LMFDB - Embedded newform 756.2.bf.c.271.8

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			271.8
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.c.703.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.145354 - 1.40672i) q^{2} +(-1.95774 + 0.408946i) q^{4} +(-3.03704 - 1.75344i) q^{5} +(0.151085 + 2.64143i) q^{7} +(0.859840 + 2.69456i) q^{8} +O(q^{10})$	\(q+(-0.145354 - 1.40672i) q^{2} +(-1.95774 + 0.408946i) q^{4} +(-3.03704 - 1.75344i) q^{5} +(0.151085 + 2.64143i) q^{7} +(0.859840 + 2.69456i) q^{8} +(-2.02516 + 4.52715i) q^{10} +(2.81992 - 1.62808i) q^{11} +2.17573i q^{13} +(3.69381 - 0.596478i) q^{14} +(3.66553 - 1.60122i) q^{16} +(-4.04232 + 2.33383i) q^{17} +(0.0375730 - 0.0650784i) q^{19} +(6.66282 + 2.19080i) q^{20} +(-2.70015 - 3.73020i) q^{22} +(2.40399 + 1.38795i) q^{23} +(3.64909 + 6.32041i) q^{25} +(3.06065 - 0.316251i) q^{26} +(-1.37599 - 5.10947i) q^{28} +8.09040 q^{29} +(3.66393 + 6.34611i) q^{31} +(-2.78528 - 4.92364i) q^{32} +(3.87063 + 5.34719i) q^{34} +(4.17274 - 8.28707i) q^{35} +(5.08610 - 8.80938i) q^{37} +(-0.0970087 - 0.0433955i) q^{38} +(2.11338 - 9.69118i) q^{40} -7.20413i q^{41} +1.49705i q^{43} +(-4.85489 + 4.34056i) q^{44} +(1.60303 - 3.58350i) q^{46} +(0.225780 - 0.391063i) q^{47} +(-6.95435 + 0.798164i) q^{49} +(8.36066 - 6.05196i) q^{50} +(-0.889757 - 4.25953i) q^{52} +(1.69463 + 2.93518i) q^{53} -11.4190 q^{55} +(-6.98760 + 2.67832i) q^{56} +(-1.17597 - 11.3810i) q^{58} +(6.23214 + 10.7944i) q^{59} +(12.7098 + 7.33802i) q^{61} +(8.39465 - 6.07656i) q^{62} +(-6.52135 + 4.63379i) q^{64} +(3.81501 - 6.60779i) q^{65} +(-8.05831 + 4.65247i) q^{67} +(6.95941 - 6.22214i) q^{68} +(-12.2641 - 4.66533i) q^{70} +11.8379i q^{71} +(-0.852826 + 0.492379i) q^{73} +(-13.1317 - 5.87426i) q^{74} +(-0.0469448 + 0.142772i) q^{76} +(4.72652 + 7.20265i) q^{77} +(3.09707 + 1.78809i) q^{79} +(-13.9400 - 1.56429i) q^{80} +(-10.1342 + 1.04715i) q^{82} -0.350331 q^{83} +16.3689 q^{85} +(2.10594 - 0.217603i) q^{86} +(6.81165 + 6.19857i) q^{88} +(3.06210 + 1.76790i) q^{89} +(-5.74705 + 0.328721i) q^{91} +(-5.27400 - 1.73414i) q^{92} +(-0.582936 - 0.260768i) q^{94} +(-0.228222 + 0.131764i) q^{95} +1.05525i q^{97} +(2.13364 + 9.66683i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.145354	−	1.40672i	−0.102781	−	0.994704i
$2$	−0.145354	−	1.40672i	−0.102781	−	0.994704i
$3$		0			0
$3$		0			0
$4$	−1.95774	+	0.408946i	−0.978872	+	0.204473i
$5$	−3.03704	−	1.75344i	−1.35821	−	0.784161i	−0.368825	−	0.929499i	$-0.620240\pi$
$5$	−3.03704	−	1.75344i	−1.35821	−	0.784161i	−0.989382	+	0.145338i	$0.953573\pi$
$6$		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
$10$	−2.02516	+	4.52715i	−0.640411	+	1.43161i
$11$	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	$0.902439\pi$
$14$	3.69381	−	0.596478i	0.987212	−	0.159416i
$15$		0			0
$16$	3.66553	−	1.60122i	0.916382	−	0.400306i
$17$	−4.04232	+	2.33383i	−0.980406	+	0.566038i	−0.902393	−	0.430915i	$-0.858191\pi$
$17$	−4.04232	+	2.33383i	−0.980406	+	0.566038i	−0.0780131	+	0.996952i	$0.524858\pi$
$18$		0			0
$19$	0.0375730	−	0.0650784i	0.00861984	−	0.0149300i	−0.861683	−	0.507446i	$-0.830590\pi$
$19$	0.0375730	−	0.0650784i	0.00861984	−	0.0149300i	0.870303	+	0.492516i	$0.163923\pi$
$20$	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
$26$	3.06065	−	0.316251i	0.600244	−	0.0620220i
$27$		0			0
$28$	−1.37599	−	5.10947i	−0.260038	−	0.965598i
$29$	8.09040			1.50235			0.751175	−	0.660104i	$-0.229488\pi$
$29$	8.09040			1.50235			0.751175	+	0.660104i	$0.229488\pi$
$30$		0			0
$31$	3.66393	+	6.34611i	0.658060	+	1.13979i	0.981117	+	0.193415i	$0.0619562\pi$
$31$	3.66393	+	6.34611i	0.658060	+	1.13979i	−0.323057	+	0.946380i	$0.604710\pi$
$32$	−2.78528	−	4.92364i	−0.492372	−	0.870385i
$33$		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	$-0.148532\pi$
$38$	−0.0970087	−	0.0433955i	−0.0157369	−	0.00703968i
$39$		0			0
$40$	2.11338	−	9.69118i	0.334155	−	1.53231i
$41$		−	7.20413i		−	1.12510i	−0.826765	−	0.562548i	$-0.809821\pi$
$41$		−	7.20413i		−	1.12510i	0.826765	−	0.562548i	$-0.190179\pi$
$42$		0			0
$43$			1.49705i			0.228299i	0.993464	+	0.114149i	$0.0364142\pi$
$43$			1.49705i			0.228299i	−0.993464	+	0.114149i	$0.963586\pi$
$44$	−4.85489	+	4.34056i	−0.731902	+	0.654364i
$45$		0			0
$46$	1.60303	−	3.58350i	0.236353	−	0.528358i
$47$	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
$52$	−0.889757	−	4.25953i	−0.123387	−	0.590690i
$53$	1.69463	+	2.93518i	0.232775	+	0.403178i	0.958624	−	0.284677i	$-0.0918862\pi$
$53$	1.69463	+	2.93518i	0.232775	+	0.403178i	−0.725849	+	0.687854i	$0.758553\pi$
$54$		0			0
$55$	−11.4190			−1.53973
$56$	−6.98760	+	2.67832i	−0.933758	+	0.357906i
$57$		0			0
$58$	−1.17597	−	11.3810i	−0.154413	−	1.49439i
$59$	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	−0.903619	−	0.428336i	$-0.859100\pi$
$67$	−8.05831	+	4.65247i	−0.984479	+	0.568389i	−0.0808598	+	0.996725i	$0.525767\pi$
