LMFDB - Embedded newform 1500.2.m.c.901.3

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			901.3
Character	$\chi$	$=$	1500.901
Dual form			1500.2.m.c.601.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{3} -0.957526 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{3} -0.957526 q^{7} +(0.309017 - 0.951057i) q^{9} +(-1.67360 - 5.15082i) q^{11} +(-0.625052 + 1.92371i) q^{13} +(0.520090 + 0.377867i) q^{17} +(4.07829 + 2.96305i) q^{19} +(0.774655 - 0.562820i) q^{21} +(1.08762 + 3.34734i) q^{23} +(0.309017 + 0.951057i) q^{27} +(-8.20405 + 5.96059i) q^{29} +(-2.98671 - 2.16997i) q^{31} +(4.38155 + 3.18338i) q^{33} +(-3.49663 + 10.7615i) q^{37} +(-0.625052 - 1.92371i) q^{39} +(1.08859 - 3.35035i) q^{41} +0.766348 q^{43} +(-3.99186 + 2.90026i) q^{47} -6.08314 q^{49} -0.642866 q^{51} +(-4.81069 + 3.49517i) q^{53} -5.04105 q^{57} +(1.45818 - 4.48783i) q^{59} +(1.34263 + 4.13219i) q^{61} +(-0.295892 + 0.910662i) q^{63} +(-7.70005 - 5.59441i) q^{67} +(-2.84742 - 2.06877i) q^{69} +(9.66368 - 7.02107i) q^{71} +(-1.67890 - 5.16713i) q^{73} +(1.60252 + 4.93205i) q^{77} +(-9.58637 + 6.96491i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(1.12784 + 0.819420i) q^{83} +(3.13367 - 9.64444i) q^{87} +(-0.527839 - 1.62452i) q^{89} +(0.598504 - 1.84200i) q^{91} +3.69178 q^{93} +(-11.8018 + 8.57451i) q^{97} -5.41590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.557919\pi$
$7$	−0.957526			−0.361911			−0.180955	+	0.983491i	$0.557919\pi$
$8$		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	−0.999555	−	0.0298404i	$-0.990500\pi$
$13$	−0.625052	+	1.92371i	−0.173358	+	0.533542i	0.826196	+	0.563382i	$0.190500\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.520090	+	0.377867i	0.126140	+	0.0916463i	0.649067	−	0.760732i	$-0.275160\pi$
$17$	0.520090	+	0.377867i	0.126140	+	0.0916463i	−0.522926	+	0.852378i	$0.675160\pi$
$18$		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	$0.0195959\pi$
$23$	1.08762	+	3.34734i	0.226784	+	0.697969i	−0.771322	+	0.636445i	$0.780404\pi$
$24$		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	$0.480292\pi$
$37$	−3.49663	+	10.7615i	−0.574842	+	1.76918i	−0.636717	+	0.771097i	$0.719708\pi$
$38$		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	$-0.481389\pi$
$43$	0.766348			0.116867			0.0584335	+	0.998291i	$0.481389\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.99186	+	2.90026i	−0.582273	+	0.423046i	−0.839543	−	0.543293i	$-0.817177\pi$
$47$	−3.99186	+	2.90026i	−0.582273	+	0.423046i	0.257270	+	0.966340i	$0.417177\pi$
$48$		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	−0.866933	−	0.498425i	$-0.833912\pi$
$53$	−4.81069	+	3.49517i	−0.660799	+	0.480099i	0.206134	+	0.978524i	$0.433912\pi$
$54$		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	0.00788103	−	0.999969i	$-0.497491\pi$
$67$	−7.70005	−	5.59441i	−0.940711	−	0.683466i	−0.948592	+	0.316503i	$0.897491\pi$
$68$		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	$-0.997007\pi$
$73$	−1.67890	−	5.16713i	−0.196500	−	0.604766i	0.803455	−	0.595365i	$-0.202993\pi$
$74$		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	0.647960	−	0.761674i	$-0.275622\pi$
$83$	1.12784	+	0.819420i	0.123796	+	0.0899431i	−0.524164	+	0.851617i	$0.675622\pi$
$84$		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	−0.994116	−	0.108325i	$-0.965451\pi$
$97$	−11.8018	+	8.57451i	−1.19829	+	0.870610i	−0.204176	+	0.978934i	$0.565451\pi$
$98$		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	−0.983413	−	0.181383i	$-0.941943\pi$
