LMFDB - Embedded newform 425.2.n.c.349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(49,425)]

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([4, 3]))

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

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

chi := DirichletCharacter("425.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.n (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			349.1
Character	$\chi$	$=$	425.349
Dual form			425.2.n.c.274.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.66305 - 1.66305i) q^{2} +(0.600564 - 1.44989i) q^{3} +3.53144i q^{4} +(-3.41000 + 1.41247i) q^{6} +(3.30945 - 1.37082i) q^{7} +(2.54686 - 2.54686i) q^{8} +(0.379815 + 0.379815i) q^{9} +(2.29362 - 0.950048i) q^{11} +(5.12021 + 2.12086i) q^{12} +1.25948 q^{13} +(-7.78350 - 3.22403i) q^{14} -1.40821 q^{16} +(1.48772 + 3.84535i) q^{17} -1.26330i q^{18} +(2.56985 - 2.56985i) q^{19} -5.62161i q^{21} +(-5.39437 - 2.23442i) q^{22} +(-3.38021 - 8.16056i) q^{23} +(-2.16312 - 5.22222i) q^{24} +(-2.09458 - 2.09458i) q^{26} +(5.12847 - 2.12428i) q^{27} +(4.84097 + 11.6871i) q^{28} +(-3.35200 + 8.09244i) q^{29} +(2.25799 + 0.935290i) q^{31} +(-2.75181 - 2.75181i) q^{32} -3.89606i q^{33} +(3.92084 - 8.86913i) q^{34} +(-1.34129 + 1.34129i) q^{36} +(-1.76094 + 4.25128i) q^{37} -8.54755 q^{38} +(0.756400 - 1.82611i) q^{39} +(-1.65510 - 3.99575i) q^{41} +(-9.34899 + 9.34899i) q^{42} +(-5.33668 + 5.33668i) q^{43} +(3.35504 + 8.09978i) q^{44} +(-7.94993 + 19.1928i) q^{46} -11.3322 q^{47} +(-0.845719 + 2.04175i) q^{48} +(4.12357 - 4.12357i) q^{49} +(6.46880 + 0.152348i) q^{51} +4.44779i q^{52} +(4.02442 + 4.02442i) q^{53} +(-12.0616 - 4.99610i) q^{54} +(4.93742 - 11.9200i) q^{56} +(-2.18264 - 5.26936i) q^{57} +(19.0326 - 7.88357i) q^{58} +(-3.16077 - 3.16077i) q^{59} +(0.0929426 + 0.224383i) q^{61} +(-2.19971 - 5.31057i) q^{62} +(1.77764 + 0.736321i) q^{63} +11.9692i q^{64} +(-6.47933 + 6.47933i) q^{66} -7.23278i q^{67} +(-13.5796 + 5.25380i) q^{68} -13.8620 q^{69} +(-1.69789 - 0.703290i) q^{71} +1.93467 q^{72} +(-5.05599 - 2.09426i) q^{73} +(9.99859 - 4.14155i) q^{74} +(9.07527 + 9.07527i) q^{76} +(6.28827 - 6.28827i) q^{77} +(-4.29484 + 1.77898i) q^{78} +(8.34789 - 3.45781i) q^{79} -7.10006i q^{81} +(-3.89262 + 9.39762i) q^{82} +(-5.17302 - 5.17302i) q^{83} +19.8524 q^{84} +17.7503 q^{86} +(9.72006 + 9.72006i) q^{87} +(3.42189 - 8.26117i) q^{88} -2.19350i q^{89} +(4.16819 - 1.72652i) q^{91} +(28.8186 - 11.9370i) q^{92} +(2.71214 - 2.71214i) q^{93} +(18.8459 + 18.8459i) q^{94} +(-5.64246 + 2.33718i) q^{96} +(9.07286 + 3.75810i) q^{97} -13.7154 q^{98} +(1.23199 + 0.510308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} + 40 q^{12} + 16 q^{13} - 24 q^{16} + 8 q^{19} - 24 q^{22} + 8 q^{23} + 8 q^{24} + 16 q^{26} + 16 q^{27} - 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} - 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 + 40 * q^12 + 16 * q^13 - 24 * q^16 + 8 * q^19 - 24 * q^22 + 8 * q^23 + 8 * q^24 + 16 * q^26 + 16 * q^27 - 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 + 16 * q^41 - 24 * q^42 - 8 * q^43 - 16 * q^44 + 8 * q^46 - 64 * q^47 - 8 * q^48 - 56 * q^51 + 24 * q^53 + 32 * q^54 + 64 * q^56 + 16 * q^57 + 56 * q^58 - 32 * q^59 + 32 * q^61 - 32 * q^62 + 80 * q^63 + 96 * q^66 + 24 * q^68 - 96 * q^69 - 24 * q^71 - 24 * q^72 - 64 * q^73 + 64 * q^74 - 8 * q^76 + 24 * q^77 + 8 * q^78 - 16 * q^82 - 96 * q^83 + 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 + 112 * q^92 - 64 * q^93 - 56 * q^94 - 168 * q^96 + 48 * q^97 + 120 * q^98 + 8 * q^99

Character values

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

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

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 $

$2$	−1.66305	−	1.66305i	−1.17595	−	1.17595i	−0.980767	−	0.195185i	$-0.937469\pi$
$2$	−1.66305	−	1.66305i	−1.17595	−	1.17595i	−0.195185	−	0.980767i	$-0.562531\pi$
$3$	0.600564	−	1.44989i	0.346736	−	0.837095i	−0.650265	−	0.759707i	$-0.725342\pi$
$3$	0.600564	−	1.44989i	0.346736	−	0.837095i	0.997001	−	0.0773874i	$-0.0246578\pi$
$4$			3.53144i			1.76572i
$5$		0			0
$5$		0			0
$6$	−3.41000	+	1.41247i	−1.39213	+	0.576638i
$7$	3.30945	−	1.37082i	1.25085	−	0.518121i	0.343764	−	0.939056i	$-0.388298\pi$
$7$	3.30945	−	1.37082i	1.25085	−	0.518121i	0.907091	+	0.420935i	$0.138298\pi$
$8$	2.54686	−	2.54686i	0.900451	−	0.900451i
$9$	0.379815	+	0.379815i	0.126605	+	0.126605i
$10$		0			0
$11$	2.29362	−	0.950048i	0.691552	−	0.286450i	−0.00909468	−	0.999959i	$-0.502895\pi$
$11$	2.29362	−	0.950048i	0.691552	−	0.286450i	0.700647	+	0.713508i	$0.252895\pi$
$12$	5.12021	+	2.12086i	1.47808	+	0.612239i
$13$	1.25948			0.349317			0.174659	−	0.984629i	$-0.444118\pi$
$13$	1.25948			0.349317			0.174659	+	0.984629i	$0.444118\pi$
$14$	−7.78350	−	3.22403i	−2.08023	−	0.861659i
$15$		0			0
$16$	−1.40821			−0.352052
$17$	1.48772	+	3.84535i	0.360825	+	0.932634i
$17$	1.48772	+	3.84535i	0.360825	+	0.932634i
$18$		−	1.26330i		−	0.297762i
$19$	2.56985	−	2.56985i	0.589563	−	0.589563i	−0.347950	−	0.937513i	$-0.613122\pi$
$19$	2.56985	−	2.56985i	0.589563	−	0.589563i	0.937513	+	0.347950i	$0.113122\pi$
$20$		0			0
$21$		−	5.62161i		−	1.22674i
$22$	−5.39437	−	2.23442i	−1.15008	−	0.476380i
$23$	−3.38021	−	8.16056i	−0.704823	−	1.70159i	−0.712547	−	0.701624i	$-0.752459\pi$
$23$	−3.38021	−	8.16056i	−0.704823	−	1.70159i	0.00772401	−	0.999970i	$-0.497541\pi$
$24$	−2.16312	−	5.22222i	−0.441544	−	1.06598i
$25$		0			0
$26$	−2.09458	−	2.09458i	−0.410780	−	0.410780i
$27$	5.12847	−	2.12428i	0.986974	−	0.408818i
$28$	4.84097	+	11.6871i	0.914857	+	2.20866i
$29$	−3.35200	+	8.09244i	−0.622451	+	1.50273i	0.226367	+	0.974042i	$0.427315\pi$
$29$	−3.35200	+	8.09244i	−0.622451	+	1.50273i	−0.848817	+	0.528686i	$0.822685\pi$
$30$		0			0
$31$	2.25799	+	0.935290i	0.405547	+	0.167983i	0.576126	−	0.817361i	$-0.304564\pi$
$31$	2.25799	+	0.935290i	0.405547	+	0.167983i	−0.170579	+	0.985344i	$0.554564\pi$
$32$	−2.75181	−	2.75181i	−0.486456	−	0.486456i
$33$		−	3.89606i		−	0.678217i
$34$	3.92084	−	8.86913i	0.672419	−	1.52104i
$35$		0			0
$36$	−1.34129	+	1.34129i	−0.223549	+	0.223549i
$37$	−1.76094	+	4.25128i	−0.289496	+	0.698906i	−0.999988	−	0.00479925i	$-0.998472\pi$
$37$	−1.76094	+	4.25128i	−0.289496	+	0.698906i	0.710492	+	0.703705i	$0.248472\pi$
$38$	−8.54755			−1.38660
$39$	0.756400	−	1.82611i	0.121121	−	0.292412i
$40$		0			0
$41$	−1.65510	−	3.99575i	−0.258483	−	0.624032i	0.740356	−	0.672215i	$-0.234657\pi$
$41$	−1.65510	−	3.99575i	−0.258483	−	0.624032i	−0.998839	+	0.0481830i	$0.984657\pi$
$42$	−9.34899	+	9.34899i	−1.44258	+	1.44258i
$43$	−5.33668	+	5.33668i	−0.813836	+	0.813836i	−0.985207	−	0.171371i	$-0.945180\pi$
$43$	−5.33668	+	5.33668i	−0.813836	+	0.813836i	0.171371	+	0.985207i	$0.445180\pi$
$44$	3.35504	+	8.09978i	0.505791	+	1.22109i
$45$		0			0
$46$	−7.94993	+	19.1928i	−1.17215	+	2.82983i
$47$	−11.3322			−1.65297			−0.826484	−	0.562961i	$-0.809662\pi$
$47$	−11.3322			−1.65297			−0.826484	+	0.562961i	$0.809662\pi$
$48$	−0.845719	+	2.04175i	−0.122069	+	0.294701i
$49$	4.12357	−	4.12357i	0.589081	−	0.589081i
$50$		0			0
$51$	6.46880	+	0.152348i	0.905814	+	0.0213330i
$52$			4.44779i			0.616797i
$53$	4.02442	+	4.02442i	0.552797	+	0.552797i	0.927247	−	0.374450i	$-0.122169\pi$
$53$	4.02442	+	4.02442i	0.552797	+	0.552797i	−0.374450	+	0.927247i	$0.622169\pi$
$54$	−12.0616	−	4.99610i	−1.64138	−	0.679883i
$55$		0			0
$56$	4.93742	−	11.9200i	0.659791	−	1.59288i
$57$	−2.18264	−	5.26936i	−0.289098	−	0.697943i
$58$	19.0326	−	7.88357i	2.49911	−	1.03516i
$59$	−3.16077	−	3.16077i	−0.411497	−	0.411497i	0.470763	−	0.882260i	$-0.343979\pi$
$59$	−3.16077	−	3.16077i	−0.411497	−	0.411497i	−0.882260	+	0.470763i	$0.843979\pi$
$60$		0			0
$61$	0.0929426	+	0.224383i	0.0119001	+	0.0287293i	0.929718	−	0.368273i	$-0.120051\pi$
$61$	0.0929426	+	0.224383i	0.0119001	+	0.0287293i	−0.917818	+	0.397002i	$0.870051\pi$
$62$	−2.19971	−	5.31057i	−0.279364	−	0.674443i
$63$	1.77764	+	0.736321i	0.223961	+	0.0927677i
$64$			11.9692i			1.49615i
$65$		0			0
