LMFDB - Embedded newform 1960.2.q.y.361.1

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			361.1
Root			$-0.939980 + 1.62809i$ of defining polynomial
Character	$\chi$	$=$	1960.361
Dual form			1960.2.q.y.961.1

$q$-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 $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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	0.456050	+	0.889954i	$0.349264\pi$
$3$	−0.939980	+	1.62809i	−0.542698	+	0.939980i	−0.998748	+	0.0500262i	$0.984070\pi$
$4$		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	−0.503377	−	0.864067i	$-0.667909\pi$
$11$	1.64709	−	2.85284i	0.496615	−	0.860163i	0.999992	+	0.00390371i	$0.00124259\pi$
$12$		0			0
$13$	−4.19292			−1.16291			−0.581453	−	0.813580i	$-0.697516\pi$
$13$	−4.19292			−1.16291			−0.581453	+	0.813580i	$0.697516\pi$
$14$		0			0
$15$	−1.87996			−0.485404
$16$		0			0
$17$	−0.718686	+	1.24480i	−0.174307	+	0.301908i	−0.939921	−	0.341392i	$-0.889102\pi$
$17$	−0.718686	+	1.24480i	−0.174307	+	0.301908i	0.765614	+	0.643300i	$0.222435\pi$
$18$		0			0
$19$	0.622226	+	1.07773i	0.142748	+	0.247248i	0.928531	−	0.371256i	$-0.121073\pi$
$19$	0.622226	+	1.07773i	0.142748	+	0.247248i	−0.785782	+	0.618503i	$0.787739\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.136414	+	0.236276i	0.0284443	+	0.0492670i	0.879897	−	0.475164i	$-0.157611\pi$
$23$	0.136414	+	0.236276i	0.0284443	+	0.0492670i	−0.851453	+	0.524431i	$0.824278\pi$
$24$		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	$-0.941972\pi$
$31$	−1.86359	+	3.22783i	−0.334710	+	0.579735i	0.648719	+	0.761028i	$0.275305\pi$
$32$		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	0.858964	−	0.512036i	$-0.171109\pi$
$37$	−0.0848805	−	0.147017i	−0.0139543	−	0.0241695i	−0.872918	+	0.487867i	$0.837775\pi$
$38$		0			0
$39$	3.94126	−	6.82647i	0.631107	−	1.09311i
$40$		0			0
$41$	−11.6630			−1.82146			−0.910730	−	0.413001i	$-0.864480\pi$
$41$	−11.6630			−1.82146			−0.910730	+	0.413001i	$0.864480\pi$
$42$		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	$-0.0934901\pi$
$47$	1.56221	+	2.70582i	0.227871	+	0.394685i	−0.729306	+	0.684188i	$0.760157\pi$
$48$		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	0.351409	+	0.936222i	$0.385703\pi$
$53$	−4.62351	+	8.00815i	−0.635088	+	1.10000i	−0.986497	+	0.163782i	$0.947631\pi$
$54$		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	−0.403692	−	0.914895i	$-0.632273\pi$
$59$	4.53553	−	7.85578i	0.590476	−	1.02273i	0.994168	−	0.107840i	$-0.0343934\pi$
$60$		0			0
$61$	3.63551	+	6.29689i	0.465479	+	0.806234i	0.999223	−	0.0394127i	$-0.0125487\pi$
$61$	3.63551	+	6.29689i	0.465479	+	0.806234i	−0.533744	+	0.845646i	$0.679215\pi$
$62$		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	−0.114809	−	0.993388i	$-0.536626\pi$
$67$	6.57197	−	11.3830i	0.802894	−	1.39065i	0.917703	−	0.397266i	$-0.130041\pi$
$68$		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	−0.0554412	+	0.998462i	$0.517657\pi$
$73$	−7.62479	+	13.2065i	−0.892414	+	1.54571i	−0.836973	+	0.547244i	$0.815677\pi$
$74$		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	−0.888998	−	0.457910i	$-0.848598\pi$