$103$	−11.3140	+	8.22008i	−1.11480	+	0.809949i	−0.131386	+	0.991331i	$0.541943\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.06727			0.876566			0.438283	−	0.898837i	$-0.355587\pi$
$107$	9.06727			0.876566			0.438283	+	0.898837i	$0.355587\pi$
$108$		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	$0.317782\pi$
$113$	−4.15238	+	12.7797i	−0.390623	+	1.20221i	−0.932318	+	0.361638i	$0.882218\pi$
$114$		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	$0.118101\pi$
$127$	4.40749	+	13.5648i	0.391101	+	1.20369i	−0.540855	+	0.841116i	$0.681899\pi$
$128$		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	$-0.700965\pi$
$137$	4.23423	−	13.0316i	0.361754	−	1.11337i	0.951989	−	0.306133i	$-0.0990354\pi$
$138$		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	$-0.325906\pi$
$157$	13.0329			1.04014			0.520070	+	0.854124i	$0.325906\pi$
$158$		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	−0.820780	−	0.571244i	$-0.806461\pi$
$163$	2.28549	−	7.03403i	0.179014	−	0.550948i	0.999794	+	0.0202964i	$0.00646098\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−16.2827	−	11.8301i	−1.25999	−	0.915438i	−0.261235	−	0.965275i	$-0.584130\pi$
$167$	−16.2827	−	11.8301i	−1.25999	−	0.915438i	−0.998757	+	0.0498368i	$0.984130\pi$
$168$		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	0.921569	−	0.388215i	$-0.126908\pi$
$173$	−0.686365	−	2.11241i	−0.0521833	−	0.160604i	−0.973752	+	0.227612i	$0.926908\pi$
$174$		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	$-0.740048\pi$
$193$	−19.0231			−1.36932			−0.684658	+	0.728864i	$0.740048\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−9.80131	+	7.12107i	−0.698315	+	0.507355i	−0.879383	−	0.476115i	$-0.842045\pi$
$197$	−9.80131	+	7.12107i	−0.698315	+	0.507355i	0.181068	+	0.983471i	$0.442045\pi$
$198$		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	$-0.811539\pi$
$223$	−7.26507	−	22.3596i	−0.486505	−	1.49731i	0.343284	−	0.939231i	$-0.388461\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.08155	−	18.7171i	−0.403647	−	1.24230i	−0.922020	−	0.387142i	$-0.873462\pi$
$227$	−6.08155	−	18.7171i	−0.403647	−	1.24230i	0.518373	−	0.855154i	$-0.326538\pi$
$228$		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	0.997132	−	0.0756813i	$-0.0241132\pi$
$233$	18.8253	+	13.6774i	1.23329	+	0.896034i	0.236154	+	0.971716i	$0.424113\pi$
$234$		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	$-0.282335\pi$
$257$	20.2556			1.26351			0.631754	+	0.775169i	$0.282335\pi$
$258$		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	$-0.502145\pi$
$263$	9.51119	−	29.2724i	0.586485	−	1.80502i	0.593223	−	0.805038i	$-0.297855\pi$
$264$		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	$0.279331\pi$
$277$	9.55583	+	29.4098i	0.574154	+	1.76706i	−0.0648872	+	0.997893i	$0.520669\pi$
$278$		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	0.283055	−	0.959104i	$-0.408652\pi$
$283$	−9.11176	−	6.62008i	−0.541638	−	0.393523i	−0.824693	+	0.565581i	$0.808652\pi$
$284$		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	$-0.393914\pi$
$293$	11.1995			0.654284			0.327142	+	0.944975i	$0.393914\pi$
$294$		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	$-0.741754\pi$
$307$	−24.1289			−1.37711			−0.688554	+	0.725185i	$0.741754\pi$
$308$		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	−0.848671	−	0.528921i	$-0.822597\pi$
