$540$	6.39164	+	16.2323i	0.275052	+	0.698528i
$541$	−0.543655	−	11.5859i	−0.0233736	−	0.498117i	−0.979040	−	0.203667i	$-0.934714\pi$
$541$	−0.543655	−	11.5859i	−0.0233736	−	0.498117i	0.955667	−	0.294451i	$-0.0951366\pi$
$542$	5.65863	−	5.27400i	0.243059	−	0.226538i
$543$	19.9264	+	11.2978i	0.855126	+	0.484837i
$544$	2.57704	−	1.15704i	0.110490	−	0.0496077i
$545$	13.9688	+	12.4203i	0.598357	+	0.532027i
$546$	−0.816672	−	0.389924i	−0.0349503	−	0.0166872i
$547$	1.72947	−	0.162665i	0.0739470	−	0.00695506i	−0.0566034	−	0.998397i	$-0.518027\pi$
$547$	1.72947	−	0.162665i	0.0739470	−	0.00695506i	0.130550	+	0.991442i	$0.458326\pi$
$548$	0.201932	−	1.42604i	0.00862612	−	0.0609174i
$549$	−2.09588	+	17.7973i	−0.0894498	+	0.759571i
$550$	1.35935	+	1.32785i	0.0579630	+	0.0566197i
$551$	40.8850	+	5.78946i	1.74176	+	0.246639i
$552$	2.64187	−	7.20007i	0.112446	−	0.306455i
$553$	−0.208138	+	0.410872i	−0.00885092	+	0.0174721i
$554$	−0.190622	+	2.70576i	−0.00809873	+	0.114957i
$555$	−12.3414	+	1.45337i	−0.523865	+	0.0616921i
$556$	2.06184	+	4.07015i	0.0874415	+	0.172613i
$557$	−30.7927	+	12.9667i	−1.30473	+	0.549418i	−0.926501	−	0.376293i	$-0.877198\pi$
$557$	−30.7927	+	12.9667i	−1.30473	+	0.549418i	−0.378230	+	0.925712i	$0.623467\pi$
$558$	4.30113	−	1.02728i	0.182081	−	0.0434882i
$559$	5.52694	−	6.83612i	0.233765	−	0.289137i
$560$	−1.54187	+	0.406693i	−0.0651561	+	0.0171859i
$561$	1.42123	−	0.0666897i	0.0600045	−	0.00281564i
$562$	8.74311	−	20.7627i	0.368806	−	0.875821i
$563$	−1.37816	−	2.30315i	−0.0580826	−	0.0970662i	0.827690	−	0.561185i	$-0.189655\pi$
$563$	−1.37816	−	2.30315i	−0.0580826	−	0.0970662i	−0.885773	+	0.464119i	$0.846371\pi$
$564$	2.87100	+	12.0206i	0.120891	+	0.506159i
$565$	6.07760	+	42.9198i	0.255686	+	1.80565i
$566$	5.71985	−	0.134125i	0.240423	−	0.00563769i
$567$	−1.28426	−	0.768479i	−0.0539339	−	0.0322731i
$568$	14.3306	+	1.34786i	0.601298	+	0.0565549i
$569$	10.1872	−	42.6529i	0.427069	−	1.78810i	−0.169488	−	0.985532i	$-0.554211\pi$
$569$	10.1872	−	42.6529i	0.427069	−	1.78810i	0.596557	−	0.802571i	$-0.296535\pi$
$570$	29.1042	−	9.15567i	1.21904	−	0.383489i
$571$	−29.5025	−	2.07846i	−1.23464	−	0.0869810i	−0.562118	−	0.827057i	$-0.690013\pi$
$571$	−29.5025	−	2.07846i	−1.23464	−	0.0869810i	−0.672523	+	0.740076i	$0.734790\pi$
$572$	0.261564	+	0.487632i	0.0109366	+	0.0203889i
$573$	0.0364130	+	0.106926i	0.00152118	+	0.00446690i
$574$	0.0929632	−	0.104553i	0.00388021	−	0.00436397i
$575$	−16.0053	−	24.1062i	−0.667467	−	1.00530i
$576$	0.966465	+	0.989393i	0.0402694	+	0.0412247i
