LMFDB - Embedded newform 1792.2.m.g.1345.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1792,2,Mod(449,1792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1792, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1792.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1792 = 2^{8} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1792.m (of order $4$, degree $2$, 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:	$14.3091920422$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1345.3
Root			$0.792206 + 1.03242i$ of defining polynomial
Character	$\chi$	$=$	1792.1345
Dual form			1792.2.m.g.449.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18265 - 1.18265i) q^{3} +(-1.87820 + 1.87820i) q^{5} +1.00000i q^{7} -0.202696i q^{9} +O(q^{10})$	\(q+(-1.18265 - 1.18265i) q^{3} +(-1.87820 + 1.87820i) q^{5} +1.00000i q^{7} -0.202696i q^{9} +(0.584413 - 0.584413i) q^{11} +(3.94057 + 3.94057i) q^{13} +4.44250 q^{15} +1.74896 q^{17} +(-4.19467 - 4.19467i) q^{19} +(1.18265 - 1.18265i) q^{21} -3.04150i q^{23} -2.05530i q^{25} +(-3.78766 + 3.78766i) q^{27} +(-4.43316 - 4.43316i) q^{29} +7.90794 q^{31} -1.38231 q^{33} +(-1.87820 - 1.87820i) q^{35} +(-5.87262 + 5.87262i) q^{37} -9.32061i q^{39} +1.38922i q^{41} +(1.73902 - 1.73902i) q^{43} +(0.380704 + 0.380704i) q^{45} -1.80017 q^{47} -1.00000 q^{49} +(-2.06840 - 2.06840i) q^{51} +(-9.73675 + 9.73675i) q^{53} +2.19529i q^{55} +9.92162i q^{57} +(-4.74002 + 4.74002i) q^{59} +(3.10257 + 3.10257i) q^{61} +0.202696 q^{63} -14.8024 q^{65} +(-4.81108 - 4.81108i) q^{67} +(-3.59702 + 3.59702i) q^{69} +1.11625i q^{71} +11.2521i q^{73} +(-2.43070 + 2.43070i) q^{75} +(0.584413 + 0.584413i) q^{77} -7.61158 q^{79} +8.35083 q^{81} +(11.1869 + 11.1869i) q^{83} +(-3.28490 + 3.28490i) q^{85} +10.4857i q^{87} +0.428825i q^{89} +(-3.94057 + 3.94057i) q^{91} +(-9.35230 - 9.35230i) q^{93} +15.7569 q^{95} -19.2163 q^{97} +(-0.118458 - 0.118458i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^3 - 4 * q^5	$ 16 q + 4 q^{3} - 4 q^{5} - 8 q^{11} + 12 q^{13} - 8 q^{17} + 4 q^{19} - 4 q^{21} - 56 q^{27} + 8 q^{31} + 16 q^{33} - 4 q^{35} - 8 q^{37} - 24 q^{43} - 36 q^{45} + 40 q^{47} - 16 q^{49} + 24 q^{51} - 32 q^{53} - 4 q^{59} - 20 q^{61} - 24 q^{63} + 72 q^{65} + 32 q^{67} + 56 q^{69} - 28 q^{75} - 8 q^{77} - 40 q^{81} + 36 q^{83} - 12 q^{91} + 8 q^{93} + 80 q^{95} - 72 q^{97} - 8 q^{99}+O(q^{100}) $ 16 * q + 4 * q^3 - 4 * q^5 - 8 * q^11 + 12 * q^13 - 8 * q^17 + 4 * q^19 - 4 * q^21 - 56 * q^27 + 8 * q^31 + 16 * q^33 - 4 * q^35 - 8 * q^37 - 24 * q^43 - 36 * q^45 + 40 * q^47 - 16 * q^49 + 24 * q^51 - 32 * q^53 - 4 * q^59 - 20 * q^61 - 24 * q^63 + 72 * q^65 + 32 * q^67 + 56 * q^69 - 28 * q^75 - 8 * q^77 - 40 * q^81 + 36 * q^83 - 12 * q^91 + 8 * q^93 + 80 * q^95 - 72 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times$.

$n$	$1023$	$1025$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.18265	−	1.18265i	−0.682801	−	0.682801i	0.277829	−	0.960630i	$-0.410385\pi$
$3$	−1.18265	−	1.18265i	−0.682801	−	0.682801i	−0.960630	+	0.277829i	$0.910385\pi$
$4$		0			0
$5$	−1.87820	+	1.87820i	−0.839958	+	0.839958i	−0.988853	−	0.148895i	$-0.952428\pi$
$5$	−1.87820	+	1.87820i	−0.839958	+	0.839958i	0.148895	+	0.988853i	$0.452428\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		0			0
$9$		−	0.202696i		−	0.0675652i
$10$		0			0
$11$	0.584413	−	0.584413i	0.176207	−	0.176207i	−0.613493	−	0.789700i	$-0.710236\pi$
$11$	0.584413	−	0.584413i	0.176207	−	0.176207i	0.789700	+	0.613493i	$0.210236\pi$
$12$		0			0
$13$	3.94057	+	3.94057i	1.09292	+	1.09292i	0.995216	+	0.0977031i	$0.0311496\pi$
$13$	3.94057	+	3.94057i	1.09292	+	1.09292i	0.0977031	+	0.995216i	$0.468850\pi$
$14$		0			0
$15$	4.44250			1.14705
$16$		0			0
$17$	1.74896			0.424185			0.212093	−	0.977250i	$-0.431972\pi$
$17$	1.74896			0.424185			0.212093	+	0.977250i	$0.431972\pi$
$18$		0			0
$19$	−4.19467	−	4.19467i	−0.962323	−	0.962323i	0.0369927	−	0.999316i	$-0.488222\pi$
$19$	−4.19467	−	4.19467i	−0.962323	−	0.962323i	−0.999316	+	0.0369927i	$0.988222\pi$
$20$		0			0
$21$	1.18265	−	1.18265i	0.258075	−	0.258075i
$22$		0			0
$23$		−	3.04150i		−	0.634198i	−0.948393	−	0.317099i	$-0.897291\pi$
$23$		−	3.04150i		−	0.634198i	0.948393	−	0.317099i	$-0.102709\pi$
$24$		0			0
$25$		−	2.05530i		−	0.411060i
$26$		0			0
$27$	−3.78766	+	3.78766i	−0.728935	+	0.728935i
$28$		0			0
$29$	−4.43316	−	4.43316i	−0.823217	−	0.823217i	0.163351	−	0.986568i	$-0.447770\pi$
$29$	−4.43316	−	4.43316i	−0.823217	−	0.823217i	−0.986568	+	0.163351i	$0.947770\pi$
$30$		0			0
$31$	7.90794			1.42031			0.710154	−	0.704046i	$-0.248625\pi$
$31$	7.90794			1.42031			0.710154	+	0.704046i	$0.248625\pi$
$32$		0			0
$33$	−1.38231			−0.240629
$34$		0			0
$35$	−1.87820	−	1.87820i	−0.317474	−	0.317474i
$36$		0			0
$37$	−5.87262	+	5.87262i	−0.965453	+	0.965453i	−0.999423	−	0.0339701i	$-0.989185\pi$
$37$	−5.87262	+	5.87262i	−0.965453	+	0.965453i	0.0339701	+	0.999423i	$0.489185\pi$
$38$		0			0
$39$		−	9.32061i		−	1.49249i
$40$		0			0
$41$			1.38922i			0.216960i	0.994099	+	0.108480i	$0.0345983\pi$
$41$			1.38922i			0.216960i	−0.994099	+	0.108480i	$0.965402\pi$
$42$		0			0
$43$	1.73902	−	1.73902i	0.265198	−	0.265198i	−0.561964	−	0.827162i	$-0.689954\pi$
$43$	1.73902	−	1.73902i	0.265198	−	0.265198i	0.827162	+	0.561964i	$0.189954\pi$
$44$		0			0
$45$	0.380704	+	0.380704i	0.0567520	+	0.0567520i
$46$		0			0
$47$	−1.80017			−0.262582			−0.131291	−	0.991344i	$-0.541912\pi$
$47$	−1.80017			−0.262582			−0.131291	+	0.991344i	$0.541912\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−2.06840	−	2.06840i	−0.289634	−	0.289634i
$52$		0			0
$53$	−9.73675	+	9.73675i	−1.33745	+	1.33745i	−0.438919	+	0.898527i	$0.644639\pi$
$53$	−9.73675	+	9.73675i	−1.33745	+	1.33745i	−0.898527	+	0.438919i	$0.855361\pi$
$54$		0			0
$55$			2.19529i			0.296013i
$56$		0			0
$57$			9.92162i			1.31415i
$58$		0			0
$59$	−4.74002	+	4.74002i	−0.617098	+	0.617098i	−0.944786	−	0.327688i	$-0.893731\pi$
$59$	−4.74002	+	4.74002i	−0.617098	+	0.617098i	0.327688	+	0.944786i	$0.393731\pi$
$60$		0			0
$61$	3.10257	+	3.10257i	0.397243	+	0.397243i	0.877260	−	0.480016i	$-0.159369\pi$
$61$	3.10257	+	3.10257i	0.397243	+	0.397243i	−0.480016	+	0.877260i	$0.659369\pi$
$62$		0			0
$63$	0.202696			0.0255372
$64$		0			0
$65$	−14.8024			−1.83601
