LMFDB - Embedded newform 819.2.et.b.271.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.5
Character	$\chi$	$=$	819.271
Dual form			819.2.et.b.136.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.270646 + 0.270646i) q^{2} -1.85350i q^{4} +(-0.959617 - 3.58134i) q^{5} +(1.30385 - 2.30217i) q^{7} +(1.04293 - 1.04293i) q^{8} +O(q^{10})$	\(q+(0.270646 + 0.270646i) q^{2} -1.85350i q^{4} +(-0.959617 - 3.58134i) q^{5} +(1.30385 - 2.30217i) q^{7} +(1.04293 - 1.04293i) q^{8} +(0.709559 - 1.22899i) q^{10} +(-0.0226729 - 0.0846164i) q^{11} +(1.63590 + 3.21307i) q^{13} +(0.975954 - 0.270190i) q^{14} -3.14247 q^{16} +5.89043 q^{17} +(-3.58643 - 0.960980i) q^{19} +(-6.63802 + 1.77865i) q^{20} +(0.0167648 - 0.0290374i) q^{22} -0.446373i q^{23} +(-7.57501 + 4.37343i) q^{25} +(-0.426856 + 1.31235i) q^{26} +(-4.26707 - 2.41669i) q^{28} +(-0.706429 - 1.22357i) q^{29} +(-1.94183 - 0.520311i) q^{31} +(-2.93637 - 2.93637i) q^{32} +(1.59422 + 1.59422i) q^{34} +(-9.49604 - 2.46033i) q^{35} +(1.87469 - 1.87469i) q^{37} +(-0.710566 - 1.23074i) q^{38} +(-4.73592 - 2.73428i) q^{40} +(-3.00264 - 0.804556i) q^{41} +(8.64788 + 4.99286i) q^{43} +(-0.156837 + 0.0420243i) q^{44} +(0.120809 - 0.120809i) q^{46} +(-8.84037 + 2.36877i) q^{47} +(-3.59995 - 6.00336i) q^{49} +(-3.23380 - 0.866493i) q^{50} +(5.95544 - 3.03214i) q^{52} +(6.28118 + 10.8793i) q^{53} +(-0.281283 + 0.162399i) q^{55} +(-1.04118 - 3.76084i) q^{56} +(0.139962 - 0.522347i) q^{58} +(-5.05813 - 5.05813i) q^{59} +(0.110587 - 0.0638473i) q^{61} +(-0.384727 - 0.666367i) q^{62} +4.69551i q^{64} +(9.93727 - 8.94203i) q^{65} +(9.61759 - 2.57703i) q^{67} -10.9179i q^{68} +(-1.90419 - 3.23594i) q^{70} +(9.83277 - 2.63468i) q^{71} +(-2.37094 + 8.84847i) q^{73} +1.01475 q^{74} +(-1.78118 + 6.64744i) q^{76} +(-0.224363 - 0.0581303i) q^{77} +(1.75744 - 3.04398i) q^{79} +(3.01557 + 11.2543i) q^{80} +(-0.594903 - 1.03040i) q^{82} +(2.17980 - 2.17980i) q^{83} +(-5.65256 - 21.0956i) q^{85} +(0.989217 + 3.69181i) q^{86} +(-0.111896 - 0.0646030i) q^{88} +(-1.19449 - 1.19449i) q^{89} +(9.53000 + 0.423256i) q^{91} -0.827354 q^{92} +(-3.03371 - 1.75151i) q^{94} +13.7664i q^{95} +(-0.452103 - 1.68727i) q^{97} +(0.650474 - 2.59910i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.270646	+	0.270646i	0.191376	+	0.191376i	0.796290	−	0.604915i	$-0.206793\pi$
$2$	0.270646	+	0.270646i	0.191376	+	0.191376i	−0.604915	+	0.796290i	$0.706793\pi$
$3$		0			0
$3$		0			0
$4$		−	1.85350i		−	0.926751i
$5$	−0.959617	−	3.58134i	−0.429154	−	1.60162i	−0.754681	−	0.656091i	$-0.772209\pi$
$5$	−0.959617	−	3.58134i	−0.429154	−	1.60162i	0.325528	−	0.945533i	$-0.394458\pi$
$6$		0			0
$7$	1.30385	−	2.30217i	0.492809	−	0.870137i
$7$	1.30385	−	2.30217i	0.492809	−	0.870137i
$8$	1.04293	−	1.04293i	0.368733	−	0.368733i
$9$		0			0
$10$	0.709559	−	1.22899i	0.224382	−	0.388641i
$11$	−0.0226729	−	0.0846164i	−0.00683614	−	0.0255128i	0.962424	−	0.271553i	$-0.0875372\pi$
$11$	−0.0226729	−	0.0846164i	−0.00683614	−	0.0255128i	−0.969260	+	0.246040i	$0.920871\pi$
$12$		0			0
$13$	1.63590	+	3.21307i	0.453716	+	0.891146i
$13$	1.63590	+	3.21307i	0.453716	+	0.891146i
$14$	0.975954	−	0.270190i	0.260835	−	0.0722114i
$15$		0			0
$16$	−3.14247			−0.785618
$17$	5.89043			1.42864			0.714319	−	0.699820i	$-0.246736\pi$
$17$	5.89043			1.42864			0.714319	+	0.699820i	$0.246736\pi$
$18$		0			0
$19$	−3.58643	−	0.960980i	−0.822782	−	0.220464i	−0.177220	−	0.984171i	$-0.556710\pi$
$19$	−3.58643	−	0.960980i	−0.822782	−	0.220464i	−0.645563	+	0.763707i	$0.723377\pi$
$20$	−6.63802	+	1.77865i	−1.48431	+	0.397719i
$21$		0			0
$22$	0.0167648	−	0.0290374i	0.00357426	−	0.00619080i
$23$		−	0.446373i		−	0.0930753i	−0.998917	−	0.0465377i	$-0.985181\pi$
$23$		−	0.446373i		−	0.0930753i	0.998917	−	0.0465377i	$-0.0148187\pi$
$24$		0			0
$25$	−7.57501	+	4.37343i	−1.51500	+	0.874686i
$26$	−0.426856	+	1.31235i	−0.0837133	+	0.257374i
$27$		0			0
$28$	−4.26707	−	2.41669i	−0.806401	−	0.456711i
$29$	−0.706429	−	1.22357i	−0.131181	−	0.227212i	0.792951	−	0.609285i	$-0.208543\pi$
$29$	−0.706429	−	1.22357i	−0.131181	−	0.227212i	−0.924132	+	0.382073i	$0.875210\pi$
$30$		0			0
$31$	−1.94183	−	0.520311i	−0.348762	−	0.0934505i	0.0801853	−	0.996780i	$-0.474449\pi$
$31$	−1.94183	−	0.520311i	−0.348762	−	0.0934505i	−0.428947	+	0.903329i	$0.641115\pi$
$32$	−2.93637	−	2.93637i	−0.519081	−	0.519081i
$33$		0			0
$34$	1.59422	+	1.59422i	0.273406	+	0.273406i
$35$	−9.49604	−	2.46033i	−1.60512	−	0.415872i
$36$		0			0
$37$	1.87469	−	1.87469i	0.308197	−	0.308197i	−0.536013	−	0.844210i	$-0.680070\pi$
$37$	1.87469	−	1.87469i	0.308197	−	0.308197i	0.844210	+	0.536013i	$0.180070\pi$
$38$	−0.710566	−	1.23074i	−0.115269	−	0.199652i
$39$		0			0
$40$	−4.73592	−	2.73428i	−0.748815	−	0.432328i
$41$	−3.00264	−	0.804556i	−0.468934	−	0.125651i	0.0166112	−	0.999862i	$-0.494712\pi$
$41$	−3.00264	−	0.804556i	−0.468934	−	0.125651i	−0.485545	+	0.874211i	$0.661379\pi$
$42$		0			0
$43$	8.64788	+	4.99286i	1.31879	+	0.761404i	0.983534	−	0.180724i	$-0.0578439\pi$
$43$	8.64788	+	4.99286i	1.31879	+	0.761404i	0.335256	+	0.942127i	$0.391177\pi$
$44$	−0.156837	+	0.0420243i	−0.0236440	+	0.00633539i
$45$		0			0
$46$	0.120809	−	0.120809i	0.0178123	−	0.0178123i
$47$	−8.84037	+	2.36877i	−1.28950	+	0.345521i	−0.837471	−	0.546482i	$-0.815967\pi$
$47$	−8.84037	+	2.36877i	−1.28950	+	0.345521i	−0.452030	+	0.892003i	$0.649300\pi$
$48$		0			0
$49$	−3.59995	−	6.00336i	−0.514278	−	0.857623i
$50$	−3.23380	−	0.866493i	−0.457328	−	0.122541i
$51$		0			0
$52$	5.95544	−	3.03214i	0.825870	−	0.420482i
$53$	6.28118	+	10.8793i	0.862786	+	1.49439i	0.869229	+	0.494410i	$0.164616\pi$
$53$	6.28118	+	10.8793i	0.862786	+	1.49439i	−0.00644326	+	0.999979i	$0.502051\pi$
$54$		0			0
$55$	−0.281283	+	0.162399i	−0.0379282	+	0.0218978i
$56$	−1.04118	−	3.76084i	−0.139133	−	0.502563i
$57$		0			0
$58$	0.139962	−	0.522347i	0.0183780	−	0.0685875i
$59$	−5.05813	−	5.05813i	−0.658513	−	0.658513i	0.296515	−	0.955028i	$-0.404175\pi$
$59$	−5.05813	−	5.05813i	−0.658513	−	0.658513i	−0.955028	+	0.296515i	$0.904175\pi$
$60$		0			0
$61$	0.110587	−	0.0638473i	0.0141592	−	0.00817481i	−0.492904	−	0.870084i	$-0.664065\pi$
$61$	0.110587	−	0.0638473i	0.0141592	−	0.00817481i	0.507063	+	0.861909i	$0.330731\pi$
$62$	−0.384727	−	0.666367i	−0.0488604	−	0.0846287i
$63$		0			0
$64$			4.69551i			0.586939i
$65$	9.93727	−	8.94203i	1.23257	−	1.10912i
$66$		0			0
$67$	9.61759	−	2.57703i	1.17498	−	0.314834i	0.382044	−	0.924144i	$-0.375220\pi$
$67$	9.61759	−	2.57703i	1.17498	−	0.314834i	0.792932	+	0.609310i	$0.208554\pi$
$68$		−	10.9179i		−	1.32399i
$69$		0			0
$70$	−1.90419	−	3.23594i	−0.227594	−	0.386769i
$71$	9.83277	−	2.63468i	1.16694	−	0.312679i	0.377203	−	0.926131i	$-0.376886\pi$
$71$	9.83277	−	2.63468i	1.16694	−	0.312679i	0.789732	+	0.613451i	$0.210219\pi$
$72$		0			0
$73$	−2.37094	+	8.84847i	−0.277498	+	1.03563i	0.676652	+	0.736303i	$0.263430\pi$
$73$	−2.37094	+	8.84847i	−0.277498	+	1.03563i	−0.954149	+	0.299332i	$0.903236\pi$
$74$	1.01475			0.117963
$75$		0			0
$76$	−1.78118	+	6.64744i	−0.204315	+	0.762514i
$77$	−0.224363	−	0.0581303i	−0.0255686	−	0.00662457i
$78$		0			0
$79$	1.75744	−	3.04398i	0.197728	−	0.342474i	−0.750064	−	0.661366i	$-0.769977\pi$
$79$	1.75744	−	3.04398i	0.197728	−	0.342474i	0.947791	+	0.318891i	$0.103311\pi$
$80$	3.01557	+	11.2543i	0.337151	+	1.25826i
$81$		0			0
$82$	−0.594903	−	1.03040i	−0.0656961	−	0.113789i
$83$	2.17980	−	2.17980i	0.239264	−	0.239264i	−0.577281	−	0.816545i	$-0.695886\pi$
$83$	2.17980	−	2.17980i	0.239264	−	0.239264i	0.816545	+	0.577281i	$0.195886\pi$
