LMFDB - Embedded newform 927.2.u.b.100.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [927,2,Mod(64,927)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(927, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([0, 20]))

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

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

chi := DirichletCharacter("927.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 927 = 3^{2} \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	927.u (of order $17$, degree $16$, 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:	$7.40213226737$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$8$ over $\Q(\zeta_{17})$
Twist minimal:	no (minimal twist has level 309)
Sato-Tate group:	$\mathrm{SU}(2)[C_{17}]$

Embedding invariants

Embedding label			100.3
Character	$\chi$	$=$	927.100
Dual form			927.2.u.b.343.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18369 + 0.732910i) q^{2} +(-0.0275108 + 0.0552492i) q^{4} +(2.15782 - 0.835944i) q^{5} +(-0.227033 + 2.45008i) q^{7} +(-0.264844 - 2.85813i) q^{8} +O(q^{10})$	\(q+(-1.18369 + 0.732910i) q^{2} +(-0.0275108 + 0.0552492i) q^{4} +(2.15782 - 0.835944i) q^{5} +(-0.227033 + 2.45008i) q^{7} +(-0.264844 - 2.85813i) q^{8} +(-1.94152 + 2.57099i) q^{10} +(-0.646803 + 0.400483i) q^{11} +(-0.169251 + 1.82651i) q^{13} +(-1.52695 - 3.06653i) q^{14} +(2.33385 + 3.09052i) q^{16} +(-4.73881 + 4.32000i) q^{17} +(1.10565 - 3.88594i) q^{19} +(-0.0131782 + 0.142215i) q^{20} +(0.472096 - 0.948097i) q^{22} +(1.32107 + 0.817969i) q^{23} +(0.262338 - 0.239153i) q^{25} +(-1.13833 - 2.28607i) q^{26} +(-0.129119 - 0.0799470i) q^{28} +(-3.77465 + 1.46231i) q^{29} +(5.80435 + 7.68620i) q^{31} +(0.325445 + 0.126078i) q^{32} +(2.44312 - 8.58666i) q^{34} +(1.55823 + 5.47661i) q^{35} +(-1.84413 - 0.344727i) q^{37} +(1.53930 + 5.41009i) q^{38} +(-2.96072 - 5.94592i) q^{40} +(5.85985 + 2.27012i) q^{41} +(-0.0530217 + 0.00991147i) q^{43} +(-0.00433230 - 0.0467530i) q^{44} -2.16323 q^{46} -6.18940 q^{47} +(0.929485 + 0.173751i) q^{49} +(-0.135250 + 0.475353i) q^{50} +(-0.0962569 - 0.0595997i) q^{52} +(-1.57530 + 5.53659i) q^{53} +(-1.06090 + 1.40486i) q^{55} +7.06275 q^{56} +(3.39627 - 4.49739i) q^{58} +(-0.0292170 - 0.315301i) q^{59} +(-1.10277 + 1.00531i) q^{61} +(-12.5038 - 4.84402i) q^{62} +(-8.09125 + 1.51252i) q^{64} +(1.16165 + 4.08276i) q^{65} +(0.265393 + 2.86404i) q^{67} +(-0.108308 - 0.380662i) q^{68} +(-5.85832 - 5.34057i) q^{70} +(-10.6673 - 4.13253i) q^{71} +(5.13108 + 1.98779i) q^{73} +(2.43553 - 0.943528i) q^{74} +(0.184278 + 0.167992i) q^{76} +(-0.834369 - 1.67564i) q^{77} +(-8.01143 + 3.10365i) q^{79} +(7.61954 + 4.71782i) q^{80} +(-8.60004 + 1.60763i) q^{82} +(-1.11119 + 11.9916i) q^{83} +(-6.61422 + 13.2831i) q^{85} +(0.0554970 - 0.0505922i) q^{86} +(1.31593 + 1.74258i) q^{88} +(1.77818 + 3.57106i) q^{89} +(-4.43666 - 0.829356i) q^{91} +(-0.0815357 + 0.0504848i) q^{92} +(7.32633 - 4.53627i) q^{94} +(-0.862645 - 9.30942i) q^{95} +(-10.0723 - 9.18211i) q^{97} +(-1.22757 + 0.475562i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - q^{2} - 3 q^{4} - 4 q^{5} + 4 q^{7} + 48 q^{8}+O(q^{10}) $ 128 * q - q^2 - 3 * q^4 - 4 * q^5 + 4 * q^7 + 48 * q^8	$ 128 q - q^{2} - 3 q^{4} - 4 q^{5} + 4 q^{7} + 48 q^{8} + 28 q^{10} + 13 q^{11} + 2 q^{13} + 51 q^{14} + 7 q^{16} - 6 q^{17} + 21 q^{19} + 43 q^{20} - 36 q^{22} - 15 q^{23} + 30 q^{25} - 7 q^{26} + 46 q^{28} - 16 q^{29} - 28 q^{31} + 8 q^{32} + 65 q^{34} + 37 q^{35} + 2 q^{37} - 30 q^{38} - 44 q^{40} + 84 q^{41} - 6 q^{43} + 62 q^{44} + 20 q^{47} - 56 q^{49} - 36 q^{50} - 86 q^{52} - 16 q^{53} + 8 q^{55} + 10 q^{56} + 32 q^{58} + 64 q^{59} + 4 q^{61} - 2 q^{62} - 58 q^{64} + 38 q^{65} - 8 q^{67} + 7 q^{68} - 140 q^{70} - 19 q^{71} + 60 q^{73} + 139 q^{74} - 76 q^{76} + 21 q^{77} + 12 q^{79} + 48 q^{80} + 207 q^{82} + 40 q^{83} - 85 q^{85} - 224 q^{86} + 87 q^{88} - 5 q^{89} - 48 q^{91} - 82 q^{92} - 214 q^{94} - 129 q^{95} - 61 q^{97} - 93 q^{98}+O(q^{100}) $ 128 * q - q^2 - 3 * q^4 - 4 * q^5 + 4 * q^7 + 48 * q^8 + 28 * q^10 + 13 * q^11 + 2 * q^13 + 51 * q^14 + 7 * q^16 - 6 * q^17 + 21 * q^19 + 43 * q^20 - 36 * q^22 - 15 * q^23 + 30 * q^25 - 7 * q^26 + 46 * q^28 - 16 * q^29 - 28 * q^31 + 8 * q^32 + 65 * q^34 + 37 * q^35 + 2 * q^37 - 30 * q^38 - 44 * q^40 + 84 * q^41 - 6 * q^43 + 62 * q^44 + 20 * q^47 - 56 * q^49 - 36 * q^50 - 86 * q^52 - 16 * q^53 + 8 * q^55 + 10 * q^56 + 32 * q^58 + 64 * q^59 + 4 * q^61 - 2 * q^62 - 58 * q^64 + 38 * q^65 - 8 * q^67 + 7 * q^68 - 140 * q^70 - 19 * q^71 + 60 * q^73 + 139 * q^74 - 76 * q^76 + 21 * q^77 + 12 * q^79 + 48 * q^80 + 207 * q^82 + 40 * q^83 - 85 * q^85 - 224 * q^86 + 87 * q^88 - 5 * q^89 - 48 * q^91 - 82 * q^92 - 214 * q^94 - 129 * q^95 - 61 * q^97 - 93 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/927\mathbb{Z}\right)^\times$.

$n$	$722$	$829$
$\chi(n)$	$1$	$e\left(\frac{15}{17}\right)$

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 $

$2$	−1.18369	+	0.732910i	−0.836996	+	0.518246i	−0.876740	−	0.480964i	$-0.840287\pi$
$2$	−1.18369	+	0.732910i	−0.836996	+	0.518246i	0.0397447	+	0.999210i	$0.487346\pi$
$3$		0			0
$3$		0			0
$4$	−0.0275108	+	0.0552492i	−0.0137554	+	0.0276246i
$5$	2.15782	−	0.835944i	0.965006	−	0.373845i	0.173383	−	0.984855i	$-0.444530\pi$
$5$	2.15782	−	0.835944i	0.965006	−	0.373845i	0.791624	+	0.611009i	$0.209236\pi$
$6$		0			0
$7$	−0.227033	+	2.45008i	−0.0858104	+	0.926042i	0.838627	+	0.544707i	$0.183359\pi$
$7$	−0.227033	+	2.45008i	−0.0858104	+	0.926042i	−0.924437	+	0.381335i	$0.875465\pi$
$8$	−0.264844	−	2.85813i	−0.0936366	−	1.01050i
$9$		0			0
$10$	−1.94152	+	2.57099i	−0.613962	+	0.813017i
$11$	−0.646803	+	0.400483i	−0.195018	+	0.120750i	−0.620468	−	0.784232i	$-0.713057\pi$
$11$	−0.646803	+	0.400483i	−0.195018	+	0.120750i	0.425449	+	0.904982i	$0.360116\pi$
$12$		0			0
$13$	−0.169251	+	1.82651i	−0.0469418	+	0.506583i	0.939509	+	0.342525i	$0.111282\pi$
$13$	−0.169251	+	1.82651i	−0.0469418	+	0.506583i	−0.986451	+	0.164058i	$0.947542\pi$
$14$	−1.52695	−	3.06653i	−0.408094	−	0.819564i
$15$		0			0
$16$	2.33385	+	3.09052i	0.583464	+	0.772631i
$17$	−4.73881	+	4.32000i	−1.14933	+	1.04775i	−0.151086	+	0.988521i	$0.548277\pi$
$17$	−4.73881	+	4.32000i	−1.14933	+	1.04775i	−0.998244	+	0.0592324i	$0.981135\pi$
$18$		0			0
$19$	1.10565	−	3.88594i	0.253653	−	0.891497i	−0.725475	−	0.688249i	$-0.758380\pi$
$19$	1.10565	−	3.88594i	0.253653	−	0.891497i	0.979127	−	0.203248i	$-0.0651497\pi$
$20$	−0.0131782	+	0.142215i	−0.00294673	+	0.0318003i
$21$		0			0
$22$	0.472096	−	0.948097i	0.100651	−	0.202135i
$23$	1.32107	+	0.817969i	0.275461	+	0.170558i	0.657209	−	0.753708i	$-0.271737\pi$
$23$	1.32107	+	0.817969i	0.275461	+	0.170558i	−0.381748	+	0.924266i	$0.624678\pi$
$24$		0			0
$25$	0.262338	−	0.239153i	0.0524676	−	0.0478305i
$26$	−1.13833	−	2.28607i	−0.223244	−	0.448335i
$27$		0			0
$28$	−0.129119	−	0.0799470i	−0.0244012	−	0.0151086i
$29$	−3.77465	+	1.46231i	−0.700934	+	0.271543i	−0.685223	−	0.728333i	$-0.740295\pi$
$29$	−3.77465	+	1.46231i	−0.700934	+	0.271543i	−0.0157112	+	0.999877i	$0.505001\pi$
$30$		0			0
$31$	5.80435	+	7.68620i	1.04249	+	1.38048i	0.921744	+	0.387799i	$0.126765\pi$
$31$	5.80435	+	7.68620i	1.04249	+	1.38048i	0.120748	+	0.992683i	$0.461471\pi$
$32$	0.325445	+	0.126078i	0.0575311	+	0.0222877i
$33$		0			0
$34$	2.44312	−	8.58666i	0.418991	−	1.47260i
$35$	1.55823	+	5.47661i	0.263389	+	0.925716i
$36$		0			0
$37$	−1.84413	−	0.344727i	−0.303172	−	0.0566727i	0.0299653	−	0.999551i	$-0.490460\pi$
$37$	−1.84413	−	0.344727i	−0.303172	−	0.0566727i	−0.333138	+	0.942878i	$0.608107\pi$
$38$	1.53930	+	5.41009i	0.249708	+	0.877633i
$39$		0			0
$40$	−2.96072	−	5.94592i	−0.468131	−	0.940133i
$41$	5.85985	+	2.27012i	0.915155	+	0.354533i	0.772335	−	0.635216i	$-0.219089\pi$
$41$	5.85985	+	2.27012i	0.915155	+	0.354533i	0.142820	+	0.989749i	$0.454383\pi$
$42$		0			0
$43$	−0.0530217	+	0.00991147i	−0.00808573	+	0.00151148i	−0.187791	−	0.982209i	$-0.560133\pi$
$43$	−0.0530217	+	0.00991147i	−0.00808573	+	0.00151148i	0.179705	+	0.983721i	$0.442486\pi$
$44$	−0.00433230	−	0.0467530i	−0.000653119	−	0.00704827i
$45$		0			0
$46$	−2.16323			−0.318951
