LMFDB - Embedded newform 756.2.ba.a.575.8

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			575.8
Character	$\chi$	$=$	756.575
Dual form			756.2.ba.a.71.8

$q$-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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

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

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	0.151201	−	0.988503i	$-0.451686\pi$
$5$	2.42137	−	1.39798i	1.08287	−	0.625195i	0.931669	+	0.363308i	$0.118353\pi$
$6$		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	−0.843992	−	0.536356i	$-0.819800\pi$
$11$	0.140963	−	0.244156i	0.0425021	−	0.0736157i	0.886494	+	0.462740i	$0.153134\pi$
$12$		0			0
$13$	−2.43776	−	4.22232i	−0.676112	−	1.17106i	−0.976143	−	0.217131i	$-0.930330\pi$
$13$	−2.43776	−	4.22232i	−0.676112	−	1.17106i	0.300031	−	0.953930i	$-0.403003\pi$
$14$	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	$-0.759037\pi$
$17$		−	5.66309i		−	1.37350i	0.726894	−	0.686750i	$-0.240963\pi$
$18$		0			0
$19$			7.39353i			1.69619i	0.529843	+	0.848096i	$0.322251\pi$
$19$			7.39353i			1.69619i	−0.529843	+	0.848096i	$0.677749\pi$
$20$	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	−0.973161	−	0.230125i	$-0.926086\pi$
$23$	−3.28934	−	5.69730i	−0.685875	−	1.18797i	0.287286	−	0.957845i	$-0.407247\pi$
$24$		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	0.522424	−	0.852686i	$-0.325028\pi$
$29$	0.243350	+	0.140498i	0.0451889	+	0.0260898i	−0.477235	+	0.878776i	$0.658361\pi$
$30$		0			0
$31$	8.09138	−	4.67156i	1.45325	−	0.839037i	0.454590	−	0.890701i	$-0.349786\pi$
$31$	8.09138	−	4.67156i	1.45325	−	0.839037i	0.998665	+	0.0516641i	$0.0164525\pi$
$32$	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	−0.448806	−	0.893629i	$-0.648151\pi$
$41$	0.644767	−	0.372257i	0.100696	−	0.0581367i	0.549502	+	0.835492i	$0.314817\pi$
$42$		0			0
$43$	−6.31743	−	3.64737i	−0.963400	−	0.556219i	−0.0661820	−	0.997808i	$-0.521082\pi$
$43$	−6.31743	−	3.64737i	−0.963400	−	0.556219i	−0.897218	+	0.441588i	$0.854415\pi$
$44$	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	−0.990745	−	0.135733i	$-0.956661\pi$
$47$	−2.59024	+	4.48642i	−0.377825	+	0.654412i	0.612921	+	0.790144i	$0.289994\pi$
$48$		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	$-0.811713\pi$
$53$		−	8.11915i		−	1.11525i	0.830093	−	0.557625i	$-0.188287\pi$
$54$		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	0.879710	−	0.475511i	$-0.157737\pi$
$59$	0.215457	+	0.373183i	0.0280501	+	0.0485843i	−0.851660	+	0.524095i	$0.824404\pi$
$60$		0			0
$61$	2.95890	−	5.12497i	0.378848	−	0.656185i	−0.612047	−	0.790822i	$-0.709654\pi$
$61$	2.95890	−	5.12497i	0.378848	−	0.656185i	0.990895	+	0.134637i	$0.0429869\pi$
$62$	−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	−0.623390	−	0.781911i	$-0.714245\pi$
$67$	−2.11124	+	1.21893i	−0.257930	+	0.148916i	0.365460	+	0.930827i	$0.380912\pi$
$68$	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	0.616226	−	0.787569i	$-0.288661\pi$
$79$	2.15347	+	1.24331i	0.242285	+	0.139883i	−0.373942	+	0.927452i	$0.621994\pi$
$80$	−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	−0.548280	−	0.836295i	$-0.684717\pi$