$84$		0			0
$85$	−5.65256	−	21.0956i	−0.613106	−	2.28814i
$86$	0.989217	+	3.69181i	0.106670	+	0.398098i
$87$		0			0
$88$	−0.111896	−	0.0646030i	−0.0119281	−	0.00688670i
$89$	−1.19449	−	1.19449i	−0.126616	−	0.126616i	0.640959	−	0.767575i	$-0.278537\pi$
$89$	−1.19449	−	1.19449i	−0.126616	−	0.126616i	−0.767575	+	0.640959i	$0.778537\pi$
$90$		0			0
$91$	9.53000	+	0.423256i	0.999015	+	0.0443693i
$92$	−0.827354			−0.0862576
$93$		0			0
$94$	−3.03371	−	1.75151i	−0.312903	−	0.180655i
$95$			13.7664i			1.41240i
$96$		0			0
$97$	−0.452103	−	1.68727i	−0.0459041	−	0.171317i	0.939168	−	0.343458i	$-0.111598\pi$
$97$	−0.452103	−	1.68727i	−0.0459041	−	0.171317i	−0.985072	+	0.172141i	$0.944932\pi$
$98$	0.650474	−	2.59910i	0.0657078	−	0.262548i
$99$		0			0
$100$	8.10616	+	14.0403i	0.810616	+	1.40403i
$101$	3.41120	−	5.90838i	0.339427	−	0.587905i	−0.644898	−	0.764269i	$-0.723100\pi$
$101$	3.41120	−	5.90838i	0.339427	−	0.587905i	0.984325	+	0.176363i	$0.0564334\pi$
$102$		0			0
$103$	5.00029	−	8.66076i	0.492693	−	0.853370i	−0.507271	−	0.861787i	$-0.669346\pi$
$103$	5.00029	−	8.66076i	0.492693	−	0.853370i	0.999965	+	0.00841640i	$0.00267906\pi$
$104$	5.05716	+	1.64489i	0.495895	+	0.161295i
$105$		0			0
$106$	−1.24447	+	4.64442i	−0.120873	+	0.451106i
$107$	0.0598871			0.00578950			0.00289475	−	0.999996i	$-0.499079\pi$
$107$	0.0598871			0.00578950			0.00289475	+	0.999996i	$0.499079\pi$
$108$		0			0
$109$	−4.25671	+	15.8862i	−0.407719	+	1.52163i	0.391267	+	0.920277i	$0.372037\pi$
$109$	−4.25671	+	15.8862i	−0.407719	+	1.52163i	−0.798986	+	0.601350i	$0.794630\pi$
$110$	−0.120081	−	0.0321755i	−0.0114492	−	0.00306781i
$111$		0			0
$112$	−4.09731	+	7.23450i	−0.387160	+	0.683596i
$113$	−2.74673	+	4.75748i	−0.258391	+	0.447546i	−0.965811	−	0.259247i	$-0.916526\pi$
$113$	−2.74673	+	4.75748i	−0.258391	+	0.447546i	0.707420	+	0.706793i	$0.249859\pi$
$114$		0			0
$115$	−1.59862	+	0.428348i	−0.149072	+	0.0399436i
$116$	−2.26789	+	1.30937i	−0.210569	+	0.121572i
$117$		0			0
$118$		−	2.73793i		−	0.252047i
$119$	7.68024	−	13.5608i	0.704046	−	1.24311i
$120$		0			0
$121$	9.51963	−	5.49616i	0.865421	−	0.499651i
$122$	0.0472098	+	0.0126498i	0.00427418	+	0.00114526i
$123$		0			0
$124$	−0.964397	+	3.59918i	−0.0866054	+	0.323216i
$125$	9.82324	+	9.82324i	0.878617	+	0.878617i
$126$		0			0
$127$	14.7405	−	8.51045i	1.30801	−	0.755180i	0.326247	−	0.945285i	$-0.394216\pi$
$127$	14.7405	−	8.51045i	1.30801	−	0.755180i	0.981764	+	0.190104i	$0.0608826\pi$
$128$	−7.14355	+	7.14355i	−0.631407	+	0.631407i
$129$		0			0
$130$	5.10960	+	0.269359i	0.448142	+	0.0236243i
$131$	−2.35567	−	1.36005i	−0.205816	−	0.118828i	0.393549	−	0.919303i	$-0.371247\pi$
$131$	−2.35567	−	1.36005i	−0.205816	−	0.118828i	−0.599365	+	0.800475i	$0.704580\pi$
$132$		0			0
$133$	−6.88850	+	7.00358i	−0.597309	+	0.607287i
$134$	3.30042	+	1.90550i	0.285113	+	0.164610i
$135$		0			0
$136$	6.14333	−	6.14333i	0.526786	−	0.526786i
$137$	3.04603	−	3.04603i	0.260240	−	0.260240i	−0.564911	−	0.825152i	$-0.691090\pi$
$137$	3.04603	−	3.04603i	0.260240	−	0.260240i	0.825152	+	0.564911i	$0.191090\pi$
$138$		0			0
$139$	−12.1251	−	7.00040i	−1.02843	−	0.593766i	−0.111898	−	0.993720i	$-0.535693\pi$
$139$	−12.1251	−	7.00040i	−1.02843	−	0.593766i	−0.916535	+	0.399953i	$0.869026\pi$
$140$	−4.56023	+	17.6009i	−0.385410	+	1.48755i
$141$		0			0
$142$	3.37426	+	1.94813i	0.283162	+	0.163484i
$143$	0.234788	−	0.211273i	0.0196340	−	0.0176676i
$144$		0			0
$145$	−3.70412	+	3.70412i	−0.307611	+	0.307611i
$146$	−3.03649	+	1.75312i	−0.251301	+	0.145089i
$147$		0			0
$148$	−3.47473	−	3.47473i	−0.285621	−	0.285621i
$149$	2.37346	−	8.85786i	0.194441	−	0.725664i	−0.797970	−	0.602698i	$-0.794092\pi$
$149$	2.37346	−	8.85786i	0.194441	−	0.725664i	0.992411	−	0.122967i	$-0.0392408\pi$
$150$		0			0
$151$	−7.33161	−	1.96450i	−0.596638	−	0.159869i	−0.0521530	−	0.998639i	$-0.516608\pi$
$151$	−7.33161	−	1.96450i	−0.596638	−	0.159869i	−0.544485	+	0.838770i	$0.683275\pi$
$152$	−4.74264	+	2.73817i	−0.384679	+	0.222095i
$153$		0			0
$154$	−0.0449902	−	0.0764557i	−0.00362542	−	0.00616098i
$155$			7.45364i			0.598691i
$156$		0			0
$157$	−0.438021	+	0.252891i	−0.0349578	+	0.0201829i	−0.517377	−	0.855758i	$-0.673092\pi$
$157$	−0.438021	+	0.252891i	−0.0349578	+	0.0201829i	0.482419	+	0.875940i	$0.339758\pi$
$158$	1.29948	−	0.348196i	0.103381	−	0.0277010i
$159$		0			0
$160$	−7.69834	+	13.3339i	−0.608607	+	1.05414i
$161$	−1.02763	−	0.582004i	−0.0809883	−	0.0458684i
$162$		0			0
$163$	−4.28976	−	1.14944i	−0.336000	−	0.0900308i	0.0868745	−	0.996219i	$-0.472312\pi$
$163$	−4.28976	−	1.14944i	−0.336000	−	0.0900308i	−0.422874	+	0.906188i	$0.638979\pi$
$164$	−1.49125	+	5.56541i	−0.116447	+	0.434585i
$165$		0			0
$166$	1.17991			0.0915785
$167$	2.07730	−	7.75258i	0.160746	−	0.599913i	−0.837798	−	0.545980i	$-0.816158\pi$
$167$	2.07730	−	7.75258i	0.160746	−	0.599913i	0.998545	−	0.0539330i	$-0.0171757\pi$
$168$		0			0
$169$	−7.64768	+	10.5125i	−0.588283	+	0.808655i
$170$	4.17960	−	7.23929i	0.320561	−	0.555228i
$171$		0			0
$172$	9.25427	−	16.0289i	0.705631	−	1.22219i
$173$	−0.631547	−	1.09387i	−0.0480157	−	0.0831656i	0.841019	−	0.541006i	$-0.181956\pi$
$173$	−0.631547	−	1.09387i	−0.0480157	−	0.0831656i	−0.889034	+	0.457841i	$0.848623\pi$
$174$		0			0
$175$	0.191697	+	23.1412i	0.0144909	+	1.74931i
$176$	0.0712489	+	0.265905i	0.00537059	+	0.0200433i
$177$		0			0
$178$		−	0.646569i		−	0.0484624i
$179$	−1.46377	−	0.845110i	−0.109408	−	0.0631665i	0.444298	−	0.895879i	$-0.353453\pi$
$179$	−1.46377	−	0.845110i	−0.109408	−	0.0631665i	−0.553705	+	0.832713i	$0.686787\pi$
$180$		0			0
$181$	−8.30825			−0.617547			−0.308774	−	0.951136i	$-0.599919\pi$
$181$	−8.30825			−0.617547			−0.308774	+	0.951136i	$0.599919\pi$
$182$	2.46470	+	2.69381i	0.182696	+	0.199678i
$183$		0			0
$184$	−0.465538	−	0.465538i	−0.0343199	−	0.0343199i
$185$	−8.51287	−	4.91491i	−0.625879	−	0.361351i
$186$		0			0
$187$	−0.133553	−	0.498427i	−0.00976637	−	0.0364486i
$188$	4.39052	+	16.3856i	0.320211	+	1.19505i
$189$		0			0
$190$	−3.72581	+	3.72581i	−0.270299	+	0.270299i
$191$	10.3140	+	17.8644i	0.746296	+	1.29262i	0.949587	+	0.313505i	$0.101503\pi$
$191$	10.3140	+	17.8644i	0.746296	+	1.29262i	−0.203290	+	0.979119i	$0.565164\pi$
$192$		0			0
$193$	−3.47003	−	12.9503i	−0.249779	−	0.932186i	−0.970921	−	0.239400i	$-0.923049\pi$
$193$	−3.47003	−	12.9503i	−0.249779	−	0.932186i	0.721143	−	0.692787i	$-0.243617\pi$
$194$	0.334293	−	0.579013i	0.0240009	−	0.0415707i
$195$		0			0
$196$	−11.1272	+	6.67251i	−0.794803	+	0.476608i
$197$	−4.28034	+	15.9744i	−0.304961	+	1.13813i	0.628017	+	0.778199i	$0.283867\pi$
$197$	−4.28034	+	15.9744i	−0.304961	+	1.13813i	−0.932979	+	0.359932i	$0.882800\pi$
$198$		0			0
$199$	12.9622			0.918863			0.459432	−	0.888213i	$-0.348053\pi$
$199$	12.9622			0.918863			0.459432	+	0.888213i	$0.348053\pi$
$200$	−3.33903	+	12.4614i	−0.236105	+	0.881157i
$201$		0			0
$202$	2.52231	−	0.675850i	0.177469	−	0.0475526i
$203$	−3.73795	+	0.0309644i	−0.262352	+	0.00217327i
$204$		0			0
$205$			11.5256i			0.804980i
$206$	3.69731	−	0.990691i	0.257604	−	0.0690247i
$207$		0			0
$208$	−5.14076	−	10.0970i	−0.356448	−	0.700100i
$209$			0.325259i			0.0224986i
$210$		0			0
$211$	−3.19052	−	5.52614i	−0.219644	−	0.380435i	0.735055	−	0.678008i	$-0.237156\pi$
$211$	−3.19052	−	5.52614i	−0.219644	−	0.380435i	−0.954699	+	0.297572i	$0.903823\pi$
$212$	20.1648	−	11.6422i	1.38493	−	0.799587i
$213$		0			0
$214$	0.0162082	+	0.0162082i	0.00110797	+	0.00110797i
