LMFDB - Embedded newform 430.2.q.a.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			271.1
Character	$\chi$	$=$	430.271
Dual form			430.2.q.a.311.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.222521 + 0.974928i) q^{2} +(-0.861302 + 0.799171i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(-0.587477 - 1.01754i) q^{6} +(-1.53300 + 2.65524i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-0.121024 + 1.61496i) q^{9} +O(q^{10})$	\(q+(-0.222521 + 0.974928i) q^{2} +(-0.861302 + 0.799171i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(-0.587477 - 1.01754i) q^{6} +(-1.53300 + 2.65524i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-0.121024 + 1.61496i) q^{9} +(0.365341 - 0.930874i) q^{10} +(1.59984 - 0.770444i) q^{11} +(1.12275 - 0.346324i) q^{12} +(-0.784440 - 1.99872i) q^{13} +(-2.24754 - 2.08542i) q^{14} +(0.970792 - 0.661875i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-5.40490 + 0.814658i) q^{17} +(-1.54754 - 0.477351i) q^{18} +(-0.568317 - 7.58367i) q^{19} +(0.826239 + 0.563320i) q^{20} +(-0.801613 - 3.51210i) q^{21} +(0.395129 + 1.73117i) q^{22} +(-5.24504 - 3.57601i) q^{23} +(0.0878044 + 1.17167i) q^{24} +(0.955573 + 0.294755i) q^{25} +(2.12316 - 0.320015i) q^{26} +(-3.38410 - 4.24353i) q^{27} +(2.53326 - 1.72714i) q^{28} +(2.13711 + 1.98294i) q^{29} +(0.429259 + 1.09373i) q^{30} +(-4.97211 + 1.53369i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(-0.762231 + 1.94213i) q^{33} +(0.408471 - 5.45067i) q^{34} +(1.91163 - 2.39710i) q^{35} +(0.809742 - 1.40251i) q^{36} +(2.20848 + 3.82520i) q^{37} +(7.51999 + 1.13346i) q^{38} +(2.27296 + 1.09460i) q^{39} +(-0.733052 + 0.680173i) q^{40} +(-0.306382 + 1.34235i) q^{41} +3.60242 q^{42} +(-5.48462 + 3.59429i) q^{43} -1.77569 q^{44} +(0.360369 - 1.57888i) q^{45} +(4.65348 - 4.31780i) q^{46} +(4.13568 + 1.99164i) q^{47} +(-1.16183 - 0.175118i) q^{48} +(-1.20020 - 2.07882i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(4.00420 - 5.02111i) q^{51} +(-0.160456 + 2.14114i) q^{52} +(0.102535 - 0.261255i) q^{53} +(4.89017 - 2.35498i) q^{54} +(-1.69680 + 0.523394i) q^{55} +(1.12014 + 2.85407i) q^{56} +(6.55014 + 6.07764i) q^{57} +(-2.40878 + 1.64228i) q^{58} +(-9.41834 - 11.8102i) q^{59} +(-1.16183 + 0.175118i) q^{60} +(11.0016 + 3.39354i) q^{61} +(-0.388841 - 5.18872i) q^{62} +(-4.10257 - 2.79708i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.477784 + 2.09331i) q^{65} +(-1.72383 - 1.17529i) q^{66} +(1.13513 + 15.1473i) q^{67} +(5.22312 + 1.61112i) q^{68} +(7.37541 - 1.11166i) q^{69} +(1.91163 + 2.39710i) q^{70} +(-8.01881 + 5.46714i) q^{71} +(1.18717 + 1.10153i) q^{72} +(-1.33757 - 3.40808i) q^{73} +(-4.22073 + 1.30192i) q^{74} +(-1.05860 + 0.509793i) q^{75} +(-2.77839 + 7.07923i) q^{76} +(-0.406852 + 5.42906i) q^{77} +(-1.57294 + 1.97240i) q^{78} +(0.640935 - 1.11013i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(1.50185 + 0.226368i) q^{81} +(-1.24051 - 0.597400i) q^{82} +(-11.1446 + 10.3406i) q^{83} +(-0.801613 + 3.51210i) q^{84} +5.46595 q^{85} +(-2.28373 - 6.14692i) q^{86} -3.42541 q^{87} +(0.395129 - 1.73117i) q^{88} +(-6.63657 + 6.15784i) q^{89} +(1.45911 + 0.702668i) q^{90} +(6.50963 + 0.981169i) q^{91} +(3.17405 + 5.49761i) q^{92} +(3.05680 - 5.29454i) q^{93} +(-2.86198 + 3.58881i) q^{94} +(-0.568317 + 7.58367i) q^{95} +(0.429259 - 1.09373i) q^{96} +(7.66768 - 3.69256i) q^{97} +(2.29377 - 0.707533i) q^{98} +(1.05061 + 2.67692i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$3$	−0.861302	+	0.799171i	−0.497273	+	0.461402i	−0.888490	−	0.458897i	$-0.848245\pi$
$3$	−0.861302	+	0.799171i	−0.497273	+	0.461402i	0.391217	+	0.920299i	$0.372054\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	−0.988831	−	0.149042i	−0.442219	−	0.0666537i
$5$	−0.988831	−	0.149042i	−0.442219	−	0.0666537i
$6$	−0.587477	−	1.01754i	−0.239836	−	0.415409i
$7$	−1.53300	+	2.65524i	−0.579421	+	1.00359i	0.416125	+	0.909308i	$0.363388\pi$
$7$	−1.53300	+	2.65524i	−0.579421	+	1.00359i	−0.995546	+	0.0942793i	$0.969945\pi$
$8$	0.623490	−	0.781831i	0.220437	−	0.276419i
$9$	−0.121024	+	1.61496i	−0.0403414	+	0.538319i
$10$	0.365341	−	0.930874i	0.115531	−	0.294368i
$11$	1.59984	−	0.770444i	0.482371	−	0.232297i	−0.176863	−	0.984235i	$-0.556595\pi$
$11$	1.59984	−	0.770444i	0.482371	−	0.232297i	0.659234	+	0.751938i	$0.270881\pi$
$12$	1.12275	−	0.346324i	0.324111	−	0.0999750i
$13$	−0.784440	−	1.99872i	−0.217564	−	0.554345i	0.779869	−	0.625943i	$-0.215286\pi$
$13$	−0.784440	−	1.99872i	−0.217564	−	0.554345i	−0.997434	+	0.0715974i	$0.977190\pi$
$14$	−2.24754	−	2.08542i	−0.600681	−	0.557351i
$15$	0.970792	−	0.661875i	0.250657	−	0.170895i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	−5.40490	+	0.814658i	−1.31088	+	0.197584i	−0.767037	−	0.641603i	$-0.778270\pi$
$17$	−5.40490	+	0.814658i	−1.31088	+	0.197584i	−0.543844	+	0.839186i	$0.683032\pi$
$18$	−1.54754	−	0.477351i	−0.364758	−	0.112513i
$19$	−0.568317	−	7.58367i	−0.130381	−	1.73981i	−0.552713	−	0.833371i	$-0.686408\pi$
$19$	−0.568317	−	7.58367i	−0.130381	−	1.73981i	0.422332	−	0.906441i	$-0.361211\pi$
$20$	0.826239	+	0.563320i	0.184753	+	0.125962i
$21$	−0.801613	−	3.51210i	−0.174926	−	0.766402i
$22$	0.395129	+	1.73117i	0.0842417	+	0.369087i
$23$	−5.24504	−	3.57601i	−1.09367	−	0.745650i	−0.124541	−	0.992214i	$-0.539746\pi$
$23$	−5.24504	−	3.57601i	−1.09367	−	0.745650i	−0.969126	+	0.246565i	$0.920698\pi$
$24$	0.0878044	+	1.17167i	0.0179230	+	0.239166i
$25$	0.955573	+	0.294755i	0.191115	+	0.0589510i
$26$	2.12316	−	0.320015i	0.416386	−	0.0627601i
$27$	−3.38410	−	4.24353i	−0.651271	−	0.816668i
$28$	2.53326	−	1.72714i	0.478740	−	0.326400i
$29$	2.13711	+	1.98294i	0.396851	+	0.368224i	0.853206	−	0.521574i	$-0.174655\pi$
$29$	2.13711	+	1.98294i	0.396851	+	0.368224i	−0.456355	+	0.889798i	$0.650845\pi$
$30$	0.429259	+	1.09373i	0.0783716	+	0.199687i
$31$	−4.97211	+	1.53369i	−0.893017	+	0.275459i	−0.707106	−	0.707107i	$-0.750000\pi$
$31$	−4.97211	+	1.53369i	−0.893017	+	0.275459i	−0.185911	+	0.982567i	$0.559524\pi$
$32$	−0.900969	+	0.433884i	−0.159270	+	0.0767005i
$33$	−0.762231	+	1.94213i	−0.132687	+	0.338082i
$34$	0.408471	−	5.45067i	0.0700522	−	0.934782i
$35$	1.91163	−	2.39710i	0.323124	−	0.405184i
$36$	0.809742	−	1.40251i	0.134957	−	0.233752i
$37$	2.20848	+	3.82520i	0.363072	+	0.628859i	0.988465	−	0.151451i	$-0.0483946\pi$
$37$	2.20848	+	3.82520i	0.363072	+	0.628859i	−0.625393	+	0.780310i	$0.715061\pi$
$38$	7.51999	+	1.13346i	1.21990	+	0.183871i
$39$	2.27296	+	1.09460i	0.363965	+	0.175276i
$40$	−0.733052	+	0.680173i	−0.115906	+	0.107545i
$41$	−0.306382	+	1.34235i	−0.0478488	+	0.209639i	−0.993201	−	0.116411i	$-0.962861\pi$
$41$	−0.306382	+	1.34235i	−0.0478488	+	0.209639i	0.945352	+	0.326051i	$0.105718\pi$
$42$	3.60242			0.555865
$43$	−5.48462	+	3.59429i	−0.836397	+	0.548124i
$43$	−5.48462	+	3.59429i	−0.836397	+	0.548124i
$44$	−1.77569			−0.267696
$45$	0.360369	−	1.57888i	0.0537207	−	0.235366i
$46$	4.65348	−	4.31780i	0.686119	−	0.636625i
$47$	4.13568	+	1.99164i	0.603251	+	0.290510i	0.710473	−	0.703725i	$-0.248481\pi$
$47$	4.13568	+	1.99164i	0.603251	+	0.290510i	−0.107222	+	0.994235i	$0.534196\pi$
$48$	−1.16183	−	0.175118i	−0.167696	−	0.0252761i
$49$	−1.20020	−	2.07882i	−0.171458	−	0.296974i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	4.00420	−	5.02111i	0.560700	−	0.703096i
$52$	−0.160456	+	2.14114i	−0.0222513	+	0.296923i
$53$	0.102535	−	0.261255i	0.0140843	−	0.0358862i	−0.923659	−	0.383216i	$-0.874816\pi$
$53$	0.102535	−	0.261255i	0.0140843	−	0.0358862i	0.937743	+	0.347330i	$0.112912\pi$
$54$	4.89017	−	2.35498i	0.665468	−	0.320472i
$55$	−1.69680	+	0.523394i	−0.228797	+	0.0705745i
$56$	1.12014	+	2.85407i	0.149685	+	0.381391i
$57$	6.55014	+	6.07764i	0.867587	+	0.805003i
$58$	−2.40878	+	1.64228i	−0.316288	+	0.215642i
$59$	−9.41834	−	11.8102i	−1.22616	−	1.53756i	−0.755339	−	0.655334i	$-0.772528\pi$
$59$	−9.41834	−	11.8102i	−1.22616	−	1.53756i	−0.470825	−	0.882227i	$-0.656044\pi$
$60$	−1.16183	+	0.175118i	−0.149992	+	0.0226076i
$61$	11.0016	+	3.39354i	1.40861	+	0.434498i	0.903511	−	0.428565i	$-0.140981\pi$
$61$	11.0016	+	3.39354i	1.40861	+	0.434498i	0.505097	+	0.863063i	$0.331457\pi$
$62$	−0.388841	−	5.18872i	−0.0493829	−	0.658969i
$63$	−4.10257	−	2.79708i	−0.516875	−	0.352399i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	0.477784	+	2.09331i	0.0592619	+	0.259643i
$66$	−1.72383	−	1.17529i	−0.212188	−	0.144668i
$67$	1.13513	+	15.1473i	0.138679	+	1.85054i	0.441217	+	0.897400i	$0.354547\pi$
$67$	1.13513	+	15.1473i	0.138679	+	1.85054i	−0.302538	+	0.953137i	$0.597834\pi$
$68$	5.22312	+	1.61112i	0.633396	+	0.195377i
$69$	7.37541	−	1.11166i	0.887895	−	0.133829i
$70$	1.91163	+	2.39710i	0.228483	+	0.286508i
$71$	−8.01881	+	5.46714i	−0.951658	+	0.648830i	−0.936355	−	0.351053i	$-0.885824\pi$
$71$	−8.01881	+	5.46714i	−0.951658	+	0.648830i	−0.0153027	+	0.999883i	$0.504871\pi$
$72$	1.18717	+	1.10153i	0.139909	+	0.129816i
$73$	−1.33757	−	3.40808i	−0.156551	−	0.398885i	0.830982	−	0.556300i	$-0.187779\pi$
$73$	−1.33757	−	3.40808i	−0.156551	−	0.398885i	−0.987533	+	0.157414i	$0.949684\pi$
$74$	−4.22073	+	1.30192i	−0.490650	+	0.151345i
$75$	−1.05860	+	0.509793i	−0.122236	+	0.0588658i
$76$	−2.77839	+	7.07923i	−0.318704	+	0.812044i
$77$	−0.406852	+	5.42906i	−0.0463651	+	0.618699i