$66$		0			0
$67$	−4.81108	−	4.81108i	−0.587767	−	0.587767i	0.349259	−	0.937026i	$-0.386433\pi$
$67$	−4.81108	−	4.81108i	−0.587767	−	0.587767i	−0.937026	+	0.349259i	$0.886433\pi$
$68$		0			0
$69$	−3.59702	+	3.59702i	−0.433031	+	0.433031i
$70$		0			0
$71$			1.11625i			0.132475i	0.997804	+	0.0662375i	$0.0210995\pi$
$71$			1.11625i			0.132475i	−0.997804	+	0.0662375i	$0.978900\pi$
$72$		0			0
$73$			11.2521i			1.31696i	0.752600	+	0.658478i	$0.228799\pi$
$73$			11.2521i			1.31696i	−0.752600	+	0.658478i	$0.771201\pi$
$74$		0			0
$75$	−2.43070	+	2.43070i	−0.280673	+	0.280673i
$76$		0			0
$77$	0.584413	+	0.584413i	0.0666000	+	0.0666000i
$78$		0			0
$79$	−7.61158			−0.856370			−0.428185	−	0.903691i	$-0.640847\pi$
$79$	−7.61158			−0.856370			−0.428185	+	0.903691i	$0.640847\pi$
$80$		0			0
$81$	8.35083			0.927870
$82$		0			0
$83$	11.1869	+	11.1869i	1.22792	+	1.22792i	0.964748	+	0.263176i	$0.0847700\pi$
$83$	11.1869	+	11.1869i	1.22792	+	1.22792i	0.263176	+	0.964748i	$0.415230\pi$
$84$		0			0
$85$	−3.28490	+	3.28490i	−0.356298	+	0.356298i
$86$		0			0
$87$			10.4857i			1.12419i
$88$		0			0
$89$			0.428825i			0.0454554i	0.999742	+	0.0227277i	$0.00723508\pi$
$89$			0.428825i			0.0454554i	−0.999742	+	0.0227277i	$0.992765\pi$
$90$		0			0
$91$	−3.94057	+	3.94057i	−0.413084	+	0.413084i
$92$		0			0
$93$	−9.35230	−	9.35230i	−0.969788	−	0.969788i
$94$		0			0
$95$	15.7569			1.61662
$96$		0			0
$97$	−19.2163			−1.95111			−0.975557	−	0.219745i	$-0.929478\pi$
$97$	−19.2163			−1.95111			−0.975557	+	0.219745i	$0.929478\pi$
$98$		0			0
$99$	−0.118458	−	0.118458i	−0.0119055	−	0.0119055i
$100$		0			0
$101$	4.87547	−	4.87547i	0.485127	−	0.485127i	−0.421637	−	0.906765i	$-0.638544\pi$
$101$	4.87547	−	4.87547i	0.485127	−	0.485127i	0.906765	+	0.421637i	$0.138544\pi$
$102$		0			0
$103$		−	6.09849i		−	0.600902i	−0.953797	−	0.300451i	$-0.902863\pi$
$103$		−	6.09849i		−	0.600902i	0.953797	−	0.300451i	$-0.0971371\pi$
$104$		0			0
$105$			4.44250i			0.433544i
$106$		0			0
$107$	−5.19989	+	5.19989i	−0.502693	+	0.502693i	−0.912274	−	0.409581i	$-0.865675\pi$
$107$	−5.19989	+	5.19989i	−0.502693	+	0.502693i	0.409581	+	0.912274i	$0.365675\pi$
$108$		0			0
$109$	7.70055	+	7.70055i	0.737579	+	0.737579i	0.972109	−	0.234530i	$-0.0753550\pi$
$109$	7.70055	+	7.70055i	0.737579	+	0.737579i	−0.234530	+	0.972109i	$0.575355\pi$
$110$		0			0
$111$	13.8905			1.31842
$112$		0			0
$113$	−14.2646			−1.34190			−0.670952	−	0.741500i	$-0.734115\pi$
$113$	−14.2646			−1.34190			−0.670952	+	0.741500i	$0.734115\pi$
$114$		0			0
$115$	5.71257	+	5.71257i	0.532700	+	0.532700i
$116$		0			0
$117$	0.798737	−	0.798737i	0.0738433	−	0.0738433i
$118$		0			0
$119$			1.74896i			0.160327i
$120$		0			0
$121$			10.3169i			0.937902i
$122$		0			0
$123$	1.64296	−	1.64296i	0.148140	−	0.148140i
$124$		0			0
$125$	−5.53074	−	5.53074i	−0.494685	−	0.494685i
$126$		0			0
$127$	−8.98310			−0.797121			−0.398561	−	0.917142i	$-0.630490\pi$
$127$	−8.98310			−0.797121			−0.398561	+	0.917142i	$0.630490\pi$
$128$		0			0
$129$	−4.11328			−0.362154
$130$		0			0
$131$	−12.7547	−	12.7547i	−1.11438	−	1.11438i	−0.992551	−	0.121828i	$-0.961124\pi$
$131$	−12.7547	−	12.7547i	−1.11438	−	1.11438i	−0.121828	−	0.992551i	$-0.538876\pi$
$132$		0			0
$133$	4.19467	−	4.19467i	0.363724	−	0.363724i
$134$		0			0
$135$		−	14.2280i		−	1.22455i
$136$		0			0
$137$		−	11.7927i		−	1.00751i	−0.863845	−	0.503757i	$-0.831951\pi$
$137$		−	11.7927i		−	1.00751i	0.863845	−	0.503757i	$-0.168049\pi$
$138$		0			0
$139$	−0.524016	+	0.524016i	−0.0444465	+	0.0444465i	−0.728981	−	0.684534i	$-0.760006\pi$
$139$	−0.524016	+	0.524016i	−0.0444465	+	0.0444465i	0.684534	+	0.728981i	$0.260006\pi$
$140$		0			0
$141$	2.12896	+	2.12896i	0.179291	+	0.179291i
$142$		0			0
$143$	4.60584			0.385160
$144$		0			0
$145$	16.6527			1.38294
$146$		0			0
$147$	1.18265	+	1.18265i	0.0975430	+	0.0975430i
$148$		0			0
$149$	−1.98859	+	1.98859i	−0.162912	+	0.162912i	−0.783855	−	0.620944i	$-0.786750\pi$
$149$	−1.98859	+	1.98859i	−0.162912	+	0.162912i	0.620944	+	0.783855i	$0.286750\pi$
$150$		0			0
$151$			15.1887i			1.23604i	0.786162	+	0.618020i	$0.212065\pi$
$151$			15.1887i			1.23604i	−0.786162	+	0.618020i	$0.787935\pi$
$152$		0			0
$153$		−	0.354507i		−	0.0286602i
$154$		0			0
$155$	−14.8527	+	14.8527i	−1.19300	+	1.19300i
$156$		0			0
$157$	7.91629	+	7.91629i	0.631789	+	0.631789i	0.948516	−	0.316728i	$-0.102584\pi$
$157$	7.91629	+	7.91629i	0.631789	+	0.631789i	−0.316728	+	0.948516i	$0.602584\pi$
$158$		0			0
$159$	23.0303			1.82642
$160$		0			0
$161$	3.04150			0.239704
$162$		0			0
$163$	6.32172	+	6.32172i	0.495155	+	0.495155i	0.909926	−	0.414771i	$-0.136138\pi$
$163$	6.32172	+	6.32172i	0.495155	+	0.495155i	−0.414771	+	0.909926i	$0.636138\pi$
$164$		0			0
$165$	2.59626	−	2.59626i	0.202118	−	0.202118i
$166$		0			0
$167$			22.5263i			1.74314i	0.490271	+	0.871570i	$0.336898\pi$
$167$			22.5263i			1.74314i	−0.490271	+	0.871570i	$0.663102\pi$
$168$		0			0
$169$			18.0563i			1.38894i
$170$		0			0
$171$	−0.850241	+	0.850241i	−0.0650195	+	0.0650195i
$172$		0			0
$173$	0.0105911	+	0.0105911i	0.000805223	+	0.000805223i	0.707509	−	0.706704i	$-0.249819\pi$
$173$	0.0105911	+	0.0105911i	0.000805223	+	0.000805223i	−0.706704	+	0.707509i	$0.749819\pi$
$174$		0			0
$175$	2.05530			0.155366
$176$		0			0
$177$	11.2115			0.842710
$178$		0			0
$179$	−14.3569	−	14.3569i	−1.07309	−	1.07309i	−0.997109	−	0.0759779i	$-0.975792\pi$
$179$	−14.3569	−	14.3569i	−1.07309	−	1.07309i	−0.0759779	−	0.997109i	$-0.524208\pi$
$180$		0			0
$181$	−8.65321	+	8.65321i	−0.643188	+	0.643188i	−0.951338	−	0.308150i	$-0.900290\pi$
$181$	−8.65321	+	8.65321i	−0.643188	+	0.643188i	0.308150	+	0.951338i	$0.400290\pi$
$182$		0			0
$183$		−	7.33848i		−	0.542476i
$184$		0			0
$185$		−	22.0600i		−	1.62188i
$186$		0			0
$187$	1.02211	−	1.02211i	0.0747444	−	0.0747444i
$188$		0			0
$189$	−3.78766	−	3.78766i	−0.275511	−	0.275511i
$190$		0			0
$191$	−17.2085			−1.24517			−0.622583	−	0.782554i	$-0.713917\pi$
$191$	−17.2085			−1.24517			−0.622583	+	0.782554i	$0.713917\pi$
$192$		0			0
$193$	7.00982			0.504578			0.252289	−	0.967652i	$-0.418817\pi$
$193$	7.00982			0.504578			0.252289	+	0.967652i	$0.418817\pi$
$194$		0			0
$195$	17.5060	+	17.5060i	1.25363	+	1.25363i
$196$		0			0
$197$	15.4175	−	15.4175i	1.09845	−	1.09845i	0.103860	−	0.994592i	$-0.466881\pi$
