LMFDB - Embedded newform 675.2.y.a.19.20

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			19.20
Character	$\chi$	$=$	675.19
Dual form			675.2.y.a.604.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.255527 - 1.20216i) q^{2} +(0.447195 + 0.199104i) q^{4} +(-0.173727 - 2.22931i) q^{5} +(-1.60284 - 0.925401i) q^{7} +(1.79842 - 2.47532i) q^{8} +O(q^{10})$	\(q+(0.255527 - 1.20216i) q^{2} +(0.447195 + 0.199104i) q^{4} +(-0.173727 - 2.22931i) q^{5} +(-1.60284 - 0.925401i) q^{7} +(1.79842 - 2.47532i) q^{8} +(-2.72438 - 0.360801i) q^{10} +(-4.46195 - 0.948417i) q^{11} +(-0.134284 - 0.631759i) q^{13} +(-1.52205 + 1.69041i) q^{14} +(-1.86108 - 2.06694i) q^{16} +(-0.197326 + 0.271596i) q^{17} +(-0.793011 - 0.576156i) q^{19} +(0.366175 - 1.03153i) q^{20} +(-2.28030 + 5.12163i) q^{22} +(3.34049 + 3.00779i) q^{23} +(-4.93964 + 0.774584i) q^{25} -0.793788 q^{26} +(-0.532532 - 0.732968i) q^{28} +(-0.971616 - 9.24431i) q^{29} +(0.167747 - 1.59601i) q^{31} +(2.33914 - 1.35050i) q^{32} +(0.276080 + 0.306618i) q^{34} +(-1.78455 + 3.73400i) q^{35} +(11.0762 + 3.59887i) q^{37} +(-0.895268 + 0.806103i) q^{38} +(-5.83068 - 3.57921i) q^{40} +(-7.28791 + 1.54909i) q^{41} +(2.66615 + 1.53930i) q^{43} +(-1.80653 - 1.31252i) q^{44} +(4.46944 - 3.24724i) q^{46} +(-2.51480 + 0.264316i) q^{47} +(-1.78727 - 3.09564i) q^{49} +(-0.331038 + 6.13616i) q^{50} +(0.0657344 - 0.309256i) q^{52} +(-6.39509 - 8.80209i) q^{53} +(-1.33915 + 10.1118i) q^{55} +(-5.17325 + 2.30328i) q^{56} +(-11.3614 - 1.19413i) q^{58} +(12.6952 - 2.69845i) q^{59} +(4.37602 + 0.930151i) q^{61} +(-1.87579 - 0.609482i) q^{62} +(-2.74477 - 8.44753i) q^{64} +(-1.38506 + 0.409115i) q^{65} +(3.78807 + 0.398142i) q^{67} +(-0.142319 + 0.0821680i) q^{68} +(4.03286 + 3.09945i) q^{70} +(-2.38521 + 1.73295i) q^{71} +(-2.05379 + 0.667318i) q^{73} +(7.15668 - 12.3957i) q^{74} +(-0.239916 - 0.415546i) q^{76} +(6.27413 + 5.64925i) q^{77} +(0.296904 + 2.82485i) q^{79} +(-4.28453 + 4.50801i) q^{80} +9.15707i q^{82} +(5.32000 + 11.9489i) q^{83} +(0.639752 + 0.392717i) q^{85} +(2.53176 - 2.81180i) q^{86} +(-10.3721 + 9.33908i) q^{88} +(2.56455 + 7.89287i) q^{89} +(-0.369393 + 1.13688i) q^{91} +(0.894989 + 2.01018i) q^{92} +(-0.324849 + 3.09073i) q^{94} +(-1.14666 + 1.86796i) q^{95} +(7.27138 - 0.764252i) q^{97} +(-4.17814 + 1.35756i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.255527	−	1.20216i	0.180685	−	0.850056i	−0.790637	−	0.612286i	$-0.790250\pi$
$2$	0.255527	−	1.20216i	0.180685	−	0.850056i	0.971321	−	0.237770i	$-0.0764165\pi$
$3$		0			0
$3$		0			0
$4$	0.447195	+	0.199104i	0.223598	+	0.0995521i
$5$	−0.173727	−	2.22931i	−0.0776932	−	0.996977i
$5$	−0.173727	−	2.22931i	−0.0776932	−	0.996977i
$6$		0			0
$7$	−1.60284	−	0.925401i	−0.605817	−	0.349769i	0.165509	−	0.986208i	$-0.447073\pi$
$7$	−1.60284	−	0.925401i	−0.605817	−	0.349769i	−0.771327	+	0.636439i	$0.780407\pi$
$8$	1.79842	−	2.47532i	0.635838	−	0.875156i
$9$		0			0
$10$	−2.72438	−	0.360801i	−0.861524	−	0.114095i
$11$	−4.46195	−	0.948417i	−1.34533	−	0.285958i	−0.521720	−	0.853117i	$-0.674709\pi$
$11$	−4.46195	−	0.948417i	−1.34533	−	0.285958i	−0.823609	+	0.567159i	$0.808043\pi$
$12$		0			0
$13$	−0.134284	−	0.631759i	−0.0372438	−	0.175218i	0.955594	−	0.294685i	$-0.0952148\pi$
$13$	−0.134284	−	0.631759i	−0.0372438	−	0.175218i	−0.992838	+	0.119467i	$0.961881\pi$
$14$	−1.52205	+	1.69041i	−0.406785	+	0.451780i
$15$		0			0
$16$	−1.86108	−	2.06694i	−0.465270	−	0.516735i
$17$	−0.197326	+	0.271596i	−0.0478586	+	0.0658717i	−0.832276	−	0.554362i	$-0.812962\pi$
$17$	−0.197326	+	0.271596i	−0.0478586	+	0.0658717i	0.784417	+	0.620234i	$0.212962\pi$
$18$		0			0
$19$	−0.793011	−	0.576156i	−0.181929	−	0.132179i	0.493093	−	0.869976i	$-0.335866\pi$
$19$	−0.793011	−	0.576156i	−0.181929	−	0.132179i	−0.675023	+	0.737797i	$0.735866\pi$
$20$	0.366175	−	1.03153i	0.0818792	−	0.230656i
$21$		0			0
$22$	−2.28030	+	5.12163i	−0.486161	+	1.09194i
$23$	3.34049	+	3.00779i	0.696541	+	0.627168i	0.939372	−	0.342900i	$-0.111409\pi$
$23$	3.34049	+	3.00779i	0.696541	+	0.627168i	−0.242831	+	0.970069i	$0.578076\pi$
$24$		0			0
$25$	−4.93964	+	0.774584i	−0.987928	+	0.154917i
$26$	−0.793788			−0.155675
$27$		0			0
$28$	−0.532532	−	0.732968i	−0.100639	−	0.138518i
$29$	−0.971616	−	9.24431i	−0.180425	−	1.71663i	−0.592580	−	0.805512i	$-0.701891\pi$
$29$	−0.971616	−	9.24431i	−0.180425	−	1.71663i	0.412155	−	0.911114i	$-0.364776\pi$
$30$		0			0
$31$	0.167747	−	1.59601i	0.0301283	−	0.286651i	−0.969076	−	0.246763i	$-0.920633\pi$
$31$	0.167747	−	1.59601i	0.0301283	−	0.286651i	0.999204	−	0.0398883i	$-0.0127002\pi$
$32$	2.33914	−	1.35050i	0.413505	−	0.238737i
$33$		0			0
$34$	0.276080	+	0.306618i	0.0473473	+	0.0525845i
$35$	−1.78455	+	3.73400i	−0.301644	+	0.631161i
$36$		0			0
$37$	11.0762	+	3.59887i	1.82091	+	0.591650i	0.999781	+	0.0209094i	$0.00665615\pi$
$37$	11.0762	+	3.59887i	1.82091	+	0.591650i	0.821130	+	0.570741i	$0.193344\pi$
$38$	−0.895268	+	0.806103i	−0.145232	+	0.130767i
$39$		0			0
$40$	−5.83068	−	3.57921i	−0.921911	−	0.565923i
$41$	−7.28791	+	1.54909i	−1.13818	+	0.241928i	−0.738191	−	0.674592i	$-0.764320\pi$
$41$	−7.28791	+	1.54909i	−1.13818	+	0.241928i	−0.399990	+	0.916520i	$0.630986\pi$
$42$		0			0
$43$	2.66615	+	1.53930i	0.406584	+	0.234741i	0.689321	−	0.724456i	$-0.257909\pi$
$43$	2.66615	+	1.53930i	0.406584	+	0.234741i	−0.282737	+	0.959197i	$0.591242\pi$
$44$	−1.80653	−	1.31252i	−0.272345	−	0.197870i
$45$		0			0
$46$	4.46944	−	3.24724i	0.658983	−	0.478779i
$47$	−2.51480	+	0.264316i	−0.366821	+	0.0385545i	−0.286146	−	0.958186i	$-0.592374\pi$
$47$	−2.51480	+	0.264316i	−0.366821	+	0.0385545i	−0.0806752	+	0.996740i	$0.525708\pi$
$48$		0			0
$49$	−1.78727	−	3.09564i	−0.255324	−	0.442234i
$50$	−0.331038	+	6.13616i	−0.0468158	+	0.867785i
$51$		0			0
$52$	0.0657344	−	0.309256i	0.00911572	−	0.0428861i
$53$	−6.39509	−	8.80209i	−0.878434	−	1.20906i	−0.976852	−	0.213915i	$-0.931378\pi$
$53$	−6.39509	−	8.80209i	−0.878434	−	1.20906i	0.0984184	−	0.995145i	$-0.468622\pi$
$54$		0			0
$55$	−1.33915	+	10.1118i	−0.180571	+	1.36348i
$56$	−5.17325	+	2.30328i	−0.691304	+	0.307788i
$57$		0			0
$58$	−11.3614	−	1.19413i	−1.49183	−	0.156797i
$59$	12.6952	−	2.69845i	1.65278	−	0.351309i	0.715156	−	0.698965i	$-0.246356\pi$
$59$	12.6952	−	2.69845i	1.65278	−	0.351309i	0.937622	+	0.347656i	$0.113022\pi$
$60$		0			0
$61$	4.37602	+	0.930151i	0.560291	+	0.119094i	0.479348	−	0.877625i	$-0.340873\pi$
$61$	4.37602	+	0.930151i	0.560291	+	0.119094i	0.0809437	+	0.996719i	$0.474207\pi$
$62$	−1.87579	−	0.609482i	−0.238226	−	0.0774042i
$63$		0			0
$64$	−2.74477	−	8.44753i	−0.343096	−	1.05594i
$65$	−1.38506	+	0.409115i	−0.171795	+	0.0507445i
$66$		0			0
$67$	3.78807	+	0.398142i	0.462786	+	0.0486408i	0.333053	−	0.942908i	$-0.391921\pi$
$67$	3.78807	+	0.398142i	0.462786	+	0.0486408i	0.129733	+	0.991549i	$0.458588\pi$
$68$	−0.142319	+	0.0821680i	−0.0172587	+	0.00996433i
$69$		0			0
$70$	4.03286	+	3.09945i	0.482019	+	0.370455i
$71$	−2.38521	+	1.73295i	−0.283072	+	0.205664i	−0.720256	−	0.693708i	$-0.755976\pi$
$71$	−2.38521	+	1.73295i	−0.283072	+	0.205664i	0.437184	+	0.899372i	$0.355976\pi$
$72$		0			0
$73$	−2.05379	+	0.667318i	−0.240378	+	0.0781036i	−0.426729	−	0.904380i	$-0.640334\pi$
$73$	−2.05379	+	0.667318i	−0.240378	+	0.0781036i	0.186350	+	0.982483i	$0.440334\pi$
$74$	7.15668	−	12.3957i	0.831947	−	1.44097i
$75$		0			0
$76$	−0.239916	−	0.415546i	−0.0275202	−	0.0476664i
$77$	6.27413	+	5.64925i	0.715004	+	0.643792i
$78$		0			0
$79$	0.296904	+	2.82485i	0.0334043	+	0.317821i	0.998446	+	0.0557248i	$0.0177470\pi$
$79$	0.296904	+	2.82485i	0.0334043	+	0.317821i	−0.965042	+	0.262096i	$0.915586\pi$
