LMFDB - Embedded newform 475.2.e.d.201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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([0, 2]))

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.e (of order $3$, degree $2$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.3518667.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 $ x^6 - x^5 + 7x^4 - 8x^3 + 43x^2 - 42x + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.2
Root			$0.610938 - 1.05818i$ of defining polynomial
Character	$\chi$	$=$	475.201
Dual form			475.2.e.d.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.610938 - 1.05818i) q^{2} +(1.14257 - 1.97899i) q^{3} +(0.253509 + 0.439091i) q^{4} +(-1.39608 - 2.41808i) q^{6} +1.28514 q^{7} +3.06327 q^{8} +(-1.11094 - 1.92420i) q^{9} +0.285142 q^{11} +1.15861 q^{12} +(-2.50000 - 4.33013i) q^{13} +(0.785142 - 1.35991i) q^{14} +(1.36445 - 2.36329i) q^{16} +(-3.11796 + 5.40046i) q^{17} -2.71486 q^{18} +(2.92771 + 3.22932i) q^{19} +(1.46837 - 2.54329i) q^{21} +(0.174204 - 0.301731i) q^{22} +(-2.61796 - 4.53443i) q^{23} +(3.50000 - 6.06218i) q^{24} -6.10938 q^{26} +1.77812 q^{27} +(0.325796 + 0.564295i) q^{28} +(-0.642571 - 1.11297i) q^{29} -1.22188 q^{31} +(1.39608 + 2.41808i) q^{32} +(0.325796 - 0.564295i) q^{33} +(3.80976 + 6.59869i) q^{34} +(0.563266 - 0.975606i) q^{36} -10.8695 q^{37} +(5.20584 - 1.12512i) q^{38} -11.4257 q^{39} +(0.420695 - 0.728665i) q^{41} +(-1.79416 - 3.10758i) q^{42} +(-2.47539 + 4.28749i) q^{43} +(0.0722863 + 0.125204i) q^{44} -6.39764 q^{46} +(2.86445 + 4.96137i) q^{47} +(-3.11796 - 5.40046i) q^{48} -5.34841 q^{49} +(7.12498 + 12.3408i) q^{51} +(1.26755 - 2.19546i) q^{52} +(6.18122 + 10.7062i) q^{53} +(1.08632 - 1.88157i) q^{54} +3.93673 q^{56} +(9.73591 - 2.10419i) q^{57} -1.57028 q^{58} +(-2.86445 + 4.96137i) q^{59} +(-2.22889 - 3.86056i) q^{61} +(-0.746491 + 1.29296i) q^{62} +(-1.42771 - 2.47287i) q^{63} +8.86946 q^{64} +(-0.398082 - 0.689498i) q^{66} +(-0.492981 - 0.853869i) q^{67} -3.16172 q^{68} -11.9648 q^{69} +(1.46135 - 2.53113i) q^{71} +(-3.40310 - 5.89434i) q^{72} +(-0.382043 + 0.661718i) q^{73} +(-6.64057 + 11.5018i) q^{74} +(-0.675762 + 2.10419i) q^{76} +0.366449 q^{77} +(-6.98040 + 12.0904i) q^{78} +(7.72889 - 13.3868i) q^{79} +(5.36445 - 9.29150i) q^{81} +(-0.514037 - 0.890339i) q^{82} -1.66563 q^{83} +1.48898 q^{84} +(3.02461 + 5.23879i) q^{86} -2.93673 q^{87} +0.873467 q^{88} +(8.01404 + 13.8807i) q^{89} +(-3.21286 - 5.56483i) q^{91} +(1.32735 - 2.29904i) q^{92} +(-1.39608 + 2.41808i) q^{93} +7.00000 q^{94} +6.38049 q^{96} +(5.87147 - 10.1697i) q^{97} +(-3.26755 + 5.65956i) q^{98} +(-0.316776 - 0.548672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + q^{3} - 7 q^{4} + 6 q^{6} - 4 q^{7} + 12 q^{8} - 4 q^{9} - 10 q^{11} + 8 q^{12} - 15 q^{13} - 7 q^{14} - 3 q^{16} + q^{17} - 28 q^{18} + 12 q^{21} - 8 q^{22} + 4 q^{23} + 21 q^{24} - 10 q^{26}+ \cdots + 13 q^{99}+O(q^{100}) $ 6 * q + q^2 + q^3 - 7 * q^4 + 6 * q^6 - 4 * q^7 + 12 * q^8 - 4 * q^9 - 10 * q^11 + 8 * q^12 - 15 * q^13 - 7 * q^14 - 3 * q^16 + q^17 - 28 * q^18 + 12 * q^21 - 8 * q^22 + 4 * q^23 + 21 * q^24 - 10 * q^26 + 16 * q^27 + 11 * q^28 + 2 * q^29 - 2 * q^31 - 6 * q^32 + 11 * q^33 + 25 * q^34 - 3 * q^36 + 4 * q^37 + 19 * q^38 - 10 * q^39 + 2 * q^41 - 23 * q^42 - q^43 + 18 * q^44 - 48 * q^46 + 6 * q^47 + q^48 - 14 * q^49 + 6 * q^51 - 35 * q^52 + 11 * q^53 - 10 * q^54 + 30 * q^56 + 19 * q^57 + 14 * q^58 - 6 * q^59 + 9 * q^61 - 13 * q^62 + 9 * q^63 - 16 * q^64 - 29 * q^66 - 20 * q^67 - 68 * q^68 - 10 * q^69 + 29 * q^71 + 11 * q^72 - 22 * q^73 + 7 * q^74 - 19 * q^76 + 32 * q^77 + 30 * q^78 + 24 * q^79 + 21 * q^81 + 31 * q^82 + 6 * q^83 - 56 * q^84 + 32 * q^86 - 24 * q^87 + 18 * q^88 + 14 * q^89 + 10 * q^91 + 41 * q^92 + 6 * q^93 + 42 * q^94 + 34 * q^96 + 7 * q^97 + 23 * q^98 + 13 * q^99

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.610938	−	1.05818i	0.431998	−	0.748243i	−0.565047	−	0.825059i	$-0.691142\pi$
$2$	0.610938	−	1.05818i	0.431998	−	0.748243i	0.997045	+	0.0768155i	$0.0244753\pi$
$3$	1.14257	−	1.97899i	0.659664	−	1.14257i	−0.321039	−	0.947066i	$-0.604032\pi$
$3$	1.14257	−	1.97899i	0.659664	−	1.14257i	0.980703	−	0.195505i	$-0.0626347\pi$
$4$	0.253509	+	0.439091i	0.126755	+	0.219546i
$5$		0			0
$5$		0			0
$6$	−1.39608	−	2.41808i	−0.569948	−	0.987178i
$7$	1.28514			0.485738			0.242869	−	0.970059i	$-0.421911\pi$
$7$	1.28514			0.485738			0.242869	+	0.970059i	$0.421911\pi$
$8$	3.06327			1.08303
$9$	−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	$0.486313\pi$
$12$	1.15861			0.334462
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	0.277350	−	0.960769i	$-0.410544\pi$
$14$	0.785142	−	1.35991i	0.209838	−	0.363450i
$15$		0			0
$16$	1.36445	−	2.36329i	0.341112	−	0.590823i
$17$	−3.11796	+	5.40046i	−0.756216	+	1.30980i	0.188552	+	0.982063i	$0.439621\pi$
$17$	−3.11796	+	5.40046i	−0.756216	+	1.30980i	−0.944768	+	0.327741i	$0.893713\pi$
$18$	−2.71486			−0.639898
$19$	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
$22$	0.174204	−	0.301731i	0.0371405	−	0.0643292i
$23$	−2.61796	−	4.53443i	−0.545882	−	0.945495i	−0.998551	−	0.0538163i	$-0.982861\pi$
$23$	−2.61796	−	4.53443i	−0.545882	−	0.945495i	0.452669	−	0.891679i	$-0.350472\pi$
$24$	3.50000	−	6.06218i	0.714435	−	1.23744i
$25$		0			0
$26$	−6.10938			−1.19815
$27$	1.77812			0.342200
$28$	0.325796	+	0.564295i	0.0615696	+	0.106642i
$29$	−0.642571	−	1.11297i	−0.119322	−	0.206673i	0.800177	−	0.599764i	$-0.204739\pi$
$29$	−0.642571	−	1.11297i	−0.119322	−	0.206673i	−0.919499	+	0.393091i	$0.871406\pi$
$30$		0			0
$31$	−1.22188			−0.219455			−0.109728	−	0.993962i	$-0.534998\pi$
$31$	−1.22188			−0.219455			−0.109728	+	0.993962i	$0.534998\pi$
$32$	1.39608	+	2.41808i	0.246795	+	0.427461i
$33$	0.325796	−	0.564295i	0.0567137	−	0.0982311i
$34$	3.80976	+	6.59869i	0.653368	+	1.13167i
$35$		0			0
$36$	0.563266	−	0.975606i	0.0938777	−	0.162601i
$37$	−10.8695			−1.78693			−0.893464	−	0.449134i	$-0.851733\pi$
$37$	−10.8695			−1.78693			−0.893464	+	0.449134i	$0.851733\pi$
$38$	5.20584	−	1.12512i	0.844498	−	0.182519i
$39$	−11.4257			−1.82958
$40$		0			0
$41$	0.420695	−	0.728665i	0.0657015	−	0.113798i	−0.831303	−	0.555819i	$-0.812405\pi$
$41$	0.420695	−	0.728665i	0.0657015	−	0.113798i	0.897005	+	0.442020i	$0.145738\pi$
$42$	−1.79416	−	3.10758i	−0.276845	−	0.479510i
$43$	−2.47539	+	4.28749i	−0.377493	+	0.653837i	−0.990697	−	0.136088i	$-0.956547\pi$
$43$	−2.47539	+	4.28749i	−0.377493	+	0.653837i	0.613204	+	0.789925i	$0.289880\pi$
$44$	0.0722863	+	0.125204i	0.0108976	+	0.0188751i
$45$		0			0
$46$	−6.39764			−0.943280
$47$	2.86445	+	4.96137i	0.417823	+	0.723690i	0.995720	−	0.0924193i	$-0.0294600\pi$
$47$	2.86445	+	4.96137i	0.417823	+	0.723690i	−0.577898	+	0.816109i	$0.696127\pi$
$48$	−3.11796	−	5.40046i	−0.450038	−	0.779489i
$49$	−5.34841			−0.764058
$50$		0			0
$51$	7.12498	+	12.3408i	0.997696	+	1.72806i
$52$	1.26755	−	2.19546i	0.175777	−	0.304455i
$53$	6.18122	+	10.7062i	0.849056	+	1.47061i	0.882051	+	0.471153i	$0.156162\pi$
$53$	6.18122	+	10.7062i	0.849056	+	1.47061i	−0.0329952	+	0.999456i	$0.510505\pi$
$54$	1.08632	−	1.88157i	0.147830	−	0.256049i
$55$		0			0
$56$	3.93673			0.526068
$57$	9.73591	−	2.10419i	1.28955	−	0.278707i
$58$	−1.57028			−0.206189
$59$	−2.86445	+	4.96137i	−0.372919	+	0.645915i	−0.990013	−	0.140974i	$-0.954977\pi$
$59$	−2.86445	+	4.96137i	−0.372919	+	0.645915i	0.617094	+	0.786889i	$0.288310\pi$
$60$		0			0
$61$	−2.22889	−	3.86056i	−0.285381	−	0.494294i	0.687321	−	0.726354i	$-0.258787\pi$
$61$	−2.22889	−	3.86056i	−0.285381	−	0.494294i	−0.972701	+	0.232060i	$0.925453\pi$
$62$	−0.746491	+	1.29296i	−0.0948044	+	0.164206i
$63$	−1.42771	−	2.47287i	−0.179875	−	0.311553i
$64$	8.86946			1.10868
