LMFDB - Embedded newform 1500.2.o.c.349.5

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			349.5
Character	$\chi$	$=$	1500.349
Dual form			1500.2.o.c.649.5

$q$-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 $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$1$

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	$-0.942081\pi$
$7$		−	0.957526i		−	0.361911i	0.983491	−	0.180955i	$-0.0579190\pi$
$8$		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
$13$	1.92371	+	0.625052i	0.533542	+	0.173358i	0.563382	−	0.826196i	$-0.309500\pi$
$13$	1.92371	+	0.625052i	0.533542	+	0.173358i	−0.0298404	+	0.999555i	$0.509500\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.377867	+	0.520090i	−0.0916463	+	0.126140i	−0.852378	−	0.522926i	$-0.824840\pi$
$17$	−0.377867	+	0.520090i	−0.0916463	+	0.126140i	0.760732	+	0.649067i	$0.224840\pi$
$18$		0			0
$19$	−4.07829	−	2.96305i	−0.935625	−	0.679771i	0.0117388	−	0.999931i	$-0.496263\pi$
$19$	−4.07829	−	2.96305i	−0.935625	−	0.679771i	−0.947364	+	0.320160i	$0.896263\pi$
$20$		0			0
$21$	0.774655	−	0.562820i	0.169044	−	0.122817i
$22$		0			0
$23$	3.34734	−	1.08762i	0.697969	−	0.226784i	0.0615235	−	0.998106i	$-0.480404\pi$
$23$	3.34734	−	1.08762i	0.697969	−	0.226784i	0.636445	+	0.771322i	$0.280404\pi$
$24$		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	0.563712	−	0.825972i	$-0.309373\pi$
$29$	8.20405	−	5.96059i	1.52345	−	1.10685i	0.959742	−	0.280882i	$-0.0906271\pi$
$30$		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
$33$	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	−0.771097	−	0.636717i	$-0.780292\pi$
$37$	−10.7615	−	3.49663i	−1.76918	−	0.574842i	−0.998084	+	0.0618753i	$0.980292\pi$
$38$		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
$43$		−	0.766348i		−	0.116867i	−0.998291	−	0.0584335i	$-0.981389\pi$
$43$		−	0.766348i		−	0.116867i	0.998291	−	0.0584335i	$-0.0186106\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.90026	−	3.99186i	−0.423046	−	0.582273i	0.543293	−	0.839543i	$-0.317177\pi$
$47$	−2.90026	−	3.99186i	−0.423046	−	0.582273i	−0.966340	+	0.257270i	$0.917177\pi$
$48$		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	0.978524	−	0.206134i	$-0.0660881\pi$
$53$	3.49517	+	4.81069i	0.480099	+	0.660799i	−0.498425	+	0.866933i	$0.666088\pi$
$54$		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	−0.999998	−	0.00194529i	$-0.999381\pi$
$59$	−1.45818	+	4.48783i	−0.189839	+	0.584265i	0.810159	+	0.586210i	$0.199381\pi$
$60$		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
$63$	0.910662	+	0.295892i	0.114733	+	0.0372789i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.59441	−	7.70005i	0.683466	−	0.940711i	−0.316503	−	0.948592i	$-0.602509\pi$
$67$	5.59441	−	7.70005i	0.683466	−	0.940711i	0.999969	+	0.00788103i	$0.00250864\pi$
$68$		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
$73$	−5.16713	+	1.67890i	−0.604766	+	0.196500i	−0.595365	−	0.803455i	$-0.702993\pi$
$73$	−5.16713	+	1.67890i	−0.604766	+	0.196500i	−0.00940128	+	0.999956i	$0.502993\pi$
$74$		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	0.101122	−	0.994874i	$-0.467757\pi$
$79$	9.58637	−	6.96491i	1.07855	−	0.783613i	0.977430	+	0.211261i	$0.0677569\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	0.819420	−	1.12784i	0.0899431	−	0.123796i	−0.761674	−	0.647960i	$-0.775622\pi$
$83$	0.819420	−	1.12784i	0.0899431	−	0.123796i	0.851617	+	0.524164i	$0.175622\pi$
