LMFDB - Embedded newform 225.2.h.d.91.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 $ x^12 + 3x^10 - 2x^9 + 34x^8 - 22x^7 + 236x^6 - 179x^5 + 877x^4 - 409x^3 + 96x^2 - 11x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.3
Root			$-0.667650 - 2.05481i$ of defining polynomial
Character	$\chi$	$=$	225.91
Dual form			225.2.h.d.136.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.74793 + 1.26995i) q^{2} +(0.824463 + 2.53744i) q^{4} +(0.460159 + 2.18821i) q^{5} -3.16056 q^{7} +(-0.446002 + 1.37265i) q^{8} +O(q^{10})$	\(q+(1.74793 + 1.26995i) q^{2} +(0.824463 + 2.53744i) q^{4} +(0.460159 + 2.18821i) q^{5} -3.16056 q^{7} +(-0.446002 + 1.37265i) q^{8} +(-1.97458 + 4.40921i) q^{10} +(1.24455 + 0.904220i) q^{11} +(4.24041 - 3.08084i) q^{13} +(-5.52444 - 4.01374i) q^{14} +(1.79417 - 1.30354i) q^{16} +(-0.398843 + 1.22751i) q^{17} +(1.68287 - 5.17933i) q^{19} +(-5.17306 + 2.97172i) q^{20} +(1.02708 + 3.16103i) q^{22} +(-5.21204 - 3.78677i) q^{23} +(-4.57651 + 2.01385i) q^{25} +11.3244 q^{26} +(-2.60577 - 8.01972i) q^{28} +(0.730396 + 2.24793i) q^{29} +(-1.37989 + 4.24687i) q^{31} +7.67809 q^{32} +(-2.25602 + 1.63910i) q^{34} +(-1.45436 - 6.91596i) q^{35} +(4.81973 - 3.50174i) q^{37} +(9.51901 - 6.91596i) q^{38} +(-3.20889 - 0.344307i) q^{40} +(-6.90269 + 5.01510i) q^{41} -8.48426 q^{43} +(-1.26831 + 3.90347i) q^{44} +(-4.30129 - 13.2380i) q^{46} +(-0.232712 - 0.716212i) q^{47} +2.98914 q^{49} +(-10.5569 - 2.29185i) q^{50} +(11.3135 + 8.21974i) q^{52} +(-3.01289 - 9.27271i) q^{53} +(-1.40593 + 3.13942i) q^{55} +(1.40962 - 4.33836i) q^{56} +(-1.57806 + 4.85678i) q^{58} +(3.32724 - 2.41738i) q^{59} +(8.65159 + 6.28574i) q^{61} +(-7.80525 + 5.67084i) q^{62} +(9.83243 + 7.14368i) q^{64} +(8.69278 + 7.86123i) q^{65} +(-0.586713 + 1.80572i) q^{67} -3.44357 q^{68} +(6.24078 - 13.9356i) q^{70} +(0.0219023 + 0.0674084i) q^{71} +(-3.24515 - 2.35774i) q^{73} +12.8716 q^{74} +14.5297 q^{76} +(-3.93348 - 2.85784i) q^{77} +(0.500141 + 1.53928i) q^{79} +(3.67802 + 3.32618i) q^{80} -18.4343 q^{82} +(-4.06322 + 12.5053i) q^{83} +(-2.86958 - 0.307901i) q^{85} +(-14.8299 - 10.7745i) q^{86} +(-1.79626 + 1.30506i) q^{88} +(5.88638 + 4.27671i) q^{89} +(-13.4021 + 9.73718i) q^{91} +(5.31155 - 16.3473i) q^{92} +(0.502787 - 1.54742i) q^{94} +(12.1078 + 1.29915i) q^{95} +(3.15009 + 9.69499i) q^{97} +(5.22480 + 3.79604i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8}+O(q^{10}) $ 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8	$ 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8} - 9 q^{10} + 4 q^{11} - 2 q^{13} - 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 26 q^{20} + 13 q^{22} - 19 q^{23} + 4 q^{25} + 56 q^{26} + q^{28} + q^{29} + 13 q^{31} + 32 q^{32} - 25 q^{34} + 10 q^{35} + 8 q^{37} + 22 q^{38} - 28 q^{40} - 8 q^{41} - 4 q^{43} - 33 q^{44} - 22 q^{46} + 13 q^{47} - 28 q^{49} - 81 q^{50} + 44 q^{52} - 44 q^{53} + 9 q^{55} - 45 q^{56} + 41 q^{58} + 22 q^{59} - 8 q^{61} - 41 q^{62} + 49 q^{64} + 38 q^{65} - 6 q^{67} + 100 q^{68} - 45 q^{70} + 21 q^{71} - 16 q^{73} + 44 q^{74} - 52 q^{76} - q^{77} + 10 q^{79} + 99 q^{80} + 26 q^{82} + 10 q^{83} + 23 q^{85} - 56 q^{86} - 16 q^{88} - 57 q^{89} - 7 q^{91} - 3 q^{92} - 23 q^{94} - 21 q^{95} + 4 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8 - 9 * q^10 + 4 * q^11 - 2 * q^13 - 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 26 * q^20 + 13 * q^22 - 19 * q^23 + 4 * q^25 + 56 * q^26 + q^28 + q^29 + 13 * q^31 + 32 * q^32 - 25 * q^34 + 10 * q^35 + 8 * q^37 + 22 * q^38 - 28 * q^40 - 8 * q^41 - 4 * q^43 - 33 * q^44 - 22 * q^46 + 13 * q^47 - 28 * q^49 - 81 * q^50 + 44 * q^52 - 44 * q^53 + 9 * q^55 - 45 * q^56 + 41 * q^58 + 22 * q^59 - 8 * q^61 - 41 * q^62 + 49 * q^64 + 38 * q^65 - 6 * q^67 + 100 * q^68 - 45 * q^70 + 21 * q^71 - 16 * q^73 + 44 * q^74 - 52 * q^76 - q^77 + 10 * q^79 + 99 * q^80 + 26 * q^82 + 10 * q^83 + 23 * q^85 - 56 * q^86 - 16 * q^88 - 57 * q^89 - 7 * q^91 - 3 * q^92 - 23 * q^94 - 21 * q^95 + 4 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.74793	+	1.26995i	1.23597	+	0.897987i	0.997323	−	0.0731189i	$-0.0232952\pi$
$2$	1.74793	+	1.26995i	1.23597	+	0.897987i	0.238650	+	0.971106i	$0.423295\pi$
$3$		0			0
$3$		0			0
$4$	0.824463	+	2.53744i	0.412232	+	1.26872i
$5$	0.460159	+	2.18821i	0.205789	+	0.978596i
$5$	0.460159	+	2.18821i	0.205789	+	0.978596i
$6$		0			0
$7$	−3.16056			−1.19458			−0.597290	−	0.802026i	$-0.703756\pi$
$7$	−3.16056			−1.19458			−0.597290	+	0.802026i	$0.703756\pi$
$8$	−0.446002	+	1.37265i	−0.157686	+	0.485307i
$9$		0			0
$10$	−1.97458	+	4.40921i	−0.624417	+	1.39431i
$11$	1.24455	+	0.904220i	0.375247	+	0.272633i	0.759383	−	0.650644i	$-0.225501\pi$
$11$	1.24455	+	0.904220i	0.375247	+	0.272633i	−0.384137	+	0.923276i	$0.625501\pi$
$12$		0			0
$13$	4.24041	−	3.08084i	1.17608	−	0.854471i	0.184355	−	0.982860i	$-0.440981\pi$
$13$	4.24041	−	3.08084i	1.17608	−	0.854471i	0.991724	+	0.128389i	$0.0409805\pi$
$14$	−5.52444	−	4.01374i	−1.47647	−	1.07272i
$15$		0			0
$16$	1.79417	−	1.30354i	0.448542	−	0.325885i
$17$	−0.398843	+	1.22751i	−0.0967337	+	0.297716i	−0.987702	−	0.156351i	$-0.950027\pi$
$17$	−0.398843	+	1.22751i	−0.0967337	+	0.297716i	0.890968	+	0.454066i	$0.150027\pi$
$18$		0			0
$19$	1.68287	−	5.17933i	0.386076	−	1.18822i	−0.549620	−	0.835415i	$-0.685228\pi$
$19$	1.68287	−	5.17933i	0.386076	−	1.18822i	0.935696	−	0.352806i	$-0.114772\pi$
$20$	−5.17306	+	2.97172i	−1.15673	+	0.664497i
$21$		0			0
$22$	1.02708	+	3.16103i	0.218974	+	0.673933i
$23$	−5.21204	−	3.78677i	−1.08679	−	0.789596i	−0.107932	−	0.994158i	$-0.534423\pi$
$23$	−5.21204	−	3.78677i	−1.08679	−	0.789596i	−0.978854	+	0.204562i	$0.934423\pi$
$24$		0			0
$25$	−4.57651	+	2.01385i	−0.915302	+	0.402769i
$26$	11.3244			2.22090
$27$		0			0
$28$	−2.60577	−	8.01972i	−0.492443	−	1.51558i
$29$	0.730396	+	2.24793i	0.135631	+	0.417430i	0.995688	−	0.0927690i	$-0.0295718\pi$
$29$	0.730396	+	2.24793i	0.135631	+	0.417430i	−0.860056	+	0.510199i	$0.829572\pi$
$30$		0			0
$31$	−1.37989	+	4.24687i	−0.247836	+	0.762760i	0.747321	+	0.664463i	$0.231340\pi$
$31$	−1.37989	+	4.24687i	−0.247836	+	0.762760i	−0.995157	+	0.0982974i	$0.968660\pi$
$32$	7.67809			1.35731
$33$		0			0
$34$	−2.25602	+	1.63910i	−0.386905	+	0.281103i
$35$	−1.45436	−	6.91596i	−0.245831	−	1.16901i
$36$		0			0
$37$	4.81973	−	3.50174i	0.792358	−	0.575682i	−0.116304	−	0.993214i	$-0.537105\pi$
$37$	4.81973	−	3.50174i	0.792358	−	0.575682i	0.908662	+	0.417532i	$0.137105\pi$
$38$	9.51901	−	6.91596i	1.54419	−	1.12192i
$39$		0			0
$40$	−3.20889	−	0.344307i	−0.507369	−	0.0544398i
$41$	−6.90269	+	5.01510i	−1.07802	+	0.783227i	−0.977336	−	0.211692i	$-0.932103\pi$
$41$	−6.90269	+	5.01510i	−1.07802	+	0.783227i	−0.100683	+	0.994919i	$0.532103\pi$
$42$		0			0
$43$	−8.48426			−1.29384			−0.646919	−	0.762559i	$-0.723943\pi$
$43$	−8.48426			−1.29384			−0.646919	+	0.762559i	$0.723943\pi$
$44$	−1.26831	+	3.90347i	−0.191206	+	0.588470i
$45$		0			0
$46$	−4.30129	−	13.2380i	−0.634191	−	1.95184i
$47$	−0.232712	−	0.716212i	−0.0339445	−	0.104470i	0.932649	−	0.360786i	$-0.117491\pi$
$47$	−0.232712	−	0.716212i	−0.0339445	−	0.104470i	−0.966593	+	0.256315i	$0.917491\pi$
$48$		0			0
$49$	2.98914			0.427020
$50$	−10.5569	−	2.29185i	−1.49297	−	0.324117i
$51$		0			0
$52$	11.3135	+	8.21974i	1.56890	+	1.13987i
$53$	−3.01289	−	9.27271i	−0.413852	−	1.27371i	−0.913274	−	0.407346i	$-0.866454\pi$
$53$	−3.01289	−	9.27271i	−0.413852	−	1.27371i	0.499422	−	0.866359i	$-0.333546\pi$
$54$		0			0
$55$	−1.40593	+	3.13942i	−0.189576	+	0.423320i
$56$	1.40962	−	4.33836i	0.188368	−	0.579737i
$57$		0			0
$58$	−1.57806	+	4.85678i	−0.207210	+	0.637727i
$59$	3.32724	−	2.41738i	0.433170	−	0.314717i	−0.349745	−	0.936845i	$-0.613732\pi$
$59$	3.32724	−	2.41738i	0.433170	−	0.314717i	0.782915	+	0.622128i	$0.213732\pi$