$65$		0			0
$66$	−0.398082	−	0.689498i	−0.0490005	−	0.0848713i
$67$	−0.492981	−	0.853869i	−0.0602273	−	0.104317i	0.834340	−	0.551251i	$-0.185849\pi$
$67$	−0.492981	−	0.853869i	−0.0602273	−	0.104317i	−0.894567	+	0.446934i	$0.852516\pi$
$68$	−3.16172			−0.383415
$69$	−11.9648			−1.44039
$70$		0			0
$71$	1.46135	−	2.53113i	0.173430	−	0.300390i	−0.766187	−	0.642618i	$-0.777848\pi$
$71$	1.46135	−	2.53113i	0.173430	−	0.300390i	0.939617	+	0.342228i	$0.111182\pi$
$72$	−3.40310	−	5.89434i	−0.401059	−	0.694655i
$73$	−0.382043	+	0.661718i	−0.0447148	+	0.0774483i	−0.887517	−	0.460776i	$-0.847571\pi$
$73$	−0.382043	+	0.661718i	−0.0447148	+	0.0774483i	0.842802	+	0.538224i	$0.180905\pi$
$74$	−6.64057	+	11.5018i	−0.771951	+	1.33706i
$75$		0			0
$76$	−0.675762	+	2.10419i	−0.0775152	+	0.241368i
$77$	0.366449			0.0417607
$78$	−6.98040	+	12.0904i	−0.790375	+	1.36897i
$79$	7.72889	−	13.3868i	0.869569	−	1.50614i	0.00713043	−	0.999975i	$-0.497730\pi$
$79$	7.72889	−	13.3868i	0.869569	−	1.50614i	0.862438	−	0.506162i	$-0.168936\pi$
$80$		0			0
$81$	5.36445	−	9.29150i	0.596050	−	1.03239i
$82$	−0.514037	−	0.890339i	−0.0567659	−	0.0983215i
$83$	−1.66563			−0.182826			−0.0914132	−	0.995813i	$-0.529138\pi$
$83$	−1.66563			−0.182826			−0.0914132	+	0.995813i	$0.529138\pi$
$84$	1.48898			0.162461
$85$		0			0
$86$	3.02461	+	5.23879i	0.326153	+	0.564913i
$87$	−2.93673			−0.314851
$88$	0.873467			0.0931119
$89$	8.01404	+	13.8807i	0.849486	+	1.47135i	0.881667	+	0.471871i	$0.156421\pi$
$89$	8.01404	+	13.8807i	0.849486	+	1.47135i	−0.0321812	+	0.999482i	$0.510245\pi$
$90$		0			0
$91$	−3.21286	−	5.56483i	−0.336799	−	0.583353i
$92$	1.32735	−	2.29904i	0.138386	−	0.239692i
$93$	−1.39608	+	2.41808i	−0.144767	+	0.250743i
$94$	7.00000			0.721995
$95$		0			0
$96$	6.38049			0.651206
$97$	5.87147	−	10.1697i	0.596157	−	1.03257i	−0.397225	−	0.917721i	$-0.630027\pi$
$97$	5.87147	−	10.1697i	0.596157	−	1.03257i	0.993382	−	0.114853i	$-0.0366398\pi$
$98$	−3.26755	+	5.65956i	−0.330072	+	0.571702i
$99$	−0.316776	−	0.548672i	−0.0318371	−	0.0551436i
$100$		0			0
$101$	3.95935	+	6.85779i	0.393970	+	0.682376i	0.992969	−	0.118374i	$-0.0377681\pi$
$101$	3.95935	+	6.85779i	0.393970	+	0.682376i	−0.598999	+	0.800750i	$0.704435\pi$
$102$	17.4117			1.72401
$103$	12.8202			1.26322			0.631608	−	0.775288i	$-0.282395\pi$
$103$	12.8202			1.26322			0.631608	+	0.775288i	$0.282395\pi$
$104$	−7.65817	−	13.2643i	−0.750945	−	1.30067i
$105$		0			0
$106$	15.1054			1.46716
$107$	−13.8062			−1.33470			−0.667348	−	0.744746i	$-0.732571\pi$
$107$	−13.8062			−1.33470			−0.667348	+	0.744746i	$0.732571\pi$
$108$	0.450771	+	0.780758i	0.0433755	+	0.0751285i
$109$	4.60192	−	7.97076i	0.440784	−	0.763460i	−0.556964	−	0.830537i	$-0.688034\pi$
$109$	4.60192	−	7.97076i	0.440784	−	0.763460i	0.997748	+	0.0670767i	$0.0213672\pi$
$110$		0			0
$111$	−12.4191	+	21.5106i	−1.17877	+	2.04169i
$112$	1.75351	−	3.03717i	0.165691	−	0.286985i
$113$	17.3273			1.63001			0.815005	−	0.579453i	$-0.196734\pi$
$113$	17.3273			1.63001			0.815005	+	0.579453i	$0.196734\pi$
$114$	3.72143	−	11.5878i	0.348544	−	1.08530i
$115$		0			0
$116$	0.325796	−	0.564295i	0.0302494	−	0.0523934i
$117$	−5.55469	+	9.62101i	−0.513531	+	0.889462i
$118$	3.50000	+	6.06218i	0.322201	+	0.558069i
$119$	−4.00702	+	6.94036i	−0.367323	+	0.636222i
$120$		0			0
$121$	−10.9187			−0.992609
$122$	−5.44687			−0.493136
$123$	−0.961348	−	1.66510i	−0.0866818	−	0.150137i
$124$	−0.309757	−	0.536515i	−0.0278170	−	0.0481805i
$125$		0			0
$126$	−3.48898			−0.310823
$127$	4.66563	+	8.08111i	0.414008	+	0.717082i	0.995324	−	0.0965956i	$-0.0307954\pi$
$127$	4.66563	+	8.08111i	0.414008	+	0.717082i	−0.581316	+	0.813678i	$0.697462\pi$
$128$	2.62653	−	4.54929i	0.232155	−	0.402104i
$129$	5.65661	+	9.79753i	0.498037	+	0.862625i
$130$		0			0
$131$	−6.21286	+	10.7610i	−0.542820	+	0.940191i	0.455921	+	0.890020i	$0.349310\pi$
$131$	−6.21286	+	10.7610i	−0.542820	+	0.940191i	−0.998741	+	0.0501711i	$0.984023\pi$
$132$	0.330369			0.0287549
$133$	3.76253	+	4.15013i	0.326253	+	0.359862i
$134$	−1.20472			−0.104072
$135$		0			0
$136$	−9.55113	+	16.5430i	−0.819003	+	1.41855i
$137$	−9.26755	−	16.0519i	−0.791780	−	1.37140i	−0.924864	−	0.380298i	$-0.875821\pi$
$137$	−9.26755	−	16.0519i	−0.791780	−	1.37140i	0.133084	−	0.991105i	$-0.457512\pi$
$138$	−7.30976	+	12.6609i	−0.622248	+	1.07776i
$139$	3.00702	+	5.20831i	0.255052	+	0.441763i	0.964910	−	0.262582i	$-0.0845741\pi$
$139$	3.00702	+	5.20831i	0.255052	+	0.441763i	−0.709858	+	0.704345i	$0.751241\pi$
$140$		0			0
$141$	13.0913			1.10249
$142$	−1.78559	−	3.09273i	−0.149843	−	0.259536i
$143$	−0.712856	−	1.23470i	−0.0596120	−	0.103251i
$144$	−6.06327			−0.505272
$145$		0			0
$146$	0.466810	+	0.808538i	0.0386334	+	0.0669151i
$147$	−6.11094	+	10.5845i	−0.504022	+	0.872991i
$148$	−2.75551	−	4.77268i	−0.226502	−	0.392312i
$149$	3.39608	−	5.88218i	0.278218	−	0.481887i	−0.692724	−	0.721203i	$-0.743590\pi$
$149$	3.39608	−	5.88218i	0.278218	−	0.481887i	0.970942	+	0.239315i	$0.0769230\pi$
$150$		0			0
$151$	−15.8875			−1.29291			−0.646453	−	0.762953i	$-0.723749\pi$
$151$	−15.8875			−1.29291			−0.646453	+	0.762953i	$0.723749\pi$
$152$	8.96837	+	9.89226i	0.727431	+	0.802368i
$153$	13.8554			1.12014
$154$	0.223877	−	0.387767i	0.0180406	−	0.0312472i
$155$		0			0
$156$	−2.89652	−	5.01693i	−0.231908	−	0.401676i
$157$	3.75351	−	6.50127i	0.299563	−	0.518858i	−0.676473	−	0.736467i	$-0.736493\pi$
$157$	3.75351	−	6.50127i	0.299563	−	0.518858i	0.976036	+	0.217609i	$0.0698259\pi$
$158$	−9.44375	−	16.3571i	−0.751305	−	1.30130i
$159$	28.2500			2.24037
$160$		0			0
$161$	−3.36445	−	5.82739i	−0.265156	−	0.459263i
$162$	−6.55469	−	11.3531i	−0.514985	−	0.891980i
$163$	−21.8202			−1.70909			−0.854546	−	0.519375i	$-0.826165\pi$
$163$	−21.8202			−1.70909			−0.854546	+	0.519375i	$0.826165\pi$
$164$	0.426600			0.0333119
$165$		0			0
$166$	−1.01760	+	1.76253i	−0.0789808	+	0.136799i
$167$	5.64257	+	9.77322i	0.436635	+	0.756274i	0.997428	−	0.0716821i	$-0.0228367\pi$
$167$	5.64257	+	9.77322i	0.436635	+	0.756274i	−0.560792	+	0.827957i	$0.689503\pi$
$168$	4.49800	−	7.79076i	0.347028	−	0.601070i
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$		0			0
$171$	2.96135	−	9.22108i	0.226460	−	0.705154i
$172$	−2.51013			−0.191396
$173$	−2.92771	+	5.07095i	−0.222590	+	0.385537i	−0.955594	−	0.294688i	$-0.904784\pi$
$173$	−2.92771	+	5.07095i	−0.222590	+	0.385537i	0.733004	+	0.680225i	$0.238118\pi$
$174$	−1.79416	+	3.10758i	−0.136015	+	0.235585i
$175$		0			0
$176$	0.389062	−	0.673875i	0.0293266	−	0.0507952i
$177$	6.54567	+	11.3374i	0.492003	+	0.852174i
$178$	19.5843			1.46791
$179$	−18.7922			−1.40459			−0.702296	−	0.711885i	$-0.747842\pi$
$179$	−18.7922			−1.40459			−0.702296	+	0.711885i	$0.747842\pi$
$180$		0			0
$181$	−6.67265	−	11.5574i	−0.495974	−	0.859052i	0.504015	−	0.863695i	$-0.331856\pi$
$181$	−6.67265	−	11.5574i	−0.495974	−	0.859052i	−0.999989	+	0.00464265i	$0.998522\pi$
$182$	−7.85142			−0.581986
$183$	−10.1867			−0.753021
$184$	−8.01950	−	13.8902i	−0.591205	−	1.02400i
$185$		0			0
$186$	1.70584	+	2.95460i	0.125078	+	0.216642i
$187$	−0.889062	+	1.53990i	−0.0650146	+	0.112609i
$188$	−1.45233	+	2.51551i	−0.105922	+	0.183462i
$189$	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	$0.507702\pi$
$192$	10.1340	−	17.5526i	0.731358	−	1.26675i
$193$	−1.88204	+	3.25979i	−0.135472	+	0.234645i	−0.925778	−	0.378068i	$-0.876589\pi$
$193$	−1.88204	+	3.25979i	−0.135472	+	0.234645i	0.790305	+	0.612713i	$0.209922\pi$
$194$	−7.17420	−	12.4261i	−0.515078	−	0.892141i
$195$		0			0
$196$	−1.35587	−	2.34844i	−0.0968480	−	0.167746i
$197$	−14.6164			−1.04138			−0.520688	−	0.853747i	$-0.674324\pi$
$197$	−14.6164			−1.04138			−0.520688	+	0.853747i	$0.674324\pi$
$198$	−0.774121			−0.0550144
