LMFDB - Embedded newform 675.2.r.a.361.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, 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 $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			361.14
Character	$\chi$	$=$	675.361
Dual form			675.2.r.a.316.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.254613 - 0.113361i) q^{2} +(-1.28628 - 1.42856i) q^{4} +(-0.148962 + 2.23110i) q^{5} +(-1.97470 - 3.42027i) q^{7} +(0.337813 + 1.03968i) q^{8} +O(q^{10})$	\(q+(-0.254613 - 0.113361i) q^{2} +(-1.28628 - 1.42856i) q^{4} +(-0.148962 + 2.23110i) q^{5} +(-1.97470 - 3.42027i) q^{7} +(0.337813 + 1.03968i) q^{8} +(0.290848 - 0.551181i) q^{10} +(-1.53404 - 0.682997i) q^{11} +(0.961615 - 0.428138i) q^{13} +(0.115058 + 1.09470i) q^{14} +(-0.370027 + 3.52057i) q^{16} +(1.25351 + 3.85792i) q^{17} +(1.85242 + 5.70117i) q^{19} +(3.37888 - 2.65703i) q^{20} +(0.313161 + 0.347800i) q^{22} +(0.564211 + 5.36811i) q^{23} +(-4.95562 - 0.664700i) q^{25} -0.293374 q^{26} +(-2.34606 + 7.22042i) q^{28} +(-6.99712 + 1.48728i) q^{29} +(-4.81399 - 1.02325i) q^{31} +(1.58649 - 2.74789i) q^{32} +(0.118177 - 1.12438i) q^{34} +(7.92513 - 3.89625i) q^{35} +(-3.92983 - 2.85519i) q^{37} +(0.174640 - 1.66158i) q^{38} +(-2.36995 + 0.598821i) q^{40} +(1.14861 - 0.511393i) q^{41} +(4.99451 + 8.65075i) q^{43} +(0.997503 + 3.07000i) q^{44} +(0.464879 - 1.43075i) q^{46} +(-4.62748 + 0.983601i) q^{47} +(-4.29885 + 7.44583i) q^{49} +(1.18641 + 0.731016i) q^{50} +(-1.84853 - 0.823020i) q^{52} +(-2.76942 + 8.52341i) q^{53} +(1.75235 - 3.32085i) q^{55} +(2.88892 - 3.20847i) q^{56} +(1.95016 + 0.414519i) q^{58} +(-5.63502 + 2.50887i) q^{59} +(-2.58041 - 1.14887i) q^{61} +(1.10971 + 0.806250i) q^{62} +(5.01233 - 3.64167i) q^{64} +(0.811976 + 2.20924i) q^{65} +(11.9904 + 2.54863i) q^{67} +(3.89891 - 6.75310i) q^{68} +(-2.45953 + 0.0936360i) q^{70} +(2.15288 - 6.62590i) q^{71} +(-4.42300 + 3.21350i) q^{73} +(0.676918 + 1.17246i) q^{74} +(5.76174 - 9.97962i) q^{76} +(0.693219 + 6.59554i) q^{77} +(11.5363 - 2.45211i) q^{79} +(-7.79963 - 1.35000i) q^{80} -0.350423 q^{82} +(3.65812 - 4.06275i) q^{83} +(-8.79413 + 2.22203i) q^{85} +(-0.291010 - 2.76878i) q^{86} +(0.191882 - 1.82563i) q^{88} +(-12.2123 + 8.87274i) q^{89} +(-3.36325 - 2.44354i) q^{91} +(6.94294 - 7.71092i) q^{92} +(1.28972 + 0.274138i) q^{94} +(-12.9958 + 3.28368i) q^{95} +(-3.26984 + 0.695025i) q^{97} +(1.93861 - 1.40848i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.254613	−	0.113361i	−0.180039	−	0.0801584i	0.314738	−	0.949179i	$-0.398083\pi$
$2$	−0.254613	−	0.113361i	−0.180039	−	0.0801584i	−0.494776	+	0.869020i	$0.664750\pi$
$3$		0			0
$3$		0			0
$4$	−1.28628	−	1.42856i	−0.643142	−	0.714282i
$5$	−0.148962	+	2.23110i	−0.0666180	+	0.997779i
$5$	−0.148962	+	2.23110i	−0.0666180	+	0.997779i
$6$		0			0
$7$	−1.97470	−	3.42027i	−0.746365	−	1.29274i	−0.949554	−	0.313603i	$-0.898464\pi$
$7$	−1.97470	−	3.42027i	−0.746365	−	1.29274i	0.203189	−	0.979140i	$-0.434869\pi$
$8$	0.337813	+	1.03968i	0.119435	+	0.367583i
$9$		0			0
$10$	0.290848	−	0.551181i	0.0919741	−	0.174299i
$11$	−1.53404	−	0.682997i	−0.462530	−	0.205931i	0.162223	−	0.986754i	$-0.448134\pi$
$11$	−1.53404	−	0.682997i	−0.462530	−	0.205931i	−0.624753	+	0.780823i	$0.714800\pi$
$12$		0			0
$13$	0.961615	−	0.428138i	0.266704	−	0.118744i	−0.269028	−	0.963132i	$-0.586702\pi$
$13$	0.961615	−	0.428138i	0.266704	−	0.118744i	0.535732	+	0.844388i	$0.320036\pi$
$14$	0.115058	+	1.09470i	0.0307504	+	0.292571i
$15$		0			0
$16$	−0.370027	+	3.52057i	−0.0925067	+	0.880143i
$17$	1.25351	+	3.85792i	0.304022	+	0.935683i	0.980040	+	0.198798i	$0.0637038\pi$
$17$	1.25351	+	3.85792i	0.304022	+	0.935683i	−0.676019	+	0.736884i	$0.736296\pi$
$18$		0			0
$19$	1.85242	+	5.70117i	0.424975	+	1.30794i	0.903019	+	0.429602i	$0.141346\pi$
$19$	1.85242	+	5.70117i	0.424975	+	1.30794i	−0.478044	+	0.878336i	$0.658654\pi$
$20$	3.37888	−	2.65703i	0.755540	−	0.594129i
$21$		0			0
$22$	0.313161	+	0.347800i	0.0667661	+	0.0741512i
$23$	0.564211	+	5.36811i	0.117646	+	1.11933i	0.880924	+	0.473257i	$0.156922\pi$
$23$	0.564211	+	5.36811i	0.117646	+	1.11933i	−0.763278	+	0.646070i	$0.776411\pi$
$24$		0			0
$25$	−4.95562	−	0.664700i	−0.991124	−	0.132940i
$26$	−0.293374			−0.0575354
$27$		0			0
$28$	−2.34606	+	7.22042i	−0.443363	+	1.36453i
$29$	−6.99712	+	1.48728i	−1.29933	+	0.276182i	−0.805096	−	0.593145i	$-0.797886\pi$
$29$	−6.99712	+	1.48728i	−1.29933	+	0.276182i	−0.494238	+	0.869327i	$0.664553\pi$
$30$		0			0
$31$	−4.81399	−	1.02325i	−0.864618	−	0.183780i	−0.245806	−	0.969319i	$-0.579053\pi$
$31$	−4.81399	−	1.02325i	−0.864618	−	0.183780i	−0.618812	+	0.785539i	$0.712386\pi$
$32$	1.58649	−	2.74789i	0.280455	−	0.485763i
$33$		0			0
$34$	0.118177	−	1.12438i	0.0202671	−	0.192829i
$35$	7.92513	−	3.89625i	1.33959	−	0.658587i
$36$		0			0
$37$	−3.92983	−	2.85519i	−0.646059	−	0.469390i	0.215867	−	0.976423i	$-0.430742\pi$
$37$	−3.92983	−	2.85519i	−0.646059	−	0.469390i	−0.861927	+	0.507033i	$0.830742\pi$
$38$	0.174640	−	1.66158i	0.0283303	−	0.269545i
$39$		0			0
$40$	−2.36995	+	0.598821i	−0.374723	+	0.0946819i
$41$	1.14861	−	0.511393i	0.179382	−	0.0798662i	−0.315080	−	0.949065i	$-0.602031\pi$
$41$	1.14861	−	0.511393i	0.179382	−	0.0798662i	0.494463	+	0.869199i	$0.335365\pi$
$42$		0			0
$43$	4.99451	+	8.65075i	0.761656	+	1.31923i	0.941997	+	0.335623i	$0.108947\pi$
$43$	4.99451	+	8.65075i	0.761656	+	1.31923i	−0.180341	+	0.983604i	$0.557720\pi$
$44$	0.997503	+	3.07000i	0.150379	+	0.462820i
$45$		0			0
$46$	0.464879	−	1.43075i	0.0685426	−	0.210952i
$47$	−4.62748	+	0.983601i	−0.674987	+	0.143473i	−0.532638	−	0.846343i	$-0.678799\pi$
$47$	−4.62748	+	0.983601i	−0.674987	+	0.143473i	−0.142350	+	0.989816i	$0.545466\pi$
$48$		0			0
$49$	−4.29885	+	7.44583i	−0.614122	+	1.06369i
$50$	1.18641	+	0.731016i	0.167784	+	0.103381i
$51$		0			0
$52$	−1.84853	−	0.823020i	−0.256345	−	0.114132i
$53$	−2.76942	+	8.52341i	−0.380410	+	1.17078i	0.559346	+	0.828934i	$0.311052\pi$
$53$	−2.76942	+	8.52341i	−0.380410	+	1.17078i	−0.939756	+	0.341846i	$0.888948\pi$
$54$		0			0
$55$	1.75235	−	3.32085i	0.236287	−	0.447783i
$56$	2.88892	−	3.20847i	0.386048	−	0.428749i
$57$		0			0
$58$	1.95016	+	0.414519i	0.256068	+	0.0544290i
$59$	−5.63502	+	2.50887i	−0.733618	+	0.326628i	−0.739318	−	0.673356i	$-0.764852\pi$
$59$	−5.63502	+	2.50887i	−0.733618	+	0.326628i	0.00570072	+	0.999984i	$0.498185\pi$
$60$		0			0
$61$	−2.58041	−	1.14887i	−0.330388	−	0.147098i	0.234838	−	0.972035i	$-0.424544\pi$
$61$	−2.58041	−	1.14887i	−0.330388	−	0.147098i	−0.565225	+	0.824937i	$0.691211\pi$
$62$	1.10971	+	0.806250i	0.140933	+	0.102394i
$63$		0			0
$64$	5.01233	−	3.64167i	0.626542	−	0.455209i
$65$	0.811976	+	2.20924i	0.100713	+	0.274022i
$66$		0			0
$67$	11.9904	+	2.54863i	1.46486	+	0.311365i	0.870233	−	0.492640i	$-0.163968\pi$
$67$	11.9904	+	2.54863i	1.46486	+	0.311365i	0.594623	+	0.804005i	$0.297301\pi$
$68$	3.89891	−	6.75310i	0.472812	−	0.818934i
$69$		0			0
$70$	−2.45953	+	0.0936360i	−0.293970	+	0.0111916i
$71$	2.15288	−	6.62590i	0.255500	−	0.786349i	−0.738230	−	0.674549i	$-0.764338\pi$
$71$	2.15288	−	6.62590i	0.255500	−	0.786349i	0.993731	−	0.111801i	$-0.0356618\pi$
$72$		0			0
$73$	−4.42300	+	3.21350i	−0.517673	+	0.376112i	−0.815727	−	0.578437i	$-0.803663\pi$
$73$	−4.42300	+	3.21350i	−0.517673	+	0.376112i	0.298053	+	0.954549i	$0.403663\pi$
$74$	0.676918	+	1.17246i	0.0786901	+	0.136295i
$75$		0			0
$76$	5.76174	−	9.97962i	0.660917	−	1.14474i
$77$	0.693219	+	6.59554i	0.0789997	+	0.751632i
$78$		0			0
$79$	11.5363	−	2.45211i	1.29793	−	0.275884i	0.493404	−	0.869800i	$-0.335753\pi$
