LMFDB - Embedded newform 1500.2.m.d.901.4

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			901.4
Character	$\chi$	$=$	1500.901
Dual form			1500.2.m.d.601.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{3} +0.957526 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{3} +0.957526 q^{7} +(0.309017 - 0.951057i) q^{9} +(-1.67360 - 5.15082i) q^{11} +(0.625052 - 1.92371i) q^{13} +(-0.520090 - 0.377867i) q^{17} +(4.07829 + 2.96305i) q^{19} +(0.774655 - 0.562820i) q^{21} +(-1.08762 - 3.34734i) q^{23} +(-0.309017 - 0.951057i) q^{27} +(-8.20405 + 5.96059i) q^{29} +(-2.98671 - 2.16997i) q^{31} +(-4.38155 - 3.18338i) q^{33} +(3.49663 - 10.7615i) q^{37} +(-0.625052 - 1.92371i) q^{39} +(1.08859 - 3.35035i) q^{41} -0.766348 q^{43} +(3.99186 - 2.90026i) q^{47} -6.08314 q^{49} -0.642866 q^{51} +(4.81069 - 3.49517i) q^{53} +5.04105 q^{57} +(1.45818 - 4.48783i) q^{59} +(1.34263 + 4.13219i) q^{61} +(0.295892 - 0.910662i) q^{63} +(7.70005 + 5.59441i) q^{67} +(-2.84742 - 2.06877i) q^{69} +(9.66368 - 7.02107i) q^{71} +(1.67890 + 5.16713i) q^{73} +(-1.60252 - 4.93205i) q^{77} +(-9.58637 + 6.96491i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-1.12784 - 0.819420i) q^{83} +(-3.13367 + 9.64444i) q^{87} +(-0.527839 - 1.62452i) q^{89} +(0.598504 - 1.84200i) q^{91} -3.69178 q^{93} +(11.8018 - 8.57451i) q^{97} -5.41590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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
$7$	0.957526			0.361911			0.180955	−	0.983491i	$-0.442081\pi$
$7$	0.957526			0.361911			0.180955	+	0.983491i	$0.442081\pi$
$8$		0			0
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	−1.67360	−	5.15082i	−0.504611	−	1.55303i	−0.801424	−	0.598096i	$-0.795924\pi$
$11$	−1.67360	−	5.15082i	−0.504611	−	1.55303i	0.296814	−	0.954935i	$-0.404076\pi$
$12$		0			0
$13$	0.625052	−	1.92371i	0.173358	−	0.533542i	−0.826196	−	0.563382i	$-0.809500\pi$
$13$	0.625052	−	1.92371i	0.173358	−	0.533542i	0.999555	+	0.0298404i	$0.00949990\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.520090	−	0.377867i	−0.126140	−	0.0916463i	0.522926	−	0.852378i	$-0.324840\pi$
$17$	−0.520090	−	0.377867i	−0.126140	−	0.0916463i	−0.649067	+	0.760732i	$0.724840\pi$
$18$		0			0
$19$	4.07829	+	2.96305i	0.935625	+	0.679771i	0.947364	−	0.320160i	$-0.103737\pi$
$19$	4.07829	+	2.96305i	0.935625	+	0.679771i	−0.0117388	+	0.999931i	$0.503737\pi$
$20$		0			0
$21$	0.774655	−	0.562820i	0.169044	−	0.122817i
$22$		0			0
$23$	−1.08762	−	3.34734i	−0.226784	−	0.697969i	−0.998106	−	0.0615235i	$-0.980404\pi$
$23$	−1.08762	−	3.34734i	−0.226784	−	0.697969i	0.771322	−	0.636445i	$-0.219596\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$		0			0
$29$	−8.20405	+	5.96059i	−1.52345	+	1.10685i	−0.563712	+	0.825972i	$0.690627\pi$
$29$	−8.20405	+	5.96059i	−1.52345	+	1.10685i	−0.959742	+	0.280882i	$0.909373\pi$
$30$		0			0
$31$	−2.98671	−	2.16997i	−0.536429	−	0.389738i	0.286328	−	0.958132i	$-0.407565\pi$
$31$	−2.98671	−	2.16997i	−0.536429	−	0.389738i	−0.822757	+	0.568393i	$0.807565\pi$
$32$		0			0
$33$	−4.38155	−	3.18338i	−0.762730	−	0.554156i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.49663	−	10.7615i	0.574842	−	1.76918i	−0.0618753	−	0.998084i	$-0.519708\pi$
$37$	3.49663	−	10.7615i	0.574842	−	1.76918i	0.636717	−	0.771097i	$-0.280292\pi$
$38$		0			0
$39$	−0.625052	−	1.92371i	−0.100088	−	0.308040i
$40$		0			0
$41$	1.08859	−	3.35035i	0.170010	−	0.523237i	−0.829361	−	0.558714i	$-0.811295\pi$
$41$	1.08859	−	3.35035i	0.170010	−	0.523237i	0.999370	+	0.0354770i	$0.0112950\pi$
$42$		0			0
$43$	−0.766348			−0.116867			−0.0584335	−	0.998291i	$-0.518611\pi$
$43$	−0.766348			−0.116867			−0.0584335	+	0.998291i	$0.518611\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.99186	−	2.90026i	0.582273	−	0.423046i	−0.257270	−	0.966340i	$-0.582823\pi$
$47$	3.99186	−	2.90026i	0.582273	−	0.423046i	0.839543	+	0.543293i	$0.182823\pi$
$48$		0			0
$49$	−6.08314			−0.869021
$50$		0			0
$51$	−0.642866			−0.0900193
$52$		0			0
$53$	4.81069	−	3.49517i	0.660799	−	0.480099i	−0.206134	−	0.978524i	$-0.566088\pi$
$53$	4.81069	−	3.49517i	0.660799	−	0.480099i	0.866933	+	0.498425i	$0.166088\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	5.04105			0.667703
$58$		0			0
$59$	1.45818	−	4.48783i	0.189839	−	0.584265i	−0.810159	−	0.586210i	$-0.800619\pi$
$59$	1.45818	−	4.48783i	0.189839	−	0.584265i	0.999998	+	0.00194529i	$0.000619206\pi$
$60$		0			0
$61$	1.34263	+	4.13219i	0.171906	+	0.529073i	0.999479	−	0.0322858i	$-0.0102787\pi$
$61$	1.34263	+	4.13219i	0.171906	+	0.529073i	−0.827572	+	0.561359i	$0.810279\pi$
$62$		0			0
$63$	0.295892	−	0.910662i	0.0372789	−	0.114733i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	7.70005	+	5.59441i	0.940711	+	0.683466i	0.948592	−	0.316503i	$-0.102509\pi$
$67$	7.70005	+	5.59441i	0.940711	+	0.683466i	−0.00788103	+	0.999969i	$0.502509\pi$
$68$		0			0
$69$	−2.84742	−	2.06877i	−0.342789	−	0.249051i
$70$		0			0
$71$	9.66368	−	7.02107i	1.14687	−	0.833248i	0.158806	−	0.987310i	$-0.449235\pi$
$71$	9.66368	−	7.02107i	1.14687	−	0.833248i	0.988061	+	0.154062i	$0.0492354\pi$
$72$		0			0
$73$	1.67890	+	5.16713i	0.196500	+	0.604766i	0.999956	+	0.00940128i	$0.00299256\pi$
$73$	1.67890	+	5.16713i	0.196500	+	0.604766i	−0.803455	+	0.595365i	$0.797007\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.60252	−	4.93205i	−0.182624	−	0.562059i
$78$		0			0
$79$	−9.58637	+	6.96491i	−1.07855	+	0.783613i	−0.977430	−	0.211261i	$-0.932243\pi$
$79$	−9.58637	+	6.96491i	−1.07855	+	0.783613i	−0.101122	+	0.994874i	$0.532243\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	−1.12784	−	0.819420i	−0.123796	−	0.0899431i	0.524164	−	0.851617i	$-0.324378\pi$
$83$	−1.12784	−	0.819420i	−0.123796	−	0.0899431i	−0.647960	+	0.761674i	$0.724378\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−3.13367	+	9.64444i	−0.335965	+	1.03399i
$88$		0			0
$89$	−0.527839	−	1.62452i	−0.0559508	−	0.172199i	0.919176	−	0.393847i	$-0.128856\pi$
$89$	−0.527839	−	1.62452i	−0.0559508	−	0.172199i	−0.975127	+	0.221649i	$0.928856\pi$
$90$		0			0
$91$	0.598504	−	1.84200i	0.0627402	−	0.193095i
$92$		0			0
