LMFDB - Embedded newform 756.2.bf.c.271.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(271,756)]

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, 0, 5]))

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

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

chi := DirichletCharacter("756.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.3
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.c.703.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29094 + 0.577482i) q^{2} +(1.33303 - 1.49098i) q^{4} +(3.03704 + 1.75344i) q^{5} +(-0.151085 - 2.64143i) q^{7} +(-0.859840 + 2.69456i) q^{8} +O(q^{10})$	\(q+(-1.29094 + 0.577482i) q^{2} +(1.33303 - 1.49098i) q^{4} +(3.03704 + 1.75344i) q^{5} +(-0.151085 - 2.64143i) q^{7} +(-0.859840 + 2.69456i) q^{8} +(-4.93321 - 0.509738i) q^{10} +(2.81992 - 1.62808i) q^{11} +2.17573i q^{13} +(1.72042 + 3.32267i) q^{14} +(-0.446063 - 3.97505i) q^{16} +(4.04232 - 2.33383i) q^{17} +(-0.0375730 + 0.0650784i) q^{19} +(6.66282 - 2.19080i) q^{20} +(-2.70015 + 3.73020i) q^{22} +(2.40399 + 1.38795i) q^{23} +(3.64909 + 6.32041i) q^{25} +(-1.25645 - 2.80873i) q^{26} +(-4.13974 - 3.29584i) q^{28} -8.09040 q^{29} +(-3.66393 - 6.34611i) q^{31} +(2.87136 + 4.87394i) q^{32} +(-3.87063 + 5.34719i) q^{34} +(4.17274 - 8.28707i) q^{35} +(5.08610 - 8.80938i) q^{37} +(0.0109228 - 0.105710i) q^{38} +(-7.33612 + 6.67583i) q^{40} +7.20413i q^{41} -1.49705i q^{43} +(1.33159 - 6.37474i) q^{44} +(-3.90491 - 0.403487i) q^{46} +(0.225780 - 0.391063i) q^{47} +(-6.95435 + 0.798164i) q^{49} +(-8.36066 - 6.05196i) q^{50} +(3.24398 + 2.90032i) q^{52} +(-1.69463 - 2.93518i) q^{53} +11.4190 q^{55} +(7.24742 + 1.86410i) q^{56} +(10.4442 - 4.67206i) q^{58} +(6.23214 + 10.7944i) q^{59} +(12.7098 + 7.33802i) q^{61} +(8.39465 + 6.07656i) q^{62} +(-6.52135 - 4.63379i) q^{64} +(-3.81501 + 6.60779i) q^{65} +(8.05831 - 4.65247i) q^{67} +(1.90882 - 9.13810i) q^{68} +(-0.601105 + 13.1078i) q^{70} +11.8379i q^{71} +(-0.852826 + 0.492379i) q^{73} +(-1.47857 + 14.3095i) q^{74} +(0.0469448 + 0.142772i) q^{76} +(-4.72652 - 7.20265i) q^{77} +(-3.09707 - 1.78809i) q^{79} +(5.61529 - 12.8545i) q^{80} +(-4.16025 - 9.30006i) q^{82} -0.350331 q^{83} +16.3689 q^{85} +(0.864522 + 1.93260i) q^{86} +(1.96229 + 8.99834i) q^{88} +(-3.06210 - 1.76790i) q^{89} +(5.74705 - 0.328721i) q^{91} +(5.27400 - 1.73414i) q^{92} +(-0.0656362 + 0.635221i) q^{94} +(-0.228222 + 0.131764i) q^{95} +1.05525i q^{97} +(8.51669 - 5.04639i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 6 q^{11} + 17 q^{14} - 4 q^{16} - 8 q^{20} + 2 q^{22} + 14 q^{25} - 15 q^{26} - 13 q^{28} - 15 q^{32} - 6 q^{35} + 4 q^{37} + q^{38} - 15 q^{40} + 42 q^{44} - 9 q^{46} + 4 q^{47} + 14 q^{49} - 9 q^{52} - 45 q^{56} + 10 q^{58} + 16 q^{59} - 42 q^{64} + 49 q^{68} - 33 q^{70} + 36 q^{73} + 54 q^{74} + 15 q^{80} - 51 q^{82} - 20 q^{83} + 16 q^{85} - 78 q^{86} - 2 q^{88} - 27 q^{94} - 24 q^{95} + 46 q^{98}+O(q^{100}) $ 32 * q + 6 * q^11 + 17 * q^14 - 4 * q^16 - 8 * q^20 + 2 * q^22 + 14 * q^25 - 15 * q^26 - 13 * q^28 - 15 * q^32 - 6 * q^35 + 4 * q^37 + q^38 - 15 * q^40 + 42 * q^44 - 9 * q^46 + 4 * q^47 + 14 * q^49 - 9 * q^52 - 45 * q^56 + 10 * q^58 + 16 * q^59 - 42 * q^64 + 49 * q^68 - 33 * q^70 + 36 * q^73 + 54 * q^74 + 15 * q^80 - 51 * q^82 - 20 * q^83 + 16 * q^85 - 78 * q^86 - 2 * q^88 - 27 * q^94 - 24 * q^95 + 46 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.29094	+	0.577482i	−0.912829	+	0.408341i
$2$	−1.29094	+	0.577482i	−0.912829	+	0.408341i
$3$		0			0
$3$		0			0
$4$	1.33303	−	1.49098i	0.666515	−	0.745492i
$5$	3.03704	+	1.75344i	1.35821	+	0.784161i	0.989382	−	0.145338i	$-0.0464268\pi$
$5$	3.03704	+	1.75344i	1.35821	+	0.784161i	0.368825	+	0.929499i	$0.379760\pi$
$6$		0			0
$7$	−0.151085	−	2.64143i	−0.0571049	−	0.998368i
$7$	−0.151085	−	2.64143i	−0.0571049	−	0.998368i
$8$	−0.859840	+	2.69456i	−0.303999	+	0.952672i
$9$		0			0
$10$	−4.93321	−	0.509738i	−1.56002	−	0.161193i
$11$	2.81992	−	1.62808i	0.850238	−	0.490885i	−0.0104932	−	0.999945i	$-0.503340\pi$
$11$	2.81992	−	1.62808i	0.850238	−	0.490885i	0.860731	+	0.509060i	$0.170007\pi$
$12$		0			0
$13$			2.17573i			0.603440i	0.953397	+	0.301720i	$0.0975607\pi$
$13$			2.17573i			0.603440i	−0.953397	+	0.301720i	$0.902439\pi$
$14$	1.72042	+	3.32267i	0.459802	+	0.888022i
$15$		0			0
$16$	−0.446063	−	3.97505i	−0.111516	−	0.993763i
$17$	4.04232	−	2.33383i	0.980406	−	0.566038i	0.0780131	−	0.996952i	$-0.475142\pi$
$17$	4.04232	−	2.33383i	0.980406	−	0.566038i	0.902393	+	0.430915i	$0.141809\pi$
$18$		0			0
$19$	−0.0375730	+	0.0650784i	−0.00861984	+	0.0149300i	−0.870303	−	0.492516i	$-0.836077\pi$
$19$	−0.0375730	+	0.0650784i	−0.00861984	+	0.0149300i	0.861683	+	0.507446i	$0.169410\pi$
$20$	6.66282	−	2.19080i	1.48985	−	0.489877i
$21$		0			0
$22$	−2.70015	+	3.73020i	−0.575674	+	0.795281i
$23$	2.40399	+	1.38795i	0.501267	+	0.289407i	0.729237	−	0.684262i	$-0.239875\pi$
$23$	2.40399	+	1.38795i	0.501267	+	0.289407i	−0.227970	+	0.973668i	$0.573209\pi$
$24$		0			0
$25$	3.64909	+	6.32041i	0.729818	+	1.26408i
$26$	−1.25645	−	2.80873i	−0.246409	−	0.550837i
$27$		0			0
$28$	−4.13974	−	3.29584i	−0.782336	−	0.622856i
$29$	−8.09040			−1.50235			−0.751175	−	0.660104i	$-0.770512\pi$
$29$	−8.09040			−1.50235			−0.751175	+	0.660104i	$0.770512\pi$
$30$		0			0
$31$	−3.66393	−	6.34611i	−0.658060	−	1.13979i	−0.981117	−	0.193415i	$-0.938044\pi$
$31$	−3.66393	−	6.34611i	−0.658060	−	1.13979i	0.323057	−	0.946380i	$-0.395290\pi$
$32$	2.87136	+	4.87394i	0.507589	+	0.861599i
$33$		0			0
$34$	−3.87063	+	5.34719i	−0.663807	+	0.917036i
$35$	4.17274	−	8.28707i	0.705321	−	1.40077i
$36$		0			0
$37$	5.08610	−	8.80938i	0.836150	−	1.44825i	−0.0569410	−	0.998378i	$-0.518135\pi$
$37$	5.08610	−	8.80938i	0.836150	−	1.44825i	0.893091	−	0.449876i	$-0.148532\pi$
$38$	0.0109228	−	0.105710i	0.00177191	−	0.0171484i
$39$		0			0
$40$	−7.33612	+	6.67583i	−1.15994	+	1.05554i
$41$			7.20413i			1.12510i	0.826765	+	0.562548i	$0.190179\pi$
$41$			7.20413i			1.12510i	−0.826765	+	0.562548i	$0.809821\pi$
$42$		0			0
$43$		−	1.49705i		−	0.228299i	−0.993464	−	0.114149i	$-0.963586\pi$
$43$		−	1.49705i		−	0.228299i	0.993464	−	0.114149i	$-0.0364142\pi$
$44$	1.33159	−	6.37474i	0.200745	−	0.961028i
$45$		0			0
$46$	−3.90491	−	0.403487i	−0.575748	−	0.0594909i
$47$	0.225780	−	0.391063i	0.0329334	−	0.0570424i	−0.849089	−	0.528250i	$-0.822848\pi$
$47$	0.225780	−	0.391063i	0.0329334	−	0.0570424i	0.882022	+	0.471208i	$0.156182\pi$
$48$		0			0
$49$	−6.95435	+	0.798164i	−0.993478	+	0.114023i
$50$	−8.36066	−	6.05196i	−1.18238	−	0.855876i
$51$		0			0
$52$	3.24398	+	2.90032i	0.449859	+	0.402201i
$53$	−1.69463	−	2.93518i	−0.232775	−	0.403178i	0.725849	−	0.687854i	$-0.241447\pi$
$53$	−1.69463	−	2.93518i	−0.232775	−	0.403178i	−0.958624	+	0.284677i	$0.908114\pi$
$54$		0			0
$55$	11.4190			1.53973
$56$	7.24742	+	1.86410i	0.968477	+	0.249101i
$57$		0			0
$58$	10.4442	−	4.67206i	1.37139	−	0.613471i
$59$	6.23214	+	10.7944i	0.811356	+	1.40531i	0.911915	+	0.410378i	$0.134603\pi$
$59$	6.23214	+	10.7944i	0.811356	+	1.40531i	−0.100560	+	0.994931i	$0.532063\pi$
$60$		0			0
$61$	12.7098	+	7.33802i	1.62733	+	0.939537i	0.984886	+	0.173202i	$0.0554112\pi$
$61$	12.7098	+	7.33802i	1.62733	+	0.939537i	0.642440	+	0.766336i	$0.277922\pi$
$62$	8.39465	+	6.07656i	1.06612	+	0.771724i
$63$		0			0
$64$	−6.52135	−	4.63379i	−0.815169	−	0.579224i
$65$	−3.81501	+	6.60779i	−0.473194	+	0.819596i
$66$		0			0
$67$	8.05831	−	4.65247i	0.984479	−	0.568389i	0.0808598	−	0.996725i	$-0.474233\pi$
$67$	8.05831	−	4.65247i	0.984479	−	0.568389i	0.903619	+	0.428336i	$0.140900\pi$
