LMFDB - Embedded newform 855.2.bs.b.766.1

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} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} + \cdots + 361 $ x^18 + 12x^16 - 8x^15 + 96x^14 - 75x^13 + 448x^12 - 405x^11 + 1521x^10 - 1294x^9 + 3333x^8 - 2616x^7 + 5113x^6 - 3126x^5 + 4032x^4 - 1359x^3 + 1698x^2 - 513x + 361
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			766.1
Root			$-0.908512 - 1.57359i$ of defining polynomial
Character	$\chi$	$=$	855.766
Dual form			855.2.bs.b.586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39192 + 1.16796i) q^{2} +(0.226016 - 1.28180i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-0.536732 + 0.929646i) q^{7} +(-0.634528 - 1.09903i) q^{8} +O(q^{10})$	\(q+(-1.39192 + 1.16796i) q^{2} +(0.226016 - 1.28180i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-0.536732 + 0.929646i) q^{7} +(-0.634528 - 1.09903i) q^{8} +(-1.39192 - 1.16796i) q^{10} +(-1.65508 - 2.86668i) q^{11} +(-2.49736 + 0.908963i) q^{13} +(-0.338702 - 1.92087i) q^{14} +(4.61300 + 1.67899i) q^{16} +(3.06411 - 2.57109i) q^{17} +(0.281925 - 4.34977i) q^{19} +1.30157 q^{20} +(5.65190 + 2.05712i) q^{22} +(-0.304541 + 1.72714i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(2.41449 - 4.18202i) q^{26} +(1.07031 + 0.898098i) q^{28} +(-1.72552 - 1.44789i) q^{29} +(4.02636 - 6.97386i) q^{31} +(-5.99689 + 2.18269i) q^{32} +(-1.26206 + 7.15751i) q^{34} +(-1.00873 - 0.367146i) q^{35} -5.64805 q^{37} +(4.68794 + 6.38382i) q^{38} +(0.972153 - 0.815733i) q^{40} +(-0.842126 - 0.306509i) q^{41} +(-1.47811 - 8.38279i) q^{43} +(-4.04858 + 1.47356i) q^{44} +(-1.59333 - 2.75973i) q^{46} +(4.82313 + 4.04709i) q^{47} +(2.92384 + 5.06424i) q^{49} +(0.908512 - 1.57359i) q^{50} +(0.600667 + 3.40655i) q^{52} +(0.590304 - 3.34778i) q^{53} +(2.53572 - 2.12772i) q^{55} +1.36228 q^{56} +4.09287 q^{58} +(1.13893 - 0.955673i) q^{59} +(2.38416 - 13.5212i) q^{61} +(2.54082 + 14.4097i) q^{62} +(0.888845 - 1.53952i) q^{64} +(-1.32882 - 2.30158i) q^{65} +(9.85110 + 8.26605i) q^{67} +(-2.60309 - 4.50868i) q^{68} +(1.83288 - 0.667113i) q^{70} +(-1.91469 - 10.8587i) q^{71} +(2.45320 + 0.892893i) q^{73} +(7.86164 - 6.59670i) q^{74} +(-5.51182 - 1.34449i) q^{76} +3.55333 q^{77} +(6.17425 + 2.24724i) q^{79} +(-0.852448 + 4.83447i) q^{80} +(1.53016 - 0.556934i) q^{82} +(1.34944 - 2.33730i) q^{83} +(3.06411 + 2.57109i) q^{85} +(11.8482 + 9.94180i) q^{86} +(-2.10038 + 3.63797i) q^{88} +(0.742205 - 0.270140i) q^{89} +(0.495396 - 2.80953i) q^{91} +(2.14502 + 0.780722i) q^{92} -11.4403 q^{94} +(4.33265 - 0.477688i) q^{95} +(-14.3388 + 12.0317i) q^{97} +(-9.98458 - 3.63409i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) $ 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8	$ 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) $ 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8 - 3 * q^10 - 3 * q^13 - 24 * q^14 + 21 * q^16 + 24 * q^17 - 12 * q^19 + 12 * q^20 + 15 * q^22 - 21 * q^23 + 21 * q^26 - 24 * q^28 + 9 * q^29 + 30 * q^31 - 45 * q^32 + 24 * q^34 + 6 * q^35 - 60 * q^37 + 15 * q^38 - 6 * q^40 + 6 * q^41 - 6 * q^43 + 30 * q^44 + 21 * q^46 - 33 * q^47 - 3 * q^49 + 9 * q^52 - 24 * q^53 - 3 * q^55 + 72 * q^56 + 36 * q^58 - 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^64 - 3 * q^65 - 24 * q^67 + 3 * q^68 + 39 * q^70 - 24 * q^71 + 6 * q^73 + 39 * q^74 + 27 * q^76 - 24 * q^77 + 9 * q^79 - 33 * q^80 - 57 * q^82 + 24 * q^85 + 33 * q^86 + 39 * q^88 + 6 * q^89 - 6 * q^91 + 66 * q^92 - 66 * q^94 + 15 * q^95 - 87 * q^97 - 39 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−1.39192	+	1.16796i	−0.984237	+	0.825873i	−0.984723	−	0.174127i	$-0.944290\pi$
$2$	−1.39192	+	1.16796i	−0.984237	+	0.825873i	0.000486534		1.00000i	$0.499845\pi$
$3$		0			0
$3$		0			0
$4$	0.226016	−	1.28180i	0.113008	−	0.640900i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$6$		0			0
$7$	−0.536732	+	0.929646i	−0.202865	+	0.351373i	−0.949451	−	0.313917i	$-0.898359\pi$
$7$	−0.536732	+	0.929646i	−0.202865	+	0.351373i	0.746585	+	0.665290i	$0.231692\pi$
$8$	−0.634528	−	1.09903i	−0.224339	−	0.388567i
$9$		0			0
$10$	−1.39192	−	1.16796i	−0.440164	−	0.369341i
$11$	−1.65508	−	2.86668i	−0.499024	−	0.864335i	0.500975	−	0.865462i	$-0.332975\pi$
$11$	−1.65508	−	2.86668i	−0.499024	−	0.864335i	−0.999999	+	0.00112649i	$0.999641\pi$
$12$		0			0
$13$	−2.49736	+	0.908963i	−0.692642	+	0.252101i	−0.664266	−	0.747496i	$-0.731256\pi$
$13$	−2.49736	+	0.908963i	−0.692642	+	0.252101i	−0.0283760	+	0.999597i	$0.509034\pi$
$14$	−0.338702	−	1.92087i	−0.0905219	−	0.513375i
$15$		0			0
$16$	4.61300	+	1.67899i	1.15325	+	0.419749i
$17$	3.06411	−	2.57109i	0.743155	−	0.623581i	−0.190528	−	0.981682i	$-0.561020\pi$
$17$	3.06411	−	2.57109i	0.743155	−	0.623581i	0.933683	+	0.358101i	$0.116576\pi$
$18$		0			0
$19$	0.281925	−	4.34977i	0.0646780	−	0.997906i
$19$	0.281925	−	4.34977i	0.0646780	−	0.997906i
$20$	1.30157			0.291041
$21$		0			0
$22$	5.65190	+	2.05712i	1.20499	+	0.438580i
$23$	−0.304541	+	1.72714i	−0.0635012	+	0.360133i	0.936455	+	0.350787i	$0.114086\pi$
$23$	−0.304541	+	1.72714i	−0.0635012	+	0.360133i	−0.999956	+	0.00934578i	$0.997025\pi$
$24$		0			0
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	2.41449	−	4.18202i	0.473520	−	0.820161i
$27$		0			0
$28$	1.07031	+	0.898098i	0.202270	+	0.169725i
$29$	−1.72552	−	1.44789i	−0.320422	−	0.268866i	0.468362	−	0.883537i	$-0.344844\pi$
$29$	−1.72552	−	1.44789i	−0.320422	−	0.268866i	−0.788784	+	0.614671i	$0.789289\pi$
$30$		0			0
$31$	4.02636	−	6.97386i	0.723156	−	1.25254i	−0.236573	−	0.971614i	$-0.576024\pi$
$31$	4.02636	−	6.97386i	0.723156	−	1.25254i	0.959729	−	0.280929i	$-0.0906425\pi$
$32$	−5.99689	+	2.18269i	−1.06011	+	0.385848i
$33$		0			0
$34$	−1.26206	+	7.15751i	−0.216442	+	1.22750i
$35$	−1.00873	−	0.367146i	−0.170506	−	0.0620590i
$36$		0			0
$37$	−5.64805			−0.928534			−0.464267	−	0.885695i	$-0.653682\pi$
$37$	−5.64805			−0.928534			−0.464267	+	0.885695i	$0.653682\pi$
$38$	4.68794	+	6.38382i	0.760485	+	1.03559i
$39$		0			0
$40$	0.972153	−	0.815733i	0.153711	−	0.128979i
$41$	−0.842126	−	0.306509i	−0.131518	−	0.0478686i	0.275423	−	0.961323i	$-0.411182\pi$
$41$	−0.842126	−	0.306509i	−0.131518	−	0.0478686i	−0.406941	+	0.913455i	$0.633404\pi$
$42$		0			0
$43$	−1.47811	−	8.38279i	−0.225410	−	1.27836i	−0.861900	−	0.507079i	$-0.830725\pi$
$43$	−1.47811	−	8.38279i	−0.225410	−	1.27836i	0.636490	−	0.771285i	$-0.280386\pi$
$44$	−4.04858	+	1.47356i	−0.610346	+	0.222148i
$45$		0			0
$46$	−1.59333	−	2.75973i	−0.234924	−	0.406900i
$47$	4.82313	+	4.04709i	0.703527	+	0.590329i	0.922775	−	0.385340i	$-0.125916\pi$
$47$	4.82313	+	4.04709i	0.703527	+	0.590329i	−0.219248	+	0.975669i	$0.570360\pi$
$48$		0			0
$49$	2.92384	+	5.06424i	0.417691	+	0.723462i
$50$	0.908512	−	1.57359i	0.128483	−	0.222539i
$51$		0			0
$52$	0.600667	+	3.40655i	0.0832976	+	0.472404i
$53$	0.590304	−	3.34778i	0.0810846	−	0.459853i	−0.917048	−	0.398776i	$-0.869435\pi$
$53$	0.590304	−	3.34778i	0.0810846	−	0.459853i	0.998133	−	0.0610776i	$-0.0194537\pi$
$54$		0			0
$55$	2.53572	−	2.12772i	0.341917	−	0.286902i
$56$	1.36228			0.182043
$57$		0			0
$58$	4.09287			0.537420
$59$	1.13893	−	0.955673i	0.148276	−	0.124418i	−0.565632	−	0.824657i	$-0.691368\pi$
$59$	1.13893	−	0.955673i	0.148276	−	0.124418i	0.713908	+	0.700239i	$0.246923\pi$
$60$		0			0
$61$	2.38416	−	13.5212i	0.305260	−	1.73122i	−0.317016	−	0.948420i	$-0.602681\pi$
$61$	2.38416	−	13.5212i	0.305260	−	1.73122i	0.622277	−	0.782797i	$-0.286208\pi$
$62$	2.54082	+	14.4097i	0.322684	+	1.83003i
$63$		0			0
$64$	0.888845	−	1.53952i	0.111106	−	0.192441i
$65$	−1.32882	−	2.30158i	−0.164819	−	0.285475i
$66$		0			0
$67$	9.85110	+	8.26605i	1.20350	+	1.00986i	0.999523	+	0.0308840i	$0.00983223\pi$
$67$	9.85110	+	8.26605i	1.20350	+	1.00986i	0.203980	+	0.978975i	$0.434612\pi$
