LMFDB - Embedded newform 945.2.bv.e.73.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(73,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 9, 2]))

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

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

chi := DirichletCharacter("945.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bv (of order $12$, degree $4$, not 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.12
Character	$\chi$	$=$	945.73
Dual form			945.2.bv.e.712.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.974511 + 0.974511i) q^{2} +0.100655i q^{4} +(1.63908 + 1.52100i) q^{5} +(1.06331 - 2.42268i) q^{7} +(-2.04711 - 2.04711i) q^{8} +O(q^{10})$	\(q+(-0.974511 + 0.974511i) q^{2} +0.100655i q^{4} +(1.63908 + 1.52100i) q^{5} +(1.06331 - 2.42268i) q^{7} +(-2.04711 - 2.04711i) q^{8} +(-3.07953 + 0.115069i) q^{10} +(0.129642 + 0.224547i) q^{11} +(2.23686 + 0.599364i) q^{13} +(1.32472 + 3.39713i) q^{14} +3.78856 q^{16} +(5.06133 - 1.35618i) q^{17} +(-1.84029 - 3.18747i) q^{19} +(-0.153096 + 0.164981i) q^{20} +(-0.345161 - 0.0924857i) q^{22} +(3.96787 - 1.06319i) q^{23} +(0.373138 + 4.98606i) q^{25} +(-2.76393 + 1.59576i) q^{26} +(0.243854 + 0.107027i) q^{28} +(1.13026 + 0.652558i) q^{29} +1.03722i q^{31} +(0.402230 - 0.402230i) q^{32} +(-3.61071 + 6.25393i) q^{34} +(5.42773 - 2.35367i) q^{35} +(7.48615 + 2.00591i) q^{37} +(4.89961 + 1.31285i) q^{38} +(-0.241721 - 6.46902i) q^{40} +(5.05188 - 2.91670i) q^{41} +(-10.5875 + 2.83692i) q^{43} +(-0.0226017 + 0.0130491i) q^{44} +(-2.83065 + 4.90283i) q^{46} +(1.49360 + 1.49360i) q^{47} +(-4.73875 - 5.15211i) q^{49} +(-5.22260 - 4.49534i) q^{50} +(-0.0603289 + 0.225151i) q^{52} +(5.97951 - 1.60220i) q^{53} +(-0.129042 + 0.565235i) q^{55} +(-7.13621 + 2.78279i) q^{56} +(-1.73738 + 0.465529i) q^{58} -4.10944 q^{59} -11.5368i q^{61} +(-1.01078 - 1.01078i) q^{62} +8.36107i q^{64} +(2.75475 + 4.38466i) q^{65} +(0.710508 - 0.710508i) q^{67} +(0.136506 + 0.509447i) q^{68} +(-2.99571 + 7.58306i) q^{70} -11.9553 q^{71} +(1.89993 + 7.09062i) q^{73} +(-9.25012 + 5.34056i) q^{74} +(0.320835 - 0.185234i) q^{76} +(0.681855 - 0.0753191i) q^{77} +15.4772i q^{79} +(6.20973 + 5.76239i) q^{80} +(-2.08075 + 7.76547i) q^{82} +(3.81672 + 14.2442i) q^{83} +(10.3586 + 5.47538i) q^{85} +(7.55305 - 13.0823i) q^{86} +(0.194280 - 0.725065i) q^{88} +(3.16633 + 5.48424i) q^{89} +(3.83054 - 4.78188i) q^{91} +(0.107015 + 0.399386i) q^{92} -2.91106 q^{94} +(1.83176 - 8.02358i) q^{95} +(-0.694682 + 0.186139i) q^{97} +(9.63876 + 0.402817i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8}+O(q^{10}) $ 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8	$ 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8} - 24 q^{10} + 16 q^{11} - 152 q^{16} + 6 q^{17} - 60 q^{20} + 8 q^{22} - 8 q^{23} + 2 q^{25} + 36 q^{26} + 22 q^{28} - 12 q^{32} + 36 q^{35} - 4 q^{37} + 18 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 44 q^{50} + 54 q^{52} - 8 q^{53} - 148 q^{56} + 28 q^{58} + 124 q^{65} - 24 q^{67} - 42 q^{68} - 34 q^{70} + 40 q^{71} + 36 q^{73} + 96 q^{76} - 58 q^{77} - 36 q^{80} - 66 q^{82} + 138 q^{83} - 20 q^{85} + 16 q^{86} + 46 q^{88} - 48 q^{91} + 26 q^{92} - 188 q^{95} + 48 q^{97} - 102 q^{98}+O(q^{100}) $ 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8 - 24 * q^10 + 16 * q^11 - 152 * q^16 + 6 * q^17 - 60 * q^20 + 8 * q^22 - 8 * q^23 + 2 * q^25 + 36 * q^26 + 22 * q^28 - 12 * q^32 + 36 * q^35 - 4 * q^37 + 18 * q^38 - 6 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 44 * q^50 + 54 * q^52 - 8 * q^53 - 148 * q^56 + 28 * q^58 + 124 * q^65 - 24 * q^67 - 42 * q^68 - 34 * q^70 + 40 * q^71 + 36 * q^73 + 96 * q^76 - 58 * q^77 - 36 * q^80 - 66 * q^82 + 138 * q^83 - 20 * q^85 + 16 * q^86 + 46 * q^88 - 48 * q^91 + 26 * q^92 - 188 * q^95 + 48 * q^97 - 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.974511	+	0.974511i	−0.689084	+	0.689084i	−0.962029	−	0.272946i	$-0.912002\pi$
$2$	−0.974511	+	0.974511i	−0.689084	+	0.689084i	0.272946	+	0.962029i	$0.412002\pi$
$3$		0			0
$3$		0			0
$4$			0.100655i			0.0503274i
$5$	1.63908	+	1.52100i	0.733017	+	0.680210i
$5$	1.63908	+	1.52100i	0.733017	+	0.680210i
$6$		0			0
$7$	1.06331	−	2.42268i	0.401892	−	0.915687i
$7$	1.06331	−	2.42268i	0.401892	−	0.915687i
$8$	−2.04711	−	2.04711i	−0.723763	−	0.723763i
$9$		0			0
$10$	−3.07953	+	0.115069i	−0.973832	+	0.0363881i
$11$	0.129642	+	0.224547i	0.0390886	+	0.0677034i	0.884908	−	0.465766i	$-0.154221\pi$
$11$	0.129642	+	0.224547i	0.0390886	+	0.0677034i	−0.845819	+	0.533470i	$0.820888\pi$
$12$		0			0
$13$	2.23686	+	0.599364i	0.620393	+	0.166234i	0.555306	−	0.831646i	$-0.312601\pi$
$13$	2.23686	+	0.599364i	0.620393	+	0.166234i	0.0650865	+	0.997880i	$0.479268\pi$
$14$	1.32472	+	3.39713i	0.354047	+	0.907922i
$15$		0			0
$16$	3.78856			0.947140
$17$	5.06133	−	1.35618i	1.22755	−	0.328922i	0.413926	−	0.910310i	$-0.364157\pi$
$17$	5.06133	−	1.35618i	1.22755	−	0.328922i	0.813626	+	0.581389i	$0.197490\pi$
$18$		0			0
$19$	−1.84029	−	3.18747i	−0.422191	−	0.731257i	0.573962	−	0.818882i	$-0.305406\pi$
$19$	−1.84029	−	3.18747i	−0.422191	−	0.731257i	−0.996154	+	0.0876251i	$0.972072\pi$
$20$	−0.153096	+	0.164981i	−0.0342332	+	0.0368909i
$21$		0			0
$22$	−0.345161	−	0.0924857i	−0.0735886	−	0.0197180i
$23$	3.96787	−	1.06319i	0.827359	−	0.221690i	0.179797	−	0.983704i	$-0.442456\pi$
$23$	3.96787	−	1.06319i	0.827359	−	0.221690i	0.647561	+	0.762014i	$0.275789\pi$
$24$		0			0
$25$	0.373138	+	4.98606i	0.0746276	+	0.997211i
$26$	−2.76393	+	1.59576i	−0.542052	+	0.312954i
$27$		0			0
$28$	0.243854	+	0.107027i	0.0460842	+	0.0202262i
$29$	1.13026	+	0.652558i	0.209885	+	0.121177i	0.601258	−	0.799055i	$-0.294667\pi$
$29$	1.13026	+	0.652558i	0.209885	+	0.121177i	−0.391373	+	0.920232i	$0.628000\pi$
$30$		0			0
$31$			1.03722i			0.186290i	0.995653	+	0.0931448i	$0.0296920\pi$
$31$			1.03722i			0.186290i	−0.995653	+	0.0931448i	$0.970308\pi$
$32$	0.402230	−	0.402230i	0.0711050	−	0.0711050i
$33$		0			0
$34$	−3.61071	+	6.25393i	−0.619232	+	1.07254i
$35$	5.42773	−	2.35367i	0.917454	−	0.397843i
$36$		0			0
$37$	7.48615	+	2.00591i	1.23072	+	0.329769i	0.814858	−	0.579661i	$-0.196815\pi$
$37$	7.48615	+	2.00591i	1.23072	+	0.329769i	0.415857	+	0.909430i	$0.363482\pi$
$38$	4.89961	+	1.31285i	0.794822	+	0.212972i
$39$		0			0
$40$	−0.241721	−	6.46902i	−0.0382194	−	1.02284i
$41$	5.05188	−	2.91670i	0.788971	−	0.455513i	−0.0506292	−	0.998718i	$-0.516123\pi$
$41$	5.05188	−	2.91670i	0.788971	−	0.455513i	0.839600	+	0.543205i	$0.182789\pi$
$42$		0			0
$43$	−10.5875	+	2.83692i	−1.61458	+	0.432626i	−0.949403	−	0.314060i	$-0.898311\pi$
$43$	−10.5875	+	2.83692i	−1.61458	+	0.432626i	−0.665178	+	0.746685i	$0.731644\pi$
$44$	−0.0226017	+	0.0130491i	−0.00340734	+	0.00196723i
$45$		0			0
$46$	−2.83065	+	4.90283i	−0.417356	+	0.722882i
$47$	1.49360	+	1.49360i	0.217864	+	0.217864i	0.807598	−	0.589734i	$-0.200767\pi$
$47$	1.49360	+	1.49360i	0.217864	+	0.217864i	−0.589734	+	0.807598i	$0.700767\pi$
$48$		0			0
$49$	−4.73875	−	5.15211i	−0.676965	−	0.736015i
$50$	−5.22260	−	4.49534i	−0.738587	−	0.635737i
$51$		0			0
$52$	−0.0603289	+	0.225151i	−0.00836612	+	0.0312228i
$53$	5.97951	−	1.60220i	0.821349	−	0.220080i	0.176413	−	0.984316i	$-0.443551\pi$
$53$	5.97951	−	1.60220i	0.821349	−	0.220080i	0.644936	+	0.764237i	$0.276884\pi$
$54$		0			0
$55$	−0.129042	+	0.565235i	−0.0174000	+	0.0762162i
$56$	−7.13621	+	2.78279i	−0.953616	+	0.371866i
$57$		0			0
$58$	−1.73738	+	0.465529i	−0.228129	+	0.0611270i
$59$	−4.10944			−0.535004			−0.267502	−	0.963557i	$-0.586198\pi$
$59$	−4.10944			−0.535004			−0.267502	+	0.963557i	$0.586198\pi$
$60$		0			0
$61$		−	11.5368i		−	1.47714i	−0.674177	−	0.738570i	$-0.735502\pi$
$61$		−	11.5368i		−	1.47714i	0.674177	−	0.738570i	$-0.264498\pi$
$62$	−1.01078	−	1.01078i	−0.128369	−	0.128369i
$63$		0			0
$64$			8.36107i			1.04513i
$65$	2.75475	+	4.38466i	0.341684	+	0.543850i
$66$		0			0
