LMFDB - Embedded newform 855.2.bs.c.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(226,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("855.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.bs (of order $9$, degree $6$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} + \cdots + 1 $ x^18 - 3x^17 + 15x^16 - 14x^15 + 72x^14 - 51x^13 + 231x^12 - 93x^11 + 438x^10 - 156x^9 + 582x^8 - 138x^7 + 437x^6 - 132x^5 + 198x^4 - 16x^3 + 15x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			541.1
Root			$-0.566185 + 0.980662i$ of defining polynomial
Character	$\chi$	$=$	855.541
Dual form			855.2.bs.c.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.370282 - 2.09998i) q^{2} +(-2.39340 + 0.871127i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-0.742812 + 1.28659i) q^{7} +(0.583208 + 1.01015i) q^{8} +O(q^{10})$	\(q+(-0.370282 - 2.09998i) q^{2} +(-2.39340 + 0.871127i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-0.742812 + 1.28659i) q^{7} +(0.583208 + 1.01015i) q^{8} +(0.370282 - 2.09998i) q^{10} +(2.34068 + 4.05417i) q^{11} +(-0.276562 - 0.232063i) q^{13} +(2.97685 + 1.08349i) q^{14} +(-1.99691 + 1.67560i) q^{16} +(0.951255 + 5.39483i) q^{17} +(-1.68540 + 4.01988i) q^{19} -2.54700 q^{20} +(7.64695 - 6.41655i) q^{22} +(-5.79545 + 2.10937i) q^{23} +(0.766044 + 0.642788i) q^{25} +(-0.384921 + 0.666703i) q^{26} +(0.657066 - 3.72641i) q^{28} +(0.155581 - 0.882346i) q^{29} +(-2.40012 + 4.15713i) q^{31} +(6.04520 + 5.07252i) q^{32} +(10.9768 - 3.99522i) q^{34} +(-1.13805 + 0.954941i) q^{35} +11.3982 q^{37} +(9.06572 + 2.05081i) q^{38} +(0.202546 + 1.14870i) q^{40} +(4.01104 - 3.36566i) q^{41} +(-6.78295 - 2.46879i) q^{43} +(-9.13387 - 7.66423i) q^{44} +(6.57558 + 11.3892i) q^{46} +(1.88678 - 10.7005i) q^{47} +(2.39646 + 4.15079i) q^{49} +(1.06619 - 1.84669i) q^{50} +(0.864081 + 0.314500i) q^{52} +(-6.12941 + 2.23092i) q^{53} +(0.812908 + 4.61023i) q^{55} -1.73286 q^{56} -1.91051 q^{58} +(1.70300 + 9.65818i) q^{59} +(-2.20795 + 0.803626i) q^{61} +(9.61858 + 3.50088i) q^{62} +(5.80697 - 10.0580i) q^{64} +(-0.180513 - 0.312658i) q^{65} +(1.53717 - 8.71774i) q^{67} +(-6.97632 - 12.0833i) q^{68} +(2.42675 + 2.03629i) q^{70} +(6.02538 + 2.19306i) q^{71} +(2.19219 - 1.83946i) q^{73} +(-4.22054 - 23.9359i) q^{74} +(0.532020 - 11.0894i) q^{76} -6.95473 q^{77} +(1.58226 - 1.32767i) q^{79} +(-2.44957 + 0.891571i) q^{80} +(-8.55302 - 7.17684i) q^{82} +(3.08199 - 5.33816i) q^{83} +(-0.951255 + 5.39483i) q^{85} +(-2.67280 + 15.1582i) q^{86} +(-2.73020 + 4.72885i) q^{88} +(2.54338 + 2.13415i) q^{89} +(0.504004 - 0.183442i) q^{91} +(12.0333 - 10.0971i) q^{92} -23.1693 q^{94} +(-2.95864 + 3.20101i) q^{95} +(0.819060 + 4.64512i) q^{97} +(7.82919 - 6.56947i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) $ 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8	$ 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8} - 3 q^{10} - 3 q^{13} + 12 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{20} + 9 q^{22} + 9 q^{23} - 3 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} - 15 q^{32} - 12 q^{34} + 36 q^{37} + 33 q^{38} - 6 q^{40} + 30 q^{41} - 36 q^{43} - 42 q^{44} + 9 q^{46} - 21 q^{47} + 9 q^{49} + 6 q^{50} - 39 q^{52} + 12 q^{53} + 3 q^{55} + 12 q^{58} - 18 q^{59} - 30 q^{61} + 24 q^{62} + 36 q^{64} + 9 q^{65} - 51 q^{68} + 33 q^{70} + 12 q^{71} + 24 q^{73} + 15 q^{74} - 33 q^{76} + 60 q^{77} - 51 q^{79} - 15 q^{80} - 15 q^{82} + 24 q^{85} - 63 q^{86} - 27 q^{88} + 54 q^{89} + 30 q^{91} + 42 q^{92} + 30 q^{94} - 15 q^{95} + 27 q^{97} + 3 q^{98}+O(q^{100}) $ 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8 - 3 * q^10 - 3 * q^13 + 12 * q^14 - 3 * q^16 - 24 * q^17 - 12 * q^20 + 9 * q^22 + 9 * q^23 - 3 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 - 15 * q^32 - 12 * q^34 + 36 * q^37 + 33 * q^38 - 6 * q^40 + 30 * q^41 - 36 * q^43 - 42 * q^44 + 9 * q^46 - 21 * q^47 + 9 * q^49 + 6 * q^50 - 39 * q^52 + 12 * q^53 + 3 * q^55 + 12 * q^58 - 18 * q^59 - 30 * q^61 + 24 * q^62 + 36 * q^64 + 9 * q^65 - 51 * q^68 + 33 * q^70 + 12 * q^71 + 24 * q^73 + 15 * q^74 - 33 * q^76 + 60 * q^77 - 51 * q^79 - 15 * q^80 - 15 * q^82 + 24 * q^85 - 63 * q^86 - 27 * q^88 + 54 * q^89 + 30 * q^91 + 42 * q^92 + 30 * q^94 - 15 * q^95 + 27 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.370282	−	2.09998i	−0.261829	−	1.48491i	−0.777915	−	0.628370i	$-0.783723\pi$
$2$	−0.370282	−	2.09998i	−0.261829	−	1.48491i	0.516086	−	0.856537i	$-0.327389\pi$
$3$		0			0
$3$		0			0
$4$	−2.39340	+	0.871127i	−1.19670	+	0.435563i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$6$		0			0
$7$	−0.742812	+	1.28659i	−0.280757	+	0.486285i	−0.971571	−	0.236747i	$-0.923919\pi$
$7$	−0.742812	+	1.28659i	−0.280757	+	0.486285i	0.690815	+	0.723032i	$0.257252\pi$
$8$	0.583208	+	1.01015i	0.206195	+	0.357140i
$9$		0			0
$10$	0.370282	−	2.09998i	0.117094	−	0.664070i
$11$	2.34068	+	4.05417i	0.705741	+	1.22238i	0.966424	+	0.256954i	$0.0827189\pi$
$11$	2.34068	+	4.05417i	0.705741	+	1.22238i	−0.260683	+	0.965424i	$0.583948\pi$
$12$		0			0
$13$	−0.276562	−	0.232063i	−0.0767046	−	0.0643628i	0.603629	−	0.797265i	$-0.293721\pi$
$13$	−0.276562	−	0.232063i	−0.0767046	−	0.0643628i	−0.680334	+	0.732902i	$0.738165\pi$
$14$	2.97685	+	1.08349i	0.795598	+	0.289574i
$15$		0			0
$16$	−1.99691	+	1.67560i	−0.499227	+	0.418901i
$17$	0.951255	+	5.39483i	0.230713	+	1.30844i	0.851456	+	0.524425i	$0.175720\pi$
$17$	0.951255	+	5.39483i	0.230713	+	1.30844i	−0.620743	+	0.784014i	$0.713169\pi$
$18$		0			0
$19$	−1.68540	+	4.01988i	−0.386658	+	0.922223i
$19$	−1.68540	+	4.01988i	−0.386658	+	0.922223i
$20$	−2.54700			−0.569527
$21$		0			0
$22$	7.64695	−	6.41655i	1.63033	−	1.36801i
$23$	−5.79545	+	2.10937i	−1.20843	+	0.439834i	−0.866161	−	0.499766i	$-0.833419\pi$
$23$	−5.79545	+	2.10937i	−1.20843	+	0.439834i	−0.342274	+	0.939600i	$0.611197\pi$
$24$		0			0
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	−0.384921	+	0.666703i	−0.0754892	+	0.130751i
$27$		0			0
$28$	0.657066	−	3.72641i	0.124174	−	0.704225i
$29$	0.155581	−	0.882346i	0.0288907	−	0.163848i	−0.966949	−	0.254970i	$-0.917934\pi$
$29$	0.155581	−	0.882346i	0.0288907	−	0.163848i	0.995840	+	0.0911225i	$0.0290455\pi$
$30$		0			0
$31$	−2.40012	+	4.15713i	−0.431074	+	0.746642i	−0.996966	−	0.0778374i	$-0.975199\pi$
$31$	−2.40012	+	4.15713i	−0.431074	+	0.746642i	0.565892	+	0.824479i	$0.308532\pi$
$32$	6.04520	+	5.07252i	1.06865	+	0.896704i
$33$		0			0
$34$	10.9768	−	3.99522i	1.88250	−	0.685175i
$35$	−1.13805	+	0.954941i	−0.192366	+	0.161415i
$36$		0			0
$37$	11.3982			1.87385			0.936924	−	0.349534i	$-0.113660\pi$
$37$	11.3982			1.87385			0.936924	+	0.349534i	$0.113660\pi$
$38$	9.06572	+	2.05081i	1.47065	+	0.332686i
$39$		0			0
$40$	0.202546	+	1.14870i	0.0320253	+	0.181625i
$41$	4.01104	−	3.36566i	0.626419	−	0.525628i	−0.273395	−	0.961902i	$-0.588147\pi$
$41$	4.01104	−	3.36566i	0.626419	−	0.525628i	0.899814	+	0.436274i	$0.143702\pi$
$42$		0			0
$43$	−6.78295	−	2.46879i	−1.03439	−	0.376487i	−0.231639	−	0.972802i	$-0.574409\pi$
$43$	−6.78295	−	2.46879i	−1.03439	−	0.376487i	−0.802751	+	0.596314i	$0.796631\pi$
$44$	−9.13387	−	7.66423i	−1.37698	−	1.15543i
$45$		0			0
$46$	6.57558	+	11.3892i	0.969516	+	1.67925i
$47$	1.88678	−	10.7005i	0.275215	−	1.56082i	−0.463062	−	0.886326i	$-0.653249\pi$
$47$	1.88678	−	10.7005i	0.275215	−	1.56082i	0.738278	−	0.674497i	$-0.235639\pi$
$48$		0			0
$49$	2.39646	+	4.15079i	0.342351	+	0.592970i
$50$	1.06619	−	1.84669i	0.150781	−	0.261161i
$51$		0			0
$52$	0.864081	+	0.314500i	0.119827	+	0.0436133i
$53$	−6.12941	+	2.23092i	−0.841940	+	0.306441i	−0.726750	−	0.686902i	$-0.758970\pi$
$53$	−6.12941	+	2.23092i	−0.841940	+	0.306441i	−0.115190	+	0.993343i	$0.536748\pi$
$54$		0			0
$55$	0.812908	+	4.61023i	0.109613	+	0.621644i
$56$	−1.73286			−0.231563
$57$		0			0
$58$	−1.91051			−0.250863
$59$	1.70300	+	9.65818i	0.221711	+	1.25739i	0.868873	+	0.495035i	$0.164845\pi$