$79$	−7.47551	−	12.9480i	−0.841061	−	1.45676i	0.0479374	−	0.998850i	$-0.484735\pi$
$80$		0			0
$81$	5.15867	−	8.93507i	0.573185	−	0.992786i
$82$		0			0
$83$	−0.167199			−0.0183524			−0.00917622	−	0.999958i	$-0.502921\pi$
$83$	−0.167199			−0.0183524			−0.00917622	+	0.999958i	$0.502921\pi$
$84$		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	$-0.114153\pi$
$89$	1.54935	+	2.68355i	0.164230	+	0.284455i	−0.772151	+	0.635439i	$0.780819\pi$
$90$		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	$-0.608911\pi$
$97$	−6.60894			−0.671037			−0.335518	+	0.942034i	$0.608911\pi$
$98$		0			0
$99$	−1.75992			−0.176879
$100$		0			0
$101$	9.41859	−	16.3135i	0.937185	−	1.62325i	0.166493	−	0.986043i	$-0.446756\pi$
$101$	9.41859	−	16.3135i	0.937185	−	1.62325i	0.770691	−	0.637209i	$-0.219911\pi$
$102$		0			0
$103$	−0.733780	−	1.27094i	−0.0723014	−	0.125230i	0.827608	−	0.561306i	$-0.189701\pi$
$103$	−0.733780	−	1.27094i	−0.0723014	−	0.125230i	−0.899910	+	0.436077i	$0.856368\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.78127	−	11.7455i	−0.655570	−	1.13548i	−0.981751	−	0.190173i	$-0.939095\pi$
$107$	−6.78127	−	11.7455i	−0.655570	−	1.13548i	0.326181	−	0.945307i	$-0.394238\pi$
$108$		0			0
$109$	−7.40701	+	12.8293i	−0.709463	+	1.22883i	0.255594	+	0.966784i	$0.417729\pi$
$109$	−7.40701	+	12.8293i	−0.709463	+	1.22883i	−0.965057	+	0.262041i	$0.915604\pi$
$110$		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	$-0.171474\pi$
$131$	−0.172854	−	0.299392i	−0.0151023	−	0.0261580i	−0.873478	+	0.486864i	$0.838141\pi$
$132$		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	−0.999816	−	0.0191800i	$-0.993894\pi$
$137$	−5.65685	+	9.79796i	−0.483298	+	0.837096i	0.516518	+	0.856276i	$0.327228\pi$
$138$		0			0
$139$	−2.68885			−0.228066			−0.114033	−	0.993477i	$-0.536377\pi$
$139$	−2.68885			−0.228066			−0.114033	+	0.993477i	$0.536377\pi$
$140$		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	−0.999012	−	0.0444372i	$-0.985851\pi$
$149$	−6.56700	−	11.3744i	−0.537990	−	0.931826i	0.461022	−	0.887389i	$-0.347483\pi$
$150$		0			0
$151$	−1.50570	+	2.60795i	−0.122532	+	0.212232i	−0.920766	−	0.390116i	$-0.872435\pi$
$151$	−1.50570	+	2.60795i	−0.122532	+	0.212232i	0.798233	+	0.602348i	$0.205768\pi$
$152$		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	−0.157194	−	0.987568i	$-0.550245\pi$
$157$	9.73155	−	16.8555i	0.776662	−	1.34522i	0.933856	−	0.357650i	$-0.116422\pi$
$158$		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	−0.999452	−	0.0331054i	$-0.989460\pi$
$163$	−6.74611	−	11.6846i	−0.528396	−	0.915209i	0.471056	−	0.882103i	$-0.343873\pi$
$164$		0			0
$165$	−3.09646	+	5.36323i	−0.241059	+	0.417527i
$166$		0			0
$167$	−12.3011			−0.951889			−0.475944	−	0.879475i	$-0.657894\pi$
$167$	−12.3011			−0.951889			−0.475944	+	0.879475i	$0.657894\pi$
$168$		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	$-0.136495\pi$
$173$	1.24487	+	2.15619i	0.0946461	+	0.163932i	−0.814815	+	0.579721i	$0.803161\pi$
$174$		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	0.431411	+	0.902156i	$0.358016\pi$
$179$	−7.56700	+	13.1064i	−0.565584	+	0.979621i	−0.996995	+	0.0774652i	$0.975317\pi$
$180$		0			0
$181$	−11.0637			−0.822357			−0.411179	−	0.911555i	$-0.634883\pi$