$47$	−6.18940			−0.902817			−0.451408	−	0.892318i	$-0.649078\pi$
$47$	−6.18940			−0.902817			−0.451408	+	0.892318i	$0.649078\pi$
$48$		0			0
$49$	0.929485	+	0.173751i	0.132784	+	0.0248215i
$50$	−0.135250	+	0.475353i	−0.0191272	+	0.0672251i
$51$		0			0
$52$	−0.0962569	−	0.0595997i	−0.0133484	−	0.00826500i
$53$	−1.57530	+	5.53659i	−0.216383	+	0.760509i	0.775276	+	0.631623i	$0.217611\pi$
$53$	−1.57530	+	5.53659i	−0.216383	+	0.760509i	−0.991659	+	0.128886i	$0.958860\pi$
$54$		0			0
$55$	−1.06090	+	1.40486i	−0.143052	+	0.189432i
$56$	7.06275			0.943800
$57$		0			0
$58$	3.39627	−	4.49739i	0.445953	−	0.590537i
$59$	−0.0292170	−	0.315301i	−0.00380372	−	0.0410487i	0.993621	−	0.112773i	$-0.0359733\pi$
$59$	−0.0292170	−	0.315301i	−0.00380372	−	0.0410487i	−0.997424	+	0.0717244i	$0.977150\pi$
$60$		0			0
$61$	−1.10277	+	1.00531i	−0.141195	+	0.128716i	−0.741212	−	0.671271i	$-0.765749\pi$
$61$	−1.10277	+	1.00531i	−0.141195	+	0.128716i	0.600017	+	0.799987i	$0.295160\pi$
$62$	−12.5038	−	4.84402i	−1.58799	−	0.615191i
$63$		0			0
$64$	−8.09125	+	1.51252i	−1.01141	+	0.189065i
$65$	1.16165	+	4.08276i	0.144084	+	0.506404i
$66$		0			0
$67$	0.265393	+	2.86404i	0.0324229	+	0.349898i	0.996456	+	0.0841162i	$0.0268067\pi$
$67$	0.265393	+	2.86404i	0.0324229	+	0.349898i	−0.964033	+	0.265782i	$0.914370\pi$
$68$	−0.108308	−	0.380662i	−0.0131342	−	0.0461620i
$69$		0			0
$70$	−5.85832	−	5.34057i	−0.700203	−	0.638320i
$71$	−10.6673	−	4.13253i	−1.26597	−	0.490441i	−0.367727	−	0.929934i	$-0.619864\pi$
$71$	−10.6673	−	4.13253i	−1.26597	−	0.490441i	−0.898246	+	0.439493i	$0.855158\pi$
$72$		0			0
$73$	5.13108	+	1.98779i	0.600548	+	0.232653i	0.642273	−	0.766476i	$-0.277991\pi$
$73$	5.13108	+	1.98779i	0.600548	+	0.232653i	−0.0417257	+	0.999129i	$0.513286\pi$
$74$	2.43553	−	0.943528i	0.283124	−	0.109683i
$75$		0			0
$76$	0.184278	+	0.167992i	0.0211381	+	0.0192700i
$77$	−0.834369	−	1.67564i	−0.0950852	−	0.190957i
$78$		0			0
$79$	−8.01143	+	3.10365i	−0.901357	+	0.349187i	−0.766926	−	0.641735i	$-0.778215\pi$
$79$	−8.01143	+	3.10365i	−0.901357	+	0.349187i	−0.134431	+	0.990923i	$0.542921\pi$
$80$	7.61954	+	4.71782i	0.851890	+	0.527468i
$81$		0			0
$82$	−8.60004	+	1.60763i	−0.949716	+	0.177533i
$83$	−1.11119	+	11.9916i	−0.121969	+	1.31625i	0.686248	+	0.727368i	$0.259257\pi$
$83$	−1.11119	+	11.9916i	−0.121969	+	1.31625i	−0.808216	+	0.588886i	$0.799567\pi$
$84$		0			0
$85$	−6.61422	+	13.2831i	−0.717413	+	1.44076i
$86$	0.0554970	−	0.0505922i	0.00598440	−	0.00545550i
$87$		0			0
$88$	1.31593	+	1.74258i	0.140279	+	0.185759i
$89$	1.77818	+	3.57106i	0.188486	+	0.378531i	0.969169	−	0.246396i	$-0.0792463\pi$
$89$	1.77818	+	3.57106i	0.188486	+	0.378531i	−0.780683	+	0.624927i	$0.785129\pi$
$90$		0			0
$91$	−4.43666	−	0.829356i	−0.465089	−	0.0869401i
$92$	−0.0815357	+	0.0504848i	−0.00850069	+	0.00526340i
$93$		0			0
$94$	7.32633	−	4.53627i	0.755653	−	0.467881i
$95$	−0.862645	−	9.30942i	−0.0885055	−	0.955127i
$96$		0			0
$97$	−10.0723	−	9.18211i	−1.02269	−	0.932302i	−0.0249593	−	0.999688i	$-0.507946\pi$
$97$	−10.0723	−	9.18211i	−1.02269	−	0.932302i	−0.997727	+	0.0673868i	$0.978534\pi$
$98$	−1.22757	+	0.475562i	−0.124003	+	0.0480390i
$99$		0			0
$100$	0.00599585	+	0.0210732i	0.000599585	+	0.00210732i
$101$	1.14856	−	0.711156i	0.114286	−	0.0707627i	−0.468099	−	0.883676i	$-0.655061\pi$
$101$	1.14856	−	0.711156i	0.114286	−	0.0707627i	0.582385	+	0.812913i	$0.302120\pi$
$102$		0			0
$103$	−6.52728	−	7.77140i	−0.643152	−	0.765739i
$103$	−6.52728	−	7.77140i	−0.643152	−	0.765739i
$104$	5.26522			0.516297
$105$		0			0
$106$	−2.19316	−	7.70816i	−0.213018	−	0.748682i
$107$	−8.44421	+	16.9583i	−0.816332	+	1.63942i	−0.0484497	+	0.998826i	$0.515428\pi$
$107$	−8.44421	+	16.9583i	−0.816332	+	1.63942i	−0.767883	+	0.640591i	$0.778690\pi$
$108$		0			0
$109$	9.64453	+	8.79215i	0.923778	+	0.842135i	0.987786	−	0.155814i	$-0.0498002\pi$
$109$	9.64453	+	8.79215i	0.923778	+	0.842135i	−0.0640083	+	0.997949i	$0.520388\pi$
$110$	0.226143	−	2.44047i	0.0215619	−	0.232689i
$111$		0			0
$112$	−8.10188	+	5.01647i	−0.765555	+	0.474012i
$113$	7.82006	−	10.3554i	0.735650	−	0.974158i	−0.264303	−	0.964440i	$-0.585142\pi$
$113$	7.82006	−	10.3554i	0.735650	−	0.974158i	0.999953	−	0.00971790i	$-0.00309335\pi$
$114$		0			0
$115$	3.53440	+	0.660693i	0.329584	+	0.0616100i
$116$	0.0230524	−	0.248775i	0.00214036	−	0.0230982i
$117$		0			0
$118$	0.265671	+	0.351806i	0.0244570	+	0.0323863i
$119$	−9.50845	−	12.5912i	−0.871638	−	1.15424i
$120$		0			0
$121$	−4.64515	+	9.32873i	−0.422287	+	0.848066i
$122$	0.568538	−	1.99820i	0.0514730	−	0.180909i
$123$		0			0
$124$	−0.584338	+	0.109232i	−0.0524751	+	0.00980930i
$125$	−4.79122	+	9.62207i	−0.428540	+	0.860624i
$126$		0			0
$127$	−7.28392	+	2.82181i	−0.646343	+	0.250395i	−0.662024	−	0.749482i	$-0.730302\pi$
$127$	−7.28392	+	2.82181i	−0.646343	+	0.250395i	0.0156811	+	0.999877i	$0.495008\pi$
$128$	7.95315	−	7.25025i	0.702966	−	0.640838i
$129$		0			0
$130$	−4.36733	−	3.98134i	−0.383040	−	0.349187i
$131$	−12.7988	−	7.92470i	−1.11824	−	0.692384i	−0.162532	−	0.986703i	$-0.551966\pi$
$131$	−12.7988	−	7.92470i	−1.11824	−	0.692384i	−0.955707	+	0.294319i	$0.904907\pi$
$132$		0			0
$133$	9.26984	+	3.59115i	0.803797	+	0.311393i
$134$	−2.41323	−	3.19563i	−0.208471	−	0.276060i
$135$		0			0
$136$	13.6021	+	12.4000i	1.16637	+	1.06329i
$137$	1.90777	−	6.70512i	0.162992	−	0.572857i	−0.836691	−	0.547675i	$-0.815513\pi$
$137$	1.90777	−	6.70512i	0.162992	−	0.572857i	0.999683	−	0.0251820i	$-0.00801654\pi$
$138$		0			0
$139$	−1.36804	−	14.7635i	−0.116036	−	1.25222i	−0.832273	−	0.554367i	$-0.812961\pi$
$139$	−1.36804	−	14.7635i	−0.116036	−	1.25222i	0.716237	−	0.697857i	$-0.245863\pi$
$140$	−0.345446	−	0.0645751i	−0.0291955	−	0.00545759i
$141$		0			0
$142$	15.6555	−	2.92653i	1.31378	−	0.245589i
$143$	−0.622015	−	1.24917i	−0.0520155	−	0.104461i
$144$		0			0
$145$	−6.92260	+	6.31078i	−0.574891	+	0.524082i
$146$	−7.53048	+	1.40769i	−0.623227	+	0.116501i
$147$		0			0
$148$	0.0697793	−	0.0924027i	0.00573582	−	0.00759545i
$149$	23.0601			1.88915			0.944577	−	0.328290i	$-0.106472\pi$
$149$	23.0601			1.88915			0.944577	+	0.328290i	$0.106472\pi$
$150$		0			0
$151$	7.97411	−	10.5594i	0.648924	−	0.859314i	−0.348016	−	0.937489i	$-0.613144\pi$
$151$	7.97411	−	10.5594i	0.648924	−	0.859314i	0.996940	+	0.0781743i	$0.0249091\pi$
$152$	−11.3993	−	2.13091i	−0.924609	−	0.172839i
$153$		0			0
$154$	2.21573	+	1.37192i	0.178548	+	0.110553i
$155$	18.9500	+	11.7333i	1.52210	+	0.942443i
$156$		0			0
$157$	21.2049	+	3.96388i	1.69233	+	0.316352i	0.939677	−	0.342062i	$-0.111125\pi$
$157$	21.2049	+	3.96388i	1.69233	+	0.316352i	0.752656	+	0.658414i	$0.228772\pi$
$158$	7.20837	−	9.54542i	0.573467	−	0.759393i
$159$		0			0
$160$	0.807646			0.0638500
$161$	−2.30401	+	3.05101i	−0.181582	+	0.240453i
$162$		0			0
$163$	−0.659864	+	0.123350i	−0.0516845	+	0.00966151i	−0.209528	−	0.977803i	$-0.567193\pi$
$163$	−0.659864	+	0.123350i	−0.0516845	+	0.00966151i	0.157844	+	0.987464i	$0.449546\pi$
$164$	−0.286631	+	0.261299i	−0.0223822	+	0.0204040i
$165$		0			0
$166$	−7.47349	−	15.0088i	−0.580055	−	1.16491i
$167$	−7.44706	+	1.39210i	−0.576271	+	0.107724i	−0.463814	−	0.885933i	$-0.653519\pi$
$167$	−7.44706	+	1.39210i	−0.576271	+	0.107724i	−0.112457	+	0.993657i	$0.535872\pi$
$168$		0			0
$169$	9.47116	+	1.77047i	0.728551	+	0.136190i
$170$	−1.90616	−	20.5708i	−0.146196	−	1.57771i
$171$		0			0
$172$	0.000911069	−	0.00320208i	6.94684e−5	−	0.000244156i
$173$	2.15103	+	1.96092i	0.163540	+	0.149086i	0.751329	−	0.659928i	$-0.229413\pi$
$173$	2.15103	+	1.96092i	0.163540	+	0.149086i	−0.587789	+	0.809014i	$0.700001\pi$
$174$		0			0
$175$	0.526383	+	0.697044i	0.0397908	+	0.0526915i
$176$	−2.74725	−	1.06429i	−0.207082	−	0.0802238i
$177$		0			0
$178$	−4.72207	−	2.92378i	−0.353934	−	0.219147i
$179$	9.36829	+	8.54033i	0.700219	+	0.638334i	0.943404	−	0.331646i	$-0.107604\pi$
$179$	9.36829	+	8.54033i	0.700219	+	0.638334i	−0.243185	+	0.969980i	$0.578192\pi$
$180$		0			0
$181$	7.80697	−	7.11699i	0.580287	−	0.529002i	−0.329457	−	0.944171i	$-0.606866\pi$
$181$	7.80697	−	7.11699i	0.580287	−	0.529002i	0.909744	+	0.415169i	$0.136277\pi$
$182$	5.85948	−	2.26997i	0.434333	−	0.168262i