$68$	−2.60309	−	4.50868i	−0.315671	−	0.546758i
$69$		0			0
$70$	1.83288	−	0.667113i	0.219071	−	0.0797352i
$71$	−1.91469	−	10.8587i	−0.227231	−	1.28869i	−0.858373	−	0.513026i	$-0.828524\pi$
$71$	−1.91469	−	10.8587i	−0.227231	−	1.28869i	0.631141	−	0.775668i	$-0.282587\pi$
$72$		0			0
$73$	2.45320	+	0.892893i	0.287126	+	0.104505i	0.481568	−	0.876409i	$-0.340067\pi$
$73$	2.45320	+	0.892893i	0.287126	+	0.104505i	−0.194442	+	0.980914i	$0.562290\pi$
$74$	7.86164	−	6.59670i	0.913897	−	0.766851i
$75$		0			0
$76$	−5.51182	−	1.34449i	−0.632249	−	0.154224i
$77$	3.55333			0.404939
$78$		0			0
$79$	6.17425	+	2.24724i	0.694657	+	0.252835i	0.665128	−	0.746729i	$-0.268377\pi$
$79$	6.17425	+	2.24724i	0.694657	+	0.252835i	0.0295293	+	0.999564i	$0.490599\pi$
$80$	−0.852448	+	4.83447i	−0.0953066	+	0.540511i
$81$		0			0
$82$	1.53016	−	0.556934i	0.168978	−	0.0615030i
$83$	1.34944	−	2.33730i	0.148120	−	0.256552i	−0.782412	−	0.622761i	$-0.786011\pi$
$83$	1.34944	−	2.33730i	0.148120	−	0.256552i	0.930533	+	0.366209i	$0.119344\pi$
$84$		0			0
$85$	3.06411	+	2.57109i	0.332349	+	0.278874i
$86$	11.8482	+	9.94180i	1.27762	+	1.07205i
$87$		0			0
$88$	−2.10038	+	3.63797i	−0.223902	+	0.387809i
$89$	0.742205	−	0.270140i	0.0786736	−	0.0286348i	−0.302384	−	0.953186i	$-0.597782\pi$
$89$	0.742205	−	0.270140i	0.0786736	−	0.0286348i	0.381057	+	0.924551i	$0.375560\pi$
$90$		0			0
$91$	0.495396	−	2.80953i	0.0519316	−	0.294519i
$92$	2.14502	+	0.780722i	0.223633	+	0.0813959i
$93$		0			0
$94$	−11.4403			−1.17997
$95$	4.33265	−	0.477688i	0.444520	−	0.0490098i
$96$		0			0
$97$	−14.3388	+	12.0317i	−1.45588	+	1.22163i	−0.527737	+	0.849408i	$0.676959\pi$
$97$	−14.3388	+	12.0317i	−1.45588	+	1.22163i	−0.928144	+	0.372222i	$0.878596\pi$
$98$	−9.98458	−	3.63409i	−1.00859	−	0.367098i
$99$		0			0
$100$	0.226016	+	1.28180i	0.0226016	+	0.128180i
$101$	17.7763	−	6.47005i	1.76881	−	0.643794i	0.768818	−	0.639467i	$-0.220845\pi$
$101$	17.7763	−	6.47005i	1.76881	−	0.643794i	0.999991	−	0.00432656i	$-0.00137719\pi$
$102$		0			0
$103$	5.82191	+	10.0838i	0.573650	+	0.993591i	0.996187	+	0.0872452i	$0.0278064\pi$
$103$	5.82191	+	10.0838i	0.573650	+	0.993591i	−0.422537	+	0.906346i	$0.638860\pi$
$104$	2.58362	+	2.16792i	0.253345	+	0.212582i
$105$		0			0
$106$	3.08842	+	5.34930i	0.299974	+	0.519570i
$107$	5.69791	−	9.86907i	0.550838	−	0.954079i	−0.447376	−	0.894346i	$-0.647642\pi$
$107$	5.69791	−	9.86907i	0.550838	−	0.954079i	0.998214	−	0.0597335i	$-0.0190251\pi$
$108$		0			0
$109$	−2.21184	−	12.5440i	−0.211856	−	1.20149i	−0.886280	−	0.463150i	$-0.846719\pi$
$109$	−2.21184	−	12.5440i	−0.211856	−	1.20149i	0.674424	−	0.738344i	$-0.264392\pi$
$110$	−1.04443	+	5.92325i	−0.0995823	+	0.564759i
$111$		0			0
$112$	−4.03681	+	3.38729i	−0.381443	+	0.320069i
$113$	−16.5894			−1.56060			−0.780300	−	0.625406i	$-0.784933\pi$
$113$	−16.5894			−1.56060			−0.780300	+	0.625406i	$0.784933\pi$
$114$		0			0
$115$	−1.75378			−0.163541
$116$	−2.24590	+	1.88453i	−0.208526	+	0.174974i
$117$		0			0
$118$	−0.469108	+	2.66044i	−0.0431849	+	0.244914i
$119$	0.745602	+	4.22852i	0.0683492	+	0.387628i
$120$		0			0
$121$	0.0214486	−	0.0371501i	0.00194987	−	0.00337728i
$122$	12.4737	+	21.6051i	1.12932	+	1.95603i
$123$		0			0
$124$	−8.02908	−	6.73720i	−0.721033	−	0.605018i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$		0			0
$127$	9.13699	−	3.32559i	0.810777	−	0.295099i	0.0968322	−	0.995301i	$-0.469129\pi$
$127$	9.13699	−	3.32559i	0.810777	−	0.295099i	0.713945	+	0.700202i	$0.246907\pi$
$128$	−1.65546	−	9.38857i	−0.146323	−	0.829840i
$129$		0			0
$130$	4.53776	+	1.65161i	0.397988	+	0.144856i
$131$	−11.3300	+	9.50703i	−0.989910	+	0.830633i	−0.985555	−	0.169358i	$-0.945831\pi$
$131$	−11.3300	+	9.50703i	−0.989910	+	0.830633i	−0.00435510	+	0.999991i	$0.501386\pi$
$132$		0			0
$133$	3.89243	+	2.59675i	0.337517	+	0.225167i
$134$	−23.3664			−2.01855
$135$		0			0
$136$	−4.76998	−	1.73613i	−0.409022	−	0.148872i
$137$	−0.624490	+	3.54166i	−0.0533538	+	0.302584i	−0.999794	−	0.0202946i	$-0.993540\pi$
$137$	−0.624490	+	3.54166i	−0.0533538	+	0.302584i	0.946440	+	0.322879i	$0.104651\pi$
$138$		0			0
$139$	5.50159	−	2.00242i	0.466639	−	0.169843i	−0.0979902	−	0.995187i	$-0.531241\pi$
$139$	5.50159	−	2.00242i	0.466639	−	0.169843i	0.564629	+	0.825345i	$0.309019\pi$
$140$	−0.698596	+	1.21000i	−0.0590421	+	0.102264i
$141$		0			0
$142$	15.3477	+	12.8782i	1.28795	+	1.08072i
$143$	6.73902	+	5.65471i	0.563545	+	0.472870i
$144$		0			0
$145$	1.12626	−	1.95073i	0.0935304	−	0.161999i
$146$	−4.45753	+	1.62241i	−0.368908	+	0.134271i
$147$		0			0
$148$	−1.27655	+	7.23968i	−0.104932	+	0.595098i
$149$	9.45957	+	3.44300i	0.774958	+	0.282062i	0.699069	−	0.715054i	$-0.253598\pi$
$149$	9.45957	+	3.44300i	0.774958	+	0.282062i	0.0758895	+	0.997116i	$0.475820\pi$
$150$		0			0
$151$	−2.12653			−0.173054			−0.0865272	−	0.996249i	$-0.527577\pi$
$151$	−2.12653			−0.173054			−0.0865272	+	0.996249i	$0.527577\pi$
$152$	−4.95944	+	2.45021i	−0.402264	+	0.198738i
$153$		0			0
$154$	−4.94595	+	4.15014i	−0.398556	+	0.334428i
$155$	7.56708	+	2.75419i	0.607803	+	0.221222i
$156$		0			0
$157$	−2.00562	−	11.3744i	−0.160066	−	0.907779i	−0.954007	−	0.299784i	$-0.903085\pi$
$157$	−2.00562	−	11.3744i	−0.160066	−	0.907779i	0.793941	−	0.607995i	$-0.208026\pi$
$158$	−11.2188	+	4.08329i	−0.892516	+	0.324849i
$159$		0			0
$160$	−3.19088	−	5.52676i	−0.252261	−	0.436929i
$161$	−1.44217	−	1.21012i	−0.113659	−	0.0953712i
$162$		0			0
$163$	−9.21567	−	15.9620i	−0.721827	−	1.25024i	−0.960267	−	0.279084i	$-0.909969\pi$
$163$	−9.21567	−	15.9620i	−0.721827	−	1.25024i	0.238439	−	0.971157i	$-0.423364\pi$
$164$	−0.583217	+	1.01016i	−0.0455416	+	0.0788804i
$165$		0			0
$166$	0.851559	+	4.82943i	0.0660938	+	0.374836i
$167$	−0.337332	+	1.91311i	−0.0261035	+	0.148041i	−0.995074	−	0.0991367i	$-0.968392\pi$
$167$	−0.337332	+	1.91311i	−0.0261035	+	0.148041i	0.968970	+	0.247177i	$0.0795030\pi$
$168$		0			0
$169$	−4.54800	+	3.81623i	−0.349846	+	0.293556i
$170$	−7.26792			−0.557424
$171$		0			0
$172$	−11.0791			−0.844777
$173$	9.23195	−	7.74653i	0.701892	−	0.588958i	−0.220419	−	0.975405i	$-0.570742\pi$
$173$	9.23195	−	7.74653i	0.701892	−	0.588958i	0.922311	+	0.386448i	$0.126298\pi$
$174$		0			0
$175$	0.186405	−	1.05715i	0.0140909	−	0.0799134i
$176$	−2.82173	−	16.0028i	−0.212696	−	1.20626i
$177$		0			0
$178$	−0.717577	+	1.24288i	−0.0537847	+	0.0931578i
$179$	−9.15519	−	15.8573i	−0.684291	−	1.18523i	−0.973659	−	0.228009i	$-0.926778\pi$
$179$	−9.15519	−	15.8573i	−0.684291	−	1.18523i	0.289368	−	0.957218i	$-0.406555\pi$
$180$		0			0
$181$	−19.6501	−	16.4884i	−1.46058	−	1.22557i	−0.924375	−	0.381486i	$-0.875412\pi$
$181$	−19.6501	−	16.4884i	−1.46058	−	1.22557i	−0.536206	−	0.844087i	$-0.680143\pi$
$182$	2.59187	+	4.48924i	0.192122	+	0.332765i
$183$		0			0
$184$	2.09142	−	0.761216i	0.154182	−	0.0561176i
$185$	−0.980774	−	5.56225i	−0.0721080	−	0.408945i
$186$		0			0
$187$	−12.4418	−	4.52845i	−0.909835	−	0.331153i
$188$	6.27767	−	5.26759i	0.457846	−	0.384178i
$189$		0			0
$190$	−5.47278	+	5.72526i	−0.397037	+	0.415354i
$191$	−9.22171			−0.667259			−0.333630	−	0.942704i	$-0.608274\pi$
$191$	−9.22171			−0.667259			−0.333630	+	0.942704i	$0.608274\pi$
$192$		0			0
$193$	−11.2782	−	4.10492i	−0.811821	−	0.295479i	−0.0974450	−	0.995241i	$-0.531067\pi$
$193$	−11.2782	−	4.10492i	−0.811821	−	0.295479i	−0.714376	+	0.699762i	$0.753289\pi$
$194$	5.90593	−	33.4942i	0.424021	−	2.40474i
$195$		0			0
$196$	7.15218	−	2.60318i	0.510870	−	0.185941i
$197$	−13.4486	+	23.2937i	−0.958174	+	1.65961i	−0.231243	+	0.972896i	$0.574279\pi$
$197$	−13.4486	+	23.2937i	−0.958174	+	1.65961i	−0.726931	+	0.686710i	$0.759054\pi$
$198$		0			0
$199$	−3.50384	−	2.94007i	−0.248381	−	0.208416i	0.510094	−	0.860119i	$-0.329611\pi$