$84$		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	0.975127	−	0.221649i	$-0.0711438\pi$
$89$	0.527839	+	1.62452i	0.0559508	+	0.172199i	−0.919176	+	0.393847i	$0.871144\pi$
$90$		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	−0.978934	−	0.204176i	$-0.934549\pi$
$97$	−8.57451	−	11.8018i	−0.870610	−	1.19829i	0.108325	−	0.994116i	$-0.465451\pi$
$98$		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	0.991331	+	0.131386i	$0.0419427\pi$
$103$	8.22008	+	11.3140i	0.809949	+	1.11480i	−0.181383	+	0.983413i	$0.558057\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			9.06727i			0.876566i	0.898837	+	0.438283i	$0.144413\pi$
$107$			9.06727i			0.876566i	−0.898837	+	0.438283i	$0.855587\pi$
$108$		0			0
$109$	−0.734025	+	2.25910i	−0.0703068	+	0.216382i	−0.980036	−	0.198820i	$-0.936289\pi$
$109$	−0.734025	+	2.25910i	−0.0703068	+	0.216382i	0.909729	+	0.415202i	$0.136289\pi$
$110$		0			0
$111$	−3.49663	−	10.7615i	−0.331885	−	1.02144i
$112$		0			0
$113$	12.7797	+	4.15238i	1.20221	+	0.390623i	0.840575	−	0.541696i	$-0.182218\pi$
$113$	12.7797	+	4.15238i	1.20221	+	0.390623i	0.361638	+	0.932318i	$0.382218\pi$
$114$		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	−0.841116	−	0.540855i	$-0.818101\pi$
$127$	−13.5648	+	4.40749i	−1.20369	+	0.391101i	−0.362570	+	0.931957i	$0.618101\pi$
$128$		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
$133$	−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	0.807232	−	0.590234i	$-0.200965\pi$
$137$	13.0316	+	4.23423i	1.11337	+	0.361754i	0.306133	+	0.951989i	$0.400965\pi$
$138$		0			0
$139$	−7.25318	−	22.3230i	−0.615206	−	1.89341i	−0.398475	−	0.917179i	$-0.630461\pi$
$139$	−7.25318	−	22.3230i	−0.615206	−	1.89341i	−0.216731	−	0.976231i	$-0.569539\pi$
$140$		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	$0.174094\pi$
$157$			13.0329i			1.04014i	−0.854124	+	0.520070i	$0.825906\pi$
$158$		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	0.0202964	−	0.999794i	$-0.493539\pi$
$163$	−7.03403	−	2.28549i	−0.550948	−	0.179014i	−0.571244	+	0.820780i	$0.693539\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.8301	−	16.2827i	0.915438	−	1.25999i	−0.0498368	−	0.998757i	$-0.515870\pi$
$167$	11.8301	−	16.2827i	0.915438	−	1.25999i	0.965275	−	0.261235i	$-0.0841299\pi$
$168$		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	−0.388215	−	0.921569i	$-0.626908\pi$
$173$	−2.11241	+	0.686365i	−0.160604	+	0.0521833i	0.227612	+	0.973752i	$0.426908\pi$
$174$		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	−0.588951	−	0.808168i	$-0.700459\pi$
$179$	−0.0312215	+	0.0226837i	−0.00233360	+	0.00169546i	0.586618	+	0.809864i	$0.300459\pi$
$180$		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
$183$	−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	−0.956064	−	0.293158i	$-0.905294\pi$
$191$	−0.142049	+	0.437183i	−0.0102783	+	0.0316335i	0.945786	+	0.324791i	$0.105294\pi$
$192$		0			0
$193$			19.0231i			1.36932i	0.728864	+	0.684658i	$0.240048\pi$
$193$			19.0231i			1.36932i	−0.728864	+	0.684658i	$0.759952\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.12107	−	9.80131i	−0.507355	−	0.698315i	0.476115	−	0.879383i	$-0.342045\pi$
$197$	−7.12107	−	9.80131i	−0.507355	−	0.698315i	−0.983471	+	0.181068i	$0.942045\pi$
$198$		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	0.935102	+	0.354378i	$0.115307\pi$