$60$		0			0
$61$	8.65159	+	6.28574i	1.10772	+	0.804807i	0.982303	−	0.187297i	$-0.0599726\pi$
$61$	8.65159	+	6.28574i	1.10772	+	0.804807i	0.125419	+	0.992104i	$0.459973\pi$
$62$	−7.80525	+	5.67084i	−0.991267	+	0.720198i
$63$		0			0
$64$	9.83243	+	7.14368i	1.22905	+	0.892960i
$65$	8.69278	+	7.86123i	1.07821	+	0.975065i
$66$		0			0
$67$	−0.586713	+	1.80572i	−0.0716785	+	0.220604i	−0.980478	−	0.196630i	$-0.937000\pi$
$67$	−0.586713	+	1.80572i	−0.0716785	+	0.220604i	0.908799	+	0.417233i	$0.137000\pi$
$68$	−3.44357			−0.417594
$69$		0			0
$70$	6.24078	−	13.9356i	0.745915	−	1.66562i
$71$	0.0219023	+	0.0674084i	0.00259933	+	0.00799990i	0.952348	−	0.305014i	$-0.0986612\pi$
$71$	0.0219023	+	0.0674084i	0.00259933	+	0.00799990i	−0.949748	+	0.313014i	$0.898661\pi$
$72$		0			0
$73$	−3.24515	−	2.35774i	−0.379816	−	0.275952i	0.381454	−	0.924388i	$-0.375424\pi$
$73$	−3.24515	−	2.35774i	−0.379816	−	0.275952i	−0.761270	+	0.648436i	$0.775424\pi$
$74$	12.8716			1.49629
$75$		0			0
$76$	14.5297			1.66667
$77$	−3.93348	−	2.85784i	−0.448262	−	0.325681i
$78$		0			0
$79$	0.500141	+	1.53928i	0.0562703	+	0.173182i	0.975242	−	0.221143i	$-0.0709786\pi$
$79$	0.500141	+	1.53928i	0.0562703	+	0.173182i	−0.918971	+	0.394325i	$0.870979\pi$
$80$	3.67802	+	3.32618i	0.411215	+	0.371878i
$81$		0			0
$82$	−18.4343			−2.03573
$83$	−4.06322	+	12.5053i	−0.445996	+	1.37263i	0.435392	+	0.900241i	$0.356610\pi$
$83$	−4.06322	+	12.5053i	−0.445996	+	1.37263i	−0.881388	+	0.472393i	$0.843390\pi$
$84$		0			0
$85$	−2.86958	−	0.307901i	−0.311250	−	0.0333966i
$86$	−14.8299	−	10.7745i	−1.59915	−	1.16185i
$87$		0			0
$88$	−1.79626	+	1.30506i	−0.191481	+	0.139119i
$89$	5.88638	+	4.27671i	0.623955	+	0.453330i	0.854301	−	0.519779i	$-0.173986\pi$
$89$	5.88638	+	4.27671i	0.623955	+	0.453330i	−0.230345	+	0.973109i	$0.573986\pi$
$90$		0			0
$91$	−13.4021	+	9.73718i	−1.40492	+	1.02073i
$92$	5.31155	−	16.3473i	0.553768	−	1.70432i
$93$		0			0
$94$	0.502787	−	1.54742i	0.0518585	−	0.159604i
$95$	12.1078	+	1.29915i	1.24224	+	0.133290i
$96$		0			0
$97$	3.15009	+	9.69499i	0.319843	+	0.984377i	0.973715	+	0.227771i	$0.0731438\pi$
$97$	3.15009	+	9.69499i	0.319843	+	0.984377i	−0.653871	+	0.756606i	$0.726856\pi$
$98$	5.22480	+	3.79604i	0.527785	+	0.383458i
$99$		0			0
$100$	−8.88317	−	9.95226i	−0.888317	−	0.995226i
$101$	−1.08759			−0.108219			−0.0541096	−	0.998535i	$-0.517232\pi$
$101$	−1.08759			−0.108219			−0.0541096	+	0.998535i	$0.517232\pi$
$102$		0			0
$103$	−1.52579	−	4.69590i	−0.150341	−	0.462701i	0.847319	−	0.531085i	$-0.178216\pi$
$103$	−1.52579	−	4.69590i	−0.150341	−	0.462701i	−0.997659	+	0.0683845i	$0.978216\pi$
$104$	2.33769	+	7.19468i	0.229230	+	0.705497i
$105$		0			0
$106$	6.50952	−	20.0343i	0.632261	−	1.94590i
$107$	−15.3059			−1.47967			−0.739837	−	0.672786i	$-0.765098\pi$
$107$	−15.3059			−1.47967			−0.739837	+	0.672786i	$0.765098\pi$
$108$		0			0
$109$	−5.38724	+	3.91406i	−0.516004	+	0.374899i	−0.815097	−	0.579325i	$-0.803316\pi$
$109$	−5.38724	+	3.91406i	−0.516004	+	0.374899i	0.299092	+	0.954224i	$0.403316\pi$
$110$	−6.44436	+	3.70204i	−0.614446	+	0.352975i
$111$		0			0
$112$	−5.67058	+	4.11991i	−0.535819	+	0.389295i
$113$	−7.25804	+	5.27328i	−0.682779	+	0.496068i	−0.874278	−	0.485425i	$-0.838665\pi$
$113$	−7.25804	+	5.27328i	−0.682779	+	0.496068i	0.191499	+	0.981493i	$0.438665\pi$
$114$		0			0
$115$	5.88787	−	13.1475i	0.549047	−	1.22601i
$116$	−5.10179	+	3.70667i	−0.473689	+	0.344155i
$117$		0			0
$118$	8.88573			0.817998
$119$	1.26057	−	3.87963i	0.115556	−	0.355645i
$120$		0			0
$121$	−2.66789	−	8.21092i	−0.242536	−	0.746448i
$122$	7.13981	+	21.9741i	0.646408	+	1.98944i
$123$		0			0
$124$	−11.9138			−1.06989
$125$	−6.51263	−	9.08766i	−0.582508	−	0.812825i
$126$		0			0
$127$	−8.10511	−	5.88870i	−0.719212	−	0.522538i	0.166920	−	0.985970i	$-0.446618\pi$
$127$	−8.10511	−	5.88870i	−0.719212	−	0.522538i	−0.886132	+	0.463432i	$0.846618\pi$
$128$	3.36899	+	10.3687i	0.297780	+	0.916471i
$129$		0			0
$130$	5.21104	+	24.7802i	0.457038	+	2.17337i
$131$	1.97111	−	6.06645i	0.172217	−	0.530029i	−0.827279	−	0.561792i	$-0.810112\pi$
$131$	1.97111	−	6.06645i	0.172217	−	0.530029i	0.999495	+	0.0317631i	$0.0101122\pi$
$132$		0			0
$133$	−5.31880	+	16.3696i	−0.461199	+	1.41942i
$134$	−3.31870	+	2.41117i	−0.286692	+	0.208294i
$135$		0			0
$136$	−1.50707	−	1.09495i	−0.129230	−	0.0938910i
$137$	−7.42461	+	5.39429i	−0.634327	+	0.460866i	−0.857897	−	0.513822i	$-0.828229\pi$
$137$	−7.42461	+	5.39429i	−0.634327	+	0.460866i	0.223570	+	0.974688i	$0.428229\pi$
$138$		0			0
$139$	7.49586	+	5.44606i	0.635790	+	0.461929i	0.858401	−	0.512979i	$-0.171458\pi$
$139$	7.49586	+	5.44606i	0.635790	+	0.461929i	−0.222611	+	0.974907i	$0.571458\pi$
$140$	16.3498	−	9.39230i	1.38181	−	0.793794i
$141$		0			0
$142$	−0.0473213	+	0.145640i	−0.00397111	+	0.0122218i
$143$	8.06317			0.674276
$144$		0			0
$145$	−4.58284	+	2.63266i	−0.380584	+	0.218631i
$146$	−2.67809	−	8.24232i	−0.221641	−	0.682140i
$147$		0			0
$148$	12.8591	+	9.34270i	1.05701	+	0.767965i
$149$	10.0817			0.825928			0.412964	−	0.910747i	$-0.364494\pi$
$149$	10.0817			0.825928			0.412964	+	0.910747i	$0.364494\pi$
$150$		0			0
$151$	10.7375			0.873804			0.436902	−	0.899509i	$-0.356076\pi$
$151$	10.7375			0.873804			0.436902	+	0.899509i	$0.356076\pi$
$152$	6.35887	+	4.61999i	0.515773	+	0.374731i
$153$		0			0
$154$	−3.24615	−	9.99061i	−0.261582	−	0.805067i
$155$	−9.92800	−	1.06526i	−0.797436	−	0.0855634i
$156$		0			0
$157$	17.4417			1.39200			0.696001	−	0.718041i	$-0.254961\pi$
$157$	17.4417			1.39200			0.696001	+	0.718041i	$0.254961\pi$
$158$	−1.08058	+	3.32570i	−0.0859667	+	0.264578i
$159$		0			0
$160$	3.53314	+	16.8013i	0.279319	+	1.32826i
$161$	16.4730	+	11.9683i	1.29825	+	0.943235i
$162$		0			0
$163$	13.1525	−	9.55586i	1.03018	−	0.748473i	0.0618392	−	0.998086i	$-0.480303\pi$
$163$	13.1525	−	9.55586i	1.03018	−	0.748473i	0.968346	+	0.249613i	$0.0803034\pi$
$164$	−18.4165	−	13.3804i	−1.43809	−	1.04483i
$165$		0			0
$166$	−22.9832	+	16.6983i	−1.78385	+	1.29604i
$167$	3.51989	−	10.8331i	0.272377	−	0.838290i	−0.717525	−	0.696533i	$-0.754725\pi$
$167$	3.51989	−	10.8331i	0.272377	−	0.838290i	0.989902	−	0.141757i	$-0.0452751\pi$
$168$		0			0
$169$	4.47230	−	13.7643i	0.344023	−	1.05879i
$170$	−4.62481	−	4.18240i	−0.354707	−	0.320776i
$171$		0			0
$172$	−6.99496	−	21.5283i	−0.533361	−	1.64152i
$173$	7.65205	+	5.55954i	0.581775	+	0.422684i	0.839363	−	0.543571i	$-0.182928\pi$
$173$	7.65205	+	5.55954i	0.581775	+	0.422684i	−0.257589	+	0.966255i	$0.582928\pi$
$174$		0			0
$175$	14.4643	−	6.36488i	1.09340	−	0.481140i
$176$	3.41162			0.257161
$177$		0			0
$178$	4.85780	+	14.9508i	0.364107	+	1.12061i
$179$	−1.26001	−	3.87790i	−0.0941773	−	0.289848i	0.892861	−	0.450332i	$-0.148694\pi$
$179$	−1.26001	−	3.87790i	−0.0941773	−	0.289848i	−0.987038	+	0.160484i	$0.948694\pi$
$180$		0			0
$181$	−3.43633	+	10.5759i	−0.255421	+	0.786104i	0.738326	+	0.674444i	$0.235617\pi$
$181$	−3.43633	+	10.5759i	−0.255421	+	0.786104i	−0.993747	+	0.111660i	$0.964383\pi$
$182$	−35.7916			−2.65305
$183$		0			0
$184$	7.52251	−	5.46542i	0.554567	−	0.402916i
$185$	9.88036	+	8.93521i	0.726419	+	0.656930i
$186$		0			0
$187$	−1.60632	+	1.16706i	−0.117466	+	0.0853440i
$188$	1.62548	−	1.18098i	0.118550	−	0.0861319i
$189$		0			0
$190$	19.5138	+	17.6471i	1.41568	+	1.28026i
$191$	2.92164	−	2.12270i	0.211403	−	0.153593i	−0.477046	−	0.878879i	$-0.658292\pi$
$191$	2.92164	−	2.12270i	0.211403	−	0.153593i	0.688448	+	0.725286i	$0.258292\pi$
$192$		0			0
$193$	−17.0562			−1.22774			−0.613868	−	0.789409i	$-0.710387\pi$
$193$	−17.0562			−1.22774			−0.613868	+	0.789409i	$0.710387\pi$
$194$	−6.80596	+	20.9466i	−0.488640	+	1.50388i
$195$		0			0
$196$	2.46443	+	7.58475i	0.176031	+	0.541768i