$66$	−6.47933	+	6.47933i	−0.797550	+	0.797550i
$67$		−	7.23278i		−	0.883625i	−0.897108	−	0.441812i	$-0.854336\pi$
$67$		−	7.23278i		−	0.883625i	0.897108	−	0.441812i	$-0.145664\pi$
$68$	−13.5796	+	5.25380i	−1.64677	+	0.637116i
$69$	−13.8620			−1.66878
$70$		0			0
$71$	−1.69789	−	0.703290i	−0.201503	−	0.0834651i	0.279650	−	0.960102i	$-0.409782\pi$
$71$	−1.69789	−	0.703290i	−0.201503	−	0.0834651i	−0.481152	+	0.876637i	$0.659782\pi$
$72$	1.93467			0.228003
$73$	−5.05599	−	2.09426i	−0.591758	−	0.245114i	0.0666485	−	0.997777i	$-0.478769\pi$
$73$	−5.05599	−	2.09426i	−0.591758	−	0.245114i	−0.658407	+	0.752662i	$0.728769\pi$
$74$	9.99859	−	4.14155i	1.16231	−	0.481446i
$75$		0			0
$76$	9.07527	+	9.07527i	1.04100	+	1.04100i
$77$	6.28827	−	6.28827i	0.716615	−	0.716615i
$78$	−4.29484	+	1.77898i	−0.486294	+	0.201430i
$79$	8.34789	−	3.45781i	0.939211	−	0.389034i	0.140046	−	0.990145i	$-0.455275\pi$
$79$	8.34789	−	3.45781i	0.939211	−	0.389034i	0.799166	+	0.601111i	$0.205275\pi$
$80$		0			0
$81$		−	7.10006i		−	0.788896i
$82$	−3.89262	+	9.39762i	−0.429868	+	1.03779i
$83$	−5.17302	−	5.17302i	−0.567812	−	0.567812i	0.363703	−	0.931515i	$-0.381512\pi$
$83$	−5.17302	−	5.17302i	−0.567812	−	0.567812i	−0.931515	+	0.363703i	$0.881512\pi$
$84$	19.8524			2.16607
$85$		0			0
$86$	17.7503			1.91406
$87$	9.72006	+	9.72006i	1.04210	+	1.04210i
$88$	3.42189	−	8.26117i	0.364774	−	0.880643i
$89$		−	2.19350i		−	0.232510i	−0.993219	−	0.116255i	$-0.962911\pi$
$89$		−	2.19350i		−	0.232510i	0.993219	−	0.116255i	$-0.0370890\pi$
$90$		0			0
$91$	4.16819	−	1.72652i	0.436945	−	0.180989i
$92$	28.8186	−	11.9370i	3.00454	−	1.24452i
$93$	2.71214	−	2.71214i	0.281235	−	0.281235i
$94$	18.8459	+	18.8459i	1.94381	+	1.94381i
$95$		0			0
$96$	−5.64246	+	2.33718i	−0.575882	+	0.238538i
$97$	9.07286	+	3.75810i	0.921209	+	0.381577i	0.792337	−	0.610084i	$-0.208864\pi$
$97$	9.07286	+	3.75810i	0.921209	+	0.381577i	0.128872	+	0.991661i	$0.458864\pi$
$98$	−13.7154			−1.38546
$99$	1.23199	+	0.510308i	0.123820	+	0.0512879i
$100$		0			0
$101$	5.46415			0.543704			0.271852	−	0.962339i	$-0.412364\pi$
$101$	5.46415			0.543704			0.271852	+	0.962339i	$0.412364\pi$
$102$	−10.5046	−	11.0113i	−1.04011	−	1.09028i
$103$			7.16074i			0.705568i	0.935705	+	0.352784i	$0.114765\pi$
$103$			7.16074i			0.705568i	−0.935705	+	0.352784i	$0.885235\pi$
$104$	3.20773	−	3.20773i	0.314543	−	0.314543i
$105$		0			0
$106$		−	13.3856i		−	1.30012i
$107$	0.575721	+	0.238471i	0.0556570	+	0.0230539i	0.410338	−	0.911933i	$-0.365411\pi$
$107$	0.575721	+	0.238471i	0.0556570	+	0.0230539i	−0.354681	+	0.934987i	$0.615411\pi$
$108$	7.50177	+	18.1109i	0.721859	+	1.74272i
$109$	−2.36863	−	5.71837i	−0.226873	−	0.547720i	0.768921	−	0.639344i	$-0.220794\pi$
$109$	−2.36863	−	5.71837i	−0.226873	−	0.547720i	−0.995794	+	0.0916242i	$0.970794\pi$
$110$		0			0
$111$	5.10633	+	5.10633i	0.484672	+	0.484672i
$112$	−4.66039	+	1.93040i	−0.440365	+	0.182405i
$113$	6.14574	+	14.8371i	0.578143	+	1.39576i	0.894478	+	0.447113i	$0.147548\pi$
$113$	6.14574	+	14.8371i	0.578143	+	1.39576i	−0.316335	+	0.948648i	$0.602452\pi$
$114$	−5.13335	+	12.3930i	−0.480782	+	1.16071i
$115$		0			0
$116$	−28.5780	−	11.8374i	−2.65340	−	1.09907i
$117$	0.478370	+	0.478370i	0.0442253	+	0.0442253i
$118$			10.5130i			0.967801i
$119$	10.1948	+	10.6866i	0.934557	+	0.979638i
$120$		0			0
$121$	−3.42008	+	3.42008i	−0.310916	+	0.310916i
$122$	0.218592	−	0.527727i	0.0197904	−	0.0477782i
$123$	−6.78740			−0.611999
$124$	−3.30292	+	7.97396i	−0.296611	+	0.716083i
$125$		0			0
$126$	−1.73175	−	4.18082i	−0.154277	−	0.372457i
$127$	4.18456	−	4.18456i	0.371320	−	0.371320i	−0.496638	−	0.867958i	$-0.665432\pi$
$127$	4.18456	−	4.18456i	0.371320	−	0.371320i	0.867958	+	0.496638i	$0.165432\pi$
$128$	14.4017	−	14.4017i	1.27294	−	1.27294i
$129$	4.53258	+	10.9426i	0.399072	+	0.963444i
$130$		0			0
$131$	6.16914	−	14.8936i	0.539000	−	1.30126i	−0.386421	−	0.922322i	$-0.626289\pi$
$131$	6.16914	−	14.8936i	0.539000	−	1.30126i	0.925422	−	0.378939i	$-0.123711\pi$
$132$	13.7587			1.19754
$133$	4.98198	−	12.0276i	0.431993	−	1.04292i
$134$	−12.0284	+	12.0284i	−1.03910	+	1.03910i
$135$		0			0
$136$	13.5826	+	6.00455i	1.16470	+	0.514886i
$137$			17.1320i			1.46369i	0.681473	+	0.731843i	$0.261339\pi$
$137$			17.1320i			1.46369i	−0.681473	+	0.731843i	$0.738661\pi$
$138$	23.0531	+	23.0531i	1.96241	+	1.96241i
$139$	−1.97070	−	0.816292i	−0.167153	−	0.0692369i	0.297538	−	0.954710i	$-0.403835\pi$
$139$	−1.97070	−	0.816292i	−0.167153	−	0.0692369i	−0.464691	+	0.885473i	$0.653835\pi$
$140$		0			0
$141$	−6.80570	+	16.4304i	−0.573143	+	1.38369i
$142$	1.65407	+	3.99327i	0.138806	+	0.335108i
$143$	2.88877	−	1.19657i	0.241571	−	0.100062i
$144$	−0.534857	−	0.534857i	−0.0445715	−	0.0445715i
$145$		0			0
$146$	4.92549	+	11.8912i	0.407636	+	0.984121i
$147$	−3.50226	−	8.45519i	−0.288861	−	0.697373i
$148$	−15.0131	−	6.21865i	−1.23407	−	0.511170i
$149$		−	18.5384i		−	1.51872i	−0.650669	−	0.759362i	$-0.725511\pi$
$149$		−	18.5384i		−	1.51872i	0.650669	−	0.759362i	$-0.274489\pi$
$150$		0			0
$151$	−6.30217	+	6.30217i	−0.512863	+	0.512863i	−0.915403	−	0.402539i	$-0.868128\pi$
$151$	−6.30217	+	6.30217i	−0.512863	+	0.512863i	0.402539	+	0.915403i	$0.368128\pi$
$152$		−	13.0901i		−	1.06175i
$153$	−0.895462	+	2.02558i	−0.0723938	+	0.163758i
$154$	−20.9154			−1.68541
$155$		0			0
$156$	6.44881	+	2.67118i	0.516318	+	0.213866i
$157$	−18.2426			−1.45592			−0.727960	−	0.685620i	$-0.759531\pi$
$157$	−18.2426			−1.45592			−0.727960	+	0.685620i	$0.759531\pi$
$158$	−19.6334	−	8.13243i	−1.56195	−	0.646982i
$159$	8.25189	−	3.41805i	0.654418	−	0.271069i
$160$		0			0
$161$	−22.3733	−	22.3733i	−1.76326	−	1.76326i
$162$	−11.8077	+	11.8077i	−0.927703	+	0.927703i
$163$	8.65222	−	3.58387i	0.677694	−	0.280710i	−0.0171684	−	0.999853i	$-0.505465\pi$
$163$	8.65222	−	3.58387i	0.677694	−	0.280710i	0.694863	+	0.719142i	$0.255465\pi$
$164$	14.1108	−	5.84488i	1.10187	−	0.456408i
$165$		0			0
$166$			17.2059i			1.33544i
$167$	−3.55181	+	8.57484i	−0.274848	+	0.663541i	−0.999678	−	0.0253869i	$-0.991918\pi$
$167$	−3.55181	+	8.57484i	−0.274848	+	0.663541i	0.724830	+	0.688928i	$0.241918\pi$
$168$	−14.3175	−	14.3175i	−1.10462	−	1.10462i
$169$	−11.4137			−0.877977
$170$		0			0
$171$	1.95213			0.149283
$172$	−18.8462	−	18.8462i	−1.43701	−	1.43701i
$173$	1.64545	−	3.97248i	0.125102	−	0.302022i	−0.848904	−	0.528548i	$-0.822737\pi$
$173$	1.64545	−	3.97248i	0.125102	−	0.302022i	0.974005	+	0.226526i	$0.0727368\pi$
$174$		−	32.3298i		−	2.45092i
$175$		0			0
$176$	−3.22989	+	1.33786i	−0.243462	+	0.100845i
$177$	−6.48102	+	2.68453i	−0.487143	+	0.201781i
$178$	−3.64789	+	3.64789i	−0.273421	+	0.273421i
$179$	0.0832109	+	0.0832109i	0.00621948	+	0.00621948i	0.710210	−	0.703990i	$-0.248600\pi$
$179$	0.0832109	+	0.0832109i	0.00621948	+	0.00621948i	−0.703990	+	0.710210i	$0.748600\pi$
$180$		0			0
$181$	−2.14676	+	0.889218i	−0.159568	+	0.0660951i	−0.461038	−	0.887381i	$-0.652523\pi$
$181$	−2.14676	+	0.889218i	−0.159568	+	0.0660951i	0.301470	+	0.953476i	$0.402523\pi$
$182$	−9.80318	−	4.06061i	−0.726660	−	0.300993i
$183$	0.381149			0.0281754
$184$	−29.3927	−	12.1749i	−2.16686	−	0.897544i
$185$		0			0
$186$	−9.02082			−0.661438
$187$	7.06552	+	7.40635i	0.516682	+	0.541606i
$188$		−	40.0189i		−	2.91868i
$189$	14.0604	−	14.0604i	1.02274	−	1.02274i
$190$		0			0
$191$			14.6622i			1.06092i	0.847710	+	0.530461i	$0.177981\pi$
$191$			14.6622i			1.06092i	−0.847710	+	0.530461i	$0.822019\pi$
$192$	17.3540	+	7.18827i	1.25242	+	0.518768i
$193$	3.21303	+	7.75695i	0.231279	+	0.558357i	0.996328	−	0.0856146i	$-0.0272854\pi$
$193$	3.21303	+	7.75695i	0.231279	+	0.558357i	−0.765049	+	0.643972i	$0.777285\pi$
$194$	−8.83869	−	21.3385i	−0.634581	−	1.53201i
$195$		0			0
$196$	14.5622	+	14.5622i	1.04015	+	1.04015i
$197$	−6.17290	+	2.55690i	−0.439801	+	0.182171i	−0.591586	−	0.806242i	$-0.701498\pi$
$197$	−6.17290	+	2.55690i	−0.439801	+	0.182171i	0.151785	+	0.988414i	$0.451498\pi$
$198$	−1.20019	−	2.89752i	−0.0852941	−	0.205918i
$199$	−7.22192	+	17.4353i	−0.511949	+	1.23595i	0.430800	+	0.902448i	$0.358232\pi$