$67$	0.710508	−	0.710508i	0.0868024	−	0.0868024i	−0.662372	−	0.749175i	$-0.730450\pi$
$67$	0.710508	−	0.710508i	0.0868024	−	0.0868024i	0.749175	+	0.662372i	$0.230450\pi$
$68$	0.136506	+	0.509447i	0.0165538	+	0.0617795i
$69$		0			0
$70$	−2.99571	+	7.58306i	−0.358056	+	0.906349i
$71$	−11.9553			−1.41883			−0.709417	−	0.704789i	$-0.751042\pi$
$71$	−11.9553			−1.41883			−0.709417	+	0.704789i	$0.751042\pi$
$72$		0			0
$73$	1.89993	+	7.09062i	0.222370	+	0.829894i	0.983441	+	0.181227i	$0.0580068\pi$
$73$	1.89993	+	7.09062i	0.222370	+	0.829894i	−0.761072	+	0.648668i	$0.775327\pi$
$74$	−9.25012	+	5.34056i	−1.07530	+	0.620827i
$75$		0			0
$76$	0.320835	−	0.185234i	0.0368023	−	0.0212478i
$77$	0.681855	−	0.0753191i	0.0777045	−	0.00858341i
$78$		0			0
$79$			15.4772i			1.74132i	0.491888	+	0.870659i	$0.336307\pi$
$79$			15.4772i			1.74132i	−0.491888	+	0.870659i	$0.663693\pi$
$80$	6.20973	+	5.76239i	0.694269	+	0.644254i
$81$		0			0
$82$	−2.08075	+	7.76547i	−0.229781	+	0.857553i
$83$	3.81672	+	14.2442i	0.418939	+	1.56350i	0.776813	+	0.629732i	$0.216835\pi$
$83$	3.81672	+	14.2442i	0.418939	+	1.56350i	−0.357874	+	0.933770i	$0.616498\pi$
$84$		0			0
$85$	10.3586	+	5.47538i	1.12355	+	0.593889i
$86$	7.55305	−	13.0823i	0.814466	−	1.41070i
$87$		0			0
$88$	0.194280	−	0.725065i	0.0207104	−	0.0772921i
$89$	3.16633	+	5.48424i	0.335630	+	0.581328i	0.983606	−	0.180333i	$-0.0577176\pi$
$89$	3.16633	+	5.48424i	0.335630	+	0.581328i	−0.647976	+	0.761661i	$0.724384\pi$
$90$		0			0
$91$	3.83054	−	4.78188i	0.401549	−	0.501277i
$92$	0.107015	+	0.399386i	0.0111571	+	0.0416388i
$93$		0			0
$94$	−2.91106			−0.300253
$95$	1.83176	−	8.02358i	0.187935	−	0.823202i
$96$		0			0
$97$	−0.694682	+	0.186139i	−0.0705342	+	0.0188996i	−0.293914	−	0.955832i	$-0.594958\pi$
$97$	−0.694682	+	0.186139i	−0.0705342	+	0.0188996i	0.223379	+	0.974732i	$0.428291\pi$
$98$	9.63876	+	0.402817i	0.973662	+	0.0406907i
$99$		0			0
$100$	−0.501871	+	0.0375581i	−0.0501871	+	0.00375581i
$101$	0.180462	−	0.104190i	0.0179566	−	0.0103673i	−0.490995	−	0.871162i	$-0.663367\pi$
$101$	0.180462	−	0.104190i	0.0179566	−	0.0103673i	0.508951	+	0.860795i	$0.330033\pi$
$102$		0			0
$103$	−0.994766	−	3.71252i	−0.0980172	−	0.365805i	0.899442	−	0.437039i	$-0.143973\pi$
$103$	−0.994766	−	3.71252i	−0.0980172	−	0.365805i	−0.997460	+	0.0712340i	$0.977306\pi$
$104$	−3.35213	−	5.80607i	−0.328704	−	0.569332i
$105$		0			0
$106$	−4.26573	+	7.38847i	−0.414325	+	0.717631i
$107$	3.72854	+	0.999060i	0.360452	+	0.0965828i	0.434500	−	0.900672i	$-0.356925\pi$
$107$	3.72854	+	0.999060i	0.360452	+	0.0965828i	−0.0740480	+	0.997255i	$0.523592\pi$
$108$		0			0
$109$	11.9798	+	6.91652i	1.14745	+	0.662482i	0.948265	−	0.317479i	$-0.102836\pi$
$109$	11.9798	+	6.91652i	1.14745	+	0.662482i	0.199188	+	0.979961i	$0.436170\pi$
$110$	−0.425075	−	0.676580i	−0.0405293	−	0.0645094i
$111$		0			0
$112$	4.02840	−	9.17846i	0.380648	−	0.867283i
$113$	−5.03053	+	18.7742i	−0.473232	+	1.76613i	0.154806	+	0.987945i	$0.450525\pi$
$113$	−5.03053	+	18.7742i	−0.473232	+	1.76613i	−0.628038	+	0.778183i	$0.716142\pi$
$114$		0			0
$115$	8.12075	+	4.29247i	0.757264	+	0.400275i
$116$	−0.0656831	+	0.113766i	−0.00609852	+	0.0105629i
$117$		0			0
$118$	4.00470	−	4.00470i	0.368662	−	0.368662i
$119$	2.09616	−	13.7040i	0.192155	−	1.25624i
$120$		0			0
$121$	5.46639	−	9.46806i	0.496944	−	0.860733i
$122$	11.2428	+	11.2428i	1.01787	+	1.01787i
$123$		0			0
$124$	−0.104401			−0.00937548
$125$	−6.97218	+	8.74007i	−0.623610	+	0.781735i
$126$		0			0
$127$	9.49671	−	9.49671i	0.842697	−	0.842697i	−0.146512	−	0.989209i	$-0.546805\pi$
$127$	9.49671	−	9.49671i	0.842697	−	0.842697i	0.989209	+	0.146512i	$0.0468047\pi$
$128$	−7.34350	−	7.34350i	−0.649080	−	0.649080i
$129$		0			0
$130$	−6.95743	−	1.58836i	−0.610207	−	0.139309i
$131$	−15.0514	−	8.68993i	−1.31505	−	0.759242i	−0.332119	−	0.943237i	$-0.607764\pi$
$131$	−15.0514	−	8.68993i	−1.31505	−	0.759242i	−0.982927	+	0.183995i	$0.941097\pi$
$132$		0			0
$133$	−9.67902	+	1.06917i	−0.839278	+	0.0927084i
$134$			1.38480i			0.119628i
$135$		0			0
$136$	−13.1374	−	7.58485i	−1.12652	−	0.650396i
$137$	−2.87345	−	0.769939i	−0.245496	−	0.0657803i	0.133973	−	0.990985i	$-0.457226\pi$
$137$	−2.87345	−	0.769939i	−0.245496	−	0.0657803i	−0.379468	+	0.925205i	$0.623893\pi$
$138$		0			0
$139$	2.18289	+	3.78087i	0.185150	+	0.320689i	0.943627	−	0.331011i	$-0.107390\pi$
$139$	2.18289	+	3.78087i	0.185150	+	0.320689i	−0.758477	+	0.651700i	$0.774056\pi$
$140$	0.236908	+	0.546327i	0.0200224	+	0.0461731i
$141$		0			0
$142$	11.6506	−	11.6506i	0.977695	−	0.977695i
$143$	0.155406	+	0.579982i	0.0129957	+	0.0485006i
$144$		0			0
$145$	0.860048	+	2.78872i	0.0714231	+	0.231590i
$146$	−8.76139	−	5.05839i	−0.725098	−	0.418635i
$147$		0			0
$148$	−0.201904	+	0.753517i	−0.0165964	+	0.0619387i
$149$	−13.3159	−	7.68793i	−1.09088	−	0.629819i	−0.157069	−	0.987588i	$-0.550204\pi$
$149$	−13.3159	−	7.68793i	−1.09088	−	0.629819i	−0.933810	+	0.357768i	$0.883538\pi$
$150$		0			0
$151$	−6.35107	−	11.0004i	−0.516843	−	0.895198i	−0.999809	−	0.0195586i	$-0.993774\pi$
$151$	−6.35107	−	11.0004i	−0.516843	−	0.895198i	0.482966	−	0.875639i	$-0.339559\pi$
$152$	−2.75784	+	10.2924i	−0.223690	+	0.834823i
$153$		0			0
$154$	−0.591076	+	0.737874i	−0.0476302	+	0.0594596i
$155$	−1.57760	+	1.70008i	−0.126716	+	0.136553i
$156$		0			0
$157$	4.13744	+	4.13744i	0.330204	+	0.330204i	0.852664	−	0.522460i	$-0.174986\pi$
$157$	4.13744	+	4.13744i	0.330204	+	0.330204i	−0.522460	+	0.852664i	$0.674986\pi$
$158$	−15.0827	−	15.0827i	−1.19991	−	1.19991i
$159$		0			0
$160$	1.27108	−	0.0474949i	0.100487	−	0.00375480i
$161$	1.64330	−	10.7434i	0.129510	−	0.846697i
$162$		0			0
$163$	3.28156	−	12.2469i	0.257032	−	0.959255i	−0.709917	−	0.704285i	$-0.751268\pi$
$163$	3.28156	−	12.2469i	0.257032	−	0.959255i	0.966949	−	0.254970i	$-0.0820655\pi$
$164$	0.293580	+	0.508496i	0.0229248	+	0.0397069i
$165$		0			0
$166$	−17.6005	−	10.1617i	−1.36607	−	0.788699i
$167$	−4.58316	+	17.1046i	−0.354655	+	1.32359i	0.526263	+	0.850322i	$0.323593\pi$
$167$	−4.58316	+	17.1046i	−0.354655	+	1.32359i	−0.880918	+	0.473269i	$0.843074\pi$
$168$		0			0
$169$	−6.61403	−	3.81861i	−0.508772	−	0.293740i
$170$	−15.4304	+	4.75879i	−1.18346	+	0.364983i
$171$		0			0
$172$	−0.285549	−	1.06568i	−0.0217729	−	0.0812577i
$173$	15.4355	−	15.4355i	1.17354	−	1.17354i	0.192184	−	0.981359i	$-0.438443\pi$
$173$	15.4355	−	15.4355i	1.17354	−	1.17354i	0.981359	−	0.192184i	$-0.0615570\pi$
$174$		0			0
$175$	12.4764	+	4.39772i	0.943126	+	0.332436i
$176$	0.491157	+	0.850709i	0.0370223	+	0.0641246i
$177$		0			0
$178$	−8.43007	−	2.25883i	−0.631861	−	0.169307i
$179$	−1.91049	−	1.10302i	−0.142796	−	0.0824436i	0.426900	−	0.904299i	$-0.359606\pi$
$179$	−1.91049	−	1.10302i	−0.142796	−	0.0824436i	−0.569696	+	0.821855i	$0.692939\pi$
$180$		0			0
$181$			8.73541i			0.649298i	0.945835	+	0.324649i	$0.105246\pi$
$181$			8.73541i			0.649298i	−0.945835	+	0.324649i	$0.894754\pi$
$182$	0.927098	+	8.39290i	0.0687211	+	0.622123i
$183$		0			0
$184$	−10.2991	−	5.94621i	−0.759263	−	0.438361i
$185$	9.21938	+	14.6742i	0.677823	+	1.07887i
$186$		0			0
$187$	0.960687	+	0.960687i	0.0702524	+	0.0702524i
$188$	−0.150338	+	0.150338i	−0.0109645	+	0.0109645i
$189$		0			0
$190$	6.03400	+	9.60415i	0.437752	+	0.696758i
$191$	−13.0841			−0.946735			−0.473367	−	0.880865i	$-0.656962\pi$
$191$	−13.0841			−0.946735			−0.473367	+	0.880865i	$0.656962\pi$
$192$		0			0
$193$	−13.8787	−	13.8787i	−0.999009	−	0.999009i	0.000990852	−	1.00000i	$-0.499685\pi$
$193$	−13.8787	−	13.8787i	−0.999009	−	0.999009i	−1.00000		0.000990852i	$0.999685\pi$
$194$	0.495580	−	0.858370i	0.0355806	−	0.0616274i
$195$		0			0
$196$	0.518585	−	0.476979i	0.0370418	−	0.0340699i
$197$	13.4777	−	13.4777i	0.960248	−	0.960248i	−0.0389913	−	0.999240i	$-0.512414\pi$
$197$	13.4777	−	13.4777i	0.960248	−	0.960248i	0.999240	+	0.0389913i	$0.0124145\pi$
$198$		0			0
$199$	1.92396	−	3.33240i	0.136386	−	0.236228i	−0.789740	−	0.613442i	$-0.789785\pi$