$79$	11.5363	−	2.45211i	1.29793	−	0.275884i	0.804526	+	0.593917i	$0.202419\pi$
$80$	−7.79963	−	1.35000i	−0.872025	−	0.150935i
$81$		0			0
$82$	−0.350423			−0.0386977
$83$	3.65812	−	4.06275i	0.401531	−	0.445945i	−0.508140	−	0.861274i	$-0.669667\pi$
$83$	3.65812	−	4.06275i	0.401531	−	0.445945i	0.909671	+	0.415329i	$0.136334\pi$
$84$		0			0
$85$	−8.79413	+	2.22203i	−0.953857	+	0.241013i
$86$	−0.291010	−	2.76878i	−0.0313804	−	0.298565i
$87$		0			0
$88$	0.191882	−	1.82563i	0.0204547	−	0.194613i
$89$	−12.2123	+	8.87274i	−1.29450	+	0.940508i	−0.999886	−	0.0151087i	$-0.995191\pi$
$89$	−12.2123	+	8.87274i	−1.29450	+	0.940508i	−0.294612	+	0.955617i	$0.595191\pi$
$90$		0			0
$91$	−3.36325	−	2.44354i	−0.352564	−	0.256153i
$92$	6.94294	−	7.71092i	0.723852	−	0.803919i
$93$		0			0
$94$	1.28972	+	0.274138i	0.133024	+	0.0282752i
$95$	−12.9958	+	3.28368i	−1.33334	+	0.336898i
$96$		0			0
$97$	−3.26984	+	0.695025i	−0.332002	+	0.0705691i	−0.370897	−	0.928674i	$-0.620950\pi$
$97$	−3.26984	+	0.695025i	−0.332002	+	0.0705691i	0.0388949	+	0.999243i	$0.487616\pi$
$98$	1.93861	−	1.40848i	0.195829	−	0.142278i
$99$		0			0
$100$	5.42477	+	7.93441i	0.542477	+	0.793441i
$101$	−3.60857	−	6.25022i	−0.359066	−	0.621920i	0.628739	−	0.777616i	$-0.283571\pi$
$101$	−3.60857	−	6.25022i	−0.359066	−	0.621920i	−0.987805	+	0.155696i	$0.950238\pi$
$102$		0			0
$103$	−3.13282	−	3.47934i	−0.308685	−	0.342830i	0.568762	−	0.822502i	$-0.307422\pi$
$103$	−3.13282	−	3.47934i	−0.308685	−	0.342830i	−0.877448	+	0.479672i	$0.840756\pi$
$104$	0.769973	+	0.855142i	0.0755021	+	0.0838535i
$105$		0			0
$106$	1.67135	−	1.85623i	0.162336	−	0.180293i
$107$	19.3140			1.86715			0.933577	−	0.358378i	$-0.116670\pi$
$107$	19.3140			1.86715			0.933577	+	0.358378i	$0.116670\pi$
$108$		0			0
$109$	−8.78758	−	6.38455i	−0.841698	−	0.611529i	0.0811466	−	0.996702i	$-0.474142\pi$
$109$	−8.78758	−	6.38455i	−0.841698	−	0.611529i	−0.922844	+	0.385173i	$0.874142\pi$
$110$	−0.822626	+	0.646884i	−0.0784343	+	0.0616779i
$111$		0			0
$112$	12.7720	−	5.68646i	1.20684	−	0.537320i
$113$	−6.21807	+	2.76846i	−0.584947	+	0.260435i	−0.677802	−	0.735245i	$-0.737067\pi$
$113$	−6.21807	+	2.76846i	−0.584947	+	0.260435i	0.0928552	+	0.995680i	$0.470401\pi$
$114$		0			0
$115$	−12.0608	+	0.459165i	−1.12468	+	0.0428173i
$116$	11.1250	+	8.08276i	1.03293	+	0.750466i
$117$		0			0
$118$	1.71916			0.158261
$119$	10.7198	−	11.9056i	0.982685	−	1.09138i
$120$		0			0
$121$	−5.47365	−	6.07911i	−0.497605	−	0.552646i
$122$	0.526769	+	0.585036i	0.0476914	+	0.0529667i
$123$		0			0
$124$	4.73039	+	8.19327i	0.424801	+	0.735778i
$125$	2.22121	−	10.9575i	0.198671	−	0.980066i
$126$		0			0
$127$	10.7288	−	7.79490i	0.952024	−	0.691686i	0.000739229	−	1.00000i	$-0.499765\pi$
$127$	10.7288	−	7.79490i	0.952024	−	0.691686i	0.951285	+	0.308314i	$0.0997647\pi$
$128$	−7.89633	+	1.67842i	−0.697944	+	0.148353i
$129$		0			0
$130$	0.0437017	−	0.654547i	0.00383289	−	0.0574075i
$131$	−13.9228	−	2.95937i	−1.21644	−	0.258562i	−0.445388	−	0.895338i	$-0.646934\pi$
$131$	−13.9228	−	2.95937i	−1.21644	−	0.258562i	−0.771049	+	0.636776i	$0.780268\pi$
$132$		0			0
$133$	15.8416	−	17.5939i	1.37364	−	1.52558i
$134$	−2.76399	−	2.00815i	−0.238772	−	0.173478i
$135$		0			0
$136$	−3.58755	+	2.60651i	−0.307630	+	0.223506i
$137$	−1.01433	+	9.65072i	−0.0866602	+	0.824516i	0.861721	+	0.507383i	$0.169387\pi$
$137$	−1.01433	+	9.65072i	−0.0866602	+	0.824516i	−0.948381	+	0.317134i	$0.897280\pi$
$138$		0			0
$139$	0.170258	+	1.61990i	0.0144411	+	0.137398i	0.999367	−	0.0355797i	$-0.0113278\pi$
$139$	0.170258	+	1.61990i	0.0144411	+	0.137398i	−0.984926	+	0.172978i	$0.944661\pi$
$140$	−15.7600	−	6.30986i	−1.33196	−	0.533281i
$141$		0			0
$142$	−1.29927	+	1.44299i	−0.109032	+	0.121093i
$143$	−1.76757			−0.147812
$144$		0			0
$145$	−2.27597	−	15.8328i	−0.189009	−	1.31485i
$146$	1.49044	−	0.316803i	0.123350	−	0.0262188i
$147$		0			0
$148$	0.976060	+	9.28659i	0.0802316	+	0.763353i
$149$	−5.52553	+	9.57050i	−0.452669	+	0.784046i	−0.998551	−	0.0538166i	$-0.982861\pi$
$149$	−5.52553	+	9.57050i	−0.452669	+	0.784046i	0.545882	+	0.837862i	$0.316195\pi$
$150$		0			0
$151$	−2.90413	−	5.03011i	−0.236335	−	0.409344i	0.723325	−	0.690508i	$-0.242613\pi$
$151$	−2.90413	−	5.03011i	−0.236335	−	0.409344i	−0.959660	+	0.281164i	$0.909280\pi$
$152$	−5.30162	+	3.85185i	−0.430018	+	0.312427i
$153$		0			0
$154$	0.571175	−	1.75790i	0.0460266	−	0.141655i
$155$	3.00007	−	10.5881i	0.240971	−	0.850454i
$156$		0			0
$157$	−1.84071	+	3.18821i	−0.146905	+	0.254447i	−0.930082	−	0.367352i	$-0.880264\pi$
$157$	−1.84071	+	3.18821i	−0.146905	+	0.254447i	0.783177	+	0.621799i	$0.213598\pi$
$158$	−3.21525	−	0.683423i	−0.255792	−	0.0543703i
$159$		0			0
$160$	5.89449	+	3.94896i	0.466000	+	0.312193i
$161$	17.2463	−	12.5301i	1.35920	−	0.987513i
$162$		0			0
$163$	−0.304317	−	0.221099i	−0.0238360	−	0.0173178i	0.575803	−	0.817588i	$-0.304689\pi$
$163$	−0.304317	−	0.221099i	−0.0238360	−	0.0173178i	−0.599639	+	0.800270i	$0.704689\pi$
$164$	−2.20799	−	0.983062i	−0.172415	−	0.0767642i
$165$		0			0
$166$	−1.39196	+	0.619742i	−0.108037	+	0.0481013i
$167$	−8.56276	−	1.82007i	−0.662606	−	0.140841i	−0.135681	−	0.990753i	$-0.543322\pi$
$167$	−8.56276	−	1.82007i	−0.662606	−	0.140841i	−0.526926	+	0.849911i	$0.676655\pi$
$168$		0			0
$169$	−7.95730	+	8.83747i	−0.612100	+	0.679806i
$170$	2.49099	+	0.431154i	0.191050	+	0.0330680i
$171$		0			0
$172$	5.93378	−	18.2623i	0.452447	−	1.39249i
$173$	1.96220	+	0.873627i	0.149183	+	0.0664206i	0.479970	−	0.877285i	$-0.340647\pi$
$173$	1.96220	+	0.873627i	0.149183	+	0.0664206i	−0.330787	+	0.943705i	$0.607314\pi$
$174$		0			0
$175$	7.51239	+	18.2622i	0.567883	+	1.38049i
$176$	2.97218	−	5.14796i	0.224036	−	0.388042i
$177$		0			0
$178$	4.11523	−	0.874718i	0.308449	−	0.0655629i
$179$	6.01883	−	18.5241i	0.449869	−	1.38455i	−0.427187	−	0.904164i	$-0.640495\pi$
$179$	6.01883	−	18.5241i	0.449869	−	1.38455i	0.877055	−	0.480390i	$-0.159505\pi$
$180$		0			0
$181$	4.60344	+	14.1679i	0.342171	+	1.05309i	0.963081	+	0.269212i	$0.0867632\pi$
$181$	4.60344	+	14.1679i	0.342171	+	1.05309i	−0.620910	+	0.783882i	$0.713237\pi$
$182$	0.579324	+	1.00342i	0.0429424	+	0.0743784i
$183$		0			0
$184$	−5.39052	+	2.40001i	−0.397394	+	0.176931i
$185$	6.95560	−	8.34252i	0.511386	−	0.613354i
$186$		0			0
$187$	0.712012	−	6.77434i	0.0520674	−	0.495389i
$188$	7.35739	+	5.34546i	0.536593	+	0.389858i
$189$		0			0
$190$	3.68115	+	0.637152i	0.267058	+	0.0462239i
$191$	−0.852384	+	8.10990i	−0.0616764	+	0.586811i	0.919418	+	0.393282i	$0.128660\pi$
$191$	−0.852384	+	8.10990i	−0.0616764	+	0.586811i	−0.981094	+	0.193530i	$0.938006\pi$
$192$		0			0
$193$	2.38184	−	4.12547i	0.171449	−	0.296958i	−0.767478	−	0.641076i	$-0.778488\pi$
$193$	2.38184	−	4.12547i	0.171449	−	0.296958i	0.938927	+	0.344117i	$0.111822\pi$
$194$	0.911332	+	0.193710i	0.0654298	+	0.0139075i
$195$		0			0
$196$	16.1664	−	3.43627i	1.15474	−	0.245448i
$197$	1.66876	−	5.13592i	0.118894	−	0.365919i	−0.873845	−	0.486205i	$-0.838381\pi$
$197$	1.66876	−	5.13592i	0.118894	−	0.365919i	0.992739	+	0.120286i	$0.0383810\pi$
$198$		0			0
$199$	−21.6479			−1.53458			−0.767291	−	0.641299i	$-0.778396\pi$
$199$	−21.6479			−1.53458			−0.767291	+	0.641299i	$0.778396\pi$
$200$	−0.982996	−	5.37681i	−0.0695083	−	0.380198i
$201$		0			0
$202$	0.210257	+	2.00046i	0.0147936	+	0.140752i
$203$	18.9041	+	20.9951i	1.32681	+	1.47357i
$204$		0			0
$205$	0.969870	+	2.63884i	0.0677387	+	0.184304i
$206$	0.403234	+	1.24103i	0.0280946	+	0.0864663i
$207$		0			0
$208$	1.15147	+	3.54386i	0.0798400	+	0.245722i
$209$	1.05220	−	10.0110i	0.0727821	−	0.692476i
$210$		0			0
$211$	−1.60139	−	15.2362i	−0.110244	−	1.04891i	−0.900121	−	0.435640i	$-0.856522\pi$