$68$	1.90882	−	9.13810i	0.231479	−	1.10816i
$69$		0			0
$70$	−0.601105	+	13.1078i	−0.0718458	+	1.56668i
$71$			11.8379i			1.40490i	0.711731	+	0.702452i	$0.247911\pi$
$71$			11.8379i			1.40490i	−0.711731	+	0.702452i	$0.752089\pi$
$72$		0			0
$73$	−0.852826	+	0.492379i	−0.0998157	+	0.0576286i	−0.549077	−	0.835772i	$-0.685021\pi$
$73$	−0.852826	+	0.492379i	−0.0998157	+	0.0576286i	0.449261	+	0.893400i	$0.351687\pi$
$74$	−1.47857	+	14.3095i	−0.171880	+	1.66344i
$75$		0			0
$76$	0.0469448	+	0.142772i	0.00538494	+	0.0163771i
$77$	−4.72652	−	7.20265i	−0.538637	−	0.820819i
$78$		0			0
$79$	−3.09707	−	1.78809i	−0.348447	−	0.201176i	0.315554	−	0.948908i	$-0.397810\pi$
$79$	−3.09707	−	1.78809i	−0.348447	−	0.201176i	−0.664001	+	0.747731i	$0.731143\pi$
$80$	5.61529	−	12.8545i	0.627809	−	1.43718i
$81$		0			0
$82$	−4.16025	−	9.30006i	−0.459423	−	1.02702i
$83$	−0.350331			−0.0384538			−0.0192269	−	0.999815i	$-0.506120\pi$
$83$	−0.350331			−0.0384538			−0.0192269	+	0.999815i	$0.506120\pi$
$84$		0			0
$85$	16.3689			1.77546
$86$	0.864522	+	1.93260i	0.0932238	+	0.208398i
$87$		0			0
$88$	1.96229	+	8.99834i	0.209181	+	0.959227i
$89$	−3.06210	−	1.76790i	−0.324582	−	0.187397i	0.328851	−	0.944382i	$-0.393339\pi$
$89$	−3.06210	−	1.76790i	−0.324582	−	0.187397i	−0.653433	+	0.756984i	$0.726672\pi$
$90$		0			0
$91$	5.74705	−	0.328721i	0.602455	−	0.0344594i
$92$	5.27400	−	1.73414i	0.549852	−	0.180797i
$93$		0			0
$94$	−0.0656362	+	0.635221i	−0.00676985	+	0.0655181i
$95$	−0.228222	+	0.131764i	−0.0234151	+	0.0135187i
$96$		0			0
$97$			1.05525i			0.107145i	0.998564	+	0.0535723i	$0.0170607\pi$
$97$			1.05525i			0.107145i	−0.998564	+	0.0535723i	$0.982939\pi$
$98$	8.51669	−	5.04639i	0.860315	−	0.509762i
$99$		0			0
$100$	14.2880	+	2.98456i	1.42880	+	0.298456i
$101$	10.8723	−	6.27713i	1.08183	−	0.624597i	0.150444	−	0.988619i	$-0.451930\pi$
$101$	10.8723	−	6.27713i	1.08183	−	0.624597i	0.931391	+	0.364021i	$0.118596\pi$
$102$		0			0
$103$	−2.80411	+	4.85686i	−0.276297	+	0.478561i	−0.970462	−	0.241256i	$-0.922441\pi$
$103$	−2.80411	+	4.85686i	−0.276297	+	0.478561i	0.694164	+	0.719817i	$0.255774\pi$
$104$	−5.86265	−	1.87078i	−0.574880	−	0.183445i
$105$		0			0
$106$	3.88266	+	2.81051i	0.377118	+	0.272981i
$107$	−15.8399	−	9.14518i	−1.53130	−	0.884098i	−0.999302	−	0.0373531i	$-0.988107\pi$
$107$	−15.8399	−	9.14518i	−1.53130	−	0.884098i	−0.532000	−	0.846744i	$-0.678559\pi$
$108$		0			0
$109$	7.43893	+	12.8846i	0.712520	+	1.23412i	0.963908	+	0.266234i	$0.0857795\pi$
$109$	7.43893	+	12.8846i	0.712520	+	1.23412i	−0.251388	+	0.967886i	$0.580887\pi$
$110$	−14.7411	+	6.59424i	−1.40551	+	0.628736i
$111$		0			0
$112$	−10.4324	+	1.77882i	−0.985773	+	0.168083i
$113$	6.67916			0.628323			0.314161	−	0.949370i	$-0.398277\pi$
$113$	6.67916			0.628323			0.314161	+	0.949370i	$0.398277\pi$
$114$		0			0
$115$	4.86735	+	8.43050i	0.453883	+	0.786149i
$116$	−10.7847	+	12.0626i	−1.00134	+	1.11999i
$117$		0			0
$118$	−14.2789	−	10.3359i	−1.31448	−	0.951498i
$119$	−6.77540	−	10.3249i	−0.621100	−	0.946482i
$120$		0			0
$121$	−0.198701	+	0.344159i	−0.0180637	+	0.0312872i
$122$	−20.6451	−	2.13322i	−1.86912	−	0.193133i
$123$		0			0
$124$	−14.3461	−	2.99670i	−1.28831	−	0.269111i
$125$			8.05942i			0.720856i
$126$		0			0
$127$		−	0.237718i		−	0.0210941i	−0.999944	−	0.0105470i	$-0.996643\pi$
$127$		−	0.237718i		−	0.0210941i	0.999944	−	0.0105470i	$-0.00335729\pi$
$128$	11.0946	+	2.21596i	0.980631	+	0.195865i
$129$		0			0
$130$	1.10905	−	10.7333i	0.0972705	−	0.941376i
$131$	−4.92994	+	8.53891i	−0.430731	+	0.746048i	−0.996936	−	0.0782164i	$-0.975077\pi$
$131$	−4.92994	+	8.53891i	−0.430731	+	0.746048i	0.566206	+	0.824264i	$0.308411\pi$
$132$		0			0
$133$	0.177577	+	0.0894143i	0.0153979	+	0.00775320i
$134$	−7.71604	+	10.6596i	−0.666565	+	0.920846i
$135$		0			0
$136$	2.81292	+	12.8990i	0.241205	+	1.10608i
$137$	3.27562	+	5.67353i	0.279855	+	0.484723i	0.971348	−	0.237660i	$-0.0763804\pi$
$137$	3.27562	+	5.67353i	0.279855	+	0.484723i	−0.691494	+	0.722382i	$0.743047\pi$
$138$		0			0
$139$	−5.30200			−0.449710			−0.224855	−	0.974392i	$-0.572191\pi$
$139$	−5.30200			−0.449710			−0.224855	+	0.974392i	$0.572191\pi$
$140$	−6.79350	−	17.2684i	−0.574155	−	1.45945i
$141$		0			0
$142$	−6.83619	−	15.2820i	−0.573680	−	1.28244i
$143$	3.54227	+	6.13539i	0.296219	+	0.513067i
$144$		0			0
$145$	−24.5709	−	14.1860i	−2.04050	−	1.17808i
$146$	0.816603	−	1.12812i	0.0675826	−	0.0933640i
$147$		0			0
$148$	−6.35472	−	19.3265i	−0.522355	−	1.58863i
$149$	−0.192950	+	0.334200i	−0.0158071	+	0.0273787i	−0.873821	−	0.486248i	$-0.838365\pi$
$149$	−0.192950	+	0.334200i	−0.0158071	+	0.0273787i	0.858014	+	0.513627i	$0.171698\pi$
$150$		0			0
$151$	−14.9039	+	8.60478i	−1.21286	+	0.700247i	−0.963382	−	0.268132i	$-0.913594\pi$
$151$	−14.9039	+	8.60478i	−1.21286	+	0.700247i	−0.249482	+	0.968380i	$0.580260\pi$
$152$	−0.143051	−	0.157200i	−0.0116030	−	0.0127506i
$153$		0			0
$154$	10.2610	+	6.56868i	0.826858	+	0.529320i
$155$		−	25.6979i		−	2.06410i
$156$		0			0
$157$	6.83943	−	3.94874i	0.545846	−	0.315144i	−0.201599	−	0.979468i	$-0.564614\pi$
$157$	6.83943	−	3.94874i	0.545846	−	0.315144i	0.747445	+	0.664324i	$0.231280\pi$
$158$	5.03071	+	0.519813i	0.400222	+	0.0413541i
$159$		0			0
$160$	0.174285	+	19.8371i	0.0137784	+	1.56826i
$161$	3.30296	−	6.55969i	0.260310	−	0.516976i
$162$		0			0
$163$	−21.1449	−	12.2080i	−1.65620	−	0.956207i	−0.974445	−	0.224625i	$-0.927884\pi$
$163$	−21.1449	−	12.2080i	−1.65620	−	0.956207i	−0.681753	−	0.731582i	$-0.738782\pi$
$164$	10.7412	+	9.60331i	0.838749	+	0.749893i
$165$		0			0
$166$	0.452254	−	0.202310i	0.0351017	−	0.0157023i
$167$	−18.5223			−1.43330			−0.716648	−	0.697435i	$-0.754325\pi$
$167$	−18.5223			−1.43330			−0.716648	+	0.697435i	$0.754325\pi$
$168$		0			0
$169$	8.26619			0.635861
$170$	−21.1312	+	9.45275i	−1.62069	+	0.724993i
$171$		0			0
$172$	−2.23208	−	1.99562i	−0.170195	−	0.152164i
$173$	−13.0506	−	7.53479i	−0.992222	−	0.572860i	−0.0862842	−	0.996271i	$-0.527499\pi$
$173$	−13.0506	−	7.53479i	−0.992222	−	0.572860i	−0.905938	+	0.423411i	$0.860833\pi$
$174$		0			0
$175$	16.1436	−	10.5937i	1.22034	−	0.800812i
$176$	−7.72957	−	10.4831i	−0.582638	−	0.790193i
$177$		0			0
$178$	4.97390	+	0.513944i	0.372810	+	0.0385217i
$179$	5.38111	−	3.10679i	0.402203	−	0.232212i	−0.285231	−	0.958459i	$-0.592070\pi$
$179$	5.38111	−	3.10679i	0.402203	−	0.232212i	0.687434	+	0.726247i	$0.258737\pi$
$180$		0			0
$181$		−	12.1266i		−	0.901366i	−0.892684	−	0.450683i	$-0.851180\pi$
$181$		−	12.1266i		−	0.901366i	0.892684	−	0.450683i	$-0.148820\pi$
$182$	−7.22924	+	3.74318i	−0.535867	+	0.277463i
$183$		0			0
$184$	−5.80696	+	5.28430i	−0.428095	+	0.389564i
$185$	30.8934	−	17.8363i	2.27133	−	1.31135i
$186$		0			0
$187$	7.59934	−	13.1624i	0.555719	−	0.962533i
$188$	−0.282097	−	0.857933i	−0.0205740	−	0.0625712i
$189$		0			0
$190$	0.218528	−	0.301893i	0.0158537	−	0.0219016i
$191$	−7.71716	−	4.45550i	−0.558394	−	0.322389i	0.194107	−	0.980980i	$-0.437819\pi$
$191$	−7.71716	−	4.45550i	−0.558394	−	0.322389i	−0.752501	+	0.658591i	$0.771153\pi$
$192$		0			0
$193$	1.51542	+	2.62478i	0.109082	+	0.188936i	0.915399	−	0.402548i	$-0.131875\pi$
$193$	1.51542	+	2.62478i	0.109082	+	0.188936i	−0.806316	+	0.591484i	$0.798542\pi$
$194$	−0.609388	−	1.36226i	−0.0437515	−	0.0978047i
$195$		0			0
$196$	−8.08030	+	11.4328i	−0.577164	+	0.816628i
$197$	−17.5070			−1.24733			−0.623663	−	0.781694i	$-0.714356\pi$
$197$	−17.5070			−1.24733			−0.623663	+	0.781694i	$0.714356\pi$
$198$		0			0
$199$	−9.12491	−	15.8048i	−0.646848	−	1.12037i	−0.983871	−	0.178877i	$-0.942753\pi$
