LMFDB - Embedded newform 1148.2.r.a.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(81,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("1148.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.r (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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			81.1
Character	$\chi$	$=$	1148.81
Dual form			1148.2.r.a.737.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.89464 - 1.67122i) q^{3} +(1.42784 + 2.47308i) q^{5} +(-1.36322 + 2.26752i) q^{7} +(4.08596 + 7.07710i) q^{9} +O(q^{10})$	\(q+(-2.89464 - 1.67122i) q^{3} +(1.42784 + 2.47308i) q^{5} +(-1.36322 + 2.26752i) q^{7} +(4.08596 + 7.07710i) q^{9} +(1.10288 + 0.636749i) q^{11} +3.41413i q^{13} -9.54492i q^{15} +(-1.97022 - 1.13751i) q^{17} +(-0.851130 + 0.491400i) q^{19} +(7.73555 - 4.28541i) q^{21} +(-3.90559 - 6.76468i) q^{23} +(-1.57743 + 2.73219i) q^{25} -17.2869i q^{27} -0.0172332i q^{29} +(-4.79997 + 8.31379i) q^{31} +(-2.12830 - 3.68632i) q^{33} +(-7.55422 - 0.133706i) q^{35} +(-4.00389 - 6.93495i) q^{37} +(5.70576 - 9.88267i) q^{39} +(4.71859 + 4.32839i) q^{41} -2.35283 q^{43} +(-11.6682 + 20.2099i) q^{45} +(3.58279 - 2.06853i) q^{47} +(-3.28328 - 6.18224i) q^{49} +(3.80205 + 6.58535i) q^{51} +(1.38918 + 0.802043i) q^{53} +3.63669i q^{55} +3.28495 q^{57} +(-3.38451 + 5.86214i) q^{59} +(-3.36290 - 5.82471i) q^{61} +(-21.6175 - 0.382618i) q^{63} +(-8.44343 + 4.87481i) q^{65} +(8.17149 + 4.71781i) q^{67} +26.1084i q^{69} -3.13702i q^{71} +(-5.62882 + 9.74940i) q^{73} +(9.13220 - 5.27248i) q^{75} +(-2.94731 + 1.63278i) q^{77} +(-1.10592 + 0.638505i) q^{79} +(-16.6323 + 28.8080i) q^{81} -3.83139 q^{83} -6.49669i q^{85} +(-0.0288004 + 0.0498838i) q^{87} +(-11.9151 + 6.87919i) q^{89} +(-7.74160 - 4.65420i) q^{91} +(27.7884 - 16.0436i) q^{93} +(-2.43055 - 1.40328i) q^{95} -10.5399i q^{97} +10.4069i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) $ 56 * q + 4 * q^5 + 32 * q^9	$ 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) $ 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.89464	−	1.67122i	−1.67122	−	0.964880i	−0.966956	−	0.254944i	$-0.917943\pi$
$3$	−2.89464	−	1.67122i	−1.67122	−	0.964880i	−0.704266	−	0.709936i	$-0.748724\pi$
$4$		0			0
$5$	1.42784	+	2.47308i	0.638548	+	1.10600i	0.985752	+	0.168207i	$0.0537979\pi$
$5$	1.42784	+	2.47308i	0.638548	+	1.10600i	−0.347204	+	0.937790i	$0.612869\pi$
$6$		0			0
$7$	−1.36322	+	2.26752i	−0.515247	+	0.857041i
$7$	−1.36322	+	2.26752i	−0.515247	+	0.857041i
$8$		0			0
$9$	4.08596	+	7.07710i	1.36199	+	2.35903i
$10$		0			0
$11$	1.10288	+	0.636749i	0.332531	+	0.191987i	0.656964	−	0.753922i	$-0.271840\pi$
$11$	1.10288	+	0.636749i	0.332531	+	0.191987i	−0.324433	+	0.945909i	$0.605174\pi$
$12$		0			0
$13$			3.41413i			0.946909i	0.880818	+	0.473454i	$0.156993\pi$
$13$			3.41413i			0.946909i	−0.880818	+	0.473454i	$0.843007\pi$
$14$		0			0
$15$		−	9.54492i		−	2.46449i
$16$		0			0
$17$	−1.97022	−	1.13751i	−0.477849	−	0.275886i	0.241671	−	0.970358i	$-0.422305\pi$
$17$	−1.97022	−	1.13751i	−0.477849	−	0.275886i	−0.719519	+	0.694472i	$0.755638\pi$
$18$		0			0
$19$	−0.851130	+	0.491400i	−0.195263	+	0.112735i	−0.594444	−	0.804137i	$-0.702628\pi$
$19$	−0.851130	+	0.491400i	−0.195263	+	0.112735i	0.399181	+	0.916872i	$0.369294\pi$
$20$		0			0
$21$	7.73555	−	4.28541i	1.68804	−	0.935154i
$22$		0			0
$23$	−3.90559	−	6.76468i	−0.814372	−	1.41053i	−0.909778	−	0.415095i	$-0.863748\pi$
$23$	−3.90559	−	6.76468i	−0.814372	−	1.41053i	0.0954064	−	0.995438i	$-0.469585\pi$
$24$		0			0
$25$	−1.57743	+	2.73219i	−0.315486	+	0.546439i
$26$		0			0
$27$		−	17.2869i		−	3.32686i
$28$		0			0
$29$		−	0.0172332i		−	0.00320012i	−0.999999	−	0.00160006i	$-0.999491\pi$
$29$		−	0.0172332i		−	0.00320012i	0.999999	−	0.00160006i	$-0.000509315\pi$
$30$		0			0
$31$	−4.79997	+	8.31379i	−0.862100	+	1.49320i	0.00779754	+	0.999970i	$0.497518\pi$
$31$	−4.79997	+	8.31379i	−0.862100	+	1.49320i	−0.869898	+	0.493232i	$0.835815\pi$
$32$		0			0
$33$	−2.12830	−	3.68632i	−0.370489	−	0.641705i
$34$		0			0
$35$	−7.55422	−	0.133706i	−1.27690	−	0.0226004i
$36$		0			0
$37$	−4.00389	−	6.93495i	−0.658236	−	1.14010i	−0.981072	−	0.193644i	$-0.937969\pi$
$37$	−4.00389	−	6.93495i	−0.658236	−	1.14010i	0.322836	−	0.946455i	$-0.395364\pi$
$38$		0			0
$39$	5.70576	−	9.88267i	0.913653	−	1.58249i
$40$		0			0
$41$	4.71859	+	4.32839i	0.736920	+	0.675980i
$41$	4.71859	+	4.32839i	0.736920	+	0.675980i
$42$		0			0
$43$	−2.35283			−0.358802			−0.179401	−	0.983776i	$-0.557416\pi$
$43$	−2.35283			−0.358802			−0.179401	+	0.983776i	$0.557416\pi$
$44$		0			0
$45$	−11.6682	+	20.2099i	−1.73939	+	3.01271i
$46$		0			0
$47$	3.58279	−	2.06853i	0.522604	−	0.301726i	−0.215395	−	0.976527i	$-0.569104\pi$
$47$	3.58279	−	2.06853i	0.522604	−	0.301726i	0.737999	+	0.674801i	$0.235771\pi$
$48$		0			0
$49$	−3.28328	−	6.18224i	−0.469040	−	0.883177i
$50$		0			0
$51$	3.80205	+	6.58535i	0.532394	+	0.922133i
$52$		0			0
$53$	1.38918	+	0.802043i	0.190819	+	0.110169i	0.592366	−	0.805669i	$-0.298194\pi$
$53$	1.38918	+	0.802043i	0.190819	+	0.110169i	−0.401547	+	0.915838i	$0.631527\pi$
$54$		0			0
$55$			3.63669i			0.490371i
$56$		0			0
$57$	3.28495			0.435103
$58$		0			0
$59$	−3.38451	+	5.86214i	−0.440625	+	0.763185i	−0.997736	−	0.0672529i	$-0.978577\pi$
$59$	−3.38451	+	5.86214i	−0.440625	+	0.763185i	0.557111	+	0.830438i	$0.311910\pi$
$60$		0			0
$61$	−3.36290	−	5.82471i	−0.430575	−	0.745778i	0.566348	−	0.824166i	$-0.308356\pi$
$61$	−3.36290	−	5.82471i	−0.430575	−	0.745778i	−0.996923	+	0.0783884i	$0.975023\pi$
$62$		0			0
$63$	−21.6175	−	0.382618i	−2.72355	−	0.0482054i
$64$		0			0
$65$	−8.44343	+	4.87481i	−1.04728	+	0.604646i
$66$		0			0
$67$	8.17149	+	4.71781i	0.998306	+	0.576372i	0.907747	−	0.419519i	$-0.137801\pi$
$67$	8.17149	+	4.71781i	0.998306	+	0.576372i	0.0905595	+	0.995891i	$0.471134\pi$
$68$		0			0
$69$			26.1084i			3.14308i
$70$		0			0
$71$		−	3.13702i		−	0.372296i	−0.982522	−	0.186148i	$-0.940400\pi$
$71$		−	3.13702i		−	0.372296i	0.982522	−	0.186148i	$-0.0596003\pi$
$72$		0			0
$73$	−5.62882	+	9.74940i	−0.658803	+	1.14108i	0.322123	+	0.946698i	$0.395604\pi$
$73$	−5.62882	+	9.74940i	−0.658803	+	1.14108i	−0.980926	+	0.194382i	$0.937730\pi$
$74$		0			0
$75$	9.13220	−	5.27248i	1.05450	−	0.608813i
$76$		0			0
$77$	−2.94731	+	1.63278i	−0.335877	+	0.186072i
$78$		0			0
