LMFDB - Embedded newform 864.2.bn.a.179.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(35,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("864.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			179.38
Character	$\chi$	$=$	864.179
Dual form			864.2.bn.a.251.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17575 + 0.785882i) q^{2} +(0.764778 + 1.84800i) q^{4} +(-2.85653 - 0.376069i) q^{5} +(-0.838984 + 3.13113i) q^{7} +(-0.553125 + 2.77382i) q^{8} +O(q^{10})$	\(q+(1.17575 + 0.785882i) q^{2} +(0.764778 + 1.84800i) q^{4} +(-2.85653 - 0.376069i) q^{5} +(-0.838984 + 3.13113i) q^{7} +(-0.553125 + 2.77382i) q^{8} +(-3.06302 - 2.68706i) q^{10} +(3.69421 - 4.81439i) q^{11} +(-3.49913 + 2.68498i) q^{13} +(-3.44714 + 3.02209i) q^{14} +(-2.83023 + 2.82662i) q^{16} -4.67934 q^{17} +(-1.17593 + 2.83895i) q^{19} +(-1.48963 - 5.56649i) q^{20} +(8.12702 - 2.75731i) q^{22} +(-3.57188 + 0.957081i) q^{23} +(3.18871 + 0.854412i) q^{25} +(-6.22418 + 0.406959i) q^{26} +(-6.42797 + 0.844175i) q^{28} +(0.568252 + 4.31631i) q^{29} +(-3.52849 - 2.03717i) q^{31} +(-5.54904 + 1.09918i) q^{32} +(-5.50174 - 3.67741i) q^{34} +(3.57410 - 8.62865i) q^{35} +(1.98078 - 0.820466i) q^{37} +(-3.61369 + 2.41376i) q^{38} +(2.62316 - 7.71547i) q^{40} +(-0.0956623 - 0.357017i) q^{41} +(0.627411 + 0.481429i) q^{43} +(11.7223 + 3.14498i) q^{44} +(-4.95179 - 1.68179i) q^{46} +(-2.98300 + 1.72224i) q^{47} +(-3.03790 - 1.75394i) q^{49} +(3.07766 + 3.51052i) q^{50} +(-7.63791 - 4.41300i) q^{52} +(6.59478 - 2.73165i) q^{53} +(-12.3632 + 12.3632i) q^{55} +(-8.22112 - 4.05909i) q^{56} +(-2.72399 + 5.52148i) q^{58} +(-0.174758 + 1.32742i) q^{59} +(-2.52080 + 0.331870i) q^{61} +(-2.54764 - 5.16818i) q^{62} +(-7.38811 - 3.06853i) q^{64} +(11.0051 - 6.35381i) q^{65} +(8.04333 - 6.17187i) q^{67} +(-3.57866 - 8.64743i) q^{68} +(10.9834 - 7.33632i) q^{70} +(-5.75858 + 5.75858i) q^{71} +(11.3191 + 11.3191i) q^{73} +(2.97369 + 0.591997i) q^{74} +(-6.14572 - 0.00195846i) q^{76} +(11.9751 + 15.6063i) q^{77} +(7.01043 + 12.1424i) q^{79} +(9.14764 - 7.00997i) q^{80} +(0.168098 - 0.494942i) q^{82} +(2.31862 + 17.6117i) q^{83} +(13.3667 + 1.75976i) q^{85} +(0.359332 + 1.05911i) q^{86} +(11.3109 + 12.9100i) q^{88} +(-2.22386 - 2.22386i) q^{89} +(-5.47130 - 13.2089i) q^{91} +(-4.50038 - 5.86888i) q^{92} +(-4.86074 - 0.319367i) q^{94} +(4.42673 - 7.66732i) q^{95} +(0.970710 + 1.68132i) q^{97} +(-2.19343 - 4.44963i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.17575	+	0.785882i	0.831381	+	0.555703i
$2$	1.17575	+	0.785882i	0.831381	+	0.555703i
$3$		0			0
$3$		0			0
$4$	0.764778	+	1.84800i	0.382389	+	0.924001i
$5$	−2.85653	−	0.376069i	−1.27748	−	0.168183i	−0.538911	−	0.842362i	$-0.681164\pi$
$5$	−2.85653	−	0.376069i	−1.27748	−	0.168183i	−0.738568	+	0.674179i	$0.764498\pi$
$6$		0			0
$7$	−0.838984	+	3.13113i	−0.317106	+	1.18346i	0.604907	+	0.796296i	$0.293210\pi$
$7$	−0.838984	+	3.13113i	−0.317106	+	1.18346i	−0.922013	+	0.387160i	$0.873456\pi$
$8$	−0.553125	+	2.77382i	−0.195559	+	0.980692i
$9$		0			0
$10$	−3.06302	−	2.68706i	−0.968612	−	0.849723i
$11$	3.69421	−	4.81439i	1.11385	−	1.45159i	0.236568	−	0.971615i	$-0.423977\pi$
$11$	3.69421	−	4.81439i	1.11385	−	1.45159i	0.877280	−	0.479980i	$-0.159356\pi$
$12$		0			0
$13$	−3.49913	+	2.68498i	−0.970485	+	0.744679i	−0.966858	−	0.255314i	$-0.917821\pi$
$13$	−3.49913	+	2.68498i	−0.970485	+	0.744679i	−0.00362678	+	0.999993i	$0.501154\pi$
$14$	−3.44714	+	3.02209i	−0.921286	+	0.807686i
$15$		0			0
$16$	−2.83023	+	2.82662i	−0.707557	+	0.706656i
$17$	−4.67934			−1.13491			−0.567453	−	0.823406i	$-0.692071\pi$
$17$	−4.67934			−1.13491			−0.567453	+	0.823406i	$0.692071\pi$
$18$		0			0
$19$	−1.17593	+	2.83895i	−0.269778	+	0.651301i	−0.999473	−	0.0324721i	$-0.989662\pi$
$19$	−1.17593	+	2.83895i	−0.269778	+	0.651301i	0.729695	+	0.683773i	$0.239662\pi$
$20$	−1.48963	−	5.56649i	−0.333092	−	1.24470i
$21$		0			0
$22$	8.12702	−	2.75731i	1.73269	−	0.587860i
$23$	−3.57188	+	0.957081i	−0.744788	+	0.199565i	−0.611205	−	0.791472i	$-0.709315\pi$
$23$	−3.57188	+	0.957081i	−0.744788	+	0.199565i	−0.133583	+	0.991038i	$0.542648\pi$
$24$		0			0
$25$	3.18871	+	0.854412i	0.637742	+	0.170882i
$26$	−6.22418	+	0.406959i	−1.22066	+	0.0798112i
$27$		0			0
$28$	−6.42797	+	0.844175i	−1.21477	+	0.159534i
$29$	0.568252	+	4.31631i	0.105522	+	0.801518i	0.959599	+	0.281371i	$0.0907893\pi$
$29$	0.568252	+	4.31631i	0.105522	+	0.801518i	−0.854077	+	0.520146i	$0.825877\pi$
$30$		0			0
$31$	−3.52849	−	2.03717i	−0.633735	−	0.365887i	0.148462	−	0.988918i	$-0.452568\pi$
$31$	−3.52849	−	2.03717i	−0.633735	−	0.365887i	−0.782197	+	0.623031i	$0.785901\pi$
$32$	−5.54904	+	1.09918i	−0.980940	+	0.194309i
$33$		0			0
$34$	−5.50174	−	3.67741i	−0.943540	−	0.630671i
$35$	3.57410	−	8.62865i	0.604134	−	1.45851i
$36$		0			0
$37$	1.98078	−	0.820466i	0.325638	−	0.134884i	−0.213875	−	0.976861i	$-0.568608\pi$
$37$	1.98078	−	0.820466i	0.325638	−	0.134884i	0.539513	+	0.841977i	$0.318608\pi$
$38$	−3.61369	+	2.41376i	−0.586217	+	0.391563i
$39$		0			0
$40$	2.62316	−	7.71547i	0.414759	−	1.21992i
$41$	−0.0956623	−	0.357017i	−0.0149399	−	0.0557566i	0.958053	−	0.286590i	$-0.0925216\pi$
$41$	−0.0956623	−	0.357017i	−0.0149399	−	0.0557566i	−0.972993	+	0.230833i	$0.925855\pi$
$42$		0			0
$43$	0.627411	+	0.481429i	0.0956793	+	0.0734173i	0.655493	−	0.755201i	$-0.272461\pi$
$43$	0.627411	+	0.481429i	0.0956793	+	0.0734173i	−0.559814	+	0.828618i	$0.689127\pi$
$44$	11.7223	+	3.14498i	1.76720	+	0.474123i
$45$		0			0
$46$	−4.95179	−	1.68179i	−0.730101	−	0.247966i
$47$	−2.98300	+	1.72224i	−0.435115	+	0.251214i	−0.701523	−	0.712646i	$-0.747496\pi$
$47$	−2.98300	+	1.72224i	−0.435115	+	0.251214i	0.266408	+	0.963860i	$0.414163\pi$
$48$		0			0
$49$	−3.03790	−	1.75394i	−0.433986	−	0.250562i
$50$	3.07766	+	3.51052i	0.435246	+	0.496463i
$51$		0			0
$52$	−7.63791	−	4.41300i	−1.05919	−	0.611972i
$53$	6.59478	−	2.73165i	0.905863	−	0.375221i	0.119391	−	0.992847i	$-0.461906\pi$
$53$	6.59478	−	2.73165i	0.905863	−	0.375221i	0.786471	+	0.617627i	$0.211906\pi$
$54$		0			0
$55$	−12.3632	+	12.3632i	−1.66705	+	1.66705i
$56$	−8.22112	−	4.05909i	−1.09859	−	0.542419i
$57$		0			0
$58$	−2.72399	+	5.52148i	−0.357677	+	0.725006i
$59$	−0.174758	+	1.32742i	−0.0227515	+	0.172815i	−0.999048	−	0.0436220i	$-0.986110\pi$
$59$	−0.174758	+	1.32742i	−0.0227515	+	0.172815i	0.976297	+	0.216437i	$0.0694436\pi$
$60$		0			0
$61$	−2.52080	+	0.331870i	−0.322756	+	0.0424916i	−0.290163	−	0.956977i	$-0.593710\pi$
$61$	−2.52080	+	0.331870i	−0.322756	+	0.0424916i	−0.0325924	+	0.999469i	$0.510376\pi$
$62$	−2.54764	−	5.16818i	−0.323551	−	0.656359i
$63$		0			0
$64$	−7.38811	−	3.06853i	−0.923513	−	0.383566i
$65$	11.0051	−	6.35381i	1.36502	−	0.788093i
$66$		0			0
$67$	8.04333	−	6.17187i	0.982650	−	0.754014i	0.0133538	−	0.999911i	$-0.495749\pi$
$67$	8.04333	−	6.17187i	0.982650	−	0.754014i	0.969296	+	0.245897i	$0.0790825\pi$
$68$	−3.57866	−	8.64743i	−0.433976	−	1.04866i
$69$		0			0
$70$	10.9834	−	7.33632i	1.31276	−	0.876857i
$71$	−5.75858	+	5.75858i	−0.683418	+	0.683418i	−0.960769	−	0.277351i	$-0.910544\pi$
$71$	−5.75858	+	5.75858i	−0.683418	+	0.683418i	0.277351	+	0.960769i	$0.410544\pi$
$72$		0			0
$73$	11.3191	+	11.3191i	1.32480	+	1.32480i	0.909843	+	0.414952i	$0.136202\pi$
$73$	11.3191	+	11.3191i	1.32480	+	1.32480i	0.414952	+	0.909843i	$0.363798\pi$
$74$	2.97369	+	0.591997i	0.345685	+	0.0688183i
$75$		0			0
$76$	−6.14572	−	0.00195846i	−0.704963	−	0.000224651i
$77$	11.9751	+	15.6063i	1.36469	+	1.77850i
$78$		0			0
$79$	7.01043	+	12.1424i	0.788735	+	1.36613i	0.926742	+	0.375697i	$0.122597\pi$