$93$	−3.69178			−0.382819
$94$		0			0
$95$		0			0
$96$		0			0
$97$	11.8018	−	8.57451i	1.19829	−	0.870610i	0.204176	−	0.978934i	$-0.434549\pi$
$97$	11.8018	−	8.57451i	1.19829	−	0.870610i	0.994116	+	0.108325i	$0.0345486\pi$
$98$		0			0
$99$	−5.41590			−0.544318
$100$		0			0
$101$	−10.2832			−1.02322			−0.511610	−	0.859218i	$-0.670951\pi$
$101$	−10.2832			−1.02322			−0.511610	+	0.859218i	$0.670951\pi$
$102$		0			0
$103$	11.3140	−	8.22008i	1.11480	−	0.809949i	0.131386	−	0.991331i	$-0.458057\pi$
$103$	11.3140	−	8.22008i	1.11480	−	0.809949i	0.983413	+	0.181383i	$0.0580573\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.06727			−0.876566			−0.438283	−	0.898837i	$-0.644413\pi$
$107$	−9.06727			−0.876566			−0.438283	+	0.898837i	$0.644413\pi$
$108$		0			0
$109$	0.734025	−	2.25910i	0.0703068	−	0.216382i	−0.909729	−	0.415202i	$-0.863711\pi$
$109$	0.734025	−	2.25910i	0.0703068	−	0.216382i	0.980036	+	0.198820i	$0.0637109\pi$
$110$		0			0
$111$	−3.49663	−	10.7615i	−0.331885	−	1.02144i
$112$		0			0
$113$	4.15238	−	12.7797i	0.390623	−	1.20221i	−0.541696	−	0.840575i	$-0.682218\pi$
$113$	4.15238	−	12.7797i	0.390623	−	1.20221i	0.932318	−	0.361638i	$-0.117782\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.63641	−	1.18892i	−0.151286	−	0.109916i
$118$		0			0
$119$	−0.498000	−	0.361818i	−0.0456515	−	0.0331678i
$120$		0			0
$121$	−14.8308	+	10.7752i	−1.34826	+	0.979567i
$122$		0			0
$123$	−1.08859	−	3.35035i	−0.0981553	−	0.302091i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−4.40749	−	13.5648i	−0.391101	−	1.20369i	−0.931957	−	0.362570i	$-0.881899\pi$
$127$	−4.40749	−	13.5648i	−0.391101	−	1.20369i	0.540855	−	0.841116i	$-0.318101\pi$
$128$		0			0
$129$	−0.619989	+	0.450448i	−0.0545869	+	0.0396597i
$130$		0			0
$131$	0.104093	+	0.0756282i	0.00909468	+	0.00660767i	0.592323	−	0.805700i	$-0.298211\pi$
$131$	0.104093	+	0.0756282i	0.00909468	+	0.00660767i	−0.583229	+	0.812308i	$0.698211\pi$
$132$		0			0
$133$	3.90507	+	2.83720i	0.338613	+	0.246017i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.23423	+	13.0316i	−0.361754	+	1.11337i	0.590234	+	0.807232i	$0.299035\pi$
$137$	−4.23423	+	13.0316i	−0.361754	+	1.11337i	−0.951989	+	0.306133i	$0.900965\pi$
$138$		0			0
$139$	7.25318	+	22.3230i	0.615206	+	1.89341i	0.398475	+	0.917179i	$0.369539\pi$
$139$	7.25318	+	22.3230i	0.615206	+	1.89341i	0.216731	+	0.976231i	$0.430461\pi$
$140$		0			0
$141$	1.52476	−	4.69272i	0.128408	−	0.395198i
$142$		0			0
$143$	−10.9548			−0.916086
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−4.92137	+	3.57558i	−0.405907	+	0.294909i
$148$		0			0
$149$	−10.6938			−0.876071			−0.438035	−	0.898958i	$-0.644326\pi$
$149$	−10.6938			−0.876071			−0.438035	+	0.898958i	$0.644326\pi$
$150$		0			0
$151$	7.37520			0.600185			0.300092	−	0.953910i	$-0.402982\pi$
$151$	7.37520			0.600185			0.300092	+	0.953910i	$0.402982\pi$
$152$		0			0
$153$	−0.520090	+	0.377867i	−0.0420468	+	0.0305488i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−13.0329			−1.04014			−0.520070	−	0.854124i	$-0.674094\pi$
$157$	−13.0329			−1.04014			−0.520070	+	0.854124i	$0.674094\pi$
$158$		0			0
$159$	1.83752	−	5.65531i	0.145725	−	0.448495i
$160$		0			0
$161$	−1.04142	−	3.20517i	−0.0820755	−	0.252603i
$162$		0			0
$163$	−2.28549	+	7.03403i	−0.179014	+	0.550948i	−0.999794	−	0.0202964i	$-0.993539\pi$
$163$	−2.28549	+	7.03403i	−0.179014	+	0.550948i	0.820780	+	0.571244i	$0.193539\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	16.2827	+	11.8301i	1.25999	+	0.915438i	0.998757	−	0.0498368i	$-0.0158701\pi$
$167$	16.2827	+	11.8301i	1.25999	+	0.915438i	0.261235	+	0.965275i	$0.415870\pi$
$168$		0			0
$169$	7.20724	+	5.23637i	0.554403	+	0.402798i
$170$		0			0
$171$	4.07829	−	2.96305i	0.311875	−	0.226590i
$172$		0			0
$173$	0.686365	+	2.11241i	0.0521833	+	0.160604i	0.973752	−	0.227612i	$-0.0730916\pi$
$173$	0.686365	+	2.11241i	0.0521833	+	0.160604i	−0.921569	+	0.388215i	$0.873092\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.45818	−	4.48783i	−0.109604	−	0.337326i
$178$		0			0
$179$	0.0312215	−	0.0226837i	0.00233360	−	0.00169546i	−0.586618	−	0.809864i	$-0.699541\pi$
$179$	0.0312215	−	0.0226837i	0.00233360	−	0.00169546i	0.588951	+	0.808168i	$0.299541\pi$
$180$		0			0
$181$	−0.118881	−	0.0863720i	−0.00883634	−	0.00641998i	0.583358	−	0.812215i	$-0.301738\pi$
$181$	−0.118881	−	0.0863720i	−0.00883634	−	0.00641998i	−0.592195	+	0.805795i	$0.701738\pi$
$182$		0			0
$183$	3.51505	+	2.55384i	0.259840	+	0.188785i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.07590	+	3.31129i	−0.0786779	+	0.242146i
$188$		0			0
$189$	−0.295892	−	0.910662i	−0.0215230	−	0.0662409i
$190$		0			0
$191$	−0.142049	+	0.437183i	−0.0102783	+	0.0316335i	−0.956064	−	0.293158i	$-0.905294\pi$
$191$	−0.142049	+	0.437183i	−0.0102783	+	0.0316335i	0.945786	+	0.324791i	$0.105294\pi$
$192$		0			0
$193$	19.0231			1.36932			0.684658	−	0.728864i	$-0.259952\pi$
$193$	19.0231			1.36932			0.684658	+	0.728864i	$0.259952\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.80131	−	7.12107i	0.698315	−	0.507355i	−0.181068	−	0.983471i	$-0.557955\pi$
$197$	9.80131	−	7.12107i	0.698315	−	0.507355i	0.879383	+	0.476115i	$0.157955\pi$
$198$		0			0
$199$	16.4872			1.16875			0.584375	−	0.811484i	$-0.301340\pi$
$199$	16.4872			1.16875			0.584375	+	0.811484i	$0.301340\pi$
$200$		0			0
$201$	9.51778			0.671333
$202$		0			0
$203$	−7.85559	+	5.70742i	−0.551355	+	0.400583i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.51960			−0.244629
$208$		0			0
$209$	8.43672	−	25.9656i	0.583580	−	1.79607i
$210$		0			0
$211$	5.61985	+	17.2961i	0.386887	+	1.19071i	0.935102	+	0.354378i	$0.115307\pi$
$211$	5.61985	+	17.2961i	0.386887	+	1.19071i	−0.548216	+	0.836337i	$0.684693\pi$
$212$		0			0
$213$	3.69120	−	11.3603i	0.252917	−	0.778397i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.85985	−	2.07780i	−0.194139	−	0.141051i
$218$		0			0
$219$	4.39542	+	3.19346i	0.297015	+	0.215794i
$220$		0			0
$221$	−1.05199	+	0.764316i	−0.0707646	+	0.0514135i
$222$		0			0
$223$	7.26507	+	22.3596i	0.486505	+	1.49731i	0.829789	+	0.558077i	$0.188461\pi$