$80$	−4.28453	+	4.50801i	−0.479025	+	0.504011i
$81$		0			0
$82$			9.15707i			1.01123i
$83$	5.32000	+	11.9489i	0.583945	+	1.31156i	0.927988	+	0.372609i	$0.121537\pi$
$83$	5.32000	+	11.9489i	0.583945	+	1.31156i	−0.344043	+	0.938954i	$0.611797\pi$
$84$		0			0
$85$	0.639752	+	0.392717i	0.0693909	+	0.0425961i
$86$	2.53176	−	2.81180i	0.273007	−	0.303205i
$87$		0			0
$88$	−10.3721	+	9.33908i	−1.10567	+	0.995549i
$89$	2.56455	+	7.89287i	0.271841	+	0.836642i	0.990038	+	0.140802i	$0.0449680\pi$
$89$	2.56455	+	7.89287i	0.271841	+	0.836642i	−0.718196	+	0.695840i	$0.755032\pi$
$90$		0			0
$91$	−0.369393	+	1.13688i	−0.0387229	+	0.119177i
$92$	0.894989	+	2.01018i	0.0933090	+	0.209576i
$93$		0			0
$94$	−0.324849	+	3.09073i	−0.0335056	+	0.318785i
$95$	−1.14666	+	1.86796i	−0.117645	+	0.191649i
$96$		0			0
$97$	7.27138	−	0.764252i	0.738296	−	0.0775981i	0.272087	−	0.962273i	$-0.412286\pi$
$97$	7.27138	−	0.764252i	0.738296	−	0.0775981i	0.466209	+	0.884675i	$0.345619\pi$
$98$	−4.17814	+	1.35756i	−0.422056	+	0.137134i
$99$		0			0
$100$	−2.36321	−	0.637112i	−0.236321	−	0.0637112i
$101$	5.83982	−	10.1149i	0.581084	−	1.00647i	−0.414267	−	0.910155i	$-0.635962\pi$
$101$	5.83982	−	10.1149i	0.581084	−	1.00647i	0.995351	−	0.0963117i	$-0.0307046\pi$
$102$		0			0
$103$	7.28028	−	16.3518i	0.717347	−	1.61119i	−0.0721207	−	0.997396i	$-0.522977\pi$
$103$	7.28028	−	16.3518i	0.717347	−	1.61119i	0.789468	−	0.613792i	$-0.210357\pi$
$104$	−1.80530	−	0.803772i	−0.177024	−	0.0788164i
$105$		0			0
$106$	−12.2156	+	5.43876i	−1.18649	+	0.528259i
$107$			15.9755i			1.54441i	0.635372	+	0.772206i	$0.280847\pi$
$107$			15.9755i			1.54441i	−0.635372	+	0.772206i	$0.719153\pi$
$108$		0			0
$109$	1.90189	−	5.85341i	0.182168	−	0.560655i	−0.817720	−	0.575616i	$-0.804762\pi$
$109$	1.90189	−	5.85341i	0.182168	−	0.560655i	0.999888	+	0.0149608i	$0.00476235\pi$
$110$	11.8139	+	4.19372i	1.12641	+	0.399856i
$111$		0			0
$112$	1.07027	+	5.03522i	0.101131	+	0.475784i
$113$	−1.46543	−	6.89429i	−0.137856	−	0.648561i	−0.991758	−	0.128127i	$-0.959104\pi$
$113$	−1.46543	−	6.89429i	−0.137856	−	0.648561i	0.853902	−	0.520434i	$-0.174230\pi$
$114$		0			0
$115$	6.12497	−	7.96953i	0.571156	−	0.743162i
$116$	1.40608	−	4.32747i	0.130551	−	0.401795i
$117$		0			0
$118$		−	15.9512i		−	1.46843i
$119$	0.567617	−	0.252720i	0.0520334	−	0.0231668i
$120$		0			0
$121$	8.96050	+	3.98947i	0.814591	+	0.362679i
$122$	2.23638	−	5.02299i	0.202472	−	0.454760i
$123$		0			0
$124$	0.392787	−	0.680327i	0.0352733	−	0.0610952i
$125$	2.58494	+	10.8774i	0.231204	+	0.972905i
$126$		0			0
$127$	3.48706	−	1.13302i	0.309427	−	0.100539i	−0.150187	−	0.988658i	$-0.547988\pi$
$127$	3.48706	−	1.13302i	0.309427	−	0.100539i	0.459614	+	0.888119i	$0.347988\pi$
$128$	−5.48424	+	0.576417i	−0.484743	+	0.0509485i
$129$		0			0
$130$	0.137903	+	1.76960i	0.0120949	+	0.155204i
$131$	−1.55861	+	14.8292i	−0.136176	+	1.29563i	0.686504	+	0.727126i	$0.259145\pi$
$131$	−1.55861	+	14.8292i	−0.136176	+	1.29563i	−0.822680	+	0.568505i	$0.807522\pi$
$132$		0			0
$133$	0.737895	+	1.65734i	0.0639837	+	0.143710i
$134$	1.44658	−	4.45213i	0.124966	−	0.384606i
$135$		0			0
$136$	0.317410	+	0.976888i	0.0272177	+	0.0837675i
$137$	11.2782	−	10.1550i	0.963565	−	0.867598i	−0.0276820	−	0.999617i	$-0.508813\pi$
$137$	11.2782	−	10.1550i	0.963565	−	0.867598i	0.991247	+	0.132019i	$0.0421459\pi$
$138$		0			0
$139$	−11.0026	+	12.2197i	−0.933230	+	1.03646i	0.0660230	+	0.997818i	$0.478969\pi$
$139$	−11.0026	+	12.2197i	−0.933230	+	1.03646i	−0.999253	+	0.0386391i	$0.987698\pi$
$140$	−1.54150	+	1.31452i	−0.130280	+	0.111097i
$141$		0			0
$142$	1.47380	+	3.31022i	0.123679	+	0.277787i
$143$			2.94623i			0.246376i
$144$		0			0
$145$	−20.4396	+	3.77202i	−1.69742	+	0.313249i
$146$	0.277423	+	2.63951i	0.0229597	+	0.218447i
$147$		0			0
$148$	4.23666	+	3.81471i	0.348252	+	0.313567i
$149$	−0.310863	−	0.538430i	−0.0254669	−	0.0441099i	0.853011	−	0.521893i	$-0.174774\pi$
$149$	−0.310863	−	0.538430i	−0.0254669	−	0.0441099i	−0.878478	+	0.477783i	$0.841441\pi$
$150$		0			0
$151$	5.87252	−	10.1715i	0.477899	−	0.827745i	−0.521780	−	0.853080i	$-0.674732\pi$
$151$	5.87252	−	10.1715i	0.477899	−	0.827745i	0.999679	+	0.0253349i	$0.00806521\pi$
$152$	−2.85234	+	0.926781i	−0.231355	+	0.0751718i
$153$		0			0
$154$	8.39452	−	6.09898i	0.676450	−	0.491470i
$155$	−3.58713	−	0.0966901i	−0.288125	−	0.00776634i
$156$		0			0
$157$	7.39876	−	4.27168i	0.590486	−	0.340917i	−0.174804	−	0.984603i	$-0.555929\pi$
$157$	7.39876	−	4.27168i	0.590486	−	0.340917i	0.765289	+	0.643686i	$0.222596\pi$
$158$	3.47179	+	0.364900i	0.276201	+	0.0290299i
$159$		0			0
$160$	−3.41705	−	4.98004i	−0.270142	−	0.393706i
$161$	−2.57087	−	7.91231i	−0.202613	−	0.623578i
$162$		0			0
$163$	0.733644	+	0.238375i	0.0574634	+	0.0186710i	0.337608	−	0.941287i	$-0.390382\pi$
$163$	0.733644	+	0.238375i	0.0574634	+	0.0186710i	−0.280144	+	0.959958i	$0.590382\pi$
$164$	−3.56755	−	0.758306i	−0.278579	−	0.0592138i
$165$		0			0
$166$	15.7239	−	3.34222i	1.22041	−	0.259407i
$167$	15.7962	+	1.66024i	1.22234	+	0.128474i	0.693633	−	0.720328i	$-0.256009\pi$
$167$	15.7962	+	1.66024i	1.22234	+	0.128474i	0.528711	+	0.848802i	$0.322676\pi$
$168$		0			0
$169$	11.4950	−	5.11791i	0.884231	−	0.393685i
$170$	0.635583	−	0.668735i	0.0487470	−	0.0512896i
$171$		0			0
$172$	0.885807	+	1.21921i	0.0675422	+	0.0929638i
$173$	−1.21388	+	5.71087i	−0.0922898	+	0.434189i	0.907607	+	0.419821i	$0.137907\pi$
$173$	−1.21388	+	5.71087i	−0.0922898	+	0.434189i	−0.999897	+	0.0143685i	$0.995426\pi$
$174$		0			0
$175$	8.63426	+	3.32961i	0.652689	+	0.251695i
$176$	6.34373	+	10.9877i	0.478176	+	0.828226i
$177$		0			0
$178$	10.1438	−	1.06616i	0.760310	−	0.0799118i
$179$	−0.206045	+	0.149700i	−0.0154005	+	0.0111891i	−0.595459	−	0.803386i	$-0.703030\pi$
$179$	−0.206045	+	0.149700i	−0.0154005	+	0.0111891i	0.580058	+	0.814575i	$0.303030\pi$
$180$		0			0
$181$	−4.74723	−	3.44906i	−0.352859	−	0.256367i	0.397209	−	0.917728i	$-0.369979\pi$
$181$	−4.74723	−	3.44906i	−0.352859	−	0.256367i	−0.750067	+	0.661361i	$0.769979\pi$
$182$	1.27232	+	0.734573i	0.0943104	+	0.0544501i
$183$		0			0
$184$	13.4529	−	2.85949i	0.991758	−	0.210805i
$185$	6.09875	−	25.3174i	0.448389	−	1.86137i
$186$		0			0
$187$	1.13804	−	1.02470i	0.0832221	−	0.0749335i
$188$	−1.17723	−	0.382506i	−0.0858586	−	0.0278971i
$189$		0			0
$190$	1.95258	+	1.85579i	0.141655	+	0.134633i
$191$	−11.8310	−	13.1396i	−0.856058	−	0.950748i	0.143184	−	0.989696i	$-0.454266\pi$
$191$	−11.8310	−	13.1396i	−0.856058	−	0.950748i	−0.999241	+	0.0389477i	$0.987599\pi$
$192$		0			0
$193$	1.74674	−	1.00848i	0.125733	−	0.0725919i	−0.435814	−	0.900037i	$-0.643540\pi$
$193$	1.74674	−	1.00848i	0.125733	−	0.0725919i	0.561547	+	0.827445i	$0.310206\pi$
$194$	0.939279	−	8.93665i	0.0674363	−	0.641614i
$195$		0			0
$196$	−0.182903	−	1.74021i	−0.0130645	−	0.124300i
$197$	10.8317	+	14.9086i	0.771727	+	1.06219i	0.996147	+	0.0876990i	$0.0279514\pi$
$197$	10.8317	+	14.9086i	0.771727	+	1.06219i	−0.224420	+	0.974493i	$0.572049\pi$
$198$		0			0
$199$	5.79952			0.411117			0.205559	−	0.978645i	$-0.434099\pi$
$199$	5.79952			0.411117			0.205559	+	0.978645i	$0.434099\pi$
$200$	−6.96622	+	13.6202i	−0.492586	+	0.963093i
$201$		0			0
$202$	−10.6675	−	9.60503i	−0.750560	−	0.675807i
$203$	−6.99735	+	15.7163i	−0.491118	+	1.10307i
$204$		0			0
$205$	4.71952	+	15.9779i	0.329625	+	1.11594i
$206$	−17.7971	−	12.9304i	−1.23999	−	0.900902i
$207$		0			0
$208$	−1.05589	+	1.45331i	−0.0732130	+	0.100769i
$209$	2.99194	+	3.32288i	0.206957	+	0.229849i
$210$		0			0
$211$	4.84831	−	5.38459i	0.333771	−	0.370690i	−0.552775	−	0.833331i	$-0.686431\pi$
$211$	4.84831	−	5.38459i	0.333771	−	0.370690i	0.886546	+	0.462640i	$0.153098\pi$
