LMFDB - Embedded newform 475.2.j.b.349.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(49,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("475.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.j (of order $6$, degree $2$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.50712647503417344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 13x^{10} + 119x^{8} - 552x^{6} + 1863x^{4} - 2450x^{2} + 2401 $ x^12 - 13x^10 + 119x^8 - 552x^6 + 1863x^4 - 2450*x^2 + 2401
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.4
Root			$1.05818 - 0.610938i$ of defining polynomial
Character	$\chi$	$=$	475.349
Dual form			475.2.j.b.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05818 - 0.610938i) q^{2} +(-1.97899 + 1.14257i) q^{3} +(-0.253509 + 0.439091i) q^{4} +(-1.39608 + 2.41808i) q^{6} -1.28514i q^{7} +3.06327i q^{8} +(1.11094 - 1.92420i) q^{9} +O(q^{10})$	\(q+(1.05818 - 0.610938i) q^{2} +(-1.97899 + 1.14257i) q^{3} +(-0.253509 + 0.439091i) q^{4} +(-1.39608 + 2.41808i) q^{6} -1.28514i q^{7} +3.06327i q^{8} +(1.11094 - 1.92420i) q^{9} +0.285142 q^{11} -1.15861i q^{12} +(-4.33013 - 2.50000i) q^{13} +(-0.785142 - 1.35991i) q^{14} +(1.36445 + 2.36329i) q^{16} +(-5.40046 + 3.11796i) q^{17} -2.71486i q^{18} +(-2.92771 + 3.22932i) q^{19} +(1.46837 + 2.54329i) q^{21} +(0.301731 - 0.174204i) q^{22} +(-4.53443 - 2.61796i) q^{23} +(-3.50000 - 6.06218i) q^{24} -6.10938 q^{26} -1.77812i q^{27} +(0.564295 + 0.325796i) q^{28} +(0.642571 - 1.11297i) q^{29} -1.22188 q^{31} +(-2.41808 - 1.39608i) q^{32} +(-0.564295 + 0.325796i) q^{33} +(-3.80976 + 6.59869i) q^{34} +(0.563266 + 0.975606i) q^{36} +10.8695i q^{37} +(-1.12512 + 5.20584i) q^{38} +11.4257 q^{39} +(0.420695 + 0.728665i) q^{41} +(3.10758 + 1.79416i) q^{42} +(4.28749 - 2.47539i) q^{43} +(-0.0722863 + 0.125204i) q^{44} -6.39764 q^{46} +(-4.96137 - 2.86445i) q^{47} +(-5.40046 - 3.11796i) q^{48} +5.34841 q^{49} +(7.12498 - 12.3408i) q^{51} +(2.19546 - 1.26755i) q^{52} +(10.7062 + 6.18122i) q^{53} +(-1.08632 - 1.88157i) q^{54} +3.93673 q^{56} +(2.10419 - 9.73591i) q^{57} -1.57028i q^{58} +(2.86445 + 4.96137i) q^{59} +(-2.22889 + 3.86056i) q^{61} +(-1.29296 + 0.746491i) q^{62} +(-2.47287 - 1.42771i) q^{63} -8.86946 q^{64} +(-0.398082 + 0.689498i) q^{66} +(0.853869 + 0.492981i) q^{67} -3.16172i q^{68} +11.9648 q^{69} +(1.46135 + 2.53113i) q^{71} +(5.89434 + 3.40310i) q^{72} +(0.661718 - 0.382043i) q^{73} +(6.64057 + 11.5018i) q^{74} +(-0.675762 - 2.10419i) q^{76} -0.366449i q^{77} +(12.0904 - 6.98040i) q^{78} +(-7.72889 - 13.3868i) q^{79} +(5.36445 + 9.29150i) q^{81} +(0.890339 + 0.514037i) q^{82} -1.66563i q^{83} -1.48898 q^{84} +(3.02461 - 5.23879i) q^{86} +2.93673i q^{87} +0.873467i q^{88} +(-8.01404 + 13.8807i) q^{89} +(-3.21286 + 5.56483i) q^{91} +(2.29904 - 1.32735i) q^{92} +(2.41808 - 1.39608i) q^{93} -7.00000 q^{94} +6.38049 q^{96} +(10.1697 - 5.87147i) q^{97} +(5.65956 - 3.26755i) q^{98} +(0.316776 - 0.548672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 14 q^{4} + 12 q^{6} + 8 q^{9}+O(q^{10}) $ 12 * q + 14 * q^4 + 12 * q^6 + 8 * q^9	$ 12 q + 14 q^{4} + 12 q^{6} + 8 q^{9} - 20 q^{11} + 14 q^{14} - 6 q^{16} + 24 q^{21} - 42 q^{24} - 20 q^{26} - 4 q^{29} - 4 q^{31} - 50 q^{34} - 6 q^{36} + 20 q^{39} + 4 q^{41} - 36 q^{44} - 96 q^{46} + 28 q^{49} + 12 q^{51} + 20 q^{54} + 60 q^{56} + 12 q^{59} + 18 q^{61} + 32 q^{64} - 58 q^{66} + 20 q^{69} + 58 q^{71} - 14 q^{74} - 38 q^{76} - 48 q^{79} + 42 q^{81} + 112 q^{84} + 64 q^{86} - 28 q^{89} + 20 q^{91} - 84 q^{94} + 68 q^{96} - 26 q^{99}+O(q^{100}) $ 12 * q + 14 * q^4 + 12 * q^6 + 8 * q^9 - 20 * q^11 + 14 * q^14 - 6 * q^16 + 24 * q^21 - 42 * q^24 - 20 * q^26 - 4 * q^29 - 4 * q^31 - 50 * q^34 - 6 * q^36 + 20 * q^39 + 4 * q^41 - 36 * q^44 - 96 * q^46 + 28 * q^49 + 12 * q^51 + 20 * q^54 + 60 * q^56 + 12 * q^59 + 18 * q^61 + 32 * q^64 - 58 * q^66 + 20 * q^69 + 58 * q^71 - 14 * q^74 - 38 * q^76 - 48 * q^79 + 42 * q^81 + 112 * q^84 + 64 * q^86 - 28 * q^89 + 20 * q^91 - 84 * q^94 + 68 * q^96 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.05818	−	0.610938i	0.748243	−	0.431998i	−0.0768155	−	0.997045i	$-0.524475\pi$
$2$	1.05818	−	0.610938i	0.748243	−	0.431998i	0.825059	+	0.565047i	$0.191142\pi$
$3$	−1.97899	+	1.14257i	−1.14257	+	0.659664i	−0.947066	−	0.321039i	$-0.895968\pi$
$3$	−1.97899	+	1.14257i	−1.14257	+	0.659664i	−0.195505	+	0.980703i	$0.562635\pi$
$4$	−0.253509	+	0.439091i	−0.126755	+	0.219546i
$5$		0			0
$5$		0			0
$6$	−1.39608	+	2.41808i	−0.569948	+	0.987178i
$7$		−	1.28514i		−	0.485738i	−0.970059	−	0.242869i	$-0.921911\pi$
$7$		−	1.28514i		−	0.485738i	0.970059	−	0.242869i	$-0.0780886\pi$
$8$			3.06327i			1.08303i
$9$	1.11094	−	1.92420i	0.370313	−	0.641400i
$10$		0			0
$11$	0.285142			0.0859737			0.0429868	−	0.999076i	$-0.486313\pi$
$11$	0.285142			0.0859737			0.0429868	+	0.999076i	$0.486313\pi$
$12$		−	1.15861i		−	0.334462i
$13$	−4.33013	−	2.50000i	−1.20096	−	0.693375i	−0.240192	−	0.970725i	$-0.577210\pi$
$13$	−4.33013	−	2.50000i	−1.20096	−	0.693375i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	−0.785142	−	1.35991i	−0.209838	−	0.363450i
$15$		0			0
$16$	1.36445	+	2.36329i	0.341112	+	0.590823i
$17$	−5.40046	+	3.11796i	−1.30980	+	0.756216i	−0.982063	−	0.188552i	$-0.939621\pi$
$17$	−5.40046	+	3.11796i	−1.30980	+	0.756216i	−0.327741	+	0.944768i	$0.606287\pi$
$18$		−	2.71486i		−	0.639898i
$19$	−2.92771	+	3.22932i	−0.671664	+	0.740856i
$19$	−2.92771	+	3.22932i	−0.671664	+	0.740856i
$20$		0			0
$21$	1.46837	+	2.54329i	0.320424	+	0.554990i
$22$	0.301731	−	0.174204i	0.0643292	−	0.0371405i
$23$	−4.53443	−	2.61796i	−0.945495	−	0.545882i	−0.0538163	−	0.998551i	$-0.517139\pi$
$23$	−4.53443	−	2.61796i	−0.945495	−	0.545882i	−0.891679	+	0.452669i	$0.850472\pi$
$24$	−3.50000	−	6.06218i	−0.714435	−	1.23744i
$25$		0			0
$26$	−6.10938			−1.19815
$27$		−	1.77812i		−	0.342200i
$28$	0.564295	+	0.325796i	0.106642	+	0.0615696i
$29$	0.642571	−	1.11297i	0.119322	−	0.206673i	−0.800177	−	0.599764i	$-0.795261\pi$
$29$	0.642571	−	1.11297i	0.119322	−	0.206673i	0.919499	+	0.393091i	$0.128594\pi$
$30$		0			0
$31$	−1.22188			−0.219455			−0.109728	−	0.993962i	$-0.534998\pi$
$31$	−1.22188			−0.219455			−0.109728	+	0.993962i	$0.534998\pi$
$32$	−2.41808	−	1.39608i	−0.427461	−	0.246795i
$33$	−0.564295	+	0.325796i	−0.0982311	+	0.0567137i
$34$	−3.80976	+	6.59869i	−0.653368	+	1.13167i
$35$		0			0
$36$	0.563266	+	0.975606i	0.0938777	+	0.162601i
$37$			10.8695i			1.78693i	0.449134	+	0.893464i	$0.351733\pi$
$37$			10.8695i			1.78693i	−0.449134	+	0.893464i	$0.648267\pi$
$38$	−1.12512	+	5.20584i	−0.182519	+	0.844498i
$39$	11.4257			1.82958
$40$		0			0
$41$	0.420695	+	0.728665i	0.0657015	+	0.113798i	0.897005	−	0.442020i	$-0.145738\pi$
$41$	0.420695	+	0.728665i	0.0657015	+	0.113798i	−0.831303	+	0.555819i	$0.812405\pi$
$42$	3.10758	+	1.79416i	0.479510	+	0.276845i
$43$	4.28749	−	2.47539i	0.653837	−	0.377493i	−0.136088	−	0.990697i	$-0.543453\pi$
$43$	4.28749	−	2.47539i	0.653837	−	0.377493i	0.789925	+	0.613204i	$0.210120\pi$
$44$	−0.0722863	+	0.125204i	−0.0108976	+	0.0188751i
$45$		0			0
$46$	−6.39764			−0.943280
$47$	−4.96137	−	2.86445i	−0.723690	−	0.417823i	0.0924193	−	0.995720i	$-0.470540\pi$
$47$	−4.96137	−	2.86445i	−0.723690	−	0.417823i	−0.816109	+	0.577898i	$0.803873\pi$
$48$	−5.40046	−	3.11796i	−0.779489	−	0.450038i
$49$	5.34841			0.764058
$50$		0			0
$51$	7.12498	−	12.3408i	0.997696	−	1.72806i
$52$	2.19546	−	1.26755i	0.304455	−	0.175777i
$53$	10.7062	+	6.18122i	1.47061	+	0.849056i	0.999456	−	0.0329952i	$-0.0105046\pi$
$53$	10.7062	+	6.18122i	1.47061	+	0.849056i	0.471153	+	0.882051i	$0.343838\pi$
$54$	−1.08632	−	1.88157i	−0.147830	−	0.256049i
$55$		0			0
$56$	3.93673			0.526068
$57$	2.10419	−	9.73591i	0.278707	−	1.28955i
$58$		−	1.57028i		−	0.206189i
$59$	2.86445	+	4.96137i	0.372919	+	0.645915i	0.990013	−	0.140974i	$-0.0450235\pi$
$59$	2.86445	+	4.96137i	0.372919	+	0.645915i	−0.617094	+	0.786889i	$0.711690\pi$
$60$		0			0