$223$	7.26507	+	22.3596i	0.486505	+	1.49731i	−0.343284	+	0.939231i	$0.611539\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.08155	+	18.7171i	0.403647	+	1.24230i	0.922020	+	0.387142i	$0.126538\pi$
$227$	6.08155	+	18.7171i	0.403647	+	1.24230i	−0.518373	+	0.855154i	$0.673462\pi$
$228$		0			0
$229$	−4.29343	+	3.11936i	−0.283718	+	0.206133i	−0.720538	−	0.693416i	$-0.756105\pi$
$229$	−4.29343	+	3.11936i	−0.283718	+	0.206133i	0.436819	+	0.899549i	$0.356105\pi$
$230$		0			0
$231$	−4.19545	−	3.04817i	−0.276040	−	0.200555i
$232$		0			0
$233$	−18.8253	−	13.6774i	−1.23329	−	0.896034i	−0.236154	−	0.971716i	$-0.575887\pi$
$233$	−18.8253	−	13.6774i	−1.23329	−	0.896034i	−0.997132	+	0.0756813i	$0.975887\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−3.66167	+	11.2695i	−0.237851	+	0.732030i
$238$		0			0
$239$	−4.65842	−	14.3371i	−0.301328	−	0.927392i	−0.981022	−	0.193897i	$-0.937887\pi$
$239$	−4.65842	−	14.3371i	−0.301328	−	0.927392i	0.679694	−	0.733496i	$-0.262113\pi$
$240$		0			0
$241$	−5.84454	+	17.9877i	−0.376480	+	1.15869i	0.565995	+	0.824409i	$0.308492\pi$
$241$	−5.84454	+	17.9877i	−0.376480	+	1.15869i	−0.942475	+	0.334278i	$0.891508\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.24921	−	5.99340i	0.524885	−	0.381351i
$248$		0			0
$249$	−1.39408			−0.0883463
$250$		0			0
$251$	−4.56761			−0.288305			−0.144153	−	0.989555i	$-0.546046\pi$
$251$	−4.56761			−0.288305			−0.144153	+	0.989555i	$0.546046\pi$
$252$		0			0
$253$	−15.4213	+	11.2042i	−0.969530	+	0.704405i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−20.2556			−1.26351			−0.631754	−	0.775169i	$-0.717665\pi$
$257$	−20.2556			−1.26351			−0.631754	+	0.775169i	$0.717665\pi$
$258$		0			0
$259$	3.34811	−	10.3044i	0.208042	−	0.640286i
$260$		0			0
$261$	3.13367	+	9.64444i	0.193969	+	0.596976i
$262$		0			0
$263$	−9.51119	+	29.2724i	−0.586485	+	1.80502i	0.00673789	+	0.999977i	$0.497855\pi$
$263$	−9.51119	+	29.2724i	−0.586485	+	1.80502i	−0.593223	+	0.805038i	$0.702145\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.38190	−	1.00401i	−0.0845709	−	0.0614443i
$268$		0			0
$269$	21.5796	+	15.6785i	1.31573	+	0.955936i	0.999975	+	0.00709610i	$0.00225878\pi$
$269$	21.5796	+	15.6785i	1.31573	+	0.955936i	0.315758	+	0.948840i	$0.397741\pi$
$270$		0			0
$271$	4.47342	−	3.25013i	0.271741	−	0.197431i	−0.443566	−	0.896242i	$-0.646287\pi$
$271$	4.47342	−	3.25013i	0.271741	−	0.197431i	0.715307	+	0.698810i	$0.246287\pi$
$272$		0			0
$273$	−0.598504	−	1.84200i	−0.0362231	−	0.111483i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−9.55583	−	29.4098i	−0.574154	−	1.76706i	−0.639041	−	0.769172i	$-0.720669\pi$
$277$	−9.55583	−	29.4098i	−0.574154	−	1.76706i	0.0648872	−	0.997893i	$-0.479331\pi$
$278$		0			0
$279$	−2.98671	+	2.16997i	−0.178810	+	0.129913i
$280$		0			0
$281$	13.6310	+	9.90352i	0.813159	+	0.590795i	0.914745	−	0.404032i	$-0.132392\pi$
$281$	13.6310	+	9.90352i	0.813159	+	0.590795i	−0.101586	+	0.994827i	$0.532392\pi$
$282$		0			0
$283$	9.11176	+	6.62008i	0.541638	+	0.393523i	0.824693	−	0.565581i	$-0.191348\pi$
$283$	9.11176	+	6.62008i	0.541638	+	0.393523i	−0.283055	+	0.959104i	$0.591348\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.04236	−	3.20805i	0.0615285	−	0.189365i
$288$		0			0
$289$	−5.12558	−	15.7749i	−0.301505	−	0.927936i
$290$		0			0
$291$	4.50789	−	13.8738i	0.264257	−	0.813299i
$292$		0			0
$293$	−11.1995			−0.654284			−0.327142	−	0.944975i	$-0.606086\pi$
$293$	−11.1995			−0.654284			−0.327142	+	0.944975i	$0.606086\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.38155	+	3.18338i	−0.254243	+	0.184719i
$298$		0			0
$299$	−7.11914			−0.411710
$300$		0			0
$301$	−0.733798			−0.0422954
$302$		0			0
$303$	−8.31931	+	6.04433i	−0.477932	+	0.347238i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	24.1289			1.37711			0.688554	−	0.725185i	$-0.258246\pi$
$307$	24.1289			1.37711			0.688554	+	0.725185i	$0.258246\pi$
$308$		0			0
$309$	4.32155	−	13.3004i	0.245844	−	0.756632i
$310$		0			0
$311$	0.640628	+	1.97165i	0.0363267	+	0.111802i	0.967576	−	0.252582i	$-0.0812797\pi$
$311$	0.640628	+	1.97165i	0.0363267	+	0.111802i	−0.931249	+	0.364384i	$0.881280\pi$
$312$		0			0
$313$	−2.63272	+	8.10268i	−0.148810	+	0.457991i	−0.997481	−	0.0709303i	$-0.977403\pi$
$313$	−2.63272	+	8.10268i	−0.148810	+	0.457991i	0.848671	+	0.528921i	$0.177403\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.0083	−	7.99798i	−0.618286	−	0.449211i	0.234036	−	0.972228i	$-0.424806\pi$
$317$	−11.0083	−	7.99798i	−0.618286	−	0.449211i	−0.852322	+	0.523017i	$0.824806\pi$
$318$		0			0
$319$	44.4323	+	32.2819i	2.48773	+	1.80744i
$320$		0			0
$321$	−7.33558	+	5.32961i	−0.409432	+	0.297470i
$322$		0			0
$323$	−1.00144	−	3.08211i	−0.0557215	−	0.171493i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.734025	−	2.25910i	−0.0405917	−	0.124928i
$328$		0			0
$329$	3.82231	−	2.77707i	0.210731	−	0.153105i
$330$		0			0
$331$	18.3097	+	13.3028i	1.00639	+	0.731187i	0.963449	−	0.267891i	$-0.0863266\pi$
$331$	18.3097	+	13.3028i	1.00639	+	0.731187i	0.0429430	+	0.999078i	$0.486327\pi$
$332$		0			0
$333$	−9.15429	−	6.65098i	−0.501652	−	0.364471i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−11.1215	+	34.2285i	−0.605828	+	1.86455i	−0.114831	+	0.993385i	$0.536633\pi$
$337$	−11.1215	+	34.2285i	−0.605828	+	1.86455i	−0.490997	+	0.871161i	$0.663367\pi$
$338$		0			0
$339$	−4.15238	−	12.7797i	−0.225526	−	0.694098i
$340$		0			0
$341$	−6.17857	+	19.0157i	−0.334588	+	1.02976i
$342$		0			0
$343$	−12.5275			−0.676419
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.25158	+	5.26858i	−0.389285	+	0.282832i	−0.765162	−	0.643837i	$-0.777341\pi$
$347$	−7.25158	+	5.26858i	−0.389285	+	0.282832i	0.375877	+	0.926669i	$0.377341\pi$
$348$		0			0
$349$	−11.8276			−0.633114			−0.316557	−	0.948573i	$-0.602527\pi$
$349$	−11.8276			−0.633114			−0.316557	+	0.948573i	$0.602527\pi$
$350$		0			0
$351$	−2.02271			−0.107964
$352$		0			0
$353$	18.6791	−	13.5712i	0.994188	−	0.722320i	0.0333537	−	0.999444i	$-0.489381\pi$
$353$	18.6791	−	13.5712i	0.994188	−	0.722320i	0.960834	+	0.277124i	$0.0893812\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.615561			−0.0325790
