LMFDB - Embedded newform 425.2.m.c.376.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			376.5
Character	$\chi$	$=$	425.376
Dual form			425.2.m.c.26.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.813283 + 0.813283i) q^{2} +(1.89910 - 0.786634i) q^{3} -0.677141i q^{4} +(2.18426 + 0.904752i) q^{6} +(0.143683 - 0.346882i) q^{7} +(2.17727 - 2.17727i) q^{8} +(0.866476 - 0.866476i) q^{9} +(0.0511675 + 0.0211943i) q^{11} +(-0.532662 - 1.28596i) q^{12} +0.388558i q^{13} +(0.398969 - 0.165258i) q^{14} +2.18720 q^{16} +(-4.08007 - 0.594174i) q^{17} +1.40938 q^{18} +(1.25108 + 1.25108i) q^{19} -0.771791i q^{21} +(0.0243767 + 0.0588507i) q^{22} +(0.948471 + 0.392870i) q^{23} +(2.42215 - 5.84758i) q^{24} +(-0.316007 + 0.316007i) q^{26} +(-1.39597 + 3.37018i) q^{27} +(-0.234888 - 0.0972938i) q^{28} +(3.23410 + 7.80781i) q^{29} +(5.59808 - 2.31880i) q^{31} +(-2.57573 - 2.57573i) q^{32} +0.113845 q^{33} +(-2.83502 - 3.80148i) q^{34} +(-0.586726 - 0.586726i) q^{36} +(-8.77594 + 3.63511i) q^{37} +2.03496i q^{38} +(0.305652 + 0.737910i) q^{39} +(2.93662 - 7.08964i) q^{41} +(0.627685 - 0.627685i) q^{42} +(-4.77818 + 4.77818i) q^{43} +(0.0143515 - 0.0346476i) q^{44} +(0.451862 + 1.09089i) q^{46} -1.84378i q^{47} +(4.15372 - 1.72053i) q^{48} +(4.85007 + 4.85007i) q^{49} +(-8.21586 + 2.08112i) q^{51} +0.263108 q^{52} +(-6.43330 - 6.43330i) q^{53} +(-3.87624 + 1.60559i) q^{54} +(-0.442420 - 1.06810i) q^{56} +(3.36006 + 1.39178i) q^{57} +(-3.71972 + 8.98020i) q^{58} +(-9.61131 + 9.61131i) q^{59} +(-2.22364 + 5.36835i) q^{61} +(6.43867 + 2.66698i) q^{62} +(-0.176067 - 0.425063i) q^{63} -8.56400i q^{64} +(0.0925878 + 0.0925878i) q^{66} +14.4112 q^{67} +(-0.402339 + 2.76278i) q^{68} +2.11029 q^{69} +(-1.04049 + 0.430984i) q^{71} -3.77311i q^{72} +(0.838594 + 2.02455i) q^{73} +(-10.0937 - 4.18095i) q^{74} +(0.847155 - 0.847155i) q^{76} +(0.0147038 - 0.0147038i) q^{77} +(-0.351548 + 0.848712i) q^{78} +(-3.64157 - 1.50839i) q^{79} +11.1746i q^{81} +(8.15419 - 3.37758i) q^{82} +(-6.67554 - 6.67554i) q^{83} -0.522611 q^{84} -7.77202 q^{86} +(12.2838 + 12.2838i) q^{87} +(0.157551 - 0.0652600i) q^{88} +2.61320i q^{89} +(0.134784 + 0.0558293i) q^{91} +(0.266028 - 0.642248i) q^{92} +(8.80728 - 8.80728i) q^{93} +(1.49951 - 1.49951i) q^{94} +(-6.91774 - 2.86542i) q^{96} +(-2.01122 - 4.85551i) q^{97} +7.88895i q^{98} +(0.0626997 - 0.0259711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} + 12 q^{9} + 4 q^{11} - 12 q^{12} - 24 q^{14} - 24 q^{16} + 4 q^{17} - 40 q^{18} - 20 q^{19} + 16 q^{22} + 8 q^{23} + 16 q^{24} + 16 q^{26} - 12 q^{27} + 48 q^{28} + 4 q^{29} + 24 q^{31}+ \cdots - 80 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 + 12 * q^9 + 4 * q^11 - 12 * q^12 - 24 * q^14 - 24 * q^16 + 4 * q^17 - 40 * q^18 - 20 * q^19 + 16 * q^22 + 8 * q^23 + 16 * q^24 + 16 * q^26 - 12 * q^27 + 48 * q^28 + 4 * q^29 + 24 * q^31 - 60 * q^32 + 48 * q^33 + 16 * q^34 + 60 * q^36 - 12 * q^37 + 8 * q^39 - 20 * q^41 + 12 * q^42 + 32 * q^43 + 64 * q^44 - 40 * q^46 - 40 * q^48 + 24 * q^49 + 16 * q^51 - 48 * q^52 - 12 * q^53 - 20 * q^54 - 32 * q^56 + 68 * q^57 - 16 * q^58 - 16 * q^59 - 64 * q^61 + 100 * q^62 - 44 * q^63 - 72 * q^66 + 40 * q^67 + 20 * q^68 - 48 * q^69 - 24 * q^71 + 32 * q^74 + 52 * q^76 + 24 * q^77 - 16 * q^78 - 48 * q^79 + 100 * q^82 + 12 * q^83 - 40 * q^84 - 16 * q^86 + 24 * q^87 + 4 * q^88 + 24 * q^91 - 88 * q^92 - 32 * q^93 - 40 * q^94 + 132 * q^96 - 88 * q^97 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	0.813283	+	0.813283i	0.575078	+	0.575078i	0.933543	−	0.358465i	$-0.116700\pi$
$2$	0.813283	+	0.813283i	0.575078	+	0.575078i	−0.358465	+	0.933543i	$0.616700\pi$
$3$	1.89910	−	0.786634i	1.09645	−	0.454163i	0.240197	−	0.970724i	$-0.422788\pi$
$3$	1.89910	−	0.786634i	1.09645	−	0.454163i	0.856250	+	0.516561i	$0.172788\pi$
$4$		−	0.677141i		−	0.338570i
$5$		0			0
$5$		0			0
$6$	2.18426	+	0.904752i	0.891722	+	0.369363i
$7$	0.143683	−	0.346882i	0.0543072	−	0.131109i	−0.894397	−	0.447273i	$-0.852395\pi$
$7$	0.143683	−	0.346882i	0.0543072	−	0.131109i	0.948704	+	0.316164i	$0.102395\pi$
$8$	2.17727	−	2.17727i	0.769782	−	0.769782i
$9$	0.866476	−	0.866476i	0.288825	−	0.288825i
$10$		0			0
$11$	0.0511675	+	0.0211943i	0.0154276	+	0.00639032i	0.390384	−	0.920652i	$-0.372342\pi$
$11$	0.0511675	+	0.0211943i	0.0154276	+	0.00639032i	−0.374956	+	0.927042i	$0.622342\pi$
$12$	−0.532662	−	1.28596i	−0.153766	−	0.371224i
$13$			0.388558i			0.107766i	0.998547	+	0.0538832i	$0.0171599\pi$
$13$			0.388558i			0.107766i	−0.998547	+	0.0538832i	$0.982840\pi$
$14$	0.398969	−	0.165258i	0.106629	−	0.0441671i
$15$		0			0
$16$	2.18720			0.546800
$17$	−4.08007	−	0.594174i	−0.989562	−	0.144108i
$17$	−4.08007	−	0.594174i	−0.989562	−	0.144108i
$18$	1.40938			0.332194
$19$	1.25108	+	1.25108i	0.287017	+	0.287017i	0.835899	−	0.548883i	$-0.184947\pi$
$19$	1.25108	+	1.25108i	0.287017	+	0.287017i	−0.548883	+	0.835899i	$0.684947\pi$
$20$		0			0
$21$		−	0.771791i		−	0.168419i
$22$	0.0243767	+	0.0588507i	0.00519714	+	0.0125470i
$23$	0.948471	+	0.392870i	0.197770	+	0.0819190i	0.479370	−	0.877613i	$-0.340865\pi$
$23$	0.948471	+	0.392870i	0.197770	+	0.0819190i	−0.281600	+	0.959532i	$0.590865\pi$
$24$	2.42215	−	5.84758i	0.494419	−	1.19363i
$25$		0			0
$26$	−0.316007	+	0.316007i	−0.0619741	+	0.0619741i
$27$	−1.39597	+	3.37018i	−0.268656	+	0.648592i
$28$	−0.234888	−	0.0972938i	−0.0443897	−	0.0183868i
$29$	3.23410	+	7.80781i	0.600557	+	1.44987i	0.873009	+	0.487704i	$0.162165\pi$
$29$	3.23410	+	7.80781i	0.600557	+	1.44987i	−0.272452	+	0.962169i	$0.587835\pi$
$30$		0			0
$31$	5.59808	−	2.31880i	1.00545	−	0.416469i	0.181654	−	0.983362i	$-0.441855\pi$
$31$	5.59808	−	2.31880i	1.00545	−	0.416469i	0.823791	+	0.566893i	$0.191855\pi$
$32$	−2.57573	−	2.57573i	−0.455330	−	0.455330i
$33$	0.113845			0.0198178
$34$	−2.83502	−	3.80148i	−0.486202	−	0.651949i
$35$		0			0
$36$	−0.586726	−	0.586726i	−0.0977876	−	0.0977876i
$37$	−8.77594	+	3.63511i	−1.44276	+	0.597609i	−0.960465	−	0.278402i	$-0.910195\pi$
$37$	−8.77594	+	3.63511i	−1.44276	+	0.597609i	−0.482291	+	0.876011i	$0.660195\pi$
$38$			2.03496i			0.330114i
$39$	0.305652	+	0.737910i	0.0489436	+	0.118160i
$40$		0			0
$41$	2.93662	−	7.08964i	0.458624	−	1.10722i	−0.510331	−	0.859978i	$-0.670477\pi$
$41$	2.93662	−	7.08964i	0.458624	−	1.10722i	0.968955	−	0.247238i	$-0.0795228\pi$
$42$	0.627685	−	0.627685i	0.0968539	−	0.0968539i
$43$	−4.77818	+	4.77818i	−0.728665	+	0.728665i	−0.970354	−	0.241689i	$-0.922299\pi$
$43$	−4.77818	+	4.77818i	−0.728665	+	0.728665i	0.241689	+	0.970354i	$0.422299\pi$
$44$	0.0143515	−	0.0346476i	0.00216357	−	0.00522332i
$45$		0			0
$46$	0.451862	+	1.09089i	0.0666233	+	0.160843i
$47$		−	1.84378i		−	0.268942i	−0.990918	−	0.134471i	$-0.957066\pi$
$47$		−	1.84378i		−	0.268942i	0.990918	−	0.134471i	$-0.0429335\pi$
$48$	4.15372	−	1.72053i	0.599537	−	0.248336i
$49$	4.85007	+	4.85007i	0.692866	+	0.692866i
$50$		0			0
$51$	−8.21586	+	2.08112i	−1.15045	+	0.291415i
$52$	0.263108			0.0364865
$53$	−6.43330	−	6.43330i	−0.883682	−	0.883682i	0.110224	−	0.993907i	$-0.464843\pi$
$53$	−6.43330	−	6.43330i	−0.883682	−	0.883682i	−0.993907	+	0.110224i	$0.964843\pi$
$54$	−3.87624	+	1.60559i	−0.527489	+	0.218493i
$55$		0			0
$56$	−0.442420	−	1.06810i	−0.0591208	−	0.142730i
$57$	3.36006	+	1.39178i	0.445051	+	0.184346i
$58$	−3.71972	+	8.98020i	−0.488423	+	1.17916i
$59$	−9.61131	+	9.61131i	−1.25129	+	1.25129i	−0.296143	+	0.955144i	$0.595700\pi$
$59$	−9.61131	+	9.61131i	−1.25129	+	1.25129i	−0.955144	+	0.296143i	$0.904300\pi$
$60$		0			0
$61$	−2.22364	+	5.36835i	−0.284708	+	0.687347i	−0.999933	−	0.0115474i	$-0.996324\pi$
$61$	−2.22364	+	5.36835i	−0.284708	+	0.687347i	0.715225	+	0.698894i	$0.246324\pi$
$62$	6.43867	+	2.66698i	0.817712	+	0.338707i
$63$	−0.176067	−	0.425063i	−0.0221823	−	0.0535529i
$64$		−	8.56400i		−	1.07050i
$65$		0			0
$66$	0.0925878	+	0.0925878i	0.0113968	+	0.0113968i
$67$	14.4112			1.76061			0.880303	−	0.474412i	$-0.157339\pi$
$67$	14.4112			1.76061			0.880303	+	0.474412i	$0.157339\pi$
$68$	−0.402339	+	2.76278i	−0.0487908	+	0.335036i
$69$	2.11029			0.254049
$70$		0			0
