LMFDB - Embedded newform 1960.2.q.x.961.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1960,2,Mod(361,1960)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1960, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1960.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1960 = 2^{3} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1960.q (of order $3$, degree $2$, 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:	$15.6506787962$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.21913473024.16
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 11x^{6} - 2x^{5} + 51x^{4} + 162x^{2} + 112x + 196 $ x^8 - 2x^7 + 11x^6 - 2x^5 + 51x^4 + 162x^2 + 112x + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.4
Root			$-0.939980 - 1.62809i$ of defining polynomial
Character	$\chi$	$=$	1960.961
Dual form			1960.2.q.x.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939980 + 1.62809i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.267126 + 0.462676i) q^{9} +O(q^{10})$	\(q+(0.939980 + 1.62809i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.267126 + 0.462676i) q^{9} +(1.64709 + 2.85284i) q^{11} +4.19292 q^{13} -1.87996 q^{15} +(0.718686 + 1.24480i) q^{17} +(-0.622226 + 1.07773i) q^{19} +(0.136414 - 0.236276i) q^{23} +(-0.500000 - 0.866025i) q^{25} +4.63551 q^{27} -2.36268 q^{29} +(1.86359 + 3.22783i) q^{31} +(-3.09646 + 5.36323i) q^{33} +(-0.0848805 + 0.147017i) q^{37} +(3.94126 + 6.82647i) q^{39} +11.6630 q^{41} -10.1458 q^{43} +(-0.267126 - 0.462676i) q^{45} +(-1.56221 + 2.70582i) q^{47} +(-1.35110 + 2.34018i) q^{51} +(-4.62351 - 8.00815i) q^{53} -3.29417 q^{55} -2.33952 q^{57} +(-4.53553 - 7.85578i) q^{59} +(-3.63551 + 6.29689i) q^{61} +(-2.09646 + 3.63117i) q^{65} +(6.57197 + 11.3830i) q^{67} +0.512907 q^{69} +6.87474 q^{71} +(7.62479 + 13.2065i) q^{73} +(0.939980 - 1.62809i) q^{75} +(-7.47551 + 12.9480i) q^{79} +(5.15867 + 8.93507i) q^{81} +0.167199 q^{83} -1.43737 q^{85} +(-2.22087 - 3.84666i) q^{87} +(-1.54935 + 2.68355i) q^{89} +(-3.50347 + 6.06819i) q^{93} +(-0.622226 - 1.07773i) q^{95} +6.60894 q^{97} -1.75992 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 4 q^{5} - 6 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 - 4 * q^5 - 6 * q^9	$ 8 q - 2 q^{3} - 4 q^{5} - 6 q^{9} - 2 q^{11} + 20 q^{13} + 4 q^{15} - 6 q^{17} + 4 q^{23} - 4 q^{25} + 28 q^{27} - 4 q^{29} + 12 q^{31} - 18 q^{33} - 14 q^{39} + 24 q^{41} - 16 q^{43} - 6 q^{45} + 2 q^{47} - 2 q^{51} + 4 q^{53} + 4 q^{55} - 16 q^{57} - 8 q^{59} - 20 q^{61} - 10 q^{65} + 8 q^{67} + 48 q^{69} + 8 q^{71} - 16 q^{73} - 2 q^{75} - 22 q^{79} + 20 q^{81} + 72 q^{83} + 12 q^{85} + 18 q^{87} - 40 q^{89} + 32 q^{93} + 52 q^{97} + 24 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 - 4 * q^5 - 6 * q^9 - 2 * q^11 + 20 * q^13 + 4 * q^15 - 6 * q^17 + 4 * q^23 - 4 * q^25 + 28 * q^27 - 4 * q^29 + 12 * q^31 - 18 * q^33 - 14 * q^39 + 24 * q^41 - 16 * q^43 - 6 * q^45 + 2 * q^47 - 2 * q^51 + 4 * q^53 + 4 * q^55 - 16 * q^57 - 8 * q^59 - 20 * q^61 - 10 * q^65 + 8 * q^67 + 48 * q^69 + 8 * q^71 - 16 * q^73 - 2 * q^75 - 22 * q^79 + 20 * q^81 + 72 * q^83 + 12 * q^85 + 18 * q^87 - 40 * q^89 + 32 * q^93 + 52 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	0.939980	+	1.62809i	0.542698	+	0.939980i	0.998748	+	0.0500262i	$0.0159305\pi$
$3$	0.939980	+	1.62809i	0.542698	+	0.939980i	−0.456050	+	0.889954i	$0.650736\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.267126	+	0.462676i	−0.0890421	+	0.154225i
$10$		0			0
$11$	1.64709	+	2.85284i	0.496615	+	0.860163i	0.999992	−	0.00390371i	$-0.00124259\pi$
$11$	1.64709	+	2.85284i	0.496615	+	0.860163i	−0.503377	+	0.864067i	$0.667909\pi$
$12$		0			0
$13$	4.19292			1.16291			0.581453	−	0.813580i	$-0.302484\pi$
$13$	4.19292			1.16291			0.581453	+	0.813580i	$0.302484\pi$
$14$		0			0
$15$	−1.87996			−0.485404
$16$		0			0
$17$	0.718686	+	1.24480i	0.174307	+	0.301908i	0.939921	−	0.341392i	$-0.110898\pi$
$17$	0.718686	+	1.24480i	0.174307	+	0.301908i	−0.765614	+	0.643300i	$0.777565\pi$
$18$		0			0
$19$	−0.622226	+	1.07773i	−0.142748	+	0.247248i	−0.928531	−	0.371256i	$-0.878927\pi$
$19$	−0.622226	+	1.07773i	−0.142748	+	0.247248i	0.785782	+	0.618503i	$0.212261\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.136414	−	0.236276i	0.0284443	−	0.0492670i	−0.851453	−	0.524431i	$-0.824278\pi$
$23$	0.136414	−	0.236276i	0.0284443	−	0.0492670i	0.879897	+	0.475164i	$0.157611\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	4.63551			0.892104
$28$		0			0
$29$	−2.36268			−0.438739			−0.219369	−	0.975642i	$-0.570400\pi$
$29$	−2.36268			−0.438739			−0.219369	+	0.975642i	$0.570400\pi$
$30$		0			0
$31$	1.86359	+	3.22783i	0.334710	+	0.579735i	0.983429	−	0.181293i	$-0.0580283\pi$
$31$	1.86359	+	3.22783i	0.334710	+	0.579735i	−0.648719	+	0.761028i	$0.724695\pi$
$32$		0			0
$33$	−3.09646	+	5.36323i	−0.539024	+	0.933618i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.0848805	+	0.147017i	−0.0139543	+	0.0241695i	−0.872918	−	0.487867i	$-0.837775\pi$
$37$	−0.0848805	+	0.147017i	−0.0139543	+	0.0241695i	0.858964	+	0.512036i	$0.171109\pi$
$38$		0			0
$39$	3.94126	+	6.82647i	0.631107	+	1.09311i
$40$		0			0
$41$	11.6630			1.82146			0.910730	−	0.413001i	$-0.135520\pi$
$41$	11.6630			1.82146			0.910730	+	0.413001i	$0.135520\pi$
$42$		0			0
$43$	−10.1458			−1.54721			−0.773607	−	0.633666i	$-0.781549\pi$
$43$	−10.1458			−1.54721			−0.773607	+	0.633666i	$0.781549\pi$
$44$		0			0
$45$	−0.267126	−	0.462676i	−0.0398208	−	0.0689717i
$46$		0			0
$47$	−1.56221	+	2.70582i	−0.227871	+	0.394685i	−0.957177	−	0.289503i	$-0.906510\pi$
$47$	−1.56221	+	2.70582i	−0.227871	+	0.394685i	0.729306	+	0.684188i	$0.239843\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.35110	+	2.34018i	−0.189192	+	0.327690i
$52$		0			0
$53$	−4.62351	−	8.00815i	−0.635088	−	1.10000i	−0.986497	−	0.163782i	$-0.947631\pi$
$53$	−4.62351	−	8.00815i	−0.635088	−	1.10000i	0.351409	−	0.936222i	$-0.385703\pi$
$54$		0			0
$55$	−3.29417			−0.444186
$56$		0			0
$57$	−2.33952			−0.309877
$58$		0			0
$59$	−4.53553	−	7.85578i	−0.590476	−	1.02273i	−0.994168	−	0.107840i	$-0.965607\pi$
$59$	−4.53553	−	7.85578i	−0.590476	−	1.02273i	0.403692	−	0.914895i	$-0.367727\pi$
$60$		0			0
$61$	−3.63551	+	6.29689i	−0.465479	+	0.806234i	−0.999223	−	0.0394127i	$-0.987451\pi$
