LMFDB - Embedded newform 756.2.ba.a.71.8

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			71.8
Character	$\chi$	$=$	756.71
Dual form			756.2.ba.a.575.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09990 + 0.888937i) q^{2} +(0.419581 - 1.95549i) q^{4} +(2.42137 + 1.39798i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.27681 + 2.52384i) q^{8} +O(q^{10})$	\(q+(-1.09990 + 0.888937i) q^{2} +(0.419581 - 1.95549i) q^{4} +(2.42137 + 1.39798i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.27681 + 2.52384i) q^{8} +(-3.90599 + 0.614803i) q^{10} +(0.140963 + 0.244156i) q^{11} +(-2.43776 + 4.22232i) q^{13} +(0.508077 - 1.31979i) q^{14} +(-3.64790 - 1.64098i) q^{16} +5.66309i q^{17} -7.39353i q^{19} +(3.74970 - 4.14841i) q^{20} +(-0.372086 - 0.143241i) q^{22} +(-3.28934 + 5.69730i) q^{23} +(1.40869 + 2.43992i) q^{25} +(-1.07208 - 6.81116i) q^{26} +(0.614378 + 1.90330i) q^{28} +(0.243350 - 0.140498i) q^{29} +(8.09138 + 4.67156i) q^{31} +(5.47107 - 1.43784i) q^{32} +(-5.03413 - 6.22886i) q^{34} -2.79596 q^{35} +4.22211 q^{37} +(6.57238 + 8.13218i) q^{38} +(-0.436639 + 7.89610i) q^{40} +(0.644767 + 0.372257i) q^{41} +(-6.31743 + 3.64737i) q^{43} +(0.536590 - 0.173210i) q^{44} +(-1.44658 - 9.19051i) q^{46} +(-2.59024 - 4.48642i) q^{47} +(0.500000 - 0.866025i) q^{49} +(-3.71837 - 1.43145i) q^{50} +(7.23387 + 6.53862i) q^{52} +8.11915i q^{53} +0.788256i q^{55} +(-2.36767 - 1.54730i) q^{56} +(-0.142768 + 0.370857i) q^{58} +(0.215457 - 0.373183i) q^{59} +(2.95890 + 5.12497i) q^{61} +(-13.0525 + 2.05446i) q^{62} +(-4.73951 + 6.44493i) q^{64} +(-11.8054 + 6.81586i) q^{65} +(-2.11124 - 1.21893i) q^{67} +(11.0741 + 2.37612i) q^{68} +(3.07529 - 2.48543i) q^{70} -2.47114 q^{71} +0.714758 q^{73} +(-4.64392 + 3.75319i) q^{74} +(-14.4580 - 3.10218i) q^{76} +(-0.244156 - 0.140963i) q^{77} +(2.15347 - 1.24331i) q^{79} +(-6.53888 - 9.07310i) q^{80} +(-1.04010 + 0.163711i) q^{82} +(4.10072 + 7.10266i) q^{83} +(-7.91688 + 13.7124i) q^{85} +(3.70629 - 9.62757i) q^{86} +(-0.436226 + 0.667509i) q^{88} +0.354223i q^{89} -4.87551i q^{91} +(9.76089 + 8.82276i) q^{92} +(6.83716 + 2.63208i) q^{94} +(10.3360 - 17.9025i) q^{95} +(-0.138992 - 0.240741i) q^{97} +(0.219890 + 1.39701i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.09990	+	0.888937i	−0.777750	+	0.628574i
$2$	−1.09990	+	0.888937i	−0.777750	+	0.628574i
$3$		0			0
$3$		0			0
$4$	0.419581	−	1.95549i	0.209791	−	0.977746i
$5$	2.42137	+	1.39798i	1.08287	+	0.625195i	0.931669	−	0.363308i	$-0.118353\pi$
$5$	2.42137	+	1.39798i	1.08287	+	0.625195i	0.151201	+	0.988503i	$0.451686\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$	1.27681	+	2.52384i	0.451421	+	0.892311i
$9$		0			0
$10$	−3.90599	+	0.614803i	−1.23518	+	0.194418i
$11$	0.140963	+	0.244156i	0.0425021	+	0.0736157i	0.886494	−	0.462740i	$-0.153134\pi$
$11$	0.140963	+	0.244156i	0.0425021	+	0.0736157i	−0.843992	+	0.536356i	$0.819800\pi$
$12$		0			0
$13$	−2.43776	+	4.22232i	−0.676112	+	1.17106i	0.300031	+	0.953930i	$0.403003\pi$
$13$	−2.43776	+	4.22232i	−0.676112	+	1.17106i	−0.976143	+	0.217131i	$0.930330\pi$
$14$	0.508077	−	1.31979i	0.135789	−	0.352730i
$15$		0			0
$16$	−3.64790	−	1.64098i	−0.911976	−	0.410244i
$17$			5.66309i			1.37350i	0.726894	+	0.686750i	$0.240963\pi$
$17$			5.66309i			1.37350i	−0.726894	+	0.686750i	$0.759037\pi$
$18$		0			0
$19$		−	7.39353i		−	1.69619i	−0.529843	−	0.848096i	$-0.677749\pi$
$19$		−	7.39353i		−	1.69619i	0.529843	−	0.848096i	$-0.322251\pi$
$20$	3.74970	−	4.14841i	0.838458	−	0.927612i
$21$		0			0
$22$	−0.372086	−	0.143241i	−0.0793289	−	0.0305390i
$23$	−3.28934	+	5.69730i	−0.685875	+	1.18797i	0.287286	+	0.957845i	$0.407247\pi$
$23$	−3.28934	+	5.69730i	−0.685875	+	1.18797i	−0.973161	+	0.230125i	$0.926086\pi$
$24$		0			0
$25$	1.40869	+	2.43992i	0.281738	+	0.487985i
$26$	−1.07208	−	6.81116i	−0.210251	−	1.33578i
$27$		0			0
$28$	0.614378	+	1.90330i	0.116107	+	0.359689i
$29$	0.243350	−	0.140498i	0.0451889	−	0.0260898i	−0.477235	−	0.878776i	$-0.658361\pi$
$29$	0.243350	−	0.140498i	0.0451889	−	0.0260898i	0.522424	+	0.852686i	$0.325028\pi$
$30$		0			0
$31$	8.09138	+	4.67156i	1.45325	+	0.839037i	0.998665	−	0.0516641i	$-0.0164525\pi$
$31$	8.09138	+	4.67156i	1.45325	+	0.839037i	0.454590	+	0.890701i	$0.349786\pi$
$32$	5.47107	−	1.43784i	0.967158	−	0.254177i
$33$		0			0
$34$	−5.03413	−	6.22886i	−0.863346	−	1.06824i
$35$	−2.79596			−0.472603
$36$		0			0
$37$	4.22211			0.694111			0.347056	−	0.937845i	$-0.387182\pi$
$37$	4.22211			0.694111			0.347056	+	0.937845i	$0.387182\pi$
$38$	6.57238	+	8.13218i	1.06618	+	1.31921i
$39$		0			0
$40$	−0.436639	+	7.89610i	−0.0690387	+	1.24848i
$41$	0.644767	+	0.372257i	0.100696	+	0.0581367i	0.549502	−	0.835492i	$-0.314817\pi$
$41$	0.644767	+	0.372257i	0.100696	+	0.0581367i	−0.448806	+	0.893629i	$0.648151\pi$
$42$		0			0
$43$	−6.31743	+	3.64737i	−0.963400	+	0.556219i	−0.897218	−	0.441588i	$-0.854415\pi$
$43$	−6.31743	+	3.64737i	−0.963400	+	0.556219i	−0.0661820	+	0.997808i	$0.521082\pi$
$44$	0.536590	−	0.173210i	0.0808941	−	0.0261124i
$45$		0			0
$46$	−1.44658	−	9.19051i	−0.213287	−	1.35507i
$47$	−2.59024	−	4.48642i	−0.377825	−	0.654412i	0.612921	−	0.790144i	$-0.289994\pi$
$47$	−2.59024	−	4.48642i	−0.377825	−	0.654412i	−0.990745	+	0.135733i	$0.956661\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−3.71837	−	1.43145i	−0.525856	−	0.202437i
$51$		0			0
$52$	7.23387	+	6.53862i	1.00316	+	0.906743i
$53$			8.11915i			1.11525i	0.830093	+	0.557625i	$0.188287\pi$
$53$			8.11915i			1.11525i	−0.830093	+	0.557625i	$0.811713\pi$
$54$		0			0
$55$			0.788256i			0.106288i
$56$	−2.36767	−	1.54730i	−0.316393	−	0.206767i
$57$		0			0
$58$	−0.142768	+	0.370857i	−0.0187463	+	0.0486959i
$59$	0.215457	−	0.373183i	0.0280501	−	0.0485843i	−0.851660	−	0.524095i	$-0.824404\pi$
$59$	0.215457	−	0.373183i	0.0280501	−	0.0485843i	0.879710	+	0.475511i	$0.157737\pi$
$60$		0			0
$61$	2.95890	+	5.12497i	0.378848	+	0.656185i	0.990895	−	0.134637i	$-0.0429869\pi$
$61$	2.95890	+	5.12497i	0.378848	+	0.656185i	−0.612047	+	0.790822i	$0.709654\pi$
$62$	−13.0525	+	2.05446i	−1.65767	+	0.260916i
$63$		0			0
$64$	−4.73951	+	6.44493i	−0.592438	+	0.805616i
$65$	−11.8054	+	6.81586i	−1.46428	+	0.845404i
$66$		0			0
$67$	−2.11124	−	1.21893i	−0.257930	−	0.148916i	0.365460	−	0.930827i	$-0.380912\pi$
$67$	−2.11124	−	1.21893i	−0.257930	−	0.148916i	−0.623390	+	0.781911i	$0.714245\pi$
$68$	11.0741	+	2.37612i	1.34293	+	0.288147i
$69$		0			0
$70$	3.07529	−	2.48543i	0.367567	−	0.297066i
$71$	−2.47114			−0.293270			−0.146635	−	0.989191i	$-0.546844\pi$
$71$	−2.47114			−0.293270			−0.146635	+	0.989191i	$0.546844\pi$
$72$		0			0
$73$	0.714758			0.0836560			0.0418280	−	0.999125i	$-0.486682\pi$
$73$	0.714758			0.0836560			0.0418280	+	0.999125i	$0.486682\pi$
$74$	−4.64392	+	3.75319i	−0.539845	+	0.436300i
$75$		0			0
$76$	−14.4580	−	3.10218i	−1.65844	−	0.355845i
$77$	−0.244156	−	0.140963i	−0.0278241	−	0.0160643i
$78$		0			0
$79$	2.15347	−	1.24331i	0.242285	−	0.139883i	−0.373942	−	0.927452i	$-0.621994\pi$
$79$	2.15347	−	1.24331i	0.242285	−	0.139883i	0.616226	+	0.787569i	$0.288661\pi$
$80$	−6.53888	−	9.07310i	−0.731069	−	1.01440i
$81$		0			0
$82$	−1.04010	+	0.163711i	−0.114859	+	0.0180788i
$83$	4.10072	+	7.10266i	0.450113	+	0.779618i	0.998393	−	0.0566769i	$-0.0180505\pi$