$577$	−2.47006	+	26.2620i	−0.102830	+	1.09330i	0.780694	+	0.624914i	$0.214866\pi$
$577$	−2.47006	+	26.2620i	−0.102830	+	1.09330i	−0.883524	+	0.468386i	$0.844836\pi$
$578$	5.16409	+	7.39557i	0.214798	+	0.307615i
$579$	−5.74792	−	2.26330i	−0.238875	−	0.0940595i
$580$	−16.0840	−	5.05975i	−0.667851	−	0.210095i
$581$	−2.41197	+	4.03082i	−0.100065	+	0.167227i
$582$	3.47391	+	4.73458i	0.143998	+	0.196255i
$583$	3.57743	+	1.60619i	0.148162	+	0.0665218i
$584$	1.09589	+	2.44084i	0.0453481	+	0.101003i
$585$	5.11558	+	3.22629i	0.211503	+	0.133391i
$586$	16.1150	+	0.377880i	0.665703	+	0.0156101i
$587$	2.16689	+	18.4003i	0.0894370	+	0.759463i	0.962392	+	0.271663i	$0.0875736\pi$
$587$	2.16689	+	18.4003i	0.0894370	+	0.759463i	−0.872955	+	0.487800i	$0.837800\pi$
$588$	−5.23098	+	6.78963i	−0.215722	+	0.280000i
$589$	−4.00420	−	24.1796i	−0.164990	−	0.996303i
$590$	−11.3172	+	7.90246i	−0.465923	+	0.325339i
$591$	3.43623	−	10.9231i	0.141348	−	0.449318i
$592$	−2.71600	+	1.53991i	−0.111627	+	0.0632898i
$593$	−2.22922	+	3.03819i	−0.0915430	+	0.124764i	−0.849607	−	0.527417i	$-0.823161\pi$
$593$	−2.22922	+	3.03819i	−0.0915430	+	0.124764i	0.758064	+	0.652181i	$0.226146\pi$
$594$	0.856761	+	2.03459i	0.0351533	+	0.0834804i
$595$	1.94085	+	4.06499i	0.0795672	+	0.166648i
$596$	2.63777	−	15.9283i	0.108047	−	0.652450i
$597$	3.68364	+	3.95228i	0.150761	+	0.161756i
$598$	−2.33941	−	8.09478i	−0.0956655	−	0.331020i
$599$	−9.19389	+	42.9238i	−0.375652	+	1.75382i	0.244798	+	0.969574i	$0.421279\pi$
$599$	−9.19389	+	42.9238i	−0.375652	+	1.75382i	−0.620450	+	0.784246i	$0.713050\pi$
$600$	−6.04010	+	0.855300i	−0.246586	+	0.0349175i
$601$	−1.56370	−	1.14733i	−0.0637846	−	0.0468007i	0.559217	−	0.829021i	$-0.311102\pi$
$601$	−1.56370	−	1.14733i	−0.0637846	−	0.0468007i	−0.623002	+	0.782221i	$0.714087\pi$
$602$	2.01549	+	2.49290i	0.0821452	+	0.101603i
$603$	10.6866	+	8.23335i	0.435192	+	0.335288i
$604$	3.15045	+	10.0147i	0.128190	+	0.407491i
$605$	−24.8281	−	23.1405i	−1.00941	−	0.940795i
$606$	−10.3920	+	12.2544i	−0.422145	+	0.497802i
$607$	−0.738778	−	7.85477i	−0.0299861	−	0.318815i	−0.997755	−	0.0669742i	$-0.978665\pi$
$607$	−0.738778	−	7.85477i	−0.0299861	−	0.318815i	0.967769	−	0.251841i	$-0.0810360\pi$
$608$	5.84645	−	4.95789i	0.237105	−	0.201069i
$609$	3.27597	−	1.20203i	0.132749	−	0.0487086i
$610$	−38.0735	−	13.9700i	−1.54155	−	0.565631i
$611$	10.3557	+	8.78178i	0.418945	+	0.355273i
$612$	2.23683	−	3.20340i	0.0904185	−	0.129490i
$613$	14.7628	−	9.80171i	0.596263	−	0.395888i	−0.218369	−	0.975866i	$-0.570074\pi$