$61$	−3.63551	+	6.29689i	−0.465479	+	0.806234i	0.533744	+	0.845646i	$0.320785\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.09646	+	3.63117i	−0.260034	+	0.450392i
$66$		0			0
$67$	6.57197	+	11.3830i	0.802894	+	1.39065i	0.917703	+	0.397266i	$0.130041\pi$
$67$	6.57197	+	11.3830i	0.802894	+	1.39065i	−0.114809	+	0.993388i	$0.536626\pi$
$68$		0			0
$69$	0.512907			0.0617467
$70$		0			0
$71$	6.87474			0.815882			0.407941	−	0.913008i	$-0.366247\pi$
$71$	6.87474			0.815882			0.407941	+	0.913008i	$0.366247\pi$
$72$		0			0
$73$	7.62479	+	13.2065i	0.892414	+	1.54571i	0.836973	+	0.547244i	$0.184323\pi$
$73$	7.62479	+	13.2065i	0.892414	+	1.54571i	0.0554412	+	0.998462i	$0.482343\pi$
$74$		0			0
$75$	0.939980	−	1.62809i	0.108540	−	0.187996i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−7.47551	+	12.9480i	−0.841061	+	1.45676i	0.0479374	+	0.998850i	$0.484735\pi$
$79$	−7.47551	+	12.9480i	−0.841061	+	1.45676i	−0.888998	+	0.457910i	$0.848598\pi$
$80$		0			0
$81$	5.15867	+	8.93507i	0.573185	+	0.992786i
$82$		0			0
$83$	0.167199			0.0183524			0.00917622	−	0.999958i	$-0.497079\pi$
$83$	0.167199			0.0183524			0.00917622	+	0.999958i	$0.497079\pi$
$84$		0			0
$85$	−1.43737			−0.155905
$86$		0			0
$87$	−2.22087	−	3.84666i	−0.238103	−	0.412406i
$88$		0			0
$89$	−1.54935	+	2.68355i	−0.164230	+	0.284455i	−0.936382	−	0.350983i	$-0.885847\pi$
$89$	−1.54935	+	2.68355i	−0.164230	+	0.284455i	0.772151	+	0.635439i	$0.219181\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−3.50347	+	6.06819i	−0.363293	+	0.629241i
$94$		0			0
$95$	−0.622226	−	1.07773i	−0.0638391	−	0.110573i
$96$		0			0
$97$	6.60894			0.671037			0.335518	−	0.942034i	$-0.391089\pi$
$97$	6.60894			0.671037			0.335518	+	0.942034i	$0.391089\pi$
$98$		0			0
$99$	−1.75992			−0.176879
$100$		0			0
$101$	−9.41859	−	16.3135i	−0.937185	−	1.62325i	−0.770691	−	0.637209i	$-0.780089\pi$
$101$	−9.41859	−	16.3135i	−0.937185	−	1.62325i	−0.166493	−	0.986043i	$-0.553244\pi$
$102$		0			0
$103$	0.733780	−	1.27094i	0.0723014	−	0.125230i	−0.827608	−	0.561306i	$-0.810299\pi$
$103$	0.733780	−	1.27094i	0.0723014	−	0.125230i	0.899910	+	0.436077i	$0.143632\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.78127	+	11.7455i	−0.655570	+	1.13548i	0.326181	+	0.945307i	$0.394238\pi$
$107$	−6.78127	+	11.7455i	−0.655570	+	1.13548i	−0.981751	+	0.190173i	$0.939095\pi$
$108$		0			0
$109$	−7.40701	−	12.8293i	−0.709463	−	1.22883i	−0.965057	−	0.262041i	$-0.915604\pi$
$109$	−7.40701	−	12.8293i	−0.709463	−	1.22883i	0.255594	−	0.966784i	$-0.417729\pi$
$110$		0			0
$111$	−0.319144			−0.0302918
$112$		0			0
$113$	−13.1903			−1.24084			−0.620418	−	0.784271i	$-0.713037\pi$
$113$	−13.1903			−1.24084			−0.620418	+	0.784271i	$0.713037\pi$
$114$		0			0
$115$	0.136414	+	0.236276i	0.0127207	+	0.0220329i
$116$		0			0
$117$	−1.12004	+	1.93996i	−0.103548	+	0.179350i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.0742075	−	0.128531i	0.00674614	−	0.0116847i
$122$		0			0
$123$	10.9630	+	18.9885i	0.988503	+	1.71214i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	6.86118			0.608831			0.304416	−	0.952539i	$-0.401539\pi$
$127$	6.86118			0.608831			0.304416	+	0.952539i	$0.401539\pi$
$128$		0			0
$129$	−9.53682	−	16.5182i	−0.839670	−	1.45435i
$130$		0			0
$131$	0.172854	−	0.299392i	0.0151023	−	0.0261580i	−0.858375	−	0.513022i	$-0.828526\pi$
$131$	0.172854	−	0.299392i	0.0151023	−	0.0261580i	0.873478	+	0.486864i	$0.161859\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.31775	+	4.01447i	−0.199481	+	0.345510i
$136$		0			0
$137$	−5.65685	−	9.79796i	−0.483298	−	0.837096i	0.516518	−	0.856276i	$-0.327228\pi$
$137$	−5.65685	−	9.79796i	−0.483298	−	0.837096i	−0.999816	+	0.0191800i	$0.993894\pi$
$138$		0			0
$139$	2.68885			0.228066			0.114033	−	0.993477i	$-0.463623\pi$
$139$	2.68885			0.228066			0.114033	+	0.993477i	$0.463623\pi$
$140$		0			0
$141$	−5.87377			−0.494661
$142$		0			0
$143$	6.90610	+	11.9617i	0.577517	+	1.00029i
$144$		0			0
$145$	1.18134	−	2.04614i	0.0981049	−	0.169923i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.56700	+	11.3744i	−0.537990	+	0.931826i	0.461022	+	0.887389i	$0.347483\pi$
$149$	−6.56700	+	11.3744i	−0.537990	+	0.931826i	−0.999012	+	0.0444372i	$0.985851\pi$
$150$		0			0
$151$	−1.50570	−	2.60795i	−0.122532	−	0.212232i	0.798233	−	0.602348i	$-0.205768\pi$
$151$	−1.50570	−	2.60795i	−0.122532	−	0.212232i	−0.920766	+	0.390116i	$0.872435\pi$
$152$		0			0
$153$	−0.767920			−0.0620826
$154$		0			0
$155$	−3.72717			−0.299374
$156$		0			0
$157$	−9.73155	−	16.8555i	−0.776662	−	1.34522i	−0.933856	−	0.357650i	$-0.883578\pi$
$157$	−9.73155	−	16.8555i	−0.776662	−	1.34522i	0.157194	−	0.987568i	$-0.449755\pi$
$158$		0			0
$159$	8.69201	−	15.0550i	0.689321	−	1.19394i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−6.74611	+	11.6846i	−0.528396	+	0.915209i	0.471056	+	0.882103i	$0.343873\pi$
$163$	−6.74611	+	11.6846i	−0.528396	+	0.915209i	−0.999452	+	0.0331054i	$0.989460\pi$
$164$		0			0
$165$	−3.09646	−	5.36323i	−0.241059	−	0.417527i
$166$		0			0
$167$	12.3011			0.951889			0.475944	−	0.879475i	$-0.342106\pi$
$167$	12.3011			0.951889			0.475944	+	0.879475i	$0.342106\pi$
$168$		0			0
$169$	4.58057			0.352351
$170$		0			0
$171$	−0.332426	−	0.575779i	−0.0254213	−	0.0440309i
$172$		0			0
$173$	−1.24487	+	2.15619i	−0.0946461	+	0.163932i	−0.909461	−	0.415790i	$-0.863505\pi$
$173$	−1.24487	+	2.15619i	−0.0946461	+	0.163932i	0.814815	+	0.579721i	$0.196839\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.52663	−	14.7685i	0.640900	−	1.11007i
$178$		0			0
$179$	−7.56700	−	13.1064i	−0.565584	−	0.979621i	−0.996995	−	0.0774652i	$-0.975317\pi$
$179$	−7.56700	−	13.1064i	−0.565584	−	0.979621i	0.431411	−	0.902156i	$-0.358016\pi$
$180$		0			0
$181$	11.0637			0.822357			0.411179	−	0.911555i	$-0.365117\pi$
$181$	11.0637			0.822357			0.411179	+	0.911555i	$0.365117\pi$
$182$		0			0
$183$	−13.6692			−1.01046
$184$		0			0
$185$	−0.0848805	−	0.147017i	−0.00624054	−	0.0108089i
$186$		0			0
$187$	−2.36748	+	4.10059i	−0.173127	+	0.299865i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.2258	−	19.4437i	0.812274	−	1.40690i	−0.0989957	−	0.995088i	$-0.531563\pi$
$191$	11.2258	−	19.4437i	0.812274	−	1.40690i	0.911269	−	0.411811i	$-0.135104\pi$
$192$		0			0
$193$	−1.55741	−	2.69751i	−0.112105	−	0.194171i	0.804514	−	0.593934i	$-0.202426\pi$
$193$	−1.55741	−	2.69751i	−0.112105	−	0.194171i	−0.916619	+	0.399763i	$0.869093\pi$