$183$		0			0
$184$	1.98798	−	3.99241i	0.146556	−	0.294324i
$185$	−4.26746	+	0.797727i	−0.313750	+	0.0586500i
$186$		0			0
$187$	1.33499	−	4.69200i	0.0976241	−	0.343113i
$188$	0.170275	−	0.341959i	0.0124186	−	0.0249399i
$189$		0			0
$190$	7.84408	+	10.3872i	0.569069	+	0.753569i
$191$	−8.31563	−	11.0117i	−0.601698	−	0.796777i	0.390612	−	0.920556i	$-0.372264\pi$
$191$	−8.31563	−	11.0117i	−0.601698	−	0.796777i	−0.992310	+	0.123778i	$0.960499\pi$
$192$		0			0
$193$	−2.09640	+	22.6237i	−0.150902	+	1.62849i	0.497690	+	0.867355i	$0.334182\pi$
$193$	−2.09640	+	22.6237i	−0.150902	+	1.62849i	−0.648592	+	0.761137i	$0.724642\pi$
$194$	18.6521	+	3.48669i	1.33915	+	0.250330i
$195$		0			0
$196$	−0.0351705	+	0.0465732i	−0.00251218	+	0.00332666i
$197$	19.1686	−	11.8687i	1.36570	−	0.845607i	0.369215	−	0.929344i	$-0.379627\pi$
$197$	19.1686	−	11.8687i	1.36570	−	0.845607i	0.996488	+	0.0837366i	$0.0266854\pi$
$198$		0			0
$199$	1.33201	−	14.3747i	0.0944235	−	1.01899i	−0.808300	−	0.588771i	$-0.799612\pi$
$199$	1.33201	−	14.3747i	0.0944235	−	1.01899i	0.902724	−	0.430221i	$-0.141564\pi$
$200$	−0.753007	−	0.686457i	−0.0532457	−	0.0485398i
$201$		0			0
$202$	−0.838322	+	1.68358i	−0.0589841	+	0.118456i
$203$	−2.72579	−	9.58016i	−0.191313	−	0.672396i
$204$		0			0
$205$	14.5422			1.01567
$206$	13.4220	+	4.41503i	0.935156	+	0.307610i
$207$		0			0
$208$	−6.03988	+	3.73973i	−0.418790	+	0.259304i
$209$	0.841121	+	2.95623i	0.0581816	+	0.204487i
$210$		0			0
$211$	1.81919	−	0.704756i	0.125238	−	0.0485174i	−0.297807	−	0.954626i	$-0.596255\pi$
$211$	1.81919	−	0.704756i	0.125238	−	0.0485174i	0.423045	+	0.906109i	$0.360961\pi$
$212$	−0.262554	−	0.239350i	−0.0180323	−	0.0164386i
$213$		0			0
$214$	−2.43355	−	26.2622i	−0.166354	−	1.79524i
$215$	−0.106126	+	0.0657103i	−0.00723772	+	0.00448140i
$216$		0			0
$217$	−20.1495	+	12.4761i	−1.36784	+	0.846931i
$218$	−17.8600	−	3.33861i	−1.20963	−	0.226119i
$219$		0			0
$220$	−0.0484312	−	0.0972629i	−0.00326523	−	0.00655746i
$221$	−7.08847	−	9.38665i	−0.476822	−	0.631414i
$222$		0			0
$223$	17.1241	−	15.6107i	1.14672	−	1.04537i	0.148311	−	0.988941i	$-0.452616\pi$
$223$	17.1241	−	15.6107i	1.14672	−	1.04537i	0.998407	−	0.0564306i	$-0.0179720\pi$
$224$	−0.382788	+	0.768741i	−0.0255761	+	0.0513637i
$225$		0			0
$226$	−1.66693	+	17.9890i	−0.110883	+	1.19661i
$227$	10.3760	−	1.93961i	0.688678	−	0.128736i	0.172233	−	0.985056i	$-0.444902\pi$
$227$	10.3760	−	1.93961i	0.688678	−	0.128736i	0.516445	+	0.856320i	$0.327255\pi$
$228$		0			0
$229$	−7.08350	−	4.38591i	−0.468091	−	0.289829i	0.272048	−	0.962284i	$-0.412299\pi$
$229$	−7.08350	−	4.38591i	−0.468091	−	0.289829i	−0.740139	+	0.672454i	$0.765240\pi$
$230$	−4.66786	+	1.80834i	−0.307790	+	0.119238i
$231$		0			0
$232$	5.17915	+	10.4011i	0.340028	+	0.682868i
$233$	12.6708	+	11.5510i	0.830093	+	0.756730i	0.972456	−	0.233085i	$-0.0748819\pi$
$233$	12.6708	+	11.5510i	0.830093	+	0.756730i	−0.142363	+	0.989814i	$0.545470\pi$
$234$		0			0
$235$	−13.3556	+	5.17399i	−0.871224	+	0.337514i
$236$	0.0182239	+	0.00705998i	0.00118628	+	0.000459566i
$237$		0			0
$238$	20.4833	+	7.93527i	1.32774	+	0.514367i
$239$	11.8152	+	10.7710i	0.764264	+	0.696719i	0.958770	−	0.284183i	$-0.0917222\pi$
$239$	11.8152	+	10.7710i	0.764264	+	0.696719i	−0.194506	+	0.980901i	$0.562310\pi$
$240$		0			0
$241$	4.84456	+	17.0269i	0.312065	+	1.09680i	0.946202	+	0.323575i	$0.104885\pi$
$241$	4.84456	+	17.0269i	0.312065	+	1.09680i	−0.634137	+	0.773221i	$0.718644\pi$
$242$	−1.33869	−	14.4468i	−0.0860545	−	0.928676i
$243$		0			0
$244$	−0.0252043	−	0.0885839i	−0.00161354	−	0.00567100i
$245$	2.15091	−	0.402074i	0.137416	−	0.0256876i
$246$		0			0
$247$	6.91058	+	2.67717i	0.439710	+	0.170345i
$248$	20.4309	−	18.6252i	1.29736	−	1.18270i
$249$		0			0
$250$	−1.38079	−	14.9011i	−0.0873288	−	0.942427i
$251$	4.85314	−	6.42660i	0.306328	−	0.405643i	−0.618649	−	0.785668i	$-0.712320\pi$
$251$	4.85314	−	6.42660i	0.306328	−	0.405643i	0.924977	+	0.380024i	$0.124084\pi$
$252$		0			0
$253$	−1.18205			−0.0743150
$254$	6.55378	−	8.67860i	0.411220	−	0.544544i
$255$		0			0
$256$	0.404979	−	1.42335i	0.0253112	−	0.0889596i
$257$	18.3968	+	11.3908i	1.14756	+	0.710539i	0.962257	−	0.272143i	$-0.0877323\pi$
$257$	18.3968	+	11.3908i	1.14756	+	0.710539i	0.185303	+	0.982682i	$0.440673\pi$
$258$		0			0
$259$	1.26328	−	4.43998i	0.0784966	−	0.275887i
$260$	−0.257527	−	0.0481401i	−0.0159711	−	0.00298553i
$261$		0			0
$262$	20.9579			1.29479
$263$	−3.29637			−0.203263			−0.101632	−	0.994822i	$-0.532406\pi$
$263$	−3.29637			−0.203263			−0.101632	+	0.994822i	$0.532406\pi$
$264$		0			0
$265$	1.22907	+	13.2638i	0.0755014	+	0.814790i
$266$	−13.6046	+	2.54314i	−0.834152	+	0.155930i
$267$		0			0
$268$	−0.165537	−	0.0641294i	−0.0101118	−	0.00391733i
$269$	−2.38235	−	4.78441i	−0.145255	−	0.291711i	0.810573	−	0.585637i	$-0.199156\pi$
$269$	−2.38235	−	4.78441i	−0.145255	−	0.291711i	−0.955828	+	0.293926i	$0.905038\pi$
$270$		0			0
$271$	−2.27140	−	7.98315i	−0.137978	−	0.484942i	0.861772	−	0.507295i	$-0.169355\pi$
$271$	−2.27140	−	7.98315i	−0.137978	−	0.484942i	−0.999750	+	0.0223535i	$0.992884\pi$
$272$	−24.4107	−	4.56316i	−1.48012	−	0.276682i
$273$		0			0
$274$	2.65604	+	9.33502i	0.160457	+	0.563949i
$275$	−0.0739043	+	0.259747i	−0.00445660	+	0.0156633i
$276$		0			0
$277$	−25.4312	−	9.85208i	−1.52801	−	0.591954i	−0.556899	−	0.830580i	$-0.688009\pi$
$277$	−25.4312	−	9.85208i	−1.52801	−	0.591954i	−0.971112	+	0.238626i	$0.923303\pi$
$278$	12.4397	+	16.4728i	0.746081	+	0.987971i
$279$		0			0
$280$	15.2401	−	5.90406i	0.910773	−	0.352835i
$281$	7.23626	+	4.48050i	0.431679	+	0.267284i	0.725026	−	0.688722i	$-0.241828\pi$
$281$	7.23626	+	4.48050i	0.431679	+	0.267284i	−0.293347	+	0.956006i	$0.594769\pi$
$282$		0			0
$283$	−4.96842	−	9.97794i	−0.295342	−	0.593127i	0.696940	−	0.717130i	$-0.254545\pi$
$283$	−4.96842	−	9.97794i	−0.295342	−	0.593127i	−0.992282	+	0.124003i	$0.960427\pi$
$284$	0.521784	−	0.475669i	0.0309622	−	0.0282258i
$285$		0			0
$286$	1.65181	+	1.02275i	0.0976733	+	0.0604768i
$287$	−6.89234	+	13.8417i	−0.406842	+	0.817049i
$288$		0			0
$289$	2.22539	−	24.0158i	0.130905	−	1.41269i
$290$	3.56898	−	12.5437i	0.209578	−	0.736589i
$291$		0			0
$292$	−0.250984	+	0.228802i	−0.0146877	+	0.0133896i
$293$	13.8317	+	18.3162i	0.808059	+	1.07004i	0.996130	+	0.0878877i	$0.0280117\pi$
$293$	13.8317	+	18.3162i	0.808059	+	1.07004i	−0.188071	+	0.982155i	$0.560224\pi$
$294$		0			0
$295$	−0.326619	−	0.655939i	−0.0190165	−	0.0381903i
$296$	−0.496866	+	5.36204i	−0.0288798	+	0.311662i
$297$		0			0
$298$	−27.2960	+	16.9010i	−1.58121	+	0.979046i
$299$	−1.71762	+	2.27450i	−0.0993326	+	0.131538i
$300$		0			0
$301$	−0.0122462	−	0.132157i	−0.000705858	−	0.00761742i
$302$	−1.69977	+	18.3434i	−0.0978106	+	1.05554i
$303$		0			0
$304$	14.5900	−	5.65220i	0.836795	−	0.324176i
$305$	−1.53920	+	3.09112i	−0.0881341	+	0.176997i
$306$		0			0
$307$	1.77605	−	1.09969i	0.101365	−	0.0627624i	−0.474814	−	0.880086i	$-0.657485\pi$
$307$	1.77605	−	1.09969i	0.101365	−	0.0627624i	0.576178	+	0.817324i	$0.304543\pi$
$308$	0.115532			0.00658304
$309$		0			0
$310$	−31.0304			−1.76241
$311$	−2.89057	+	1.78977i	−0.163909	+	0.101488i	−0.605935	−	0.795514i	$-0.707201\pi$
$311$	−2.89057	+	1.78977i	−0.163909	+	0.101488i	0.442026	+	0.897002i	$0.354260\pi$
$312$		0			0
$313$	9.55364	−	19.1863i	0.540004	−	1.08447i	−0.442246	−	0.896894i	$-0.645818\pi$
$313$	9.55364	−	19.1863i	0.540004	−	1.08447i	0.982249	−	0.187580i	$-0.0600643\pi$
$314$	−28.0052	+	10.8493i	−1.58042	+	0.612259i
$315$		0			0
$316$	0.0489272	−	0.528009i	0.00275237	−	0.0297028i
$317$	−0.820058	−	8.84984i	−0.0460590	−	0.497056i	−0.987250	−	0.159180i	$-0.949115\pi$
$317$	−0.820058	−	8.84984i	−0.0460590	−	0.497056i	0.941191	−	0.337876i	$-0.109709\pi$
$318$		0			0
$319$	1.85582	−	2.45751i	0.103906	−	0.137594i
$320$	−16.1951	+	10.0276i	−0.905332	+	0.560558i
$321$		0			0
$322$	0.491125	−	5.30008i	0.0273693	−	0.295362i
$323$	11.5478	+	23.1911i	0.642538	+	1.29039i
$324$		0			0
$325$	0.392414	+	0.519640i	0.0217672	+	0.0288244i
$326$	0.690670	−	0.629629i	0.0382527	−	0.0348719i
$327$		0			0
$328$	4.93634	−	17.3494i	0.272564	−	0.957961i
$329$	1.40520	−	15.1645i	0.0774710	−	0.836046i
