LMFDB - Embedded newform 525.2.t.j.26.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(26,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("525.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.t (of order $6$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.11
Character	$\chi$	$=$	525.26
Dual form			525.2.t.j.101.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.17197 + 1.25399i) q^{2} +(-0.831052 + 1.51966i) q^{3} +(2.14497 + 3.71520i) q^{4} +(-3.71065 + 2.25852i) q^{6} +(2.06025 + 1.65993i) q^{7} +5.74313i q^{8} +(-1.61871 - 2.52582i) q^{9} +O(q^{10})$	\(q+(2.17197 + 1.25399i) q^{2} +(-0.831052 + 1.51966i) q^{3} +(2.14497 + 3.71520i) q^{4} +(-3.71065 + 2.25852i) q^{6} +(2.06025 + 1.65993i) q^{7} +5.74313i q^{8} +(-1.61871 - 2.52582i) q^{9} +(1.48843 - 0.859346i) q^{11} +(-7.42841 + 0.172094i) q^{12} +0.360784i q^{13} +(2.39327 + 6.18885i) q^{14} +(-2.91187 + 5.04351i) q^{16} +(-1.27144 - 2.20219i) q^{17} +(-0.348428 - 7.51586i) q^{18} +(-4.93492 - 2.84918i) q^{19} +(-4.23470 + 1.75138i) q^{21} +4.31044 q^{22} +(2.17197 + 1.25399i) q^{23} +(-8.72758 - 4.77284i) q^{24} +(-0.452418 + 0.783611i) q^{26} +(5.18361 - 0.360784i) q^{27} +(-1.74780 + 11.2147i) q^{28} -3.76228i q^{29} +(-2.41187 + 1.39249i) q^{31} +(-2.70160 + 1.55977i) q^{32} +(0.0689466 + 2.97606i) q^{33} -6.37747i q^{34} +(5.91187 - 11.4316i) q^{36} +(-1.65283 + 2.86279i) q^{37} +(-7.14567 - 12.3767i) q^{38} +(-0.548267 - 0.299830i) q^{39} -2.63477 q^{41} +(-11.3939 - 1.50631i) q^{42} +10.0606 q^{43} +(6.38529 + 3.68655i) q^{44} +(3.14497 + 5.44725i) q^{46} +(2.91152 - 5.04290i) q^{47} +(-5.24448 - 8.61645i) q^{48} +(1.48925 + 6.83975i) q^{49} +(4.40320 - 0.102009i) q^{51} +(-1.34038 + 0.773871i) q^{52} +(1.25950 - 0.727175i) q^{53} +(11.7111 + 5.71658i) q^{54} +(-9.53320 + 11.8323i) q^{56} +(8.43094 - 5.13156i) q^{57} +(4.71786 - 8.17157i) q^{58} +(3.42928 + 5.93969i) q^{59} +(1.38882 + 0.801836i) q^{61} -6.98468 q^{62} +(0.857759 - 7.89077i) q^{63} +3.82374 q^{64} +(-3.58220 + 6.55038i) q^{66} +(-1.24541 - 2.15712i) q^{67} +(5.45439 - 9.44729i) q^{68} +(-3.71065 + 2.25852i) q^{69} -13.1790i q^{71} +(14.5061 - 9.29643i) q^{72} +(-10.0838 + 5.82187i) q^{73} +(-7.17980 + 4.14526i) q^{74} -24.4456i q^{76} +(4.49300 + 0.700227i) q^{77} +(-0.814836 - 1.33874i) q^{78} +(-6.93492 + 12.0116i) q^{79} +(-3.75958 + 8.17713i) q^{81} +(-5.72264 - 3.30396i) q^{82} +3.50427 q^{83} +(-15.5900 - 11.9761i) q^{84} +(21.8514 + 12.6159i) q^{86} +(5.71737 + 3.12665i) q^{87} +(4.93534 + 8.54825i) q^{88} +(6.10392 - 10.5723i) q^{89} +(-0.598876 + 0.743304i) q^{91} +10.7591i q^{92} +(-0.111722 - 4.82244i) q^{93} +(12.6475 - 7.30202i) q^{94} +(-0.125143 - 5.40176i) q^{96} +8.18747i q^{97} +(-5.34234 + 16.7232i) q^{98} +(-4.57989 - 2.36849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 6 q^{9}+O(q^{10}) $ 24 * q + 12 * q^4 + 6 * q^9	$ 24 q + 12 q^{4} + 6 q^{9} - 12 q^{16} - 6 q^{21} - 18 q^{24} + 84 q^{36} + 12 q^{39} + 36 q^{46} + 12 q^{49} - 12 q^{51} + 36 q^{54} + 36 q^{61} - 24 q^{64} - 72 q^{66} - 48 q^{79} - 6 q^{81} - 48 q^{84} - 96 q^{91} + 72 q^{94} - 90 q^{96} + 48 q^{99}+O(q^{100}) $ 24 * q + 12 * q^4 + 6 * q^9 - 12 * q^16 - 6 * q^21 - 18 * q^24 + 84 * q^36 + 12 * q^39 + 36 * q^46 + 12 * q^49 - 12 * q^51 + 36 * q^54 + 36 * q^61 - 24 * q^64 - 72 * q^66 - 48 * q^79 - 6 * q^81 - 48 * q^84 - 96 * q^91 + 72 * q^94 - 90 * q^96 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.17197	+	1.25399i	1.53582	+	0.886704i	0.999077	+	0.0429549i	$0.0136772\pi$
$2$	2.17197	+	1.25399i	1.53582	+	0.886704i	0.536739	+	0.843749i	$0.319656\pi$
$3$	−0.831052	+	1.51966i	−0.479808	+	0.877374i
$3$	−0.831052	+	1.51966i	−0.479808	+	0.877374i
$4$	2.14497	+	3.71520i	1.07249	+	1.85760i
$5$		0			0
$5$		0			0
$6$	−3.71065	+	2.25852i	−1.51487	+	0.922036i
$7$	2.06025	+	1.65993i	0.778701	+	0.627395i
$7$	2.06025	+	1.65993i	0.778701	+	0.627395i
$8$			5.74313i			2.03050i
$9$	−1.61871	−	2.52582i	−0.539569	−	0.841942i
$10$		0			0
$11$	1.48843	−	0.859346i	0.448779	−	0.259103i	−0.258535	−	0.966002i	$-0.583240\pi$
$11$	1.48843	−	0.859346i	0.448779	−	0.259103i	0.707314	+	0.706899i	$0.249907\pi$
$12$	−7.42841	+	0.172094i	−2.14440	+	0.0496794i
$13$			0.360784i			0.100063i	0.998748	+	0.0500317i	$0.0159322\pi$
$13$			0.360784i			0.100063i	−0.998748	+	0.0500317i	$0.984068\pi$
$14$	2.39327	+	6.18885i	0.639628	+	1.65404i
$15$		0			0
$16$	−2.91187	+	5.04351i	−0.727967	+	1.26088i
$17$	−1.27144	−	2.20219i	−0.308369	−	0.534110i	0.669637	−	0.742689i	$-0.266450\pi$
$17$	−1.27144	−	2.20219i	−0.308369	−	0.534110i	−0.978006	+	0.208578i	$0.933116\pi$
$18$	−0.348428	−	7.51586i	−0.0821252	−	1.77150i
$19$	−4.93492	−	2.84918i	−1.13215	−	0.653646i	−0.187674	−	0.982231i	$-0.560095\pi$
$19$	−4.93492	−	2.84918i	−1.13215	−	0.653646i	−0.944474	+	0.328586i	$0.893428\pi$
$20$		0			0
$21$	−4.23470	+	1.75138i	−0.924087	+	0.382182i
$22$	4.31044			0.918989
$23$	2.17197	+	1.25399i	0.452887	+	0.261475i	0.709049	−	0.705159i	$-0.249125\pi$
$23$	2.17197	+	1.25399i	0.452887	+	0.261475i	−0.256162	+	0.966634i	$0.582458\pi$
$24$	−8.72758	−	4.77284i	−1.78151	−	0.974251i
$25$		0			0
$26$	−0.452418	+	0.783611i	−0.0887265	+	0.153679i
$27$	5.18361	−	0.360784i	0.997587	−	0.0694328i
$28$	−1.74780	+	11.2147i	−0.330303	+	2.11939i
$29$		−	3.76228i		−	0.698638i	−0.937004	−	0.349319i	$-0.886413\pi$
$29$		−	3.76228i		−	0.698638i	0.937004	−	0.349319i	$-0.113587\pi$
$30$		0			0
$31$	−2.41187	+	1.39249i	−0.433185	+	0.250099i	−0.700702	−	0.713454i	$-0.747130\pi$
$31$	−2.41187	+	1.39249i	−0.433185	+	0.250099i	0.267518	+	0.963553i	$0.413797\pi$
$32$	−2.70160	+	1.55977i	−0.477580	+	0.275731i
$33$	0.0689466	+	2.97606i	0.0120021	+	0.518066i
$34$		−	6.37747i		−	1.09373i
$35$		0			0
$36$	5.91187	−	11.4316i	0.985312	−	1.90527i
$37$	−1.65283	+	2.86279i	−0.271724	+	0.470639i	−0.969303	−	0.245868i	$-0.920927\pi$
$37$	−1.65283	+	2.86279i	−0.271724	+	0.470639i	0.697580	+	0.716507i	$0.254260\pi$
$38$	−7.14567	−	12.3767i	−1.15918	−	2.00776i
$39$	−0.548267	−	0.299830i	−0.0877929	−	0.0480112i
$40$		0			0
$41$	−2.63477			−0.411481			−0.205741	−	0.978607i	$-0.565960\pi$
$41$	−2.63477			−0.411481			−0.205741	+	0.978607i	$0.565960\pi$
$42$	−11.3939	−	1.50631i	−1.75811	−	0.232429i
$43$	10.0606			1.53423			0.767114	−	0.641510i	$-0.221692\pi$
$43$	10.0606			1.53423			0.767114	+	0.641510i	$0.221692\pi$
$44$	6.38529	+	3.68655i	0.962618	+	0.555768i
$45$		0			0
$46$	3.14497	+	5.44725i	0.463701	+	0.803154i
$47$	2.91152	−	5.04290i	0.424689	−	0.735583i	−0.571702	−	0.820461i	$-0.693717\pi$
$47$	2.91152	−	5.04290i	0.424689	−	0.735583i	0.996391	+	0.0848783i	$0.0270501\pi$
$48$	−5.24448	−	8.61645i	−0.756975	−	1.24368i
$49$	1.48925	+	6.83975i	0.212751	+	0.977107i
$50$		0			0
$51$	4.40320	−	0.102009i	0.616572	−	0.0142842i
$52$	−1.34038	+	0.773871i	−0.185878	+	0.107317i
$53$	1.25950	−	0.727175i	0.173006	−	0.0998852i	−0.410996	−	0.911637i	$-0.634819\pi$
$53$	1.25950	−	0.727175i	0.173006	−	0.0998852i	0.584003	+	0.811752i	$0.301486\pi$
$54$	11.7111	+	5.71658i	1.59368	+	0.777928i
$55$		0			0
$56$	−9.53320	+	11.8323i	−1.27393	+	1.58115i
$57$	8.43094	−	5.13156i	1.11671	−	0.679692i
$58$	4.71786	−	8.17157i	0.619485	−	1.07298i
$59$	3.42928	+	5.93969i	0.446454	+	0.773282i	0.998152	−	0.0607624i	$-0.0193532\pi$
$59$	3.42928	+	5.93969i	0.446454	+	0.773282i	−0.551698	+	0.834044i	$0.686020\pi$
$60$		0			0
$61$	1.38882	+	0.801836i	0.177820	+	0.102665i	0.586268	−	0.810117i	$-0.300596\pi$
$61$	1.38882	+	0.801836i	0.177820	+	0.102665i	−0.408448	+	0.912782i	$0.633930\pi$
$62$	−6.98468			−0.887055
$63$	0.857759	−	7.89077i	0.108067	−	0.994144i
$64$	3.82374			0.477967
$65$		0			0
$66$	−3.58220	+	6.55038i	−0.440938	+	0.806296i
$67$	−1.24541	−	2.15712i	−0.152151	−	0.263534i	0.779867	−	0.625946i	$-0.215287\pi$
$67$	−1.24541	−	2.15712i	−0.152151	−	0.263534i	−0.932018	+	0.362412i	$0.881953\pi$
$68$	5.45439	−	9.44729i	0.661442	−	1.14565i
$69$	−3.71065	+	2.25852i	−0.446710	+	0.271894i
$70$		0			0
$71$		−	13.1790i		−	1.56406i	−0.623243	−	0.782028i	$-0.714185\pi$
$71$		−	13.1790i		−	1.56406i	0.623243	−	0.782028i	$-0.285815\pi$
$72$	14.5061	−	9.29643i	1.70956	−	1.09560i
$73$	−10.0838	+	5.82187i	−1.18022	+	0.681398i	−0.956065	−	0.293156i	$-0.905294\pi$
