LMFDB - Embedded newform 756.2.ba.a.71.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(71,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("756.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ba (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.16
Character	$\chi$	$=$	756.71
Dual form			756.2.ba.a.575.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.246614 - 1.39255i) q^{2} +(-1.87836 + 0.686842i) q^{4} +(3.28588 + 1.89710i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.41969 + 2.44632i) q^{8} +O(q^{10})$	\(q+(-0.246614 - 1.39255i) q^{2} +(-1.87836 + 0.686842i) q^{4} +(3.28588 + 1.89710i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.41969 + 2.44632i) q^{8} +(1.83146 - 5.04359i) q^{10} +(-0.147235 - 0.255018i) q^{11} +(-1.99299 + 3.45197i) q^{13} +(0.909846 + 1.08267i) q^{14} +(3.05650 - 2.58028i) q^{16} -3.60857i q^{17} +6.02570i q^{19} +(-7.47508 - 1.30657i) q^{20} +(-0.318814 + 0.267922i) q^{22} +(-2.37532 + 4.11418i) q^{23} +(4.69800 + 8.13717i) q^{25} +(5.29852 + 1.92403i) q^{26} +(1.28329 - 1.53400i) q^{28} +(-0.904457 + 0.522189i) q^{29} +(5.56802 + 3.21470i) q^{31} +(-4.34693 - 3.61998i) q^{32} +(-5.02510 + 0.889923i) q^{34} -3.79421 q^{35} -3.86636 q^{37} +(8.39106 - 1.48602i) q^{38} +(0.0240018 + 10.7316i) q^{40} +(10.6945 + 6.17450i) q^{41} +(-0.852502 + 0.492192i) q^{43} +(0.451718 + 0.377890i) q^{44} +(6.31496 + 2.29313i) q^{46} +(-1.68371 - 2.91626i) q^{47} +(0.500000 - 0.866025i) q^{49} +(10.1728 - 8.54892i) q^{50} +(1.37261 - 7.85292i) q^{52} -2.03029i q^{53} -1.11728i q^{55} +(-2.45265 - 1.40873i) q^{56} +(0.950223 + 1.13072i) q^{58} +(4.15275 - 7.19278i) q^{59} +(-5.48589 - 9.50184i) q^{61} +(3.10346 - 8.54650i) q^{62} +(-3.96897 + 6.94603i) q^{64} +(-13.0975 + 7.56183i) q^{65} +(9.26153 + 5.34715i) q^{67} +(2.47852 + 6.77821i) q^{68} +(0.935704 + 5.28360i) q^{70} -2.73284 q^{71} +8.63292 q^{73} +(0.953498 + 5.38408i) q^{74} +(-4.13870 - 11.3185i) q^{76} +(0.255018 + 0.147235i) q^{77} +(4.74756 - 2.74100i) q^{79} +(14.9383 - 2.67999i) q^{80} +(5.96084 - 16.4153i) q^{82} +(-4.07096 - 7.05111i) q^{83} +(6.84583 - 11.8573i) q^{85} +(0.895639 + 1.06577i) q^{86} +(0.414829 - 0.722231i) q^{88} -3.35572i q^{89} -3.98599i q^{91} +(1.63593 - 9.35939i) q^{92} +(-3.64580 + 3.06383i) q^{94} +(-11.4314 + 19.7997i) q^{95} +(6.74076 + 11.6753i) q^{97} +(-1.32929 - 0.482699i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) $ 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−0.246614	−	1.39255i	−0.174382	−	0.984678i
$2$	−0.246614	−	1.39255i	−0.174382	−	0.984678i
$3$		0			0
$3$		0			0
$4$	−1.87836	+	0.686842i	−0.939182	+	0.343421i
$5$	3.28588	+	1.89710i	1.46949	+	0.848410i	0.999414	−	0.0342161i	$-0.0108934\pi$
$5$	3.28588	+	1.89710i	1.46949	+	0.848410i	0.470075	+	0.882626i	$0.344227\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$	1.41969	+	2.44632i	0.501936	+	0.864905i
$9$		0			0
$10$	1.83146	−	5.04359i	0.579158	−	1.59492i
$11$	−0.147235	−	0.255018i	−0.0443930	−	0.0768909i	0.842975	−	0.537953i	$-0.180802\pi$
$11$	−0.147235	−	0.255018i	−0.0443930	−	0.0768909i	−0.887368	+	0.461062i	$0.847469\pi$
$12$		0			0
$13$	−1.99299	+	3.45197i	−0.552757	+	0.957404i	0.445317	+	0.895373i	$0.353091\pi$
$13$	−1.99299	+	3.45197i	−0.552757	+	0.957404i	−0.998074	+	0.0620307i	$0.980242\pi$
$14$	0.909846	+	1.08267i	0.243167	+	0.289356i
$15$		0			0
$16$	3.05650	−	2.58028i	0.764124	−	0.645069i
$17$		−	3.60857i		−	0.875207i	−0.899168	−	0.437603i	$-0.855827\pi$
$17$		−	3.60857i		−	0.875207i	0.899168	−	0.437603i	$-0.144173\pi$
$18$		0			0
$19$			6.02570i			1.38239i	0.722668	+	0.691195i	$0.242915\pi$
$19$			6.02570i			1.38239i	−0.722668	+	0.691195i	$0.757085\pi$
$20$	−7.47508	−	1.30657i	−1.67148	−	0.292158i
$21$		0			0
$22$	−0.318814	+	0.267922i	−0.0679715	+	0.0571212i
$23$	−2.37532	+	4.11418i	−0.495289	+	0.857865i	−0.999985	−	0.00543156i	$-0.998271\pi$
$23$	−2.37532	+	4.11418i	−0.495289	+	0.857865i	0.504696	+	0.863297i	$0.331604\pi$
$24$		0			0
$25$	4.69800	+	8.13717i	0.939600	+	1.62743i
$26$	5.29852	+	1.92403i	1.03913	+	0.377334i
$27$		0			0
$28$	1.28329	−	1.53400i	0.242519	−	0.289900i
$29$	−0.904457	+	0.522189i	−0.167954	+	0.0969680i	−0.581621	−	0.813460i	$-0.697581\pi$
$29$	−0.904457	+	0.522189i	−0.167954	+	0.0969680i	0.413667	+	0.910428i	$0.364248\pi$
$30$		0			0
$31$	5.56802	+	3.21470i	1.00005	+	0.577376i	0.908262	−	0.418403i	$-0.137410\pi$
$31$	5.56802	+	3.21470i	1.00005	+	0.577376i	0.0917836	+	0.995779i	$0.470743\pi$
$32$	−4.34693	−	3.61998i	−0.768435	−	0.639928i
$33$		0			0
$34$	−5.02510	+	0.889923i	−0.861797	+	0.152621i
$35$	−3.79421			−0.641338
$36$		0			0
$37$	−3.86636			−0.635626			−0.317813	−	0.948153i	$-0.602948\pi$
$37$	−3.86636			−0.635626			−0.317813	+	0.948153i	$0.602948\pi$
$38$	8.39106	−	1.48602i	1.36121	−	0.241064i
$39$		0			0
$40$	0.0240018	+	10.7316i	0.00379502	+	1.69682i
$41$	10.6945	+	6.17450i	1.67021	+	0.964295i	0.967520	+	0.252796i	$0.0813501\pi$
$41$	10.6945	+	6.17450i	1.67021	+	0.964295i	0.702687	+	0.711499i	$0.251983\pi$
$42$		0			0
$43$	−0.852502	+	0.492192i	−0.130005	+	0.0750586i	−0.563592	−	0.826053i	$-0.690581\pi$
$43$	−0.852502	+	0.492192i	−0.130005	+	0.0750586i	0.433587	+	0.901112i	$0.357248\pi$
$44$	0.451718	+	0.377890i	0.0680991	+	0.0569691i
$45$		0			0
$46$	6.31496	+	2.29313i	0.931091	+	0.338103i
$47$	−1.68371	−	2.91626i	−0.245594	−	0.425381i	0.716705	−	0.697377i	$-0.245650\pi$
$47$	−1.68371	−	2.91626i	−0.245594	−	0.425381i	−0.962298	+	0.271996i	$0.912316\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	10.1728	−	8.54892i	1.43865	−	1.20900i
$51$		0			0
$52$	1.37261	−	7.85292i	0.190347	−	1.08900i
$53$		−	2.03029i		−	0.278882i	−0.990230	−	0.139441i	$-0.955469\pi$
$53$		−	2.03029i		−	0.278882i	0.990230	−	0.139441i	$-0.0445306\pi$
$54$		0			0
$55$		−	1.11728i		−	0.150654i
$56$	−2.45265	−	1.40873i	−0.327749	−	0.188250i
$57$		0			0
$58$	0.950223	+	1.13072i	0.124770	+	0.148471i
$59$	4.15275	−	7.19278i	0.540642	−	0.936420i	−0.458225	−	0.888836i	$-0.651515\pi$
$59$	4.15275	−	7.19278i	0.540642	−	0.936420i	0.998867	−	0.0475837i	$-0.0151521\pi$
$60$		0			0
$61$	−5.48589	−	9.50184i	−0.702397	−	1.21659i	−0.967623	−	0.252400i	$-0.918780\pi$
$61$	−5.48589	−	9.50184i	−0.702397	−	1.21659i	0.265226	−	0.964186i	$-0.414553\pi$
$62$	3.10346	−	8.54650i	0.394140	−	1.08541i
$63$		0			0
$64$	−3.96897	+	6.94603i	−0.496121	+	0.868253i
$65$	−13.0975	+	7.56183i	−1.62454	+	0.937930i
$66$		0			0
$67$	9.26153	+	5.34715i	1.13148	+	0.653258i	0.944306	−	0.329069i	$-0.106735\pi$
$67$	9.26153	+	5.34715i	1.13148	+	0.653258i	0.187170	+	0.982327i	$0.440068\pi$
$68$	2.47852	+	6.77821i	0.300564	+	0.821978i
$69$		0			0
$70$	0.935704	+	5.28360i	0.111838	+	0.631511i
$71$	−2.73284			−0.324329			−0.162164	−	0.986764i	$-0.551848\pi$
$71$	−2.73284			−0.324329			−0.162164	+	0.986764i	$0.551848\pi$
$72$		0			0
$73$	8.63292			1.01041			0.505203	−	0.863000i	$-0.331417\pi$
$73$	8.63292			1.01041			0.505203	+	0.863000i	$0.331417\pi$
$74$	0.953498	+	5.38408i	0.110842	+	0.625886i
$75$		0			0
$76$	−4.13870	−	11.3185i	−0.474742	−	1.29832i
$77$	0.255018	+	0.147235i	0.0290620	+	0.0167790i
$78$		0			0
$79$	4.74756	−	2.74100i	0.534142	−	0.308387i	−0.208560	−	0.978010i	$-0.566878\pi$
$79$	4.74756	−	2.74100i	0.534142	−	0.308387i	0.742701	+	0.669623i	$0.233544\pi$