$79$	−1.10592	+	0.638505i	−0.124426	+	0.0718375i	−0.560921	−	0.827869i	$-0.689553\pi$
$79$	−1.10592	+	0.638505i	−0.124426	+	0.0718375i	0.436495	+	0.899707i	$0.356220\pi$
$80$		0			0
$81$	−16.6323	+	28.8080i	−1.84803	+	3.20089i
$82$		0			0
$83$	−3.83139			−0.420550			−0.210275	−	0.977642i	$-0.567436\pi$
$83$	−3.83139			−0.420550			−0.210275	+	0.977642i	$0.567436\pi$
$84$		0			0
$85$		−	6.49669i		−	0.704665i
$86$		0			0
$87$	−0.0288004	+	0.0498838i	−0.00308773	+	0.00534810i
$88$		0			0
$89$	−11.9151	+	6.87919i	−1.26300	+	0.729193i	−0.973654	−	0.228032i	$-0.926771\pi$
$89$	−11.9151	+	6.87919i	−1.26300	+	0.729193i	−0.289345	+	0.957225i	$0.593438\pi$
$90$		0			0
$91$	−7.74160	−	4.65420i	−0.811540	−	0.487892i
$92$		0			0
$93$	27.7884	−	16.0436i	2.88152	−	1.66365i
$94$		0			0
$95$	−2.43055	−	1.40328i	−0.249369	−	0.143973i
$96$		0			0
$97$		−	10.5399i		−	1.07017i	−0.844798	−	0.535085i	$-0.820280\pi$
$97$		−	10.5399i		−	1.07017i	0.844798	−	0.535085i	$-0.179720\pi$
$98$		0			0
$99$			10.4069i			1.04594i
$100$		0			0
$101$	−16.0930	−	9.29128i	−1.60131	−	0.924517i	−0.991226	−	0.132181i	$-0.957802\pi$
$101$	−16.0930	−	9.29128i	−1.60131	−	0.924517i	−0.610085	−	0.792336i	$-0.708865\pi$
$102$		0			0
$103$	−2.66295	−	4.61237i	−0.262389	−	0.454470i	0.704488	−	0.709716i	$-0.251177\pi$
$103$	−2.66295	−	4.61237i	−0.262389	−	0.454470i	−0.966876	+	0.255246i	$0.917844\pi$
$104$		0			0
$105$	21.6433	+	13.0118i	2.11217	+	1.26982i
$106$		0			0
$107$	−4.41227	−	7.64228i	−0.426550	−	0.738807i	0.570013	−	0.821635i	$-0.306938\pi$
$107$	−4.41227	−	7.64228i	−0.426550	−	0.738807i	−0.996564	+	0.0828285i	$0.973605\pi$
$108$		0			0
$109$	12.7691	+	7.37222i	1.22305	+	0.706131i	0.965568	−	0.260151i	$-0.0837723\pi$
$109$	12.7691	+	7.37222i	1.22305	+	0.706131i	0.257487	+	0.966282i	$0.417106\pi$
$110$		0			0
$111$			26.7656i			2.54048i
$112$		0			0
$113$	−5.57000			−0.523982			−0.261991	−	0.965070i	$-0.584379\pi$
$113$	−5.57000			−0.523982			−0.261991	+	0.965070i	$0.584379\pi$
$114$		0			0
$115$	11.1531	−	19.3177i	1.04003	−	1.80139i
$116$		0			0
$117$	−24.1621	+	13.9500i	−2.23379	+	1.28968i
$118$		0			0
$119$	5.26516	−	2.91684i	0.482656	−	0.267386i
$120$		0			0
$121$	−4.68910	−	8.12176i	−0.426282	−	0.738342i
$122$		0			0
$123$	−6.42492	−	20.4149i	−0.579316	−	1.84075i
$124$		0			0
$125$	5.26910			0.471283
$126$		0			0
$127$	−11.7889			−1.04610			−0.523049	−	0.852302i	$-0.675206\pi$
$127$	−11.7889			−1.04610			−0.523049	+	0.852302i	$0.675206\pi$
$128$		0			0
$129$	6.81058	+	3.93209i	0.599638	+	0.346201i
$130$		0			0
$131$	3.27601	+	5.67422i	0.286227	+	0.495759i	0.972906	−	0.231202i	$-0.0742657\pi$
$131$	3.27601	+	5.67422i	0.286227	+	0.495759i	−0.686679	+	0.726960i	$0.740932\pi$
$132$		0			0
$133$	0.0460158	−	2.59984i	0.00399007	−	0.225435i
$134$		0			0
$135$	42.7519	−	24.6828i	3.67950	−	2.12436i
$136$		0			0
$137$	−11.7173	−	6.76496i	−1.00107	−	0.577970i	−0.0925076	−	0.995712i	$-0.529488\pi$
$137$	−11.7173	−	6.76496i	−1.00107	−	0.577970i	−0.908566	+	0.417742i	$0.862822\pi$
$138$		0			0
$139$	12.1594			1.03135			0.515673	−	0.856785i	$-0.327542\pi$
$139$	12.1594			1.03135			0.515673	+	0.856785i	$0.327542\pi$
$140$		0			0
$141$	−13.8279			−1.16452
$142$		0			0
$143$	−2.17394	+	3.76538i	−0.181794	+	0.314877i
$144$		0			0
$145$	0.0426191	−	0.0246061i	0.00353932	−	0.00204343i
$146$		0			0
$147$	−0.827974	+	23.3824i	−0.0682901	+	1.92855i
$148$		0			0
$149$	1.02593	−	0.592323i	0.0840477	−	0.0485250i	−0.457387	−	0.889268i	$-0.651215\pi$
$149$	1.02593	−	0.592323i	0.0840477	−	0.0485250i	0.541435	+	0.840743i	$0.317881\pi$
$150$		0			0
$151$	−16.9980	−	9.81380i	−1.38328	−	0.798635i	−0.390731	−	0.920505i	$-0.627778\pi$
$151$	−16.9980	−	9.81380i	−1.38328	−	0.798635i	−0.992546	+	0.121869i	$0.961111\pi$
$152$		0			0
$153$		−	18.5912i		−	1.50301i
$154$		0			0
$155$	−27.4143			−2.20197
$156$		0			0
$157$	−0.469171	−	0.270876i	−0.0374439	−	0.0216183i	0.481161	−	0.876632i	$-0.340215\pi$
$157$	−0.469171	−	0.270876i	−0.0374439	−	0.0216183i	−0.518605	+	0.855014i	$0.673549\pi$
$158$		0			0
$159$	−2.68078	−	4.64325i	−0.212600	−	0.368234i
$160$		0			0
$161$	20.6632	+	0.365728i	1.62849	+	0.0288234i
$162$		0			0
$163$	12.7168	+	22.0262i	0.996057	+	1.72522i	0.574856	+	0.818254i	$0.305058\pi$
$163$	12.7168	+	22.0262i	0.996057	+	1.72522i	0.421201	+	0.906967i	$0.361609\pi$
$164$		0			0
$165$	6.07772	−	10.5269i	0.473150	−	0.819519i
$166$		0			0
$167$			6.26023i			0.484431i	0.970222	+	0.242216i	$0.0778742\pi$
$167$			6.26023i			0.484431i	−0.970222	+	0.242216i	$0.922126\pi$
$168$		0			0
$169$	1.34373			0.103364
$170$		0			0
$171$	−6.95537	−	4.01569i	−0.531891	−	0.307087i
$172$		0			0
$173$	9.34229	+	16.1813i	0.710281	+	1.23024i	0.964751	+	0.263163i	$0.0847657\pi$
$173$	9.34229	+	16.1813i	0.710281	+	1.23024i	−0.254470	+	0.967081i	$0.581901\pi$
$174$		0			0
$175$	−4.04492	−	7.30143i	−0.305767	−	0.551936i
$176$		0			0
$177$	19.5939	−	11.3125i	1.47276	−	0.850301i
$178$		0			0
$179$	13.6712	+	7.89306i	1.02183	+	0.589955i	0.914634	−	0.404283i	$-0.132479\pi$
$179$	13.6712	+	7.89306i	1.02183	+	0.589955i	0.107198	+	0.994238i	$0.465812\pi$
$180$		0			0
$181$			4.35013i			0.323342i	0.986845	+	0.161671i	$0.0516884\pi$
$181$			4.35013i			0.323342i	−0.986845	+	0.161671i	$0.948312\pi$
$182$		0			0
$183$			22.4806i			1.66181i
$184$		0			0
$185$	11.4338	−	19.8039i	0.840631	−	1.45601i
$186$		0			0
$187$	−1.44861	−	2.50907i	−0.105933	−	0.183481i
$188$		0			0
$189$	39.1983	+	23.5658i	2.85126	+	1.71416i
$190$		0			0
$191$	−18.9422	+	10.9363i	−1.37061	+	0.791323i	−0.991005	−	0.133825i	$-0.957274\pi$
$191$	−18.9422	+	10.9363i	−1.37061	+	0.791323i	−0.379607	+	0.925148i	$0.623941\pi$
$192$		0			0
$193$	−15.9608	−	9.21496i	−1.14888	−	0.663308i	−0.200268	−	0.979741i	$-0.564181\pi$
$193$	−15.9608	−	9.21496i	−1.14888	−	0.663308i	−0.948615	+	0.316434i	$0.897515\pi$
$194$		0			0
$195$	32.5876			2.33365
$196$		0			0
$197$	19.4760			1.38761			0.693803	−	0.720165i	$-0.255934\pi$
$197$	19.4760			1.38761			0.693803	+	0.720165i	$0.255934\pi$
$198$		0			0
$199$	−2.75202	−	1.58888i	−0.195085	−	0.112633i	0.399276	−	0.916831i	$-0.369262\pi$
$199$	−2.75202	−	1.58888i	−0.195085	−	0.112633i	−0.594361	+	0.804198i	$0.702595\pi$
$200$		0			0
$201$	−15.7690	−	27.3127i	−1.11226	−	1.92649i
$202$		0			0
$203$	0.0390765	+	0.0234925i	0.00274263	+	0.00164885i
$204$		0			0
$205$	−3.96710	+	17.8497i	−0.277074	+	1.24668i