$211$	−1.60139	−	15.2362i	−0.110244	−	1.04891i	0.789877	−	0.613266i	$-0.210145\pi$
$212$	15.7385	−	7.00723i	1.08092	−	0.481259i
$213$		0			0
$214$	−4.91759	−	2.18945i	−0.336160	−	0.149668i
$215$	−20.0447	+	9.85462i	−1.36704	+	0.672080i
$216$		0			0
$217$	6.00639	+	18.4858i	0.407740	+	1.25490i
$218$	1.51367	+	2.62176i	0.102519	+	0.177568i
$219$		0			0
$220$	−6.99807	+	1.76822i	−0.471809	+	0.119213i
$221$	2.85712	+	3.17315i	0.192191	+	0.213449i
$222$		0			0
$223$	18.7205	+	8.33491i	1.25362	+	0.558147i	0.922702	−	0.385513i	$-0.125976\pi$
$223$	18.7205	+	8.33491i	1.25362	+	0.558147i	0.330916	+	0.943660i	$0.392642\pi$
$224$	−12.5314			−0.837288
$225$		0			0
$226$	1.89704			0.126189
$227$	2.16300	+	0.963030i	0.143563	+	0.0639186i	0.477261	−	0.878762i	$-0.341630\pi$
$227$	2.16300	+	0.963030i	0.143563	+	0.0639186i	−0.333697	+	0.942680i	$0.608296\pi$
$228$		0			0
$229$	2.18473	+	2.42639i	0.144371	+	0.160341i	0.810993	−	0.585055i	$-0.198927\pi$
$229$	2.18473	+	2.42639i	0.144371	+	0.160341i	−0.666622	+	0.745396i	$0.732261\pi$
$230$	3.12290	+	1.25032i	0.205918	+	0.0824436i
$231$		0			0
$232$	−3.91002	−	6.77235i	−0.256705	−	0.444627i
$233$	−0.388396	−	1.19536i	−0.0254446	−	0.0783106i	0.937528	−	0.347910i	$-0.113109\pi$
$233$	−0.388396	−	1.19536i	−0.0254446	−	0.0783106i	−0.962972	+	0.269600i	$0.913109\pi$
$234$		0			0
$235$	−1.50519	−	10.4709i	−0.0981880	−	0.683046i
$236$	10.8323	+	4.82286i	0.705124	+	0.313942i
$237$		0			0
$238$	−4.07904	+	1.81610i	−0.264405	+	0.117721i
$239$	−1.36041	−	12.9434i	−0.0879974	−	0.837240i	−0.946125	−	0.323802i	$-0.895039\pi$
$239$	−1.36041	−	12.9434i	−0.0879974	−	0.837240i	0.858127	−	0.513437i	$-0.171628\pi$
$240$		0			0
$241$	−0.129158	+	1.22886i	−0.00831982	+	0.0791578i	−0.997894	−	0.0648668i	$-0.979338\pi$
$241$	−0.129158	+	1.22886i	−0.00831982	+	0.0791578i	0.989574	+	0.144025i	$0.0460044\pi$
$242$	0.704529	+	2.16832i	0.0452889	+	0.139385i
$243$		0			0
$244$	1.67790	+	5.16406i	0.107417	+	0.330595i
$245$	−15.9720	−	10.7003i	−1.02042	−	0.683618i
$246$		0			0
$247$	4.22220	+	4.68923i	0.268652	+	0.298369i
$248$	−0.562379	−	5.35068i	−0.0357111	−	0.339768i
$249$		0			0
$250$	−1.80770	+	2.53812i	−0.114329	+	0.160525i
$251$	−16.1915			−1.02200			−0.511000	−	0.859581i	$-0.670725\pi$
$251$	−16.1915			−1.02200			−0.511000	+	0.859581i	$0.670725\pi$
$252$		0			0
$253$	2.80088	−	8.62023i	0.176090	−	0.541949i
$254$	−3.61532	+	0.768460i	−0.226845	+	0.0482175i
$255$		0			0
$256$	−9.91962	−	2.10848i	−0.619976	−	0.131780i
$257$	12.5307	−	21.7037i	0.781641	−	1.35384i	−0.149345	−	0.988785i	$-0.547716\pi$
$257$	12.5307	−	21.7037i	0.781641	−	1.35384i	0.930986	−	0.365056i	$-0.118950\pi$
$258$		0			0
$259$	−2.00531	+	19.0792i	−0.124604	+	1.18552i
$260$	2.11160	−	4.00166i	0.130956	−	0.248173i
$261$		0			0
$262$	3.20944	+	2.33179i	0.198280	+	0.144059i
$263$	−2.02669	+	19.2826i	−0.124971	+	1.18902i	0.734781	+	0.678305i	$0.237285\pi$
$263$	−2.02669	+	19.2826i	−0.124971	+	1.18902i	−0.859751	+	0.510713i	$0.829382\pi$
$264$		0			0
$265$	−18.6041	−	7.44853i	−1.14284	−	0.457560i
$266$	−6.02793	+	2.68381i	−0.369596	+	0.164555i
$267$		0			0
$268$	−11.7821	−	20.4073i	−0.719708	−	1.24657i
$269$	1.15306	+	3.54876i	0.0703034	+	0.216372i	0.980035	−	0.198825i	$-0.0637127\pi$
$269$	1.15306	+	3.54876i	0.0703034	+	0.216372i	−0.909732	+	0.415197i	$0.863713\pi$
$270$		0			0
$271$	−6.82902	+	21.0175i	−0.414833	+	1.27673i	0.497567	+	0.867426i	$0.334227\pi$
$271$	−6.82902	+	21.0175i	−0.414833	+	1.27673i	−0.912400	+	0.409300i	$0.865773\pi$
$272$	−14.0459	+	2.98555i	−0.851658	+	0.181026i
$273$		0			0
$274$	1.35228	−	2.34221i	0.0816941	−	0.141498i
$275$	7.14812	+	4.40435i	0.431048	+	0.265592i
$276$		0			0
$277$	−10.9247	−	4.86399i	−0.656401	−	0.292249i	0.0513814	−	0.998679i	$-0.483638\pi$
$277$	−10.9247	−	4.86399i	−0.656401	−	0.292249i	−0.707782	+	0.706431i	$0.750304\pi$
$278$	0.140284	−	0.431748i	0.00841365	−	0.0258945i
$279$		0			0
$280$	6.72807	+	6.92340i	0.402079	+	0.413752i
$281$	−18.2979	+	20.3219i	−1.09156	+	1.21230i	−0.115843	+	0.993267i	$0.536957\pi$
$281$	−18.2979	+	20.3219i	−1.09156	+	1.21230i	−0.975717	+	0.219034i	$0.929710\pi$
$282$		0			0
$283$	3.04324	+	0.646861i	0.180902	+	0.0384519i	0.297472	−	0.954731i	$-0.403857\pi$
$283$	3.04324	+	0.646861i	0.180902	+	0.0384519i	−0.116570	+	0.993182i	$0.537190\pi$
$284$	−12.2347	+	5.44725i	−0.725998	+	0.323235i
$285$		0			0
$286$	0.450047	+	0.200374i	0.0266118	+	0.0118483i
$287$	−4.01726	−	2.91871i	−0.237131	−	0.172286i
$288$		0			0
$289$	0.441053	−	0.320444i	0.0259443	−	0.0188496i
$290$	−1.21533	+	4.28925i	−0.0713669	+	0.251874i
$291$		0			0
$292$	10.2799	+	2.18507i	0.601587	+	0.127871i
$293$	−1.08652	+	1.88191i	−0.0634752	+	0.109942i	−0.896017	−	0.444021i	$-0.853552\pi$
$293$	−1.08652	+	1.88191i	−0.0634752	+	0.109942i	0.832541	+	0.553963i	$0.186885\pi$
$294$		0			0
$295$	−4.75814	−	12.9460i	−0.277030	−	0.753747i
$296$	1.64094	−	5.05028i	0.0953775	−	0.293542i
$297$		0			0
$298$	2.49179	−	1.81039i	0.144346	−	0.104873i
$299$	2.84085	+	4.92049i	0.164290	+	0.284559i
$300$		0			0
$301$	19.7253	−	34.1652i	1.13695	−	1.96925i
$302$	0.169212	+	1.60995i	0.00973707	+	0.0926420i
$303$		0			0
$304$	−20.7568	+	4.41200i	−1.19048	+	0.253045i
$305$	2.94763	−	5.58602i	0.168781	−	0.319854i
$306$		0			0
$307$	6.16436			0.351818			0.175909	−	0.984406i	$-0.443713\pi$
$307$	6.16436			0.351818			0.175909	+	0.984406i	$0.443713\pi$
$308$	8.53047	−	9.47405i	0.486069	−	0.539834i
$309$		0			0
$310$	−1.96413	+	2.35577i	−0.111555	+	0.133799i
$311$	−0.412568	−	3.92532i	−0.0233946	−	0.222584i	−0.999972	−	0.00742028i	$-0.997638\pi$
$311$	−0.412568	−	3.92532i	−0.0233946	−	0.222584i	0.976578	−	0.215164i	$-0.0690286\pi$
$312$		0			0
$313$	−0.256506	+	2.44049i	−0.0144986	+	0.137945i	−0.999377	−	0.0353045i	$-0.988760\pi$
$313$	−0.256506	+	2.44049i	−0.0144986	+	0.137945i	0.984878	+	0.173249i	$0.0554266\pi$
$314$	0.830088	−	0.603094i	0.0468446	−	0.0340346i
$315$		0			0
$316$	−18.3419	−	13.3262i	−1.03181	−	0.749655i
$317$	6.30981	−	7.00775i	0.354394	−	0.393594i	−0.539417	−	0.842039i	$-0.681355\pi$
$317$	6.30981	−	7.00775i	0.354394	−	0.393594i	0.893811	+	0.448445i	$0.148022\pi$
$318$		0			0
$319$	11.7497	+	2.49747i	0.657855	+	0.139831i
$320$	7.37829	+	11.7255i	0.412459	+	0.655475i
$321$		0			0
$322$	−5.81155	+	1.23528i	−0.323865	+	0.0688396i
$323$	−19.6726	+	14.2930i	−1.09461	+	0.795283i
$324$		0			0
$325$	−5.04998	+	1.48251i	−0.280123	+	0.0822346i
$326$	0.0524191	+	0.0907925i	0.00290323	+	0.00502853i
$327$		0			0
$328$	0.919700	+	1.02143i	0.0507819	+	0.0563990i
$329$	12.5021	+	13.8849i	0.689261	+	0.765501i
$330$		0			0
$331$	−13.8019	+	15.3285i	−0.758619	+	0.842531i	−0.991518	−	0.129970i	$-0.958512\pi$
$331$	−13.8019	+	15.3285i	−0.758619	+	0.842531i	0.232899	+	0.972501i	$0.425179\pi$
$332$	−10.5093			−0.576772
$333$		0			0
$334$	1.97387	+	1.43410i	0.108005	+	0.0784703i
$335$	−7.47236	+	26.3721i	−0.408259	+	1.44086i
$336$		0			0
$337$	−24.7265	+	11.0089i	−1.34694	+	0.599695i	−0.948289	−	0.317409i	$-0.897187\pi$
$337$	−24.7265	+	11.0089i	−1.34694	+	0.599695i	−0.398649	+	0.917104i	$0.630521\pi$
$338$	3.02786	−	1.34809i	0.164694	−	0.0733264i
$339$		0			0
$340$	14.4861	+	9.70481i	0.785617	+	0.526317i
$341$	6.68597	+	4.85764i	0.362065	+	0.263056i
$342$		0			0
$343$	6.30996			0.340706
$344$	−7.30681	+	8.11503i	−0.393957	+	0.437533i
$345$		0			0
$346$	−0.400566	−	0.444874i	−0.0215346	−	0.0239166i
$347$	22.5406	+	25.0339i	1.21004	+	1.34389i	0.922441	+	0.386139i	$0.126192\pi$
$347$	22.5406	+	25.0339i	1.21004	+	1.34389i	0.287603	+	0.957750i	$0.407142\pi$
$348$		0			0