$215$	9.58246	−	35.7622i	0.653519	−	2.43896i
$216$		0			0
$217$	−3.72969	+	3.79200i	−0.253188	+	0.257418i
$218$	−5.45161	+	3.14749i	−0.369229	+	0.213175i
$219$		0			0
$220$	0.301006	+	0.521358i	0.0202938	+	0.0351500i
$221$	9.63614	+	18.9264i	0.648197	+	1.27313i
$222$		0			0
$223$	12.3622	+	3.31244i	0.827834	+	0.221817i	0.647769	−	0.761837i	$-0.275702\pi$
$223$	12.3622	+	3.31244i	0.827834	+	0.221817i	0.180065	+	0.983655i	$0.442369\pi$
$224$	−10.5886	+	2.93142i	−0.707480	+	0.195864i
$225$		0			0
$226$	−2.03098	+	0.544201i	−0.135099	+	0.0361997i
$227$	8.38467	−	8.38467i	0.556510	−	0.556510i	−0.371802	−	0.928312i	$-0.621260\pi$
$227$	8.38467	−	8.38467i	0.556510	−	0.556510i	0.928312	+	0.371802i	$0.121260\pi$
$228$		0			0
$229$	15.2594	−	4.08875i	1.00837	−	0.270192i	0.283423	−	0.958995i	$-0.408530\pi$
$229$	15.2594	−	4.08875i	1.00837	−	0.270192i	0.724949	+	0.688803i	$0.241863\pi$
$230$	−0.548589	−	0.316728i	−0.0361729	−	0.0208844i
$231$		0			0
$232$	−2.01286	−	0.539345i	−0.132151	−	0.0354098i
$233$	−11.6063	−	6.70088i	−0.760352	−	0.438989i	0.0690703	−	0.997612i	$-0.477997\pi$
$233$	−11.6063	−	6.70088i	−0.760352	−	0.438989i	−0.829422	+	0.558623i	$0.811330\pi$
$234$		0			0
$235$	16.9667	+	29.3873i	1.10679	+	1.91701i
$236$	−9.37526	+	9.37526i	−0.610277	+	0.610277i
$237$		0			0
$238$	5.74879	−	1.59154i	0.372638	−	0.103164i
$239$	14.4526	+	14.4526i	0.934861	+	0.934861i	0.998004	−	0.0631438i	$-0.0201127\pi$
$239$	14.4526	+	14.4526i	0.934861	+	0.934861i	−0.0631438	+	0.998004i	$0.520113\pi$
$240$		0			0
$241$	0.721809	+	0.721809i	0.0464958	+	0.0464958i	0.729972	−	0.683477i	$-0.239533\pi$
$241$	0.721809	+	0.721809i	0.0464958	+	0.0464958i	−0.683477	+	0.729972i	$0.739533\pi$
$242$	4.06396	+	1.08894i	0.261241	+	0.0699994i
$243$		0			0
$244$	−0.118341	−	0.204973i	−0.00757601	−	0.0131220i
$245$	−18.0455	+	18.6536i	−1.15289	+	1.19173i
$246$		0			0
$247$	−2.77933	−	13.0955i	−0.176844	−	0.833247i
$248$	−2.56785	+	1.48255i	−0.163058	+	0.0941418i
$249$		0			0
$250$			5.31724i			0.336292i
$251$	5.59470	−	9.69030i	0.353134	−	0.611646i	−0.633663	−	0.773609i	$-0.718449\pi$
$251$	5.59470	−	9.69030i	0.353134	−	0.611646i	0.986797	+	0.161963i	$0.0517826\pi$
$252$		0			0
$253$	−0.0377705	+	0.0101206i	−0.00237461	+	0.000636275i
$254$	6.29278	+	1.68615i	0.394844	+	0.105798i
$255$		0			0
$256$	5.52428			0.345267
$257$	9.42673			0.588023			0.294012	−	0.955802i	$-0.405010\pi$
$257$	9.42673			0.588023			0.294012	+	0.955802i	$0.405010\pi$
$258$		0			0
$259$	−1.87153	−	6.76015i	−0.116291	−	0.420055i
$260$	−16.5741	−	18.4187i	−1.02788	−	1.14228i
$261$		0			0
$262$	−0.269462	−	1.00564i	−0.0166474	−	0.0621289i
$263$	6.87360	−	11.9054i	0.423844	−	0.734120i	−0.572467	−	0.819928i	$-0.694014\pi$
$263$	6.87360	−	11.9054i	0.423844	−	0.734120i	0.996312	+	0.0858074i	$0.0273470\pi$
$264$		0			0
$265$	32.9350	−	32.9350i	2.02318	−	2.02318i
$266$	−3.75983	+	0.0311457i	−0.230530	+	0.00190966i
$267$		0			0
$268$	−4.77652	−	17.8262i	−0.291772	−	1.08891i
$269$			23.5848i			1.43799i	0.695015	+	0.718995i	$0.255398\pi$
$269$			23.5848i			1.43799i	−0.695015	+	0.718995i	$0.744602\pi$
$270$		0			0
$271$	−6.42801	−	6.42801i	−0.390474	−	0.390474i	0.484382	−	0.874856i	$-0.339044\pi$
$271$	−6.42801	−	6.42801i	−0.390474	−	0.390474i	−0.874856	+	0.484382i	$0.839044\pi$
$272$	−18.5105			−1.12236
$273$		0			0
$274$	1.64879			0.0996072
$275$	0.541811	+	0.541811i	0.0326725	+	0.0326725i
$276$		0			0
$277$			12.6627i			0.760828i	0.924816	+	0.380414i	$0.124219\pi$
$277$			12.6627i			0.760828i	−0.924816	+	0.380414i	$0.875781\pi$
$278$	−1.38697	−	5.17622i	−0.0831846	−	0.310449i
$279$		0			0
$280$	−12.4697	+	7.33778i	−0.745208	+	0.438516i
$281$	23.5896	−	23.5896i	1.40724	−	1.40724i	0.633468	−	0.773769i	$-0.281631\pi$
$281$	23.5896	−	23.5896i	1.40724	−	1.40724i	0.773769	−	0.633468i	$-0.218369\pi$
$282$		0			0
$283$	−11.4194	+	19.7790i	−0.678813	+	1.17574i	0.296526	+	0.955025i	$0.404172\pi$
$283$	−11.4194	+	19.7790i	−0.678813	+	1.17574i	−0.975339	+	0.220713i	$0.929162\pi$
$284$	−4.88339	−	18.2251i	−0.289776	−	1.08146i
$285$		0			0
$286$	0.120725	+	0.00636415i	0.00713860	+	0.000376320i
$287$	−5.76722	+	5.86357i	−0.340428	+	0.346115i
$288$		0			0
$289$	17.6971			1.04101
$290$	−2.00501			−0.117738
$291$		0			0
$292$	16.4007	+	4.39454i	0.959776	+	0.257171i
$293$	−11.5762	+	3.10184i	−0.676290	+	0.181211i	−0.580587	−	0.814198i	$-0.697177\pi$
$293$	−11.5762	+	3.10184i	−0.676290	+	0.181211i	−0.0957036	+	0.995410i	$0.530510\pi$
$294$		0			0
$295$	−13.2610	+	22.9688i	−0.772087	+	1.33729i
$296$		−	3.91035i		−	0.227284i
$297$		0			0
$298$	3.03971	−	1.75498i	0.176086	−	0.101663i
$299$	1.43423	−	0.730221i	0.0829437	−	0.0422298i
$300$		0			0
$301$	22.7699	−	13.3989i	1.31244	−	0.772302i
$302$	−1.45259	−	2.51596i	−0.0835870	−	0.144777i
$303$		0			0
$304$	11.2702	+	3.01985i	0.646393	+	0.173200i
$305$	−0.334780	−	0.334780i	−0.0191694	−	0.0191694i
$306$		0			0
$307$	−18.9842	−	18.9842i	−1.08348	−	1.08348i	−0.996182	−	0.0873012i	$-0.972176\pi$
$307$	−18.9842	−	18.9842i	−1.08348	−	1.08348i	−0.0873012	−	0.996182i	$-0.527824\pi$
$308$	−0.107745	+	0.415858i	−0.00613932	+	0.0236957i
$309$		0			0
$310$	−2.01730	+	2.01730i	−0.114575	+	0.114575i
$311$	14.8991	+	25.8060i	0.844851	+	1.46333i	0.885750	+	0.464162i	$0.153644\pi$
$311$	14.8991	+	25.8060i	0.844851	+	1.46333i	−0.0408993	+	0.999163i	$0.513022\pi$
$312$		0			0
$313$	14.1617	+	8.17629i	0.800469	+	0.462151i	0.843635	−	0.536917i	$-0.180411\pi$
$313$	14.1617	+	8.17629i	0.800469	+	0.462151i	−0.0431661	+	0.999068i	$0.513744\pi$
$314$	−0.186992	−	0.0501045i	−0.0105526	−	0.00282756i
$315$		0			0
$316$	−5.64202	−	3.25742i	−0.317388	−	0.183244i
$317$	16.4961	−	4.42013i	0.926516	−	0.248259i	0.236147	−	0.971717i	$-0.424115\pi$
$317$	16.4961	−	4.42013i	0.926516	−	0.248259i	0.690368	+	0.723458i	$0.257449\pi$
$318$		0			0
$319$	−0.0875174	+	0.0875174i	−0.00490004	+	0.00490004i
$320$	16.8162	−	4.50589i	0.940056	−	0.251887i
$321$		0			0
$322$	−0.120606	−	0.435640i	−0.00672110	−	0.0242773i
$323$	−21.1256	−	5.66058i	−1.17546	−	0.314963i
$324$		0			0
$325$	−26.4441	−	17.1846i	−1.46685	−	0.953228i
$326$	−0.849915	−	1.47210i	−0.0470724	−	0.0815318i
$327$		0			0
$328$	−3.97066	+	2.29246i	−0.219243	+	0.126580i
$329$	−6.07321	+	23.4405i	−0.334827	+	1.29232i
$330$		0			0
$331$	5.63617	−	21.0345i	0.309792	−	1.15616i	−0.618950	−	0.785430i	$-0.712442\pi$
$331$	5.63617	−	21.0345i	0.309792	−	1.15616i	0.928742	−	0.370728i	$-0.120892\pi$
$332$	−4.04026	−	4.04026i	−0.221738	−	0.221738i
$333$		0			0
$334$	2.66042	−	1.53599i	0.145571	−	0.0840457i
$335$	−18.4584	−	31.9709i	−1.00849	−	1.74676i
$336$		0			0
$337$			22.6556i			1.23413i	0.786912	+	0.617066i	$0.211679\pi$
$337$			22.6556i			1.23413i	−0.786912	+	0.617066i	$0.788321\pi$
$338$	−4.91498	+	0.775358i	−0.267340	+	0.0421739i
$339$		0			0
$340$	−39.1008	+	10.4770i	−2.12054	+	0.568196i
$341$			0.176107i			0.00953674i
$342$		0			0
$343$	−18.5145	+	0.460196i	−0.999691	+	0.0248483i
$344$	14.2264	−	3.81195i	0.767036	−	0.205527i
$345$		0			0
$346$	0.125126	−	0.466978i	0.00672683	−	0.0251049i
$347$	−11.8708			−0.637259			−0.318630	−	0.947879i	$-0.603223\pi$
$347$	−11.8708			−0.637259			−0.318630	+	0.947879i	$0.603223\pi$
$348$		0			0
$349$	−5.38273	+	20.0886i	−0.288131	+	1.07532i	0.658390	+	0.752677i	$0.271238\pi$
$349$	−5.38273	+	20.0886i	−0.288131	+	1.07532i	−0.946521	+	0.322642i	$0.895429\pi$
$350$	−6.21120	+	6.31496i	−0.332002	+	0.337549i
$351$		0			0
$352$	−0.181889	+	0.315041i	−0.00969470	+	0.0167917i
