LMFDB - Embedded newform 675.2.y.a.19.9

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			19.9
Character	$\chi$	$=$	675.19
Dual form			675.2.y.a.604.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.250369 + 1.17789i) q^{2} +(0.502342 + 0.223657i) q^{4} +(1.04324 - 1.97779i) q^{5} +(2.32094 + 1.33999i) q^{7} +(-1.80485 + 2.48416i) q^{8} +O(q^{10})$	\(q+(-0.250369 + 1.17789i) q^{2} +(0.502342 + 0.223657i) q^{4} +(1.04324 - 1.97779i) q^{5} +(2.32094 + 1.33999i) q^{7} +(-1.80485 + 2.48416i) q^{8} +(2.06843 + 1.72401i) q^{10} +(-1.37561 - 0.292396i) q^{11} +(-0.0338103 - 0.159065i) q^{13} +(-2.15946 + 2.39833i) q^{14} +(-1.73831 - 1.93059i) q^{16} +(-0.113531 + 0.156262i) q^{17} +(6.07397 + 4.41300i) q^{19} +(0.966411 - 0.760196i) q^{20} +(0.688822 - 1.54712i) q^{22} +(4.38392 + 3.94730i) q^{23} +(-2.82328 - 4.12663i) q^{25} +0.195827 q^{26} +(0.866205 + 1.19223i) q^{28} +(-0.636956 - 6.06023i) q^{29} +(0.0629147 - 0.598594i) q^{31} +(-2.60917 + 1.50640i) q^{32} +(-0.155636 - 0.172851i) q^{34} +(5.07153 - 3.19238i) q^{35} +(0.888903 + 0.288822i) q^{37} +(-6.71878 + 6.04962i) q^{38} +(3.03024 + 6.16119i) q^{40} +(5.53191 - 1.17584i) q^{41} +(5.91893 + 3.41730i) q^{43} +(-0.625632 - 0.454548i) q^{44} +(-5.74710 + 4.17551i) q^{46} +(0.217685 - 0.0228796i) q^{47} +(0.0911727 + 0.157916i) q^{49} +(5.56760 - 2.29234i) q^{50} +(0.0185917 - 0.0874669i) q^{52} +(7.64631 + 10.5242i) q^{53} +(-2.01340 + 2.41563i) q^{55} +(-7.51770 + 3.34710i) q^{56} +(7.29779 + 0.767028i) q^{58} +(-5.81390 + 1.23578i) q^{59} +(-13.7973 - 2.93271i) q^{61} +(0.689328 + 0.223976i) q^{62} +(-2.72670 - 8.39191i) q^{64} +(-0.349869 - 0.0990742i) q^{65} +(-6.42391 - 0.675180i) q^{67} +(-0.0919806 + 0.0531050i) q^{68} +(2.49053 + 6.77300i) q^{70} +(-2.90460 + 2.11032i) q^{71} +(-11.0652 + 3.59530i) q^{73} +(-0.562756 + 0.974721i) q^{74} +(2.06421 + 3.57532i) q^{76} +(-2.80091 - 2.52195i) q^{77} +(-1.42166 - 13.5262i) q^{79} +(-5.63178 + 1.42393i) q^{80} +6.81040i q^{82} +(-5.96001 - 13.3864i) q^{83} +(0.190613 + 0.387560i) q^{85} +(-5.50713 + 6.11629i) q^{86} +(3.20913 - 2.88951i) q^{88} +(3.38521 + 10.4186i) q^{89} +(0.134675 - 0.414486i) q^{91} +(1.31938 + 2.96339i) q^{92} +(-0.0275518 + 0.262138i) q^{94} +(15.0646 - 7.40918i) q^{95} +(3.08167 - 0.323896i) q^{97} +(-0.208835 + 0.0678546i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.250369	+	1.17789i	−0.177038	+	0.832897i	0.796548	+	0.604575i	$0.206657\pi$
$2$	−0.250369	+	1.17789i	−0.177038	+	0.832897i	−0.973586	+	0.228322i	$0.926676\pi$
$3$		0			0
$3$		0			0
$4$	0.502342	+	0.223657i	0.251171	+	0.111828i
$5$	1.04324	−	1.97779i	0.466553	−	0.884493i
$5$	1.04324	−	1.97779i	0.466553	−	0.884493i
$6$		0			0
$7$	2.32094	+	1.33999i	0.877233	+	0.506470i	0.869745	−	0.493501i	$-0.164283\pi$
$7$	2.32094	+	1.33999i	0.877233	+	0.506470i	0.00748764	+	0.999972i	$0.497617\pi$
$8$	−1.80485	+	2.48416i	−0.638110	+	0.878283i
$9$		0			0
$10$	2.06843	+	1.72401i	0.654094	+	0.545179i
$11$	−1.37561	−	0.292396i	−0.414763	−	0.0881606i	−0.00419636	−	0.999991i	$-0.501336\pi$
$11$	−1.37561	−	0.292396i	−0.414763	−	0.0881606i	−0.410567	+	0.911831i	$0.634669\pi$
$12$		0			0
$13$	−0.0338103	−	0.159065i	−0.00937729	−	0.0441167i	0.973210	−	0.229917i	$-0.0738455\pi$
$13$	−0.0338103	−	0.159065i	−0.00937729	−	0.0441167i	−0.982587	+	0.185800i	$0.940512\pi$
$14$	−2.15946	+	2.39833i	−0.577141	+	0.640980i
$15$		0			0
$16$	−1.73831	−	1.93059i	−0.434578	−	0.482648i
$17$	−0.113531	+	0.156262i	−0.0275354	+	0.0378992i	−0.822563	−	0.568674i	$-0.807456\pi$
$17$	−0.113531	+	0.156262i	−0.0275354	+	0.0378992i	0.795027	+	0.606574i	$0.207456\pi$
$18$		0			0
$19$	6.07397	+	4.41300i	1.39346	+	1.01241i	0.995475	+	0.0950213i	$0.0302919\pi$
$19$	6.07397	+	4.41300i	1.39346	+	1.01241i	0.397989	+	0.917390i	$0.369708\pi$
$20$	0.966411	−	0.760196i	0.216096	−	0.169985i
$21$		0			0
$22$	0.688822	−	1.54712i	0.146857	−	0.329847i
$23$	4.38392	+	3.94730i	0.914110	+	0.823069i	0.984668	−	0.174439i	$-0.0558112\pi$
$23$	4.38392	+	3.94730i	0.914110	+	0.823069i	−0.0705575	+	0.997508i	$0.522478\pi$
$24$		0			0
$25$	−2.82328	−	4.12663i	−0.564656	−	0.825326i
$26$	0.195827			0.0384048
$27$		0			0
$28$	0.866205	+	1.19223i	0.163697	+	0.225310i
$29$	−0.636956	−	6.06023i	−0.118280	−	1.12536i	−0.879180	−	0.476489i	$-0.841909\pi$
$29$	−0.636956	−	6.06023i	−0.118280	−	1.12536i	0.760901	−	0.648868i	$-0.224757\pi$
$30$		0			0
$31$	0.0629147	−	0.598594i	0.0112998	−	0.107511i	−0.987418	−	0.158131i	$-0.949453\pi$
$31$	0.0629147	−	0.598594i	0.0112998	−	0.107511i	0.998718	+	0.0506203i	$0.0161198\pi$
$32$	−2.60917	+	1.50640i	−0.461240	+	0.266297i
$33$		0			0
$34$	−0.155636	−	0.172851i	−0.0266913	−	0.0296437i
$35$	5.07153	−	3.19238i	0.857245	−	0.539611i
$36$		0			0
$37$	0.888903	+	0.288822i	0.146135	+	0.0474821i	0.381171	−	0.924505i	$-0.375521\pi$
$37$	0.888903	+	0.288822i	0.146135	+	0.0474821i	−0.235036	+	0.971987i	$0.575521\pi$
$38$	−6.71878	+	6.04962i	−1.08993	+	0.981377i
$39$		0			0
$40$	3.03024	+	6.16119i	0.479123	+	0.974169i
$41$	5.53191	−	1.17584i	0.863940	−	0.183636i	0.245431	−	0.969414i	$-0.421071\pi$
$41$	5.53191	−	1.17584i	0.863940	−	0.183636i	0.618509	+	0.785778i	$0.287737\pi$
$42$		0			0
$43$	5.91893	+	3.41730i	0.902629	+	0.521133i	0.878052	−	0.478565i	$-0.158843\pi$
$43$	5.91893	+	3.41730i	0.902629	+	0.521133i	0.0245768	+	0.999698i	$0.492176\pi$
$44$	−0.625632	−	0.454548i	−0.0943175	−	0.0685257i
$45$		0			0
$46$	−5.74710	+	4.17551i	−0.847363	+	0.615645i
$47$	0.217685	−	0.0228796i	0.0317525	−	0.00333733i	−0.0886389	−	0.996064i	$-0.528252\pi$
$47$	0.217685	−	0.0228796i	0.0317525	−	0.00333733i	0.120391	+	0.992727i	$0.461585\pi$
$48$		0			0
$49$	0.0911727	+	0.157916i	0.0130247	+	0.0225594i
$50$	5.56760	−	2.29234i	0.787377	−	0.324186i
$51$		0			0
$52$	0.0185917	−	0.0874669i	0.00257820	−	0.0121295i
$53$	7.64631	+	10.5242i	1.05030	+	1.44562i	0.888547	+	0.458785i	$0.151715\pi$
$53$	7.64631	+	10.5242i	1.05030	+	1.44562i	0.161754	+	0.986831i	$0.448285\pi$
$54$		0			0
$55$	−2.01340	+	2.41563i	−0.271486	+	0.325723i
$56$	−7.51770	+	3.34710i	−1.00460	+	0.447275i
$57$		0			0
$58$	7.29779	+	0.767028i	0.958246	+	0.100716i
$59$	−5.81390	+	1.23578i	−0.756905	+	0.160885i	−0.570172	−	0.821525i	$-0.693123\pi$
$59$	−5.81390	+	1.23578i	−0.756905	+	0.160885i	−0.186733	+	0.982411i	$0.559790\pi$
$60$		0			0
$61$	−13.7973	−	2.93271i	−1.76656	−	0.375495i	−0.793961	−	0.607969i	$-0.791984\pi$
$61$	−13.7973	−	2.93271i	−1.76656	−	0.375495i	−0.972602	+	0.232475i	$0.925318\pi$
$62$	0.689328	+	0.223976i	0.0875447	+	0.0284450i
$63$		0			0
$64$	−2.72670	−	8.39191i	−0.340837	−	1.04899i
$65$	−0.349869	−	0.0990742i	−0.0433959	−	0.0122886i
$66$		0			0
$67$	−6.42391	−	0.675180i	−0.784805	−	0.0824863i	−0.296355	−	0.955078i	$-0.595771\pi$
$67$	−6.42391	−	0.675180i	−0.784805	−	0.0824863i	−0.488450	+	0.872592i	$0.662438\pi$
$68$	−0.0919806	+	0.0531050i	−0.0111543	+	0.00643993i
$69$		0			0
$70$	2.49053	+	6.77300i	0.297675	+	0.809528i
$71$	−2.90460	+	2.11032i	−0.344713	+	0.250449i	−0.746648	−	0.665220i	$-0.768338\pi$
$71$	−2.90460	+	2.11032i	−0.344713	+	0.250449i	0.401935	+	0.915668i	$0.368338\pi$
$72$		0			0
