LMFDB - Embedded newform 1500.2.m.d.601.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(301,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("1500.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.m (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			601.3
Character	$\chi$	$=$	1500.601
Dual form			1500.2.m.d.901.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{3} -2.44380 q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{3} -2.44380 q^{7} +(0.309017 + 0.951057i) q^{9} +(-0.178298 + 0.548744i) q^{11} +(-1.99206 - 6.13093i) q^{13} +(1.53529 - 1.11545i) q^{17} +(-6.69438 + 4.86375i) q^{19} +(-1.97708 - 1.43643i) q^{21} +(-1.30065 + 4.00298i) q^{23} +(-0.309017 + 0.951057i) q^{27} +(-5.28988 - 3.84332i) q^{29} +(-3.93738 + 2.86068i) q^{31} +(-0.466789 + 0.339142i) q^{33} +(0.0673673 + 0.207335i) q^{37} +(1.99206 - 6.13093i) q^{39} +(1.99456 + 6.13862i) q^{41} +3.42419 q^{43} +(-7.78140 - 5.65351i) q^{47} -1.02783 q^{49} +1.89772 q^{51} +(-11.3199 - 8.22441i) q^{53} -8.27470 q^{57} +(-3.72459 - 11.4631i) q^{59} +(-1.48657 + 4.57520i) q^{61} +(-0.755176 - 2.32419i) q^{63} +(3.13165 - 2.27528i) q^{67} +(-3.40513 + 2.47398i) q^{69} +(5.24443 + 3.81030i) q^{71} +(3.10590 - 9.55897i) q^{73} +(0.435724 - 1.34102i) q^{77} +(3.83854 + 2.78887i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(2.77831 - 2.01856i) q^{83} +(-2.02055 - 6.21862i) q^{87} +(-1.75719 + 5.40807i) q^{89} +(4.86820 + 14.9828i) q^{91} -4.86687 q^{93} +(5.32717 + 3.87042i) q^{97} -0.576983 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9	$ 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9} - 6 q^{11} + 4 q^{17} - 10 q^{19} - 4 q^{21} + 14 q^{23} + 6 q^{27} - 4 q^{29} + 6 q^{31} - 4 q^{33} - 8 q^{37} - 10 q^{41} - 56 q^{43} + 26 q^{47} + 56 q^{49} + 16 q^{51} - 32 q^{53} - 20 q^{57} + 36 q^{59} - 12 q^{61} + 4 q^{63} + 36 q^{67} - 4 q^{69} + 40 q^{71} + 32 q^{73} - 46 q^{77} - 8 q^{79} - 6 q^{81} - 6 q^{83} + 4 q^{87} - 30 q^{91} + 4 q^{93} + 48 q^{97} + 4 q^{99}+O(q^{100}) $ 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9 - 6 * q^11 + 4 * q^17 - 10 * q^19 - 4 * q^21 + 14 * q^23 + 6 * q^27 - 4 * q^29 + 6 * q^31 - 4 * q^33 - 8 * q^37 - 10 * q^41 - 56 * q^43 + 26 * q^47 + 56 * q^49 + 16 * q^51 - 32 * q^53 - 20 * q^57 + 36 * q^59 - 12 * q^61 + 4 * q^63 + 36 * q^67 - 4 * q^69 + 40 * q^71 + 32 * q^73 - 46 * q^77 - 8 * q^79 - 6 * q^81 - 6 * q^83 + 4 * q^87 - 30 * q^91 + 4 * q^93 + 48 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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			0
$2$		0			0
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.44380			−0.923670			−0.461835	−	0.886966i	$-0.652809\pi$
$7$	−2.44380			−0.923670			−0.461835	+	0.886966i	$0.652809\pi$
$8$		0			0
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	−0.178298	+	0.548744i	−0.0537588	+	0.165452i	−0.974331	−	0.225120i	$-0.927723\pi$
$11$	−0.178298	+	0.548744i	−0.0537588	+	0.165452i	0.920572	+	0.390572i	$0.127723\pi$
$12$		0			0
$13$	−1.99206	−	6.13093i	−0.552498	−	1.70042i	−0.702460	−	0.711723i	$-0.747915\pi$
$13$	−1.99206	−	6.13093i	−0.552498	−	1.70042i	0.149962	−	0.988692i	$-0.452085\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.53529	−	1.11545i	0.372362	−	0.270537i	−0.385828	−	0.922571i	$-0.626084\pi$
$17$	1.53529	−	1.11545i	0.372362	−	0.270537i	0.758190	+	0.652034i	$0.226084\pi$
$18$		0			0
$19$	−6.69438	+	4.86375i	−1.53580	+	1.11582i	−0.582890	+	0.812551i	$0.698078\pi$
$19$	−6.69438	+	4.86375i	−1.53580	+	1.11582i	−0.952905	+	0.303269i	$0.901922\pi$
$20$		0			0
$21$	−1.97708	−	1.43643i	−0.431434	−	0.313455i
$22$		0			0
$23$	−1.30065	+	4.00298i	−0.271203	+	0.834678i	0.718996	+	0.695015i	$0.244602\pi$
$23$	−1.30065	+	4.00298i	−0.271203	+	0.834678i	−0.990199	+	0.139664i	$0.955398\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$		0			0
$29$	−5.28988	−	3.84332i	−0.982306	−	0.713687i	−0.0240828	−	0.999710i	$-0.507667\pi$
$29$	−5.28988	−	3.84332i	−0.982306	−	0.713687i	−0.958223	+	0.286023i	$0.907667\pi$
$30$		0			0
$31$	−3.93738	+	2.86068i	−0.707175	+	0.513793i	−0.882261	−	0.470760i	$-0.843980\pi$
$31$	−3.93738	+	2.86068i	−0.707175	+	0.513793i	0.175086	+	0.984553i	$0.443980\pi$
$32$		0			0
$33$	−0.466789	+	0.339142i	−0.0812576	+	0.0590371i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.0673673	+	0.207335i	0.0110751	+	0.0340857i	0.956441	−	0.291925i	$-0.0942956\pi$
$37$	0.0673673	+	0.207335i	0.0110751	+	0.0340857i	−0.945366	+	0.326010i	$0.894296\pi$
$38$		0			0
$39$	1.99206	−	6.13093i	0.318985	−	0.981735i
$40$		0			0
$41$	1.99456	+	6.13862i	0.311498	+	0.958691i	0.977172	+	0.212449i	$0.0681439\pi$
$41$	1.99456	+	6.13862i	0.311498	+	0.958691i	−0.665675	+	0.746242i	$0.731856\pi$
$42$		0			0
$43$	3.42419			0.522184			0.261092	−	0.965314i	$-0.415917\pi$
$43$	3.42419			0.522184			0.261092	+	0.965314i	$0.415917\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.78140	−	5.65351i	−1.13503	−	0.824650i	−0.148614	−	0.988895i	$-0.547481\pi$
$47$	−7.78140	−	5.65351i	−1.13503	−	0.824650i	−0.986419	+	0.164245i	$0.947481\pi$
$48$		0			0
$49$	−1.02783			−0.146833
$50$		0			0
$51$	1.89772			0.265734
$52$		0			0
$53$	−11.3199	−	8.22441i	−1.55491	−	1.12971i	−0.940031	−	0.341090i	$-0.889204\pi$
$53$	−11.3199	−	8.22441i	−1.55491	−	1.12971i	−0.614881	−	0.788620i	$-0.710796\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−8.27470			−1.09601
$58$		0			0
$59$	−3.72459	−	11.4631i	−0.484901	−	1.49237i	−0.832125	−	0.554589i	$-0.812876\pi$
$59$	−3.72459	−	11.4631i	−0.484901	−	1.49237i	0.347224	−	0.937782i	$-0.387124\pi$
$60$		0			0
$61$	−1.48657	+	4.57520i	−0.190336	+	0.585795i	−0.999999	−	0.00110016i	$-0.999650\pi$
$61$	−1.48657	+	4.57520i	−0.190336	+	0.585795i	0.809663	+	0.586895i	$0.199650\pi$
$62$		0			0
$63$	−0.755176	−	2.32419i	−0.0951433	−	0.292821i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	3.13165	−	2.27528i	0.382592	−	0.277970i	−0.379821	−	0.925060i	$-0.624014\pi$
$67$	3.13165	−	2.27528i	0.382592	−	0.277970i	0.762413	+	0.647090i	$0.224014\pi$
$68$		0			0
$69$	−3.40513	+	2.47398i	−0.409930	+	0.297832i
$70$		0			0
$71$	5.24443	+	3.81030i	0.622399	+	0.452200i	0.853759	−	0.520669i	$-0.174317\pi$
$71$	5.24443	+	3.81030i	0.622399	+	0.452200i	−0.231359	+	0.972868i	$0.574317\pi$
$72$		0			0
$73$	3.10590	−	9.55897i	0.363518	−	1.11879i	−0.587386	−	0.809307i	$-0.699843\pi$