$61$	−2.22889	+	3.86056i	−0.285381	+	0.494294i	−0.972701	−	0.232060i	$-0.925453\pi$
$61$	−2.22889	+	3.86056i	−0.285381	+	0.494294i	0.687321	+	0.726354i	$0.258787\pi$
$62$	−1.29296	+	0.746491i	−0.164206	+	0.0948044i
$63$	−2.47287	−	1.42771i	−0.311553	−	0.179875i
$64$	−8.86946			−1.10868
$65$		0			0
$66$	−0.398082	+	0.689498i	−0.0490005	+	0.0848713i
$67$	0.853869	+	0.492981i	0.104317	+	0.0602273i	0.551251	−	0.834340i	$-0.314151\pi$
$67$	0.853869	+	0.492981i	0.104317	+	0.0602273i	−0.446934	+	0.894567i	$0.647484\pi$
$68$		−	3.16172i		−	0.383415i
$69$	11.9648			1.44039
$70$		0			0
$71$	1.46135	+	2.53113i	0.173430	+	0.300390i	0.939617	−	0.342228i	$-0.111182\pi$
$71$	1.46135	+	2.53113i	0.173430	+	0.300390i	−0.766187	+	0.642618i	$0.777848\pi$
$72$	5.89434	+	3.40310i	0.694655	+	0.401059i
$73$	0.661718	−	0.382043i	0.0774483	−	0.0447148i	−0.460776	−	0.887517i	$-0.652429\pi$
$73$	0.661718	−	0.382043i	0.0774483	−	0.0447148i	0.538224	+	0.842802i	$0.319095\pi$
$74$	6.64057	+	11.5018i	0.771951	+	1.33706i
$75$		0			0
$76$	−0.675762	−	2.10419i	−0.0775152	−	0.241368i
$77$		−	0.366449i		−	0.0417607i
$78$	12.0904	−	6.98040i	1.36897	−	0.790375i
$79$	−7.72889	−	13.3868i	−0.869569	−	1.50614i	−0.862438	−	0.506162i	$-0.831064\pi$
$79$	−7.72889	−	13.3868i	−0.869569	−	1.50614i	−0.00713043	−	0.999975i	$-0.502270\pi$
$80$		0			0
$81$	5.36445	+	9.29150i	0.596050	+	1.03239i
$82$	0.890339	+	0.514037i	0.0983215	+	0.0567659i
$83$		−	1.66563i		−	0.182826i	−0.995813	−	0.0914132i	$-0.970862\pi$
$83$		−	1.66563i		−	0.182826i	0.995813	−	0.0914132i	$-0.0291384\pi$
$84$	−1.48898			−0.162461
$85$		0			0
$86$	3.02461	−	5.23879i	0.326153	−	0.564913i
$87$			2.93673i			0.314851i
$88$			0.873467i			0.0931119i
$89$	−8.01404	+	13.8807i	−0.849486	+	1.47135i	0.0321812	+	0.999482i	$0.489755\pi$
$89$	−8.01404	+	13.8807i	−0.849486	+	1.47135i	−0.881667	+	0.471871i	$0.843579\pi$
$90$		0			0
$91$	−3.21286	+	5.56483i	−0.336799	+	0.583353i
$92$	2.29904	−	1.32735i	0.239692	−	0.138386i
$93$	2.41808	−	1.39608i	0.250743	−	0.144767i
$94$	−7.00000			−0.721995
$95$		0			0
$96$	6.38049			0.651206
$97$	10.1697	−	5.87147i	1.03257	−	0.596157i	0.114853	−	0.993382i	$-0.463360\pi$
$97$	10.1697	−	5.87147i	1.03257	−	0.596157i	0.917721	+	0.397225i	$0.130027\pi$
$98$	5.65956	−	3.26755i	0.571702	−	0.330072i
$99$	0.316776	−	0.548672i	0.0318371	−	0.0551436i
$100$		0			0
$101$	3.95935	−	6.85779i	0.393970	−	0.682376i	−0.598999	−	0.800750i	$-0.704435\pi$
$101$	3.95935	−	6.85779i	0.393970	−	0.682376i	0.992969	+	0.118374i	$0.0377681\pi$
$102$		−	17.4117i		−	1.72401i
$103$			12.8202i			1.26322i	0.775288	+	0.631608i	$0.217605\pi$
$103$			12.8202i			1.26322i	−0.775288	+	0.631608i	$0.782395\pi$
$104$	7.65817	−	13.2643i	0.750945	−	1.30067i
$105$		0			0
$106$	15.1054			1.46716
$107$			13.8062i			1.33470i	0.744746	+	0.667348i	$0.232571\pi$
$107$			13.8062i			1.33470i	−0.744746	+	0.667348i	$0.767429\pi$
$108$	0.780758	+	0.450771i	0.0751285	+	0.0433755i
$109$	−4.60192	−	7.97076i	−0.440784	−	0.763460i	0.556964	−	0.830537i	$-0.311966\pi$
$109$	−4.60192	−	7.97076i	−0.440784	−	0.763460i	−0.997748	+	0.0670767i	$0.978633\pi$
$110$		0			0
$111$	−12.4191	−	21.5106i	−1.17877	−	2.04169i
$112$	3.03717	−	1.75351i	0.286985	−	0.165691i
$113$			17.3273i			1.63001i	0.579453	+	0.815005i	$0.303266\pi$
$113$			17.3273i			1.63001i	−0.579453	+	0.815005i	$0.696734\pi$
$114$	−3.72143	−	11.5878i	−0.348544	−	1.08530i
$115$		0			0
$116$	0.325796	+	0.564295i	0.0302494	+	0.0523934i
$117$	−9.62101	+	5.55469i	−0.889462	+	0.513531i
$118$	6.06218	+	3.50000i	0.558069	+	0.322201i
$119$	4.00702	+	6.94036i	0.367323	+	0.636222i
$120$		0			0
$121$	−10.9187			−0.992609
$122$			5.44687i			0.493136i
$123$	−1.66510	−	0.961348i	−0.150137	−	0.0866818i
$124$	0.309757	−	0.536515i	0.0278170	−	0.0481805i
$125$		0			0
$126$	−3.48898			−0.310823
$127$	−8.08111	−	4.66563i	−0.717082	−	0.414008i	0.0965956	−	0.995324i	$-0.469205\pi$
$127$	−8.08111	−	4.66563i	−0.717082	−	0.414008i	−0.813678	+	0.581316i	$0.802538\pi$
$128$	−4.54929	+	2.62653i	−0.402104	+	0.232155i
$129$	−5.65661	+	9.79753i	−0.498037	+	0.862625i
$130$		0			0
$131$	−6.21286	−	10.7610i	−0.542820	−	0.940191i	−0.998741	−	0.0501711i	$-0.984023\pi$
$131$	−6.21286	−	10.7610i	−0.542820	−	0.940191i	0.455921	−	0.890020i	$-0.349310\pi$
$132$		−	0.330369i		−	0.0287549i
$133$	4.15013	+	3.76253i	0.359862	+	0.326253i
$134$	1.20472			0.104072
$135$		0			0
$136$	−9.55113	−	16.5430i	−0.819003	−	1.41855i
$137$	16.0519	+	9.26755i	1.37140	+	0.791780i	0.991105	−	0.133084i	$-0.0424880\pi$
$137$	16.0519	+	9.26755i	1.37140	+	0.791780i	0.380298	+	0.924864i	$0.375821\pi$
$138$	12.6609	−	7.30976i	1.07776	−	0.622248i
$139$	−3.00702	+	5.20831i	−0.255052	+	0.441763i	−0.964910	−	0.262582i	$-0.915426\pi$
$139$	−3.00702	+	5.20831i	−0.255052	+	0.441763i	0.709858	+	0.704345i	$0.248759\pi$
$140$		0			0
$141$	13.0913			1.10249
$142$	3.09273	+	1.78559i	0.259536	+	0.149843i
$143$	−1.23470	−	0.712856i	−0.103251	−	0.0596120i
$144$	6.06327			0.505272
$145$		0			0
$146$	0.466810	−	0.808538i	0.0386334	−	0.0669151i
$147$	−10.5845	+	6.11094i	−0.872991	+	0.504022i
$148$	−4.77268	−	2.75551i	−0.392312	−	0.226502i
$149$	−3.39608	−	5.88218i	−0.278218	−	0.481887i	0.692724	−	0.721203i	$-0.256410\pi$
$149$	−3.39608	−	5.88218i	−0.278218	−	0.481887i	−0.970942	+	0.239315i	$0.923077\pi$
$150$		0			0
$151$	−15.8875			−1.29291			−0.646453	−	0.762953i	$-0.723749\pi$
$151$	−15.8875			−1.29291			−0.646453	+	0.762953i	$0.723749\pi$
$152$	−9.89226	−	8.96837i	−0.802368	−	0.727431i
$153$			13.8554i			1.12014i
$154$	−0.223877	−	0.387767i	−0.0180406	−	0.0312472i
$155$		0			0
$156$	−2.89652	+	5.01693i	−0.231908	+	0.401676i
$157$	6.50127	−	3.75351i	0.518858	−	0.299563i	−0.217609	−	0.976036i	$-0.569826\pi$
$157$	6.50127	−	3.75351i	0.518858	−	0.299563i	0.736467	+	0.676473i	$0.236493\pi$
$158$	−16.3571	−	9.44375i	−1.30130	−	0.751305i
$159$	−28.2500			−2.24037
$160$		0			0
$161$	−3.36445	+	5.82739i	−0.265156	+	0.459263i
$162$	11.3531	+	6.55469i	0.891980	+	0.514985i
$163$		−	21.8202i		−	1.70909i	−0.519375	−	0.854546i	$-0.673835\pi$
$163$		−	21.8202i		−	1.70909i	0.519375	−	0.854546i	$-0.326165\pi$
$164$	−0.426600			−0.0333119
$165$		0			0
$166$	−1.01760	−	1.76253i	−0.0789808	−	0.136799i
$167$	−9.77322	−	5.64257i	−0.756274	−	0.436635i	0.0716821	−	0.997428i	$-0.477163\pi$
$167$	−9.77322	−	5.64257i	−0.756274	−	0.436635i	−0.827957	+	0.560792i	$0.810497\pi$
$168$	−7.79076	+	4.49800i	−0.601070	+	0.347028i
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$	2.96135	+	9.22108i	0.226460	+	0.705154i
$172$			2.51013i			0.191396i
$173$	5.07095	−	2.92771i	0.385537	−	0.222590i	−0.294688	−	0.955594i	$-0.595216\pi$
$173$	5.07095	−	2.92771i	0.385537	−	0.222590i	0.680225	+	0.733004i	$0.261882\pi$
$174$	1.79416	+	3.10758i	0.136015	+	0.235585i
$175$		0			0
$176$	0.389062	+	0.673875i	0.0293266	+	0.0507952i
$177$	−11.3374	−	6.54567i	−0.852174	−	0.492003i
$178$			19.5843i			1.46791i
$179$	18.7922			1.40459			0.702296	−	0.711885i	$-0.252158\pi$
$179$	18.7922			1.40459			0.702296	+	0.711885i	$0.252158\pi$
$180$		0			0
$181$	−6.67265	+	11.5574i	−0.495974	+	0.859052i	−0.999989	−	0.00464265i	$-0.998522\pi$
$181$	−6.67265	+	11.5574i	−0.495974	+	0.859052i	0.504015	+	0.863695i	$0.331856\pi$
$182$			7.85142i			0.581986i
$183$		−	10.1867i		−	0.753021i
$184$	8.01950	−	13.8902i	0.591205	−	1.02400i
$185$		0			0
$186$	1.70584	−	2.95460i	0.125078	−	0.216642i
$187$	−1.53990	+	0.889062i	−0.112609	+	0.0650146i
$188$	2.51551	−	1.45233i	0.183462	−	0.105922i
$189$	−2.28514			−0.166220
$190$		0			0
$191$	−0.668743			−0.0483885			−0.0241943	−	0.999707i	$-0.507702\pi$
$191$	−0.668743			−0.0483885			−0.0241943	+	0.999707i	$0.507702\pi$
$192$	17.5526	−	10.1340i	1.26675	−	0.731358i
$193$	3.25979	−	1.88204i	0.234645	−	0.135472i	−0.378068	−	0.925778i	$-0.623411\pi$
$193$	3.25979	−	1.88204i	0.234645	−	0.135472i	0.612713	+	0.790305i	$0.290078\pi$
$194$	7.17420	−	12.4261i	0.515078	−	0.892141i
$195$		0			0
$196$	−1.35587	+	2.34844i	−0.0968480	+	0.167746i