$83$	4.10072	+	7.10266i	0.450113	+	0.779618i	−0.548280	+	0.836295i	$0.684717\pi$
$84$		0			0
$85$	−7.91688	+	13.7124i	−0.858706	+	1.48732i
$86$	3.70629	−	9.62757i	0.399660	−	1.03817i
$87$		0			0
$88$	−0.436226	+	0.667509i	−0.0465018	+	0.0711568i
$89$			0.354223i			0.0375476i	0.999824	+	0.0187738i	$0.00597624\pi$
$89$			0.354223i			0.0375476i	−0.999824	+	0.0187738i	$0.994024\pi$
$90$		0			0
$91$		−	4.87551i		−	0.511093i
$92$	9.76089	+	8.82276i	1.01764	+	0.919836i
$93$		0			0
$94$	6.83716	+	2.63208i	0.705199	+	0.271478i
$95$	10.3360	−	17.9025i	1.06045	−	1.83675i
$96$		0			0
$97$	−0.138992	−	0.240741i	−0.0141125	−	0.0244435i	0.858883	−	0.512172i	$-0.171159\pi$
$97$	−0.138992	−	0.240741i	−0.0141125	−	0.0244435i	−0.872995	+	0.487728i	$0.837826\pi$
$98$	0.219890	+	1.39701i	0.0222122	+	0.141120i
$99$		0			0
$100$	5.36231	−	1.73094i	0.536231	−	0.173094i
$101$	−12.2098	+	7.04936i	−1.21493	+	0.701437i	−0.963828	−	0.266525i	$-0.914125\pi$
$101$	−12.2098	+	7.04936i	−1.21493	+	0.701437i	−0.251097	+	0.967962i	$0.580791\pi$
$102$		0			0
$103$	−9.34581	−	5.39581i	−0.920870	−	0.531665i	−0.0369577	−	0.999317i	$-0.511767\pi$
$103$	−9.34581	−	5.39581i	−0.920870	−	0.531665i	−0.883913	+	0.467652i	$0.845100\pi$
$104$	−13.7690	−	0.761398i	−1.35016	−	0.0746613i
$105$		0			0
$106$	−7.21741	−	8.93029i	−0.701017	−	0.867387i
$107$	−3.76330			−0.363811			−0.181906	−	0.983316i	$-0.558227\pi$
$107$	−3.76330			−0.363811			−0.181906	+	0.983316i	$0.558227\pi$
$108$		0			0
$109$	6.11566			0.585774			0.292887	−	0.956147i	$-0.405384\pi$
$109$	6.11566			0.585774			0.292887	+	0.956147i	$0.405384\pi$
$110$	−0.700710	−	0.867006i	−0.0668101	−	0.0826658i
$111$		0			0
$112$	3.97966	−	0.402825i	0.376043	−	0.0380634i
$113$	−1.77771	−	1.02636i	−0.167233	−	0.0965519i	0.414048	−	0.910255i	$-0.364115\pi$
$113$	−1.77771	−	1.02636i	−0.167233	−	0.0965519i	−0.581280	+	0.813703i	$0.697448\pi$
$114$		0			0
$115$	−15.9294	+	9.19686i	−1.48543	+	0.857611i
$116$	−0.172638	−	0.534819i	−0.0160290	−	0.0496567i
$117$		0			0
$118$	0.0947537	+	0.601993i	0.00872278	+	0.0554180i
$119$	−2.83154	−	4.90438i	−0.259567	−	0.449583i
$120$		0			0
$121$	5.46026	−	9.45745i	0.496387	−	0.859768i
$122$	−7.81028	−	3.00670i	−0.707110	−	0.272214i
$123$		0			0
$124$	12.5302	−	13.8625i	1.12524	−	1.24489i
$125$		−	6.10251i		−	0.545825i
$126$		0			0
$127$			12.5913i			1.11729i	0.829406	+	0.558647i	$0.188679\pi$
$127$			12.5913i			1.11729i	−0.829406	+	0.558647i	$0.811321\pi$
$128$	−0.516127	−	11.3019i	−0.0456196	−	0.998959i
$129$		0			0
$130$	6.92597	−	17.9911i	0.607447	−	1.57792i
$131$	4.13063	−	7.15447i	0.360895	−	0.625089i	−0.627213	−	0.778848i	$-0.715805\pi$
$131$	4.13063	−	7.15447i	0.360895	−	0.625089i	0.988108	+	0.153759i	$0.0491379\pi$
$132$		0			0
$133$	3.69676	+	6.40298i	0.320550	+	0.555209i
$134$	3.40572	−	0.536060i	0.294209	−	0.0463085i
$135$		0			0
$136$	−14.2927	+	7.23069i	−1.22559	+	0.620027i
$137$	14.5034	−	8.37353i	1.23911	−	0.715399i	0.270195	−	0.962806i	$-0.412912\pi$
$137$	14.5034	−	8.37353i	1.23911	−	0.715399i	0.968912	+	0.247407i	$0.0795784\pi$
$138$		0			0
$139$	20.1639	+	11.6416i	1.71028	+	0.987430i	0.934169	+	0.356831i	$0.116143\pi$
$139$	20.1639	+	11.6416i	1.71028	+	0.987430i	0.776110	+	0.630598i	$0.217190\pi$
$140$	−1.17313	+	5.46748i	−0.0991477	+	0.462086i
$141$		0			0
$142$	2.71802	−	2.19669i	0.228091	−	0.184342i
$143$	−1.37454			−0.114945
$144$		0			0
$145$	0.785654			0.0652450
$146$	−0.786165	+	0.635375i	−0.0650635	+	0.0525840i
$147$		0			0
$148$	1.77152	−	8.25631i	0.145618	−	0.678665i
$149$	9.96222	+	5.75169i	0.816137	+	0.471197i	0.849083	−	0.528260i	$-0.177155\pi$
$149$	9.96222	+	5.75169i	0.816137	+	0.471197i	−0.0329454	+	0.999457i	$0.510489\pi$
$150$		0			0
$151$	−4.20513	+	2.42783i	−0.342209	+	0.197574i	−0.661248	−	0.750167i	$-0.729973\pi$
$151$	−4.20513	+	2.42783i	−0.342209	+	0.197574i	0.319040	+	0.947741i	$0.396640\pi$
$152$	18.6601	−	9.44014i	1.51353	−	0.765696i
$153$		0			0
$154$	0.393856	−	0.0619928i	0.0317378	−	0.00499553i
$155$	13.0615	+	22.6232i	1.04912	+	1.81714i
$156$		0			0
$157$	10.1032	−	17.4992i	0.806322	−	1.39659i	−0.109073	−	0.994034i	$-0.534788\pi$
$157$	10.1032	−	17.4992i	0.806322	−	1.39659i	0.915395	−	0.402557i	$-0.131878\pi$
$158$	−1.26339	+	3.28182i	−0.100510	+	0.261088i
$159$		0			0
$160$	15.2576	+	4.16690i	1.20622	+	0.329422i
$161$		−	6.57868i		−	0.518473i
$162$		0			0
$163$		−	16.5798i		−	1.29863i	−0.760518	−	0.649317i	$-0.775055\pi$
$163$		−	16.5798i		−	1.29863i	0.760518	−	0.649317i	$-0.224945\pi$
$164$	0.998477	−	1.10465i	0.0779680	−	0.0862584i
$165$		0			0
$166$	−10.8242	−	4.16696i	−0.840122	−	0.323419i
$167$	3.38550	−	5.86386i	0.261978	−	0.453759i	−0.704789	−	0.709417i	$-0.748958\pi$
$167$	3.38550	−	5.86386i	0.261978	−	0.453759i	0.966768	+	0.255657i	$0.0822918\pi$
$168$		0			0
$169$	−5.38531	−	9.32763i	−0.414255	−	0.717510i
$170$	−3.48168	−	22.1200i	−0.267033	−	1.69652i
$171$		0			0
$172$	4.48173	+	13.8841i	0.341729	+	1.05865i
$173$	8.38112	−	4.83884i	0.637204	−	0.367890i	−0.146332	−	0.989235i	$-0.546747\pi$
$173$	8.38112	−	4.83884i	0.637204	−	0.367890i	0.783537	+	0.621345i	$0.213414\pi$
$174$		0			0
$175$	−2.43992	−	1.40869i	−0.184441	−	0.106487i
$176$	−0.113567	−	1.12197i	−0.00856045	−	0.0845720i
$177$		0			0
$178$	−0.314882	−	0.389612i	−0.0236014	−	0.0292027i
$179$	6.71304			0.501756			0.250878	−	0.968019i	$-0.419281\pi$
$179$	6.71304			0.501756			0.250878	+	0.968019i	$0.419281\pi$
$180$		0			0
$181$	10.5763			0.786129			0.393065	−	0.919511i	$-0.371415\pi$
$181$	10.5763			0.786129			0.393065	+	0.919511i	$0.371415\pi$
$182$	4.33402	+	5.36260i	0.321259	+	0.397502i
$183$		0			0
$184$	−18.5789	−	1.02738i	−1.36966	−	0.0757393i
$185$	10.2233	+	5.90243i	0.751632	+	0.433955i
$186$		0			0
$187$	−1.38268	+	0.798288i	−0.101111	+	0.0583766i
$188$	−9.85997	+	3.18277i	−0.719113	+	0.232127i
$189$		0			0
$190$	4.54556	+	28.8791i	0.329770	+	2.09511i
$191$	4.68386	+	8.11268i	0.338912	+	0.587013i	0.984228	−	0.176903i	$-0.0566078\pi$
$191$	4.68386	+	8.11268i	0.338912	+	0.587013i	−0.645316	+	0.763915i	$0.723274\pi$
$192$		0			0
$193$	−0.439681	+	0.761550i	−0.0316489	+	0.0548176i	−0.881416	−	0.472341i	$-0.843409\pi$
$193$	−0.439681	+	0.761550i	−0.0316489	+	0.0548176i	0.849767	+	0.527158i	$0.176743\pi$
$194$	0.366882	+	0.141237i	0.0263406	+	0.0101402i
$195$		0			0
$196$	−1.48372	−	1.34111i	−0.105980	−	0.0957939i
$197$		−	14.4709i		−	1.03101i	−0.856887	−	0.515504i	$-0.827605\pi$
$197$		−	14.4709i		−	1.03101i	0.856887	−	0.515504i	$-0.172395\pi$
$198$		0			0
$199$			0.507764i			0.0359945i	0.999838	+	0.0179972i	$0.00572901\pi$
$199$			0.507764i			0.0359945i	−0.999838	+	0.0179972i	$0.994271\pi$
$200$	−4.35934	+	6.67063i	−0.308252	+	0.471685i
$201$		0			0
$202$	7.16323	−	18.6074i	0.504003	−	1.30921i
$203$	−0.140498	+	0.243350i	−0.00986103	+	0.0170798i
$204$		0			0
$205$	1.04081	+	1.80274i	0.0726936	+	0.125909i
$206$	15.0760	−	2.37297i	1.05040	−	0.165332i
$207$		0			0
$208$	15.8214	−	11.4023i	1.09702	−	0.790608i
$209$	1.80517	−	1.04222i	0.124866	−	0.0720916i
$210$		0			0
$211$	10.0333	+	5.79273i	0.690721	+	0.398788i	0.803882	−	0.594789i	$-0.202764\pi$
$211$	10.0333	+	5.79273i	0.690721	+	0.398788i	−0.113161	+	0.993577i	$0.536098\pi$
$212$	15.8769	+	3.40664i	1.09043	+	0.233969i
$213$		0			0
$214$	4.13927	−	3.34533i	0.282954	−	0.228682i