$73$	3.10590	−	9.55897i	0.363518	−	1.11879i	0.950904	−	0.309486i	$-0.100157\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.435724	−	1.34102i	0.0496554	−	0.152824i
$78$		0			0
$79$	3.83854	+	2.78887i	0.431870	+	0.313772i	0.782396	−	0.622781i	$-0.213997\pi$
$79$	3.83854	+	2.78887i	0.431870	+	0.313772i	−0.350526	+	0.936553i	$0.613997\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	2.77831	−	2.01856i	0.304959	−	0.221566i	−0.424772	−	0.905301i	$-0.639646\pi$
$83$	2.77831	−	2.01856i	0.304959	−	0.221566i	0.729730	+	0.683735i	$0.239646\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.02055	−	6.21862i	−0.216626	−	0.666706i
$88$		0			0
$89$	−1.75719	+	5.40807i	−0.186262	+	0.573254i	−0.999968	−	0.00802201i	$-0.997446\pi$
$89$	−1.75719	+	5.40807i	−0.186262	+	0.573254i	0.813706	+	0.581276i	$0.197446\pi$
$90$		0			0
$91$	4.86820	+	14.9828i	0.510326	+	1.57062i
$92$		0			0
$93$	−4.86687			−0.504671
$94$		0			0
$95$		0			0
$96$		0			0
$97$	5.32717	+	3.87042i	0.540893	+	0.392982i	0.824416	−	0.565984i	$-0.191503\pi$
$97$	5.32717	+	3.87042i	0.540893	+	0.392982i	−0.283524	+	0.958965i	$0.591503\pi$
$98$		0			0
$99$	−0.576983			−0.0579890
$100$		0			0
$101$	−12.0363			−1.19766			−0.598828	−	0.800877i	$-0.704367\pi$
$101$	−12.0363			−1.19766			−0.598828	+	0.800877i	$0.704367\pi$
$102$		0			0
$103$	−4.68117	−	3.40107i	−0.461249	−	0.335117i	0.332772	−	0.943007i	$-0.392016\pi$
$103$	−4.68117	−	3.40107i	−0.461249	−	0.335117i	−0.794021	+	0.607890i	$0.792016\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.07081			−0.393540			−0.196770	−	0.980450i	$-0.563045\pi$
$107$	−4.07081			−0.393540			−0.196770	+	0.980450i	$0.563045\pi$
$108$		0			0
$109$	−0.450471	−	1.38641i	−0.0431473	−	0.132794i	0.927162	−	0.374660i	$-0.122241\pi$
$109$	−0.450471	−	1.38641i	−0.0431473	−	0.132794i	−0.970310	+	0.241866i	$0.922241\pi$
$110$		0			0
$111$	−0.0673673	+	0.207335i	−0.00639422	+	0.0196794i
$112$		0			0
$113$	1.81017	+	5.57114i	0.170287	+	0.524089i	0.999387	−	0.0350111i	$-0.0111467\pi$
$113$	1.81017	+	5.57114i	0.170287	+	0.524089i	−0.829100	+	0.559100i	$0.811147\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	5.21528	−	3.78913i	0.482153	−	0.350305i
$118$		0			0
$119$	−3.75194	+	2.72595i	−0.343940	+	0.249887i
$120$		0			0
$121$	8.62986	+	6.26996i	0.784532	+	0.569996i
$122$		0			0
$123$	−1.99456	+	6.13862i	−0.179843	+	0.553500i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−4.72346	+	14.5373i	−0.419139	+	1.28998i	0.489357	+	0.872084i	$0.337232\pi$
$127$	−4.72346	+	14.5373i	−0.419139	+	1.28998i	−0.908496	+	0.417894i	$0.862768\pi$
$128$		0			0
$129$	2.77023	+	2.01269i	0.243905	+	0.177207i
$130$		0			0
$131$	3.03698	−	2.20650i	0.265343	−	0.192783i	−0.447156	−	0.894456i	$-0.647563\pi$
$131$	3.03698	−	2.20650i	0.265343	−	0.192783i	0.712499	+	0.701673i	$0.247563\pi$
$132$		0			0
$133$	16.3597	−	11.8860i	1.41857	−	1.03065i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.25793	−	19.2599i	−0.534651	−	1.64549i	−0.744402	−	0.667732i	$-0.767265\pi$
$137$	−6.25793	−	19.2599i	−0.534651	−	1.64549i	0.209751	−	0.977755i	$-0.432735\pi$
$138$		0			0
$139$	−0.287036	+	0.883406i	−0.0243461	+	0.0749295i	−0.962491	−	0.271312i	$-0.912542\pi$
$139$	−0.287036	+	0.883406i	−0.0243461	+	0.0749295i	0.938145	+	0.346242i	$0.112542\pi$
$140$		0			0
$141$	−2.97223	−	9.14758i	−0.250307	−	0.770365i
$142$		0			0
$143$	3.71949			0.311040
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.831532	−	0.604143i	−0.0685836	−	0.0498289i
$148$		0			0
$149$	13.1432			1.07673			0.538364	−	0.842712i	$-0.319042\pi$
$149$	13.1432			1.07673			0.538364	+	0.842712i	$0.319042\pi$
$150$		0			0
$151$	17.5864			1.43116			0.715580	−	0.698531i	$-0.246163\pi$
$151$	17.5864			1.43116			0.715580	+	0.698531i	$0.246163\pi$
$152$		0			0
$153$	1.53529	+	1.11545i	0.124121	+	0.0901790i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−8.68198			−0.692897			−0.346449	−	0.938069i	$-0.612613\pi$
$157$	−8.68198			−0.692897			−0.346449	+	0.938069i	$0.612613\pi$
$158$		0			0
$159$	−4.32383	−	13.3074i	−0.342902	−	1.05534i
$160$		0			0
$161$	3.17852	−	9.78248i	0.250503	−	0.770968i
$162$		0			0
$163$	0.435068	+	1.33900i	0.0340771	+	0.104879i	0.966648	−	0.256108i	$-0.0824401\pi$
$163$	0.435068	+	1.33900i	0.0340771	+	0.104879i	−0.932571	+	0.360986i	$0.882440\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.13128	+	5.18118i	−0.551835	+	0.400932i	−0.828462	−	0.560046i	$-0.810784\pi$
$167$	−7.13128	+	5.18118i	−0.551835	+	0.400932i	0.276626	+	0.960978i	$0.410784\pi$
$168$		0			0
$169$	−23.1028	+	16.7852i	−1.77714	+	1.29117i
$170$		0			0
$171$	−6.69438	−	4.86375i	−0.511932	−	0.371940i
$172$		0			0
$173$	2.44219	−	7.51629i	0.185676	−	0.571453i	−0.814283	−	0.580468i	$-0.802870\pi$
$173$	2.44219	−	7.51629i	0.185676	−	0.571453i	0.999959	+	0.00901487i	$0.00286956\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.72459	−	11.4631i	0.279958	−	0.861621i
$178$		0			0
$179$	9.29450	+	6.75285i	0.694704	+	0.504732i	0.878203	−	0.478288i	$-0.158742\pi$
$179$	9.29450	+	6.75285i	0.694704	+	0.504732i	−0.183499	+	0.983020i	$0.558742\pi$
$180$		0			0
$181$	−3.17383	+	2.30592i	−0.235909	+	0.171398i	−0.699459	−	0.714673i	$-0.746576\pi$
$181$	−3.17383	+	2.30592i	−0.235909	+	0.171398i	0.463550	+	0.886071i	$0.346576\pi$
$182$		0			0
$183$	−3.89190	+	2.82763i	−0.287698	+	0.209024i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.338359	+	1.04136i	0.0247433	+	0.0761520i
$188$		0			0
$189$	0.755176	−	2.32419i	0.0549310	−	0.169060i
$190$		0			0
$191$	−7.89402	−	24.2953i	−0.571191	−	1.75795i	−0.648797	−	0.760961i	$-0.724728\pi$
$191$	−7.89402	−	24.2953i	−0.571191	−	1.75795i	0.0776060	−	0.996984i	$-0.475272\pi$
$192$		0			0
$193$	−0.421651			−0.0303511			−0.0151756	−	0.999885i	$-0.504831\pi$
$193$	−0.421651			−0.0303511			−0.0151756	+	0.999885i	$0.504831\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.84224	+	4.24463i	0.416242	+	0.302418i	0.776124	−	0.630580i	$-0.217183\pi$
$197$	5.84224	+	4.24463i	0.416242	+	0.302418i	−0.359882	+	0.932998i	$0.617183\pi$
$198$		0			0
$199$	3.93505			0.278949			0.139474	−	0.990226i	$-0.455459\pi$
$199$	3.93505			0.278949			0.139474	+	0.990226i	$0.455459\pi$
$200$		0			0
$201$	3.87094			0.273035
$202$		0			0
$203$	12.9274	+	9.39232i	0.907327	+	0.659211i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−4.20898			−0.292544
$208$		0			0