$197$	15.4175	−	15.4175i	1.09845	−	1.09845i	0.994592	−	0.103860i	$-0.0331194\pi$
$198$		0			0
$199$			15.3483i			1.08801i	0.839082	+	0.544005i	$0.183093\pi$
$199$			15.3483i			1.08801i	−0.839082	+	0.544005i	$0.816907\pi$
$200$		0			0
$201$			11.3796i			0.802656i
$202$		0			0
$203$	4.43316	−	4.43316i	0.311147	−	0.311147i
$204$		0			0
$205$	−2.60924	−	2.60924i	−0.182237	−	0.182237i
$206$		0			0
$207$	−0.616500			−0.0428497
$208$		0			0
$209$	−4.90283			−0.339136
$210$		0			0
$211$	−4.38104	−	4.38104i	−0.301603	−	0.301603i	0.540038	−	0.841641i	$-0.318410\pi$
$211$	−4.38104	−	4.38104i	−0.301603	−	0.301603i	−0.841641	+	0.540038i	$0.818410\pi$
$212$		0			0
$213$	1.32013	−	1.32013i	0.0904541	−	0.0904541i
$214$		0			0
$215$			6.53246i			0.445510i
$216$		0			0
$217$			7.90794i			0.536826i
$218$		0			0
$219$	13.3072	−	13.3072i	0.899219	−	0.899219i
$220$		0			0
$221$	6.89191	+	6.89191i	0.463600	+	0.463600i
$222$		0			0
$223$	0.528935			0.0354201			0.0177101	−	0.999843i	$-0.494362\pi$
$223$	0.528935			0.0354201			0.0177101	+	0.999843i	$0.494362\pi$
$224$		0			0
$225$	−0.416601			−0.0277734
$226$		0			0
$227$	−17.8735	−	17.8735i	−1.18631	−	1.18631i	−0.978081	−	0.208224i	$-0.933232\pi$
$227$	−17.8735	−	17.8735i	−1.18631	−	1.18631i	−0.208224	−	0.978081i	$-0.566768\pi$
$228$		0			0
$229$	8.73248	−	8.73248i	0.577059	−	0.577059i	−0.357033	−	0.934092i	$-0.616212\pi$
$229$	8.73248	−	8.73248i	0.577059	−	0.577059i	0.934092	+	0.357033i	$0.116212\pi$
$230$		0			0
$231$		−	1.38231i		−	0.0909491i
$232$		0			0
$233$			26.9485i			1.76545i	0.469885	+	0.882727i	$0.344295\pi$
$233$			26.9485i			1.76545i	−0.469885	+	0.882727i	$0.655705\pi$
$234$		0			0
$235$	3.38109	−	3.38109i	0.220558	−	0.220558i
$236$		0			0
$237$	9.00181	+	9.00181i	0.584730	+	0.584730i
$238$		0			0
$239$	−19.8050			−1.28108			−0.640539	−	0.767926i	$-0.721289\pi$
$239$	−19.8050			−1.28108			−0.640539	+	0.767926i	$0.721289\pi$
$240$		0			0
$241$	3.73993			0.240910			0.120455	−	0.992719i	$-0.461565\pi$
$241$	3.73993			0.240910			0.120455	+	0.992719i	$0.461565\pi$
$242$		0			0
$243$	1.48689	+	1.48689i	0.0953842	+	0.0953842i
$244$		0			0
$245$	1.87820	−	1.87820i	0.119994	−	0.119994i
$246$		0			0
$247$		−	33.0588i		−	2.10348i
$248$		0			0
$249$		−	26.4603i		−	1.67686i
$250$		0			0
$251$	10.1476	−	10.1476i	0.640510	−	0.640510i	−0.310171	−	0.950681i	$-0.600386\pi$
$251$	10.1476	−	10.1476i	0.640510	−	0.640510i	0.950681	+	0.310171i	$0.100386\pi$
$252$		0			0
$253$	−1.77749	−	1.77749i	−0.111750	−	0.111750i
$254$		0			0
$255$	7.76976			0.486561
$256$		0			0
$257$	12.6111			0.786657			0.393328	−	0.919398i	$-0.371324\pi$
$257$	12.6111			0.786657			0.393328	+	0.919398i	$0.371324\pi$
$258$		0			0
$259$	−5.87262	−	5.87262i	−0.364907	−	0.364907i
$260$		0			0
$261$	−0.898582	+	0.898582i	−0.0556208	+	0.0556208i
$262$		0			0
$263$		−	7.01176i		−	0.432364i	−0.976353	−	0.216182i	$-0.930640\pi$
$263$		−	7.01176i		−	0.432364i	0.976353	−	0.216182i	$-0.0693604\pi$
$264$		0			0
$265$		−	36.5752i		−	2.24680i
$266$		0			0
$267$	0.507149	−	0.507149i	0.0310370	−	0.0310370i
$268$		0			0
$269$	3.92307	+	3.92307i	0.239194	+	0.239194i	0.816516	−	0.577323i	$-0.195902\pi$
$269$	3.92307	+	3.92307i	0.239194	+	0.239194i	−0.577323	+	0.816516i	$0.695902\pi$
$270$		0			0
$271$	−23.5746			−1.43205			−0.716026	−	0.698073i	$-0.754041\pi$
$271$	−23.5746			−1.43205			−0.716026	+	0.698073i	$0.754041\pi$
$272$		0			0
$273$	9.32061			0.564109
$274$		0			0
$275$	−1.20114	−	1.20114i	−0.0724318	−	0.0724318i
$276$		0			0
$277$	−7.89677	+	7.89677i	−0.474471	+	0.474471i	−0.903358	−	0.428887i	$-0.858906\pi$
$277$	−7.89677	+	7.89677i	−0.474471	+	0.474471i	0.428887	+	0.903358i	$0.358906\pi$
$278$		0			0
$279$		−	1.60290i		−	0.0959634i
$280$		0			0
$281$		−	33.1753i		−	1.97907i	−0.144288	−	0.989536i	$-0.546089\pi$
$281$		−	33.1753i		−	1.97907i	0.144288	−	0.989536i	$-0.453911\pi$
$282$		0			0
$283$	−2.06245	+	2.06245i	−0.122600	+	0.122600i	−0.765745	−	0.643145i	$-0.777629\pi$
$283$	−2.06245	+	2.06245i	−0.122600	+	0.122600i	0.643145	+	0.765745i	$0.277629\pi$
$284$		0			0
$285$	−18.6348	−	18.6348i	−1.10383	−	1.10383i
$286$		0			0
$287$	−1.38922			−0.0820030
$288$		0			0
$289$	−13.9411			−0.820067
$290$		0			0
$291$	22.7260	+	22.7260i	1.33222	+	1.33222i
$292$		0			0
$293$	−5.32453	+	5.32453i	−0.311062	+	0.311062i	−0.845321	−	0.534259i	$-0.820591\pi$
$293$	−5.32453	+	5.32453i	−0.311062	+	0.311062i	0.534259	+	0.845321i	$0.320591\pi$
$294$		0			0
$295$		−	17.8054i		−	1.03667i
$296$		0			0
$297$			4.42711i			0.256887i
$298$		0			0
$299$	11.9853	−	11.9853i	0.693126	−	0.693126i
$300$		0			0
$301$	1.73902	+	1.73902i	0.100235	+	0.100235i
$302$		0			0
$303$	−11.5319			−0.662491
$304$		0			0
$305$	−11.6545			−0.667336
$306$		0			0
$307$	9.92446	+	9.92446i	0.566419	+	0.566419i	0.931123	−	0.364705i	$-0.118830\pi$
$307$	9.92446	+	9.92446i	0.566419	+	0.566419i	−0.364705	+	0.931123i	$0.618830\pi$
$308$		0			0
$309$	−7.21235	+	7.21235i	−0.410296	+	0.410296i
$310$		0			0
$311$		−	9.78126i		−	0.554644i	−0.960777	−	0.277322i	$-0.910553\pi$
$311$		−	9.78126i		−	0.554644i	0.960777	−	0.277322i	$-0.0894469\pi$
$312$		0			0
$313$		−	5.68720i		−	0.321460i	−0.986998	−	0.160730i	$-0.948615\pi$
$313$		−	5.68720i		−	0.321460i	0.986998	−	0.160730i	$-0.0513848\pi$
$314$		0			0
$315$	−0.380704	+	0.380704i	−0.0214502	+	0.0214502i
$316$		0			0
$317$	−21.8662	−	21.8662i	−1.22813	−	1.22813i	−0.964671	−	0.263457i	$-0.915137\pi$
$317$	−21.8662	−	21.8662i	−1.22813	−	1.22813i	−0.263457	−	0.964671i	$-0.584863\pi$
$318$		0			0
$319$	−5.18159			−0.290113
$320$		0			0
$321$	12.2993			0.686478
$322$		0			0
$323$	−7.33631	−	7.33631i	−0.408203	−	0.408203i
$324$		0			0
$325$	8.09907	−	8.09907i	0.449256	−	0.449256i
$326$		0			0
$327$		−	18.2141i		−	1.00724i
$328$		0			0
$329$		−	1.80017i		−	0.0992466i
$330$		0			0
$331$	−8.75943	+	8.75943i	−0.481462	+	0.481462i	−0.905598	−	0.424137i	$-0.860578\pi$
$331$	−8.75943	+	8.75943i	−0.481462	+	0.481462i	0.424137	+	0.905598i	$0.360578\pi$
$332$		0			0
$333$	1.19035	+	1.19035i	0.0652310	+	0.0652310i
$334$		0			0
$335$	18.0724			0.987400
$336$		0			0
$337$	19.1758			1.04457			0.522286	−	0.852771i	$-0.325079\pi$
$337$	19.1758			1.04457			0.522286	+	0.852771i	$0.325079\pi$
$338$		0			0
$339$	16.8700	+	16.8700i	0.916254	+	0.916254i