$79$	7.01043	+	12.1424i	0.788735	+	1.36613i	−0.138008	+	0.990431i	$0.544070\pi$
$80$	9.14764	−	7.00997i	1.02274	−	0.783739i
$81$		0			0
$82$	0.168098	−	0.494942i	0.0185633	−	0.0546572i
$83$	2.31862	+	17.6117i	0.254502	+	1.93313i	0.347957	+	0.937510i	$0.386875\pi$
$83$	2.31862	+	17.6117i	0.254502	+	1.93313i	−0.0934556	+	0.995623i	$0.529791\pi$
$84$		0			0
$85$	13.3667	+	1.75976i	1.44982	+	0.190872i
$86$	0.359332	+	1.05911i	0.0387478	+	0.114207i
$87$		0			0
$88$	11.3109	+	12.9100i	1.20574	+	1.37621i
$89$	−2.22386	−	2.22386i	−0.235728	−	0.235728i	0.579350	−	0.815079i	$-0.303306\pi$
$89$	−2.22386	−	2.22386i	−0.235728	−	0.235728i	−0.815079	+	0.579350i	$0.803306\pi$
$90$		0			0
$91$	−5.47130	−	13.2089i	−0.573548	−	1.38467i
$92$	−4.50038	−	5.86888i	−0.469197	−	0.611873i
$93$		0			0
$94$	−4.86074	−	0.319367i	−0.501347	−	0.0329402i
$95$	4.42673	−	7.66732i	0.454173	−	0.786651i
$96$		0			0
$97$	0.970710	+	1.68132i	0.0985606	+	0.170712i	0.911089	−	0.412210i	$-0.135243\pi$
$97$	0.970710	+	1.68132i	0.0985606	+	0.170712i	−0.812528	+	0.582922i	$0.801909\pi$
$98$	−2.19343	−	4.44963i	−0.221570	−	0.449480i
$99$		0			0
$100$	0.859698	+	6.54618i	0.0859698	+	0.654618i
$101$	7.65091	−	9.97086i	0.761294	−	0.992138i	−0.238485	−	0.971146i	$-0.576651\pi$
$101$	7.65091	−	9.97086i	0.761294	−	0.992138i	0.999780	−	0.0209918i	$-0.00668239\pi$
$102$		0			0
$103$	−3.04623	+	0.816235i	−0.300154	+	0.0804261i	−0.405753	−	0.913983i	$-0.632991\pi$
$103$	−3.04623	+	0.816235i	−0.300154	+	0.0804261i	0.105599	+	0.994409i	$0.466324\pi$
$104$	−5.51218	−	11.1911i	−0.540514	−	1.09738i
$105$		0			0
$106$	9.90057	+	1.97099i	0.961628	+	0.191439i
$107$	1.96372	+	4.74085i	0.189840	+	0.458315i	0.989929	−	0.141567i	$-0.0452141\pi$
$107$	1.96372	+	4.74085i	0.189840	+	0.458315i	−0.800088	+	0.599882i	$0.795214\pi$
$108$		0			0
$109$	6.27216	+	2.59801i	0.600764	+	0.248845i	0.662274	−	0.749262i	$-0.269592\pi$
$109$	6.27216	+	2.59801i	0.600764	+	0.248845i	−0.0615097	+	0.998106i	$0.519592\pi$
$110$	−24.2520	+	4.82001i	−2.31234	+	0.459570i
$111$		0			0
$112$	−6.47601	−	11.2333i	−0.611926	−	1.06145i
$113$	−0.221857	+	0.384268i	−0.0208706	+	0.0361489i	−0.876272	−	0.481817i	$-0.839977\pi$
$113$	−0.221857	+	0.384268i	−0.0208706	+	0.0361489i	0.855401	+	0.517966i	$0.173310\pi$
$114$		0			0
$115$	10.5631	−	1.39066i	0.985014	−	0.129680i
$116$	−7.54196	+	4.35115i	−0.700253	+	0.403994i
$117$		0			0
$118$	−1.24867	+	1.42337i	−0.114949	+	0.131032i
$119$	3.92589	−	14.6516i	0.359886	−	1.34311i
$120$		0			0
$121$	−6.68416	−	24.9456i	−0.607651	−	2.26778i
$122$	−3.22465	−	1.59086i	−0.291946	−	0.144030i
$123$		0			0
$124$	1.06619	−	8.07864i	0.0957468	−	0.725483i
$125$	4.52199	+	1.87307i	0.404459	+	0.167532i
$126$		0			0
$127$		−	0.759969i		−	0.0674364i	−0.999431	−	0.0337182i	$-0.989265\pi$
$127$		−	0.759969i		−	0.0674364i	0.999431	−	0.0337182i	$-0.0107349\pi$
$128$	−6.27506	−	9.41401i	−0.554643	−	0.832089i
$129$		0			0
$130$	17.9326	+	1.17824i	1.57279	+	0.103338i
$131$	−3.83035	−	4.99180i	−0.334659	−	0.436136i	0.595465	−	0.803381i	$-0.296968\pi$
$131$	−3.83035	−	4.99180i	−0.334659	−	0.436136i	−0.930124	+	0.367245i	$0.880301\pi$
$132$		0			0
$133$	−7.90254	−	6.06383i	−0.685237	−	0.525801i
$134$	14.3073	−	0.935462i	1.23596	−	0.0808116i
$135$		0			0
$136$	2.58826	−	12.9796i	0.221941	−	1.11299i
$137$	−13.8441	−	3.70952i	−1.18278	−	0.316926i	−0.386754	−	0.922183i	$-0.626404\pi$
$137$	−13.8441	−	3.70952i	−1.18278	−	0.316926i	−0.796030	+	0.605257i	$0.793070\pi$
$138$		0			0
$139$	−1.77167	+	13.4571i	−0.150271	+	1.14142i	0.735576	+	0.677442i	$0.236912\pi$
$139$	−1.77167	+	13.4571i	−0.150271	+	1.14142i	−0.885847	+	0.463978i	$0.846422\pi$
$140$	18.6792	+	0.00595250i	1.57868	+	0.000503078i
$141$		0			0
$142$	−11.2962	+	2.24509i	−0.947958	+	0.188404i
$143$			26.7651i			2.23821i
$144$		0			0
$145$		−	12.5434i		−	1.04167i
$146$	4.41294	+	22.2038i	0.365217	+	1.83760i
$147$		0			0
$148$	3.03108	+	3.03301i	0.249153	+	0.249312i
$149$	1.08494	−	8.24090i	0.0888814	−	0.675121i	−0.887770	−	0.460288i	$-0.847746\pi$
$149$	1.08494	−	8.24090i	0.0888814	−	0.675121i	0.976651	−	0.214833i	$-0.0689206\pi$
$150$		0			0
$151$	0.395426	+	0.105954i	0.0321793	+	0.00862241i	0.274873	−	0.961481i	$-0.411364\pi$
$151$	0.395426	+	0.105954i	0.0321793	+	0.00862241i	−0.242693	+	0.970103i	$0.578031\pi$
$152$	−7.22430	−	4.83212i	−0.585968	−	0.391936i
$153$		0			0
$154$	1.81505	+	27.7601i	0.146261	+	2.23697i
$155$	9.31311	+	7.14620i	0.748047	+	0.573996i
$156$		0			0
$157$	8.63965	+	11.2594i	0.689519	+	0.898599i	0.998625	−	0.0524290i	$-0.0166963\pi$
$157$	8.63965	+	11.2594i	0.689519	+	0.898599i	−0.309106	+	0.951028i	$0.600030\pi$
$158$	−1.30000	+	19.7858i	−0.103422	+	1.57408i
$159$		0			0
$160$	16.2644	−	1.05301i	1.28581	−	0.0832477i
$161$		−	11.9870i		−	0.944707i
$162$		0			0
$163$	7.16640	+	2.96842i	0.561316	+	0.232505i	0.645256	−	0.763966i	$-0.276751\pi$
$163$	7.16640	+	2.96842i	0.561316	+	0.232505i	−0.0839407	+	0.996471i	$0.526751\pi$
$164$	0.586608	−	0.449823i	0.0458064	−	0.0351253i
$165$		0			0
$166$	−11.1146	+	22.5291i	−0.862660	+	1.74860i
$167$	−3.88696	−	14.5063i	−0.300782	−	1.12253i	−0.936516	−	0.350625i	$-0.885969\pi$
$167$	−3.88696	−	14.5063i	−0.300782	−	1.12253i	0.635734	−	0.771908i	$-0.280698\pi$
$168$		0			0
$169$	1.67017	−	6.23316i	0.128475	−	0.479474i
$170$	14.3329	+	12.5737i	1.09928	+	0.964356i
$171$		0			0
$172$	−0.409853	+	1.52764i	−0.0312510	+	0.116482i
$173$	11.4938	−	1.51319i	0.873861	−	0.115046i	0.319763	−	0.947497i	$-0.396397\pi$
$173$	11.4938	−	1.51319i	0.873861	−	0.115046i	0.554098	+	0.832451i	$0.313063\pi$
$174$		0			0
$175$	−5.35055	+	9.26742i	−0.404463	+	0.700551i
$176$	3.15301	+	24.0680i	0.237667	+	1.81419i
$177$		0			0
$178$	−0.867011	−	4.36239i	−0.0649852	−	0.326975i
$179$	−19.6993	−	8.15971i	−1.47239	−	0.609886i	−0.504990	−	0.863125i	$-0.668504\pi$
$179$	−19.6993	−	8.15971i	−1.47239	−	0.609886i	−0.967404	+	0.253239i	$0.918504\pi$
$180$		0			0
$181$	−0.746186	−	1.80145i	−0.0554636	−	0.133901i	0.893719	−	0.448628i	$-0.148087\pi$
$181$	−0.746186	−	1.80145i	−0.0554636	−	0.133901i	−0.949182	+	0.314727i	$0.898087\pi$
$182$	3.94775	−	19.8302i	0.292627	−	1.46991i
$183$		0			0
$184$	−0.679074	−	10.4371i	−0.0500620	−	0.769434i
$185$	−5.96671	+	1.59878i	−0.438681	+	0.117544i
$186$		0			0
$187$	−17.2865	+	22.5282i	−1.26411	+	1.64742i
$188$	−5.46403	−	4.19546i	−0.398505	−	0.305986i
$189$		0			0
$190$	11.2303	−	5.53597i	0.814735	−	0.401621i
$191$	6.06876	+	10.5114i	0.439120	+	0.760578i	0.997622	−	0.0689251i	$-0.0219569\pi$
$191$	6.06876	+	10.5114i	0.439120	+	0.760578i	−0.558502	+	0.829503i	$0.688624\pi$
$192$		0			0
$193$	1.87855	−	3.25374i	0.135221	−	0.234210i	−0.790461	−	0.612512i	$-0.790159\pi$
$193$	1.87855	−	3.25374i	0.135221	−	0.234210i	0.925682	+	0.378303i	$0.123492\pi$
$194$	−0.180006	+	2.73967i	−0.0129237	+	0.196697i
$195$		0			0
$196$	0.917954	−	6.95543i	0.0655682	−	0.496816i
$197$	8.91962	+	21.5339i	0.635497	+	1.53422i	0.832619	+	0.553846i	$0.186840\pi$
$197$	8.91962	+	21.5339i	0.635497	+	1.53422i	−0.197122	+	0.980379i	$0.563160\pi$
$198$		0			0
$199$	−13.5124	−	13.5124i	−0.957872	−	0.957872i	0.0412759	−	0.999148i	$-0.486858\pi$
$199$	−13.5124	−	13.5124i	−0.957872	−	0.957872i	−0.999148	+	0.0412759i	$0.986858\pi$
$200$	−4.13373	+	8.37229i	−0.292299	+	0.592010i
$201$		0			0
$202$	16.8315	−	5.71053i	1.18426	−	0.401791i
$203$	−13.9917	−	1.84204i	−0.982023	−	0.129286i
$204$		0			0
$205$	0.138999	+	1.05580i	0.00970814	+	0.0737406i
$206$	−4.22307	−	1.43429i	−0.294235	−	0.0999318i
$207$		0			0
$208$	2.31392	−	17.4898i	0.160442	−	1.21270i
$209$	9.32369	+	16.1491i	0.644933	+	1.11706i
$210$		0			0