$199$	−5.76053	−	9.97753i	−0.408353	−	0.707288i	0.586352	−	0.810056i	$-0.300563\pi$
$199$	−5.76053	−	9.97753i	−0.408353	−	0.707288i	−0.994705	+	0.102768i	$0.967230\pi$
$200$		0			0
$201$	−2.25307			−0.158919
$202$	9.67566			0.680777
$203$	−0.825796	−	1.43032i	−0.0579595	−	0.100389i
$204$	−3.61250	+	6.25703i	−0.252925	+	0.438079i
$205$		0			0
$206$	7.83237	−	13.5661i	0.545707	−	0.945192i
$207$	−5.81678	+	10.0750i	−0.404294	+	0.700257i
$208$	−13.6445			−0.946074
$209$	0.834816	+	0.920816i	0.0577454	+	0.0636941i
$210$		0			0
$211$	8.57028	−	14.8442i	0.590003	−	1.02191i	−0.404229	−	0.914658i	$-0.632460\pi$
$211$	8.57028	−	14.8442i	0.590003	−	1.02191i	0.994231	−	0.107257i	$-0.0342067\pi$
$212$	−3.13400	+	5.42824i	−0.215244	+	0.372813i
$213$	−3.33939	−	5.78399i	−0.228811	−	0.396313i
$214$	−8.43473	+	14.6094i	−0.576586	+	0.998677i
$215$		0			0
$216$	5.44687			0.370612
$217$	−1.57028			−0.106598
$218$	−5.62297	−	9.73928i	−0.380836	−	0.659627i
$219$	0.873023	+	1.51212i	0.0589934	+	0.102180i
$220$		0			0
$221$	31.1796			2.09736
$222$	15.1746	+	26.2833i	1.01846	+	1.76402i
$223$	0.762085	−	1.31997i	0.0510330	−	0.0883918i	−0.839380	−	0.543544i	$-0.817082\pi$
$223$	0.762085	−	1.31997i	0.0510330	−	0.0883918i	0.890413	+	0.455153i	$0.150415\pi$
$224$	1.79416	+	3.10758i	0.119878	+	0.207634i
$225$		0			0
$226$	10.5859	−	18.3353i	0.704162	−	1.21964i
$227$	−4.00000			−0.265489			−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000			−0.265489			−0.132745	+	0.991150i	$0.542379\pi$
$228$	3.39208	+	3.74152i	0.224646	+	0.247788i
$229$	18.4397			1.21853			0.609266	−	0.792966i	$-0.291464\pi$
$229$	18.4397			1.21853			0.609266	+	0.792966i	$0.291464\pi$
$230$		0			0
$231$	0.418694	−	0.725199i	0.0275480	−	0.0477146i
$232$	−1.96837	−	3.40931i	−0.129230	−	0.223832i
$233$	6.35587	−	11.0087i	0.416387	−	0.721203i	−0.579186	−	0.815195i	$-0.696629\pi$
$233$	6.35587	−	11.0087i	0.416387	−	0.721203i	0.995573	+	0.0939920i	$0.0299628\pi$
$234$	6.78714	+	11.7557i	0.443689	+	0.768493i
$235$		0			0
$236$	−2.90466			−0.189077
$237$	−17.6616	−	30.5908i	−1.14725	−	1.98709i
$238$	4.89608	+	8.48026i	0.317366	+	0.549694i
$239$	−10.8343			−0.700811			−0.350405	−	0.936598i	$-0.613956\pi$
$239$	−10.8343			−0.700811			−0.350405	+	0.936598i	$0.613956\pi$
$240$		0			0
$241$	4.93673	+	8.55067i	0.318003	+	0.550797i	0.980071	−	0.198646i	$-0.0636545\pi$
$241$	4.93673	+	8.55067i	0.318003	+	0.550797i	−0.662068	+	0.749444i	$0.730321\pi$
$242$	−6.67065	+	11.5539i	−0.428805	+	0.742713i
$243$	−9.59134	−	16.6127i	−0.615285	−	1.06570i
$244$	1.13009	−	1.95738i	0.0723467	−	0.125308i
$245$		0			0
$246$	−2.34930			−0.149786
$247$	6.66407	−	20.7507i	0.424025	−	1.32033i
$248$	−3.74293			−0.237676
$249$	−1.90310	+	3.29626i	−0.120604	+	0.208892i
$250$		0			0
$251$	−8.88550	−	15.3901i	−0.560848	−	0.971417i	−0.997423	−	0.0717492i	$-0.977142\pi$
$251$	−8.88550	−	15.3901i	−0.560848	−	0.971417i	0.436575	−	0.899668i	$-0.356191\pi$
$252$	0.723877	−	1.25379i	0.0456000	−	0.0789815i
$253$	−0.746491	−	1.29296i	−0.0469315	−	0.0812877i
$254$	11.4016			0.715403
$255$		0			0
$256$	5.66017	+	9.80370i	0.353760	+	0.612731i
$257$	4.07930	+	7.06556i	0.254460	+	0.440738i	0.964749	−	0.263173i	$-0.0847689\pi$
$257$	4.07930	+	7.06556i	0.254460	+	0.440738i	−0.710289	+	0.703911i	$0.751436\pi$
$258$	13.8234			0.860604
$259$	−13.9688			−0.867980
$260$		0			0
$261$	−1.42771	+	2.47287i	−0.0883733	+	0.153067i
$262$	7.59134	+	13.1486i	0.468995	+	0.812322i
$263$	3.15861	−	5.47087i	0.194768	−	0.337348i	−0.752056	−	0.659099i	$-0.770938\pi$
$263$	3.15861	−	5.47087i	0.194768	−	0.337348i	0.946825	+	0.321750i	$0.104271\pi$
$264$	0.997999	−	1.72858i	0.0614226	−	0.106387i
$265$		0			0
$266$	6.69024	−	1.44594i	0.410205	−	0.0886565i
$267$	36.6264			2.24150
$268$	0.249951	−	0.432927i	0.0152682	−	0.0264452i
$269$	−4.11951	+	7.13521i	−0.251171	+	0.435041i	−0.963849	−	0.266451i	$-0.914149\pi$
$269$	−4.11951	+	7.13521i	−0.251171	+	0.435041i	0.712677	+	0.701492i	$0.247482\pi$
$270$		0			0
$271$	2.11094	−	3.65625i	0.128230	−	0.222101i	−0.794761	−	0.606923i	$-0.792404\pi$
$271$	2.11094	−	3.65625i	0.128230	−	0.222101i	0.922991	+	0.384821i	$0.125737\pi$
$272$	8.50858	+	14.7373i	0.515908	+	0.893579i
$273$	−14.6837			−0.888696
$274$	−22.6476			−1.36819
$275$		0			0
$276$	−3.03319	−	5.25364i	−0.182577	−	0.316232i
$277$	9.83739			0.591071			0.295536	−	0.955332i	$-0.404502\pi$
$277$	9.83739			0.591071			0.295536	+	0.955332i	$0.404502\pi$
$278$	7.34841			0.440728
$279$	1.35743	+	2.35114i	0.0812671	+	0.140759i
$280$		0			0
$281$	−2.69024	−	4.65964i	−0.160486	−	0.277971i	0.774557	−	0.632504i	$-0.217973\pi$
$281$	−2.69024	−	4.65964i	−0.160486	−	0.277971i	−0.935043	+	0.354534i	$0.884640\pi$
$282$	7.99800	−	13.8529i	0.476274	−	0.824931i
$283$	−2.48240	+	4.29965i	−0.147564	+	0.255588i	−0.930326	−	0.366732i	$-0.880476\pi$
$283$	−2.48240	+	4.29965i	−0.147564	+	0.255588i	0.782763	+	0.622320i	$0.213810\pi$
$284$	1.48186			0.0879323
$285$		0			0
$286$	−1.74204			−0.103009
$287$	0.540653	−	0.936439i	0.0319137	−	0.0552762i
$288$	3.10192	−	5.37268i	0.182782	−	0.316588i
$289$	−10.9433	−	18.9544i	−0.643724	−	1.11496i
$290$		0			0
$291$	−13.4171	−	23.2392i	−0.786526	−	1.36230i
$292$	−0.387406			−0.0226712
$293$	3.80620			0.222360			0.111180	−	0.993800i	$-0.464537\pi$
$293$	3.80620			0.222360			0.111180	+	0.993800i	$0.464537\pi$
$294$	7.46681	+	12.9329i	0.435473	+	0.754262i
$295$		0			0
$296$	−33.2961			−1.93529
$297$	0.507019			0.0294202
$298$	−4.14959	−	7.18730i	−0.240379	−	0.416349i
$299$	−13.0898	+	22.6722i	−0.757002	+	1.31117i
$300$		0			0
$301$	−3.18122	+	5.51004i	−0.183363	+	0.317593i
$302$	−9.70628	+	16.8118i	−0.558534	+	0.967409i
$303$	18.0953			1.03955
$304$	11.6265	−	2.51281i	0.666827	−	0.144119i
$305$		0			0
$306$	8.46481	−	14.6615i	0.483901	−	0.838141i
$307$	0.287144	−	0.497348i	0.0163882	−	0.0283851i	−0.857715	−	0.514125i	$-0.828117\pi$
$307$	0.287144	−	0.497348i	0.0163882	−	0.0283851i	0.874103	+	0.485740i	$0.161450\pi$
$308$	0.0928982	+	0.160904i	0.00529336	+	0.00916838i
$309$	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	$0.578557\pi$
$312$	−35.0000			−1.98148
$313$	−17.0617	−	29.5517i	−0.964385	−	1.67036i	−0.711259	−	0.702930i	$-0.751875\pi$
$313$	−17.0617	−	29.5517i	−0.964385	−	1.67036i	−0.253126	−	0.967433i	$-0.581459\pi$
$314$	−4.58632	−	7.94375i	−0.258821	−	0.448291i
$315$		0			0
$316$	7.83739			0.440887
$317$	−5.53865	−	9.59323i	−0.311082	−	0.538809i	0.667515	−	0.744596i	$-0.267358\pi$
$317$	−5.53865	−	9.59323i	−0.311082	−	0.538809i	−0.978597	+	0.205787i	$0.934025\pi$
$318$	17.2590	−	29.8934i	0.967835	−	1.67634i
$319$	−0.183224	−	0.317354i	−0.0102586	−	0.0177684i
$320$		0			0
$321$	−15.7746	+	27.3223i	−0.880450	+	1.52498i
$322$	−8.22188			−0.458187
$323$	−26.5683	+	5.74213i	−1.47830	+	0.319500i
$324$	5.43975			0.302208
$325$		0			0
$326$	−13.3308	+	23.0896i	−0.738325	+	1.27882i
$327$	−10.5160	−	18.2143i	−0.581538	−	1.00725i
$328$	1.28870	−	2.23210i	0.0711566	−	0.123247i
$329$	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	$0.443617\pi$
$332$	−0.422252	−	0.731363i	−0.0231741	−	0.0401387i
$333$	12.0753	+	20.9150i	0.661722	+	1.14614i
$334$	13.7890			0.754503
$335$		0			0
$336$	−4.00702	−	6.94036i	−0.218601	−	0.378628i
$337$	−12.6336	+	21.8820i	−0.688193	+	1.19199i	0.284228	+	0.958757i	$0.408263\pi$
$337$	−12.6336	+	21.8820i	−0.688193	+	1.19199i	−0.972422	+	0.233229i	$0.925071\pi$
$338$	7.33126	+	12.6981i	0.398768	+	0.690686i
$339$	19.7976	−	34.2905i	1.07526	−	1.86240i
$340$		0			0
$341$	−0.348409			−0.0188674
$342$	−7.94833	−	8.76714i	−0.429796	−	0.474072i
$343$	−15.8695			−0.856871
$344$	−7.58276	+	13.1337i	−0.408835	+	0.708123i
$345$		0			0
$346$	3.57730	+	6.19607i	0.192317	+	0.333103i