$197$	1.36129	+	4.18963i	0.0969880	+	0.298498i	0.987767	−	0.155939i	$-0.0498403\pi$
$197$	1.36129	+	4.18963i	0.0969880	+	0.298498i	−0.890779	+	0.454437i	$0.849840\pi$
$198$		0			0
$199$	16.5956			1.17643			0.588214	−	0.808705i	$-0.299831\pi$
$199$	16.5956			1.17643			0.588214	+	0.808705i	$0.299831\pi$
$200$	−0.723180	−	7.18014i	−0.0511365	−	0.507713i
$201$		0			0
$202$	−1.90103	−	1.38118i	−0.133756	−	0.0971795i
$203$	−2.30846	−	7.10471i	−0.162022	−	0.498653i
$204$		0			0
$205$	−14.1504	−	12.7968i	−0.988307	−	0.893766i
$206$	3.29656	−	10.1458i	0.229682	−	0.706889i
$207$		0			0
$208$	3.59202	−	11.0551i	0.249061	−	0.766532i
$209$	6.77768	−	4.92427i	0.468822	−	0.340619i
$210$		0			0
$211$	−15.0035	−	10.9007i	−1.03288	−	0.750434i	−0.0640001	−	0.997950i	$-0.520386\pi$
$211$	−15.0035	−	10.9007i	−1.03288	−	0.750434i	−0.968884	+	0.247516i	$0.920386\pi$
$212$	21.0449	−	15.2900i	1.44537	−	1.05012i
$213$		0			0
$214$	−26.7536	−	19.4376i	−1.82884	−	1.32873i
$215$	−3.90410	−	18.5653i	−0.266258	−	1.26614i
$216$		0			0
$217$	4.36123	−	13.4225i	0.296060	−	0.911178i
$218$	−14.3872			−0.974422
$219$		0			0
$220$	−9.12523	−	0.979120i	−0.615223	−	0.0660122i
$221$	2.09051	+	6.43393i	0.140623	+	0.432793i
$222$		0			0
$223$	0.624203	+	0.453510i	0.0417997	+	0.0303693i	0.608489	−	0.793562i	$-0.291776\pi$
$223$	0.624203	+	0.453510i	0.0417997	+	0.0303693i	−0.566689	+	0.823932i	$0.691776\pi$
$224$	−24.2671			−1.62141
$225$		0			0
$226$	−19.3833			−1.28936
$227$	9.24817	+	6.71919i	0.613823	+	0.445968i	0.850758	−	0.525557i	$-0.176143\pi$
$227$	9.24817	+	6.71919i	0.613823	+	0.445968i	−0.236936	+	0.971525i	$0.576143\pi$
$228$		0			0
$229$	3.15962	+	9.72432i	0.208794	+	0.642601i	0.999536	+	0.0304520i	$0.00969467\pi$
$229$	3.15962	+	9.72432i	0.208794	+	0.642601i	−0.790743	+	0.612149i	$0.790305\pi$
$230$	26.9883	−	15.5037i	1.77955	−	1.02228i
$231$		0			0
$232$	−3.41139			−0.223969
$233$	6.95997	−	21.4206i	0.455963	−	1.40331i	−0.414038	−	0.910260i	$-0.635882\pi$
$233$	6.95997	−	21.4206i	0.455963	−	1.40331i	0.870001	−	0.493050i	$-0.164118\pi$
$234$		0			0
$235$	1.46014	−	0.838793i	0.0952489	−	0.0547168i
$236$	8.87715	+	6.44963i	0.577853	+	0.419835i
$237$		0			0
$238$	7.13030	−	5.18047i	0.462189	−	0.335800i
$239$	−0.476571	−	0.346249i	−0.0308268	−	0.0223970i	0.572265	−	0.820069i	$-0.306065\pi$
$239$	−0.476571	−	0.346249i	−0.0308268	−	0.0223970i	−0.603092	+	0.797672i	$0.706065\pi$
$240$		0			0
$241$	−1.22110	+	0.887185i	−0.0786583	+	0.0571486i	−0.626419	−	0.779486i	$-0.715480\pi$
$241$	−1.22110	+	0.887185i	−0.0786583	+	0.0571486i	0.547761	+	0.836635i	$0.315480\pi$
$242$	5.76414	−	17.7402i	0.370533	−	1.14038i
$243$		0			0
$244$	−8.81677	+	27.1352i	−0.564436	+	1.73715i
$245$	1.37548	+	6.54086i	0.0878760	+	0.417880i
$246$		0			0
$247$	−8.82065	−	27.1472i	−0.561244	−	1.72733i
$248$	−5.21405	−	3.78823i	−0.331093	−	0.240553i
$249$		0			0
$250$	0.157212	−	24.1553i	0.00994296	−	1.52771i
$251$	−11.8953			−0.750823			−0.375412	−	0.926858i	$-0.622499\pi$
$251$	−11.8953			−0.750823			−0.375412	+	0.926858i	$0.622499\pi$
$252$		0			0
$253$	−3.06258	−	9.42567i	−0.192543	−	0.592587i
$254$	−6.68882	−	20.5861i	−0.419694	−	1.29169i
$255$		0			0
$256$	0.232398	−	0.715248i	0.0145249	−	0.0447030i
$257$	18.0492			1.12588			0.562939	−	0.826498i	$-0.309671\pi$
$257$	18.0492			1.12588			0.562939	+	0.826498i	$0.309671\pi$
$258$		0			0
$259$	−15.2330	+	11.0674i	−0.946534	+	0.687698i
$260$	−12.7805	+	28.5387i	−0.792612	+	1.76989i
$261$		0			0
$262$	11.1494	−	8.10053i	0.688814	−	0.500453i
$263$	−15.4576	+	11.2306i	−0.953157	+	0.692509i	−0.951551	−	0.307490i	$-0.900511\pi$
$263$	−15.4576	+	11.2306i	−0.953157	+	0.692509i	−0.00160518	+	0.999999i	$0.500511\pi$
$264$		0			0
$265$	18.9042	−	10.8597i	1.16128	−	0.667109i
$266$	−30.0854	+	21.8583i	−1.84465	+	1.34022i
$267$		0			0
$268$	−5.06562			−0.309432
$269$	6.86791	−	21.1372i	0.418744	−	1.28876i	−0.490115	−	0.871658i	$-0.663045\pi$
$269$	6.86791	−	21.1372i	0.418744	−	1.28876i	0.908859	−	0.417103i	$-0.136955\pi$
$270$		0			0
$271$	6.24546	+	19.2216i	0.379385	+	1.16763i	0.940472	+	0.339870i	$0.110383\pi$
$271$	6.24546	+	19.2216i	0.379385	+	1.16763i	−0.561088	+	0.827756i	$0.689617\pi$
$272$	0.884520	+	2.72227i	0.0536319	+	0.165062i
$273$		0			0
$274$	−19.8281			−1.19786
$275$	−7.51666	−	1.63184i	−0.453272	−	0.0984034i
$276$		0			0
$277$	12.9777	+	9.42882i	0.779752	+	0.566523i	0.904904	−	0.425615i	$-0.139942\pi$
$277$	12.9777	+	9.42882i	0.779752	+	0.566523i	−0.125153	+	0.992137i	$0.539942\pi$
$278$	6.18604	+	19.0387i	0.371014	+	1.14186i
$279$		0			0
$280$	10.1419	+	1.08820i	0.606093	+	0.0650326i
$281$	−2.58742	+	7.96327i	−0.154353	+	0.475049i	−0.998095	−	0.0617001i	$-0.980348\pi$
$281$	−2.58742	+	7.96327i	−0.154353	+	0.475049i	0.843742	+	0.536749i	$0.180348\pi$
$282$		0			0
$283$	−0.349174	+	1.07465i	−0.0207562	+	0.0638811i	−0.960898	−	0.276902i	$-0.910692\pi$
$283$	−0.349174	+	1.07465i	−0.0207562	+	0.0638811i	0.940142	+	0.340783i	$0.110692\pi$
$284$	−0.152987	+	0.111151i	−0.00907810	+	0.00659563i
$285$		0			0
$286$	14.0939	+	10.2398i	0.833387	+	0.605491i
$287$	21.8164	−	15.8505i	1.28778	−	0.935626i
$288$		0			0
$289$	12.4056	+	9.01318i	0.729740	+	0.530187i
$290$	−11.3538	−	1.21824i	−0.666719	−	0.0715377i
$291$		0			0
$292$	3.30711	−	10.1782i	0.193534	−	0.595636i
$293$	2.37857			0.138958			0.0694789	−	0.997583i	$-0.477866\pi$
$293$	2.37857			0.138958			0.0694789	+	0.997583i	$0.477866\pi$
$294$		0			0
$295$	6.82080	+	6.16832i	0.397122	+	0.359134i
$296$	2.65706	+	8.17760i	0.154439	+	0.475313i
$297$		0			0
$298$	17.6222	+	12.8032i	1.02082	+	0.741672i
$299$	−33.7676			−1.95283
$300$		0			0
$301$	26.8150			1.54559
$302$	18.7684	+	13.6360i	1.08000	+	0.784665i
$303$		0			0
$304$	−3.73212	−	11.4863i	−0.214052	−	0.658783i
$305$	−9.77342	+	21.8239i	−0.559624	+	1.24963i
$306$		0			0
$307$	2.89366			0.165150			0.0825748	−	0.996585i	$-0.473686\pi$
$307$	2.89366			0.165150			0.0825748	+	0.996585i	$0.473686\pi$
$308$	4.00858	−	12.3371i	0.228410	−	0.702974i
$309$		0			0
$310$	−16.0006	−	14.4700i	−0.908775	−	0.821842i
$311$	−5.78079	−	4.19999i	−0.327799	−	0.238160i	0.411697	−	0.911321i	$-0.364936\pi$
$311$	−5.78079	−	4.19999i	−0.327799	−	0.238160i	−0.739496	+	0.673161i	$0.764936\pi$
$312$		0			0
$313$	−18.6331	+	13.5378i	−1.05321	+	0.765200i	−0.972820	−	0.231563i	$-0.925616\pi$
$313$	−18.6331	+	13.5378i	−1.05321	+	0.765200i	−0.0803879	+	0.996764i	$0.525616\pi$
$314$	30.4869	+	22.1500i	1.72048	+	1.25000i
$315$		0			0
$316$	−3.49347	+	2.53815i	−0.196523	+	0.142782i
$317$	6.41981	−	19.7582i	0.360573	−	1.10973i	−0.592135	−	0.805839i	$-0.701715\pi$
$317$	6.41981	−	19.7582i	0.360573	−	1.10973i	0.952707	−	0.303890i	$-0.0982854\pi$
$318$		0			0
$319$	−1.12361	+	3.45810i	−0.0629098	+	0.193617i
$320$	−11.1074	+	24.8026i	−0.620921	+	1.38651i
$321$		0			0
$322$	13.5945	+	41.8395i	0.757591	+	2.33163i
$323$	5.68650	+	4.13148i	0.316405	+	0.229882i
$324$		0			0
$325$	−13.2019	+	22.6390i	−0.732312	+	1.25579i
$326$	35.1251			1.94540
$327$		0			0
$328$	−3.80538	−	11.7118i	−0.210117	−	0.646673i
$329$	0.735499	+	2.26363i	0.0405494	+	0.124798i
$330$		0			0
$331$	−5.94869	+	18.3082i	−0.326969	+	1.00631i	0.643574	+	0.765383i	$0.277451\pi$
$331$	−5.94869	+	18.3082i	−0.326969	+	1.00631i	−0.970544	+	0.240925i	$0.922549\pi$
$332$	−35.0814			−1.92534
$333$		0			0
$334$	19.9099	−	14.4654i	1.08942	−	0.791513i
$335$	−4.22127	−	0.452934i	−0.230633	−	0.0247464i
$336$		0			0
$337$	−17.5609	+	12.7587i	−0.956602	+	0.695012i	−0.952359	−	0.304979i	$-0.901351\pi$
$337$	−17.5609	+	12.7587i	−0.956602	+	0.695012i	−0.00424305	+	0.999991i	$0.501351\pi$
$338$	25.2972	−	18.3795i	1.37599	−	0.999712i
$339$		0			0
$340$	−1.58459	−	7.53524i	−0.0859363	−	0.408656i
$341$	−5.55745	+	4.03773i	−0.300953	+	0.218655i
$342$		0			0