$358$		0			0
$359$	6.52607	−	20.0852i	0.344433	−	1.06005i	−0.617454	−	0.786607i	$-0.711836\pi$
$359$	6.52607	−	20.0852i	0.344433	−	1.06005i	0.961887	−	0.273448i	$-0.0881641\pi$
$360$		0			0
$361$	1.98147	+	6.09833i	0.104288	+	0.320965i
$362$		0			0
$363$	−5.66488	+	17.4347i	−0.297329	+	0.915085i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	6.78801	+	4.93178i	0.354331	+	0.257437i	0.750684	−	0.660662i	$-0.229724\pi$
$367$	6.78801	+	4.93178i	0.354331	+	0.257437i	−0.396353	+	0.918098i	$0.629724\pi$
$368$		0			0
$369$	−2.84998	−	2.07063i	−0.148364	−	0.107793i
$370$		0			0
$371$	4.60636	−	3.34672i	0.239150	−	0.173753i
$372$		0			0
$373$	−1.95565	−	6.01888i	−0.101260	−	0.311646i	0.887575	−	0.460664i	$-0.152389\pi$
$373$	−1.95565	−	6.01888i	−0.101260	−	0.311646i	−0.988834	+	0.149018i	$0.952389\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.33850	+	19.5079i	0.326450	+	1.00471i
$378$		0			0
$379$	−12.1990	+	8.86310i	−0.626621	+	0.455267i	−0.855228	−	0.518252i	$-0.826583\pi$
$379$	−12.1990	+	8.86310i	−0.626621	+	0.455267i	0.228607	+	0.973519i	$0.426583\pi$
$380$		0			0
$381$	−11.5389	−	8.38354i	−0.591158	−	0.429502i
$382$		0			0
$383$	26.3563	+	19.1490i	1.34674	+	0.978466i	0.999167	+	0.0408145i	$0.0129953\pi$
$383$	26.3563	+	19.1490i	1.34674	+	0.978466i	0.347576	+	0.937652i	$0.387005\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.236815	+	0.728840i	−0.0120380	+	0.0370490i
$388$		0			0
$389$	−1.69084	−	5.20388i	−0.0857292	−	0.263847i	0.898998	−	0.437953i	$-0.144296\pi$
$389$	−1.69084	−	5.20388i	−0.0857292	−	0.263847i	−0.984727	+	0.174106i	$0.944296\pi$
$390$		0			0
$391$	−0.699192	+	2.15189i	−0.0353597	+	0.108826i
$392$		0			0
$393$	0.128666			0.00649036
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−11.5435	+	8.38686i	−0.579353	+	0.420925i	−0.838491	−	0.544916i	$-0.816562\pi$
$397$	−11.5435	+	8.38686i	−0.579353	+	0.420925i	0.259138	+	0.965840i	$0.416562\pi$
$398$		0			0
$399$	4.82694			0.241649
$400$		0			0
$401$	17.8291			0.890342			0.445171	−	0.895446i	$-0.353143\pi$
$401$	17.8291			0.890342			0.445171	+	0.895446i	$0.353143\pi$
$402$		0			0
$403$	−6.04125	+	4.38923i	−0.300936	+	0.218643i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−61.2826			−3.03767
$408$		0			0
$409$	7.42964	−	22.8661i	0.367372	−	1.13065i	−0.581110	−	0.813825i	$-0.697382\pi$
$409$	7.42964	−	22.8661i	0.367372	−	1.13065i	0.948482	−	0.316830i	$-0.102618\pi$
$410$		0			0
$411$	4.23423	+	13.0316i	0.208859	+	0.642802i
$412$		0			0
$413$	1.39625	−	4.29721i	0.0687049	−	0.211452i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	18.9891	+	13.7964i	0.929898	+	0.675611i
$418$		0			0
$419$	22.7180	+	16.5056i	1.10984	+	0.806349i	0.982639	−	0.185527i	$-0.0593992\pi$
$419$	22.7180	+	16.5056i	1.10984	+	0.806349i	0.127206	+	0.991876i	$0.459399\pi$
$420$		0			0
$421$	−16.3383	+	11.8704i	−0.796278	+	0.578530i	−0.909820	−	0.415003i	$-0.863780\pi$
$421$	−16.3383	+	11.8704i	−0.796278	+	0.578530i	0.113542	+	0.993533i	$0.463780\pi$
$422$		0			0
$423$	−1.52476	−	4.69272i	−0.0741362	−	0.228168i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.28560	+	3.95668i	0.0622148	+	0.191477i
$428$		0			0
$429$	−8.86261	+	6.43907i	−0.427891	+	0.310881i
$430$		0			0
$431$	3.35912	+	2.44055i	0.161803	+	0.117557i	0.665741	−	0.746183i	$-0.268116\pi$
$431$	3.35912	+	2.44055i	0.161803	+	0.117557i	−0.503937	+	0.863740i	$0.668116\pi$
$432$		0			0
$433$	24.5295	+	17.8217i	1.17881	+	0.856456i	0.992037	−	0.125947i	$-0.0401970\pi$
$433$	24.5295	+	17.8217i	1.17881	+	0.856456i	0.186773	+	0.982403i	$0.440197\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.48273	−	16.8741i	0.262275	−	0.807198i
$438$		0			0
$439$	−0.984067	−	3.02865i	−0.0469670	−	0.144549i	0.924823	−	0.380398i	$-0.124213\pi$
$439$	−0.984067	−	3.02865i	−0.0469670	−	0.144549i	−0.971790	+	0.235849i	$0.924213\pi$
$440$		0			0
$441$	−1.87979	+	5.78541i	−0.0895140	+	0.275496i
$442$		0			0
$443$	30.4607			1.44723			0.723615	−	0.690204i	$-0.242479\pi$
$443$	30.4607			1.44723			0.723615	+	0.690204i	$0.242479\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−8.65147	+	6.28566i	−0.409201	+	0.297302i
$448$		0			0
$449$	1.35787			0.0640820			0.0320410	−	0.999487i	$-0.489799\pi$
$449$	1.35787			0.0640820			0.0320410	+	0.999487i	$0.489799\pi$
$450$		0			0
$451$	−19.0789			−0.898392
$452$		0			0
$453$	5.96666	−	4.33503i	0.280338	−	0.203678i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	9.89208			0.462732			0.231366	−	0.972867i	$-0.425680\pi$
$457$	9.89208			0.462732			0.231366	+	0.972867i	$0.425680\pi$
$458$		0			0
$459$	−0.198657	+	0.611402i	−0.00927250	+	0.0285378i
$460$		0			0
$461$	−6.51515	−	20.0516i	−0.303441	−	0.933894i	−0.980255	−	0.197740i	$-0.936640\pi$
$461$	−6.51515	−	20.0516i	−0.303441	−	0.933894i	0.676814	−	0.736154i	$-0.263360\pi$
$462$		0			0
$463$	−0.158879	+	0.488978i	−0.00738372	+	0.0227248i	−0.954681	−	0.297633i	$-0.903803\pi$
$463$	−0.158879	+	0.488978i	−0.00738372	+	0.0227248i	0.947297	+	0.320357i	$0.103803\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	15.0267	+	10.9175i	0.695352	+	0.505202i	0.878415	−	0.477899i	$-0.158601\pi$
$467$	15.0267	+	10.9175i	0.695352	+	0.505202i	−0.183063	+	0.983101i	$0.558601\pi$
$468$		0			0
$469$	7.37300	+	5.35680i	0.340453	+	0.247354i
$470$		0			0
$471$	−10.5439	+	7.66056i	−0.485835	+	0.352980i
$472$		0			0
$473$	1.28256	+	3.94732i	0.0589723	+	0.181498i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.83752	−	5.65531i	−0.0841343	−	0.258939i
$478$		0			0
$479$	−18.3847	+	13.3573i	−0.840017	+	0.610308i	−0.922376	−	0.386294i	$-0.873755\pi$
$479$	−18.3847	+	13.3573i	−0.840017	+	0.610308i	0.0823581	+	0.996603i	$0.473755\pi$
$480$		0			0
$481$	−18.5165	−	13.4530i	−0.844279	−	0.613404i
$482$		0			0
$483$	−2.72648	−	1.98090i	−0.124059	−	0.0901342i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−8.21528	+	25.2840i	−0.372270	+	1.14573i	0.573032	+	0.819533i	$0.305767\pi$
$487$	−8.21528	+	25.2840i	−0.372270	+	1.14573i	−0.945302	+	0.326196i	$0.894233\pi$
$488$		0			0
$489$	2.28549	+	7.03403i	0.103354	+	0.318090i
$490$		0			0