$73$	−10.0838	+	5.82187i	−1.18022	+	0.681398i	−0.224151	+	0.974554i	$0.571961\pi$
$74$	−7.17980	+	4.14526i	−0.834635	+	0.481877i
$75$		0			0
$76$		−	24.4456i		−	2.80410i
$77$	4.49300	+	0.700227i	0.512024	+	0.0797982i
$78$	−0.814836	−	1.33874i	−0.0922621	−	0.151583i
$79$	−6.93492	+	12.0116i	−0.780239	+	1.35141i	0.151563	+	0.988448i	$0.451569\pi$
$79$	−6.93492	+	12.0116i	−0.780239	+	1.35141i	−0.931802	+	0.362966i	$0.881764\pi$
$80$		0			0
$81$	−3.75958	+	8.17713i	−0.417732	+	0.908571i
$82$	−5.72264	−	3.30396i	−0.631959	−	0.364862i
$83$	3.50427			0.384644			0.192322	−	0.981332i	$-0.438398\pi$
$83$	3.50427			0.384644			0.192322	+	0.981332i	$0.438398\pi$
$84$	−15.5900	−	11.9761i	−1.70101	−	1.30670i
$85$		0			0
$86$	21.8514	+	12.6159i	2.35629	+	1.36041i
$87$	5.71737	+	3.12665i	0.612967	+	0.335212i
$88$	4.93534	+	8.54825i	0.526108	+	0.911247i
$89$	6.10392	−	10.5723i	0.647014	−	1.12066i	−0.336818	−	0.941570i	$-0.609351\pi$
$89$	6.10392	−	10.5723i	0.647014	−	1.12066i	0.983832	−	0.179092i	$-0.0573158\pi$
$90$		0			0
$91$	−0.598876	+	0.743304i	−0.0627793	+	0.0779194i
$92$			10.7591i			1.12171i
$93$	−0.111722	−	4.82244i	−0.0115850	−	0.500064i
$94$	12.6475	−	7.30202i	1.30449	−	0.753146i
$95$		0			0
$96$	−0.125143	−	5.40176i	−0.0127723	−	0.551314i
$97$			8.18747i			0.831311i	0.909522	+	0.415656i	$0.136448\pi$
$97$			8.18747i			0.831311i	−0.909522	+	0.415656i	$0.863552\pi$
$98$	−5.34234	+	16.7232i	−0.539658	+	1.68930i
$99$	−4.57989	−	2.36849i	−0.460296	−	0.238042i
$100$		0			0
$101$	−0.623467	−	1.07988i	−0.0620372	−	0.107452i	0.833339	−	0.552763i	$-0.186426\pi$
$101$	−0.623467	−	1.07988i	−0.0620372	−	0.107452i	−0.895376	+	0.445311i	$0.853093\pi$
$102$	9.69155	+	5.30001i	0.959607	+	0.524779i
$103$	−3.59057	−	2.07302i	−0.353790	−	0.204261i	0.312563	−	0.949897i	$-0.398812\pi$
$103$	−3.59057	−	2.07302i	−0.353790	−	0.204261i	−0.666353	+	0.745636i	$0.732146\pi$
$104$	−2.07203			−0.203179
$105$		0			0
$106$	3.64748			0.354274
$107$	0.959143	+	0.553762i	0.0927239	+	0.0535342i	0.545645	−	0.838016i	$-0.316285\pi$
$107$	0.959143	+	0.553762i	0.0927239	+	0.0535342i	−0.452921	+	0.891551i	$0.649618\pi$
$108$	12.4591	+	18.4843i	1.19888	+	1.77865i
$109$	−4.55684	−	7.89268i	−0.436466	−	0.755982i	0.560948	−	0.827851i	$-0.310437\pi$
$109$	−4.55684	−	7.89268i	−0.436466	−	0.755982i	−0.997414	+	0.0718694i	$0.977104\pi$
$110$		0			0
$111$	−2.97686	−	4.89086i	−0.282551	−	0.464220i
$112$	−14.3711	+	5.55738i	−1.35794	+	0.525123i
$113$		−	3.79282i		−	0.356799i	−0.983958	−	0.178399i	$-0.942908\pi$
$113$		−	3.79282i		−	0.356799i	0.983958	−	0.178399i	$-0.0570919\pi$
$114$	24.7467	−	0.573307i	2.31774	−	0.0536952i
$115$		0			0
$116$	13.9776	−	8.06999i	1.29779	−	0.749280i
$117$	0.911276	−	0.584002i	0.0842475	−	0.0539910i
$118$			17.2011i			1.58349i
$119$	1.03601	−	6.64757i	0.0949712	−	0.609381i
$120$		0			0
$121$	−4.02305	+	6.96812i	−0.365732	+	0.633466i
$122$	2.01099	+	3.48313i	0.182066	+	0.315348i
$123$	2.18963	−	4.00394i	0.197432	−	0.361023i
$124$	−10.3468	−	5.97372i	−0.929169	−	0.536456i
$125$		0			0
$126$	11.7580	−	16.0629i	1.04748	−	1.43100i
$127$	−5.98643			−0.531210			−0.265605	−	0.964082i	$-0.585572\pi$
$127$	−5.98643			−0.531210			−0.265605	+	0.964082i	$0.585572\pi$
$128$	13.7083	+	7.91447i	1.21165	+	0.699547i
$129$	−8.36089	+	15.2887i	−0.736135	+	1.34609i
$130$		0			0
$131$	7.29012	−	12.6269i	0.636941	−	1.10321i	−0.349159	−	0.937063i	$-0.613533\pi$
$131$	7.29012	−	12.6269i	0.636941	−	1.10321i	0.986100	−	0.166151i	$-0.0531339\pi$
$132$	−10.9088	+	6.63973i	−0.949488	+	0.577914i
$133$	−5.43772	−	14.0616i	−0.471510	−	1.21930i
$134$		−	6.24693i		−	0.539653i
$135$		0			0
$136$	12.6475	−	7.30202i	1.08451	−	0.626143i
$137$	−13.6081	+	7.85666i	−1.16262	+	0.671240i	−0.951931	−	0.306313i	$-0.900905\pi$
$137$	−13.6081	+	7.85666i	−1.16262	+	0.671240i	−0.210691	+	0.977553i	$0.567571\pi$
$138$	−10.8916	+	0.252326i	−0.927153	+	0.0214794i
$139$		−	14.7324i		−	1.24959i	−0.780790	−	0.624794i	$-0.785183\pi$
$139$		−	14.7324i		−	1.24959i	0.780790	−	0.624794i	$-0.214817\pi$
$140$		0			0
$141$	5.24385	+	8.61542i	0.441612	+	0.725549i
$142$	16.5263	−	28.6243i	1.38685	−	2.40210i
$143$	0.310038	+	0.537001i	0.0259267	+	0.0449063i
$144$	17.4525	−	0.809079i	1.45437	−	0.0674232i
$145$		0			0
$146$	−29.2022			−2.41679
$147$	−11.6317	−	3.42103i	−0.959367	−	0.282162i
$148$	−14.1811			−1.16568
$149$	−11.0008	−	6.35130i	−0.901219	−	0.520319i	−0.0236233	−	0.999721i	$-0.507520\pi$
$149$	−11.0008	−	6.35130i	−0.901219	−	0.520319i	−0.877595	+	0.479402i	$0.840854\pi$
$150$		0			0
$151$	−8.34679	−	14.4571i	−0.679252	−	1.17650i	−0.975207	−	0.221297i	$-0.928971\pi$
$151$	−8.34679	−	14.4571i	−0.679252	−	1.17650i	0.295955	−	0.955202i	$-0.404362\pi$
$152$	16.3632	−	28.3419i	1.32723	−	2.29883i
$153$	−3.50427	+	6.77613i	−0.283304	+	0.547818i
$154$	8.88058	+	7.15503i	0.715618	+	0.576569i
$155$		0			0
$156$	−0.0620888	−	2.68005i	−0.00497108	−	0.214576i
$157$	−1.24979	+	0.721567i	−0.0997442	+	0.0575873i	−0.549042	−	0.835795i	$-0.685007\pi$
$157$	−1.24979	+	0.721567i	−0.0997442	+	0.0575873i	0.449298	+	0.893382i	$0.351674\pi$
$158$	−30.1249	+	17.3926i	−2.39661	+	1.38368i
$159$	0.0583424	+	2.51833i	0.00462685	+	0.199717i
$160$		0			0
$161$	2.39327	+	6.18885i	0.188616	+	0.487750i
$162$	−18.4197	+	13.0460i	−1.44719	+	1.02499i
$163$	−8.43094	+	14.6028i	−0.660362	+	1.14378i	0.320158	+	0.947364i	$0.396264\pi$
$163$	−8.43094	+	14.6028i	−0.660362	+	1.14378i	−0.980521	+	0.196417i	$0.937069\pi$
$164$	−5.65150	−	9.78869i	−0.441308	−	0.764368i
$165$		0			0
$166$	7.61118	+	4.39432i	0.590742	+	0.341065i
$167$	7.20879			0.557833			0.278916	−	0.960315i	$-0.410025\pi$
$167$	7.20879			0.557833			0.278916	+	0.960315i	$0.410025\pi$
$168$	−10.0584	−	24.3204i	−0.776022	−	1.87636i
$169$	12.8698			0.989987
$170$		0			0
$171$	0.791659	+	17.0767i	0.0605397	+	1.30589i
$172$	21.5797	+	37.3772i	1.64544	+	2.84998i
$173$	−4.49300	+	7.78210i	−0.341596	+	0.591662i	−0.984729	−	0.174093i	$-0.944301\pi$
$173$	−4.49300	+	7.78210i	−0.341596	+	0.591662i	0.643133	+	0.765754i	$0.277634\pi$
$174$	8.49719	+	13.9605i	0.644170	+	1.05834i
$175$		0			0
$176$			10.0092i			0.754473i
$177$	−11.8762	+	0.275136i	−0.892669	+	0.0206805i
$178$	26.5151	−	15.3085i	1.98739	−	1.14742i
$179$	−9.49333	+	5.48098i	−0.709565	+	0.409667i	−0.810900	−	0.585185i	$-0.801022\pi$
$179$	−9.49333	+	5.48098i	−0.709565	+	0.409667i	0.101335	+	0.994852i	$0.467689\pi$
$180$		0			0
$181$			5.39306i			0.400863i	0.979708	+	0.200431i	$0.0642344\pi$
$181$			5.39306i			0.400863i	−0.979708	+	0.200431i	$0.935766\pi$
$182$	−2.23284	+	0.863452i	−0.165509	+	0.0640033i
$183$	−2.37270	+	1.44416i	−0.175395	+	0.106756i
$184$	−7.20181	+	12.4739i	−0.530925	+	0.919589i
$185$		0			0
$186$	5.80463	−	10.6143i	0.425616	−	0.778279i
$187$	−3.78489	−	2.18521i	−0.276779	−	0.159798i
$188$	24.9805			1.82189
$189$	11.2784	+	7.86114i	0.820384	+	0.571814i
$190$		0			0
$191$	−18.4619	−	10.6590i	−1.33586	−	0.771259i	−0.349669	−	0.936873i	$-0.613706\pi$
$191$	−18.4619	−	10.6590i	−1.33586	−	0.771259i	−0.986191	+	0.165614i	$0.947039\pi$
$192$	−3.17773	+	5.81077i	−0.229333	+	0.419356i
$193$	6.96805	+	12.0690i	0.501571	+	0.868747i	0.999998	+	0.00181508i	$0.000577759\pi$
$193$	6.96805	+	12.0690i	0.501571	+	0.868747i	−0.498427	+	0.866932i	$0.666089\pi$
$194$	−10.2670	+	17.7829i	−0.737127	+	1.27674i
$195$		0			0
$196$	−22.2166	+	20.2039i	−1.58690	+	1.44314i
$197$		−	2.01202i		−	0.143350i	−0.997428	−	0.0716752i	$-0.977165\pi$
$197$		−	2.01202i		−	0.143350i	0.997428	−	0.0716752i	$-0.0228345\pi$
$198$	−6.97733	−	10.8874i	−0.495857	−	0.773735i
$199$	−6.90207	+	3.98491i	−0.489275	+	0.282483i	−0.724274	−	0.689513i	$-0.757825\pi$
$199$	−6.90207	+	3.98491i	−0.489275	+	0.282483i	0.234999	+	0.971996i	$0.424491\pi$
$200$		0			0
$201$	4.31308	−	0.0999214i	0.304221	−	0.00704791i
$202$		−	3.12728i		−	0.220035i
$203$	6.24513	−	7.75124i	0.438322	−	0.544030i
$204$	9.82374	+	16.1400i	0.687799	+	1.13003i
$205$		0			0
$206$	−5.19908	−	9.00507i	−0.362237	−	0.627413i
$207$	−0.348428	−	7.51586i	−0.0242174	−	0.522388i
$208$	−1.81961	−	1.05055i	−0.126168	−	0.0728428i
$209$	−9.79371			−0.677445
$210$		0			0
$211$	−4.95390			−0.341041			−0.170520	−	0.985354i	$-0.554545\pi$