$194$		0			0
$195$	−7.88252			−0.564479
$196$		0			0
$197$	1.38765			0.0988659			0.0494330	−	0.998777i	$-0.484259\pi$
$197$	1.38765			0.0988659			0.0494330	+	0.998777i	$0.484259\pi$
$198$		0			0
$199$	0.206732	+	0.358070i	0.0146548	+	0.0253829i	0.873260	−	0.487255i	$-0.162002\pi$
$199$	0.206732	+	0.358070i	0.0146548	+	0.0253829i	−0.858605	+	0.512638i	$0.828668\pi$
$200$		0			0
$201$	−12.3551	+	21.3996i	−0.871458	+	1.50941i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−5.83152	+	10.1005i	−0.407291	+	0.705449i
$206$		0			0
$207$	0.0728797	+	0.126231i	0.00506549	+	0.00877368i
$208$		0			0
$209$	−4.09944			−0.283564
$210$		0			0
$211$	24.6203			1.69493			0.847464	−	0.530853i	$-0.178128\pi$
$211$	24.6203			1.69493			0.847464	+	0.530853i	$0.178128\pi$
$212$		0			0
$213$	6.46212	+	11.1927i	0.442777	+	0.766913i
$214$		0			0
$215$	5.07288	−	8.78649i	0.345968	−	0.599233i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−14.3343	+	24.8277i	−0.968622	+	1.67770i
$220$		0			0
$221$	3.01339	+	5.21935i	0.202703	+	0.351091i
$222$		0			0
$223$	−17.9065			−1.19911			−0.599555	−	0.800334i	$-0.704656\pi$
$223$	−17.9065			−1.19911			−0.599555	+	0.800334i	$0.704656\pi$
$224$		0			0
$225$	0.534253			0.0356168
$226$		0			0
$227$	6.27428	+	10.8674i	0.416439	+	0.721293i	0.995578	−	0.0939352i	$-0.0299447\pi$
$227$	6.27428	+	10.8674i	0.416439	+	0.721293i	−0.579139	+	0.815229i	$0.696611\pi$
$228$		0			0
$229$	7.91768	−	13.7138i	0.523215	−	0.906235i	−0.476420	−	0.879218i	$-0.658066\pi$
$229$	7.91768	−	13.7138i	0.523215	−	0.906235i	0.999635	−	0.0270173i	$-0.00860092\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	11.6896	−	20.2470i	0.765811	−	1.32642i	−0.174005	−	0.984745i	$-0.555671\pi$
$233$	11.6896	−	20.2470i	0.765811	−	1.32642i	0.939817	−	0.341680i	$-0.110996\pi$
$234$		0			0
$235$	−1.56221	−	2.70582i	−0.101907	−	0.176508i
$236$		0			0
$237$	−28.1073			−1.82577
$238$		0			0
$239$	20.9135			1.35278			0.676390	−	0.736544i	$-0.263544\pi$
$239$	20.9135			1.35278			0.676390	+	0.736544i	$0.263544\pi$
$240$		0			0
$241$	1.67873	+	2.90765i	0.108137	+	0.187298i	0.915015	−	0.403419i	$-0.132178\pi$
$241$	1.67873	+	2.90765i	0.108137	+	0.187298i	−0.806879	+	0.590717i	$0.798845\pi$
$242$		0			0
$243$	−2.74483	+	4.75418i	−0.176081	+	0.304981i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.60894	+	4.51882i	−0.166003	+	0.287526i
$248$		0			0
$249$	0.157163	+	0.272215i	0.00995983	+	0.0172509i
$250$		0			0
$251$	16.5717			1.04600			0.522999	−	0.852333i	$-0.324813\pi$
$251$	16.5717			1.04600			0.522999	+	0.852333i	$0.324813\pi$
$252$		0			0
$253$	0.898744			0.0565036
$254$		0			0
$255$	−1.35110	−	2.34018i	−0.0846092	−	0.146547i
$256$		0			0
$257$	−6.57069	+	11.3808i	−0.409869	+	0.709913i	−0.994875	−	0.101116i	$-0.967759\pi$
$257$	−6.57069	+	11.3808i	−0.409869	+	0.709913i	0.585006	+	0.811029i	$0.301092\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.631134	−	1.09316i	0.0390662	−	0.0676647i
$262$		0			0
$263$	1.87740	+	3.25175i	0.115765	+	0.200511i	0.918085	−	0.396383i	$-0.129735\pi$
$263$	1.87740	+	3.25175i	0.115765	+	0.200511i	−0.802320	+	0.596894i	$0.796401\pi$
$264$		0			0
$265$	9.24701			0.568040
$266$		0			0
$267$	−5.82542			−0.356510
$268$		0			0
$269$	−8.24761	−	14.2853i	−0.502866	−	0.870989i	−0.999995	−	0.00331226i	$-0.998946\pi$
$269$	−8.24761	−	14.2853i	−0.502866	−	0.870989i	0.497129	−	0.867677i	$-0.334388\pi$
$270$		0			0
$271$	11.2710	−	19.5220i	0.684665	−	1.18588i	−0.288876	−	0.957366i	$-0.593282\pi$
$271$	11.2710	−	19.5220i	0.684665	−	1.18588i	0.973542	−	0.228509i	$-0.0733850\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.64709	−	2.85284i	0.0993231	−	0.172033i
$276$		0			0
$277$	7.49909	+	12.9888i	0.450577	+	0.780422i	0.998422	−	0.0561578i	$-0.0178850\pi$
$277$	7.49909	+	12.9888i	0.450577	+	0.780422i	−0.547845	+	0.836580i	$0.684552\pi$
$278$		0			0
$279$	−1.99125			−0.119213
$280$		0			0
$281$	−28.0283			−1.67203			−0.836014	−	0.548709i	$-0.815120\pi$
$281$	−28.0283			−1.67203			−0.836014	+	0.548709i	$0.815120\pi$
$282$		0			0
$283$	13.0857	+	22.6652i	0.777866	+	1.34730i	0.933169	+	0.359437i	$0.117031\pi$
$283$	13.0857	+	22.6652i	0.777866	+	1.34730i	−0.155303	+	0.987867i	$0.549635\pi$
$284$		0			0
$285$	1.16976	−	2.02609i	0.0692907	−	0.120015i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.46698	−	12.9332i	0.439234	−	0.760776i
$290$		0			0
$291$	6.21228	+	10.7600i	0.364170	+	0.630761i
$292$		0			0
$293$	15.6061			0.911716			0.455858	−	0.890052i	$-0.349332\pi$
$293$	15.6061			0.911716			0.455858	+	0.890052i	$0.349332\pi$
$294$		0			0
$295$	9.07107			0.528138
$296$		0			0
$297$	7.63509	+	13.2244i	0.443033	+	0.767355i
$298$		0			0
$299$	0.571974	−	0.990688i	0.0330781	−	0.0572929i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	17.7066	−	30.6687i	1.01722	−	1.76187i
$304$		0			0
$305$	−3.63551	−	6.29689i	−0.208169	−	0.360559i
$306$		0			0
$307$	21.3055			1.21597			0.607984	−	0.793949i	$-0.291978\pi$
$307$	21.3055			1.21597			0.607984	+	0.793949i	$0.291978\pi$
$308$		0			0
$309$	2.75895			0.156951
$310$		0			0
$311$	7.43993	+	12.8863i	0.421880	+	0.730717i	0.996123	−	0.0879671i	$-0.0280370\pi$
$311$	7.43993	+	12.8863i	0.421880	+	0.730717i	−0.574243	+	0.818685i	$0.694704\pi$
$312$		0			0
$313$	−1.08137	+	1.87298i	−0.0611224	+	0.105867i	−0.894967	−	0.446132i	$-0.852801\pi$
$313$	−1.08137	+	1.87298i	−0.0611224	+	0.105867i	0.833845	+	0.551999i	$0.186135\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.7297	−	18.5844i	0.602642	−	1.04381i	−0.389777	−	0.920909i	$-0.627448\pi$
$317$	10.7297	−	18.5844i	0.602642	−	1.04381i	0.992419	−	0.122897i	$-0.0392186\pi$
$318$		0			0
$319$	−3.89154	−	6.74034i	−0.217884	−	0.377387i
$320$		0			0
$321$	−25.4970			−1.42311
$322$		0			0
$323$	−1.78874			−0.0995282
$324$		0			0
$325$	−2.09646	−	3.63117i	−0.116291	−	0.201421i
$326$		0			0
$327$	13.9249	−	24.1186i	0.770048	−	1.33376i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	5.83461	−	10.1058i	0.320699	−	0.555468i	−0.659933	−	0.751324i	$-0.729415\pi$
$331$	5.83461	−	10.1058i	0.320699	−	0.555468i	0.980633	+	0.195857i	$0.0627488\pi$
$332$		0			0
$333$	−0.0453476	−	0.0785444i	−0.00248504	−	0.00430421i
$334$		0			0
$335$	−13.1439			−0.718131
$336$		0			0
$337$	17.1403			0.933693			0.466846	−	0.884338i	$-0.345390\pi$