$83$	4.10072	−	7.10266i	0.450113	−	0.779618i	0.998393	+	0.0566769i	$0.0180505\pi$
$84$		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	$-0.994024\pi$
$89$		−	0.354223i		−	0.0375476i	0.999824	−	0.0187738i	$-0.00597624\pi$
$90$		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	−0.872995	−	0.487728i	$-0.837826\pi$
$97$	−0.138992	+	0.240741i	−0.0141125	+	0.0244435i	0.858883	+	0.512172i	$0.171159\pi$
$98$	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	−0.251097	−	0.967962i	$-0.580791\pi$
$101$	−12.2098	−	7.04936i	−1.21493	−	0.701437i	−0.963828	+	0.266525i	$0.914125\pi$
$102$		0			0
$103$	−9.34581	+	5.39581i	−0.920870	+	0.531665i	−0.883913	−	0.467652i	$-0.845100\pi$
$103$	−9.34581	+	5.39581i	−0.920870	+	0.531665i	−0.0369577	+	0.999317i	$0.511767\pi$
$104$	−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	−0.581280	−	0.813703i	$-0.697448\pi$
$113$	−1.77771	+	1.02636i	−0.167233	+	0.0965519i	0.414048	+	0.910255i	$0.364115\pi$
$114$		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	$-0.811321\pi$
$127$		−	12.5913i		−	1.11729i	0.829406	−	0.558647i	$-0.188679\pi$
$128$	−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	0.988108	−	0.153759i	$-0.0491379\pi$
$131$	4.13063	+	7.15447i	0.360895	+	0.625089i	−0.627213	+	0.778848i	$0.715805\pi$
$132$		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	0.968912	−	0.247407i	$-0.0795784\pi$
$137$	14.5034	+	8.37353i	1.23911	+	0.715399i	0.270195	+	0.962806i	$0.412912\pi$
$138$		0			0
$139$	20.1639	−	11.6416i	1.71028	−	0.987430i	0.776110	−	0.630598i	$-0.217190\pi$
$139$	20.1639	−	11.6416i	1.71028	−	0.987430i	0.934169	−	0.356831i	$-0.116143\pi$
$140$	−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	−0.0329454	−	0.999457i	$-0.510489\pi$
$149$	9.96222	−	5.75169i	0.816137	−	0.471197i	0.849083	+	0.528260i	$0.177155\pi$
$150$		0			0
$151$	−4.20513	−	2.42783i	−0.342209	−	0.197574i	0.319040	−	0.947741i	$-0.396640\pi$
$151$	−4.20513	−	2.42783i	−0.342209	−	0.197574i	−0.661248	+	0.750167i	$0.729973\pi$
$152$	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	0.915395	+	0.402557i	$0.131878\pi$
$157$	10.1032	+	17.4992i	0.806322	+	1.39659i	−0.109073	+	0.994034i	$0.534788\pi$
$158$	−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	$0.224945\pi$
$163$			16.5798i			1.29863i	−0.760518	+	0.649317i	$0.775055\pi$
$164$	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	0.966768	−	0.255657i	$-0.0822918\pi$
$167$	3.38550	+	5.86386i	0.261978	+	0.453759i	−0.704789	+	0.709417i	$0.748958\pi$
$168$		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	0.783537	−	0.621345i	$-0.213414\pi$
$173$	8.38112	+	4.83884i	0.637204	+	0.367890i	−0.146332	+	0.989235i	$0.546747\pi$
$174$		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	−0.645316	−	0.763915i	$-0.723274\pi$
$191$	4.68386	−	8.11268i	0.338912	−	0.587013i	0.984228	+	0.176903i	$0.0566078\pi$
$192$		0			0
$193$	−0.439681	−	0.761550i	−0.0316489	−	0.0548176i	0.849767	−	0.527158i	$-0.176743\pi$
$193$	−0.439681	−	0.761550i	−0.0316489	−	0.0548176i	−0.881416	+	0.472341i	$0.843409\pi$
$194$	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	$0.172395\pi$