$491$	1.66601	−	5.12746i	0.0751860	−	0.231399i	−0.906400	−	0.422421i	$-0.861180\pi$
$491$	1.66601	−	5.12746i	0.0751860	−	0.231399i	0.981586	+	0.191022i	$0.0611803\pi$
$492$		0			0
$493$	6.51915			0.293608
$494$		0			0
$495$		0			0
$496$		0			0
$497$	9.25323	−	6.72286i	0.415064	−	0.301562i
$498$		0			0
$499$	−14.5574			−0.651677			−0.325839	−	0.945425i	$-0.605647\pi$
$499$	−14.5574			−0.651677			−0.325839	+	0.945425i	$0.605647\pi$
$500$		0			0
$501$	20.1265			0.899187
$502$		0			0
$503$	−27.4386	+	19.9353i	−1.22343	+	0.888873i	−0.996380	−	0.0850104i	$-0.972908\pi$
$503$	−27.4386	+	19.9353i	−1.22343	+	0.888873i	−0.227049	+	0.973883i	$0.572908\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	8.90864			0.395647
$508$		0			0
$509$	−5.18882	+	15.9695i	−0.229990	+	0.707838i	0.767756	+	0.640742i	$0.221373\pi$
$509$	−5.18882	+	15.9695i	−0.229990	+	0.707838i	−0.997747	+	0.0670956i	$0.978627\pi$
$510$		0			0
$511$	1.60759	+	4.94766i	0.0711157	+	0.218872i
$512$		0			0
$513$	1.55777	−	4.79432i	0.0687772	−	0.211674i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−21.6195	−	15.7075i	−0.950825	−	0.690815i
$518$		0			0
$519$	1.79693	+	1.30554i	0.0788763	+	0.0573070i
$520$		0			0
$521$	13.8271	−	10.0460i	0.605777	−	0.440123i	−0.242148	−	0.970239i	$-0.577852\pi$
$521$	13.8271	−	10.0460i	0.605777	−	0.440123i	0.847925	+	0.530117i	$0.177852\pi$
$522$		0			0
$523$	−6.38135	−	19.6398i	−0.279037	−	0.858788i	−0.988123	−	0.153666i	$-0.950892\pi$
$523$	−6.38135	−	19.6398i	−0.279037	−	0.858788i	0.709086	−	0.705122i	$-0.249108\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.733396	+	2.25716i	0.0319472	+	0.0983234i
$528$		0			0
$529$	8.58561	−	6.23781i	0.373287	−	0.271209i
$530$		0			0
$531$	−3.81757	−	2.77363i	−0.165669	−	0.120365i
$532$		0			0
$533$	−5.76468	−	4.18829i	−0.249696	−	0.181415i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.0119255	−	0.0367031i	0.000514625	−	0.00158385i
$538$		0			0
$539$	10.1808	+	31.3332i	0.438517	+	1.34962i
$540$		0			0
$541$	−3.75968	+	11.5711i	−0.161641	+	0.497480i	−0.998773	−	0.0495207i	$-0.984231\pi$
$541$	−3.75968	+	11.5711i	−0.161641	+	0.497480i	0.837132	+	0.547001i	$0.184231\pi$
$542$		0			0
$543$	−0.146945			−0.00630600
$544$		0			0
$545$		0			0
$546$		0			0
$547$	9.03427	−	6.56378i	0.386278	−	0.280647i	−0.377651	−	0.925948i	$-0.623268\pi$
$547$	9.03427	−	6.56378i	0.386278	−	0.280647i	0.763928	+	0.645301i	$0.223268\pi$
$548$		0			0
$549$	4.34485			0.185434
$550$		0			0
$551$	−51.1201			−2.17779
$552$		0			0
$553$	−9.17921	+	6.66908i	−0.390340	+	0.283598i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−12.9282			−0.547787			−0.273894	−	0.961760i	$-0.588312\pi$
$557$	−12.9282			−0.547787			−0.273894	+	0.961760i	$0.588312\pi$
$558$		0			0
$559$	−0.479007	+	1.47423i	−0.0202598	+	0.0623534i
$560$		0			0
$561$	1.07590	+	3.31129i	0.0454247	+	0.139803i
$562$		0			0
$563$	9.80354	−	30.1722i	0.413170	−	1.27161i	−0.500708	−	0.865616i	$-0.666927\pi$
$563$	9.80354	−	30.1722i	0.413170	−	1.27161i	0.913878	−	0.405989i	$-0.133073\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.774655	−	0.562820i	−0.0325325	−	0.0236362i
$568$		0			0
$569$	−23.3050	−	16.9321i	−0.976997	−	0.709830i	−0.0199619	−	0.999801i	$-0.506354\pi$
$569$	−23.3050	−	16.9321i	−0.976997	−	0.709830i	−0.957036	+	0.289971i	$0.906354\pi$
$570$		0			0
$571$	14.6999	−	10.6801i	0.615173	−	0.446950i	−0.236059	−	0.971739i	$-0.575856\pi$
$571$	14.6999	−	10.6801i	0.615173	−	0.446950i	0.851232	+	0.524789i	$0.175856\pi$
$572$		0			0
$573$	0.142049	+	0.437183i	0.00593420	+	0.0182636i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−12.6065	−	38.7990i	−0.524817	−	1.61522i	−0.764677	−	0.644414i	$-0.777101\pi$
$577$	−12.6065	−	38.7990i	−0.524817	−	1.61522i	0.239859	−	0.970808i	$-0.422899\pi$
$578$		0			0
$579$	15.3900	−	11.1815i	0.639589	−	0.464688i
$580$		0			0
$581$	−1.07993	−	0.784616i	−0.0448031	−	0.0325514i
$582$		0			0
$583$	−26.0542	−	18.9295i	−1.07905	−	0.783979i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.84446	−	8.75436i	0.117404	−	0.361331i	−0.875037	−	0.484056i	$-0.839163\pi$
$587$	2.84446	−	8.75436i	0.117404	−	0.361331i	0.992441	+	0.122725i	$0.0391632\pi$
$588$		0			0
$589$	−5.75094	−	17.6996i	−0.236963	−	0.729298i
$590$		0			0
$591$	3.74377	−	11.5221i	0.153998	−	0.473957i
$592$		0			0
$593$	12.3856			0.508614			0.254307	−	0.967124i	$-0.418153\pi$
$593$	12.3856			0.508614			0.254307	+	0.967124i	$0.418153\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	13.3385	−	9.69096i	0.545907	−	0.396625i
$598$		0			0
$599$	−18.1732			−0.742536			−0.371268	−	0.928526i	$-0.621077\pi$
$599$	−18.1732			−0.742536			−0.371268	+	0.928526i	$0.621077\pi$
$600$		0			0
$601$	29.8155			1.21620			0.608099	−	0.793861i	$-0.291932\pi$
$601$	29.8155			1.21620			0.608099	+	0.793861i	$0.291932\pi$
$602$		0			0
$603$	7.70005	−	5.59441i	0.313570	−	0.227822i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	9.16747			0.372096			0.186048	−	0.982541i	$-0.440432\pi$
$607$	9.16747			0.372096			0.186048	+	0.982541i	$0.440432\pi$
$608$		0			0
$609$	−3.00057	+	9.23480i	−0.121589	+	0.374213i
$610$		0			0
$611$	−3.08414	−	9.49201i	−0.124771	−	0.384006i
$612$		0			0
$613$	4.34294	−	13.3662i	0.175410	−	0.539855i	−0.824242	−	0.566237i	$-0.808399\pi$
$613$	4.34294	−	13.3662i	0.175410	−	0.539855i	0.999652	+	0.0263819i	$0.00839859\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	29.3141	+	21.2980i	1.18014	+	0.857424i	0.992188	−	0.124754i	$-0.0398141\pi$
$617$	29.3141	+	21.2980i	1.18014	+	0.857424i	0.187955	+	0.982178i	$0.439814\pi$
$618$		0			0
$619$	−20.7716	−	15.0915i	−0.834882	−	0.606577i	0.0860542	−	0.996290i	$-0.472574\pi$
$619$	−20.7716	−	15.0915i	−0.834882	−	0.606577i	−0.920936	+	0.389713i	$0.872574\pi$
$620$		0			0
$621$	−2.84742	+	2.06877i	−0.114263	+	0.0830169i
$622$		0			0
$623$	−0.505419	−	1.55552i	−0.0202492	−	0.0623206i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−8.43672	−	25.9656i	−0.336930	−	1.03696i
$628$		0			0
$629$	−5.88498	+	4.27569i	−0.234650	+	0.170483i
$630$		0			0
$631$	19.9603	+	14.5020i	0.794608	+	0.577317i	0.909327	−	0.416081i	$-0.136597\pi$