$199$	−7.22192	+	17.4353i	−0.511949	+	1.23595i	−0.942748	+	0.333506i	$0.891768\pi$
$200$		0			0
$201$	−10.4867	−	4.34375i	−0.739678	−	0.306384i
$202$	−9.08714	−	9.08714i	−0.639369	−	0.639369i
$203$			31.3765i			2.20220i
$204$	−0.538009	+	22.8442i	−0.0376681	+	1.59942i
$205$		0			0
$206$	11.9086	−	11.9086i	0.829714	−	0.829714i
$207$	1.81565	−	4.38336i	0.126196	−	0.304664i
$208$	−1.77361			−0.122978
$209$	3.45277	−	8.33572i	0.238833	−	0.576594i
$210$		0			0
$211$	2.53326	+	6.11583i	0.174397	+	0.421031i	0.986774	−	0.162101i	$-0.0518270\pi$
$211$	2.53326	+	6.11583i	0.174397	+	0.421031i	−0.812377	+	0.583132i	$0.801827\pi$
$212$	−14.2120	+	14.2120i	−0.976085	+	0.976085i
$213$	−2.03939	+	2.03939i	−0.139736	+	0.139736i
$214$	−0.560861	−	1.35404i	−0.0383397	−	0.0925602i
$215$		0			0
$216$	7.65124	−	18.4717i	0.520601	−	1.25684i
$217$	8.75482			0.594316
$218$	−5.57077	+	13.4490i	−0.377300	+	0.910884i
$219$	−6.07289	+	6.07289i	−0.410368	+	0.410368i
$220$		0			0
$221$	1.87376	+	4.84315i	0.126042	+	0.325785i
$222$		−	16.9841i		−	1.13990i
$223$	2.08077	+	2.08077i	0.139339	+	0.139339i	0.773336	−	0.633997i	$-0.218587\pi$
$223$	2.08077	+	2.08077i	0.139339	+	0.139339i	−0.633997	+	0.773336i	$0.718587\pi$
$224$	−12.8792	−	5.33474i	−0.860529	−	0.356443i
$225$		0			0
$226$	14.4542	−	34.8955i	0.961478	−	2.32121i
$227$	8.23750	+	19.8871i	0.546742	+	1.31995i	0.919889	+	0.392180i	$0.128279\pi$
$227$	8.23750	+	19.8871i	0.546742	+	1.31995i	−0.373147	+	0.927772i	$0.621721\pi$
$228$	18.6084	−	7.70786i	1.23237	−	0.510466i
$229$	−8.44347	−	8.44347i	−0.557960	−	0.557960i	0.370766	−	0.928726i	$-0.379095\pi$
$229$	−8.44347	−	8.44347i	−0.557960	−	0.557960i	−0.928726	+	0.370766i	$0.879095\pi$
$230$		0			0
$231$	−5.34080	−	12.8938i	−0.351399	−	0.848351i
$232$	12.0732	+	29.1474i	0.792647	+	1.91362i
$233$	−9.30228	−	3.85313i	−0.609412	−	0.252427i	0.0565648	−	0.998399i	$-0.481985\pi$
$233$	−9.30228	−	3.85313i	−0.609412	−	0.252427i	−0.665977	+	0.745972i	$0.731985\pi$
$234$		−	1.59110i		−	0.104014i
$235$		0			0
$236$	11.1621	−	11.1621i	0.726590	−	0.726590i
$237$		−	14.1802i		−	0.921101i
$238$	0.817856	−	34.7267i	0.0530137	−	2.25100i
$239$	16.6253			1.07540			0.537701	−	0.843135i	$-0.319293\pi$
$239$	16.6253			1.07540			0.537701	+	0.843135i	$0.319293\pi$
$240$		0			0
$241$	5.47122	+	2.26625i	0.352432	+	0.145982i	0.551874	−	0.833928i	$-0.313913\pi$
$241$	5.47122	+	2.26625i	0.352432	+	0.145982i	−0.199442	+	0.979910i	$0.563913\pi$
$242$	11.3755			0.731245
$243$	5.09108	+	2.10879i	0.326593	+	0.135279i
$244$	−0.792397	+	0.328221i	−0.0507280	+	0.0210122i
$245$		0			0
$246$	11.2878	+	11.2878i	0.719681	+	0.719681i
$247$	3.23668	−	3.23668i	0.205945	−	0.205945i
$248$	8.13284	−	3.36873i	0.516436	−	0.213915i
$249$	−10.6070	+	4.39358i	−0.672194	+	0.278432i
$250$		0			0
$251$			7.77270i			0.490608i	0.969446	+	0.245304i	$0.0788878\pi$
$251$			7.77270i			0.490608i	−0.969446	+	0.245304i	$0.921112\pi$
$252$	−2.60027	+	6.27762i	−0.163802	+	0.395453i
$253$	−15.5058	−	15.5058i	−0.974844	−	0.974844i
$254$	−13.9182			−0.873307
$255$		0			0
$256$	−23.9630			−1.49768
$257$	5.70344	+	5.70344i	0.355771	+	0.355771i	0.862251	−	0.506481i	$-0.169054\pi$
$257$	5.70344	+	5.70344i	0.355771	+	0.355771i	−0.506481	+	0.862251i	$0.669054\pi$
$258$	10.6602	−	25.7360i	0.663674	−	1.60225i
$259$			16.4833i			1.02422i
$260$		0			0
$261$	−4.34677	+	1.80049i	−0.269058	+	0.111448i
$262$	−35.0283	+	14.5092i	−2.16406	+	0.896382i
$263$	−15.0792	+	15.0792i	−0.929822	+	0.929822i	−0.997694	−	0.0678724i	$-0.978379\pi$
$263$	−15.0792	+	15.0792i	−0.929822	+	0.929822i	0.0678724	+	0.997694i	$0.478379\pi$
$264$	−9.92273	−	9.92273i	−0.610702	−	0.610702i
$265$		0			0
$266$	−28.2877	+	11.7171i	−1.73443	+	0.718424i
$267$	−3.18033	−	1.31734i	−0.194633	−	0.0806197i
$268$	25.5422			1.56024
$269$	−3.88200	−	1.60798i	−0.236690	−	0.0980401i	0.261186	−	0.965289i	$-0.415886\pi$
$269$	−3.88200	−	1.60798i	−0.236690	−	0.0980401i	−0.497876	+	0.867248i	$0.665886\pi$
$270$		0			0
$271$	−24.7136			−1.50124			−0.750621	−	0.660733i	$-0.770245\pi$
$271$	−24.7136			−1.50124			−0.750621	+	0.660733i	$0.770245\pi$
$272$	−2.09502	−	5.41504i	−0.127029	−	0.328335i
$273$		−	7.08031i		−	0.428520i
$274$	28.4913	−	28.4913i	1.72122	−	1.72122i
$275$		0			0
$276$		−	48.9527i		−	2.94661i
$277$	−18.5355	−	7.67765i	−1.11369	−	0.461305i	−0.251483	−	0.967862i	$-0.580918\pi$
$277$	−18.5355	−	7.67765i	−1.11369	−	0.461305i	−0.862207	+	0.506556i	$0.830918\pi$
$278$	1.91984	+	4.63490i	0.115144	+	0.277983i
$279$	0.502381	+	1.21285i	0.0300768	+	0.0726117i
$280$		0			0
$281$	17.8053	+	17.8053i	1.06218	+	1.06218i	0.997934	+	0.0642430i	$0.0204633\pi$
$281$	17.8053	+	17.8053i	1.06218	+	1.06218i	0.0642430	+	0.997934i	$0.479537\pi$
$282$	38.6427	−	16.0063i	2.30114	−	0.953164i
$283$	3.24768	+	7.84059i	0.193054	+	0.466075i	0.990533	−	0.137272i	$-0.0438335\pi$
$283$	3.24768	+	7.84059i	0.193054	+	0.466075i	−0.797479	+	0.603347i	$0.793833\pi$
$284$	2.48363	−	5.99601i	0.147376	−	0.355798i
$285$		0			0
$286$	−6.79411	−	2.81421i	−0.401744	−	0.166408i
$287$	−10.9549	−	10.9549i	−0.646648	−	0.646648i
$288$		−	2.09036i		−	0.123175i
$289$	−12.5734	+	11.4416i	−0.739611	+	0.673035i
$290$		0			0
$291$	10.8977	−	10.8977i	0.638833	−	0.638833i
$292$	7.39575	−	17.8549i	0.432804	−	1.04488i
$293$	25.9873			1.51820			0.759098	−	0.650977i	$-0.225640\pi$
$293$	25.9873			1.51820			0.759098	+	0.650977i	$0.225640\pi$
$294$	−8.23696	+	19.8858i	−0.480389	+	1.15976i
$295$		0			0
$296$	6.34255	+	15.3123i	0.368653	+	0.890008i
$297$	9.74457	−	9.74457i	0.565438	−	0.565438i
$298$	−30.8302	+	30.8302i	−1.78594	+	1.78594i
$299$	−4.25732	−	10.2781i	−0.246207	−	0.594397i
$300$		0			0
$301$	−10.3458	+	24.9771i	−0.596325	+	1.43966i
$302$	20.9616			1.20620
$303$	3.28158	−	7.92243i	0.188522	−	0.455132i
$304$	−3.61887	+	3.61887i	−0.207557	+	0.207557i
$305$		0			0
$306$	4.85782	−	1.87943i	0.277703	−	0.107440i
$307$		−	16.9475i		−	0.967245i	−0.875277	−	0.483622i	$-0.839321\pi$
$307$		−	16.9475i		−	0.967245i	0.875277	−	0.483622i	$-0.160679\pi$
$308$	22.2067	+	22.2067i	1.26534	+	1.26534i
$309$	10.3823	+	4.30048i	0.590628	+	0.244646i
$310$		0			0
$311$	−6.57851	+	15.8819i	−0.373033	+	0.900581i	0.620200	+	0.784444i	$0.287051\pi$
$311$	−6.57851	+	15.8819i	−0.373033	+	0.900581i	−0.993233	+	0.116138i	$0.962949\pi$
$312$	−2.72441	−	6.57730i	−0.154239	−	0.372366i
$313$	5.46463	−	2.26352i	0.308879	−	0.127942i	−0.222859	−	0.974851i	$-0.571539\pi$
$313$	5.46463	−	2.26352i	0.308879	−	0.127942i	0.531738	+	0.846909i	$0.321539\pi$
$314$	30.3383	+	30.3383i	1.71209	+	1.71209i
$315$		0			0
$316$	12.2111	+	29.4801i	0.686926	+	1.65839i
$317$	0.245137	+	0.591813i	0.0137683	+	0.0332395i	0.930614	−	0.366002i	$-0.119274\pi$
$317$	0.245137	+	0.591813i	0.0137683	+	0.0332395i	−0.916846	+	0.399241i	$0.869274\pi$
$318$	−19.4076	−	8.03891i	−1.08833	−	0.450800i
$319$			21.7455i			1.21752i
$320$		0			0
$321$	0.691515	−	0.691515i	0.0385966	−	0.0385966i
$322$			74.4157i			4.14702i
$323$	13.7052	+	6.05874i	0.762576	+	0.337117i
$324$	25.0735			1.39297
$325$		0			0
$326$	−20.3492	−	8.42891i	−1.12704	−	0.466834i
$327$	−9.71352			−0.537159
$328$	−14.3919	−	5.96133i	−0.794661	−	0.329160i
$329$	−37.5033	+	15.5344i	−2.06762	+	0.856437i
$330$		0			0
$331$	−8.24547	−	8.24547i	−0.453212	−	0.453212i	0.443207	−	0.896419i	$-0.353841\pi$
$331$	−8.24547	−	8.24547i	−0.453212	−	0.453212i	−0.896419	+	0.443207i	$0.853841\pi$
$332$	18.2682	−	18.2682i	1.00260	−	1.00260i
$333$	−2.28353	+	0.945868i	−0.125137	+	0.0518333i
$334$	20.1672	−	8.35352i	1.10350	−	0.457084i
$335$		0			0
$336$			7.91638i			0.431874i
$337$	11.8175	−	28.5300i	0.643740	−	1.55413i	−0.177856	−	0.984056i	$-0.556916\pi$
$337$	11.8175	−	28.5300i	0.643740	−	1.55413i	0.821596	−	0.570070i	$-0.193084\pi$
$338$	18.9815	+	18.9815i	1.03246	+	1.03246i
$339$	25.2031			1.36885
$340$		0			0
$341$	6.06754			0.328576
$342$	−3.24648	−	3.24648i	−0.175550	−	0.175550i
$343$	−1.60166	+	3.86674i	−0.0864813	+	0.208784i
$344$			27.1836i			1.46564i
$345$		0			0
$346$	−9.34288	+	3.86995i	−0.502276	+	0.208050i