$181$	−11.0637			−0.822357			−0.411179	+	0.911555i	$0.634883\pi$
$182$		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	0.911269	+	0.411811i	$0.135104\pi$
$191$	11.2258	+	19.4437i	0.812274	+	1.40690i	−0.0989957	+	0.995088i	$0.531563\pi$
$192$		0			0
$193$	−1.55741	+	2.69751i	−0.112105	+	0.194171i	−0.916619	−	0.399763i	$-0.869093\pi$
$193$	−1.55741	+	2.69751i	−0.112105	+	0.194171i	0.804514	+	0.593934i	$0.202426\pi$
$194$		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	$-0.837998\pi$
$199$	−0.206732	+	0.358070i	−0.0146548	+	0.0253829i	0.858605	+	0.512638i	$0.171332\pi$
$200$		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	$-0.295344\pi$
$223$	17.9065			1.19911			0.599555	+	0.800334i	$0.295344\pi$
$224$		0			0
$225$	0.534253			0.0356168
$226$		0			0
$227$	−6.27428	+	10.8674i	−0.416439	+	0.721293i	−0.995578	−	0.0939352i	$-0.970055\pi$
$227$	−6.27428	+	10.8674i	−0.416439	+	0.721293i	0.579139	+	0.815229i	$0.303389\pi$
$228$		0			0
$229$	−7.91768	−	13.7138i	−0.523215	−	0.906235i	−0.999635	−	0.0270173i	$-0.991399\pi$
$229$	−7.91768	−	13.7138i	−0.523215	−	0.906235i	0.476420	−	0.879218i	$-0.341934\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	11.6896	+	20.2470i	0.765811	+	1.32642i	0.939817	+	0.341680i	$0.110996\pi$
$233$	11.6896	+	20.2470i	0.765811	+	1.32642i	−0.174005	+	0.984745i	$0.555671\pi$
$234$		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	$-0.867822\pi$
$241$	−1.67873	+	2.90765i	−0.108137	+	0.187298i	0.806879	+	0.590717i	$0.201155\pi$
$242$		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	$-0.675187\pi$
$251$	−16.5717			−1.04600			−0.522999	+	0.852333i	$0.675187\pi$
$252$		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	$-0.0322412\pi$
$257$	6.57069	+	11.3808i	0.409869	+	0.709913i	−0.585006	+	0.811029i	$0.698908\pi$
$258$		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	−0.802320	−	0.596894i	$-0.796401\pi$
$263$	1.87740	−	3.25175i	0.115765	−	0.200511i	0.918085	+	0.396383i	$0.129735\pi$
$264$		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	−0.497129	−	0.867677i	$-0.665612\pi$
$269$	8.24761	−	14.2853i	0.502866	−	0.870989i	0.999995	−	0.00331226i	$-0.00105433\pi$
$270$		0			0
$271$	−11.2710	−	19.5220i	−0.684665	−	1.18588i	−0.973542	−	0.228509i	$-0.926615\pi$
$271$	−11.2710	−	19.5220i	−0.684665	−	1.18588i	0.288876	−	0.957366i	$-0.406718\pi$
$272$		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	−0.547845	−	0.836580i	$-0.684552\pi$
$277$	7.49909	−	12.9888i	0.450577	−	0.780422i	0.998422	+	0.0561578i	$0.0178850\pi$
$278$		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	0.155303	+	0.987867i	$0.450365\pi$
$283$	−13.0857	+	22.6652i	−0.777866	+	1.34730i	−0.933169	+	0.359437i	$0.882969\pi$
$284$		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	$-0.650668\pi$
$293$	−15.6061			−0.911716			−0.455858	+	0.890052i	$0.650668\pi$
$294$		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	$-0.708022\pi$
$307$	−21.3055			−1.21597			−0.607984	+	0.793949i	$0.708022\pi$
$308$		0			0
$309$	2.75895			0.156951
$310$		0			0
$311$	−7.43993	+	12.8863i	−0.421880	+	0.730717i	−0.996123	−	0.0879671i	$-0.971963\pi$