$211$	5.61985	+	17.2961i	0.386887	+	1.19071i	−0.548216	+	0.836337i	$0.684693\pi$
$212$		0			0
$213$	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	−0.939231	−	0.343284i	$-0.888461\pi$
$223$	−22.3596	+	7.26507i	−1.49731	+	0.486505i	−0.558077	+	0.829789i	$0.688461\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	18.7171	−	6.08155i	1.24230	−	0.403647i	0.387142	−	0.922020i	$-0.373462\pi$
$227$	18.7171	−	6.08155i	1.24230	−	0.403647i	0.855154	+	0.518373i	$0.173462\pi$
$228$		0			0
$229$	4.29343	−	3.11936i	0.283718	−	0.206133i	−0.436819	−	0.899549i	$-0.643895\pi$
$229$	4.29343	−	3.11936i	0.283718	−	0.206133i	0.720538	+	0.693416i	$0.243895\pi$
$230$		0			0
$231$	−4.19545	−	3.04817i	−0.276040	−	0.200555i
$232$		0			0
$233$	13.6774	−	18.8253i	0.896034	−	1.23329i	−0.0756813	−	0.997132i	$-0.524113\pi$
$233$	13.6774	−	18.8253i	0.896034	−	1.23329i	0.971716	−	0.236154i	$-0.0758868\pi$
$234$		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	0.981022	+	0.193897i	$0.0621126\pi$
$239$	4.65842	+	14.3371i	0.301328	+	0.927392i	−0.679694	+	0.733496i	$0.737887\pi$
$240$		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
$243$		−	1.00000i		−	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	$0.217665\pi$
$257$			20.2556i			1.26351i	−0.775169	+	0.631754i	$0.782335\pi$
$258$		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	−0.805038	−	0.593223i	$-0.797855\pi$
$263$	−29.2724	−	9.51119i	−1.80502	−	0.586485i	−0.999977	+	0.00673789i	$0.997855\pi$
$264$		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	−0.999975	−	0.00709610i	$-0.997741\pi$
$269$	−21.5796	−	15.6785i	−1.31573	−	0.955936i	−0.315758	−	0.948840i	$-0.602259\pi$
$270$		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
$273$	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	−0.997893	−	0.0648872i	$-0.979331\pi$
$277$	−29.4098	+	9.55583i	−1.76706	+	0.574154i	−0.769172	+	0.639041i	$0.779331\pi$
$278$		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
$283$	−6.62008	+	9.11176i	−0.393523	+	0.541638i	−0.959104	−	0.283055i	$-0.908652\pi$
$283$	−6.62008	+	9.11176i	−0.393523	+	0.541638i	0.565581	+	0.824693i	$0.308652\pi$
$284$		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	$-0.893914\pi$
$293$		−	11.1995i		−	0.654284i	0.944975	−	0.327142i	$-0.106086\pi$
$294$		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	$-0.758246\pi$
$307$		−	24.1289i		−	1.37711i	0.725185	−	0.688554i	$-0.241754\pi$
$308$		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
$313$	−8.10268	−	2.63272i	−0.457991	−	0.148810i	0.0709303	−	0.997481i	$-0.477403\pi$
$313$	−8.10268	−	2.63272i	−0.457991	−	0.148810i	−0.528921	+	0.848671i	$0.677403\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.99798	+	11.0083i	−0.449211	+	0.618286i	−0.972228	−	0.234036i	$-0.924806\pi$
$317$	−7.99798	+	11.0083i	−0.449211	+	0.618286i	0.523017	+	0.852322i	$0.324806\pi$
$318$		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	0.963449	−	0.267891i	$-0.0863266\pi$
$331$	18.3097	+	13.3028i	1.00639	+	0.731187i	0.0429430	+	0.999078i	$0.486327\pi$
$332$		0			0
$333$	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	0.993385	+	0.114831i	$0.0366327\pi$
$337$	34.2285	+	11.1215i	1.86455	+	0.605828i	0.871161	+	0.490997i	$0.163367\pi$
$338$		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	0.926669	−	0.375877i	$-0.122659\pi$
$347$	5.26858	+	7.25158i	0.282832	+	0.389285i	−0.643837	+	0.765162i	$0.722659\pi$