$199$	−9.12491	−	15.8048i	−0.646848	−	1.12037i	0.337023	−	0.941496i	$-0.390580\pi$
$200$	−20.1684	+	4.39816i	−1.42612	+	0.310997i
$201$		0			0
$202$	−10.4105	+	14.3819i	−0.732481	+	1.01191i
$203$	1.22234	+	21.3703i	0.0857915	+	1.49990i
$204$		0			0
$205$	−12.6320	+	21.8792i	−0.882256	+	1.52811i
$206$	0.815177	−	7.88922i	0.0567961	−	0.549668i
$207$		0			0
$208$	8.64865	−	0.970514i	0.599676	−	0.0672930i
$209$			0.244688i			0.0169254i
$210$		0			0
$211$			20.8486i			1.43528i	0.696414	+	0.717640i	$0.254778\pi$
$211$			20.8486i			1.43528i	−0.696414	+	0.717640i	$0.745222\pi$
$212$	−6.63529	−	1.38602i	−0.455713	−	0.0951923i
$213$		0			0
$214$	25.7295	+	2.65858i	1.75883	+	0.181737i
$215$	2.62499	−	4.54662i	0.179023	−	0.310077i
$216$		0			0
$217$	−16.2093	+	10.6368i	−1.10036	+	0.722074i
$218$	−17.0438	−	12.3373i	−1.15435	−	0.835590i
$219$		0			0
$220$	15.2218	−	17.0255i	1.02625	−	1.14786i
$221$	5.07779	+	8.79500i	0.341569	+	0.591616i
$222$		0			0
$223$	23.6765			1.58550			0.792748	−	0.609550i	$-0.208650\pi$
$223$	23.6765			1.58550			0.792748	+	0.609550i	$0.208650\pi$
$224$	12.4404	−	8.32088i	0.831207	−	0.555962i
$225$		0			0
$226$	−8.62237	+	3.85710i	−0.573552	+	0.256570i
$227$	0.833064	+	1.44291i	0.0552924	+	0.0957692i	0.892347	−	0.451350i	$-0.149058\pi$
$227$	0.833064	+	1.44291i	0.0552924	+	0.0957692i	−0.837054	+	0.547120i	$0.815724\pi$
$228$		0			0
$229$	−19.6839	−	11.3645i	−1.30075	−	0.750989i	−0.320218	−	0.947344i	$-0.603756\pi$
$229$	−19.6839	−	11.3645i	−1.30075	−	0.750989i	−0.980533	+	0.196355i	$0.937089\pi$
$230$	−11.1519	−	8.07243i	−0.735335	−	0.532280i
$231$		0			0
$232$	6.95645	−	21.8001i	0.456713	−	1.43125i
$233$	−0.739972	+	1.28167i	−0.0484772	+	0.0839649i	−0.889246	−	0.457430i	$-0.848770\pi$
$233$	−0.739972	+	1.28167i	−0.0484772	+	0.0839649i	0.840769	+	0.541395i	$0.182103\pi$
$234$		0			0
$235$	1.37141	−	0.791784i	0.0894609	−	0.0516503i
$236$	24.4019	+	5.09722i	1.58843	+	0.331801i
$237$		0			0
$238$	14.7090	+	9.41612i	0.953446	+	0.610356i
$239$			7.69359i			0.497657i	0.968548	+	0.248829i	$0.0800456\pi$
$239$			7.69359i			0.497657i	−0.968548	+	0.248829i	$0.919954\pi$
$240$		0			0
$241$	−1.47981	+	0.854368i	−0.0953229	+	0.0550347i	−0.546904	−	0.837196i	$-0.684194\pi$
$241$	−1.47981	+	0.854368i	−0.0953229	+	0.0550347i	0.451581	+	0.892230i	$0.350860\pi$
$242$	0.0577639	−	0.559034i	0.00371320	−	0.0359360i
$243$		0			0
$244$	27.8834	−	9.16834i	1.78505	−	0.586943i
$245$	−22.5202	−	9.76995i	−1.43876	−	0.624180i
$246$		0			0
$247$	−0.141593	−	0.0817488i	−0.00900936	−	0.00520155i
$248$	20.2504	−	4.41605i	1.28590	−	0.280419i
$249$		0			0
$250$	−4.65417	−	10.4042i	−0.294355	−	0.658019i
$251$	−15.5203			−0.979630			−0.489815	−	0.871826i	$-0.662936\pi$
$251$	−15.5203			−0.979630			−0.489815	+	0.871826i	$0.662936\pi$
$252$		0			0
$253$	9.03876			0.568262
$254$	0.137278	+	0.306879i	0.00861358	+	0.0192553i
$255$		0			0
$256$	−15.6021	+	3.54625i	−0.975128	+	0.221640i
$257$	11.3136	+	6.53193i	0.705726	+	0.407451i	0.809476	−	0.587152i	$-0.199751\pi$
$257$	11.3136	+	6.53193i	0.705726	+	0.407451i	−0.103751	+	0.994603i	$0.533084\pi$
$258$		0			0
$259$	−24.0378	−	12.1036i	−1.49364	−	0.752083i
$260$	4.76659	+	14.4965i	0.295611	+	0.899035i
$261$		0			0
$262$	1.43317	−	13.8701i	0.0885417	−	0.856899i
$263$	−6.59070	+	3.80514i	−0.406400	+	0.234635i	−0.689242	−	0.724531i	$-0.742056\pi$
$263$	−6.59070	+	3.80514i	−0.406400	+	0.234635i	0.282842	+	0.959167i	$0.408723\pi$
$264$		0			0
$265$		−	11.8857i		−	0.730132i
$266$	−0.280876	−	0.0128806i	−0.0172216	−	0.000789761i
$267$		0			0
$268$	3.80522	−	18.2167i	0.232441	−	1.11276i
$269$	−14.2226	+	8.21140i	−0.867165	+	0.500658i	−0.866405	−	0.499342i	$-0.833575\pi$
$269$	−14.2226	+	8.21140i	−0.867165	+	0.500658i	−0.000759905		1.00000i	$0.500242\pi$
$270$		0			0
$271$	−7.95296	+	13.7749i	−0.483108	+	0.836767i	−0.999812	−	0.0193968i	$-0.993825\pi$
$271$	−7.95296	+	13.7749i	−0.483108	+	0.836767i	0.516704	+	0.856164i	$0.327159\pi$
$272$	−11.0802	−	15.0274i	−0.671838	−	0.911169i
$273$		0			0
$274$	−7.50497	−	5.43256i	−0.453392	−	0.328193i
$275$	20.5803	+	11.8820i	1.24104	+	0.716513i
$276$		0			0
$277$	−14.9147	−	25.8330i	−0.896136	−	1.55215i	−0.832392	−	0.554187i	$-0.813029\pi$
$277$	−14.9147	−	25.8330i	−0.896136	−	1.55215i	−0.0637443	−	0.997966i	$-0.520304\pi$
$278$	6.84454	−	3.06181i	0.410508	−	0.183635i
$279$		0			0
$280$	18.7421	+	18.3693i	1.12006	+	1.09777i
$281$	−12.6113			−0.752324			−0.376162	−	0.926554i	$-0.622756\pi$
$281$	−12.6113			−0.752324			−0.376162	+	0.926554i	$0.622756\pi$
$282$		0			0
$283$	4.00631	+	6.93912i	0.238150	+	0.412488i	0.960183	−	0.279370i	$-0.0901256\pi$
$283$	4.00631	+	6.93912i	0.238150	+	0.412488i	−0.722033	+	0.691858i	$0.756792\pi$
$284$	17.6502	+	15.7803i	1.04734	+	0.936389i
$285$		0			0
$286$	−8.11592	−	5.87480i	−0.479904	−	0.347384i
$287$	19.0292	−	1.08844i	1.12326	−	0.0642485i
$288$		0			0
$289$	2.39355	−	4.14575i	0.140797	−	0.243868i
$290$	39.9116	+	4.12399i	2.34369	+	0.242169i
$291$		0			0
$292$	−0.402713	+	1.92791i	−0.0235670	+	0.112822i
$293$		−	16.8878i		−	0.986596i	−0.869861	−	0.493298i	$-0.835791\pi$
$293$		−	16.8878i		−	0.986596i	0.869861	−	0.493298i	$-0.164209\pi$
$294$		0			0
$295$			43.7107i			2.54493i
$296$	19.3642	+	21.2795i	1.12552	+	1.23685i
$297$		0			0
$298$	0.0560922	−	0.542855i	0.00324933	−	0.0314468i
$299$	−3.01980	+	5.23044i	−0.174639	+	0.302484i
$300$		0			0
$301$	−3.95437	+	0.226183i	−0.227926	+	0.0130370i
$302$	14.2709	−	19.7150i	0.821198	−	1.13447i
$303$		0			0
$304$	0.275450	+	0.120326i	0.0157981	+	0.00690115i
$305$	25.7335	+	44.5718i	1.47350	+	2.55217i
$306$		0			0
$307$	17.3886			0.992420			0.496210	−	0.868202i	$-0.334725\pi$
$307$	17.3886			0.992420			0.496210	+	0.868202i	$0.334725\pi$
$308$	−17.0396	−	2.55419i	−0.970923	−	0.145539i
$309$		0			0
$310$	14.8400	+	33.1743i	0.842858	+	1.88417i
$311$	−4.32502	−	7.49115i	−0.245249	−	0.424784i	0.716952	−	0.697122i	$-0.245537\pi$
$311$	−4.32502	−	7.49115i	−0.245249	−	0.424784i	−0.962202	+	0.272338i	$0.912203\pi$
$312$		0			0
$313$	7.49650	+	4.32810i	0.423727	+	0.244639i	0.696671	−	0.717391i	$-0.254664\pi$
$313$	7.49650	+	4.32810i	0.423727	+	0.244639i	−0.272944	+	0.962030i	$0.587997\pi$
$314$	−6.54893	+	9.04722i	−0.369578	+	0.510564i
$315$		0			0
$316$	−6.79450	+	2.23410i	−0.382221	+	0.125678i
$317$	−3.65839	+	6.33651i	−0.205475	+	0.355894i	−0.950284	−	0.311384i	$-0.899207\pi$
$317$	−3.65839	+	6.33651i	−0.205475	+	0.355894i	0.744809	+	0.667278i	$0.232541\pi$
$318$		0			0
$319$	−22.8143	+	13.1718i	−1.27735	+	0.737481i
$320$	−11.6806	−	25.5078i	−0.652963	−	1.42593i
$321$		0			0
$322$	−0.475809	+	10.3755i	−0.0265158	+	0.578206i
$323$			0.350757i			0.0195166i
$324$		0			0
$325$	−13.7515	+	7.93944i	−0.762797	+	0.440401i
$326$	34.3467	+	3.54897i	1.90229	+	0.196559i
$327$		0			0
$328$	−19.4120	−	6.19440i	−1.07185	−	0.342028i
$329$	−1.06708	−	0.537300i	−0.0588300	−	0.0296223i
$330$		0			0
$331$	−13.1557	−	7.59544i	−0.723102	−	0.417483i	0.0927914	−	0.995686i	$-0.470421\pi$
$331$	−13.1557	−	7.59544i	−0.723102	−	0.417483i	−0.815893	+	0.578203i	$0.803754\pi$
$332$	−0.467001	+	0.522337i	−0.0256300	+	0.0286670i
$333$		0			0
$334$	23.9111	−	10.6963i	1.30836	−	0.585274i
$335$	32.6312			1.78284
$336$		0			0
$337$	−8.46246			−0.460980			−0.230490	−	0.973075i	$-0.574033\pi$
$337$	−8.46246			−0.460980			−0.230490	+	0.973075i	$0.574033\pi$
$338$	−10.6711	+	4.77357i	−0.580432	+	0.259648i
$339$		0			0
$340$	21.8203	−	24.4058i	1.18337	−	1.32359i
$341$	−20.6640	−	11.9303i	−1.11902	−	0.646064i
$342$		0			0
$343$	3.15900	+	18.2489i	0.170570	+	0.985346i