$80$	14.9383	−	2.67999i	1.67016	−	0.299632i
$81$		0			0
$82$	5.96084	−	16.4153i	0.658265	−	1.81277i
$83$	−4.07096	−	7.05111i	−0.446846	−	0.773960i	0.551333	−	0.834286i	$-0.314120\pi$
$83$	−4.07096	−	7.05111i	−0.446846	−	0.773960i	−0.998179	+	0.0603253i	$0.980786\pi$
$84$		0			0
$85$	6.84583	−	11.8573i	0.742534	−	1.28611i
$86$	0.895639	+	1.06577i	0.0965792	+	0.114925i
$87$		0			0
$88$	0.414829	−	0.722231i	0.0442209	−	0.0769900i
$89$		−	3.35572i		−	0.355706i	−0.984057	−	0.177853i	$-0.943085\pi$
$89$		−	3.35572i		−	0.355706i	0.984057	−	0.177853i	$-0.0569151\pi$
$90$		0			0
$91$		−	3.98599i		−	0.417845i
$92$	1.63593	−	9.35939i	0.170557	−	0.975784i
$93$		0			0
$94$	−3.64580	+	3.06383i	−0.376036	+	0.316010i
$95$	−11.4314	+	19.7997i	−1.17283	+	2.03141i
$96$		0			0
$97$	6.74076	+	11.6753i	0.684421	+	1.18545i	0.973619	+	0.228182i	$0.0732781\pi$
$97$	6.74076	+	11.6753i	0.684421	+	1.18545i	−0.289198	+	0.957269i	$0.593389\pi$
$98$	−1.32929	−	0.482699i	−0.134278	−	0.0487599i
$99$		0			0
$100$	−14.4135	−	12.0578i	−1.44135	−	1.20578i
$101$	11.1419	−	6.43278i	1.10866	−	0.640085i	0.170178	−	0.985413i	$-0.445566\pi$
$101$	11.1419	−	6.43278i	1.10866	−	0.640085i	0.938482	+	0.345328i	$0.112232\pi$
$102$		0			0
$103$	−7.71860	−	4.45634i	−0.760537	−	0.439096i	0.0689517	−	0.997620i	$-0.478035\pi$
$103$	−7.71860	−	4.45634i	−0.760537	−	0.439096i	−0.829488	+	0.558524i	$0.811368\pi$
$104$	−11.2741	+	0.0252150i	−1.10551	+	0.00247254i
$105$		0			0
$106$	−2.82728	+	0.500699i	−0.274609	+	0.0486322i
$107$	2.28113			0.220525			0.110263	−	0.993902i	$-0.464831\pi$
$107$	2.28113			0.220525			0.110263	+	0.993902i	$0.464831\pi$
$108$		0			0
$109$	−10.0544			−0.963032			−0.481516	−	0.876437i	$-0.659914\pi$
$109$	−10.0544			−0.963032			−0.481516	+	0.876437i	$0.659914\pi$
$110$	−1.55586	+	0.275537i	−0.148346	+	0.0262714i
$111$		0			0
$112$	−1.35687	+	3.76283i	−0.128212	+	0.355554i
$113$	−6.07706	−	3.50859i	−0.571682	−	0.330061i	0.186139	−	0.982523i	$-0.440403\pi$
$113$	−6.07706	−	3.50859i	−0.571682	−	0.330061i	−0.757821	+	0.652463i	$0.773736\pi$
$114$		0			0
$115$	−15.6100	+	9.01246i	−1.45564	+	0.840416i
$116$	1.34024	−	1.60208i	0.124438	−	0.148749i
$117$		0			0
$118$	−11.0404	−	4.00906i	−1.01635	−	0.369064i
$119$	1.80429	+	3.12511i	0.165399	+	0.286479i
$120$		0			0
$121$	5.45664	−	9.45118i	0.496059	−	0.859199i
$122$	−11.8788	+	9.98264i	−1.07546	+	0.903786i
$123$		0			0
$124$	−12.6667	−	2.21402i	−1.13751	−	0.198825i
$125$			16.6793i			1.49184i
$126$		0			0
$127$			6.98999i			0.620262i	0.950694	+	0.310131i	$0.100373\pi$
$127$			6.98999i			0.620262i	−0.950694	+	0.310131i	$0.899627\pi$
$128$	10.6515	+	3.81398i	0.941465	+	0.337112i
$129$		0			0
$130$	13.7602	+	16.3740i	1.20685	+	1.43609i
$131$	−5.94819	+	10.3026i	−0.519696	+	0.900139i	0.480042	+	0.877245i	$0.340621\pi$
$131$	−5.94819	+	10.3026i	−0.519696	+	0.900139i	−0.999738	+	0.0228940i	$0.992712\pi$
$132$		0			0
$133$	−3.01285	−	5.21841i	−0.261247	−	0.452493i
$134$	5.16212	−	14.2158i	0.445939	−	1.22806i
$135$		0			0
$136$	8.82772	−	5.12305i	0.756971	−	0.439297i
$137$	0.240419	−	0.138806i	0.0205404	−	0.0118590i	−0.489695	−	0.871894i	$-0.662892\pi$
$137$	0.240419	−	0.138806i	0.0205404	−	0.0118590i	0.510235	+	0.860035i	$0.329558\pi$
$138$		0			0
$139$	−9.51784	−	5.49513i	−0.807293	−	0.466091i	0.0387220	−	0.999250i	$-0.487671\pi$
$139$	−9.51784	−	5.49513i	−0.807293	−	0.466091i	−0.846015	+	0.533159i	$0.821005\pi$
$140$	7.12690	−	2.60602i	0.602333	−	0.220249i
$141$		0			0
$142$	0.673957	+	3.80561i	0.0565572	+	0.319360i
$143$	1.17375			0.0981542
$144$		0			0
$145$	−3.96258			−0.329075
$146$	−2.12900	−	12.0217i	−0.176197	−	0.994925i
$147$		0			0
$148$	7.26243	−	2.65558i	0.596968	−	0.218287i
$149$	−7.22393	−	4.17074i	−0.591808	−	0.341680i	0.174004	−	0.984745i	$-0.444329\pi$
$149$	−7.22393	−	4.17074i	−0.591808	−	0.341680i	−0.765812	+	0.643065i	$0.777663\pi$
$150$		0			0
$151$	4.58601	−	2.64773i	0.373204	−	0.215469i	−0.301653	−	0.953418i	$-0.597539\pi$
$151$	4.58601	−	2.64773i	0.373204	−	0.215469i	0.674857	+	0.737948i	$0.264205\pi$
$152$	−14.7408	+	8.55462i	−1.19564	+	0.693871i
$153$		0			0
$154$	0.142140	−	0.391435i	0.0114540	−	0.0315427i
$155$	12.1972	+	21.1262i	0.979704	+	1.69690i
$156$		0			0
$157$	4.66952	−	8.08784i	0.372668	−	0.645480i	−0.617307	−	0.786722i	$-0.711776\pi$
$157$	4.66952	−	8.08784i	0.372668	−	0.645480i	0.989975	+	0.141242i	$0.0451097\pi$
$158$	−4.98778	−	5.93522i	−0.396807	−	0.472180i
$159$		0			0
$160$	−7.41600	−	20.1414i	−0.586286	−	1.59232i
$161$		−	4.75064i		−	0.374403i
$162$		0			0
$163$			15.6620i			1.22674i	0.789794	+	0.613372i	$0.210187\pi$
$163$			15.6620i			1.22674i	−0.789794	+	0.613372i	$0.789813\pi$
$164$	−24.3291	−	4.25249i	−1.89979	−	0.332064i
$165$		0			0
$166$	−8.81504	+	7.40790i	−0.684179	+	0.574965i
$167$	−1.43448	+	2.48460i	−0.111004	+	0.192264i	−0.916175	−	0.400778i	$-0.868740\pi$
$167$	−1.43448	+	2.48460i	−0.111004	+	0.192264i	0.805172	+	0.593042i	$0.202073\pi$
$168$		0			0
$169$	−1.44406	−	2.50118i	−0.111081	−	0.192398i
$170$	−18.2001	−	6.60895i	−1.39589	−	0.506883i
$171$		0			0
$172$	1.26325	−	1.51005i	0.0963219	−	0.115140i
$173$	−5.95609	+	3.43875i	−0.452833	+	0.261443i	−0.709026	−	0.705182i	$-0.750865\pi$
$173$	−5.95609	+	3.43875i	−0.452833	+	0.261443i	0.256193	+	0.966626i	$0.417532\pi$
$174$		0			0
$175$	−8.13717	−	4.69800i	−0.615113	−	0.355135i
$176$	−1.10804	−	0.399556i	−0.0835217	−	0.0301177i
$177$		0			0
$178$	−4.67299	+	0.827567i	−0.350255	+	0.0620288i
$179$	19.3475			1.44610			0.723050	−	0.690796i	$-0.242740\pi$
$179$	19.3475			1.44610			0.723050	+	0.690796i	$0.242740\pi$
$180$		0			0
$181$	−12.6872			−0.943032			−0.471516	−	0.881858i	$-0.656293\pi$
$181$	−12.6872			−0.943032			−0.471516	+	0.881858i	$0.656293\pi$
$182$	−5.55067	+	0.983000i	−0.411443	+	0.0728648i
$183$		0			0
$184$	−13.4368	+	0.0300522i	−0.990575	+	0.00221547i
$185$	−12.7044	−	7.33488i	−0.934045	−	0.539271i
$186$		0			0
$187$	−0.920252	+	0.531308i	−0.0672955	+	0.0388531i
$188$	5.16562	+	4.32136i	0.376742	+	0.315168i
$189$		0			0
$190$	30.3911	+	11.0358i	2.20480	+	0.800622i
$191$	−4.15917	−	7.20389i	−0.300947	−	0.521255i	0.675404	−	0.737448i	$-0.263969\pi$
$191$	−4.15917	−	7.20389i	−0.300947	−	0.521255i	−0.976351	+	0.216193i	$0.930636\pi$
$192$		0			0
$193$	5.39565	−	9.34554i	0.388387	−	0.672707i	−0.603845	−	0.797101i	$-0.706366\pi$
$193$	5.39565	−	9.34554i	0.388387	−	0.672707i	0.992233	+	0.124395i	$0.0396989\pi$
$194$	14.5961	−	12.2661i	1.04794	−	0.880656i
$195$		0			0
$196$	−0.344359	+	1.97013i	−0.0245971	+	0.140724i
$197$		−	14.3939i		−	1.02553i	−0.858530	−	0.512763i	$-0.828622\pi$
$197$		−	14.3939i		−	1.02553i	0.858530	−	0.512763i	$-0.171378\pi$
$198$		0			0
$199$			14.9925i			1.06279i	0.847124	+	0.531395i	$0.178332\pi$
$199$			14.9925i			1.06279i	−0.847124	+	0.531395i	$0.821668\pi$
$200$	−13.2364	+	23.0451i	−0.935958	+	1.62953i
$201$		0			0
$202$	−11.7057	−	13.9292i	−0.823609	−	0.980054i
$203$	0.522189	−	0.904457i	0.0366505	−	0.0634805i
$204$		0			0
$205$	23.4273	+	40.5773i	1.63623	+	2.83404i
$206$	−4.30214	+	11.8475i	−0.299744	+	0.825454i
$207$		0			0
$208$	2.81545	+	15.6934i	0.195216	+	1.08814i
$209$	1.53666	−	0.887194i	0.106293	−	0.0613685i
$210$		0			0
$211$	2.48466	+	1.43452i	0.171051	+	0.0987564i	0.583081	−	0.812414i	$-0.301847\pi$