$209$	−1.47536	−	4.54069i	−0.102053	−	0.314086i
$210$		0			0
$211$	−7.65156	+	23.5491i	−0.526755	+	1.62119i	0.234064	+	0.972221i	$0.424798\pi$
$211$	−7.65156	+	23.5491i	−0.526755	+	1.62119i	−0.760819	+	0.648964i	$0.775202\pi$
$212$		0			0
$213$	2.00319	+	6.16520i	0.137257	+	0.422432i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	9.62219	−	6.99093i	0.653197	−	0.474575i
$218$		0			0
$219$	8.13134	−	5.90777i	0.549465	−	0.399210i
$220$		0			0
$221$	−9.89715	−	7.19070i	−0.665755	−	0.483699i
$222$		0			0
$223$	−6.07919	+	18.7098i	−0.407093	+	1.25290i	0.512043	+	0.858960i	$0.328889\pi$
$223$	−6.07919	+	18.7098i	−0.407093	+	1.25290i	−0.919135	+	0.393942i	$0.871111\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.15025	+	25.0839i	−0.540951	+	1.66488i	0.189476	+	0.981885i	$0.439321\pi$
$227$	−8.15025	+	25.0839i	−0.540951	+	1.66488i	−0.730427	+	0.682991i	$0.760679\pi$
$228$		0			0
$229$	12.9614	+	9.41703i	0.856515	+	0.622295i	0.926935	−	0.375223i	$-0.122434\pi$
$229$	12.9614	+	9.41703i	0.856515	+	0.622295i	−0.0704195	+	0.997517i	$0.522434\pi$
$230$		0			0
$231$	1.14074	−	0.828797i	0.0750552	−	0.0545308i
$232$		0			0
$233$	−23.7129	+	17.2285i	−1.55349	+	1.12867i	−0.612379	+	0.790564i	$0.709787\pi$
$233$	−23.7129	+	17.2285i	−1.55349	+	1.12867i	−0.941107	+	0.338109i	$0.890213\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.46619	+	4.51248i	0.0952395	+	0.293117i
$238$		0			0
$239$	7.98989	−	24.5904i	0.516823	−	1.59062i	−0.263117	−	0.964764i	$-0.584750\pi$
$239$	7.98989	−	24.5904i	0.516823	−	1.59062i	0.779940	−	0.625854i	$-0.215250\pi$
$240$		0			0
$241$	−2.88671	−	8.88437i	−0.185949	−	0.572292i	0.814014	−	0.580845i	$-0.197278\pi$
$241$	−2.88671	−	8.88437i	−0.185949	−	0.572292i	−0.999963	+	0.00855232i	$0.997278\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$		0			0
$246$		0			0
$247$	43.1549	+	31.3539i	2.74588	+	1.99500i
$248$		0			0
$249$	3.43418			0.217632
$250$		0			0
$251$	−13.5088			−0.852666			−0.426333	−	0.904566i	$-0.640195\pi$
$251$	−13.5088			−0.852666			−0.426333	+	0.904566i	$0.640195\pi$
$252$		0			0
$253$	−1.96471	−	1.42744i	−0.123520	−	0.0897425i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.0662			0.815044			0.407522	−	0.913195i	$-0.366393\pi$
$257$	13.0662			0.815044			0.407522	+	0.913195i	$0.366393\pi$
$258$		0			0
$259$	−0.164632	−	0.506686i	−0.0102298	−	0.0314839i
$260$		0			0
$261$	2.02055	−	6.21862i	0.125069	−	0.384923i
$262$		0			0
$263$	−1.36915	−	4.21380i	−0.0844251	−	0.259834i	0.899929	−	0.436037i	$-0.143618\pi$
$263$	−1.36915	−	4.21380i	−0.0844251	−	0.259834i	−0.984354	+	0.176203i	$0.943618\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−4.60038	+	3.34237i	−0.281539	+	0.204550i
$268$		0			0
$269$	−22.6936	+	16.4879i	−1.38366	+	1.00528i	−0.387127	+	0.922026i	$0.626533\pi$
$269$	−22.6936	+	16.4879i	−1.38366	+	1.00528i	−0.996528	+	0.0832584i	$0.973467\pi$
$270$		0			0
$271$	−4.84207	−	3.51797i	−0.294135	−	0.213701i	0.430924	−	0.902388i	$-0.358188\pi$
$271$	−4.84207	−	3.51797i	−0.294135	−	0.213701i	−0.725059	+	0.688687i	$0.758188\pi$
$272$		0			0
$273$	−4.86820	+	14.9828i	−0.294637	+	0.906800i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.56694	−	4.82254i	0.0941481	−	0.289758i	−0.892883	−	0.450290i	$-0.851321\pi$
$277$	1.56694	−	4.82254i	0.0941481	−	0.289758i	0.987031	+	0.160531i	$0.0513208\pi$
$278$		0			0
$279$	−3.93738	−	2.86068i	−0.235725	−	0.171264i
$280$		0			0
$281$	14.6885	−	10.6718i	0.876239	−	0.636625i	−0.0560144	−	0.998430i	$-0.517839\pi$
$281$	14.6885	−	10.6718i	0.876239	−	0.636625i	0.932254	+	0.361805i	$0.117839\pi$
$282$		0			0
$283$	3.80009	−	2.76092i	0.225892	−	0.164120i	−0.469083	−	0.883154i	$-0.655416\pi$
$283$	3.80009	−	2.76092i	0.225892	−	0.164120i	0.694975	+	0.719034i	$0.255416\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.87430	−	15.0016i	−0.287721	−	0.885514i
$288$		0			0
$289$	−4.14041	+	12.7429i	−0.243554	+	0.749581i
$290$		0			0
$291$	2.03480	+	6.26247i	0.119282	+	0.367112i
$292$		0			0
$293$	9.60771			0.561288			0.280644	−	0.959812i	$-0.409452\pi$
$293$	9.60771			0.561288			0.280644	+	0.959812i	$0.409452\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.466789	−	0.339142i	−0.0270859	−	0.0196790i
$298$		0			0
$299$	27.1329			1.56914
$300$		0			0
$301$	−8.36804			−0.482326
$302$		0			0
$303$	−9.73757	−	7.07476i	−0.559409	−	0.406434i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	13.5400			0.772771			0.386386	−	0.922337i	$-0.373723\pi$
$307$	13.5400			0.772771			0.386386	+	0.922337i	$0.373723\pi$
$308$		0			0
$309$	−1.78805	−	5.50304i	−0.101718	−	0.313057i
$310$		0			0
$311$	−0.916931	+	2.82202i	−0.0519944	+	0.160022i	−0.973682	−	0.227910i	$-0.926811\pi$
$311$	−0.916931	+	2.82202i	−0.0519944	+	0.160022i	0.921688	+	0.387933i	$0.126811\pi$
$312$		0			0
$313$	−4.32802	−	13.3203i	−0.244634	−	0.752906i	−0.995696	−	0.0926747i	$-0.970458\pi$
$313$	−4.32802	−	13.3203i	−0.244634	−	0.752906i	0.751063	−	0.660231i	$-0.229542\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	21.8577	−	15.8806i	1.22765	−	0.891941i	0.230939	−	0.972968i	$-0.425820\pi$
$317$	21.8577	−	15.8806i	1.22765	−	0.891941i	0.996712	+	0.0810273i	$0.0258201\pi$
$318$		0			0
$319$	3.05217	−	2.21753i	0.170889	−	0.124158i
$320$		0			0
$321$	−3.29336	−	2.39276i	−0.183817	−	0.133551i
$322$		0			0
$323$	−4.85252	+	14.9345i	−0.270001	+	0.830979i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.450471	−	1.38641i	0.0249111	−	0.0766686i
$328$		0			0
$329$	19.0162	+	13.8161i	1.04840	+	0.761705i
$330$		0			0
$331$	5.38394	−	3.91166i	0.295928	−	0.215004i	−0.429907	−	0.902873i	$-0.641454\pi$
$331$	5.38394	−	3.91166i	0.295928	−	0.215004i	0.725835	+	0.687869i	$0.241454\pi$
$332$		0			0
$333$	−0.176370	+	0.128140i	−0.00966501	+	0.00702204i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	5.93398	+	18.2629i	0.323245	+	0.994844i	0.972227	+	0.234041i	$0.0751950\pi$
$337$	5.93398	+	18.2629i	0.323245	+	0.994844i	−0.648982	+	0.760804i	$0.724805\pi$
$338$		0			0
$339$	−1.81017	+	5.57114i	−0.0983152	+	0.302583i
$340$		0			0
$341$	−0.867752	−	2.67067i	−0.0469914	−	0.144625i
$342$		0			0
$343$	19.6184			1.05930
$344$		0			0
$345$		0			0
$346$		0			0
$347$	13.5584	+	9.85076i	0.727853	+	0.528816i	0.888884	−	0.458133i	$-0.151482\pi$
$347$	13.5584	+	9.85076i	0.727853	+	0.528816i	−0.161030	+	0.986949i	$0.551482\pi$
$348$		0			0