$197$			14.4709i			1.03101i	−0.856887	+	0.515504i	$0.827605\pi$
$198$		0			0
$199$		−	0.507764i		−	0.0359945i	−0.999838	−	0.0179972i	$-0.994271\pi$
$199$		−	0.507764i		−	0.0359945i	0.999838	−	0.0179972i	$-0.00572901\pi$
$200$	−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	−0.113161	−	0.993577i	$-0.536098\pi$
$211$	10.0333	−	5.79273i	0.690721	−	0.398788i	0.803882	+	0.594789i	$0.202764\pi$
$212$	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	0.833138	−	0.553065i	$-0.186542\pi$
$223$	11.5096	+	6.64507i	0.770739	+	0.444987i	−0.0623990	+	0.998051i	$0.519875\pi$
$224$	−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	−0.971981	−	0.235061i	$-0.924471\pi$
$227$	−4.25510	+	7.37006i	−0.282421	+	0.489168i	0.689559	+	0.724229i	$0.257804\pi$
$228$		0			0
$229$	5.27466	+	9.13598i	0.348559	+	0.603722i	0.985994	−	0.166782i	$-0.0533377\pi$
$229$	5.27466	+	9.13598i	0.348559	+	0.603722i	−0.637435	+	0.770505i	$0.720004\pi$
$230$	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	$0.0265148\pi$
$233$			2.54006i			0.166405i	−0.996533	+	0.0832024i	$0.973485\pi$
$234$		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	−0.921010	−	0.389538i	$-0.872635\pi$
$239$	−12.3345	−	21.3640i	−0.797855	−	1.38193i	0.123155	−	0.992387i	$-0.460699\pi$
$240$		0			0
$241$	−7.33435	+	12.7035i	−0.472447	+	0.818303i	−0.999503	−	0.0315281i	$-0.989963\pi$
$241$	−7.33435	+	12.7035i	−0.472447	+	0.818303i	0.527056	+	0.849831i	$0.323296\pi$
$242$	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	−0.611477	−	0.791262i	$-0.709424\pi$
$257$	−3.71863	+	2.14695i	−0.231962	+	0.133923i	0.379515	+	0.925186i	$0.376091\pi$
$258$		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	−0.679143	−	0.734006i	$-0.737648\pi$
$263$	4.80188	−	8.31711i	0.296097	−	0.512855i	0.975239	+	0.221152i	$0.0709815\pi$
$264$		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	$0.221563\pi$
$269$			21.0329i			1.28240i	−0.767375	+	0.641199i	$0.778437\pi$
$270$		0			0
$271$			12.1109i			0.735682i	0.929889	+	0.367841i	$0.119903\pi$
$271$			12.1109i			0.735682i	−0.929889	+	0.367841i	$0.880097\pi$
$272$	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	−0.821851	−	0.569703i	$-0.807058\pi$
$277$	1.37227	−	2.37683i	0.0824514	−	0.142810i	0.904302	+	0.426893i	$0.140392\pi$
$278$	−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	0.336209	−	0.941787i	$-0.390855\pi$
$281$	−5.21831	−	3.01279i	−0.311298	−	0.179728i	−0.647507	+	0.762059i	$0.724188\pi$
$282$		0			0
$283$	−24.0259	+	13.8713i	−1.42819	+	0.824565i	−0.996978	−	0.0776854i	$-0.975247\pi$
$283$	−24.0259	+	13.8713i	−1.42819	+	0.824565i	−0.431211	+	0.902251i	$0.641914\pi$
$284$	−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	−0.781859	−	0.623455i	$-0.785729\pi$
$293$	−10.8328	+	6.25434i	−0.632861	+	0.365383i	0.148998	+	0.988837i	$0.452395\pi$
$294$		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	$0.0247594\pi$
$307$			2.72302i			0.155411i	−0.996976	+	0.0777054i	$0.975241\pi$
$308$	−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	0.960642	−	0.277788i	$-0.0896013\pi$