$199$	1.92396	−	3.33240i	0.136386	−	0.236228i	0.926126	+	0.377214i	$0.123118\pi$
$200$	9.44316	−	10.9709i	0.667733	−	0.775758i
$201$		0			0
$202$	−0.0743282	+	0.277396i	−0.00522971	+	0.0195175i
$203$	2.78275	−	2.04440i	0.195311	−	0.143488i
$204$		0			0
$205$	12.7167	+	2.90319i	0.888173	+	0.202768i
$206$	4.58730	+	2.64848i	0.319613	+	0.184528i
$207$		0			0
$208$	8.47447	+	2.27073i	0.587599	+	0.157447i
$209$	0.477158	−	0.826462i	0.0330057	−	0.0571676i
$210$		0			0
$211$	2.11219	+	3.65842i	0.145409	+	0.251856i	0.929526	−	0.368758i	$-0.120217\pi$
$211$	2.11219	+	3.65842i	0.145409	+	0.251856i	−0.784116	+	0.620614i	$0.786883\pi$
$212$	0.161270	+	0.601867i	0.0110760	+	0.0413364i
$213$		0			0
$214$	−4.60710	+	2.65991i	−0.314935	+	0.181828i
$215$	−21.6687	−	11.4537i	−1.47779	−	0.781133i
$216$		0			0
$217$	2.51284	+	1.10288i	0.170583	+	0.0748684i
$218$	−18.4146	+	4.93419i	−1.24720	+	0.334185i
$219$		0			0
$220$	−0.0568936	−	0.0129887i	−0.00383577	−	0.000875696i
$221$	12.1343			0.816242
$222$		0			0
$223$	−5.75589	−	21.4813i	−0.385443	−	1.43849i	−0.837467	−	0.546487i	$-0.815965\pi$
$223$	−5.75589	−	21.4813i	−0.385443	−	1.43849i	0.452025	−	0.892005i	$-0.350702\pi$
$224$	−0.546781	−	1.40217i	−0.0365333	−	0.0936864i
$225$		0			0
$226$	−13.3934	−	23.1980i	−0.890913	−	1.54311i
$227$	5.72367	−	21.3610i	0.379893	−	1.41778i	−0.466168	−	0.884696i	$-0.654366\pi$
$227$	5.72367	−	21.3610i	0.379893	−	1.41778i	0.846062	−	0.533085i	$-0.178967\pi$
$228$		0			0
$229$	2.50533	−	4.33936i	0.165557	−	0.286753i	−0.771296	−	0.636477i	$-0.780391\pi$
$229$	2.50533	−	4.33936i	0.165557	−	0.286753i	0.936853	+	0.349724i	$0.113725\pi$
$230$	−12.0968	+	3.73070i	−0.797641	+	0.245995i
$231$		0			0
$232$	−0.977916	−	3.64963i	−0.0642033	−	0.239610i
$233$	6.51408	−	24.3109i	0.426751	−	1.59266i	−0.333317	−	0.942815i	$-0.608168\pi$
$233$	6.51408	−	24.3109i	0.426751	−	1.59266i	0.760069	−	0.649843i	$-0.225165\pi$
$234$		0			0
$235$	0.176363	+	4.71989i	0.0115046	+	0.307892i
$236$		−	0.413635i		−	0.0269254i
$237$		0			0
$238$	11.3120	+	15.3974i	0.733247	+	0.998068i
$239$	2.65588	−	1.53337i	0.171794	−	0.0991856i	−0.411637	−	0.911348i	$-0.635043\pi$
$239$	2.65588	−	1.53337i	0.171794	−	0.0991856i	0.583432	+	0.812162i	$0.301710\pi$
$240$		0			0
$241$	−18.0020	+	10.3935i	−1.15961	+	0.669501i	−0.951210	−	0.308543i	$-0.900159\pi$
$241$	−18.0020	+	10.3935i	−1.15961	+	0.669501i	−0.208399	+	0.978044i	$0.566825\pi$
$242$	3.89968	+	14.5538i	0.250681	+	0.935553i
$243$		0			0
$244$	1.16124			0.0743406
$245$	0.0691615	−	15.6523i	0.00441856	−	0.999990i
$246$		0			0
$247$	−2.20601	−	8.23293i	−0.140365	−	0.523849i
$248$	2.12330	−	2.12330i	0.134830	−	0.134830i
$249$		0			0
$250$	−1.72283	−	15.3118i	−0.108961	−	0.968401i
$251$			22.8147i			1.44005i	0.693946	+	0.720027i	$0.255871\pi$
$251$			22.8147i			1.44005i	−0.693946	+	0.720027i	$0.744129\pi$
$252$		0			0
$253$	0.753139	+	0.753139i	0.0473494	+	0.0473494i
$254$			18.5093i			1.16138i
$255$		0			0
$256$	−2.40950			−0.150593
$257$	−9.67818	+	2.59326i	−0.603708	+	0.161763i	−0.547711	−	0.836668i	$-0.684501\pi$
$257$	−9.67818	+	2.59326i	−0.603708	+	0.161763i	−0.0559975	+	0.998431i	$0.517834\pi$
$258$		0			0
$259$	12.8197	−	16.0036i	0.796580	−	0.994418i
$260$	−0.441337	+	0.277279i	−0.0273706	+	0.0171961i
$261$		0			0
$262$	23.1362	−	6.19932i	1.42936	−	0.382995i
$263$	−2.05244	+	7.65982i	−0.126559	+	0.472325i	−0.999890	−	0.0148019i	$-0.995288\pi$
$263$	−2.05244	+	7.65982i	−0.126559	+	0.472325i	0.873331	+	0.487126i	$0.161955\pi$
$264$		0			0
$265$	12.2378	+	6.46868i	0.751763	+	0.397368i
$266$	8.39040	−	10.4742i	0.514449	−	0.642216i
$267$		0			0
$268$	0.0715161	+	0.0715161i	0.00436854	+	0.00436854i
$269$	−6.74817	+	11.6882i	−0.411443	+	0.712641i	−0.995048	−	0.0993972i	$-0.968309\pi$
$269$	−6.74817	+	11.6882i	−0.411443	+	0.712641i	0.583604	+	0.812038i	$0.301642\pi$
$270$		0			0
$271$	8.72237	−	5.03586i	0.529846	−	0.305907i	−0.211107	−	0.977463i	$-0.567707\pi$
$271$	8.72237	−	5.03586i	0.529846	−	0.305907i	0.740954	+	0.671556i	$0.234374\pi$
$272$	19.1751	−	5.13796i	1.16266	−	0.311535i
$273$		0			0
$274$	3.55053	−	2.04990i	0.214495	−	0.123839i
$275$	−1.07123	+	0.730190i	−0.0645975	+	0.0440321i
$276$		0			0
$277$	−8.31693	−	2.22851i	−0.499716	−	0.133898i	0.000152404	−	1.00000i	$-0.499951\pi$
$277$	−8.31693	−	2.22851i	−0.499716	−	0.133898i	−0.499868	+	0.866102i	$0.666618\pi$
$278$	−5.81175	−	1.55725i	−0.348565	−	0.0933978i
$279$		0			0
$280$	−15.9294	−	6.29295i	−0.951963	−	0.376076i
$281$	8.22404	−	14.2445i	0.490605	−	0.849753i	−0.509336	−	0.860568i	$-0.670109\pi$
$281$	8.22404	−	14.2445i	0.490605	−	0.849753i	0.999942	+	0.0108144i	$0.00344240\pi$
$282$		0			0
$283$	2.14679	−	2.14679i	0.127613	−	0.127613i	−0.640415	−	0.768029i	$-0.721238\pi$
$283$	2.14679	−	2.14679i	0.127613	−	0.127613i	0.768029	+	0.640415i	$0.221238\pi$
$284$		−	1.20336i		−	0.0714062i
$285$		0			0
$286$	−0.716644	−	0.413755i	−0.0423761	−	0.0244658i
$287$	−1.69454	−	15.3404i	−0.100025	−	0.905517i
$288$		0			0
$289$	9.05538	−	5.22812i	0.532669	−	0.307537i
$290$	−3.55576	−	1.87951i	−0.208802	−	0.110369i
$291$		0			0
$292$	−0.713705	+	0.191237i	−0.0417665	+	0.0111913i
$293$	7.46580	+	2.00045i	0.436157	+	0.116868i	0.470215	−	0.882552i	$-0.344176\pi$
$293$	7.46580	+	2.00045i	0.436157	+	0.116868i	−0.0340582	+	0.999420i	$0.510843\pi$
$294$		0			0
$295$	−6.73568	−	6.25045i	−0.392167	−	0.363915i
$296$	−11.2187	−	19.4313i	−0.652072	−	1.12942i
$297$		0			0
$298$	20.4684	−	5.48450i	1.18571	−	0.317709i
$299$	9.51280			0.550140
$300$		0			0
$301$	−4.38485	+	28.6667i	−0.252738	+	1.65232i
$302$	16.9092	+	4.53080i	0.973014	+	0.260718i
$303$		0			0
$304$	−6.97204	−	12.0759i	−0.399874	−	0.692602i
$305$	17.5475	−	18.9097i	1.00477	−	1.08277i
$306$		0			0
$307$	15.0183	+	15.0183i	0.857140	+	0.857140i	0.991000	−	0.133860i	$-0.0427372\pi$
$307$	15.0183	+	15.0183i	0.857140	+	0.857140i	−0.133860	+	0.991000i	$0.542737\pi$
$308$	0.00758124	+	0.0686320i	0.000431981	+	0.00391067i
$309$		0			0
$310$	−0.119352	−	3.19414i	−0.00677872	−	0.181415i
$311$			15.1169i			0.857202i	0.903494	+	0.428601i	$0.140993\pi$
$311$			15.1169i			0.857202i	−0.903494	+	0.428601i	$0.859007\pi$
$312$		0			0
$313$	−6.59443	+	6.59443i	−0.372739	+	0.372739i	−0.868474	−	0.495735i	$-0.834899\pi$
$313$	−6.59443	+	6.59443i	−0.372739	+	0.372739i	0.495735	+	0.868474i	$0.334899\pi$
$314$	−8.06397			−0.455076
$315$		0			0
$316$	−1.55785			−0.0876360
$317$	13.0603	−	13.0603i	0.733537	−	0.733537i	−0.237782	−	0.971319i	$-0.576420\pi$
$317$	13.0603	−	13.0603i	0.733537	−	0.733537i	0.971319	+	0.237782i	$0.0764202\pi$
$318$		0			0
$319$			0.338396i			0.0189465i
$320$	−12.7172	+	13.7044i	−0.710911	+	0.766101i
$321$		0			0
$322$	8.86813	+	12.0710i	0.494201	+	0.672689i
$323$	−13.6371	−	13.6371i	−0.758788	−	0.758788i
$324$		0			0
$325$	−2.15381	+	11.3767i	−0.119472	+	0.631068i
$326$	8.73687	+	15.1327i	0.483891	+	0.838123i
$327$		0			0
$328$	−16.3126	−	4.37094i	−0.900712	−	0.241345i
$329$	5.20668	−	2.03036i	0.287053	−	0.111937i
$330$		0			0
$331$	5.99394			0.329457			0.164728	−	0.986339i	$-0.447325\pi$
$331$	5.99394			0.329457			0.164728	+	0.986339i	$0.447325\pi$
$332$	−1.43375	+	0.384171i	−0.0786870	+	0.0210841i
$333$		0			0
$334$	−12.2023	−	21.1349i	−0.667678	−	1.15645i
$335$	2.24526	−	0.0838960i	0.122672	−	0.00458373i
$336$		0			0
$337$	−20.3805	−	5.46095i	−1.11020	−	0.297477i	−0.343288	−	0.939230i	$-0.611541\pi$
$337$	−20.3805	−	5.46095i	−1.11020	−	0.297477i	−0.766911	+	0.641753i	$0.778207\pi$
$338$	10.1667	−	2.72417i	0.552997	−	0.148175i
$339$		0			0
$340$	−0.551124	+	1.04265i	−0.0298889	+	0.0565455i
$341$	−0.232904	+	0.134467i	−0.0126124	+	0.00728180i
$342$		0			0
$343$	−17.5207	+	6.00221i	−0.946027	+	0.324089i
$344$	27.4813	+	15.8663i	1.48169	+	0.855456i
$345$		0			0
$346$			30.0842i			1.61734i
$347$	−4.40393	+	4.40393i	−0.236415	+	0.236415i	−0.815364	−	0.578949i	$-0.803463\pi$