$197$			14.6164i			1.04138i	0.853747	+	0.520688i	$0.174324\pi$
$197$			14.6164i			1.04138i	−0.853747	+	0.520688i	$0.825676\pi$
$198$		−	0.774121i		−	0.0550144i
$199$	5.76053	−	9.97753i	0.408353	−	0.707288i	−0.586352	−	0.810056i	$-0.699437\pi$
$199$	5.76053	−	9.97753i	0.408353	−	0.707288i	0.994705	+	0.102768i	$0.0327699\pi$
$200$		0			0
$201$	−2.25307			−0.158919
$202$		−	9.67566i		−	0.680777i
$203$	−1.43032	−	0.825796i	−0.100389	−	0.0579595i
$204$	3.61250	+	6.25703i	0.252925	+	0.438079i
$205$		0			0
$206$	7.83237	+	13.5661i	0.545707	+	0.945192i
$207$	−10.0750	+	5.81678i	−0.700257	+	0.404294i
$208$		−	13.6445i		−	0.946074i
$209$	−0.834816	+	0.920816i	−0.0577454	+	0.0636941i
$210$		0			0
$211$	8.57028	+	14.8442i	0.590003	+	1.02191i	0.994231	+	0.107257i	$0.0342067\pi$
$211$	8.57028	+	14.8442i	0.590003	+	1.02191i	−0.404229	+	0.914658i	$0.632460\pi$
$212$	−5.42824	+	3.13400i	−0.372813	+	0.215244i
$213$	−5.78399	−	3.33939i	−0.396313	−	0.228811i
$214$	8.43473	+	14.6094i	0.576586	+	0.998677i
$215$		0			0
$216$	5.44687			0.370612
$217$			1.57028i			0.106598i
$218$	−9.73928	−	5.62297i	−0.659627	−	0.380836i
$219$	−0.873023	+	1.51212i	−0.0589934	+	0.102180i
$220$		0			0
$221$	31.1796			2.09736
$222$	−26.2833	−	15.1746i	−1.76402	−	1.01846i
$223$	−1.31997	+	0.762085i	−0.0883918	+	0.0510330i	−0.543544	−	0.839380i	$-0.682918\pi$
$223$	−1.31997	+	0.762085i	−0.0883918	+	0.0510330i	0.455153	+	0.890413i	$0.349585\pi$
$224$	−1.79416	+	3.10758i	−0.119878	+	0.207634i
$225$		0			0
$226$	10.5859	+	18.3353i	0.704162	+	1.21964i
$227$			4.00000i			0.265489i	0.991150	+	0.132745i	$0.0423790\pi$
$227$			4.00000i			0.265489i	−0.991150	+	0.132745i	$0.957621\pi$
$228$	3.74152	+	3.39208i	0.247788	+	0.224646i
$229$	−18.4397			−1.21853			−0.609266	−	0.792966i	$-0.708536\pi$
$229$	−18.4397			−1.21853			−0.609266	+	0.792966i	$0.708536\pi$
$230$		0			0
$231$	0.418694	+	0.725199i	0.0275480	+	0.0477146i
$232$	3.40931	+	1.96837i	0.223832	+	0.129230i
$233$	−11.0087	+	6.35587i	−0.721203	+	0.416387i	−0.815195	−	0.579186i	$-0.803371\pi$
$233$	−11.0087	+	6.35587i	−0.721203	+	0.416387i	0.0939920	+	0.995573i	$0.470037\pi$
$234$	−6.78714	+	11.7557i	−0.443689	+	0.768493i
$235$		0			0
$236$	−2.90466			−0.189077
$237$	30.5908	+	17.6616i	1.98709	+	1.14725i
$238$	8.48026	+	4.89608i	0.549694	+	0.317366i
$239$	10.8343			0.700811			0.350405	−	0.936598i	$-0.386044\pi$
$239$	10.8343			0.700811			0.350405	+	0.936598i	$0.386044\pi$
$240$		0			0
$241$	4.93673	−	8.55067i	0.318003	−	0.550797i	−0.662068	−	0.749444i	$-0.730321\pi$
$241$	4.93673	−	8.55067i	0.318003	−	0.550797i	0.980071	+	0.198646i	$0.0636545\pi$
$242$	−11.5539	+	6.67065i	−0.742713	+	0.428805i
$243$	−16.6127	−	9.59134i	−1.06570	−	0.615285i
$244$	−1.13009	−	1.95738i	−0.0723467	−	0.125308i
$245$		0			0
$246$	−2.34930			−0.149786
$247$	20.7507	−	6.66407i	1.32033	−	0.424025i
$248$		−	3.74293i		−	0.237676i
$249$	1.90310	+	3.29626i	0.120604	+	0.208892i
$250$		0			0
$251$	−8.88550	+	15.3901i	−0.560848	+	0.971417i	0.436575	+	0.899668i	$0.356191\pi$
$251$	−8.88550	+	15.3901i	−0.560848	+	0.971417i	−0.997423	+	0.0717492i	$0.977142\pi$
$252$	1.25379	−	0.723877i	0.0789815	−	0.0456000i
$253$	−1.29296	−	0.746491i	−0.0812877	−	0.0469315i
$254$	−11.4016			−0.715403
$255$		0			0
$256$	5.66017	−	9.80370i	0.353760	−	0.612731i
$257$	−7.06556	−	4.07930i	−0.440738	−	0.254460i	0.263173	−	0.964749i	$-0.415231\pi$
$257$	−7.06556	−	4.07930i	−0.440738	−	0.254460i	−0.703911	+	0.710289i	$0.748564\pi$
$258$			13.8234i			0.860604i
$259$	13.9688			0.867980
$260$		0			0
$261$	−1.42771	−	2.47287i	−0.0883733	−	0.153067i
$262$	−13.1486	−	7.59134i	−0.812322	−	0.468995i
$263$	−5.47087	+	3.15861i	−0.337348	+	0.194768i	−0.659099	−	0.752056i	$-0.729062\pi$
$263$	−5.47087	+	3.15861i	−0.337348	+	0.194768i	0.321750	+	0.946825i	$0.395729\pi$
$264$	−0.997999	−	1.72858i	−0.0614226	−	0.106387i
$265$		0			0
$266$	6.69024	+	1.44594i	0.410205	+	0.0886565i
$267$		−	36.6264i		−	2.24150i
$268$	−0.432927	+	0.249951i	−0.0264452	+	0.0152682i
$269$	4.11951	+	7.13521i	0.251171	+	0.435041i	0.963849	−	0.266451i	$-0.0858510\pi$
$269$	4.11951	+	7.13521i	0.251171	+	0.435041i	−0.712677	+	0.701492i	$0.752518\pi$
$270$		0			0
$271$	2.11094	+	3.65625i	0.128230	+	0.222101i	0.922991	−	0.384821i	$-0.125737\pi$
$271$	2.11094	+	3.65625i	0.128230	+	0.222101i	−0.794761	+	0.606923i	$0.792404\pi$
$272$	−14.7373	−	8.50858i	−0.893579	−	0.515908i
$273$		−	14.6837i		−	0.888696i
$274$	22.6476			1.36819
$275$		0			0
$276$	−3.03319	+	5.25364i	−0.182577	+	0.316232i
$277$		−	9.83739i		−	0.591071i	−0.955332	−	0.295536i	$-0.904502\pi$
$277$		−	9.83739i		−	0.591071i	0.955332	−	0.295536i	$-0.0954981\pi$
$278$			7.34841i			0.440728i
$279$	−1.35743	+	2.35114i	−0.0812671	+	0.140759i
$280$		0			0
$281$	−2.69024	+	4.65964i	−0.160486	+	0.277971i	−0.935043	−	0.354534i	$-0.884640\pi$
$281$	−2.69024	+	4.65964i	−0.160486	+	0.277971i	0.774557	+	0.632504i	$0.217973\pi$
$282$	13.8529	−	7.99800i	0.824931	−	0.476274i
$283$	4.29965	−	2.48240i	0.255588	−	0.147564i	−0.366732	−	0.930326i	$-0.619524\pi$
$283$	4.29965	−	2.48240i	0.255588	−	0.147564i	0.622320	+	0.782763i	$0.286190\pi$
$284$	−1.48186			−0.0879323
$285$		0			0
$286$	−1.74204			−0.103009
$287$	0.936439	−	0.540653i	0.0552762	−	0.0319137i
$288$	−5.37268	+	3.10192i	−0.316588	+	0.182782i
$289$	10.9433	−	18.9544i	0.643724	−	1.11496i
$290$		0			0
$291$	−13.4171	+	23.2392i	−0.786526	+	1.36230i
$292$			0.387406i			0.0226712i
$293$			3.80620i			0.222360i	0.993800	+	0.111180i	$0.0354631\pi$
$293$			3.80620i			0.222360i	−0.993800	+	0.111180i	$0.964537\pi$
$294$	−7.46681	+	12.9329i	−0.435473	+	0.754262i
$295$		0			0
$296$	−33.2961			−1.93529
$297$		−	0.507019i		−	0.0294202i
$298$	−7.18730	−	4.14959i	−0.416349	−	0.240379i
$299$	13.0898	+	22.6722i	0.757002	+	1.31117i
$300$		0			0
$301$	−3.18122	−	5.51004i	−0.183363	−	0.317593i
$302$	−16.8118	+	9.70628i	−0.967409	+	0.558534i
$303$			18.0953i			1.03955i
$304$	−11.6265	−	2.51281i	−0.666827	−	0.144119i
$305$		0			0
$306$	8.46481	+	14.6615i	0.483901	+	0.838141i
$307$	0.497348	−	0.287144i	0.0283851	−	0.0163882i	−0.485740	−	0.874103i	$-0.661450\pi$
$307$	0.497348	−	0.287144i	0.0283851	−	0.0163882i	0.514125	+	0.857715i	$0.328117\pi$
$308$	0.160904	+	0.0928982i	0.00916838	+	0.00529336i
$309$	−14.6480	−	25.3711i	−0.833297	−	1.44331i
$310$		0			0
$311$	−8.61640			−0.488591			−0.244296	−	0.969701i	$-0.578557\pi$
$311$	−8.61640			−0.488591			−0.244296	+	0.969701i	$0.578557\pi$
$312$			35.0000i			1.98148i
$313$	−29.5517	−	17.0617i	−1.67036	−	0.964385i	−0.967433	−	0.253126i	$-0.918541\pi$
$313$	−29.5517	−	17.0617i	−1.67036	−	0.964385i	−0.702930	−	0.711259i	$-0.748125\pi$
$314$	4.58632	−	7.94375i	0.258821	−	0.448291i
$315$		0			0
$316$	7.83739			0.440887
$317$	9.59323	+	5.53865i	0.538809	+	0.311082i	0.744596	−	0.667515i	$-0.232642\pi$
$317$	9.59323	+	5.53865i	0.538809	+	0.311082i	−0.205787	+	0.978597i	$0.565975\pi$
$318$	−29.8934	+	17.2590i	−1.67634	+	0.967835i
$319$	0.183224	−	0.317354i	0.0102586	−	0.0177684i
$320$		0			0
$321$	−15.7746	−	27.3223i	−0.880450	−	1.52498i
$322$			8.22188i			0.458187i
$323$	5.74213	−	26.5683i	0.319500	−	1.47830i
$324$	−5.43975			−0.302208
$325$		0			0
$326$	−13.3308	−	23.0896i	−0.738325	−	1.27882i
$327$	18.2143	+	10.5160i	1.00725	+	0.581538i
$328$	−2.23210	+	1.28870i	−0.123247	+	0.0711566i
$329$	−3.68122	+	6.37607i	−0.202952	+	0.351524i
$330$		0			0
$331$	6.41168			0.352418			0.176209	−	0.984353i	$-0.443617\pi$
$331$	6.41168			0.352418			0.176209	+	0.984353i	$0.443617\pi$
$332$	0.731363	+	0.422252i	0.0401387	+	0.0231741i
$333$	20.9150	+	12.0753i	1.14614	+	0.661722i
$334$	−13.7890			−0.754503
$335$		0			0
$336$	−4.00702	+	6.94036i	−0.218601	+	0.378628i
$337$	−21.8820	+	12.6336i	−1.19199	+	0.688193i	−0.958757	−	0.284228i	$-0.908263\pi$
$337$	−21.8820	+	12.6336i	−1.19199	+	0.688193i	−0.233229	+	0.972422i	$0.574929\pi$
$338$	12.6981	+	7.33126i	0.690686	+	0.398768i
$339$	−19.7976	−	34.2905i	−1.07526	−	1.86240i
$340$		0			0
