LMFDB - Embedded newform 845.2.bg.a.621.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(36,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 47]))

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

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

chi := DirichletCharacter("845.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.bg (of order $78$, degree $24$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$1440$
Relative dimension:	$60$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			621.38
Character	$\chi$	$=$	845.621
Dual form			845.2.bg.a.381.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.748238 + 0.610917i) q^{2} +(2.54521 + 0.205471i) q^{3} +(-0.213412 - 1.04536i) q^{4} +(0.992709 - 0.120537i) q^{5} +(1.77890 + 1.70865i) q^{6} +(0.816244 + 1.29079i) q^{7} +(1.37675 - 2.62318i) q^{8} +(3.47473 + 0.564699i) q^{9} +O(q^{10})$	\(q+(0.748238 + 0.610917i) q^{2} +(2.54521 + 0.205471i) q^{3} +(-0.213412 - 1.04536i) q^{4} +(0.992709 - 0.120537i) q^{5} +(1.77890 + 1.70865i) q^{6} +(0.816244 + 1.29079i) q^{7} +(1.37675 - 2.62318i) q^{8} +(3.47473 + 0.564699i) q^{9} +(0.816420 + 0.516273i) q^{10} +(0.0511583 + 0.314790i) q^{11} +(-0.328387 - 2.70451i) q^{12} +(-2.58328 - 2.51528i) q^{13} +(-0.177819 + 1.46447i) q^{14} +(2.55142 - 0.102819i) q^{15} +(0.669598 - 0.285289i) q^{16} +(2.39056 - 1.51170i) q^{17} +(2.25494 + 2.54530i) q^{18} +(-0.441706 - 0.255019i) q^{19} +(-0.337860 - 1.01201i) q^{20} +(1.81229 + 3.45304i) q^{21} +(-0.154032 + 0.266791i) q^{22} +(1.02998 + 1.78397i) q^{23} +(4.04312 - 6.39368i) q^{24} +(0.970942 - 0.239316i) q^{25} +(-0.396280 - 3.46020i) q^{26} +(1.29002 + 0.317961i) q^{27} +(1.17514 - 1.12874i) q^{28} +(-4.40937 + 5.40050i) q^{29} +(1.97188 + 1.48177i) q^{30} +(-1.61913 + 6.56905i) q^{31} +(-5.01581 - 1.45285i) q^{32} +(0.0655286 + 0.811718i) q^{33} +(2.71223 + 0.329324i) q^{34} +(0.965880 + 1.18299i) q^{35} +(-0.151235 - 3.75285i) q^{36} +(-4.21522 + 1.22095i) q^{37} +(-0.174706 - 0.460661i) q^{38} +(-6.05818 - 6.93272i) q^{39} +(1.05053 - 2.77001i) q^{40} +(-0.399262 + 4.94574i) q^{41} +(-0.753494 + 3.69086i) q^{42} +(1.14952 - 3.96861i) q^{43} +(0.318150 - 0.120658i) q^{44} +(3.51746 + 0.141749i) q^{45} +(-0.319191 + 1.96406i) q^{46} +(-1.12331 + 1.26796i) q^{47} +(1.76289 - 0.588538i) q^{48} +(2.00097 - 4.21696i) q^{49} +(0.872697 + 0.414100i) q^{50} +(6.39508 - 3.35640i) q^{51} +(-2.07807 + 3.23725i) q^{52} +(11.7778 + 6.18148i) q^{53} +(0.770992 + 1.02600i) q^{54} +(0.0887290 + 0.306328i) q^{55} +(4.50974 - 0.364064i) q^{56} +(-1.07184 - 0.739836i) q^{57} +(-6.59851 + 1.34710i) q^{58} +(2.81219 - 6.60045i) q^{59} +(-0.651985 - 2.64521i) q^{60} +(-0.125926 + 3.12483i) q^{61} +(-5.22464 + 3.92606i) q^{62} +(2.10732 + 4.94607i) q^{63} +(-3.69237 - 5.34932i) q^{64} +(-2.86763 - 2.18556i) q^{65} +(-0.446861 + 0.647390i) q^{66} +(-8.86382 - 1.80956i) q^{67} +(-2.09044 - 2.17638i) q^{68} +(2.25495 + 4.75221i) q^{69} +1.47523i q^{70} +(4.82951 - 2.29163i) q^{71} +(6.26516 - 8.33741i) q^{72} +(1.26270 + 0.478881i) q^{73} +(-3.89988 - 1.66159i) q^{74} +(2.52042 - 0.409609i) q^{75} +(-0.172321 + 0.516166i) q^{76} +(-0.364569 + 0.322980i) q^{77} +(-0.297645 - 8.88837i) q^{78} +(2.35816 + 2.08915i) q^{79} +(0.630328 - 0.363920i) q^{80} +(-6.79941 - 2.26998i) q^{81} +(-3.32018 + 3.45668i) q^{82} +(-2.78409 + 1.92172i) q^{83} +(3.22290 - 2.63142i) q^{84} +(2.19091 - 1.78882i) q^{85} +(3.28461 - 2.26720i) q^{86} +(-12.3324 + 12.8394i) q^{87} +(0.896184 + 0.299190i) q^{88} +(0.167715 - 0.0968301i) q^{89} +(2.54530 + 2.25494i) q^{90} +(1.13811 - 5.38755i) q^{91} +(1.64508 - 1.45741i) q^{92} +(-5.47077 + 16.3869i) q^{93} +(-1.61512 + 0.262483i) q^{94} +(-0.469225 - 0.199918i) q^{95} +(-12.4678 - 4.72840i) q^{96} +(-8.33676 + 11.0942i) q^{97} +(4.07341 - 1.93286i) q^{98} +1.12270i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1440 q - 2 q^{3} - 58 q^{4} + 18 q^{6} + 6 q^{7} + 60 q^{9}+O(q^{10}) $ 1440 * q - 2 * q^3 - 58 * q^4 + 18 * q^6 + 6 * q^7 + 60 * q^9	$ 1440 q - 2 q^{3} - 58 q^{4} + 18 q^{6} + 6 q^{7} + 60 q^{9} + 2 q^{10} - 20 q^{12} + 26 q^{13} + 4 q^{14} + 6 q^{15} + 58 q^{16} + 6 q^{17} - 156 q^{18} - 12 q^{19} - 12 q^{20} + 60 q^{22} - 146 q^{23} - 144 q^{24} + 120 q^{25} - 10 q^{26} + 4 q^{27} + 18 q^{28} + 4 q^{29} - 4 q^{30} + 52 q^{31} + 20 q^{32} - 42 q^{33} + 130 q^{34} - 10 q^{35} - 56 q^{36} - 6 q^{37} - 162 q^{38} + 12 q^{40} - 12 q^{41} - 24 q^{42} + 2 q^{43} + 42 q^{46} - 156 q^{47} + 30 q^{48} + 18 q^{49} - 124 q^{52} + 48 q^{53} - 330 q^{54} - 4 q^{55} + 20 q^{56} + 78 q^{57} + 68 q^{58} - 196 q^{59} + 12 q^{61} - 118 q^{62} + 24 q^{63} + 96 q^{64} + 8 q^{65} + 44 q^{66} + 98 q^{67} + 120 q^{68} + 28 q^{69} - 156 q^{71} + 386 q^{72} - 30 q^{74} + 2 q^{75} - 392 q^{76} + 4 q^{77} - 204 q^{78} + 40 q^{79} + 40 q^{81} - 244 q^{82} + 30 q^{84} - 18 q^{85} - 30 q^{87} + 30 q^{88} - 24 q^{89} - 56 q^{90} + 76 q^{91} + 20 q^{92} - 130 q^{93} - 148 q^{94} + 16 q^{95} - 338 q^{96} + 30 q^{97} - 72 q^{98}+O(q^{100}) $ 1440 * q - 2 * q^3 - 58 * q^4 + 18 * q^6 + 6 * q^7 + 60 * q^9 + 2 * q^10 - 20 * q^12 + 26 * q^13 + 4 * q^14 + 6 * q^15 + 58 * q^16 + 6 * q^17 - 156 * q^18 - 12 * q^19 - 12 * q^20 + 60 * q^22 - 146 * q^23 - 144 * q^24 + 120 * q^25 - 10 * q^26 + 4 * q^27 + 18 * q^28 + 4 * q^29 - 4 * q^30 + 52 * q^31 + 20 * q^32 - 42 * q^33 + 130 * q^34 - 10 * q^35 - 56 * q^36 - 6 * q^37 - 162 * q^38 + 12 * q^40 - 12 * q^41 - 24 * q^42 + 2 * q^43 + 42 * q^46 - 156 * q^47 + 30 * q^48 + 18 * q^49 - 124 * q^52 + 48 * q^53 - 330 * q^54 - 4 * q^55 + 20 * q^56 + 78 * q^57 + 68 * q^58 - 196 * q^59 + 12 * q^61 - 118 * q^62 + 24 * q^63 + 96 * q^64 + 8 * q^65 + 44 * q^66 + 98 * q^67 + 120 * q^68 + 28 * q^69 - 156 * q^71 + 386 * q^72 - 30 * q^74 + 2 * q^75 - 392 * q^76 + 4 * q^77 - 204 * q^78 + 40 * q^79 + 40 * q^81 - 244 * q^82 + 30 * q^84 - 18 * q^85 - 30 * q^87 + 30 * q^88 - 24 * q^89 - 56 * q^90 + 76 * q^91 + 20 * q^92 - 130 * q^93 - 148 * q^94 + 16 * q^95 - 338 * q^96 + 30 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{17}{78}\right)$	$1$

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 $

$2$	0.748238	+	0.610917i	0.529084	+	0.431984i	0.858962	−	0.512040i	$-0.171110\pi$
$2$	0.748238	+	0.610917i	0.529084	+	0.431984i	−0.329878	+	0.944024i	$0.607007\pi$
$3$	2.54521	+	0.205471i	1.46948	+	0.118629i	0.789115	−	0.614246i	$-0.210540\pi$
$3$	2.54521	+	0.205471i	1.46948	+	0.118629i	0.680364	+	0.732875i	$0.261822\pi$
$4$	−0.213412	−	1.04536i	−0.106706	−	0.522679i
$5$	0.992709	−	0.120537i	0.443953	−	0.0539056i
$5$	0.992709	−	0.120537i	0.443953	−	0.0539056i
$6$	1.77890	+	1.70865i	0.726232	+	0.697555i
$7$	0.816244	+	1.29079i	0.308511	+	0.487872i	0.963478	−	0.267786i	$-0.0862919\pi$
$7$	0.816244	+	1.29079i	0.308511	+	0.487872i	−0.654967	+	0.755657i	$0.727318\pi$
$8$	1.37675	−	2.62318i	0.486756	−	0.927436i
$9$	3.47473	+	0.564699i	1.15824	+	0.188233i
$10$	0.816420	+	0.516273i	0.258175	+	0.163260i
$11$	0.0511583	+	0.314790i	0.0154248	+	0.0949126i	0.993621	−	0.112769i	$-0.0359721\pi$
$11$	0.0511583	+	0.314790i	0.0154248	+	0.0949126i	−0.978196	+	0.207682i	$0.933408\pi$
$12$	−0.328387	−	2.70451i	−0.0947971	−	0.780724i
$13$	−2.58328	−	2.51528i	−0.716474	−	0.697614i
$13$	−2.58328	−	2.51528i	−0.716474	−	0.697614i
$14$	−0.177819	+	1.46447i	−0.0475242	+	0.391397i
$15$	2.55142	−	0.102819i	0.658774	−	0.0265477i
$16$	0.669598	−	0.285289i	0.167399	−	0.0713222i
$17$	2.39056	−	1.51170i	0.579795	−	0.366640i	−0.212146	−	0.977238i	$-0.568045\pi$
$17$	2.39056	−	1.51170i	0.579795	−	0.366640i	0.791941	+	0.610598i	$0.209071\pi$
$18$	2.25494	+	2.54530i	0.531494	+	0.599933i
$19$	−0.441706	−	0.255019i	−0.101334	−	0.0585054i	0.448476	−	0.893795i	$-0.351967\pi$
$19$	−0.441706	−	0.255019i	−0.101334	−	0.0585054i	−0.549811	+	0.835289i	$0.685300\pi$
$20$	−0.337860	−	1.01201i	−0.0755477	−	0.226293i
$21$	1.81229	+	3.45304i	0.395475	+	0.753515i
$22$	−0.154032	+	0.266791i	−0.0328397	+	0.0568800i
$23$	1.02998	+	1.78397i	0.214765	+	0.371983i	0.953200	−	0.302341i	$-0.0977682\pi$
$23$	1.02998	+	1.78397i	0.214765	+	0.371983i	−0.738435	+	0.674325i	$0.764435\pi$
$24$	4.04312	−	6.39368i	0.825297	−	1.30510i
$25$	0.970942	−	0.239316i	0.194188	−	0.0478631i
$26$	−0.396280	−	3.46020i	−0.0777168	−	0.678601i
$27$	1.29002	+	0.317961i	0.248264	+	0.0611916i
$28$	1.17514	−	1.12874i	0.222080	−	0.213311i
$29$	−4.40937	+	5.40050i	−0.818799	+	1.00285i	0.181013	+	0.983481i	$0.442062\pi$
$29$	−4.40937	+	5.40050i	−0.818799	+	1.00285i	−0.999812	+	0.0193663i	$0.993835\pi$
$30$	1.97188	+	1.48177i	0.360015	+	0.270534i
$31$	−1.61913	+	6.56905i	−0.290804	+	1.17984i	0.625782	+	0.779998i	$0.284780\pi$
$31$	−1.61913	+	6.56905i	−0.290804	+	1.17984i	−0.916586	+	0.399839i	$0.869066\pi$
$32$	−5.01581	−	1.45285i	−0.886678	−	0.256829i
$33$	0.0655286	+	0.811718i	0.0114071	+	0.141302i
$34$	2.71223	+	0.329324i	0.465143	+	0.0564786i
$35$	0.965880	+	1.18299i	0.163264	+	0.199962i
$36$	−0.151235	−	3.75285i	−0.0252058	−	0.625475i
$37$	−4.21522	+	1.22095i	−0.692977	+	0.200723i	−0.605974	−	0.795485i	$-0.707216\pi$
$37$	−4.21522	+	1.22095i	−0.692977	+	0.200723i	−0.0870036	+	0.996208i	$0.527729\pi$
$38$	−0.174706	−	0.460661i	−0.0283410	−	0.0747291i
$39$	−6.05818	−	6.93272i	−0.970086	−	1.11012i
$40$	1.05053	−	2.77001i	0.166103	−	0.437977i
$41$	−0.399262	+	4.94574i	−0.0623542	+	0.772395i	0.887723	+	0.460379i	$0.152286\pi$
$41$	−0.399262	+	4.94574i	−0.0623542	+	0.772395i	−0.950077	+	0.312016i	$0.898996\pi$
$42$	−0.753494	+	3.69086i	−0.116267	+	0.569512i
$43$	1.14952	−	3.96861i	0.175301	−	0.605208i	−0.823956	−	0.566654i	$-0.808238\pi$
$43$	1.14952	−	3.96861i	0.175301	−	0.605208i	0.999257	−	0.0385539i	$-0.0122751\pi$
$44$	0.318150	−	0.120658i	0.0479630	−	0.0181900i
$45$	3.51746	+	0.141749i	0.524352	+	0.0211307i
$46$	−0.319191	+	1.96406i	−0.0470622	+	0.289585i
$47$	−1.12331	+	1.26796i	−0.163852	+	0.184951i	−0.824702	−	0.565567i	$-0.808657\pi$
$47$	−1.12331	+	1.26796i	−0.163852	+	0.184951i	0.660850	+	0.750518i	$0.270196\pi$