$311$	−7.43993	+	12.8863i	−0.421880	+	0.730717i	0.574243	+	0.818685i	$0.305296\pi$
$312$		0			0
$313$	1.08137	+	1.87298i	0.0611224	+	0.105867i	0.894967	−	0.446132i	$-0.147199\pi$
$313$	1.08137	+	1.87298i	0.0611224	+	0.105867i	−0.833845	+	0.551999i	$0.813865\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.7297	+	18.5844i	0.602642	+	1.04381i	0.992419	+	0.122897i	$0.0392186\pi$
$317$	10.7297	+	18.5844i	0.602642	+	1.04381i	−0.389777	+	0.920909i	$0.627448\pi$
$318$		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	0.980633	−	0.195857i	$-0.0627488\pi$
$331$	5.83461	+	10.1058i	0.320699	+	0.555468i	−0.659933	+	0.751324i	$0.729415\pi$
$332$		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	−0.927343	−	0.374212i	$-0.877913\pi$
$347$	−2.60035	+	4.50394i	−0.139594	+	0.241784i	0.787749	+	0.615996i	$0.211246\pi$
$348$		0			0
$349$	33.8645			1.81272			0.906362	−	0.422501i	$-0.138848\pi$
$349$	33.8645			1.81272			0.906362	+	0.422501i	$0.138848\pi$
$350$		0			0
$351$	19.4363			1.03743
$352$		0			0
$353$	−11.6226	+	20.1309i	−0.618606	+	1.07146i	0.371134	+	0.928579i	$0.378969\pi$
$353$	−11.6226	+	20.1309i	−0.618606	+	1.07146i	−0.989740	+	0.142878i	$0.954364\pi$
$354$		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	0.999150	+	0.0412304i	$0.0131278\pi$
$359$	10.1421	+	17.5667i	0.535281	+	0.927135i	−0.463868	+	0.885904i	$0.653539\pi$
$360$		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	$-0.945944\pi$
$367$	−6.63690	+	11.4954i	−0.346443	+	0.600057i	0.639172	+	0.769064i	$0.279277\pi$
$368$		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	0.792439	+	0.609951i	$0.208811\pi$
$373$	17.8541	+	30.9243i	0.924453	+	1.60120i	0.132014	+	0.991248i	$0.457856\pi$
$374$		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	0.775812	+	0.630964i	$0.217340\pi$
$383$	18.2853	+	31.6711i	0.934337	+	1.61832i	0.158525	+	0.987355i	$0.449326\pi$
$384$		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	0.177868	+	0.984054i	$0.443080\pi$
$389$	−15.0543	+	26.0748i	−0.763282	+	1.32204i	−0.941150	+	0.337989i	$0.890253\pi$
$390$		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	$-0.226670\pi$
$397$	−3.73378	−	6.46710i	−0.187393	−	0.324574i	−0.944380	+	0.328855i	$0.893337\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.86657	+	10.1612i	0.292963	+	0.507426i	0.974509	−	0.224349i	$-0.0720255\pi$
$401$	5.86657	+	10.1612i	0.292963	+	0.507426i	−0.681546	+	0.731775i	$0.738692\pi$
$402$		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	$-0.696471\pi$
$409$	8.43006	−	14.6013i	0.416840	−	0.721987i	0.995620	+	0.0934964i	$0.0298044\pi$
$410$		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	$-0.418335\pi$
$419$	10.3884			0.507507			0.253753	+	0.967269i	$0.418335\pi$
$420$		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	0.221840	+	0.975083i	$0.428794\pi$
$431$	−15.2284	+	26.3764i	−0.733527	+	1.27051i	−0.955367	+	0.295422i	$0.904540\pi$
$432$		0			0
$433$	−25.9182			−1.24555			−0.622774	−	0.782402i	$-0.713994\pi$
$433$	−25.9182			−1.24555			−0.622774	+	0.782402i	$0.713994\pi$
$434$		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	−0.984777	−	0.173821i	$-0.944388\pi$
