LMFDB - Embedded newform 1500.2.o.a.349.3

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{60})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 $ x^16 + x^14 - x^10 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.3
Root			$-0.406737 - 0.913545i$ of defining polynomial
Character	$\chi$	$=$	1500.349
Dual form			1500.2.o.a.649.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{3} -0.511170i q^{7} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{3} -0.511170i q^{7} +(-0.309017 + 0.951057i) q^{9} +(-0.564602 - 1.73767i) q^{11} +(-5.82203 - 1.89169i) q^{13} +(1.51852 - 2.09007i) q^{17} +(-3.93444 - 2.85854i) q^{19} +(0.413545 - 0.300458i) q^{21} +(-6.30818 + 2.04965i) q^{23} +(-0.951057 + 0.309017i) q^{27} +(-6.46980 + 4.70059i) q^{29} +(3.95252 + 2.87167i) q^{31} +(1.07394 - 1.47815i) q^{33} +(-7.07355 - 2.29833i) q^{37} +(-1.89169 - 5.82203i) q^{39} +(1.77084 - 5.45007i) q^{41} +2.05126i q^{43} +(-4.67547 - 6.43523i) q^{47} +6.73870 q^{49} +2.58347 q^{51} +(0.781240 + 1.07528i) q^{53} -4.86324i q^{57} +(3.11882 - 9.59875i) q^{59} +(1.47437 + 4.53764i) q^{61} +(0.486152 + 0.157960i) q^{63} +(-8.42500 + 11.5960i) q^{67} +(-5.36606 - 3.89867i) q^{69} +(4.34421 - 3.15625i) q^{71} +(-3.31031 + 1.07559i) q^{73} +(-0.888244 + 0.288608i) q^{77} +(-1.06789 + 0.775869i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-0.536407 + 0.738301i) q^{83} +(-7.60571 - 2.47124i) q^{87} +(-3.63893 - 11.1995i) q^{89} +(-0.966977 + 2.97605i) q^{91} +4.88558i q^{93} +(4.34952 + 5.98660i) q^{97} +1.82709 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^9	$ 16 q + 4 q^{9} - 4 q^{11} - 10 q^{19} - 6 q^{21} - 54 q^{29} - 6 q^{31} + 40 q^{41} + 16 q^{49} - 16 q^{51} - 4 q^{59} - 28 q^{61} - 4 q^{69} - 30 q^{71} - 48 q^{79} - 4 q^{81} + 10 q^{91} + 4 q^{99}+O(q^{100}) $ 16 * q + 4 * q^9 - 4 * q^11 - 10 * q^19 - 6 * q^21 - 54 * q^29 - 6 * q^31 + 40 * q^41 + 16 * q^49 - 16 * q^51 - 4 * q^59 - 28 * q^61 - 4 * q^69 - 30 * q^71 - 48 * q^79 - 4 * q^81 + 10 * q^91 + 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
$7$		−	0.511170i		−	0.193204i	−0.995323	−	0.0966021i	$-0.969203\pi$
$7$		−	0.511170i		−	0.193204i	0.995323	−	0.0966021i	$-0.0307974\pi$
$8$		0			0
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$		0			0
$11$	−0.564602	−	1.73767i	−0.170234	−	0.523926i	0.829150	−	0.559026i	$-0.188825\pi$
$11$	−0.564602	−	1.73767i	−0.170234	−	0.523926i	−0.999384	+	0.0351002i	$0.988825\pi$
$12$		0			0
$13$	−5.82203	−	1.89169i	−1.61474	−	0.524661i	−0.644048	−	0.764985i	$-0.722746\pi$
$13$	−5.82203	−	1.89169i	−1.61474	−	0.524661i	−0.970693	+	0.240323i	$0.922746\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.51852	−	2.09007i	0.368296	−	0.506916i	−0.584141	−	0.811652i	$-0.698568\pi$
$17$	1.51852	−	2.09007i	0.368296	−	0.506916i	0.952437	+	0.304736i	$0.0985684\pi$
$18$		0			0
$19$	−3.93444	−	2.85854i	−0.902623	−	0.655794i	0.0365153	−	0.999333i	$-0.488374\pi$
$19$	−3.93444	−	2.85854i	−0.902623	−	0.655794i	−0.939138	+	0.343539i	$0.888374\pi$
$20$		0			0
$21$	0.413545	−	0.300458i	0.0902430	−	0.0655654i
$22$		0			0
$23$	−6.30818	+	2.04965i	−1.31535	+	0.427382i	−0.880895	−	0.473312i	$-0.843058\pi$
$23$	−6.30818	+	2.04965i	−1.31535	+	0.427382i	−0.434453	+	0.900695i	$0.643058\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$		0			0
$29$	−6.46980	+	4.70059i	−1.20141	+	0.872877i	−0.994423	−	0.105466i	$-0.966366\pi$
$29$	−6.46980	+	4.70059i	−1.20141	+	0.872877i	−0.206989	+	0.978343i	$0.566366\pi$
$30$		0			0
$31$	3.95252	+	2.87167i	0.709893	+	0.515767i	0.883139	−	0.469111i	$-0.155426\pi$
$31$	3.95252	+	2.87167i	0.709893	+	0.515767i	−0.173246	+	0.984879i	$0.555426\pi$
$32$		0			0
$33$	1.07394	−	1.47815i	0.186948	−	0.257312i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−7.07355	−	2.29833i	−1.16288	−	0.377844i	−0.336902	−	0.941540i	$-0.609379\pi$
$37$	−7.07355	−	2.29833i	−1.16288	−	0.377844i	−0.825982	+	0.563696i	$0.809379\pi$
$38$		0			0
$39$	−1.89169	−	5.82203i	−0.302913	−	0.932271i
$40$		0			0
$41$	1.77084	−	5.45007i	0.276558	−	0.851158i	−0.712245	−	0.701931i	$-0.752321\pi$
$41$	1.77084	−	5.45007i	0.276558	−	0.851158i	0.988803	−	0.149227i	$-0.0476786\pi$
$42$		0			0
$43$			2.05126i			0.312814i	0.987693	+	0.156407i	$0.0499912\pi$
$43$			2.05126i			0.312814i	−0.987693	+	0.156407i	$0.950009\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.67547	−	6.43523i	−0.681987	−	0.938675i	0.317968	−	0.948101i	$-0.396999\pi$
$47$	−4.67547	−	6.43523i	−0.681987	−	0.938675i	−0.999956	+	0.00942623i	$0.996999\pi$
$48$		0			0
$49$	6.73870			0.962672
$50$		0			0
$51$	2.58347			0.361758
$52$		0			0
$53$	0.781240	+	1.07528i	0.107312	+	0.147702i	0.859295	−	0.511480i	$-0.170903\pi$
$53$	0.781240	+	1.07528i	0.107312	+	0.147702i	−0.751983	+	0.659182i	$0.770903\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	4.86324i		−	0.644152i
$58$		0			0
$59$	3.11882	−	9.59875i	0.406036	−	1.24965i	−0.513991	−	0.857796i	$-0.671833\pi$
$59$	3.11882	−	9.59875i	0.406036	−	1.24965i	0.920027	−	0.391855i	$-0.128167\pi$
$60$		0			0
$61$	1.47437	+	4.53764i	0.188774	+	0.580985i	0.999993	−	0.00375653i	$-0.00119574\pi$
$61$	1.47437	+	4.53764i	0.188774	+	0.580985i	−0.811219	+	0.584742i	$0.801196\pi$
$62$		0			0
$63$	0.486152	+	0.157960i	0.0612494	+	0.0199011i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−8.42500	+	11.5960i	−1.02928	+	1.41668i	−0.123789	+	0.992309i	$0.539505\pi$
$67$	−8.42500	+	11.5960i	−1.02928	+	1.41668i	−0.905489	+	0.424370i	$0.860495\pi$
$68$		0			0
$69$	−5.36606	−	3.89867i	−0.645998	−	0.469345i
$70$		0			0
$71$	4.34421	−	3.15625i	0.515563	−	0.374578i	−0.299367	−	0.954138i	$-0.596775\pi$
$71$	4.34421	−	3.15625i	0.515563	−	0.374578i	0.814930	+	0.579560i	$0.196775\pi$
$72$		0			0
$73$	−3.31031	+	1.07559i	−0.387443	+	0.125888i	−0.496260	−	0.868174i	$-0.665294\pi$
$73$	−3.31031	+	1.07559i	−0.387443	+	0.125888i	0.108817	+	0.994062i	$0.465294\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.888244	+	0.288608i	−0.101225	+	0.0328899i
$78$		0			0
$79$	−1.06789	+	0.775869i	−0.120147	+	0.0872921i	−0.646236	−	0.763137i	$-0.723658\pi$
$79$	−1.06789	+	0.775869i	−0.120147	+	0.0872921i	0.526089	+	0.850430i	$0.323658\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	−0.536407	+	0.738301i	−0.0588783	+	0.0810391i	−0.837441	−	0.546528i	$-0.815949\pi$