$78$	−1.57294	+	1.97240i	−0.178100	+	0.223330i
$79$	0.640935	−	1.11013i	0.0721108	−	0.124900i	−0.827715	−	0.561148i	$-0.810360\pi$
$79$	0.640935	−	1.11013i	0.0721108	−	0.124900i	0.899826	+	0.436249i	$0.143693\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	1.50185	+	0.226368i	0.166872	+	0.0251520i
$82$	−1.24051	−	0.597400i	−0.136992	−	0.0659718i
$83$	−11.1446	+	10.3406i	−1.22328	+	1.13503i	−0.236725	+	0.971577i	$0.576074\pi$
$83$	−11.1446	+	10.3406i	−1.22328	+	1.13503i	−0.986551	+	0.163457i	$0.947736\pi$
$84$	−0.801613	+	3.51210i	−0.0874632	+	0.383201i
$85$	5.46595			0.592866
$86$	−2.28373	−	6.14692i	−0.246261	−	0.662839i
$87$	−3.42541			−0.367242
$88$	0.395129	−	1.73117i	0.0421208	−	0.184543i
$89$	−6.63657	+	6.15784i	−0.703475	+	0.652730i	−0.948496	−	0.316788i	$-0.897396\pi$
$89$	−6.63657	+	6.15784i	−0.703475	+	0.652730i	0.245021	+	0.969518i	$0.421205\pi$
$90$	1.45911	+	0.702668i	0.153803	+	0.0740677i
$91$	6.50963	+	0.981169i	0.682395	+	0.102854i
$92$	3.17405	+	5.49761i	0.330917	+	0.573166i
$93$	3.05680	−	5.29454i	0.316976	−	0.549018i
$94$	−2.86198	+	3.58881i	−0.295190	+	0.370157i
$95$	−0.568317	+	7.58367i	−0.0583081	+	0.778068i
$96$	0.429259	−	1.09373i	0.0438110	−	0.111629i
$97$	7.66768	−	3.69256i	0.778535	−	0.374923i	−0.00202966	−	0.999998i	$-0.500646\pi$
$97$	7.66768	−	3.69256i	0.778535	−	0.374923i	0.780564	+	0.625075i	$0.214932\pi$
$98$	2.29377	−	0.707533i	0.231705	−	0.0714716i
$99$	1.05061	+	2.67692i	0.105591	+	0.269040i
$100$	−0.733052	−	0.680173i	−0.0733052	−	0.0680173i
$101$	−10.0716	+	6.86672i	−1.00216	+	0.683264i	−0.948985	−	0.315321i	$-0.897888\pi$
$101$	−10.0716	+	6.86672i	−1.00216	+	0.683264i	−0.0531788	+	0.998585i	$0.516935\pi$
$102$	4.00420	+	5.02111i	0.396475	+	0.497164i
$103$	13.0992	−	1.97438i	1.29070	−	0.194542i	0.532426	−	0.846477i	$-0.321281\pi$
$103$	13.0992	−	1.97438i	1.29070	−	0.194542i	0.758275	+	0.651935i	$0.226043\pi$
$104$	−2.05175	−	0.632882i	−0.201191	−	0.0620592i
$105$	0.269209	+	3.59234i	0.0262721	+	0.350577i
$106$	0.231889	+	0.158099i	0.0225230	+	0.0153559i
$107$	−0.0459463	−	0.201304i	−0.00444180	−	0.0194608i	0.972658	−	0.232240i	$-0.0746056\pi$
$107$	−0.0459463	−	0.201304i	−0.00444180	−	0.0194608i	−0.977100	+	0.212779i	$0.931748\pi$
$108$	1.20777	+	5.29160i	0.116218	+	0.509184i
$109$	−0.841126	−	0.573470i	−0.0805653	−	0.0549285i	0.522368	−	0.852720i	$-0.325049\pi$
$109$	−0.841126	−	0.573470i	−0.0805653	−	0.0549285i	−0.602933	+	0.797792i	$0.706001\pi$
$110$	−0.132698	−	1.77073i	−0.0126522	−	0.168832i
$111$	−4.95916	−	1.52970i	−0.470702	−	0.145192i
$112$	−3.03176	+	0.456965i	−0.286475	+	0.0431791i
$113$	−10.1409	−	12.7162i	−0.953971	−	1.19624i	−0.980485	−	0.196594i	$-0.937012\pi$
$113$	−10.1409	−	12.7162i	−0.953971	−	1.19624i	0.0265136	−	0.999648i	$-0.491559\pi$
$114$	−7.38281	+	5.03351i	−0.691463	+	0.471432i
$115$	4.65348	+	4.31780i	0.433940	+	0.402637i
$116$	−1.06510	−	2.71383i	−0.0988919	−	0.251973i
$117$	3.32278	−	1.02494i	0.307191	−	0.0947559i
$118$	13.6099	−	6.55418i	1.25289	−	0.603361i
$119$	6.12262	−	15.6002i	0.561260	−	1.43007i
$120$	0.0878044	−	1.17167i	0.00801541	−	0.106958i
$121$	−4.89247	+	6.13497i	−0.444770	+	0.557724i
$122$	−5.75654	+	9.97061i	−0.521172	+	0.902697i
$123$	−0.808877	−	1.40102i	−0.0729340	−	0.126325i
$124$	5.14516	+	0.775508i	0.462049	+	0.0696427i
$125$	−0.900969	−	0.433884i	−0.0805851	−	0.0388077i
$126$	3.63986	−	3.37730i	0.324265	−	0.300874i
$127$	−2.28599	+	10.0156i	−0.202849	+	0.888738i	0.766343	+	0.642431i	$0.222074\pi$
$127$	−2.28599	+	10.0156i	−0.202849	+	0.888738i	−0.969192	+	0.246306i	$0.920783\pi$
$128$	1.00000			0.0883883
$129$	1.85147	−	7.47892i	0.163012	−	0.658482i
$130$	−2.14714			−0.188317
$131$	2.18209	−	9.56034i	0.190650	−	0.835291i	−0.785616	−	0.618714i	$-0.787654\pi$
$131$	2.18209	−	9.56034i	0.190650	−	0.835291i	0.976266	−	0.216576i	$-0.0694890\pi$
$132$	1.52941	−	1.41908i	0.133118	−	0.123515i
$133$	21.0077	+	10.1168i	1.82160	+	0.877236i
$134$	−15.0201	−	2.26392i	−1.29754	−	0.195573i
$135$	2.71384	+	4.70051i	0.233570	+	0.404555i
$136$	−2.73298	+	4.73365i	−0.234351	+	0.405907i
$137$	−5.55556	+	6.96645i	−0.474644	+	0.595184i	−0.960301	−	0.278965i	$-0.910009\pi$
$137$	−5.55556	+	6.96645i	−0.474644	+	0.595184i	0.485658	+	0.874149i	$0.338580\pi$
$138$	−0.557391	+	7.43786i	−0.0474483	+	0.633153i
$139$	−2.29910	+	5.85802i	−0.195007	+	0.496870i	−0.994613	−	0.103654i	$-0.966946\pi$
$139$	−2.29910	+	5.85802i	−0.195007	+	0.496870i	0.799606	+	0.600525i	$0.205042\pi$
$140$	−2.76238	+	1.33029i	−0.233464	+	0.112430i
$141$	−5.15373	+	1.58971i	−0.434022	+	0.133878i
$142$	−3.54571	−	9.03432i	−0.297549	−	0.758143i
$143$	−2.79488	−	2.59327i	−0.233720	−	0.216860i
$144$	−1.33808	+	0.912288i	−0.111507	+	0.0760240i
$145$	−1.81769	−	2.27932i	−0.150951	−	0.189287i
$146$	3.62027	−	0.545668i	0.299616	−	0.0451598i
$147$	2.69507	+	0.831318i	0.222285	+	0.0685660i
$148$	−0.330080	−	4.40461i	−0.0271324	−	0.362057i
$149$	12.0985	+	8.24861i	0.991147	+	0.675753i	0.946316	−	0.323242i	$-0.104773\pi$
$149$	12.0985	+	8.24861i	0.991147	+	0.675753i	0.0448306	+	0.998995i	$0.485725\pi$
$150$	−0.261452	−	1.14549i	−0.0213474	−	0.0935293i
$151$	−0.845776	−	3.70559i	−0.0688283	−	0.301556i	0.928784	−	0.370622i	$-0.120855\pi$
$151$	−0.845776	−	3.70559i	−0.0688283	−	0.301556i	−0.997612	+	0.0690655i	$0.977998\pi$
$152$	−6.28349	−	4.28401i	−0.509658	−	0.347479i
$153$	−0.661513	−	8.82727i	−0.0534801	−	0.713643i
$154$	−5.20241	−	1.60473i	−0.419222	−	0.129313i
$155$	5.14516	−	0.775508i	0.413269	−	0.0622903i
$156$	−1.57294	−	1.97240i	−0.125936	−	0.157918i
$157$	3.98911	−	2.71973i	0.318366	−	0.217058i	−0.393584	−	0.919289i	$-0.628765\pi$
$157$	3.98911	−	2.71973i	0.318366	−	0.217058i	0.711949	+	0.702231i	$0.247812\pi$
$158$	0.939677	+	0.871892i	0.0747567	+	0.0693640i
$159$	0.120474	+	0.306963i	0.00955421	+	0.0243437i
$160$	0.955573	−	0.294755i	0.0755447	−	0.0233024i
$161$	17.5358	−	8.44482i	1.38202	−	0.665545i
$162$	−0.554886	+	1.41383i	−0.0435960	+	0.111081i
$163$	0.255888	−	3.41459i	0.0200427	−	0.267451i	−0.978175	−	0.207781i	$-0.933376\pi$
$163$	0.255888	−	3.41459i	0.0200427	−	0.267451i	0.998218	−	0.0596705i	$-0.0190050\pi$
$164$	0.858462	−	1.07648i	0.0670346	−	0.0840588i
$165$	1.04318	−	1.80684i	0.0812112	−	0.140662i
$166$	−7.60149	−	13.1662i	−0.589990	−	1.02189i
$167$	−11.7635	−	1.77307i	−0.910289	−	0.137204i	−0.322829	−	0.946457i	$-0.604634\pi$
$167$	−11.7635	−	1.77307i	−0.910289	−	0.137204i	−0.587460	+	0.809253i	$0.699872\pi$
$168$	−3.24567	−	1.56303i	−0.250409	−	0.120590i
$169$	6.15014	−	5.70650i	0.473088	−	0.438961i
$170$	−1.21629	+	5.32891i	−0.0932851	+	0.408709i
$171$	12.3161			0.941833
$172$	6.50098	−	0.858652i	0.495695	−	0.0654716i
$173$	−9.68262			−0.736156			−0.368078	−	0.929795i	$-0.619984\pi$
$173$	−9.68262			−0.736156			−0.368078	+	0.929795i	$0.619984\pi$
$174$	0.762225	−	3.33952i	0.0577841	−	0.253169i
$175$	−2.24754	+	2.08542i	−0.169898	+	0.157643i
$176$	1.59984	+	0.770444i	0.120593	+	0.0580744i
$177$	17.5504	+	2.64530i	1.31917	+	0.198833i
$178$	−4.52667	−	7.84043i	−0.339288	−	0.587665i
$179$	−6.24005	+	10.8081i	−0.466403	+	0.807834i	−0.999264	−	0.0383689i	$-0.987784\pi$
$179$	−6.24005	+	10.8081i	−0.466403	+	0.807834i	0.532860	+	0.846203i	$0.321117\pi$
$180$	−1.00973	+	1.26616i	−0.0752610	+	0.0943743i
$181$	−0.210939	+	2.81479i	−0.0156790	+	0.209222i	0.983862	+	0.178929i	$0.0572631\pi$
$181$	−0.210939	+	2.81479i	−0.0156790	+	0.209222i	−0.999541	+	0.0302931i	$0.990356\pi$
$182$	−2.40510	+	6.12809i	−0.178278	+	0.454244i
$183$	−12.1877	+	5.86928i	−0.900940	+	0.433870i
$184$	−6.06607	+	1.87113i	−0.447197	+	0.137942i
$185$	−1.61370	−	4.11163i	−0.118641	−	0.302293i
$186$	4.48159	+	4.15831i	0.328606	+	0.304902i
$187$	−8.01935	+	5.46750i	−0.586433	+	0.399823i
$188$	−2.86198	−	3.58881i	−0.208731	−	0.261741i
$189$	16.4554	−	2.48026i	1.19696	−	0.180412i
$190$	−7.26707	−	2.24159i	−0.527208	−	0.162622i
$191$	−1.35215	−	18.0432i	−0.0978381	−	1.30556i	−0.802772	−	0.596286i	$-0.796642\pi$
$191$	−1.35215	−	18.0432i	−0.0978381	−	1.30556i	0.704934	−	0.709273i	$-0.250977\pi$
$192$	0.970792	+	0.661875i	0.0700609	+	0.0477667i
$193$	2.67825	+	11.7342i	0.192784	+	0.844644i	0.975101	+	0.221762i	$0.0711809\pi$
$193$	2.67825	+	11.7342i	0.192784	+	0.844644i	−0.782316	+	0.622881i	$0.785962\pi$
$194$	1.89376	+	8.29710i	0.135964	+	0.595697i
$195$	−2.08443	−	1.42114i	−0.149269	−	0.101770i
$196$	0.179383	+	2.39370i	0.0128131	+	0.170978i
$197$	5.10578	+	1.57492i	0.363772	+	0.112209i	0.471252	−	0.881999i	$-0.343802\pi$
$197$	5.10578	+	1.57492i	0.363772	+	0.112209i	−0.107481	+	0.994207i	$0.534278\pi$
$198$	−2.84359	+	0.428602i	−0.202085	+	0.0304594i
$199$	−1.63649	−	2.05209i	−0.116008	−	0.145469i	0.720437	−	0.693520i	$-0.243941\pi$
$199$	−1.63649	−	2.05209i	−0.116008	−	0.145469i	−0.836445	+	0.548051i	$0.815370\pi$
$200$	0.826239	−	0.563320i	0.0584239	−	0.0398327i
$201$	−13.0830	−	12.1392i	−0.922802	−	0.856235i
$202$	−4.45341	−	11.3471i	−0.313341	−	0.798379i
$203$	−8.54139	+	2.63467i	−0.599488	+	0.184918i
$204$	−5.78624	+	2.78651i	−0.405118	+	0.195094i
$205$	0.503026	−	1.28169i	0.0351329	−	0.0895171i
$206$	−0.989960	+	13.2101i	−0.0689738	+	0.920391i
$207$	6.40988	−	8.03773i	0.445517	−	0.558661i
$208$	1.07357	−	1.85948i	0.0744388	−	0.128932i
$209$	−6.75201	−	11.6948i	−0.467046	−	0.808947i