$211$	−2.02558	−	2.63979i	−0.139447	−	0.181730i	0.718409	−	0.695621i	$-0.244871\pi$
$211$	−2.02558	−	2.63979i	−0.139447	−	0.181730i	−0.857856	+	0.513890i	$0.828204\pi$
$212$	10.0916	+	10.0981i	0.693096	+	0.693538i
$213$		0			0
$214$	−1.41690	+	7.11731i	−0.0968573	+	0.486529i
$215$	−1.61117	−	1.61117i	−0.109881	−	0.109881i
$216$		0			0
$217$	9.33899	−	9.33899i	0.633972	−	0.633972i
$218$	5.33276	+	7.98380i	0.361180	+	0.540731i
$219$		0			0
$220$	−32.3023	−	13.3921i	−2.17782	−	0.902896i
$221$	16.3736	−	12.5639i	1.10141	−	0.845142i
$222$		0			0
$223$	8.66983	−	5.00553i	0.580574	−	0.335195i	−0.180787	−	0.983522i	$-0.557865\pi$
$223$	8.66983	−	5.00553i	0.580574	−	0.335195i	0.761362	+	0.648327i	$0.224531\pi$
$224$	1.21389	−	18.2969i	0.0811061	−	1.22252i
$225$		0			0
$226$	−0.562839	+	0.277450i	−0.0374395	+	0.0184557i
$227$	−14.9664	+	1.97036i	−0.993352	+	0.130777i	−0.609642	−	0.792677i	$-0.708687\pi$
$227$	−14.9664	+	1.97036i	−0.993352	+	0.130777i	−0.383710	+	0.923454i	$0.625354\pi$
$228$		0			0
$229$	2.27583	−	17.2867i	0.150391	−	1.14234i	−0.735193	−	0.677857i	$-0.762909\pi$
$229$	2.27583	−	17.2867i	0.150391	−	1.14234i	0.885585	−	0.464478i	$-0.153758\pi$
$230$	13.5125	+	6.66629i	0.890985	+	0.439562i
$231$		0			0
$232$	−12.2870	−	0.811228i	−0.806678	−	0.0532597i
$233$	−15.6723	+	15.6723i	−1.02673	+	1.02673i	−0.0270935	+	0.999633i	$0.508625\pi$
$233$	−15.6723	+	15.6723i	−1.02673	+	1.02673i	−0.999633	+	0.0270935i	$0.991375\pi$
$234$		0			0
$235$	9.16871	−	3.79780i	0.598101	−	0.247741i
$236$	−2.58672	+	0.692227i	−0.168381	+	0.0450602i
$237$		0			0
$238$	16.1303	−	14.1414i	1.04557	−	0.916648i
$239$	−14.9128	−	8.60993i	−0.964632	−	0.556930i	−0.0670362	−	0.997751i	$-0.521354\pi$
$239$	−14.9128	−	8.60993i	−0.964632	−	0.556930i	−0.897595	+	0.440820i	$0.854688\pi$
$240$		0			0
$241$	10.9425	−	6.31766i	0.704869	−	0.406956i	−0.104290	−	0.994547i	$-0.533257\pi$
$241$	10.9425	−	6.31766i	0.704869	−	0.406956i	0.809158	+	0.587591i	$0.199924\pi$
$242$	11.7454	−	34.5828i	0.755025	−	2.22307i
$243$		0			0
$244$	−2.54115	−	4.40464i	−0.162681	−	0.281978i
$245$	8.01827	+	6.15263i	0.512268	+	0.393077i
$246$		0			0
$247$	−3.50778	−	13.0912i	−0.223195	−	0.832975i
$248$	7.60243	−	8.66056i	0.482755	−	0.549946i
$249$		0			0
$250$	3.84472	+	5.75601i	0.243161	+	0.364042i
$251$	−6.30328	+	2.61090i	−0.397859	+	0.164799i	−0.572637	−	0.819809i	$-0.694079\pi$
$251$	−6.30328	+	2.61090i	−0.397859	+	0.164799i	0.174777	+	0.984608i	$0.444079\pi$
$252$		0			0
$253$	−8.58751	+	20.7321i	−0.539892	+	1.30341i
$254$	0.597246	−	0.893534i	0.0374746	−	0.0560653i
$255$		0			0
$256$	0.0203949	−	16.0000i	0.00127468	−	0.999999i
$257$	24.2199	+	13.9834i	1.51079	+	0.872258i	0.999921	+	0.0126022i	$0.00401150\pi$
$257$	24.2199	+	13.9834i	1.51079	+	0.872258i	0.510874	+	0.859656i	$0.329322\pi$
$258$		0			0
$259$	0.907144	+	6.89044i	0.0563672	+	0.428151i
$260$	20.1583	+	15.4782i	1.25017	+	0.959920i
$261$		0			0
$262$	−0.580560	−	8.87932i	−0.0358671	−	0.548566i
$263$	0.270431	+	0.0724618i	0.0166755	+	0.00446819i	0.267147	−	0.963656i	$-0.413919\pi$
$263$	0.270431	+	0.0724618i	0.0166755	+	0.00446819i	−0.250472	+	0.968124i	$0.580586\pi$
$264$		0			0
$265$	−19.8655	+	5.32294i	−1.22033	+	0.326986i
$266$	−4.52596	−	13.3400i	−0.277504	−	0.817929i
$267$		0			0
$268$	17.5570	+	10.1440i	1.07246	+	0.619643i
$269$	−2.02799	+	4.89600i	−0.123649	+	0.298515i	−0.973568	−	0.228399i	$-0.926651\pi$
$269$	−2.02799	+	4.89600i	−0.123649	+	0.298515i	0.849919	+	0.526914i	$0.176651\pi$
$270$		0			0
$271$	−22.5843			−1.37190			−0.685949	−	0.727649i	$-0.740613\pi$
$271$	−22.5843			−1.37190			−0.685949	+	0.727649i	$0.740613\pi$
$272$	13.2436	−	13.2267i	0.803012	−	0.801989i
$273$		0			0
$274$	−13.3620	−	15.2413i	−0.807227	−	0.920762i
$275$	15.8932	−	12.1953i	0.958399	−	0.735405i
$276$		0			0
$277$	−8.06669	+	10.5127i	−0.484680	+	0.631648i	−0.970121	−	0.242622i	$-0.921993\pi$
$277$	−8.06669	+	10.5127i	−0.484680	+	0.631648i	0.485440	+	0.874270i	$0.338659\pi$
$278$	−12.6588	+	14.4299i	−0.759223	+	0.865449i
$279$		0			0
$280$	21.9574	+	14.6866i	1.31220	+	0.877694i
$281$	4.05619	−	15.1379i	0.241972	−	0.903053i	−0.732909	−	0.680327i	$-0.761838\pi$
$281$	4.05619	−	15.1379i	0.241972	−	0.903053i	0.974881	−	0.222726i	$-0.0714955\pi$
$282$		0			0
$283$	−0.743339	−	0.0978624i	−0.0441869	−	0.00581732i	0.108400	−	0.994107i	$-0.465427\pi$
$283$	−0.743339	−	0.0978624i	−0.0441869	−	0.00581732i	−0.152587	+	0.988290i	$0.548761\pi$
$284$	−15.0459	−	6.23784i	−0.892811	−	0.370148i
$285$		0			0
$286$	−21.0342	+	31.4691i	−1.24378	+	1.86081i
$287$	1.19813			0.0707231
$288$		0			0
$289$	4.89622			0.288013
$290$	9.85761	−	14.7479i	0.578859	−	0.866024i
$291$		0			0
$292$	−12.2611	+	29.5742i	−0.717526	+	1.73070i
$293$	−1.09834	−	0.144599i	−0.0641658	−	0.00844758i	0.0983750	−	0.995149i	$-0.468636\pi$
$293$	−1.09834	−	0.144599i	−0.0641658	−	0.00844758i	−0.162541	+	0.986702i	$0.551969\pi$
$294$		0			0
$295$	0.998403	−	3.72609i	0.0581293	−	0.216941i
$296$	1.18020	+	5.94814i	0.0685979	+	0.345729i
$297$		0			0
$298$	7.75199	−	8.83661i	0.449061	−	0.511891i
$299$	9.92873	−	12.9394i	0.574193	−	0.748303i
$300$		0			0
$301$	−2.03381	+	1.56059i	−0.117227	+	0.0899511i
$302$	0.381654	+	0.435333i	0.0219617	+	0.0250506i
$303$		0			0
$304$	−4.69649	−	11.3588i	−0.269362	−	0.651472i
$305$	7.32556			0.419460
$306$		0			0
$307$	5.62180	−	13.5722i	0.320853	−	0.774607i	−0.678352	−	0.734737i	$-0.737306\pi$
$307$	5.62180	−	13.5722i	0.320853	−	0.774607i	0.999205	−	0.0398702i	$-0.0126944\pi$
$308$	−19.6821	+	34.0654i	−1.12149	+	1.94105i
$309$		0			0
$310$	5.33382	+	15.7212i	0.302941	+	0.892901i
$311$	−15.9966	+	4.28627i	−0.907083	+	0.243052i	−0.682056	−	0.731300i	$-0.738914\pi$
$311$	−15.9966	+	4.28627i	−0.907083	+	0.243052i	−0.225027	+	0.974352i	$0.572247\pi$
$312$		0			0
$313$	2.04004	+	0.546628i	0.115310	+	0.0308972i	0.316013	−	0.948755i	$-0.397656\pi$
$313$	2.04004	+	0.546628i	0.115310	+	0.0308972i	−0.200703	+	0.979652i	$0.564322\pi$
$314$	1.30950	+	20.0280i	0.0738994	+	1.13025i
$315$		0			0
$316$	−17.0778	+	22.2415i	−0.960701	+	1.25118i
$317$	2.28300	+	17.3411i	0.128226	+	0.973974i	0.927714	+	0.373292i	$0.121771\pi$
$317$	2.28300	+	17.3411i	0.128226	+	0.973974i	−0.799488	+	0.600682i	$0.794896\pi$
$318$		0			0
$319$	22.8796	+	13.2096i	1.28101	+	0.739594i
$320$	19.9504	+	11.5438i	1.11526	+	0.645318i
$321$		0			0
$322$	9.42036	−	14.0937i	0.524976	−	0.785411i
$323$	5.50259	−	13.2844i	0.306172	−	0.739165i
$324$		0			0
$325$	−13.4518	+	5.57191i	−0.746171	+	0.309074i
$326$	6.09307	+	9.12206i	0.337464	+	0.505224i
$327$		0			0
$328$	1.04321	−	0.0678749i	0.0576017	−	0.00374777i
$329$	−2.88986	−	10.7851i	−0.159323	−	0.594601i
$330$		0			0
$331$	−6.80198	−	5.21934i	−0.373871	−	0.286881i	0.404686	−	0.914456i	$-0.367381\pi$
$331$	−6.80198	−	5.21934i	−0.373871	−	0.286881i	−0.778556	+	0.627575i	$0.784048\pi$
$332$	−30.7732	+	17.7539i	−1.68890	+	0.974369i
$333$		0			0
$334$	6.83017	−	20.1105i	0.373730	−	1.10040i
$335$	−25.2971	+	14.6053i	−1.38213	+	0.797971i
$336$		0			0
$337$	9.96360	+	5.75249i	0.542752	+	0.313358i	0.746193	−	0.665729i	$-0.231879\pi$
$337$	9.96360	+	5.75249i	0.542752	+	0.313358i	−0.203442	+	0.979087i	$0.565213\pi$
$338$	6.86224	−	6.01609i	0.373257	−	0.327232i
$339$		0			0
$340$	6.97051	+	26.0475i	0.378029	+	1.41262i
$341$	−22.8427	+	9.46177i	−1.23700	+	0.512384i
$342$		0			0
$343$	−8.00447	+	8.00447i	−0.432201	+	0.432201i
$344$	−1.68243	+	1.47403i	−0.0907107	+	0.0794745i
$345$		0			0
$346$	14.7031	+	7.25367i	0.790443	+	0.389960i
$347$	2.84116	−	21.5808i	0.152521	−	1.15852i	−0.728366	−	0.685189i	$-0.759720\pi$