$59$	1.70300	+	9.65818i	0.221711	+	1.25739i	−0.647162	+	0.762353i	$0.724044\pi$
$60$		0			0
$61$	−2.20795	+	0.803626i	−0.282698	+	0.102894i	−0.479478	−	0.877554i	$-0.659174\pi$
$61$	−2.20795	+	0.803626i	−0.282698	+	0.102894i	0.196779	+	0.980448i	$0.436952\pi$
$62$	9.61858	+	3.50088i	1.22156	+	0.444612i
$63$		0			0
$64$	5.80697	−	10.0580i	0.725871	−	1.25725i
$65$	−0.180513	−	0.312658i	−0.0223899	−	0.0387805i
$66$		0			0
$67$	1.53717	−	8.71774i	0.187796	−	1.06504i	−0.734515	−	0.678592i	$-0.762590\pi$
$67$	1.53717	−	8.71774i	0.187796	−	1.06504i	0.922311	−	0.386449i	$-0.126299\pi$
$68$	−6.97632	−	12.0833i	−0.846003	−	1.46532i
$69$		0			0
$70$	2.42675	+	2.03629i	0.290053	+	0.243383i
$71$	6.02538	+	2.19306i	0.715081	+	0.260268i	0.673836	−	0.738881i	$-0.264645\pi$
$71$	6.02538	+	2.19306i	0.715081	+	0.260268i	0.0412447	+	0.999149i	$0.486868\pi$
$72$		0			0
$73$	2.19219	−	1.83946i	0.256576	−	0.215293i	−0.505422	−	0.862872i	$-0.668663\pi$
$73$	2.19219	−	1.83946i	0.256576	−	0.215293i	0.761998	+	0.647580i	$0.224219\pi$
$74$	−4.22054	−	23.9359i	−0.490628	−	2.78249i
$75$		0			0
$76$	0.532020	−	11.0894i	0.0610268	−	1.27204i
$77$	−6.95473			−0.792566
$78$		0			0
$79$	1.58226	−	1.32767i	0.178018	−	0.149375i	−0.549425	−	0.835543i	$-0.685153\pi$
$79$	1.58226	−	1.32767i	0.178018	−	0.149375i	0.727443	+	0.686168i	$0.240709\pi$
$80$	−2.44957	+	0.891571i	−0.273870	+	0.0996806i
$81$		0			0
$82$	−8.55302	−	7.17684i	−0.944523	−	0.792549i
$83$	3.08199	−	5.33816i	0.338292	−	0.585939i	−0.645820	−	0.763490i	$-0.723484\pi$
$83$	3.08199	−	5.33816i	0.338292	−	0.585939i	0.984112	+	0.177551i	$0.0568176\pi$
$84$		0			0
$85$	−0.951255	+	5.39483i	−0.103178	+	0.585152i
$86$	−2.67280	+	15.1582i	−0.288215	+	1.63455i
$87$		0			0
$88$	−2.73020	+	4.72885i	−0.291040	+	0.504097i
$89$	2.54338	+	2.13415i	0.269598	+	0.226220i	0.767556	−	0.640981i	$-0.221472\pi$
$89$	2.54338	+	2.13415i	0.269598	+	0.226220i	−0.497959	+	0.867201i	$0.665917\pi$
$90$		0			0
$91$	0.504004	−	0.183442i	0.0528340	−	0.0192300i
$92$	12.0333	−	10.0971i	1.25456	−	1.05270i
$93$		0			0
$94$	−23.1693			−2.38974
$95$	−2.95864	+	3.20101i	−0.303550	+	0.328417i
$96$		0			0
$97$	0.819060	+	4.64512i	0.0831630	+	0.471641i	0.997738	+	0.0672241i	$0.0214143\pi$
$97$	0.819060	+	4.64512i	0.0831630	+	0.471641i	−0.914575	+	0.404416i	$0.867475\pi$
$98$	7.82919	−	6.56947i	0.790867	−	0.663617i
$99$		0			0
$100$	−2.39340	−	0.871127i	−0.239340	−	0.0871127i
$101$	−6.92692	−	5.81237i	−0.689254	−	0.578353i	0.229440	−	0.973323i	$-0.426310\pi$
$101$	−6.92692	−	5.81237i	−0.689254	−	0.578353i	−0.918694	+	0.394970i	$0.870755\pi$
$102$		0			0
$103$	−3.89934	−	6.75385i	−0.384213	−	0.665476i	0.607447	−	0.794360i	$-0.292194\pi$
$103$	−3.89934	−	6.75385i	−0.384213	−	0.665476i	−0.991660	+	0.128884i	$0.958860\pi$
$104$	0.0731245	−	0.414709i	0.00717044	−	0.0406656i
$105$		0			0
$106$	6.95450	+	12.0455i	0.675481	+	1.16997i
$107$	0.259152	−	0.448864i	0.0250531	−	0.0433933i	−0.853227	−	0.521540i	$-0.825358\pi$
$107$	0.259152	−	0.448864i	0.0250531	−	0.0433933i	0.878280	+	0.478146i	$0.158691\pi$
$108$		0			0
$109$	2.59771	+	0.945488i	0.248815	+	0.0905614i	0.463417	−	0.886140i	$-0.346623\pi$
$109$	2.59771	+	0.945488i	0.248815	+	0.0905614i	−0.214602	+	0.976702i	$0.568845\pi$
$110$	9.38037	−	3.41417i	0.894383	−	0.325529i
$111$		0			0
$112$	−0.672486	−	3.81386i	−0.0635440	−	0.360376i
$113$	−12.4325			−1.16955			−0.584774	−	0.811197i	$-0.698817\pi$
$113$	−12.4325			−1.16955			−0.584774	+	0.811197i	$0.698817\pi$
$114$		0			0
$115$	−6.16739			−0.575112
$116$	0.396266	+	2.24734i	0.0367924	+	0.208660i
$117$		0			0
$118$	19.6513	−	7.15250i	1.80905	−	0.658441i
$119$	−7.64754	−	2.78348i	−0.701049	−	0.255161i
$120$		0			0
$121$	−5.45753	+	9.45272i	−0.496139	+	0.859339i
$122$	2.50516	+	4.33906i	0.226806	+	0.392840i
$123$		0			0
$124$	2.12306	−	12.0405i	0.190656	−	1.08127i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$		0			0
$127$	−1.04258	−	0.874829i	−0.0925141	−	0.0776285i	0.595358	−	0.803461i	$-0.297010\pi$
$127$	−1.04258	−	0.874829i	−0.0925141	−	0.0776285i	−0.687872	+	0.725832i	$0.741455\pi$
$128$	−8.44062	−	3.07213i	−0.746052	−	0.271541i
$129$		0			0
$130$	−0.589733	+	0.494845i	−0.0517230	+	0.0434008i
$131$	3.39033	+	19.2275i	0.296214	+	1.67991i	0.662226	+	0.749305i	$0.269612\pi$
$131$	3.39033	+	19.2275i	0.296214	+	1.67991i	−0.366011	+	0.930610i	$0.619277\pi$
$132$		0			0
$133$	−3.91999	−	5.15444i	−0.339907	−	0.446946i
$134$	−18.8762			−1.63066
$135$		0			0
$136$	−4.89479	+	4.10721i	−0.419725	+	0.352191i
$137$	10.0363	−	3.65291i	0.857458	−	0.312089i	0.124381	−	0.992235i	$-0.460306\pi$
$137$	10.0363	−	3.65291i	0.857458	−	0.312089i	0.733077	+	0.680145i	$0.238083\pi$
$138$		0			0
$139$	−5.50879	−	4.62243i	−0.467250	−	0.392069i	0.378541	−	0.925585i	$-0.376426\pi$
$139$	−5.50879	−	4.62243i	−0.467250	−	0.392069i	−0.845790	+	0.533516i	$0.820871\pi$
$140$	1.89195	−	3.27695i	0.159899	−	0.276953i
$141$		0			0
$142$	2.37428	−	13.4652i	0.199245	−	1.12997i
$143$	0.293481	−	1.66442i	0.0245422	−	0.139185i
$144$		0			0
$145$	0.447979	−	0.775922i	0.0372026	−	0.0644368i
$146$	−4.67455	−	3.92241i	−0.386869	−	0.324621i
$147$		0			0
$148$	−27.2804	+	9.92925i	−2.24243	+	0.816179i
$149$	−3.25360	+	2.73009i	−0.266545	+	0.223658i	−0.766258	−	0.642533i	$-0.777883\pi$
$149$	−3.25360	+	2.73009i	−0.266545	+	0.223658i	0.499713	+	0.866191i	$0.333439\pi$
$150$		0			0
$151$	−19.5373			−1.58992			−0.794961	−	0.606660i	$-0.792509\pi$
$151$	−19.5373			−1.58992			−0.794961	+	0.606660i	$0.792509\pi$
$152$	−5.04360	+	0.641923i	−0.409090	+	0.0520668i
$153$		0			0
$154$	2.57521	+	14.6048i	0.207517	+	1.17689i
$155$	−3.67719	+	3.08553i	−0.295359	+	0.247836i
$156$		0			0
$157$	−0.269149	−	0.0979622i	−0.0214804	−	0.00781823i	0.331258	−	0.943540i	$-0.392527\pi$
$157$	−0.269149	−	0.0979622i	−0.0214804	−	0.00781823i	−0.352738	+	0.935722i	$0.614749\pi$
$158$	−3.37396	−	2.83109i	−0.268418	−	0.225230i
$159$		0			0
$160$	3.94572	+	6.83419i	0.311937	+	0.540291i
$161$	1.59104	−	9.02323i	0.125391	−	0.711130i
$162$		0			0
$163$	10.3128	+	17.8622i	0.807759	+	1.39908i	0.914413	+	0.404783i	$0.132653\pi$
$163$	10.3128	+	17.8622i	0.807759	+	1.39908i	−0.106654	+	0.994296i	$0.534014\pi$
$164$	−6.66811	+	11.5495i	−0.520692	+	0.901864i
$165$		0			0
$166$	−12.3512	−	4.49547i	−0.958639	−	0.348916i
$167$	10.1993	−	3.71223i	0.789243	−	0.287261i	0.0842218	−	0.996447i	$-0.473160\pi$
$167$	10.1993	−	3.71223i	0.789243	−	0.287261i	0.705021	+	0.709186i	$0.250937\pi$
$168$		0			0
$169$	−2.23479	−	12.6741i	−0.171907	−	0.974934i
$170$	11.6812			0.895911
$171$		0			0
$172$	18.3850			1.40184
$173$	3.04734	+	17.2823i	0.231685	+	1.31395i	0.849483	+	0.527616i	$0.176914\pi$
$173$	3.04734	+	17.2823i	0.231685	+	1.31395i	−0.617798	+	0.786337i	$0.711975\pi$
$174$		0			0
$175$	−1.39603	+	0.508114i	−0.105530	+	0.0384098i
$176$	−11.4673	−	4.17376i	−0.864380	−	0.314609i
$177$		0			0
$178$	3.53989	−	6.13128i	0.265326	−	0.459559i
$179$	7.53220	+	13.0462i	0.562983	+	0.975116i	0.997234	+	0.0743239i	$0.0236799\pi$
$179$	7.53220	+	13.0462i	0.562983	+	0.975116i	−0.434251	+	0.900792i	$0.642987\pi$
$180$		0			0
$181$	2.59091	−	14.6938i	0.192581	−	1.09218i	−0.723241	−	0.690596i	$-0.757348\pi$
$181$	2.59091	−	14.6938i	0.192581	−	1.09218i	0.915822	−	0.401585i	$-0.131541\pi$
$182$	−0.571848	−	0.990471i	−0.0423882	−	0.0734186i
$183$		0			0
$184$	−5.51072	−	4.62405i	−0.406256	−	0.340889i
$185$	10.7108	+	3.89840i	0.787472	+	0.286616i
$186$		0			0
$187$	−19.6450	+	16.4841i	−1.43658	+	1.20544i
$188$	4.80564	+	27.2541i	0.350487	+	1.98771i
$189$		0			0
$190$	7.81757	+	5.02779i	0.567146	+	0.364754i
$191$	0.00677854			0.000490478			0.000245239	−	1.00000i	$-0.499922\pi$
$191$	0.00677854			0.000490478			0.000245239		1.00000i	$0.499922\pi$
$192$		0			0
$193$	10.5149	−	8.82305i	0.756880	−	0.635097i	−0.180433	−	0.983587i	$-0.557750\pi$
$193$	10.5149	−	8.82305i	0.756880	−	0.635097i	0.937313	+	0.348490i	$0.113305\pi$
$194$	9.45136	−	3.44001i	0.678568	−	0.246978i
$195$		0			0