$341$	−0.348409			−0.0188674
$342$	8.76714	+	7.94833i	0.474072	+	0.429796i
$343$		−	15.8695i		−	0.856871i
$344$	7.58276	+	13.1337i	0.408835	+	0.708123i
$345$		0			0
$346$	3.57730	−	6.19607i	0.192317	−	0.333103i
$347$	10.7461	−	6.20428i	0.576882	−	0.333063i	−0.183011	−	0.983111i	$-0.558584\pi$
$347$	10.7461	−	6.20428i	0.576882	−	0.333063i	0.759893	+	0.650048i	$0.225251\pi$
$348$	−1.28949	−	0.744489i	−0.0691241	−	0.0399088i
$349$	−6.20384			−0.332084			−0.166042	−	0.986119i	$-0.553099\pi$
$349$	−6.20384			−0.332084			−0.166042	+	0.986119i	$0.553099\pi$
$350$		0			0
$351$	−4.44531	+	7.69950i	−0.237273	+	0.410969i
$352$	−0.689498	−	0.398082i	−0.0367504	−	0.0212178i
$353$			23.3484i			1.24271i	0.783529	+	0.621355i	$0.213418\pi$
$353$			23.3484i			1.24271i	−0.783529	+	0.621355i	$0.786582\pi$
$354$	−15.9960			−0.850178
$355$		0			0
$356$	−4.06327	−	7.03778i	−0.215353	−	0.373002i
$357$	−15.8597	−	9.15661i	−0.839385	−	0.484619i
$358$	19.8854	−	11.4808i	1.05098	−	0.606782i
$359$	−18.8609	−	32.6680i	−0.995440	−	1.72415i	−0.580333	−	0.814379i	$-0.697078\pi$
$359$	−18.8609	−	32.6680i	−0.995440	−	1.72415i	−0.415107	−	0.909773i	$-0.636256\pi$
$360$		0			0
$361$	−1.85698	−	18.9090i	−0.0977360	−	0.995212i
$362$			16.3063i			0.857040i
$363$	21.6080	−	12.4754i	1.13413	−	0.654788i
$364$	−1.62898	−	2.82147i	−0.0853816	−	0.147885i
$365$		0			0
$366$	−6.22343	−	10.7793i	−0.325304	−	0.563443i
$367$	−25.4678	−	14.7038i	−1.32941	−	0.767534i	−0.344200	−	0.938896i	$-0.611850\pi$
$367$	−25.4678	−	14.7038i	−1.32941	−	0.767534i	−0.985208	+	0.171362i	$0.945183\pi$
$368$		−	14.2883i		−	0.744827i
$369$	1.86946			0.0973204
$370$		0			0
$371$	7.94375	−	13.7590i	0.412419	−	0.714331i
$372$			1.41568i			0.0733995i
$373$			21.5491i			1.11577i	0.829918	+	0.557886i	$0.188387\pi$
$373$			21.5491i			1.11577i	−0.829918	+	0.557886i	$0.811613\pi$
$374$	−1.08632	+	1.88157i	−0.0561725	+	0.0972935i
$375$		0			0
$376$	8.77457	−	15.1980i	0.452514	−	0.783777i
$377$	−5.56483	+	3.21286i	−0.286603	+	0.165471i
$378$	−2.41808	+	1.39608i	−0.124373	+	0.0718066i
$379$	19.3945			0.996230			0.498115	−	0.867111i	$-0.334026\pi$
$379$	19.3945			0.996230			0.498115	+	0.867111i	$0.334026\pi$
$380$		0			0
$381$	21.3233			1.09242
$382$	−0.707648	+	0.408561i	−0.0362064	+	0.0209038i
$383$	−16.3563	+	9.44331i	−0.835767	+	0.482531i	−0.855823	−	0.517268i	$-0.826949\pi$
$383$	−16.3563	+	9.44331i	−0.835767	+	0.482531i	0.0200559	+	0.999799i	$0.493616\pi$
$384$	6.00200	−	10.3958i	0.306288	−	0.530507i
$385$		0			0
$386$	2.29962	−	3.98307i	0.117048	−	0.202733i
$387$		−	11.0000i		−	0.559161i
$388$			5.95389i			0.302263i
$389$	−4.54021	+	7.86387i	−0.230198	+	0.398714i	−0.957866	−	0.287215i	$-0.907271\pi$
$389$	−4.54021	+	7.86387i	−0.230198	+	0.398714i	0.727668	+	0.685929i	$0.240604\pi$
$390$		0			0
$391$	32.6507			1.65122
$392$			16.3836i			0.827497i
$393$	24.5904	+	14.1973i	1.24042	+	0.716157i
$394$	8.92972	+	15.4667i	0.449873	+	0.779202i
$395$		0			0
$396$	0.160611	+	0.278187i	0.00807101	+	0.0139794i
$397$	14.7190	−	8.49800i	0.738724	−	0.426502i	−0.0828814	−	0.996559i	$-0.526412\pi$
$397$	14.7190	−	8.49800i	0.738724	−	0.426502i	0.821605	+	0.570057i	$0.193079\pi$
$398$		−	14.0773i		−	0.705631i
$399$	−12.5120	−	2.70419i	−0.626385	−	0.135379i
$400$		0			0
$401$	−0.795720	−	1.37823i	−0.0397363	−	0.0688254i	0.845473	−	0.534018i	$-0.179318\pi$
$401$	−0.795720	−	1.37823i	−0.0397363	−	0.0688254i	−0.885210	+	0.465192i	$0.845985\pi$
$402$	−2.38414	+	1.37648i	−0.118910	+	0.0686528i
$403$	5.29088	+	3.05469i	0.263557	+	0.152165i
$404$	2.00746	+	3.47703i	0.0998750	+	0.172989i
$405$		0			0
$406$	−2.01804			−0.100154
$407$			3.09935i			0.153629i
$408$	37.8032	+	21.8257i	1.87154	+	1.08053i
$409$	−0.998443	+	1.72935i	−0.0493698	+	0.0855110i	−0.889654	−	0.456635i	$-0.849055\pi$
$409$	−0.998443	+	1.72935i	−0.0493698	+	0.0855110i	0.840284	+	0.542146i	$0.182388\pi$
$410$		0			0
$411$	−42.3553			−2.08923
$412$	−5.62925	−	3.25005i	−0.277333	−	0.160118i
$413$	6.37607	−	3.68122i	0.313746	−	0.181141i
$414$	−7.10738	+	12.3103i	−0.349309	+	0.605020i
$415$		0			0
$416$	6.98040	+	12.0904i	0.342242	+	0.592781i
$417$		−	13.7429i		−	0.672994i
$418$	−0.320820	+	1.48441i	−0.0156918	+	0.0726046i
$419$	22.7781			1.11278			0.556392	−	0.830920i	$-0.312185\pi$
$419$	22.7781			1.11278			0.556392	+	0.830920i	$0.312185\pi$
$420$		0			0
$421$	6.92070	+	11.9870i	0.337294	+	0.584210i	0.983923	−	0.178594i	$-0.0571550\pi$
$421$	6.92070	+	11.9870i	0.337294	+	0.584210i	−0.646629	+	0.762805i	$0.723822\pi$
$422$	18.1377	+	10.4718i	0.882931	+	0.509761i
$423$	−11.0235	+	6.36445i	−0.535983	+	0.309450i
$424$	−18.9347	+	32.7959i	−0.919552	+	1.59271i
$425$		0			0
$426$	−8.16064			−0.395384
$427$	4.96137	+	2.86445i	0.240097	+	0.138620i
$428$	−6.06218	−	3.50000i	−0.293026	−	0.169179i
$429$	3.25796			0.157296
$430$		0			0
$431$	−1.71987	+	2.97891i	−0.0828435	+	0.143489i	−0.904470	−	0.426537i	$-0.859733\pi$
$431$	−1.71987	+	2.97891i	−0.0828435	+	0.143489i	0.821627	+	0.570026i	$0.193067\pi$
$432$	4.20223	−	2.42616i	0.202180	−	0.116729i
$433$	−7.96806	−	4.60036i	−0.382920	−	0.221079i	0.296168	−	0.955136i	$-0.404291\pi$
$433$	−7.96806	−	4.60036i	−0.382920	−	0.221079i	−0.679088	+	0.734057i	$0.737625\pi$
$434$	0.959347	+	1.66164i	0.0460501	+	0.0797612i
$435$		0			0
$436$	4.66652			0.223486
$437$	21.7297	−	6.97850i	1.03947	−	0.333827i
$438$			2.13345i			0.101940i
$439$	−18.7550	−	32.4846i	−0.895126	−	1.55040i	−0.833649	−	0.552295i	$-0.813752\pi$
$439$	−18.7550	−	32.4846i	−0.895126	−	1.55040i	−0.0614769	−	0.998109i	$-0.519581\pi$
$440$		0			0
$441$	5.94175	−	10.2914i	0.282941	−	0.490067i
$442$	32.9935	−	19.0488i	1.56934	−	0.906058i
$443$	12.7122	+	7.33939i	0.603975	+	0.348705i	0.770604	−	0.637315i	$-0.219955\pi$
$443$	12.7122	+	7.33939i	0.603975	+	0.348705i	−0.166629	+	0.986020i	$0.553288\pi$
$444$	12.5935			0.597660
$445$		0			0
$446$	−0.931174	+	1.61284i	−0.0440924	+	0.0763702i
$447$	13.4416	+	7.76053i	0.635767	+	0.367060i
$448$			11.3985i			0.538530i
$449$	7.39052			0.348780			0.174390	−	0.984677i	$-0.444205\pi$
$449$	7.39052			0.348780			0.174390	+	0.984677i	$0.444205\pi$
$450$		0			0
$451$	0.119958	+	0.207773i	0.00564860	+	0.00978367i
$452$	−7.60824	−	4.39262i	−0.357862	−	0.206611i
$453$	31.4412	−	18.1526i	1.47724	−	0.852884i
$454$	2.44375	+	4.23270i	0.114691	+	0.198651i
$455$		0			0
$456$	29.8237	+	6.44571i	1.39662	+	0.301848i
$457$			2.30007i			0.107593i	0.998552	+	0.0537963i	$0.0171322\pi$
$457$			2.30007i			0.107593i	−0.998552	+	0.0537963i	$0.982868\pi$
$458$	−19.5125	+	11.2655i	−0.911759	+	0.526404i
$459$	5.54411	+	9.60269i	0.258777	+	0.448215i
$460$		0			0
$461$	−9.87848	−	17.1100i	−0.460087	−	0.796894i	0.538878	−	0.842384i	$-0.318848\pi$
$461$	−9.87848	−	17.1100i	−0.460087	−	0.796894i	−0.998965	+	0.0454900i	$0.985515\pi$
$462$	0.886103	+	0.511592i	0.0412253	+	0.0238014i
$463$		−	28.9468i		−	1.34527i	−0.739974	−	0.672635i	$-0.765162\pi$
$463$		−	28.9468i		−	1.34527i	0.739974	−	0.672635i	$-0.234838\pi$
$464$	3.50702			0.162809
$465$		0			0
$466$	−7.76609	+	13.4513i	−0.359757	+	0.623118i
$467$		−	3.31722i		−	0.153503i	−0.997050	−	0.0767513i	$-0.975545\pi$
$467$		−	3.31722i		−	0.153503i	0.997050	−	0.0767513i	$-0.0244548\pi$
$468$		−	5.63266i		−	0.260370i
$469$	0.633551	−	1.09734i	0.0292547	−	0.0506706i
$470$		0			0
$471$	−8.57730	+	14.8563i	−0.395221	+	0.684543i
$472$	−15.1980	+	8.77457i	−0.699544	+	0.403882i
$473$	1.22255	−	0.705838i	0.0562127	−	0.0324544i
$474$	43.1606			1.98243
$475$		0			0
$476$	−4.06327			−0.186240
$477$	23.7878	−	13.7339i	1.08917	−	0.628833i
$478$	11.4646	−	6.61907i	0.524377	−	0.302749i
$479$	−19.7535	+	34.2141i	−0.902561	+	1.56328i	−0.0784026	+	0.996922i	$0.524982\pi$
$479$	−19.7535	+	34.2141i	−0.902561	+	1.56328i	−0.824158	+	0.566360i	$0.808351\pi$
$480$		0			0
$481$	27.1737	−	47.0662i	1.23901	−	2.14603i
$482$		−	12.0642i		−	0.549507i
$483$		−	15.3765i		−	0.699654i
$484$	2.76799	−	4.79430i	0.125818	−	0.217923i
$485$		0			0
$486$	−23.4389			−1.06321