$439$	−13.4707	−	23.3320i	−0.642922	−	1.11357i	0.341855	−	0.939753i	$-0.388945\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.19292	+	14.1906i	0.389257	+	0.674213i	0.992350	−	0.123458i	$-0.0393984\pi$
$443$	8.19292	+	14.1906i	0.389257	+	0.674213i	−0.603093	+	0.797671i	$0.706065\pi$
$444$		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	0.984312	−	0.176436i	$-0.0564569\pi$
$457$	7.25464	+	12.5654i	0.339358	+	0.587785i	−0.644954	+	0.764221i	$0.723124\pi$
$458$		0			0
$459$	3.33147	−	5.77028i	0.155500	−	0.269334i
$460$		0			0
$461$	17.8933			0.833374			0.416687	−	0.909050i	$-0.363191\pi$
$461$	17.8933			0.833374			0.416687	+	0.909050i	$0.363191\pi$
$462$		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	0.998616	+	0.0526029i	$0.0167518\pi$
$467$	11.7746	+	20.3942i	0.544863	+	0.943731i	−0.453752	+	0.891128i	$0.649915\pi$
$468$		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	$-0.799391\pi$
$479$	2.32933	−	4.03452i	0.106430	−	0.184342i	0.914322	+	0.404989i	$0.132725\pi$
$480$		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	−0.966517	−	0.256603i	$-0.917397\pi$
$487$	−5.76052	+	9.97751i	−0.261034	+	0.452124i	0.705483	+	0.708727i	$0.250730\pi$
$488$		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	−0.899836	−	0.436228i	$-0.856314\pi$
$499$	−18.4895	−	32.0247i	−0.827703	−	1.43362i	0.0721332	−	0.997395i	$-0.477019\pi$
$500$		0			0
$501$	11.5628	−	20.0274i	0.516588	−	0.894757i
$502$		0			0
$503$	8.08985			0.360709			0.180354	−	0.983602i	$-0.442276\pi$
$503$	8.08985			0.360709			0.180354	+	0.983602i	$0.442276\pi$
$504$		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	−0.989052	−	0.147569i	$-0.952855\pi$
$509$	−14.0403	−	24.3185i	−0.622325	−	1.07790i	0.366727	−	0.930329i	$-0.380478\pi$
$510$		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	$-0.922207\pi$
$521$	−6.29048	+	10.8954i	−0.275591	+	0.477338i	0.694693	+	0.719306i	$0.255540\pi$
$522$		0			0
$523$	−0.742265	−	1.28564i	−0.0324570	−	0.0562172i	0.849341	−	0.527845i	$-0.177000\pi$
$523$	−0.742265	−	1.28564i	−0.0324570	−	0.0562172i	−0.881798	+	0.471628i	$0.843667\pi$
$524$		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	0.587927	−	0.808914i	$-0.299944\pi$
$541$	−9.45673	−	16.3795i	−0.406577	−	0.704211i	−0.994504	+	0.104703i	$0.966611\pi$
$542$		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	−0.994551	−	0.104252i	$-0.966755\pi$
$557$	−9.60532	+	16.6369i	−0.406990	+	0.704928i	0.587560	+	0.809180i	$0.300088\pi$
$558$		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	−0.251899	−	0.967754i	$-0.581055\pi$
$563$	16.8976	−	29.2675i	0.712150	−	1.23348i	0.964049	−	0.265726i	$-0.0856116\pi$
$564$		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	0.813335	−	0.581796i	$-0.197650\pi$
$569$	−2.31818	−	4.01520i	−0.0971830	−	0.168326i	−0.910518	+	0.413470i	$0.864317\pi$
$570$		0			0
$571$	−21.9341	+	37.9909i	−0.917912	+	1.58987i	−0.115330	+	0.993327i	$0.536793\pi$
$571$	−21.9341	+	37.9909i	−0.917912	+	1.58987i	−0.802581	+	0.596543i	$0.796541\pi$
$572$		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	$-0.771474\pi$
$577$	4.63878	−	8.03460i	0.193115	−	0.334485i	0.946281	+	0.323346i	$0.104808\pi$