$48$	1.76289	−	0.588538i	0.254451	−	0.0849481i
$49$	2.00097	−	4.21696i	0.285853	−	0.602423i
$50$	0.872697	+	0.414100i	0.123418	+	0.0585626i
$51$	6.39508	−	3.35640i	0.895490	−	0.469990i
$52$	−2.07807	+	3.23725i	−0.288177	+	0.448925i
$53$	11.7778	+	6.18148i	1.61781	+	0.849091i	0.997924	+	0.0643971i	$0.0205124\pi$
$53$	11.7778	+	6.18148i	1.61781	+	0.849091i	0.619883	+	0.784694i	$0.287180\pi$
$54$	0.770992	+	1.02600i	0.104919	+	0.139622i
$55$	0.0887290	+	0.306328i	0.0119642	+	0.0413053i
$56$	4.50974	−	0.364064i	0.602639	−	0.0486501i
$57$	−1.07184	−	0.739836i	−0.141968	−	0.0979936i
$58$	−6.59851	+	1.34710i	−0.866427	+	0.176882i
$59$	2.81219	−	6.60045i	0.366116	−	0.859306i	−0.630429	−	0.776247i	$-0.717121\pi$
$59$	2.81219	−	6.60045i	0.366116	−	0.859306i	0.996545	−	0.0830587i	$-0.0264689\pi$
$60$	−0.651985	−	2.64521i	−0.0841709	−	0.341495i
$61$	−0.125926	+	3.12483i	−0.0161232	+	0.400093i	0.970897	+	0.239497i	$0.0769826\pi$
$61$	−0.125926	+	3.12483i	−0.0161232	+	0.400093i	−0.987020	+	0.160596i	$0.948658\pi$
$62$	−5.22464	+	3.92606i	−0.663530	+	0.498610i
$63$	2.10732	+	4.94607i	0.265498	+	0.623146i
$64$	−3.69237	−	5.34932i	−0.461546	−	0.668665i
$65$	−2.86763	−	2.18556i	−0.355686	−	0.271086i
$66$	−0.446861	+	0.647390i	−0.0550048	+	0.0796882i
$67$	−8.86382	−	1.80956i	−1.08289	−	0.221073i	−0.374735	−	0.927132i	$-0.622266\pi$
$67$	−8.86382	−	1.80956i	−1.08289	−	0.221073i	−0.708153	+	0.706059i	$0.750471\pi$
$68$	−2.09044	−	2.17638i	−0.253503	−	0.263924i
$69$	2.25495	+	4.75221i	0.271464	+	0.572099i
$70$			1.47523i			0.176324i
$71$	4.82951	−	2.29163i	0.573157	−	0.271966i	−0.119975	−	0.992777i	$-0.538282\pi$
$71$	4.82951	−	2.29163i	0.573157	−	0.271966i	0.693132	+	0.720811i	$0.256230\pi$
$72$	6.26516	−	8.33741i	0.738356	−	0.982573i
$73$	1.26270	+	0.478881i	0.147788	+	0.0560487i	0.427390	−	0.904067i	$-0.359433\pi$
$73$	1.26270	+	0.478881i	0.147788	+	0.0560487i	−0.279602	+	0.960116i	$0.590202\pi$
$74$	−3.89988	−	1.66159i	−0.453352	−	0.193155i
$75$	2.52042	−	0.409609i	0.291034	−	0.0472975i
$76$	−0.172321	+	0.516166i	−0.0197666	+	0.0592083i
$77$	−0.364569	+	0.322980i	−0.0415465	+	0.0368070i
$78$	−0.297645	−	8.88837i	−0.0337017	−	1.00641i
$79$	2.35816	+	2.08915i	0.265314	+	0.235047i	0.785282	−	0.619138i	$-0.212518\pi$
$79$	2.35816	+	2.08915i	0.265314	+	0.235047i	−0.519969	+	0.854185i	$0.674056\pi$
$80$	0.630328	−	0.363920i	0.0704728	−	0.0406875i
$81$	−6.79941	−	2.26998i	−0.755490	−	0.252220i
$82$	−3.32018	+	3.45668i	−0.366653	+	0.381726i
$83$	−2.78409	+	1.92172i	−0.305594	+	0.210936i	−0.710985	−	0.703207i	$-0.751751\pi$
$83$	−2.78409	+	1.92172i	−0.305594	+	0.210936i	0.405391	+	0.914143i	$0.367135\pi$
$84$	3.22290	−	2.63142i	0.351647	−	0.287111i
$85$	2.19091	−	1.78882i	0.237638	−	0.194025i
$86$	3.28461	−	2.26720i	0.354189	−	0.244479i
$87$	−12.3324	+	12.8394i	−1.32217	+	1.37653i
$88$	0.896184	+	0.299190i	0.0955335	+	0.0318938i
$89$	0.167715	−	0.0968301i	0.0177777	−	0.0102640i	−0.491085	−	0.871112i	$-0.663399\pi$
$89$	0.167715	−	0.0968301i	0.0177777	−	0.0102640i	0.508863	+	0.860848i	$0.330066\pi$
$90$	2.54530	+	2.25494i	0.268298	+	0.237692i
$91$	1.13811	−	5.38755i	0.119306	−	0.564769i
$92$	1.64508	−	1.45741i	0.171511	−	0.151946i
$93$	−5.47077	+	16.3869i	−0.567292	+	1.69925i
$94$	−1.61512	+	0.262483i	−0.166587	+	0.0270730i
$95$	−0.469225	−	0.199918i	−0.0481415	−	0.0205112i
$96$	−12.4678	−	4.72840i	−1.27249	−	0.482591i
$97$	−8.33676	+	11.0942i	−0.846469	+	1.12645i	0.144118	+	0.989561i	$0.453966\pi$
$97$	−8.33676	+	11.0942i	−0.846469	+	1.12645i	−0.990587	+	0.136885i	$0.956291\pi$
$98$	4.07341	−	1.93286i	0.411477	−	0.195248i
$99$			1.12270i			0.112835i
$100$	−0.457381	−	0.963910i	−0.0457381	−	0.0963910i
$101$	−11.5163	−	11.9897i	−1.14591	−	1.19302i	−0.978306	−	0.207165i	$-0.933576\pi$
$101$	−11.5163	−	11.9897i	−1.14591	−	1.19302i	−0.167604	−	0.985854i	$-0.553603\pi$
$102$	6.83552	+	1.39548i	0.676817	+	0.138173i
$103$	4.79712	−	6.94983i	0.472675	−	0.684787i	−0.512040	−	0.858961i	$-0.671110\pi$
$103$	4.79712	−	6.94983i	0.472675	−	0.684787i	0.984715	+	0.174174i	$0.0557255\pi$
$104$	−10.1546	+	3.31350i	−0.995740	+	0.324916i
$105$	2.21530	+	3.20941i	0.216191	+	0.313207i
$106$	5.03624	+	11.8205i	0.489163	+	1.14811i
$107$	−13.8427	+	10.4021i	−1.33822	+	1.00561i	−0.340358	+	0.940296i	$0.610548\pi$
$107$	−13.8427	+	10.4021i	−1.33822	+	1.00561i	−0.997865	+	0.0653138i	$0.979195\pi$
$108$	0.0570785	−	1.41639i	0.00549238	−	0.136292i
$109$	3.48392	+	14.1348i	0.333699	+	1.35387i	0.862900	+	0.505375i	$0.168646\pi$
$109$	3.48392	+	14.1348i	0.333699	+	1.35387i	−0.529200	+	0.848497i	$0.677508\pi$
$110$	−0.120751	+	0.283412i	−0.0115131	+	0.0270223i
$111$	−10.9795	+	2.24148i	−1.04213	+	0.212752i
$112$	0.914802	+	0.631442i	0.0864407	+	0.0596657i
$113$	−3.42339	+	0.276365i	−0.322045	+	0.0259982i	−0.240432	−	0.970666i	$-0.577289\pi$
$113$	−3.42339	+	0.276365i	−0.322045	+	0.0259982i	−0.0816131	+	0.996664i	$0.526007\pi$
$114$	−0.350010	−	1.20838i	−0.0327815	−	0.113175i
$115$	1.23750	+	1.64681i	0.115397	+	0.153566i
$116$	6.58647	+	3.45684i	0.611538	+	0.320960i
$117$	−7.55583	−	10.1987i	−0.698537	−	0.942871i
$118$	6.13652	−	3.22069i	0.564912	−	0.296489i
$119$	3.90256	+	1.85179i	0.357747	+	0.169753i
$120$	3.24296	−	6.83440i	0.296041	−	0.623893i
$121$	10.3374	−	3.45114i	0.939766	−	0.313740i
$122$	−2.00323	+	2.26118i	−0.181364	+	0.204718i
$123$	−2.03241	+	12.5059i	−0.183256	+	1.12762i
$124$	7.21256	+	0.290656i	0.647707	+	0.0261017i
$125$	0.935016	−	0.354605i	0.0836304	−	0.0317168i
$126$	−1.44486	+	4.98823i	−0.128718	+	0.444387i
$127$	−0.268455	+	1.31498i	−0.0238216	+	0.116686i	−0.989963	−	0.141328i	$-0.954863\pi$
$127$	−0.268455	+	1.31498i	−0.0238216	+	0.116686i	0.966141	+	0.258014i	$0.0830679\pi$
$128$	−0.335168	+	4.15181i	−0.0296250	+	0.366971i
$129$	3.74121	−	9.86476i	0.329395	−	0.868544i
$130$	−0.810471	−	3.38721i	−0.0710830	−	0.297078i
$131$	−5.08394	−	13.4052i	−0.444186	−	1.17122i	−0.951007	−	0.309170i	$-0.899949\pi$
$131$	−5.08394	−	13.4052i	−0.444186	−	1.17122i	0.506821	−	0.862051i	$-0.330820\pi$
$132$	0.834551	−	0.241731i	0.0726384	−	0.0210400i
$133$	−0.0313647	−	0.778307i	−0.00271966	−	0.0674878i
$134$	−5.52675	−	6.76904i	−0.477439	−	0.584756i
$135$	1.31894	+	0.160148i	0.113516	+	0.0137834i
$136$	−0.674252	−	8.35210i	−0.0578166	−	0.716187i
$137$	2.83883	+	0.822278i	0.242538	+	0.0702520i	0.397260	−	0.917706i	$-0.369961\pi$
$137$	2.83883	+	0.822278i	0.242538	+	0.0702520i	−0.154722	+	0.987958i	$0.549448\pi$
$138$	−1.21597	+	4.93337i	−0.103510	+	0.419956i
$139$	−5.65044	−	4.24603i	−0.479264	−	0.360144i	0.333487	−	0.942755i	$-0.391775\pi$
$139$	−5.65044	−	4.24603i	−0.479264	−	0.360144i	−0.812751	+	0.582611i	$0.802031\pi$
$140$	1.03052	−	1.26215i	0.0870946	−	0.106672i
$141$	−3.11960	+	2.99641i	−0.262717	+	0.252343i
$142$	5.01361	+	1.23574i	0.420733	+	0.103701i
$143$	0.659629	−	0.941868i	0.0551609	−	0.0787630i
$144$	2.48777	−	0.613181i	0.207314	−	0.0510984i
$145$	−3.72626	+	5.89261i	−0.309449	+	0.489355i
$146$	0.652247	+	1.12972i	0.0539803	+	0.0934967i
$147$	5.95936	−	10.3219i	0.491519	−	0.851337i
$148$	2.17591	+	4.14585i	0.178859	+	0.340787i
$149$	0.174570	+	0.522900i	0.0143013	+	0.0428377i	0.955445	−	0.295168i	$-0.0953758\pi$
$149$	0.174570	+	0.522900i	0.0143013	+	0.0428377i	−0.941144	+	0.338006i	$0.890248\pi$
$150$	2.13611	+	1.23329i	0.174413	+	0.100697i
$151$	−5.45174	−	6.15375i	−0.443657	−	0.500785i	0.483560	−	0.875311i	$-0.339344\pi$
$151$	−5.45174	−	6.15375i	−0.443657	−	0.500785i	−0.927216	+	0.374527i	$0.877805\pi$
$152$	−1.27708	+	0.807579i	−0.103585	+	0.0655033i
$153$	9.16019	−	3.90279i	0.740558	−	0.315522i
$154$	−0.470098	+	0.0189443i	−0.0378816	+	0.00152657i
$155$	−0.815509	+	6.71632i	−0.0655033	+	0.539468i
$156$	−5.95429	+	7.81249i	−0.476725	+	0.625500i
$157$	−0.279319	−	2.30040i	−0.0222921	−	0.183592i	0.977310	−	0.211816i	$-0.0679378\pi$
$157$	−0.279319	−	2.30040i	−0.0222921	−	0.183592i	−0.999602	+	0.0282243i	$0.991015\pi$
$158$	0.488168	+	3.00382i	0.0388366	+	0.238971i
$159$	28.7069	+	18.1532i	2.27661	+	1.43964i
$160$	−5.15436	−	0.837665i	−0.407488	−	0.0662232i
$161$	−1.46201	+	2.78563i	−0.115223	+	0.219539i
$162$	−3.70081	−	5.85236i	−0.290763	−	0.459805i
$163$	1.78269	+	1.71230i	0.139631	+	0.134117i	0.759286	−	0.650757i	$-0.225548\pi$
$163$	1.78269	+	1.71230i	0.139631	+	0.134117i	−0.619655	+	0.784874i	$0.712728\pi$
$164$	5.25528	−	0.638107i	0.410369	−	0.0498278i
$165$	0.162893	+	0.797901i	0.0126812	+	0.0621165i
$166$	−3.25717	−	0.262946i	−0.252806	−	0.0204086i
$167$	5.46529	+	4.46227i	0.422917	+	0.345301i	0.819882	−	0.572533i	$-0.194039\pi$
$167$	5.46529	+	4.46227i	0.422917	+	0.345301i	−0.396965	+	0.917834i	$0.629937\pi$
$168$	11.5530			0.891337
$169$	0.346698	+	12.9954i	0.0266690	+	0.999644i
$170$	2.73215			0.209546
$171$	−1.39080	−	1.13555i	−0.106357	−	0.0868380i
$172$	−4.39394	−	0.354716i	−0.335035	−	0.0270468i
$173$	−4.86448	−	23.8278i	−0.369839	−	1.81159i	−0.558447	−	0.829540i	$-0.688602\pi$
$173$	−4.86448	−	23.8278i	−0.369839	−	1.81159i	0.188607	−	0.982053i	$-0.439603\pi$
$174$	−17.0714	+	2.07284i	−1.29418	+	0.157142i
$175$	1.10143	+	1.05794i	0.0832604	+	0.0799727i
$176$	0.124061	+	0.196187i	0.00935148	+	0.0147882i
$177$	8.51382	−	16.2217i	0.639938	−	1.21930i
$178$	0.184646	+	0.0300078i	0.0138398	+	0.00224918i
$179$	−10.4795	−	6.62683i	−0.783274	−	0.495312i	0.0819875	−	0.996633i	$-0.473873\pi$
$179$	−10.4795	−	6.62683i	−0.783274	−	0.495312i	−0.865261	+	0.501321i	$0.832848\pi$
$180$	−0.602488	−	3.70726i	−0.0449068	−	0.276323i
$181$	1.73903	+	14.3222i	0.129261	+	1.06456i	0.902574	+	0.430534i	$0.141675\pi$
$181$	1.73903	+	14.3222i	0.129261	+	1.06456i	−0.773314	+	0.634024i	$0.781402\pi$
$182$	4.14292	−	3.33588i	0.307094	−	0.247272i
$183$	−0.962569	+	7.92747i	−0.0711551	+	0.586015i
$184$	6.09770	−	0.245729i	0.449529	−	0.0181154i
$185$	−4.03731	+	1.72014i	−0.296829	+	0.126467i
$186$	−14.1045	+	8.91914i	−1.03419	+	0.653983i
$187$	0.598163	+	0.675187i	0.0437420	+	0.0493745i
$188$	1.56520	+	0.903668i	0.114154	+	0.0659067i