$83$	−0.536407	+	0.738301i	−0.0588783	+	0.0810391i	0.778562	+	0.627567i	$0.215949\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−7.60571	−	2.47124i	−0.815417	−	0.264945i
$88$		0			0
$89$	−3.63893	−	11.1995i	−0.385726	−	1.18714i	−0.935952	−	0.352127i	$-0.885459\pi$
$89$	−3.63893	−	11.1995i	−0.385726	−	1.18714i	0.550226	−	0.835016i	$-0.314541\pi$
$90$		0			0
$91$	−0.966977	+	2.97605i	−0.101367	+	0.311975i
$92$		0			0
$93$			4.88558i			0.506611i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.34952	+	5.98660i	0.441627	+	0.607847i	0.970573	−	0.240809i	$-0.0774126\pi$
$97$	4.34952	+	5.98660i	0.441627	+	0.607847i	−0.528946	+	0.848655i	$0.677413\pi$
$98$		0			0
$99$	1.82709			0.183630
$100$		0			0
$101$	13.0962			1.30312			0.651561	−	0.758596i	$-0.274114\pi$
$101$	13.0962			1.30312			0.651561	+	0.758596i	$0.274114\pi$
$102$		0			0
$103$	−6.48337	−	8.92360i	−0.638826	−	0.879268i	0.359727	−	0.933058i	$-0.382870\pi$
$103$	−6.48337	−	8.92360i	−0.638826	−	0.879268i	−0.998552	+	0.0537897i	$0.982870\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	8.08083i		−	0.781203i	−0.920560	−	0.390602i	$-0.872267\pi$
$107$		−	8.08083i		−	0.781203i	0.920560	−	0.390602i	$-0.127733\pi$
$108$		0			0
$109$	−3.49904	+	10.7690i	−0.335148	+	1.03148i	0.631502	+	0.775375i	$0.282439\pi$
$109$	−3.49904	+	10.7690i	−0.335148	+	1.03148i	−0.966649	+	0.256104i	$0.917561\pi$
$110$		0			0
$111$	−2.29833	−	7.07355i	−0.218148	−	0.671391i
$112$		0			0
$113$	−3.58415	−	1.16456i	−0.337169	−	0.109553i	0.135539	−	0.990772i	$-0.456723\pi$
$113$	−3.58415	−	1.16456i	−0.337169	−	0.109553i	−0.472708	+	0.881219i	$0.656723\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.59821	−	4.95252i	0.332655	−	0.457860i
$118$		0			0
$119$	−1.06838	−	0.776224i	−0.0979383	−	0.0711563i
$120$		0			0
$121$	6.19848	−	4.50346i	0.563498	−	0.409405i
$122$		0			0
$123$	5.45007	−	1.77084i	0.491416	−	0.159671i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	3.96774	−	1.28920i	0.352080	−	0.114398i	−0.127637	−	0.991821i	$-0.540739\pi$
$127$	3.96774	−	1.28920i	0.352080	−	0.114398i	0.479717	+	0.877423i	$0.340739\pi$
$128$		0			0
$129$	−1.65951	+	1.20570i	−0.146111	+	0.106156i
$130$		0			0
$131$	−11.9660	−	8.69382i	−1.04548	−	0.759583i	−0.0741292	−	0.997249i	$-0.523618\pi$
$131$	−11.9660	−	8.69382i	−1.04548	−	0.759583i	−0.971347	+	0.237666i	$0.923618\pi$
$132$		0			0
$133$	−1.46120	+	2.01117i	−0.126702	+	0.174391i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.16688	−	0.379143i	−0.0996934	−	0.0323923i	0.258746	−	0.965946i	$-0.416691\pi$
$137$	−1.16688	−	0.379143i	−0.0996934	−	0.0323923i	−0.358439	+	0.933553i	$0.616691\pi$
$138$		0			0
$139$	−2.80764	−	8.64102i	−0.238141	−	0.732922i	−0.996689	−	0.0813051i	$-0.974091\pi$
$139$	−2.80764	−	8.64102i	−0.238141	−	0.732922i	0.758549	−	0.651616i	$-0.225909\pi$
$140$		0			0
$141$	2.45804	−	7.56507i	0.207004	−	0.637094i
$142$		0			0
$143$			11.1848i			0.935320i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.96091	+	5.45173i	0.326690	+	0.449651i
$148$		0			0
$149$	−1.90097			−0.155733			−0.0778666	−	0.996964i	$-0.524811\pi$
$149$	−1.90097			−0.155733			−0.0778666	+	0.996964i	$0.524811\pi$
$150$		0			0
$151$	−4.60292			−0.374580			−0.187290	−	0.982305i	$-0.559970\pi$
$151$	−4.60292			−0.374580			−0.187290	+	0.982305i	$0.559970\pi$
$152$		0			0
$153$	1.51852	+	2.09007i	0.122765	+	0.168972i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			3.96076i			0.316103i	0.987431	+	0.158052i	$0.0505212\pi$
$157$			3.96076i			0.316103i	−0.987431	+	0.158052i	$0.949479\pi$
$158$		0			0
$159$	−0.410722	+	1.26407i	−0.0325724	+	0.100247i
$160$		0			0
$161$	1.04772	+	3.22456i	0.0825721	+	0.254131i
$162$		0			0
$163$	−19.9527	−	6.48302i	−1.56281	−	0.507789i	−0.605256	−	0.796031i	$-0.706929\pi$
$163$	−19.9527	−	6.48302i	−1.56281	−	0.507789i	−0.957558	+	0.288241i	$0.906929\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.6021	+	14.5925i	−0.820413	+	1.12920i	0.169219	+	0.985578i	$0.445875\pi$
$167$	−10.6021	+	14.5925i	−0.820413	+	1.12920i	−0.989632	+	0.143624i	$0.954125\pi$
$168$		0			0
$169$	19.8003	+	14.3858i	1.52310	+	1.10660i
$170$		0			0
$171$	3.93444	−	2.85854i	0.300874	−	0.218598i
$172$		0			0
$173$	24.3447	−	7.91007i	1.85089	−	0.601391i	0.854217	−	0.519917i	$-0.174037\pi$
$173$	24.3447	−	7.91007i	1.85089	−	0.601391i	0.996675	−	0.0814747i	$-0.0259630\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	9.59875	−	3.11882i	0.721486	−	0.234425i
$178$		0			0
$179$	−6.81056	+	4.94816i	−0.509045	+	0.369843i	−0.812461	−	0.583015i	$-0.801873\pi$
$179$	−6.81056	+	4.94816i	−0.509045	+	0.369843i	0.303416	+	0.952858i	$0.401873\pi$
$180$		0			0
$181$	16.2350	+	11.7955i	1.20674	+	0.876749i	0.994931	−	0.100561i	$-0.0320639\pi$
$181$	16.2350	+	11.7955i	1.20674	+	0.876749i	0.211811	+	0.977311i	$0.432064\pi$
$182$		0			0
$183$	−2.80442	+	3.85995i	−0.207308	+	0.285336i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−4.48920	−	1.45863i	−0.328283	−	0.106666i
$188$		0			0
$189$	0.157960	+	0.486152i	0.0114899	+	0.0353623i
$190$		0			0
$191$	1.19381	−	3.67416i	0.0863808	−	0.265853i	−0.898531	−	0.438910i	$-0.855365\pi$
$191$	1.19381	−	3.67416i	0.0863808	−	0.265853i	0.984912	+	0.173057i	$0.0553646\pi$
$192$		0			0
$193$		−	10.6925i		−	0.769662i	−0.922987	−	0.384831i	$-0.874260\pi$
$193$		−	10.6925i		−	0.769662i	0.922987	−	0.384831i	$-0.125740\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.44778	+	3.36909i	0.174397	+	0.240037i	0.887264	−	0.461263i	$-0.152603\pi$
$197$	2.44778	+	3.36909i	0.174397	+	0.240037i	−0.712866	+	0.701300i	$0.752603\pi$
$198$		0			0
$199$	27.5965			1.95627			0.978134	−	0.207978i	$-0.0666882\pi$
$199$	27.5965			1.95627			0.978134	+	0.207978i	$0.0666882\pi$
$200$		0			0
$201$	−14.3335			−1.01100
$202$		0			0
$203$	2.40280	+	3.30717i	0.168643	+	0.232118i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	6.63282i		−	0.461013i
$208$		0			0
$209$	−2.74580	+	8.45069i	−0.189931	+	0.584546i
$210$		0			0
$211$	0.597913	+	1.84019i	0.0411621	+	0.126684i	0.969526	−	0.244989i	$-0.0787843\pi$
$211$	0.597913	+	1.84019i	0.0411621	+	0.126684i	−0.928364	+	0.371673i	$0.878784\pi$
$212$		0			0