$344$	4.03391	+	1.28723i	0.217494	+	0.0694027i
$345$		0			0
$346$	21.1987	+	2.19042i	1.13965	+	0.117758i
$347$	−18.7881	+	10.8473i	−1.00860	+	0.582313i	−0.910780	−	0.412892i	$-0.864519\pi$
$347$	−18.7881	+	10.8473i	−1.00860	+	0.582313i	−0.0978156	+	0.995205i	$0.531186\pi$
$348$		0			0
$349$		−	34.5359i		−	1.84867i	−0.381586	−	0.924333i	$-0.624622\pi$
$349$		−	34.5359i		−	1.84867i	0.381586	−	0.924333i	$-0.375378\pi$
$350$	−14.7227	+	22.9985i	−0.786960	+	1.22932i
$351$		0			0
$352$	16.0322	+	9.06932i	0.854518	+	0.483396i
$353$	−7.93449	+	4.58098i	−0.422311	+	0.243821i	−0.696065	−	0.717978i	$-0.745068\pi$
$353$	−7.93449	+	4.58098i	−0.422311	+	0.243821i	0.273755	+	0.961799i	$0.411734\pi$
$354$		0			0
$355$	−20.7571	+	35.9523i	−1.10167	+	1.90815i
$356$	−6.71778	+	2.20887i	−0.356042	+	0.117070i
$357$		0			0
$358$	−5.15256	+	7.11815i	−0.272321	+	0.376206i
$359$	13.6912	+	7.90464i	0.722596	+	0.417191i	0.815707	−	0.578465i	$-0.196348\pi$
$359$	13.6912	+	7.90464i	0.722596	+	0.417191i	−0.0931113	+	0.995656i	$0.529681\pi$
$360$		0			0
$361$	9.49718	+	16.4496i	0.499851	+	0.865768i
$362$	7.00291	+	15.6547i	0.368065	+	0.822793i
$363$		0			0
$364$	7.17087	−	9.00696i	0.375856	−	0.472093i
$365$	−3.45343			−0.180761
$366$		0			0
$367$	−0.321922	−	0.557586i	−0.0168042	−	0.0291057i	0.857501	−	0.514482i	$-0.172016\pi$
$367$	−0.321922	−	0.557586i	−0.0168042	−	0.0291057i	−0.874305	+	0.485377i	$0.838683\pi$
$368$	4.44482	−	10.1751i	0.231702	−	0.530414i
$369$		0			0
$370$	−29.5813	+	40.8659i	−1.53786	+	2.12452i
$371$	−7.49704	+	4.91970i	−0.389227	+	0.255418i
$372$		0			0
$373$	−14.4675	+	25.0584i	−0.749098	+	1.29748i	0.199158	+	0.979967i	$0.436179\pi$
$373$	−14.4675	+	25.0584i	−0.749098	+	1.29748i	−0.948256	+	0.317508i	$0.897154\pi$
$374$	−2.20919	+	21.3803i	−0.114234	+	1.10555i
$375$		0			0
$376$	0.859609	+	0.944631i	0.0443310	+	0.0487156i
$377$		−	17.6025i		−	0.906577i
$378$		0			0
$379$			20.6164i			1.05899i	0.848312	+	0.529496i	$0.177619\pi$
$379$			20.6164i			1.05899i	−0.848312	+	0.529496i	$0.822381\pi$
$380$	−0.107769	+	0.515920i	−0.00552842	+	0.0264661i
$381$		0			0
$382$	12.5353	+	1.29525i	0.641363	+	0.0662708i
$383$	11.1672	−	19.3421i	0.570616	−	0.988336i	−0.425886	−	0.904777i	$-0.640038\pi$
$383$	11.1672	−	19.3421i	0.570616	−	0.988336i	0.996503	−	0.0835599i	$-0.0266290\pi$
$384$		0			0
$385$	−1.72524	−	30.1624i	−0.0879263	−	1.53722i
$386$	−3.47207	−	2.51330i	−0.176724	−	0.127924i
$387$		0			0
$388$	1.57336	+	1.40668i	0.0798753	+	0.0714134i
$389$	−0.312454	−	0.541186i	−0.0158420	−	0.0274392i	0.857996	−	0.513657i	$-0.171710\pi$
$389$	−0.312454	−	0.541186i	−0.0158420	−	0.0274392i	−0.873838	+	0.486218i	$0.838376\pi$
$390$		0			0
$391$	12.9569			0.655260
$392$	3.82892	−	19.4252i	0.193390	−	0.981122i
$393$		0			0
$394$	22.6005	−	10.1100i	1.13860	−	0.509334i
$395$	−6.27062	−	10.8610i	−0.315509	−	0.546478i
$396$		0			0
$397$	14.4487	+	8.34197i	0.725160	+	0.418671i	0.816649	−	0.577135i	$-0.195829\pi$
$397$	14.4487	+	8.34197i	0.725160	+	0.418671i	−0.0914889	+	0.995806i	$0.529163\pi$
$398$	20.9067	+	15.1335i	1.04796	+	0.758575i
$399$		0			0
$400$	23.4962	−	17.3246i	1.17481	−	0.866231i
$401$	−3.39351	+	5.87773i	−0.169464	+	0.293520i	−0.938231	−	0.346008i	$-0.887537\pi$
$401$	−3.39351	+	5.87773i	−0.169464	+	0.293520i	0.768768	+	0.639528i	$0.220870\pi$
$402$		0			0
$403$	13.8074	−	7.97172i	0.687797	−	0.397100i
$404$	5.13401	−	24.5780i	0.255427	−	1.22280i
$405$		0			0
$406$	−13.9189	−	26.8817i	−0.690783	−	1.33412i
$407$		−	33.1223i		−	1.64181i
$408$		0			0
$409$	−0.576150	+	0.332640i	−0.0284888	+	0.0164480i	−0.514177	−	0.857684i	$-0.671902\pi$
$409$	−0.576150	+	0.332640i	−0.0284888	+	0.0164480i	0.485688	+	0.874132i	$0.338569\pi$
$410$	3.67222	−	35.5394i	0.181358	−	1.75517i
$411$		0			0
$412$	3.50354	+	10.6552i	0.172607	+	0.524945i
$413$	27.5711	−	18.0927i	1.35668	−	0.890282i
$414$		0			0
$415$	−1.06397	−	0.614283i	−0.0522282	−	0.0301540i
$416$	−10.6044	+	6.24731i	−0.519923	+	0.306299i
$417$		0			0
$418$	−0.141303	−	0.315876i	−0.00691134	−	0.0154500i
$419$	34.3592			1.67856			0.839278	−	0.543702i	$-0.182978\pi$
$419$	34.3592			1.67856			0.839278	+	0.543702i	$0.182978\pi$
$420$		0			0
$421$	−31.1909			−1.52015			−0.760076	−	0.649835i	$-0.774838\pi$
$421$	−31.1909			−1.52015			−0.760076	+	0.649835i	$0.774838\pi$
$422$	−12.0397	−	26.9143i	−0.586084	−	1.31017i
$423$		0			0
$424$	9.36613	−	2.04249i	0.454859	−	0.0991922i
$425$	29.5015	+	17.0327i	1.43103	+	0.826208i
$426$		0			0
$427$	17.4626	−	34.6808i	0.845076	−	1.67832i
$428$	−34.7504	+	11.4263i	−1.67972	+	0.552309i
$429$		0			0
$430$	−0.763106	+	7.38528i	−0.0368003	+	0.356150i
$431$	5.25944	−	3.03654i	0.253339	−	0.146265i	−0.367953	−	0.929844i	$-0.619941\pi$
$431$	5.25944	−	3.03654i	0.253339	−	0.146265i	0.621292	+	0.783579i	$0.286608\pi$
$432$		0			0
$433$		−	9.56176i		−	0.459509i	−0.973249	−	0.229754i	$-0.926208\pi$
$433$		−	9.56176i		−	0.459509i	0.973249	−	0.229754i	$-0.0737923\pi$
$434$	14.7825	−	23.0920i	0.709584	−	1.10845i
$435$		0			0
$436$	29.1270	+	6.08424i	1.39493	+	0.291382i
$437$	−0.180651	+	0.104299i	−0.00864169	+	0.00498928i
$438$		0			0
$439$	13.6732	−	23.6827i	0.652586	−	1.13031i	−0.329907	−	0.944013i	$-0.607017\pi$
$439$	13.6732	−	23.6827i	0.652586	−	1.13031i	0.982493	−	0.186299i	$-0.0596493\pi$
$440$	−9.81848	+	30.7691i	−0.468078	+	1.46686i
$441$		0			0
$442$	−11.6341	−	8.42144i	−0.553376	−	0.400567i
$443$	20.2373	+	11.6840i	0.961502	+	0.555123i	0.896635	−	0.442770i	$-0.146004\pi$
$443$	20.2373	+	11.6840i	0.961502	+	0.555123i	0.0648670	+	0.997894i	$0.479338\pi$
$444$		0			0
$445$	−6.19982	−	10.7384i	−0.293900	−	0.509049i
$446$	−30.5648	+	13.6727i	−1.44729	+	0.647423i
$447$		0			0
$448$	−11.2546	+	17.9258i	−0.531728	+	0.846915i
$449$	18.8468			0.889436			0.444718	−	0.895671i	$-0.353304\pi$
$449$	18.8468			0.889436			0.444718	+	0.895671i	$0.353304\pi$
$450$		0			0
$451$	11.7289	+	20.3151i	0.552293	+	0.956599i
$452$	8.90353	−	9.95852i	0.418787	−	0.468410i
$453$		0			0
$454$	−1.90869	−	1.38162i	−0.0895790	−	0.0648428i
$455$	18.0304	+	9.07876i	0.845280	+	0.425619i
$456$		0			0
$457$	−3.63991	+	6.30451i	−0.170268	+	0.294913i	−0.938513	−	0.345243i	$-0.887797\pi$
$457$	−3.63991	+	6.30451i	−0.170268	+	0.294913i	0.768246	+	0.640155i	$0.221130\pi$
$458$	31.9735	+	3.30376i	1.49402	+	0.154374i
$459$		0			0
$460$	19.0581	+	3.98097i	0.888587	+	0.185614i
$461$			3.58604i			0.167019i	0.996507	+	0.0835093i	$0.0266128\pi$
$461$			3.58604i			0.167019i	−0.996507	+	0.0835093i	$0.973387\pi$
$462$		0			0
$463$		−	28.4541i		−	1.32237i	−0.750221	−	0.661187i	$-0.770053\pi$
$463$		−	28.4541i		−	1.32237i	0.750221	−	0.661187i	$-0.229947\pi$
$464$	3.60883	+	32.1597i	0.167536	+	1.49298i
$465$		0			0
$466$	0.215116	−	2.08187i	0.00996504	−	0.0964409i
$467$	12.4728	−	21.6035i	0.577173	−	0.999692i	−0.418629	−	0.908157i	$-0.637489\pi$
$467$	12.4728	−	21.6035i	0.577173	−	0.999692i	0.995802	−	0.0915351i	$-0.0291774\pi$
$468$		0			0
$469$	−13.5067	−	20.5826i	−0.623680	−	0.950415i
$470$	−1.31316	+	1.81411i	−0.0605716	+	0.0836784i
$471$		0			0
$472$	−34.4448	+	7.51146i	−1.58545	+	0.345743i
$473$	−2.43733	−	4.22157i	−0.112068	−	0.194108i
$474$		0			0
$475$	−0.548429			−0.0251637
$476$	−24.4261	−	3.66140i	−1.11957	−	0.167820i
$477$		0			0
$478$	−4.44291	−	9.93193i	−0.203214	−	0.454276i
$479$	−1.73949	−	3.01289i	−0.0794795	−	0.137662i	0.823546	−	0.567249i	$-0.191992\pi$
$479$	−1.73949	−	3.01289i	−0.0794795	−	0.137662i	−0.903025	+	0.429587i	$0.858659\pi$
$480$		0			0
$481$	19.1669	+	11.0660i	0.873934	+	0.504566i
$482$	1.41696	−	1.95750i	0.0645406	−	0.0891615i