$211$	−4.95390			−0.341041			−0.170520	+	0.985354i	$0.554545\pi$
$212$	5.40321	+	3.11954i	0.371094	+	0.214251i
$213$	20.0275	+	10.9524i	1.37226	+	0.750447i
$214$	1.38882	+	2.40551i	0.0949379	+	0.164437i
$215$		0			0
$216$	2.07203	+	29.7701i	0.140984	+	2.02560i
$217$	−7.28050	−	1.13465i	−0.494232	−	0.0770254i
$218$		−	22.8569i		−	1.54806i
$219$	−0.467097	−	20.1621i	−0.0315635	−	1.36243i
$220$		0			0
$221$	0.794515	−	0.458713i	0.0534449	−	0.0308564i
$222$	−0.332581	−	14.3558i	−0.0223213	−	0.963495i
$223$		−	15.6534i		−	1.04823i	−0.851648	−	0.524114i	$-0.824397\pi$
$223$		−	15.6534i		−	1.04823i	0.851648	−	0.524114i	$-0.175603\pi$
$224$	−8.15509	−	1.27096i	−0.544885	−	0.0849195i
$225$		0			0
$226$	4.75615	−	8.23790i	0.316374	−	0.547977i
$227$	−6.30600	−	10.9223i	−0.418544	−	0.724939i	0.577250	−	0.816568i	$-0.304126\pi$
$227$	−6.30600	−	10.9223i	−0.418544	−	0.724939i	−0.995793	+	0.0916289i	$0.970793\pi$
$228$	37.1489	+	20.3156i	2.46025	+	1.34543i
$229$	5.18951	+	2.99617i	0.342933	+	0.197992i	0.661568	−	0.749885i	$-0.269891\pi$
$229$	5.18951	+	2.99617i	0.342933	+	0.197992i	−0.318636	+	0.947877i	$0.603225\pi$
$230$		0			0
$231$	−4.79802	+	6.24588i	−0.315686	+	0.410949i
$232$	21.6073			1.41859
$233$	−18.8822	−	10.9016i	−1.23701	−	0.714190i	−0.268531	−	0.963271i	$-0.586538\pi$
$233$	−18.8822	−	10.9016i	−1.23701	−	0.714190i	−0.968483	+	0.249081i	$0.919871\pi$
$234$	2.71160	−	0.125707i	0.177263	−	0.00821772i
$235$		0			0
$236$	−14.7114	+	25.4809i	−0.957632	+	1.65867i
$237$	−12.4903	−	20.5210i	−0.811330	−	1.33298i
$238$	10.5862	−	13.1392i	0.686199	−	0.851686i
$239$		−	24.9069i		−	1.61109i	−0.592533	−	0.805546i	$-0.701872\pi$
$239$		−	24.9069i		−	1.61109i	0.592533	−	0.805546i	$-0.298128\pi$
$240$		0			0
$241$	14.7454	−	8.51326i	0.949835	−	0.548388i	0.0568054	−	0.998385i	$-0.481909\pi$
$241$	14.7454	−	8.51326i	0.949835	−	0.548388i	0.893030	+	0.449998i	$0.148575\pi$
$242$	−17.4759	+	10.0897i	−1.12339	+	0.648591i
$243$	−9.30202	−	12.5089i	−0.596725	−	0.802446i
$244$			6.87967i			0.440426i
$245$		0			0
$246$	9.77670	−	5.95067i	0.623339	−	0.379401i
$247$	1.02794	−	1.78044i	0.0654060	−	0.113286i
$248$	−7.99727	−	13.8517i	−0.507827	−	0.879582i
$249$	−2.91223	+	5.32529i	−0.184555	+	0.337476i
$250$		0			0
$251$	27.3925			1.72900			0.864501	−	0.502631i	$-0.167635\pi$
$251$	27.3925			1.72900			0.864501	+	0.502631i	$0.167635\pi$
$252$	31.1557	−	13.7387i	1.96262	−	0.865459i
$253$	4.31044			0.270995
$254$	−13.0024	−	7.50691i	−0.815840	−	0.471026i
$255$		0			0
$256$	16.0256	+	27.7571i	1.00160	+	1.73482i
$257$	−15.1941	+	26.3170i	−0.947783	+	1.64161i	−0.197703	+	0.980262i	$0.563348\pi$
$257$	−15.1941	+	26.3170i	−0.947783	+	1.64161i	−0.750080	+	0.661347i	$0.769985\pi$
$258$	−37.3314	+	22.7221i	−2.32415	+	1.41461i
$259$	−8.15728	+	3.15447i	−0.506868	+	0.196009i
$260$		0			0
$261$	−9.50287	+	6.09003i	−0.588213	+	0.376963i
$262$	31.6679	−	18.2835i	1.95645	−	1.12956i
$263$	−16.7460	+	9.66832i	−1.03260	+	0.596174i	−0.917729	−	0.397206i	$-0.869980\pi$
$263$	−16.7460	+	9.66832i	−1.03260	+	0.596174i	−0.114874	+	0.993380i	$0.536646\pi$
$264$	−17.0919	+	0.395969i	−1.05193	+	0.0243702i
$265$		0			0
$266$	5.82255	−	37.3603i	0.357003	−	2.29071i
$267$	10.9936	+	18.0620i	0.672796	+	1.10538i
$268$	5.34275	−	9.25392i	0.326361	−	0.565273i
$269$	11.0008	+	19.0539i	0.670729	+	1.16174i	0.977698	+	0.210017i	$0.0673520\pi$
$269$	11.0008	+	19.0539i	0.670729	+	1.16174i	−0.306969	+	0.951720i	$0.599315\pi$
$270$		0			0
$271$	−13.0404	−	7.52886i	−0.792146	−	0.457345i	0.0485718	−	0.998820i	$-0.484533\pi$
$271$	−13.0404	−	7.52886i	−0.792146	−	0.457345i	−0.840717	+	0.541474i	$0.817866\pi$
$272$	14.8090			0.897929
$273$	−0.631869	−	1.52781i	−0.0382425	−	0.0924672i
$274$	−39.4086			−2.38076
$275$		0			0
$276$	−16.3501	−	8.94135i	−0.984160	−	0.538206i
$277$	−0.837995	−	1.45145i	−0.0503502	−	0.0872092i	0.839752	−	0.542970i	$-0.182700\pi$
$277$	−0.837995	−	1.45145i	−0.0503502	−	0.0872092i	−0.890102	+	0.455761i	$0.849367\pi$
$278$	18.4743	−	31.9984i	1.10801	−	1.91914i
$279$	7.42130	+	3.83792i	0.444302	+	0.229770i
$280$		0			0
$281$			2.10086i			0.125327i	0.998035	+	0.0626633i	$0.0199594\pi$
$281$			2.10086i			0.125327i	−0.998035	+	0.0626633i	$0.980041\pi$
$282$	0.585852	+	25.2882i	0.0348870	+	1.50589i
$283$	4.33360	−	2.50200i	0.257606	−	0.148729i	−0.365636	−	0.930758i	$-0.619149\pi$
$283$	4.33360	−	2.50200i	0.257606	−	0.148729i	0.623242	+	0.782029i	$0.285815\pi$
$284$	48.9625	−	28.2685i	2.90539	−	1.67743i
$285$		0			0
$286$			1.55514i			0.0919571i
$287$	−5.42827	−	4.37353i	−0.320421	−	0.258161i
$288$	8.31281	+	4.29897i	0.489837	+	0.253319i
$289$	5.26690	−	9.12253i	0.309817	−	0.536620i
$290$		0			0
$291$	−12.4421	−	6.80421i	−0.729371	−	0.398870i
$292$	−43.2588	−	24.9755i	−2.53153	−	1.46158i
$293$	17.2734			1.00912			0.504561	−	0.863376i	$-0.331654\pi$
$293$	17.2734			1.00912			0.504561	+	0.863376i	$0.331654\pi$
$294$	−20.9738	−	22.0164i	−1.22322	−	1.28402i
$295$		0			0
$296$	−16.4414	−	9.49242i	−0.955634	−	0.551736i
$297$	7.40541	−	4.99152i	0.429706	−	0.289637i
$298$	−15.9289	−	27.5897i	−0.922737	−	1.59823i
$299$	−0.452418	+	0.783611i	−0.0261640	+	0.0453174i
$300$		0			0
$301$	20.7274	+	16.6999i	1.19471	+	0.962568i
$302$		−	41.8671i		−	2.40918i
$303$	2.15917	−	0.0500217i	0.124041	−	0.00287367i
$304$	28.7397	−	16.5929i	1.64833	−	0.951666i
$305$		0			0
$306$	−16.1084	+	10.3232i	−0.920854	+	0.590140i
$307$			10.2324i			0.583994i	0.956419	+	0.291997i	$0.0943197\pi$
$307$			10.2324i			0.583994i	−0.956419	+	0.291997i	$0.905680\pi$
$308$	7.03587	+	18.1943i	0.400906	+	1.03672i
$309$	6.13423	−	3.73365i	0.348964	−	0.212400i
$310$		0			0
$311$	5.23895	+	9.07413i	0.297074	+	0.514547i	0.975465	−	0.220154i	$-0.0706559\pi$
$311$	5.23895	+	9.07413i	0.297074	+	0.514547i	−0.678391	+	0.734701i	$0.737323\pi$
$312$	1.72196	−	3.14877i	0.0974868	−	0.178264i
$313$	−0.221855	−	0.128088i	−0.0125400	−	0.00723997i	0.493717	−	0.869623i	$-0.335638\pi$
$313$	−0.221855	−	0.128088i	−0.0125400	−	0.00723997i	−0.506257	+	0.862383i	$0.668971\pi$
$314$	−3.61935			−0.204252
$315$		0			0
$316$	−59.5008			−3.34718
$317$	26.7935	+	15.4693i	1.50487	+	0.868840i	0.999984	+	0.00565618i	$0.00180043\pi$
$317$	26.7935	+	15.4693i	1.50487	+	0.868840i	0.504890	+	0.863183i	$0.331533\pi$
$318$	−3.03124	+	5.54291i	−0.169984	+	0.310831i
$319$	−3.23310	−	5.59990i	−0.181019	−	0.313534i
$320$		0			0
$321$	−1.63862	+	0.997363i	−0.0914591	+	0.0556674i
$322$	−2.56264	+	16.4431i	−0.142810	+	0.916340i
$323$			14.4902i			0.806256i
$324$	−38.4439	+	3.57212i	−2.13577	+	0.198451i
$325$		0			0
$326$	−36.6235	+	21.1446i	−2.02839	+	1.17109i
$327$	15.7811	−	0.365602i	0.872698	−	0.0202179i
$328$		−	15.1318i		−	0.835514i
$329$	14.3693	−	5.55671i	0.792207	−	0.306351i
$330$		0			0
$331$	4.18951	−	7.25645i	0.230276	−	0.398850i	−0.727613	−	0.685988i	$-0.759370\pi$
$331$	4.18951	−	7.25645i	0.230276	−	0.398850i	0.957889	+	0.287137i	$0.0927036\pi$
$332$	7.51657	+	13.0191i	0.412525	+	0.714515i
$333$	9.90635	−	0.459248i	0.542865	−	0.0251666i
$334$	15.6573	+	9.03973i	0.856728	+	0.494632i
$335$		0			0
$336$	3.49779	−	26.4575i	0.190820	−	1.44338i
$337$	−11.7454			−0.639810			−0.319905	−	0.947450i	$-0.603651\pi$
$337$	−11.7454			−0.639810			−0.319905	+	0.947450i	$0.603651\pi$
$338$	27.9529	+	16.1386i	1.52044	+	0.877825i
$339$	5.76378	+	3.15203i	0.313046	+	0.171195i
$340$		0			0
$341$	−2.39327	+	4.14526i	−0.129603	+	0.224478i
$342$	−19.6945	+	38.0829i	−1.06496	+	2.05929i
$343$	−8.28527	+	16.5636i	−0.447363	+	0.894353i
$344$			57.7794i			3.11526i
$345$		0			0
$346$	−19.5173	+	11.2683i	−1.04926	+	0.605789i
$347$	−0.382835	+	0.221030i	−0.0205516	+	0.0118655i	−0.510241	−	0.860032i	$-0.670444\pi$
$347$	−0.382835	+	0.221030i	−0.0205516	+	0.0118655i	0.489689	+	0.871897i	$0.337110\pi$
$348$	0.647468	+	27.9478i	0.0347079	+	1.49816i
$349$			21.7405i			1.16374i	0.813282	+	0.581870i	$0.197679\pi$
$349$			21.7405i			1.16374i	−0.813282	+	0.581870i	$0.802321\pi$
$350$		0			0
$351$	0.130165	+	1.87016i	0.00694768	+	0.0998219i
$352$	−2.68077	+	4.64322i	−0.142885	+	0.247485i
$353$	−11.3917	−	19.7311i	−0.606321	−	1.05018i	−0.991841	−	0.127480i	$-0.959311\pi$
$353$	−11.3917	−	19.7311i	−0.606321	−	1.05018i	0.385520	−	0.922700i	$-0.374022\pi$