$196$	−9.35155	−	7.84688i	−0.667968	−	0.560492i
$197$	0.239890	−	0.415502i	0.0170915	−	0.0296033i	−0.857353	−	0.514729i	$-0.827893\pi$
$197$	0.239890	−	0.415502i	0.0170915	−	0.0296033i	0.874445	+	0.485125i	$0.161226\pi$
$198$		0			0
$199$	−4.65737	+	26.4133i	−0.330152	+	1.87239i	0.140517	+	0.990078i	$0.455123\pi$
$199$	−4.65737	+	26.4133i	−0.330152	+	1.87239i	−0.470670	+	0.882309i	$0.655988\pi$
$200$	−0.202546	+	1.14870i	−0.0143222	+	0.0812250i
$201$		0			0
$202$	−9.64092	+	16.6986i	−0.678333	+	1.17491i
$203$	1.01965	+	0.855587i	0.0715653	+	0.0600504i
$204$		0			0
$205$	4.92027	−	1.79083i	0.343646	−	0.125077i
$206$	−12.7391	+	10.6893i	−0.887572	+	0.744761i
$207$		0			0
$208$	0.941116			0.0652547
$209$	−20.2423	+	2.57633i	−1.40019	+	0.178208i
$210$		0			0
$211$	1.43107	+	8.11599i	0.0985188	+	0.558728i	0.993612	+	0.112849i	$0.0359976\pi$
$211$	1.43107	+	8.11599i	0.0985188	+	0.558728i	−0.895093	+	0.445879i	$0.852891\pi$
$212$	12.7267	−	10.6790i	0.874075	−	0.733436i
$213$		0			0
$214$	−1.03856	−	0.378006i	−0.0709946	−	0.0258399i
$215$	−5.52951	−	4.63981i	−0.377110	−	0.316433i
$216$		0			0
$217$	−3.56567	−	6.17593i	−0.242054	−	0.419249i
$218$	1.02362	−	5.80522i	0.0693281	−	0.393179i
$219$		0			0
$220$	−5.96171	−	10.3260i	−0.401939	−	0.696178i
$221$	0.988862	−	1.71276i	0.0665181	−	0.115213i
$222$		0			0
$223$	−1.61443	−	0.587605i	−0.108110	−	0.0393489i	0.287399	−	0.957811i	$-0.407210\pi$
$223$	−1.61443	−	0.587605i	−0.108110	−	0.0393489i	−0.395509	+	0.918462i	$0.629432\pi$
$224$	−11.0167	+	4.00975i	−0.736085	+	0.267913i
$225$		0			0
$226$	4.60352	+	26.1079i	0.306222	+	1.73667i
$227$	−4.22601			−0.280490			−0.140245	−	0.990117i	$-0.544789\pi$
$227$	−4.22601			−0.280490			−0.140245	+	0.990117i	$0.544789\pi$
$228$		0			0
$229$	5.52322			0.364985			0.182492	−	0.983207i	$-0.441583\pi$
$229$	5.52322			0.364985			0.182492	+	0.983207i	$0.441583\pi$
$230$	2.28367	+	12.9514i	0.150581	+	0.853988i
$231$		0			0
$232$	0.982034	−	0.357431i	0.0644737	−	0.0234665i
$233$	26.4955	+	9.64357i	1.73578	+	0.631771i	0.999015	−	0.0443807i	$-0.0141315\pi$
$233$	26.4955	+	9.64357i	1.73578	+	0.631771i	0.736762	+	0.676152i	$0.236354\pi$
$234$		0			0
$235$	5.43277	−	9.40983i	0.354395	−	0.613829i
$236$	−12.4895	−	21.6324i	−0.812994	−	1.40815i
$237$		0			0
$238$	−3.01348	+	17.0903i	−0.195335	+	1.10780i
$239$	−5.66020	−	9.80375i	−0.366128	−	0.634152i	0.622829	−	0.782358i	$-0.285983\pi$
$239$	−5.66020	−	9.80375i	−0.366128	−	0.634152i	−0.988956	+	0.148206i	$0.952650\pi$
$240$		0			0
$241$	12.5356	+	10.5186i	0.807488	+	0.677563i	0.950007	−	0.312229i	$-0.101076\pi$
$241$	12.5356	+	10.5186i	0.807488	+	0.677563i	−0.142519	+	0.989792i	$0.545520\pi$
$242$	21.8713	+	7.96051i	1.40594	+	0.511721i
$243$		0			0
$244$	4.58444	−	3.84680i	0.293489	−	0.246266i
$245$	0.832282	+	4.72010i	0.0531725	+	0.301556i
$246$		0			0
$247$	1.39899	−	0.720627i	0.0890153	−	0.0458524i
$248$	−5.59907			−0.355541
$249$		0			0
$250$	1.63349	−	1.37066i	0.103311	−	0.0866882i
$251$	−6.90186	+	2.51207i	−0.435641	+	0.158560i	−0.550525	−	0.834818i	$-0.685573\pi$
$251$	−6.90186	+	2.51207i	−0.435641	+	0.158560i	0.114884	+	0.993379i	$0.463350\pi$
$252$		0			0
$253$	−22.1170	−	18.5584i	−1.39049	−	1.16676i
$254$	−1.45107	+	2.51333i	−0.0910482	+	0.157700i
$255$		0			0
$256$	0.707484	−	4.01234i	0.0442178	−	0.250771i
$257$	1.04416	−	5.92171i	0.0651327	−	0.369386i	−0.934768	−	0.355260i	$-0.884392\pi$
$257$	1.04416	−	5.92171i	0.0651327	−	0.369386i	0.999900	−	0.0141259i	$-0.00449655\pi$
$258$		0			0
$259$	−8.46670	+	14.6648i	−0.526095	+	0.911224i
$260$	0.704405	+	0.591066i	0.0436854	+	0.0366564i
$261$		0			0
$262$	39.1219	−	14.2392i	2.41696	−	0.879701i
$263$	−5.65251	+	4.74302i	−0.348549	+	0.292467i	−0.800207	−	0.599724i	$-0.795277\pi$
$263$	−5.65251	+	4.74302i	−0.348549	+	0.292467i	0.451658	+	0.892191i	$0.350833\pi$
$264$		0			0
$265$	−6.52279			−0.400692
$266$	−9.37268	+	10.1405i	−0.574676	+	0.621753i
$267$		0			0
$268$	3.91519	+	22.2041i	0.239158	+	1.35633i
$269$	8.32148	−	6.98255i	0.507370	−	0.425734i	−0.352833	−	0.935686i	$-0.614782\pi$
$269$	8.32148	−	6.98255i	0.507370	−	0.425734i	0.860203	+	0.509953i	$0.170337\pi$
$270$		0			0
$271$	−2.67693	−	0.974323i	−0.162612	−	0.0591859i	0.259432	−	0.965762i	$-0.416465\pi$
$271$	−2.67693	−	0.974323i	−0.162612	−	0.0591859i	−0.422043	+	0.906576i	$0.638687\pi$
$272$	−10.9392	−	9.17906i	−0.663285	−	0.556562i
$273$		0			0
$274$	−11.3873	−	19.7233i	−0.687931	−	1.19153i
$275$	−0.812908	+	4.61023i	−0.0490202	+	0.278007i
$276$		0			0
$277$	8.07213	+	13.9813i	0.485008	+	0.840058i	0.999852	−	0.0172261i	$-0.00548351\pi$
$277$	8.07213	+	13.9813i	0.485008	+	0.840058i	−0.514844	+	0.857284i	$0.672150\pi$
$278$	−7.66717	+	13.2799i	−0.459846	+	0.796477i
$279$		0			0
$280$	−1.62835	−	0.592672i	−0.0973127	−	0.0354189i
$281$	3.02211	−	1.09996i	0.180284	−	0.0656179i	−0.250301	−	0.968168i	$-0.580530\pi$
$281$	3.02211	−	1.09996i	0.180284	−	0.0656179i	0.430585	+	0.902550i	$0.358307\pi$
$282$		0			0
$283$	2.23560	+	12.6787i	0.132893	+	0.753671i	0.976304	+	0.216403i	$0.0694325\pi$
$283$	2.23560	+	12.6787i	0.132893	+	0.753671i	−0.843412	+	0.537268i	$0.819456\pi$
$284$	−16.3316			−0.969101
$285$		0			0
$286$	−3.60390			−0.213103
$287$	1.35077	+	7.66061i	0.0797336	+	0.452192i
$288$		0			0
$289$	−12.2246	+	4.44938i	−0.719092	+	0.261728i
$290$	−1.79530	−	0.653434i	−0.105423	−	0.0383710i
$291$		0			0
$292$	−3.64437	+	6.31224i	−0.213271	+	0.369396i
$293$	−15.4055	−	26.6831i	−0.899999	−	1.55884i	−0.827493	−	0.561476i	$-0.810234\pi$
$293$	−15.4055	−	26.6831i	−0.899999	−	1.55884i	−0.0725066	−	0.997368i	$-0.523100\pi$
$294$		0			0
$295$	−1.70300	+	9.65818i	−0.0991523	+	0.562321i
$296$	6.64750	+	11.5138i	0.386378	+	0.669227i
$297$		0			0
$298$	6.93788	+	5.82157i	0.401900	+	0.337234i
$299$	2.09231	+	0.761539i	0.121001	+	0.0440409i
$300$		0			0
$301$	8.21478	−	6.89302i	0.473492	−	0.397307i
$302$	7.23432	+	41.0278i	0.416288	+	2.36089i
$303$		0			0
$304$	−3.37013	−	10.8514i	−0.193290	−	0.622370i
$305$	−2.34965			−0.134540
$306$		0			0
$307$	12.5488	−	10.5297i	0.716196	−	0.600959i	−0.210134	−	0.977673i	$-0.567390\pi$
$307$	12.5488	−	10.5297i	0.716196	−	0.600959i	0.926330	+	0.376713i	$0.122946\pi$
$308$	16.6455	−	6.05846i	0.948464	−	0.345213i
$309$		0			0
$310$	7.84114	+	6.57950i	0.445347	+	0.373690i
$311$	12.3873	−	21.4555i	0.702420	−	1.21663i	−0.265195	−	0.964195i	$-0.585436\pi$
$311$	12.3873	−	21.4555i	0.702420	−	1.21663i	0.967615	−	0.252432i	$-0.0812304\pi$
$312$		0			0
$313$	1.78395	−	10.1173i	0.100835	−	0.571863i	−0.891968	−	0.452099i	$-0.850675\pi$
$313$	1.78395	−	10.1173i	0.100835	−	0.571863i	0.992802	−	0.119763i	$-0.0382136\pi$
$314$	−0.106057	+	0.601480i	−0.00598515	+	0.0339435i
$315$		0			0
$316$	−2.63041	+	4.55600i	−0.147972	+	0.256295i
$317$	−4.65473	−	3.90578i	−0.261436	−	0.219371i	0.502642	−	0.864495i	$-0.332361\pi$
$317$	−4.65473	−	3.90578i	−0.261436	−	0.219371i	−0.764078	+	0.645124i	$0.776806\pi$
$318$		0			0
$319$	3.94135	−	1.43453i	0.220673	−	0.0803184i
$320$	8.89679	−	7.46529i	0.497346	−	0.417323i
$321$		0			0
$322$	−19.5377			−1.08879
$323$	−23.2898	−	5.26854i	−1.29588	−	0.293149i
$324$		0			0
$325$	−0.0626916	−	0.355542i	−0.00347750	−	0.0197219i
$326$	33.6916	−	28.2706i	1.86601	−	1.56577i
$327$		0			0
$328$	5.73908	+	2.08885i	0.316888	+	0.115338i
$329$	12.3656	+	10.3759i	0.681736	+	0.572044i
$330$		0			0
$331$	−5.90549	−	10.2286i	−0.324595	−	0.562215i	0.656835	−	0.754034i	$-0.271895\pi$
$331$	−5.90549	−	10.2286i	−0.324595	−	0.562215i	−0.981430	+	0.191819i	$0.938561\pi$
$332$	−2.72622	+	15.4611i	−0.149621	+	0.848541i
$333$		0			0
$334$	−11.5722	−	20.0436i	−0.633203	−	1.09674i
$335$	4.42611	−	7.66625i	0.241824	−	0.418852i
$336$		0			0
$337$	−14.3082	−	5.20776i	−0.779417	−	0.283685i	−0.0784877	−	0.996915i	$-0.525009\pi$
$337$	−14.3082	−	5.20776i	−0.779417	−	0.283685i	−0.700930	+	0.713230i	$0.747231\pi$
$338$	−25.7879	+	9.38602i	−1.40268	+	0.510532i
$339$		0			0