$613$	14.7628	−	9.80171i	0.596263	−	0.395888i	0.814632	+	0.579979i	$0.196939\pi$
$614$	3.54284	−	7.89087i	0.142977	−	0.318450i
$615$	0.816845	−	0.726295i	0.0329384	−	0.0292870i
$616$	−0.193856	+	0.0560249i	−0.00781070	+	0.00225731i
$617$	7.53705	+	28.5748i	0.303430	+	1.15038i	0.928960	+	0.370179i	$0.120704\pi$
$617$	7.53705	+	28.5748i	0.303430	+	1.15038i	−0.625530	+	0.780200i	$0.715117\pi$
$618$	−3.58288	+	5.39633i	−0.144125	+	0.217072i
$619$	1.68541	−	0.319872i	0.0677425	−	0.0128567i	−0.152478	−	0.988307i	$-0.548725\pi$
$619$	1.68541	−	0.319872i	0.0677425	−	0.0128567i	0.220220	+	0.975450i	$0.429322\pi$
$620$			10.0077i			0.401919i
$621$	−6.26803	−	33.0264i	−0.251528	−	1.32530i
$622$	−0.713044	−	10.1212i	−0.0285905	−	0.405824i
$623$	4.64542	+	1.95617i	0.186115	+	0.0783724i
$624$	−1.75254	−	0.290225i	−0.0701579	−	0.0116183i
$625$	12.2765	−	22.8869i	0.491059	−	0.915477i
$626$	3.35607	−	5.32135i	0.134135	−	0.212684i
$627$	3.65481	−	1.24462i	0.145959	−	0.0497055i
$628$	−0.499744	+	10.6501i	−0.0199419	+	0.424985i
$629$	5.70434	+	6.72668i	0.227447	+	0.268210i
$630$	−1.54113	+	1.57770i	−0.0614002	+	0.0628569i
$631$	36.2427	+	6.87844i	1.44280	+	0.273826i	0.847977	−	0.530033i	$-0.177820\pi$
$631$	36.2427	+	6.87844i	1.44280	+	0.273826i	0.594820	+	0.803859i	$0.297223\pi$
$632$	−0.168577	+	0.888234i	−0.00670562	+	0.0353321i
$633$	−4.61692	−	0.543704i	−0.183506	−	0.0216103i
$634$	0.210889	+	0.574751i	0.00837549	+	0.0228263i
$635$	1.38335	+	6.45851i	0.0548967	+	0.256298i
$636$	−11.0937	+	5.95064i	−0.439895	+	0.235958i
$637$	−0.220748	+	9.41395i	−0.00874635	+	0.372994i
$638$	−2.04980	−	0.592396i	−0.0811523	−	0.0234532i
$639$	17.9654	−	8.57765i	0.710698	−	0.339327i
$640$	−2.68595	+	1.60722i	−0.106171	+	0.0635310i
$641$	−36.2978	+	22.8923i	−1.43368	+	0.904191i	−0.433682	+	0.901066i	$0.642786\pi$
$641$	−36.2978	+	22.8923i	−1.43368	+	0.904191i	−0.999995	+	0.00312516i	$0.999005\pi$
$642$	−20.1996	−	13.4115i	−0.797214	−	0.529309i
$643$	−25.7015	+	10.1202i	−1.01357	+	0.399102i	−0.814052	−	0.580792i	$-0.802743\pi$
$643$	−25.7015	+	10.1202i	−1.01357	+	0.399102i	−0.199515	+	0.979895i	$0.563937\pi$
$644$	3.06510	−	0.215937i	0.120782	−	0.00850912i
$645$	13.3605	+	21.1843i	0.526070	+	0.834132i
$646$	−16.8392	−	13.6144i	−0.662531	−	0.535651i
$647$	−42.7782	−	9.16269i	−1.68178	−	0.360223i	−0.734004	−	0.679146i	$-0.762350\pi$
$647$	−42.7782	−	9.16269i	−1.68178	−	0.360223i	−0.947781	+	0.318923i	$0.896679\pi$
$648$	−2.84061	−	0.749254i	−0.111590	−	0.0294335i
$649$	−1.40830	+	1.03332i	−0.0552807	+	0.0405612i