$210$	−3.56218	−	0.536912i	−0.245814	−	0.0370505i
$211$	−16.8996	−	8.13841i	−1.16342	−	0.560271i	−0.250378	−	0.968148i	$-0.580555\pi$
$211$	−16.8996	−	8.13841i	−1.16342	−	0.560271i	−0.913037	+	0.407877i	$0.866269\pi$
$212$	−0.205735	+	0.190895i	−0.0141300	+	0.0131107i
$213$	2.53744	−	11.1173i	0.173863	−	0.761742i
$214$	0.206481			0.0141147
$215$	5.95907	−	2.73670i	0.406405	−	0.186641i
$216$	−5.42768			−0.369307
$217$	3.54994	−	15.5533i	0.240986	−	1.05583i
$218$	0.746260	−	0.692428i	0.0505431	−	0.0468972i
$219$	3.87569	+	1.86643i	0.261895	+	0.126122i
$220$	1.75586	+	0.264653i	0.118380	+	0.0178429i
$221$	5.86809	+	10.1638i	0.394731	+	0.683693i
$222$	2.59486	−	4.49443i	0.174156	−	0.301647i
$223$	12.0767	−	15.1437i	0.808717	−	1.01410i	−0.190756	−	0.981637i	$-0.561094\pi$
$223$	12.0767	−	15.1437i	0.808717	−	1.01410i	0.999473	−	0.0324612i	$-0.0103345\pi$
$224$	0.229123	−	3.05744i	0.0153089	−	0.204283i
$225$	−0.591664	+	1.50754i	−0.0394443	+	0.100502i
$226$	14.6540	−	7.05698i	0.974767	−	0.469423i
$227$	12.7216	−	3.92408i	0.844359	−	0.260450i	0.157752	−	0.987479i	$-0.449575\pi$
$227$	12.7216	−	3.92408i	0.844359	−	0.260450i	0.686607	+	0.727028i	$0.259099\pi$
$228$	−3.26448	−	8.31777i	−0.216196	−	0.550858i
$229$	18.8836	+	17.5215i	1.24787	+	1.15785i	0.980977	+	0.194124i	$0.0621864\pi$
$229$	18.8836	+	17.5215i	1.24787	+	1.15785i	0.266890	+	0.963727i	$0.414004\pi$
$230$	−5.24504	+	3.57601i	−0.345848	+	0.235795i
$231$	−3.98833	−	5.00121i	−0.262413	−	0.329055i
$232$	2.88279	−	0.434511i	0.189265	−	0.0285271i
$233$	−8.26657	−	2.54990i	−0.541561	−	0.167049i	0.0118929	−	0.999929i	$-0.496214\pi$
$233$	−8.26657	−	2.54990i	−0.541561	−	0.167049i	−0.553454	+	0.832880i	$0.686690\pi$
$234$	0.259856	+	3.46754i	0.0169873	+	0.226680i
$235$	−3.79265	−	2.58578i	−0.247405	−	0.168678i
$236$	3.36137	+	14.7271i	0.218806	+	0.958654i
$237$	0.335147	+	1.46837i	0.0217701	+	0.0953812i
$238$	13.8467	+	9.44049i	0.897545	+	0.611936i
$239$	−1.03542	−	13.8167i	−0.0669757	−	0.893729i	−0.924963	−	0.380058i	$-0.875904\pi$
$239$	−1.03542	−	13.8167i	−0.0669757	−	0.893729i	0.857987	−	0.513671i	$-0.171715\pi$
$240$	1.12275	+	0.346324i	0.0724734	+	0.0223551i
$241$	−22.7030	+	3.42193i	−1.46243	+	0.220426i	−0.831548	−	0.555453i	$-0.812545\pi$
$241$	−22.7030	+	3.42193i	−1.46243	+	0.220426i	−0.630882	+	0.775879i	$0.717307\pi$
$242$	−4.89247	−	6.13497i	−0.314500	−	0.394371i
$243$	11.9792	−	8.16730i	0.768467	−	0.523932i
$244$	−8.43968	−	7.83088i	−0.540295	−	0.501320i
$245$	0.876968	+	2.23448i	0.0560274	+	0.142756i
$246$	1.54588	−	0.476841i	0.0985618	−	0.0304023i
$247$	−14.7118	+	7.08484i	−0.936090	+	0.450797i
$248$	−1.90097	+	4.84359i	−0.120712	+	0.307568i
$249$	1.33489	−	17.8128i	0.0845951	−	1.12884i
$250$	0.623490	−	0.781831i	0.0394330	−	0.0494474i
$251$	−6.49183	+	11.2442i	−0.409760	+	0.709726i	−0.994863	−	0.101234i	$-0.967721\pi$
$251$	−6.49183	+	11.2442i	−0.409760	+	0.709726i	0.585102	+	0.810960i	$0.301054\pi$
$252$	2.48268	+	4.30012i	0.156394	+	0.270882i
$253$	−11.1464	−	1.68004i	−0.700766	−	0.105623i
$254$	−9.25577	−	4.45734i	−0.580759	−	0.279679i
$255$	−4.70783	+	4.36823i	−0.294816	+	0.273549i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	14.5122			0.905244			0.452622	−	0.891702i	$-0.350489\pi$
$257$	14.5122			0.905244			0.452622	+	0.891702i	$0.350489\pi$
$258$	6.87942	+	3.46926i	0.428294	+	0.215987i
$259$	−13.5424			−0.841486
$260$	0.477784	−	2.09331i	0.0296309	−	0.129822i
$261$	−3.46101	+	3.21135i	−0.214231	+	0.198777i
$262$	8.83508	+	4.25475i	0.545833	+	0.262859i
$263$	5.47223	+	0.824806i	0.337432	+	0.0508597i	0.315573	−	0.948901i	$-0.397803\pi$
$263$	5.47223	+	0.824806i	0.337432	+	0.0508597i	0.0218593	+	0.999761i	$0.493041\pi$
$264$	1.04318	+	1.80684i	0.0642031	+	0.111203i
$265$	−0.140328	+	0.243055i	−0.00862028	+	0.0149308i
$266$	−14.5378	+	18.2298i	−0.891368	+	1.11774i
$267$	0.794923	−	10.6075i	0.0486485	−	0.649169i
$268$	5.54945	−	14.1398i	0.338987	−	0.863724i
$269$	12.0035	−	5.78059i	0.731868	−	0.352449i	−0.0305508	−	0.999533i	$-0.509726\pi$
$269$	12.0035	−	5.78059i	0.731868	−	0.352449i	0.762418	+	0.647084i	$0.224012\pi$
$270$	−5.18654	+	1.59984i	−0.315643	+	0.0973629i
$271$	8.62302	+	21.9711i	0.523811	+	1.33465i	0.910908	+	0.412610i	$0.135383\pi$
$271$	8.62302	+	21.9711i	0.523811	+	1.33465i	−0.387096	+	0.922039i	$0.626522\pi$
$272$	−4.00683	−	3.71779i	−0.242950	−	0.225424i
$273$	−6.39088	+	4.35723i	−0.386794	+	0.263711i
$274$	−5.55556	−	6.96645i	−0.335624	−	0.420859i
$275$	1.75586	−	0.264653i	0.105882	−	0.0159592i
$276$	−7.12735	−	2.19850i	−0.429016	−	0.132334i
$277$	−1.05336	−	14.0561i	−0.0632902	−	0.844550i	−0.935027	−	0.354576i	$-0.884625\pi$
$277$	−1.05336	−	14.0561i	−0.0632902	−	0.844550i	0.871737	−	0.489974i	$-0.162994\pi$
$278$	−5.19955	−	3.54499i	−0.311848	−	0.212614i
$279$	−1.87510	−	8.21535i	−0.112259	−	0.491840i
$280$	−0.682251	−	2.98914i	−0.0407723	−	0.178635i
$281$	6.73452	+	4.59152i	0.401748	+	0.273907i	0.747292	−	0.664495i	$-0.231353\pi$
$281$	6.73452	+	4.59152i	0.401748	+	0.273907i	−0.345545	+	0.938402i	$0.612306\pi$
$282$	−0.403045	−	5.37826i	−0.0240010	−	0.320270i
$283$	−13.5314	−	4.17389i	−0.804359	−	0.248112i	−0.134802	−	0.990873i	$-0.543040\pi$
$283$	−13.5314	−	4.17389i	−0.804359	−	0.248112i	−0.669557	+	0.742761i	$0.733516\pi$
$284$	9.59680	−	1.44649i	0.569465	−	0.0858331i
$285$	−5.57116	−	6.98601i	−0.330007	−	0.413815i
$286$	3.15017	−	2.14775i	0.186274	−	0.126999i
$287$	−3.09457	−	2.87134i	−0.182667	−	0.169490i
$288$	−0.591664	−	1.50754i	−0.0348641	−	0.0888324i
$289$	12.3046	−	3.79545i	0.723798	−	0.223262i
$290$	2.62664	−	1.26493i	0.154242	−	0.0742790i
$291$	−3.65320	+	9.30820i	−0.214154	+	0.545656i
$292$	−0.273599	+	3.65092i	−0.0160112	+	0.213654i
$293$	−20.5073	+	25.7153i	−1.19805	+	1.50230i	−0.382157	+	0.924098i	$0.624818\pi$
$293$	−20.5073	+	25.7153i	−1.19805	+	1.50230i	−0.815891	+	0.578206i	$0.803753\pi$
$294$	−1.41018	+	2.44251i	−0.0822436	+	0.142450i
$295$	7.55292	+	13.0820i	0.439748	+	0.761666i
$296$	4.36763	+	0.658314i	0.253863	+	0.0382637i
$297$	−8.68343	−	4.18172i	−0.503864	−	0.242648i
$298$	−10.7340	+	9.95967i	−0.621802	+	0.576948i
$299$	−3.03302	+	13.2885i	−0.175404	+	0.768496i
$300$	1.17495			0.0678360
$301$	−1.13575	−	20.0731i	−0.0654634	−	1.15699i
$302$	3.80088			0.218716
$303$	3.18702	−	13.9633i	0.183090	−	0.802169i
$304$	5.57481	−	5.17267i	0.319737	−	0.296673i
$305$	−10.3729	−	4.99533i	−0.593952	−	0.286032i
$306$	8.75316	+	1.31933i	0.500385	+	0.0754208i
$307$	−14.6235	−	25.3287i	−0.834610	−	1.44559i	−0.894348	−	0.447372i	$-0.852360\pi$
$307$	−14.6235	−	25.3287i	−0.834610	−	1.44559i	0.0597382	−	0.998214i	$-0.480973\pi$
$308$	2.72214	−	4.71489i	0.155108	−	0.268656i
$309$	−9.70447	+	12.1690i	−0.552068	+	0.692272i
$310$	−0.388841	+	5.18872i	−0.0220847	+	0.294700i
$311$	−0.885125	+	2.25526i	−0.0501908	+	0.127884i	−0.953770	−	0.300536i	$-0.902834\pi$
$311$	−0.885125	+	2.25526i	−0.0501908	+	0.127884i	0.903580	+	0.428420i	$0.140930\pi$
$312$	2.27296	−	1.09460i	0.128681	−	0.0619695i
$313$	26.0496	−	8.03523i	1.47241	−	0.454178i	0.548292	−	0.836287i	$-0.315278\pi$
$313$	26.0496	−	8.03523i	1.47241	−	0.454178i	0.924117	+	0.382109i	$0.124802\pi$
$314$	1.76388	+	4.49429i	0.0995415	+	0.253628i
$315$	3.63986	+	3.37730i	0.205083	+	0.190289i
$316$	−1.05913	+	0.722103i	−0.0595807	+	0.0406214i
$317$	−10.3428	−	12.9694i	−0.580907	−	0.728435i	0.401360	−	0.915920i	$-0.368538\pi$
$317$	−10.3428	−	12.9694i	−0.580907	−	0.728435i	−0.982267	+	0.187486i	$0.939966\pi$
$318$	−0.326075	+	0.0491478i	−0.0182854	+	0.00275607i
$319$	4.94678	+	1.52588i	0.276967	+	0.0854329i
$320$	0.0747301	+	0.997204i	0.00417754	+	0.0557454i
$321$	0.200450	+	0.136664i	0.0111880	+	0.00762786i
$322$	4.33100	+	18.9753i	0.241357	+	1.05745i
$323$	9.24979	+	40.5260i	0.514672	+	2.25493i
$324$	−1.25490	−	0.855580i	−0.0697169	−	0.0475322i
$325$	−0.160456	−	2.14114i	−0.00890051	−	0.118769i
$326$	3.27204	+	1.00929i	0.181221	+	0.0558994i
$327$	1.18276	−	0.178273i	0.0654070	−	0.00985852i
$328$	0.858462	+	1.07648i	0.0474007	+	0.0594385i
$329$	−11.6283	+	7.92803i	−0.641088	+	0.437087i
$330$	1.52941	+	1.41908i	0.0841910	+	0.0781179i
$331$	8.69976	+	22.1666i	0.478182	+	1.21839i	0.942944	+	0.332952i	$0.108045\pi$
$331$	8.69976	+	22.1666i	0.478182	+	1.21839i	−0.464761	+	0.885436i	$0.653860\pi$
$332$	14.5275	−	4.48115i	0.797303	−	0.245935i
$333$	−6.44481	+	3.10366i	−0.353173	+	0.170079i
$334$	4.34624	−	11.0740i	0.237816	−	0.605945i
$335$	1.13513	−	15.1473i	0.0620190	−	0.827586i
$336$	2.24607	−	2.81648i	0.122533	−	0.153652i
$337$	−8.51782	+	14.7533i	−0.463995	+	0.803663i	−0.999156	−	0.0410871i	$-0.986918\pi$
$337$	−8.51782	+	14.7533i	−0.463995	+	0.803663i	0.535160	+	0.844751i	$0.320251\pi$
$338$	4.19489	+	7.26576i	0.228172	+	0.395205i
$339$	18.8968	+	2.84823i	1.02633	+	0.154695i
$340$	−4.92465	−	2.37159i	−0.267077	−	0.128617i
$341$	−6.77297	+	6.28439i	−0.366777	+	0.340319i
$342$	−2.74058	+	12.0073i	−0.148194	+	0.649279i
$343$	−14.1024			−0.761457
$344$	−0.609480	+	6.52905i	−0.0328610	+	0.352023i
$345$	−7.45872			−0.401564
$346$	2.15459	−	9.43986i	0.115831	−	0.507490i
$347$	17.4194	−	16.1629i	0.935124	−	0.867668i	−0.0562917	−	0.998414i	$-0.517928\pi$
$347$	17.4194	−	16.1629i	0.935124	−	0.867668i	0.991416	+	0.130746i	$0.0417372\pi$