$189$	0.642550	+	1.92467i	0.0467386	+	0.139999i
$190$	−0.228958	−	0.436244i	−0.0166104	−	0.0316485i
$191$	−1.36678	+	2.36733i	−0.0988967	+	0.171294i	−0.911228	−	0.411902i	$-0.864865\pi$
$191$	−1.36678	+	2.36733i	−0.0988967	+	0.171294i	0.812332	+	0.583196i	$0.198198\pi$
$192$	−8.29873	−	14.3738i	−0.598909	−	1.03734i
$193$	4.94638	−	7.82208i	0.356048	−	0.563045i	−0.618902	−	0.785468i	$-0.712422\pi$
$193$	4.94638	−	7.82208i	0.356048	−	0.563045i	0.974950	+	0.222423i	$0.0713965\pi$
$194$	−13.0155	+	3.20804i	−0.934460	+	0.230324i
$195$	−6.84966	−	6.15194i	−0.490514	−	0.440549i
$196$	−4.83526	−	1.19179i	−0.345376	−	0.0851275i
$197$	13.3348	−	12.8083i	0.950066	−	0.912551i	−0.0461963	−	0.998932i	$-0.514710\pi$
$197$	13.3348	−	12.8083i	0.950066	−	0.912551i	0.996262	+	0.0863818i	$0.0275305\pi$
$198$	−0.685876	+	0.840045i	−0.0487431	+	0.0596994i
$199$	4.47795	+	3.36496i	0.317434	+	0.238536i	0.747501	−	0.664261i	$-0.231254\pi$
$199$	4.47795	+	3.36496i	0.317434	+	0.238536i	−0.430067	+	0.902797i	$0.641510\pi$
$200$	0.708978	−	2.87644i	0.0501323	−	0.203395i
$201$	−22.1885	−	6.42697i	−1.56505	−	0.453324i
$202$	−1.29219	−	16.0066i	−0.0909180	−	1.12622i
$203$	−10.5700	−	1.28343i	−0.741869	−	0.0900793i
$204$	−4.87342	−	5.96886i	−0.341208	−	0.417904i
$205$	0.199793	+	4.95781i	0.0139541	+	0.346268i
$206$	7.83516	−	2.26948i	0.545902	−	0.158122i
$207$	2.57148	+	6.78044i	0.178730	+	0.471273i
$208$	−2.44734	−	0.947246i	−0.169693	−	0.0656797i
$209$	0.0576805	−	0.152091i	0.00398984	−	0.0105203i
$210$	−0.303116	+	3.75477i	−0.0209170	+	0.259104i
$211$	5.30744	−	25.9975i	0.365379	−	1.78974i	−0.216301	−	0.976327i	$-0.569399\pi$
$211$	5.30744	−	25.9975i	0.365379	−	1.78974i	0.581680	−	0.813418i	$-0.302396\pi$
$212$	3.94834	−	13.6312i	0.271173	−	0.936198i
$213$	12.7630	−	4.84036i	0.874505	−	0.331656i
$214$	−16.7124	−	0.673489i	−1.14244	−	0.0460387i
$215$	0.662778	−	4.07824i	0.0452011	−	0.278133i
$216$	2.61011	−	2.94620i	0.177595	−	0.200464i
$217$	−9.80085	+	3.27200i	−0.665325	+	0.222118i
$218$	−6.02841	+	12.7046i	−0.408296	+	0.860465i
$219$	3.11545	+	1.47830i	0.210523	+	0.0998943i
$220$	0.301287	−	0.158128i	0.0203128	−	0.0106610i
$221$	−9.97783	−	2.10779i	−0.671181	−	0.141785i
$222$	−9.58462	−	5.03040i	−0.643278	−	0.337618i
$223$	0.761711	+	1.01365i	0.0510079	+	0.0678792i	0.824226	−	0.566261i	$-0.191611\pi$
$223$	0.761711	+	1.01365i	0.0510079	+	0.0678792i	−0.773218	+	0.634140i	$0.781354\pi$
$224$	−2.21881	−	7.66022i	−0.148250	−	0.511820i
$225$	3.50890	−	0.283268i	0.233927	−	0.0188845i
$226$	−2.73035	−	1.88462i	−0.181620	−	0.125363i
$227$	3.05863	−	0.624424i	0.203008	−	0.0414445i	−0.0974452	−	0.995241i	$-0.531067\pi$
$227$	3.05863	−	0.624424i	0.203008	−	0.0414445i	0.300454	+	0.953796i	$0.402862\pi$
$228$	−0.544651	+	1.27834i	−0.0360704	+	0.0846604i
$229$	0.172597	+	0.700252i	0.0114055	+	0.0462740i	0.976369	−	0.216111i	$-0.0693372\pi$
$229$	0.172597	+	0.700252i	0.0114055	+	0.0462740i	−0.964963	+	0.262385i	$0.915491\pi$
$230$	−0.0801224	+	1.98822i	−0.00528312	+	0.131099i
$231$	−0.994267	+	0.747143i	−0.0654180	+	0.0491584i
$232$	8.09588	+	19.0017i	0.531521	+	1.24753i
$233$	1.44779	+	2.09748i	0.0948478	+	0.137411i	0.867535	−	0.497376i	$-0.165703\pi$
$233$	1.44779	+	2.09748i	0.0948478	+	0.137411i	−0.772687	+	0.634787i	$0.781088\pi$
$234$	0.577007	−	12.2470i	0.0377201	−	0.800614i
$235$	−0.962287	+	1.39411i	−0.0627727	+	0.0909419i
$236$	−7.50000	−	1.53114i	−0.488208	−	0.0996684i
$237$	5.57275	+	5.80185i	0.361989	+	0.376871i
$238$	1.78875	+	3.76971i	0.115948	+	0.244354i
$239$		−	3.29263i		−	0.212983i	−0.994314	−	0.106491i	$-0.966038\pi$
$239$		−	3.29263i		−	0.212983i	0.994314	−	0.106491i	$-0.0339616\pi$
$240$	1.67909	−	0.796739i	0.108385	−	0.0514293i
$241$	−13.4595	+	17.9113i	−0.867000	+	1.15377i	0.119956	+	0.992779i	$0.461725\pi$
$241$	−13.4595	+	17.9113i	−0.867000	+	1.15377i	−0.986956	+	0.160989i	$0.948532\pi$
$242$	9.84321	+	3.73304i	0.632746	+	0.239969i
$243$	−20.5064	−	8.73698i	−1.31549	−	0.560478i
$244$	3.29344	−	0.535236i	0.210841	−	0.0342650i
$245$	1.47808	−	4.42740i	0.0944313	−	0.282856i
$246$	−9.16081	+	8.11577i	−0.584072	+	0.517443i
$247$	0.499606	+	1.76980i	0.0317892	+	0.112610i
$248$	15.0027	+	13.2912i	0.952672	+	0.843994i
$249$	−7.48096	+	4.31913i	−0.474087	+	0.273714i
$250$	0.916249	+	0.305889i	0.0579487	+	0.0193461i
$251$	13.7766	−	14.3430i	0.869572	−	0.905321i	−0.126669	−	0.991945i	$-0.540429\pi$
$251$	13.7766	−	14.3430i	0.869572	−	0.905321i	0.996241	+	0.0866244i	$0.0276080\pi$
$252$	4.72069	−	3.25846i	0.297375	−	0.205263i
$253$	−0.508883	+	0.415490i	−0.0319932	+	0.0261217i
$254$	−1.00421	+	0.819915i	−0.0630099	+	0.0514460i
$255$	5.94388	−	4.10277i	0.372220	−	0.256925i
$256$	−11.7925	+	12.2773i	−0.737030	+	0.767330i
$257$	3.86508	+	1.29035i	0.241097	+	0.0804900i	0.434649	−	0.900600i	$-0.356873\pi$
$257$	3.86508	+	1.29035i	0.241097	+	0.0804900i	−0.193552	+	0.981090i	$0.562001\pi$
$258$	8.82587	−	5.09562i	0.549475	−	0.317239i
$259$	−5.01664	−	4.44435i	−0.311719	−	0.276159i
$260$	−1.67271	+	3.46413i	−0.103737	+	0.214836i
$261$	−18.3710	+	16.2753i	−1.13714	+	1.00742i
$262$	4.38550	−	13.1362i	0.270937	−	0.811555i
$263$	22.6627	−	3.68304i	1.39744	−	0.227106i	0.585418	−	0.810732i	$-0.300931\pi$
$263$	22.6627	−	3.68304i	1.39744	−	0.227106i	0.812023	+	0.583626i	$0.198366\pi$
$264$	2.21950	+	0.945641i	0.136601	+	0.0582002i
$265$	12.4370	+	4.71675i	0.764001	+	0.289747i
$266$	0.452013	−	0.601520i	0.0277147	−	0.0368815i
$267$	0.446765	−	0.211993i	0.0273416	−	0.0129737i
$268$			9.65205i			0.589593i
$269$	−7.44643	−	15.6930i	−0.454017	−	0.956820i	−0.993394	−	0.114755i	$-0.963392\pi$
$269$	−7.44643	−	15.6930i	−0.454017	−	0.956820i	0.539377	−	0.842064i	$-0.318660\pi$
$270$	0.889042	+	0.925591i	0.0541054	+	0.0563297i
$271$	21.3296	+	4.35448i	1.29568	+	0.264516i	0.797902	−	0.602787i	$-0.205943\pi$
$271$	21.3296	+	4.35448i	1.29568	+	0.264516i	0.497781	+	0.867303i	$0.334148\pi$
$272$	1.16944	−	1.69423i	0.0709078	−	0.102728i
$273$	4.00370	−	13.4786i	0.242315	−	0.815763i
$274$	1.62178	+	2.34955i	0.0979752	+	0.141942i
$275$	0.125006	+	0.293399i	0.00753813	+	0.0176927i
$276$	4.48653	−	3.37141i	0.270057	−	0.202935i
$277$	0.509861	−	12.6521i	0.0306346	−	0.760189i	−0.908753	−	0.417333i	$-0.862965\pi$
$277$	0.509861	−	12.6521i	0.0306346	−	0.760189i	0.939388	−	0.342856i	$-0.111394\pi$
$278$	−1.63390	−	6.62900i	−0.0979949	−	0.397581i
$279$	−9.33556	+	21.9114i	−0.558905	+	1.31180i
$280$	4.43298	−	0.904998i	0.264921	−	0.0540840i
$281$	−19.0641	−	13.1590i	−1.13727	−	0.784999i	−0.157974	−	0.987443i	$-0.550496\pi$
$281$	−19.0641	−	13.1590i	−1.13727	−	0.784999i	−0.979294	+	0.202444i	$0.935112\pi$
$282$	−4.16476	+	0.336214i	−0.248008	+	0.0200213i
$283$	4.54451	+	15.6895i	0.270143	+	0.932642i	0.974798	+	0.223091i	$0.0716149\pi$
$283$	4.54451	+	15.6895i	0.270143	+	0.932642i	−0.704654	+	0.709551i	$0.748898\pi$
$284$	−3.42625	−	4.55951i	−0.203310	−	0.270557i
$285$	−1.15320	−	0.605246i	−0.0683096	−	0.0358517i
$286$	1.06896	−	0.301763i	0.0632091	−	0.0178436i
$287$	−6.70980	+	3.52157i	−0.396067	+	0.207872i
$288$	−16.6082	−	7.88067i	−0.978645	−	0.464373i
$289$	−3.85824	+	8.13107i	−0.226955	+	0.478298i
$290$	−6.38803	+	2.13264i	−0.375118	+	0.125233i
$291$	−23.4983	+	26.5241i	−1.37750	+	1.55487i
$292$	0.231126	−	1.42218i	0.0135257	−	0.0832267i
$293$	−5.20695	−	0.209833i	−0.304193	−	0.0122586i	−0.112300	−	0.993674i	$-0.535822\pi$
$293$	−5.20695	−	0.209833i	−0.304193	−	0.0122586i	−0.191893	+	0.981416i	$0.561463\pi$
$294$	10.7648	−	4.08257i	0.627819	−	0.238100i
$295$	1.99609	−	6.89130i	0.116217	−	0.401227i
$296$	−2.60053	+	12.7382i	−0.151153	+	0.740395i
$297$	−0.0340957	+	0.422351i	−0.00197843	+	0.0245073i
$298$	−0.188829	+	0.497902i	−0.0109386	+	0.0288427i
$299$	1.82647	−	7.19918i	0.105628	−	0.416339i
$300$	−0.966076	−	2.54733i	−0.0557764	−	0.147070i
$301$	6.06092	−	1.75557i	0.349346	−	0.101189i
$302$	−0.319771	−	7.93503i	−0.0184007	−	0.456610i
$303$	−26.8478	−	32.8826i	−1.54236	−	1.88905i
$304$	−0.368520	−	0.0447464i	−0.0211361	−	0.00256638i
$305$	0.251648	+	3.11722i	0.0144093	+	0.178492i
$306$	9.23828	+	2.67590i	0.528118	+	0.152971i
$307$	−2.88828	+	11.7182i	−0.164843	+	0.668793i	0.829120	+	0.559071i	$0.188842\pi$
$307$	−2.88828	+	11.7182i	−0.164843	+	0.668793i	−0.993962	+	0.109722i	$0.965004\pi$
$308$	0.415433	+	0.312177i	0.0236715	+	0.0177880i
$309$	13.6377	−	16.7031i	0.775820	−	0.950208i
$310$	−4.71331	+	4.52720i	−0.267698	+	0.257127i
$311$	−2.29409	−	0.565442i	−0.130086	−	0.0320633i	0.173735	−	0.984792i	$-0.444416\pi$
$311$	−2.29409	−	0.565442i	−0.130086	−	0.0320633i	−0.303821	+	0.952729i	$0.598262\pi$
$312$	−26.5264	+	6.34709i	−1.50176	+	0.359333i
$313$	20.9153	−	5.15517i	1.18220	−	0.291387i	0.401246	−	0.915970i	$-0.368577\pi$
$313$	20.9153	−	5.15517i	1.18220	−	0.291387i	0.780958	+	0.624583i	$0.214731\pi$
$314$	1.19636	−	1.89189i	0.0675143	−	0.106765i
$315$	2.68814	+	4.65600i	0.151460	+	0.262336i
$316$	1.68065	−	2.91097i	0.0945439	−	0.163755i
$317$	12.8715	+	24.5245i	0.722934	+	1.37743i	0.917974	+	0.396640i	$0.129824\pi$
$317$	12.8715	+	24.5245i	0.722934	+	1.37743i	−0.195041	+	0.980795i	$0.562484\pi$
$318$	10.3895	+	31.1204i	0.582616	+	1.74515i
$319$	−1.92560	−	1.11174i	−0.107813	−	0.0622457i
$320$	−4.31024	−	4.86525i	−0.240950	−	0.271976i
$321$	−37.3699	+	23.6313i	−2.08578	+	1.31897i
$322$	−2.79573	+	1.19115i	−0.155800	+	0.0663800i
$323$	−1.44144	+	0.0580879i	−0.0802036	+	0.00323210i
$324$	−0.921868	+	7.59226i	−0.0512149	+	0.421792i
$325$	−3.11016	−	1.82397i	−0.172521	−	0.101176i
$326$	0.287804	+	2.37028i	0.0159400	+	0.131278i
$327$	5.96303	+	36.6920i	0.329756	+	2.02907i
$328$	12.4239	+	7.85641i	0.685996	+	0.433797i
$329$	−2.55356	−	0.414994i	−0.140782	−	0.0228794i
$330$	−0.365569	+	0.696533i	−0.0201239	+	0.0383429i
$331$	−7.14257	−	11.2951i	−0.392591	−	0.620833i	0.589826	−	0.807530i	$-0.299196\pi$
$331$	−7.14257	−	11.2951i	−0.392591	−	0.620833i	−0.982418	+	0.186697i	$0.940222\pi$
$332$	2.60304	+	2.50026i	0.142861	+	0.137219i
$333$	−15.3362	+	1.86215i	−0.840419	+	0.102045i