$650$	−4.79437	+	4.68326i	−0.188050	+	0.183693i
$651$	−1.26406	−	1.64070i	−0.0495423	−	0.0643043i
$652$	8.85286	−	9.49849i	0.346705	−	0.371989i
$653$	−34.1957	−	17.3227i	−1.33818	−	0.677891i	−0.370210	−	0.928948i	$-0.620714\pi$
$653$	−34.1957	−	17.3227i	−1.33818	−	0.677891i	−0.967972	+	0.251057i	$0.919222\pi$
$654$	−7.42507	+	1.59038i	−0.290343	+	0.0621888i
$655$	−24.1340	−	1.13246i	−0.942994	−	0.0442489i
$656$	0.118325	−	0.247825i	0.00461983	−	0.00967593i
$657$	3.03408	+	2.11860i	0.118371	+	0.0826546i
$658$	−3.92232	+	3.02189i	−0.152908	+	0.117806i
$659$	32.7303	+	7.81727i	1.27499	+	0.304518i	0.812946	−	0.582339i	$-0.197863\pi$
$659$	32.7303	+	7.81727i	1.27499	+	0.304518i	0.462044	+	0.886857i	$0.347116\pi$
$660$	−1.55534	+	0.257569i	−0.0605417	+	0.0100259i
$661$	5.80388	−	17.0430i	0.225745	−	0.662895i	−0.773820	−	0.633405i	$-0.781657\pi$
$661$	5.80388	−	17.0430i	0.225745	−	0.662895i	0.999565	−	0.0294893i	$-0.00938811\pi$
$662$	−0.469420	−	0.827934i	−0.0182445	−	0.0321786i
$663$	0.117638	+	5.01675i	0.00456868	+	0.194834i
$664$	−2.35163	+	8.91561i	−0.0912610	+	0.345993i
$665$	8.12227	+	9.13491i	0.314968	+	0.354236i
$666$	−2.12984	+	3.75648i	−0.0825296	+	0.145561i
$667$	28.6312	+	15.3577i	1.10860	+	0.594651i
$668$	−4.28871	+	14.8397i	−0.165935	+	0.574166i
$669$	−2.07052	+	1.04887i	−0.0800508	+	0.0405518i
$670$	−23.7415	+	19.1948i	−0.917214	+	0.741559i
$671$	−4.85813	−	1.65441i	−0.187546	−	0.0638677i
$672$	0.237340	−	0.602753i	0.00915559	−	0.0232517i
$673$	18.8467	−	47.8635i	0.726488	−	1.84500i	0.241762	−	0.970336i	$-0.422275\pi$
$673$	18.8467	−	47.8635i	0.726488	−	1.84500i	0.484726	−	0.874666i	$-0.338919\pi$
$674$	28.0728	+	9.56004i	1.08133	+	0.368239i
$675$	−20.7928	+	16.8108i	−0.800316	+	0.647048i
$676$	9.85588	−	4.99275i	0.379072	−	0.192029i
$677$	−9.62892	+	33.3178i	−0.370069	+	1.28051i	0.531199	+	0.847247i	$0.321742\pi$
$677$	−9.62892	+	33.3178i	−0.370069	+	1.28051i	−0.901269	+	0.433261i	$0.857363\pi$
$678$	−15.5183	−	8.32394i	−0.595975	−	0.319679i
$679$	−1.16039	+	2.04663i	−0.0445317	+	0.0785423i
$680$	5.87533	+	6.60782i	0.225308	+	0.253399i
$681$	5.32009	−	20.1698i	0.203866	−	0.772908i
$682$	0.0296882	+	1.26608i	0.00113682	+	0.0484805i
$683$	−8.75074	−	15.4340i	−0.334838	−	0.590567i	0.650838	−	0.759216i	$-0.274418\pi$
$683$	−8.75074	−	15.4340i	−0.334838	−	0.590567i	−0.985676	+	0.168650i	$0.946059\pi$
$684$	3.41780	−	10.0363i	0.130683	−	0.383747i
$685$	4.44759	−	0.736532i	0.169934	−	0.0281415i
$686$	−6.80851	−	1.62614i	−0.259950	−	0.0620863i