$348$	3.08618	+	1.48623i	0.165437	+	0.0796702i
$349$	34.1008	+	5.13987i	1.82537	+	0.275131i	0.970040	−	0.242945i	$-0.0781136\pi$
$349$	34.1008	+	5.13987i	1.82537	+	0.275131i	0.855334	+	0.518076i	$0.173352\pi$
$350$	−1.53300	−	2.65524i	−0.0819425	−	0.141929i
$351$	−5.82700	+	10.0927i	−0.311022	+	0.538707i
$352$	−1.10713	+	1.38829i	−0.0590100	+	0.0739962i
$353$	−1.49954	+	20.0100i	−0.0798125	+	1.06502i	0.803211	+	0.595695i	$0.203123\pi$
$353$	−1.49954	+	20.0100i	−0.0798125	+	1.06502i	−0.883023	+	0.469329i	$0.844496\pi$
$354$	−6.48432	+	16.5218i	−0.344638	+	0.878122i
$355$	8.74409	−	4.21093i	0.464088	−	0.223493i
$356$	8.65113	−	2.66852i	0.458509	−	0.141431i
$357$	7.19380	+	18.3295i	0.380736	+	0.970100i
$358$	−9.14856	−	8.48863i	−0.483517	−	0.448638i
$359$	11.9502	−	8.14754i	0.630710	−	0.430011i	−0.205320	−	0.978695i	$-0.565823\pi$
$359$	11.9502	−	8.14754i	0.630710	−	0.430011i	0.836030	+	0.548684i	$0.184871\pi$
$360$	−1.00973	−	1.26616i	−0.0532176	−	0.0667327i
$361$	−38.4012	+	5.78805i	−2.02112	+	0.304634i
$362$	−2.69728	−	0.832000i	−0.141766	−	0.0437290i
$363$	−0.688994	−	9.19399i	−0.0361628	−	0.482559i
$364$	−5.43926	−	3.70843i	−0.285095	−	0.194374i
$365$	0.814685	+	3.56937i	0.0426426	+	0.186829i
$366$	−3.01011	−	13.1882i	−0.157341	−	0.689356i
$367$	−3.78854	−	2.58298i	−0.197760	−	0.134831i	0.460391	−	0.887716i	$-0.347709\pi$
$367$	−3.78854	−	2.58298i	−0.197760	−	0.134831i	−0.658152	+	0.752885i	$0.728661\pi$
$368$	−0.474394	−	6.33035i	−0.0247295	−	0.329992i
$369$	−2.13075	−	0.657249i	−0.110922	−	0.0342150i
$370$	4.36763	−	0.658314i	0.227062	−	0.0342241i
$371$	0.536509	+	0.672761i	0.0278542	+	0.0349280i
$372$	−5.05130	+	3.44392i	−0.261898	+	0.178559i
$373$	11.1984	+	10.3906i	0.579829	+	0.538003i	0.914633	−	0.404285i	$-0.132480\pi$
$373$	11.1984	+	10.3906i	0.579829	+	0.538003i	−0.334804	+	0.942288i	$0.608670\pi$
$374$	−3.54594	−	9.03492i	−0.183356	−	0.467184i
$375$	1.12275	−	0.346324i	0.0579787	−	0.0178841i
$376$	4.13568	−	1.99164i	0.213281	−	0.102711i
$377$	2.28692	−	5.82698i	0.117782	−	0.300105i
$378$	−1.24361	+	16.5948i	−0.0639642	+	0.853543i
$379$	−2.00280	+	2.51143i	−0.102877	+	0.129003i	−0.830605	−	0.556863i	$-0.812005\pi$
$379$	−2.00280	+	2.51143i	−0.102877	+	0.129003i	0.727728	+	0.685866i	$0.240576\pi$
$380$	3.80247	−	6.58606i	0.195062	−	0.337858i
$381$	−6.03523	−	10.4533i	−0.309194	−	0.535540i
$382$	17.8917	+	2.69674i	0.915418	+	0.137977i
$383$	−21.0885	−	10.1557i	−1.07757	−	0.518931i	−0.191032	−	0.981584i	$-0.561183\pi$
$383$	−21.0885	−	10.1557i	−1.07757	−	0.518931i	−0.886539	+	0.462653i	$0.846898\pi$
$384$	−0.861302	+	0.799171i	−0.0439531	+	0.0407825i
$385$	1.21147	−	5.30779i	0.0617421	−	0.270510i
$386$	−12.0359			−0.612613
$387$	−5.14084	−	9.29242i	−0.261324	−	0.472360i
$388$	−8.51048			−0.432054
$389$	−7.41296	+	32.4783i	−0.375852	+	1.64672i	0.334152	+	0.942519i	$0.391550\pi$
$389$	−7.41296	+	32.4783i	−0.375852	+	1.64672i	−0.710005	+	0.704197i	$0.751307\pi$
$390$	1.84934	−	1.71594i	0.0936449	−	0.0868898i
$391$	31.2622	+	15.0551i	1.58100	+	0.761368i
$392$	−2.37360	−	0.357762i	−0.119885	−	0.0180697i
$393$	5.76092	+	9.97820i	0.290600	+	0.503334i
$394$	−2.67158	+	4.62731i	−0.134592	+	0.233121i
$395$	−0.799232	+	1.00221i	−0.0402137	+	0.0504264i
$396$	0.214902	−	2.86766i	0.0107992	−	0.144106i
$397$	4.41087	−	11.2387i	0.221375	−	0.564055i	−0.776435	−	0.630197i	$-0.782974\pi$
$397$	4.41087	−	11.2387i	0.221375	−	0.564055i	0.997810	+	0.0661424i	$0.0210692\pi$
$398$	2.36480	−	1.13883i	0.118537	−	0.0570842i
$399$	−26.1790	+	8.07515i	−1.31059	+	0.404263i
$400$	0.365341	+	0.930874i	0.0182671	+	0.0465437i
$401$	−8.82830	−	8.19146i	−0.440864	−	0.409062i	0.428260	−	0.903655i	$-0.359127\pi$
$401$	−8.82830	−	8.19146i	−0.440864	−	0.409062i	−0.869125	+	0.494593i	$0.835317\pi$
$402$	14.7461	−	10.0537i	0.735469	−	0.501435i
$403$	6.96574	+	8.73476i	0.346988	+	0.435109i
$404$	12.0536	−	1.81678i	0.599688	−	0.0903884i
$405$	−1.45134	−	0.447679i	−0.0721176	−	0.0222453i
$406$	−0.667975	−	8.91351i	−0.0331511	−	0.442370i
$407$	6.48032	+	4.41821i	0.321218	+	0.219002i
$408$	−1.42908	−	6.26122i	−0.0707501	−	0.309977i
$409$	4.45033	+	19.4982i	0.220055	+	0.964123i	0.957436	+	0.288646i	$0.0932050\pi$
$409$	4.45033	+	19.4982i	0.220055	+	0.964123i	−0.737381	+	0.675477i	$0.763938\pi$
$410$	1.13762	+	0.775617i	0.0561831	+	0.0383050i
$411$	−0.782374	−	10.4401i	−0.0385917	−	0.514970i
$412$	−12.6586	−	3.90466i	−0.623645	−	0.192369i
$413$	45.7974	−	6.90284i	2.25354	−	0.339667i
$414$	6.40988	+	8.03773i	0.315028	+	0.395033i
$415$	12.5613	−	8.56414i	0.616609	−	0.420397i
$416$	1.57397	+	1.46043i	0.0771701	+	0.0716034i
$417$	−2.70134	−	6.88290i	−0.132285	−	0.337057i
$418$	12.9041	−	3.98038i	0.631159	−	0.194687i
$419$	−5.72268	+	2.75590i	−0.279571	+	0.134634i	−0.568415	−	0.822742i	$-0.692443\pi$
$419$	−5.72268	+	2.75590i	−0.279571	+	0.134634i	0.288844	+	0.957376i	$0.406729\pi$
$420$	1.31611	−	3.35340i	0.0642196	−	0.163629i
$421$	0.488378	−	6.51695i	0.0238021	−	0.317616i	−0.972576	−	0.232585i	$-0.925282\pi$
$421$	0.488378	−	6.51695i	0.0238021	−	0.317616i	0.996378	−	0.0850319i	$-0.0270992\pi$
$422$	11.6949	−	14.6649i	0.569298	−	0.713877i
$423$	−3.71692	+	6.43790i	−0.180723	+	0.313021i
$424$	−0.140328	−	0.243055i	−0.00681493	−	0.0118038i
$425$	−5.40490	−	0.814658i	−0.262176	−	0.0395167i
$426$	10.2739	+	4.94765i	0.497772	+	0.239714i
$427$	−25.8761	+	24.0095i	−1.25223	+	1.16190i
$428$	−0.0459463	+	0.201304i	−0.00222090	+	0.00973039i
$429$	4.47970			0.216282
$430$	1.34207	+	6.41863i	0.0647203	+	0.309534i
$431$	5.85423			0.281988			0.140994	−	0.990010i	$-0.454970\pi$
$431$	5.85423			0.281988			0.140994	+	0.990010i	$0.454970\pi$
$432$	1.20777	−	5.29160i	0.0581090	−	0.254592i
$433$	1.16564	−	1.08155i	0.0560169	−	0.0519761i	−0.651668	−	0.758505i	$-0.725930\pi$
$433$	1.16564	−	1.08155i	0.0560169	−	0.0519761i	0.707685	+	0.706529i	$0.249740\pi$
$434$	14.3734	+	6.92187i	0.689946	+	0.332260i
$435$	3.38715	+	0.510530i	0.162401	+	0.0244781i
$436$	0.509009	+	0.881630i	0.0243771	+	0.0422224i
$437$	−24.1384	+	41.8090i	−1.15470	+	1.99999i
$438$	−2.68206	+	3.36320i	−0.128154	+	0.160700i
$439$	−1.22745	+	16.3791i	−0.0585828	+	0.781734i	0.888117	+	0.459617i	$0.152013\pi$
$439$	−1.22745	+	16.3791i	−0.0585828	+	0.781734i	−0.946700	+	0.322117i	$0.895606\pi$
$440$	−0.648733	+	1.65294i	−0.0309271	+	0.0788010i
$441$	3.50245	−	1.68669i	0.166783	−	0.0803186i
$442$	−11.2148	+	3.45930i	−0.533433	+	0.164542i
$443$	10.4695	+	26.6759i	0.497422	+	1.26741i	0.930579	+	0.366091i	$0.119304\pi$
$443$	10.4695	+	26.6759i	0.497422	+	1.26741i	−0.433157	+	0.901318i	$0.642601\pi$
$444$	3.80434	+	3.52991i	0.180546	+	0.167522i
$445$	7.48022	−	5.09993i	0.354597	−	0.241760i
$446$	12.0767	+	15.1437i	0.571849	+	0.717076i
$447$	−17.0125	+	2.56422i	−0.804664	+	0.121284i
$448$	2.92979	+	0.903722i	0.138420	+	0.0426968i
$449$	−0.280775	−	3.74668i	−0.0132506	−	0.176817i	−0.999902	−	0.0139726i	$-0.995552\pi$
$449$	−0.280775	−	3.74668i	−0.0132506	−	0.176817i	0.986652	−	0.162844i	$-0.0520668\pi$
$450$	−1.33808	−	0.912288i	−0.0630777	−	0.0430057i
$451$	0.544039	+	2.38359i	0.0256178	+	0.112239i
$452$	3.61923	+	15.8569i	0.170234	+	0.745845i
$453$	3.68987	+	2.51571i	0.173365	+	0.118198i
$454$	0.994883	+	13.2758i	0.0466922	+	0.623064i
$455$	−6.29069	−	1.94042i	−0.294912	−	0.0909683i
$456$	8.83564	−	1.33176i	0.413767	−	0.0623653i
$457$	−12.0703	−	15.1356i	−0.564623	−	0.708014i	0.414782	−	0.909921i	$-0.363858\pi$
$457$	−12.0703	−	15.1356i	−0.564623	−	0.708014i	−0.979405	+	0.201906i	$0.935286\pi$
$458$	−21.2842	+	14.5113i	−0.994544	+	0.678069i
$459$	21.7478	+	20.1790i	1.01510	+	0.941874i
$460$	−2.31922	−	5.90928i	−0.108134	−	0.275521i
$461$	15.4411	−	4.76295i	0.719164	−	0.221833i	0.0864920	−	0.996253i	$-0.472434\pi$
$461$	15.4411	−	4.76295i	0.719164	−	0.221833i	0.632672	+	0.774420i	$0.281958\pi$
$462$	5.76330	−	2.77546i	0.268133	−	0.129126i
$463$	2.07198	−	5.27931i	0.0962929	−	0.245350i	−0.874609	−	0.484830i	$-0.838882\pi$
$463$	2.07198	−	5.27931i	0.0962929	−	0.245350i	0.970901	+	0.239479i	$0.0769768\pi$
$464$	−0.217865	+	2.90720i	−0.0101141	+	0.134964i
$465$	−3.81177	+	4.77981i	−0.176767	+	0.221658i
$466$	4.32545	−	7.49190i	0.200373	−	0.347056i
$467$	−6.43784	−	11.1507i	−0.297908	−	0.515991i	0.677750	−	0.735293i	$-0.262955\pi$
$467$	−6.43784	−	11.1507i	−0.297908	−	0.515991i	−0.975657	+	0.219302i	$0.929622\pi$
$468$	−3.43843	−	0.518260i	−0.158941	−	0.0239566i
$469$	−41.9599	−	20.2068i	−1.93753	−	0.933065i
$470$	3.36490	−	3.12217i	0.155211	−	0.144015i
$471$	−1.26230	+	5.53049i	−0.0581637	+	0.254832i
$472$	−15.1058			−0.695303
$473$	−6.00534	+	9.97589i	−0.276126	+	0.458692i
$474$	−1.50614			−0.0691791
$475$	1.69226	−	7.41426i	0.0776461	−	0.340190i
$476$	−12.2850	+	11.3988i	−0.563080	+	0.522462i
$477$	0.409507	+	0.197208i	0.0187500	+	0.00902953i
$478$	13.7007	+	2.06505i	0.626656	+	0.0944532i
$479$	−12.3825	−	21.4471i	−0.565770	−	0.979943i	−0.996978	−	0.0776899i	$-0.975246\pi$
$479$	−12.3825	−	21.4471i	−0.565770	−	0.979943i	0.431207	−	0.902253i	$-0.358088\pi$
$480$	−0.587477	+	1.01754i	−0.0268145	+	0.0464441i
$481$	5.91308	−	7.41477i	0.269613	−	0.338084i
$482$	1.71576	−	22.8953i	0.0781509	−	1.04285i
$483$	−8.35480	+	21.2877i	−0.380157	+	0.968623i
$484$	7.06983	−	3.40465i	0.321356	−	0.154757i