$487$		−	24.7781i		−	1.12280i	−0.827543	−	0.561402i	$-0.810262\pi$
$487$		−	24.7781i		−	1.12280i	0.827543	−	0.561402i	$-0.189738\pi$
$488$	−11.8259	−	6.82770i	−0.535334	−	0.309075i
$489$	24.9312	+	43.1821i	1.12743	+	1.95276i
$490$		0			0
$491$	6.81176	+	11.7983i	0.307410	+	0.532450i	0.977795	−	0.209563i	$-0.0672042\pi$
$491$	6.81176	+	11.7983i	0.307410	+	0.532450i	−0.670385	+	0.742014i	$0.733871\pi$
$492$	0.844239	−	0.487421i	0.0380612	−	0.0219747i
$493$			8.01404i			0.360934i
$494$	17.8865	−	19.7291i	0.804752	−	0.887656i
$495$		0			0
$496$	−1.66719	−	2.88765i	−0.0748589	−	0.129659i
$497$	3.25286	−	1.87804i	0.145911	−	0.0842416i
$498$	4.02763	+	2.32535i	0.180482	+	0.104201i
$499$	4.09490	+	7.09257i	0.183313	+	0.317507i	0.943007	−	0.332774i	$-0.107985\pi$
$499$	4.09490	+	7.09257i	0.183313	+	0.317507i	−0.759694	+	0.650281i	$0.774651\pi$
$500$		0			0
$501$	25.7882			1.15213
$502$			21.7140i			0.969142i
$503$	15.8354	+	9.14257i	0.706065	+	0.407647i	0.809603	−	0.586978i	$-0.199683\pi$
$503$	15.8354	+	9.14257i	0.706065	+	0.407647i	−0.103537	+	0.994626i	$0.533016\pi$
$504$	4.37347	−	7.57507i	0.194810	−	0.337420i
$505$		0			0
$506$	−1.82424			−0.0810973
$507$	−23.7479	−	13.7109i	−1.05468	−	0.608920i
$508$	4.09727	−	2.36556i	0.181787	−	0.104955i
$509$	5.94220	−	10.2922i	0.263383	−	0.456193i	−0.703756	−	0.710442i	$-0.748495\pi$
$509$	5.94220	−	10.2922i	0.263383	−	0.456193i	0.967139	+	0.254249i	$0.0818283\pi$
$510$		0			0
$511$	−0.490980	−	0.850402i	−0.0217197	−	0.0376196i
$512$		−	24.3382i		−	1.07561i
$513$	5.74213	+	5.20584i	0.253521	+	0.229843i
$514$	−9.96881			−0.439705
$515$		0			0
$516$	−2.86801	−	4.96753i	−0.126257	−	0.218683i
$517$	−1.41470	−	0.816776i	−0.0622183	−	0.0359218i
$518$	14.7815	−	8.53408i	0.649460	−	0.374966i
$519$	−6.69024	+	11.5878i	−0.293669	+	0.508650i
$520$		0			0
$521$	21.3725			0.936345			0.468173	−	0.883637i	$-0.344913\pi$
$521$	21.3725			0.936345			0.468173	+	0.883637i	$0.344913\pi$
$522$	−3.02154	−	1.74449i	−0.132249	−	0.0763542i
$523$	−5.00323	−	2.88862i	−0.218776	−	0.126310i	0.386607	−	0.922244i	$-0.373647\pi$
$523$	−5.00323	−	2.88862i	−0.218776	−	0.126310i	−0.605383	+	0.795934i	$0.706980\pi$
$524$	6.30007			0.275220
$525$		0			0
$526$	−3.85943	+	6.68473i	−0.168279	+	0.291468i
$527$	6.59869	−	3.80976i	0.287444	−	0.165956i
$528$	−1.53990	−	0.889062i	−0.0670156	−	0.0386915i
$529$	2.20739	+	3.82332i	0.0959737	+	0.166231i
$530$		0			0
$531$	12.7289			0.552387
$532$	−2.70419	+	0.868450i	−0.117242	+	0.0376521i
$533$		−	4.20695i		−	0.182223i
$534$	−22.3765	−	38.7572i	−0.968325	−	1.67719i
$535$		0			0
$536$	−1.51013	+	2.61563i	−0.0652278	+	0.112978i
$537$	−37.1895	+	21.4714i	−1.60485	+	0.926559i
$538$	8.71834	+	5.03354i	0.375874	+	0.217011i
$539$	1.52506			0.0656889
$540$		0			0
$541$	−1.31678	+	2.28072i	−0.0566126	+	0.0980559i	−0.892943	−	0.450170i	$-0.851363\pi$
$541$	−1.31678	+	2.28072i	−0.0566126	+	0.0980559i	0.836330	+	0.548226i	$0.184697\pi$
$542$	4.46749	+	2.57930i	0.191895	+	0.110791i
$543$		−	30.4959i		−	1.30870i
$544$	17.4117			0.746519
$545$		0			0
$546$	−8.97081	−	15.5379i	−0.383915	−	0.664961i
$547$	31.4908	+	18.1812i	1.34645	+	0.777373i	0.987745	−	0.156078i	$-0.0498852\pi$
$547$	31.4908	+	18.1812i	1.34645	+	0.777373i	0.358705	+	0.933451i	$0.383218\pi$
$548$	−8.13859	+	4.69882i	−0.347663	+	0.200724i
$549$	4.95233	+	8.57768i	0.211360	+	0.366087i
$550$		0			0
$551$	1.71286	+	5.33351i	0.0729701	+	0.227215i
$552$			36.6514i			1.55999i
$553$	−17.2040	+	9.93273i	−0.731588	+	0.422383i
$554$	−6.01003	−	10.4097i	−0.255342	−	0.442265i
$555$		0			0
$556$	−1.52461	−	2.64071i	−0.0646581	−	0.111991i
$557$	−20.7541	−	11.9824i	−0.879381	−	0.507711i	−0.00892662	−	0.999960i	$-0.502841\pi$
$557$	−20.7541	−	11.9824i	−0.879381	−	0.507711i	−0.870454	+	0.492249i	$0.836175\pi$
$558$			3.31722i			0.140429i
$559$	−24.7539			−1.04698
$560$		0			0
$561$	2.03163	−	3.51889i	0.0857756	−	0.148568i
$562$			6.57429i			0.277320i
$563$			8.52017i			0.359082i	0.983750	+	0.179541i	$0.0574613\pi$
$563$			8.52017i			0.359082i	−0.983750	+	0.179541i	$0.942539\pi$
$564$	−3.31878	+	5.74829i	−0.139746	+	0.242047i
$565$		0			0
$566$	3.03319	−	5.25364i	0.127495	−	0.220827i
$567$	11.9409	−	6.89408i	0.501470	−	0.289524i
$568$	−7.75352	+	4.47650i	−0.325331	+	0.187830i
$569$	−16.3734			−0.686407			−0.343204	−	0.939261i	$-0.611512\pi$
$569$	−16.3734			−0.686407			−0.343204	+	0.939261i	$0.611512\pi$
$570$		0			0
$571$	−5.21876			−0.218398			−0.109199	−	0.994020i	$-0.534829\pi$
$571$	−5.21876			−0.218398			−0.109199	+	0.994020i	$0.534829\pi$
$572$	0.626018	−	0.361431i	0.0261751	−	0.0151122i
$573$	1.32344	−	0.764087i	0.0552874	−	0.0319202i
$574$	0.660611	−	1.14421i	0.0275734	−	0.0477585i
$575$		0			0
$576$	−9.85343	+	17.0666i	−0.410559	+	0.711110i
$577$		−	32.0390i		−	1.33380i	−0.745147	−	0.666900i	$-0.767621\pi$
$577$		−	32.0390i		−	1.33380i	0.745147	−	0.666900i	$-0.232379\pi$
$578$		−	26.7427i		−	1.11235i
$579$	−4.30074	+	7.44910i	−0.178733	+	0.309574i
$580$		0			0
$581$	−2.14057			−0.0888058
$582$			32.7882i			1.35911i
$583$	3.05279	+	1.76253i	0.126434	+	0.0729965i
$584$	1.17030	+	2.02702i	0.0484274	+	0.0838787i
$585$		0			0
$586$	2.32535	+	4.02763i	0.0960594	+	0.166380i
$587$	−2.89634	+	1.67220i	−0.119545	+	0.0690192i	−0.558580	−	0.829451i	$-0.688654\pi$
$587$	−2.89634	+	1.67220i	−0.119545	+	0.0690192i	0.439035	+	0.898470i	$0.355320\pi$
$588$		−	6.19672i		−	0.255548i
$589$	3.57730	−	3.94583i	0.147400	−	0.162585i
$590$		0			0
$591$	−16.7003	−	28.9257i	−0.686958	−	1.18985i
$592$	−25.6877	+	14.8308i	−1.05576	+	0.609543i
$593$	36.5556	+	21.1054i	1.50116	+	0.866694i	0.999999	+	0.00133875i	$0.000426138\pi$
$593$	36.5556	+	21.1054i	1.50116	+	0.866694i	0.501159	+	0.865355i	$0.332907\pi$
$594$	−0.309757	−	0.536515i	−0.0127095	−	0.0220135i
$595$		0			0
$596$	3.44375			0.141062
$597$			26.3273i			1.07750i
$598$	27.7026	+	15.9941i	1.13284	+	0.654047i
$599$	−2.60938	+	4.51958i	−0.106616	+	0.184665i	−0.914397	−	0.404818i	$-0.867335\pi$
$599$	−2.60938	+	4.51958i	−0.106616	+	0.184665i	0.807781	+	0.589483i	$0.200668\pi$
$600$		0			0
$601$	−10.1546			−0.414215			−0.207108	−	0.978318i	$-0.566405\pi$
$601$	−10.1546			−0.414215			−0.207108	+	0.978318i	$0.566405\pi$
$602$	−6.73259	−	3.88706i	−0.274400	−	0.158425i
$603$	1.89719	−	1.09534i	0.0772596	−	0.0446058i
$604$	4.02763	−	6.97606i	0.163882	−	0.283852i
$605$		0			0
$606$	11.0551	+	19.1481i	0.449084	+	0.777837i
$607$			42.8764i			1.74030i	0.492788	+	0.870149i	$0.335978\pi$
$607$			42.8764i			1.74030i	−0.492788	+	0.870149i	$0.664022\pi$
$608$	11.5878	−	3.72143i	0.469949	−	0.150924i
$609$	3.77412			0.152935
$610$		0			0
$611$	14.3222	+	24.8068i	0.579416	+	1.00358i
$612$	−6.08379	−	3.51248i	−0.245923	−	0.141984i
$613$	−21.7141	+	12.5367i	−0.877025	+	0.506351i	−0.869676	−	0.493622i	$-0.835672\pi$
$613$	−21.7141	+	12.5367i	−0.877025	+	0.506351i	−0.00734857	+	0.999973i	$0.502339\pi$
$614$	0.350854	−	0.607697i	0.0141593	−	0.0245247i
$615$		0			0
$616$	1.12253			0.0452280
$617$	4.76053	+	2.74849i	0.191652	+	0.110650i	0.592756	−	0.805382i	$-0.298040\pi$
$617$	4.76053	+	2.74849i	0.191652	+	0.110650i	−0.401104	+	0.916033i	$0.631373\pi$
$618$	−31.0004	−	17.8981i	−1.24702	−	0.719966i
$619$	−15.4899			−0.622590			−0.311295	−	0.950313i	$-0.600763\pi$
$619$	−15.4899			−0.622590			−0.311295	+	0.950313i	$0.600763\pi$
$620$		0			0
$621$	−4.65505	+	8.06279i	−0.186801	+	0.323548i
$622$	−9.11767	+	5.26409i	−0.365585	+	0.211071i
$623$	17.8387	+	10.2992i	0.714693	+	0.412628i
$624$	15.5898	+	27.0023i	0.624091	+	1.08096i
$625$		0			0
$626$	−41.6946			−1.66645
$627$	0.599995	−	2.77612i	0.0239615	−	0.110868i
$628$			3.80620i			0.151884i
$629$	−33.8905	−	58.7001i	−1.35130	−	2.34053i
$630$		0			0
$631$	−20.6616	+	35.7870i	−0.822526	+	1.42466i	0.0812689	+	0.996692i	$0.474103\pi$
$631$	−20.6616	+	35.7870i	−0.822526	+	1.42466i	−0.903795	+	0.427965i	$0.859231\pi$
$632$	41.0075	−	23.6757i	1.63119	−	0.941767i
$633$	−33.9210	−	19.5843i	−1.34824	−	0.778407i