$199$	−3.50384	−	2.94007i	−0.248381	−	0.208416i	−0.758475	+	0.651702i	$0.774055\pi$
$200$	0.972153	+	0.815733i	0.0687416	+	0.0576810i
$201$		0			0
$202$	−17.1865	+	29.7678i	−1.20923	+	2.09446i
$203$	2.27217	−	0.827000i	0.159475	−	0.0580441i
$204$		0			0
$205$	0.155619	−	0.882557i	0.0108689	−	0.0616405i
$206$	−19.8812	−	7.23615i	−1.38519	−	0.504167i
$207$		0			0
$208$	−13.0465			−0.904609
$209$	−12.9360	+	6.39102i	−0.894801	+	0.442076i
$210$		0			0
$211$	−11.9217	+	10.0035i	−0.820721	+	0.688667i	−0.953141	−	0.302527i	$-0.902170\pi$
$211$	−11.9217	+	10.0035i	−0.820721	+	0.688667i	0.132419	+	0.991194i	$0.457725\pi$
$212$	−4.15777	−	1.51331i	−0.285557	−	0.103934i
$213$		0			0
$214$	3.59564	+	20.3919i	0.245793	+	1.39396i
$215$	7.99877	−	2.91131i	0.545511	−	0.198550i
$216$		0			0
$217$	4.32215	+	7.48618i	0.293407	+	0.508195i
$218$	17.7296	+	14.8769i	1.20080	+	1.00759i
$219$		0			0
$220$	−2.15420	−	3.73119i	−0.145236	−	0.251557i
$221$	−5.31514	+	9.20609i	−0.357535	+	0.619269i
$222$		0			0
$223$	−3.49526	−	19.8226i	−0.234060	−	1.32742i	−0.844584	−	0.535423i	$-0.820152\pi$
$223$	−3.49526	−	19.8226i	−0.234060	−	1.32742i	0.610524	−	0.791998i	$-0.290959\pi$
$224$	1.18959	−	6.74650i	0.0794828	−	0.450770i
$225$		0			0
$226$	23.0911	−	19.3758i	1.53600	−	1.28886i
$227$	−13.8680			−0.920453			−0.460226	−	0.887802i	$-0.652232\pi$
$227$	−13.8680			−0.920453			−0.460226	+	0.887802i	$0.652232\pi$
$228$		0			0
$229$	8.70352			0.575145			0.287572	−	0.957759i	$-0.407152\pi$
$229$	8.70352			0.575145			0.287572	+	0.957759i	$0.407152\pi$
$230$	2.44113	−	2.04835i	0.160963	−	0.135064i
$231$		0			0
$232$	−0.496384	+	2.81513i	−0.0325892	+	0.184823i
$233$	−2.72986	−	15.4818i	−0.178839	−	1.01425i	−0.933619	−	0.358268i	$-0.883367\pi$
$233$	−2.72986	−	15.4818i	−0.178839	−	1.01425i	0.754780	−	0.655978i	$-0.227744\pi$
$234$		0			0
$235$	−3.14808	+	5.45263i	−0.205358	+	0.355690i
$236$	−0.967567	−	1.67587i	−0.0629832	−	0.109090i
$237$		0			0
$238$	−5.97656	−	5.01493i	−0.387403	−	0.325070i
$239$	−6.91731	−	11.9811i	−0.447443	−	0.774995i	0.550775	−	0.834653i	$-0.314332\pi$
$239$	−6.91731	−	11.9811i	−0.447443	−	0.774995i	−0.998219	+	0.0596587i	$0.980999\pi$
$240$		0			0
$241$	−11.4424	+	4.16469i	−0.737070	+	0.268271i	−0.683154	−	0.730274i	$-0.739392\pi$
$241$	−11.4424	+	4.16469i	−0.737070	+	0.268271i	−0.0539155	+	0.998546i	$0.517170\pi$
$242$	0.0135351	+	0.0767611i	0.000870066	+	0.00493439i
$243$		0			0
$244$	−16.7927	−	6.11203i	−1.07504	−	0.391283i
$245$	−4.47958	+	3.75881i	−0.286190	+	0.240142i
$246$		0			0
$247$	3.24972	+	11.1192i	0.206775	+	0.707497i
$248$	−10.2194			−0.648929
$249$		0			0
$250$	1.70744	+	0.621459i	0.107988	+	0.0393045i
$251$	−0.761116	+	4.31650i	−0.0480412	+	0.272455i	−0.999361	−	0.0357511i	$-0.988618\pi$
$251$	−0.761116	+	4.31650i	−0.0480412	+	0.272455i	0.951320	+	0.308206i	$0.0997288\pi$
$252$		0			0
$253$	5.45518	−	1.98552i	0.342964	−	0.124829i
$254$	−8.83381	+	15.3006i	−0.554282	+	0.960045i
$255$		0			0
$256$	15.9933	+	13.4200i	0.999582	+	0.838749i
$257$	−17.7403	−	14.8859i	−1.10661	−	0.928558i	−0.108761	−	0.994068i	$-0.534688\pi$
$257$	−17.7403	−	14.8859i	−1.10661	−	0.928558i	−0.997852	+	0.0655097i	$0.979133\pi$
$258$		0			0
$259$	3.03149	−	5.25069i	0.188368	−	0.326262i
$260$	−3.25050	+	1.18308i	−0.201587	+	0.0733717i
$261$		0			0
$262$	4.66668	−	26.4661i	0.288308	−	1.63508i
$263$	30.0779	+	10.9475i	1.85468	+	0.675050i	0.982611	+	0.185675i	$0.0594473\pi$
$263$	30.0779	+	10.9475i	1.85468	+	0.675050i	0.872074	+	0.489375i	$0.162775\pi$
$264$		0			0
$265$	3.39943			0.208825
$266$	−8.45086	+	0.931735i	−0.518155	+	0.0571283i
$267$		0			0
$268$	12.8219	−	10.7589i	0.783224	−	0.657203i
$269$	3.55876	+	1.29528i	0.216981	+	0.0789748i	0.448224	−	0.893921i	$-0.352057\pi$
$269$	3.55876	+	1.29528i	0.216981	+	0.0789748i	−0.231242	+	0.972896i	$0.574279\pi$
$270$		0			0
$271$	2.90657	+	16.4840i	0.176562	+	1.00133i	0.936326	+	0.351132i	$0.114203\pi$
$271$	2.90657	+	16.4840i	0.176562	+	1.00133i	−0.759764	+	0.650199i	$0.774686\pi$
$272$	18.4516	−	6.71582i	1.11879	−	0.407207i
$273$		0			0
$274$	−3.26728	−	5.65909i	−0.197383	−	0.341878i
$275$	2.53572	+	2.12772i	0.152910	+	0.128307i
$276$		0			0
$277$	−5.79462	−	10.0366i	−0.348165	−	0.603040i	0.637758	−	0.770236i	$-0.279862\pi$
$277$	−5.79462	−	10.0366i	−0.348165	−	0.603040i	−0.985924	+	0.167197i	$0.946528\pi$
$278$	−5.31904	+	9.21285i	−0.319015	+	0.552550i
$279$		0			0
$280$	0.236558	+	1.34159i	0.0141371	+	0.0801752i
$281$	0.442986	−	2.51230i	0.0264263	−	0.149871i	−0.968739	−	0.248080i	$-0.920200\pi$
$281$	0.442986	−	2.51230i	0.0264263	−	0.149871i	0.995166	+	0.0982092i	$0.0313114\pi$
$282$		0			0
$283$	−0.397495	+	0.333538i	−0.0236286	+	0.0198268i	−0.654525	−	0.756040i	$-0.727132\pi$
$283$	−0.397495	+	0.333538i	−0.0236286	+	0.0198268i	0.630897	+	0.775867i	$0.282687\pi$
$284$	−14.3515			−0.851603
$285$		0			0
$286$	−15.9847			−0.945192
$287$	0.736940	−	0.618366i	0.0435002	−	0.0365010i
$288$		0			0
$289$	−0.173778	+	0.985542i	−0.0102222	+	0.0579731i
$290$	0.710719	+	4.03069i	0.0417348	+	0.236690i
$291$		0			0
$292$	1.69897	−	2.94271i	0.0994250	−	0.172209i
$293$	0.580211	+	1.00495i	0.0338963	+	0.0587100i	0.882476	−	0.470358i	$-0.155875\pi$
$293$	0.580211	+	1.00495i	0.0338963	+	0.0587100i	−0.848580	+	0.529068i	$0.822542\pi$
$294$		0			0
$295$	1.13893	+	0.955673i	0.0663109	+	0.0556414i
$296$	3.58385	+	6.20741i	0.208307	+	0.360798i
$297$		0			0
$298$	−17.1883	+	6.25602i	−0.995689	+	0.362401i
$299$	−0.809358	−	4.59010i	−0.0468064	−	0.265452i
$300$		0			0
$301$	8.58638	+	3.12519i	0.494911	+	0.180133i
$302$	2.95996	−	2.48370i	0.170327	−	0.142921i
$303$		0			0
$304$	8.60376	−	19.5922i	0.493460	−	1.12369i
$305$	13.7298			0.786168
$306$		0			0
$307$	14.0684	+	5.12048i	0.802926	+	0.292241i	0.710698	−	0.703497i	$-0.248379\pi$
$307$	14.0684	+	5.12048i	0.802926	+	0.292241i	0.0922276	+	0.995738i	$0.470601\pi$
$308$	0.803108	−	4.55465i	0.0457614	−	0.259526i
$309$		0			0
$310$	−13.7496	+	5.00443i	−0.780923	+	0.284233i
$311$	5.60315	−	9.70495i	0.317726	−	0.550317i	−0.662287	−	0.749250i	$-0.730414\pi$
$311$	5.60315	−	9.70495i	0.317726	−	0.550317i	0.980013	+	0.198933i	$0.0637475\pi$
$312$		0			0
$313$	10.4368	+	8.75749i	0.589921	+	0.495003i	0.888188	−	0.459480i	$-0.151964\pi$
$313$	10.4368	+	8.75749i	0.589921	+	0.495003i	−0.298267	+	0.954482i	$0.596409\pi$
$314$	16.0765	+	13.4898i	0.907252	+	0.761275i
$315$		0			0
$316$	4.27600	−	7.40624i	0.240544	−	0.416634i
$317$	−8.16123	+	2.97044i	−0.458380	+	0.166837i	−0.560881	−	0.827896i	$-0.689538\pi$
$317$	−8.16123	+	2.97044i	−0.458380	+	0.166837i	0.102501	+	0.994733i	$0.467315\pi$
$318$		0			0
$319$	−1.29475	+	7.34288i	−0.0724919	+	0.411122i
$320$	1.67048	+	0.608006i	0.0933828	+	0.0339886i
$321$		0			0
$322$	3.42076			0.190632
$323$	−10.3198	−	14.0530i	−0.574210	−	0.781931i
$324$		0			0
$325$	2.03586	−	1.70829i	0.112929	−	0.0947590i
$326$	31.4705	+	11.4543i	1.74299	+	0.634396i
$327$		0			0
$328$	0.197489	+	1.12001i	0.0109045	+	0.0618424i
$329$	−6.35109	+	2.31161i	−0.350147	+	0.127443i
$330$		0			0
$331$	11.6700	+	20.2130i	0.641439	+	1.11101i	0.985112	+	0.171916i	$0.0549957\pi$
$331$	11.6700	+	20.2130i	0.641439	+	1.11101i	−0.343672	+	0.939090i	$0.611671\pi$
$332$	−2.69096	−	2.25798i	−0.147685	−	0.123923i
$333$		0			0
$334$	−1.76489	−	3.05688i	−0.0965706	−	0.167265i
$335$	−6.42985	+	11.1368i	−0.351300	+	0.608470i
$336$		0			0
$337$	−2.23209	−	12.6588i	−0.121589	−	0.689568i	−0.983275	−	0.182126i	$-0.941702\pi$
$337$	−2.23209	−	12.6588i	−0.121589	−	0.689568i	0.861686	−	0.507442i	$-0.169409\pi$
$338$	1.87326	−	10.6238i	0.101892	−	0.577857i
$339$		0			0
$340$	3.98816	−	3.34647i	0.216288	−	0.181488i
$341$	−26.6557			−1.44349
$342$		0			0
$343$	−13.7915			−0.744671
$344$	−8.27507	+	6.94361i	−0.446162	+	0.374374i