$485$	−8.13238	+	2.50851i	−0.369273	+	0.113905i
$486$	5.29690	+	13.4963i	0.240272	+	0.612203i
$487$	−2.95336	−	2.74032i	−0.133830	−	0.124176i	0.610418	−	0.792079i	$-0.291001\pi$
$487$	−2.95336	−	2.74032i	−0.133830	−	0.124176i	−0.744248	+	0.667904i	$0.767192\pi$
$488$	9.51254	−	6.48554i	0.430613	−	0.293587i
$489$	2.50845	+	3.14549i	0.113436	+	0.142244i
$490$	−2.37360	+	0.357762i	−0.107228	+	0.0161621i
$491$	33.9659	+	10.4771i	1.53286	+	0.472824i	0.942469	−	0.334294i	$-0.108498\pi$
$491$	33.9659	+	10.4771i	1.53286	+	0.472824i	0.590390	+	0.807118i	$0.298974\pi$
$492$	0.120895	+	1.61323i	0.00545036	+	0.0727301i
$493$	−13.1663	−	8.97661i	−0.592979	−	0.404286i
$494$	−3.63352	−	15.9195i	−0.163480	−	0.716251i
$495$	−0.639904	−	2.80360i	−0.0287616	−	0.126013i
$496$	−4.29915	−	2.93111i	−0.193037	−	0.131611i
$497$	−2.22369	−	29.6730i	−0.0997460	−	1.33102i
$498$	17.0692	+	5.26515i	0.764889	+	0.235937i
$499$	17.4362	−	2.62808i	0.780551	−	0.117649i	0.253333	−	0.967379i	$-0.418473\pi$
$499$	17.4362	−	2.62808i	0.780551	−	0.117649i	0.527218	+	0.849730i	$0.323235\pi$
$500$	0.623490	+	0.781831i	0.0278833	+	0.0349646i
$501$	11.5489	−	7.87393i	0.515968	−	0.351781i
$502$	−9.51769	−	8.83113i	−0.424795	−	0.394152i
$503$	−2.40339	−	6.12375i	−0.107162	−	0.273044i	0.867227	−	0.497913i	$-0.165900\pi$
$503$	−2.40339	−	6.12375i	−0.107162	−	0.273044i	−0.974389	+	0.224868i	$0.927805\pi$
$504$	−4.74476	+	1.46356i	−0.211348	+	0.0651923i
$505$	10.9826	−	5.28892i	0.488718	−	0.235354i
$506$	4.11822	−	10.4931i	0.183077	−	0.466473i
$507$	−0.736659	+	9.83003i	−0.0327162	+	0.436567i
$508$	6.40519	−	8.03186i	0.284184	−	0.356356i
$509$	1.45297	−	2.51662i	0.0644018	−	0.111547i	−0.832027	−	0.554736i	$-0.812819\pi$
$509$	1.45297	−	2.51662i	0.0644018	−	0.111547i	0.896428	+	0.443188i	$0.146153\pi$
$510$	−3.21112	−	5.56182i	−0.142191	−	0.246282i
$511$	11.0998	+	1.67302i	0.491025	+	0.0740101i
$512$	−0.900969	−	0.433884i	−0.0398176	−	0.0191751i
$513$	−30.2583	+	28.0756i	−1.33594	+	1.23957i
$514$	−3.22926	+	14.1483i	−0.142437	+	0.624056i
$515$	−13.2471			−0.583739
$516$	−4.91309	+	5.93495i	−0.216287	+	0.261272i
$517$	8.15088			0.358475
$518$	3.01348	−	13.2029i	0.132405	−	0.580102i
$519$	8.33966	−	7.73807i	0.366070	−	0.339664i
$520$	1.93451	+	0.931611i	0.0848339	+	0.0408538i
$521$	13.7668	+	2.07502i	0.603136	+	0.0909081i	0.443510	−	0.896269i	$-0.353733\pi$
$521$	13.7668	+	2.07502i	0.603136	+	0.0909081i	0.159626	+	0.987178i	$0.448971\pi$
$522$	−2.36069	−	4.08883i	−0.103324	−	0.178963i
$523$	14.2275	−	24.6428i	0.622126	−	1.07755i	−0.366964	−	0.930235i	$-0.619603\pi$
$523$	14.2275	−	24.6428i	0.622126	−	1.07755i	0.989089	−	0.147318i	$-0.0470640\pi$
$524$	−6.11407	+	7.66680i	−0.267094	+	0.334926i
$525$	0.269209	−	3.59234i	0.0117492	−	0.156783i
$526$	−2.02181	+	5.15149i	−0.0881552	+	0.224616i
$527$	25.6243	−	12.3400i	1.11621	−	0.537540i
$528$	−1.99366	+	0.614964i	−0.0867631	+	0.0267629i
$529$	6.31979	+	16.1026i	0.274774	+	0.700112i
$530$	−0.205735	−	0.190895i	−0.00893657	−	0.00829193i
$531$	20.2128	−	13.7809i	0.877163	−	0.598040i
$532$	−14.5378	−	18.2298i	−0.630293	−	0.790362i
$533$	2.92331	−	0.440618i	0.126623	−	0.0190853i
$534$	10.1647	+	3.13539i	0.439868	+	0.135681i
$535$	0.0154303	+	0.205903i	0.000667111	+	0.00890198i
$536$	12.5504	+	8.55671i	0.542094	+	0.369593i
$537$	−3.26294	−	14.2959i	−0.140806	−	0.616913i
$538$	2.96463	+	12.9889i	0.127814	+	0.559990i
$539$	−3.52175	−	2.40109i	−0.151692	−	0.103422i
$540$	−0.405611	−	5.41250i	−0.0174547	−	0.232917i
$541$	−41.3001	−	12.7394i	−1.77563	−	0.547710i	−0.778801	−	0.627271i	$-0.784172\pi$
$541$	−41.3001	−	12.7394i	−1.77563	−	0.547710i	−0.996830	+	0.0795609i	$0.974648\pi$
$542$	−23.3390	+	3.51780i	−1.00250	+	0.151102i
$543$	−2.06782	−	2.59296i	−0.0887385	−	0.111275i
$544$	4.51618	−	3.07908i	0.193630	−	0.132014i
$545$	0.746260	+	0.692428i	0.0319663	+	0.0296604i
$546$	−2.82588	−	7.20022i	−0.120936	−	0.308141i
$547$	−19.2805	+	5.94725i	−0.824375	+	0.254286i	−0.678111	−	0.734959i	$-0.737201\pi$
$547$	−19.2805	+	5.94725i	−0.824375	+	0.254286i	−0.146264	+	0.989246i	$0.546725\pi$
$548$	8.02802	−	3.86609i	0.342940	−	0.165151i
$549$	−6.81187	+	17.3564i	−0.290724	+	0.740752i
$550$	−0.132698	+	1.77073i	−0.00565824	+	0.0755040i
$551$	13.8234	−	17.3340i	0.588898	−	0.738455i
$552$	3.72936	−	6.45944i	0.158732	−	0.274932i
$553$	1.96511	+	3.40367i	0.0835650	+	0.144739i
$554$	13.9381	+	2.10083i	0.592172	+	0.0892556i
$555$	4.67578	+	2.25174i	0.198476	+	0.0955809i
$556$	4.61312	−	4.28035i	0.195640	−	0.181527i
$557$	9.14690	−	40.0752i	0.387567	−	1.69804i	−0.285434	−	0.958398i	$-0.592138\pi$
$557$	9.14690	−	40.0752i	0.387567	−	1.69804i	0.673001	−	0.739642i	$-0.265005\pi$
$558$	8.42662			0.356727
$559$	11.4863	+	8.14272i	0.485820	+	0.344401i
$560$	3.06601			0.129563
$561$	2.53761	−	11.1180i	0.107138	−	0.469402i
$562$	−5.97497	+	5.54396i	−0.252039	+	0.233858i
$563$	−12.6724	−	6.10270i	−0.534077	−	0.257198i	0.147349	−	0.989085i	$-0.452926\pi$
$563$	−12.6724	−	6.10270i	−0.534077	−	0.257198i	−0.681427	+	0.731887i	$0.738640\pi$
$564$	5.33310	+	0.803835i	0.224564	+	0.0338476i
$565$	8.13233	+	14.0856i	0.342130	+	0.592586i
$566$	7.08026	−	12.2634i	0.297606	−	0.515468i
$567$	−2.90341	+	3.64076i	−0.121932	+	0.152897i
$568$	−0.725271	+	9.67806i	−0.0304317	+	0.406083i
$569$	7.05219	−	17.9687i	0.295643	−	0.753286i	−0.703452	−	0.710743i	$-0.748359\pi$
$569$	7.05219	−	17.9687i	0.295643	−	0.753286i	0.999095	−	0.0425431i	$-0.0135460\pi$
$570$	8.05055	−	3.87694i	0.337201	−	0.162387i
$571$	−16.2014	+	4.99746i	−0.678006	+	0.209137i	−0.614586	−	0.788850i	$-0.710677\pi$
$571$	−16.2014	+	4.99746i	−0.678006	+	0.209137i	−0.0634198	+	0.997987i	$0.520201\pi$
$572$	1.39292	+	3.54911i	0.0582410	+	0.148396i
$573$	15.5842	+	14.4600i	0.651039	+	0.604076i
$574$	3.48795	−	2.37805i	0.145584	−	0.0992578i
$575$	−3.95797	−	4.96314i	−0.165059	−	0.206977i
$576$	1.60140	−	0.241372i	0.0667248	−	0.0100572i
$577$	−13.3705	−	4.12426i	−0.556622	−	0.171695i	0.00366578	−	0.999993i	$-0.498833\pi$
$577$	−13.3705	−	4.12426i	−0.556622	−	0.171695i	−0.560287	+	0.828298i	$0.689309\pi$
$578$	0.962272	+	12.8406i	0.0400252	+	0.534100i
$579$	−11.6844	−	7.96628i	−0.485587	−	0.331067i
$580$	0.648727	+	2.84226i	0.0269369	+	0.118018i
$581$	−10.3722	−	45.4438i	−0.430313	−	1.88533i
$582$	−8.26191	−	5.63287i	−0.342467	−	0.233490i
$583$	−0.0372424	−	0.496965i	−0.00154242	−	0.0205822i
$584$	−3.49851	−	1.07915i	−0.144769	−	0.0446554i
$585$	−3.43843	+	0.518260i	−0.142161	+	0.0214274i
$586$	−20.5073	−	25.7153i	−0.847147	−	1.06229i
$587$	−11.7765	+	8.02910i	−0.486070	+	0.331397i	−0.781434	−	0.623988i	$-0.785511\pi$
$587$	−11.7765	+	8.02910i	−0.486070	+	0.331397i	0.295364	+	0.955385i	$0.404559\pi$
$588$	−2.06748	−	1.91834i	−0.0852613	−	0.0791109i
$589$	14.4567	+	36.8352i	0.595680	+	1.51777i
$590$	−14.4347	+	4.45253i	−0.594269	+	0.183308i
$591$	−5.65625	+	2.72391i	−0.232667	+	0.112047i
$592$	−1.61370	+	4.11163i	−0.0663225	+	0.168987i
$593$	2.61622	−	34.9111i	0.107435	−	1.43363i	−0.639532	−	0.768765i	$-0.720872\pi$
$593$	2.61622	−	34.9111i	0.107435	−	1.43363i	0.746967	−	0.664861i	$-0.231509\pi$
$594$	6.00912	−	7.53520i	0.246557	−	0.309173i
$595$	−8.37933	+	14.5134i	−0.343519	+	0.594992i
$596$	−7.32142	−	12.6811i	−0.299897	−	0.519437i
$597$	3.04949	+	0.459636i	0.124807	+	0.0188116i
$598$	−12.2805	−	5.91396i	−0.502185	−	0.241840i
$599$	−22.7229	+	21.0837i	−0.928431	+	0.861458i	−0.990625	−	0.136606i	$-0.956380\pi$
$599$	−22.7229	+	21.0837i	−0.928431	+	0.861458i	0.0621947	+	0.998064i	$0.480190\pi$
$600$	−0.261452	+	1.14549i	−0.0106737	+	0.0467646i
$601$	−25.4296			−1.03730			−0.518648	−	0.854988i	$-0.673564\pi$
$601$	−25.4296			−1.03730			−0.518648	+	0.854988i	$0.673564\pi$
$602$	19.8225	+	3.35940i	0.807905	+	0.136919i
$603$	−24.5996			−1.00177
$604$	−0.845776	+	3.70559i	−0.0344141	+	0.150778i
$605$	5.75220	−	5.33726i	0.233860	−	0.216991i
$606$	12.9040	+	6.21424i	0.524189	+	0.252436i
$607$	30.4534	+	4.59012i	1.23607	+	0.186307i	0.734378	−	0.678741i	$-0.237474\pi$
$607$	30.4534	+	4.59012i	1.23607	+	0.186307i	0.501689	+	0.865048i	$0.332712\pi$
$608$	3.80247	+	6.58606i	0.154210	+	0.267100i
$609$	5.25116	−	9.09528i	0.212788	−	0.368559i
$610$	7.17828	−	9.00128i	0.290640	−	0.364451i
$611$	0.736535	−	9.82838i	0.0297970	−	0.397614i
$612$	−3.23401	+	8.24012i	−0.130727	+	0.333087i
$613$	4.25744	−	2.05028i	0.171957	−	0.0828099i	−0.345925	−	0.938262i	$-0.612435\pi$
$613$	4.25744	−	2.05028i	0.171957	−	0.0828099i	0.517882	+	0.855452i	$0.326721\pi$
$614$	27.9477	−	8.62073i	1.12788	−	0.347904i
$615$	0.591032	+	1.50592i	0.0238327	+	0.0607248i
$616$	3.99094	+	3.70305i	0.160800	+	0.149200i
$617$	−20.1798	+	13.7583i	−0.812406	+	0.553889i	−0.896745	−	0.442548i	$-0.854075\pi$
$617$	−20.1798	+	13.7583i	−0.812406	+	0.553889i	0.0843385	+	0.996437i	$0.473122\pi$
$618$	−9.70447	−	12.1690i	−0.390371	−	0.489510i
$619$	−38.6844	+	5.83073i	−1.55486	+	0.234357i	−0.869530	−	0.493879i	$-0.835578\pi$
$619$	−38.6844	+	5.83073i	−1.55486	+	0.234357i	−0.685326	+	0.728236i	$0.740340\pi$
$620$	−4.97211	−	1.53369i	−0.199685	−	0.0615946i
$621$	2.57486	+	34.3591i	0.103325	+	1.37878i
$622$	−2.00176	−	1.36478i	−0.0802632	−	0.0547225i
$623$	−6.17665	−	27.0617i	−0.247462	−	1.08420i
$624$	0.561374	+	2.45954i	0.0224730	+	0.0984605i