$340$	−2.42285	−	13.7407i	−0.131397	−	0.745192i
$341$	−22.4716			−1.21691
$342$		0			0
$343$	−17.5199			−0.945983
$344$	−1.46203	−	8.29159i	−0.0788274	−	0.447052i
$345$		0			0
$346$	35.1641	−	12.7987i	1.89044	−	0.688062i
$347$	−28.3603	−	10.3223i	−1.52246	−	0.554131i	−0.560700	−	0.828019i	$-0.689468\pi$
$347$	−28.3603	−	10.3223i	−1.52246	−	0.554131i	−0.961762	+	0.273888i	$0.911690\pi$
$348$		0			0
$349$	1.36886	−	2.37093i	0.0732732	−	0.126913i	−0.827061	−	0.562112i	$-0.809989\pi$
$349$	1.36886	−	2.37093i	0.0732732	−	0.126913i	0.900334	+	0.435200i	$0.143322\pi$
$350$	1.58395	+	2.74348i	0.0846658	+	0.146645i
$351$		0			0
$352$	−6.41502	+	36.3814i	−0.341922	+	1.93914i
$353$	−2.30462	−	3.99172i	−0.122663	−	0.212458i	0.798154	−	0.602453i	$-0.205810\pi$
$353$	−2.30462	−	3.99172i	−0.122663	−	0.212458i	−0.920817	+	0.389995i	$0.872477\pi$
$354$		0			0
$355$	4.91193	+	4.12160i	0.260698	+	0.218752i
$356$	−7.94645	−	2.89227i	−0.421161	−	0.153290i
$357$		0			0
$358$	24.6076	−	20.6482i	1.30055	−	1.09129i
$359$	−2.14281	−	12.1525i	−0.113093	−	0.641383i	−0.987677	−	0.156508i	$-0.949976\pi$
$359$	−2.14281	−	12.1525i	−0.113093	−	0.641383i	0.874584	−	0.484875i	$-0.161135\pi$
$360$		0			0
$361$	−13.3188	−	13.5502i	−0.700992	−	0.713170i
$362$	−31.8160			−1.67221
$363$		0			0
$364$	−1.04648	+	0.878103i	−0.0548506	+	0.0460251i
$365$	2.68911	−	0.978757i	0.140755	−	0.0512305i
$366$		0			0
$367$	−1.25334	−	1.05168i	−0.0654239	−	0.0548972i	0.609489	−	0.792794i	$-0.291375\pi$
$367$	−1.25334	−	1.05168i	−0.0654239	−	0.0548972i	−0.674913	+	0.737897i	$0.735819\pi$
$368$	8.03851	−	13.9231i	0.419036	−	0.725792i
$369$		0			0
$370$	4.22054	−	23.9359i	0.219415	−	1.24437i
$371$	1.68272	−	9.54319i	0.0873626	−	0.495458i
$372$		0			0
$373$	7.37936	−	12.7814i	0.382089	−	0.661797i	−0.609272	−	0.792961i	$-0.708538\pi$
$373$	7.37936	−	12.7814i	0.382089	−	0.661797i	0.991361	+	0.131164i	$0.0418715\pi$
$374$	41.8904	+	35.1502i	2.16610	+	1.81758i
$375$		0			0
$376$	11.9094	−	4.33467i	0.614181	−	0.223544i
$377$	−0.247788	+	0.207919i	−0.0127617	+	0.0107084i
$378$		0			0
$379$	−1.75865			−0.0903358			−0.0451679	−	0.998979i	$-0.514382\pi$
$379$	−1.75865			−0.0903358			−0.0451679	+	0.998979i	$0.514382\pi$
$380$	4.29273	−	10.2386i	0.220212	−	0.525231i
$381$		0			0
$382$	−0.00250997	−	0.0142348i	−0.000128421	−	0.000728314i
$383$	6.51031	−	5.46280i	0.332661	−	0.279136i	−0.461122	−	0.887337i	$-0.652553\pi$
$383$	6.51031	−	5.46280i	0.332661	−	0.279136i	0.793783	+	0.608201i	$0.208108\pi$
$384$		0			0
$385$	−6.53531	−	2.37866i	−0.333070	−	0.121228i
$386$	−22.4217	−	18.8140i	−1.14123	−	0.957609i
$387$		0			0
$388$	−6.00683	−	10.4041i	−0.304951	−	0.528190i
$389$	5.89390	−	33.4260i	0.298833	−	1.69476i	−0.352370	−	0.935861i	$-0.614624\pi$
$389$	5.89390	−	33.4260i	0.298833	−	1.69476i	0.651203	−	0.758904i	$-0.274265\pi$
$390$		0			0
$391$	−16.8927	−	29.2589i	−0.854298	−	1.47969i
$392$	−2.79527	+	4.84155i	−0.141182	+	0.244535i
$393$		0			0
$394$	−0.961370	−	0.349910i	−0.0484331	−	0.0176282i
$395$	1.94093	−	0.706440i	0.0976587	−	0.0355449i
$396$		0			0
$397$	1.35048	+	7.65893i	0.0677785	+	0.384391i	0.999760	+	0.0218863i	$0.00696718\pi$
$397$	1.35048	+	7.65893i	0.0677785	+	0.384391i	−0.931982	+	0.362505i	$0.881922\pi$
$398$	57.1918			2.86676
$399$		0			0
$400$	−2.60678			−0.130339
$401$	−5.41570	−	30.7140i	−0.270447	−	1.53378i	−0.753062	−	0.657950i	$-0.771424\pi$
$401$	−5.41570	−	30.7140i	−0.270447	−	1.53378i	0.482615	−	0.875833i	$-0.339687\pi$
$402$		0			0
$403$	1.62850	−	0.592725i	0.0811213	−	0.0295257i
$404$	21.6422	+	7.87712i	1.07674	+	0.391901i
$405$		0			0
$406$	1.41915	−	2.45805i	0.0704314	−	0.121991i
$407$	26.6794	+	46.2101i	1.32245	+	2.29055i
$408$		0			0
$409$	−2.54836	+	14.4525i	−0.126008	+	0.714629i	0.854695	+	0.519130i	$0.173744\pi$
$409$	−2.54836	+	14.4525i	−0.126008	+	0.714629i	−0.980704	+	0.195499i	$0.937367\pi$
$410$	−5.58259	−	9.66933i	−0.275704	−	0.477534i
$411$		0			0
$412$	15.2161	+	12.7679i	0.749645	+	0.629027i
$413$	−13.6911	−	4.98316i	−0.673696	−	0.245205i
$414$		0			0
$415$	4.72188	−	3.96212i	0.231788	−	0.194493i
$416$	−0.494727	−	2.80574i	−0.0242560	−	0.137563i
$417$		0			0
$418$	12.9056	+	41.5543i	0.631232	+	2.03249i
$419$	20.6063			1.00668			0.503341	−	0.864088i	$-0.332104\pi$
$419$	20.6063			1.00668			0.503341	+	0.864088i	$0.332104\pi$
$420$		0			0
$421$	21.2034	−	17.7918i	1.03339	−	0.867119i	0.0421416	−	0.999112i	$-0.486582\pi$
$421$	21.2034	−	17.7918i	1.03339	−	0.867119i	0.991251	+	0.131993i	$0.0421375\pi$
$422$	16.5135	−	6.01041i	0.803864	−	0.292582i
$423$		0			0
$424$	−5.82828	−	4.89051i	−0.283046	−	0.237504i
$425$	−2.73903	+	4.74414i	−0.132862	+	0.230124i
$426$		0			0
$427$	0.606153	−	3.43766i	0.0293338	−	0.166360i
$428$	−0.229237	+	1.30007i	−0.0110806	+	0.0628410i
$429$		0			0
$430$	−7.69601	+	13.3299i	−0.371134	+	0.642824i
$431$	16.0072	+	13.4317i	0.771042	+	0.646981i	0.940976	−	0.338475i	$-0.109911\pi$
$431$	16.0072	+	13.4317i	0.771042	+	0.646981i	−0.169934	+	0.985455i	$0.554355\pi$
$432$		0			0
$433$	−1.80980	+	0.658712i	−0.0869732	+	0.0316557i	−0.385140	−	0.922858i	$-0.625847\pi$
$433$	−1.80980	+	0.658712i	−0.0869732	+	0.0316557i	0.298167	+	0.954514i	$0.403625\pi$
$434$	−11.6490	+	9.77467i	−0.559170	+	0.469199i
$435$		0			0
$436$	−7.04100			−0.337203
$437$	1.28825	−	26.8521i	0.0616252	−	1.28451i
$438$		0			0
$439$	6.02549	+	34.1723i	0.287581	+	1.63095i	0.695918	+	0.718121i	$0.254998\pi$
$439$	6.02549	+	34.1723i	0.287581	+	1.63095i	−0.408337	+	0.912831i	$0.633891\pi$
$440$	−4.18291	+	3.50988i	−0.199412	+	0.167327i
$441$		0			0
$442$	−3.96291	−	1.44238i	−0.188496	−	0.0686071i
$443$	−20.1629	−	16.9187i	−0.957970	−	0.803832i	0.0226514	−	0.999743i	$-0.492789\pi$
$443$	−20.1629	−	16.9187i	−0.957970	−	0.803832i	−0.980622	+	0.195911i	$0.937234\pi$
$444$		0			0
$445$	1.66007	+	2.87533i	0.0786951	+	0.136304i
$446$	−0.636160	+	3.60784i	−0.0301231	+	0.170836i
$447$		0			0
$448$	8.62698	+	14.9424i	0.407586	+	0.705960i
$449$	−6.71581	+	11.6321i	−0.316939	+	0.548954i	−0.979848	−	0.199746i	$-0.935988\pi$
$449$	−6.71581	+	11.6321i	−0.316939	+	0.548954i	0.662909	+	0.748700i	$0.269322\pi$
$450$		0			0
$451$	23.0335	+	8.38351i	1.08461	+	0.394764i
$452$	29.7559	−	10.8302i	1.39960	−	0.509412i
$453$		0			0
$454$	1.56482	+	8.87452i	0.0734405	+	0.416502i
$455$	0.536350			0.0251445
$456$		0			0
$457$	0.205882			0.00963073			0.00481537	−	0.999988i	$-0.498467\pi$
$457$	0.205882			0.00963073			0.00481537	+	0.999988i	$0.498467\pi$
$458$	−2.04515	−	11.5986i	−0.0955637	−	0.541969i
$459$		0			0
$460$	14.7610	−	5.37258i	0.688237	−	0.250498i
$461$	36.6739	+	13.3482i	1.70807	+	0.621688i	0.996704	−	0.0811290i	$-0.0258526\pi$
$461$	36.6739	+	13.3482i	1.70807	+	0.621688i	0.711371	+	0.702817i	$0.248075\pi$
$462$		0			0
$463$	3.71234	−	6.42997i	0.172527	−	0.298826i	−0.766776	−	0.641915i	$-0.778140\pi$
$463$	3.71234	−	6.42997i	0.172527	−	0.298826i	0.939303	+	0.343089i	$0.111473\pi$
$464$	1.16778	+	2.02266i	0.0542129	+	0.0938995i
$465$		0			0
$466$	10.4404	−	59.2107i	0.483644	−	2.74288i
$467$	10.9627	+	18.9880i	0.507295	+	0.878660i	0.999964	+	0.00844368i	$0.00268774\pi$
$467$	10.9627	+	18.9880i	0.507295	+	0.878660i	−0.492670	+	0.870216i	$0.663979\pi$
$468$		0			0
$469$	10.0743	+	8.45336i	0.465189	+	0.390340i
$470$	−21.7721	−	7.92438i	−1.00427	−	0.365524i
$471$		0			0
$472$	−8.76296	+	7.35300i	−0.403348	+	0.338449i
$473$	−5.86779	−	33.2779i	−0.269801	−	1.53012i
$474$		0			0
$475$	−3.87502	+	1.99605i	−0.177798	+	0.0915850i
$476$	20.7284			0.950084
$477$		0			0
$478$	−18.4918	+	15.5164i	−0.845794	+	0.709705i
$479$	−26.3861	+	9.60376i	−1.20561	+	0.438807i	−0.865180	−	0.501462i	$-0.832796\pi$
$479$	−26.3861	+	9.60376i	−1.20561	+	0.438807i	−0.340433	+	0.940269i	$0.610573\pi$
$480$		0			0
$481$	−3.15230	−	2.64510i	−0.143733	−	0.120606i
$482$	17.4471	−	30.2193i	0.794694	−	1.37645i
$483$		0			0
$484$	4.82754	−	27.3784i	0.219434	−	1.24447i
$485$	−0.819060	+	4.64512i	−0.0371916	+	0.210924i