$71$	−1.04049	+	0.430984i	−0.123483	+	0.0511484i	−0.443570	−	0.896240i	$-0.646288\pi$
$71$	−1.04049	+	0.430984i	−0.123483	+	0.0511484i	0.320086	+	0.947388i	$0.396288\pi$
$72$		−	3.77311i		−	0.444665i
$73$	0.838594	+	2.02455i	0.0981500	+	0.236955i	0.965326	−	0.261046i	$-0.0840675\pi$
$73$	0.838594	+	2.02455i	0.0981500	+	0.236955i	−0.867176	+	0.498001i	$0.834067\pi$
$74$	−10.0937	−	4.18095i	−1.17337	−	0.486025i
$75$		0			0
$76$	0.847155	−	0.847155i	0.0971753	−	0.0971753i
$77$	0.0147038	−	0.0147038i	0.00167566	−	0.00167566i
$78$	−0.351548	+	0.848712i	−0.0398050	+	0.0960977i
$79$	−3.64157	−	1.50839i	−0.409709	−	0.169707i	0.168303	−	0.985735i	$-0.446171\pi$
$79$	−3.64157	−	1.50839i	−0.409709	−	0.169707i	−0.578012	+	0.816028i	$0.696171\pi$
$80$		0			0
$81$			11.1746i			1.24162i
$82$	8.15419	−	3.37758i	0.900480	−	0.372991i
$83$	−6.67554	−	6.67554i	−0.732735	−	0.732735i	0.238425	−	0.971161i	$-0.423369\pi$
$83$	−6.67554	−	6.67554i	−0.732735	−	0.732735i	−0.971161	+	0.238425i	$0.923369\pi$
$84$	−0.522611			−0.0570215
$85$		0			0
$86$	−7.77202			−0.838079
$87$	12.2838	+	12.2838i	1.31696	+	1.31696i
$88$	0.157551	−	0.0652600i	0.0167950	−	0.00695674i
$89$			2.61320i			0.276998i	0.990363	+	0.138499i	$0.0442278\pi$
$89$			2.61320i			0.276998i	−0.990363	+	0.138499i	$0.955772\pi$
$90$		0			0
$91$	0.134784	+	0.0558293i	0.0141292	+	0.00585250i
$92$	0.266028	−	0.642248i	0.0277353	−	0.0669590i
$93$	8.80728	−	8.80728i	0.913273	−	0.913273i
$94$	1.49951	−	1.49951i	0.154663	−	0.154663i
$95$		0			0
$96$	−6.91774	−	2.86542i	−0.706039	−	0.292451i
$97$	−2.01122	−	4.85551i	−0.204208	−	0.493002i	0.788284	−	0.615312i	$-0.210970\pi$
$97$	−2.01122	−	4.85551i	−0.204208	−	0.493002i	−0.992492	+	0.122310i	$0.960970\pi$
$98$			7.88895i			0.796905i
$99$	0.0626997	−	0.0259711i	0.00630156	−	0.00261019i
$100$		0			0
$101$	−4.03337			−0.401335			−0.200668	−	0.979659i	$-0.564311\pi$
$101$	−4.03337			−0.401335			−0.200668	+	0.979659i	$0.564311\pi$
$102$	−8.37437	−	4.98928i	−0.829186	−	0.494013i
$103$	3.21586			0.316868			0.158434	−	0.987370i	$-0.449355\pi$
$103$	3.21586			0.316868			0.158434	+	0.987370i	$0.449355\pi$
$104$	0.845996	+	0.845996i	0.0829567	+	0.0829567i
$105$		0			0
$106$		−	10.4642i		−	1.01637i
$107$	−4.54399	−	10.9702i	−0.439284	−	1.06052i	−0.976197	−	0.216887i	$-0.930410\pi$
$107$	−4.54399	−	10.9702i	−0.439284	−	1.06052i	0.536913	−	0.843638i	$-0.319590\pi$
$108$	2.28209	+	0.945271i	0.219594	+	0.0909588i
$109$	7.92218	−	19.1258i	0.758807	−	1.83192i	0.258701	−	0.965957i	$-0.416706\pi$
$109$	7.92218	−	19.1258i	0.758807	−	1.83192i	0.500106	−	0.865964i	$-0.333294\pi$
$110$		0			0
$111$	−13.8069	+	13.8069i	−1.31049	+	1.31049i
$112$	0.314264	−	0.758701i	0.0296952	−	0.0716905i
$113$	−4.23196	−	1.75294i	−0.398109	−	0.164902i	0.174641	−	0.984632i	$-0.444124\pi$
$113$	−4.23196	−	1.75294i	−0.398109	−	0.164902i	−0.572750	+	0.819730i	$0.694124\pi$
$114$	1.60077	+	3.86460i	0.149926	+	0.361953i
$115$		0			0
$116$	5.28698	−	2.18994i	0.490884	−	0.203331i
$117$	0.336676	+	0.336676i	0.0311257	+	0.0311257i
$118$	−15.6334			−1.43917
$119$	−0.792346	+	1.32993i	−0.0726343	+	0.121915i
$120$		0			0
$121$	−7.77601	−	7.77601i	−0.706910	−	0.706910i
$122$	−6.17444	+	2.55754i	−0.559008	+	0.231549i
$123$		−	15.7740i		−	1.42229i
$124$	−1.57015	−	3.79069i	−0.141004	−	0.340414i
$125$		0			0
$126$	0.202505	−	0.488889i	0.0180405	−	0.0435537i
$127$	−0.0614833	+	0.0614833i	−0.00545576	+	0.00545576i	−0.709829	−	0.704374i	$-0.751228\pi$
$127$	−0.0614833	+	0.0614833i	−0.00545576	+	0.00545576i	0.704374	+	0.709829i	$0.251228\pi$
$128$	1.81349	−	1.81349i	0.160292	−	0.160292i
$129$	−5.31557	+	12.8329i	−0.468010	+	1.12988i
$130$		0			0
$131$	3.00793	+	7.26179i	0.262804	+	0.634465i	0.999110	−	0.0421837i	$-0.0134315\pi$
$131$	3.00793	+	7.26179i	0.262804	+	0.634465i	−0.736306	+	0.676649i	$0.763431\pi$
$132$		−	0.0770887i		−	0.00670971i
$133$	0.613736	−	0.254218i	0.0532176	−	0.0220435i
$134$	11.7204	+	11.7204i	1.01249	+	1.01249i
$135$		0			0
$136$	−10.1771	+	7.58975i	−0.872680	+	0.650815i
$137$	−14.3733			−1.22800			−0.613999	−	0.789307i	$-0.710440\pi$
$137$	−14.3733			−1.22800			−0.613999	+	0.789307i	$0.710440\pi$
$138$	1.71626	+	1.71626i	0.146098	+	0.146098i
$139$	10.2198	−	4.23320i	0.866836	−	0.359055i	0.0954589	−	0.995433i	$-0.469568\pi$
$139$	10.2198	−	4.23320i	0.866836	−	0.359055i	0.771377	+	0.636378i	$0.219568\pi$
$140$		0			0
$141$	−1.45038	−	3.50152i	−0.122144	−	0.294881i
$142$	−1.19672	−	0.495699i	−0.100427	−	0.0415981i
$143$	−0.00823520	+	0.0198815i	−0.000688662	+	0.00166258i
$144$	1.89516	−	1.89516i	0.157930	−	0.157930i
$145$		0			0
$146$	−0.964514	+	2.32854i	−0.0798238	+	0.192712i
$147$	13.0260	+	5.39554i	1.07437	+	0.445017i
$148$	2.46148	+	5.94254i	0.202333	+	0.488474i
$149$		−	5.19432i		−	0.425535i	−0.977103	−	0.212768i	$-0.931752\pi$
$149$		−	5.19432i		−	0.425535i	0.977103	−	0.212768i	$-0.0682478\pi$
$150$		0			0
$151$	4.97988	+	4.97988i	0.405257	+	0.405257i	0.880081	−	0.474824i	$-0.157488\pi$
$151$	4.97988	+	4.97988i	0.405257	+	0.405257i	−0.474824	+	0.880081i	$0.657488\pi$
$152$	5.44787			0.441881
$153$	−4.05012	+	3.02044i	−0.327433	+	0.244188i
$154$	0.0239168			0.00192727
$155$		0			0
$156$	0.499669	−	0.206970i	0.0400055	−	0.0165708i
$157$		−	15.8006i		−	1.26103i	−0.776178	−	0.630514i	$-0.782844\pi$
$157$		−	15.8006i		−	1.26103i	0.776178	−	0.630514i	$-0.217156\pi$
$158$	−1.73488	−	4.18838i	−0.138020	−	0.333209i
$159$	−17.2782	−	7.15685i	−1.37025	−	0.567575i
$160$		0			0
$161$	0.272559	−	0.272559i	0.0214807	−	0.0214807i
$162$	−9.08810	+	9.08810i	−0.714029	+	0.714029i
$163$	−3.94819	+	9.53178i	−0.309246	+	0.746587i	0.690483	+	0.723348i	$0.257398\pi$
$163$	−3.94819	+	9.53178i	−0.309246	+	0.746587i	−0.999730	+	0.0232388i	$0.992602\pi$
$164$	−4.80068	−	1.98851i	−0.374870	−	0.155276i
$165$		0			0
$166$		−	10.8582i		−	0.842760i
$167$	7.64004	−	3.16461i	0.591204	−	0.244885i	−0.0669645	−	0.997755i	$-0.521331\pi$
$167$	7.64004	−	3.16461i	0.591204	−	0.244885i	0.658168	+	0.752871i	$0.271331\pi$
$168$	−1.68040	−	1.68040i	−0.129646	−	0.129646i
$169$	12.8490			0.988386
$170$		0			0
$171$	2.16806			0.165795
$172$	3.23550	+	3.23550i	0.246704	+	0.246704i
$173$	13.4048	−	5.55244i	1.01915	−	0.422144i	0.190362	−	0.981714i	$-0.439034\pi$
$173$	13.4048	−	5.55244i	1.01915	−	0.422144i	0.828783	+	0.559570i	$0.189034\pi$
$174$			19.9804i			1.51471i
$175$		0			0
$176$	0.111914	+	0.0463561i	0.00843581	+	0.00349423i
$177$	−10.6923	+	25.8134i	−0.803681	+	1.94026i
$178$	−2.12527	+	2.12527i	−0.159296	+	0.159296i
$179$	−10.9353	+	10.9353i	−0.817342	+	0.817342i	−0.985722	−	0.168380i	$-0.946146\pi$
$179$	−10.9353	+	10.9353i	−0.817342	+	0.817342i	0.168380	+	0.985722i	$0.446146\pi$
$180$		0			0
$181$	22.1058	+	9.15653i	1.64311	+	0.680600i	0.996607	−	0.0823091i	$-0.0262295\pi$
$181$	22.1058	+	9.15653i	1.64311	+	0.680600i	0.646506	+	0.762909i	$0.276229\pi$
$182$	0.0642124	+	0.155022i	0.00475974	+	0.0114910i
$183$			11.9442i			0.882944i
$184$	2.92047	−	1.20970i	0.215300	−	0.0891800i
$185$		0			0
$186$	14.3256			1.05041
$187$	−0.196174	−	0.116877i	−0.0143457	−	0.00854686i
$188$	−1.24849			−0.0910558
$189$	0.968478	+	0.968478i	0.0704464	+	0.0704464i
$190$		0			0
$191$		−	22.0393i		−	1.59471i	−0.603511	−	0.797355i	$-0.706232\pi$
$191$		−	22.0393i		−	1.59471i	0.603511	−	0.797355i	$-0.293768\pi$
$192$	−6.73673	−	16.2639i	−0.486182	−	1.17375i
$193$	13.5616	+	5.61741i	0.976187	+	0.404350i	0.813012	−	0.582247i	$-0.197826\pi$
$193$	13.5616	+	5.61741i	0.976187	+	0.404350i	0.163175	+	0.986597i	$0.447826\pi$
$194$	2.31321	−	5.58459i	0.166079	−	0.400950i
$195$		0			0
$196$	3.28418	−	3.28418i	0.234584	−	0.234584i
$197$	−3.74992	+	9.05311i	−0.267171	+	0.645007i	−0.999348	−	0.0361070i	$-0.988504\pi$
$197$	−3.74992	+	9.05311i	−0.267171	+	0.645007i	0.732177	+	0.681114i	$0.238504\pi$
$198$	0.0721145	+	0.0298708i	0.00512495	+	0.00212283i
$199$	−5.41887	−	13.0823i	−0.384134	−	0.927381i	−0.991157	−	0.132697i	$-0.957636\pi$
$199$	−5.41887	−	13.0823i	−0.384134	−	0.927381i	0.607023	−	0.794684i	$-0.292364\pi$
$200$		0			0
$201$	27.3683	−	11.3363i	1.93041	−	0.799603i
$202$	−3.28027	−	3.28027i	−0.230799	−	0.230799i