$349$	2.68244	+	4.64613i	0.143588	+	0.248702i	0.928845	−	0.370468i	$-0.120803\pi$
$349$	2.68244	+	4.64613i	0.143588	+	0.248702i	−0.785257	+	0.619170i	$0.787469\pi$
$350$	0.157466	−	5.50140i	0.00841689	−	0.294062i
$351$		0			0
$352$	−4.31054	+	3.13179i	−0.229753	+	0.166925i
$353$	−22.9425	+	4.87657i	−1.22110	+	0.259554i	−0.772988	−	0.634421i	$-0.781239\pi$
$353$	−22.9425	+	4.87657i	−1.22110	+	0.259554i	−0.448117	+	0.893975i	$0.647905\pi$
$354$		0			0
$355$	14.4623	+	5.79031i	0.767582	+	0.307318i
$356$	28.3837	+	6.03315i	1.50433	+	0.319756i
$357$		0			0
$358$	−3.63238	+	4.03417i	−0.191977	+	0.213212i
$359$	12.6673	+	9.20330i	0.668552	+	0.485732i	0.869540	−	0.493862i	$-0.164415\pi$
$359$	12.6673	+	9.20330i	0.668552	+	0.485732i	−0.200988	+	0.979594i	$0.564415\pi$
$360$		0			0
$361$	−13.7005	+	9.95401i	−0.721080	+	0.523895i
$362$	0.433995	−	4.12919i	0.0228103	−	0.217025i
$363$		0			0
$364$	0.835337	+	7.94770i	0.0437836	+	0.416573i
$365$	−6.51078	−	10.3469i	−0.340790	−	0.541579i
$366$		0			0
$367$	−12.2743	+	13.6320i	−0.640713	+	0.711584i	−0.972795	−	0.231666i	$-0.925582\pi$
$367$	−12.2743	+	13.6320i	−0.640713	+	0.711584i	0.332082	+	0.943251i	$0.392249\pi$
$368$	−19.1076			−0.996051
$369$		0			0
$370$	−2.71670	+	1.33562i	−0.141235	+	0.0694356i
$371$	34.6212	−	7.35896i	1.79744	−	0.382058i
$372$		0			0
$373$	1.53017	+	14.5586i	0.0792291	+	0.753815i	0.959949	+	0.280176i	$0.0903930\pi$
$373$	1.53017	+	14.5586i	0.0792291	+	0.753815i	−0.880719	+	0.473638i	$0.842940\pi$
$374$	−0.949233	+	1.64412i	−0.0490837	+	0.0850154i
$375$		0			0
$376$	−2.58585	−	4.47883i	−0.133355	−	0.230978i
$377$	−6.09177	+	4.42593i	−0.313742	+	0.227947i
$378$		0			0
$379$	1.91579	−	5.89620i	0.0984077	−	0.302868i	−0.889719	−	0.456508i	$-0.849100\pi$
$379$	1.91579	−	5.89620i	0.0984077	−	0.302868i	0.988127	+	0.153641i	$0.0490998\pi$
$380$	21.4073	+	14.3416i	1.09817	+	0.735709i
$381$		0			0
$382$	1.13637	−	1.96826i	0.0581420	−	0.100705i
$383$	11.7942	+	2.50693i	0.602654	+	0.128098i	0.499127	−	0.866529i	$-0.333654\pi$
$383$	11.7942	+	2.50693i	0.602654	+	0.128098i	0.103527	+	0.994627i	$0.466987\pi$
$384$		0			0
$385$	−14.8186	+	0.564154i	−0.755225	+	0.0287520i
$386$	−1.07412	+	0.780391i	−0.0546711	+	0.0397209i
$387$		0			0
$388$	5.19883	+	3.77717i	0.263930	+	0.191757i
$389$	27.9727	+	12.4542i	1.41827	+	0.631455i	0.965555	−	0.260200i	$-0.0837885\pi$
$389$	27.9727	+	12.4542i	1.41827	+	0.631455i	0.452716	+	0.891655i	$0.350455\pi$
$390$		0			0
$391$	−20.0025	+	8.90567i	−1.01157	+	0.450379i
$392$	−9.19349	−	1.95414i	−0.464342	−	0.0986988i
$393$		0			0
$394$	−1.00710	+	1.11850i	−0.0507370	+	0.0563492i
$395$	3.75243	+	26.1038i	0.188805	+	1.31343i
$396$		0			0
$397$	4.04467	−	12.4482i	0.202996	−	0.624758i	−0.796794	−	0.604252i	$-0.793472\pi$
$397$	4.04467	−	12.4482i	0.202996	−	0.624758i	0.999790	−	0.0205064i	$-0.00652785\pi$
$398$	5.51185	+	2.45403i	0.276284	+	0.123010i
$399$		0			0
$400$	4.17384	−	17.2007i	0.208692	−	0.860033i
$401$	1.28841	−	2.23159i	0.0643399	−	0.111440i	−0.832061	−	0.554684i	$-0.812839\pi$
$401$	1.28841	−	2.23159i	0.0643399	−	0.111440i	0.896401	+	0.443244i	$0.146172\pi$
$402$		0			0
$403$	−5.06729	+	1.07709i	−0.252420	+	0.0536535i
$404$	−4.28719	+	13.1946i	−0.213296	+	0.656457i
$405$		0			0
$406$	−2.43320	−	7.48863i	−0.120758	−	0.371654i
$407$	4.07842	+	7.06402i	0.202160	+	0.350151i
$408$		0			0
$409$	36.2080	−	16.1208i	1.79037	−	0.797124i	0.814048	−	0.580798i	$-0.197259\pi$
$409$	36.2080	−	16.1208i	1.79037	−	0.797124i	0.976321	−	0.216325i	$-0.0694072\pi$
$410$	0.0521998	−	0.781828i	0.00257796	−	0.0386117i
$411$		0			0
$412$	−0.940772	+	8.95085i	−0.0463485	+	0.440977i
$413$	19.7085	+	14.3191i	0.969792	+	0.704595i
$414$		0			0
$415$	8.51949	+	8.76683i	0.418205	+	0.430347i
$416$	0.349119	−	3.32165i	0.0171170	−	0.162857i
$417$		0			0
$418$	−1.40276	+	2.42965i	−0.0686113	+	0.118838i
$419$	15.7915	+	3.35660i	0.771468	+	0.163981i	0.576796	−	0.816888i	$-0.304303\pi$
$419$	15.7915	+	3.35660i	0.771468	+	0.163981i	0.194671	+	0.980869i	$0.437636\pi$
$420$		0			0
$421$	29.8599	−	6.34692i	1.45528	−	0.309330i	0.588696	−	0.808355i	$-0.299642\pi$
$421$	29.8599	−	6.34692i	1.45528	−	0.309330i	0.866588	+	0.499025i	$0.166308\pi$
$422$	−1.31946	+	4.06088i	−0.0642303	+	0.197681i
$423$		0			0
$424$	−9.79717			−0.475793
$425$	−3.64758	−	19.9516i	−0.176934	−	0.967794i
$426$		0			0
$427$	1.16607	+	11.0944i	0.0564299	+	0.536895i
$428$	−24.8433	−	27.5912i	−1.20084	−	1.33367i
$429$		0			0
$430$	6.22077	−	0.236829i	0.299992	−	0.0114209i
$431$	−4.75754	−	14.6422i	−0.229162	−	0.705290i	−0.997842	−	0.0656558i	$-0.979086\pi$
$431$	−4.75754	−	14.6422i	−0.229162	−	0.705290i	0.768680	−	0.639634i	$-0.220914\pi$
$432$		0			0
$433$	12.3339	+	37.9599i	0.592730	+	1.82424i	0.565716	+	0.824600i	$0.308600\pi$
$433$	12.3339	+	37.9599i	0.592730	+	1.82424i	0.0270144	+	0.999635i	$0.491400\pi$
$434$	0.566260	−	5.38761i	0.0271814	−	0.258613i
$435$		0			0
$436$	2.18259	+	20.7660i	0.104527	+	0.994509i
$437$	−29.5593	+	13.1607i	−1.41401	+	0.629559i
$438$		0			0
$439$	21.8459	+	9.72643i	1.04265	+	0.464217i	0.855331	−	0.518082i	$-0.173354\pi$
$439$	21.8459	+	9.72643i	1.04265	+	0.464217i	0.187318	+	0.982299i	$0.440021\pi$
$440$	4.04459	+	0.700059i	0.192818	+	0.0333740i
$441$		0			0
$442$	−0.367748	−	1.13181i	−0.0174920	−	0.0538348i
$443$	−10.1099	−	17.5109i	−0.480337	−	0.831968i	0.519409	−	0.854526i	$-0.326152\pi$
$443$	−10.1099	−	17.5109i	−0.480337	−	0.831968i	−0.999746	+	0.0225580i	$0.992819\pi$
$444$		0			0
$445$	−17.9768	−	28.5685i	−0.852182	−	1.35428i
$446$	−3.82163	−	4.24436i	−0.180960	−	0.200976i
$447$		0			0
$448$	−22.3534	−	9.95236i	−1.05610	−	0.470205i
$449$	−7.79598			−0.367915			−0.183957	−	0.982934i	$-0.558891\pi$
$449$	−7.79598			−0.367915			−0.183957	+	0.982934i	$0.558891\pi$
$450$		0			0
$451$	−2.11129			−0.0994166
$452$	11.9531	+	5.32188i	0.562228	+	0.250320i
$453$		0			0
$454$	−0.441558	−	0.490400i	−0.0207234	−	0.0230156i
$455$	5.95279	−	7.13975i	0.279071	−	0.334717i
$456$		0			0
$457$	5.97766	+	10.3536i	0.279623	+	0.484321i	0.971291	−	0.237894i	$-0.0764572\pi$
$457$	5.97766	+	10.3536i	0.279623	+	0.484321i	−0.691668	+	0.722216i	$0.743124\pi$
$458$	−0.281204	−	0.865455i	−0.0131398	−	0.0404401i
$459$		0			0
$460$	16.1696	+	16.6390i	0.753912	+	0.775799i
$461$	−21.0765	−	9.38384i	−0.981629	−	0.437049i	−0.147767	−	0.989022i	$-0.547208\pi$
$461$	−21.0765	−	9.38384i	−0.981629	−	0.437049i	−0.833862	+	0.551973i	$0.813875\pi$
$462$		0			0
$463$	−17.7625	+	7.90838i	−0.825494	+	0.367534i	−0.775603	−	0.631221i	$-0.782554\pi$
$463$	−17.7625	+	7.90838i	−0.825494	+	0.367534i	−0.0498910	+	0.998755i	$0.515887\pi$
$464$	−2.64697	−	25.1842i	−0.122882	−	1.16915i
$465$		0			0
$466$	−0.0366165	+	0.348383i	−0.00169623	+	0.0161385i
$467$	−4.78120	−	14.7150i	−0.221248	−	0.680931i	−0.998651	−	0.0519278i	$-0.983463\pi$
$467$	−4.78120	−	14.7150i	−0.221248	−	0.680931i	0.777403	−	0.629003i	$-0.216537\pi$
$468$		0			0
$469$	−14.9603	−	46.0431i	−0.690803	−	2.12607i
$470$	−0.803750	+	2.83666i	−0.0370742	+	0.130845i
$471$		0			0
$472$	−4.51201	−	5.01110i	−0.207682	−	0.230654i
$473$	−1.75333	−	16.6818i	−0.0806182	−	0.767030i
$474$		0			0
$475$	−5.39033	−	29.4841i	−0.247325	−	1.35282i
$476$	−30.7966			−1.41156
$477$		0			0
$478$	−1.12090	+	3.44978i	−0.0512688	+	0.157789i
$479$	−29.8968	+	6.35475i	−1.36602	+	0.290356i	−0.831840	−	0.555016i	$-0.812712\pi$
$479$	−29.8968	+	6.35475i	−1.36602	+	0.290356i	−0.534178	+	0.845372i	$0.679379\pi$
$480$		0			0
$481$	−5.00139	−	1.06308i	−0.228044	−	0.0484722i
$482$	0.172190	−	0.298242i	0.00784305	−	0.0135846i
$483$		0			0