$625$	0.826239	+	0.563320i	0.0330496	+	0.0225328i
$626$	2.03719	+	27.1845i	0.0814227	+	1.08651i
$627$	15.1617	+	4.67676i	0.605499	+	0.186772i
$628$	−4.77411	+	0.719582i	−0.190508	+	0.0287144i
$629$	−15.0529	−	18.8757i	−0.600196	−	0.752623i
$630$	−4.10257	+	2.79708i	−0.163450	+	0.111438i
$631$	7.76769	+	7.20737i	0.309227	+	0.286921i	0.819485	−	0.573101i	$-0.194260\pi$
$631$	7.76769	+	7.20737i	0.309227	+	0.286921i	−0.510258	+	0.860021i	$0.670450\pi$
$632$	−0.468319	−	1.19326i	−0.0186287	−	0.0474653i
$633$	21.0596	−	6.49603i	0.837045	−	0.258194i
$634$	14.9457	−	7.19748i	0.593570	−	0.285848i
$635$	3.75320	−	9.56299i	0.148941	−	0.379496i
$636$	0.0246428	−	0.328836i	0.000977151	−	0.0130392i
$637$	−3.21348	+	4.02958i	−0.127323	+	0.159658i
$638$	−2.58839	+	4.48321i	−0.102475	+	0.177492i
$639$	−7.85871	−	13.6117i	−0.310886	−	0.538470i
$640$	−0.988831	−	0.149042i	−0.0390870	−	0.00589141i
$641$	−18.6484	−	8.98059i	−0.736567	−	0.354712i	0.0276963	−	0.999616i	$-0.491183\pi$
$641$	−18.6484	−	8.98059i	−0.736567	−	0.354712i	−0.764263	+	0.644904i	$0.776897\pi$
$642$	−0.177842	+	0.165013i	−0.00701887	+	0.00651256i
$643$	5.05378	−	22.1421i	0.199302	−	0.873198i	−0.772052	−	0.635560i	$-0.780769\pi$
$643$	5.05378	−	22.1421i	0.199302	−	0.873198i	0.971354	−	0.237639i	$-0.0763734\pi$
$644$	−19.4633			−0.766962
$645$	−2.94546	+	7.11944i	−0.115977	+	0.280328i
$646$	−41.5682			−1.63548
$647$	−5.71696	+	25.0477i	−0.224757	+	0.984725i	0.729087	+	0.684421i	$0.239945\pi$
$647$	−5.71696	+	25.0477i	−0.224757	+	0.984725i	−0.953844	+	0.300303i	$0.902912\pi$
$648$	1.11337	−	1.03306i	0.0437374	−	0.0405823i
$649$	−24.1670	−	11.6382i	−0.948637	−	0.456840i
$650$	2.12316	+	0.320015i	0.0832773	+	0.0125520i
$651$	9.37218	+	16.2331i	0.367325	+	0.636225i
$652$	−1.71208	+	2.96541i	−0.0670503	+	0.116135i
$653$	−23.1863	+	29.0747i	−0.907350	+	1.13778i	0.0826315	+	0.996580i	$0.473668\pi$
$653$	−23.1863	+	29.0747i	−0.907350	+	1.13778i	−0.989981	+	0.141200i	$0.954904\pi$
$654$	−0.0893865	+	1.19278i	−0.00349529	+	0.0466414i
$655$	−3.58261	+	9.12834i	−0.139984	+	0.356674i
$656$	−1.24051	+	0.597400i	−0.0484339	+	0.0233246i
$657$	5.66578	−	1.74766i	0.221043	−	0.0681827i
$658$	−5.14172	−	13.1009i	−0.200445	−	0.510726i
$659$	−9.53826	−	8.85021i	−0.371558	−	0.344755i	0.472188	−	0.881498i	$-0.343464\pi$
$659$	−9.53826	−	8.85021i	−0.371558	−	0.344755i	−0.843746	+	0.536742i	$0.819655\pi$
$660$	−1.72383	+	1.17529i	−0.0670999	+	0.0457479i
$661$	−11.5063	−	14.4285i	−0.447544	−	0.561203i	0.505970	−	0.862551i	$-0.331135\pi$
$661$	−11.5063	−	14.4285i	−0.447544	−	0.561203i	−0.953514	+	0.301348i	$0.902563\pi$
$662$	−23.5467	+	3.54910i	−0.915170	+	0.137940i
$663$	−13.1768	−	4.06452i	−0.511746	−	0.157853i
$664$	1.13612	+	15.1605i	0.0440900	+	0.588340i
$665$	−19.2652	−	13.1348i	−0.747074	−	0.509346i
$666$	−1.59174	−	6.97385i	−0.0616785	−	0.270231i
$667$	−4.11819	−	18.0429i	−0.159457	−	0.698626i
$668$	9.82927	+	6.70148i	0.380306	+	0.259288i
$669$	1.70073	+	22.6947i	0.0657541	+	0.877427i
$670$	14.5149	+	4.47727i	0.560761	+	0.172972i
$671$	20.2153	−	3.04697i	0.780404	−	0.117627i
$672$	2.24607	+	2.81648i	0.0866440	+	0.108648i
$673$	−18.1576	+	12.3796i	−0.699924	+	0.477200i	−0.860256	−	0.509863i	$-0.829696\pi$
$673$	−18.1576	+	12.3796i	−0.699924	+	0.477200i	0.160331	+	0.987063i	$0.448744\pi$
$674$	−12.4880	−	11.5872i	−0.481020	−	0.446321i
$675$	−1.98295	−	5.05248i	−0.0763239	−	0.194470i
$676$	−8.01704	+	2.47293i	−0.308348	+	0.0951127i
$677$	13.0683	−	6.29337i	0.502257	−	0.241874i	−0.165560	−	0.986200i	$-0.552943\pi$
$677$	13.0683	−	6.29337i	0.502257	−	0.241874i	0.667817	+	0.744326i	$0.267229\pi$
$678$	−6.98175	+	17.7892i	−0.268132	+	0.683190i
$679$	−1.94995	+	26.0202i	−0.0748321	+	0.998565i
$680$	3.40797	−	4.27345i	0.130690	−	0.163879i
$681$	−7.82109	+	13.5465i	−0.299705	+	0.519104i
$682$	−4.61970	−	8.00156i	−0.176898	−	0.306396i
$683$	24.6341	+	3.71299i	0.942597	+	0.142074i	0.602323	−	0.798252i	$-0.294242\pi$
$683$	24.6341	+	3.71299i	0.942597	+	0.142074i	0.340274	+	0.940326i	$0.389480\pi$
$684$	−11.0964	−	5.34374i	−0.424281	−	0.204323i
$685$	6.53180	−	6.06063i	0.249567	−	0.231565i
$686$	3.13808	−	13.7488i	0.119812	−	0.524932i
$687$	−30.2672			−1.15476
$688$	−6.22973	−	2.04705i	−0.237506	−	0.0780431i
$689$	−0.602609			−0.0229576
$690$	1.65972	−	7.27171i	0.0631845	−	0.276829i
$691$	−8.31226	+	7.71265i	−0.316213	+	0.293403i	−0.822271	−	0.569097i	$-0.807293\pi$
$691$	−8.31226	+	7.71265i	−0.316213	+	0.293403i	0.506057	+	0.862500i	$0.331102\pi$
$692$	8.72374	+	4.20113i	0.331627	+	0.159703i
$693$	−8.71846	−	1.31410i	−0.331187	−	0.0499184i
$694$	11.8814	+	20.5793i	0.451014	+	0.781178i
$695$	3.14652	−	5.44992i	0.119354	−	0.206727i
$696$	−2.13571	+	2.67809i	−0.0809537	+	0.101513i
$697$	0.562410	−	7.50484i	0.0213028	−	0.284266i
$698$	−12.5991	+	32.1021i	−0.476885	+	1.21508i
$699$	9.15782	−	4.41017i	0.346380	−	0.166808i
$700$	2.92979	−	0.903722i	0.110736	−	0.0341575i
$701$	13.4740	+	34.3312i	0.508905	+	1.29667i	0.922426	+	0.386175i	$0.126204\pi$
$701$	13.4740	+	34.3312i	0.508905	+	1.29667i	−0.413520	+	0.910495i	$0.635701\pi$
$702$	−8.54299	−	7.92674i	−0.322434	−	0.299175i
$703$	27.7539	−	18.9223i	1.04676	−	0.713668i
$704$	−1.10713	−	1.38829i	−0.0417264	−	0.0523232i
$705$	5.33310	−	0.803835i	0.200856	−	0.0302742i
$706$	−19.1746	−	5.91458i	−0.721646	−	0.222598i
$707$	−2.79295	−	37.2693i	−0.105040	−	1.40166i
$708$	−14.6646	−	9.99818i	−0.551131	−	0.375755i
$709$	−1.72855	−	7.57328i	−0.0649172	−	0.284421i	0.932042	−	0.362351i	$-0.118026\pi$
$709$	−1.72855	−	7.57328i	−0.0649172	−	0.284421i	−0.996959	+	0.0779305i	$0.975169\pi$
$710$	2.15961	+	9.46187i	0.0810487	+	0.355098i
$711$	1.71524	+	1.16943i	0.0643267	+	0.0438572i
$712$	0.676557	+	9.02803i	0.0253551	+	0.338340i
$713$	31.5634	+	9.73603i	1.18206	+	0.364617i
$714$	−19.4707	+	2.93474i	−0.728673	+	0.109830i
$715$	2.37716	+	2.98086i	0.0889006	+	0.111478i
$716$	10.3115	−	7.03029i	0.385361	−	0.262734i
$717$	11.9337	+	11.0729i	0.445673	+	0.413525i
$718$	5.28408	+	13.4636i	0.197200	+	0.502458i
$719$	14.7022	−	4.53501i	0.548298	−	0.169127i	−0.00821540	−	0.999966i	$-0.502615\pi$
$719$	14.7022	−	4.53501i	0.548298	−	0.169127i	0.556513	+	0.830839i	$0.312139\pi$
$720$	1.45911	−	0.702668i	0.0543776	−	0.0261869i
$721$	−14.8386	+	37.8082i	−0.552619	+	1.40805i
$722$	2.90214	−	38.7264i	0.108007	−	1.44125i
$723$	16.8194	−	21.0909i	0.625522	−	0.784380i
$724$	1.41134	−	2.44451i	0.0524521	−	0.0908497i
$725$	1.45768	+	2.52477i	0.0541368	+	0.0937677i
$726$	9.11679	+	1.37413i	0.338356	+	0.0509989i
$727$	−11.9947	−	5.77633i	−0.444858	−	0.214232i	0.198025	−	0.980197i	$-0.436547\pi$
$727$	−11.9947	−	5.77633i	−0.444858	−	0.214232i	−0.642882	+	0.765965i	$0.722262\pi$
$728$	4.82580	−	4.47769i	0.178856	−	0.165954i
$729$	−4.80456	+	21.0502i	−0.177947	+	0.779636i
$730$	−3.66116			−0.135506
$731$	26.7157	−	23.8949i	0.988117	−	0.883783i
$732$	13.5273			0.499984
$733$	9.24464	−	40.5034i	0.341459	−	1.49603i	−0.454538	−	0.890727i	$-0.650196\pi$
$733$	9.24464	−	40.5034i	0.341459	−	1.49603i	0.795997	−	0.605301i	$-0.206947\pi$
$734$	3.36125	−	3.11879i	0.124066	−	0.115117i
$735$	−2.54106	−	1.22371i	−0.0937286	−	0.0451373i
$736$	6.27719	+	0.946135i	0.231380	+	0.0348750i
$737$	13.4862	+	23.3587i	0.496770	+	0.860430i
$738$	1.11491	−	1.93108i	0.0410403	−	0.0710839i
$739$	13.8130	−	17.3210i	0.508121	−	0.637164i	−0.459919	−	0.887961i	$-0.652121\pi$
$739$	13.8130	−	17.3210i	0.508121	−	0.637164i	0.968040	+	0.250798i	$0.0806928\pi$
$740$	−0.330080	+	4.40461i	−0.0121340	+	0.161917i
$741$	7.00931	−	17.8594i	0.257494	−	0.656083i
$742$	−0.775278	+	0.373354i	−0.0284613	+	0.0137063i
$743$	15.4616	−	4.76926i	0.567230	−	0.174967i	0.00214159	−	0.999998i	$-0.499318\pi$
$743$	15.4616	−	4.76926i	0.567230	−	0.174967i	0.565088	+	0.825030i	$0.308842\pi$
$744$	−2.23355	−	5.69099i	−0.0818859	−	0.208642i
$745$	−10.7340	−	9.95967i	−0.393262	−	0.364894i
$746$	−12.6219	+	8.60548i	−0.462121	+	0.315069i
$747$	−15.3509	−	19.2495i	−0.561661	−	0.704301i
$748$	9.59744	−	1.44658i	0.350917	−	0.0528922i
$749$	0.604946	+	0.186601i	0.0221043	+	0.00681826i
$750$	0.0878044	+	1.17167i	0.00320616	+	0.0427833i
$751$	14.9481	+	10.1915i	0.545465	+	0.371891i	0.804478	−	0.593982i	$-0.202445\pi$
$751$	14.9481	+	10.1915i	0.545465	+	0.371891i	−0.259014	+	0.965874i	$0.583397\pi$
$752$	1.02143	+	4.47517i	0.0372476	+	0.163193i
$753$	−3.39460	−	14.8727i	−0.123706	−	0.541992i
$754$	5.17199	+	3.52621i	0.188353	+	0.128417i
$755$	0.284040	+	3.79025i	0.0103373	+	0.137941i
$756$	−15.9020	−	4.90511i	−0.578350	−	0.178397i
$757$	35.5861	−	5.36374i	1.29340	−	0.194949i	0.533950	−	0.845516i	$-0.320707\pi$
$757$	35.5861	−	5.36374i	1.29340	−	0.194949i	0.759449	+	0.650567i	$0.225469\pi$
$758$	−2.00280	−	2.51143i	−0.0727449	−	0.0912192i
$759$	10.9430	−	7.46083i	0.397207	−	0.270811i
$760$	5.57481	+	5.17267i	0.202220	+	0.187632i
$761$	−8.88948	−	22.6500i	−0.322243	−	0.821063i	−0.996580	−	0.0826382i	$-0.973665\pi$
$761$	−8.88948	−	22.6500i	−0.322243	−	0.821063i	0.674336	−	0.738424i	$-0.264430\pi$
$762$	11.5342	−	3.55783i	0.417840	−	0.128887i
$763$	2.81215	−	1.35426i	0.101807	−	0.0490275i
$764$	−6.61040	+	16.8430i	−0.239156	+	0.609359i
$765$	−0.661513	+	8.82727i	−0.0239170	+	0.319151i
$766$	14.5937	−	18.2999i	0.527291	−	0.661202i