$345$		0			0
$346$	−3.80251	+	21.5651i	−0.204424	+	1.15935i
$347$	5.63215	+	31.9415i	0.302350	+	1.71471i	0.635725	+	0.771916i	$0.280701\pi$
$347$	5.63215	+	31.9415i	0.302350	+	1.71471i	−0.333376	+	0.942794i	$0.608188\pi$
$348$		0			0
$349$	−6.05424	+	10.4863i	−0.324076	+	0.561316i	−0.981325	−	0.192357i	$-0.938387\pi$
$349$	−6.05424	+	10.4863i	−0.324076	+	0.561316i	0.657249	+	0.753674i	$0.271720\pi$
$350$	0.975254	+	1.68919i	0.0521295	+	0.0902910i
$351$		0			0
$352$	16.1824	+	13.5786i	0.862523	+	0.723742i
$353$	−11.5481	−	20.0019i	−0.614643	−	1.06459i	−0.990447	−	0.137894i	$-0.955967\pi$
$353$	−11.5481	−	20.0019i	−0.614643	−	1.06459i	0.375804	−	0.926699i	$-0.377367\pi$
$354$		0			0
$355$	10.3613	−	3.77120i	0.549919	−	0.200154i
$356$	−0.178516	−	1.01241i	−0.00946133	−	0.0536579i
$357$		0			0
$358$	31.2639	+	11.3791i	1.65235	+	0.601406i
$359$	4.93802	−	4.14349i	0.260619	−	0.218685i	−0.503110	−	0.864222i	$-0.667811\pi$
$359$	4.93802	−	4.14349i	0.260619	−	0.218685i	0.763729	+	0.645537i	$0.223366\pi$
$360$		0			0
$361$	−18.8410	−	2.45262i	−0.991634	−	0.129085i
$362$	46.6092			2.44972
$363$		0			0
$364$	−3.48929	−	1.27000i	−0.182888	−	0.0665659i
$365$	−0.453334	+	2.57098i	−0.0237286	+	0.134571i
$366$		0			0
$367$	8.09901	−	2.94780i	0.422765	−	0.153874i	−0.121872	−	0.992546i	$-0.538890\pi$
$367$	8.09901	−	2.94780i	0.422765	−	0.153874i	0.544637	+	0.838672i	$0.316667\pi$
$368$	−4.30470	+	7.45597i	−0.224398	+	0.388669i
$369$		0			0
$370$	7.86164	+	6.59670i	0.408707	+	0.342946i
$371$	2.79542	+	2.34563i	0.145131	+	0.121779i
$372$		0			0
$373$	4.75291	−	8.23228i	0.246096	−	0.426251i	−0.716343	−	0.697748i	$-0.754185\pi$
$373$	4.75291	−	8.23228i	0.246096	−	0.426251i	0.962439	+	0.271497i	$0.0875188\pi$
$374$	22.6071	−	8.22830i	1.16898	−	0.425475i
$375$		0			0
$376$	1.38748	−	7.86878i	0.0715538	−	0.405801i
$377$	5.62532	+	2.04745i	0.289719	+	0.105449i
$378$		0			0
$379$	−11.3635			−0.583706			−0.291853	−	0.956463i	$-0.594272\pi$
$379$	−11.3635			−0.583706			−0.291853	+	0.956463i	$0.594272\pi$
$380$	0.366946	−	5.66155i	0.0188239	−	0.290432i
$381$		0			0
$382$	12.8359	−	10.7706i	0.656741	−	0.551071i
$383$	−2.56808	−	0.934706i	−0.131223	−	0.0477612i	0.275574	−	0.961280i	$-0.411132\pi$
$383$	−2.56808	−	0.934706i	−0.131223	−	0.0477612i	−0.406797	+	0.913519i	$0.633354\pi$
$384$		0			0
$385$	0.617028	+	3.49934i	0.0314467	+	0.178343i
$386$	20.4927	−	7.45874i	1.04305	−	0.379640i
$387$		0			0
$388$	12.1814	+	21.0988i	0.618416	+	1.07113i
$389$	16.9706	+	14.2400i	0.860445	+	0.721999i	0.962064	−	0.272824i	$-0.0879578\pi$
$389$	16.9706	+	14.2400i	0.860445	+	0.721999i	−0.101619	+	0.994823i	$0.532402\pi$
$390$		0			0
$391$	3.50748	+	6.07514i	0.177381	+	0.307233i
$392$	3.71051	−	6.42680i	0.187409	−	0.324602i
$393$		0			0
$394$	−8.48669	−	48.1304i	−0.427553	−	2.42478i
$395$	−1.14096	+	6.47068i	−0.0574077	+	0.325575i
$396$		0			0
$397$	12.9927	−	10.9022i	0.652086	−	0.547165i	−0.255617	−	0.966778i	$-0.582279\pi$
$397$	12.9927	−	10.9022i	0.652086	−	0.547165i	0.907703	+	0.419613i	$0.137834\pi$
$398$	8.31096			0.416591
$399$		0			0
$400$	−4.90905			−0.245453
$401$	−5.07050	+	4.25465i	−0.253208	+	0.212467i	−0.760552	−	0.649276i	$-0.775072\pi$
$401$	−5.07050	+	4.25465i	−0.253208	+	0.212467i	0.507344	+	0.861744i	$0.330627\pi$
$402$		0			0
$403$	−3.71627	+	21.0760i	−0.185121	+	1.04987i
$404$	−4.27558	−	24.2480i	−0.212718	−	1.20638i
$405$		0			0
$406$	−2.19677	+	3.80492i	−0.109024	+	0.188835i
$407$	9.34796	+	16.1911i	0.463361	+	0.802565i
$408$		0			0
$409$	27.3969	+	22.9888i	1.35469	+	1.13672i	0.977583	+	0.210552i	$0.0675263\pi$
$409$	27.3969	+	22.9888i	1.35469	+	1.13672i	0.377109	+	0.926169i	$0.376918\pi$
$410$	0.814183	+	1.41021i	0.0402096	+	0.0696451i
$411$		0			0
$412$	14.2413	−	5.18342i	0.701620	−	0.255369i
$413$	0.277140	+	1.57174i	0.0136372	+	0.0773402i
$414$		0			0
$415$	2.53612	+	0.923072i	0.124493	+	0.0453118i
$416$	12.9924	−	10.9019i	0.637004	−	0.534510i
$417$		0			0
$418$	10.5414	−	24.0045i	0.515598	−	1.17410i
$419$	29.6681			1.44938			0.724691	−	0.689074i	$-0.241982\pi$
$419$	29.6681			1.44938			0.724691	+	0.689074i	$0.241982\pi$
$420$		0			0
$421$	−11.6019	−	4.22276i	−0.565444	−	0.205805i	0.0434509	−	0.999056i	$-0.486165\pi$
$421$	−11.6019	−	4.22276i	−0.565444	−	0.205805i	−0.608895	+	0.793251i	$0.708387\pi$
$422$	4.91037	−	27.8481i	0.239033	−	1.35562i
$423$		0			0
$424$	−4.05389	+	1.47550i	−0.196874	+	0.0716564i
$425$	−1.99995	+	3.46402i	−0.0970120	+	0.168030i
$426$		0			0
$427$	11.2903	+	9.47370i	0.546377	+	0.458465i
$428$	−11.3624	−	9.53416i	−0.549221	−	0.460851i
$429$		0			0
$430$	−7.73335	+	13.3946i	−0.372935	+	0.645943i
$431$	−16.0374	+	5.83712i	−0.772492	+	0.281164i	−0.698038	−	0.716060i	$-0.745944\pi$
$431$	−16.0374	+	5.83712i	−0.772492	+	0.281164i	−0.0744539	+	0.997224i	$0.523721\pi$
$432$		0			0
$433$	−0.486245	+	2.75763i	−0.0233674	+	0.132523i	−0.994260	−	0.106993i	$-0.965878\pi$
$433$	−0.486245	+	2.75763i	−0.0233674	+	0.132523i	0.970892	+	0.239516i	$0.0769889\pi$
$434$	−14.7597	−	5.37207i	−0.708486	−	0.257868i
$435$		0			0
$436$	−16.5788			−0.793979
$437$	7.42680	+	1.81161i	0.355272	+	0.0866609i
$438$		0			0
$439$	16.2517	−	13.6368i	0.775651	−	0.650848i	−0.166498	−	0.986042i	$-0.553246\pi$
$439$	16.2517	−	13.6368i	0.775651	−	0.650848i	0.942149	+	0.335193i	$0.108802\pi$
$440$	−3.94743	−	1.43675i	−0.188186	−	0.0684942i
$441$		0			0
$442$	−3.35410	−	19.0220i	−0.159538	−	0.904785i
$443$	21.4052	−	7.79086i	1.01699	−	0.370155i	0.220878	−	0.975301i	$-0.429108\pi$
$443$	21.4052	−	7.79086i	1.01699	−	0.370155i	0.796114	+	0.605146i	$0.206885\pi$
$444$		0			0
$445$	0.394919	+	0.684020i	0.0187210	+	0.0324256i
$446$	28.0172	+	23.5092i	1.32665	+	1.11319i
$447$		0			0
$448$	0.954142	+	1.65262i	0.0450790	+	0.0780791i
$449$	−14.8849	+	25.7814i	−0.702461	+	1.21670i	0.265139	+	0.964210i	$0.414582\pi$
$449$	−14.8849	+	25.7814i	−0.702461	+	1.21670i	−0.967600	+	0.252488i	$0.918751\pi$
$450$		0			0
$451$	0.515121	+	2.92140i	0.0242561	+	0.137563i
$452$	−3.74947	+	21.2643i	−0.176360	+	1.00019i
$453$		0			0
$454$	19.3032	−	16.1973i	0.905943	−	0.760177i
$455$	2.85287			0.133745
$456$		0			0
$457$	−36.7666			−1.71987			−0.859934	−	0.510406i	$-0.829495\pi$
$457$	−36.7666			−1.71987			−0.859934	+	0.510406i	$0.829495\pi$
$458$	−12.1146	+	10.1654i	−0.566078	+	0.474996i
$459$		0			0
$460$	−0.396383	+	2.24800i	−0.0184814	+	0.104813i
$461$	4.46796	+	25.3390i	0.208093	+	1.18016i	0.892497	+	0.451053i	$0.148952\pi$
$461$	4.46796	+	25.3390i	0.208093	+	1.18016i	−0.684404	+	0.729103i	$0.739937\pi$
$462$		0			0
$463$	17.7844	−	30.8035i	0.826511	−	1.43156i	−0.0742472	−	0.997240i	$-0.523655\pi$
$463$	17.7844	−	30.8035i	0.826511	−	1.43156i	0.900759	−	0.434320i	$-0.143011\pi$
$464$	−5.52885	−	9.57625i	−0.256670	−	0.444566i
$465$		0			0
$466$	21.8819	+	18.3611i	1.01366	+	0.850560i
$467$	−3.55785	−	6.16238i	−0.164638	−	0.285161i	0.771889	−	0.635758i	$-0.219312\pi$
$467$	−3.55785	−	6.16238i	−0.164638	−	0.285161i	−0.936527	+	0.350596i	$0.885979\pi$
$468$		0			0
$469$	−12.9719	+	4.72139i	−0.598987	+	0.218013i
$470$	−1.98658	−	11.2665i	−0.0916341	−	0.519683i
$471$		0			0
$472$	−1.77300	−	0.645319i	−0.0816089	−	0.0297032i
$473$	−21.5844	+	18.1114i	−0.992449	+	0.832764i
$474$		0			0
$475$	1.22279	+	4.18387i	0.0561053	+	0.191969i
$476$	5.58864			0.256155
$477$		0			0
$478$	23.6218	+	8.59764i	1.08044	+	0.393247i
$479$	1.53032	−	8.67887i	0.0699220	−	0.396547i	−0.929681	−	0.368366i	$-0.879917\pi$
$479$	1.53032	−	8.67887i	0.0699220	−	0.396547i	0.999603	−	0.0281814i	$-0.00897159\pi$
$480$		0			0
$481$	14.1052	−	5.13387i	0.643142	−	0.234085i
$482$	11.0627	−	19.1612i	0.503893	−	0.872768i
$483$		0			0
$484$	−0.0427713	−	0.0358894i	−0.00194415	−	0.00163133i
$485$	−14.3388	−	12.0317i	−0.651090	−	0.546329i
$486$		0			0