$311$	4.22803	+	7.32317i	0.239750	+	0.415259i	−0.720893	+	0.693047i	$0.756268\pi$
$312$		0			0
$313$	−13.8676	+	24.0195i	−0.783845	+	1.35766i	0.145841	+	0.989308i	$0.453411\pi$
$313$	−13.8676	+	24.0195i	−0.783845	+	1.35766i	−0.929687	+	0.368352i	$0.879922\pi$
$314$	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	0.952198	−	0.305482i	$-0.0988176\pi$
$317$	20.7198	+	11.9626i	1.16374	+	0.671886i	0.211544	+	0.977369i	$0.432151\pi$
$318$		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	0.989210	−	0.146506i	$-0.0468029\pi$
$331$	24.6873	+	14.2532i	1.35694	+	0.783427i	0.367727	+	0.929934i	$0.380136\pi$
$332$	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	0.921053	−	0.389437i	$-0.127331\pi$
$337$	2.26282	+	3.91932i	0.123264	+	0.213499i	−0.797789	+	0.602937i	$0.793997\pi$
$338$	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	−0.918367	−	0.395729i	$-0.870492\pi$
$347$	−14.9377	−	25.8728i	−0.801895	−	1.38892i	0.116472	−	0.993194i	$-0.462841\pi$
$348$		0			0
$349$	−9.43250	+	16.3376i	−0.504910	+	0.874530i	0.495074	+	0.868851i	$0.335141\pi$
$349$	−9.43250	+	16.3376i	−0.504910	+	0.874530i	−0.999984	+	0.00567921i	$0.998192\pi$
$350$	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	−0.417598	−	0.908632i	$-0.637128\pi$
$353$	−26.5534	−	15.3306i	−1.41330	−	0.815967i	−0.995697	+	0.0926650i	$0.970461\pi$
$354$		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	0.374194	−	0.927351i	$-0.377919\pi$
$367$	−4.63257	−	2.67462i	−0.241818	−	0.139614i	−0.616012	+	0.787737i	$0.711253\pi$
$368$	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	0.603336	−	0.797487i	$-0.293838\pi$
$373$	−7.51238	−	13.0118i	−0.388976	−	0.673727i	−0.992312	+	0.123760i	$0.960505\pi$
$374$	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	$-0.967475\pi$
$379$		−	3.97151i		−	0.204003i	0.994784	−	0.102001i	$-0.0325246\pi$
$380$	−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	0.999867	+	0.0162963i	$0.00518751\pi$
$383$	10.0601	+	17.4246i	0.514047	+	0.890355i	−0.485821	+	0.874059i	$0.661479\pi$
$384$		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	0.996548	+	0.0830175i	$0.0264558\pi$
$389$	30.9005	+	17.8404i	1.56672	+	0.904545i	0.570169	+	0.821527i	$0.306878\pi$
$390$		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	−0.900545	−	0.434762i	$-0.856832\pi$
$401$	−19.5104	+	11.2643i	−0.974302	+	0.562514i	−0.0737572	+	0.997276i	$0.523499\pi$
$402$		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	0.623839	−	0.781553i	$-0.285572\pi$
$409$	−7.38017	−	12.7828i	−0.364926	−	0.632070i	−0.988764	+	0.149483i	$0.952239\pi$
$410$	−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	−0.953567	−	0.301181i	$-0.902619\pi$
$419$	−15.0986	−	26.1515i	−0.737614	−	1.27759i	0.215953	−	0.976404i	$-0.430714\pi$
$420$		0			0
$421$	12.0519	−	20.8744i	0.587372	−	1.01736i	−0.407203	−	0.913338i	$-0.633496\pi$
$421$	12.0519	−	20.8744i	0.587372	−	1.01736i	0.994575	−	0.104021i	$-0.0331708\pi$
$422$	−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	0.235935	−	0.971769i	$-0.424185\pi$
$439$	−10.2179	−	5.89931i	−0.487674	−	0.281559i	−0.723609	+	0.690210i	$0.757518\pi$