$337$	17.1403			0.933693			0.466846	+	0.884338i	$0.345390\pi$
$338$		0			0
$339$	−12.3986	−	21.4750i	−0.673399	−	1.16636i
$340$		0			0
$341$	−6.13898	+	10.6330i	−0.332444	+	0.575810i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−0.256453	+	0.444190i	−0.0138070	+	0.0239144i
$346$		0			0
$347$	−2.60035	−	4.50394i	−0.139594	−	0.241784i	0.787749	−	0.615996i	$-0.211246\pi$
$347$	−2.60035	−	4.50394i	−0.139594	−	0.241784i	−0.927343	+	0.374212i	$0.877913\pi$
$348$		0			0
$349$	−33.8645			−1.81272			−0.906362	−	0.422501i	$-0.861152\pi$
$349$	−33.8645			−1.81272			−0.906362	+	0.422501i	$0.861152\pi$
$350$		0			0
$351$	19.4363			1.03743
$352$		0			0
$353$	11.6226	+	20.1309i	0.618606	+	1.07146i	0.989740	+	0.142878i	$0.0456357\pi$
$353$	11.6226	+	20.1309i	0.618606	+	1.07146i	−0.371134	+	0.928579i	$0.621031\pi$
$354$		0			0
$355$	−3.43737	+	5.95370i	−0.182437	+	0.315990i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.1421	−	17.5667i	0.535281	−	0.927135i	−0.463868	−	0.885904i	$-0.653539\pi$
$359$	10.1421	−	17.5667i	0.535281	−	0.927135i	0.999150	−	0.0412304i	$-0.0131278\pi$
$360$		0			0
$361$	8.72567	+	15.1133i	0.459246	+	0.795437i
$362$		0			0
$363$	0.279014			0.0146445
$364$		0			0
$365$	−15.2496			−0.798199
$366$		0			0
$367$	6.63690	+	11.4954i	0.346443	+	0.600057i	0.985615	−	0.169007i	$-0.0540560\pi$
$367$	6.63690	+	11.4954i	0.346443	+	0.600057i	−0.639172	+	0.769064i	$0.720723\pi$
$368$		0			0
$369$	−3.11551	+	5.39621i	−0.162187	+	0.280916i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	17.8541	−	30.9243i	0.924453	−	1.60120i	0.132014	−	0.991248i	$-0.457856\pi$
$373$	17.8541	−	30.9243i	0.924453	−	1.60120i	0.792439	−	0.609951i	$-0.208811\pi$
$374$		0			0
$375$	0.939980	+	1.62809i	0.0485404	+	0.0840744i
$376$		0			0
$377$	−9.90652			−0.510212
$378$		0			0
$379$	−12.6878			−0.651728			−0.325864	−	0.945417i	$-0.605655\pi$
$379$	−12.6878			−0.651728			−0.325864	+	0.945417i	$0.605655\pi$
$380$		0			0
$381$	6.44937	+	11.1706i	0.330411	+	0.572289i
$382$		0			0
$383$	−18.2853	+	31.6711i	−0.934337	+	1.61832i	−0.158525	+	0.987355i	$0.550674\pi$
$383$	−18.2853	+	31.6711i	−0.934337	+	1.61832i	−0.775812	+	0.630964i	$0.782660\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.71020	−	4.69420i	0.137767	−	0.238620i
$388$		0			0
$389$	−15.0543	−	26.0748i	−0.763282	−	1.32204i	−0.941150	−	0.337989i	$-0.890253\pi$
$389$	−15.0543	−	26.0748i	−0.763282	−	1.32204i	0.177868	−	0.984054i	$-0.443080\pi$
$390$		0			0
$391$	0.392156			0.0198322
$392$		0			0
$393$	0.649918			0.0327840
$394$		0			0
$395$	−7.47551	−	12.9480i	−0.376134	−	0.651483i
$396$		0			0
$397$	3.73378	−	6.46710i	0.187393	−	0.324574i	−0.756987	−	0.653430i	$-0.773330\pi$
$397$	3.73378	−	6.46710i	0.187393	−	0.324574i	0.944380	+	0.328855i	$0.106663\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.86657	−	10.1612i	0.292963	−	0.507426i	−0.681546	−	0.731775i	$-0.738692\pi$
$401$	5.86657	−	10.1612i	0.292963	−	0.507426i	0.974509	+	0.224349i	$0.0720255\pi$
$402$		0			0
$403$	7.81386	+	13.5340i	0.389236	+	0.674177i
$404$		0			0
$405$	−10.3173			−0.512672
$406$		0			0
$407$	−0.559222			−0.0277196
$408$		0			0
$409$	−8.43006	−	14.6013i	−0.416840	−	0.721987i	0.578780	−	0.815484i	$-0.303529\pi$
$409$	−8.43006	−	14.6013i	−0.416840	−	0.721987i	−0.995620	+	0.0934964i	$0.970196\pi$
$410$		0			0
$411$	10.6347	−	18.4198i	0.524569	−	0.908581i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−0.0835993	+	0.144798i	−0.00410373	+	0.00710787i
$416$		0			0
$417$	2.52747	+	4.37771i	0.123771	+	0.214377i
$418$		0			0
$419$	−10.3884			−0.507507			−0.253753	−	0.967269i	$-0.581665\pi$
$419$	−10.3884			−0.507507			−0.253753	+	0.967269i	$0.581665\pi$
$420$		0			0
$421$	13.7758			0.671393			0.335696	−	0.941970i	$-0.391028\pi$
$421$	13.7758			0.671393			0.335696	+	0.941970i	$0.391028\pi$
$422$		0			0
$423$	−0.834613	−	1.44559i	−0.0405803	−	0.0702871i
$424$		0			0
$425$	0.718686	−	1.24480i	0.0348614	−	0.0603817i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−12.9832	+	22.4876i	−0.626835	+	1.08571i
$430$		0			0
$431$	−15.2284	−	26.3764i	−0.733527	−	1.27051i	−0.955367	−	0.295422i	$-0.904540\pi$
$431$	−15.2284	−	26.3764i	−0.733527	−	1.27051i	0.221840	−	0.975083i	$-0.428794\pi$
$432$		0			0
$433$	25.9182			1.24555			0.622774	−	0.782402i	$-0.286006\pi$
$433$	25.9182			1.24555			0.622774	+	0.782402i	$0.286006\pi$
$434$		0			0
$435$	4.44175			0.212965
$436$		0			0
$437$	0.169761	+	0.294035i	0.00812077	+	0.0140656i
$438$		0			0
$439$	13.4707	−	23.3320i	0.642922	−	1.11357i	−0.341855	−	0.939753i	$-0.611055\pi$
$439$	13.4707	−	23.3320i	0.642922	−	1.11357i	0.984777	−	0.173821i	$-0.0556115\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.19292	−	14.1906i	0.389257	−	0.674213i	−0.603093	−	0.797671i	$-0.706065\pi$
$443$	8.19292	−	14.1906i	0.389257	−	0.674213i	0.992350	+	0.123458i	$0.0393984\pi$
$444$		0			0
$445$	−1.54935	−	2.68355i	−0.0734461	−	0.127212i
$446$		0			0
$447$	−24.6914			−1.16786
$448$		0			0
$449$	14.2152			0.670858			0.335429	−	0.942065i	$-0.391119\pi$
$449$	14.2152			0.670858			0.335429	+	0.942065i	$0.391119\pi$
$450$		0			0
$451$	19.2100	+	33.2728i	0.904566	+	1.56675i
$452$		0			0
$453$	2.83066	−	4.90285i	0.132996	−	0.230356i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	7.25464	−	12.5654i	0.339358	−	0.587785i	−0.644954	−	0.764221i	$-0.723124\pi$
$457$	7.25464	−	12.5654i	0.339358	−	0.587785i	0.984312	+	0.176436i	$0.0564569\pi$
$458$		0			0
$459$	3.33147	+	5.77028i	0.155500	+	0.269334i
$460$		0			0
$461$	−17.8933			−0.833374			−0.416687	−	0.909050i	$-0.636809\pi$
$461$	−17.8933			−0.833374			−0.416687	+	0.909050i	$0.636809\pi$
$462$		0			0
$463$	15.2657			0.709457			0.354729	−	0.934969i	$-0.384573\pi$
$463$	15.2657			0.709457			0.354729	+	0.934969i	$0.384573\pi$
$464$		0			0
$465$	−3.50347	−	6.06819i	−0.162469	−	0.281405i
$466$		0			0
$467$	−11.7746	+	20.3942i	−0.544863	+	0.943731i	0.453752	+	0.891128i	$0.350085\pi$
$467$	−11.7746	+	20.3942i	−0.544863	+	0.943731i	−0.998616	+	0.0526029i	$0.983248\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	18.2949	−	31.6877i	0.842986	−	1.46009i
$472$		0			0
$473$	−16.7110	−	28.9442i	−0.768370	−	1.33086i
$474$		0			0
$475$	1.24445			0.0570994
$476$		0			0
$477$	4.94024			0.226198
$478$		0			0
$479$	−2.32933	−	4.03452i	−0.106430	−	0.184342i	0.807892	−	0.589331i	$-0.200609\pi$