$354$	−26.1398	−	14.2950i	−1.38931	−	0.759771i
$355$		0			0
$356$	52.3709			2.77565
$357$	9.24103	+	7.09885i	0.489087	+	0.375711i
$358$	−27.4923			−1.45301
$359$	21.6706	+	12.5115i	1.14373	+	0.660333i	0.947351	−	0.320195i	$-0.103749\pi$
$359$	21.6706	+	12.5115i	1.14373	+	0.660333i	0.196378	+	0.980528i	$0.437082\pi$
$360$		0			0
$361$	6.73561	+	11.6664i	0.354506	+	0.614022i
$362$	−6.76283	+	11.7136i	−0.355447	+	0.615651i
$363$	−7.24579	−	11.9045i	−0.380305	−	0.624825i
$364$	−4.04610	−	0.630578i	−0.212073	−	0.0330513i
$365$		0			0
$366$	−6.96439	+	0.161344i	−0.364035	+	0.00843361i
$367$	−18.4872	+	10.6736i	−0.965023	+	0.557156i	−0.897715	−	0.440576i	$-0.854774\pi$
$367$	−18.4872	+	10.6736i	−0.965023	+	0.557156i	−0.0673073	+	0.997732i	$0.521441\pi$
$368$	−12.6490	+	7.30290i	−0.659374	+	0.380690i
$369$	4.26491	+	6.65496i	0.222022	+	0.346443i
$370$		0			0
$371$	3.80196	+	0.592529i	0.197388	+	0.0307626i
$372$	17.6767	−	10.7591i	0.916495	−	0.557832i
$373$	−7.06740	+	12.2411i	−0.365936	+	0.633820i	−0.988926	−	0.148410i	$-0.952584\pi$
$373$	−7.06740	+	12.2411i	−0.365936	+	0.633820i	0.622990	+	0.782230i	$0.285918\pi$
$374$	−5.48045	−	9.49242i	−0.283387	−	0.490841i
$375$		0			0
$376$	28.9620	+	16.7212i	1.49360	+	0.862332i
$377$	1.35737			0.0699081
$378$	14.6386	+	31.2172i	0.752929	+	1.60564i
$379$	9.53880			0.489975			0.244988	−	0.969526i	$-0.421216\pi$
$379$	9.53880			0.489975			0.244988	+	0.969526i	$0.421216\pi$
$380$		0			0
$381$	4.97503	−	9.09731i	0.254879	−	0.466069i
$382$	−26.7325	−	46.3021i	−1.36776	−	2.36902i
$383$	−7.88522	+	13.6576i	−0.402916	+	0.697870i	−0.994076	−	0.108683i	$-0.965337\pi$
$383$	−7.88522	+	13.6576i	−0.402916	+	0.697870i	0.591161	+	0.806554i	$0.298670\pi$
$384$	−23.4195	+	14.2545i	−1.19512	+	0.727422i
$385$		0			0
$386$			34.9514i			1.77898i
$387$	−16.2852	−	25.4113i	−0.827822	−	1.29173i
$388$	−30.4181	+	17.5619i	−1.54424	+	0.891570i
$389$	−29.5749	+	17.0751i	−1.49951	+	0.865740i	−1.00000		0.000570006i	$-0.999819\pi$
$389$	−29.5749	+	17.0751i	−1.49951	+	0.865740i	−0.499506	+	0.866310i	$0.666485\pi$
$390$		0			0
$391$		−	6.37747i		−	0.322522i
$392$	−39.2815	+	8.55298i	−1.98402	+	0.431991i
$393$	13.1300	+	21.5721i	0.662322	+	1.08817i
$394$	2.52305	−	4.37005i	0.127109	−	0.220160i
$395$		0			0
$396$	−1.02433	−	22.0956i	−0.0514744	−	1.11034i
$397$	−3.70870	−	2.14122i	−0.186134	−	0.107465i	0.404037	−	0.914743i	$-0.367607\pi$
$397$	−3.70870	−	2.14122i	−0.186134	−	0.107465i	−0.590172	+	0.807278i	$0.700940\pi$
$398$	−19.9881			−1.00191
$399$	25.8879	+	3.42248i	1.29601	+	0.171338i
$400$		0			0
$401$	−10.8316	−	6.25361i	−0.540903	−	0.312290i	0.204542	−	0.978858i	$-0.434429\pi$
$401$	−10.8316	−	6.25361i	−0.540903	−	0.312290i	−0.745445	+	0.666568i	$0.767763\pi$
$402$	9.49319	+	5.19152i	0.473477	+	0.258930i
$403$	−0.502389	−	0.870163i	−0.0250258	−	0.0433459i
$404$	2.67464	−	4.63261i	0.133068	−	0.230481i
$405$		0			0
$406$	23.2842	−	9.00415i	1.15558	−	0.446868i
$407$			5.68142i			0.281617i
$408$	0.585852	+	25.2882i	0.0290040	+	1.25195i
$409$	−5.59219	+	3.22865i	−0.276516	+	0.159647i	−0.631845	−	0.775095i	$-0.717702\pi$
$409$	−5.59219	+	3.22865i	−0.276516	+	0.159647i	0.355329	+	0.934741i	$0.384369\pi$
$410$		0			0
$411$	−0.630352	−	27.2090i	−0.0310930	−	1.34212i
$412$		−	17.7863i		−	0.876267i
$413$	−2.79430	+	17.9296i	−0.137499	+	0.882258i
$414$	8.66802	−	16.7611i	0.426010	−	0.823766i
$415$		0			0
$416$	−0.562740	−	0.974694i	−0.0275906	−	0.0477883i
$417$	22.3882	+	12.2434i	1.09636	+	0.599562i
$418$	−21.2717	−	12.2812i	−1.04043	−	0.600693i
$419$	10.0144			0.489233			0.244617	−	0.969620i	$-0.421338\pi$
$419$	10.0144			0.489233			0.244617	+	0.969620i	$0.421338\pi$
$420$		0			0
$421$	17.7858			0.866825			0.433413	−	0.901196i	$-0.357309\pi$
$421$	17.7858			0.866825			0.433413	+	0.901196i	$0.357309\pi$
$422$	−10.7597	−	6.21214i	−0.523776	−	0.302402i
$423$	−17.4504	+	0.808982i	−0.848467	+	0.0393341i
$424$	4.17626	+	7.23350i	0.202817	+	0.351290i
$425$		0			0
$426$	29.7649	+	48.9025i	1.44212	+	2.36934i
$427$	1.53032	+	3.95733i	0.0740576	+	0.191509i
$428$			4.75121i			0.229659i
$429$	−1.07371	+	0.0248748i	−0.0518394	+	0.00120097i
$430$		0			0
$431$	−2.54530	+	1.46953i	−0.122603	+	0.0707847i	−0.560047	−	0.828461i	$-0.689217\pi$
$431$	−2.54530	+	1.46953i	−0.122603	+	0.0707847i	0.437444	+	0.899245i	$0.355884\pi$
$432$	−13.2744	+	27.1941i	−0.638664	+	1.30838i
$433$		−	31.6675i		−	1.52184i	−0.648843	−	0.760922i	$-0.724747\pi$
$433$		−	31.6675i		−	1.52184i	0.648843	−	0.760922i	$-0.275253\pi$
$434$	−14.3902	−	11.5941i	−0.690751	−	0.556534i
$435$		0			0
$436$	19.5486	−	33.8592i	0.936208	−	1.62156i
$437$	−7.14567	−	12.3767i	−0.341824	−	0.592056i
$438$	24.2685	−	44.3773i	1.15960	−	2.12043i
$439$	18.6152	+	10.7475i	0.888457	+	0.512951i	0.873437	−	0.486936i	$-0.161886\pi$
$439$	18.6152	+	10.7475i	0.888457	+	0.512951i	0.0150195	+	0.999887i	$0.495219\pi$
$440$		0			0
$441$	14.8653	−	14.8331i	0.707873	−	0.706340i
$442$	2.30088			0.109442
$443$	22.7499	+	13.1347i	1.08088	+	0.624048i	0.931134	−	0.364676i	$-0.118820\pi$
$443$	22.7499	+	13.1347i	1.08088	+	0.624048i	0.149748	+	0.988724i	$0.452154\pi$
$444$	11.7852	−	21.5504i	0.559303	−	1.02274i
$445$		0			0
$446$	19.6291	−	33.9987i	0.929467	−	1.60988i
$447$	18.7940	−	11.4391i	0.888926	−	0.541052i
$448$	7.87786	+	6.34714i	0.372194	+	0.299874i
$449$			36.0069i			1.69927i	0.527369	+	0.849636i	$0.323179\pi$
$449$			36.0069i			1.69927i	−0.527369	+	0.849636i	$0.676821\pi$
$450$		0			0
$451$	−3.92167	+	2.26418i	−0.184664	+	0.106616i
$452$	14.0911	−	8.13550i	0.662789	−	0.382662i
$453$	28.9064	−	0.669675i	1.35814	−	0.0314641i
$454$		−	31.6306i		−	1.48450i
$455$		0			0
$456$	29.4712	+	48.4200i	1.38012	+	2.26747i
$457$	−9.12327	+	15.8020i	−0.426768	+	0.739185i	−0.996584	−	0.0825881i	$-0.973681\pi$
$457$	−9.12327	+	15.8020i	−0.426768	+	0.739185i	0.569815	+	0.821773i	$0.307015\pi$
$458$	7.51431	+	13.0152i	0.351121	+	0.608159i
$459$	−7.38515	−	10.9566i	−0.344709	−	0.511410i
$460$		0			0
$461$	−22.8072			−1.06224			−0.531119	−	0.847298i	$-0.678228\pi$
$461$	−22.8072			−1.06224			−0.531119	+	0.847298i	$0.678228\pi$
$462$	−18.2534	+	7.54922i	−0.849226	+	0.351221i
$463$	23.3718			1.08618			0.543090	−	0.839674i	$-0.317254\pi$
$463$	23.3718			1.08618			0.543090	+	0.839674i	$0.317254\pi$
$464$	18.9751	+	10.9553i	0.880897	+	0.508586i
$465$		0			0
$466$	−27.3411	−	47.3561i	−1.26655	−	2.19373i
$467$	5.44472	−	9.43053i	0.251951	−	0.436393i	−0.712112	−	0.702066i	$-0.752261\pi$
$467$	5.44472	−	9.43053i	0.251951	−	0.436393i	0.964063	+	0.265674i	$0.0855943\pi$
$468$	4.12435	+	2.13291i	0.190648	+	0.0985936i
$469$	1.01481	−	6.51150i	0.0468595	−	0.300673i
$470$		0			0
$471$	−0.0578924	−	2.49891i	−0.00266754	−	0.115144i
$472$	−34.1124	+	19.6948i	−1.57015	+	0.906527i
$473$	14.9745	−	8.64555i	0.688530	−	0.397523i
$474$	−1.39544	−	60.2336i	−0.0640945	−	2.76662i
$475$		0			0
$476$	26.9193	−	10.4098i	1.23384	−	0.477135i
$477$	−3.87549	−	2.00421i	−0.177446	−	0.0917663i
$478$	31.2329	−	54.0970i	1.42856	−	2.47434i
$479$	5.13835	+	8.89989i	0.234777	+	0.406646i	0.959208	−	0.282701i	$-0.0912305\pi$
$479$	5.13835	+	8.89989i	0.234777	+	0.406646i	−0.724431	+	0.689348i	$0.757897\pi$
$480$		0			0
$481$	−1.03285	−	0.596314i	−0.0470938	−	0.0271896i
$482$	42.7021			1.94503
$483$	−11.3939	−	1.50631i	−0.518438	−	0.0685397i
$484$	−34.5173			−1.56897
$485$		0			0
$486$	−4.51771	−	38.8336i	−0.204928	−	1.76153i
$487$	6.92377	+	11.9923i	0.313746	+	0.543424i	0.979170	−	0.203041i	$-0.0650826\pi$
$487$	6.92377	+	11.9923i	0.313746	+	0.543424i	−0.665424	+	0.746466i	$0.731749\pi$
$488$	−4.60505	+	7.97618i	−0.208461	+	0.361065i
$489$	−15.1847	−	24.9478i	−0.686676	−	1.12818i
$490$		0			0
$491$			13.5981i			0.613672i	0.951762	+	0.306836i	$0.0992704\pi$
$491$			13.5981i			0.613672i	−0.951762	+	0.306836i	$0.900730\pi$
$492$	19.5721	−	0.453428i	0.882379	−	0.0204421i
$493$	−8.28527	+	4.78350i	−0.373150	+	0.215438i
$494$	4.46529	−	2.57804i	0.200903	−	0.115991i
$495$		0			0
$496$		−	16.2190i		−	0.728256i
$497$	21.8762	−	27.1520i	0.981281	−	1.21793i
$498$	−13.0031	+	7.91447i	−0.582684	+	0.354656i
$499$	18.1054	−	31.3595i	0.810511	−	1.40385i	−0.101996	−	0.994785i	$-0.532523\pi$
$499$	18.1054	−	31.3595i	0.810511	−	1.40385i	0.912507	−	0.409061i	$-0.134144\pi$