$486$		0			0
$487$	7.06739	−	12.2411i	0.320254	−	0.554697i	−0.660286	−	0.751014i	$-0.729565\pi$
$487$	7.06739	−	12.2411i	0.320254	−	0.554697i	0.980540	+	0.196318i	$0.0628983\pi$
$488$	−2.09947	−	1.76167i	−0.0950386	−	0.0797468i
$489$		0			0
$490$	9.60392	−	3.49554i	0.433861	−	0.157912i
$491$	17.7677	−	14.9089i	0.801847	−	0.672830i	−0.146800	−	0.989166i	$-0.546897\pi$
$491$	17.7677	−	14.9089i	0.801847	−	0.672830i	0.948647	+	0.316337i	$0.102453\pi$
$492$		0			0
$493$	4.90811			0.221050
$494$	−2.03132	−	2.67100i	−0.0913933	−	0.120174i
$495$		0			0
$496$	−2.17289	−	12.3230i	−0.0975654	−	0.553321i
$497$	−7.29729	+	6.12315i	−0.327328	+	0.274661i
$498$		0			0
$499$	39.8744	+	14.5131i	1.78502	+	0.649695i	0.999525	+	0.0308294i	$0.00981485\pi$
$499$	39.8744	+	14.5131i	1.78502	+	0.649695i	0.785497	+	0.618865i	$0.212407\pi$
$500$	−1.95112	−	1.63718i	−0.0872567	−	0.0732170i
$501$		0			0
$502$	7.83092	+	13.5635i	0.349511	+	0.605371i
$503$	−1.01542	+	5.75873i	−0.0452753	+	0.256769i	−0.999041	−	0.0437817i	$-0.986059\pi$
$503$	−1.01542	+	5.75873i	−0.0452753	+	0.256769i	0.953766	+	0.300551i	$0.0971705\pi$
$504$		0			0
$505$	−4.52122	−	7.83099i	−0.201192	−	0.348474i
$506$	−30.7826	+	53.3170i	−1.36845	+	2.37023i
$507$		0			0
$508$	3.25740	+	1.18560i	0.144524	+	0.0526023i
$509$	7.84135	−	2.85402i	0.347562	−	0.126502i	−0.162340	−	0.986735i	$-0.551904\pi$
$509$	7.84135	−	2.85402i	0.347562	−	0.126502i	0.509902	+	0.860233i	$0.329682\pi$
$510$		0			0
$511$	0.738249	+	4.18682i	0.0326582	+	0.185214i
$512$	−26.6524			−1.17788
$513$		0			0
$514$	−12.8221			−0.565557
$515$	−1.35423	−	7.68019i	−0.0596743	−	0.338430i
$516$		0			0
$517$	47.7978	−	17.3970i	2.10215	−	0.765119i
$518$	33.9307	+	12.3498i	1.49083	+	0.542618i
$519$		0			0
$520$	0.210553	−	0.364689i	0.00923338	−	0.0159927i
$521$	15.4419	+	26.7461i	0.676521	+	1.17177i	0.976022	+	0.217673i	$0.0698465\pi$
$521$	15.4419	+	26.7461i	0.676521	+	1.17177i	−0.299501	+	0.954096i	$0.596820\pi$
$522$		0			0
$523$	3.97753	−	22.5577i	0.173925	−	0.986380i	−0.765452	−	0.643494i	$-0.777484\pi$
$523$	3.97753	−	22.5577i	0.173925	−	0.986380i	0.939377	−	0.342886i	$-0.111405\pi$
$524$	−24.8640	−	43.0657i	−1.08619	−	1.88134i
$525$		0			0
$526$	12.0532	+	10.1139i	0.525547	+	0.440986i
$527$	−24.7101	−	8.99375i	−1.07639	−	0.391774i
$528$		0			0
$529$	11.5188	−	9.66540i	0.500816	−	0.420235i
$530$	2.41527	+	13.6977i	0.104913	+	0.594990i
$531$		0			0
$532$	13.8723	+	8.92182i	0.601440	+	0.386810i
$533$	−1.89035			−0.0818801
$534$		0			0
$535$	0.397043	−	0.333159i	0.0171657	−	0.0144037i
$536$	9.70268	−	3.53149i	0.419092	−	0.152537i
$537$		0			0
$538$	−17.7445	−	14.8894i	−0.765019	−	0.641927i
$539$	−11.2187	+	19.4313i	−0.483222	+	0.836966i
$540$		0			0
$541$	−0.695195	+	3.94265i	−0.0298888	+	0.169508i	−0.996098	−	0.0882501i	$-0.971873\pi$
$541$	−0.695195	+	3.94265i	−0.0298888	+	0.169508i	0.966210	+	0.257758i	$0.0829837\pi$
$542$	−1.05483	+	5.98226i	−0.0453090	+	0.256960i
$543$		0			0
$544$	−21.6149	+	37.4381i	−0.926731	+	1.60515i
$545$	2.11767	+	1.77694i	0.0907110	+	0.0761156i
$546$		0			0
$547$	−39.1590	+	14.2527i	−1.67432	+	0.609402i	−0.992514	−	0.122133i	$-0.961027\pi$
$547$	−39.1590	+	14.2527i	−1.67432	+	0.609402i	−0.681804	+	0.731535i	$0.738804\pi$
$548$	−20.8387	+	17.4858i	−0.890186	+	0.746954i
$549$		0			0
$550$	9.98238			0.425650
$551$	3.28471	+	2.11253i	0.139933	+	0.0899966i
$552$		0			0
$553$	0.532848	+	3.02193i	0.0226590	+	0.128506i
$554$	26.3715	−	22.1283i	1.12042	−	0.940142i
$555$		0			0
$556$	17.2115	+	6.26446i	0.729929	+	0.265672i
$557$	2.43219	+	2.04085i	0.103055	+	0.0864735i	0.692859	−	0.721073i	$-0.256351\pi$
$557$	2.43219	+	2.04085i	0.103055	+	0.0864735i	−0.589804	+	0.807546i	$0.700795\pi$
$558$		0			0
$559$	1.30299	+	2.25685i	0.0551107	+	0.0954546i
$560$	0.672486	−	3.81386i	0.0284177	−	0.161165i
$561$		0			0
$562$	−3.42891	−	5.93905i	−0.144640	−	0.250524i
$563$	7.20295	−	12.4759i	0.303568	−	0.525796i	−0.673373	−	0.739303i	$-0.735155\pi$
$563$	7.20295	−	12.4759i	0.303568	−	0.525796i	0.976942	+	0.213507i	$0.0684886\pi$
$564$		0			0
$565$	−11.6827	−	4.25215i	−0.491494	−	0.178889i
$566$	25.7972	−	9.38940i	1.08434	−	0.394666i
$567$		0			0
$568$	1.29874	+	7.36552i	0.0544939	+	0.309050i
$569$	−24.9795			−1.04719			−0.523597	−	0.851966i	$-0.675410\pi$
$569$	−24.9795			−1.04719			−0.523597	+	0.851966i	$0.675410\pi$
$570$		0			0
$571$	13.1086			0.548579			0.274289	−	0.961647i	$-0.411557\pi$
$571$	13.1086			0.548579			0.274289	+	0.961647i	$0.411557\pi$
$572$	0.747499	+	4.23928i	0.0312545	+	0.177253i
$573$		0			0
$574$	15.5869	−	5.67318i	0.650586	−	0.236794i
$575$	−5.79545	−	2.10937i	−0.241687	−	0.0879669i
$576$		0			0
$577$	−4.12748	+	7.14901i	−0.171829	+	0.297617i	−0.939059	−	0.343755i	$-0.888301\pi$
$577$	−4.12748	+	7.14901i	−0.171829	+	0.297617i	0.767230	+	0.641372i	$0.221634\pi$
$578$	13.8701	+	24.0238i	0.576921	+	0.999257i
$579$		0			0
$580$	−0.396266	+	2.24734i	−0.0164541	+	0.0933157i
$581$	4.57867	+	7.93050i	0.189955	+	0.329012i
$582$		0			0
$583$	−23.3915	−	19.6278i	−0.968778	−	0.812901i
$584$	3.13662	+	1.14164i	0.129794	+	0.0472413i
$585$		0			0
$586$	−50.3295	+	42.2315i	−2.07909	+	1.74457i
$587$	1.37287	+	7.78595i	0.0566646	+	0.321361i	0.999943	−	0.0106409i	$-0.00338717\pi$
$587$	1.37287	+	7.78595i	0.0566646	+	0.321361i	−0.943279	+	0.332002i	$0.892276\pi$
$588$		0			0
$589$	−12.6660	−	16.6546i	−0.521892	−	0.686241i
$590$	20.9125			0.860955
$591$		0			0
$592$	−22.7611	+	19.0988i	−0.935475	+	0.784957i
$593$	−3.34124	+	1.21611i	−0.137208	+	0.0499398i	−0.409712	−	0.912215i	$-0.634371\pi$
$593$	−3.34124	+	1.21611i	−0.137208	+	0.0499398i	0.272503	+	0.962155i	$0.412148\pi$
$594$		0			0
$595$	−6.23433	−	5.23122i	−0.255583	−	0.214459i
$596$	5.40891	−	9.36850i	0.221557	−	0.383749i
$597$		0			0
$598$	0.824467	−	4.67579i	0.0337150	−	0.191207i
$599$	−1.91987	+	10.8881i	−0.0784437	+	0.444876i	0.920136	+	0.391599i	$0.128078\pi$
$599$	−1.91987	+	10.8881i	−0.0784437	+	0.444876i	−0.998580	+	0.0532774i	$0.983033\pi$
$600$		0			0
$601$	22.7722	−	39.4426i	0.928898	−	1.60890i	0.143728	−	0.989617i	$-0.454091\pi$
$601$	22.7722	−	39.4426i	0.928898	−	1.60890i	0.785170	−	0.619281i	$-0.212576\pi$
$602$	−17.5170	−	14.6985i	−0.713938	−	0.599065i
$603$		0			0
$604$	46.7606	−	17.0195i	1.90266	−	0.692512i
$605$	−8.36143	+	7.01607i	−0.339940	+	0.285244i
$606$		0			0
$607$	36.4498			1.47945			0.739727	−	0.672907i	$-0.234955\pi$
$607$	36.4498			1.47945			0.739727	+	0.672907i	$0.234955\pi$
$608$	−30.5795	+	15.7517i	−1.24016	+	0.638817i
$609$		0			0
$610$	0.870032	+	4.93420i	0.0352266	+	0.199780i
$611$	−3.00500	+	2.52149i	−0.121569	+	0.102009i
$612$		0			0
$613$	−6.33713	−	2.30653i	−0.255954	−	0.0931597i	0.210856	−	0.977517i	$-0.432375\pi$
$613$	−6.33713	−	2.30653i	−0.255954	−	0.0931597i	−0.466811	+	0.884357i	$0.654597\pi$
$614$	−26.7586	−	22.4531i	−1.07989	−	0.906135i
$615$		0			0
$616$	−4.05606	−	7.02529i	−0.163423	−	0.283057i
$617$	−4.38423	+	24.8642i	−0.176503	+	1.00100i	0.759893	+	0.650049i	$0.225252\pi$
$617$	−4.38423	+	24.8642i	−0.176503	+	1.00100i	−0.936395	+	0.350947i	$0.885860\pi$
$618$		0			0
$619$	−11.1611	−	19.3317i	−0.448604	−	0.777006i	0.549691	−	0.835368i	$-0.314745\pi$
$619$	−11.1611	−	19.3317i	−0.448604	−	0.777006i	−0.998295	+	0.0583624i	$0.981412\pi$
$620$	6.11311	−	10.5882i	0.245508	−	0.425233i
$621$		0			0
$622$	−49.6427	−	18.0685i	−1.99049	−	0.724480i
$623$	−4.63503	+	1.68701i	−0.185699	+	0.0675887i
$624$		0			0
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	−21.9066			−0.875564
$627$		0			0
$628$	0.729519			0.0291110
$629$	10.8426	+	61.4912i	0.432321	+	2.45182i
$630$		0			0
$631$	−3.32590	+	1.21053i	−0.132402	+	0.0481904i	−0.407371	−	0.913263i	$-0.633555\pi$
$631$	−3.32590	+	1.21053i	−0.132402	+	0.0481904i	0.274969	+	0.961453i	$0.411332\pi$
$632$	2.26393	+	0.824003i	0.0900543	+	0.0327771i
$633$		0			0
$634$	−6.47848	+	11.2211i	−0.257293	+	0.445645i
$635$	−0.680496	−	1.17865i	−0.0270047	−	0.0467734i