$349$	22.9371			1.22780			0.613898	−	0.789385i	$-0.289601\pi$
$349$	22.9371			1.22780			0.613898	+	0.789385i	$0.289601\pi$
$350$		0			0
$351$	6.44645			0.344086
$352$		0			0
$353$	5.67455	+	4.12280i	0.302026	+	0.219434i	0.728467	−	0.685081i	$-0.240233\pi$
$353$	5.67455	+	4.12280i	0.302026	+	0.219434i	−0.426442	+	0.904515i	$0.640233\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−4.63766			−0.245451
$358$		0			0
$359$	−4.61051	−	14.1897i	−0.243333	−	0.748903i	−0.995906	−	0.0903940i	$-0.971187\pi$
$359$	−4.61051	−	14.1897i	−0.243333	−	0.748903i	0.752573	−	0.658509i	$-0.228813\pi$
$360$		0			0
$361$	15.2873	−	47.0494i	0.804594	−	2.47629i
$362$		0			0
$363$	3.29631	+	10.1450i	0.173012	+	0.532475i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.550914	−	0.400262i	0.0287575	−	0.0208935i	−0.573314	−	0.819336i	$-0.694342\pi$
$367$	0.550914	−	0.400262i	0.0287575	−	0.0208935i	0.602071	+	0.798442i	$0.294342\pi$
$368$		0			0
$369$	−5.22182	+	3.79387i	−0.271837	+	0.197501i
$370$		0			0
$371$	27.6637	+	20.0988i	1.43623	+	1.04348i
$372$		0			0
$373$	8.84935	−	27.2355i	0.458202	−	1.41020i	−0.409133	−	0.912475i	$-0.634169\pi$
$373$	8.84935	−	27.2355i	0.458202	−	1.41020i	0.867335	−	0.497725i	$-0.165831\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−13.0254	+	40.0880i	−0.670842	+	2.06464i
$378$		0			0
$379$	17.7191	+	12.8737i	0.910167	+	0.661275i	0.941057	−	0.338247i	$-0.109834\pi$
$379$	17.7191	+	12.8737i	0.910167	+	0.661275i	−0.0308898	+	0.999523i	$0.509834\pi$
$380$		0			0
$381$	−12.3662	+	8.98455i	−0.633538	+	0.460293i
$382$		0			0
$383$	−3.69391	+	2.68378i	−0.188750	+	0.137135i	−0.678147	−	0.734926i	$-0.737217\pi$
$383$	−3.69391	+	2.68378i	−0.188750	+	0.137135i	0.489397	+	0.872061i	$0.337217\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.05813	+	3.25660i	0.0537879	+	0.165542i
$388$		0			0
$389$	6.71865	−	20.6779i	0.340649	−	1.04841i	−0.623223	−	0.782044i	$-0.714177\pi$
$389$	6.71865	−	20.6779i	0.340649	−	1.04841i	0.963872	−	0.266366i	$-0.0858229\pi$
$390$		0			0
$391$	2.46826	+	7.59653i	0.124825	+	0.384173i
$392$		0			0
$393$	3.75392			0.189360
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−12.6396	−	9.18318i	−0.634361	−	0.460891i	0.223547	−	0.974693i	$-0.428236\pi$
$397$	−12.6396	−	9.18318i	−0.634361	−	0.460891i	−0.857908	+	0.513803i	$0.828236\pi$
$398$		0			0
$399$	20.2217			1.01235
$400$		0			0
$401$	−19.9417			−0.995841			−0.497920	−	0.867223i	$-0.665903\pi$
$401$	−19.9417			−0.995841			−0.497920	+	0.867223i	$0.665903\pi$
$402$		0			0
$403$	25.3821	+	18.4412i	1.26437	+	0.918622i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.125785			−0.00623495
$408$		0			0
$409$	−5.32001	−	16.3733i	−0.263058	−	0.809608i	−0.992134	−	0.125176i	$-0.960050\pi$
$409$	−5.32001	−	16.3733i	−0.263058	−	0.809608i	0.729077	−	0.684432i	$-0.239950\pi$
$410$		0			0
$411$	6.25793	−	19.2599i	0.308681	−	0.950022i
$412$		0			0
$413$	9.10217	+	28.0136i	0.447888	+	1.37846i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.751470	+	0.545975i	−0.0367996	+	0.0267365i
$418$		0			0
$419$	−10.6230	+	7.71804i	−0.518966	+	0.377051i	−0.816214	−	0.577749i	$-0.803931\pi$
$419$	−10.6230	+	7.71804i	−0.518966	+	0.377051i	0.297248	+	0.954800i	$0.403931\pi$
$420$		0			0
$421$	−13.7712	−	10.0054i	−0.671169	−	0.487633i	0.199248	−	0.979949i	$-0.436150\pi$
$421$	−13.7712	−	10.0054i	−0.671169	−	0.487633i	−0.870416	+	0.492317i	$0.836150\pi$
$422$		0			0
$423$	2.97223	−	9.14758i	0.144515	−	0.444770i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.63289	−	11.1809i	0.175808	−	0.541081i
$428$		0			0
$429$	3.00913	+	2.18626i	0.145282	+	0.105554i
$430$		0			0
$431$	10.1246	−	7.35594i	0.487684	−	0.354323i	−0.316609	−	0.948556i	$-0.602544\pi$
$431$	10.1246	−	7.35594i	0.487684	−	0.354323i	0.804293	+	0.594233i	$0.202544\pi$
$432$		0			0
$433$	−16.7848	+	12.1949i	−0.806626	+	0.586048i	−0.912850	−	0.408294i	$-0.866124\pi$
$433$	−16.7848	+	12.1949i	−0.806626	+	0.586048i	0.106225	+	0.994342i	$0.466124\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.7625	−	33.1234i	−0.514838	−	1.58451i
$438$		0			0
$439$	−10.2225	+	31.4615i	−0.487891	+	1.50157i	0.339858	+	0.940477i	$0.389621\pi$
$439$	−10.2225	+	31.4615i	−0.487891	+	1.50157i	−0.827749	+	0.561098i	$0.810379\pi$
$440$		0			0
$441$	−0.317617	−	0.977524i	−0.0151246	−	0.0465488i
$442$		0			0
$443$	−23.4802			−1.11558			−0.557788	−	0.829984i	$-0.688350\pi$
$443$	−23.4802			−1.11558			−0.557788	+	0.829984i	$0.688350\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	10.6330	+	7.72535i	0.502925	+	0.365397i
$448$		0			0
$449$	−31.6965			−1.49585			−0.747925	−	0.663783i	$-0.768950\pi$
$449$	−31.6965			−1.49585			−0.747925	+	0.663783i	$0.768950\pi$
$450$		0			0
$451$	−3.72415			−0.175363
$452$		0			0
$453$	14.2277	+	10.3370i	0.668475	+	0.485676i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−28.2267			−1.32039			−0.660196	−	0.751094i	$-0.729527\pi$
$457$	−28.2267			−1.32039			−0.660196	+	0.751094i	$0.729527\pi$
$458$		0			0
$459$	0.586428	+	1.80484i	0.0273721	+	0.0842427i
$460$		0			0
$461$	−1.52737	+	4.70075i	−0.0711365	+	0.218936i	−0.980304	−	0.197495i	$-0.936719\pi$
$461$	−1.52737	+	4.70075i	−0.0711365	+	0.218936i	0.909167	+	0.416431i	$0.136719\pi$
$462$		0			0
$463$	5.70022	+	17.5435i	0.264912	+	0.815314i	0.991714	+	0.128467i	$0.0410057\pi$
$463$	5.70022	+	17.5435i	0.264912	+	0.815314i	−0.726802	+	0.686847i	$0.758994\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	13.9969	−	10.1693i	0.647699	−	0.470581i	−0.214788	−	0.976661i	$-0.568906\pi$
$467$	13.9969	−	10.1693i	0.647699	−	0.470581i	0.862487	+	0.506080i	$0.168906\pi$
$468$		0			0
$469$	−7.65314	+	5.56033i	−0.353389	+	0.256752i
$470$		0			0
$471$	−7.02387	−	5.10314i	−0.323643	−	0.235140i
$472$		0			0
$473$	−0.610525	+	1.87900i	−0.0280719	+	0.0863966i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	4.32383	−	13.3074i	0.197974	−	0.609303i
$478$		0			0
$479$	27.8105	+	20.2055i	1.27069	+	0.923212i	0.999230	−	0.0392366i	$-0.0124926\pi$
$479$	27.8105	+	20.2055i	1.27069	+	0.923212i	0.271463	+	0.962449i	$0.412493\pi$
$480$		0			0
$481$	1.13696	−	0.826049i	0.0518408	−	0.0376646i
$482$		0			0
$483$	8.32148	−	6.04591i	0.378640	−	0.275098i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	1.55809	+	4.79530i	0.0706037	+	0.217296i	0.980132	−	0.198346i	$-0.0635570\pi$