$347$	6.20428	−	10.7461i	0.333063	−	0.576882i	−0.650048	−	0.759893i	$-0.725251\pi$
$347$	6.20428	−	10.7461i	0.333063	−	0.576882i	0.983111	+	0.183011i	$0.0585844\pi$
$348$	−0.744489	−	1.28949i	−0.0399088	−	0.0691241i
$349$	6.20384			0.332084			0.166042	−	0.986119i	$-0.446901\pi$
$349$	6.20384			0.332084			0.166042	+	0.986119i	$0.446901\pi$
$350$		0			0
$351$	−4.44531	−	7.69950i	−0.237273	−	0.410969i
$352$	0.398082	+	0.689498i	0.0212178	+	0.0367504i
$353$	23.3484			1.24271			0.621355	−	0.783529i	$-0.286582\pi$
$353$	23.3484			1.24271			0.621355	+	0.783529i	$0.286582\pi$
$354$	15.9960			0.850178
$355$		0			0
$356$	−4.06327	+	7.03778i	−0.215353	+	0.373002i
$357$	9.15661	+	15.8597i	0.484619	+	0.839385i
$358$	−11.4808	+	19.8854i	−0.606782	+	1.05098i
$359$	18.8609	−	32.6680i	0.995440	−	1.72415i	0.415107	−	0.909773i	$-0.363744\pi$
$359$	18.8609	−	32.6680i	0.995440	−	1.72415i	0.580333	−	0.814379i	$-0.302922\pi$
$360$		0			0
$361$	−1.85698	+	18.9090i	−0.0977360	+	0.995212i
$362$	−16.3063			−0.857040
$363$	−12.4754	+	21.6080i	−0.654788	+	1.13413i
$364$	1.62898	−	2.82147i	0.0853816	−	0.147885i
$365$		0			0
$366$	−6.22343	+	10.7793i	−0.325304	+	0.563443i
$367$	14.7038	+	25.4678i	0.767534	+	1.32941i	0.938896	+	0.344200i	$0.111850\pi$
$367$	14.7038	+	25.4678i	0.767534	+	1.32941i	−0.171362	+	0.985208i	$0.554817\pi$
$368$	−14.2883			−0.744827
$369$	−1.86946			−0.0973204
$370$		0			0
$371$	7.94375	+	13.7590i	0.412419	+	0.714331i
$372$	−1.41568			−0.0733995
$373$	21.5491			1.11577			0.557886	−	0.829918i	$-0.311613\pi$
$373$	21.5491			1.11577			0.557886	+	0.829918i	$0.311613\pi$
$374$	1.08632	+	1.88157i	0.0561725	+	0.0972935i
$375$		0			0
$376$	8.77457	+	15.1980i	0.452514	+	0.783777i
$377$	−3.21286	+	5.56483i	−0.165471	+	0.286603i
$378$	1.39608	−	2.41808i	0.0718066	−	0.124373i
$379$	−19.3945			−0.996230			−0.498115	−	0.867111i	$-0.665974\pi$
$379$	−19.3945			−0.996230			−0.498115	+	0.867111i	$0.665974\pi$
$380$		0			0
$381$	21.3233			1.09242
$382$	−0.408561	+	0.707648i	−0.0209038	+	0.0362064i
$383$	9.44331	−	16.3563i	0.482531	−	0.835767i	−0.517268	−	0.855823i	$-0.673051\pi$
$383$	9.44331	−	16.3563i	0.482531	−	0.835767i	0.999799	+	0.0200559i	$0.00638442\pi$
$384$	−6.00200	−	10.3958i	−0.306288	−	0.530507i
$385$		0			0
$386$	2.29962	+	3.98307i	0.117048	+	0.202733i
$387$	11.0000			0.559161
$388$	5.95389			0.302263
$389$	4.54021	+	7.86387i	0.230198	+	0.398714i	0.957866	−	0.287215i	$-0.0927294\pi$
$389$	4.54021	+	7.86387i	0.230198	+	0.398714i	−0.727668	+	0.685929i	$0.759396\pi$
$390$		0			0
$391$	32.6507			1.65122
$392$	−16.3836			−0.827497
$393$	14.1973	+	24.5904i	0.716157	+	1.24042i
$394$	−8.92972	+	15.4667i	−0.449873	+	0.779202i
$395$		0			0
$396$	0.160611	−	0.278187i	0.00807101	−	0.0139794i
$397$	8.49800	−	14.7190i	0.426502	−	0.738724i	−0.570057	−	0.821605i	$-0.693079\pi$
$397$	8.49800	−	14.7190i	0.426502	−	0.738724i	0.996559	+	0.0828814i	$0.0264123\pi$
$398$	−14.0773			−0.705631
$399$	12.5120	−	2.70419i	0.626385	−	0.135379i
$400$		0			0
$401$	−0.795720	+	1.37823i	−0.0397363	+	0.0688254i	−0.885210	−	0.465192i	$-0.845985\pi$
$401$	−0.795720	+	1.37823i	−0.0397363	+	0.0688254i	0.845473	+	0.534018i	$0.179318\pi$
$402$	−1.37648	+	2.38414i	−0.0686528	+	0.118910i
$403$	3.05469	+	5.29088i	0.152165	+	0.263557i
$404$	−2.00746	+	3.47703i	−0.0998750	+	0.172989i
$405$		0			0
$406$	−2.01804			−0.100154
$407$	−3.09935			−0.153629
$408$	21.8257	+	37.8032i	1.08053	+	1.87154i
$409$	0.998443	+	1.72935i	0.0493698	+	0.0855110i	0.889654	−	0.456635i	$-0.150945\pi$
$409$	0.998443	+	1.72935i	0.0493698	+	0.0855110i	−0.840284	+	0.542146i	$0.817612\pi$
$410$		0			0
$411$	−42.3553			−2.08923
$412$	3.25005	+	5.62925i	0.160118	+	0.277333i
$413$	−3.68122	+	6.37607i	−0.181141	+	0.313746i
$414$	7.10738	+	12.3103i	0.349309	+	0.605020i
$415$		0			0
$416$	6.98040	−	12.0904i	0.342242	−	0.592781i
$417$	13.7429			0.672994
$418$	1.48441	−	0.320820i	0.0726046	−	0.0156918i
$419$	−22.7781			−1.11278			−0.556392	−	0.830920i	$-0.687815\pi$
$419$	−22.7781			−1.11278			−0.556392	+	0.830920i	$0.687815\pi$
$420$		0			0
$421$	6.92070	−	11.9870i	0.337294	−	0.584210i	−0.646629	−	0.762805i	$-0.723822\pi$
$421$	6.92070	−	11.9870i	0.337294	−	0.584210i	0.983923	+	0.178594i	$0.0571550\pi$
$422$	−10.4718	−	18.1377i	−0.509761	−	0.882931i
$423$	6.36445	−	11.0235i	0.309450	−	0.535983i
$424$	18.9347	+	32.7959i	0.919552	+	1.59271i
$425$		0			0
$426$	−8.16064			−0.395384
$427$	−2.86445	−	4.96137i	−0.138620	−	0.240097i
$428$	−3.50000	−	6.06218i	−0.169179	−	0.293026i
$429$	−3.25796			−0.157296
$430$		0			0
$431$	−1.71987	−	2.97891i	−0.0828435	−	0.143489i	0.821627	−	0.570026i	$-0.193067\pi$
$431$	−1.71987	−	2.97891i	−0.0828435	−	0.143489i	−0.904470	+	0.426537i	$0.859733\pi$
$432$	2.42616	−	4.20223i	0.116729	−	0.202180i
$433$	−4.60036	−	7.96806i	−0.221079	−	0.382920i	0.734057	−	0.679088i	$-0.237625\pi$
$433$	−4.60036	−	7.96806i	−0.221079	−	0.382920i	−0.955136	+	0.296168i	$0.904291\pi$
$434$	−0.959347	+	1.66164i	−0.0460501	+	0.0797612i
$435$		0			0
$436$	4.66652			0.223486
$437$	6.97850	−	21.7297i	0.333827	−	1.03947i
$438$	2.13345			0.101940
$439$	18.7550	−	32.4846i	0.895126	−	1.55040i	0.0614769	−	0.998109i	$-0.480419\pi$
$439$	18.7550	−	32.4846i	0.895126	−	1.55040i	0.833649	−	0.552295i	$-0.186248\pi$
$440$		0			0
$441$	5.94175	+	10.2914i	0.282941	+	0.490067i
$442$	19.0488	−	32.9935i	0.906058	−	1.56934i
$443$	7.33939	+	12.7122i	0.348705	+	0.603975i	0.986020	−	0.166629i	$-0.0532882\pi$
$443$	7.33939	+	12.7122i	0.348705	+	0.603975i	−0.637315	+	0.770604i	$0.719955\pi$
$444$	−12.5935			−0.597660
$445$		0			0
$446$	−0.931174	−	1.61284i	−0.0440924	−	0.0763702i
$447$	−7.76053	−	13.4416i	−0.367060	−	0.635767i
$448$	11.3985			0.538530
$449$	−7.39052			−0.348780			−0.174390	−	0.984677i	$-0.555795\pi$
$449$	−7.39052			−0.348780			−0.174390	+	0.984677i	$0.555795\pi$
$450$		0			0
$451$	0.119958	−	0.207773i	0.00564860	−	0.00978367i
$452$	4.39262	+	7.60824i	0.206611	+	0.357862i
$453$	−18.1526	+	31.4412i	−0.852884	+	1.47724i
$454$	−2.44375	+	4.23270i	−0.114691	+	0.198651i
$455$		0			0
$456$	29.8237	−	6.44571i	1.39662	−	0.301848i
$457$	−2.30007			−0.107593			−0.0537963	−	0.998552i	$-0.517132\pi$
$457$	−2.30007			−0.107593			−0.0537963	+	0.998552i	$0.517132\pi$
$458$	11.2655	−	19.5125i	0.526404	−	0.911759i
$459$	−5.54411	+	9.60269i	−0.258777	+	0.448215i
$460$		0			0
$461$	−9.87848	+	17.1100i	−0.460087	+	0.796894i	−0.998965	−	0.0454900i	$-0.985515\pi$
$461$	−9.87848	+	17.1100i	−0.460087	+	0.796894i	0.538878	+	0.842384i	$0.318848\pi$
$462$	−0.511592	−	0.886103i	−0.0238014	−	0.0412253i
$463$	−28.9468			−1.34527			−0.672635	−	0.739974i	$-0.734838\pi$
$463$	−28.9468			−1.34527			−0.672635	+	0.739974i	$0.734838\pi$
$464$	−3.50702			−0.162809
$465$		0			0
$466$	−7.76609	−	13.4513i	−0.359757	−	0.623118i
$467$	3.31722			0.153503			0.0767513	−	0.997050i	$-0.475545\pi$
$467$	3.31722			0.153503			0.0767513	+	0.997050i	$0.475545\pi$
$468$	−5.63266			−0.260370
$469$	−0.633551	−	1.09734i	−0.0292547	−	0.0506706i
$470$		0			0
$471$	−8.57730	−	14.8563i	−0.395221	−	0.684543i
$472$	−8.77457	+	15.1980i	−0.403882	+	0.699544i
$473$	−0.705838	+	1.22255i	−0.0324544	+	0.0562127i
$474$	−43.1606			−1.98243
$475$		0			0
$476$	−4.06327			−0.186240
$477$	13.7339	−	23.7878i	0.628833	−	1.08917i
$478$	−6.61907	+	11.4646i	−0.302749	+	0.524377i
$479$	19.7535	+	34.2141i	0.902561	+	1.56328i	0.824158	+	0.566360i	$0.191649\pi$
$479$	19.7535	+	34.2141i	0.902561	+	1.56328i	0.0784026	+	0.996922i	$0.475018\pi$
$480$		0			0
$481$	27.1737	+	47.0662i	1.23901	+	2.14603i
$482$	12.0642			0.549507
$483$	−15.3765			−0.699654
$484$	−2.76799	−	4.79430i	−0.125818	−	0.217923i
$485$		0			0
$486$	−23.4389			−1.06321
$487$	24.7781			1.12280			0.561402	−	0.827543i	$-0.310262\pi$