$334$	1.36326	+	6.67768i	0.0745942	+	0.365386i
$335$	−9.01731	−	0.727953i	−0.492668	−	0.0397723i
$336$	2.19862	+	1.79512i	0.119945	+	0.0979318i
$337$	15.7539			0.858170			0.429085	−	0.903264i	$-0.358836\pi$
$337$	15.7539			0.858170			0.429085	+	0.903264i	$0.358836\pi$
$338$	−7.67969	+	9.93543i	−0.417720	+	0.540416i
$339$	−8.77003			−0.476323
$340$	−2.33753	−	1.90853i	−0.126770	−	0.103505i
$341$	−2.15070	−	0.173623i	−0.116467	−	0.00940219i
$342$	−0.346920	−	1.69933i	−0.0187593	−	0.0918892i
$343$	17.6890	−	2.14784i	0.955118	−	0.115972i
$344$	−8.82779	−	8.47921i	−0.475963	−	0.457168i
$345$	2.81133	+	4.44576i	0.151357	+	0.239351i
$346$	10.9170	−	20.8006i	0.586903	−	1.11825i
$347$	−27.2110	−	4.42222i	−1.46076	−	0.237397i	−0.622482	−	0.782634i	$-0.713876\pi$
$347$	−27.2110	−	4.42222i	−1.46076	−	0.237397i	−0.838282	+	0.545237i	$0.816440\pi$
$348$	16.0537	+	10.1517i	0.860567	+	0.544189i
$349$	4.20059	+	25.8472i	0.224852	+	1.38357i	0.816486	+	0.577365i	$0.195919\pi$
$349$	4.20059	+	25.8472i	0.224852	+	1.38357i	−0.591634	+	0.806207i	$0.701517\pi$
$350$	0.177819	+	1.46447i	0.00950484	+	0.0782794i
$351$	−2.53272	−	4.06614i	−0.135187	−	0.217035i
$352$	0.200741	−	1.65325i	0.0106995	−	0.0881185i
$353$	22.1336	−	0.891954i	1.17805	−	0.0474739i	0.556502	−	0.830847i	$-0.312143\pi$
$353$	22.1336	−	0.891954i	1.17805	−	0.0474739i	0.621552	+	0.783373i	$0.286502\pi$
$354$	16.2805	−	6.93647i	0.865298	−	0.368669i
$355$	4.51807	−	2.85705i	0.239794	−	0.151637i
$356$	−0.137014	−	0.154657i	−0.00726175	−	0.00819682i
$357$	9.55234	+	5.51505i	0.505563	+	0.291887i
$358$	−3.79271	−	11.3605i	−0.200451	−	0.600423i
$359$	−8.44315	−	16.0871i	−0.445612	−	0.849043i	−0.999861	−	0.0166919i	$-0.994687\pi$
$359$	−8.44315	−	16.0871i	−0.445612	−	0.849043i	0.554248	−	0.832351i	$-0.313006\pi$
$360$	5.21451	−	9.03180i	0.274829	−	0.476018i
$361$	−9.36993	−	16.2292i	−0.493154	−	0.854168i
$362$	−7.44845	+	11.7788i	−0.391482	+	0.619079i
$363$	27.0200	−	6.65984i	1.41818	−	0.349551i
$364$	−5.87481	−	0.0399629i	−0.307924	−	0.00209463i
$365$	1.31122	+	0.323187i	0.0686324	+	0.0169164i
$366$	−5.56326	+	5.34358i	−0.290796	+	0.279313i
$367$	3.55952	−	4.35962i	0.185806	−	0.227570i	−0.673299	−	0.739370i	$-0.735123\pi$
$367$	3.55952	−	4.35962i	0.185806	−	0.227570i	0.859105	+	0.511799i	$0.171021\pi$
$368$	1.19862	+	0.900701i	0.0624822	+	0.0469523i
$369$	−4.18018	+	16.9597i	−0.217612	+	0.882885i
$370$	−4.07173	−	1.17939i	−0.211679	−	0.0613136i
$371$	1.63461	+	20.2482i	0.0848646	+	1.05124i
$372$	18.2978	+	2.22175i	0.948695	+	0.115192i
$373$	0.0482934	+	0.0591487i	0.00250054	+	0.00306260i	0.775854	−	0.630913i	$-0.217319\pi$
$373$	0.0482934	+	0.0591487i	0.00250054	+	0.00306260i	−0.773353	+	0.633975i	$0.781422\pi$
$374$	0.0350851	+	0.870628i	0.00181421	+	0.0450191i
$375$	2.45267	−	0.710426i	0.126656	−	0.0366862i
$376$	1.77956	+	4.69232i	0.0917739	+	0.241988i
$377$	24.9744	−	2.86020i	1.28625	−	0.147308i
$378$	−0.695035	+	1.83266i	−0.0357488	+	0.0942617i
$379$	−1.20309	+	14.9030i	−0.0617987	+	0.765514i	0.889439	+	0.457054i	$0.151096\pi$
$379$	−1.20309	+	14.9030i	−0.0617987	+	0.765514i	−0.951237	+	0.308460i	$0.900187\pi$
$380$	−0.108848	+	0.533173i	−0.00558379	+	0.0273512i
$381$	−0.953466	+	3.29175i	−0.0488475	+	0.168641i
$382$	−2.46892	+	0.936338i	−0.126321	+	0.0479072i
$383$	−9.02940	−	0.363872i	−0.461381	−	0.0185930i	−0.191512	−	0.981490i	$-0.561339\pi$
$383$	−9.02940	−	0.363872i	−0.461381	−	0.0185930i	−0.269868	+	0.962897i	$0.586980\pi$
$384$	−1.70615	+	10.4984i	−0.0870665	+	0.535742i
$385$	−0.322980	+	0.364569i	−0.0164606	+	0.0185801i
$386$	8.47971	−	2.83094i	0.431606	−	0.144091i
$387$	6.23535	−	13.1407i	0.316961	−	0.667980i
$388$	13.3766	+	6.34727i	0.679093	+	0.322234i
$389$	2.72638	−	1.43092i	0.138233	−	0.0725503i	−0.394189	−	0.919030i	$-0.628974\pi$
$389$	2.72638	−	1.43092i	0.138233	−	0.0725503i	0.532422	+	0.846479i	$0.321282\pi$
$390$	−1.36685	−	8.78768i	−0.0692131	−	0.444982i
$391$	5.15904	+	2.70767i	0.260904	+	0.136933i
$392$	−8.30702	−	11.0546i	−0.419568	−	0.558343i
$393$	−10.1853	−	35.1638i	−0.513781	−	1.77378i
$394$	17.8024	−	1.43716i	0.896872	−	0.0724030i
$395$	2.59278	+	1.78967i	0.130457	+	0.0900480i
$396$	1.17362	−	0.239597i	0.0589767	−	0.0120402i
$397$	2.52267	−	5.92093i	0.126609	−	0.297163i	−0.844597	−	0.535402i	$-0.820160\pi$
$397$	2.52267	−	5.92093i	0.126609	−	0.297163i	0.971206	+	0.238239i	$0.0765702\pi$
$398$	1.29486	+	5.25345i	0.0649055	+	0.263332i
$399$	0.0800895	−	1.98740i	0.00400949	−	0.0994944i
$400$	0.581866	−	0.437244i	0.0290933	−	0.0218622i
$401$	−6.81010	−	15.9839i	−0.340080	−	0.798197i	−0.998944	−	0.0459356i	$-0.985373\pi$
$401$	−6.81010	−	15.9839i	−0.340080	−	0.798197i	0.658864	−	0.752262i	$-0.271037\pi$
$402$	−12.6759	−	18.3642i	−0.632217	−	0.915924i
$403$	20.7057	−	12.8972i	1.03142	−	0.642453i
$404$	−10.0758	+	14.5974i	−0.501291	+	0.726246i
$405$	−7.02345	−	1.43385i	−0.348998	−	0.0712485i
$406$	−7.12481	−	7.41771i	−0.353598	−	0.368135i
$407$	−0.599986	−	1.26444i	−0.0297402	−	0.0626762i
$408$		−	21.3964i		−	1.05928i
$409$	28.9646	−	13.7439i	1.43221	−	0.679591i	0.454729	−	0.890630i	$-0.349736\pi$
$409$	28.9646	−	13.7439i	1.43221	−	0.679591i	0.977478	+	0.211039i	$0.0676847\pi$
$410$	−2.87932	+	3.83168i	−0.142199	+	0.189233i
$411$	7.05648	+	2.67617i	0.348070	+	0.132006i
$412$	−8.28883	−	3.53154i	−0.408361	−	0.173987i
$413$	10.8152	−	1.75764i	0.532182	−	0.0864880i
$414$	−2.21821	+	6.64434i	−0.109019	+	0.326552i
$415$	−2.53216	+	2.24329i	−0.124299	+	0.110119i
$416$	9.30293	+	16.3693i	0.456114	+	0.802571i
$417$	−13.5091	−	11.9681i	−0.661545	−	0.586078i
$418$	0.136074	−	0.0785622i	0.00665558	−	0.00384260i
$419$	27.9577	+	9.33366i	1.36582	+	0.455979i	0.902683	−	0.430306i	$-0.141594\pi$
$419$	27.9577	+	9.33366i	1.36582	+	0.455979i	0.463141	+	0.886285i	$0.346723\pi$
$420$	2.88222	−	3.00071i	0.140638	−	0.146420i
$421$	−2.32442	+	1.60443i	−0.113286	+	0.0781954i	−0.623360	−	0.781935i	$-0.714233\pi$
$421$	−2.32442	+	1.60443i	−0.113286	+	0.0781954i	0.510075	+	0.860130i	$0.329618\pi$
$422$	19.8536	−	16.2099i	0.966457	−	0.789087i
$423$	−4.61922	+	3.77148i	−0.224594	+	0.183376i
$424$	32.4303	−	22.3850i	1.57495	−	1.08711i
$425$	1.95932	−	2.03987i	0.0950409	−	0.0989481i
$426$	12.5068	+	4.17538i	0.605956	+	0.202298i
$427$	−4.13627	+	2.38808i	−0.200168	+	0.115567i
$428$	13.8281	+	12.2506i	0.668407	+	0.592157i
$429$	1.87242	−	2.26172i	0.0904013	−	0.109197i
$430$	2.98738	−	2.64659i	0.144064	−	0.127630i
$431$	5.62475	−	16.8482i	0.270934	−	0.811548i	−0.721894	−	0.692003i	$-0.756728\pi$
$431$	5.62475	−	16.8482i	0.270934	−	0.811548i	0.992829	−	0.119545i	$-0.0381434\pi$
$432$	0.954504	−	0.155122i	0.0459236	−	0.00746331i
$433$	8.16523	+	3.47888i	0.392396	+	0.167184i	0.579147	−	0.815223i	$-0.303386\pi$
$433$	8.16523	+	3.47888i	0.392396	+	0.167184i	−0.186751	+	0.982407i	$0.559796\pi$
$434$	−9.33229	−	3.53927i	−0.447964	−	0.169890i
$435$	−10.6949	+	14.2323i	−0.512780	+	0.682387i
$436$	14.0325	−	6.65849i	0.672033	−	0.318884i
$437$		−	1.05065i		−	0.0502596i
$438$	1.42798	+	3.00941i	0.0682315	+	0.143795i
$439$	13.8075	+	14.3751i	0.658997	+	0.686088i	0.963891	−	0.266298i	$-0.0858005\pi$
$439$	13.8075	+	14.3751i	0.658997	+	0.686088i	−0.304894	+	0.952386i	$0.598621\pi$
$440$	0.925713	+	0.188986i	0.0441316	+	0.00900954i
$441$	9.33415	−	13.5228i	0.444483	−	0.643945i
$442$	−6.17810	−	7.67275i	−0.293862	−	0.364956i
$443$	10.4507	+	15.1405i	0.496528	+	0.719345i	0.988492	−	0.151270i	$-0.0483363\pi$
$443$	10.4507	+	15.1405i	0.496528	+	0.719345i	−0.491964	+	0.870615i	$0.663721\pi$
$444$	4.68630	+	10.9991i	0.222402	+	0.521996i
$445$	0.154820	−	0.116340i	0.00733918	−	0.00551504i
$446$	−0.0493173	+	1.22380i	−0.00233524	+	0.0579484i
$447$	0.336876	+	1.36676i	0.0159337	+	0.0646456i
$448$	3.89096	−	9.13241i	0.183830	−	0.431466i
$449$	6.48159	−	1.32323i	0.305885	−	0.0624469i	−0.0446312	−	0.999004i	$-0.514211\pi$
$449$	6.48159	−	1.32323i	0.305885	−	0.0624469i	0.350516	+	0.936557i	$0.386006\pi$
$450$	2.79855	+	1.93170i	0.131925	+	0.0910611i
$451$	−1.57729	+	0.127332i	−0.0742719	+	0.00599585i
$452$	1.01949	+	3.51969i	0.0479528	+	0.165552i
$453$	−12.6114	−	16.7828i	−0.592536	−	0.788523i
$454$	2.67005	+	1.40135i	0.125312	+	0.0657687i
$455$	0.480410	−	5.48546i	0.0225220	−	0.257162i
$456$	−3.41638	+	1.79305i	−0.159987	+	0.0839675i
$457$	28.7920	+	13.6620i	1.34683	+	0.639080i	0.959198	−	0.282734i	$-0.0912414\pi$
$457$	28.7920	+	13.6620i	1.34683	+	0.639080i	0.387633	+	0.921814i	$0.373293\pi$
$458$	−0.298653	+	0.629398i	−0.0139551	+	0.0294098i
$459$	3.56452	−	1.19001i	0.166378	−	0.0555450i
$460$	1.45741	−	1.64508i	0.0679523	−	0.0767022i
$461$	−1.04457	+	6.42750i	−0.0486505	+	0.299359i	−0.999961	−	0.00887685i	$-0.997174\pi$
$461$	−1.04457	+	6.42750i	−0.0486505	+	0.299359i	0.951310	+	0.308235i	$0.0997385\pi$
$462$	−1.20039	−	0.0483741i	−0.0558472	−	0.00225057i
$463$	19.3128	−	7.32439i	0.897543	−	0.340393i	0.137680	−	0.990477i	$-0.456035\pi$
$463$	19.3128	−	7.32439i	0.897543	−	0.340393i	0.759863	+	0.650083i	$0.225266\pi$
$464$	−1.41180	+	4.87410i	−0.0655412	+	0.226275i
$465$	−3.45565	+	16.9269i	−0.160252	+	0.784966i
$466$	−0.198099	+	2.45390i	−0.00917676	+	0.113675i
$467$	5.71169	−	15.0605i	0.264305	−	0.696916i	−0.735506	−	0.677518i	$-0.763056\pi$
$467$	5.71169	−	15.0605i	0.264305	−	0.696916i	0.999812	−	0.0193984i	$-0.00617508\pi$
$468$	−9.04881	+	10.0751i	−0.418281	+	0.465721i
$469$	−4.89928	−	12.9183i	−0.226228	−	0.596514i
$470$	−1.57171	+	0.455251i	−0.0724974	+	0.0209991i
$471$	−0.238261	−	5.91239i	−0.0109785	−	0.272429i
$472$	−13.4425	−	16.4641i	−0.618742	−	0.757821i
$473$	1.30809	+	0.158830i	0.0601458	+	0.00730303i
$474$	0.625294	+	7.74565i	0.0287207	+	0.355770i
$475$	−0.489901	−	0.141902i	−0.0224782	−	0.00651089i
$476$	1.10293	−	4.47476i	0.0505527	−	0.205100i
$477$	37.4341	+	28.1299i	1.71399	+	1.28798i
$478$	2.01153	−	2.46367i	0.0920050	−	0.112686i
$479$	−21.0571	+	20.2256i	−0.962123	+	0.924132i	−0.997164	−	0.0752538i	$-0.976023\pi$
$479$	−21.0571	+	20.2256i	−0.962123	+	0.924132i	0.0350410	+	0.999386i	$0.488844\pi$
