LMFDB - Embedded newform 675.2.y.a.154.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(19,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 27]))

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

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

chi := DirichletCharacter("675.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.y (of order $30$, degree $8$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			154.9
Character	$\chi$	$=$	675.154
Dual form			675.2.y.a.469.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.894901 + 0.805773i) q^{2} +(-0.0574783 + 0.546869i) q^{4} +(-2.23444 - 0.0854168i) q^{5} +(-2.32094 - 1.33999i) q^{7} +(-1.80485 - 2.48416i) q^{8} +O(q^{10})$	\(q+(-0.894901 + 0.805773i) q^{2} +(-0.0574783 + 0.546869i) q^{4} +(-2.23444 - 0.0854168i) q^{5} +(-2.32094 - 1.33999i) q^{7} +(-1.80485 - 2.48416i) q^{8} +(2.06843 - 1.72401i) q^{10} +(0.941029 + 1.04512i) q^{11} +(-0.120849 - 0.108813i) q^{13} +(3.15674 - 0.670987i) q^{14} +(2.54110 + 0.540127i) q^{16} +(-0.113531 - 0.156262i) q^{17} +(6.07397 - 4.41300i) q^{19} +(0.175143 - 1.21703i) q^{20} +(-1.68426 - 0.177022i) q^{22} +(1.22650 + 5.77024i) q^{23} +(4.98541 + 0.381717i) q^{25} +0.195827 q^{26} +(0.866205 - 1.19223i) q^{28} +(5.56680 - 2.47850i) q^{29} +(-0.549855 - 0.244811i) q^{31} +(2.60917 - 1.50640i) q^{32} +(0.227511 + 0.0483590i) q^{34} +(5.07153 + 3.19238i) q^{35} +(0.888903 - 0.288822i) q^{37} +(-1.87973 + 8.84344i) q^{38} +(3.82063 + 5.70486i) q^{40} +(-3.78427 + 4.20285i) q^{41} +(-5.91893 - 3.41730i) q^{43} +(-0.625632 + 0.454548i) q^{44} +(-5.74710 - 4.17551i) q^{46} +(-0.0890280 - 0.199960i) q^{47} +(0.0911727 + 0.157916i) q^{49} +(-4.76903 + 3.67551i) q^{50} +(0.0664527 - 0.0598343i) q^{52} +(7.64631 - 10.5242i) q^{53} +(-2.01340 - 2.41563i) q^{55} +(0.860180 + 8.18407i) q^{56} +(-2.98463 + 6.70358i) q^{58} +(3.97717 - 4.41709i) q^{59} +(9.43845 + 10.4825i) q^{61} +(0.689328 - 0.223976i) q^{62} +(-2.72670 + 8.39191i) q^{64} +(0.260735 + 0.253458i) q^{65} +(2.62723 - 5.90086i) q^{67} +(0.0919806 - 0.0531050i) q^{68} +(-7.11085 + 1.22964i) q^{70} +(-2.90460 - 2.11032i) q^{71} +(-11.0652 - 3.59530i) q^{73} +(-0.562756 + 0.974721i) q^{74} +(2.06421 + 3.57532i) q^{76} +(-0.783617 - 3.68663i) q^{77} +(12.4249 - 5.53192i) q^{79} +(-5.63178 - 1.42393i) q^{80} -6.81040i q^{82} +(14.5730 - 1.53168i) q^{83} +(0.240331 + 0.358856i) q^{85} +(8.05043 - 1.71117i) q^{86} +(0.897827 - 4.22394i) q^{88} +(3.38521 - 10.4186i) q^{89} +(0.134675 + 0.414486i) q^{91} +(-3.22606 + 0.339073i) q^{92} +(0.240794 + 0.107208i) q^{94} +(-13.9488 + 9.34174i) q^{95} +(-1.26033 - 2.83075i) q^{97} +(-0.208835 - 0.0678546i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.894901	+	0.805773i	−0.632791	+	0.569767i	−0.921851	−	0.387543i	$-0.873324\pi$
$2$	−0.894901	+	0.805773i	−0.632791	+	0.569767i	0.289061	+	0.957311i	$0.406657\pi$
$3$		0			0
$3$		0			0
$4$	−0.0574783	+	0.546869i	−0.0287391	+	0.273435i
$5$	−2.23444	−	0.0854168i	−0.999270	−	0.0381996i
$5$	−2.23444	−	0.0854168i	−0.999270	−	0.0381996i
$6$		0			0
$7$	−2.32094	−	1.33999i	−0.877233	−	0.506470i	−0.00748764	−	0.999972i	$-0.502383\pi$
$7$	−2.32094	−	1.33999i	−0.877233	−	0.506470i	−0.869745	+	0.493501i	$0.835717\pi$
$8$	−1.80485	−	2.48416i	−0.638110	−	0.878283i
$9$		0			0
$10$	2.06843	−	1.72401i	0.654094	−	0.545179i
$11$	0.941029	+	1.04512i	0.283731	+	0.315115i	0.868116	−	0.496361i	$-0.165331\pi$
$11$	0.941029	+	1.04512i	0.283731	+	0.315115i	−0.584385	+	0.811476i	$0.698664\pi$
$12$		0			0
$13$	−0.120849	−	0.108813i	−0.0335175	−	0.0301793i	0.652202	−	0.758045i	$-0.273846\pi$
$13$	−0.120849	−	0.108813i	−0.0335175	−	0.0301793i	−0.685719	+	0.727866i	$0.740512\pi$
$14$	3.15674	−	0.670987i	0.843675	−	0.179329i
$15$		0			0
$16$	2.54110	+	0.540127i	0.635274	+	0.135032i
$17$	−0.113531	−	0.156262i	−0.0275354	−	0.0378992i	0.795027	−	0.606574i	$-0.207456\pi$
$17$	−0.113531	−	0.156262i	−0.0275354	−	0.0378992i	−0.822563	+	0.568674i	$0.807456\pi$
$18$		0			0
$19$	6.07397	−	4.41300i	1.39346	−	1.01241i	0.397989	−	0.917390i	$-0.369708\pi$
$19$	6.07397	−	4.41300i	1.39346	−	1.01241i	0.995475	−	0.0950213i	$-0.0302919\pi$
$20$	0.175143	−	1.21703i	0.0391632	−	0.272137i
$21$		0			0
$22$	−1.68426	−	0.177022i	−0.359085	−	0.0377413i
$23$	1.22650	+	5.77024i	0.255743	+	1.20318i	0.899146	+	0.437649i	$0.144189\pi$
$23$	1.22650	+	5.77024i	0.255743	+	1.20318i	−0.643403	+	0.765528i	$0.722478\pi$
$24$		0			0
$25$	4.98541	+	0.381717i	0.997082	+	0.0763434i
$26$	0.195827			0.0384048
$27$		0			0
$28$	0.866205	−	1.19223i	0.163697	−	0.225310i
$29$	5.56680	−	2.47850i	1.03373	−	0.460245i	0.181486	−	0.983393i	$-0.441909\pi$
$29$	5.56680	−	2.47850i	1.03373	−	0.460245i	0.852242	+	0.523148i	$0.175243\pi$
$30$		0			0
$31$	−0.549855	−	0.244811i	−0.0987568	−	0.0439694i	0.356764	−	0.934195i	$-0.383880\pi$
$31$	−0.549855	−	0.244811i	−0.0987568	−	0.0439694i	−0.455520	+	0.890225i	$0.650547\pi$
$32$	2.60917	−	1.50640i	0.461240	−	0.266297i
$33$		0			0
$34$	0.227511	+	0.0483590i	0.0390178	+	0.00829350i
$35$	5.07153	+	3.19238i	0.857245	+	0.539611i
$36$		0			0
$37$	0.888903	−	0.288822i	0.146135	−	0.0474821i	−0.235036	−	0.971987i	$-0.575521\pi$
$37$	0.888903	−	0.288822i	0.146135	−	0.0474821i	0.381171	+	0.924505i	$0.375521\pi$
$38$	−1.87973	+	8.84344i	−0.304933	+	1.43460i
$39$		0			0
$40$	3.82063	+	5.70486i	0.604094	+	0.902017i
$41$	−3.78427	+	4.20285i	−0.591003	+	0.656376i	−0.962253	−	0.272158i	$-0.912263\pi$
$41$	−3.78427	+	4.20285i	−0.591003	+	0.656376i	0.371249	+	0.928533i	$0.378929\pi$
$42$		0			0
$43$	−5.91893	−	3.41730i	−0.902629	−	0.521133i	−0.0245768	−	0.999698i	$-0.507824\pi$
$43$	−5.91893	−	3.41730i	−0.902629	−	0.521133i	−0.878052	+	0.478565i	$0.841157\pi$
$44$	−0.625632	+	0.454548i	−0.0943175	+	0.0685257i
$45$		0			0
$46$	−5.74710	−	4.17551i	−0.847363	−	0.615645i
$47$	−0.0890280	−	0.199960i	−0.0129861	−	0.0291672i	0.906936	−	0.421268i	$-0.138415\pi$
$47$	−0.0890280	−	0.199960i	−0.0129861	−	0.0291672i	−0.919922	+	0.392101i	$0.871748\pi$
$48$		0			0
$49$	0.0911727	+	0.157916i	0.0130247	+	0.0225594i
$50$	−4.76903	+	3.67551i	−0.674442	+	0.519795i
$51$		0			0
$52$	0.0664527	−	0.0598343i	0.00921534	−	0.00829753i
$53$	7.64631	−	10.5242i	1.05030	−	1.44562i	0.161754	−	0.986831i	$-0.448285\pi$
$53$	7.64631	−	10.5242i	1.05030	−	1.44562i	0.888547	−	0.458785i	$-0.151715\pi$
$54$		0			0
$55$	−2.01340	−	2.41563i	−0.271486	−	0.325723i
$56$	0.860180	+	8.18407i	0.114946	+	1.09364i
$57$		0			0
$58$	−2.98463	+	6.70358i	−0.391901	+	0.880224i
$59$	3.97717	−	4.41709i	0.517783	−	0.575057i	−0.426376	−	0.904546i	$-0.640210\pi$
$59$	3.97717	−	4.41709i	0.517783	−	0.575057i	0.944159	+	0.329489i	$0.106877\pi$
$60$		0			0
$61$	9.43845	+	10.4825i	1.20847	+	1.34214i	0.923497	+	0.383606i	$0.125318\pi$
$61$	9.43845	+	10.4825i	1.20847	+	1.34214i	0.284972	+	0.958536i	$0.408016\pi$
$62$	0.689328	−	0.223976i	0.0875447	−	0.0284450i
$63$		0			0
$64$	−2.72670	+	8.39191i	−0.340837	+	1.04899i
$65$	0.260735	+	0.253458i	0.0323402	+	0.0314377i
$66$		0			0
$67$	2.62723	−	5.90086i	0.320967	−	0.720904i	−0.678945	−	0.734190i	$-0.737562\pi$
$67$	2.62723	−	5.90086i	0.320967	−	0.720904i	0.999912	+	0.0132854i	$0.00422899\pi$
$68$	0.0919806	−	0.0531050i	0.0111543	−	0.00643993i
$69$		0			0
$70$	−7.11085	+	1.22964i	−0.849910	+	0.146970i
$71$	−2.90460	−	2.11032i	−0.344713	−	0.250449i	0.401935	−	0.915668i	$-0.368338\pi$
$71$	−2.90460	−	2.11032i	−0.344713	−	0.250449i	−0.746648	+	0.665220i	$0.768338\pi$
$72$		0			0
$73$	−11.0652	−	3.59530i	−1.29508	−	0.420798i	−0.421215	−	0.906961i	$-0.638396\pi$
$73$	−11.0652	−	3.59530i	−1.29508	−	0.420798i	−0.873868	+	0.486163i	$0.838396\pi$
$74$	−0.562756	+	0.974721i	−0.0654190	+	0.113309i
$75$		0			0