$203$	3.17308			0.222706
$204$	1.40921	+	5.56329i	0.0986646	+	0.389508i
$205$		0			0
$206$	2.61541	+	2.61541i	0.182224	+	0.182224i
$207$	1.16224	−	0.481415i	0.0807812	−	0.0334607i
$208$			0.849853i			0.0589267i
$209$	0.0374988	+	0.0905302i	0.00259385	+	0.00626211i
$210$		0			0
$211$	2.00706	−	4.84546i	0.138172	−	0.333576i	−0.839614	−	0.543184i	$-0.817219\pi$
$211$	2.00706	−	4.84546i	0.138172	−	0.333576i	0.977786	+	0.209608i	$0.0672188\pi$
$212$	−4.35625	+	4.35625i	−0.299189	+	0.299189i
$213$	−1.63697	+	1.63697i	−0.112163	+	0.112163i
$214$	5.22629	−	12.6174i	0.357262	−	0.862507i
$215$		0			0
$216$	4.29839	+	10.3772i	0.292468	+	0.706081i
$217$		−	2.27505i		−	0.154440i
$218$	21.9977	−	9.11174i	1.48987	−	0.617125i
$219$	3.18515	+	3.18515i	0.215233	+	0.215233i
$220$		0			0
$221$	0.230871	−	1.58534i	0.0155300	−	0.106642i
$222$	−22.4578			−1.50727
$223$	−9.59168	−	9.59168i	−0.642306	−	0.642306i	0.308816	−	0.951122i	$-0.400067\pi$
$223$	−9.59168	−	9.59168i	−0.642306	−	0.642306i	−0.951122	+	0.308816i	$0.900067\pi$
$224$	−1.26357	+	0.523387i	−0.0844256	+	0.0349702i
$225$		0			0
$226$	−2.01615	−	4.86742i	−0.134112	−	0.323776i
$227$	12.4165	+	5.14308i	0.824112	+	0.341358i	0.754569	−	0.656221i	$-0.227846\pi$
$227$	12.4165	+	5.14308i	0.824112	+	0.341358i	0.0695428	+	0.997579i	$0.477846\pi$
$228$	0.942433	−	2.27523i	0.0624142	−	0.150681i
$229$	−7.22635	+	7.22635i	−0.477530	+	0.477530i	−0.904341	−	0.426811i	$-0.859637\pi$
$229$	−7.22635	+	7.22635i	−0.477530	+	0.477530i	0.426811	+	0.904341i	$0.359637\pi$
$230$		0			0
$231$	0.0163576	−	0.0394906i	0.00107625	−	0.00259829i
$232$	24.0413	+	9.95821i	1.57839	+	0.653789i
$233$	7.23347	+	17.4631i	0.473880	+	1.14405i	0.962434	+	0.271514i	$0.0875244\pi$
$233$	7.23347	+	17.4631i	0.473880	+	1.14405i	−0.488554	+	0.872534i	$0.662476\pi$
$234$			0.547625i			0.0357994i
$235$		0			0
$236$	6.50821	+	6.50821i	0.423648	+	0.423648i
$237$	−8.10226			−0.526299
$238$	−1.72601	+	0.437208i	−0.111881	+	0.0283400i
$239$	17.0192			1.10088			0.550440	−	0.834874i	$-0.314460\pi$
$239$	17.0192			1.10088			0.550440	+	0.834874i	$0.314460\pi$
$240$		0			0
$241$	22.9284	−	9.49726i	1.47695	−	0.611772i	0.508517	−	0.861052i	$-0.330194\pi$
$241$	22.9284	−	9.49726i	1.47695	−	0.611772i	0.968432	+	0.249279i	$0.0801937\pi$
$242$		−	12.6482i		−	0.813057i
$243$	4.60238	+	11.1111i	0.295243	+	0.712779i
$244$	3.63513	+	1.50572i	0.232715	+	0.0963938i
$245$		0			0
$246$	12.8287	−	12.8287i	0.817930	−	0.817930i
$247$	−0.486115	+	0.486115i	−0.0309308	+	0.0309308i
$248$	7.13989	−	17.2372i	0.453384	−	1.09457i
$249$	−17.9287	−	7.42632i	−1.13619	−	0.470624i
$250$		0			0
$251$			18.0171i			1.13723i	0.822604	+	0.568614i	$0.192520\pi$
$251$			18.0171i			1.13723i	−0.822604	+	0.568614i	$0.807480\pi$
$252$	−0.287828	+	0.119222i	−0.0181314	+	0.00751028i
$253$	0.0402043	+	0.0402043i	0.00252763	+	0.00252763i
$254$	−0.100007			−0.00627497
$255$		0			0
$256$	−14.1782			−0.886140
$257$	4.67554	+	4.67554i	0.291652	+	0.291652i	0.837733	−	0.546080i	$-0.183881\pi$
$257$	4.67554	+	4.67554i	0.291652	+	0.291652i	−0.546080	+	0.837733i	$0.683881\pi$
$258$	−14.7599	+	6.11374i	−0.918909	+	0.380625i
$259$			3.56652i			0.221613i
$260$		0			0
$261$	9.56754	+	3.96301i	0.592216	+	0.245304i
$262$	−3.45959	+	8.35219i	−0.213734	+	0.516000i
$263$	−7.47288	+	7.47288i	−0.460798	+	0.460798i	−0.898917	−	0.438119i	$-0.855645\pi$
$263$	−7.47288	+	7.47288i	−0.460798	+	0.460798i	0.438119	+	0.898917i	$0.355645\pi$
$264$	0.247871	−	0.247871i	0.0152554	−	0.0152554i
$265$		0			0
$266$	0.705892	+	0.292390i	0.0432810	+	0.0179276i
$267$	2.05563	+	4.96273i	0.125802	+	0.303714i
$268$		−	9.75840i		−	0.596089i
$269$	3.50830	−	1.45319i	0.213905	−	0.0886024i	−0.273158	−	0.961969i	$-0.588068\pi$
$269$	3.50830	−	1.45319i	0.213905	−	0.0886024i	0.487063	+	0.873367i	$0.338068\pi$
$270$		0			0
$271$	−24.1996			−1.47002			−0.735010	−	0.678056i	$-0.762822\pi$
$271$	−24.1996			−1.47002			−0.735010	+	0.678056i	$0.762822\pi$
$272$	−8.92392	−	1.29958i	−0.541092	−	0.0787984i
$273$	0.299885			0.0181499
$274$	−11.6896	−	11.6896i	−0.706194	−	0.706194i
$275$		0			0
$276$		−	1.42896i		−	0.0860134i
$277$	−8.69785	−	20.9985i	−0.522603	−	1.26168i	−0.936281	−	0.351252i	$-0.885756\pi$
$277$	−8.69785	−	20.9985i	−0.522603	−	1.26168i	0.413678	−	0.910423i	$-0.364244\pi$
$278$	11.7544	+	4.86884i	0.704983	+	0.292014i
$279$	2.84142	−	6.85979i	0.170111	−	0.410685i
$280$		0			0
$281$	−7.92609	+	7.92609i	−0.472831	+	0.472831i	−0.902830	−	0.429998i	$-0.858514\pi$
$281$	−7.92609	+	7.92609i	−0.472831	+	0.472831i	0.429998	+	0.902830i	$0.358514\pi$
$282$	1.66816	−	4.02729i	0.0993374	−	0.239822i
$283$	12.9735	+	5.37381i	0.771196	+	0.319440i	0.733357	−	0.679844i	$-0.237952\pi$
$283$	12.9735	+	5.37381i	0.771196	+	0.319440i	0.0378394	+	0.999284i	$0.487952\pi$
$284$	0.291837	+	0.704556i	0.0173173	+	0.0418077i
$285$		0			0
$286$	−0.0228669	+	0.00947177i	−0.00135215	+	0.000560077i
$287$	−2.03733	−	2.03733i	−0.120260	−	0.120260i
$288$	−4.46362			−0.263021
$289$	16.2939	+	4.84854i	0.958466	+	0.285208i
$290$		0			0
$291$	−7.63901	−	7.63901i	−0.447807	−	0.447807i
$292$	1.37090	−	0.567846i	0.0802259	−	0.0332307i
$293$		−	27.9654i		−	1.63376i	−0.576811	−	0.816878i	$-0.695703\pi$
$293$		−	27.9654i		−	1.63376i	0.576811	−	0.816878i	$-0.304297\pi$
$294$	6.20572	+	14.9819i	0.361925	+	0.873764i
$295$		0			0
$296$	−11.1930	+	27.0223i	−0.650579	+	1.57064i
$297$	−0.142857	+	0.142857i	−0.00828941	+	0.00828941i
$298$	4.22446	−	4.22446i	0.244716	−	0.244716i
$299$	−0.152652	+	0.368536i	−0.00882812	+	0.0213130i
$300$		0			0
$301$	0.970921	+	2.34401i	0.0559629	+	0.135106i
$302$			8.10011i			0.466109i
$303$	−7.65978	+	3.17278i	−0.440043	+	0.182272i
$304$	2.73636	+	2.73636i	0.156941	+	0.156941i
$305$		0			0
$306$	−5.75037	−	0.837417i	−0.328727	−	0.0478719i
$307$	−20.4310			−1.16606			−0.583029	−	0.812451i	$-0.698133\pi$
$307$	−20.4310			−1.16606			−0.583029	+	0.812451i	$0.698133\pi$
$308$	−0.00995657	−	0.00995657i	−0.000567328	−	0.000567328i
$309$	6.10725	−	2.52971i	0.347429	−	0.143910i
$310$		0			0
$311$	−4.76779	−	11.5105i	−0.270356	−	0.652698i	0.729142	−	0.684362i	$-0.239919\pi$
$311$	−4.76779	−	11.5105i	−0.270356	−	0.652698i	−0.999499	+	0.0316642i	$0.989919\pi$
$312$	2.27212	+	0.941144i	0.128634	+	0.0532818i
$313$	−3.52347	+	8.50641i	−0.199158	+	0.480811i	−0.991632	−	0.129095i	$-0.958793\pi$
$313$	−3.52347	+	8.50641i	−0.199158	+	0.480811i	0.792474	+	0.609906i	$0.208793\pi$
$314$	12.8504	−	12.8504i	0.725189	−	0.725189i
$315$		0			0
$316$	−1.02139	+	2.46586i	−0.0574577	+	0.138715i
$317$	1.67569	+	0.694093i	0.0941160	+	0.0389841i	0.429245	−	0.903188i	$-0.358780\pi$
$317$	1.67569	+	0.694093i	0.0941160	+	0.0389841i	−0.335129	+	0.942172i	$0.608780\pi$
$318$	−8.23149	−	19.8726i	−0.461599	−	1.11440i
$319$			0.468051i			0.0262058i
$320$		0			0
$321$	−17.2590	−	17.2590i	−0.963303	−	0.963303i
$322$	0.443336			0.0247061
$323$	−4.36112	−	5.84784i	−0.242659	−	0.325382i
$324$	7.56676			0.420376
$325$		0			0
$326$	−10.9630	+	4.54104i	−0.607187	+	0.251505i
$327$		−	42.5537i		−	2.35323i
$328$	−9.04225	−	21.8299i	−0.499275	−	1.20536i
$329$	−0.639573	−	0.264920i	−0.0352608	−	0.0146055i
$330$		0			0
$331$	−12.9804	+	12.9804i	−0.713470	+	0.713470i	−0.967259	−	0.253790i	$-0.918323\pi$
$331$	−12.9804	+	12.9804i	−0.713470	+	0.713470i	0.253790	+	0.967259i	$0.418323\pi$
$332$	−4.52028	+	4.52028i	−0.248082	+	0.248082i
$333$	−4.45440	+	10.7539i	−0.244100	+	0.589309i
$334$	8.78724	+	3.63979i	0.480816	+	0.199161i
$335$		0			0
$336$		−	1.68806i		−	0.0920913i
$337$	9.82922	−	4.07140i	0.535432	−	0.221783i	−0.0985486	−	0.995132i	$-0.531420\pi$
$337$	9.82922	−	4.07140i	0.535432	−	0.221783i	0.633980	+	0.773349i	$0.281420\pi$
$338$	10.4499	+	10.4499i	0.568399	+	0.568399i
$339$	−9.41585			−0.511399
$340$		0			0
$341$	0.335585			0.0181730
$342$	1.76324	+	1.76324i	0.0953453	+	0.0953453i
$343$	4.80745	−	1.99131i	0.259578	−	0.107521i
$344$			20.8068i			1.12183i
$345$		0			0
$346$	15.4176	+	6.38617i	0.828854	+	0.343323i
$347$	−9.14186	+	22.0704i	−0.490761	+	1.18480i	0.463573	+	0.886059i	$0.346567\pi$