$484$	−1.64372	+	15.6389i	−0.0747144	+	0.710860i
$485$	−1.06359	−	7.39887i	−0.0482951	−	0.335965i
$486$		0			0
$487$	−7.57800	−	5.50574i	−0.343392	−	0.249489i	0.402700	−	0.915332i	$-0.368072\pi$
$487$	−7.57800	−	5.50574i	−0.343392	−	0.249489i	−0.746092	+	0.665843i	$0.768072\pi$
$488$	0.322765	−	3.07091i	0.0146109	−	0.139013i
$489$		0			0
$490$	2.85369	+	4.53505i	0.128916	+	0.204873i
$491$	16.8465	−	7.50055i	0.760273	−	0.338495i	0.0102850	−	0.999947i	$-0.496726\pi$
$491$	16.8465	−	7.50055i	0.760273	−	0.338495i	0.749988	+	0.661452i	$0.230059\pi$
$492$		0			0
$493$	−14.5088	−	25.1300i	−0.653444	−	1.13180i
$494$	−0.543452	−	1.67257i	−0.0244511	−	0.0752526i
$495$		0			0
$496$	5.38371	−	16.5694i	0.241736	−	0.743986i
$497$	−26.9137	+	5.72068i	−1.20724	+	0.256608i
$498$		0			0
$499$	13.8809	−	24.0424i	0.621393	−	1.07628i	−0.367833	−	0.929892i	$-0.619900\pi$
$499$	13.8809	−	24.0424i	0.621393	−	1.07628i	0.989227	−	0.146393i	$-0.0467664\pi$
$500$	−18.5106	+	10.9213i	−0.827817	+	0.488414i
$501$		0			0
$502$	4.12258	+	1.83549i	0.184000	+	0.0819219i
$503$	12.4716	−	38.3835i	0.556080	−	1.71144i	−0.136996	−	0.990572i	$-0.543745\pi$
$503$	12.4716	−	38.3835i	0.556080	−	1.71144i	0.693075	−	0.720865i	$-0.256255\pi$
$504$		0			0
$505$	14.4824	−	7.12003i	0.644459	−	0.316837i
$506$	−1.69034	+	1.87731i	−0.0751448	+	0.0834567i
$507$		0			0
$508$	−24.9358	−	5.30026i	−1.10635	−	0.235161i
$509$	16.6460	−	7.41126i	0.737819	−	0.328498i	−0.00318840	−	0.999995i	$-0.501015\pi$
$509$	16.6460	−	7.41126i	0.737819	−	0.328498i	0.741008	+	0.671497i	$0.234348\pi$
$510$		0			0
$511$	19.7251	+	8.78220i	0.872589	+	0.388502i
$512$	15.3486	+	11.1514i	0.678319	+	0.492828i
$513$		0			0
$514$	−5.65082	+	4.10556i	−0.249247	+	0.181089i
$515$	8.22944	−	6.47133i	0.362632	−	0.285161i
$516$		0			0
$517$	7.77052	+	1.65168i	0.341747	+	0.0726406i
$518$	2.67342	−	4.63049i	0.117463	−	0.203452i
$519$		0			0
$520$	−2.02260	+	1.59050i	−0.0886971	+	0.0697482i
$521$	−5.30810	+	16.3367i	−0.232552	+	0.715722i	0.764884	+	0.644168i	$0.222796\pi$
$521$	−5.30810	+	16.3367i	−0.232552	+	0.715722i	−0.997437	+	0.0715548i	$0.977204\pi$
$522$		0			0
$523$	−9.32851	+	6.77756i	−0.407907	+	0.296362i	−0.772754	−	0.634706i	$-0.781121\pi$
$523$	−9.32851	+	6.77756i	−0.407907	+	0.296362i	0.364847	+	0.931068i	$0.381121\pi$
$524$	13.6810	+	23.6961i	0.597656	+	1.03517i
$525$		0			0
$526$	2.70192	−	4.67986i	0.117809	−	0.204052i
$527$	−2.08681	−	19.8546i	−0.0909027	−	0.864881i
$528$		0			0
$529$	−6.00083	+	1.27552i	−0.260906	+	0.0554572i
$530$	3.89246	+	4.00547i	0.169078	+	0.173986i
$531$		0			0
$532$	−45.5107			−1.97314
$533$	0.885571	−	0.983526i	0.0383583	−	0.0426012i
$534$		0			0
$535$	−2.87706	+	43.0914i	−0.124386	+	1.86301i
$536$	1.40074	+	13.3271i	0.0605026	+	0.575643i
$537$		0			0
$538$	0.108706	−	1.03427i	0.00468666	−	0.0445906i
$539$	11.6801	−	8.48608i	0.503097	−	0.365521i
$540$		0			0
$541$	15.1965	+	11.0409i	0.653350	+	0.474687i	0.864411	−	0.502786i	$-0.167692\pi$
$541$	15.1965	+	11.0409i	0.653350	+	0.474687i	−0.211061	+	0.977473i	$0.567692\pi$
$542$	4.12133	−	4.57720i	0.177026	−	0.196607i
$543$		0			0
$544$	12.5898	+	2.67605i	0.539784	+	0.114735i
$545$	15.5536	−	18.6549i	0.666243	−	0.799089i
$546$		0			0
$547$	5.71030	−	1.21376i	0.244155	−	0.0518967i	−0.0842086	−	0.996448i	$-0.526836\pi$
$547$	5.71030	−	1.21376i	0.244155	−	0.0518967i	0.328364	+	0.944551i	$0.393503\pi$
$548$	15.0914	−	10.9645i	0.644672	−	0.468381i
$549$		0			0
$550$	−1.32072	−	1.93172i	−0.0563158	−	0.0823690i
$551$	−21.4409	−	37.1367i	−0.913412	−	1.58208i
$552$		0			0
$553$	−31.1675	−	34.6150i	−1.32538	−	1.47198i
$554$	2.23018	+	2.47687i	0.0947514	+	0.105232i
$555$		0			0
$556$	2.09513	−	2.32688i	0.0888532	−	0.0986815i
$557$	−21.0555			−0.892151			−0.446076	−	0.894995i	$-0.647179\pi$
$557$	−21.0555			−0.892151			−0.446076	+	0.894995i	$0.647179\pi$
$558$		0			0
$559$	8.50652	+	6.18034i	0.359787	+	0.261401i
$560$	10.7845	+	29.3427i	0.455729	+	1.23996i
$561$		0			0
$562$	6.96259	−	3.09995i	0.293699	−	0.130763i
$563$	−12.1123	+	5.39273i	−0.510471	+	0.227277i	−0.645775	−	0.763528i	$-0.723466\pi$
$563$	−12.1123	+	5.39273i	−0.510471	+	0.227277i	0.135304	+	0.990804i	$0.456799\pi$
$564$		0			0
$565$	−5.25046	−	14.2855i	−0.220889	−	0.600997i
$566$	−0.701520	−	0.509684i	−0.0294871	−	0.0214236i
$567$		0			0
$568$	7.61609			0.319564
$569$	7.07709	−	7.85990i	0.296687	−	0.329504i	−0.576309	−	0.817232i	$-0.695507\pi$
$569$	7.07709	−	7.85990i	0.296687	−	0.329504i	0.872996	+	0.487728i	$0.162174\pi$
$570$		0			0
$571$	27.0260	+	30.0154i	1.13100	+	1.25610i	0.962760	+	0.270358i	$0.0871421\pi$
$571$	27.0260	+	30.0154i	1.13100	+	1.25610i	0.168241	+	0.985746i	$0.446191\pi$
$572$	2.27360	+	2.52509i	0.0950639	+	0.105579i
$573$		0			0
$574$	0.691978	+	1.19854i	0.0288826	+	0.0500261i
$575$	0.772167	−	26.9773i	0.0322016	−	1.12503i
$576$		0			0
$577$	11.4589	−	8.32536i	0.477039	−	0.346589i	−0.323139	−	0.946351i	$-0.604738\pi$
$577$	11.4589	−	8.32536i	0.477039	−	0.346589i	0.800178	+	0.599762i	$0.204738\pi$
$578$	−0.148624	+	0.0315910i	−0.00618193	+	0.00131401i
$579$		0			0
$580$	−19.6907	+	23.6169i	−0.817610	+	0.980638i
$581$	−21.1194	−	4.48907i	−0.876181	−	0.186238i
$582$		0			0
$583$	10.0699	−	11.1837i	0.417051	−	0.463182i
$584$	−4.83516	−	3.51295i	−0.200080	−	0.145367i
$585$		0			0
$586$	0.489977	−	0.355989i	0.0202408	−	0.0147058i
$587$	−1.08785	+	10.3502i	−0.0449003	+	0.427198i	0.948863	+	0.315688i	$0.102235\pi$
$587$	−1.08785	+	10.3502i	−0.0449003	+	0.427198i	−0.993763	+	0.111510i	$0.964431\pi$
$588$		0			0
$589$	−3.08385	−	29.3408i	−0.127068	−	1.20897i
$590$	−0.256090	+	3.83562i	−0.0105431	+	0.157910i
$591$		0			0
$592$	11.5060	−	12.7787i	0.472895	−	0.525203i
$593$	−33.1998			−1.36335			−0.681676	−	0.731654i	$-0.738749\pi$
$593$	−33.1998			−1.36335			−0.681676	+	0.731654i	$0.738749\pi$
$594$		0			0
$595$	24.9657	+	25.6905i	1.02349	+	1.05321i
$596$	20.7795	−	4.41681i	0.851160	−	0.180920i
$597$		0			0
$598$	−0.165525	−	1.57486i	−0.00676881	−	0.0644009i
$599$	16.0799	−	27.8512i	0.657007	−	1.13797i	−0.324379	−	0.945927i	$-0.605155\pi$
$599$	16.0799	−	27.8512i	0.657007	−	1.13797i	0.981387	−	0.192043i	$-0.0615112\pi$
$600$		0			0
$601$	3.24834	+	5.62629i	0.132503	+	0.229501i	0.924641	−	0.380841i	$-0.124365\pi$
$601$	3.24834	+	5.62629i	0.132503	+	0.229501i	−0.792138	+	0.610342i	$0.791032\pi$
$602$	−8.89532	+	6.46283i	−0.362546	+	0.263405i
$603$		0			0
$604$	−3.45029	+	10.6189i	−0.140390	+	0.432076i
$605$	14.3785	−	11.3067i	0.584568	−	0.459683i
$606$		0			0
$607$	−4.92697	+	8.53376i	−0.199979	+	0.346375i	−0.948521	−	0.316713i	$-0.897421\pi$
$607$	−4.92697	+	8.53376i	−0.199979	+	0.346375i	0.748542	+	0.663087i	$0.230754\pi$
$608$	18.6050	+	3.95462i	0.754534	+	0.160381i
$609$		0			0
$610$	−1.38374	+	1.08813i	−0.0560261	+	0.0440569i
$611$	−4.02874	+	2.92705i	−0.162985	+	0.118416i
$612$		0			0
$613$	21.3372	+	15.5024i	0.861801	+	0.626135i	0.928374	−	0.371646i	$-0.121207\pi$
$613$	21.3372	+	15.5024i	0.861801	+	0.626135i	−0.0665732	+	0.997782i	$0.521207\pi$
$614$	−1.56953	−	0.698798i	−0.0633409	−	0.0282012i
$615$		0			0
$616$	−6.62308	+	2.94878i	−0.266851	+	0.118810i
$617$	−16.5737	−	3.52285i	−0.667232	−	0.141825i	−0.138171	−	0.990408i	$-0.544122\pi$
$617$	−16.5737	−	3.52285i	−0.667232	−	0.141825i	−0.529061	+	0.848584i	$0.677456\pi$
$618$		0			0
$619$	18.2999	−	20.3241i	0.735536	−	0.816896i	−0.253066	−	0.967449i	$-0.581439\pi$
$619$	18.2999	−	20.3241i	0.735536	−	0.816896i	0.988602	+	0.150553i	$0.0481055\pi$
$620$	−18.9847	+	9.33348i	−0.762443	+	0.374842i
$621$		0			0
$622$	−0.339933	+	1.04621i	−0.0136301	+	0.0419491i
