LMFDB - Embedded newform 855.2.dl.a.667.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(127,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 9, 10]))

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

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

chi := DirichletCharacter("855.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.dl (of order $36$, degree $12$, 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:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			667.1
Character	$\chi$	$=$	855.667
Dual form			855.2.dl.a.523.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31842 - 1.88289i) q^{2} +(-1.12303 + 3.08549i) q^{4} +(1.96769 + 1.06216i) q^{5} +(0.282738 - 1.05519i) q^{7} +(2.84973 - 0.763583i) q^{8} +O(q^{10})$	\(q+(-1.31842 - 1.88289i) q^{2} +(-1.12303 + 3.08549i) q^{4} +(1.96769 + 1.06216i) q^{5} +(0.282738 - 1.05519i) q^{7} +(2.84973 - 0.763583i) q^{8} +(-0.594310 - 5.10532i) q^{10} +(-0.454581 + 0.787357i) q^{11} +(-2.13403 - 0.186703i) q^{13} +(-2.35958 + 0.858817i) q^{14} +(-0.164249 - 0.137821i) q^{16} +(1.23292 - 0.863300i) q^{17} +(-3.39576 - 2.73291i) q^{19} +(-5.48705 + 4.87847i) q^{20} +(2.08184 - 0.182137i) q^{22} +(7.05313 - 3.28893i) q^{23} +(2.74364 + 4.18000i) q^{25} +(2.46200 + 4.26430i) q^{26} +(2.93826 + 2.05739i) q^{28} +(1.08928 + 6.17764i) q^{29} +(3.92386 - 2.26544i) q^{31} +(0.471310 - 5.38709i) q^{32} +(-3.25100 - 1.18327i) q^{34} +(1.67712 - 1.77598i) q^{35} +(7.47953 - 7.47953i) q^{37} +(-0.668763 + 9.99697i) q^{38} +(6.41844 + 1.52437i) q^{40} +(4.59540 - 5.47659i) q^{41} +(-1.92558 + 4.12943i) q^{43} +(-1.91887 - 2.28683i) q^{44} +(-15.4917 - 8.94412i) q^{46} +(6.83296 - 9.75847i) q^{47} +(5.02869 + 2.90331i) q^{49} +(4.25324 - 10.6770i) q^{50} +(2.97264 - 6.37485i) q^{52} +(1.04592 + 2.24298i) q^{53} +(-1.73077 + 1.06644i) q^{55} -3.22291i q^{56} +(10.1957 - 10.1957i) q^{58} +(-0.443312 + 2.51415i) q^{59} +(-0.234183 - 0.0852357i) q^{61} +(-9.43886 - 4.40141i) q^{62} +(-11.1361 + 6.42942i) q^{64} +(-4.00081 - 2.63405i) q^{65} +(7.54653 + 5.28414i) q^{67} +(1.27910 + 4.77367i) q^{68} +(-5.55513 - 0.816358i) q^{70} +(-2.90257 - 7.97473i) q^{71} +(6.65286 - 0.582050i) q^{73} +(-23.9443 - 4.22203i) q^{74} +(12.2459 - 7.40844i) q^{76} +(0.702285 + 0.702285i) q^{77} +(-4.80677 - 4.03336i) q^{79} +(-0.176804 - 0.445648i) q^{80} +(-16.3705 - 1.43223i) q^{82} +(0.217902 + 0.0583867i) q^{83} +(3.34297 - 0.389154i) q^{85} +(10.3140 - 1.81864i) q^{86} +(-0.694220 + 2.59086i) q^{88} +(-10.4217 + 8.74483i) q^{89} +(-0.800379 + 2.19902i) q^{91} +(2.22710 + 25.4559i) q^{92} -27.3828 q^{94} +(-3.77903 - 8.98437i) q^{95} +(-7.78495 - 11.1181i) q^{97} +(-1.16327 - 13.2963i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8}+O(q^{10}) $ 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8	$ 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40} - 12 q^{41} + 48 q^{43} - 36 q^{46} + 24 q^{47} - 126 q^{50} + 30 q^{53} + 18 q^{55} + 120 q^{58} - 48 q^{61} - 60 q^{62} - 72 q^{65} + 108 q^{67} - 18 q^{68} + 36 q^{70} + 24 q^{71} + 6 q^{73} + 60 q^{76} - 168 q^{77} + 60 q^{80} + 60 q^{82} - 36 q^{85} + 180 q^{86} - 198 q^{88} - 24 q^{91} + 72 q^{92} + 24 q^{95} - 72 q^{97} + 90 q^{98}+O(q^{100}) $ 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 + 12 * q^16 + 30 * q^17 + 84 * q^20 - 24 * q^22 + 12 * q^25 + 48 * q^26 - 36 * q^31 - 18 * q^32 + 30 * q^35 - 54 * q^38 + 54 * q^40 - 12 * q^41 + 48 * q^43 - 36 * q^46 + 24 * q^47 - 126 * q^50 + 30 * q^53 + 18 * q^55 + 120 * q^58 - 48 * q^61 - 60 * q^62 - 72 * q^65 + 108 * q^67 - 18 * q^68 + 36 * q^70 + 24 * q^71 + 6 * q^73 + 60 * q^76 - 168 * q^77 + 60 * q^80 + 60 * q^82 - 36 * q^85 + 180 * q^86 - 198 * q^88 - 24 * q^91 + 72 * q^92 + 24 * q^95 - 72 * q^97 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−1.31842	−	1.88289i	−0.932261	−	1.33141i	−0.943466	−	0.331469i	$-0.892456\pi$
$2$	−1.31842	−	1.88289i	−0.932261	−	1.33141i	0.0112050	−	0.999937i	$-0.496433\pi$
$3$		0			0
$3$		0			0
$4$	−1.12303	+	3.08549i	−0.561513	+	1.54274i
$5$	1.96769	+	1.06216i	0.879980	+	0.475011i
$5$	1.96769	+	1.06216i	0.879980	+	0.475011i
$6$		0			0
$7$	0.282738	−	1.05519i	0.106865	−	0.398825i	−0.891685	−	0.452656i	$-0.850477\pi$
$7$	0.282738	−	1.05519i	0.106865	−	0.398825i	0.998550	+	0.0538310i	$0.0171432\pi$
$8$	2.84973	−	0.763583i	1.00753	−	0.269967i
$9$		0			0
$10$	−0.594310	−	5.10532i	−0.187937	−	1.61445i
$11$	−0.454581	+	0.787357i	−0.137061	+	0.237397i	−0.926383	−	0.376583i	$-0.877099\pi$
$11$	−0.454581	+	0.787357i	−0.137061	+	0.237397i	0.789322	+	0.613980i	$0.210432\pi$
$12$		0			0
$13$	−2.13403	−	0.186703i	−0.591873	−	0.0517822i	−0.212716	−	0.977114i	$-0.568231\pi$
$13$	−2.13403	−	0.186703i	−0.591873	−	0.0517822i	−0.379158	+	0.925332i	$0.623786\pi$
$14$	−2.35958	+	0.858817i	−0.630624	+	0.229528i
$15$		0			0
$16$	−0.164249	−	0.137821i	−0.0410622	−	0.0344553i
$17$	1.23292	−	0.863300i	0.299027	−	0.209381i	−0.414428	−	0.910082i	$-0.636018\pi$
$17$	1.23292	−	0.863300i	0.299027	−	0.209381i	0.713455	+	0.700701i	$0.247129\pi$
$18$		0			0
$19$	−3.39576	−	2.73291i	−0.779041	−	0.626974i
$19$	−3.39576	−	2.73291i	−0.779041	−	0.626974i
$20$	−5.48705	+	4.87847i	−1.22694	+	1.09086i
$21$		0			0
$22$	2.08184	−	0.182137i	0.443849	−	0.0388317i
$23$	7.05313	−	3.28893i	1.47068	−	0.685789i	0.488298	−	0.872677i	$-0.337618\pi$
$23$	7.05313	−	3.28893i	1.47068	−	0.685789i	0.982381	+	0.186887i	$0.0598400\pi$
$24$		0			0
$25$	2.74364	+	4.18000i	0.548728	+	0.836001i
$26$	2.46200	+	4.26430i	0.482837	+	0.836299i
$27$		0			0
$28$	2.93826	+	2.05739i	0.555279	+	0.388811i
$29$	1.08928	+	6.17764i	0.202275	+	1.14716i	0.901670	+	0.432424i	$0.142342\pi$
$29$	1.08928	+	6.17764i	0.202275	+	1.14716i	−0.699395	+	0.714735i	$0.746547\pi$
$30$		0			0
$31$	3.92386	−	2.26544i	0.704746	−	0.406885i	−0.104367	−	0.994539i	$-0.533282\pi$
$31$	3.92386	−	2.26544i	0.704746	−	0.406885i	0.809113	+	0.587654i	$0.199948\pi$
$32$	0.471310	−	5.38709i	0.0833166	−	0.952313i
$33$		0			0
$34$	−3.25100	−	1.18327i	−0.557542	−	0.202929i
$35$	1.67712	−	1.77598i	0.283485	−	0.300196i
$36$		0			0
$37$	7.47953	−	7.47953i	1.22963	−	1.22963i	0.265523	−	0.964104i	$-0.414455\pi$
$37$	7.47953	−	7.47953i	1.22963	−	1.22963i	0.964104	−	0.265523i	$-0.0855447\pi$
$38$	−0.668763	+	9.99697i	−0.108488	+	1.62172i
$39$		0			0
$40$	6.41844	+	1.52437i	1.01485	+	0.241023i
$41$	4.59540	−	5.47659i	0.717681	−	0.855299i	−0.276722	−	0.960950i	$-0.589248\pi$
$41$	4.59540	−	5.47659i	0.717681	−	0.855299i	0.994403	+	0.105651i	$0.0336926\pi$
$42$		0			0
$43$	−1.92558	+	4.12943i	−0.293649	+	0.629732i	−0.996679	−	0.0814279i	$-0.974052\pi$
$43$	−1.92558	+	4.12943i	−0.293649	+	0.629732i	0.703030	+	0.711160i	$0.251830\pi$
$44$	−1.91887	−	2.28683i	−0.289281	−	0.344752i
$45$		0			0
$46$	−15.4917	−	8.94412i	−2.28412	−	1.31874i
$47$	6.83296	−	9.75847i	0.996689	−	1.42342i	0.0927839	−	0.995686i	$-0.470423\pi$
$47$	6.83296	−	9.75847i	0.996689	−	1.42342i	0.903905	−	0.427733i	$-0.140688\pi$
$48$		0			0
$49$	5.02869	+	2.90331i	0.718384	+	0.414759i
$50$	4.25324	−	10.6770i	0.601499	−	1.50995i
$51$		0			0
$52$	2.97264	−	6.37485i	0.412231	−	0.884033i
$53$	1.04592	+	2.24298i	0.143668	+	0.308097i	0.964954	−	0.262420i	$-0.0845206\pi$
$53$	1.04592	+	2.24298i	0.143668	+	0.308097i	−0.821286	+	0.570517i	$0.806743\pi$
$54$		0			0
$55$	−1.73077	+	1.06644i	−0.233377	+	0.143799i
$56$		−	3.22291i		−	0.430679i
$57$		0			0
$58$	10.1957	−	10.1957i	1.33876	−	1.33876i
$59$	−0.443312	+	2.51415i	−0.0577143	+	0.327314i	−0.999971	−	0.00757669i	$-0.997588\pi$
$59$	−0.443312	+	2.51415i	−0.0577143	+	0.327314i	0.942257	+	0.334891i	$0.108699\pi$
$60$		0			0
$61$	−0.234183	−	0.0852357i	−0.0299841	−	0.0109133i	0.326985	−	0.945030i	$-0.393967\pi$
$61$	−0.234183	−	0.0852357i	−0.0299841	−	0.0109133i	−0.356969	+	0.934116i	$0.616190\pi$
$62$	−9.43886	−	4.40141i	−1.19874	−	0.558980i
$63$		0			0
$64$	−11.1361	+	6.42942i	−1.39201	+	0.803677i
$65$	−4.00081	−	2.63405i	−0.496239	−	0.326714i