$578$		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	$-0.704204\pi$
$587$	−28.9971			−1.19684			−0.598420	+	0.801183i	$0.704204\pi$
$588$		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	−0.999608	−	0.0279933i	$-0.991088\pi$
$593$	−12.7614	−	22.1034i	−0.524047	−	0.907676i	0.475561	−	0.879683i	$-0.342245\pi$
$594$		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	0.352657	+	0.935752i	$0.385278\pi$
$599$	−15.5182	+	26.8783i	−0.634057	+	1.09822i	−0.986714	+	0.162466i	$0.948055\pi$
$600$		0			0
$601$	−3.56479			−0.145411			−0.0727054	−	0.997353i	$-0.523163\pi$
$601$	−3.56479			−0.145411			−0.0727054	+	0.997353i	$0.523163\pi$
$602$		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	$-0.210253\pi$
$607$	−3.36310	−	5.82506i	−0.136504	−	0.236432i	−0.926171	+	0.377104i	$0.876920\pi$
$608$		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	−0.594874	−	0.803819i	$-0.702798\pi$
$613$	9.87112	−	17.0973i	0.398691	−	0.690553i	0.993565	+	0.113266i	$0.0361314\pi$
$614$		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	−0.248710	−	0.968578i	$-0.580006\pi$
$619$	17.7755	−	30.7881i	0.714458	−	1.23748i	0.963168	−	0.268900i	$-0.0866602\pi$
$620$		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	−0.991823	−	0.127621i	$-0.959266\pi$
$641$	−9.75727	+	16.9001i	−0.385389	+	0.667513i	0.606434	+	0.795134i	$0.292599\pi$
$642$		0			0
$643$	18.9895			0.748872			0.374436	−	0.927253i	$-0.377836\pi$
$643$	18.9895			0.748872			0.374436	+	0.927253i	$0.377836\pi$
$644$		0			0
$645$	19.0736			0.751023
$646$		0			0
$647$	20.6285	−	35.7296i	0.810989	−	1.40467i	−0.101183	−	0.994868i	$-0.532263\pi$
$647$	20.6285	−	35.7296i	0.810989	−	1.40467i	0.912172	−	0.409807i	$-0.134404\pi$
$648$		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	0.991966	−	0.126503i	$-0.0403753\pi$
$653$	9.87474	+	17.1036i	0.386429	+	0.669314i	−0.605538	+	0.795817i	$0.707042\pi$
$654$		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	$-0.850618\pi$
$661$	−1.39543	+	2.41696i	−0.0542759	+	0.0940087i	0.837611	+	0.546267i	$0.183952\pi$
$662$		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	$-0.0137261\pi$
$677$	12.0261	+	20.8299i	0.462202	+	0.800558i	−0.536868	+	0.843666i	$0.680393\pi$
$678$		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	−0.225136	−	0.974327i	$-0.572283\pi$
$683$	19.1100	−	33.0995i	0.731224	−	1.26652i	0.956360	−	0.292190i	$-0.0943839\pi$
$684$		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	0.999993	+	0.00385805i	$0.00122806\pi$
$691$	13.2312	+	22.9171i	0.503337	+	0.871806i	−0.496655	+	0.867948i	$0.665439\pi$
$692$		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	0.799557	−	0.600590i	$-0.205068\pi$
$709$	−3.20450	−	5.55035i	−0.120347	−	0.208448i	−0.919905	+	0.392142i	$0.871734\pi$
$710$		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	0.961039	+	0.276413i	$0.0891456\pi$
$719$	19.3035	+	33.4347i	0.719900	+	1.24690i	−0.241139	+	0.970491i	$0.577521\pi$
$720$		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	$-0.362816\pi$
$727$	22.5280			0.835516			0.417758	+	0.908558i	$0.362816\pi$
$728$		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	$-0.210907\pi$