$347$	−4.40393	+	4.40393i	−0.236415	+	0.236415i	0.578949	+	0.815364i	$0.303463\pi$
$348$		0			0
$349$	−8.70295	+	15.0740i	−0.465858	+	0.806890i	−0.999240	−	0.0389846i	$-0.987588\pi$
$349$	−8.70295	+	15.0740i	−0.465858	+	0.806890i	0.533382	+	0.845875i	$0.320921\pi$
$350$	−16.4440	+	7.87275i	−0.878969	+	0.420816i
$351$		0			0
$352$	0.142466	+	0.0381735i	0.00759344	+	0.00203466i
$353$	0.429560	+	0.115100i	0.0228632	+	0.00612618i	0.270233	−	0.962795i	$-0.412899\pi$
$353$	0.429560	+	0.115100i	0.0228632	+	0.00612618i	−0.247369	+	0.968921i	$0.579566\pi$
$354$		0			0
$355$	−19.5956	−	18.1840i	−1.04003	−	0.965105i
$356$	−0.552015	+	0.318706i	−0.0292567	+	0.0168914i
$357$		0			0
$358$	2.93670	−	0.786885i	0.155209	−	0.0415882i
$359$	5.72792	−	3.30701i	0.302308	−	0.174538i	−0.341171	−	0.940001i	$-0.610824\pi$
$359$	5.72792	−	3.30701i	0.302308	−	0.174538i	0.643479	+	0.765464i	$0.277490\pi$
$360$		0			0
$361$	2.72667	−	4.72274i	0.143509	−	0.248565i
$362$	−8.51276	−	8.51276i	−0.447421	−	0.447421i
$363$		0			0
$364$	0.481320	+	0.385562i	0.0252280	+	0.0202089i
$365$	−7.67069	+	14.5118i	−0.401502	+	0.759585i
$366$		0			0
$367$	−7.80222	+	29.1183i	−0.407273	+	1.51996i	0.392553	+	0.919729i	$0.371592\pi$
$367$	−7.80222	+	29.1183i	−0.407273	+	1.51996i	−0.799826	+	0.600232i	$0.795075\pi$
$368$	15.0325	−	4.02795i	0.783624	−	0.209971i
$369$		0			0
$370$	−23.2846	−	5.31582i	−1.21051	−	0.276356i
$371$	2.47643	−	16.1901i	0.128570	−	0.840547i
$372$		0			0
$373$	32.0897	−	8.59841i	1.66154	−	0.445209i	0.698730	−	0.715385i	$-0.253749\pi$
$373$	32.0897	−	8.59841i	1.66154	−	0.445209i	0.962811	+	0.270176i	$0.0870820\pi$
$374$	−1.87240			−0.0968195
$375$		0			0
$376$		−	6.11514i		−	0.315364i
$377$	2.13712	+	2.13712i	0.110067	+	0.110067i
$378$		0			0
$379$			2.84911i			0.146349i	0.997319	+	0.0731746i	$0.0233130\pi$
$379$			2.84911i			0.146349i	−0.997319	+	0.0731746i	$0.976687\pi$
$380$	0.807613	+	0.184376i	0.0414297	+	0.00945829i
$381$		0			0
$382$	12.7506	−	12.7506i	0.652380	−	0.652380i
$383$	−8.04591	−	30.0278i	−0.411127	−	1.53435i	−0.792469	−	0.609912i	$-0.791205\pi$
$383$	−8.04591	−	30.0278i	−0.411127	−	1.53435i	0.381342	−	0.924434i	$-0.375462\pi$
$384$		0			0
$385$	1.23217	+	0.913645i	0.0627973	+	0.0465636i
$386$	27.0498			1.37680
$387$		0			0
$388$	−0.0187358	−	0.0699231i	−0.000951168	−	0.00354981i
$389$	−26.8083	+	15.4778i	−1.35923	+	0.784753i	−0.989520	−	0.144393i	$-0.953877\pi$
$389$	−26.8083	+	15.4778i	−1.35923	+	0.784753i	−0.369712	+	0.929146i	$0.620544\pi$
$390$		0			0
$391$	18.6408	−	10.7623i	0.942707	−	0.544272i
$392$	−0.846180	+	20.2477i	−0.0427385	+	1.02266i
$393$		0			0
$394$			26.2684i			1.32338i
$395$	−23.5407	+	25.3682i	−1.18446	+	1.27642i
$396$		0			0
$397$	−6.86987	+	25.6387i	−0.344789	+	1.28677i	0.548070	+	0.836433i	$0.315363\pi$
$397$	−6.86987	+	25.6387i	−0.344789	+	1.28677i	−0.892859	+	0.450337i	$0.851304\pi$
$398$	1.37254	+	5.12239i	0.0687993	+	0.256762i
$399$		0			0
$400$	1.41366	+	18.8900i	0.0706828	+	0.944499i
$401$	4.40300	−	7.62621i	0.219875	−	0.380835i	−0.734895	−	0.678181i	$-0.762768\pi$
$401$	4.40300	−	7.62621i	0.219875	−	0.380835i	0.954770	+	0.297347i	$0.0961017\pi$
$402$		0			0
$403$	−0.621671	+	2.32011i	−0.0309676	+	0.115573i
$404$	0.0104872	+	0.0181644i	0.000521758	+	0.000903712i
$405$		0			0
$406$	−0.719540	+	4.70411i	−0.0357102	+	0.233461i
$407$	0.520100	+	1.94104i	0.0257804	+	0.0962138i
$408$		0			0
$409$	−15.2558			−0.754350			−0.377175	−	0.926142i	$-0.623105\pi$
$409$	−15.2558			−0.754350			−0.377175	+	0.926142i	$0.623105\pi$
$410$	−15.2218	+	9.56338i	−0.751750	+	0.472302i
$411$		0			0
$412$	0.373683	−	0.100128i	0.0184100	−	0.00493296i
$413$	−4.36960	+	9.95586i	−0.215014	+	0.489896i
$414$		0			0
$415$	−15.4095	+	29.1525i	−0.756421	+	1.43104i
$416$	1.14081	−	0.658650i	0.0559330	−	0.0322930i
$417$		0			0
$418$	0.340401	+	1.27039i	0.0166495	+	0.0621369i
$419$	−1.97540	−	3.42149i	−0.0965046	−	0.167151i	0.813731	−	0.581242i	$-0.197433\pi$
$419$	−1.97540	−	3.42149i	−0.0965046	−	0.167151i	−0.910236	+	0.414091i	$0.864100\pi$
$420$		0			0
$421$	−4.13167	+	7.15626i	−0.201365	+	0.348775i	−0.948969	−	0.315371i	$-0.897871\pi$
$421$	−4.13167	+	7.15626i	−0.201365	+	0.348775i	0.747603	+	0.664145i	$0.231204\pi$
$422$	−5.62353	−	1.50682i	−0.273749	−	0.0733509i
$423$		0			0
$424$	−15.5206	−	8.96083i	−0.753748	−	0.435177i
$425$	8.65056	+	24.7300i	0.419614	+	1.19958i
$426$		0			0
$427$	−27.9500	−	12.2672i	−1.35260	−	0.593651i
$428$	−0.100560	+	0.375296i	−0.00486076	+	0.0181406i
$429$		0			0
$430$	32.2781	−	9.95466i	1.55659	−	0.480056i
$431$	−14.3973	+	24.9369i	−0.693495	+	1.20117i	0.277191	+	0.960815i	$0.410597\pi$
$431$	−14.3973	+	24.9369i	−0.693495	+	1.20117i	−0.970686	+	0.240353i	$0.922737\pi$
$432$		0			0
$433$	−21.8648	+	21.8648i	−1.05076	+	1.05076i	−0.0521139	+	0.998641i	$0.516596\pi$
$433$	−21.8648	+	21.8648i	−1.05076	+	1.05076i	−0.998641	+	0.0521139i	$0.983404\pi$
$434$	−3.52356	+	1.37403i	−0.169137	+	0.0659553i
$435$		0			0
$436$	−0.696181	+	1.20582i	−0.0333410	+	0.0577483i
$437$	−10.6909	−	10.6909i	−0.511416	−	0.511416i
$438$		0			0
$439$	38.8430			1.85387			0.926937	−	0.375217i	$-0.122432\pi$
$439$	38.8430			1.85387			0.926937	+	0.375217i	$0.122432\pi$
$440$	1.42126	−	0.892936i	0.0677560	−	0.0425690i
$441$		0			0
$442$	−11.8250	+	11.8250i	−0.562459	+	0.562459i
$443$	2.47565	+	2.47565i	0.117622	+	0.117622i	0.763468	−	0.645846i	$-0.223495\pi$
$443$	2.47565	+	2.47565i	0.117622	+	0.117622i	−0.645846	+	0.763468i	$0.723495\pi$
$444$		0			0
$445$	−3.15166	+	13.8050i	−0.149403	+	0.654422i
$446$	26.5429	+	15.3246i	1.25684	+	0.725639i
$447$		0			0
$448$	20.2562	+	8.89039i	0.957016	+	0.420032i
$449$			1.32063i			0.0623244i	0.999514	+	0.0311622i	$0.00992085\pi$
$449$			1.32063i			0.0623244i	−0.999514	+	0.0311622i	$0.990079\pi$
$450$		0			0
$451$	1.30987	+	0.756256i	0.0616795	+	0.0356107i
$452$	−1.88971	−	0.506347i	−0.0888847	−	0.0238166i
$453$		0			0
$454$	15.2388	+	26.3943i	0.715191	+	1.23875i
$455$	13.5518	−	2.01163i	0.635317	−	0.0943069i
$456$		0			0
$457$	8.25041	−	8.25041i	0.385938	−	0.385938i	−0.487298	−	0.873236i	$-0.662017\pi$
$457$	8.25041	−	8.25041i	0.385938	−	0.385938i	0.873236	+	0.487298i	$0.162017\pi$
$458$	1.78728	+	6.67023i	0.0835142	+	0.311679i
$459$		0			0
$460$	−0.432058	+	0.817393i	−0.0201448	+	0.0381111i
$461$	−12.3918	−	7.15441i	−0.577143	−	0.333214i	0.182854	−	0.983140i	$-0.441466\pi$
$461$	−12.3918	−	7.15441i	−0.577143	−	0.333214i	−0.759997	+	0.649926i	$0.774800\pi$
$462$		0			0
$463$	11.0882	−	41.3816i	0.515311	−	1.92317i	0.166164	−	0.986098i	$-0.446862\pi$
$463$	11.0882	−	41.3816i	0.515311	−	1.92317i	0.349146	−	0.937068i	$-0.386472\pi$
$464$	4.28207	+	2.47225i	0.198790	+	0.114771i
$465$		0			0
$466$	17.3432	+	30.0393i	0.803407	+	1.39154i
$467$	−1.68405	+	6.28495i	−0.0779284	+	0.290833i	−0.993881	−	0.110453i	$-0.964770\pi$
$467$	−1.68405	+	6.28495i	−0.0779284	+	0.290833i	0.915953	+	0.401286i	$0.131437\pi$
$468$		0			0
$469$	−0.965845	−	2.47682i	−0.0445986	−	0.114369i
$470$	−4.77145	−	4.42772i	−0.220091	−	0.204235i
$471$		0			0
$472$	8.41249	+	8.41249i	0.387216	+	0.387216i
$473$	−2.00961	−	2.00961i	−0.0924019	−	0.0924019i
$474$		0			0
$475$	15.2062	−	10.3652i	0.697710	−	0.475586i
$476$	1.37937	+	0.210989i	0.0632235	+	0.00967065i
$477$		0			0
$478$	−1.09390	+	4.08247i	−0.0500336	+	0.186728i
$479$	−12.6979	−	21.9934i	−0.580182	−	1.00490i	−0.995457	−	0.0952084i	$-0.969648\pi$
$479$	−12.6979	−	21.9934i	−0.580182	−	1.00490i	0.415276	−	0.909696i	$-0.363685\pi$
$480$		0			0
$481$	15.5432	+	8.97386i	0.708708	+	0.409173i
$482$	7.41460	−	27.6717i	0.337726	−	1.26041i
$483$		0			0
$484$	0.953006	+	0.550218i	0.0433185	+	0.0250099i
$485$	−1.42175	−	0.751512i	−0.0645585	−	0.0341244i
$486$		0			0
$487$	−10.4599	−	39.0369i	−0.473983	−	1.76893i	−0.625237	−	0.780435i	$-0.714998\pi$
$487$	−10.4599	−	39.0369i	−0.473983	−	1.76893i	0.151254	−	0.988495i	$-0.451669\pi$