$767$	−16.2172	+	28.0890i	−0.585570	+	1.01424i
$768$	−0.587477	−	1.01754i	−0.0211987	−	0.0367173i
$769$	−40.0182	−	6.03178i	−1.44309	−	0.217511i	−0.619636	−	0.784889i	$-0.712720\pi$
$769$	−40.0182	−	6.03178i	−1.44309	−	0.217511i	−0.823458	+	0.567378i	$0.807958\pi$
$770$	4.90513	+	2.36219i	0.176769	+	0.0851273i
$771$	−12.4994	+	11.5977i	−0.450153	+	0.417681i
$772$	2.67825	−	11.7342i	0.0963922	−	0.422322i
$773$	7.77692			0.279716			0.139858	−	0.990172i	$-0.455335\pi$
$773$	7.77692			0.279716			0.139858	+	0.990172i	$0.455335\pi$
$774$	10.2034	−	2.94419i	0.366753	−	0.105827i
$775$	−5.20327			−0.186907
$776$	1.89376	−	8.29710i	0.0679820	−	0.297849i
$777$	11.6641	−	10.8227i	0.418448	−	0.388263i
$778$	−30.0145	−	14.4542i	−1.07607	−	0.518209i
$779$	10.3540	+	1.56062i	0.370971	+	0.0559150i
$780$	1.26140	+	2.18480i	0.0451652	+	0.0782285i
$781$	−8.61672	+	14.9246i	−0.308331	+	0.534044i
$782$	−21.6341	+	27.1283i	−0.773634	+	0.970106i
$783$	1.18250	−	15.7794i	0.0422591	−	0.563908i
$784$	0.876968	−	2.23448i	0.0313203	−	0.0798028i
$785$	−4.34991	+	2.09481i	−0.155255	+	0.0747669i
$786$	−11.0099	+	3.39612i	−0.392712	+	0.121136i
$787$	−13.5550	−	34.5377i	−0.483185	−	1.23114i	−0.939878	−	0.341511i	$-0.889061\pi$
$787$	−13.5550	−	34.5377i	−0.483185	−	1.23114i	0.456693	−	0.889624i	$-0.349034\pi$
$788$	−3.91681	−	3.63427i	−0.139531	−	0.129466i
$789$	−5.37240	+	3.66284i	−0.191263	+	0.130401i
$790$	−0.799232	−	1.00221i	−0.0284354	−	0.0356569i
$791$	49.3106	−	7.43238i	1.75328	−	0.264265i
$792$	2.74795	+	0.847629i	0.0976440	+	0.0301192i
$793$	−1.84734	−	24.6511i	−0.0656011	−	0.875386i
$794$	9.97543	+	6.80113i	0.354015	+	0.241363i
$795$	−0.0733780	−	0.321490i	−0.00260245	−	0.0114021i
$796$	0.584056	+	2.55892i	0.0207013	+	0.0906984i
$797$	36.2528	+	24.7168i	1.28414	+	0.875513i	0.996611	−	0.0822586i	$-0.0262134\pi$
$797$	36.2528	+	24.7168i	1.28414	+	0.875513i	0.287530	+	0.957771i	$0.407166\pi$
$798$	−2.04732	−	27.3195i	−0.0724742	−	0.967101i
$799$	−23.9754	−	7.39544i	−0.848190	−	0.261632i
$800$	−0.988831	+	0.149042i	−0.0349604	+	0.00526944i
$801$	−9.14145	−	11.4630i	−0.322997	−	0.405026i
$802$	9.95057	−	6.78418i	0.351367	−	0.239558i
$803$	−4.76564	−	4.42187i	−0.168176	−	0.156044i
$804$	6.52034	+	16.6136i	0.229955	+	0.585915i
$805$	−18.5986	+	5.73691i	−0.655515	+	0.202200i
$806$	−10.0658	+	4.84743i	−0.354552	+	0.170743i
$807$	−5.71897	+	14.5717i	−0.201317	+	0.512948i
$808$	−0.910939	+	12.1556i	−0.0320467	+	0.427634i
$809$	−4.09183	+	5.13100i	−0.143861	+	0.180396i	−0.848542	−	0.529129i	$-0.822519\pi$
$809$	−4.09183	+	5.13100i	−0.143861	+	0.180396i	0.704680	+	0.709525i	$0.251090\pi$
$810$	0.759408	−	1.31533i	0.0266829	−	0.0462161i
$811$	3.76299	+	6.51768i	0.132136	+	0.228867i	0.924500	−	0.381182i	$-0.124483\pi$
$811$	3.76299	+	6.51768i	0.132136	+	0.228867i	−0.792364	+	0.610049i	$0.791150\pi$
$812$	8.83867	+	1.33221i	0.310176	+	0.0467516i
$813$	−24.9857	−	12.0325i	−0.876287	−	0.421998i
$814$	−5.74944	+	5.33470i	−0.201518	+	0.186981i
$815$	−0.761948	+	3.33831i	−0.0266899	+	0.116936i
$816$	6.42224			0.224823
$817$	30.3749	+	39.5509i	1.06268	+	1.38371i
$818$	−19.9996			−0.699270
$819$	−2.37237	+	10.3940i	−0.0828973	+	0.363197i
$820$	−1.00931	+	0.936507i	−0.0352468	+	0.0327043i
$821$	48.9677	+	23.5816i	1.70898	+	0.823004i	0.992047	+	0.125867i	$0.0401711\pi$
$821$	48.9677	+	23.5816i	1.70898	+	0.823004i	0.716938	+	0.697137i	$0.245543\pi$
$822$	10.3524	+	1.56037i	0.361081	+	0.0544243i
$823$	9.47314	+	16.4080i	0.330213	+	0.571946i	0.982553	−	0.185980i	$-0.0595461\pi$
$823$	9.47314	+	16.4080i	0.330213	+	0.571946i	−0.652340	+	0.757926i	$0.726213\pi$
$824$	6.62357	−	11.4724i	0.230743	−	0.399658i
$825$	−1.30082	+	1.63118i	−0.0452888	+	0.0567903i
$826$	−3.46110	+	46.1852i	−0.120427	+	1.60699i
$827$	8.07458	−	20.5737i	0.280781	−	0.715418i	−0.719011	−	0.694999i	$-0.755405\pi$
$827$	8.07458	−	20.5737i	0.280781	−	0.715418i	0.999792	−	0.0204187i	$-0.00649993\pi$
$828$	−9.26254	+	4.46061i	−0.321896	+	0.155017i
$829$	24.1337	−	7.44426i	0.838197	−	0.258550i	0.154205	−	0.988039i	$-0.450718\pi$
$829$	24.1337	−	7.44426i	0.838197	−	0.258550i	0.683992	+	0.729489i	$0.260242\pi$
$830$	5.55427	+	14.1520i	0.192791	+	0.491225i
$831$	12.1405	+	11.2647i	0.421149	+	0.390769i
$832$	−1.77405	+	1.20953i	−0.0615042	+	0.0419329i
$833$	8.18051	+	10.2580i	0.283438	+	0.355420i
$834$	7.31143	−	1.10202i	0.253174	−	0.0381599i
$835$	11.3679	+	3.50653i	0.393402	+	0.121348i
$836$	1.00916	+	13.4663i	0.0349024	+	0.465740i
$837$	23.3344	+	15.9091i	0.806554	+	0.549900i
$838$	−1.41338	−	6.19244i	−0.0488245	−	0.213914i
$839$	10.9507	+	47.9780i	0.378059	+	1.65638i	0.703406	+	0.710789i	$0.251662\pi$
$839$	10.9507	+	47.9780i	0.378059	+	1.65638i	−0.325347	+	0.945595i	$0.605481\pi$
$840$	2.97646	+	2.02931i	0.102698	+	0.0700180i
$841$	−1.53202	−	20.4434i	−0.0528283	−	0.704944i
$842$	6.24488	+	1.92629i	0.215213	+	0.0663843i
$843$	−9.46986	+	1.42735i	−0.326159	+	0.0491606i
$844$	11.6949	+	14.6649i	0.402554	+	0.504787i
$845$	−6.93196	+	4.72613i	−0.238467	+	0.162584i
$846$	−5.44940	−	5.05630i	−0.187354	−	0.173839i
$847$	−8.78964	−	22.3956i	−0.302016	−	0.769523i
$848$	0.268187	−	0.0827248i	0.00920959	−	0.00284078i
$849$	14.9903	−	7.21894i	0.514465	−	0.247753i
$850$	1.99694	−	5.08811i	0.0684944	−	0.174521i
$851$	2.09538	−	27.9609i	0.0718287	−	0.958487i
$852$	−7.10975	+	8.91535i	−0.243576	+	0.305435i
$853$	−18.7491	+	32.4744i	−0.641958	+	1.11190i	0.343038	+	0.939322i	$0.388544\pi$
$853$	−18.7491	+	32.4744i	−0.641958	+	1.11190i	−0.984995	+	0.172581i	$0.944789\pi$
$854$	−17.6496	−	30.5700i	−0.603956	−	1.04608i
$855$	−12.1785	−	1.83561i	−0.416496	−	0.0627767i
$856$	−0.186033	−	0.0895886i	−0.00635847	−	0.00306208i
$857$	−20.9970	+	19.4824i	−0.717244	+	0.665505i	−0.951843	−	0.306587i	$-0.900813\pi$
$857$	−20.9970	+	19.4824i	−0.717244	+	0.665505i	0.234599	+	0.972092i	$0.424622\pi$
$858$	−0.996828	+	4.36739i	−0.0340311	+	0.149100i
$859$	23.7307			0.809680			0.404840	−	0.914388i	$-0.367327\pi$
$859$	23.7307			0.809680			0.404840	+	0.914388i	$0.367327\pi$
$860$	−6.55634	−	0.119859i	−0.223569	−	0.00408716i
$861$	4.96005			0.169038
$862$	−1.30269	+	5.70745i	−0.0443697	+	0.194397i
$863$	−2.39856	+	2.22554i	−0.0816479	+	0.0757582i	−0.719941	−	0.694035i	$-0.755831\pi$
$863$	−2.39856	+	2.22554i	−0.0816479	+	0.0757582i	0.638293	+	0.769793i	$0.279641\pi$
$864$	4.89017	+	2.35498i	0.166367	+	0.0801181i
$865$	9.57448	+	1.44312i	0.325542	+	0.0490676i
$866$	0.795057	+	1.37708i	0.0270172	+	0.0467951i
$867$	−7.56472	+	13.1025i	−0.256911	+	0.444984i
$868$	−9.94671	+	12.4728i	−0.337613	+	0.423354i
$869$	0.170101	−	2.26984i	0.00577028	−	0.0769990i
$870$	−1.25144	+	3.18862i	−0.0424278	+	0.108104i
$871$	29.3848	−	14.1510i	0.995665	−	0.479487i
$872$	−0.972791	+	0.300066i	−0.0329429	+	0.0101615i
$873$	5.03535	+	12.8299i	0.170421	+	0.434225i
$874$	−35.3894	−	32.8366i	−1.19707	−	1.11071i
$875$	2.53326	−	1.72714i	0.0856397	−	0.0583881i
$876$	−2.68206	−	3.36320i	−0.0906185	−	0.113632i
$877$	7.10103	−	1.07031i	0.239785	−	0.0361417i	−0.0280503	−	0.999607i	$-0.508930\pi$
$877$	7.10103	−	1.07031i	0.239785	−	0.0361417i	0.267835	+	0.963465i	$0.413692\pi$
$878$	−15.6953	−	4.84137i	−0.529692	−	0.163388i
$879$	−2.88798	−	38.5374i	−0.0974092	−	1.29984i
$880$	−1.46715	−	1.00028i	−0.0494575	−	0.0337195i
$881$	−5.32309	−	23.3220i	−0.179340	−	0.785738i	−0.981936	−	0.189215i	$-0.939406\pi$
$881$	−5.32309	−	23.3220i	−0.179340	−	0.785738i	0.802596	−	0.596523i	$-0.203451\pi$
$882$	0.865033	+	3.78996i	0.0291272	+	0.127615i
$883$	26.3384	+	17.9572i	0.886358	+	0.604308i	0.918607	−	0.395171i	$-0.129315\pi$
$883$	26.3384	+	17.9572i	0.886358	+	0.604308i	−0.0322498	+	0.999480i	$0.510267\pi$
$884$	−0.877046	−	11.7034i	−0.0294983	−	0.393627i
$885$	−16.9601	−	5.23151i	−0.570109	−	0.175855i
$886$	−28.3368	+	4.27108i	−0.951992	+	0.143490i
$887$	25.8762	+	32.4478i	0.868839	+	1.08949i	0.995235	+	0.0975101i	$0.0310878\pi$
$887$	25.8762	+	32.4478i	0.868839	+	1.08949i	−0.126395	+	0.991980i	$0.540341\pi$
$888$	−4.28795	+	2.92348i	−0.143894	+	0.0981054i
$889$	−23.0893	−	21.4237i	−0.774391	−	0.718529i
$890$	3.30756	+	8.42752i	0.110870	+	0.282491i
$891$	2.57713	−	0.794940i	0.0863371	−	0.0266315i
$892$	−17.4514	+	8.40413i	−0.584315	+	0.281391i
$893$	12.7535	−	32.4955i	0.426781	−	1.08742i
$894$	1.28571	−	17.1566i	0.0430005	−	0.573801i
$895$	7.78122	−	9.75734i	0.260097	−	0.326152i
$896$	−1.53300	+	2.65524i	−0.0512141	+	0.0887054i
$897$	−8.00747	−	13.8693i	−0.267362	−	0.463084i
$898$	3.71522	+	0.559980i	0.123979	+	0.0186868i
$899$	−13.6671	−	6.58175i	−0.455825	−	0.219514i
$900$	1.18717	−	1.10153i	0.0395722	−	0.0367176i
$901$	−0.341359	+	1.49559i	−0.0113723	+	0.0498253i
$902$	−2.44489			−0.0814059
$903$	17.0200	+	16.3813i	0.566391	+	0.545136i
$904$	−16.2647			−0.540955
$905$	0.628106	−	2.75191i	0.0208789	−	0.0914766i
$906$	−3.27371	+	3.03756i	−0.108762	+	0.100916i
$907$	41.3241	+	19.9006i	1.37214	+	0.660789i	0.967309	−	0.253601i	$-0.0816150\pi$
$907$	41.3241	+	19.9006i	1.37214	+	0.660789i	0.404834	+	0.914390i	$0.367329\pi$
$908$	−13.1643	−	1.98420i	−0.436873	−	0.0658481i
$909$	−9.87053	−	17.0963i	−0.327385	−	0.567047i
$910$	3.29158	−	5.70118i	0.109115	−	0.188992i
$911$	2.57174	−	3.22486i	0.0852055	−	0.106844i	−0.737401	−	0.675455i	$-0.763947\pi$