$66$		0			0
$67$	7.54653	+	5.28414i	0.921956	+	0.645560i	0.935112	−	0.354353i	$-0.115299\pi$
$67$	7.54653	+	5.28414i	0.921956	+	0.645560i	−0.0131559	+	0.999913i	$0.504188\pi$
$68$	1.27910	+	4.77367i	0.155114	+	0.578892i
$69$		0			0
$70$	−5.55513	−	0.816358i	−0.663965	−	0.0975734i
$71$	−2.90257	−	7.97473i	−0.344471	−	0.946427i	−0.984080	−	0.177726i	$-0.943126\pi$
$71$	−2.90257	−	7.97473i	−0.344471	−	0.946427i	0.639609	−	0.768701i	$-0.279096\pi$
$72$		0			0
$73$	6.65286	−	0.582050i	0.778658	−	0.0681238i	0.309105	−	0.951028i	$-0.399971\pi$
$73$	6.65286	−	0.582050i	0.778658	−	0.0681238i	0.469553	+	0.882904i	$0.344415\pi$
$74$	−23.9443	−	4.22203i	−2.78347	−	0.490801i
$75$		0			0
$76$	12.2459	−	7.40844i	1.40470	−	0.849807i
$77$	0.702285	+	0.702285i	0.0800328	+	0.0800328i
$78$		0			0
$79$	−4.80677	−	4.03336i	−0.540803	−	0.453788i	0.331009	−	0.943628i	$-0.392611\pi$
$79$	−4.80677	−	4.03336i	−0.540803	−	0.453788i	−0.871813	+	0.489840i	$0.837055\pi$
$80$	−0.176804	−	0.445648i	−0.0197672	−	0.0498250i
$81$		0			0
$82$	−16.3705	−	1.43223i	−1.80782	−	0.158163i
$83$	0.217902	+	0.0583867i	0.0239178	+	0.00640877i	0.270758	−	0.962647i	$-0.412726\pi$
$83$	0.217902	+	0.0583867i	0.0239178	+	0.00640877i	−0.246840	+	0.969056i	$0.579392\pi$
$84$		0			0
$85$	3.34297	−	0.389154i	0.362596	−	0.0422097i
$86$	10.3140	−	1.81864i	1.11219	−	0.196108i
$87$		0			0
$88$	−0.694220	+	2.59086i	−0.0740041	+	0.276187i
$89$	−10.4217	+	8.74483i	−1.10470	+	0.926951i	−0.997732	−	0.0673123i	$-0.978558\pi$
$89$	−10.4217	+	8.74483i	−1.10470	+	0.926951i	−0.106965	+	0.994263i	$0.534113\pi$
$90$		0			0
$91$	−0.800379	+	2.19902i	−0.0839025	+	0.230520i
$92$	2.22710	+	25.4559i	0.232192	+	2.65396i
$93$		0			0
$94$	−27.3828			−2.82432
$95$	−3.77903	−	8.98437i	−0.387720	−	0.921777i
$96$		0			0
$97$	−7.78495	−	11.1181i	−0.790442	−	1.12887i	−0.988874	−	0.148753i	$-0.952474\pi$
$97$	−7.78495	−	11.1181i	−0.790442	−	1.12887i	0.198432	−	0.980115i	$-0.436415\pi$
$98$	−1.16327	−	13.2963i	−0.117508	−	1.34313i
$99$		0			0
$100$	−15.9785	+	3.77122i	−1.59785	+	0.377122i
$101$	−10.7952	+	9.05824i	−1.07416	+	0.901328i	−0.995423	−	0.0955669i	$-0.969534\pi$
$101$	−10.7952	+	9.05824i	−1.07416	+	0.901328i	−0.0787384	+	0.996895i	$0.525089\pi$
$102$		0			0
$103$	−7.94148	+	2.12791i	−0.782498	+	0.209670i	−0.627886	−	0.778306i	$-0.716079\pi$
$103$	−7.94148	+	2.12791i	−0.782498	+	0.209670i	−0.154612	+	0.987975i	$0.549413\pi$
$104$	−6.22397	+	1.09745i	−0.610311	+	0.107614i
$105$		0			0
$106$	2.84434	−	4.92654i	0.276266	−	0.478508i
$107$	9.88619	+	2.64900i	0.955734	+	0.256088i	0.702794	−	0.711394i	$-0.251936\pi$
$107$	9.88619	+	2.64900i	0.955734	+	0.256088i	0.252941	+	0.967482i	$0.418602\pi$
$108$		0			0
$109$	0.358229	−	0.130385i	0.0343121	−	0.0124886i	−0.324807	−	0.945780i	$-0.605299\pi$
$109$	0.358229	−	0.130385i	0.0343121	−	0.0124886i	0.359119	+	0.933292i	$0.383077\pi$
$110$	4.28987	+	1.85285i	0.409023	+	0.176662i
$111$		0			0
$112$	−0.191867	+	0.134347i	−0.0181297	+	0.0126946i
$113$	−6.83708	−	6.83708i	−0.643179	−	0.643179i	0.308157	−	0.951336i	$-0.400288\pi$
$113$	−6.83708	−	6.83708i	−0.643179	−	0.643179i	−0.951336	+	0.308157i	$0.900288\pi$
$114$		0			0
$115$	17.3718	+	1.01993i	1.61993	+	0.0951092i
$116$	−20.2843	−	3.57668i	−1.88335	−	0.332086i
$117$		0			0
$118$	5.31834	−	2.47998i	0.489593	−	0.228301i
$119$	−0.562354	−	1.54505i	−0.0515509	−	0.141635i
$120$		0			0
$121$	5.08671	+	8.81045i	0.462428	+	0.800950i
$122$	0.148261	+	0.553318i	0.0134229	+	0.0500951i
$123$		0			0
$124$	2.58340	+	14.6512i	0.231996	+	1.31571i
$125$	0.958823	+	11.1391i	0.0857597	+	0.996316i
$126$		0			0
$127$	0.160223	−	1.83136i	0.0142175	−	0.162507i	−0.985767	−	0.168119i	$-0.946231\pi$
$127$	0.160223	−	1.83136i	0.0142175	−	0.162507i	0.999984	+	0.00561197i	$0.00178636\pi$
$128$	16.9859	+	7.92064i	1.50135	+	0.700092i
$129$		0			0
$130$	0.315093	+	11.0059i	0.0276355	+	0.965279i
$131$	0.135174	−	0.766611i	0.0118102	−	0.0669791i	−0.978333	−	0.207037i	$-0.933618\pi$
$131$	0.135174	−	0.766611i	0.0118102	−	0.0669791i	0.990143	+	0.140058i	$0.0447290\pi$
$132$		0			0
$133$	−3.84386	+	2.81048i	−0.333305	+	0.243699i
$134$		−	21.1760i		−	1.82933i
$135$		0			0
$136$	2.85429	−	3.40161i	0.244753	−	0.291686i
$137$	1.76496	+	3.78496i	0.150791	+	0.323371i	0.967164	−	0.254153i	$-0.0817967\pi$
$137$	1.76496	+	3.78496i	0.150791	+	0.323371i	−0.816374	+	0.577524i	$0.804019\pi$
$138$		0			0
$139$	9.27490	+	11.0534i	0.786686	+	0.937536i	0.999215	−	0.0396186i	$-0.0126143\pi$
$139$	9.27490	+	11.0534i	0.786686	+	0.937536i	−0.212529	+	0.977155i	$0.568170\pi$
$140$	3.59632	+	7.16922i	0.303945	+	0.605909i
$141$		0			0
$142$	−11.1888	+	15.9792i	−0.938942	+	1.34095i
$143$	1.11709	−	1.59537i	0.0934158	−	0.133412i
$144$		0			0
$145$	−4.41825	+	13.3127i	−0.366916	+	1.10556i
$146$	−9.86718	−	11.7592i	−0.816613	−	0.973202i
$147$		0			0
$148$	14.6783	+	31.4777i	1.20655	+	2.58745i
$149$	11.0863	−	13.2122i	0.908227	−	1.08238i	−0.0880455	−	0.996116i	$-0.528062\pi$
$149$	11.0863	−	13.2122i	0.908227	−	1.08238i	0.996272	−	0.0862659i	$-0.0274935\pi$
$150$		0			0
$151$		−	21.2078i		−	1.72586i	−0.505320	−	0.862932i	$-0.668625\pi$
$151$		−	21.2078i		−	1.72586i	0.505320	−	0.862932i	$-0.331375\pi$
$152$	−11.7638	−	5.19513i	−0.954171	−	0.421380i
$153$		0			0
$154$	0.396424	−	2.24823i	0.0319448	−	0.181168i
$155$	10.1272	−	0.289937i	0.813437	−	0.0232883i
$156$		0			0
$157$	4.48064	+	2.08936i	0.357594	+	0.166749i	0.593110	−	0.805122i	$-0.297900\pi$
$157$	4.48064	+	2.08936i	0.357594	+	0.166749i	−0.235515	+	0.971871i	$0.575678\pi$
$158$	−1.25706	+	14.3683i	−0.100006	+	1.14308i
$159$		0			0
$160$	6.64934	−	10.0995i	0.525676	−	0.798439i
$161$	−1.47626	−	8.37231i	−0.116346	−	0.659831i
$162$		0			0
$163$	−3.59357	−	13.4114i	−0.281470	−	1.05046i	−0.951380	−	0.308018i	$-0.900334\pi$
$163$	−3.59357	−	13.4114i	−0.281470	−	1.05046i	0.669910	−	0.742442i	$-0.266332\pi$
$164$	11.7372	+	20.3294i	0.916520	+	1.58746i
$165$		0			0
$166$	−0.177350	−	0.487264i	−0.0137650	−	0.0378190i
$167$	−11.8240	+	5.51364i	−0.914971	+	0.426658i	−0.822310	−	0.569040i	$-0.807315\pi$
$167$	−11.8240	+	5.51364i	−0.914971	+	0.426658i	−0.0926609	+	0.995698i	$0.529537\pi$
$168$		0			0
$169$	−8.28327	−	1.46056i	−0.637175	−	0.112351i
$170$	−5.14016	−	5.78139i	−0.394232	−	0.443412i
$171$		0			0
$172$	−10.5788	−	10.5788i	−0.806628	−	0.806628i
$173$	2.36420	−	1.65543i	0.179746	−	0.125860i	−0.480241	−	0.877137i	$-0.659451\pi$
$173$	2.36420	−	1.65543i	0.179746	−	0.125860i	0.659987	+	0.751277i	$0.270562\pi$
$174$		0			0
$175$	5.18644	−	1.71322i	0.392058	−	0.129507i
$176$	0.183179	−	0.0666716i	0.0138076	−	0.00502556i
$177$		0			0
$178$	30.2057	+	8.09360i	2.26401	+	0.606641i
$179$	5.86898	−	10.1654i	0.438668	−	0.759796i	−0.558919	−	0.829222i	$-0.688784\pi$
$179$	5.86898	−	10.1654i	0.438668	−	0.759796i	0.997587	+	0.0694265i	$0.0221169\pi$
$180$		0			0
$181$	−15.5664	+	2.74478i	−1.15704	+	0.204018i	−0.719049	−	0.694959i	$-0.755423\pi$
$181$	−15.5664	+	2.74478i	−1.15704	+	0.204018i	−0.437995	+	0.898977i	$0.644311\pi$
$182$	5.19576	−	1.39220i	0.385135	−	0.103197i
$183$		0			0
$184$	17.5882	−	14.7582i	1.29662	−	1.08799i
$185$	22.6619	−	6.77299i	1.66613	−	0.497960i
$186$		0			0
$187$	0.119263	+	1.36319i	0.00872140	+	0.0996861i
$188$	22.4361	+	32.0420i	1.63632	+	2.33690i
$189$		0			0
$190$	−11.9343	+	18.9606i	−0.865804	+	1.37555i
$191$	19.3049			1.39685			0.698425	−	0.715683i	$-0.253884\pi$
$191$	19.3049			1.39685			0.698425	+	0.715683i	$0.253884\pi$
$192$		0			0
$193$	−0.291357	−	3.33023i	−0.0209723	−	0.239715i	−0.999444	−	0.0333348i	$-0.989387\pi$
$193$	−0.291357	−	3.33023i	−0.0209723	−	0.239715i	0.978472	−	0.206380i	$-0.0661683\pi$
$194$	−10.6703	+	29.3165i	−0.766084	+	2.10480i
$195$		0			0
$196$	−14.6055	+	12.2555i	−1.04325	+	0.875390i
$197$	−3.33413	+	12.4431i	−0.237547	+	0.886537i	0.739437	+	0.673225i	$0.235092\pi$
$197$	−3.33413	+	12.4431i	−0.237547	+	0.886537i	−0.976984	+	0.213312i	$0.931575\pi$
$198$		0			0