$213$	5.10692	+	1.65934i	0.349921	+	0.113696i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.46791	−	2.02041i	0.0996484	−	0.137154i
$218$		0			0
$219$	−2.81592	−	2.04589i	−0.190282	−	0.138248i
$220$		0			0
$221$	−12.7947	+	9.29586i	−0.860662	+	0.625307i
$222$		0			0
$223$	−17.5067	+	5.68828i	−1.17234	+	0.380916i	−0.829515	−	0.558485i	$-0.811383\pi$
$223$	−17.5067	+	5.68828i	−1.17234	+	0.380916i	−0.342823	+	0.939400i	$0.611383\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	18.3170	−	5.95154i	1.21574	−	0.395018i	0.370211	−	0.928948i	$-0.379286\pi$
$227$	18.3170	−	5.95154i	1.21574	−	0.395018i	0.845529	+	0.533930i	$0.179286\pi$
$228$		0			0
$229$	−21.3918	+	15.5420i	−1.41361	+	1.02705i	−0.420824	+	0.907142i	$0.638259\pi$
$229$	−21.3918	+	15.5420i	−1.41361	+	1.02705i	−0.992785	+	0.119905i	$0.961741\pi$
$230$		0			0
$231$	−0.755585	−	0.548965i	−0.0497139	−	0.0361192i
$232$		0			0
$233$	9.26399	−	12.7508i	0.606904	−	0.835332i	−0.389414	−	0.921063i	$-0.627323\pi$
$233$	9.26399	−	12.7508i	0.606904	−	0.835332i	0.996318	+	0.0857308i	$0.0273225\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.25538	−	0.407899i	−0.0815459	−	0.0264959i
$238$		0			0
$239$	−5.67518	−	17.4664i	−0.367097	−	1.12981i	−0.948658	−	0.316305i	$-0.897558\pi$
$239$	−5.67518	−	17.4664i	−0.367097	−	1.12981i	0.581561	−	0.813503i	$-0.302442\pi$
$240$		0			0
$241$	−7.81517	+	24.0526i	−0.503419	+	1.54936i	0.299993	+	0.953941i	$0.403016\pi$
$241$	−7.81517	+	24.0526i	−0.503419	+	1.54936i	−0.803412	+	0.595423i	$0.796984\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	17.4990	+	24.0853i	1.11343	+	1.53251i
$248$		0			0
$249$	−0.912590			−0.0578331
$250$		0			0
$251$	−17.4297			−1.10015			−0.550076	−	0.835115i	$-0.685401\pi$
$251$	−17.4297			−1.10015			−0.550076	+	0.835115i	$0.685401\pi$
$252$		0			0
$253$	7.12323	+	9.80428i	0.447834	+	0.616390i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	29.6169i		−	1.84745i	−0.383052	−	0.923727i	$-0.625127\pi$
$257$		−	29.6169i		−	1.84745i	0.383052	−	0.923727i	$-0.374873\pi$
$258$		0			0
$259$	−1.17484	+	3.61579i	−0.0730010	+	0.224674i
$260$		0			0
$261$	−2.47124	−	7.60571i	−0.152966	−	0.470781i
$262$		0			0
$263$	15.9159	+	5.17140i	0.981419	+	0.318882i	0.755417	−	0.655244i	$-0.227434\pi$
$263$	15.9159	+	5.17140i	0.981419	+	0.318882i	0.226002	+	0.974127i	$0.427434\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	6.92166	−	9.52685i	0.423599	−	0.583034i
$268$		0			0
$269$	−10.3471	−	7.51758i	−0.630872	−	0.458355i	0.225830	−	0.974167i	$-0.427491\pi$
$269$	−10.3471	−	7.51758i	−0.630872	−	0.458355i	−0.856702	+	0.515811i	$0.827491\pi$
$270$		0			0
$271$	−23.1964	+	16.8532i	−1.40908	+	1.02376i	−0.415628	+	0.909535i	$0.636438\pi$
$271$	−23.1964	+	16.8532i	−1.40908	+	1.02376i	−0.993455	+	0.114224i	$0.963562\pi$
$272$		0			0
$273$	−2.97605	+	0.966977i	−0.180119	+	0.0585241i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−5.07610	+	1.64932i	−0.304993	+	0.0990983i	−0.457515	−	0.889202i	$-0.651261\pi$
$277$	−5.07610	+	1.64932i	−0.304993	+	0.0990983i	0.152522	+	0.988300i	$0.451261\pi$
$278$		0			0
$279$	−3.95252	+	2.87167i	−0.236631	+	0.171922i
$280$		0			0
$281$	5.19975	+	3.77784i	0.310191	+	0.225367i	0.731979	−	0.681328i	$-0.238597\pi$
$281$	5.19975	+	3.77784i	0.310191	+	0.225367i	−0.421787	+	0.906695i	$0.638597\pi$
$282$		0			0
$283$	6.15038	−	8.46527i	0.365602	−	0.503208i	−0.586097	−	0.810241i	$-0.699336\pi$
$283$	6.15038	−	8.46527i	0.365602	−	0.503208i	0.951699	+	0.307033i	$0.0993362\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.78591	−	0.905199i	−0.164447	−	0.0534322i
$288$		0			0
$289$	3.19082	+	9.82033i	0.187695	+	0.577666i
$290$		0			0
$291$	−2.28668	+	7.03767i	−0.134047	+	0.412555i
$292$		0			0
$293$		−	4.63761i		−	0.270932i	−0.990782	−	0.135466i	$-0.956747\pi$
$293$		−	4.63761i		−	0.270932i	0.990782	−	0.135466i	$-0.0432532\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.07394	+	1.47815i	0.0623162	+	0.0857708i
$298$		0			0
$299$	40.6038			2.34818
$300$		0			0
$301$	1.04854			0.0604371
$302$		0			0
$303$	7.69776	+	10.5951i	0.442225	+	0.608670i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			17.5664i			1.00257i	0.865282	+	0.501285i	$0.167139\pi$
$307$			17.5664i			1.00257i	−0.865282	+	0.501285i	$0.832861\pi$
$308$		0			0
$309$	3.40851	−	10.4903i	0.193903	−	0.596773i
$310$		0			0
$311$	5.67507	+	17.4661i	0.321803	+	0.990409i	0.972863	+	0.231382i	$0.0743249\pi$
$311$	5.67507	+	17.4661i	0.321803	+	0.990409i	−0.651059	+	0.759027i	$0.725675\pi$
$312$		0			0
$313$	24.1128	+	7.83472i	1.36294	+	0.442845i	0.897022	−	0.441986i	$-0.145726\pi$
$313$	24.1128	+	7.83472i	1.36294	+	0.442845i	0.465914	+	0.884830i	$0.345726\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.9019	+	19.1343i	−0.780808	+	1.07469i	0.214385	+	0.976749i	$0.431225\pi$
$317$	−13.9019	+	19.1343i	−0.780808	+	1.07469i	−0.995192	+	0.0979401i	$0.968775\pi$
$318$		0			0
$319$	11.8209	+	8.58840i	0.661844	+	0.480858i
$320$		0			0
$321$	6.53753	−	4.74979i	0.364889	−	0.265108i
$322$		0			0
$323$	−11.9491	+	3.88249i	−0.664865	+	0.216028i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−10.7690	+	3.49904i	−0.595524	+	0.193498i
$328$		0			0
$329$	−3.28950	+	2.38996i	−0.181356	+	0.131763i
$330$		0			0
$331$	−26.6188	−	19.3397i	−1.46310	−	1.06301i	−0.982541	−	0.186045i	$-0.940433\pi$
$331$	−26.6188	−	19.3397i	−1.46310	−	1.06301i	−0.480561	−	0.876961i	$-0.659567\pi$
$332$		0			0
$333$	4.37169	−	6.01712i	0.239567	−	0.329736i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	4.94935	+	1.60814i	0.269608	+	0.0876011i	0.440701	−	0.897654i	$-0.354730\pi$
$337$	4.94935	+	1.60814i	0.269608	+	0.0876011i	−0.171093	+	0.985255i	$0.554730\pi$
$338$		0			0
$339$	−1.16456	−	3.58415i	−0.0632503	−	0.194665i
$340$		0			0
$341$	2.75841	−	8.48951i	0.149376	−	0.459733i
$342$		0			0
$343$		−	7.02282i		−	0.379197i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.96493	−	2.70449i	−0.105483	−	0.145185i	0.753012	−	0.658007i	$-0.228600\pi$
$347$	−1.96493	−	2.70449i	−0.105483	−	0.145185i	−0.858495	+	0.512822i	$0.828600\pi$
$348$		0			0
$349$	28.9138			1.54772			0.773859	−	0.633358i	$-0.218324\pi$
$349$	28.9138			1.54772			0.773859	+	0.633358i	$0.218324\pi$
$350$		0			0
$351$	6.12165			0.326749
$352$		0			0
$353$	11.9531	+	16.4521i	0.636201	+	0.875656i	0.998406	−	0.0564426i	$-0.0179758\pi$