$487$	24.7781			1.12280			0.561402	+	0.827543i	$0.310262\pi$
$488$	−6.82770	−	11.8259i	−0.309075	−	0.535334i
$489$	−24.9312	+	43.1821i	−1.12743	+	1.95276i
$490$		0			0
$491$	6.81176	−	11.7983i	0.307410	−	0.532450i	−0.670385	−	0.742014i	$-0.733871\pi$
$491$	6.81176	−	11.7983i	0.307410	−	0.532450i	0.977795	+	0.209563i	$0.0672042\pi$
$492$	0.487421	−	0.844239i	0.0219747	−	0.0380612i
$493$	8.01404			0.360934
$494$	−17.8865	−	19.7291i	−0.804752	−	0.887656i
$495$		0			0
$496$	−1.66719	+	2.88765i	−0.0748589	+	0.129659i
$497$	1.87804	−	3.25286i	0.0842416	−	0.145911i
$498$	2.32535	+	4.02763i	0.104201	+	0.180482i
$499$	−4.09490	+	7.09257i	−0.183313	+	0.317507i	−0.943007	−	0.332774i	$-0.892015\pi$
$499$	−4.09490	+	7.09257i	−0.183313	+	0.317507i	0.759694	+	0.650281i	$0.225349\pi$
$500$		0			0
$501$	25.7882			1.15213
$502$	−21.7140			−0.969142
$503$	9.14257	+	15.8354i	0.407647	+	0.706065i	0.994626	−	0.103537i	$-0.0330160\pi$
$503$	9.14257	+	15.8354i	0.407647	+	0.706065i	−0.586978	+	0.809603i	$0.699683\pi$
$504$	−4.37347	−	7.57507i	−0.194810	−	0.337420i
$505$		0			0
$506$	−1.82424			−0.0810973
$507$	13.7109	+	23.7479i	0.608920	+	1.05468i
$508$	−2.36556	+	4.09727i	−0.104955	+	0.181787i
$509$	−5.94220	−	10.2922i	−0.263383	−	0.456193i	0.703756	−	0.710442i	$-0.251505\pi$
$509$	−5.94220	−	10.2922i	−0.263383	−	0.456193i	−0.967139	+	0.254249i	$0.918172\pi$
$510$		0			0
$511$	−0.490980	+	0.850402i	−0.0217197	+	0.0376196i
$512$	24.3382			1.07561
$513$	5.20584	+	5.74213i	0.229843	+	0.253521i
$514$	9.96881			0.439705
$515$		0			0
$516$	−2.86801	+	4.96753i	−0.126257	+	0.218683i
$517$	0.816776	+	1.41470i	0.0359218	+	0.0622183i
$518$	−8.53408	+	14.7815i	−0.374966	+	0.649460i
$519$	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	$0.344913\pi$
$522$	1.74449	+	3.02154i	0.0763542	+	0.132249i
$523$	−2.88862	−	5.00323i	−0.126310	−	0.218776i	0.795934	−	0.605383i	$-0.206980\pi$
$523$	−2.88862	−	5.00323i	−0.126310	−	0.218776i	−0.922244	+	0.386607i	$0.873647\pi$
$524$	−6.30007			−0.275220
$525$		0			0
$526$	−3.85943	−	6.68473i	−0.168279	−	0.291468i
$527$	3.80976	−	6.59869i	0.165956	−	0.287444i
$528$	−0.889062	−	1.53990i	−0.0386915	−	0.0670156i
$529$	−2.20739	+	3.82332i	−0.0959737	+	0.166231i
$530$		0			0
$531$	12.7289			0.552387
$532$	−0.868450	+	2.70419i	−0.0376521	+	0.117242i
$533$	−4.20695			−0.182223
$534$	22.3765	−	38.7572i	0.968325	−	1.67719i
$535$		0			0
$536$	−1.51013	−	2.61563i	−0.0652278	−	0.112978i
$537$	−21.4714	+	37.1895i	−0.926559	+	1.60485i
$538$	5.03354	+	8.71834i	0.217011	+	0.375874i
$539$	−1.52506			−0.0656889
$540$		0			0
$541$	−1.31678	−	2.28072i	−0.0566126	−	0.0980559i	0.836330	−	0.548226i	$-0.184697\pi$
$541$	−1.31678	−	2.28072i	−0.0566126	−	0.0980559i	−0.892943	+	0.450170i	$0.851363\pi$
$542$	−2.57930	−	4.46749i	−0.110791	−	0.191895i
$543$	−30.4959			−1.30870
$544$	−17.4117			−0.746519
$545$		0			0
$546$	−8.97081	+	15.5379i	−0.383915	+	0.664961i
$547$	−18.1812	−	31.4908i	−0.777373	−	1.34645i	−0.933451	−	0.358705i	$-0.883218\pi$
$547$	−18.1812	−	31.4908i	−0.777373	−	1.34645i	0.156078	−	0.987745i	$-0.450115\pi$
$548$	4.69882	−	8.13859i	0.200724	−	0.347663i
$549$	−4.95233	+	8.57768i	−0.211360	+	0.366087i
$550$		0			0
$551$	1.71286	−	5.33351i	0.0729701	−	0.227215i
$552$	−36.6514			−1.55999
$553$	9.93273	−	17.2040i	0.422383	−	0.731588i
$554$	6.01003	−	10.4097i	0.255342	−	0.442265i
$555$		0			0
$556$	−1.52461	+	2.64071i	−0.0646581	+	0.111991i
$557$	11.9824	+	20.7541i	0.507711	+	0.879381i	0.999960	+	0.00892662i	$0.00284147\pi$
$557$	11.9824	+	20.7541i	0.507711	+	0.879381i	−0.492249	+	0.870454i	$0.663825\pi$
$558$	3.31722			0.140429
$559$	24.7539			1.04698
$560$		0			0
$561$	2.03163	+	3.51889i	0.0857756	+	0.148568i
$562$	−6.57429			−0.277320
$563$	8.52017			0.359082			0.179541	−	0.983750i	$-0.442539\pi$
$563$	8.52017			0.359082			0.179541	+	0.983750i	$0.442539\pi$
$564$	3.31878	+	5.74829i	0.139746	+	0.242047i
$565$		0			0
$566$	3.03319	+	5.25364i	0.127495	+	0.220827i
$567$	6.89408	−	11.9409i	0.289524	−	0.501470i
$568$	4.47650	−	7.75352i	0.187830	−	0.325331i
$569$	16.3734			0.686407			0.343204	−	0.939261i	$-0.388488\pi$
$569$	16.3734			0.686407			0.343204	+	0.939261i	$0.388488\pi$
$570$		0			0
$571$	−5.21876			−0.218398			−0.109199	−	0.994020i	$-0.534829\pi$
$571$	−5.21876			−0.218398			−0.109199	+	0.994020i	$0.534829\pi$
$572$	0.361431	−	0.626018i	0.0151122	−	0.0261751i
$573$	−0.764087	+	1.32344i	−0.0319202	+	0.0552874i
$574$	−0.660611	−	1.14421i	−0.0275734	−	0.0477585i
$575$		0			0
$576$	−9.85343	−	17.0666i	−0.410559	−	0.711110i
$577$	32.0390			1.33380			0.666900	−	0.745147i	$-0.267621\pi$
$577$	32.0390			1.33380			0.666900	+	0.745147i	$0.267621\pi$
$578$	−26.7427			−1.11235
$579$	4.30074	+	7.44910i	0.178733	+	0.309574i
$580$		0			0
$581$	−2.14057			−0.0888058
$582$	−32.7882			−1.35911
$583$	1.76253	+	3.05279i	0.0729965	+	0.126434i
$584$	−1.17030	+	2.02702i	−0.0484274	+	0.0838787i
$585$		0			0
$586$	2.32535	−	4.02763i	0.0960594	−	0.166380i
$587$	−1.67220	+	2.89634i	−0.0690192	+	0.119545i	−0.898470	−	0.439035i	$-0.855320\pi$
$587$	−1.67220	+	2.89634i	−0.0690192	+	0.119545i	0.829451	+	0.558580i	$0.188654\pi$
$588$	−6.19672			−0.255548
$589$	−3.57730	−	3.94583i	−0.147400	−	0.162585i
$590$		0			0
$591$	−16.7003	+	28.9257i	−0.686958	+	1.18985i
$592$	−14.8308	+	25.6877i	−0.609543	+	1.05576i
$593$	21.1054	+	36.5556i	0.866694	+	1.50116i	0.865355	+	0.501159i	$0.167093\pi$
$593$	21.1054	+	36.5556i	0.866694	+	1.50116i	0.00133875	+	0.999999i	$0.499574\pi$
$594$	0.309757	−	0.536515i	0.0127095	−	0.0220135i
$595$		0			0
$596$	3.44375			0.141062
$597$	−26.3273			−1.07750
$598$	15.9941	+	27.7026i	0.654047	+	1.13284i
$599$	2.60938	+	4.51958i	0.106616	+	0.184665i	0.914397	−	0.404818i	$-0.132665\pi$
$599$	2.60938	+	4.51958i	0.106616	+	0.184665i	−0.807781	+	0.589483i	$0.799332\pi$
$600$		0			0
$601$	−10.1546			−0.414215			−0.207108	−	0.978318i	$-0.566405\pi$
$601$	−10.1546			−0.414215			−0.207108	+	0.978318i	$0.566405\pi$
$602$	3.88706	+	6.73259i	0.158425	+	0.274400i
$603$	−1.09534	+	1.89719i	−0.0446058	+	0.0772596i
$604$	−4.02763	−	6.97606i	−0.163882	−	0.283852i
$605$		0			0
$606$	11.0551	−	19.1481i	0.449084	−	0.777837i
$607$	−42.8764			−1.74030			−0.870149	−	0.492788i	$-0.835978\pi$
$607$	−42.8764			−1.74030			−0.870149	+	0.492788i	$0.835978\pi$
$608$	−3.72143	+	11.5878i	−0.150924	+	0.469949i
$609$	−3.77412			−0.152935
$610$		0			0
$611$	14.3222	−	24.8068i	0.579416	−	1.00358i
$612$	3.51248	+	6.08379i	0.141984	+	0.245923i
$613$	12.5367	−	21.7141i	0.506351	−	0.877025i	−0.493622	−	0.869676i	$-0.664328\pi$
$613$	12.5367	−	21.7141i	0.506351	−	0.877025i	0.999973	−	0.00734857i	$-0.00233914\pi$
$614$	−0.350854	−	0.607697i	−0.0141593	−	0.0245247i
$615$		0			0
$616$	1.12253			0.0452280
$617$	−2.74849	−	4.76053i	−0.110650	−	0.191652i	0.805382	−	0.592756i	$-0.201960\pi$
$617$	−2.74849	−	4.76053i	−0.110650	−	0.191652i	−0.916033	+	0.401104i	$0.868627\pi$
$618$	−17.8981	−	31.0004i	−0.719966	−	1.24702i
$619$	15.4899			0.622590			0.311295	−	0.950313i	$-0.399237\pi$
$619$	15.4899			0.622590			0.311295	+	0.950313i	$0.399237\pi$
$620$		0			0
$621$	−4.65505	−	8.06279i	−0.186801	−	0.323548i
$622$	−5.26409	+	9.11767i	−0.211071	+	0.365585i
$623$	10.2992	+	17.8387i	0.412628	+	0.714693i
$624$	−15.5898	+	27.0023i	−0.624091	+	1.08096i
$625$		0			0
$626$	−41.6946			−1.66645
$627$	2.77612	−	0.599995i	0.110868	−	0.0239615i
$628$	3.80620			0.151884
$629$	33.8905	−	58.7001i	1.35130	−	2.34053i
$630$		0			0
$631$	−20.6616	−	35.7870i	−0.822526	−	1.42466i	−0.903795	−	0.427965i	$-0.859231\pi$
$631$	−20.6616	−	35.7870i	−0.822526	−	1.42466i	0.0812689	−	0.996692i	$-0.474103\pi$
$632$	23.6757	−	41.0075i	0.941767	−	1.63119i