$340$		0			0
$341$	4.62150	−	4.62150i	0.250268	−	0.250268i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$		−	13.5119i		−	0.727456i
$346$		0			0
$347$	6.37041	−	6.37041i	0.341982	−	0.341982i	−0.515130	−	0.857112i	$-0.672256\pi$
$347$	6.37041	−	6.37041i	0.341982	−	0.341982i	0.857112	+	0.515130i	$0.172256\pi$
$348$		0			0
$349$	14.0831	+	14.0831i	0.753850	+	0.753850i	0.975195	−	0.221346i	$-0.0710450\pi$
$349$	14.0831	+	14.0831i	0.753850	+	0.753850i	−0.221346	+	0.975195i	$0.571045\pi$
$350$		0			0
$351$	−29.8511			−1.59333
$352$		0			0
$353$	12.8957			0.686371			0.343185	−	0.939268i	$-0.388494\pi$
$353$	12.8957			0.686371			0.343185	+	0.939268i	$0.388494\pi$
$354$		0			0
$355$	−2.09655	−	2.09655i	−0.111274	−	0.111274i
$356$		0			0
$357$	2.06840	−	2.06840i	0.109471	−	0.109471i
$358$		0			0
$359$			33.5832i			1.77245i	0.463252	+	0.886227i	$0.346682\pi$
$359$			33.5832i			1.77245i	−0.463252	+	0.886227i	$0.653318\pi$
$360$		0			0
$361$			16.1905i			0.852130i
$362$		0			0
$363$	12.2013	−	12.2013i	0.640401	−	0.640401i
$364$		0			0
$365$	−21.1337	−	21.1337i	−1.10619	−	1.10619i
$366$		0			0
$367$	−7.74580			−0.404328			−0.202164	−	0.979352i	$-0.564797\pi$
$367$	−7.74580			−0.404328			−0.202164	+	0.979352i	$0.564797\pi$
$368$		0			0
$369$	0.281589			0.0146589
$370$		0			0
$371$	−9.73675	−	9.73675i	−0.505507	−	0.505507i
$372$		0			0
$373$	1.84606	−	1.84606i	0.0955855	−	0.0955855i	−0.657697	−	0.753283i	$-0.728469\pi$
$373$	1.84606	−	1.84606i	0.0955855	−	0.0955855i	0.753283	+	0.657697i	$0.228469\pi$
$374$		0			0
$375$			13.0818i			0.675543i
$376$		0			0
$377$		−	34.9384i		−	1.79942i
$378$		0			0
$379$	24.4450	−	24.4450i	1.25566	−	1.25566i	0.302511	−	0.953146i	$-0.402175\pi$
$379$	24.4450	−	24.4450i	1.25566	−	1.25566i	0.953146	−	0.302511i	$-0.0978250\pi$
$380$		0			0
$381$	10.6238	+	10.6238i	0.544275	+	0.544275i
$382$		0			0
$383$	−22.2480			−1.13682			−0.568411	−	0.822745i	$-0.692441\pi$
$383$	−22.2480			−1.13682			−0.568411	+	0.822745i	$0.692441\pi$
$384$		0			0
$385$	−2.19529			−0.111882
$386$		0			0
$387$	−0.352491	−	0.352491i	−0.0179181	−	0.0179181i
$388$		0			0
$389$	6.93666	−	6.93666i	0.351703	−	0.351703i	−0.509040	−	0.860743i	$-0.670000\pi$
$389$	6.93666	−	6.93666i	0.351703	−	0.351703i	0.860743	+	0.509040i	$0.170000\pi$
$390$		0			0
$391$		−	5.31947i		−	0.269017i
$392$		0			0
$393$			30.1685i			1.52180i
$394$		0			0
$395$	14.2961	−	14.2961i	0.719315	−	0.719315i
$396$		0			0
$397$	16.4042	+	16.4042i	0.823304	+	0.823304i	0.986580	−	0.163277i	$-0.0522063\pi$
$397$	16.4042	+	16.4042i	0.823304	+	0.823304i	−0.163277	+	0.986580i	$0.552206\pi$
$398$		0			0
$399$	−9.92162			−0.496702
$400$		0			0
$401$	−22.8150			−1.13932			−0.569662	−	0.821879i	$-0.692926\pi$
$401$	−22.8150			−1.13932			−0.569662	+	0.821879i	$0.692926\pi$
$402$		0			0
$403$	31.1618	+	31.1618i	1.55228	+	1.55228i
$404$		0			0
$405$	−15.6846	+	15.6846i	−0.779372	+	0.779372i
$406$		0			0
$407$			6.86407i			0.340239i
$408$		0			0
$409$		−	13.9196i		−	0.688281i	−0.938918	−	0.344140i	$-0.888170\pi$
$409$		−	13.9196i		−	0.688281i	0.938918	−	0.344140i	$-0.111830\pi$
$410$		0			0
$411$	−13.9465	+	13.9465i	−0.687932	+	0.687932i
$412$		0			0
$413$	−4.74002	−	4.74002i	−0.233241	−	0.233241i
$414$		0			0
$415$	−42.0226			−2.06281
$416$		0			0
$417$	1.23945			0.0606962
$418$		0			0
$419$	25.1837	+	25.1837i	1.23030	+	1.23030i	0.963847	+	0.266455i	$0.0858523\pi$
$419$	25.1837	+	25.1837i	1.23030	+	1.23030i	0.266455	+	0.963847i	$0.414148\pi$
$420$		0			0
$421$	16.0774	−	16.0774i	0.783566	−	0.783566i	−0.196865	−	0.980431i	$-0.563076\pi$
$421$	16.0774	−	16.0774i	0.783566	−	0.783566i	0.980431	+	0.196865i	$0.0630761\pi$
$422$		0			0
$423$			0.364887i			0.0177414i
$424$		0			0
$425$		−	3.59464i		−	0.174366i
$426$		0			0
$427$	−3.10257	+	3.10257i	−0.150144	+	0.150144i
$428$		0			0
$429$	−5.44708	−	5.44708i	−0.262988	−	0.262988i
$430$		0			0
$431$	0.695976			0.0335240			0.0167620	−	0.999860i	$-0.494664\pi$
$431$	0.695976			0.0335240			0.0167620	+	0.999860i	$0.494664\pi$
$432$		0			0
$433$	26.4982			1.27342			0.636711	−	0.771103i	$-0.280295\pi$
$433$	26.4982			1.27342			0.636711	+	0.771103i	$0.280295\pi$
$434$		0			0
$435$	−19.6943	−	19.6943i	−0.944270	−	0.944270i
$436$		0			0
$437$	−12.7581	+	12.7581i	−0.610303	+	0.610303i
$438$		0			0
$439$			5.34131i			0.254927i	0.991843	+	0.127463i	$0.0406835\pi$
$439$			5.34131i			0.254927i	−0.991843	+	0.127463i	$0.959316\pi$
$440$		0			0
$441$			0.202696i			0.00965217i
$442$		0			0
$443$	18.0337	−	18.0337i	0.856805	−	0.856805i	−0.134155	−	0.990960i	$-0.542832\pi$
$443$	18.0337	−	18.0337i	0.856805	−	0.856805i	0.990960	+	0.134155i	$0.0428321\pi$
$444$		0			0
$445$	−0.805422	−	0.805422i	−0.0381807	−	0.0381807i
$446$		0			0
$447$	4.70360			0.222473
$448$		0			0
$449$	5.57561			0.263129			0.131565	−	0.991308i	$-0.458000\pi$
$449$	5.57561			0.263129			0.131565	+	0.991308i	$0.458000\pi$
$450$		0			0
$451$	0.811878	+	0.811878i	0.0382298	+	0.0382298i
$452$		0			0
$453$	17.9629	−	17.9629i	0.843970	−	0.843970i
$454$		0			0
$455$		−	14.8024i		−	0.693948i
$456$		0			0
$457$		−	11.8678i		−	0.555151i	−0.960704	−	0.277576i	$-0.910469\pi$
$457$		−	11.8678i		−	0.555151i	0.960704	−	0.277576i	$-0.0895309\pi$
$458$		0			0
$459$	−6.62446	+	6.62446i	−0.309203	+	0.309203i
$460$		0			0
$461$	25.1973	+	25.1973i	1.17356	+	1.17356i	0.981356	+	0.192200i	$0.0615624\pi$
$461$	25.1973	+	25.1973i	1.17356	+	1.17356i	0.192200	+	0.981356i	$0.438438\pi$
$462$		0			0
$463$	31.1785			1.44899			0.724494	−	0.689281i	$-0.242074\pi$
$463$	31.1785			1.44899			0.724494	+	0.689281i	$0.242074\pi$
$464$		0			0
$465$	35.1310			1.62916
$466$		0			0
$467$	−4.86260	−	4.86260i	−0.225014	−	0.225014i	0.585592	−	0.810606i	$-0.300862\pi$
$467$	−4.86260	−	4.86260i	−0.225014	−	0.225014i	−0.810606	+	0.585592i	$0.800862\pi$
$468$		0			0
$469$	4.81108	−	4.81108i	0.222155	−	0.222155i
$470$		0			0
$471$		−	18.7243i		−	0.862772i
$472$		0			0
$473$		−	2.03261i		−	0.0934594i
$474$		0			0
$475$	−8.62131	+	8.62131i	−0.395573	+	0.395573i
$476$		0			0
$477$	1.97360	+	1.97360i	0.0903648	+	0.0903648i
$478$		0			0
$479$	13.2313			0.604555			0.302277	−	0.953220i	$-0.402253\pi$
$479$	13.2313			0.604555			0.302277	+	0.953220i	$0.402253\pi$
$480$		0			0
$481$	−46.2830			−2.11032
$482$		0			0