$215$	−20.3958			−1.39098
$216$		0			0
$217$	−9.34312			−0.634252
$218$	−6.72665	+	5.43644i	−0.455586	+	0.368202i
$219$		0			0
$220$	1.54143	+	0.330737i	0.103923	+	0.0222983i
$221$	−23.9113	−	13.8052i	−1.60845	−	0.928640i
$222$		0			0
$223$	11.5096	−	6.64507i	0.770739	−	0.444987i	−0.0623990	−	0.998051i	$-0.519875\pi$
$223$	11.5096	−	6.64507i	0.770739	−	0.444987i	0.833138	+	0.553065i	$0.186542\pi$
$224$	−4.01917	+	3.98074i	−0.268542	+	0.265974i
$225$		0			0
$226$	2.86768	−	0.451373i	0.190755	−	0.0300249i
$227$	−4.25510	−	7.37006i	−0.282421	−	0.489168i	0.689559	−	0.724229i	$-0.257804\pi$
$227$	−4.25510	−	7.37006i	−0.282421	−	0.489168i	−0.971981	+	0.235061i	$0.924471\pi$
$228$		0			0
$229$	5.27466	−	9.13598i	0.348559	−	0.603722i	−0.637435	−	0.770505i	$-0.720004\pi$
$229$	5.27466	−	9.13598i	0.348559	−	0.603722i	0.985994	+	0.166782i	$0.0533377\pi$
$230$	9.34542	−	24.2759i	0.616219	−	1.60071i
$231$		0			0
$232$	0.665306	+	0.434786i	0.0436795	+	0.0285451i
$233$		−	2.54006i		−	0.166405i	−0.996533	−	0.0832024i	$-0.973485\pi$
$233$		−	2.54006i		−	0.166405i	0.996533	−	0.0832024i	$-0.0265148\pi$
$234$		0			0
$235$		−	14.4844i		−	0.944857i
$236$	−0.639354	−	0.577905i	−0.0416184	−	0.0376184i
$237$		0			0
$238$	7.47411	+	2.87728i	0.484475	+	0.186507i
$239$	−12.3345	+	21.3640i	−0.797855	+	1.38193i	0.123155	+	0.992387i	$0.460699\pi$
$239$	−12.3345	+	21.3640i	−0.797855	+	1.38193i	−0.921010	+	0.389538i	$0.872635\pi$
$240$		0			0
$241$	−7.33435	−	12.7035i	−0.472447	−	0.818303i	0.527056	−	0.849831i	$-0.323296\pi$
$241$	−7.33435	−	12.7035i	−0.472447	−	0.818303i	−0.999503	+	0.0315281i	$0.989963\pi$
$242$	2.40131	+	15.2561i	0.154362	+	0.980700i
$243$		0			0
$244$	11.2633	−	3.63577i	0.721061	−	0.232756i
$245$	2.42137	−	1.39798i	0.154696	−	0.0893136i
$246$		0			0
$247$	31.2178	+	18.0236i	1.98634	+	1.14682i
$248$	−1.45909	+	26.3860i	−0.0926526	+	1.67551i
$249$		0			0
$250$	5.42475	+	6.71218i	0.343091	+	0.424516i
$251$	−15.0697			−0.951191			−0.475595	−	0.879664i	$-0.657767\pi$
$251$	−15.0697			−0.951191			−0.475595	+	0.879664i	$0.657767\pi$
$252$		0			0
$253$	−1.85471			−0.116604
$254$	−11.1928	−	13.8492i	−0.702301	−	0.868975i
$255$		0			0
$256$	10.6144	+	11.9722i	0.663400	+	0.748265i
$257$	−3.71863	−	2.14695i	−0.231962	−	0.133923i	0.379515	−	0.925186i	$-0.376091\pi$
$257$	−3.71863	−	2.14695i	−0.231962	−	0.133923i	−0.611477	+	0.791262i	$0.709424\pi$
$258$		0			0
$259$	−3.65646	+	2.11106i	−0.227201	+	0.131175i
$260$	8.37504	+	25.9452i	0.519398	+	1.60905i
$261$		0			0
$262$	1.81657	+	11.5411i	0.112228	+	0.713012i
$263$	4.80188	+	8.31711i	0.296097	+	0.512855i	0.975239	−	0.221152i	$-0.0709815\pi$
$263$	4.80188	+	8.31711i	0.296097	+	0.512855i	−0.679143	+	0.734006i	$0.737648\pi$
$264$		0			0
$265$	−11.3504	+	19.6595i	−0.697250	+	1.20767i
$266$	−9.75794	−	3.75648i	−0.598297	−	0.230325i
$267$		0			0
$268$	−3.26944	+	3.61708i	−0.199713	+	0.220949i
$269$		−	21.0329i		−	1.28240i	−0.767375	−	0.641199i	$-0.778437\pi$
$269$		−	21.0329i		−	1.28240i	0.767375	−	0.641199i	$-0.221563\pi$
$270$		0			0
$271$		−	12.1109i		−	0.735682i	−0.929889	−	0.367841i	$-0.880097\pi$
$271$		−	12.1109i		−	0.735682i	0.929889	−	0.367841i	$-0.119903\pi$
$272$	9.29299	−	20.6584i	0.563470	−	1.25260i
$273$		0			0
$274$	−8.50879	+	22.1027i	−0.514035	+	1.33527i
$275$	−0.397148	+	0.687880i	−0.0239489	+	0.0414807i
$276$		0			0
$277$	1.37227	+	2.37683i	0.0824514	+	0.142810i	0.904302	−	0.426893i	$-0.140392\pi$
$277$	1.37227	+	2.37683i	0.0824514	+	0.142810i	−0.821851	+	0.569703i	$0.807058\pi$
$278$	−32.5270	+	5.11975i	−1.95084	+	0.307062i
$279$		0			0
$280$	−3.56991	−	7.05654i	−0.213343	−	0.421709i
$281$	−5.21831	+	3.01279i	−0.311298	+	0.179728i	−0.647507	−	0.762059i	$-0.724188\pi$
$281$	−5.21831	+	3.01279i	−0.311298	+	0.179728i	0.336209	+	0.941787i	$0.390855\pi$
$282$		0			0
$283$	−24.0259	−	13.8713i	−1.42819	−	0.824565i	−0.431211	−	0.902251i	$-0.641914\pi$
$283$	−24.0259	−	13.8713i	−1.42819	−	0.824565i	−0.996978	+	0.0776854i	$0.975247\pi$
$284$	−1.03684	+	4.83230i	−0.0615254	+	0.286744i
$285$		0			0
$286$	1.51186	−	1.22188i	0.0893982	−	0.0722511i
$287$	−0.744513			−0.0439472
$288$		0			0
$289$	−15.0705			−0.886503
$290$	−0.864144	+	0.698397i	−0.0507443	+	0.0410113i
$291$		0			0
$292$	0.299899	−	1.39770i	0.0175502	−	0.0817944i
$293$	−10.8328	−	6.25434i	−0.632861	−	0.365383i	0.148998	−	0.988837i	$-0.452395\pi$
$293$	−10.8328	−	6.25434i	−0.632861	−	0.365383i	−0.781859	+	0.623455i	$0.785729\pi$
$294$		0			0
$295$	1.04340	−	0.602409i	0.0607493	−	0.0350736i
$296$	5.39084	+	10.6559i	0.313336	+	0.619363i
$297$		0			0
$298$	−16.0704	+	2.52948i	−0.930933	+	0.146529i
$299$	−16.0372	−	27.7773i	−0.927456	−	1.60640i
$300$		0			0
$301$	3.64737	−	6.31743i	0.210231	−	0.364131i
$302$	2.46705	−	6.40848i	0.141963	−	0.368767i
$303$		0			0
$304$	−12.1326	+	26.9709i	−0.695852	+	1.54689i
$305$			16.5459i			0.947417i
$306$		0			0
$307$		−	2.72302i		−	0.155411i	−0.996976	−	0.0777054i	$-0.975241\pi$
$307$		−	2.72302i		−	0.155411i	0.996976	−	0.0777054i	$-0.0247594\pi$
$308$	−0.378096	+	0.418299i	−0.0215440	+	0.0238348i
$309$		0			0
$310$	−34.4770	−	13.2725i	−1.95816	−	0.753826i
$311$	4.22803	−	7.32317i	0.239750	−	0.415259i	−0.720893	−	0.693047i	$-0.756268\pi$
$311$	4.22803	−	7.32317i	0.239750	−	0.415259i	0.960642	+	0.277788i	$0.0896013\pi$
$312$		0			0
$313$	−13.8676	−	24.0195i	−0.783845	−	1.35766i	−0.929687	−	0.368352i	$-0.879922\pi$
$313$	−13.8676	−	24.0195i	−0.783845	−	1.35766i	0.145841	−	0.989308i	$-0.453411\pi$
$314$	4.44318	+	28.2286i	0.250743	+	1.59303i
$315$		0			0
$316$	−1.52772	−	4.73277i	−0.0859411	−	0.266239i
$317$	20.7198	−	11.9626i	1.16374	−	0.671886i	0.211544	−	0.977369i	$-0.432151\pi$
$317$	20.7198	−	11.9626i	1.16374	−	0.671886i	0.952198	+	0.305482i	$0.0988176\pi$
$318$		0			0
$319$	0.0686069	+	0.0396102i	0.00384125	+	0.00221774i
$320$	−20.4860	+	8.97982i	−1.14520	+	0.501987i
$321$		0			0
$322$	5.84803	+	7.23592i	0.325898	+	0.403242i
$323$	41.8702			2.32972
$324$		0			0
$325$	−13.7362			−0.761946
$326$	14.7384	+	18.2363i	0.816287	+	1.01001i
$327$		0			0
$328$	−0.116269	+	2.10259i	−0.00641988	+	0.116096i
$329$	4.48642	+	2.59024i	0.247344	+	0.142804i
$330$		0			0
$331$	24.6873	−	14.2532i	1.35694	−	0.783427i	0.367727	−	0.929934i	$-0.380136\pi$
$331$	24.6873	−	14.2532i	1.35694	−	0.783427i	0.989210	+	0.146506i	$0.0468029\pi$
$332$	15.6098	−	5.03879i	0.856698	−	0.276539i
$333$		0			0
$334$	1.48888	+	9.45919i	0.0814677	+	0.517584i
$335$	−3.40807	−	5.90295i	−0.186203	−	0.322513i
$336$		0			0
$337$	2.26282	−	3.91932i	0.123264	−	0.213499i	−0.797789	−	0.602937i	$-0.793997\pi$
$337$	2.26282	−	3.91932i	0.123264	−	0.213499i	0.921053	+	0.389437i	$0.127331\pi$
$338$	14.2150	+	5.47230i	0.773194	+	0.297654i
$339$		0			0
$340$	23.4928	+	21.2349i	1.27408	+	1.15162i
$341$			2.63408i			0.142643i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−17.2715	−	11.2872i	−0.931219	−	0.608563i
$345$		0			0
$346$	−4.91700	+	12.7725i	−0.264340	+	0.686656i
$347$	−14.9377	+	25.8728i	−0.801895	+	1.38892i	0.116472	+	0.993194i	$0.462841\pi$
$347$	−14.9377	+	25.8728i	−0.801895	+	1.38892i	−0.918367	+	0.395729i	$0.870492\pi$
$348$		0			0
$349$	−9.43250	−	16.3376i	−0.504910	−	0.874530i	−0.999984	−	0.00567921i	$-0.998192\pi$
$349$	−9.43250	−	16.3376i	−0.504910	−	0.874530i	0.495074	−	0.868851i	$-0.335141\pi$