$480$	−12.9468	−	3.19110i	−0.590939	−	0.145653i
$481$	13.9601	+	7.44840i	0.636527	+	0.339618i
$482$	−21.0132	+	5.17929i	−0.957125	+	0.235910i
$483$	−4.29350	+	6.78963i	−0.195361	+	0.308939i
$484$	−5.81380	−	10.0698i	−0.264264	−	0.457718i
$485$	−6.93871	+	12.0182i	−0.315071	+	0.545718i
$486$	−10.0061	−	19.0651i	−0.453887	−	0.864810i
$487$	10.7713	+	32.2640i	0.488094	+	1.46202i	0.848485	+	0.529219i	$0.177515\pi$
$487$	10.7713	+	32.2640i	0.488094	+	1.46202i	−0.360391	+	0.932801i	$0.617357\pi$
$488$	8.02363	+	4.63244i	0.363212	+	0.209701i
$489$	4.18549	+	4.72445i	0.189275	+	0.213647i
$490$	3.81073	−	2.40976i	0.172151	−	0.108862i
$491$	−18.4923	+	7.87883i	−0.834546	+	0.355567i	−0.766602	−	0.642122i	$-0.778054\pi$
$491$	−18.4923	+	7.87883i	−0.834546	+	0.355567i	−0.0679436	+	0.997689i	$0.521644\pi$
$492$	13.5069	−	0.544310i	0.608939	−	0.0245394i
$493$	−2.37693	+	19.5758i	−0.107052	+	0.881650i
$494$	−0.707379	+	1.62945i	−0.0318265	+	0.0733125i
$495$	0.135326	+	1.11451i	0.00608246	+	0.0500936i
$496$	0.789915	+	4.86054i	0.0354682	+	0.218245i
$497$	6.90006	+	4.36333i	0.309510	+	0.195722i
$498$	−8.23617	−	1.33851i	−0.369072	−	0.0599800i
$499$	−11.8238	+	22.5283i	−0.529305	+	1.00851i	0.463195	+	0.886257i	$0.346703\pi$
$499$	−11.8238	+	22.5283i	−0.529305	+	1.00851i	−0.992499	+	0.122249i	$0.960989\pi$
$500$	−0.570233	−	0.901751i	−0.0255016	−	0.0403275i
$501$	12.9935	+	12.4804i	0.580505	+	0.557582i
$502$	19.0706	−	2.31558i	0.851161	−	0.103350i
$503$	−6.92410	−	33.9165i	−0.308730	−	1.51226i	−0.777468	−	0.628923i	$-0.783496\pi$
$503$	−6.92410	−	33.9165i	−0.308730	−	1.51226i	0.468738	−	0.883337i	$-0.344709\pi$
$504$	15.8757	+	1.28162i	0.707160	+	0.0570879i
$505$	−12.8775	−	10.5141i	−0.573041	−	0.467873i
$506$	−0.634596			−0.0282112
$507$	−1.78775	+	33.1472i	−0.0793968	+	1.47212i
$508$	1.43192			0.0635311
$509$	1.02169	+	0.834182i	0.0452855	+	0.0369745i	0.654818	−	0.755787i	$-0.272745\pi$
$509$	1.02169	+	0.834182i	0.0452855	+	0.0369745i	−0.609532	+	0.792761i	$0.708643\pi$
$510$	6.95389	+	0.561376i	0.307923	+	0.0248581i
$511$	0.412542	+	2.02077i	0.0182498	+	0.0893934i
$512$	−8.05410	+	0.977944i	−0.355944	+	0.0432194i
$513$	−0.488723	−	0.469425i	−0.0215776	−	0.0207256i
$514$	2.10370	+	3.32673i	0.0927901	+	0.146736i
$515$	3.92444	−	7.47739i	0.172931	−	0.329493i
$516$	−11.1106	−	1.80565i	−0.489118	−	0.0794895i
$517$	−0.456607	−	0.288741i	−0.0200815	−	0.0126988i
$518$	−1.03851	−	6.39018i	−0.0456293	−	0.280768i
$519$	−7.48521	−	61.6462i	−0.328564	−	2.70597i
$520$	−9.68116	+	4.51334i	−0.424547	+	0.197923i
$521$	1.33595	−	11.0026i	0.0585291	−	0.482031i	−0.933742	−	0.357945i	$-0.883477\pi$
$521$	1.33595	−	11.0026i	0.0585291	−	0.482031i	0.992272	−	0.124085i	$-0.0395996\pi$
$522$	−23.6888	+	0.954624i	−1.03683	+	0.0417828i
$523$	29.0307	−	12.3688i	1.26942	−	0.540851i	0.350973	−	0.936386i	$-0.385851\pi$
$523$	29.0307	−	12.3688i	1.26942	−	0.540851i	0.918451	+	0.395535i	$0.129441\pi$
$524$	−12.9283	+	8.17537i	−0.564776	+	0.357143i
$525$	2.58600	+	2.91899i	0.112862	+	0.127395i
$526$	19.2071	+	11.0892i	0.837469	+	0.483513i
$527$	6.05980	+	18.1513i	0.263969	+	0.790684i
$528$	0.275452	+	0.524830i	0.0119875	+	0.0228403i
$529$	9.37830	−	16.2437i	0.407752	−	0.706248i
$530$	6.42432	+	11.1272i	0.279055	+	0.483337i
$531$	13.4989	−	21.3468i	0.585801	−	0.926370i
$532$	−0.806916	+	0.198887i	−0.0349843	+	0.00862284i
$533$	13.4714	−	11.7720i	0.583509	−	0.509902i
$534$	0.463796	+	0.114316i	0.0200704	+	0.00494692i
$535$	−12.4879	+	11.9948i	−0.539900	+	0.518581i
$536$	−16.9501	+	20.7601i	−0.732133	+	0.896700i
$537$	−25.3109	−	19.0199i	−1.09225	−	0.820769i
$538$	4.01543	−	16.2913i	0.173118	−	0.702366i
$539$	1.42982	+	0.414153i	0.0615868	+	0.0178388i
$540$	−0.114064	−	1.41294i	−0.00490855	−	0.0608033i
$541$	23.5178	+	2.85558i	1.01111	+	0.122771i	0.609290	−	0.792948i	$-0.291455\pi$
$541$	23.5178	+	2.85558i	1.01111	+	0.122771i	0.401820	+	0.915719i	$0.368378\pi$
$542$	13.2994	+	16.2888i	0.571259	+	0.699665i
$543$	1.48340	+	36.8102i	0.0636589	+	1.57968i
$544$	−14.1868	+	4.10927i	−0.608256	+	0.176183i
$545$	5.16229	+	13.6118i	0.221128	+	0.583067i
$546$	11.2300	−	7.63927i	0.480601	−	0.326931i
$547$	−2.78057	+	7.33176i	−0.118889	+	0.313484i	−0.981229	−	0.192845i	$-0.938229\pi$
$547$	−2.78057	+	7.33176i	−0.118889	+	0.313484i	0.862341	+	0.506329i	$0.168998\pi$
$548$	0.253736	−	3.14308i	0.0108391	−	0.134266i
$549$	−2.20214	+	10.7868i	−0.0939852	+	0.460370i
$550$	−0.0857087	+	0.295901i	−0.00365463	+	0.0126172i
$551$	3.32488	−	1.26096i	0.141645	−	0.0537187i
$552$	15.5704	+	0.627467i	0.662722	+	0.0267068i
$553$	−0.771809	+	4.74913i	−0.0328207	+	0.201954i
$554$	8.11087	−	9.15528i	0.344598	−	0.388970i
$555$	−10.6293	+	3.54857i	−0.451187	+	0.150628i
$556$	−3.23276	+	6.81289i	−0.137099	+	0.288931i
$557$	21.3907	+	10.1500i	0.906354	+	0.430070i	0.824037	−	0.566536i	$-0.191717\pi$
$557$	21.3907	+	10.1500i	0.906354	+	0.430070i	0.0823169	+	0.996606i	$0.473768\pi$
$558$	−20.3713	+	10.6917i	−0.862384	+	0.452614i
$559$	−12.9517	+	7.36067i	−0.547800	+	0.311323i
$560$	0.984244	+	0.516571i	0.0415919	+	0.0218291i
$561$	1.38372	+	1.84140i	0.0584207	+	0.0777439i
$562$	−6.22542	−	21.4926i	−0.262603	−	0.906612i
$563$	−39.3120	+	3.17359i	−1.65680	+	0.133751i	−0.873152	−	0.487448i	$-0.837928\pi$
$563$	−39.3120	+	3.17359i	−1.65680	+	0.133751i	−0.783652	+	0.621200i	$0.786646\pi$
$564$	3.79808	+	2.62163i	0.159928	+	0.110390i
$565$	−3.36512	+	0.686994i	−0.141572	+	0.0289020i
$566$	−6.18459	+	14.5158i	−0.259958	+	0.610143i
$567$	−2.61992	−	10.6294i	−0.110026	−	0.446395i
$568$	0.637673	−	15.8237i	0.0267562	−	0.663947i
$569$	−22.4818	+	16.8940i	−0.942485	+	0.708231i	−0.956519	−	0.291670i	$-0.905789\pi$
$569$	−22.4818	+	16.8940i	−0.942485	+	0.708231i	0.0140341	+	0.999902i	$0.495533\pi$
$570$	−0.493112	−	1.15738i	−0.0206542	−	0.0484772i
$571$	−8.70509	−	12.6115i	−0.364297	−	0.527775i	0.597381	−	0.801958i	$-0.296208\pi$
$571$	−8.70509	−	12.6115i	−0.364297	−	0.527775i	−0.961678	+	0.274183i	$0.911593\pi$
$572$	−1.12536	−	0.488543i	−0.0470538	−	0.0204270i
$573$	−3.96516	+	5.74453i	−0.165647	+	0.239981i
$574$	−7.17191	−	1.46416i	−0.299350	−	0.0611127i
$575$	1.42698	+	1.48564i	0.0595091	+	0.0619555i
$576$	−9.80923	−	20.6725i	−0.408718	−	0.861355i
$577$			8.87348i			0.369408i	0.982794	+	0.184704i	$0.0591326\pi$
$577$			8.87348i			0.369408i	−0.982794	+	0.184704i	$0.940867\pi$
$578$	−7.85429	+	3.72691i	−0.326695	+	0.155019i
$579$	14.1968	−	18.8925i	0.589999	−	0.785145i
$580$	6.95512	+	2.63773i	0.288796	+	0.109526i
$581$	−4.75303	−	2.02508i	−0.197189	−	0.0840144i
$582$	−33.7864	+	5.49082i	−1.40049	+	0.227602i
$583$	−1.34333	+	4.02377i	−0.0556351	+	0.166647i
$584$	2.99463	−	2.65301i	0.123918	−	0.109782i
$585$	−8.73006	−	9.21359i	−0.360944	−	0.380935i
$586$	−3.76785	−	3.33802i	−0.155648	−	0.137892i
$587$	−7.63500	+	4.40807i	−0.315130	+	0.181941i	−0.649220	−	0.760601i	$-0.724905\pi$
$587$	−7.63500	+	4.40807i	−0.315130	+	0.181941i	0.334090	+	0.942541i	$0.391571\pi$
$588$	−12.0619	−	4.02685i	−0.497424	−	0.166065i
$589$	2.39041	−	2.48868i	0.0984953	−	0.102544i
$590$	5.70356	−	3.93689i	0.234812	−	0.162079i
$591$	36.5716	−	29.8598i	1.50436	−	1.22827i
$592$	−2.47417	+	2.02010i	−0.101688	+	0.0830256i
$593$	−27.8427	+	19.2184i	−1.14336	+	0.789207i	−0.980321	−	0.197412i	$-0.936746\pi$
$593$	−27.8427	+	19.2184i	−1.14336	+	0.789207i	−0.163043	+	0.986619i	$0.552131\pi$
$594$	−0.283533	+	0.295189i	−0.0116335	+	0.0121118i
$595$	4.09731	+	1.36788i	0.167973	+	0.0560777i
$596$	0.509363	−	0.294081i	0.0208643	−	0.0120460i
$597$	10.7059	+	9.48463i	0.438165	+	0.388180i
$598$	5.76474	−	4.27087i	0.235738	−	0.174649i
$599$	−35.4480	+	31.4042i	−1.44837	+	1.28314i	−0.556494	+	0.830851i	$0.687854\pi$
$599$	−35.4480	+	31.4042i	−1.44837	+	1.28314i	−0.891872	+	0.452289i	$0.850608\pi$
$600$	2.39552	−	7.17547i	0.0977968	−	0.292937i
$601$	27.3303	−	4.44160i	1.11482	−	0.181177i	0.425028	−	0.905180i	$-0.360264\pi$
$601$	27.3303	−	4.44160i	1.11482	−	0.181177i	0.689796	+	0.724004i	$0.257700\pi$
$602$	5.60752	+	2.38914i	0.228545	+	0.0973741i
$603$	−29.7775	−	11.2931i	−1.21263	−	0.459892i
$604$	−5.26941	+	7.01231i	−0.214409	+	0.285327i
$605$	9.84607	−	4.67202i	0.400299	−	0.189944i
$606$		−	41.0057i		−	1.66574i
$607$	3.41160	+	7.18979i	0.138472	+	0.291824i	0.960826	−	0.277152i	$-0.0893907\pi$
$607$	3.41160	+	7.18979i	0.138472	+	0.291824i	−0.822354	+	0.568977i	$0.807339\pi$
$608$	1.84501	+	1.92086i	0.0748251	+	0.0779011i
$609$	−26.6392	−	5.43843i	−1.07947	−	0.220376i
$610$	−1.71607	+	2.48616i	−0.0694817	+	0.100662i
$611$	6.09111	−	0.450044i	0.246420	−	0.0182068i
$612$	−6.03471	−	8.74278i	−0.243939	−	0.353406i
$613$	−8.84551	−	20.7612i	−0.357267	−	0.838536i	−0.997521	−	0.0703725i	$-0.977581\pi$
$613$	−8.84551	−	20.7612i	−0.357267	−	0.838536i	0.640254	−	0.768163i	$-0.278829\pi$
$614$	−9.31997	+	7.00350i	−0.376123	+	0.282638i
$615$	−0.510169	+	12.6597i	−0.0205720	+	0.510489i
$616$	0.345314	+	1.40099i	0.0139131	+	0.0564477i
$617$	2.37054	−	5.56385i	0.0954342	−	0.223992i	−0.865420	−	0.501047i	$-0.832948\pi$
$617$	2.37054	−	5.56385i	0.0954342	−	0.223992i	0.960854	+	0.277055i	$0.0893585\pi$
$618$	20.4085	−	4.16642i	0.820948	−	0.167598i
$619$	−36.9872	−	25.5304i	−1.48664	−	1.02616i	−0.987143	−	0.159841i	$-0.948902\pi$
$619$	−36.9872	−	25.5304i	−1.48664	−	1.02616i	−0.499499	−	0.866314i	$-0.666483\pi$
$620$	7.19500	−	0.580841i	0.288958	−	0.0233271i
$621$	0.761454	+	2.62885i	0.0305561	+	0.105492i
$622$	−1.37109	−	1.82458i	−0.0549756	−	0.0731592i
$623$	0.261883	+	0.137447i	0.0104921	+	0.00550669i
$624$	−6.03437	−	2.91380i	−0.241568	−	0.116645i
$625$	0.885456	−	0.464723i	0.0354182	−	0.0185889i
$626$	18.7990	+	8.92025i	0.751360	+	0.356525i
$627$	0.178059	−	0.375252i	0.00711100	−	0.0149861i
$628$	−2.34513	+	0.782920i	−0.0935810	+	0.0312419i
$629$	−8.23100	+	9.29088i	−0.328192	+	0.370452i
$630$	−0.833060	+	5.12602i	−0.0331899	+	0.204226i
$631$	31.9481	+	1.28746i	1.27183	+	0.0512531i	0.666974	−	0.745081i	$-0.267589\pi$