$206$		0			0
$207$	31.9162	−	55.2805i	2.21833	−	3.84226i
$208$		0			0
$209$	−1.25159			−0.0865745
$210$		0			0
$211$		−	20.5647i		−	1.41573i	−0.706345	−	0.707867i	$-0.749657\pi$
$211$		−	20.5647i		−	1.41573i	0.706345	−	0.707867i	$-0.250343\pi$
$212$		0			0
$213$	−5.24265	+	9.08054i	−0.359221	+	0.622188i
$214$		0			0
$215$	−3.35945	−	5.81874i	−0.229113	−	0.396835i
$216$		0			0
$217$	−12.3083	−	22.2175i	−0.835541	−	1.50822i
$218$		0			0
$219$	32.5868	−	18.8140i	2.20201	−	1.27133i
$220$		0			0
$221$	3.88359	−	6.72658i	0.261239	−	0.452479i
$222$		0			0
$223$	−22.3009			−1.49338			−0.746689	−	0.665173i	$-0.768358\pi$
$223$	−22.3009			−1.49338			−0.746689	+	0.665173i	$0.768358\pi$
$224$		0			0
$225$	−25.7813			−1.71875
$226$		0			0
$227$	−9.05944	−	5.23047i	−0.601296	−	0.347159i	0.168255	−	0.985744i	$-0.446187\pi$
$227$	−9.05944	−	5.23047i	−0.601296	−	0.347159i	−0.769551	+	0.638585i	$0.779520\pi$
$228$		0			0
$229$	−17.9503	+	10.3636i	−1.18619	+	0.684847i	−0.957439	−	0.288637i	$-0.906798\pi$
$229$	−17.9503	+	10.3636i	−1.18619	+	0.684847i	−0.228752	+	0.973485i	$0.573465\pi$
$230$		0			0
$231$	11.2601	+	0.199298i	0.740862	+	0.0131129i
$232$		0			0
$233$	19.9415	−	11.5132i	1.30641	−	0.754255i	0.324913	−	0.945744i	$-0.394665\pi$
$233$	19.9415	−	11.5132i	1.30641	−	0.754255i	0.981495	+	0.191489i	$0.0613316\pi$
$234$		0			0
$235$	10.2313	+	5.90703i	0.667415	+	0.385332i
$236$		0			0
$237$	4.26833			0.277258
$238$		0			0
$239$			9.34289i			0.604341i	0.953254	+	0.302171i	$0.0977112\pi$
$239$			9.34289i			0.604341i	−0.953254	+	0.302171i	$0.902289\pi$
$240$		0			0
$241$	7.94995	−	13.7697i	0.512101	−	0.886986i	−0.487800	−	0.872955i	$-0.662201\pi$
$241$	7.94995	−	13.7697i	0.512101	−	0.886986i	0.999902	−	0.0140303i	$-0.00446612\pi$
$242$		0			0
$243$	51.3765	−	29.6622i	3.29580	−	1.90283i
$244$		0			0
$245$	10.6012	−	16.9471i	0.677287	−	1.08271i
$246$		0			0
$247$	−1.67770	−	2.90587i	−0.106750	−	0.184896i
$248$		0			0
$249$	11.0905	+	6.40311i	0.702833	+	0.405781i
$250$		0			0
$251$	10.4444			0.659247			0.329624	−	0.944112i	$-0.393078\pi$
$251$	10.4444			0.659247			0.329624	+	0.944112i	$0.393078\pi$
$252$		0			0
$253$		−	9.94752i		−	0.625395i
$254$		0			0
$255$	−10.8574	+	18.8056i	−0.679918	+	1.17765i
$256$		0			0
$257$	2.28526	−	1.31940i	0.142551	−	0.0823018i	−0.427028	−	0.904238i	$-0.640440\pi$
$257$	2.28526	−	1.31940i	0.142551	−	0.0823018i	0.569579	+	0.821936i	$0.307106\pi$
$258$		0			0
$259$	21.1833	+	0.374933i	1.31627	+	0.0232972i
$260$		0			0
$261$	0.121961	−	0.0704141i	0.00754918	−	0.00435852i
$262$		0			0
$263$	12.7942	+	7.38672i	0.788922	+	0.455484i	0.839583	−	0.543232i	$-0.182799\pi$
$263$	12.7942	+	7.38672i	0.788922	+	0.455484i	−0.0506608	+	0.998716i	$0.516133\pi$
$264$		0			0
$265$			4.58075i			0.281393i
$266$		0			0
$267$	45.9866			2.81434
$268$		0			0
$269$	−3.59737	+	6.23082i	−0.219335	+	0.379900i	−0.954605	−	0.297875i	$-0.903722\pi$
$269$	−3.59737	+	6.23082i	−0.219335	+	0.379900i	0.735270	+	0.677775i	$0.237056\pi$
$270$		0			0
$271$	−12.8734	−	22.2973i	−0.782002	−	1.35447i	−0.930774	−	0.365595i	$-0.880866\pi$
$271$	−12.8734	−	22.2973i	−0.782002	−	1.35447i	0.148773	−	0.988871i	$-0.452468\pi$
$272$		0			0
$273$	14.6309	+	26.4101i	0.885505	+	1.59841i
$274$		0			0
$275$	−3.47944	+	2.00886i	−0.209818	+	0.121139i
$276$		0			0
$277$	5.04779	−	8.74302i	0.303292	−	0.525317i	−0.673588	−	0.739107i	$-0.735248\pi$
$277$	5.04779	−	8.74302i	0.303292	−	0.525317i	0.976880	+	0.213790i	$0.0685809\pi$
$278$		0			0
$279$	−78.4500			−4.69668
$280$		0			0
$281$			31.4886i			1.87845i	0.343300	+	0.939226i	$0.388455\pi$
$281$			31.4886i			1.87845i	−0.343300	+	0.939226i	$0.611545\pi$
$282$		0			0
$283$	−10.9374	+	18.9441i	−0.650161	+	1.12611i	0.332922	+	0.942954i	$0.391965\pi$
$283$	−10.9374	+	18.9441i	−0.650161	+	1.12611i	−0.983083	+	0.183158i	$0.941368\pi$
$284$		0			0
$285$	4.69038	+	8.12397i	0.277834	+	0.481223i
$286$		0			0
$287$	−16.2472	+	4.79896i	−0.959039	+	0.283273i
$288$		0			0
$289$	−5.91216	−	10.2402i	−0.347774	−	0.602362i
$290$		0			0
$291$	−17.6146	+	30.5094i	−1.03259	+	1.78849i
$292$		0			0
$293$			2.76984i			0.161816i	0.996722	+	0.0809080i	$0.0257820\pi$
$293$			2.76984i			0.161816i	−0.996722	+	0.0809080i	$0.974218\pi$
$294$		0			0
$295$	−19.3301			−1.12544
$296$		0			0
$297$	11.0074	−	19.0654i	0.638714	−	1.10628i
$298$		0			0
$299$	23.0955	−	13.3342i	1.33565	−	0.771136i
$300$		0			0
$301$	3.20741	−	5.33507i	0.184872	−	0.307509i
$302$		0			0
$303$	31.0556	+	53.7898i	1.78410	+	3.09015i
$304$		0			0
$305$	9.60334	−	16.6335i	0.549886	−	0.952430i
$306$		0			0
$307$	−6.90088			−0.393854			−0.196927	−	0.980418i	$-0.563096\pi$
$307$	−6.90088			−0.393854			−0.196927	+	0.980418i	$0.563096\pi$
$308$		0			0
$309$			17.8015i			1.01269i
$310$		0			0
$311$	0.268231	+	0.154863i	0.0152100	+	0.00878148i	0.507586	−	0.861601i	$-0.330538\pi$
$311$	0.268231	+	0.154863i	0.0152100	+	0.00878148i	−0.492376	+	0.870383i	$0.663871\pi$
$312$		0			0
$313$	6.57240	−	3.79458i	0.371494	−	0.214482i	−0.302617	−	0.953112i	$-0.597860\pi$
$313$	6.57240	−	3.79458i	0.371494	−	0.214482i	0.674111	+	0.738630i	$0.264527\pi$
$314$		0			0
$315$	−29.9200	−	54.0082i	−1.68580	−	3.04302i
$316$		0			0
$317$	−16.0085	+	9.24253i	−0.899129	+	0.519112i	−0.876918	−	0.480641i	$-0.840404\pi$
$317$	−16.0085	+	9.24253i	−0.899129	+	0.519112i	−0.0222115	+	0.999753i	$0.507071\pi$
$318$		0			0
$319$	0.0109732	−	0.0190061i	0.000614381	−	0.00106414i
$320$		0			0
$321$			29.4955i			1.64628i
$322$		0			0
$323$	2.23588			0.124408
$324$		0			0
$325$	−9.32806	−	5.38556i	−0.517427	−	0.298737i
$326$		0			0
$327$	−24.6412	−	42.6799i	−1.36266	−	2.36020i
$328$		0			0
$329$	−0.193701	+	10.9439i	−0.0106791	+	0.603357i
$330$		0			0
$331$	−4.75436	+	2.74493i	−0.261323	+	0.150875i	−0.624938	−	0.780674i	$-0.714876\pi$
$331$	−4.75436	+	2.74493i	−0.261323	+	0.150875i	0.363615	+	0.931549i	$0.381542\pi$
$332$		0			0
$333$	32.7195	−	56.6719i	1.79302	−	3.10560i
$334$		0			0
$335$			26.9450i			1.47217i
$336$		0			0
$337$	−10.4452			−0.568986			−0.284493	−	0.958678i	$-0.591825\pi$
$337$	−10.4452			−0.568986			−0.284493	+	0.958678i	$0.591825\pi$
$338$		0			0
$339$	16.1232	+	9.30871i	0.875689	+	0.505580i
$340$		0			0
$341$	−10.5876	+	6.11275i	−0.573350	+	0.331024i
$342$		0			0
$343$	18.4942	+	0.982832i	0.998591	+	0.0530680i
$344$		0			0