$487$	1.55809	+	4.79530i	0.0706037	+	0.217296i	−0.909528	+	0.415642i	$0.863557\pi$
$488$		0			0
$489$	−0.435068	+	1.33900i	−0.0196744	+	0.0605517i
$490$		0			0
$491$	−8.03949	−	24.7430i	−0.362817	−	1.11664i	−0.951337	−	0.308153i	$-0.900289\pi$
$491$	−8.03949	−	24.7430i	−0.362817	−	1.11664i	0.588520	−	0.808483i	$-0.299711\pi$
$492$		0			0
$493$	−12.4085			−0.558852
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.8163	−	9.31162i	−0.574892	−	0.417683i
$498$		0			0
$499$	2.49658			0.111762			0.0558812	−	0.998437i	$-0.482203\pi$
$499$	2.49658			0.111762			0.0558812	+	0.998437i	$0.482203\pi$
$500$		0			0
$501$	−8.81475			−0.393814
$502$		0			0
$503$	11.5366	+	8.38184i	0.514392	+	0.373728i	0.814487	−	0.580181i	$-0.197018\pi$
$503$	11.5366	+	8.38184i	0.514392	+	0.373728i	−0.300095	+	0.953909i	$0.597018\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−28.5567			−1.26825
$508$		0			0
$509$	−4.82569	−	14.8520i	−0.213895	−	0.658301i	−0.999230	−	0.0392303i	$-0.987509\pi$
$509$	−4.82569	−	14.8520i	−0.213895	−	0.658301i	0.785335	−	0.619071i	$-0.212491\pi$
$510$		0			0
$511$	−7.59020	+	23.3602i	−0.335771	+	1.03340i
$512$		0			0
$513$	−2.55702	−	7.86971i	−0.112895	−	0.347456i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	4.48974	−	3.26198i	0.197458	−	0.143462i
$518$		0			0
$519$	6.39374	−	4.64533i	0.280654	−	0.203907i
$520$		0			0
$521$	−11.6277	−	8.44804i	−0.509420	−	0.370115i	0.303183	−	0.952932i	$-0.401951\pi$
$521$	−11.6277	−	8.44804i	−0.509420	−	0.370115i	−0.812604	+	0.582817i	$0.801951\pi$
$522$		0			0
$523$	1.36427	−	4.19878i	0.0596552	−	0.183600i	−0.916788	−	0.399374i	$-0.869228\pi$
$523$	1.36427	−	4.19878i	0.0596552	−	0.183600i	0.976443	+	0.215774i	$0.0692275\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.85407	+	8.78393i	−0.124325	+	0.382634i
$528$		0			0
$529$	4.27526	+	3.10615i	0.185881	+	0.135050i
$530$		0			0
$531$	9.75111	−	7.08460i	0.423162	−	0.307445i
$532$		0			0
$533$	33.6622	−	24.4570i	1.45807	−	1.05935i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	3.55018	+	10.9263i	0.153202	+	0.471507i
$538$		0			0
$539$	0.183260	−	0.564015i	0.00789355	−	0.0242939i
$540$		0			0
$541$	11.1361	+	34.2734i	0.478778	+	1.47353i	0.840794	+	0.541355i	$0.182088\pi$
$541$	11.1361	+	34.2734i	0.478778	+	1.47353i	−0.362016	+	0.932172i	$0.617912\pi$
$542$		0			0
$543$	−3.92307			−0.168355
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−9.79172	−	7.11410i	−0.418664	−	0.304177i	0.358436	−	0.933554i	$-0.383310\pi$
$547$	−9.79172	−	7.11410i	−0.418664	−	0.304177i	−0.777100	+	0.629377i	$0.783310\pi$
$548$		0			0
$549$	−4.81065			−0.205314
$550$		0			0
$551$	54.1054			2.30497
$552$		0			0
$553$	−9.38064	−	6.81544i	−0.398906	−	0.289822i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	24.0437			1.01876			0.509382	−	0.860541i	$-0.329874\pi$
$557$	24.0437			1.01876			0.509382	+	0.860541i	$0.329874\pi$
$558$		0			0
$559$	−6.82119	−	20.9935i	−0.288506	−	0.887929i
$560$		0			0
$561$	−0.338359	+	1.04136i	−0.0142855	+	0.0439664i
$562$		0			0
$563$	−5.85371	−	18.0159i	−0.246704	−	0.759278i	−0.995351	−	0.0963092i	$-0.969296\pi$
$563$	−5.85371	−	18.0159i	−0.246704	−	0.759278i	0.748647	−	0.662969i	$-0.230704\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.97708	−	1.43643i	0.0830295	−	0.0603244i
$568$		0			0
$569$	25.2591	−	18.3518i	1.05892	−	0.769348i	0.0850293	−	0.996378i	$-0.472902\pi$
$569$	25.2591	−	18.3518i	1.05892	−	0.769348i	0.973888	+	0.227030i	$0.0729016\pi$
$570$		0			0
$571$	0.0316916	+	0.0230253i	0.00132625	+	0.000963578i	0.588448	−	0.808535i	$-0.299739\pi$
$571$	0.0316916	+	0.0230253i	0.00132625	+	0.000963578i	−0.587122	+	0.809499i	$0.699739\pi$
$572$		0			0
$573$	7.89402	−	24.2953i	0.329777	−	1.01495i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−6.22035	+	19.1443i	−0.258957	+	0.796986i	0.734068	+	0.679076i	$0.237619\pi$
$577$	−6.22035	+	19.1443i	−0.258957	+	0.796986i	−0.993024	+	0.117910i	$0.962381\pi$
$578$		0			0
$579$	−0.341123	−	0.247840i	−0.0141766	−	0.0102999i
$580$		0			0
$581$	−6.78964	+	4.93296i	−0.281682	+	0.204654i
$582$		0			0
$583$	6.53141	−	4.74535i	0.270503	−	0.196532i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.08070	−	9.48143i	−0.127154	−	0.391341i	0.867133	−	0.498076i	$-0.165960\pi$
$587$	−3.08070	−	9.48143i	−0.127154	−	0.391341i	−0.994287	+	0.106736i	$0.965960\pi$
$588$		0			0
$589$	12.4447	−	38.3009i	0.512776	−	1.57816i
$590$		0			0
$591$	2.23154	+	6.86796i	0.0917931	+	0.282510i
$592$		0			0
$593$	−20.3619			−0.836163			−0.418082	−	0.908410i	$-0.637297\pi$
$593$	−20.3619			−0.836163			−0.418082	+	0.908410i	$0.637297\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.18353	+	2.31297i	0.130293	+	0.0946634i
$598$		0			0
$599$	−24.1075			−0.985007			−0.492503	−	0.870311i	$-0.663918\pi$
$599$	−24.1075			−0.985007			−0.492503	+	0.870311i	$0.663918\pi$
$600$		0			0
$601$	37.2054			1.51764			0.758820	−	0.651300i	$-0.225776\pi$
$601$	37.2054			1.51764			0.758820	+	0.651300i	$0.225776\pi$
$602$		0			0
$603$	3.13165	+	2.27528i	0.127531	+	0.0926565i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−40.5752			−1.64690			−0.823448	−	0.567392i	$-0.807952\pi$
$607$	−40.5752			−1.64690			−0.823448	+	0.567392i	$0.807952\pi$
$608$		0			0
$609$	4.93783	+	15.1971i	0.200091	+	0.615817i
$610$		0			0
$611$	−19.1603	+	58.9694i	−0.775143	+	2.38565i
$612$		0			0
$613$	1.58698	+	4.88423i	0.0640977	+	0.197272i	0.977977	−	0.208714i	$-0.0669279\pi$
$613$	1.58698	+	4.88423i	0.0640977	+	0.197272i	−0.913879	+	0.405987i	$0.866928\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.2531	−	9.62895i	0.533550	−	0.387647i	−0.288134	−	0.957590i	$-0.593035\pi$
$617$	13.2531	−	9.62895i	0.533550	−	0.387647i	0.821684	+	0.569943i	$0.193035\pi$
$618$		0			0
$619$	−14.9251	+	10.8437i	−0.599892	+	0.435847i	−0.845841	−	0.533436i	$-0.820901\pi$
$619$	−14.9251	+	10.8437i	−0.599892	+	0.435847i	0.245948	+	0.969283i	$0.420901\pi$
$620$		0			0
$621$	−3.40513	−	2.47398i	−0.136643	−	0.0992772i
$622$		0			0
$623$	4.29422	−	13.2163i	0.172044	−	0.529498i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.47536	−	4.54069i	0.0589202	−	0.181338i
$628$		0			0
$629$	0.334701	+	0.243174i	0.0133454	+	0.00969600i
$630$		0			0
$631$	−31.1970	+	22.6659i	−1.24193	+	0.902316i	−0.997726	−	0.0674068i	$-0.978527\pi$
$631$	−31.1970	+	22.6659i	−1.24193	+	0.902316i	−0.244206	+	0.969723i	$0.578527\pi$
$632$		0			0