$68$	6.95941	−	6.22214i	0.843953	−	0.754545i
$69$		0			0
$70$	−12.2641	−	4.66533i	−1.46585	−	0.557614i
$71$			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	$0.351687\pi$
$74$	−13.1317	−	5.87426i	−1.52652	−	0.682869i
$75$		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	0.664001	−	0.747731i	$-0.268857\pi$
$79$	3.09707	+	1.78809i	0.348447	+	0.201176i	−0.315554	+	0.948908i	$0.602190\pi$
$80$	−13.9400	−	1.56429i	−1.55854	−	0.174893i
$81$		0			0
$82$	−10.1342	+	1.04715i	−1.11914	+	0.115638i
$83$	−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
$86$	2.10594	−	0.217603i	0.227090	−	0.0234647i
$87$		0			0
$88$	6.81165	+	6.19857i	0.726124	+	0.660769i
$89$	3.06210	+	1.76790i	0.324582	+	0.187397i	0.653433	−	0.756984i	$-0.273328\pi$
$89$	3.06210	+	1.76790i	0.324582	+	0.187397i	−0.328851	+	0.944382i	$0.606661\pi$
$90$		0			0
$91$	−5.74705	+	0.328721i	−0.602455	+	0.0344594i
$92$	−5.27400	−	1.73414i	−0.549852	−	0.180797i
$93$		0			0
$94$	−0.582936	−	0.260768i	−0.0601252	−	0.0268962i
$95$	−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	$0.982939\pi$
$98$	2.13364	+	9.66683i	0.215530	+	0.976497i
$99$		0			0
$100$	−9.72869	−	10.8815i	−0.972869	−	1.08815i
$101$	−10.8723	+	6.27713i	−1.08183	+	0.624597i	−0.931391	−	0.364021i	$-0.881404\pi$
$101$	−10.8723	+	6.27713i	−1.08183	+	0.624597i	−0.150444	+	0.988619i	$0.548070\pi$
$102$		0			0
$103$	2.80411	−	4.85686i	0.276297	−	0.478561i	−0.694164	−	0.719817i	$-0.744226\pi$
$103$	2.80411	−	4.85686i	0.276297	−	0.478561i	0.970462	+	0.241256i	$0.0775593\pi$
$104$	−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	$0.580887\pi$
$110$	1.65979	+	16.0633i	0.158255	+	1.53158i
$111$		0			0
$112$	4.78333	+	9.44032i	0.451982	+	0.892027i
$113$	−6.67916			−0.628323			−0.314161	−	0.949370i	$-0.601723\pi$
$113$	−6.67916			−0.628323			−0.314161	+	0.949370i	$0.601723\pi$
$114$		0			0
$115$	−4.86735	−	8.43050i	−0.453883	−	0.786149i
$116$	−15.8389	+	3.30854i	−1.47061	+	0.307190i
$117$		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
$122$	8.47515	−	18.9458i	0.767304	−	1.71527i
$123$		0			0
$124$	−9.76824	−	10.9257i	−0.877214	−	0.981157i
$125$		−	8.05942i		−	0.720856i
$126$		0			0
$127$			0.237718i			0.0210941i	0.999944	+	0.0105470i	$0.00335729\pi$
$127$			0.237718i			0.0210941i	−0.999944	+	0.0105470i	$0.996643\pi$
$128$	7.46637	+	8.50020i	0.659940	+	0.751319i
$129$		0			0
$130$	−9.84987	−	4.40620i	−0.863891	−	0.386449i
$131$	−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
$136$	−9.76441	−	8.88556i	−0.837291	−	0.761930i
$137$	−3.27562	−	5.67353i	−0.279855	−	0.484723i	0.691494	−	0.722382i	$-0.256953\pi$
$137$	−3.27562	−	5.67353i	−0.279855	−	0.484723i	−0.971348	+	0.237660i	$0.923620\pi$
$138$		0			0
$139$	5.30200			0.449710			0.224855	−	0.974392i	$-0.427809\pi$
$139$	5.30200			0.449710			0.224855	+	0.974392i	$0.427809\pi$
$140$	−4.78019	+	17.9304i	−0.404000	+	1.51539i
$141$		0			0
$142$	16.6527	−	1.72069i	1.39746	−	0.144397i
$143$	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	−0.858014	−	0.513627i	$-0.828302\pi$
$149$	0.192950	−	0.334200i	0.0158071	−	0.0273787i	0.873821	+	0.486248i	$0.161635\pi$
$150$		0			0
$151$	14.9039	−	8.60478i	1.21286	−	0.700247i	0.249482	−	0.968380i	$-0.419740\pi$
$151$	14.9039	−	8.60478i	1.21286	−	0.700247i	0.963382	+	0.268132i	$0.0864065\pi$
$152$	0.207665	+	0.0452859i	0.0168438	+	0.00367317i
$153$		0			0
$154$	9.44513	−	7.69584i	0.761110	−	0.620149i
$155$		−	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	$0.231280\pi$
$158$	2.06518	−	4.61663i	0.164297	−	0.367279i
$159$		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	$0.0721156\pi$
$163$	21.1449	+	12.2080i	1.65620	+	0.956207i	0.681753	+	0.731582i	$0.261218\pi$
$164$	2.94610	+	14.1038i	0.230052	+	1.10132i
$165$		0			0
$166$	0.0509220	+	0.492819i	0.00395231	+	0.0382501i
$167$	−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
$170$	−2.37929	−	23.0266i	−0.182483	−	1.76606i
$171$		0			0
$172$	−0.612215	−	2.93085i	−0.0466809	−	0.223475i
$173$	13.0506	+	7.53479i	0.992222	+	0.572860i	0.905938	−	0.423411i	$-0.139167\pi$
$173$	13.0506	+	7.53479i	0.992222	+	0.572860i	0.0862842	+	0.996271i	$0.472501\pi$
$174$		0			0
$175$	−16.1436	+	10.5937i	−1.22034	+	0.800812i
$176$	7.72957	−	10.4831i	0.582638	−	0.790193i
$177$		0			0
$178$	2.04186	−	4.56450i	0.153044	−	0.342124i
$179$	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	$-0.148820\pi$
$182$	1.29778	+	8.03674i	0.0961977	+	0.595722i
$183$		0			0
$184$	−1.67286	+	7.67112i	−0.123325	+	0.565523i
$185$	−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	$0.798542\pi$
$194$	1.48445	−	0.153385i	0.106577	−	0.0110124i
$195$		0			0
$196$	13.2884	−	4.40655i	0.949173	−	0.314754i
$197$	17.5070			1.24733			0.623663	−	0.781694i	$-0.285644\pi$
$197$	17.5070			1.24733			0.623663	+	0.781694i	$0.285644\pi$
$198$		0			0
$199$	9.12491	+	15.8048i	0.646848	+	1.12037i	0.983871	+	0.178877i	$0.0572465\pi$
