LMFDB - Embedded newform 1500.2.o.c.649.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(49,1500)]

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, 7]))

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

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

chi := DirichletCharacter("1500.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.o (of order $10$, 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 $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			649.5
Character	$\chi$	$=$	1500.649
Dual form			1500.2.o.c.349.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{3} +0.957526i q^{7} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{3} +0.957526i q^{7} +(-0.309017 - 0.951057i) q^{9} +(-1.67360 + 5.15082i) q^{11} +(1.92371 - 0.625052i) q^{13} +(-0.377867 - 0.520090i) q^{17} +(-4.07829 + 2.96305i) q^{19} +(0.774655 + 0.562820i) q^{21} +(3.34734 + 1.08762i) q^{23} +(-0.951057 - 0.309017i) q^{27} +(8.20405 + 5.96059i) q^{29} +(-2.98671 + 2.16997i) q^{31} +(3.18338 + 4.38155i) q^{33} +(-10.7615 + 3.49663i) q^{37} +(0.625052 - 1.92371i) q^{39} +(1.08859 + 3.35035i) q^{41} +0.766348i q^{43} +(-2.90026 + 3.99186i) q^{47} +6.08314 q^{49} -0.642866 q^{51} +(3.49517 - 4.81069i) q^{53} +5.04105i q^{57} +(-1.45818 - 4.48783i) q^{59} +(1.34263 - 4.13219i) q^{61} +(0.910662 - 0.295892i) q^{63} +(5.59441 + 7.70005i) q^{67} +(2.84742 - 2.06877i) q^{69} +(9.66368 + 7.02107i) q^{71} +(-5.16713 - 1.67890i) q^{73} +(-4.93205 - 1.60252i) q^{77} +(9.58637 + 6.96491i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(0.819420 + 1.12784i) q^{83} +(9.64444 - 3.13367i) q^{87} +(0.527839 - 1.62452i) q^{89} +(0.598504 + 1.84200i) q^{91} +3.69178i q^{93} +(-8.57451 + 11.8018i) q^{97} +5.41590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^9	$ 24 q + 6 q^{9} - 6 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{21} - 40 q^{23} + 4 q^{29} + 6 q^{31} - 10 q^{33} - 10 q^{41} + 40 q^{47} - 56 q^{49} + 16 q^{51} + 60 q^{53} - 36 q^{59} - 12 q^{61} + 10 q^{63} - 20 q^{67} + 4 q^{69} + 40 q^{71} - 60 q^{73} + 40 q^{77} + 8 q^{79} - 6 q^{81} + 50 q^{83} + 20 q^{87} - 30 q^{91} + 40 q^{97} - 4 q^{99}+O(q^{100}) $ 24 * q + 6 * q^9 - 6 * q^11 - 10 * q^17 + 10 * q^19 - 4 * q^21 - 40 * q^23 + 4 * q^29 + 6 * q^31 - 10 * q^33 - 10 * q^41 + 40 * q^47 - 56 * q^49 + 16 * q^51 + 60 * q^53 - 36 * q^59 - 12 * q^61 + 10 * q^63 - 20 * q^67 + 4 * q^69 + 40 * q^71 - 60 * q^73 + 40 * q^77 + 8 * q^79 - 6 * q^81 + 50 * q^83 + 20 * q^87 - 30 * q^91 + 40 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$1$

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
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			0.957526i			0.361911i	0.983491	+	0.180955i	$0.0579190\pi$
$7$			0.957526i			0.361911i	−0.983491	+	0.180955i	$0.942081\pi$
$8$		0			0
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$		0			0
$11$	−1.67360	+	5.15082i	−0.504611	+	1.55303i	0.296814	+	0.954935i	$0.404076\pi$
$11$	−1.67360	+	5.15082i	−0.504611	+	1.55303i	−0.801424	+	0.598096i	$0.795924\pi$
$12$		0			0
$13$	1.92371	−	0.625052i	0.533542	−	0.173358i	−0.0298404	−	0.999555i	$-0.509500\pi$
$13$	1.92371	−	0.625052i	0.533542	−	0.173358i	0.563382	+	0.826196i	$0.309500\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.377867	−	0.520090i	−0.0916463	−	0.126140i	0.760732	−	0.649067i	$-0.224840\pi$
$17$	−0.377867	−	0.520090i	−0.0916463	−	0.126140i	−0.852378	+	0.522926i	$0.824840\pi$
$18$		0			0
$19$	−4.07829	+	2.96305i	−0.935625	+	0.679771i	−0.947364	−	0.320160i	$-0.896263\pi$
$19$	−4.07829	+	2.96305i	−0.935625	+	0.679771i	0.0117388	+	0.999931i	$0.496263\pi$
$20$		0			0
$21$	0.774655	+	0.562820i	0.169044	+	0.122817i
$22$		0			0
$23$	3.34734	+	1.08762i	0.697969	+	0.226784i	0.636445	−	0.771322i	$-0.280404\pi$
$23$	3.34734	+	1.08762i	0.697969	+	0.226784i	0.0615235	+	0.998106i	$0.480404\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$		0			0
$29$	8.20405	+	5.96059i	1.52345	+	1.10685i	0.959742	+	0.280882i	$0.0906271\pi$
$29$	8.20405	+	5.96059i	1.52345	+	1.10685i	0.563712	+	0.825972i	$0.309373\pi$
$30$		0			0
$31$	−2.98671	+	2.16997i	−0.536429	+	0.389738i	−0.822757	−	0.568393i	$-0.807565\pi$
$31$	−2.98671	+	2.16997i	−0.536429	+	0.389738i	0.286328	+	0.958132i	$0.407565\pi$
$32$		0			0
$33$	3.18338	+	4.38155i	0.554156	+	0.762730i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−10.7615	+	3.49663i	−1.76918	+	0.574842i	−0.998084	−	0.0618753i	$-0.980292\pi$
$37$	−10.7615	+	3.49663i	−1.76918	+	0.574842i	−0.771097	+	0.636717i	$0.780292\pi$
$38$		0			0
$39$	0.625052	−	1.92371i	0.100088	−	0.308040i
$40$		0			0
$41$	1.08859	+	3.35035i	0.170010	+	0.523237i	0.999370	−	0.0354770i	$-0.0112950\pi$
$41$	1.08859	+	3.35035i	0.170010	+	0.523237i	−0.829361	+	0.558714i	$0.811295\pi$
$42$		0			0
$43$			0.766348i			0.116867i	0.998291	+	0.0584335i	$0.0186106\pi$
$43$			0.766348i			0.116867i	−0.998291	+	0.0584335i	$0.981389\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.90026	+	3.99186i	−0.423046	+	0.582273i	−0.966340	−	0.257270i	$-0.917177\pi$
$47$	−2.90026	+	3.99186i	−0.423046	+	0.582273i	0.543293	+	0.839543i	$0.317177\pi$
$48$		0			0
$49$	6.08314			0.869021
$50$		0			0
$51$	−0.642866			−0.0900193
$52$		0			0
$53$	3.49517	−	4.81069i	0.480099	−	0.660799i	−0.498425	−	0.866933i	$-0.666088\pi$
$53$	3.49517	−	4.81069i	0.480099	−	0.660799i	0.978524	+	0.206134i	$0.0660881\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			5.04105i			0.667703i
$58$		0			0
$59$	−1.45818	−	4.48783i	−0.189839	−	0.584265i	0.810159	−	0.586210i	$-0.199381\pi$
$59$	−1.45818	−	4.48783i	−0.189839	−	0.584265i	−0.999998	+	0.00194529i	$0.999381\pi$
$60$		0			0
$61$	1.34263	−	4.13219i	0.171906	−	0.529073i	−0.827572	−	0.561359i	$-0.810279\pi$
$61$	1.34263	−	4.13219i	0.171906	−	0.529073i	0.999479	+	0.0322858i	$0.0102787\pi$
$62$		0			0
$63$	0.910662	−	0.295892i	0.114733	−	0.0372789i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.59441	+	7.70005i	0.683466	+	0.940711i	0.999969	−	0.00788103i	$-0.00250864\pi$