$633$	−20.0320	+	14.5541i	−0.796202	+	0.578475i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	2.04750	+	6.30156i	0.0811249	+	0.249677i
$638$		0			0
$639$	−2.00319	+	6.16520i	−0.0792451	+	0.243891i
$640$		0			0
$641$	5.87099	+	18.0690i	0.231890	+	0.713684i	0.997519	+	0.0704016i	$0.0224281\pi$
$641$	5.87099	+	18.0690i	0.231890	+	0.713684i	−0.765629	+	0.643283i	$0.777572\pi$
$642$		0			0
$643$	−37.6504			−1.48479			−0.742393	−	0.669964i	$-0.766309\pi$
$643$	−37.6504			−1.48479			−0.742393	+	0.669964i	$0.766309\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.63937	−	3.37070i	−0.182392	−	0.132516i	0.492843	−	0.870118i	$-0.335958\pi$
$647$	−4.63937	−	3.37070i	−0.182392	−	0.132516i	−0.675235	+	0.737603i	$0.735958\pi$
$648$		0			0
$649$	6.95440			0.272984
$650$		0			0
$651$	11.8937			0.466150
$652$		0			0
$653$	−32.4262	−	23.5590i	−1.26894	−	0.921936i	−0.269777	−	0.962923i	$-0.586950\pi$
$653$	−32.4262	−	23.5590i	−1.26894	−	0.921936i	−0.999160	+	0.0409866i	$0.986950\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	10.0509			0.392123
$658$		0			0
$659$	−9.75714	−	30.0294i	−0.380084	−	1.16978i	−0.939984	−	0.341218i	$-0.889160\pi$
$659$	−9.75714	−	30.0294i	−0.380084	−	1.16978i	0.559900	−	0.828560i	$-0.310840\pi$
$660$		0			0
$661$	9.68781	−	29.8160i	0.376812	−	1.15971i	−0.565436	−	0.824792i	$-0.691292\pi$
$661$	9.68781	−	29.8160i	0.376812	−	1.15971i	0.942248	−	0.334916i	$-0.108708\pi$
$662$		0			0
$663$	−3.78038	−	11.6348i	−0.146818	−	0.451858i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	22.2650	−	16.1765i	0.862103	−	0.626355i
$668$		0			0
$669$	−15.9155	+	11.5633i	−0.615330	+	0.447063i
$670$		0			0
$671$	−2.24556	−	1.63150i	−0.0866889	−	0.0629832i
$672$		0			0
$673$	1.38278	−	4.25575i	0.0533021	−	0.164047i	−0.920862	−	0.389889i	$-0.872513\pi$
$673$	1.38278	−	4.25575i	0.0533021	−	0.164047i	0.974164	+	0.225842i	$0.0725133\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.35181	+	13.3935i	−0.167254	+	0.514754i	−0.999195	−	0.0401092i	$-0.987229\pi$
$677$	−4.35181	+	13.3935i	−0.167254	+	0.514754i	0.831942	+	0.554863i	$0.187229\pi$
$678$		0			0
$679$	−13.0186	−	9.45854i	−0.499607	−	0.362985i
$680$		0			0
$681$	−21.3376	+	15.5027i	−0.817660	+	0.594065i
$682$		0			0
$683$	9.57528	−	6.95685i	0.366388	−	0.266196i	−0.389324	−	0.921101i	$-0.627291\pi$
$683$	9.57528	−	6.95685i	0.366388	−	0.266196i	0.755711	+	0.654905i	$0.227291\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	4.95082	+	15.2371i	0.188886	+	0.581330i
$688$		0			0
$689$	−27.8733	+	85.7853i	−1.06189	+	3.26816i
$690$		0			0
$691$	−11.6676	−	35.9091i	−0.443855	−	1.36605i	−0.883734	−	0.467989i	$-0.844979\pi$
$691$	−11.6676	−	35.9091i	−0.443855	−	1.36605i	0.439879	−	0.898057i	$-0.355021\pi$
$692$		0			0
$693$	1.41003			0.0535627
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.90956	+	7.19971i	0.375351	+	0.272709i
$698$		0			0
$699$	−29.3108			−1.10864
$700$		0			0
$701$	−39.1678			−1.47935			−0.739674	−	0.672965i	$-0.765020\pi$
$701$	−39.1678			−1.47935			−0.739674	+	0.672965i	$0.765020\pi$
$702$		0			0
$703$	−1.45941	−	1.06032i	−0.0550426	−	0.0399908i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	29.4143			1.10624
$708$		0			0
$709$	−13.1296	−	40.4089i	−0.493094	−	1.51759i	−0.819906	−	0.572498i	$-0.805974\pi$
$709$	−13.1296	−	40.4089i	−0.493094	−	1.51759i	0.326812	−	0.945089i	$-0.394026\pi$
$710$		0			0
$711$	−1.46619	+	4.51248i	−0.0549866	+	0.169231i
$712$		0			0
$713$	−6.33008	−	19.4820i	−0.237063	−	0.729606i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	20.9178	−	15.1977i	0.781190	−	0.567568i
$718$		0			0
$719$	−24.0261	+	17.4560i	−0.896022	+	0.650998i	−0.937441	−	0.348143i	$-0.886812\pi$
$719$	−24.0261	+	17.4560i	−0.896022	+	0.650998i	0.0414189	+	0.999142i	$0.486812\pi$
$720$		0			0
$721$	11.4399	+	8.31154i	0.426042	+	0.309538i
$722$		0			0
$723$	2.88671	−	8.88437i	0.107358	−	0.330413i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	12.9577	−	39.8796i	0.480573	−	1.47905i	−0.357719	−	0.933829i	$-0.616445\pi$
$727$	12.9577	−	39.8796i	0.480573	−	1.47905i	0.838292	−	0.545222i	$-0.183555\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	5.25712	−	3.81952i	0.194441	−	0.141270i
$732$		0			0
$733$	−23.6317	+	17.1695i	−0.872858	+	0.634168i	−0.931352	−	0.364119i	$-0.881370\pi$
$733$	−23.6317	+	17.1695i	−0.872858	+	0.634168i	0.0584945	+	0.998288i	$0.481370\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.690179	+	2.12415i	0.0254231	+	0.0782441i
$738$		0			0
$739$	8.00979	−	24.6516i	0.294645	−	0.906824i	−0.688695	−	0.725051i	$-0.741816\pi$
$739$	8.00979	−	24.6516i	0.294645	−	0.906824i	0.983340	−	0.181773i	$-0.0581837\pi$
$740$		0			0
$741$	16.4837	+	50.7317i	0.605544	+	1.86367i
$742$		0			0
$743$	−9.22935			−0.338592			−0.169296	−	0.985565i	$-0.554149\pi$
$743$	−9.22935			−0.338592			−0.169296	+	0.985565i	$0.554149\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.77831	+	2.01856i	0.101653	+	0.0738552i
$748$		0			0
$749$	9.94826			0.363502
$750$		0			0
$751$	−37.2805			−1.36038			−0.680192	−	0.733034i	$-0.738103\pi$
$751$	−37.2805			−1.36038			−0.680192	+	0.733034i	$0.738103\pi$
$752$		0			0
$753$	−10.9288	−	7.94025i	−0.398268	−	0.289359i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−27.6758			−1.00589			−0.502947	−	0.864317i	$-0.667751\pi$
$757$	−27.6758			−1.00589			−0.502947	+	0.864317i	$0.667751\pi$
$758$		0			0
$759$	−0.750451	−	2.30965i	−0.0272396	−	0.0838350i
$760$		0			0
$761$	−4.21264	+	12.9652i	−0.152708	+	0.469988i	−0.997921	−	0.0644416i	$-0.979473\pi$
$761$	−4.21264	+	12.9652i	−0.152708	+	0.469988i	0.845213	+	0.534429i	$0.179473\pi$
$762$		0			0
$763$	1.10086	+	3.38811i	0.0398539	+	0.122658i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−62.8600	+	45.6705i	−2.26974	+	1.64906i
$768$		0			0
$769$	24.6838	−	17.9339i	0.890122	−	0.646712i	−0.0457876	−	0.998951i	$-0.514580\pi$
$769$	24.6838	−	17.9339i	0.890122	−	0.646712i	0.935910	+	0.352239i	$0.114580\pi$
$770$		0			0
$771$	10.5707	+	7.68009i	0.380696	+	0.276592i
$772$		0			0
$773$	−2.60967	+	8.03172i	−0.0938631	+	0.288881i	−0.986956	−	0.160992i	$-0.948531\pi$
$773$	−2.60967	+	8.03172i	−0.0938631	+	0.288881i	0.893093	+	0.449873i	$0.148531\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.164632	−	0.506686i	0.00590615	−	0.0181773i
$778$		0			0
$779$	−43.2090	−	31.3932i	−1.54812	−	1.12478i