$313$	2.63272	−	8.10268i	0.148810	−	0.457991i	0.997481	+	0.0709303i	$0.0225968\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.0083	+	7.99798i	0.618286	+	0.449211i	0.852322	−	0.523017i	$-0.175194\pi$
$317$	11.0083	+	7.99798i	0.618286	+	0.449211i	−0.234036	+	0.972228i	$0.575194\pi$
$318$		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	$-0.463367\pi$
$337$	11.1215	−	34.2285i	0.605828	−	1.86455i	0.490997	−	0.871161i	$-0.336633\pi$
$338$		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	−0.375877	−	0.926669i	$-0.622659\pi$
$347$	7.25158	−	5.26858i	0.389285	−	0.282832i	0.765162	+	0.643837i	$0.222659\pi$
$348$		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	−0.960834	−	0.277124i	$-0.910619\pi$
$353$	−18.6791	+	13.5712i	−0.994188	+	0.722320i	−0.0333537	+	0.999444i	$0.510619\pi$
$354$		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	0.396353	−	0.918098i	$-0.370276\pi$
$367$	−6.78801	−	4.93178i	−0.354331	−	0.257437i	−0.750684	+	0.660662i	$0.770276\pi$
$368$		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	0.988834	−	0.149018i	$-0.0476113\pi$
$373$	1.95565	+	6.01888i	0.101260	+	0.311646i	−0.887575	+	0.460664i	$0.847611\pi$
$374$		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	$-0.987005\pi$
$383$	−26.3563	−	19.1490i	−1.34674	−	0.978466i	−0.347576	−	0.937652i	$-0.612995\pi$
$384$		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	−0.259138	−	0.965840i	$-0.583438\pi$
$397$	11.5435	−	8.38686i	0.579353	−	0.420925i	0.838491	+	0.544916i	$0.183438\pi$
$398$		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	−0.186773	−	0.982403i	$-0.559803\pi$
$433$	−24.5295	−	17.8217i	−1.17881	−	0.856456i	−0.992037	+	0.125947i	$0.959803\pi$
$434$		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	$-0.757521\pi$
$443$	−30.4607			−1.44723			−0.723615	+	0.690204i	$0.757521\pi$
$444$		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	$-0.574320\pi$
$457$	−9.89208			−0.462732			−0.231366	+	0.972867i	$0.574320\pi$
$458$		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	−0.947297	−	0.320357i	$-0.896197\pi$
$463$	0.158879	−	0.488978i	0.00738372	−	0.0227248i	0.954681	+	0.297633i	$0.0961970\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−15.0267	−	10.9175i	−0.695352	−	0.505202i	0.183063	−	0.983101i	$-0.441399\pi$
$467$	−15.0267	−	10.9175i	−0.695352	−	0.505202i	−0.878415	+	0.477899i	$0.841399\pi$
$468$		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	$-0.694233\pi$
$487$	8.21528	−	25.2840i	0.372270	−	1.14573i	0.945302	−	0.326196i	$-0.105767\pi$
$488$		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	0.227049	−	0.973883i	$-0.427092\pi$
$503$	27.4386	−	19.9353i	1.22343	−	0.888873i	0.996380	+	0.0850104i	$0.0270924\pi$
$504$		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	$0.0491078\pi$
$523$	6.38135	+	19.6398i	0.279037	+	0.858788i	−0.709086	+	0.705122i	$0.750892\pi$
$524$		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	−0.763928	−	0.645301i	$-0.776732\pi$
$547$	−9.03427	+	6.56378i	−0.386278	+	0.280647i	0.377651	+	0.925948i	$0.376732\pi$
$548$		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	$-0.411688\pi$
$557$	12.9282			0.547787			0.273894	+	0.961760i	$0.411688\pi$
$558$		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	$0.333073\pi$
$563$	−9.80354	+	30.1722i	−0.413170	+	1.27161i	−0.913878	+	0.405989i	$0.866927\pi$
$564$		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	$0.222899\pi$
$577$	12.6065	+	38.7990i	0.524817	+	1.61522i	−0.239859	+	0.970808i	$0.577101\pi$