$199$	9.12491	+	15.8048i	0.646848	+	1.12037i	−0.337023	+	0.941496i	$0.609420\pi$
$200$	−13.8931	+	15.2672i	−0.982391	+	1.07956i
$201$		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
$206$	−7.23985	−	3.23864i	−0.504424	−	0.225647i
$207$		0			0
$208$	3.48383	+	7.97520i	0.241560	+	0.552981i
$209$		−	0.244688i		−	0.0169254i
$210$		0			0
$211$		−	20.8486i		−	1.43528i	−0.696414	−	0.717640i	$-0.745222\pi$
$211$		−	20.8486i		−	1.43528i	0.696414	−	0.717640i	$-0.254778\pi$
$212$	−4.51797	−	5.05332i	−0.310296	−	0.347063i
$213$		0			0
$214$	−10.5623	+	23.6117i	−0.722027	+	1.61406i
$215$	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
$220$	22.3554	−	4.66974i	1.50720	−	0.314834i
$221$	−5.07779	−	8.79500i	−0.341569	−	0.591616i
$222$		0			0
$223$	−23.6765			−1.58550			−0.792748	−	0.609550i	$-0.791350\pi$
$223$	−23.6765			−1.58550			−0.792748	+	0.609550i	$0.791350\pi$
$224$	12.5847	−	8.10102i	0.840848	−	0.541272i
$225$		0			0
$226$	0.970843	+	9.39574i	0.0645795	+	0.624995i
$227$	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	−0.840769	−	0.541395i	$-0.817897\pi$
$233$	0.739972	−	1.28167i	0.0484772	−	0.0839649i	0.889246	+	0.457430i	$0.151230\pi$
$234$		0			0
$235$	−1.37141	+	0.791784i	−0.0894609	+	0.0516503i
$236$	−16.6153	−	18.5840i	−1.08156	−	1.20972i
$237$		0			0
$238$	−13.5395	+	11.0319i	−0.877633	+	0.715091i
$239$			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	$0.350860\pi$
$242$	0.513019	+	0.229492i	0.0329781	+	0.0147523i
$243$		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
$248$	−13.9496	+	15.3293i	−0.885800	+	0.973413i
$249$		0			0
$250$	−11.3374	+	1.17147i	−0.717039	+	0.0740902i
$251$	−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
$254$	0.334404	−	0.0345533i	0.0209824	−	0.00216807i
$255$		0			0
$256$	10.8722	−	11.7387i	0.679510	−	0.733666i
$257$	−11.3136	−	6.53193i	−0.705726	−	0.407451i	0.103751	−	0.994603i	$-0.466916\pi$
$257$	−11.3136	−	6.53193i	−0.705726	−	0.407451i	−0.809476	+	0.587152i	$0.800249\pi$
$258$		0			0
$259$	24.0378	+	12.1036i	1.49364	+	0.752083i
$260$	−4.76659	+	14.4965i	−0.295611	+	0.899035i
$261$		0			0
$262$	12.7285	+	5.69390i	0.786368	+	0.351770i
$263$	−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
$266$	0.0999697	−	0.262799i	0.00612953	−	0.0161132i
$267$		0			0
$268$	13.8735	−	12.4038i	0.847459	−	0.757680i
$269$	14.2226	−	8.21140i	0.867165	−	0.500658i	0.000759905	−	1.00000i	$-0.499758\pi$
$269$	14.2226	−	8.21140i	0.867165	−	0.500658i	0.866405	+	0.499342i	$0.166425\pi$
$270$		0			0
$271$	7.95296	−	13.7749i	0.483108	−	0.836767i	−0.516704	−	0.856164i	$-0.672841\pi$
$271$	7.95296	−	13.7749i	0.483108	−	0.836767i	0.999812	+	0.0193968i	$0.00617457\pi$
$272$	−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	$-0.520304\pi$
$278$	−0.770667	−	7.45845i	−0.0462216	−	0.447328i
$279$		0			0
$280$	25.9179	+	4.11815i	1.54889	+	0.246107i
$281$	12.6113			0.752324			0.376162	−	0.926554i	$-0.377244\pi$
$281$	12.6113			0.752324			0.376162	+	0.926554i	$0.377244\pi$
$282$		0			0
$283$	−4.00631	−	6.93912i	−0.238150	−	0.412488i	0.722033	−	0.691858i	$-0.243208\pi$
$283$	−4.00631	−	6.93912i	−0.238150	−	0.412488i	−0.960183	+	0.279370i	$0.909874\pi$
$284$	−4.84107	−	23.1756i	−0.287265	−	1.37522i
$285$		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
$290$	−16.3843	+	36.6264i	−0.962120	+	2.15078i
$291$		0			0
$292$	1.46826	−	1.31271i	0.0859233	−	0.0768207i
$293$			16.8878i			0.986596i	0.869861	+	0.493298i	$0.164209\pi$
$293$			16.8878i			0.986596i	−0.869861	+	0.493298i	$0.835791\pi$
$294$		0			0
$295$		−	43.7107i		−	2.54493i
$296$	28.1107	+	6.13016i	1.63390	+	0.356308i
$297$		0			0
$298$	−0.498173	−	0.222850i	−0.0288584	−	0.0129094i
$299$	−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
$304$	0.0335199	−	0.298709i	0.00192250	−	0.0171322i
$305$	−25.7335	−	44.5718i	−1.47350	−	2.55217i
$306$		0			0
$307$	−17.3886			−0.992420			−0.496210	−	0.868202i	$-0.665275\pi$
$307$	−17.3886			−0.992420			−0.496210	+	0.868202i	$0.665275\pi$
$308$	−12.1988	−	12.1681i	−0.695092	−	0.693340i
$309$		0			0
$310$	−36.1498	+	3.73529i	−2.05317	+	0.212150i
$311$	−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	−0.744809	−	0.667278i	$-0.767459\pi$
$317$	3.65839	−	6.33651i	0.205475	−	0.355894i	0.950284	+	0.311384i	$0.100793\pi$
$318$		0			0
$319$	22.8143	−	13.1718i	1.27735	−	0.737481i
$320$	27.9307	−	2.63823i	1.56137	−	0.147482i
$321$		0			0
$322$	9.70777	+	3.69287i	0.540993	+	0.205796i
$323$			0.350757i			0.0195166i
$324$		0			0
$325$	−13.7515	+	7.93944i	−0.762797	+	0.440401i
$326$	14.0998	−	31.5196i	0.780917	−	1.74571i
$327$		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	0.815893	−	0.578203i	$-0.196246\pi$
$331$	13.1557	+	7.59544i	0.723102	+	0.417483i	−0.0927914	+	0.995686i	$0.529579\pi$
$332$	0.685858	−	0.143266i	0.0376413	−	0.00786276i
$333$		0			0
$334$	2.69229	+	26.0557i	0.147315	+	1.42571i
$335$	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	$0.574033\pi$