$67$	5.59441	+	7.70005i	0.683466	+	0.940711i	−0.316503	+	0.948592i	$0.602509\pi$
$68$		0			0
$69$	2.84742	−	2.06877i	0.342789	−	0.249051i
$70$		0			0
$71$	9.66368	+	7.02107i	1.14687	+	0.833248i	0.988061	−	0.154062i	$-0.0492354\pi$
$71$	9.66368	+	7.02107i	1.14687	+	0.833248i	0.158806	+	0.987310i	$0.449235\pi$
$72$		0			0
$73$	−5.16713	−	1.67890i	−0.604766	−	0.196500i	−0.00940128	−	0.999956i	$-0.502993\pi$
$73$	−5.16713	−	1.67890i	−0.604766	−	0.196500i	−0.595365	+	0.803455i	$0.702993\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.93205	−	1.60252i	−0.562059	−	0.182624i
$78$		0			0
$79$	9.58637	+	6.96491i	1.07855	+	0.783613i	0.977430	−	0.211261i	$-0.0677569\pi$
$79$	9.58637	+	6.96491i	1.07855	+	0.783613i	0.101122	+	0.994874i	$0.467757\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	0.819420	+	1.12784i	0.0899431	+	0.123796i	0.851617	−	0.524164i	$-0.175622\pi$
$83$	0.819420	+	1.12784i	0.0899431	+	0.123796i	−0.761674	+	0.647960i	$0.775622\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	9.64444	−	3.13367i	1.03399	−	0.335965i
$88$		0			0
$89$	0.527839	−	1.62452i	0.0559508	−	0.172199i	−0.919176	−	0.393847i	$-0.871144\pi$
$89$	0.527839	−	1.62452i	0.0559508	−	0.172199i	0.975127	+	0.221649i	$0.0711438\pi$
$90$		0			0
$91$	0.598504	+	1.84200i	0.0627402	+	0.193095i
$92$		0			0
$93$			3.69178i			0.382819i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−8.57451	+	11.8018i	−0.870610	+	1.19829i	0.108325	+	0.994116i	$0.465451\pi$
$97$	−8.57451	+	11.8018i	−0.870610	+	1.19829i	−0.978934	+	0.204176i	$0.934549\pi$
$98$		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
$103$	8.22008	−	11.3140i	0.809949	−	1.11480i	−0.181383	−	0.983413i	$-0.558057\pi$
$103$	8.22008	−	11.3140i	0.809949	−	1.11480i	0.991331	−	0.131386i	$-0.0419427\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	9.06727i		−	0.876566i	−0.898837	−	0.438283i	$-0.855587\pi$
$107$		−	9.06727i		−	0.876566i	0.898837	−	0.438283i	$-0.144413\pi$
$108$		0			0
$109$	−0.734025	−	2.25910i	−0.0703068	−	0.216382i	0.909729	−	0.415202i	$-0.136289\pi$
$109$	−0.734025	−	2.25910i	−0.0703068	−	0.216382i	−0.980036	+	0.198820i	$0.936289\pi$
$110$		0			0
$111$	−3.49663	+	10.7615i	−0.331885	+	1.02144i
$112$		0			0
$113$	12.7797	−	4.15238i	1.20221	−	0.390623i	0.361638	−	0.932318i	$-0.382218\pi$
$113$	12.7797	−	4.15238i	1.20221	−	0.390623i	0.840575	+	0.541696i	$0.182218\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.18892	−	1.63641i	−0.109916	−	0.151286i
$118$		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
$123$	3.35035	+	1.08859i	0.302091	+	0.0981553i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−13.5648	−	4.40749i	−1.20369	−	0.391101i	−0.362570	−	0.931957i	$-0.618101\pi$
$127$	−13.5648	−	4.40749i	−1.20369	−	0.391101i	−0.841116	+	0.540855i	$0.818101\pi$
$128$		0			0
$129$	0.619989	+	0.450448i	0.0545869	+	0.0396597i
$130$		0			0
$131$	0.104093	−	0.0756282i	0.00909468	−	0.00660767i	−0.583229	−	0.812308i	$-0.698211\pi$
$131$	0.104093	−	0.0756282i	0.00909468	−	0.00660767i	0.592323	+	0.805700i	$0.298211\pi$
$132$		0			0
$133$	−2.83720	−	3.90507i	−0.246017	−	0.338613i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.0316	−	4.23423i	1.11337	−	0.361754i	0.306133	−	0.951989i	$-0.400965\pi$
$137$	13.0316	−	4.23423i	1.11337	−	0.361754i	0.807232	+	0.590234i	$0.200965\pi$
$138$		0			0
$139$	−7.25318	+	22.3230i	−0.615206	+	1.89341i	−0.216731	+	0.976231i	$0.569539\pi$
$139$	−7.25318	+	22.3230i	−0.615206	+	1.89341i	−0.398475	+	0.917179i	$0.630461\pi$
$140$		0			0
$141$	1.52476	+	4.69272i	0.128408	+	0.395198i
$142$		0			0
$143$			10.9548i			0.916086i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.57558	−	4.92137i	0.294909	−	0.405907i
$148$		0			0
$149$	10.6938			0.876071			0.438035	−	0.898958i	$-0.355674\pi$
$149$	10.6938			0.876071			0.438035	+	0.898958i	$0.355674\pi$
$150$		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
$153$	−0.377867	+	0.520090i	−0.0305488	+	0.0420468i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	13.0329i		−	1.04014i	−0.854124	−	0.520070i	$-0.825906\pi$
$157$		−	13.0329i		−	1.04014i	0.854124	−	0.520070i	$-0.174094\pi$
$158$		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
$163$	−7.03403	+	2.28549i	−0.550948	+	0.179014i	−0.571244	−	0.820780i	$-0.693539\pi$
$163$	−7.03403	+	2.28549i	−0.550948	+	0.179014i	0.0202964	+	0.999794i	$0.493539\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.8301	+	16.2827i	0.915438	+	1.25999i	0.965275	+	0.261235i	$0.0841299\pi$
$167$	11.8301	+	16.2827i	0.915438	+	1.25999i	−0.0498368	+	0.998757i	$0.515870\pi$
$168$		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
$173$	−2.11241	−	0.686365i	−0.160604	−	0.0521833i	0.227612	−	0.973752i	$-0.426908\pi$
$173$	−2.11241	−	0.686365i	−0.160604	−	0.0521833i	−0.388215	+	0.921569i	$0.626908\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.48783	−	1.45818i	−0.337326	−	0.109604i
$178$		0			0
$179$	−0.0312215	−	0.0226837i	−0.00233360	−	0.00169546i	0.586618	−	0.809864i	$-0.300459\pi$
$179$	−0.0312215	−	0.0226837i	−0.00233360	−	0.00169546i	−0.588951	+	0.808168i	$0.700459\pi$
$180$		0			0
$181$	−0.118881	+	0.0863720i	−0.00883634	+	0.00641998i	−0.592195	−	0.805795i	$-0.701738\pi$
$181$	−0.118881	+	0.0863720i	−0.00883634	+	0.00641998i	0.583358	+	0.812215i	$0.301738\pi$
$182$		0			0
$183$	−2.55384	−	3.51505i	−0.188785	−	0.259840i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.31129	−	1.07590i	0.242146	−	0.0786779i
$188$		0			0
$189$	0.295892	−	0.910662i	0.0215230	−	0.0662409i
$190$		0			0
$191$	−0.142049	−	0.437183i	−0.0102783	−	0.0316335i	0.945786	−	0.324791i	$-0.105294\pi$
$191$	−0.142049	−	0.437183i	−0.0102783	−	0.0316335i	−0.956064	+	0.293158i	$0.905294\pi$
$192$		0			0
$193$		−	19.0231i		−	1.36932i	−0.728864	−	0.684658i	$-0.759952\pi$
$193$		−	19.0231i		−	1.36932i	0.728864	−	0.684658i	$-0.240048\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.12107	+	9.80131i	−0.507355	+	0.698315i	−0.983471	−	0.181068i	$-0.942045\pi$
$197$	−7.12107	+	9.80131i	−0.507355	+	0.698315i	0.476115	+	0.879383i	$0.342045\pi$