$348$		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	0.999444	+	0.0333537i	$0.0106188\pi$
$353$	13.5712	+	18.6791i	0.722320	+	0.994188i	−0.277124	+	0.960834i	$0.589381\pi$
$354$		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	0.617454	+	0.786607i	$0.288164\pi$
$359$	−6.52607	+	20.0852i	−0.344433	+	1.06005i	−0.961887	+	0.273448i	$0.911836\pi$
$360$		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	−0.660662	−	0.750684i	$-0.729724\pi$
$367$	4.93178	−	6.78801i	0.257437	−	0.354331i	0.918098	+	0.396353i	$0.129724\pi$
$368$		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	−0.149018	−	0.988834i	$-0.547611\pi$
$373$	6.01888	−	1.95565i	0.311646	−	0.101260i	0.460664	+	0.887575i	$0.347611\pi$
$374$		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	−0.228607	−	0.973519i	$-0.573417\pi$
$379$	12.1990	−	8.86310i	0.626621	−	0.455267i	0.855228	+	0.518252i	$0.173417\pi$
$380$		0			0
$381$	−11.5389	−	8.38354i	−0.591158	−	0.429502i
$382$		0			0
$383$	−19.1490	+	26.3563i	−0.978466	+	1.34674i	−0.0408145	+	0.999167i	$0.512995\pi$
$383$	−19.1490	+	26.3563i	−0.978466	+	1.34674i	−0.937652	+	0.347576i	$0.887005\pi$
$384$		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	0.984727	−	0.174106i	$-0.0557035\pi$
$389$	1.69084	+	5.20388i	0.0857292	+	0.263847i	−0.898998	+	0.437953i	$0.855704\pi$
$390$		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	0.965840	−	0.259138i	$-0.0834384\pi$
$397$	8.38686	+	11.5435i	0.420925	+	0.579353i	−0.544916	+	0.838491i	$0.683438\pi$
$398$		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	0.581110	+	0.813825i	$0.302618\pi$
$409$	−7.42964	+	22.8661i	−0.367372	+	1.13065i	−0.948482	+	0.316830i	$0.897382\pi$
$410$		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	−0.127206	−	0.991876i	$-0.540601\pi$
$419$	−22.7180	−	16.5056i	−1.10984	−	0.806349i	−0.982639	+	0.185527i	$0.940601\pi$
$420$		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
$423$	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	0.665741	−	0.746183i	$-0.268116\pi$
$431$	3.35912	+	2.44055i	0.161803	+	0.117557i	−0.503937	+	0.863740i	$0.668116\pi$
$432$		0			0
$433$	−17.8217	+	24.5295i	−0.856456	+	1.17881i	0.125947	+	0.992037i	$0.459803\pi$
$433$	−17.8217	+	24.5295i	−0.856456	+	1.17881i	−0.982403	+	0.186773i	$0.940197\pi$
$434$		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	0.971790	−	0.235849i	$-0.0757870\pi$
$439$	0.984067	+	3.02865i	0.0469670	+	0.144549i	−0.924823	+	0.380398i	$0.875787\pi$
$440$		0			0
$441$	−1.87979	+	5.78541i	−0.0895140	+	0.275496i
$442$		0			0
$443$			30.4607i			1.44723i	0.690204	+	0.723615i	$0.257521\pi$
$443$			30.4607i			1.44723i	−0.690204	+	0.723615i	$0.742479\pi$
$444$		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	$-0.925680\pi$
$457$		−	9.89208i		−	0.462732i	0.972867	−	0.231366i	$-0.0743195\pi$
$458$		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
$463$	−0.488978	−	0.158879i	−0.0227248	−	0.00738372i	0.297633	−	0.954681i	$-0.403803\pi$
$463$	−0.488978	−	0.158879i	−0.0227248	−	0.00738372i	−0.320357	+	0.947297i	$0.603803\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.9175	−	15.0267i	0.505202	−	0.695352i	−0.477899	−	0.878415i	$-0.658601\pi$
$467$	10.9175	−	15.0267i	0.505202	−	0.695352i	0.983101	+	0.183063i	$0.0586014\pi$
$468$		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	−0.0823581	−	0.996603i	$-0.526245\pi$