$199$	8.35913	−	1.47394i	0.592563	−	0.104485i	0.130678	−	0.991425i	$-0.458285\pi$
$199$	8.35913	−	1.47394i	0.592563	−	0.104485i	0.461885	+	0.886940i	$0.347173\pi$
$200$	11.0104	+	9.81689i	0.778554	+	0.694159i
$201$		0			0
$202$	31.2882	+	8.38366i	2.20143	+	0.589872i
$203$	6.82658	+	0.597248i	0.479132	+	0.0419186i
$204$		0			0
$205$	14.8593	−	5.89520i	1.03782	−	0.411739i
$206$	14.4768	+	12.1475i	1.00865	+	0.846356i
$207$		0			0
$208$	0.324780	+	0.324780i	0.0225195	+	0.0225195i
$209$	3.69542	−	1.43134i	0.255618	−	0.0990081i
$210$		0			0
$211$	−15.9594	−	2.81408i	−1.09869	−	0.193729i	−0.405225	−	0.914217i	$-0.632807\pi$
$211$	−15.9594	−	2.81408i	−1.09869	−	0.193729i	−0.693468	+	0.720488i	$0.743918\pi$
$212$	−8.09529	+	0.708246i	−0.555987	+	0.0486425i
$213$		0			0
$214$	−8.04634	−	22.1071i	−0.550036	−	1.51121i
$215$	−8.17506	+	6.08018i	−0.557535	+	0.414665i
$216$		0			0
$217$	−1.28105	−	4.78095i	−0.0869634	−	0.324552i
$218$	−0.717795	−	0.502606i	−0.0486152	−	0.0340407i
$219$		0			0
$220$	−1.34679	−	6.53792i	−0.0908005	−	0.440787i
$221$	−2.79227	+	1.61212i	−0.187828	+	0.108443i
$222$		0			0
$223$	10.1610	+	4.73817i	0.680433	+	0.317291i	0.731928	−	0.681382i	$-0.238621\pi$
$223$	10.1610	+	4.73817i	0.680433	+	0.317291i	−0.0514946	+	0.998673i	$0.516398\pi$
$224$	−5.55116	−	2.02046i	−0.370903	−	0.134997i
$225$		0			0
$226$	−3.85938	+	21.8876i	−0.256722	+	1.45594i
$227$	−9.99402	+	9.99402i	−0.663326	+	0.663326i	−0.956163	−	0.292836i	$-0.905401\pi$
$227$	−9.99402	+	9.99402i	−0.663326	+	0.663326i	0.292836	+	0.956163i	$0.405401\pi$
$228$		0			0
$229$			14.2210i			0.939752i	0.882732	+	0.469876i	$0.155701\pi$
$229$			14.2210i			0.939752i	−0.882732	+	0.469876i	$0.844299\pi$
$230$	−20.9828	−	34.0539i	−1.38356	−	2.24545i
$231$		0			0
$232$	7.82131	+	16.7729i	0.513494	+	1.10119i
$233$	−7.88812	+	16.9161i	−0.516768	+	1.10821i	0.458805	+	0.888537i	$0.348278\pi$
$233$	−7.88812	+	16.9161i	−0.516768	+	1.10821i	−0.975573	+	0.219676i	$0.929500\pi$
$234$		0			0
$235$	23.8102	−	11.9440i	1.55321	−	0.779141i
$236$	−7.25952	−	4.19128i	−0.472554	−	0.272829i
$237$		0			0
$238$	−2.16776	+	3.09588i	−0.140515	+	0.200676i
$239$	8.54720	+	4.93473i	0.552873	+	0.319201i	0.750280	−	0.661120i	$-0.229919\pi$
$239$	8.54720	+	4.93473i	0.552873	+	0.319201i	−0.197407	+	0.980322i	$0.563252\pi$
$240$		0			0
$241$	15.2762	+	18.2054i	0.984024	+	1.17271i	0.984972	+	0.172714i	$0.0552537\pi$
$241$	15.2762	+	18.2054i	0.984024	+	1.17271i	−0.000948389		1.00000i	$0.500302\pi$
$242$	9.88272	−	21.1936i	0.635286	−	1.36237i
$243$		0			0
$244$	0.525988	−	0.626848i	0.0336729	−	0.0401298i
$245$	6.81114	+	11.0541i	0.435148	+	0.706220i
$246$		0			0
$247$	6.73641	+	6.46612i	0.428627	+	0.411429i
$248$	9.45209	−	9.45209i	0.600208	−	0.600208i
$249$		0			0
$250$	19.7097	−	16.4914i	1.24655	−	1.04301i
$251$	−2.64175	−	0.961518i	−0.166746	−	0.0606905i	0.257298	−	0.966332i	$-0.417168\pi$
$251$	−2.64175	−	0.961518i	−0.166746	−	0.0606905i	−0.424044	+	0.905641i	$0.639390\pi$
$252$		0			0
$253$	−0.616656	+	7.04841i	−0.0387689	+	0.443130i
$254$	−3.65949	+	2.11281i	−0.229617	+	0.132569i
$255$		0			0
$256$	−3.01489	−	17.0983i	−0.188431	−	1.06864i
$257$	10.5469	+	7.38504i	0.657899	+	0.460666i	0.854246	−	0.519868i	$-0.174019\pi$
$257$	10.5469	+	7.38504i	0.657899	+	0.460666i	−0.196347	+	0.980534i	$0.562908\pi$
$258$		0			0
$259$	−5.77760	−	10.0071i	−0.359002	−	0.621810i
$260$	12.6204	−	9.38635i	0.782681	−	0.582116i
$261$		0			0
$262$	−1.62166	+	0.756194i	−0.100187	+	0.0467178i
$263$	−7.47719	+	0.654169i	−0.461063	+	0.0403378i	−0.315322	−	0.948985i	$-0.602112\pi$
$263$	−7.47719	+	0.654169i	−0.461063	+	0.0403378i	−0.145742	+	0.989323i	$0.546557\pi$
$264$		0			0
$265$	−0.324351	+	5.52443i	−0.0199247	+	0.339363i
$266$	10.3596	+	3.53220i	0.635190	+	0.216573i
$267$		0			0
$268$	−24.7791	+	17.3505i	−1.51362	+	1.05985i
$269$	−0.573855	−	0.481521i	−0.0349885	−	0.0293589i	0.625126	−	0.780524i	$-0.285048\pi$
$269$	−0.573855	−	0.481521i	−0.0349885	−	0.0293589i	−0.660114	+	0.751165i	$0.729492\pi$
$270$		0			0
$271$	−9.00533	+	3.27767i	−0.547035	+	0.199104i	−0.600728	−	0.799453i	$-0.705123\pi$
$271$	−9.00533	+	3.27767i	−0.547035	+	0.199104i	0.0536939	+	0.998557i	$0.482900\pi$
$272$	−0.321487	−	0.0281264i	−0.0194930	−	0.00170542i
$273$		0			0
$274$	4.79974	−	8.31339i	0.289963	−	0.502230i
$275$	−4.53836	+	0.260076i	−0.273673	+	0.0156831i
$276$		0			0
$277$	−7.97600	+	2.13716i	−0.479231	+	0.128410i	−0.490345	−	0.871529i	$-0.663129\pi$
$277$	−7.97600	+	2.13716i	−0.479231	+	0.128410i	0.0111135	+	0.999938i	$0.496462\pi$
$278$	8.58418	−	32.0366i	0.514845	−	1.92143i
$279$		0			0
$280$	3.42324	−	6.34169i	0.204577	−	0.378989i
$281$	−1.54859	+	4.25472i	−0.0923813	+	0.253815i	−0.977274	−	0.211979i	$-0.932009\pi$
$281$	−1.54859	+	4.25472i	−0.0923813	+	0.253815i	0.884893	+	0.465794i	$0.154231\pi$
$282$		0			0
$283$	−6.87627	−	9.82032i	−0.408752	−	0.583758i	0.561011	−	0.827808i	$-0.310413\pi$
$283$	−6.87627	−	9.82032i	−0.408752	−	0.583758i	−0.969762	+	0.244051i	$0.921524\pi$
$284$	27.8656			1.65352
$285$		0			0
$286$	−4.47670			−0.264713
$287$	−4.47956	−	6.39747i	−0.264420	−	0.377631i
$288$		0			0
$289$	−5.03954	+	13.8460i	−0.296443	+	0.814472i
$290$	30.8915	−	9.23259i	1.81401	−	0.542156i
$291$		0			0
$292$	−5.67543	+	21.1810i	−0.332129	+	1.23952i
$293$	−12.8467	+	3.44227i	−0.750514	+	0.201100i	−0.613746	−	0.789504i	$-0.710338\pi$
$293$	−12.8467	+	3.44227i	−0.750514	+	0.201100i	−0.136768	+	0.990603i	$0.543671\pi$
$294$		0			0
$295$	−3.54272	+	4.47620i	−0.206265	+	0.260615i
$296$	15.6034	−	27.0259i	0.906930	−	1.57085i
$297$		0			0
$298$	−39.4935	−	3.45523i	−2.28780	−	0.200156i
$299$	−15.6657	+	5.70183i	−0.905968	+	0.329745i
$300$		0			0
$301$	3.81290	+	3.19941i	0.219772	+	0.184411i
$302$	−39.9320	+	27.9607i	−2.29783	+	1.60896i
$303$		0			0
$304$	0.181096	+	0.916885i	0.0103866	+	0.0525870i
$305$	−0.370267	−	0.416458i	−0.0212014	−	0.0238463i
$306$		0			0
$307$	−17.6640	+	1.54540i	−1.00814	+	0.0882008i	−0.579245	−	0.815154i	$-0.696652\pi$
$307$	−17.6640	+	1.54540i	−1.00814	+	0.0882008i	−0.428895	+	0.903355i	$0.641097\pi$
$308$	−2.95558	+	1.37821i	−0.168410	+	0.0785307i
$309$		0			0
$310$	−13.8978	−	18.6862i	−0.789342	−	1.06130i
$311$	1.33370	+	2.31004i	0.0756274	+	0.130990i	0.901359	−	0.433073i	$-0.142571\pi$
$311$	1.33370	+	2.31004i	0.0756274	+	0.130990i	−0.825732	+	0.564063i	$0.809237\pi$
$312$		0			0
$313$	−1.21369	−	0.849832i	−0.0686016	−	0.0480354i	0.538773	−	0.842451i	$-0.318888\pi$
$313$	−1.21369	−	0.849832i	−0.0686016	−	0.0480354i	−0.607374	+	0.794416i	$0.707777\pi$
$314$	−1.97331	−	11.1912i	−0.111361	−	0.631557i
$315$		0			0
$316$	17.8430	−	10.3017i	1.00375	−	0.579514i
$317$	−0.0833060	+	0.952192i	−0.00467893	+	0.0534804i	−0.998175	−	0.0603841i	$-0.980767\pi$
$317$	−0.0833060	+	0.952192i	−0.00467893	+	0.0534804i	0.993496	+	0.113865i	$0.0363230\pi$
$318$		0			0
$319$	−5.35918	−	1.95058i	−0.300056	−	0.109212i
$320$	−28.7415	+	0.822855i	−1.60670	+	0.0459990i
$321$		0			0
$322$	−13.8178	+	13.8178i	−0.770038	+	0.770038i
$323$	−6.54602	−	0.437906i	−0.364230	−	0.0243658i
$324$		0			0
$325$	−5.07459	−	9.43250i	−0.281488	−	0.523221i
$326$	−20.5144	+	24.4481i	−1.13619	+	1.35405i
$327$		0			0
$328$	8.91383	−	19.1158i	0.492184	−	1.05549i
$329$	−8.36513	−	9.96917i	−0.461184	−	0.549618i
$330$		0			0
$331$	22.9198	+	13.2327i	1.25979	+	0.727338i	0.973033	−	0.230667i	$-0.0740908\pi$
$331$	22.9198	+	13.2327i	1.25979	+	0.727338i	0.286753	+	0.958005i	$0.407424\pi$
$332$	−0.424861	+	0.606764i	−0.0233173	+	0.0333005i
$333$		0			0
$334$	25.9706	+	14.9941i	1.42105	+	0.820442i
$335$	9.23668	+	18.4132i	0.504654	+	1.00602i
$336$		0			0
$337$	−1.77790	+	3.81272i	−0.0968485	+	0.207692i	−0.948763	−	0.315989i	$-0.897664\pi$
$337$	−1.77790	+	3.81272i	−0.0968485	+	0.207692i	0.851914	+	0.523681i	$0.175442\pi$
$338$	8.17071	+	17.5222i	0.444428	+	0.953080i
$339$		0			0
$340$	−2.55351	+	10.7517i	−0.138484	+	0.583094i
$341$			4.11930i			0.223073i
$342$		0			0