$76$	2.06421	+	3.57532i	0.236781	+	0.410117i
$77$	−0.783617	−	3.68663i	−0.0893015	−	0.420130i
$78$		0			0
$79$	12.4249	−	5.53192i	1.39791	−	0.622390i	0.437053	−	0.899436i	$-0.356022\pi$
$79$	12.4249	−	5.53192i	1.39791	−	0.622390i	0.960857	+	0.277046i	$0.0893554\pi$
$80$	−5.63178	−	1.42393i	−0.629653	−	0.159200i
$81$		0			0
$82$		−	6.81040i		−	0.752083i
$83$	14.5730	−	1.53168i	1.59959	−	0.168124i	0.737668	−	0.675164i	$-0.235927\pi$
$83$	14.5730	−	1.53168i	1.59959	−	0.168124i	0.861922	+	0.507040i	$0.169260\pi$
$84$		0			0
$85$	0.240331	+	0.358856i	0.0260675	+	0.0389234i
$86$	8.05043	−	1.71117i	0.868100	−	0.184520i
$87$		0			0
$88$	0.897827	−	4.22394i	0.0957087	−	0.450274i
$89$	3.38521	−	10.4186i	0.358831	−	1.10437i	−0.594923	−	0.803783i	$-0.702817\pi$
$89$	3.38521	−	10.4186i	0.358831	−	1.10437i	0.953754	−	0.300587i	$-0.0971825\pi$
$90$		0			0
$91$	0.134675	+	0.414486i	0.0141177	+	0.0434499i
$92$	−3.22606	+	0.339073i	−0.336340	+	0.0353508i
$93$		0			0
$94$	0.240794	+	0.107208i	0.0248360	+	0.0110577i
$95$	−13.9488	+	9.34174i	−1.43112	+	0.958443i
$96$		0			0
$97$	−1.26033	−	2.83075i	−0.127967	−	0.287419i	0.838188	−	0.545382i	$-0.183615\pi$
$97$	−1.26033	−	2.83075i	−0.127967	−	0.287419i	−0.966155	+	0.257963i	$0.916949\pi$
$98$	−0.208835	−	0.0678546i	−0.0210955	−	0.00685435i
$99$		0			0
$100$	−0.495302	+	2.70443i	−0.0495302	+	0.270443i
$101$	−4.01857	+	6.96037i	−0.399863	+	0.692583i	−0.993709	−	0.111996i	$-0.964276\pi$
$101$	−4.01857	+	6.96037i	−0.399863	+	0.692583i	0.593846	+	0.804579i	$0.297609\pi$
$102$		0			0
$103$	−0.536843	−	0.0564245i	−0.0528968	−	0.00555967i	0.0780431	−	0.996950i	$-0.475133\pi$
$103$	−0.536843	−	0.0564245i	−0.0528968	−	0.00555967i	−0.130940	+	0.991390i	$0.541799\pi$
$104$	−0.0521947	+	0.496600i	−0.00511811	+	0.0486956i
$105$		0			0
$106$	1.63746	+	15.5794i	0.159044	+	1.51320i
$107$		−	0.671621i		−	0.0649281i	−0.999473	−	0.0324640i	$-0.989665\pi$
$107$		−	0.671621i		−	0.0649281i	0.999473	−	0.0324640i	$-0.0103354\pi$
$108$		0			0
$109$	4.32136	+	13.2998i	0.413911	+	1.27389i	0.913221	+	0.407464i	$0.133587\pi$
$109$	4.32136	+	13.2998i	0.413911	+	1.27389i	−0.499310	+	0.866423i	$0.666413\pi$
$110$	3.74824	+	0.539409i	0.357381	+	0.0514306i
$111$		0			0
$112$	−5.17397	−	4.65866i	−0.488894	−	0.440202i
$113$	2.75193	+	2.47785i	0.258880	+	0.233097i	0.788342	−	0.615237i	$-0.210940\pi$
$113$	2.75193	+	2.47785i	0.258880	+	0.233097i	−0.529462	+	0.848333i	$0.677606\pi$
$114$		0			0
$115$	−2.24766	−	12.9980i	−0.209596	−	1.21207i
$116$	1.03544	+	3.18677i	0.0961386	+	0.295884i
$117$		0			0
$118$			7.15756i			0.658907i
$119$	0.0541083	+	0.514807i	0.00496010	+	0.0471922i
$120$		0			0
$121$	0.943076	−	8.97277i	0.0857342	−	0.815706i
$122$	−16.8930	−	1.77552i	−1.52942	−	0.160748i
$123$		0			0
$124$	0.165484	−	0.286627i	0.0148609	−	0.0257399i
$125$	−11.1070	−	1.27876i	−0.993438	−	0.114376i
$126$		0			0
$127$	13.6104	+	4.42230i	1.20773	+	0.392416i	0.842600	−	0.538540i	$-0.181024\pi$
$127$	13.6104	+	4.42230i	1.20773	+	0.392416i	0.365132	+	0.930956i	$0.381024\pi$
$128$	−1.87101	−	4.20237i	−0.165376	−	0.371440i
$129$		0			0
$130$	−0.437562	−	0.0167269i	−0.0383768	−	0.00146705i
$131$	−10.6971	−	4.76265i	−0.934608	−	0.416114i	−0.117809	−	0.993036i	$-0.537587\pi$
$131$	−10.6971	−	4.76265i	−0.934608	−	0.416114i	−0.816799	+	0.576922i	$0.804254\pi$
$132$		0			0
$133$	−20.0107	+	2.10321i	−1.73515	+	0.182372i
$134$	2.40364	+	7.39763i	0.207643	+	0.639058i
$135$		0			0
$136$	−0.183274	+	0.564059i	−0.0157156	+	0.0483677i
$137$	4.27866	−	20.1295i	0.365550	−	1.71978i	−0.283447	−	0.958988i	$-0.591478\pi$
$137$	4.27866	−	20.1295i	0.365550	−	1.71978i	0.648997	−	0.760791i	$-0.275189\pi$
$138$		0			0
$139$	0.891271	−	0.189445i	0.0755966	−	0.0160686i	−0.169958	−	0.985451i	$-0.554363\pi$
$139$	0.891271	−	0.189445i	0.0755966	−	0.0160686i	0.245555	+	0.969383i	$0.421030\pi$
$140$	−2.03732	+	2.58997i	−0.172185	+	0.218893i
$141$		0			0
$142$	4.29977	−	0.451924i	0.360829	−	0.0379246i
$143$		−	0.228698i		−	0.0191247i
$144$		0			0
$145$	−12.6504	+	5.06254i	−1.05055	+	0.420421i
$146$	12.7993	−	5.69860i	1.05927	−	0.471619i
$147$		0			0
$148$	0.106855	+	0.502715i	0.00878345	+	0.0413229i
$149$	−10.6085	−	18.3745i	−0.869083	−	1.50530i	−0.862935	−	0.505315i	$-0.831376\pi$
$149$	−10.6085	−	18.3745i	−0.869083	−	1.50530i	−0.00614869	−	0.999981i	$-0.501957\pi$
$150$		0			0
$151$	−2.66528	+	4.61641i	−0.216898	+	0.375678i	−0.953858	−	0.300258i	$-0.902927\pi$
$151$	−2.66528	+	4.61641i	−0.216898	+	0.375678i	0.736960	+	0.675936i	$0.236260\pi$
$152$	−21.9252	−	7.12392i	−1.77837	−	0.577826i
$153$		0			0
$154$	3.67185	+	2.66775i	0.295886	+	0.214974i
$155$	1.20770	+	0.593982i	0.0970051	+	0.0477098i
$156$		0			0
$157$	−10.4979	+	6.06096i	−0.837823	+	0.483717i	−0.856524	−	0.516108i	$-0.827380\pi$
$157$	−10.4979	+	6.06096i	−0.837823	+	0.483717i	0.0187007	+	0.999825i	$0.494047\pi$
$158$	−6.66159	+	14.9622i	−0.529967	+	1.19033i
$159$		0			0
$160$	−5.95868	+	3.14309i	−0.471075	+	0.248483i
$161$	4.88545	−	15.0359i	0.385027	−	1.18499i
$162$		0			0
$163$	−0.508454	+	0.165207i	−0.0398252	+	0.0129400i	−0.328862	−	0.944378i	$-0.606665\pi$
$163$	−0.508454	+	0.165207i	−0.0398252	+	0.0129400i	0.289037	+	0.957318i	$0.406665\pi$
$164$	−2.08090	−	2.31107i	−0.162491	−	0.180464i
$165$		0			0
$166$	−11.8072	+	13.1132i	−0.916415	+	1.01778i
$167$	4.43413	−	9.95922i	0.343123	−	0.770668i	−0.656740	−	0.754117i	$-0.728065\pi$
$167$	4.43413	−	9.95922i	0.343123	−	0.770668i	0.999863	−	0.0165503i	$-0.00526835\pi$
$168$		0			0
$169$	−1.35611	−	12.9025i	−0.104316	−	0.992499i
$170$	−0.504228	−	0.127488i	−0.0386726	−	0.00977791i
$171$		0			0
$172$	2.20903	−	3.04046i	0.168437	−	0.231833i
$173$	−7.80136	+	7.02437i	−0.593126	+	0.534053i	−0.910104	−	0.414380i	$-0.863999\pi$
$173$	−7.80136	+	7.02437i	−0.593126	+	0.534053i	0.316978	+	0.948433i	$0.397332\pi$
$174$		0			0
$175$	−11.0593	−	7.56636i	−0.836007	−	0.571963i
$176$	1.82675	+	3.16402i	0.137696	+	0.238497i
$177$		0			0
$178$	5.36560	+	12.0513i	0.402169	+	0.903285i
$179$	11.1491	+	8.10027i	0.833321	+	0.605443i	0.920497	−	0.390750i	$-0.127784\pi$
$179$	11.1491	+	8.10027i	0.833321	+	0.605443i	−0.0871761	+	0.996193i	$0.527784\pi$
$180$		0			0
$181$	−5.95243	+	4.32469i	−0.442441	+	0.321452i	−0.786604	−	0.617458i	$-0.788163\pi$
$181$	−5.95243	+	4.32469i	−0.442441	+	0.321452i	0.344163	+	0.938910i	$0.388163\pi$
$182$	−0.454502	−	0.262407i	−0.0336899	−	0.0194509i
$183$		0			0
$184$	12.1205	−	13.4612i	0.893538	−	0.992374i
$185$	−2.01087	+	0.569427i	−0.147842	+	0.0418651i
$186$		0			0
$187$	0.0564765	−	0.265701i	0.00412997	−	0.0194300i
$188$	0.114469	−	0.0371933i	0.00834852	−	0.00271260i
$189$		0			0
$190$	4.95552	−	19.5995i	0.359511	−	1.42190i
$191$	1.09062	+	0.231818i	0.0789142	+	0.0167737i	0.247200	−	0.968965i	$-0.420490\pi$
$191$	1.09062	+	0.231818i	0.0789142	+	0.0167737i	−0.168285	+	0.985738i	$0.553823\pi$
$192$		0			0
$193$	21.9469	−	12.6711i	1.57977	−	0.912083i	0.584884	−	0.811117i	$-0.301140\pi$
$193$	21.9469	−	12.6711i	1.57977	−	0.912083i	0.994890	−	0.100966i	$-0.0321934\pi$
$194$	3.40881	+	1.51770i	0.244738	+	0.108965i
$195$		0			0
$196$	−0.0915997	+	0.0407828i	−0.00654284	+	0.00291306i
$197$	−9.37839	+	12.9082i	−0.668182	+	0.919674i	−0.999717	−	0.0237688i	$-0.992433\pi$
$197$	−9.37839	+	12.9082i	−0.668182	+	0.919674i	0.331535	+	0.943443i	$0.392433\pi$
$198$		0			0
$199$	−19.2943			−1.36774			−0.683868	−	0.729606i	$-0.739704\pi$
$199$	−19.2943			−1.36774			−0.683868	+	0.729606i	$0.739704\pi$
$200$	−8.04965	−	13.0735i	−0.569196	−	0.924435i
$201$		0			0
$202$	−2.01225	−	9.46690i	−0.141582	−	0.666089i
$203$	−16.2414	−	1.70704i	−1.13992	−	0.119810i
$204$		0			0
$205$	8.81470	−	9.06777i	0.615645	−	0.633320i