$330$		0			0
$331$	10.5099	−	21.1067i	0.577677	−	1.16013i	−0.392954	−	0.919558i	$-0.628547\pi$
$331$	10.5099	−	21.1067i	0.577677	−	1.16013i	0.970631	−	0.240573i	$-0.0773355\pi$
$332$	−0.631958	−	0.391292i	−0.0346832	−	0.0214749i
$333$		0			0
$334$	7.79473	−	7.10584i	0.426509	−	0.388814i
$335$	2.96685	+	5.95823i	0.162096	+	0.325533i
$336$		0			0
$337$	−9.08580	−	5.62569i	−0.494935	−	0.306451i	0.256172	−	0.966631i	$-0.417539\pi$
$337$	−9.08580	−	5.62569i	−0.494935	−	0.306451i	−0.751107	+	0.660180i	$0.770480\pi$
$338$	−12.5085	+	4.84582i	−0.680373	+	0.263578i
$339$		0			0
$340$	−0.551920	−	0.730861i	−0.0299321	−	0.0396365i
$341$	−6.83247	−	2.64691i	−0.369999	−	0.143338i
$342$		0			0
$343$	−5.35030	+	18.8044i	−0.288889	+	1.01534i
$344$	0.0423707	+	0.148918i	0.00228448	+	0.00802910i
$345$		0			0
$346$	−3.98334	−	0.744615i	−0.214146	−	0.0400307i
$347$	1.81949	+	6.39486i	0.0976756	+	0.343294i	0.995223	−	0.0976229i	$-0.0311239\pi$
$347$	1.81949	+	6.39486i	0.0976756	+	0.343294i	−0.897548	+	0.440917i	$0.854653\pi$
$348$		0			0
$349$	−9.84419	−	19.7698i	−0.526947	−	1.05825i	−0.985514	−	0.169593i	$-0.945755\pi$
$349$	−9.84419	−	19.7698i	−0.526947	−	1.05825i	0.458567	−	0.888660i	$-0.348363\pi$
$350$	−1.13394	−	0.439293i	−0.0606119	−	0.0234812i
$351$		0			0
$352$	−0.260991	+	0.0487877i	−0.0139109	+	0.00260039i
$353$	−1.87240	−	20.2064i	−0.0996579	−	1.07548i	−0.887876	−	0.460083i	$-0.847820\pi$
$353$	−1.87240	−	20.2064i	−0.0996579	−	1.07548i	0.788218	−	0.615396i	$-0.211004\pi$
$354$		0			0
$355$	−26.4726			−1.40502
$356$	−0.246217			−0.0130495
$357$		0			0
$358$	−17.3485	−	3.24299i	−0.916894	−	0.171397i
$359$	9.16572	−	32.2142i	0.483748	−	1.70020i	−0.208058	−	0.978116i	$-0.566714\pi$
$359$	9.16572	−	32.2142i	0.483748	−	1.70020i	0.691807	−	0.722083i	$-0.256815\pi$
$360$		0			0
$361$	2.27602	+	1.40925i	0.119790	+	0.0741710i
$362$	−4.02492	+	14.1461i	−0.211545	+	0.743503i
$363$		0			0
$364$	0.167877	−	0.222306i	0.00879917	−	0.0116520i
$365$	12.7336			0.666509
$366$		0			0
$367$	−3.88080	+	5.13901i	−0.202576	+	0.268254i	−0.887953	−	0.459934i	$-0.847873\pi$
$367$	−3.88080	+	5.13901i	−0.202576	+	0.268254i	0.685377	+	0.728189i	$0.259638\pi$
$368$	0.555222	+	5.99180i	0.0289430	+	0.312344i
$369$		0			0
$370$	4.46669	−	4.07193i	0.232212	−	0.211689i
$371$	−13.2074	−	5.11658i	−0.685695	−	0.265640i
$372$		0			0
$373$	−3.88620	+	0.726457i	−0.201220	+	0.0376145i	−0.283394	−	0.959003i	$-0.591461\pi$
$373$	−3.88620	+	0.726457i	−0.201220	+	0.0376145i	0.0821746	+	0.996618i	$0.473813\pi$
$374$	1.85860	+	6.53231i	0.0961060	+	0.337777i
$375$		0			0
$376$	1.63923	+	17.6901i	0.0845367	+	0.912296i
$377$	−2.03205	−	7.14193i	−0.104656	−	0.367828i
$378$		0			0
$379$	10.0603	+	9.17118i	0.516763	+	0.471092i	0.889558	−	0.456822i	$-0.151012\pi$
$379$	10.0603	+	9.17118i	0.516763	+	0.471092i	−0.372795	+	0.927914i	$0.621601\pi$
$380$	0.538070	+	0.208449i	0.0276024	+	0.0106932i
$381$		0			0
$382$	17.9137	+	6.93981i	0.916545	+	0.355071i
$383$	−23.1089	+	8.95243i	−1.18081	+	0.457448i	−0.870013	−	0.493029i	$-0.835890\pi$
$383$	−23.1089	+	8.95243i	−1.18081	+	0.457448i	−0.310796	+	0.950477i	$0.600596\pi$
$384$		0			0
$385$	−3.20116	−	2.91824i	−0.163146	−	0.148727i
$386$	−14.0997	−	28.3160i	−0.717655	−	1.44124i
$387$		0			0
$388$	0.784401	−	0.303878i	0.0398219	−	0.0154271i
$389$	12.7667	+	7.90479i	0.647296	+	0.400789i	0.810447	−	0.585813i	$-0.199225\pi$
$389$	12.7667	+	7.90479i	0.647296	+	0.400789i	−0.163151	+	0.986601i	$0.552166\pi$
$390$		0			0
$391$	−9.79391	+	1.83080i	−0.495299	+	0.0925874i
$392$	0.250433	−	2.70260i	0.0126488	−	0.136502i
$393$		0			0
$394$	−13.9910	+	28.0977i	−0.704855	+	1.41554i
$395$	−14.6928	+	13.3942i	−0.739273	+	0.673936i
$396$		0			0
$397$	17.3292	+	22.9476i	0.869727	+	1.15171i	0.987336	+	0.158645i	$0.0507126\pi$
$397$	17.3292	+	22.9476i	0.869727	+	1.15171i	−0.117608	+	0.993060i	$0.537523\pi$
$398$	8.95864	+	17.9914i	0.449056	+	0.901826i
$399$		0			0
$400$	1.35137	+	0.252614i	0.0675683	+	0.0126307i
$401$	21.1188	−	13.0762i	1.05462	−	0.652994i	0.114357	−	0.993440i	$-0.463519\pi$
$401$	21.1188	−	13.0762i	1.05462	−	0.652994i	0.940264	+	0.340446i	$0.110578\pi$
$402$		0			0
$403$	−15.0213	+	9.30080i	−0.748265	+	0.463306i
$404$	0.00769305	+	0.0830213i	0.000382744	+	0.00413046i
$405$		0			0
$406$	10.2479	+	9.34219i	0.508594	+	0.463645i
$407$	1.33084	−	0.515571i	0.0659675	−	0.0255559i
$408$		0			0
$409$	−0.495356	−	1.74099i	−0.0244938	−	0.0860867i	0.948615	−	0.316432i	$-0.102485\pi$
$409$	−0.495356	−	1.74099i	−0.0244938	−	0.0860867i	−0.973109	+	0.230345i	$0.926014\pi$
$410$	−17.2135	+	10.6581i	−0.850112	+	0.526367i
$411$		0			0
$412$	0.608934	−	0.146829i	0.0300000	−	0.00723374i
$413$	0.779145			0.0383392
$414$		0			0
$415$	7.62659	+	26.8047i	0.374375	+	1.31579i
$416$	−0.285365	+	0.573090i	−0.0139912	+	0.0280980i
$417$		0			0
$418$	−3.16228	−	2.88280i	−0.154672	−	0.141002i
$419$	0.101667	−	1.09716i	0.00496677	−	0.0536000i	−0.992890	−	0.119035i	$-0.962020\pi$
$419$	0.101667	−	1.09716i	0.00496677	−	0.0536000i	0.997857	+	0.0654350i	$0.0208435\pi$
$420$		0			0
$421$	17.6073	−	10.9020i	0.858127	−	0.531329i	−0.0254178	−	0.999677i	$-0.508092\pi$
$421$	17.6073	−	10.9020i	0.858127	−	0.531329i	0.883544	+	0.468347i	$0.155150\pi$
$422$	−1.63683	+	2.16751i	−0.0796796	+	0.105513i
$423$		0			0
$424$	16.2415	+	3.03606i	0.788756	+	0.147444i
$425$	−0.210031	+	2.26660i	−0.0101880	+	0.109946i
$426$		0			0
$427$	−2.21271	−	2.93010i	−0.107081	−	0.141798i
$428$	−0.704622	−	0.933071i	−0.0340592	−	0.0451017i
$429$		0			0
$430$	0.0774603	−	0.155561i	0.00373547	−	0.00750183i
$431$	−8.63286	+	30.3413i	−0.415830	+	1.46149i	0.417480	+	0.908686i	$0.362913\pi$
$431$	−8.63286	+	30.3413i	−0.415830	+	1.46149i	−0.833311	+	0.552805i	$0.813557\pi$
$432$		0			0
$433$	−28.9578	+	5.41315i	−1.39162	+	0.260139i	−0.825602	−	0.564252i	$-0.809164\pi$
$433$	−28.9578	+	5.41315i	−1.39162	+	0.260139i	−0.566020	+	0.824392i	$0.691517\pi$
$434$	14.7070	−	29.5356i	0.705958	−	1.41775i
$435$		0			0
$436$	−0.751088	+	0.290973i	−0.0359706	+	0.0139351i
$437$	4.63922	−	4.22920i	0.221924	−	0.202310i
$438$		0			0
$439$	18.8614	+	17.1945i	0.900207	+	0.820647i	0.984426	−	0.175800i	$-0.0562513\pi$
$439$	18.8614	+	17.1945i	0.900207	+	0.820647i	−0.0842189	+	0.996447i	$0.526839\pi$
$440$	4.29625	+	2.66012i	0.204815	+	0.126816i
$441$		0			0
$442$	15.2701	+	5.91568i	0.726325	+	0.281380i
$443$	9.76122	+	12.9259i	0.463769	+	0.614130i	0.968460	−	0.249171i	$-0.0801580\pi$
$443$	9.76122	+	12.9259i	0.463769	+	0.614130i	−0.504690	+	0.863300i	$0.668393\pi$
$444$		0			0
$445$	6.82218	+	6.21924i	0.323403	+	0.294820i
$446$	−8.82843	+	31.0287i	−0.418038	+	1.46925i
$447$		0			0
$448$	−1.86880	−	20.1676i	−0.0882925	−	0.952828i
$449$	−25.6088	−	4.78711i	−1.20855	−	0.225918i	−0.459348	−	0.888256i	$-0.651917\pi$
$449$	−25.6088	−	4.78711i	−1.20855	−	0.225918i	−0.749205	+	0.662339i	$0.769564\pi$
$450$		0			0
$451$	−4.69931	+	0.878454i	−0.221282	+	0.0413648i
$452$	0.356993	+	0.716938i	0.0167915	+	0.0337219i
$453$		0			0
$454$	−10.8604	+	9.90055i	−0.509703	+	0.464656i
$455$	−10.2668	+	1.91920i	−0.481315	+	0.0899734i
$456$		0			0
$457$	−22.3698	+	29.6225i	−1.04642	+	1.38568i	−0.127224	+	0.991874i	$0.540607\pi$
$457$	−22.3698	+	29.6225i	−1.04642	+	1.38568i	−0.919193	+	0.393807i	$0.871158\pi$
$458$	11.5991			0.541993
$459$		0			0
$460$	−0.133737	+	0.177096i	−0.00623552	+	0.00825716i
$461$	2.48329	+	0.464207i	0.115658	+	0.0216203i	0.241260	−	0.970460i	$-0.422439\pi$
$461$	2.48329	+	0.464207i	0.115658	+	0.0216203i	−0.125602	+	0.992081i	$0.540086\pi$
$462$		0			0
$463$	8.53295	+	5.28338i	0.396560	+	0.245539i	0.710196	−	0.704004i	$-0.248606\pi$
$463$	8.53295	+	5.28338i	0.396560	+	0.245539i	−0.313637	+	0.949543i	$0.601547\pi$
$464$	−13.3288	−	8.25282i	−0.618772	−	0.383128i
$465$		0			0
$466$	−23.4642	−	4.38621i	−1.08696	−	0.203187i
$467$	7.61216	−	10.0801i	0.352249	−	0.466453i	−0.587051	−	0.809550i	$-0.699711\pi$
$467$	7.61216	−	10.0801i	0.352249	−	0.466453i	0.939300	+	0.343097i	$0.111476\pi$
$468$		0			0
$469$	−7.07737			−0.326803
$470$	12.0168	−	15.9129i	0.554295	−	0.734005i
$471$		0			0
$472$	−0.893433	+	0.167011i	−0.0411236	+	0.00768733i