$343$	9.89253	−	9.89253i	0.534147	−	0.534147i
$344$	−2.33423	+	13.2381i	−0.125853	+	0.713750i
$345$		0			0
$346$	−6.23399	−	2.26899i	−0.335141	−	0.121981i
$347$	−18.0091	−	8.39777i	−0.966777	−	0.450816i	−0.125901	−	0.992043i	$-0.540182\pi$
$347$	−18.0091	−	8.39777i	−0.966777	−	0.450816i	−0.840876	+	0.541227i	$0.817960\pi$
$348$		0			0
$349$	−20.6312	+	11.9114i	−1.10436	+	0.637603i	−0.937363	−	0.348354i	$-0.886741\pi$
$349$	−20.6312	+	11.9114i	−1.10436	+	0.637603i	−0.166998	+	0.985957i	$0.553407\pi$
$350$	−10.0637	−	7.50677i	−0.537927	−	0.401254i
$351$		0			0
$352$	4.02732	+	2.81996i	0.214657	+	0.150304i
$353$	−8.36473	−	31.2176i	−0.445210	−	1.66155i	−0.715382	−	0.698734i	$-0.753747\pi$
$353$	−8.36473	−	31.2176i	−0.445210	−	1.66155i	0.270172	−	0.962812i	$-0.412919\pi$
$354$		0			0
$355$	2.75906	−	18.7748i	0.146436	−	0.996464i
$356$	−15.2783	−	41.9767i	−0.809746	−	2.22476i
$357$		0			0
$358$	−26.8781	+	2.35153i	−1.42055	+	0.124282i
$359$	−27.9067	−	4.92071i	−1.47286	−	0.259705i	−0.621139	−	0.783700i	$-0.713330\pi$
$359$	−27.9067	−	4.92071i	−1.47286	−	0.259705i	−0.851721	+	0.523995i	$0.824441\pi$
$360$		0			0
$361$	4.06236	+	18.5606i	0.213808	+	0.976876i
$362$	25.6912	+	25.6912i	1.35030	+	1.35030i
$363$		0			0
$364$	−5.88622	−	4.93912i	−0.308522	−	0.258880i
$365$	13.7090	+	5.92109i	0.717563	+	0.309924i
$366$		0			0
$367$	15.9385	+	1.39444i	0.831982	+	0.0727890i	0.495184	−	0.868788i	$-0.335101\pi$
$367$	15.9385	+	1.39444i	0.831982	+	0.0727890i	0.336798	+	0.941577i	$0.390656\pi$
$368$	−1.61175	−	0.431868i	−0.0840184	−	0.0225127i
$369$		0			0
$370$	−42.6306	−	33.7403i	−2.21626	−	1.75407i
$371$	2.66250	−	0.469470i	0.138230	−	0.0243737i
$372$		0			0
$373$	0.128165	−	0.478317i	0.00663611	−	0.0247663i	−0.962528	−	0.271181i	$-0.912586\pi$
$373$	0.128165	−	0.478317i	0.00663611	−	0.0247663i	0.969165	+	0.246415i	$0.0792525\pi$
$374$	2.40950	−	2.02181i	0.124592	−	0.104545i
$375$		0			0
$376$	12.0207	−	33.0265i	0.619919	−	1.70321i
$377$	−1.17118	−	13.3866i	−0.0603188	−	0.689447i
$378$		0			0
$379$	0.914413			0.0469702			0.0234851	−	0.999724i	$-0.492524\pi$
$379$	0.914413			0.0469702			0.0234851	+	0.999724i	$0.492524\pi$
$380$	31.9651	−	1.57047i	1.63978	−	0.0805632i
$381$		0			0
$382$	−25.4518	−	36.3490i	−1.30223	−	1.85978i
$383$	1.24683	+	14.2513i	0.0637100	+	0.728209i	0.959126	+	0.282979i	$0.0913226\pi$
$383$	1.24683	+	14.2513i	0.0637100	+	0.728209i	−0.895416	+	0.445230i	$0.853122\pi$
$384$		0			0
$385$	0.635945	+	2.12782i	0.0324108	+	0.108444i
$386$	−5.88633	+	4.93922i	−0.299606	+	0.251400i
$387$		0			0
$388$	43.0474	−	11.5345i	2.18540	−	0.585576i
$389$	14.4079	−	2.54050i	0.730508	−	0.128808i	0.203991	−	0.978973i	$-0.434609\pi$
$389$	14.4079	−	2.54050i	0.730508	−	0.128808i	0.526517	+	0.850164i	$0.323498\pi$
$390$		0			0
$391$	5.85661	−	10.1440i	0.296182	−	0.513002i
$392$	16.5473	+	4.43384i	0.835766	+	0.223943i
$393$		0			0
$394$	27.8249	−	10.1274i	1.40180	−	0.510212i
$395$	−5.17419	−	13.0420i	−0.260342	−	0.656212i
$396$		0			0
$397$	−8.45661	+	5.92138i	−0.424425	+	0.297186i	−0.766207	−	0.642594i	$-0.777858\pi$
$397$	−8.45661	+	5.92138i	−0.424425	+	0.297186i	0.341782	+	0.939779i	$0.388970\pi$
$398$	−13.7961	−	13.7961i	−0.691535	−	0.691535i
$399$		0			0
$400$	0.125453	−	1.06469i	0.00627265	−	0.0532346i
$401$	−4.46270	−	0.786895i	−0.222857	−	0.0392956i	0.0611047	−	0.998131i	$-0.480538\pi$
$401$	−4.46270	−	0.786895i	−0.222857	−	0.0392956i	−0.283961	+	0.958836i	$0.591649\pi$
$402$		0			0
$403$	−8.79660	+	4.10192i	−0.438190	+	0.204331i
$404$	−15.8258	−	43.4811i	−0.787364	−	2.16326i
$405$		0			0
$406$	−7.87572	−	13.6411i	−0.390865	−	0.676999i
$407$	2.48901	+	9.28911i	0.123376	+	0.460444i
$408$		0			0
$409$	0.693246	+	3.93159i	0.0342788	+	0.194405i	0.997138	−	0.0755979i	$-0.0240865\pi$
$409$	0.693246	+	3.93159i	0.0342788	+	0.194405i	−0.962860	+	0.270003i	$0.912975\pi$
$410$	−30.6908	−	20.2062i	−1.51571	−	0.997914i
$411$		0			0
$412$	2.35284	−	26.8931i	0.115916	−	1.32493i
$413$	2.52757	+	1.17862i	0.124373	+	0.0579963i
$414$		0			0
$415$	0.366749	+	0.346333i	0.0180030	+	0.0170008i
$416$	−2.01158	+	11.4082i	−0.0986257	+	0.559334i
$417$		0			0
$418$	−7.56717	−	5.07098i	−0.370123	−	0.248030i
$419$			24.8998i			1.21644i	0.793770	+	0.608218i	$0.208115\pi$
$419$			24.8998i			1.21644i	−0.793770	+	0.608218i	$0.791885\pi$
$420$		0			0
$421$	−6.21912	+	7.41166i	−0.303101	+	0.361222i	−0.895999	−	0.444056i	$-0.853539\pi$
$421$	−6.21912	+	7.41166i	−0.303101	+	0.361222i	0.592898	+	0.805278i	$0.297984\pi$
$422$	15.7426	+	33.7600i	0.766336	+	1.64341i
$423$		0			0
$424$	4.69329	+	5.59324i	0.227926	+	0.271632i
$425$	6.99129	+	2.78503i	0.339127	+	0.135094i
$426$		0			0
$427$	−0.156153	+	0.223009i	−0.00755675	+	0.0107922i
$428$	−19.2759	+	27.5288i	−0.931736	+	1.33066i
$429$		0			0
$430$	22.2265	+	7.37657i	1.07186	+	0.355730i
$431$	8.83156	+	10.5250i	0.425401	+	0.506973i	0.935590	−	0.353089i	$-0.114869\pi$
$431$	8.83156	+	10.5250i	0.425401	+	0.506973i	−0.510188	+	0.860063i	$0.670424\pi$
$432$		0			0
$433$	−10.1383	−	21.7417i	−0.487217	−	1.04484i	−0.984197	−	0.177078i	$-0.943336\pi$
$433$	−10.1383	−	21.7417i	−0.487217	−	1.04484i	0.496980	−	0.867762i	$-0.334442\pi$
$434$	−7.31306	+	8.71536i	−0.351038	+	0.418351i
$435$		0			0
$436$			1.25174i			0.0599473i
$437$	−32.9391	−	8.10719i	−1.57569	−	0.387820i
$438$		0			0
$439$	3.39505	−	19.2543i	0.162037	−	0.918957i	−0.790030	−	0.613068i	$-0.789935\pi$
$439$	3.39505	−	19.2543i	0.162037	−	0.918957i	0.952067	−	0.305889i	$-0.0989537\pi$
$440$	−4.11792	+	4.36066i	−0.196314	+	0.207886i
$441$		0			0
$442$	6.71682	+	3.13210i	0.319486	+	0.148979i
$443$	1.64937	−	18.8524i	0.0783639	−	0.895703i	−0.850668	−	0.525703i	$-0.823802\pi$
$443$	1.64937	−	18.8524i	0.0783639	−	0.895703i	0.929032	−	0.370000i	$-0.120642\pi$
$444$		0			0
$445$	−29.7951	+	6.13768i	−1.41242	+	0.290954i
$446$	−4.47501	−	25.3790i	−0.211898	−	1.20173i
$447$		0			0
$448$	3.63568	+	13.5685i	0.171770	+	0.641053i
$449$	12.2119	+	21.1517i	0.576317	+	0.998211i	0.995897	+	0.0904922i	$0.0288440\pi$
$449$	12.2119	+	21.1517i	0.576317	+	0.998211i	−0.419580	+	0.907718i	$0.637823\pi$
$450$		0			0
$451$	2.22305	+	6.10777i	0.104679	+	0.287604i
$452$	28.7740	−	13.4175i	1.35341	−	0.631107i
$453$		0			0
$454$	31.9939	+	5.64139i	1.50155	+	0.264764i
$455$	−3.91061	+	3.47688i	−0.183332	+	0.162998i
$456$		0			0
$457$	−0.109557	−	0.109557i	−0.00512484	−	0.00512484i	0.704540	−	0.709665i	$-0.251153\pi$
$457$	−0.109557	−	0.109557i	−0.00512484	−	0.00512484i	−0.709665	+	0.704540i	$0.751153\pi$
$458$	26.7767	−	18.7492i	1.25119	−	0.876094i
$459$		0			0
$460$	−22.6559	+	52.4550i	−1.05634	+	2.44573i
$461$	−17.6438	+	6.42183i	−0.821755	+	0.299094i	−0.718470	−	0.695558i	$-0.755157\pi$
$461$	−17.6438	+	6.42183i	−0.821755	+	0.299094i	−0.103284	+	0.994652i	$0.532935\pi$
$462$		0			0
$463$	−13.5335	−	3.62629i	−0.628956	−	0.168528i	−0.0697600	−	0.997564i	$-0.522223\pi$
$463$	−13.5335	−	3.62629i	−0.628956	−	0.168528i	−0.559196	+	0.829036i	$0.688890\pi$
$464$	0.672496	−	1.16480i	0.0312198	−	0.0540743i
$465$		0			0
$466$	42.2511	−	7.45001i	1.95724	−	0.345115i
$467$	7.97555	−	2.13704i	0.369065	−	0.0988905i	−0.0695198	−	0.997581i	$-0.522147\pi$
$467$	7.97555	−	2.13704i	0.369065	−	0.0988905i	0.438584	+	0.898690i	$0.355480\pi$
$468$		0			0
$469$	7.70947	−	6.46902i	0.355990	−	0.298711i
$470$	−53.8811	−	29.0849i	−2.48535	−	1.34159i
$471$		0			0
$472$	0.656440	+	7.50314i	0.0302151	+	0.345360i
$473$	−2.37600	−	3.39328i	−0.109249	−	0.156023i
$474$		0			0
$475$	2.10685	−	21.6924i	0.0966688	−	0.995317i
$476$	5.39879			0.247453
$477$		0			0
$478$	−1.97720	−	22.5995i	−0.0904350	−	1.03368i
$479$	12.0572	−	33.1269i	0.550907	−	1.51361i	−0.281567	−	0.959542i	$-0.590854\pi$
$479$	12.0572	−	33.1269i	0.550907	−	1.51361i	0.832474	−	0.554064i	$-0.186924\pi$
$480$		0			0
$481$	−17.3580	+	14.5651i	−0.791457	+	0.664111i
$482$	14.1385	−	52.7657i	0.643992	−	2.40341i
$483$		0			0
$484$	−32.8970	+	5.80064i	−1.49532	+	0.263665i