$198$		0			0
$199$	−16.4872			−1.16875			−0.584375	−	0.811484i	$-0.698660\pi$
$199$	−16.4872			−1.16875			−0.584375	+	0.811484i	$0.698660\pi$
$200$		0			0
$201$	9.51778			0.671333
$202$		0			0
$203$	−5.70742	+	7.85559i	−0.400583	+	0.551355i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	3.51960i		−	0.244629i
$208$		0			0
$209$	−8.43672	−	25.9656i	−0.583580	−	1.79607i
$210$		0			0
$211$	5.61985	−	17.2961i	0.386887	−	1.19071i	−0.548216	−	0.836337i	$-0.684693\pi$
$211$	5.61985	−	17.2961i	0.386887	−	1.19071i	0.935102	−	0.354378i	$-0.115307\pi$
$212$		0			0
$213$	11.3603	−	3.69120i	0.778397	−	0.252917i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.07780	−	2.85985i	−0.141051	−	0.194139i
$218$		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
$223$	−22.3596	−	7.26507i	−1.49731	−	0.486505i	−0.558077	−	0.829789i	$-0.688461\pi$
$223$	−22.3596	−	7.26507i	−1.49731	−	0.486505i	−0.939231	+	0.343284i	$0.888461\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	18.7171	+	6.08155i	1.24230	+	0.403647i	0.855154	−	0.518373i	$-0.173462\pi$
$227$	18.7171	+	6.08155i	1.24230	+	0.403647i	0.387142	+	0.922020i	$0.373462\pi$
$228$		0			0
$229$	4.29343	+	3.11936i	0.283718	+	0.206133i	0.720538	−	0.693416i	$-0.243895\pi$
$229$	4.29343	+	3.11936i	0.283718	+	0.206133i	−0.436819	+	0.899549i	$0.643895\pi$
$230$		0			0
$231$	−4.19545	+	3.04817i	−0.276040	+	0.200555i
$232$		0			0
$233$	13.6774	+	18.8253i	0.896034	+	1.23329i	0.971716	+	0.236154i	$0.0758868\pi$
$233$	13.6774	+	18.8253i	0.896034	+	1.23329i	−0.0756813	+	0.997132i	$0.524113\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	11.2695	−	3.66167i	0.732030	−	0.237851i
$238$		0			0
$239$	4.65842	−	14.3371i	0.301328	−	0.927392i	−0.679694	−	0.733496i	$-0.737887\pi$
$239$	4.65842	−	14.3371i	0.301328	−	0.927392i	0.981022	−	0.193897i	$-0.0621126\pi$
$240$		0			0
$241$	−5.84454	−	17.9877i	−0.376480	−	1.15869i	−0.942475	−	0.334278i	$-0.891508\pi$
$241$	−5.84454	−	17.9877i	−0.376480	−	1.15869i	0.565995	−	0.824409i	$-0.308492\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5.99340	+	8.24921i	−0.381351	+	0.524885i
$248$		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
$253$	−11.2042	+	15.4213i	−0.704405	+	0.969530i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	20.2556i		−	1.26351i	−0.775169	−	0.631754i	$-0.782335\pi$
$257$		−	20.2556i		−	1.26351i	0.775169	−	0.631754i	$-0.217665\pi$
$258$		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
$263$	−29.2724	+	9.51119i	−1.80502	+	0.586485i	−0.999977	−	0.00673789i	$-0.997855\pi$
$263$	−29.2724	+	9.51119i	−1.80502	+	0.586485i	−0.805038	+	0.593223i	$0.797855\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.00401	−	1.38190i	−0.0614443	−	0.0845709i
$268$		0			0
$269$	−21.5796	+	15.6785i	−1.31573	+	0.955936i	−0.315758	+	0.948840i	$0.602259\pi$
$269$	−21.5796	+	15.6785i	−1.31573	+	0.955936i	−0.999975	+	0.00709610i	$0.997741\pi$
$270$		0			0
$271$	4.47342	+	3.25013i	0.271741	+	0.197431i	0.715307	−	0.698810i	$-0.246287\pi$
$271$	4.47342	+	3.25013i	0.271741	+	0.197431i	−0.443566	+	0.896242i	$0.646287\pi$
$272$		0			0
$273$	1.84200	+	0.598504i	0.111483	+	0.0362231i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−29.4098	−	9.55583i	−1.76706	−	0.574154i	−0.769172	−	0.639041i	$-0.779331\pi$
$277$	−29.4098	−	9.55583i	−1.76706	−	0.574154i	−0.997893	+	0.0648872i	$0.979331\pi$
$278$		0			0
$279$	2.98671	+	2.16997i	0.178810	+	0.129913i
$280$		0			0
$281$	13.6310	−	9.90352i	0.813159	−	0.590795i	−0.101586	−	0.994827i	$-0.532392\pi$
$281$	13.6310	−	9.90352i	0.813159	−	0.590795i	0.914745	+	0.404032i	$0.132392\pi$
$282$		0			0
$283$	−6.62008	−	9.11176i	−0.393523	−	0.541638i	0.565581	−	0.824693i	$-0.308652\pi$
$283$	−6.62008	−	9.11176i	−0.393523	−	0.541638i	−0.959104	+	0.283055i	$0.908652\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.20805	+	1.04236i	−0.189365	+	0.0615285i
$288$		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
$293$			11.1995i			0.654284i	0.944975	+	0.327142i	$0.106086\pi$
$293$			11.1995i			0.654284i	−0.944975	+	0.327142i	$0.893914\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.18338	−	4.38155i	0.184719	−	0.254243i
$298$		0			0
$299$	7.11914			0.411710
$300$		0			0
$301$	−0.733798			−0.0422954
$302$		0			0
$303$	−6.04433	+	8.31931i	−0.347238	+	0.477932i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			24.1289i			1.37711i	0.725185	+	0.688554i	$0.241754\pi$
$307$			24.1289i			1.37711i	−0.725185	+	0.688554i	$0.758246\pi$
$308$		0			0
$309$	−4.32155	−	13.3004i	−0.245844	−	0.756632i
$310$		0			0
$311$	0.640628	−	1.97165i	0.0363267	−	0.111802i	−0.931249	−	0.364384i	$-0.881280\pi$
$311$	0.640628	−	1.97165i	0.0363267	−	0.111802i	0.967576	+	0.252582i	$0.0812797\pi$
$312$		0			0
$313$	−8.10268	+	2.63272i	−0.457991	+	0.148810i	−0.528921	−	0.848671i	$-0.677403\pi$
$313$	−8.10268	+	2.63272i	−0.457991	+	0.148810i	0.0709303	+	0.997481i	$0.477403\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.99798	−	11.0083i	−0.449211	−	0.618286i	0.523017	−	0.852322i	$-0.324806\pi$
$317$	−7.99798	−	11.0083i	−0.449211	−	0.618286i	−0.972228	+	0.234036i	$0.924806\pi$
$318$		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
$323$	3.08211	+	1.00144i	0.171493	+	0.0557215i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.25910	−	0.734025i	−0.124928	−	0.0405917i
$328$		0			0
$329$	−3.82231	−	2.77707i	−0.210731	−	0.153105i
$330$		0			0
$331$	18.3097	−	13.3028i	1.00639	−	0.731187i	0.0429430	−	0.999078i	$-0.486327\pi$
$331$	18.3097	−	13.3028i	1.00639	−	0.731187i	0.963449	+	0.267891i	$0.0863266\pi$
$332$		0			0
$333$	6.65098	+	9.15429i	0.364471	+	0.501652i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	34.2285	−	11.1215i	1.86455	−	0.605828i	0.871161	−	0.490997i	$-0.163367\pi$
$337$	34.2285	−	11.1215i	1.86455	−	0.605828i	0.993385	−	0.114831i	$-0.0366327\pi$
$338$		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
$343$			12.5275i			0.676419i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.26858	−	7.25158i	0.282832	−	0.389285i	−0.643837	−	0.765162i	$-0.722659\pi$