$343$	12.6766			0.684470
$344$	3.78400	−	11.6460i	0.204020	−	0.627908i
$345$		0			0
$346$	6.31493	+	19.4354i	0.339493	+	1.04485i
$347$	0.529944	+	1.63100i	0.0284489	+	0.0875567i	0.964273	−	0.264911i	$-0.0853426\pi$
$347$	0.529944	+	1.63100i	0.0284489	+	0.0875567i	−0.935824	+	0.352468i	$0.885343\pi$
$348$		0			0
$349$	−15.5553			−0.832654			−0.416327	−	0.909215i	$-0.636683\pi$
$349$	−15.5553			−0.832654			−0.416327	+	0.909215i	$0.636683\pi$
$350$	33.3657	+	7.24354i	1.78347	+	0.387184i
$351$		0			0
$352$	9.55579	+	6.94268i	0.509325	+	0.370046i
$353$	−4.80632	−	14.7923i	−0.255814	−	0.787316i	−0.993668	−	0.112355i	$-0.964161\pi$
$353$	−4.80632	−	14.7923i	−0.255814	−	0.787316i	0.737854	−	0.674961i	$-0.235839\pi$
$354$		0			0
$355$	−0.137425	+	0.0789454i	−0.00729376	+	0.00418998i
$356$	−5.99877	+	18.4623i	−0.317934	+	0.978501i
$357$		0			0
$358$	2.72232	−	8.37844i	0.143879	−	0.442814i
$359$	−19.8509	+	14.4225i	−1.04769	+	0.761191i	−0.971772	−	0.235923i	$-0.924189\pi$
$359$	−19.8509	+	14.4225i	−1.04769	+	0.761191i	−0.0759181	+	0.997114i	$0.524189\pi$
$360$		0			0
$361$	−8.62214	−	6.26435i	−0.453797	−	0.329703i
$362$	−19.4373	+	14.1221i	−1.02160	+	0.742239i
$363$		0			0
$364$	−35.7570	−	25.9790i	−1.87418	−	1.36167i
$365$	3.66594	−	8.18600i	0.191884	−	0.428475i
$366$		0			0
$367$	8.68548	−	26.7311i	0.453378	−	1.39535i	−0.419651	−	0.907686i	$-0.637847\pi$
$367$	8.68548	−	26.7311i	0.453378	−	1.39535i	0.873029	−	0.487669i	$-0.162153\pi$
$368$	−14.2875			−0.744786
$369$		0			0
$370$	5.92296	+	28.1656i	0.307920	+	1.46426i
$371$	9.52241	+	29.3070i	0.494379	+	1.52154i
$372$		0			0
$373$	7.85414	+	5.70637i	0.406672	+	0.295464i	0.772253	−	0.635315i	$-0.219130\pi$
$373$	7.85414	+	5.70637i	0.406672	+	0.295464i	−0.365581	+	0.930779i	$0.619130\pi$
$374$	−4.28984			−0.221823
$375$		0			0
$376$	1.08690			0.0560527
$377$	10.0227	+	7.28191i	0.516195	+	0.375037i
$378$		0			0
$379$	−6.88071	−	21.1767i	−0.353438	−	1.08777i	−0.956909	−	0.290387i	$-0.906216\pi$
$379$	−6.88071	−	21.1767i	−0.353438	−	1.08777i	0.603471	−	0.797385i	$-0.293784\pi$
$380$	6.68596	+	31.7940i	0.342983	+	1.63100i
$381$		0			0
$382$	7.80253			0.399212
$383$	4.21189	−	12.9628i	0.215217	−	0.662371i	−0.783921	−	0.620861i	$-0.786783\pi$
$383$	4.21189	−	12.9628i	0.215217	−	0.662371i	0.999138	−	0.0415099i	$-0.0132168\pi$
$384$		0			0
$385$	4.44353	−	9.92234i	0.226463	−	0.505689i
$386$	−29.8131	−	21.6605i	−1.51745	−	1.10249i
$387$		0			0
$388$	−22.0033	+	15.9863i	−1.11705	+	0.811582i
$389$	15.5577	+	11.3034i	0.788808	+	0.573103i	0.907610	−	0.419815i	$-0.137905\pi$
$389$	15.5577	+	11.3034i	0.788808	+	0.573103i	−0.118801	+	0.992918i	$0.537905\pi$
$390$		0			0
$391$	6.72710	−	4.88752i	0.340204	−	0.247173i
$392$	−1.33316	+	4.10305i	−0.0673349	+	0.207236i
$393$		0			0
$394$	−2.94115	+	9.05194i	−0.148173	+	0.456030i
$395$	−3.13811	+	1.80272i	−0.157895	+	0.0907049i
$396$		0			0
$397$	6.86887	+	21.1402i	0.344739	+	1.06100i	0.961723	+	0.274022i	$0.0883541\pi$
$397$	6.86887	+	21.1402i	0.344739	+	1.06100i	−0.616984	+	0.786975i	$0.711646\pi$
$398$	29.0079	+	21.0755i	1.45403	+	1.05642i
$399$		0			0
$400$	−5.58590	+	9.57884i	−0.279295	+	0.478942i
$401$	−4.71728			−0.235570			−0.117785	−	0.993039i	$-0.537579\pi$
$401$	−4.71728			−0.235570			−0.117785	+	0.993039i	$0.537579\pi$
$402$		0			0
$403$	7.23261	+	22.2597i	0.360282	+	1.10883i
$404$	−0.896678	−	2.75969i	−0.0446114	−	0.137300i
$405$		0			0
$406$	4.98757	−	15.3502i	0.247529	−	0.761815i
$407$	9.16474			0.454279
$408$		0			0
$409$	10.0971	−	7.33597i	0.499269	−	0.362740i	−0.309469	−	0.950910i	$-0.600151\pi$
$409$	10.0971	−	7.33597i	0.499269	−	0.362740i	0.808738	+	0.588169i	$0.200151\pi$
$410$	−8.48271	−	40.3381i	−0.418931	−	1.99216i
$411$		0			0
$412$	10.6576	−	7.74319i	0.525062	−	0.381480i
$413$	−10.5160	+	7.64029i	−0.517456	+	0.375954i
$414$		0			0
$415$	−29.2339	−	3.13674i	−1.43504	−	0.153977i
$416$	32.5583	−	23.6550i	1.59630	−	1.15978i
$417$		0			0
$418$	18.1005			0.885322
$419$	−10.7996	+	33.2379i	−0.527597	+	1.62378i	0.231527	+	0.972829i	$0.425628\pi$
$419$	−10.7996	+	33.2379i	−0.527597	+	1.62378i	−0.759123	+	0.650947i	$0.774372\pi$
$420$		0			0
$421$	−12.2247	−	37.6239i	−0.595797	−	1.83368i	−0.550717	−	0.834692i	$-0.685646\pi$
$421$	−12.2247	−	37.6239i	−0.595797	−	1.83368i	−0.0450804	−	0.998983i	$-0.514354\pi$
$422$	−12.3818	−	38.1073i	−0.602737	−	1.85503i
$423$		0			0
$424$	14.0720			0.683396
$425$	−0.646712	−	6.42093i	−0.0313702	−	0.311461i
$426$		0			0
$427$	−27.3439	−	19.8665i	−1.32326	−	0.961406i
$428$	−12.6191	−	38.8377i	−0.609969	−	1.87729i
$429$		0			0
$430$	16.7528	−	37.4089i	0.807894	−	1.80402i
$431$	4.34429	−	13.3703i	0.209257	−	0.644027i	−0.790255	−	0.612778i	$-0.790052\pi$
$431$	4.34429	−	13.3703i	0.209257	−	0.644027i	0.999512	−	0.0312481i	$-0.00994821\pi$
$432$		0			0
$433$	−0.169860	+	0.522775i	−0.00816294	+	0.0251230i	−0.955055	−	0.296429i	$-0.904204\pi$
$433$	−0.169860	+	0.522775i	−0.00816294	+	0.0251230i	0.946892	+	0.321552i	$0.104204\pi$
$434$	24.6689	−	17.9230i	1.18415	−	0.860333i
$435$		0			0
$436$	−14.3733	−	10.4428i	−0.688355	−	0.500119i
$437$	−28.3841	+	20.6223i	−1.35780	+	0.986497i
$438$		0			0
$439$	2.40583	+	1.74794i	0.114824	+	0.0834245i	0.643715	−	0.765265i	$-0.277392\pi$
$439$	2.40583	+	1.74794i	0.114824	+	0.0834245i	−0.528891	+	0.848690i	$0.677392\pi$
$440$	−3.68230	−	3.33005i	−0.175547	−	0.158754i
$441$		0			0
$442$	−4.51667	+	13.9009i	−0.214836	+	0.661198i
$443$	36.6893			1.74316			0.871580	−	0.490253i	$-0.163095\pi$
$443$	36.6893			1.74316			0.871580	+	0.490253i	$0.163095\pi$
$444$		0			0
$445$	−6.64966	+	14.8486i	−0.315224	+	0.703891i
$446$	0.515130	+	1.58541i	0.0243921	+	0.0750712i
$447$		0			0
$448$	−31.0760	−	22.5780i	−1.46820	−	1.06671i
$449$	17.8432			0.842071			0.421036	−	0.907044i	$-0.361667\pi$
$449$	17.8432			0.842071			0.421036	+	0.907044i	$0.361667\pi$
$450$		0			0
$451$	−13.1255			−0.618056
$452$	−19.3646	−	14.0692i	−0.910834	−	0.661759i
$453$		0			0
$454$	7.63215	+	23.4893i	0.358195	+	1.10241i
$455$	−27.4740	−	24.8459i	−1.28800	−	1.16479i
$456$		0			0
$457$	−24.1784			−1.13102			−0.565509	−	0.824742i	$-0.691320\pi$
$457$	−24.1784			−1.13102			−0.565509	+	0.824742i	$0.691320\pi$
$458$	−6.82655	+	21.0100i	−0.318984	+	0.981731i
$459$		0			0
$460$	38.2154	+	4.10044i	1.78180	+	0.191184i
$461$	−30.2470	−	21.9757i	−1.40874	−	1.02351i	−0.993504	−	0.113800i	$-0.963698\pi$
$461$	−30.2470	−	21.9757i	−1.40874	−	1.02351i	−0.415240	−	0.909712i	$-0.636302\pi$
$462$		0			0
$463$	−16.5294	+	12.0093i	−0.768186	+	0.558120i	−0.901410	−	0.432966i	$-0.857467\pi$
$463$	−16.5294	+	12.0093i	−0.768186	+	0.558120i	0.133224	+	0.991086i	$0.457467\pi$
$464$	4.24072	+	3.08106i	0.196870	+	0.143035i
$465$		0			0
$466$	39.3685	−	28.6029i	1.82371	−	1.32500i
$467$	−9.64517	+	29.6848i	−0.446325	+	1.37365i	0.434699	+	0.900576i	$0.356855\pi$
$467$	−9.64517	+	29.6848i	−0.446325	+	1.37365i	−0.881024	+	0.473072i	$0.843145\pi$
$468$		0			0
$469$	1.85434	−	5.70708i	0.0856256	−	0.263529i
$470$	3.61744	+	0.388144i	0.166860	+	0.0179038i
$471$		0			0
$472$	1.83427	+	5.64532i	0.0844293	+	0.259847i
$473$	−10.5591	−	7.67164i	−0.485508	−	0.352742i
$474$		0			0
$475$	2.72872	+	27.0923i	0.125202	+	1.24308i
$476$	10.8836			0.498849
$477$		0			0
$478$	−0.393295	−	1.21044i	−0.0179889	−	0.0553641i
$479$	−3.42915	−	10.5538i	−0.156682	−	0.482217i	0.841646	−	0.540030i	$-0.181587\pi$
$479$	−3.42915	−	10.5538i	−0.156682	−	0.482217i	−0.998327	+	0.0578133i	$0.981587\pi$
$480$		0			0
$481$	9.64933	−	29.6976i	0.439972	−	1.35409i
$482$	−3.26108			−0.148538
$483$		0			0
$484$	18.6351	−	13.5392i	0.847051	−	0.615418i
$485$	−19.7651	+	11.3543i	−0.897487	+	0.515572i
$486$		0			0
$487$	−5.77397	+	4.19504i	−0.261644	+	0.190095i	−0.710871	−	0.703322i	$-0.751699\pi$