$636$		0			0
$637$	0.300476	−	1.70408i	0.0119053	−	0.0675182i
$638$	−4.47189	−	7.74555i	−0.177044	−	0.306649i
$639$		0			0
$640$	−6.88085	−	5.77372i	−0.271990	−	0.228226i
$641$	24.7767	+	9.01799i	0.978622	+	0.356189i	0.781304	−	0.624150i	$-0.214555\pi$
$641$	24.7767	+	9.01799i	0.978622	+	0.356189i	0.197318	+	0.980340i	$0.436777\pi$
$642$		0			0
$643$	−11.2983	+	9.48043i	−0.445563	+	0.373872i	−0.837786	−	0.545998i	$-0.816150\pi$
$643$	−11.2983	+	9.48043i	−0.445563	+	0.373872i	0.392223	+	0.919870i	$0.371706\pi$
$644$	4.05238	+	22.9822i	0.159686	+	0.905626i
$645$		0			0
$646$	−2.43999	+	50.8589i	−0.0960000	+	2.00102i
$647$	−5.04555			−0.198361			−0.0991804	−	0.995069i	$-0.531622\pi$
$647$	−5.04555			−0.198361			−0.0991804	+	0.995069i	$0.531622\pi$
$648$		0			0
$649$	−35.1697	+	29.5109i	−1.38053	+	1.15840i
$650$	−0.723415	+	0.263302i	−0.0283747	+	0.0103275i
$651$		0			0
$652$	−40.2429	−	33.7678i	−1.57603	−	1.32245i
$653$	−22.3362	+	38.6875i	−0.874084	+	1.51396i	−0.0163488	+	0.999866i	$0.505204\pi$
$653$	−22.3362	+	38.6875i	−0.874084	+	1.51396i	−0.857735	+	0.514092i	$0.828129\pi$
$654$		0			0
$655$	−3.39033	+	19.2275i	−0.132471	+	0.751281i
$656$	−2.37016	+	13.4418i	−0.0925391	+	0.524815i
$657$		0			0
$658$	17.2105	−	29.8094i	0.670934	−	1.16209i
$659$	−22.5147	−	18.8921i	−0.877049	−	0.735931i	0.0885212	−	0.996074i	$-0.471786\pi$
$659$	−22.5147	−	18.8921i	−0.877049	−	0.735931i	−0.965570	+	0.260143i	$0.916230\pi$
$660$		0			0
$661$	19.0049	−	6.91721i	0.739204	−	0.269048i	0.0551486	−	0.998478i	$-0.482437\pi$
$661$	19.0049	−	6.91721i	0.739204	−	0.269048i	0.684056	+	0.729430i	$0.260215\pi$
$662$	−19.2931	+	16.1889i	−0.749849	+	0.629198i
$663$		0			0
$664$	7.18975			0.279016
$665$	−1.92067	−	6.18430i	−0.0744803	−	0.239817i
$666$		0			0
$667$	0.959531	+	5.44177i	0.0371532	+	0.210706i
$668$	−21.1771	+	17.7697i	−0.819367	+	0.687531i
$669$		0			0
$670$	−17.7379	−	6.45605i	−0.685273	−	0.249419i
$671$	−8.42612	−	7.07036i	−0.325287	−	0.272948i
$672$		0			0
$673$	13.8331	+	23.9597i	0.533227	+	0.923577i	0.999247	+	0.0388026i	$0.0123543\pi$
$673$	13.8331	+	23.9597i	0.533227	+	0.923577i	−0.466019	+	0.884774i	$0.654312\pi$
$674$	−5.63809	+	31.9752i	−0.217171	+	1.23164i
$675$		0			0
$676$	16.3895	+	28.3875i	0.630367	+	1.09183i
$677$	15.8370	−	27.4305i	0.608665	−	1.05424i	−0.382796	−	0.923833i	$-0.625039\pi$
$677$	15.8370	−	27.4305i	0.608665	−	1.05424i	0.991461	−	0.130405i	$-0.0416279\pi$
$678$		0			0
$679$	−6.58477	−	2.39666i	−0.252700	−	0.0919754i
$680$	−6.00435	+	2.18540i	−0.230256	+	0.0838064i
$681$		0			0
$682$	8.32083	+	47.1898i	0.318621	+	1.80699i
$683$	4.75181			0.181823			0.0909114	−	0.995859i	$-0.471022\pi$
$683$	4.75181			0.181823			0.0909114	+	0.995859i	$0.471022\pi$
$684$		0			0
$685$	10.6804			0.408077
$686$	6.48729	+	36.7913i	0.247686	+	1.40470i
$687$		0			0
$688$	17.6816	−	6.43559i	0.674106	−	0.245355i
$689$	2.21288	+	0.805423i	0.0843040	+	0.0306842i
$690$		0			0
$691$	0.211770	−	0.366797i	0.00805613	−	0.0139536i	−0.861969	−	0.506961i	$-0.830769\pi$
$691$	0.211770	−	0.366797i	0.00805613	−	0.0139536i	0.870025	+	0.493007i	$0.164102\pi$
$692$	−22.3486	−	38.7090i	−0.849568	−	1.47149i
$693$		0			0
$694$	−11.1753	+	63.3781i	−0.424208	+	2.40580i
$695$	−3.59561	−	6.22778i	−0.136389	−	0.236233i
$696$		0			0
$697$	21.9727	+	18.4373i	0.832275	+	0.698362i
$698$	−5.48575	−	1.99665i	−0.207639	−	0.0755743i
$699$		0			0
$700$	2.89863	−	2.43224i	0.109558	−	0.0919300i
$701$	−1.37980	−	7.82526i	−0.0521145	−	0.295556i	0.947600	−	0.319460i	$-0.103501\pi$
$701$	−1.37980	−	7.82526i	−0.0521145	−	0.295556i	−0.999714	+	0.0239040i	$0.992390\pi$
$702$		0			0
$703$	−19.2105	+	45.8193i	−0.724538	+	1.72811i
$704$	54.3689			2.04911
$705$		0			0
$706$	−7.52915	+	6.31771i	−0.283363	+	0.237770i
$707$	12.6235	−	4.59459i	0.474757	−	0.172797i
$708$		0			0
$709$	8.99170	+	7.54493i	0.337690	+	0.283356i	0.795825	−	0.605527i	$-0.207038\pi$
$709$	8.99170	+	7.54493i	0.337690	+	0.283356i	−0.458134	+	0.888883i	$0.651482\pi$
$710$	6.83646	−	11.8411i	0.256568	−	0.444388i
$711$		0			0
$712$	−0.672483	+	3.81384i	−0.0252024	+	0.142930i
$713$	5.14084	−	29.1552i	0.192526	−	1.09187i
$714$		0			0
$715$	0.845046	−	1.46366i	0.0316029	−	0.0547379i
$716$	−29.3924	−	24.6632i	−1.09845	−	0.921707i
$717$		0			0
$718$	−24.7264	+	8.99969i	−0.922783	+	0.335865i
$719$	38.6452	−	32.4272i	1.44122	−	1.20933i	0.502536	−	0.864556i	$-0.332400\pi$
$719$	38.6452	−	32.4272i	1.44122	−	1.20933i	0.938686	−	0.344773i	$-0.112044\pi$
$720$		0			0
$721$	11.5859			0.431481
$722$	−23.5234	+	32.9866i	−0.875450	+	1.22764i
$723$		0			0
$724$	6.59907	+	37.4252i	0.245252	+	1.39090i
$725$	0.686343	−	0.575910i	0.0254902	−	0.0213888i
$726$		0			0
$727$	−24.4935	−	8.91490i	−0.908414	−	0.330636i	−0.154794	−	0.987947i	$-0.549471\pi$
$727$	−24.4935	−	8.91490i	−0.908414	−	0.330636i	−0.753619	+	0.657311i	$0.771694\pi$
$728$	0.479243	+	0.402132i	0.0177619	+	0.0149040i
$729$		0			0
$730$	−3.05110	−	5.28466i	−0.112926	−	0.195594i
$731$	6.86641	−	38.9413i	0.253963	−	1.44030i
$732$		0			0
$733$	−8.54306	−	14.7970i	−0.315545	−	0.546540i	0.664008	−	0.747725i	$-0.268854\pi$
$733$	−8.54306	−	14.7970i	−0.315545	−	0.546540i	−0.979553	+	0.201185i	$0.935521\pi$
$734$	−1.74441	+	3.02141i	−0.0643873	+	0.111522i
$735$		0			0
$736$	−45.7345	−	16.6460i	−1.68580	−	0.613580i
$737$	38.9412	−	14.1734i	1.43442	−	0.522086i
$738$		0			0
$739$	−4.27432	−	24.2409i	−0.157233	−	0.891715i	−0.956715	−	0.291025i	$-0.906004\pi$
$739$	−4.27432	−	24.2409i	−0.157233	−	0.891715i	0.799482	−	0.600690i	$-0.205107\pi$
$740$	−29.0312			−1.06721
$741$		0			0
$742$	−20.6636			−0.758583
$743$	1.33186	+	7.55333i	0.0488610	+	0.277105i	0.999443	−	0.0333687i	$-0.0106236\pi$
$743$	1.33186	+	7.55333i	0.0488610	+	0.277105i	−0.950582	+	0.310473i	$0.899512\pi$
$744$		0			0
$745$	−3.99113	+	1.45265i	−0.146224	+	0.0532210i
$746$	−29.5731	−	10.7637i	−1.08275	−	0.394089i
$747$		0			0
$748$	32.6586	−	56.5664i	1.19412	−	2.06827i
$749$	0.385002	+	0.666843i	0.0140677	+	0.0243659i
$750$		0			0
$751$	3.65755	−	20.7430i	0.133466	−	0.756923i	−0.842450	−	0.538775i	$-0.818887\pi$
$751$	3.65755	−	20.7430i	0.133466	−	0.756923i	0.975916	−	0.218148i	$-0.0700017\pi$
$752$	14.1620	+	24.5293i	0.516436	+	0.894493i
$753$		0			0
$754$	0.528376	+	0.443360i	0.0192423	+	0.0161462i
$755$	−18.3591	−	6.68215i	−0.668154	−	0.243188i
$756$		0			0
$757$	3.29957	−	2.76867i	0.119925	−	0.100629i	−0.580853	−	0.814009i	$-0.697281\pi$
$757$	3.29957	−	2.76867i	0.119925	−	0.100629i	0.700778	+	0.713379i	$0.252836\pi$
$758$	0.651197	+	3.69312i	0.0236525	+	0.134140i
$759$		0			0
$760$	−4.95899	−	1.12180i	−0.179881	−	0.0406921i
$761$	1.11318			0.0403529			0.0201764	−	0.999796i	$-0.493577\pi$
$761$	1.11318			0.0403529			0.0201764	+	0.999796i	$0.493577\pi$
$762$		0			0
$763$	−3.14606	+	2.63986i	−0.113895	+	0.0955694i
$764$	−0.0162238	+	0.00590497i	−0.000586956	+	0.000213634i
$765$		0			0
$766$	−13.8824	−	11.6487i	−0.501591	−	0.420885i
$767$	1.77032	−	3.06629i	0.0639227	−	0.110717i
$768$		0			0
$769$	1.71410	−	9.72113i	0.0618119	−	0.350553i	−0.938178	−	0.346152i	$-0.887488\pi$
$769$	1.71410	−	9.72113i	0.0618119	−	0.350553i	0.999990	−	0.00440066i	$-0.00140078\pi$
$770$	−2.57521	+	14.6048i	−0.0928043	+	0.526319i
$771$		0			0
$772$	−17.4804	+	30.2769i	−0.629133	+	1.08969i
$773$	13.0788	+	10.9744i	0.470410	+	0.394721i	0.846944	−	0.531682i	$-0.178440\pi$
$773$	13.0788	+	10.9744i	0.470410	+	0.394721i	−0.376534	+	0.926403i	$0.622884\pi$
$774$		0			0
$775$	−4.51075	+	1.64178i	−0.162031	+	0.0589744i
$776$	−4.21457	+	3.53644i	−0.151294	+	0.126951i
$777$		0			0
$778$	−72.3761			−2.59481
$779$	6.76933	+	21.7964i	0.242537	+	0.780936i
$780$		0			0
$781$	5.21243	+	29.5611i	0.186515	+	1.05778i
$782$	−55.1880	+	46.3082i	−1.97352	+	1.65598i
$783$		0			0
$784$	−11.7406	−	4.27323i	−0.419307	−	0.152615i
$785$	−0.219412	−	0.184109i	−0.00783116	−	0.00657112i
$786$		0			0
$787$	5.82825	+	10.0948i	0.207755	+	0.359842i	0.951007	−	0.309170i	$-0.100051\pi$