$353$	−7.23488	−	27.0009i	−0.385074	−	1.43712i	−0.838050	−	0.545593i	$-0.816305\pi$
$353$	−7.23488	−	27.0009i	−0.385074	−	1.43712i	0.452977	−	0.891522i	$-0.350362\pi$
$354$		0			0
$355$	−18.8714	−	32.6862i	−1.00159	−	1.73480i
$356$	−2.21400	+	2.21400i	−0.117342	+	0.117342i
$357$		0			0
$358$	−0.167439	−	0.624890i	−0.00884941	−	0.0330265i
$359$	−4.06106	−	15.1561i	−0.214334	−	0.799907i	−0.986400	−	0.164364i	$-0.947443\pi$
$359$	−4.06106	−	15.1561i	−0.214334	−	0.799907i	0.772065	−	0.635543i	$-0.219224\pi$
$360$		0			0
$361$	−4.51552	−	2.60704i	−0.237659	−	0.137212i
$362$	−2.24859	−	2.24859i	−0.118183	−	0.118183i
$363$		0			0
$364$	0.784506	−	17.6639i	0.0411193	−	0.925838i
$365$	33.9646			1.77779
$366$		0			0
$367$	4.15012	+	2.39607i	0.216635	+	0.125074i	0.604391	−	0.796688i	$-0.293416\pi$
$367$	4.15012	+	2.39607i	0.216635	+	0.125074i	−0.387756	+	0.921762i	$0.626750\pi$
$368$			1.40272i			0.0731216i
$369$		0			0
$370$	−0.973774	−	3.63417i	−0.0506241	−	0.188932i
$371$	33.2357	−	0.275318i	1.72551	−	0.0142938i
$372$		0			0
$373$	−0.941886	−	1.63140i	−0.0487690	−	0.0844704i	0.840610	−	0.541640i	$-0.182196\pi$
$373$	−0.941886	−	1.63140i	−0.0487690	−	0.0844704i	−0.889379	+	0.457170i	$0.848863\pi$
$374$	0.0987516	−	0.171043i	0.00510632	−	0.00884441i
$375$		0			0
$376$	−6.74945	+	11.6904i	−0.348076	+	0.602886i
$377$	2.77578	−	4.27145i	0.142960	−	0.219991i
$378$		0			0
$379$	−0.368612	+	1.37568i	−0.0189343	+	0.0706638i	−0.974747	−	0.223314i	$-0.928312\pi$
$379$	−0.368612	+	1.37568i	−0.0189343	+	0.0706638i	0.955812	+	0.293978i	$0.0949792\pi$
$380$	25.5160			1.30894
$381$		0			0
$382$	−2.04348	+	7.62638i	−0.104554	+	0.390199i
$383$	−10.5704	−	2.83233i	−0.540122	−	0.144725i	−0.0215638	−	0.999767i	$-0.506865\pi$
$383$	−10.5704	−	2.83233i	−0.540122	−	0.144725i	−0.518559	+	0.855042i	$0.673531\pi$
$384$		0			0
$385$	0.00711829	+	0.859304i	0.000362782	+	0.0437942i
$386$	2.56581	−	4.44411i	0.130596	−	0.226199i
$387$		0			0
$388$	−3.12736	+	0.837974i	−0.158768	+	0.0425417i
$389$	−23.9984	+	13.8555i	−1.21677	+	0.702502i	−0.964225	−	0.265084i	$-0.914600\pi$
$389$	−23.9984	+	13.8555i	−1.21677	+	0.702502i	−0.252544	+	0.967586i	$0.581267\pi$
$390$		0			0
$391$		−	2.62933i		−	0.132971i
$392$	−10.0156	−	2.50660i	−0.505865	−	0.126603i
$393$		0			0
$394$	−5.48187	+	3.16496i	−0.276173	+	0.159448i
$395$	−12.5880	−	3.37294i	−0.633371	−	0.169711i
$396$		0			0
$397$	−3.25335	+	12.1417i	−0.163281	+	0.609373i	0.834972	+	0.550292i	$0.185484\pi$
$397$	−3.25335	+	12.1417i	−0.163281	+	0.609373i	−0.998253	+	0.0590806i	$0.981183\pi$
$398$	3.50816	+	3.50816i	0.175848	+	0.175848i
$399$		0			0
$400$	23.8042	−	13.7434i	1.19021	−	0.687169i
$401$	17.4913	−	17.4913i	0.873475	−	0.873475i	−0.119374	−	0.992849i	$-0.538089\pi$
$401$	17.4913	−	17.4913i	0.873475	−	0.873475i	0.992849	+	0.119374i	$0.0380887\pi$
$402$		0			0
$403$	−1.50483	−	7.09040i	−0.0749610	−	0.353198i
$404$	−10.9512	−	6.32267i	−0.544842	−	0.314565i
$405$		0			0
$406$	−1.02004	−	1.00328i	−0.0506237	−	0.0497919i
$407$	−0.201134	−	0.116125i	−0.00996983	−	0.00575609i
$408$		0			0
$409$	8.05291	−	8.05291i	0.398191	−	0.398191i	−0.479404	−	0.877594i	$-0.659147\pi$
$409$	8.05291	−	8.05291i	0.398191	−	0.398191i	0.877594	+	0.479404i	$0.159147\pi$
$410$	−3.11934	+	3.11934i	−0.154053	+	0.154053i
$411$		0			0
$412$	−16.0527	−	9.26805i	−0.790861	−	0.456604i
$413$	−18.2397	+	5.04962i	−0.897518	+	0.248476i
$414$		0			0
$415$	−9.89837	−	5.71482i	−0.485892	−	0.280530i
$416$	4.63116	−	14.2384i	0.227061	−	0.698093i
$417$		0			0
$418$	−0.0880299	+	0.0880299i	−0.00430568	+	0.00430568i
$419$	−25.2233	+	14.5627i	−1.23224	+	0.711435i	−0.967497	−	0.252884i	$-0.918621\pi$
$419$	−25.2233	+	14.5627i	−1.23224	+	0.711435i	−0.264744	+	0.964319i	$0.585288\pi$
$420$		0			0
$421$	24.9431	+	24.9431i	1.21565	+	1.21565i	0.969140	+	0.246512i	$0.0792845\pi$
$421$	24.9431	+	24.9431i	1.21565	+	1.21565i	0.246512	+	0.969140i	$0.420715\pi$
$422$	0.632127	−	2.35913i	0.0307714	−	0.114841i
$423$		0			0
$424$	17.8973	+	4.79556i	0.869168	+	0.232893i
$425$	−44.6200	+	25.7614i	−2.16439	+	1.24961i
$426$		0			0
$427$	−0.00279857	−	0.337836i	−0.000135432	−	0.0163491i
$428$		−	0.111001i		−	0.00536543i
$429$		0			0
$430$	12.2724	−	7.08545i	0.591826	−	0.341691i
$431$	−3.15664	+	0.845820i	−0.152050	+	0.0407417i	−0.334041	−	0.942558i	$-0.608412\pi$
$431$	−3.15664	+	0.845820i	−0.152050	+	0.0407417i	0.181991	+	0.983300i	$0.441746\pi$
$432$		0			0
$433$	−9.82888	+	17.0241i	−0.472346	+	0.818127i	−0.999499	−	0.0316430i	$-0.989926\pi$
$433$	−9.82888	+	17.0241i	−0.472346	+	0.818127i	0.527153	+	0.849770i	$0.323259\pi$
$434$	−2.03572	+	0.0168634i	−0.0977174	+	0.000809471i
$435$		0			0
$436$	29.4452	+	7.88981i	1.41017	+	0.377854i
$437$	−0.428956	+	1.60089i	−0.0205197	+	0.0765807i
$438$		0			0
$439$	−37.8075			−1.80445			−0.902226	−	0.431263i	$-0.858068\pi$
$439$	−37.8075			−1.80445			−0.902226	+	0.431263i	$0.858068\pi$
$440$	−0.123988	+	0.462731i	−0.00591091	+	0.0220598i
$441$		0			0
$442$	−2.51436	+	7.73033i	−0.119596	+	0.367694i
$443$	−2.31623	+	4.01183i	−0.110047	+	0.190608i	−0.915789	−	0.401659i	$-0.868434\pi$
$443$	−2.31623	+	4.01183i	−0.110047	+	0.190608i	0.805742	+	0.592267i	$0.201767\pi$
$444$		0			0
$445$	−3.13163	+	5.42414i	−0.148454	+	0.257129i
$446$	2.44928	+	4.24228i	0.115977	+	0.200878i
$447$		0			0
$448$	10.8099	+	6.12225i	0.510718	+	0.289249i
$449$	3.43957	+	12.8367i	0.162324	+	0.605800i	0.998366	+	0.0571356i	$0.0181967\pi$
$449$	3.43957	+	12.8367i	0.162324	+	0.605800i	−0.836043	+	0.548664i	$0.815137\pi$
$450$		0			0
$451$			0.272315i			0.0128228i
$452$	8.81800	+	5.09107i	0.414764	+	0.239464i
$453$		0			0
$454$	4.53855			0.213005
$455$	−7.62933	−	34.5363i	−0.357668	−	1.61909i
$456$		0			0
$457$	−0.254661	−	0.254661i	−0.0119125	−	0.0119125i	0.701125	−	0.713038i	$-0.252681\pi$
$457$	−0.254661	−	0.254661i	−0.0119125	−	0.0119125i	−0.713038	+	0.701125i	$0.752681\pi$
$458$	5.23651	+	3.02330i	0.244686	+	0.141270i
$459$		0			0
$460$	0.793943	+	2.96304i	0.0370178	+	0.138152i
$461$	6.55396	+	24.4597i	0.305249	+	1.13920i	0.932731	+	0.360573i	$0.117419\pi$
$461$	6.55396	+	24.4597i	0.305249	+	1.13920i	−0.627483	+	0.778631i	$0.715915\pi$
$462$		0			0
$463$	18.4801	−	18.4801i	0.858844	−	0.858844i	−0.132358	−	0.991202i	$-0.542255\pi$
$463$	18.4801	−	18.4801i	0.858844	−	0.858844i	0.991202	+	0.132358i	$0.0422548\pi$
$464$	2.21993	+	3.84504i	0.103058	+	0.178501i
$465$		0			0
$466$	−1.32762	−	4.95475i	−0.0615009	−	0.229525i
$467$	15.6223	−	27.0587i	0.722916	−	1.25213i	−0.236911	−	0.971531i	$-0.576135\pi$
$467$	15.6223	−	27.0587i	0.722916	−	1.25213i	0.959826	−	0.280595i	$-0.0905318\pi$
$468$		0			0
$469$	6.60715	−	25.5014i	0.305090	−	1.17754i
$470$	−3.36156	+	12.5455i	−0.155057	+	0.578682i
$471$		0			0
$472$	−10.5506			−0.485631
$473$	0.226405	−	0.844955i	0.0104101	−	0.0388511i
$474$		0			0
$475$	31.3700	−	8.40556i	1.43935	−	0.385673i
$476$	−25.1349	−	14.2353i	−1.15206	−	0.652475i
$477$		0			0
$478$			7.82307i			0.357819i
$479$	−28.7805	+	7.71172i	−1.31502	+	0.352357i	−0.847108	−	0.531420i	$-0.821659\pi$
$479$	−28.7805	+	7.71172i	−1.31502	+	0.352357i	−0.467907	+	0.883778i	$0.654992\pi$
$480$		0			0
$481$	9.09030	+	2.95671i	0.414482	+	0.134814i
$482$			0.390709i			0.0177963i
$483$		0			0
$484$	−10.1871	−	17.6447i	−0.463052	−	0.802030i
$485$	−5.60885	+	3.23827i	−0.254685	+	0.147042i
$486$		0			0
$487$	−10.1388	−	10.1388i	−0.459433	−	0.459433i	0.439037	−	0.898469i	$-0.355320\pi$
$487$	−10.1388	−	10.1388i	−0.459433	−	0.459433i	−0.898469	+	0.439037i	$0.855320\pi$