$479$	−2.32933	−	4.03452i	−0.106430	−	0.184342i	−0.914322	+	0.404989i	$0.867275\pi$
$480$		0			0
$481$	−0.355897	+	0.616432i	−0.0162275	+	0.0281069i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.30447	+	5.72351i	−0.150048	+	0.259891i
$486$		0			0
$487$	−5.76052	−	9.97751i	−0.261034	−	0.452124i	0.705483	−	0.708727i	$-0.250730\pi$
$487$	−5.76052	−	9.97751i	−0.261034	−	0.452124i	−0.966517	+	0.256603i	$0.917397\pi$
$488$		0			0
$489$	−25.3648			−1.14704
$490$		0			0
$491$	−14.2771			−0.644317			−0.322158	−	0.946686i	$-0.604408\pi$
$491$	−14.2771			−0.644317			−0.322158	+	0.946686i	$0.604408\pi$
$492$		0			0
$493$	−1.69802	−	2.94106i	−0.0764752	−	0.132459i
$494$		0			0
$495$	0.879961	−	1.52414i	0.0395513	−	0.0685049i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−18.4895	+	32.0247i	−0.827703	+	1.43362i	0.0721332	+	0.997395i	$0.477019\pi$
$499$	−18.4895	+	32.0247i	−0.827703	+	1.43362i	−0.899836	+	0.436228i	$0.856314\pi$
$500$		0			0
$501$	11.5628	+	20.0274i	0.516588	+	0.894757i
$502$		0			0
$503$	−8.08985			−0.360709			−0.180354	−	0.983602i	$-0.557724\pi$
$503$	−8.08985			−0.360709			−0.180354	+	0.983602i	$0.557724\pi$
$504$		0			0
$505$	18.8372			0.838243
$506$		0			0
$507$	4.30564	+	7.45760i	0.191220	+	0.331203i
$508$		0			0
$509$	14.0403	−	24.3185i	0.622325	−	1.07790i	−0.366727	−	0.930329i	$-0.619522\pi$
$509$	14.0403	−	24.3185i	0.622325	−	1.07790i	0.989052	−	0.147569i	$-0.0471449\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.88434	+	4.99581i	−0.127347	+	0.220571i
$514$		0			0
$515$	0.733780	+	1.27094i	0.0323342	+	0.0560045i
$516$		0			0
$517$	−10.2924			−0.452658
$518$		0			0
$519$	−4.68063			−0.205457
$520$		0			0
$521$	6.29048	+	10.8954i	0.275591	+	0.477338i	0.970284	−	0.241969i	$-0.0777931\pi$
$521$	6.29048	+	10.8954i	0.275591	+	0.477338i	−0.694693	+	0.719306i	$0.744460\pi$
$522$		0			0
$523$	0.742265	−	1.28564i	0.0324570	−	0.0562172i	−0.849341	−	0.527845i	$-0.823000\pi$
$523$	0.742265	−	1.28564i	0.0324570	−	0.0562172i	0.881798	+	0.471628i	$0.156333\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.67866	+	4.63958i	−0.116684	+	0.202103i
$528$		0			0
$529$	11.4628	+	19.8541i	0.498382	+	0.863223i
$530$		0			0
$531$	4.84624			0.210309
$532$		0			0
$533$	48.9022			2.11819
$534$		0			0
$535$	−6.78127	−	11.7455i	−0.293180	−	0.507802i
$536$		0			0
$537$	14.2257	−	24.6396i	0.613883	−	1.06328i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−9.45673	+	16.3795i	−0.406577	+	0.704211i	−0.994504	−	0.104703i	$-0.966611\pi$
$541$	−9.45673	+	16.3795i	−0.406577	+	0.704211i	0.587927	+	0.808914i	$0.299944\pi$
$542$		0			0
$543$	10.3997	+	18.0127i	0.446292	+	0.773000i
$544$		0			0
$545$	14.8140			0.634563
$546$		0			0
$547$	−17.4403			−0.745693			−0.372846	−	0.927893i	$-0.621618\pi$
$547$	−17.4403			−0.745693			−0.372846	+	0.927893i	$0.621618\pi$
$548$		0			0
$549$	−1.94228	−	3.36413i	−0.0828945	−	0.143577i
$550$		0			0
$551$	1.47012	−	2.54633i	0.0626293	−	0.108477i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	0.159572	−	0.276387i	0.00677346	−	0.0117320i
$556$		0			0
$557$	−9.60532	−	16.6369i	−0.406990	−	0.704928i	0.587560	−	0.809180i	$-0.300088\pi$
$557$	−9.60532	−	16.6369i	−0.406990	−	0.704928i	−0.994551	+	0.104252i	$0.966755\pi$
$558$		0			0
$559$	−42.5403			−1.79926
$560$		0			0
$561$	−8.90152			−0.375823
$562$		0			0
$563$	−16.8976	−	29.2675i	−0.712150	−	1.23348i	−0.964049	−	0.265726i	$-0.914388\pi$
$563$	−16.8976	−	29.2675i	−0.712150	−	1.23348i	0.251899	−	0.967754i	$-0.418945\pi$
$564$		0			0
$565$	6.59513	−	11.4231i	0.277459	−	0.480574i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.31818	+	4.01520i	−0.0971830	+	0.168326i	−0.910518	−	0.413470i	$-0.864317\pi$
$569$	−2.31818	+	4.01520i	−0.0971830	+	0.168326i	0.813335	+	0.581796i	$0.197650\pi$
$570$		0			0
$571$	−21.9341	−	37.9909i	−0.917912	−	1.58987i	−0.802581	−	0.596543i	$-0.796541\pi$
$571$	−21.9341	−	37.9909i	−0.917912	−	1.58987i	−0.115330	−	0.993327i	$-0.536793\pi$
$572$		0			0
$573$	42.2083			1.76328
$574$		0			0
$575$	−0.272828			−0.0113777
$576$		0			0
$577$	−4.63878	−	8.03460i	−0.193115	−	0.334485i	0.753166	−	0.657830i	$-0.228526\pi$
$577$	−4.63878	−	8.03460i	−0.193115	−	0.334485i	−0.946281	+	0.323346i	$0.895192\pi$
$578$		0			0
$579$	2.92787	−	5.07122i	0.121678	−	0.210753i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	15.2306	−	26.3802i	0.630789	−	1.09256i
$584$		0			0
$585$	−1.12004	−	1.93996i	−0.0463079	−	0.0802077i
$586$		0			0
$587$	28.9971			1.19684			0.598420	−	0.801183i	$-0.295796\pi$
$587$	28.9971			1.19684			0.598420	+	0.801183i	$0.295796\pi$
$588$		0			0
$589$	−4.63829			−0.191117
$590$		0			0
$591$	1.30436	+	2.25922i	0.0536543	+	0.0929320i
$592$		0			0
$593$	12.7614	−	22.1034i	0.524047	−	0.907676i	−0.475561	−	0.879683i	$-0.657755\pi$
$593$	12.7614	−	22.1034i	0.524047	−	0.907676i	0.999608	−	0.0279933i	$-0.00891171\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.388647	+	0.673157i	−0.0159063	+	0.0275505i
$598$		0			0
$599$	−15.5182	−	26.8783i	−0.634057	−	1.09822i	−0.986714	−	0.162466i	$-0.948055\pi$
$599$	−15.5182	−	26.8783i	−0.634057	−	1.09822i	0.352657	−	0.935752i	$-0.385278\pi$
$600$		0			0
$601$	3.56479			0.145411			0.0727054	−	0.997353i	$-0.476837\pi$
$601$	3.56479			0.145411			0.0727054	+	0.997353i	$0.476837\pi$
$602$		0			0
$603$	−7.02219			−0.285966
$604$		0			0
$605$	0.0742075	+	0.128531i	0.00301697	+	0.00522554i
$606$		0			0
$607$	3.36310	−	5.82506i	0.136504	−	0.236432i	−0.789667	−	0.613536i	$-0.789747\pi$
$607$	3.36310	−	5.82506i	0.136504	−	0.236432i	0.926171	+	0.377104i	$0.123080\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.55021	+	11.3453i	−0.264993	+	0.458981i
$612$		0			0
$613$	9.87112	+	17.0973i	0.398691	+	0.690553i	0.993565	−	0.113266i	$-0.0361314\pi$
$613$	9.87112	+	17.0973i	0.398691	+	0.690553i	−0.594874	+	0.803819i	$0.702798\pi$
$614$		0			0
$615$	−21.9261			−0.884144
$616$		0			0
$617$	−16.3958			−0.660069			−0.330035	−	0.943969i	$-0.607060\pi$
$617$	−16.3958			−0.660069			−0.330035	+	0.943969i	$0.607060\pi$
$618$		0			0
$619$	−17.7755	−	30.7881i	−0.714458	−	1.23748i	−0.963168	−	0.268900i	$-0.913340\pi$
$619$	−17.7755	−	30.7881i	−0.714458	−	1.23748i	0.248710	−	0.968578i	$-0.419994\pi$
$620$		0			0
$621$	0.632349	−	1.09526i	0.0253753	−	0.0439513i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−3.85340	−	6.67428i	−0.153890	−	0.266545i