$73$	−11.0652	+	3.59530i	−1.29508	+	0.420798i	−0.873868	−	0.486163i	$-0.838396\pi$
$73$	−11.0652	+	3.59530i	−1.29508	+	0.420798i	−0.421215	+	0.906961i	$0.638396\pi$
$74$	−0.562756	+	0.974721i	−0.0654190	+	0.113309i
$75$		0			0
$76$	2.06421	+	3.57532i	0.236781	+	0.410117i
$77$	−2.80091	−	2.52195i	−0.319193	−	0.287403i
$78$		0			0
$79$	−1.42166	−	13.5262i	−0.159950	−	1.52182i	−0.720357	−	0.693603i	$-0.756022\pi$
$79$	−1.42166	−	13.5262i	−0.159950	−	1.52182i	0.560407	−	0.828217i	$-0.310645\pi$
$80$	−5.63178	+	1.42393i	−0.629653	+	0.159200i
$81$		0			0
$82$			6.81040i			0.752083i
$83$	−5.96001	−	13.3864i	−0.654196	−	1.46935i	−0.870071	−	0.492927i	$-0.835927\pi$
$83$	−5.96001	−	13.3864i	−0.654196	−	1.46935i	0.215875	−	0.976421i	$-0.430740\pi$
$84$		0			0
$85$	0.190613	+	0.387560i	0.0206748	+	0.0420368i
$86$	−5.50713	+	6.11629i	−0.593849	+	0.659537i
$87$		0			0
$88$	3.20913	−	2.88951i	0.342094	−	0.308023i
$89$	3.38521	+	10.4186i	0.358831	+	1.10437i	0.953754	+	0.300587i	$0.0971825\pi$
$89$	3.38521	+	10.4186i	0.358831	+	1.10437i	−0.594923	+	0.803783i	$0.702817\pi$
$90$		0			0
$91$	0.134675	−	0.414486i	0.0141177	−	0.0434499i
$92$	1.31938	+	2.96339i	0.137555	+	0.308954i
$93$		0			0
$94$	−0.0275518	+	0.262138i	−0.00284175	+	0.0270374i
$95$	15.0646	−	7.40918i	1.54560	−	0.760166i
$96$		0			0
$97$	3.08167	−	0.323896i	0.312896	−	0.0328867i	0.0532209	−	0.998583i	$-0.483051\pi$
$97$	3.08167	−	0.323896i	0.312896	−	0.0328867i	0.259675	+	0.965696i	$0.416385\pi$
$98$	−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
$103$	0.219557	−	0.493132i	0.0216336	−	0.0485898i	−0.902406	−	0.430888i	$-0.858201\pi$
$103$	0.219557	−	0.493132i	0.0216336	−	0.0485898i	0.924039	+	0.382298i	$0.124867\pi$
$104$	0.456165	+	0.203098i	0.0447307	+	0.0199154i
$105$		0			0
$106$	−14.3108	+	6.37160i	−1.38999	+	0.618864i
$107$			0.671621i			0.0649281i	0.999473	+	0.0324640i	$0.0103354\pi$
$107$			0.671621i			0.0649281i	−0.999473	+	0.0324640i	$0.989665\pi$
$108$		0			0
$109$	4.32136	−	13.2998i	0.413911	−	1.27389i	−0.499310	−	0.866423i	$-0.666413\pi$
$109$	4.32136	−	13.2998i	0.413911	−	1.27389i	0.913221	−	0.407464i	$-0.133587\pi$
$110$	−2.34126	−	2.97637i	−0.223231	−	0.283785i
$111$		0			0
$112$	−1.44753	−	6.81012i	−0.136779	−	0.643495i
$113$	0.769916	+	3.62217i	0.0724276	+	0.340745i	0.999409	−	0.0343611i	$-0.0109396\pi$
$113$	0.769916	+	3.62217i	0.0724276	+	0.340745i	−0.926982	+	0.375106i	$0.877606\pi$
$114$		0			0
$115$	12.3804	−	4.55246i	1.15448	−	0.424519i
$116$	1.03544	−	3.18677i	0.0961386	−	0.295884i
$117$		0			0
$118$		−	7.15756i		−	0.658907i
$119$	−0.472890	+	0.210544i	−0.0433497	+	0.0193005i
$120$		0			0
$121$	−8.24218	−	3.66966i	−0.749289	−	0.333605i
$122$	6.90883	−	15.5175i	0.625496	−	1.40489i
$123$		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	0.365132	−	0.930956i	$-0.381024\pi$
$127$	13.6104	−	4.42230i	1.20773	−	0.392416i	0.842600	+	0.538540i	$0.181024\pi$
$128$	4.57486	−	0.480838i	0.404365	−	0.0425004i
$129$		0			0
$130$	0.204295	−	0.387304i	0.0179179	−	0.0339688i
$131$	1.22397	−	11.6453i	0.106938	−	1.01745i	−0.801090	−	0.598543i	$-0.795746\pi$
$131$	1.22397	−	11.6453i	0.106938	−	1.01745i	0.908029	−	0.418908i	$-0.137587\pi$
$132$		0			0
$133$	8.18392	+	18.3814i	0.709636	+	1.59387i
$134$	2.40364	−	7.39763i	0.207643	−	0.639058i
$135$		0			0
$136$	−0.183274	−	0.564059i	−0.0157156	−	0.0483677i
$137$	15.2933	−	13.7702i	1.30660	−	1.17647i	0.334366	−	0.942443i	$-0.391478\pi$
$137$	15.2933	−	13.7702i	1.30660	−	1.17647i	0.972231	−	0.234022i	$-0.0751888\pi$
$138$		0			0
$139$	−0.609700	+	0.677140i	−0.0517141	+	0.0574343i	−0.768447	−	0.639914i	$-0.778970\pi$
$139$	−0.609700	+	0.677140i	−0.0517141	+	0.0574343i	0.716733	+	0.697348i	$0.245637\pi$
$140$	3.26164	−	0.469382i	0.275659	−	0.0396701i
$141$		0			0
$142$	−1.75851	−	3.94967i	−0.147571	−	0.331449i
$143$			0.228698i			0.0191247i
$144$		0			0
$145$	−12.6504	−	5.06254i	−1.05055	−	0.420421i
$146$	−1.46450	−	13.9338i	−0.121203	−	1.15317i
$147$		0			0
$148$	0.381936	+	0.343897i	0.0313949	+	0.0282681i
$149$	−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
$155$	−1.11826	−	0.748912i	−0.0898204	−	0.0601540i
$156$		0			0
$157$	10.4979	−	6.06096i	0.837823	−	0.483717i	−0.0187007	−	0.999825i	$-0.505953\pi$
$157$	10.4979	−	6.06096i	0.837823	−	0.483717i	0.856524	+	0.516108i	$0.172620\pi$
$158$	16.2884	+	1.71198i	1.29584	+	0.136198i
$159$		0			0
$160$	0.257344	+	6.73192i	0.0203448	+	0.532205i
$161$	4.88545	+	15.0359i	0.385027	+	1.18499i
$162$		0			0
$163$	−0.508454	−	0.165207i	−0.0398252	−	0.0129400i	0.289037	−	0.957318i	$-0.406665\pi$
$163$	−0.508454	−	0.165207i	−0.0398252	−	0.0129400i	−0.328862	+	0.944378i	$0.606665\pi$
$164$	3.04190	+	0.646575i	0.237532	+	0.0504890i
$165$		0			0
$166$	17.2600	−	3.66872i	1.33963	−	0.284748i
$167$	−10.8420	−	1.13954i	−0.838979	−	0.0881803i	−0.324715	−	0.945812i	$-0.605268\pi$
$167$	−10.8420	−	1.13954i	−0.838979	−	0.0881803i	−0.514264	+	0.857632i	$0.671935\pi$
$168$		0			0
$169$	11.8519	−	5.27682i	0.911687	−	0.405909i
$170$	−0.504228	+	0.127488i	−0.0386726	+	0.00977791i
$171$		0			0
$172$	2.20903	+	3.04046i	0.168437	+	0.231833i
$173$	−2.18261	+	10.2684i	−0.165941	+	0.780689i	0.813915	+	0.580983i	$0.197332\pi$
$173$	−2.18261	+	10.2684i	−0.165941	+	0.780689i	−0.979856	+	0.199706i	$0.936001\pi$
$174$		0			0
$175$	−1.02300	−	13.3608i	−0.0773313	−	1.00998i
$176$	1.82675	+	3.16402i	0.137696	+	0.238497i
$177$		0			0
$178$	−13.1196	+	1.37892i	−0.983352	+	0.103355i
$179$	11.1491	−	8.10027i	0.833321	−	0.605443i	−0.0871761	−	0.996193i	$-0.527784\pi$
$179$	11.1491	−	8.10027i	0.833321	−	0.605443i	0.920497	+	0.390750i	$0.127784\pi$
$180$		0			0
$181$	−5.95243	−	4.32469i	−0.442441	−	0.321452i	0.344163	−	0.938910i	$-0.388163\pi$
$181$	−5.95243	−	4.32469i	−0.442441	−	0.321452i	−0.786604	+	0.617458i	$0.788163\pi$
$182$	0.454502	+	0.262407i	0.0336899	+	0.0194509i
$183$		0			0
$184$	−17.7180	+	3.76608i	−1.30619	+	0.277639i
$185$	1.49857	−	1.45675i	0.110177	−	0.107102i
$186$		0			0
$187$	0.201865	−	0.181760i	0.0147619	−	0.0132916i
$188$	0.114469	+	0.0371933i	0.00834852	+	0.00271260i
$189$		0			0
$190$	4.95552	+	19.5995i	0.359511	+	1.42190i
$191$	−0.746068	−	0.828592i	−0.0539836	−	0.0599548i	0.715548	−	0.698563i	$-0.246177\pi$
$191$	−0.746068	−	0.828592i	−0.0539836	−	0.0599548i	−0.769532	+	0.638609i	$0.779510\pi$
$192$		0			0
$193$	−21.9469	+	12.6711i	−1.57977	+	0.912083i	−0.584884	+	0.811117i	$0.698860\pi$
$193$	−21.9469	+	12.6711i	−1.57977	+	0.912083i	−0.994890	+	0.100966i	$0.967807\pi$
$194$	−0.390039	+	3.71097i	−0.0280031	+	0.266432i
$195$		0			0
$196$	0.0104809	+	0.0997191i	0.000748636	+	0.00712279i
$197$	−9.37839	−	12.9082i	−0.668182	−	0.919674i	0.331535	−	0.943443i	$-0.392433\pi$
$197$	−9.37839	−	12.9082i	−0.668182	−	0.919674i	−0.999717	+	0.0237688i	$0.992433\pi$
$198$		0			0
$199$	−19.2943			−1.36774			−0.683868	−	0.729606i	$-0.739704\pi$
$199$	−19.2943			−1.36774			−0.683868	+	0.729606i	$0.739704\pi$
$200$	15.3468	+	0.434461i	1.08518	+	0.0307210i
$201$		0			0
$202$	−7.19245	−	6.47611i	−0.506059	−	0.455658i
$203$	6.64235	−	14.9190i	0.466201	−	1.04711i
$204$		0			0
$205$	3.44557	−	12.1676i	0.240649	−	0.849825i
$206$	0.525887	+	0.382080i	0.0366403	+	0.0266207i