$488$	0.0487462	−	0.181923i	0.00220664	−	0.00823528i
$489$		0			0
$490$	−9.93246	+	0.164568i	−0.448703	+	0.00743443i
$491$	−16.5417	+	9.55034i	−0.746515	+	0.431001i	−0.824433	−	0.565959i	$-0.808506\pi$
$491$	−16.5417	+	9.55034i	−0.746515	+	0.431001i	0.0779183	+	0.996960i	$0.475173\pi$
$492$		0			0
$493$	−4.16117	−	7.20736i	−0.187410	−	0.324603i
$494$	2.79203	−	4.29646i	0.125619	−	0.193307i
$495$		0			0
$496$	6.10213	+	1.63506i	0.273994	+	0.0734164i
$497$	6.75498	−	26.0719i	0.303002	−	1.16949i
$498$		0			0
$499$	−22.3030	+	5.97607i	−0.998420	+	0.267526i	−0.720783	−	0.693160i	$-0.756218\pi$
$499$	−22.3030	+	5.97607i	−0.998420	+	0.267526i	−0.277636	+	0.960686i	$0.589551\pi$
$500$	18.2074	−	18.2074i	0.814259	−	0.814259i
$501$		0			0
$502$	4.13682	−	1.10846i	0.184635	−	0.0494729i
$503$	−10.9978	−	6.34957i	−0.490367	−	0.283113i	0.234360	−	0.972150i	$-0.424701\pi$
$503$	−10.9978	−	6.34957i	−0.490367	−	0.283113i	−0.724727	+	0.689036i	$0.758034\pi$
$504$		0			0
$505$	−24.4334	−	6.54690i	−1.08727	−	0.291333i
$506$	−0.0129615	−	0.00748334i	−0.000576210	−	0.000332675i
$507$		0			0
$508$	−15.7741	−	27.3216i	−0.699864	−	1.21220i
$509$	−7.68399	+	7.68399i	−0.340587	+	0.340587i	−0.856588	−	0.516001i	$-0.827420\pi$
$509$	−7.68399	+	7.68399i	−0.340587	+	0.340587i	0.516001	+	0.856588i	$0.327420\pi$
$510$		0			0
$511$	17.2793	+	16.9954i	0.764391	+	0.751831i
$512$	15.7822	+	15.7822i	0.697483	+	0.697483i
$513$		0			0
$514$	2.55130	+	2.55130i	0.112533	+	0.112533i
$515$	−35.8155	−	9.59673i	−1.57822	−	0.422883i
$516$		0			0
$517$	0.400874	+	0.694333i	0.0176304	+	0.0305367i
$518$	1.32309	−	2.33613i	0.0581330	−	0.102644i
$519$		0			0
$520$	1.03798	−	19.6899i	0.0455182	−	0.863458i
$521$	28.6041	−	16.5146i	1.25317	−	0.723518i	0.281432	−	0.959581i	$-0.409191\pi$
$521$	28.6041	−	16.5146i	1.25317	−	0.723518i	0.971738	+	0.236064i	$0.0758574\pi$
$522$		0			0
$523$		−	15.6359i		−	0.683712i	−0.939752	−	0.341856i	$-0.888945\pi$
$523$		−	15.6359i		−	0.683712i	0.939752	−	0.341856i	$-0.111055\pi$
$524$	−2.52085	+	4.36624i	−0.110124	+	0.190740i
$525$		0			0
$526$	5.08247	−	1.36184i	0.221606	−	0.0593792i
$527$	−11.4382	−	3.06485i	−0.498255	−	0.133507i
$528$		0			0
$529$	22.8008			0.991337
$530$	17.8274			0.774375
$531$		0			0
$532$	12.9811	+	12.7678i	0.562804	+	0.553556i
$533$	−2.32692	−	10.9639i	−0.100790	−	0.474899i
$534$		0			0
$535$	−0.0574687	−	0.214476i	−0.00248459	−	0.00927261i
$536$	7.34285	−	12.7182i	0.317163	−	0.549342i
$537$		0			0
$538$	−6.38313	+	6.38313i	−0.275196	+	0.275196i
$539$	−0.426362	+	0.440728i	−0.0183647	+	0.0189835i
$540$		0			0
$541$	3.18712	+	11.8945i	0.137025	+	0.511384i	0.999981	+	0.00610564i	$0.00194350\pi$
$541$	3.18712	+	11.8945i	0.137025	+	0.511384i	−0.862956	+	0.505278i	$0.831390\pi$
$542$		−	3.47943i		−	0.149454i
$543$		0			0
$544$	−17.2965	−	17.2965i	−0.741579	−	0.741579i
$545$	60.9789			2.61205
$546$		0			0
$547$	3.99754			0.170922			0.0854611	−	0.996342i	$-0.472764\pi$
$547$	3.99754			0.170922			0.0854611	+	0.996342i	$0.472764\pi$
$548$	−5.64583	−	5.64583i	−0.241178	−	0.241178i
$549$		0			0
$550$			0.293278i			0.0125054i
$551$	1.35773	+	5.06711i	0.0578412	+	0.215866i
$552$		0			0
$553$	−4.71631	−	8.01482i	−0.200558	−	0.340825i
$554$	−3.42711	+	3.42711i	−0.145604	+	0.145604i
$555$		0			0
$556$	−12.9753	+	22.4738i	−0.550273	+	0.953101i
$557$	3.31424	+	12.3689i	0.140429	+	0.524088i	0.999916	+	0.0129309i	$0.00411614\pi$
$557$	3.31424	+	12.3689i	0.140429	+	0.524088i	−0.859488	+	0.511157i	$0.829217\pi$
$558$		0			0
$559$	−1.89536	+	35.9541i	−0.0801653	+	1.52070i
$560$	29.8410	+	7.73152i	1.26101	+	0.326717i
$561$		0			0
$562$	12.7689			0.538621
$563$	10.0474			0.423447			0.211723	−	0.977330i	$-0.432092\pi$
$563$	10.0474			0.423447			0.211723	+	0.977330i	$0.432092\pi$
$564$		0			0
$565$	19.6740	+	5.27162i	0.827690	+	0.221779i
$566$	−8.44371	+	2.26249i	−0.354916	+	0.0950993i
$567$		0			0
$568$	7.50713	−	13.0027i	0.314992	−	0.545583i
$569$			5.89515i			0.247138i	0.992336	+	0.123569i	$0.0394340\pi$
$569$			5.89515i			0.247138i	−0.992336	+	0.123569i	$0.960566\pi$
$570$		0			0
$571$	0.761139	−	0.439444i	0.0318527	−	0.0183901i	−0.483989	−	0.875074i	$-0.660813\pi$
$571$	0.761139	−	0.439444i	0.0318527	−	0.0183901i	0.515842	+	0.856684i	$0.327479\pi$
$572$	−0.391596	−	0.435180i	−0.0163734	−	0.0181958i
$573$		0			0
$574$	−3.14782	+	0.0260759i	−0.131388	+	0.00108839i
$575$	1.95218	+	3.38128i	0.0814117	+	0.141009i
$576$		0			0
$577$	−0.150636	−	0.0403629i	−0.00627107	−	0.00168033i	0.255682	−	0.966761i	$-0.417700\pi$
$577$	−0.150636	−	0.0403629i	−0.00627107	−	0.00168033i	−0.261953	+	0.965081i	$0.584367\pi$
$578$	4.78966	+	4.78966i	0.199224	+	0.199224i
$579$		0			0
$580$	6.86560	+	6.86560i	0.285079	+	0.285079i
$581$	−2.17613	−	7.86039i	−0.0902810	−	0.326104i
$582$		0			0
$583$	0.778156	−	0.778156i	0.0322279	−	0.0322279i
$584$	6.75564	+	11.7011i	0.279550	+	0.484195i
$585$		0			0
$586$	−3.97256	−	2.29356i	−0.164105	−	0.0947460i
$587$	38.7558	+	10.3846i	1.59962	+	0.428617i	0.944928	−	0.327278i	$-0.106131\pi$
$587$	38.7558	+	10.3846i	1.59962	+	0.428617i	0.654693	+	0.755895i	$0.272798\pi$
$588$		0			0
$589$	6.46420	+	3.73211i	0.266353	+	0.153779i
$590$	−9.80544	+	2.62736i	−0.403684	+	0.108167i
$591$		0			0
$592$	−5.89115	+	5.89115i	−0.242125	+	0.242125i
$593$	2.34322	−	0.627863i	0.0962244	−	0.0257833i	−0.210386	−	0.977618i	$-0.567472\pi$
$593$	2.34322	−	0.627863i	0.0962244	−	0.0257833i	0.306610	+	0.951835i	$0.400805\pi$
$594$		0			0
$595$	−55.9357	−	14.4924i	−2.29314	−	0.594131i
$596$	−16.4181	−	4.39921i	−0.672510	−	0.180199i
$597$		0			0
$598$	0.585800	+	0.190537i	0.0239551	+	0.00779164i
$599$	−5.34796	−	9.26293i	−0.218512	−	0.378473i	0.735842	−	0.677154i	$-0.236787\pi$
$599$	−5.34796	−	9.26293i	−0.218512	−	0.378473i	−0.954353	+	0.298681i	$0.903453\pi$
$600$		0			0
$601$	−30.2246	+	17.4502i	−1.23289	+	0.711807i	−0.967630	−	0.252371i	$-0.918790\pi$
$601$	−30.2246	+	17.4502i	−1.23289	+	0.711807i	−0.265255	+	0.964178i	$0.585456\pi$
$602$	9.78896	+	2.53622i	0.398968	+	0.103369i
$603$		0			0
$604$	−3.64120	+	13.5892i	−0.148159	+	0.552935i
$605$	−28.8188	−	28.8188i	−1.17165	−	1.17165i
$606$		0			0
$607$	−12.7887	+	7.38356i	−0.519078	+	0.299690i	−0.736557	−	0.676375i	$-0.763550\pi$
$607$	−12.7887	+	7.38356i	−0.519078	+	0.299690i	0.217480	+	0.976065i	$0.430216\pi$
$608$	7.70927	+	13.3528i	0.312652	+	0.541529i
$609$		0			0
$610$		−	0.181214i		−	0.00733712i
$611$	−22.0730	−	24.5297i	−0.892977	−	0.992365i
$612$		0			0
$613$	13.1947	−	3.53552i	0.532930	−	0.142798i	0.0176892	−	0.999844i	$-0.494369\pi$
$613$	13.1947	−	3.53552i	0.532930	−	0.142798i	0.515241	+	0.857045i	$0.327702\pi$
$614$		−	10.2760i		−	0.414704i
$615$		0			0
$616$	−0.294622	+	0.173370i	−0.0118707	+	0.00698527i
$617$	14.8331	−	3.97453i	0.597160	−	0.160008i	0.0524363	−	0.998624i	$-0.483301\pi$
$617$	14.8331	−	3.97453i	0.597160	−	0.160008i	0.544723	+	0.838616i	$0.316635\pi$
$618$		0			0
$619$	1.22023	−	4.55397i	0.0490453	−	0.183039i	−0.937058	−	0.349174i	$-0.886462\pi$
$619$	1.22023	−	4.55397i	0.0490453	−	0.183039i	0.986103	+	0.166135i	$0.0531287\pi$
$620$	13.8153			0.554837
$621$		0			0
$622$	−2.95191	+	11.0167i	−0.118361	+	0.441728i
$623$	−4.30736	+	1.19248i	−0.172571	+	0.0477758i
$624$		0			0
$625$	3.88665	−	6.73187i	0.155466	−	0.269275i
$626$	1.61994	+	6.04570i	0.0647458	+	0.241635i
$627$		0			0
$628$	0.468734	+	0.811872i	0.0187045	+	0.0323972i
$629$	11.0427	−	11.0427i	0.440302	−	0.440302i
$630$		0			0
$631$	−4.57205	−	17.0631i	−0.182011	−	0.679273i	−0.995251	−	0.0973445i	$-0.968965\pi$