$780$		0			0
$781$	−3.02595	+	2.19848i	−0.108277	+	0.0786678i
$782$		0			0
$783$	5.28988	−	3.84332i	0.189045	−	0.137349i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−12.6251	−	38.8560i	−0.450036	−	1.38507i	−0.876865	−	0.480736i	$-0.840369\pi$
$787$	−12.6251	−	38.8560i	−0.450036	−	1.38507i	0.426829	−	0.904332i	$-0.359631\pi$
$788$		0			0
$789$	1.36915	−	4.21380i	0.0487429	−	0.150015i
$790$		0			0
$791$	−4.42371	−	13.6148i	−0.157289	−	0.484086i
$792$		0			0
$793$	31.0116			1.10125
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−23.9082	−	17.3703i	−0.846871	−	0.615288i	0.0774107	−	0.996999i	$-0.475335\pi$
$797$	−23.9082	−	17.3703i	−0.846871	−	0.615288i	−0.924281	+	0.381712i	$0.875335\pi$
$798$		0			0
$799$	−18.2529			−0.645742
$800$		0			0
$801$	−5.68638			−0.200918
$802$		0			0
$803$	4.69165	+	3.40868i	0.165565	+	0.120290i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−28.0509			−0.987438
$808$		0			0
$809$	7.69396	+	23.6796i	0.270505	+	0.832529i	0.990374	+	0.138419i	$0.0442020\pi$
$809$	7.69396	+	23.6796i	0.270505	+	0.832529i	−0.719869	+	0.694110i	$0.755798\pi$
$810$		0			0
$811$	7.52723	−	23.1664i	0.264317	−	0.813483i	−0.727533	−	0.686072i	$-0.759333\pi$
$811$	7.52723	−	23.1664i	0.264317	−	0.813483i	0.991850	−	0.127411i	$-0.0406667\pi$
$812$		0			0
$813$	−1.84950	−	5.69219i	−0.0648650	−	0.199634i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−22.9228	+	16.6544i	−0.801967	+	0.582663i
$818$		0			0
$819$	−12.7451	+	9.25987i	−0.445351	+	0.323566i
$820$		0			0
$821$	44.8023	+	32.5508i	1.56361	+	1.13603i	0.932969	+	0.359956i	$0.117208\pi$
$821$	44.8023	+	32.5508i	1.56361	+	1.13603i	0.630642	+	0.776074i	$0.282792\pi$
$822$		0			0
$823$	−5.39695	+	16.6101i	−0.188126	+	0.578992i	−0.999988	−	0.00485678i	$-0.998454\pi$
$823$	−5.39695	+	16.6101i	−0.188126	+	0.578992i	0.811862	+	0.583849i	$0.198454\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−7.22601	+	22.2394i	−0.251273	+	0.773338i	0.743268	+	0.668993i	$0.233275\pi$
$827$	−7.22601	+	22.2394i	−0.251273	+	0.773338i	−0.994541	+	0.104345i	$0.966725\pi$
$828$		0			0
$829$	−29.1866	−	21.2053i	−1.01369	−	0.736491i	−0.0487125	−	0.998813i	$-0.515512\pi$
$829$	−29.1866	−	21.2053i	−1.01369	−	0.736491i	−0.964980	+	0.262322i	$0.915512\pi$
$830$		0			0
$831$	4.10230	−	2.98049i	0.142307	−	0.103392i
$832$		0			0
$833$	−1.57802	+	1.14650i	−0.0546750	+	0.0397237i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.50395	−	4.62867i	−0.0519840	−	0.159990i
$838$		0			0
$839$	5.88419	−	18.1097i	0.203145	−	0.625215i	−0.796640	−	0.604454i	$-0.793391\pi$
$839$	5.88419	−	18.1097i	0.203145	−	0.625215i	0.999784	−	0.0207608i	$-0.00660885\pi$
$840$		0			0
$841$	4.25019	+	13.0808i	0.146558	+	0.451060i
$842$		0			0
$843$	18.1559			0.625323
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−21.0897	−	15.3225i	−0.724649	−	0.526489i
$848$		0			0
$849$	4.69717			0.161206
$850$		0			0
$851$	−0.917579			−0.0314542
$852$		0			0
$853$	−14.6027	−	10.6095i	−0.499986	−	0.363261i	0.309026	−	0.951054i	$-0.399997\pi$
$853$	−14.6027	−	10.6095i	−0.499986	−	0.363261i	−0.809012	+	0.587793i	$0.799997\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.4435			−0.425061			−0.212531	−	0.977154i	$-0.568171\pi$
$857$	−12.4435			−0.425061			−0.212531	+	0.977154i	$0.568171\pi$
$858$		0			0
$859$	14.2156	+	43.7511i	0.485029	+	1.49277i	0.831938	+	0.554868i	$0.187231\pi$
$859$	14.2156	+	43.7511i	0.485029	+	1.49277i	−0.346909	+	0.937899i	$0.612769\pi$
$860$		0			0
$861$	4.87430	−	15.0016i	0.166116	−	0.511252i
$862$		0			0
$863$	−14.6311	−	45.0298i	−0.498048	−	1.53283i	−0.812153	−	0.583445i	$-0.801704\pi$
$863$	−14.6311	−	45.0298i	−0.498048	−	1.53283i	0.314105	−	0.949388i	$-0.398296\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−10.8397	+	7.87553i	−0.368137	+	0.267467i
$868$		0			0
$869$	−2.21478	+	1.60913i	−0.0751311	+	0.0545860i
$870$		0			0
$871$	−20.1880	−	14.6675i	−0.684045	−	0.496988i
$872$		0			0
$873$	−2.03480	+	6.26247i	−0.0688675	+	0.211952i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	9.87543	−	30.3934i	0.333470	−	1.02631i	−0.634001	−	0.773332i	$-0.718589\pi$
$877$	9.87543	−	30.3934i	0.333470	−	1.02631i	0.967471	−	0.252982i	$-0.0814113\pi$
$878$		0			0
$879$	7.77280	+	5.64727i	0.262170	+	0.190478i
$880$		0			0
$881$	6.41518	−	4.66090i	0.216133	−	0.157030i	−0.474451	−	0.880282i	$-0.657353\pi$
$881$	6.41518	−	4.66090i	0.216133	−	0.157030i	0.690584	+	0.723252i	$0.257353\pi$
$882$		0			0
$883$	−30.1363	+	21.8953i	−1.01417	+	0.736836i	−0.965079	−	0.261958i	$-0.915632\pi$
$883$	−30.1363	+	21.8953i	−1.01417	+	0.736836i	−0.0490886	+	0.998794i	$0.515632\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.07245	−	15.6114i	−0.170316	−	0.524179i	0.829072	−	0.559141i	$-0.188869\pi$
$887$	−5.07245	−	15.6114i	−0.170316	−	0.524179i	−0.999389	+	0.0349619i	$0.988869\pi$
$888$		0			0
$889$	11.5432	−	35.5263i	0.387147	−	1.19151i
$890$		0			0
$891$	−0.178298	−	0.548744i	−0.00597320	−	0.0183836i
$892$		0			0
$893$	79.5889			2.66334
$894$		0			0
$895$		0			0
$896$		0			0
$897$	21.9510	+	15.9483i	0.732923	+	0.532500i
$898$		0			0
$899$	31.8228			1.06135
$900$		0			0
$901$	−26.5533			−0.884619
$902$		0			0
$903$	−6.76988	−	4.91861i	−0.225288	−	0.163681i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.85782			0.0616880			0.0308440	−	0.999524i	$-0.490181\pi$
$907$	1.85782			0.0616880			0.0308440	+	0.999524i	$0.490181\pi$
$908$		0			0
$909$	−3.71942	−	11.4472i	−0.123365	−	0.379680i
$910$		0			0
$911$	−6.95487	+	21.4049i	−0.230425	+	0.709176i	0.767270	+	0.641324i	$0.221615\pi$
$911$	−6.95487	+	21.4049i	−0.230425	+	0.709176i	−0.997695	+	0.0678519i	$0.978385\pi$
$912$		0			0
$913$	0.612306	+	1.88448i	0.0202644	+	0.0623673i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−7.42179	+	5.39225i	−0.245089	+	0.178068i
$918$		0			0
$919$	−16.9124	+	12.2876i	−0.557890	+	0.405331i	−0.830686	−	0.556741i	$-0.812052\pi$
$919$	−16.9124	+	12.2876i	−0.557890	+	0.405331i	0.272796	+	0.962072i	$0.412052\pi$
$920$		0			0
$921$	10.9541	+	7.95864i	0.360951	+	0.262246i
$922$		0			0
$923$	12.9135	−	39.7436i	0.425052	−	1.30818i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.78805	−	5.50304i	0.0587272	−	0.180744i
$928$		0			0
$929$	−11.3058	−	8.21417i	−0.370933	−	0.269498i	0.386665	−	0.922220i	$-0.373627\pi$
$929$	−11.3058	−	8.21417i	−0.370933	−	0.269498i	−0.757598	+	0.652722i	$0.773627\pi$