$347$	2.84116	−	21.5808i	0.152521	−	1.15852i	0.880887	−	0.473327i	$-0.156947\pi$
$348$		0			0
$349$	24.0250	−	3.16295i	1.28603	−	0.169309i	0.543663	−	0.839304i	$-0.317037\pi$
$349$	24.0250	−	3.16295i	1.28603	−	0.169309i	0.742366	+	0.669995i	$0.233704\pi$
$350$	−13.5740	+	6.69127i	−0.725561	+	0.357664i
$351$		0			0
$352$	−15.2075	+	30.7758i	−0.810560	+	1.64036i
$353$	−15.5162	+	8.95827i	−0.825843	+	0.476801i	−0.852427	−	0.522846i	$-0.824870\pi$
$353$	−15.5162	+	8.95827i	−0.825843	+	0.476801i	0.0265842	+	0.999647i	$0.491537\pi$
$354$		0			0
$355$	18.6152	−	14.2839i	0.987992	−	0.758113i
$356$	2.40894	−	5.81045i	0.127673	−	0.307953i
$357$		0			0
$358$	−16.7489	−	25.0751i	−0.885205	−	1.32526i
$359$	4.22376	−	4.22376i	0.222921	−	0.222921i	−0.586806	−	0.809727i	$-0.699615\pi$
$359$	4.22376	−	4.22376i	0.222921	−	0.222921i	0.809727	+	0.586806i	$0.199615\pi$
$360$		0			0
$361$	6.75819	+	6.75819i	0.355694	+	0.355694i
$362$	0.538401	−	2.70447i	0.0282977	−	0.142144i
$363$		0			0
$364$	20.2257	−	20.2129i	1.06012	−	1.05944i
$365$	−28.0765	−	36.5900i	−1.46959	−	1.91521i
$366$		0			0
$367$	1.50986	+	2.61515i	0.0788140	+	0.136510i	0.902738	−	0.430190i	$-0.141553\pi$
$367$	1.50986	+	2.61515i	0.0788140	+	0.136510i	−0.823925	+	0.566700i	$0.808220\pi$
$368$	7.40392	−	12.8051i	0.385956	−	0.667512i
$369$		0			0
$370$	−8.27181	−	2.80937i	−0.430031	−	0.146052i
$371$	3.02023	+	22.9409i	0.156803	+	1.19103i
$372$		0			0
$373$	−19.5198	−	2.56982i	−1.01069	−	0.133060i	−0.393049	−	0.919517i	$-0.628580\pi$
$373$	−19.5198	−	2.56982i	−1.01069	−	0.133060i	−0.617645	+	0.786457i	$0.711913\pi$
$374$	−38.0291	+	12.9024i	−1.96644	+	0.667166i
$375$		0			0
$376$	−3.12719	−	9.22690i	−0.161273	−	0.475841i
$377$	−13.5776	−	13.5776i	−0.699281	−	0.699281i
$378$		0			0
$379$	12.4650	+	30.0933i	0.640286	+	1.54579i	0.826294	+	0.563239i	$0.190445\pi$
$379$	12.4650	+	30.0933i	0.640286	+	1.54579i	−0.186008	+	0.982548i	$0.559555\pi$
$380$	17.5547	+	2.31681i	0.900537	+	0.118850i
$381$		0			0
$382$	−1.12538	+	17.1281i	−0.0575793	+	0.876351i
$383$	−11.8673	+	20.5548i	−0.606392	+	1.05030i	0.385437	+	0.922734i	$0.374051\pi$
$383$	−11.8673	+	20.5548i	−0.606392	+	1.05030i	−0.991830	+	0.127568i	$0.959283\pi$
$384$		0			0
$385$	−28.3382	−	49.0832i	−1.44425	−	2.50151i
$386$	4.76576	−	2.34927i	0.242571	−	0.119575i
$387$		0			0
$388$	−2.36470	+	3.07971i	−0.120050	+	0.156349i
$389$	3.54858	−	4.62460i	0.179920	−	0.234476i	−0.694683	−	0.719316i	$-0.744455\pi$
$389$	3.54858	−	4.62460i	0.179920	−	0.234476i	0.874603	+	0.484840i	$0.161122\pi$
$390$		0			0
$391$	16.7140	−	4.47851i	0.845264	−	0.226488i
$392$	6.54543	−	7.45644i	0.330594	−	0.376607i
$393$		0			0
$394$	−6.43584	+	32.3282i	−0.324233	+	1.62867i
$395$	−15.4591	−	37.3216i	−0.777832	−	1.87785i
$396$		0			0
$397$	−17.4731	−	7.23758i	−0.876948	−	0.363244i	−0.101636	−	0.994822i	$-0.532408\pi$
$397$	−17.4731	−	7.23758i	−0.876948	−	0.363244i	−0.775312	+	0.631578i	$0.782408\pi$
$398$	−5.26807	−	26.5065i	−0.264065	−	1.32865i
$399$		0			0
$400$	−11.4399	+	6.59510i	−0.571994	+	0.329755i
$401$	−6.30036	+	10.9125i	−0.314625	+	0.544947i	−0.979358	−	0.202135i	$-0.935212\pi$
$401$	−6.30036	+	10.9125i	−0.314625	+	0.544947i	0.664733	+	0.747081i	$0.268545\pi$
$402$		0			0
$403$	17.8164	−	2.34557i	0.887498	−	0.116841i
$404$	24.2774	+	6.51341i	1.20785	+	0.324054i
$405$		0			0
$406$	−15.0031	−	13.1616i	−0.744591	−	0.653198i
$407$	3.36738	−	12.5672i	0.166915	−	0.622935i
$408$		0			0
$409$	8.06455	+	30.0973i	0.398766	+	1.48822i	0.815269	+	0.579082i	$0.196589\pi$
$409$	8.06455	+	30.0973i	0.398766	+	1.48822i	−0.416503	+	0.909134i	$0.636744\pi$
$410$	−0.666310	+	1.35060i	−0.0329067	+	0.0667014i
$411$		0			0
$412$	−3.83810	−	5.00521i	−0.189089	−	0.246589i
$413$	−4.00970	−	1.66087i	−0.197304	−	0.0817262i
$414$		0			0
$415$		−	51.1803i		−	2.51234i
$416$	16.4656	−	18.7452i	0.807290	−	0.919060i
$417$		0			0
$418$	−1.72896	+	26.3146i	−0.0845664	+	1.28709i
$419$	−2.70599	−	3.52651i	−0.132196	−	0.172282i	0.722565	−	0.691303i	$-0.242963\pi$
$419$	−2.70599	−	3.52651i	−0.132196	−	0.172282i	−0.854761	+	0.519022i	$0.826296\pi$
$420$		0			0
$421$	−20.6981	−	15.8822i	−1.00877	−	0.774053i	−0.0344885	−	0.999405i	$-0.510980\pi$
$421$	−20.6981	−	15.8822i	−1.00877	−	0.774053i	−0.974277	+	0.225352i	$0.927647\pi$
$422$	−0.307014	−	4.69560i	−0.0149452	−	0.228578i
$423$		0			0
$424$	3.92935	+	19.8036i	0.190826	+	0.961750i
$425$	−14.9210	−	3.99808i	−0.723777	−	0.193936i
$426$		0			0
$427$	1.07578	−	8.17140i	0.0520609	−	0.395442i
$428$	−7.25929	+	7.25466i	−0.350891	+	0.350667i
$429$		0			0
$430$	−0.628143	−	3.16052i	−0.0302917	−	0.152414i
$431$		−	3.86711i		−	0.186272i	−0.995653	−	0.0931362i	$-0.970311\pi$
$431$		−	3.86711i		−	0.186272i	0.995653	−	0.0931362i	$-0.0296892\pi$
$432$		0			0
$433$		−	33.7121i		−	1.62010i	−0.586360	−	0.810050i	$-0.699440\pi$
$433$		−	33.7121i		−	1.62010i	0.586360	−	0.810050i	$-0.300560\pi$
$434$	18.3197	−	3.64098i	0.879372	−	0.174772i
$435$		0			0
$436$	−0.00432687	+	13.5779i	−0.000207220	+	0.650262i
$437$	1.48318	−	11.2659i	0.0709500	−	0.538919i
$438$		0			0
$439$	3.17739	+	0.851379i	0.151648	+	0.0406341i	0.333845	−	0.942628i	$-0.391654\pi$
$439$	3.17739	+	0.851379i	0.151648	+	0.0406341i	−0.182196	+	0.983262i	$0.558321\pi$
$440$	−27.4548	−	41.1316i	−1.30886	−	1.96087i
$441$		0			0
$442$	29.1251	−	1.90430i	1.38534	−	0.0905782i
$443$	−24.0366	−	18.4439i	−1.14201	−	0.876297i	−0.148376	−	0.988931i	$-0.547405\pi$
$443$	−24.0366	−	18.4439i	−1.14201	−	0.876297i	−0.993637	+	0.112634i	$0.964071\pi$
$444$		0			0
$445$	5.51619	+	7.18884i	0.261493	+	0.340784i
$446$	14.1273	+	0.928213i	0.668947	+	0.0439522i
$447$		0			0
$448$	15.8065	−	20.5587i	0.746786	−	0.971306i
$449$		−	15.8644i		−	0.748686i	−0.927290	−	0.374343i	$-0.877868\pi$
$449$		−	15.8644i		−	0.748686i	0.927290	−	0.374343i	$-0.122132\pi$
$450$		0			0
$451$	−2.07222	−	0.858340i	−0.0975769	−	0.0404177i
$452$	−0.879800	−	0.116113i	−0.0413823	−	0.00546150i
$453$		0			0
$454$	−19.1452	−	9.44515i	−0.898527	−	0.443283i
$455$	10.6615	+	39.7892i	0.499818	+	1.86535i
$456$		0			0
$457$	−0.391338	+	1.46049i	−0.0183060	+	0.0683191i	−0.974475	−	0.224498i	$-0.927926\pi$
$457$	−0.391338	+	1.46049i	−0.0183060	+	0.0683191i	0.956169	+	0.292817i	$0.0945926\pi$
$458$	16.2611	−	18.5363i	0.759831	−	0.866143i
$459$		0			0
$460$	10.6484	+	18.4571i	0.496483	+	0.860566i
$461$	−2.13606	+	0.281217i	−0.0994860	+	0.0130976i	−0.180105	−	0.983647i	$-0.557644\pi$
$461$	−2.13606	+	0.281217i	−0.0994860	+	0.0130976i	0.0806188	+	0.996745i	$0.474310\pi$
$462$		0			0
$463$	−9.17201	+	15.8864i	−0.426259	+	0.738303i	−0.996537	−	0.0831491i	$-0.973502\pi$
$463$	−9.17201	+	15.8864i	−0.426259	+	0.738303i	0.570278	+	0.821452i	$0.306836\pi$
$464$	−13.8089	−	10.6099i	−0.641060	−	0.492552i
$465$		0			0
$466$	−30.7433	+	6.11013i	−1.42416	+	0.283046i
$467$	32.6812	+	13.5370i	1.51230	+	0.626417i	0.976032	−	0.217629i	$-0.0698322\pi$
$467$	32.6812	+	13.5370i	1.51230	+	0.626417i	0.536272	+	0.844045i	$0.319832\pi$
$468$		0			0
$469$	12.5767	+	30.3628i	0.580738	+	1.40203i
$470$	13.7647	+	2.74026i	0.634920	+	0.126399i
$471$		0			0
$472$	−3.58535	−	1.21897i	−0.165029	−	0.0561078i
$473$	4.63558	−	1.24210i	0.213144	−	0.0571118i
$474$		0			0
$475$	−6.17534	+	8.04786i	−0.283344	+	0.369261i
$476$	30.0787	−	3.95018i	1.37865	−	0.181056i
$477$		0			0
$478$	−10.7674	−	21.8429i	−0.492489	−	0.999070i
$479$	−3.52666	−	6.10836i	−0.161137	−	0.279098i	0.774139	−	0.633015i	$-0.218183\pi$
$479$	−3.52666	−	6.10836i	−0.161137	−	0.279098i	−0.935277	+	0.353917i	$0.884850\pi$
$480$		0			0
$481$	−4.72808	+	8.18928i	−0.215582	+	0.373399i
$482$	17.8306	+	1.17153i	0.812161	+	0.0533618i