$347$	−0.0138574	+	0.00573993i	−0.000743905	+	0.000308135i	−0.383055	−	0.923725i	$-0.625128\pi$
$347$	−0.0138574	+	0.00573993i	−0.000743905	+	0.000308135i	0.382311	+	0.924034i	$0.375128\pi$
$348$	−34.3259	+	34.3259i	−1.84006	+	1.84006i
$349$	2.58441	+	2.58441i	0.138340	+	0.138340i	0.772886	−	0.634545i	$-0.218813\pi$
$349$	2.58441	+	2.58441i	0.138340	+	0.138340i	−0.634545	+	0.772886i	$0.718813\pi$
$350$		0			0
$351$	6.45921	−	2.67549i	0.344767	−	0.142807i
$352$	−8.92595	−	3.69725i	−0.475755	−	0.197064i
$353$	−3.82333			−0.203495			−0.101748	−	0.994810i	$-0.532443\pi$
$353$	−3.82333			−0.203495			−0.101748	+	0.994810i	$0.532443\pi$
$354$	15.2427	+	6.31374i	0.810141	+	0.335572i
$355$		0			0
$356$	7.74622			0.410549
$357$	21.6170	−	8.36337i	1.14409	−	0.442637i
$358$		−	0.276767i		−	0.0146276i
$359$	4.73532	−	4.73532i	0.249921	−	0.249921i	−0.571017	−	0.820938i	$-0.693451\pi$
$359$	4.73532	−	4.73532i	0.249921	−	0.249921i	0.820938	+	0.571017i	$0.193451\pi$
$360$		0			0
$361$			5.79178i			0.304830i
$362$	5.04897	+	2.09135i	0.265368	+	0.109919i
$363$	2.90476	+	7.01272i	0.152461	+	0.368072i
$364$	6.09712	+	14.7197i	0.319576	+	0.771524i
$365$		0			0
$366$	−0.633869	−	0.633869i	−0.0331328	−	0.0331328i
$367$	−21.2747	+	8.81227i	−1.11053	+	0.459997i	−0.861120	−	0.508401i	$-0.830237\pi$
$367$	−21.2747	+	8.81227i	−1.11053	+	0.459997i	−0.249410	+	0.968398i	$0.580237\pi$
$368$	4.76004	+	11.4917i	0.248134	+	0.599049i
$369$	0.889017	−	2.14628i	0.0462804	−	0.111731i
$370$		0			0
$371$	18.8354	+	7.80187i	0.977884	+	0.405053i
$372$	9.57776	+	9.57776i	0.496584	+	0.496584i
$373$		−	23.7303i		−	1.22871i	−0.789030	−	0.614355i	$-0.789416\pi$
$373$		−	23.7303i		−	1.22871i	0.789030	−	0.614355i	$-0.210584\pi$
$374$	0.566816	−	24.0674i	0.0293094	−	1.24450i
$375$		0			0
$376$	−28.8615	+	28.8615i	−1.48842	+	1.48842i
$377$	−4.22178	+	10.1923i	−0.217433	+	0.524929i
$378$	−46.7662			−2.40539
$379$	−1.13970	+	2.75149i	−0.0585427	+	0.141335i	−0.950444	−	0.310895i	$-0.899371\pi$
$379$	−1.13970	+	2.75149i	−0.0585427	+	0.141335i	0.891902	+	0.452230i	$0.149371\pi$
$380$		0			0
$381$	−3.55406	−	8.58025i	−0.182080	−	0.439580i
$382$	24.3839	−	24.3839i	1.24759	−	1.24759i
$383$	17.2691	−	17.2691i	0.882408	−	0.882408i	−0.111371	−	0.993779i	$-0.535524\pi$
$383$	17.2691	−	17.2691i	0.882408	−	0.882408i	0.993779	+	0.111371i	$0.0355241\pi$
$384$	−12.2317	−	29.5300i	−0.624198	−	1.50695i
$385$		0			0
$386$	7.55674	−	18.2436i	0.384628	−	0.928574i
$387$	−4.05390			−0.206071
$388$	−13.2715	+	32.0403i	−0.673759	+	1.62660i
$389$	1.19407	−	1.19407i	0.0605418	−	0.0605418i	−0.676188	−	0.736729i	$-0.736369\pi$
$389$	1.19407	−	1.19407i	0.0605418	−	0.0605418i	0.736729	+	0.676188i	$0.236369\pi$
$390$		0			0
$391$	26.3514	−	25.1387i	1.33265	−	1.27132i
$392$		−	21.0043i		−	1.06088i
$393$	−17.8892	−	17.8892i	−0.902389	−	0.902389i
$394$	14.5181	+	6.01357i	0.731409	+	0.302960i
$395$		0			0
$396$	−1.80212	+	4.35071i	−0.0905601	+	0.218631i
$397$	12.0643	+	29.1259i	0.605491	+	1.46178i	0.867856	+	0.496816i	$0.165498\pi$
$397$	12.0643	+	29.1259i	0.605491	+	1.46178i	−0.262365	+	0.964969i	$0.584502\pi$
$398$	41.0060	−	16.9853i	2.05545	−	0.851394i
$399$	−14.4467	−	14.4467i	−0.723238	−	0.723238i
$400$		0			0
$401$	1.93870	+	4.68044i	0.0968141	+	0.233730i	0.964865	−	0.262745i	$-0.0846276\pi$
$401$	1.93870	+	4.68044i	0.0968141	+	0.233730i	−0.868051	+	0.496474i	$0.834628\pi$
$402$	10.2161	+	24.6638i	0.509531	+	1.23012i
$403$	2.84390	+	1.17798i	0.141665	+	0.0586794i
$404$			19.2964i			0.960029i
$405$		0			0
$406$	52.1806	−	52.1806i	2.58968	−	2.58968i
$407$			11.4238i			0.566256i
$408$	16.8632	−	16.0871i	0.834850	−	0.796432i
$409$	26.1178			1.29144			0.645722	−	0.763573i	$-0.276557\pi$
$409$	26.1178			1.29144			0.645722	+	0.763573i	$0.276557\pi$
$410$		0			0
$411$	24.8395	+	10.2889i	1.22524	+	0.507513i
$412$	−25.2877			−1.24584
$413$	−14.7933	−	6.12757i	−0.727929	−	0.301518i
$414$	−10.3092	+	4.27022i	−0.506671	+	0.209870i
$415$		0			0
$416$	−3.46586	−	3.46586i	−0.169928	−	0.169928i
$417$	−2.36707	+	2.36707i	−0.115916	+	0.115916i
$418$	−19.6048	+	8.12058i	−0.958903	+	0.397190i
$419$	−6.74298	+	2.79303i	−0.329416	+	0.136449i	−0.541261	−	0.840855i	$-0.682053\pi$
$419$	−6.74298	+	2.79303i	−0.329416	+	0.136449i	0.211845	+	0.977303i	$0.432053\pi$
$420$		0			0
$421$		−	21.0644i		−	1.02662i	−0.858204	−	0.513309i	$-0.828420\pi$
$421$		−	21.0644i		−	1.02662i	0.858204	−	0.513309i	$-0.171580\pi$
$422$	5.95798	−	14.3838i	0.290030	−	0.700194i
$423$	−4.30413	−	4.30413i	−0.209274	−	0.209274i
$424$	20.4993			0.995533
$425$		0			0
$426$	6.78319			0.328646
$427$	0.615178	+	0.615178i	0.0297705	+	0.0297705i
$428$	−0.842148	+	2.03313i	−0.0407068	+	0.0982749i
$429$		−	4.90702i		−	0.236913i
$430$		0			0
$431$	−19.4414	+	8.05290i	−0.936460	+	0.387894i	−0.798126	−	0.602491i	$-0.794175\pi$
$431$	−19.4414	+	8.05290i	−0.936460	+	0.387894i	−0.138334	+	0.990386i	$0.544175\pi$
$432$	−7.22194	+	2.99142i	−0.347466	+	0.143925i
$433$	26.2522	−	26.2522i	1.26160	−	1.26160i	0.311280	−	0.950318i	$-0.399242\pi$
$433$	26.2522	−	26.2522i	1.26160	−	1.26160i	0.950318	−	0.311280i	$-0.100758\pi$
$434$	−14.5597	−	14.5597i	−0.698886	−	0.698886i
$435$		0			0
$436$	20.1941	−	8.36467i	0.967121	−	0.400595i
$437$	−29.6580	−	12.2848i	−1.41874	−	0.587659i
$438$	20.1990			0.965145
$439$	−0.435448	−	0.180369i	−0.0207828	−	0.00860852i	0.372268	−	0.928125i	$-0.378580\pi$
$439$	−0.435448	−	0.180369i	−0.0207828	−	0.00860852i	−0.393051	+	0.919517i	$0.628580\pi$
$440$		0			0
$441$	3.13238			0.149161
$442$	4.93823	−	11.1705i	0.234888	−	0.531327i
$443$		−	11.0249i		−	0.523808i	−0.965094	−	0.261904i	$-0.915650\pi$
$443$		−	11.0249i		−	0.523808i	0.965094	−	0.261904i	$-0.0843504\pi$
$444$	−18.0327	+	18.0327i	−0.855795	+	0.855795i
$445$		0			0
$446$		−	6.92084i		−	0.327711i
$447$	−26.8786	−	11.1335i	−1.27132	−	0.526596i
$448$	16.4076	+	39.6114i	0.775186	+	1.87146i
$449$	−6.60636	−	15.9492i	−0.311773	−	0.752688i	−0.999639	−	0.0268500i	$-0.991452\pi$
$449$	−6.60636	−	15.9492i	−0.311773	−	0.752688i	0.687866	−	0.725838i	$-0.258548\pi$
$450$		0			0
$451$	−7.59232	−	7.59232i	−0.357508	−	0.357508i
$452$	−52.3965	+	21.7033i	−2.46452	+	1.02084i
$453$	5.35260	+	12.9223i	0.251487	+	0.607143i
$454$	19.3738	−	46.7725i	0.909257	−	2.19514i
$455$		0			0
$456$	−18.9792	−	7.86144i	−0.888782	−	0.368146i
$457$	7.96742	+	7.96742i	0.372700	+	0.372700i	0.868460	−	0.495760i	$-0.165110\pi$
$457$	7.96742	+	7.96742i	0.372700	+	0.372700i	−0.495760	+	0.868460i	$0.665110\pi$
$458$			28.0837i			1.31227i
$459$	15.7983	+	16.5604i	0.737402	+	0.772973i
$460$		0			0
$461$	21.2185	−	21.2185i	0.988244	−	0.988244i	−0.0116873	−	0.999932i	$-0.503720\pi$
$461$	21.2185	−	21.2185i	0.988244	−	0.988244i	0.999932	+	0.0116873i	$0.00372025\pi$
$462$	−12.5610	+	30.3250i	−0.584392	+	1.41085i
$463$	−17.1592			−0.797457			−0.398728	−	0.917069i	$-0.630548\pi$
$463$	−17.1592			−0.797457			−0.398728	+	0.917069i	$0.630548\pi$
$464$	4.72031	−	11.3958i	0.219135	−	0.529038i
$465$		0			0
$466$	9.06218	+	21.8780i	0.419798	+	1.01348i
$467$	18.8030	−	18.8030i	0.870099	−	0.870099i	−0.122384	−	0.992483i	$-0.539054\pi$
$467$	18.8030	−	18.8030i	0.870099	−	0.870099i	0.992483	+	0.122384i	$0.0390540\pi$
$468$	−1.68934	+	1.68934i	−0.0780896	+	0.0780896i
$469$	−9.91483	−	23.9365i	−0.457824	−	1.10529i
$470$		0			0
$471$	−10.9559	+	26.4498i	−0.504820	+	1.21874i
$472$	−16.1001			−0.741066
$473$	−7.17020	+	17.3104i	−0.329686	+	0.795933i
$474$	−23.5823	+	23.5823i	−1.08317	+	1.08317i
$475$		0			0
$476$	−37.7391	+	36.0024i	−1.72977	+	1.65017i
$477$			3.05707i			0.139974i
$478$	−27.6487	−	27.6487i	−1.26462	−	1.26462i
$479$	21.1662	+	8.76732i	0.967107	+	0.400589i	0.809635	−	0.586934i	$-0.199665\pi$
$479$	21.1662	+	8.76732i	0.967107	+	0.400589i	0.157473	+	0.987523i	$0.449665\pi$
$480$		0			0
$481$	−2.21787	+	5.35441i	−0.101126	+	0.244140i
$482$	−5.33000	−	12.8678i	−0.242775	−	0.586111i
$483$	−45.8755	+	19.0022i	−2.08741	+	0.864632i
$484$	−12.0778	−	12.0778i	−0.548992	−	0.548992i
$485$		0			0
$486$	−4.95968	−	11.9737i	−0.224975	−	0.543139i