$633$	−19.5843	−	33.9210i	−0.778407	−	1.34824i
$634$	−13.5351			−0.537547
$635$		0			0
$636$	7.16163	+	12.4043i	0.283977	+	0.491862i
$637$	13.3710	+	23.1593i	0.529779	+	0.917604i
$638$	−0.447755			−0.0177268
$639$	−6.49387			−0.256894
$640$		0			0
$641$	15.3358	−	26.5624i	0.605729	−	1.04915i	−0.386207	−	0.922412i	$-0.626215\pi$
$641$	15.3358	−	26.5624i	0.605729	−	1.04915i	0.991936	−	0.126741i	$-0.0404517\pi$
$642$	19.2746	+	33.3845i	0.760706	+	1.31758i
$643$	−4.00902	+	6.94383i	−0.158100	+	0.273838i	−0.934184	−	0.356793i	$-0.883870\pi$
$643$	−4.00902	+	6.94383i	−0.158100	+	0.273838i	0.776083	+	0.630630i	$0.217204\pi$
$644$	1.70584	−	2.95460i	0.0672194	−	0.116427i
$645$		0			0
$646$	−10.1554	+	31.6220i	−0.399559	+	1.24415i
$647$	−10.0272			−0.394209			−0.197105	−	0.980382i	$-0.563154\pi$
$647$	−10.0272			−0.394209			−0.197105	+	0.980382i	$0.563154\pi$
$648$	16.4327	−	28.4623i	0.645539	−	1.11811i
$649$	−0.816776	+	1.41470i	−0.0320612	+	0.0555317i
$650$		0			0
$651$	−1.79416	+	3.10758i	−0.0703188	+	0.121796i
$652$	−5.53163	−	9.58107i	−0.216635	−	0.375224i
$653$	−20.4117			−0.798771			−0.399385	−	0.916783i	$-0.630776\pi$
$653$	−20.4117			−0.798771			−0.399385	+	0.916783i	$0.630776\pi$
$654$	−25.6986			−1.00489
$655$		0			0
$656$	−1.14803	−	1.98845i	−0.0448231	−	0.0776360i
$657$	1.69771			0.0662338
$658$	8.99600			0.350700
$659$	18.4874	+	32.0212i	0.720168	+	1.24737i	0.960932	+	0.276783i	$0.0892685\pi$
$659$	18.4874	+	32.0212i	0.720168	+	1.24737i	−0.240765	+	0.970584i	$0.577398\pi$
$660$		0			0
$661$	−1.59646	−	2.76514i	−0.0620950	−	0.107552i	0.833307	−	0.552811i	$-0.186445\pi$
$661$	−1.59646	−	2.76514i	−0.0620950	−	0.107552i	−0.895402	+	0.445259i	$0.853112\pi$
$662$	3.91714	−	6.78468i	0.152244	−	0.263694i
$663$	35.6249	−	61.7041i	1.38356	−	2.39639i
$664$	−5.10226			−0.198006
$665$		0			0
$666$	29.5090			1.14345
$667$	−3.36445	+	5.82739i	−0.130272	+	0.225638i
$668$	−2.86089	+	4.95520i	−0.110691	+	0.191723i
$669$	−1.74147	−	3.01632i	−0.0673292	−	0.116618i
$670$		0			0
$671$	−0.635553	−	1.10081i	−0.0245352	−	0.0424963i
$672$	8.19983			0.316315
$673$	15.0742			0.581067			0.290534	−	0.956865i	$-0.406167\pi$
$673$	15.0742			0.581067			0.290534	+	0.956865i	$0.406167\pi$
$674$	15.4366	+	26.7370i	0.594597	+	1.02987i
$675$		0			0
$676$	−6.08422			−0.234009
$677$	−17.9648			−0.690444			−0.345222	−	0.938521i	$-0.612196\pi$
$677$	−17.9648			−0.690444			−0.345222	+	0.938521i	$0.612196\pi$
$678$	−24.1902	−	41.8987i	−0.929021	−	1.60911i
$679$	7.54567	−	13.0695i	0.289576	−	0.501561i
$680$		0			0
$681$	−4.57028	+	7.91597i	−0.175134	+	0.303340i
$682$	−0.212856	+	0.368678i	−0.00815069	+	0.0141174i
$683$	3.78524			0.144838			0.0724191	−	0.997374i	$-0.476928\pi$
$683$	3.78524			0.144838			0.0724191	+	0.997374i	$0.476928\pi$
$684$	4.79962	−	1.03733i	0.183518	−	0.0396633i
$685$		0			0
$686$	−9.69526	+	16.7927i	−0.370167	+	0.641148i
$687$	21.0687	−	36.4921i	0.803822	−	1.39226i
$688$	6.75507	+	11.7001i	0.257534	+	0.446063i
$689$	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	$0.562974\pi$
$692$	−2.96881			−0.112857
$693$	−0.407102	−	0.705121i	−0.0154645	−	0.0267853i
$694$	−7.58086	−	13.1304i	−0.287766	−	0.498425i
$695$		0			0
$696$	−8.99600			−0.340992
$697$	2.62342	+	4.54389i	0.0993690	+	0.172112i
$698$	3.79016	−	6.56475i	0.143460	−	0.248479i
$699$	−14.5241	−	25.1564i	−0.549351	−	0.951504i
$700$		0			0
$701$	−17.9980	+	31.1734i	−0.679775	+	1.17740i	0.295273	+	0.955413i	$0.404589\pi$
$701$	−17.9980	+	31.1734i	−0.679775	+	1.17740i	−0.975048	+	0.221992i	$0.928744\pi$
$702$	−10.8632			−0.410006
$703$	−31.8227	−	35.1010i	−1.20022	−	1.32386i
$704$	2.52906			0.0953176
$705$		0			0
$706$	14.2644	−	24.7067i	0.536849	−	0.929850i
$707$	5.08832	+	8.81324i	0.191366	+	0.331456i
$708$	−3.31878	+	5.74829i	−0.124727	+	0.216034i
$709$	−4.40266	−	7.62562i	−0.165345	−	0.286386i	0.771433	−	0.636311i	$-0.219540\pi$
$709$	−4.40266	−	7.62562i	−0.165345	−	0.286386i	−0.936778	+	0.349925i	$0.886207\pi$
$710$		0			0
$711$	−34.3453			−1.28805
$712$	24.5491	+	42.5203i	0.920018	+	1.59352i
$713$	3.19882	+	5.54052i	0.119797	+	0.207494i
$714$	22.3765			0.837419
$715$		0			0
$716$	−4.76399	−	8.25147i	−0.178039	−	0.308372i
$717$	−12.3789	+	21.4409i	−0.462300	+	0.800726i
$718$	−23.0457	−	39.9163i	−0.860057	−	1.48966i
$719$	−9.49600	+	16.4475i	−0.354141	+	0.613390i	−0.986971	−	0.160901i	$-0.948560\pi$
$719$	−9.49600	+	16.4475i	−0.354141	+	0.613390i	0.632830	+	0.774291i	$0.281893\pi$
$720$		0			0
$721$	16.4758			0.613592
$722$	18.8746	+	13.5173i	0.702439	+	0.503061i
$723$	22.5623			0.839100
$724$	3.38316	−	5.85980i	0.125734	−	0.217778i
$725$		0			0
$726$	15.2434	+	26.4023i	0.565735	+	0.979881i
$727$	2.04567	−	3.54321i	0.0758697	−	0.131410i	−0.825594	−	0.564264i	$-0.809160\pi$
$727$	2.04567	−	3.54321i	0.0758697	−	0.131410i	0.901464	+	0.432854i	$0.142493\pi$
$728$	−9.84183	−	17.0466i	−0.364763	−	0.631787i
$729$	−11.6485			−0.431425
$730$		0			0
$731$	−15.4363	−	26.7364i	−0.570932	−	0.988883i
$732$	−2.58242	−	4.47288i	−0.0954490	−	0.165322i
$733$	50.4678			1.86407			0.932036	−	0.362366i	$-0.118031\pi$
$733$	50.4678			1.86407			0.932036	+	0.362366i	$0.118031\pi$
$734$	35.9325			1.32629
$735$		0			0
$736$	7.30976	−	12.6609i	0.269441	−	0.466686i
$737$	−0.140570	−	0.243474i	−0.00517796	−	0.00896849i
$738$	−1.14213	+	1.97822i	−0.0420423	+	0.0728194i
$739$	−17.1148	+	29.6438i	−0.629580	+	1.09046i	0.358056	+	0.933700i	$0.383440\pi$
$739$	−17.1148	+	29.6438i	−0.629580	+	1.09046i	−0.987636	+	0.156764i	$0.949894\pi$
$740$		0			0
$741$	−33.4512	−	36.8973i	−1.22886	−	1.35545i
$742$	19.4126			0.712658
$743$	11.2996	−	19.5715i	0.414543	−	0.718010i	−0.580837	−	0.814020i	$-0.697275\pi$
$743$	11.2996	−	19.5715i	0.414543	−	0.718010i	0.995380	+	0.0960101i	$0.0306081\pi$
$744$	−4.27657	+	7.40723i	−0.156787	+	0.271562i
$745$		0			0
$746$	13.1652	−	22.8028i	0.482012	−	0.834869i
$747$	1.85041	+	3.20500i	0.0677030	+	0.117265i
$748$	−0.901542			−0.0329636
$749$	−17.7429			−0.648313
$750$		0			0
$751$	12.7199	+	22.0315i	0.464155	+	0.803940i	0.999163	−	0.0409072i	$-0.0130248\pi$
$751$	12.7199	+	22.0315i	0.464155	+	0.803940i	−0.535008	+	0.844847i	$0.679691\pi$
$752$	15.6336			0.570097
$753$	−40.6093			−1.47988
$754$	3.92571	+	6.79953i	0.142966	+	0.247624i
$755$		0			0
$756$	0.579305	+	1.00339i	0.0210691	+	0.0364928i
$757$	21.4015	−	37.0686i	0.777852	−	1.34728i	−0.155325	−	0.987863i	$-0.549643\pi$
$757$	21.4015	−	37.0686i	0.777852	−	1.34728i	0.933177	−	0.359416i	$-0.117024\pi$
$758$	−11.8489	+	20.5228i	−0.430370	+	0.745422i
$759$	−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	$0.682271\pi$
$762$	13.0272	−	22.5637i	0.471925	−	0.817398i
$763$	5.91412	−	10.2436i	0.214106	−	0.370842i
$764$	−0.169533	−	0.293639i	−0.00613347	−	0.0106235i
$765$		0			0
$766$	−11.5386	−	19.9854i	−0.416905	−	0.722100i
$767$	28.6445			1.03429
$768$	25.8686			0.933452
$769$	8.32179	+	14.4138i	0.300092	+	0.519774i	0.976156	−	0.217068i	$-0.0696494\pi$
$769$	8.32179	+	14.4138i	0.300092	+	0.519774i	−0.676065	+	0.736842i	$0.736316\pi$
$770$		0			0
$771$	18.6436			0.671432
$772$	−1.90846			−0.0686871
$773$	3.05669	+	5.29435i	0.109942	+	0.190424i	0.915746	−	0.401757i	$-0.131600\pi$
$773$	3.05669	+	5.29435i	0.109942	+	0.190424i	−0.805805	+	0.592181i	$0.798267\pi$
$774$	6.72032	−	11.6399i	0.241557	−	0.418389i
$775$		0			0
$776$	17.9859	−	31.1524i	0.645655	−	1.11831i
$777$	−15.9604	+	27.6442i	−0.572575	+	0.991729i
$778$	11.0951			0.397780
$779$	3.58477	−	0.774765i	0.128438	−	0.0277588i
$780$		0			0
$781$	0.416692	−	0.721732i	0.0149104	−	0.0258256i
$782$	19.9476	−	34.5502i	0.713323	−	1.23551i
$783$	−1.14257	−	1.97899i	−0.0408322	−	0.0707234i
$784$	−7.29762	+	12.6399i	−0.260629	+	0.451423i
$785$		0			0
$786$	34.6946			1.23752