$206$	0.525887	−	0.382080i	0.0366403	−	0.0266207i
$207$		0			0
$208$	−0.248317	−	0.341779i	−0.0172177	−	0.0236981i
$209$	10.3279	+	2.19526i	0.714395	+	0.151849i
$210$		0			0
$211$	−2.96507	+	0.630245i	−0.204124	+	0.0433879i	−0.308839	−	0.951114i	$-0.599940\pi$
$211$	−2.96507	+	0.630245i	−0.204124	+	0.0433879i	0.104715	+	0.994502i	$0.466607\pi$
$212$	5.31589	+	4.78645i	0.365097	+	0.328735i
$213$		0			0
$214$	0.541174	+	0.601035i	0.0369939	+	0.0410859i
$215$	12.9336	+	8.14131i	0.882063	+	0.555233i
$216$		0			0
$217$	0.948134	+	1.30499i	0.0643635	+	0.0885888i
$218$	−14.5838	−	8.41995i	−0.987738	−	0.570271i
$219$		0			0
$220$	1.43676	−	0.962219i	0.0968663	−	0.0648728i
$221$	−0.00328323	+	0.0312379i	−0.000220854	+	0.00210129i
$222$		0			0
$223$	−13.5387	+	12.1903i	−0.906616	+	0.816321i	−0.983535	−	0.180716i	$-0.942158\pi$
$223$	−13.5387	+	12.1903i	−0.906616	+	0.816321i	0.0769189	+	0.997037i	$0.475492\pi$
$224$	−8.07429			−0.539486
$225$		0			0
$226$	−4.45929			−0.296628
$227$	6.28780	−	5.66156i	0.417336	−	0.375771i	−0.433543	−	0.901133i	$-0.642737\pi$
$227$	6.28780	−	5.66156i	0.417336	−	0.375771i	0.850879	+	0.525362i	$0.176070\pi$
$228$		0			0
$229$	1.02248	−	9.72823i	0.0675673	−	0.642860i	−0.907363	−	0.420348i	$-0.861908\pi$
$229$	1.02248	−	9.72823i	0.0675673	−	0.642860i	0.974930	−	0.222511i	$-0.0714255\pi$
$230$	12.4849	+	9.82081i	0.823227	+	0.647565i
$231$		0			0
$232$	−16.2042	−	9.35550i	−1.06386	−	0.614218i
$233$	1.49631	+	2.05949i	0.0980263	+	0.134922i	0.855213	−	0.518277i	$-0.173427\pi$
$233$	1.49631	+	2.05949i	0.0980263	+	0.134922i	−0.757186	+	0.653199i	$0.773427\pi$
$234$		0			0
$235$	0.181847	+	0.454403i	0.0118624	+	0.0296420i
$236$	2.18697	+	2.42888i	0.142360	+	0.158107i
$237$		0			0
$238$	−0.463239	−	0.417102i	−0.0300273	−	0.0270367i
$239$	10.3206	−	2.19372i	0.667586	−	0.141900i	0.138362	−	0.990382i	$-0.455816\pi$
$239$	10.3206	−	2.19372i	0.667586	−	0.141900i	0.529224	+	0.848482i	$0.322483\pi$
$240$		0			0
$241$	3.00671	+	0.639097i	0.193680	+	0.0411679i	0.303730	−	0.952758i	$-0.401768\pi$
$241$	3.00671	+	0.639097i	0.193680	+	0.0411679i	−0.110050	+	0.993926i	$0.535101\pi$
$242$	6.38605	+	8.78965i	0.410511	+	0.565020i
$243$		0			0
$244$	−6.27504	+	4.55908i	−0.401718	+	0.291865i
$245$	−0.190231	−	0.360640i	−0.0121534	−	0.0230405i
$246$		0			0
$247$	−1.21423	−	0.127620i	−0.0772594	−	0.00812029i
$248$	0.384254	+	1.80777i	0.0244002	+	0.114794i
$249$		0			0
$250$	10.9700	−	7.80533i	0.693806	−	0.493652i
$251$	23.8819			1.50741			0.753707	−	0.657211i	$-0.228264\pi$
$251$	23.8819			1.50741			0.753707	+	0.657211i	$0.228264\pi$
$252$		0			0
$253$	−4.87640	+	6.71180i	−0.306577	+	0.421967i
$254$	−15.7434	+	7.00940i	−0.987827	+	0.439809i
$255$		0			0
$256$	−11.0613	−	4.92482i	−0.691333	−	0.307801i
$257$	−4.15137	+	2.39680i	−0.258955	+	0.149508i	−0.623858	−	0.781538i	$-0.714436\pi$
$257$	−4.15137	+	2.39680i	−0.258955	+	0.149508i	0.364903	+	0.931046i	$0.381102\pi$
$258$		0			0
$259$	−2.45011	−	0.520787i	−0.152242	−	0.0323601i
$260$	−0.153595	+	0.128020i	−0.00952557	+	0.00793945i
$261$		0			0
$262$	13.4104	−	4.35732i	0.828500	−	0.269196i
$263$	−4.83640	+	22.7535i	−0.298225	+	1.40304i	0.532535	+	0.846408i	$0.321239\pi$
$263$	−4.83640	+	22.7535i	−0.298225	+	1.40304i	−0.830760	+	0.556631i	$0.812094\pi$
$264$		0			0
$265$	−17.9841	+	22.8626i	−1.10476	+	1.40444i
$266$	16.2129	−	18.0063i	0.994077	−	1.10403i
$267$		0			0
$268$	3.07599	+	1.77592i	0.187896	+	0.108482i
$269$	−6.79619	+	4.93772i	−0.414371	+	0.301058i	−0.775369	−	0.631508i	$-0.782436\pi$
$269$	−6.79619	+	4.93772i	−0.414371	+	0.301058i	0.360998	+	0.932567i	$0.382436\pi$
$270$		0			0
$271$	16.4715	+	11.9673i	1.00058	+	0.726960i	0.962211	−	0.272304i	$-0.0877855\pi$
$271$	16.4715	+	11.9673i	1.00058	+	0.726960i	0.0383636	+	0.999264i	$0.487785\pi$
$272$	−0.204092	−	0.458399i	−0.0123749	−	0.0277945i
$273$		0			0
$274$	12.3908	+	21.4615i	0.748557	+	1.29654i
$275$	4.29247	+	5.56955i	0.258846	+	0.335856i
$276$		0			0
$277$	−7.58456	+	6.82917i	−0.455712	+	0.410325i	−0.864758	−	0.502189i	$-0.832528\pi$
$277$	−7.58456	+	6.82917i	−0.455712	+	0.410325i	0.409046	+	0.912514i	$0.365862\pi$
$278$	−0.644950	+	0.887697i	−0.0386815	+	0.0532405i
$279$		0			0
$280$	−1.22296	−	18.3602i	−0.0730859	−	1.09723i
$281$	2.45064	+	23.3163i	0.146193	+	1.39093i	0.784011	+	0.620747i	$0.213171\pi$
$281$	2.45064	+	23.3163i	0.146193	+	1.39093i	−0.637818	+	0.770187i	$0.720163\pi$
$282$		0			0
$283$	6.59912	−	14.8219i	0.392277	−	0.881069i	−0.604171	−	0.796855i	$-0.706495\pi$
$283$	6.59912	−	14.8219i	0.392277	−	0.881069i	0.996448	−	0.0842137i	$-0.0268378\pi$
$284$	1.32102	−	1.46714i	0.0783881	−	0.0870588i
$285$		0			0
$286$	0.184279	+	0.204662i	0.0108966	+	0.0121019i
$287$	14.4149	−	4.68367i	0.850882	−	0.276468i
$288$		0			0
$289$	5.24176	−	16.1325i	0.308339	−	0.948969i
$290$	7.24156	−	14.7238i	0.425239	−	0.864611i
$291$		0			0
$292$	2.60217	−	5.84456i	0.152280	−	0.342027i
$293$	−2.77885	+	1.60437i	−0.162342	+	0.0937283i	−0.578970	−	0.815349i	$-0.696545\pi$
$293$	−2.77885	+	1.60437i	−0.162342	+	0.0937283i	0.416628	+	0.909077i	$0.363212\pi$
$294$		0			0
$295$	−9.26402	+	9.53000i	−0.539372	+	0.554858i
$296$	−2.32181	−	1.68690i	−0.134953	−	0.0980489i
$297$		0			0
$298$	24.2992	+	7.89530i	1.40762	+	0.457363i
$299$	0.479656	−	0.830788i	0.0277392	−	0.0480457i
$300$		0			0
$301$	9.15833	+	15.8627i	0.527877	+	0.914310i
$302$	−1.33461	−	6.27884i	−0.0767981	−	0.361307i
$303$		0			0
$304$	17.8181	−	7.93314i	1.02194	−	0.454997i
$305$	−20.1942	−	24.2286i	−1.15632	−	1.38732i
$306$		0			0
$307$			16.5271i			0.943250i	0.881799	+	0.471625i	$0.156332\pi$
$307$			16.5271i			0.943250i	−0.881799	+	0.471625i	$0.843668\pi$
$308$	2.06115	−	0.216635i	0.117445	−	0.0123439i
$309$		0			0
$310$	−1.55939	+	0.441580i	−0.0885674	+	0.0250801i
$311$	18.3936	−	3.90968i	1.04301	−	0.221698i	0.345606	−	0.938380i	$-0.387673\pi$
$311$	18.3936	−	3.90968i	1.04301	−	0.221698i	0.697400	+	0.716682i	$0.254340\pi$
$312$		0			0
$313$	0.657406	−	3.09285i	0.0371588	−	0.174818i	−0.955655	−	0.294489i	$-0.904851\pi$
$313$	0.657406	−	3.09285i	0.0371588	−	0.174818i	0.992814	+	0.119671i	$0.0381839\pi$
$314$	4.51082	−	13.8829i	0.254560	−	0.783456i
$315$		0			0
$316$	2.31108	+	7.11276i	0.130008	+	0.400124i
$317$	−0.398908	+	0.0419269i	−0.0224049	+	0.00235485i	−0.115724	−	0.993281i	$-0.536919\pi$
$317$	−0.398908	+	0.0419269i	−0.0224049	+	0.00235485i	0.0933194	+	0.995636i	$0.470252\pi$
$318$		0			0
$319$	7.82884	+	3.48562i	0.438331	+	0.195157i
$320$	6.80944	−	18.5183i	0.380659	−	1.03520i
$321$		0			0
$322$	7.74350	+	17.3922i	0.431528	+	0.969229i
$323$	−1.37917	−	0.448120i	−0.0767391	−	0.0249340i
$324$		0			0
$325$	−0.560947	−	0.588608i	−0.0311157	−	0.0326501i
$326$	0.321897	−	0.557543i	0.0178282	−	0.0308794i
$327$		0			0
$328$	17.2706	+	1.81521i	0.953608	+	0.100228i
$329$	−0.0613170	+	0.583392i	−0.00338052	+	0.0321635i
$330$		0			0
$331$	−2.52674	−	24.0403i	−0.138882	−	1.32138i	−0.812789	−	0.582559i	$-0.802052\pi$
$331$	−2.52674	−	24.0403i	−0.138882	−	1.32138i	0.673906	−	0.738817i	$-0.264615\pi$
$332$			8.05754i			0.442215i
$333$		0			0
$334$	4.05676	+	12.4854i	0.221976	+	0.683172i
$335$	−6.37441	+	12.9607i	−0.348271	+	0.708117i
$336$		0			0
$337$	24.8166	+	22.3450i	1.35185	+	1.21721i	0.954018	+	0.299750i	$0.0969032\pi$
$337$	24.8166	+	22.3450i	1.35185	+	1.21721i	0.397830	+	0.917459i	$0.369763\pi$
$338$	11.6101	+	10.4537i	0.631504	+	0.568608i
$339$		0			0
$340$	−0.210061	+	0.110803i	−0.0113921	+	0.00600914i
$341$	−0.261573	−	0.805038i	−0.0141649	−	0.0435952i
$342$		0			0
$343$			18.2712i			0.986554i
$344$	2.19366	+	20.8713i	0.118274	+	1.12530i
$345$		0			0
$346$	1.32140	−	12.5722i	0.0710387	−	0.675888i
$347$	3.72354	+	0.391360i	0.199890	+	0.0210093i	0.203944	−	0.978982i	$-0.434624\pi$