$347$	5.26858	−	7.25158i	0.282832	−	0.389285i	0.926669	+	0.375877i	$0.122659\pi$
$348$		0			0
$349$	11.8276			0.633114			0.316557	−	0.948573i	$-0.397473\pi$
$349$	11.8276			0.633114			0.316557	+	0.948573i	$0.397473\pi$
$350$		0			0
$351$	−2.02271			−0.107964
$352$		0			0
$353$	13.5712	−	18.6791i	0.722320	−	0.994188i	−0.277124	−	0.960834i	$-0.589381\pi$
$353$	13.5712	−	18.6791i	0.722320	−	0.994188i	0.999444	−	0.0333537i	$-0.0106188\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	0.615561i		−	0.0325790i
$358$		0			0
$359$	−6.52607	−	20.0852i	−0.344433	−	1.06005i	−0.961887	−	0.273448i	$-0.911836\pi$
$359$	−6.52607	−	20.0852i	−0.344433	−	1.06005i	0.617454	−	0.786607i	$-0.288164\pi$
$360$		0			0
$361$	1.98147	−	6.09833i	0.104288	−	0.320965i
$362$		0			0
$363$	−17.4347	+	5.66488i	−0.915085	+	0.297329i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	4.93178	+	6.78801i	0.257437	+	0.354331i	0.918098	−	0.396353i	$-0.129724\pi$
$367$	4.93178	+	6.78801i	0.257437	+	0.354331i	−0.660662	+	0.750684i	$0.729724\pi$
$368$		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
$373$	6.01888	+	1.95565i	0.311646	+	0.101260i	0.460664	−	0.887575i	$-0.347611\pi$
$373$	6.01888	+	1.95565i	0.311646	+	0.101260i	−0.149018	+	0.988834i	$0.547611\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	19.5079	+	6.33850i	1.00471	+	0.326450i
$378$		0			0
$379$	12.1990	+	8.86310i	0.626621	+	0.455267i	0.855228	−	0.518252i	$-0.173417\pi$
$379$	12.1990	+	8.86310i	0.626621	+	0.455267i	−0.228607	+	0.973519i	$0.573417\pi$
$380$		0			0
$381$	−11.5389	+	8.38354i	−0.591158	+	0.429502i
$382$		0			0
$383$	−19.1490	−	26.3563i	−0.978466	−	1.34674i	−0.937652	−	0.347576i	$-0.887005\pi$
$383$	−19.1490	−	26.3563i	−0.978466	−	1.34674i	−0.0408145	−	0.999167i	$-0.512995\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.728840	−	0.236815i	0.0370490	−	0.0120380i
$388$		0			0
$389$	1.69084	−	5.20388i	0.0857292	−	0.263847i	−0.898998	−	0.437953i	$-0.855704\pi$
$389$	1.69084	−	5.20388i	0.0857292	−	0.263847i	0.984727	+	0.174106i	$0.0557035\pi$
$390$		0			0
$391$	−0.699192	−	2.15189i	−0.0353597	−	0.108826i
$392$		0			0
$393$		−	0.128666i		−	0.00649036i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	8.38686	−	11.5435i	0.420925	−	0.579353i	−0.544916	−	0.838491i	$-0.683438\pi$
$397$	8.38686	−	11.5435i	0.420925	−	0.579353i	0.965840	+	0.259138i	$0.0834384\pi$
$398$		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
$403$	−4.38923	+	6.04125i	−0.218643	+	0.300936i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	61.2826i		−	3.03767i
$408$		0			0
$409$	−7.42964	−	22.8661i	−0.367372	−	1.13065i	−0.948482	−	0.316830i	$-0.897382\pi$
$409$	−7.42964	−	22.8661i	−0.367372	−	1.13065i	0.581110	−	0.813825i	$-0.302618\pi$
$410$		0			0
$411$	4.23423	−	13.0316i	0.208859	−	0.642802i
$412$		0			0
$413$	4.29721	−	1.39625i	0.211452	−	0.0687049i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	13.7964	+	18.9891i	0.675611	+	0.929898i
$418$		0			0
$419$	−22.7180	+	16.5056i	−1.10984	+	0.806349i	−0.982639	−	0.185527i	$-0.940601\pi$
$419$	−22.7180	+	16.5056i	−1.10984	+	0.806349i	−0.127206	+	0.991876i	$0.540601\pi$
$420$		0			0
$421$	−16.3383	−	11.8704i	−0.796278	−	0.578530i	0.113542	−	0.993533i	$-0.463780\pi$
$421$	−16.3383	−	11.8704i	−0.796278	−	0.578530i	−0.909820	+	0.415003i	$0.863780\pi$
$422$		0			0
$423$	4.69272	+	1.52476i	0.228168	+	0.0741362i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.95668	+	1.28560i	0.191477	+	0.0622148i
$428$		0			0
$429$	8.86261	+	6.43907i	0.427891	+	0.310881i
$430$		0			0
$431$	3.35912	−	2.44055i	0.161803	−	0.117557i	−0.503937	−	0.863740i	$-0.668116\pi$
$431$	3.35912	−	2.44055i	0.161803	−	0.117557i	0.665741	+	0.746183i	$0.268116\pi$
$432$		0			0
$433$	−17.8217	−	24.5295i	−0.856456	−	1.17881i	−0.982403	−	0.186773i	$-0.940197\pi$
$433$	−17.8217	−	24.5295i	−0.856456	−	1.17881i	0.125947	−	0.992037i	$-0.459803\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−16.8741	+	5.48273i	−0.807198	+	0.262275i
$438$		0			0
$439$	0.984067	−	3.02865i	0.0469670	−	0.144549i	−0.924823	−	0.380398i	$-0.875787\pi$
$439$	0.984067	−	3.02865i	0.0469670	−	0.144549i	0.971790	+	0.235849i	$0.0757870\pi$
$440$		0			0
$441$	−1.87979	−	5.78541i	−0.0895140	−	0.275496i
$442$		0			0
$443$		−	30.4607i		−	1.44723i	−0.690204	−	0.723615i	$-0.742479\pi$
$443$		−	30.4607i		−	1.44723i	0.690204	−	0.723615i	$-0.257521\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	6.28566	−	8.65147i	0.297302	−	0.409201i
$448$		0			0
$449$	−1.35787			−0.0640820			−0.0320410	−	0.999487i	$-0.510201\pi$
$449$	−1.35787			−0.0640820			−0.0320410	+	0.999487i	$0.510201\pi$
$450$		0			0
$451$	−19.0789			−0.898392
$452$		0			0
$453$	4.33503	−	5.96666i	0.203678	−	0.280338i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			9.89208i			0.462732i	0.972867	+	0.231366i	$0.0743195\pi$
$457$			9.89208i			0.462732i	−0.972867	+	0.231366i	$0.925680\pi$
$458$		0			0
$459$	0.198657	+	0.611402i	0.00927250	+	0.0285378i
$460$		0			0
$461$	−6.51515	+	20.0516i	−0.303441	+	0.933894i	0.676814	+	0.736154i	$0.263360\pi$
$461$	−6.51515	+	20.0516i	−0.303441	+	0.933894i	−0.980255	+	0.197740i	$0.936640\pi$
$462$		0			0
$463$	−0.488978	+	0.158879i	−0.0227248	+	0.00738372i	−0.320357	−	0.947297i	$-0.603803\pi$
$463$	−0.488978	+	0.158879i	−0.0227248	+	0.00738372i	0.297633	+	0.954681i	$0.403803\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.9175	+	15.0267i	0.505202	+	0.695352i	0.983101	−	0.183063i	$-0.0586014\pi$
$467$	10.9175	+	15.0267i	0.505202	+	0.695352i	−0.477899	+	0.878415i	$0.658601\pi$
$468$		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
$473$	−3.94732	−	1.28256i	−0.181498	−	0.0589723i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−5.65531	−	1.83752i	−0.258939	−	0.0841343i
$478$		0			0
$479$	18.3847	+	13.3573i	0.840017	+	0.610308i	0.922376	−	0.386294i	$-0.126245\pi$
$479$	18.3847	+	13.3573i	0.840017	+	0.610308i	−0.0823581	+	0.996603i	$0.526245\pi$
$480$		0			0
$481$	−18.5165	+	13.4530i	−0.844279	+	0.613404i