$733$	−3.75075	−	6.49649i	−0.138537	−	0.239953i	−0.926943	+	0.375202i	$0.877573\pi$
$734$		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	0.338888	+	0.940827i	$0.389949\pi$
$739$	−17.5432	+	30.3857i	−0.645336	+	1.11776i	−0.984224	+	0.176928i	$0.943384\pi$
$740$		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	0.608991	−	0.793177i	$-0.291575\pi$
$751$	−10.4799	−	18.1517i	−0.382417	−	0.662365i	−0.991407	+	0.130813i	$0.958241\pi$
$752$		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	$-0.180850\pi$
$761$	−1.22876	−	2.12828i	−0.0445426	−	0.0771500i	−0.887437	+	0.460929i	$0.847516\pi$
$762$		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	$-0.627957\pi$
$769$	−21.6994			−0.782501			−0.391250	+	0.920284i	$0.627957\pi$
$770$		0			0
$771$	−24.7053			−0.889739
$772$		0			0
$773$	7.84900	−	13.5949i	0.282309	−	0.488973i	−0.689644	−	0.724149i	$-0.742233\pi$
$773$	7.84900	−	13.5949i	0.282309	−	0.488973i	0.971953	+	0.235175i	$0.0755663\pi$
$774$		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	$-0.977220\pi$
$787$	−12.2537	+	21.2240i	−0.436797	+	0.756554i	0.560644	+	0.828057i	$0.310554\pi$
$788$		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	$-0.532390\pi$
$797$	−5.73557			−0.203164			−0.101582	+	0.994827i	$0.532390\pi$
$798$		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	−0.895025	−	0.446016i	$-0.852842\pi$
$809$	−1.74216	+	3.01750i	−0.0612510	+	0.106090i	0.833774	+	0.552106i	$0.186176\pi$
$810$		0			0
$811$	−25.9953			−0.912819			−0.456409	−	0.889770i	$-0.650865\pi$
$811$	−25.9953			−0.912819			−0.456409	+	0.889770i	$0.650865\pi$
$812$		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	0.849997	+	0.526788i	$0.176604\pi$
$821$	25.2494	+	43.7332i	0.881210	+	1.52630i	0.0312136	+	0.999513i	$0.490063\pi$
$822$		0			0
$823$	22.4350	−	38.8585i	0.782034	−	1.35452i	−0.148722	−	0.988879i	$-0.547516\pi$
$823$	22.4350	−	38.8585i	0.782034	−	1.35452i	0.930755	−	0.365643i	$-0.119151\pi$
$824$		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	−0.0703811	+	0.997520i	$0.522422\pi$
$829$	−25.8863	+	44.8364i	−0.899068	+	1.55723i	−0.828687	+	0.559712i	$0.810912\pi$
$830$		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	$-0.484272\pi$
$839$	2.86118			0.0987788			0.0493894	+	0.998780i	$0.484272\pi$
$840$		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	$-0.787432\pi$
$853$	−45.8645			−1.57037			−0.785185	+	0.619261i	$0.787432\pi$
$854$		0			0
$855$	0.664852			0.0227375
$856$		0			0
$857$	−11.5751	+	20.0486i	−0.395397	+	0.684847i	−0.993152	−	0.116832i	$-0.962726\pi$
$857$	−11.5751	+	20.0486i	−0.395397	+	0.684847i	0.597755	+	0.801679i	$0.296060\pi$
$858$		0			0
$859$	−4.23192	−	7.32990i	−0.144391	−	0.250093i	0.784754	−	0.619807i	$-0.212789\pi$
$859$	−4.23192	−	7.32990i	−0.144391	−	0.250093i	−0.929146	+	0.369714i	$0.879456\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	17.5462	+	30.3908i	0.597278	+	1.03452i	0.993221	+	0.116241i	$0.0370845\pi$
$863$	17.5462	+	30.3908i	0.597278	+	1.03452i	−0.395943	+	0.918275i	$0.629582\pi$
$864$		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	0.655326	−	0.755346i	$-0.272531\pi$
$877$	−9.66861	−	16.7465i	−0.326486	−	0.565490i	−0.981812	+	0.189856i	$0.939198\pi$