$787$	18.7781			0.669368			0.334684	−	0.942330i	$-0.391370\pi$
$787$	18.7781			0.669368			0.334684	+	0.942330i	$0.391370\pi$
$788$	−3.70539	−	6.41793i	−0.131999	−	0.228629i
$789$	−7.21787	−	12.5017i	−0.256963	−	0.445073i
$790$		0			0
$791$	22.2680			0.791759
$792$	−0.970368	−	1.68073i	−0.0344805	−	0.0597220i
$793$	−11.1445	+	19.3028i	−0.395752	+	0.685462i
$794$	−10.3835	−	17.9848i	−0.368497	−	0.638255i
$795$		0			0
$796$	2.92070	−	5.05879i	0.103521	−	0.179304i
$797$	−30.2851			−1.07275			−0.536377	−	0.843978i	$-0.680208\pi$
$797$	−30.2851			−1.07275			−0.536377	+	0.843978i	$0.680208\pi$
$798$	4.78257	−	14.8920i	0.169301	−	0.527172i
$799$	−35.7249			−1.26386
$800$		0			0
$801$	17.8062	−	30.8412i	0.629151	−	1.08972i
$802$	0.972271	+	1.68402i	0.0343321	+	0.0594649i
$803$	−0.108937	+	0.188684i	−0.00384430	+	0.00665851i
$804$	−0.571173	−	0.989301i	−0.0201437	−	0.0348899i
$805$		0			0
$806$	7.46491			0.262940
$807$	9.41368	+	16.3050i	0.331377	+	0.573962i
$808$	12.1285	+	21.0072i	0.426680	+	0.739032i
$809$	13.6015			0.478202			0.239101	−	0.970995i	$-0.423147\pi$
$809$	13.6015			0.478202			0.239101	+	0.970995i	$0.423147\pi$
$810$		0			0
$811$	−0.799180	−	1.38422i	−0.0280630	−	0.0486065i	0.851653	−	0.524106i	$-0.175601\pi$
$811$	−0.799180	−	1.38422i	−0.0280630	−	0.0486065i	−0.879716	+	0.475500i	$0.842267\pi$
$812$	0.418694	−	0.725199i	0.0146933	−	0.0254495i
$813$	−4.82379	−	8.35506i	−0.169178	−	0.293025i
$814$	−1.89351	+	3.27965i	−0.0663674	+	0.114952i
$815$		0			0
$816$	38.8866			1.36130
$817$	−21.0929	+	4.55875i	−0.737947	+	0.159490i
$818$	2.43995			0.0853107
$819$	−7.13857	+	12.3644i	−0.249442	+	0.432046i
$820$		0			0
$821$	9.40110	+	16.2832i	0.328101	+	0.568287i	0.982135	−	0.188178i	$-0.0602582\pi$
$821$	9.40110	+	16.2832i	0.328101	+	0.568287i	−0.654034	+	0.756465i	$0.726925\pi$
$822$	−25.8765	+	44.8194i	−0.902546	+	1.56326i
$823$	26.5984	+	46.0697i	0.927161	+	1.60589i	0.788049	+	0.615612i	$0.211091\pi$
$823$	26.5984	+	46.0697i	0.927161	+	1.60589i	0.139111	+	0.990277i	$0.455575\pi$
$824$	39.2718			1.36810
$825$		0			0
$826$	4.49800	+	7.79076i	0.156505	+	0.271075i
$827$	−12.5371	−	21.7149i	−0.435957	−	0.755101i	0.561416	−	0.827534i	$-0.310257\pi$
$827$	−12.5371	−	21.7149i	−0.435957	−	0.755101i	−0.997373	+	0.0724334i	$0.976924\pi$
$828$	−5.89843			−0.204985
$829$	−28.2740			−0.981997			−0.490999	−	0.871160i	$-0.663368\pi$
$829$	−28.2740			−0.981997			−0.490999	+	0.871160i	$0.663368\pi$
$830$		0			0
$831$	11.2399	−	19.4681i	0.389908	−	0.675341i
$832$	−22.1737	−	38.4059i	−0.768733	−	1.33149i
$833$	16.6761	−	28.8839i	0.577793	−	1.00077i
$834$	8.39608	−	14.5424i	0.290732	−	0.503563i
$835$		0			0
$836$	−0.192688	+	0.599995i	−0.00666427	+	0.0207513i
$837$	−2.17265			−0.0750977
$838$	−13.9160	+	24.1033i	−0.480721	+	0.832633i
$839$	−7.33983	+	12.7130i	−0.253399	+	0.438900i	−0.964459	−	0.264231i	$-0.914882\pi$
$839$	−7.33983	+	12.7130i	−0.253399	+	0.438900i	0.711060	+	0.703131i	$0.248215\pi$
$840$		0			0
$841$	13.6742	−	23.6844i	0.471524	−	0.816704i
$842$	−8.45623	−	14.6466i	−0.291421	−	0.504756i
$843$	−12.2952			−0.423468
$844$	8.69059			0.299142
$845$		0			0
$846$	−7.77657	−	13.4694i	−0.267364	−	0.463088i
$847$	−14.0321			−0.482148
$848$	33.7358			1.15849
$849$	5.67265	+	9.82531i	0.194685	+	0.337204i
$850$		0			0
$851$	28.4558	+	49.2869i	0.975452	+	1.68953i
$852$	1.69313	−	2.93259i	0.0580058	−	0.100469i
$853$	−12.9523	+	22.4341i	−0.443479	+	0.768129i	−0.997945	−	0.0640780i	$-0.979589\pi$
$853$	−12.9523	+	22.4341i	−0.443479	+	0.768129i	0.554466	+	0.832207i	$0.312923\pi$
$854$	−7.00000			−0.239535
$855$		0			0
$856$	−42.2921			−1.44551
$857$	−6.45277	+	11.1765i	−0.220423	+	0.381783i	−0.954936	−	0.296811i	$-0.904077\pi$
$857$	−6.45277	+	11.1765i	−0.220423	+	0.381783i	0.734514	+	0.678594i	$0.237410\pi$
$858$	−1.99041	+	3.44749i	−0.0679515	+	0.117695i
$859$	14.3589	+	24.8703i	0.489919	+	0.848564i	0.999933	−	0.0116018i	$-0.00369304\pi$
$859$	14.3589	+	24.8703i	0.489919	+	0.848564i	−0.510014	+	0.860166i	$0.670360\pi$
$860$		0			0
$861$	−1.23547	−	2.13990i	−0.0421047	−	0.0729275i
$862$	−4.20295			−0.143153
$863$	3.04300			0.103585			0.0517925	−	0.998658i	$-0.483507\pi$
$863$	3.04300			0.103585			0.0517925	+	0.998658i	$0.483507\pi$
$864$	2.48240	+	4.29965i	0.0844531	+	0.146277i
$865$		0			0
$866$	−11.2421			−0.382024
$867$	−50.0140			−1.69857
$868$	−0.398082	−	0.689498i	−0.0135118	−	0.0234031i
$869$	2.20384	−	3.81716i	0.0747600	−	0.129488i
$870$		0			0
$871$	−2.46491	+	4.26934i	−0.0835202	+	0.144661i
$872$	14.0969	−	24.4165i	0.477381	−	0.826849i
$873$	−26.0913			−0.883058
$874$	−18.7305	−	20.6600i	−0.633567	−	0.698835i
$875$		0			0
$876$	−0.442639	+	0.766673i	−0.0149554	+	0.0259035i
$877$	5.68468	−	9.84616i	0.191958	−	0.332481i	−0.753941	−	0.656942i	$-0.771850\pi$
$877$	5.68468	−	9.84616i	0.191958	−	0.332481i	0.945899	+	0.324461i	$0.105183\pi$
$878$	−22.9162	−	39.6921i	−0.773386	−	1.33954i
$879$	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	$0.289883\pi$
$882$	14.5202			0.488919
$883$	−24.8839	−	43.1003i	−0.837411	−	1.45044i	−0.892052	−	0.451933i	$-0.850735\pi$
$883$	−24.8839	−	43.1003i	−0.837411	−	1.45044i	0.0546404	−	0.998506i	$-0.482599\pi$
$884$	7.90431	+	13.6907i	0.265851	+	0.460467i
$885$		0			0
$886$	17.9356			0.602560
$887$	−7.84885	−	13.5946i	−0.263539	−	0.456462i	0.703641	−	0.710556i	$-0.251556\pi$
$887$	−7.84885	−	13.5946i	−0.263539	−	0.456462i	−0.967180	+	0.254093i	$0.918223\pi$
$888$	−38.0431	+	65.8926i	−1.27664	+	2.21121i
$889$	5.99600	+	10.3854i	0.201099	+	0.348314i
$890$		0			0
$891$	1.52963	−	2.64940i	0.0512446	−	0.0887582i
$892$	0.772783			0.0258747
$893$	−7.63555	+	23.7757i	−0.255514	+	0.795623i
$894$	−18.9648			−0.634278
$895$		0			0
$896$	3.37547	−	5.84648i	0.112766	−	0.195317i
$897$	29.9120	+	51.8091i	0.998733	+	1.72986i
$898$	−4.51515	+	7.82047i	−0.150673	+	0.260972i
$899$	0.785142	+	1.35991i	0.0261860	+	0.0453554i
$900$		0			0
$901$	−77.0911			−2.56828
$902$	−0.146574	−	0.253873i	−0.00488038	−	0.00845306i
$903$	7.26955	+	12.5912i	0.241915	+	0.419010i
$904$	53.0780			1.76535
$905$		0			0
$906$	22.1802	+	38.4173i	0.736889	+	1.27633i
$907$	−16.4578	+	28.5057i	−0.546472	+	0.946517i	0.452041	+	0.891997i	$0.350696\pi$
$907$	−16.4578	+	28.5057i	−0.546472	+	0.946517i	−0.998513	+	0.0545199i	$0.982637\pi$
$908$	−1.01404	−	1.75636i	−0.0336520	−	0.0582870i
$909$	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	$0.600315\pi$
$912$	8.31131	−	25.8799i	0.275215	−	0.856968i
$913$	−0.474941			−0.0157183
$914$	−1.40520	+	2.43388i	−0.0464799	+	0.0805055i
$915$		0			0
$916$	4.67465	+	8.09673i	0.154455	+	0.267523i
$917$	−7.98441	+	13.8294i	−0.263668	+	0.456687i
$918$	6.77422	+	11.7333i	0.223583	+	0.387256i
$919$	−50.9506			−1.68070			−0.840352	−	0.542041i	$-0.817652\pi$
$919$	−50.9506			−1.68070			−0.840352	+	0.542041i	$0.817652\pi$
$920$		0			0
$921$	−0.656164	−	1.13651i	−0.0216214	−	0.0374493i
$922$	12.0703	+	20.9063i	0.397514	+	0.688514i
$923$	−14.6135			−0.481009
$924$	0.424571			0.0139674
$925$		0			0
$926$	−17.6847	+	30.6308i	−0.581155	+	1.00659i
$927$	−14.2425	−	24.6687i	−0.467785	−	0.810227i
$928$	1.79416	−	3.10758i	0.0588963	−	0.102011i
$929$	−5.74249	+	9.94628i	−0.188405	+	0.326327i	−0.944719	−	0.327882i	$-0.893665\pi$
$929$	−5.74249	+	9.94628i	−0.188405	+	0.326327i	0.756314	+	0.654209i	$0.226998\pi$
$930$		0			0
$931$	−15.6586	−	17.2717i	−0.513190	−	0.566057i
$932$	6.44509			0.211116
$933$	−9.84485	+	17.0518i	−0.322306	+	0.558250i
$934$	2.02662	−	3.51020i	0.0663129	−	0.114857i
$935$		0			0
$936$	−17.0155	+	29.4717i	−0.556169	+	0.963313i
$937$	8.08477	+	14.0032i	0.264118	+	0.457465i	0.967332	−	0.253512i	$-0.0815859\pi$
$937$	8.08477	+	14.0032i	0.264118	+	0.457465i	−0.703214	+	0.710978i	$0.748253\pi$