$787$	5.82825	+	10.0948i	0.207755	+	0.359842i	−0.743252	+	0.669011i	$0.766718\pi$
$788$	−0.212198	+	1.20344i	−0.00755925	+	0.0428707i
$789$		0			0
$790$	−2.20220	−	3.81432i	−0.0783507	−	0.135707i
$791$	9.23498	−	15.9955i	0.328358	−	0.568733i
$792$		0			0
$793$	0.797127	+	0.290130i	0.0283068	+	0.0103028i
$794$	15.5835	−	5.67194i	0.553038	−	0.201289i
$795$		0			0
$796$	−11.8624	−	67.2747i	−0.420450	−	2.38449i
$797$	29.8609			1.05773			0.528864	−	0.848707i	$-0.322618\pi$
$797$	29.8609			1.05773			0.528864	+	0.848707i	$0.322618\pi$
$798$		0			0
$799$	59.5220			2.10574
$800$	1.37034	+	7.77156i	0.0484487	+	0.274766i
$801$		0			0
$802$	−62.4932	+	22.7457i	−2.20671	+	0.803178i
$803$	12.5887	+	4.58191i	0.444245	+	0.161692i
$804$		0			0
$805$	4.58121	−	7.93490i	0.161467	−	0.279668i
$806$	−1.84771	−	3.20033i	−0.0650829	−	0.112727i
$807$		0			0
$808$	1.83151	−	10.3870i	0.0644323	−	0.365414i
$809$	−19.1756	−	33.2132i	−0.674180	−	1.16771i	−0.976708	−	0.214573i	$-0.931164\pi$
$809$	−19.1756	−	33.2132i	−0.674180	−	1.16771i	0.302528	−	0.953140i	$-0.402169\pi$
$810$		0			0
$811$	8.55127	+	7.17537i	0.300276	+	0.251961i	0.780459	−	0.625207i	$-0.214985\pi$
$811$	8.55127	+	7.17537i	0.300276	+	0.251961i	−0.480183	+	0.877168i	$0.659430\pi$
$812$	−3.18575	−	1.15952i	−0.111798	−	0.0406911i
$813$		0			0
$814$	87.1612	−	73.1369i	3.05500	−	2.56345i
$815$	3.58159	+	20.3122i	0.125458	+	0.711505i
$816$		0			0
$817$	21.3562	−	23.1057i	0.747160	−	0.808367i
$818$	31.2935			1.09415
$819$		0			0
$820$	−10.2161	+	8.57235i	−0.356763	+	0.299360i
$821$	7.18934	−	2.61671i	0.250910	−	0.0913236i	−0.213504	−	0.976942i	$-0.568487\pi$
$821$	7.18934	−	2.61671i	0.250910	−	0.0913236i	0.464413	+	0.885619i	$0.346265\pi$
$822$		0			0
$823$	25.4494	+	21.3546i	0.887110	+	0.744373i	0.967628	−	0.252380i	$-0.0812132\pi$
$823$	25.4494	+	21.3546i	0.887110	+	0.744373i	−0.0805185	+	0.996753i	$0.525658\pi$
$824$	4.54825	−	7.87779i	0.158446	−	0.274436i
$825$		0			0
$826$	−5.39493	+	30.5962i	−0.187714	+	1.06458i
$827$	0.591681	−	3.35559i	0.0205748	−	0.116685i	−0.972791	−	0.231686i	$-0.925576\pi$
$827$	0.591681	−	3.35559i	0.0205748	−	0.116685i	0.993365	+	0.115001i	$0.0366870\pi$
$828$		0			0
$829$	−2.21217	+	3.83160i	−0.0768320	+	0.133077i	−0.901881	−	0.431984i	$-0.857814\pi$
$829$	−2.21217	+	3.83160i	−0.0768320	+	0.133077i	0.825049	+	0.565060i	$0.191147\pi$
$830$	−10.0688	−	8.44872i	−0.349493	−	0.293259i
$831$		0			0
$832$	−3.94007	+	1.43407i	−0.136597	+	0.0497174i
$833$	−20.1132	+	16.8770i	−0.696880	+	0.584752i
$834$		0			0
$835$	10.8538			0.375613
$836$	46.2035	−	23.7998i	1.59798	−	0.823132i
$837$		0			0
$838$	−7.63013	−	43.2726i	−0.263579	−	1.49483i
$839$	18.2406	−	15.3057i	0.629736	−	0.528411i	−0.271111	−	0.962548i	$-0.587391\pi$
$839$	18.2406	−	15.3057i	0.629736	−	0.528411i	0.900847	+	0.434137i	$0.142947\pi$
$840$		0			0
$841$	26.4968	+	9.64403i	0.913681	+	0.332553i
$842$	−45.2136	−	37.9387i	−1.55816	−	1.30745i
$843$		0			0
$844$	−10.4952	−	18.1782i	−0.361259	−	0.625719i
$845$	2.23479	−	12.6741i	0.0768792	−	0.436004i
$846$		0			0
$847$	−8.10785	−	14.0432i	−0.278589	−	0.482530i
$848$	8.50173	−	14.7254i	0.291951	−	0.505673i
$849$		0			0
$850$	10.9768	+	3.99522i	0.376501	+	0.137035i
$851$	−66.0575	+	24.0430i	−2.26442	+	0.824183i
$852$		0			0
$853$	−0.769903	−	4.36634i	−0.0263610	−	0.149501i	0.968786	−	0.247898i	$-0.0797396\pi$
$853$	−0.769903	−	4.36634i	−0.0263610	−	0.149501i	−0.995147	+	0.0983970i	$0.968629\pi$
$854$	−7.44345			−0.254710
$855$		0			0
$856$	0.604557			0.0206633
$857$	−4.68808	−	26.5874i	−0.160142	−	0.908208i	−0.953933	−	0.300019i	$-0.903007\pi$
$857$	−4.68808	−	26.5874i	−0.160142	−	0.908208i	0.793792	−	0.608190i	$-0.208104\pi$
$858$		0			0
$859$	12.8850	−	4.68976i	0.439631	−	0.160013i	−0.112715	−	0.993627i	$-0.535955\pi$
$859$	12.8850	−	4.68976i	0.439631	−	0.160013i	0.552346	+	0.833615i	$0.313733\pi$
$860$	17.2762	+	6.28802i	0.589114	+	0.214420i
$861$		0			0
$862$	22.2790	−	38.5883i	0.758825	−	1.31432i
$863$	26.2240	+	45.4213i	0.892676	+	1.54616i	0.836655	+	0.547730i	$0.184508\pi$
$863$	26.2240	+	45.4213i	0.892676	+	1.54616i	0.0560208	+	0.998430i	$0.482159\pi$
$864$		0			0
$865$	−3.04734	+	17.2823i	−0.103613	+	0.587618i
$866$	2.05341	+	3.55662i	0.0697778	+	0.120859i
$867$		0			0
$868$	13.9141	+	11.6753i	0.472276	+	0.396286i
$869$	9.08617	+	3.30710i	0.308227	+	0.112186i
$870$		0			0
$871$	−2.44819	+	2.05428i	−0.0829538	+	0.0696065i
$872$	0.559923	+	3.17548i	0.0189614	+	0.107535i
$873$		0			0
$874$	−56.8658	+	7.23758i	−1.92352	+	0.244815i
$875$	−1.48562			−0.0502233
$876$		0			0
$877$	−31.2742	+	26.2422i	−1.05606	+	0.886136i	−0.993717	−	0.111919i	$-0.964300\pi$
$877$	−31.2742	+	26.2422i	−1.05606	+	0.886136i	−0.0623382	+	0.998055i	$0.519856\pi$
$878$	69.5298	−	25.3068i	2.34652	−	0.854062i
$879$		0			0
$880$	−9.34823	−	7.84410i	−0.315129	−	0.264424i
$881$	−23.8807	+	41.3627i	−0.804563	+	1.39354i	0.112023	+	0.993706i	$0.464267\pi$
$881$	−23.8807	+	41.3627i	−0.804563	+	1.39354i	−0.916586	+	0.399838i	$0.869066\pi$
$882$		0			0
$883$	5.57488	−	31.6167i	0.187610	−	1.06399i	−0.734946	−	0.678125i	$-0.762793\pi$
$883$	5.57488	−	31.6167i	0.187610	−	1.06399i	0.922556	−	0.385863i	$-0.126096\pi$
$884$	−0.874713	+	4.96074i	−0.0294198	+	0.166848i
$885$		0			0
$886$	−28.0629	+	48.6064i	−0.942792	+	1.63296i
$887$	6.75510	+	5.66820i	0.226814	+	0.190319i	0.749112	−	0.662444i	$-0.230481\pi$
$887$	6.75510	+	5.66820i	0.226814	+	0.190319i	−0.522298	+	0.852763i	$0.674925\pi$
$888$		0			0
$889$	1.89999	−	0.691539i	0.0637235	−	0.0231935i
$890$	5.42343	−	4.55080i	0.181794	−	0.152543i
$891$		0			0
$892$	4.37586			0.146515
$893$	39.8346	+	25.6192i	1.33301	+	0.857314i
$894$		0			0
$895$	2.61591	+	14.8355i	0.0874401	+	0.495898i
$896$	10.2224	−	8.57759i	0.341505	−	0.286557i
$897$		0			0
$898$	26.9139	+	9.79587i	0.898130	+	0.326892i
$899$	3.29461	+	2.76451i	0.109881	+	0.0922014i
$900$		0			0
$901$	−17.8661	−	30.9450i	−0.595206	−	1.03093i
$902$	9.07627	−	51.4741i	0.302207	−	1.71390i
$903$		0			0
$904$	−7.25071	−	12.5586i	−0.241155	−	0.417693i
$905$	7.46024	−	12.9215i	0.247987	−	0.429525i
$906$		0			0
$907$	−9.71693	−	3.53667i	−0.322645	−	0.117433i	0.175620	−	0.984458i	$-0.443807\pi$
$907$	−9.71693	−	3.53667i	−0.322645	−	0.117433i	−0.498265	+	0.867025i	$0.666029\pi$
$908$	10.1145	−	3.68139i	0.335663	−	0.122171i
$909$		0			0
$910$	−0.198601	−	1.12632i	−0.00658356	−	0.0373372i
$911$	−5.25941			−0.174252			−0.0871260	−	0.996197i	$-0.527768\pi$
$911$	−5.25941			−0.174252			−0.0871260	+	0.996197i	$0.527768\pi$
$912$		0			0
$913$	28.8557			0.954985
$914$	−0.0762343	−	0.432346i	−0.00252161	−	0.0143007i
$915$		0			0
$916$	−13.2193	+	4.81143i	−0.436778	+	0.158974i
$917$	−27.2563	−	9.92047i	−0.900081	−	0.327603i
$918$		0			0
$919$	−0.101184	+	0.175255i	−0.00333774	+	0.00578114i	−0.867689	−	0.497107i	$-0.834396\pi$
$919$	−0.101184	+	0.175255i	−0.00333774	+	0.00578114i	0.864352	+	0.502888i	$0.167729\pi$
$920$	−3.59687	−	6.22996i	−0.118585	−	0.205396i
$921$		0			0
$922$	14.4512	−	81.9569i	0.475925	−	2.69911i
$923$	−1.15746	−	2.00479i	−0.0380984	−	0.0659883i
$924$		0			0
$925$	8.73151	+	7.32660i	0.287090	+	0.240897i
$926$	−14.8774	−	5.41492i	−0.488901	−	0.177945i
$927$		0			0
$928$	5.41624	−	4.54477i	0.177797	−	0.149189i
$929$	−3.23698	−	18.3578i	−0.106202	−	0.602301i	−0.990733	−	0.135821i	$-0.956633\pi$
$929$	−3.23698	−	18.3578i	−0.106202	−	0.602301i	0.884532	−	0.466480i	$-0.154478\pi$
$930$		0			0
$931$	−20.7247	+	2.63773i	−0.679223	+	0.0864480i
$932$	−71.8151			−2.35238
$933$		0			0
$934$	35.8150	−	30.0524i	1.17190	−	0.983344i
$935$	−24.0982	+	8.77101i	−0.788094	+	0.286843i
$936$		0			0
$937$	−38.6935	−	32.4677i	−1.26406	−	1.06067i	−0.995237	−	0.0974836i	$-0.968921\pi$
$937$	−38.6935	−	32.4677i	−1.26406	−	1.06067i	−0.268824	−	0.963189i	$-0.586635\pi$
$938$	14.0215	−	24.2859i	0.457818	−	0.792964i
$939$		0			0
$940$	−4.80564	+	27.2541i	−0.156743	+	0.888931i