$487$	−5.77397	+	4.19504i	−0.261644	+	0.190095i	0.449228	+	0.893417i	$0.351699\pi$
$488$	−12.4868	+	9.07218i	−0.565250	+	0.410678i
$489$		0			0
$490$	−5.90229	+	13.1797i	−0.266638	+	0.595400i
$491$	5.85201	−	4.25173i	0.264097	−	0.191878i	−0.447854	−	0.894107i	$-0.647812\pi$
$491$	5.85201	−	4.25173i	0.264097	−	0.191878i	0.711951	+	0.702229i	$0.247812\pi$
$492$		0			0
$493$	−3.05067			−0.137395
$494$	19.0575	−	58.6531i	0.857439	−	2.63893i
$495$		0			0
$496$	3.06020	+	9.41834i	0.137407	+	0.422896i
$497$	−0.0692236	−	0.213048i	−0.00310510	−	0.00955652i
$498$		0			0
$499$	16.0169			0.717014			0.358507	−	0.933527i	$-0.383286\pi$
$499$	16.0169			0.717014			0.358507	+	0.933527i	$0.383286\pi$
$500$	17.6899	−	24.0178i	0.791118	−	1.07411i
$501$		0			0
$502$	−20.7921	−	15.1063i	−0.927997	−	0.674229i
$503$	10.4436	+	32.1422i	0.465659	+	1.43315i	0.858152	+	0.513396i	$0.171613\pi$
$503$	10.4436	+	32.1422i	0.465659	+	1.43315i	−0.392492	+	0.919755i	$0.628387\pi$
$504$		0			0
$505$	−0.500464	−	2.37987i	−0.0222703	−	0.105903i
$506$	6.61690	−	20.3647i	0.294157	−	0.905322i
$507$		0			0
$508$	8.25985	−	25.4212i	0.366472	−	1.12788i
$509$	−29.4701	+	21.4113i	−1.30624	+	0.949038i	−0.999996	−	0.00291563i	$-0.999072\pi$
$509$	−29.4701	+	21.4113i	−1.30624	+	0.949038i	−0.306243	+	0.951953i	$0.599072\pi$
$510$		0			0
$511$	10.2565	+	7.45178i	0.453720	+	0.329647i
$512$	18.9548	−	13.7715i	0.837692	−	0.608619i
$513$		0			0
$514$	31.5487	+	22.9215i	1.39156	+	1.01102i
$515$	9.57350	−	5.49960i	0.421859	−	0.242341i
$516$		0			0
$517$	0.357992	−	1.10179i	0.0157445	−	0.0484565i
$518$	−40.6813			−1.78743
$519$		0			0
$520$	−14.6678	+	8.42606i	−0.643223	+	0.369507i
$521$	−7.87972	−	24.2513i	−0.345217	−	1.06247i	−0.961468	−	0.274918i	$-0.911349\pi$
$521$	−7.87972	−	24.2513i	−0.345217	−	1.06247i	0.616251	−	0.787550i	$-0.288651\pi$
$522$		0			0
$523$	5.68880	+	4.13315i	0.248754	+	0.180730i	0.705174	−	0.709034i	$-0.250869\pi$
$523$	5.68880	+	4.13315i	0.248754	+	0.180730i	−0.456420	+	0.889764i	$0.650869\pi$
$524$	17.0184			0.743450
$525$		0			0
$526$	−41.2811			−1.79994
$527$	−4.66273	−	3.38767i	−0.203112	−	0.147569i
$528$		0			0
$529$	5.71836	+	17.5993i	0.248624	+	0.765187i
$530$	46.8345	+	5.02526i	2.03436	+	0.218283i
$531$		0			0
$532$	−45.9220			−1.99097
$533$	−13.8195	+	42.5322i	−0.598590	+	1.84227i
$534$		0			0
$535$	−7.04313	−	33.4924i	−0.304501	−	1.44800i
$536$	−2.21695	−	1.61071i	−0.0957577	−	0.0695721i
$537$		0			0
$538$	38.8478	−	28.2246i	1.67485	−	1.21685i
$539$	3.72014	+	2.70284i	0.160238	+	0.116420i
$540$		0			0
$541$	21.9629	−	15.9570i	0.944258	−	0.686044i	−0.00518365	−	0.999987i	$-0.501650\pi$
$541$	21.9629	−	15.9570i	0.944258	−	0.686044i	0.949442	+	0.313943i	$0.101650\pi$
$542$	−13.4937	+	41.5293i	−0.579604	+	1.78384i
$543$		0			0
$544$	−3.06235	+	9.42496i	−0.131297	+	0.404092i
$545$	−11.0438	−	9.98732i	−0.473063	−	0.427810i
$546$		0			0
$547$	13.6205	+	41.9196i	0.582371	+	1.79235i	0.609582	+	0.792723i	$0.291337\pi$
$547$	13.6205	+	41.9196i	0.582371	+	1.79235i	−0.0272113	+	0.999630i	$0.508663\pi$
$548$	−19.8090	−	14.3921i	−0.846198	−	0.614799i
$549$		0			0
$550$	−11.0663	−	12.3981i	−0.471867	−	0.528656i
$551$	12.8719			0.548363
$552$		0			0
$553$	−1.58073	−	4.86497i	−0.0672193	−	0.206880i
$554$	10.7099	+	32.9618i	0.455022	+	1.40041i
$555$		0			0
$556$	−7.63897	+	23.5103i	−0.323965	+	0.997061i
$557$	9.85667			0.417641			0.208820	−	0.977954i	$-0.433038\pi$
$557$	9.85667			0.417641			0.208820	+	0.977954i	$0.433038\pi$
$558$		0			0
$559$	−35.9768	+	26.1386i	−1.52165	+	1.10555i
$560$	−11.6246	−	10.5126i	−0.491229	−	0.444238i
$561$		0			0
$562$	−14.6356	+	10.6334i	−0.617363	+	0.448541i
$563$	−10.0251	+	7.28367i	−0.422508	+	0.306970i	−0.778646	−	0.627463i	$-0.784093\pi$
$563$	−10.0251	+	7.28367i	−0.422508	+	0.306970i	0.356138	+	0.934433i	$0.384093\pi$
$564$		0			0
$565$	−14.8789	−	13.4556i	−0.625959	−	0.566080i
$566$	−1.97507	+	1.43497i	−0.0830185	+	0.0603165i
$567$		0			0
$568$	−0.102297			−0.00429228
$569$	3.62037	−	11.1424i	0.151774	−	0.467112i	−0.846046	−	0.533110i	$-0.821023\pi$
$569$	3.62037	−	11.1424i	0.151774	−	0.467112i	0.997820	+	0.0659983i	$0.0210232\pi$
$570$		0			0
$571$	8.95523	+	27.5614i	0.374765	+	1.15341i	0.943637	+	0.330982i	$0.107380\pi$
$571$	8.95523	+	27.5614i	0.374765	+	1.15341i	−0.568872	+	0.822426i	$0.692620\pi$
$572$	6.64779	+	20.4598i	0.277958	+	0.855467i
$573$		0			0
$574$	58.2628			2.43184
$575$	31.4789	+	6.83394i	1.31276	+	0.284995i
$576$		0			0
$577$	26.5377	+	19.2808i	1.10478	+	0.802668i	0.981833	−	0.189745i	$-0.0607662\pi$
$577$	26.5377	+	19.2808i	1.10478	+	0.802668i	0.122945	+	0.992414i	$0.460766\pi$
$578$	10.2378	+	31.5088i	0.425838	+	1.31059i
$579$		0			0
$580$	−10.4586	−	9.45812i	−0.434269	−	0.392727i
$581$	12.8420	−	39.5237i	0.532777	−	1.63972i
$582$		0			0
$583$	4.63488	−	14.2647i	0.191957	−	0.590783i
$584$	4.68371	−	3.40291i	0.193813	−	0.140813i
$585$		0			0
$586$	4.15758	+	3.02066i	0.171748	+	0.124782i
$587$	15.0797	−	10.9560i	0.622405	−	0.452203i	−0.231356	−	0.972869i	$-0.574316\pi$
$587$	15.0797	−	10.9560i	0.622405	−	0.452203i	0.853761	+	0.520666i	$0.174316\pi$
$588$		0			0
$589$	19.6738	+	14.2938i	0.810644	+	0.588967i
$590$	4.08885	+	19.4438i	0.168335	+	0.800490i
$591$		0			0
$592$	4.08275	−	12.5654i	0.167800	−	0.516435i
$593$	−1.55882			−0.0640129			−0.0320064	−	0.999488i	$-0.510190\pi$
$593$	−1.55882			−0.0640129			−0.0320064	+	0.999488i	$0.510190\pi$
$594$		0			0
$595$	9.06949	+	0.973140i	0.371813	+	0.0398948i
$596$	8.31202	+	25.5818i	0.340474	+	1.04787i
$597$		0			0
$598$	−59.0234	−	42.8830i	−2.41365	−	1.75362i
$599$	31.5470			1.28898			0.644489	−	0.764614i	$-0.277070\pi$
$599$	31.5470			1.28898			0.644489	+	0.764614i	$0.277070\pi$
$600$		0			0
$601$	−32.3999			−1.32162			−0.660809	−	0.750554i	$-0.729787\pi$
$601$	−32.3999			−1.32162			−0.660809	+	0.750554i	$0.729787\pi$
$602$	46.8707	+	34.0536i	1.91031	+	1.38792i
$603$		0			0
$604$	8.85266	+	27.2457i	0.360210	+	1.10861i
$605$	16.7396	−	9.61623i	0.680560	−	0.390955i
$606$		0			0
$607$	24.8410			1.00827			0.504133	−	0.863626i	$-0.331812\pi$
$607$	24.8410			1.00827			0.504133	+	0.863626i	$0.331812\pi$
$608$	12.9212	−	39.7674i	0.524024	−	1.61278i
$609$		0			0
$610$	−44.7984	+	25.7350i	−1.81383	+	1.04198i
$611$	−3.19333	−	2.32009i	−0.129188	−	0.0938607i
$612$		0			0
$613$	3.19204	−	2.31915i	0.128925	−	0.0936697i	−0.521454	−	0.853280i	$-0.674610\pi$
$613$	3.19204	−	2.31915i	0.128925	−	0.0936697i	0.650379	+	0.759610i	$0.274610\pi$
$614$	5.05791	+	3.67478i	0.204120	+	0.148302i
$615$		0			0
$616$	5.67717	−	4.12471i	0.228740	−	0.166189i
$617$	5.40225	−	16.6264i	0.217486	−	0.669354i	−0.781481	−	0.623929i	$-0.785536\pi$
$617$	5.40225	−	16.6264i	0.217486	−	0.669354i	0.998968	−	0.0454257i	$-0.0144644\pi$
$618$		0			0
$619$	−4.44581	+	13.6828i	−0.178692	+	0.549958i	−0.999783	−	0.0208398i	$-0.993366\pi$
$619$	−4.44581	+	13.6828i	−0.178692	+	0.549958i	0.821091	+	0.570798i	$0.193366\pi$
$620$	−5.48225	−	26.0699i	−0.220173	−	1.04699i
$621$		0			0
$622$	−4.77066	−	14.6826i	−0.191286	−	0.588718i
$623$	−18.6043	−	13.5168i	−0.745364	−	0.541539i
$624$		0			0
$625$	16.8889	−	18.4328i	0.675554	−	0.737310i
$626$	−49.7617			−1.98888
$627$		0			0
$628$	14.3801	+	44.2573i	0.573827	+	1.76606i
$629$	2.37611	+	7.31292i	0.0947418	+	0.291585i
$630$		0			0
$631$	−5.46214	+	16.8107i	−0.217444	+	0.669225i	0.781527	+	0.623872i	$0.214441\pi$
$631$	−5.46214	+	16.8107i	−0.217444	+	0.669225i	−0.998971	+	0.0453529i	$0.985559\pi$
$632$	−2.33596			−0.0929194
$633$		0			0
$634$	36.3132	−	26.3831i	1.44218	−	1.04781i
$635$	9.15608	−	20.4454i	0.363348	−	0.811351i
$636$		0			0
$637$	12.6752	−	9.20905i	0.502209	−	0.364876i
$638$	−6.35559	+	4.61760i	−0.251620	+	0.182813i
$639$		0			0
$640$	−21.1386	+	12.1433i	−0.835576	+	0.480006i