$211$	2.48466	+	1.43452i	0.171051	+	0.0987564i	−0.412030	+	0.911170i	$0.635180\pi$
$212$	1.39449	+	3.81363i	0.0957740	+	0.261921i
$213$		0			0
$214$	−0.562559	−	3.17658i	−0.0384557	−	0.217147i
$215$	−3.73496			−0.254722
$216$		0			0
$217$	−6.42939			−0.436456
$218$	2.47954	+	14.0011i	0.167936	+	0.948277i
$219$		0			0
$220$	0.767394	+	2.09866i	0.0517377	+	0.141491i
$221$	12.4567	+	7.19186i	0.837926	+	0.483777i
$222$		0			0
$223$	14.5462	−	8.39828i	0.974088	−	0.562390i	0.0736082	−	0.997287i	$-0.476549\pi$
$223$	14.5462	−	8.39828i	0.974088	−	0.562390i	0.900480	+	0.434897i	$0.143215\pi$
$224$	5.57454	+	0.961530i	0.372464	+	0.0642449i
$225$		0			0
$226$	−3.38719	+	9.32785i	−0.225312	+	0.620479i
$227$	−14.3890	−	24.9225i	−0.955033	−	1.65417i	−0.734291	−	0.678834i	$-0.762485\pi$
$227$	−14.3890	−	24.9225i	−0.955033	−	1.65417i	−0.220742	−	0.975332i	$-0.570848\pi$
$228$		0			0
$229$	−9.30663	+	16.1196i	−0.614999	+	1.06521i	0.375385	+	0.926869i	$0.377510\pi$
$229$	−9.30663	+	16.1196i	−0.614999	+	1.06521i	−0.990385	+	0.138341i	$0.955823\pi$
$230$	16.3999	+	19.5151i	1.08138	+	1.28679i
$231$		0			0
$232$	−2.56149	−	1.47125i	−0.168170	−	0.0965921i
$233$			25.3473i			1.66056i	0.557348	+	0.830279i	$0.311819\pi$
$233$			25.3473i			1.66056i	−0.557348	+	0.830279i	$0.688181\pi$
$234$		0			0
$235$		−	12.7767i		−	0.833457i
$236$	−2.86008	+	16.3629i	−0.186175	+	1.06514i
$237$		0			0
$238$	3.90690	−	3.28324i	0.253247	−	0.212821i
$239$	12.5884	−	21.8038i	0.814279	−	1.41037i	−0.0955656	−	0.995423i	$-0.530466\pi$
$239$	12.5884	−	21.8038i	0.814279	−	1.41037i	0.909845	−	0.414949i	$-0.136201\pi$
$240$		0			0
$241$	−4.83687	−	8.37771i	−0.311570	−	0.539656i	0.667132	−	0.744939i	$-0.267522\pi$
$241$	−4.83687	−	8.37771i	−0.311570	−	0.539656i	−0.978703	+	0.205284i	$0.934188\pi$
$242$	−14.5069	−	5.26783i	−0.932538	−	0.338629i
$243$		0			0
$244$	16.8308	+	14.0800i	1.07748	+	0.901378i
$245$	3.28588	−	1.89710i	0.209927	−	0.121201i
$246$		0			0
$247$	−20.8005	−	12.0092i	−1.32351	−	0.764126i
$248$	0.0406718	+	18.1850i	0.00258266	+	1.15475i
$249$		0			0
$250$	23.2267	−	4.11335i	1.46899	−	0.260151i
$251$	−9.27090			−0.585174			−0.292587	−	0.956239i	$-0.594516\pi$
$251$	−9.27090			−0.585174			−0.292587	+	0.956239i	$0.594516\pi$
$252$		0			0
$253$	1.39892			0.0879494
$254$	9.73388	−	1.72383i	0.610758	−	0.108163i
$255$		0			0
$256$	2.68435	−	15.7732i	0.167772	−	0.985826i
$257$	−12.1695	−	7.02607i	−0.759113	−	0.438274i	0.0698640	−	0.997557i	$-0.477743\pi$
$257$	−12.1695	−	7.02607i	−0.759113	−	0.438274i	−0.828977	+	0.559282i	$0.811077\pi$
$258$		0			0
$259$	3.34837	−	1.93318i	0.208057	−	0.120122i
$260$	19.4080	−	23.1998i	1.20364	−	1.43879i
$261$		0			0
$262$	15.8137	+	5.74237i	0.976973	+	0.354765i
$263$	−3.96550	−	6.86845i	−0.244523	−	0.423527i	0.717474	−	0.696585i	$-0.245298\pi$
$263$	−3.96550	−	6.86845i	−0.244523	−	0.423527i	−0.961997	+	0.273058i	$0.911965\pi$
$264$		0			0
$265$	3.85168	−	6.67130i	0.236607	−	0.409815i
$266$	−6.52386	+	5.48246i	−0.400003	+	0.336151i
$267$		0			0
$268$	−21.0692	−	3.68268i	−1.28700	−	0.224955i
$269$			6.36470i			0.388062i	0.980995	+	0.194031i	$0.0621563\pi$
$269$			6.36470i			0.388062i	−0.980995	+	0.194031i	$0.937844\pi$
$270$		0			0
$271$		−	2.98241i		−	0.181169i	−0.995889	−	0.0905844i	$-0.971127\pi$
$271$		−	2.98241i		−	0.181169i	0.995889	−	0.0905844i	$-0.0288735\pi$
$272$	−9.31111	−	11.0296i	−0.564569	−	0.668767i
$273$		0			0
$274$	−0.252584	−	0.300563i	−0.0152592	−	0.0181577i
$275$	1.38342	−	2.39615i	0.0834233	−	0.144493i
$276$		0			0
$277$	−10.7876	−	18.6847i	−0.648164	−	1.12265i	−0.983561	−	0.180576i	$-0.942204\pi$
$277$	−10.7876	−	18.6847i	−0.648164	−	1.12265i	0.335397	−	0.942077i	$-0.391130\pi$
$278$	−5.30498	+	14.6092i	−0.318172	+	0.876202i
$279$		0			0
$280$	−5.38659	−	9.28184i	−0.321910	−	0.554696i
$281$	7.00028	−	4.04161i	0.417602	−	0.241103i	−0.276449	−	0.961029i	$-0.589158\pi$
$281$	7.00028	−	4.04161i	0.417602	−	0.241103i	0.694051	+	0.719926i	$0.255824\pi$
$282$		0			0
$283$	−0.719769	−	0.415559i	−0.0427858	−	0.0247024i	0.478455	−	0.878112i	$-0.341197\pi$
$283$	−0.719769	−	0.415559i	−0.0427858	−	0.0247024i	−0.521240	+	0.853410i	$0.674530\pi$
$284$	5.13327	−	1.87703i	0.304604	−	0.111381i
$285$		0			0
$286$	−0.289464	−	1.63451i	−0.0171164	−	0.0966503i
$287$	−12.3490			−0.728938
$288$		0			0
$289$	3.97822			0.234013
$290$	0.977228	+	5.51808i	0.0573848	+	0.324033i
$291$		0			0
$292$	−16.2158	+	5.92945i	−0.948956	+	0.346995i
$293$	−11.2950	−	6.52120i	−0.659864	−	0.380972i	0.132361	−	0.991202i	$-0.457744\pi$
$293$	−11.2950	−	6.52120i	−0.659864	−	0.380972i	−0.792225	+	0.610229i	$0.791077\pi$
$294$		0			0
$295$	27.2909	−	15.7564i	1.58894	−	0.917373i
$296$	−5.48903	−	9.45835i	−0.319043	−	0.549756i
$297$		0			0
$298$	−4.02642	+	11.0882i	−0.233244	+	0.642323i
$299$	−9.46801	−	16.3991i	−0.547549	−	0.948383i
$300$		0			0
$301$	0.492192	−	0.852502i	0.0283695	−	0.0491374i
$302$	−4.81806	−	5.73325i	−0.277248	−	0.329912i
$303$		0			0
$304$	15.5480	+	18.4175i	0.891737	+	1.05632i
$305$		−	41.6292i		−	2.38368i
$306$		0			0
$307$		−	32.6077i		−	1.86102i	−0.366266	−	0.930510i	$-0.619364\pi$
$307$		−	32.6077i		−	1.86102i	0.366266	−	0.930510i	$-0.380636\pi$
$308$	−0.580144	−	0.101403i	−0.0330568	−	0.00577800i
$309$		0			0
$310$	26.4112	−	22.1952i	1.50005	−	1.26060i
$311$	6.47968	−	11.2231i	0.367429	−	0.636406i	−0.621734	−	0.783229i	$-0.713571\pi$
$311$	6.47968	−	11.2231i	0.367429	−	0.636406i	0.989163	+	0.146823i	$0.0469047\pi$
$312$		0			0
$313$	−3.72105	−	6.44505i	−0.210326	−	0.364296i	0.741490	−	0.670963i	$-0.234119\pi$
$313$	−3.72105	−	6.44505i	−0.210326	−	0.364296i	−0.951817	+	0.306668i	$0.900786\pi$
$314$	−12.4142	−	4.50794i	−0.700576	−	0.254398i
$315$		0			0
$316$	−7.03500	+	8.40942i	−0.395750	+	0.473067i
$317$	0.272234	−	0.157175i	0.0152902	−	0.00882780i	−0.492335	−	0.870406i	$-0.663857\pi$
$317$	0.272234	−	0.157175i	0.0152902	−	0.00882780i	0.507626	+	0.861578i	$0.330523\pi$
$318$		0			0
$319$	0.266336	+	0.153769i	0.0149119	+	0.00860940i
$320$	−26.2189	+	15.2943i	−1.46568	+	0.854975i
$321$		0			0
$322$	−6.61548	+	1.17157i	−0.368667	+	0.0652893i
$323$	21.7442			1.20988
$324$		0			0
$325$	−37.4524			−2.07748
$326$	21.8101	−	3.86247i	1.20795	−	0.213923i
$327$		0			0
$328$	0.0781187	+	34.9281i	0.00431338	+	1.92858i
$329$	2.91626	+	1.68371i	0.160779	+	0.0928257i
$330$		0			0
$331$	18.2481	−	10.5356i	1.00301	−	0.579087i	0.0938717	−	0.995584i	$-0.470076\pi$
$331$	18.2481	−	10.5356i	1.00301	−	0.579087i	0.909137	+	0.416497i	$0.136742\pi$
$332$	12.4897	+	10.4484i	0.685464	+	0.573433i
$333$		0			0
$334$	3.81367	+	1.38484i	0.208675	+	0.0757753i
$335$	20.2882	+	35.1402i	1.10846	+	1.91991i
$336$		0			0
$337$	−4.76860	+	8.25945i	−0.259762	+	0.449921i	−0.966178	−	0.257876i	$-0.916977\pi$
$337$	−4.76860	+	8.25945i	−0.259762	+	0.449921i	0.706416	+	0.707797i	$0.250311\pi$
$338$	−3.12688	+	2.62774i	−0.170080	+	0.142930i
$339$		0			0
$340$	−4.71485	+	26.9744i	−0.255699	+	1.46289i
$341$		−	1.89326i		−	0.102526i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−2.41435	−	1.38673i	−0.130173	−	0.0747677i
$345$		0			0
$346$	6.25746	+	7.44608i	0.336403	+	0.400303i
$347$	6.87336	−	11.9050i	0.368981	−	0.639095i	−0.620425	−	0.784266i	$-0.713040\pi$
$347$	6.87336	−	11.9050i	0.368981	−	0.639095i	0.989407	+	0.145171i	$0.0463733\pi$