$207$		0			0
$208$	−0.248317	+	0.341779i	−0.0172177	+	0.0236981i
$209$	−7.06509	−	7.84658i	−0.488703	−	0.542759i
$210$		0			0
$211$	2.02834	−	2.25270i	0.139637	−	0.155082i	−0.669270	−	0.743019i	$-0.733393\pi$
$211$	2.02834	−	2.25270i	0.139637	−	0.155082i	0.808907	+	0.587937i	$0.200060\pi$
$212$	1.48724	+	6.99692i	0.102144	+	0.480550i
$213$		0			0
$214$	−0.791098	−	0.168153i	−0.0540784	−	0.0114947i
$215$	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
$220$	−1.55169	+	0.763161i	−0.104615	+	0.0514523i
$221$	0.0286944	+	0.0127756i	0.00193019	+	0.000859378i
$222$		0			0
$223$	−3.78775	+	17.8200i	−0.253647	+	1.19331i	0.648273	+	0.761408i	$0.275492\pi$
$223$	−3.78775	+	17.8200i	−0.253647	+	1.19331i	−0.901919	+	0.431905i	$0.857842\pi$
$224$	−8.07429			−0.539486
$225$		0			0
$226$	−4.45929			−0.296628
$227$	1.75915	−	8.27617i	0.116759	−	0.549309i	−0.880416	−	0.474202i	$-0.842737\pi$
$227$	1.75915	−	8.27617i	0.116759	−	0.549309i	0.997175	−	0.0751071i	$-0.0239299\pi$
$228$		0			0
$229$	−8.93614	−	3.97862i	−0.590517	−	0.262915i	0.0896491	−	0.995973i	$-0.471425\pi$
$229$	−8.93614	−	3.97862i	−0.590517	−	0.262915i	−0.680166	+	0.733059i	$0.738092\pi$
$230$	2.26264	+	15.7226i	0.149194	+	1.03672i
$231$		0			0
$232$	16.2042	+	9.35550i	1.06386	+	0.614218i
$233$	1.49631	−	2.05949i	0.0980263	−	0.134922i	−0.757186	−	0.653199i	$-0.773427\pi$
$233$	1.49631	−	2.05949i	0.0980263	−	0.134922i	0.855213	+	0.518277i	$0.173427\pi$
$234$		0			0
$235$	0.181847	−	0.454403i	0.0118624	−	0.0296420i
$236$	−3.19696	−	0.679534i	−0.208104	−	0.0442339i
$237$		0			0
$238$	−0.129602	−	0.609728i	−0.00840082	−	0.0395228i
$239$	−7.06013	+	7.84107i	−0.456682	+	0.507197i	−0.926877	−	0.375366i	$-0.877517\pi$
$239$	−7.06013	+	7.84107i	−0.456682	+	0.507197i	0.470195	+	0.882563i	$0.344184\pi$
$240$		0			0
$241$	−2.05683	−	2.28434i	−0.132492	−	0.147147i	0.673248	−	0.739417i	$-0.264899\pi$
$241$	−2.05683	−	2.28434i	−0.132492	−	0.147147i	−0.805740	+	0.592270i	$0.798232\pi$
$242$	6.38605	−	8.78965i	0.410511	−	0.565020i
$243$		0			0
$244$	−6.27504	−	4.55908i	−0.401718	−	0.291865i
$245$	0.407439	−	0.0155754i	0.0260303	−	0.000995074i
$246$		0			0
$247$	0.496591	−	1.11536i	0.0315973	−	0.0709687i
$248$	1.37345	+	1.23666i	0.0872142	+	0.0785280i
$249$		0			0
$250$	1.27460	−	13.4030i	0.0806127	−	0.847680i
$251$	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
$254$	1.80137	+	17.1389i	0.113028	+	1.07539i
$255$		0			0
$256$	1.26564	−	12.0418i	0.0791027	−	0.752612i
$257$	4.15137	−	2.39680i	0.258955	−	0.149508i	−0.364903	−	0.931046i	$-0.618898\pi$
$257$	4.15137	−	2.39680i	0.258955	−	0.149508i	0.623858	+	0.781538i	$0.285564\pi$
$258$		0			0
$259$	1.67607	+	1.86146i	0.104146	+	0.115666i
$260$	−0.153595	−	0.128020i	−0.00952557	−	0.00793945i
$261$		0			0
$262$	13.4104	+	4.35732i	0.828500	+	0.269196i
$263$	−17.2869	+	15.5652i	−1.06595	+	0.959790i	−0.999278	−	0.0379848i	$-0.987906\pi$
$263$	−17.2869	+	15.5652i	−1.06595	+	0.959790i	−0.0666763	+	0.997775i	$0.521239\pi$
$264$		0			0
$265$	28.7917	−	4.14341i	1.76866	−	0.254528i
$266$	−23.7003	+	5.03766i	−1.45316	+	0.308879i
$267$		0			0
$268$	−3.07599	−	1.77592i	−0.187896	−	0.108482i
$269$	−6.79619	−	4.93772i	−0.414371	−	0.301058i	0.360998	−	0.932567i	$-0.382436\pi$
$269$	−6.79619	−	4.93772i	−0.414371	−	0.301058i	−0.775369	+	0.631508i	$0.782436\pi$
$270$		0			0
$271$	16.4715	−	11.9673i	1.00058	−	0.726960i	0.0383636	−	0.999264i	$-0.487785\pi$
$271$	16.4715	−	11.9673i	1.00058	−	0.726960i	0.962211	+	0.272304i	$0.0877855\pi$
$272$	0.499031	−	0.0524503i	0.0302582	−	0.00318027i
$273$		0			0
$274$	12.3908	+	21.4615i	0.748557	+	1.29654i
$275$	2.67713	+	6.50216i	0.161437	+	0.392095i
$276$		0			0
$277$	−2.12195	+	9.98301i	−0.127496	+	0.599821i	0.867287	+	0.497808i	$0.165862\pi$
$277$	−2.12195	+	9.98301i	−0.127496	+	0.599821i	−0.994783	+	0.102013i	$0.967472\pi$
$278$	−0.644950	−	0.887697i	−0.0386815	−	0.0532405i
$279$		0			0
$280$	−1.22296	+	18.3602i	−0.0730859	+	1.09723i
$281$	−21.4178	+	9.53583i	−1.27768	+	0.568860i	−0.929588	−	0.368600i	$-0.879837\pi$
$281$	−21.4178	+	9.53583i	−1.27768	+	0.568860i	−0.348093	+	0.937460i	$0.613171\pi$
$282$		0			0
$283$	−16.1357	−	1.69593i	−0.959166	−	0.100812i	−0.388011	−	0.921655i	$-0.626838\pi$
$283$	−16.1357	−	1.69593i	−0.959166	−	0.100812i	−0.571155	+	0.820842i	$0.693505\pi$
$284$	−1.93109	+	0.410466i	−0.114589	+	0.0243567i
$285$		0			0
$286$	−0.269382	−	0.0572589i	−0.0159289	−	0.00338579i
$287$	14.4149	+	4.68367i	0.850882	+	0.276468i
$288$		0			0
$289$	5.24176	+	16.1325i	0.308339	+	0.948969i
$290$	9.13040	−	13.6333i	0.536155	−	0.800573i
$291$		0			0
$292$	−6.36263	−	0.668739i	−0.372344	−	0.0391350i
$293$	2.77885	−	1.60437i	0.162342	−	0.0937283i	−0.416628	−	0.909077i	$-0.636788\pi$
$293$	2.77885	−	1.60437i	0.162342	−	0.0937283i	0.578970	+	0.815349i	$0.303455\pi$
$294$		0			0
$295$	−3.62121	+	12.7879i	−0.210835	+	0.744539i
$296$	−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
$302$	−4.77033	−	4.29523i	−0.274502	−	0.247162i
$303$		0			0
$304$	−2.03876	−	19.3975i	−0.116931	−	1.11252i
$305$	−20.1942	+	24.2286i	−1.15632	+	1.38732i
$306$		0			0
$307$		−	16.5271i		−	0.943250i	−0.881799	−	0.471625i	$-0.843668\pi$
$307$		−	16.5271i		−	0.943250i	0.881799	−	0.471625i	$-0.156332\pi$
$308$	−0.842961	−	1.89332i	−0.0480322	−	0.107882i
$309$		0			0
$310$	1.16212	−	1.12968i	0.0660037	−	0.0641616i
$311$	−12.5827	+	13.9745i	−0.713499	+	0.792421i	−0.985464	−	0.169886i	$-0.945660\pi$
$311$	−12.5827	+	13.9745i	−0.713499	+	0.792421i	0.271965	+	0.962307i	$0.412327\pi$
$312$		0			0
$313$	2.34979	−	2.11576i	0.132818	−	0.119590i	−0.600045	−	0.799967i	$-0.704851\pi$
$313$	2.34979	−	2.11576i	0.132818	−	0.119590i	0.732862	+	0.680377i	$0.238184\pi$
$314$	4.51082	+	13.8829i	0.254560	+	0.783456i
$315$		0			0
$316$	2.31108	−	7.11276i	0.130008	−	0.400124i
$317$	0.163144	+	0.366428i	0.00916309	+	0.0205806i	0.918069	−	0.396421i	$-0.129748\pi$
$317$	0.163144	+	0.366428i	0.00916309	+	0.0205806i	−0.908906	+	0.417001i	$0.863081\pi$
$318$		0			0
$319$	−0.895781	+	8.52278i	−0.0501541	+	0.477184i
$320$	−19.4420	−	3.36199i	−1.08684	−	0.187941i
$321$		0			0
$322$	−18.9338	+	1.99003i	−1.05514	+	0.110900i
$323$	−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
$328$	−7.06327	+	15.8644i	−0.390004	+	0.875963i
$329$	0.535891	+	0.238594i	0.0295446	+	0.0131541i
$330$		0			0
$331$	22.0829	−	9.83194i	1.21379	−	0.540412i	0.302881	−	0.953028i	$-0.402052\pi$
$331$	22.0829	−	9.83194i	1.21379	−	0.540412i	0.910905	+	0.412616i	$0.135385\pi$
$332$		−	8.05754i		−	0.442215i
$333$		0			0
$334$	4.05676	−	12.4854i	0.221976	−	0.683172i
$335$	−8.03707	+	12.0007i	−0.439112	+	0.655670i
$336$		0			0
$337$	6.94302	+	32.6643i	0.378210	+	1.77934i	0.595628	+	0.803260i	$0.296903\pi$
$337$	6.94302	+	32.6643i	0.378210	+	1.77934i	−0.217418	+	0.976079i	$0.569763\pi$
$338$	3.24818	+	15.2815i	0.176678	+	0.831202i
$339$		0			0
$340$	0.00907213	+	0.237320i	0.000492005	+	0.0128705i
$341$	−0.261573	+	0.805038i	−0.0141649	+	0.0435952i
$342$		0			0
$343$		−	18.2712i		−	0.986554i
$344$	−19.1719	+	8.53587i	−1.03368	+	0.460223i
$345$		0			0
$346$	−11.5486	−	5.14176i	−0.620856	−	0.276423i