$483$	−3.59702	−	3.59702i	−0.163670	−	0.163670i
$484$		0			0
$485$	36.0920	−	36.0920i	1.63886	−	1.63886i
$486$		0			0
$487$			27.6451i			1.25272i	0.779534	+	0.626360i	$0.215456\pi$
$487$			27.6451i			1.25272i	−0.779534	+	0.626360i	$0.784544\pi$
$488$		0			0
$489$		−	14.9527i		−	0.676185i
$490$		0			0
$491$	5.28148	−	5.28148i	0.238350	−	0.238350i	−0.577817	−	0.816167i	$-0.696095\pi$
$491$	5.28148	−	5.28148i	0.238350	−	0.238350i	0.816167	+	0.577817i	$0.196095\pi$
$492$		0			0
$493$	−7.75342	−	7.75342i	−0.349196	−	0.349196i
$494$		0			0
$495$	0.444976			0.0200002
$496$		0			0
$497$	−1.11625			−0.0500709
$498$		0			0
$499$	−28.8375	−	28.8375i	−1.29094	−	1.29094i	−0.934203	−	0.356741i	$-0.883888\pi$
$499$	−28.8375	−	28.8375i	−1.29094	−	1.29094i	−0.356741	−	0.934203i	$-0.616112\pi$
$500$		0			0
$501$	26.6407	−	26.6407i	1.19022	−	1.19022i
$502$		0			0
$503$			16.8595i			0.751729i	0.926675	+	0.375864i	$0.122654\pi$
$503$			16.8595i			0.751729i	−0.926675	+	0.375864i	$0.877346\pi$
$504$		0			0
$505$			18.3142i			0.814973i
$506$		0			0
$507$	21.3542	−	21.3542i	0.948372	−	0.948372i
$508$		0			0
$509$	−21.3899	−	21.3899i	−0.948093	−	0.948093i	0.0506250	−	0.998718i	$-0.483879\pi$
$509$	−21.3899	−	21.3899i	−0.948093	−	0.948093i	−0.998718	+	0.0506250i	$0.983879\pi$
$510$		0			0
$511$	−11.2521			−0.497762
$512$		0			0
$513$	31.7759			1.40294
$514$		0			0
$515$	11.4542	+	11.4542i	0.504732	+	0.504732i
$516$		0			0
$517$	−1.05204	+	1.05204i	−0.0462688	+	0.0462688i
$518$		0			0
$519$		−	0.0250509i		−	0.00109961i
$520$		0			0
$521$		−	29.9153i		−	1.31061i	−0.755363	−	0.655307i	$-0.772539\pi$
$521$		−	29.9153i		−	1.31061i	0.755363	−	0.655307i	$-0.227461\pi$
$522$		0			0
$523$	−12.6212	+	12.6212i	−0.551885	+	0.551885i	−0.926985	−	0.375099i	$-0.877609\pi$
$523$	−12.6212	+	12.6212i	−0.551885	+	0.551885i	0.375099	+	0.926985i	$0.377609\pi$
$524$		0			0
$525$	−2.43070	−	2.43070i	−0.106084	−	0.106084i
$526$		0			0
$527$	13.8307			0.602473
$528$		0			0
$529$	13.7492			0.597793
$530$		0			0
$531$	0.960781	+	0.960781i	0.0416943	+	0.0416943i
$532$		0			0
$533$	−5.47432	+	5.47432i	−0.237119	+	0.237119i
$534$		0			0
$535$		−	19.5329i		−	0.844482i
$536$		0			0
$537$			33.9583i			1.46541i
$538$		0			0
$539$	−0.584413	+	0.584413i	−0.0251724	+	0.0251724i
$540$		0			0
$541$	6.98421	+	6.98421i	0.300275	+	0.300275i	0.841121	−	0.540847i	$-0.181896\pi$
$541$	6.98421	+	6.98421i	0.300275	+	0.300275i	−0.540847	+	0.841121i	$0.681896\pi$
$542$		0			0
$543$	20.4674			0.878339
$544$		0			0
$545$	−28.9264			−1.23907
$546$		0			0
$547$	19.0691	+	19.0691i	0.815337	+	0.815337i	0.985428	−	0.170091i	$-0.0544062\pi$
$547$	19.0691	+	19.0691i	0.815337	+	0.815337i	−0.170091	+	0.985428i	$0.554406\pi$
$548$		0			0
$549$	0.628877	−	0.628877i	0.0268398	−	0.0268398i
$550$		0			0
$551$			37.1912i			1.58440i
$552$		0			0
$553$		−	7.61158i		−	0.323677i
$554$		0			0
$555$	−26.0891	+	26.0891i	−1.10742	+	1.10742i
$556$		0			0
$557$	10.7024	+	10.7024i	0.453474	+	0.453474i	0.896506	−	0.443032i	$-0.146097\pi$
$557$	10.7024	+	10.7024i	0.453474	+	0.453474i	−0.443032	+	0.896506i	$0.646097\pi$
$558$		0			0
$559$	13.7055			0.579679
$560$		0			0
$561$	−2.41760			−0.102071
$562$		0			0
$563$	6.53316	+	6.53316i	0.275340	+	0.275340i	0.831246	−	0.555905i	$-0.187628\pi$
$563$	6.53316	+	6.53316i	0.275340	+	0.275340i	−0.555905	+	0.831246i	$0.687628\pi$
$564$		0			0
$565$	26.7919	−	26.7919i	1.12714	−	1.12714i
$566$		0			0
$567$			8.35083i			0.350702i
$568$		0			0
$569$			36.7286i			1.53974i	0.638199	+	0.769871i	$0.279680\pi$
$569$			36.7286i			1.53974i	−0.638199	+	0.769871i	$0.720320\pi$
$570$		0			0
$571$	−23.7908	+	23.7908i	−0.995613	+	0.995613i	−0.999990	−	0.00437721i	$-0.998607\pi$
$571$	−23.7908	+	23.7908i	−0.995613	+	0.995613i	0.00437721	+	0.999990i	$0.498607\pi$
$572$		0			0
$573$	20.3516	+	20.3516i	0.850200	+	0.850200i
$574$		0			0
$575$	−6.25121			−0.260694
$576$		0			0
$577$	−5.87217			−0.244462			−0.122231	−	0.992502i	$-0.539005\pi$
$577$	−5.87217			−0.244462			−0.122231	+	0.992502i	$0.539005\pi$
$578$		0			0
$579$	−8.29014	−	8.29014i	−0.344527	−	0.344527i
$580$		0			0
$581$	−11.1869	+	11.1869i	−0.464112	+	0.464112i
$582$		0			0
$583$			11.3806i			0.471335i
$584$		0			0
$585$			3.00038i			0.124051i
$586$		0			0
$587$	−11.0010	+	11.0010i	−0.454060	+	0.454060i	−0.896700	−	0.442639i	$-0.854042\pi$
$587$	−11.0010	+	11.0010i	−0.454060	+	0.454060i	0.442639	+	0.896700i	$0.354042\pi$
$588$		0			0
$589$	−33.1712	−	33.1712i	−1.36679	−	1.36679i
$590$		0			0
$591$	−36.4669			−1.50005
$592$		0			0
$593$	26.8167			1.10123			0.550616	−	0.834759i	$-0.314393\pi$
$593$	26.8167			1.10123			0.550616	+	0.834759i	$0.314393\pi$
$594$		0			0
$595$	−3.28490	−	3.28490i	−0.134668	−	0.134668i
$596$		0			0
$597$	18.1516	−	18.1516i	0.742894	−	0.742894i
$598$		0			0
$599$			44.9307i			1.83582i	0.396791	+	0.917909i	$0.370124\pi$
$599$			44.9307i			1.83582i	−0.396791	+	0.917909i	$0.629876\pi$
$600$		0			0
$601$		−	40.2092i		−	1.64017i	−0.572244	−	0.820083i	$-0.693927\pi$
$601$		−	40.2092i		−	1.64017i	0.572244	−	0.820083i	$-0.306073\pi$
$602$		0			0
$603$	−0.975185	+	0.975185i	−0.0397126	+	0.0397126i
$604$		0			0
$605$	−19.3773	−	19.3773i	−0.787799	−	0.787799i
$606$		0			0
$607$	−20.7271			−0.841286			−0.420643	−	0.907226i	$-0.638195\pi$
$607$	−20.7271			−0.841286			−0.420643	+	0.907226i	$0.638195\pi$
$608$		0			0
$609$	−10.4857			−0.424903
$610$		0			0
$611$	−7.09371	−	7.09371i	−0.286981	−	0.286981i
$612$		0			0
$613$	5.43581	−	5.43581i	0.219550	−	0.219550i	−0.588759	−	0.808309i	$-0.700383\pi$
$613$	5.43581	−	5.43581i	0.219550	−	0.219550i	0.808309	+	0.588759i	$0.200383\pi$
$614$		0			0
$615$			6.17161i			0.248863i
$616$		0			0
$617$			24.8297i			0.999607i	0.866139	+	0.499803i	$0.166594\pi$
$617$			24.8297i			0.999607i	−0.866139	+	0.499803i	$0.833406\pi$
$618$		0			0
$619$	−13.2178	+	13.2178i	−0.531267	+	0.531267i	−0.920949	−	0.389683i	$-0.872585\pi$
$619$	−13.2178	+	13.2178i	−0.531267	+	0.531267i	0.389683	+	0.920949i	$0.372585\pi$
$620$		0			0
$621$	11.5202	+	11.5202i	0.462289	+	0.462289i
$622$		0			0
$623$	−0.428825			−0.0171805
$624$		0			0
$625$	31.0522			1.24209
$626$		0			0
$627$	5.79832	+	5.79832i	0.231563	+	0.231563i
$628$		0			0
$629$	−10.2710	+	10.2710i	−0.409531	+	0.409531i
$630$		0			0
$631$		−	30.4138i		−	1.21075i	−0.795939	−	0.605377i	$-0.793022\pi$