$338$	−1.20152	−	11.6282i	−0.0653543	−	0.632493i
$339$		0			0
$340$	−32.0462	+	6.69400i	−1.73795	+	0.363033i
$341$	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
$346$	8.70241	−	19.4539i	0.467844	−	1.04585i
$347$	−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	$-0.375378\pi$
$350$	17.2490	+	21.1698i	0.921999	+	1.13157i
$351$		0			0
$352$	−15.8703	−	9.34961i	−0.845892	−	0.498336i
$353$	7.93449	−	4.58098i	0.422311	−	0.243821i	−0.273755	−	0.961799i	$-0.588266\pi$
$353$	7.93449	−	4.58098i	0.422311	−	0.243821i	0.696065	+	0.717978i	$0.254932\pi$
$354$		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
$362$	−17.0588	+	1.76266i	−0.896592	+	0.0926431i
$363$		0			0
$364$	11.1168	−	2.99379i	0.582680	−	0.156917i
$365$	3.45343			0.180761
$366$		0			0
$367$	0.321922	+	0.557586i	0.0168042	+	0.0291057i	0.874305	−	0.485377i	$-0.161317\pi$
$367$	0.321922	+	0.557586i	0.0168042	+	0.0291057i	−0.857501	+	0.514482i	$0.827984\pi$
$368$	11.0343	+	1.23822i	0.575203	+	0.0645468i
$369$		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	$0.897154\pi$
$374$	19.6205	+	8.77696i	1.01455	+	0.453846i
$375$		0			0
$376$	1.24788	+	0.272128i	0.0643545	+	0.0140339i
$377$			17.6025i			0.906577i
$378$		0			0
$379$		−	20.6164i		−	1.05899i	−0.848312	−	0.529496i	$-0.822381\pi$
$379$		−	20.6164i		−	1.05899i	0.848312	−	0.529496i	$-0.177619\pi$
$380$	0.392916	−	0.351291i	0.0201562	−	0.0180208i
$381$		0			0
$382$	−5.14594	+	11.5035i	−0.263289	+	0.588572i
$383$	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
$388$	−0.431541	−	2.06591i	−0.0219082	−	0.104881i
$389$	0.312454	+	0.541186i	0.0158420	+	0.0274392i	0.873838	−	0.486218i	$-0.161624\pi$
$389$	0.312454	+	0.541186i	0.0158420	+	0.0274392i	−0.857996	+	0.513657i	$0.828290\pi$
$390$		0			0
$391$	−12.9569			−0.655260
$392$	−8.13033	−	18.0526i	−0.410644	−	0.911796i
$393$		0			0
$394$	−2.54472	−	24.6276i	−0.128201	−	1.24072i
$395$	−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	−0.768768	−	0.639528i	$-0.779130\pi$
$401$	3.39351	−	5.87773i	0.169464	−	0.293520i	0.938231	+	0.346008i	$0.112463\pi$
$402$		0			0
$403$	−13.8074	+	7.97172i	−0.687797	+	0.397100i
$404$	18.7182	−	16.7352i	0.931264	−	0.832607i
$405$		0			0
$406$	29.8844	−	4.82575i	1.48314	−	0.239498i
$407$		−	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	$0.338569\pi$
$410$	32.6142	+	14.5895i	1.61070	+	0.720523i
$411$		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
$416$	10.7125	−	6.06002i	0.525225	−	0.297117i
$417$		0			0
$418$	−0.344208	+	0.0355664i	−0.0168358	+	0.00173961i
$419$	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	$0.774838\pi$
$422$	−29.3283	+	3.03043i	−1.42768	+	0.147519i
$423$		0			0
$424$	−6.45192	+	7.09006i	−0.313333	+	0.344324i
$425$	−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
$430$	−6.77739	−	3.03177i	−0.326835	−	0.146205i
$431$	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	$-0.0737923\pi$
$434$	17.3192	+	21.2558i	0.831346	+	1.02031i
$435$		0			0
$436$	−19.8326	−	22.1826i	−0.949810	−	1.06236i
$437$	0.180651	−	0.104299i	0.00864169	−	0.00498928i
$438$		0			0
$439$	−13.6732	+	23.6827i	−0.652586	+	1.13031i	0.329907	+	0.944013i	$0.392983\pi$
$439$	−13.6732	+	23.6827i	−0.652586	+	1.13031i	−0.982493	+	0.186299i	$0.940351\pi$
$440$	−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
$446$	3.44147	+	33.3063i	0.162959	+	1.57710i
$447$		0			0
$448$	−13.2251	−	16.5256i	−0.624828	−	0.780762i
$449$	−18.8468			−0.889436			−0.444718	−	0.895671i	$-0.646696\pi$
$449$	−18.8468			−0.889436			−0.444718	+	0.895671i	$0.646696\pi$
$450$		0			0
$451$	−11.7289	−	20.3151i	−0.552293	−	0.956599i
$452$	13.0761	−	2.73142i	0.615048	−	0.128475i
$453$		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	$0.221130\pi$
$458$	−13.1256	+	29.3417i	−0.613319	+	1.37105i
$459$		0			0
$460$	12.9767	+	14.5143i	0.605040	+	0.676732i
$461$		−	3.58604i		−	0.167019i	−0.996507	−	0.0835093i	$-0.973387\pi$
$461$		−	3.58604i		−	0.167019i	0.996507	−	0.0835093i	$-0.0266128\pi$
$462$		0			0
$463$			28.4541i			1.32237i	0.750221	+	0.661187i	$0.229947\pi$
$463$			28.4541i			1.32237i	−0.750221	+	0.661187i	$0.770053\pi$
$464$	29.6556	−	12.9545i	1.37673	−	0.601399i
$465$		0			0
$466$	−1.91051	−	0.854640i	−0.0885028	−	0.0395904i
$467$	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
$472$	−23.7275	+	26.0744i	−1.09215	+	1.20017i
$473$	2.43733	+	4.22157i	0.112068	+	0.194108i
$474$		0			0
$475$	0.548429			0.0251637
$476$	17.4868	+	17.4428i	0.801507	+	0.799487i
$477$		0			0
$478$	10.8228	−	1.11829i	0.495022	−	0.0511496i
$479$	−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	−0.160413	−	0.987050i	$-0.551283\pi$
$487$	13.5540	−	7.82541i	0.614191	−	0.354603i	0.774604	+	0.632447i	$0.217949\pi$
$488$	−8.84435	+	40.5570i	−0.400365	+	1.83593i
$489$		0			0
$490$	10.4702	−	33.0998i	0.472997	−	1.49530i
$491$		−	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
$494$	0.0944169	−	0.211065i	0.00424802	−	0.00949626i