$488$	−23.6172	+	23.6172i	−1.06910	+	1.06910i
$489$		0			0
$490$	15.1860	+	15.3208i	0.686032	+	0.692122i
$491$	−3.12056	−	5.40496i	−0.140829	−	0.243923i	0.786980	−	0.616978i	$-0.211643\pi$
$491$	−3.12056	−	5.40496i	−0.140829	−	0.243923i	−0.927809	+	0.373056i	$0.878310\pi$
$492$		0			0
$493$	6.60561	+	1.76997i	0.297502	+	0.0797154i
$494$	10.1729	+	5.87331i	0.457699	+	0.264253i
$495$		0			0
$496$			3.92956i			0.176442i
$497$	−12.7122	+	28.9639i	−0.570218	+	1.29921i
$498$		0			0
$499$	−6.23526	−	3.59993i	−0.279128	−	0.161155i	0.353900	−	0.935283i	$-0.384855\pi$
$499$	−6.23526	−	3.59993i	−0.279128	−	0.161155i	−0.633029	+	0.774128i	$0.718189\pi$
$500$	−0.879730	−	0.701783i	−0.0393427	−	0.0313847i
$501$		0			0
$502$	−22.2332	−	22.2332i	−0.992318	−	0.992318i
$503$	7.68911	−	7.68911i	0.342840	−	0.342840i	−0.514594	−	0.857434i	$-0.672057\pi$
$503$	7.68911	−	7.68911i	0.342840	−	0.342840i	0.857434	+	0.514594i	$0.172057\pi$
$504$		0			0
$505$	0.454263	+	0.103707i	0.0202145	+	0.00461491i
$506$	−1.46789			−0.0652555
$507$		0			0
$508$	0.955890	+	0.955890i	0.0424108	+	0.0424108i
$509$	−6.95962	+	12.0544i	−0.308480	+	0.534303i	−0.978030	−	0.208464i	$-0.933154\pi$
$509$	−6.95962	+	12.0544i	−0.308480	+	0.534303i	0.669550	+	0.742767i	$0.266487\pi$
$510$		0			0
$511$	19.1985	+	2.93660i	0.849292	+	0.129907i
$512$	17.0351	−	17.0351i	0.752851	−	0.752851i
$513$		0			0
$514$	6.90434	−	11.9587i	0.304537	−	0.527474i
$515$	4.01623	−	7.59814i	0.176976	−	0.334814i
$516$		0			0
$517$	−0.141750	+	0.529017i	−0.00623415	+	0.0232662i
$518$	3.10274	+	28.0887i	0.136327	+	1.23415i
$519$		0			0
$520$	3.33661	−	14.6152i	0.146320	−	0.640917i
$521$	−0.885586	−	0.511293i	−0.0387982	−	0.0224002i	0.480475	−	0.877008i	$-0.340464\pi$
$521$	−0.885586	−	0.511293i	−0.0387982	−	0.0224002i	−0.519274	+	0.854608i	$0.673797\pi$
$522$		0			0
$523$	8.78408	+	2.35369i	0.384101	+	0.102920i	0.445702	−	0.895181i	$-0.352954\pi$
$523$	8.78408	+	2.35369i	0.384101	+	0.102920i	−0.0616011	+	0.998101i	$0.519621\pi$
$524$	0.874683	−	1.51500i	0.0382107	−	0.0661829i
$525$		0			0
$526$	−5.46445	−	9.46471i	−0.238261	−	0.412681i
$527$	1.40665	+	5.24969i	0.0612747	+	0.228680i
$528$		0			0
$529$	−5.30494	+	3.06281i	−0.230650	+	0.133166i
$530$	−18.2297	+	5.62209i	−0.791847	+	0.244208i
$531$		0			0
$532$	−0.107617	−	0.974240i	−0.00466578	−	0.0422387i
$533$	13.0485	−	3.49634i	0.565193	−	0.151443i
$534$		0			0
$535$	4.59180	+	7.30864i	0.198521	+	0.315980i
$536$	−2.90898			−0.125649
$537$		0			0
$538$	−4.81409	−	17.9664i	−0.207550	−	0.774588i
$539$	0.542547	−	1.73200i	0.0233691	−	0.0746026i
$540$		0			0
$541$	−3.50184	−	6.06537i	−0.150556	−	0.260771i	0.780876	−	0.624686i	$-0.214773\pi$
$541$	−3.50184	−	6.06537i	−0.150556	−	0.260771i	−0.931432	+	0.363915i	$0.881440\pi$
$542$	−3.59254	+	13.4076i	−0.154313	+	0.575904i
$543$		0			0
$544$	1.49032	−	2.58132i	0.0638971	−	0.110673i
$545$	9.11573	+	29.5579i	0.390475	+	1.26612i
$546$		0			0
$547$	2.38131	+	8.88717i	0.101817	+	0.379988i	0.997965	−	0.0637689i	$-0.0203121\pi$
$547$	2.38131	+	8.88717i	0.101817	+	0.379988i	−0.896147	+	0.443757i	$0.853645\pi$
$548$	0.0774981	−	0.289227i	0.00331055	−	0.0123552i
$549$		0			0
$550$	0.332346	−	1.75550i	0.0141713	−	0.0748549i
$551$		−	4.80358i		−	0.204639i
$552$		0			0
$553$	37.4962	+	16.4570i	1.59450	+	0.699822i
$554$	10.2767	−	5.93323i	0.436613	−	0.252079i
$555$		0			0
$556$	−0.380563	+	0.219718i	−0.0161395	+	0.00931812i
$557$	5.66350	+	21.1365i	0.239970	+	0.895580i	0.975845	+	0.218463i	$0.0701043\pi$
$557$	5.66350	+	21.1365i	0.239970	+	0.895580i	−0.735875	+	0.677117i	$0.763229\pi$
$558$		0			0
$559$	−25.3831			−1.07359
$560$	20.5633	−	8.91701i	0.868957	−	0.376812i
$561$		0			0
$562$	5.86696	+	21.8958i	0.247483	+	0.923619i
$563$	17.6627	−	17.6627i	0.744395	−	0.744395i	−0.229026	−	0.973420i	$-0.573554\pi$
$563$	17.6627	−	17.6627i	0.744395	−	0.744395i	0.973420	+	0.229026i	$0.0735540\pi$
$564$		0			0
$565$	−36.8009	+	23.1209i	−1.54823	+	0.972704i
$566$			4.18414i			0.175872i
$567$		0			0
$568$	24.4738	+	24.4738i	1.02690	+	1.02690i
$569$			32.4429i			1.36008i	0.733176	+	0.680039i	$0.238037\pi$
$569$			32.4429i			1.36008i	−0.733176	+	0.680039i	$0.761963\pi$
$570$		0			0
$571$	1.22790			0.0513862			0.0256931	−	0.999670i	$-0.491821\pi$
$571$	1.22790			0.0513862			0.0256931	+	0.999670i	$0.491821\pi$
$572$	−0.0583780	+	0.0156423i	−0.00244091	+	0.000654039i
$573$		0			0
$574$	16.6008	+	13.2981i	0.692903	+	0.555051i
$575$	6.78168	+	19.3873i	0.282816	+	0.808507i
$576$		0			0
$577$	−3.55002	+	0.951225i	−0.147789	+	0.0396000i	−0.331955	−	0.943295i	$-0.607708\pi$
$577$	−3.55002	+	0.951225i	−0.147789	+	0.0396000i	0.184166	+	0.982895i	$0.441042\pi$
$578$	−3.72970	+	13.9194i	−0.155135	+	0.578972i
$579$		0			0
$580$	−0.280698	+	0.0865680i	−0.0116553	+	0.00359454i
$581$	38.5674	+	5.89926i	1.60005	+	0.244743i
$582$		0			0
$583$	1.13497	+	1.13497i	0.0470055	+	0.0470055i
$584$	10.6259	−	18.4047i	0.439704	−	0.761590i
$585$		0			0
$586$	−9.22497	+	5.32604i	−0.381080	+	0.220017i
$587$	−29.5276	+	7.91189i	−1.21873	+	0.326559i	−0.810183	−	0.586177i	$-0.800632\pi$
$587$	−29.5276	+	7.91189i	−1.21873	+	0.326559i	−0.408551	+	0.912736i	$0.633966\pi$
$588$		0			0
$589$	3.30610	−	1.90878i	0.136226	−	0.0786498i
$590$	12.6551	−	0.472870i	0.521003	−	0.0194678i
$591$		0			0
$592$	28.3617	+	7.59950i	1.16566	+	0.312337i
$593$	9.32116	+	2.49760i	0.382774	+	0.102564i	0.445075	−	0.895493i	$-0.353177\pi$
$593$	9.32116	+	2.49760i	0.382774	+	0.102564i	−0.0623006	+	0.998057i	$0.519844\pi$
$594$		0			0
$595$	24.2795	−	19.2737i	0.995363	−	0.790143i
$596$	0.773827	−	1.34031i	0.0316972	−	0.0549011i
$597$		0			0
$598$	−9.27034	+	9.27034i	−0.379092	+	0.379092i
$599$		−	26.5311i		−	1.08403i	−0.840368	−	0.542016i	$-0.817661\pi$
$599$		−	26.5311i		−	1.08403i	0.840368	−	0.542016i	$-0.182339\pi$
$600$		0			0
$601$	−37.0964	−	21.4176i	−1.51319	−	0.873643i	−0.999881	−	0.0154416i	$-0.995085\pi$
$601$	−37.0964	−	21.4176i	−1.51319	−	0.873643i	−0.513313	−	0.858201i	$-0.671582\pi$
$602$	−23.6629	−	32.2091i	−0.964429	−	1.31274i
$603$		0			0
$604$	1.10724	−	0.639266i	0.0450530	−	0.0260114i
$605$	23.3607	−	7.20451i	0.949748	−	0.292905i
$606$		0			0
$607$	−42.1612	+	11.2971i	−1.71127	+	0.458534i	−0.975736	−	0.218952i	$-0.929736\pi$
$607$	−42.1612	+	11.2971i	−1.71127	+	0.458534i	−0.735536	+	0.677486i	$0.763070\pi$
$608$	−2.02232	−	0.541879i	−0.0820159	−	0.0219761i
$609$		0			0
$610$	1.32753	+	35.5280i	0.0537503	+	1.43849i
$611$	2.44576	+	4.23619i	0.0989450	+	0.171378i
$612$		0			0
$613$	−45.9091	+	12.3013i	−1.85425	+	0.496845i	−0.999745	−	0.0225980i	$-0.992806\pi$
$613$	−45.9091	+	12.3013i	−1.85425	+	0.496845i	−0.854505	+	0.519443i	$0.826140\pi$
$614$	−29.2710			−1.18128
$615$		0			0
$616$	−1.55002	−	1.24165i	−0.0624521	−	0.0500273i
$617$	−35.0083	−	9.38045i	−1.40938	−	0.377643i	−0.527678	−	0.849445i	$-0.676937\pi$
$617$	−35.0083	−	9.38045i	−1.40938	−	0.377643i	−0.881705	+	0.471802i	$0.843604\pi$
$618$		0			0
$619$	1.75588	+	3.04128i	0.0705748	+	0.122239i	0.899153	−	0.437634i	$-0.144183\pi$
$619$	1.75588	+	3.04128i	0.0705748	+	0.122239i	−0.828579	+	0.559873i	$0.810850\pi$
$620$	−0.171121	−	0.158793i	−0.00687238	−	0.00637730i
$621$		0			0
$622$	−14.7316	−	14.7316i	−0.590684	−	0.590684i
$623$	16.6533	−	1.83956i	0.667201	−	0.0737005i
$624$		0			0
$625$	−24.7215	+	3.72097i	−0.988861	+	0.148839i
$626$		−	12.8527i		−	0.513697i
$627$		0			0
$628$	−0.416454	+	0.416454i	−0.0166183	+	0.0166183i
$629$	40.6102			1.61923
$630$		0			0
$631$	−5.04974			−0.201027			−0.100513	−	0.994936i	$-0.532049\pi$
$631$	−5.04974			−0.201027			−0.100513	+	0.994936i	$0.532049\pi$
$632$	31.6835	−	31.6835i	1.26030	−	1.26030i
$633$		0			0
$634$			25.4547i			1.01094i
$635$	30.0103	−	1.12136i	1.19092	−	0.0444999i
$636$		0			0
$637$	−7.51193	−	14.3648i	−0.297634	−	0.569153i
$638$	−0.329771	−	0.329771i	−0.0130557	−	0.0130557i
$639$		0			0
$640$	−0.867113	−	23.2060i	−0.0342756	−	0.917298i