$347$	−9.14186	+	22.0704i	−0.490761	+	1.18480i	−0.954334	+	0.298743i	$0.903433\pi$
$348$	8.31784	−	8.31784i	0.445883	−	0.445883i
$349$	18.5777	−	18.5777i	0.994441	−	0.994441i	−0.00554356	−	0.999985i	$-0.501765\pi$
$349$	18.5777	−	18.5777i	0.994441	−	0.994441i	0.999985	+	0.00554356i	$0.00176458\pi$
$350$		0			0
$351$	−1.30951	−	0.542417i	−0.0698964	−	0.0289521i
$352$	−0.0772031	−	0.186385i	−0.00411494	−	0.00993434i
$353$			4.10448i			0.218460i	0.994017	+	0.109230i	$0.0348384\pi$
$353$			4.10448i			0.218460i	−0.994017	+	0.109230i	$0.965162\pi$
$354$	−29.6895	+	12.2978i	−1.57798	+	0.653620i
$355$		0			0
$356$	1.76950			0.0937834
$357$	−0.458578	+	3.14896i	−0.0242705	+	0.166661i
$358$	−17.7870			−0.940071
$359$	−11.2487	−	11.2487i	−0.593683	−	0.593683i	0.344941	−	0.938624i	$-0.387899\pi$
$359$	−11.2487	−	11.2487i	−0.593683	−	0.593683i	−0.938624	+	0.344941i	$0.887899\pi$
$360$		0			0
$361$		−	15.8696i		−	0.835243i
$362$	10.5314	+	25.4252i	0.553520	+	1.33632i
$363$	−20.8843	−	8.65056i	−1.09614	−	0.454037i
$364$	0.0378042	−	0.0912675i	0.00198148	−	0.00478372i
$365$		0			0
$366$	−9.71405	+	9.71405i	−0.507762	+	0.507762i
$367$	6.66981	−	16.1023i	0.348161	−	0.840535i	−0.648676	−	0.761064i	$-0.724677\pi$
$367$	6.66981	−	16.1023i	0.348161	−	0.840535i	0.996837	−	0.0794705i	$-0.0253229\pi$
$368$	2.07450	+	0.859284i	0.108141	+	0.0447933i
$369$	−3.59848	−	8.68751i	−0.187330	−	0.452254i
$370$		0			0
$371$	−3.15596	+	1.30724i	−0.163849	+	0.0678686i
$372$	−5.96377	−	5.96377i	−0.309207	−	0.309207i
$373$	26.1546			1.35423			0.677117	−	0.735875i	$-0.263229\pi$
$373$	26.1546			1.35423			0.677117	+	0.735875i	$0.263229\pi$
$374$	−0.0644912	−	0.254599i	−0.00333476	−	0.0131650i
$375$		0			0
$376$	−4.01440	−	4.01440i	−0.207027	−	0.207027i
$377$	−3.03378	+	1.25663i	−0.156248	+	0.0647199i
$378$			1.57529i			0.0810244i
$379$	6.79575	+	16.4064i	0.349074	+	0.842740i	0.996730	+	0.0808066i	$0.0257496\pi$
$379$	6.79575	+	16.4064i	0.349074	+	0.842740i	−0.647656	+	0.761933i	$0.724250\pi$
$380$		0			0
$381$	−0.0683982	+	0.165128i	−0.00350414	+	0.00845975i
$382$	17.9242	−	17.9242i	0.917083	−	0.917083i
$383$	−20.3547	+	20.3547i	−1.04008	+	1.04008i	−0.0409141	+	0.999163i	$0.513027\pi$
$383$	−20.3547	+	20.3547i	−1.04008	+	1.04008i	−0.999163	+	0.0409141i	$0.986973\pi$
$384$	2.01745	−	4.87056i	0.102953	−	0.248550i
$385$		0			0
$386$	6.46090	+	15.5980i	0.328851	+	0.793916i
$387$			8.28035i			0.420914i
$388$	−3.28786	+	1.36188i	−0.166916	+	0.0691388i
$389$	−18.9994	−	18.9994i	−0.963308	−	0.963308i	0.0360421	−	0.999350i	$-0.488525\pi$
$389$	−18.9994	−	18.9994i	−0.963308	−	0.963308i	−0.999350	+	0.0360421i	$0.988525\pi$
$390$		0			0
$391$	−3.63639	−	2.16649i	−0.183900	−	0.109564i
$392$	21.1198			1.06671
$393$	11.4247	+	11.4247i	0.576302	+	0.576302i
$394$	−10.4125	+	4.31299i	−0.524574	+	0.217285i
$395$		0			0
$396$	−0.0175861	−	0.0424565i	−0.000883733	−	0.00213352i
$397$	24.6038	+	10.1912i	1.23483	+	0.511484i	0.902096	−	0.431536i	$-0.142028\pi$
$397$	24.6038	+	10.1912i	1.23483	+	0.511484i	0.332736	+	0.943020i	$0.392028\pi$
$398$	6.23255	−	15.0467i	0.312410	−	0.754223i
$399$	0.965570	−	0.965570i	0.0483390	−	0.0483390i
$400$		0			0
$401$	1.03533	−	2.49950i	0.0517018	−	0.124819i	−0.895918	−	0.444219i	$-0.853481\pi$
$401$	1.03533	−	2.49950i	0.0517018	−	0.124819i	0.947620	+	0.319400i	$0.103481\pi$
$402$	31.4778	+	13.0385i	1.56997	+	0.650303i
$403$	0.900988	+	2.17518i	0.0448814	+	0.108353i
$404$			2.73116i			0.135880i
$405$		0			0
$406$	2.58061	+	2.58061i	0.128074	+	0.128074i
$407$	−0.526087			−0.0260771
$408$	−13.3570	+	22.4194i	−0.661271	+	1.10992i
$409$	−0.665597			−0.0329117			−0.0164558	−	0.999865i	$-0.505238\pi$
$409$	−0.665597			−0.0329117			−0.0164558	+	0.999865i	$0.505238\pi$
$410$		0			0
$411$	−27.2964	+	11.3066i	−1.34643	+	0.557711i
$412$		−	2.17759i		−	0.107282i
$413$	1.95301	+	4.71498i	0.0961013	+	0.232009i
$414$	1.33676	+	0.553703i	0.0656980	+	0.0272130i
$415$		0			0
$416$	1.00082	−	1.00082i	0.0490693	−	0.0490693i
$417$	16.0786	−	16.0786i	0.787370	−	0.787370i
$418$	−0.0431295	+	0.104124i	−0.00210953	+	0.00509287i
$419$	−30.4600	−	12.6170i	−1.48807	−	0.616379i	−0.517175	−	0.855880i	$-0.673016\pi$
$419$	−30.4600	−	12.6170i	−1.48807	−	0.616379i	−0.970896	+	0.239501i	$0.923016\pi$
$420$		0			0
$421$			5.35373i			0.260925i	0.991453	+	0.130462i	$0.0416462\pi$
$421$			5.35373i			0.260925i	−0.991453	+	0.130462i	$0.958354\pi$
$422$	5.57304	−	2.30843i	0.271291	−	0.112373i
$423$	−1.59759	−	1.59759i	−0.0776773	−	0.0776773i
$424$	−28.0141			−1.36049
$425$		0			0
$426$	−2.66263			−0.129005
$427$	1.54269	+	1.54269i	0.0746558	+	0.0746558i
$428$	−7.42833	+	3.07692i	−0.359062	+	0.148728i
$429$			0.0442351i			0.00213569i
$430$		0			0
$431$	−10.2043	−	4.22676i	−0.491524	−	0.203596i	0.123134	−	0.992390i	$-0.460706\pi$
$431$	−10.2043	−	4.22676i	−0.491524	−	0.203596i	−0.614657	+	0.788794i	$0.710706\pi$
$432$	−3.05328	+	7.37126i	−0.146901	+	0.354650i
$433$	−9.87103	+	9.87103i	−0.474372	+	0.474372i	−0.903326	−	0.428954i	$-0.858882\pi$
$433$	−9.87103	+	9.87103i	−0.474372	+	0.474372i	0.428954	+	0.903326i	$0.358882\pi$
$434$	1.85026	−	1.85026i	0.0888153	−	0.0888153i
$435$		0			0
$436$	−12.9509	−	5.36443i	−0.620234	−	0.256909i
$437$	0.695100	+	1.67812i	0.0332512	+	0.0802754i
$438$			5.18086i			0.247551i
$439$	−29.3045	+	12.1383i	−1.39863	+	0.579330i	−0.949395	−	0.314086i	$-0.898302\pi$
$439$	−29.3045	+	12.1383i	−1.39863	+	0.579330i	−0.449231	+	0.893416i	$0.648302\pi$
$440$		0			0
$441$	8.40493			0.400235
$442$	1.47709	−	1.10157i	0.0702582	−	0.0523963i
$443$	−37.4994			−1.78165			−0.890826	−	0.454345i	$-0.849873\pi$
$443$	−37.4994			−1.78165			−0.890826	+	0.454345i	$0.849873\pi$
$444$	9.34921	+	9.34921i	0.443694	+	0.443694i
$445$		0			0
$446$		−	15.6015i		−	0.738753i
$447$	−4.08603	−	9.86455i	−0.193263	−	0.466577i
$448$	−2.97070	−	1.23050i	−0.140352	−	0.0581359i
$449$	−4.39688	+	10.6150i	−0.207502	+	0.500953i	−0.993029	−	0.117874i	$-0.962392\pi$
$449$	−4.39688	+	10.6150i	−0.207502	+	0.500953i	0.785527	+	0.618827i	$0.212392\pi$
$450$		0			0
$451$	0.300520	−	0.300520i	0.0141509	−	0.0141509i
$452$	−1.18698	+	2.86563i	−0.0558310	+	0.134788i
$453$	13.3746	+	5.53996i	0.628395	+	0.260290i
$454$	5.91535	+	14.2809i	0.277621	+	0.670236i
$455$		0			0
$456$	10.3461	−	4.28548i	0.484499	−	0.200686i
$457$	−17.1448	−	17.1448i	−0.802002	−	0.802002i	0.181407	−	0.983408i	$-0.441935\pi$
$457$	−17.1448	−	17.1448i	−0.802002	−	0.802002i	−0.983408	+	0.181407i	$0.941935\pi$
$458$	−11.7541			−0.549235
$459$	7.69815	−	12.9211i	0.359319	−	0.603106i
$460$		0			0
$461$	18.7157	+	18.7157i	0.871675	+	0.871675i	0.992655	−	0.120980i	$-0.0386037\pi$
$461$	18.7157	+	18.7157i	0.871675	+	0.871675i	−0.120980	+	0.992655i	$0.538604\pi$
$462$	0.0454204	−	0.0188138i	0.00211315	−	0.000875295i
$463$			16.0633i			0.746523i	0.927726	+	0.373261i	$0.121761\pi$
$463$			16.0633i			0.746523i	−0.927726	+	0.373261i	$0.878239\pi$
$464$	7.07362	+	17.0772i	0.328385	+	0.792791i
$465$		0			0
$466$	−8.31962	+	20.0853i	−0.385399	+	0.930435i
$467$	13.7863	−	13.7863i	0.637955	−	0.637955i	−0.312096	−	0.950051i	$-0.601031\pi$
$467$	13.7863	−	13.7863i	0.637955	−	0.637955i	0.950051	+	0.312096i	$0.101031\pi$
$468$	0.227977	−	0.227977i	0.0105382	−	0.0105382i
$469$	2.07065	−	4.99898i	0.0956136	−	0.230832i
$470$		0			0
$471$	−12.4293	−	30.0070i	−0.572712	−	1.38265i
$472$			41.8529i			1.92644i
$473$	−0.345758	+	0.143217i	−0.0158980	+	0.00658515i
$474$	−6.58944	−	6.58944i	−0.302663	−	0.302663i
$475$		0			0
$476$	0.900550	+	0.536530i	0.0412766	+	0.0245918i
$477$	−11.1486			−0.510459
$478$	13.8414	+	13.8414i	0.633093	+	0.633093i
$479$	22.3277	−	9.24842i	1.02018	−	0.422571i	0.191020	−	0.981586i	$-0.438821\pi$
$479$	22.3277	−	9.24842i	1.02018	−	0.422571i	0.829158	+	0.559015i	$0.188821\pi$
$480$		0			0
$481$	−1.41245	−	3.40996i	−0.0644022	−	0.155481i
$482$	26.3713	+	10.9233i	1.20118	+	0.497544i
$483$	0.303213	−	0.732022i	0.0137967	−	0.0333081i
$484$	−5.26545	+	5.26545i	−0.239339	+	0.239339i
$485$		0			0
$486$	−5.29346	+	12.7795i	−0.240116	+	0.579692i
$487$	−33.6285	−	13.9294i	−1.52385	−	0.631200i	−0.545493	−	0.838115i	$-0.683658\pi$