$631$	19.9603	+	14.5020i	0.794608	+	0.577317i	−0.114719	+	0.993398i	$0.536597\pi$
$632$		0			0
$633$	14.7130	+	10.6896i	0.584788	+	0.424873i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−3.80228	+	11.7022i	−0.150652	+	0.463659i
$638$		0			0
$639$	−3.69120	−	11.3603i	−0.146021	−	0.449408i
$640$		0			0
$641$	−9.25128	+	28.4725i	−0.365404	+	1.12460i	0.584324	+	0.811520i	$0.301360\pi$
$641$	−9.25128	+	28.4725i	−0.365404	+	1.12460i	−0.949728	+	0.313077i	$0.898640\pi$
$642$		0			0
$643$	−10.1343			−0.399658			−0.199829	−	0.979831i	$-0.564039\pi$
$643$	−10.1343			−0.399658			−0.199829	+	0.979831i	$0.564039\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	36.6155	−	26.6027i	1.43950	−	1.04586i	0.451358	−	0.892343i	$-0.350940\pi$
$647$	36.6155	−	26.6027i	1.43950	−	1.04586i	0.988146	−	0.153518i	$-0.0490603\pi$
$648$		0			0
$649$	−25.5564			−1.00318
$650$		0			0
$651$	−3.53497			−0.138547
$652$		0			0
$653$	−26.6853	+	19.3880i	−1.04428	+	0.758711i	−0.971116	−	0.238609i	$-0.923309\pi$
$653$	−26.6853	+	19.3880i	−1.04428	+	0.758711i	−0.0731608	+	0.997320i	$0.523309\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	5.43304			0.211963
$658$		0			0
$659$	0.789392	−	2.42950i	0.0307504	−	0.0946398i	−0.934503	−	0.355954i	$-0.884156\pi$
$659$	0.789392	−	2.42950i	0.0307504	−	0.0946398i	0.965254	+	0.261314i	$0.0841559\pi$
$660$		0			0
$661$	−14.0332	−	43.1898i	−0.545829	−	1.67989i	−0.719011	−	0.694999i	$-0.755405\pi$
$661$	−14.0332	−	43.1898i	−0.545829	−	1.67989i	0.173182	−	0.984890i	$-0.444595\pi$
$662$		0			0
$663$	−0.401825	+	1.23669i	−0.0156056	+	0.0480290i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	28.8750	+	20.9789i	1.11804	+	0.812307i
$668$		0			0
$669$	19.0202	+	13.8190i	0.735363	+	0.534273i
$670$		0			0
$671$	19.0372	−	13.8313i	0.734922	−	0.533952i
$672$		0			0
$673$	−3.50508	−	10.7875i	−0.135111	−	0.415828i	0.860496	−	0.509456i	$-0.170153\pi$
$673$	−3.50508	−	10.7875i	−0.135111	−	0.415828i	−0.995607	+	0.0936282i	$0.970153\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4.78000	+	14.7113i	0.183710	+	0.565402i	0.999924	−	0.0123484i	$-0.00393071\pi$
$677$	4.78000	+	14.7113i	0.183710	+	0.565402i	−0.816213	+	0.577750i	$0.803931\pi$
$678$		0			0
$679$	11.3005	−	8.21032i	0.433675	−	0.315083i
$680$		0			0
$681$	15.9217	+	11.5678i	0.610121	+	0.443279i
$682$		0			0
$683$	5.49567	+	3.99284i	0.210286	+	0.152782i	0.687943	−	0.725765i	$-0.258514\pi$
$683$	5.49567	+	3.99284i	0.210286	+	0.152782i	−0.477657	+	0.878546i	$0.658514\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−1.63995	+	5.04724i	−0.0625678	+	0.192564i
$688$		0			0
$689$	−3.71677	−	11.4390i	−0.141598	−	0.435793i
$690$		0			0
$691$	13.0774	−	40.2482i	0.497489	−	1.53111i	−0.315552	−	0.948908i	$-0.602190\pi$
$691$	13.0774	−	40.2482i	0.497489	−	1.53111i	0.813041	−	0.582206i	$-0.197810\pi$
$692$		0			0
$693$	−5.18586			−0.196995
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.83215	+	1.33114i	−0.0693978	+	0.0504205i
$698$		0			0
$699$	−23.2693			−0.880127
$700$		0			0
$701$	32.2924			1.21967			0.609834	−	0.792529i	$-0.291236\pi$
$701$	32.2924			1.21967			0.609834	+	0.792529i	$0.291236\pi$
$702$		0			0
$703$	46.1472	−	33.5279i	1.74047	−	1.26453i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.84647			−0.370314
$708$		0			0
$709$	−0.667116	+	2.05317i	−0.0250541	+	0.0771085i	−0.962802	−	0.270209i	$-0.912907\pi$
$709$	−0.667116	+	2.05317i	−0.0250541	+	0.0771085i	0.937748	+	0.347317i	$0.112907\pi$
$710$		0			0
$711$	3.66167	+	11.2695i	0.137323	+	0.422638i
$712$		0			0
$713$	−4.01524	+	12.3576i	−0.150372	+	0.462797i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−12.1959	−	8.86084i	−0.455464	−	0.330914i
$718$		0			0
$719$	−1.28757	−	0.935472i	−0.0480181	−	0.0348872i	0.563517	−	0.826104i	$-0.309448\pi$
$719$	−1.28757	−	0.935472i	−0.0480181	−	0.0348872i	−0.611535	+	0.791217i	$0.709448\pi$
$720$		0			0
$721$	10.8334	−	7.87094i	0.403458	−	0.293129i
$722$		0			0
$723$	5.84454	+	17.9877i	0.217361	+	0.668968i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	0.414026	+	1.27424i	0.0153554	+	0.0472589i	0.958441	−	0.285292i	$-0.0920906\pi$
$727$	0.414026	+	1.27424i	0.0153554	+	0.0472589i	−0.943085	+	0.332551i	$0.892091\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	0.398570	+	0.289578i	0.0147416	+	0.0107104i
$732$		0			0
$733$	−35.4759	−	25.7748i	−1.31033	−	0.952013i	−0.999999	−	0.00138578i	$-0.999559\pi$
$733$	−35.4759	−	25.7748i	−1.31033	−	0.952013i	−0.310335	−	0.950627i	$-0.600441\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	15.9290	−	49.0244i	0.586752	−	1.80584i
$738$		0			0
$739$	5.67584	+	17.4684i	0.208789	+	0.642587i	0.999536	+	0.0304443i	$0.00969221\pi$
$739$	5.67584	+	17.4684i	0.208789	+	0.642587i	−0.790747	+	0.612143i	$0.790308\pi$
$740$		0			0
$741$	3.15092	−	9.69753i	0.115752	−	0.356248i
$742$		0			0
$743$	−21.5051			−0.788947			−0.394474	−	0.918907i	$-0.629073\pi$
$743$	−21.5051			−0.788947			−0.394474	+	0.918907i	$0.629073\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.12784	+	0.819420i	−0.0412653	+	0.0299810i
$748$		0			0
$749$	−8.68215			−0.317239
$750$		0			0
$751$	−7.02810			−0.256459			−0.128230	−	0.991745i	$-0.540929\pi$
$751$	−7.02810			−0.256459			−0.128230	+	0.991745i	$0.540929\pi$
$752$		0			0
$753$	−3.69528	+	2.68477i	−0.134663	+	0.0978386i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	5.39361			0.196034			0.0980171	−	0.995185i	$-0.468750\pi$
$757$	5.39361			0.196034			0.0980171	+	0.995185i	$0.468750\pi$
$758$		0			0
$759$	−5.89042	+	18.1289i	−0.213809	+	0.658036i
$760$		0			0
$761$	−6.22670	−	19.1638i	−0.225718	−	0.694688i	−0.998218	−	0.0596731i	$-0.980994\pi$
$761$	−6.22670	−	19.1638i	−0.225718	−	0.694688i	0.772500	−	0.635014i	$-0.219006\pi$
$762$		0			0
$763$	0.702848	−	2.16314i	0.0254448	−	0.0783111i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.72184	−	5.61025i	−0.278820	−	0.202574i
$768$		0			0
$769$	−25.0121	−	18.1724i	−0.901960	−	0.655312i	0.0370088	−	0.999315i	$-0.488217\pi$
$769$	−25.0121	−	18.1724i	−0.901960	−	0.655312i	−0.938969	+	0.344003i	$0.888217\pi$
$770$		0			0
$771$	−16.3871	+	11.9059i	−0.590167	+	0.428781i