$348$		0			0
$349$	8.69604	+	15.0620i	0.465488	+	0.806249i	0.999223	−	0.0394024i	$-0.0125454\pi$
$349$	8.69604	+	15.0620i	0.465488	+	0.806249i	−0.533735	+	0.845652i	$0.679212\pi$
$350$	−4.53544	+	12.4900i	−0.242429	+	0.667617i
$351$		0			0
$352$	−0.283142	+	1.64153i	−0.0150915	+	0.0874940i
$353$	16.2716	−	9.39439i	0.866047	−	0.500013i	1.46597e−5	−	1.00000i	$-0.499995\pi$
$353$	16.2716	−	9.39439i	0.866047	−	0.500013i	0.866033	+	0.499987i	$0.166662\pi$
$354$		0			0
$355$	−8.97979	−	5.18449i	−0.476598	−	0.275164i
$356$	2.30485	+	6.30326i	0.122157	+	0.334072i
$357$		0			0
$358$	−4.77136	−	26.9423i	−0.252174	−	1.42394i
$359$	14.2512			0.752151			0.376076	−	0.926589i	$-0.377273\pi$
$359$	14.2512			0.752151			0.376076	+	0.926589i	$0.377273\pi$
$360$		0			0
$361$	−17.3091			−0.911003
$362$	3.12884	+	17.6675i	0.164448	+	0.928582i
$363$		0			0
$364$	2.73774	+	7.48714i	0.143497	+	0.392433i
$365$	28.3667	+	16.3775i	1.48478	+	0.857240i
$366$		0			0
$367$	−1.87665	+	1.08348i	−0.0979604	+	0.0565574i	−0.548180	−	0.836360i	$-0.684679\pi$
$367$	−1.87665	+	1.08348i	−0.0979604	+	0.0565574i	0.450219	+	0.892918i	$0.351346\pi$
$368$	3.35555	+	18.7040i	0.174920	+	0.975011i
$369$		0			0
$370$	−7.08107	+	19.5003i	−0.368128	+	1.01377i
$371$	1.01515	+	1.75829i	0.0527038	+	0.0912857i
$372$		0			0
$373$	−16.7324	+	28.9814i	−0.866370	+	1.50060i	−0.000690393		1.00000i	$0.500220\pi$
$373$	−16.7324	+	28.9814i	−0.866370	+	1.50060i	−0.865680	+	0.500598i	$0.833114\pi$
$374$	0.966817	+	1.15046i	0.0499929	+	0.0594891i
$375$		0			0
$376$	4.74378	−	8.25907i	0.244642	−	0.425929i
$377$		−	4.16288i		−	0.214399i
$378$		0			0
$379$			6.82998i			0.350832i	0.984494	+	0.175416i	$0.0561271\pi$
$379$			6.82998i			0.350832i	−0.984494	+	0.175416i	$0.943873\pi$
$380$	7.87300	−	45.0426i	0.403876	−	2.31064i
$381$		0			0
$382$	−9.00603	+	7.56841i	−0.460789	+	0.387233i
$383$	3.69911	−	6.40704i	0.189016	−	0.327384i	−0.755907	−	0.654679i	$-0.772804\pi$
$383$	3.69911	−	6.40704i	0.189016	−	0.327384i	0.944922	+	0.327295i	$0.106137\pi$
$384$		0			0
$385$	0.558640	+	0.967592i	0.0284709	+	0.0493131i
$386$	−14.3447	−	5.20895i	−0.730128	−	0.265128i
$387$		0			0
$388$	−20.6807	−	17.3007i	−1.04990	−	0.878310i
$389$	−15.0318	+	8.67863i	−0.762144	+	0.440024i	−0.830065	−	0.557667i	$-0.811697\pi$
$389$	−15.0318	+	8.67863i	−0.762144	+	0.440024i	0.0679209	+	0.997691i	$0.478363\pi$
$390$		0			0
$391$	14.8463	+	8.57151i	0.750810	+	0.433480i
$392$	2.82842	−	0.00632591i	0.142857	−	0.000319507i
$393$		0			0
$394$	−20.0442	+	3.54975i	−1.00981	+	0.178834i
$395$	20.7999			1.04655
$396$		0			0
$397$	4.91004			0.246428			0.123214	−	0.992380i	$-0.460680\pi$
$397$	4.91004			0.246428			0.123214	+	0.992380i	$0.460680\pi$
$398$	20.8777	−	3.69736i	1.04651	−	0.185332i
$399$		0			0
$400$	35.3556	+	12.7491i	1.76778	+	0.637455i
$401$	21.0371	+	12.1458i	1.05054	+	0.606532i	0.922802	−	0.385276i	$-0.125894\pi$
$401$	21.0371	+	12.1458i	1.05054	+	0.606532i	0.127742	+	0.991807i	$0.459227\pi$
$402$		0			0
$403$	−22.1941	+	12.8137i	−1.10556	+	0.638298i
$404$	−16.5102	+	19.7358i	−0.821415	+	0.981894i
$405$		0			0
$406$	−1.38828	−	0.504120i	−0.0688990	−	0.0250190i
$407$	0.569263	+	0.985993i	0.0282173	+	0.0488738i
$408$		0			0
$409$	19.1299	−	33.1340i	0.945915	−	1.63837i	0.192006	−	0.981394i	$-0.438501\pi$
$409$	19.1299	−	33.1340i	0.945915	−	1.63837i	0.753909	−	0.656979i	$-0.228166\pi$
$410$	50.7282	−	42.6305i	2.50529	−	2.10537i
$411$		0			0
$412$	17.5591	+	3.06916i	0.865077	+	0.151207i
$413$			8.30551i			0.408687i
$414$		0			0
$415$		−	30.8921i		−	1.51644i
$416$	21.1594	−	7.79085i	1.03743	−	0.381978i
$417$		0			0
$418$	−1.61442	−	1.92108i	−0.0789638	−	0.0939631i
$419$	9.47453	−	16.4104i	0.462861	−	0.801699i	−0.536241	−	0.844065i	$-0.680156\pi$
$419$	9.47453	−	16.4104i	0.462861	−	0.801699i	0.999102	+	0.0423659i	$0.0134895\pi$
$420$		0			0
$421$	10.6034	+	18.3656i	0.516777	+	0.895084i	0.999810	+	0.0194821i	$0.00620175\pi$
$421$	10.6034	+	18.3656i	0.516777	+	0.895084i	−0.483033	+	0.875602i	$0.660465\pi$
$422$	1.38488	−	3.81377i	0.0674150	−	0.185652i
$423$		0			0
$424$	4.96675	−	2.88239i	0.241207	−	0.139981i
$425$	29.3636	−	16.9531i	1.42434	−	0.822344i
$426$		0			0
$427$	9.50184	+	5.48589i	0.459827	+	0.265481i
$428$	−4.28480	+	1.56678i	−0.207113	+	0.0757330i
$429$		0			0
$430$	0.921092	+	5.20110i	0.0444190	+	0.250819i
$431$	6.24043			0.300591			0.150295	−	0.988641i	$-0.451977\pi$
$431$	6.24043			0.300591			0.150295	+	0.988641i	$0.451977\pi$
$432$		0			0
$433$	12.2312			0.587795			0.293897	−	0.955837i	$-0.405048\pi$
$433$	12.2312			0.587795			0.293897	+	0.955837i	$0.405048\pi$
$434$	1.58558	+	8.95322i	0.0761101	+	0.429768i
$435$		0			0
$436$	18.8857	−	6.90575i	0.904462	−	0.330725i
$437$	−24.7908	−	14.3130i	−1.18590	−	0.684682i
$438$		0			0
$439$	17.4636	−	10.0826i	0.833492	−	0.481217i	−0.0215550	−	0.999768i	$-0.506862\pi$
$439$	17.4636	−	10.0826i	0.833492	−	0.481217i	0.855047	+	0.518551i	$0.173528\pi$
$440$	2.73322	−	1.58619i	0.130301	−	0.0756186i
$441$		0			0
$442$	6.94300	−	19.1201i	0.330245	−	0.909450i
$443$	14.2028	+	24.6000i	0.674795	+	1.16878i	0.976529	+	0.215387i	$0.0691014\pi$
$443$	14.2028	+	24.6000i	0.674795	+	1.16878i	−0.301733	+	0.953392i	$0.597565\pi$
$444$		0			0
$445$	6.36615	−	11.0265i	0.301784	−	0.522706i
$446$	−15.2823	−	18.1852i	−0.723637	−	0.861093i
$447$		0			0
$448$	−0.0357847	−	7.99992i	−0.00169067	−	0.377961i
$449$		−	8.88596i		−	0.419354i	−0.977771	−	0.209677i	$-0.932759\pi$
$449$		−	8.88596i		−	0.419354i	0.977771	−	0.209677i	$-0.0672413\pi$
$450$		0			0
$451$		−	3.63641i		−	0.171232i
$452$	13.8248	+	2.41643i	0.650263	+	0.113659i
$453$		0			0
$454$	−31.1572	+	26.1836i	−1.46228	+	1.22886i
$455$	7.56183	−	13.0975i	0.354504	−	0.614019i
$456$		0			0
$457$	5.43702	+	9.41720i	0.254333	+	0.440518i	0.964714	−	0.263299i	$-0.0848106\pi$
$457$	5.43702	+	9.41720i	0.254333	+	0.440518i	−0.710381	+	0.703817i	$0.751477\pi$
$458$	24.7423	+	8.98459i	1.15613	+	0.419822i
$459$		0			0
$460$	23.1312	−	27.6503i	1.07850	−	1.28920i
$461$	−31.3246	+	18.0853i	−1.45893	+	0.842316i	−0.998959	−	0.0456166i	$-0.985475\pi$
$461$	−31.3246	+	18.0853i	−1.45893	+	0.842316i	−0.459974	+	0.887932i	$0.652141\pi$
$462$		0			0
$463$	−7.50957	−	4.33565i	−0.348999	−	0.201495i	0.315245	−	0.949010i	$-0.397913\pi$
$463$	−7.50957	−	4.33565i	−0.348999	−	0.201495i	−0.664244	+	0.747516i	$0.731247\pi$
$464$	−1.41708	+	3.92982i	−0.0657863	+	0.182437i
$465$		0			0
$466$	35.2973	−	6.25100i	1.63511	−	0.289572i
$467$	−13.4993			−0.624671			−0.312336	−	0.949972i	$-0.601111\pi$
$467$	−13.4993			−0.624671			−0.312336	+	0.949972i	$0.601111\pi$
$468$		0			0
$469$	−10.6943			−0.493817
$470$	−17.7921	+	3.15090i	−0.820687	+	0.145340i
$471$		0			0
$472$	23.4915	−	0.0525399i	1.08128	−	0.00241835i
$473$	0.251036	+	0.144936i	0.0115427	+	0.00666416i
$474$		0			0
$475$	−49.0322	+	28.3087i	−2.24975	+	1.29889i
$476$	−5.53556	−	4.63084i	−0.253722	−	0.212254i
$477$		0			0
$478$	−33.4673	−	12.1529i	−1.53076	−	0.555859i
$479$	19.1408	+	33.1529i	0.874567	+	1.51480i	0.857223	+	0.514945i	$0.172188\pi$
$479$	19.1408	+	33.1529i	0.874567	+	1.51480i	0.0173444	+	0.999850i	$0.494479\pi$
$480$		0			0
$481$	7.70563	−	13.3465i	0.351347	−	0.608550i
$482$	−10.4735	+	8.80163i	−0.477055	+	0.400903i
$483$		0			0
$484$	−3.75809	+	21.5006i	−0.170822	+	0.977300i