$941$	2.87903	−	16.3278i	0.0938538	−	0.532271i	−0.901239	−	0.433323i	$-0.857341\pi$
$941$	2.87903	−	16.3278i	0.0938538	−	0.532271i	0.995093	−	0.0989484i	$-0.0315479\pi$
$942$		0			0
$943$	−16.1463	+	27.9663i	−0.525797	+	0.910708i
$944$	−19.5840	−	16.4329i	−0.637405	−	0.534847i
$945$		0			0
$946$	−67.7100	+	24.6444i	−2.20144	+	0.801259i
$947$	−28.6765	+	24.0625i	−0.931862	+	0.781925i	−0.976151	−	0.217094i	$-0.930342\pi$
$947$	−28.6765	+	24.0625i	−0.931862	+	0.781925i	0.0442887	+	0.999019i	$0.485898\pi$
$948$		0			0
$949$	−1.03315			−0.0335374
$950$	5.62651	+	7.39835i	0.182548	+	0.240034i
$951$		0			0
$952$	−1.64839	−	9.34847i	−0.0534245	−	0.302986i
$953$	−32.5326	+	27.2981i	−1.05384	+	0.884273i	−0.993492	−	0.113905i	$-0.963664\pi$
$953$	−32.5326	+	27.2981i	−1.05384	+	0.884273i	−0.0603438	+	0.998178i	$0.519220\pi$
$954$		0			0
$955$	0.00636975	+	0.00231840i	0.000206120	+	7.50216e-5i
$956$	22.0874	+	18.5336i	0.714359	+	0.599418i
$957$		0			0
$958$	29.9380	+	51.8541i	0.967252	+	1.67533i
$959$	−2.75529	+	15.6260i	−0.0889728	+	0.504590i
$960$		0			0
$961$	3.97887	+	6.89160i	0.128351	+	0.222310i
$962$	−4.38740	+	7.59919i	−0.141455	+	0.245008i
$963$		0			0
$964$	−39.1657	−	14.2552i	−1.26144	−	0.459128i
$965$	12.8984	−	4.69465i	0.415216	−	0.151126i
$966$		0			0
$967$	2.81797	+	15.9815i	0.0906197	+	0.513930i	0.996002	+	0.0893324i	$0.0284733\pi$
$967$	2.81797	+	15.9815i	0.0906197	+	0.513930i	−0.905382	+	0.424598i	$0.860416\pi$
$968$	−12.7315			−0.409206
$969$		0			0
$970$	10.0579			0.322940
$971$	3.05833	+	17.3447i	0.0981465	+	0.556617i	0.993738	+	0.111738i	$0.0356419\pi$
$971$	3.05833	+	17.3447i	0.0981465	+	0.556617i	−0.895591	+	0.444878i	$0.853247\pi$
$972$		0			0
$973$	10.0392	−	3.65396i	0.321841	−	0.117140i
$974$	−28.3229	−	10.3087i	−0.907524	−	0.330312i
$975$		0			0
$976$	3.06250	−	5.30441i	0.0980283	−	0.169790i
$977$	0.0604375	+	0.104681i	0.00193357	+	0.00334903i	0.866991	−	0.498325i	$-0.166051\pi$
$977$	0.0604375	+	0.104681i	0.00193357	+	0.00334903i	−0.865057	+	0.501674i	$0.832718\pi$
$978$		0			0
$979$	−2.69898	+	15.3067i	−0.0862597	+	0.489203i
$980$	−6.10379	−	10.5721i	−0.194978	−	0.337713i
$981$		0			0
$982$	−37.8874	−	31.7913i	−1.20904	−	1.01450i
$983$	21.3108	+	7.75648i	0.679708	+	0.247393i	0.658722	−	0.752386i	$-0.271097\pi$
$983$	21.3108	+	7.75648i	0.679708	+	0.247393i	0.0209857	+	0.999780i	$0.493320\pi$
$984$		0			0
$985$	0.367533	−	0.308397i	0.0117106	−	0.00982633i
$986$	−1.81738	−	10.3069i	−0.0578773	−	0.328239i
$987$		0			0
$988$	−2.72058	+	2.94344i	−0.0865530	+	0.0936434i
$989$	44.5179			1.41559
$990$		0			0
$991$	−41.1874	+	34.5603i	−1.30836	+	1.09784i	−0.319725	+	0.947510i	$0.603591\pi$
$991$	−41.1874	+	34.5603i	−1.30836	+	1.09784i	−0.988635	+	0.150334i	$0.951965\pi$
$992$	−35.5963	+	12.9560i	−1.13018	+	0.411353i
$993$		0			0
$994$	15.5605	+	13.0568i	0.493550	+	0.414137i
$995$	−13.4104	+	23.2274i	−0.425137	+	0.736360i
$996$		0			0
$997$	6.38045	−	36.1853i	0.202071	−	1.14600i	−0.699912	−	0.714229i	$-0.746777\pi$
$997$	6.38045	−	36.1853i	0.202071	−	1.14600i	0.901983	−	0.431772i	$-0.142111\pi$
$998$	15.7123	−	89.1091i	0.497365	−	2.82070i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.bs.c.541.1		18
3.2	odd	2		95.2.k.a.66.3	yes	18
15.2	even	4		475.2.u.b.199.2		36
15.8	even	4		475.2.u.b.199.5		36
15.14	odd	2		475.2.l.c.351.1		18
19.17	even	9	inner	855.2.bs.c.226.1		18
57.17	odd	18		95.2.k.a.36.3	✓	18
57.32	even	18		1805.2.a.s.1.3		9
57.44	odd	18		1805.2.a.v.1.7		9
285.17	even	36		475.2.u.b.74.5		36
285.44	odd	18		9025.2.a.cc.1.3		9
285.74	odd	18		475.2.l.c.226.1		18
285.89	even	18		9025.2.a.cf.1.7		9
285.188	even	36		475.2.u.b.74.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.36.3	✓	18	57.17	odd	18
95.2.k.a.66.3	yes	18	3.2	odd	2
475.2.l.c.226.1		18	285.74	odd	18
475.2.l.c.351.1		18	15.14	odd	2
475.2.u.b.74.2		36	285.188	even	36
475.2.u.b.74.5		36	285.17	even	36
475.2.u.b.199.2		36	15.2	even	4
475.2.u.b.199.5		36	15.8	even	4
855.2.bs.c.226.1		18	19.17	even	9	inner
855.2.bs.c.541.1		18	1.1	even	1	trivial
1805.2.a.s.1.3		9	57.32	even	18
1805.2.a.v.1.7		9	57.44	odd	18
9025.2.a.cc.1.3		9	285.44	odd	18
9025.2.a.cf.1.7		9	285.89	even	18

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bs (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.370282 - 2.09998i) q^{2} +(-2.39340 + 0.871127i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-0.742812 + 1.28659i) q^{7} +(0.583208 + 1.01015i) q^{8} +O(q^{10})\)	\(q+(-0.370282 - 2.09998i) q^{2} +(-2.39340 + 0.871127i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-0.742812 + 1.28659i) q^{7} +(0.583208 + 1.01015i) q^{8} +(0.370282 - 2.09998i) q^{10} +(2.34068 + 4.05417i) q^{11} +(-0.276562 - 0.232063i) q^{13} +(2.97685 + 1.08349i) q^{14} +(-1.99691 + 1.67560i) q^{16} +(0.951255 + 5.39483i) q^{17} +(-1.68540 + 4.01988i) q^{19} -2.54700 q^{20} +(7.64695 - 6.41655i) q^{22} +(-5.79545 + 2.10937i) q^{23} +(0.766044 + 0.642788i) q^{25} +(-0.384921 + 0.666703i) q^{26} +(0.657066 - 3.72641i) q^{28} +(0.155581 - 0.882346i) q^{29} +(-2.40012 + 4.15713i) q^{31} +(6.04520 + 5.07252i) q^{32} +(10.9768 - 3.99522i) q^{34} +(-1.13805 + 0.954941i) q^{35} +11.3982 q^{37} +(9.06572 + 2.05081i) q^{38} +(0.202546 + 1.14870i) q^{40} +(4.01104 - 3.36566i) q^{41} +(-6.78295 - 2.46879i) q^{43} +(-9.13387 - 7.66423i) q^{44} +(6.57558 + 11.3892i) q^{46} +(1.88678 - 10.7005i) q^{47} +(2.39646 + 4.15079i) q^{49} +(1.06619 - 1.84669i) q^{50} +(0.864081 + 0.314500i) q^{52} +(-6.12941 + 2.23092i) q^{53} +(0.812908 + 4.61023i) q^{55} -1.73286 q^{56} -1.91051 q^{58} +(1.70300 + 9.65818i) q^{59} +(-2.20795 + 0.803626i) q^{61} +(9.61858 + 3.50088i) q^{62} +(5.80697 - 10.0580i) q^{64} +(-0.180513 - 0.312658i) q^{65} +(1.53717 - 8.71774i) q^{67} +(-6.97632 - 12.0833i) q^{68} +(2.42675 + 2.03629i) q^{70} +(6.02538 + 2.19306i) q^{71} +(2.19219 - 1.83946i) q^{73} +(-4.22054 - 23.9359i) q^{74} +(0.532020 - 11.0894i) q^{76} -6.95473 q^{77} +(1.58226 - 1.32767i) q^{79} +(-2.44957 + 0.891571i) q^{80} +(-8.55302 - 7.17684i) q^{82} +(3.08199 - 5.33816i) q^{83} +(-0.951255 + 5.39483i) q^{85} +(-2.67280 + 15.1582i) q^{86} +(-2.73020 + 4.72885i) q^{88} +(2.54338 + 2.13415i) q^{89} +(0.504004 - 0.183442i) q^{91} +(12.0333 - 10.0971i) q^{92} -23.1693 q^{94} +(-2.95864 + 3.20101i) q^{95} +(0.819060 + 4.64512i) q^{97} +(7.82919 - 6.56947i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) \) 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8	\( 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8} - 3 q^{10} - 3 q^{13} + 12 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{20} + 9 q^{22} + 9 q^{23} - 3 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} - 15 q^{32} - 12 q^{34} + 36 q^{37} + 33 q^{38} - 6 q^{40} + 30 q^{41} - 36 q^{43} - 42 q^{44} + 9 q^{46} - 21 q^{47} + 9 q^{49} + 6 q^{50} - 39 q^{52} + 12 q^{53} + 3 q^{55} + 12 q^{58} - 18 q^{59} - 30 q^{61} + 24 q^{62} + 36 q^{64} + 9 q^{65} - 51 q^{68} + 33 q^{70} + 12 q^{71} + 24 q^{73} + 15 q^{74} - 33 q^{76} + 60 q^{77} - 51 q^{79} - 15 q^{80} - 15 q^{82} + 24 q^{85} - 63 q^{86} - 27 q^{88} + 54 q^{89} + 30 q^{91} + 42 q^{92} + 30 q^{94} - 15 q^{95} + 27 q^{97} + 3 q^{98}+O(q^{100}) \) 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8 - 3 * q^10 - 3 * q^13 + 12 * q^14 - 3 * q^16 - 24 * q^17 - 12 * q^20 + 9 * q^22 + 9 * q^23 - 3 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 - 15 * q^32 - 12 * q^34 + 36 * q^37 + 33 * q^38 - 6 * q^40 + 30 * q^41 - 36 * q^43 - 42 * q^44 + 9 * q^46 - 21 * q^47 + 9 * q^49 + 6 * q^50 - 39 * q^52 + 12 * q^53 + 3 * q^55 + 12 * q^58 - 18 * q^59 - 30 * q^61 + 24 * q^62 + 36 * q^64 + 9 * q^65 - 51 * q^68 + 33 * q^70 + 12 * q^71 + 24 * q^73 + 15 * q^74 - 33 * q^76 + 60 * q^77 - 51 * q^79 - 15 * q^80 - 15 * q^82 + 24 * q^85 - 63 * q^86 - 27 * q^88 + 54 * q^89 + 30 * q^91 + 42 * q^92 + 30 * q^94 - 15 * q^95 + 27 * q^97 + 3 * q^98

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