$212$	−1.10732	−	5.20954i	−0.0760513	−	0.357793i
$213$		0			0
$214$	19.2052	+	4.08218i	1.31284	+	0.279052i
$215$	2.96839	−	6.21108i	0.202443	−	0.423592i
$216$		0			0
$217$	−1.74582	+	2.40291i	−0.118514	+	0.163120i
$218$	−6.55076	−	3.78208i	−0.443673	−	0.256155i
$219$		0			0
$220$	−2.61217	+	4.25533i	−0.176112	+	0.286894i
$221$	0.198081	+	0.0881913i	0.0133244	+	0.00593239i
$222$		0			0
$223$	−0.383673	+	1.80504i	−0.0256926	+	0.120874i	−0.989125	−	0.147077i	$-0.953013\pi$
$223$	−0.383673	+	1.80504i	−0.0256926	+	0.120874i	0.963432	+	0.267952i	$0.0863467\pi$
$224$	−4.99902			−0.334011
$225$		0			0
$226$	−8.66250			−0.576221
$227$	2.34711	−	11.0423i	0.155783	−	0.732903i	−0.829019	−	0.559221i	$-0.811100\pi$
$227$	2.34711	−	11.0423i	0.155783	−	0.732903i	0.984802	−	0.173682i	$-0.0555664\pi$
$228$		0			0
$229$	25.2326	+	11.2343i	1.66741	+	0.742381i	0.999997	−	0.00230334i	$-0.000733176\pi$
$229$	25.2326	+	11.2343i	1.66741	+	0.742381i	0.667417	+	0.744684i	$0.267400\pi$
$230$	−8.01556	−	9.39962i	−0.528530	−	0.619793i
$231$		0			0
$232$	−24.6300	−	14.2201i	−1.61704	−	0.933596i
$233$	−2.64302	+	3.63780i	−0.173150	+	0.238320i	−0.886768	−	0.462214i	$-0.847055\pi$
$233$	−2.64302	+	3.63780i	−0.173150	+	0.238320i	0.713618	+	0.700535i	$0.247055\pi$
$234$		0			0
$235$	1.02613	+	5.56035i	0.0669375	+	0.362717i
$236$	6.21452	+	1.32094i	0.404531	+	0.0859857i
$237$		0			0
$238$	−0.158768	−	0.746944i	−0.0102914	−	0.0484172i
$239$	−13.6422	+	15.1512i	−0.882441	+	0.980050i	−0.999915	−	0.0130256i	$-0.995854\pi$
$239$	−13.6422	+	15.1512i	−0.882441	+	0.980050i	0.117474	+	0.993076i	$0.462520\pi$
$240$		0			0
$241$	−16.9551	−	18.8305i	−1.09217	−	1.21298i	−0.975544	−	0.219804i	$-0.929458\pi$
$241$	−16.9551	−	18.8305i	−1.09217	−	1.21298i	−0.116628	−	0.993176i	$-0.537208\pi$
$242$	7.08563	−	9.75254i	0.455482	−	0.626917i
$243$		0			0
$244$	1.77174	+	1.28724i	0.113424	+	0.0824072i
$245$	−6.59063	+	4.52216i	−0.421060	+	0.288910i
$246$		0			0
$247$	−0.257503	+	0.578360i	−0.0163845	+	0.0368002i
$248$	−3.64894	−	3.28552i	−0.231708	−	0.208631i
$249$		0			0
$250$	13.7369	−	0.328034i	0.868799	−	0.0207467i
$251$	−10.6512			−0.672301			−0.336150	−	0.941808i	$-0.609125\pi$
$251$	−10.6512			−0.672301			−0.336150	+	0.941808i	$0.609125\pi$
$252$		0			0
$253$	−12.0525	−	16.5888i	−0.757732	−	1.04293i
$254$	−0.471027	−	4.48153i	−0.0295549	−	0.281196i
$255$		0			0
$256$	1.14847	−	10.9270i	0.0717795	−	0.682936i
$257$	−15.8671	+	9.16088i	−0.989763	+	0.571440i	−0.905204	−	0.424978i	$-0.860282\pi$
$257$	−15.8671	+	9.16088i	−0.989763	+	0.571440i	−0.0845598	+	0.996418i	$0.526948\pi$
$258$		0			0
$259$	−14.4230	−	16.0183i	−0.896199	−	0.995330i
$260$	−0.700847	−	0.0928161i	−0.0434647	−	0.00575621i
$261$		0			0
$262$	17.4288	+	5.66295i	1.07675	+	0.349858i
$263$	−6.37256	+	5.73788i	−0.392949	+	0.353813i	−0.841796	−	0.539796i	$-0.818501\pi$
$263$	−6.37256	+	5.73788i	−0.392949	+	0.353813i	0.448847	+	0.893609i	$0.351835\pi$
$264$		0			0
$265$	−18.5116	+	15.7858i	−1.13716	+	0.969714i
$266$	2.18094	−	0.463573i	0.133722	−	0.0284235i
$267$		0			0
$268$	1.61474	+	0.932268i	0.0986356	+	0.0569473i
$269$	−2.10031	−	1.52597i	−0.128058	−	0.0930398i	0.521912	−	0.852999i	$-0.325219\pi$
$269$	−2.10031	−	1.52597i	−0.128058	−	0.0930398i	−0.649971	+	0.759959i	$0.725219\pi$
$270$		0			0
$271$	−23.7606	+	17.2631i	−1.44336	+	1.04866i	−0.456029	+	0.889965i	$0.650729\pi$
$271$	−23.7606	+	17.2631i	−1.44336	+	1.04866i	−0.987328	+	0.158695i	$0.949271\pi$
$272$	0.928612	−	0.0976010i	0.0563054	−	0.00591793i
$273$		0			0
$274$	−9.32601	−	16.1531i	−0.563405	−	0.975846i
$275$	22.7750	+	1.22868i	1.37339	+	0.0740923i
$276$		0			0
$277$	−4.52895	+	21.3070i	−0.272118	+	1.28022i	0.603559	+	0.797319i	$0.293749\pi$
$277$	−4.52895	+	21.3070i	−0.272118	+	1.28022i	−0.875677	+	0.482897i	$0.839584\pi$
$278$	11.8785	+	16.3494i	0.712426	+	0.980570i
$279$		0			0
$280$	6.03345	+	11.1326i	0.360568	+	0.665301i
$281$	16.7337	−	7.45034i	0.998252	−	0.444450i	0.158464	−	0.987365i	$-0.449346\pi$
$281$	16.7337	−	7.45034i	0.998252	−	0.444450i	0.839788	+	0.542915i	$0.182679\pi$
$282$		0			0
$283$	−23.7401	−	2.49518i	−1.41120	−	0.148323i	−0.631938	−	0.775019i	$-0.717740\pi$
$283$	−23.7401	−	2.49518i	−1.41120	−	0.148323i	−0.779264	+	0.626696i	$0.784407\pi$
$284$	−1.41169	+	0.300064i	−0.0837685	+	0.0178055i
$285$		0			0
$286$	3.54184	+	0.752842i	0.209434	+	0.0445165i
$287$	13.1149	+	4.26129i	0.774148	+	0.251536i
$288$		0			0
$289$	5.21846	+	16.0608i	0.306968	+	0.944751i
$290$	−0.688304	+	25.5356i	−0.0404186	+	1.49950i
$291$		0			0
$292$	−1.05131	−	0.110497i	−0.0615234	−	0.00646637i
$293$	−10.9893	+	6.34465i	−0.641999	+	0.370658i	−0.785384	−	0.619009i	$-0.787535\pi$
$293$	−10.9893	+	6.34465i	−0.641999	+	0.370658i	0.143385	+	0.989667i	$0.454201\pi$
$294$		0			0
$295$	−8.22120	−	27.8328i	−0.478657	−	1.62049i
$296$	28.8280	−	20.9447i	1.67559	−	1.21739i
$297$		0			0
$298$	−0.726713	+	0.236123i	−0.0420974	+	0.0136783i
$299$	1.45162	−	2.51429i	0.0839495	−	0.145405i
$300$		0			0
$301$	−2.84894	−	4.93451i	−0.164210	−	0.284420i
$302$	−10.7272	−	9.65880i	−0.617280	−	0.555802i
$303$		0			0
$304$	0.284977	+	2.71138i	0.0163446	+	0.155508i
$305$	1.31336	−	9.91708i	0.0752028	−	0.567851i
$306$		0			0
$307$			9.69140i			0.553117i	0.960997	+	0.276559i	$0.0891940\pi$
$307$			9.69140i			0.553117i	−0.960997	+	0.276559i	$0.910806\pi$
$308$	1.68097	+	3.77553i	0.0957823	+	0.215131i
$309$		0			0
$310$	−1.03285	+	4.28760i	−0.0586618	+	0.243519i
$311$	−3.82823	+	4.25168i	−0.217079	+	0.241091i	−0.841842	−	0.539723i	$-0.818529\pi$
$311$	−3.82823	+	4.25168i	−0.217079	+	0.241091i	0.624763	+	0.780814i	$0.285195\pi$
$312$		0			0
$313$	−1.24890	+	1.12452i	−0.0705921	+	0.0635614i	−0.703672	−	0.710525i	$-0.748457\pi$
$313$	−1.24890	+	1.12452i	−0.0705921	+	0.0635614i	0.633079	+	0.774087i	$0.281791\pi$
$314$	−3.24466	−	9.98603i	−0.183107	−	0.563544i
$315$		0			0
$316$	−0.429666	+	1.32238i	−0.0241706	+	0.0743894i
$317$	8.95041	+	20.1029i	0.502705	+	1.12909i	0.969581	+	0.244771i	$0.0787128\pi$
$317$	8.95041	+	20.1029i	0.502705	+	1.12909i	−0.466876	+	0.884323i	$0.654621\pi$
$318$		0			0
$319$	−4.43215	+	42.1691i	−0.248153	+	2.36102i
$320$	−18.3553	+	7.58651i	−1.02609	+	0.424099i
$321$		0			0
$322$	−10.1688	+	1.06878i	−0.566685	+	0.0595610i
$323$	0.312963	−	0.101688i	0.0174137	−	0.00565807i
$324$		0			0
$325$	1.15267	+	3.01664i	0.0639384	+	0.167333i
$326$	0.474031	−	0.821046i	0.0262542	−	0.0454736i
$327$		0			0
$328$	−9.27225	+	20.8258i	−0.511974	+	1.14991i
$329$	4.27543	+	1.90354i	0.235712	+	0.104946i
$330$		0			0
$331$	−11.7901	+	5.24930i	−0.648044	+	0.288528i	−0.704315	−	0.709888i	$-0.748746\pi$
$331$	−11.7901	+	5.24930i	−0.648044	+	0.288528i	0.0562709	+	0.998416i	$0.482079\pi$
$332$			6.40273i			0.351395i
$333$		0			0
$334$	6.03223	−	18.5653i	0.330069	−	1.01585i
$335$	0.229491	−	8.51395i	0.0125384	−	0.465167i
$336$		0			0
$337$	−3.89454	−	18.3224i	−0.212149	−	0.998083i	−0.947342	−	0.320224i	$-0.896242\pi$
$337$	−3.89454	−	18.3224i	−0.212149	−	0.998083i	0.735193	−	0.677858i	$-0.237092\pi$
$338$	−3.21526	−	15.1266i	−0.174887	−	0.822779i
$339$		0			0
$340$	0.207903	+	0.302999i	0.0112751	+	0.0164324i
$341$	−2.26216	+	6.96220i	−0.122503	+	0.377025i
$342$		0			0
$343$			19.5714i			1.05675i
$344$	8.60511	−	3.83124i	0.463957	−	0.206567i
$345$		0			0
$346$	6.55520	+	2.91856i	0.352410	+	0.156903i
$347$	14.4295	−	32.4092i	0.774617	−	1.73982i	0.108341	−	0.994114i	$-0.465446\pi$
$347$	14.4295	−	32.4092i	0.774617	−	1.73982i	0.666276	−	0.745705i	$-0.267887\pi$
$348$		0			0
$349$	−9.87776	+	17.1088i	−0.528744	+	0.915812i	0.470694	+	0.882297i	$0.344004\pi$