$631$	31.9481	+	1.28746i	1.27183	+	0.0512531i	0.604858	+	0.796334i	$0.293230\pi$
$632$	8.72682	−	3.30965i	0.347134	−	0.131651i
$633$	18.8503	−	65.0787i	0.749231	−	2.58665i
$634$	−5.35154	+	26.2136i	−0.212537	+	1.04107i
$635$	−0.107995	+	1.33775i	−0.00428563	+	0.0530871i
$636$	12.8502	−	33.8831i	0.509543	−	1.34355i
$637$	−15.7759	+	5.86058i	−0.625065	+	0.232205i
$638$	−0.761620	−	2.00823i	−0.0301528	−	0.0795065i
$639$	18.0753	−	5.23558i	0.715048	−	0.207116i
$640$	0.167720	+	4.16193i	0.00662972	+	0.164515i
$641$	−8.11953	−	9.94462i	−0.320702	−	0.392789i	0.588943	−	0.808174i	$-0.299544\pi$
$641$	−8.11953	−	9.94462i	−0.320702	−	0.392789i	−0.909645	+	0.415386i	$0.863647\pi$
$642$	−42.3983	−	5.14809i	−1.67333	−	0.203179i
$643$	0.664884	+	8.23607i	0.0262205	+	0.324799i	0.996549	+	0.0830081i	$0.0264527\pi$
$643$	0.664884	+	8.23607i	0.0262205	+	0.324799i	−0.970328	+	0.241791i	$0.922265\pi$
$644$	3.22400	+	0.933842i	0.127043	+	0.0367985i
$645$	2.52487	−	10.2438i	0.0994166	−	0.403349i
$646$	−1.11402	−	0.837134i	−0.0438307	−	0.0329366i
$647$	6.43773	−	7.88479i	0.253093	−	0.309983i	−0.632394	−	0.774647i	$-0.717927\pi$
$647$	6.43773	−	7.88479i	0.253093	−	0.309983i	0.885487	+	0.464664i	$0.153825\pi$
$648$	−15.3157	+	14.7109i	−0.601657	+	0.577899i
$649$	2.22162	+	0.547580i	0.0872063	+	0.0214944i
$650$	−1.21284	−	3.26482i	−0.0475717	−	0.128057i
$651$	−25.6175	+	6.31415i	−1.00403	+	0.247471i
$652$	1.40952	−	2.22897i	0.0552010	−	0.0872933i
$653$	16.7505	+	29.0128i	0.655499	+	1.13536i	0.981768	+	0.190081i	$0.0608749\pi$
$653$	16.7505	+	29.0128i	0.655499	+	1.13536i	−0.326270	+	0.945277i	$0.605792\pi$
$654$	−17.9540	+	31.0972i	−0.702057	+	1.21600i
$655$	−6.66269	−	12.6947i	−0.260333	−	0.496023i
$656$	1.14362	+	3.42556i	0.0446509	+	0.133746i
$657$	4.11713	+	2.37703i	0.160625	+	0.0927367i
$658$	−1.65714	−	1.87053i	−0.0646022	−	0.0729208i
$659$	27.7164	−	17.5268i	1.07968	−	0.682748i	0.128600	−	0.991696i	$-0.458952\pi$
$659$	27.7164	−	17.5268i	1.07968	−	0.682748i	0.951079	+	0.308949i	$0.0999772\pi$
$660$	0.799329	−	0.340562i	0.0311138	−	0.0132564i
$661$	13.8245	−	0.557108i	0.537711	−	0.0216690i	0.230074	−	0.973173i	$-0.426103\pi$
$661$	13.8245	−	0.557108i	0.537711	−	0.0216690i	0.307636	+	0.951504i	$0.400462\pi$
$662$	1.55601	−	12.8149i	0.0604762	−	0.498066i
$663$	−24.9626	−	7.41492i	−0.969467	−	0.287972i
$664$	1.20802	+	9.94892i	0.0468802	+	0.386093i
$665$	−0.124951	−	0.768851i	−0.00484537	−	0.0298148i
$666$	−12.6128	−	7.97582i	−0.488734	−	0.309057i
$667$	−14.1759	−	2.30380i	−0.548892	−	0.0892036i
$668$	3.49832	−	6.66549i	0.135354	−	0.257895i
$669$	1.73044	+	2.73647i	0.0669026	+	0.105798i
$670$	−6.30237	−	6.05351i	−0.243482	−	0.233868i
$671$	−0.990105	+	0.120221i	−0.0382226	+	0.00464106i
$672$	−4.07339	−	19.9528i	−0.157134	−	0.769695i
$673$	−40.0370	−	3.23212i	−1.54331	−	0.124589i	−0.720722	−	0.693224i	$-0.756190\pi$
$673$	−40.0370	−	3.23212i	−1.54331	−	0.124589i	−0.822590	+	0.568635i	$0.807472\pi$
$674$	11.7877	+	9.62433i	0.454044	+	0.370716i
$675$	1.32863			0.0511388
$676$	13.5108	−	3.13579i	0.519648	−	0.120607i
$677$	15.8781			0.610246			0.305123	−	0.952313i	$-0.401302\pi$
$677$	15.8781			0.610246			0.305123	+	0.952313i	$0.401302\pi$
$678$	−6.56207	−	5.35776i	−0.252015	−	0.205764i
$679$	−21.1251	−	1.70539i	−0.810706	−	0.0654470i
$680$	−1.67607	−	8.20994i	−0.0642744	−	0.314837i
$681$	7.91316	−	0.960831i	0.303233	−	0.0368191i
$682$	−1.50317	−	1.44381i	−0.0575592	−	0.0552864i
$683$	6.72254	+	10.6308i	0.257231	+	0.406778i	0.948969	−	0.315371i	$-0.102129\pi$
$683$	6.72254	+	10.6308i	0.257231	+	0.406778i	−0.691738	+	0.722149i	$0.743155\pi$
$684$	−0.890248	+	1.69623i	−0.0340395	+	0.0648568i
$685$	2.91725	+	0.474099i	0.111462	+	0.0181144i
$686$	14.5478	+	9.19944i	0.555436	+	0.351236i
$687$	0.295414	+	1.81775i	0.0112707	+	0.0693516i
$688$	−0.362483	−	2.98532i	−0.0138195	−	0.113814i
$689$	−14.8773	−	45.5931i	−0.566779	−	1.73696i
$690$	−0.612449	+	5.04397i	−0.0233155	+	0.192021i
$691$	37.5261	−	1.51225i	1.42756	−	0.0575286i	0.685602	−	0.727977i	$-0.259539\pi$
$691$	37.5261	−	1.51225i	1.42756	−	0.0575286i	0.741957	+	0.670448i	$0.233898\pi$
$692$	−23.8704	+	10.1702i	−0.907418	+	0.386615i
$693$	−1.44916	+	0.916396i	−0.0550492	+	0.0348110i
$694$	−17.6587	−	19.9325i	−0.670315	−	0.756629i
$695$	−6.12105	−	3.53399i	−0.232185	−	0.134052i
$696$	16.7014	+	50.0269i	0.633066	+	1.89626i
$697$	6.52200	+	12.4266i	0.247039	+	0.470693i
$698$	−12.6475	+	21.9061i	−0.478714	+	0.829158i
$699$	3.25396	+	5.63602i	0.123076	+	0.213174i
$700$	0.870868	−	1.37717i	0.0329157	−	0.0520520i
$701$	10.1480	−	2.50125i	0.383284	−	0.0944711i	−0.0429657	−	0.999077i	$-0.513681\pi$
$701$	10.1480	−	2.50125i	0.383284	−	0.0944711i	0.426250	+	0.904605i	$0.359834\pi$
$702$	0.589001	−	4.58972i	0.0222304	−	0.173228i
$703$	2.17325	+	0.535659i	0.0819658	+	0.0202028i
$704$	1.49502	−	1.43598i	0.0563455	−	0.0541206i
$705$	−2.73567	+	3.35059i	−0.103031	+	0.126191i
$706$	17.1061	+	12.8544i	0.643797	+	0.483782i
$707$	6.07606	−	24.6516i	0.228514	−	0.927117i
$708$	−18.7745	−	5.43809i	−0.705588	−	0.204376i
$709$	−0.595750	−	7.37969i	−0.0223739	−	0.277150i	−0.998264	−	0.0588899i	$-0.981244\pi$
$709$	−0.595750	−	7.37969i	−0.0223739	−	0.277150i	0.975891	−	0.218260i	$-0.0700382\pi$
$710$	5.12601	+	0.622410i	0.192376	+	0.0233586i
$711$	7.01423	+	8.59087i	0.263054	+	0.322183i
$712$	−0.0231015	−	0.573258i	−0.000865765	−	0.0214837i
$713$	−13.3867	+	3.87749i	−0.501334	+	0.145213i
$714$	3.77818	+	9.96225i	0.141395	+	0.372828i
$715$	0.541290	−	1.01451i	0.0202431	−	0.0379405i
$716$	−4.69097	+	12.3691i	−0.175310	+	0.462254i
$717$	0.676539	−	8.38044i	0.0252658	−	0.312973i
$718$	3.51039	−	17.1950i	0.131007	−	0.641712i
$719$	−5.07882	+	17.5341i	−0.189408	+	0.653913i	0.808454	+	0.588559i	$0.200305\pi$
$719$	−5.07882	+	17.5341i	−0.189408	+	0.653913i	−0.997862	+	0.0653534i	$0.979183\pi$
$720$	2.39572	−	0.908578i	0.0892833	−	0.0338607i
$721$	12.8864	+	0.519303i	0.479914	+	0.0193399i
$722$	2.90376	−	17.8675i	0.108067	−	0.664961i
$723$	−37.9374	+	42.8225i	−1.41091	+	1.59259i
$724$	14.6007	−	4.87442i	0.542630	−	0.181156i
$725$	−2.98882	+	6.29880i	−0.111002	+	0.233932i
$726$	24.2860	+	11.5239i	0.901339	+	0.427691i
$727$	−9.32659	+	4.89497i	−0.345904	+	0.181544i	−0.628724	−	0.777629i	$-0.716422\pi$
$727$	−9.32659	+	4.89497i	−0.345904	+	0.181544i	0.282820	+	0.959173i	$0.408730\pi$
$728$	−12.5657	−	10.4028i	−0.465714	−	0.385553i
$729$	−31.3563	−	16.4571i	−1.16135	−	0.609522i
$730$	0.783664	+	1.04287i	0.0290047	+	0.0385983i
$731$	−3.25134	−	11.2249i	−0.120255	−	0.415169i
$732$	8.49247	−	0.685583i	0.313891	−	0.0253399i
$733$	20.5328	+	14.1727i	0.758395	+	0.523482i	0.883369	−	0.468678i	$-0.155270\pi$
$733$	20.5328	+	14.1727i	0.758395	+	0.523482i	−0.124974	+	0.992160i	$0.539885\pi$
$734$	5.32674	−	1.08746i	0.196613	−	0.0401389i
$735$	4.67174	−	10.9650i	0.172320	−	0.404449i
$736$	−2.57433	−	10.4444i	−0.0948909	−	0.384988i
$737$	0.116173	−	2.88281i	0.00427930	−	0.106190i
$738$	−13.4887	+	10.1361i	−0.496527	+	0.373115i
$739$	−6.09074	−	14.2955i	−0.224052	−	0.525869i	0.769579	−	0.638551i	$-0.220466\pi$
$739$	−6.09074	−	14.2955i	−0.224052	−	0.525869i	−0.993631	+	0.112683i	$0.964056\pi$
$740$	2.65977	+	3.85334i	0.0977751	+	0.141652i
$741$	0.907961	+	4.60718i	0.0333548	+	0.169249i
$742$	−11.1469	+	16.1491i	−0.409217	+	0.592853i
$743$	−47.0199	−	9.59918i	−1.72499	−	0.352160i	−0.767596	−	0.640935i	$-0.778547\pi$
$743$	−47.0199	−	9.59918i	−1.72499	−	0.352160i	−0.957397	+	0.288775i	$0.906752\pi$
$744$	35.4541	+	36.9116i	1.29981	+	1.35325i
$745$	0.236326	+	0.498046i	0.00865830	+	0.0182470i
$746$			0.0737606i			0.00270057i
$747$	−10.7592	+	5.10529i	−0.393657	+	0.186793i
$748$	0.578157	−	0.769388i	0.0211395	−	0.0281316i
$749$	−24.7259	−	9.37730i	−0.903465	−	0.342639i
$750$	2.26919	+	0.966814i	0.0828593	+	0.0353030i
$751$	20.1667	−	3.27740i	0.735892	−	0.119594i	0.219097	−	0.975703i	$-0.429689\pi$
$751$	20.1667	−	3.27740i	0.735892	−	0.119594i	0.516795	+	0.856109i	$0.327125\pi$
$752$	−0.390433	+	1.16949i	−0.0142376	+	0.0426469i
$753$	38.0115	−	33.6752i	1.38521	−	1.22719i
$754$	20.4341	+	13.1172i	0.744168	+	0.477700i
$755$	−6.15375	−	5.45174i	−0.223958	−	0.198409i
$756$	1.87485	−	1.08244i	0.0681875	−	0.0393680i
$757$	18.4712	+	6.16659i	0.671347	+	0.224129i	0.631849	−	0.775091i	$-0.282296\pi$
$757$	18.4712	+	6.16659i	0.671347	+	0.224129i	0.0394974	+	0.999220i	$0.487424\pi$
$758$	−10.0047	+	10.4160i	−0.363386	+	0.378325i
$759$	−1.38059	+	0.952950i	−0.0501121	+	0.0345899i
$760$	−1.17043	+	0.955626i	−0.0424559	+	0.0346642i
$761$	1.11183	−	0.907781i	0.0403038	−	0.0329070i	−0.612079	−	0.790796i	$-0.709667\pi$
$761$	1.11183	−	0.907781i	0.0403038	−	0.0329070i	0.652383	+	0.757889i	$0.273769\pi$
$762$	−2.72440	+	1.88052i	−0.0986947	+	0.0681240i
$763$	−15.4013	+	16.0345i	−0.557566	+	0.580487i
$764$	2.76640	+	0.923559i	0.100085	+	0.0334132i
$765$	8.62297	−	4.97848i	0.311764	−	0.179997i
$766$	−6.53384	−	5.78848i	−0.236077	−	0.209146i
$767$	−23.8667	+	9.97738i	−0.861776	+	0.360262i
$768$	−32.5370	+	28.8253i	−1.17408	+	1.04014i
$769$	5.93605	−	17.7806i	0.214059	−	0.641186i	−0.785686	−	0.618626i	$-0.787690\pi$
$769$	5.93605	−	17.7806i	0.214059	−	0.641186i	0.999745	−	0.0225609i	$-0.00718198\pi$
$770$	−0.464387	+	0.0754702i	−0.0167353	+	0.00271976i
$771$	9.57231	+	4.07838i	0.344738	+	0.146879i
$772$	−9.23249	−	3.50142i	−0.332285	−	0.126019i
$773$	−21.0728	+	28.0429i	−0.757938	+	1.00863i	0.241333	+	0.970442i	$0.422415\pi$
$773$	−21.0728	+	28.0429i	−0.757938	+	1.00863i	−0.999271	+	0.0381895i	$0.987841\pi$
$774$	12.6934	−	6.02310i	0.456255	−	0.216496i
$775$			6.76565i			0.243029i
$776$	17.6245	+	37.1428i	0.632683	+	1.33335i
$777$	−11.8552	−	12.3426i	−0.425303	−	0.442788i
$778$	2.91415	+	0.594928i	0.104477	+	0.0213292i
$779$	1.43762	−	2.08275i	0.0515079	−	0.0746221i
$780$	−4.96918	+	8.47324i	−0.177925	+	0.303391i
$781$	0.968450	+	1.40304i	0.0346539	+	0.0502048i
$782$	2.20602	+	5.17772i	0.0788872	+	0.185155i
$783$	−7.40531	+	5.56473i	−0.264644	+	0.198867i