$687$	−3.34216	+	2.57492i	−0.127511	+	0.0982393i
$688$	5.15931	+	3.60258i	0.196697	+	0.137347i
$689$	−5.95919	+	12.4812i	−0.227027	+	0.475494i
$690$	23.9797	+	1.12522i	0.912892	+	0.0428364i
$691$	−2.61150	+	0.559358i	−0.0993460	+	0.0212790i	−0.258843	−	0.965919i	$-0.583341\pi$
$691$	−2.61150	+	0.559358i	−0.0993460	+	0.0212790i	0.159497	+	0.987198i	$0.449013\pi$
$692$	−6.70672	−	3.39746i	−0.254951	−	0.129152i
$693$	−0.190289	+	0.204166i	−0.00722848	+	0.00775564i
$694$	−0.118825	−	0.154231i	−0.00451053	−	0.00585452i
$695$	−10.2161	+	9.97938i	−0.387520	+	0.378539i
$696$	5.52257	−	4.05208i	0.209332	−	0.153594i
$697$	−0.750120	−	0.197856i	−0.0284128	−	0.00749433i
$698$	−27.6935	−	5.93169i	−1.04821	−	0.224518i
$699$	−16.2894	−	13.1698i	−0.616121	−	0.498128i
$700$	−1.30378	−	2.06726i	−0.0492781	−	0.0781349i
$701$	−24.1907	+	1.70424i	−0.913670	+	0.0643684i	−0.519308	−	0.854587i	$-0.673810\pi$
$701$	−24.1907	+	1.70424i	−0.913670	+	0.0643684i	−0.394362	+	0.918955i	$0.629034\pi$
$702$	−7.24477	+	2.85270i	−0.273436	+	0.107668i
$703$	19.9388	+	13.2383i	0.752004	+	0.499292i
$704$	−0.335032	+	0.211298i	−0.0126270	+	0.00796359i
$705$	−33.1949	+	19.8632i	−1.25019	+	0.748091i
$706$	2.37293	−	1.13297i	0.0893066	−	0.0426399i
$707$	−6.18420	−	1.78725i	−0.232581	−	0.0672164i
$708$	0.131453	−	5.60590i	0.00494030	−	0.210683i
$709$	−9.88873	+	5.30428i	−0.371379	+	0.199206i	−0.647765	−	0.761840i	$-0.724296\pi$
$709$	−9.88873	+	5.30428i	−0.371379	+	0.199206i	0.276386	+	0.961047i	$0.410863\pi$
$710$	9.43612	+	44.0548i	0.354131	+	1.65335i
$711$	0.430736	+	1.17391i	0.0161539	+	0.0440252i
$712$	9.82619	+	1.15717i	0.368252	+	0.0433666i
$713$	3.59571	−	18.9459i	0.134660	−	0.709529i
$714$	−1.79785	−	0.341211i	−0.0672829	−	0.0127695i
$715$	−1.21030	+	1.23902i	−0.0452628	+	0.0463366i
$716$	−4.55165	−	5.36741i	−0.170103	−	0.200589i
$717$	−0.259834	+	5.53736i	−0.00970369	+	0.206797i
$718$	4.27843	−	1.45699i	0.159669	−	0.0543745i
$719$	12.5189	−	19.8499i	0.466877	−	0.740276i	−0.527107	−	0.849799i	$-0.676723\pi$
$719$	12.5189	−	19.8499i	0.466877	−	0.740276i	0.993984	+	0.109523i	$0.0349323\pi$
$720$	−2.04637	+	3.81503i	−0.0762638	+	0.142178i
$721$	−2.56026	−	0.423986i	−0.0953491	−	0.0157900i
$722$	−36.6452	−	15.4312i	−1.36379	−	0.574289i
$723$	−0.583845	−	8.28732i	−0.0217134	−	0.308209i
$724$	3.35893	+	17.6983i	0.124834	+	0.657752i
$725$		−	25.8429i		−	0.959781i
$726$	13.5460	−	2.57088i	0.502740	−	0.0954143i
$727$	−10.9938	+	16.5582i	−0.407736	+	0.614109i	−0.978312	−	0.207136i	$-0.933586\pi$