$483$		0			0
$484$	40.9877	−	31.4302i	1.86308	−	1.42865i
$485$	−2.14057	−	5.16779i	−0.0971982	−	0.234657i
$486$		0			0
$487$	−0.127493	−	0.127493i	−0.00577726	−	0.00577726i	0.704212	−	0.709990i	$-0.251300\pi$
$487$	−0.127493	−	0.127493i	−0.00577726	−	0.00577726i	−0.709990	+	0.704212i	$0.751300\pi$
$488$	0.473772	−	7.17581i	0.0214467	−	0.324834i
$489$		0			0
$490$	4.59223	+	13.5354i	0.207456	+	0.611466i
$491$	20.3157	+	2.67461i	0.916833	+	0.120703i	0.574152	−	0.818749i	$-0.305332\pi$
$491$	20.3157	+	2.67461i	0.916833	+	0.120703i	0.342681	+	0.939452i	$0.388665\pi$
$492$		0			0
$493$	−2.65905	−	20.1975i	−0.119757	−	0.909648i
$494$	6.16389	−	18.1487i	0.277326	−	0.816550i
$495$		0			0
$496$	15.7447	−	4.20804i	0.706960	−	0.188946i
$497$	−13.1995	−	22.8622i	−0.592079	−	1.02551i
$498$		0			0
$499$	6.83554	+	8.90825i	0.306001	+	0.398788i	0.920888	−	0.389827i	$-0.127465\pi$
$499$	6.83554	+	8.90825i	0.306001	+	0.398788i	−0.614887	+	0.788615i	$0.710798\pi$
$500$	−0.00311951	+	9.78913i	−0.000139509	+	0.437783i
$501$		0			0
$502$	−9.46294	−	1.88386i	−0.422352	−	0.0840809i
$503$	23.8196	+	23.8196i	1.06206	+	1.06206i	0.997942	+	0.0641209i	$0.0204243\pi$
$503$	23.8196	+	23.8196i	1.06206	+	1.06206i	0.0641209	+	0.997942i	$0.479576\pi$
$504$		0			0
$505$	−25.6048	+	25.6048i	−1.13940	+	1.13940i
$506$	−26.3897	+	17.6270i	−1.17317	+	0.783615i
$507$		0			0
$508$	1.40443	−	0.581208i	0.0623113	−	0.0257869i
$509$	8.91776	−	6.84284i	0.395273	−	0.303304i	−0.391933	−	0.919994i	$-0.628194\pi$
$509$	8.91776	−	6.84284i	0.395273	−	0.303304i	0.787206	+	0.616690i	$0.211527\pi$
$510$		0			0
$511$	−44.9379	+	25.9449i	−1.98794	+	1.14774i
$512$	12.5981	−	18.7960i	0.556762	−	0.830672i
$513$		0			0
$514$	17.4873	+	35.4749i	0.771330	+	1.56473i
$515$	9.00862	−	1.18601i	0.396967	−	0.0522617i
$516$		0			0
$517$	−2.72832	+	20.7236i	−0.119991	+	0.911425i
$518$	−4.34850	+	8.81435i	−0.191062	+	0.387280i
$519$		0			0
$520$	11.5371	+	34.0406i	0.505935	+	1.49278i
$521$	−21.7451	+	21.7451i	−0.952672	+	0.952672i	−0.998930	−	0.0462579i	$-0.985270\pi$
$521$	−21.7451	+	21.7451i	−0.952672	+	0.952672i	0.0462579	+	0.998930i	$0.485270\pi$
$522$		0			0
$523$	−20.4000	+	8.44994i	−0.892028	+	0.369490i	−0.781150	−	0.624344i	$-0.785366\pi$
$523$	−20.4000	+	8.44994i	−0.892028	+	0.369490i	−0.110879	+	0.993834i	$0.535366\pi$
$524$	6.29550	−	10.8961i	0.275020	−	0.475999i
$525$		0			0
$526$	0.261013	+	0.297724i	0.0113807	+	0.0129814i
$527$	16.5110	+	9.53262i	0.719230	+	0.415247i
$528$		0			0
$529$	−8.07629	+	4.66285i	−0.351143	+	0.202733i
$530$	−27.5400	−	9.35348i	−1.19626	−	0.406289i
$531$		0			0
$532$	5.16229	−	19.2414i	0.223814	−	0.834221i
$533$	1.29332	+	0.992398i	0.0560198	+	0.0429855i
$534$		0			0
$535$	−3.82655	−	14.2809i	−0.165436	−	0.617416i
$536$	12.6707	+	25.7245i	0.547289	+	1.11113i
$537$		0			0
$538$	−6.23209	+	4.16272i	−0.268685	+	0.179467i
$539$	−19.6668	+	8.14626i	−0.847109	+	0.350884i
$540$		0			0
$541$	9.30148	−	22.4558i	0.399902	−	0.965449i	−0.587787	−	0.809016i	$-0.700001\pi$
$541$	9.30148	−	22.4558i	0.399902	−	0.965449i	0.987689	−	0.156433i	$-0.0499995\pi$
$542$	−26.5535	−	17.7486i	−1.14057	−	0.762368i
$543$		0			0
$544$	25.9658	−	5.14342i	1.11328	−	0.220522i
$545$	−16.9396	−	9.78007i	−0.725612	−	0.418932i
$546$		0			0
$547$	−5.35307	−	40.6606i	−0.228881	−	1.73852i	−0.591252	−	0.806487i	$-0.701366\pi$
$547$	−5.35307	−	40.6606i	−0.228881	−	1.73852i	0.362372	−	0.932034i	$-0.381967\pi$
$548$	−3.73248	−	28.4210i	−0.159443	−	1.21408i
$549$		0			0
$550$	28.2706	−	1.84843i	1.20546	−	0.0788172i
$551$	−12.9220	−	3.46244i	−0.550496	−	0.147505i
$552$		0			0
$553$	−43.9011	+	11.7633i	−1.86687	+	0.500225i
$554$	−17.7462	+	6.02086i	−0.753963	+	0.255802i
$555$		0			0
$556$	−26.2238	+	7.01768i	−1.11214	+	0.297616i
$557$	−5.08956	+	12.2873i	−0.215651	+	0.520628i	−0.994274	−	0.106865i	$-0.965919\pi$
$557$	−5.08956	+	12.2873i	−0.215651	+	0.520628i	0.778622	+	0.627493i	$0.215919\pi$
$558$		0			0
$559$	−3.48802			−0.147528
$560$	14.2744	+	34.5237i	0.603204	+	1.45889i
$561$		0			0
$562$	16.6657	−	14.6107i	0.703000	−	0.616316i
$563$	5.98768	−	4.59451i	0.252351	−	0.193635i	−0.474838	−	0.880073i	$-0.657493\pi$
$563$	5.98768	−	4.59451i	0.252351	−	0.193635i	0.727188	+	0.686438i	$0.240827\pi$
$564$		0			0
$565$	0.778254	−	1.01424i	0.0327414	−	0.0426694i
$566$	−0.797073	−	0.699239i	−0.0335035	−	0.0293912i
$567$		0			0
$568$	−12.7880	−	19.1585i	−0.536574	−	0.803871i
$569$	0.558495	−	2.08433i	0.0234133	−	0.0873797i	−0.953231	−	0.302244i	$-0.902264\pi$
$569$	0.558495	−	2.08433i	0.0234133	−	0.0873797i	0.976644	+	0.214864i	$0.0689309\pi$
$570$		0			0
$571$	20.1241	+	2.64939i	0.842167	+	0.110873i	0.539252	−	0.842144i	$-0.318707\pi$
$571$	20.1241	+	2.64939i	0.842167	+	0.110873i	0.302915	+	0.953018i	$0.402040\pi$
$572$	−49.4620	+	20.4694i	−2.06811	+	0.855867i
$573$		0			0
$574$	1.40870	+	0.941585i	0.0587978	+	0.0393010i
$575$	−12.2074			−0.509084
$576$		0			0
$577$	22.7617			0.947583			0.473791	−	0.880637i	$-0.342885\pi$
$577$	22.7617			0.947583			0.473791	+	0.880637i	$0.342885\pi$
$578$	5.75674	+	3.84786i	0.239449	+	0.160050i
$579$		0			0
$580$	23.1802	−	9.59289i	0.962504	−	0.398323i
$581$	−57.0898	−	7.51601i	−2.36848	−	0.311817i
$582$		0			0
$583$	11.2113	−	41.8412i	0.464325	−	1.73288i
$584$	−37.6578	+	25.1361i	−1.55829	+	1.04014i
$585$		0			0
$586$	−1.17774	−	1.03318i	−0.0486519	−	0.0426802i
$587$	−4.11805	+	5.36674i	−0.169970	+	0.221509i	−0.870569	−	0.492046i	$-0.836249\pi$
$587$	−4.11805	+	5.36674i	−0.169970	+	0.221509i	0.700599	+	0.713555i	$0.252916\pi$
$588$		0			0
$589$	9.93270	−	7.62163i	0.409270	−	0.314044i
$590$	4.10214	−	3.59632i	0.168882	−	0.148058i
$591$		0			0
$592$	−3.28691	+	7.92103i	−0.135091	+	0.325552i
$593$	24.0199			0.986380			0.493190	−	0.869922i	$-0.335831\pi$
$593$	24.0199			0.986380			0.493190	+	0.869922i	$0.335831\pi$
$594$		0			0
$595$	−16.7245	+	40.3764i	−0.685636	+	1.65527i
$596$	16.0589	−	4.29750i	0.657800	−	0.176032i
$597$		0			0
$598$	21.8425	−	7.41066i	0.893207	−	0.303044i
$599$	30.5456	−	8.18468i	1.24806	−	0.334417i	0.426474	−	0.904500i	$-0.359756\pi$
$599$	30.5456	−	8.18468i	1.24806	−	0.334417i	0.821587	+	0.570083i	$0.193089\pi$
$600$		0			0
$601$	20.0266	+	5.36611i	0.816901	+	0.218888i	0.642991	−	0.765873i	$-0.277693\pi$
$601$	20.0266	+	5.36611i	0.816901	+	0.218888i	0.173910	+	0.984762i	$0.444360\pi$
$602$	−3.61769	+	0.236537i	−0.147446	+	0.00964053i
$603$		0			0
$604$	0.106610	+	0.811779i	0.00433788	+	0.0330308i
$605$	9.71222	+	73.7717i	0.394858	+	2.99924i
$606$		0			0
$607$	−35.8101	−	20.6750i	−1.45349	−	0.839172i	−0.454812	−	0.890588i	$-0.650293\pi$
$607$	−35.8101	−	20.6750i	−1.45349	−	0.839172i	−0.998677	+	0.0514155i	$0.983627\pi$
$608$	3.40478	−	17.0460i	0.138082	−	0.691307i
$609$		0			0
$610$	8.61303	+	5.75703i	0.348731	+	0.233095i
$611$	5.81375	−	14.0356i	0.235199	−	0.567821i
$612$		0			0
$613$	39.4122	−	16.3251i	1.59185	−	0.659364i	0.601612	−	0.798788i	$-0.294525\pi$
$613$	39.4122	−	16.3251i	1.59185	−	0.659364i	0.990233	+	0.139424i	$0.0445252\pi$
$614$	17.2760	−	11.5395i	0.697202	−	0.465695i
$615$		0			0
$616$	−49.9126	+	24.5845i	−2.01104	+	0.990539i
$617$	2.15431	+	8.04000i	0.0867293	+	0.323678i	0.995636	−	0.0933213i	$-0.0297484\pi$
$617$	2.15431	+	8.04000i	0.0867293	+	0.323678i	−0.908907	+	0.416999i	$0.863082\pi$
$618$		0			0
$619$	−19.3738	−	14.8660i	−0.778697	−	0.597516i	0.141061	−	0.990001i	$-0.454949\pi$
$619$	−19.3738	−	14.8660i	−0.778697	−	0.597516i	−0.919758	+	0.392485i	$0.871615\pi$
$620$	−6.08374	+	22.6759i	−0.244329	+	0.910686i
$621$		0			0
$622$	−22.1765	−	7.53184i	−0.889196	−	0.301999i