$353$	11.9531	+	16.4521i	0.636201	+	0.875656i	−0.362204	+	0.932099i	$0.617976\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	1.32059i		−	0.0698931i
$358$		0			0
$359$	−11.4959	+	35.3806i	−0.606729	+	1.86732i	−0.122289	+	0.992494i	$0.539024\pi$
$359$	−11.4959	+	35.3806i	−0.606729	+	1.86732i	−0.484439	+	0.874825i	$0.660976\pi$
$360$		0			0
$361$	1.43727	+	4.42345i	0.0756456	+	0.232813i
$362$		0			0
$363$	7.28675	+	2.36761i	0.382455	+	0.124267i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.16352	−	2.97782i	0.112935	−	0.155441i	−0.748808	−	0.662787i	$-0.769373\pi$
$367$	2.16352	−	2.97782i	0.112935	−	0.155441i	0.861742	+	0.507346i	$0.169373\pi$
$368$		0			0
$369$	4.63611	+	3.36833i	0.241346	+	0.175348i
$370$		0			0
$371$	0.549653	−	0.399347i	0.0285366	−	0.0207330i
$372$		0			0
$373$	19.3625	−	6.29124i	1.00255	−	0.325748i	0.238666	−	0.971102i	$-0.423290\pi$
$373$	19.3625	−	6.29124i	1.00255	−	0.325748i	0.763884	+	0.645353i	$0.223290\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	46.5595	−	15.1281i	2.39793	−	0.779136i
$378$		0			0
$379$	−5.17476	+	3.75968i	−0.265809	+	0.193122i	−0.712704	−	0.701465i	$-0.752530\pi$
$379$	−5.17476	+	3.75968i	−0.265809	+	0.193122i	0.446895	+	0.894586i	$0.352530\pi$
$380$		0			0
$381$	3.37516	+	2.45220i	0.172915	+	0.125630i
$382$		0			0
$383$	1.45146	−	1.99777i	0.0741663	−	0.102081i	−0.770322	−	0.637655i	$-0.779905\pi$
$383$	1.45146	−	1.99777i	0.0741663	−	0.102081i	0.844488	+	0.535574i	$0.179905\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.95087	−	0.633875i	−0.0991681	−	0.0322217i
$388$		0			0
$389$	−4.50293	−	13.8586i	−0.228307	−	0.702658i	−0.997939	−	0.0641697i	$-0.979560\pi$
$389$	−4.50293	−	13.8586i	−0.228307	−	0.702658i	0.769632	−	0.638488i	$-0.220440\pi$
$390$		0			0
$391$	−5.29521	+	16.2970i	−0.267790	+	0.824174i
$392$		0			0
$393$		−	14.7908i		−	0.746098i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	14.5325	+	20.0023i	0.729365	+	1.00389i	0.999160	+	0.0409675i	$0.0130440\pi$
$397$	14.5325	+	20.0023i	0.729365	+	1.00389i	−0.269795	+	0.962918i	$0.586956\pi$
$398$		0			0
$399$	−2.48594			−0.124453
$400$		0			0
$401$	6.50743			0.324966			0.162483	−	0.986711i	$-0.448050\pi$
$401$	6.50743			0.324966			0.162483	+	0.986711i	$0.448050\pi$
$402$		0			0
$403$	−17.5794	−	24.1959i	−0.875690	−	1.20528i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			13.5891i			0.673587i
$408$		0			0
$409$	−3.41434	+	10.5082i	−0.168828	+	0.519599i	−0.999298	−	0.0374642i	$-0.988072\pi$
$409$	−3.41434	+	10.5082i	−0.168828	+	0.519599i	0.830470	+	0.557063i	$0.188072\pi$
$410$		0			0
$411$	−0.379143	−	1.16688i	−0.0187017	−	0.0575580i
$412$		0			0
$413$	−4.90660	−	1.59425i	−0.241438	−	0.0784479i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.34044	−	7.35049i	0.261523	−	0.359955i
$418$		0			0
$419$	15.0550	+	10.9381i	0.735483	+	0.534360i	0.891293	−	0.453427i	$-0.149799\pi$
$419$	15.0550	+	10.9381i	0.735483	+	0.534360i	−0.155810	+	0.987787i	$0.549799\pi$
$420$		0			0
$421$	11.0426	−	8.02291i	0.538183	−	0.391013i	−0.285227	−	0.958460i	$-0.592069\pi$
$421$	11.0426	−	8.02291i	0.538183	−	0.391013i	0.823410	+	0.567447i	$0.192069\pi$
$422$		0			0
$423$	7.56507	−	2.45804i	0.367826	−	0.119514i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	2.31951	−	0.753654i	0.112249	−	0.0364719i
$428$		0			0
$429$	−9.04870	+	6.57426i	−0.436875	+	0.317408i
$430$		0			0
$431$	−27.6903	−	20.1182i	−1.33379	−	0.969058i	−0.999648	−	0.0265371i	$-0.991552\pi$
$431$	−27.6903	−	20.1182i	−1.33379	−	0.969058i	−0.334146	−	0.942521i	$-0.608448\pi$
$432$		0			0
$433$	−5.30277	+	7.29864i	−0.254835	+	0.350750i	−0.917197	−	0.398434i	$-0.869554\pi$
$433$	−5.30277	+	7.29864i	−0.254835	+	0.350750i	0.662362	+	0.749184i	$0.269554\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	30.6782	+	9.96795i	1.46754	+	0.476832i
$438$		0			0
$439$	−5.87343	−	18.0766i	−0.280324	−	0.862747i	−0.987761	−	0.155972i	$-0.950149\pi$
$439$	−5.87343	−	18.0766i	−0.280324	−	0.862747i	0.707438	−	0.706776i	$-0.249851\pi$
$440$		0			0
$441$	−2.08237	+	6.40889i	−0.0991607	+	0.305185i
$442$		0			0
$443$			1.68124i			0.0798779i	0.999202	+	0.0399390i	$0.0127163\pi$
$443$			1.68124i			0.0798779i	−0.999202	+	0.0399390i	$0.987284\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−1.11736	−	1.53791i	−0.0528493	−	0.0727408i
$448$		0			0
$449$	14.1334			0.666997			0.333499	−	0.942751i	$-0.391771\pi$
$449$	14.1334			0.666997			0.333499	+	0.942751i	$0.391771\pi$
$450$		0			0
$451$	−10.4702			−0.493024
$452$		0			0
$453$	−2.70553	−	3.72384i	−0.127117	−	0.174961i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	24.8188i		−	1.16097i	−0.814269	−	0.580487i	$-0.802862\pi$
$457$		−	24.8188i		−	1.16097i	0.814269	−	0.580487i	$-0.197138\pi$
$458$		0			0
$459$	−0.798335	+	2.45702i	−0.0372631	+	0.114684i
$460$		0			0
$461$	−10.4642	−	32.2054i	−0.487365	−	1.49996i	−0.828526	−	0.559951i	$-0.810820\pi$
$461$	−10.4642	−	32.2054i	−0.487365	−	1.49996i	0.341161	−	0.940005i	$-0.389180\pi$
$462$		0			0
$463$	−2.60378	−	0.846018i	−0.121008	−	0.0393178i	0.247887	−	0.968789i	$-0.420264\pi$
$463$	−2.60378	−	0.846018i	−0.121008	−	0.0393178i	−0.368895	+	0.929471i	$0.620264\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−20.3823	+	28.0538i	−0.943179	+	1.29817i	0.0113121	+	0.999936i	$0.496399\pi$
$467$	−20.3823	+	28.0538i	−0.943179	+	1.29817i	−0.954491	+	0.298239i	$0.903601\pi$
$468$		0			0
$469$	5.92754	+	4.30661i	0.273708	+	0.198861i
$470$		0			0
$471$	−3.20432	+	2.32808i	−0.147647	+	0.107272i
$472$		0			0
$473$	3.56441	−	1.15815i	0.163892	−	0.0532516i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.26407	+	0.410722i	−0.0578779	+	0.0188057i
$478$		0			0
$479$	4.41726	−	3.20933i	0.201830	−	0.146638i	−0.482280	−	0.876017i	$-0.660191\pi$
$479$	4.41726	−	3.20933i	0.201830	−	0.146638i	0.684109	+	0.729379i	$0.260191\pi$
$480$		0			0
$481$	36.8347	+	26.7620i	1.67952	+	1.22024i
$482$		0			0
$483$	−1.99289	+	2.74297i	−0.0906794	+	0.124810i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−22.4471	−	7.29352i	−1.01718	−	0.330501i	−0.247468	−	0.968896i	$-0.579599\pi$
$487$	−22.4471	−	7.29352i	−1.01718	−	0.330501i	−0.769709	+	0.638395i	$0.779599\pi$
$488$		0			0
$489$	−6.48302	−	19.9527i	−0.293172	−	0.902291i