$878$		0			0
$879$	14.6694	−	25.4081i	0.494787	−	0.856996i
$880$		0			0
$881$	33.0573			1.11373			0.556865	−	0.830603i	$-0.312004\pi$
$881$	33.0573			1.11373			0.556865	+	0.830603i	$0.312004\pi$
$882$		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	$-0.0625998\pi$
$887$	9.56444	+	16.5661i	0.321142	+	0.556235i	−0.659582	+	0.751633i	$0.729266\pi$
$888$		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	−0.0380931	−	0.999274i	$-0.512128\pi$
$907$	25.4891	−	44.1483i	0.846350	−	1.46592i	0.884443	−	0.466648i	$-0.154538\pi$
$908$		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	0.977855	+	0.209285i	$0.0671136\pi$
$919$	20.3163	+	35.1889i	0.670173	+	1.16077i	−0.307681	+	0.951489i	$0.599553\pi$
$920$		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	$-0.248976\pi$
$929$	−7.79395	−	13.4995i	−0.255711	−	0.442905i	−0.965088	+	0.261924i	$0.915643\pi$
$930$		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	$-0.391427\pi$
$937$	20.4794			0.669034			0.334517	+	0.942390i	$0.391427\pi$
$938$		0			0
$939$	−4.06585			−0.132684
$940$		0			0
$941$	8.39362	−	14.5382i	0.273624	−	0.473931i	−0.696163	−	0.717884i	$-0.745111\pi$
$941$	8.39362	−	14.5382i	0.273624	−	0.473931i	0.969787	+	0.243953i	$0.0784442\pi$
$942$		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	0.892613	−	0.450825i	$-0.148870\pi$
$947$	1.71964	+	2.97850i	0.0558807	+	0.0967883i	−0.836732	+	0.547613i	$0.815537\pi$
$948$		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	0.999964	+	0.00853421i	$0.00271656\pi$
$971$	15.8102	+	27.3840i	0.507373	+	0.878795i	−0.492591	+	0.870261i	$0.663950\pi$
$972$		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	−0.673769	−	0.738942i	$-0.735326\pi$
$977$	9.47268	−	16.4072i	0.303058	−	0.524912i	0.976827	+	0.214030i	$0.0686591\pi$
$978$		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	$-0.755300\pi$
$983$	7.60937	−	13.1798i	0.242701	−	0.420371i	0.961483	+	0.274865i	$0.0886332\pi$
$984$		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	−0.999995	−	0.00317464i	$-0.998989\pi$
$991$	−15.6534	+	27.1126i	−0.497248	+	0.861259i	0.502747	+	0.864434i	$0.332323\pi$
$992$		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	−0.351424	−	0.936217i	$-0.614302\pi$
$997$	20.0527	−	34.7323i	0.635076	−	1.09998i	0.986499	−	0.163767i	$-0.0523644\pi$
$998$		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.y.361.1		8
7.2	even	3	inner	1960.2.q.y.961.1		8
7.3	odd	6		1960.2.a.y.1.1	yes	4
7.4	even	3		1960.2.a.x.1.4	✓	4
7.5	odd	6		1960.2.q.x.961.4		8
7.6	odd	2		1960.2.q.x.361.4		8
28.3	even	6		3920.2.a.cd.1.4		4
28.11	odd	6		3920.2.a.ce.1.1		4
35.4	even	6		9800.2.a.cs.1.1		4
35.24	odd	6		9800.2.a.cl.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.2.a.x.1.4	✓	4	7.4	even	3
1960.2.a.y.1.1	yes	4	7.3	odd	6
1960.2.q.x.361.4		8	7.6	odd	2
1960.2.q.x.961.4		8	7.5	odd	6
1960.2.q.y.361.1		8	1.1	even	1	trivial
1960.2.q.y.961.1		8	7.2	even	3	inner
3920.2.a.cd.1.4		4	28.3	even	6
3920.2.a.ce.1.1		4	28.11	odd	6
9800.2.a.cl.1.4		4	35.24	odd	6
9800.2.a.cs.1.1		4	35.4	even	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

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