$349$	−9.87776	+	17.1088i	−0.528744	+	0.915812i	−0.999438	+	0.0335153i	$0.989330\pi$
$350$	6.20901	−	9.52896i	0.331886	−	0.509344i
$351$		0			0
$352$	−11.7179	+	3.80739i	−0.624568	+	0.202935i
$353$	−7.30722	+	0.768020i	−0.388924	+	0.0408776i	−0.296973	−	0.954886i	$-0.595977\pi$
$353$	−7.30722	+	0.768020i	−0.388924	+	0.0408776i	−0.0919513	+	0.995764i	$0.529310\pi$
$354$		0			0
$355$	4.27766	+	5.01630i	0.227035	+	0.266238i
$356$	−0.424649	+	4.04026i	−0.0225063	+	0.214134i
$357$		0			0
$358$	0.127314	+	0.285951i	0.00672873	+	0.0151130i
$359$	−0.458883	+	1.41230i	−0.0242189	+	0.0745381i	−0.962435	−	0.271511i	$-0.912477\pi$
$359$	−0.458883	+	1.41230i	−0.0242189	+	0.0745381i	0.938217	+	0.346049i	$0.112477\pi$
$360$		0			0
$361$	−5.57441	−	17.1563i	−0.293390	−	0.902962i
$362$	−5.35937	+	4.82560i	−0.281682	+	0.253628i
$363$		0			0
$364$	−0.391548	+	0.434858i	−0.0205227	+	0.0227927i
$365$	1.84446	+	4.46261i	0.0965433	+	0.233584i
$366$		0			0
$367$	11.6063	+	26.0682i	0.605845	+	1.36075i	0.912557	+	0.408949i	$0.134105\pi$
$367$	11.6063	+	26.0682i	0.605845	+	1.36075i	−0.306712	+	0.951802i	$0.599229\pi$
$368$		−	12.5023i		−	0.651730i
$369$		0			0
$370$	−28.8772	−	13.8010i	−1.50126	−	0.717478i
$371$	2.10486	+	20.0264i	0.109279	+	1.03972i
$372$		0			0
$373$	−20.6705	−	18.6118i	−1.07028	−	0.963681i	−0.0708479	−	0.997487i	$-0.522570\pi$
$373$	−20.6705	−	18.6118i	−1.07028	−	0.963681i	−0.999428	+	0.0338060i	$0.989237\pi$
$374$	−0.941052	−	1.62995i	−0.0486607	−	0.0842827i
$375$		0			0
$376$	−3.86841	+	6.70028i	−0.199498	+	0.345541i
$377$	−5.70970	+	1.85519i	−0.294064	+	0.0955473i
$378$		0			0
$379$	15.0490	−	10.9338i	0.773017	−	0.561629i	−0.129858	−	0.991533i	$-0.541452\pi$
$379$	15.0490	−	10.9338i	0.773017	−	0.561629i	0.902875	+	0.429903i	$0.141452\pi$
$380$	−0.884701	+	0.607038i	−0.0453842	+	0.0311404i
$381$		0			0
$382$	−18.8190	+	10.8652i	−0.962866	+	0.555911i
$383$	3.42797	+	0.360295i	0.175161	+	0.0184102i	0.191703	−	0.981453i	$-0.438599\pi$
$383$	3.42797	+	0.360295i	0.175161	+	0.0184102i	−0.0165417	+	0.999863i	$0.505266\pi$
$384$		0			0
$385$	11.5039	−	14.9684i	0.586295	−	0.762861i
$386$	−0.766015	−	2.35755i	−0.0389891	−	0.119996i
$387$		0			0
$388$	3.40389	+	1.10599i	0.172806	+	0.0561482i
$389$	−29.1494	−	6.19589i	−1.47793	−	0.314144i	−0.602747	−	0.797932i	$-0.705927\pi$
$389$	−29.1494	−	6.19589i	−1.47793	−	0.314144i	−0.875185	+	0.483788i	$0.839261\pi$
$390$		0			0
$391$	−1.47607	+	0.313749i	−0.0746481	+	0.0158669i
$392$	−10.8769	−	1.14321i	−0.549368	−	0.0577409i
$393$		0			0
$394$	20.6903	−	9.21191i	1.04236	−	0.464089i
$395$	6.24589	−	1.15264i	0.314265	−	0.0579958i
$396$		0			0
$397$	−14.0335	−	19.3155i	−0.704323	−	0.969417i	−0.999901	−	0.0140985i	$-0.995512\pi$
$397$	−14.0335	−	19.3155i	−0.704323	−	0.969417i	0.295578	−	0.955319i	$-0.404488\pi$
$398$	1.48194	−	6.97196i	0.0742827	−	0.349473i
$399$		0			0
$400$	10.7941	+	8.76837i	0.539704	+	0.438418i
$401$	−17.1301	−	29.6702i	−0.855435	−	1.48166i	−0.876241	−	0.481874i	$-0.839956\pi$
$401$	−17.1301	−	29.6702i	−0.855435	−	1.48166i	0.0208054	−	0.999784i	$-0.493377\pi$
$402$		0			0
$403$	−1.03082	+	0.108343i	−0.0513486	+	0.00539696i
$404$	4.62545	−	3.36059i	0.230125	−	0.167196i
$405$		0			0
$406$	17.1055	+	12.4279i	0.848932	+	0.616785i
$407$	−46.0081	−	26.5628i	−2.28054	−	1.31667i
$408$		0			0
$409$	−32.7895	+	6.96961i	−1.62133	+	0.344625i	−0.927010	−	0.375037i	$-0.877630\pi$
$409$	−32.7895	+	6.96961i	−1.62133	+	0.344625i	−0.694324	+	0.719662i	$0.744297\pi$
$410$	20.4139	−	1.59083i	1.00817	−	0.0785657i
$411$		0			0
$412$	6.51141	−	5.86290i	0.320794	−	0.288844i
$413$	−22.8456	−	7.42298i	−1.12416	−	0.365261i
$414$		0			0
$415$	25.7136	−	13.9358i	1.26223	−	0.684080i
$416$	−1.16730	−	1.29642i	−0.0572316	−	0.0635621i
$417$		0			0
$418$	4.75916	−	2.74770i	0.232778	−	0.134395i
$419$	−1.52842	+	14.5419i	−0.0746681	+	0.710420i	0.891590	+	0.452844i	$0.149590\pi$
$419$	−1.52842	+	14.5419i	−0.0746681	+	0.710420i	−0.966258	+	0.257576i	$0.917076\pi$
$420$		0			0
$421$	−1.50616	−	14.3302i	−0.0734057	−	0.698409i	−0.967901	−	0.251332i	$-0.919132\pi$
$421$	−1.50616	−	14.3302i	−0.0734057	−	0.698409i	0.894495	−	0.447077i	$-0.147535\pi$
$422$	−5.23427	−	7.20435i	−0.254800	−	0.350702i
$423$		0			0
$424$	−33.2890			−1.61666
$425$	0.764345	−	1.49443i	0.0370762	−	0.0724905i
$426$		0			0
$427$	−6.15330	−	5.54045i	−0.297779	−	0.268121i
$428$	−3.18080	+	7.14418i	−0.153750	+	0.345327i
$429$		0			0
$430$	−6.70821	−	5.15559i	−0.323499	−	0.248624i
$431$	12.4642	+	9.05574i	0.600377	+	0.436199i	0.846013	−	0.533163i	$-0.178997\pi$
$431$	12.4642	+	9.05574i	0.600377	+	0.436199i	−0.245636	+	0.969362i	$0.578997\pi$
$432$		0			0
$433$	13.6828	−	18.8327i	0.657552	−	0.905042i	−0.341846	−	0.939756i	$-0.611052\pi$
$433$	13.6828	−	18.8327i	0.657552	−	0.905042i	0.999397	+	0.0347139i	$0.0110520\pi$
$434$	2.44258	+	2.71276i	0.117248	+	0.130217i
$435$		0			0
$436$	2.01595	−	2.23894i	0.0965467	−	0.107226i
$437$	−0.916089	−	4.30986i	−0.0438225	−	0.206169i
$438$		0			0
$439$	5.34703	+	1.13655i	0.255200	+	0.0542444i	0.333735	−	0.942667i	$-0.391691\pi$
$439$	5.34703	+	1.13655i	0.255200	+	0.0542444i	−0.0785351	+	0.996911i	$0.525024\pi$
$440$	22.6216	+	21.5002i	1.07844	+	1.02498i
$441$		0			0
$442$	0.156635	−	0.215590i	0.00745037	−	0.0102546i
$443$	7.99920	+	4.61834i	0.380054	+	0.219424i	0.677842	−	0.735208i	$-0.262916\pi$
$443$	7.99920	+	4.61834i	0.380054	+	0.219424i	−0.297788	+	0.954632i	$0.596249\pi$
$444$		0			0
$445$	17.1501	−	7.08837i	0.812993	−	0.336021i
$446$	2.07191	+	0.922472i	0.0981076	+	0.0436803i
$447$		0			0
$448$	−3.41792	+	16.0801i	−0.161482	+	0.759712i
$449$	0.00721973			0.000340720			0.000170360	−	1.00000i	$-0.499946\pi$
$449$	0.00721973			0.000340720			0.000170360		1.00000i	$0.499946\pi$
$450$		0			0
$451$	33.9875			1.60041
$452$	0.717350	−	3.37487i	0.0337413	−	0.158740i
$453$		0			0
$454$	−12.6749	−	5.64321i	−0.594861	−	0.264849i
$455$	2.59862	+	0.625986i	0.121825	+	0.0293467i
$456$		0			0
$457$	−7.80178	−	4.50436i	−0.364952	−	0.210705i	0.306299	−	0.951935i	$-0.400909\pi$
$457$	−7.80178	−	4.50436i	−0.364952	−	0.210705i	−0.671251	+	0.741230i	$0.734243\pi$
$458$	19.9530	−	27.4629i	0.932342	−	1.28326i
$459$		0			0
$460$	4.32582	−	2.34443i	0.201693	−	0.109310i
$461$	22.5011	+	4.78275i	1.04798	+	0.222755i	0.699553	−	0.714581i	$-0.253382\pi$
$461$	22.5011	+	4.78275i	1.04798	+	0.222755i	0.348427	+	0.937336i	$0.386716\pi$
$462$		0			0
$463$	2.18706	+	10.2893i	0.101641	+	0.478184i	0.999297	+	0.0374869i	$0.0119353\pi$
$463$	2.18706	+	10.2893i	0.101641	+	0.478184i	−0.897656	+	0.440697i	$0.854731\pi$
$464$	−17.2992	+	19.2127i	−0.803094	+	0.891926i
$465$		0			0
$466$	3.69786	+	4.10689i	0.171300	+	0.190248i
$467$	6.78515	−	9.33896i	0.313979	−	0.432155i	−0.622638	−	0.782510i	$-0.713939\pi$
$467$	6.78515	−	9.33896i	0.313979	−	0.432155i	0.936617	+	0.350355i	$0.113939\pi$
$468$		0			0
$469$	−5.70323	−	4.14364i	−0.263351	−	0.191336i
$470$	6.94664	+	0.187245i	0.320424	+	0.00863695i
$471$		0			0
$472$	16.1519	−	36.2777i	0.743449	−	1.66981i
$473$	−10.4363	−	9.39690i	−0.479862	−	0.432070i
$474$		0			0
$475$	4.36347	+	2.23175i	0.200210	+	0.102400i
$476$	0.304153			0.0139408
$477$		0			0
$478$	14.7282	+	20.2717i	0.673654	+	0.927205i
$479$	2.20580	+	20.9868i	0.100785	+	0.958910i	0.921712	+	0.387876i	$0.126791\pi$
$479$	2.20580	+	20.9868i	0.100785	+	0.958910i	−0.820926	+	0.571034i	$0.806542\pi$
$480$		0			0
$481$	0.786257	−	7.48074i	0.0358502	−	0.341092i
$482$	−26.9698	+	15.5710i	−1.22844	+	0.709240i
$483$		0			0
$484$	3.21277	+	3.56815i	0.146035	+	0.162188i
$485$	−2.96699	−	16.0774i	−0.134724	−	0.730036i
$486$		0			0