$487$	−6.01330	−	14.5174i	−0.272489	−	0.657846i	0.727100	−	0.686532i	$-0.240868\pi$
$487$	−6.01330	−	14.5174i	−0.272489	−	0.657846i	−0.999588	+	0.0286857i	$0.990868\pi$
$488$	0.808185	+	0.334761i	0.0365848	+	0.0151539i
$489$		−	14.6971i		−	0.664627i
$490$		0			0
$491$	0.607534	−	0.607534i	0.0274176	−	0.0274176i	−0.693265	−	0.720683i	$-0.743828\pi$
$491$	0.607534	−	0.607534i	0.0274176	−	0.0274176i	0.720683	+	0.693265i	$0.243828\pi$
$492$		−	23.9693i		−	1.08062i
$493$	−36.1051	−	0.850318i	−1.62609	−	0.0382964i
$494$	−10.7655			−0.484362
$495$		0			0
$496$	−3.17972	−	1.31708i	−0.142773	−	0.0591387i
$497$	−6.58317			−0.295296
$498$	24.9467	+	10.3333i	1.11789	+	0.463045i
$499$	20.9163	−	8.66380i	0.936340	−	0.387845i	0.138260	−	0.990396i	$-0.455849\pi$
$499$	20.9163	−	8.66380i	0.936340	−	0.387845i	0.798080	+	0.602551i	$0.205849\pi$
$500$		0			0
$501$	10.2995	+	10.2995i	0.460147	+	0.460147i
$502$	12.9264	−	12.9264i	0.576931	−	0.576931i
$503$	−15.8122	+	6.54963i	−0.705032	+	0.292034i	−0.706247	−	0.707966i	$-0.749613\pi$
$503$	−15.8122	+	6.54963i	−0.705032	+	0.292034i	0.00121517	+	0.999999i	$0.499613\pi$
$504$	6.40270	−	2.65208i	0.285199	−	0.118133i
$505$		0			0
$506$			51.5739i			2.29274i
$507$	−6.85467	+	16.5486i	−0.304426	+	0.734950i
$508$	14.7775	+	14.7775i	0.655647	+	0.655647i
$509$	−29.7081			−1.31679			−0.658393	−	0.752674i	$-0.728764\pi$
$509$	−29.7081			−1.31679			−0.658393	+	0.752674i	$0.728764\pi$
$510$		0			0
$511$	−19.6034			−0.867203
$512$	11.0481	+	11.0481i	0.488263	+	0.488263i
$513$	7.72030	−	18.6384i	0.340859	−	0.822907i
$514$		−	18.9701i		−	0.836737i
$515$		0			0
$516$	−38.6432	+	16.0066i	−1.70117	+	0.704649i
$517$	−25.9917	+	10.7661i	−1.14311	+	0.473493i
$518$	27.4125	−	27.4125i	1.20444	−	1.20444i
$519$	−4.77146	−	4.77146i	−0.209444	−	0.209444i
$520$		0			0
$521$	−35.7139	+	14.7932i	−1.56465	+	0.648101i	−0.985890	−	0.167395i	$-0.946465\pi$
$521$	−35.7139	+	14.7932i	−1.56465	+	0.648101i	−0.578764	+	0.815495i	$0.696465\pi$
$522$	10.2232	+	4.23458i	0.447456	+	0.185342i
$523$	−0.599508			−0.0262147			−0.0131073	−	0.999914i	$-0.504172\pi$
$523$	−0.599508			−0.0262147			−0.0131073	+	0.999914i	$0.504172\pi$
$524$	52.5960	+	21.7860i	2.29767	+	0.951724i
$525$		0			0
$526$	50.1547			2.18685
$527$	−0.237259	+	10.0742i	−0.0103352	+	0.438839i
$528$			5.48646i			0.238767i
$529$	−38.9054	+	38.9054i	−1.69154	+	1.69154i
$530$		0			0
$531$		−	2.40101i		−	0.104195i
$532$	42.4747	+	17.5936i	1.84151	+	0.762779i
$533$	−2.08456	−	5.03258i	−0.0902925	−	0.217985i
$534$	3.09825	+	7.47983i	0.134074	+	0.323684i
$535$		0			0
$536$	−18.4209	−	18.4209i	−0.795661	−	0.795661i
$537$	0.170620	−	0.0706732i	0.00736281	−	0.00304977i
$538$	3.78181	+	9.13009i	0.163045	+	0.393626i
$539$	5.54031	−	13.3755i	0.238638	−	0.576123i
$540$		0			0
$541$	36.6847	+	15.1953i	1.57720	+	0.653297i	0.987966	−	0.154668i	$-0.0494308\pi$
$541$	36.6847	+	15.1953i	1.57720	+	0.653297i	0.589231	+	0.807965i	$0.299431\pi$
$542$	41.0998	+	41.0998i	1.76539	+	1.76539i
$543$			3.64660i			0.156491i
$544$	6.48774	−	14.6756i	0.278160	−	0.629211i
$545$		0			0
$546$	−11.7749	+	11.7749i	−0.503919	+	0.503919i
$547$	−1.54516	+	3.73035i	−0.0660663	+	0.159498i	−0.953464	−	0.301506i	$-0.902511\pi$
$547$	−1.54516	+	3.73035i	−0.0660663	+	0.159498i	0.887398	+	0.461004i	$0.152511\pi$
$548$	−60.5007			−2.58446
$549$	−0.0499231	+	0.120525i	−0.00213067	+	0.00514388i
$550$		0			0
$551$	12.1822	+	29.4105i	0.518980	+	1.25293i
$552$	−35.3045	+	35.3045i	−1.50266	+	1.50266i
$553$	22.8869	−	22.8869i	0.973250	−	0.973250i
$554$	18.0571	+	43.5937i	0.767172	+	1.85212i
$555$		0			0
$556$	2.88269	−	6.95942i	0.122253	−	0.295145i
$557$	5.42781			0.229984			0.114992	−	0.993366i	$-0.463316\pi$
$557$	5.42781			0.229984			0.114992	+	0.993366i	$0.463316\pi$
$558$	1.18155	−	2.85252i	0.0500190	−	0.120757i
$559$	−6.72145	+	6.72145i	−0.284287	+	0.284287i
$560$		0			0
$561$	14.9817	−	5.79624i	0.632528	−	0.244718i
$562$		−	59.2222i		−	2.49814i
$563$	−3.66888	−	3.66888i	−0.154625	−	0.154625i	0.625555	−	0.780180i	$-0.284873\pi$
$563$	−3.66888	−	3.66888i	−0.154625	−	0.154625i	−0.780180	+	0.625555i	$0.784873\pi$
$564$	−58.0231	−	24.0339i	−2.44321	−	1.01201i
$565$		0			0
$566$	7.63822	−	18.4403i	0.321058	−	0.775104i
$567$	−9.73290	−	23.4973i	−0.408744	−	0.986794i
$568$	−6.11547	+	2.53311i	−0.256600	+	0.106287i
$569$	−8.48266	−	8.48266i	−0.355611	−	0.355611i	0.506581	−	0.862192i	$-0.330909\pi$
$569$	−8.48266	−	8.48266i	−0.355611	−	0.355611i	−0.862192	+	0.506581i	$0.830909\pi$
$570$		0			0
$571$	−16.6512	−	40.1996i	−0.696833	−	1.68230i	−0.730539	−	0.682871i	$-0.760731\pi$
$571$	−16.6512	−	40.1996i	−0.696833	−	1.68230i	0.0337061	−	0.999432i	$-0.489269\pi$
$572$	4.22561	+	10.2015i	0.176682	+	0.426548i
$573$	21.2586	+	8.80561i	0.888092	+	0.367860i
$574$			36.4371i			1.52085i
$575$		0			0
$576$	−4.54607	+	4.54607i	−0.189420	+	0.189420i
$577$		−	27.7097i		−	1.15357i	−0.816897	−	0.576784i	$-0.804307\pi$
$577$		−	27.7097i		−	1.15357i	0.816897	−	0.576784i	$-0.195693\pi$
$578$	39.9380	+	1.88222i	1.66120	+	0.0782900i
$579$	13.1764			0.547591
$580$		0			0
$581$	−24.2111	−	10.0286i	−1.00445	−	0.416055i
$582$	−36.2467			−1.50247
$583$	13.0539	+	5.40709i	0.540636	+	0.223939i
$584$	−18.2107	+	7.54311i	−0.753563	+	0.312136i
$585$		0			0
$586$	−43.2181	−	43.2181i	−1.78532	−	1.78532i
$587$	3.09653	−	3.09653i	0.127808	−	0.127808i	−0.640309	−	0.768117i	$-0.721194\pi$
$587$	3.09653	−	3.09653i	0.127808	−	0.127808i	0.768117	+	0.640309i	$0.221194\pi$
$588$	29.8590	−	12.3680i	1.23137	−	0.510048i
$589$	8.20624	−	3.39914i	0.338132	−	0.140059i
$590$		0			0
$591$			10.4856i			0.431320i
$592$	2.47976	−	5.98668i	0.101918	−	0.246051i
$593$	25.3698	+	25.3698i	1.04181	+	1.04181i	0.999087	+	0.0427255i	$0.0136041\pi$
$593$	25.3698	+	25.3698i	1.04181	+	1.04181i	0.0427255	+	0.999087i	$0.486396\pi$
$594$	−32.4114			−1.32985
$595$		0			0
$596$	65.4673			2.68164
$597$	20.9420	+	20.9420i	0.857099	+	0.857099i
$598$	−10.0128	+	24.1730i	−0.409454	+	0.988509i
$599$			11.1415i			0.455230i	0.973751	+	0.227615i	$0.0730928\pi$
$599$			11.1415i			0.455230i	−0.973751	+	0.227615i	$0.926907\pi$
$600$		0			0
$601$	18.8938	−	7.82606i	0.770693	−	0.319232i	0.0375402	−	0.999295i	$-0.488048\pi$
$601$	18.8938	−	7.82606i	0.770693	−	0.319232i	0.733153	+	0.680063i	$0.238048\pi$
$602$	58.7437	−	24.3324i	2.39421	−	0.991716i
$603$	2.74712	−	2.74712i	0.111871	−	0.111871i
$604$	−22.2558	−	22.2558i	−0.905574	−	0.905574i
$605$		0			0
$606$	−18.6328	+	7.71795i	−0.756905	+	0.313520i
$607$	−1.45561	−	0.602934i	−0.0590814	−	0.0244723i	0.352947	−	0.935643i	$-0.385180\pi$
$607$	−1.45561	−	0.602934i	−0.0590814	−	0.0244723i	−0.412028	+	0.911171i	$0.635180\pi$
$608$	−14.1435			−0.573593
$609$	45.4925	+	18.8436i	1.84345	+	0.763582i
$610$		0			0
$611$	−14.2727			−0.577410
$612$	−7.15321	−	3.16227i	−0.289151	−	0.127827i
$613$		−	22.4800i		−	0.907959i	−0.891012	−	0.453980i	$-0.850004\pi$
$613$		−	22.4800i		−	0.907959i	0.891012	−	0.453980i	$-0.149996\pi$
$614$	−28.1845	+	28.1845i	−1.13743	+	1.13743i
$615$		0			0
$616$		−	32.0307i		−	1.29055i
$617$	−25.1273	−	10.4081i	−1.01159	−	0.419013i	−0.185554	−	0.982634i	$-0.559408\pi$
$617$	−25.1273	−	10.4081i	−1.01159	−	0.419013i	−0.826034	+	0.563621i	$0.809408\pi$
$618$	−10.1143	−	24.4181i	−0.406858	−	0.982241i
$619$	−5.49924	−	13.2763i	−0.221033	−	0.533621i	0.773998	−	0.633188i	$-0.218254\pi$
$619$	−5.49924	−	13.2763i	−0.221033	−	0.533621i	−0.995031	+	0.0995671i	$0.968254\pi$
$620$		0			0
$621$	−34.6706	−	34.6706i	−1.39128	−	1.39128i
$622$	37.3527	−	15.4720i	1.49771	−	0.620371i
$623$	−3.00689	−	7.25927i	−0.120469	−	0.290837i
$624$	−1.06517	+	2.57154i	−0.0426408	+	0.102944i
$625$		0			0
$626$	−12.8523	−	5.32358i	−0.513680	−	0.212773i
$627$	−10.0123	−	10.0123i	−0.399852	−	0.399852i
$628$		−	64.4228i		−	2.57075i
$629$	−18.9674	−	0.446705i	−0.756280	−	0.0178113i
$630$		0			0
$631$	−16.4538	+	16.4538i	−0.655014	+	0.655014i	−0.954196	−	0.299182i	$-0.903286\pi$
$631$	−16.4538	+	16.4538i	−0.655014	+	0.655014i	0.299182	+	0.954196i	$0.403286\pi$
$632$	12.4544	−	30.0675i	0.495408	−	1.19602i
$633$	10.3887			0.412913