$440$	−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	−0.596292	−	0.802768i	$-0.703360\pi$
$443$	8.35739	−	14.4754i	0.397071	−	0.687748i	0.993363	+	0.115020i	$0.0366932\pi$
$444$		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	$-0.670556\pi$
$449$		−	36.4399i		−	1.71970i	0.510543	−	0.859852i	$-0.329444\pi$
$450$		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	−0.175136	−	0.984544i	$-0.556036\pi$
$457$	16.3554	−	28.3283i	0.765072	−	1.32514i	0.940208	−	0.340600i	$-0.110630\pi$
$458$	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	0.935040	−	0.354541i	$-0.115363\pi$
$461$	23.5218	+	13.5803i	1.09552	+	0.632498i	0.160479	+	0.987039i	$0.448696\pi$
$462$		0			0
$463$	15.5298	−	8.96612i	0.721730	−	0.416691i	−0.0936592	−	0.995604i	$-0.529856\pi$
$463$	15.5298	−	8.96612i	0.721730	−	0.416691i	0.815389	+	0.578913i	$0.196523\pi$
$464$	−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	−0.993662	−	0.112406i	$-0.964144\pi$
$479$	−8.74315	+	15.1436i	−0.399485	+	0.691928i	0.594177	+	0.804334i	$0.297478\pi$
$480$		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	$0.0417050\pi$
$487$			5.76620i			0.261291i	−0.991429	+	0.130646i	$0.958295\pi$
$488$	−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	0.946234	+	0.323482i	$0.104854\pi$
$491$	16.6911	+	28.9099i	0.753261	+	1.30469i	−0.192973	+	0.981204i	$0.561813\pi$
$492$		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	0.578362	−	0.815780i	$-0.303692\pi$
$499$	35.1612	−	20.3003i	1.57403	−	0.908766i	0.995667	−	0.0929863i	$-0.0296413\pi$
$500$	−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	−0.510103	−	0.860113i	$-0.670393\pi$
$509$	−0.457413	+	0.264088i	−0.0202745	+	0.0117055i	0.489829	+	0.871819i	$0.337059\pi$
$510$		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	$0.329563\pi$
$521$			39.2616i			1.72008i	−0.510224	+	0.860042i	$0.670437\pi$
$522$		0			0
$523$		−	12.1444i		−	0.531036i	−0.964106	−	0.265518i	$-0.914457\pi$
$523$		−	12.1444i		−	0.531036i	0.964106	−	0.265518i	$-0.0855430\pi$
$524$	−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	0.321593	−	0.946878i	$-0.395782\pi$
$547$	−7.89651	−	4.55905i	−0.337631	−	0.194931i	−0.659224	+	0.751947i	$0.729115\pi$
$548$	−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	$0.0818070\pi$
$557$			11.9979i			0.508369i	−0.967156	+	0.254184i	$0.918193\pi$
$558$		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	0.594032	−	0.804441i	$-0.297535\pi$
$563$	−9.48276	−	16.4246i	−0.399651	−	0.692216i	−0.993683	+	0.112226i	$0.964202\pi$
$564$		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	0.00181529	−	0.999998i	$-0.499422\pi$
$569$	−20.5929	−	11.8893i	−0.863301	−	0.498427i	−0.865116	+	0.501571i	$0.832756\pi$
$570$		0			0
$571$	9.65431	−	5.57392i	0.404020	−	0.233261i	−0.284197	−	0.958766i	$-0.591727\pi$
$571$	9.65431	−	5.57392i	0.404020	−	0.233261i	0.688217	+	0.725505i	$0.258394\pi$
$572$	−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	−0.832530	−	0.553981i	$-0.813108\pi$
$587$	1.53840	−	2.66458i	0.0634965	−	0.109979i	0.896026	+	0.444001i	$0.146441\pi$
$588$		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	$0.0285169\pi$