$772$		0			0
$773$	−9.88584	−	30.4255i	−0.355569	−	1.09433i	−0.955679	−	0.294411i	$-0.904876\pi$
$773$	−9.88584	−	30.4255i	−0.355569	−	1.09433i	0.600110	−	0.799918i	$-0.295124\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−3.34811	−	10.3044i	−0.120113	−	0.369669i
$778$		0			0
$779$	14.3669	−	10.4381i	0.514747	−	0.373985i
$780$		0			0
$781$	−52.3375	−	38.0254i	−1.87278	−	1.36066i
$782$		0			0
$783$	8.20405	+	5.96059i	0.293189	+	0.213014i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	7.54681	−	23.2267i	0.269015	−	0.827942i	−0.721726	−	0.692178i	$-0.756651\pi$
$787$	7.54681	−	23.2267i	0.269015	−	0.827942i	0.990741	−	0.135764i	$-0.0433489\pi$
$788$		0			0
$789$	9.51119	+	29.2724i	0.338607	+	1.04213i
$790$		0			0
$791$	3.97601	−	12.2369i	0.141371	−	0.435094i
$792$		0			0
$793$	8.78837			0.312084
$794$		0			0
$795$		0			0
$796$		0			0
$797$	40.1580	−	29.1765i	1.42247	−	1.03348i	0.431110	−	0.902300i	$-0.358122\pi$
$797$	40.1580	−	29.1765i	1.42247	−	1.03348i	0.991358	−	0.131184i	$-0.0418778\pi$
$798$		0			0
$799$	−3.17204			−0.112219
$800$		0			0
$801$	−1.70812			−0.0603535
$802$		0			0
$803$	23.8051	−	17.2954i	0.840065	−	0.610343i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	26.6739			0.938965
$808$		0			0
$809$	−5.82162	+	17.9171i	−0.204677	+	0.629932i	0.795049	+	0.606545i	$0.207445\pi$
$809$	−5.82162	+	17.9171i	−0.204677	+	0.629932i	−0.999726	+	0.0233871i	$0.992555\pi$
$810$		0			0
$811$	5.77928	+	17.7868i	0.202938	+	0.624578i	0.999792	+	0.0204064i	$0.00649600\pi$
$811$	5.77928	+	17.7868i	0.202938	+	0.624578i	−0.796854	+	0.604172i	$0.793504\pi$
$812$		0			0
$813$	1.70869	−	5.25882i	0.0599265	−	0.184435i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−3.12539	−	2.27073i	−0.109344	−	0.0794428i
$818$		0			0
$819$	−1.56690	−	1.13842i	−0.0547520	−	0.0397797i
$820$		0			0
$821$	−29.7103	+	21.5858i	−1.03690	+	0.753350i	−0.969678	−	0.244388i	$-0.921413\pi$
$821$	−29.7103	+	21.5858i	−1.03690	+	0.753350i	−0.0672202	+	0.997738i	$0.521413\pi$
$822$		0			0
$823$	−12.5200	−	38.5327i	−0.436421	−	1.34317i	−0.891623	−	0.452779i	$-0.850433\pi$
$823$	−12.5200	−	38.5327i	−0.436421	−	1.34317i	0.455202	−	0.890388i	$-0.349567\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−3.45274	−	10.6264i	−0.120063	−	0.369517i	0.872906	−	0.487889i	$-0.162233\pi$
$827$	−3.45274	−	10.6264i	−0.120063	−	0.369517i	−0.992969	+	0.118371i	$0.962233\pi$
$828$		0			0
$829$	−29.8314	+	21.6738i	−1.03609	+	0.752762i	−0.969518	−	0.245019i	$-0.921206\pi$
$829$	−29.8314	+	21.6738i	−1.03609	+	0.752762i	−0.0665703	+	0.997782i	$0.521206\pi$
$830$		0			0
$831$	−25.0175	−	18.1763i	−0.867847	−	0.630528i
$832$		0			0
$833$	3.16378	+	2.29862i	0.109618	+	0.0796425i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.14082	+	3.51109i	−0.0394326	+	0.121361i
$838$		0			0
$839$	−3.53480	−	10.8790i	−0.122035	−	0.375585i	0.871314	−	0.490725i	$-0.163268\pi$
$839$	−3.53480	−	10.8790i	−0.122035	−	0.375585i	−0.993349	+	0.115140i	$0.963268\pi$
$840$		0			0
$841$	22.8163	−	70.2213i	0.786769	−	2.42143i
$842$		0			0
$843$	16.8489			0.580306
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−14.2009	+	10.3176i	−0.487950	+	0.354516i
$848$		0			0
$849$	11.2627			0.386537
$850$		0			0
$851$	−39.8254			−1.36520
$852$		0			0
$853$	−19.9368	+	14.4849i	−0.682623	+	0.495954i	−0.874227	−	0.485518i	$-0.838631\pi$
$853$	−19.9368	+	14.4849i	−0.682623	+	0.495954i	0.191604	+	0.981472i	$0.438631\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.2342			−0.383752			−0.191876	−	0.981419i	$-0.561457\pi$
$857$	−11.2342			−0.383752			−0.191876	+	0.981419i	$0.561457\pi$
$858$		0			0
$859$	−4.79573	+	14.7597i	−0.163628	+	0.503595i	−0.998933	−	0.0461922i	$-0.985291\pi$
$859$	−4.79573	+	14.7597i	−0.163628	+	0.503595i	0.835305	+	0.549788i	$0.185291\pi$
$860$		0			0
$861$	−1.04236	−	3.20805i	−0.0355235	−	0.109330i
$862$		0			0
$863$	6.03168	−	18.5636i	0.205321	−	0.631912i	−0.794379	−	0.607422i	$-0.792204\pi$
$863$	6.03168	−	18.5636i	0.205321	−	0.631912i	0.999700	−	0.0244902i	$-0.00779625\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−13.4189	−	9.74943i	−0.455731	−	0.331108i
$868$		0			0
$869$	51.9188	+	37.7212i	1.76123	+	1.27960i
$870$		0			0
$871$	15.5750	−	11.3159i	0.527738	−	0.383424i
$872$		0			0
$873$	−4.50789	−	13.8738i	−0.152569	−	0.469559i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	4.24470	+	13.0638i	0.143333	+	0.441134i	0.996793	−	0.0800245i	$-0.0254999\pi$
$877$	4.24470	+	13.0638i	0.143333	+	0.441134i	−0.853460	+	0.521159i	$0.825500\pi$
$878$		0			0
$879$	−9.06061	+	6.58292i	−0.305607	+	0.222036i
$880$		0			0
$881$	42.4014	+	30.8064i	1.42854	+	1.03789i	0.990286	+	0.139042i	$0.0444024\pi$
$881$	42.4014	+	30.8064i	1.42854	+	1.03789i	0.438253	+	0.898852i	$0.355598\pi$
$882$		0			0
$883$	−13.5119	−	9.81699i	−0.454713	−	0.330368i	0.336741	−	0.941597i	$-0.390675\pi$
$883$	−13.5119	−	9.81699i	−0.454713	−	0.330368i	−0.791454	+	0.611229i	$0.790675\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.00379	−	24.6331i	0.268741	−	0.827099i	−0.722067	−	0.691823i	$-0.756808\pi$
$887$	8.00379	−	24.6331i	0.268741	−	0.827099i	0.990808	−	0.135276i	$-0.0431922\pi$
$888$		0			0
$889$	−4.22028	−	12.9887i	−0.141544	−	0.435627i
$890$		0			0
$891$	−1.67360	+	5.15082i	−0.0560678	+	0.172559i
$892$		0			0
$893$	24.8736			0.832364
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−5.75950	+	4.18452i	−0.192304	+	0.139717i
$898$		0			0
$899$	37.4374			1.24861
$900$		0			0
$901$	−3.82270			−0.127353
$902$		0			0
$903$	−0.593655	+	0.431316i	−0.0197556	+	0.0143533i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−4.74821			−0.157662			−0.0788308	−	0.996888i	$-0.525119\pi$
$907$	−4.74821			−0.157662			−0.0788308	+	0.996888i	$0.525119\pi$
$908$		0			0
$909$	−3.17769	+	9.77994i	−0.105397	+	0.324380i
$910$		0			0
$911$	−3.79559	−	11.6816i	−0.125753	−	0.387029i	0.868284	−	0.496067i	$-0.165223\pi$
$911$	−3.79559	−	11.6816i	−0.125753	−	0.387029i	−0.994038	+	0.109038i	$0.965223\pi$
$912$		0			0
$913$	−2.33314	+	7.18067i	−0.0772156	+	0.237645i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.0996721	+	0.0724160i	0.00329146	+	0.00239139i