$485$	−3.50927	−	30.1458i	−0.159348	−	1.36885i
$486$		0			0
$487$	25.8535	+	6.92743i	1.17153	+	0.313912i	0.791564	−	0.611086i	$-0.209267\pi$
$487$	25.8535	+	6.92743i	1.17153	+	0.313912i	0.379971	+	0.924998i	$0.375934\pi$
$488$	−0.732444	−	0.0640805i	−0.0331562	−	0.00290079i
$489$		0			0
$490$	11.8338	−	27.3986i	0.534595	−	1.23774i
$491$	27.0749	+	22.7185i	1.22187	+	1.02527i	0.998725	+	0.0504874i	$0.0160775\pi$
$491$	27.0749	+	22.7185i	1.22187	+	1.02527i	0.223147	+	0.974785i	$0.428367\pi$
$492$		0			0
$493$	6.67616	+	6.67616i	0.300679	+	0.300679i
$494$	3.29363	−	21.2090i	0.148187	−	0.954237i
$495$		0			0
$496$	−0.956715	−	0.168695i	−0.0429578	−	0.00757461i
$497$	−9.23554	+	0.808005i	−0.414271	+	0.0362440i
$498$		0			0
$499$	1.69866	+	4.66702i	0.0760422	+	0.208924i	0.971889	−	0.235438i	$-0.0756525\pi$
$499$	1.69866	+	4.66702i	0.0760422	+	0.208924i	−0.895847	+	0.444362i	$0.853430\pi$
$500$	−35.4465	−	9.55112i	−1.58522	−	0.427139i
$501$		0			0
$502$	1.67249	+	6.24181i	0.0746468	+	0.278586i
$503$	−9.45287	−	6.61897i	−0.421483	−	0.295125i	0.343529	−	0.939142i	$-0.388378\pi$
$503$	−9.45287	−	6.61897i	−0.421483	−	0.295125i	−0.765011	+	0.644017i	$0.777267\pi$
$504$		0			0
$505$	−30.8629	+	6.35765i	−1.37338	+	0.282912i
$506$	14.0844	−	8.13164i	0.626129	−	0.361496i
$507$		0			0
$508$	5.47070	+	2.55103i	0.242723	+	0.113184i
$509$	14.9519	+	5.44206i	0.662733	+	0.241215i	0.651416	−	0.758721i	$-0.274175\pi$
$509$	14.9519	+	5.44206i	0.662733	+	0.241215i	0.0113170	+	0.999936i	$0.496398\pi$
$510$		0			0
$511$	1.26684	−	7.18461i	0.0560417	−	0.317829i
$512$	−1.71446	+	1.71446i	−0.0757690	+	0.0757690i
$513$		0			0
$514$		−	29.5953i		−	1.30539i
$515$	−17.8866	−	4.24803i	−0.788177	−	0.187190i
$516$		0			0
$517$	4.57727	+	9.81598i	0.201308	+	0.431707i
$518$	−11.2250	+	24.0721i	−0.493199	+	1.05767i
$519$		0			0
$520$	−13.4125	−	4.45139i	−0.588179	−	0.195206i
$521$	−16.4641	−	9.50554i	−0.721305	−	0.416445i	0.0939281	−	0.995579i	$-0.470058\pi$
$521$	−16.4641	−	9.50554i	−0.721305	−	0.416445i	−0.815233	+	0.579134i	$0.803391\pi$
$522$		0			0
$523$	23.9327	−	34.1794i	1.04650	−	1.49456i	0.187718	−	0.982223i	$-0.439891\pi$
$523$	23.9327	−	34.1794i	1.04650	−	1.49456i	0.858784	−	0.512338i	$-0.171220\pi$
$524$	2.21357	+	1.27800i	0.0967001	+	0.0558298i
$525$		0			0
$526$	11.0898	+	13.2163i	0.483537	+	0.576257i
$527$	2.88205	−	6.18057i	0.125544	−	0.269230i
$528$		0			0
$529$	24.1455	−	28.7755i	1.04980	−	1.25111i
$530$	10.8295	−	6.67278i	0.470405	−	0.289847i
$531$		0			0
$532$	−4.35495	−	15.0164i	−0.188811	−	0.651045i
$533$	−10.8292	+	10.8292i	−0.469066	+	0.469066i
$534$		0			0
$535$	16.6394	+	15.7131i	0.719382	+	0.679337i
$536$	25.5405	+	9.29597i	1.10318	+	0.401525i
$537$		0			0
$538$	−0.150074	+	1.71535i	−0.00647014	+	0.0739541i
$539$	−4.57189	+	2.63958i	−0.196925	+	0.113695i
$540$		0			0
$541$	−3.67444	−	20.8388i	−0.157976	−	0.895929i	−0.956014	−	0.293321i	$-0.905239\pi$
$541$	−3.67444	−	20.8388i	−0.157976	−	0.895929i	0.798038	−	0.602608i	$-0.205872\pi$
$542$	18.0443	+	12.6347i	0.775068	+	0.542708i
$543$		0			0
$544$	−4.06959	−	7.04874i	−0.174482	−	0.302212i
$545$	0.843374	+	0.123938i	0.0361262	+	0.00530894i
$546$		0			0
$547$	−24.6252	+	11.4829i	−1.05290	+	0.490974i	−0.870458	−	0.492243i	$-0.836177\pi$
$547$	−24.6252	+	11.4829i	−1.05290	+	0.490974i	−0.182440	+	0.983217i	$0.558400\pi$
$548$	−13.6606	+	1.19514i	−0.583550	+	0.0510540i
$549$		0			0
$550$	6.47314	+	8.20236i	0.276016	+	0.349750i
$551$	13.1840	−	23.9547i	0.561658	−	1.02050i
$552$		0			0
$553$	−5.61502	+	3.93168i	−0.238775	+	0.167192i
$554$	14.5397	+	12.2003i	0.617734	+	0.518340i
$555$		0			0
$556$	−44.5211	+	16.2043i	−1.88811	+	0.687217i
$557$	−7.29200	−	0.637967i	−0.308972	−	0.0270315i	−0.0683846	−	0.997659i	$-0.521785\pi$
$557$	−7.29200	−	0.637967i	−0.308972	−	0.0270315i	−0.240587	+	0.970627i	$0.577340\pi$
$558$		0			0
$559$	4.88023	−	8.45281i	0.206412	−	0.357516i
$560$	−0.520233	+	0.0605602i	−0.0219839	+	0.00255914i
$561$		0			0
$562$	10.0529	−	2.69366i	0.424055	−	0.113625i
$563$	0.570779	−	2.13018i	0.0240555	−	0.0897762i	−0.952855	−	0.303428i	$-0.901869\pi$
$563$	0.570779	−	2.13018i	0.0240555	−	0.0897762i	0.976910	+	0.213651i	$0.0685356\pi$
$564$		0			0
$565$	−6.19123	−	20.7153i	−0.260467	−	0.871501i
$566$	−9.42485	+	25.8945i	−0.396156	+	1.08843i
$567$		0			0
$568$	−14.3609	−	20.5095i	−0.602570	−	0.860559i
$569$	−37.6654			−1.57902			−0.789508	−	0.613740i	$-0.789664\pi$
$569$	−37.6654			−1.57902			−0.789508	+	0.613740i	$0.789664\pi$
$570$		0			0
$571$	−28.1049			−1.17615			−0.588077	−	0.808805i	$-0.700115\pi$
$571$	−28.1049			−1.17615			−0.588077	+	0.808805i	$0.700115\pi$
$572$	3.66798	+	5.23841i	0.153366	+	0.219029i
$573$		0			0
$574$	−6.13983	+	16.8691i	−0.256272	+	0.704101i
$575$	33.0990	+	20.4585i	1.38032	+	0.853178i
$576$		0			0
$577$	5.60166	−	20.9057i	0.233200	−	0.870314i	−0.745752	−	0.666224i	$-0.767910\pi$
$577$	5.60166	−	20.9057i	0.233200	−	0.870314i	0.978952	−	0.204091i	$-0.0654237\pi$
$578$	32.7148	−	8.76590i	1.36076	−	0.364613i
$579$		0			0
$580$	−36.1144	−	28.5830i	−1.49957	−	1.18684i
$581$	0.123218	−	0.213420i	0.00511195	−	0.00885417i
$582$		0			0
$583$	−2.24148	−	0.196104i	−0.0928326	−	0.00812180i
$584$	18.5144	−	6.73870i	0.766132	−	0.278849i
$585$		0			0
$586$	23.4188	+	19.6507i	0.967420	+	0.811762i
$587$	−0.751166	+	0.525972i	−0.0310039	+	0.0217092i	−0.588976	−	0.808151i	$-0.700469\pi$
$587$	−0.751166	+	0.525972i	−0.0310039	+	0.0217092i	0.557972	+	0.829860i	$0.311580\pi$
$588$		0			0
$589$	−19.5157	−	3.03068i	−0.804132	−	0.124877i
$590$	13.0990	+	0.769069i	0.539277	+	0.0316621i
$591$		0			0
$592$	−2.25934	+	0.197667i	−0.0928584	+	0.00812406i
$593$	20.5889	−	9.60074i	0.845483	−	0.394255i	0.0489143	−	0.998803i	$-0.484424\pi$
$593$	20.5889	−	9.60074i	0.845483	−	0.394255i	0.796569	+	0.604548i	$0.206646\pi$
$594$		0			0
$595$	0.534551	−	3.63750i	0.0219145	−	0.149123i
$596$	28.3157	+	49.0443i	1.15986	+	2.00893i
$597$		0			0
$598$	31.3898	+	21.9794i	1.28362	+	0.898803i
$599$	4.59419	+	26.0549i	0.187713	+	1.06458i	0.922419	+	0.386190i	$0.126209\pi$
$599$	4.59419	+	26.0549i	0.187713	+	1.06458i	−0.734706	+	0.678386i	$0.762680\pi$
$600$		0			0
$601$	−14.0085	+	8.08784i	−0.571420	+	0.329910i	−0.757716	−	0.652584i	$-0.773685\pi$
$601$	−14.0085	+	8.08784i	−0.571420	+	0.329910i	0.186296	+	0.982494i	$0.440352\pi$
$602$	0.997147	−	11.3974i	0.0406407	−	0.464525i
$603$		0			0
$604$	65.4364	+	23.8169i	2.66257	+	0.969095i
$605$	0.651012	+	22.7392i	0.0264674	+	0.924478i
$606$		0			0
$607$	−26.7277	+	26.7277i	−1.08484	+	1.08484i	−0.0887942	+	0.996050i	$0.528301\pi$
$607$	−26.7277	+	26.7277i	−1.08484	+	1.08484i	−0.996050	+	0.0887942i	$0.971699\pi$
$608$	−16.3229	+	17.0052i	−0.661982	+	0.689653i
$609$		0			0
$610$	−0.295979	+	1.24624i	−0.0119838	+	0.0504587i
$611$	−16.4037	+	19.5491i	−0.663622	+	0.790873i
$612$		0			0
$613$	4.91970	−	10.5503i	0.198705	−	0.426124i	−0.781555	−	0.623836i	$-0.785573\pi$
$613$	4.91970	−	10.5503i	0.198705	−	0.426124i	0.980260	+	0.197712i	$0.0633512\pi$
$614$	26.1984	+	31.2220i	1.05728	+	1.26002i
$615$		0			0
$616$	2.53758	+	1.46507i	0.102242	+	0.0590294i
$617$	−16.7231	+	23.8831i	−0.673248	+	0.961497i	0.326619	+	0.945156i	$0.394091\pi$
$617$	−16.7231	+	23.8831i	−0.673248	+	0.961497i	−0.999866	+	0.0163411i	$0.994798\pi$
$618$		0			0
$619$	6.64467	+	3.83630i	0.267072	+	0.154194i	0.627556	−	0.778571i	$-0.284055\pi$
$619$	6.64467	+	3.83630i	0.267072	+	0.154194i	−0.360484	+	0.932765i	$0.617389\pi$
$620$	−10.4785	+	31.5730i	−0.420828	+	1.26800i
$621$		0			0
$622$	2.59119	−	5.55682i	0.103897	−	0.222808i
$623$	6.28087	+	13.4694i	0.251638	+	0.539639i
$624$		0			0
$625$	−9.94487	+	22.9369i	−0.397795	+	0.917474i
$626$			3.40567i			0.136118i
$627$		0			0
$628$	−11.4786	+	11.4786i	−0.458045	+	0.458045i
$629$	2.76459	−	15.6787i	0.110231	−	0.625153i
$630$		0			0
$631$	46.5410	+	16.9396i	1.85277	+	0.674353i	0.983741	+	0.179591i	$0.0574775\pi$
$631$	46.5410	+	16.9396i	1.85277	+	0.674353i	0.869029	+	0.494762i	$0.164745\pi$