$487$	2.39153	−	4.14225i	0.108370	−	0.187703i	−0.806740	−	0.590907i	$-0.798770\pi$
$487$	2.39153	−	4.14225i	0.108370	−	0.187703i	0.915110	+	0.403204i	$0.132103\pi$
$488$	−16.3731	+	5.95933i	−0.741177	+	0.269766i
$489$		0			0
$490$	1.84508	−	10.4639i	0.0833520	−	0.472713i
$491$	9.46362	+	3.44448i	0.427087	+	0.155447i	0.546615	−	0.837384i	$-0.315916\pi$
$491$	9.46362	+	3.44448i	0.427087	+	0.155447i	−0.119528	+	0.992831i	$0.538138\pi$
$492$		0			0
$493$	−9.00984			−0.405783
$494$	−17.5101	−	11.6815i	−0.787818	−	0.525575i
$495$		0			0
$496$	30.2827	−	25.4102i	1.35973	−	1.14095i
$497$	11.1224	+	4.04824i	0.498910	+	0.181588i
$498$		0			0
$499$	−0.333774	−	1.89292i	−0.0149418	−	0.0847390i	0.976425	−	0.215857i	$-0.0692545\pi$
$499$	−0.333774	−	1.89292i	−0.0149418	−	0.0847390i	−0.991367	+	0.131118i	$0.958143\pi$
$500$	−1.22308	+	0.445165i	−0.0546978	+	0.0199084i
$501$		0			0
$502$	−3.98209	−	6.89718i	−0.177729	−	0.307836i
$503$	12.4324	+	10.4320i	0.554332	+	0.465140i	0.876405	−	0.481575i	$-0.159935\pi$
$503$	12.4324	+	10.4320i	0.554332	+	0.465140i	−0.322073	+	0.946715i	$0.604380\pi$
$504$		0			0
$505$	9.45858	+	16.3827i	0.420901	+	0.729022i
$506$	−5.27417	+	9.13513i	−0.234465	+	0.406106i
$507$		0			0
$508$	−2.19764	−	12.4634i	−0.0975045	−	0.552976i
$509$	5.87363	−	33.3110i	0.260344	−	1.47649i	−0.521629	−	0.853173i	$-0.674675\pi$
$509$	5.87363	−	33.3110i	0.260344	−	1.47649i	0.781973	−	0.623313i	$-0.214214\pi$
$510$		0			0
$511$	−2.14679	+	1.80137i	−0.0949683	+	0.0796878i
$512$	−18.8686			−0.833884
$513$		0			0
$514$	42.0793			1.85604
$515$	−8.91969	+	7.48451i	−0.393048	+	0.329807i
$516$		0			0
$517$	3.61904	−	20.5246i	0.159165	−	0.902671i
$518$	1.91301	+	10.8492i	0.0840527	+	0.476687i
$519$		0			0
$520$	−1.68634	+	2.92083i	−0.0739509	+	0.128087i
$521$	3.44419	+	5.96551i	0.150893	+	0.261354i	0.931556	−	0.363598i	$-0.118452\pi$
$521$	3.44419	+	5.96551i	0.150893	+	0.261354i	−0.780663	+	0.624952i	$0.785119\pi$
$522$		0			0
$523$	−15.4658	−	12.9773i	−0.676271	−	0.567459i	0.238643	−	0.971107i	$-0.423297\pi$
$523$	−15.4658	−	12.9773i	−0.676271	−	0.567459i	−0.914914	+	0.403648i	$0.867742\pi$
$524$	9.62535	+	16.6716i	0.420485	+	0.728302i
$525$		0			0
$526$	−54.6523	+	19.8918i	−2.38295	+	0.867324i
$527$	−5.59323	−	31.7208i	−0.243645	−	1.38178i
$528$		0			0
$529$	18.7227	+	6.81449i	0.814029	+	0.296282i
$530$	−4.73173	+	3.97040i	−0.205533	+	0.172463i
$531$		0			0
$532$	4.20827	−	4.40241i	0.182452	−	0.190869i
$533$	2.38169			0.103163
$534$		0			0
$535$	10.7086	+	3.89760i	0.462972	+	0.168508i
$536$	2.83388	−	16.0717i	0.122405	−	0.694193i
$537$		0			0
$538$	−6.46635	+	2.35356i	−0.278784	+	0.101469i
$539$	9.67835	−	16.7634i	0.416876	−	0.722050i
$540$		0			0
$541$	2.00813	+	1.68502i	0.0863363	+	0.0724447i	0.684934	−	0.728605i	$-0.259831\pi$
$541$	2.00813	+	1.68502i	0.0863363	+	0.0724447i	−0.598598	+	0.801050i	$0.704275\pi$
$542$	−23.2983	−	19.5496i	−1.00075	−	0.839729i
$543$		0			0
$544$	−12.7632	+	22.1065i	−0.547218	+	0.947810i
$545$	11.9693	−	4.35647i	0.512709	−	0.186611i
$546$		0			0
$547$	4.61386	−	26.1665i	0.197274	−	1.11880i	−0.711868	−	0.702313i	$-0.752151\pi$
$547$	4.61386	−	26.1665i	0.197274	−	1.11880i	0.909143	−	0.416485i	$-0.136738\pi$
$548$	4.39856	+	1.60094i	0.187897	+	0.0683889i
$549$		0			0
$550$	−6.01462			−0.256464
$551$	−6.78444	+	7.09744i	−0.289027	+	0.302361i
$552$		0			0
$553$	−5.40306	+	4.53370i	−0.229761	+	0.192793i
$554$	19.7880	+	7.20224i	0.840711	+	0.305994i
$555$		0			0
$556$	−1.32325	−	7.50453i	−0.0561183	−	0.318263i
$557$	16.3758	−	5.96029i	0.693864	−	0.252546i	0.0290750	−	0.999577i	$-0.490744\pi$
$557$	16.3758	−	5.96029i	0.693864	−	0.252546i	0.664789	+	0.747032i	$0.268522\pi$
$558$		0			0
$559$	11.3110	+	19.5913i	0.478405	+	0.828622i
$560$	−4.03681	−	3.38729i	−0.170587	−	0.143139i
$561$		0			0
$562$	2.31766	+	4.01431i	0.0977647	+	0.169333i
$563$	−1.12668	+	1.95146i	−0.0474838	+	0.0822443i	−0.888790	−	0.458314i	$-0.848454\pi$
$563$	−1.12668	+	1.95146i	−0.0474838	+	0.0822443i	0.841307	+	0.540558i	$0.181787\pi$
$564$		0			0
$565$	−2.88072	−	16.3374i	−0.121193	−	0.687318i
$566$	0.163723	−	0.928516i	0.00688177	−	0.0390285i
$567$		0			0
$568$	−10.7192	+	8.99447i	−0.449767	+	0.377400i
$569$	8.49148			0.355982			0.177991	−	0.984032i	$-0.443040\pi$
$569$	8.49148			0.355982			0.177991	+	0.984032i	$0.443040\pi$
$570$		0			0
$571$	−2.29006			−0.0958359			−0.0479179	−	0.998851i	$-0.515259\pi$
$571$	−2.29006			−0.0958359			−0.0479179	+	0.998851i	$0.515259\pi$
$572$	8.77133	−	7.36002i	0.366748	−	0.307738i
$573$		0			0
$574$	−0.303535	+	1.72143i	−0.0126693	+	0.0718513i
$575$	−0.304541	−	1.72714i	−0.0127002	−	0.0720266i
$576$		0			0
$577$	1.00458	−	1.73999i	0.0418213	−	0.0724366i	−0.844357	−	0.535781i	$-0.820017\pi$
$577$	1.00458	−	1.73999i	0.0418213	−	0.0724366i	0.886178	+	0.463344i	$0.153351\pi$
$578$	−0.909189	−	1.57476i	−0.0378173	−	0.0655015i
$579$		0			0
$580$	−2.24590	−	1.88453i	−0.0932558	−	0.0782509i
$581$	1.44857	+	2.50900i	0.0600970	+	0.104091i
$582$		0			0
$583$	−10.5740	+	3.84862i	−0.437931	+	0.159394i
$584$	−0.575306	−	3.26272i	−0.0238063	−	0.135012i
$585$		0			0
$586$	−1.98135	−	0.721154i	−0.0818490	−	0.0297906i
$587$	5.66052	−	4.74974i	0.233635	−	0.196043i	−0.518452	−	0.855106i	$-0.673492\pi$
$587$	5.66052	−	4.74974i	0.233635	−	0.196043i	0.752087	+	0.659064i	$0.229047\pi$
$588$		0			0
$589$	−29.1996	−	19.4799i	−1.20315	−	0.802654i
$590$	−2.70148			−0.111218
$591$		0			0
$592$	−26.0545	−	9.48305i	−1.07083	−	0.389751i
$593$	4.07647	−	23.1188i	0.167401	−	0.949377i	−0.779154	−	0.626833i	$-0.784351\pi$
$593$	4.07647	−	23.1188i	0.167401	−	0.949377i	0.946555	−	0.322544i	$-0.104538\pi$
$594$		0			0
$595$	−4.03481	+	1.46855i	−0.165411	+	0.0602047i
$596$	6.55126	−	11.3471i	0.268350	−	0.464796i
$597$		0			0
$598$	6.48761	+	5.44375i	0.265298	+	0.222612i
$599$	24.7199	+	20.7425i	1.01003	+	0.847514i	0.988342	−	0.152251i	$-0.0486522\pi$
$599$	24.7199	+	20.7425i	1.01003	+	0.847514i	0.0216857	+	0.999765i	$0.493097\pi$
$600$		0			0
$601$	−14.9179	+	25.8385i	−0.608513	+	1.05397i	0.382973	+	0.923759i	$0.374900\pi$
$601$	−14.9179	+	25.8385i	−0.608513	+	1.05397i	−0.991486	+	0.130215i	$0.958433\pi$
$602$	−15.6017	+	5.67854i	−0.635876	+	0.231440i
$603$		0			0
$604$	−0.480630	+	2.72579i	−0.0195565	+	0.110911i
$605$	0.0403102	+	0.0146717i	0.00163884	+	0.000596490i
$606$		0			0
$607$	−9.11607			−0.370010			−0.185005	−	0.982738i	$-0.559230\pi$
$607$	−9.11607			−0.370010			−0.185005	+	0.982738i	$0.559230\pi$
$608$	7.80353	+	26.7004i	0.316475	+	1.08285i
$609$		0			0
$610$	−19.1108	+	16.0359i	−0.773775	+	0.649274i
$611$	−15.7237	−	5.72298i	−0.636115	−	0.231527i
$612$		0			0
$613$	7.30218	+	41.4127i	0.294932	+	1.67264i	0.667477	+	0.744631i	$0.267374\pi$
$613$	7.30218	+	41.4127i	0.294932	+	1.67264i	−0.372544	+	0.928014i	$0.621515\pi$
$614$	−25.5626	+	9.30403i	−1.03162	+	0.375480i
$615$		0			0
$616$	−2.25468	−	3.90523i	−0.0908438	−	0.157346i
$617$	−25.8029	−	21.6512i	−1.03878	−	0.871643i	−0.0469138	−	0.998899i	$-0.514939\pi$
$617$	−25.8029	−	21.6512i	−1.03878	−	0.871643i	−0.991870	+	0.127256i	$0.959383\pi$
$618$		0			0
$619$	20.8458	+	36.1060i	0.837865	+	1.45122i	0.891676	+	0.452673i	$0.149530\pi$
$619$	20.8458	+	36.1060i	0.837865	+	1.45122i	−0.0538116	+	0.998551i	$0.517137\pi$
$620$	5.24061	−	9.07700i	0.210468	−	0.364541i
$621$		0			0
$622$	3.53585	+	20.0528i	0.141775	+	0.804043i
$623$	−0.147230	+	0.834981i	−0.00589863	+	0.0334528i
$624$		0			0
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	−24.7556			−0.989431
$627$		0			0
$628$	−15.0331			−0.599884
$629$	−17.3062	+	14.5217i	−0.690045	+	0.579016i
$630$		0			0
$631$	−1.44547	+	8.19764i	−0.0575431	+	0.326343i	−0.999967	−	0.00807654i	$-0.997429\pi$
$631$	−1.44547	+	8.19764i	−0.0575431	+	0.326343i	0.942424	+	0.334420i	$0.108540\pi$