$473$	0.0303252	−	0.0276451i	0.00139435	−	0.00127112i
$474$		0			0
$475$	−0.639281	−	1.28385i	−0.0293322	−	0.0589070i
$476$	0.957240	−	0.178939i	0.0438750	−	0.00820166i
$477$		0			0
$478$	−21.8798	−	4.09004i	−1.00076	−	0.187074i
$479$	−0.744216	−	8.03137i	−0.0340041	−	0.366963i	−0.995685	−	0.0927929i	$-0.970421\pi$
$479$	−0.744216	−	8.03137i	−0.0340041	−	0.366963i	0.961681	−	0.274170i	$-0.0884030\pi$
$480$		0			0
$481$	0.941767	−	3.30997i	0.0429409	−	0.150922i
$482$	−18.2136	−	16.6039i	−0.829607	−	0.756287i
$483$		0			0
$484$	−0.387612	−	0.513282i	−0.0176187	−	0.0233310i
$485$	−29.4099	−	11.3935i	−1.33544	−	0.517350i
$486$		0			0
$487$	−17.6383	−	10.9212i	−0.799269	−	0.494887i	0.0650187	−	0.997884i	$-0.479289\pi$
$487$	−17.6383	−	10.9212i	−0.799269	−	0.494887i	−0.864288	+	0.502998i	$0.832230\pi$
$488$	3.16535	+	2.88560i	0.143289	+	0.130625i
$489$		0			0
$490$	−2.25132	+	2.05235i	−0.101704	+	0.0927158i
$491$	−19.8151	+	7.67642i	−0.894244	+	0.346432i	−0.764126	−	0.645067i	$-0.776830\pi$
$491$	−19.8151	+	7.67642i	−0.894244	+	0.346432i	−0.130117	+	0.991499i	$0.541535\pi$
$492$		0			0
$493$	11.5702	−	23.2361i	0.521095	−	1.04650i
$494$	−10.1421	+	1.89589i	−0.456316	+	0.0853002i
$495$		0			0
$496$	−10.2079	+	35.8769i	−0.458347	+	1.61092i
$497$	12.5468	−	25.1974i	0.562802	−	1.13026i
$498$		0			0
$499$	5.52456	+	7.31570i	0.247313	+	0.327495i	0.904693	−	0.426064i	$-0.140100\pi$
$499$	5.52456	+	7.31570i	0.247313	+	0.327495i	−0.657380	+	0.753559i	$0.728335\pi$
$500$	−0.399801	−	0.529422i	−0.0178796	−	0.0236765i
$501$		0			0
$502$	−1.03450	+	11.1640i	−0.0461720	+	0.498275i
$503$	−23.0578	−	4.31024i	−1.02810	−	0.192184i	−0.357426	−	0.933941i	$-0.616346\pi$
$503$	−23.0578	−	4.31024i	−1.02810	−	0.192184i	−0.670669	+	0.741757i	$0.733993\pi$
$504$		0			0
$505$	1.88389	−	2.49467i	0.0838320	−	0.111012i
$506$	1.39918	−	0.866338i	0.0622013	−	0.0385134i
$507$		0			0
$508$	0.0444842	−	0.480061i	0.00197367	−	0.0212992i
$509$	−23.3485	−	21.2850i	−1.03490	−	0.943439i	−0.0364665	−	0.999335i	$-0.511610\pi$
$509$	−23.3485	−	21.2850i	−1.03490	−	0.943439i	−0.998437	+	0.0558960i	$0.982198\pi$
$510$		0			0
$511$	−6.03516	+	12.1202i	−0.266980	+	0.536168i
$512$	6.45410	+	22.6838i	0.285233	+	1.00249i
$513$		0			0
$514$	−30.1245			−1.32874
$515$	−20.5811	−	11.3128i	−0.906913	−	0.498504i
$516$		0			0
$517$	4.00332	−	2.47875i	0.176066	−	0.109015i
$518$	1.75877	+	6.18144i	0.0772760	+	0.271597i
$519$		0			0
$520$	11.3614	−	4.40143i	0.498230	−	0.193015i
$521$	0.0449391	+	0.0409674i	0.00196882	+	0.00179481i	0.674679	−	0.738111i	$-0.264282\pi$
$521$	0.0449391	+	0.0409674i	0.00196882	+	0.00179481i	−0.672711	+	0.739906i	$0.734870\pi$
$522$		0			0
$523$	−1.91278	−	20.6422i	−0.0836402	−	0.902621i	−0.929404	−	0.369064i	$-0.879678\pi$
$523$	−1.91278	−	20.6422i	−0.0836402	−	0.902621i	0.845764	−	0.533557i	$-0.179145\pi$
$524$	0.789939	−	0.489110i	0.0345087	−	0.0213669i
$525$		0			0
$526$	3.90189	−	2.41595i	0.170130	−	0.105340i
$527$	−60.7101	−	11.3487i	−2.64457	−	0.494356i
$528$		0			0
$529$	−9.17584	−	18.4276i	−0.398950	−	0.801199i
$530$	−11.1760	−	14.7995i	−0.485456	−	0.642847i
$531$		0			0
$532$	−0.453429	+	0.413355i	−0.0196586	+	0.0179212i
$533$	−5.13818	+	10.3189i	−0.222559	+	0.446959i
$534$		0			0
$535$	−4.04493	+	43.6517i	−0.174878	+	1.88723i
$536$	8.11551	−	1.51705i	0.350536	−	0.0655266i
$537$		0			0
$538$	6.32651	+	3.91721i	0.272755	+	0.168883i
$539$	−0.670778	+	0.259861i	−0.0288925	+	0.0111930i
$540$		0			0
$541$	10.8734	+	21.8367i	0.467484	+	0.938834i	0.995952	+	0.0898814i	$0.0286488\pi$
$541$	10.8734	+	21.8367i	0.467484	+	0.938834i	−0.528469	+	0.848953i	$0.677234\pi$
$542$	8.53957	+	7.78484i	0.366806	+	0.334388i
$543$		0			0
$544$	−2.08688	+	0.808461i	−0.0894742	+	0.0346625i
$545$	28.1609	+	10.9096i	1.20628	+	0.467315i
$546$		0			0
$547$	−11.8055	−	4.57348i	−0.504768	−	0.195548i	0.0953744	−	0.995441i	$-0.469595\pi$
$547$	−11.8055	−	4.57348i	−0.504768	−	0.195548i	−0.600142	+	0.799893i	$0.704889\pi$
$548$	0.317968	+	0.289866i	0.0135829	+	0.0123825i
$549$		0			0
$550$	−0.102891	−	0.361625i	−0.00438729	−	0.0154197i
$551$	1.50901	+	16.2849i	0.0642862	+	0.693758i
$552$		0			0
$553$	−5.78531	−	20.3333i	−0.246016	−	0.864658i
$554$	37.3233	−	6.97694i	1.58572	−	0.296422i
$555$		0			0
$556$	0.853307	+	0.330573i	0.0361883	+	0.0140194i
$557$	−20.0831	+	18.3082i	−0.850950	+	0.775743i	−0.976312	−	0.216368i	$-0.930579\pi$
$557$	−20.0831	+	18.3082i	−0.850950	+	0.775743i	0.125362	+	0.992111i	$0.459991\pi$
$558$		0			0
$559$	−0.00912942	−	0.0985221i	−0.000386133	−	0.00416704i
$560$	−13.2889	+	17.5973i	−0.561558	+	0.743624i
$561$		0			0
$562$	−11.8493			−0.499832
$563$	−5.95927	+	7.89135i	−0.251153	+	0.332581i	−0.906076	−	0.423115i	$-0.860937\pi$
$563$	−5.95927	+	7.89135i	−0.251153	+	0.332581i	0.654923	+	0.755696i	$0.272701\pi$
$564$		0			0
$565$	8.21772	−	28.8823i	0.345722	−	1.21509i
$566$	13.1940	+	8.16939i	0.554586	+	0.343385i
$567$		0			0
$568$	−8.98611	+	31.5829i	−0.377049	+	1.32519i
$569$	−11.9880	−	2.24094i	−0.502562	−	0.0939452i	−0.0736370	−	0.997285i	$-0.523461\pi$
$569$	−11.9880	−	2.24094i	−0.502562	−	0.0939452i	−0.428925	+	0.903340i	$0.641108\pi$
$570$		0			0
$571$	35.5972			1.48970			0.744848	−	0.667234i	$-0.232522\pi$
$571$	35.5972			1.48970			0.744848	+	0.667234i	$0.232522\pi$
$572$	0.0861280			0.00360119
$573$		0			0
$574$	−1.98631	−	21.4357i	−0.0829071	−	0.894711i
$575$	0.542185	−	0.101352i	0.0226107	−	0.00422667i
$576$		0			0
$577$	32.8073	+	12.7096i	1.36578	+	0.529108i	0.928874	−	0.370397i	$-0.120778\pi$
$577$	32.8073	+	12.7096i	1.36578	+	0.529108i	0.436911	+	0.899505i	$0.356073\pi$
$578$	14.9672	+	30.0583i	0.622555	+	1.25026i
$579$		0			0
$580$	−0.158219	−	0.556083i	−0.00656969	−	0.0230901i
$581$	−29.1281	−	5.44499i	−1.20844	−	0.225896i
$582$		0			0
$583$	−1.19841	−	4.21196i	−0.0496329	−	0.174442i
$584$	4.32242	−	15.1917i	0.178863	−	0.628638i
$585$		0			0
$586$	−29.7966	−	11.5433i	−1.23089	−	0.476848i
$587$	26.4455	+	35.0195i	1.09152	+	1.44541i	0.884184	+	0.467139i	$0.154715\pi$
$587$	26.4455	+	35.0195i	1.09152	+	1.44541i	0.207338	+	0.978269i	$0.433520\pi$
$588$		0			0
$589$	36.2857	−	14.0572i	1.49513	−	0.579215i
$590$	0.867360	+	0.537047i	0.0357087	+	0.0221099i
$591$		0			0
$592$	−3.23853	−	6.50385i	−0.133103	−	0.267307i
$593$	7.96802	−	7.26381i	0.327207	−	0.298289i	−0.493376	−	0.869816i	$-0.664237\pi$
$593$	7.96802	−	7.26381i	0.327207	−	0.298289i	0.820583	+	0.571527i	$0.193649\pi$
$594$		0			0
$595$	−31.0431	−	19.2211i	−1.27264	−	0.787987i
$596$	−0.634401	+	1.27405i	−0.0259861	+	0.0521871i
$597$		0			0
$598$	0.366129	−	3.95116i	0.0149721	−	0.161575i
$599$	10.7252	−	37.6952i	0.438220	−	1.54018i	−0.357143	−	0.934050i	$-0.616249\pi$
$599$	10.7252	−	37.6952i	0.438220	−	1.54018i	0.795363	−	0.606134i	$-0.207280\pi$
$600$		0			0
$601$	16.9468	−	15.4491i	0.691276	−	0.630181i	−0.249831	−	0.968289i	$-0.580375\pi$
$601$	16.9468	−	15.4491i	0.691276	−	0.630181i	0.941107	+	0.338108i	$0.109787\pi$
$602$	0.111355	+	0.147458i	0.00453850	+	0.00600994i
$603$		0			0
$604$	0.364025	+	0.731062i	0.0148120	+	0.0297465i
$605$	−2.22511	+	24.0128i	−0.0904637	+	0.976259i
$606$		0			0
$607$	−26.3558	+	16.3188i	−1.06975	+	0.662361i	−0.944082	−	0.329711i	$-0.893049\pi$
$607$	−26.3558	+	16.3188i	−1.06975	+	0.662361i	−0.125668	+	0.992072i	$0.540107\pi$
$608$	0.849759	−	1.12526i	0.0344623	−	0.0456355i
$609$		0			0
$610$	−0.443583	−	4.78702i	−0.0179602	−	0.193821i
$611$	1.04756	−	11.3050i	0.0423798	−	0.457351i
$612$		0			0
$613$	−33.8993	+	13.1326i	−1.36918	+	0.530423i	−0.929862	−	0.367909i	$-0.880074\pi$
$613$	−33.8993	+	13.1326i	−1.36918	+	0.530423i	−0.439317	+	0.898332i	$0.644780\pi$
$614$	−1.29633	+	2.60338i	−0.0523155	+	0.105064i
$615$		0			0
$616$	−4.56821	+	2.82852i	−0.184058	+	0.113964i
$617$	−14.4586			−0.582082			−0.291041	−	0.956711i	$-0.594002\pi$
$617$	−14.4586			−0.582082			−0.291041	+	0.956711i	$0.594002\pi$
$618$		0			0
$619$	−5.12903			−0.206153			−0.103077	−	0.994673i	$-0.532869\pi$
$619$	−5.12903			−0.206153			−0.103077	+	0.994673i	$0.532869\pi$
$620$	−1.16959	+	0.724176i	−0.0469717	+	0.0290836i
$621$		0			0
$622$	2.10981	−	4.23706i	0.0845955	−	0.169891i