$487$	25.2926	+	8.21806i	1.14612	+	0.372396i	0.819679	−	0.572823i	$-0.194152\pi$
$487$	25.2926	+	8.21806i	1.14612	+	0.372396i	0.326437	+	0.945219i	$0.394152\pi$
$488$	10.1723	−	9.15922i	0.460480	−	0.414618i
$489$		0			0
$490$	3.75228	+	9.07853i	0.169511	+	0.410126i
$491$	10.3798	−	2.20629i	0.468434	−	0.0995687i	0.0323536	−	0.999476i	$-0.489700\pi$
$491$	10.3798	−	2.20629i	0.468434	−	0.0995687i	0.436080	+	0.899908i	$0.356366\pi$
$492$		0			0
$493$	2.70244	+	1.56026i	0.121712	+	0.0702704i
$494$	0.629483	+	0.457346i	0.0283218	+	0.0205770i
$495$		0			0
$496$	−3.61104	+	2.62357i	−0.162140	+	0.117802i
$497$	5.42678	−	0.570378i	0.243425	−	0.0255849i
$498$		0			0
$499$	−12.3320	−	21.3596i	−0.552054	−	0.956186i	−0.998126	−	0.0611891i	$-0.980511\pi$
$499$	−12.3320	−	21.3596i	−0.552054	−	0.956186i	0.446072	−	0.894997i	$-0.352823\pi$
$500$	−1.00977	+	5.37900i	−0.0451582	+	0.240556i
$501$		0			0
$502$	−2.72168	+	12.8045i	−0.121475	+	0.571493i
$503$	2.09000	+	2.87664i	0.0931885	+	0.128263i	0.853065	−	0.521804i	$-0.174741\pi$
$503$	2.09000	+	2.87664i	0.0931885	+	0.128263i	−0.759877	+	0.650067i	$0.774741\pi$
$504$		0			0
$505$	−23.5637	−	11.2615i	−1.04857	−	0.501132i
$506$	−23.0221	+	10.2501i	−1.02346	+	0.455673i
$507$		0			0
$508$	1.78499	+	0.187610i	0.0791960	+	0.00832383i
$509$	22.6518	−	4.81478i	1.00402	−	0.213411i	0.323570	−	0.946204i	$-0.395117\pi$
$509$	22.6518	−	4.81478i	1.00402	−	0.213411i	0.680452	+	0.732793i	$0.261784\pi$
$510$		0			0
$511$	3.90944	+	0.830977i	0.172944	+	0.0367603i
$512$	−23.3316	−	7.58090i	−1.03112	−	0.335032i
$513$		0			0
$514$	6.95837	+	21.4157i	0.306921	+	0.944605i
$515$	−37.7179	−	13.3892i	−1.66205	−	0.590000i
$516$		0			0
$517$	11.4716	+	1.20571i	0.504520	+	0.0530272i
$518$	−22.9420	+	13.2456i	−1.00802	+	0.581978i
$519$		0			0
$520$	−1.47823	+	4.16421i	−0.0648245	+	0.182613i
$521$	−0.621037	+	0.451210i	−0.0272081	+	0.0197678i	−0.601306	−	0.799019i	$-0.705353\pi$
$521$	−0.621037	+	0.451210i	−0.0272081	+	0.0197678i	0.574098	+	0.818787i	$0.305353\pi$
$522$		0			0
$523$	13.7519	−	4.46826i	0.601328	−	0.195383i	0.00749560	−	0.999972i	$-0.497614\pi$
$523$	13.7519	−	4.46826i	0.601328	−	0.195383i	0.593833	+	0.804588i	$0.297614\pi$
$524$	−3.64955	+	6.32121i	−0.159431	+	0.276143i
$525$		0			0
$526$	5.26949	+	9.12702i	0.229761	+	0.397957i
$527$	0.400368	+	0.360493i	0.0174403	+	0.0157033i
$528$		0			0
$529$	−0.292081	−	2.77897i	−0.0126992	−	0.120825i
$530$	14.2469	+	26.2876i	0.618844	+	1.14186i
$531$		0			0
$532$			0.888073i			0.0385028i
$533$	1.95731	+	4.39618i	0.0847803	+	0.190420i
$534$		0			0
$535$	35.6144	−	2.77539i	1.53974	−	0.119990i
$536$	7.79808	−	8.66064i	0.336826	−	0.374083i
$537$		0			0
$538$	−2.37114	+	2.13499i	−0.102227	+	0.0920458i
$539$	5.03874	+	15.5076i	0.217034	+	0.667961i
$540$		0			0
$541$	−5.60541	+	17.2517i	−0.240996	+	0.741708i	0.755274	+	0.655409i	$0.227504\pi$
$541$	−5.60541	+	17.2517i	−0.240996	+	0.741708i	−0.996269	+	0.0862986i	$0.972496\pi$
$542$	14.6815	+	32.9753i	0.630627	+	1.41641i
$543$		0			0
$544$	−0.0947818	+	0.901788i	−0.00406373	+	0.0386639i
$545$	−13.3795	−	3.22300i	−0.573114	−	0.138058i
$546$		0			0
$547$	−22.0698	+	2.31963i	−0.943638	+	0.0991803i	−0.563835	−	0.825887i	$-0.690675\pi$
$547$	−22.0698	+	2.31963i	−0.943638	+	0.0991803i	−0.379802	+	0.925068i	$0.624008\pi$
$548$	7.06547	−	2.29571i	0.301822	−	0.0980680i
$549$		0			0
$550$	7.29671	−	27.0653i	0.311133	−	1.15407i
$551$	−4.55566	+	7.89064i	−0.194078	+	0.336153i
$552$		0			0
$553$	2.13823	−	4.80254i	0.0909268	−	0.204225i
$554$	24.4572	+	10.8891i	1.03909	+	0.462632i
$555$		0			0
$556$	−7.35331	+	3.27390i	−0.311850	+	0.138844i
$557$		−	33.0199i		−	1.39910i	−0.714584	−	0.699549i	$-0.753384\pi$
$557$		−	33.0199i		−	1.39910i	0.714584	−	0.699549i	$-0.246616\pi$
$558$		0			0
$559$	0.614444	−	1.89106i	0.0259882	−	0.0799835i
$560$	11.0391	−	3.26072i	0.466488	−	0.137790i
$561$		0			0
$562$	−4.68058	−	22.0204i	−0.197438	−	0.928875i
$563$	−2.77449	−	13.0529i	−0.116931	−	0.550115i	−0.997143	−	0.0755356i	$-0.975933\pi$
$563$	−2.77449	−	13.0529i	−0.116931	−	0.550115i	0.880212	−	0.474580i	$-0.157400\pi$
$564$		0			0
$565$	−15.1149	+	4.46462i	−0.635890	+	0.187828i
$566$	−9.06585	+	27.9018i	−0.381066	+	1.17280i
$567$		0			0
$568$			9.02072i			0.378501i
$569$	−1.23753	+	0.550985i	−0.0518800	+	0.0230985i	−0.432513	−	0.901628i	$-0.642373\pi$
$569$	−1.23753	+	0.550985i	−0.0518800	+	0.0230985i	0.380633	+	0.924726i	$0.375706\pi$
$570$		0			0
$571$	11.0515	+	4.92047i	0.462493	+	0.205915i	0.624737	−	0.780836i	$-0.285206\pi$
$571$	11.0515	+	4.92047i	0.462493	+	0.205915i	−0.162244	+	0.986751i	$0.551873\pi$
$572$	−0.586607	+	1.31754i	−0.0245273	+	0.0550892i
$573$		0			0
$574$	8.47396	−	14.6773i	0.353696	−	0.612620i
$575$	−18.8306	−	12.2699i	−0.785291	−	0.511691i
$576$		0			0
$577$	−6.08341	+	1.97662i	−0.253256	+	0.0822877i	−0.432894	−	0.901445i	$-0.642507\pi$
$577$	−6.08341	+	1.97662i	−0.253256	+	0.0822877i	0.179638	+	0.983733i	$0.442507\pi$
$578$	20.6411	−	2.16947i	0.858556	−	0.0902379i
$579$		0			0
$580$	−9.89153	−	2.38279i	−0.410723	−	0.0989398i
$581$	2.53042	−	24.0753i	0.104980	−	0.998813i
$582$		0			0
$583$	20.1865	+	45.3397i	0.836041	+	1.87778i
$584$	−2.04176	+	6.28391i	−0.0844888	+	0.260030i
$585$		0			0
$586$	4.81924	+	14.8321i	0.199081	+	0.612708i
$587$	−3.75246	+	3.37873i	−0.154881	+	0.139455i	−0.742928	−	0.669371i	$-0.766564\pi$
$587$	−3.75246	+	3.37873i	−0.154881	+	0.139455i	0.588047	+	0.808826i	$0.299897\pi$
$588$		0			0
$589$	−1.05257	+	1.16900i	−0.0433706	+	0.0481679i
$590$	−35.5602	+	2.77116i	−1.46399	+	0.114087i
$591$		0			0
$592$	−13.1750	−	29.5916i	−0.541490	−	1.21621i
$593$		−	15.4520i		−	0.634536i	−0.948336	−	0.317268i	$-0.897235\pi$
$593$		−	15.4520i		−	0.634536i	0.948336	−	0.317268i	$-0.102765\pi$
$594$		0			0
$595$	−0.662001	−	1.22149i	−0.0271394	−	0.0500762i
$596$	−0.0318127	−	0.302677i	−0.00130310	−	0.0123981i
$597$		0			0
$598$	−2.65165	−	2.38755i	−0.108434	−	0.0976343i
$599$	−14.5998	−	25.2875i	−0.596530	−	1.03322i	−0.993329	−	0.115315i	$-0.963212\pi$
$599$	−14.5998	−	25.2875i	−0.596530	−	1.03322i	0.396799	−	0.917905i	$-0.370121\pi$
$600$		0			0
$601$	6.04982	−	10.4786i	0.246777	−	0.427431i	−0.715853	−	0.698251i	$-0.753962\pi$
$601$	6.04982	−	10.4786i	0.246777	−	0.427431i	0.962630	+	0.270821i	$0.0872951\pi$
$602$	−6.66005	+	2.16398i	−0.271444	+	0.0881974i
$603$		0			0
$604$	4.65135	−	3.37941i	0.189261	−	0.137506i
$605$	7.33708	−	20.6688i	0.298295	−	0.840306i
$606$		0			0
$607$	6.77456	−	3.91130i	0.274971	−	0.158755i	−0.356174	−	0.934420i	$-0.615919\pi$
$607$	6.77456	−	3.91130i	0.274971	−	0.158755i	0.631145	+	0.775665i	$0.282585\pi$
$608$	−2.63306	−	0.276746i	−0.106785	−	0.0112235i
$609$		0			0
$610$	−11.5863	−	4.11295i	−0.469117	−	0.166529i
$611$	0.504683	+	1.55325i	0.0204173	+	0.0628379i
$612$		0			0
$613$	41.1658	+	13.3756i	1.66267	+	0.540235i	0.981429	−	0.191824i	$-0.0614403\pi$
$613$	41.1658	+	13.3756i	1.66267	+	0.540235i	0.681242	+	0.732059i	$0.261440\pi$
$614$	11.6506	+	2.47641i	0.470181	+	0.0999400i
$615$		0			0
$616$	25.2672	−	5.37072i	1.01805	−	0.216392i
$617$	41.5681	+	4.36898i	1.67347	+	0.175888i	0.893231	−	0.449597i	$-0.148433\pi$
$617$	41.5681	+	4.36898i	1.67347	+	0.175888i	0.780236	+	0.625486i	$0.215099\pi$
$618$		0			0
$619$	−41.0840	+	18.2918i	−1.65130	+	0.735208i	−0.999727	−	0.0233746i	$-0.992559\pi$
$619$	−41.0840	+	18.2918i	−1.65130	+	0.735208i	−0.651577	+	0.758582i	$0.725892\pi$
$620$	−1.58490	−	0.757453i	−0.0636510	−	0.0304200i
$621$		0			0
$622$	4.13299	+	5.68857i	0.165718	+	0.228091i
$623$	3.19350	−	15.0242i	0.127945	−	0.601934i
$624$		0			0
$625$	23.8000	−	7.65232i	0.952002	−	0.306093i