$930$		0			0
$931$	6.88068	−	4.99911i	0.225505	−	0.163839i
$932$		0			0
$933$	−2.40056	+	1.74411i	−0.0785907	+	0.0570995i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−10.1229	−	31.1551i	−0.330701	−	1.01779i	−0.968801	−	0.247840i	$-0.920279\pi$
$937$	−10.1229	−	31.1551i	−0.330701	−	1.01779i	0.638100	−	0.769954i	$-0.279721\pi$
$938$		0			0
$939$	4.32802	−	13.3203i	0.141239	−	0.434690i
$940$		0			0
$941$	−7.99456	−	24.6047i	−0.260615	−	0.802091i	−0.992671	−	0.120847i	$-0.961439\pi$
$941$	−7.99456	−	24.6047i	−0.260615	−	0.802091i	0.732056	−	0.681244i	$-0.238561\pi$
$942$		0			0
$943$	−27.1669			−0.884677
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−45.1202	−	32.7818i	−1.46621	−	1.06526i	−0.981690	−	0.190485i	$-0.938994\pi$
$947$	−45.1202	−	32.7818i	−1.46621	−	1.06526i	−0.484521	−	0.874780i	$-0.661006\pi$
$948$		0			0
$949$	−64.7925			−2.10325
$950$		0			0
$951$	27.0176			0.876106
$952$		0			0
$953$	20.1685	+	14.6533i	0.653322	+	0.474666i	0.864401	−	0.502803i	$-0.167698\pi$
$953$	20.1685	+	14.6533i	0.653322	+	0.474666i	−0.211079	+	0.977469i	$0.567698\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	3.77269			0.121954
$958$		0			0
$959$	15.2931	+	47.0675i	0.493841	+	1.51989i
$960$		0			0
$961$	−2.26000	+	6.95558i	−0.0729034	+	0.224373i
$962$		0			0
$963$	−1.25795	−	3.87157i	−0.0405369	−	0.124760i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	7.02876	−	5.10669i	0.226030	−	0.164220i	−0.469007	−	0.883194i	$-0.655388\pi$
$967$	7.02876	−	5.10669i	0.226030	−	0.164220i	0.695037	+	0.718974i	$0.255388\pi$
$968$		0			0
$969$	−12.7041	+	9.23004i	−0.408113	+	0.296512i
$970$		0			0
$971$	−19.9663	−	14.5064i	−0.640750	−	0.465532i	0.219358	−	0.975645i	$-0.429604\pi$
$971$	−19.9663	−	14.5064i	−0.640750	−	0.465532i	−0.860108	+	0.510112i	$0.829604\pi$
$972$		0			0
$973$	0.701459	−	2.15887i	0.0224877	−	0.0692102i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11.0003	+	33.8554i	−0.351930	+	1.08313i	0.605838	+	0.795588i	$0.292838\pi$
$977$	−11.0003	+	33.8554i	−0.351930	+	1.08313i	−0.957768	+	0.287542i	$0.907162\pi$
$978$		0			0
$979$	−2.65434	−	1.92849i	−0.0848332	−	0.0616349i
$980$		0			0
$981$	1.17935	−	0.856848i	0.0376537	−	0.0273570i
$982$		0			0
$983$	4.80656	−	3.49217i	0.153305	−	0.111383i	−0.508488	−	0.861069i	$-0.669795\pi$
$983$	4.80656	−	3.49217i	0.153305	−	0.111383i	0.661794	+	0.749686i	$0.269795\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	7.26354	+	22.3549i	0.231201	+	0.711563i
$988$		0			0
$989$	−4.45365	+	13.7069i	−0.141618	+	0.435855i
$990$		0			0
$991$	1.30614	+	4.01987i	0.0414908	+	0.127695i	0.969656	−	0.244472i	$-0.0786147\pi$
$991$	1.30614	+	4.01987i	0.0414908	+	0.127695i	−0.928166	+	0.372168i	$0.878615\pi$
$992$		0			0
$993$	6.65492			0.211187
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−10.1495	−	7.37405i	−0.321438	−	0.233538i	0.415351	−	0.909661i	$-0.363659\pi$
$997$	−10.1495	−	7.37405i	−0.321438	−	0.233538i	−0.736789	+	0.676123i	$0.763659\pi$
$998$		0			0
$999$	−0.218005			−0.00689738

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.m.d.601.3		24
5.2	odd	4		300.2.o.a.229.6	yes	24
5.3	odd	4		1500.2.o.c.649.1		24
5.4	even	2		1500.2.m.c.601.4		24
15.2	even	4		900.2.w.c.829.2		24
25.6	even	5	inner	1500.2.m.d.901.3		24
25.8	odd	20		300.2.o.a.169.6	✓	24
25.9	even	10		7500.2.a.n.1.8		12
25.12	odd	20		7500.2.d.g.1249.17		24
25.13	odd	20		7500.2.d.g.1249.8		24
25.16	even	5		7500.2.a.m.1.5		12
25.17	odd	20		1500.2.o.c.349.1		24
25.19	even	10		1500.2.m.c.901.4		24
75.8	even	20		900.2.w.c.469.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.6	✓	24	25.8	odd	20
300.2.o.a.229.6	yes	24	5.2	odd	4
900.2.w.c.469.2		24	75.8	even	20
900.2.w.c.829.2		24	15.2	even	4
1500.2.m.c.601.4		24	5.4	even	2
1500.2.m.c.901.4		24	25.19	even	10
1500.2.m.d.601.3		24	1.1	even	1	trivial
1500.2.m.d.901.3		24	25.6	even	5	inner
1500.2.o.c.349.1		24	25.17	odd	20
1500.2.o.c.649.1		24	5.3	odd	4
7500.2.a.m.1.5		12	25.16	even	5
7500.2.a.n.1.8		12	25.9	even	10
7500.2.d.g.1249.8		24	25.13	odd	20
7500.2.d.g.1249.17		24	25.12	odd	20

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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{3} -2.44380 q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{3} -2.44380 q^{7} +(0.309017 + 0.951057i) q^{9} +(-0.178298 + 0.548744i) q^{11} +(-1.99206 - 6.13093i) q^{13} +(1.53529 - 1.11545i) q^{17} +(-6.69438 + 4.86375i) q^{19} +(-1.97708 - 1.43643i) q^{21} +(-1.30065 + 4.00298i) q^{23} +(-0.309017 + 0.951057i) q^{27} +(-5.28988 - 3.84332i) q^{29} +(-3.93738 + 2.86068i) q^{31} +(-0.466789 + 0.339142i) q^{33} +(0.0673673 + 0.207335i) q^{37} +(1.99206 - 6.13093i) q^{39} +(1.99456 + 6.13862i) q^{41} +3.42419 q^{43} +(-7.78140 - 5.65351i) q^{47} -1.02783 q^{49} +1.89772 q^{51} +(-11.3199 - 8.22441i) q^{53} -8.27470 q^{57} +(-3.72459 - 11.4631i) q^{59} +(-1.48657 + 4.57520i) q^{61} +(-0.755176 - 2.32419i) q^{63} +(3.13165 - 2.27528i) q^{67} +(-3.40513 + 2.47398i) q^{69} +(5.24443 + 3.81030i) q^{71} +(3.10590 - 9.55897i) q^{73} +(0.435724 - 1.34102i) q^{77} +(3.83854 + 2.78887i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(2.77831 - 2.01856i) q^{83} +(-2.02055 - 6.21862i) q^{87} +(-1.75719 + 5.40807i) q^{89} +(4.86820 + 14.9828i) q^{91} -4.86687 q^{93} +(5.32717 + 3.87042i) q^{97} -0.576983 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9	\( 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9} - 6 q^{11} + 4 q^{17} - 10 q^{19} - 4 q^{21} + 14 q^{23} + 6 q^{27} - 4 q^{29} + 6 q^{31} - 4 q^{33} - 8 q^{37} - 10 q^{41} - 56 q^{43} + 26 q^{47} + 56 q^{49} + 16 q^{51} - 32 q^{53} - 20 q^{57} + 36 q^{59} - 12 q^{61} + 4 q^{63} + 36 q^{67} - 4 q^{69} + 40 q^{71} + 32 q^{73} - 46 q^{77} - 8 q^{79} - 6 q^{81} - 6 q^{83} + 4 q^{87} - 30 q^{91} + 4 q^{93} + 48 q^{97} + 4 q^{99}+O(q^{100}) \) 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9 - 6 * q^11 + 4 * q^17 - 10 * q^19 - 4 * q^21 + 14 * q^23 + 6 * q^27 - 4 * q^29 + 6 * q^31 - 4 * q^33 - 8 * q^37 - 10 * q^41 - 56 * q^43 + 26 * q^47 + 56 * q^49 + 16 * q^51 - 32 * q^53 - 20 * q^57 + 36 * q^59 - 12 * q^61 + 4 * q^63 + 36 * q^67 - 4 * q^69 + 40 * q^71 + 32 * q^73 - 46 * q^77 - 8 * q^79 - 6 * q^81 - 6 * q^83 + 4 * q^87 - 30 * q^91 + 4 * q^93 + 48 * q^97 + 4 * q^99

Introduction

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