$632$	−1.44794	−	8.21165i	−0.0575958	−	0.326642i
$633$		0			0
$634$	7.89042	−	13.6666i	0.313369	−	0.542770i
$635$	4.86169	+	8.42070i	0.192930	+	0.334165i
$636$		0			0
$637$	−11.9051	−	9.98954i	−0.471696	−	0.395800i
$638$	−6.77400	−	11.7329i	−0.268185	−	0.464511i
$639$		0			0
$640$	8.95847	−	3.26062i	0.354115	−	0.128887i
$641$	1.26074	+	7.15002i	0.0497963	+	0.282409i	0.999530	−	0.0306495i	$-0.00975756\pi$
$641$	1.26074	+	7.15002i	0.0497963	+	0.282409i	−0.949734	+	0.313058i	$0.898646\pi$
$642$		0			0
$643$	−3.35653	−	1.22168i	−0.132369	−	0.0481783i	0.274986	−	0.961448i	$-0.411327\pi$
$643$	−3.35653	−	1.22168i	−0.132369	−	0.0481783i	−0.407355	+	0.913270i	$0.633549\pi$
$644$	−1.87709	+	1.57507i	−0.0739678	+	0.0620664i
$645$		0			0
$646$	30.7777	+	7.50756i	1.21093	+	0.295381i
$647$	−21.0229			−0.826494			−0.413247	−	0.910619i	$-0.635605\pi$
$647$	−21.0229			−0.826494			−0.413247	+	0.910619i	$0.635605\pi$
$648$		0			0
$649$	−4.62461	−	1.68322i	−0.181532	−	0.0660722i
$650$	−0.838543	+	4.75562i	−0.0328904	+	0.186531i
$651$		0			0
$652$	−22.5430	+	8.20498i	−0.882852	+	0.321332i
$653$	−11.6323	+	20.1477i	−0.455207	+	0.788441i	−0.998700	−	0.0509725i	$-0.983768\pi$
$653$	−11.6323	+	20.1477i	−0.455207	+	0.788441i	0.543494	+	0.839413i	$0.317101\pi$
$654$		0			0
$655$	−11.3300	−	9.50703i	−0.442701	−	0.371470i
$656$	−3.37010	−	2.82785i	−0.131580	−	0.110409i
$657$		0			0
$658$	6.14035	−	10.6354i	0.239376	−	0.414611i
$659$	−22.1075	+	8.04649i	−0.861188	+	0.313447i	−0.734593	−	0.678508i	$-0.762627\pi$
$659$	−22.1075	+	8.04649i	−0.861188	+	0.313447i	−0.126595	+	0.991955i	$0.540405\pi$
$660$		0			0
$661$	−3.70008	+	20.9842i	−0.143916	+	0.816190i	0.824315	+	0.566132i	$0.191561\pi$
$661$	−3.70008	+	20.9842i	−0.143916	+	0.816190i	−0.968231	+	0.250058i	$0.919550\pi$
$662$	−39.8516	−	14.5048i	−1.54888	−	0.563745i
$663$		0			0
$664$	−3.42503			−0.132917
$665$	−1.88139	+	4.28422i	−0.0729570	+	0.166135i
$666$		0			0
$667$	3.02619	−	2.53928i	0.117175	−	0.0983212i
$668$	2.37598	+	0.864785i	0.0919293	+	0.0334595i
$669$		0			0
$670$	−4.05753	−	23.0114i	−0.156756	−	0.889007i
$671$	−42.7070	+	15.5441i	−1.64868	+	0.600072i
$672$		0			0
$673$	−3.87301	−	6.70824i	−0.149293	−	0.258584i	0.781673	−	0.623688i	$-0.214367\pi$
$673$	−3.87301	−	6.70824i	−0.149293	−	0.258584i	−0.930967	+	0.365105i	$0.881033\pi$
$674$	17.8919	+	15.0130i	0.689168	+	0.578281i
$675$		0			0
$676$	3.86372	+	6.69216i	0.148605	+	0.257391i
$677$	−1.65573	+	2.86781i	−0.0636348	+	0.110219i	−0.896088	−	0.443877i	$-0.853603\pi$
$677$	−1.65573	+	2.86781i	−0.0636348	+	0.110219i	0.832453	+	0.554096i	$0.186936\pi$
$678$		0			0
$679$	−3.48911	−	19.7877i	−0.133900	−	0.759384i
$680$	0.881456	−	4.99899i	0.0338023	−	0.191702i
$681$		0			0
$682$	37.1027	−	31.1328i	1.42073	−	1.19214i
$683$	4.09964			0.156868			0.0784342	−	0.996919i	$-0.475008\pi$
$683$	4.09964			0.156868			0.0784342	+	0.996919i	$0.475008\pi$
$684$		0			0
$685$	−3.59629			−0.137407
$686$	19.1967	−	16.1079i	0.732933	−	0.615004i
$687$		0			0
$688$	7.25613	−	41.1516i	0.276637	−	1.56889i
$689$	1.56881	+	8.89717i	0.0597670	+	0.338955i
$690$		0			0
$691$	11.4219	−	19.7832i	0.434508	−	0.752590i	−0.562747	−	0.826629i	$-0.690256\pi$
$691$	11.4219	−	19.7832i	0.434508	−	0.752590i	0.997255	+	0.0740389i	$0.0235889\pi$
$692$	−7.84294	−	13.5844i	−0.298144	−	0.516400i
$693$		0			0
$694$	−45.1459	−	37.8819i	−1.71372	−	1.43798i
$695$	2.92734	+	5.07030i	0.111040	+	0.192327i
$696$		0			0
$697$	−3.36843	+	1.22601i	−0.127588	+	0.0464383i
$698$	−3.82050	−	21.6671i	−0.144608	−	0.820113i
$699$		0			0
$700$	−1.31293	−	0.477868i	−0.0496241	−	0.0180617i
$701$	33.0796	−	27.7571i	1.24940	−	1.04837i	0.252671	−	0.967552i	$-0.418691\pi$
$701$	33.0796	−	27.7571i	1.24940	−	1.04837i	0.996729	−	0.0808184i	$-0.0257534\pi$
$702$		0			0
$703$	−1.59233	+	24.5677i	−0.0600557	+	0.926590i
$704$	−5.88442			−0.221778
$705$		0			0
$706$	39.4354	+	14.3533i	1.48417	+	0.540194i
$707$	−3.52625	+	19.9984i	−0.132618	+	0.752116i
$708$		0			0
$709$	−11.7936	+	4.29251i	−0.442917	+	0.161209i	−0.553845	−	0.832620i	$-0.686840\pi$
$709$	−11.7936	+	4.29251i	−0.442917	+	0.161209i	0.110928	+	0.993828i	$0.464618\pi$
$710$	−10.0175	+	17.3508i	−0.375949	+	0.651163i
$711$		0			0
$712$	−0.767843	−	0.644297i	−0.0287761	−	0.0241461i
$713$	10.8186	+	9.07791i	0.405161	+	0.339970i
$714$		0			0
$715$	−4.39858	+	7.61857i	−0.164498	+	0.284918i
$716$	−22.3951	+	8.15114i	−0.836943	+	0.304622i
$717$		0			0
$718$	−2.03390	+	11.5348i	−0.0759045	+	0.430476i
$719$	21.1132	+	7.68458i	0.787390	+	0.286587i	0.704251	−	0.709951i	$-0.251283\pi$
$719$	21.1132	+	7.68458i	0.787390	+	0.286587i	0.0831393	+	0.996538i	$0.473505\pi$
$720$		0			0
$721$	−12.4992			−0.465495
$722$	29.0898	−	18.5917i	1.08261	−	0.691913i
$723$		0			0
$724$	−25.5761	+	21.4609i	−0.950527	+	0.797587i
$725$	2.11667	+	0.770404i	0.0786111	+	0.0286121i
$726$		0			0
$727$	5.13769	+	29.1373i	0.190546	+	1.08064i	0.918620	+	0.395143i	$0.129305\pi$
$727$	5.13769	+	29.1373i	0.190546	+	1.08064i	−0.728073	+	0.685499i	$0.759584\pi$
$728$	−3.40211	+	1.23827i	−0.126091	+	0.0458932i
$729$		0			0
$730$	−2.37180	−	4.10808i	−0.0877843	−	0.152047i
$731$	−26.0820	−	21.8854i	−0.964678	−	0.809461i
$732$		0			0
$733$	−23.4156	−	40.5570i	−0.864876	−	1.49801i	−0.867171	−	0.498011i	$-0.834064\pi$
$733$	−23.4156	−	40.5570i	−0.864876	−	1.49801i	0.00229524	−	0.999997i	$-0.499269\pi$
$734$	−7.83027	+	13.5624i	−0.289021	+	0.500598i
$735$		0			0
$736$	−1.94351	−	11.0222i	−0.0716386	−	0.406283i
$737$	7.39178	−	41.9208i	0.272280	−	1.54417i
$738$		0			0
$739$	29.8695	−	25.0635i	1.09877	−	0.921976i	0.101427	−	0.994843i	$-0.467659\pi$
$739$	29.8695	−	25.0635i	1.09877	−	0.921976i	0.997342	+	0.0728667i	$0.0232148\pi$
$740$	−7.35136			−0.270241
$741$		0			0
$742$	−6.63061			−0.243417
$743$	−9.29569	+	7.80001i	−0.341026	+	0.286155i	−0.797174	−	0.603749i	$-0.793673\pi$
$743$	−9.29569	+	7.80001i	−0.341026	+	0.286155i	0.456149	+	0.889904i	$0.349228\pi$
$744$		0			0
$745$	−1.74806	+	9.91373i	−0.0640439	+	0.363211i
$746$	2.99930	+	17.0099i	0.109812	+	0.622776i
$747$		0			0
$748$	−8.61662	+	14.9244i	−0.315055	+	0.545691i
$749$	6.11650	+	10.5941i	0.223492	+	0.387099i
$750$		0			0
$751$	−4.07011	−	3.41523i	−0.148521	−	0.124624i	0.565500	−	0.824748i	$-0.308683\pi$
$751$	−4.07011	−	3.41523i	−0.148521	−	0.124624i	−0.714021	+	0.700125i	$0.753128\pi$
$752$	15.4541	+	26.7673i	0.563552	+	0.976101i
$753$		0			0
$754$	−10.2213	+	3.72027i	−0.372239	+	0.135484i
$755$	−0.369268	−	2.09422i	−0.0134390	−	0.0762165i
$756$		0			0
$757$	19.9629	+	7.26590i	0.725564	+	0.264084i	0.678286	−	0.734798i	$-0.262723\pi$
$757$	19.9629	+	7.26590i	0.725564	+	0.264084i	0.0472781	+	0.998882i	$0.484945\pi$
$758$	15.8172	−	13.2722i	0.574505	−	0.482067i
$759$		0			0
$760$	−3.27418	−	4.45862i	−0.118767	−	0.161731i
$761$	−37.4718			−1.35835			−0.679176	−	0.733975i	$-0.737663\pi$
$761$	−37.4718			−1.35835			−0.679176	+	0.733975i	$0.737663\pi$
$762$		0			0
$763$	12.8486	+	4.67651i	0.465151	+	0.169301i
$764$	−2.08425	+	11.8204i	−0.0754057	+	0.427647i
$765$		0			0
$766$	4.66627	−	1.69838i	0.168599	−	0.0613650i
$767$	−1.97563	+	3.42190i	−0.0713360	+	0.123558i
$768$		0			0
$769$	−2.29530	−	1.92599i	−0.0827707	−	0.0694529i	0.600464	−	0.799652i	$-0.294983\pi$
$769$	−2.29530	−	1.92599i	−0.0827707	−	0.0694529i	−0.683234	+	0.730199i	$0.739427\pi$
$770$	−4.94595	−	4.15014i	−0.178240	−	0.149561i
$771$		0			0
$772$	−7.81074	+	13.5286i	−0.281115	+	0.486905i
$773$	14.9175	−	5.42954i	0.536547	−	0.195287i	−0.0595125	−	0.998228i	$-0.518955\pi$
$773$	14.9175	−	5.42954i	0.536547	−	0.195287i	0.596059	+	0.802941i	$0.296732\pi$
$774$		0			0
$775$	−1.39834	+	7.93038i	−0.0502299	+	0.284868i
$776$	22.3215	+	8.12438i	0.801297	+	0.291648i
$777$		0			0