$623$	54.4627	+	24.2484i	2.18200	+	0.971490i
$624$		0			0
$625$	24.1163	+	6.58800i	0.964654	+	0.263520i
$626$	0.341966	−	0.592303i	0.0136677	−	0.0236732i
$627$		0			0
$628$	6.92223	−	1.47137i	0.276227	−	0.0587139i
$629$	6.08898	−	18.7400i	0.242784	−	0.747211i
$630$		0			0
$631$	−6.22922	−	19.1716i	−0.247981	−	0.763208i	−0.995132	−	0.0985529i	$-0.968579\pi$
$631$	−6.22922	−	19.1716i	−0.247981	−	0.763208i	0.747151	−	0.664655i	$-0.231421\pi$
$632$	6.44650	+	11.1657i	0.256428	+	0.444147i
$633$		0			0
$634$	−2.40096	+	1.06898i	−0.0953545	+	0.0424546i
$635$	15.7930	+	25.0981i	0.626727	+	0.995988i
$636$		0			0
$637$	−0.945993	+	9.00052i	−0.0374816	+	0.356614i
$638$	−2.70850	−	1.96784i	−0.107231	−	0.0779076i
$639$		0			0
$640$	−2.56846	−	17.8675i	−0.101527	−	0.706276i
$641$	−2.51268	+	23.9066i	−0.0992450	+	0.944253i	0.825689	+	0.564126i	$0.190787\pi$
$641$	−2.51268	+	23.9066i	−0.0992450	+	0.944253i	−0.924934	+	0.380128i	$0.875880\pi$
$642$		0			0
$643$	6.17193	−	10.6901i	0.243397	−	0.421576i	−0.718283	−	0.695752i	$-0.755071\pi$
$643$	6.17193	−	10.6901i	0.243397	−	0.421576i	0.961680	+	0.274175i	$0.0884048\pi$
$644$	−40.0837	−	8.52005i	−1.57952	−	0.335737i
$645$		0			0
$646$	6.62917	−	1.40907i	0.260821	−	0.0554392i
$647$	13.9688	−	42.9917i	0.549172	−	1.69018i	−0.161687	−	0.986842i	$-0.551693\pi$
$647$	13.9688	−	42.9917i	0.549172	−	1.69018i	0.710858	−	0.703335i	$-0.248307\pi$
$648$		0			0
$649$	10.3579			0.406583
$650$	1.45385	+	0.195006i	0.0570247	+	0.00764875i
$651$		0			0
$652$	0.0755840	+	0.719133i	0.00296010	+	0.0281634i
$653$	6.72082	+	7.46423i	0.263006	+	0.292098i	0.860155	−	0.510032i	$-0.170367\pi$
$653$	6.72082	+	7.46423i	0.263006	+	0.292098i	−0.597149	+	0.802130i	$0.703700\pi$
$654$		0			0
$655$	8.67662	−	30.6222i	0.339024	−	1.19651i
$656$	1.37538	+	4.23298i	0.0536996	+	0.165270i
$657$		0			0
$658$	−1.60918	−	4.95253i	−0.0627322	−	0.193070i
$659$	−3.83346	+	36.4729i	−0.149330	+	1.42078i	0.621336	+	0.783545i	$0.286590\pi$
$659$	−3.83346	+	36.4729i	−0.149330	+	1.42078i	−0.770666	+	0.637239i	$0.780076\pi$
$660$		0			0
$661$	−1.19894	−	11.4072i	−0.0466334	−	0.443687i	−0.992780	−	0.119949i	$-0.961727\pi$
$661$	−1.19894	−	11.4072i	−0.0466334	−	0.443687i	0.946147	−	0.323738i	$-0.104940\pi$
$662$	5.25179	−	2.33825i	0.204117	−	0.0908785i
$663$		0			0
$664$	5.45973	+	2.43083i	0.211879	+	0.0943344i
$665$	36.8939	+	37.9650i	1.43068	+	1.47222i
$666$		0			0
$667$	−11.9318	−	36.7222i	−0.461999	−	1.42189i
$668$	8.41406	+	14.5736i	0.325550	+	0.563869i
$669$		0			0
$670$	4.89212	−	5.86759i	0.188999	−	0.226685i
$671$	3.17377	+	3.52483i	0.122522	+	0.136074i
$672$		0			0
$673$	32.2055	+	14.3388i	1.24143	+	0.552721i	0.919144	−	0.393921i	$-0.128882\pi$
$673$	32.2055	+	14.3388i	1.24143	+	0.552721i	0.322288	+	0.946642i	$0.395548\pi$
$674$	7.54367			0.290571
$675$		0			0
$676$	22.8602			0.879240
$677$	−1.28253	−	0.571021i	−0.0492918	−	0.0219461i	0.381943	−	0.924186i	$-0.375255\pi$
$677$	−1.28253	−	0.571021i	−0.0492918	−	0.0219461i	−0.431234	+	0.902240i	$0.641922\pi$
$678$		0			0
$679$	8.83411	+	9.81128i	0.339022	+	0.376522i
$680$	−5.28097	−	8.39246i	−0.202516	−	0.321836i
$681$		0			0
$682$	−1.15167	−	1.99475i	−0.0440996	−	0.0763828i
$683$	−13.5005	−	41.5502i	−0.516582	−	1.58987i	−0.780386	−	0.625298i	$-0.784977\pi$
$683$	−13.5005	−	41.5502i	−0.516582	−	1.58987i	0.263804	−	0.964576i	$-0.415023\pi$
$684$		0			0
$685$	−21.3806	−	3.70067i	−0.816912	−	0.141395i
$686$	−1.60660	−	0.715304i	−0.0613402	−	0.0273104i
$687$		0			0
$688$	−32.3037	+	14.3825i	−1.23157	+	0.548329i
$689$	0.986081	+	9.38194i	0.0375667	+	0.357423i
$690$		0			0
$691$	−4.73461	+	45.0468i	−0.180113	+	1.71366i	0.414834	+	0.909897i	$0.363840\pi$
$691$	−4.73461	+	45.0468i	−0.180113	+	1.71366i	−0.594947	+	0.803765i	$0.702827\pi$
$692$	−1.27591	−	3.92686i	−0.0485029	−	0.149277i
$693$		0			0
$694$	−2.90127	−	8.92918i	−0.110131	−	0.338947i
$695$	−3.63952	+	0.138559i	−0.138055	+	0.00525585i
$696$		0			0
$697$	3.41271	+	3.79020i	0.129266	+	0.143564i
$698$	−0.156295	−	1.48705i	−0.00591586	−	0.0562857i
$699$		0			0
$700$	16.4256	−	34.2223i	0.620829	−	1.29348i
$701$	−29.7825			−1.12487			−0.562435	−	0.826841i	$-0.690136\pi$
$701$	−29.7825			−1.12487			−0.562435	+	0.826841i	$0.690136\pi$
$702$		0			0
$703$	8.99820	−	27.6936i	0.339373	−	1.04448i
$704$	−10.1764	+	2.16305i	−0.383536	+	0.0815231i
$705$		0			0
$706$	6.39427	+	1.35914i	0.240651	+	0.0511520i
$707$	−14.2516	+	24.6846i	−0.535988	+	0.928359i
$708$		0			0
$709$	2.20660	−	20.9944i	0.0828707	−	0.788462i	−0.871612	−	0.490196i	$-0.836925\pi$
$709$	2.20660	−	20.9944i	0.0828707	−	0.788462i	0.954483	−	0.298266i	$-0.0964083\pi$
$710$	−3.02591	−	3.11376i	−0.113560	−	0.116857i
$711$		0			0
$712$	−13.3503	−	9.69954i	−0.500323	−	0.363506i
$713$	2.77678	−	26.4193i	0.103991	−	0.989412i
$714$		0			0
$715$	0.263302	−	3.94363i	0.00984692	−	0.147483i
$716$	−34.2047	+	15.2289i	−1.27829	+	0.569132i
$717$		0			0
$718$	−2.18195	−	3.77925i	−0.0814298	−	0.141040i
$719$	3.25698	+	10.0240i	0.121465	+	0.373831i	0.993240	−	0.116075i	$-0.0370312\pi$
$719$	3.25698	+	10.0240i	0.121465	+	0.373831i	−0.871775	+	0.489906i	$0.837031\pi$
$720$		0			0
$721$	−5.71395	+	17.5857i	−0.212799	+	0.654927i
$722$	4.61673	−	0.981316i	0.171817	−	0.0365208i
$723$		0			0
$724$	14.3184	−	24.8003i	0.532141	−	0.921695i
$725$	35.6637	−	2.71943i	1.32452	−	0.100997i
$726$		0			0
$727$	−5.05053	−	2.24864i	−0.187314	−	0.0833974i	0.310937	−	0.950431i	$-0.399357\pi$
$727$	−5.05053	−	2.24864i	−0.187314	−	0.0833974i	−0.498250	+	0.867033i	$0.666024\pi$
$728$	1.40436	−	4.32216i	0.0520489	−	0.160190i
$729$		0			0
$730$	0.484800	+	3.37251i	0.0179432	+	0.124822i
$731$	−27.1132	+	30.1123i	−1.00282	+	1.11374i
$732$		0			0
$733$	8.41306	+	1.78825i	0.310744	+	0.0660506i	0.360644	−	0.932704i	$-0.382557\pi$
$733$	8.41306	+	1.78825i	0.310744	+	0.0660506i	−0.0499002	+	0.998754i	$0.515890\pi$
$734$	4.67053	−	2.07946i	0.172393	−	0.0767541i
$735$		0			0
$736$	15.6461	+	6.96608i	0.576722	+	0.256773i
$737$	−16.6530	−	12.0991i	−0.613419	−	0.445675i
$738$		0			0
$739$	−5.63541	+	4.09436i	−0.207302	+	0.150614i	−0.686592	−	0.727043i	$-0.740894\pi$
$739$	−5.63541	+	4.09436i	−0.207302	+	0.150614i	0.479290	+	0.877656i	$0.340894\pi$
$740$	−20.8647	+	0.794335i	−0.767002	+	0.0292003i
$741$		0			0
$742$	−9.64922	−	2.05101i	−0.354234	−	0.0752948i
$743$	1.69867	−	2.94218i	0.0623180	−	0.107938i	−0.833183	−	0.552997i	$-0.813484\pi$
$743$	1.69867	−	2.94218i	0.0623180	−	0.107938i	0.895501	+	0.445059i	$0.146817\pi$
$744$		0			0
$745$	−20.5296	−	13.7537i	−0.752148	−	0.503895i
$746$	1.26078	−	3.88027i	0.0461603	−	0.142067i
$747$		0			0
$748$	−10.5934	+	7.69657i	−0.387334	+	0.281414i
$749$	−38.1393	−	66.0591i	−1.39358	−	2.41375i
$750$		0			0
$751$	−8.22782	+	14.2510i	−0.300238	+	0.520027i	−0.976190	−	0.216919i	$-0.930399\pi$
$751$	−8.22782	+	14.2510i	−0.300238	+	0.520027i	0.675952	+	0.736946i	$0.263733\pi$
$752$	−1.75055	−	16.6553i	−0.0638358	−	0.607357i
$753$		0			0
$754$	2.05277	−	0.436330i	0.0747576	−	0.0158902i
$755$	11.6553	−	5.73012i	0.424179	−	0.208540i
$756$		0			0
$757$	32.9922			1.19912			0.599560	−	0.800330i	$-0.295342\pi$
$757$	32.9922			1.19912			0.599560	+	0.800330i	$0.295342\pi$
$758$	−1.15619	+	1.28407i	−0.0419946	+	0.0466397i
$759$		0			0
$760$	−7.80413	−	12.4022i	−0.283086	−	0.449876i
$761$	2.66928	+	25.3965i	0.0967614	+	0.920624i	0.929963	+	0.367654i	$0.119839\pi$
$761$	2.66928	+	25.3965i	0.0967614	+	0.920624i	−0.833201	+	0.552970i	$0.813494\pi$
$762$		0			0
$763$	−4.48411	+	42.6635i	−0.162336	+	1.54452i
$764$	12.6819	−	9.21394i	0.458815	−	0.333349i
$765$		0			0
$766$	−2.71876	−	1.97530i	−0.0982328	−	0.0713703i