$634$	13.5351			0.537547
$635$		0			0
$636$	7.16163	−	12.4043i	0.283977	−	0.491862i
$637$	−23.1593	−	13.3710i	−0.917604	−	0.529779i
$638$		−	0.447755i		−	0.0177268i
$639$	6.49387			0.256894
$640$		0			0
$641$	15.3358	+	26.5624i	0.605729	+	1.04915i	0.991936	+	0.126741i	$0.0404517\pi$
$641$	15.3358	+	26.5624i	0.605729	+	1.04915i	−0.386207	+	0.922412i	$0.626215\pi$
$642$	−33.3845	−	19.2746i	−1.31758	−	0.760706i
$643$	6.94383	−	4.00902i	0.273838	−	0.158100i	−0.356793	−	0.934184i	$-0.616130\pi$
$643$	6.94383	−	4.00902i	0.273838	−	0.158100i	0.630630	+	0.776083i	$0.282796\pi$
$644$	−1.70584	−	2.95460i	−0.0672194	−	0.116427i
$645$		0			0
$646$	−10.1554	−	31.6220i	−0.399559	−	1.24415i
$647$			10.0272i			0.394209i	0.980382	+	0.197105i	$0.0631539\pi$
$647$			10.0272i			0.394209i	−0.980382	+	0.197105i	$0.936846\pi$
$648$	−28.4623	+	16.4327i	−1.11811	+	0.645539i
$649$	0.816776	+	1.41470i	0.0320612	+	0.0555317i
$650$		0			0
$651$	−1.79416	−	3.10758i	−0.0703188	−	0.121796i
$652$	9.58107	+	5.53163i	0.375224	+	0.216635i
$653$		−	20.4117i		−	0.798771i	−0.916783	−	0.399385i	$-0.869224\pi$
$653$		−	20.4117i		−	0.798771i	0.916783	−	0.399385i	$-0.130776\pi$
$654$	25.6986			1.00489
$655$		0			0
$656$	−1.14803	+	1.98845i	−0.0448231	+	0.0776360i
$657$		−	1.69771i		−	0.0662338i
$658$			8.99600i			0.350700i
$659$	−18.4874	+	32.0212i	−0.720168	+	1.24737i	0.240765	+	0.970584i	$0.422602\pi$
$659$	−18.4874	+	32.0212i	−0.720168	+	1.24737i	−0.960932	+	0.276783i	$0.910732\pi$
$660$		0			0
$661$	−1.59646	+	2.76514i	−0.0620950	+	0.107552i	−0.895402	−	0.445259i	$-0.853112\pi$
$661$	−1.59646	+	2.76514i	−0.0620950	+	0.107552i	0.833307	+	0.552811i	$0.186445\pi$
$662$	6.78468	−	3.91714i	0.263694	−	0.152244i
$663$	−61.7041	+	35.6249i	−2.39639	+	1.38356i
$664$	5.10226			0.198006
$665$		0			0
$666$	29.5090			1.14345
$667$	−5.82739	+	3.36445i	−0.225638	+	0.130272i
$668$	4.95520	−	2.86089i	0.191723	−	0.110691i
$669$	1.74147	−	3.01632i	0.0673292	−	0.116618i
$670$		0			0
$671$	−0.635553	+	1.10081i	−0.0245352	+	0.0424963i
$672$		−	8.19983i		−	0.316315i
$673$			15.0742i			0.581067i	0.956865	+	0.290534i	$0.0938328\pi$
$673$			15.0742i			0.581067i	−0.956865	+	0.290534i	$0.906167\pi$
$674$	−15.4366	+	26.7370i	−0.594597	+	1.02987i
$675$		0			0
$676$	−6.08422			−0.234009
$677$			17.9648i			0.690444i	0.938521	+	0.345222i	$0.112196\pi$
$677$			17.9648i			0.690444i	−0.938521	+	0.345222i	$0.887804\pi$
$678$	−41.8987	−	24.1902i	−1.60911	−	0.929021i
$679$	−7.54567	−	13.0695i	−0.289576	−	0.501561i
$680$		0			0
$681$	−4.57028	−	7.91597i	−0.175134	−	0.303340i
$682$	−0.368678	+	0.212856i	−0.0141174	+	0.00815069i
$683$			3.78524i			0.144838i	0.997374	+	0.0724191i	$0.0230719\pi$
$683$			3.78524i			0.144838i	−0.997374	+	0.0724191i	$0.976928\pi$
$684$	−4.79962	−	1.03733i	−0.183518	−	0.0396633i
$685$		0			0
$686$	−9.69526	−	16.7927i	−0.370167	−	0.641148i
$687$	36.4921	−	21.0687i	1.39226	−	0.803822i
$688$	11.7001	+	6.75507i	0.446063	+	0.257534i
$689$	−30.9061	−	53.5310i	−1.17743	−	2.03937i
$690$		0			0
$691$	−10.3335			−0.393104			−0.196552	−	0.980493i	$-0.562974\pi$
$691$	−10.3335			−0.393104			−0.196552	+	0.980493i	$0.562974\pi$
$692$			2.96881i			0.112857i
$693$	−0.705121	−	0.407102i	−0.0267853	−	0.0154645i
$694$	7.58086	−	13.1304i	0.287766	−	0.498425i
$695$		0			0
$696$	−8.99600			−0.340992
$697$	−4.54389	−	2.62342i	−0.172112	−	0.0993690i
$698$	−6.56475	+	3.79016i	−0.248479	+	0.143460i
$699$	14.5241	−	25.1564i	0.549351	−	0.951504i
$700$		0			0
$701$	−17.9980	−	31.1734i	−0.679775	−	1.17740i	−0.975048	−	0.221992i	$-0.928744\pi$
$701$	−17.9980	−	31.1734i	−0.679775	−	1.17740i	0.295273	−	0.955413i	$-0.404589\pi$
$702$			10.8632i			0.410006i
$703$	−35.1010	−	31.8227i	−1.32386	−	1.20022i
$704$	−2.52906			−0.0953176
$705$		0			0
$706$	14.2644	+	24.7067i	0.536849	+	0.929850i
$707$	−8.81324	−	5.08832i	−0.331456	−	0.191366i
$708$	5.74829	−	3.31878i	0.216034	−	0.124727i
$709$	4.40266	−	7.62562i	0.165345	−	0.286386i	−0.771433	−	0.636311i	$-0.780460\pi$
$709$	4.40266	−	7.62562i	0.165345	−	0.286386i	0.936778	+	0.349925i	$0.113793\pi$
$710$		0			0
$711$	−34.3453			−1.28805
$712$	−42.5203	−	24.5491i	−1.59352	−	0.920018i
$713$	5.54052	+	3.19882i	0.207494	+	0.119797i
$714$	−22.3765			−0.837419
$715$		0			0
$716$	−4.76399	+	8.25147i	−0.178039	+	0.308372i
$717$	−21.4409	+	12.3789i	−0.800726	+	0.462300i
$718$	−39.9163	−	23.0457i	−1.48966	−	0.860057i
$719$	9.49600	+	16.4475i	0.354141	+	0.613390i	0.986971	−	0.160901i	$-0.0514400\pi$
$719$	9.49600	+	16.4475i	0.354141	+	0.613390i	−0.632830	+	0.774291i	$0.718107\pi$
$720$		0			0
$721$	16.4758			0.613592
$722$	−13.5173	−	18.8746i	−0.503061	−	0.702439i
$723$			22.5623i			0.839100i
$724$	−3.38316	−	5.85980i	−0.125734	−	0.217778i
$725$		0			0
$726$	15.2434	−	26.4023i	0.565735	−	0.979881i
$727$	3.54321	−	2.04567i	0.131410	−	0.0758697i	−0.432854	−	0.901464i	$-0.642493\pi$
$727$	3.54321	−	2.04567i	0.131410	−	0.0758697i	0.564264	+	0.825594i	$0.309160\pi$
$728$	−17.0466	−	9.84183i	−0.631787	−	0.364763i
$729$	11.6485			0.431425
$730$		0			0
$731$	−15.4363	+	26.7364i	−0.570932	+	0.988883i
$732$	4.47288	+	2.58242i	0.165322	+	0.0954490i
$733$			50.4678i			1.86407i	0.362366	+	0.932036i	$0.381969\pi$
$733$			50.4678i			1.86407i	−0.362366	+	0.932036i	$0.618031\pi$
$734$	−35.9325			−1.32629
$735$		0			0
$736$	7.30976	+	12.6609i	0.269441	+	0.466686i
$737$	0.243474	+	0.140570i	0.00896849	+	0.00517796i
$738$	1.97822	−	1.14213i	0.0728194	−	0.0420423i
$739$	17.1148	+	29.6438i	0.629580	+	1.09046i	0.987636	+	0.156764i	$0.0501062\pi$
$739$	17.1148	+	29.6438i	0.629580	+	1.09046i	−0.358056	+	0.933700i	$0.616560\pi$
$740$		0			0
$741$	−33.4512	+	36.8973i	−1.22886	+	1.35545i
$742$		−	19.4126i		−	0.712658i
$743$	−19.5715	+	11.2996i	−0.718010	+	0.414543i	−0.814020	−	0.580837i	$-0.802725\pi$
$743$	−19.5715	+	11.2996i	−0.718010	+	0.414543i	0.0960101	+	0.995380i	$0.469392\pi$
$744$	4.27657	+	7.40723i	0.156787	+	0.271562i
$745$		0			0
$746$	13.1652	+	22.8028i	0.482012	+	0.834869i
$747$	−3.20500	−	1.85041i	−0.117265	−	0.0677030i
$748$		−	0.901542i		−	0.0329636i
$749$	17.7429			0.648313
$750$		0			0
$751$	12.7199	−	22.0315i	0.464155	−	0.803940i	−0.535008	−	0.844847i	$-0.679691\pi$
$751$	12.7199	−	22.0315i	0.464155	−	0.803940i	0.999163	+	0.0409072i	$0.0130248\pi$
$752$		−	15.6336i		−	0.570097i
$753$		−	40.6093i		−	1.47988i
$754$	−3.92571	+	6.79953i	−0.142966	+	0.247624i
$755$		0			0
$756$	0.579305	−	1.00339i	0.0210691	−	0.0364928i
$757$	37.0686	−	21.4015i	1.34728	−	0.777852i	0.359416	−	0.933177i	$-0.382976\pi$
$757$	37.0686	−	21.4015i	1.34728	−	0.777852i	0.987863	+	0.155325i	$0.0496425\pi$
$758$	20.5228	−	11.8489i	0.745422	−	0.430370i
$759$	3.41168			0.123836
$760$		0			0
$761$	−29.8944			−1.08367			−0.541836	−	0.840484i	$-0.682271\pi$
$761$	−29.8944			−1.08367			−0.541836	+	0.840484i	$0.682271\pi$
$762$	22.5637	−	13.0272i	0.817398	−	0.471925i
$763$	−10.2436	+	5.91412i	−0.370842	+	0.214106i
$764$	0.169533	−	0.293639i	0.00613347	−	0.0106235i
$765$		0			0
$766$	−11.5386	+	19.9854i	−0.416905	+	0.722100i
$767$		−	28.6445i		−	1.03429i
$768$			25.8686i			0.933452i
$769$	−8.32179	+	14.4138i	−0.300092	+	0.519774i	−0.976156	−	0.217068i	$-0.930351\pi$
$769$	−8.32179	+	14.4138i	−0.300092	+	0.519774i	0.676065	+	0.736842i	$0.263684\pi$
$770$		0			0
$771$	18.6436			0.671432
$772$			1.90846i			0.0686871i
$773$	5.29435	+	3.05669i	0.190424	+	0.109942i	0.592181	−	0.805805i	$-0.298267\pi$
$773$	5.29435	+	3.05669i	0.190424	+	0.109942i	−0.401757	+	0.915746i	$0.631600\pi$
$774$	−6.72032	−	11.6399i	−0.241557	−	0.418389i
$775$		0			0
$776$	17.9859	+	31.1524i	0.645655	+	1.11831i
$777$	−27.6442	+	15.9604i	−0.991729	+	0.572575i
$778$			11.0951i			0.397780i
$779$	−3.58477	−	0.774765i	−0.128438	−	0.0277588i
$780$		0			0
$781$	0.416692	+	0.721732i	0.0149104	+	0.0258256i
$782$	34.5502	−	19.9476i	1.23551	−	0.713323i
$783$	−1.97899	−	1.14257i	−0.0707234	−	0.0408322i
$784$	7.29762	+	12.6399i	0.260629	+	0.451423i