$495$		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	0.387310	−	0.921950i	$-0.373404\pi$
$499$	−4.85785	−	2.80468i	−0.217467	−	0.125555i	−0.604777	+	0.796395i	$0.706738\pi$
$500$	3.29587	+	15.7783i	0.147396	+	0.705626i
$501$		0			0
$502$	2.25593	+	21.8327i	0.100687	+	0.974442i
$503$	−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
$506$	−1.31382	−	12.7150i	−0.0584064	−	0.565252i
$507$		0			0
$508$	−0.0972139	−	0.465392i	−0.00431317	−	0.0206484i
$509$	21.5238	+	12.4268i	0.954026	+	0.550807i	0.894329	−	0.447409i	$-0.147653\pi$
$509$	21.5238	+	12.4268i	0.954026	+	0.550807i	0.0596966	+	0.998217i	$0.480987\pi$
$510$		0			0
$511$	−1.42944	−	2.17829i	−0.0632346	−	0.0963620i
$512$	−18.0934	−	13.5879i	−0.799621	−	0.600505i
$513$		0			0
$514$	−7.54414	+	16.8646i	−0.332758	+	0.743866i
$515$	−17.0324	+	9.83367i	−0.750538	+	0.433323i
$516$		0			0
$517$		−	1.47036i		−	0.0646662i
$518$	13.5325	−	35.5739i	0.594583	−	1.56303i
$519$		0			0
$520$	21.0854	+	4.59815i	0.924657	+	0.201642i
$521$	13.3491	−	7.70713i	0.584837	−	0.337656i	−0.178217	−	0.983991i	$-0.557033\pi$
$521$	13.3491	−	7.70713i	0.584837	−	0.337656i	0.763053	+	0.646336i	$0.223699\pi$
$522$		0			0
$523$	7.33526	−	12.7050i	0.320748	−	0.555553i	−0.659894	−	0.751358i	$-0.729399\pi$
$523$	7.33526	−	12.7050i	0.320748	−	0.555553i	0.980643	+	0.195806i	$0.0627323\pi$
$524$	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
$530$	−16.7199	+	1.72763i	−0.726265	+	0.0750435i
$531$		0			0
$532$	−0.384216	−	0.102431i	−0.0166579	−	0.00444094i
$533$	15.6742			0.678927
$534$		0			0
$535$	32.0710	+	55.5486i	1.38655	+	2.40158i
$536$	−19.4652	−	17.7133i	−0.840770	−	0.765096i
$537$		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	$0.303324\pi$
$542$	−20.5335	−	9.18538i	−0.881990	−	0.394546i
$543$		0			0
$544$	22.7499	+	13.4025i	0.975395	+	0.574629i
$545$		−	52.1748i		−	2.23492i
$546$		0			0
$547$		−	15.2986i		−	0.654120i	−0.945004	−	0.327060i	$-0.893942\pi$
$547$		−	15.2986i		−	0.654120i	0.945004	−	0.327060i	$-0.106058\pi$
$548$	8.73299	+	9.76778i	0.373055	+	0.417259i
$549$		0			0
$550$	13.7233	−	30.6779i	0.585164	−	1.30811i
$551$	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
$556$	−10.3800	+	2.16823i	−0.440209	+	0.0919535i
$557$	3.01197	+	5.21688i	0.127621	+	0.221046i	0.922754	−	0.385388i	$-0.125933\pi$
$557$	3.01197	+	5.21688i	0.127621	+	0.221046i	−0.795133	+	0.606435i	$0.792599\pi$
$558$		0			0
$559$	−3.25719			−0.137764
$560$	2.02583	−	37.0580i	0.0856070	−	1.56598i
$561$		0			0
$562$	−1.83310	−	17.7406i	−0.0773245	−	0.748340i
$563$	−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	−0.989537	−	0.144278i	$-0.953914\pi$
$569$	−8.82158	+	15.2794i	−0.369820	+	0.640547i	0.619717	+	0.784825i	$0.287247\pi$
$570$		0			0
$571$	22.3514	−	12.9046i	0.935378	−	0.540041i	0.0468695	−	0.998901i	$-0.485076\pi$
$571$	22.3514	−	12.9046i	0.935378	−	0.540041i	0.888508	+	0.458860i	$0.151742\pi$
$572$	−9.44390	−	10.5629i	−0.394869	−	0.441658i
$573$		0			0
$574$	−4.29711	−	26.6107i	−0.179358	−	1.11071i
$575$			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	$0.294344\pi$
$578$	−6.17983	−	2.76446i	−0.257047	−	0.114986i
$579$		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
$584$	−2.06004	−	1.87463i	−0.0852451	−	0.0775726i
$585$		0			0
$586$	23.7565	−	2.45471i	0.981371	−	0.101403i
$587$	−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
$590$	−61.4889	+	6.35353i	−2.53146	+	0.261570i
$591$		0			0
$592$	4.53744	−	40.4350i	0.186488	−	1.66187i
$593$	5.75014	+	3.31984i	0.236130	+	0.136330i	0.613397	−	0.789775i	$-0.289803\pi$
$593$	5.75014	+	3.31984i	0.236130	+	0.136330i	−0.377267	+	0.926105i	$0.623136\pi$
$594$		0			0
$595$	2.47310	+	43.2374i	0.101387	+	1.77256i
$596$	−0.241078	+	0.733183i	−0.00987492	+	0.0300324i
$597$		0			0
$598$	7.79673	+	3.48776i	0.318832	+	0.142625i
$599$	−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	$-0.0212869\pi$
$602$	0.892961	+	5.52983i	0.0363944	+	0.225379i
$603$		0			0
$604$	−25.6592	+	22.9409i	−1.04406	+	0.933450i
$605$	1.20692	−	0.696818i	0.0490685	−	0.0283297i
$606$		0			0
$607$	−0.148269	+	0.256810i	−0.00601806	+	0.0104236i	−0.869019	−	0.494779i	$-0.835249\pi$
$607$	−0.148269	+	0.256810i	−0.00601806	+	0.0104236i	0.863001	+	0.505203i	$0.168582\pi$
$608$	−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	$0.790462\pi$
$614$	2.52750	+	24.4610i	0.102002	+	0.987164i
$615$		0			0
$616$	−15.3440	+	18.9290i	−0.618226	+	0.762673i
$617$	−0.955148			−0.0384528			−0.0192264	−	0.999815i	$-0.506120\pi$
$617$	−0.955148			−0.0384528			−0.0192264	+	0.999815i	$0.506120\pi$
$618$		0			0
$619$	−6.38442	−	11.0581i	−0.256611	−	0.444464i	0.708721	−	0.705489i	$-0.249273\pi$
$619$	−6.38442	−	11.0581i	−0.256611	−	0.444464i	−0.965332	+	0.261025i	$0.915939\pi$
$620$	10.5090	+	50.3098i	0.422053	+	2.02049i
$621$		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
$626$	4.99880	−	11.1746i	0.199792	−	0.446627i