$347$	3.72354	+	0.391360i	0.199890	+	0.0210093i	−0.00405417	+	0.999992i	$0.501290\pi$
$348$		0			0
$349$	−8.67752	+	15.0299i	−0.464497	+	0.804532i	−0.999179	−	0.0405213i	$-0.987098\pi$
$349$	−8.67752	+	15.0299i	−0.464497	+	0.804532i	0.534682	+	0.845053i	$0.320431\pi$
$350$	15.9938	−	2.14016i	0.854904	−	0.114396i
$351$		0			0
$352$	4.02967	+	1.30932i	0.214782	+	0.0697869i
$353$	2.24699	+	5.04682i	0.119595	+	0.268615i	0.963416	−	0.268009i	$-0.0863659\pi$
$353$	2.24699	+	5.04682i	0.119595	+	0.268615i	−0.843821	+	0.536624i	$0.819699\pi$
$354$		0			0
$355$	6.30990	+	4.96347i	0.334895	+	0.263434i
$356$	5.50304	+	2.45011i	0.291660	+	0.129856i
$357$		0			0
$358$	−16.5043	+	1.73467i	−0.872279	+	0.0916803i
$359$	4.30244	+	13.2416i	0.227074	+	0.698863i	0.998074	+	0.0620276i	$0.0197567\pi$
$359$	4.30244	+	13.2416i	0.227074	+	0.698863i	−0.771000	+	0.636835i	$0.780243\pi$
$360$		0			0
$361$	11.5473	−	35.5388i	0.607750	−	1.87046i
$362$	1.84212	−	8.66648i	0.0968196	−	0.455500i
$363$		0			0
$364$	−0.234410	+	0.0498255i	−0.0122864	+	0.00261156i
$365$	24.4174	+	8.97862i	1.27806	+	0.469963i
$366$		0			0
$367$	36.4865	−	3.83489i	1.90458	−	0.200179i	0.922153	−	0.386825i	$-0.126428\pi$
$367$	36.4865	−	3.83489i	1.90458	−	0.200179i	0.982427	+	0.186645i	$0.0597615\pi$
$368$			15.3252i			0.798881i
$369$		0			0
$370$	1.34070	−	2.12988i	0.0696996	−	0.110727i
$371$	−31.8491	+	14.1801i	−1.65352	+	0.736195i
$372$		0			0
$373$	−3.88898	−	18.2962i	−0.201364	−	0.947342i	−0.956491	−	0.291763i	$-0.905758\pi$
$373$	−3.88898	−	18.2962i	−0.201364	−	0.947342i	0.755127	−	0.655579i	$-0.227575\pi$
$374$	0.163554	+	0.283283i	0.00845716	+	0.0146482i
$375$		0			0
$376$	−0.336051	+	0.582057i	−0.0173305	+	0.0300173i
$377$	−0.942436	−	0.306216i	−0.0485379	−	0.0157709i
$378$		0			0
$379$	1.54812	+	1.12477i	0.0795216	+	0.0577758i	0.626836	−	0.779151i	$-0.284350\pi$
$379$	1.54812	+	1.12477i	0.0795216	+	0.0577758i	−0.547314	+	0.836927i	$0.684350\pi$
$380$	−4.30696	−	8.16514i	−0.220942	−	0.418863i
$381$		0			0
$382$	−1.16279	+	0.671335i	−0.0594933	+	0.0343485i
$383$	3.92887	−	8.82440i	0.200756	−	0.450906i	−0.784911	−	0.619609i	$-0.787291\pi$
$383$	3.92887	−	8.82440i	0.200756	−	0.450906i	0.985667	+	0.168703i	$0.0539579\pi$
$384$		0			0
$385$	1.43604	+	8.30447i	0.0731875	+	0.423235i
$386$	−9.43034	+	29.0236i	−0.479991	+	1.47726i
$387$		0			0
$388$	1.62049	−	0.526529i	0.0822680	−	0.0267305i
$389$	−15.2919	−	16.9834i	−0.775332	−	0.861093i	0.218052	−	0.975937i	$-0.430030\pi$
$389$	−15.2919	−	16.9834i	−0.775332	−	0.861093i	−0.993384	+	0.114844i	$0.963363\pi$
$390$		0			0
$391$	0.762424	−	0.846758i	0.0385574	−	0.0428224i
$392$	0.227735	−	0.511501i	0.0115024	−	0.0258347i
$393$		0			0
$394$	−2.00838	−	19.1085i	−0.101181	−	0.962670i
$395$	−28.2352	+	11.2994i	−1.42066	+	0.568536i
$396$		0			0
$397$	5.64077	−	7.76385i	0.283102	−	0.389657i	−0.643656	−	0.765315i	$-0.722583\pi$
$397$	5.64077	−	7.76385i	0.283102	−	0.389657i	0.926758	+	0.375658i	$0.122583\pi$
$398$	17.2665	−	15.5468i	0.865491	−	0.779291i
$399$		0			0
$400$	12.4622	+	3.66273i	0.623112	+	0.183137i
$401$	3.09035	+	5.35264i	0.154325	+	0.267298i	0.932813	−	0.360361i	$-0.117347\pi$
$401$	3.09035	+	5.35264i	0.154325	+	0.267298i	−0.778488	+	0.627659i	$0.784013\pi$
$402$		0			0
$403$	0.0398109	+	0.0894166i	0.00198312	+	0.00445416i
$404$	−3.57543	−	2.59770i	−0.177884	−	0.129241i
$405$		0			0
$406$	15.9099	−	11.5592i	0.789595	−	0.573675i
$407$	1.13834	+	0.657219i	0.0564252	+	0.0325771i
$408$		0			0
$409$	−1.96923	+	2.18705i	−0.0973722	+	0.108143i	−0.789861	−	0.613286i	$-0.789847\pi$
$409$	−1.96923	+	2.18705i	−0.0973722	+	0.108143i	0.692489	+	0.721428i	$0.256514\pi$
$410$	−0.581723	+	15.2174i	−0.0287292	+	0.751534i
$411$		0			0
$412$	0.0617137	−	0.290340i	0.00304041	−	0.0143040i
$413$	−15.1497	+	4.92242i	−0.745466	+	0.242216i
$414$		0			0
$415$	−32.6932	+	2.17766i	−1.60484	+	0.106897i
$416$	−0.479232	−	0.101864i	−0.0234963	−	0.00499429i
$417$		0			0
$418$	−11.0113	+	6.35739i	−0.538581	+	0.310950i
$419$	−5.57816	−	2.48356i	−0.272511	−	0.121330i	0.265932	−	0.963992i	$-0.414320\pi$
$419$	−5.57816	−	2.48356i	−0.272511	−	0.121330i	−0.538443	+	0.842662i	$0.680987\pi$
$420$		0			0
$421$	1.22140	−	0.543804i	0.0595276	−	0.0265034i	−0.376757	−	0.926312i	$-0.622961\pi$
$421$	1.22140	−	0.543804i	0.0595276	−	0.0265034i	0.436285	+	0.899809i	$0.356294\pi$
$422$	2.14561	−	2.95318i	0.104447	−	0.143759i
$423$		0			0
$424$	−39.9443			−1.93987
$425$	−0.506351	−	0.822368i	−0.0245617	−	0.0398907i
$426$		0			0
$427$	−7.85962	−	36.9766i	−0.380354	−	1.78942i
$428$	0.367289	+	0.0386036i	0.0177536	+	0.00186598i
$429$		0			0
$430$	−18.1343	+	3.13586i	−0.874515	+	0.151225i
$431$	26.8953	−	19.5406i	1.29550	−	0.941237i	0.295600	−	0.955312i	$-0.404480\pi$
$431$	26.8953	−	19.5406i	1.29550	−	0.941237i	0.999901	+	0.0140751i	$0.00448038\pi$
$432$		0			0
$433$	−6.84957	−	9.42763i	−0.329169	−	0.453063i	0.612070	−	0.790804i	$-0.290337\pi$
$433$	−6.84957	−	9.42763i	−0.329169	−	0.453063i	−0.941239	+	0.337741i	$0.890337\pi$
$434$	−1.90002	−	0.403861i	−0.0912037	−	0.0193859i
$435$		0			0
$436$	−7.52162	+	1.59877i	−0.360220	+	0.0765672i
$437$	32.9138	+	29.6357i	1.57448	+	1.41767i
$438$		0			0
$439$	−14.8478	−	16.4901i	−0.708646	−	0.787031i	0.276081	−	0.961134i	$-0.410964\pi$
$439$	−14.8478	−	16.4901i	−0.708646	−	0.787031i	−0.984727	+	0.174103i	$0.944297\pi$
$440$	−2.36693	+	9.36144i	−0.112839	+	0.446289i
$441$		0			0
$442$	−0.0222324	−	0.0306003i	−0.00105749	−	0.00145551i
$443$	6.90522	+	3.98673i	0.328077	+	0.189415i	0.654987	−	0.755640i	$-0.272674\pi$
$443$	6.90522	+	3.98673i	0.328077	+	0.189415i	−0.326910	+	0.945055i	$0.606007\pi$
$444$		0			0
$445$	−8.45396	+	22.9905i	−0.400756	+	1.08986i
$446$	2.29318	−	21.8182i	0.108585	−	1.03312i
$447$		0			0
$448$	17.5736	−	15.8234i	0.830276	−	0.747583i
$449$	−19.4821			−0.919419			−0.459710	−	0.888069i	$-0.652047\pi$
$449$	−19.4821			−0.919419			−0.459710	+	0.888069i	$0.652047\pi$
$450$		0			0
$451$	−7.95358			−0.374520
$452$	−1.51324	+	1.36252i	−0.0711767	+	0.0640878i
$453$		0			0
$454$	−1.06503	+	10.1331i	−0.0499843	+	0.475569i
$455$	−0.265518	−	0.937646i	−0.0124477	−	0.0439575i
$456$		0			0
$457$	−15.0307	−	8.67800i	−0.703108	−	0.405940i	0.105396	−	0.994430i	$-0.466389\pi$
$457$	−15.0307	−	8.67800i	−0.703108	−	0.405940i	−0.808504	+	0.588491i	$0.799722\pi$
$458$	6.92373	+	9.52970i	0.323525	+	0.445293i
$459$		0			0
$460$	7.23739	−	0.482076i	0.337445	−	0.0224769i
$461$	−19.9699	−	22.1788i	−0.930089	−	1.03297i	−0.999374	−	0.0353718i	$-0.988738\pi$
$461$	−19.9699	−	22.1788i	−0.930089	−	1.03297i	0.0692850	−	0.997597i	$-0.477928\pi$
$462$		0			0
$463$	8.67871	+	7.81435i	0.403334	+	0.363163i	0.845689	−	0.533677i	$-0.179190\pi$
$463$	8.67871	+	7.81435i	0.403334	+	0.363163i	−0.442355	+	0.896840i	$0.645857\pi$
$464$	15.4845	−	3.29133i	0.718849	−	0.152796i
$465$		0			0
$466$	−2.99853	−	0.637357i	−0.138904	−	0.0295250i
$467$	8.44207	+	11.6195i	0.390652	+	0.537687i	0.958367	−	0.285538i	$-0.0921724\pi$
$467$	8.44207	+	11.6195i	0.390652	+	0.537687i	−0.567715	+	0.823225i	$0.692172\pi$
$468$		0			0
$469$	−14.0048	+	10.1751i	−0.646680	+	0.469840i
$470$	−0.528881	−	0.260118i	−0.0243954	−	0.0119983i
$471$		0			0
$472$	−18.1509	−	1.90774i	−0.835465	−	0.0878109i
$473$	−1.99841	−	9.40176i	−0.0918868	−	0.432293i
$474$		0			0
$475$	31.9657	−	19.6821i	1.46669	−	0.903075i
$476$	−0.284642			−0.0130465
$477$		0			0
$478$	−7.46831	+	10.2792i	−0.341592	+	0.470162i
$479$	−4.69795	+	2.09166i	−0.214655	+	0.0955705i	−0.511247	−	0.859434i	$-0.670816\pi$
$479$	−4.69795	+	2.09166i	−0.214655	+	0.0955705i	0.296592	+	0.955004i	$0.404150\pi$
$480$		0			0
$481$	−0.138851	−	0.0618204i	−0.00633105	−	0.00281877i