$631$		−	30.4138i		−	1.21075i	0.795939	−	0.605377i	$-0.206978\pi$
$632$		0			0
$633$			10.3624i			0.411870i
$634$		0			0
$635$	16.8721	−	16.8721i	0.669549	−	0.669549i
$636$		0			0
$637$	−3.94057	−	3.94057i	−0.156131	−	0.156131i
$638$		0			0
$639$	0.226260			0.00895071
$640$		0			0
$641$	−41.7486			−1.64897			−0.824485	−	0.565884i	$-0.808535\pi$
$641$	−41.7486			−1.64897			−0.824485	+	0.565884i	$0.808535\pi$
$642$		0			0
$643$	15.4137	+	15.4137i	0.607857	+	0.607857i	0.942386	−	0.334529i	$-0.108577\pi$
$643$	15.4137	+	15.4137i	0.607857	+	0.607857i	−0.334529	+	0.942386i	$0.608577\pi$
$644$		0			0
$645$	7.72559	−	7.72559i	0.304195	−	0.304195i
$646$		0			0
$647$			8.85923i			0.348292i	0.984720	+	0.174146i	$0.0557165\pi$
$647$			8.85923i			0.348292i	−0.984720	+	0.174146i	$0.944283\pi$
$648$		0			0
$649$			5.54026i			0.217474i
$650$		0			0
$651$	9.35230	−	9.35230i	0.366545	−	0.366545i
$652$		0			0
$653$	−2.42659	−	2.42659i	−0.0949598	−	0.0949598i	0.658031	−	0.752991i	$-0.271390\pi$
$653$	−2.42659	−	2.42659i	−0.0949598	−	0.0949598i	−0.752991	+	0.658031i	$0.771390\pi$
$654$		0			0
$655$	47.9117			1.87206
$656$		0			0
$657$	2.28075			0.0889804
$658$		0			0
$659$	−23.3045	−	23.3045i	−0.907815	−	0.907815i	0.0882806	−	0.996096i	$-0.471863\pi$
$659$	−23.3045	−	23.3045i	−0.907815	−	0.907815i	−0.996096	+	0.0882806i	$0.971863\pi$
$660$		0			0
$661$	−23.2433	+	23.2433i	−0.904059	+	0.904059i	−0.995784	−	0.0917252i	$-0.970762\pi$
$661$	−23.2433	+	23.2433i	−0.904059	+	0.904059i	0.0917252	+	0.995784i	$0.470762\pi$
$662$		0			0
$663$		−	16.3014i		−	0.633093i
$664$		0			0
$665$			15.7569i			0.611026i
$666$		0			0
$667$	−13.4835	+	13.4835i	−0.522082	+	0.522082i
$668$		0			0
$669$	−0.625543	−	0.625543i	−0.0241849	−	0.0241849i
$670$		0			0
$671$	3.62636			0.139994
$672$		0			0
$673$	46.7430			1.80181			0.900906	−	0.434014i	$-0.142903\pi$
$673$	46.7430			1.80181			0.900906	+	0.434014i	$0.142903\pi$
$674$		0			0
$675$	7.78478	+	7.78478i	0.299636	+	0.299636i
$676$		0			0
$677$	−30.0928	+	30.0928i	−1.15656	+	1.15656i	−0.171351	+	0.985210i	$0.554813\pi$
$677$	−30.0928	+	30.0928i	−1.15656	+	1.15656i	−0.985210	+	0.171351i	$0.945187\pi$
$678$		0			0
$679$		−	19.2163i		−	0.737452i
$680$		0			0
$681$			42.2760i			1.62002i
$682$		0			0
$683$	25.4691	−	25.4691i	0.974548	−	0.974548i	−0.0251358	−	0.999684i	$-0.508002\pi$
$683$	25.4691	−	25.4691i	0.974548	−	0.974548i	0.999684	+	0.0251358i	$0.00800181\pi$
$684$		0			0
$685$	22.1490	+	22.1490i	0.846270	+	0.846270i
$686$		0			0
$687$	−20.6549			−0.788033
$688$		0			0
$689$	−76.7368			−2.92344
$690$		0			0
$691$	15.5437	+	15.5437i	0.591311	+	0.591311i	0.937986	−	0.346674i	$-0.112689\pi$
$691$	15.5437	+	15.5437i	0.591311	+	0.591311i	−0.346674	+	0.937986i	$0.612689\pi$
$692$		0			0
$693$	0.118458	−	0.118458i	0.00449984	−	0.00449984i
$694$		0			0
$695$		−	1.96842i		−	0.0746664i
$696$		0			0
$697$			2.42969i			0.0920311i
$698$		0			0
$699$	31.8705	−	31.8705i	1.20545	−	1.20545i
$700$		0			0
$701$	5.59915	+	5.59915i	0.211477	+	0.211477i	0.804895	−	0.593418i	$-0.202222\pi$
$701$	5.59915	+	5.59915i	0.211477	+	0.211477i	−0.593418	+	0.804895i	$0.702222\pi$
$702$		0			0
$703$	49.2674			1.85815
$704$		0			0
$705$	−7.99726			−0.301194
$706$		0			0
$707$	4.87547	+	4.87547i	0.183361	+	0.183361i
$708$		0			0
$709$	0.685858	−	0.685858i	0.0257579	−	0.0257579i	−0.694111	−	0.719868i	$-0.744202\pi$
$709$	0.685858	−	0.685858i	0.0257579	−	0.0257579i	0.719868	+	0.694111i	$0.244202\pi$
$710$		0			0
$711$			1.54283i			0.0578608i
$712$		0			0
$713$		−	24.0520i		−	0.900756i
$714$		0			0
$715$	−8.65072	+	8.65072i	−0.323518	+	0.323518i
$716$		0			0
$717$	23.4223	+	23.4223i	0.874721	+	0.874721i
$718$		0			0
$719$	−10.0440			−0.374579			−0.187289	−	0.982305i	$-0.559970\pi$
$719$	−10.0440			−0.374579			−0.187289	+	0.982305i	$0.559970\pi$
$720$		0			0
$721$	6.09849			0.227119
$722$		0			0
$723$	−4.42302	−	4.42302i	−0.164494	−	0.164494i
$724$		0			0
$725$	−9.11148	+	9.11148i	−0.338392	+	0.338392i
$726$		0			0
$727$			5.53235i			0.205184i	0.994724	+	0.102592i	$0.0327135\pi$
$727$			5.53235i			0.205184i	−0.994724	+	0.102592i	$0.967286\pi$
$728$		0			0
$729$		−	28.5694i		−	1.05813i
$730$		0			0
$731$	3.04147	−	3.04147i	0.112493	−	0.112493i
$732$		0			0
$733$	−3.98509	−	3.98509i	−0.147193	−	0.147193i	0.629670	−	0.776863i	$-0.283190\pi$
$733$	−3.98509	−	3.98509i	−0.147193	−	0.147193i	−0.776863	+	0.629670i	$0.783190\pi$
$734$		0			0
$735$	−4.44250			−0.163864
$736$		0			0
$737$	−5.62331			−0.207137
$738$		0			0
$739$	−2.19669	−	2.19669i	−0.0808065	−	0.0808065i	0.665548	−	0.746355i	$-0.268198\pi$
$739$	−2.19669	−	2.19669i	−0.0808065	−	0.0808065i	−0.746355	+	0.665548i	$0.768198\pi$
$740$		0			0
$741$	−39.0969	+	39.0969i	−1.43626	+	1.43626i
$742$		0			0
$743$		−	22.5404i		−	0.826927i	−0.910521	−	0.413464i	$-0.864319\pi$
$743$		−	22.5404i		−	0.826927i	0.910521	−	0.413464i	$-0.135681\pi$
$744$		0			0
$745$		−	7.46996i		−	0.273678i
$746$		0			0
$747$	2.26754	−	2.26754i	0.0829649	−	0.0829649i
$748$		0			0
$749$	−5.19989	−	5.19989i	−0.190000	−	0.190000i
$750$		0			0
$751$	14.8752			0.542805			0.271403	−	0.962466i	$-0.412513\pi$
$751$	14.8752			0.542805			0.271403	+	0.962466i	$0.412513\pi$
$752$		0			0
$753$	−24.0020			−0.874682
$754$		0			0
$755$	−28.5275	−	28.5275i	−1.03822	−	1.03822i
$756$		0			0
$757$	−0.982488	+	0.982488i	−0.0357091	+	0.0357091i	−0.724736	−	0.689027i	$-0.758038\pi$
$757$	−0.982488	+	0.982488i	−0.0357091	+	0.0357091i	0.689027	+	0.724736i	$0.258038\pi$
$758$		0			0
$759$			4.20429i			0.152606i
$760$		0			0
$761$			19.9186i			0.722049i	0.932556	+	0.361024i	$0.117573\pi$
$761$			19.9186i			0.722049i	−0.932556	+	0.361024i	$0.882427\pi$
$762$		0			0
$763$	−7.70055	+	7.70055i	−0.278779	+	0.278779i
$764$		0			0
$765$	0.665836	+	0.665836i	0.0240733	+	0.0240733i
$766$		0			0
$767$	−37.3568			−1.34888
$768$		0			0
$769$	−9.78665			−0.352915			−0.176458	−	0.984308i	$-0.556464\pi$
$769$	−9.78665			−0.352915			−0.176458	+	0.984308i	$0.556464\pi$
$770$		0			0
$771$	−14.9144	−	14.9144i	−0.537130	−	0.537130i
$772$		0			0
$773$	−19.6983	+	19.6983i	−0.708499	+	0.708499i	−0.966220	−	0.257720i	$-0.917029\pi$
$773$	−19.6983	+	19.6983i	−0.708499	+	0.708499i	0.257720	+	0.966220i	$0.417029\pi$
$774$		0			0