$785$		0			0
$786$	34.6946			1.23752
$787$		−	18.7781i		−	0.669368i	−0.942330	−	0.334684i	$-0.891370\pi$
$787$		−	18.7781i		−	0.669368i	0.942330	−	0.334684i	$-0.108630\pi$
$788$	−6.41793	−	3.70539i	−0.228629	−	0.131999i
$789$	7.21787	−	12.5017i	0.256963	−	0.445073i
$790$		0			0
$791$	22.2680			0.791759
$792$	1.68073	+	0.970368i	0.0597220	+	0.0344805i
$793$	19.3028	−	11.1445i	0.685462	−	0.395752i
$794$	10.3835	−	17.9848i	0.368497	−	0.638255i
$795$		0			0
$796$	2.92070	+	5.05879i	0.103521	+	0.179304i
$797$			30.2851i			1.07275i	0.843978	+	0.536377i	$0.180208\pi$
$797$			30.2851i			1.07275i	−0.843978	+	0.536377i	$0.819792\pi$
$798$	−14.8920	+	4.78257i	−0.527172	+	0.169301i
$799$	35.7249			1.26386
$800$		0			0
$801$	17.8062	+	30.8412i	0.629151	+	1.08972i
$802$	−1.68402	−	0.972271i	−0.0594649	−	0.0343321i
$803$	0.188684	−	0.108937i	0.00665851	−	0.00384430i
$804$	0.571173	−	0.989301i	0.0201437	−	0.0348899i
$805$		0			0
$806$	7.46491			0.262940
$807$	−16.3050	−	9.41368i	−0.573962	−	0.331377i
$808$	21.0072	+	12.1285i	0.739032	+	0.426680i
$809$	−13.6015			−0.478202			−0.239101	−	0.970995i	$-0.576853\pi$
$809$	−13.6015			−0.478202			−0.239101	+	0.970995i	$0.576853\pi$
$810$		0			0
$811$	−0.799180	+	1.38422i	−0.0280630	+	0.0486065i	−0.879716	−	0.475500i	$-0.842267\pi$
$811$	−0.799180	+	1.38422i	−0.0280630	+	0.0486065i	0.851653	+	0.524106i	$0.175601\pi$
$812$	0.725199	−	0.418694i	0.0254495	−	0.0146933i
$813$	−8.35506	−	4.82379i	−0.293025	−	0.169178i
$814$	1.89351	+	3.27965i	0.0663674	+	0.114952i
$815$		0			0
$816$	38.8866			1.36130
$817$	−4.55875	+	21.0929i	−0.159490	+	0.737947i
$818$			2.43995i			0.0853107i
$819$	7.13857	+	12.3644i	0.249442	+	0.432046i
$820$		0			0
$821$	9.40110	−	16.2832i	0.328101	−	0.568287i	−0.654034	−	0.756465i	$-0.726925\pi$
$821$	9.40110	−	16.2832i	0.328101	−	0.568287i	0.982135	+	0.188178i	$0.0602582\pi$
$822$	−44.8194	+	25.8765i	−1.56326	+	0.902546i
$823$	46.0697	+	26.5984i	1.60589	+	0.927161i	0.990277	+	0.139111i	$0.0444246\pi$
$823$	46.0697	+	26.5984i	1.60589	+	0.927161i	0.615612	+	0.788049i	$0.288909\pi$
$824$	−39.2718			−1.36810
$825$		0			0
$826$	4.49800	−	7.79076i	0.156505	−	0.271075i
$827$	21.7149	+	12.5371i	0.755101	+	0.435957i	0.827534	−	0.561416i	$-0.189743\pi$
$827$	21.7149	+	12.5371i	0.755101	+	0.435957i	−0.0724334	+	0.997373i	$0.523076\pi$
$828$		−	5.89843i		−	0.204985i
$829$	28.2740			0.981997			0.490999	−	0.871160i	$-0.336632\pi$
$829$	28.2740			0.981997			0.490999	+	0.871160i	$0.336632\pi$
$830$		0			0
$831$	11.2399	+	19.4681i	0.389908	+	0.675341i
$832$	38.4059	+	22.1737i	1.33149	+	0.768733i
$833$	−28.8839	+	16.6761i	−1.00077	+	0.577793i
$834$	−8.39608	−	14.5424i	−0.290732	−	0.503563i
$835$		0			0
$836$	−0.192688	−	0.599995i	−0.00666427	−	0.0207513i
$837$			2.17265i			0.0750977i
$838$	24.1033	−	13.9160i	0.832633	−	0.480721i
$839$	7.33983	+	12.7130i	0.253399	+	0.438900i	0.964459	−	0.264231i	$-0.0851181\pi$
$839$	7.33983	+	12.7130i	0.253399	+	0.438900i	−0.711060	+	0.703131i	$0.751785\pi$
$840$		0			0
$841$	13.6742	+	23.6844i	0.471524	+	0.816704i
$842$	14.6466	+	8.45623i	0.504756	+	0.291421i
$843$		−	12.2952i		−	0.423468i
$844$	−8.69059			−0.299142
$845$		0			0
$846$	−7.77657	+	13.4694i	−0.267364	+	0.463088i
$847$			14.0321i			0.482148i
$848$			33.7358i			1.15849i
$849$	−5.67265	+	9.82531i	−0.194685	+	0.337204i
$850$		0			0
$851$	28.4558	−	49.2869i	0.975452	−	1.68953i
$852$	2.93259	−	1.69313i	0.100469	−	0.0580058i
$853$	22.4341	−	12.9523i	0.768129	−	0.443479i	−0.0640780	−	0.997945i	$-0.520411\pi$
$853$	22.4341	−	12.9523i	0.768129	−	0.443479i	0.832207	+	0.554466i	$0.187077\pi$
$854$	7.00000			0.239535
$855$		0			0
$856$	−42.2921			−1.44551
$857$	−11.1765	+	6.45277i	−0.381783	+	0.220423i	−0.678594	−	0.734514i	$-0.737410\pi$
$857$	−11.1765	+	6.45277i	−0.381783	+	0.220423i	0.296811	+	0.954936i	$0.404077\pi$
$858$	3.44749	−	1.99041i	0.117695	−	0.0679515i
$859$	−14.3589	+	24.8703i	−0.489919	+	0.848564i	−0.999933	−	0.0116018i	$-0.996307\pi$
$859$	−14.3589	+	24.8703i	−0.489919	+	0.848564i	0.510014	+	0.860166i	$0.329640\pi$
$860$		0			0
$861$	−1.23547	+	2.13990i	−0.0421047	+	0.0729275i
$862$			4.20295i			0.143153i
$863$			3.04300i			0.103585i	0.998658	+	0.0517925i	$0.0164934\pi$
$863$			3.04300i			0.103585i	−0.998658	+	0.0517925i	$0.983507\pi$
$864$	−2.48240	+	4.29965i	−0.0844531	+	0.146277i
$865$		0			0
$866$	−11.2421			−0.382024
$867$			50.0140i			1.69857i
$868$	−0.689498	−	0.398082i	−0.0234031	−	0.0135118i
$869$	−2.20384	−	3.81716i	−0.0747600	−	0.129488i
$870$		0			0
$871$	−2.46491	−	4.26934i	−0.0835202	−	0.144661i
$872$	24.4165	−	14.0969i	0.826849	−	0.477381i
$873$		−	26.0913i		−	0.883058i
$874$	18.7305	−	20.6600i	0.633567	−	0.698835i
$875$		0			0
$876$	−0.442639	−	0.766673i	−0.0149554	−	0.0259035i
$877$	9.84616	−	5.68468i	0.332481	−	0.191958i	−0.324461	−	0.945899i	$-0.605183\pi$
$877$	9.84616	−	5.68468i	0.332481	−	0.191958i	0.656942	+	0.753941i	$0.271850\pi$
$878$	−39.6921	−	22.9162i	−1.33954	−	0.773386i
$879$	−4.34885	−	7.53243i	−0.146683	−	0.254063i
$880$		0			0
$881$	36.4014			1.22640			0.613198	−	0.789929i	$-0.289883\pi$
$881$	36.4014			1.22640			0.613198	+	0.789929i	$0.289883\pi$
$882$		−	14.5202i		−	0.488919i
$883$	−43.1003	−	24.8839i	−1.45044	−	0.837411i	−0.451933	−	0.892052i	$-0.649265\pi$
$883$	−43.1003	−	24.8839i	−1.45044	−	0.837411i	−0.998506	+	0.0546404i	$0.982599\pi$
$884$	−7.90431	+	13.6907i	−0.265851	+	0.460467i
$885$		0			0
$886$	17.9356			0.602560
$887$	13.5946	+	7.84885i	0.456462	+	0.263539i	0.710556	−	0.703641i	$-0.248444\pi$
$887$	13.5946	+	7.84885i	0.456462	+	0.263539i	−0.254093	+	0.967180i	$0.581777\pi$
$888$	65.8926	−	38.0431i	2.21121	−	1.27664i
$889$	−5.99600	+	10.3854i	−0.201099	+	0.348314i
$890$		0			0
$891$	1.52963	+	2.64940i	0.0512446	+	0.0887582i
$892$		−	0.772783i		−	0.0258747i
$893$	23.7757	−	7.63555i	0.795623	−	0.255514i
$894$	18.9648			0.634278
$895$		0			0
$896$	3.37547	+	5.84648i	0.112766	+	0.195317i
$897$	−51.8091	−	29.9120i	−1.72986	−	0.998733i
$898$	7.82047	−	4.51515i	0.260972	−	0.150673i
$899$	−0.785142	+	1.35991i	−0.0261860	+	0.0453554i
$900$		0			0
$901$	−77.0911			−2.56828
$902$	0.253873	+	0.146574i	0.00845306	+	0.00488038i
$903$	12.5912	+	7.26955i	0.419010	+	0.241915i
$904$	−53.0780			−1.76535
$905$		0			0
$906$	22.1802	−	38.4173i	0.736889	−	1.27633i
$907$	−28.5057	+	16.4578i	−0.946517	+	0.546472i	−0.891997	−	0.452041i	$-0.850696\pi$
$907$	−28.5057	+	16.4578i	−0.946517	+	0.546472i	−0.0545199	+	0.998513i	$0.517363\pi$
$908$	−1.75636	−	1.01404i	−0.0582870	−	0.0336520i
$909$	−8.79718	−	15.2372i	−0.291784	−	0.505385i
$910$		0			0
$911$	−18.7109			−0.619918			−0.309959	−	0.950750i	$-0.600315\pi$
$911$	−18.7109			−0.619918			−0.309959	+	0.950750i	$0.600315\pi$
$912$	25.8799	−	8.31131i	0.856968	−	0.275215i
$913$		−	0.474941i		−	0.0157183i
$914$	1.40520	+	2.43388i	0.0464799	+	0.0805055i
$915$		0			0
$916$	4.67465	−	8.09673i	0.154455	−	0.267523i
$917$	−13.8294	+	7.98441i	−0.456687	+	0.263668i
$918$	11.7333	+	6.77422i	0.387256	+	0.223583i
$919$	50.9506			1.68070			0.840352	−	0.542041i	$-0.182348\pi$
$919$	50.9506			1.68070			0.840352	+	0.542041i	$0.182348\pi$
$920$		0			0
$921$	−0.656164	+	1.13651i	−0.0216214	+	0.0374493i
$922$	−20.9063	−	12.0703i	−0.688514	−	0.397514i
$923$		−	14.6135i		−	0.481009i
$924$	−0.424571			−0.0139674
$925$		0			0
$926$	−17.6847	−	30.6308i	−0.581155	−	1.00659i
$927$	24.6687	+	14.2425i	0.810227	+	0.467785i
$928$	−3.10758	+	1.79416i	−0.102011	+	0.0588963i
$929$	5.74249	+	9.94628i	0.188405	+	0.326327i	0.944719	−	0.327882i	$-0.106335\pi$
$929$	5.74249	+	9.94628i	0.188405	+	0.326327i	−0.756314	+	0.654209i	$0.773002\pi$
$930$		0			0
$931$	−15.6586	+	17.2717i	−0.513190	+	0.566057i
$932$		−	6.44509i		−	0.211116i
$933$	17.0518	−	9.84485i	0.558250	−	0.322306i
$934$	−2.02662	−	3.51020i	−0.0663129	−	0.114857i
$935$		0			0
$936$	−17.0155	−	29.4717i	−0.556169	−	0.963313i
$937$	−14.0032	−	8.08477i	−0.457465	−	0.264118i	0.253512	−	0.967332i	$-0.418414\pi$