$345$	−64.5683	+	37.2786i	−3.47624	+	2.00701i
$346$		0			0
$347$	21.4144	+	12.3636i	1.14958	+	0.663712i	0.948786	−	0.315920i	$-0.102313\pi$
$347$	21.4144	+	12.3636i	1.14958	+	0.663712i	0.200798	+	0.979633i	$0.435647\pi$
$348$		0			0
$349$	−3.15478			−0.168872			−0.0844359	−	0.996429i	$-0.526909\pi$
$349$	−3.15478			−0.168872			−0.0844359	+	0.996429i	$0.526909\pi$
$350$		0			0
$351$	59.0196			3.15023
$352$		0			0
$353$	0.697880	−	1.20876i	0.0371444	−	0.0643360i	−0.846856	−	0.531823i	$-0.821507\pi$
$353$	0.697880	−	1.20876i	0.0371444	−	0.0643360i	0.884000	+	0.467487i	$0.154841\pi$
$354$		0			0
$355$	7.75811	−	4.47915i	0.411758	−	0.237729i
$356$		0			0
$357$	−20.1154	−	0.356032i	−1.06462	−	0.0188432i
$358$		0			0
$359$	0.470898	+	0.815619i	0.0248530	+	0.0430467i	0.878184	−	0.478322i	$-0.158755\pi$
$359$	0.470898	+	0.815619i	0.0248530	+	0.0430467i	−0.853331	+	0.521369i	$0.825422\pi$
$360$		0			0
$361$	−9.01705	+	15.6180i	−0.474582	+	0.822000i
$362$		0			0
$363$			31.3461i			1.64524i
$364$		0			0
$365$	−32.1481			−1.68271
$366$		0			0
$367$	−15.9467	+	27.6205i	−0.832411	+	1.44178i	0.0637108	+	0.997968i	$0.479706\pi$
$367$	−15.9467	+	27.6205i	−0.832411	+	1.44178i	−0.896121	+	0.443809i	$0.853627\pi$
$368$		0			0
$369$	−11.3524	+	51.0795i	−0.590984	+	2.65909i
$370$		0			0
$371$	−3.71240	+	2.05663i	−0.192738	+	0.106775i
$372$		0			0
$373$	−3.36868	−	5.83472i	−0.174424	−	0.302110i	0.765538	−	0.643391i	$-0.222473\pi$
$373$	−3.36868	−	5.83472i	−0.174424	−	0.302110i	−0.939962	+	0.341280i	$0.889140\pi$
$374$		0			0
$375$	−15.2522	−	8.80584i	−0.787618	−	0.454731i
$376$		0			0
$377$	0.0588362			0.00303022
$378$		0			0
$379$	21.0763			1.08262			0.541308	−	0.840825i	$-0.317929\pi$
$379$	21.0763			1.08262			0.541308	+	0.840825i	$0.317929\pi$
$380$		0			0
$381$	34.1247	+	19.7019i	1.74826	+	1.00936i
$382$		0			0
$383$	−8.45613	+	4.88215i	−0.432088	+	0.249466i	−0.700236	−	0.713912i	$-0.746922\pi$
$383$	−8.45613	+	4.88215i	−0.432088	+	0.249466i	0.268148	+	0.963378i	$0.413588\pi$
$384$		0			0
$385$	−8.24626	−	4.95760i	−0.420269	−	0.252663i
$386$		0			0
$387$	−9.61356	−	16.6512i	−0.488685	−	0.846427i
$388$		0			0
$389$	−8.89671	+	15.4095i	−0.451081	+	0.781295i	−0.998453	−	0.0555939i	$-0.982295\pi$
$389$	−8.89671	+	15.4095i	−0.451081	+	0.781295i	0.547372	+	0.836889i	$0.315628\pi$
$390$		0			0
$391$			17.7705i			0.898695i
$392$		0			0
$393$		−	21.8998i		−	1.10470i
$394$		0			0
$395$	−3.15816	−	1.82336i	−0.158904	−	0.0917433i
$396$		0			0
$397$	−22.2634	+	12.8538i	−1.11737	+	0.645113i	−0.940728	−	0.339162i	$-0.889856\pi$
$397$	−22.2634	+	12.8538i	−1.11737	+	0.645113i	−0.176641	+	0.984275i	$0.556523\pi$
$398$		0			0
$399$	−4.47811	+	7.44870i	−0.224186	+	0.372901i
$400$		0			0
$401$	11.6874	+	20.2432i	0.583642	+	1.01090i	0.995043	+	0.0994438i	$0.0317064\pi$
$401$	11.6874	+	20.2432i	0.583642	+	1.01090i	−0.411401	+	0.911455i	$0.634960\pi$
$402$		0			0
$403$	−28.3844	−	16.3877i	−1.41393	−	0.816330i
$404$		0			0
$405$	−94.9928			−4.72023
$406$		0			0
$407$		−	10.1979i		−	0.505491i
$408$		0			0
$409$	8.07479	−	13.9860i	0.399273	−	0.691561i	−0.594363	−	0.804197i	$-0.702596\pi$
$409$	8.07479	−	13.9860i	0.399273	−	0.691561i	0.993636	+	0.112636i	$0.0359293\pi$
$410$		0			0
$411$	22.6115	+	39.1643i	1.11534	+	1.93183i
$412$		0			0
$413$	−8.67869	−	15.6658i	−0.427050	−	0.770863i
$414$		0			0
$415$	−5.47060	−	9.47536i	−0.268541	−	0.465127i
$416$		0			0
$417$	−35.1971	−	20.3211i	−1.72361	−	0.995126i
$418$		0			0
$419$	−0.145809			−0.00712322			−0.00356161	−	0.999994i	$-0.501134\pi$
$419$	−0.145809			−0.00712322			−0.00356161	+	0.999994i	$0.501134\pi$
$420$		0			0
$421$		−	29.9240i		−	1.45840i	−0.684298	−	0.729202i	$-0.739891\pi$
$421$		−	29.9240i		−	1.45840i	0.684298	−	0.729202i	$-0.260109\pi$
$422$		0			0
$423$	29.2783	+	16.9038i	1.42356	+	0.821893i
$424$		0			0
$425$	6.21578	−	3.58868i	0.301509	−	0.174077i
$426$		0			0
$427$	17.7920	+	0.314909i	0.861015	+	0.0152395i
$428$		0			0
$429$	12.5856	−	7.26627i	0.607636	−	0.350819i
$430$		0			0
$431$	−2.55062	+	4.41781i	−0.122859	+	0.212798i	−0.920894	−	0.389813i	$-0.872540\pi$
$431$	−2.55062	+	4.41781i	−0.122859	+	0.212798i	0.798035	+	0.602611i	$0.205873\pi$
$432$		0			0
$433$	−16.4540			−0.790727			−0.395363	−	0.918525i	$-0.629381\pi$
$433$	−16.4540			−0.790727			−0.395363	+	0.918525i	$0.629381\pi$
$434$		0			0
$435$	−0.164489			−0.00788665
$436$		0			0
$437$	6.64833	+	3.83842i	0.318033	+	0.183616i
$438$		0			0
$439$	−10.7398	+	6.20060i	−0.512581	+	0.295939i	−0.733894	−	0.679264i	$-0.762299\pi$
$439$	−10.7398	+	6.20060i	−0.512581	+	0.295939i	0.221313	+	0.975203i	$0.428966\pi$
$440$		0			0
$441$	30.3369	−	48.4965i	1.44462	−	2.30936i
$442$		0			0
$443$	−9.08072	−	15.7283i	−0.431438	−	0.747272i	0.565559	−	0.824708i	$-0.308660\pi$
$443$	−9.08072	−	15.7283i	−0.431438	−	0.747272i	−0.996997	+	0.0774351i	$0.975327\pi$
$444$		0			0
$445$	−34.0257	−	19.6447i	−1.61297	−	0.931249i
$446$		0			0
$447$	−3.95961			−0.187283
$448$		0			0
$449$	−0.727275			−0.0343222			−0.0171611	−	0.999853i	$-0.505463\pi$
$449$	−0.727275			−0.0343222			−0.0171611	+	0.999853i	$0.505463\pi$
$450$		0			0
$451$	2.44795	+	7.77825i	0.115269	+	0.366263i
$452$		0			0
$453$	32.8021	+	56.8148i	1.54118	+	2.66939i
$454$		0			0
$455$	0.456488	−	25.7911i	0.0214005	−	1.20910i
$456$		0			0
$457$	28.1671	−	16.2623i	1.31760	−	0.760719i	0.334261	−	0.942481i	$-0.391513\pi$
$457$	28.1671	−	16.2623i	1.31760	−	0.760719i	0.983343	+	0.181762i	$0.0581800\pi$
$458$		0			0
$459$	−19.6639	+	34.0589i	−0.917834	+	1.58974i
$460$		0			0
$461$	31.5168			1.46789			0.733943	−	0.679211i	$-0.237678\pi$
$461$	31.5168			1.46789			0.733943	+	0.679211i	$0.237678\pi$
$462$		0			0
$463$			39.8842i			1.85358i	0.375583	+	0.926789i	$0.377442\pi$
$463$			39.8842i			1.85358i	−0.375583	+	0.926789i	$0.622558\pi$
$464$		0			0
$465$	79.3545	+	45.8154i	3.67998	+	2.12464i
$466$		0			0
$467$	9.76790	+	16.9185i	0.452005	+	0.782895i	0.998510	−	0.0545604i	$-0.0173757\pi$
$467$	9.76790	+	16.9185i	0.452005	+	0.782895i	−0.546506	+	0.837455i	$0.684042\pi$
$468$		0			0
$469$	−21.8372	+	12.0976i	−1.00835	+	0.558615i
$470$		0			0
$471$	0.905388	+	1.56818i	0.0417181	+	0.0722578i
$472$		0			0
$473$	−2.59489	−	1.49816i	−0.119313	−	0.0688854i
$474$		0			0
$475$		−	3.10060i		−	0.142265i
$476$		0			0
$477$			13.1085i			0.600196i
$478$		0			0