$350$	3.93592	−	0.619514i	0.210384	−	0.0331144i
$351$		0			0
$352$	1.12228	+	1.13311i	0.0598176	+	0.0603950i
$353$	−26.5534	+	15.3306i	−1.41330	+	0.815967i	−0.995697	−	0.0926650i	$-0.970461\pi$
$353$	−26.5534	+	15.3306i	−1.41330	+	0.815967i	−0.417598	+	0.908632i	$0.637128\pi$
$354$		0			0
$355$	−5.98355	−	3.45460i	−0.317574	−	0.183351i
$356$	0.692681	+	0.148625i	0.0367120	+	0.00787713i
$357$		0			0
$358$	−7.38370	+	5.96747i	−0.390241	+	0.315391i
$359$	18.8963			0.997310			0.498655	−	0.866801i	$-0.333828\pi$
$359$	18.8963			0.997310			0.498655	+	0.866801i	$0.333828\pi$
$360$		0			0
$361$	−35.6642			−1.87706
$362$	−11.6329	+	9.40165i	−0.611412	+	0.494140i
$363$		0			0
$364$	−9.53403	−	2.04567i	−0.499719	−	0.107222i
$365$	1.73069	+	0.999216i	0.0905886	+	0.0523014i
$366$		0			0
$367$	−4.63257	+	2.67462i	−0.241818	+	0.139614i	−0.616012	−	0.787737i	$-0.711253\pi$
$367$	−4.63257	+	2.67462i	−0.241818	+	0.139614i	0.374194	+	0.927351i	$0.377919\pi$
$368$	21.3483	−	15.3855i	1.11286	−	0.802024i
$369$		0			0
$370$	−16.4915	+	2.59577i	−0.857355	+	0.134947i
$371$	−4.05957	−	7.03139i	−0.210763	−	0.365052i
$372$		0			0
$373$	−7.51238	+	13.0118i	−0.388976	+	0.673727i	−0.992312	−	0.123760i	$-0.960505\pi$
$373$	−7.51238	+	13.0118i	−0.388976	+	0.673727i	0.603336	+	0.797487i	$0.293838\pi$
$374$	0.811183	−	2.10715i	0.0419453	−	0.108958i
$375$		0			0
$376$	8.01575	−	12.2656i	0.413381	−	0.632552i
$377$			1.37000i			0.0705586i
$378$		0			0
$379$			3.97151i			0.204003i	0.994784	+	0.102001i	$0.0325246\pi$
$379$			3.97151i			0.204003i	−0.994784	+	0.102001i	$0.967475\pi$
$380$	−30.6714	−	27.7235i	−1.57341	−	1.42219i
$381$		0			0
$382$	−12.3635	−	4.75952i	−0.632569	−	0.243518i
$383$	10.0601	−	17.4246i	0.514047	−	0.890355i	−0.485821	−	0.874059i	$-0.661479\pi$
$383$	10.0601	−	17.4246i	0.514047	−	0.890355i	0.999867	−	0.0162963i	$-0.00518751\pi$
$384$		0			0
$385$	−0.394128	−	0.682649i	−0.0200866	−	0.0347910i
$386$	−0.193363	−	1.22848i	−0.00984191	−	0.0625281i
$387$		0			0
$388$	−0.529086	+	0.170787i	−0.0268603	+	0.00867041i
$389$	30.9005	−	17.8404i	1.56672	−	0.904545i	0.570169	−	0.821527i	$-0.306878\pi$
$389$	30.9005	−	17.8404i	1.56672	−	0.904545i	0.996548	−	0.0830175i	$-0.0264558\pi$
$390$		0			0
$391$	−32.2643	−	18.6278i	−1.63168	−	0.942049i
$392$	2.82411	+	0.156168i	0.142639	+	0.00788767i
$393$		0			0
$394$	12.8637	+	15.9166i	0.648064	+	0.801866i
$395$	6.95247			0.349817
$396$		0			0
$397$	26.7209			1.34108			0.670541	−	0.741873i	$-0.266062\pi$
$397$	26.7209			1.34108			0.670541	+	0.741873i	$0.266062\pi$
$398$	−0.451371	−	0.558492i	−0.0226252	−	0.0279947i
$399$		0			0
$400$	−1.13491	−	11.2122i	−0.0567456	−	0.560612i
$401$	−19.5104	−	11.2643i	−0.974302	−	0.562514i	−0.0737572	−	0.997276i	$-0.523499\pi$
$401$	−19.5104	−	11.2643i	−0.974302	−	0.562514i	−0.900545	+	0.434762i	$0.856832\pi$
$402$		0			0
$403$	−39.4496	+	22.7762i	−1.96513	+	1.13457i
$404$	8.66195	+	26.8340i	0.430948	+	1.33504i
$405$		0			0
$406$	−0.0617882	−	0.392556i	−0.00306650	−	0.0194822i
$407$	0.595164	+	1.03085i	0.0295012	+	0.0510975i
$408$		0			0
$409$	−7.38017	+	12.7828i	−0.364926	+	0.632070i	−0.988764	−	0.149483i	$-0.952239\pi$
$409$	−7.38017	+	12.7828i	−0.364926	+	0.632070i	0.623839	+	0.781553i	$0.285572\pi$
$410$	−2.74732	−	1.05763i	−0.135681	−	0.0522325i
$411$		0			0
$412$	−14.4728	+	16.0117i	−0.713023	+	0.788839i
$413$			0.430914i			0.0212039i
$414$		0			0
$415$			22.9309i			1.12563i
$416$	−7.26612	+	26.6057i	−0.356251	+	1.30445i
$417$		0			0
$418$	−1.05905	+	2.75102i	−0.0518000	+	0.134557i
$419$	−15.0986	+	26.1515i	−0.737614	+	1.27759i	0.215953	+	0.976404i	$0.430714\pi$
$419$	−15.0986	+	26.1515i	−0.737614	+	1.27759i	−0.953567	+	0.301181i	$0.902619\pi$
$420$		0			0
$421$	12.0519	+	20.8744i	0.587372	+	1.01736i	0.994575	+	0.104021i	$0.0331708\pi$
$421$	12.0519	+	20.8744i	0.587372	+	1.01736i	−0.407203	+	0.913338i	$0.633496\pi$
$422$	−16.1850	+	2.54752i	−0.787875	+	0.124011i
$423$		0			0
$424$	−20.4914	+	10.3666i	−0.995151	+	0.503448i
$425$	−13.8175	+	7.97754i	−0.670247	+	0.386967i
$426$		0			0
$427$	−5.12497	−	2.95890i	−0.248014	−	0.143191i
$428$	−1.57901	+	7.35910i	−0.0763242	+	0.355715i
$429$		0			0
$430$	22.4334	−	18.1306i	1.08184	−	0.874335i
$431$	−26.8450			−1.29308			−0.646538	−	0.762882i	$-0.723784\pi$
$431$	−26.8450			−1.29308			−0.646538	+	0.762882i	$0.723784\pi$
$432$		0			0
$433$	16.4401			0.790063			0.395031	−	0.918668i	$-0.370734\pi$
$433$	16.4401			0.790063			0.395031	+	0.918668i	$0.370734\pi$
$434$	10.2765	−	8.30545i	0.493290	−	0.398674i
$435$		0			0
$436$	2.56602	−	11.9591i	0.122890	−	0.572739i
$437$	42.1232	+	24.3198i	2.01502	+	1.16337i
$438$		0			0
$439$	−10.2179	+	5.89931i	−0.487674	+	0.281559i	−0.723609	−	0.690210i	$-0.757518\pi$
$439$	−10.2179	+	5.89931i	−0.487674	+	0.281559i	0.235935	+	0.971769i	$0.424185\pi$
$440$	−1.98943	+	1.00645i	−0.0948423	+	0.0479808i
$441$		0			0
$442$	38.5722	−	6.07126i	1.83469	−	0.288780i
$443$	8.35739	+	14.4754i	0.397071	+	0.687748i	0.993363	−	0.115020i	$-0.0366932\pi$
$443$	8.35739	+	14.4754i	0.397071	+	0.687748i	−0.596292	+	0.802768i	$0.703360\pi$
$444$		0			0
$445$	−0.495197	+	0.857706i	−0.0234746	+	0.0406592i
$446$	−6.75241	+	17.5402i	−0.319736	+	0.830555i
$447$		0			0
$448$	0.882071	−	7.95122i	0.0416740	−	0.375660i
$449$			36.4399i			1.71970i	0.510543	+	0.859852i	$0.329444\pi$
$449$			36.4399i			1.71970i	−0.510543	+	0.859852i	$0.670556\pi$
$450$		0			0
$451$			0.209898i			0.00988372i
$452$	−2.75293	+	3.04566i	−0.129487	+	0.143256i
$453$		0			0
$454$	11.2317	+	4.32384i	0.527131	+	0.202928i
$455$	6.81586	−	11.8054i	0.319533	−	0.553447i
$456$		0			0
$457$	16.3554	+	28.3283i	0.765072	+	1.32514i	0.940208	+	0.340600i	$0.110630\pi$
$457$	16.3554	+	28.3283i	0.765072	+	1.32514i	−0.175136	+	0.984544i	$0.556036\pi$
$458$	2.31969	+	14.7375i	0.108392	+	0.688640i
$459$		0			0
$460$	11.3007	+	35.0087i	0.526898	+	1.63229i
$461$	23.5218	−	13.5803i	1.09552	−	0.632498i	0.160479	−	0.987039i	$-0.448696\pi$
$461$	23.5218	−	13.5803i	1.09552	−	0.632498i	0.935040	+	0.354541i	$0.115363\pi$
$462$		0			0
$463$	15.5298	+	8.96612i	0.721730	+	0.416691i	0.815389	−	0.578913i	$-0.196523\pi$
$463$	15.5298	+	8.96612i	0.721730	+	0.416691i	−0.0936592	+	0.995604i	$0.529856\pi$
$464$	−1.11827	+	0.113192i	−0.0519144	+	0.00525482i
$465$		0			0
$466$	2.25795	+	2.79382i	0.104598	+	0.129421i
$467$	24.3536			1.12695			0.563474	−	0.826134i	$-0.309464\pi$
$467$	24.3536			1.12695			0.563474	+	0.826134i	$0.309464\pi$
$468$		0			0
$469$	2.43786			0.112570
$470$	12.8757	+	15.9314i	0.593912	+	0.734862i
$471$		0			0
$472$	1.21695	+	0.0672950i	0.0560147	+	0.00309750i
$473$	−1.78105	−	1.02829i	−0.0818930	−	0.0472809i
$474$		0			0
$475$	18.0396	−	10.4152i	0.827716	−	0.477882i
$476$	−10.7785	+	3.47928i	−0.494033	+	0.159472i
$477$		0			0
$478$	−5.42448	−	34.4630i	−0.248110	−	1.57630i
$479$	−8.74315	−	15.1436i	−0.399485	−	0.691928i	0.594177	−	0.804334i	$-0.297478\pi$
$479$	−8.74315	−	15.1436i	−0.399485	−	0.691928i	−0.993662	+	0.112406i	$0.964144\pi$
$480$		0			0
$481$	−10.2925	+	17.8271i	−0.469297	+	0.812846i
$482$	19.3597	+	7.45283i	0.881809	+	0.339467i
$483$		0			0
$484$	−16.2029	−	14.6457i	−0.736497	−	0.665712i
$485$		−	0.777231i		−	0.0352922i
$486$		0			0