$482$		0			0
$483$	1.98090	+	2.72648i	0.0901342	+	0.124059i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	25.2840	−	8.21528i	1.14573	−	0.372270i	0.326196	−	0.945302i	$-0.394233\pi$
$487$	25.2840	−	8.21528i	1.14573	−	0.372270i	0.819533	+	0.573032i	$0.194233\pi$
$488$		0			0
$489$	−2.28549	+	7.03403i	−0.103354	+	0.318090i
$490$		0			0
$491$	1.66601	+	5.12746i	0.0751860	+	0.231399i	0.981586	−	0.191022i	$-0.0611803\pi$
$491$	1.66601	+	5.12746i	0.0751860	+	0.231399i	−0.906400	+	0.422421i	$0.861180\pi$
$492$		0			0
$493$		−	6.51915i		−	0.293608i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.72286	+	9.25323i	−0.301562	+	0.415064i
$498$		0			0
$499$	14.5574			0.651677			0.325839	−	0.945425i	$-0.394353\pi$
$499$	14.5574			0.651677			0.325839	+	0.945425i	$0.394353\pi$
$500$		0			0
$501$	20.1265			0.899187
$502$		0			0
$503$	−19.9353	+	27.4386i	−0.888873	+	1.22343i	0.0850104	+	0.996380i	$0.472908\pi$
$503$	−19.9353	+	27.4386i	−0.888873	+	1.22343i	−0.973883	+	0.227049i	$0.927092\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			8.90864i			0.395647i
$508$		0			0
$509$	5.18882	+	15.9695i	0.229990	+	0.707838i	0.997747	+	0.0670956i	$0.0213733\pi$
$509$	5.18882	+	15.9695i	0.229990	+	0.707838i	−0.767756	+	0.640742i	$0.778627\pi$
$510$		0			0
$511$	1.60759	−	4.94766i	0.0711157	−	0.218872i
$512$		0			0
$513$	4.79432	−	1.55777i	0.211674	−	0.0687772i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−15.7075	−	21.6195i	−0.690815	−	0.950825i
$518$		0			0
$519$	−1.79693	+	1.30554i	−0.0788763	+	0.0573070i
$520$		0			0
$521$	13.8271	+	10.0460i	0.605777	+	0.440123i	0.847925	−	0.530117i	$-0.177852\pi$
$521$	13.8271	+	10.0460i	0.605777	+	0.440123i	−0.242148	+	0.970239i	$0.577852\pi$
$522$		0			0
$523$	19.6398	+	6.38135i	0.858788	+	0.279037i	0.705122	−	0.709086i	$-0.250892\pi$
$523$	19.6398	+	6.38135i	0.858788	+	0.279037i	0.153666	+	0.988123i	$0.450892\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.25716	+	0.733396i	0.0983234	+	0.0319472i
$528$		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
$533$	4.18829	+	5.76468i	0.181415	+	0.249696i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.0367031	+	0.0119255i	−0.00158385	+	0.000514625i
$538$		0			0
$539$	−10.1808	+	31.3332i	−0.438517	+	1.34962i
$540$		0			0
$541$	−3.75968	−	11.5711i	−0.161641	−	0.497480i	0.837132	−	0.547001i	$-0.184231\pi$
$541$	−3.75968	−	11.5711i	−0.161641	−	0.497480i	−0.998773	+	0.0495207i	$0.984231\pi$
$542$		0			0
$543$			0.146945i			0.00630600i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−6.56378	+	9.03427i	−0.280647	+	0.386278i	−0.925948	−	0.377651i	$-0.876732\pi$
$547$	−6.56378	+	9.03427i	−0.280647	+	0.386278i	0.645301	+	0.763928i	$0.276732\pi$
$548$		0			0
$549$	−4.34485			−0.185434
$550$		0			0
$551$	−51.1201			−2.17779
$552$		0			0
$553$	−6.66908	+	9.17921i	−0.283598	+	0.390340i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	12.9282i		−	0.547787i	−0.961760	−	0.273894i	$-0.911688\pi$
$557$		−	12.9282i		−	0.547787i	0.961760	−	0.273894i	$-0.0883116\pi$
$558$		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
$563$	30.1722	−	9.80354i	1.27161	−	0.413170i	0.405989	−	0.913878i	$-0.366927\pi$
$563$	30.1722	−	9.80354i	1.27161	−	0.413170i	0.865616	+	0.500708i	$0.166927\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.562820	−	0.774655i	−0.0236362	−	0.0325325i
$568$		0			0
$569$	23.3050	−	16.9321i	0.976997	−	0.709830i	0.0199619	−	0.999801i	$-0.493646\pi$
$569$	23.3050	−	16.9321i	0.976997	−	0.709830i	0.957036	+	0.289971i	$0.0936455\pi$
$570$		0			0
$571$	14.6999	+	10.6801i	0.615173	+	0.446950i	0.851232	−	0.524789i	$-0.175856\pi$
$571$	14.6999	+	10.6801i	0.615173	+	0.446950i	−0.236059	+	0.971739i	$0.575856\pi$
$572$		0			0
$573$	−0.437183	−	0.142049i	−0.0182636	−	0.00593420i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−38.7990	−	12.6065i	−1.61522	−	0.524817i	−0.644414	−	0.764677i	$-0.722899\pi$
$577$	−38.7990	−	12.6065i	−1.61522	−	0.524817i	−0.970808	+	0.239859i	$0.922899\pi$
$578$		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
$583$	18.9295	+	26.0542i	0.783979	+	1.07905i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.75436	+	2.84446i	−0.361331	+	0.117404i	−0.484056	−	0.875037i	$-0.660837\pi$
$587$	−8.75436	+	2.84446i	−0.361331	+	0.117404i	0.122725	+	0.992441i	$0.460837\pi$
$588$		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
$593$		−	12.3856i		−	0.508614i	−0.967124	−	0.254307i	$-0.918153\pi$
$593$		−	12.3856i		−	0.508614i	0.967124	−	0.254307i	$-0.0818474\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−9.69096	+	13.3385i	−0.396625	+	0.545907i
$598$		0			0
$599$	18.1732			0.742536			0.371268	−	0.928526i	$-0.378923\pi$
$599$	18.1732			0.742536			0.371268	+	0.928526i	$0.378923\pi$
$600$		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
$603$	5.59441	−	7.70005i	0.227822	−	0.313570i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			9.16747i			0.372096i	0.982541	+	0.186048i	$0.0595680\pi$
$607$			9.16747i			0.372096i	−0.982541	+	0.186048i	$0.940432\pi$
$608$		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
$613$	13.3662	−	4.34294i	0.539855	−	0.175410i	−0.0263819	−	0.999652i	$-0.508399\pi$
$613$	13.3662	−	4.34294i	0.539855	−	0.175410i	0.566237	+	0.824242i	$0.308399\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	21.2980	+	29.3141i	0.857424	+	1.18014i	0.982178	+	0.187955i	$0.0601859\pi$
$617$	21.2980	+	29.3141i	0.857424	+	1.18014i	−0.124754	+	0.992188i	$0.539814\pi$
$618$		0			0
$619$	20.7716	−	15.0915i	0.834882	−	0.606577i	−0.0860542	−	0.996290i	$-0.527426\pi$
$619$	20.7716	−	15.0915i	0.834882	−	0.606577i	0.920936	+	0.389713i	$0.127426\pi$
$620$		0			0
$621$	−2.84742	−	2.06877i	−0.114263	−	0.0830169i
$622$		0			0
$623$	1.55552	+	0.505419i	0.0623206	+	0.0202492i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−25.9656	−	8.43672i	−1.03696	−	0.336930i
$628$		0			0
$629$	5.88498	+	4.27569i	0.234650	+	0.170483i
$630$		0			0
$631$	19.9603	−	14.5020i	0.794608	−	0.577317i	−0.114719	−	0.993398i	$-0.536597\pi$