$593$			4.35742i			0.178938i	−0.995990	+	0.0894688i	$0.971483\pi$
$594$		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	0.982205	+	0.187812i	$0.0601397\pi$
$599$	16.0003	+	27.7133i	0.653753	+	1.13233i	−0.328452	+	0.944521i	$0.606527\pi$
$600$		0			0
$601$	−17.6951	+	30.6489i	−0.721799	+	1.25019i	0.238478	+	0.971148i	$0.423351\pi$
$601$	−17.6951	+	30.6489i	−0.721799	+	1.25019i	−0.960278	+	0.279045i	$0.909982\pi$
$602$	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	−0.546509	−	0.837453i	$-0.684044\pi$
$607$	−2.32842	+	1.34431i	−0.0945076	+	0.0545640i	0.452001	+	0.892017i	$0.350710\pi$
$608$	−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	−0.892031	−	0.451974i	$-0.850720\pi$
$617$	−23.5137	+	13.5756i	−0.946626	+	0.546534i	−0.0545945	+	0.998509i	$0.517387\pi$
$618$		0			0
$619$	−8.12323	−	4.68995i	−0.326500	−	0.188505i	0.327786	−	0.944752i	$-0.393698\pi$
$619$	−8.12323	−	4.68995i	−0.326500	−	0.188505i	−0.654286	+	0.756247i	$0.727031\pi$
$620$	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	$-0.887461\pi$
$631$		−	17.3945i		−	0.692463i	0.938149	−	0.346232i	$-0.112539\pi$
$632$	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	−0.0839224	−	0.996472i	$-0.526745\pi$
$641$	−25.0358	−	14.4544i	−0.988854	−	0.570915i	−0.904932	+	0.425557i	$0.860078\pi$
$642$		0			0
$643$	12.0530	−	6.95879i	0.475323	−	0.274428i	−0.243142	−	0.969991i	$-0.578178\pi$
$643$	12.0530	−	6.95879i	0.475323	−	0.274428i	0.718465	+	0.695563i	$0.244845\pi$
$644$	−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	−0.419073	−	0.907953i	$-0.637645\pi$
$653$	4.02988	−	2.32665i	0.157701	−	0.0910489i	0.576774	+	0.816904i	$0.304311\pi$
$654$		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	0.474684	+	0.880156i	$0.342562\pi$
$659$	−13.4746	+	23.3387i	−0.524895	+	0.909145i	−0.999580	+	0.0289894i	$0.990771\pi$
$660$		0			0
$661$	−15.9921	−	27.6992i	−0.622022	−	1.07737i	−0.989109	−	0.147186i	$-0.952978\pi$
$661$	−15.9921	−	27.6992i	−0.622022	−	1.07737i	0.367087	−	0.930187i	$-0.380355\pi$
$662$	−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	−0.781997	−	0.623282i	$-0.785799\pi$
$673$	3.85968	−	6.68517i	0.148780	−	0.257694i	0.930777	+	0.365588i	$0.119132\pi$
$674$	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	0.635877	−	0.771790i	$-0.280638\pi$
$677$	7.42656	+	4.28773i	0.285426	+	0.164791i	−0.350451	+	0.936581i	$0.613972\pi$
$678$		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	0.734095	−	0.679047i	$-0.237607\pi$
$691$	13.4870	+	7.78675i	0.513071	+	0.296222i	−0.221024	+	0.975268i	$0.570940\pi$
$692$	−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	$-0.936457\pi$
$701$		−	10.5008i		−	0.396609i	0.980140	−	0.198304i	$-0.0635435\pi$
$702$		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	−0.791390	−	0.611312i	$-0.790642\pi$
$709$	3.56049	−	6.16695i	0.133717	−	0.231605i	0.925107	+	0.379708i	$0.123975\pi$
$710$	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	0.276931	−	0.960890i	$-0.410683\pi$
$727$	−11.2371	−	6.48771i	−0.416759	−	0.240616i	−0.693690	+	0.720274i	$0.744016\pi$
$728$	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	0.544571	−	0.838715i	$-0.316693\pi$