$483$		0			0
$484$	0.248262	+	0.755034i	0.0112846	+	0.0343197i
$485$	−1.85032	+	3.20484i	−0.0840186	+	0.145524i
$486$		0			0
$487$	−13.5540	+	7.82541i	−0.614191	+	0.354603i	−0.774604	−	0.632447i	$-0.782051\pi$
$487$	−13.5540	+	7.82541i	−0.614191	+	0.354603i	0.160413	+	0.987050i	$0.448717\pi$
$488$	−30.7012	+	27.9379i	−1.38978	+	1.26469i
$489$		0			0
$490$	34.7141	−	0.392610i	1.56822	−	0.0177363i
$491$		−	2.07316i		−	0.0935606i	−0.998905	−	0.0467803i	$-0.985104\pi$
$491$		−	2.07316i		−	0.0935606i	0.998905	−	0.0467803i	$-0.0148961\pi$
$492$		0			0
$493$	−32.7039	+	18.8816i	−1.47291	+	0.850386i
$494$	0.229996	+	0.0237650i	0.0103480	+	0.00106924i
$495$		0			0
$496$	−23.5917	+	17.3951i	−1.05930	+	0.781061i
$497$	31.2691	−	1.78854i	1.40261	−	0.0802269i
$498$		0			0
$499$	4.85785	+	2.80468i	0.217467	+	0.125555i	0.604777	−	0.796395i	$-0.293262\pi$
$499$	4.85785	+	2.80468i	0.217467	+	0.125555i	−0.387310	+	0.921950i	$0.626596\pi$
$500$	12.0165	+	10.7434i	0.537393	+	0.480462i
$501$		0			0
$502$	20.0357	−	8.96267i	0.894235	−	0.400023i
$503$	−16.2015			−0.722390			−0.361195	−	0.932490i	$-0.617631\pi$
$503$	−16.2015			−0.722390			−0.361195	+	0.932490i	$0.617631\pi$
$504$		0			0
$505$	44.0262			1.95914
$506$	−11.6685	+	5.21972i	−0.518726	+	0.232045i
$507$		0			0
$508$	−0.354434	−	0.316885i	−0.0157255	−	0.0140595i
$509$	−21.5238	−	12.4268i	−0.954026	−	0.550807i	−0.0596966	−	0.998217i	$-0.519013\pi$
$509$	−21.5238	−	12.4268i	−0.954026	−	0.550807i	−0.894329	+	0.447409i	$0.852347\pi$
$510$		0			0
$511$	1.42944	+	2.17829i	0.0632346	+	0.0963620i
$512$	18.0934	−	13.5879i	0.799621	−	0.600505i
$513$		0			0
$514$	−18.3773	−	1.89889i	−0.810586	−	0.0837563i
$515$	−17.0324	+	9.83367i	−0.750538	+	0.433323i
$516$		0			0
$517$		−	1.47036i		−	0.0646662i
$518$	38.0209	+	1.74359i	1.67054	+	0.0766091i
$519$		0			0
$520$	−14.5248	−	15.9614i	−0.636956	−	0.699955i
$521$	−13.3491	+	7.70713i	−0.584837	+	0.337656i	−0.763053	−	0.646336i	$-0.776301\pi$
$521$	−13.3491	+	7.70713i	−0.584837	+	0.337656i	0.178217	+	0.983991i	$0.442967\pi$
$522$		0			0
$523$	−7.33526	+	12.7050i	−0.320748	+	0.555553i	−0.980643	−	0.195806i	$-0.937268\pi$
$523$	−7.33526	+	12.7050i	−0.320748	+	0.555553i	0.659894	+	0.751358i	$0.270601\pi$
$524$	6.15961	+	18.7331i	0.269084	+	0.818358i
$525$		0			0
$526$	6.31077	−	8.71820i	0.275163	−	0.380132i
$527$	−29.6215	−	17.1020i	−1.29033	−	0.744974i
$528$		0			0
$529$	−7.64721	−	13.2454i	−0.332487	−	0.575885i
$530$	6.86376	+	15.3436i	0.298143	+	0.666485i
$531$		0			0
$532$	0.370031	−	0.145572i	0.0160429	−	0.00631137i
$533$	−15.6742			−0.678927
$534$		0			0
$535$	−32.0710	−	55.5486i	−1.38655	−	2.40158i
$536$	5.60751	+	25.7140i	0.242208	+	1.11068i
$537$		0			0
$538$	13.6185	−	18.8137i	0.587134	−	0.811114i
$539$	−18.3112	+	13.5730i	−0.788720	+	0.584631i
$540$		0			0
$541$	−9.68184	+	16.7694i	−0.416255	+	0.720975i	−0.995559	−	0.0941366i	$-0.969991\pi$
$541$	−9.68184	+	16.7694i	−0.416255	+	0.720975i	0.579304	+	0.815111i	$0.303324\pi$
$542$	2.31199	−	22.3752i	0.0993084	−	0.961099i
$543$		0			0
$544$	22.9819	+	13.0007i	0.985341	+	0.557402i
$545$			52.1748i			2.23492i
$546$		0			0
$547$			15.2986i			0.654120i	0.945004	+	0.327060i	$0.106058\pi$
$547$			15.2986i			0.654120i	−0.945004	+	0.327060i	$0.893942\pi$
$548$	12.8256	+	2.67910i	0.547884	+	0.114445i
$549$		0			0
$550$	−33.4295	−	3.45420i	−1.42544	−	0.147288i
$551$	0.303981	−	0.526510i	0.0129500	−	0.0224301i
$552$		0			0
$553$	−4.25521	+	8.45086i	−0.180950	+	0.359367i
$554$	34.1720	+	24.7358i	1.45183	+	1.05092i
$555$		0			0
$556$	−7.06773	+	7.90520i	−0.299738	+	0.335255i
$557$	−3.01197	−	5.21688i	−0.127621	−	0.221046i	0.795133	−	0.606435i	$-0.207401\pi$
$557$	−3.01197	−	5.21688i	−0.127621	−	0.221046i	−0.922754	+	0.385388i	$0.874067\pi$
$558$		0			0
$559$	3.25719			0.137764
$560$	−34.8028	−	12.8903i	−1.47069	−	0.544714i
$561$		0			0
$562$	16.2803	−	7.28277i	0.686744	−	0.307205i
$563$	−7.04736	−	12.2064i	−0.297011	−	0.514438i	0.678440	−	0.734656i	$-0.262656\pi$
$563$	−7.04736	−	12.2064i	−0.297011	−	0.514438i	−0.975451	+	0.220218i	$0.929323\pi$
$564$		0			0
$565$	20.2849	+	11.7115i	0.853393	+	0.492706i
$566$	−9.17910	−	6.64439i	−0.385826	−	0.279285i
$567$		0			0
$568$	−31.8981	−	10.1787i	−1.33841	−	0.427090i
$569$	8.82158	−	15.2794i	0.369820	−	0.640547i	−0.619717	−	0.784825i	$-0.712753\pi$
$569$	8.82158	−	15.2794i	0.369820	−	0.640547i	0.989537	+	0.144278i	$0.0460861\pi$
$570$		0			0
$571$	−22.3514	+	12.9046i	−0.935378	+	0.540041i	−0.888508	−	0.458860i	$-0.848258\pi$
$571$	−22.3514	+	12.9046i	−0.935378	+	0.540041i	−0.0468695	+	0.998901i	$0.514924\pi$
$572$	13.8697	+	2.89719i	0.579922	+	0.121138i
$573$		0			0
$574$	−23.9369	+	12.3941i	−0.999109	+	0.517321i
$575$			20.2589i			0.844857i
$576$		0			0
$577$	5.08344	−	2.93493i	0.211626	−	0.122183i	−0.390441	−	0.920628i	$-0.627677\pi$
$577$	5.08344	−	2.93493i	0.211626	−	0.122183i	0.602067	+	0.798446i	$0.294344\pi$
$578$	−0.695824	+	6.73412i	−0.0289425	+	0.280103i
$579$		0			0
$580$	−53.9048	+	17.7244i	−2.23828	+	0.735966i
$581$	0.0529298	+	0.925375i	0.00219590	+	0.0383910i
$582$		0			0
$583$	−9.55742	−	5.51798i	−0.395828	−	0.228531i
$584$	−0.593454	−	2.72136i	−0.0245573	−	0.112611i
$585$		0			0
$586$	9.75239	+	21.8011i	0.402868	+	0.900593i
$587$	−1.21088			−0.0499786			−0.0249893	−	0.999688i	$-0.507955\pi$
$587$	−1.21088			−0.0499786			−0.0249893	+	0.999688i	$0.507955\pi$
$588$		0			0
$589$	0.550659			0.0226895
$590$	−25.2421	−	56.4277i	−1.03920	−	2.32309i
$591$		0			0
$592$	−37.2865	−	16.2880i	−1.53246	−	0.669431i
$593$	−5.75014	−	3.31984i	−0.236130	−	0.136330i	0.377267	−	0.926105i	$-0.376864\pi$
$593$	−5.75014	−	3.31984i	−0.236130	−	0.136330i	−0.613397	+	0.789775i	$0.710197\pi$
$594$		0			0
$595$	−2.47310	−	43.2374i	−0.101387	−	1.77256i
$596$	0.241078	+	0.733183i	0.00987492	+	0.0300324i
$597$		0			0
$598$	0.877880	−	8.49605i	0.0358992	−	0.347429i
$599$	−36.2905	+	20.9523i	−1.48279	+	0.856089i	−0.999809	−	0.0195424i	$-0.993779\pi$
$599$	−36.2905	+	20.9523i	−1.48279	+	0.856089i	−0.482980	+	0.875631i	$0.660446\pi$
$600$		0			0
$601$		−	3.27647i		−	0.133650i	−0.997765	−	0.0668250i	$-0.978713\pi$
$601$		−	3.27647i		−	0.133650i	0.997765	−	0.0668250i	$-0.0212869\pi$
$602$	4.97422	−	2.57556i	0.202734	−	0.104972i
$603$		0			0
$604$	−7.03778	+	33.6919i	−0.286363	+	1.37090i
$605$	−1.20692	+	0.696818i	−0.0490685	+	0.0283297i
$606$		0			0
$607$	0.148269	−	0.256810i	0.00601806	−	0.0104236i	−0.863001	−	0.505203i	$-0.831418\pi$
$607$	0.148269	−	0.256810i	0.00601806	−	0.0104236i	0.869019	+	0.494779i	$0.164751\pi$
$608$	−0.425074	+	0.00373461i	−0.0172390	+	0.000151459i
$609$		0			0
$610$	−58.9597	−	42.6787i	−2.38721	−	1.72801i
$611$	0.850848	+	0.491238i	0.0344216	+	0.0198733i
$612$		0			0
$613$	3.32452	+	5.75823i	0.134276	+	0.232573i	0.925321	−	0.379186i	$-0.123796\pi$
$613$	3.32452	+	5.75823i	0.134276	+	0.232573i	−0.791045	+	0.611758i	$0.790462\pi$
$614$	−22.4476	+	10.0416i	−0.905910	+	0.405246i
$615$		0			0
$616$	23.4721	−	6.54278i	0.945716	−	0.263616i
$617$	0.955148			0.0384528			0.0192264	−	0.999815i	$-0.493880\pi$
$617$	0.955148			0.0384528			0.0192264	+	0.999815i	$0.493880\pi$
$618$		0			0
$619$	6.38442	+	11.0581i	0.256611	+	0.444464i	0.965332	−	0.261025i	$-0.0840606\pi$
$619$	6.38442	+	11.0581i	0.256611	+	0.444464i	−0.708721	+	0.705489i	$0.750727\pi$
$620$	−38.3151	−	34.2560i	−1.53877	−	1.37575i
$621$		0			0
$622$	9.90933	+	7.17298i	0.397328	+	0.287610i
$623$	−4.20716	+	8.35543i	−0.168556	+	0.334753i
$624$		0			0
$625$	4.11375	−	7.12522i	0.164550	−	0.285009i