$487$	−33.6285	−	13.9294i	−1.52385	−	0.631200i	−0.978359	+	0.206915i	$0.933658\pi$
$488$	6.84689	+	16.5299i	0.309944	+	0.748271i
$489$			21.2076i			0.959041i
$490$		0			0
$491$	−27.2688	−	27.2688i	−1.23063	−	1.23063i	−0.963724	−	0.266902i	$-0.914000\pi$
$491$	−27.2688	−	27.2688i	−1.23063	−	1.23063i	−0.266902	−	0.963724i	$-0.586000\pi$
$492$	−10.6812			−0.481546
$493$	−8.55615	−	33.7780i	−0.385350	−	1.52128i
$494$	−0.790699			−0.0355752
$495$		0			0
$496$	12.2441	−	5.07168i	0.549778	−	0.227725i
$497$			0.422852i			0.0189675i
$498$	−8.54143	−	20.6208i	−0.382751	−	0.924042i
$499$	33.5365	+	13.8913i	1.50130	+	0.621859i	0.973741	−	0.227659i	$-0.0731072\pi$
$499$	33.5365	+	13.8913i	1.50130	+	0.621859i	0.527559	+	0.849518i	$0.323107\pi$
$500$		0			0
$501$	12.0198	−	12.0198i	0.537006	−	0.537006i
$502$	−14.6530	+	14.6530i	−0.653995	+	0.653995i
$503$	−3.85574	+	9.30858i	−0.171919	+	0.415049i	−0.986230	−	0.165380i	$-0.947115\pi$
$503$	−3.85574	+	9.30858i	−0.171919	+	0.415049i	0.814311	+	0.580429i	$0.197115\pi$
$504$	−1.30882	−	0.542133i	−0.0582997	−	0.0241485i
$505$		0			0
$506$			0.0653950i			0.00290716i
$507$	24.4016	−	10.1075i	1.08371	−	0.448889i
$508$	0.0416328	+	0.0416328i	0.00184716	+	0.00184716i
$509$	−17.8399			−0.790740			−0.395370	−	0.918522i	$-0.629384\pi$
$509$	−17.8399			−0.790740			−0.395370	+	0.918522i	$0.629384\pi$
$510$		0			0
$511$	0.822771			0.0363972
$512$	−15.1579	−	15.1579i	−0.669891	−	0.669891i
$513$	−5.96283	+	2.46988i	−0.263265	+	0.109048i
$514$			7.60508i			0.335446i
$515$		0			0
$516$	8.68969	+	3.59939i	0.382542	+	0.158454i
$517$	0.0390775	−	0.0943414i	0.00171863	−	0.00414913i
$518$	−2.90059	+	2.90059i	−0.127445	+	0.127445i
$519$	21.0893	−	21.0893i	0.925717	−	0.925717i
$520$		0			0
$521$	33.1134	+	13.7160i	1.45073	+	0.600910i	0.962372	−	0.271736i	$-0.0875976\pi$
$521$	33.1134	+	13.7160i	1.45073	+	0.600910i	0.488354	+	0.872646i	$0.337598\pi$
$522$	4.55808	+	11.0042i	0.199502	+	0.481639i
$523$		−	16.7275i		−	0.731444i	−0.930724	−	0.365722i	$-0.880822\pi$
$523$		−	16.7275i		−	0.731444i	0.930724	−	0.365722i	$-0.119178\pi$
$524$	4.91725	−	2.03679i	0.214811	−	0.0889777i
$525$		0			0
$526$	−12.1551			−0.529989
$527$	−24.2183	+	6.13464i	−1.05497	+	0.267229i
$528$	0.249001			0.0108364
$529$	−15.5182	−	15.5182i	−0.674705	−	0.674705i
$530$		0			0
$531$			16.6559i			0.722806i
$532$	−0.172141	−	0.415585i	−0.00746326	−	0.0180179i
$533$	2.75473	+	1.14105i	0.119321	+	0.0494242i
$534$	−2.36430	+	5.70791i	−0.102313	+	0.247006i
$535$		0			0
$536$	31.3771	−	31.3771i	1.35528	−	1.35528i
$537$	−12.1652	+	29.3693i	−0.524966	+	1.26738i
$538$	4.03510	+	1.67139i	0.173965	+	0.0720588i
$539$	0.145372	+	0.350960i	0.00626162	+	0.0151169i
$540$		0			0
$541$	−12.1694	+	5.04072i	−0.523203	+	0.216718i	−0.628623	−	0.777710i	$-0.716381\pi$
$541$	−12.1694	+	5.04072i	−0.523203	+	0.216718i	0.105420	+	0.994428i	$0.466381\pi$
$542$	−19.6811	−	19.6811i	−0.845376	−	0.845376i
$543$	49.1841			2.11069
$544$	8.97874	+	12.0396i	0.384960	+	0.516194i
$545$		0			0
$546$	0.243892	+	0.243892i	0.0104376	+	0.0104376i
$547$	−12.1445	+	5.03041i	−0.519260	+	0.215085i	−0.626892	−	0.779106i	$-0.715673\pi$
$547$	−12.1445	+	5.03041i	−0.519260	+	0.215085i	0.107632	+	0.994191i	$0.465673\pi$
$548$			9.73277i			0.415763i
$549$	2.72481	+	6.57828i	0.116292	+	0.280754i
$550$		0			0
$551$	−5.72206	+	13.8143i	−0.243768	+	0.588508i
$552$	4.59468	−	4.59468i	0.195562	−	0.195562i
$553$	−1.04647	+	1.04647i	−0.0445003	+	0.0445003i
$554$	10.0039	−	24.1515i	0.425024	−	1.02610i
$555$		0			0
$556$	−2.86647	−	6.92027i	−0.121565	−	0.293485i
$557$		−	1.81038i		−	0.0767084i	−0.999264	−	0.0383542i	$-0.987788\pi$
$557$		−	1.81038i		−	0.0767084i	0.999264	−	0.0383542i	$-0.0122115\pi$
$558$	7.88983	−	3.26807i	0.334003	−	0.138349i
$559$	−1.85660	−	1.85660i	−0.0785257	−	0.0785257i
$560$		0			0
$561$	−0.464493	−	0.0676434i	−0.0196109	−	0.00285591i
$562$	−12.8923			−0.543830
$563$	−15.2557	−	15.2557i	−0.642950	−	0.642950i	0.308330	−	0.951280i	$-0.400230\pi$
$563$	−15.2557	−	15.2557i	−0.642950	−	0.642950i	−0.951280	+	0.308330i	$0.900230\pi$
$564$	−2.37102	+	0.982108i	−0.0998379	+	0.0413542i
$565$		0			0
$566$	6.18072	+	14.9216i	0.259795	+	0.627201i
$567$	3.87627	+	1.60560i	0.162788	+	0.0674289i
$568$	−1.32706	+	3.20380i	−0.0556820	+	0.134428i
$569$	−1.85776	+	1.85776i	−0.0778815	+	0.0778815i	−0.744974	−	0.667093i	$-0.767538\pi$
$569$	−1.85776	+	1.85776i	−0.0778815	+	0.0778815i	0.667093	+	0.744974i	$0.267538\pi$
$570$		0			0
$571$	2.24262	−	5.41417i	0.0938509	−	0.226576i	−0.869982	−	0.493084i	$-0.835870\pi$
$571$	2.24262	−	5.41417i	0.0938509	−	0.226576i	0.963833	+	0.266507i	$0.0858697\pi$
$572$	0.0134626	+	0.00557639i	0.000562899	+	0.000233160i
$573$	−17.3369	−	41.8549i	−0.724259	−	1.74851i
$574$		−	3.31385i		−	0.138317i
$575$		0			0
$576$	−7.42050	−	7.42050i	−0.309187	−	0.309187i
$577$	20.9381			0.871663			0.435832	−	0.900028i	$-0.356454\pi$
$577$	20.9381			0.871663			0.435832	+	0.900028i	$0.356454\pi$
$578$	9.30833	+	17.1948i	0.387176	+	0.715210i
$579$	30.1737			1.25398
$580$		0			0
$581$	−3.27479	+	1.35646i	−0.135861	+	0.0562755i
$582$		−	12.4254i		−	0.515048i
$583$	−0.192827	−	0.465526i	−0.00798608	−	0.0192801i
$584$	6.23384	+	2.58214i	0.257958	+	0.106850i
$585$		0			0
$586$	22.7438	−	22.7438i	0.939537	−	0.939537i
$587$	−13.7302	+	13.7302i	−0.566706	+	0.566706i	−0.931204	−	0.364498i	$-0.881240\pi$
$587$	−13.7302	+	13.7302i	−0.566706	+	0.566706i	0.364498	+	0.931204i	$0.381240\pi$
$588$	3.65354	−	8.82043i	0.150669	−	0.363748i
$589$	9.90463	+	4.10263i	0.408113	+	0.169046i
$590$		0			0
$591$			20.1426i			0.828555i
$592$	−19.1947	+	7.95072i	−0.788898	+	0.326772i
$593$	14.9131	+	14.9131i	0.612407	+	0.612407i	0.943573	−	0.331166i	$-0.107442\pi$
$593$	14.9131	+	14.9131i	0.612407	+	0.612407i	−0.331166	+	0.943573i	$0.607442\pi$
$594$	−0.232367			−0.00953412
$595$		0			0
$596$	−3.51729			−0.144074
$597$	−20.5820	−	20.5820i	−0.842365	−	0.842365i
$598$	−0.423874	+	0.175574i	−0.0173335	+	0.00717976i
$599$		−	23.7029i		−	0.968476i	−0.874936	−	0.484238i	$-0.839097\pi$
$599$		−	23.7029i		−	0.968476i	0.874936	−	0.484238i	$-0.160903\pi$
$600$		0			0
$601$	19.7112	+	8.16463i	0.804035	+	0.333042i	0.746571	−	0.665305i	$-0.231699\pi$
$601$	19.7112	+	8.16463i	0.804035	+	0.333042i	0.0574636	+	0.998348i	$0.481699\pi$
$602$	−1.11671	+	2.69598i	−0.0455137	+	0.109880i
$603$	12.4869	−	12.4869i	0.508507	−	0.508507i
$604$	3.37208	−	3.37208i	0.137208	−	0.137208i
$605$		0			0
$606$	−8.80994	−	3.64920i	−0.357880	−	0.148239i
$607$	−11.1029	−	26.8048i	−0.450653	−	1.08797i	−0.972074	−	0.234673i	$-0.924598\pi$
$607$	−11.1029	−	26.8048i	−0.450653	−	1.08797i	0.521421	−	0.853299i	$-0.325402\pi$
$608$		−	6.44488i		−	0.261375i
$609$	6.02600	−	2.49605i	0.244186	−	0.101145i
$610$		0			0
$611$	0.716413			0.0289830
$612$	2.04526	+	2.74250i	0.0826749	+	0.110859i
$613$	26.9206			1.08731			0.543657	−	0.839308i	$-0.317039\pi$
$613$	26.9206			1.08731			0.543657	+	0.839308i	$0.317039\pi$
$614$	−16.6162	−	16.6162i	−0.670574	−	0.670574i
$615$		0			0
$616$		−	0.0640286i		−	0.00257979i
$617$	5.70499	+	13.7731i	0.229674	+	0.554483i	0.996138	−	0.0878053i	$-0.0279853\pi$
$617$	5.70499	+	13.7731i	0.229674	+	0.554483i	−0.766463	+	0.642288i	$0.777985\pi$
$618$	7.02429	+	2.90956i	0.282558	+	0.117040i
$619$	−13.1072	+	31.6435i	−0.526822	+	1.27186i	0.406772	+	0.913530i	$0.366654\pi$
$619$	−13.1072	+	31.6435i	−0.526822	+	1.27186i	−0.933594	+	0.358332i	$0.883346\pi$
$620$		0			0
$621$	−2.64808	+	2.64808i	−0.106264	+	0.106264i
$622$	5.48370	−	13.2388i	0.219876	−	0.530828i
$623$	0.906472	+	0.375473i	0.0363170	+	0.0150430i
$624$	0.668523	+	1.61396i	0.0267623	+	0.0646100i
$625$		0			0
$626$	−9.78370	+	4.05254i	−0.391035	+	0.161972i
$627$	0.142428	+	0.142428i	0.00568804	+	0.00568804i
$628$	−10.6992			−0.426946
$629$	37.9663	−	9.61707i	1.51382	−	0.383458i
$630$		0			0
$631$	22.2493	+	22.2493i	0.885730	+	0.885730i	0.994110	−	0.108380i	$-0.0345662\pi$
$631$	22.2493	+	22.2493i	0.885730	+	0.885730i	−0.108380	+	0.994110i	$0.534566\pi$
$632$	−11.2129	+	4.64452i	−0.446024	+	0.184749i
$633$		−	10.7809i		−	0.428500i