$487$		−	5.76620i		−	0.261291i	−0.991429	−	0.130646i	$-0.958295\pi$
$487$		−	5.76620i		−	0.261291i	0.991429	−	0.130646i	$-0.0417050\pi$
$488$	−9.15662	+	14.0114i	−0.414501	+	0.634266i
$489$		0			0
$490$	−1.42056	+	3.69009i	−0.0641744	+	0.166701i
$491$	16.6911	−	28.9099i	0.753261	−	1.30469i	−0.192973	−	0.981204i	$-0.561813\pi$
$491$	16.6911	−	28.9099i	0.753261	−	1.30469i	0.946234	−	0.323482i	$-0.104854\pi$
$492$		0			0
$493$	0.795653	+	1.37811i	0.0358344	+	0.0620670i
$494$	−50.3585	+	7.92642i	−2.26574	+	0.356626i
$495$		0			0
$496$	−21.8506	−	30.3192i	−0.981123	−	1.36137i
$497$	2.14007	−	1.23557i	0.0959953	−	0.0554229i
$498$		0			0
$499$	35.1612	+	20.3003i	1.57403	+	0.908766i	0.995667	+	0.0929863i	$0.0296413\pi$
$499$	35.1612	+	20.3003i	1.57403	+	0.908766i	0.578362	+	0.815780i	$0.303692\pi$
$500$	−11.9334	−	2.56050i	−0.533678	−	0.114509i
$501$		0			0
$502$	16.5752	−	13.3960i	0.739789	−	0.597893i
$503$	16.0809			0.717012			0.358506	−	0.933528i	$-0.383286\pi$
$503$	16.0809			0.717012			0.358506	+	0.933528i	$0.383286\pi$
$504$		0			0
$505$	−39.4194			−1.75414
$506$	2.04000	−	1.64872i	0.0906891	−	0.0732944i
$507$		0			0
$508$	24.6221	+	5.28305i	1.09243	+	0.234398i
$509$	−0.457413	−	0.264088i	−0.0202745	−	0.0117055i	0.489829	−	0.871819i	$-0.337059\pi$
$509$	−0.457413	−	0.264088i	−0.0202745	−	0.0117055i	−0.510103	+	0.860113i	$0.670393\pi$
$510$		0			0
$511$	−0.618998	+	0.357379i	−0.0273829	+	0.0158095i
$512$	−22.3174	−	3.73279i	−0.986299	−	0.164968i
$513$		0			0
$514$	5.99864	−	0.944185i	0.264589	−	0.0416462i
$515$	−15.0865	−	26.1305i	−0.664788	−	1.15145i
$516$		0			0
$517$	0.730257	−	1.26484i	0.0321167	−	0.0556277i
$518$	2.14516	−	5.57232i	0.0942528	−	0.244834i
$519$		0			0
$520$	−32.2754	−	21.0924i	−1.41537	−	0.924963i
$521$		−	39.2616i		−	1.72008i	−0.510224	−	0.860042i	$-0.670437\pi$
$521$		−	39.2616i		−	1.72008i	0.510224	−	0.860042i	$-0.329563\pi$
$522$		0			0
$523$			12.1444i			0.531036i	0.964106	+	0.265518i	$0.0855430\pi$
$523$			12.1444i			0.531036i	−0.964106	+	0.265518i	$0.914457\pi$
$524$	−12.2574	−	11.0793i	−0.535466	−	0.484002i
$525$		0			0
$526$	−12.6750	−	4.87945i	−0.552656	−	0.212754i
$527$	−26.4554	+	45.8222i	−1.15242	+	1.99605i
$528$		0			0
$529$	−10.1395	−	17.5621i	−0.440848	−	0.763572i
$530$	−4.99168	−	31.7133i	−0.216825	−	1.37754i
$531$		0			0
$532$	14.0721	−	4.54242i	0.610102	−	0.196939i
$533$	−3.14357	+	1.81494i	−0.136163	+	0.0786138i
$534$		0			0
$535$	−9.11233	−	5.26101i	−0.393961	−	0.227453i
$536$	0.380715	−	6.88478i	0.0164444	−	0.297377i
$537$		0			0
$538$	18.6969	+	23.1342i	0.806081	+	0.997385i
$539$	0.281927			0.0121434
$540$		0			0
$541$	−22.5265			−0.968490			−0.484245	−	0.874933i	$-0.660906\pi$
$541$	−22.5265			−0.968490			−0.484245	+	0.874933i	$0.660906\pi$
$542$	10.7658	+	13.3208i	0.462430	+	0.572177i
$543$		0			0
$544$	8.14261	+	30.9831i	0.349112	+	1.32839i
$545$	14.8083	+	8.54957i	0.634317	+	0.366223i
$546$		0			0
$547$	−7.89651	+	4.55905i	−0.337631	+	0.194931i	−0.659224	−	0.751947i	$-0.729115\pi$
$547$	−7.89651	+	4.55905i	−0.337631	+	0.194931i	0.321593	+	0.946878i	$0.395782\pi$
$548$	−10.2890	−	31.8746i	−0.439525	−	1.36162i
$549$		0			0
$550$	−0.174657	−	1.10964i	−0.00744742	−	0.0473153i
$551$	−1.03878	−	1.79921i	−0.0442534	−	0.0766491i
$552$		0			0
$553$	−1.24331	+	2.15347i	−0.0528708	+	0.0915750i
$554$	−3.62222	−	1.39443i	−0.153893	−	0.0592438i
$555$		0			0
$556$	31.2255	−	34.5457i	1.32426	−	1.46506i
$557$		−	11.9979i		−	0.508369i	−0.967156	−	0.254184i	$-0.918193\pi$
$557$		−	11.9979i		−	0.508369i	0.967156	−	0.254184i	$-0.0818070\pi$
$558$		0			0
$559$		−	35.5656i		−	1.50427i
$560$	10.1994	+	4.58810i	0.431003	+	0.193883i
$561$		0			0
$562$	3.06146	−	7.95253i	0.129140	−	0.335457i
$563$	−9.48276	+	16.4246i	−0.399651	+	0.692216i	−0.993683	−	0.112226i	$-0.964202\pi$
$563$	−9.48276	+	16.4246i	−0.399651	+	0.692216i	0.594032	+	0.804441i	$0.297535\pi$
$564$		0			0
$565$	−2.86966	−	4.97040i	−0.120728	−	0.209106i
$566$	38.7569	−	6.10033i	1.62907	−	0.256416i
$567$		0			0
$568$	−3.15518	−	6.23676i	−0.132388	−	0.261688i
$569$	−20.5929	+	11.8893i	−0.863301	+	0.498427i	−0.865116	−	0.501571i	$-0.832756\pi$
$569$	−20.5929	+	11.8893i	−0.863301	+	0.498427i	0.00181529	+	0.999998i	$0.499422\pi$
$570$		0			0
$571$	9.65431	+	5.57392i	0.404020	+	0.233261i	0.688217	−	0.725505i	$-0.258394\pi$
$571$	9.65431	+	5.57392i	0.404020	+	0.233261i	−0.284197	+	0.958766i	$0.591727\pi$
$572$	−0.576730	+	2.68790i	−0.0241143	+	0.112387i
$573$		0			0
$574$	0.818894	−	0.661826i	0.0341800	−	0.0276241i
$575$	−18.5346			−0.772948
$576$		0			0
$577$	26.0394			1.08404			0.542018	−	0.840367i	$-0.317660\pi$
$577$	26.0394			1.08404			0.542018	+	0.840367i	$0.317660\pi$
$578$	16.5762	−	13.3968i	0.689478	−	0.557232i
$579$		0			0
$580$	0.329645	−	1.53634i	0.0136878	−	0.0637930i
$581$	−7.10266	−	4.10072i	−0.294668	−	0.170127i
$582$		0			0
$583$	−1.98234	+	1.14450i	−0.0821000	+	0.0474005i
$584$	0.912610	+	1.80393i	0.0377641	+	0.0746472i
$585$		0			0
$586$	17.4748	−	2.75053i	0.721878	−	0.113623i
$587$	1.53840	+	2.66458i	0.0634965	+	0.109979i	0.896026	−	0.444001i	$-0.146441\pi$
$587$	1.53840	+	2.66458i	0.0634965	+	0.109979i	−0.832530	+	0.553981i	$0.813108\pi$
$588$		0			0
$589$	34.5393	−	59.8238i	1.42317	−	2.46500i
$590$	−0.612140	+	1.59011i	−0.0252014	+	0.0654639i
$591$		0			0
$592$	−15.4019	−	6.92839i	−0.633013	−	0.284755i
$593$		−	4.35742i		−	0.178938i	−0.995990	−	0.0894688i	$-0.971483\pi$
$593$		−	4.35742i		−	0.178938i	0.995990	−	0.0894688i	$-0.0285169\pi$
$594$		0			0
$595$		−	15.8338i		−	0.649121i
$596$	15.4274	−	17.0678i	0.631929	−	0.699122i
$597$		0			0
$598$	42.3317	+	16.2963i	1.73107	+	0.666404i
$599$	16.0003	−	27.7133i	0.653753	−	1.13233i	−0.328452	−	0.944521i	$-0.606527\pi$
$599$	16.0003	−	27.7133i	0.653753	−	1.13233i	0.982205	−	0.187812i	$-0.0601397\pi$
$600$		0			0
$601$	−17.6951	−	30.6489i	−0.721799	−	1.25019i	−0.960278	−	0.279045i	$-0.909982\pi$
$601$	−17.6951	−	30.6489i	−0.721799	−	1.25019i	0.238478	−	0.971148i	$-0.423351\pi$
$602$	1.60404	+	10.1909i	0.0653758	+	0.415349i
$603$		0			0
$604$	2.98322	+	9.24178i	0.121385	+	0.376043i
$605$	26.4426	−	15.2667i	1.07505	−	0.620678i
$606$		0			0
$607$	−2.32842	−	1.34431i	−0.0945076	−	0.0545640i	0.452001	−	0.892017i	$-0.350710\pi$
$607$	−2.32842	−	1.34431i	−0.0945076	−	0.0545640i	−0.546509	+	0.837453i	$0.684044\pi$
$608$	−10.6307	−	40.4505i	−0.431132	−	1.64048i
$609$		0			0
$610$	−14.7083	−	18.1989i	−0.595521	−	0.736854i
$611$	25.2574			1.02181
$612$		0			0
$613$	41.2533			1.66621			0.833103	−	0.553117i	$-0.186562\pi$
$613$	41.2533			1.66621			0.833103	+	0.553117i	$0.186562\pi$
$614$	2.42059	+	2.99506i	0.0976872	+	0.120871i
$615$		0			0
$616$	0.0440279	−	0.796193i	0.00177394	−	0.0320795i
$617$	−23.5137	−	13.5756i	−0.946626	−	0.546534i	−0.0545945	−	0.998509i	$-0.517387\pi$
$617$	−23.5137	−	13.5756i	−0.946626	−	0.546534i	−0.892031	+	0.451974i	$0.850720\pi$
$618$		0			0
$619$	−8.12323	+	4.68995i	−0.326500	+	0.188505i	−0.654286	−	0.756247i	$-0.727031\pi$
$619$	−8.12323	+	4.68995i	−0.326500	+	0.188505i	0.327786	+	0.944752i	$0.393698\pi$
$620$	49.7198	−	16.0494i	1.99679	−	0.644559i
$621$		0			0
$622$	1.85940	+	11.8132i	0.0745553	+	0.473668i
$623$	−0.177112	−	0.306766i	−0.00709583	−	0.0122903i
$624$		0			0
$625$	15.5746	−	26.9761i	0.622985	−	1.07904i