$490$		0			0
$491$	4.07930	−	12.5548i	0.184096	−	0.566590i	−0.815835	−	0.578284i	$-0.803722\pi$
$491$	4.07930	−	12.5548i	0.184096	−	0.566590i	0.999932	+	0.0116942i	$0.00372245\pi$
$492$		0			0
$493$			20.6603i			0.930492i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.61338	−	2.22063i	−0.0723701	−	0.0996089i
$498$		0			0
$499$	−25.5183			−1.14235			−0.571177	−	0.820827i	$-0.693513\pi$
$499$	−25.5183			−1.14235			−0.571177	+	0.820827i	$0.693513\pi$
$500$		0			0
$501$	−18.0373			−0.805848
$502$		0			0
$503$	−17.1563	−	23.6136i	−0.764960	−	1.05288i	−0.996785	−	0.0801193i	$-0.974470\pi$
$503$	−17.1563	−	23.6136i	−0.764960	−	1.05288i	0.231826	−	0.972757i	$-0.425530\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			24.4746i			1.08695i
$508$		0			0
$509$	−8.87540	+	27.3157i	−0.393395	+	1.21075i	0.536809	+	0.843704i	$0.319630\pi$
$509$	−8.87540	+	27.3157i	−0.393395	+	1.21075i	−0.930204	+	0.367042i	$0.880370\pi$
$510$		0			0
$511$	0.549808	+	1.69213i	0.0243221	+	0.0748556i
$512$		0			0
$513$	4.62521	+	1.50282i	0.204208	+	0.0663513i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−8.54251	+	11.7578i	−0.375699	+	0.517105i
$518$		0			0
$519$	20.7088	+	15.0458i	0.909017	+	0.660439i
$520$		0			0
$521$	−27.6502	+	20.0890i	−1.21138	+	0.880116i	−0.995355	−	0.0962724i	$-0.969308\pi$
$521$	−27.6502	+	20.0890i	−1.21138	+	0.880116i	−0.216021	+	0.976389i	$0.569308\pi$
$522$		0			0
$523$	14.3199	−	4.65282i	0.626166	−	0.203454i	0.0212901	−	0.999773i	$-0.493223\pi$
$523$	14.3199	−	4.65282i	0.626166	−	0.203454i	0.604876	+	0.796320i	$0.293223\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	12.0040	−	3.90033i	0.522901	−	0.169901i
$528$		0			0
$529$	16.9847	−	12.3401i	0.738466	−	0.536527i
$530$		0			0
$531$	8.16519	+	5.93236i	0.354339	+	0.257442i
$532$		0			0
$533$	−20.6197	+	28.3806i	−0.893139	+	1.22930i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−8.00630	−	2.60140i	−0.345497	−	0.112259i
$538$		0			0
$539$	−3.80469	−	11.7096i	−0.163879	−	0.504369i
$540$		0			0
$541$	13.5497	−	41.7016i	0.582546	−	1.79289i	−0.0263633	−	0.999652i	$-0.508393\pi$
$541$	13.5497	−	41.7016i	0.582546	−	1.79289i	0.608909	−	0.793240i	$-0.291607\pi$
$542$		0			0
$543$			20.0676i			0.861184i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	6.09587	+	8.39025i	0.260641	+	0.358741i	0.919202	−	0.393786i	$-0.128835\pi$
$547$	6.09587	+	8.39025i	0.260641	+	0.358741i	−0.658562	+	0.752527i	$0.728835\pi$
$548$		0			0
$549$	−4.77116			−0.203628
$550$		0			0
$551$	38.8919			1.65685
$552$		0			0
$553$	0.396601	+	0.545875i	0.0168652	+	0.0232130i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	24.3856i		−	1.03325i	−0.856212	−	0.516625i	$-0.827188\pi$
$557$		−	24.3856i		−	1.03325i	0.856212	−	0.516625i	$-0.172812\pi$
$558$		0			0
$559$	3.88036	−	11.9425i	0.164122	−	0.505114i
$560$		0			0
$561$	−1.45863	−	4.48920i	−0.0615834	−	0.189534i
$562$		0			0
$563$	27.3359	+	8.88197i	1.15207	+	0.374330i	0.821923	−	0.569599i	$-0.192902\pi$
$563$	27.3359	+	8.88197i	1.15207	+	0.374330i	0.330147	+	0.943929i	$0.392902\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.300458	+	0.413545i	−0.0126181	+	0.0173673i
$568$		0			0
$569$	14.1571	+	10.2858i	0.593498	+	0.431202i	0.843565	−	0.537027i	$-0.180453\pi$
$569$	14.1571	+	10.2858i	0.593498	+	0.431202i	−0.250067	+	0.968229i	$0.580453\pi$
$570$		0			0
$571$	15.5117	−	11.2699i	0.649146	−	0.471632i	−0.213834	−	0.976870i	$-0.568595\pi$
$571$	15.5117	−	11.2699i	0.649146	−	0.471632i	0.862980	+	0.505238i	$0.168595\pi$
$572$		0			0
$573$	3.67416	−	1.19381i	0.153490	−	0.0498720i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−8.83072	+	2.86928i	−0.367628	+	0.119450i	−0.487004	−	0.873400i	$-0.661910\pi$
$577$	−8.83072	+	2.86928i	−0.367628	+	0.119450i	0.119377	+	0.992849i	$0.461910\pi$
$578$		0			0
$579$	8.65040	−	6.28489i	0.359498	−	0.261191i
$580$		0			0
$581$	0.377398	+	0.274195i	0.0156571	+	0.0113755i
$582$		0			0
$583$	1.42740	−	1.96464i	0.0591167	−	0.0813672i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−16.8370	−	5.47068i	−0.694938	−	0.225799i	−0.0598141	−	0.998210i	$-0.519051\pi$
$587$	−16.8370	−	5.47068i	−0.694938	−	0.225799i	−0.635123	+	0.772411i	$0.719051\pi$
$588$		0			0
$589$	−7.34216	−	22.5969i	−0.302529	−	0.931087i
$590$		0			0
$591$	−1.28688	+	3.96060i	−0.0529350	+	0.162917i
$592$		0			0
$593$		−	25.8975i		−	1.06348i	−0.846907	−	0.531742i	$-0.821538\pi$
$593$		−	25.8975i		−	1.06348i	0.846907	−	0.531742i	$-0.178462\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	16.2208	+	22.3261i	0.663875	+	0.913745i
$598$		0			0
$599$	−10.0259			−0.409646			−0.204823	−	0.978799i	$-0.565662\pi$
$599$	−10.0259			−0.409646			−0.204823	+	0.978799i	$0.565662\pi$
$600$		0			0
$601$	−1.69846			−0.0692818			−0.0346409	−	0.999400i	$-0.511029\pi$
$601$	−1.69846			−0.0692818			−0.0346409	+	0.999400i	$0.511029\pi$
$602$		0			0
$603$	−8.42500	−	11.5960i	−0.343092	−	0.472226i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	13.3043i		−	0.540005i	−0.962860	−	0.270002i	$-0.912976\pi$
$607$		−	13.3043i		−	0.540005i	0.962860	−	0.270002i	$-0.0870245\pi$
$608$		0			0
$609$	−1.26323	+	3.88781i	−0.0511885	+	0.157542i
$610$		0			0
$611$	15.0473	+	46.3107i	0.608747	+	1.87353i
$612$		0			0
$613$	6.68433	+	2.17187i	0.269977	+	0.0877210i	0.440877	−	0.897567i	$-0.354667\pi$
$613$	6.68433	+	2.17187i	0.269977	+	0.0877210i	−0.170900	+	0.985288i	$0.554667\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.84267	+	8.04174i	−0.235217	+	0.323748i	−0.910266	−	0.414025i	$-0.864123\pi$
$617$	−5.84267	+	8.04174i	−0.235217	+	0.323748i	0.675049	+	0.737773i	$0.264123\pi$
$618$		0			0
$619$	−20.2765	−	14.7317i	−0.814980	−	0.592118i	0.100290	−	0.994958i	$-0.468023\pi$
$619$	−20.2765	−	14.7317i	−0.814980	−	0.592118i	−0.915270	+	0.402840i	$0.868023\pi$
$620$		0			0
$621$	5.36606	−	3.89867i	0.215333	−	0.156448i
$622$		0			0
$623$	−5.72484	+	1.86011i	−0.229361	+	0.0745239i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−8.45069	+	2.74580i	−0.337488	+	0.109656i
$628$		0			0
$629$	−15.5450	+	11.2941i	−0.619821	+	0.450326i
$630$		0			0
$631$	−8.20614	−	5.96211i	−0.326681	−	0.237348i	0.412340	−	0.911030i	$-0.364712\pi$
$631$	−8.20614	−	5.96211i	−0.326681	−	0.237348i	−0.739021	+	0.673682i	$0.764712\pi$