$485$			51.1517i			2.32268i
$486$		0			0
$487$			13.3113i			0.603193i	0.953436	+	0.301597i	$0.0975196\pi$
$487$			13.3113i			0.603193i	−0.953436	+	0.301597i	$0.902480\pi$
$488$	15.4563	−	26.9099i	0.699674	−	1.21815i
$489$		0			0
$490$	−3.45214	−	4.10788i	−0.155952	−	0.185575i
$491$	−1.46735	+	2.54153i	−0.0662207	+	0.114698i	−0.897235	−	0.441554i	$-0.854427\pi$
$491$	−1.46735	+	2.54153i	−0.0662207	+	0.114698i	0.831014	+	0.556251i	$0.187761\pi$
$492$		0			0
$493$	1.88435	+	3.26380i	0.0848671	+	0.146994i
$494$	−11.5936	+	31.9273i	−0.521622	+	1.43648i
$495$		0			0
$496$	25.3134	−	4.54131i	1.13661	−	0.203911i
$497$	2.36671	−	1.36642i	0.106162	−	0.0612924i
$498$		0			0
$499$	32.3491	+	18.6768i	1.44815	+	0.836088i	0.998371	−	0.0570538i	$-0.0181707\pi$
$499$	32.3491	+	18.6768i	1.44815	+	0.836088i	0.449775	+	0.893142i	$0.351504\pi$
$500$	−11.4561	−	31.3298i	−0.512331	−	1.40111i
$501$		0			0
$502$	2.28633	+	12.9101i	0.102044	+	0.576208i
$503$	−29.1509			−1.29978			−0.649888	−	0.760030i	$-0.725184\pi$
$503$	−29.1509			−1.29978			−0.649888	+	0.760030i	$0.725184\pi$
$504$		0			0
$505$	48.8146			2.17222
$506$	−0.344993	−	1.94806i	−0.0153368	−	0.0866019i
$507$		0			0
$508$	−4.80102	−	13.1297i	−0.213011	−	0.582538i
$509$	19.4308	+	11.2184i	0.861255	+	0.497246i	0.864432	−	0.502749i	$-0.167678\pi$
$509$	19.4308	+	11.2184i	0.861255	+	0.497246i	−0.00317707	+	0.999995i	$0.501011\pi$
$510$		0			0
$511$	−7.47633	+	4.31646i	−0.330733	+	0.190949i
$512$	−22.6269	+	0.151821i	−0.999977	+	0.00670960i
$513$		0			0
$514$	−6.78295	+	18.6793i	−0.299183	+	0.823909i
$515$	−16.9083	−	29.2860i	−0.745067	−	1.29049i
$516$		0			0
$517$	−0.495801	+	0.858752i	−0.0218053	+	0.0377679i
$518$	−3.51779	−	4.18600i	−0.154563	−	0.183922i
$519$		0			0
$520$	−37.0930	−	21.3052i	−1.62664	−	0.934294i
$521$		−	19.1422i		−	0.838636i	−0.907839	−	0.419318i	$-0.862269\pi$
$521$		−	19.1422i		−	0.838636i	0.907839	−	0.419318i	$-0.137731\pi$
$522$		0			0
$523$		−	7.09271i		−	0.310143i	−0.987903	−	0.155071i	$-0.950439\pi$
$523$		−	7.09271i		−	0.310143i	0.987903	−	0.155071i	$-0.0495607\pi$
$524$	4.09663	−	23.4374i	0.178962	−	1.02387i
$525$		0			0
$526$	−8.58668	+	7.21600i	−0.374397	+	0.314632i
$527$	11.6005	−	20.0926i	0.505324	−	0.875246i
$528$		0			0
$529$	0.215696	+	0.373597i	0.00937809	+	0.0162433i
$530$	−10.2400	−	3.71840i	−0.444796	−	0.161517i
$531$		0			0
$532$	9.24345	+	7.73272i	0.400754	+	0.335256i
$533$	−42.6283	+	24.6115i	−1.84644	+	1.06604i
$534$		0			0
$535$	7.49553	+	4.32754i	0.324060	+	0.187096i
$536$	0.0676512	+	30.2480i	0.00292209	+	1.30651i
$537$		0			0
$538$	8.86313	−	1.56962i	0.382116	−	0.0676712i
$539$	−0.294470			−0.0126837
$540$		0			0
$541$	15.6391			0.672376			0.336188	−	0.941795i	$-0.390862\pi$
$541$	15.6391			0.672376			0.336188	+	0.941795i	$0.390862\pi$
$542$	−4.15315	+	0.735505i	−0.178393	+	0.0315926i
$543$		0			0
$544$	−13.0629	+	15.6862i	−0.560069	+	0.672540i
$545$	−33.0374	−	19.0741i	−1.41517	−	0.817047i
$546$		0			0
$547$	5.46377	−	3.15451i	0.233614	−	0.134877i	−0.378624	−	0.925551i	$-0.623603\pi$
$547$	5.46377	−	3.15451i	0.233614	−	0.134877i	0.612238	+	0.790673i	$0.290269\pi$
$548$	−0.356257	+	0.425858i	−0.0152185	+	0.0181918i
$549$		0			0
$550$	−3.67792	−	1.33555i	−0.156827	−	0.0569480i
$551$	−3.14655	−	5.44999i	−0.134048	−	0.232177i
$552$		0			0
$553$	−2.74100	+	4.74756i	−0.116559	+	0.201887i
$554$	−23.3589	+	19.6301i	−0.992424	+	0.834004i
$555$		0			0
$556$	21.6523	+	3.78460i	0.918260	+	0.160503i
$557$			22.2489i			0.942714i	0.881942	+	0.471357i	$0.156236\pi$
$557$			22.2489i			0.942714i	−0.881942	+	0.471357i	$0.843764\pi$
$558$		0			0
$559$		−	3.92375i		−	0.165957i
$560$	−11.5970	+	9.79010i	−0.490062	+	0.413707i
$561$		0			0
$562$	−7.35450	−	8.75149i	−0.310231	−	0.369159i
$563$	−18.9723	+	32.8609i	−0.799585	+	1.38492i	0.120301	+	0.992737i	$0.461614\pi$
$563$	−18.9723	+	32.8609i	−0.799585	+	1.38492i	−0.919887	+	0.392185i	$0.871719\pi$
$564$		0			0
$565$	−13.3123	−	23.0576i	−0.560054	−	0.970042i
$566$	−0.401179	+	1.10479i	−0.0168628	+	0.0464379i
$567$		0			0
$568$	−3.87979	−	6.68541i	−0.162792	−	0.280514i
$569$	−8.24731	+	4.76159i	−0.345745	+	0.199616i	−0.662810	−	0.748788i	$-0.730636\pi$
$569$	−8.24731	+	4.76159i	−0.345745	+	0.199616i	0.317064	+	0.948404i	$0.397303\pi$
$570$		0			0
$571$	−21.0510	−	12.1538i	−0.880958	−	0.508621i	−0.00998391	−	0.999950i	$-0.503178\pi$
$571$	−21.0510	−	12.1538i	−0.880958	−	0.508621i	−0.870974	+	0.491329i	$0.836511\pi$
$572$	−2.20474	+	0.806183i	−0.0921847	+	0.0337082i
$573$		0			0
$574$	3.04543	+	17.1965i	0.127114	+	0.717769i
$575$	−44.6370			−1.86149
$576$		0			0
$577$	−13.6033			−0.566311			−0.283156	−	0.959074i	$-0.591381\pi$
$577$	−13.6033			−0.566311			−0.283156	+	0.959074i	$0.591381\pi$
$578$	−0.981085	−	5.53985i	−0.0408077	−	0.230428i
$579$		0			0
$580$	7.44317	−	2.72167i	0.309061	−	0.113011i
$581$	7.05111	+	4.07096i	0.292529	+	0.168892i
$582$		0			0
$583$	−0.517763	+	0.298930i	−0.0214435	+	0.0123804i
$584$	12.2561	+	21.1189i	0.507159	+	0.873906i
$585$		0			0
$586$	−6.29555	+	17.3371i	−0.260067	+	0.716188i
$587$	−3.27395	−	5.67065i	−0.135130	−	0.234053i	0.790517	−	0.612440i	$-0.209812\pi$
$587$	−3.27395	−	5.67065i	−0.135130	−	0.234053i	−0.925647	+	0.378388i	$0.876479\pi$
$588$		0			0
$589$	−19.3708	+	33.5512i	−0.798159	+	1.38245i
$590$	−28.6718	−	34.1180i	−1.18040	−	1.40462i
$591$		0			0
$592$	−11.8175	+	9.97628i	−0.485697	+	0.410022i
$593$		−	11.1137i		−	0.456386i	−0.973616	−	0.228193i	$-0.926718\pi$
$593$		−	11.1137i		−	0.456386i	0.973616	−	0.228193i	$-0.0732818\pi$
$594$		0			0
$595$			13.6917i			0.561303i
$596$	16.4338	+	2.87247i	0.673155	+	0.117661i
$597$		0			0
$598$	−20.5015	+	17.2289i	−0.838369	+	0.704541i
$599$	6.36905	−	11.0315i	0.260232	−	0.450736i	−0.706071	−	0.708141i	$-0.749534\pi$
$599$	6.36905	−	11.0315i	0.260232	−	0.450736i	0.966304	+	0.257405i	$0.0828675\pi$
$600$		0			0
$601$	−14.5547	−	25.2095i	−0.593699	−	1.02832i	−0.993729	−	0.111815i	$-0.964334\pi$
$601$	−14.5547	−	25.2095i	−0.593699	−	1.02832i	0.400030	−	0.916502i	$-0.369000\pi$
$602$	−1.30853	−	0.475161i	−0.0533317	−	0.0193661i
$603$		0			0
$604$	−6.79561	+	8.12326i	−0.276510	+	0.330531i
$605$	35.8597	−	20.7036i	1.45791	−	0.841722i
$606$		0			0
$607$	−32.5285	−	18.7804i	−1.32029	−	0.762272i	−0.336518	−	0.941677i	$-0.609249\pi$
$607$	−32.5285	−	18.7804i	−1.32029	−	0.762272i	−0.983775	+	0.179406i	$0.942583\pi$
$608$	21.8129	−	26.1933i	0.884630	−	1.06228i
$609$		0			0
$610$	−57.9706	+	10.2663i	−2.34716	+	0.415672i
$611$	13.4225			0.543015
$612$		0			0
$613$	20.5622			0.830501			0.415250	−	0.909707i	$-0.363694\pi$
$613$	20.5622			0.830501			0.415250	+	0.909707i	$0.363694\pi$
$614$	−45.4077	+	8.04151i	−1.83251	+	0.324529i
$615$		0			0
$616$	0.00186279	+	0.832885i	7.50540e−5	+	0.0335579i
$617$	−29.4852	−	17.0233i	−1.18703	−	0.685333i	−0.229400	−	0.973332i	$-0.573677\pi$
$617$	−29.4852	−	17.0233i	−1.18703	−	0.685333i	−0.957631	+	0.288000i	$0.907010\pi$
$618$		0			0
$619$	32.9073	−	18.9990i	1.32265	−	0.763635i	0.338503	−	0.940965i	$-0.390079\pi$
$619$	32.9073	−	18.9990i	1.32265	−	0.763635i	0.984151	+	0.177330i	$0.0567461\pi$
$620$	−37.4212	−	31.3051i	−1.50287	−	1.25724i
$621$		0			0
$622$	−17.2267	−	6.25547i	−0.690728	−	0.250821i
$623$	1.67786	+	2.90614i	0.0672220	+	0.116432i