$626$	−12.1769	−	1.25821i	−0.486687	−	0.0502884i
$627$		0			0
$628$	3.22965	−	15.4613i	0.128877	−	0.616972i
$629$		−	47.4804i		−	1.89317i
$630$		0			0
$631$			11.9142i			0.474298i	0.971473	+	0.237149i	$0.0762129\pi$
$631$			11.9142i			0.474298i	−0.971473	+	0.237149i	$0.923787\pi$
$632$	7.48111	−	6.80777i	0.297583	−	0.270799i
$633$		0			0
$634$	1.06352	−	10.2927i	0.0422379	−	0.408774i
$635$	0.416824	−	0.721961i	0.0165412	−	0.0286501i
$636$		0			0
$637$	−1.73659	−	15.1308i	−0.0688063	−	0.599504i
$638$	21.8453	−	30.1788i	0.864863	−	1.19479i
$639$		0			0
$640$	29.8091	+	26.1836i	1.17831	+	1.03500i
$641$	0.801420	+	1.38810i	0.0316542	+	0.0548266i	0.881419	−	0.472336i	$-0.156589\pi$
$641$	0.801420	+	1.38810i	0.0316542	+	0.0548266i	−0.849764	+	0.527163i	$0.823256\pi$
$642$		0			0
$643$	20.7304			0.817525			0.408763	−	0.912641i	$-0.365960\pi$
$643$	20.7304			0.817525			0.408763	+	0.912641i	$0.365960\pi$
$644$	−5.37744	−	13.6689i	−0.211901	−	0.538631i
$645$		0			0
$646$	−0.202556	−	0.452804i	−0.00796944	−	0.0178153i
$647$	7.97304	+	13.8097i	0.313452	+	0.542916i	0.979107	−	0.203344i	$-0.0651810\pi$
$647$	7.97304	+	13.8097i	0.313452	+	0.542916i	−0.665655	+	0.746260i	$0.731848\pi$
$648$		0			0
$649$	35.1483	+	20.2929i	1.37969	+	0.796565i
$650$	13.1674	−	18.1906i	0.516469	−	0.713492i
$651$		0			0
$652$	−46.3888	+	15.2531i	−1.81673	+	0.597356i
$653$	−16.5069	+	28.5908i	−0.645966	+	1.11885i	0.338112	+	0.941106i	$0.390212\pi$
$653$	−16.5069	+	28.5908i	−0.645966	+	1.11885i	−0.984078	+	0.177740i	$0.943122\pi$
$654$		0			0
$655$	−29.9449	+	17.2887i	−1.17004	+	0.675525i
$656$	28.6368	−	3.21349i	1.11808	−	0.125466i
$657$		0			0
$658$	1.68781	+	0.0774009i	0.0657977	+	0.00301740i
$659$			34.3288i			1.33726i	0.743595	+	0.668630i	$0.233119\pi$
$659$			34.3288i			1.33726i	−0.743595	+	0.668630i	$0.766881\pi$
$660$		0			0
$661$	−1.72551	+	0.996223i	−0.0671145	+	0.0387486i	−0.533182	−	0.846001i	$-0.679004\pi$
$661$	−1.72551	+	0.996223i	−0.0671145	+	0.0387486i	0.466067	+	0.884749i	$0.345670\pi$
$662$	21.3694	+	2.20805i	0.830544	+	0.0858185i
$663$		0			0
$664$	0.301228	−	0.943988i	0.0116899	−	0.0366339i
$665$	0.382527	+	0.582925i	0.0148338	+	0.0226049i
$666$		0			0
$667$	−19.4493	−	11.2290i	−0.753078	−	0.434790i
$668$	−24.6907	+	27.6164i	−0.955313	+	1.06851i
$669$		0			0
$670$	−42.1248	+	18.8439i	−1.62742	+	0.728005i
$671$	47.7876			1.84482
$672$		0			0
$673$	21.6634			0.835063			0.417531	−	0.908663i	$-0.362895\pi$
$673$	21.6634			0.835063			0.417531	+	0.908663i	$0.362895\pi$
$674$	10.9245	−	4.88692i	0.420796	−	0.188237i
$675$		0			0
$676$	11.0191	−	12.3248i	0.423811	−	0.474029i
$677$	−18.4674	−	10.6622i	−0.709760	−	0.409780i	0.101212	−	0.994865i	$-0.467728\pi$
$677$	−18.4674	−	10.6622i	−0.709760	−	0.409780i	−0.810972	+	0.585085i	$0.801061\pi$
$678$		0			0
$679$	2.78738	−	0.159433i	0.106970	−	0.00611848i
$680$	−14.0747	+	44.1071i	−0.539738	+	1.69143i
$681$		0			0
$682$	33.5654	+	3.46825i	1.28529	+	0.132806i
$683$	24.6393	−	14.2255i	0.942798	−	0.544325i	0.0519619	−	0.998649i	$-0.483453\pi$
$683$	24.6393	−	14.2255i	0.942798	−	0.544325i	0.890836	+	0.454324i	$0.150119\pi$
$684$		0			0
$685$			22.9744i			0.877805i
$686$	−14.6164	−	21.7338i	−0.558058	−	0.829802i
$687$		0			0
$688$	−5.95087	+	0.667781i	−0.226875	+	0.0254589i
$689$	6.38616	−	3.68705i	0.243293	−	0.140465i
$690$		0			0
$691$	21.4507	−	37.1536i	0.816022	−	1.41339i	−0.0925703	−	0.995706i	$-0.529508\pi$
$691$	21.4507	−	37.1536i	0.816022	−	1.41339i	0.908592	−	0.417685i	$-0.137158\pi$
$692$	−28.6311	+	9.41419i	−1.08839	+	0.357874i
$693$		0			0
$694$	17.9901	−	24.8529i	0.682893	−	0.943404i
$695$	−16.1024	−	9.29673i	−0.610799	−	0.352645i
$696$		0			0
$697$	16.8132	+	29.1214i	0.636846	+	1.10305i
$698$	19.9439	+	44.5837i	0.754887	+	1.68752i
$699$		0			0
$700$	5.72482	−	38.1916i	0.216378	−	1.44351i
$701$	−29.6874			−1.12128			−0.560639	−	0.828061i	$-0.689444\pi$
$701$	−29.6874			−1.12128			−0.560639	+	0.828061i	$0.689444\pi$
$702$		0			0
$703$	0.382200	+	0.661991i	0.0144150	+	0.0249674i
$704$	−25.9339	−	2.44962i	−0.977420	−	0.0923236i
$705$		0			0
$706$	7.59749	−	10.4958i	0.285935	−	0.395014i
$707$	−18.2233	−	27.7701i	−0.685356	−	1.04440i
$708$		0			0
$709$	10.3262	−	17.8854i	0.387807	−	0.671702i	−0.604347	−	0.796721i	$-0.706566\pi$
$709$	10.3262	−	17.8854i	0.387807	−	0.671702i	0.992154	+	0.125019i	$0.0398993\pi$
$710$	6.03425	−	58.3990i	0.226461	−	2.19167i
$711$		0			0
$712$	7.39664	−	6.73091i	0.277201	−	0.252251i
$713$		−	20.3413i		−	0.761789i
$714$		0			0
$715$			24.8446i			0.929135i
$716$	2.54101	−	12.1646i	0.0949622	−	0.454612i
$717$		0			0
$718$	−22.2393	−	2.29794i	−0.829963	−	0.0857585i
$719$	−20.9300	+	36.2519i	−0.780559	+	1.35197i	0.151058	+	0.988525i	$0.451732\pi$
$719$	−20.9300	+	36.2519i	−0.780559	+	1.35197i	−0.931617	+	0.363443i	$0.881601\pi$
$720$		0			0
$721$	13.2527	+	6.67307i	0.493558	+	0.248518i
$722$	−21.7596	−	15.7509i	−0.809808	−	0.586189i
$723$		0			0
$724$	−18.0806	−	16.1652i	−0.671961	−	0.600774i
$725$	−29.5226	−	51.1346i	−1.09644	−	1.89909i
$726$		0			0
$727$	32.7901			1.21612			0.608059	−	0.793892i	$-0.291949\pi$
$727$	32.7901			1.21612			0.608059	+	0.793892i	$0.291949\pi$
$728$	−4.05579	+	15.7684i	−0.150317	+	0.584418i
$729$		0			0
$730$	4.45815	−	1.99429i	0.165004	−	0.0738120i
$731$	−3.49388	−	6.05157i	−0.129226	−	0.223825i
$732$		0			0
$733$	27.1489	+	15.6744i	1.00277	+	0.578948i	0.909066	−	0.416652i	$-0.136797\pi$
$733$	27.1489	+	15.6744i	1.00277	+	0.578948i	0.0937014	+	0.995600i	$0.470130\pi$
$734$	0.737576	+	0.533903i	0.0272244	+	0.0197067i
$735$		0			0
$736$	0.137956	+	15.7022i	0.00508514	+	0.578791i
$737$	15.1492	−	26.2392i	0.558028	−	0.966532i
$738$		0			0
$739$	26.6466	−	15.3844i	0.980211	−	0.565925i	0.0778770	−	0.996963i	$-0.475186\pi$
$739$	26.6466	−	15.3844i	0.980211	−	0.565925i	0.902334	+	0.431038i	$0.141853\pi$
$740$	14.5882	−	69.8379i	0.536272	−	2.56729i
$741$		0			0
$742$	6.83716	−	10.6804i	0.251000	−	0.392091i
$743$			24.1452i			0.885801i	0.896571	+	0.442901i	$0.146051\pi$
$743$			24.1452i			0.885801i	−0.896571	+	0.442901i	$0.853949\pi$
$744$		0			0
$745$	−1.17200	+	0.676652i	−0.0429386	+	0.0247906i
$746$	4.20581	−	40.7035i	0.153986	−	1.49026i
$747$		0			0
$748$	−9.49484	−	28.8764i	−0.347166	−	1.05583i
$749$	−21.7632	+	43.2218i	−0.795210	+	1.57929i
$750$		0			0
$751$	32.7871	+	18.9297i	1.19642	+	0.690753i	0.959755	−	0.280838i	$-0.0906124\pi$
$751$	32.7871	+	18.9297i	1.19642	+	0.690753i	0.236665	+	0.971591i	$0.423946\pi$
$752$	−1.65521	−	0.723050i	−0.0603592	−	0.0263669i
$753$		0			0
$754$	10.1651	+	22.7237i	0.370193	+	0.827550i
$755$	−60.3518			−2.19643
$756$		0			0
$757$	−22.5471			−0.819489			−0.409744	−	0.912200i	$-0.634382\pi$
$757$	−22.5471			−0.819489			−0.409744	+	0.912200i	$0.634382\pi$
$758$	−11.9056	−	26.6144i	−0.432430	−	0.966679i
$759$		0			0
$760$	−0.158812	−	0.728254i	−0.00576072	−	0.0264166i
$761$	12.8446	+	7.41584i	0.465617	+	0.268824i	0.714403	−	0.699734i	$-0.246698\pi$
$761$	12.8446	+	7.41584i	0.465617	+	0.268824i	−0.248786	+	0.968558i	$0.580032\pi$
$762$		0			0
$763$	32.9099	−	21.5961i	1.19142	−	0.781832i
$764$	−16.9303	+	5.56684i	−0.612516	+	0.201401i
$765$		0			0
$766$	−3.24639	+	31.4183i	−0.117297	+	1.13519i
$767$	−23.4857	+	13.5595i	−0.848019	+	0.489604i
$768$		0			0
$769$		−	41.7367i		−	1.50506i	−0.658556	−	0.752532i	$-0.728833\pi$
$769$		−	41.7367i		−	1.50506i	0.658556	−	0.752532i	$-0.271167\pi$
$770$	19.6454	+	37.9415i	0.707972	+	1.36732i
$771$		0			0
$772$	5.93361	+	1.23945i	0.213555	+	0.0446088i
$773$	−17.7798	+	10.2652i	−0.639497	+	0.369214i	−0.784421	−	0.620229i	$-0.787040\pi$