$482$	−3.20568	+	1.85080i	−0.146015	+	0.0843016i
$483$		0			0
$484$	4.85272	+	1.03148i	0.220578	+	0.0468854i
$485$	2.57433	+	6.43278i	0.116895	+	0.292098i
$486$		0			0
$487$	38.7356	−	12.5860i	1.75528	−	0.570324i	0.758584	−	0.651575i	$-0.225892\pi$
$487$	38.7356	−	12.5860i	1.75528	−	0.570324i	0.996694	+	0.0812511i	$0.0258916\pi$
$488$	9.00514	−	42.3658i	0.407643	−	1.91781i
$489$		0			0
$490$	0.460832	+	0.169455i	0.0208183	+	0.00765518i
$491$	−26.8216	+	29.7884i	−1.21044	+	1.34433i	−0.288271	+	0.957549i	$0.593080\pi$
$491$	−26.8216	+	29.7884i	−1.21044	+	1.34433i	−0.922171	+	0.386783i	$0.873586\pi$
$492$		0			0
$493$	−1.01930	−	0.588493i	−0.0459070	−	0.0265044i
$494$	1.18945	−	0.864183i	0.0535157	−	0.0388814i
$495$		0			0
$496$	−1.26501	−	0.919080i	−0.0568004	−	0.0412679i
$497$	3.91359	+	8.79008i	0.175549	+	0.394289i
$498$		0			0
$499$	14.6136	+	25.3114i	0.654193	+	1.13310i	0.982096	+	0.188384i	$0.0603249\pi$
$499$	14.6136	+	25.3114i	0.654193	+	1.13310i	−0.327903	+	0.944712i	$0.606342\pi$
$500$	1.33772	−	6.00056i	0.0598248	−	0.268353i
$501$		0			0
$502$	−21.3720	+	19.2434i	−0.953878	+	0.858875i
$503$	−4.96862	+	6.83872i	−0.221540	+	0.304923i	−0.905291	−	0.424792i	$-0.860347\pi$
$503$	−4.96862	+	6.83872i	−0.221540	+	0.304923i	0.683751	+	0.729715i	$0.260347\pi$
$504$		0			0
$505$	9.57377	−	15.2092i	0.426027	−	0.676803i
$506$	−1.04428	−	9.93567i	−0.0464240	−	0.441694i
$507$		0			0
$508$	−3.20072	+	7.18895i	−0.142009	+	0.318958i
$509$	−8.40814	+	9.33819i	−0.372684	+	0.413908i	−0.900089	−	0.435706i	$-0.856499\pi$
$509$	−8.40814	+	9.33819i	−0.372684	+	0.413908i	0.527404	+	0.849614i	$0.323165\pi$
$510$		0			0
$511$	20.8640	+	23.1718i	0.922968	+	1.02506i
$512$	22.6169	−	7.34868i	0.999536	−	0.324769i
$513$		0			0
$514$	1.78380	−	5.48996i	0.0786799	−	0.242152i
$515$	1.19472	+	0.171932i	0.0526458	+	0.00757625i
$516$		0			0
$517$	0.125204	−	0.281213i	0.00550647	−	0.0123677i
$518$	2.61224	−	1.50818i	0.114775	−	0.0662656i
$519$		0			0
$520$	0.159044	−	1.10516i	0.00697453	−	0.0484646i
$521$	−15.5846	−	11.3229i	−0.682773	−	0.496063i	0.191504	−	0.981492i	$-0.438664\pi$
$521$	−15.5846	−	11.3229i	−0.682773	−	0.496063i	−0.874276	+	0.485429i	$0.838664\pi$
$522$		0			0
$523$	24.3250	+	7.90367i	1.06366	+	0.345604i	0.788015	−	0.615656i	$-0.211109\pi$
$523$	24.3250	+	7.90367i	1.06366	+	0.345604i	0.275644	+	0.961260i	$0.411109\pi$
$524$	3.21939	−	5.57615i	0.140640	−	0.243595i
$525$		0			0
$526$	−14.0060	−	24.2591i	−0.610692	−	1.05775i
$527$	0.0241709	+	0.113715i	0.00105290	+	0.00495352i
$528$		0			0
$529$	−10.7798	+	4.79946i	−0.468685	+	0.208672i
$530$	−2.32805	−	34.9509i	−0.101124	−	1.51817i
$531$		0			0
$532$		−	11.0641i		−	0.479691i
$533$	0.914651	−	0.0961337i	0.0396179	−	0.00416401i
$534$		0			0
$535$	−0.0573678	+	1.50069i	−0.00248022	+	0.0648807i
$536$	−19.4004	+	4.12368i	−0.837970	+	0.178116i
$537$		0			0
$538$	2.10324	−	9.89496i	0.0906771	−	0.426602i
$539$	−0.0792445	+	0.243890i	−0.00341330	+	0.0105051i
$540$		0			0
$541$	−11.8581	−	36.4956i	−0.509821	−	1.56907i	−0.792511	−	0.609858i	$-0.791227\pi$
$541$	−11.8581	−	36.4956i	−0.509821	−	1.56907i	0.282690	−	0.959211i	$-0.408773\pi$
$542$	−24.3833	+	2.56279i	−1.04735	+	0.110081i
$543$		0			0
$544$	−0.531616	−	0.236690i	−0.0227928	−	0.0101480i
$545$	−8.51977	−	30.0866i	−0.364947	−	1.28877i
$546$		0			0
$547$	12.7170	+	28.5628i	0.543739	+	1.22126i	0.951353	+	0.308104i	$0.0996944\pi$
$547$	12.7170	+	28.5628i	0.543739	+	1.22126i	−0.407613	+	0.913155i	$0.633639\pi$
$548$	10.7623	+	3.49687i	0.459741	+	0.149379i
$549$		0			0
$550$	−8.32913	−	1.52544i	−0.355155	−	0.0650449i
$551$	22.8750	−	39.6206i	0.974506	−	1.68789i
$552$		0			0
$553$	−36.2502	−	3.81005i	−1.54151	−	0.162020i
$554$	1.28468	−	12.2229i	0.0545806	−	0.519300i
$555$		0			0
$556$	0.0523732	+	0.498298i	0.00222112	+	0.0211325i
$557$			24.3166i			1.03033i	0.857091	+	0.515165i	$0.172269\pi$
$557$			24.3166i			1.03033i	−0.857091	+	0.515165i	$0.827731\pi$
$558$		0			0
$559$	0.343452	+	1.05704i	0.0145265	+	0.0447078i
$560$	11.1630	+	10.8514i	0.471721	+	0.458556i
$561$		0			0
$562$	−20.9807	−	18.8911i	−0.885019	−	0.796874i
$563$	−12.1037	−	10.8982i	−0.510109	−	0.459304i	0.373432	−	0.927657i	$-0.378181\pi$
$563$	−12.1037	−	10.8982i	−0.510109	−	0.459304i	−0.883541	+	0.468353i	$0.844847\pi$
$564$		0			0
$565$	−5.93737	−	5.77166i	−0.249787	−	0.242816i
$566$	6.03750	+	18.5815i	0.253775	+	0.781039i
$567$		0			0
$568$			11.0243i			0.462569i
$569$	−2.00198	−	19.0476i	−0.0839276	−	0.798517i	−0.952824	−	0.303523i	$-0.901837\pi$
$569$	−2.00198	−	19.0476i	−0.0839276	−	0.798517i	0.868896	−	0.494994i	$-0.164830\pi$
$570$		0			0
$571$	−0.480995	+	4.57636i	−0.0201290	+	0.191515i	−0.999966	−	0.00828549i	$-0.997363\pi$
$571$	−0.480995	+	4.57636i	−0.0201290	+	0.191515i	0.979837	+	0.199800i	$0.0640293\pi$
$572$	0.125068	+	0.0131452i	0.00522935	+	0.000549627i
$573$		0			0
$574$	−9.12590	+	15.8065i	−0.380908	+	0.659752i
$575$	3.91201	+	29.2352i	0.163142	+	1.21919i
$576$		0			0
$577$	−36.5521	−	11.8765i	−1.52168	−	0.494425i	−0.575429	−	0.817852i	$-0.695165\pi$
$577$	−36.5521	−	11.8765i	−1.52168	−	0.494425i	−0.946253	+	0.323427i	$0.895165\pi$
$578$	8.30826	+	18.6606i	0.345578	+	0.776181i
$579$		0			0
$580$	−2.04143	−	7.20907i	−0.0847657	−	0.299341i
$581$	−35.8754	−	15.9728i	−1.48836	−	0.662662i
$582$		0			0
$583$	18.1945	−	1.91232i	0.753538	−	0.0792001i
$584$	11.0397	+	33.9767i	0.456826	+	1.40597i
$585$		0			0
$586$	1.19404	−	3.67487i	0.0493253	−	0.151808i
$587$	−5.40305	+	25.4193i	−0.223008	+	1.04917i	0.714077	+	0.700067i	$0.246847\pi$
$587$	−5.40305	+	25.4193i	−0.223008	+	1.04917i	−0.937085	+	0.349102i	$0.886487\pi$
$588$		0			0
$589$	−4.42015	+	0.939533i	−0.182129	+	0.0387128i
$590$	0.611376	−	15.9931i	0.0251700	−	0.658426i
$591$		0			0
$592$	2.41479	−	0.253805i	0.0992472	−	0.0104313i
$593$		−	32.5216i		−	1.33550i	−0.744385	−	0.667750i	$-0.767257\pi$
$593$		−	32.5216i		−	1.33550i	0.744385	−	0.667750i	$-0.232743\pi$
$594$		0			0
$595$	−0.0769285	−	1.15492i	−0.00315376	−	0.0473473i
$596$	10.6582	−	4.74534i	0.436577	−	0.194377i
$597$		0			0
$598$	0.240182	+	1.12997i	0.00982176	+	0.0462078i
$599$	−5.00962	−	8.67692i	−0.204688	−	0.354529i	0.745346	−	0.666678i	$-0.232285\pi$
$599$	−5.00962	−	8.67692i	−0.204688	−	0.354529i	−0.950033	+	0.312149i	$0.898951\pi$
$600$		0			0
$601$	6.09862	−	10.5631i	0.248768	−	0.430878i	−0.714416	−	0.699721i	$-0.753308\pi$
$601$	6.09862	−	10.5631i	0.248768	−	0.430878i	0.963184	+	0.268842i	$0.0866411\pi$
$602$	−20.9775	−	6.81601i	−0.854980	−	0.277800i
$603$		0			0
$604$	−2.37137	−	1.72290i	−0.0964899	−	0.0701040i
$605$	−2.87367	+	19.9685i	−0.116831	+	0.811836i
$606$		0			0
$607$	−18.1063	+	10.4537i	−0.734910	+	0.424301i	−0.820216	−	0.572054i	$-0.806147\pi$
$607$	−18.1063	+	10.4537i	−0.734910	+	0.424301i	0.0853054	+	0.996355i	$0.472813\pi$
$608$	9.20024	−	20.6641i	0.373119	−	0.838039i
$609$		0			0
$610$	37.5946	+	5.41023i	1.52216	+	0.219054i
$611$	−0.0109993	+	0.0338524i	−0.000444985	+	0.00136952i
$612$		0			0
$613$	−3.43863	+	1.11728i	−0.138885	+	0.0451265i	−0.377635	−	0.925955i	$-0.623262\pi$
$613$	−3.43863	+	1.11728i	−0.138885	+	0.0451265i	0.238750	+	0.971081i	$0.423262\pi$
$614$	−13.3171	−	14.7901i	−0.537433	−	0.596880i
$615$		0			0
$616$	−7.74386	+	8.60043i	−0.312009	+	0.346521i
$617$	2.39310	−	5.37500i	0.0963427	−	0.216389i	−0.858945	−	0.512069i	$-0.828879\pi$
$617$	2.39310	−	5.37500i	0.0963427	−	0.216389i	0.955287	+	0.295679i	$0.0955460\pi$
$618$		0			0
$619$	2.88523	+	27.4512i	0.115967	+	1.10336i	0.885465	+	0.464706i	$0.153840\pi$
$619$	2.88523	+	27.4512i	0.115967	+	1.10336i	−0.769498	+	0.638649i	$0.779493\pi$
$620$	−0.394247	+	0.626315i	−0.0158333	+	0.0251534i
$621$		0			0