$624$		0			0
$625$	−8.15241	+	14.1204i	−0.326096	+	0.564815i
$626$	−8.05736	+	6.77117i	−0.322037	+	0.270630i
$627$		0			0
$628$	−3.21598	+	18.3991i	−0.128332	+	0.734205i
$629$			13.9520i			0.556304i
$630$		0			0
$631$			46.8749i			1.86606i	0.359799	+	0.933030i	$0.382845\pi$
$631$			46.8749i			1.86606i	−0.359799	+	0.933030i	$0.617155\pi$
$632$	13.4454	+	7.72267i	0.534830	+	0.307191i
$633$		0			0
$634$	−0.286009	−	0.340337i	−0.0113589	−	0.0135165i
$635$	−13.2607	+	22.9683i	−0.526236	+	0.911468i
$636$		0			0
$637$	1.99299	+	3.45197i	0.0789653	+	0.136772i
$638$	0.148448	−	0.408806i	0.00587712	−	0.0161848i
$639$		0			0
$640$	27.7639	+	32.7392i	1.09746	+	1.29413i
$641$	22.8062	−	13.1672i	0.900792	−	0.520073i	0.0233352	−	0.999728i	$-0.492571\pi$
$641$	22.8062	−	13.1672i	0.900792	−	0.520073i	0.877457	+	0.479655i	$0.159238\pi$
$642$		0			0
$643$	33.1788	+	19.1558i	1.30844	+	0.755430i	0.981836	−	0.189730i	$-0.0607611\pi$
$643$	33.1788	+	19.1558i	1.30844	+	0.755430i	0.326608	+	0.945160i	$0.394094\pi$
$644$	3.26294	+	8.92343i	0.128578	+	0.351633i
$645$		0			0
$646$	−5.36241	−	30.2797i	−0.210981	−	1.19134i
$647$	−31.8925			−1.25382			−0.626912	−	0.779090i	$-0.715682\pi$
$647$	−31.8925			−1.25382			−0.626912	+	0.779090i	$0.715682\pi$
$648$		0			0
$649$	−2.44572			−0.0960030
$650$	9.23627	+	52.1541i	0.362276	+	2.04565i
$651$		0			0
$652$	−10.7573	−	29.4190i	−0.421290	−	1.15214i
$653$	−4.99048	−	2.88125i	−0.195292	−	0.112752i	0.399165	−	0.916879i	$-0.369300\pi$
$653$	−4.99048	−	2.88125i	−0.195292	−	0.112752i	−0.594458	+	0.804127i	$0.702633\pi$
$654$		0			0
$655$	−39.0901	+	22.5687i	−1.52738	+	0.881830i
$656$	48.6197	−	8.72255i	1.89828	−	0.340558i
$657$		0			0
$658$	1.62545	−	4.47625i	0.0633664	−	0.174503i
$659$	8.37638	+	14.5083i	0.326298	+	0.565164i	0.981774	−	0.190052i	$-0.0608655\pi$
$659$	8.37638	+	14.5083i	0.326298	+	0.565164i	−0.655477	+	0.755216i	$0.727532\pi$
$660$		0			0
$661$	−8.26733	+	14.3194i	−0.321562	+	0.556961i	−0.980810	−	0.194964i	$-0.937541\pi$
$661$	−8.26733	+	14.3194i	−0.321562	+	0.556961i	0.659249	+	0.751925i	$0.270874\pi$
$662$	−19.1715	−	22.8131i	−0.745122	−	0.886658i
$663$		0			0
$664$	11.4698	−	19.9693i	0.445114	−	0.774958i
$665$		−	22.8627i		−	0.886579i
$666$		0			0
$667$		−	4.96146i		−	0.192109i
$668$	0.987954	−	5.65223i	0.0382251	−	0.218692i
$669$		0			0
$670$	43.9309	−	36.9183i	1.69720	−	1.42628i
$671$	−1.61543	+	2.79801i	−0.0623630	+	0.108016i
$672$		0			0
$673$	−6.04519	−	10.4706i	−0.233025	−	0.403611i	0.725672	−	0.688041i	$-0.241529\pi$
$673$	−6.04519	−	10.4706i	−0.233025	−	0.403611i	−0.958697	+	0.284430i	$0.908196\pi$
$674$	12.6777	+	4.60359i	0.488325	+	0.177324i
$675$		0			0
$676$	4.43038	+	3.70628i	0.170399	+	0.142549i
$677$	21.2204	−	12.2516i	0.815567	−	0.470868i	−0.0333185	−	0.999445i	$-0.510608\pi$
$677$	21.2204	−	12.2516i	0.815567	−	0.470868i	0.848885	+	0.528577i	$0.177274\pi$
$678$		0			0
$679$	−11.6753	−	6.74076i	−0.448058	−	0.258687i
$680$	38.7258	−	0.0866122i	1.48507	−	0.00332143i
$681$		0			0
$682$	−2.63645	+	0.466905i	−0.100955	+	0.0178787i
$683$	−50.4915			−1.93200			−0.966002	−	0.258534i	$-0.916761\pi$
$683$	−50.4915			−1.93200			−0.966002	+	0.258534i	$0.916761\pi$
$684$		0			0
$685$	1.05332			0.0402452
$686$	1.39255	−	0.246614i	0.0531676	−	0.00941576i
$687$		0			0
$688$	−1.33568	+	3.70408i	−0.0509222	+	0.141217i
$689$	7.00851	+	4.04637i	0.267003	+	0.154154i
$690$		0			0
$691$	7.62153	−	4.40029i	0.289937	−	0.167395i	−0.347977	−	0.937503i	$-0.613131\pi$
$691$	7.62153	−	4.40029i	0.289937	−	0.167395i	0.637913	+	0.770108i	$0.279798\pi$
$692$	8.82582	−	10.5501i	0.335507	−	0.401055i
$693$		0			0
$694$	−18.2733	−	6.63553i	−0.693646	−	0.251881i
$695$	−20.8497	−	36.1127i	−0.790872	−	1.36983i
$696$		0			0
$697$	22.2811	−	38.5920i	0.843957	−	1.46178i
$698$	18.8299	−	15.8241i	0.712723	−	0.598952i
$699$		0			0
$700$	18.5114	+	3.23560i	0.699663	+	0.122294i
$701$			40.0613i			1.51309i	0.653940	+	0.756546i	$0.273115\pi$
$701$			40.0613i			1.51309i	−0.653940	+	0.756546i	$0.726885\pi$
$702$		0			0
$703$		−	23.2975i		−	0.878682i
$704$	2.35574	−	0.0105375i	0.0887851	−	0.000397147i
$705$		0			0
$706$	−17.0949	−	20.3421i	−0.643375	−	0.765584i
$707$	−6.43278	+	11.1419i	−0.241930	+	0.419034i
$708$		0			0
$709$	−13.4387	−	23.2765i	−0.504701	−	0.874169i	−0.999985	−	0.00543734i	$-0.998269\pi$
$709$	−13.4387	−	23.2765i	−0.504701	−	0.874169i	0.495284	−	0.868731i	$-0.335064\pi$
$710$	−5.00509	+	13.7833i	−0.187838	+	0.517279i
$711$		0			0
$712$	8.20917	−	4.76408i	0.307652	−	0.178541i
$713$	−26.4517	+	15.2719i	−0.990622	+	0.571936i
$714$		0			0
$715$	3.85681	+	2.22673i	0.144237	+	0.0832751i
$716$	−36.3416	+	13.2887i	−1.35815	+	0.496621i
$717$		0			0
$718$	−3.51455	−	19.8455i	−0.131162	−	0.740627i
$719$	40.6857			1.51732			0.758661	−	0.651486i	$-0.225854\pi$
$719$	40.6857			1.51732			0.758661	+	0.651486i	$0.225854\pi$
$720$		0			0
$721$	8.91268			0.331925
$722$	4.26865	+	24.1036i	0.158863	+	0.897044i
$723$		0			0
$724$	23.8312	−	8.71409i	0.885678	−	0.323857i
$725$	−8.49828	−	4.90649i	−0.315618	−	0.182222i
$726$		0			0
$727$	−3.36949	+	1.94538i	−0.124968	+	0.0721501i	−0.561181	−	0.827693i	$-0.689653\pi$
$727$	−3.36949	+	1.94538i	−0.124968	+	0.0721501i	0.436213	+	0.899843i	$0.356319\pi$
$728$	9.75101	−	5.65886i	0.361396	−	0.209731i
$729$		0			0
$730$	15.8108	−	43.5409i	0.585185	−	1.61152i
$731$	1.77611	+	3.07631i	0.0656918	+	0.113782i
$732$		0			0
$733$	−11.2371	+	19.4633i	−0.415053	+	0.718893i	−0.995434	−	0.0954521i	$-0.969570\pi$
$733$	−11.2371	+	19.4633i	−0.415053	+	0.718893i	0.580381	+	0.814345i	$0.302904\pi$
$734$	1.97161	+	2.34612i	0.0727734	+	0.0865968i
$735$		0			0
$736$	25.2186	−	9.28541i	0.929569	−	0.342265i
$737$		−	3.14915i		−	0.116000i
$738$		0			0
$739$		−	34.2290i		−	1.25913i	−0.776947	−	0.629567i	$-0.783232\pi$
$739$		−	34.2290i		−	1.25913i	0.776947	−	0.629567i	$-0.216768\pi$
$740$	28.9014	+	5.05167i	1.06244	+	0.185703i
$741$		0			0
$742$	2.19814	−	1.84726i	0.0806964	−	0.0678149i
$743$	14.2792	−	24.7322i	0.523851	−	0.907337i	−0.475763	−	0.879573i	$-0.657828\pi$
$743$	14.2792	−	24.7322i	0.523851	−	0.907337i	0.999615	−	0.0277637i	$-0.00883859\pi$
$744$		0			0
$745$	−15.8246	−	27.4091i	−0.579770	−	1.00419i
$746$	44.4843	+	16.1534i	1.62869	+	0.591418i
$747$		0			0
$748$	1.36364	−	1.63006i	0.0498597	−	0.0596008i
$749$	−1.97552	+	1.14057i	−0.0721839	+	0.0416754i
$750$		0			0
$751$	−3.64406	−	2.10390i	−0.132974	−	0.0767723i	0.432038	−	0.901856i	$-0.357795\pi$
$751$	−3.64406	−	2.10390i	−0.132974	−	0.0767723i	−0.565011	+	0.825083i	$0.691128\pi$
$752$	−12.6710	−	4.56913i	−0.462064	−	0.166619i
$753$		0			0
$754$	−5.79700	+	1.02662i	−0.211114	+	0.0373874i
$755$	20.0921			0.731226
$756$		0			0
$757$	−5.18894			−0.188595			−0.0942977	−	0.995544i	$-0.530061\pi$
$757$	−5.18894			−0.188595			−0.0942977	+	0.995544i	$0.530061\pi$
$758$	9.51105	−	1.68437i	0.345457	−	0.0611790i
$759$		0			0
$760$	−64.6654	+	0.144628i	−2.34566	+	0.00524620i
$761$	−0.558714	−	0.322574i	−0.0202534	−	0.0116933i	0.489839	−	0.871813i	$-0.337056\pi$
$761$	−0.558714	−	0.322574i	−0.0202534	−	0.0116933i	−0.510092	+	0.860120i	$0.670389\pi$
$762$		0			0
$763$	8.70733	−	5.02718i	0.315226	−	0.181996i
$764$	12.7604	+	10.6748i	0.461654	+	0.386202i
$765$		0			0
$766$	−9.83434	−	3.57111i	−0.355329	−	0.129029i