$500$		0			0
$501$	−5.99087	+	10.9549i	−0.267653	+	0.489428i
$502$	59.4958	+	34.3499i	2.65543	+	1.53311i
$503$	0.513189			0.0228819			0.0114410	−	0.999935i	$-0.496358\pi$
$503$	0.513189			0.0228819			0.0114410	+	0.999935i	$0.496358\pi$
$504$	45.3177	+	4.92622i	2.01861	+	0.219431i
$505$		0			0
$506$	9.36215	+	5.40524i	0.416198	+	0.240292i
$507$	−10.6955	+	19.5577i	−0.475004	+	0.868589i
$508$	−12.8407	−	22.2408i	−0.569715	−	0.986776i
$509$	9.40202	−	16.2848i	0.416737	−	0.721810i	−0.578872	−	0.815419i	$-0.696507\pi$
$509$	9.40202	−	16.2848i	0.416737	−	0.721810i	0.995609	+	0.0936084i	$0.0298402\pi$
$510$		0			0
$511$	−30.4390	−	4.74387i	−1.34654	−	0.209856i
$512$			48.7256i			2.15339i
$513$	−26.6086	−	12.9886i	−1.17480	−	0.573460i
$514$	−66.0024	+	38.1065i	−2.91124	+	1.68081i
$515$		0			0
$516$	−74.7343	+	1.73137i	−3.29000	+	0.0762195i
$517$		−	10.0080i		−	0.440152i
$518$	−21.6730	−	3.37771i	−0.952258	−	0.148408i
$519$	−8.09219	−	13.2951i	−0.355208	−	0.583591i
$520$		0			0
$521$	15.1847	+	26.3007i	0.665254	+	1.15225i	0.979216	+	0.202818i	$0.0650100\pi$
$521$	15.1847	+	26.3007i	0.665254	+	1.15225i	−0.313963	+	0.949435i	$0.601657\pi$
$522$	−28.2768	+	1.31088i	−1.23764	+	0.0573758i
$523$	33.7999	+	19.5144i	1.47797	+	0.853305i	0.999690	−	0.0249028i	$-0.00792764\pi$
$523$	33.7999	+	19.5144i	1.47797	+	0.853305i	0.478278	+	0.878208i	$0.341261\pi$
$524$	62.5485			2.73244
$525$		0			0
$526$	−48.4958			−2.11452
$527$	6.13308	+	3.54093i	0.267161	+	0.154246i
$528$	−15.2106	−	8.31818i	−0.661955	−	0.362002i
$529$	−8.35503	−	14.4713i	−0.363262	−	0.629188i
$530$		0			0
$531$	9.45162	−	18.2764i	0.410165	−	0.793127i
$532$	40.5781	−	50.3641i	1.75928	−	2.18356i
$533$		−	0.950580i		−	0.0411742i
$534$	1.22822	+	53.0159i	0.0531504	+	2.29422i
$535$		0			0
$536$	12.3886	−	7.15257i	0.535106	−	0.308944i
$537$	−0.439747	−	18.9816i	−0.0189765	−	0.819115i
$538$			55.1794i			2.37895i
$539$	8.09436	+	8.90071i	0.348649	+	0.383381i
$540$		0			0
$541$	5.25615	−	9.10392i	0.225980	−	0.391408i	−0.730633	−	0.682770i	$-0.760775\pi$
$541$	5.25615	−	9.10392i	0.225980	−	0.391408i	0.956613	+	0.291362i	$0.0941084\pi$
$542$	−18.8822	−	32.7049i	−0.811060	−	1.40480i
$543$	−8.19559	−	4.48191i	−0.351706	−	0.192337i
$544$	6.86984	+	3.96630i	0.294542	+	0.170054i
$545$		0			0
$546$	0.543453	−	4.11071i	0.0232577	−	0.175922i
$547$	25.2465			1.07946			0.539731	−	0.841837i	$-0.318526\pi$
$547$	25.2465			1.07946			0.539731	+	0.841837i	$0.318526\pi$
$548$	−58.3782	−	33.7046i	−2.49379	−	1.43979i
$549$	−0.222795	−	4.80586i	−0.00950864	−	0.205109i
$550$		0			0
$551$	−10.7194	+	18.5666i	−0.456662	+	0.790962i
$552$	−12.9710	−	21.3107i	−0.552081	−	0.907045i
$553$	−34.2261	+	13.2355i	−1.45544	+	0.562829i
$554$		−	4.20334i		−	0.178583i
$555$		0			0
$556$	54.7339	−	31.6007i	2.32124	−	1.34017i
$557$	17.6227	−	10.1745i	0.746697	−	0.431106i	−0.0778021	−	0.996969i	$-0.524790\pi$
$557$	17.6227	−	10.1745i	0.746697	−	0.431106i	0.824499	+	0.565863i	$0.191457\pi$
$558$	11.3061	+	17.6421i	0.478627	+	0.746849i
$559$			3.62970i			0.153520i
$560$		0			0
$561$	6.46621	−	3.93571i	0.273003	−	0.166166i
$562$	−2.63445	+	4.56300i	−0.111128	+	0.192479i
$563$	−17.8326	−	30.8870i	−0.751555	−	1.30173i	−0.947069	−	0.321030i	$-0.895971\pi$
$563$	−17.8326	−	30.8870i	−0.751555	−	1.30173i	0.195514	−	0.980701i	$-0.437362\pi$
$564$	−20.7601	+	37.9618i	−0.874158	+	1.59848i
$565$		0			0
$566$	12.5499			0.527513
$567$	−21.3192	+	10.6063i	−0.895321	+	0.445422i
$568$	75.6885			3.17582
$569$	−21.8018	−	12.5873i	−0.913977	−	0.527685i	−0.0322687	−	0.999479i	$-0.510273\pi$
$569$	−21.8018	−	12.5873i	−0.913977	−	0.527685i	−0.881709	+	0.471794i	$0.843607\pi$
$570$		0			0
$571$	−2.49020	−	4.31316i	−0.104212	−	0.180500i	0.809204	−	0.587528i	$-0.199899\pi$
$571$	−2.49020	−	4.31316i	−0.104212	−	0.180500i	−0.913416	+	0.407028i	$0.866565\pi$
$572$	−1.33005	+	2.30371i	−0.0556120	+	0.0963228i
$573$	31.5409	−	19.1976i	1.31764	−	0.801992i
$574$	−6.30570	−	16.3062i	−0.263195	−	0.680607i
$575$		0			0
$576$	−6.18951	−	9.65809i	−0.257896	−	0.402421i
$577$	18.9939	−	10.9662i	0.790728	−	0.456527i	−0.0494908	−	0.998775i	$-0.515760\pi$
$577$	18.9939	−	10.9662i	0.790728	−	0.456527i	0.840219	+	0.542248i	$0.182427\pi$
$578$	22.8791	−	13.2093i	0.951645	−	0.549432i
$579$	−24.1316	+	0.559057i	−1.00287	+	0.0232336i
$580$		0			0
$581$	7.21968	+	5.81685i	0.299523	+	0.241324i
$582$	−18.4915	−	30.3808i	−0.766499	−	1.25933i
$583$	1.24979	−	2.16470i	0.0517610	−	0.0896528i
$584$	−33.4357	−	57.9124i	−1.38358	−	2.39643i
$585$		0			0
$586$	37.5173	+	21.6606i	1.54983	+	0.894792i
$587$	−31.8719			−1.31549			−0.657746	−	0.753240i	$-0.728490\pi$
$587$	−31.8719			−1.31549			−0.657746	+	0.753240i	$0.728490\pi$
$588$	−12.2399	−	50.5521i	−0.504764	−	2.08474i
$589$	15.8698			0.653905
$590$		0			0
$591$	3.05758	+	1.67209i	0.125772	+	0.0687807i
$592$	−9.62566	−	16.6721i	−0.395612	−	0.685220i
$593$	16.4536	−	28.4985i	0.675669	−	1.17029i	−0.300603	−	0.953749i	$-0.597188\pi$
$593$	16.4536	−	28.4985i	0.675669	−	1.17029i	0.976273	−	0.216545i	$-0.0694787\pi$
$594$	22.3436	−	1.55514i	0.916771	−	0.0638080i
$595$		0			0
$596$		−	54.4935i		−	2.23214i
$597$	−0.319716	−	13.8004i	−0.0130851	−	0.564814i
$598$	−1.96528	+	1.13465i	−0.0803662	+	0.0463995i
$599$	−18.8935	+	10.9082i	−0.771968	+	0.445696i	−0.833576	−	0.552404i	$-0.813710\pi$
$599$	−18.8935	+	10.9082i	−0.771968	+	0.445696i	0.0616082	+	0.998100i	$0.480377\pi$
$600$		0			0
$601$			23.9262i			0.975969i	0.872852	+	0.487985i	$0.162268\pi$
$601$			23.9262i			0.975969i	−0.872852	+	0.487985i	$0.837732\pi$
$602$	24.0777	+	62.2636i	0.981335	+	2.53768i
$603$	−3.43255	+	6.63744i	−0.139784	+	0.270297i
$604$	35.8073	−	62.0200i	1.45698	−	2.52356i
$605$		0			0
$606$	4.75239	+	2.59893i	0.193053	+	0.105574i
$607$	38.3634	+	22.1491i	1.55712	+	0.899005i	0.997530	+	0.0702358i	$0.0223752\pi$
$607$	38.3634	+	22.1491i	1.55712	+	0.899005i	0.559591	+	0.828769i	$0.310958\pi$
$608$	17.7763			0.720922
$609$	6.58919	+	15.9321i	0.267007	+	0.645603i
$610$		0			0
$611$	1.81940	+	1.05043i	0.0736049	+	0.0424958i
$612$	−32.6913	+	1.51553i	−1.32147	+	0.0612618i
$613$	−4.02115	−	6.96484i	−0.162413	−	0.281307i	0.773321	−	0.634015i	$-0.218594\pi$
$613$	−4.02115	−	6.96484i	−0.162413	−	0.281307i	−0.935733	+	0.352708i	$0.885261\pi$
$614$	−12.8313	+	22.2245i	−0.517829	+	0.896907i
$615$		0			0
$616$	−4.02149	+	25.8038i	−0.162030	+	1.03967i
$617$		−	13.1311i		−	0.528637i	−0.964435	−	0.264318i	$-0.914853\pi$
$617$		−	13.1311i		−	0.528637i	0.964435	−	0.264318i	$-0.0851470\pi$
$618$	18.0053	−	0.417130i	0.724280	−	0.0167794i
$619$	21.7909	−	12.5810i	0.875850	−	0.505672i	0.00656210	−	0.999978i	$-0.497911\pi$
$619$	21.7909	−	12.5810i	0.875850	−	0.505672i	0.869288	+	0.494306i	$0.164578\pi$
$620$		0			0
$621$	11.7111	+	5.71658i	0.469949	+	0.229398i
$622$			26.2783i			1.05367i
$623$	30.1249	−	11.6495i	1.20693	−	0.466727i
$624$	3.10867	−	1.89212i	0.124447	−	0.0757455i
$625$		0			0
$626$	−0.321242	−	0.556407i	−0.0128394	−	0.0222385i
$627$	8.13908	−	14.8831i	0.325044	−	0.594373i
$628$	−5.36153	−	3.09548i	−0.213948	−	0.123523i
$629$	8.40588			0.335164
$630$		0			0
$631$	−9.42011			−0.375009			−0.187504	−	0.982264i	$-0.560040\pi$
$631$	−9.42011			−0.375009			−0.187504	+	0.982264i	$0.560040\pi$
$632$	−68.9843	−	39.8281i	−2.74405	−	1.58428i
$633$	4.11695	−	7.52823i	0.163634	−	0.299220i
$634$	38.7965	+	67.1975i	1.54081	+	2.66875i
$635$		0			0
$636$	−9.23097	+	5.61851i	−0.366032	+	0.222788i
$637$	−2.46767	+	0.537299i	−0.0977725	+	0.0212885i
$638$		−	16.2171i		−	0.642041i
$639$	−33.2878	+	21.3329i	−1.31684	+	0.843915i
$640$		0			0
$641$	−4.25254	+	2.45520i	−0.167965	+	0.0969747i	−0.581626	−	0.813456i	$-0.697583\pi$
$641$	−4.25254	+	2.45520i	−0.167965	+	0.0969747i	0.413661	+	0.910431i	$0.364250\pi$
$642$	−4.80973	+	0.111427i	−0.189825	+	0.00439768i
$643$			8.98926i			0.354502i	0.984166	+	0.177251i	$0.0567204\pi$
$643$			8.98926i			0.354502i	−0.984166	+	0.177251i	$0.943280\pi$
$644$	−17.8593	+	22.1664i	−0.703756	+	0.873478i
$645$		0			0
$646$	−18.1705	+	31.4723i	−0.714910	+	1.23826i
$647$	−0.119473	−	0.206934i	−0.00469699	−	0.00813542i	0.863667	−	0.504062i	$-0.168162\pi$