$347$	−1.52284	+	3.42036i	−0.0817505	+	0.183615i	−0.949796	−	0.312870i	$-0.898710\pi$
$347$	−1.52284	+	3.42036i	−0.0817505	+	0.183615i	0.868045	+	0.496485i	$0.165376\pi$
$348$		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
$353$	−5.49417	+	0.577460i	−0.292425	+	0.0307351i	−0.249605	−	0.968348i	$-0.580301\pi$
$353$	−5.49417	+	0.577460i	−0.292425	+	0.0307351i	−0.0428198	+	0.999083i	$0.513634\pi$
$354$		0			0
$355$	1.14355	+	7.94627i	0.0606932	+	0.421744i
$356$	−0.629661	+	5.99082i	−0.0333720	+	0.317513i
$357$		0			0
$358$	6.74988	+	15.1605i	0.356742	+	0.801256i
$359$	4.30244	−	13.2416i	0.227074	−	0.698863i	−0.771000	−	0.636835i	$-0.780243\pi$
$359$	4.30244	−	13.2416i	0.227074	−	0.698863i	0.998074	−	0.0620276i	$-0.0197567\pi$
$360$		0			0
$361$	11.5473	+	35.5388i	0.607750	+	1.87046i
$362$	6.58434	−	5.92856i	0.346065	−	0.311598i
$363$		0			0
$364$	0.160355	−	0.178093i	0.00840490	−	0.00933459i
$365$	−4.43297	+	25.6354i	−0.232032	+	1.34182i
$366$		0			0
$367$	−14.9221	−	33.5157i	−0.778930	−	1.74950i	−0.652853	−	0.757484i	$-0.726428\pi$
$367$	−14.9221	−	33.5157i	−0.778930	−	1.74950i	−0.126077	−	0.992021i	$-0.540239\pi$
$368$		−	15.3252i		−	0.798881i
$369$		0			0
$370$	1.34070	+	2.12988i	0.0696996	+	0.110727i
$371$	3.64419	+	34.6721i	0.189197	+	1.80009i
$372$		0			0
$373$	−13.9005	−	12.5161i	−0.719740	−	0.648057i	0.225571	−	0.974227i	$-0.427575\pi$
$373$	−13.9005	−	12.5161i	−0.719740	−	0.648057i	−0.945311	+	0.326170i	$0.894242\pi$
$374$	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	−0.547314	−	0.836927i	$-0.684350\pi$
$379$	1.54812	−	1.12477i	0.0795216	−	0.0577758i	0.626836	+	0.779151i	$0.284350\pi$
$380$	9.22470	−	0.352637i	0.473217	−	0.0180899i
$381$		0			0
$382$	1.16279	−	0.671335i	0.0594933	−	0.0343485i
$383$	−9.60659	−	1.00969i	−0.490874	−	0.0515929i	−0.144142	−	0.989557i	$-0.546042\pi$
$383$	−9.60659	−	1.00969i	−0.490874	−	0.0515929i	−0.346732	+	0.937964i	$0.612709\pi$
$384$		0			0
$385$	−7.90990	+	2.90859i	−0.403126	+	0.148235i
$386$	−9.43034	−	29.0236i	−0.479991	−	1.47726i
$387$		0			0
$388$	1.62049	+	0.526529i	0.0822680	+	0.0267305i
$389$	22.3540	+	4.75150i	1.13339	+	0.240910i	0.736161	−	0.676807i	$-0.236637\pi$
$389$	22.3540	+	4.75150i	1.13339	+	0.240910i	0.397234	+	0.917717i	$0.369970\pi$
$390$		0			0
$391$	−1.11453	+	0.236900i	−0.0563640	+	0.0119805i
$392$	−0.556841	−	0.0585263i	−0.0281247	−	0.00295603i
$393$		0			0
$394$	17.5526	−	7.81492i	0.884287	−	0.393710i
$395$	−28.2352	−	11.2994i	−1.42066	−	0.568536i
$396$		0			0
$397$	5.64077	+	7.76385i	0.283102	+	0.389657i	0.926758	−	0.375658i	$-0.122583\pi$
$397$	5.64077	+	7.76385i	0.283102	+	0.389657i	−0.643656	+	0.765315i	$0.722583\pi$
$398$	4.83069	−	22.7266i	0.242141	−	1.13918i
$399$		0			0
$400$	−3.05910	+	12.6240i	−0.152955	+	0.631199i
$401$	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
$403$	−0.0973425	+	0.0102311i	−0.00484898	+	0.000509648i
$404$	−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
$409$	2.87866	−	0.611877i	0.142340	−	0.0302554i	−0.136190	−	0.990683i	$-0.543486\pi$
$409$	2.87866	−	0.611877i	0.142340	−	0.0302554i	0.278531	+	0.960427i	$0.410153\pi$
$410$	13.4695	+	7.10492i	0.665212	+	0.350887i
$411$		0			0
$412$	0.220585	−	0.198616i	0.0108674	−	0.00978509i
$413$	−15.1497	−	4.92242i	−0.745466	−	0.242216i
$414$		0			0
$415$	−32.6932	−	2.17766i	−1.60484	−	0.106897i
$416$	0.327833	+	0.364095i	0.0160733	+	0.0178512i
$417$		0			0
$418$	11.0113	−	6.35739i	0.538581	−	0.310950i
$419$	0.638257	−	6.07261i	0.0311809	−	0.296666i	−0.967807	−	0.251692i	$-0.919013\pi$
$419$	0.638257	−	6.07261i	0.0311809	−	0.296666i	0.998988	−	0.0449739i	$-0.0143205\pi$
$420$		0			0
$421$	−0.139754	−	1.32967i	−0.00681119	−	0.0648041i	0.990588	−	0.136875i	$-0.0437059\pi$
$421$	−0.139754	−	1.32967i	−0.00681119	−	0.0648041i	−0.997400	+	0.0720709i	$0.977039\pi$
$422$	2.14561	+	2.95318i	0.104447	+	0.143759i
$423$		0			0
$424$	−39.9443			−1.93987
$425$	0.965367	+	0.0273291i	0.0468272	+	0.00132566i
$426$		0			0
$427$	−28.0929	−	25.2949i	−1.35951	−	1.22411i
$428$	−0.150213	+	0.337383i	−0.00726081	+	0.0163080i
$429$		0			0
$430$	6.35143	+	17.2727i	0.306293	+	0.832965i
$431$	26.8953	+	19.5406i	1.29550	+	0.941237i	0.999901	−	0.0140751i	$-0.00448038\pi$
$431$	26.8953	+	19.5406i	1.29550	+	0.941237i	0.295600	+	0.955312i	$0.404480\pi$
$432$		0			0
$433$	−6.84957	+	9.42763i	−0.329169	+	0.453063i	−0.941239	−	0.337741i	$-0.890337\pi$
$433$	−6.84957	+	9.42763i	−0.329169	+	0.453063i	0.612070	+	0.790804i	$0.290337\pi$
$434$	1.29976	+	1.44353i	0.0623905	+	0.0692917i
$435$		0			0
$436$	5.14538	−	5.71453i	0.246419	−	0.273676i
$437$	9.20838	+	43.3220i	0.440496	+	2.07237i
$438$		0			0
$439$	21.7048	+	4.61349i	1.03591	+	0.220190i	0.694326	−	0.719661i	$-0.255703\pi$
$439$	21.7048	+	4.61349i	1.03591	+	0.220190i	0.341586	+	0.939851i	$0.389036\pi$
$440$	−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	0.326910	−	0.945055i	$-0.393993\pi$
$443$	−6.90522	−	3.98673i	−0.328077	−	0.189415i	−0.654987	+	0.755640i	$0.727326\pi$
$444$		0			0
$445$	24.1374	+	4.17393i	1.14422	+	0.197863i
$446$	−20.0417	−	8.92314i	−0.949002	−	0.422523i
$447$		0			0
$448$	4.91662	−	23.1309i	0.232289	−	1.09283i
$449$	−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
$452$	−0.423362	+	1.99176i	−0.0199133	+	0.0936847i
$453$		0			0
$454$	9.30801	+	4.14419i	0.436847	+	0.194497i
$455$	−0.679266	−	0.698768i	−0.0318445	−	0.0327587i
$456$		0			0
$457$	15.0307	+	8.67800i	0.703108	+	0.405940i	0.808504	−	0.588491i	$-0.200278\pi$
$457$	15.0307	+	8.67800i	0.703108	+	0.405940i	−0.105396	+	0.994430i	$0.533611\pi$
$458$	6.92373	−	9.52970i	0.323525	−	0.445293i
$459$		0			0
$460$	7.23739	+	0.482076i	0.337445	+	0.0224769i
$461$	29.1923	+	6.20502i	1.35962	+	0.288997i	0.829302	−	0.558801i	$-0.188738\pi$
$461$	29.1923	+	6.20502i	1.35962	+	0.288997i	0.530320	+	0.847798i	$0.322072\pi$
$462$		0			0
$463$	2.42807	+	11.4232i	0.112842	+	0.530879i	0.997864	+	0.0653297i	$0.0208099\pi$
$463$	2.42807	+	11.4232i	0.112842	+	0.530879i	−0.885022	+	0.465549i	$0.845857\pi$
$464$	−10.5926	+	11.7643i	−0.491750	+	0.546143i
$465$		0			0
$466$	2.05123	+	2.27812i	0.0950214	+	0.105532i
$467$	8.44207	−	11.6195i	0.390652	−	0.537687i	−0.567715	−	0.823225i	$-0.692172\pi$
$467$	8.44207	−	11.6195i	0.390652	−	0.537687i	0.958367	+	0.285538i	$0.0921724\pi$
$468$		0			0
$469$	−14.0048	−	10.1751i	−0.646680	−	0.469840i
$470$	0.489709	+	0.327965i	0.0225886	+	0.0151279i
$471$		0			0
$472$	7.42332	−	16.6731i	0.341686	−	0.767439i
$473$	−7.14296	−	6.43155i	−0.328434	−	0.295723i
$474$		0			0
$475$	1.06229	−	37.5242i	0.0487414	−	1.72173i
$476$	−0.284642			−0.0130465
$477$		0			0
$478$	−7.46831	−	10.2792i	−0.341592	−	0.470162i
$479$	0.537542	+	5.11437i	0.0245609	+	0.233682i	0.999915	+	0.0130363i	$0.00414970\pi$
$479$	0.537542	+	5.11437i	0.0245609	+	0.233682i	−0.975354	+	0.220645i	$0.929184\pi$
$480$		0			0
$481$	0.0158874	−	0.151159i	0.000724403	−	0.00689224i
$482$	3.20568	−	1.85080i	0.146015	−	0.0843016i
$483$		0			0
$484$	−3.31965	−	3.68684i	−0.150893	−	0.167584i
$485$	2.57433	−	6.43278i	0.116895	−	0.292098i
$486$		0			0
$487$	38.7356	+	12.5860i	1.75528	+	0.570324i	0.996694	−	0.0812511i	$-0.0258916\pi$