$578$		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	−0.992441	−	0.122725i	$-0.960837\pi$
$587$	−2.84446	+	8.75436i	−0.117404	+	0.361331i	0.875037	+	0.484056i	$0.160837\pi$
$588$		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	$-0.581847\pi$
$593$	−12.3856			−0.508614			−0.254307	+	0.967124i	$0.581847\pi$
$594$		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	$-0.559568\pi$
$607$	−9.16747			−0.372096			−0.186048	+	0.982541i	$0.559568\pi$
$608$		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	−0.999652	−	0.0263819i	$-0.991601\pi$
$613$	−4.34294	+	13.3662i	−0.175410	+	0.539855i	0.824242	+	0.566237i	$0.191601\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−29.3141	−	21.2980i	−1.18014	−	0.857424i	−0.187955	−	0.982178i	$-0.560186\pi$
$617$	−29.3141	−	21.2980i	−1.18014	−	0.857424i	−0.992188	+	0.124754i	$0.960186\pi$
$618$		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	$-0.435961\pi$
$643$	10.1343			0.399658			0.199829	+	0.979831i	$0.435961\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−36.6155	+	26.6027i	−1.43950	+	1.04586i	−0.451358	+	0.892343i	$0.649060\pi$
$647$	−36.6155	+	26.6027i	−1.43950	+	1.04586i	−0.988146	+	0.153518i	$0.950940\pi$
$648$		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	0.0731608	−	0.997320i	$-0.476691\pi$
$653$	26.6853	−	19.3880i	1.04428	−	0.758711i	0.971116	+	0.238609i	$0.0766914\pi$
$654$		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	0.995607	−	0.0936282i	$-0.0298465\pi$
$673$	3.50508	+	10.7875i	0.135111	+	0.415828i	−0.860496	+	0.509456i	$0.829847\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.78000	−	14.7113i	−0.183710	−	0.565402i	0.816213	−	0.577750i	$-0.196069\pi$
$677$	−4.78000	−	14.7113i	−0.183710	−	0.565402i	−0.999924	+	0.0123484i	$0.996069\pi$
$678$		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	0.477657	−	0.878546i	$-0.341486\pi$
$683$	−5.49567	−	3.99284i	−0.210286	−	0.152782i	−0.687943	+	0.725765i	$0.741486\pi$
$684$		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	0.943085	−	0.332551i	$-0.107909\pi$
$727$	−0.414026	−	1.27424i	−0.0153554	−	0.0472589i	−0.958441	+	0.285292i	$0.907909\pi$
$728$		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	$0.000441109\pi$
$733$	35.4759	+	25.7748i	1.31033	+	0.952013i	0.310335	+	0.950627i	$0.399559\pi$
$734$		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	$-0.370927\pi$
$743$	21.5051			0.788947			0.394474	+	0.918907i	$0.370927\pi$
$744$		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	$-0.531250\pi$
$757$	−5.39361			−0.196034			−0.0980171	+	0.995185i	$0.531250\pi$
$758$		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	$0.0951235\pi$
$773$	9.88584	+	30.4255i	0.355569	+	1.09433i	−0.600110	+	0.799918i	$0.704876\pi$
$774$		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	$0.243349\pi$
$787$	−7.54681	+	23.2267i	−0.269015	+	0.827942i	−0.990741	+	0.135764i	$0.956651\pi$
$788$		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	$0.641878\pi$
$797$	−40.1580	+	29.1765i	−1.42247	+	1.03348i	−0.991358	+	0.131184i	$0.958122\pi$
$798$		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	$0.149567\pi$
$823$	12.5200	+	38.5327i	0.436421	+	1.34317i	−0.455202	+	0.890388i	$0.650433\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	3.45274	+	10.6264i	0.120063	+	0.369517i	0.992969	−	0.118371i	$-0.0377673\pi$
$827$	3.45274	+	10.6264i	0.120063	+	0.369517i	−0.872906	+	0.487889i	$0.837767\pi$
$828$		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	−0.191604	−	0.981472i	$-0.561369\pi$