$641$	0.232246	+	0.402262i	0.00917317	+	0.0158884i	0.870576	−	0.492035i	$-0.163747\pi$
$641$	0.232246	+	0.402262i	0.00917317	+	0.0158884i	−0.861402	+	0.507923i	$0.830413\pi$
$642$		0			0
$643$	−16.1803	−	4.33549i	−0.638087	−	0.170975i	−0.0747505	−	0.997202i	$-0.523816\pi$
$643$	−16.1803	−	4.33549i	−0.638087	−	0.170975i	−0.563337	+	0.826227i	$0.690483\pi$
$644$	1.08137	+	0.165407i	0.0426121	+	0.00651793i
$645$		0			0
$646$	26.5790			1.04574
$647$	−19.4718	+	5.21745i	−0.765515	+	0.205119i	−0.620389	−	0.784294i	$-0.713025\pi$
$647$	−19.4718	+	5.21745i	−0.765515	+	0.205119i	−0.145126	+	0.989413i	$0.546359\pi$
$648$		0			0
$649$	−0.532757	−	0.922762i	−0.0209125	−	0.0362216i
$650$	−8.98786	−	13.1857i	−0.352533	−	0.517185i
$651$		0			0
$652$	1.23271	+	0.330305i	0.0482768	+	0.0129357i
$653$	−15.7307	+	4.21502i	−0.615588	+	0.164946i	−0.553121	−	0.833101i	$-0.686563\pi$
$653$	−15.7307	+	4.21502i	−0.615588	+	0.164946i	−0.0624670	+	0.998047i	$0.519897\pi$
$654$		0			0
$655$	−11.4530	−	37.1366i	−0.447507	−	1.45105i
$656$	19.1393	−	11.0501i	0.747266	−	0.431434i
$657$		0			0
$658$	−3.09536	+	7.05258i	−0.120670	+	0.274938i
$659$	6.34444	+	3.66296i	0.247144	+	0.142689i	0.618456	−	0.785820i	$-0.287759\pi$
$659$	6.34444	+	3.66296i	0.247144	+	0.142689i	−0.371312	+	0.928508i	$0.621092\pi$
$660$		0			0
$661$			11.4679i			0.446048i	0.974813	+	0.223024i	$0.0715929\pi$
$661$			11.4679i			0.446048i	−0.974813	+	0.223024i	$0.928407\pi$
$662$	−5.84117	+	5.84117i	−0.227023	+	0.227023i
$663$		0			0
$664$	21.3462	−	36.9727i	0.828393	−	1.43482i
$665$	−17.4908	−	12.9693i	−0.678266	−	0.502929i
$666$		0			0
$667$	5.17853	+	1.38758i	0.200513	+	0.0537274i
$668$	−1.72166	−	0.461317i	−0.0666129	−	0.0178489i
$669$		0			0
$670$	−2.10627	+	2.26979i	−0.0813724	+	0.0876895i
$671$	2.59056	−	1.49566i	0.100007	−	0.0577393i
$672$		0			0
$673$	−21.2878	+	5.70404i	−0.820584	+	0.219875i	−0.644602	−	0.764519i	$-0.722977\pi$
$673$	−21.2878	+	5.70404i	−0.820584	+	0.219875i	−0.175982	+	0.984393i	$0.556310\pi$
$674$	25.1828	−	14.5393i	0.970007	−	0.560034i
$675$		0			0
$676$	0.384362	−	0.665735i	0.0147832	−	0.0256052i
$677$	25.5821	+	25.5821i	0.983199	+	0.983199i	0.999861	−	0.0166625i	$-0.00530407\pi$
$677$	25.5821	+	25.5821i	0.983199	+	0.983199i	−0.0166625	+	0.999861i	$0.505304\pi$
$678$		0			0
$679$	−0.287704	+	1.88091i	−0.0110411	+	0.0721829i
$680$	−9.99658	−	32.4140i	−0.383351	−	1.24302i
$681$		0			0
$682$	0.0959277	−	0.358007i	0.00367326	−	0.0137088i
$683$	−8.45814	+	2.26635i	−0.323642	+	0.0867195i	−0.416982	−	0.908915i	$-0.636912\pi$
$683$	−8.45814	+	2.26635i	−0.323642	+	0.0867195i	0.0933404	+	0.995634i	$0.470246\pi$
$684$		0			0
$685$	−3.53873	−	5.63250i	−0.135208	−	0.215207i
$686$	11.2249	−	22.9233i	0.428567	−	0.875216i
$687$		0			0
$688$	−40.1114	+	10.7478i	−1.52923	+	0.409757i
$689$	14.3356			0.546144
$690$		0			0
$691$			10.6959i			0.406891i	0.979086	+	0.203445i	$0.0652139\pi$
$691$			10.6959i			0.406891i	−0.979086	+	0.203445i	$0.934786\pi$
$692$	1.55366	+	1.55366i	0.0590614	+	0.0590614i
$693$		0			0
$694$		−	8.58336i		−	0.325820i
$695$	−2.17277	+	9.51729i	−0.0824180	+	0.361011i
$696$		0			0
$697$	21.6136	−	21.6136i	0.818675	−	0.818675i
$698$	−6.20861	−	23.1709i	−0.235000	−	0.877030i
$699$		0			0
$700$	−0.442652	+	1.25581i	−0.0167307	+	0.0474651i
$701$	13.4460			0.507848			0.253924	−	0.967224i	$-0.418279\pi$
$701$	13.4460			0.507848			0.253924	+	0.967224i	$0.418279\pi$
$702$		0			0
$703$	−7.38290	−	27.5533i	−0.278451	−	1.03919i
$704$	−1.87745	+	1.08395i	−0.0707592	+	0.0408528i
$705$		0			0
$706$	−0.530778	+	0.306445i	−0.0199761	+	0.0115332i
$707$	−0.0605319	−	0.547988i	−0.00227654	−	0.0206092i
$708$		0			0
$709$		−	13.8943i		−	0.521811i	−0.965364	−	0.260906i	$-0.915979\pi$
$709$		−	13.8943i		−	0.521811i	0.965364	−	0.260906i	$-0.0840211\pi$
$710$	36.8167	−	1.37569i	1.38171	−	0.0516286i
$711$		0			0
$712$	4.74502	−	17.7087i	0.177827	−	0.663660i
$713$	1.10276	+	4.11554i	0.0412986	+	0.154128i
$714$		0			0
$715$	−0.627429	+	1.18701i	−0.0234645	+	0.0443915i
$716$	0.111024	−	0.192300i	0.00414917	−	0.00718658i
$717$		0			0
$718$	−2.35920	+	8.80464i	−0.0880445	+	0.328586i
$719$	−14.3592	−	24.8708i	−0.535506	−	0.927524i	−0.999139	−	0.0414962i	$-0.986788\pi$
$719$	−14.3592	−	24.8708i	−0.535506	−	0.927524i	0.463633	−	0.886028i	$-0.346546\pi$
$720$		0			0
$721$	−10.0520	−	1.53755i	−0.374356	−	0.0572613i
$722$	1.94519	+	7.25954i	0.0723924	+	0.270172i
$723$		0			0
$724$	−0.879262			−0.0326775
$725$	−2.83195	+	5.87905i	−0.105176	+	0.218342i
$726$		0			0
$727$	−6.27347	+	1.68097i	−0.232670	+	0.0623438i	−0.373270	−	0.927723i	$-0.621764\pi$
$727$	−6.27347	+	1.68097i	−0.232670	+	0.0623438i	0.140600	+	0.990066i	$0.455097\pi$
$728$	−17.6306	+	1.94751i	−0.653433	+	0.0721796i
$729$		0			0
$730$	−6.66679	−	21.6171i	−0.246749	−	0.800086i
$731$	−49.7395	+	28.7171i	−1.83968	+	1.06214i
$732$		0			0
$733$	7.11383	+	26.5492i	0.262755	+	0.980616i	0.963610	+	0.267312i	$0.0861355\pi$
$733$	7.11383	+	26.5492i	0.262755	+	0.980616i	−0.700855	+	0.713304i	$0.747198\pi$
$734$	−20.7727	−	35.9794i	−0.766736	−	1.32803i
$735$		0			0
$736$	1.16835	−	2.02365i	0.0430660	−	0.0745926i
$737$	0.251654	+	0.0674305i	0.00926980	+	0.00248384i
$738$		0			0
$739$	24.7020	+	14.2617i	0.908679	+	0.524626i	0.880006	−	0.474963i	$-0.157539\pi$
$739$	24.7020	+	14.2617i	0.908679	+	0.524626i	0.0286729	+	0.999589i	$0.490872\pi$
$740$	−1.47703	+	0.927976i	−0.0542968	+	0.0341131i
$741$		0			0
$742$	13.3641	+	18.1907i	0.490612	+	0.667802i
$743$	−5.77016	+	21.5345i	−0.211687	+	0.790025i	0.775620	+	0.631200i	$0.217437\pi$
$743$	−5.77016	+	21.5345i	−0.211687	+	0.790025i	−0.987307	+	0.158825i	$0.949229\pi$
$744$		0			0
$745$	−10.1324	−	32.8545i	−0.371223	−	1.20370i
$746$	−22.8925	+	39.6510i	−0.838155	+	1.45173i
$747$		0			0
$748$	−0.0966978	+	0.0966978i	−0.00353562	+	0.00353562i
$749$	6.38499	−	7.97076i	0.233302	−	0.291245i
$750$		0			0
$751$	7.96033	−	13.7877i	0.290477	−	0.503120i	−0.683446	−	0.730001i	$-0.739520\pi$
$751$	7.96033	−	13.7877i	0.290477	−	0.503120i	0.973922	+	0.226881i	$0.0728528\pi$
$752$	5.65860	+	5.65860i	0.206348	+	0.206348i
$753$		0			0
$754$	−4.16529			−0.151691
$755$	6.32165	−	27.6904i	0.230068	−	1.00776i
$756$		0			0
$757$	15.6132	−	15.6132i	0.567471	−	0.567471i	−0.363948	−	0.931419i	$-0.618572\pi$
$757$	15.6132	−	15.6132i	0.567471	−	0.567471i	0.931419	+	0.363948i	$0.118572\pi$
$758$	−2.77649	−	2.77649i	−0.100847	−	0.100847i
$759$		0			0
$760$	−20.1750	+	12.6753i	−0.731824	+	0.459783i
$761$	−22.5862	−	13.0402i	−0.818750	−	0.472706i	0.0312349	−	0.999512i	$-0.490056\pi$
$761$	−22.5862	−	13.0402i	−0.818750	−	0.472706i	−0.849985	+	0.526806i	$0.823389\pi$
$762$		0			0
$763$	29.4947	−	21.6687i	1.06778	−	0.784461i
$764$		−	1.31698i		−	0.0476467i
$765$		0			0
$766$	37.1032	+	21.4216i	1.34059	+	0.773992i
$767$	−9.19223	−	2.46305i	−0.331912	−	0.0889356i
$768$		0			0
$769$	1.24982	+	2.16475i	0.0450695	+	0.0780627i	0.887680	−	0.460461i	$-0.152316\pi$
$769$	1.24982	+	2.16475i	0.0450695	+	0.0780627i	−0.842611	+	0.538523i	$0.818982\pi$
$770$	−2.09112	+	0.310408i	−0.0753588	+	0.0111863i
$771$		0			0
$772$	1.39696	−	1.39696i	0.0502775	−	0.0502775i
$773$	−1.75890	−	6.56432i	−0.0632634	−	0.236102i	0.927053	−	0.374930i	$-0.122333\pi$
$773$	−1.75890	−	6.56432i	−0.0632634	−	0.236102i	−0.990317	+	0.138828i	$0.955667\pi$
$774$		0			0
$775$	−5.17162	+	0.387025i	−0.185770	+	0.0139023i
$776$	1.80314	+	1.04104i	0.0647289	+	0.0373713i
$777$		0			0
$778$	11.0417	−	41.2082i	0.395864	−	1.47739i
$779$	−18.5938	−	10.7352i	−0.666193	−	0.384627i
$780$		0			0
$781$	−1.54991	−	2.68453i	−0.0554602	−	0.0960599i
$782$	−7.67773	+	28.6537i	−0.274555	+	1.02465i
$783$		0			0
$784$	−17.9530	−	19.5191i	−0.641180	−	0.697109i
$785$	0.488545	+	13.0746i	0.0174369	+	0.466653i
$786$		0			0
$787$	11.0114	+	11.0114i	0.392514	+	0.392514i	0.875582	−	0.483069i	$-0.160478\pi$