$627$		0			0
$628$	−11.7750	+	10.5276i	−0.469875	+	0.420096i
$629$			47.4804i			1.89317i
$630$		0			0
$631$		−	11.9142i		−	0.474298i	−0.971473	−	0.237149i	$-0.923787\pi$
$631$		−	11.9142i		−	0.474298i	0.971473	−	0.237149i	$-0.0762129\pi$
$632$	−2.15515	+	9.88272i	−0.0857272	+	0.393114i
$633$		0			0
$634$	−9.44548	−	4.22530i	−0.375128	−	0.167808i
$635$	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
$640$	−7.77110	−	38.9073i	−0.307180	−	1.53795i
$641$	−0.801420	−	1.38810i	−0.0316542	−	0.0548266i	0.849764	−	0.527163i	$-0.176744\pi$
$641$	−0.801420	−	1.38810i	−0.0316542	−	0.0548266i	−0.881419	+	0.472336i	$0.843411\pi$
$642$		0			0
$643$	−20.7304			−0.817525			−0.408763	−	0.912641i	$-0.634040\pi$
$643$	−20.7304			−0.817525			−0.408763	+	0.912641i	$0.634040\pi$
$644$	3.78379	−	14.1929i	0.149102	−	0.559279i
$645$		0			0
$646$	0.493418	−	0.0509839i	0.0194133	−	0.00200593i
$647$	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	$-0.609788\pi$
$653$	16.5069	−	28.5908i	0.645966	−	1.11885i	0.984078	−	0.177740i	$-0.0568785\pi$
$654$		0			0
$655$	29.9449	−	17.2887i	1.17004	−	0.675525i
$656$	−11.5354	−	26.4069i	−0.450382	−	1.03102i
$657$		0			0
$658$	0.600728	−	1.57918i	0.0234188	−	0.0615630i
$659$			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	$0.345670\pi$
$662$	8.77245	−	19.6104i	0.340951	−	0.762182i
$663$		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
$668$	36.2619	−	7.57461i	1.40301	−	0.293070i
$669$		0			0
$670$	−4.74308	−	45.9032i	−0.183241	−	1.77339i
$671$	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	$0.362895\pi$
$674$	1.23005	+	11.9043i	0.0473799	+	0.458538i
$675$		0			0
$676$	−16.1831	+	3.38042i	−0.622426	+	0.130016i
$677$	18.4674	+	10.6622i	0.709760	+	0.409780i	0.810972	−	0.585085i	$-0.198939\pi$
$677$	18.4674	+	10.6622i	0.709760	+	0.409780i	−0.101212	+	0.994865i	$0.532272\pi$
$678$		0			0
$679$	−2.78738	+	0.159433i	−0.106970	+	0.00611848i
$680$	14.0747	+	44.1071i	0.539738	+	1.69143i
$681$		0			0
$682$	13.7791	−	30.8026i	0.527629	−	1.17949i
$683$	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
$686$	−25.2119	+	7.09638i	−0.962596	+	0.270941i
$687$		0			0
$688$	2.39712	+	5.48749i	0.0913893	+	0.209209i
$689$	−6.38616	+	3.68705i	−0.243293	+	0.140465i
$690$		0			0
$691$	−21.4507	+	37.1536i	−0.816022	+	1.41339i	0.0925703	+	0.995706i	$0.470492\pi$
$691$	−21.4507	+	37.1536i	−0.816022	+	1.41339i	−0.908592	+	0.417685i	$0.862842\pi$
$692$	−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
$698$	−48.5825	+	5.01994i	−1.83888	+	0.190007i
$699$		0			0
$700$	27.2728	−	27.3417i	1.03081	−	1.03342i
$701$	29.6874			1.12128			0.560639	−	0.828061i	$-0.310556\pi$
$701$	29.6874			1.12128			0.560639	+	0.828061i	$0.310556\pi$
$702$		0			0
$703$	−0.382200	−	0.661991i	−0.0144150	−	0.0249674i
$704$	−10.8455	+	23.6842i	−0.408755	+	0.892632i
$705$		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	$0.0398993\pi$
$710$	−53.5921	−	23.9737i	−2.01128	−	0.899716i
$711$		0			0
$712$	−2.13081	+	9.77113i	−0.0798556	+	0.366189i
$713$			20.3413i			0.761789i
$714$		0			0
$715$		−	24.8446i		−	0.929135i
$716$	−9.26433	+	8.28288i	−0.346224	+	0.309546i
$717$		0			0
$718$	9.12957	−	20.4088i	0.340713	−	0.761649i
$719$	−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
$724$	4.95914	+	23.7409i	0.184305	+	0.882322i
$725$	29.5226	+	51.1346i	1.09644	+	1.89909i
$726$		0			0
$727$	−32.7901			−1.21612			−0.608059	−	0.793892i	$-0.708051\pi$
$727$	−32.7901			−1.21612			−0.608059	+	0.793892i	$0.708051\pi$
$728$	−5.82731	−	15.2032i	−0.215974	−	0.563466i
$729$		0			0
$730$	−0.501969	−	4.85802i	−0.0185787	−	0.179803i
$731$	−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	−0.902334	−	0.431038i	$-0.858147\pi$
$739$	−26.6466	+	15.3844i	−0.980211	+	0.565925i	−0.0778770	+	0.996963i	$0.524814\pi$
$740$	53.1873	−	47.5527i	1.95520	−	1.74807i
$741$		0			0
$742$	8.01039	+	9.83117i	0.294071	+	0.360914i
$743$			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
$746$	37.3532	+	16.7094i	1.36760	+	0.611775i
$747$		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	−0.236665	−	0.971591i	$-0.576054\pi$
$751$	−32.7871	−	18.9297i	−1.19642	−	0.690753i	−0.959755	+	0.280838i	$0.909388\pi$
$752$	0.201425	−	1.79498i	0.00734520	−	0.0654561i
$753$		0			0
$754$	24.7619	−	2.55860i	0.901776	−	0.0931787i
$755$	−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	$0.634382\pi$
$758$	−29.0015	+	2.99667i	−1.05338	+	0.108844i
$759$		0			0
$760$	−0.551281	−	0.501662i	−0.0199971	−	0.0181972i
$761$	−12.8446	−	7.41584i	−0.465617	−	0.268824i	0.248786	−	0.968558i	$-0.419968\pi$
$761$	−12.8446	−	7.41584i	−0.465617	−	0.268824i	−0.714403	+	0.699734i	$0.753302\pi$
$762$		0			0
$763$	−32.9099	+	21.5961i	−1.19142	+	0.781832i
$764$	16.9303	+	5.56684i	0.612516	+	0.201401i
$765$		0			0
$766$	−28.8322	−	12.8977i	−1.04175	−	0.466012i
$767$	−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	$-0.271167\pi$