$918$		0			0
$919$	−16.7306	−	12.1555i	−0.551893	−	0.400974i	0.276590	−	0.960988i	$-0.410796\pi$
$919$	−16.7306	−	12.1555i	−0.551893	−	0.400974i	−0.828483	+	0.560014i	$0.810796\pi$
$920$		0			0
$921$	19.5207	−	14.1826i	0.643228	−	0.467332i
$922$		0			0
$923$	−7.46622	−	22.9787i	−0.245754	−	0.756352i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−4.32155	−	13.3004i	−0.141938	−	0.436841i
$928$		0			0
$929$	−19.4753	+	14.1496i	−0.638964	+	0.464235i	−0.859494	−	0.511145i	$-0.829221\pi$
$929$	−19.4753	+	14.1496i	−0.638964	+	0.464235i	0.220530	+	0.975380i	$0.429221\pi$
$930$		0			0
$931$	−24.8088	−	18.0247i	−0.813077	−	0.590735i
$932$		0			0
$933$	1.67719	+	1.21855i	0.0549086	+	0.0398934i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−13.8438	+	42.6067i	−0.452256	+	1.39190i	0.422071	+	0.906563i	$0.361303\pi$
$937$	−13.8438	+	42.6067i	−0.452256	+	1.39190i	−0.874327	+	0.485338i	$0.838697\pi$
$938$		0			0
$939$	2.63272	+	8.10268i	0.0859156	+	0.264421i
$940$		0			0
$941$	−14.5501	+	44.7806i	−0.474319	+	1.45980i	0.372554	+	0.928010i	$0.378482\pi$
$941$	−14.5501	+	44.7806i	−0.474319	+	1.45980i	−0.846874	+	0.531794i	$0.821518\pi$
$942$		0			0
$943$	−12.3987			−0.403759
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.5424	+	10.5656i	−0.472563	+	0.343337i	−0.798439	−	0.602075i	$-0.794341\pi$
$947$	−14.5424	+	10.5656i	−0.472563	+	0.343337i	0.325876	+	0.945412i	$0.394341\pi$
$948$		0			0
$949$	10.9895			0.356733
$950$		0			0
$951$	−13.6070			−0.441236
$952$		0			0
$953$	29.0854	−	21.1318i	0.942169	−	0.684526i	−0.00677250	−	0.999977i	$-0.502156\pi$
$953$	29.0854	−	21.1318i	0.942169	−	0.684526i	0.948942	+	0.315451i	$0.102156\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	54.9213			1.77535
$958$		0			0
$959$	−4.05438	+	12.4781i	−0.130923	+	0.402939i
$960$		0			0
$961$	−5.36787	−	16.5206i	−0.173157	−	0.532923i
$962$		0			0
$963$	−2.80194	+	8.62349i	−0.0902913	+	0.277888i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−7.76589	−	5.64225i	−0.249734	−	0.181443i	0.455875	−	0.890044i	$-0.349326\pi$
$967$	−7.76589	−	5.64225i	−0.249734	−	0.181443i	−0.705609	+	0.708601i	$0.749326\pi$
$968$		0			0
$969$	−2.62180	−	1.90485i	−0.0842243	−	0.0611925i
$970$		0			0
$971$	22.5625	−	16.3926i	0.724066	−	0.526065i	−0.163615	−	0.986524i	$-0.552315\pi$
$971$	22.5625	−	16.3926i	0.724066	−	0.526065i	0.887681	+	0.460460i	$0.152315\pi$
$972$		0			0
$973$	6.94511	+	21.3748i	0.222650	+	0.685246i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	17.5347	+	53.9664i	0.560986	+	1.72654i	0.679587	+	0.733595i	$0.262159\pi$
$977$	17.5347	+	53.9664i	0.560986	+	1.72654i	−0.118601	+	0.992942i	$0.537841\pi$
$978$		0			0
$979$	−7.48423	+	5.43761i	−0.239197	+	0.173787i
$980$		0			0
$981$	−1.92170	−	1.39620i	−0.0613552	−	0.0445772i
$982$		0			0
$983$	9.10235	+	6.61324i	0.290320	+	0.210930i	0.723406	−	0.690423i	$-0.242575\pi$
$983$	9.10235	+	6.61324i	0.290320	+	0.210930i	−0.433086	+	0.901352i	$0.642575\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	1.45999	−	4.49340i	0.0464721	−	0.143026i
$988$		0			0
$989$	0.833493	+	2.56523i	0.0265035	+	0.0815695i
$990$		0			0
$991$	10.6488	−	32.7735i	0.338269	−	1.04109i	−0.626820	−	0.779164i	$-0.715644\pi$
$991$	10.6488	−	32.7735i	0.338269	−	1.04109i	0.965089	−	0.261921i	$-0.0843561\pi$
$992$		0			0
$993$	22.6320			0.718206
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−41.4138	+	30.0889i	−1.31159	+	0.952924i	−0.311591	+	0.950216i	$0.600862\pi$
$997$	−41.4138	+	30.0889i	−1.31159	+	0.952924i	−0.999996	+	0.00270782i	$0.999138\pi$
$998$		0			0
$999$	−11.3153			−0.358001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.m.d.901.4		24
5.2	odd	4		300.2.o.a.169.2	✓	24
5.3	odd	4		1500.2.o.c.349.5		24
5.4	even	2		1500.2.m.c.901.3		24
15.2	even	4		900.2.w.c.469.4		24
25.2	odd	20		7500.2.d.g.1249.20		24
25.3	odd	20		300.2.o.a.229.2	yes	24
25.4	even	10		1500.2.m.c.601.3		24
25.11	even	5		7500.2.a.m.1.8		12
25.14	even	10		7500.2.a.n.1.5		12
25.21	even	5	inner	1500.2.m.d.601.4		24
25.22	odd	20		1500.2.o.c.649.5		24
25.23	odd	20		7500.2.d.g.1249.5		24
75.53	even	20		900.2.w.c.829.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.2	✓	24	5.2	odd	4
300.2.o.a.229.2	yes	24	25.3	odd	20
900.2.w.c.469.4		24	15.2	even	4
900.2.w.c.829.4		24	75.53	even	20
1500.2.m.c.601.3		24	25.4	even	10
1500.2.m.c.901.3		24	5.4	even	2
1500.2.m.d.601.4		24	25.21	even	5	inner
1500.2.m.d.901.4		24	1.1	even	1	trivial
1500.2.o.c.349.5		24	5.3	odd	4
1500.2.o.c.649.5		24	25.22	odd	20
7500.2.a.m.1.8		12	25.11	even	5
7500.2.a.n.1.5		12	25.14	even	10
7500.2.d.g.1249.5		24	25.23	odd	20
7500.2.d.g.1249.20		24	25.2	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)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{3} +0.957526 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{3} +0.957526 q^{7} +(0.309017 - 0.951057i) q^{9} +(-1.67360 - 5.15082i) q^{11} +(0.625052 - 1.92371i) q^{13} +(-0.520090 - 0.377867i) q^{17} +(4.07829 + 2.96305i) q^{19} +(0.774655 - 0.562820i) q^{21} +(-1.08762 - 3.34734i) q^{23} +(-0.309017 - 0.951057i) q^{27} +(-8.20405 + 5.96059i) q^{29} +(-2.98671 - 2.16997i) q^{31} +(-4.38155 - 3.18338i) q^{33} +(3.49663 - 10.7615i) q^{37} +(-0.625052 - 1.92371i) q^{39} +(1.08859 - 3.35035i) q^{41} -0.766348 q^{43} +(3.99186 - 2.90026i) q^{47} -6.08314 q^{49} -0.642866 q^{51} +(4.81069 - 3.49517i) q^{53} +5.04105 q^{57} +(1.45818 - 4.48783i) q^{59} +(1.34263 + 4.13219i) q^{61} +(0.295892 - 0.910662i) q^{63} +(7.70005 + 5.59441i) q^{67} +(-2.84742 - 2.06877i) q^{69} +(9.66368 - 7.02107i) q^{71} +(1.67890 + 5.16713i) q^{73} +(-1.60252 - 4.93205i) q^{77} +(-9.58637 + 6.96491i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-1.12784 - 0.819420i) q^{83} +(-3.13367 + 9.64444i) q^{87} +(-0.527839 - 1.62452i) q^{89} +(0.598504 - 1.84200i) q^{91} -3.69178 q^{93} +(11.8018 - 8.57451i) q^{97} -5.41590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9}+O(q^{10}) \) 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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