$623$	8.82897	−	5.09741i	0.353725	−	0.204223i
$624$		0			0
$625$	−26.5074	−	15.3040i	−1.06030	−	0.612162i
$626$	1.96900	+	2.24593i	0.0786969	+	0.0897655i
$627$		0			0
$628$	−14.2000	+	24.5770i	−0.566642	+	0.980731i
$629$	−9.26875	+	3.83924i	−0.369569	+	0.153081i
$630$		0			0
$631$	−3.80915	+	3.80915i	−0.151640	+	0.151640i	−0.778850	−	0.627210i	$-0.784197\pi$
$631$	−3.80915	+	3.80915i	−0.151640	+	0.151640i	0.627210	+	0.778850i	$0.284197\pi$
$632$	−37.5585	+	12.7294i	−1.49400	+	0.506347i
$633$		0			0
$634$	−10.9438	+	22.1830i	−0.434635	+	0.880999i
$635$	−0.285801	+	2.17088i	−0.0113417	+	0.0861486i
$636$		0			0
$637$	15.3393	−	2.01946i	0.607766	−	0.0800139i
$638$	16.5196	+	33.5119i	0.654017	+	1.32675i
$639$		0			0
$640$	14.3846	+	29.2513i	0.568601	+	1.15626i
$641$	18.5594	−	10.7153i	0.733051	−	0.423227i	−0.0864863	−	0.996253i	$-0.527564\pi$
$641$	18.5594	−	10.7153i	0.733051	−	0.423227i	0.819537	+	0.573026i	$0.194231\pi$
$642$		0			0
$643$	−20.0541	+	15.3880i	−0.790855	+	0.606845i	−0.923183	−	0.384361i	$-0.874422\pi$
$643$	−20.0541	+	15.3880i	−0.790855	+	0.606845i	0.132327	+	0.991206i	$0.457755\pi$
$644$	22.1520	−	9.16738i	0.872910	−	0.361245i
$645$		0			0
$646$	16.9097	−	11.2948i	0.665302	−	0.444387i
$647$	1.32295	−	1.32295i	0.0520104	−	0.0520104i	−0.680623	−	0.732634i	$-0.738291\pi$
$647$	1.32295	−	1.32295i	0.0520104	−	0.0520104i	0.732634	+	0.680623i	$0.238291\pi$
$648$		0			0
$649$	5.74512	+	5.74512i	0.225516	+	0.225516i
$650$	−20.1948	−	4.02034i	−0.792106	−	0.157691i
$651$		0			0
$652$	−0.00494376	+	15.5137i	−0.000193613	+	0.607564i
$653$	−15.5873	−	20.3137i	−0.609977	−	0.794937i	0.381618	−	0.924320i	$-0.375367\pi$
$653$	−15.5873	−	20.3137i	−0.609977	−	0.794937i	−0.991595	+	0.129383i	$0.958700\pi$
$654$		0			0
$655$	9.06424	+	15.6997i	0.354169	+	0.613439i
$656$	1.27990	+	0.740038i	0.0499716	+	0.0288936i
$657$		0			0
$658$	5.07806	−	14.9517i	0.197963	−	0.582876i
$659$	0.168711	+	1.28149i	0.00657206	+	0.0499197i	0.994417	−	0.105525i	$-0.0336523\pi$
$659$	0.168711	+	1.28149i	0.00657206	+	0.0499197i	−0.987845	+	0.155445i	$0.950319\pi$
$660$		0			0
$661$	−24.1790	−	3.18323i	−0.940456	−	0.123813i	−0.355316	−	0.934746i	$-0.615627\pi$
$661$	−24.1790	−	3.18323i	−0.940456	−	0.123813i	−0.585139	+	0.810933i	$0.698960\pi$
$662$	−3.89564	−	11.4822i	−0.151408	−	0.446268i
$663$		0			0
$664$	−50.1341	−	3.31003i	−1.94558	−	0.128454i
$665$	20.2934	+	20.2934i	0.786946	+	0.786946i
$666$		0			0
$667$	−6.16078	−	14.8734i	−0.238546	−	0.575902i
$668$	23.8351	−	18.2772i	0.922207	−	0.707167i
$669$		0			0
$670$	−41.2211	−	2.70837i	−1.59251	−	0.104633i
$671$	−7.71463	+	13.3621i	−0.297820	+	0.515840i
$672$		0			0
$673$	1.54203	+	2.67087i	0.0594407	+	0.102954i	0.894214	−	0.447639i	$-0.147735\pi$
$673$	1.54203	+	2.67087i	0.0594407	+	0.102954i	−0.834774	+	0.550593i	$0.814402\pi$
$674$	7.19393	+	14.5937i	0.277100	+	0.562129i
$675$		0			0
$676$	12.7962	−	1.68051i	0.492162	−	0.0646348i
$677$	14.1128	−	18.3921i	0.542397	−	0.706866i	−0.439079	−	0.898448i	$-0.644695\pi$
$677$	14.1128	−	18.3921i	0.542397	−	0.706866i	0.981477	+	0.191582i	$0.0613619\pi$
$678$		0			0
$679$	−6.07884	+	1.62882i	−0.233284	+	0.0625084i
$680$	−12.2747	+	36.1033i	−0.470712	+	1.38450i
$681$		0			0
$682$	−34.2932	−	6.82702i	−1.31315	−	0.261420i
$683$	8.07633	+	19.4980i	0.309032	+	0.746070i	0.999737	+	0.0229330i	$0.00730044\pi$
$683$	8.07633	+	19.4980i	0.309032	+	0.746070i	−0.690705	+	0.723137i	$0.742700\pi$
$684$		0			0
$685$	38.1511	+	15.8027i	1.45768	+	0.603791i
$686$	−15.7018	+	3.12069i	−0.599499	+	0.119148i
$687$		0			0
$688$	−3.13654	+	0.410899i	−0.119579	+	0.0156654i
$689$	−15.7416	+	27.2652i	−0.599707	+	1.03872i
$690$		0			0
$691$	30.9251	−	4.07137i	1.17645	−	0.154882i	0.483152	−	0.875537i	$-0.339492\pi$
$691$	30.9251	−	4.07137i	1.17645	−	0.154882i	0.693294	+	0.720655i	$0.256159\pi$
$692$	11.5866	+	20.0834i	0.440458	+	0.763457i
$693$		0			0
$694$	20.3004	−	23.1408i	0.770594	−	0.878411i
$695$	10.1216	−	37.7745i	0.383936	−	1.43287i
$696$		0			0
$697$	0.447637	+	1.67060i	0.0169554	+	0.0632786i
$698$	30.7331	+	15.1620i	1.16327	+	0.573889i
$699$		0			0
$700$	−21.2182	−	2.80031i	−0.801973	−	0.105842i
$701$	33.4570	+	13.8584i	1.26365	+	0.523423i	0.911029	−	0.412341i	$-0.135289\pi$
$701$	33.4570	+	13.8584i	1.26365	+	0.523423i	0.352626	+	0.935765i	$0.385289\pi$
$702$		0			0
$703$			6.58816i			0.248477i
$704$	−42.0664	+	24.2334i	−1.58544	+	0.913332i
$705$		0			0
$706$	−25.2833	−	1.66120i	−0.951550	−	0.0625201i
$707$	24.8011	+	32.3214i	0.932740	+	1.21557i
$708$		0			0
$709$	4.18727	+	3.21300i	0.157256	+	0.120667i	0.684392	−	0.729114i	$-0.260068\pi$
$709$	4.18727	+	3.21300i	0.157256	+	0.120667i	−0.527136	+	0.849781i	$0.676734\pi$
$710$	33.1123	−	2.16500i	1.24268	−	0.0812509i
$711$		0			0
$712$	7.39864	−	4.93850i	0.277276	−	0.185078i
$713$	14.5531	+	3.89948i	0.545016	+	0.146037i
$714$		0			0
$715$	10.0655	−	76.4553i	0.376430	−	2.85927i
$716$	0.0135896	−	42.6447i	0.000507868	−	1.59371i
$717$		0			0
$718$	8.28546	−	1.64671i	0.309211	−	0.0614546i
$719$			40.9430i			1.52691i	0.645858	+	0.763457i	$0.276500\pi$
$719$			40.9430i			1.52691i	−0.645858	+	0.763457i	$0.723500\pi$
$720$		0			0
$721$		−	10.2230i		−	0.380723i
$722$	2.63480	+	13.2571i	0.0980572	+	0.493378i
$723$		0			0
$724$	2.75842	−	2.75666i	0.102516	−	0.102451i
$725$	−1.87591	+	14.2490i	−0.0696696	+	0.529193i
$726$		0			0
$727$	−18.2625	−	4.89343i	−0.677320	−	0.181487i	−0.0962700	−	0.995355i	$-0.530691\pi$
$727$	−18.2625	−	4.89343i	−0.677320	−	0.181487i	−0.581050	+	0.813868i	$0.697358\pi$
$728$	39.6654	−	7.87022i	1.47010	−	0.291690i
$729$		0			0
$730$	−4.25551	−	65.0855i	−0.157504	−	2.40892i
$731$	−2.93587	−	2.25277i	−0.108587	−	0.0833218i
$732$		0			0
$733$	30.1492	+	39.2912i	1.11359	+	1.45125i	0.877534	+	0.479515i	$0.159187\pi$
$733$	30.1492	+	39.2912i	1.11359	+	1.45125i	0.236053	+	0.971740i	$0.424146\pi$
$734$	−0.279985	+	4.26134i	−0.0103344	+	0.157289i
$735$		0			0
$736$	18.7685	−	9.23700i	0.691815	−	0.340480i
$737$		−	61.5240i		−	2.26627i
$738$		0			0
$739$	24.3973	+	10.1057i	0.897468	+	0.371743i	0.783246	−	0.621712i	$-0.213563\pi$
$739$	24.3973	+	10.1057i	0.897468	+	0.371743i	0.114222	+	0.993455i	$0.463563\pi$
$740$	−7.51775	−	9.80379i	−0.276358	−	0.360395i
$741$		0			0
$742$	−14.4778	+	29.3463i	−0.531498	+	1.07734i
$743$	6.18952	+	23.0996i	0.227072	+	0.847443i	0.981564	+	0.191134i	$0.0612165\pi$
$743$	6.18952	+	23.0996i	0.227072	+	0.847443i	−0.754492	+	0.656309i	$0.772117\pi$
$744$		0			0
$745$	−6.19830	+	23.1324i	−0.227088	+	0.847505i
$746$	−20.9308	−	18.3617i	−0.766330	−	0.672270i
$747$		0			0
$748$	−54.8525	−	14.7164i	−2.00561	−	0.538085i
$749$	−16.4917	+	2.17118i	−0.602595	+	0.0793332i
$750$		0			0
$751$	9.25320	−	16.0270i	0.337654	−	0.584834i	−0.646337	−	0.763052i	$-0.723700\pi$
$751$	9.25320	−	16.0270i	0.337654	−	0.584834i	0.983991	+	0.178218i	$0.0570332\pi$
$752$	3.57446	−	13.3061i	0.130347	−	0.485225i
$753$		0			0
$754$	−5.29347	−	26.6342i	−0.192777	−	0.969962i
$755$	−1.08970	−	0.451368i	−0.0396582	−	0.0164270i
$756$		0			0
$757$	19.5190	+	47.1230i	0.709430	+	1.71272i	0.701420	+	0.712748i	$0.252550\pi$
$757$	19.5190	+	47.1230i	0.709430	+	1.71272i	0.00801046	+	0.999968i	$0.497450\pi$
$758$	−8.99399	+	45.1782i	−0.326676	+	1.64095i
$759$		0			0
$760$	18.8192	+	16.5199i	0.682644	+	0.599241i
$761$	−15.5130	+	4.15670i	−0.562346	+	0.150680i	−0.528784	−	0.848757i	$-0.677352\pi$
$761$	−15.5130	+	4.15670i	−0.562346	+	0.150680i	−0.0335620	+	0.999437i	$0.510685\pi$
$762$		0			0
$763$	−13.3970	+	17.4593i	−0.485003	+	0.632068i
$764$	−14.7838	+	19.2540i	−0.534861	+	0.696584i
$765$		0			0
$766$	−30.1067	+	14.8410i	−1.08780	+	0.536228i