$775$		−	16.2532i		−	0.583832i
$776$		0			0
$777$			13.8905i			0.498318i
$778$		0			0
$779$	5.82731	−	5.82731i	0.208785	−	0.208785i
$780$		0			0
$781$	0.652354	+	0.652354i	0.0233430	+	0.0233430i
$782$		0			0
$783$	33.5825			1.20014
$784$		0			0
$785$	−29.7368			−1.06135
$786$		0			0
$787$	30.9238	+	30.9238i	1.10231	+	1.10231i	0.994131	+	0.108184i	$0.0345035\pi$
$787$	30.9238	+	30.9238i	1.10231	+	1.10231i	0.108184	+	0.994131i	$0.465496\pi$
$788$		0			0
$789$	−8.29244	+	8.29244i	−0.295219	+	0.295219i
$790$		0			0
$791$		−	14.2646i		−	0.507192i
$792$		0			0
$793$			24.4518i			0.868309i
$794$		0			0
$795$	−43.2555	+	43.2555i	−1.53412	+	1.53412i
$796$		0			0
$797$	−32.5005	−	32.5005i	−1.15123	−	1.15123i	−0.986307	−	0.164919i	$-0.947264\pi$
$797$	−32.5005	−	32.5005i	−1.15123	−	1.15123i	−0.164919	−	0.986307i	$-0.552736\pi$
$798$		0			0
$799$	−3.14843			−0.111383
$800$		0			0
$801$	0.0869210			0.00307120
$802$		0			0
$803$	6.57585	+	6.57585i	0.232057	+	0.232057i
$804$		0			0
$805$	−5.71257	+	5.71257i	−0.201342	+	0.201342i
$806$		0			0
$807$		−	9.27920i		−	0.326643i
$808$		0			0
$809$		−	20.8417i		−	0.732756i	−0.930466	−	0.366378i	$-0.880598\pi$
$809$		−	20.8417i		−	0.732756i	0.930466	−	0.366378i	$-0.119402\pi$
$810$		0			0
$811$	1.93354	−	1.93354i	0.0678959	−	0.0678959i	−0.672343	−	0.740239i	$-0.734712\pi$
$811$	1.93354	−	1.93354i	0.0678959	−	0.0678959i	0.740239	+	0.672343i	$0.234712\pi$
$812$		0			0
$813$	27.8804	+	27.8804i	0.977807	+	0.977807i
$814$		0			0
$815$	−23.7469			−0.831819
$816$		0			0
$817$	−14.5892			−0.510411
$818$		0			0
$819$	0.798737	+	0.798737i	0.0279101	+	0.0279101i
$820$		0			0
$821$	6.76535	−	6.76535i	0.236112	−	0.236112i	−0.579126	−	0.815238i	$-0.696606\pi$
$821$	6.76535	−	6.76535i	0.236112	−	0.236112i	0.815238	+	0.579126i	$0.196606\pi$
$822$		0			0
$823$		−	35.9651i		−	1.25366i	−0.779154	−	0.626832i	$-0.784351\pi$
$823$		−	35.9651i		−	1.25366i	0.779154	−	0.626832i	$-0.215649\pi$
$824$		0			0
$825$			2.84106i			0.0989130i
$826$		0			0
$827$	−23.1871	+	23.1871i	−0.806296	+	0.806296i	−0.984071	−	0.177775i	$-0.943110\pi$
$827$	−23.1871	+	23.1871i	−0.806296	+	0.806296i	0.177775	+	0.984071i	$0.443110\pi$
$828$		0			0
$829$	−18.4289	−	18.4289i	−0.640063	−	0.640063i	0.310508	−	0.950571i	$-0.399501\pi$
$829$	−18.4289	−	18.4289i	−0.640063	−	0.640063i	−0.950571	+	0.310508i	$0.899501\pi$
$830$		0			0
$831$	18.6782			0.647938
$832$		0			0
$833$	−1.74896			−0.0605979
$834$		0			0
$835$	−42.3091	−	42.3091i	−1.46417	−	1.46417i
$836$		0			0
$837$	−29.9526	+	29.9526i	−1.03531	+	1.03531i
$838$		0			0
$839$			34.0165i			1.17438i	0.809449	+	0.587191i	$0.199766\pi$
$839$			34.0165i			1.17438i	−0.809449	+	0.587191i	$0.800234\pi$
$840$		0			0
$841$			10.3058i			0.355371i
$842$		0			0
$843$	−39.2346	+	39.2346i	−1.35131	+	1.35131i
$844$		0			0
$845$	−33.9133	−	33.9133i	−1.16665	−	1.16665i
$846$		0			0
$847$	−10.3169			−0.354494
$848$		0			0
$849$	4.87829			0.167423
$850$		0			0
$851$	17.8616	+	17.8616i	0.612288	+	0.612288i
$852$		0			0
$853$	11.0005	−	11.0005i	0.376649	−	0.376649i	−0.493243	−	0.869892i	$-0.664188\pi$
$853$	11.0005	−	11.0005i	0.376649	−	0.376649i	0.869892	+	0.493243i	$0.164188\pi$
$854$		0			0
$855$		−	3.19385i		−	0.109227i
$856$		0			0
$857$			0.996249i			0.0340312i	0.999855	+	0.0170156i	$0.00541650\pi$
$857$			0.996249i			0.0340312i	−0.999855	+	0.0170156i	$0.994584\pi$
$858$		0			0
$859$	−23.5504	+	23.5504i	−0.803530	+	0.803530i	−0.983645	−	0.180116i	$-0.942353\pi$
$859$	−23.5504	+	23.5504i	−0.803530	+	0.803530i	0.180116	+	0.983645i	$0.442353\pi$
$860$		0			0
$861$	1.64296	+	1.64296i	0.0559918	+	0.0559918i
$862$		0			0
$863$	45.1680			1.53754			0.768768	−	0.639528i	$-0.220870\pi$
$863$	45.1680			1.53754			0.768768	+	0.639528i	$0.220870\pi$
$864$		0			0
$865$	−0.0397843			−0.00135271
$866$		0			0
$867$	16.4874	+	16.4874i	0.559943	+	0.559943i
$868$		0			0
$869$	−4.44831	+	4.44831i	−0.150898	+	0.150898i
$870$		0			0
$871$		−	37.9168i		−	1.28476i
$872$		0			0
$873$			3.89505i			0.131827i
$874$		0			0
$875$	5.53074	−	5.53074i	0.186973	−	0.186973i
$876$		0			0
$877$	4.57165	+	4.57165i	0.154374	+	0.154374i	0.780068	−	0.625695i	$-0.215184\pi$
$877$	4.57165	+	4.57165i	0.154374	+	0.154374i	−0.625695	+	0.780068i	$0.715184\pi$
$878$		0			0
$879$	12.5941			0.424788
$880$		0			0
$881$	29.5811			0.996613			0.498306	−	0.867001i	$-0.333955\pi$
$881$	29.5811			0.996613			0.498306	+	0.867001i	$0.333955\pi$
$882$		0			0
$883$	−20.9519	−	20.9519i	−0.705087	−	0.705087i	0.260411	−	0.965498i	$-0.416142\pi$
$883$	−20.9519	−	20.9519i	−0.705087	−	0.705087i	−0.965498	+	0.260411i	$0.916142\pi$
$884$		0			0
$885$	−21.0575	+	21.0575i	−0.707842	+	0.707842i
$886$		0			0
$887$		−	33.7805i		−	1.13424i	−0.823635	−	0.567120i	$-0.808058\pi$
$887$		−	33.7805i		−	1.13424i	0.823635	−	0.567120i	$-0.191942\pi$
$888$		0			0
$889$		−	8.98310i		−	0.301284i
$890$		0			0
$891$	4.88033	−	4.88033i	0.163497	−	0.163497i
$892$		0			0
$893$	7.55112	+	7.55112i	0.252688	+	0.252688i
$894$		0			0
$895$	53.9305			1.80270
$896$		0			0
$897$	−28.3487			−0.946535
$898$		0			0
$899$	−35.0571	−	35.0571i	−1.16922	−	1.16922i
$900$		0			0
$901$	−17.0292	+	17.0292i	−0.567325	+	0.567325i
$902$		0			0
$903$		−	4.11328i		−	0.136881i
$904$		0			0
$905$		−	32.5050i		−	1.08050i
$906$		0			0
$907$	37.9368	−	37.9368i	1.25967	−	1.25967i	0.308418	−	0.951251i	$-0.400200\pi$
$907$	37.9368	−	37.9368i	1.25967	−	1.25967i	0.951251	−	0.308418i	$-0.0997997\pi$
$908$		0			0
$909$	−0.988236	−	0.988236i	−0.0327777	−	0.0327777i
$910$		0			0
$911$	−16.3562			−0.541906			−0.270953	−	0.962593i	$-0.587339\pi$
$911$	−16.3562			−0.541906			−0.270953	+	0.962593i	$0.587339\pi$
$912$		0			0
$913$	13.0756			0.432738
$914$		0			0
$915$	13.7832	+	13.7832i	0.455658	+	0.455658i
$916$		0			0
$917$	12.7547	−	12.7547i	0.421196	−	0.421196i
$918$		0			0
$919$		−	6.74372i		−	0.222455i	−0.993795	−	0.111227i	$-0.964522\pi$
$919$		−	6.74372i		−	0.222455i	0.993795	−	0.111227i	$-0.0354782\pi$
$920$		0			0
$921$		−	23.4742i		−	0.773503i
$922$		0			0
$923$	−4.39869	+	4.39869i	−0.144785	+	0.144785i
$924$		0			0
$925$	12.0700	+	12.0700i	0.396859	+	0.396859i
$926$		0			0
$927$	−1.23614			−0.0406000
$928$		0			0
$929$	−3.61776			−0.118695			−0.0593475	−	0.998237i	$-0.518902\pi$
$929$	−3.61776			−0.118695			−0.0593475	+	0.998237i	$0.518902\pi$