$778$	−40.2536			−1.44316
$779$	−1.57066	+	3.57664i	−0.0562747	+	0.128147i
$780$		0			0
$781$	−27.9595	+	23.4608i	−1.00047	+	0.839493i
$782$	−11.9777	−	4.35951i	−0.428320	−	0.155896i
$783$		0			0
$784$	4.98484	+	28.2704i	0.178030	+	1.00966i
$785$	10.8534	−	3.95030i	0.387373	−	0.140992i
$786$		0			0
$787$	−2.42508	−	4.20037i	−0.0864449	−	0.149727i	0.819561	−	0.572992i	$-0.194217\pi$
$787$	−2.42508	−	4.20037i	−0.0864449	−	0.149727i	−0.906006	+	0.423265i	$0.860884\pi$
$788$	26.8183	+	22.5032i	0.955361	+	0.801643i
$789$		0			0
$790$	−5.96938	−	10.3393i	−0.212381	−	0.367854i
$791$	8.90405	−	15.4223i	0.316592	−	0.548353i
$792$		0			0
$793$	6.33622	+	35.9345i	0.225006	+	1.27607i
$794$	−5.35152	+	30.3500i	−0.189918	+	1.07708i
$795$		0			0
$796$	−4.56051	+	3.82673i	−0.161643	+	0.135635i
$797$	−42.7169			−1.51311			−0.756555	−	0.653930i	$-0.773119\pi$
$797$	−42.7169			−1.51311			−0.756555	+	0.653930i	$0.773119\pi$
$798$		0			0
$799$	25.1840			0.890947
$800$	4.88871	−	4.10211i	0.172842	−	0.145032i
$801$		0			0
$802$	2.08847	−	11.8443i	0.0737463	−	0.418236i
$803$	−1.50060	−	8.51035i	−0.0529552	−	0.300324i
$804$		0			0
$805$	0.941310	−	1.63040i	0.0331768	−	0.0574639i
$806$	−19.4432	−	33.6766i	−0.684858	−	1.18621i
$807$		0			0
$808$	−18.3904	−	15.4314i	−0.646971	−	0.542873i
$809$	7.67860	+	13.2997i	0.269965	+	0.467593i	0.968853	−	0.247638i	$-0.0796545\pi$
$809$	7.67860	+	13.2997i	0.269965	+	0.467593i	−0.698887	+	0.715232i	$0.746321\pi$
$810$		0			0
$811$	26.8518	−	9.77325i	0.942894	−	0.343185i	0.175586	−	0.984464i	$-0.443818\pi$
$811$	26.8518	−	9.77325i	0.942894	−	0.343185i	0.767308	+	0.641279i	$0.221596\pi$
$812$	−0.546504	−	3.09938i	−0.0191785	−	0.108767i
$813$		0			0
$814$	−31.9222	−	11.6187i	−1.11887	−	0.407237i
$815$	14.1192	−	11.8474i	0.494575	−	0.414998i
$816$		0			0
$817$	−36.8799	+	4.06614i	−1.29027	+	0.142256i
$818$	−64.9843			−2.27212
$819$		0			0
$820$	−1.09609	−	0.398944i	−0.0382771	−	0.0139317i
$821$	0.156048	−	0.884994i	0.00544612	−	0.0308865i	−0.981964	−	0.189070i	$-0.939453\pi$
$821$	0.156048	−	0.884994i	0.00544612	−	0.0308865i	0.987410	+	0.158184i	$0.0505638\pi$
$822$		0			0
$823$	34.4963	−	12.5556i	1.20246	−	0.437661i	0.338381	−	0.941009i	$-0.390121\pi$
$823$	34.4963	−	12.5556i	1.20246	−	0.437661i	0.864084	+	0.503348i	$0.167899\pi$
$824$	7.38833	−	12.7970i	0.257385	−	0.445803i
$825$		0			0
$826$	−2.22149	−	1.86405i	−0.0772954	−	0.0648585i
$827$	32.4484	+	27.2274i	1.12834	+	0.946791i	0.998996	−	0.0448083i	$-0.0142677\pi$
$827$	32.4484	+	27.2274i	1.12834	+	0.946791i	0.129346	+	0.991599i	$0.458712\pi$
$828$		0			0
$829$	−12.1944	+	21.1213i	−0.423530	+	0.733575i	−0.996282	−	0.0861537i	$-0.972542\pi$
$829$	−12.1944	+	21.1213i	−0.423530	+	0.733575i	0.572752	+	0.819729i	$0.305876\pi$
$830$	−4.60819	+	1.67724i	−0.159953	+	0.0582180i
$831$		0			0
$832$	−0.820391	+	4.65267i	−0.0284420	+	0.161302i
$833$	21.9796	+	7.99991i	0.761547	+	0.277180i
$834$		0			0
$835$	−1.94262			−0.0672271
$836$	5.26827	+	18.0258i	0.182207	+	0.623437i
$837$		0			0
$838$	−41.2957	+	34.6512i	−1.42654	+	1.19701i
$839$	−22.0649	−	8.03097i	−0.761765	−	0.277260i	−0.0682173	−	0.997670i	$-0.521731\pi$
$839$	−22.0649	−	8.03097i	−0.761765	−	0.277260i	−0.693548	+	0.720411i	$0.743953\pi$
$840$		0			0
$841$	−4.15474	−	23.5627i	−0.143267	−	0.812507i
$842$	21.0810	−	7.67286i	0.726500	−	0.264424i
$843$		0			0
$844$	10.1280	+	17.5421i	0.348619	+	0.603826i
$845$	−4.54800	−	3.81623i	−0.156456	−	0.131282i
$846$		0			0
$847$	0.0230243	+	0.0398792i	0.000791124	+	0.00137027i
$848$	8.34399	−	14.4522i	0.286534	−	0.496291i
$849$		0			0
$850$	−1.26206	−	7.15751i	−0.0432884	−	0.245501i
$851$	1.72006	−	9.75497i	0.0589630	−	0.334396i
$852$		0			0
$853$	4.47350	−	3.75372i	0.153170	−	0.128525i	−0.562982	−	0.826469i	$-0.690346\pi$
$853$	4.47350	−	3.75372i	0.153170	−	0.128525i	0.716152	+	0.697944i	$0.245902\pi$
$854$	−26.7801			−0.916397
$855$		0			0
$856$	−14.4619			−0.494299
$857$	20.6838	−	17.3558i	0.706546	−	0.592862i	−0.217082	−	0.976153i	$-0.569654\pi$
$857$	20.6838	−	17.3558i	0.706546	−	0.592862i	0.923628	+	0.383291i	$0.125209\pi$
$858$		0			0
$859$	−0.553337	+	3.13813i	−0.0188796	+	0.107072i	−0.992791	−	0.119856i	$-0.961757\pi$
$859$	−0.553337	+	3.13813i	−0.0188796	+	0.107072i	0.973912	+	0.226927i	$0.0728680\pi$
$860$	−1.92387	−	10.9108i	−0.0656035	−	0.372056i
$861$		0			0
$862$	15.5052	−	26.8558i	0.528109	−	0.914712i
$863$	4.21087	+	7.29344i	0.143340	+	0.248272i	0.928752	−	0.370701i	$-0.120883\pi$
$863$	4.21087	+	7.29344i	0.143340	+	0.248272i	−0.785413	+	0.618973i	$0.787549\pi$
$864$		0			0
$865$	9.23195	+	7.74653i	0.313896	+	0.263390i
$866$	−2.54399	−	4.40632i	−0.0864483	−	0.149733i
$867$		0			0
$868$	10.5727	−	3.84814i	0.358860	−	0.130614i
$869$	−3.77673	−	21.4189i	−0.128117	−	0.726587i
$870$		0			0
$871$	−32.1152	−	11.6890i	−1.08818	−	0.396066i
$872$	−12.3828	+	10.3904i	−0.419334	+	0.351863i
$873$		0			0
$874$	−12.4534	+	6.15259i	−0.421243	+	0.208115i
$875$	1.07346			0.0362897
$876$		0			0
$877$	39.2887	+	14.2999i	1.32669	+	0.482874i	0.905595	−	0.424144i	$-0.139425\pi$
$877$	39.2887	+	14.2999i	1.32669	+	0.482874i	0.421091	+	0.907018i	$0.361647\pi$
$878$	−6.69384	+	37.9627i	−0.225906	+	1.28118i
$879$		0			0
$880$	15.2697	−	5.55773i	0.514743	−	0.187351i
$881$	−13.9233	+	24.1158i	−0.469087	+	0.812482i	−0.999376	−	0.0353351i	$-0.988750\pi$
$881$	−13.9233	+	24.1158i	−0.469087	+	0.812482i	0.530289	+	0.847817i	$0.322083\pi$
$882$		0			0
$883$	21.5180	+	18.0558i	0.724139	+	0.607625i	0.928527	−	0.371265i	$-0.121076\pi$
$883$	21.5180	+	18.0558i	0.724139	+	0.607625i	−0.204388	+	0.978890i	$0.565520\pi$
$884$	10.5991	+	8.89367i	0.356485	+	0.299127i
$885$		0			0
$886$	−20.6950	+	35.8447i	−0.695261	+	1.20423i
$887$	0.105586	−	0.0384300i	0.00354522	−	0.00129035i	−0.340247	−	0.940336i	$-0.610511\pi$
$887$	0.105586	−	0.0384300i	0.00354522	−	0.00129035i	0.343792	+	0.939046i	$0.388288\pi$
$888$		0			0
$889$	−1.81249	+	10.2791i	−0.0607888	+	0.344751i
$890$	−1.34860	−	0.490852i	−0.0452053	−	0.0164534i
$891$		0			0
$892$	−26.1986			−0.877195
$893$	18.9637	−	19.8386i	0.634595	−	0.663872i
$894$		0			0
$895$	14.0266	−	11.7697i	0.468856	−	0.393417i
$896$	9.61658	+	3.50015i	0.321268	+	0.116932i
$897$		0			0
$898$	−9.39304	−	53.2706i	−0.313450	−	1.77766i
$899$	−17.0449	+	6.20385i	−0.568481	+	0.206910i
$900$		0			0
$901$	−6.79870	−	11.7757i	−0.226497	−	0.392305i
$902$	−4.12908	−	3.46471i	−0.137483	−	0.115362i
$903$		0			0
$904$	10.5264	+	18.2323i	0.350104	+	0.606398i
$905$	12.8257	−	22.2148i	0.426341	−	0.738444i
$906$		0			0
$907$	6.26402	+	35.5251i	0.207994	+	1.17959i	0.892659	+	0.450733i	$0.148837\pi$
$907$	6.26402	+	35.5251i	0.207994	+	1.17959i	−0.684666	+	0.728857i	$0.740052\pi$
$908$	−3.13439	+	17.7760i	−0.104019	+	0.589918i
$909$		0			0
$910$	−3.97097	+	3.33204i	−0.131636	+	0.110456i
$911$	51.0528			1.69145			0.845727	−	0.533615i	$-0.179167\pi$
$911$	51.0528			1.69145			0.845727	+	0.533615i	$0.179167\pi$
$912$		0			0
$913$	−8.93370			−0.295662
$914$	51.1761	−	42.9419i	1.69276	−	1.42039i
$915$		0			0
$916$	1.96713	−	11.1562i	0.0649960	−	0.368610i
$917$	−2.75699	−	15.6356i	−0.0910437	−	0.516335i
$918$		0			0
$919$	−20.6112	+	35.6996i	−0.679900	+	1.17762i	0.295110	+	0.955463i	$0.404644\pi$
$919$	−20.6112	+	35.6996i	−0.679900	+	1.17762i	−0.975011	+	0.222159i	$0.928690\pi$
$920$	1.11282	+	1.92747i	0.0366887	+	0.0635467i
$921$		0			0
$922$	−35.8140	−	30.0515i	−1.17947	−	0.989695i
$923$	14.6518	+	25.3777i	0.482271	+	0.835318i
$924$		0			0
$925$	5.30743	−	1.93175i	0.174507	−	0.0635155i
$926$	11.2228	+	63.6475i	0.368803	+	2.09159i
$927$		0			0
$928$	13.5081	+	4.91653i	0.443424	+	0.161393i
$929$	−9.91750	+	8.32177i	−0.325383	+	0.273029i	−0.790815	−	0.612055i	$-0.790343\pi$