$767$	−4.34458	+	4.82514i	−0.156874	+	0.174226i
$768$		0			0
$769$	−26.2553	−	5.58075i	−0.946792	−	0.201247i	−0.291456	−	0.956584i	$-0.594140\pi$
$769$	−26.2553	−	5.58075i	−0.946792	−	0.201247i	−0.655336	+	0.755337i	$0.727473\pi$
$770$	3.83696	+	1.53621i	0.138274	+	0.0553611i
$771$		0			0
$772$	−8.95723	+	1.90392i	−0.322378	+	0.0685235i
$773$	33.5830	−	24.3995i	1.20790	−	0.877588i	0.212858	−	0.977083i	$-0.431723\pi$
$773$	33.5830	−	24.3995i	1.20790	−	0.877588i	0.995038	+	0.0994950i	$0.0317227\pi$
$774$		0			0
$775$	23.1762	+	8.27067i	0.832512	+	0.297091i
$776$	−1.82720	−	3.16480i	−0.0655926	−	0.113610i
$777$		0			0
$778$	−5.71038	−	6.34202i	−0.204727	−	0.227372i
$779$	5.04324	+	5.60109i	0.180693	+	0.200680i
$780$		0			0
$781$	−7.82808	+	8.69396i	−0.280111	+	0.311094i
$782$	6.10245			0.218223
$783$		0			0
$784$	−24.6229	−	17.8896i	−0.879389	−	0.638913i
$785$	−6.83901	−	4.58174i	−0.244095	−	0.163529i
$786$		0			0
$787$	13.4214	−	5.97558i	0.478420	−	0.213006i	−0.153335	−	0.988174i	$-0.549001\pi$
$787$	13.4214	−	5.97558i	0.478420	−	0.213006i	0.631755	+	0.775168i	$0.282335\pi$
$788$	−9.48349	+	4.22232i	−0.337835	+	0.150414i
$789$		0			0
$790$	2.00374	−	7.07175i	0.0712898	−	0.251602i
$791$	21.7477	+	15.8006i	0.773259	+	0.561806i
$792$		0			0
$793$	−2.97324			−0.105583
$794$	−2.44097	+	2.71097i	−0.0866267	+	0.0962087i
$795$		0			0
$796$	27.8454	+	30.9254i	0.986954	+	1.09612i
$797$	6.10534	+	6.78067i	0.216262	+	0.240184i	0.841508	−	0.540244i	$-0.181668\pi$
$797$	6.10534	+	6.78067i	0.216262	+	0.240184i	−0.625246	+	0.780428i	$0.715001\pi$
$798$		0			0
$799$	−9.59526	−	16.6195i	−0.339456	−	0.587955i
$800$	−9.68859	+	12.5629i	−0.342543	+	0.444167i
$801$		0			0
$802$	−0.581020	+	0.422136i	−0.0205165	+	0.0149061i
$803$	8.97987	−	1.90873i	0.316893	−	0.0673576i
$804$		0			0
$805$	25.3870	+	40.3446i	0.894772	+	1.42196i
$806$	1.41230	+	0.300193i	0.0497461	+	0.0105739i
$807$		0			0
$808$	5.27921	−	5.86316i	0.185722	−	0.206265i
$809$	19.4810	+	14.1538i	0.684916	+	0.497621i	0.874985	−	0.484150i	$-0.160871\pi$
$809$	19.4810	+	14.1538i	0.684916	+	0.497621i	−0.190069	+	0.981771i	$0.560871\pi$
$810$		0			0
$811$	−16.5638	+	12.0343i	−0.581635	+	0.422582i	−0.839313	−	0.543648i	$-0.817043\pi$
$811$	−16.5638	+	12.0343i	−0.581635	+	0.422582i	0.257678	+	0.966231i	$0.417043\pi$
$812$	5.67683	−	54.0114i	0.199218	−	1.89543i
$813$		0			0
$814$	−0.237633	−	2.26093i	−0.00832903	−	0.0792454i
$815$	0.538627	−	0.646027i	0.0188673	−	0.0226293i
$816$		0			0
$817$	−40.0674	+	44.4994i	−1.40178	+	1.55684i
$818$	−11.0465			−0.386232
$819$		0			0
$820$	2.52222	−	4.77982i	0.0880797	−	0.166918i
$821$	26.5774	−	5.64921i	0.927559	−	0.197159i	0.280724	−	0.959789i	$-0.409425\pi$
$821$	26.5774	−	5.64921i	0.927559	−	0.197159i	0.646835	+	0.762630i	$0.276092\pi$
$822$		0			0
$823$	−1.82685	−	17.3813i	−0.0636799	−	0.605874i	−0.979101	−	0.203376i	$-0.934809\pi$
$823$	−1.82685	−	17.3813i	−0.0636799	−	0.605874i	0.915421	−	0.402498i	$-0.131858\pi$
$824$	2.55910	−	4.43249i	0.0891505	−	0.154413i
$825$		0			0
$826$	−3.39482	−	5.88000i	−0.118121	−	0.204591i
$827$	−10.7163	+	7.78583i	−0.372641	+	0.270740i	−0.758305	−	0.651900i	$-0.773972\pi$
$827$	−10.7163	+	7.78583i	−0.372641	+	0.270740i	0.385664	+	0.922639i	$0.373972\pi$
$828$		0			0
$829$	0.853479	−	2.62674i	0.0296425	−	0.0912304i	−0.935141	−	0.354277i	$-0.884727\pi$
$829$	0.853479	−	2.62674i	0.0296425	−	0.0912304i	0.964783	+	0.263046i	$0.0847272\pi$
$830$	−1.17536	−	3.19793i	−0.0407972	−	0.111002i
$831$		0			0
$832$	3.26079	−	5.64786i	0.113048	−	0.195804i
$833$	−34.1141	−	7.25117i	−1.18198	−	0.251238i
$834$		0			0
$835$	5.33629	−	18.8333i	0.184670	−	0.651752i
$836$	−15.6548	+	11.3739i	−0.541432	+	0.393373i
$837$		0			0
$838$	−3.64023	−	2.64478i	−0.125750	−	0.0913624i
$839$	−1.85839	−	0.827407i	−0.0641587	−	0.0285653i	0.374406	−	0.927265i	$-0.377846\pi$
$839$	−1.85839	−	0.827407i	−0.0641587	−	0.0285653i	−0.438565	+	0.898699i	$0.644513\pi$
$840$		0			0
$841$	20.2549	−	9.01806i	0.698445	−	0.310968i
$842$	−8.32222	−	1.76894i	−0.286803	−	0.0609618i
$843$		0			0
$844$	−19.7061	+	21.8858i	−0.678311	+	0.753341i
$845$	−18.5320	−	19.0700i	−0.637519	−	0.656027i
$846$		0			0
$847$	−9.98341	+	30.7258i	−0.343034	+	1.05575i
$848$	−28.9825	−	12.9038i	−0.995264	−	0.443120i
$849$		0			0
$850$	−1.33301	+	5.49343i	−0.0457219	+	0.188423i
$851$	13.1097	−	22.7067i	0.449394	−	0.778374i
$852$		0			0
$853$	−26.3288	+	5.59636i	−0.901481	+	0.191616i	−0.635262	−	0.772297i	$-0.719108\pi$
$853$	−26.3288	+	5.59636i	−0.901481	+	0.191616i	−0.266219	+	0.963913i	$0.585775\pi$
$854$	0.960775	−	2.95696i	0.0328771	−	0.101185i
$855$		0			0
$856$	6.52451	+	20.0804i	0.223003	+	0.686333i
$857$	0.867885	+	1.50322i	0.0296464	+	0.0513490i	0.880468	−	0.474106i	$-0.157229\pi$
$857$	0.867885	+	1.50322i	0.0296464	+	0.0513490i	−0.850822	+	0.525455i	$0.823895\pi$
$858$		0			0
$859$	−15.3532	+	6.83571i	−0.523846	+	0.233231i	−0.651584	−	0.758577i	$-0.725895\pi$
$859$	−15.3532	+	6.83571i	−0.523846	+	0.233231i	0.127738	+	0.991808i	$0.459228\pi$
$860$	39.8611	+	15.9593i	1.35925	+	0.544206i
$861$		0			0
$862$	−0.448523	+	4.26741i	−0.0152768	+	0.145349i
$863$	37.0757	+	26.9371i	1.26207	+	0.916949i	0.998857	−	0.0477885i	$-0.0152173\pi$
$863$	37.0757	+	26.9371i	1.26207	+	0.916949i	0.263214	+	0.964737i	$0.415217\pi$
$864$		0			0
$865$	−2.24144	+	4.24772i	−0.0762113	+	0.144427i
$866$	1.16280	−	11.0633i	0.0395134	−	0.375945i
$867$		0			0
$868$	18.6822	−	32.3585i	0.634114	−	1.09832i
$869$	−19.3718	−	4.11761i	−0.657144	−	0.139680i
$870$		0			0
$871$	12.6213	−	2.68273i	0.427656	−	0.0909010i
$872$	3.66934	−	11.2931i	0.124260	−	0.382431i
$873$		0			0
$874$	9.01809			0.305042
$875$	−41.8638	+	14.0405i	−1.41525	+	0.474656i
$876$		0			0
$877$	−0.595243	−	5.66336i	−0.0200999	−	0.191238i	0.979865	−	0.199663i	$-0.0639848\pi$
$877$	−0.595243	−	5.66336i	−0.0200999	−	0.191238i	−0.999965	+	0.00842524i	$0.997318\pi$
$878$	−4.45966	−	4.95295i	−0.150506	−	0.167154i
$879$		0			0
$880$	11.0429	+	7.39808i	0.372255	+	0.249389i
$881$	15.5751	+	47.9353i	0.524739	+	1.61498i	0.764832	+	0.644230i	$0.222822\pi$
$881$	15.5751	+	47.9353i	0.524739	+	1.61498i	−0.240093	+	0.970750i	$0.577178\pi$
$882$		0			0
$883$	−11.3213	−	34.8432i	−0.380990	−	1.17257i	−0.939347	−	0.342967i	$-0.888568\pi$
$883$	−11.3213	−	34.8432i	−0.380990	−	1.17257i	0.558357	−	0.829601i	$-0.311432\pi$
$884$	0.857982	−	8.16315i	0.0288571	−	0.274557i
$885$		0			0
$886$	0.589065	+	5.60458i	0.0197900	+	0.188289i
$887$	−17.7941	+	7.92244i	−0.597467	+	0.266010i	−0.683109	−	0.730316i	$-0.739373\pi$
$887$	−17.7941	+	7.92244i	−0.597467	+	0.266010i	0.0856417	+	0.996326i	$0.472706\pi$
$888$		0			0
$889$	−47.8468	−	21.3028i	−1.60473	−	0.714471i
$890$	1.33857	+	9.31179i	0.0448690	+	0.312132i
$891$		0			0
$892$	−12.1730	−	37.4645i	−0.407581	−	1.25440i
$893$	−14.1797	−	24.5600i	−0.474506	−	0.821869i
$894$		0			0
$895$	40.4325	+	16.1880i	1.35151	+	0.541105i
$896$	21.3335	+	23.6933i	0.712702	+	0.791536i
$897$		0			0
$898$	1.98496	+	0.883760i	0.0662389	+	0.0294914i
$899$	35.2059			1.17418
$900$		0			0
$901$	−36.3541			−1.21113
$902$	0.537561	+	0.239338i	0.0178988	+	0.00796907i
$903$		0			0
$904$	−4.97886	−	5.52958i	−0.165594	−	0.183911i
$905$	−32.2958	+	8.16025i	−1.07355	+	0.271256i
$906$		0			0
$907$	14.8967	+	25.8019i	0.494638	+	0.856738i	0.999981	−	0.00618063i	$-0.00196737\pi$
$907$	14.8967	+	25.8019i	0.494638	+	0.856738i	−0.505343	+	0.862919i	$0.668634\pi$
$908$	−1.40648	−	4.32871i	−0.0466758	−	0.143653i
$909$		0			0
$910$	−2.32503	+	1.14306i	−0.0770739	+	0.0378920i