$631$	−4.57205	−	17.0631i	−0.182011	−	0.679273i	0.813240	−	0.581928i	$-0.197702\pi$
$632$	−1.34177	−	5.00757i	−0.0533729	−	0.199190i
$633$		0			0
$634$	5.66090	+	3.26832i	0.224823	+	0.129802i
$635$	−44.6241	−	44.6241i	−1.77085	−	1.77085i
$636$		0			0
$637$	13.4001	−	21.3878i	0.530931	−	0.847415i
$638$	−0.0473725			−0.00187549
$639$		0			0
$640$	32.4386	+	18.7284i	1.28225	+	0.740306i
$641$			37.2148i			1.46990i	0.678124	+	0.734948i	$0.262793\pi$
$641$			37.2148i			1.46990i	−0.678124	+	0.734948i	$0.737207\pi$
$642$		0			0
$643$	2.17224	+	8.10691i	0.0856648	+	0.319705i	0.995439	−	0.0953976i	$-0.0304122\pi$
$643$	2.17224	+	8.10691i	0.0856648	+	0.319705i	−0.909774	+	0.415103i	$0.863746\pi$
$644$	−1.07875	+	1.90471i	−0.0425085	+	0.0750560i
$645$		0			0
$646$	−4.18554	−	7.24956i	−0.164678	−	0.285230i
$647$	−12.9222	+	22.3819i	−0.508024	+	0.879923i	0.491933	+	0.870633i	$0.336290\pi$
$647$	−12.9222	+	22.3819i	−0.508024	+	0.879923i	−0.999957	+	0.00928983i	$0.997043\pi$
$648$		0			0
$649$	−0.313319	+	0.542684i	−0.0122988	+	0.0213022i
$650$	−2.50605	−	11.8079i	−0.0982955	−	0.463144i
$651$		0			0
$652$	−2.13048	+	7.95107i	−0.0834362	+	0.311388i
$653$	−32.0109			−1.25268			−0.626341	−	0.779549i	$-0.715448\pi$
$653$	−32.0109			−1.25268			−0.626341	+	0.779549i	$0.715448\pi$
$654$		0			0
$655$	−2.61025	+	9.74159i	−0.101991	+	0.380636i
$656$	9.43572	+	2.52829i	0.368403	+	0.0987133i
$657$		0			0
$658$	−7.98777	+	4.70039i	−0.311396	+	0.183240i
$659$	−1.93932	+	3.35900i	−0.0755452	+	0.130848i	−0.901323	−	0.433147i	$-0.857403\pi$
$659$	−1.93932	+	3.35900i	−0.0755452	+	0.130848i	0.825778	+	0.563995i	$0.190736\pi$
$660$		0			0
$661$	−8.97619	+	2.40516i	−0.349133	+	0.0935500i	−0.429124	−	0.903246i	$-0.641178\pi$
$661$	−8.97619	+	2.40516i	−0.349133	+	0.0935500i	0.0799905	+	0.996796i	$0.474511\pi$
$662$	7.21829	−	4.16748i	0.280547	−	0.161974i
$663$		0			0
$664$		−	4.54677i		−	0.176449i
$665$	31.6925	+	17.9493i	1.22898	+	0.696044i
$666$		0			0
$667$	−0.546170	+	0.315331i	−0.0211478	+	0.0122097i
$668$	−14.3694	−	3.85027i	−0.555969	−	0.148972i
$669$		0			0
$670$	3.65710	−	13.6485i	0.141286	−	0.527287i
$671$	−0.00790985	−	0.00790985i	−0.000305356	−	0.000305356i
$672$		0			0
$673$	24.3896	−	14.0814i	0.940151	−	0.542797i	0.0501436	−	0.998742i	$-0.484032\pi$
$673$	24.3896	−	14.0814i	0.940151	−	0.542797i	0.890008	+	0.455945i	$0.150699\pi$
$674$	−6.13166	+	6.13166i	−0.236183	+	0.236183i
$675$		0			0
$676$	19.4850	+	14.1750i	0.749422	+	0.545192i
$677$	24.5782	+	14.1902i	0.944617	+	0.545375i	0.891405	−	0.453209i	$-0.149721\pi$
$677$	24.5782	+	14.1902i	0.944617	+	0.545375i	0.0532122	+	0.998583i	$0.483054\pi$
$678$		0			0
$679$	−4.47386	−	1.15913i	−0.171691	−	0.0444835i
$680$	−27.8966	−	16.1061i	−1.06979	−	0.617641i
$681$		0			0
$682$	−0.0476627	+	0.0476627i	−0.00182510	+	0.00182510i
$683$	−17.2778	+	17.2778i	−0.661118	+	0.661118i	−0.955644	−	0.294526i	$-0.904838\pi$
$683$	−17.2778	+	17.2778i	−0.661118	+	0.661118i	0.294526	+	0.955644i	$0.404838\pi$
$684$		0			0
$685$	−13.8319	−	7.98586i	−0.528490	−	0.305124i
$686$	−5.13543	−	4.88633i	−0.196072	−	0.186561i
$687$		0			0
$688$	−27.1757	−	15.6899i	−1.03606	−	0.598172i
$689$	−24.6807	+	37.9793i	−0.940259	+	1.44690i
$690$		0			0
$691$	−22.9402	+	22.9402i	−0.872688	+	0.872688i	−0.992765	−	0.120077i	$-0.961686\pi$
$691$	−22.9402	+	22.9402i	−0.872688	+	0.872688i	0.120077	+	0.992765i	$0.461686\pi$
$692$	−2.02749	+	1.17057i	−0.0770738	+	0.0444986i
$693$		0			0
$694$	−3.21279	−	3.21279i	−0.121956	−	0.121956i
$695$	−13.4354	+	50.1416i	−0.509634	+	1.90198i
$696$		0			0
$697$	−17.6869	−	4.73918i	−0.669937	−	0.179509i
$698$	−6.89372	+	3.98009i	−0.260931	+	0.150649i
$699$		0			0
$700$	42.8923	−	0.355311i	1.62118	−	0.0134295i
$701$			49.4461i			1.86755i	0.357856	+	0.933777i	$0.383508\pi$
$701$			49.4461i			1.86755i	−0.357856	+	0.933777i	$0.616492\pi$
$702$		0			0
$703$	−8.52496	+	4.92189i	−0.321525	+	0.185632i
$704$	0.397317	−	0.106461i	0.0149745	−	0.00401240i
$705$		0			0
$706$	5.34960	−	9.26578i	0.201335	−	0.348722i
$707$	−9.15437	−	15.5568i	−0.344286	−	0.585074i
$708$		0			0
$709$	17.2101	+	4.61145i	0.646341	+	0.173186i	0.567074	−	0.823667i	$-0.308075\pi$
$709$	17.2101	+	4.61145i	0.646341	+	0.173186i	0.0792669	+	0.996853i	$0.474742\pi$
$710$	3.73892	−	13.9539i	0.140319	−	0.523679i
$711$		0			0
$712$	−2.49156			−0.0933750
$713$	−0.232253	+	0.866779i	−0.00869794	+	0.0324611i
$714$		0			0
$715$	−0.981949	−	0.638115i	−0.0367228	−	0.0238641i
$716$	−1.56641	+	2.71311i	−0.0585396	+	0.101394i
$717$		0			0
$718$	3.00282	−	5.20104i	0.112064	−	0.194101i
$719$	13.9168	+	24.1047i	0.519011	+	0.898953i	0.999756	+	0.0220927i	$0.00703289\pi$
$719$	13.9168	+	24.1047i	0.519011	+	0.898953i	−0.480745	+	0.876860i	$0.659634\pi$
$720$		0			0
$721$	−13.4189	−	22.8038i	−0.499745	−	0.849260i
$722$	−0.516523	−	1.92769i	−0.0192230	−	0.0717412i
$723$		0			0
$724$			15.3994i			0.572312i
$725$	10.7024	+	6.17904i	0.397478	+	0.229484i
$726$		0			0
$727$	47.3797			1.75722			0.878608	−	0.477544i	$-0.158473\pi$
$727$	47.3797			1.75722			0.878608	+	0.477544i	$0.158473\pi$
$728$	10.3806	−	9.49773i	0.384730	−	0.352009i
$729$		0			0
$730$	9.19237	+	9.19237i	0.340225	+	0.340225i
$731$	50.9397	+	29.4101i	1.88407	+	1.08777i
$732$		0			0
$733$	7.74821	+	28.9167i	0.286187	+	1.06806i	0.947968	+	0.318366i	$0.103134\pi$
$733$	7.74821	+	28.9167i	0.286187	+	1.06806i	−0.661781	+	0.749697i	$0.730199\pi$
$734$	0.474726	+	1.77170i	0.0175225	+	0.0653947i
$735$		0			0
$736$	−1.31072	+	1.31072i	−0.0483136	+	0.0483136i
$737$	−0.436117	−	0.755377i	−0.0160646	−	0.0278247i
$738$		0			0
$739$	3.28151	+	12.2468i	0.120712	+	0.450505i	0.999651	−	0.0264308i	$-0.00841417\pi$
$739$	3.28151	+	12.2468i	0.120712	+	0.450505i	−0.878938	+	0.476936i	$0.841748\pi$
$740$	−9.10979	+	15.7786i	−0.334883	+	0.580034i
$741$		0			0
$742$	9.06962	+	8.92060i	0.332956	+	0.327485i
$743$	5.17566	−	19.3158i	0.189877	−	0.708629i	−0.803657	−	0.595093i	$-0.797115\pi$
$743$	5.17566	−	19.3158i	0.189877	−	0.708629i	0.993534	−	0.113537i	$-0.0362180\pi$
$744$		0			0
$745$	−34.0006			−1.24569
$746$	0.186613	−	0.696448i	0.00683238	−	0.0254988i
$747$		0			0
$748$	−0.923835	+	0.247541i	−0.0337788	+	0.00905099i
$749$	0.0780838	−	0.137870i	0.00285312	−	0.00503766i
$750$		0			0
$751$			31.9306i			1.16516i	0.812772	+	0.582582i	$0.197958\pi$
$751$			31.9306i			1.16516i	−0.812772	+	0.582582i	$0.802042\pi$
$752$	27.7806	−	7.44379i	1.01305	−	0.271447i
$753$		0			0
$754$	1.90730	−	0.404797i	0.0694599	−	0.0147418i
$755$			28.1422i			1.02420i
$756$		0			0
$757$	0.983838	+	1.70406i	0.0357582	+	0.0619350i	0.883351	−	0.468713i	$-0.155282\pi$
$757$	0.983838	+	1.70406i	0.0357582	+	0.0619350i	−0.847592	+	0.530648i	$0.821949\pi$
$758$	−0.472085	+	0.272558i	−0.0171469	+	0.00989976i
$759$		0			0
$760$	14.3574	+	14.3574i	0.520799	+	0.520799i
$761$	−1.79980	+	6.71695i	−0.0652427	+	0.243489i	−0.990844	−	0.135010i	$-0.956893\pi$
$761$	−1.79980	+	6.71695i	−0.0652427	+	0.243489i	0.925601	+	0.378500i	$0.123560\pi$
$762$		0			0
$763$	31.0227	+	30.5129i	1.12310	+	1.10464i
$764$	33.1117	−	19.1171i	1.19794	−	0.691631i
$765$		0			0
$766$	−2.09428	−	3.62739i	−0.0756693	−	0.131063i
$767$	7.97756	−	24.5267i	0.288053	−	0.885609i
$768$		0			0
$769$	2.45316	+	0.657322i	0.0884631	+	0.0237036i	0.302779	−	0.953061i	$-0.402086\pi$
$769$	2.45316	+	0.657322i	0.0884631	+	0.0237036i	−0.214316	+	0.976764i	$0.568752\pi$
$770$	−0.230640	+	0.234494i	−0.00831171	+	0.00845056i
$771$		0			0
$772$	−24.0035	+	6.43171i	−0.863904	+	0.231482i