$634$	0.798315	+	1.92730i	0.0317051	+	0.0765430i
$635$		0			0
$636$	−4.84619	+	11.6997i	−0.192164	+	0.463925i
$637$	−1.88453	+	1.88453i	−0.0746678	+	0.0746678i
$638$	−0.380658	+	0.380658i	−0.0150704	+	0.0150704i
$639$	−0.528120	+	1.27499i	−0.0208921	+	0.0504380i
$640$		0			0
$641$	−7.38863	−	17.8377i	−0.291833	−	0.704548i	0.708166	−	0.706046i	$-0.249523\pi$
$641$	−7.38863	−	17.8377i	−0.291833	−	0.704548i	−0.999999	+	0.00149842i	$0.999523\pi$
$642$		−	28.0729i		−	1.10795i
$643$	16.0593	−	6.65200i	0.633319	−	0.262329i	−0.0428438	−	0.999082i	$-0.513642\pi$
$643$	16.0593	−	6.65200i	0.633319	−	0.262329i	0.676162	+	0.736753i	$0.263642\pi$
$644$	−0.184561	−	0.184561i	−0.00727271	−	0.00727271i
$645$		0			0
$646$	1.20912	−	8.30278i	0.0475722	−	0.326668i
$647$	39.9032			1.56876			0.784378	−	0.620283i	$-0.212982\pi$
$647$	39.9032			1.56876			0.784378	+	0.620283i	$0.212982\pi$
$648$	24.3301	+	24.3301i	0.955778	+	0.955778i
$649$	−0.695492	+	0.288082i	−0.0273005	+	0.0113082i
$650$		0			0
$651$	−1.78963	−	4.32055i	−0.0701412	−	0.169336i
$652$	6.45436	+	2.67348i	0.252772	+	0.104702i
$653$	4.79886	−	11.5855i	0.187794	−	0.453374i	−0.801740	−	0.597672i	$-0.796092\pi$
$653$	4.79886	−	11.5855i	0.187794	−	0.453374i	0.989534	+	0.144298i	$0.0460924\pi$
$654$	34.6083	−	34.6083i	1.35329	−	1.35329i
$655$		0			0
$656$	6.42298	−	15.5065i	0.250775	−	0.605425i
$657$	2.48084	+	1.02760i	0.0967868	+	0.0400904i
$658$	−0.304699	−	0.735609i	−0.0118784	−	0.0286770i
$659$			10.7616i			0.419214i	0.977786	+	0.209607i	$0.0672184\pi$
$659$			10.7616i			0.419214i	−0.977786	+	0.209607i	$0.932782\pi$
$660$		0			0
$661$	4.37383	+	4.37383i	0.170122	+	0.170122i	0.787033	−	0.616911i	$-0.211616\pi$
$661$	4.37383	+	4.37383i	0.170122	+	0.170122i	−0.616911	+	0.787033i	$0.711616\pi$
$662$	−21.1136			−0.820602
$663$	−0.808636	−	3.19234i	−0.0314048	−	0.123980i
$664$	−29.0689			−1.12809
$665$		0			0
$666$	−12.3686	+	5.12326i	−0.479275	+	0.198522i
$667$			8.67606i			0.335938i
$668$	−2.14288	−	5.17338i	−0.0829107	−	0.200164i
$669$	−25.7607	−	10.6704i	−0.995967	−	0.412543i
$670$		0			0
$671$	−0.227557	+	0.227557i	−0.00878473	+	0.00878473i
$672$	−1.98793	+	1.98793i	−0.0766860	+	0.0766860i
$673$	1.84710	−	4.45929i	0.0712004	−	0.171893i	−0.884273	−	0.466970i	$-0.845345\pi$
$673$	1.84710	−	4.45929i	0.0712004	−	0.171893i	0.955473	+	0.295077i	$0.0953454\pi$
$674$	11.3051	+	4.68274i	0.435458	+	0.180373i
$675$		0			0
$676$		−	8.70059i		−	0.334638i
$677$	25.8295	−	10.6989i	0.992709	−	0.411193i	0.173590	−	0.984818i	$-0.444463\pi$
$677$	25.8295	−	10.6989i	0.992709	−	0.411193i	0.819118	+	0.573625i	$0.194463\pi$
$678$	−7.65775	−	7.65775i	−0.294094	−	0.294094i
$679$	−1.97327			−0.0757271
$680$		0			0
$681$	27.6259			1.05863
$682$	0.272926	+	0.272926i	0.0104509	+	0.0104509i
$683$	−10.7779	+	4.46436i	−0.412405	+	0.170824i	−0.579233	−	0.815162i	$-0.696648\pi$
$683$	−10.7779	+	4.46436i	−0.412405	+	0.170824i	0.166827	+	0.985986i	$0.446648\pi$
$684$		−	1.46808i		−	0.0561334i
$685$		0			0
$686$	5.52932	+	2.29032i	0.211110	+	0.0874448i
$687$	−8.03908	+	19.4081i	−0.306710	+	0.740464i
$688$	−10.4508	+	10.4508i	−0.398434	+	0.398434i
$689$	2.49971	−	2.49971i	0.0952313	−	0.0952313i
$690$		0			0
$691$	35.3606	+	14.6468i	1.34518	+	0.557192i	0.934946	−	0.354789i	$-0.115447\pi$
$691$	35.3606	+	14.6468i	1.34518	+	0.557192i	0.410233	+	0.911981i	$0.365447\pi$
$692$	−3.75978	−	9.07691i	−0.142925	−	0.345052i
$693$		−	0.0254810i		−	0.000967945i
$694$	−25.3844	+	10.5146i	−0.963580	+	0.399128i
$695$		0			0
$696$	53.4903			2.02754
$697$	−16.1941	+	27.1813i	−0.613395	+	1.02957i
$698$	30.2179			1.14376
$699$	27.4742	+	27.4742i	1.03917	+	1.03917i
$700$		0			0
$701$			13.5092i			0.510234i	0.966910	+	0.255117i	$0.0821141\pi$
$701$			13.5092i			0.510234i	−0.966910	+	0.255117i	$0.917886\pi$
$702$	−0.623864	−	1.50614i	−0.0235462	−	0.0568456i
$703$	−15.5272	−	6.43157i	−0.585619	−	0.242571i
$704$	0.181508	−	0.438199i	0.00684084	−	0.0165152i
$705$		0			0
$706$	−3.33811	+	3.33811i	−0.125631	+	0.125631i
$707$	−0.579528	+	1.39910i	−0.0217954	+	0.0526187i
$708$	17.4793	+	7.24018i	0.656914	+	0.272102i
$709$	−9.05657	−	21.8645i	−0.340127	−	0.821138i	−0.997702	−	0.0677499i	$-0.978418\pi$
$709$	−9.05657	−	21.8645i	−0.340127	−	0.821138i	0.657576	−	0.753388i	$-0.271582\pi$
$710$		0			0
$711$	−4.46231	+	1.84835i	−0.167350	+	0.0693186i
$712$	5.68965	+	5.68965i	0.213229	+	0.213229i
$713$	6.22061			0.232964
$714$	−2.93395	+	2.18804i	−0.109800	+	0.0818855i
$715$		0			0
$716$	7.40473	+	7.40473i	0.276728	+	0.276728i
$717$	32.3212	−	13.3879i	1.20706	−	0.499980i
$718$		−	18.2968i		−	0.682829i
$719$	−6.74163	−	16.2757i	−0.251420	−	0.606982i	0.746899	−	0.664938i	$-0.231542\pi$
$719$	−6.74163	−	16.2757i	−0.251420	−	0.606982i	−0.998319	+	0.0579555i	$0.981542\pi$
$720$		0			0
$721$	0.462066	−	1.11553i	0.0172082	−	0.0415443i
$722$	12.9065	−	12.9065i	0.480330	−	0.480330i
$723$	36.0725	−	36.0725i	1.34155	−	1.34155i
$724$	6.20026	−	14.9687i	0.230431	−	0.556309i
$725$		0			0
$726$	−9.94950	−	24.0202i	−0.369260	−	0.891473i
$727$			38.2375i			1.41815i	0.705132	+	0.709076i	$0.250888\pi$
$727$			38.2375i			1.41815i	−0.705132	+	0.709076i	$0.749112\pi$
$728$	0.415017	−	0.171906i	0.0153815	−	0.00637124i
$729$	−6.22409	−	6.22409i	−0.230522	−	0.230522i
$730$		0			0
$731$	22.3344	−	16.6562i	0.826066	−	0.616053i
$732$	8.08793			0.298939
$733$	25.7052	+	25.7052i	0.949443	+	0.949443i	0.998782	−	0.0493393i	$-0.0157116\pi$
$733$	25.7052	+	25.7052i	0.949443	+	0.949443i	−0.0493393	+	0.998782i	$0.515712\pi$
$734$	18.5202	−	7.67132i	0.683593	−	0.283154i
$735$		0			0
$736$	−1.43108	−	3.45494i	−0.0527504	−	0.127351i
$737$	0.737385	+	0.305435i	0.0271619	+	0.0112508i
$738$	4.13882	−	9.99200i	0.152352	−	0.367810i
$739$	−31.5666	+	31.5666i	−1.16120	+	1.16120i	−0.176982	+	0.984214i	$0.556634\pi$
$739$	−31.5666	+	31.5666i	−1.16120	+	1.16120i	−0.984214	+	0.176982i	$0.943366\pi$
$740$		0			0
$741$	−0.540788	+	1.30558i	−0.0198663	+	0.0479616i
$742$	−3.62985	−	1.50353i	−0.133256	−	0.0551964i
$743$	1.24279	+	3.00035i	0.0455935	+	0.110072i	0.945036	−	0.326968i	$-0.106027\pi$
$743$	1.24279	+	3.00035i	0.0455935	+	0.110072i	−0.899442	+	0.437040i	$0.856027\pi$
$744$		−	38.3517i		−	1.40604i
$745$		0			0
$746$	21.2711	+	21.2711i	0.778790	+	0.778790i
$747$	−11.5684			−0.423265
$748$	−0.0791418	+	0.132837i	−0.00289371	+	0.00485701i
$749$	−4.45825			−0.162901
$750$		0			0
$751$	1.51618	−	0.628022i	0.0553262	−	0.0229169i	−0.354849	−	0.934924i	$-0.615468\pi$
$751$	1.51618	−	0.628022i	0.0553262	−	0.0229169i	0.410175	+	0.912007i	$0.365468\pi$
$752$		−	4.03270i		−	0.147058i
$753$	14.1729	+	34.2163i	0.516487	+	1.24691i
$754$	−3.48932	−	1.44533i	−0.127074	−	0.0526356i
$755$		0			0
$756$	0.655796	−	0.655796i	0.0238511	−	0.0238511i
$757$	−6.36808	+	6.36808i	−0.231452	+	0.231452i	−0.813298	−	0.581847i	$-0.802330\pi$
$757$	−6.36808	+	6.36808i	−0.231452	+	0.231452i	0.581847	+	0.813298i	$0.302330\pi$
$758$	−7.81618	+	18.8699i	−0.283896	+	0.685386i
$759$	0.107978	+	0.0447261i	0.00391936	+	0.00162345i
$760$		0			0
$761$		−	40.8543i		−	1.48097i	−0.672075	−	0.740484i	$-0.734597\pi$
$761$		−	40.8543i		−	1.48097i	0.672075	−	0.740484i	$-0.265403\pi$
$762$	−0.189923	+	0.0786686i	−0.00688018	+	0.00284986i
$763$	−5.49613	−	5.49613i	−0.198973	−	0.198973i
$764$	−14.9237			−0.539921
$765$		0			0
$766$	−33.1083			−1.19625
$767$	−3.73455	−	3.73455i	−0.134847	−	0.134847i
$768$	−26.9259	+	11.1531i	−0.971606	+	0.402452i
$769$			15.1859i			0.547617i	0.961784	+	0.273809i	$0.0882835\pi$
$769$			15.1859i			0.547617i	−0.961784	+	0.273809i	$0.911716\pi$
$770$		0			0
$771$	12.5573	+	5.20139i	0.452239	+	0.187324i
$772$	3.80377	−	9.18312i	0.136901	−	0.330508i
$773$	−16.3437	+	16.3437i	−0.587842	+	0.587842i	−0.937047	−	0.349204i	$-0.886452\pi$
$773$	−16.3437	+	16.3437i	−0.587842	+	0.587842i	0.349204	+	0.937047i	$0.386452\pi$
$774$	−6.73427	+	6.73427i	−0.242058	+	0.242058i
$775$		0			0
$776$	−14.9507	−	6.19280i	−0.536700	−	0.222308i
$777$	2.80555	+	6.77319i	0.100648	+	0.242987i
$778$		−	30.9038i		−	1.10795i
$779$	12.5436	−	5.19574i	0.449422	−	0.186157i
$780$		0			0