$628$		0			0
$629$	−0.244010			−0.00972930
$630$		0			0
$631$	−9.58569			−0.381600			−0.190800	−	0.981629i	$-0.561108\pi$
$631$	−9.58569			−0.381600			−0.190800	+	0.981629i	$0.561108\pi$
$632$		0			0
$633$	23.1426	+	40.0841i	0.919834	+	1.59320i
$634$		0			0
$635$	−3.43059	+	5.94195i	−0.136139	+	0.235799i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−1.83643	+	3.18078i	−0.0726479	+	0.125830i
$640$		0			0
$641$	−9.75727	−	16.9001i	−0.385389	−	0.667513i	0.606434	−	0.795134i	$-0.292599\pi$
$641$	−9.75727	−	16.9001i	−0.385389	−	0.667513i	−0.991823	+	0.127621i	$0.959266\pi$
$642$		0			0
$643$	−18.9895			−0.748872			−0.374436	−	0.927253i	$-0.622164\pi$
$643$	−18.9895			−0.748872			−0.374436	+	0.927253i	$0.622164\pi$
$644$		0			0
$645$	19.0736			0.751023
$646$		0			0
$647$	−20.6285	−	35.7296i	−0.810989	−	1.40467i	−0.912172	−	0.409807i	$-0.865596\pi$
$647$	−20.6285	−	35.7296i	−0.810989	−	1.40467i	0.101183	−	0.994868i	$-0.467737\pi$
$648$		0			0
$649$	14.9408	−	25.8783i	0.586479	−	1.01581i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.87474	−	17.1036i	0.386429	−	0.669314i	−0.605538	−	0.795817i	$-0.707042\pi$
$653$	9.87474	−	17.1036i	0.386429	−	0.669314i	0.991966	+	0.126503i	$0.0403753\pi$
$654$		0			0
$655$	0.172854	+	0.299392i	0.00675397	+	0.0116982i
$656$		0			0
$657$	−8.14713			−0.317850
$658$		0			0
$659$	10.1830			0.396672			0.198336	−	0.980134i	$-0.436446\pi$
$659$	10.1830			0.396672			0.198336	+	0.980134i	$0.436446\pi$
$660$		0			0
$661$	1.39543	+	2.41696i	0.0542759	+	0.0940087i	0.891887	−	0.452259i	$-0.149382\pi$
$661$	1.39543	+	2.41696i	0.0542759	+	0.0940087i	−0.837611	+	0.546267i	$0.816048\pi$
$662$		0			0
$663$	−5.66506	+	9.81217i	−0.220013	+	0.381073i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.322303	+	0.558245i	−0.0124796	+	0.0216153i
$668$		0			0
$669$	−16.8318	−	29.1535i	−0.650754	−	1.12714i
$670$		0			0
$671$	−23.9520			−0.924657
$672$		0			0
$673$	18.2879			0.704947			0.352473	−	0.935822i	$-0.385341\pi$
$673$	18.2879			0.704947			0.352473	+	0.935822i	$0.385341\pi$
$674$		0			0
$675$	−2.31775	−	4.01447i	−0.0892104	−	0.154517i
$676$		0			0
$677$	−12.0261	+	20.8299i	−0.462202	+	0.800558i	−0.999070	−	0.0431084i	$-0.986274\pi$
$677$	−12.0261	+	20.8299i	−0.462202	+	0.800558i	0.536868	+	0.843666i	$0.319607\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−11.7954	+	20.4302i	−0.452001	+	0.782889i
$682$		0			0
$683$	19.1100	+	33.0995i	0.731224	+	1.26652i	0.956360	+	0.292190i	$0.0943839\pi$
$683$	19.1100	+	33.0995i	0.731224	+	1.26652i	−0.225136	+	0.974327i	$0.572283\pi$
$684$		0			0
$685$	11.3137			0.432275
$686$		0			0
$687$	29.7699			1.13579
$688$		0			0
$689$	−19.3860	−	33.5775i	−0.738547	−	1.27920i
$690$		0			0
$691$	−13.2312	+	22.9171i	−0.503337	+	0.871806i	0.496655	+	0.867948i	$0.334561\pi$
$691$	−13.2312	+	22.9171i	−0.503337	+	0.871806i	−0.999993	+	0.00385805i	$0.998772\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.34443	+	2.32862i	−0.0509970	+	0.0883294i
$696$		0			0
$697$	8.38206	+	14.5182i	0.317493	+	0.549914i
$698$		0			0
$699$	43.9520			1.66242
$700$		0			0
$701$	−34.5136			−1.30356			−0.651780	−	0.758408i	$-0.725977\pi$
$701$	−34.5136			−1.30356			−0.651780	+	0.758408i	$0.725977\pi$
$702$		0			0
$703$	−0.105630	−	0.182956i	−0.00398390	−	0.00690032i
$704$		0			0
$705$	2.93689	−	5.08684i	0.110610	−	0.191581i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−3.20450	+	5.55035i	−0.120347	+	0.208448i	−0.919905	−	0.392142i	$-0.871734\pi$
$709$	−3.20450	+	5.55035i	−0.120347	+	0.208448i	0.799557	+	0.600590i	$0.205068\pi$
$710$		0			0
$711$	−3.99381	−	6.91749i	−0.149780	−	0.259426i
$712$		0			0
$713$	1.01688			0.0380824
$714$		0			0
$715$	−13.8122			−0.516547
$716$		0			0
$717$	19.6582	+	34.0491i	0.734151	+	1.27159i
$718$		0			0
$719$	−19.3035	+	33.4347i	−0.719900	+	1.24690i	0.241139	+	0.970491i	$0.422479\pi$
$719$	−19.3035	+	33.4347i	−0.719900	+	1.24690i	−0.961039	+	0.276413i	$0.910854\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−3.15595	+	5.46626i	−0.117371	+	0.203293i
$724$		0			0
$725$	1.18134	+	2.04614i	0.0438739	+	0.0759918i
$726$		0			0
$727$	−22.5280			−0.835516			−0.417758	−	0.908558i	$-0.637184\pi$
$727$	−22.5280			−0.835516			−0.417758	+	0.908558i	$0.637184\pi$
$728$		0			0
$729$	20.6317			0.764136
$730$		0			0
$731$	−7.29161	−	12.6294i	−0.269690	−	0.467117i
$732$		0			0
$733$	3.75075	−	6.49649i	0.138537	−	0.239953i	−0.788406	−	0.615155i	$-0.789093\pi$
$733$	3.75075	−	6.49649i	0.138537	−	0.239953i	0.926943	+	0.375202i	$0.122427\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−21.6492	+	37.4976i	−0.797460	+	1.38124i
$738$		0			0
$739$	−17.5432	−	30.3857i	−0.645336	−	1.11776i	−0.984224	−	0.176928i	$-0.943384\pi$
$739$	−17.5432	−	30.3857i	−0.645336	−	1.11776i	0.338888	−	0.940827i	$-0.389949\pi$
$740$		0			0
$741$	−9.80943			−0.360358
$742$		0			0
$743$	−2.42902			−0.0891122			−0.0445561	−	0.999007i	$-0.514187\pi$
$743$	−2.42902			−0.0891122			−0.0445561	+	0.999007i	$0.514187\pi$
$744$		0			0
$745$	−6.56700	−	11.3744i	−0.240596	−	0.416725i
$746$		0			0
$747$	−0.0446632	+	0.0773589i	−0.00163414	+	0.00283041i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−10.4799	+	18.1517i	−0.382417	+	0.662365i	−0.991407	−	0.130813i	$-0.958241\pi$
$751$	−10.4799	+	18.1517i	−0.382417	+	0.662365i	0.608991	+	0.793177i	$0.291575\pi$
$752$		0			0
$753$	15.5771	+	26.9803i	0.567661	+	0.983218i
$754$		0			0
$755$	3.01140			0.109596
$756$		0			0
$757$	−35.9748			−1.30753			−0.653763	−	0.756699i	$-0.726811\pi$
$757$	−35.9748			−1.30753			−0.653763	+	0.756699i	$0.726811\pi$
$758$		0			0
$759$	0.844802	+	1.46324i	0.0306644	+	0.0531123i
$760$		0			0
$761$	1.22876	−	2.12828i	0.0445426	−	0.0771500i	−0.842895	−	0.538079i	$-0.819150\pi$
$761$	1.22876	−	2.12828i	0.0445426	−	0.0771500i	0.887437	+	0.460929i	$0.152484\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.383960	−	0.665038i	0.0138821	−	0.0240445i
$766$		0			0
$767$	−19.0171	−	32.9386i	−0.686669	−	1.18934i
$768$		0			0
$769$	21.6994			0.782501			0.391250	−	0.920284i	$-0.372043\pi$
$769$	21.6994			0.782501			0.391250	+	0.920284i	$0.372043\pi$
$770$		0			0
$771$	−24.7053			−0.889739
$772$		0			0
$773$	−7.84900	−	13.5949i	−0.282309	−	0.488973i	0.689644	−	0.724149i	$-0.257767\pi$