$487$	38.7356	+	12.5860i	1.75528	+	0.570324i	0.758584	+	0.651575i	$0.225892\pi$
$488$	32.1873	−	28.9816i	1.45705	−	1.31194i
$489$		0			0
$490$	−0.0836640	+	0.483820i	−0.00377956	+	0.0218568i
$491$	39.2083	−	8.33398i	1.76945	−	0.376107i	0.796049	−	0.605232i	$-0.206920\pi$
$491$	39.2083	−	8.33398i	1.76945	−	0.376107i	0.973397	+	0.229125i	$0.0735864\pi$
$492$		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
$497$	−9.56923	+	1.00577i	−0.429239	+	0.0451148i
$498$		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	$0.606342\pi$
$500$	−5.86550	−	1.84178i	−0.262313	−	0.0823667i
$501$		0			0
$502$	−5.97930	+	28.1304i	−0.266869	+	1.25552i
$503$	−4.96862	−	6.83872i	−0.221540	−	0.304923i	0.683751	−	0.729715i	$-0.260347\pi$
$503$	−4.96862	−	6.83872i	−0.221540	−	0.304923i	−0.905291	+	0.424792i	$0.860347\pi$
$504$		0			0
$505$	9.57377	+	15.2092i	0.426027	+	0.676803i
$506$	9.12668	−	4.06346i	0.405731	−	0.180643i
$507$		0			0
$508$	7.82617	+	0.822564i	0.347230	+	0.0364954i
$509$	12.2912	−	2.61257i	0.544797	−	0.115800i	0.0727116	−	0.997353i	$-0.476835\pi$
$509$	12.2912	−	2.61257i	0.544797	−	0.115800i	0.472085	+	0.881553i	$0.343501\pi$
$510$		0			0
$511$	−30.4993	−	6.48283i	−1.34921	−	0.286784i
$512$	22.6169	+	7.34868i	0.999536	+	0.324769i
$513$		0			0
$514$	1.78380	+	5.48996i	0.0786799	+	0.242152i
$515$	−0.746259	−	0.948694i	−0.0328841	−	0.0418045i
$516$		0			0
$517$	−0.306140	−	0.0321766i	−0.0134640	−	0.00141512i
$518$	−2.61224	+	1.50818i	−0.114775	+	0.0662656i
$519$		0			0
$520$	0.877576	−	0.690317i	0.0384843	−	0.0302724i
$521$	−15.5846	+	11.3229i	−0.682773	+	0.496063i	−0.874276	−	0.485429i	$-0.838664\pi$
$521$	−15.5846	+	11.3229i	−0.682773	+	0.496063i	0.191504	+	0.981492i	$0.438664\pi$
$522$		0			0
$523$	24.3250	−	7.90367i	1.06366	−	0.345604i	0.275644	−	0.961260i	$-0.411109\pi$
$523$	24.3250	−	7.90367i	1.06366	−	0.345604i	0.788015	+	0.615656i	$0.211109\pi$
$524$	3.21939	−	5.57615i	0.140640	−	0.243595i
$525$		0			0
$526$	−14.0060	−	24.2591i	−0.610692	−	1.05775i
$527$	0.0863949	+	0.0777903i	0.00376342	+	0.00338860i
$528$		0			0
$529$	1.23343	+	11.7353i	0.0536273	+	0.510230i
$530$	−2.32805	+	34.9509i	−0.101124	+	1.51817i
$531$		0			0
$532$			11.0641i			0.479691i
$533$	−0.374071	−	0.840178i	−0.0162028	−	0.0363922i
$534$		0			0
$535$	1.32832	+	0.700665i	0.0574284	+	0.0302924i
$536$	13.2714	−	14.7394i	0.573238	−	0.636645i
$537$		0			0
$538$	7.51767	−	6.76894i	0.324110	−	0.291830i
$539$	−0.0792445	−	0.243890i	−0.00341330	−	0.0105051i
$540$		0			0
$541$	−11.8581	+	36.4956i	−0.509821	+	1.56907i	0.282690	+	0.959211i	$0.408773\pi$
$541$	−11.8581	+	36.4956i	−0.509821	+	1.56907i	−0.792511	+	0.609858i	$0.791227\pi$
$542$	9.97222	+	22.3980i	0.428343	+	0.962075i
$543$		0			0
$544$	0.0608278	−	0.578738i	0.00260797	−	0.0248132i
$545$	−21.7959	−	22.4216i	−0.933633	−	0.960437i
$546$		0			0
$547$	−31.0946	+	3.26818i	−1.32951	+	0.139737i	−0.742502	−	0.669844i	$-0.766361\pi$
$547$	−31.0946	+	3.26818i	−1.32951	+	0.139737i	−0.587008	+	0.809581i	$0.699694\pi$
$548$	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
$553$	14.8255	−	33.2986i	0.630444	−	1.41600i
$554$	−11.2277	−	4.99887i	−0.477017	−	0.212382i
$555$		0			0
$556$	−0.457725	+	0.203792i	−0.0194119	+	0.00864272i
$557$		−	24.3166i		−	1.03033i	−0.857091	−	0.515165i	$-0.827731\pi$
$557$		−	24.3166i		−	1.03033i	0.857091	−	0.515165i	$-0.172269\pi$
$558$		0			0
$559$	0.343452	−	1.05704i	0.0145265	−	0.0447078i
$560$	−14.9791	−	4.24170i	−0.632982	−	0.179245i
$561$		0			0
$562$	−5.86984	−	27.6154i	−0.247604	−	1.16489i
$563$	−3.38628	−	15.9312i	−0.142715	−	0.671419i	−0.990091	−	0.140427i	$-0.955153\pi$
$563$	−3.38628	−	15.9312i	−0.142715	−	0.671419i	0.847376	−	0.530993i	$-0.178181\pi$
$564$		0			0
$565$	7.96709	+	2.25608i	0.335178	+	0.0949140i
$566$	6.03750	−	18.5815i	0.253775	−	0.781039i
$567$		0			0
$568$		−	11.0243i		−	0.462569i
$569$	17.4967	−	7.79004i	0.733500	−	0.326575i	−0.00577081	−	0.999983i	$-0.501837\pi$
$569$	17.4967	−	7.79004i	0.733500	−	0.326575i	0.739271	+	0.673408i	$0.235170\pi$
$570$		0			0
$571$	4.20374	+	1.87163i	0.175921	+	0.0783251i	0.492807	−	0.870138i	$-0.335971\pi$
$571$	4.20374	+	1.87163i	0.175921	+	0.0783251i	−0.316886	+	0.948464i	$0.602637\pi$
$572$	−0.0511499	+	0.114885i	−0.00213868	+	0.00480356i
$573$		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	−0.946253	−	0.323427i	$-0.895165\pi$
$577$	−36.5521	+	11.8765i	−1.52168	+	0.494425i	−0.575429	+	0.817852i	$0.695165\pi$
$578$	−20.3147	+	2.13516i	−0.844981	+	0.0888111i
$579$		0			0
$580$	−5.22253	−	5.37247i	−0.216854	−	0.223080i
$581$	4.10489	−	39.0554i	0.170299	−	1.62029i
$582$		0			0
$583$	−7.44112	−	16.7130i	−0.308180	−	0.692183i
$584$	11.0397	−	33.9767i	0.456826	−	1.40597i
$585$		0			0
$586$	1.19404	+	3.67487i	0.0493253	+	0.151808i
$587$	−19.3123	+	17.3889i	−0.797103	+	0.717715i	−0.963314	−	0.268375i	$-0.913513\pi$
$587$	−19.3123	+	17.3889i	−0.797103	+	0.717715i	0.166211	+	0.986090i	$0.446847\pi$
$588$		0			0
$589$	3.02374	−	3.35820i	0.124591	−	0.138372i
$590$	−14.1561	−	7.46709i	−0.582798	−	0.307415i
$591$		0			0
$592$	−0.987594	−	2.21817i	−0.0405898	−	0.0911663i
$593$			32.5216i			1.33550i	0.744385	+	0.667750i	$0.232743\pi$
$593$			32.5216i			1.33550i	−0.744385	+	0.667750i	$0.767257\pi$
$594$		0			0
$595$	−0.0769285	+	1.15492i	−0.00315376	+	0.0473473i
$596$	−1.21952	−	11.6029i	−0.0499534	−	0.475275i
$597$		0			0
$598$	0.858489	+	0.772987i	0.0351062	+	0.0316098i
$599$	−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
$605$	−15.8564	+	12.4729i	−0.644655	+	0.507097i
$606$		0			0
$607$	18.1063	−	10.4537i	0.734910	−	0.424301i	−0.0853054	−	0.996355i	$-0.527187\pi$
$607$	18.1063	−	10.4537i	0.734910	−	0.424301i	0.820216	+	0.572054i	$0.193853\pi$
$608$	−22.4957	−	2.36440i	−0.912323	−	0.0958890i
$609$		0			0
$610$	−23.4827	−	29.8527i	−0.950786	−	1.20870i
$611$	−0.0109993	−	0.0338524i	−0.000444985	−	0.00136952i
$612$		0			0
$613$	−3.43863	−	1.11728i	−0.138885	−	0.0451265i	0.238750	−	0.971081i	$-0.423262\pi$
$613$	−3.43863	−	1.11728i	−0.138885	−	0.0451265i	−0.377635	+	0.925955i	$0.623262\pi$
$614$	19.4671	+	4.13787i	0.785630	+	0.166991i
$615$		0			0
$616$	11.3201	−	2.40617i	0.456101	−	0.0969472i
$617$	−5.85144	−	0.615011i	−0.235570	−	0.0247594i	−0.0139922	−	0.999902i	$-0.504454\pi$
$617$	−5.85144	−	0.615011i	−0.235570	−	0.0247594i	−0.221578	+	0.975143i	$0.571121\pi$
$618$		0			0
$619$	−25.2160	+	11.2269i	−1.01352	+	0.451247i	−0.845180	−	0.534482i	$-0.820507\pi$
$619$	−25.2160	+	11.2269i	−1.01352	+	0.451247i	−0.168338	+	0.985729i	$0.553840\pi$
$620$	−0.394247	−	0.626315i	−0.0158333	−	0.0251534i
$621$		0			0
$622$	−13.3102	−	18.3199i	−0.533689	−	0.734559i
$623$	−6.10401	+	28.7171i	−0.244552	+	1.15053i
$624$		0			0
$625$	−9.05817	+	23.3013i	−0.362327	+	0.932051i
$626$	1.90382	+	3.29752i	0.0760921	+	0.131795i
$627$		0			0
$628$	6.62910	−	0.696747i	0.264530	−	0.0278032i
$629$	−0.146050	+	0.106112i	−0.00582340	+	0.00423095i
$630$		0			0
$631$	−5.50355	−	3.99857i	−0.219093	−	0.159180i	0.472825	−	0.881156i	$-0.343234\pi$
$631$	−5.50355	−	3.99857i	−0.219093	−	0.159180i	−0.691918	+	0.721976i	$0.743234\pi$
$632$	36.1672	+	20.8811i	1.43865	+	0.830607i