$911$	2.57174	−	3.22486i	0.0852055	−	0.106844i	0.822607	+	0.568610i	$0.192519\pi$
$912$	−0.667746	+	8.91045i	−0.0221113	+	0.295055i
$913$	−9.86267	+	25.1297i	−0.326407	+	0.831671i
$914$	17.4420	−	8.39963i	0.576931	−	0.277835i
$915$	12.9263	−	3.98725i	0.427332	−	0.131814i
$916$	−9.41130	−	23.9796i	−0.310958	−	0.792308i
$917$	22.0399	+	20.4500i	0.727820	+	0.675319i
$918$	−24.5124	+	16.7123i	−0.809029	+	0.551587i
$919$	28.1554	+	35.3057i	0.928760	+	1.16463i	0.986080	+	0.166272i	$0.0531729\pi$
$919$	28.1554	+	35.3057i	0.928760	+	1.16463i	−0.0573203	+	0.998356i	$0.518256\pi$
$920$	6.27719	−	0.946135i	0.206953	−	0.0311931i
$921$	32.8373	+	10.1290i	1.08202	+	0.333760i
$922$	1.20756	+	16.1138i	0.0397690	+	0.530680i
$923$	17.2175	+	11.7387i	0.566722	+	0.386385i
$924$	1.42342	+	6.23640i	0.0468270	+	0.205163i
$925$	0.982866	+	4.30622i	0.0323164	+	0.141588i
$926$	4.68589	+	3.19478i	0.153988	+	0.104987i
$927$	1.60322	+	21.3935i	0.0526568	+	0.702656i
$928$	−2.78583	−	0.859316i	−0.0914495	−	0.0282084i
$929$	11.2889	−	1.70153i	0.370378	−	0.0558255i	0.0387837	−	0.999248i	$-0.487652\pi$
$929$	11.2889	−	1.70153i	0.370378	−	0.0558255i	0.331594	+	0.943422i	$0.392414\pi$
$930$	−3.81177	−	4.77981i	−0.124993	−	0.156736i
$931$	−15.0829	+	10.2834i	−0.494324	+	0.337024i
$932$	6.34156	+	5.88411i	0.207725	+	0.192740i
$933$	−1.03998	−	2.64983i	−0.0340474	−	0.0867514i
$934$	12.3036	−	3.79517i	0.402587	−	0.124182i
$935$	8.74466	−	4.21121i	0.285981	−	0.137721i
$936$	1.27039	−	3.23690i	0.0415239	−	0.105801i
$937$	3.19211	−	42.5958i	0.104282	−	1.39154i	−0.662224	−	0.749306i	$-0.730387\pi$
$937$	3.19211	−	42.5958i	0.104282	−	1.39154i	0.766506	−	0.642238i	$-0.221994\pi$
$938$	29.0372	−	36.4114i	0.948097	−	1.18888i
$939$	−16.0150	+	27.7388i	−0.522631	+	0.905223i
$940$	2.29513	+	3.97528i	0.0748588	+	0.129659i
$941$	−21.0472	−	3.17236i	−0.686120	−	0.103416i	−0.203275	−	0.979122i	$-0.565158\pi$
$941$	−21.0472	−	3.17236i	−0.686120	−	0.103416i	−0.482845	+	0.875706i	$0.660397\pi$
$942$	−5.11094	−	2.46130i	−0.166524	−	0.0801935i
$943$	6.40723	−	5.94504i	0.208648	−	0.193597i
$944$	3.36137	−	14.7271i	0.109403	−	0.479327i
$945$	−16.6413			−0.541342
$946$	−8.38946	−	8.07462i	−0.272765	−	0.262528i
$947$	50.8820			1.65344			0.826721	−	0.562612i	$-0.190203\pi$
$947$	50.8820			1.65344			0.826721	+	0.562612i	$0.190203\pi$
$948$	0.335147	−	1.46837i	0.0108851	−	0.0476906i
$949$	−5.76255	+	5.34686i	−0.187060	+	0.173567i
$950$	6.85181	+	3.29966i	0.222302	+	0.107055i
$951$	19.2730	+	2.90494i	0.624970	+	0.0941991i
$952$	−8.37933	−	14.5134i	−0.271576	−	0.470383i
$953$	−1.61682	+	2.80042i	−0.0523740	+	0.0907144i	−0.891024	−	0.453957i	$-0.850012\pi$
$953$	−1.61682	+	2.80042i	−0.0523740	+	0.0907144i	0.838650	+	0.544671i	$0.183345\pi$
$954$	−0.283387	+	0.355356i	−0.00917500	+	0.0115051i
$955$	−1.35215	+	18.0432i	−0.0437545	+	0.583864i
$956$	−5.06197	+	12.8977i	−0.163716	+	0.417141i
$957$	−5.48011	+	2.63908i	−0.177147	+	0.0853094i
$958$	23.6647	−	7.29960i	0.764573	−	0.235839i
$959$	−9.98091	−	25.4310i	−0.322301	−	0.821208i
$960$	−0.861302	−	0.799171i	−0.0277984	−	0.0257931i
$961$	−3.24376	+	2.21156i	−0.104637	+	0.0713406i
$962$	5.91308	+	7.41477i	0.190645	+	0.239062i
$963$	0.330658	−	0.0498386i	0.0106553	−	0.00160603i
$964$	21.9394	+	6.76742i	0.706622	+	0.217964i
$965$	−0.899446	−	12.0023i	−0.0289542	−	0.386367i
$966$	−18.8948	−	12.8823i	−0.607931	−	0.414481i
$967$	6.51368	+	28.5383i	0.209466	+	0.917730i	0.964923	+	0.262532i	$0.0845576\pi$
$967$	6.51368	+	28.5383i	0.209466	+	0.917730i	−0.755457	+	0.655198i	$0.772585\pi$
$968$	1.74610	+	7.65018i	0.0561219	+	0.245886i
$969$	−40.3541	−	27.5129i	−1.29636	−	0.883843i
$970$	−0.635989	−	8.48668i	−0.0204204	−	0.272491i
$971$	−27.7456	−	8.55840i	−0.890400	−	0.274652i	−0.184389	−	0.982853i	$-0.559031\pi$
$971$	−27.7456	−	8.55840i	−0.890400	−	0.274652i	−0.706011	+	0.708201i	$0.749507\pi$
$972$	−14.3366	+	2.16089i	−0.459845	+	0.0693105i
$973$	−12.0299	−	15.0850i	−0.385661	−	0.483604i
$974$	3.32880	−	2.26954i	0.106662	−	0.0727207i
$975$	1.84934	+	1.71594i	0.0592262	+	0.0549539i
$976$	4.20620	+	10.7172i	0.134637	+	0.343050i
$977$	−18.2785	+	5.63817i	−0.584781	+	0.180381i	−0.573008	−	0.819550i	$-0.694224\pi$
$977$	−18.2785	+	5.63817i	−0.584781	+	0.180381i	−0.0117726	+	0.999931i	$0.503747\pi$
$978$	−3.62481	+	1.74562i	−0.115909	+	0.0558186i
$979$	−5.87320	+	14.9647i	−0.187708	+	0.478273i
$980$	0.179383	−	2.39370i	0.00573017	−	0.0764638i
$981$	1.02793	−	1.28898i	0.0328192	−	0.0411539i
$982$	−17.7725	+	30.7829i	−0.567144	+	0.982322i
$983$	16.7381	+	28.9912i	0.533862	+	0.924675i	0.999218	+	0.0395518i	$0.0125930\pi$
$983$	16.7381	+	28.9912i	0.533862	+	0.924675i	−0.465356	+	0.885124i	$0.654074\pi$
$984$	−1.59969	−	0.241114i	−0.0509961	−	0.00768643i
$985$	−4.81402	−	2.31831i	−0.153387	−	0.0738675i
$986$	11.6813	−	10.8387i	0.372009	−	0.345174i
$987$	3.67961	−	16.1214i	0.117123	−	0.513151i
$988$	16.3289			0.519491
$989$	41.6203	+	0.760877i	1.32345	+	0.0241945i
$990$	2.87570			0.0913959
$991$	−11.8937	+	52.1096i	−0.377815	+	1.65532i	0.326328	+	0.945257i	$0.394189\pi$
$991$	−11.8937	+	52.1096i	−0.377815	+	1.65532i	−0.704143	+	0.710058i	$0.748668\pi$
$992$	3.81427	−	3.53913i	0.121103	−	0.112367i
$993$	−25.2081	−	12.1396i	−0.799953	−	0.385237i
$994$	29.4239	+	4.43494i	0.933269	+	0.140668i
$995$	1.31236	+	2.27308i	0.0416047	+	0.0720614i
$996$	−8.93139	+	15.4696i	−0.283002	+	0.490174i
$997$	−20.6396	+	25.8813i	−0.653664	+	0.819669i	−0.992637	−	0.121128i	$-0.961349\pi$
$997$	−20.6396	+	25.8813i	−0.653664	+	0.819669i	0.338973	+	0.940796i	$0.389920\pi$
$998$	−1.31773	+	17.5838i	−0.0417119	+	0.556606i
$999$	8.75863	−	22.3166i	0.277111	−	0.706067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.a.271.1	✓	36
43.10	even	21	inner	430.2.q.a.311.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.a.271.1	✓	36	1.1	even	1	trivial
430.2.q.a.311.1	yes	36	43.10	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.222521 + 0.974928i) q^{2} +(-0.861302 + 0.799171i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(-0.587477 - 1.01754i) q^{6} +(-1.53300 + 2.65524i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-0.121024 + 1.61496i) q^{9} +O(q^{10})\)	\(q+(-0.222521 + 0.974928i) q^{2} +(-0.861302 + 0.799171i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(-0.587477 - 1.01754i) q^{6} +(-1.53300 + 2.65524i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-0.121024 + 1.61496i) q^{9} +(0.365341 - 0.930874i) q^{10} +(1.59984 - 0.770444i) q^{11} +(1.12275 - 0.346324i) q^{12} +(-0.784440 - 1.99872i) q^{13} +(-2.24754 - 2.08542i) q^{14} +(0.970792 - 0.661875i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-5.40490 + 0.814658i) q^{17} +(-1.54754 - 0.477351i) q^{18} +(-0.568317 - 7.58367i) q^{19} +(0.826239 + 0.563320i) q^{20} +(-0.801613 - 3.51210i) q^{21} +(0.395129 + 1.73117i) q^{22} +(-5.24504 - 3.57601i) q^{23} +(0.0878044 + 1.17167i) q^{24} +(0.955573 + 0.294755i) q^{25} +(2.12316 - 0.320015i) q^{26} +(-3.38410 - 4.24353i) q^{27} +(2.53326 - 1.72714i) q^{28} +(2.13711 + 1.98294i) q^{29} +(0.429259 + 1.09373i) q^{30} +(-4.97211 + 1.53369i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(-0.762231 + 1.94213i) q^{33} +(0.408471 - 5.45067i) q^{34} +(1.91163 - 2.39710i) q^{35} +(0.809742 - 1.40251i) q^{36} +(2.20848 + 3.82520i) q^{37} +(7.51999 + 1.13346i) q^{38} +(2.27296 + 1.09460i) q^{39} +(-0.733052 + 0.680173i) q^{40} +(-0.306382 + 1.34235i) q^{41} +3.60242 q^{42} +(-5.48462 + 3.59429i) q^{43} -1.77569 q^{44} +(0.360369 - 1.57888i) q^{45} +(4.65348 - 4.31780i) q^{46} +(4.13568 + 1.99164i) q^{47} +(-1.16183 - 0.175118i) q^{48} +(-1.20020 - 2.07882i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(4.00420 - 5.02111i) q^{51} +(-0.160456 + 2.14114i) q^{52} +(0.102535 - 0.261255i) q^{53} +(4.89017 - 2.35498i) q^{54} +(-1.69680 + 0.523394i) q^{55} +(1.12014 + 2.85407i) q^{56} +(6.55014 + 6.07764i) q^{57} +(-2.40878 + 1.64228i) q^{58} +(-9.41834 - 11.8102i) q^{59} +(-1.16183 + 0.175118i) q^{60} +(11.0016 + 3.39354i) q^{61} +(-0.388841 - 5.18872i) q^{62} +(-4.10257 - 2.79708i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.477784 + 2.09331i) q^{65} +(-1.72383 - 1.17529i) q^{66} +(1.13513 + 15.1473i) q^{67} +(5.22312 + 1.61112i) q^{68} +(7.37541 - 1.11166i) q^{69} +(1.91163 + 2.39710i) q^{70} +(-8.01881 + 5.46714i) q^{71} +(1.18717 + 1.10153i) q^{72} +(-1.33757 - 3.40808i) q^{73} +(-4.22073 + 1.30192i) q^{74} +(-1.05860 + 0.509793i) q^{75} +(-2.77839 + 7.07923i) q^{76} +(-0.406852 + 5.42906i) q^{77} +(-1.57294 + 1.97240i) q^{78} +(0.640935 - 1.11013i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(1.50185 + 0.226368i) q^{81} +(-1.24051 - 0.597400i) q^{82} +(-11.1446 + 10.3406i) q^{83} +(-0.801613 + 3.51210i) q^{84} +5.46595 q^{85} +(-2.28373 - 6.14692i) q^{86} -3.42541 q^{87} +(0.395129 - 1.73117i) q^{88} +(-6.63657 + 6.15784i) q^{89} +(1.45911 + 0.702668i) q^{90} +(6.50963 + 0.981169i) q^{91} +(3.17405 + 5.49761i) q^{92} +(3.05680 - 5.29454i) q^{93} +(-2.86198 + 3.58881i) q^{94} +(-0.568317 + 7.58367i) q^{95} +(0.429259 - 1.09373i) q^{96} +(7.66768 - 3.69256i) q^{97} +(2.29377 - 0.707533i) q^{98} +(1.05061 + 2.67692i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Introduction

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