$647$	−0.119473	−	0.206934i	−0.00469699	−	0.00813542i	−0.868364	+	0.495927i	$0.834828\pi$
$648$	−46.9623	−	21.5918i	−1.84485	−	0.848205i
$649$	10.2085	+	5.89388i	0.400719	+	0.231355i
$650$		0			0
$651$	7.77475	−	10.1209i	0.304717	−	0.396669i
$652$	−72.3365			−2.83292
$653$	1.69578	+	0.979061i	0.0663611	+	0.0383136i	0.532813	−	0.846233i	$-0.321135\pi$
$653$	1.69578	+	0.979061i	0.0663611	+	0.0383136i	−0.466452	+	0.884546i	$0.654468\pi$
$654$	34.7346	+	18.9953i	1.35823	+	0.742774i
$655$		0			0
$656$	7.67209	−	13.2885i	0.299545	−	0.518827i
$657$	31.0277	+	16.0459i	1.21050	+	0.626012i
$658$	38.1778	+	5.94996i	1.48833	+	0.231953i
$659$		−	31.6741i		−	1.23385i	−0.787023	−	0.616924i	$-0.788379\pi$
$659$		−	31.6741i		−	1.23385i	0.787023	−	0.616924i	$-0.211621\pi$
$660$		0			0
$661$	−24.8549	+	14.3500i	−0.966744	+	0.558150i	−0.898242	−	0.439501i	$-0.855155\pi$
$661$	−24.8549	+	14.3500i	−0.966744	+	0.558150i	−0.0685020	+	0.997651i	$0.521822\pi$
$662$	18.1990	−	10.5072i	0.707324	−	0.408374i
$663$	0.0368033	+	1.58860i	0.00142932	+	0.0616963i
$664$			20.1255i			0.781020i
$665$		0			0
$666$	22.0922	+	11.4250i	0.856055	+	0.442709i
$667$	4.71786	−	8.17157i	0.182676	−	0.316404i
$668$	15.4626	+	26.7821i	0.598268	+	1.03623i
$669$	23.7877	+	13.0088i	0.919687	+	0.502948i
$670$		0			0
$671$	2.75622			0.106403
$672$	8.70872	−	11.3367i	0.335946	−	0.437322i
$673$	−33.9688			−1.30940			−0.654700	−	0.755889i	$-0.727205\pi$
$673$	−33.9688			−1.30940			−0.654700	+	0.755889i	$0.727205\pi$
$674$	−25.5106	−	14.7285i	−0.982631	−	0.567322i
$675$		0			0
$676$	27.6054	+	47.8140i	1.06175	+	1.83900i
$677$	3.59472	−	6.22623i	0.138156	−	0.239294i	−0.788643	−	0.614852i	$-0.789216\pi$
$677$	3.59472	−	6.22623i	0.138156	−	0.239294i	0.926799	+	0.375558i	$0.122549\pi$
$678$	8.56616	+	14.0738i	0.328981	+	0.540502i
$679$	−13.5906	+	16.8682i	−0.521561	+	0.647343i
$680$		0			0
$681$	21.8388	−	0.505940i	0.836863	−	0.0193876i
$682$	−10.3962	+	6.00226i	−0.398092	+	0.229838i
$683$	−6.96307	+	4.02013i	−0.266435	+	0.153826i	−0.627266	−	0.778805i	$-0.715826\pi$
$683$	−6.96307	+	4.02013i	−0.266435	+	0.153826i	0.360832	+	0.932631i	$0.382493\pi$
$684$	−61.7454	+	39.5703i	−2.36089	+	1.51301i
$685$		0			0
$686$	−38.7660	+	25.5861i	−1.48009	+	0.976883i
$687$	−8.86589	+	5.39630i	−0.338255	+	0.205882i
$688$	−29.2952	+	50.7407i	−1.11687	+	1.93447i
$689$	0.262353	+	0.454409i	0.00999485	+	0.0173116i
$690$		0			0
$691$	38.3278	+	22.1286i	1.45806	+	0.841810i	0.998916	−	0.0465523i	$-0.0148234\pi$
$691$	38.3278	+	22.1286i	1.45806	+	0.841810i	0.459142	+	0.888363i	$0.348157\pi$
$692$	−38.5494			−1.46543
$693$	−5.50419	−	12.4820i	−0.209087	−	0.474151i
$694$	−1.10867			−0.0420847
$695$		0			0
$696$	−17.9568	+	32.8356i	−0.680649	+	1.24463i
$697$	3.34994	+	5.80226i	0.126888	+	0.219776i
$698$	−27.2623	+	47.2197i	−1.03189	+	1.78729i
$699$	32.2588	−	19.6346i	1.22014	−	0.742649i
$700$		0			0
$701$		−	0.779307i		−	0.0294340i	−0.999892	−	0.0147170i	$-0.995315\pi$
$701$		−	0.779307i		−	0.0294340i	0.999892	−	0.0147170i	$-0.00468474\pi$
$702$	−2.06245	+	4.22516i	−0.0778420	+	0.159468i
$703$	16.3132	−	9.41841i	0.615263	−	0.355222i
$704$	5.69137	−	3.28592i	0.214502	−	0.123843i
$705$		0			0
$706$		−	57.1404i		−	2.15051i
$707$	0.508023	−	3.25973i	0.0191062	−	0.122595i
$708$	−26.4963	−	43.5323i	−0.995792	−	1.63604i
$709$	−4.63267	+	8.02402i	−0.173984	+	0.301348i	−0.939809	−	0.341700i	$-0.888997\pi$
$709$	−4.63267	+	8.02402i	−0.173984	+	0.301348i	0.765825	+	0.643048i	$0.222331\pi$
$710$		0			0
$711$	41.5649	−	1.92691i	1.55880	−	0.0722646i
$712$	60.7181	+	35.0556i	2.27551	+	1.31376i
$713$	−6.98468			−0.261578
$714$	11.1694	+	27.0066i	0.418003	+	1.01070i
$715$		0			0
$716$	−40.7259	−	23.5131i	−1.52200	−	0.878725i
$717$	37.8499	+	20.6989i	1.41353	+	0.773015i
$718$	31.3786	+	54.3493i	1.17104	+	2.02830i
$719$	−9.09980	+	15.7613i	−0.339365	+	0.587798i	−0.984313	−	0.176428i	$-0.943546\pi$
$719$	−9.09980	+	15.7613i	−0.339365	+	0.587798i	0.644948	+	0.764226i	$0.276879\pi$
$720$		0			0
$721$	−3.95641	−	10.2310i	−0.147344	−	0.381024i
$722$			33.7855i			1.25737i
$723$	0.683032	+	29.4829i	0.0254022	+	1.09648i
$724$	−20.0363	+	11.5680i	−0.744643	+	0.429920i
$725$		0			0
$726$	−0.809513	−	34.9424i	−0.0300438	−	1.29683i
$727$		−	31.6357i		−	1.17330i	−0.809839	−	0.586652i	$-0.800446\pi$
$727$		−	31.6357i		−	1.17330i	0.809839	−	0.586652i	$-0.199554\pi$
$728$	−4.26889	−	3.43942i	−0.158216	−	0.127473i
$729$	26.7397	−	3.74032i	0.990358	−	0.138531i
$730$		0			0
$731$	−12.7914	−	22.1554i	−0.473108	−	0.819447i
$732$	−10.4547	−	5.71736i	−0.386418	−	0.211320i
$733$	−14.7298	−	8.50426i	−0.544058	−	0.314112i	0.202664	−	0.979248i	$-0.435040\pi$
$733$	−14.7298	−	8.50426i	−0.544058	−	0.314112i	−0.746722	+	0.665136i	$0.768373\pi$
$734$	−53.5381			−1.97613
$735$		0			0
$736$	−7.82374			−0.288387
$737$	−3.70742	−	2.14048i	−0.136565	−	0.0788457i
$738$	0.918025	+	19.8025i	0.0337930	+	0.728941i
$739$	−9.49020	−	16.4375i	−0.349103	−	0.604664i	0.636988	−	0.770874i	$-0.280180\pi$
$739$	−9.49020	−	16.4375i	−0.349103	−	0.604664i	−0.986090	+	0.166210i	$0.946847\pi$
$740$		0			0
$741$	1.85138	+	3.04174i	0.0680123	+	0.111741i
$742$	7.51471	+	6.05456i	0.275874	+	0.222270i
$743$		−	3.80063i		−	0.139432i	−0.997567	−	0.0697159i	$-0.977791\pi$
$743$		−	3.80063i		−	0.139432i	0.997567	−	0.0697159i	$-0.0222093\pi$
$744$	27.6959	−	0.641633i	1.01538	−	0.0235234i
$745$		0			0
$746$	−30.7004	+	17.7249i	−1.12402	+	0.648953i
$747$	−5.67239	−	8.85118i	−0.207542	−	0.323848i
$748$		−	18.7489i		−	0.685526i
$749$	1.05687	+	2.73300i	0.0386171	+	0.0998616i
$750$		0			0
$751$	6.32279	−	10.9514i	0.230722	−	0.399622i	−0.727299	−	0.686321i	$-0.759225\pi$
$751$	6.32279	−	10.9514i	0.230722	−	0.399622i	0.958021	+	0.286699i	$0.0925579\pi$
$752$	16.9559	+	29.3685i	0.618319	+	1.07096i
$753$	−22.7646	+	41.6272i	−0.829589	+	1.51698i
$754$	2.94817	+	1.70213i	0.107366	+	0.0619878i
$755$		0			0
$756$	−5.01383	+	58.7635i	−0.182351	+	2.13721i
$757$	−6.50118			−0.236289			−0.118145	−	0.992996i	$-0.537695\pi$
$757$	−6.50118			−0.236289			−0.118145	+	0.992996i	$0.537695\pi$
$758$	20.7180	+	11.9615i	0.752512	+	0.434463i
$759$	−3.58220	+	6.55038i	−0.130026	+	0.237764i
$760$		0			0
$761$	−21.8912	+	37.9167i	−0.793556	+	1.37448i	0.130195	+	0.991488i	$0.458440\pi$
$761$	−21.8912	+	37.9167i	−0.793556	+	1.37448i	−0.923752	+	0.382992i	$0.874894\pi$
$762$	22.2135	−	13.5205i	0.804712	−	0.489795i
$763$	3.71308	−	23.8249i	0.134423	−	0.862521i
$764$		−	91.4531i		−	3.30866i
$765$		0			0
$766$	−34.2529	+	19.7759i	−1.23761	+	0.714533i
$767$	−2.14294	+	1.23723i	−0.0773771	+	0.0446737i
$768$	−55.4993	+	1.28575i	−2.00266	+	0.0463957i
$769$			33.3141i			1.20134i	0.799498	+	0.600668i	$0.205099\pi$
$769$			33.3141i			1.20134i	−0.799498	+	0.600668i	$0.794901\pi$
$770$		0			0
$771$	−27.3657	−	44.9606i	−0.985550	−	1.61922i
$772$	−29.8925	+	51.7754i	−1.07586	+	1.86344i
$773$	21.1662	+	36.6610i	0.761296	+	1.31860i	0.942183	+	0.335099i	$0.108770\pi$
$773$	21.1662	+	36.6610i	0.761296	+	1.31860i	−0.180887	+	0.983504i	$0.557897\pi$
$774$	−3.50539	−	75.6141i	−0.125999	−	2.71789i
$775$		0			0
$776$	−47.0217			−1.68798
$777$	1.98541	−	15.0178i	0.0712262	−	0.538760i
$778$	−85.6477			−3.07062
$779$	13.0024	+	7.50691i	0.465858	+	0.268963i
$780$		0			0
$781$	−11.3253	−	19.6160i	−0.405251	−	0.701915i
$782$	7.99727	−	13.8517i	0.285982	−	0.495335i
$783$	−1.35737	−	19.5022i	−0.0485084	−	0.696952i
$784$	−38.8328	−	12.4054i	−1.38689	−	0.443049i
$785$		0			0
$786$	1.46691	+	63.3188i	0.0523229	+	2.25851i
$787$	−22.4388	+	12.9551i	−0.799859	+	0.461799i	−0.843422	−	0.537252i	$-0.819462\pi$
$787$	−22.4388	+	12.9551i	−0.799859	+	0.461799i	0.0435632	+	0.999051i	$0.486129\pi$
$788$	7.47506	−	4.31573i	0.266288	−	0.153741i
$789$	−0.775704	−	33.4830i	−0.0276158	−	1.19203i
$790$		0			0
$791$	6.29582	−	7.81416i	0.223854	−	0.277839i
$792$	13.6025	−	26.3029i	0.483345	−	0.934633i
$793$	−0.289289	+	0.501064i	−0.0102730	+	0.0177933i
$794$	−5.37013	−	9.30134i	−0.190579	−	0.330092i
$795$		0			0
$796$	−29.6095	−	17.0951i	−1.04948	−	0.605918i
$797$	−27.5780			−0.976865			−0.488432	−	0.872602i	$-0.662431\pi$
$797$	−27.5780			−0.976865			−0.488432	+	0.872602i	$0.662431\pi$
$798$	51.9360	+	39.8966i	1.83851	+	1.41233i