$631$	19.9603	−	14.5020i	0.794608	−	0.577317i	0.909327	+	0.416081i	$0.136597\pi$
$632$		0			0
$633$	−10.6896	−	14.7130i	−0.424873	−	0.584788i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	11.7022	−	3.80228i	0.463659	−	0.150652i
$638$		0			0
$639$	3.69120	−	11.3603i	0.146021	−	0.449408i
$640$		0			0
$641$	−9.25128	−	28.4725i	−0.365404	−	1.12460i	−0.949728	−	0.313077i	$-0.898640\pi$
$641$	−9.25128	−	28.4725i	−0.365404	−	1.12460i	0.584324	−	0.811520i	$-0.301360\pi$
$642$		0			0
$643$			10.1343i			0.399658i	0.979831	+	0.199829i	$0.0640387\pi$
$643$			10.1343i			0.399658i	−0.979831	+	0.199829i	$0.935961\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−26.6027	+	36.6155i	−1.04586	+	1.43950i	−0.153518	+	0.988146i	$0.549060\pi$
$647$	−26.6027	+	36.6155i	−1.04586	+	1.43950i	−0.892343	+	0.451358i	$0.850940\pi$
$648$		0			0
$649$	25.5564			1.00318
$650$		0			0
$651$	−3.53497			−0.138547
$652$		0			0
$653$	−19.3880	+	26.6853i	−0.758711	+	1.04428i	0.238609	+	0.971116i	$0.423309\pi$
$653$	−19.3880	+	26.6853i	−0.758711	+	1.04428i	−0.997320	+	0.0731608i	$0.976691\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			5.43304i			0.211963i
$658$		0			0
$659$	−0.789392	−	2.42950i	−0.0307504	−	0.0946398i	0.934503	−	0.355954i	$-0.115844\pi$
$659$	−0.789392	−	2.42950i	−0.0307504	−	0.0946398i	−0.965254	+	0.261314i	$0.915844\pi$
$660$		0			0
$661$	−14.0332	+	43.1898i	−0.545829	+	1.67989i	0.173182	+	0.984890i	$0.444595\pi$
$661$	−14.0332	+	43.1898i	−0.545829	+	1.67989i	−0.719011	+	0.694999i	$0.755405\pi$
$662$		0			0
$663$	−1.23669	+	0.401825i	−0.0480290	+	0.0156056i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	20.9789	+	28.8750i	0.812307	+	1.11804i
$668$		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
$673$	10.7875	+	3.50508i	0.415828	+	0.135111i	0.509456	−	0.860496i	$-0.329847\pi$
$673$	10.7875	+	3.50508i	0.415828	+	0.135111i	−0.0936282	+	0.995607i	$0.529847\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.7113	+	4.78000i	0.565402	+	0.183710i	0.577750	−	0.816213i	$-0.303931\pi$
$677$	14.7113	+	4.78000i	0.565402	+	0.183710i	−0.0123484	+	0.999924i	$0.503931\pi$
$678$		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
$683$	−3.99284	−	5.49567i	−0.152782	−	0.210286i	0.725765	−	0.687943i	$-0.241486\pi$
$683$	−3.99284	−	5.49567i	−0.152782	−	0.210286i	−0.878546	+	0.477657i	$0.841486\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	5.04724	−	1.63995i	0.192564	−	0.0625678i
$688$		0			0
$689$	3.71677	−	11.4390i	0.141598	−	0.435793i
$690$		0			0
$691$	13.0774	+	40.2482i	0.497489	+	1.53111i	0.813041	+	0.582206i	$0.197810\pi$
$691$	13.0774	+	40.2482i	0.497489	+	1.53111i	−0.315552	+	0.948908i	$0.602190\pi$
$692$		0			0
$693$			5.18586i			0.196995i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.33114	−	1.83215i	0.0504205	−	0.0693978i
$698$		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
$703$	33.5279	−	46.1472i	1.26453	−	1.74047i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	9.84647i		−	0.370314i
$708$		0			0
$709$	0.667116	+	2.05317i	0.0250541	+	0.0771085i	0.962802	−	0.270209i	$-0.0870927\pi$
$709$	0.667116	+	2.05317i	0.0250541	+	0.0771085i	−0.937748	+	0.347317i	$0.887093\pi$
$710$		0			0
$711$	3.66167	−	11.2695i	0.137323	−	0.422638i
$712$		0			0
$713$	−12.3576	+	4.01524i	−0.462797	+	0.150372i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−8.86084	−	12.1959i	−0.330914	−	0.455464i
$718$		0			0
$719$	1.28757	−	0.935472i	0.0480181	−	0.0348872i	−0.563517	−	0.826104i	$-0.690552\pi$
$719$	1.28757	−	0.935472i	0.0480181	−	0.0348872i	0.611535	+	0.791217i	$0.290552\pi$
$720$		0			0
$721$	10.8334	+	7.87094i	0.403458	+	0.293129i
$722$		0			0
$723$	−17.9877	−	5.84454i	−0.668968	−	0.217361i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	1.27424	+	0.414026i	0.0472589	+	0.0153554i	0.332551	−	0.943085i	$-0.392091\pi$
$727$	1.27424	+	0.414026i	0.0472589	+	0.0153554i	−0.285292	+	0.958441i	$0.592091\pi$
$728$		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
$733$	25.7748	+	35.4759i	0.952013	+	1.31033i	0.950627	+	0.310335i	$0.100441\pi$
$733$	25.7748	+	35.4759i	0.952013	+	1.31033i	0.00138578	+	0.999999i	$0.499559\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−49.0244	+	15.9290i	−1.80584	+	0.586752i
$738$		0			0
$739$	−5.67584	+	17.4684i	−0.208789	+	0.642587i	0.790747	+	0.612143i	$0.209692\pi$
$739$	−5.67584	+	17.4684i	−0.208789	+	0.642587i	−0.999536	+	0.0304443i	$0.990308\pi$
$740$		0			0
$741$	3.15092	+	9.69753i	0.115752	+	0.356248i
$742$		0			0
$743$			21.5051i			0.788947i	0.918907	+	0.394474i	$0.129073\pi$
$743$			21.5051i			0.788947i	−0.918907	+	0.394474i	$0.870927\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.819420	−	1.12784i	0.0299810	−	0.0412653i
$748$		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
$753$	−2.68477	+	3.69528i	−0.0978386	+	0.134663i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			5.39361i			0.196034i	0.995185	+	0.0980171i	$0.0312500\pi$
$757$			5.39361i			0.196034i	−0.995185	+	0.0980171i	$0.968750\pi$
$758$		0			0
$759$	5.89042	+	18.1289i	0.213809	+	0.658036i
$760$		0			0
$761$	−6.22670	+	19.1638i	−0.225718	+	0.694688i	0.772500	+	0.635014i	$0.219006\pi$
$761$	−6.22670	+	19.1638i	−0.225718	+	0.694688i	−0.998218	+	0.0596731i	$0.980994\pi$
$762$		0			0
$763$	2.16314	−	0.702848i	0.0783111	−	0.0254448i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.61025	−	7.72184i	−0.202574	−	0.278820i
$768$		0			0
$769$	25.0121	−	18.1724i	0.901960	−	0.655312i	−0.0370088	−	0.999315i	$-0.511783\pi$
$769$	25.0121	−	18.1724i	0.901960	−	0.655312i	0.938969	+	0.344003i	$0.111783\pi$
$770$		0			0
$771$	−16.3871	−	11.9059i	−0.590167	−	0.428781i
$772$		0			0
$773$	30.4255	+	9.88584i	1.09433	+	0.355569i	0.799918	−	0.600110i	$-0.204876\pi$
$773$	30.4255	+	9.88584i	1.09433	+	0.355569i	0.294411	+	0.955679i	$0.404876\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−10.3044	−	3.34811i	−0.369669	−	0.120113i
$778$		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