$784$	0.136794	−	3.39452i	0.00488552	−	0.121233i
$785$	−0.554565	−	2.24996i	−0.0197933	−	0.0803045i
$786$	13.8611	−	32.5332i	0.494410	−	1.16042i
$787$	−30.0994	+	6.14484i	−1.07293	+	0.219040i	−0.703843	−	0.710355i	$-0.748534\pi$
$787$	−30.0994	+	6.14484i	−1.07293	+	0.219040i	−0.369086	+	0.929395i	$0.620329\pi$
$788$	−16.2350	−	11.2062i	−0.578349	−	0.399205i
$789$	58.4380	−	4.71761i	2.08045	−	0.167951i
$790$	0.846679	+	2.92307i	0.0301235	+	0.103998i
$791$	−3.15105	−	4.19329i	−0.112038	−	0.149096i
$792$	2.94504	+	1.54568i	0.104648	+	0.0549233i
$793$	8.18513	−	7.75557i	0.290662	−	0.275408i
$794$	5.50476	−	2.88912i	0.195357	−	0.102531i
$795$	30.6857	+	14.5606i	1.08831	+	0.516410i
$796$	2.56195	−	5.39919i	0.0908058	−	0.191369i
$797$	29.1524	−	9.73250i	1.03263	−	0.344743i	0.250672	−	0.968072i	$-0.419349\pi$
$797$	29.1524	−	9.73250i	1.03263	−	0.344743i	0.781960	+	0.623329i	$0.214220\pi$
$798$	1.27406	−	1.43812i	0.0451013	−	0.0509089i
$799$	−0.768575	+	4.72923i	−0.0271902	+	0.167308i
$800$	−5.21775	−	0.210268i	−0.184475	−	0.00743410i
$801$	0.637443	−	0.241750i	0.0225229	−	0.00854182i
$802$	4.66926	−	16.1202i	0.164877	−	0.569223i
$803$	−0.0861489	+	0.421985i	−0.00304013	+	0.0148915i
$804$	−1.98321	+	24.5665i	−0.0699426	+	0.866394i
$805$	−1.11558	+	2.94155i	−0.0393191	+	0.103676i
$806$	23.3719	+	2.99932i	0.823239	+	0.105647i
$807$	−15.7283	−	41.4720i	−0.553661	−	1.45989i
$808$	−47.3062	+	13.7024i	−1.66423	+	0.482049i
$809$	−0.671268	−	16.6574i	−0.0236005	−	0.585641i	−0.967119	−	0.254323i	$-0.918148\pi$
$809$	−0.671268	−	16.6574i	−0.0236005	−	0.585641i	0.943519	−	0.331319i	$-0.107494\pi$
$810$	−4.37925	−	5.36361i	−0.153871	−	0.188458i
$811$	−43.8775	−	5.32770i	−1.54075	−	0.187081i	−0.694353	−	0.719635i	$-0.744309\pi$
$811$	−43.8775	−	5.32770i	−1.54075	−	0.187081i	−0.846396	+	0.532554i	$0.821232\pi$
$812$	0.914116	+	11.3234i	0.0320792	+	0.397372i
$813$	53.3937	+	15.4657i	1.87260	+	0.542405i
$814$	0.323538	−	1.31265i	0.0113400	−	0.0460083i
$815$	1.97609	+	1.48493i	0.0692193	+	0.0520149i
$816$	3.32459	−	4.07188i	0.116384	−	0.142544i
$817$	−1.51982	+	1.45981i	−0.0531719	+	0.0510723i
$818$	30.0688	+	7.41129i	1.05133	+	0.259130i
$819$	6.99695	−	18.0776i	0.244493	−	0.631683i
$820$	5.14005	−	1.26691i	0.179498	−	0.0442424i
$821$	16.8681	−	26.6747i	0.588699	−	0.930953i	−0.411113	−	0.911584i	$-0.634860\pi$
$821$	16.8681	−	26.6747i	0.588699	−	0.930953i	0.999812	−	0.0193689i	$-0.00616571\pi$
$822$	3.64500	+	6.31333i	0.127134	+	0.220203i
$823$	−20.1488	+	34.8987i	−0.702342	+	1.21649i	0.265300	+	0.964166i	$0.414529\pi$
$823$	−20.1488	+	34.8987i	−0.702342	+	1.21649i	−0.967642	+	0.252326i	$0.918804\pi$
$824$	−11.6262	−	22.1519i	−0.405019	−	0.771700i
$825$	0.257881	+	0.772449i	0.00897827	+	0.0268932i
$826$	9.16613	+	5.29207i	0.318930	+	0.184134i
$827$	−20.3065	−	22.9213i	−0.706126	−	0.797052i	0.280534	−	0.959844i	$-0.409488\pi$
$827$	−20.3065	−	22.9213i	−0.706126	−	0.797052i	−0.986660	+	0.162792i	$0.947950\pi$
$828$	6.53921	−	4.13514i	0.227253	−	0.143706i
$829$	−18.4613	+	7.86564i	−0.641188	+	0.273185i	−0.687991	−	0.725719i	$-0.741507\pi$
$829$	−18.4613	+	7.86564i	−0.641188	+	0.273185i	0.0468025	+	0.998904i	$0.485097\pi$
$830$	−3.26512	+	0.131580i	−0.113334	+	0.00456720i
$831$	3.89733	−	32.0974i	0.135197	−	1.11345i
$832$	−3.91662	+	23.1062i	−0.135785	+	0.801062i
$833$	−1.59132	−	13.1057i	−0.0551361	−	0.454087i
$834$	−2.79656	−	17.2079i	−0.0968369	−	0.595861i
$835$	5.96331	+	3.77097i	0.206369	+	0.130500i
$836$	−0.171299	−	0.0278388i	−0.00592451	−	0.000962826i
$837$	−4.17740	+	7.95938i	−0.144392	+	0.275116i
$838$	15.2169	+	24.0636i	0.525660	+	0.831265i
$839$	−13.4863	−	12.9538i	−0.465600	−	0.447215i	0.422842	−	0.906203i	$-0.361033\pi$
$839$	−13.4863	−	12.9538i	−0.465600	−	0.447215i	−0.888442	+	0.458988i	$0.848212\pi$
$840$	11.4688	−	1.39257i	0.395711	−	0.0480481i
$841$	−3.92208	−	19.2116i	−0.135244	−	0.662470i
$842$	−2.71940	−	0.219533i	−0.0937167	−	0.00756559i
$843$	−45.8183	−	37.4095i	−1.57807	−	1.28845i
$844$	−28.3094			−0.974451
$845$	1.91059	+	12.8588i	0.0657263	+	0.442357i
$846$	−5.76034			−0.198044
$847$	12.8926	+	10.5264i	0.442993	+	0.361693i
$848$	9.64990	+	0.779021i	0.331379	+	0.0267517i
$849$	8.34301	+	40.8668i	0.286331	+	1.40254i
$850$	2.71223	−	0.329324i	0.0930286	−	0.0112957i
$851$	−6.51971	−	6.26227i	−0.223493	−	0.214668i
$852$	−7.78368	−	12.3089i	−0.266664	−	0.421696i
$853$	−2.33744	+	4.45362i	−0.0800323	+	0.152489i	−0.922183	−	0.386753i	$-0.873597\pi$
$853$	−2.33744	+	4.45362i	−0.0800323	+	0.152489i	0.842151	+	0.539242i	$0.181289\pi$
$854$	−4.55383	−	0.740070i	−0.155829	−	0.0253247i
$855$	−1.51754	−	0.959632i	−0.0518987	−	0.0328187i
$856$	8.22867	+	50.6331i	0.281250	+	1.73060i
$857$	−1.37027	−	11.2852i	−0.0468075	−	0.385494i	−0.997221	−	0.0745043i	$-0.976263\pi$
$857$	−1.37027	−	11.2852i	−0.0468075	−	0.385494i	0.950413	−	0.310990i	$-0.100661\pi$
$858$	2.78274	−	0.548409i	0.0950011	−	0.0187224i
$859$	3.37374	−	27.7853i	0.115111	−	0.948021i	−0.814675	−	0.579918i	$-0.803084\pi$
$859$	3.37374	−	27.7853i	0.115111	−	0.948021i	0.929785	−	0.368102i	$-0.119992\pi$
$860$	−4.40466	+	0.177502i	−0.150198	+	0.00605276i
$861$	−17.8014	+	7.58448i	−0.606671	+	0.258478i
$862$	14.5015	−	9.17018i	0.493923	−	0.312338i
$863$	−36.8066	−	41.5461i	−1.25291	−	1.41425i	−0.871906	−	0.489672i	$-0.837116\pi$
$863$	−36.8066	−	41.5461i	−1.25291	−	1.41425i	−0.381005	−	0.924573i	$-0.624422\pi$
$864$	−6.00854	−	3.46903i	−0.204415	−	0.118019i
$865$	−7.70113	−	23.0677i	−0.261846	−	0.784326i
$866$	3.98423	+	7.59131i	0.135390	+	0.257963i
$867$	−11.4907	+	19.9025i	−0.390246	+	0.675925i
$868$	5.51203	+	9.54712i	0.187091	+	0.324050i
$869$	−0.537002	+	0.849201i	−0.0182166	+	0.0288072i
$870$	−16.6971	+	4.11546i	−0.566084	+	0.139527i
$871$	18.3462	+	26.9696i	0.621637	+	0.913831i
$872$	41.8748	+	10.3212i	1.41806	+	0.349520i
$873$	−35.2329	+	33.8416i	−1.19245	+	1.14537i
$874$	0.641863	−	0.786139i	0.0217113	−	0.0265916i
$875$	1.22092	+	0.917463i	0.0412747	+	0.0310159i
$876$	0.880481	−	3.57225i	0.0297487	−	0.120695i
$877$	−14.3598	−	4.15936i	−0.484895	−	0.140452i	0.0267611	−	0.999642i	$-0.491481\pi$
$877$	−14.3598	−	4.15936i	−0.484895	−	0.140452i	−0.511656	+	0.859190i	$0.670968\pi$
$878$	1.54928	+	19.1913i	0.0522857	+	0.647674i
$879$	−13.2097	−	1.60395i	−0.445551	−	0.0540997i
$880$	0.146805	+	0.179803i	0.00494879	+	0.00606116i
$881$	−1.43260	−	35.5496i	−0.0482655	−	1.19770i	−0.823983	−	0.566615i	$-0.808253\pi$
$881$	−1.43260	−	35.5496i	−0.0482655	−	1.19770i	0.775717	−	0.631081i	$-0.217388\pi$
$882$	15.2455	−	4.41591i	0.513343	−	0.148692i
$883$	4.97848	+	13.1272i	0.167539	+	0.441765i	0.992321	−	0.123686i	$-0.0394716\pi$
$883$	4.97848	+	13.1272i	0.167539	+	0.441765i	−0.824782	+	0.565451i	$0.808702\pi$
$884$	−0.0740119	+	10.8802i	−0.00248929	+	0.365942i
$885$	6.49643	−	17.1297i	0.218375	−	0.575808i
$886$	−1.42996	+	17.7132i	−0.0480403	+	0.595086i
$887$	−1.85182	+	9.07080i	−0.0621779	+	0.304568i	−0.998973	−	0.0453111i	$-0.985572\pi$
$887$	−1.85182	+	9.07080i	−0.0621779	+	0.304568i	0.936795	+	0.349879i	$0.113777\pi$
$888$	−9.23623	+	31.8872i	−0.309948	+	1.07006i
$889$	−1.91649	+	0.726827i	−0.0642769	+	0.0243770i
$890$	0.186916	+	0.00753247i	0.00626545	+	0.000252489i
$891$	0.366719	−	2.25651i	0.0122855	−	0.0755960i
$892$	0.897073	−	1.01259i	0.0300362	−	0.0339039i
$893$	0.819528	−	0.273599i	0.0274245	−	0.00915563i
$894$	−0.582914	+	1.22847i	−0.0194956	+	0.0410860i
$895$	−11.2019	−	5.31535i	−0.374437	−	0.177672i
$896$	−5.63268	+	2.95626i	−0.188174	+	0.0987616i
$897$	6.12798	−	17.9481i	0.204607	−	0.599271i
$898$	5.65815	+	2.96963i	0.188815	+	0.0990977i
$899$	−28.3368	−	37.7095i	−0.945086	−	1.25768i
$900$	−1.04496	−	3.60761i	−0.0348319	−	0.120254i
$901$	37.5001	−	3.02732i	1.24931	−	0.100855i
$902$	−1.25798	−	0.868321i	−0.0418862	−	0.0289119i
$903$	15.7870	−	3.22295i	0.525360	−	0.107253i
$904$	−3.98821	+	9.36067i	−0.132646	+	0.311331i
$905$	3.45269	+	14.0081i	0.114771	+	0.465646i
$906$	0.816532	−	20.2620i	0.0271275	−	0.673161i
$907$	−42.3871	+	31.8518i	−1.40744	+	1.05762i	−0.418677	+	0.908135i	$0.637506\pi$
$907$	−42.3871	+	31.8518i	−1.40744	+	1.05762i	−0.988764	+	0.149488i	$0.952238\pi$
$908$	−1.30549	−	3.06411i	−0.0433243	−	0.101686i
$909$	−33.2453	−	48.1642i	−1.10268	−	1.59750i
$910$	3.71062	−	3.81093i	0.123006	−	0.126331i
$911$	−5.41119	+	7.83947i	−0.179281	+	0.259733i	−0.902313	−	0.431081i	$-0.858132\pi$
$911$	−5.41119	+	7.83947i	−0.179281	+	0.259733i	0.723032	+	0.690814i	$0.242748\pi$
$912$	−0.928766	−	0.189609i	−0.0307545	−	0.00627858i
$913$	−0.747367	−	0.778091i	−0.0247342	−	0.0257511i
$914$	13.1969	+	27.8119i	0.436515	+	0.919936i
$915$			7.98569i			0.263999i
$916$	0.695181	−	0.329867i	0.0229694	−	0.0108991i
$917$	13.1536	−	17.5042i	0.434369	−	0.578040i
$918$	3.39411	+	1.28722i	0.112022	+	0.0424844i
$919$	−46.3903	−	19.7651i	−1.53028	−	0.651989i	−0.547502	−	0.836804i	$-0.684421\pi$
$919$	−46.3903	−	19.7651i	−1.53028	−	0.651989i	−0.982773	+	0.184815i	$0.940831\pi$
$920$	6.02363	−	0.978934i	0.198593	−	0.0322745i
$921$	−9.75902	+	29.2318i	−0.321571	+	0.963222i
$922$	−4.70826	+	4.17115i	−0.155058	+	0.137370i
$923$	−18.2401	−	6.22765i	−0.600379	−	0.204986i
$924$	0.993221	+	0.879917i	0.0326746	+	0.0289471i
$925$	−3.80054	+	2.19424i	−0.124961	+	0.0721462i
$926$	18.9252	+	6.31816i	0.621920	+	0.207627i
$927$	20.5933	−	21.4399i	0.676372	−	0.704178i
$928$	29.9626	−	20.6817i	0.983572	−	0.678911i
$929$	32.1131	−	26.2195i	1.05360	−	0.860234i	0.0631317	−	0.998005i	$-0.479891\pi$
$929$	32.1131	−	26.2195i	1.05360	−	0.860234i	0.990464	+	0.137771i	$0.0439938\pi$
$930$	−12.9266	+	10.5542i	−0.423879	+	0.346087i
$931$	−1.95925	+	1.35237i	−0.0642117	+	0.0443222i
$932$	1.88365	−	1.96109i	0.0617010	−	0.0642375i
$933$	−5.72276	−	1.91054i	−0.187355	−	0.0625482i
$934$	13.4744	−	7.77945i	0.440896	−	0.254552i
$935$	0.675187	+	0.598163i	0.0220810	+	0.0195620i
$936$	−37.1556	+	5.77924i	−1.21447	+	0.188900i
$937$	−1.85641	+	1.64464i	−0.0606464	+	0.0537280i	−0.692901	−	0.721032i	$-0.743668\pi$