$770$	−42.1794	+	6.81116i	−1.52004	+	0.245457i
$771$		0			0
$772$	−4.04020	−	4.51893i	−0.145410	−	0.162640i
$773$	17.7798	−	10.2652i	0.639497	−	0.369214i	−0.144924	−	0.989443i	$-0.546294\pi$
$773$	17.7798	−	10.2652i	0.639497	−	0.369214i	0.784421	+	0.620229i	$0.212960\pi$
$774$		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
$782$	1.88334	+	18.2268i	0.0673482	+	0.651790i
$783$		0			0
$784$	−24.2133	+	14.0612i	−0.864761	+	0.502184i
$785$	−27.6955			−0.988495
$786$		0			0
$787$	−4.37470	−	7.57720i	−0.155941	−	0.270098i	0.777460	−	0.628932i	$-0.216508\pi$
$787$	−4.37470	−	7.57720i	−0.155941	−	0.270098i	−0.933401	+	0.358834i	$0.883174\pi$
$788$	−34.2743	+	7.15944i	−1.22097	+	0.255044i
$789$		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
$794$	9.63467	−	21.5379i	0.341922	−	0.764351i
$795$		0			0
$796$	−24.3276	−	27.2102i	−0.862268	−	0.964440i
$797$		−	11.5319i		−	0.408480i	−0.978921	−	0.204240i	$-0.934528\pi$
$797$		−	11.5319i		−	0.408480i	0.978921	−	0.204240i	$-0.0654722\pi$
$798$		0			0
$799$			2.10773i			0.0745663i
$800$	20.9557	−	35.5709i	0.740895	−	1.25762i
$801$		0			0
$802$	−8.76160	−	3.91938i	−0.309383	−	0.138398i
$803$	−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
$808$	−26.2626	−	23.8988i	−0.923914	−	0.840756i
$809$	−17.0250	−	29.4882i	−0.598567	−	1.03675i	−0.993033	−	0.117838i	$-0.962404\pi$
$809$	−17.0250	−	29.4882i	−0.598567	−	1.03675i	0.394465	−	0.918911i	$-0.370930\pi$
$810$		0			0
$811$	9.87280			0.346681			0.173340	−	0.984862i	$-0.444544\pi$
$811$	9.87280			0.346681			0.173340	+	0.984862i	$0.444544\pi$
$812$	−11.1323	−	41.3376i	−0.390667	−	1.45067i
$813$		0			0
$814$	−46.5940	+	4.81447i	−1.63312	+	0.168747i
$815$	−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	$0.448426\pi$
$821$	−22.1782	+	38.4138i	−0.774024	+	1.34065i	−0.935341	+	0.353747i	$0.884908\pi$
$822$		0			0
$823$	−23.6005	+	13.6257i	−0.822660	+	0.474963i	−0.851333	−	0.524626i	$-0.824205\pi$
$823$	−23.6005	+	13.6257i	−0.822660	+	0.474963i	0.0286727	+	0.999589i	$0.490872\pi$
$824$	15.4982	+	3.37973i	0.539906	+	0.117738i
$825$		0			0
$826$	29.4590	+	36.1550i	1.02501	+	1.25799i
$827$		−	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	$0.169819\pi$
$830$	0.709474	−	1.58600i	0.0246262	−	0.0550509i
$831$		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
$836$	0.100064	+	0.479036i	0.00346079	+	0.0165678i
$837$		0			0
$838$	−4.99425	−	48.3339i	−0.172523	−	1.66967i
$839$	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
$842$	4.53372	+	43.8770i	0.156242	+	1.51210i
$843$		0			0
$844$	8.52597	+	40.8163i	0.293476	+	1.40496i
$845$	−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
$850$	−19.6722	+	43.9763i	−0.674750	+	1.50837i
$851$	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	$0.916588\pi$
$854$	51.3246	+	19.5241i	1.75629	+	0.668101i
$855$		0			0
$856$	11.0225	−	50.5450i	0.376740	−	1.72759i
$857$	−16.9075	+	9.76153i	−0.577548	+	0.333447i	−0.760158	−	0.649738i	$-0.774879\pi$
$857$	−16.9075	+	9.76153i	−0.577548	+	0.333447i	0.182610	+	0.983185i	$0.441545\pi$
$858$		0			0
$859$	28.4937	−	49.3526i	0.972193	−	1.68389i	0.283290	−	0.959034i	$-0.408574\pi$
$859$	28.4937	−	49.3526i	0.972193	−	1.68389i	0.688903	−	0.724854i	$-0.258093\pi$
$860$	−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
$866$	−13.4508	+	1.38984i	−0.457075	+	0.0472287i
$867$		0			0
$868$	27.3837	−	27.4529i	0.929463	−	0.931812i
$869$	11.6446			0.395018
$870$		0			0
$871$	−10.1225	−	17.5327i	−0.342989	−	0.594074i
$872$	−28.3221	+	31.1234i	−0.959107	+	1.05397i
$873$		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	$0.959498\pi$
$878$	35.3024	+	15.7920i	1.19140	+	0.532956i
$879$		0			0
$880$	−41.8565	+	18.2843i	−1.41098	+	0.616364i
$881$		−	10.6024i		−	0.357203i	−0.983921	−	0.178601i	$-0.942843\pi$
$881$		−	10.6024i		−	0.357203i	0.983921	−	0.178601i	$-0.0571573\pi$
$882$		0			0
$883$		−	7.32656i		−	0.246558i	−0.992372	−	0.123279i	$-0.960659\pi$
$883$		−	7.32656i		−	0.246558i	0.992372	−	0.123279i	$-0.0393410\pi$
$884$	13.5377	+	15.1418i	0.455322	+	0.509274i
$885$		0			0
$886$	13.4946	−	30.1666i	0.453360	−	1.01347i
$887$	−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
$892$	46.3525	−	9.68241i	1.55200	−	0.324191i
$893$	−0.0169665	−	0.0293868i	−0.000567762	−	0.000983393i
$894$		0			0
$895$	−21.7902			−0.728367
$896$	−21.3247	+	21.0062i	−0.712407	+	0.701767i
$897$		0			0
$898$	2.73946	+	26.5123i	0.0914170	+	0.884726i
$899$	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	−0.942372	−	0.334568i	$-0.891410\pi$
$907$	−33.8453	+	19.5406i	−1.12381	+	0.648834i	−0.181441	+	0.983402i	$0.558076\pi$
$908$	−2.22100	−	2.48417i	−0.0737064	−	0.0824400i
$909$		0			0
$910$	10.1505	−	26.6835i	0.336486	−	0.884549i
$911$			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
$914$	9.39778	+	4.20396i	0.310851	+	0.139055i
$915$		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	0.809924	−	0.586535i	$-0.199508\pi$