$727$	−10.9938	+	16.5582i	−0.407736	+	0.614109i	0.570576	+	0.821245i	$0.306720\pi$
$728$	−0.181515	−	0.688166i	−0.00672738	−	0.0255051i
$729$	−24.3287	+	7.03105i	−0.901064	+	0.260409i
$730$	−6.25857	+	5.56479i	−0.231640	+	0.205962i
$731$	7.28081	−	16.2163i	0.269290	−	0.599783i
$732$	13.7255	−	9.11304i	0.507311	−	0.336828i
$733$	25.1910	−	36.0764i	0.930451	−	1.33251i	−0.0126200	−	0.999920i	$-0.504017\pi$
$733$	25.1910	−	36.0764i	0.930451	−	1.33251i	0.943071	−	0.332592i	$-0.107923\pi$
$734$	15.3098	+	12.9830i	0.565096	+	0.479211i
$735$	−25.1861	−	9.24138i	−0.929005	−	0.340873i
$736$	5.66232	−	2.07764i	0.208716	−	0.0765827i
$737$	−2.94660	+	2.49877i	−0.108539	+	0.0920432i
$738$	−0.0355679	−	0.378161i	−0.00130927	−	0.0139203i
$739$	4.52583	−	5.33696i	0.166485	−	0.196323i	−0.673099	−	0.739552i	$-0.735037\pi$
$739$	4.52583	−	5.33696i	0.166485	−	0.196323i	0.839585	+	0.543229i	$0.182798\pi$
$740$	−7.14903	−	6.66310i	−0.262803	−	0.244940i
$741$	4.08634	+	12.9897i	0.150115	+	0.477189i
$742$	−3.99537	−	3.07818i	−0.146675	−	0.113003i
$743$	18.6361	+	23.0504i	0.683690	+	0.845638i	0.994489	−	0.104838i	$-0.0334324\pi$
$743$	18.6361	+	23.0504i	0.683690	+	0.845638i	−0.310799	+	0.950476i	$0.600597\pi$
$744$	−3.27785	−	2.40506i	−0.120172	−	0.0881739i
$745$	50.0370	−	7.08542i	1.83321	−	0.259590i
$746$	−3.19740	+	14.9278i	−0.117065	+	0.546547i
$747$	3.54071	+	12.2515i	0.129548	+	0.448259i
$748$	0.762891	+	0.818528i	0.0278941	+	0.0299284i
$749$	1.58707	−	9.58359i	0.0579902	−	0.350177i
$750$	0.347304	+	0.727407i	0.0126818	+	0.0265612i
$751$	−12.5900	−	29.8981i	−0.459417	−	1.09100i	−0.972551	−	0.232691i	$-0.925247\pi$
$751$	−12.5900	−	29.8981i	−0.459417	−	1.09100i	0.513134	−	0.858308i	$-0.328484\pi$
$752$	−5.74962	+	7.83614i	−0.209667	+	0.285755i
$753$	−19.6188	+	11.1234i	−0.714950	+	0.405360i
$754$	2.25826	−	7.17857i	0.0822408	−	0.261428i
$755$	−26.9430	+	18.8134i	−0.980555	+	0.684691i
$756$	−0.463887	−	2.80121i	−0.0168714	−	0.101879i
$757$	5.26643	−	6.83565i	0.191412	−	0.248446i	−0.686656	−	0.726983i	$-0.740922\pi$
$757$	5.26643	−	6.83565i	0.191412	−	0.248446i	0.878068	+	0.478536i	$0.158833\pi$
$758$	−1.71476	−	14.5611i	−0.0622829	−	0.528881i
$759$	3.03702	+	0.0712151i	0.110237	+	0.00258494i
$760$	20.2950	+	12.7996i	0.736176	+	0.464291i
$761$	−0.173494	−	0.386419i	−0.00628916	−	0.0140077i	0.909098	−	0.416582i	$-0.136772\pi$
$761$	−0.173494	−	0.386419i	−0.00628916	−	0.0140077i	−0.915387	+	0.402574i	$0.868115\pi$
$762$	−2.44783	−	1.09903i	−0.0886755	−	0.0398135i
$763$	−1.79971	−	2.45282i	−0.0651540	−	0.0887982i