$937$	−1.85641	+	1.64464i	−0.0606464	+	0.0537280i	0.632255	+	0.774760i	$0.282129\pi$
$938$	4.22621	−	12.6591i	0.137991	−	0.413333i
$939$	54.2932	−	8.82350i	1.77179	−	0.287944i
$940$	1.66271	+	0.708415i	0.0542317	+	0.0231060i
$941$	−28.6484	−	10.8649i	−0.933910	−	0.354185i	−0.159737	−	0.987160i	$-0.551065\pi$
$941$	−28.6484	−	10.8649i	−0.933910	−	0.354185i	−0.774173	+	0.632974i	$0.781834\pi$
$942$	3.43371	−	4.56943i	0.111876	−	0.148880i
$943$	−9.23429	+	4.38172i	−0.300710	+	0.142689i
$944$		−	5.22193i		−	0.169959i
$945$	0.869859	+	1.83319i	0.0282965	+	0.0596336i
$946$	0.881727	+	0.917975i	0.0286674	+	0.0298459i
$947$	25.7307	+	5.25297i	0.836136	+	0.170698i	0.598971	−	0.800771i	$-0.295577\pi$
$947$	25.7307	+	5.25297i	0.836136	+	0.170698i	0.237165	+	0.971469i	$0.423782\pi$
$948$	4.87573	−	7.06371i	0.158356	−	0.229419i
$949$	−2.05740	−	4.41314i	−0.0667861	−	0.143257i
$950$	−0.279872	−	0.405465i	−0.00908026	−	0.0131550i
$951$	27.7215	+	65.0648i	0.898932	+	2.10987i
$952$	10.2304	−	7.68767i	0.331570	−	0.249159i
$953$	2.01445	−	49.9881i	0.0652544	−	1.61927i	−0.552922	−	0.833233i	$-0.686487\pi$
$953$	2.01445	−	49.9881i	0.0652544	−	1.61927i	0.618177	−	0.786039i	$-0.287872\pi$
$954$	10.8246	+	43.9170i	0.350458	+	1.42186i
$955$	−1.07146	+	2.51482i	−0.0346718	+	0.0813776i
$956$	−3.44198	+	0.702686i	−0.111322	+	0.0227265i
$957$	−4.67262	−	3.22527i	−0.151044	−	0.104258i
$958$	−28.1119	+	2.26943i	−0.908254	+	0.0733219i
$959$	1.25580	+	4.33551i	0.0405517	+	0.140001i
$960$	−9.97080	−	13.2687i	−0.321806	−	0.428246i
$961$	−13.0818	−	6.86583i	−0.421992	−	0.221478i
$962$	5.89515	+	14.1017i	0.190067	+	0.454656i
$963$	−53.9737	+	28.3276i	−1.73928	+	0.912843i
$964$	21.5961	+	10.2475i	0.695565	+	0.330050i
$965$	3.96747	−	8.36127i	0.127717	−	0.269159i
$966$	−7.36046	+	2.45728i	−0.236819	+	0.0790617i
$967$	−23.8809	+	26.9559i	−0.767957	+	0.866845i	−0.994236	−	0.107218i	$-0.965806\pi$
$967$	−23.8809	+	26.9559i	−0.767957	+	0.866845i	0.226278	+	0.974063i	$0.427344\pi$
$968$	5.17911	−	31.8683i	0.166463	−	1.02429i
$969$	−3.68069	−	0.148327i	−0.118241	−	0.00476495i
$970$	−12.5339	+	4.75349i	−0.402440	+	0.152625i
$971$	−6.52702	+	22.5339i	−0.209462	+	0.723146i	0.785134	+	0.619326i	$0.212594\pi$
$971$	−6.52702	+	22.5339i	−0.209462	+	0.723146i	−0.994596	+	0.103821i	$0.966893\pi$
$972$	−4.75697	+	23.3012i	−0.152580	+	0.747385i
$973$	0.868582	−	10.7593i	0.0278455	−	0.344928i
$974$	−11.6511	+	30.7215i	−0.373326	+	0.984380i
$975$	−7.54125	−	5.28145i	−0.241513	−	0.169142i
$976$	0.807158	+	2.12830i	0.0258365	+	0.0681253i
$977$	49.8187	−	14.4302i	1.59384	−	0.461662i	0.641609	−	0.767032i	$-0.278267\pi$
$977$	49.8187	−	14.4302i	1.59384	−	0.461662i	0.952234	+	0.305370i	$0.0987802\pi$
$978$	0.245499	+	6.09200i	0.00785020	+	0.194801i
$979$	0.0390611	+	0.0478412i	0.00124840	+	0.00152901i
$980$	−4.94366	−	0.600269i	−0.157920	−	0.0191749i
$981$	4.12377	+	51.0821i	0.131662	+	1.63093i
$982$	−18.6499	−	5.40202i	−0.595144	−	0.172386i
$983$	−12.0071	+	48.7146i	−0.382966	+	1.55375i	0.390917	+	0.920426i	$0.372158\pi$
$983$	−12.0071	+	48.7146i	−0.382966	+	1.55375i	−0.773883	+	0.633329i	$0.781688\pi$
$984$	30.0072	+	22.5490i	0.956595	+	0.718835i
$985$	11.6937	−	14.3222i	0.372593	−	0.456343i
$986$	−13.7377	+	13.1953i	−0.437498	+	0.420223i
$987$	−6.41408	−	1.58093i	−0.204162	−	0.0503215i
$988$	1.74346	−	0.899964i	0.0554668	−	0.0286317i
$989$	8.26386	−	2.03686i	0.262776	−	0.0647684i
$990$	−0.579618	+	0.916593i	−0.0184215	+	0.0291312i
$991$	2.68231	+	4.64590i	0.0852064	+	0.147582i	0.905479	−	0.424391i	$-0.139512\pi$
$991$	2.68231	+	4.64590i	0.0852064	+	0.147582i	−0.820273	+	0.571973i	$0.806178\pi$
$992$	17.6651	−	30.5968i	0.560866	−	0.971449i
$993$	−15.8585	−	30.2159i	−0.503256	−	0.958874i
$994$	2.49725	+	7.48018i	0.0792080	+	0.237257i
$995$	4.85091	+	2.80067i	0.153784	+	0.0887873i
$996$	6.11157	+	6.89853i	0.193652	+	0.218588i
$997$	−14.1179	+	8.92763i	−0.447119	+	0.282741i	−0.738989	−	0.673717i	$-0.764697\pi$
$997$	−14.1179	+	8.92763i	−0.447119	+	0.282741i	0.291871	+	0.956458i	$0.405722\pi$
$998$	−22.6099	+	9.63319i	−0.715705	+	0.304933i
$999$	−5.82592	+	0.234777i	−0.184324	+	0.00742800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.bg.a.621.38	yes	1440
169.43	even	78	inner	845.2.bg.a.381.38	✓	1440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.bg.a.381.38	✓	1440	169.43	even	78	inner
845.2.bg.a.621.38	yes	1440	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.bg (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.748238 + 0.610917i) q^{2} +(2.54521 + 0.205471i) q^{3} +(-0.213412 - 1.04536i) q^{4} +(0.992709 - 0.120537i) q^{5} +(1.77890 + 1.70865i) q^{6} +(0.816244 + 1.29079i) q^{7} +(1.37675 - 2.62318i) q^{8} +(3.47473 + 0.564699i) q^{9} +O(q^{10})\)	\(q+(0.748238 + 0.610917i) q^{2} +(2.54521 + 0.205471i) q^{3} +(-0.213412 - 1.04536i) q^{4} +(0.992709 - 0.120537i) q^{5} +(1.77890 + 1.70865i) q^{6} +(0.816244 + 1.29079i) q^{7} +(1.37675 - 2.62318i) q^{8} +(3.47473 + 0.564699i) q^{9} +(0.816420 + 0.516273i) q^{10} +(0.0511583 + 0.314790i) q^{11} +(-0.328387 - 2.70451i) q^{12} +(-2.58328 - 2.51528i) q^{13} +(-0.177819 + 1.46447i) q^{14} +(2.55142 - 0.102819i) q^{15} +(0.669598 - 0.285289i) q^{16} +(2.39056 - 1.51170i) q^{17} +(2.25494 + 2.54530i) q^{18} +(-0.441706 - 0.255019i) q^{19} +(-0.337860 - 1.01201i) q^{20} +(1.81229 + 3.45304i) q^{21} +(-0.154032 + 0.266791i) q^{22} +(1.02998 + 1.78397i) q^{23} +(4.04312 - 6.39368i) q^{24} +(0.970942 - 0.239316i) q^{25} +(-0.396280 - 3.46020i) q^{26} +(1.29002 + 0.317961i) q^{27} +(1.17514 - 1.12874i) q^{28} +(-4.40937 + 5.40050i) q^{29} +(1.97188 + 1.48177i) q^{30} +(-1.61913 + 6.56905i) q^{31} +(-5.01581 - 1.45285i) q^{32} +(0.0655286 + 0.811718i) q^{33} +(2.71223 + 0.329324i) q^{34} +(0.965880 + 1.18299i) q^{35} +(-0.151235 - 3.75285i) q^{36} +(-4.21522 + 1.22095i) q^{37} +(-0.174706 - 0.460661i) q^{38} +(-6.05818 - 6.93272i) q^{39} +(1.05053 - 2.77001i) q^{40} +(-0.399262 + 4.94574i) q^{41} +(-0.753494 + 3.69086i) q^{42} +(1.14952 - 3.96861i) q^{43} +(0.318150 - 0.120658i) q^{44} +(3.51746 + 0.141749i) q^{45} +(-0.319191 + 1.96406i) q^{46} +(-1.12331 + 1.26796i) q^{47} +(1.76289 - 0.588538i) q^{48} +(2.00097 - 4.21696i) q^{49} +(0.872697 + 0.414100i) q^{50} +(6.39508 - 3.35640i) q^{51} +(-2.07807 + 3.23725i) q^{52} +(11.7778 + 6.18148i) q^{53} +(0.770992 + 1.02600i) q^{54} +(0.0887290 + 0.306328i) q^{55} +(4.50974 - 0.364064i) q^{56} +(-1.07184 - 0.739836i) q^{57} +(-6.59851 + 1.34710i) q^{58} +(2.81219 - 6.60045i) q^{59} +(-0.651985 - 2.64521i) q^{60} +(-0.125926 + 3.12483i) q^{61} +(-5.22464 + 3.92606i) q^{62} +(2.10732 + 4.94607i) q^{63} +(-3.69237 - 5.34932i) q^{64} +(-2.86763 - 2.18556i) q^{65} +(-0.446861 + 0.647390i) q^{66} +(-8.86382 - 1.80956i) q^{67} +(-2.09044 - 2.17638i) q^{68} +(2.25495 + 4.75221i) q^{69} +1.47523i q^{70} +(4.82951 - 2.29163i) q^{71} +(6.26516 - 8.33741i) q^{72} +(1.26270 + 0.478881i) q^{73} +(-3.89988 - 1.66159i) q^{74} +(2.52042 - 0.409609i) q^{75} +(-0.172321 + 0.516166i) q^{76} +(-0.364569 + 0.322980i) q^{77} +(-0.297645 - 8.88837i) q^{78} +(2.35816 + 2.08915i) q^{79} +(0.630328 - 0.363920i) q^{80} +(-6.79941 - 2.26998i) q^{81} +(-3.32018 + 3.45668i) q^{82} +(-2.78409 + 1.92172i) q^{83} +(3.22290 - 2.63142i) q^{84} +(2.19091 - 1.78882i) q^{85} +(3.28461 - 2.26720i) q^{86} +(-12.3324 + 12.8394i) q^{87} +(0.896184 + 0.299190i) q^{88} +(0.167715 - 0.0968301i) q^{89} +(2.54530 + 2.25494i) q^{90} +(1.13811 - 5.38755i) q^{91} +(1.64508 - 1.45741i) q^{92} +(-5.47077 + 16.3869i) q^{93} +(-1.61512 + 0.262483i) q^{94} +(-0.469225 - 0.199918i) q^{95} +(-12.4678 - 4.72840i) q^{96} +(-8.33676 + 11.0942i) q^{97} +(4.07341 - 1.93286i) q^{98} +1.12270i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1440 q - 2 q^{3} - 58 q^{4} + 18 q^{6} + 6 q^{7} + 60 q^{9}+O(q^{10}) \) 1440 * q - 2 * q^3 - 58 * q^4 + 18 * q^6 + 6 * q^7 + 60 * q^9	\( 1440 q - 2 q^{3} - 58 q^{4} + 18 q^{6} + 6 q^{7} + 60 q^{9} + 2 q^{10} - 20 q^{12} + 26 q^{13} + 4 q^{14} + 6 q^{15} + 58 q^{16} + 6 q^{17} - 156 q^{18} - 12 q^{19} - 12 q^{20} + 60 q^{22} - 146 q^{23} - 144 q^{24} + 120 q^{25} - 10 q^{26} + 4 q^{27} + 18 q^{28} + 4 q^{29} - 4 q^{30} + 52 q^{31} + 20 q^{32} - 42 q^{33} + 130 q^{34} - 10 q^{35} - 56 q^{36} - 6 q^{37} - 162 q^{38} + 12 q^{40} - 12 q^{41} - 24 q^{42} + 2 q^{43} + 42 q^{46} - 156 q^{47} + 30 q^{48} + 18 q^{49} - 124 q^{52} + 48 q^{53} - 330 q^{54} - 4 q^{55} + 20 q^{56} + 78 q^{57} + 68 q^{58} - 196 q^{59} + 12 q^{61} - 118 q^{62} + 24 q^{63} + 96 q^{64} + 8 q^{65} + 44 q^{66} + 98 q^{67} + 120 q^{68} + 28 q^{69} - 156 q^{71} + 386 q^{72} - 30 q^{74} + 2 q^{75} - 392 q^{76} + 4 q^{77} - 204 q^{78} + 40 q^{79} + 40 q^{81} - 244 q^{82} + 30 q^{84} - 18 q^{85} - 30 q^{87} + 30 q^{88} - 24 q^{89} - 56 q^{90} + 76 q^{91} + 20 q^{92} - 130 q^{93} - 148 q^{94} + 16 q^{95} - 338 q^{96} + 30 q^{97} - 72 q^{98}+O(q^{100}) \) 1440 * q - 2 * q^3 - 58 * q^4 + 18 * q^6 + 6 * q^7 + 60 * q^9 + 2 * q^10 - 20 * q^12 + 26 * q^13 + 4 * q^14 + 6 * q^15 + 58 * q^16 + 6 * q^17 - 156 * q^18 - 12 * q^19 - 12 * q^20 + 60 * q^22 - 146 * q^23 - 144 * q^24 + 120 * q^25 - 10 * q^26 + 4 * q^27 + 18 * q^28 + 4 * q^29 - 4 * q^30 + 52 * q^31 + 20 * q^32 - 42 * q^33 + 130 * q^34 - 10 * q^35 - 56 * q^36 - 6 * q^37 - 162 * q^38 + 12 * q^40 - 12 * q^41 - 24 * q^42 + 2 * q^43 + 42 * q^46 - 156 * q^47 + 30 * q^48 + 18 * q^49 - 124 * q^52 + 48 * q^53 - 330 * q^54 - 4 * q^55 + 20 * q^56 + 78 * q^57 + 68 * q^58 - 196 * q^59 + 12 * q^61 - 118 * q^62 + 24 * q^63 + 96 * q^64 + 8 * q^65 + 44 * q^66 + 98 * q^67 + 120 * q^68 + 28 * q^69 - 156 * q^71 + 386 * q^72 - 30 * q^74 + 2 * q^75 - 392 * q^76 + 4 * q^77 - 204 * q^78 + 40 * q^79 + 40 * q^81 - 244 * q^82 + 30 * q^84 - 18 * q^85 - 30 * q^87 + 30 * q^88 - 24 * q^89 - 56 * q^90 + 76 * q^91 + 20 * q^92 - 130 * q^93 - 148 * q^94 + 16 * q^95 - 338 * q^96 + 30 * q^97 - 72 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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