$479$	15.8197	+	9.13352i	0.722822	+	0.417321i	0.815790	−	0.578348i	$-0.196302\pi$
$479$	15.8197	+	9.13352i	0.722822	+	0.417321i	−0.0929686	+	0.995669i	$0.529636\pi$
$480$		0			0
$481$	23.6768	−	13.6698i	1.07957	−	0.623290i
$482$		0			0
$483$	−59.2013	−	35.5914i	−2.69375	−	1.61947i
$484$		0			0
$485$	26.0662	−	15.0493i	1.18360	−	0.683354i
$486$		0			0
$487$	−2.37745	+	4.11786i	−0.107732	+	0.186598i	−0.914851	−	0.403791i	$-0.867692\pi$
$487$	−2.37745	+	4.11786i	−0.107732	+	0.186598i	0.807119	+	0.590389i	$0.201026\pi$
$488$		0			0
$489$		−	85.0104i		−	3.84430i
$490$		0			0
$491$	23.6740			1.06839			0.534196	−	0.845361i	$-0.320614\pi$
$491$	23.6740			1.06839			0.534196	+	0.845361i	$0.320614\pi$
$492$		0			0
$493$	−0.0196028	+	0.0339531i	−0.000882867	+	0.00152917i
$494$		0			0
$495$	−25.7372	+	14.8594i	−1.15680	+	0.667880i
$496$		0			0
$497$	7.11325	+	4.27644i	0.319073	+	0.191824i
$498$		0			0
$499$	−5.70632	+	3.29454i	−0.255450	+	0.147484i	−0.622257	−	0.782813i	$-0.713784\pi$
$499$	−5.70632	+	3.29454i	−0.255450	+	0.147484i	0.366807	+	0.930297i	$0.380451\pi$
$500$		0			0
$501$	10.4622	−	18.1211i	0.467418	−	0.809592i
$502$		0			0
$503$			10.5303i			0.469522i	0.972053	+	0.234761i	$0.0754308\pi$
$503$			10.5303i			0.469522i	−0.972053	+	0.234761i	$0.924569\pi$
$504$		0			0
$505$		−	53.0657i		−	2.36139i
$506$		0			0
$507$	−3.88963	−	2.24568i	−0.172744	−	0.0997340i
$508$		0			0
$509$	31.8073	−	18.3640i	1.40983	−	0.813968i	0.414463	−	0.910066i	$-0.363970\pi$
$509$	31.8073	−	18.3640i	1.40983	−	0.813968i	0.995372	+	0.0960979i	$0.0306362\pi$
$510$		0			0
$511$	−14.4336	−	26.0540i	−0.638507	−	1.15256i
$512$		0			0
$513$	8.49477	+	14.7134i	0.375053	+	0.649611i
$514$		0			0
$515$	7.60452	−	13.1714i	0.335095	−	0.580402i
$516$		0			0
$517$	5.26852			0.231709
$518$		0			0
$519$		−	62.4522i		−	2.74135i
$520$		0			0
$521$	16.3222	+	9.42362i	0.715088	+	0.412856i	0.812942	−	0.582344i	$-0.197864\pi$
$521$	16.3222	+	9.42362i	0.715088	+	0.412856i	−0.0978540	+	0.995201i	$0.531198\pi$
$522$		0			0
$523$	−8.62436	−	14.9378i	−0.377117	−	0.653185i	0.613525	−	0.789676i	$-0.289751\pi$
$523$	−8.62436	−	14.9378i	−0.377117	−	0.653185i	−0.990641	+	0.136490i	$0.956418\pi$
$524$		0			0
$525$	−0.493726	+	27.8950i	−0.0215480	+	1.21744i
$526$		0			0
$527$	18.9140	−	10.9200i	0.823907	−	0.475683i
$528$		0			0
$529$	−19.0073	+	32.9215i	−0.826403	+	1.43137i
$530$		0			0
$531$	−55.3159			−2.40050
$532$		0			0
$533$	−14.7777	+	16.1099i	−0.640092	+	0.697795i
$534$		0			0
$535$	12.6000	−	21.8238i	0.544746	−	0.943527i
$536$		0			0
$537$	−26.3821	−	45.6951i	−1.13847	−	1.97189i
$538$		0			0
$539$	0.315465	−	8.90890i	0.0135880	−	0.383733i
$540$		0			0
$541$	21.6967	+	37.5798i	0.932814	+	1.61568i	0.778487	+	0.627661i	$0.215988\pi$
$541$	21.6967	+	37.5798i	0.932814	+	1.61568i	0.154327	+	0.988020i	$0.450679\pi$
$542$		0			0
$543$	7.27003	−	12.5921i	0.311987	−	0.540377i
$544$		0			0
$545$			42.1053i			1.80359i
$546$		0			0
$547$		−	12.8757i		−	0.550527i	−0.961369	−	0.275263i	$-0.911235\pi$
$547$		−	12.8757i		−	0.550527i	0.961369	−	0.275263i	$-0.0887650\pi$
$548$		0			0
$549$	27.4814	−	47.5991i	1.17288	−	2.03148i
$550$		0			0
$551$	0.00846838	+	0.0146677i	0.000360765	+	0.000624863i
$552$		0			0
$553$	0.0597910	−	3.37812i	0.00254257	−	0.143652i
$554$		0			0
$555$	−66.1936	+	38.2169i	−2.80976	+	1.62222i
$556$		0			0
$557$	−30.3677	−	17.5328i	−1.28672	−	0.742888i	−0.308651	−	0.951175i	$-0.599878\pi$
$557$	−30.3677	−	17.5328i	−1.28672	−	0.742888i	−0.978068	+	0.208288i	$0.933211\pi$
$558$		0			0
$559$		−	8.03284i		−	0.339753i
$560$		0			0
$561$			9.68381i			0.408851i
$562$		0			0
$563$	−34.6461	−	20.0029i	−1.46016	−	0.843024i	−0.461142	−	0.887326i	$-0.652560\pi$
$563$	−34.6461	−	20.0029i	−1.46016	−	0.843024i	−0.999018	+	0.0443026i	$0.985893\pi$
$564$		0			0
$565$	−7.95305	−	13.7751i	−0.334587	−	0.579522i
$566$		0			0
$567$	−42.6492	−	76.9856i	−1.79110	−	3.23309i
$568$		0			0
$569$	−5.60021	−	9.69985i	−0.234773	−	0.406639i	0.724434	−	0.689345i	$-0.242101\pi$
$569$	−5.60021	−	9.69985i	−0.234773	−	0.406639i	−0.959207	+	0.282706i	$0.908768\pi$
$570$		0			0
$571$	24.8072	+	14.3224i	1.03815	+	0.599376i	0.919308	−	0.393538i	$-0.128749\pi$
$571$	24.8072	+	14.3224i	1.03815	+	0.599376i	0.118840	+	0.992913i	$0.462082\pi$
$572$		0			0
$573$	73.1080			3.05413
$574$		0			0
$575$	24.6432			1.02769
$576$		0			0
$577$	−7.53352	−	4.34948i	−0.313625	−	0.181071i	0.334923	−	0.942246i	$-0.391290\pi$
$577$	−7.53352	−	4.34948i	−0.313625	−	0.181071i	−0.648547	+	0.761174i	$0.724623\pi$
$578$		0			0
$579$	30.8005	+	53.3480i	1.28002	+	2.21707i
$580$		0			0
$581$	5.22302	−	8.68776i	0.216687	−	0.360429i
$582$		0			0
$583$	1.02140	+	1.76912i	0.0423021	+	0.0732693i
$584$		0			0
$585$	−68.9991	−	39.8366i	−2.85276	−	1.64704i
$586$		0			0
$587$		−	8.55700i		−	0.353185i	−0.984284	−	0.176593i	$-0.943492\pi$
$587$		−	8.55700i		−	0.353185i	0.984284	−	0.176593i	$-0.0565075\pi$
$588$		0			0
$589$		−	9.43483i		−	0.388755i
$590$		0			0
$591$	−56.3759	−	32.5487i	−2.31900	−	1.33887i
$592$		0			0
$593$	28.5590	−	16.4886i	1.17278	−	0.677104i	0.218446	−	0.975849i	$-0.429901\pi$
$593$	28.5590	−	16.4886i	1.17278	−	0.677104i	0.954333	+	0.298745i	$0.0965680\pi$
$594$		0			0
$595$	14.7314	+	8.85640i	0.603928	+	0.363077i
$596$		0			0
$597$	5.31073	+	9.19846i	0.217354	+	0.376468i
$598$		0			0
$599$	−13.8917	+	24.0612i	−0.567600	+	0.983113i	0.429202	+	0.903208i	$0.358795\pi$
$599$	−13.8917	+	24.0612i	−0.567600	+	0.983113i	−0.996803	+	0.0799042i	$0.974539\pi$
$600$		0			0
$601$		−	3.12765i		−	0.127580i	−0.997963	−	0.0637898i	$-0.979681\pi$
$601$		−	3.12765i		−	0.127580i	0.997963	−	0.0637898i	$-0.0203187\pi$
$602$		0			0
$603$			77.1072i			3.14005i
$604$		0			0
$605$	13.3905	−	23.1931i	0.544403	−	0.942933i
$606$		0			0
$607$	−1.66790	−	2.88889i	−0.0676980	−	0.117256i	0.830190	−	0.557481i	$-0.188232\pi$
$607$	−1.66790	−	2.88889i	−0.0676980	−	0.117256i	−0.897888	+	0.440225i	$0.854899\pi$
$608$		0			0
$609$	−0.0738512	−	0.133308i	−0.00299260	−	0.00540191i
$610$		0			0
$611$	7.06221	+	12.2321i	0.285706	+	0.494858i
$612$		0			0
$613$	−10.7528	+	18.6244i	−0.434302	+	0.752233i	−0.997238	−	0.0742672i	$-0.976338\pi$
$613$	−10.7528	+	18.6244i	−0.434302	+	0.752233i	0.562936	+	0.826500i	$0.309672\pi$
$614$		0			0
$615$	41.3141	−	45.0386i	1.66595	−	1.81613i
$616$		0			0
$617$	28.5261			1.14842			0.574210	−	0.818708i	$-0.305309\pi$