$641$	−2.21774	+	1.61128i	−0.0875954	+	0.0636417i	−0.630721	−	0.776010i	$-0.717241\pi$
$641$	−2.21774	+	1.61128i	−0.0875954	+	0.0636417i	0.543126	+	0.839651i	$0.317241\pi$
$642$		0			0
$643$	20.9276			0.825303			0.412651	−	0.910889i	$-0.364603\pi$
$643$	20.9276			0.825303			0.412651	+	0.910889i	$0.364603\pi$
$644$	−16.7875	+	51.6665i	−0.661519	+	2.03595i
$645$		0			0
$646$	4.69284	+	14.4431i	0.184637	+	0.568256i
$647$	0.570653	+	1.75629i	0.0224347	+	0.0690469i	0.961647	−	0.274290i	$-0.0884428\pi$
$647$	0.570653	+	1.75629i	0.0224347	+	0.0690469i	−0.939212	+	0.343337i	$0.888443\pi$
$648$		0			0
$649$	6.32678			0.248348
$650$	−51.8264	+	22.8057i	−2.03280	+	0.894512i
$651$		0			0
$652$	35.0912	+	25.4952i	1.37428	+	0.998470i
$653$	5.69002	+	17.5121i	0.222667	+	0.685300i	0.998520	+	0.0543858i	$0.0173201\pi$
$653$	5.69002	+	17.5121i	0.222667	+	0.685300i	−0.775853	+	0.630914i	$0.782680\pi$
$654$		0			0
$655$	14.1817	+	1.52167i	0.554124	+	0.0594565i
$656$	−5.84721	+	17.9959i	−0.228295	+	0.702620i
$657$		0			0
$658$	−1.58909	+	4.89071i	−0.0619491	+	0.190660i
$659$	−10.8246	+	7.86455i	−0.421668	+	0.306360i	−0.778308	−	0.627882i	$-0.783922\pi$
$659$	−10.8246	+	7.86455i	−0.421668	+	0.306360i	0.356641	+	0.934242i	$0.383922\pi$
$660$		0			0
$661$	−31.7001	−	23.0315i	−1.23299	−	0.895820i	−0.235879	−	0.971782i	$-0.575797\pi$
$661$	−31.7001	−	23.0315i	−1.23299	−	0.895820i	−0.997111	+	0.0759628i	$0.975797\pi$
$662$	−33.6483	+	24.4469i	−1.30778	+	0.950155i
$663$		0			0
$664$	−15.3532	−	11.1548i	−0.595821	−	0.432890i
$665$	−38.2676	−	4.10604i	−1.48395	−	0.159225i
$666$		0			0
$667$	4.70553	−	14.4821i	0.182199	−	0.560751i
$668$	30.3903			1.17584
$669$		0			0
$670$	−6.80328	−	6.15248i	−0.262834	−	0.237691i
$671$	5.08365	+	15.6459i	0.196252	+	0.604002i
$672$		0			0
$673$	−15.6877	−	11.3978i	−0.604718	−	0.439353i	0.242832	−	0.970068i	$-0.421923\pi$
$673$	−15.6877	−	11.3978i	−0.604718	−	0.439353i	−0.847550	+	0.530715i	$0.821923\pi$
$674$	−46.8981			−1.80645
$675$		0			0
$676$	38.6133			1.48513
$677$	−36.9588	−	26.8522i	−1.42044	−	1.03201i	−0.991698	−	0.128587i	$-0.958956\pi$
$677$	−36.9588	−	26.8522i	−1.42044	−	1.03201i	−0.428746	−	0.903425i	$-0.641044\pi$
$678$		0			0
$679$	−9.95606	−	30.6416i	−0.382078	−	1.17592i
$680$	1.70248	−	3.80162i	0.0652873	−	0.145786i
$681$		0			0
$682$	−14.8417			−0.568319
$683$	−3.58128	+	11.0220i	−0.137034	+	0.421747i	−0.995901	−	0.0904520i	$-0.971169\pi$
$683$	−3.58128	+	11.0220i	−0.137034	+	0.421747i	0.858867	+	0.512199i	$0.171169\pi$
$684$		0			0
$685$	−15.2203	−	13.7644i	−0.581539	−	0.525909i
$686$	22.1577	+	16.0985i	0.845987	+	0.614645i
$687$		0			0
$688$	−15.2222	+	11.0596i	−0.580340	+	0.421642i
$689$	−41.3436	−	30.0379i	−1.57507	−	1.14435i
$690$		0			0
$691$	17.5091	−	12.7211i	0.666077	−	0.483934i	−0.202632	−	0.979255i	$-0.564950\pi$
$691$	17.5091	−	12.7211i	0.666077	−	0.483934i	0.868710	+	0.495321i	$0.164950\pi$
$692$	−7.79815	+	24.0002i	−0.296441	+	0.912352i
$693$		0			0
$694$	−1.14498	+	3.52388i	−0.0434627	+	0.133764i
$695$	−8.46783	+	18.9086i	−0.321203	+	0.717242i
$696$		0			0
$697$	−3.40301	−	10.4734i	−0.128898	−	0.396707i
$698$	−27.1895	−	19.7543i	−1.02914	−	0.747713i
$699$		0			0
$700$	28.0758	+	31.4547i	1.06116	+	1.18888i
$701$	8.61904			0.325537			0.162768	−	0.986664i	$-0.447958\pi$
$701$	8.61904			0.325537			0.162768	+	0.986664i	$0.447958\pi$
$702$		0			0
$703$	−10.0257	−	30.8559i	−0.378126	−	1.16375i
$704$	5.77751	+	17.7814i	0.217748	+	0.670160i
$705$		0			0
$706$	10.3843	−	31.9597i	0.390820	−	1.20282i
$707$	3.43739			0.129276
$708$		0			0
$709$	−12.9443	+	9.40460i	−0.486134	+	0.353197i	−0.803696	−	0.595041i	$-0.797136\pi$
$709$	−12.9443	+	9.40460i	−0.486134	+	0.353197i	0.317562	+	0.948238i	$0.397136\pi$
$710$	−0.340466	−	0.0365313i	−0.0127774	−	0.00137100i
$711$		0			0
$712$	−8.49579	+	6.17255i	−0.318393	+	0.231326i
$713$	23.2740	−	16.9095i	0.871617	−	0.633267i
$714$		0			0
$715$	3.71034	+	17.6439i	0.138759	+	0.659844i
$716$	8.80110	−	6.39437i	0.328913	−	0.238969i
$717$		0			0
$718$	−53.0138			−1.97846
$719$	15.0132	−	46.2060i	0.559899	−	1.72319i	−0.122743	−	0.992438i	$-0.539169\pi$
$719$	15.0132	−	46.2060i	0.559899	−	1.72319i	0.682642	−	0.730753i	$-0.260831\pi$
$720$		0			0
$721$	4.82235	+	14.8417i	0.179594	+	0.552733i
$722$	−7.11551	−	21.8993i	−0.264812	−	0.815007i
$723$		0			0
$724$	−29.6689			−1.10264
$725$	−7.86964	−	8.81676i	−0.292271	−	0.327446i
$726$		0			0
$727$	−20.5756	−	14.9490i	−0.763106	−	0.554429i	0.136755	−	0.990605i	$-0.456333\pi$
$727$	−20.5756	−	14.9490i	−0.763106	−	0.554429i	−0.899861	+	0.436176i	$0.856333\pi$
$728$	−7.38842	−	22.7392i	−0.273833	−	0.842772i
$729$		0			0
$730$	16.8036	−	9.65300i	0.621928	−	0.357274i
$731$	3.38389	−	10.4145i	0.125158	−	0.385196i
$732$		0			0
$733$	−5.75358	+	17.7077i	−0.212513	+	0.654049i	0.786807	+	0.617199i	$0.211733\pi$
$733$	−5.75358	+	17.7077i	−0.212513	+	0.654049i	−0.999321	+	0.0368505i	$0.988267\pi$
$734$	49.1287	−	35.6941i	1.81337	−	1.31749i
$735$		0			0
$736$	−40.0185	−	29.0752i	−1.47510	−	1.07172i
$737$	−2.36296	+	1.71679i	−0.0870408	+	0.0632389i
$738$		0			0
$739$	−37.9326	−	27.5596i	−1.39537	−	1.01380i	−0.995252	−	0.0973351i	$-0.968968\pi$
$739$	−37.9326	−	27.5596i	−1.39537	−	1.01380i	−0.400121	−	0.916462i	$-0.631032\pi$
$740$	−14.5265	+	32.4375i	−0.534006	+	1.19243i
$741$		0			0
$742$	−20.5737	+	63.3194i	−0.755286	+	2.32453i
$743$	42.7061			1.56674			0.783368	−	0.621558i	$-0.213500\pi$
$743$	42.7061			1.56674			0.783368	+	0.621558i	$0.213500\pi$
$744$		0			0
$745$	4.63920	+	22.0609i	0.169967	+	0.808250i
$746$	6.48171	+	19.9487i	0.237312	+	0.730372i
$747$		0			0
$748$	−4.28570	−	3.11374i	−0.156701	−	0.113850i
$749$	48.3751			1.76759
$750$		0			0
$751$	−2.64893			−0.0966608			−0.0483304	−	0.998831i	$-0.515390\pi$
$751$	−2.64893			−0.0966608			−0.0483304	+	0.998831i	$0.515390\pi$
$752$	−1.35113	−	0.981657i	−0.0492708	−	0.0357973i
$753$		0			0
$754$	8.27133	+	25.4565i	0.301224	+	0.927072i
$755$	4.94095	+	23.4959i	0.179819	+	0.855102i
$756$		0			0
$757$	52.9153			1.92324			0.961620	−	0.274383i	$-0.0884737\pi$
$757$	52.9153			1.92324			0.961620	+	0.274383i	$0.0884737\pi$
$758$	14.8662	−	45.7534i	0.539964	−	1.66184i
$759$		0			0
$760$	−7.18341	+	16.0405i	−0.260570	+	0.581849i
$761$	41.0808	+	29.8470i	1.48918	+	1.08195i	0.974451	+	0.224598i	$0.0721070\pi$
$761$	41.0808	+	29.8470i	1.48918	+	1.08195i	0.514728	+	0.857354i	$0.327893\pi$
$762$		0			0
$763$	17.0267	−	12.3706i	0.616408	−	0.447847i
$764$	7.79499	+	5.66339i	0.282013	+	0.204894i
$765$		0			0
$766$	23.8242	−	17.3093i	0.860803	−	0.625410i
$767$	6.66131	−	20.5014i	0.240526	−	0.740263i
$768$		0			0
$769$	7.59580	−	23.3775i	0.273912	−	0.843013i	−0.715594	−	0.698517i	$-0.753844\pi$
$769$	7.59580	−	23.3775i	0.273912	−	0.843013i	0.989505	−	0.144496i	$-0.0461562\pi$
$770$	20.3678	−	11.7005i	0.734004	−	0.421657i
$771$		0			0
$772$	−14.0622	−	43.2791i	−0.506111	−	1.55765i
$773$	−16.1894	−	11.7623i	−0.582293	−	0.423061i	0.257257	−	0.966343i	$-0.417181\pi$
$773$	−16.1894	−	11.7623i	−0.582293	−	0.423061i	−0.839550	+	0.543282i	$0.817181\pi$
$774$		0			0
$775$	−2.23745	−	22.2147i	−0.0803717	−	0.797976i
$776$	−14.7128			−0.528159
$777$		0			0
$778$	12.8392	+	39.5149i	0.460307	+	1.41668i
$779$	14.3586	+	44.1911i	0.514449	+	1.58331i
$780$		0			0
$781$	−0.0336934	+	0.103698i	−0.00120565	+	0.00371060i
$782$	17.9654			0.642441
$783$		0			0
$784$	5.36302	−	3.89646i	0.191536	−	0.139159i
$785$	8.02596	+	38.1661i	0.286459	+	1.36221i
$786$		0			0
$787$	−7.27526	+	5.28579i	−0.259335	+	0.188418i	−0.709854	−	0.704349i	$-0.751239\pi$
$787$	−7.27526	+	5.28579i	−0.259335	+	0.188418i	0.450519	+	0.892767i	$0.351239\pi$
$788$	−9.50857	+	6.90838i	−0.338729	+	0.246101i
$789$		0			0
$790$	−7.77456	−	0.834195i	−0.276606	−	0.0296793i