$929$	−9.91750	+	8.32177i	−0.325383	+	0.273029i	0.465433	+	0.885083i	$0.345899\pi$
$930$		0			0
$931$	22.8526	−	11.2903i	0.748963	−	0.370025i
$932$	−20.4616			−0.670241
$933$		0			0
$934$	12.1497	+	4.42212i	0.397549	+	0.144696i
$935$	2.29915	−	13.0391i	0.0751904	−	0.426426i
$936$		0			0
$937$	−29.2049	+	10.6297i	−0.954082	+	0.347258i	−0.771712	−	0.635972i	$-0.780599\pi$
$937$	−29.2049	+	10.6297i	−0.954082	+	0.347258i	−0.182370	+	0.983230i	$0.558377\pi$
$938$	12.5415	−	21.7225i	0.409493	−	0.709263i
$939$		0			0
$940$	6.27767	+	5.26759i	0.204755	+	0.171810i
$941$	−1.29987	−	1.09072i	−0.0423745	−	0.0355564i	0.621354	−	0.783530i	$-0.286583\pi$
$941$	−1.29987	−	1.09072i	−0.0423745	−	0.0355564i	−0.663729	+	0.747973i	$0.731027\pi$
$942$		0			0
$943$	0.785845	−	1.36112i	0.0255906	−	0.0443243i
$944$	6.85844	−	2.49627i	0.223223	−	0.0812466i
$945$		0			0
$946$	8.89029	−	50.4193i	0.289048	−	1.63927i
$947$	−44.2831	−	16.1177i	−1.43901	−	0.523756i	−0.499509	−	0.866309i	$-0.666486\pi$
$947$	−44.2831	−	16.1177i	−1.43901	−	0.523756i	−0.939499	+	0.342553i	$0.888709\pi$
$948$		0			0
$949$	−6.93813			−0.225221
$950$	−6.58862	−	4.39545i	−0.213763	−	0.142607i
$951$		0			0
$952$	4.17418	−	3.50256i	0.135286	−	0.113518i
$953$	48.5905	+	17.6855i	1.57400	+	0.572889i	0.973888	−	0.227028i	$-0.0729008\pi$
$953$	48.5905	+	17.6855i	1.57400	+	0.572889i	0.600111	+	0.799917i	$0.295123\pi$
$954$		0			0
$955$	−1.60133	−	9.08161i	−0.0518179	−	0.293874i
$956$	−16.9208	+	6.15868i	−0.547259	+	0.199186i
$957$		0			0
$958$	8.00649	+	13.8676i	0.258678	+	0.448043i
$959$	−2.95731	−	2.48147i	−0.0954964	−	0.0801310i
$960$		0			0
$961$	−16.9232	−	29.3118i	−0.545909	−	0.945541i
$962$	−13.6372	+	23.6203i	−0.439680	+	0.761548i
$963$		0			0
$964$	2.75214	+	15.6082i	0.0886405	+	0.502705i
$965$	2.08412	−	11.8196i	0.0670903	−	0.380488i
$966$		0			0
$967$	−8.87003	+	7.44284i	−0.285241	+	0.239346i	−0.774170	−	0.632978i	$-0.781832\pi$
$967$	−8.87003	+	7.44284i	−0.285241	+	0.239346i	0.488929	+	0.872324i	$0.337388\pi$
$968$	−0.0544390			−0.00174973
$969$		0			0
$970$	34.0109			1.09202
$971$	45.4143	−	38.1071i	1.45742	−	1.22292i	0.530478	−	0.847698i	$-0.322012\pi$
$971$	45.4143	−	38.1071i	1.45742	−	1.22292i	0.926937	−	0.375218i	$-0.122432\pi$
$972$		0			0
$973$	−1.09134	+	6.18930i	−0.0349868	+	0.198420i
$974$	1.50916	+	8.55889i	0.0483567	+	0.274245i
$975$		0			0
$976$	33.7002	−	58.3705i	1.07872	−	1.86839i
$977$	10.9939	+	19.0420i	0.351727	+	0.609209i	0.986552	−	0.163447i	$-0.0522613\pi$
$977$	10.9939	+	19.0420i	0.351727	+	0.609209i	−0.634825	+	0.772656i	$0.718928\pi$
$978$		0			0
$979$	−2.00281	−	1.68056i	−0.0640101	−	0.0537108i
$980$	3.80559	+	6.59148i	0.121565	+	0.210557i
$981$		0			0
$982$	−17.1956	+	6.25869i	−0.548734	+	0.199723i
$983$	−3.42195	−	19.4068i	−0.109143	−	0.618982i	−0.989484	−	0.144641i	$-0.953797\pi$
$983$	−3.42195	−	19.4068i	−0.109143	−	0.618982i	0.880341	−	0.474341i	$-0.157314\pi$
$984$		0			0
$985$	−25.2751	−	9.19939i	−0.805333	−	0.293117i
$986$	12.5410	−	10.5231i	0.399386	−	0.335125i
$987$		0			0
$988$	14.9871	−	1.65237i	0.476802	−	0.0525690i
$989$	14.9284			0.474695
$990$		0			0
$991$	43.9295	+	15.9890i	1.39547	+	0.507909i	0.926830	−	0.375482i	$-0.122523\pi$
$991$	43.9295	+	15.9890i	1.39547	+	0.507909i	0.468638	+	0.883390i	$0.344745\pi$
$992$	−8.92386	+	50.6097i	−0.283333	+	1.60686i
$993$		0			0
$994$	−20.2097	+	7.35575i	−0.641014	+	0.233310i
$995$	2.28697	−	3.96115i	0.0725019	−	0.125577i
$996$		0			0
$997$	8.89467	+	7.46351i	0.281697	+	0.236372i	0.772678	−	0.634799i	$-0.218917\pi$
$997$	8.89467	+	7.46351i	0.281697	+	0.236372i	−0.490981	+	0.871170i	$0.663361\pi$
$998$	2.67545	+	2.24497i	0.0846898	+	0.0710632i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.bs.b.766.1		18
3.2	odd	2		95.2.k.b.6.3	✓	18
15.2	even	4		475.2.u.c.424.6		36
15.8	even	4		475.2.u.c.424.1		36
15.14	odd	2		475.2.l.b.101.1		18
19.16	even	9	inner	855.2.bs.b.586.1		18
57.23	odd	18		1805.2.a.t.1.8		9
57.35	odd	18		95.2.k.b.16.3	yes	18
57.53	even	18		1805.2.a.u.1.2		9
285.92	even	36		475.2.u.c.149.1		36
285.149	odd	18		475.2.l.b.301.1		18
285.194	odd	18		9025.2.a.ce.1.2		9
285.224	even	18		9025.2.a.cd.1.8		9
285.263	even	36		475.2.u.c.149.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.6.3	✓	18	3.2	odd	2
95.2.k.b.16.3	yes	18	57.35	odd	18
475.2.l.b.101.1		18	15.14	odd	2
475.2.l.b.301.1		18	285.149	odd	18
475.2.u.c.149.1		36	285.92	even	36
475.2.u.c.149.6		36	285.263	even	36
475.2.u.c.424.1		36	15.8	even	4
475.2.u.c.424.6		36	15.2	even	4
855.2.bs.b.586.1		18	19.16	even	9	inner
855.2.bs.b.766.1		18	1.1	even	1	trivial
1805.2.a.t.1.8		9	57.23	odd	18
1805.2.a.u.1.2		9	57.53	even	18
9025.2.a.cd.1.8		9	285.224	even	18
9025.2.a.ce.1.2		9	285.194	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.39192 + 1.16796i) q^{2} +(0.226016 - 1.28180i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-0.536732 + 0.929646i) q^{7} +(-0.634528 - 1.09903i) q^{8} +O(q^{10})\)	\(q+(-1.39192 + 1.16796i) q^{2} +(0.226016 - 1.28180i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-0.536732 + 0.929646i) q^{7} +(-0.634528 - 1.09903i) q^{8} +(-1.39192 - 1.16796i) q^{10} +(-1.65508 - 2.86668i) q^{11} +(-2.49736 + 0.908963i) q^{13} +(-0.338702 - 1.92087i) q^{14} +(4.61300 + 1.67899i) q^{16} +(3.06411 - 2.57109i) q^{17} +(0.281925 - 4.34977i) q^{19} +1.30157 q^{20} +(5.65190 + 2.05712i) q^{22} +(-0.304541 + 1.72714i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(2.41449 - 4.18202i) q^{26} +(1.07031 + 0.898098i) q^{28} +(-1.72552 - 1.44789i) q^{29} +(4.02636 - 6.97386i) q^{31} +(-5.99689 + 2.18269i) q^{32} +(-1.26206 + 7.15751i) q^{34} +(-1.00873 - 0.367146i) q^{35} -5.64805 q^{37} +(4.68794 + 6.38382i) q^{38} +(0.972153 - 0.815733i) q^{40} +(-0.842126 - 0.306509i) q^{41} +(-1.47811 - 8.38279i) q^{43} +(-4.04858 + 1.47356i) q^{44} +(-1.59333 - 2.75973i) q^{46} +(4.82313 + 4.04709i) q^{47} +(2.92384 + 5.06424i) q^{49} +(0.908512 - 1.57359i) q^{50} +(0.600667 + 3.40655i) q^{52} +(0.590304 - 3.34778i) q^{53} +(2.53572 - 2.12772i) q^{55} +1.36228 q^{56} +4.09287 q^{58} +(1.13893 - 0.955673i) q^{59} +(2.38416 - 13.5212i) q^{61} +(2.54082 + 14.4097i) q^{62} +(0.888845 - 1.53952i) q^{64} +(-1.32882 - 2.30158i) q^{65} +(9.85110 + 8.26605i) q^{67} +(-2.60309 - 4.50868i) q^{68} +(1.83288 - 0.667113i) q^{70} +(-1.91469 - 10.8587i) q^{71} +(2.45320 + 0.892893i) q^{73} +(7.86164 - 6.59670i) q^{74} +(-5.51182 - 1.34449i) q^{76} +3.55333 q^{77} +(6.17425 + 2.24724i) q^{79} +(-0.852448 + 4.83447i) q^{80} +(1.53016 - 0.556934i) q^{82} +(1.34944 - 2.33730i) q^{83} +(3.06411 + 2.57109i) q^{85} +(11.8482 + 9.94180i) q^{86} +(-2.10038 + 3.63797i) q^{88} +(0.742205 - 0.270140i) q^{89} +(0.495396 - 2.80953i) q^{91} +(2.14502 + 0.780722i) q^{92} -11.4403 q^{94} +(4.33265 - 0.477688i) q^{95} +(-14.3388 + 12.0317i) q^{97} +(-9.98458 - 3.63409i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) \) 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8	\( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) \) 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8 - 3 * q^10 - 3 * q^13 - 24 * q^14 + 21 * q^16 + 24 * q^17 - 12 * q^19 + 12 * q^20 + 15 * q^22 - 21 * q^23 + 21 * q^26 - 24 * q^28 + 9 * q^29 + 30 * q^31 - 45 * q^32 + 24 * q^34 + 6 * q^35 - 60 * q^37 + 15 * q^38 - 6 * q^40 + 6 * q^41 - 6 * q^43 + 30 * q^44 + 21 * q^46 - 33 * q^47 - 3 * q^49 + 9 * q^52 - 24 * q^53 - 3 * q^55 + 72 * q^56 + 36 * q^58 - 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^64 - 3 * q^65 - 24 * q^67 + 3 * q^68 + 39 * q^70 - 24 * q^71 + 6 * q^73 + 39 * q^74 + 27 * q^76 - 24 * q^77 + 9 * q^79 - 33 * q^80 - 57 * q^82 + 24 * q^85 + 33 * q^86 + 39 * q^88 + 6 * q^89 - 6 * q^91 + 66 * q^92 - 66 * q^94 + 15 * q^95 - 87 * q^97 - 39 * q^98

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