$632$	−16.7778	−	7.82361i	−0.667385	−	0.311207i
$633$		0			0
$634$	1.90271	−	1.09853i	0.0755662	−	0.0436282i
$635$	2.26046	−	3.43337i	0.0897037	−	0.136249i
$636$		0			0
$637$	−10.1893	−	7.13463i	−0.403715	−	0.282685i
$638$	3.39289	+	12.6624i	0.134326	+	0.501310i
$639$		0			0
$640$	25.0100	+	33.6271i	0.988608	+	1.32923i
$641$	6.68223	+	18.3593i	0.263932	+	0.725148i	0.998893	+	0.0470384i	$0.0149783\pi$
$641$	6.68223	+	18.3593i	0.263932	+	0.725148i	−0.734961	+	0.678110i	$0.762799\pi$
$642$		0			0
$643$	−37.5158	+	3.28220i	−1.47948	+	0.129438i	−0.798113	−	0.602507i	$-0.794168\pi$
$643$	−37.5158	+	3.28220i	−1.47948	+	0.129438i	−0.681364	+	0.731945i	$0.738613\pi$
$644$	27.4906	+	4.84733i	1.08328	+	0.191011i
$645$		0			0
$646$	7.80585	+	12.9028i	0.307117	+	0.507654i
$647$	−26.8404	−	26.8404i	−1.05520	−	1.05520i	−0.998384	−	0.0568195i	$-0.981904\pi$
$647$	−26.8404	−	26.8404i	−1.05520	−	1.05520i	−0.0568195	−	0.998384i	$-0.518096\pi$
$648$		0			0
$649$	−1.77801	−	1.49193i	−0.0697929	−	0.0585632i
$650$	−11.0700	+	21.9909i	−0.434200	+	0.862553i
$651$		0			0
$652$	45.4163	+	3.97341i	1.77864	+	0.155611i
$653$	−8.97909	−	2.40594i	−0.351379	−	0.0941517i	0.0788123	−	0.996889i	$-0.474887\pi$
$653$	−8.97909	−	2.40594i	−0.351379	−	0.0941517i	−0.430191	+	0.902738i	$0.641554\pi$
$654$		0			0
$655$	1.08024	−	1.36488i	0.0422086	−	0.0533303i
$656$	−1.50958	+	0.266179i	−0.0589391	+	0.0103926i
$657$		0			0
$658$	−7.74217	+	28.8942i	−0.301821	+	1.12641i
$659$	27.5139	−	23.0869i	1.07179	−	0.899339i	0.0765770	−	0.997064i	$-0.475601\pi$
$659$	27.5139	−	23.0869i	1.07179	−	0.899339i	0.995213	+	0.0977247i	$0.0311565\pi$
$660$		0			0
$661$	−1.30561	+	3.58715i	−0.0507825	+	0.139524i	−0.962491	−	0.271314i	$-0.912542\pi$
$661$	−1.30561	+	3.58715i	−0.0507825	+	0.139524i	0.911708	+	0.410838i	$0.134764\pi$
$662$	−5.30197	−	60.6018i	−0.206067	−	2.35536i
$663$		0			0
$664$	0.665545			0.0258282
$665$	−10.5487	+	1.44738i	−0.409061	+	0.0561269i
$666$		0			0
$667$	28.0007	+	39.9891i	1.08419	+	1.54839i
$668$	−3.73357	−	42.6749i	−0.144456	−	1.65114i
$669$		0			0
$670$	22.4923	−	41.6679i	0.868952	−	1.60977i
$671$	0.173566	−	0.145639i	0.00670045	−	0.00562234i
$672$		0			0
$673$	6.36664	−	1.70594i	0.245416	−	0.0657590i	−0.134014	−	0.990979i	$-0.542787\pi$
$673$	6.36664	−	1.70594i	0.245416	−	0.0657590i	0.379430	+	0.925220i	$0.376120\pi$
$674$	9.52297	−	1.67916i	0.366811	−	0.0646787i
$675$		0			0
$676$	13.8089	−	23.9177i	0.531111	−	0.919911i
$677$	47.5516	+	12.7414i	1.82755	+	0.489692i	0.997669	−	0.0682414i	$-0.0217388\pi$
$677$	47.5516	+	12.7414i	1.82755	+	0.489692i	0.829886	+	0.557933i	$0.188405\pi$
$678$		0			0
$679$	−13.9328	+	5.07112i	−0.534691	+	0.194612i
$680$	9.22941	−	3.66162i	0.353932	−	0.140417i
$681$		0			0
$682$	7.75621	−	5.43095i	0.297000	−	0.207962i
$683$	−9.35713	−	9.35713i	−0.358041	−	0.358041i	0.505050	−	0.863090i	$-0.331474\pi$
$683$	−9.35713	−	9.35713i	−0.358041	−	0.358041i	−0.863090	+	0.505050i	$0.831474\pi$
$684$		0			0
$685$	−0.547332	+	9.32232i	−0.0209125	+	0.356187i
$686$	−31.6691	−	5.58411i	−1.20913	−	0.213202i
$687$		0			0
$688$	0.885397	−	0.412867i	0.0337554	−	0.0157404i
$689$	−1.81325	−	4.98187i	−0.0690794	−	0.189794i
$690$		0			0
$691$	11.7412	+	20.3363i	0.446656	+	0.773631i	0.998166	−	0.0605375i	$-0.0192815\pi$
$691$	11.7412	+	20.3363i	0.446656	+	0.773631i	−0.551510	+	0.834168i	$0.685948\pi$
$692$	2.45275	+	9.15379i	0.0932396	+	0.347975i
$693$		0			0
$694$	7.93135	+	44.9809i	0.301070	+	1.70745i
$695$	6.50971	+	31.6011i	0.246927	+	1.19870i
$696$		0			0
$697$	0.937826	−	10.7194i	0.0355227	−	0.406026i
$698$	49.6284	+	23.1421i	1.87846	+	0.875942i
$699$		0			0
$700$	−0.538375	+	17.9267i	−0.0203487	+	0.677565i
$701$	−2.02579	+	11.4888i	−0.0765130	+	0.433927i	0.922354	+	0.386345i	$0.126263\pi$
$701$	−2.02579	+	11.4888i	−0.0765130	+	0.433927i	−0.998867	+	0.0475819i	$0.984849\pi$
$702$		0			0
$703$	−45.8396	+	4.95777i	−1.72887	+	0.186986i
$704$		−	11.6908i		−	0.440612i
$705$		0			0
$706$	−47.7512	+	56.9077i	−1.79714	+	2.14175i
$707$	6.50597	+	13.9521i	0.244682	+	0.524723i
$708$		0			0
$709$	−2.17987	−	2.59787i	−0.0818668	−	0.0975650i	0.723556	−	0.690265i	$-0.242506\pi$
$709$	−2.17987	−	2.59787i	−0.0818668	−	0.0975650i	−0.805423	+	0.592700i	$0.798062\pi$
$710$	−38.9886	+	19.5580i	−1.46322	+	0.733999i
$711$		0			0
$712$	−23.0216	+	32.8782i	−0.862771	+	1.23216i
$713$	20.2246	−	28.8837i	0.757418	−	1.08170i
$714$		0			0
$715$	3.89263	−	1.95268i	0.145576	−	0.0730259i
$716$	24.7741	+	29.5247i	0.925853	+	1.10339i
$717$		0			0
$718$	27.5275	+	59.0329i	1.02732	+	2.20309i
$719$	10.4802	−	12.4898i	0.390844	−	0.465790i	−0.534361	−	0.845256i	$-0.679448\pi$
$719$	10.4802	−	12.4898i	0.390844	−	0.465790i	0.925206	+	0.379466i	$0.123892\pi$
$720$		0			0
$721$			8.98143i			0.334486i
$722$	29.5918	−	32.1196i	1.10129	−	1.19537i
$723$		0			0
$724$	9.01252	−	51.1126i	0.334948	−	1.89958i
$725$	−22.8340	+	21.5024i	−0.848032	+	0.798581i
$726$		0			0
$727$	−47.2763	−	22.0453i	−1.75338	−	0.817615i	−0.983847	−	0.179011i	$-0.942710\pi$
$727$	−47.2763	−	22.0453i	−1.75338	−	0.817615i	−0.769535	−	0.638605i	$-0.779512\pi$
$728$	−0.601728	+	6.87778i	−0.0223015	+	0.254907i
$729$		0			0
$730$	−6.92541	−	33.6191i	−0.256321	−	1.24430i
$731$	1.19084	+	6.75361i	0.0440449	+	0.249791i
$732$		0			0
$733$	11.2613	+	42.0276i	0.415944	+	1.55233i	0.782937	+	0.622101i	$0.213721\pi$
$733$	11.2613	+	42.0276i	0.415944	+	1.55233i	−0.366992	+	0.930224i	$0.619612\pi$
$734$	−18.3880	−	31.8489i	−0.678713	−	1.17556i
$735$		0			0
$736$	−14.3936	−	39.5460i	−0.530554	−	1.45768i
$737$	−7.59101	+	3.53975i	−0.279618	+	0.130388i
$738$		0			0
$739$	−26.2077	−	4.62112i	−0.964066	−	0.169991i	−0.330608	−	0.943768i	$-0.607254\pi$
$739$	−26.2077	−	4.62112i	−0.964066	−	0.169991i	−0.633458	+	0.773777i	$0.718365\pi$
$740$	−4.55190	+	77.5292i	−0.167331	+	2.85003i
$741$		0			0
$742$	−4.39424	−	4.39424i	−0.161318	−	0.161318i
$743$	8.30405	−	5.81456i	0.304646	−	0.213315i	−0.411250	−	0.911523i	$-0.634908\pi$
$743$	8.30405	−	5.81456i	0.304646	−	0.213315i	0.715896	+	0.698207i	$0.246019\pi$
$744$		0			0
$745$	35.8479	−	14.2221i	1.31336	−	0.521056i
$746$	−1.06959	+	0.389300i	−0.0391606	+	0.0142533i
$747$		0			0
$748$	−4.34003	−	1.16291i	−0.158687	−	0.0425202i
$749$	5.59040	−	9.68286i	0.204269	−	0.353804i
$750$		0			0
$751$	11.6832	−	2.06006i	0.426326	−	0.0751727i	0.0436312	−	0.999048i	$-0.486107\pi$
$751$	11.6832	−	2.06006i	0.426326	−	0.0751727i	0.382694	+	0.923875i	$0.374996\pi$
$752$	−2.46723	+	0.661092i	−0.0899706	+	0.0241075i
$753$		0			0
$754$	−23.6615	+	19.8544i	−0.861702	+	0.723054i
$755$	22.5260	−	41.7304i	0.819805	−	1.51873i
$756$		0			0
$757$	−1.75655	−	20.0775i	−0.0638431	−	0.729729i	−0.958894	−	0.283765i	$-0.908416\pi$
$757$	−1.75655	−	20.0775i	−0.0638431	−	0.729729i	0.895051	−	0.445964i	$-0.147139\pi$
$758$	−1.20558	−	1.72174i	−0.0437885	−	0.0625365i
$759$		0			0
$760$	−17.6295	−	22.7174i	−0.639490	−	0.824048i
$761$	24.8234			0.899848			0.449924	−	0.893067i	$-0.351451\pi$
$761$	24.8234			0.899848			0.449924	+	0.893067i	$0.351451\pi$
$762$		0			0
$763$	−0.0362960	−	0.414865i	−0.00131400	−	0.0150191i
$764$	−21.6799	+	59.5649i	−0.784350	+	2.15498i
$765$		0			0
$766$	25.1899	−	21.1368i	0.910148	−	0.763705i
$767$	1.41544	−	5.28249i	0.0511086	−	0.190740i
$768$		0			0
$769$	10.2756	−	1.81187i	0.370548	−	0.0653377i	0.0147267	−	0.999892i	$-0.495312\pi$
$769$	10.2756	−	1.81187i	0.370548	−	0.0653377i	0.355822	+	0.934554i	$0.384201\pi$
$770$	3.16802	−	4.00277i	0.114167	−	0.144250i
$771$		0			0
$772$	10.6026	+	2.84095i	0.381595	+	0.102248i
$773$	−37.6398	−	3.29305i	−1.35381	−	0.118443i	−0.612959	−	0.790115i	$-0.710021\pi$
$773$	−37.6398	−	3.29305i	−1.35381	−	0.118443i	−0.740849	+	0.671672i	$0.765577\pi$
$774$		0			0
$775$	20.2352	+	10.1862i	0.726870	+	0.365899i
$776$	−30.6746	−	25.7390i	−1.10115	−	0.923977i
$777$		0			0
$778$	−23.7791	−	23.7791i	−0.852521	−	0.852521i
$779$	−30.5719	+	6.03833i	−1.09535	+	0.216346i