$773$	−7.84900	−	13.5949i	−0.282309	−	0.488973i	−0.971953	+	0.235175i	$0.924434\pi$
$774$		0			0
$775$	1.86359	−	3.22783i	0.0669420	−	0.115947i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−7.25705	+	12.5696i	−0.260011	+	0.450352i
$780$		0			0
$781$	11.3233	+	19.6125i	0.405180	+	0.701792i
$782$		0			0
$783$	−10.9522			−0.391400
$784$		0			0
$785$	19.4631			0.694668
$786$		0			0
$787$	12.2537	+	21.2240i	0.436797	+	0.756554i	0.997440	−	0.0715029i	$-0.0227795\pi$
$787$	12.2537	+	21.2240i	0.436797	+	0.756554i	−0.560644	+	0.828057i	$0.689446\pi$
$788$		0			0
$789$	−3.52944	+	6.11316i	−0.125651	+	0.217634i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−15.2434	+	26.4023i	−0.541309	+	0.937574i
$794$		0			0
$795$	8.69201	+	15.0550i	0.308274	+	0.533946i
$796$		0			0
$797$	5.73557			0.203164			0.101582	−	0.994827i	$-0.467610\pi$
$797$	5.73557			0.203164			0.101582	+	0.994827i	$0.467610\pi$
$798$		0			0
$799$	−4.49094			−0.158878
$800$		0			0
$801$	−0.827743	−	1.43369i	−0.0292468	−	0.0506570i
$802$		0			0
$803$	−25.1174	+	43.5046i	−0.886373	+	1.53524i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	15.5052	−	26.8558i	0.545808	−	0.945368i
$808$		0			0
$809$	−1.74216	−	3.01750i	−0.0612510	−	0.106090i	0.833774	−	0.552106i	$-0.186176\pi$
$809$	−1.74216	−	3.01750i	−0.0612510	−	0.106090i	−0.895025	+	0.446016i	$0.852842\pi$
$810$		0			0
$811$	25.9953			0.912819			0.456409	−	0.889770i	$-0.349135\pi$
$811$	25.9953			0.912819			0.456409	+	0.889770i	$0.349135\pi$
$812$		0			0
$813$	42.3781			1.48627
$814$		0			0
$815$	−6.74611	−	11.6846i	−0.236306	−	0.409294i
$816$		0			0
$817$	6.31296	−	10.9344i	0.220862	−	0.382545i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	25.2494	−	43.7332i	0.881210	−	1.52630i	0.0312136	−	0.999513i	$-0.490063\pi$
$821$	25.2494	−	43.7332i	0.881210	−	1.52630i	0.849997	−	0.526788i	$-0.176604\pi$
$822$		0			0
$823$	22.4350	+	38.8585i	0.782034	+	1.35452i	0.930755	+	0.365643i	$0.119151\pi$
$823$	22.4350	+	38.8585i	0.782034	+	1.35452i	−0.148722	+	0.988879i	$0.547516\pi$
$824$		0			0
$825$	6.19292			0.215610
$826$		0			0
$827$	−15.7323			−0.547066			−0.273533	−	0.961863i	$-0.588192\pi$
$827$	−15.7323			−0.547066			−0.273533	+	0.961863i	$0.588192\pi$
$828$		0			0
$829$	25.8863	+	44.8364i	0.899068	+	1.55723i	0.828687	+	0.559712i	$0.189088\pi$
$829$	25.8863	+	44.8364i	0.899068	+	1.55723i	0.0703811	+	0.997520i	$0.477578\pi$
$830$		0			0
$831$	−14.0980	+	24.4185i	−0.489054	+	0.847067i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−6.15056	+	10.6531i	−0.212849	+	0.368665i
$836$		0			0
$837$	8.63867	+	14.9626i	0.298596	+	0.517183i
$838$		0			0
$839$	−2.86118			−0.0987788			−0.0493894	−	0.998780i	$-0.515728\pi$
$839$	−2.86118			−0.0987788			−0.0493894	+	0.998780i	$0.515728\pi$
$840$		0			0
$841$	−23.4177			−0.807508
$842$		0			0
$843$	−26.3460	−	45.6327i	−0.907406	−	1.57167i
$844$		0			0
$845$	−2.29028	+	3.96689i	−0.0787882	+	0.136465i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−24.6007	+	42.6096i	−0.844293	+	1.46236i
$850$		0			0
$851$	0.0231578	+	0.0401105i	0.000793840	+	0.00137497i
$852$		0			0
$853$	45.8645			1.57037			0.785185	−	0.619261i	$-0.212568\pi$
$853$	45.8645			1.57037			0.785185	+	0.619261i	$0.212568\pi$
$854$		0			0
$855$	0.664852			0.0227375
$856$		0			0
$857$	11.5751	+	20.0486i	0.395397	+	0.684847i	0.993152	−	0.116832i	$-0.0372738\pi$
$857$	11.5751	+	20.0486i	0.395397	+	0.684847i	−0.597755	+	0.801679i	$0.703940\pi$
$858$		0			0
$859$	4.23192	−	7.32990i	0.144391	−	0.250093i	−0.784754	−	0.619807i	$-0.787211\pi$
$859$	4.23192	−	7.32990i	0.144391	−	0.250093i	0.929146	+	0.369714i	$0.120544\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	17.5462	−	30.3908i	0.597278	−	1.03452i	−0.395943	−	0.918275i	$-0.629582\pi$
$863$	17.5462	−	30.3908i	0.597278	−	1.03452i	0.993221	−	0.116241i	$-0.0370845\pi$
$864$		0			0
$865$	−1.24487	−	2.15619i	−0.0423270	−	0.0733125i
$866$		0			0
$867$	28.0753			0.953486
$868$		0			0
$869$	−49.2513			−1.67074
$870$		0			0
$871$	27.5558	+	47.7280i	0.933691	+	1.61720i
$872$		0			0
$873$	−1.76542	+	3.05780i	−0.0597505	+	0.103491i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−9.66861	+	16.7465i	−0.326486	+	0.565490i	−0.981812	−	0.189856i	$-0.939198\pi$
$877$	−9.66861	+	16.7465i	−0.326486	+	0.565490i	0.655326	+	0.755346i	$0.272531\pi$
$878$		0			0
$879$	14.6694	+	25.4081i	0.494787	+	0.856996i
$880$		0			0
$881$	−33.0573			−1.11373			−0.556865	−	0.830603i	$-0.687996\pi$
$881$	−33.0573			−1.11373			−0.556865	+	0.830603i	$0.687996\pi$
$882$		0			0
$883$	−28.6238			−0.963267			−0.481634	−	0.876373i	$-0.659956\pi$
$883$	−28.6238			−0.963267			−0.481634	+	0.876373i	$0.659956\pi$
$884$		0			0
$885$	8.52663	+	14.7685i	0.286619	+	0.496439i
$886$		0			0
$887$	−9.56444	+	16.5661i	−0.321142	+	0.556235i	−0.980724	−	0.195398i	$-0.937400\pi$
$887$	−9.56444	+	16.5661i	−0.321142	+	0.556235i	0.659582	+	0.751633i	$0.270734\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−16.9935	+	29.4337i	−0.569305	+	0.986066i
$892$		0			0
$893$	−1.94409	−	3.36727i	−0.0650566	−	0.112681i
$894$		0			0
$895$	15.1340			0.505874
$896$		0			0
$897$	2.15058			0.0718057
$898$		0			0
$899$	−4.40306	−	7.62632i	−0.146850	−	0.254352i
$900$		0			0
$901$	6.64570	−	11.5107i	0.221400	−	0.383477i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−5.53184	+	9.58144i	−0.183885	+	0.318498i
$906$		0			0
$907$	25.4891	+	44.1483i	0.846350	+	1.46592i	0.884443	+	0.466648i	$0.154538\pi$
$907$	25.4891	+	44.1483i	0.846350	+	1.46592i	−0.0380931	+	0.999274i	$0.512128\pi$
$908$		0			0
$909$	10.0638			0.333796
$910$		0			0
$911$	−5.52585			−0.183080			−0.0915399	−	0.995801i	$-0.529179\pi$
$911$	−5.52585			−0.183080			−0.0915399	+	0.995801i	$0.529179\pi$
$912$		0			0
$913$	0.275391	+	0.476991i	0.00911410	+	0.0157861i
$914$		0			0
$915$	6.83461	−	11.8379i	0.225945	−	0.391349i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	20.3163	−	35.1889i	0.670173	−	1.16077i	−0.307681	−	0.951489i	$-0.599553\pi$
$919$	20.3163	−	35.1889i	0.670173	−	1.16077i	0.977855	−	0.209285i	$-0.0671136\pi$
$920$		0			0
$921$	20.0267	+	34.6873i	0.659903	+	1.14299i
$922$		0			0
$923$	28.8252			0.948794
$924$		0			0
$925$	0.169761			0.00558171
$926$		0			0
$927$	0.392024	+	0.679005i	0.0128757	+	0.0223015i
$928$		0			0
$929$	7.79395	−	13.4995i	0.255711	−	0.442905i	−0.709377	−	0.704829i	$-0.751024\pi$