$623$	−9.15306	+	3.54592i	−0.366710	+	0.142064i
$624$		0			0
$625$	−2.45885	+	26.5352i	−0.0983541	+	1.06141i
$626$	2.75328	+	29.7126i	0.110043	+	1.18755i
$627$		0			0
$628$	−0.802364	+	1.06250i	−0.0320178	+	0.0423984i
$629$	10.2282	−	6.33302i	0.407824	−	0.252514i
$630$		0			0
$631$	3.82357	−	41.2629i	0.152214	−	1.64265i	−0.486843	−	0.873489i	$-0.661852\pi$
$631$	3.82357	−	41.2629i	0.152214	−	1.64265i	0.639057	−	0.769159i	$-0.279325\pi$
$632$	10.9924	+	22.0757i	0.437254	+	0.878124i
$633$		0			0
$634$	7.45683	+	9.87444i	0.296148	+	0.392164i
$635$	−13.3585	+	12.1779i	−0.530116	+	0.483265i
$636$		0			0
$637$	−0.474674	+	1.66831i	−0.0188073	+	0.0661007i
$638$	−0.395589	+	4.26908i	−0.0156615	+	0.169015i
$639$		0			0
$640$	11.1007	−	22.2931i	0.438792	−	0.881213i
$641$	−6.02996	−	3.73360i	−0.238169	−	0.147468i	0.402158	−	0.915570i	$-0.368260\pi$
$641$	−6.02996	−	3.73360i	−0.238169	−	0.147468i	−0.640327	+	0.768102i	$0.721201\pi$
$642$		0			0
$643$	34.1119	−	31.0971i	1.34524	−	1.22635i	0.393548	−	0.919304i	$-0.371247\pi$
$643$	34.1119	−	31.0971i	1.34524	−	1.22635i	0.951694	−	0.307047i	$-0.0993409\pi$
$644$	−0.105180	−	0.211230i	−0.00414468	−	0.00832364i
$645$		0			0
$646$	−30.6661	−	18.9876i	−1.20654	−	0.747058i
$647$	45.8964	−	17.7804i	1.80438	−	0.699019i	0.810871	−	0.585225i	$-0.198994\pi$
$647$	45.8964	−	17.7804i	1.80438	−	0.699019i	0.993504	−	0.113794i	$-0.0363004\pi$
$648$		0			0
$649$	0.145171	+	0.192237i	0.00569844	+	0.00754596i
$650$	−0.845346	−	0.327489i	−0.0331572	−	0.0128452i
$651$		0			0
$652$	0.0113384	−	0.0398504i	0.000444046	−	0.00156066i
$653$	6.21411	+	21.8403i	0.243177	+	0.854678i	0.983267	+	0.182171i	$0.0583123\pi$
$653$	6.21411	+	21.8403i	0.243177	+	0.854678i	−0.740090	+	0.672508i	$0.765217\pi$
$654$		0			0
$655$	−34.2422	−	6.40097i	−1.33795	−	0.250107i
$656$	6.66019	+	23.4081i	0.260037	+	0.913934i
$657$		0			0
$658$	9.45089	+	18.9800i	0.368434	+	0.739916i
$659$	18.8821	+	7.31495i	0.735541	+	0.284950i	0.699729	−	0.714409i	$-0.253304\pi$
$659$	18.8821	+	7.31495i	0.735541	+	0.284950i	0.0358119	+	0.999359i	$0.488598\pi$
$660$		0			0
$661$	38.4078	−	7.17966i	1.49389	−	0.279256i	0.627497	−	0.778619i	$-0.284080\pi$
$661$	38.4078	−	7.17966i	1.49389	−	0.279256i	0.866393	+	0.499363i	$0.166433\pi$
$662$	3.02887	+	32.6867i	0.117720	+	1.27040i
$663$		0			0
$664$	34.5679			1.34149
$665$	23.0046			0.892082
$666$		0			0
$667$	−6.18268	−	1.15574i	−0.239394	−	0.0447505i
$668$	0.127963	−	0.449742i	0.00495102	−	0.0174010i
$669$		0			0
$670$	−7.87868	−	4.87827i	−0.304380	−	0.188464i
$671$	0.310666	−	1.09188i	0.0119931	−	0.0421514i
$672$		0			0
$673$	19.0971	−	25.2887i	0.736140	−	0.974807i	−0.263808	−	0.964575i	$-0.584978\pi$
$673$	19.0971	−	25.2887i	0.736140	−	0.974807i	0.999948	−	0.0102316i	$-0.00325688\pi$
$674$	14.8779			0.573075
$675$		0			0
$676$	−0.358376	+	0.474567i	−0.0137837	+	0.0182526i
$677$	1.83753	+	19.8301i	0.0706221	+	0.762134i	0.955243	+	0.295823i	$0.0955937\pi$
$677$	1.83753	+	19.8301i	0.0706221	+	0.762134i	−0.884621	+	0.466311i	$0.845583\pi$
$678$		0			0
$679$	24.7836	−	22.5932i	0.951107	−	0.867049i
$680$	39.7167	+	15.3863i	1.52306	+	0.590038i
$681$		0			0
$682$	10.0275	−	1.87446i	0.383972	−	0.0717768i
$683$	−7.94177	−	27.9124i	−0.303883	−	1.06804i	−0.951899	−	0.306412i	$-0.900872\pi$
$683$	−7.94177	−	27.9124i	−0.303883	−	1.06804i	0.648016	−	0.761627i	$-0.275599\pi$
$684$		0			0
$685$	−1.48848	−	16.0632i	−0.0568718	−	0.613745i
$686$	−7.44880	−	26.1798i	−0.284397	−	0.999550i
$687$		0			0
$688$	−0.154376	−	0.140733i	−0.00588555	−	0.00536538i
$689$	−9.84601	−	3.81437i	−0.375103	−	0.145316i
$690$		0			0
$691$	33.8989	+	13.1325i	1.28958	+	0.499584i	0.905746	−	0.423820i	$-0.139311\pi$
$691$	33.8989	+	13.1325i	1.28958	+	0.499584i	0.383829	+	0.923404i	$0.374605\pi$
$692$	−0.167516	+	0.0648961i	−0.00636800	+	0.00246698i
$693$		0			0
$694$	−6.84058	−	6.23601i	−0.259665	−	0.236716i
$695$	−15.2934	−	30.7134i	−0.580113	−	1.16502i
$696$		0			0
$697$	−37.5756	+	14.5569i	−1.42328	+	0.551381i
$698$	26.1419	+	16.1864i	0.989487	+	0.612665i
$699$		0			0
$700$	−0.0529923	+	0.00990598i	−0.00200292	+	0.000374411i
$701$	1.27274	−	13.7351i	0.0480708	−	0.518766i	−0.937321	−	0.348466i	$-0.886703\pi$
$701$	1.27274	−	13.7351i	0.0480708	−	0.518766i	0.985392	−	0.170300i	$-0.0544738\pi$
$702$		0			0
$703$	−3.37854	+	6.78502i	−0.127424	+	0.255902i
$704$	4.62771	−	4.21871i	0.174413	−	0.158999i
$705$		0			0
$706$	17.0258	+	22.5459i	0.640776	+	0.848524i
$707$	1.48163	+	2.97551i	0.0557223	+	0.111905i
$708$		0			0
$709$	11.1068	+	2.07621i	0.417123	+	0.0779739i	0.388128	−	0.921606i	$-0.373122\pi$
$709$	11.1068	+	2.07621i	0.417123	+	0.0779739i	0.0289958	+	0.999580i	$0.490769\pi$
$710$	31.3354	−	19.4021i	1.17600	−	0.728146i
$711$		0			0
$712$	9.73559	−	6.02802i	0.364857	−	0.225910i
$713$	1.38085	+	14.9018i	0.0517133	+	0.558075i
$714$		0			0
$715$	−2.38644	−	2.17552i	−0.0892476	−	0.0813600i
$716$	−0.729575	+	0.282639i	−0.0272655	+	0.0105627i
$717$		0			0
$718$	12.7607	+	44.8493i	0.476226	+	1.67376i
$719$	13.5398	−	8.38352i	0.504951	−	0.312653i	−0.250210	−	0.968192i	$-0.580500\pi$
$719$	13.5398	−	8.38352i	0.504951	−	0.312653i	0.755161	+	0.655539i	$0.227559\pi$
$720$		0			0
$721$	20.5224	−	14.2280i	0.764295	−	0.529877i
$722$	−3.72695			−0.138703
$723$		0			0
$724$	0.178432	+	0.627123i	0.00663136	+	0.0233068i
$725$	−0.640519	+	1.28634i	−0.0237883	+	0.0477733i
$726$		0			0
$727$	36.3307	+	33.1198i	1.34743	+	1.22835i	0.950586	+	0.310461i	$0.100484\pi$
$727$	36.3307	+	33.1198i	1.34743	+	1.22835i	0.396846	+	0.917885i	$0.370105\pi$
$728$	−1.19538	+	12.9002i	−0.0443037	+	0.478113i
$729$		0			0
$730$	−15.0727	+	9.33260i	−0.557865	+	0.345415i
$731$	0.208442	−	0.276022i	0.00770951	−	0.0102090i
$732$		0			0
$733$	−35.9918	−	6.72804i	−1.32939	−	0.248506i	−0.529324	−	0.848420i	$-0.677554\pi$
$733$	−35.9918	−	6.72804i	−1.32939	−	0.248506i	−0.800064	+	0.599914i	$0.795201\pi$
$734$	0.827234	−	8.92728i	0.0305338	−	0.329512i
$735$		0			0
$736$	0.326806	+	0.432761i	0.0120462	+	0.0159518i
$737$	−1.31866	−	1.74619i	−0.0485734	−	0.0643216i
$738$		0			0
$739$	1.66354	−	3.34085i	0.0611944	−	0.122895i	−0.862455	−	0.506134i	$-0.831074\pi$
$739$	1.66354	−	3.34085i	0.0611944	−	0.122895i	0.923649	+	0.383239i	$0.125192\pi$
$740$	0.0733276	−	0.257720i	0.00269558	−	0.00947397i
$741$		0			0
$742$	19.3835	−	3.62340i	0.711590	−	0.133019i
$743$	23.3585	−	46.9103i	0.856942	−	1.72097i	0.181727	−	0.983349i	$-0.441831\pi$
$743$	23.3585	−	46.9103i	0.856942	−	1.72097i	0.675214	−	0.737622i	$-0.264051\pi$
$744$		0			0
$745$	49.7594	−	19.2769i	1.82304	−	0.706251i
$746$	4.06763	−	3.70813i	0.148927	−	0.135764i
$747$		0			0
$748$	0.222503	+	0.202838i	0.00813550	+	0.00741649i
$749$	−39.6319	−	24.5390i	−1.44812	−	0.896637i
$750$		0			0
$751$	29.2002	+	11.3122i	1.06553	+	0.412789i	0.829240	−	0.558893i	$-0.188774\pi$
$751$	29.2002	+	11.3122i	1.06553	+	0.412789i	0.236292	+	0.971682i	$0.424068\pi$
$752$	−14.4452	−	19.1285i	−0.526761	−	0.697544i
$753$		0			0
$754$	7.63971	+	6.96452i	0.278222	+	0.253633i
$755$	8.37961	−	29.4513i	0.304965	−	1.07184i
$756$		0			0
$757$	1.67560	+	18.0826i	0.0609006	+	0.657222i	0.970398	+	0.241512i	$0.0776434\pi$
$757$	1.67560	+	18.0826i	0.0609006	+	0.657222i	−0.909497	+	0.415710i	$0.863533\pi$
$758$	−18.6299	−	3.48254i	−0.676670	−	0.126491i
$759$		0			0
$760$	−26.3790	+	4.93110i	−0.956868	+	0.178870i
$761$	3.87305	+	7.77814i	0.140398	+	0.281957i	0.954191	−	0.299197i	$-0.0967188\pi$
$761$	3.87305	+	7.77814i	0.140398	+	0.281957i	−0.813793	+	0.581155i	$0.802601\pi$
$762$		0			0
$763$	−23.7311	+	21.6337i	−0.859122	+	0.783193i
$764$	0.837156	−	0.156492i	0.0302872	−	0.00566167i
$765$		0			0
$766$	20.7924	−	27.5336i	0.751261	−	0.994831i
$767$	0.580846			0.0209731
$768$		0			0
$769$	18.0707	−	23.9295i	0.651647	−	0.862920i	−0.345499	−	0.938419i	$-0.612290\pi$
$769$	18.0707	−	23.9295i	0.651647	−	0.862920i	0.997146	+	0.0754990i	$0.0240550\pi$
$770$	5.92799	+	1.10813i	0.213630	+	0.0399343i
$771$		0			0
$772$	−1.19227	−	0.738221i	−0.0429107	−	0.0265692i
$773$	41.9089	+	25.9489i	1.50736	+	0.933316i	0.997320	+	0.0731630i	$0.0233093\pi$
$773$	41.9089	+	25.9489i	1.50736	+	0.933316i	0.510037	+	0.860153i	$0.329632\pi$