$780$		0			0
$781$	7.59841	+	1.33980i	0.271892	+	0.0479420i
$782$	−26.8214	+	2.34657i	−0.959133	+	0.0839132i
$783$		0			0
$784$	−0.425818	−	1.16993i	−0.0152078	−	0.0417830i
$785$	6.59731	+	8.87037i	0.235468	+	0.316597i
$786$		0			0
$787$	−1.79456	−	6.69740i	−0.0639693	−	0.238737i	0.926537	−	0.376203i	$-0.122771\pi$
$787$	−1.79456	−	6.69740i	−0.0639693	−	0.238737i	−0.990506	+	0.137467i	$0.956104\pi$
$788$	−34.6489	−	24.2614i	−1.23431	−	0.864276i
$789$		0			0
$790$	−17.7349	+	26.9372i	−0.630979	+	0.958381i
$791$	−9.14753	+	5.28133i	−0.325249	+	0.187783i
$792$		0			0
$793$	0.483840	+	0.225618i	0.0171817	+	0.00801195i
$794$	22.2987	+	8.11605i	0.791350	+	0.288028i
$795$		0			0
$796$	−4.83969	+	27.4473i	−0.171538	+	0.972843i
$797$	17.7625	−	17.7625i	0.629179	−	0.629179i	−0.318682	−	0.947862i	$-0.603240\pi$
$797$	17.7625	−	17.7625i	0.629179	−	0.629179i	0.947862	+	0.318682i	$0.103240\pi$
$798$		0			0
$799$		−	17.9303i		−	0.634329i
$800$	23.8112	−	12.8102i	0.841852	−	0.452908i
$801$		0			0
$802$	4.40206	+	9.44025i	0.155442	+	0.333347i
$803$	−2.56598	+	5.50276i	−0.0905515	+	0.194188i
$804$		0			0
$805$	5.98788	−	18.0422i	0.211045	−	0.635903i
$806$	19.3211	+	11.1550i	0.680555	+	0.392919i
$807$		0			0
$808$	−23.8467	+	34.0566i	−0.838923	+	1.19811i
$809$	40.4029	+	23.3266i	1.42049	+	0.820120i	0.996341	−	0.0854725i	$-0.0272400\pi$
$809$	40.4029	+	23.3266i	1.42049	+	0.820120i	0.424149	+	0.905592i	$0.360573\pi$
$810$		0			0
$811$	1.01348	+	1.20782i	0.0355880	+	0.0424121i	0.783545	−	0.621335i	$-0.213409\pi$
$811$	1.01348	+	1.20782i	0.0355880	+	0.0424121i	−0.747957	+	0.663747i	$0.768965\pi$
$812$	−9.50923	+	20.3926i	−0.333709	+	0.715640i
$813$		0			0
$814$	14.2089	−	16.9335i	0.498020	−	0.593517i
$815$	7.17396	−	30.2064i	0.251293	−	1.05809i
$816$		0			0
$817$	17.8242	−	8.76009i	0.623589	−	0.306477i
$818$	6.48878	−	6.48878i	0.226875	−	0.226875i
$819$		0			0
$820$	1.50216	+	52.4688i	0.0524576	+	1.83229i
$821$	−16.0517	−	5.84233i	−0.560207	−	0.203899i	0.0463686	−	0.998924i	$-0.485235\pi$
$821$	−16.0517	−	5.84233i	−0.560207	−	0.203899i	−0.606576	+	0.795026i	$0.707457\pi$
$822$		0			0
$823$	1.42696	−	16.3102i	0.0497406	−	0.568537i	−0.929905	−	0.367801i	$-0.880111\pi$
$823$	1.42696	−	16.3102i	0.0497406	−	0.568537i	0.979645	−	0.200737i	$-0.0643336\pi$
$824$	−21.0062	+	12.1280i	−0.731787	+	0.422498i
$825$		0			0
$826$	−1.11316	−	6.31305i	−0.0387318	−	0.219659i
$827$	−31.2397	−	21.8743i	−1.08631	−	0.760643i	−0.113801	−	0.993504i	$-0.536303\pi$
$827$	−31.2397	−	21.8743i	−1.08631	−	0.760643i	−0.972510	+	0.232860i	$0.925191\pi$
$828$		0			0
$829$	23.1294	+	40.0614i	0.803319	+	1.39139i	0.917420	+	0.397919i	$0.130268\pi$
$829$	23.1294	+	40.0614i	0.803319	+	1.39139i	−0.114102	+	0.993469i	$0.536399\pi$
$830$	0.168582	−	1.14716i	0.00585155	−	0.0398185i
$831$		0			0
$832$	24.9651	−	11.6414i	0.865510	−	0.403594i
$833$	8.70640	−	0.761711i	0.301659	−	0.0263917i
$834$		0			0
$835$	−29.1224	−	1.70984i	−1.00782	−	0.0591714i
$836$	0.266337	+	13.0096i	0.00921145	+	0.449947i
$837$		0			0
$838$	46.8837	−	32.8283i	1.61957	−	1.13404i
$839$	−26.4145	−	22.1644i	−0.911928	−	0.765199i	0.0605565	−	0.998165i	$-0.480712\pi$
$839$	−26.4145	−	22.1644i	−0.911928	−	0.765199i	−0.972485	+	0.232966i	$0.925157\pi$
$840$		0			0
$841$	−9.72563	+	3.53984i	−0.335367	+	0.122063i
$842$	22.1547	+	1.93829i	0.763503	+	0.0667979i
$843$		0			0
$844$	26.6057	−	46.0824i	0.915805	−	1.58622i
$845$	−14.7476	−	11.6721i	−0.507333	−	0.401532i
$846$		0			0
$847$	10.7349	−	2.87641i	0.368856	−	0.0988347i
$848$	0.137339	−	0.512557i	0.00471625	−	0.0176013i
$849$		0			0
$850$	−3.97352	−	16.8357i	−0.136291	−	0.577459i
$851$	28.1545	−	77.3538i	0.965123	−	2.65165i
$852$		0			0
$853$	−1.55285	−	2.21770i	−0.0531685	−	0.0759324i	0.791688	−	0.610926i	$-0.209203\pi$
$853$	−1.55285	−	2.21770i	−0.0531685	−	0.0759324i	−0.844856	+	0.534994i	$0.820314\pi$
$854$	0.625776			0.0214136
$855$		0			0
$856$	30.1957			1.03207
$857$	−0.496284	−	0.708768i	−0.0169528	−	0.0242110i	0.810586	−	0.585619i	$-0.199149\pi$
$857$	−0.496284	−	0.708768i	−0.0169528	−	0.0242110i	−0.827539	+	0.561408i	$0.810260\pi$
$858$		0			0
$859$	1.69553	−	4.65844i	0.0578508	−	0.158944i	−0.907401	−	0.420267i	$-0.861937\pi$
$859$	1.69553	−	4.65844i	0.0578508	−	0.158944i	0.965251	+	0.261323i	$0.0841587\pi$
$860$	−9.57951	−	32.0523i	−0.326659	−	1.09297i
$861$		0			0
$862$	8.17386	−	30.5053i	0.278403	−	1.03901i
$863$	−11.9228	+	3.19471i	−0.405858	+	0.108749i	−0.455972	−	0.889994i	$-0.650708\pi$
$863$	−11.9228	+	3.19471i	−0.405858	+	0.108749i	0.0501141	+	0.998744i	$0.484042\pi$
$864$		0			0
$865$	6.41034	−	0.746226i	0.217958	−	0.0253725i
$866$	−27.5708	+	47.7540i	−0.936893	+	1.62275i
$867$		0			0
$868$	16.1902	+	1.41646i	0.549532	+	0.0480778i
$869$	5.36075	−	1.95115i	0.181851	−	0.0661884i
$870$		0			0
$871$	−15.1180	−	12.6855i	−0.512253	−	0.429831i
$872$	0.921296	−	0.645099i	0.0311990	−	0.0218458i
$873$		0			0
$874$	28.1625	+	72.7095i	0.952609	+	2.45943i
$875$	12.0250	+	2.13772i	0.406520	+	0.0722680i
$876$		0			0
$877$	−11.6269	+	1.01722i	−0.392614	+	0.0343492i	−0.281754	−	0.959487i	$-0.590916\pi$
$877$	−11.6269	+	1.01722i	−0.392614	+	0.0343492i	−0.110860	+	0.993836i	$0.535361\pi$
$878$	−40.7299	+	18.9926i	−1.37457	+	0.640971i
$879$		0			0
$880$	0.431255	+	0.0633754i	0.0145376	+	0.00213638i
$881$	−15.5870	−	26.9974i	−0.525138	−	0.909566i	−0.999571	−	0.0292745i	$-0.990680\pi$
$881$	−15.5870	−	26.9974i	−0.525138	−	0.909566i	0.474433	−	0.880291i	$-0.342653\pi$
$882$		0			0
$883$	−3.84160	−	2.68992i	−0.129280	−	0.0905229i	0.507148	−	0.861859i	$-0.330700\pi$
$883$	−3.84160	−	2.68992i	−0.129280	−	0.0905229i	−0.636428	+	0.771336i	$0.719589\pi$
$884$	−1.83838	−	10.4260i	−0.0618314	−	0.350663i
$885$		0			0
$886$	−37.6716	+	21.7497i	−1.26560	+	0.730695i
$887$	−2.97829	+	34.0421i	−0.100001	+	1.14302i	0.765953	+	0.642897i	$0.222268\pi$
$887$	−2.97829	+	34.0421i	−0.100001	+	1.14302i	−0.865954	+	0.500124i	$0.833288\pi$
$888$		0			0
$889$	−1.88713	−	0.686860i	−0.0632924	−	0.0230366i
$890$	50.8389	+	48.0090i	1.70412	+	1.60926i
$891$		0			0
$892$	−26.0307	+	26.0307i	−0.871572	+	0.871572i
$893$	−49.8721	+	14.4635i	−1.66891	+	0.484004i
$894$		0			0
$895$	22.3456	−	13.7686i	0.746931	−	0.460232i
$896$	13.1603	−	15.6839i	0.439656	−	0.523962i
$897$		0			0
$898$	23.7260	−	50.8805i	0.791746	−	1.69791i
$899$	18.2693	+	21.7725i	0.609315	+	0.726153i
$900$		0			0
$901$	3.22590	+	1.86247i	0.107470	+	0.0620480i
$902$	8.56938	−	12.2383i	0.285329	−	0.407492i
$903$		0			0
$904$	−24.7045	−	14.2632i	−0.821660	−	0.474386i
$905$	−33.5454	−	11.1331i	−1.11509	−	0.370078i
$906$		0			0
$907$	10.3231	−	22.1380i	0.342773	−	0.735079i	−0.657051	−	0.753846i	$-0.728196\pi$
$907$	10.3231	−	22.1380i	0.342773	−	0.735079i	0.999824	+	0.0187673i	$0.00597417\pi$
$908$	−19.6129	−	42.0600i	−0.650876	−	1.39581i
$909$		0			0
$910$	11.7024	+	2.77929i	0.387931	+	0.0921327i
$911$		−	10.6067i		−	0.351414i	−0.984443	−	0.175707i	$-0.943779\pi$
$911$		−	10.6067i		−	0.351414i	0.984443	−	0.175707i	$-0.0562211\pi$
$912$		0			0
$913$	−0.145025	+	0.145025i	−0.00479963	+	0.00479963i
$914$	−0.0618422	+	0.350725i	−0.00204556	+	0.0116009i
$915$		0			0
$916$	−43.8788	−	15.9706i	−1.44980	−	0.527683i
$917$	−0.770703	−	0.359385i	−0.0254509	−	0.0118679i
$918$		0			0
$919$	−35.6084	+	20.5585i	−1.17461	+	0.678163i	−0.954762	−	0.297371i	$-0.903890\pi$
$919$	−35.6084	+	20.5585i	−1.17461	+	0.678163i	−0.219851	+	0.975534i	$0.570557\pi$
$920$	50.2837	−	10.3583i	1.65780	−	0.341502i
$921$		0			0
$922$	35.3535	+	24.7548i	1.16431	+	0.815256i
$923$	4.70525	+	17.5602i	0.154875	+	0.578002i
$924$		0			0
$925$	51.7856	+	10.7433i	1.70270	+	0.353238i
$926$	11.0149	+	30.2631i	0.361971	+	0.994508i
$927$		0			0
$928$	33.7929	−	2.95650i	1.10931	−	0.0970518i
$929$	−29.4849	−	5.19898i	−0.967367	−	0.170573i	−0.332423	−	0.943131i	$-0.607866\pi$
$929$	−29.4849	−	5.19898i	−0.967367	−	0.170573i	−0.634945	+	0.772558i	$0.718977\pi$
$930$		0			0