$733$	−12.2933	−	21.2926i	−0.454063	−	0.786460i	−0.998634	+	0.0522545i	$0.983359\pi$
$734$	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	$-0.717678\pi$
$739$		−	42.1439i		−	1.55029i	0.631785	−	0.775144i	$-0.282322\pi$
$740$	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	0.864453	−	0.502714i	$-0.167665\pi$
$743$	−0.0854917	−	0.148076i	−0.00313639	−	0.00543238i	−0.867589	+	0.497281i	$0.834332\pi$
$744$		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	−0.683587	−	0.729869i	$-0.739581\pi$
$751$	−10.7780	+	6.22269i	−0.393295	+	0.227069i	0.290292	+	0.956938i	$0.406248\pi$
$752$	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	−0.324090	−	0.946026i	$-0.605058\pi$
$761$	9.19028	−	5.30601i	0.333148	−	0.192343i	0.657238	+	0.753683i	$0.271725\pi$
$762$		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	0.775793	−	0.630987i	$-0.217350\pi$
$769$	−4.39685	−	7.61557i	−0.158554	−	0.274624i	−0.934348	+	0.356363i	$0.884017\pi$
$770$	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	$0.00712279\pi$
$773$			1.24418i			0.0447501i	−0.999750	+	0.0223751i	$0.992877\pi$
$774$		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	−0.638106	−	0.769949i	$-0.720282\pi$
$787$	−8.14573	+	4.70294i	−0.290364	+	0.167642i	0.347742	+	0.937590i	$0.386948\pi$
$788$	−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	−0.777395	−	0.629013i	$-0.783459\pi$
$797$	−17.5415	+	10.1276i	−0.621351	+	0.358737i	0.156044	+	0.987750i	$0.450126\pi$
$798$		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	$-0.796337\pi$
$809$		−	33.9641i		−	1.19411i	0.802199	−	0.597057i	$-0.203663\pi$
$810$		0			0
$811$		−	53.9712i		−	1.89518i	−0.319482	−	0.947592i	$-0.603509\pi$
$811$		−	53.9712i		−	1.89518i	0.319482	−	0.947592i	$-0.396491\pi$
$812$	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	0.0820442	−	0.996629i	$-0.473855\pi$
$821$	−21.2044	−	12.2424i	−0.740039	−	0.427262i	−0.822084	+	0.569367i	$0.807188\pi$
$822$		0			0
$823$	−38.5728	+	22.2700i	−1.34456	+	0.776284i	−0.987473	−	0.157786i	$-0.949564\pi$
$823$	−38.5728	+	22.2700i	−1.34456	+	0.776284i	−0.357090	+	0.934070i	$0.616231\pi$
$824$	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	−0.233798	−	0.972285i	$-0.575115\pi$
$839$	21.0036	−	36.3793i	0.725125	−	1.25595i	0.958923	−	0.283668i	$-0.0915512\pi$
$840$		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	−0.471736	−	0.881740i	$-0.656372\pi$
$853$	15.4133	−	26.6966i	0.527741	−	0.914075i	0.999477	−	0.0323350i	$-0.0102943\pi$
$854$	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	0.281222	−	0.959643i	$-0.409260\pi$
$857$	−11.9804	−	6.91687i	−0.409242	−	0.236276i	−0.690464	+	0.723367i	$0.742594\pi$
$858$		0			0
$859$	−32.0674	+	18.5141i	−1.09413	+	0.631694i	−0.934672	−	0.355511i	$-0.884307\pi$
$859$	−32.0674	+	18.5141i	−1.09413	+	0.631694i	−0.159455	+	0.987205i	$0.550974\pi$
$860$	−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	0.990941	−	0.134296i	$-0.0428774\pi$
$877$	11.2287	+	19.4487i	0.379167	+	0.656736i	−0.611775	+	0.791032i	$0.709544\pi$
$878$	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	$0.0115290\pi$