$634$	0.576538	−	1.39189i	0.0228972	−	0.0552788i
$635$		0			0
$636$	12.0706	+	29.1411i	0.478632	+	1.15552i
$637$	5.19356	−	5.19356i	0.205776	−	0.205776i
$638$	36.1638	−	36.1638i	1.43174	−	1.43174i
$639$	−0.377764	−	0.912004i	−0.0149441	−	0.0360783i
$640$		0			0
$641$	−2.06038	+	4.97419i	−0.0813800	+	0.196469i	−0.959332	−	0.282280i	$-0.908909\pi$
$641$	−2.06038	+	4.97419i	−0.0813800	+	0.196469i	0.877952	+	0.478748i	$0.158909\pi$
$642$	−2.30004			−0.0907754
$643$	−6.19532	+	14.9568i	−0.244319	+	0.589839i	−0.997703	−	0.0677421i	$-0.978420\pi$
$643$	−6.19532	+	14.9568i	−0.244319	+	0.589839i	0.753383	+	0.657582i	$0.228420\pi$
$644$	79.0101	−	79.0101i	3.11343	−	3.11343i
$645$		0			0
$646$	−12.7163	−	32.8683i	−0.500318	−	1.29319i
$647$			25.8383i			1.01581i	0.861413	+	0.507904i	$0.169580\pi$
$647$			25.8383i			1.01581i	−0.861413	+	0.507904i	$0.830420\pi$
$648$	−18.0829	−	18.0829i	−0.710362	−	0.710362i
$649$	−10.2525	−	4.24672i	−0.402445	−	0.166698i
$650$		0			0
$651$	5.25783	−	12.6935i	0.206071	−	0.497499i
$652$	12.6562	+	30.5548i	0.495656	+	1.19662i
$653$	11.5286	−	4.77529i	0.451148	−	0.186872i	−0.145528	−	0.989354i	$-0.546488\pi$
$653$	11.5286	−	4.77529i	0.451148	−	0.186872i	0.596675	+	0.802483i	$0.296488\pi$
$654$	16.1540	+	16.1540i	0.631672	+	0.631672i
$655$		0			0
$656$	2.33072	+	5.62685i	0.0909992	+	0.219691i
$657$	−1.12491	−	2.71577i	−0.0438868	−	0.105952i
$658$	88.2040	+	36.5353i	3.43855	+	1.42429i
$659$		−	41.7109i		−	1.62483i	−0.583082	−	0.812413i	$-0.698153\pi$
$659$		−	41.7109i		−	1.62483i	0.583082	−	0.812413i	$-0.301847\pi$
$660$		0			0
$661$	−12.8495	+	12.8495i	−0.499789	+	0.499789i	−0.911372	−	0.411583i	$-0.864976\pi$
$661$	−12.8495	+	12.8495i	−0.499789	+	0.499789i	0.411583	+	0.911372i	$0.364976\pi$
$662$			27.4252i			1.06591i
$663$	8.14734	+	0.191880i	0.316417	+	0.00745199i
$664$	−26.3499			−1.02257
$665$		0			0
$666$	5.37063	+	2.22459i	0.208108	+	0.0862011i
$667$	77.3693			2.99575
$668$	−30.2815	−	12.5430i	−1.17163	−	0.485304i
$669$	4.26653	−	1.76726i	0.164954	−	0.0683260i
$670$		0			0
$671$	0.426350	+	0.426350i	0.0164590	+	0.0164590i
$672$	−15.4696	+	15.4696i	−0.596753	+	0.596753i
$673$	−5.90984	+	2.44794i	−0.227808	+	0.0943610i	−0.493668	−	0.869651i	$-0.664344\pi$
$673$	−5.90984	+	2.44794i	−0.227808	+	0.0943610i	0.265860	+	0.964012i	$0.414344\pi$
$674$	−67.0997	+	27.7936i	−2.58458	+	1.07057i
$675$		0			0
$676$		−	40.3069i		−	1.55026i
$677$	−16.0301	+	38.7001i	−0.616087	+	1.48737i	0.240125	+	0.970742i	$0.422811\pi$
$677$	−16.0301	+	38.7001i	−0.616087	+	1.48737i	−0.856212	+	0.516624i	$0.827189\pi$
$678$	−41.9140	−	41.9140i	−1.60970	−	1.60970i
$679$	35.1779			1.35000
$680$		0			0
$681$	33.7812			1.29450
$682$	−10.0906	−	10.0906i	−0.386389	−	0.386389i
$683$	−11.5977	+	27.9994i	−0.443775	+	1.07137i	0.530838	+	0.847473i	$0.321877\pi$
$683$	−11.5977	+	27.9994i	−0.443775	+	1.07137i	−0.974613	+	0.223895i	$0.928123\pi$
$684$			6.89384i			0.263593i
$685$		0			0
$686$	9.09419	−	3.76694i	0.347218	−	0.143822i
$687$	−17.3130	+	7.17126i	−0.660530	+	0.273601i
$688$	7.51514	−	7.51514i	0.286512	−	0.286512i
$689$	5.06869	+	5.06869i	0.193102	+	0.193102i
$690$		0			0
$691$	5.35185	−	2.21681i	0.203594	−	0.0843314i	−0.278556	−	0.960420i	$-0.589856\pi$
$691$	5.35185	−	2.21681i	0.203594	−	0.0843314i	0.482150	+	0.876088i	$0.339856\pi$
$692$	14.0286	+	5.81083i	0.533287	+	0.220895i
$693$	4.77676			0.181454
$694$	0.0325913	+	0.0134997i	0.00123715	+	0.000512443i
$695$		0			0
$696$	49.5113			1.87672
$697$	12.9027	−	12.3090i	0.488726	−	0.466236i
$698$		−	8.59600i		−	0.325363i
$699$	−11.1732	+	11.1732i	−0.422611	+	0.422611i
$700$		0			0
$701$		−	5.24783i		−	0.198208i	−0.995077	−	0.0991039i	$-0.968402\pi$
$701$		−	5.24783i		−	0.198208i	0.995077	−	0.0991039i	$-0.0315976\pi$
$702$	−15.1914	−	6.29250i	−0.573364	−	0.237495i
$703$	6.39979	+	15.4505i	0.241373	+	0.582726i
$704$	11.3713	+	27.4527i	0.428572	+	1.03466i
$705$		0			0
$706$	6.35837	+	6.35837i	0.239300	+	0.239300i
$707$	18.0833	−	7.49037i	0.680094	−	0.281704i
$708$	−9.48025	−	22.8873i	−0.356290	−	0.860159i
$709$	−15.9798	+	38.5786i	−0.600134	+	1.44885i	0.273310	+	0.961926i	$0.411882\pi$
$709$	−15.9798	+	38.5786i	−0.600134	+	1.44885i	−0.873444	+	0.486925i	$0.838118\pi$
$710$		0			0
$711$	4.48398	+	1.85733i	0.168162	+	0.0696551i
$712$	−5.58654	−	5.58654i	−0.209364	−	0.209364i
$713$		−	21.5879i		−	0.808475i
$714$	−49.8588	−	22.0414i	−1.86592	−	0.824880i
$715$		0			0
$716$	−0.293855	+	0.293855i	−0.0109819	+	0.0109819i
$717$	9.98458	−	24.1049i	0.372881	−	0.900214i
$718$	−15.7501			−0.587789
$719$	−3.89643	+	9.40681i	−0.145312	+	0.350815i	−0.979731	−	0.200316i	$-0.935803\pi$
$719$	−3.89643	+	9.40681i	−0.145312	+	0.350815i	0.834419	+	0.551130i	$0.185803\pi$
$720$		0			0
$721$	9.81608	+	23.6981i	0.365570	+	0.882564i
$722$	9.63199	−	9.63199i	0.358465	−	0.358465i
$723$	6.57164	−	6.57164i	0.244402	−	0.244402i
$724$	−3.14022	−	7.58117i	−0.116705	−	0.281752i
$725$		0			0
$726$	6.83172	−	16.4932i	0.253549	−	0.612121i
$727$	46.0182			1.70672			0.853361	−	0.521321i	$-0.174561\pi$
$727$	46.0182			1.70672			0.853361	+	0.521321i	$0.174561\pi$
$728$	6.21860	−	15.0130i	0.230477	−	0.556420i
$729$	21.1766	−	21.1766i	0.784317	−	0.784317i
$730$		0			0
$731$	−28.4609	−	12.5819i	−1.05266	−	0.465358i
$732$			1.34601i			0.0497498i
$733$	−1.80962	−	1.80962i	−0.0668398	−	0.0668398i	0.672897	−	0.739736i	$-0.265050\pi$
$733$	−1.80962	−	1.80962i	−0.0668398	−	0.0668398i	−0.739736	+	0.672897i	$0.765050\pi$
$734$	50.0360	+	20.7256i	1.84686	+	0.764996i
$735$		0			0
$736$	−13.1546	+	31.7580i	−0.484885	+	1.17062i
$737$	−6.87149	−	16.5892i	−0.253114	−	0.611072i
$738$	−5.04783	+	2.09088i	−0.185813	+	0.0769664i
$739$	−1.75127	−	1.75127i	−0.0644215	−	0.0644215i	0.674162	−	0.738583i	$-0.264505\pi$
$739$	−1.75127	−	1.75127i	−0.0644215	−	0.0644215i	−0.738583	+	0.674162i	$0.764505\pi$
$740$		0			0
$741$	−2.74899	−	6.63666i	−0.100987	−	0.243804i
$742$	−18.3492	−	44.2989i	−0.673621	−	1.62627i
$743$	1.47337	+	0.610291i	0.0540528	+	0.0223894i	0.409546	−	0.912289i	$-0.365687\pi$
$743$	1.47337	+	0.610291i	0.0540528	+	0.0223894i	−0.355493	+	0.934679i	$0.615687\pi$
$744$		−	13.8149i		−	0.506478i
$745$		0			0
$746$	−39.4646	+	39.4646i	−1.44490	+	1.44490i
$747$		−	3.92957i		−	0.143776i
$748$	−26.1551	+	24.9515i	−0.956326	+	0.912317i
$749$	2.23222			0.0815636
$750$		0			0
$751$	11.7741	+	4.87697i	0.429641	+	0.177963i	0.587015	−	0.809576i	$-0.300303\pi$
$751$	11.7741	+	4.87697i	0.429641	+	0.177963i	−0.157374	+	0.987539i	$0.550303\pi$
$752$	15.9580			0.581930
$753$	11.2696	+	4.66801i	0.410686	+	0.170112i
$754$	23.9713	−	9.92922i	0.872982	−	0.361601i
$755$		0			0
$756$	49.6535	+	49.6535i	1.80588	+	1.80588i
$757$	−32.5674	+	32.5674i	−1.18368	+	1.18368i	−0.204901	+	0.978783i	$0.565687\pi$
$757$	−32.5674	+	32.5674i	−1.18368	+	1.18368i	−0.978783	+	0.204901i	$0.934313\pi$
$758$	6.47123	−	2.68047i	0.235046	−	0.0973592i
$759$	−31.7940	+	13.1695i	−1.15405	+	0.478023i
$760$		0			0
$761$		−	29.7003i		−	1.07664i	−0.842742	−	0.538318i	$-0.819060\pi$
$761$		−	29.7003i		−	1.07664i	0.842742	−	0.538318i	$-0.180940\pi$
$762$	−8.35879	+	20.1799i	−0.302807	+	0.731041i
$763$	−15.6777	−	15.6777i	−0.567571	−	0.567571i
$764$	−51.7788			−1.87329
$765$		0			0
$766$	−57.4385			−2.07534
$767$	−3.98093	−	3.98093i	−0.143743	−	0.143743i
$768$	−14.3913	+	34.7437i	−0.519301	+	1.25370i
$769$			43.8299i			1.58055i	0.612755	+	0.790273i	$0.290061\pi$
$769$			43.8299i			1.58055i	−0.612755	+	0.790273i	$0.709939\pi$
$770$		0			0
$771$	11.6946	−	4.84408i	0.421172	−	0.174455i
$772$	−27.3932	+	11.3466i	−0.985904	+	0.408375i
$773$	−19.7369	+	19.7369i	−0.709887	+	0.709887i	−0.966511	−	0.256624i	$-0.917390\pi$
$773$	−19.7369	+	19.7369i	−0.709887	+	0.709887i	0.256624	+	0.966511i	$0.417390\pi$
$774$	6.74182	+	6.74182i	0.242330	+	0.242330i
$775$		0			0
$776$	32.6787	−	13.5359i	1.17310	−	0.485912i
$777$	23.8990	+	9.89930i	0.857372	+	0.355135i
$778$	−3.97159			−0.142388
$779$	−14.5218	−	6.01513i	−0.520298	−	0.215515i
$780$		0			0
$781$	−4.56247			−0.163258
$782$	−85.6304	−	2.01670i	−3.06214	−	0.0721170i