$773$	−17.7798	+	10.2652i	−0.639497	+	0.369214i	0.144924	+	0.989443i	$0.453706\pi$
$774$		0			0
$775$	26.7400	−	46.3150i	0.960528	−	1.66368i
$776$	−2.84344	−	0.907347i	−0.102074	−	0.0325719i
$777$		0			0
$778$	0.715882	+	0.518199i	0.0256656	+	0.0185784i
$779$	−0.468833	−	0.270681i	−0.0167977	−	0.00969815i
$780$		0			0
$781$	19.2731	+	33.3820i	0.689646	+	1.19450i
$782$	−16.7266	+	7.48239i	−0.598141	+	0.267570i
$783$		0			0
$784$	6.27482	+	27.2878i	0.224101	+	0.974566i
$785$	27.6955			0.988495
$786$		0			0
$787$	4.37470	+	7.57720i	0.155941	+	0.270098i	0.933401	−	0.358834i	$-0.116826\pi$
$787$	4.37470	+	7.57720i	0.155941	+	0.270098i	−0.777460	+	0.628932i	$0.783492\pi$
$788$	−23.3374	+	26.1027i	−0.831361	+	0.929871i
$789$		0			0
$790$	14.3670	+	10.3997i	0.511155	+	0.370006i
$791$	−1.00912	−	17.6426i	−0.0358803	−	0.627298i
$792$		0			0
$793$	−15.9656	+	27.6532i	−0.566954	+	0.981993i
$794$	−23.4697	−	2.42508i	−0.832908	−	0.0860628i
$795$		0			0
$796$	−35.7285	−	7.46319i	−1.26636	−	0.264526i
$797$			11.5319i			0.408480i	0.978921	+	0.204240i	$0.0654722\pi$
$797$			11.5319i			0.408480i	−0.978921	+	0.204240i	$0.934528\pi$
$798$		0			0
$799$		−	2.10773i		−	0.0745663i
$800$	−20.3275	+	35.9336i	−0.718684	+	1.27044i
$801$		0			0
$802$	0.986520	−	9.54746i	0.0348352	−	0.337132i
$803$	−1.60327	+	2.77694i	−0.0565781	+	0.0979961i
$804$		0			0
$805$	21.5332	−	14.1305i	0.758947	−	0.498035i
$806$	−13.2210	+	18.2645i	−0.465689	+	0.643340i
$807$		0			0
$808$	7.56568	+	34.6934i	0.266160	+	1.22051i
$809$	17.0250	+	29.4882i	0.598567	+	1.03675i	0.993033	+	0.117838i	$0.0375965\pi$
$809$	17.0250	+	29.4882i	0.598567	+	1.03675i	−0.394465	+	0.918911i	$0.629070\pi$
$810$		0			0
$811$	−9.87280			−0.346681			−0.173340	−	0.984862i	$-0.555456\pi$
$811$	−9.87280			−0.346681			−0.173340	+	0.984862i	$0.555456\pi$
$812$	33.4921	+	26.6647i	1.17534	+	0.935747i
$813$		0			0
$814$	19.1275	+	42.7588i	0.670420	+	1.49870i
$815$	−42.8120	−	74.1526i	−1.49964	−	2.59745i
$816$		0			0
$817$	0.0974259	+	0.0562489i	0.00340850	+	0.00196790i
$818$	0.551679	−	0.762133i	0.0192890	−	0.0266474i
$819$		0			0
$820$	15.7828	+	47.9998i	0.551158	+	1.67622i
$821$	22.1782	−	38.4138i	0.774024	−	1.34065i	−0.161317	−	0.986903i	$-0.551574\pi$
$821$	22.1782	−	38.4138i	0.774024	−	1.34065i	0.935341	−	0.353747i	$-0.115092\pi$
$822$		0			0
$823$	23.6005	−	13.6257i	0.822660	−	0.474963i	−0.0286727	−	0.999589i	$-0.509128\pi$
$823$	23.6005	−	13.6257i	0.822660	−	0.474963i	0.851333	+	0.524626i	$0.175795\pi$
$824$	−10.6760	−	11.7320i	−0.371917	−	0.408703i
$825$		0			0
$826$	−25.1443	+	39.2783i	−0.874882	+	1.36667i
$827$		−	31.6550i		−	1.10075i	−0.834917	−	0.550376i	$-0.814485\pi$
$827$		−	31.6550i		−	1.10075i	0.834917	−	0.550376i	$-0.185515\pi$
$828$		0			0
$829$	24.5060	−	14.1485i	0.851128	−	0.491399i	−0.00990312	−	0.999951i	$-0.503152\pi$
$829$	24.5060	−	14.1485i	0.851128	−	0.491399i	0.861031	+	0.508552i	$0.169819\pi$
$830$	1.72825	+	0.178577i	0.0599886	+	0.00619850i
$831$		0			0
$832$	10.0819	−	14.1887i	0.349526	−	0.491905i
$833$	−26.2489	+	19.4567i	−0.909470	+	0.674135i
$834$		0			0
$835$	−56.2529	−	32.4777i	−1.94671	−	1.12394i
$836$	0.364825	+	0.326176i	0.0126178	+	0.0112810i
$837$		0			0
$838$	−44.3555	+	19.8418i	−1.53224	+	0.685424i
$839$	20.6201			0.711884			0.355942	−	0.934508i	$-0.384160\pi$
$839$	20.6201			0.711884			0.355942	+	0.934508i	$0.384160\pi$
$840$		0			0
$841$	36.4545			1.25705
$842$	40.2654	−	18.0122i	1.38764	−	0.620740i
$843$		0			0
$844$	31.0850	+	27.7919i	1.06999	+	0.956635i
$845$	25.1048	+	14.4942i	0.863631	+	0.498617i
$846$		0			0
$847$	0.939095	+	0.472857i	0.0322677	+	0.0162476i
$848$	−10.9116	+	8.04550i	−0.374705	+	0.276283i
$849$		0			0
$850$	−47.9207	−	4.95155i	−1.64367	−	0.169837i
$851$	24.4539	−	14.1185i	0.838269	−	0.483975i
$852$		0			0
$853$			15.1322i			0.518116i	0.965862	+	0.259058i	$0.0834121\pi$
$853$			15.1322i			0.518116i	−0.965862	+	0.259058i	$0.916588\pi$
$854$	−2.51559	+	54.8551i	−0.0860816	+	1.87710i
$855$		0			0
$856$	38.2621	−	34.8183i	1.30777	−	1.19006i
$857$	16.9075	−	9.76153i	0.577548	−	0.333447i	−0.182610	−	0.983185i	$-0.558455\pi$
$857$	16.9075	−	9.76153i	0.577548	−	0.333447i	0.760158	+	0.649738i	$0.225121\pi$
$858$		0			0
$859$	−28.4937	+	49.3526i	−0.972193	+	1.68389i	−0.283290	+	0.959034i	$0.591426\pi$
$859$	−28.4937	+	49.3526i	−0.972193	+	1.68389i	−0.688903	+	0.724854i	$0.741907\pi$
$860$	−3.27974	−	9.97460i	−0.111838	−	0.340131i
$861$		0			0
$862$	−5.03606	+	6.95721i	−0.171529	+	0.236964i
$863$	−27.0749	−	15.6317i	−0.921640	−	0.532109i	−0.0374820	−	0.999297i	$-0.511934\pi$
$863$	−27.0749	−	15.6317i	−0.921640	−	0.532109i	−0.884158	+	0.467188i	$0.845267\pi$
$864$		0			0
$865$	−26.4236	−	45.7670i	−0.898429	−	1.55612i
$866$	5.52174	+	12.3436i	0.187636	+	0.419453i
$867$		0			0
$868$	−5.74809	+	38.3469i	−0.195103	+	1.30158i
$869$	−11.6446			−0.395018
$870$		0			0
$871$	10.1225	+	17.5327i	0.342989	+	0.594074i
$872$	−41.1147	+	8.96597i	−1.39232	+	0.303626i
$873$		0			0
$874$	0.172978	−	0.238965i	0.00585106	−	0.00808312i
$875$	21.2884	−	1.21766i	0.719680	−	0.0411644i
$876$		0			0
$877$	−17.9419	+	31.0762i	−0.605853	+	1.04937i	0.386063	+	0.922473i	$0.373835\pi$
$877$	−17.9419	+	31.0762i	−0.605853	+	1.04937i	−0.991916	+	0.126896i	$0.959498\pi$
$878$	−3.97491	+	38.4688i	−0.134147	+	1.29826i
$879$		0			0
$880$	−5.09358	−	45.3909i	−0.171704	−	1.53013i
$881$			10.6024i			0.357203i	0.983921	+	0.178601i	$0.0571573\pi$
$881$			10.6024i			0.357203i	−0.983921	+	0.178601i	$0.942843\pi$
$882$		0			0
$883$			7.32656i			0.246558i	0.992372	+	0.123279i	$0.0393410\pi$
$883$			7.32656i			0.246558i	−0.992372	+	0.123279i	$0.960659\pi$
$884$	19.8820	+	4.15309i	0.668706	+	0.139683i
$885$		0			0
$886$	−32.8723	−	3.39663i	−1.10437	−	0.114112i
$887$	−1.07737	+	1.86607i	−0.0361747	+	0.0626564i	−0.883546	−	0.468345i	$-0.844851\pi$
$887$	−1.07737	+	1.86607i	−0.0361747	+	0.0626564i	0.847371	+	0.531001i	$0.178184\pi$
$888$		0			0
$889$	−0.627917	+	0.0359157i	−0.0210597	+	0.00120458i
$890$	14.2048	+	10.2823i	0.476146	+	0.344663i
$891$		0			0
$892$	31.5615	−	35.3013i	1.05676	−	1.18197i
$893$	0.0169665	+	0.0293868i	0.000567762	+	0.000983393i
$894$		0			0
$895$	21.7902			0.728367
$896$	4.17709	−	29.6404i	0.139547	−	0.990215i
$897$		0			0
$898$	−24.3300	+	10.8837i	−0.811904	+	0.363193i
$899$	29.6426	+	51.3425i	0.988637	+	1.71237i
$900$		0			0
$901$	−13.7004	−	7.90994i	−0.456427	−	0.263518i
$902$	−26.8728	−	19.4522i	−0.894768	−	0.647688i
$903$		0			0
$904$	−5.74301	+	17.9974i	−0.191010	+	0.598586i
$905$	21.2633	−	36.8291i	0.706816	−	1.22424i
$906$		0			0
$907$	33.8453	−	19.5406i	1.12381	−	0.648834i	0.181441	−	0.983402i	$-0.441924\pi$
$907$	33.8453	−	19.5406i	1.12381	−	0.648834i	0.942372	+	0.334568i	$0.108590\pi$
$908$	3.26185	+	0.681356i	0.108248	+	0.0226116i
$909$		0			0
$910$	−28.5190	−	1.30784i	−0.945394	−	0.0433546i
$911$			46.5980i			1.54386i	0.635708	+	0.771930i	$0.280708\pi$
$911$			46.5980i			1.54386i	−0.635708	+	0.771930i	$0.719292\pi$
$912$		0			0
$913$	−0.987905	+	0.570367i	−0.0326949	+	0.0188764i
$914$	1.05815	−	10.2407i	0.0350005	−	0.338732i
$915$		0			0
$916$	−43.1836	+	14.1992i	−1.42683	+	0.469154i
$917$	23.2998	+	11.7320i	0.769427	+	0.387425i
$918$		0			0
$919$	−21.4307	−	12.3730i	−0.706932	−	0.408148i	0.102992	−	0.994682i	$-0.467158\pi$
$919$	−21.4307	−	12.3730i	−0.706932	−	0.408148i	−0.809924	+	0.586535i	$0.800492\pi$
$920$	−26.9017	+	5.86651i	−0.886922	+	0.193413i
$921$		0			0
$922$	−2.07087	−	4.62935i	−0.0682006	−	0.152459i
$923$	−25.7562			−0.847775
$924$		0			0
$925$	74.2385			2.44095