$783$	−5.96059	−	8.20405i	−0.213014	−	0.293189i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−23.2267	+	7.54681i	−0.827942	+	0.269015i	−0.692178	−	0.721726i	$-0.743349\pi$
$787$	−23.2267	+	7.54681i	−0.827942	+	0.269015i	−0.135764	+	0.990741i	$0.543349\pi$
$788$		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
$793$		−	8.78837i		−	0.312084i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−29.1765	+	40.1580i	−1.03348	+	1.42247i	−0.131184	+	0.991358i	$0.541878\pi$
$797$	−29.1765	+	40.1580i	−1.03348	+	1.42247i	−0.902300	+	0.431110i	$0.858122\pi$
$798$		0			0
$799$	3.17204			0.112219
$800$		0			0
$801$	−1.70812			−0.0603535
$802$		0			0
$803$	17.2954	−	23.8051i	0.610343	−	0.840065i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			26.6739i			0.938965i
$808$		0			0
$809$	5.82162	+	17.9171i	0.204677	+	0.629932i	0.999726	+	0.0233871i	$0.00744501\pi$
$809$	5.82162	+	17.9171i	0.204677	+	0.629932i	−0.795049	+	0.606545i	$0.792555\pi$
$810$		0			0
$811$	5.77928	−	17.7868i	0.202938	−	0.624578i	−0.796854	−	0.604172i	$-0.793504\pi$
$811$	5.77928	−	17.7868i	0.202938	−	0.624578i	0.999792	−	0.0204064i	$-0.00649600\pi$
$812$		0			0
$813$	5.25882	−	1.70869i	0.184435	−	0.0599265i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.27073	−	3.12539i	−0.0794428	−	0.109344i
$818$		0			0
$819$	1.56690	−	1.13842i	0.0547520	−	0.0397797i
$820$		0			0
$821$	−29.7103	−	21.5858i	−1.03690	−	0.753350i	−0.0672202	−	0.997738i	$-0.521413\pi$
$821$	−29.7103	−	21.5858i	−1.03690	−	0.753350i	−0.969678	+	0.244388i	$0.921413\pi$
$822$		0			0
$823$	38.5327	+	12.5200i	1.34317	+	0.436421i	0.890388	−	0.455202i	$-0.150433\pi$
$823$	38.5327	+	12.5200i	1.34317	+	0.436421i	0.452779	+	0.891623i	$0.350433\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−10.6264	−	3.45274i	−0.369517	−	0.120063i	0.118371	−	0.992969i	$-0.462233\pi$
$827$	−10.6264	−	3.45274i	−0.369517	−	0.120063i	−0.487889	+	0.872906i	$0.662233\pi$
$828$		0			0
$829$	29.8314	+	21.6738i	1.03609	+	0.752762i	0.969518	−	0.245019i	$-0.0787943\pi$
$829$	29.8314	+	21.6738i	1.03609	+	0.752762i	0.0665703	+	0.997782i	$0.478794\pi$
$830$		0			0
$831$	−25.0175	+	18.1763i	−0.867847	+	0.630528i
$832$		0			0
$833$	−2.29862	−	3.16378i	−0.0796425	−	0.109618i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	3.51109	−	1.14082i	0.121361	−	0.0394326i
$838$		0			0
$839$	3.53480	−	10.8790i	0.122035	−	0.375585i	−0.871314	−	0.490725i	$-0.836732\pi$
$839$	3.53480	−	10.8790i	0.122035	−	0.375585i	0.993349	+	0.115140i	$0.0367318\pi$
$840$		0			0
$841$	22.8163	+	70.2213i	0.786769	+	2.42143i
$842$		0			0
$843$		−	16.8489i		−	0.580306i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	10.3176	−	14.2009i	0.354516	−	0.487950i
$848$		0			0
$849$	−11.2627			−0.386537
$850$		0			0
$851$	−39.8254			−1.36520
$852$		0			0
$853$	−14.4849	+	19.9368i	−0.495954	+	0.682623i	−0.981472	−	0.191604i	$-0.938631\pi$
$853$	−14.4849	+	19.9368i	−0.495954	+	0.682623i	0.485518	+	0.874227i	$0.338631\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	11.2342i		−	0.383752i	−0.981419	−	0.191876i	$-0.938543\pi$
$857$		−	11.2342i		−	0.383752i	0.981419	−	0.191876i	$-0.0614571\pi$
$858$		0			0
$859$	4.79573	+	14.7597i	0.163628	+	0.503595i	0.998933	−	0.0461922i	$-0.0147087\pi$
$859$	4.79573	+	14.7597i	0.163628	+	0.503595i	−0.835305	+	0.549788i	$0.814709\pi$
$860$		0			0
$861$	−1.04236	+	3.20805i	−0.0355235	+	0.109330i
$862$		0			0
$863$	18.5636	−	6.03168i	0.631912	−	0.205321i	0.0244902	−	0.999700i	$-0.492204\pi$
$863$	18.5636	−	6.03168i	0.631912	−	0.205321i	0.607422	+	0.794379i	$0.292204\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−9.74943	−	13.4189i	−0.331108	−	0.455731i
$868$		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
$873$	13.8738	+	4.50789i	0.469559	+	0.152569i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	13.0638	+	4.24470i	0.441134	+	0.143333i	0.521159	−	0.853460i	$-0.325500\pi$
$877$	13.0638	+	4.24470i	0.441134	+	0.143333i	−0.0800245	+	0.996793i	$0.525500\pi$
$878$		0			0
$879$	9.06061	+	6.58292i	0.305607	+	0.222036i
$880$		0			0
$881$	42.4014	−	30.8064i	1.42854	−	1.03789i	0.438253	−	0.898852i	$-0.355598\pi$
$881$	42.4014	−	30.8064i	1.42854	−	1.03789i	0.990286	−	0.139042i	$-0.0444024\pi$
$882$		0			0
$883$	9.81699	+	13.5119i	0.330368	+	0.454713i	0.941597	−	0.336741i	$-0.109325\pi$
$883$	9.81699	+	13.5119i	0.330368	+	0.454713i	−0.611229	+	0.791454i	$0.709325\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.6331	+	8.00379i	−0.827099	+	0.268741i	−0.691823	−	0.722067i	$-0.743192\pi$
$887$	−24.6331	+	8.00379i	−0.827099	+	0.268741i	−0.135276	+	0.990808i	$0.543192\pi$
$888$		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
$893$		−	24.8736i		−	0.832364i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	4.18452	−	5.75950i	0.139717	−	0.192304i
$898$		0			0
$899$	−37.4374			−1.24861
$900$		0			0
$901$	−3.82270			−0.127353
$902$		0			0
$903$	−0.431316	+	0.593655i	−0.0143533	+	0.0197556i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	4.74821i		−	0.157662i	−0.996888	−	0.0788308i	$-0.974881\pi$
$907$		−	4.74821i		−	0.157662i	0.996888	−	0.0788308i	$-0.0251187\pi$
$908$		0			0
$909$	3.17769	+	9.77994i	0.105397	+	0.324380i
$910$		0			0
$911$	−3.79559	+	11.6816i	−0.125753	+	0.387029i	−0.994038	−	0.109038i	$-0.965223\pi$
$911$	−3.79559	+	11.6816i	−0.125753	+	0.387029i	0.868284	+	0.496067i	$0.165223\pi$
$912$		0			0
$913$	−7.18067	+	2.33314i	−0.237645	+	0.0772156i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.0724160	+	0.0996721i	0.00239139	+	0.00329146i
$918$		0			0
$919$	16.7306	−	12.1555i	0.551893	−	0.400974i	−0.276590	−	0.960988i	$-0.589204\pi$
$919$	16.7306	−	12.1555i	0.551893	−	0.400974i	0.828483	+	0.560014i	$0.189204\pi$
$920$		0			0
$921$	19.5207	+	14.1826i	0.643228	+	0.467332i
$922$		0			0
$923$	22.9787	+	7.46622i	0.756352	+	0.245754i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−13.3004	−	4.32155i	−0.436841	−	0.141938i
$928$		0			0
$929$	19.4753	+	14.1496i	0.638964	+	0.464235i	0.859494	−	0.511145i	$-0.170779\pi$
$929$	19.4753	+	14.1496i	0.638964	+	0.464235i	−0.220530	+	0.975380i	$0.570779\pi$