$783$			48.6224i			1.73762i
$784$	−5.80684	+	5.80684i	−0.207387	+	0.207387i
$785$		0			0
$786$			59.5010i			2.12233i
$787$	−27.7373	−	11.4892i	−0.988728	−	0.409544i	−0.171076	−	0.985258i	$-0.554724\pi$
$787$	−27.7373	−	11.4892i	−0.988728	−	0.409544i	−0.817652	+	0.575713i	$0.804724\pi$
$788$	−9.02954	−	21.7992i	−0.321664	−	0.776566i
$789$	12.8071	+	30.9192i	0.455946	+	1.10075i
$790$		0			0
$791$	40.6781	+	40.6781i	1.44635	+	1.44635i
$792$	4.43740	−	1.83803i	0.157676	−	0.0653115i
$793$	0.117060	+	0.282607i	0.00415691	+	0.0100357i
$794$	28.3741	−	68.5012i	1.00696	−	2.43102i
$795$		0			0
$796$	−61.5717	−	25.5038i	−2.18235	−	0.903959i
$797$	−3.65013	−	3.65013i	−0.129294	−	0.129294i	0.639498	−	0.768793i	$-0.279142\pi$
$797$	−3.65013	−	3.65013i	−0.129294	−	0.129294i	−0.768793	+	0.639498i	$0.779142\pi$
$798$			48.0509i			1.70099i
$799$	−16.8591	−	43.5761i	−0.596432	−	1.54161i
$800$		0			0
$801$	0.833123	−	0.833123i	0.0294370	−	0.0294370i
$802$	4.55963	−	11.0079i	0.161006	−	0.388704i
$803$	−13.5861			−0.479445
$804$	15.3397	−	37.0333i	0.540990	−	1.30606i
$805$		0			0
$806$	−2.77050	−	6.68857i	−0.0975866	−	0.235595i
$807$	−4.66278	+	4.66278i	−0.164138	+	0.164138i
$808$	13.9164	−	13.9164i	0.489579	−	0.489579i
$809$	−8.50871	−	20.5418i	−0.299150	−	0.722213i	−0.999961	−	0.00886509i	$-0.997178\pi$
$809$	−8.50871	−	20.5418i	−0.299150	−	0.722213i	0.700810	−	0.713348i	$-0.252822\pi$
$810$		0			0
$811$	−5.99450	+	14.4720i	−0.210495	+	0.508181i	−0.993500	−	0.113836i	$-0.963686\pi$
$811$	−5.99450	+	14.4720i	−0.210495	+	0.508181i	0.783004	+	0.622016i	$0.213686\pi$
$812$	−110.804			−3.88847
$813$	−14.8421	+	35.8320i	−0.520535	+	1.25668i
$814$	18.9983	−	18.9983i	0.665889	−	0.665889i
$815$		0			0
$816$	−9.10941	−	0.214537i	−0.318893	−	0.00751031i
$817$			27.4289i			0.959615i
$818$	−43.4351	−	43.4351i	−1.51867	−	1.51867i
$819$	2.23890	+	0.927383i	0.0782335	+	0.0324054i
$820$		0			0
$821$	13.3707	−	32.2797i	0.466640	−	1.12657i	−0.498981	−	0.866613i	$-0.666292\pi$
$821$	13.3707	−	32.2797i	0.466640	−	1.12657i	0.965621	−	0.259955i	$-0.0837077\pi$
$822$	−24.1984	−	58.4201i	−0.844017	−	2.03764i
$823$	−2.25811	+	0.935339i	−0.0787127	+	0.0326039i	−0.421692	−	0.906739i	$-0.638564\pi$
$823$	−2.25811	+	0.935339i	−0.0787127	+	0.0326039i	0.342980	+	0.939343i	$0.388564\pi$
$824$	18.2374	+	18.2374i	0.635330	+	0.635330i
$825$		0			0
$826$	14.4114	+	34.7923i	0.501438	+	1.21058i
$827$	19.4487	+	46.9533i	0.676298	+	1.63273i	0.770703	+	0.637194i	$0.219905\pi$
$827$	19.4487	+	46.9533i	0.676298	+	1.63273i	−0.0944054	+	0.995534i	$0.530095\pi$
$828$	15.4796	+	6.41185i	0.537952	+	0.222827i
$829$		−	41.5846i		−	1.44429i	−0.691740	−	0.722147i	$-0.743156\pi$
$829$		−	41.5846i		−	1.44429i	0.691740	−	0.722147i	$-0.256844\pi$
$830$		0			0
$831$	−22.2635	+	22.2635i	−0.772313	+	0.772313i
$832$			15.0750i			0.522631i
$833$	21.9913	+	9.72184i	0.761952	+	0.336842i
$834$	7.87308			0.272623
$835$		0			0
$836$	29.4371	+	12.1933i	1.01810	+	0.421713i
$837$	13.5668			0.468939
$838$	15.8588	+	6.56894i	0.547834	+	0.226920i
$839$	−4.10912	+	1.70205i	−0.141863	+	0.0587614i	−0.452485	−	0.891772i	$-0.649462\pi$
$839$	−4.10912	+	1.70205i	−0.141863	+	0.0587614i	0.310623	+	0.950533i	$0.399462\pi$
$840$		0			0
$841$	−33.7456	−	33.7456i	−1.16364	−	1.16364i
$842$	−35.0311	+	35.0311i	−1.20725	+	1.20725i
$843$	36.5090	−	15.1225i	1.25744	−	0.520848i
$844$	−21.5977	+	8.94607i	−0.743424	+	0.307936i
$845$		0			0
$846$			14.3159i			0.492191i
$847$	−6.63027	+	16.0069i	−0.227819	+	0.550004i
$848$	−5.66721	−	5.66721i	−0.194613	−	0.194613i
$849$	13.3184			0.457088
$850$		0			0
$851$	40.6451			1.39330
$852$	−7.20198	−	7.20198i	−0.246736	−	0.246736i
$853$	−6.84491	+	16.5251i	−0.234365	+	0.565808i	−0.996682	−	0.0813967i	$-0.974062\pi$
$853$	−6.84491	+	16.5251i	−0.234365	+	0.565808i	0.762317	+	0.647204i	$0.224062\pi$
$854$		−	2.04614i		−	0.0700174i
$855$		0			0
$856$	2.07363	−	0.858928i	0.0708754	−	0.0293575i
$857$	35.6234	−	14.7557i	1.21687	−	0.504045i	0.320458	−	0.947263i	$-0.396163\pi$
$857$	35.6234	−	14.7557i	1.21687	−	0.504045i	0.896414	+	0.443218i	$0.146163\pi$
$858$	−8.16060	+	8.16060i	−0.278598	+	0.278598i
$859$	−2.48184	−	2.48184i	−0.0846792	−	0.0846792i	0.663498	−	0.748178i	$-0.269071\pi$
$859$	−2.48184	−	2.48184i	−0.0846792	−	0.0846792i	−0.748178	+	0.663498i	$0.769071\pi$
$860$		0			0
$861$	−22.4626	+	9.30430i	−0.765522	+	0.317090i
$862$	45.7243	+	18.9396i	1.55738	+	0.645086i
$863$	21.9552			0.747365			0.373683	−	0.927557i	$-0.378095\pi$
$863$	21.9552			0.747365			0.373683	+	0.927557i	$0.378095\pi$
$864$	−19.9582	−	8.26695i	−0.678991	−	0.281247i
$865$		0			0
$866$	−87.3171			−2.96715
$867$	9.03793	+	25.1014i	0.306944	+	0.852490i
$868$			30.9171i			1.04940i
$869$	15.8618	−	15.8618i	0.538075	−	0.538075i
$870$		0			0
$871$		−	9.10956i		−	0.308666i
$872$	−20.5964	−	8.53133i	−0.697484	−	0.288907i
$873$	2.01862	+	4.87339i	0.0683200	+	0.164939i
$874$	28.8925	+	69.7528i	0.977305	+	2.35942i
$875$		0			0
$876$	−21.4461	−	21.4461i	−0.724596	−	0.724596i
$877$	5.22542	−	2.16444i	0.176450	−	0.0730879i	−0.292710	−	0.956201i	$-0.594557\pi$
$877$	5.22542	−	2.16444i	0.176450	−	0.0730879i	0.469159	+	0.883113i	$0.344557\pi$
$878$	0.424209	+	1.02413i	0.0143164	+	0.0345628i
$879$	15.6071	−	37.6788i	0.526413	−	1.27087i
$880$		0			0
$881$	31.7736	+	13.1611i	1.07048	+	0.443407i	0.847160	−	0.531338i	$-0.178311\pi$
$881$	31.7736	+	13.1611i	1.07048	+	0.443407i	0.223320	+	0.974745i	$0.428311\pi$
$882$	−5.20930	−	5.20930i	−0.175406	−	0.175406i
$883$		−	58.3115i		−	1.96234i	−0.193148	−	0.981170i	$-0.561870\pi$
$883$		−	58.3115i		−	1.96234i	0.193148	−	0.981170i	$-0.438130\pi$
$884$	−17.1033	+	6.61706i	−0.575246	+	0.222556i
$885$		0			0
$886$	−18.3349	+	18.3349i	−0.615973	+	0.615973i
$887$	17.0299	−	41.1137i	0.571807	−	1.38046i	−0.328208	−	0.944605i	$-0.606445\pi$
$887$	17.0299	−	41.1137i	0.571807	−	1.38046i	0.900015	−	0.435859i	$-0.143555\pi$
$888$	26.0102			0.872846
$889$	8.11232	−	19.5849i	0.272078	−	0.656855i
$890$		0			0
$891$	−6.74540	−	16.2848i	−0.225979	−	0.545563i
$892$	−7.34813	+	7.34813i	−0.246034	+	0.246034i
$893$	−29.1220	+	29.1220i	−0.974529	+	0.974529i
$894$	26.1849	+	63.2159i	0.875754	+	2.11426i
$895$		0			0
$896$	27.9196	−	67.4038i	0.932727	−	2.25180i
$897$	−17.4589			−0.582935
$898$	−15.5375	+	37.5109i	−0.518494	+	1.25175i
$899$	−15.1376	+	15.1376i	−0.504866	+	0.504866i
$900$		0			0
$901$	−9.48808	+	21.4625i	−0.316094	+	0.715019i
$902$			25.2527i			0.840824i
$903$	30.0007	+	30.0007i	0.998361	+	0.998361i
$904$	53.4405	+	22.1358i	1.77740	+	0.736225i
$905$		0			0
$906$	12.5888	−	30.3920i	0.418234	−	1.00971i
$907$	13.5365	+	32.6800i	0.449472	+	1.08512i	0.972520	+	0.232819i	$0.0747949\pi$
$907$	13.5365	+	32.6800i	0.449472	+	1.08512i	−0.523048	+	0.852303i	$0.675205\pi$
$908$	−70.2301	+	29.0903i	−2.33067	+	0.965394i
$909$	2.07537	+	2.07537i	0.0688355	+	0.0688355i
$910$		0			0
$911$	−18.8207	−	45.4373i	−0.623559	−	1.50540i	−0.847496	−	0.530801i	$-0.821891\pi$
$911$	−18.8207	−	45.4373i	−0.623559	−	1.50540i	0.223937	−	0.974604i	$-0.428109\pi$
$912$	3.07361	+	7.42034i	0.101777	+	0.245712i
$913$	−16.7795	−	6.95031i	−0.555322	−	0.230022i
$914$		−	26.5004i		−	0.876554i
$915$		0			0
$916$	29.8176	−	29.8176i	0.985202	−	0.985202i
$917$		−	57.7465i		−	1.90696i
$918$	1.26738	−	53.8140i	0.0418299	−	1.77613i
$919$	−49.6635			−1.63825			−0.819123	−	0.573618i	$-0.805540\pi$
$919$	−49.6635			−1.63825			−0.819123	+	0.573618i	$0.805540\pi$
$920$		0			0
$921$	−24.5720	−	10.1781i	−0.809676	−	0.335379i
$922$	−70.5747			−2.32425
$923$	−2.13846	−	0.885781i	−0.0703884	−	0.0291558i
$924$	45.5338	−	18.8607i	1.49795	−	0.620472i
$925$		0			0
$926$	28.5366	+	28.5366i	0.937770	+	0.937770i
$927$	−2.71975	+	2.71975i	−0.0893284	+	0.0893284i
$928$	31.4929	−	13.0448i	1.03381	−	0.428216i
$929$	31.5196	−	13.0558i	1.03412	−	0.428348i	0.199924	−	0.979811i	$-0.435930\pi$
$929$	31.5196	−	13.0558i	1.03412	−	0.428348i	0.834199	+	0.551463i	$0.185930\pi$
$930$		0			0
$931$		−	21.1939i		−	0.694601i
$932$	13.6071	−	32.8505i	0.445716	−	1.07605i