$626$	36.6049	+	14.0917i	1.46302	+	0.563216i
$627$		0			0
$628$	−29.9805	−	27.0991i	−1.19635	−	1.08137i
$629$			23.9102i			0.953362i
$630$		0			0
$631$			17.3945i			0.692463i	0.938149	+	0.346232i	$0.112539\pi$
$631$			17.3945i			0.692463i	−0.938149	+	0.346232i	$0.887461\pi$
$632$	5.88748	+	3.84755i	0.234192	+	0.153047i
$633$		0			0
$634$	−12.1558	+	31.5763i	−0.482770	+	1.25406i
$635$	−17.6023	+	30.4881i	−0.698526	+	1.20988i
$636$		0			0
$637$	2.43776	+	4.22232i	0.0965874	+	0.167294i
$638$	−0.110672	+	0.0174198i	−0.00438155	+	0.000689655i
$639$		0			0
$640$	14.5501	−	28.0877i	0.575144	−	1.11026i
$641$	−25.0358	+	14.4544i	−0.988854	+	0.570915i	−0.904932	−	0.425557i	$-0.860078\pi$
$641$	−25.0358	+	14.4544i	−0.988854	+	0.570915i	−0.0839224	+	0.996472i	$0.526745\pi$
$642$		0			0
$643$	12.0530	+	6.95879i	0.475323	+	0.274428i	0.718465	−	0.695563i	$-0.244845\pi$
$643$	12.0530	+	6.95879i	0.475323	+	0.274428i	−0.243142	+	0.969991i	$0.578178\pi$
$644$	−12.8646	−	2.76029i	−0.506935	−	0.108771i
$645$		0			0
$646$	−46.0532	+	37.2200i	−1.81194	+	1.46440i
$647$	20.5491			0.807868			0.403934	−	0.914788i	$-0.367643\pi$
$647$	20.5491			0.807868			0.403934	+	0.914788i	$0.367643\pi$
$648$		0			0
$649$	0.121486			0.00476875
$650$	15.1085	−	12.2106i	0.592604	−	0.478939i
$651$		0			0
$652$	−32.4218	−	6.95659i	−1.26973	−	0.272441i
$653$	4.02988	+	2.32665i	0.157701	+	0.0910489i	0.576774	−	0.816904i	$-0.304311\pi$
$653$	4.02988	+	2.32665i	0.157701	+	0.0910489i	−0.419073	+	0.907953i	$0.637645\pi$
$654$		0			0
$655$	20.0036	−	11.5491i	0.781605	−	0.451260i
$656$	−1.74118	−	2.41600i	−0.0679818	−	0.0943291i
$657$		0			0
$658$	−7.23719	+	1.13913i	−0.282135	+	0.0444080i
$659$	−13.4746	−	23.3387i	−0.524895	−	0.909145i	−0.999580	−	0.0289894i	$-0.990771\pi$
$659$	−13.4746	−	23.3387i	−0.524895	−	0.909145i	0.474684	−	0.880156i	$-0.342562\pi$
$660$		0			0
$661$	−15.9921	+	27.6992i	−0.622022	+	1.07737i	0.367087	+	0.930187i	$0.380355\pi$
$661$	−15.9921	+	27.6992i	−0.622022	+	1.07737i	−0.989109	+	0.147186i	$0.952978\pi$
$662$	−14.4835	+	37.6226i	−0.562916	+	1.46225i
$663$		0			0
$664$	−12.6901	+	19.4183i	−0.492472	+	0.753576i
$665$			20.6720i			0.801625i
$666$		0			0
$667$			1.84858i			0.0715775i
$668$	−10.0463	−	9.08070i	−0.388701	−	0.351343i
$669$		0			0
$670$	8.99591	+	3.46312i	0.347542	+	0.133792i
$671$	−0.834193	+	1.44487i	−0.0322037	+	0.0557784i
$672$		0			0
$673$	3.85968	+	6.68517i	0.148780	+	0.257694i	0.930777	−	0.365588i	$-0.119132\pi$
$673$	3.85968	+	6.68517i	0.148780	+	0.257694i	−0.781997	+	0.623282i	$0.785799\pi$
$674$	0.995143	+	6.32239i	0.0383315	+	0.243529i
$675$		0			0
$676$	−20.4997	+	6.61724i	−0.788449	+	0.254509i
$677$	7.42656	−	4.28773i	0.285426	−	0.164791i	−0.350451	−	0.936581i	$-0.613972\pi$
$677$	7.42656	−	4.28773i	0.285426	−	0.164791i	0.635877	+	0.771790i	$0.280638\pi$
$678$		0			0
$679$	0.240741	+	0.138992i	0.00923879	+	0.00533402i
$680$	−44.7163	−	2.47272i	−1.71479	−	0.0948246i
$681$		0			0
$682$	−2.34153	−	2.89723i	−0.0896617	−	0.110941i
$683$	−5.18082			−0.198238			−0.0991192	−	0.995076i	$-0.531603\pi$
$683$	−5.18082			−0.198238			−0.0991192	+	0.995076i	$0.531603\pi$
$684$		0			0
$685$	46.8241			1.78906
$686$	−0.888937	−	1.09990i	−0.0339398	−	0.0419946i
$687$		0			0
$688$	29.0306	−	2.93850i	1.10678	−	0.112029i
$689$	−34.2816	−	19.7925i	−1.30603	−	0.754034i
$690$		0			0
$691$	13.4870	−	7.78675i	0.513071	−	0.296222i	−0.221024	−	0.975268i	$-0.570940\pi$
$691$	13.4870	−	7.78675i	0.513071	−	0.296222i	0.734095	+	0.679047i	$0.237607\pi$
$692$	−5.94576	−	18.4195i	−0.226024	−	0.700204i
$693$		0			0
$694$	−6.56928	−	41.7362i	−0.249366	−	1.58429i
$695$	32.5495	+	56.3774i	1.23467	+	2.13852i
$696$		0			0
$697$	−2.10812	+	3.65137i	−0.0798508	+	0.138306i
$698$	24.8979	+	9.58487i	0.942401	+	0.362793i
$699$		0			0
$700$	−3.77843	+	4.18019i	−0.142811	+	0.157996i
$701$			10.5008i			0.396609i	0.980140	+	0.198304i	$0.0635435\pi$
$701$			10.5008i			0.396609i	−0.980140	+	0.198304i	$0.936457\pi$
$702$		0			0
$703$		−	31.2163i		−	1.17735i
$704$	−2.24166	−	0.248680i	−0.0844859	−	0.00937246i
$705$		0			0
$706$	15.5783	−	40.4665i	0.586296	−	1.52298i
$707$	7.04936	−	12.2098i	0.265118	−	0.459199i
$708$		0			0
$709$	3.56049	+	6.16695i	0.133717	+	0.231605i	0.925107	−	0.379708i	$-0.123975\pi$
$709$	3.56049	+	6.16695i	0.133717	+	0.231605i	−0.791390	+	0.611312i	$0.790642\pi$
$710$	9.65226	−	1.51926i	0.362243	−	0.0570170i
$711$		0			0
$712$	−0.894002	+	0.452276i	−0.0335041	+	0.0169498i
$713$	−53.2306	+	30.7327i	−1.99350	+	1.15095i
$714$		0			0
$715$	−3.32827	−	1.92157i	−0.124470	−	0.0718628i
$716$	2.81666	−	13.1273i	0.105264	−	0.490590i
$717$		0			0
$718$	−20.7842	+	16.7976i	−0.775658	+	0.626882i
$719$	−11.4166			−0.425766			−0.212883	−	0.977078i	$-0.568285\pi$
$719$	−11.4166			−0.425766			−0.212883	+	0.977078i	$0.568285\pi$
$720$		0			0
$721$	10.7916			0.401901
$722$	39.2273	−	31.7033i	1.45989	−	1.17987i
$723$		0			0
$724$	4.43761	−	20.6818i	0.164922	−	0.768635i
$725$	0.685609	+	0.395837i	0.0254629	+	0.0147010i
$726$		0			0
$727$	−11.2371	+	6.48771i	−0.416759	+	0.240616i	−0.693690	−	0.720274i	$-0.744016\pi$
$727$	−11.2371	+	6.48771i	−0.416759	+	0.240616i	0.276931	+	0.960890i	$0.410683\pi$
$728$	12.3050	−	6.22511i	0.456054	−	0.230718i
$729$		0			0
$730$	−2.79184	+	0.439435i	−0.103331	+	0.0162642i
$731$	−20.6554	−	35.7762i	−0.763967	−	1.32323i
$732$		0			0
$733$	−12.2933	+	21.2926i	−0.454063	+	0.786460i	−0.998634	−	0.0522545i	$-0.983359\pi$
$733$	−12.2933	+	21.2926i	−0.454063	+	0.786460i	0.544571	+	0.838715i	$0.316693\pi$
$734$	2.71782	−	7.05989i	0.100317	−	0.260585i
$735$		0			0
$736$	−9.80440	+	35.8999i	−0.361395	+	1.32329i
$737$		−	0.687297i		−	0.0253169i
$738$		0			0
$739$			42.1439i			1.55029i	0.631785	+	0.775144i	$0.282322\pi$
$739$			42.1439i			1.55029i	−0.631785	+	0.775144i	$0.717678\pi$
$740$	15.8317	−	17.5150i	0.581983	−	0.643866i
$741$		0			0
$742$	10.7156	+	4.12515i	0.393382	+	0.151439i
$743$	−0.0854917	+	0.148076i	−0.00313639	+	0.00543238i	−0.867589	−	0.497281i	$-0.834332\pi$
$743$	−0.0854917	+	0.148076i	−0.00313639	+	0.00543238i	0.864453	+	0.502714i	$0.167665\pi$
$744$		0			0
$745$	16.0815	+	27.8540i	0.589180	+	1.02049i
$746$	−3.30379	−	20.9898i	−0.120960	−	0.768491i
$747$		0			0
$748$	0.980902	+	3.03876i	0.0358653	+	0.111108i
$749$	3.25911	−	1.88165i	0.119085	−	0.0687539i
$750$		0			0
$751$	−10.7780	−	6.22269i	−0.393295	−	0.227069i	0.290292	−	0.956938i	$-0.406248\pi$
$751$	−10.7780	−	6.22269i	−0.393295	−	0.227069i	−0.683587	+	0.729869i	$0.739581\pi$
$752$	2.08682	+	20.6165i	0.0760986	+	0.751808i
$753$		0			0
$754$	−1.21784	−	1.50687i	−0.0443513	−	0.0548770i
$755$	−13.5762			−0.494090
$756$		0			0
$757$	34.3261			1.24760			0.623801	−	0.781583i	$-0.285587\pi$
$757$	34.3261			1.24760			0.623801	+	0.781583i	$0.285587\pi$
$758$	−3.53043	−	4.36829i	−0.128231	−	0.158663i
$759$		0			0
$760$	58.3800	+	3.22830i	2.11767	+	0.117103i
$761$	9.19028	+	5.30601i	0.333148	+	0.192343i	0.657238	−	0.753683i	$-0.271725\pi$
$761$	9.19028	+	5.30601i	0.333148	+	0.192343i	−0.324090	+	0.946026i	$0.605058\pi$
$762$		0			0
$763$	−5.29632	+	3.05783i	−0.191740	+	0.110701i
$764$	17.8295	−	5.75532i	0.645050	−	0.208220i
$765$		0			0
$766$	4.42422	+	28.1082i	0.159854	+	1.01559i
$767$	1.05046	+	1.81946i	0.0379301	+	0.0656968i
$768$		0			0