$787$	11.0114	+	11.0114i	0.392514	+	0.392514i	−0.483069	+	0.875582i	$0.660478\pi$
$788$	1.35660	+	1.35660i	0.0483268	+	0.0483268i
$789$		0			0
$790$	−1.78095	−	47.6623i	−0.0633632	−	1.69575i
$791$	40.1349	+	32.1501i	1.42703	+	1.14313i
$792$		0			0
$793$	6.91476	−	25.8062i	0.245550	−	0.916407i
$794$	−18.2904	−	31.6800i	−0.649104	−	1.12428i
$795$		0			0
$796$	0.335423	+	0.193656i	0.0118887	+	0.00686397i
$797$	1.54239	−	5.75626i	0.0546341	−	0.203897i	−0.933214	−	0.359322i	$-0.883008\pi$
$797$	1.54239	−	5.75626i	0.0546341	−	0.203897i	0.987848	+	0.155425i	$0.0496746\pi$
$798$		0			0
$799$	9.58520	+	5.53402i	0.339100	+	0.195779i
$800$	2.15563	+	1.85546i	0.0762131	+	0.0656003i
$801$		0			0
$802$	3.14106	+	11.7226i	0.110915	+	0.413939i
$803$	−1.34587	+	1.34587i	−0.0474946	+	0.0474946i
$804$		0			0
$805$	19.0341	−	15.1098i	0.670865	−	0.532549i
$806$	−1.65515	−	2.86680i	−0.0583000	−	0.100979i
$807$		0			0
$808$	−0.582714	−	0.156138i	−0.0204998	−	0.00549291i
$809$	−7.57041	−	4.37078i	−0.266161	−	0.153668i	0.360981	−	0.932573i	$-0.382442\pi$
$809$	−7.57041	−	4.37078i	−0.266161	−	0.153668i	−0.627142	+	0.778905i	$0.715775\pi$
$810$		0			0
$811$			45.3232i			1.59151i	0.605617	+	0.795757i	$0.292927\pi$
$811$			45.3232i			1.59151i	−0.605617	+	0.795757i	$0.707073\pi$
$812$	0.205778	+	0.280098i	0.00722140	+	0.00982950i
$813$		0			0
$814$	−2.39841	−	1.38472i	−0.0840642	−	0.0485345i
$815$	24.0063	−	15.0824i	0.840903	−	0.528314i
$816$		0			0
$817$	28.5267	+	28.5267i	0.998022	+	0.998022i
$818$	14.8669	−	14.8669i	0.519810	−	0.519810i
$819$		0			0
$820$	−0.292220	+	1.28000i	−0.0102048	+	0.0446995i
$821$	−39.3824			−1.37446			−0.687228	−	0.726442i	$-0.741173\pi$
$821$	−39.3824			−1.37446			−0.687228	+	0.726442i	$0.741173\pi$
$822$		0			0
$823$	11.9183	+	11.9183i	0.415446	+	0.415446i	0.883631	−	0.468185i	$-0.155092\pi$
$823$	11.9183	+	11.9183i	0.415446	+	0.415446i	−0.468185	+	0.883631i	$0.655092\pi$
$824$	−5.56354	+	9.63634i	−0.193815	+	0.335698i
$825$		0			0
$826$	−5.44387	−	13.9603i	−0.189417	−	0.485742i
$827$	−3.57234	+	3.57234i	−0.124222	+	0.124222i	−0.766485	−	0.642262i	$-0.777996\pi$
$827$	−3.57234	+	3.57234i	−0.124222	+	0.124222i	0.642262	+	0.766485i	$0.277996\pi$
$828$		0			0
$829$	−23.9683	+	41.5144i	−0.832455	+	1.44185i	0.0636314	+	0.997973i	$0.479732\pi$
$829$	−23.9683	+	41.5144i	−0.832455	+	1.44185i	−0.896086	+	0.443880i	$0.853602\pi$
$830$	−13.3927	−	43.4261i	−0.464869	−	1.50734i
$831$		0			0
$832$	−5.01133	+	18.7025i	−0.173737	+	0.648394i
$833$	−30.9716	−	19.6499i	−1.07310	−	0.680829i
$834$		0			0
$835$	−33.5281	+	21.0647i	−1.16029	+	0.728975i
$836$	0.0831874	+	0.0480283i	0.00287710	+	0.00166109i
$837$		0			0
$838$	5.25934	+	1.40923i	0.181681	+	0.0486812i
$839$	−0.252625	+	0.437560i	−0.00872159	+	0.0151062i	−0.870353	−	0.492428i	$-0.836110\pi$
$839$	−0.252625	+	0.437560i	−0.00872159	+	0.0151062i	0.861632	+	0.507534i	$0.169443\pi$
$840$		0			0
$841$	−13.6483	−	23.6396i	−0.470632	−	0.815159i
$842$	−2.94750	−	11.0002i	−0.101577	−	0.379092i
$843$		0			0
$844$	−0.368238	+	0.212602i	−0.0126753	+	0.00731808i
$845$	−5.03280	−	16.3189i	−0.173134	−	0.561388i
$846$		0			0
$847$	−17.1256	−	23.3108i	−0.588443	−	0.800967i
$848$	22.6537	−	6.07005i	0.777932	−	0.208446i
$849$		0			0
$850$	−32.5298	−	15.6696i	−1.11576	−	0.537464i
$851$	31.8367			1.09135
$852$		0			0
$853$	−3.59160	−	13.4040i	−0.122974	−	0.458945i	0.876785	−	0.480882i	$-0.159683\pi$
$853$	−3.59160	−	13.4040i	−0.122974	−	0.458945i	−0.999759	+	0.0219369i	$0.993017\pi$
$854$	39.1922	−	15.2831i	1.34113	−	0.522977i
$855$		0			0
$856$	−5.58756	−	9.67793i	−0.190979	−	0.330785i
$857$	−10.4502	+	39.0005i	−0.356971	+	1.33223i	0.521015	+	0.853547i	$0.325553\pi$
$857$	−10.4502	+	39.0005i	−0.356971	+	1.33223i	−0.877986	+	0.478686i	$0.841113\pi$
$858$		0			0
$859$	−9.98473	+	17.2941i	−0.340675	+	0.590066i	−0.984558	−	0.175058i	$-0.943989\pi$
$859$	−9.98473	+	17.2941i	−0.340675	+	0.590066i	0.643884	+	0.765123i	$0.277322\pi$
$860$	1.15287	−	2.18106i	0.0393124	−	0.0743734i
$861$		0			0
$862$	−10.2709	−	38.3316i	−0.349829	−	1.30558i
$863$	3.35773	−	12.5312i	0.114298	−	0.426567i	−0.884935	−	0.465714i	$-0.845797\pi$
$863$	3.35773	−	12.5312i	0.114298	−	0.426567i	0.999233	+	0.0391471i	$0.0124641\pi$
$864$		0			0
$865$	48.7774	−	1.82261i	1.65848	−	0.0619707i
$866$		−	42.6150i		−	1.44812i
$867$		0			0
$868$	−0.111010	+	0.252930i	−0.00376793	+	0.00858500i
$869$	−3.47535	+	2.00649i	−0.117893	+	0.0680656i
$870$		0			0
$871$	2.01516	−	1.16345i	0.0682811	−	0.0394221i
$872$	−10.3650	−	38.6828i	−0.351004	−	1.30996i
$873$		0			0
$874$	20.8368			0.704817
$875$	13.7608	+	26.1847i	0.465200	+	0.885205i
$876$		0			0
$877$	−0.00254408	−	0.00949463i	−8.59074e−5	−	0.000320611i	0.965883	−	0.258979i	$-0.0833862\pi$
$877$	−0.00254408	−	0.00949463i	−8.59074e−5	−	0.000320611i	−0.965969	+	0.258659i	$0.916719\pi$
$878$	−37.8529	+	37.8529i	−1.27747	+	1.27747i
$879$		0			0
$880$	−0.488882	+	2.14142i	−0.0164802	+	0.0721874i
$881$		−	4.53219i		−	0.152693i	−0.997081	−	0.0763466i	$-0.975674\pi$
$881$		−	4.53219i		−	0.152693i	0.997081	−	0.0763466i	$-0.0243256\pi$
$882$		0			0
$883$	−8.97475	−	8.97475i	−0.302024	−	0.302024i	0.539781	−	0.841805i	$-0.318507\pi$
$883$	−8.97475	−	8.97475i	−0.302024	−	0.302024i	−0.841805	+	0.539781i	$0.818507\pi$
$884$			1.22138i			0.0410794i
$885$		0			0
$886$	−4.82510			−0.162102
$887$	−19.1735	+	5.13752i	−0.643782	+	0.172501i	−0.565916	−	0.824463i	$-0.691477\pi$
$887$	−19.1735	+	5.13752i	−0.643782	+	0.172501i	−0.0778662	+	0.996964i	$0.524811\pi$
$888$		0			0
$889$	−12.9096	−	33.1054i	−0.432973	−	1.11032i
$890$	−10.3818	−	16.5245i	−0.348000	−	0.553903i
$891$		0			0
$892$	2.16219	−	0.579358i	0.0723956	−	0.0193984i
$893$	2.01216	−	7.50948i	0.0673343	−	0.251295i
$894$		0			0
$895$	−1.45374	−	4.71378i	−0.0485932	−	0.157564i
$896$	−25.5994	+	9.98255i	−0.855214	+	0.333494i
$897$		0			0
$898$	−1.28697	−	1.28697i	−0.0429468	−	0.0429468i
$899$	−0.676844	+	1.17233i	−0.0225740	+	0.0390993i
$900$		0			0
$901$	28.0914	−	16.2186i	0.935859	−	0.540319i
$902$	−2.01347	+	0.539507i	−0.0670411	+	0.0179636i
$903$		0			0
$904$	48.7309	−	28.1348i	1.62077	−	0.935750i
$905$	−13.2865	+	14.3180i	−0.441659	+	0.475947i
$906$		0			0
$907$	9.64984	+	2.58567i	0.320418	+	0.0858556i	0.415443	−	0.909619i	$-0.363627\pi$
$907$	9.64984	+	2.58567i	0.320418	+	0.0858556i	−0.0950254	+	0.995475i	$0.530293\pi$
$908$	2.15009	+	0.576115i	0.0713533	+	0.0191191i
$909$		0			0
$910$	−11.2460	+	15.1667i	−0.372801	+	0.502772i
$911$	−16.8443	+	29.1751i	−0.558076	+	0.966615i	0.439582	+	0.898203i	$0.355127\pi$
$911$	−16.8443	+	29.1751i	−0.558076	+	0.966615i	−0.997657	+	0.0684125i	$0.978207\pi$
$912$		0			0
$913$	−2.70368	+	2.70368i	−0.0894787	+	0.0894787i
$914$			16.0802i			0.531887i
$915$		0			0
$916$	0.436777	+	0.252174i	0.0144315	+	0.00833205i
$917$	−37.0572	+	27.2246i	−1.22374	+	0.899037i
$918$		0			0
$919$	16.4930	−	9.52221i	0.544052	−	0.314109i	−0.202667	−	0.979248i	$-0.564961\pi$
$919$	16.4930	−	9.52221i	0.544052	−	0.314109i	0.746720	+	0.665139i	$0.231628\pi$
$920$	−7.83691	−	25.4113i	−0.258375	−	0.837784i
$921$		0			0
$922$	19.0480	−	5.10389i	0.627312	−	0.168088i
$923$	−26.7423	−	7.16558i	−0.880234	−	0.235858i
$924$		0			0
$925$	−7.20820	+	38.0748i	−0.237004	+	1.25189i
$926$	29.5213	+	51.1324i	0.970130	+	1.68031i
$927$		0			0
$928$	0.717105	−	0.192148i	0.0235401	−	0.00630755i
$929$	−13.5354			−0.444081			−0.222041	−	0.975037i	$-0.571272\pi$
$929$	−13.5354			−0.444081			−0.222041	+	0.975037i	$0.571272\pi$
$930$		0			0
$931$	−7.70153	+	24.5860i	−0.252407	+	0.805774i
$932$	2.44701	+	0.655673i	0.0801544	+	0.0214773i
$933$		0			0
$934$	−4.48363	−	7.76588i	−0.146709	−	0.254107i
$935$	0.113437	+	3.03584i	0.00370978	+	0.0992826i
$936$		0			0
$937$	−41.4550	−	41.4550i	−1.35428	−	1.35428i	−0.880813	−	0.473464i	$-0.843004\pi$
$937$	−41.4550	−	41.4550i	−1.35428	−	1.35428i	−0.473464	−	0.880813i	$-0.656996\pi$
$938$	3.35492	+	1.47246i	0.109542	+	0.0480777i