$911$	−21.1134	−	9.40029i	−0.699518	−	0.311446i	0.0259870	−	0.999662i	$-0.491727\pi$
$911$	−21.1134	−	9.40029i	−0.699518	−	0.311446i	−0.725505	+	0.688217i	$0.758394\pi$
$912$		0			0
$913$	−8.38655	+	3.73393i	−0.277554	+	0.123575i
$914$	−0.348294	−	3.31380i	−0.0115205	−	0.109611i
$915$		0			0
$916$	0.656067	−	6.24206i	0.0216771	−	0.206244i
$917$	17.3713	+	53.4635i	0.573652	+	1.76552i
$918$		0			0
$919$	15.8586	+	48.8077i	0.523126	+	1.61002i	0.767992	+	0.640460i	$0.221256\pi$
$919$	15.8586	+	48.8077i	0.523126	+	1.61002i	−0.244865	+	0.969557i	$0.578744\pi$
$920$	−4.55169	−	12.3843i	−0.150065	−	0.408298i
$921$		0			0
$922$	4.30258	+	4.77850i	0.141698	+	0.157371i
$923$	−0.766556	−	7.29329i	−0.0252315	−	0.240062i
$924$		0			0
$925$	17.5769	+	16.7614i	0.577924	+	0.551111i
$926$	5.41907			0.178082
$927$		0			0
$928$	−7.01400	+	21.5869i	−0.230246	+	0.708624i
$929$	53.4901	−	11.3697i	1.75495	−	0.373027i	0.785607	−	0.618726i	$-0.212351\pi$
$929$	53.4901	−	11.3697i	1.75495	−	0.373027i	0.969346	+	0.245700i	$0.0790177\pi$
$930$		0			0
$931$	−50.4132	−	10.7157i	−1.65223	−	0.351192i
$932$	−1.20806	+	2.09242i	−0.0395713	+	0.0685395i
$933$		0			0
$934$	−0.450754	+	4.28864i	−0.0147491	+	0.140329i
$935$	15.0082	+	2.59769i	0.490819	+	0.0849536i
$936$		0			0
$937$	44.5714	+	32.3830i	1.45608	+	1.05791i	0.984362	+	0.176160i	$0.0563675\pi$
$937$	44.5714	+	32.3830i	1.45608	+	1.05791i	0.471722	+	0.881747i	$0.343632\pi$
$938$	−1.41040	+	13.4191i	−0.0460513	+	0.438149i
$939$		0			0
$940$	−13.0222	+	15.6188i	−0.424738	+	0.509429i
$941$	−32.5595	+	14.4964i	−1.06141	+	0.472569i	−0.861769	−	0.507300i	$-0.830643\pi$
$941$	−32.5595	+	14.4964i	−1.06141	+	0.472569i	−0.199639	+	0.979870i	$0.563977\pi$
$942$		0			0
$943$	3.39327	+	5.87731i	0.110500	+	0.191392i
$944$	−6.74756	−	20.7668i	−0.219614	−	0.675903i
$945$		0			0
$946$	−1.44465	+	4.44617i	−0.0469695	+	0.144557i
$947$	41.6883	−	8.86113i	1.35469	−	0.287948i	0.527348	−	0.849649i	$-0.323186\pi$
$947$	41.6883	−	8.86113i	1.35469	−	0.287948i	0.827340	+	0.561701i	$0.189853\pi$
$948$		0			0
$949$	−2.87740	+	4.98381i	−0.0934044	+	0.161781i
$950$	−1.96990	+	8.11810i	−0.0639121	+	0.263386i
$951$		0			0
$952$	15.9993	+	7.12335i	0.518540	+	0.230869i
$953$	−6.79715	+	20.9195i	−0.220181	+	0.677649i	0.778564	+	0.627566i	$0.215949\pi$
$953$	−6.79715	+	20.9195i	−0.220181	+	0.677649i	−0.998745	+	0.0500831i	$0.984051\pi$
$954$		0			0
$955$	−17.9670	−	3.10982i	−0.581399	−	0.100632i
$956$	−16.7406	+	18.5923i	−0.541430	+	0.601319i
$957$		0			0
$958$	8.33249	+	1.77113i	0.269210	+	0.0572225i
$959$	35.0111	−	15.5879i	1.13057	−	0.503361i
$960$		0			0
$961$	−6.19244	−	2.75705i	−0.199756	−	0.0889372i
$962$	1.15291	+	0.837637i	0.0371713	+	0.0270065i
$963$		0			0
$964$	1.92164	−	1.39615i	0.0618918	−	0.0449670i
$965$	8.84954	+	5.92867i	0.284877	+	0.190851i
$966$		0			0
$967$	−21.1184	−	4.48886i	−0.679122	−	0.144352i	−0.144579	−	0.989493i	$-0.546183\pi$
$967$	−21.1184	−	4.48886i	−0.679122	−	0.144352i	−0.534543	+	0.845141i	$0.679516\pi$
$968$	4.47126	−	7.74445i	0.143712	−	0.248916i
$969$		0			0
$970$	−0.567940	+	2.00442i	−0.0182355	+	0.0643580i
$971$	11.5867	−	35.6601i	0.371834	−	1.14439i	−0.573757	−	0.819026i	$-0.694514\pi$
$971$	11.5867	−	35.6601i	0.371834	−	1.14439i	0.945590	−	0.325360i	$-0.105486\pi$
$972$		0			0
$973$	5.20429	−	3.78114i	0.166842	−	0.121218i
$974$	1.30532	+	2.26088i	0.0418252	+	0.0724434i
$975$		0			0
$976$	4.99951	−	8.65940i	0.160030	−	0.277181i
$977$	2.57745	+	24.5228i	0.0824601	+	0.784555i	0.955119	+	0.296224i	$0.0957275\pi$
$977$	2.57745	+	24.5228i	0.0824601	+	0.784555i	−0.872658	+	0.488331i	$0.837606\pi$
$978$		0			0
$979$	24.7941	−	5.27016i	0.792424	−	0.168435i
$980$	5.25848	+	36.5807i	0.167976	+	1.16853i
$981$		0			0
$982$	−5.13961			−0.164012
$983$	17.5110	−	19.4479i	0.558514	−	0.620293i	−0.396075	−	0.918218i	$-0.629628\pi$
$983$	17.5110	−	19.4479i	0.558514	−	0.620293i	0.954589	+	0.297925i	$0.0962947\pi$
$984$		0			0
$985$	11.2102	+	4.48823i	0.357186	+	0.143007i
$986$	0.845370	+	8.04316i	0.0269221	+	0.256146i
$987$		0			0
$988$	1.26791	−	12.0634i	0.0403376	−	0.383787i
$989$	−43.6202	+	31.6919i	−1.38704	+	1.00774i
$990$		0			0
$991$	−24.1262	−	17.5287i	−0.766396	−	0.556819i	0.134470	−	0.990918i	$-0.457067\pi$
$991$	−24.1262	−	17.5287i	−0.766396	−	0.556819i	−0.900865	+	0.434099i	$0.857067\pi$
$992$	−10.4491	+	11.6049i	−0.331760	+	0.368457i
$993$		0			0
$994$	7.50108	+	1.59440i	0.237920	+	0.0505714i
$995$	3.22473	−	48.2987i	0.102231	−	1.53117i
$996$		0			0
$997$	−5.99911	+	1.27515i	−0.189994	+	0.0403844i	−0.301926	−	0.953331i	$-0.597629\pi$
$997$	−5.99911	+	1.27515i	−0.189994	+	0.0403844i	0.111932	+	0.993716i	$0.464296\pi$
$998$	−6.25972	+	4.54795i	−0.198148	+	0.143963i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.361.14		224
3.2	odd	2		225.2.q.a.211.15	yes	224
9.2	odd	6		225.2.q.a.61.14	yes	224
9.7	even	3	inner	675.2.r.a.586.15		224
25.16	even	5	inner	675.2.r.a.91.15		224
75.41	odd	10		225.2.q.a.166.14	yes	224
225.16	even	15	inner	675.2.r.a.316.14		224
225.191	odd	30		225.2.q.a.16.15	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.15	✓	224	225.191	odd	30
225.2.q.a.61.14	yes	224	9.2	odd	6
225.2.q.a.166.14	yes	224	75.41	odd	10
225.2.q.a.211.15	yes	224	3.2	odd	2
675.2.r.a.91.15		224	25.16	even	5	inner
675.2.r.a.316.14		224	225.16	even	15	inner
675.2.r.a.361.14		224	1.1	even	1	trivial
675.2.r.a.586.15		224	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.254613 - 0.113361i) q^{2} +(-1.28628 - 1.42856i) q^{4} +(-0.148962 + 2.23110i) q^{5} +(-1.97470 - 3.42027i) q^{7} +(0.337813 + 1.03968i) q^{8} +O(q^{10})\)	\(q+(-0.254613 - 0.113361i) q^{2} +(-1.28628 - 1.42856i) q^{4} +(-0.148962 + 2.23110i) q^{5} +(-1.97470 - 3.42027i) q^{7} +(0.337813 + 1.03968i) q^{8} +(0.290848 - 0.551181i) q^{10} +(-1.53404 - 0.682997i) q^{11} +(0.961615 - 0.428138i) q^{13} +(0.115058 + 1.09470i) q^{14} +(-0.370027 + 3.52057i) q^{16} +(1.25351 + 3.85792i) q^{17} +(1.85242 + 5.70117i) q^{19} +(3.37888 - 2.65703i) q^{20} +(0.313161 + 0.347800i) q^{22} +(0.564211 + 5.36811i) q^{23} +(-4.95562 - 0.664700i) q^{25} -0.293374 q^{26} +(-2.34606 + 7.22042i) q^{28} +(-6.99712 + 1.48728i) q^{29} +(-4.81399 - 1.02325i) q^{31} +(1.58649 - 2.74789i) q^{32} +(0.118177 - 1.12438i) q^{34} +(7.92513 - 3.89625i) q^{35} +(-3.92983 - 2.85519i) q^{37} +(0.174640 - 1.66158i) q^{38} +(-2.36995 + 0.598821i) q^{40} +(1.14861 - 0.511393i) q^{41} +(4.99451 + 8.65075i) q^{43} +(0.997503 + 3.07000i) q^{44} +(0.464879 - 1.43075i) q^{46} +(-4.62748 + 0.983601i) q^{47} +(-4.29885 + 7.44583i) q^{49} +(1.18641 + 0.731016i) q^{50} +(-1.84853 - 0.823020i) q^{52} +(-2.76942 + 8.52341i) q^{53} +(1.75235 - 3.32085i) q^{55} +(2.88892 - 3.20847i) q^{56} +(1.95016 + 0.414519i) q^{58} +(-5.63502 + 2.50887i) q^{59} +(-2.58041 - 1.14887i) q^{61} +(1.10971 + 0.806250i) q^{62} +(5.01233 - 3.64167i) q^{64} +(0.811976 + 2.20924i) q^{65} +(11.9904 + 2.54863i) q^{67} +(3.89891 - 6.75310i) q^{68} +(-2.45953 + 0.0936360i) q^{70} +(2.15288 - 6.62590i) q^{71} +(-4.42300 + 3.21350i) q^{73} +(0.676918 + 1.17246i) q^{74} +(5.76174 - 9.97962i) q^{76} +(0.693219 + 6.59554i) q^{77} +(11.5363 - 2.45211i) q^{79} +(-7.79963 - 1.35000i) q^{80} -0.350423 q^{82} +(3.65812 - 4.06275i) q^{83} +(-8.79413 + 2.22203i) q^{85} +(-0.291010 - 2.76878i) q^{86} +(0.191882 - 1.82563i) q^{88} +(-12.2123 + 8.87274i) q^{89} +(-3.36325 - 2.44354i) q^{91} +(6.94294 - 7.71092i) q^{92} +(1.28972 + 0.274138i) q^{94} +(-12.9958 + 3.28368i) q^{95} +(-3.26984 + 0.695025i) q^{97} +(1.93861 - 1.40848i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

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