$622$	−13.3102	+	18.3199i	−0.533689	+	0.734559i
$623$	−21.8177	+	19.6448i	−0.874109	+	0.787051i
$624$		0			0
$625$	24.7086	+	3.80603i	0.988343	+	0.152241i
$626$	1.90382	+	3.29752i	0.0760921	+	0.131795i
$627$		0			0
$628$	−2.71115	−	6.08935i	−0.108187	−	0.242991i
$629$	−0.146050	−	0.106112i	−0.00582340	−	0.00423095i
$630$		0			0
$631$	−5.50355	+	3.99857i	−0.219093	+	0.159180i	−0.691918	−	0.721976i	$-0.743234\pi$
$631$	−5.50355	+	3.99857i	−0.219093	+	0.159180i	0.472825	+	0.881156i	$0.343234\pi$
$632$	−36.1672	−	20.8811i	−1.43865	−	0.830607i
$633$		0			0
$634$	0.323200	−	0.358950i	0.0128359	−	0.0142557i
$635$	−30.0339	−	11.0439i	−1.19186	−	0.438264i
$636$		0			0
$637$	0.00616516	−	0.0290048i	0.000244272	−	0.00114921i
$638$	−9.81466	+	3.18898i	−0.388566	+	0.126253i
$639$		0			0
$640$	3.82171	+	9.54974i	0.151066	+	0.377486i
$641$	1.85596	+	0.394497i	0.0733060	+	0.0155817i	0.244419	−	0.969670i	$-0.421403\pi$
$641$	1.85596	+	0.394497i	0.0733060	+	0.0155817i	−0.171113	+	0.985251i	$0.554736\pi$
$642$		0			0
$643$	13.7142	−	7.91791i	0.540836	−	0.312252i	−0.204581	−	0.978850i	$-0.565583\pi$
$643$	13.7142	−	7.91791i	0.540836	−	0.312252i	0.745418	+	0.666598i	$0.232250\pi$
$644$	7.94185	+	3.53594i	0.312953	+	0.139335i
$645$		0			0
$646$	1.59530	−	0.710275i	0.0627664	−	0.0279454i
$647$	1.30998	−	1.80303i	0.0515007	−	0.0708846i	−0.782490	−	0.622663i	$-0.786051\pi$
$647$	1.30998	−	1.80303i	0.0515007	−	0.0708846i	0.833991	+	0.551779i	$0.186051\pi$
$648$		0			0
$649$	8.35902			0.328120
$650$	0.976276	+	0.0747504i	0.0382927	+	0.00293195i
$651$		0			0
$652$	−0.0611215	−	0.287554i	−0.00239370	−	0.0112615i
$653$	1.00426	+	0.105552i	0.0392999	+	0.00413058i	0.124158	−	0.992262i	$-0.460377\pi$
$653$	1.00426	+	0.105552i	0.0392999	+	0.00413058i	−0.0848581	+	0.996393i	$0.527044\pi$
$654$		0			0
$655$	23.4951	+	11.5555i	0.918030	+	0.451512i
$656$	−11.8863	+	8.63588i	−0.464081	+	0.337174i
$657$		0			0
$658$	−0.415209	−	0.571486i	−0.0161865	−	0.0222788i
$659$	14.3529	+	3.05080i	0.559109	+	0.118842i	0.478794	−	0.877927i	$-0.341074\pi$
$659$	14.3529	+	3.05080i	0.559109	+	0.118842i	0.0803150	+	0.996770i	$0.474407\pi$
$660$		0			0
$661$	−30.9764	+	6.58425i	−1.20484	+	0.256098i	−0.766223	−	0.642575i	$-0.777866\pi$
$661$	−30.9764	+	6.58425i	−1.20484	+	0.256098i	−0.438621	+	0.898672i	$0.644533\pi$
$662$	21.6322	+	19.4777i	0.840760	+	0.757024i
$663$		0			0
$664$	−30.1069	−	33.4371i	−1.16837	−	1.29761i
$665$	44.8923	−	2.99024i	1.74085	−	0.115956i
$666$		0			0
$667$	21.1292	+	29.0818i	0.818126	+	1.12605i
$668$	5.19152	+	2.99733i	0.200866	+	0.115970i
$669$		0			0
$670$	−4.73889	−	16.7349i	−0.183079	−	0.646524i
$671$	−2.07356	+	19.7286i	−0.0800488	+	0.761614i
$672$		0			0
$673$	−30.0916	+	27.0946i	−1.15995	+	1.04442i	−0.161605	+	0.986856i	$0.551667\pi$
$673$	−30.0916	+	27.0946i	−1.15995	+	1.04442i	−0.998342	+	0.0575650i	$0.981666\pi$
$674$	−40.2134			−1.54896
$675$		0			0
$676$	7.13392			0.274381
$677$	−1.87592	+	1.68909i	−0.0720975	+	0.0649169i	−0.704392	−	0.709812i	$-0.748780\pi$
$677$	−1.87592	+	1.68909i	−0.0720975	+	0.0649169i	0.632294	+	0.774728i	$0.282113\pi$
$678$		0			0
$679$	−0.868038	+	8.25883i	−0.0333123	+	0.316945i
$680$	0.457694	−	1.24470i	0.0175518	−	0.0477320i
$681$		0			0
$682$	0.882759	+	0.509661i	0.0338026	+	0.0195159i
$683$	−12.8169	−	17.6409i	−0.490425	−	0.675012i	0.490042	−	0.871699i	$-0.336982\pi$
$683$	−12.8169	−	17.6409i	−0.490425	−	0.675012i	−0.980466	+	0.196687i	$0.936982\pi$
$684$		0			0
$685$	−11.2798	+	44.6126i	−0.430978	+	1.70456i
$686$	−14.7225	−	16.3510i	−0.562107	−	0.624283i
$687$		0			0
$688$	−13.1948	−	11.8807i	−0.503048	−	0.452946i
$689$	−2.06923	+	0.439828i	−0.0788312	+	0.0167561i
$690$		0			0
$691$	−12.5345	−	2.66428i	−0.476833	−	0.101354i	−0.0367757	−	0.999324i	$-0.511709\pi$
$691$	−12.5345	−	2.66428i	−0.476833	−	0.101354i	−0.440058	+	0.897969i	$0.645042\pi$
$692$	−3.39301	−	4.67007i	−0.128983	−	0.177529i
$693$		0			0
$694$	−3.64755	+	2.65010i	−0.138459	+	0.100596i
$695$	−2.00767	+	0.347174i	−0.0761552	+	0.0131691i
$696$		0			0
$697$	1.08638	+	0.114183i	0.0411496	+	0.00432500i
$698$	−4.34516	−	20.4424i	−0.164467	−	0.773756i
$699$		0			0
$700$	4.77348	−	5.61311i	0.180421	−	0.212155i
$701$	−48.5879			−1.83514			−0.917569	−	0.397577i	$-0.869851\pi$
$701$	−48.5879			−1.83514			−0.917569	+	0.397577i	$0.869851\pi$
$702$		0			0
$703$	4.12460	−	5.67702i	0.155562	−	0.214113i
$704$	−11.3364	+	5.04731i	−0.427258	+	0.190228i
$705$		0			0
$706$	−6.07742	−	2.70584i	−0.228727	−	0.101836i
$707$	18.6537	−	10.7697i	0.701545	−	0.405037i
$708$		0			0
$709$	7.36006	+	1.56443i	0.276413	+	0.0587533i	0.344032	−	0.938958i	$-0.388207\pi$
$709$	7.36006	+	1.56443i	0.276413	+	0.0587533i	−0.0676195	+	0.997711i	$0.521540\pi$
$710$	−9.64617	+	0.642523i	−0.362014	+	0.0241135i
$711$		0			0
$712$	−31.9912	+	10.3946i	−1.19892	+	0.389554i
$713$	0.738220	−	3.47305i	0.0276466	−	0.130067i
$714$		0			0
$715$	−0.0195347	+	0.511011i	−0.000730555	+	0.0191107i
$716$	−5.07062	+	5.63149i	−0.189498	+	0.210459i
$717$		0			0
$718$	−14.5199	−	8.38310i	−0.541880	−	0.312854i
$719$	35.5528	−	25.8307i	1.32590	−	0.963321i	0.326059	−	0.945349i	$-0.394279\pi$
$719$	35.5528	−	25.8307i	1.32590	−	0.963321i	0.999839	−	0.0179714i	$-0.00572079\pi$
$720$		0			0
$721$	1.17037	+	0.850325i	0.0435869	+	0.0316678i
$722$	18.3025	+	41.1082i	0.681150	+	1.52989i
$723$		0			0
$724$	−2.02291	−	3.50378i	−0.0751807	−	0.130217i
$725$	28.6988	−	10.2314i	1.06585	−	0.379984i
$726$		0			0
$727$	−27.6361	+	24.8837i	−1.02497	+	0.922884i	−0.997052	−	0.0767266i	$-0.975553\pi$
$727$	−27.6361	+	24.8837i	−1.02497	+	0.922884i	−0.0279140	+	0.999610i	$0.508886\pi$
$728$	0.786582	−	1.08264i	0.0291527	−	0.0401252i
$729$		0			0
$730$	−29.0859	+	11.6399i	−1.07652	+	0.430811i
$731$	0.137989	+	1.31288i	0.00510370	+	0.0485585i
$732$		0			0
$733$	2.24663	−	5.04602i	0.0829813	−	0.186379i	−0.867289	−	0.497804i	$-0.834140\pi$
$733$	2.24663	−	5.04602i	0.0829813	−	0.186379i	0.950271	+	0.311425i	$0.100806\pi$
$734$	−29.5618	+	32.8317i	−1.09115	+	1.21184i
$735$		0			0
$736$	11.8924	+	13.2079i	0.438361	+	0.486849i
$737$	8.63939	−	2.80711i	0.318236	−	0.103401i
$738$		0			0
$739$	13.0729	−	40.2342i	0.480894	−	1.48004i	−0.356946	−	0.934125i	$-0.616182\pi$
$739$	13.0729	−	40.2342i	0.480894	−	1.48004i	0.837840	−	0.545915i	$-0.183818\pi$
$740$	−0.195821	−	1.13241i	−0.00719852	−	0.0416282i
$741$		0			0
$742$	17.0758	−	38.3529i	0.626873	−	1.40798i
$743$	16.0074	−	9.24189i	0.587256	−	0.339052i	−0.176756	−	0.984255i	$-0.556560\pi$
$743$	16.0074	−	9.24189i	0.587256	−	0.339052i	0.764012	+	0.645203i	$0.223227\pi$
$744$		0			0
$745$	22.1346	+	41.9628i	0.810947	+	1.53740i
$746$	18.2228	+	13.2397i	0.667186	+	0.484739i
$747$		0			0
$748$	0.142057	+	0.0461573i	0.00519413	+	0.00168768i
$749$	−0.899969	+	1.55879i	−0.0328841	+	0.0569570i
$750$		0			0
$751$	12.6388	+	21.8911i	0.461197	+	0.798816i	0.999021	−	0.0442409i	$-0.0140869\pi$
$751$	12.6388	+	21.8911i	0.461197	+	0.798816i	−0.537824	+	0.843057i	$0.680754\pi$
$752$	−0.118225	−	0.556205i	−0.00431122	−	0.0202827i
$753$		0			0
$754$	1.09013	−	0.485356i	0.0397001	−	0.0176756i
$755$	6.34972	−	10.0874i	0.231090	−	0.367118i
$756$		0			0
$757$			14.6646i			0.532993i	0.963836	+	0.266497i	$0.0858661\pi$
$757$			14.6646i			0.532993i	−0.963836	+	0.266497i	$0.914134\pi$
$758$	−2.29173	+	0.240870i	−0.0832393	+	0.00874880i
$759$		0			0
$760$	48.3819	+	17.7907i	1.75500	+	0.645338i
$761$	9.76945	−	2.07656i	0.354142	−	0.0752752i	−0.0274055	−	0.999624i	$-0.508725\pi$
$761$	9.76945	−	2.07656i	0.354142	−	0.0752752i	0.381548	+	0.924349i	$0.375391\pi$
$762$		0			0
$763$	7.79202	−	36.6586i	0.282090	−	1.32713i
$764$	−0.189461	+	0.583100i	−0.00685444	+	0.0210958i
$765$		0			0