$764$	−0.0456128	+	0.0762269i	−0.00165021	+	0.00275779i
$765$	11.6658	+	3.66988i	0.421780	+	0.132685i
$766$	25.3013	+	9.96262i	0.914171	+	0.359964i
$767$	−3.52701	−	5.05108i	−0.127353	−	0.182384i

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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	538.e (of order \(134\), degree \(66\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366380 - 0.930465i) q^{2} +(0.0596016 + 1.27018i) q^{3} +(-0.731531 + 0.681808i) q^{4} +(-2.72289 - 1.54381i) q^{5} +(1.16002 - 0.520825i) q^{6} +(0.380715 + 0.338511i) q^{7} +(0.902417 + 0.430864i) q^{8} +(1.37702 - 0.129515i) q^{9} +O(q^{10})\)	\(q+(-0.366380 - 0.930465i) q^{2} +(0.0596016 + 1.27018i) q^{3} +(-0.731531 + 0.681808i) q^{4} +(-2.72289 - 1.54381i) q^{5} +(1.16002 - 0.520825i) q^{6} +(0.380715 + 0.338511i) q^{7} +(0.902417 + 0.430864i) q^{8} +(1.37702 - 0.129515i) q^{9} +(-0.438854 + 3.09917i) q^{10} +(-0.0463257 + 0.393379i) q^{11} +(-0.909618 - 0.888538i) q^{12} +(-1.38322 - 0.195868i) q^{13} +(0.175487 - 0.478266i) q^{14} +(1.79863 - 3.55057i) q^{15} +(0.0702762 - 0.997528i) q^{16} +(-2.80548 + 0.330384i) q^{17} +(-0.625021 - 1.23382i) q^{18} +(-7.06479 + 2.97496i) q^{19} +(3.04446 - 0.727137i) q^{20} +(-0.407279 + 0.503752i) q^{21} +(0.382999 - 0.101022i) q^{22} +(-6.02483 + 0.282708i) q^{23} +(-0.493488 + 1.17191i) q^{24} +(2.46338 + 4.11674i) q^{25} +(0.324534 + 1.35880i) q^{26} +(0.781423 + 5.51839i) q^{27} +(-0.509305 + 0.0119427i) q^{28} +(-4.62241 - 2.76596i) q^{29} +(-3.96266 - 0.372707i) q^{30} +(-0.742739 + 3.10978i) q^{31} +(-0.953913 + 0.300085i) q^{32} +(-0.502423 - 0.0353959i) q^{33} +(1.33528 + 2.48936i) q^{34} +(-0.514045 - 1.50948i) q^{35} +(-0.919028 + 1.03361i) q^{36} +(-1.72697 - 2.60106i) q^{37} +(5.35650 + 5.48357i) q^{38} +(0.166346 - 1.76861i) q^{39} +(-1.79201 - 2.56636i) q^{40} +(0.255528 + 0.100617i) q^{41} +(0.617942 + 0.194394i) q^{42} +(-3.23110 + 5.39973i) q^{43} +(-0.234320 - 0.319354i) q^{44} +(-3.94941 - 1.77321i) q^{45} +(2.47043 + 5.50232i) q^{46} +(-8.22082 - 5.18471i) q^{47} +(1.27123 + 0.0298090i) q^{48} +(-0.788333 - 6.69421i) q^{49} +(2.92795 - 3.80038i) q^{50} +(-0.586857 - 3.54377i) q^{51} +(1.14541 - 0.799804i) q^{52} +(2.97091 - 9.44397i) q^{53} +(4.84837 - 2.74891i) q^{54} +(0.733444 - 0.999609i) q^{55} +(0.197711 + 0.469515i) q^{56} +(-4.19981 - 8.79623i) q^{57} +(-0.880075 + 5.31439i) q^{58} +(3.00666 + 3.22594i) q^{59} +(1.10505 + 3.82367i) q^{60} +(-2.71365 + 12.6693i) q^{61} +(3.16567 - 0.448270i) q^{62} +(0.568094 + 