$781$	−0.0623736			−0.00223190
$782$	−1.19545	−	4.71939i	−0.0427491	−	0.168765i
$783$	−30.8285			−1.10172
$784$	10.6081	+	10.6081i	0.378859	+	0.378859i
$785$		0			0
$786$			18.5831i			0.662837i
$787$	13.1280	+	31.6938i	0.467962	+	1.12976i	0.965051	+	0.262061i	$0.0844023\pi$
$787$	13.1280	+	31.6938i	0.467962	+	1.12976i	−0.497089	+	0.867700i	$0.665598\pi$
$788$	6.13023	+	2.53922i	0.218380	+	0.0904561i
$789$	−8.31335	+	20.0702i	−0.295963	+	0.714518i
$790$		0			0
$791$	−1.21612	+	1.21612i	−0.0432404	+	0.0432404i
$792$	0.0799683	−	0.193061i	0.00284155	−	0.00686011i
$793$	−2.08591	−	0.864014i	−0.0740730	−	0.0306820i
$794$	11.7215	+	28.2983i	0.415981	+	1.00427i
$795$		0			0
$796$	−8.85857	+	3.66934i	−0.313984	+	0.130056i
$797$	7.47651	+	7.47651i	0.264832	+	0.264832i	0.827014	−	0.562182i	$-0.190038\pi$
$797$	7.47651	+	7.47651i	0.264832	+	0.264832i	−0.562182	+	0.827014i	$0.690038\pi$
$798$	1.57056			0.0555974
$799$	−1.09552	+	7.52273i	−0.0387568	+	0.266135i
$800$		0			0
$801$	2.26427	+	2.26427i	0.0800041	+	0.0800041i
$802$	2.87482	−	1.19079i	0.101513	−	0.0420482i
$803$			0.121364i			0.00428286i
$804$	−7.67628	−	18.5322i	−0.270722	−	0.653580i
$805$		0			0
$806$	−1.03628	+	2.50179i	−0.0365013	+	0.0881219i
$807$	5.51950	−	5.51950i	0.194296	−	0.194296i
$808$	−8.78175	+	8.78175i	−0.308941	+	0.308941i
$809$	−15.7502	+	38.0243i	−0.553747	+	1.33686i	0.360897	+	0.932606i	$0.382471\pi$
$809$	−15.7502	+	38.0243i	−0.553747	+	1.33686i	−0.914645	+	0.404259i	$0.867529\pi$
$810$		0			0
$811$	1.73158	+	4.18040i	0.0608039	+	0.146794i	0.951361	−	0.308077i	$-0.0996855\pi$
$811$	1.73158	+	4.18040i	0.0608039	+	0.146794i	−0.890558	+	0.454871i	$0.849685\pi$
$812$		−	2.14862i		−	0.0754017i
$813$	−45.9575	+	19.0362i	−1.61180	+	0.667629i
$814$	−0.427857	−	0.427857i	−0.0149964	−	0.0149964i
$815$		0			0
$816$	−17.9697	+	4.55183i	−0.629067	+	0.159346i
$817$	−11.9557			−0.418278
$818$	−0.541319	−	0.541319i	−0.0189268	−	0.0189268i
$819$	0.165162	−	0.0684121i	0.00577121	−	0.00239051i
$820$		0			0
$821$	−7.96209	−	19.2222i	−0.277879	−	0.670859i	0.721898	−	0.692000i	$-0.243270\pi$
$821$	−7.96209	−	19.2222i	−0.277879	−	0.670859i	−0.999777	+	0.0211408i	$0.993270\pi$
$822$	−31.3952	−	13.0043i	−1.09503	−	0.453577i
$823$	−17.5594	+	42.3922i	−0.612083	+	1.47770i	0.248626	+	0.968600i	$0.420021\pi$
$823$	−17.5594	+	42.3922i	−0.612083	+	1.47770i	−0.860708	+	0.509099i	$0.829979\pi$
$824$	7.00181	−	7.00181i	0.243920	−	0.243920i
$825$		0			0
$826$	−2.24627	+	5.42296i	−0.0781576	+	0.188689i
$827$	−35.1805	−	14.5723i	−1.22335	−	0.506727i	−0.324875	−	0.945757i	$-0.605322\pi$
$827$	−35.1805	−	14.5723i	−1.22335	−	0.506727i	−0.898472	+	0.439030i	$0.855322\pi$
$828$	−0.325986	−	0.786999i	−0.0113288	−	0.0273501i
$829$			36.1886i			1.25688i	0.777857	+	0.628441i	$0.216307\pi$
$829$			36.1886i			1.25688i	−0.777857	+	0.628441i	$0.783693\pi$
$830$		0			0
$831$	−33.0362	−	33.0362i	−1.14601	−	1.14601i
$832$	3.32761			0.115364
$833$	−16.9068	−	22.6704i	−0.585786	−	0.785482i
$834$	26.1528			0.905599
$835$		0			0
$836$	0.0613017	−	0.0253920i	0.00212016	−	0.000878200i
$837$			22.1035i			0.764010i
$838$	−14.5115	−	35.0338i	−0.501291	−	1.21022i
$839$	−12.7679	−	5.28865i	−0.440798	−	0.182585i	0.151236	−	0.988498i	$-0.451675\pi$
$839$	−12.7679	−	5.28865i	−0.440798	−	0.182585i	−0.592034	+	0.805913i	$0.701675\pi$
$840$		0			0
$841$	−29.9964	+	29.9964i	−1.03436	+	1.03436i
$842$	−4.35410	+	4.35410i	−0.150052	+	0.150052i
$843$	−8.81753	+	21.2874i	−0.303692	+	0.733177i
$844$	−3.28106	−	1.35906i	−0.112939	−	0.0467808i
$845$		0			0
$846$		−	2.59858i		−	0.0893410i
$847$	−3.81464	+	1.58008i	−0.131073	+	0.0542921i
$848$	−14.0709	−	14.0709i	−0.483197	−	0.483197i
$849$	28.8653			0.990654
$850$		0			0
$851$	−9.75185			−0.334289
$852$	1.10846	+	1.10846i	0.0379751	+	0.0379751i
$853$	3.03652	−	1.25777i	0.103968	−	0.0430651i	−0.330093	−	0.943948i	$-0.607080\pi$
$853$	3.03652	−	1.25777i	0.103968	−	0.0430651i	0.434061	+	0.900883i	$0.357080\pi$
$854$			2.50928i			0.0858658i
$855$		0			0
$856$	−33.7785	−	13.9915i	−1.15453	−	0.478220i
$857$	12.2568	−	29.5906i	0.418686	−	1.01080i	−0.564043	−	0.825745i	$-0.690755\pi$
$857$	12.2568	−	29.5906i	0.418686	−	1.01080i	0.982729	−	0.185051i	$-0.0592452\pi$
$858$	−0.0359757	+	0.0359757i	−0.00122819	+	0.00122819i
$859$	−22.5032	+	22.5032i	−0.767801	+	0.767801i	−0.977719	−	0.209918i	$-0.932680\pi$
$859$	−22.5032	+	22.5032i	−0.767801	+	0.767801i	0.209918	+	0.977719i	$0.432680\pi$
$860$		0			0
$861$	−5.47172	−	2.26646i	−0.186476	−	0.0772408i
$862$	−4.86143	−	11.7365i	−0.165581	−	0.399748i
$863$			35.8941i			1.22185i	0.791688	+	0.610925i	$0.209202\pi$
$863$			35.8941i			1.22185i	−0.791688	+	0.610925i	$0.790798\pi$
$864$	12.2764	−	5.08503i	0.417650	−	0.172996i
$865$		0			0
$866$	−16.0559			−0.545602
$867$	34.7578	−	3.60947i	1.18044	−	0.122584i
$868$	−1.54053			−0.0522889
$869$	−0.154361	−	0.154361i	−0.00523634	−	0.00523634i
$870$		0			0
$871$			5.59957i			0.189734i
$872$	−24.3934	−	58.8909i	−0.826065	−	1.99430i
$873$	−5.94985	−	2.46451i	−0.201372	−	0.0834109i
$874$	−0.799474	+	1.93010i	−0.0270426	+	0.0652867i
$875$		0			0
$876$	2.15680	−	2.15680i	0.0728714	−	0.0728714i
$877$	−12.4156	+	29.9738i	−0.419243	+	1.01214i	0.563324	+	0.826236i	$0.309522\pi$
$877$	−12.4156	+	29.9738i	−0.419243	+	1.01214i	−0.982567	+	0.185907i	$0.940478\pi$
$878$	−33.7047	−	13.9609i	−1.13748	−	0.471159i
$879$	−21.9985	−	53.1091i	−0.741992	−	1.79133i
$880$		0			0
$881$	−37.0581	+	15.3500i	−1.24852	+	0.517154i	−0.906368	−	0.422490i	$-0.861156\pi$
$881$	−37.0581	+	15.3500i	−1.24852	+	0.517154i	−0.342153	+	0.939644i	$0.611156\pi$
$882$	6.83559	+	6.83559i	0.230166	+	0.230166i
$883$	−10.0633			−0.338656			−0.169328	−	0.985560i	$-0.554160\pi$
$883$	−10.0633			−0.338656			−0.169328	+	0.985560i	$0.554160\pi$
$884$	−1.07350	−	0.156332i	−0.0361057	−	0.00525801i
$885$		0			0
$886$	−30.4977	−	30.4977i	−1.02459	−	1.02459i
$887$	24.5160	−	10.1549i	0.823167	−	0.340967i	0.0689728	−	0.997619i	$-0.478028\pi$
$887$	24.5160	−	10.1549i	0.823167	−	0.340967i	0.754194	+	0.656652i	$0.228028\pi$
$888$			60.1228i			2.01759i
$889$	0.0124933	+	0.0301616i	0.000419013	+	0.00101159i
$890$		0			0
$891$	−0.236837	+	0.571776i	−0.00793435	+	0.0191552i
$892$	−6.49491	+	6.49491i	−0.217466	+	0.217466i
$893$	2.30670	−	2.30670i	0.0771909	−	0.0771909i
$894$	4.69957	−	11.3458i	0.157177	−	0.379459i
$895$		0			0
$896$	−0.368500	−	0.889637i	−0.0123107	−	0.0297207i
$897$			0.819968i			0.0273779i
$898$	−12.2089	+	5.05710i	−0.407417	+	0.168758i
$899$	36.2095	+	36.2095i	1.20766	+	1.20766i
$900$		0			0
$901$	22.4258	+	30.0708i	0.747112	+	1.00180i
$902$	0.488815			0.0162758
$903$	3.68776	+	3.68776i	0.122721	+	0.122721i
$904$	−13.0308	+	5.39752i	−0.433397	+	0.179519i
$905$		0			0
$906$	6.37182	+	15.3829i	0.211689	+	0.511064i
$907$	−7.64833	−	3.16804i	−0.253959	−	0.105193i	0.252072	−	0.967708i	$-0.418888\pi$
$907$	−7.64833	−	3.16804i	−0.253959	−	0.105193i	−0.506031	+	0.862515i	$0.668888\pi$
$908$	3.48259	−	8.40771i	0.115574	−	0.279020i
$909$	−3.49482	+	3.49482i	−0.115916	+	0.115916i
$910$		0			0
$911$	13.6431	−	32.9374i	0.452017	−	1.09126i	−0.519538	−	0.854448i	$-0.673896\pi$
$911$	13.6431	−	32.9374i	0.452017	−	1.09126i	0.971554	−	0.236817i	$-0.0761042\pi$
$912$	7.34913	+	3.04411i	0.243354	+	0.100801i
$913$	−0.200088	−	0.483054i	−0.00662193	−	0.0159868i
$914$		−	27.8872i		−	0.922427i
$915$		0			0
$916$	4.89325	+	4.89325i	0.161678	+	0.161678i
$917$	2.95118			0.0974564
$918$	16.7693	−	4.24776i	0.553470	−	0.140197i
$919$	−44.5065			−1.46813			−0.734067	−	0.679077i	$-0.762380\pi$
$919$	−44.5065			−1.46813			−0.734067	+	0.679077i	$0.762380\pi$
$920$		0			0
$921$	−38.8005	+	16.0717i	−1.27852	+	0.529581i
$922$			30.4423i			1.00256i
$923$	−0.167462	−	0.404289i	−0.00551208	−	0.0133073i
$924$	−0.0267407	−	0.0110764i	−0.000879705	−	0.000364386i
$925$		0			0
$926$	−13.0640	+	13.0640i	−0.429309	+	0.429309i
$927$	2.78647	−	2.78647i	0.0915195	−	0.0915195i
$928$	11.7807	−	28.4410i	0.386719	−	0.933622i
$929$	3.92217	+	1.62462i	0.128682	+	0.0533019i	0.446095	−	0.894985i	$-0.352814\pi$
$929$	3.92217	+	1.62462i	0.128682	+	0.0533019i	−0.317413	+	0.948287i	$0.602814\pi$