$931$	−9.14170	−	23.6019i	−0.299607	−	0.773522i
$932$	−43.3360	−	43.3360i	−1.41952	−	1.41952i
$933$		0			0
$934$	−14.5389	−	12.1996i	−0.475728	−	0.399183i
$935$	−1.21325	+	2.80901i	−0.0396774	+	0.0918645i
$936$		0			0
$937$	−36.7446	−	3.21474i	−1.20039	−	0.105021i	−0.530636	−	0.847600i	$-0.678047\pi$
$937$	−36.7446	−	3.21474i	−1.20039	−	0.105021i	−0.669758	+	0.742579i	$0.733602\pi$
$938$	−22.3448	−	5.98726i	−0.729582	−	0.195491i
$939$		0			0
$940$	10.1136	+	86.8796i	0.329870	+	2.83370i
$941$	42.9712	−	7.57699i	1.40082	−	0.247003i	0.578341	−	0.815795i	$-0.303700\pi$
$941$	42.9712	−	7.57699i	1.40082	−	0.247003i	0.822481	+	0.568793i	$0.192589\pi$
$942$		0			0
$943$	14.3999	−	53.7410i	0.468924	−	1.75005i
$944$	0.419316	−	0.351848i	0.0136476	−	0.0114517i
$945$		0			0
$946$	−3.25663	+	8.94751i	−0.105882	+	0.290909i
$947$	3.07055	+	35.0966i	0.0997796	+	1.14049i	0.866729	+	0.498779i	$0.166218\pi$
$947$	3.07055	+	35.0966i	0.0997796	+	1.14049i	−0.766950	+	0.641707i	$0.778226\pi$
$948$		0			0
$949$	−14.3061			−0.464395
$950$	−43.6222	+	24.6327i	−1.41529	+	0.799189i
$951$		0			0
$952$	−2.78233	−	3.97359i	−0.0901760	−	0.128785i
$953$	−1.39310	−	15.9232i	−0.0451268	−	0.515802i	−0.984796	−	0.173717i	$-0.944422\pi$
$953$	−1.39310	−	15.9232i	−0.0451268	−	0.515802i	0.939669	−	0.342085i	$-0.111133\pi$
$954$		0			0
$955$	37.9861	+	20.5048i	1.22920	+	0.663520i
$956$	−24.8248	+	20.8305i	−0.802891	+	0.673706i
$957$		0			0
$958$	−78.2708	+	20.9726i	−2.52881	+	0.677594i
$959$	4.49288	−	0.792217i	0.145083	−	0.0255820i
$960$		0			0
$961$	−5.23556	+	9.06825i	−0.168889	+	0.292524i
$962$	50.3096	+	13.4804i	1.62205	+	0.434626i
$963$		0			0
$964$	−73.3281	+	26.6893i	−2.36174	+	0.859603i
$965$	2.96392	−	6.86233i	0.0954121	−	0.220906i
$966$		0			0
$967$	18.6250	−	13.0414i	0.598939	−	0.419382i	−0.234403	−	0.972140i	$-0.575313\pi$
$967$	18.6250	−	13.0414i	0.598939	−	0.419382i	0.833342	+	0.552758i	$0.186425\pi$
$968$	21.2233	+	21.2233i	0.682142	+	0.682142i
$969$		0			0
$970$	−52.1346	+	46.3523i	−1.67394	+	1.48828i
$971$	−11.8099	−	2.08241i	−0.378999	−	0.0668277i	−0.0190962	−	0.999818i	$-0.506079\pi$
$971$	−11.8099	−	2.08241i	−0.378999	−	0.0668277i	−0.359902	+	0.932990i	$0.617190\pi$
$972$		0			0
$973$	14.2858	−	6.66158i	0.457982	−	0.213561i
$974$	−21.0421	−	57.8127i	−0.674232	−	1.85244i
$975$		0			0
$976$	0.0267170	+	0.0462753i	0.000855192	+	0.00148124i
$977$	12.7075	+	47.4252i	0.406550	+	1.51727i	0.801178	+	0.598426i	$0.204207\pi$
$977$	12.7075	+	47.4252i	0.406550	+	1.51727i	−0.394628	+	0.918841i	$0.629127\pi$
$978$		0			0
$979$	−2.14781	−	12.1808i	−0.0686442	−	0.389301i
$980$	−41.7564	+	8.60167i	−1.33386	+	0.274770i
$981$		0			0
$982$	7.08059	−	80.9316i	0.225951	−	2.58263i
$983$	−16.4975	−	7.69293i	−0.526190	−	0.245366i	0.141324	−	0.989963i	$-0.454864\pi$
$983$	−16.4975	−	7.69293i	−0.526190	−	0.245366i	−0.667514	+	0.744597i	$0.732642\pi$
$984$		0			0
$985$	−19.7771	+	20.9429i	−0.630152	+	0.667297i
$986$	3.76854	−	21.3724i	0.120015	−	0.680637i
$987$		0			0
$988$	−27.5163	+	13.5235i	−0.875410	+	0.430239i
$989$			35.4585i			1.12751i
$990$		0			0
$991$	−13.0219	+	15.5189i	−0.413655	+	0.492975i	−0.932133	−	0.362116i	$-0.882054\pi$
$991$	−13.0219	+	15.5189i	−0.413655	+	0.492975i	0.518478	+	0.855091i	$0.326499\pi$
$992$	−10.3548	−	22.2059i	−0.328765	−	0.705039i
$993$		0			0
$994$	13.6977	+	16.3242i	0.434464	+	0.517774i
$995$	18.0138	+	5.97845i	0.571075	+	0.189530i
$996$		0			0
$997$	−22.2188	+	31.7318i	−0.703677	+	1.00496i	0.295098	+	0.955467i	$0.404648\pi$
$997$	−22.2188	+	31.7318i	−0.703677	+	1.00496i	−0.998775	+	0.0494880i	$0.984241\pi$
$998$	6.54796	−	9.35146i	0.207272	−	0.296015i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.dl.a.667.1		96
3.2	odd	2		95.2.r.a.2.8	✓	96
5.3	odd	4	inner	855.2.dl.a.838.1		96
15.2	even	4		475.2.bb.b.268.1		96
15.8	even	4		95.2.r.a.78.8	yes	96
15.14	odd	2		475.2.bb.b.382.1		96
19.10	odd	18	inner	855.2.dl.a.352.1		96
57.29	even	18		95.2.r.a.67.8	yes	96
95.48	even	36	inner	855.2.dl.a.523.1		96
285.29	even	18		475.2.bb.b.257.1		96
285.143	odd	36		95.2.r.a.48.8	yes	96
285.257	odd	36		475.2.bb.b.143.1		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.2.8	✓	96	3.2	odd	2
95.2.r.a.48.8	yes	96	285.143	odd	36
95.2.r.a.67.8	yes	96	57.29	even	18
95.2.r.a.78.8	yes	96	15.8	even	4
475.2.bb.b.143.1		96	285.257	odd	36
475.2.bb.b.257.1		96	285.29	even	18
475.2.bb.b.268.1		96	15.2	even	4
475.2.bb.b.382.1		96	15.14	odd	2
855.2.dl.a.352.1		96	19.10	odd	18	inner
855.2.dl.a.523.1		96	95.48	even	36	inner
855.2.dl.a.667.1		96	1.1	even	1	trivial
855.2.dl.a.838.1		96	5.3	odd	4	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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.dl (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31842 - 1.88289i) q^{2} +(-1.12303 + 3.08549i) q^{4} +(1.96769 + 1.06216i) q^{5} +(0.282738 - 1.05519i) q^{7} +(2.84973 - 0.763583i) q^{8} +O(q^{10})\)	\(q+(-1.31842 - 1.88289i) q^{2} +(-1.12303 + 3.08549i) q^{4} +(1.96769 + 1.06216i) q^{5} +(0.282738 - 1.05519i) q^{7} +(2.84973 - 0.763583i) q^{8} +(-0.594310 - 5.10532i) q^{10} +(-0.454581 + 0.787357i) q^{11} +(-2.13403 - 0.186703i) q^{13} +(-2.35958 + 0.858817i) q^{14} +(-0.164249 - 0.137821i) q^{16} +(1.23292 - 0.863300i) q^{17} +(-3.39576 - 2.73291i) q^{19} +(-5.48705 + 4.87847i) q^{20} +(2.08184 - 0.182137i) q^{22} +(7.05313 - 3.28893i) q^{23} +(2.74364 + 4.18000i) q^{25} +(2.46200 + 4.26430i) q^{26} +(2.93826 + 2.05739i) q^{28} +(1.08928 + 6.17764i) q^{29} +(3.92386 - 2.26544i) q^{31} +(0.471310 - 5.38709i) q^{32} +(-3.25100 - 1.18327i) q^{34} +(1.67712 - 1.77598i) q^{35} +(7.47953 - 7.47953i) q^{37} +(-0.668763 + 9.99697i) q^{38} +(6.41844 + 1.52437i) q^{40} +(4.59540 - 5.47659i) q^{41} +(-1.92558 + 4.12943i) q^{43} +(-1.91887 - 2.28683i) q^{44} +(-15.4917 - 8.94412i) q^{46} +(6.83296 - 9.75847i) q^{47} +(5.02869 + 2.90331i) q^{49} +(4.25324 - 10.6770i) q^{50} +(2.97264 - 6.37485i) q^{52} +(1.04592 + 2.24298i) q^{53} +(-1.73077 + 1.06644i) q^{55} -3.22291i q^{56} +(10.1957 - 10.1957i) q^{58} +(-0.443312 + 2.51415i) q^{59} +(-0.234183 - 0.0852357i) q^{61} +(-9.43886 - 4.40141i) q^{62} +(-11.1361 + 6.42942i) q^{64} +(-4.00081 - 2.63405i) q^{65} +(7.54653 + 5.28414i) q^{67} +(1.27910 + 4.77367i) q^{68} +(-5.55513 - 0.816358i) q^{70} +(-2.90257 - 7.97473i) q^{71} +(6.65286 - 0.582050i) q^{73} +(-23.9443 - 4.22203i) q^{74} +(12.2459 - 7.40844i) q^{76} +(0.702285 + 0.702285i) q^{77} +(-4.80677 - 4.03336i) q^{79} +(-0.176804 - 0.445648i) q^{80} +(-16.3705 - 1.43223i) q^{82} +(0.217902 + 0.0583867i) q^{83} +(3.34297 - 0.389154i) q^{85} +(10.3140 - 1.81864i) q^{86} +(-0.694220 + 2.59086i) q^{88} +(-10.4217 + 8.74483i) q^{89} +(-0.800379 + 2.19902i) q^{91} +(2.22710 + 25.4559i) q^{92} -27.3828 q^{94} +(-3.77903 - 8.98437i) q^{95} +(-7.78495 - 11.1181i) q^{97} +(-1.16327 - 13.2963i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8}+O(q^{10}) \) 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8	\( 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40} - 12 q^{41} + 48 q^{43} - 36 q^{46} + 24 q^{47} - 126 q^{50} + 30 q^{53} + 18 q^{55} + 120 q^{58} - 48 q^{61} - 60 q^{62} - 72 q^{65} + 108 q^{67} - 18 q^{68} + 36 q^{70} + 24 q^{71} + 6 q^{73} + 60 q^{76} - 168 q^{77} + 60 q^{80} + 60 q^{82} - 36 q^{85} + 180 q^{86} - 198 q^{88} - 24 q^{91} + 72 q^{92} + 24 q^{95} - 72 q^{97} + 90 q^{98}+O(q^{100}) \) 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 + 12 * q^16 + 30 * q^17 + 84 * q^20 - 24 * q^22 + 12 * q^25 + 48 * q^26 - 36 * q^31 - 18 * q^32 + 30 * q^35 - 54 * q^38 + 54 * q^40 - 12 * q^41 + 48 * q^43 - 36 * q^46 + 24 * q^47 - 126 * q^50 + 30 * q^53 + 18 * q^55 + 120 * q^58 - 48 * q^61 - 60 * q^62 - 72 * q^65 + 108 * q^67 - 18 * q^68 + 36 * q^70 + 24 * q^71 + 6 * q^73 + 60 * q^76 - 168 * q^77 + 60 * q^80 + 60 * q^82 - 36 * q^85 + 180 * q^86 - 198 * q^88 - 24 * q^91 + 72 * q^92 + 24 * q^95 - 72 * q^97 + 90 * q^98

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