$853$	19.9368	−	14.4849i	0.682623	−	0.495954i	0.874227	+	0.485518i	$0.161369\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	11.2342			0.383752			0.191876	−	0.981419i	$-0.438543\pi$
$857$	11.2342			0.383752			0.191876	+	0.981419i	$0.438543\pi$
$858$		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	$0.207796\pi$
$863$	−6.03168	+	18.5636i	−0.205321	+	0.631912i	−0.999700	+	0.0244902i	$0.992204\pi$
$864$		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	0.853460	−	0.521159i	$-0.174500\pi$
$877$	−4.24470	−	13.0638i	−0.143333	−	0.441134i	−0.996793	+	0.0800245i	$0.974500\pi$
$878$		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	0.791454	−	0.611229i	$-0.209325\pi$
$883$	13.5119	+	9.81699i	0.454713	+	0.330368i	−0.336741	+	0.941597i	$0.609325\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−8.00379	+	24.6331i	−0.268741	+	0.827099i	0.722067	+	0.691823i	$0.243192\pi$
$887$	−8.00379	+	24.6331i	−0.268741	+	0.827099i	−0.990808	+	0.135276i	$0.956808\pi$
$888$		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	$-0.474881\pi$
$907$	4.74821			0.157662			0.0788308	+	0.996888i	$0.474881\pi$
$908$		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	$-0.638697\pi$
$937$	13.8438	−	42.6067i	0.452256	−	1.39190i	0.874327	−	0.485338i	$-0.161303\pi$
$938$		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	−0.325876	−	0.945412i	$-0.605659\pi$
$947$	14.5424	−	10.5656i	0.472563	−	0.343337i	0.798439	+	0.602075i	$0.205659\pi$
$948$		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	−0.948942	−	0.315451i	$-0.897844\pi$
$953$	−29.0854	+	21.1318i	−0.942169	+	0.684526i	0.00677250	+	0.999977i	$0.497844\pi$
$954$		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	0.705609	−	0.708601i	$-0.250674\pi$
$967$	7.76589	+	5.64225i	0.249734	+	0.181443i	−0.455875	+	0.890044i	$0.650674\pi$
$968$		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	$-0.737841\pi$
$977$	−17.5347	−	53.9664i	−0.560986	−	1.72654i	0.118601	−	0.992942i	$-0.462159\pi$
$978$		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	0.433086	−	0.901352i	$-0.357425\pi$
$983$	−9.10235	−	6.61324i	−0.290320	−	0.210930i	−0.723406	+	0.690423i	$0.757425\pi$
$984$		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	$-0.399138\pi$
$997$	41.4138	−	30.0889i	1.31159	−	0.952924i	0.999996	−	0.00270782i	$-0.000861928\pi$
$998$		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.c.901.3		24
5.2	odd	4		1500.2.o.c.349.5		24
5.3	odd	4		300.2.o.a.169.2	✓	24
5.4	even	2		1500.2.m.d.901.4		24
15.8	even	4		900.2.w.c.469.4		24
25.2	odd	20		7500.2.d.g.1249.5		24
25.3	odd	20		1500.2.o.c.649.5		24
25.4	even	10		1500.2.m.d.601.4		24
25.11	even	5		7500.2.a.n.1.5		12
25.14	even	10		7500.2.a.m.1.8		12
25.21	even	5	inner	1500.2.m.c.601.3		24
25.22	odd	20		300.2.o.a.229.2	yes	24
25.23	odd	20		7500.2.d.g.1249.20		24
75.47	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	5.3	odd	4
300.2.o.a.229.2	yes	24	25.22	odd	20
900.2.w.c.469.4		24	15.8	even	4
900.2.w.c.829.4		24	75.47	even	20
1500.2.m.c.601.3		24	25.21	even	5	inner
1500.2.m.c.901.3		24	1.1	even	1	trivial
1500.2.m.d.601.4		24	25.4	even	10
1500.2.m.d.901.4		24	5.4	even	2
1500.2.o.c.349.5		24	5.2	odd	4
1500.2.o.c.649.5		24	25.3	odd	20
7500.2.a.m.1.8		12	25.14	even	10
7500.2.a.n.1.5		12	25.11	even	5
7500.2.d.g.1249.5		24	25.2	odd	20
7500.2.d.g.1249.20		24	25.23	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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