$767$	16.5528	+	28.6703i	0.597688	+	1.03523i
$768$		0			0
$769$	−12.6215	+	21.8612i	−0.455145	+	0.788333i	−0.998697	−	0.0510420i	$-0.983746\pi$
$769$	−12.6215	+	21.8612i	−0.455145	+	0.788333i	0.543552	+	0.839376i	$0.317079\pi$
$770$	1.20965	−	1.01655i	0.0435927	−	0.0366340i
$771$		0			0
$772$	−3.71608	+	21.2603i	−0.133745	+	0.765174i
$773$		−	8.72610i		−	0.313856i	−0.987610	−	0.156928i	$-0.949841\pi$
$773$		−	8.72610i		−	0.313856i	0.987610	−	0.156928i	$-0.0501591\pi$
$774$		0			0
$775$			60.4106i			2.17001i
$776$	−18.9918	+	33.0654i	−0.681768	+	1.18698i
$777$		0			0
$778$	15.7924	+	18.7922i	0.566187	+	0.673734i
$779$	−37.2057	+	64.4421i	−1.33303	+	2.30888i
$780$		0			0
$781$	0.402370	+	0.696926i	0.0143979	+	0.0249380i
$782$	8.27492	−	22.7880i	0.295910	−	0.814897i
$783$		0			0
$784$	−0.706337	−	3.93714i	−0.0252263	−	0.140612i
$785$	30.6869	−	17.7171i	1.09526	−	0.632351i
$786$		0			0
$787$	−16.8392	−	9.72212i	−0.600253	−	0.346556i	0.168888	−	0.985635i	$-0.445982\pi$
$787$	−16.8392	−	9.72212i	−0.600253	−	0.346556i	−0.769141	+	0.639079i	$0.779316\pi$
$788$	9.88636	+	27.0370i	0.352187	+	0.963155i
$789$		0			0
$790$	−5.12953	−	28.9647i	−0.182501	−	1.03052i
$791$	7.01719			0.249502
$792$		0			0
$793$	43.7334			1.55302
$794$	−1.21088	−	6.83745i	−0.0429727	−	0.242652i
$795$		0			0
$796$	−10.2975	−	28.1614i	−0.364984	−	0.998153i
$797$	46.9719	+	27.1193i	1.66383	+	0.960614i	0.970859	+	0.239649i	$0.0770325\pi$
$797$	46.9719	+	27.1193i	1.66383	+	0.960614i	0.692972	+	0.720964i	$0.256301\pi$
$798$		0			0
$799$	−10.5235	+	6.07577i	−0.372296	+	0.214945i
$800$	9.03453	−	52.3783i	0.319419	−	1.85185i
$801$		0			0
$802$	11.7255	−	32.2905i	0.414042	−	1.14022i
$803$	−1.27107	−	2.20155i	−0.0448550	−	0.0776911i
$804$		0			0
$805$	9.01246	−	15.6100i	0.317647	−	0.550182i
$806$	23.3171	+	27.7462i	0.821309	+	0.977317i
$807$		0			0
$808$	31.5547	+	18.1241i	1.11009	+	0.637604i
$809$		−	33.5957i		−	1.18116i	−0.806979	−	0.590581i	$-0.798899\pi$
$809$		−	33.5957i		−	1.18116i	0.806979	−	0.590581i	$-0.201101\pi$
$810$		0			0
$811$			6.28139i			0.220570i	0.993900	+	0.110285i	$0.0351763\pi$
$811$			6.28139i			0.220570i	−0.993900	+	0.110285i	$0.964824\pi$
$812$	−0.359641	+	2.05756i	−0.0126209	+	0.0722062i
$813$		0			0
$814$	1.23265	−	1.03588i	0.0432044	−	0.0363077i
$815$	−29.7125	+	51.4635i	−1.04078	+	1.80269i
$816$		0			0
$817$	−2.96580	−	5.13692i	−0.103760	−	0.179718i
$818$	−50.8583	−	18.4680i	−1.77822	−	0.645718i
$819$		0			0
$820$	−71.8752	−	60.1281i	−2.50999	−	2.09976i
$821$	−16.5450	+	9.55229i	−0.577426	+	0.333377i	−0.760110	−	0.649795i	$-0.774855\pi$
$821$	−16.5450	+	9.55229i	−0.577426	+	0.333377i	0.182684	+	0.983172i	$0.441522\pi$
$822$		0			0
$823$	43.0543	+	24.8574i	1.50078	+	0.866476i	1.00000		0.000901331i	$0.000286903\pi$
$823$	43.0543	+	24.8574i	1.50078	+	0.866476i	0.500780	+	0.865574i	$0.333046\pi$
$824$	−0.0563808	−	25.2088i	−0.00196412	−	0.878190i
$825$		0			0
$826$	11.5658	−	2.04825i	0.402425	−	0.0712678i
$827$	−4.74479			−0.164992			−0.0824962	−	0.996591i	$-0.526289\pi$
$827$	−4.74479			−0.164992			−0.0824962	+	0.996591i	$0.526289\pi$
$828$		0			0
$829$	11.3890			0.395558			0.197779	−	0.980247i	$-0.436627\pi$
$829$	11.3890			0.395558			0.197779	+	0.980247i	$0.436627\pi$
$830$	−43.0187	+	7.61843i	−1.49320	+	0.264440i
$831$		0			0
$832$	−16.0673	−	27.5442i	−0.557034	−	0.954922i
$833$	−3.12511	−	1.80429i	−0.108279	−	0.0625148i
$834$		0			0
$835$	−9.42707	+	5.44272i	−0.326237	+	0.188353i
$836$	−2.27705	+	2.72192i	−0.0787535	+	0.0941395i
$837$		0			0
$838$	−25.1887	−	9.14669i	−0.870130	−	0.315967i
$839$	17.0108	+	29.4636i	0.587279	+	1.01720i	0.994587	+	0.103906i	$0.0331343\pi$
$839$	17.0108	+	29.4636i	0.587279	+	1.01720i	−0.407308	+	0.913291i	$0.633532\pi$
$840$		0			0
$841$	−13.9546	+	24.1701i	−0.481194	+	0.833453i
$842$	22.9600	−	19.2949i	0.791253	−	0.664946i
$843$		0			0
$844$	−5.65238	−	0.987980i	−0.194563	−	0.0340077i
$845$		−	10.9581i		−	0.376970i
$846$		0			0
$847$			10.9133i			0.374985i
$848$	−5.23872	−	6.20559i	−0.179898	−	0.213101i
$849$		0			0
$850$	−30.8494	−	36.7092i	−1.05812	−	1.25912i
$851$	9.18385	−	15.9069i	0.314818	−	0.545281i
$852$		0			0
$853$	8.54802	+	14.8056i	0.292679	+	0.506934i	0.974442	−	0.224638i	$-0.0721201\pi$
$853$	8.54802	+	14.8056i	0.292679	+	0.506934i	−0.681764	+	0.731573i	$0.738787\pi$
$854$	5.29607	−	14.5846i	0.181228	−	0.499076i
$855$		0			0
$856$	3.23850	+	5.58038i	0.110690	+	0.190734i
$857$	4.25999	−	2.45951i	0.145518	−	0.0840151i	−0.425473	−	0.904971i	$-0.639892\pi$
$857$	4.25999	−	2.45951i	0.145518	−	0.0840151i	0.570991	+	0.820956i	$0.306559\pi$
$858$		0			0
$859$	25.8381	+	14.9176i	0.881585	+	0.508983i	0.871181	−	0.490963i	$-0.163355\pi$
$859$	25.8381	+	14.9176i	0.881585	+	0.508983i	0.0104044	+	0.999946i	$0.496688\pi$
$860$	7.01561	−	2.56533i	0.239230	−	0.0874769i
$861$		0			0
$862$	−1.53898	−	8.69008i	−0.0524177	−	0.295985i
$863$	−7.21912			−0.245742			−0.122871	−	0.992423i	$-0.539210\pi$
$863$	−7.21912			−0.245742			−0.122871	+	0.992423i	$0.539210\pi$
$864$		0			0
$865$	−26.0946			−0.887244
$866$	−3.01639	−	17.0325i	−0.102501	−	0.578788i
$867$		0			0
$868$	12.0767	−	4.41597i	0.409911	−	0.149888i
$869$	−1.39801	−	0.807143i	−0.0474243	−	0.0273804i
$870$		0			0
$871$	−36.9164	+	21.3137i	−1.25086	+	0.722186i
$872$	−14.2741	−	24.5962i	−0.483380	−	0.832932i
$873$		0			0
$874$	−13.8177	+	38.0521i	−0.467391	+	1.28713i
$875$	−8.33966	−	14.4447i	−0.281932	−	0.488321i
$876$		0			0
$877$	−4.56875	+	7.91331i	−0.154276	+	0.267214i	−0.932795	−	0.360407i	$-0.882638\pi$
$877$	−4.56875	+	7.91331i	−0.154276	+	0.267214i	0.778519	+	0.627621i	$0.215971\pi$
$878$	−18.3472	−	21.8323i	−0.619190	−	0.736805i
$879$		0			0
$880$	−2.88289	−	3.41496i	−0.0971822	−	0.115118i
$881$		−	18.1037i		−	0.609930i	−0.952364	−	0.304965i	$-0.901355\pi$
$881$		−	18.1037i		−	0.609930i	0.952364	−	0.304965i	$-0.0986447\pi$
$882$		0			0
$883$			10.5545i			0.355187i	0.984104	+	0.177593i	$0.0568311\pi$
$883$			10.5545i			0.355187i	−0.984104	+	0.177593i	$0.943169\pi$
$884$	−28.3378	−	4.95317i	−0.953104	−	0.166593i
$885$		0			0
$886$	30.7540	−	25.8447i	1.03320	−	0.868271i
$887$	4.71464	−	8.16599i	0.158302	−	0.274187i	−0.775954	−	0.630789i	$-0.782731\pi$
$887$	4.71464	−	8.16599i	0.158302	−	0.274187i	0.934256	+	0.356602i	$0.116065\pi$
$888$		0			0
$889$	−3.49500	−	6.05351i	−0.117218	−	0.203028i
$890$	−16.9249	−	6.14586i	−0.567323	−	0.206010i
$891$		0			0
$892$	−21.5548	+	25.7660i	−0.721709	+	0.862709i
$893$	17.5725	−	10.1455i	0.588042	−	0.339506i
$894$		0			0
$895$	63.5735	+	36.7042i	2.12503	+	1.22689i
$896$	−11.1314	+	2.02272i	−0.371875	+	0.0675744i
$897$		0			0
$898$	−12.3741	+	2.19140i	−0.412929	+	0.0731280i
$899$	−6.71471			−0.223948
$900$		0			0
$901$	−7.32646			−0.244080
$902$	−5.06386	+	0.896788i	−0.168608	+	0.0298598i
$903$		0			0
$904$	−0.0443901	−	19.8476i	−0.00147639	−	0.660120i
$905$	−41.6886	−	24.0689i	−1.38578	−	0.800078i
$906$		0			0
$907$	5.60015	−	3.23325i	0.185950	−	0.107358i	−0.404135	−	0.914699i	$-0.632428\pi$
$907$	5.60015	−	3.23325i	0.185950	−	0.107358i	0.590085	+	0.807341i	$0.299094\pi$
$908$	44.1457	+	36.9306i	1.46503	+	1.22558i
$909$		0			0
$910$	−20.1037	−	7.30017i	−0.666431	−	0.241998i
$911$	−17.1240	−	29.6597i	−0.567345	−	0.982670i	−0.996827	−	0.0795950i	$-0.974637\pi$