$791$	22.9395	−	16.6665i	0.815634	−	0.592593i
$792$		0			0
$793$	56.0517			1.99045
$794$	−14.8406	+	45.6747i	−0.526674	+	1.62093i
$795$		0			0
$796$	13.6824	+	42.1102i	0.484961	+	1.49256i
$797$	11.6674	+	35.9084i	0.413279	+	1.27194i	0.913781	+	0.406207i	$0.133149\pi$
$797$	11.6674	+	35.9084i	0.413279	+	1.27194i	−0.500502	+	0.865735i	$0.666851\pi$
$798$		0			0
$799$	0.971976			0.0343860
$800$	−35.1388	+	15.4625i	−1.24235	+	0.546682i
$801$		0			0
$802$	−8.24547	−	5.99069i	−0.291158	−	0.211538i
$803$	−1.90684	−	5.86866i	−0.0672910	−	0.207100i
$804$		0			0
$805$	−18.6090	+	41.5536i	−0.655880	+	1.46457i
$806$	−15.6265	+	48.0934i	−0.550420	+	1.69402i
$807$		0			0
$808$	0.485068	−	1.49289i	0.0170646	−	0.0525195i
$809$	−39.5610	+	28.7428i	−1.39089	+	1.01054i	−0.395124	+	0.918628i	$0.629298\pi$
$809$	−39.5610	+	28.7428i	−1.39089	+	1.01054i	−0.995767	+	0.0919140i	$0.970702\pi$
$810$		0			0
$811$	14.6069	+	10.6125i	0.512916	+	0.372655i	0.813929	−	0.580965i	$-0.197325\pi$
$811$	14.6069	+	10.6125i	0.512916	+	0.372655i	−0.301013	+	0.953620i	$0.597325\pi$
$812$	16.1245	−	11.7151i	0.565860	−	0.411121i
$813$		0			0
$814$	16.0193	+	11.6387i	0.561477	+	0.407937i
$815$	26.9625	+	24.3832i	0.944454	+	0.854107i
$816$		0			0
$817$	−14.2779	+	43.9428i	−0.499520	+	1.53736i
$818$	26.9653			0.942819
$819$		0			0
$820$	20.8045	−	46.4562i	0.726526	−	1.62232i
$821$	−15.6393	−	48.1327i	−0.545814	−	1.67984i	−0.719046	−	0.694962i	$-0.755421\pi$
$821$	−15.6393	−	48.1327i	−0.545814	−	1.67984i	0.173232	−	0.984881i	$-0.444579\pi$
$822$		0			0
$823$	21.6873	+	15.7568i	0.755972	+	0.549246i	0.897672	−	0.440664i	$-0.145257\pi$
$823$	21.6873	+	15.7568i	0.755972	+	0.549246i	−0.141700	+	0.989910i	$0.545257\pi$
$824$	7.12635			0.248258
$825$		0			0
$826$	−28.0839			−0.977163
$827$	−17.2845	−	12.5580i	−0.601042	−	0.436683i	0.245206	−	0.969471i	$-0.421144\pi$
$827$	−17.2845	−	12.5580i	−0.601042	−	0.436683i	−0.846249	+	0.532788i	$0.821144\pi$
$828$		0			0
$829$	−14.8675	−	45.7575i	−0.516370	−	1.58922i	−0.780775	−	0.624812i	$-0.785176\pi$
$829$	−14.8675	−	45.7575i	−0.516370	−	1.58922i	0.264405	−	0.964412i	$-0.414824\pi$
$830$	−47.1153	−	42.6083i	−1.63540	−	1.47895i
$831$		0			0
$832$	63.7021			2.20847
$833$	−1.19220	+	3.66921i	−0.0413072	+	0.127130i
$834$		0			0
$835$	25.3248	+	2.71730i	0.876400	+	0.0940361i
$836$	18.0830	+	13.1380i	0.625412	+	0.454389i
$837$		0			0
$838$	−61.0873	+	44.3825i	−2.11022	+	1.53317i
$839$	−33.8606	−	24.6012i	−1.16900	−	0.849327i	−0.178110	−	0.984011i	$-0.556998\pi$
$839$	−33.8606	−	24.6012i	−1.16900	−	0.849327i	−0.990889	+	0.134684i	$0.956998\pi$
$840$		0			0
$841$	18.9418	−	13.7620i	0.653165	−	0.474552i
$842$	26.4123	−	81.2886i	0.910227	−	2.80139i
$843$		0			0
$844$	15.2900	−	47.0577i	0.526302	−	1.61979i
$845$	32.1772	+	3.45255i	1.10693	+	0.118771i
$846$		0			0
$847$	8.43203	+	25.9511i	0.289728	+	0.891691i
$848$	−17.4930	−	12.7094i	−0.600711	−	0.436442i
$849$		0			0
$850$	7.02382	−	12.0446i	0.240915	−	0.413127i
$851$	−38.3809			−1.31568
$852$		0			0
$853$	−17.9855	−	55.3537i	−0.615812	−	1.89527i	−0.388485	−	0.921455i	$-0.627002\pi$
$853$	−17.9855	−	55.3537i	−0.615812	−	1.89527i	−0.227327	−	0.973819i	$-0.572998\pi$
$854$	−22.5658	−	69.4504i	−0.772186	−	2.37654i
$855$		0			0
$856$	6.82646	−	21.0097i	0.233324	−	0.718096i
$857$	3.22045			0.110008			0.0550042	−	0.998486i	$-0.482483\pi$
$857$	3.22045			0.110008			0.0550042	+	0.998486i	$0.482483\pi$
$858$		0			0
$859$	−40.0003	+	29.0619i	−1.36479	+	0.991580i	−0.366669	+	0.930351i	$0.619502\pi$
$859$	−40.0003	+	29.0619i	−1.36479	+	0.991580i	−0.998124	+	0.0612288i	$0.980498\pi$
$860$	43.8895	−	25.2128i	1.49662	−	0.859751i
$861$		0			0
$862$	24.5731	−	17.8534i	0.836963	−	0.608089i
$863$	17.3878	−	12.6329i	0.591886	−	0.430030i	−0.251104	−	0.967960i	$-0.580793\pi$
$863$	17.3878	−	12.6329i	0.591886	−	0.430030i	0.842990	+	0.537930i	$0.180793\pi$
$864$		0			0
$865$	−8.64427	+	19.3025i	−0.293914	+	0.656306i
$866$	−0.960798	+	0.698061i	−0.0326493	+	0.0237211i
$867$		0			0
$868$	37.6544			1.27807
$869$	−0.769392	+	2.36795i	−0.0260999	+	0.0803271i
$870$		0			0
$871$	3.07522	+	9.46456i	0.104200	+	0.320694i
$872$	−2.96993	−	9.14051i	−0.100575	−	0.309537i
$873$		0			0
$874$	−75.8026			−2.56406
$875$	20.5836	+	28.7221i	0.695851	+	0.970984i
$876$		0			0
$877$	−12.4421	−	9.03971i	−0.420140	−	0.305249i	0.357554	−	0.933892i	$-0.383611\pi$
$877$	−12.4421	−	9.03971i	−0.420140	−	0.305249i	−0.777694	+	0.628643i	$0.783611\pi$
$878$	1.98544	+	6.11054i	0.0670052	+	0.206221i
$879$		0			0
$880$	1.56989	+	7.46534i	0.0529209	+	0.251657i
$881$	−5.84891	+	18.0011i	−0.197055	+	0.606472i	0.802892	+	0.596125i	$0.203294\pi$
$881$	−5.84891	+	18.0011i	−0.197055	+	0.606472i	−0.999946	+	0.0103472i	$0.996706\pi$
$882$		0			0
$883$	1.95208	−	6.00790i	0.0656928	−	0.202182i	−0.912822	−	0.408357i	$-0.866102\pi$
$883$	1.95208	−	6.00790i	0.0656928	−	0.202182i	0.978515	+	0.206175i	$0.0661018\pi$
$884$	−14.6021	+	10.6091i	−0.491123	+	0.356822i
$885$		0			0
$886$	64.1303	+	46.5934i	2.15450	+	1.56534i
$887$	0.0583776	−	0.0424138i	0.00196013	−	0.00142412i	−0.586805	−	0.809728i	$-0.699614\pi$
$887$	0.0583776	−	0.0424138i	0.00196013	−	0.00142412i	0.588765	+	0.808304i	$0.299614\pi$
$888$		0			0
$889$	25.6167	+	18.6116i	0.859156	+	0.624213i
$890$	−30.4800	+	17.5096i	−1.02169	+	0.586923i
$891$		0			0
$892$	−0.636120	+	1.95778i	−0.0212989	+	0.0655512i
$893$	−4.10113			−0.137239
$894$		0			0
$895$	7.90585	−	4.54161i	0.264263	−	0.151809i
$896$	−10.6479	−	32.7709i	−0.355721	−	1.09480i
$897$		0			0
$898$	31.1886	+	22.6599i	1.04078	+	0.756169i
$899$	−10.5545			−0.352013
$900$		0			0
$901$	12.5840			0.419235
$902$	−22.9425	−	16.6687i	−0.763901	−	0.555006i
$903$		0			0
$904$	−4.00128	−	12.3147i	−0.133081	−	0.409580i
$905$	−24.7236	−	2.65280i	−0.821841	−	0.0881820i
$906$		0			0
$907$	−25.4951			−0.846550			−0.423275	−	0.906001i	$-0.639120\pi$
$907$	−25.4951			−0.846550			−0.423275	+	0.906001i	$0.639120\pi$
$908$	−9.42474	+	29.0064i	−0.312771	+	0.962610i
$909$		0			0
$910$	−16.4698	−	78.3194i	−0.545968	−	2.59626i
$911$	2.87851	+	2.09136i	0.0953692	+	0.0692898i	0.634448	−	0.772966i	$-0.281227\pi$
$911$	2.87851	+	2.09136i	0.0953692	+	0.0692898i	−0.539079	+	0.842255i	$0.681227\pi$
$912$		0			0
$913$	−16.3644	+	11.8894i	−0.541583	+	0.393483i
$914$	−42.2621	−	30.7052i	−1.39791	−	1.01564i
$915$		0			0
$916$	−22.0698	+	16.0347i	−0.729208	+	0.529801i
$917$	−6.22981	+	19.1734i	−0.205727	+	0.633161i
$918$		0			0
$919$	2.46277	−	7.57962i	0.0812392	−	0.250029i	−0.902185	−	0.431350i	$-0.858037\pi$
$919$	2.46277	−	7.57962i	0.0812392	−	0.250029i	0.983424	+	0.181321i	$0.0580374\pi$
$920$	15.4210	+	13.9459i	0.508416	+	0.459781i
$921$		0			0
$922$	−24.9617	−	76.8241i	−0.822068	−	2.53007i
$923$	0.300549	+	0.218362i	0.00989270	+	0.00718747i
$924$		0			0
$925$	−15.0056	+	25.7319i	−0.493380	+	0.846060i
$926$	−44.1434			−1.45064
$927$		0			0
$928$	5.60805	+	17.2598i	0.184093	+	0.566581i
$929$	−15.0004	−	46.1666i	−0.492149	−	1.51468i	−0.821354	−	0.570419i	$-0.806781\pi$
$929$	−15.0004	−	46.1666i	−0.492149	−	1.51468i	0.329205	−	0.944258i	$-0.393219\pi$
$930$		0			0
$931$	5.03032	−	15.4817i	0.164862	−	0.507394i
$932$	60.0916			1.96837
$933$		0			0
$934$	−54.5571	+	39.6381i	−1.78516	+	1.29700i
$935$	−3.29294	−	2.97794i	−0.107691	−	0.0973889i
$936$		0			0
$937$	−25.6698	+	18.6502i	−0.838594	+	0.609274i	−0.921978	−	0.387243i	$-0.873427\pi$
$937$	−25.6698	+	18.6502i	−0.838594	+	0.609274i	0.0833833	+	0.996518i	$0.473427\pi$
$938$	10.4889	−	7.62066i	0.342476	−	0.248823i
$939$		0			0
$940$	3.33221	+	3.01345i	0.108685	+	0.0982880i
$941$	33.1752	−	24.1032i	1.08148	−	0.785742i	0.103541	−	0.994625i	$-0.466983\pi$
$941$	33.1752	−	24.1032i	1.08148	−	0.785742i	0.977941	+	0.208883i	$0.0669827\pi$