$633$		0			0
$634$	−0.472460	+	0.100424i	−0.0187638	+	0.00398836i
$635$	5.45266	−	31.5321i	0.216382	−	1.25131i
$636$		0			0
$637$	0.0220363	−	0.0198416i	0.000873110	−	0.000786152i
$638$	−9.81466	−	3.18898i	−0.388566	−	0.126253i
$639$		0			0
$640$	3.82171	−	9.54974i	0.151066	−	0.377486i
$641$	−1.26962	−	1.41006i	−0.0501471	−	0.0556940i	0.717549	−	0.696508i	$-0.245264\pi$
$641$	−1.26962	−	1.41006i	−0.0501471	−	0.0556940i	−0.767696	+	0.640814i	$0.778597\pi$
$642$		0			0
$643$	−13.7142	+	7.91791i	−0.540836	+	0.312252i	−0.745418	−	0.666598i	$-0.767750\pi$
$643$	−13.7142	+	7.91791i	−0.540836	+	0.312252i	0.204581	+	0.978850i	$0.434417\pi$
$644$	−0.908711	+	8.64581i	−0.0358082	+	0.340693i
$645$		0			0
$646$	−0.182536	−	1.73671i	−0.00718177	−	0.0683300i
$647$	1.30998	+	1.80303i	0.0515007	+	0.0708846i	0.833991	−	0.551779i	$-0.186051\pi$
$647$	1.30998	+	1.80303i	0.0515007	+	0.0708846i	−0.782490	+	0.622663i	$0.786051\pi$
$648$		0			0
$649$	8.35902			0.328120
$650$	−0.552874	−	0.808105i	−0.0216855	−	0.0316965i
$651$		0			0
$652$	−0.218468	−	0.196710i	−0.00855588	−	0.00770375i
$653$	−0.410721	+	0.922493i	−0.0160727	+	0.0361000i	−0.921403	−	0.388607i	$-0.872956\pi$
$653$	−0.410721	+	0.922493i	−0.0160727	+	0.0361000i	0.905331	+	0.424707i	$0.139623\pi$
$654$		0			0
$655$	−21.7549	−	14.5696i	−0.850036	−	0.569282i
$656$	−11.8863	−	8.63588i	−0.464081	−	0.337174i
$657$		0			0
$658$	−0.415209	+	0.571486i	−0.0161865	+	0.0222788i
$659$	−9.81851	−	10.9046i	−0.382475	−	0.424782i	0.520910	−	0.853611i	$-0.325593\pi$
$659$	−9.81851	−	10.9046i	−0.382475	−	0.424782i	−0.903385	+	0.428830i	$0.858926\pi$
$660$		0			0
$661$	21.1903	−	23.5343i	0.824209	−	0.915377i	−0.173374	−	0.984856i	$-0.555467\pi$
$661$	21.1903	−	23.5343i	0.824209	−	0.915377i	0.997583	+	0.0694791i	$0.0221337\pi$
$662$	6.05211	+	28.4729i	0.235222	+	1.10663i
$663$		0			0
$664$	44.0108	+	9.35479i	1.70795	+	0.363036i
$665$	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
$670$	−12.1234	−	12.4714i	−0.468366	−	0.481813i
$671$	18.1222	+	8.06854i	0.699601	+	0.311483i
$672$		0			0
$673$	−8.41881	+	39.6074i	−0.324521	+	1.52675i	0.449318	+	0.893372i	$0.351667\pi$
$673$	−8.41881	+	39.6074i	−0.324521	+	1.52675i	−0.773840	+	0.633382i	$0.781666\pi$
$674$	−40.2134			−1.54896
$675$		0			0
$676$	7.13392			0.274381
$677$	−0.524831	+	2.46914i	−0.0201709	+	0.0948967i	−0.987082	−	0.160219i	$-0.948780\pi$
$677$	−0.524831	+	2.46914i	−0.0201709	+	0.0948967i	0.966911	+	0.255115i	$0.0821134\pi$
$678$		0			0
$679$	7.58638	+	3.37767i	0.291138	+	0.129623i
$680$	−1.30679	−	0.225975i	−0.0501130	−	0.00866575i
$681$		0			0
$682$	−0.882759	−	0.509661i	−0.0338026	−	0.0195159i
$683$	−12.8169	+	17.6409i	−0.490425	+	0.675012i	−0.980466	−	0.196687i	$-0.936982\pi$
$683$	−12.8169	+	17.6409i	−0.490425	+	0.675012i	0.490042	+	0.871699i	$0.336982\pi$
$684$		0			0
$685$	−11.2798	−	44.6126i	−0.430978	−	1.70456i
$686$	21.5216	+	4.57455i	0.821698	+	0.174657i
$687$		0			0
$688$	−3.69155	−	17.3674i	−0.140739	−	0.662125i
$689$	1.41551	−	1.57209i	0.0539268	−	0.0598918i
$690$		0			0
$691$	8.57457	+	9.52302i	0.326192	+	0.362273i	0.883827	−	0.467813i	$-0.154958\pi$
$691$	8.57457	+	9.52302i	0.326192	+	0.362273i	−0.557635	+	0.830086i	$0.688291\pi$
$692$	−3.39301	+	4.67007i	−0.128983	+	0.177529i
$693$		0			0
$694$	−3.64755	−	2.65010i	−0.138459	−	0.100596i
$695$	0.703173	+	1.91228i	0.0266729	+	0.0725369i
$696$		0			0
$697$	−0.444305	+	0.997924i	−0.0168292	+	0.0377991i
$698$	−15.5310	−	13.9842i	−0.587859	−	0.529310i
$699$		0			0
$700$	2.47435	−	6.94051i	0.0935217	−	0.262327i
$701$	−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
$704$	1.29712	+	12.3413i	0.0488872	+	0.465130i
$705$		0			0
$706$	0.695382	−	6.61612i	0.0261711	−	0.249001i
$707$	−18.6537	+	10.7697i	−0.701545	+	0.405037i
$708$		0			0
$709$	−5.03486	−	5.59178i	−0.189088	−	0.210004i	0.641145	−	0.767420i	$-0.278460\pi$
$709$	−5.03486	−	5.59178i	−0.189088	−	0.210004i	−0.830233	+	0.557416i	$0.811793\pi$
$710$	−9.64617	−	0.642523i	−0.362014	−	0.0241135i
$711$		0			0
$712$	−31.9912	−	10.3946i	−1.19892	−	0.389554i
$713$	2.63864	−	2.37584i	0.0988179	−	0.0889761i
$714$		0			0
$715$	0.452316	+	0.238588i	0.0169157	+	0.00892268i
$716$	7.41233	−	1.57554i	0.277012	−	0.0588806i
$717$		0			0
$718$	14.5199	+	8.38310i	0.541880	+	0.312854i
$719$	35.5528	+	25.8307i	1.32590	+	0.963321i	0.999839	+	0.0179714i	$0.00572079\pi$
$719$	35.5528	+	25.8307i	1.32590	+	0.963321i	0.326059	+	0.945349i	$0.394279\pi$
$720$		0			0
$721$	1.17037	−	0.850325i	0.0435869	−	0.0316678i
$722$	−44.7520	+	4.70362i	−1.66550	+	0.175051i
$723$		0			0
$724$	−2.02291	−	3.50378i	−0.0751807	−	0.130217i
$725$	−23.2100	+	19.7382i	−0.862000	+	0.733059i
$726$		0			0
$727$	−7.73183	+	36.3754i	−0.286758	+	1.34909i	0.564973	+	0.825109i	$0.308886\pi$
$727$	−7.73183	+	36.3754i	−0.286758	+	1.34909i	−0.851731	+	0.523979i	$0.824447\pi$
$728$	0.786582	+	1.08264i	0.0291527	+	0.0401252i
$729$		0			0
$730$	−29.0859	−	11.6399i	−1.07652	−	0.430811i
$731$	−1.20598	+	0.536936i	−0.0446047	+	0.0198593i
$732$		0			0
$733$	−5.49330	−	0.577369i	−0.202900	−	0.0213256i	0.00253335	−	0.999997i	$-0.499194\pi$
$733$	−5.49330	−	0.577369i	−0.202900	−	0.0213256i	−0.205433	+	0.978671i	$0.565860\pi$
$734$	43.2140	−	9.18541i	1.59506	−	0.339040i
$735$		0			0
$736$	−17.3846	−	3.69521i	−0.640804	−	0.136207i
$737$	8.63939	+	2.80711i	0.318236	+	0.103401i
$738$		0			0
$739$	13.0729	+	40.2342i	0.480894	+	1.48004i	0.837840	+	0.545915i	$0.183818\pi$
$739$	13.0729	+	40.2342i	0.480894	+	1.48004i	−0.356946	+	0.934125i	$0.616182\pi$
$740$	1.07861	−	0.396619i	0.0396504	−	0.0145800i
$741$		0			0
$742$	−41.7525	−	4.38836i	−1.53278	−	0.161102i
$743$	−16.0074	+	9.24189i	−0.587256	+	0.339052i	−0.764012	−	0.645203i	$-0.776773\pi$
$743$	−16.0074	+	9.24189i	−0.587256	+	0.339052i	0.176756	+	0.984255i	$0.443440\pi$
$744$		0			0
$745$	−47.4081	+	1.81229i	−1.73690	+	0.0663972i
$746$	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	$0.680754\pi$
$752$	−0.422575	−	0.380488i	−0.0154097	−	0.0138750i
$753$		0			0
$754$	−0.124733	−	1.18676i	−0.00454251	−	0.0432191i
$755$	6.34972	+	10.0874i	0.231090	+	0.367118i
$756$		0			0
$757$		−	14.6646i		−	0.532993i	−0.963836	−	0.266497i	$-0.914134\pi$
$757$		−	14.6646i		−	0.532993i	0.963836	−	0.266497i	$-0.0858661\pi$
$758$	0.937264	+	2.10513i	0.0340430	+	0.0764617i
$759$		0			0
$760$	−8.78373	+	50.7953i	−0.318619	+	1.84254i
$761$	−6.68308	+	7.42231i	−0.242261	+	0.269059i	−0.851997	−	0.523546i	$-0.824609\pi$
$761$	−6.68308	+	7.42231i	−0.242261	+	0.269059i	0.609736	+	0.792605i	$0.291275\pi$
$762$		0			0
$763$	27.8512	−	25.0774i	1.00828	−	0.907861i
$764$	−0.189461	−	0.583100i	−0.00685444	−	0.0210958i
$765$		0			0
$766$	3.59450	−	11.0627i	0.129875	−	0.399713i
$767$	0.393140	+	0.883006i	0.0141954	+	0.0318835i
$768$		0			0
$769$	1.93245	−	18.3860i	0.0696860	−	0.663018i	−0.902801	−	0.430059i	$-0.858493\pi$
$769$	1.93245	−	18.3860i	0.0696860	−	0.663018i	0.972487	−	0.232958i	$-0.0748406\pi$
$770$	−1.44561	−	10.0452i	−0.0520962	−	0.362006i
$771$		0			0
$772$	−13.8588	+	1.45662i	−0.498790	+	0.0524250i
$773$	−3.41227	+	1.10871i	−0.122731	+	0.0398777i	−0.369739	−	0.929136i	$-0.620553\pi$