$881$			2.14963i			0.0724228i	−0.999344	+	0.0362114i	$0.988471\pi$
$882$		0			0
$883$			55.0001i			1.85090i	0.378868	+	0.925451i	$0.376313\pi$
$883$			55.0001i			1.85090i	−0.378868	+	0.925451i	$0.623687\pi$
$884$	−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	0.986269	−	0.165149i	$-0.0528106\pi$
$887$	10.4272	+	18.0604i	0.350111	+	0.606410i	−0.636158	+	0.771559i	$0.719477\pi$
$888$		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	0.986817	−	0.161840i	$-0.0517429\pi$
$907$	40.3581	+	23.3007i	1.34007	+	0.773689i	0.353251	+	0.935529i	$0.385076\pi$
$908$	−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	0.264635	−	0.964349i	$-0.414749\pi$
$911$	29.2009	−	50.5774i	0.967468	−	1.67570i	0.702833	−	0.711355i	$-0.251918\pi$
$912$		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	$-0.966603\pi$
$919$		−	6.34959i		−	0.209454i	0.994501	−	0.104727i	$-0.0333968\pi$
$920$	−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	0.757595	−	0.652725i	$-0.226374\pi$
$929$	17.4073	+	10.0501i	0.571116	+	0.329734i	−0.186479	+	0.982459i	$0.559708\pi$
$930$		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	0.452678	−	0.891674i	$-0.350469\pi$
$941$	44.5175	−	25.7022i	1.45123	−	0.837868i	0.998551	+	0.0538064i	$0.0171354\pi$
$942$		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	0.234107	+	0.972211i	$0.424783\pi$
$947$	−22.3078	+	38.6382i	−0.724906	+	1.25557i	−0.959013	+	0.283363i	$0.908550\pi$
$948$		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	$-0.683577\pi$
$953$		−	51.7549i		−	1.67651i	0.545281	−	0.838253i	$-0.316423\pi$
$954$		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	−0.777776	−	0.628542i	$-0.783652\pi$
$967$	−19.3524	+	11.1731i	−0.622331	+	0.359303i	0.155445	+	0.987845i	$0.450319\pi$
$968$	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	−0.647539	−	0.762033i	$-0.724202\pi$
$977$	−9.73245	+	5.61903i	−0.311369	+	0.179769i	0.336170	+	0.941801i	$0.390868\pi$
$978$		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	0.344865	+	0.938652i	$0.387925\pi$
$983$	−20.0804	+	34.7802i	−0.640464	+	1.10932i	−0.985329	+	0.170664i	$0.945409\pi$
$984$		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	$-0.903111\pi$
$991$		−	18.8697i		−	0.599417i	0.954031	−	0.299709i	$-0.0968894\pi$
$992$	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	−0.846441	−	0.532483i	$-0.821259\pi$
$997$	1.19746	−	2.07405i	0.0379238	−	0.0656860i	0.884364	+	0.466797i	$0.154592\pi$
$998$	−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.575.8		72
3.2	odd	2		252.2.ba.a.155.29	✓	72
4.3	odd	2	inner	756.2.ba.a.575.5		72
9.4	even	3		252.2.ba.a.239.32	yes	72
9.5	odd	6	inner	756.2.ba.a.71.5		72
12.11	even	2		252.2.ba.a.155.32	yes	72
36.23	even	6	inner	756.2.ba.a.71.8		72
36.31	odd	6		252.2.ba.a.239.29	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.29	✓	72	3.2	odd	2
252.2.ba.a.155.32	yes	72	12.11	even	2
252.2.ba.a.239.29	yes	72	36.31	odd	6
252.2.ba.a.239.32	yes	72	9.4	even	3
756.2.ba.a.71.5		72	9.5	odd	6	inner
756.2.ba.a.71.8		72	36.23	even	6	inner
756.2.ba.a.575.5		72	4.3	odd	2	inner
756.2.ba.a.575.8		72	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more