$774$		0			0
$775$	3.36088	+	0.628257i	0.120726	+	0.0225677i
$776$	−23.5760	+	31.2197i	−0.846330	+	1.12072i
$777$		0			0
$778$	−20.9053			−0.749491
$779$	15.3005	−	20.2611i	0.548197	−	0.725930i
$780$		0			0
$781$	8.55464	−	1.59914i	0.306109	−	0.0572217i
$782$	10.2511	−	9.34515i	0.366580	−	0.334182i
$783$		0			0
$784$	1.63230	+	3.27810i	0.0582965	+	0.117075i
$785$	49.0699	−	9.17275i	1.75138	−	0.327389i
$786$		0			0
$787$	−8.07362	−	1.50922i	−0.287794	−	0.0537979i	0.0378732	−	0.999283i	$-0.487942\pi$
$787$	−8.07362	−	1.50922i	−0.287794	−	0.0537979i	−0.325667	+	0.945485i	$0.605589\pi$
$788$	0.128391	+	1.38556i	0.00457375	+	0.0493586i
$789$		0			0
$790$	7.57492	−	26.6231i	0.269503	−	0.947207i
$791$	23.5962	+	21.5108i	0.838984	+	0.764835i
$792$		0			0
$793$	−1.64956	−	2.18437i	−0.0585775	−	0.0775692i
$794$	−37.3309	−	14.4621i	−1.32482	−	0.513240i
$795$		0			0
$796$	0.757543	+	0.469051i	0.0268504	+	0.0166251i
$797$	8.83013	+	8.04973i	0.312779	+	0.285136i	0.814827	−	0.579704i	$-0.196832\pi$
$797$	8.83013	+	8.04973i	0.312779	+	0.285136i	−0.502048	+	0.864840i	$0.667420\pi$
$798$		0			0
$799$	29.3304	−	26.7382i	1.03763	−	0.945929i
$800$	0.115529	−	0.0447560i	0.00408455	−	0.00158236i
$801$		0			0
$802$	−15.4144	+	30.9563i	−0.544302	+	1.09311i
$803$	−4.11488	+	0.769204i	−0.145211	+	0.0271446i
$804$		0			0
$805$	−2.42117	+	8.50954i	−0.0853352	+	0.299922i
$806$	10.9639	−	22.0185i	0.386188	−	0.775570i
$807$		0			0
$808$	−2.33676	−	3.09437i	−0.0822070	−	0.108860i
$809$	−15.4634	−	20.4768i	−0.543663	−	0.719926i	0.440389	−	0.897807i	$-0.354840\pi$
$809$	−15.4634	−	20.4768i	−0.543663	−	0.719926i	−0.984052	+	0.177881i	$0.943076\pi$
$810$		0			0
$811$	−1.79266	+	19.3459i	−0.0629488	+	0.679326i	0.904536	+	0.426397i	$0.140217\pi$
$811$	−1.79266	+	19.3459i	−0.0629488	+	0.679326i	−0.967485	+	0.252929i	$0.918606\pi$
$812$	0.604285	+	0.112960i	0.0212062	+	0.00396413i
$813$		0			0
$814$	−1.19744	+	1.58567i	−0.0419702	+	0.0555775i
$815$	−1.32075	+	0.817776i	−0.0462640	+	0.0286454i
$816$		0			0
$817$	−0.0201078	+	0.216998i	−0.000703483	+	0.00759179i
$818$	1.86234	+	1.69775i	0.0651152	+	0.0593604i
$819$		0			0
$820$	−0.400068	+	0.803444i	−0.0139710	+	0.0280575i
$821$	−1.37422	−	4.82987i	−0.0479605	−	0.168564i	0.934146	−	0.356892i	$-0.116164\pi$
$821$	−1.37422	−	4.82987i	−0.0479605	−	0.168564i	−0.982106	+	0.188329i	$0.939693\pi$
$822$		0			0
$823$	−4.57425			−0.159448			−0.0797242	−	0.996817i	$-0.525404\pi$
$823$	−4.57425			−0.159448			−0.0797242	+	0.996817i	$0.525404\pi$
$824$	−20.4829	+	20.7140i	−0.713557	+	0.721606i
$825$		0			0
$826$	−0.922267	+	0.571043i	−0.0320898	+	0.0198691i
$827$	−0.0460449	−	0.161831i	−0.00160114	−	0.00562741i	0.961021	−	0.276476i	$-0.0891665\pi$
$827$	−0.0460449	−	0.161831i	−0.00160114	−	0.00562741i	−0.962622	+	0.270848i	$0.912696\pi$
$828$		0			0
$829$	−28.2781	+	10.9550i	−0.982140	+	0.380483i	−0.798159	−	0.602447i	$-0.794192\pi$
$829$	−28.2781	+	10.9550i	−0.982140	+	0.380483i	−0.183981	+	0.982930i	$0.558898\pi$
$830$	−28.6729	−	26.1388i	−0.995253	−	0.907293i
$831$		0			0
$832$	−1.39317	−	15.0347i	−0.0482996	−	0.521236i
$833$	−5.15526	+	3.19200i	−0.178619	+	0.110596i
$834$		0			0
$835$	−14.9057	+	9.22922i	−0.515833	+	0.319390i
$836$	−0.186469	−	0.0348572i	−0.00644918	−	0.00120556i
$837$		0			0
$838$	0.683780	+	1.37322i	0.0236208	+	0.0474369i
$839$	−15.5803	−	20.6317i	−0.537892	−	0.712284i	0.445193	−	0.895435i	$-0.353135\pi$
$839$	−15.5803	−	20.6317i	−0.537892	−	0.712284i	−0.983085	+	0.183150i	$0.941370\pi$
$840$		0			0
$841$	−9.32164	+	8.49780i	−0.321436	+	0.293027i
$842$	−12.8514	+	25.8091i	−0.442889	+	0.889441i
$843$		0			0
$844$	−0.0111101	+	0.119897i	−0.000382425	+	0.00412702i
$845$	21.9171	−	4.09701i	0.753970	−	0.140941i
$846$		0			0
$847$	−21.8015	−	13.4989i	−0.749108	−	0.463828i
$848$	−20.7875	+	8.05310i	−0.713844	+	0.276545i
$849$		0			0
$850$	−1.41260	−	2.83689i	−0.0484518	−	0.0973044i
$851$	−2.15424	−	1.96384i	−0.0738462	−	0.0673197i
$852$		0			0
$853$	−38.4902	+	14.9112i	−1.31788	+	0.510549i	−0.914538	−	0.404501i	$-0.867445\pi$
$853$	−38.4902	+	14.9112i	−1.31788	+	0.510549i	−0.403341	+	0.915050i	$0.632151\pi$
$854$	4.76667	+	1.84662i	0.163112	+	0.0631900i
$855$		0			0
$856$	50.7052	+	19.6433i	1.73307	+	0.671394i
$857$	−1.47947	−	1.34872i	−0.0505379	−	0.0460714i	0.648033	−	0.761612i	$-0.275592\pi$
$857$	−1.47947	−	1.34872i	−0.0505379	−	0.0460714i	−0.698571	+	0.715541i	$0.746180\pi$
$858$		0			0
$859$	0.0341779	+	0.120123i	0.00116614	+	0.00409854i	0.962407	−	0.271613i	$-0.0875571\pi$
$859$	0.0341779	+	0.120123i	0.00116614	+	0.00409854i	−0.961240	+	0.275712i	$0.911087\pi$
$860$	−0.000710832	−	0.00767110i	−2.42392e−5	−	0.000261582i
$861$		0			0
$862$	−12.0188	−	42.2419i	−0.409364	−	1.43876i
$863$	−38.0359	+	7.11015i	−1.29476	+	0.242032i	−0.785650	−	0.618671i	$-0.787672\pi$
$863$	−38.0359	+	7.11015i	−1.29476	+	0.242032i	−0.509108	+	0.860703i	$0.670024\pi$
$864$		0			0
$865$	6.28076	+	2.43318i	0.213552	+	0.0827306i
$866$	30.3097	−	27.6309i	1.02997	−	0.938938i
$867$		0			0
$868$	−0.134962	−	1.45647i	−0.00458091	−	0.0494359i
$869$	3.93886	−	5.21589i	0.133617	−	0.176937i
$870$		0			0
$871$	−5.27612			−0.178774
$872$	22.5748	−	29.8938i	0.764478	−	1.01233i
$873$		0			0
$874$	−2.39177	+	8.40620i	−0.0809028	+	0.284344i
$875$	−22.4870	−	13.9234i	−0.760200	−	0.470696i
$876$		0			0
$877$	2.21369	−	7.78030i	0.0747509	−	0.262722i	−0.915438	−	0.402460i	$-0.868155\pi$
$877$	2.21369	−	7.78030i	0.0747509	−	0.262722i	0.990189	+	0.139738i	$0.0446259\pi$
$878$	−34.9281	−	6.52919i	−1.17877	−	0.220350i
$879$		0			0
$880$	−6.81775			−0.229826
$881$	22.5751			0.760574			0.380287	−	0.924868i	$-0.375825\pi$
$881$	22.5751			0.760574			0.380287	+	0.924868i	$0.375825\pi$
$882$		0			0
$883$	−4.52650	−	48.8487i	−0.152329	−	1.64389i	−0.638208	−	0.769864i	$-0.720324\pi$
$883$	−4.52650	−	48.8487i	−0.152329	−	1.64389i	0.485879	−	0.874026i	$-0.338500\pi$
$884$	0.713614	−	0.133398i	0.0240014	−	0.00448665i
$885$		0			0
$886$	−21.0278	−	8.14622i	−0.706443	−	0.273677i
$887$	−12.9568	−	26.0208i	−0.435047	−	0.873691i	−0.998858	−	0.0477874i	$-0.984783\pi$
$887$	−12.9568	−	26.0208i	−0.435047	−	0.873691i	0.563811	−	0.825904i	$-0.309335\pi$
$888$		0			0
$889$	−5.25995	−	18.4868i	−0.176413	−	0.620027i
$890$	−12.6335	−	2.36161i	−0.423476	−	0.0791614i
$891$		0			0
$892$	0.391380	+	1.37556i	0.0131044	+	0.0460571i
$893$	−6.84329	+	24.0517i	−0.229002	+	0.804858i
$894$		0			0
$895$	27.3543	+	10.5971i	0.914354	+	0.354223i
$896$	15.9580	+	21.1319i	0.533121	+	0.705966i
$897$		0			0
$898$	33.8214	−	13.1025i	1.12863	−	0.437235i
$899$	−33.1489	−	20.5250i	−1.10558	−	0.684546i
$900$		0			0
$901$	−16.4530	−	33.0421i	−0.548129	−	1.10079i
$902$	4.91871	−	4.48399i	0.163775	−	0.149301i
$903$		0			0
$904$	−31.6682	−	19.6081i	−1.05327	−	0.652157i
$905$	10.8966	−	21.8834i	0.362216	−	0.727428i
$906$		0			0
$907$	−3.54604	+	38.2679i	−0.117744	+	1.27067i	0.707834	+	0.706378i	$0.249672\pi$
$907$	−3.54604	+	38.2679i	−0.117744	+	1.27067i	−0.825579	+	0.564287i	$0.809151\pi$
$908$	−0.178290	+	0.626624i	−0.00591676	+	0.0207953i
$909$		0			0
$910$	10.7461	−	9.79639i	0.356231	−	0.324747i
$911$	19.2361	+	25.4727i	0.637321	+	0.843949i	0.995985	−	0.0895174i	$-0.0285325\pi$
$911$	19.2361	+	25.4727i	0.637321	+	0.843949i	−0.358664	+	0.933467i	$0.616768\pi$
$912$		0			0
$913$	−4.08373	−	8.20124i	−0.135152	−	0.271421i
$914$	4.76837	−	51.4589i	0.157724	−	1.70211i
$915$		0			0
$916$	0.437191	−	0.270697i	0.0144452	−	0.00894408i
$917$	22.3219	−	29.5589i	0.737133	−	0.976122i
$918$		0			0
$919$	1.91171	+	20.6307i	0.0630615	+	0.680542i	0.967320	+	0.253558i	$0.0816007\pi$
$919$	1.91171	+	20.6307i	0.0630615	+	0.680542i	−0.904259	+	0.426985i	$0.859576\pi$
$920$	0.952280	−	10.2767i	0.0313957	−	0.338814i
$921$		0			0
$922$	−3.27967	+	1.27055i	−0.108010	+	0.0418433i
$923$	9.35355	−	18.7845i	0.307876	−	0.618298i
$924$		0			0
$925$	−0.566227	+	0.350593i	−0.0186174	+	0.0115274i
$926$	−13.9726			−0.459168
$927$		0			0
$928$	−1.41280			−0.0463776
$929$	8.08649	−	5.00694i	0.265309	−	0.164272i	−0.387331	−	0.921941i	$-0.626603\pi$
$929$	8.08649	−	5.00694i	0.265309	−	0.164272i	0.652640	+	0.757668i	$0.273662\pi$
$930$		0			0