$939$		0			0
$940$	−0.475080	+	0.0177518i	−0.0154954	+	0.000578999i
$941$			9.38896i			0.306071i	0.988221	+	0.153036i	$0.0489049\pi$
$941$			9.38896i			0.306071i	−0.988221	+	0.153036i	$0.951095\pi$
$942$		0			0
$943$	16.9442	−	16.9442i	0.551779	−	0.551779i
$944$	−15.5689			−0.506723
$945$		0			0
$946$	3.91677			0.127345
$947$	10.8245	−	10.8245i	0.351748	−	0.351748i	−0.509011	−	0.860760i	$-0.669989\pi$
$947$	10.8245	−	10.8245i	0.351748	−	0.351748i	0.860760	+	0.509011i	$0.169989\pi$
$948$		0			0
$949$			16.9995i			0.551826i
$950$	−4.71770	+	24.9196i	−0.153062	+	0.808499i
$951$		0			0
$952$	−32.3447	+	23.7626i	−1.04830	+	0.770149i
$953$	18.5010	+	18.5010i	0.599306	+	0.599306i	0.940128	−	0.340822i	$-0.110705\pi$
$953$	18.5010	+	18.5010i	0.599306	+	0.599306i	−0.340822	+	0.940128i	$0.610705\pi$
$954$		0			0
$955$	−21.4459	−	19.9009i	−0.693973	−	0.643979i
$956$	0.154341	+	0.267327i	0.00499176	+	0.00864597i
$957$		0			0
$958$	33.8071	+	9.05857i	1.09226	+	0.292669i
$959$	−4.92068	+	6.14277i	−0.158897	+	0.198360i
$960$		0			0
$961$	29.9242			0.965296
$962$	−23.8921	+	6.40188i	−0.770313	+	0.206405i
$963$		0			0
$964$	−1.04615	−	1.81199i	−0.0336943	−	0.0583602i
$965$	−1.63878	−	43.8576i	−0.0527542	−	1.41183i
$966$		0			0
$967$	−27.2779	−	7.30909i	−0.877198	−	0.235045i	−0.208000	−	0.978129i	$-0.566696\pi$
$967$	−27.2779	−	7.30909i	−0.877198	−	0.235045i	−0.669198	+	0.743084i	$0.733362\pi$
$968$	−30.5725	+	8.19187i	−0.982637	+	0.263297i
$969$		0			0
$970$	2.11787	−	0.653158i	0.0680008	−	0.0209716i
$971$	5.42391	−	3.13150i	0.174062	−	0.100494i	−0.410438	−	0.911888i	$-0.634624\pi$
$971$	5.42391	−	3.13150i	0.174062	−	0.100494i	0.584500	+	0.811394i	$0.301291\pi$
$972$		0			0
$973$	11.4809	−	1.26821i	0.368061	−	0.0406568i
$974$	48.2352	+	27.8486i	1.54555	+	0.892327i
$975$		0			0
$976$		−	43.7080i		−	1.39906i
$977$	39.5668	−	39.5668i	1.26585	−	1.26585i	0.317642	−	0.948211i	$-0.397109\pi$
$977$	39.5668	−	39.5668i	1.26585	−	1.26585i	0.948211	−	0.317642i	$-0.102891\pi$
$978$		0			0
$979$	−0.820978	+	1.42198i	−0.0262386	+	0.0454466i
$980$	1.57548	+	0.00696144i	0.0503269	+	0.000222375i
$981$		0			0
$982$	8.30822	+	2.22618i	0.265126	+	0.0710403i
$983$	30.4609	+	8.16197i	0.971551	+	0.260326i	0.709483	−	0.704723i	$-0.248929\pi$
$983$	30.4609	+	8.16197i	0.971551	+	0.260326i	0.262069	+	0.965049i	$0.415595\pi$
$984$		0			0
$985$	42.5906	−	1.59144i	1.35705	−	0.0507073i
$986$	−8.16210	+	4.71239i	−0.259934	+	0.150073i
$987$		0			0
$988$	0.828684	−	0.222045i	0.0263640	−	0.00706420i
$989$	−38.9937	+	22.5130i	−1.23993	+	0.715873i
$990$		0			0
$991$	2.85314	−	4.94179i	0.0906330	−	0.156981i	−0.817145	−	0.576433i	$-0.804444\pi$
$991$	2.85314	−	4.94179i	0.0906330	−	0.156981i	0.907778	+	0.419452i	$0.137778\pi$
$992$	0.417200	+	0.417200i	0.0132461	+	0.0132461i
$993$		0			0
$994$	−15.8375	−	40.6138i	−0.502334	−	1.28819i
$995$	8.22210	−	2.53572i	0.260658	−	0.0803877i
$996$		0			0
$997$	−6.41453	+	23.9394i	−0.203150	+	0.758167i	0.786855	+	0.617138i	$0.211708\pi$
$997$	−6.41453	+	23.9394i	−0.203150	+	0.758167i	−0.990005	+	0.141029i	$0.954959\pi$
$998$	9.58450	−	2.56816i	0.303392	−	0.0812936i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bv.e.73.12		160
3.2	odd	2		315.2.bs.e.178.29	yes	160
5.2	odd	4	inner	945.2.bv.e.262.12		160
7.5	odd	6		945.2.cj.e.208.29		160
9.4	even	3		945.2.cj.e.388.12		160
9.5	odd	6		315.2.cg.e.283.29	yes	160
15.2	even	4		315.2.bs.e.52.29	✓	160
21.5	even	6		315.2.cg.e.313.12	yes	160
35.12	even	12		945.2.cj.e.397.12		160
45.22	odd	12		945.2.cj.e.577.29		160
45.32	even	12		315.2.cg.e.157.12	yes	160
63.5	even	6		315.2.bs.e.103.29	yes	160
63.40	odd	6	inner	945.2.bv.e.523.12		160
105.47	odd	12		315.2.cg.e.187.29	yes	160
315.257	odd	12		315.2.bs.e.292.29	yes	160
315.292	even	12	inner	945.2.bv.e.712.12		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.29	✓	160	15.2	even	4
315.2.bs.e.103.29	yes	160	63.5	even	6
315.2.bs.e.178.29	yes	160	3.2	odd	2
315.2.bs.e.292.29	yes	160	315.257	odd	12
315.2.cg.e.157.12	yes	160	45.32	even	12
315.2.cg.e.187.29	yes	160	105.47	odd	12
315.2.cg.e.283.29	yes	160	9.5	odd	6
315.2.cg.e.313.12	yes	160	21.5	even	6
945.2.bv.e.73.12		160	1.1	even	1	trivial
945.2.bv.e.262.12		160	5.2	odd	4	inner
945.2.bv.e.523.12		160	63.40	odd	6	inner
945.2.bv.e.712.12		160	315.292	even	12	inner
945.2.cj.e.208.29		160	7.5	odd	6
945.2.cj.e.388.12		160	9.4	even	3
945.2.cj.e.397.12		160	35.12	even	12
945.2.cj.e.577.29		160	45.22	odd	12

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bv (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.974511 + 0.974511i) q^{2} +0.100655i q^{4} +(1.63908 + 1.52100i) q^{5} +(1.06331 - 2.42268i) q^{7} +(-2.04711 - 2.04711i) q^{8} +O(q^{10})\)	\(q+(-0.974511 + 0.974511i) q^{2} +0.100655i q^{4} +(1.63908 + 1.52100i) q^{5} +(1.06331 - 2.42268i) q^{7} +(-2.04711 - 2.04711i) q^{8} +(-3.07953 + 0.115069i) q^{10} +(0.129642 + 0.224547i) q^{11} +(2.23686 + 0.599364i) q^{13} +(1.32472 + 3.39713i) q^{14} +3.78856 q^{16} +(5.06133 - 1.35618i) q^{17} +(-1.84029 - 3.18747i) q^{19} +(-0.153096 + 0.164981i) q^{20} +(-0.345161 - 0.0924857i) q^{22} +(3.96787 - 1.06319i) q^{23} +(0.373138 + 4.98606i) q^{25} +(-2.76393 + 1.59576i) q^{26} +(0.243854 + 0.107027i) q^{28} +(1.13026 + 0.652558i) q^{29} +1.03722i q^{31} +(0.402230 - 0.402230i) q^{32} +(-3.61071 + 6.25393i) q^{34} +(5.42773 - 2.35367i) q^{35} +(7.48615 + 2.00591i) q^{37} +(4.89961 + 1.31285i) q^{38} +(-0.241721 - 6.46902i) q^{40} +(5.05188 - 2.91670i) q^{41} +(-10.5875 + 2.83692i) q^{43} +(-0.0226017 + 0.0130491i) q^{44} +(-2.83065 + 4.90283i) q^{46} +(1.49360 + 1.49360i) q^{47} +(-4.73875 - 5.15211i) q^{49} +(-5.22260 - 4.49534i) q^{50} +(-0.0603289 + 0.225151i) q^{52} +(5.97951 - 1.60220i) q^{53} +(-0.129042 + 0.565235i) q^{55} +(-7.13621 + 2.78279i) q^{56} +(-1.73738 + 0.465529i) q^{58} -4.10944 q^{59} -11.5368i q^{61} +(-1.01078 - 1.01078i) q^{62} +8.36107i q^{64} +(2.75475 + 4.38466i) q^{65} +(0.710508 - 0.710508i) q^{67} +(0.136506 + 0.509447i) q^{68} +(-2.99571 + 7.58306i) q^{70} -11.9553 q^{71} +(1.89993 + 7.09062i) q^{73} +(-9.25012 + 5.34056i) q^{74} +(0.320835 - 0.185234i) q^{76} +(0.681855 - 0.0753191i) q^{77} +15.4772i q^{79} +(6.20973 + 5.76239i) q^{80} +(-2.08075 + 7.76547i) q^{82} +(3.81672 + 14.2442i) q^{83} +(10.3586 + 5.47538i) q^{85} +(7.55305 - 13.0823i) q^{86} +(0.194280 - 0.725065i) q^{88} +(3.16633 + 5.48424i) q^{89} +(3.83054 - 4.78188i) q^{91} +(0.107015 + 0.399386i) q^{92} -2.91106 q^{94} +(1.83176 - 8.02358i) q^{95} +(-0.694682 + 0.186139i) q^{97} +(9.63876 + 0.402817i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8}+O(q^{10}) \) 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8	\( 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8} - 24 q^{10} + 16 q^{11} - 152 q^{16} + 6 q^{17} - 60 q^{20} + 8 q^{22} - 8 q^{23} + 2 q^{25} + 36 q^{26} + 22 q^{28} - 12 q^{32} + 36 q^{35} - 4 q^{37} + 18 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 44 q^{50} + 54 q^{52} - 8 q^{53} - 148 q^{56} + 28 q^{58} + 124 q^{65} - 24 q^{67} - 42 q^{68} - 34 q^{70} + 40 q^{71} + 36 q^{73} + 96 q^{76} - 58 q^{77} - 36 q^{80} - 66 q^{82} + 138 q^{83} - 20 q^{85} + 16 q^{86} + 46 q^{88} - 48 q^{91} + 26 q^{92} - 188 q^{95} + 48 q^{97} - 102 q^{98}+O(q^{100}) \) 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8 - 24 * q^10 + 16 * q^11 - 152 * q^16 + 6 * q^17 - 60 * q^20 + 8 * q^22 - 8 * q^23 + 2 * q^25 + 36 * q^26 + 22 * q^28 - 12 * q^32 + 36 * q^35 - 4 * q^37 + 18 * q^38 - 6 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 44 * q^50 + 54 * q^52 - 8 * q^53 - 148 * q^56 + 28 * q^58 + 124 * q^65 - 24 * q^67 - 42 * q^68 - 34 * q^70 + 40 * q^71 + 36 * q^73 + 96 * q^76 - 58 * q^77 - 36 * q^80 - 66 * q^82 + 138 * q^83 - 20 * q^85 + 16 * q^86 + 46 * q^88 - 48 * q^91 + 26 * q^92 - 188 * q^95 + 48 * q^97 - 102 * q^98

Introduction

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