$773$	6.08636	−	6.08636i	0.218911	−	0.218911i	−0.589128	−	0.808039i	$-0.700529\pi$
$773$	6.08636	−	6.08636i	0.218911	−	0.218911i	0.808039	+	0.589128i	$0.200529\pi$
$774$		0			0
$775$	16.9849	−	4.55109i	0.610115	−	0.163480i
$776$	−2.23123	−	1.28820i	−0.0800964	−	0.0462437i
$777$		0			0
$778$	−10.2450	−	2.74514i	−0.367302	−	0.0984181i
$779$	9.99560	+	5.77096i	0.358129	+	0.206766i
$780$		0			0
$781$	−0.445875	−	0.772278i	−0.0159547	−	0.0276343i
$782$	0.711618	−	0.711618i	0.0254474	−	0.0254474i
$783$		0			0
$784$	11.3127	+	18.8654i	0.404026	+	0.673764i
$785$	1.32602	+	1.32602i	0.0473277	+	0.0473277i
$786$		0			0
$787$	4.29200	+	4.29200i	0.152993	+	0.152993i	0.779453	−	0.626460i	$-0.215497\pi$
$787$	4.29200	+	4.29200i	0.152993	+	0.152993i	−0.626460	+	0.779453i	$0.715497\pi$
$788$	29.6086	+	7.93361i	1.05476	+	0.282623i
$789$		0			0
$790$	−2.49402	−	4.31976i	−0.0887331	−	0.153690i
$791$	7.37119	+	12.5265i	0.262089	+	0.445390i
$792$		0			0
$793$	0.386055	+	0.250876i	0.0137092	+	0.00890885i
$794$	−4.16660	+	2.40559i	−0.147867	+	0.0853710i
$795$		0			0
$796$		−	24.0254i		−	0.851557i
$797$	−0.799767	+	1.38524i	−0.0283292	+	0.0490676i	−0.879842	−	0.475266i	$-0.842352\pi$
$797$	−0.799767	+	1.38524i	−0.0283292	+	0.0490676i	0.851513	+	0.524333i	$0.175685\pi$
$798$		0			0
$799$	−52.0736	+	13.9531i	−1.84223	+	0.493624i
$800$	35.0850	+	9.40099i	1.24044	+	0.332375i
$801$		0			0
$802$	9.46791			0.334324
$803$	0.802482			0.0283190
$804$		0			0
$805$	−1.09823	+	4.23878i	−0.0387074	+	0.149397i
$806$	1.51171	−	2.32626i	0.0532478	−	0.0819392i
$807$		0			0
$808$	−2.60439	−	9.71971i	−0.0916221	−	0.341938i
$809$	21.3018	−	36.8958i	0.748932	−	1.29719i	−0.199403	−	0.979918i	$-0.563900\pi$
$809$	21.3018	−	36.8958i	0.748932	−	1.29719i	0.948335	−	0.317270i	$-0.102766\pi$
$810$		0			0
$811$	36.5518	−	36.5518i	1.28351	−	1.28351i	0.344850	−	0.938658i	$-0.387930\pi$
$811$	36.5518	−	36.5518i	1.28351	−	1.28351i	0.938658	−	0.344850i	$-0.112070\pi$
$812$	0.0573925	+	6.92829i	0.00201408	+	0.243135i
$813$		0			0
$814$	−0.0230074	−	0.0858647i	−0.000806408	−	0.00300956i
$815$			16.4661i			0.576782i
$816$		0			0
$817$	−26.2169	−	26.2169i	−0.917215	−	0.917215i
$818$	4.35897			0.152408
$819$		0			0
$820$	21.3626			0.746016
$821$	14.6049	+	14.6049i	0.509714	+	0.509714i	0.914439	−	0.404725i	$-0.132633\pi$
$821$	14.6049	+	14.6049i	0.509714	+	0.509714i	−0.404725	+	0.914439i	$0.632633\pi$
$822$		0			0
$823$		−	51.9954i		−	1.81245i	−0.422799	−	0.906224i	$-0.638952\pi$
$823$		−	51.9954i		−	1.81245i	0.422799	−	0.906224i	$-0.361048\pi$
$824$	−3.81763	−	14.2476i	−0.132993	−	0.496338i
$825$		0			0
$826$	−6.30316	−	3.56985i	−0.219315	−	0.124211i
$827$	−30.9176	+	30.9176i	−1.07511	+	1.07511i	−0.0781709	+	0.996940i	$0.524908\pi$
$827$	−30.9176	+	30.9176i	−1.07511	+	1.07511i	−0.996940	+	0.0781709i	$0.975092\pi$
$828$		0			0
$829$	22.5718	−	39.0955i	0.783951	−	1.35784i	−0.145673	−	0.989333i	$-0.546535\pi$
$829$	22.5718	−	39.0955i	0.783951	−	1.35784i	0.929624	−	0.368510i	$-0.120132\pi$
$830$	−1.13226	−	4.22565i	−0.0393013	−	0.146674i
$831$		0			0
$832$	−15.0870	+	7.68138i	−0.523048	+	0.266304i
$833$	−21.2052	−	35.3624i	−0.734718	−	1.22523i
$834$		0			0
$835$	−29.7580			−1.02982
$836$	0.602867			0.0208506
$837$		0			0
$838$	−10.7679	−	2.88526i	−0.371972	−	0.0996696i
$839$	29.8547	−	7.99955i	1.03070	−	0.276175i	0.296445	−	0.955050i	$-0.404199\pi$
$839$	29.8547	−	7.99955i	1.03070	−	0.276175i	0.734254	+	0.678875i	$0.237532\pi$
$840$		0			0
$841$	13.5019	−	23.3860i	0.465583	−	0.806414i
$842$			13.5015i			0.465292i
$843$		0			0
$844$	−10.2427	+	5.91363i	−0.352569	+	0.203556i
$845$	44.9877	+	17.3009i	1.54763	+	0.595170i
$846$		0			0
$847$	−0.240909	−	29.0820i	−0.00827773	−	0.999268i
$848$	−19.7384	−	34.1879i	−0.677820	−	1.17402i
$849$		0			0
$850$	−19.0484	−	5.10401i	−0.653356	−	0.175066i
$851$	−0.836810	−	0.836810i	−0.0286855	−	0.0286855i
$852$		0			0
$853$	22.8132	+	22.8132i	0.781108	+	0.781108i	0.980018	−	0.198910i	$-0.0637401\pi$
$853$	22.8132	+	22.8132i	0.781108	+	0.781108i	−0.198910	+	0.980018i	$0.563740\pi$
$854$	0.0906766	−	0.0921915i	0.00310289	−	0.00315473i
$855$		0			0
$856$	0.0624583	−	0.0624583i	0.00213478	−	0.00213478i
$857$	−12.8148	−	22.1959i	−0.437745	−	0.758196i	0.559771	−	0.828648i	$-0.310889\pi$
$857$	−12.8148	−	22.1959i	−0.437745	−	0.758196i	−0.997515	+	0.0704518i	$0.977556\pi$
$858$		0			0
$859$	5.71477	+	3.29942i	0.194985	+	0.112575i	0.594314	−	0.804233i	$-0.297424\pi$
$859$	5.71477	+	3.29942i	0.194985	+	0.112575i	−0.399329	+	0.916808i	$0.630757\pi$
$860$	−66.2854	−	17.7611i	−2.26031	−	0.605649i
$861$		0			0
$862$	−1.08325	−	0.625415i	−0.0368956	−	0.0213017i
$863$	−42.9816	+	11.5169i	−1.46311	+	0.392039i	−0.900563	−	0.434725i	$-0.856846\pi$
$863$	−42.9816	+	11.5169i	−1.46311	+	0.392039i	−0.562548	+	0.826765i	$0.690179\pi$
$864$		0			0
$865$	−3.31148	+	3.31148i	−0.112594	+	0.112594i
$866$	−7.26766	+	1.94736i	−0.246965	+	0.0661741i
$867$		0			0
$868$	7.02848	+	6.91299i	0.238562	+	0.234642i
$869$	−0.297417	−	0.0796926i	−0.0100892	−	0.00270339i
$870$		0			0
$871$	24.0136	+	26.6863i	0.813669	+	0.904230i
$872$	12.1288	+	21.0078i	0.410735	+	0.711413i
$873$		0			0
$874$	−0.549368	+	0.317178i	−0.0185827	+	0.0107287i
$875$	35.4228	−	9.80670i	1.19751	−	0.331527i
$876$		0			0
$877$	−13.6400	+	50.9050i	−0.460589	+	1.71894i	0.210527	+	0.977588i	$0.432482\pi$
$877$	−13.6400	+	50.9050i	−0.460589	+	1.71894i	−0.671115	+	0.741353i	$0.734185\pi$
$878$	−10.2324	−	10.2324i	−0.345328	−	0.345328i
$879$		0			0
$880$	0.883923	−	0.510333i	0.0297970	−	0.0172033i
$881$	−14.4790	−	25.0784i	−0.487811	−	0.844914i	0.512090	−	0.858932i	$-0.328871\pi$
$881$	−14.4790	−	25.0784i	−0.487811	−	0.844914i	−0.999902	+	0.0140175i	$0.995538\pi$
$882$		0			0
$883$			56.4022i			1.89808i	0.315149	+	0.949042i	$0.397946\pi$
$883$			56.4022i			1.89808i	−0.315149	+	0.949042i	$0.602054\pi$
$884$	35.0801	−	17.8606i	1.17987	−	0.600717i
$885$		0			0
$886$	−1.71266	+	0.458907i	−0.0575381	+	0.0154173i
$887$			44.1021i			1.48080i	0.672165	+	0.740402i	$0.265365\pi$
$887$			44.1021i			1.48080i	−0.672165	+	0.740402i	$0.734635\pi$
$888$		0			0
$889$	−0.373032	−	45.0315i	−0.0125111	−	1.51031i
$890$	−2.31558	+	0.620459i	−0.0776186	+	0.0207978i
$891$		0			0
$892$	6.13962	−	22.9134i	0.205570	−	0.767196i
$893$	33.9817			1.13715
$894$		0			0
$895$	−1.62196	+	6.05325i	−0.0542163	+	0.202338i
$896$	7.13153	+	25.7598i	0.238248	+	0.860574i
$897$		0			0
$898$	−2.54328	+	4.40510i	−0.0848705	+	0.147000i
$899$	0.735125	+	2.74353i	0.0245178	+	0.0915017i
$900$		0			0
$901$	36.9988	+	64.0838i	1.23261	+	2.13494i
$902$	−0.0737008	+	0.0737008i	−0.00245397	+	0.00245397i
$903$		0			0
$904$	2.09708	+	7.82640i	0.0697478	+	0.260302i
$905$	7.97274	+	29.7547i	0.265023	+	0.989079i
$906$		0			0
$907$	8.56547	+	4.94528i	0.284412	+	0.164205i	0.635419	−	0.772168i	$-0.280827\pi$
$907$	8.56547	+	4.94528i	0.284412	+	0.164205i	−0.351007	+	0.936373i	$0.614161\pi$
$908$	−15.5410	−	15.5410i	−0.515746	−	0.515746i
$909$		0			0
$910$	7.28227	−	11.4120i	0.241405	−	0.378303i
$911$	−11.6807			−0.387000			−0.193500	−	0.981100i	$-0.561984\pi$
$911$	−11.6807			−0.387000			−0.193500	+	0.981100i	$0.561984\pi$
$912$		0			0
$913$	−0.233869	−	0.135024i	−0.00773993	−	0.00446865i
$914$		−	0.137846i		−	0.00455953i
$915$		0			0
$916$	−7.57851	−	28.2834i	−0.250401	−	0.934510i
$917$	−6.20250	+	3.64985i	−0.204825	+	0.120529i
$918$		0			0
$919$	4.44586	+	7.70045i	0.146655	+	0.254014i	0.929989	−	0.367587i	$-0.119816\pi$