$766$	3.59450	+	11.0627i	0.129875	+	0.399713i
$767$	−0.961275	+	0.101034i	−0.0347096	+	0.00364813i
$768$		0			0
$769$	−16.8890	−	7.51947i	−0.609033	−	0.271159i	0.0789582	−	0.996878i	$-0.474841\pi$
$769$	−16.8890	−	7.51947i	−0.609033	−	0.271159i	−0.687991	+	0.725719i	$0.741507\pi$
$770$	−7.97663	−	6.27456i	−0.287458	−	0.226119i
$771$		0			0
$772$	5.66794	+	12.7304i	0.203994	+	0.458177i
$773$	−3.41227	−	1.10871i	−0.122731	−	0.0398777i	0.247008	−	0.969014i	$-0.420553\pi$
$773$	−3.41227	−	1.10871i	−0.122731	−	0.0398777i	−0.369739	+	0.929136i	$0.620553\pi$
$774$		0			0
$775$	−2.64780	−	1.43037i	−0.0951119	−	0.0513805i
$776$	−4.75733	+	8.23993i	−0.170778	+	0.295796i
$777$		0			0
$778$	27.3695	+	2.87666i	0.981246	+	0.103133i
$779$	−4.43834	+	42.2280i	−0.159020	+	1.51297i
$780$		0			0
$781$	−0.527784	−	5.02153i	−0.0188856	−	0.179684i
$782$			1.37211i			0.0490664i
$783$		0			0
$784$	0.146384	+	0.450524i	0.00522801	+	0.0160902i
$785$	23.9746	−	12.6461i	0.855689	−	0.451360i
$786$		0			0
$787$	12.0214	+	10.8241i	0.428517	+	0.385839i	0.854975	−	0.518669i	$-0.173572\pi$
$787$	12.0214	+	10.8241i	0.428517	+	0.385839i	−0.426458	+	0.904507i	$0.640239\pi$
$788$	−6.52007	−	5.87069i	−0.232268	−	0.209135i
$789$		0			0
$790$	16.1629	−	32.8630i	0.575050	−	1.16921i
$791$	−3.06676	−	9.43852i	−0.109041	−	0.335595i
$792$		0			0
$793$		−	2.29382i		−	0.0814561i
$794$	1.20797	+	11.4931i	0.0428692	+	0.407874i
$795$		0			0
$796$	1.10900	−	10.5514i	0.0393075	−	0.373986i
$797$	−18.9150	−	1.98804i	−0.670003	−	0.0704202i	−0.236582	−	0.971612i	$-0.576027\pi$
$797$	−18.9150	−	1.98804i	−0.670003	−	0.0704202i	−0.433421	+	0.901191i	$0.642694\pi$
$798$		0			0
$799$	−0.0211388	+	0.0366134i	−0.000747836	+	0.00129529i
$800$	13.5828	−	6.51407i	0.480224	−	0.230307i
$801$		0			0
$802$	−7.07857	−	2.29997i	−0.249953	−	0.0812146i
$803$	−6.65515	−	14.9477i	−0.234855	−	0.527494i
$804$		0			0
$805$	−12.2005	+	33.1794i	−0.430013	+	1.16942i
$806$	−0.107676	−	0.0479406i	−0.00379274	−	0.00168863i
$807$		0			0
$808$	24.5436	−	2.57963i	0.863440	−	0.0907512i
$809$	−3.06508	−	9.43335i	−0.107763	−	0.331659i	0.882606	−	0.470113i	$-0.155787\pi$
$809$	−3.06508	−	9.43335i	−0.107763	−	0.331659i	−0.990369	+	0.138454i	$0.955787\pi$
$810$		0			0
$811$	8.46694	−	26.0585i	0.297314	−	0.915039i	−0.685120	−	0.728430i	$-0.740250\pi$
$811$	8.46694	−	26.0585i	0.297314	−	0.915039i	0.982434	−	0.186609i	$-0.0597498\pi$
$812$	1.86705	−	8.78379i	0.0655207	−	0.308250i
$813$		0			0
$814$	−1.54827	+	0.329094i	−0.0542668	+	0.0115348i
$815$	1.15022	−	0.325714i	0.0402905	−	0.0114092i
$816$		0			0
$817$	−51.0320	+	5.36368i	−1.78538	+	0.187651i
$818$		−	3.54395i		−	0.123911i
$819$		0			0
$820$	4.45223	+	5.34169i	0.155479	+	0.186540i
$821$	8.76982	−	3.90458i	0.306069	−	0.136271i	−0.247955	−	0.968772i	$-0.579758\pi$
$821$	8.76982	−	3.90458i	0.306069	−	0.136271i	0.554024	+	0.832501i	$0.313092\pi$
$822$		0			0
$823$	−7.15784	−	33.6750i	−0.249507	−	1.17384i	−0.907249	−	0.420594i	$-0.861822\pi$
$823$	−7.15784	−	33.6750i	−0.249507	−	1.17384i	0.657742	−	0.753243i	$-0.271512\pi$
$824$	0.828753	+	1.43544i	0.0288710	+	0.0500060i
$825$		0			0
$826$	9.59109	−	16.6123i	0.333717	−	0.578014i
$827$	−25.3249	−	8.22855i	−0.880632	−	0.286135i	−0.166412	−	0.986056i	$-0.553218\pi$
$827$	−25.3249	−	8.22855i	−0.880632	−	0.286135i	−0.714220	+	0.699922i	$0.753218\pi$
$828$		0			0
$829$	28.0528	+	20.3815i	0.974314	+	0.707880i	0.956431	−	0.291960i	$-0.0943073\pi$
$829$	28.0528	+	20.3815i	0.974314	+	0.707880i	0.0178831	+	0.999840i	$0.494307\pi$
$830$	27.5025	−	28.2921i	0.954625	−	0.982032i
$831$		0			0
$832$	1.24267	−	0.717456i	0.0430818	−	0.0248733i
$833$	0.0143253	−	0.0321752i	0.000496344	−	0.00111481i
$834$		0			0
$835$	−10.7585	+	21.8745i	−0.372312	+	0.756998i
$836$	−1.79415	+	5.52182i	−0.0620519	+	0.190976i
$837$		0			0
$838$	6.99309	−	2.27219i	0.241572	−	0.0784916i
$839$	−3.14488	−	3.49274i	−0.108573	−	0.120583i	0.686408	−	0.727216i	$-0.259186\pi$
$839$	−3.14488	−	3.49274i	−0.108573	−	0.120583i	−0.794982	+	0.606633i	$0.792520\pi$
$840$		0			0
$841$	5.44148	−	6.04337i	0.187637	−	0.208392i
$842$	−0.654854	+	1.47083i	−0.0225677	+	0.0506880i
$843$		0			0
$844$	−0.174235	−	1.65773i	−0.00599740	−	0.0570614i
$845$	1.92804	+	28.9456i	0.0663267	+	0.995759i
$846$		0			0
$847$	−14.2123	+	19.5615i	−0.488340	+	0.672142i
$848$	25.1144	−	22.6132i	0.862434	−	0.776539i
$849$		0			0
$850$	1.11578	+	0.327934i	0.0382708	+	0.0112480i
$851$	2.75681	+	4.77494i	0.0945023	+	0.163683i
$852$		0			0
$853$	−7.63819	−	17.1556i	−0.261527	−	0.587398i	0.734284	−	0.678843i	$-0.237518\pi$
$853$	−7.63819	−	17.1556i	−0.261527	−	0.587398i	−0.995810	+	0.0914446i	$0.970852\pi$
$854$	36.8283	+	26.7574i	1.26024	+	0.915618i
$855$		0			0
$856$	−1.66841	+	1.21217i	−0.0570252	+	0.0414312i
$857$	28.3893	+	16.3906i	0.969759	+	0.559891i	0.899163	−	0.437614i	$-0.144176\pi$
$857$	28.3893	+	16.3906i	0.969759	+	0.559891i	0.0705962	+	0.997505i	$0.477510\pi$
$858$		0			0
$859$	6.34105	−	7.04245i	0.216354	−	0.240285i	−0.625192	−	0.780471i	$-0.714979\pi$
$859$	6.34105	−	7.04245i	0.216354	−	0.240285i	0.841546	+	0.540186i	$0.181646\pi$
$860$	−5.19563	+	6.60503i	−0.177170	+	0.225230i
$861$		0			0
$862$	−8.32337	+	39.1584i	−0.283495	+	1.33374i
$863$	32.4083	−	10.5301i	1.10319	−	0.358449i	0.299862	−	0.953983i	$-0.403059\pi$
$863$	32.4083	−	10.5301i	1.10319	−	0.358449i	0.803330	+	0.595534i	$0.203059\pi$
$864$		0			0
$865$	18.0316	−	15.0291i	0.613094	−	0.511006i
$866$	13.7262	+	2.91760i	0.466436	+	0.0991440i
$867$		0			0
$868$	−0.768158	+	0.443496i	−0.0260730	+	0.0150532i
$869$	17.4737	+	7.77979i	0.592754	+	0.263911i
$870$		0			0
$871$	−0.959589	+	0.427237i	−0.0325144	+	0.0144764i
$872$	25.2394	−	34.7390i	0.854712	−	1.17641i
$873$		0			0
$874$	−53.3342			−1.80406
$875$	24.0651	+	17.8512i	0.813548	+	0.603481i
$876$		0			0
$877$	5.61830	+	26.4320i	0.189716	+	0.892546i	0.965268	+	0.261262i	$0.0841385\pi$
$877$	5.61830	+	26.4320i	0.189716	+	0.892546i	−0.775552	+	0.631284i	$0.782528\pi$
$878$	26.5746	+	2.79310i	0.896849	+	0.0942627i
$879$		0			0
$880$	−3.81149	−	7.22584i	−0.128485	−	0.243583i
$881$	−44.5745	+	32.3853i	−1.50175	+	1.09109i	−0.532078	+	0.846695i	$0.678589\pi$
$881$	−44.5745	+	32.3853i	−1.50175	+	1.09109i	−0.969676	+	0.244393i	$0.921411\pi$
$882$		0			0
$883$	23.9914	+	33.0214i	0.807376	+	1.11126i	0.991723	+	0.128396i	$0.0409829\pi$
$883$	23.9914	+	33.0214i	0.807376	+	1.11126i	−0.184347	+	0.982861i	$0.559017\pi$
$884$	−0.0168943	−	0.00359100i	−0.000568217	−	0.000120778i
$885$		0			0
$886$	−9.39189	+	1.99631i	−0.315527	+	0.0670673i
$887$	−21.7243	−	19.5606i	−0.729430	−	0.656782i	0.218290	−	0.975884i	$-0.429952\pi$
$887$	−21.7243	−	19.5606i	−0.729430	−	0.656782i	−0.947720	+	0.319102i	$0.896619\pi$
$888$		0			0
$889$	−25.6632	−	28.5018i	−0.860714	−	0.955920i
$890$	−10.9597	−	27.3862i	−0.367370	−	0.917989i
$891$		0			0
$892$	−5.88831	−	8.10456i	−0.197155	−	0.271361i
$893$	−1.42318	−	0.821672i	−0.0476248	−	0.0274962i
$894$		0			0
$895$	−24.2200	−	19.0519i	−0.809585	−	0.636834i
$896$	−1.28864	+	12.2606i	−0.0430504	+	0.409598i
$897$		0			0
$898$	17.4346	−	15.6982i	0.581800	−	0.523855i
$899$	−3.66769			−0.122324
$900$		0			0
$901$	−2.51264			−0.0837081
$902$	7.11767	−	6.40878i	0.236993	−	0.213389i
$903$		0			0
$904$	1.18856	−	11.3084i	0.0395309	−	0.376111i
$905$	13.6697	−	9.15482i	0.454397	−	0.304316i
$906$		0			0
$907$	−26.5281	−	15.3160i	−0.880851	−	0.508560i	−0.00991216	−	0.999951i	$-0.503155\pi$
$907$	−26.5281	−	15.3160i	−0.880851	−	0.508560i	−0.870939	+	0.491391i	$0.836489\pi$
$908$	2.73472	+	3.76402i	0.0907548	+	0.124913i
$909$		0			0
$910$	0.993142	+	0.625153i	0.0329223	+	0.0207236i
$911$	6.81616	+	7.57012i	0.225830	+	0.250809i	0.845402	−	0.534130i	$-0.179361\pi$