$938$	−1.54824			−0.0505519
$939$	−77.9769			−2.54468
$940$		0			0
$941$	12.6937	+	21.9861i	0.413803	+	0.716728i	0.995302	−	0.0968194i	$-0.0308669\pi$
$941$	12.6937	+	21.9861i	0.413803	+	0.716728i	−0.581499	+	0.813547i	$0.697534\pi$
$942$	−20.9608			−0.682940
$943$	−4.40545			−0.143461
$944$	7.81678	+	13.5391i	0.254414	+	0.440659i
$945$		0			0
$946$	0.862446	+	1.49380i	0.0280405	+	0.0485676i
$947$	11.6902	−	20.2481i	0.379882	−	0.657975i	−0.611163	−	0.791505i	$-0.709298\pi$
$947$	11.6902	−	20.2481i	0.379882	−	0.657975i	0.991045	+	0.133530i	$0.0426313\pi$
$948$	8.95477	−	15.5101i	0.290838	−	0.503745i
$949$	3.82043			0.124016
$950$		0			0
$951$	−25.3132			−0.820837
$952$	−12.2746	+	21.2602i	−0.397821	+	0.689046i
$953$	−11.0893	+	19.2073i	−0.359219	+	0.622185i	−0.987831	−	0.155534i	$-0.950290\pi$
$953$	−11.0893	+	19.2073i	−0.359219	+	0.622185i	0.628612	+	0.777719i	$0.283624\pi$
$954$	−16.7811	−	29.0658i	−0.543309	−	0.941040i
$955$		0			0
$956$	−2.74659	−	4.75723i	−0.0888310	−	0.153860i
$957$	−0.837388			−0.0270689
$958$	48.2727			1.55962
$959$	−11.9101	−	20.6289i	−0.384598	−	0.666143i
$960$		0			0
$961$	−29.5070			−0.951839
$962$	66.4057			2.14101
$963$	15.3378	+	26.5659i	0.494255	+	0.856074i
$964$	−2.50302	+	4.33535i	−0.0806167	+	0.139632i
$965$		0			0
$966$	−9.39408	+	16.2710i	−0.302250	+	0.523512i
$967$	−20.4297	+	35.3853i	−0.656975	+	1.13791i	0.324419	+	0.945913i	$0.394831\pi$
$967$	−20.4297	+	35.3853i	−0.656975	+	1.13791i	−0.981395	+	0.192001i	$0.938502\pi$
$968$	−33.4469			−1.07502
$969$	−18.9925	+	59.1392i	−0.610128	+	1.89982i
$970$		0			0
$971$	−12.3238	+	21.3454i	−0.395489	+	0.685008i	−0.993164	−	0.116731i	$-0.962758\pi$
$971$	−12.3238	+	21.3454i	−0.395489	+	0.685008i	0.597674	+	0.801739i	$0.296092\pi$
$972$	4.86299	−	8.42294i	0.155980	−	0.270166i
$973$	3.86445	+	6.69342i	0.123888	+	0.214581i
$974$	15.1379	−	26.2196i	0.485050	−	0.840131i
$975$		0			0
$976$	−12.1648			−0.389387
$977$	13.7077			0.438549			0.219275	−	0.975663i	$-0.429631\pi$
$977$	13.7077			0.438549			0.219275	+	0.975663i	$0.429631\pi$
$978$	30.4628	+	52.7631i	0.974093	+	1.68718i
$979$	2.28514	+	3.95798i	0.0730335	+	0.126498i
$980$		0			0
$981$	−20.4498			−0.652911
$982$	−8.32313	−	14.4161i	−0.265602	−	0.460035i
$983$	0.141014	−	0.244243i	0.00449765	−	0.00779015i	−0.863768	−	0.503890i	$-0.831902\pi$
$983$	0.141014	−	0.244243i	0.00449765	−	0.00779015i	0.868265	+	0.496100i	$0.165235\pi$
$984$	−2.94487	−	5.10066i	−0.0938789	−	0.162603i
$985$		0			0
$986$	4.89608	−	8.48026i	0.155923	−	0.270067i
$987$	16.8242			0.535521
$988$	10.8008	−	2.33435i	0.343620	−	0.0742657i
$989$	25.9218			0.824266
$990$		0			0
$991$	−12.2992	+	21.3028i	−0.390696	+	0.676706i	−0.992542	−	0.121907i	$-0.961099\pi$
$991$	−12.2992	+	21.3028i	−0.390696	+	0.676706i	0.601845	+	0.798613i	$0.294432\pi$
$992$	−1.70584	−	2.95460i	−0.0541604	−	0.0938086i
$993$	7.32580	−	12.6887i	0.232477	−	0.402662i
$994$	−2.29473	−	3.97459i	−0.0727845	−	0.126066i
$995$		0			0
$996$	−1.92981			−0.0611485
$997$	−11.5913	−	20.0768i	−0.367101	−	0.635838i	0.622010	−	0.783010i	$-0.286316\pi$
$997$	−11.5913	−	20.0768i	−0.367101	−	0.635838i	−0.989111	+	0.147171i	$0.952983\pi$
$998$	5.00346	+	8.66625i	0.158382	+	0.274325i
$999$	−19.3273			−0.611487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.d.201.2		6
5.2	odd	4		475.2.j.b.49.4		12
5.3	odd	4		475.2.j.b.49.3		12
5.4	even	2		95.2.e.b.11.2	✓	6
15.14	odd	2		855.2.k.g.676.2		6
19.7	even	3	inner	475.2.e.d.26.2		6
19.8	odd	6		9025.2.a.ba.1.2		3
19.11	even	3		9025.2.a.z.1.2		3
20.19	odd	2		1520.2.q.j.961.3		6
95.7	odd	12		475.2.j.b.349.3		12
95.49	even	6		1805.2.a.h.1.2		3
95.64	even	6		95.2.e.b.26.2	yes	6
95.83	odd	12		475.2.j.b.349.4		12
95.84	odd	6		1805.2.a.g.1.2		3
285.254	odd	6		855.2.k.g.406.2		6
380.159	odd	6		1520.2.q.j.881.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.b.11.2	✓	6	5.4	even	2
95.2.e.b.26.2	yes	6	95.64	even	6
475.2.e.d.26.2		6	19.7	even	3	inner
475.2.e.d.201.2		6	1.1	even	1	trivial
475.2.j.b.49.3		12	5.3	odd	4
475.2.j.b.49.4		12	5.2	odd	4
475.2.j.b.349.3		12	95.7	odd	12
475.2.j.b.349.4		12	95.83	odd	12
855.2.k.g.406.2		6	285.254	odd	6
855.2.k.g.676.2		6	15.14	odd	2
1520.2.q.j.881.3		6	380.159	odd	6
1520.2.q.j.961.3		6	20.19	odd	2
1805.2.a.g.1.2		3	95.84	odd	6
1805.2.a.h.1.2		3	95.49	even	6
9025.2.a.z.1.2		3	19.11	even	3
9025.2.a.ba.1.2		3	19.8	odd	6

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.610938 - 1.05818i) q^{2} +(1.14257 - 1.97899i) q^{3} +(0.253509 + 0.439091i) q^{4} +(-1.39608 - 2.41808i) q^{6} +1.28514 q^{7} +3.06327 q^{8} +(-1.11094 - 1.92420i) q^{9} +0.285142 q^{11} +1.15861 q^{12} +(-2.50000 - 4.33013i) q^{13} +(0.785142 - 1.35991i) q^{14} +(1.36445 - 2.36329i) q^{16} +(-3.11796 + 5.40046i) q^{17} -2.71486 q^{18} +(2.92771 + 3.22932i) q^{19} +(1.46837 - 2.54329i) q^{21} +(0.174204 - 0.301731i) q^{22} +(-2.61796 - 4.53443i) q^{23} +(3.50000 - 6.06218i) q^{24} -6.10938 q^{26} +1.77812 q^{27} +(0.325796 + 0.564295i) q^{28} +(-0.642571 - 1.11297i) q^{29} -1.22188 q^{31} +(1.39608 + 2.41808i) q^{32} +(0.325796 - 0.564295i) q^{33} +(3.80976 + 6.59869i) q^{34} +(0.563266 - 0.975606i) q^{36} -10.8695 q^{37} +(5.20584 - 1.12512i) q^{38} -11.4257 q^{39} +(0.420695 - 0.728665i) q^{41} +(-1.79416 - 3.10758i) q^{42} +(-2.47539 + 4.28749i) q^{43} +(0.0722863 + 0.125204i) q^{44} -6.39764 q^{46} +(2.86445 + 4.96137i) q^{47} +(-3.11796 - 5.40046i) q^{48} -5.34841 q^{49} +(7.12498 + 12.3408i) q^{51} +(1.26755 - 2.19546i) q^{52} +(6.18122 + 10.7062i) q^{53} +(1.08632 - 1.88157i) q^{54} +3.93673 q^{56} +(9.73591 - 2.10419i) q^{57} -1.57028 q^{58} +(-2.86445 + 4.96137i) q^{59} +(-2.22889 - 3.86056i) q^{61} +(-0.746491 + 1.29296i) q^{62} +(-1.42771 - 2.47287i) q^{63} +8.86946 q^{64} +(-0.398082 - 0.689498i) q^{66} +(-0.492981 - 0.853869i) q^{67} -3.16172 q^{68} -11.9648 q^{69} +(1.46135 - 2.53113i) q^{71} +(-3.40310 - 5.89434i) q^{72} +(-0.382043 + 0.661718i) q^{73} +(-6.64057 + 11.5018i) q^{74} +(-0.675762 + 2.10419i) q^{76} +0.366449 q^{77} +(-6.98040 + 12.0904i) q^{78} +(7.72889 - 13.3868i) q^{79} +(5.36445 - 9.29150i) q^{81} +(-0.514037 - 0.890339i) q^{82} -1.66563 q^{83} +1.48898 q^{84} +(3.02461 + 5.23879i) q^{86} -2.93673 q^{87} +0.873467 q^{88} +(8.01404 + 13.8807i) q^{89} +(-3.21286 - 5.56483i) q^{91} +(1.32735 - 2.29904i) q^{92} +(-1.39608 + 2.41808i) q^{93} +7.00000 q^{94} +6.38049 q^{96} +(5.87147 - 10.1697i) q^{97} +(-3.26755 + 5.65956i) q^{98} +(-0.316776 - 0.548672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + q^{3} - 7 q^{4} + 6 q^{6} - 4 q^{7} + 12 q^{8} - 4 q^{9} - 10 q^{11} + 8 q^{12} - 15 q^{13} - 7 q^{14} - 3 q^{16} + q^{17} - 28 q^{18} + 12 q^{21} - 8 q^{22} + 4 q^{23} + 21 q^{24} - 10 q^{26}+ \cdots + 13 q^{99}+O(q^{100}) \) 6 * q + q^2 + q^3 - 7 * q^4 + 6 * q^6 - 4 * q^7 + 12 * q^8 - 4 * q^9 - 10 * q^11 + 8 * q^12 - 15 * q^13 - 7 * q^14 - 3 * q^16 + q^17 - 28 * q^18 + 12 * q^21 - 8 * q^22 + 4 * q^23 + 21 * q^24 - 10 * q^26 + 16 * q^27 + 11 * q^28 + 2 * q^29 - 2 * q^31 - 6 * q^32 + 11 * q^33 + 25 * q^34 - 3 * q^36 + 4 * q^37 + 19 * q^38 - 10 * q^39 + 2 * q^41 - 23 * q^42 - q^43 + 18 * q^44 - 48 * q^46 + 6 * q^47 + q^48 - 14 * q^49 + 6 * q^51 - 35 * q^52 + 11 * q^53 - 10 * q^54 + 30 * q^56 + 19 * q^57 + 14 * q^58 - 6 * q^59 + 9 * q^61 - 13 * q^62 + 9 * q^63 - 16 * q^64 - 29 * q^66 - 20 * q^67 - 68 * q^68 - 10 * q^69 + 29 * q^71 + 11 * q^72 - 22 * q^73 + 7 * q^74 - 19 * q^76 + 32 * q^77 + 30 * q^78 + 24 * q^79 + 21 * q^81 + 31 * q^82 + 6 * q^83 - 56 * q^84 + 32 * q^86 - 24 * q^87 + 18 * q^88 + 14 * q^89 + 10 * q^91 + 41 * q^92 + 6 * q^93 + 42 * q^94 + 34 * q^96 + 7 * q^97 + 23 * q^98 + 13 * q^99

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