$926$	16.4317	+	36.7324i	0.539980	+	1.20710i
$927$		0			0
$928$	−23.2304	−	39.4321i	−0.762576	−	1.29442i
$929$	28.3285	+	16.3555i	0.929429	+	0.536606i	0.886631	−	0.462478i	$-0.153040\pi$
$929$	28.3285	+	16.3555i	0.929429	+	0.536606i	0.0427979	+	0.999084i	$0.486373\pi$
$930$		0			0
$931$	0.209353	−	0.482567i	0.00686125	−	0.0158155i
$932$	0.924542	+	2.81179i	0.0302844	+	0.0921032i
$933$		0			0
$934$	−3.62595	+	35.0916i	−0.118645	+	1.14823i
$935$	46.1590	−	26.6499i	1.50956	−	0.871546i
$936$		0			0
$937$			13.6897i			0.447223i	0.974678	+	0.223611i	$0.0717846\pi$
$937$			13.6897i			0.447223i	−0.974678	+	0.223611i	$0.928215\pi$
$938$	29.3223	+	18.7709i	0.957407	+	0.612892i
$939$		0			0
$940$	0.647593	−	3.10022i	0.0211222	−	0.101118i
$941$	−4.94838	+	2.85695i	−0.161313	+	0.0931338i	−0.578483	−	0.815694i	$-0.696355\pi$
$941$	−4.94838	+	2.85695i	−0.161313	+	0.0931338i	0.417171	+	0.908828i	$0.363022\pi$
$942$		0			0
$943$	−9.99894	+	17.3187i	−0.325610	+	0.563973i
$944$	40.1283	−	29.5881i	1.30607	−	0.963009i
$945$		0			0
$946$	5.58432	+	4.04227i	0.181562	+	0.131426i
$947$	2.09868	+	1.21167i	0.0681980	+	0.0393741i	0.533711	−	0.845667i	$-0.320797\pi$
$947$	2.09868	+	1.21167i	0.0681980	+	0.0393741i	−0.465513	+	0.885041i	$0.654130\pi$
$948$		0			0
$949$	−1.07129	−	1.85552i	−0.0347754	−	0.0602328i
$950$	0.707987	−	0.316708i	0.0229701	−	0.0102754i
$951$		0			0
$952$	33.6469	−	9.37898i	1.09050	−	0.303975i
$953$	56.4286			1.82790			0.913950	−	0.405827i	$-0.133016\pi$
$953$	56.4286			1.82790			0.913950	+	0.405827i	$0.133016\pi$
$954$		0			0
$955$	−15.6249	−	27.0631i	−0.505610	−	0.875742i
$956$	11.4710	+	10.2558i	0.370999	+	0.331696i
$957$		0			0
$958$	3.98546	+	2.88492i	0.128764	+	0.0932076i
$959$	14.4914	−	9.50951i	0.467951	−	0.307078i
$960$		0			0
$961$	−11.3487	+	19.6565i	−0.366087	+	0.634082i
$962$	−31.1336	−	3.21697i	−1.00379	−	0.103719i
$963$		0			0
$964$	−0.698781	+	3.34527i	−0.0225062	+	0.107744i
$965$			10.6288i			0.342152i
$966$		0			0
$967$		−	10.0918i		−	0.324531i	−0.986747	−	0.162265i	$-0.948120\pi$
$967$		−	10.0918i		−	0.324531i	0.986747	−	0.162265i	$-0.0518801\pi$
$968$	−0.756509	−	0.831333i	−0.0243151	−	0.0267201i
$969$		0			0
$970$	0.537902	−	5.20577i	0.0172710	−	0.167147i
$971$	0.0300724	−	0.0520869i	0.000965069	−	0.00167155i	−0.865542	−	0.500836i	$-0.833026\pi$
$971$	0.0300724	−	0.0520869i	0.000965069	−	0.00167155i	0.866508	+	0.499164i	$0.166359\pi$
$972$		0			0
$973$	0.801055	+	14.0049i	0.0256806	+	0.448976i
$974$	12.9783	−	17.9293i	0.415852	−	0.574492i
$975$		0			0
$976$	23.4996	−	53.7954i	0.752205	−	1.72195i
$977$	−26.7586	−	46.3473i	−0.856084	−	1.48278i	−0.875636	−	0.482971i	$-0.839557\pi$
$977$	−26.7586	−	46.3473i	−0.856084	−	1.48278i	0.0195525	−	0.999809i	$-0.493776\pi$
$978$		0			0
$979$	−11.5132			−0.367962
$980$	−44.5869	+	20.5536i	−1.42428	+	0.656560i
$981$		0			0
$982$	1.19721	+	2.67632i	0.0382046	+	0.0854048i
$983$	22.7855	+	39.4657i	0.726745	+	1.25876i	0.958252	+	0.285926i	$0.0923011\pi$
$983$	22.7855	+	39.4657i	0.726745	+	1.25876i	−0.231507	+	0.972833i	$0.574366\pi$
$984$		0			0
$985$	−53.1697	−	30.6975i	−1.69413	−	0.978104i
$986$	31.3149	−	43.2609i	0.997269	−	1.37771i
$987$		0			0
$988$	−0.310634	+	0.102139i	−0.00988259	+	0.00324949i
$989$	2.07783	−	3.59891i	0.0660712	−	0.114439i
$990$		0			0
$991$	−27.2624	+	15.7399i	−0.866018	+	0.499996i	−0.866023	−	0.500004i	$-0.833332\pi$
$991$	−27.2624	+	15.7399i	−0.866018	+	0.499996i	4.71668e−6		1.00000i	$0.499998\pi$
$992$	20.4101	−	36.0797i	0.648021	−	1.14553i
$993$		0			0
$994$	−39.3336	+	20.3662i	−1.24758	+	0.645978i
$995$		−	63.9999i		−	2.02893i
$996$		0			0
$997$	41.7278	−	24.0916i	1.32153	−	0.762988i	0.337561	−	0.941304i	$-0.390398\pi$
$997$	41.7278	−	24.0916i	1.32153	−	0.762988i	0.983973	+	0.178316i	$0.0570649\pi$
$998$	−7.89082	−	0.815343i	−0.249779	−	0.0258092i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bf.c.271.3	yes	32
3.2	odd	2		756.2.bf.b.271.14	yes	32
4.3	odd	2		756.2.bf.b.271.9	✓	32
7.3	odd	6		756.2.bf.b.703.9	yes	32
12.11	even	2	inner	756.2.bf.c.271.8	yes	32
21.17	even	6	inner	756.2.bf.c.703.8	yes	32
28.3	even	6	inner	756.2.bf.c.703.3	yes	32
84.59	odd	6		756.2.bf.b.703.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.b.271.9	✓	32	4.3	odd	2
756.2.bf.b.271.14	yes	32	3.2	odd	2
756.2.bf.b.703.9	yes	32	7.3	odd	6
756.2.bf.b.703.14	yes	32	84.59	odd	6
756.2.bf.c.271.3	yes	32	1.1	even	1	trivial
756.2.bf.c.271.8	yes	32	12.11	even	2	inner
756.2.bf.c.703.3	yes	32	28.3	even	6	inner
756.2.bf.c.703.8	yes	32	21.17	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.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29094 + 0.577482i) q^{2} +(1.33303 - 1.49098i) q^{4} +(3.03704 + 1.75344i) q^{5} +(-0.151085 - 2.64143i) q^{7} +(-0.859840 + 2.69456i) q^{8} +O(q^{10})\)	\(q+(-1.29094 + 0.577482i) q^{2} +(1.33303 - 1.49098i) q^{4} +(3.03704 + 1.75344i) q^{5} +(-0.151085 - 2.64143i) q^{7} +(-0.859840 + 2.69456i) q^{8} +(-4.93321 - 0.509738i) q^{10} +(2.81992 - 1.62808i) q^{11} +2.17573i q^{13} +(1.72042 + 3.32267i) q^{14} +(-0.446063 - 3.97505i) q^{16} +(4.04232 - 2.33383i) q^{17} +(-0.0375730 + 0.0650784i) q^{19} +(6.66282 - 2.19080i) q^{20} +(-2.70015 + 3.73020i) q^{22} +(2.40399 + 1.38795i) q^{23} +(3.64909 + 6.32041i) q^{25} +(-1.25645 - 2.80873i) q^{26} +(-4.13974 - 3.29584i) q^{28} -8.09040 q^{29} +(-3.66393 - 6.34611i) q^{31} +(2.87136 + 4.87394i) q^{32} +(-3.87063 + 5.34719i) q^{34} +(4.17274 - 8.28707i) q^{35} +(5.08610 - 8.80938i) q^{37} +(0.0109228 - 0.105710i) q^{38} +(-7.33612 + 6.67583i) q^{40} +7.20413i q^{41} -1.49705i q^{43} +(1.33159 - 6.37474i) q^{44} +(-3.90491 - 0.403487i) q^{46} +(0.225780 - 0.391063i) q^{47} +(-6.95435 + 0.798164i) q^{49} +(-8.36066 - 6.05196i) q^{50} +(3.24398 + 2.90032i) q^{52} +(-1.69463 - 2.93518i) q^{53} +11.4190 q^{55} +(7.24742 + 1.86410i) q^{56} +(10.4442 - 4.67206i) q^{58} +(6.23214 + 10.7944i) q^{59} +(12.7098 + 7.33802i) q^{61} +(8.39465 + 6.07656i) q^{62} +(-6.52135 - 4.63379i) q^{64} +(-3.81501 + 6.60779i) q^{65} +(8.05831 - 4.65247i) q^{67} +(1.90882 - 9.13810i) q^{68} +(-0.601105 + 13.1078i) q^{70} +11.8379i q^{71} +(-0.852826 + 0.492379i) q^{73} +(-1.47857 + 14.3095i) q^{74} +(0.0469448 + 0.142772i) q^{76} +(-4.72652 - 7.20265i) q^{77} +(-3.09707 - 1.78809i) q^{79} +(5.61529 - 12.8545i) q^{80} +(-4.16025 - 9.30006i) q^{82} -0.350331 q^{83} +16.3689 q^{85} +(0.864522 + 1.93260i) q^{86} +(1.96229 + 8.99834i) q^{88} +(-3.06210 - 1.76790i) q^{89} +(5.74705 - 0.328721i) q^{91} +(5.27400 - 1.73414i) q^{92} +(-0.0656362 + 0.635221i) q^{94} +(-0.228222 + 0.131764i) q^{95} +1.05525i q^{97} +(8.51669 - 5.04639i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 6 q^{11} + 17 q^{14} - 4 q^{16} - 8 q^{20} + 2 q^{22} + 14 q^{25} - 15 q^{26} - 13 q^{28} - 15 q^{32} - 6 q^{35} + 4 q^{37} + q^{38} - 15 q^{40} + 42 q^{44} - 9 q^{46} + 4 q^{47} + 14 q^{49} - 9 q^{52} - 45 q^{56} + 10 q^{58} + 16 q^{59} - 42 q^{64} + 49 q^{68} - 33 q^{70} + 36 q^{73} + 54 q^{74} + 15 q^{80} - 51 q^{82} - 20 q^{83} + 16 q^{85} - 78 q^{86} - 2 q^{88} - 27 q^{94} - 24 q^{95} + 46 q^{98}+O(q^{100}) \) 32 * q + 6 * q^11 + 17 * q^14 - 4 * q^16 - 8 * q^20 + 2 * q^22 + 14 * q^25 - 15 * q^26 - 13 * q^28 - 15 * q^32 - 6 * q^35 + 4 * q^37 + q^38 - 15 * q^40 + 42 * q^44 - 9 * q^46 + 4 * q^47 + 14 * q^49 - 9 * q^52 - 45 * q^56 + 10 * q^58 + 16 * q^59 - 42 * q^64 + 49 * q^68 - 33 * q^70 + 36 * q^73 + 54 * q^74 + 15 * q^80 - 51 * q^82 - 20 * q^83 + 16 * q^85 - 78 * q^86 - 2 * q^88 - 27 * q^94 - 24 * q^95 + 46 * q^98

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