$617$	28.5261			1.14842			0.574210	+	0.818708i	$0.305309\pi$
$618$		0			0
$619$	−13.4267	+	23.2556i	−0.539663	+	0.934723i	0.459259	+	0.888302i	$0.348115\pi$
$619$	−13.4267	+	23.2556i	−0.539663	+	0.934723i	−0.998922	+	0.0464209i	$0.985218\pi$
$620$		0			0
$621$	−116.940	+	67.5154i	−4.69265	+	2.70930i
$622$		0			0
$623$	0.644182	−	36.3956i	0.0258086	−	1.45816i
$624$		0			0
$625$	15.4106	+	26.6919i	0.616423	+	1.06768i
$626$		0			0
$627$	3.62291	+	2.09169i	0.144685	+	0.0835341i
$628$		0			0
$629$			18.2178i			0.726393i
$630$		0			0
$631$	22.7854			0.907072			0.453536	−	0.891238i	$-0.350162\pi$
$631$	22.7854			0.907072			0.453536	+	0.891238i	$0.350162\pi$
$632$		0			0
$633$	−34.3682	+	59.5275i	−1.36601	+	2.36601i
$634$		0			0
$635$	−16.8327	−	29.1550i	−0.667984	−	1.15698i
$636$		0			0
$637$	21.1069	−	11.2095i	0.836288	−	0.444138i
$638$		0			0
$639$	22.2010	−	12.8177i	0.878257	−	0.507062i
$640$		0			0
$641$	2.90828	+	1.67910i	0.114870	+	0.0663203i	0.556334	−	0.830959i	$-0.312207\pi$
$641$	2.90828	+	1.67910i	0.114870	+	0.0663203i	−0.441464	+	0.897279i	$0.645541\pi$
$642$		0			0
$643$		−	3.07260i		−	0.121171i	−0.998163	−	0.0605857i	$-0.980703\pi$
$643$		−	3.07260i		−	0.121171i	0.998163	−	0.0605857i	$-0.0192968\pi$
$644$		0			0
$645$			22.4575i			0.884265i
$646$		0			0
$647$	18.2697	−	31.6440i	0.718255	−	1.24405i	−0.243436	−	0.969917i	$-0.578275\pi$
$647$	18.2697	−	31.6440i	0.718255	−	1.24405i	0.961691	−	0.274136i	$-0.0883920\pi$
$648$		0			0
$649$	−7.46542	+	4.31016i	−0.293043	+	0.169189i
$650$		0			0
$651$	−1.50236	+	84.8816i	−0.0588822	+	3.32677i
$652$		0			0
$653$	−30.6308	+	17.6847i	−1.19868	+	0.692056i	−0.960260	−	0.279107i	$-0.909962\pi$
$653$	−30.6308	+	17.6847i	−1.19868	+	0.692056i	−0.238416	+	0.971163i	$0.576628\pi$
$654$		0			0
$655$	−9.35522	+	16.2037i	−0.365539	+	0.633132i
$656$		0			0
$657$	−91.9965			−3.58913
$658$		0			0
$659$			39.9277i			1.55536i	0.628659	+	0.777681i	$0.283604\pi$
$659$			39.9277i			1.55536i	−0.628659	+	0.777681i	$0.716396\pi$
$660$		0			0
$661$	−9.01545	+	15.6152i	−0.350660	+	0.607362i	−0.986365	−	0.164571i	$-0.947376\pi$
$661$	−9.01545	+	15.6152i	−0.350660	+	0.607362i	0.635705	+	0.771932i	$0.280709\pi$
$662$		0			0
$663$	−22.4832	+	12.9807i	−0.873176	+	0.504128i
$664$		0			0
$665$	6.49532	−	3.59834i	0.251878	−	0.139538i
$666$		0			0
$667$	−0.116577	+	0.0673056i	−0.00451387	+	0.00260608i
$668$		0			0
$669$	64.5531	+	37.2697i	2.49577	+	1.44093i
$670$		0			0
$671$		−	8.56529i		−	0.330659i
$672$		0			0
$673$		−	3.02214i		−	0.116495i	−0.998302	−	0.0582476i	$-0.981449\pi$
$673$		−	3.02214i		−	0.116495i	0.998302	−	0.0582476i	$-0.0185513\pi$
$674$		0			0
$675$	47.2311	+	27.2689i	1.81792	+	1.04958i
$676$		0			0
$677$	17.2286	+	29.8409i	0.662151	+	1.14688i	0.980049	+	0.198754i	$0.0636895\pi$
$677$	17.2286	+	29.8409i	0.662151	+	1.14688i	−0.317899	+	0.948125i	$0.602977\pi$
$678$		0			0
$679$	23.8995	+	14.3682i	0.917180	+	0.551402i
$680$		0			0
$681$	17.4826	+	30.2807i	0.669933	+	1.16036i
$682$		0			0
$683$	−9.61335	−	5.55027i	−0.367844	−	0.212375i	0.304672	−	0.952457i	$-0.401453\pi$
$683$	−9.61335	−	5.55027i	−0.367844	−	0.212375i	−0.672516	+	0.740082i	$0.734787\pi$
$684$		0			0
$685$		−	38.6370i		−	1.47625i
$686$		0			0
$687$	69.2796			2.64318
$688$		0			0
$689$	−2.73828	+	4.74284i	−0.104320	+	0.180688i
$690$		0			0
$691$	25.1725	−	14.5333i	0.957607	−	0.552875i	0.0621711	−	0.998066i	$-0.480198\pi$
$691$	25.1725	−	14.5333i	0.957607	−	0.552875i	0.895436	+	0.445191i	$0.146864\pi$
$692$		0			0
$693$	−23.5979	−	14.1869i	−0.896410	−	0.538916i
$694$		0			0
$695$	17.3616	+	30.0712i	0.658564	+	1.14067i
$696$		0			0
$697$	−4.37309	−	13.8953i	−0.165642	−	0.526322i
$698$		0			0
$699$	−76.9645			−2.91106
$700$		0			0
$701$	−33.8934			−1.28014			−0.640068	−	0.768319i	$-0.721094\pi$
$701$	−33.8934			−1.28014			−0.640068	+	0.768319i	$0.721094\pi$
$702$		0			0
$703$	6.81567	+	3.93503i	0.257058	+	0.148412i
$704$		0			0
$705$	−19.7439	−	34.1975i	−0.743599	−	1.28795i
$706$		0			0
$707$	43.0064	−	23.8251i	1.61742	−	0.896034i
$708$		0			0
$709$	−22.3457	+	12.9013i	−0.839209	+	0.484518i	−0.856995	−	0.515324i	$-0.827671\pi$
$709$	−22.3457	+	12.9013i	−0.839209	+	0.484518i	0.0177863	+	0.999842i	$0.494338\pi$
$710$		0			0
$711$	−9.03753	−	5.21782i	−0.338934	−	0.195683i
$712$		0			0
$713$	74.9869			2.80828
$714$		0			0
$715$	−12.4161			−0.464337
$716$		0			0
$717$	15.6140	−	27.0443i	0.583117	−	1.00999i
$718$		0			0
$719$	36.8802	−	21.2928i	1.37540	−	0.794086i	0.383796	−	0.923418i	$-0.374617\pi$
$719$	36.8802	−	21.2928i	1.37540	−	0.794086i	0.991601	+	0.129332i	$0.0412832\pi$
$720$		0			0
$721$	14.0888	+	0.249365i	0.524695	+	0.00928683i
$722$		0			0
$723$	−46.0245	+	26.5723i	−1.71167	+	0.988233i
$724$		0			0
$725$	0.0470843	+	0.0271841i	0.00174867	+	0.00100959i
$726$		0			0
$727$		−	18.7582i		−	0.695704i	−0.937549	−	0.347852i	$-0.886911\pi$
$727$		−	18.7582i		−	0.695704i	0.937549	−	0.347852i	$-0.113089\pi$
$728$		0			0
$729$	−98.4948			−3.64795
$730$		0			0
$731$	4.63558	+	2.67636i	0.171453	+	0.0989886i
$732$		0			0
$733$	7.63365	+	13.2219i	0.281955	+	0.488361i	0.971866	−	0.235533i	$-0.0756837\pi$
$733$	7.63365	+	13.2219i	0.281955	+	0.488361i	−0.689911	+	0.723894i	$0.742350\pi$
$734$		0			0
$735$	−59.0090	+	31.3387i	−2.17658	+	1.15594i
$736$		0			0
$737$	6.00812	+	10.4064i	0.221312	+	0.383324i
$738$		0			0
$739$	13.4654	−	23.3227i	0.495331	−	0.857939i	−0.504654	−	0.863322i	$-0.668380\pi$
$739$	13.4654	−	23.3227i	0.495331	−	0.857939i	0.999986	+	0.00538236i	$0.00171327\pi$
$740$		0			0
$741$			11.2153i			0.412003i
$742$		0			0
$743$	−38.2812			−1.40440			−0.702201	−	0.711979i	$-0.747799\pi$
$743$	−38.2812			−1.40440			−0.702201	+	0.711979i	$0.747799\pi$
$744$		0			0
$745$	2.92973	+	1.69148i	0.107337	+	0.0619710i
$746$		0			0
$747$	−15.6549	−	27.1151i	−0.572784	−	0.992091i
$748$		0			0
$749$	23.3439	+	0.413175i	0.852967	+	0.0150971i
$750$		0			0
$751$	−23.9073	+	13.8029i	−0.872389	+	0.503674i	−0.868142	−	0.496317i	$-0.834685\pi$
$751$	−23.9073	+	13.8029i	−0.872389	+	0.503674i	−0.00424786	+	0.999991i	$0.501352\pi$
$752$		0			0
$753$	−30.2329	−	17.4550i	−1.10175	−	0.636095i
$754$		0			0
$755$		−	56.0500i		−	2.03987i
$756$		0			0
$757$		−	23.3325i		−	0.848035i	−0.905654	−	0.424017i	$-0.860620\pi$
$757$		−	23.3325i		−	0.848035i	0.905654	−	0.424017i	$-0.139380\pi$