$479$	18.3847	−	13.3573i	0.840017	−	0.610308i	0.922376	+	0.386294i	$0.126245\pi$
$480$		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	0.819533	−	0.573032i	$-0.194233\pi$
$487$	25.2840	+	8.21528i	1.14573	+	0.372270i	0.326196	+	0.945302i	$0.394233\pi$
$488$		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
$493$			6.51915i			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	−0.973883	−	0.227049i	$-0.927092\pi$
$503$	−19.9353	−	27.4386i	−0.888873	−	1.22343i	0.0850104	−	0.996380i	$-0.472908\pi$
$504$		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	−0.767756	−	0.640742i	$-0.778627\pi$
$509$	5.18882	−	15.9695i	0.229990	−	0.707838i	0.997747	−	0.0670956i	$-0.0213733\pi$
$510$		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	−0.242148	−	0.970239i	$-0.577852\pi$
$521$	13.8271	−	10.0460i	0.605777	−	0.440123i	0.847925	+	0.530117i	$0.177852\pi$
$522$		0			0
$523$	19.6398	−	6.38135i	0.858788	−	0.279037i	0.153666	−	0.988123i	$-0.450892\pi$
$523$	19.6398	−	6.38135i	0.858788	−	0.279037i	0.705122	+	0.709086i	$0.250892\pi$
$524$		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	−0.998773	−	0.0495207i	$-0.984231\pi$
$541$	−3.75968	+	11.5711i	−0.161641	+	0.497480i	0.837132	+	0.547001i	$0.184231\pi$
$542$		0			0
$543$		−	0.146945i		−	0.00630600i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−6.56378	−	9.03427i	−0.280647	−	0.386278i	0.645301	−	0.763928i	$-0.276732\pi$
$547$	−6.56378	−	9.03427i	−0.280647	−	0.386278i	−0.925948	+	0.377651i	$0.876732\pi$
$548$		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	$0.0883116\pi$
$557$			12.9282i			0.547787i	−0.961760	+	0.273894i	$0.911688\pi$
$558$		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	0.865616	−	0.500708i	$-0.166927\pi$
$563$	30.1722	+	9.80354i	1.27161	+	0.413170i	0.405989	+	0.913878i	$0.366927\pi$
$564$		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	0.957036	−	0.289971i	$-0.0936455\pi$
$569$	23.3050	+	16.9321i	0.976997	+	0.709830i	0.0199619	+	0.999801i	$0.493646\pi$
$570$		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
$573$	−0.437183	+	0.142049i	−0.0182636	+	0.00593420i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−38.7990	+	12.6065i	−1.61522	+	0.524817i	−0.970808	−	0.239859i	$-0.922899\pi$
$577$	−38.7990	+	12.6065i	−1.61522	+	0.524817i	−0.644414	+	0.764677i	$0.722899\pi$
$578$		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	0.122725	−	0.992441i	$-0.460837\pi$
$587$	−8.75436	−	2.84446i	−0.361331	−	0.117404i	−0.484056	+	0.875037i	$0.660837\pi$
$588$		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	$0.0818474\pi$
$593$			12.3856i			0.508614i	−0.967124	+	0.254307i	$0.918153\pi$
$594$		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	$-0.940432\pi$
$607$		−	9.16747i		−	0.372096i	0.982541	−	0.186048i	$-0.0595680\pi$
$608$		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	0.566237	−	0.824242i	$-0.308399\pi$
$613$	13.3662	+	4.34294i	0.539855	+	0.175410i	−0.0263819	+	0.999652i	$0.508399\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	21.2980	−	29.3141i	0.857424	−	1.18014i	−0.124754	−	0.992188i	$-0.539814\pi$
$617$	21.2980	−	29.3141i	0.857424	−	1.18014i	0.982178	−	0.187955i	$-0.0601859\pi$
$618$		0			0
$619$	20.7716	+	15.0915i	0.834882	+	0.606577i	0.920936	−	0.389713i	$-0.127426\pi$
$619$	20.7716	+	15.0915i	0.834882	+	0.606577i	−0.0860542	+	0.996290i	$0.527426\pi$