$942$		0			0
$943$	54.9681			1.79001
$944$	2.81848	−	8.67439i	0.0917337	−	0.282327i
$945$		0			0
$946$	−8.71401	−	26.8190i	−0.283317	−	0.871960i
$947$	3.03389	+	9.33737i	0.0985883	+	0.303424i	0.988172	−	0.153348i	$-0.0490056\pi$
$947$	3.03389	+	9.33737i	0.0985883	+	0.303424i	−0.889584	+	0.456772i	$0.849006\pi$
$948$		0			0
$949$	−21.0246			−0.682487
$950$	−29.6361	+	50.8208i	−0.961523	+	1.64884i
$951$		0			0
$952$	4.76317	+	3.46065i	0.154375	+	0.112160i
$953$	−16.4125	−	50.5123i	−0.531652	−	1.63626i	−0.750775	−	0.660558i	$-0.770320\pi$
$953$	−16.4125	−	50.5123i	−0.531652	−	1.63626i	0.219123	−	0.975697i	$-0.429680\pi$
$954$		0			0
$955$	5.98932	+	5.41638i	0.193810	+	0.175270i
$956$	0.485670	−	1.49474i	0.0157077	−	0.0483433i
$957$		0			0
$958$	7.40888	−	22.8022i	0.239370	−	0.736705i
$959$	23.4659	−	17.0490i	0.757754	−	0.550540i
$960$		0			0
$961$	8.94773	+	6.50090i	0.288636	+	0.209707i
$962$	54.5807	−	39.6552i	1.75975	−	1.27853i
$963$		0			0
$964$	−3.25793	−	2.36703i	−0.104931	−	0.0762368i
$965$	−7.84858	−	37.3226i	−0.252655	−	1.20146i
$966$		0			0
$967$	−0.756262	+	2.32754i	−0.0243198	+	0.0748485i	−0.962480	−	0.271353i	$-0.912529\pi$
$967$	−0.756262	+	2.32754i	−0.0243198	+	0.0748485i	0.938160	+	0.346202i	$0.112529\pi$
$968$	12.4606			0.400500
$969$		0			0
$970$	−48.9673	−	5.25410i	−1.57225	−	0.168699i
$971$	14.8230	+	45.6205i	0.475693	+	1.46403i	0.845021	+	0.534734i	$0.179588\pi$
$971$	14.8230	+	45.6205i	0.475693	+	1.46403i	−0.369328	+	0.929299i	$0.620412\pi$
$972$		0			0
$973$	−23.6911	−	17.2126i	−0.759502	−	0.551811i
$974$	−15.4200			−0.494088
$975$		0			0
$976$	23.7161			0.759134
$977$	19.1696	+	13.9276i	0.613291	+	0.445582i	0.850572	−	0.525859i	$-0.176256\pi$
$977$	19.1696	+	13.9276i	0.613291	+	0.445582i	−0.237280	+	0.971441i	$0.576256\pi$
$978$		0			0
$979$	3.45883	+	10.6452i	0.110545	+	0.340221i
$980$	−15.4630	+	8.88288i	−0.493947	+	0.283753i
$981$		0			0
$982$	15.6284			0.498721
$983$	−4.00193	+	12.3167i	−0.127642	+	0.392841i	−0.994373	−	0.105934i	$-0.966217\pi$
$983$	−4.00193	+	12.3167i	−0.127642	+	0.392841i	0.866731	+	0.498775i	$0.166217\pi$
$984$		0			0
$985$	−8.54136	+	4.90668i	−0.272150	+	0.156340i
$986$	−5.33236	−	3.87419i	−0.169817	−	0.123379i
$987$		0			0
$988$	61.6119	−	44.7637i	1.96014	−	1.42412i
$989$	44.2203	+	32.1279i	1.40612	+	1.02161i
$990$		0			0
$991$	−35.9986	+	26.1545i	−1.14353	+	0.830826i	−0.987608	−	0.156943i	$-0.949836\pi$
$991$	−35.9986	+	26.1545i	−1.14353	+	0.830826i	−0.155926	+	0.987769i	$0.549836\pi$
$992$	−10.5949	+	32.6079i	−0.336389	+	1.03530i
$993$		0			0
$994$	0.149562	−	0.460303i	0.00474381	−	0.0145999i
$995$	7.63660	+	36.3146i	0.242096	+	1.15125i
$996$		0			0
$997$	−17.1663	−	52.8324i	−0.543662	−	1.67322i	−0.724150	−	0.689642i	$-0.757768\pi$
$997$	−17.1663	−	52.8324i	−0.543662	−	1.67322i	0.180488	−	0.983577i	$-0.442232\pi$
$998$	27.9964	+	20.3406i	0.886209	+	0.643869i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.d.91.3		12
3.2	odd	2		75.2.g.c.16.1	✓	12
15.2	even	4		375.2.i.d.49.6		24
15.8	even	4		375.2.i.d.49.1		24
15.14	odd	2		375.2.g.c.76.3		12
25.6	even	5		5625.2.a.p.1.2		6
25.11	even	5	inner	225.2.h.d.136.3		12
25.19	even	10		5625.2.a.q.1.5		6
75.2	even	20		375.2.i.d.199.1		24
75.8	even	20		1875.2.b.f.1249.3		12
75.11	odd	10		75.2.g.c.61.1	yes	12
75.14	odd	10		375.2.g.c.301.3		12
75.17	even	20		1875.2.b.f.1249.10		12
75.23	even	20		375.2.i.d.199.6		24
75.44	odd	10		1875.2.a.k.1.2		6
75.56	odd	10		1875.2.a.j.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.1	✓	12	3.2	odd	2
75.2.g.c.61.1	yes	12	75.11	odd	10
225.2.h.d.91.3		12	1.1	even	1	trivial
225.2.h.d.136.3		12	25.11	even	5	inner
375.2.g.c.76.3		12	15.14	odd	2
375.2.g.c.301.3		12	75.14	odd	10
375.2.i.d.49.1		24	15.8	even	4
375.2.i.d.49.6		24	15.2	even	4
375.2.i.d.199.1		24	75.2	even	20
375.2.i.d.199.6		24	75.23	even	20
1875.2.a.j.1.5		6	75.56	odd	10
1875.2.a.k.1.2		6	75.44	odd	10
1875.2.b.f.1249.3		12	75.8	even	20
1875.2.b.f.1249.10		12	75.17	even	20
5625.2.a.p.1.2		6	25.6	even	5
5625.2.a.q.1.5		6	25.19	even	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.74793 + 1.26995i) q^{2} +(0.824463 + 2.53744i) q^{4} +(0.460159 + 2.18821i) q^{5} -3.16056 q^{7} +(-0.446002 + 1.37265i) q^{8} +O(q^{10})\)	\(q+(1.74793 + 1.26995i) q^{2} +(0.824463 + 2.53744i) q^{4} +(0.460159 + 2.18821i) q^{5} -3.16056 q^{7} +(-0.446002 + 1.37265i) q^{8} +(-1.97458 + 4.40921i) q^{10} +(1.24455 + 0.904220i) q^{11} +(4.24041 - 3.08084i) q^{13} +(-5.52444 - 4.01374i) q^{14} +(1.79417 - 1.30354i) q^{16} +(-0.398843 + 1.22751i) q^{17} +(1.68287 - 5.17933i) q^{19} +(-5.17306 + 2.97172i) q^{20} +(1.02708 + 3.16103i) q^{22} +(-5.21204 - 3.78677i) q^{23} +(-4.57651 + 2.01385i) q^{25} +11.3244 q^{26} +(-2.60577 - 8.01972i) q^{28} +(0.730396 + 2.24793i) q^{29} +(-1.37989 + 4.24687i) q^{31} +7.67809 q^{32} +(-2.25602 + 1.63910i) q^{34} +(-1.45436 - 6.91596i) q^{35} +(4.81973 - 3.50174i) q^{37} +(9.51901 - 6.91596i) q^{38} +(-3.20889 - 0.344307i) q^{40} +(-6.90269 + 5.01510i) q^{41} -8.48426 q^{43} +(-1.26831 + 3.90347i) q^{44} +(-4.30129 - 13.2380i) q^{46} +(-0.232712 - 0.716212i) q^{47} +2.98914 q^{49} +(-10.5569 - 2.29185i) q^{50} +(11.3135 + 8.21974i) q^{52} +(-3.01289 - 9.27271i) q^{53} +(-1.40593 + 3.13942i) q^{55} +(1.40962 - 4.33836i) q^{56} +(-1.57806 + 4.85678i) q^{58} +(3.32724 - 2.41738i) q^{59} +(8.65159 + 6.28574i) q^{61} +(-7.80525 + 5.67084i) q^{62} +(9.83243 + 7.14368i) q^{64} +(8.69278 + 7.86123i) q^{65} +(-0.586713 + 1.80572i) q^{67} -3.44357 q^{68} +(6.24078 - 13.9356i) q^{70} +(0.0219023 + 0.0674084i) q^{71} +(-3.24515 - 2.35774i) q^{73} +12.8716 q^{74} +14.5297 q^{76} +(-3.93348 - 2.85784i) q^{77} +(0.500141 + 1.53928i) q^{79} +(3.67802 + 3.32618i) q^{80} -18.4343 q^{82} +(-4.06322 + 12.5053i) q^{83} +(-2.86958 - 0.307901i) q^{85} +(-14.8299 - 10.7745i) q^{86} +(-1.79626 + 1.30506i) q^{88} +(5.88638 + 4.27671i) q^{89} +(-13.4021 + 9.73718i) q^{91} +(5.31155 - 16.3473i) q^{92} +(0.502787 - 1.54742i) q^{94} +(12.1078 + 1.29915i) q^{95} +(3.15009 + 9.69499i) q^{97} +(5.22480 + 3.79604i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8}+O(q^{10}) \) 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8	\( 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8} - 9 q^{10} + 4 q^{11} - 2 q^{13} - 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 26 q^{20} + 13 q^{22} - 19 q^{23} + 4 q^{25} + 56 q^{26} + q^{28} + q^{29} + 13 q^{31} + 32 q^{32} - 25 q^{34} + 10 q^{35} + 8 q^{37} + 22 q^{38} - 28 q^{40} - 8 q^{41} - 4 q^{43} - 33 q^{44} - 22 q^{46} + 13 q^{47} - 28 q^{49} - 81 q^{50} + 44 q^{52} - 44 q^{53} + 9 q^{55} - 45 q^{56} + 41 q^{58} + 22 q^{59} - 8 q^{61} - 41 q^{62} + 49 q^{64} + 38 q^{65} - 6 q^{67} + 100 q^{68} - 45 q^{70} + 21 q^{71} - 16 q^{73} + 44 q^{74} - 52 q^{76} - q^{77} + 10 q^{79} + 99 q^{80} + 26 q^{82} + 10 q^{83} + 23 q^{85} - 56 q^{86} - 16 q^{88} - 57 q^{89} - 7 q^{91} - 3 q^{92} - 23 q^{94} - 21 q^{95} + 4 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8 - 9 * q^10 + 4 * q^11 - 2 * q^13 - 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 26 * q^20 + 13 * q^22 - 19 * q^23 + 4 * q^25 + 56 * q^26 + q^28 + q^29 + 13 * q^31 + 32 * q^32 - 25 * q^34 + 10 * q^35 + 8 * q^37 + 22 * q^38 - 28 * q^40 - 8 * q^41 - 4 * q^43 - 33 * q^44 - 22 * q^46 + 13 * q^47 - 28 * q^49 - 81 * q^50 + 44 * q^52 - 44 * q^53 + 9 * q^55 - 45 * q^56 + 41 * q^58 + 22 * q^59 - 8 * q^61 - 41 * q^62 + 49 * q^64 + 38 * q^65 - 6 * q^67 + 100 * q^68 - 45 * q^70 + 21 * q^71 - 16 * q^73 + 44 * q^74 - 52 * q^76 - q^77 + 10 * q^79 + 99 * q^80 + 26 * q^82 + 10 * q^83 + 23 * q^85 - 56 * q^86 - 16 * q^88 - 57 * q^89 - 7 * q^91 - 3 * q^92 - 23 * q^94 - 21 * q^95 + 4 * q^97 + 18 * q^98

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