$799$	−14.8073			−0.523843
$800$		0			0
$801$	−36.5842	+	1.69601i	−1.29264	+	0.0599255i
$802$	−15.6839	−	27.1653i	−0.553818	−	0.959240i
$803$	−10.0060	+	17.3309i	−0.353104	+	0.611594i
$804$	9.62267	+	15.8096i	0.339365	+	0.557563i
$805$		0			0
$806$		−	2.51996i		−	0.0887617i
$807$	−38.0976	+	0.882609i	−1.34110	+	0.0310693i
$808$	6.20187	−	3.58065i	0.218181	−	0.125967i
$809$	27.0106	−	15.5946i	0.949641	−	0.548275i	0.0566716	−	0.998393i	$-0.481951\pi$
$809$	27.0106	−	15.5946i	0.949641	−	0.548275i	0.892969	+	0.450117i	$0.148618\pi$
$810$		0			0
$811$		−	17.5174i		−	0.615120i	−0.951529	−	0.307560i	$-0.900488\pi$
$811$		−	17.5174i		−	0.615120i	0.951529	−	0.307560i	$-0.0995124\pi$
$812$	42.1931	+	6.57572i	1.48069	+	0.230763i
$813$	22.2785	−	13.5600i	0.781341	−	0.475569i
$814$	−7.12443	+	12.3399i	−0.249711	+	0.432512i
$815$		0			0
$816$	−12.3071	+	22.5046i	−0.430834	+	0.787820i
$817$	−49.6483	−	28.6645i	−1.73697	−	1.00284i
$818$	−16.1948			−0.566237
$819$	2.84686	+	0.309465i	0.0994773	+	0.0108136i
$820$		0			0
$821$	30.7324	+	17.7433i	1.07257	+	0.619247i	0.928882	−	0.370377i	$-0.120771\pi$
$821$	30.7324	+	17.7433i	1.07257	+	0.619247i	0.143685	+	0.989623i	$0.454105\pi$
$822$	32.7506	−	59.8876i	1.14231	−	2.08882i
$823$	15.0235	+	26.0214i	0.523686	+	0.907050i	0.999620	+	0.0275693i	$0.00877670\pi$
$823$	15.0235	+	26.0214i	0.523686	+	0.907050i	−0.475934	+	0.879481i	$0.657890\pi$
$824$	11.9056	−	20.6211i	0.414752	−	0.718371i
$825$		0			0
$826$	−28.5527	+	35.4386i	−0.993474	+	1.23307i
$827$			21.6751i			0.753717i	0.926271	+	0.376859i	$0.122996\pi$
$827$			21.6751i			0.753717i	−0.926271	+	0.376859i	$0.877004\pi$
$828$	27.1756	−	17.4158i	0.944416	−	0.605240i
$829$	7.93492	−	4.58123i	0.275591	−	0.159113i	−0.355835	−	0.934549i	$-0.615803\pi$
$829$	7.93492	−	4.58123i	0.275591	−	0.159113i	0.631426	+	0.775436i	$0.282470\pi$
$830$		0			0
$831$	2.90212	−	0.0672336i	0.100673	−	0.00233231i
$832$			1.37954i			0.0478270i
$833$	13.1689	−	11.9759i	0.456277	−	0.414941i
$834$	33.2735	+	54.6669i	1.15217	+	1.89296i
$835$		0			0
$836$	−21.0072	−	36.3856i	−0.726551	−	1.25842i
$837$	−11.9998	+	8.08831i	−0.414774	+	0.279573i
$838$	21.7509	+	12.5579i	0.751372	+	0.433805i
$839$	−31.7155			−1.09494			−0.547471	−	0.836825i	$-0.684409\pi$
$839$	−31.7155			−1.09494			−0.547471	+	0.836825i	$0.684409\pi$
$840$		0			0
$841$	14.8452			0.511904
$842$	38.6302	+	22.3031i	1.33128	+	0.768617i
$843$	−3.19258	−	1.74592i	−0.109958	−	0.0601327i
$844$	−10.6260	−	18.4047i	−0.365762	−	0.633518i
$845$		0			0
$846$	−38.9162	−	20.1255i	−1.33797	−	0.691928i
$847$	−19.8551	+	7.67809i	−0.682229	+	0.263822i
$848$			8.46976i			0.290853i
$849$	0.200740	+	8.66487i	0.00688936	+	0.297378i
$850$		0			0
$851$	−7.17980	+	4.14526i	−0.246120	+	0.142098i
$852$	2.26803	+	97.8988i	0.0777013	+	3.35396i
$853$			10.2006i			0.349262i	0.984634	+	0.174631i	$0.0558732\pi$
$853$			10.2006i			0.349262i	−0.984634	+	0.174631i	$0.944127\pi$
$854$	−1.63862	+	10.5142i	−0.0560726	+	0.359789i
$855$		0			0
$856$	−3.18032	+	5.50848i	−0.108701	+	0.188276i
$857$	−0.902790	−	1.56368i	−0.0308387	−	0.0534142i	0.850194	−	0.526469i	$-0.176484\pi$
$857$	−0.902790	−	1.56368i	−0.0308387	−	0.0534142i	−0.881033	+	0.473055i	$0.843151\pi$
$858$	−2.36327	−	1.29240i	−0.0806807	−	0.0441218i
$859$	−6.67971	−	3.85653i	−0.227909	−	0.131583i	0.381698	−	0.924287i	$-0.375339\pi$
$859$	−6.67971	−	3.85653i	−0.227909	−	0.131583i	−0.609607	+	0.792704i	$0.708673\pi$
$860$		0			0
$861$	11.1574	−	4.61448i	0.380244	−	0.157261i
$862$	−7.37109			−0.251060
$863$	−19.3584	−	11.1766i	−0.658967	−	0.380455i	0.132916	−	0.991127i	$-0.457566\pi$
$863$	−19.3584	−	11.1766i	−0.658967	−	0.380455i	−0.791883	+	0.610673i	$0.790899\pi$
$864$	−13.4413	+	9.05994i	−0.457283	+	0.308226i
$865$		0			0
$866$	39.7107	−	68.7809i	1.34942	−	2.33727i
$867$	9.48604	+	15.5852i	0.322163	+	0.529300i
$868$	−11.4010	−	29.4823i	−0.386975	−	1.00069i
$869$			23.8380i			0.808648i
$870$		0			0
$871$	0.778253	−	0.449324i	0.0263701	−	0.0152248i
$872$	45.3287	−	26.1705i	1.53502	−	0.886246i
$873$	20.6801	−	13.2531i	0.699916	−	0.448549i
$874$		−	35.8423i		−	1.21238i
$875$		0			0
$876$	73.9045	−	44.9826i	2.49700	−	1.51982i
$877$	−25.8714	+	44.8106i	−0.873615	+	1.51315i	−0.0153839	+	0.999882i	$0.504897\pi$
$877$	−25.8714	+	44.8106i	−0.873615	+	1.51315i	−0.858231	+	0.513264i	$0.828436\pi$
$878$	26.9545	+	46.6866i	0.909671	+	1.57560i
$879$	−14.3551	+	26.2496i	−0.484185	+	0.885377i
$880$		0			0
$881$	−40.9882			−1.38093			−0.690464	−	0.723367i	$-0.742594\pi$
$881$	−40.9882			−1.38093			−0.690464	+	0.723367i	$0.742594\pi$
$882$	50.8877	−	13.5762i	1.71348	−	0.457134i
$883$	10.6943			0.359891			0.179945	−	0.983677i	$-0.442408\pi$
$883$	10.6943			0.359891			0.179945	+	0.983677i	$0.442408\pi$
$884$	3.40843	+	1.96786i	0.114638	+	0.0661861i
$885$		0			0
$886$	32.9415	+	57.0563i	1.10669	+	1.91684i
$887$	−23.5424	+	40.7766i	−0.790476	+	1.36914i	0.135196	+	0.990819i	$0.456833\pi$
$887$	−23.5424	+	40.7766i	−0.790476	+	1.36914i	−0.925672	+	0.378326i	$0.876500\pi$
$888$	28.0888	−	17.0965i	0.942599	−	0.573721i
$889$	−12.3335	−	9.93706i	−0.413654	−	0.333278i
$890$		0			0
$891$	1.43111	+	15.4019i	0.0479439	+	0.515983i
$892$	58.1554	−	33.5760i	1.94719	−	1.12421i
$893$	−28.7362	+	16.5909i	−0.961621	+	0.555192i
$894$	55.1646	−	1.27800i	1.84498	−	0.0427427i
$895$		0			0
$896$	15.1050	+	39.0605i	0.504621	+	1.30492i
$897$	−0.814836	−	1.33874i	−0.0272066	−	0.0446993i
$898$	−45.1523	+	78.2061i	−1.50675	+	2.60977i
$899$	5.23895	+	9.07413i	0.174729	+	0.302639i
$900$		0			0
$901$	−3.20276	−	1.84912i	−0.106699	−	0.0616030i
$902$	−11.3570			−0.378147
$903$	−42.6037	+	17.6200i	−1.41776	+	0.586355i
$904$	21.7827			0.724480
$905$		0			0
$906$	63.6236	+	34.7937i	2.11375	+	1.15594i
$907$	−4.35909	−	7.55017i	−0.144741	−	0.250699i	0.784535	−	0.620084i	$-0.212902\pi$
$907$	−4.35909	−	7.55017i	−0.144741	−	0.250699i	−0.929276	+	0.369385i	$0.879568\pi$
$908$	27.0524	−	46.8561i	0.897765	−	1.55497i
$909$	−1.71837	+	3.32277i	−0.0569947	+	0.110209i
$910$		0			0
$911$			4.85314i			0.160792i	0.996763	+	0.0803958i	$0.0256184\pi$
$911$			4.85314i			0.160792i	−0.996763	+	0.0803958i	$0.974382\pi$
$912$	1.33127	+	57.4639i	0.0440827	+	1.90282i
$913$	5.21587	−	3.01138i	0.172620	−	0.0996622i
$914$	−39.6310	+	22.8809i	−1.31088	+	0.756834i
$915$		0			0
$916$			25.7068i			0.849376i
$917$	35.9792	−	13.9134i	1.18814	−	0.459460i
$918$	−2.30088	−	33.0583i	−0.0759405	−	1.09109i
$919$	−17.9292	+	31.0543i	−0.591429	+	1.02439i	0.402611	+	0.915371i	$0.368103\pi$
$919$	−17.9292	+	31.0543i	−0.591429	+	1.02439i	−0.994040	+	0.109014i	$0.965231\pi$
$920$		0			0
$921$	−15.5497	−	8.50365i	−0.512381	−	0.280205i
$922$	−49.5366	−	28.6000i	−1.63140	−	0.941889i
$923$	4.75475			0.156505
$924$	−33.4963	−	4.42835i	−1.10195	−	0.145682i
$925$		0			0
$926$	50.7629	+	29.3080i	1.66817	+	0.963120i
$927$	0.576000	+	12.4248i	0.0189183	+	0.408083i
$928$	5.86830	+	10.1642i	0.192636	+	0.333656i
$929$	12.7001	−	21.9973i	0.416678	−	0.721707i	−0.578925	−	0.815381i	$-0.696528\pi$
$929$	12.7001	−	21.9973i	0.416678	−	0.721707i	0.995603	+	0.0936737i	$0.0298611\pi$
$930$		0			0
$931$	12.1383	−	37.9967i	0.397816	−	1.24529i
$932$		−	93.5349i		−	3.06384i
$933$	−18.1434	+	0.420329i	−0.593988	+	0.0137610i
$934$	23.6515	−	13.6552i	0.773902	−	0.446813i
$935$		0			0
$936$	3.35400	+	5.23357i	0.109629	+	0.171065i
$937$		−	40.3037i		−	1.31667i	−0.752727	−	0.658333i	$-0.771262\pi$
$937$		−	40.3037i		−	1.31667i	0.752727	−	0.658333i	$-0.228738\pi$
$938$	10.3695	−	12.8702i	0.338576	−	0.420228i
$939$	0.379023	−	0.230695i	0.0123689	−	0.00752846i
$940$		0			0
$941$	−9.12065	−	15.7974i	−0.297325	−	0.514982i	0.678198	−	0.734879i	$-0.262761\pi$
$941$	−9.12065	−	15.7974i	−0.297325	−	0.514982i	−0.975523	+	0.219897i	$0.929428\pi$
$942$	3.00786	−	5.50016i	0.0980015	−	0.179205i
$943$	−5.72264	−	3.30396i	−0.186355	−	0.107592i
$944$	−39.9425			−1.30002
$945$		0			0
$946$	43.3657			1.40994
$947$	16.3233	+	9.42425i	0.530435	+	0.306247i	0.741194	−	0.671291i	$-0.234260\pi$
$947$	16.3233	+	9.42425i	0.530435	+	0.306247i	−0.210759	+	0.977538i	$0.567593\pi$
$948$	49.4483	−	90.4208i	1.60601	−	2.93673i
$949$	−2.10043	−	3.63806i	−0.0681830	−	0.118096i
$950$		0			0