$632$		0			0
$633$	−1.13730	+	1.56536i	−0.0452036	+	0.0622174i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−39.2330	−	12.7476i	−1.55447	−	0.505077i
$638$		0			0
$639$	1.65934	+	5.10692i	0.0656425	+	0.202027i
$640$		0			0
$641$	4.53631	−	13.9613i	0.179174	−	0.551440i	−0.820626	−	0.571466i	$-0.806375\pi$
$641$	4.53631	−	13.9613i	0.179174	−	0.551440i	0.999799	+	0.0200262i	$0.00637497\pi$
$642$		0			0
$643$		−	8.52311i		−	0.336119i	−0.985777	−	0.168059i	$-0.946250\pi$
$643$		−	8.52311i		−	0.336119i	0.985777	−	0.168059i	$-0.0537500\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−22.4796	−	30.9405i	−0.883764	−	1.21640i	−0.975364	−	0.220600i	$-0.929198\pi$
$647$	−22.4796	−	30.9405i	−0.883764	−	1.21640i	0.0916006	−	0.995796i	$-0.470802\pi$
$648$		0			0
$649$	−18.4403			−0.723846
$650$		0			0
$651$	2.49736			0.0978794
$652$		0			0
$653$	−4.93572	−	6.79344i	−0.193150	−	0.265848i	0.701448	−	0.712721i	$-0.252537\pi$
$653$	−4.93572	−	6.79344i	−0.193150	−	0.265848i	−0.894597	+	0.446873i	$0.852537\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	3.48067i		−	0.135794i
$658$		0			0
$659$	14.5953	−	44.9197i	0.568552	−	1.74982i	−0.0886012	−	0.996067i	$-0.528240\pi$
$659$	14.5953	−	44.9197i	0.568552	−	1.74982i	0.657153	−	0.753757i	$-0.271760\pi$
$660$		0			0
$661$	−7.82323	−	24.0774i	−0.304288	−	0.936503i	−0.979942	−	0.199284i	$-0.936138\pi$
$661$	−7.82323	−	24.0774i	−0.304288	−	0.936503i	0.675654	−	0.737219i	$-0.263862\pi$
$662$		0			0
$663$	−15.0410	−	4.88712i	−0.584145	−	0.189800i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	31.1781	−	42.9130i	1.20722	−	1.66160i
$668$		0			0
$669$	−14.8921	−	10.8198i	−0.575763	−	0.418316i
$670$		0			0
$671$	7.05248	−	5.12392i	0.272258	−	0.197807i
$672$		0			0
$673$	−15.0789	+	4.89943i	−0.581248	+	0.188859i	−0.584860	−	0.811135i	$-0.698850\pi$
$673$	−15.0789	+	4.89943i	−0.581248	+	0.188859i	0.00361149	+	0.999993i	$0.498850\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−32.8299	+	10.6671i	−1.26176	+	0.409970i	−0.862120	−	0.506704i	$-0.830864\pi$
$677$	−32.8299	+	10.6671i	−1.26176	+	0.409970i	−0.399637	+	0.916674i	$0.630864\pi$
$678$		0			0
$679$	3.06017	−	2.22334i	0.117439	−	0.0853241i
$680$		0			0
$681$	15.5813	+	11.3205i	0.597078	+	0.433803i
$682$		0			0
$683$	−14.7183	+	20.2580i	−0.563181	+	0.775152i	−0.991727	−	0.128368i	$-0.959026\pi$
$683$	−14.7183	+	20.2580i	−0.563181	+	0.775152i	0.428546	+	0.903520i	$0.359026\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−25.1476	−	8.17094i	−0.959439	−	0.311741i
$688$		0			0
$689$	−2.51430	−	7.73821i	−0.0957870	−	0.294802i
$690$		0			0
$691$	−8.49860	+	26.1560i	−0.323302	+	0.995021i	0.648899	+	0.760874i	$0.275230\pi$
$691$	−8.49860	+	26.1560i	−0.323302	+	0.995021i	−0.972201	+	0.234147i	$0.924770\pi$
$692$		0			0
$693$		−	0.933955i		−	0.0354780i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−8.70196	−	11.9772i	−0.329610	−	0.453670i
$698$		0			0
$699$	15.7608			0.596130
$700$		0			0
$701$	−5.38643			−0.203443			−0.101721	−	0.994813i	$-0.532435\pi$
$701$	−5.38643			−0.203443			−0.101721	+	0.994813i	$0.532435\pi$
$702$		0			0
$703$	21.2606	+	29.2627i	0.801858	+	1.10366i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	6.69440i		−	0.251769i
$708$		0			0
$709$	−6.33013	+	19.4821i	−0.237733	+	0.731667i	0.759014	+	0.651074i	$0.225681\pi$
$709$	−6.33013	+	19.4821i	−0.237733	+	0.731667i	−0.996747	+	0.0805929i	$0.974319\pi$
$710$		0			0
$711$	−0.407899	−	1.25538i	−0.0152974	−	0.0470805i
$712$		0			0
$713$	−30.8191	−	10.0137i	−1.15419	−	0.375018i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	10.7948	−	14.8578i	0.403141	−	0.554875i
$718$		0			0
$719$	−27.6232	−	20.0694i	−1.03017	−	0.748464i	−0.0618291	−	0.998087i	$-0.519693\pi$
$719$	−27.6232	−	20.0694i	−1.03017	−	0.748464i	−0.968343	+	0.249623i	$0.919693\pi$
$720$		0			0
$721$	−4.56148	+	3.31411i	−0.169878	+	0.123424i
$722$		0			0
$723$	−24.0526	+	7.81517i	−0.894526	+	0.290649i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	29.1350	−	9.46652i	1.08056	−	0.351094i	0.285966	−	0.958240i	$-0.407686\pi$
$727$	29.1350	−	9.46652i	1.08056	−	0.351094i	0.794590	+	0.607146i	$0.207686\pi$
$728$		0			0
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	4.28728	+	3.11489i	0.158571	+	0.115208i
$732$		0			0
$733$	−21.7270	+	29.9046i	−0.802505	+	1.10455i	0.189932	+	0.981797i	$0.439173\pi$
$733$	−21.7270	+	29.9046i	−0.802505	+	1.10455i	−0.992437	+	0.122756i	$0.960827\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	24.9068	+	8.09270i	0.917453	+	0.298099i
$738$		0			0
$739$	−10.2391	−	31.5127i	−0.376652	−	1.15922i	−0.942357	−	0.334608i	$-0.891396\pi$
$739$	−10.2391	−	31.5127i	−0.376652	−	1.15922i	0.565706	−	0.824607i	$-0.308604\pi$
$740$		0			0
$741$	−9.19975	+	28.3139i	−0.337961	+	1.04014i
$742$		0			0
$743$		−	18.9855i		−	0.696512i	−0.937400	−	0.348256i	$-0.886774\pi$
$743$		−	18.9855i		−	0.696512i	0.937400	−	0.348256i	$-0.113226\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.536407	−	0.738301i	−0.0196261	−	0.0270130i
$748$		0			0
$749$	−4.13068			−0.150932
$750$		0			0
$751$	−7.10651			−0.259320			−0.129660	−	0.991559i	$-0.541389\pi$
$751$	−7.10651			−0.259320			−0.129660	+	0.991559i	$0.541389\pi$
$752$		0			0
$753$	−10.2449	−	14.1009i	−0.373345	−	0.513866i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	8.77180i		−	0.318817i	−0.987213	−	0.159408i	$-0.949041\pi$
$757$		−	8.77180i		−	0.318817i	0.987213	−	0.159408i	$-0.0509586\pi$
$758$		0			0
$759$	−3.74490	+	11.5256i	−0.135931	+	0.418354i
$760$		0			0
$761$	6.40922	+	19.7255i	0.232334	+	0.715050i	0.997464	+	0.0711744i	$0.0226747\pi$
$761$	6.40922	+	19.7255i	0.232334	+	0.715050i	−0.765130	+	0.643876i	$0.777325\pi$
$762$		0			0
$763$	5.50477	+	1.78861i	0.199286	+	0.0647520i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−36.3158	+	49.9844i	−1.31129	+	1.80483i
$768$		0			0
$769$	−11.0923	−	8.05906i	−0.400000	−	0.290617i	0.369541	−	0.929214i	$-0.379515\pi$
$769$	−11.0923	−	8.05906i	−0.400000	−	0.290617i	−0.769541	+	0.638597i	$0.779515\pi$
$770$		0			0
$771$	23.9606	−	17.4084i	0.862920	−	0.626948i
$772$		0			0
$773$	−25.5597	+	8.30485i	−0.919318	+	0.298705i	−0.730187	−	0.683247i	$-0.760567\pi$