$626$	1.03272	+	1.78872i	0.0412758	+	0.0714918i
$627$		0			0
$628$	4.15920	−	0.437150i	0.165970	−	0.0174442i
$629$	−3.16305	+	2.29809i	−0.126119	+	0.0916310i
$630$		0			0
$631$	−15.8591	−	11.5223i	−0.631340	−	0.458695i	0.225524	−	0.974238i	$-0.427591\pi$
$631$	−15.8591	−	11.5223i	−0.631340	−	0.458695i	−0.856864	+	0.515542i	$0.827591\pi$
$632$	7.52636	+	4.34534i	0.299382	+	0.172849i
$633$		0			0
$634$	26.4540	−	5.62298i	1.05062	−	0.223317i
$635$	−3.13164	−	7.57691i	−0.124275	−	0.300680i
$636$		0			0
$637$	−1.71569	+	1.54482i	−0.0679782	+	0.0612078i
$638$	49.5615	+	16.1035i	1.96216	+	0.637544i
$639$		0			0
$640$	2.23777	+	12.1259i	0.0884558	+	0.479319i
$641$	18.5093	+	20.5567i	0.731074	+	0.811940i	0.987994	−	0.154492i	$-0.0493742\pi$
$641$	18.5093	+	20.5567i	0.731074	+	0.811940i	−0.256920	+	0.966433i	$0.582708\pi$
$642$		0			0
$643$	−0.471475	+	0.272206i	−0.0185932	+	0.0107348i	−0.509268	−	0.860608i	$-0.670084\pi$
$643$	−0.471475	+	0.272206i	−0.0185932	+	0.0107348i	0.490675	+	0.871343i	$0.336750\pi$
$644$	0.425695	−	4.05022i	0.0167747	−	0.159601i
$645$		0			0
$646$	−0.0422746	−	0.402216i	−0.00166327	−	0.0158250i
$647$	7.85818	+	10.8159i	0.308937	+	0.425215i	0.935049	−	0.354518i	$-0.115355\pi$
$647$	7.85818	+	10.8159i	0.308937	+	0.425215i	−0.626112	+	0.779733i	$0.715355\pi$
$648$		0			0
$649$	−59.2047			−2.32399
$650$	3.92103	−	0.614855i	0.153795	−	0.0241166i
$651$		0			0
$652$	0.280621	+	0.252672i	0.0109900	+	0.00989540i
$653$	6.82865	−	15.3374i	0.267226	−	0.600199i	−0.729235	−	0.684264i	$-0.760124\pi$
$653$	6.82865	−	15.3374i	0.267226	−	0.600199i	0.996460	+	0.0840650i	$0.0267903\pi$
$654$		0			0
$655$	33.3296	+	0.898389i	1.30229	+	0.0351030i
$656$	16.7653	+	12.1807i	0.654574	+	0.475576i
$657$		0			0
$658$	3.38085	−	4.65334i	0.131799	−	0.181406i
$659$	18.7080	+	20.7774i	0.728761	+	0.809371i	0.987673	−	0.156530i	$-0.0500308\pi$
$659$	18.7080	+	20.7774i	0.728761	+	0.809371i	−0.258913	+	0.965901i	$0.583364\pi$
$660$		0			0
$661$	−25.5742	+	28.4031i	−0.994722	+	1.10475i	−0.000223648		1.00000i	$0.500071\pi$
$661$	−25.5742	+	28.4031i	−0.994722	+	1.10475i	−0.994498	+	0.104751i	$0.966595\pi$
$662$	3.29781	+	15.5150i	0.128173	+	0.603006i
$663$		0			0
$664$	39.1449	+	8.32051i	1.51912	+	0.322898i
$665$	3.56653	−	1.93292i	0.138304	−	0.0749555i
$666$		0			0
$667$	24.5593	−	33.8030i	0.950940	−	1.30886i
$668$	6.73341	+	3.88754i	0.260524	+	0.150413i
$669$		0			0
$670$	−10.1765	−	2.45143i	−0.393152	−	0.0947069i
$671$	−18.6434	−	8.30057i	−0.719720	−	0.320440i
$672$		0			0
$673$	3.66100	−	17.2236i	0.141121	−	0.663922i	−0.849534	−	0.527533i	$-0.823117\pi$
$673$	3.66100	−	17.2236i	0.141121	−	0.663922i	0.990655	−	0.136389i	$-0.0435497\pi$
$674$	−23.0216			−0.886758
$675$		0			0
$676$	6.15951			0.236904
$677$	−2.61929	+	12.3228i	−0.100668	+	0.473604i	0.898717	+	0.438529i	$0.144500\pi$
$677$	−2.61929	+	12.3228i	−0.100668	+	0.473604i	−0.999385	+	0.0350748i	$0.988833\pi$
$678$		0			0
$679$	−12.3621	−	5.50396i	−0.474414	−	0.211223i
$680$	2.12264	−	0.877318i	0.0813996	−	0.0336436i
$681$		0			0
$682$	7.79164	+	4.49851i	0.298357	+	0.172257i
$683$	−8.54082	+	11.7554i	−0.326806	+	0.449809i	−0.940530	−	0.339711i	$-0.889671\pi$
$683$	−8.54082	+	11.7554i	−0.326806	+	0.449809i	0.613724	+	0.789520i	$0.289671\pi$
$684$		0			0
$685$	−24.5979	−	23.3785i	−0.939838	−	0.893246i
$686$	23.5279	+	5.00101i	0.898300	+	0.190940i
$687$		0			0
$688$	−1.78027	−	8.37553i	−0.0678723	−	0.319314i
$689$	−4.70204	+	5.22214i	−0.179133	+	0.198948i
$690$		0			0
$691$	−11.8506	−	13.1614i	−0.450819	−	0.500685i	0.474300	−	0.880363i	$-0.342701\pi$
$691$	−11.8506	−	13.1614i	−0.450819	−	0.500685i	−0.925118	+	0.379679i	$0.876035\pi$
$692$	−1.67990	+	2.31219i	−0.0638602	+	0.0878961i
$693$		0			0
$694$	−35.2740	−	25.6280i	−1.33898	−	0.972827i
$695$	29.1528	+	22.4054i	1.10583	+	0.849884i
$696$		0			0
$697$	1.01737	−	2.28504i	0.0385355	−	0.0865522i
$698$	18.0435	+	16.2464i	0.682955	+	0.614935i
$699$		0			0
$700$	3.19826	+	3.20810i	0.120883	+	0.121255i
$701$	−12.2885			−0.464130			−0.232065	−	0.972700i	$-0.574548\pi$
$701$	−12.2885			−0.464130			−0.232065	+	0.972700i	$0.574548\pi$
$702$		0			0
$703$	−6.71002	−	9.23555i	−0.253073	−	0.348325i
$704$	4.23524	+	40.2956i	0.159622	+	1.51870i
$705$		0			0
$706$	−0.943910	+	8.98070i	−0.0355245	+	0.337993i
$707$	−18.7206	+	10.8084i	−0.704061	+	0.406490i
$708$		0			0
$709$	26.2005	+	29.0986i	0.983982	+	1.09282i	0.995676	+	0.0928908i	$0.0296107\pi$
$709$	26.2005	+	29.0986i	0.983982	+	1.09282i	−0.0116946	+	0.999932i	$0.503723\pi$
$710$	7.12346	−	3.86064i	0.267339	−	0.144887i
$711$		0			0
$712$	24.1495	+	7.84664i	0.905040	+	0.294065i
$713$	5.36082	−	4.82690i	0.200764	−	0.180769i
$714$		0			0
$715$	6.56806	−	0.511841i	0.245632	−	0.0191418i
$716$	−0.121948	+	0.0259209i	−0.00455741	+	0.000968708i
$717$		0			0
$718$	1.58055	+	0.912530i	0.0589856	+	0.0340553i
$719$	34.6825	+	25.1983i	1.29344	+	0.939737i	0.999869	−	0.0162007i	$-0.00515708\pi$
$719$	34.6825	+	25.1983i	1.29344	+	0.939737i	0.293569	+	0.955938i	$0.405157\pi$
$720$		0			0
$721$	−26.8011	+	19.4721i	−0.998124	+	0.725180i
$722$	−22.0490	+	2.31744i	−0.820579	+	0.0862464i
$723$		0			0
$724$	−1.43622	−	2.48760i	−0.0533765	−	0.0924509i
$725$	11.9599	+	44.9109i	0.444180	+	1.66795i
$726$		0			0
$727$	−3.25029	+	15.2914i	−0.120546	+	0.567127i	0.875870	+	0.482547i	$0.160288\pi$
$727$	−3.25029	+	15.2914i	−0.120546	+	0.567127i	−0.996417	+	0.0845798i	$0.973045\pi$
$728$	2.14980	+	2.95895i	0.0796770	+	0.109666i
$729$		0			0
$730$	5.83608	−	1.07702i	0.216003	−	0.0398622i
$731$	−0.944168	+	0.420371i	−0.0349213	+	0.0155480i
$732$		0			0
$733$	−2.16196	−	0.227232i	−0.0798539	−	0.00839299i	0.0645172	−	0.997917i	$-0.479449\pi$
$733$	−2.16196	−	0.227232i	−0.0798539	−	0.00839299i	−0.144371	+	0.989524i	$0.546116\pi$
$734$	34.3039	−	7.29153i	1.26618	−	0.269135i
$735$		0			0
$736$	11.8759	+	2.52430i	0.437751	+	0.0930469i
$737$	−16.5246	−	5.36916i	−0.608690	−	0.197775i
$738$		0			0
$739$	−2.39623	−	7.37485i	−0.0881469	−	0.271288i	0.897260	−	0.441502i	$-0.145554\pi$
$739$	−2.39623	−	7.37485i	−0.0881469	−	0.271288i	−0.985407	+	0.170214i	$0.945554\pi$
$740$	7.76814	−	10.1076i	0.285563	−	0.371561i
$741$		0			0
$742$	24.6128	+	2.58691i	0.903564	+	0.0949684i
$743$	44.0124	−	25.4106i	1.61466	−	0.932223i	0.626386	−	0.779513i	$-0.284533\pi$
$743$	44.0124	−	25.4106i	1.61466	−	0.932223i	0.988271	−	0.152710i	$-0.0488001\pi$
$744$		0			0
$745$	−1.14632	+	0.786549i	−0.0419980	+	0.0288169i
$746$	−27.6562	+	20.0934i	−1.01257	+	0.735672i
$747$		0			0
$748$	0.712950	−	0.231652i	0.0260680	−	0.00847002i
$749$	14.7838	−	25.6062i	0.540187	−	0.935632i
$750$		0			0
$751$	−11.6420	−	20.1646i	−0.424824	−	0.735817i	0.571580	−	0.820546i	$-0.306331\pi$
$751$	−11.6420	−	20.1646i	−0.424824	−	0.735817i	−0.996404	+	0.0847294i	$0.972997\pi$
$752$	5.22657	+	4.70603i	0.190594	+	0.171611i
$753$		0			0
$754$	0.771258	+	7.33803i	0.0280875	+	0.267235i
$755$	−23.6956	−	11.3246i	−0.862373	−	0.412144i
$756$		0			0
$757$			6.38289i			0.231990i	0.993250	+	0.115995i	$0.0370056\pi$
$757$			6.38289i			0.231990i	−0.993250	+	0.115995i	$0.962994\pi$
$758$	−9.29870	−	20.8852i	−0.337744	−	0.758585i
$759$		0			0
$760$	2.56161	+	6.19773i	0.0929193	+	0.224815i
$761$	−13.9838	+	15.5306i	−0.506912	+	0.562983i	−0.941226	−	0.337779i	$-0.890324\pi$
$761$	−13.9838	+	15.5306i	−0.506912	+	0.562983i	0.434313	+	0.900762i	$0.356991\pi$
$762$		0			0
$763$	−8.46518	+	7.62208i	−0.306460	+	0.275938i
$764$	−2.67460	−	8.23156i	−0.0967635	−	0.297807i
$765$		0			0
$766$	1.30907	−	4.02891i	0.0472987	−	0.145570i
$767$	−3.40954	−	7.65796i	−0.123111	−	0.276513i
$768$		0			0