$929$	7.79395	−	13.4995i	0.255711	−	0.442905i	0.965088	+	0.261924i	$0.0843570\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−13.9868	+	24.2258i	−0.457907	+	0.793118i
$934$		0			0
$935$	−2.36748	−	4.10059i	−0.0774247	−	0.134104i
$936$		0			0
$937$	−20.4794			−0.669034			−0.334517	−	0.942390i	$-0.608573\pi$
$937$	−20.4794			−0.669034			−0.334517	+	0.942390i	$0.608573\pi$
$938$		0			0
$939$	−4.06585			−0.132684
$940$		0			0
$941$	−8.39362	−	14.5382i	−0.273624	−	0.473931i	0.696163	−	0.717884i	$-0.254889\pi$
$941$	−8.39362	−	14.5382i	−0.273624	−	0.473931i	−0.969787	+	0.243953i	$0.921556\pi$
$942$		0			0
$943$	1.59100	−	2.75570i	0.0518102	−	0.0897380i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.71964	−	2.97850i	0.0558807	−	0.0967883i	−0.836732	−	0.547613i	$-0.815537\pi$
$947$	1.71964	−	2.97850i	0.0558807	−	0.0967883i	0.892613	+	0.450825i	$0.148870\pi$
$948$		0			0
$949$	31.9701	+	55.3739i	1.03779	+	1.79751i
$950$		0			0
$951$	40.3430			1.30821
$952$		0			0
$953$	−30.8610			−0.999686			−0.499843	−	0.866116i	$-0.666609\pi$
$953$	−30.8610			−0.999686			−0.499843	+	0.866116i	$0.666609\pi$
$954$		0			0
$955$	11.2258	+	19.4437i	0.363260	+	0.629184i
$956$		0			0
$957$	7.31594	−	12.6716i	0.236491	−	0.409614i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	8.55410	−	14.8161i	0.275939	−	0.477940i
$962$		0			0
$963$	−3.62291	−	6.27507i	−0.116747	−	0.202211i
$964$		0			0
$965$	3.11482			0.100270
$966$		0			0
$967$	−34.3195			−1.10364			−0.551820	−	0.833964i	$-0.686066\pi$
$967$	−34.3195			−1.10364			−0.551820	+	0.833964i	$0.686066\pi$
$968$		0			0
$969$	−1.68138	−	2.91224i	−0.0540137	−	0.0935545i
$970$		0			0
$971$	−15.8102	+	27.3840i	−0.507373	+	0.878795i	0.492591	+	0.870261i	$0.336050\pi$
$971$	−15.8102	+	27.3840i	−0.507373	+	0.878795i	−0.999964	+	0.00853421i	$0.997283\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	3.94126	−	6.82647i	0.126221	−	0.218622i
$976$		0			0
$977$	9.47268	+	16.4072i	0.303058	+	0.524912i	0.976827	−	0.214030i	$-0.0686591\pi$
$977$	9.47268	+	16.4072i	0.303058	+	0.524912i	−0.673769	+	0.738942i	$0.735326\pi$
$978$		0			0
$979$	−10.2076			−0.326237
$980$		0			0
$981$	7.91443			0.252688
$982$		0			0
$983$	−7.60937	−	13.1798i	−0.242701	−	0.420371i	0.718782	−	0.695236i	$-0.244700\pi$
$983$	−7.60937	−	13.1798i	−0.242701	−	0.420371i	−0.961483	+	0.274865i	$0.911367\pi$
$984$		0			0
$985$	−0.693825	+	1.20174i	−0.0221071	+	0.0382906i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.38403	+	2.39720i	−0.0440095	+	0.0762266i
$990$		0			0
$991$	−15.6534	−	27.1126i	−0.497248	−	0.861259i	0.502747	−	0.864434i	$-0.332323\pi$
$991$	−15.6534	−	27.1126i	−0.497248	−	0.861259i	−0.999995	+	0.00317464i	$0.998989\pi$
$992$		0			0
$993$	21.9377			0.696172
$994$		0			0
$995$	−0.413463			−0.0131077
$996$		0			0
$997$	−20.0527	−	34.7323i	−0.635076	−	1.09998i	−0.986499	−	0.163767i	$-0.947636\pi$
$997$	−20.0527	−	34.7323i	−0.635076	−	1.09998i	0.351424	−	0.936217i	$-0.385698\pi$
$998$		0			0
$999$	−0.393464	+	0.681500i	−0.0124487	+	0.0215617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.x.961.4		8
7.2	even	3		1960.2.a.y.1.1	yes	4
7.3	odd	6		1960.2.q.y.361.1		8
7.4	even	3	inner	1960.2.q.x.361.4		8
7.5	odd	6		1960.2.a.x.1.4	✓	4
7.6	odd	2		1960.2.q.y.961.1		8
28.19	even	6		3920.2.a.ce.1.1		4
28.23	odd	6		3920.2.a.cd.1.4		4
35.9	even	6		9800.2.a.cl.1.4		4
35.19	odd	6		9800.2.a.cs.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.2.a.x.1.4	✓	4	7.5	odd	6
1960.2.a.y.1.1	yes	4	7.2	even	3
1960.2.q.x.361.4		8	7.4	even	3	inner
1960.2.q.x.961.4		8	1.1	even	1	trivial
1960.2.q.y.361.1		8	7.3	odd	6
1960.2.q.y.961.1		8	7.6	odd	2
3920.2.a.cd.1.4		4	28.23	odd	6
3920.2.a.ce.1.1		4	28.19	even	6
9800.2.a.cl.1.4		4	35.9	even	6
9800.2.a.cs.1.1		4	35.19	odd	6

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:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1960.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.939980 + 1.62809i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.267126 + 0.462676i) q^{9} +O(q^{10})\)	\(q+(0.939980 + 1.62809i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.267126 + 0.462676i) q^{9} +(1.64709 + 2.85284i) q^{11} +4.19292 q^{13} -1.87996 q^{15} +(0.718686 + 1.24480i) q^{17} +(-0.622226 + 1.07773i) q^{19} +(0.136414 - 0.236276i) q^{23} +(-0.500000 - 0.866025i) q^{25} +4.63551 q^{27} -2.36268 q^{29} +(1.86359 + 3.22783i) q^{31} +(-3.09646 + 5.36323i) q^{33} +(-0.0848805 + 0.147017i) q^{37} +(3.94126 + 6.82647i) q^{39} +11.6630 q^{41} -10.1458 q^{43} +(-0.267126 - 0.462676i) q^{45} +(-1.56221 + 2.70582i) q^{47} +(-1.35110 + 2.34018i) q^{51} +(-4.62351 - 8.00815i) q^{53} -3.29417 q^{55} -2.33952 q^{57} +(-4.53553 - 7.85578i) q^{59} +(-3.63551 + 6.29689i) q^{61} +(-2.09646 + 3.63117i) q^{65} +(6.57197 + 11.3830i) q^{67} +0.512907 q^{69} +6.87474 q^{71} +(7.62479 + 13.2065i) q^{73} +(0.939980 - 1.62809i) q^{75} +(-7.47551 + 12.9480i) q^{79} +(5.15867 + 8.93507i) q^{81} +0.167199 q^{83} -1.43737 q^{85} +(-2.22087 - 3.84666i) q^{87} +(-1.54935 + 2.68355i) q^{89} +(-3.50347 + 6.06819i) q^{93} +(-0.622226 - 1.07773i) q^{95} +6.60894 q^{97} -1.75992 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 4 q^{5} - 6 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 - 4 * q^5 - 6 * q^9	\( 8 q - 2 q^{3} - 4 q^{5} - 6 q^{9} - 2 q^{11} + 20 q^{13} + 4 q^{15} - 6 q^{17} + 4 q^{23} - 4 q^{25} + 28 q^{27} - 4 q^{29} + 12 q^{31} - 18 q^{33} - 14 q^{39} + 24 q^{41} - 16 q^{43} - 6 q^{45} + 2 q^{47} - 2 q^{51} + 4 q^{53} + 4 q^{55} - 16 q^{57} - 8 q^{59} - 20 q^{61} - 10 q^{65} + 8 q^{67} + 48 q^{69} + 8 q^{71} - 16 q^{73} - 2 q^{75} - 22 q^{79} + 20 q^{81} + 72 q^{83} + 12 q^{85} + 18 q^{87} - 40 q^{89} + 32 q^{93} + 52 q^{97} + 24 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 4 * q^5 - 6 * q^9 - 2 * q^11 + 20 * q^13 + 4 * q^15 - 6 * q^17 + 4 * q^23 - 4 * q^25 + 28 * q^27 - 4 * q^29 + 12 * q^31 - 18 * q^33 - 14 * q^39 + 24 * q^41 - 16 * q^43 - 6 * q^45 + 2 * q^47 - 2 * q^51 + 4 * q^53 + 4 * q^55 - 16 * q^57 - 8 * q^59 - 20 * q^61 - 10 * q^65 + 8 * q^67 + 48 * q^69 + 8 * q^71 - 16 * q^73 - 2 * q^75 - 22 * q^79 + 20 * q^81 + 72 * q^83 + 12 * q^85 + 18 * q^87 - 40 * q^89 + 32 * q^93 + 52 * q^97 + 24 * q^99

Introduction

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