$951$	−45.7747	+	27.8612i	−1.48435	+	0.903461i
$952$	38.1778	+	5.94996i	1.23735	+	0.192839i
$953$			25.3110i			0.819903i	0.912107	+	0.409952i	$0.134454\pi$
$953$			25.3110i			0.819903i	−0.912107	+	0.409952i	$0.865546\pi$
$954$	−5.90419	−	9.21289i	−0.191155	−	0.298278i
$955$		0			0
$956$	92.5341	−	53.4246i	2.99277	−	1.72787i
$957$	11.1968	−	0.259397i	0.361941	−	0.00838511i
$958$			25.7737i			0.832712i
$959$	−41.0777	−	6.40189i	−1.32647	−	0.206728i
$960$		0			0
$961$	−11.6219	+	20.1298i	−0.374901	+	0.649347i
$962$	−1.49554	−	2.59035i	−0.0482182	−	0.0835164i
$963$	−0.153866	−	3.31901i	−0.00495825	−	0.106953i
$964$	63.2570	+	36.5214i	2.03737	+	1.17628i
$965$		0			0
$966$	−22.8582	−	17.5594i	−0.735451	−	0.564965i
$967$	32.2840			1.03818			0.519092	−	0.854718i	$-0.326270\pi$
$967$	32.2840			1.03818			0.519092	+	0.854718i	$0.326270\pi$
$968$	−40.0188	−	23.1049i	−1.28625	−	0.742619i
$969$	−22.0201	−	12.0421i	−0.707387	−	0.386848i
$970$		0			0
$971$	0.693916	−	1.20190i	0.0222688	−	0.0385707i	−0.854676	−	0.519161i	$-0.826244\pi$
$971$	0.693916	−	1.20190i	0.0222688	−	0.0385707i	0.876945	+	0.480591i	$0.159578\pi$
$972$	26.5205	−	61.3901i	0.850645	−	1.96909i
$973$	24.4548	−	30.3525i	0.783986	−	0.973056i
$974$			34.7293i			1.11280i
$975$		0			0
$976$	−8.08813	+	4.66968i	−0.258895	+	0.149473i
$977$	−50.0663	+	28.9058i	−1.60176	+	0.924779i	−0.610630	+	0.791916i	$0.709084\pi$
$977$	−50.0663	+	28.9058i	−1.60176	+	0.924779i	−0.991134	+	0.132863i	$0.957583\pi$
$978$	−1.69646	−	73.2274i	−0.0542469	−	2.34155i
$979$		−	20.9815i		−	0.670572i
$980$		0			0
$981$	−12.5593	+	24.2857i	−0.400989	+	0.775383i
$982$	−17.0518	+	29.5346i	−0.544145	+	0.942487i
$983$	−13.0057	−	22.5265i	−0.414818	−	0.718485i	0.580592	−	0.814195i	$-0.302821\pi$
$983$	−13.0057	−	22.5265i	−0.414818	−	0.718485i	−0.995409	+	0.0957097i	$0.969488\pi$
$984$	22.9951	+	12.5753i	0.733058	+	0.400886i
$985$		0			0
$986$	−23.9938			−0.764119
$987$	−3.49737	+	26.4543i	−0.111323	+	0.842051i
$988$	8.81958			0.280588
$989$	21.8514	+	12.6159i	0.694833	+	0.401162i
$990$		0			0
$991$	18.1162	+	31.3782i	0.575480	+	0.996760i	0.995989	+	0.0894720i	$0.0285180\pi$
$991$	18.1162	+	31.3782i	0.575480	+	0.996760i	−0.420510	+	0.907288i	$0.638149\pi$
$992$	4.34394	−	7.52393i	0.137920	−	0.238885i
$993$	7.54560	+	12.3971i	0.239452	+	0.393410i
$994$	81.5627	−	31.5408i	2.58701	−	1.00041i
$995$		0			0
$996$	−26.0312	+	0.603066i	−0.824829	+	0.0191089i
$997$	29.9600	−	17.2974i	0.948842	−	0.547814i	0.0561210	−	0.998424i	$-0.482127\pi$
$997$	29.9600	−	17.2974i	0.948842	−	0.547814i	0.892721	+	0.450610i	$0.148793\pi$
$998$	78.6490	−	45.4080i	2.48959	−	1.43737i
$999$	−7.53479	+	15.4359i	−0.238390	+	0.488370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.j.26.11		24
3.2	odd	2	inner	525.2.t.j.26.1		24
5.2	odd	4		105.2.p.a.89.2	yes	24
5.3	odd	4		105.2.p.a.89.11	yes	24
5.4	even	2	inner	525.2.t.j.26.2		24
7.3	odd	6	inner	525.2.t.j.101.1		24
15.2	even	4		105.2.p.a.89.12	yes	24
15.8	even	4		105.2.p.a.89.1	yes	24
15.14	odd	2	inner	525.2.t.j.26.12		24
21.17	even	6	inner	525.2.t.j.101.11		24
35.2	odd	12		735.2.g.b.734.22		24
35.3	even	12		105.2.p.a.59.12	yes	24
35.12	even	12		735.2.g.b.734.23		24
35.13	even	4		735.2.p.f.509.12		24
35.17	even	12		105.2.p.a.59.1	✓	24
35.18	odd	12		735.2.p.f.374.11		24
35.23	odd	12		735.2.g.b.734.3		24
35.24	odd	6	inner	525.2.t.j.101.12		24
35.27	even	4		735.2.p.f.509.1		24
35.32	odd	12		735.2.p.f.374.2		24
35.33	even	12		735.2.g.b.734.2		24
105.2	even	12		735.2.g.b.734.1		24
105.17	odd	12		105.2.p.a.59.11	yes	24
105.23	even	12		735.2.g.b.734.24		24
105.32	even	12		735.2.p.f.374.12		24
105.38	odd	12		105.2.p.a.59.2	yes	24
105.47	odd	12		735.2.g.b.734.4		24
105.53	even	12		735.2.p.f.374.1		24
105.59	even	6	inner	525.2.t.j.101.2		24
105.62	odd	4		735.2.p.f.509.11		24
105.68	odd	12		735.2.g.b.734.21		24
105.83	odd	4		735.2.p.f.509.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.1	✓	24	35.17	even	12
105.2.p.a.59.2	yes	24	105.38	odd	12
105.2.p.a.59.11	yes	24	105.17	odd	12
105.2.p.a.59.12	yes	24	35.3	even	12
105.2.p.a.89.1	yes	24	15.8	even	4
105.2.p.a.89.2	yes	24	5.2	odd	4
105.2.p.a.89.11	yes	24	5.3	odd	4
105.2.p.a.89.12	yes	24	15.2	even	4
525.2.t.j.26.1		24	3.2	odd	2	inner
525.2.t.j.26.2		24	5.4	even	2	inner
525.2.t.j.26.11		24	1.1	even	1	trivial
525.2.t.j.26.12		24	15.14	odd	2	inner
525.2.t.j.101.1		24	7.3	odd	6	inner
525.2.t.j.101.2		24	105.59	even	6	inner
525.2.t.j.101.11		24	21.17	even	6	inner
525.2.t.j.101.12		24	35.24	odd	6	inner
735.2.g.b.734.1		24	105.2	even	12
735.2.g.b.734.2		24	35.33	even	12
735.2.g.b.734.3		24	35.23	odd	12
735.2.g.b.734.4		24	105.47	odd	12
735.2.g.b.734.21		24	105.68	odd	12
735.2.g.b.734.22		24	35.2	odd	12
735.2.g.b.734.23		24	35.12	even	12
735.2.g.b.734.24		24	105.23	even	12
735.2.p.f.374.1		24	105.53	even	12
735.2.p.f.374.2		24	35.32	odd	12
735.2.p.f.374.11		24	35.18	odd	12
735.2.p.f.374.12		24	105.32	even	12
735.2.p.f.509.1		24	35.27	even	4
735.2.p.f.509.2		24	105.83	odd	4
735.2.p.f.509.11		24	105.62	odd	4
735.2.p.f.509.12		24	35.13	even	4

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.17197 + 1.25399i) q^{2} +(-0.831052 + 1.51966i) q^{3} +(2.14497 + 3.71520i) q^{4} +(-3.71065 + 2.25852i) q^{6} +(2.06025 + 1.65993i) q^{7} +5.74313i q^{8} +(-1.61871 - 2.52582i) q^{9} +O(q^{10})\)	\(q+(2.17197 + 1.25399i) q^{2} +(-0.831052 + 1.51966i) q^{3} +(2.14497 + 3.71520i) q^{4} +(-3.71065 + 2.25852i) q^{6} +(2.06025 + 1.65993i) q^{7} +5.74313i q^{8} +(-1.61871 - 2.52582i) q^{9} +(1.48843 - 0.859346i) q^{11} +(-7.42841 + 0.172094i) q^{12} +0.360784i q^{13} +(2.39327 + 6.18885i) q^{14} +(-2.91187 + 5.04351i) q^{16} +(-1.27144 - 2.20219i) q^{17} +(-0.348428 - 7.51586i) q^{18} +(-4.93492 - 2.84918i) q^{19} +(-4.23470 + 1.75138i) q^{21} +4.31044 q^{22} +(2.17197 + 1.25399i) q^{23} +(-8.72758 - 4.77284i) q^{24} +(-0.452418 + 0.783611i) q^{26} +(5.18361 - 0.360784i) q^{27} +(-1.74780 + 11.2147i) q^{28} -3.76228i q^{29} +(-2.41187 + 1.39249i) q^{31} +(-2.70160 + 1.55977i) q^{32} +(0.0689466 + 2.97606i) q^{33} -6.37747i q^{34} +(5.91187 - 11.4316i) q^{36} +(-1.65283 + 2.86279i) q^{37} +(-7.14567 - 12.3767i) q^{38} +(-0.548267 - 0.299830i) q^{39} -2.63477 q^{41} +(-11.3939 - 1.50631i) q^{42} +10.0606 q^{43} +(6.38529 + 3.68655i) q^{44} +(3.14497 + 5.44725i) q^{46} +(2.91152 - 5.04290i) q^{47} +(-5.24448 - 8.61645i) q^{48} +(1.48925 + 6.83975i) q^{49} +(4.40320 - 0.102009i) q^{51} +(-1.34038 + 0.773871i) q^{52} +(1.25950 - 0.727175i) q^{53} +(11.7111 + 5.71658i) q^{54} +(-9.53320 + 11.8323i) q^{56} +(8.43094 - 5.13156i) q^{57} +(4.71786 - 8.17157i) q^{58} +(3.42928 + 5.93969i) q^{59} +(1.38882 + 0.801836i) q^{61} -6.98468 q^{62} +(0.857759 - 7.89077i) q^{63} +3.82374 q^{64} +(-3.58220 + 6.55038i) q^{66} +(-1.24541 - 2.15712i) q^{67} +(5.45439 - 9.44729i) q^{68} +(-3.71065 + 2.25852i) q^{69} -13.1790i q^{71} +(14.5061 - 9.29643i) q^{72} +(-10.0838 + 5.82187i) q^{73} +(-7.17980 + 4.14526i) q^{74} -24.4456i q^{76} +(4.49300 + 0.700227i) q^{77} +(-0.814836 - 1.33874i) q^{78} +(-6.93492 + 12.0116i) q^{79} +(-3.75958 + 8.17713i) q^{81} +(-5.72264 - 3.30396i) q^{82} +3.50427 q^{83} +(-15.5900 - 11.9761i) q^{84} +(21.8514 + 12.6159i) q^{86} +(5.71737 + 3.12665i) q^{87} +(4.93534 + 8.54825i) q^{88} +(6.10392 - 10.5723i) q^{89} +(-0.598876 + 0.743304i) q^{91} +10.7591i q^{92} +(-0.111722 - 4.82244i) q^{93} +(12.6475 - 7.30202i) q^{94} +(-0.125143 - 5.40176i) q^{96} +8.18747i q^{97} +(-5.34234 + 16.7232i) q^{98} +(-4.57989 - 2.36849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 6 q^{9}+O(q^{10}) \) 24 * q + 12 * q^4 + 6 * q^9	\( 24 q + 12 q^{4} + 6 q^{9} - 12 q^{16} - 6 q^{21} - 18 q^{24} + 84 q^{36} + 12 q^{39} + 36 q^{46} + 12 q^{49} - 12 q^{51} + 36 q^{54} + 36 q^{61} - 24 q^{64} - 72 q^{66} - 48 q^{79} - 6 q^{81} - 48 q^{84} - 96 q^{91} + 72 q^{94} - 90 q^{96} + 48 q^{99}+O(q^{100}) \) 24 * q + 12 * q^4 + 6 * q^9 - 12 * q^16 - 6 * q^21 - 18 * q^24 + 84 * q^36 + 12 * q^39 + 36 * q^46 + 12 * q^49 - 12 * q^51 + 36 * q^54 + 36 * q^61 - 24 * q^64 - 72 * q^66 - 48 * q^79 - 6 * q^81 - 48 * q^84 - 96 * q^91 + 72 * q^94 - 90 * q^96 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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