$769$	−4.39685	+	7.61557i	−0.158554	+	0.274624i	−0.934348	−	0.356363i	$-0.884017\pi$
$769$	−4.39685	+	7.61557i	−0.158554	+	0.274624i	0.775793	+	0.630987i	$0.217350\pi$
$770$	1.04034	+	0.400494i	0.0374911	+	0.0144328i
$771$		0			0
$772$	1.30472	+	1.17933i	0.0469580	+	0.0424449i
$773$		−	1.24418i		−	0.0447501i	−0.999750	−	0.0223751i	$-0.992877\pi$
$773$		−	1.24418i		−	0.0447501i	0.999750	−	0.0223751i	$-0.00712279\pi$
$774$		0			0
$775$			26.3231i			0.945555i
$776$	0.430125	−	0.658174i	0.0154406	−	0.0236271i
$777$		0			0
$778$	−18.1286	+	47.0914i	−0.649942	+	1.68831i
$779$	2.75229	−	4.76710i	0.0986110	−	0.170799i
$780$		0			0
$781$	−0.348340	−	0.603343i	−0.0124646	−	0.0215893i
$782$	52.0466	−	8.19213i	1.86118	−	0.292950i
$783$		0			0
$784$	−3.24508	+	2.33869i	−0.115896	+	0.0835246i
$785$	48.9271	−	28.2481i	1.74628	−	1.00822i
$786$		0			0
$787$	−8.14573	−	4.70294i	−0.290364	−	0.167642i	0.347742	−	0.937590i	$-0.386948\pi$
$787$	−8.14573	−	4.70294i	−0.290364	−	0.167642i	−0.638106	+	0.769949i	$0.720282\pi$
$788$	−28.2977	−	6.07171i	−1.00806	−	0.216296i
$789$		0			0
$790$	−7.64706	+	6.18031i	−0.272070	+	0.219886i
$791$	2.05272			0.0729864
$792$		0			0
$793$	−28.8523			−1.02458
$794$	−29.3904	+	23.7532i	−1.04303	+	0.842968i
$795$		0			0
$796$	0.992929	+	0.213048i	0.0351935	+	0.00755130i
$797$	−17.5415	−	10.1276i	−0.621351	−	0.358737i	0.156044	−	0.987750i	$-0.450126\pi$
$797$	−17.5415	−	10.1276i	−0.621351	−	0.358737i	−0.777395	+	0.629013i	$0.783459\pi$
$798$		0			0
$799$	25.4070	−	14.6687i	0.898834	−	0.518942i
$800$	11.2153	+	11.3235i	0.396520	+	0.400347i
$801$		0			0
$802$	31.4729	−	4.95382i	1.11135	−	0.174926i
$803$	0.100755	+	0.174512i	0.00355555	+	0.00615840i
$804$		0			0
$805$	9.19686	−	15.9294i	0.324147	−	0.561438i
$806$	23.1442	−	60.1199i	0.815218	−	2.11763i
$807$		0			0
$808$	−33.3811	−	21.8150i	−1.17434	−	0.767448i
$809$			33.9641i			1.19411i	0.802199	+	0.597057i	$0.203663\pi$
$809$			33.9641i			1.19411i	−0.802199	+	0.597057i	$0.796337\pi$
$810$		0			0
$811$			53.9712i			1.89518i	0.319482	+	0.947592i	$0.396491\pi$
$811$			53.9712i			1.89518i	−0.319482	+	0.947592i	$0.603509\pi$
$812$	0.416918	+	0.376848i	0.0146310	+	0.0132248i
$813$		0			0
$814$	−1.57099	−	0.604778i	−0.0550631	−	0.0211974i
$815$	23.1783	−	40.1460i	0.811900	−	1.40625i
$816$		0			0
$817$	26.9669	+	46.7081i	0.943454	+	1.63411i
$818$	−3.24565	−	20.6204i	−0.113481	−	0.720975i
$819$		0			0
$820$	3.96196	−	1.27891i	0.138357	−	0.0446614i
$821$	−21.2044	+	12.2424i	−0.740039	+	0.427262i	−0.822084	−	0.569367i	$-0.807188\pi$
$821$	−21.2044	+	12.2424i	−0.740039	+	0.427262i	0.0820442	+	0.996629i	$0.473855\pi$
$822$		0			0
$823$	−38.5728	−	22.2700i	−1.34456	−	0.776284i	−0.357090	−	0.934070i	$-0.616231\pi$
$823$	−38.5728	−	22.2700i	−1.34456	−	0.776284i	−0.987473	+	0.157786i	$0.949564\pi$
$824$	1.68530	−	30.4767i	0.0587103	−	1.06171i
$825$		0			0
$826$	−0.383056	−	0.473965i	−0.0133282	−	0.0164913i
$827$	−44.8362			−1.55911			−0.779554	−	0.626335i	$-0.784554\pi$
$827$	−44.8362			−1.55911			−0.779554	+	0.626335i	$0.784554\pi$
$828$		0			0
$829$	−1.25945			−0.0437424			−0.0218712	−	0.999761i	$-0.506962\pi$
$829$	−1.25945			−0.0437424			−0.0218712	+	0.999761i	$0.506962\pi$
$830$	−20.3841	−	25.2218i	−0.707543	−	0.875461i
$831$		0			0
$832$	−15.6588	−	35.7229i	−0.542870	−	1.23847i
$833$	4.90438	+	2.83154i	0.169927	+	0.0981072i
$834$		0			0
$835$	16.3951	−	9.46573i	0.567377	−	0.327575i
$836$	−1.28063	−	3.96730i	−0.0442915	−	0.137212i
$837$		0			0
$838$	−6.64005	−	42.1859i	−0.229377	−	1.45729i
$839$	21.0036	+	36.3793i	0.725125	+	1.25595i	0.958923	+	0.283668i	$0.0915512\pi$
$839$	21.0036	+	36.3793i	0.725125	+	1.25595i	−0.233798	+	0.972285i	$0.575115\pi$
$840$		0			0
$841$	−14.4605	+	25.0464i	−0.498639	+	0.863667i
$842$	−31.8120	−	12.2466i	−1.09631	−	0.422044i
$843$		0			0
$844$	15.5374	−	17.1895i	0.534820	−	0.591688i
$845$		−	30.1142i		−	1.03596i
$846$		0			0
$847$			10.9205i			0.375233i
$848$	13.3233	−	29.6179i	0.457525	−	1.01708i
$849$		0			0
$850$	8.10640	−	21.0574i	0.278047	−	0.722264i
$851$	−13.8880	+	24.0547i	−0.476073	+	0.824583i
$852$		0			0
$853$	15.4133	+	26.6966i	0.527741	+	0.914075i	0.999477	+	0.0323350i	$0.0102943\pi$
$853$	15.4133	+	26.6966i	0.527741	+	0.914075i	−0.471736	+	0.881740i	$0.656372\pi$
$854$	8.26725	−	1.30126i	0.282900	−	0.0445283i
$855$		0			0
$856$	−4.80502	−	9.49794i	−0.164232	−	0.324633i
$857$	−11.9804	+	6.91687i	−0.409242	+	0.236276i	−0.690464	−	0.723367i	$-0.742594\pi$
$857$	−11.9804	+	6.91687i	−0.409242	+	0.236276i	0.281222	+	0.959643i	$0.409260\pi$
$858$		0			0
$859$	−32.0674	−	18.5141i	−1.09413	−	0.631694i	−0.159455	−	0.987205i	$-0.550974\pi$
$859$	−32.0674	−	18.5141i	−1.09413	−	0.631694i	−0.934672	+	0.355511i	$0.884307\pi$
$860$	−8.55769	+	39.8838i	−0.291815	+	1.36003i
$861$		0			0
$862$	29.5269	−	23.8635i	1.00569	−	0.812793i
$863$	−40.7856			−1.38836			−0.694178	−	0.719803i	$-0.744232\pi$
$863$	−40.7856			−1.38836			−0.694178	+	0.719803i	$0.744232\pi$
$864$		0			0
$865$	27.0584			0.920013
$866$	−18.0826	+	14.6143i	−0.614472	+	0.496613i
$867$		0			0
$868$	−3.92020	+	18.2704i	−0.133060	+	0.620138i
$869$	0.607122	+	0.350522i	0.0205952	+	0.0118906i
$870$		0			0
$871$	10.2934	−	5.94290i	0.348778	−	0.201367i
$872$	7.80854	+	15.4349i	0.264431	+	0.522693i
$873$		0			0
$874$	−67.9503	+	10.6954i	−2.29845	+	0.361776i
$875$	3.05125	+	5.28493i	0.103151	+	0.178663i
$876$		0			0
$877$	11.2287	−	19.4487i	0.379167	−	0.656736i	−0.611775	−	0.791032i	$-0.709544\pi$
$877$	11.2287	−	19.4487i	0.379167	−	0.656736i	0.990941	+	0.134296i	$0.0428774\pi$
$878$	5.99461	−	15.5718i	0.202308	−	0.525522i
$879$		0			0
$880$	1.29351	−	2.87548i	0.0436042	−	0.0969324i
$881$		−	2.14963i		−	0.0724228i	−0.999344	−	0.0362114i	$-0.988471\pi$
$881$		−	2.14963i		−	0.0724228i	0.999344	−	0.0362114i	$-0.0115290\pi$
$882$		0			0
$883$		−	55.0001i		−	1.85090i	−0.378868	−	0.925451i	$-0.623687\pi$
$883$		−	55.0001i		−	1.85090i	0.378868	−	0.925451i	$-0.376313\pi$
$884$	−37.0288	+	40.9661i	−1.24541	+	1.37784i
$885$		0			0
$886$	−22.0601	−	8.49239i	−0.741122	−	0.285307i
$887$	10.4272	−	18.0604i	0.350111	−	0.606410i	−0.636158	−	0.771559i	$-0.719477\pi$
$887$	10.4272	−	18.0604i	0.350111	−	0.606410i	0.986269	+	0.165149i	$0.0528106\pi$
$888$		0			0
$889$	−6.29563	−	10.9043i	−0.211149	−	0.365720i
$890$	−0.217778	−	1.38359i	−0.00729992	−	0.0463782i
$891$		0			0
$892$	−8.16517	−	25.2951i	−0.273390	−	0.846942i
$893$	−33.1705	+	19.1510i	−1.11001	+	0.640863i
$894$		0			0
$895$	16.2548	+	9.38468i	0.543336	+	0.313695i
$896$	6.09794	+	9.52969i	0.203718	+	0.318365i
$897$		0			0
$898$	−32.3928	−	40.0804i	−1.08096	−	1.33750i
$899$	2.62538			0.0875614
$900$		0			0
$901$	−45.9794			−1.53180
$902$	−0.186586	−	0.230868i	−0.00621265	−	0.00768707i
$903$		0			0
$904$	0.320569	−	5.79712i	0.0106620	−	0.192809i
$905$	25.6091	+	14.7854i	0.851275	+	0.491484i
$906$		0			0
$907$	40.3581	−	23.3007i	1.34007	−	0.773689i	0.353251	−	0.935529i	$-0.385076\pi$
$907$	40.3581	−	23.3007i	1.34007	−	0.773689i	0.986817	+	0.161840i	$0.0517429\pi$
$908$	−16.1975	+	5.22849i	−0.537531	+	0.173513i
$909$		0			0
$910$	2.99748	+	19.0437i	0.0993654	+	0.631293i
$911$	29.2009	+	50.5774i	0.967468	+	1.67570i	0.702833	+	0.711355i	$0.251918\pi$
$911$	29.2009	+	50.5774i	0.967468	+	1.67570i	0.264635	+	0.964349i	$0.414749\pi$