$773$	−3.41227	+	1.10871i	−0.122731	+	0.0398777i	0.247008	+	0.969014i	$0.420553\pi$
$774$		0			0
$775$	−2.64780	+	1.43037i	−0.0951119	+	0.0513805i
$776$	−4.75733	+	8.23993i	−0.170778	+	0.295796i
$777$		0			0
$778$	−11.1935	+	25.1411i	−0.401307	+	0.901350i
$779$	38.7897	+	17.2703i	1.38978	+	0.618772i
$780$		0			0
$781$	4.61266	−	2.05369i	0.165054	−	0.0734868i
$782$		−	1.37211i		−	0.0490664i
$783$		0			0
$784$	0.146384	−	0.450524i	0.00522801	−	0.0160902i
$785$	−1.03542	−	27.0857i	−0.0369556	−	0.966728i
$786$		0			0
$787$	3.36327	+	15.8229i	0.119888	+	0.564026i	0.996555	+	0.0829303i	$0.0264279\pi$
$787$	3.36327	+	15.8229i	0.119888	+	0.564026i	−0.876668	+	0.481096i	$0.840239\pi$
$788$	−1.82414	−	8.58189i	−0.0649822	−	0.305717i
$789$		0			0
$790$	20.3787	−	30.4290i	0.725043	−	1.08261i
$791$	−3.06676	+	9.43852i	−0.109041	+	0.335595i
$792$		0			0
$793$			2.29382i			0.0814561i
$794$	−10.5573	+	4.70040i	−0.374664	+	0.166811i
$795$		0			0
$796$	−9.69232	−	4.31530i	−0.343535	−	0.152952i
$797$	7.73579	−	17.3749i	0.274016	−	0.615450i	−0.723149	−	0.690692i	$-0.757306\pi$
$797$	7.73579	−	17.3749i	0.274016	−	0.615450i	0.997165	+	0.0752419i	$0.0239729\pi$
$798$		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
$803$	16.2727	−	1.71033i	0.574251	−	0.0603562i
$804$		0			0
$805$	34.8345	+	6.02372i	1.22775	+	0.212308i
$806$	0.0123204	−	0.117221i	0.000433967	−	0.00412892i
$807$		0			0
$808$	−10.0378	−	22.5452i	−0.353127	−	0.793137i
$809$	−3.06508	+	9.43335i	−0.107763	+	0.331659i	−0.990369	−	0.138454i	$-0.955787\pi$
$809$	−3.06508	+	9.43335i	−0.107763	+	0.331659i	0.882606	+	0.470113i	$0.155787\pi$
$810$		0			0
$811$	8.46694	+	26.0585i	0.297314	+	0.915039i	0.982434	+	0.186609i	$0.0597498\pi$
$811$	8.46694	+	26.0585i	0.297314	+	0.915039i	−0.685120	+	0.728430i	$0.740250\pi$
$812$	6.67346	−	6.00881i	0.234192	−	0.210868i
$813$		0			0
$814$	1.05914	−	1.17629i	0.0371228	−	0.0412290i
$815$	−0.857186	+	0.833263i	−0.0300259	+	0.0291879i
$816$		0			0
$817$	20.8709	+	46.8768i	0.730181	+	1.64001i
$818$			3.54395i			0.123911i
$819$		0			0
$820$	4.45223	−	5.34169i	0.155479	−	0.186540i
$821$	−1.00345	−	9.54718i	−0.0350206	−	0.333199i	−0.997979	−	0.0635480i	$-0.979758\pi$
$821$	−1.00345	−	9.54718i	−0.0350206	−	0.333199i	0.962958	−	0.269651i	$-0.0869083\pi$
$822$		0			0
$823$	−25.5845	−	23.0364i	−0.891819	−	0.802998i	0.0893794	−	0.995998i	$-0.471512\pi$
$823$	−25.5845	−	23.0364i	−0.891819	−	0.802998i	−0.981199	+	0.193000i	$0.938178\pi$
$824$	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	−0.714220	−	0.699922i	$-0.753218\pi$
$827$	−25.3249	+	8.22855i	−0.880632	+	0.286135i	−0.166412	+	0.986056i	$0.553218\pi$
$828$		0			0
$829$	28.0528	−	20.3815i	0.974314	−	0.707880i	0.0178831	−	0.999840i	$-0.494307\pi$
$829$	28.0528	−	20.3815i	0.974314	−	0.707880i	0.956431	+	0.291960i	$0.0943073\pi$
$830$	10.7504	−	37.9639i	0.373152	−	1.31775i
$831$		0			0
$832$	−1.24267	+	0.717456i	−0.0430818	+	0.0248733i
$833$	−0.0350272	−	0.00368151i	−0.00121362	−	0.000127557i
$834$		0			0
$835$	−13.5646	+	20.2543i	−0.469423	+	0.700931i
$836$	−1.79415	−	5.52182i	−0.0620519	−	0.190976i
$837$		0			0
$838$	6.99309	+	2.27219i	0.241572	+	0.0784916i
$839$	4.59725	+	0.977175i	0.158715	+	0.0337358i	0.286584	−	0.958055i	$-0.407480\pi$
$839$	4.59725	+	0.977175i	0.158715	+	0.0337358i	−0.127869	+	0.991791i	$0.540814\pi$
$840$		0			0
$841$	−7.95445	+	1.69077i	−0.274291	+	0.0583024i
$842$	1.60120	+	0.168293i	0.0551810	+	0.00579975i
$843$		0			0
$844$	1.52275	−	0.677974i	0.0524154	−	0.0233368i
$845$	1.92804	−	28.9456i	0.0663267	−	0.995759i
$846$		0			0
$847$	−14.2123	−	19.5615i	−0.488340	−	0.672142i
$848$	7.02634	−	33.0563i	0.241285	−	1.13516i
$849$		0			0
$850$	−0.273889	+	1.13026i	−0.00939431	+	0.0387675i
$851$	2.75681	+	4.77494i	0.0945023	+	0.163683i
$852$		0			0
$853$	18.6763	−	1.96296i	0.639465	−	0.0672105i	0.220753	−	0.975330i	$-0.429148\pi$
$853$	18.6763	−	1.96296i	0.639465	−	0.0672105i	0.418712	+	0.908119i	$0.362482\pi$
$854$	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	−0.0705962	−	0.997505i	$-0.522490\pi$
$857$	−28.3893	−	16.3906i	−0.969759	−	0.559891i	−0.899163	+	0.437614i	$0.855824\pi$
$858$		0			0
$859$	−9.26946	+	1.97028i	−0.316270	+	0.0672252i	−0.363312	−	0.931668i	$-0.618354\pi$
$859$	−9.26946	+	1.97028i	−0.316270	+	0.0672252i	0.0470417	+	0.998893i	$0.485021\pi$
$860$	8.31794	−	1.19703i	0.283639	−	0.0408185i
$861$		0			0
$862$	−29.7505	+	26.7875i	−1.01331	+	0.912384i
$863$	32.4083	+	10.5301i	1.10319	+	0.358449i	0.803330	−	0.595534i	$-0.203059\pi$
$863$	32.4083	+	10.5301i	1.10319	+	0.358449i	0.299862	+	0.953983i	$0.403059\pi$
$864$		0			0
$865$	18.0316	+	15.0291i	0.613094	+	0.511006i
$866$	−9.38982	−	10.4285i	−0.319079	−	0.354373i
$867$		0			0
$868$	0.768158	−	0.443496i	0.0260730	−	0.0150532i
$869$	−1.99935	+	19.0226i	−0.0678233	+	0.645296i
$870$		0			0
$871$	0.109797	+	1.04465i	0.00372032	+	0.0353965i
$872$	25.2394	+	34.7390i	0.854712	+	1.17641i
$873$		0			0
$874$	−53.3342			−1.80406
$875$	−27.4921	−	11.9154i	−0.929404	−	0.402813i
$876$		0			0
$877$	20.0817	+	18.0816i	0.678109	+	0.610572i	0.934484	−	0.356005i	$-0.115861\pi$
$877$	20.0817	+	18.0816i	0.678109	+	0.610572i	−0.256375	+	0.966577i	$0.582528\pi$
$878$	−10.8684	+	24.4108i	−0.366791	+	0.823826i
$879$		0			0
$880$	8.16351	−	0.312070i	0.275192	−	0.0105199i
$881$	−44.5745	−	32.3853i	−1.50175	−	1.09109i	−0.969676	−	0.244393i	$-0.921411\pi$
$881$	−44.5745	−	32.3853i	−1.50175	−	1.09109i	−0.532078	−	0.846695i	$-0.678589\pi$
$882$		0			0
$883$	23.9914	−	33.0214i	0.807376	−	1.11126i	−0.184347	−	0.982861i	$-0.559017\pi$
$883$	23.9914	−	33.0214i	0.807376	−	1.11126i	0.991723	−	0.128396i	$-0.0409829\pi$
$884$	0.0115570	+	0.0128354i	0.000388706	+	0.000431701i
$885$		0			0
$886$	6.42480	−	7.13546i	0.215845	−	0.239721i
$887$	−6.07787	−	28.5941i	−0.204075	−	0.960096i	−0.954285	−	0.298897i	$-0.903381\pi$
$887$	−6.07787	−	28.5941i	−0.204075	−	0.960096i	0.750211	−	0.661199i	$-0.229952\pi$
$888$		0			0
$889$	37.5149	+	7.97403i	1.25821	+	0.267440i
$890$	−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
$895$	−4.38940	−	30.5011i	−0.146722	−	1.01954i
$896$	11.2623	+	5.01430i	0.376247	+	0.167516i
$897$		0			0
$898$	4.87773	−	22.9479i	0.162772	−	0.765781i
$899$	−3.66769			−0.122324
$900$		0			0
$901$	−2.51264			−0.0837081
$902$	1.99133	−	9.36848i	0.0663041	−	0.311936i
$903$		0			0
$904$	−10.3876	−	4.62487i	−0.345487	−	0.153821i
$905$	−14.7632	+	7.26093i	−0.490744	+	0.241361i
$906$		0			0
$907$	26.5281	+	15.3160i	0.880851	+	0.508560i	0.870939	−	0.491391i	$-0.163511\pi$
$907$	26.5281	+	15.3160i	0.880851	+	0.508560i	0.00991216	+	0.999951i	$0.496845\pi$
$908$	2.73472	−	3.76402i	0.0907548	−	0.124913i
$909$		0			0
$910$	0.993142	−	0.625153i	0.0329223	−	0.0207236i
$911$	−9.96400	−	2.11791i	−0.330122	−	0.0701696i	0.0398691	−	0.999205i	$-0.487306\pi$
$911$	−9.96400	−	2.11791i	−0.330122	−	0.0701696i	−0.369991	+	0.929035i	$0.620639\pi$
$912$		0			0
$913$	4.28454	+	20.1572i	0.141798	+	0.667105i
$914$	−13.9850	+	15.5319i	−0.462583	+	0.513750i
$915$		0			0
$916$	−3.59915	−	3.99726i	−0.118919	−	0.132073i
$917$	18.4453	−	25.3878i	0.609119	−	0.838380i
$918$		0			0