$769$	2.99572	−	28.5024i	0.108028	−	1.02782i	−0.797437	−	0.603402i	$-0.793811\pi$
$769$	2.99572	−	28.5024i	0.108028	−	1.02782i	0.905466	−	0.424420i	$-0.139522\pi$
$770$	−15.0549	−	17.6544i	−0.542539	−	0.636221i
$771$		0			0
$772$	0.981924	−	0.103204i	0.0353402	−	0.00371441i
$773$	1.63527	−	0.531331i	0.0588165	−	0.0191106i	−0.279461	−	0.960157i	$-0.590156\pi$
$773$	1.63527	−	0.531331i	0.0588165	−	0.0191106i	0.338277	+	0.941046i	$0.390156\pi$
$774$		0			0
$775$	0.407631	+	8.01363i	0.0146425	+	0.287858i
$776$	11.1852	−	19.3734i	0.401527	−	0.695464i
$777$		0			0
$778$	−14.8969	+	33.4590i	−0.534080	+	1.19956i
$779$	6.67191	+	2.97053i	0.239046	+	0.106430i
$780$		0			0
$781$	12.2862	−	5.47018i	0.439636	−	0.195738i
$782$			1.85465i			0.0663220i
$783$		0			0
$784$	−3.07224	+	9.45540i	−0.109723	+	0.337693i
$785$	−10.8083	−	15.7520i	−0.385763	−	0.562214i
$786$		0			0
$787$	5.63866	+	26.5278i	0.200996	+	0.945614i	0.956785	+	0.290798i	$0.0939207\pi$
$787$	5.63866	+	26.5278i	0.200996	+	0.945614i	−0.755788	+	0.654816i	$0.772746\pi$
$788$	1.87553	+	8.82368i	0.0668130	+	0.314331i
$789$		0			0
$790$	0.210330	−	7.80309i	0.00748321	−	0.277621i
$791$	−4.03114	+	12.4066i	−0.143331	+	0.441127i
$792$		0			0
$793$		−	2.88949i		−	0.102609i
$794$	−26.8063	+	11.9349i	−0.951319	+	0.423555i
$795$		0			0
$796$	2.59352	+	1.15471i	0.0919249	+	0.0409276i
$797$	4.65755	−	10.4610i	0.164979	−	0.370549i	−0.812071	−	0.583558i	$-0.801660\pi$
$797$	4.65755	−	10.4610i	0.164979	−	0.370549i	0.977050	+	0.213010i	$0.0683266\pi$
$798$		0			0
$799$	0.424448	−	0.735166i	0.0150159	−	0.0260083i
$800$	−10.5084	+	8.48284i	−0.371528	+	0.299914i
$801$		0			0
$802$	−40.0455	+	13.0116i	−1.41406	+	0.459455i
$803$	9.79682	−	1.02969i	0.345722	−	0.0363369i
$804$		0			0
$805$	−17.1924	+	7.10584i	−0.605951	+	0.250448i
$806$	−0.133156	+	1.26689i	−0.00469021	+	0.0446243i
$807$		0			0
$808$	−14.5350	−	32.6462i	−0.511341	−	1.14849i
$809$	4.76883	−	14.6770i	0.167663	−	0.516014i	−0.831559	−	0.555436i	$-0.812551\pi$
$809$	4.76883	−	14.6770i	0.167663	−	0.516014i	0.999223	+	0.0394214i	$0.0125515\pi$
$810$		0			0
$811$	11.0366	+	33.9670i	0.387546	+	1.19274i	0.934617	+	0.355657i	$0.115743\pi$
$811$	11.0366	+	33.9670i	0.387546	+	1.19274i	−0.547071	+	0.837086i	$0.684257\pi$
$812$	−6.25836	+	5.63505i	−0.219625	+	0.197752i
$813$		0			0
$814$	−43.6890	+	48.5216i	−1.53130	+	1.70068i
$815$	0.403958	−	1.67693i	0.0141500	−	0.0587403i
$816$		0			0
$817$	−1.22741	−	2.75680i	−0.0429415	−	0.0964482i
$818$			41.1991i			1.44049i
$819$		0			0
$820$	−1.07072	+	8.08491i	−0.0373911	+	0.282337i
$821$	3.18813	+	30.3331i	0.111267	+	1.05863i	0.897595	+	0.440822i	$0.145313\pi$
$821$	3.18813	+	30.3331i	0.111267	+	1.05863i	−0.786328	+	0.617809i	$0.788020\pi$
$822$		0			0
$823$	25.3011	+	22.7812i	0.881941	+	0.794104i	0.979567	−	0.201120i	$-0.0644580\pi$
$823$	25.3011	+	22.7812i	0.881941	+	0.794104i	−0.0976252	+	0.995223i	$0.531125\pi$
$824$	−27.3828	−	47.4284i	−0.953925	−	1.65225i
$825$		0			0
$826$	−14.7613	+	25.5673i	−0.513611	+	0.889600i
$827$	−23.0112	+	7.47679i	−0.800178	+	0.259994i	−0.680432	−	0.732811i	$-0.738208\pi$
$827$	−23.0112	+	7.47679i	−0.800178	+	0.259994i	−0.119746	+	0.992805i	$0.538208\pi$
$828$		0			0
$829$	−5.52136	+	4.01150i	−0.191765	+	0.139325i	−0.679525	−	0.733652i	$-0.737814\pi$
$829$	−5.52136	+	4.01150i	−0.191765	+	0.139325i	0.487760	+	0.872978i	$0.337814\pi$
$830$	−10.1825	−	34.4728i	−0.353440	−	1.19657i
$831$		0			0
$832$	−4.96822	+	2.86840i	−0.172242	+	0.0994440i
$833$	1.19344	+	0.125435i	0.0413501	+	0.00434607i
$834$		0			0
$835$	0.956972	−	35.5030i	0.0331174	−	1.22863i
$836$	0.676381	+	2.08169i	0.0233931	+	0.0719966i
$837$		0			0
$838$	17.0912	+	5.55326i	0.590405	+	0.191834i
$839$	−47.2868	−	10.0511i	−1.63252	−	0.347003i	−0.701699	−	0.712474i	$-0.747575\pi$
$839$	−47.2868	−	10.0511i	−1.63252	−	0.347003i	−0.930823	+	0.365470i	$0.880908\pi$
$840$		0			0
$841$	−56.1469	+	11.9344i	−1.93610	+	0.411531i
$842$	−17.6120	−	1.85110i	−0.606950	−	0.0637930i
$843$		0			0
$844$	3.24023	−	1.44265i	0.111533	−	0.0496579i
$845$	−13.4064	−	24.7368i	−0.461194	−	0.850972i
$846$		0			0
$847$	−10.6704	−	14.6865i	−0.366639	−	0.504636i
$848$	−6.29161	+	29.5997i	−0.216055	+	1.01646i
$849$		0			0
$850$	−1.60123	−	1.30073i	−0.0549219	−	0.0446148i
$851$	26.1752	+	45.3368i	0.897276	+	1.55413i
$852$		0			0
$853$	3.49922	−	0.367783i	0.119811	−	0.0125926i	−0.0444332	−	0.999012i	$-0.514148\pi$
$853$	3.49922	−	0.367783i	0.119811	−	0.0125926i	0.164244	+	0.986420i	$0.447482\pi$
$854$	−8.23285	+	5.98151i	−0.281722	+	0.204683i
$855$		0			0
$856$	39.5445	+	28.7308i	1.35160	+	0.981997i
$857$	−11.8768	−	6.85708i	−0.405704	−	0.234233i	0.283238	−	0.959050i	$-0.408591\pi$
$857$	−11.8768	−	6.85708i	−0.405704	−	0.234233i	−0.688942	+	0.724816i	$0.741925\pi$
$858$		0			0
$859$	42.6150	−	9.05809i	1.45400	−	0.309058i	0.587905	−	0.808930i	$-0.299953\pi$
$859$	42.6150	−	9.05809i	1.45400	−	0.309058i	0.866099	+	0.499872i	$0.166620\pi$
$860$	2.56410	−	2.18655i	0.0874352	−	0.0745607i
$861$		0			0
$862$	14.0714	−	12.6699i	0.479273	−	0.431539i
$863$	4.61438	+	1.49930i	0.157075	+	0.0510369i	0.386499	−	0.922290i	$-0.373684\pi$
$863$	4.61438	+	1.49930i	0.157075	+	0.0510369i	−0.229424	+	0.973327i	$0.573684\pi$
$864$		0			0
$865$	12.9422	+	1.71399i	0.440047	+	0.0582773i
$866$	−19.1436	−	21.2611i	−0.650527	−	0.722483i
$867$		0			0
$868$	−1.25915	+	0.726971i	−0.0427384	+	0.0246750i
$869$	1.35437	−	12.8859i	0.0459437	−	0.437125i
$870$		0			0
$871$	−0.257149	−	2.44661i	−0.00871316	−	0.0829002i
$872$	−11.0686	−	15.2347i	−0.374832	−	0.515911i
$873$		0			0
$874$	−5.41523			−0.183173
$875$	5.92273	−	19.8269i	0.200225	−	0.670271i
$876$		0			0
$877$	4.30337	+	3.87477i	0.145314	+	0.130842i	0.738582	−	0.674164i	$-0.235496\pi$
$877$	4.30337	+	3.87477i	0.145314	+	0.130842i	−0.593268	+	0.805005i	$0.702162\pi$
$878$	2.73262	−	6.13757i	0.0922215	−	0.207133i
$879$		0			0
$880$	23.3928	−	16.0510i	0.788571	−	0.541079i
$881$	39.7428	+	28.8749i	1.33897	+	0.972819i	0.999481	+	0.0322087i	$0.0102541\pi$
$881$	39.7428	+	28.8749i	1.33897	+	0.972819i	0.339489	+	0.940610i	$0.389746\pi$
$882$		0			0
$883$	18.5769	−	25.5689i	0.625162	−	0.860461i	−0.372554	−	0.928010i	$-0.621518\pi$
$883$	18.5769	−	25.5689i	0.625162	−	0.860461i	0.997716	+	0.0675491i	$0.0215179\pi$
$884$	0.0710216	+	0.0788774i	0.00238871	+	0.00265294i
$885$		0			0
$886$	7.59600	−	8.43621i	0.255193	−	0.283420i
$887$	5.20653	+	24.4948i	0.174818	+	0.822454i	0.974914	+	0.222582i	$0.0714485\pi$
$887$	5.20653	+	24.4948i	0.174818	+	0.822454i	−0.800096	+	0.599872i	$0.795218\pi$
$888$		0			0
$889$	−6.63771	−	1.41089i	−0.222621	−	0.0473197i
$890$	−4.13905	−	22.4284i	−0.138741	−	0.751803i
$891$		0			0
$892$	−0.530967	+	0.730814i	−0.0177781	+	0.0244694i
$893$	2.14655	+	1.23931i	0.0718316	+	0.0414720i
$894$		0			0
$895$	0.369523	+	0.433330i	0.0123518	+	0.0144846i
$896$	9.32379	+	4.15122i	0.311486	+	0.138682i
$897$		0			0
$898$	0.00184484	−	0.00867928i	6.15630e−5	−	0.000289631i
$899$	−14.9170			−0.497508
$900$		0			0
$901$	3.65253			0.121683
$902$	8.68472	−	40.8584i	0.289170	−	1.36044i
$903$		0			0
$904$	−19.7010	−	8.77146i	−0.655246	−	0.291734i
$905$	−6.86431	+	11.1822i	−0.228177	+	0.371710i
$906$		0			0
$907$	24.7390	+	14.2831i	0.821446	+	0.474262i	0.850915	−	0.525304i	$-0.176048\pi$
$907$	24.7390	+	14.2831i	0.821446	+	0.474262i	−0.0294688	+	0.999566i	$0.509382\pi$
$908$	3.24818	−	4.47074i	0.107795	−	0.148367i
$909$		0			0
$910$	1.41655	−	2.96400i	0.0469583	−	0.0982558i
$911$	−32.7084	−	6.95237i	−1.08368	−	0.230342i	−0.368740	−	0.929533i	$-0.620211\pi$
$911$	−32.7084	−	6.95237i	−1.08368	−	0.230342i	−0.714936	+	0.699190i	$0.753544\pi$