$912$		0			0
$913$	−1.15610	+	2.00243i	−0.0382614	+	0.0662708i
$914$	−43.1715	−	16.6196i	−1.42799	−	0.549727i
$915$		0			0
$916$	−15.6522	−	14.1478i	−0.517163	−	0.467458i
$917$			8.26127i			0.272811i
$918$		0			0
$919$			6.34959i			0.209454i	0.994501	+	0.104727i	$0.0333968\pi$
$919$			6.34959i			0.209454i	−0.994501	+	0.104727i	$0.966603\pi$
$920$	−43.5502	−	28.4606i	−1.43581	−	0.938319i
$921$		0			0
$922$	−13.7997	+	35.8465i	−0.454469	+	1.18054i
$923$	6.02404	−	10.4339i	0.198284	−	0.343437i
$924$		0			0
$925$	5.94765	+	10.3016i	0.195558	+	0.338716i
$926$	−25.0516	+	3.94312i	−0.823246	+	0.129579i
$927$		0			0
$928$	1.12937	−	1.11857i	0.0370734	−	0.0367190i
$929$	17.4073	−	10.0501i	0.571116	−	0.329734i	−0.186479	−	0.982459i	$-0.559708\pi$
$929$	17.4073	−	10.0501i	0.571116	−	0.329734i	0.757595	+	0.652725i	$0.226374\pi$
$930$		0			0
$931$	−6.40298	−	3.69676i	−0.209849	−	0.121157i
$932$	−4.96707	−	1.06576i	−0.162702	−	0.0349102i
$933$		0			0
$934$	−26.7866	+	21.6488i	−0.876484	+	0.708370i
$935$	−4.46396			−0.145987
$936$		0			0
$937$	−10.9126			−0.356501			−0.178250	−	0.983985i	$-0.557044\pi$
$937$	−10.9126			−0.356501			−0.178250	+	0.983985i	$0.557044\pi$
$938$	−2.68141	+	2.16710i	−0.0875511	+	0.0707583i
$939$		0			0
$940$	−28.3241	−	6.07737i	−0.923830	−	0.198222i
$941$	44.5175	+	25.7022i	1.45123	+	0.837868i	0.998551	−	0.0538064i	$-0.0171354\pi$
$941$	44.5175	+	25.7022i	1.45123	+	0.837868i	0.452678	+	0.891674i	$0.350469\pi$
$942$		0			0
$943$	−4.24172	+	2.44896i	−0.138129	+	0.0797490i
$944$	−1.39835	+	1.00777i	−0.0455124	+	0.0328003i
$945$		0			0
$946$	2.87308	−	0.452222i	0.0934118	−	0.0147030i
$947$	−22.3078	−	38.6382i	−0.724906	−	1.25557i	−0.959013	−	0.283363i	$-0.908550\pi$
$947$	−22.3078	−	38.6382i	−0.724906	−	1.25557i	0.234107	−	0.972211i	$-0.424783\pi$
$948$		0			0
$949$	−1.74240	+	3.01793i	−0.0565608	+	0.0979663i
$950$	−10.5834	+	27.4918i	−0.343372	+	0.891953i
$951$		0			0
$952$	8.76250	−	13.4083i	0.283994	−	0.434566i
$953$			51.7549i			1.67651i	0.545281	+	0.838253i	$0.316423\pi$
$953$			51.7549i			1.67651i	−0.545281	+	0.838253i	$0.683577\pi$
$954$		0			0
$955$			26.1917i			0.847545i
$956$	36.6019	+	33.0841i	1.18379	+	1.07001i
$957$		0			0
$958$	23.0783	+	8.88439i	0.745627	+	0.287042i
$959$	−8.37353	+	14.5034i	−0.270395	+	0.468338i
$960$		0			0
$961$	28.1469	+	48.7519i	0.907966	+	1.57264i
$962$	−4.52642	−	28.7575i	−0.145938	−	0.927179i
$963$		0			0
$964$	−27.9189	+	9.01214i	−0.899208	+	0.290261i
$965$	−2.12926	+	1.22933i	−0.0685434	+	0.0395735i
$966$		0			0
$967$	−19.3524	−	11.1731i	−0.622331	−	0.359303i	0.155445	−	0.987845i	$-0.450319\pi$
$967$	−19.3524	−	11.1731i	−0.622331	−	0.359303i	−0.777776	+	0.628542i	$0.783652\pi$
$968$	30.8408	+	1.70543i	0.991260	+	0.0548147i
$969$		0			0
$970$	0.690910	+	0.854880i	0.0221838	+	0.0274485i
$971$	−11.2412			−0.360747			−0.180373	−	0.983598i	$-0.557731\pi$
$971$	−11.2412			−0.360747			−0.180373	+	0.983598i	$0.557731\pi$
$972$		0			0
$973$	−23.2832			−0.746427
$974$	5.12579	+	6.34227i	0.164241	+	0.203219i
$975$		0			0
$976$	−2.38384	−	23.5509i	−0.0763048	−	0.753845i
$977$	−9.73245	−	5.61903i	−0.311369	−	0.179769i	0.336170	−	0.941801i	$-0.390868\pi$
$977$	−9.73245	−	5.61903i	−0.311369	−	0.179769i	−0.647539	+	0.762033i	$0.724202\pi$
$978$		0			0
$979$	−0.0864857	+	0.0499325i	−0.00276409	+	0.00159585i
$980$	−1.71778	−	5.32154i	−0.0548723	−	0.169990i
$981$		0			0
$982$	7.34043	+	46.6355i	0.234242	+	1.48820i
$983$	−20.0804	−	34.7802i	−0.640464	−	1.10932i	−0.985329	−	0.170664i	$-0.945409\pi$
$983$	−20.0804	−	34.7802i	−0.640464	−	1.10932i	0.344865	−	0.938652i	$-0.387925\pi$
$984$		0			0
$985$	20.2300	−	35.0394i	0.644581	−	1.11645i
$986$	−2.10020	−	0.808506i	−0.0668839	−	0.0257481i
$987$		0			0
$988$	48.3435	−	53.4838i	1.53801	−	1.70155i
$989$		−	47.9898i		−	1.52599i
$990$		0			0
$991$			18.8697i			0.599417i	0.954031	+	0.299709i	$0.0968894\pi$
$991$			18.8697i			0.599417i	−0.954031	+	0.299709i	$0.903111\pi$
$992$	50.9855	+	13.9243i	1.61879	+	0.442098i
$993$		0			0
$994$	−1.25553	+	3.26140i	−0.0398230	+	0.103445i
$995$	−0.709844	+	1.22949i	−0.0225036	+	0.0389773i
$996$		0			0
$997$	1.19746	+	2.07405i	0.0379238	+	0.0656860i	0.884364	−	0.466797i	$-0.154592\pi$
$997$	1.19746	+	2.07405i	0.0379238	+	0.0656860i	−0.846441	+	0.532483i	$0.821259\pi$
$998$	−56.7196	+	8.92766i	−1.79543	+	0.282600i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ba.a.71.8		72
3.2	odd	2		252.2.ba.a.239.29	yes	72
4.3	odd	2	inner	756.2.ba.a.71.5		72
9.2	odd	6	inner	756.2.ba.a.575.5		72
9.7	even	3		252.2.ba.a.155.32	yes	72
12.11	even	2		252.2.ba.a.239.32	yes	72
36.7	odd	6		252.2.ba.a.155.29	✓	72
36.11	even	6	inner	756.2.ba.a.575.8		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.29	✓	72	36.7	odd	6
252.2.ba.a.155.32	yes	72	9.7	even	3
252.2.ba.a.239.29	yes	72	3.2	odd	2
252.2.ba.a.239.32	yes	72	12.11	even	2
756.2.ba.a.71.5		72	4.3	odd	2	inner
756.2.ba.a.71.8		72	1.1	even	1	trivial
756.2.ba.a.575.5		72	9.2	odd	6	inner
756.2.ba.a.575.8		72	36.11	even	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)

\(f(q)\)	\(=\)	\(q+(-1.09990 + 0.888937i) q^{2} +(0.419581 - 1.95549i) q^{4} +(2.42137 + 1.39798i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.27681 + 2.52384i) q^{8} +O(q^{10})\)	\(q+(-1.09990 + 0.888937i) q^{2} +(0.419581 - 1.95549i) q^{4} +(2.42137 + 1.39798i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.27681 + 2.52384i) q^{8} +(-3.90599 + 0.614803i) q^{10} +(0.140963 + 0.244156i) q^{11} +(-2.43776 + 4.22232i) q^{13} +(0.508077 - 1.31979i) q^{14} +(-3.64790 - 1.64098i) q^{16} +5.66309i q^{17} -7.39353i q^{19} +(3.74970 - 4.14841i) q^{20} +(-0.372086 - 0.143241i) q^{22} +(-3.28934 + 5.69730i) q^{23} +(1.40869 + 2.43992i) q^{25} +(-1.07208 - 6.81116i) q^{26} +(0.614378 + 1.90330i) q^{28} +(0.243350 - 0.140498i) q^{29} +(8.09138 + 4.67156i) q^{31} +(5.47107 - 1.43784i) q^{32} +(-5.03413 - 6.22886i) q^{34} -2.79596 q^{35} +4.22211 q^{37} +(6.57238 + 8.13218i) q^{38} +(-0.436639 + 7.89610i) q^{40} +(0.644767 + 0.372257i) q^{41} +(-6.31743 + 3.64737i) q^{43} +(0.536590 - 0.173210i) q^{44} +(-1.44658 - 9.19051i) q^{46} +(-2.59024 - 4.48642i) q^{47} +(0.500000 - 0.866025i) q^{49} +(-3.71837 - 1.43145i) q^{50} +(7.23387 + 6.53862i) q^{52} +8.11915i q^{53} +0.788256i q^{55} +(-2.36767 - 1.54730i) q^{56} +(-0.142768 + 0.370857i) q^{58} +(0.215457 - 0.373183i) q^{59} +(2.95890 + 5.12497i) q^{61} +(-13.0525 + 2.05446i) q^{62} +(-4.73951 + 6.44493i) q^{64} +(-11.8054 + 6.81586i) q^{65} +(-2.11124 - 1.21893i) q^{67} +(11.0741 + 2.37612i) q^{68} +(3.07529 - 2.48543i) q^{70} -2.47114 q^{71} +0.714758 q^{73} +(-4.64392 + 3.75319i) q^{74} +(-14.4580 - 3.10218i) q^{76} +(-0.244156 - 0.140963i) q^{77} +(2.15347 - 1.24331i) q^{79} +(-6.53888 - 9.07310i) q^{80} +(-1.04010 + 0.163711i) q^{82} +(4.10072 + 7.10266i) q^{83} +(-7.91688 + 13.7124i) q^{85} +(3.70629 - 9.62757i) q^{86} +(-0.436226 + 0.667509i) q^{88} +0.354223i q^{89} -4.87551i q^{91} +(9.76089 + 8.82276i) q^{92} +(6.83716 + 2.63208i) q^{94} +(10.3360 - 17.9025i) q^{95} +(-0.138992 - 0.240741i) q^{97} +(0.219890 + 1.39701i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 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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