$758$		0			0
$759$	−16.6245	+	28.7945i	−0.603431	+	1.04517i
$760$		0			0
$761$	14.3816	+	24.9097i	0.521332	+	0.902974i	0.999692	+	0.0248103i	$0.00789816\pi$
$761$	14.3816	+	24.9097i	0.521332	+	0.902974i	−0.478360	+	0.878164i	$0.658769\pi$
$762$		0			0
$763$	−34.1237	+	18.9042i	−1.23536	+	0.684376i
$764$		0			0
$765$	45.9777	−	26.5453i	1.66233	−	0.959746i
$766$		0			0
$767$	−20.0141	−	11.5551i	−0.722667	−	0.417232i
$768$		0			0
$769$	16.1204			0.581318			0.290659	−	0.956827i	$-0.406126\pi$
$769$	16.1204			0.581318			0.290659	+	0.956827i	$0.406126\pi$
$770$		0			0
$771$	−8.82003			−0.317645
$772$		0			0
$773$	43.4003	+	25.0572i	1.56100	+	0.901244i	0.997156	+	0.0753630i	$0.0240115\pi$
$773$	43.4003	+	25.0572i	1.56100	+	0.901244i	0.563844	+	0.825881i	$0.309322\pi$
$774$		0			0
$775$	−15.1433	−	26.2289i	−0.543962	−	0.942170i
$776$		0			0
$777$	−60.6915	−	36.4873i	−2.17729	−	1.30897i
$778$		0			0
$779$	−6.14310	−	1.36531i	−0.220099	−	0.0489171i
$780$		0			0
$781$	1.99749	−	3.45976i	0.0714759	−	0.123800i
$782$		0			0
$783$	−0.297907			−0.0106463
$784$		0			0
$785$		−	1.54707i		−	0.0552172i
$786$		0			0
$787$	13.7910	−	23.8867i	0.491596	−	0.851470i	−0.508357	−	0.861146i	$-0.669747\pi$
$787$	13.7910	−	23.8867i	0.491596	−	0.851470i	0.999953	+	0.00967687i	$0.00308029\pi$
$788$		0			0
$789$	−24.6897	−	42.7638i	−0.878976	−	1.52243i
$790$		0			0
$791$	7.59312	−	12.6301i	0.269980	−	0.449074i
$792$		0			0
$793$	19.8863	−	11.4814i	0.706184	−	0.407715i
$794$		0			0
$795$	7.65544	−	13.2596i	0.271511	−	0.470270i
$796$		0			0
$797$	−37.4626			−1.32699			−0.663496	−	0.748180i	$-0.730928\pi$
$797$	−37.4626			−1.32699			−0.663496	+	0.748180i	$0.730928\pi$
$798$		0			0
$799$	−9.41185			−0.332967
$800$		0			0
$801$	−97.3694	−	56.2163i	−3.44038	−	1.98630i
$802$		0			0
$803$	−12.4158	+	7.16828i	−0.438145	+	0.252963i
$804$		0			0
$805$	28.5992	+	51.6241i	1.00799	+	1.81951i
$806$		0			0
$807$	20.8262	−	12.0240i	0.733116	−	0.423265i
$808$		0			0
$809$	−22.1564	−	12.7920i	−0.778977	−	0.449743i	0.0570906	−	0.998369i	$-0.481818\pi$
$809$	−22.1564	−	12.7920i	−0.778977	−	0.449743i	−0.836068	+	0.548626i	$0.815151\pi$
$810$		0			0
$811$	6.33968			0.222616			0.111308	−	0.993786i	$-0.464496\pi$
$811$	6.33968			0.222616			0.111308	+	0.993786i	$0.464496\pi$
$812$		0			0
$813$			86.0570i			3.01815i
$814$		0			0
$815$	−36.3150	+	62.8995i	−1.27206	+	2.20327i
$816$		0			0
$817$	2.00256	−	1.15618i	0.0700607	−	0.0404496i
$818$		0			0
$819$	1.30631	−	73.8049i	0.0456461	−	2.57895i
$820$		0			0
$821$	14.9064	+	25.8187i	0.520238	+	0.901079i	0.999723	+	0.0235286i	$0.00749009\pi$
$821$	14.9064	+	25.8187i	0.520238	+	0.901079i	−0.479485	+	0.877550i	$0.659177\pi$
$822$		0			0
$823$	20.5749	+	11.8789i	0.717195	+	0.414073i	0.813719	−	0.581258i	$-0.197439\pi$
$823$	20.5749	+	11.8789i	0.717195	+	0.414073i	−0.0965245	+	0.995331i	$0.530773\pi$
$824$		0			0
$825$	13.4290			0.467537
$826$		0			0
$827$		−	15.7429i		−	0.547434i	−0.961810	−	0.273717i	$-0.911747\pi$
$827$		−	15.7429i		−	0.547434i	0.961810	−	0.273717i	$-0.0882531\pi$
$828$		0			0
$829$	13.6466	−	23.6366i	0.473965	−	0.820932i	−0.525591	−	0.850738i	$-0.676156\pi$
$829$	13.6466	−	23.6366i	0.473965	−	0.820932i	0.999556	+	0.0298060i	$0.00948896\pi$
$830$		0			0
$831$	−29.2231	+	16.8719i	−1.01374	+	0.585281i
$832$		0			0
$833$	−0.563555	+	15.9151i	−0.0195260	+	0.551426i
$834$		0			0
$835$	−15.4821	+	8.93859i	−0.535780	+	0.309333i
$836$		0			0
$837$	143.719	+	82.9765i	4.96767	+	2.86809i
$838$		0			0
$839$			45.3952i			1.56722i	0.621255	+	0.783609i	$0.286623\pi$
$839$			45.3952i			1.56722i	−0.621255	+	0.783609i	$0.713377\pi$
$840$		0			0
$841$	28.9997			0.999990
$842$		0			0
$843$	52.6244	−	91.1481i	1.81248	−	3.13931i
$844$		0			0
$845$	1.91863	+	3.32317i	0.0660029	+	0.114320i
$846$		0			0
$847$	24.8085	+	0.439098i	0.852431	+	0.0150876i
$848$		0			0
$849$	63.3197	−	36.5577i	2.17313	−	1.25466i
$850$		0			0
$851$	−31.2751	+	54.1701i	−1.07210	+	1.85693i
$852$		0			0
$853$	−19.9508			−0.683102			−0.341551	−	0.939863i	$-0.610952\pi$
$853$	−19.9508			−0.683102			−0.341551	+	0.939863i	$0.610952\pi$
$854$		0			0
$855$		−	22.9350i		−	0.784359i
$856$		0			0
$857$	−4.97078	+	8.60964i	−0.169798	+	0.294100i	−0.938349	−	0.345690i	$-0.887645\pi$
$857$	−4.97078	+	8.60964i	−0.169798	+	0.294100i	0.768550	+	0.639789i	$0.220978\pi$
$858$		0			0
$859$	−4.58450	−	7.94059i	−0.156421	−	0.270929i	0.777154	−	0.629310i	$-0.216662\pi$
$859$	−4.58450	−	7.94059i	−0.156421	−	0.270929i	−0.933576	+	0.358381i	$0.883329\pi$
$860$		0			0
$861$	55.0498	+	13.2613i	1.87609	+	0.451945i
$862$		0			0
$863$	20.1781	+	34.9495i	0.686871	+	1.18970i	0.972845	+	0.231458i	$0.0743496\pi$
$863$	20.1781	+	34.9495i	0.686871	+	1.18970i	−0.285974	+	0.958237i	$0.592317\pi$
$864$		0			0
$865$	−26.6785	+	46.2086i	−0.907097	+	1.57114i
$866$		0			0
$867$			39.5221i			1.34224i
$868$		0			0
$869$	−1.62627			−0.0551674
$870$		0			0
$871$	−16.1072	+	27.8985i	−0.545772	+	0.945305i
$872$		0			0
$873$	74.5922	−	43.0658i	2.52456	−	1.45756i
$874$		0			0
$875$	−7.18293	+	11.9478i	−0.242827	+	0.403909i
$876$		0			0
$877$	−7.63603	−	13.2260i	−0.257850	−	0.446610i	0.707815	−	0.706397i	$-0.249681\pi$
$877$	−7.63603	−	13.2260i	−0.257850	−	0.446610i	−0.965666	+	0.259787i	$0.916348\pi$
$878$		0			0
$879$	4.62902	−	8.01770i	0.156133	−	0.270430i
$880$		0			0
$881$	−24.0412			−0.809967			−0.404984	−	0.914324i	$-0.632723\pi$
$881$	−24.0412			−0.809967			−0.404984	+	0.914324i	$0.632723\pi$
$882$		0			0
$883$			5.11357i			0.172085i	0.996291	+	0.0860426i	$0.0274221\pi$
$883$			5.11357i			0.172085i	−0.996291	+	0.0860426i	$0.972578\pi$
$884$		0			0
$885$	55.9537	+	32.3049i	1.88086	+	1.08592i
$886$		0			0
$887$	−12.2220	+	7.05638i	−0.410375	+	0.236930i	−0.690951	−	0.722902i	$-0.742808\pi$
$887$	−12.2220	+	7.05638i	−0.410375	+	0.236930i	0.280576	+	0.959832i	$0.409475\pi$
$888$		0			0
$889$	16.0709	−	26.7316i	0.539000	−	0.896550i
$890$		0			0
$891$	−36.6869	+	21.1812i	−1.22906	+	0.709597i
$892$		0			0
$893$	−2.03295	+	3.52117i	−0.0680300	+	0.117831i
$894$		0			0
$895$			45.0800i			1.50686i
$896$		0			0
$897$	−89.1375			−2.97621
$898$		0			0
$899$	0.143273	+	0.0827187i	0.00477842	+	0.00275882i
$900$		0			0
$901$	−1.82466	−	3.16040i	−0.0607882	−	0.105288i
$902$		0			0
$903$	−18.2004	+	10.0828i	−0.605671	+	0.335536i
$904$		0			0
$905$	−10.7582	+	6.21127i	−0.357616	+	0.206470i