$931$	1.70287	−	3.41982i	0.0558092	−	0.112080i
$932$	−0.986767	+	0.382275i	−0.0323226	+	0.0125218i
$933$		0			0
$934$	−1.62261	+	17.5108i	−0.0530935	+	0.572971i
$935$	−1.04158	−	11.2405i	−0.0340634	−	0.367603i
$936$		0			0
$937$	−34.0081	+	45.0340i	−1.11100	+	1.47120i	−0.246101	+	0.969244i	$0.579149\pi$
$937$	−34.0081	+	45.0340i	−1.11100	+	1.47120i	−0.864895	+	0.501952i	$0.832615\pi$
$938$	8.37742	−	5.18708i	0.273532	−	0.169364i
$939$		0			0
$940$	0.0815650	−	0.880227i	0.00266036	−	0.0287098i
$941$	13.5371	+	27.1861i	0.441296	+	0.886242i	0.998440	+	0.0558266i	$0.0177794\pi$
$941$	13.5371	+	27.1861i	0.441296	+	0.886242i	−0.557144	+	0.830416i	$0.688103\pi$
$942$		0			0
$943$	5.88436	+	7.79216i	0.191621	+	0.253747i
$944$	0.906257	−	0.826163i	0.0294962	−	0.0268893i
$945$		0			0
$946$	−0.0156343	+	0.0549488i	−0.000508315	+	0.00178654i
$947$	0.0583389	−	0.629577i	0.00189576	−	0.0204585i	−0.994734	−	0.102493i	$-0.967318\pi$
$947$	0.0583389	−	0.629577i	0.00189576	−	0.0204585i	0.996630	+	0.0820342i	$0.0261417\pi$
$948$		0			0
$949$	−4.49916	+	9.03553i	−0.146049	+	0.293306i
$950$	1.69766	+	1.05114i	0.0550793	+	0.0341036i
$951$		0			0
$952$	−33.4690	+	30.5111i	−1.08474	+	0.988869i
$953$	14.8422	+	29.8072i	0.480787	+	0.965551i	0.994214	+	0.107417i	$0.0342581\pi$
$953$	14.8422	+	29.8072i	0.480787	+	0.965551i	−0.513427	+	0.858133i	$0.671624\pi$
$954$		0			0
$955$	−27.1488	−	16.8098i	−0.878514	−	0.543953i
$956$	−0.920136	+	0.356463i	−0.0297593	+	0.0115288i
$957$		0			0
$958$	6.76719	+	8.96121i	0.218638	+	0.289524i
$959$	15.9949	+	6.19647i	0.516503	+	0.200094i
$960$		0			0
$961$	−16.9037	+	59.4102i	−0.545279	+	1.91646i
$962$	1.31115	+	4.60821i	0.0422731	+	0.148575i
$963$		0			0
$964$	−1.07400	−	0.200765i	−0.0345911	−	0.00646620i
$965$	14.3885	+	50.5704i	0.463183	+	1.62792i
$966$		0			0
$967$	1.49247	+	2.99729i	0.0479948	+	0.0963865i	0.917862	−	0.396899i	$-0.129914\pi$
$967$	1.49247	+	2.99729i	0.0479948	+	0.0963865i	−0.869868	+	0.493285i	$0.835796\pi$
$968$	27.8929	+	10.8058i	0.896512	+	0.347311i
$969$		0			0
$970$	43.1626	−	8.06849i	1.38587	−	0.259064i
$971$	−0.260077	−	2.80667i	−0.00834626	−	0.0900705i	0.990542	−	0.137209i	$-0.0438133\pi$
$971$	−0.260077	−	2.80667i	−0.00834626	−	0.0900705i	−0.998888	+	0.0471387i	$0.984990\pi$
$972$		0			0
$973$	36.4823			1.16957
$974$	28.8826			0.925458
$975$		0			0
$976$	−5.68062	−	1.06189i	−0.181832	−	0.0339904i
$977$	0.0783153	−	0.275250i	0.00250553	−	0.00880602i	−0.960563	−	0.278063i	$-0.910308\pi$
$977$	0.0783153	−	0.275250i	0.00250553	−	0.00880602i	0.963068	+	0.269257i	$0.0867781\pi$
$978$		0			0
$979$	−2.58028	−	1.59764i	−0.0824661	−	0.0510608i
$980$	−0.0369589	+	0.129897i	−0.00118061	+	0.00414941i
$981$		0			0
$982$	17.8288	−	23.6092i	0.568941	−	0.753400i
$983$	−36.3197			−1.15842			−0.579209	−	0.815179i	$-0.696639\pi$
$983$	−36.3197			−1.15842			−0.579209	+	0.815179i	$0.696639\pi$
$984$		0			0
$985$	31.4407	−	41.6343i	1.00179	−	1.32658i
$986$	3.33443	+	35.9842i	0.106190	+	1.14597i
$987$		0			0
$988$	−0.338027	+	0.308153i	−0.0107541	+	0.00980364i
$989$	−0.0781524	−	0.0302764i	−0.00248510	−	0.000962733i
$990$		0			0
$991$	−32.9238	+	6.15452i	−1.04586	+	0.195505i	−0.678519	−	0.734582i	$-0.737378\pi$
$991$	−32.9238	+	6.15452i	−1.04586	+	0.195505i	−0.367339	+	0.930087i	$0.619731\pi$
$992$	0.919935	+	3.23324i	0.0292080	+	0.102655i
$993$		0			0
$994$	3.61589	+	39.0217i	0.114689	+	1.23769i
$995$	−9.14217	−	32.1314i	−0.289826	−	1.01863i
$996$		0			0
$997$	13.2153	+	12.0474i	0.418534	+	0.381544i	0.855387	−	0.517989i	$-0.173319\pi$
$997$	13.2153	+	12.0474i	0.418534	+	0.381544i	−0.436854	+	0.899533i	$0.643907\pi$
$998$	−11.9011	−	4.61052i	−0.376723	−	0.145943i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	927.2.u.b.100.3		128
3.2	odd	2		309.2.i.a.100.6	yes	128
103.34	even	17	inner	927.2.u.b.343.3		128
309.137	odd	34		309.2.i.a.34.6	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.2.i.a.34.6	✓	128	309.137	odd	34
309.2.i.a.100.6	yes	128	3.2	odd	2
927.2.u.b.100.3		128	1.1	even	1	trivial
927.2.u.b.343.3		128	103.34	even	17	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:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.u (of order \(17\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18369 + 0.732910i) q^{2} +(-0.0275108 + 0.0552492i) q^{4} +(2.15782 - 0.835944i) q^{5} +(-0.227033 + 2.45008i) q^{7} +(-0.264844 - 2.85813i) q^{8} +O(q^{10})\)	\(q+(-1.18369 + 0.732910i) q^{2} +(-0.0275108 + 0.0552492i) q^{4} +(2.15782 - 0.835944i) q^{5} +(-0.227033 + 2.45008i) q^{7} +(-0.264844 - 2.85813i) q^{8} +(-1.94152 + 2.57099i) q^{10} +(-0.646803 + 0.400483i) q^{11} +(-0.169251 + 1.82651i) q^{13} +(-1.52695 - 3.06653i) q^{14} +(2.33385 + 3.09052i) q^{16} +(-4.73881 + 4.32000i) q^{17} +(1.10565 - 3.88594i) q^{19} +(-0.0131782 + 0.142215i) q^{20} +(0.472096 - 0.948097i) q^{22} +(1.32107 + 0.817969i) q^{23} +(0.262338 - 0.239153i) q^{25} +(-1.13833 - 2.28607i) q^{26} +(-0.129119 - 0.0799470i) q^{28} +(-3.77465 + 1.46231i) q^{29} +(5.80435 + 7.68620i) q^{31} +(0.325445 + 0.126078i) q^{32} +(2.44312 - 8.58666i) q^{34} +(1.55823 + 5.47661i) q^{35} +(-1.84413 - 0.344727i) q^{37} +(1.53930 + 5.41009i) q^{38} +(-2.96072 - 5.94592i) q^{40} +(5.85985 + 2.27012i) q^{41} +(-0.0530217 + 0.00991147i) q^{43} +(-0.00433230 - 0.0467530i) q^{44} -2.16323 q^{46} -6.18940 q^{47} +(0.929485 + 0.173751i) q^{49} +(-0.135250 + 0.475353i) q^{50} +(-0.0962569 - 0.0595997i) q^{52} +(-1.57530 + 5.53659i) q^{53} +(-1.06090 + 1.40486i) q^{55} +7.06275 q^{56} +(3.39627 - 4.49739i) q^{58} +(-0.0292170 - 0.315301i) q^{59} +(-1.10277 + 1.00531i) q^{61} +(-12.5038 - 4.84402i) q^{62} +(-8.09125 + 1.51252i) q^{64} +(1.16165 + 4.08276i) q^{65} +(0.265393 + 2.86404i) q^{67} +(-0.108308 - 0.380662i) q^{68} +(-5.85832 - 5.34057i) q^{70} +(-10.6673 - 4.13253i) q^{71} +(5.13108 + 1.98779i) q^{73} +(2.43553 - 0.943528i) q^{74} +(0.184278 + 0.167992i) q^{76} +(-0.834369 - 1.67564i) q^{77} +(-8.01143 + 3.10365i) q^{79} +(7.61954 + 4.71782i) q^{80} +(-8.60004 + 1.60763i) q^{82} +(-1.11119 + 11.9916i) q^{83} +(-6.61422 + 13.2831i) q^{85} +(0.0554970 - 0.0505922i) q^{86} +(1.31593 + 1.74258i) q^{88} +(1.77818 + 3.57106i) q^{89} +(-4.43666 - 0.829356i) q^{91} +(-0.0815357 + 0.0504848i) q^{92} +(7.32633 - 4.53627i) q^{94} +(-0.862645 - 9.30942i) q^{95} +(-10.0723 - 9.18211i) q^{97} +(-1.22757 + 0.475562i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - q^{2} - 3 q^{4} - 4 q^{5} + 4 q^{7} + 48 q^{8}+O(q^{10}) \) 128 * q - q^2 - 3 * q^4 - 4 * q^5 + 4 * q^7 + 48 * q^8	\( 128 q - q^{2} - 3 q^{4} - 4 q^{5} + 4 q^{7} + 48 q^{8} + 28 q^{10} + 13 q^{11} + 2 q^{13} + 51 q^{14} + 7 q^{16} - 6 q^{17} + 21 q^{19} + 43 q^{20} - 36 q^{22} - 15 q^{23} + 30 q^{25} - 7 q^{26} + 46 q^{28} - 16 q^{29} - 28 q^{31} + 8 q^{32} + 65 q^{34} + 37 q^{35} + 2 q^{37} - 30 q^{38} - 44 q^{40} + 84 q^{41} - 6 q^{43} + 62 q^{44} + 20 q^{47} - 56 q^{49} - 36 q^{50} - 86 q^{52} - 16 q^{53} + 8 q^{55} + 10 q^{56} + 32 q^{58} + 64 q^{59} + 4 q^{61} - 2 q^{62} - 58 q^{64} + 38 q^{65} - 8 q^{67} + 7 q^{68} - 140 q^{70} - 19 q^{71} + 60 q^{73} + 139 q^{74} - 76 q^{76} + 21 q^{77} + 12 q^{79} + 48 q^{80} + 207 q^{82} + 40 q^{83} - 85 q^{85} - 224 q^{86} + 87 q^{88} - 5 q^{89} - 48 q^{91} - 82 q^{92} - 214 q^{94} - 129 q^{95} - 61 q^{97} - 93 q^{98}+O(q^{100}) \) 128 * q - q^2 - 3 * q^4 - 4 * q^5 + 4 * q^7 + 48 * q^8 + 28 * q^10 + 13 * q^11 + 2 * q^13 + 51 * q^14 + 7 * q^16 - 6 * q^17 + 21 * q^19 + 43 * q^20 - 36 * q^22 - 15 * q^23 + 30 * q^25 - 7 * q^26 + 46 * q^28 - 16 * q^29 - 28 * q^31 + 8 * q^32 + 65 * q^34 + 37 * q^35 + 2 * q^37 - 30 * q^38 - 44 * q^40 + 84 * q^41 - 6 * q^43 + 62 * q^44 + 20 * q^47 - 56 * q^49 - 36 * q^50 - 86 * q^52 - 16 * q^53 + 8 * q^55 + 10 * q^56 + 32 * q^58 + 64 * q^59 + 4 * q^61 - 2 * q^62 - 58 * q^64 + 38 * q^65 - 8 * q^67 + 7 * q^68 - 140 * q^70 - 19 * q^71 + 60 * q^73 + 139 * q^74 - 76 * q^76 + 21 * q^77 + 12 * q^79 + 48 * q^80 + 207 * q^82 + 40 * q^83 - 85 * q^85 - 224 * q^86 + 87 * q^88 - 5 * q^89 - 48 * q^91 - 82 * q^92 - 214 * q^94 - 129 * q^95 - 61 * q^97 - 93 * q^98

Introduction

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