$933$	19.0762	+	19.0762i	0.624528	+	0.624528i
$934$	−62.5405			−2.04639
$935$		0			0
$936$	2.43668			0.0796455
$937$	27.2430	+	27.2430i	0.889991	+	0.889991i	0.994522	−	0.104530i	$-0.0333340\pi$
$937$	27.2430	+	27.2430i	0.889991	+	0.889991i	−0.104530	+	0.994522i	$0.533334\pi$
$938$	−23.3187	+	56.2964i	−0.761383	+	1.83814i
$939$		−	9.28250i		−	0.302923i
$940$		0			0
$941$	34.3095	−	14.2115i	1.11846	−	0.463280i	0.254615	−	0.967043i	$-0.418051\pi$
$941$	34.3095	−	14.2115i	1.11846	−	0.463280i	0.863842	+	0.503762i	$0.168051\pi$
$942$	62.2074	−	25.7671i	2.02683	−	0.839539i
$943$	−27.0130	+	27.0130i	−0.879665	+	0.879665i
$944$	4.45102	+	4.45102i	0.144868	+	0.144868i
$945$		0			0
$946$	40.7124	−	16.8636i	1.32367	−	0.548283i
$947$	2.06130	+	0.853817i	0.0669832	+	0.0277453i	0.415923	−	0.909400i	$-0.363458\pi$
$947$	2.06130	+	0.853817i	0.0669832	+	0.0277453i	−0.348940	+	0.937145i	$0.613458\pi$
$948$	50.0765			1.62641
$949$	−6.36792	−	2.63768i	−0.206712	−	0.0856227i
$950$		0			0
$951$	1.00528			0.0325986
$952$	53.1820	+	1.25250i	1.72364	+	0.0405938i
$953$			25.8280i			0.836651i	0.908297	+	0.418326i	$0.137383\pi$
$953$			25.8280i			0.836651i	−0.908297	+	0.418326i	$0.862617\pi$
$954$	5.08404	−	5.08404i	0.164602	−	0.164602i
$955$		0			0
$956$			58.7114i			1.89886i
$957$	31.5286	+	13.0596i	1.01918	+	0.422157i
$958$	−20.6199	−	49.7808i	−0.666198	−	1.60834i
$959$	23.4849	+	56.6975i	0.758366	+	1.83086i
$960$		0			0
$961$	−17.6966	−	17.6966i	−0.570857	−	0.570857i
$962$	12.5930	−	5.21621i	0.406016	−	0.168177i
$963$	0.128092	+	0.309242i	0.00412772	+	0.00996519i
$964$	−8.00314	+	19.3213i	−0.257764	+	0.622297i
$965$		0			0
$966$	107.895	+	44.6914i	3.47145	+	1.43792i
$967$	−22.2041	−	22.2041i	−0.714035	−	0.714035i	0.253341	−	0.967377i	$-0.418470\pi$
$967$	−22.2041	−	22.2041i	−0.714035	−	0.714035i	−0.967377	+	0.253341i	$0.918470\pi$
$968$			17.4209i			0.559930i
$969$	17.0153	−	16.2323i	0.546612	−	0.521457i
$970$		0			0
$971$	29.0808	−	29.0808i	0.933248	−	0.933248i	−0.0646590	−	0.997907i	$-0.520596\pi$
$971$	29.0808	−	29.0808i	0.933248	−	0.933248i	0.997907	+	0.0646590i	$0.0205960\pi$
$972$	−7.44709	+	17.9789i	−0.238865	+	0.576672i
$973$	−7.64093			−0.244957
$974$	−14.1427	+	34.1435i	−0.453161	+	1.09403i
$975$		0			0
$976$	−0.130882	−	0.315978i	−0.00418944	−	0.0101142i
$977$	−19.7205	+	19.7205i	−0.630916	+	0.630916i	−0.948298	−	0.317382i	$-0.897196\pi$
$977$	−19.7205	+	19.7205i	−0.630916	+	0.630916i	0.317382	+	0.948298i	$0.397196\pi$
$978$	−24.4420	+	24.4420i	−0.781569	+	0.781569i
$979$	−2.08393	−	5.03105i	−0.0666026	−	0.160793i
$980$		0			0
$981$	1.27228	−	3.07156i	0.0406208	−	0.0980673i
$982$	−2.02071			−0.0644836
$983$	21.6956	−	52.3778i	0.691982	−	1.67059i	−0.0487673	−	0.998810i	$-0.515529\pi$
$983$	21.6956	−	52.3778i	0.691982	−	1.67059i	0.740749	−	0.671782i	$-0.234471\pi$
$984$	−17.2866	+	17.2866i	−0.551075	+	0.551075i
$985$		0			0
$986$	58.6303	+	61.4585i	1.86717	+	1.95724i
$987$			63.7050i			2.02775i
$988$	11.4301	+	11.4301i	0.363641	+	0.363641i
$989$	61.5894	+	25.5112i	1.95843	+	0.811208i
$990$		0			0
$991$	−13.7333	+	33.1551i	−0.436252	+	1.05321i	0.540980	+	0.841035i	$0.318053\pi$
$991$	−13.7333	+	33.1551i	−0.436252	+	1.05321i	−0.977233	+	0.212171i	$0.931947\pi$
$992$	−3.63982	−	8.78730i	−0.115564	−	0.278997i
$993$	−16.9070	+	7.00310i	−0.536526	+	0.222237i
$994$	10.9481	+	10.9481i	0.347253	+	0.347253i
$995$		0			0
$996$	−15.5157	−	37.4581i	−0.491633	−	1.18691i
$997$	−12.6113	−	30.4465i	−0.399405	−	0.964249i	−0.987807	−	0.155681i	$-0.950243\pi$
$997$	−12.6113	−	30.4465i	−0.399405	−	0.964249i	0.588402	−	0.808568i	$-0.299757\pi$
$998$	−49.1930	−	20.3764i	−1.55718	−	0.645004i
$999$			25.5433i			0.808153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.c.349.1		24
5.2	odd	4		85.2.l.a.26.6	✓	24
5.3	odd	4		425.2.m.b.26.1		24
5.4	even	2		425.2.n.f.349.6		24
15.2	even	4		765.2.be.b.451.1		24
17.2	even	8		425.2.n.f.274.6		24
85.2	odd	8		85.2.l.a.36.6	yes	24
85.7	even	16		1445.2.d.j.866.1		24
85.19	even	8	inner	425.2.n.c.274.1		24
85.23	even	16		7225.2.a.bs.1.1		12
85.27	even	16		1445.2.d.j.866.2		24
85.28	even	16		7225.2.a.bq.1.1		12
85.53	odd	8		425.2.m.b.376.1		24
85.57	even	16		1445.2.a.p.1.12		12
85.62	even	16		1445.2.a.q.1.12		12
255.2	even	8		765.2.be.b.631.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.6	✓	24	5.2	odd	4
85.2.l.a.36.6	yes	24	85.2	odd	8
425.2.m.b.26.1		24	5.3	odd	4
425.2.m.b.376.1		24	85.53	odd	8
425.2.n.c.274.1		24	85.19	even	8	inner
425.2.n.c.349.1		24	1.1	even	1	trivial
425.2.n.f.274.6		24	17.2	even	8
425.2.n.f.349.6		24	5.4	even	2
765.2.be.b.451.1		24	15.2	even	4
765.2.be.b.631.1		24	255.2	even	8
1445.2.a.p.1.12		12	85.57	even	16
1445.2.a.q.1.12		12	85.62	even	16
1445.2.d.j.866.1		24	85.7	even	16
1445.2.d.j.866.2		24	85.27	even	16
7225.2.a.bq.1.1		12	85.28	even	16
7225.2.a.bs.1.1		12	85.23	even	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.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.66305 - 1.66305i) q^{2} +(0.600564 - 1.44989i) q^{3} +3.53144i q^{4} +(-3.41000 + 1.41247i) q^{6} +(3.30945 - 1.37082i) q^{7} +(2.54686 - 2.54686i) q^{8} +(0.379815 + 0.379815i) q^{9} +(2.29362 - 0.950048i) q^{11} +(5.12021 + 2.12086i) q^{12} +1.25948 q^{13} +(-7.78350 - 3.22403i) q^{14} -1.40821 q^{16} +(1.48772 + 3.84535i) q^{17} -1.26330i q^{18} +(2.56985 - 2.56985i) q^{19} -5.62161i q^{21} +(-5.39437 - 2.23442i) q^{22} +(-3.38021 - 8.16056i) q^{23} +(-2.16312 - 5.22222i) q^{24} +(-2.09458 - 2.09458i) q^{26} +(5.12847 - 2.12428i) q^{27} +(4.84097 + 11.6871i) q^{28} +(-3.35200 + 8.09244i) q^{29} +(2.25799 + 0.935290i) q^{31} +(-2.75181 - 2.75181i) q^{32} -3.89606i q^{33} +(3.92084 - 8.86913i) q^{34} +(-1.34129 + 1.34129i) q^{36} +(-1.76094 + 4.25128i) q^{37} -8.54755 q^{38} +(0.756400 - 1.82611i) q^{39} +(-1.65510 - 3.99575i) q^{41} +(-9.34899 + 9.34899i) q^{42} +(-5.33668 + 5.33668i) q^{43} +(3.35504 + 8.09978i) q^{44} +(-7.94993 + 19.1928i) q^{46} -11.3322 q^{47} +(-0.845719 + 2.04175i) q^{48} +(4.12357 - 4.12357i) q^{49} +(6.46880 + 0.152348i) q^{51} +4.44779i q^{52} +(4.02442 + 4.02442i) q^{53} +(-12.0616 - 4.99610i) q^{54} +(4.93742 - 11.9200i) q^{56} +(-2.18264 - 5.26936i) q^{57} +(19.0326 - 7.88357i) q^{58} +(-3.16077 - 3.16077i) q^{59} +(0.0929426 + 0.224383i) q^{61} +(-2.19971 - 5.31057i) q^{62} +(1.77764 + 0.736321i) q^{63} +11.9692i q^{64} +(-6.47933 + 6.47933i) q^{66} -7.23278i q^{67} +(-13.5796 + 5.25380i) q^{68} -13.8620 q^{69} +(-1.69789 - 0.703290i) q^{71} +1.93467 q^{72} +(-5.05599 - 2.09426i) q^{73} +(9.99859 - 4.14155i) q^{74} +(9.07527 + 9.07527i) q^{76} +(6.28827 - 6.28827i) q^{77} +(-4.29484 + 1.77898i) q^{78} +(8.34789 - 3.45781i) q^{79} -7.10006i q^{81} +(-3.89262 + 9.39762i) q^{82} +(-5.17302 - 5.17302i) q^{83} +19.8524 q^{84} +17.7503 q^{86} +(9.72006 + 9.72006i) q^{87} +(3.42189 - 8.26117i) q^{88} -2.19350i q^{89} +(4.16819 - 1.72652i) q^{91} +(28.8186 - 11.9370i) q^{92} +(2.71214 - 2.71214i) q^{93} +(18.8459 + 18.8459i) q^{94} +(-5.64246 + 2.33718i) q^{96} +(9.07286 + 3.75810i) q^{97} -13.7154 q^{98} +(1.23199 + 0.510308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} + 40 q^{12} + 16 q^{13} - 24 q^{16} + 8 q^{19} - 24 q^{22} + 8 q^{23} + 8 q^{24} + 16 q^{26} + 16 q^{27} - 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} - 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 + 40 * q^12 + 16 * q^13 - 24 * q^16 + 8 * q^19 - 24 * q^22 + 8 * q^23 + 8 * q^24 + 16 * q^26 + 16 * q^27 - 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 + 16 * q^41 - 24 * q^42 - 8 * q^43 - 16 * q^44 + 8 * q^46 - 64 * q^47 - 8 * q^48 - 56 * q^51 + 24 * q^53 + 32 * q^54 + 64 * q^56 + 16 * q^57 + 56 * q^58 - 32 * q^59 + 32 * q^61 - 32 * q^62 + 80 * q^63 + 96 * q^66 + 24 * q^68 - 96 * q^69 - 24 * q^71 - 24 * q^72 - 64 * q^73 + 64 * q^74 - 8 * q^76 + 24 * q^77 + 8 * q^78 - 16 * q^82 - 96 * q^83 + 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 + 112 * q^92 - 64 * q^93 - 56 * q^94 - 168 * q^96 + 48 * q^97 + 120 * q^98 + 8 * q^99

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