$937$	−14.0032	−	8.08477i	−0.457465	−	0.264118i	−0.710978	+	0.703214i	$0.751747\pi$
$938$		−	1.54824i		−	0.0505519i
$939$	77.9769			2.54468
$940$		0			0
$941$	12.6937	−	21.9861i	0.413803	−	0.716728i	−0.581499	−	0.813547i	$-0.697534\pi$
$941$	12.6937	−	21.9861i	0.413803	−	0.716728i	0.995302	+	0.0968194i	$0.0308669\pi$
$942$			20.9608i			0.682940i
$943$		−	4.40545i		−	0.143461i
$944$	−7.81678	+	13.5391i	−0.254414	+	0.440659i
$945$		0			0
$946$	0.862446	−	1.49380i	0.0280405	−	0.0485676i
$947$	20.2481	−	11.6902i	0.657975	−	0.379882i	−0.133530	−	0.991045i	$-0.542631\pi$
$947$	20.2481	−	11.6902i	0.657975	−	0.379882i	0.791505	+	0.611163i	$0.209298\pi$
$948$	−15.5101	+	8.95477i	−0.503745	+	0.290838i
$949$	−3.82043			−0.124016
$950$		0			0
$951$	−25.3132			−0.820837
$952$	−21.2602	+	12.2746i	−0.689046	+	0.397821i
$953$	19.2073	−	11.0893i	0.622185	−	0.359219i	−0.155534	−	0.987831i	$-0.549710\pi$
$953$	19.2073	−	11.0893i	0.622185	−	0.359219i	0.777719	+	0.628612i	$0.216376\pi$
$954$	16.7811	−	29.0658i	0.543309	−	0.941040i
$955$		0			0
$956$	−2.74659	+	4.75723i	−0.0888310	+	0.153860i
$957$			0.837388i			0.0270689i
$958$			48.2727i			1.55962i
$959$	11.9101	−	20.6289i	0.384598	−	0.666143i
$960$		0			0
$961$	−29.5070			−0.951839
$962$		−	66.4057i		−	2.14101i
$963$	26.5659	+	15.3378i	0.856074	+	0.494255i
$964$	2.50302	+	4.33535i	0.0806167	+	0.139632i
$965$		0			0
$966$	−9.39408	−	16.2710i	−0.302250	−	0.523512i
$967$	−35.3853	+	20.4297i	−1.13791	+	0.656975i	−0.945913	−	0.324419i	$-0.894831\pi$
$967$	−35.3853	+	20.4297i	−1.13791	+	0.656975i	−0.192001	+	0.981395i	$0.561498\pi$
$968$		−	33.4469i		−	1.07502i
$969$	18.9925	+	59.1392i	0.610128	+	1.89982i
$970$		0			0
$971$	−12.3238	−	21.3454i	−0.395489	−	0.685008i	0.597674	−	0.801739i	$-0.296092\pi$
$971$	−12.3238	−	21.3454i	−0.395489	−	0.685008i	−0.993164	+	0.116731i	$0.962758\pi$
$972$	8.42294	−	4.86299i	0.270166	−	0.155980i
$973$	6.69342	+	3.86445i	0.214581	+	0.123888i
$974$	−15.1379	−	26.2196i	−0.485050	−	0.840131i
$975$		0			0
$976$	−12.1648			−0.389387
$977$		−	13.7077i		−	0.438549i	−0.975663	−	0.219275i	$-0.929631\pi$
$977$		−	13.7077i		−	0.438549i	0.975663	−	0.219275i	$-0.0703691\pi$
$978$	52.7631	+	30.4628i	1.68718	+	0.974093i
$979$	−2.28514	+	3.95798i	−0.0730335	+	0.126498i
$980$		0			0
$981$	−20.4498			−0.652911
$982$	14.4161	+	8.32313i	0.460035	+	0.265602i
$983$	−0.244243	+	0.141014i	−0.00779015	+	0.00449765i	−0.503890	−	0.863768i	$-0.668098\pi$
$983$	−0.244243	+	0.141014i	−0.00779015	+	0.00449765i	0.496100	+	0.868265i	$0.334765\pi$
$984$	2.94487	−	5.10066i	0.0938789	−	0.162603i
$985$		0			0
$986$	4.89608	+	8.48026i	0.155923	+	0.270067i
$987$		−	16.8242i		−	0.535521i
$988$	−2.33435	+	10.8008i	−0.0742657	+	0.343620i
$989$	−25.9218			−0.824266
$990$		0			0
$991$	−12.2992	−	21.3028i	−0.390696	−	0.676706i	0.601845	−	0.798613i	$-0.294432\pi$
$991$	−12.2992	−	21.3028i	−0.390696	−	0.676706i	−0.992542	+	0.121907i	$0.961099\pi$
$992$	2.95460	+	1.70584i	0.0938086	+	0.0541604i
$993$	−12.6887	+	7.32580i	−0.402662	+	0.232477i
$994$	2.29473	−	3.97459i	0.0727845	−	0.126066i
$995$		0			0
$996$	−1.92981			−0.0611485
$997$	20.0768	+	11.5913i	0.635838	+	0.367101i	0.783010	−	0.622010i	$-0.213684\pi$
$997$	20.0768	+	11.5913i	0.635838	+	0.367101i	−0.147171	+	0.989111i	$0.547017\pi$
$998$	8.66625	+	5.00346i	0.274325	+	0.158382i
$999$	19.3273			0.611487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.j.b.349.4		12
5.2	odd	4		475.2.e.d.26.2		6
5.3	odd	4		95.2.e.b.26.2	yes	6
5.4	even	2	inner	475.2.j.b.349.3		12
15.8	even	4		855.2.k.g.406.2		6
19.11	even	3	inner	475.2.j.b.49.3		12
20.3	even	4		1520.2.q.j.881.3		6
95.7	odd	12		9025.2.a.z.1.2		3
95.12	even	12		9025.2.a.ba.1.2		3
95.49	even	6	inner	475.2.j.b.49.4		12
95.68	odd	12		95.2.e.b.11.2	✓	6
95.83	odd	12		1805.2.a.h.1.2		3
95.87	odd	12		475.2.e.d.201.2		6
95.88	even	12		1805.2.a.g.1.2		3
285.68	even	12		855.2.k.g.676.2		6
380.163	even	12		1520.2.q.j.961.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.b.11.2	✓	6	95.68	odd	12
95.2.e.b.26.2	yes	6	5.3	odd	4
475.2.e.d.26.2		6	5.2	odd	4
475.2.e.d.201.2		6	95.87	odd	12
475.2.j.b.49.3		12	19.11	even	3	inner
475.2.j.b.49.4		12	95.49	even	6	inner
475.2.j.b.349.3		12	5.4	even	2	inner
475.2.j.b.349.4		12	1.1	even	1	trivial
855.2.k.g.406.2		6	15.8	even	4
855.2.k.g.676.2		6	285.68	even	12
1520.2.q.j.881.3		6	20.3	even	4
1520.2.q.j.961.3		6	380.163	even	12
1805.2.a.g.1.2		3	95.88	even	12
1805.2.a.h.1.2		3	95.83	odd	12
9025.2.a.z.1.2		3	95.7	odd	12
9025.2.a.ba.1.2		3	95.12	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.05818 - 0.610938i) q^{2} +(-1.97899 + 1.14257i) q^{3} +(-0.253509 + 0.439091i) q^{4} +(-1.39608 + 2.41808i) q^{6} -1.28514i q^{7} +3.06327i q^{8} +(1.11094 - 1.92420i) q^{9} +O(q^{10})\)	\(q+(1.05818 - 0.610938i) q^{2} +(-1.97899 + 1.14257i) q^{3} +(-0.253509 + 0.439091i) q^{4} +(-1.39608 + 2.41808i) q^{6} -1.28514i q^{7} +3.06327i q^{8} +(1.11094 - 1.92420i) q^{9} +0.285142 q^{11} -1.15861i q^{12} +(-4.33013 - 2.50000i) q^{13} +(-0.785142 - 1.35991i) q^{14} +(1.36445 + 2.36329i) q^{16} +(-5.40046 + 3.11796i) q^{17} -2.71486i q^{18} +(-2.92771 + 3.22932i) q^{19} +(1.46837 + 2.54329i) q^{21} +(0.301731 - 0.174204i) q^{22} +(-4.53443 - 2.61796i) q^{23} +(-3.50000 - 6.06218i) q^{24} -6.10938 q^{26} -1.77812i q^{27} +(0.564295 + 0.325796i) q^{28} +(0.642571 - 1.11297i) q^{29} -1.22188 q^{31} +(-2.41808 - 1.39608i) q^{32} +(-0.564295 + 0.325796i) q^{33} +(-3.80976 + 6.59869i) q^{34} +(0.563266 + 0.975606i) q^{36} +10.8695i q^{37} +(-1.12512 + 5.20584i) q^{38} +11.4257 q^{39} +(0.420695 + 0.728665i) q^{41} +(3.10758 + 1.79416i) q^{42} +(4.28749 - 2.47539i) q^{43} +(-0.0722863 + 0.125204i) q^{44} -6.39764 q^{46} +(-4.96137 - 2.86445i) q^{47} +(-5.40046 - 3.11796i) q^{48} +5.34841 q^{49} +(7.12498 - 12.3408i) q^{51} +(2.19546 - 1.26755i) q^{52} +(10.7062 + 6.18122i) q^{53} +(-1.08632 - 1.88157i) q^{54} +3.93673 q^{56} +(2.10419 - 9.73591i) q^{57} -1.57028i q^{58} +(2.86445 + 4.96137i) q^{59} +(-2.22889 + 3.86056i) q^{61} +(-1.29296 + 0.746491i) q^{62} +(-2.47287 - 1.42771i) q^{63} -8.86946 q^{64} +(-0.398082 + 0.689498i) q^{66} +(0.853869 + 0.492981i) q^{67} -3.16172i q^{68} +11.9648 q^{69} +(1.46135 + 2.53113i) q^{71} +(5.89434 + 3.40310i) q^{72} +(0.661718 - 0.382043i) q^{73} +(6.64057 + 11.5018i) q^{74} +(-0.675762 - 2.10419i) q^{76} -0.366449i q^{77} +(12.0904 - 6.98040i) q^{78} +(-7.72889 - 13.3868i) q^{79} +(5.36445 + 9.29150i) q^{81} +(0.890339 + 0.514037i) q^{82} -1.66563i q^{83} -1.48898 q^{84} +(3.02461 - 5.23879i) q^{86} +2.93673i q^{87} +0.873467i q^{88} +(-8.01404 + 13.8807i) q^{89} +(-3.21286 + 5.56483i) q^{91} +(2.29904 - 1.32735i) q^{92} +(2.41808 - 1.39608i) q^{93} -7.00000 q^{94} +6.38049 q^{96} +(10.1697 - 5.87147i) q^{97} +(5.65956 - 3.26755i) q^{98} +(0.316776 - 0.548672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 14 q^{4} + 12 q^{6} + 8 q^{9}+O(q^{10}) \) 12 * q + 14 * q^4 + 12 * q^6 + 8 * q^9	\( 12 q + 14 q^{4} + 12 q^{6} + 8 q^{9} - 20 q^{11} + 14 q^{14} - 6 q^{16} + 24 q^{21} - 42 q^{24} - 20 q^{26} - 4 q^{29} - 4 q^{31} - 50 q^{34} - 6 q^{36} + 20 q^{39} + 4 q^{41} - 36 q^{44} - 96 q^{46} + 28 q^{49} + 12 q^{51} + 20 q^{54} + 60 q^{56} + 12 q^{59} + 18 q^{61} + 32 q^{64} - 58 q^{66} + 20 q^{69} + 58 q^{71} - 14 q^{74} - 38 q^{76} - 48 q^{79} + 42 q^{81} + 112 q^{84} + 64 q^{86} - 28 q^{89} + 20 q^{91} - 84 q^{94} + 68 q^{96} - 26 q^{99}+O(q^{100}) \) 12 * q + 14 * q^4 + 12 * q^6 + 8 * q^9 - 20 * q^11 + 14 * q^14 - 6 * q^16 + 24 * q^21 - 42 * q^24 - 20 * q^26 - 4 * q^29 - 4 * q^31 - 50 * q^34 - 6 * q^36 + 20 * q^39 + 4 * q^41 - 36 * q^44 - 96 * q^46 + 28 * q^49 + 12 * q^51 + 20 * q^54 + 60 * q^56 + 12 * q^59 + 18 * q^61 + 32 * q^64 - 58 * q^66 + 20 * q^69 + 58 * q^71 - 14 * q^74 - 38 * q^76 - 48 * q^79 + 42 * q^81 + 112 * q^84 + 64 * q^86 - 28 * q^89 + 20 * q^91 - 84 * q^94 + 68 * q^96 - 26 * q^99

Introduction

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