$930$		0			0
$931$	−24.8088	+	18.0247i	−0.813077	+	0.590735i
$932$		0			0
$933$	−1.21855	−	1.67719i	−0.0398934	−	0.0549086i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	42.6067	−	13.8438i	1.39190	−	0.452256i	0.485338	−	0.874327i	$-0.338697\pi$
$937$	42.6067	−	13.8438i	1.39190	−	0.452256i	0.906563	+	0.422071i	$0.138697\pi$
$938$		0			0
$939$	−2.63272	+	8.10268i	−0.0859156	+	0.264421i
$940$		0			0
$941$	−14.5501	−	44.7806i	−0.474319	−	1.45980i	−0.846874	−	0.531794i	$-0.821518\pi$
$941$	−14.5501	−	44.7806i	−0.474319	−	1.45980i	0.372554	−	0.928010i	$-0.378482\pi$
$942$		0			0
$943$			12.3987i			0.403759i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.5656	−	14.5424i	0.343337	−	0.472563i	−0.602075	−	0.798439i	$-0.705659\pi$
$947$	10.5656	−	14.5424i	0.343337	−	0.472563i	0.945412	+	0.325876i	$0.105659\pi$
$948$		0			0
$949$	−10.9895			−0.356733
$950$		0			0
$951$	−13.6070			−0.441236
$952$		0			0
$953$	21.1318	−	29.0854i	0.684526	−	0.942169i	−0.315451	−	0.948942i	$-0.602156\pi$
$953$	21.1318	−	29.0854i	0.684526	−	0.942169i	0.999977	+	0.00677250i	$0.00215577\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			54.9213i			1.77535i
$958$		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
$963$	−8.62349	+	2.80194i	−0.277888	+	0.0902913i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−5.64225	−	7.76589i	−0.181443	−	0.249734i	0.708601	−	0.705609i	$-0.249326\pi$
$967$	−5.64225	−	7.76589i	−0.181443	−	0.249734i	−0.890044	+	0.455875i	$0.849326\pi$
$968$		0			0
$969$	2.62180	−	1.90485i	0.0842243	−	0.0611925i
$970$		0			0
$971$	22.5625	+	16.3926i	0.724066	+	0.526065i	0.887681	−	0.460460i	$-0.152315\pi$
$971$	22.5625	+	16.3926i	0.724066	+	0.526065i	−0.163615	+	0.986524i	$0.552315\pi$
$972$		0			0
$973$	−21.3748	−	6.94511i	−0.685246	−	0.222650i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	53.9664	+	17.5347i	1.72654	+	0.560986i	0.992942	−	0.118601i	$-0.0378409\pi$
$977$	53.9664	+	17.5347i	1.72654	+	0.560986i	0.733595	+	0.679587i	$0.237841\pi$
$978$		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
$983$	−6.61324	−	9.10235i	−0.210930	−	0.290320i	0.690423	−	0.723406i	$-0.257425\pi$
$983$	−6.61324	−	9.10235i	−0.210930	−	0.290320i	−0.901352	+	0.433086i	$0.857425\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.49340	+	1.45999i	−0.143026	+	0.0464721i
$988$		0			0
$989$	−0.833493	+	2.56523i	−0.0265035	+	0.0815695i
$990$		0			0
$991$	10.6488	+	32.7735i	0.338269	+	1.04109i	0.965089	+	0.261921i	$0.0843561\pi$
$991$	10.6488	+	32.7735i	0.338269	+	1.04109i	−0.626820	+	0.779164i	$0.715644\pi$
$992$		0			0
$993$		−	22.6320i		−	0.718206i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	30.0889	−	41.4138i	0.952924	−	1.31159i	0.00270782	−	0.999996i	$-0.499138\pi$
$997$	30.0889	−	41.4138i	0.952924	−	1.31159i	0.950216	−	0.311591i	$-0.100862\pi$
$998$		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.o.c.649.5		24
5.2	odd	4		1500.2.m.c.601.3		24
5.3	odd	4		1500.2.m.d.601.4		24
5.4	even	2		300.2.o.a.229.2	yes	24
15.14	odd	2		900.2.w.c.829.4		24
25.6	even	5		300.2.o.a.169.2	✓	24
25.8	odd	20		1500.2.m.d.901.4		24
25.9	even	10		7500.2.d.g.1249.5		24
25.12	odd	20		7500.2.a.n.1.5		12
25.13	odd	20		7500.2.a.m.1.8		12
25.16	even	5		7500.2.d.g.1249.20		24
25.17	odd	20		1500.2.m.c.901.3		24
25.19	even	10	inner	1500.2.o.c.349.5		24
75.56	odd	10		900.2.w.c.469.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.2	✓	24	25.6	even	5
300.2.o.a.229.2	yes	24	5.4	even	2
900.2.w.c.469.4		24	75.56	odd	10
900.2.w.c.829.4		24	15.14	odd	2
1500.2.m.c.601.3		24	5.2	odd	4
1500.2.m.c.901.3		24	25.17	odd	20
1500.2.m.d.601.4		24	5.3	odd	4
1500.2.m.d.901.4		24	25.8	odd	20
1500.2.o.c.349.5		24	25.19	even	10	inner
1500.2.o.c.649.5		24	1.1	even	1	trivial
7500.2.a.m.1.8		12	25.13	odd	20
7500.2.a.n.1.5		12	25.12	odd	20
7500.2.d.g.1249.5		24	25.9	even	10
7500.2.d.g.1249.20		24	25.16	even	5

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.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{3} +0.957526i q^{7} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{3} +0.957526i q^{7} +(-0.309017 - 0.951057i) q^{9} +(-1.67360 + 5.15082i) q^{11} +(1.92371 - 0.625052i) q^{13} +(-0.377867 - 0.520090i) q^{17} +(-4.07829 + 2.96305i) q^{19} +(0.774655 + 0.562820i) q^{21} +(3.34734 + 1.08762i) q^{23} +(-0.951057 - 0.309017i) q^{27} +(8.20405 + 5.96059i) q^{29} +(-2.98671 + 2.16997i) q^{31} +(3.18338 + 4.38155i) q^{33} +(-10.7615 + 3.49663i) q^{37} +(0.625052 - 1.92371i) q^{39} +(1.08859 + 3.35035i) q^{41} +0.766348i q^{43} +(-2.90026 + 3.99186i) q^{47} +6.08314 q^{49} -0.642866 q^{51} +(3.49517 - 4.81069i) q^{53} +5.04105i q^{57} +(-1.45818 - 4.48783i) q^{59} +(1.34263 - 4.13219i) q^{61} +(0.910662 - 0.295892i) q^{63} +(5.59441 + 7.70005i) q^{67} +(2.84742 - 2.06877i) q^{69} +(9.66368 + 7.02107i) q^{71} +(-5.16713 - 1.67890i) q^{73} +(-4.93205 - 1.60252i) q^{77} +(9.58637 + 6.96491i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(0.819420 + 1.12784i) q^{83} +(9.64444 - 3.13367i) q^{87} +(0.527839 - 1.62452i) q^{89} +(0.598504 + 1.84200i) q^{91} +3.69178i q^{93} +(-8.57451 + 11.8018i) q^{97} +5.41590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^9	\( 24 q + 6 q^{9} - 6 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{21} - 40 q^{23} + 4 q^{29} + 6 q^{31} - 10 q^{33} - 10 q^{41} + 40 q^{47} - 56 q^{49} + 16 q^{51} + 60 q^{53} - 36 q^{59} - 12 q^{61} + 10 q^{63} - 20 q^{67} + 4 q^{69} + 40 q^{71} - 60 q^{73} + 40 q^{77} + 8 q^{79} - 6 q^{81} + 50 q^{83} + 20 q^{87} - 30 q^{91} + 40 q^{97} - 4 q^{99}+O(q^{100}) \) 24 * q + 6 * q^9 - 6 * q^11 - 10 * q^17 + 10 * q^19 - 4 * q^21 - 40 * q^23 + 4 * q^29 + 6 * q^31 - 10 * q^33 - 10 * q^41 + 40 * q^47 - 56 * q^49 + 16 * q^51 + 60 * q^53 - 36 * q^59 - 12 * q^61 + 10 * q^63 - 20 * q^67 + 4 * q^69 + 40 * q^71 - 60 * q^73 + 40 * q^77 + 8 * q^79 - 6 * q^81 + 50 * q^83 + 20 * q^87 - 30 * q^91 + 40 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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