$919$	21.8946	+	15.9074i	0.722236	+	0.524735i	0.887098	−	0.461581i	$-0.152718\pi$
$919$	21.8946	+	15.9074i	0.722236	+	0.524735i	−0.164862	+	0.986317i	$0.552718\pi$
$920$	−11.0357	+	38.9714i	−0.363837	+	1.28485i
$921$		0			0
$922$	−14.6177	+	32.8319i	−0.481409	+	1.08126i
$923$	0.433884	+	0.390670i	0.0142814	+	0.0128591i
$924$		0			0
$925$	−1.31776	−	4.48360i	−0.0433277	−	0.147420i
$926$	−14.0632			−0.462145
$927$		0			0
$928$	10.7911	+	14.8526i	0.354234	+	0.487562i
$929$	−2.13333	−	20.2972i	−0.0699922	−	0.665931i	−0.972123	−	0.234470i	$-0.924665\pi$
$929$	−2.13333	−	20.2972i	−0.0699922	−	0.665931i	0.902131	−	0.431462i	$-0.142002\pi$
$930$		0			0
$931$	−0.143102	+	1.36152i	−0.00468997	+	0.0446221i
$932$	1.21228	−	0.699908i	0.0397094	−	0.0229262i
$933$		0			0
$934$	11.5729	+	12.8530i	0.378677	+	0.420564i
$935$	−0.148888	−	0.588867i	−0.00486917	−	0.0192580i
$936$		0			0
$937$	19.4195	+	6.30978i	0.634408	+	0.206132i	0.608527	−	0.793533i	$-0.291761\pi$
$937$	19.4195	+	6.30978i	0.634408	+	0.206132i	0.0258811	+	0.999665i	$0.491761\pi$
$938$	15.4915	−	13.9486i	0.505815	−	0.455438i
$939$		0			0
$940$	0.192980	−	0.187594i	0.00629431	−	0.00611864i
$941$	−0.576816	+	0.122606i	−0.0188037	+	0.00399684i	−0.217304	−	0.976104i	$-0.569726\pi$
$941$	−0.576816	+	0.122606i	−0.0188037	+	0.00399684i	0.198500	+	0.980101i	$0.436393\pi$
$942$		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
$947$	−26.8317	+	2.82012i	−0.871913	+	0.0916417i	−0.529907	−	0.848056i	$-0.677773\pi$
$947$	−26.8317	+	2.82012i	−0.871913	+	0.0916417i	−0.342006	+	0.939698i	$0.611106\pi$
$948$		0			0
$949$	0.946005	+	1.63853i	0.0307086	+	0.0531889i
$950$	43.9335	+	10.6462i	1.42539	+	0.345407i
$951$		0			0
$952$	0.330469	−	1.55473i	0.0107106	−	0.0503892i
$953$	10.0812	+	13.8756i	0.326563	+	0.449475i	0.940457	−	0.339913i	$-0.110398\pi$
$953$	10.0812	+	13.8756i	0.326563	+	0.449475i	−0.613894	+	0.789388i	$0.710398\pi$
$954$		0			0
$955$	−2.41711	+	0.611139i	−0.0782159	+	0.0197760i
$956$	−5.30031	+	2.35985i	−0.171424	+	0.0763230i
$957$		0			0
$958$	−6.15877	−	0.647313i	−0.198981	−	0.0209137i
$959$	53.9469	−	11.4668i	1.74203	−	0.370281i
$960$		0			0
$961$	29.9682	+	6.36994i	0.966717	+	0.205482i
$962$	0.174071	+	0.0565591i	0.00561227	+	0.00182354i
$963$		0			0
$964$	−0.522323	−	1.60755i	−0.0168229	−	0.0517756i
$965$	2.16464	+	56.6254i	0.0696824	+	1.82283i
$966$		0			0
$967$	−13.3682	−	1.40505i	−0.429892	−	0.0451835i	−0.112888	−	0.993608i	$-0.536010\pi$
$967$	−13.3682	−	1.40505i	−0.429892	−	0.0451835i	−0.317004	+	0.948424i	$0.602677\pi$
$968$	23.9919	−	13.8517i	0.771129	−	0.445211i
$969$		0			0
$970$	6.93260	+	4.64286i	0.222592	+	0.149073i
$971$	17.9377	−	13.0325i	0.575648	−	0.418232i	−0.261505	−	0.965202i	$-0.584219\pi$
$971$	17.9377	−	13.0325i	0.575648	−	0.418232i	0.837152	+	0.546970i	$0.184219\pi$
$972$		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
$977$	15.5249	+	13.9787i	0.496687	+	0.447219i	0.879006	−	0.476812i	$-0.158208\pi$
$977$	15.5249	+	13.9787i	0.496687	+	0.447219i	−0.382318	+	0.924031i	$0.624874\pi$
$978$		0			0
$979$	−1.61038	−	15.3218i	−0.0514681	−	0.489686i
$980$	0.208157	+	0.0833025i	0.00664934	+	0.00266100i
$981$		0			0
$982$			48.2698i			1.54035i
$983$	11.1398	+	25.0205i	0.355306	+	0.798030i	0.999451	+	0.0331270i	$0.0105466\pi$
$983$	11.1398	+	25.0205i	0.355306	+	0.798030i	−0.644145	+	0.764903i	$0.722787\pi$
$984$		0			0
$985$	−35.3137	+	5.08199i	−1.12519	+	0.161926i
$986$	−0.948384	+	1.05329i	−0.0302027	+	0.0335435i
$987$		0			0
$988$	0.498917	−	0.449227i	0.0158727	−	0.0142918i
$989$	12.4590	+	38.3450i	0.396174	+	1.21930i
$990$		0			0
$991$	−4.58088	+	14.0985i	−0.145516	+	0.447854i	−0.997077	−	0.0764026i	$-0.975657\pi$
$991$	−4.58088	+	14.0985i	−0.145516	+	0.447854i	0.851561	+	0.524256i	$0.175657\pi$
$992$	0.737568	+	1.65660i	0.0234178	+	0.0525973i
$993$		0			0
$994$	1.21115	−	11.5233i	0.0384154	−	0.365498i
$995$	−20.1287	+	38.1600i	−0.638122	+	1.20975i
$996$		0			0
$997$	−2.06076	+	0.216595i	−0.0652651	+	0.00685964i	−0.137105	−	0.990557i	$-0.543780\pi$
$997$	−2.06076	+	0.216595i	−0.0652651	+	0.00685964i	0.0718396	+	0.997416i	$0.477113\pi$
$998$	−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.19.9		224
3.2	odd	2		225.2.u.a.169.20	yes	224
9.4	even	3	inner	675.2.y.a.469.9		224
9.5	odd	6		225.2.u.a.94.20	yes	224
25.4	even	10	inner	675.2.y.a.154.9		224
75.29	odd	10		225.2.u.a.79.20	yes	224
225.4	even	30	inner	675.2.y.a.604.9		224
225.104	odd	30		225.2.u.a.4.20	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.20	✓	224	225.104	odd	30
225.2.u.a.79.20	yes	224	75.29	odd	10
225.2.u.a.94.20	yes	224	9.5	odd	6
225.2.u.a.169.20	yes	224	3.2	odd	2
675.2.y.a.19.9		224	1.1	even	1	trivial
675.2.y.a.154.9		224	25.4	even	10	inner
675.2.y.a.469.9		224	9.4	even	3	inner
675.2.y.a.604.9		224	225.4	even	30	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)

\(f(q)\)	\(=\)	\(q+(-0.250369 + 1.17789i) q^{2} +(0.502342 + 0.223657i) q^{4} +(1.04324 - 1.97779i) q^{5} +(2.32094 + 1.33999i) q^{7} +(-1.80485 + 2.48416i) q^{8} +O(q^{10})\)	\(q+(-0.250369 + 1.17789i) q^{2} +(0.502342 + 0.223657i) q^{4} +(1.04324 - 1.97779i) q^{5} +(2.32094 + 1.33999i) q^{7} +(-1.80485 + 2.48416i) q^{8} +(2.06843 + 1.72401i) q^{10} +(-1.37561 - 0.292396i) q^{11} +(-0.0338103 - 0.159065i) q^{13} +(-2.15946 + 2.39833i) q^{14} +(-1.73831 - 1.93059i) q^{16} +(-0.113531 + 0.156262i) q^{17} +(6.07397 + 4.41300i) q^{19} +(0.966411 - 0.760196i) q^{20} +(0.688822 - 1.54712i) q^{22} +(4.38392 + 3.94730i) q^{23} +(-2.82328 - 4.12663i) q^{25} +0.195827 q^{26} +(0.866205 + 1.19223i) q^{28} +(-0.636956 - 6.06023i) q^{29} +(0.0629147 - 0.598594i) q^{31} +(-2.60917 + 1.50640i) q^{32} +(-0.155636 - 0.172851i) q^{34} +(5.07153 - 3.19238i) q^{35} +(0.888903 + 0.288822i) q^{37} +(-6.71878 + 6.04962i) q^{38} +(3.03024 + 6.16119i) q^{40} +(5.53191 - 1.17584i) q^{41} +(5.91893 + 3.41730i) q^{43} +(-0.625632 - 0.454548i) q^{44} +(-5.74710 + 4.17551i) q^{46} +(0.217685 - 0.0228796i) q^{47} +(0.0911727 + 0.157916i) q^{49} +(5.56760 - 2.29234i) q^{50} +(0.0185917 - 0.0874669i) q^{52} +(7.64631 + 10.5242i) q^{53} +(-2.01340 + 2.41563i) q^{55} +(-7.51770 + 3.34710i) q^{56} +(7.29779 + 0.767028i) q^{58} +(-5.81390 + 1.23578i) q^{59} +(-13.7973 - 2.93271i) q^{61} +(0.689328 + 0.223976i) q^{62} +(-2.72670 - 8.39191i) q^{64} +(-0.349869 - 0.0990742i) q^{65} +(-6.42391 - 0.675180i) q^{67} +(-0.0919806 + 0.0531050i) q^{68} +(2.49053 + 6.77300i) q^{70} +(-2.90460 + 2.11032i) q^{71} +(-11.0652 + 3.59530i) q^{73} +(-0.562756 + 0.974721i) q^{74} +(2.06421 + 3.57532i) q^{76} +(-2.80091 - 2.52195i) q^{77} +(-1.42166 - 13.5262i) q^{79} +(-5.63178 + 1.42393i) q^{80} +6.81040i q^{82} +(-5.96001 - 13.3864i) q^{83} +(0.190613 + 0.387560i) q^{85} +(-5.50713 + 6.11629i) q^{86} +(3.20913 - 2.88951i) q^{88} +(3.38521 + 10.4186i) q^{89} +(0.134675 - 0.414486i) q^{91} +(1.31938 + 2.96339i) q^{92} +(-0.0275518 + 0.262138i) q^{94} +(15.0646 - 7.40918i) q^{95} +(3.08167 - 0.323896i) q^{97} +(-0.208835 + 0.0678546i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) \) 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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