$906$		0			0
$907$	−12.9635	+	22.4534i	−0.430445	+	0.745552i	−0.996912	−	0.0785324i	$-0.974977\pi$
$907$	−12.9635	+	22.4534i	−0.430445	+	0.745552i	0.566467	+	0.824085i	$0.308310\pi$
$908$		0			0
$909$		−	151.855i		−	5.03672i
$910$		0			0
$911$	−12.1565			−0.402763			−0.201382	−	0.979513i	$-0.564543\pi$
$911$	−12.1565			−0.402763			−0.201382	+	0.979513i	$0.564543\pi$
$912$		0			0
$913$	−4.22557	−	2.43964i	−0.139846	−	0.0807401i
$914$		0			0
$915$	−55.5964	+	32.0986i	−1.83796	+	1.06115i
$916$		0			0
$917$	−17.3323	−	0.306773i	−0.572363	−	0.0101305i
$918$		0			0
$919$	28.2671	−	16.3200i	0.932445	−	0.538347i	0.0448608	−	0.998993i	$-0.485716\pi$
$919$	28.2671	−	16.3200i	0.932445	−	0.538347i	0.887584	+	0.460646i	$0.152382\pi$
$920$		0			0
$921$	19.9756	+	11.5329i	0.658217	+	0.380022i
$922$		0			0
$923$	10.7102			0.352530
$924$		0			0
$925$	25.2635			0.830659
$926$		0			0
$927$	21.7615	−	37.6920i	0.714740	−	1.23797i
$928$		0			0
$929$	−25.0610	+	14.4690i	−0.822224	+	0.474711i	−0.851183	−	0.524870i	$-0.824114\pi$
$929$	−25.0610	+	14.4690i	−0.822224	+	0.474711i	0.0289590	+	0.999581i	$0.490781\pi$
$930$		0			0
$931$	5.83245	+	3.64848i	0.191151	+	0.119574i
$932$		0			0
$933$	−0.517621	−	0.896546i	−0.0169461	−	0.0293516i
$934$		0			0
$935$	4.13676	−	7.16508i	0.135287	−	0.234323i
$936$		0			0
$937$			20.1555i			0.658452i	0.944251	+	0.329226i	$0.106788\pi$
$937$			20.1555i			0.658452i	−0.944251	+	0.329226i	$0.893212\pi$
$938$		0			0
$939$	−25.3663			−0.827799
$940$		0			0
$941$	30.3519	−	52.5710i	0.989443	−	1.71376i	0.369213	−	0.929345i	$-0.379627\pi$
$941$	30.3519	−	52.5710i	0.989443	−	1.71376i	0.620230	−	0.784420i	$-0.287039\pi$
$942$		0			0
$943$	10.8513	−	48.8246i	0.353366	−	1.58995i
$944$		0			0
$945$	−2.31135	+	130.589i	−0.0751883	+	4.24805i
$946$		0			0
$947$	3.92380	+	6.79623i	0.127506	+	0.220848i	0.922710	−	0.385495i	$-0.125969\pi$
$947$	3.92380	+	6.79623i	0.127506	+	0.220848i	−0.795203	+	0.606343i	$0.792636\pi$
$948$		0			0
$949$	−33.2857	−	19.2175i	−1.08050	−	0.623826i
$950$		0			0
$951$	61.7853			2.00353
$952$		0			0
$953$	−15.6709			−0.507631			−0.253815	−	0.967253i	$-0.581686\pi$
$953$	−15.6709			−0.507631			−0.253815	+	0.967253i	$0.581686\pi$
$954$		0			0
$955$	−54.0928	−	31.2305i	−1.75040	−	1.01060i
$956$		0			0
$957$	−0.0635269	+	0.0366773i	−0.00205353	+	0.00118561i
$958$		0			0
$959$	31.3129	−	17.3470i	1.01114	−	0.560164i
$960$		0			0
$961$	−30.5794	−	52.9652i	−0.986434	−	1.70855i
$962$		0			0
$963$	36.0568	−	62.4521i	1.16191	−	2.01249i
$964$		0			0
$965$		−	52.6298i		−	1.69421i
$966$		0			0
$967$			14.7669i			0.474870i	0.971403	+	0.237435i	$0.0763067\pi$
$967$			14.7669i			0.474870i	−0.971403	+	0.237435i	$0.923693\pi$
$968$		0			0
$969$	−6.47208	−	3.73666i	−0.207913	−	0.120039i
$970$		0			0
$971$	8.46712	−	4.88849i	0.271723	−	0.156879i	−0.357947	−	0.933742i	$-0.616523\pi$
$971$	8.46712	−	4.88849i	0.271723	−	0.156879i	0.629670	+	0.776862i	$0.283190\pi$
$972$		0			0
$973$	−16.5759	+	27.5717i	−0.531399	+	0.883907i
$974$		0			0
$975$	18.0009	+	31.1785i	0.576491	+	0.998511i
$976$		0			0
$977$	5.95563	+	3.43848i	0.190537	+	0.110007i	0.592234	−	0.805766i	$-0.298246\pi$
$977$	5.95563	+	3.43848i	0.190537	+	0.110007i	−0.401697	+	0.915773i	$0.631579\pi$
$978$		0			0
$979$	−17.5213			−0.559982
$980$		0			0
$981$			120.491i			3.84697i
$982$		0			0
$983$	−16.3611	+	28.3382i	−0.521837	+	0.903848i	0.477840	+	0.878447i	$0.341420\pi$
$983$	−16.3611	+	28.3382i	−0.521837	+	0.903848i	−0.999677	+	0.0254015i	$0.991914\pi$
$984$		0			0
$985$	27.8085	+	48.1657i	0.886052	+	1.53469i
$986$		0			0
$987$	18.8504	−	31.3549i	0.600014	−	0.998038i
$988$		0			0
$989$	9.18917	+	15.9161i	0.292199	+	0.506103i
$990$		0			0
$991$	36.8188	+	21.2573i	1.16959	+	0.675262i	0.953583	−	0.301131i	$-0.0973641\pi$
$991$	36.8188	+	21.2573i	1.16959	+	0.675262i	0.216004	+	0.976392i	$0.430697\pi$
$992$		0			0
$993$	18.3496			0.582306
$994$		0			0
$995$		−	9.07463i		−	0.287685i
$996$		0			0
$997$	30.9108	+	17.8463i	0.978954	+	0.565199i	0.901954	−	0.431832i	$-0.142133\pi$
$997$	30.9108	+	17.8463i	0.978954	+	0.565199i	0.0769995	+	0.997031i	$0.475466\pi$
$998$		0			0
$999$	−119.884	+	69.2148i	−3.79295	+	2.18986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.r.a.81.1	✓	56
7.2	even	3	inner	1148.2.r.a.737.28	yes	56
41.40	even	2	inner	1148.2.r.a.81.28	yes	56
287.163	even	6	inner	1148.2.r.a.737.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.r.a.81.1	✓	56	1.1	even	1	trivial
1148.2.r.a.81.28	yes	56	41.40	even	2	inner
1148.2.r.a.737.1	yes	56	287.163	even	6	inner
1148.2.r.a.737.28	yes	56	7.2	even	3	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.89464 - 1.67122i) q^{3} +(1.42784 + 2.47308i) q^{5} +(-1.36322 + 2.26752i) q^{7} +(4.08596 + 7.07710i) q^{9} +O(q^{10})\)	\(q+(-2.89464 - 1.67122i) q^{3} +(1.42784 + 2.47308i) q^{5} +(-1.36322 + 2.26752i) q^{7} +(4.08596 + 7.07710i) q^{9} +(1.10288 + 0.636749i) q^{11} +3.41413i q^{13} -9.54492i q^{15} +(-1.97022 - 1.13751i) q^{17} +(-0.851130 + 0.491400i) q^{19} +(7.73555 - 4.28541i) q^{21} +(-3.90559 - 6.76468i) q^{23} +(-1.57743 + 2.73219i) q^{25} -17.2869i q^{27} -0.0172332i q^{29} +(-4.79997 + 8.31379i) q^{31} +(-2.12830 - 3.68632i) q^{33} +(-7.55422 - 0.133706i) q^{35} +(-4.00389 - 6.93495i) q^{37} +(5.70576 - 9.88267i) q^{39} +(4.71859 + 4.32839i) q^{41} -2.35283 q^{43} +(-11.6682 + 20.2099i) q^{45} +(3.58279 - 2.06853i) q^{47} +(-3.28328 - 6.18224i) q^{49} +(3.80205 + 6.58535i) q^{51} +(1.38918 + 0.802043i) q^{53} +3.63669i q^{55} +3.28495 q^{57} +(-3.38451 + 5.86214i) q^{59} +(-3.36290 - 5.82471i) q^{61} +(-21.6175 - 0.382618i) q^{63} +(-8.44343 + 4.87481i) q^{65} +(8.17149 + 4.71781i) q^{67} +26.1084i q^{69} -3.13702i q^{71} +(-5.62882 + 9.74940i) q^{73} +(9.13220 - 5.27248i) q^{75} +(-2.94731 + 1.63278i) q^{77} +(-1.10592 + 0.638505i) q^{79} +(-16.6323 + 28.8080i) q^{81} -3.83139 q^{83} -6.49669i q^{85} +(-0.0288004 + 0.0498838i) q^{87} +(-11.9151 + 6.87919i) q^{89} +(-7.74160 - 4.65420i) q^{91} +(27.7884 - 16.0436i) q^{93} +(-2.43055 - 1.40328i) q^{95} -10.5399i q^{97} +10.4069i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) \) 56 * q + 4 * q^5 + 32 * q^9	\( 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) \) 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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