$620$		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	0.909327	−	0.416081i	$-0.136597\pi$
$631$	19.9603	+	14.5020i	0.794608	+	0.577317i	−0.114719	+	0.993398i	$0.536597\pi$
$632$		0			0
$633$	−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	0.584324	+	0.811520i	$0.301360\pi$
$641$	−9.25128	+	28.4725i	−0.365404	+	1.12460i	−0.949728	+	0.313077i	$0.898640\pi$
$642$		0			0
$643$		−	10.1343i		−	0.399658i	−0.979831	−	0.199829i	$-0.935961\pi$
$643$		−	10.1343i		−	0.399658i	0.979831	−	0.199829i	$-0.0640387\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−26.6027	−	36.6155i	−1.04586	−	1.43950i	−0.892343	−	0.451358i	$-0.850940\pi$
$647$	−26.6027	−	36.6155i	−1.04586	−	1.43950i	−0.153518	−	0.988146i	$-0.549060\pi$
$648$		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	−0.997320	−	0.0731608i	$-0.976691\pi$
$653$	−19.3880	−	26.6853i	−0.758711	−	1.04428i	0.238609	−	0.971116i	$-0.423309\pi$
$654$		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	−0.965254	−	0.261314i	$-0.915844\pi$
$659$	−0.789392	+	2.42950i	−0.0307504	+	0.0946398i	0.934503	+	0.355954i	$0.115844\pi$
$660$		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
$663$	−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	−0.0936282	−	0.995607i	$-0.529847\pi$
$673$	10.7875	−	3.50508i	0.415828	−	0.135111i	0.509456	+	0.860496i	$0.329847\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.7113	−	4.78000i	0.565402	−	0.183710i	−0.0123484	−	0.999924i	$-0.503931\pi$
$677$	14.7113	−	4.78000i	0.565402	−	0.183710i	0.577750	+	0.816213i	$0.303931\pi$
$678$		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	−0.878546	−	0.477657i	$-0.841486\pi$
$683$	−3.99284	+	5.49567i	−0.152782	+	0.210286i	0.725765	+	0.687943i	$0.241486\pi$
$684$		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	−0.315552	−	0.948908i	$-0.602190\pi$
$691$	13.0774	−	40.2482i	0.497489	−	1.53111i	0.813041	−	0.582206i	$-0.197810\pi$
$692$		0			0
$693$		−	5.18586i		−	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	−0.937748	−	0.347317i	$-0.887093\pi$
$709$	0.667116	−	2.05317i	0.0250541	−	0.0771085i	0.962802	+	0.270209i	$0.0870927\pi$
$710$		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	0.611535	−	0.791217i	$-0.290552\pi$
$719$	1.28757	+	0.935472i	0.0480181	+	0.0348872i	−0.563517	+	0.826104i	$0.690552\pi$
$720$		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	−0.285292	−	0.958441i	$-0.592091\pi$
$727$	1.27424	−	0.414026i	0.0472589	−	0.0153554i	0.332551	+	0.943085i	$0.392091\pi$
$728$		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	0.00138578	−	0.999999i	$-0.499559\pi$
$733$	25.7748	−	35.4759i	0.952013	−	1.31033i	0.950627	−	0.310335i	$-0.100441\pi$
$734$		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	−0.999536	−	0.0304443i	$-0.990308\pi$
$739$	−5.67584	−	17.4684i	−0.208789	−	0.642587i	0.790747	−	0.612143i	$-0.209692\pi$
$740$		0			0
$741$	3.15092	−	9.69753i	0.115752	−	0.356248i
$742$		0			0
$743$		−	21.5051i		−	0.788947i	−0.918907	−	0.394474i	$-0.870927\pi$
$743$		−	21.5051i		−	0.788947i	0.918907	−	0.394474i	$-0.129073\pi$
$744$		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	$-0.968750\pi$
$757$		−	5.39361i		−	0.196034i	0.995185	−	0.0980171i	$-0.0312500\pi$
$758$		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
$763$	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	0.938969	−	0.344003i	$-0.111783\pi$