$767$	−2.95259	−	5.11404i	−0.106612	−	0.184657i
$768$		0			0
$769$	−0.485057	+	0.840144i	−0.0174916	+	0.0302964i	−0.874639	−	0.484775i	$-0.838901\pi$
$769$	−0.485057	+	0.840144i	−0.0174916	+	0.0302964i	0.857147	+	0.515072i	$0.172235\pi$
$770$	5.25497	−	79.9802i	0.189376	−	2.88228i
$771$		0			0
$772$	7.44960	+	0.983174i	0.268117	+	0.0353852i
$773$	−11.5933	−	27.9886i	−0.416980	−	1.00668i	−0.983218	−	0.182437i	$-0.941601\pi$
$773$	−11.5933	−	27.9886i	−0.416980	−	1.00668i	0.566237	−	0.824242i	$-0.308399\pi$
$774$		0			0
$775$	−9.51072	−	9.51072i	−0.341635	−	0.341635i
$776$	−5.20059	+	1.76259i	−0.186690	+	0.0632733i
$777$		0			0
$778$	7.80663	−	2.64861i	0.279881	−	0.0949572i
$779$	1.12605	+	0.148247i	0.0403448	+	0.00531149i
$780$		0			0
$781$	6.45065	+	48.9975i	0.230822	+	1.75327i
$782$	23.1711	+	7.86965i	0.828597	+	0.281418i
$783$		0			0
$784$	13.5557	−	3.62298i	0.484131	−	0.129392i
$785$	−20.4451	−	35.4120i	−0.729717	−	1.26391i
$786$		0			0
$787$	−2.22969	−	2.90579i	−0.0794799	−	0.103580i	0.751921	−	0.659253i	$-0.229127\pi$
$787$	−2.22969	−	2.90579i	−0.0794799	−	0.103580i	−0.831401	+	0.555673i	$0.812461\pi$
$788$	−32.9731	+	32.9521i	−1.17462	+	1.17387i
$789$		0			0
$790$	11.1543	−	56.0299i	0.396853	−	1.99345i
$791$	−1.01706	−	1.01706i	−0.0361625	−	0.0361625i
$792$		0			0
$793$	7.92956	−	7.92956i	0.281587	−	0.281587i
$794$	−14.8561	−	22.2414i	−0.527223	−	0.789317i
$795$		0			0
$796$	14.6370	−	35.3051i	0.518795	−	1.25135i
$797$	−3.87216	+	2.97121i	−0.137159	+	0.105246i	−0.675062	−	0.737761i	$-0.735883\pi$
$797$	−3.87216	+	2.97121i	−0.137159	+	0.105246i	0.537903	+	0.843007i	$0.319217\pi$
$798$		0			0
$799$	13.9585	−	8.05893i	0.493815	−	0.285104i
$800$	−18.6334	−	1.23621i	−0.658790	−	0.0437065i
$801$		0			0
$802$	−15.9836	+	7.87909i	−0.564402	+	0.278220i
$803$	96.3094	−	12.6794i	3.39869	−	0.447445i
$804$		0			0
$805$	−4.50794	+	34.2412i	−0.158884	+	1.20684i
$806$	22.7910	+	11.2438i	0.802778	+	0.396046i
$807$		0			0
$808$	23.4254	+	26.7373i	0.824104	+	0.940617i
$809$	28.0570	−	28.0570i	0.986431	−	0.986431i	−0.0134785	−	0.999909i	$-0.504290\pi$
$809$	28.0570	−	28.0570i	0.986431	−	0.986431i	0.999909	+	0.0134785i	$0.00429047\pi$
$810$		0			0
$811$	29.9705	−	12.4142i	1.05240	−	0.435920i	0.211655	−	0.977344i	$-0.432115\pi$
$811$	29.9705	−	12.4142i	1.05240	−	0.435920i	0.840750	+	0.541424i	$0.182115\pi$
$812$	−7.29643	−	27.2654i	−0.256054	−	0.956828i
$813$		0			0
$814$	13.8356	−	12.1296i	0.484937	−	0.425141i
$815$	−19.3547	−	11.1744i	−0.677966	−	0.391424i
$816$		0			0
$817$	−2.10455	+	1.21506i	−0.0736288	+	0.0425096i
$818$	−14.1710	+	41.7247i	−0.495479	+	1.45887i
$819$		0			0
$820$	−1.84483	+	1.06433i	−0.0644241	+	0.0371679i
$821$	−22.2068	−	17.0399i	−0.775022	−	0.594695i	0.143690	−	0.989623i	$-0.454103\pi$
$821$	−22.2068	−	17.0399i	−0.775022	−	0.594695i	−0.918712	+	0.394927i	$0.870770\pi$
$822$		0			0
$823$	2.78458	+	10.3922i	0.0970645	+	0.362250i	0.997324	−	0.0731033i	$-0.0232903\pi$
$823$	2.78458	+	10.3922i	0.0970645	+	0.362250i	−0.900260	+	0.435353i	$0.856624\pi$
$824$	−0.579140	−	8.90117i	−0.0201753	−	0.310087i
$825$		0			0
$826$	−3.40916	−	5.10392i	−0.118620	−	0.177588i
$827$	−13.0122	+	5.38984i	−0.452480	+	0.187423i	−0.597272	−	0.802039i	$-0.703749\pi$
$827$	−13.0122	+	5.38984i	−0.452480	+	0.187423i	0.144792	+	0.989462i	$0.453749\pi$
$828$		0			0
$829$	11.6899	−	28.2220i	0.406009	−	0.980191i	−0.580169	−	0.814496i	$-0.697013\pi$
$829$	11.6899	−	28.2220i	0.406009	−	0.980191i	0.986177	−	0.165695i	$-0.0529867\pi$
$830$	40.2217	−	60.1752i	1.39611	−	2.08871i
$831$		0			0
$832$	34.0909	−	9.09971i	1.18189	−	0.315476i
$833$	14.2154	+	8.20726i	0.492534	+	0.284365i
$834$		0			0
$835$	5.64783	+	42.8995i	0.195451	+	1.48460i
$836$	−22.7130	+	29.5807i	−0.785547	+	1.02307i
$837$		0			0
$838$	−0.410143	−	6.27289i	−0.0141682	−	0.216693i
$839$	23.1112	+	6.19264i	0.797889	+	0.213794i	0.634657	−	0.772794i	$-0.281141\pi$
$839$	23.1112	+	6.19264i	0.797889	+	0.213794i	0.163232	+	0.986588i	$0.447808\pi$
$840$		0			0
$841$	9.70426	−	2.60025i	0.334630	−	0.0896638i
$842$	−11.8543	−	34.9399i	−0.408525	−	1.20411i
$843$		0			0
$844$	3.32921	−	5.76213i	0.114596	−	0.198341i
$845$	−7.11500	+	17.1771i	−0.244763	+	0.590911i
$846$		0			0
$847$	83.7159			2.87651
$848$	−10.9434	+	26.3721i	−0.375798	+	0.905623i
$849$		0			0
$850$	−14.4014	−	16.4269i	−0.493964	−	0.563439i
$851$	−6.28985	+	4.82637i	−0.215613	+	0.165446i
$852$		0			0
$853$	26.1872	−	34.1278i	0.896631	−	1.16851i	−0.0883910	−	0.996086i	$-0.528172\pi$
$853$	26.1872	−	34.1278i	0.896631	−	1.16851i	0.985022	−	0.172427i	$-0.0551608\pi$
$854$	7.68661	−	8.76208i	0.263030	−	0.299832i
$855$		0			0
$856$	−14.2364	+	2.82473i	−0.486591	+	0.0965472i
$857$	−6.49577	+	24.2426i	−0.221891	+	0.828110i	0.761735	+	0.647889i	$0.224348\pi$
$857$	−6.49577	+	24.2426i	−0.221891	+	0.828110i	−0.983626	+	0.180221i	$0.942319\pi$
$858$		0			0
$859$	21.5218	+	2.83339i	0.734313	+	0.0966741i	0.488403	−	0.872618i	$-0.337580\pi$
$859$	21.5218	+	2.83339i	0.734313	+	0.0966741i	0.245910	+	0.969293i	$0.420913\pi$
$860$	1.74526	−	4.20963i	0.0595128	−	0.143547i
$861$		0			0
$862$	3.03910	−	4.54676i	0.103512	−	0.154863i
$863$	−7.05846			−0.240273			−0.120136	−	0.992757i	$-0.538333\pi$
$863$	−7.05846			−0.240273			−0.120136	+	0.992757i	$0.538333\pi$
$864$		0			0
$865$	−33.4016			−1.13569
$866$	26.4938	−	39.6370i	0.900294	−	1.34692i
$867$		0			0
$868$	24.4007	+	10.1162i	0.828215	+	0.343367i
$869$	84.3564	+	11.1057i	2.86159	+	0.376736i
$870$		0			0
$871$	−11.5734	+	43.1924i	−0.392148	+	1.46352i
$872$	−10.6757	+	15.9608i	−0.361525	+	0.540501i
$873$		0			0
$874$	10.5975	−	12.0802i	0.358465	−	0.408620i
$875$	−9.65870	+	12.5875i	−0.326524	+	0.425534i
$876$		0			0
$877$	−31.8089	+	24.4079i	−1.07411	+	0.824195i	−0.985125	−	0.171838i	$-0.945029\pi$
$877$	−31.8089	+	24.4079i	−1.07411	+	0.824195i	−0.0889861	+	0.996033i	$0.528363\pi$
$878$	3.06673	+	3.49806i	0.103497	+	0.118054i
$879$		0			0
$880$	0.0445736	−	69.9367i	0.00150257	−	2.35757i
$881$	13.6983			0.461509			0.230754	−	0.973012i	$-0.425881\pi$
$881$	13.6983			0.461509			0.230754	+	0.973012i	$0.425881\pi$
$882$		0			0
$883$	20.9737	−	50.6349i	0.705820	−	1.70400i	−0.00436881	−	0.999990i	$-0.501391\pi$
$883$	20.9737	−	50.6349i	0.705820	−	1.70400i	0.710189	−	0.704011i	$-0.248609\pi$
$884$	35.7404	+	20.6499i	1.20208	+	0.694531i
$885$		0			0
$886$	−13.7663	−	40.5754i	−0.462487	−	1.36316i
$887$	−27.8064	+	7.45071i	−0.933649	+	0.250170i	−0.693410	−	0.720543i	$-0.743892\pi$
$887$	−27.8064	+	7.45071i	−0.933649	+	0.250170i	−0.240239	+	0.970714i	$0.577226\pi$
$888$		0			0
$889$	2.37956	+	0.637602i	0.0798080	+	0.0213845i
$890$	0.836082	+	12.7874i	0.0280255	+	0.428633i
$891$		0			0
$892$	15.8807	+	12.1937i	0.531726	+	0.408277i
$893$	−1.38154	−	10.4938i	−0.0462314	−	0.351163i
$894$		0			0
$895$	53.2030	+	30.7168i	1.77838	+	1.02675i
$896$	34.7412	−	11.7498i	1.16062	−	0.392535i
$897$		0			0
$898$	12.4675	−	18.6525i	0.416047	−	0.622443i
$899$	6.78799	−	16.3877i	0.226392	−	0.546559i
$900$		0			0
$901$	−30.8592	+	12.7823i	−1.02807	+	0.425840i
$902$	−1.76186	−	2.63771i	−0.0586634	−	0.0878262i
$903$		0			0
$904$	−0.943174	−	0.827940i	−0.0313695	−	0.0275369i
$905$	1.45403	+	5.42652i	0.0483336	+	0.180384i
$906$		0			0
$907$	40.4805	+	31.0618i	1.34413	+	1.03139i	0.995562	+	0.0941078i	$0.0299998\pi$
$907$	40.4805	+	31.0618i	1.34413	+	1.03139i	0.348572	+	0.937282i	$0.386667\pi$
$908$	−15.0872	−	26.1510i	−0.500685	−	0.867851i
$909$		0			0
$910$	−18.7344	+	55.1608i	−0.621039	+	1.82856i
$911$	3.77486	−	2.17941i	0.125067	−	0.0722072i	−0.436162	−	0.899868i	$-0.643662\pi$