$930$		0			0
$931$			12.1356i			0.397729i
$932$	11.8250	−	4.89807i	0.387341	−	0.160442i
$933$	−18.1090	−	18.1090i	−0.592863	−	0.592863i
$934$	22.4244			0.733748
$935$		0			0
$936$	1.46607			0.0479200
$937$	−7.19384	−	7.19384i	−0.235012	−	0.235012i	0.579769	−	0.814781i	$-0.303143\pi$
$937$	−7.19384	−	7.19384i	−0.235012	−	0.235012i	−0.814781	+	0.579769i	$0.803143\pi$
$938$	5.74961	−	2.38157i	0.187732	−	0.0777609i
$939$			18.9262i			0.617634i
$940$		0			0
$941$	−28.1724	−	11.6694i	−0.918395	−	0.380412i	−0.127131	−	0.991886i	$-0.540577\pi$
$941$	−28.1724	−	11.6694i	−0.918395	−	0.380412i	−0.791264	+	0.611474i	$0.790577\pi$
$942$	14.2956	−	34.5127i	0.465777	−	1.12449i
$943$	5.57061	−	5.57061i	0.181404	−	0.181404i
$944$	−21.0219	+	21.0219i	−0.684203	+	0.684203i
$945$		0			0
$946$	−0.397675	−	0.164722i	−0.0129295	−	0.00535559i
$947$	16.7053	+	40.3302i	0.542850	+	1.31056i	0.922704	+	0.385509i	$0.125974\pi$
$947$	16.7053	+	40.3302i	0.542850	+	1.31056i	−0.379854	+	0.925047i	$0.624026\pi$
$948$			5.48637i			0.178189i
$949$	−0.786652	+	0.325842i	−0.0255358	+	0.0105773i
$950$		0			0
$951$	3.72830			0.120898
$952$	1.17047	+	4.62078i	0.0379351	+	0.149760i
$953$	−6.19010			−0.200517			−0.100258	−	0.994961i	$-0.531967\pi$
$953$	−6.19010			−0.200517			−0.100258	+	0.994961i	$0.531967\pi$
$954$	−9.06697	−	9.06697i	−0.293554	−	0.293554i
$955$		0			0
$956$		−	11.5244i		−	0.372726i
$957$	0.368184	+	0.888876i	0.0119017	+	0.0287333i
$958$	25.6803	+	10.6371i	0.829693	+	0.343670i
$959$	−2.06521	+	4.98586i	−0.0666891	+	0.161002i
$960$		0			0
$961$	4.04139	−	4.04139i	0.130367	−	0.130367i
$962$	1.62454	−	3.92198i	0.0523772	−	0.126450i
$963$	−13.4426	−	5.56812i	−0.433182	−	0.179430i
$964$	−6.43098	−	15.5258i	−0.207128	−	0.500051i
$965$		0			0
$966$	0.841939	−	0.348743i	0.0270890	−	0.0112206i
$967$	31.3914	+	31.3914i	1.00948	+	1.00948i	0.999955	+	0.00952406i	$0.00303165\pi$
$967$	31.3914	+	31.3914i	1.00948	+	1.00948i	0.00952406	+	0.999955i	$0.496968\pi$
$968$	−33.8610			−1.08833
$969$	−12.8823	−	7.67503i	−0.413840	−	0.246558i
$970$		0			0
$971$	34.3536	+	34.3536i	1.10246	+	1.10246i	0.994113	+	0.108345i	$0.0345552\pi$
$971$	34.3536	+	34.3536i	1.10246	+	1.10246i	0.108345	+	0.994113i	$0.465445\pi$
$972$	7.52380	−	3.11646i	0.241326	−	0.0999605i
$973$		−	4.15333i		−	0.133149i
$974$	−16.0210	−	38.6780i	−0.513345	−	1.23932i
$975$		0			0
$976$	−4.86355	+	11.7417i	−0.155679	+	0.375841i
$977$	−5.46940	+	5.46940i	−0.174982	+	0.174982i	−0.789164	−	0.614182i	$-0.789486\pi$
$977$	−5.46940	+	5.46940i	−0.174982	+	0.174982i	0.614182	+	0.789164i	$0.289486\pi$
$978$	−17.2478	+	17.2478i	−0.551524	+	0.551524i
$979$	−0.0553849	+	0.133711i	−0.00177011	+	0.00427342i
$980$		0			0
$981$	−9.70769	−	23.4364i	−0.309943	−	0.748268i
$982$		−	44.3546i		−	1.41541i
$983$	17.5989	−	7.28969i	0.561317	−	0.232505i	−0.0839398	−	0.996471i	$-0.526750\pi$
$983$	17.5989	−	7.28969i	0.561317	−	0.232505i	0.645257	+	0.763966i	$0.276750\pi$
$984$	−34.3443	−	34.3443i	−1.09486	−	1.09486i
$985$		0			0
$986$	20.5125	−	34.4297i	0.653251	−	1.09646i
$987$	−1.42301			−0.0452949
$988$	0.329168	+	0.329168i	0.0104722	+	0.0104722i
$989$	−6.40917	+	2.65476i	−0.203800	+	0.0844166i
$990$		0			0
$991$	4.66953	+	11.2732i	0.148332	+	0.358106i	0.980529	−	0.196375i	$-0.0629169\pi$
$991$	4.66953	+	11.2732i	0.148332	+	0.358106i	−0.832196	+	0.554481i	$0.812917\pi$
$992$	−20.3918	−	8.44656i	−0.647440	−	0.268178i
$993$	−14.4403	+	34.8621i	−0.458250	+	1.10631i
$994$	−0.343898	+	0.343898i	−0.0109078	+	0.0109078i
$995$		0			0
$996$	−5.02866	+	12.1403i	−0.159339	+	0.384679i
$997$	20.3986	+	8.44938i	0.646031	+	0.267595i	0.681547	−	0.731774i	$-0.261308\pi$
$997$	20.3986	+	8.44938i	0.646031	+	0.267595i	−0.0355163	+	0.999369i	$0.511308\pi$
$998$	15.9771	+	38.5722i	0.505747	+	1.22098i
$999$		−	34.6510i		−	1.09631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.c.376.5	yes	24
5.2	odd	4		425.2.n.e.274.2		24
5.3	odd	4		425.2.n.d.274.5		24
5.4	even	2		425.2.m.d.376.2	yes	24
17.3	odd	16		7225.2.a.bx.1.18		24
17.9	even	8	inner	425.2.m.c.26.5	✓	24
17.14	odd	16		7225.2.a.bx.1.17		24
85.9	even	8		425.2.m.d.26.2	yes	24
85.14	odd	16		7225.2.a.cb.1.8		24
85.43	odd	8		425.2.n.e.349.2		24
85.54	odd	16		7225.2.a.cb.1.7		24
85.77	odd	8		425.2.n.d.349.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.26.5	✓	24	17.9	even	8	inner
425.2.m.c.376.5	yes	24	1.1	even	1	trivial
425.2.m.d.26.2	yes	24	85.9	even	8
425.2.m.d.376.2	yes	24	5.4	even	2
425.2.n.d.274.5		24	5.3	odd	4
425.2.n.d.349.5		24	85.77	odd	8
425.2.n.e.274.2		24	5.2	odd	4
425.2.n.e.349.2		24	85.43	odd	8
7225.2.a.bx.1.17		24	17.14	odd	16
7225.2.a.bx.1.18		24	17.3	odd	16
7225.2.a.cb.1.7		24	85.54	odd	16
7225.2.a.cb.1.8		24	85.14	odd	16

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.813283 + 0.813283i) q^{2} +(1.89910 - 0.786634i) q^{3} -0.677141i q^{4} +(2.18426 + 0.904752i) q^{6} +(0.143683 - 0.346882i) q^{7} +(2.17727 - 2.17727i) q^{8} +(0.866476 - 0.866476i) q^{9} +(0.0511675 + 0.0211943i) q^{11} +(-0.532662 - 1.28596i) q^{12} +0.388558i q^{13} +(0.398969 - 0.165258i) q^{14} +2.18720 q^{16} +(-4.08007 - 0.594174i) q^{17} +1.40938 q^{18} +(1.25108 + 1.25108i) q^{19} -0.771791i q^{21} +(0.0243767 + 0.0588507i) q^{22} +(0.948471 + 0.392870i) q^{23} +(2.42215 - 5.84758i) q^{24} +(-0.316007 + 0.316007i) q^{26} +(-1.39597 + 3.37018i) q^{27} +(-0.234888 - 0.0972938i) q^{28} +(3.23410 + 7.80781i) q^{29} +(5.59808 - 2.31880i) q^{31} +(-2.57573 - 2.57573i) q^{32} +0.113845 q^{33} +(-2.83502 - 3.80148i) q^{34} +(-0.586726 - 0.586726i) q^{36} +(-8.77594 + 3.63511i) q^{37} +2.03496i q^{38} +(0.305652 + 0.737910i) q^{39} +(2.93662 - 7.08964i) q^{41} +(0.627685 - 0.627685i) q^{42} +(-4.77818 + 4.77818i) q^{43} +(0.0143515 - 0.0346476i) q^{44} +(0.451862 + 1.09089i) q^{46} -1.84378i q^{47} +(4.15372 - 1.72053i) q^{48} +(4.85007 + 4.85007i) q^{49} +(-8.21586 + 2.08112i) q^{51} +0.263108 q^{52} +(-6.43330 - 6.43330i) q^{53} +(-3.87624 + 1.60559i) q^{54} +(-0.442420 - 1.06810i) q^{56} +(3.36006 + 1.39178i) q^{57} +(-3.71972 + 8.98020i) q^{58} +(-9.61131 + 9.61131i) q^{59} +(-2.22364 + 5.36835i) q^{61} +(6.43867 + 2.66698i) q^{62} +(-0.176067 - 0.425063i) q^{63} -8.56400i q^{64} +(0.0925878 + 0.0925878i) q^{66} +14.4112 q^{67} +(-0.402339 + 2.76278i) q^{68} +2.11029 q^{69} +(-1.04049 + 0.430984i) q^{71} -3.77311i q^{72} +(0.838594 + 2.02455i) q^{73} +(-10.0937 - 4.18095i) q^{74} +(0.847155 - 0.847155i) q^{76} +(0.0147038 - 0.0147038i) q^{77} +(-0.351548 + 0.848712i) q^{78} +(-3.64157 - 1.50839i) q^{79} +11.1746i q^{81} +(8.15419 - 3.37758i) q^{82} +(-6.67554 - 6.67554i) q^{83} -0.522611 q^{84} -7.77202 q^{86} +(12.2838 + 12.2838i) q^{87} +(0.157551 - 0.0652600i) q^{88} +2.61320i q^{89} +(0.134784 + 0.0558293i) q^{91} +(0.266028 - 0.642248i) q^{92} +(8.80728 - 8.80728i) q^{93} +(1.49951 - 1.49951i) q^{94} +(-6.91774 - 2.86542i) q^{96} +(-2.01122 - 4.85551i) q^{97} +7.88895i q^{98} +(0.0626997 - 0.0259711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} + 12 q^{9} + 4 q^{11} - 12 q^{12} - 24 q^{14} - 24 q^{16} + 4 q^{17} - 40 q^{18} - 20 q^{19} + 16 q^{22} + 8 q^{23} + 16 q^{24} + 16 q^{26} - 12 q^{27} + 48 q^{28} + 4 q^{29} + 24 q^{31}+ \cdots - 80 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 + 12 * q^9 + 4 * q^11 - 12 * q^12 - 24 * q^14 - 24 * q^16 + 4 * q^17 - 40 * q^18 - 20 * q^19 + 16 * q^22 + 8 * q^23 + 16 * q^24 + 16 * q^26 - 12 * q^27 + 48 * q^28 + 4 * q^29 + 24 * q^31 - 60 * q^32 + 48 * q^33 + 16 * q^34 + 60 * q^36 - 12 * q^37 + 8 * q^39 - 20 * q^41 + 12 * q^42 + 32 * q^43 + 64 * q^44 - 40 * q^46 - 40 * q^48 + 24 * q^49 + 16 * q^51 - 48 * q^52 - 12 * q^53 - 20 * q^54 - 32 * q^56 + 68 * q^57 - 16 * q^58 - 16 * q^59 - 64 * q^61 + 100 * q^62 - 44 * q^63 - 72 * q^66 + 40 * q^67 + 20 * q^68 - 48 * q^69 - 24 * q^71 + 32 * q^74 + 52 * q^76 + 24 * q^77 - 16 * q^78 - 48 * q^79 + 100 * q^82 + 12 * q^83 - 40 * q^84 - 16 * q^86 + 24 * q^87 + 4 * q^88 + 24 * q^91 - 88 * q^92 - 32 * q^93 - 40 * q^94 + 132 * q^96 - 88 * q^97 - 80 * q^99

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