$769$	25.0121	+	18.1724i	0.901960	+	0.655312i	−0.0370088	+	0.999315i	$0.511783\pi$
$770$		0			0
$771$	−16.3871	+	11.9059i	−0.590167	+	0.428781i
$772$		0			0
$773$	30.4255	−	9.88584i	1.09433	−	0.355569i	0.294411	−	0.955679i	$-0.404876\pi$
$773$	30.4255	−	9.88584i	1.09433	−	0.355569i	0.799918	+	0.600110i	$0.204876\pi$
$774$		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	−0.135764	−	0.990741i	$-0.543349\pi$
$787$	−23.2267	−	7.54681i	−0.827942	−	0.269015i	−0.692178	+	0.721726i	$0.743349\pi$
$788$		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	−0.902300	−	0.431110i	$-0.858122\pi$
$797$	−29.1765	−	40.1580i	−1.03348	−	1.42247i	−0.131184	−	0.991358i	$-0.541878\pi$
$798$		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	−0.795049	−	0.606545i	$-0.792555\pi$
$809$	5.82162	−	17.9171i	0.204677	−	0.629932i	0.999726	−	0.0233871i	$-0.00744501\pi$
$810$		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
$813$	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	−0.969678	−	0.244388i	$-0.921413\pi$
$821$	−29.7103	+	21.5858i	−1.03690	+	0.753350i	−0.0672202	+	0.997738i	$0.521413\pi$
$822$		0			0
$823$	38.5327	−	12.5200i	1.34317	−	0.436421i	0.452779	−	0.891623i	$-0.350433\pi$
$823$	38.5327	−	12.5200i	1.34317	−	0.436421i	0.890388	+	0.455202i	$0.150433\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−10.6264	+	3.45274i	−0.369517	+	0.120063i	−0.487889	−	0.872906i	$-0.662233\pi$
$827$	−10.6264	+	3.45274i	−0.369517	+	0.120063i	0.118371	+	0.992969i	$0.462233\pi$
$828$		0			0
$829$	29.8314	−	21.6738i	1.03609	−	0.752762i	0.0665703	−	0.997782i	$-0.478794\pi$
$829$	29.8314	−	21.6738i	1.03609	−	0.752762i	0.969518	+	0.245019i	$0.0787943\pi$
$830$		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	0.993349	−	0.115140i	$-0.0367318\pi$
$839$	3.53480	+	10.8790i	0.122035	+	0.375585i	−0.871314	+	0.490725i	$0.836732\pi$
$840$		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	0.485518	−	0.874227i	$-0.338631\pi$
$853$	−14.4849	−	19.9368i	−0.495954	−	0.682623i	−0.981472	+	0.191604i	$0.938631\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			11.2342i			0.383752i	0.981419	+	0.191876i	$0.0614571\pi$
$857$			11.2342i			0.383752i	−0.981419	+	0.191876i	$0.938543\pi$
$858$		0			0
$859$	4.79573	−	14.7597i	0.163628	−	0.503595i	−0.835305	−	0.549788i	$-0.814709\pi$
$859$	4.79573	−	14.7597i	0.163628	−	0.503595i	0.998933	+	0.0461922i	$0.0147087\pi$
$860$		0			0
$861$	−1.04236	−	3.20805i	−0.0355235	−	0.109330i
$862$		0			0
$863$	18.5636	+	6.03168i	0.631912	+	0.205321i	0.607422	−	0.794379i	$-0.292204\pi$
$863$	18.5636	+	6.03168i	0.631912	+	0.205321i	0.0244902	+	0.999700i	$0.492204\pi$
$864$		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	−0.0800245	−	0.996793i	$-0.525500\pi$
$877$	13.0638	−	4.24470i	0.441134	−	0.143333i	0.521159	+	0.853460i	$0.325500\pi$
$878$		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
$883$	9.81699	−	13.5119i	0.330368	−	0.454713i	−0.611229	−	0.791454i	$-0.709325\pi$
$883$	9.81699	−	13.5119i	0.330368	−	0.454713i	0.941597	+	0.336741i	$0.109325\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.6331	−	8.00379i	−0.827099	−	0.268741i	−0.135276	−	0.990808i	$-0.543192\pi$
$887$	−24.6331	−	8.00379i	−0.827099	−	0.268741i	−0.691823	+	0.722067i	$0.743192\pi$
$888$		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	$0.0251187\pi$
$907$			4.74821i			0.157662i	−0.996888	+	0.0788308i	$0.974881\pi$