$930$		0			0
$931$	4.19467	+	4.19467i	0.137475	+	0.137475i
$932$		0			0
$933$	−11.5678	+	11.5678i	−0.378712	+	0.378712i
$934$		0			0
$935$			3.83948i			0.125564i
$936$		0			0
$937$		−	2.79455i		−	0.0912940i	−0.998958	−	0.0456470i	$-0.985465\pi$
$937$		−	2.79455i		−	0.0912940i	0.998958	−	0.0456470i	$-0.0145349\pi$
$938$		0			0
$939$	−6.72595	+	6.72595i	−0.219493	+	0.219493i
$940$		0			0
$941$	17.3862	+	17.3862i	0.566775	+	0.566775i	0.931224	−	0.364448i	$-0.118742\pi$
$941$	17.3862	+	17.3862i	0.566775	+	0.566775i	−0.364448	+	0.931224i	$0.618742\pi$
$942$		0			0
$943$	4.22532			0.137595
$944$		0			0
$945$	14.2280			0.462836
$946$		0			0
$947$	−29.8903	−	29.8903i	−0.971304	−	0.971304i	0.0282955	−	0.999600i	$-0.490992\pi$
$947$	−29.8903	−	29.8903i	−0.971304	−	0.971304i	−0.999600	+	0.0282955i	$0.990992\pi$
$948$		0			0
$949$	−44.3396	+	44.3396i	−1.43933	+	1.43933i
$950$		0			0
$951$			51.7199i			1.67713i
$952$		0			0
$953$			26.9944i			0.874434i	0.899356	+	0.437217i	$0.144036\pi$
$953$			26.9944i			0.874434i	−0.899356	+	0.437217i	$0.855964\pi$
$954$		0			0
$955$	32.3211	−	32.3211i	1.04589	−	1.04589i
$956$		0			0
$957$	6.12799	+	6.12799i	0.198090	+	0.198090i
$958$		0			0
$959$	11.7927			0.380805
$960$		0			0
$961$	31.5355			1.01727
$962$		0			0
$963$	1.05400	+	1.05400i	0.0339645	+	0.0339645i
$964$		0			0
$965$	−13.1659	+	13.1659i	−0.423825	+	0.423825i
$966$		0			0
$967$			3.64431i			0.117193i	0.998282	+	0.0585966i	$0.0186626\pi$
$967$			3.64431i			0.117193i	−0.998282	+	0.0585966i	$0.981337\pi$
$968$		0			0
$969$			17.3525i			0.557443i
$970$		0			0
$971$	−10.3490	+	10.3490i	−0.332114	+	0.332114i	−0.853389	−	0.521275i	$-0.825457\pi$
$971$	−10.3490	+	10.3490i	−0.332114	+	0.332114i	0.521275	+	0.853389i	$0.325457\pi$
$972$		0			0
$973$	−0.524016	−	0.524016i	−0.0167992	−	0.0167992i
$974$		0			0
$975$	−19.1567			−0.613504
$976$		0			0
$977$	−11.7791			−0.376846			−0.188423	−	0.982088i	$-0.560338\pi$
$977$	−11.7791			−0.376846			−0.188423	+	0.982088i	$0.560338\pi$
$978$		0			0
$979$	0.250611	+	0.250611i	0.00800956	+	0.00800956i
$980$		0			0
$981$	1.56087	−	1.56087i	0.0498347	−	0.0498347i
$982$		0			0
$983$		−	3.39640i		−	0.108328i	−0.998532	−	0.0541642i	$-0.982751\pi$
$983$		−	3.39640i		−	0.108328i	0.998532	−	0.0541642i	$-0.0172494\pi$
$984$		0			0
$985$			57.9145i			1.84531i
$986$		0			0
$987$	−2.12896	+	2.12896i	−0.0677657	+	0.0677657i
$988$		0			0
$989$	−5.28923	−	5.28923i	−0.168188	−	0.168188i
$990$		0			0
$991$	−24.0326			−0.763421			−0.381710	−	0.924282i	$-0.624665\pi$
$991$	−24.0326			−0.763421			−0.381710	+	0.924282i	$0.624665\pi$
$992$		0			0
$993$	20.7186			0.657485
$994$		0			0
$995$	−28.8272	−	28.8272i	−0.913883	−	0.913883i
$996$		0			0
$997$	1.71006	−	1.71006i	0.0541583	−	0.0541583i	−0.679509	−	0.733667i	$-0.737807\pi$
$997$	1.71006	−	1.71006i	0.0541583	−	0.0541583i	0.733667	+	0.679509i	$0.237807\pi$
$998$		0			0
$999$		−	44.4869i		−	1.40750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1792.2.m.g.1345.3	yes	16
4.3	odd	2		1792.2.m.e.1345.6	yes	16
8.3	odd	2		1792.2.m.h.1345.3	yes	16
8.5	even	2		1792.2.m.f.1345.6	yes	16
16.3	odd	4		1792.2.m.h.449.3	yes	16
16.5	even	4	inner	1792.2.m.g.449.3	yes	16
16.11	odd	4		1792.2.m.e.449.6	✓	16
16.13	even	4		1792.2.m.f.449.6	yes	16
32.5	even	8		7168.2.a.be.1.6		8
32.11	odd	8		7168.2.a.bb.1.6		8
32.21	even	8		7168.2.a.ba.1.3		8
32.27	odd	8		7168.2.a.bf.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1792.2.m.e.449.6	✓	16	16.11	odd	4
1792.2.m.e.1345.6	yes	16	4.3	odd	2
1792.2.m.f.449.6	yes	16	16.13	even	4
1792.2.m.f.1345.6	yes	16	8.5	even	2
1792.2.m.g.449.3	yes	16	16.5	even	4	inner
1792.2.m.g.1345.3	yes	16	1.1	even	1	trivial
1792.2.m.h.449.3	yes	16	16.3	odd	4
1792.2.m.h.1345.3	yes	16	8.3	odd	2
7168.2.a.ba.1.3		8	32.21	even	8
7168.2.a.bb.1.6		8	32.11	odd	8
7168.2.a.be.1.6		8	32.5	even	8
7168.2.a.bf.1.3		8	32.27	odd	8

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:	\( N \)	\(=\)	\( 1792 = 2^{8} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1792.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18265 - 1.18265i) q^{3} +(-1.87820 + 1.87820i) q^{5} +1.00000i q^{7} -0.202696i q^{9} +O(q^{10})\)	\(q+(-1.18265 - 1.18265i) q^{3} +(-1.87820 + 1.87820i) q^{5} +1.00000i q^{7} -0.202696i q^{9} +(0.584413 - 0.584413i) q^{11} +(3.94057 + 3.94057i) q^{13} +4.44250 q^{15} +1.74896 q^{17} +(-4.19467 - 4.19467i) q^{19} +(1.18265 - 1.18265i) q^{21} -3.04150i q^{23} -2.05530i q^{25} +(-3.78766 + 3.78766i) q^{27} +(-4.43316 - 4.43316i) q^{29} +7.90794 q^{31} -1.38231 q^{33} +(-1.87820 - 1.87820i) q^{35} +(-5.87262 + 5.87262i) q^{37} -9.32061i q^{39} +1.38922i q^{41} +(1.73902 - 1.73902i) q^{43} +(0.380704 + 0.380704i) q^{45} -1.80017 q^{47} -1.00000 q^{49} +(-2.06840 - 2.06840i) q^{51} +(-9.73675 + 9.73675i) q^{53} +2.19529i q^{55} +9.92162i q^{57} +(-4.74002 + 4.74002i) q^{59} +(3.10257 + 3.10257i) q^{61} +0.202696 q^{63} -14.8024 q^{65} +(-4.81108 - 4.81108i) q^{67} +(-3.59702 + 3.59702i) q^{69} +1.11625i q^{71} +11.2521i q^{73} +(-2.43070 + 2.43070i) q^{75} +(0.584413 + 0.584413i) q^{77} -7.61158 q^{79} +8.35083 q^{81} +(11.1869 + 11.1869i) q^{83} +(-3.28490 + 3.28490i) q^{85} +10.4857i q^{87} +0.428825i q^{89} +(-3.94057 + 3.94057i) q^{91} +(-9.35230 - 9.35230i) q^{93} +15.7569 q^{95} -19.2163 q^{97} +(-0.118458 - 0.118458i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^3 - 4 * q^5	\( 16 q + 4 q^{3} - 4 q^{5} - 8 q^{11} + 12 q^{13} - 8 q^{17} + 4 q^{19} - 4 q^{21} - 56 q^{27} + 8 q^{31} + 16 q^{33} - 4 q^{35} - 8 q^{37} - 24 q^{43} - 36 q^{45} + 40 q^{47} - 16 q^{49} + 24 q^{51} - 32 q^{53} - 4 q^{59} - 20 q^{61} - 24 q^{63} + 72 q^{65} + 32 q^{67} + 56 q^{69} - 28 q^{75} - 8 q^{77} - 40 q^{81} + 36 q^{83} - 12 q^{91} + 8 q^{93} + 80 q^{95} - 72 q^{97} - 8 q^{99}+O(q^{100}) \) 16 * q + 4 * q^3 - 4 * q^5 - 8 * q^11 + 12 * q^13 - 8 * q^17 + 4 * q^19 - 4 * q^21 - 56 * q^27 + 8 * q^31 + 16 * q^33 - 4 * q^35 - 8 * q^37 - 24 * q^43 - 36 * q^45 + 40 * q^47 - 16 * q^49 + 24 * q^51 - 32 * q^53 - 4 * q^59 - 20 * q^61 - 24 * q^63 + 72 * q^65 + 32 * q^67 + 56 * q^69 - 28 * q^75 - 8 * q^77 - 40 * q^81 + 36 * q^83 - 12 * q^91 + 8 * q^93 + 80 * q^95 - 72 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

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