$911$	3.77486	−	2.17941i	0.125067	−	0.0722072i	0.561228	+	0.827661i	$0.310329\pi$
$912$		0			0
$913$	93.3551	+	53.8986i	3.08960	+	1.78378i
$914$	−1.60789	+	1.40963i	−0.0531844	+	0.0466265i
$915$		0			0
$916$	33.6863	−	9.01472i	1.11303	−	0.297855i
$917$	18.8436	−	7.80527i	0.622270	−	0.257753i
$918$		0			0
$919$	−6.43591	+	6.43591i	−0.212301	+	0.212301i	−0.805244	−	0.592943i	$-0.797966\pi$
$919$	−6.43591	+	6.43591i	−0.212301	+	0.212301i	0.592943	+	0.805244i	$0.297966\pi$
$920$	−1.98528	+	30.0693i	−0.0654528	+	0.991355i
$921$		0			0
$922$	−2.73247	−	1.34805i	−0.0899892	−	0.0443956i
$923$	4.68837	−	35.6117i	0.154320	−	1.17217i
$924$		0			0
$925$	7.01715	−	0.923825i	0.230722	−	0.0303752i
$926$	−23.2688	+	11.4703i	−0.764661	+	0.376938i
$927$		0			0
$928$	−7.89764	−	23.3267i	−0.259253	−	0.765737i
$929$	−19.6087	+	11.3211i	−0.643341	+	0.371433i	−0.785900	−	0.618353i	$-0.787800\pi$
$929$	−19.6087	+	11.3211i	−0.643341	+	0.371433i	0.142559	+	0.989786i	$0.454467\pi$
$930$		0			0
$931$	8.55171	−	6.56196i	0.280271	−	0.215060i
$932$	−40.9483	−	16.9766i	−1.34131	−	0.556088i
$933$		0			0
$934$	27.7864	+	41.5996i	0.909199	+	1.36118i
$935$	57.8515	−	57.8515i	1.89195	−	1.89195i
$936$		0			0
$937$	−14.5093	−	14.5093i	−0.473998	−	0.473998i	0.429207	−	0.903206i	$-0.358793\pi$
$937$	−14.5093	−	14.5093i	−0.473998	−	0.473998i	−0.903206	+	0.429207i	$0.858793\pi$
$938$	−9.07455	+	45.5829i	−0.296295	+	1.48833i
$939$		0			0
$940$	14.0304	+	14.0393i	0.457621	+	0.457912i
$941$	3.50418	+	4.56674i	0.114233	+	0.148871i	0.846970	−	0.531640i	$-0.178424\pi$
$941$	3.50418	+	4.56674i	0.114233	+	0.148871i	−0.732737	+	0.680512i	$0.761758\pi$
$942$		0			0
$943$	0.683388	+	1.18366i	0.0222542	+	0.0385454i
$944$	−3.25751	−	4.25087i	−0.106023	−	0.138354i
$945$		0			0
$946$	6.42643	+	2.18262i	0.208941	+	0.0709632i
$947$	−1.94795	−	14.7961i	−0.0632998	−	0.480810i	−0.993507	−	0.113774i	$-0.963706\pi$
$947$	−1.94795	−	14.7961i	−0.0632998	−	0.480810i	0.930207	−	0.367036i	$-0.119627\pi$
$948$		0			0
$949$	−69.9983	−	9.21545i	−2.27224	−	0.299146i
$950$	−13.5853	+	4.60918i	−0.440766	+	0.149542i
$951$		0			0
$952$	38.4694	+	18.9939i	1.24680	+	0.615595i
$953$	17.8843	+	17.8843i	0.579330	+	0.579330i	0.934719	−	0.355389i	$-0.115652\pi$
$953$	17.8843	+	17.8843i	0.579330	+	0.579330i	−0.355389	+	0.934719i	$0.615652\pi$
$954$		0			0
$955$	−13.3826	−	32.3084i	−0.433050	−	1.04548i
$956$	4.50617	−	34.1437i	0.145740	−	1.10429i
$957$		0			0
$958$	0.653976	−	9.95345i	0.0211290	−	0.321581i
$959$	23.2300	−	40.2355i	0.750136	−	1.29927i
$960$		0			0
$961$	−7.19986	−	12.4705i	−0.232254	−	0.402275i
$962$	−11.9949	+	5.91283i	−0.386730	+	0.190637i
$963$		0			0
$964$	20.0436	+	15.3902i	0.645562	+	0.495684i
$965$	−6.58977	+	8.58795i	−0.212132	+	0.276456i
$966$		0			0
$967$	27.7620	−	7.43881i	0.892767	−	0.239216i	0.216859	−	0.976203i	$-0.430419\pi$
$967$	27.7620	−	7.43881i	0.892767	−	0.239216i	0.675907	+	0.736987i	$0.263752\pi$
$968$	72.8918	−	4.74259i	2.34283	−	0.152433i
$969$		0			0
$970$	1.54450	−	7.75827i	0.0495909	−	0.249103i
$971$	−3.64747	−	8.80578i	−0.117053	−	0.282591i	0.854484	−	0.519477i	$-0.173873\pi$
$971$	−3.64747	−	8.80578i	−0.117053	−	0.282591i	−0.971537	+	0.236886i	$0.923873\pi$
$972$		0			0
$973$	−40.6497	−	16.8376i	−1.30317	−	0.539790i
$974$	−0.0497055	−	0.250095i	−0.00159267	−	0.00801355i
$975$		0			0
$976$	6.19638	−	8.06463i	0.198341	−	0.258143i
$977$	−23.9495	+	41.4818i	−0.766214	+	1.32712i	0.173388	+	0.984854i	$0.444528\pi$
$977$	−23.9495	+	41.4818i	−0.766214	+	1.32712i	−0.939602	+	0.342268i	$0.888805\pi$
$978$		0			0
$979$	−18.9219	+	2.49112i	−0.604748	+	0.0796165i
$980$	−5.23789	+	19.5232i	−0.167318	+	0.623645i
$981$		0			0
$982$	21.7842	+	19.1104i	0.695162	+	0.609837i
$983$	−1.15926	+	4.32640i	−0.0369745	+	0.137991i	−0.981946	−	0.189163i	$-0.939423\pi$
$983$	−1.15926	+	4.32640i	−0.0369745	+	0.137991i	0.944971	+	0.327153i	$0.106089\pi$
$984$		0			0
$985$	−17.3809	−	64.8665i	−0.553803	−	2.06682i
$986$	12.7465	−	25.8369i	0.405930	−	0.822814i
$987$		0			0
$988$	21.5100	−	16.4943i	0.684323	−	0.524753i
$989$	−2.70180	−	1.11912i	−0.0859123	−	0.0355860i
$990$		0			0
$991$			61.1681i			1.94307i	0.236901	+	0.971534i	$0.423868\pi$
$991$			61.1681i			1.94307i	−0.236901	+	0.971534i	$0.576132\pi$
$992$	21.8189	+	7.42591i	0.692751	+	0.235773i
$993$		0			0
$994$	2.44769	−	37.2535i	0.0776359	−	1.18161i
$995$	33.5171	+	43.6803i	1.06256	+	1.38476i
$996$		0			0
$997$	−45.7959	−	35.1404i	−1.45037	−	1.11291i	−0.972064	−	0.234716i	$-0.924584\pi$
$997$	−45.7959	−	35.1404i	−1.45037	−	1.11291i	−0.478307	−	0.878193i	$-0.658749\pi$
$998$	1.03605	+	15.8458i	0.0327957	+	0.501590i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.179.38		368
3.2	odd	2		288.2.bf.a.275.9	yes	368
9.2	odd	6	inner	864.2.bn.a.467.22		368
9.7	even	3		288.2.bf.a.83.25	yes	368
32.27	odd	8	inner	864.2.bn.a.827.22		368
96.59	even	8		288.2.bf.a.59.25	✓	368
288.155	even	24	inner	864.2.bn.a.251.38		368
288.187	odd	24		288.2.bf.a.155.9	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.59.25	✓	368	96.59	even	8
288.2.bf.a.83.25	yes	368	9.7	even	3
288.2.bf.a.155.9	yes	368	288.187	odd	24
288.2.bf.a.275.9	yes	368	3.2	odd	2
864.2.bn.a.179.38		368	1.1	even	1	trivial
864.2.bn.a.251.38		368	288.155	even	24	inner
864.2.bn.a.467.22		368	9.2	odd	6	inner
864.2.bn.a.827.22		368	32.27	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.17575 + 0.785882i) q^{2} +(0.764778 + 1.84800i) q^{4} +(-2.85653 - 0.376069i) q^{5} +(-0.838984 + 3.13113i) q^{7} +(-0.553125 + 2.77382i) q^{8} +O(q^{10})\)	\(q+(1.17575 + 0.785882i) q^{2} +(0.764778 + 1.84800i) q^{4} +(-2.85653 - 0.376069i) q^{5} +(-0.838984 + 3.13113i) q^{7} +(-0.553125 + 2.77382i) q^{8} +(-3.06302 - 2.68706i) q^{10} +(3.69421 - 4.81439i) q^{11} +(-3.49913 + 2.68498i) q^{13} +(-3.44714 + 3.02209i) q^{14} +(-2.83023 + 2.82662i) q^{16} -4.67934 q^{17} +(-1.17593 + 2.83895i) q^{19} +(-1.48963 - 5.56649i) q^{20} +(8.12702 - 2.75731i) q^{22} +(-3.57188 + 0.957081i) q^{23} +(3.18871 + 0.854412i) q^{25} +(-6.22418 + 0.406959i) q^{26} +(-6.42797 + 0.844175i) q^{28} +(0.568252 + 4.31631i) q^{29} +(-3.52849 - 2.03717i) q^{31} +(-5.54904 + 1.09918i) q^{32} +(-5.50174 - 3.67741i) q^{34} +(3.57410 - 8.62865i) q^{35} +(1.98078 - 0.820466i) q^{37} +(-3.61369 + 2.41376i) q^{38} +(2.62316 - 7.71547i) q^{40} +(-0.0956623 - 0.357017i) q^{41} +(0.627411 + 0.481429i) q^{43} +(11.7223 + 3.14498i) q^{44} +(-4.95179 - 1.68179i) q^{46} +(-2.98300 + 1.72224i) q^{47} +(-3.03790 - 1.75394i) q^{49} +(3.07766 + 3.51052i) q^{50} +(-7.63791 - 4.41300i) q^{52} +(6.59478 - 2.73165i) q^{53} +(-12.3632 + 12.3632i) q^{55} +(-8.22112 - 4.05909i) q^{56} +(-2.72399 + 5.52148i) q^{58} +(-0.174758 + 1.32742i) q^{59} +(-2.52080 + 0.331870i) q^{61} +(-2.54764 - 5.16818i) q^{62} +(-7.38811 - 3.06853i) q^{64} +(11.0051 - 6.35381i) q^{65} +(8.04333 - 6.17187i) q^{67} +(-3.57866 - 8.64743i) q^{68} +(10.9834 - 7.33632i) q^{70} +(-5.75858 + 5.75858i) q^{71} +(11.3191 + 11.3191i) q^{73} +(2.97369 + 0.591997i) q^{74} +(-6.14572 - 0.00195846i) q^{76} +(11.9751 + 15.6063i) q^{77} +(7.01043 + 12.1424i) q^{79} +(9.14764 - 7.00997i) q^{80} +(0.168098 - 0.494942i) q^{82} +(2.31862 + 17.6117i) q^{83} +(13.3667 + 1.75976i) q^{85} +(0.359332 + 1.05911i) q^{86} +(11.3109 + 12.9100i) q^{88} +(-2.22386 - 2.22386i) q^{89} +(-5.47130 - 13.2089i) q^{91} +(-4.50038 - 5.86888i) q^{92} +(-4.86074 - 0.319367i) q^{94} +(4.42673 - 7.66732i) q^{95} +(0.970710 + 1.68132i) q^{97} +(-2.19343 - 4.44963i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

L-functions

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