$912$		0			0
$913$	−12.4050	−	58.3610i	−0.410546	−	1.93147i
$914$	−7.40853	+	8.22800i	−0.245052	+	0.272158i
$915$		0			0
$916$	9.04710	+	10.0478i	0.298924	+	0.331989i
$917$	16.2211	−	22.3265i	0.535669	−	0.737285i
$918$		0			0
$919$	10.0278	+	7.28564i	0.330787	+	0.240331i	0.740765	−	0.671765i	$-0.234463\pi$
$919$	10.0278	+	7.28564i	0.330787	+	0.240331i	−0.409977	+	0.912096i	$0.634463\pi$
$920$	−8.71182	−	29.4938i	−0.287220	−	0.972382i
$921$		0			0
$922$	11.4993	−	25.8278i	0.378709	−	0.850593i
$923$	1.41510	+	1.27417i	0.0465787	+	0.0419397i
$924$		0			0
$925$	−57.4999	−	9.19768i	−1.89059	−	0.302418i
$926$	12.9282			0.424848
$927$		0			0
$928$	−14.7572	−	20.3115i	−0.484428	−	0.666758i
$929$	2.34881	+	22.3475i	0.0770620	+	0.733196i	0.963020	+	0.269430i	$0.0868354\pi$
$929$	2.34881	+	22.3475i	0.0770620	+	0.733196i	−0.885958	+	0.463766i	$0.846498\pi$
$930$		0			0
$931$	−0.366248	+	3.48462i	−0.0120033	+	0.114204i
$932$	−1.90625	+	1.10057i	−0.0624412	+	0.0360505i
$933$		0			0
$934$	−9.49314	−	10.5432i	−0.310625	−	0.344984i
$935$	−2.48208	−	2.35903i	−0.0811728	−	0.0771487i
$936$		0			0
$937$	−11.7007	−	3.80179i	−0.382246	−	0.124199i	0.111590	−	0.993754i	$-0.464406\pi$
$937$	−11.7007	−	3.80179i	−0.382246	−	0.124199i	−0.493836	+	0.869555i	$0.664406\pi$
$938$	−6.43865	+	5.79739i	−0.210229	+	0.189291i
$939$		0			0
$940$	−0.648207	+	2.69087i	−0.0211422	+	0.0877665i
$941$	−4.50020	+	0.956546i	−0.146702	+	0.0311825i	−0.280677	−	0.959802i	$-0.590559\pi$
$941$	−4.50020	+	0.956546i	−0.146702	+	0.0311825i	0.133975	+	0.990985i	$0.457226\pi$
$942$		0			0
$943$	−29.0046	−	16.7458i	−0.944519	−	0.545318i
$944$	−29.2044	−	21.2182i	−0.950522	−	0.690594i
$945$		0			0
$946$	−13.9633	+	10.1450i	−0.453987	+	0.329841i
$947$	−13.9528	+	1.46650i	−0.453404	+	0.0476547i	−0.328479	−	0.944511i	$-0.606536\pi$
$947$	−13.9528	+	1.46650i	−0.453404	+	0.0476547i	−0.124926	+	0.992166i	$0.539869\pi$
$948$		0			0
$949$	0.697376	+	1.20789i	0.0226378	+	0.0392098i
$950$	3.79791	−	4.67532i	0.123220	−	0.151687i
$951$		0			0
$952$	0.395255	−	1.85953i	0.0128103	−	0.0602677i
$953$	−19.0044	−	26.1573i	−0.615613	−	0.847318i	0.381412	−	0.924405i	$-0.375438\pi$
$953$	−19.0044	−	26.1573i	−0.615613	−	0.847318i	−0.997024	+	0.0770871i	$0.975438\pi$
$954$		0			0
$955$	−27.2369	+	28.6576i	−0.881365	+	0.927337i
$956$	−9.11740	+	4.05933i	−0.294878	+	0.131288i
$957$		0			0
$958$	25.7931	+	2.71096i	0.833337	+	0.0875873i
$959$	−27.4747	+	5.83992i	−0.887203	+	0.188581i
$960$		0			0
$961$	27.8035	+	5.90981i	0.896886	+	0.190639i
$962$	−8.79214	−	2.85674i	−0.283470	−	0.0921050i
$963$		0			0
$964$	−3.83299	−	11.7967i	−0.123452	−	0.379947i
$965$	−2.55167	−	3.71881i	−0.0821410	−	0.119713i
$966$		0			0
$967$	−16.9110	−	1.77742i	−0.543822	−	0.0571580i	−0.171365	−	0.985208i	$-0.554818\pi$
$967$	−16.9110	−	1.77742i	−0.543822	−	0.0571580i	−0.372457	+	0.928049i	$0.621485\pi$
$968$	25.9900	−	15.0053i	0.835349	−	0.482289i
$969$		0			0
$970$	−20.0857	−	0.541405i	−0.644914	−	0.0173835i
$971$	21.1843	−	15.3913i	0.679837	−	0.493930i	−0.193467	−	0.981107i	$-0.561973\pi$
$971$	21.1843	−	15.3913i	0.679837	−	0.493930i	0.873304	+	0.487176i	$0.161973\pi$
$972$		0			0
$973$	28.9435	−	9.40433i	0.927887	−	0.301489i
$974$	16.3424	−	28.3058i	0.523643	−	0.906977i
$975$		0			0
$976$	−6.22155	−	10.7760i	−0.199147	−	0.344933i
$977$	31.1907	+	28.0842i	0.997877	+	0.898493i	0.994835	−	0.101502i	$-0.0323650\pi$
$977$	31.1907	+	28.0842i	0.997877	+	0.898493i	0.00304215	+	0.999995i	$0.499032\pi$
$978$		0			0
$979$	−3.95716	−	37.6498i	−0.126471	−	1.20329i
$980$	−3.84768	+	0.710068i	−0.122910	+	0.0226823i
$981$		0			0
$982$		−	13.0420i		−	0.416185i
$983$	−7.18555	−	16.1390i	−0.229184	−	0.514755i	0.761948	−	0.647638i	$-0.224243\pi$
$983$	−7.18555	−	16.1390i	−0.229184	−	0.514755i	−0.991132	+	0.132883i	$0.957576\pi$
$984$		0			0
$985$	31.3540	−	26.7373i	0.999023	−	0.851920i
$986$	2.56622	−	2.85008i	0.0817252	−	0.0907651i
$987$		0			0
$988$	−0.230308	+	0.207370i	−0.00732707	+	0.00659732i
$989$	4.27635	+	13.1612i	0.135980	+	0.418503i
$990$		0			0
$991$	−6.40434	+	19.7105i	−0.203440	+	0.626125i	0.796333	+	0.604858i	$0.206770\pi$
$991$	−6.40434	+	19.7105i	−0.203440	+	0.626125i	−0.999774	+	0.0212674i	$0.993230\pi$
$992$	−1.76302	−	3.95982i	−0.0559761	−	0.125724i
$993$		0			0
$994$	0.701004	−	6.66961i	0.0222345	−	0.211547i
$995$	−1.00754	−	12.9289i	−0.0319410	−	0.409875i
$996$		0			0
$997$	−58.7053	+	6.17018i	−1.85922	+	0.195412i	−0.966754	−	0.255709i	$-0.917691\pi$
$997$	−58.7053	+	6.17018i	−1.85922	+	0.195412i	−0.892463	+	0.451121i	$0.851024\pi$
$998$	−28.8288	+	9.36704i	−0.912560	+	0.296509i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.y.a.19.20		224
3.2	odd	2		225.2.u.a.169.9	yes	224
9.4	even	3	inner	675.2.y.a.469.20		224
9.5	odd	6		225.2.u.a.94.9	yes	224
25.4	even	10	inner	675.2.y.a.154.20		224
75.29	odd	10		225.2.u.a.79.9	yes	224
225.4	even	30	inner	675.2.y.a.604.20		224
225.104	odd	30		225.2.u.a.4.9	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.9	✓	224	225.104	odd	30
225.2.u.a.79.9	yes	224	75.29	odd	10
225.2.u.a.94.9	yes	224	9.5	odd	6
225.2.u.a.169.9	yes	224	3.2	odd	2
675.2.y.a.19.20		224	1.1	even	1	trivial
675.2.y.a.154.20		224	25.4	even	10	inner
675.2.y.a.469.20		224	9.4	even	3	inner
675.2.y.a.604.20		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)

\(f(q)\)	\(=\)	\(q+(0.255527 - 1.20216i) q^{2} +(0.447195 + 0.199104i) q^{4} +(-0.173727 - 2.22931i) q^{5} +(-1.60284 - 0.925401i) q^{7} +(1.79842 - 2.47532i) q^{8} +O(q^{10})\)	\(q+(0.255527 - 1.20216i) q^{2} +(0.447195 + 0.199104i) q^{4} +(-0.173727 - 2.22931i) q^{5} +(-1.60284 - 0.925401i) q^{7} +(1.79842 - 2.47532i) q^{8} +(-2.72438 - 0.360801i) q^{10} +(-4.46195 - 0.948417i) q^{11} +(-0.134284 - 0.631759i) q^{13} +(-1.52205 + 1.69041i) q^{14} +(-1.86108 - 2.06694i) q^{16} +(-0.197326 + 0.271596i) q^{17} +(-0.793011 - 0.576156i) q^{19} +(0.366175 - 1.03153i) q^{20} +(-2.28030 + 5.12163i) q^{22} +(3.34049 + 3.00779i) q^{23} +(-4.93964 + 0.774584i) q^{25} -0.793788 q^{26} +(-0.532532 - 0.732968i) q^{28} +(-0.971616 - 9.24431i) q^{29} +(0.167747 - 1.59601i) q^{31} +(2.33914 - 1.35050i) q^{32} +(0.276080 + 0.306618i) q^{34} +(-1.78455 + 3.73400i) q^{35} +(11.0762 + 3.59887i) q^{37} +(-0.895268 + 0.806103i) q^{38} +(-5.83068 - 3.57921i) q^{40} +(-7.28791 + 1.54909i) q^{41} +(2.66615 + 1.53930i) q^{43} +(-1.80653 - 1.31252i) q^{44} +(4.46944 - 3.24724i) q^{46} +(-2.51480 + 0.264316i) q^{47} +(-1.78727 - 3.09564i) q^{49} +(-0.331038 + 6.13616i) q^{50} +(0.0657344 - 0.309256i) q^{52} +(-6.39509 - 8.80209i) q^{53} +(-1.33915 + 10.1118i) q^{55} +(-5.17325 + 2.30328i) q^{56} +(-11.3614 - 1.19413i) q^{58} +(12.6952 - 2.69845i) q^{59} +(4.37602 + 0.930151i) q^{61} +(-1.87579 - 0.609482i) q^{62} +(-2.74477 - 8.44753i) q^{64} +(-1.38506 + 0.409115i) q^{65} +(3.78807 + 0.398142i) q^{67} +(-0.142319 + 0.0821680i) q^{68} +(4.03286 + 3.09945i) q^{70} +(-2.38521 + 1.73295i) q^{71} +(-2.05379 + 0.667318i) q^{73} +(7.15668 - 12.3957i) q^{74} +(-0.239916 - 0.415546i) q^{76} +(6.27413 + 5.64925i) q^{77} +(0.296904 + 2.82485i) q^{79} +(-4.28453 + 4.50801i) q^{80} +9.15707i q^{82} +(5.32000 + 11.9489i) q^{83} +(0.639752 + 0.392717i) q^{85} +(2.53176 - 2.81180i) q^{86} +(-10.3721 + 9.33908i) q^{88} +(2.56455 + 7.89287i) q^{89} +(-0.369393 + 1.13688i) q^{91} +(0.894989 + 2.01018i) q^{92} +(-0.324849 + 3.09073i) q^{94} +(-1.14666 + 1.86796i) q^{95} +(7.27138 - 0.764252i) q^{97} +(-4.17814 + 1.35756i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) \) 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

Introduction

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