$911$	−17.1240	−	29.6597i	−0.567345	−	0.982670i	0.429482	−	0.903075i	$-0.358696\pi$
$912$		0			0
$913$	−1.19878	+	2.07634i	−0.0396737	+	0.0687168i
$914$	11.7730	−	9.89371i	0.389417	−	0.327255i
$915$		0			0
$916$	6.40965	−	36.6706i	0.211781	−	1.21163i
$917$		−	11.8964i		−	0.392853i
$918$		0			0
$919$			7.16854i			0.236468i	0.992986	+	0.118234i	$0.0377233\pi$
$919$			7.16854i			0.236468i	−0.992986	+	0.118234i	$0.962277\pi$
$920$	−44.2088	−	25.3923i	−1.45752	−	0.837158i
$921$		0			0
$922$	32.9097	+	39.1609i	1.08382	+	1.28969i
$923$	5.44654	−	9.43369i	0.179275	−	0.310514i
$924$		0			0
$925$	−18.1642	−	31.4612i	−0.597234	−	1.03444i
$926$	−4.18562	+	11.5266i	−0.137548	+	0.378789i
$927$		0			0
$928$	5.82192	+	1.00420i	0.191114	+	0.0329645i
$929$	−20.4211	+	11.7901i	−0.669993	+	0.386821i	−0.796074	−	0.605199i	$-0.793093\pi$
$929$	−20.4211	+	11.7901i	−0.669993	+	0.386821i	0.126081	+	0.992020i	$0.459760\pi$
$930$		0			0
$931$	5.21841	+	3.01285i	0.171026	+	0.0987422i
$932$	−17.4096	−	47.6115i	−0.570270	−	1.55957i
$933$		0			0
$934$	3.32910	+	18.7983i	0.108932	+	0.615100i
$935$	−4.03178			−0.131853
$936$		0			0
$937$	28.9176			0.944698			0.472349	−	0.881411i	$-0.343406\pi$
$937$	28.9176			0.944698			0.472349	+	0.881411i	$0.343406\pi$
$938$	2.63736	+	14.8923i	0.0861129	+	0.486250i
$939$		0			0
$940$	8.77554	+	23.9992i	0.286227	+	0.782767i
$941$	7.14862	+	4.12726i	0.233038	+	0.134545i	0.611973	−	0.790879i	$-0.290376\pi$
$941$	7.14862	+	4.12726i	0.233038	+	0.134545i	−0.378935	+	0.925423i	$0.623709\pi$
$942$		0			0
$943$	−50.8060	+	29.3328i	−1.65447	+	0.955208i
$944$	−5.86648	−	32.7000i	−0.190938	−	1.06429i
$945$		0			0
$946$	0.139921	−	0.385322i	0.00454921	−	0.0125279i
$947$	13.0431	+	22.5914i	0.423845	+	0.734121i	0.996312	−	0.0858067i	$-0.0273468\pi$
$947$	13.0431	+	22.5914i	0.423845	+	0.734121i	−0.572467	+	0.819928i	$0.694013\pi$
$948$		0			0
$949$	−17.2054	+	29.8006i	−0.558510	+	0.967367i
$950$	51.5132	+	61.2982i	1.67131	+	1.98878i
$951$		0			0
$952$	−5.08351	+	8.85055i	−0.164757	+	0.286848i
$953$			8.16427i			0.264467i	0.991219	+	0.132233i	$0.0422148\pi$
$953$			8.16427i			0.264467i	−0.991219	+	0.132233i	$0.957785\pi$
$954$		0			0
$955$		−	31.5615i		−	1.02131i
$956$	−8.66990	+	49.6018i	−0.280404	+	1.60424i
$957$		0			0
$958$	41.4465	−	34.8304i	1.33908	−	1.12532i
$959$	−0.138806	+	0.240419i	−0.00448228	+	0.00776354i
$960$		0			0
$961$	5.16854	+	8.95217i	0.166727	+	0.288780i
$962$	−20.4860	−	7.43900i	−0.660495	−	0.239843i
$963$		0			0
$964$	14.8396	+	12.4142i	0.477950	+	0.399835i
$965$	35.4589	−	20.4722i	1.14146	−	0.659024i
$966$		0			0
$967$	−47.9368	−	27.6763i	−1.54154	−	0.890010i	−0.998742	−	0.0501481i	$-0.984031\pi$
$967$	−47.9368	−	27.6763i	−1.54154	−	0.890010i	−0.542800	−	0.839862i	$-0.682636\pi$
$968$	30.8674	−	0.0690365i	0.992115	−	0.00221892i
$969$		0			0
$970$	71.2310	−	12.6147i	2.28709	−	0.405034i
$971$	−11.2138			−0.359869			−0.179935	−	0.983679i	$-0.557589\pi$
$971$	−11.2138			−0.359869			−0.179935	+	0.983679i	$0.557589\pi$
$972$		0			0
$973$	10.9903			0.352332
$974$	18.5366	−	3.28275i	0.593951	−	0.105186i
$975$		0			0
$976$	−41.2850	−	14.8872i	−1.32150	−	0.476529i
$977$	20.0276	+	11.5629i	0.640740	+	0.369931i	0.784899	−	0.619623i	$-0.212715\pi$
$977$	20.0276	+	11.5629i	0.640740	+	0.369931i	−0.144160	+	0.989554i	$0.546048\pi$
$978$		0			0
$979$	−0.855770	+	0.494079i	−0.0273505	+	0.0157908i
$980$	−4.86906	+	5.82033i	−0.155537	+	0.185924i
$981$		0			0
$982$	3.90106	+	1.41658i	0.124488	+	0.0452048i
$983$	−16.6695	−	28.8724i	−0.531673	−	0.920885i	−0.999316	−	0.0369680i	$-0.988230\pi$
$983$	−16.6695	−	28.8724i	−0.531673	−	0.920885i	0.467643	−	0.883917i	$-0.345103\pi$
$984$		0			0
$985$	27.3068	−	47.2967i	0.870067	−	1.50700i
$986$	4.08028	−	3.42895i	0.129943	−	0.109200i
$987$		0			0
$988$	47.3193	+	8.27095i	1.50543	+	0.263134i
$989$		−	4.67646i		−	0.148703i
$990$		0			0
$991$			27.6317i			0.877749i	0.898548	+	0.438875i	$0.144623\pi$
$991$			27.6317i			0.877749i	−0.898548	+	0.438875i	$0.855377\pi$
$992$	−12.5666	−	34.1301i	−0.398991	−	1.08363i
$993$		0			0
$994$	−2.48647	−	2.95877i	−0.0788660	−	0.0938466i
$995$	−28.4423	+	49.2635i	−0.901682	+	1.56176i
$996$		0			0
$997$	10.1065	+	17.5050i	0.320077	+	0.554390i	0.980504	−	0.196500i	$-0.0629577\pi$
$997$	10.1065	+	17.5050i	0.320077	+	0.554390i	−0.660426	+	0.750891i	$0.729624\pi$
$998$	18.0305	−	49.6536i	0.570746	−	1.57176i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ba.a.71.16		72
3.2	odd	2		252.2.ba.a.239.21	yes	72
4.3	odd	2	inner	756.2.ba.a.71.27		72
9.2	odd	6	inner	756.2.ba.a.575.27		72
9.7	even	3		252.2.ba.a.155.10	✓	72
12.11	even	2		252.2.ba.a.239.10	yes	72
36.7	odd	6		252.2.ba.a.155.21	yes	72
36.11	even	6	inner	756.2.ba.a.575.16		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.10	✓	72	9.7	even	3
252.2.ba.a.155.21	yes	72	36.7	odd	6
252.2.ba.a.239.10	yes	72	12.11	even	2
252.2.ba.a.239.21	yes	72	3.2	odd	2
756.2.ba.a.71.16		72	1.1	even	1	trivial
756.2.ba.a.71.27		72	4.3	odd	2	inner
756.2.ba.a.575.16		72	36.11	even	6	inner
756.2.ba.a.575.27		72	9.2	odd	6	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.246614 - 1.39255i) q^{2} +(-1.87836 + 0.686842i) q^{4} +(3.28588 + 1.89710i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.41969 + 2.44632i) q^{8} +O(q^{10})\)	\(q+(-0.246614 - 1.39255i) q^{2} +(-1.87836 + 0.686842i) q^{4} +(3.28588 + 1.89710i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.41969 + 2.44632i) q^{8} +(1.83146 - 5.04359i) q^{10} +(-0.147235 - 0.255018i) q^{11} +(-1.99299 + 3.45197i) q^{13} +(0.909846 + 1.08267i) q^{14} +(3.05650 - 2.58028i) q^{16} -3.60857i q^{17} +6.02570i q^{19} +(-7.47508 - 1.30657i) q^{20} +(-0.318814 + 0.267922i) q^{22} +(-2.37532 + 4.11418i) q^{23} +(4.69800 + 8.13717i) q^{25} +(5.29852 + 1.92403i) q^{26} +(1.28329 - 1.53400i) q^{28} +(-0.904457 + 0.522189i) q^{29} +(5.56802 + 3.21470i) q^{31} +(-4.34693 - 3.61998i) q^{32} +(-5.02510 + 0.889923i) q^{34} -3.79421 q^{35} -3.86636 q^{37} +(8.39106 - 1.48602i) q^{38} +(0.0240018 + 10.7316i) q^{40} +(10.6945 + 6.17450i) q^{41} +(-0.852502 + 0.492192i) q^{43} +(0.451718 + 0.377890i) q^{44} +(6.31496 + 2.29313i) q^{46} +(-1.68371 - 2.91626i) q^{47} +(0.500000 - 0.866025i) q^{49} +(10.1728 - 8.54892i) q^{50} +(1.37261 - 7.85292i) q^{52} -2.03029i q^{53} -1.11728i q^{55} +(-2.45265 - 1.40873i) q^{56} +(0.950223 + 1.13072i) q^{58} +(4.15275 - 7.19278i) q^{59} +(-5.48589 - 9.50184i) q^{61} +(3.10346 - 8.54650i) q^{62} +(-3.96897 + 6.94603i) q^{64} +(-13.0975 + 7.56183i) q^{65} +(9.26153 + 5.34715i) q^{67} +(2.47852 + 6.77821i) q^{68} +(0.935704 + 5.28360i) q^{70} -2.73284 q^{71} +8.63292 q^{73} +(0.953498 + 5.38408i) q^{74} +(-4.13870 - 11.3185i) q^{76} +(0.255018 + 0.147235i) q^{77} +(4.74756 - 2.74100i) q^{79} +(14.9383 - 2.67999i) q^{80} +(5.96084 - 16.4153i) q^{82} +(-4.07096 - 7.05111i) q^{83} +(6.84583 - 11.8573i) q^{85} +(0.895639 + 1.06577i) q^{86} +(0.414829 - 0.722231i) q^{88} -3.35572i q^{89} -3.98599i q^{91} +(1.63593 - 9.35939i) q^{92} +(-3.64580 + 3.06383i) q^{94} +(-11.4314 + 19.7997i) q^{95} +(6.74076 + 11.6753i) q^{97} +(-1.32929 - 0.482699i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) \) 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Introduction

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