$773$	−25.5597	+	8.30485i	−0.919318	+	0.298705i	−0.189131	+	0.981952i	$0.560567\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−3.61579	+	1.17484i	−0.129716	+	0.0421472i
$778$		0			0
$779$	−22.5465	+	16.3810i	−0.807812	+	0.586910i
$780$		0			0
$781$	−7.93727	−	5.76676i	−0.284018	−	0.206351i
$782$		0			0
$783$	4.70059	−	6.46980i	0.167985	−	0.231212i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−1.38209	−	0.449069i	−0.0492662	−	0.0160076i	0.284280	−	0.958741i	$-0.408245\pi$
$787$	−1.38209	−	0.449069i	−0.0492662	−	0.0160076i	−0.333546	+	0.942734i	$0.608245\pi$
$788$		0			0
$789$	5.17140	+	15.9159i	0.184107	+	0.566623i
$790$		0			0
$791$	−0.595290	+	1.83211i	−0.0211661	+	0.0651424i
$792$		0			0
$793$		−	29.2074i		−	1.03718i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−29.0555	−	39.9915i	−1.02920	−	1.41657i	−0.905547	−	0.424247i	$-0.860539\pi$
$797$	−29.0555	−	39.9915i	−1.02920	−	1.41657i	−0.123653	−	0.992325i	$-0.539461\pi$
$798$		0			0
$799$	−20.5499			−0.727003
$800$		0			0
$801$	11.7758			0.416078
$802$		0			0
$803$	3.73802	+	5.14494i	0.131912	+	0.181561i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	12.7897i		−	0.450218i
$808$		0			0
$809$	13.2003	−	40.6264i	0.464099	−	1.42835i	−0.396014	−	0.918244i	$-0.629607\pi$
$809$	13.2003	−	40.6264i	0.464099	−	1.42835i	0.860113	−	0.510104i	$-0.170393\pi$
$810$		0			0
$811$	−10.7851	−	33.1931i	−0.378715	−	1.16557i	−0.940938	−	0.338580i	$-0.890054\pi$
$811$	−10.7851	−	33.1931i	−0.378715	−	1.16557i	0.562222	−	0.826986i	$-0.309946\pi$
$812$		0			0
$813$	−27.2690	−	8.86025i	−0.956367	−	0.310743i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	5.86361	−	8.07057i	0.205142	−	0.282354i
$818$		0			0
$819$	−2.53158	−	1.83930i	−0.0884605	−	0.0642703i
$820$		0			0
$821$	0.210535	−	0.152962i	0.00734771	−	0.00533843i	−0.584105	−	0.811678i	$-0.698555\pi$
$821$	0.210535	−	0.152962i	0.00734771	−	0.00533843i	0.591453	+	0.806339i	$0.298555\pi$
$822$		0			0
$823$	−21.9788	+	7.14135i	−0.766133	+	0.248932i	−0.665909	−	0.746033i	$-0.731956\pi$
$823$	−21.9788	+	7.14135i	−0.766133	+	0.248932i	−0.100224	+	0.994965i	$0.531956\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.05965	+	1.96890i	−0.210715	+	0.0684654i	−0.412472	−	0.910970i	$-0.635335\pi$
$827$	−6.05965	+	1.96890i	−0.210715	+	0.0684654i	0.201758	+	0.979435i	$0.435335\pi$
$828$		0			0
$829$	−20.3689	+	14.7989i	−0.707442	+	0.513987i	−0.882347	−	0.470599i	$-0.844038\pi$
$829$	−20.3689	+	14.7989i	−0.707442	+	0.513987i	0.174905	+	0.984585i	$0.444038\pi$
$830$		0			0
$831$	−4.31799	−	3.13720i	−0.149789	−	0.108828i
$832$		0			0
$833$	10.2329	−	14.0844i	0.354548	−	0.487994i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−4.64646	−	1.50973i	−0.160605	−	0.0521838i
$838$		0			0
$839$	12.5553	+	38.6411i	0.433455	+	1.33404i	0.894661	+	0.446745i	$0.147417\pi$
$839$	12.5553	+	38.6411i	0.433455	+	1.33404i	−0.461206	+	0.887293i	$0.652583\pi$
$840$		0			0
$841$	10.8013	−	33.2431i	0.372460	−	1.14631i
$842$		0			0
$843$			6.42725i			0.221366i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−2.30203	−	3.16848i	−0.0790988	−	0.108870i
$848$		0			0
$849$	10.4636			0.359111
$850$		0			0
$851$	49.3320			1.69108
$852$		0			0
$853$	15.3618	+	21.1437i	0.525979	+	0.723947i	0.986511	−	0.163696i	$-0.0523415\pi$
$853$	15.3618	+	21.1437i	0.525979	+	0.723947i	−0.460532	+	0.887643i	$0.652341\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			30.0649i			1.02700i	0.858091	+	0.513498i	$0.171651\pi$
$857$			30.0649i			1.02700i	−0.858091	+	0.513498i	$0.828349\pi$
$858$		0			0
$859$	−3.09348	+	9.52077i	−0.105548	+	0.324844i	−0.989859	−	0.142055i	$-0.954629\pi$
$859$	−3.09348	+	9.52077i	−0.105548	+	0.324844i	0.884310	+	0.466899i	$0.154629\pi$
$860$		0			0
$861$	−0.905199	−	2.78591i	−0.0308491	−	0.0949437i
$862$		0			0
$863$	−11.8765	−	3.85892i	−0.404282	−	0.131359i	0.0998156	−	0.995006i	$-0.468175\pi$
$863$	−11.8765	−	3.85892i	−0.404282	−	0.131359i	−0.504097	+	0.863647i	$0.668175\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−6.06930	+	8.35367i	−0.206124	+	0.283705i
$868$		0			0
$869$	1.95114	+	1.41758i	0.0661878	+	0.0480882i
$870$		0			0
$871$	70.9867	−	51.5749i	2.40529	−	1.74755i
$872$		0			0
$873$	−7.03767	+	2.28668i	−0.238189	+	0.0773923i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−33.4142	+	10.8569i	−1.12832	+	0.366612i	−0.812936	−	0.582353i	$-0.802132\pi$
$877$	−33.4142	+	10.8569i	−1.12832	+	0.366612i	−0.315381	+	0.948965i	$0.602132\pi$
$878$		0			0
$879$	3.75191	−	2.72592i	0.126549	−	0.0919430i
$880$		0			0
$881$	5.56613	+	4.04403i	0.187528	+	0.136247i	0.677588	−	0.735442i	$-0.263025\pi$
$881$	5.56613	+	4.04403i	0.187528	+	0.136247i	−0.490060	+	0.871688i	$0.663025\pi$
$882$		0			0
$883$	11.0141	−	15.1596i	0.370654	−	0.510161i	−0.582424	−	0.812885i	$-0.697896\pi$
$883$	11.0141	−	15.1596i	0.370654	−	0.510161i	0.953078	+	0.302723i	$0.0978958\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	28.3346	+	9.20647i	0.951383	+	0.309123i	0.743277	−	0.668983i	$-0.233270\pi$
$887$	28.3346	+	9.20647i	0.951383	+	0.309123i	0.208106	+	0.978106i	$0.433270\pi$
$888$		0			0
$889$	−0.659000	−	2.02819i	−0.0221021	−	0.0680234i
$890$		0			0
$891$	−0.564602	+	1.73767i	−0.0189149	+	0.0582140i
$892$		0			0
$893$			38.6841i			1.29451i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	23.8663	+	32.8491i	0.796872	+	1.09680i
$898$		0			0
$899$	−39.0705			−1.30308
$900$		0			0
$901$	3.43375			0.114395
$902$		0			0
$903$	0.616319	+	0.848290i	0.0205098	+	0.0282293i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	14.5112i		−	0.481838i	−0.970545	−	0.240919i	$-0.922551\pi$
$907$		−	14.5112i		−	0.481838i	0.970545	−	0.240919i	$-0.0774488\pi$
$908$		0			0
$909$	−4.04695	+	12.4552i	−0.134229	+	0.413114i
$910$		0			0
$911$	10.4651	+	32.2084i	0.346726	+	1.06711i	0.960653	+	0.277750i	$0.0895886\pi$
$911$	10.4651	+	32.2084i	0.346726	+	1.06711i	−0.613928	+	0.789362i	$0.710411\pi$
$912$		0			0
$913$	1.58578	+	0.515250i	0.0524816	+	0.0170523i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.44402	+	6.11668i	−0.146755	+	0.201990i
$918$		0			0
$919$	−25.5931	−	18.5945i	−0.844239	−	0.613376i	0.0793122	−	0.996850i	$-0.474728\pi$
$919$	−25.5931	−	18.5945i	−0.844239	−	0.613376i	−0.923552	+	0.383474i	$0.874728\pi$
$920$		0			0