0.416828i) q^{63} +(0.628713 + 0.777638i) q^{64} +(3.46396 + 2.66876i) q^{65} +(0.151143 + 0.480455i) q^{66} +(7.13520 + 6.65021i) q^{67} +(1.82704 - 2.15449i) q^{68} +(-0.718179 - 7.63576i) q^{69} +(-1.21618 + 1.03135i) q^{70} +(13.5129 - 4.95820i) q^{71} +(1.29845 + 0.476431i) q^{72} +(2.04061 + 1.73047i) q^{73} +(-1.78747 + 2.55986i) q^{74} +(-5.08217 + 3.37430i) q^{75} +(3.13976 - 6.99311i) q^{76} +(-0.150800 + 0.134084i) q^{77} +(-1.70657 + 0.493203i) q^{78} +(0.230582 + 0.874191i) q^{79} +(-1.73135 + 2.60766i) q^{80} +(-2.88624 + 0.547775i) q^{81} -0.274623i q^{82} +(1.71926 + 9.05883i) q^{83} +(-0.0455247 - 0.646196i) q^{84} +(8.14907 + 3.43155i) q^{85} +(6.20807 + 1.02807i) q^{86} +(3.23776 - 6.03614i) q^{87} +(-0.211298 + 0.335032i) q^{88} +(9.36590 - 3.18950i) q^{89} +(-0.202920 + 4.32446i) q^{90} +(-0.460308 - 0.542805i) q^{91} +(4.21460 - 4.31459i) q^{92} +(-3.99425 - 0.758062i) q^{93} +(-1.81225 + 9.54877i) q^{94} +(23.8294 + 2.80624i) q^{95} +(-0.438016 - 1.19375i) q^{96} +(0.967228 + 4.51573i) q^{97} +(-5.93990 + 3.18614i) q^{98} +(-0.0128428 + 0.547690i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) \) 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9	\( 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + 2 q^{11} - 10 q^{13} + 12 q^{14} - 22 q^{16} + 2 q^{20} + 12 q^{21} - 4 q^{23} - 2 q^{24} - 24 q^{25} - 8 q^{30} - 12 q^{34} - 20 q^{36} - 396 q^{37} - 2 q^{38} + 24 q^{41} + 14 q^{43} - 2 q^{44} - 42 q^{45} - 402 q^{47} + 22 q^{49} + 12 q^{51} + 10 q^{52} - 10 q^{53} - 8 q^{54} - 4 q^{55} - 12 q^{56} + 16 q^{57} - 18 q^{58} - 268 q^{60} - 2 q^{61} + 4 q^{62} + 22 q^{64} + 16 q^{65} + 40 q^{66} + 6 q^{67} - 106 q^{73} + 40 q^{78} + 40 q^{79} - 2 q^{80} - 14 q^{81} - 402 q^{83} - 12 q^{84} - 100 q^{87} + 4 q^{92} - 340 q^{93} + 2 q^{96} - 64 q^{97} + 18 q^{99}+O(q^{100}) \) 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9 + 2 * q^11 - 10 * q^13 + 12 * q^14 - 22 * q^16 + 2 * q^20 + 12 * q^21 - 4 * q^23 - 2 * q^24 - 24 * q^25 - 8 * q^30 - 12 * q^34 - 20 * q^36 - 396 * q^37 - 2 * q^38 + 24 * q^41 + 14 * q^43 - 2 * q^44 - 42 * q^45 - 402 * q^47 + 22 * q^49 + 12 * q^51 + 10 * q^52 - 10 * q^53 - 8 * q^54 - 4 * q^55 - 12 * q^56 + 16 * q^57 - 18 * q^58 - 268 * q^60 - 2 * q^61 + 4 * q^62 + 22 * q^64 + 16 * q^65 + 40 * q^66 + 6 * q^67 - 106 * q^73 + 40 * q^78 + 40 * q^79 - 2 * q^80 - 14 * q^81 - 402 * q^83 - 12 * q^84 - 100 * q^87 + 4 * q^92 - 340 * q^93 + 2 * q^96 - 64 * q^97 + 18 * q^99

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