$908$		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
$913$	−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	0.828483	−	0.560014i	$-0.189204\pi$
$919$	16.7306	+	12.1555i	0.551893	+	0.400974i	−0.276590	+	0.960988i	$0.589204\pi$
$920$		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	−0.220530	−	0.975380i	$-0.570779\pi$
$929$	19.4753	−	14.1496i	0.638964	−	0.464235i	0.859494	+	0.511145i	$0.170779\pi$
$930$		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	0.906563	−	0.422071i	$-0.138697\pi$
$937$	42.6067	+	13.8438i	1.39190	+	0.452256i	0.485338	+	0.874327i	$0.338697\pi$
$938$		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
$943$		−	12.3987i		−	0.403759i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.5656	+	14.5424i	0.343337	+	0.472563i	0.945412	−	0.325876i	$-0.105659\pi$
$947$	10.5656	+	14.5424i	0.343337	+	0.472563i	−0.602075	+	0.798439i	$0.705659\pi$
$948$		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	0.999977	−	0.00677250i	$-0.00215577\pi$
$953$	21.1318	+	29.0854i	0.684526	+	0.942169i	−0.315451	+	0.948942i	$0.602156\pi$
$954$		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	−0.890044	−	0.455875i	$-0.849326\pi$
$967$	−5.64225	+	7.76589i	−0.181443	+	0.249734i	0.708601	+	0.705609i	$0.249326\pi$
$968$		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
$973$	−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	0.733595	−	0.679587i	$-0.237841\pi$
$977$	53.9664	−	17.5347i	1.72654	−	0.560986i	0.992942	+	0.118601i	$0.0378409\pi$
$978$		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	−0.901352	−	0.433086i	$-0.857425\pi$
$983$	−6.61324	+	9.10235i	−0.210930	+	0.290320i	0.690423	+	0.723406i	$0.257425\pi$
$984$		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	−0.626820	−	0.779164i	$-0.715644\pi$
$991$	10.6488	−	32.7735i	0.338269	−	1.04109i	0.965089	−	0.261921i	$-0.0843561\pi$
$992$		0			0
$993$			22.6320i			0.718206i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	30.0889	+	41.4138i	0.952924	+	1.31159i	0.950216	+	0.311591i	$0.100862\pi$
$997$	30.0889	+	41.4138i	0.952924	+	1.31159i	0.00270782	+	0.999996i	$0.499138\pi$
$998$		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.349.5		24
5.2	odd	4		1500.2.m.d.901.4		24
5.3	odd	4		1500.2.m.c.901.3		24
5.4	even	2		300.2.o.a.169.2	✓	24
15.14	odd	2		900.2.w.c.469.4		24
25.2	odd	20		7500.2.a.m.1.8		12
25.3	odd	20		1500.2.m.c.601.3		24
25.4	even	10	inner	1500.2.o.c.649.5		24
25.11	even	5		7500.2.d.g.1249.5		24
25.14	even	10		7500.2.d.g.1249.20		24
25.21	even	5		300.2.o.a.229.2	yes	24
25.22	odd	20		1500.2.m.d.601.4		24
25.23	odd	20		7500.2.a.n.1.5		12
75.71	odd	10		900.2.w.c.829.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.2	✓	24	5.4	even	2
300.2.o.a.229.2	yes	24	25.21	even	5
900.2.w.c.469.4		24	15.14	odd	2
900.2.w.c.829.4		24	75.71	odd	10
1500.2.m.c.601.3		24	25.3	odd	20
1500.2.m.c.901.3		24	5.3	odd	4
1500.2.m.d.601.4		24	25.22	odd	20
1500.2.m.d.901.4		24	5.2	odd	4
1500.2.o.c.349.5		24	1.1	even	1	trivial
1500.2.o.c.649.5		24	25.4	even	10	inner
7500.2.a.m.1.8		12	25.2	odd	20
7500.2.a.n.1.5		12	25.23	odd	20
7500.2.d.g.1249.5		24	25.11	even	5
7500.2.d.g.1249.20		24	25.14	even	10

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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Representations

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Database

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