$921$	−14.2116	+	10.3253i	−0.468286	+	0.340230i
$922$		0			0
$923$	−31.2628	+	10.1579i	−1.02903	+	0.334351i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	10.4903	−	3.40851i	0.344547	−	0.111950i
$928$		0			0
$929$	35.8848	−	26.0718i	1.17734	−	0.855389i	0.185472	−	0.982649i	$-0.440618\pi$
$929$	35.8848	−	26.0718i	1.17734	−	0.855389i	0.991869	+	0.127261i	$0.0406185\pi$
$930$		0			0
$931$	−26.5130	−	19.2629i	−0.868930	−	0.631315i
$932$		0			0
$933$	−10.7946	+	14.8575i	−0.353400	+	0.486413i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−25.0081	−	8.12561i	−0.816978	−	0.265452i	−0.129427	−	0.991589i	$-0.541314\pi$
$937$	−25.0081	−	8.12561i	−0.816978	−	0.265452i	−0.687550	+	0.726137i	$0.741314\pi$
$938$		0			0
$939$	7.83472	+	24.1128i	0.255676	+	0.786891i
$940$		0			0
$941$	4.60549	−	14.1742i	0.150135	−	0.462067i	−0.847501	−	0.530794i	$-0.821894\pi$
$941$	4.60549	−	14.1742i	0.150135	−	0.462067i	0.997636	+	0.0687270i	$0.0218937\pi$
$942$		0			0
$943$			38.0097i			1.23776i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.20300	−	8.53769i	−0.201570	−	0.277438i	0.696250	−	0.717799i	$-0.254850\pi$
$947$	−6.20300	−	8.53769i	−0.201570	−	0.277438i	−0.897821	+	0.440361i	$0.854850\pi$
$948$		0			0
$949$	21.3074			0.691668
$950$		0			0
$951$	−23.6513			−0.766946
$952$		0			0
$953$	−15.7788	−	21.7177i	−0.511126	−	0.703504i	0.472983	−	0.881071i	$-0.343177\pi$
$953$	−15.7788	−	21.7177i	−0.511126	−	0.703504i	−0.984109	+	0.177568i	$0.943177\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			14.6115i			0.472321i
$958$		0			0
$959$	−0.193806	+	0.596475i	−0.00625834	+	0.0192612i
$960$		0			0
$961$	−2.20364	−	6.78209i	−0.0710850	−	0.218777i
$962$		0			0
$963$	7.68533	+	2.49711i	0.247656	+	0.0804684i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	29.7228	−	40.9100i	0.955822	−	1.31558i	0.00692933	−	0.999976i	$-0.497794\pi$
$967$	29.7228	−	40.9100i	0.955822	−	1.31558i	0.948892	−	0.315600i	$-0.102206\pi$
$968$		0			0
$969$	−10.1645	−	7.38494i	−0.326531	−	0.237238i
$970$		0			0
$971$	−21.3040	+	15.4782i	−0.683676	+	0.496720i	−0.874575	−	0.484890i	$-0.838860\pi$
$971$	−21.3040	+	15.4782i	−0.683676	+	0.496720i	0.190899	+	0.981610i	$0.438860\pi$
$972$		0			0
$973$	−4.41703	+	1.43518i	−0.141604	+	0.0460098i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.05744	−	1.96818i	0.193795	−	0.0629677i	−0.210512	−	0.977591i	$-0.567513\pi$
$977$	6.05744	−	1.96818i	0.193795	−	0.0629677i	0.404306	+	0.914624i	$0.367513\pi$
$978$		0			0
$979$	−17.4064	+	12.6465i	−0.556311	+	0.404184i
$980$		0			0
$981$	−9.16062	−	6.65558i	−0.292476	−	0.212496i
$982$		0			0
$983$	33.4030	−	45.9752i	1.06539	−	1.46638i	0.190731	−	0.981642i	$-0.438914\pi$
$983$	33.4030	−	45.9752i	1.06539	−	1.46638i	0.874658	−	0.484740i	$-0.161086\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−3.86704	−	1.25648i	−0.123089	−	0.0399941i
$988$		0			0
$989$	−4.20438	−	12.9397i	−0.133691	−	0.411460i
$990$		0			0
$991$	4.11746	−	12.6722i	0.130795	−	0.402547i	−0.864117	−	0.503291i	$-0.832122\pi$
$991$	4.11746	−	12.6722i	0.130795	−	0.402547i	0.994912	+	0.100744i	$0.0321224\pi$
$992$		0			0
$993$		−	32.9027i		−	1.04413i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−15.0437	−	20.7058i	−0.476438	−	0.655761i	0.501378	−	0.865229i	$-0.332827\pi$
$997$	−15.0437	−	20.7058i	−0.476438	−	0.655761i	−0.977815	+	0.209468i	$0.932827\pi$
$998$		0			0
$999$	7.43757			0.235314

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.o.a.349.3		16
5.2	odd	4		1500.2.m.b.901.2		8
5.3	odd	4		300.2.m.a.181.1	yes	8
5.4	even	2	inner	1500.2.o.a.349.2		16
15.8	even	4		900.2.n.a.181.2		8
25.2	odd	20		7500.2.a.d.1.3		4
25.3	odd	20		300.2.m.a.121.1	✓	8
25.4	even	10	inner	1500.2.o.a.649.4		16
25.11	even	5		7500.2.d.d.1249.2		8
25.14	even	10		7500.2.d.d.1249.7		8
25.21	even	5	inner	1500.2.o.a.649.1		16
25.22	odd	20		1500.2.m.b.601.2		8
25.23	odd	20		7500.2.a.g.1.2		4
75.53	even	20		900.2.n.a.721.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.a.121.1	✓	8	25.3	odd	20
300.2.m.a.181.1	yes	8	5.3	odd	4
900.2.n.a.181.2		8	15.8	even	4
900.2.n.a.721.2		8	75.53	even	20
1500.2.m.b.601.2		8	25.22	odd	20
1500.2.m.b.901.2		8	5.2	odd	4
1500.2.o.a.349.2		16	5.4	even	2	inner
1500.2.o.a.349.3		16	1.1	even	1	trivial
1500.2.o.a.649.1		16	25.21	even	5	inner
1500.2.o.a.649.4		16	25.4	even	10	inner
7500.2.a.d.1.3		4	25.2	odd	20
7500.2.a.g.1.2		4	25.23	odd	20
7500.2.d.d.1249.2		8	25.11	even	5
7500.2.d.d.1249.7		8	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)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{3} -0.511170i q^{7} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{3} -0.511170i q^{7} +(-0.309017 + 0.951057i) q^{9} +(-0.564602 - 1.73767i) q^{11} +(-5.82203 - 1.89169i) q^{13} +(1.51852 - 2.09007i) q^{17} +(-3.93444 - 2.85854i) q^{19} +(0.413545 - 0.300458i) q^{21} +(-6.30818 + 2.04965i) q^{23} +(-0.951057 + 0.309017i) q^{27} +(-6.46980 + 4.70059i) q^{29} +(3.95252 + 2.87167i) q^{31} +(1.07394 - 1.47815i) q^{33} +(-7.07355 - 2.29833i) q^{37} +(-1.89169 - 5.82203i) q^{39} +(1.77084 - 5.45007i) q^{41} +2.05126i q^{43} +(-4.67547 - 6.43523i) q^{47} +6.73870 q^{49} +2.58347 q^{51} +(0.781240 + 1.07528i) q^{53} -4.86324i q^{57} +(3.11882 - 9.59875i) q^{59} +(1.47437 + 4.53764i) q^{61} +(0.486152 + 0.157960i) q^{63} +(-8.42500 + 11.5960i) q^{67} +(-5.36606 - 3.89867i) q^{69} +(4.34421 - 3.15625i) q^{71} +(-3.31031 + 1.07559i) q^{73} +(-0.888244 + 0.288608i) q^{77} +(-1.06789 + 0.775869i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-0.536407 + 0.738301i) q^{83} +(-7.60571 - 2.47124i) q^{87} +(-3.63893 - 11.1995i) q^{89} +(-0.966977 + 2.97605i) q^{91} +4.88558i q^{93} +(4.34952 + 5.98660i) q^{97} +1.82709 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^9	\( 16 q + 4 q^{9} - 4 q^{11} - 10 q^{19} - 6 q^{21} - 54 q^{29} - 6 q^{31} + 40 q^{41} + 16 q^{49} - 16 q^{51} - 4 q^{59} - 28 q^{61} - 4 q^{69} - 30 q^{71} - 48 q^{79} - 4 q^{81} + 10 q^{91} + 4 q^{99}+O(q^{100}) \) 16 * q + 4 * q^9 - 4 * q^11 - 10 * q^19 - 6 * q^21 - 54 * q^29 - 6 * q^31 + 40 * q^41 + 16 * q^49 - 16 * q^51 - 4 * q^59 - 28 * q^61 - 4 * q^69 - 30 * q^71 - 48 * q^79 - 4 * q^81 + 10 * q^91 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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