$919$	4.44586	+	7.70045i	0.146655	+	0.254014i	−0.783334	+	0.621601i	$0.786483\pi$
$920$	−1.22051	+	2.11399i	−0.0402391	+	0.0696962i
$921$		0			0
$922$	−4.84612	+	8.39373i	−0.159598	+	0.276433i
$923$	24.5508	+	27.2833i	0.808101	+	0.898042i
$924$		0			0
$925$	−6.00195	+	22.3996i	−0.197343	+	0.736493i
$926$	10.0031			0.328724
$927$		0			0
$928$	−1.51852	+	5.66719i	−0.0498478	+	0.186035i
$929$	4.93637	+	1.32270i	0.161957	+	0.0433963i	0.338886	−	0.940827i	$-0.389950\pi$
$929$	4.93637	+	1.32270i	0.161957	+	0.0433963i	−0.176929	+	0.984224i	$0.556616\pi$
$930$		0			0
$931$	7.14184	+	24.9901i	0.234064	+	0.819017i
$932$	−12.4201	+	21.5122i	−0.406834	+	0.704657i
$933$		0			0
$934$	11.5514	−	3.09520i	0.377975	−	0.101278i
$935$	−1.65688	+	0.956598i	−0.0541856	+	0.0312841i
$936$		0			0
$937$			19.6472i			0.641846i	0.947105	+	0.320923i	$0.103993\pi$
$937$			19.6472i			0.641846i	−0.947105	+	0.320923i	$0.896007\pi$
$938$	8.69004	−	5.11364i	0.283740	−	0.166966i
$939$		0			0
$940$	54.4693	−	31.4479i	1.77659	−	1.02572i
$941$	−22.9818	−	6.15795i	−0.749185	−	0.200743i	−0.136028	−	0.990705i	$-0.543434\pi$
$941$	−22.9818	−	6.15795i	−0.749185	−	0.200743i	−0.613156	+	0.789962i	$0.710100\pi$
$942$		0			0
$943$	−0.359132	+	1.34030i	−0.0116950	+	0.0436462i
$944$	15.8950	+	15.8950i	0.517339	+	0.517339i
$945$		0			0
$946$	0.289959	−	0.167408i	0.00942739	−	0.00544291i
$947$	−38.2822	+	38.2822i	−1.24400	+	1.24400i	−0.285678	+	0.958326i	$0.592219\pi$
$947$	−38.2822	+	38.2822i	−1.24400	+	1.24400i	−0.958326	+	0.285678i	$0.907781\pi$
$948$		0			0
$949$	−32.3094	+	6.85719i	−1.04881	+	0.222594i
$950$	10.7651	+	6.21522i	0.349265	+	0.201648i
$951$		0			0
$952$	−6.13299	−	22.1530i	−0.198771	−	0.717981i
$953$	−33.5390	−	19.3637i	−1.08643	−	0.627253i	−0.153809	−	0.988101i	$-0.549154\pi$
$953$	−33.5390	−	19.3637i	−1.08643	−	0.627253i	−0.932625	+	0.360848i	$0.882487\pi$
$954$		0			0
$955$	54.0810	−	54.0810i	1.75002	−	1.75002i
$956$	26.7879	−	26.7879i	0.866383	−	0.866383i
$957$		0			0
$958$	−9.87648	−	5.70219i	−0.319094	−	0.184229i
$959$	−3.04091	−	10.9841i	−0.0981960	−	0.354693i
$960$		0			0
$961$	−23.3468	−	13.4793i	−0.753123	−	0.434816i
$962$	1.66003	+	3.26047i	0.0535216	+	0.105122i
$963$		0			0
$964$	1.33787	−	1.33787i	0.0430900	−	0.0430900i
$965$	−43.0497	+	24.8547i	−1.38582	+	0.800103i
$966$		0			0
$967$	1.90329	+	1.90329i	0.0612056	+	0.0612056i	0.737047	−	0.675841i	$-0.236220\pi$
$967$	1.90329	+	1.90329i	0.0612056	+	0.0612056i	−0.675841	+	0.737047i	$0.736220\pi$
$968$	4.19622	−	15.6605i	0.134871	−	0.503347i
$969$		0			0
$970$	−2.39444	−	0.641587i	−0.0768807	−	0.0206001i
$971$	0.711680	−	0.410888i	0.0228389	−	0.0131860i	−0.488537	−	0.872543i	$-0.662469\pi$
$971$	0.711680	−	0.410888i	0.0228389	−	0.0131860i	0.511376	+	0.859357i	$0.329136\pi$
$972$		0			0
$973$	−31.9253	+	18.7864i	−1.02348	+	0.602265i
$974$		−	5.48805i		−	0.175848i
$975$		0			0
$976$	−0.347516	+	0.200638i	−0.0111237	+	0.00642227i
$977$	−11.3007	+	3.02801i	−0.361540	+	0.0968745i	−0.435016	−	0.900423i	$-0.643257\pi$
$977$	−11.3007	+	3.02801i	−0.361540	+	0.0968745i	0.0734760	+	0.997297i	$0.476591\pi$
$978$		0			0
$979$	−0.0739911	+	0.128156i	−0.00236477	+	0.00409589i
$980$	34.5744	+	33.4474i	1.10444	+	1.06844i
$981$		0			0
$982$	−7.06169	−	1.89217i	−0.225348	−	0.0603817i
$983$	3.25273	−	12.1393i	0.103746	−	0.387185i	−0.894454	−	0.447160i	$-0.852435\pi$
$983$	3.25273	−	12.1393i	0.103746	−	0.387185i	0.998200	+	0.0599750i	$0.0191021\pi$
$984$		0			0
$985$	61.3174			1.95373
$986$	0.824439	−	3.07685i	0.0262555	−	0.0979868i
$987$		0			0
$988$	−24.2726	+	5.15149i	−0.772213	+	0.163891i
$989$	2.22868	−	3.86019i	0.0708679	−	0.122747i
$990$		0			0
$991$	5.39652	−	9.34706i	0.171426	−	0.296919i	−0.767492	−	0.641058i	$-0.778496\pi$
$991$	5.39652	−	9.34706i	0.171426	−	0.296919i	0.938919	+	0.344139i	$0.111829\pi$
$992$	4.17409	+	7.22973i	0.132527	+	0.229544i
$993$		0			0
$994$	8.88446	−	5.22805i	0.281798	−	0.165824i
$995$	−12.4387	−	46.4219i	−0.394334	−	1.47167i
$996$		0			0
$997$			35.3997i			1.12112i	0.828114	+	0.560560i	$0.189414\pi$
$997$			35.3997i			1.12112i	−0.828114	+	0.560560i	$0.810586\pi$
$998$	−7.65362	−	4.41882i	−0.242271	−	0.139875i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.b.271.5		28
3.2	odd	2		91.2.ba.a.89.3	yes	28
7.3	odd	6		819.2.gh.b.388.3		28
13.6	odd	12		819.2.gh.b.19.3		28
21.2	odd	6		637.2.bd.b.440.3		28
21.5	even	6		637.2.bd.a.440.3		28
21.11	odd	6		637.2.x.a.570.5		28
21.17	even	6		91.2.w.a.24.5	yes	28
21.20	even	2		637.2.bb.a.362.3		28
39.32	even	12		91.2.w.a.19.5	✓	28
91.45	even	12	inner	819.2.et.b.136.5		28
273.32	even	12		637.2.bb.a.227.3		28
273.110	odd	12		637.2.bd.b.97.3		28
273.149	even	12		637.2.bd.a.97.3		28
273.188	odd	12		637.2.x.a.19.5		28
273.227	odd	12		91.2.ba.a.45.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.5	✓	28	39.32	even	12
91.2.w.a.24.5	yes	28	21.17	even	6
91.2.ba.a.45.3	yes	28	273.227	odd	12
91.2.ba.a.89.3	yes	28	3.2	odd	2
637.2.x.a.19.5		28	273.188	odd	12
637.2.x.a.570.5		28	21.11	odd	6
637.2.bb.a.227.3		28	273.32	even	12
637.2.bb.a.362.3		28	21.20	even	2
637.2.bd.a.97.3		28	273.149	even	12
637.2.bd.a.440.3		28	21.5	even	6
637.2.bd.b.97.3		28	273.110	odd	12
637.2.bd.b.440.3		28	21.2	odd	6
819.2.et.b.136.5		28	91.45	even	12	inner
819.2.et.b.271.5		28	1.1	even	1	trivial
819.2.gh.b.19.3		28	13.6	odd	12
819.2.gh.b.388.3		28	7.3	odd	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.270646 + 0.270646i) q^{2} -1.85350i q^{4} +(-0.959617 - 3.58134i) q^{5} +(1.30385 - 2.30217i) q^{7} +(1.04293 - 1.04293i) q^{8} +O(q^{10})\)	\(q+(0.270646 + 0.270646i) q^{2} -1.85350i q^{4} +(-0.959617 - 3.58134i) q^{5} +(1.30385 - 2.30217i) q^{7} +(1.04293 - 1.04293i) q^{8} +(0.709559 - 1.22899i) q^{10} +(-0.0226729 - 0.0846164i) q^{11} +(1.63590 + 3.21307i) q^{13} +(0.975954 - 0.270190i) q^{14} -3.14247 q^{16} +5.89043 q^{17} +(-3.58643 - 0.960980i) q^{19} +(-6.63802 + 1.77865i) q^{20} +(0.0167648 - 0.0290374i) q^{22} -0.446373i q^{23} +(-7.57501 + 4.37343i) q^{25} +(-0.426856 + 1.31235i) q^{26} +(-4.26707 - 2.41669i) q^{28} +(-0.706429 - 1.22357i) q^{29} +(-1.94183 - 0.520311i) q^{31} +(-2.93637 - 2.93637i) q^{32} +(1.59422 + 1.59422i) q^{34} +(-9.49604 - 2.46033i) q^{35} +(1.87469 - 1.87469i) q^{37} +(-0.710566 - 1.23074i) q^{38} +(-4.73592 - 2.73428i) q^{40} +(-3.00264 - 0.804556i) q^{41} +(8.64788 + 4.99286i) q^{43} +(-0.156837 + 0.0420243i) q^{44} +(0.120809 - 0.120809i) q^{46} +(-8.84037 + 2.36877i) q^{47} +(-3.59995 - 6.00336i) q^{49} +(-3.23380 - 0.866493i) q^{50} +(5.95544 - 3.03214i) q^{52} +(6.28118 + 10.8793i) q^{53} +(-0.281283 + 0.162399i) q^{55} +(-1.04118 - 3.76084i) q^{56} +(0.139962 - 0.522347i) q^{58} +(-5.05813 - 5.05813i) q^{59} +(0.110587 - 0.0638473i) q^{61} +(-0.384727 - 0.666367i) q^{62} +4.69551i q^{64} +(9.93727 - 8.94203i) q^{65} +(9.61759 - 2.57703i) q^{67} -10.9179i q^{68} +(-1.90419 - 3.23594i) q^{70} +(9.83277 - 2.63468i) q^{71} +(-2.37094 + 8.84847i) q^{73} +1.01475 q^{74} +(-1.78118 + 6.64744i) q^{76} +(-0.224363 - 0.0581303i) q^{77} +(1.75744 - 3.04398i) q^{79} +(3.01557 + 11.2543i) q^{80} +(-0.594903 - 1.03040i) q^{82} +(2.17980 - 2.17980i) q^{83} +(-5.65256 - 21.0956i) q^{85} +(0.989217 + 3.69181i) q^{86} +(-0.111896 - 0.0646030i) q^{88} +(-1.19449 - 1.19449i) q^{89} +(9.53000 + 0.423256i) q^{91} -0.827354 q^{92} +(-3.03371 - 1.75151i) q^{94} +13.7664i q^{95} +(-0.452103 - 1.68727i) q^{97} +(0.650474 - 2.59910i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

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