$911$	6.81616	+	7.57012i	0.225830	+	0.250809i	−0.619573	+	0.784939i	$0.712694\pi$
$912$		0			0
$913$	15.3144	+	13.7891i	0.506831	+	0.456353i
$914$	20.4435	−	4.34541i	0.676212	−	0.143733i
$915$		0			0
$916$	5.26130	+	1.11832i	0.173838	+	0.0369505i
$917$	18.4453	+	25.3878i	0.609119	+	0.838380i
$918$		0			0
$919$	21.8946	−	15.9074i	0.722236	−	0.524735i	−0.164862	−	0.986317i	$-0.552718\pi$
$919$	21.8946	−	15.9074i	0.722236	−	0.524735i	0.887098	+	0.461581i	$0.152718\pi$
$920$	−28.2324	+	29.0429i	−0.930794	+	0.957517i
$921$		0			0
$922$	35.7421	+	3.75665i	1.17710	+	0.123719i
$923$	0.121389	+	0.571089i	0.00399556	+	0.0187976i
$924$		0			0
$925$	4.54179	−	1.10059i	0.149333	−	0.0361871i
$926$	−14.0632			−0.462145
$927$		0			0
$928$	10.7911	−	14.8526i	0.354234	−	0.487562i
$929$	18.6446	−	8.30111i	0.611709	−	0.272351i	−0.0774089	−	0.996999i	$-0.524665\pi$
$929$	18.6446	−	8.30111i	0.611709	−	0.272351i	0.689118	+	0.724649i	$0.257998\pi$
$930$		0			0
$931$	1.25066	+	0.556831i	0.0409888	+	0.0182494i
$932$	−1.21228	+	0.699908i	−0.0397094	+	0.0229262i
$933$		0			0
$934$	−16.9175	−	3.59593i	−0.553558	−	0.117662i
$935$	−0.148888	+	0.588867i	−0.00486917	+	0.0192580i
$936$		0			0
$937$	19.4195	−	6.30978i	0.634408	−	0.206132i	0.0258811	−	0.999665i	$-0.491761\pi$
$937$	19.4195	−	6.30978i	0.634408	−	0.206132i	0.608527	+	0.793533i	$0.291761\pi$
$938$	4.33410	−	20.3903i	0.141513	−	0.665768i
$939$		0			0
$940$	−0.258951	+	0.0733284i	−0.00844605	+	0.00239171i
$941$	0.394588	−	0.438234i	0.0128632	−	0.0142860i	−0.736679	−	0.676243i	$-0.763607\pi$
$941$	0.394588	−	0.438234i	0.0128632	−	0.0142860i	0.749542	+	0.661957i	$0.230274\pi$
$942$		0			0
$943$	−28.8929	−	16.6813i	−0.940881	−	0.543218i
$944$	12.4922	−	9.07609i	0.406585	−	0.295402i
$945$		0			0
$946$	9.36406	+	6.80339i	0.304452	+	0.221197i
$947$	10.9735	+	24.6470i	0.356592	+	0.800919i	0.999391	+	0.0348845i	$0.0111063\pi$
$947$	10.9735	+	24.6470i	0.356592	+	0.800919i	−0.642799	+	0.766035i	$0.722227\pi$
$948$		0			0
$949$	0.946005	+	1.63853i	0.0307086	+	0.0531889i
$950$	−12.7469	+	43.3706i	−0.413565	+	1.40713i
$951$		0			0
$952$	1.18120	−	1.06356i	0.0382830	−	0.0344702i
$953$	10.0812	−	13.8756i	0.326563	−	0.449475i	−0.613894	−	0.789388i	$-0.710398\pi$
$953$	10.0812	−	13.8756i	0.326563	−	0.449475i	0.940457	+	0.339913i	$0.110398\pi$
$954$		0			0
$955$	−2.41711	−	0.611139i	−0.0782159	−	0.0197760i
$956$	0.606465	+	5.77012i	0.0196145	+	0.186619i
$957$		0			0
$958$	2.51880	−	5.65731i	0.0813786	−	0.182779i
$959$	−36.9039	+	40.9860i	−1.19169	+	1.32351i
$960$		0			0
$961$	−20.5006	−	22.7683i	−0.661311	−	0.734460i
$962$	0.174071	−	0.0565591i	0.00561227	−	0.00182354i
$963$		0			0
$964$	−0.522323	+	1.60755i	−0.0168229	+	0.0517756i
$965$	−50.1213	+	26.4380i	−1.61346	+	0.851071i
$966$		0			0
$967$	5.46728	−	12.2797i	0.175816	−	0.394889i	−0.804045	−	0.594568i	$-0.797323\pi$
$967$	5.46728	−	12.2797i	0.175816	−	0.394889i	0.979861	+	0.199679i	$0.0639898\pi$
$968$	−23.9919	+	13.8517i	−0.771129	+	0.445211i
$969$		0			0
$970$	−7.48714	−	3.68238i	−0.240397	−	0.118234i
$971$	17.9377	+	13.0325i	0.575648	+	0.418232i	0.837152	−	0.546970i	$-0.184219\pi$
$971$	17.9377	+	13.0325i	0.575648	+	0.418232i	−0.261505	+	0.965202i	$0.584219\pi$
$972$		0			0
$973$	−2.32244	−	0.754607i	−0.0744541	−	0.0241916i
$974$	−24.5231	+	42.4753i	−0.785771	+	1.36100i
$975$		0			0
$976$	18.3222	+	31.7349i	0.586478	+	1.01581i
$977$	4.34346	+	20.4344i	0.138960	+	0.653753i	0.991393	+	0.130918i	$0.0417924\pi$
$977$	4.34346	+	20.4344i	0.138960	+	0.653753i	−0.852434	+	0.522835i	$0.824874\pi$
$978$		0			0
$979$	14.0742	−	6.26626i	0.449815	−	0.200271i
$980$	0.208157	−	0.0833025i	0.00664934	−	0.00266100i
$981$		0			0
$982$		−	48.2698i		−	1.54035i
$983$	−27.2383	+	2.86286i	−0.868767	+	0.0913111i	−0.528414	−	0.848987i	$-0.677213\pi$
$983$	−27.2383	+	2.86286i	−0.868767	+	0.0913111i	−0.340353	+	0.940298i	$0.610547\pi$
$984$		0			0
$985$	22.0580	−	28.0416i	0.702826	−	0.893479i
$986$	1.38637	−	0.294681i	0.0441509	−	0.00938456i
$987$		0			0
$988$	0.139583	−	0.656688i	0.00444074	−	0.0208920i
$989$	12.4590	−	38.3450i	0.396174	−	1.21930i
$990$		0			0
$991$	−4.58088	−	14.0985i	−0.145516	−	0.447854i	0.851561	−	0.524256i	$-0.175657\pi$
$991$	−4.58088	−	14.0985i	−0.145516	−	0.447854i	−0.997077	+	0.0764026i	$0.975657\pi$
$992$	−1.80345	+	0.189550i	−0.0572595	+	0.00601821i
$993$		0			0
$994$	−10.5851	−	4.71278i	−0.335739	−	0.149480i
$995$	43.1118	+	1.64806i	1.36674	+	0.0522469i
$996$		0			0
$997$	0.842806	+	1.89297i	0.0266919	+	0.0599510i	0.926400	−	0.376542i	$-0.122887\pi$
$997$	0.842806	+	1.89297i	0.0266919	+	0.0599510i	−0.899708	+	0.436493i	$0.856220\pi$
$998$	−33.4730	−	10.8760i	−1.05957	−	0.344275i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.y.a.154.9		224
3.2	odd	2		225.2.u.a.79.20	yes	224
9.4	even	3	inner	675.2.y.a.604.9		224
9.5	odd	6		225.2.u.a.4.20	✓	224
25.19	even	10	inner	675.2.y.a.19.9		224
75.44	odd	10		225.2.u.a.169.20	yes	224
225.94	even	30	inner	675.2.y.a.469.9		224
225.194	odd	30		225.2.u.a.94.20	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.20	✓	224	9.5	odd	6
225.2.u.a.79.20	yes	224	3.2	odd	2
225.2.u.a.94.20	yes	224	225.194	odd	30
225.2.u.a.169.20	yes	224	75.44	odd	10
675.2.y.a.19.9		224	25.19	even	10	inner
675.2.y.a.154.9		224	1.1	even	1	trivial
675.2.y.a.469.9		224	225.94	even	30	inner
675.2.y.a.604.9		224	9.4	even	3	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.y (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.894901 + 0.805773i) q^{2} +(-0.0574783 + 0.546869i) q^{4} +(-2.23444 - 0.0854168i) q^{5} +(-2.32094 - 1.33999i) q^{7} +(-1.80485 - 2.48416i) q^{8} +O(q^{10})\)	\(q+(-0.894901 + 0.805773i) q^{2} +(-0.0574783 + 0.546869i) q^{4} +(-2.23444 - 0.0854168i) q^{5} +(-2.32094 - 1.33999i) q^{7} +(-1.80485 - 2.48416i) q^{8} +(2.06843 - 1.72401i) q^{10} +(0.941029 + 1.04512i) q^{11} +(-0.120849 - 0.108813i) q^{13} +(3.15674 - 0.670987i) q^{14} +(2.54110 + 0.540127i) q^{16} +(-0.113531 - 0.156262i) q^{17} +(6.07397 - 4.41300i) q^{19} +(0.175143 - 1.21703i) q^{20} +(-1.68426 - 0.177022i) q^{22} +(1.22650 + 5.77024i) q^{23} +(4.98541 + 0.381717i) q^{25} +0.195827 q^{26} +(0.866205 - 1.19223i) q^{28} +(5.56680 - 2.47850i) q^{29} +(-0.549855 - 0.244811i) q^{31} +(2.60917 - 1.50640i) q^{32} +(0.227511 + 0.0483590i) q^{34} +(5.07153 + 3.19238i) q^{35} +(0.888903 - 0.288822i) q^{37} +(-1.87973 + 8.84344i) q^{38} +(3.82063 + 5.70486i) q^{40} +(-3.78427 + 4.20285i) q^{41} +(-5.91893 - 3.41730i) q^{43} +(-0.625632 + 0.454548i) q^{44} +(-5.74710 - 4.17551i) q^{46} +(-0.0890280 - 0.199960i) q^{47} +(0.0911727 + 0.157916i) q^{49} +(-4.76903 + 3.67551i) q^{50} +(0.0664527 - 0.0598343i) q^{52} +(7.64631 - 10.5242i) q^{53} +(-2.01340 - 2.41563i) q^{55} +(0.860180 + 8.18407i) q^{56} +(-2.98463 + 6.70358i) q^{58} +(3.97717 - 4.41709i) q^{59} +(9.43845 + 10.4825i) q^{61} +(0.689328 - 0.223976i) q^{62} +(-2.72670 + 8.39191i) q^{64} +(0.260735 + 0.253458i) q^{65} +(2.62723 - 5.90086i) q^{67} +(0.0919806 - 0.0531050i) q^{68} +(-7.11085 + 1.22964i) q^{70} +(-2.90460 - 2.11032i) q^{71} +(-11.0652 - 3.59530i) q^{73} +(-0.562756 + 0.974721i) q^{74} +(2.06421 + 3.57532i) q^{76} +(-0.783617 - 3.68663i) q^{77} +(12.4249 - 5.53192i) q^{79} +(-5.63178 - 1.42393i) q^{80} -6.81040i q^{82} +(14.5730 - 1.53168i) q^{83} +(0.240331 + 0.358856i) q^{85} +(8.05043 - 1.71117i) q^{86} +(0.897827 - 4.22394i) q^{88} +(3.38521 - 10.4186i) q^{89} +(0.134675 + 0.414486i) q^{91} +(-3.22606 + 0.339073i) q^{92} +(0.240794 + 0.107208i) q^{94} +(-13.9488 + 9.34174i) q^{95} +(-1.26033 - 2.83075i) q^{97} +(-0.208835 - 0.0678546i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

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