$919$	21.4307	+	12.3730i	0.706932	+	0.408148i	−0.102992	+	0.994682i	$0.532842\pi$
$920$	18.5314	−	20.3643i	0.610962	−	0.671390i
$921$		0			0
$922$	−5.04457	+	0.521245i	−0.166134	+	0.0171663i
$923$	−25.7562			−0.847775
$924$		0			0
$925$	74.2385			2.44095
$926$	40.0271	−	4.13592i	1.31537	−	0.135915i
$927$		0			0
$928$	−22.5340	−	39.8342i	−0.739715	−	1.30762i
$929$	−28.3285	−	16.3555i	−0.929429	−	0.536606i	−0.0427979	−	0.999084i	$-0.513627\pi$
$929$	−28.3285	−	16.3555i	−0.929429	−	0.536606i	−0.886631	+	0.462478i	$0.846960\pi$
$930$		0			0
$931$	−0.209353	+	0.482567i	−0.00686125	+	0.0158155i
$932$	−0.924542	+	2.81179i	−0.0302844	+	0.0921032i
$933$		0			0
$934$	−32.2032	−	14.4056i	−1.05372	−	0.471367i
$935$	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	$0.928215\pi$
$938$	−26.9907	+	21.9919i	−0.881279	+	0.718062i
$939$		0			0
$940$	2.36107	−	2.11094i	0.0770097	−	0.0688513i
$941$	4.94838	−	2.85695i	0.161313	−	0.0931338i	−0.417171	−	0.908828i	$-0.636978\pi$
$941$	4.94838	−	2.85695i	0.161313	−	0.0931338i	0.578483	+	0.815694i	$0.303645\pi$
$942$		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
$950$	−0.0797164	−	0.771488i	−0.00258634	−	0.0250304i
$951$		0			0
$952$	21.9954	−	27.1345i	0.712874	−	0.879435i
$953$	−56.4286			−1.82790			−0.913950	−	0.405827i	$-0.866984\pi$
$953$	−56.4286			−1.82790			−0.913950	+	0.405827i	$0.866984\pi$
$954$		0			0
$955$	15.6249	+	27.0631i	0.505610	+	0.875742i
$956$	−3.14626	−	15.0621i	−0.101757	−	0.487143i
$957$		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
$962$	12.7808	−	28.5710i	0.412070	−	0.921165i
$963$		0			0
$964$	2.54770	−	2.27780i	0.0820558	−	0.0733629i
$965$		−	10.6288i		−	0.342152i
$966$		0			0
$967$			10.0918i			0.324531i	0.986747	+	0.162265i	$0.0518801\pi$
$967$			10.0918i			0.324531i	−0.986747	+	0.162265i	$0.948120\pi$
$968$	−1.09821	−	0.239489i	−0.0352978	−	0.00769748i
$969$		0			0
$970$	−4.77728	−	2.13705i	−0.153389	−	0.0686165i
$971$	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
$976$	58.3380	+	6.54644i	1.86735	+	0.209546i
$977$	26.7586	+	46.3473i	0.856084	+	1.48278i	0.875636	+	0.482971i	$0.160443\pi$
$977$	26.7586	+	46.3473i	0.856084	+	1.48278i	−0.0195525	+	0.999809i	$0.506224\pi$
$978$		0			0
$979$	11.5132			0.367962
$980$	−48.0841	−	9.91754i	−1.53599	−	0.316804i
$981$		0			0
$982$	−2.91637	+	0.301343i	−0.0930651	+	0.00961623i
$983$	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	−4.71668e−6	−	1.00000i	$-0.500002\pi$
$991$	27.2624	−	15.7399i	0.866018	−	0.499996i	0.866023	+	0.500004i	$0.166668\pi$
$992$	21.0409	−	35.7155i	0.668049	−	1.13397i
$993$		0			0
$994$	7.06107	+	43.7270i	0.223964	+	1.38694i
$995$		−	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	$0.0570649\pi$
$998$	−3.23930	+	7.24132i	−0.102538	+	0.229220i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.145354 - 1.40672i) q^{2} +(-1.95774 + 0.408946i) q^{4} +(-3.03704 - 1.75344i) q^{5} +(0.151085 + 2.64143i) q^{7} +(0.859840 + 2.69456i) q^{8} +O(q^{10})\)	\(q+(-0.145354 - 1.40672i) q^{2} +(-1.95774 + 0.408946i) q^{4} +(-3.03704 - 1.75344i) q^{5} +(0.151085 + 2.64143i) q^{7} +(0.859840 + 2.69456i) q^{8} +(-2.02516 + 4.52715i) q^{10} +(2.81992 - 1.62808i) q^{11} +2.17573i q^{13} +(3.69381 - 0.596478i) q^{14} +(3.66553 - 1.60122i) q^{16} +(-4.04232 + 2.33383i) q^{17} +(0.0375730 - 0.0650784i) q^{19} +(6.66282 + 2.19080i) q^{20} +(-2.70015 - 3.73020i) q^{22} +(2.40399 + 1.38795i) q^{23} +(3.64909 + 6.32041i) q^{25} +(3.06065 - 0.316251i) q^{26} +(-1.37599 - 5.10947i) q^{28} +8.09040 q^{29} +(3.66393 + 6.34611i) q^{31} +(-2.78528 - 4.92364i) q^{32} +(3.87063 + 5.34719i) q^{34} +(4.17274 - 8.28707i) q^{35} +(5.08610 - 8.80938i) q^{37} +(-0.0970087 - 0.0433955i) q^{38} +(2.11338 - 9.69118i) q^{40} -7.20413i q^{41} +1.49705i q^{43} +(-4.85489 + 4.34056i) q^{44} +(1.60303 - 3.58350i) q^{46} +(0.225780 - 0.391063i) q^{47} +(-6.95435 + 0.798164i) q^{49} +(8.36066 - 6.05196i) q^{50} +(-0.889757 - 4.25953i) q^{52} +(1.69463 + 2.93518i) q^{53} -11.4190 q^{55} +(-6.98760 + 2.67832i) q^{56} +(-1.17597 - 11.3810i) q^{58} +(6.23214 + 10.7944i) q^{59} +(12.7098 + 7.33802i) q^{61} +(8.39465 - 6.07656i) q^{62} +(-6.52135 + 4.63379i) q^{64} +(3.81501 - 6.60779i) q^{65} +(-8.05831 + 4.65247i) q^{67} +(6.95941 - 6.22214i) q^{68} +(-12.2641 - 4.66533i) q^{70} +11.8379i q^{71} +(-0.852826 + 0.492379i) q^{73} +(-13.1317 - 5.87426i) q^{74} +(-0.0469448 + 0.142772i) q^{76} +(4.72652 + 7.20265i) q^{77} +(3.09707 + 1.78809i) q^{79} +(-13.9400 - 1.56429i) q^{80} +(-10.1342 + 1.04715i) q^{82} -0.350331 q^{83} +16.3689 q^{85} +(2.10594 - 0.217603i) q^{86} +(6.81165 + 6.19857i) q^{88} +(3.06210 + 1.76790i) q^{89} +(-5.74705 + 0.328721i) q^{91} +(-5.27400 - 1.73414i) q^{92} +(-0.582936 - 0.260768i) q^{94} +(-0.228222 + 0.131764i) q^{95} +1.05525i q^{97} +(2.13364 + 9.66683i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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