LMFDB - Embedded newform 513.2.h.c.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [513,2,Mod(235,513)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(513, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("513.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.h (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:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Character	$\chi$	$=$	513.235
Dual form			513.2.h.c.334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46808 q^{2} +4.09140 q^{4} +(0.957619 - 1.65865i) q^{5} +(-0.324708 + 0.562412i) q^{7} -5.16173 q^{8} +O(q^{10})$	\(q-2.46808 q^{2} +4.09140 q^{4} +(0.957619 - 1.65865i) q^{5} +(-0.324708 + 0.562412i) q^{7} -5.16173 q^{8} +(-2.36348 + 4.09366i) q^{10} +(-2.93240 + 5.07906i) q^{11} -0.655382 q^{13} +(0.801405 - 1.38807i) q^{14} +4.55674 q^{16} +(1.93700 + 3.35499i) q^{17} +(-4.28438 + 0.802530i) q^{19} +(3.91800 - 6.78618i) q^{20} +(7.23738 - 12.5355i) q^{22} +1.92354 q^{23} +(0.665931 + 1.15343i) q^{25} +1.61753 q^{26} +(-1.32851 + 2.30105i) q^{28} +(-3.26819 - 5.66068i) q^{29} +(1.54544 + 2.67678i) q^{31} -0.922922 q^{32} +(-4.78067 - 8.28037i) q^{34} +(0.621894 + 1.07715i) q^{35} +2.23125 q^{37} +(10.5742 - 1.98070i) q^{38} +(-4.94297 + 8.56147i) q^{40} +(-3.48405 + 6.03455i) q^{41} -8.93879 q^{43} +(-11.9976 + 20.7805i) q^{44} -4.74743 q^{46} +(5.77487 + 10.0024i) q^{47} +(3.28913 + 5.69694i) q^{49} +(-1.64357 - 2.84674i) q^{50} -2.68143 q^{52} +(6.35124 - 11.0007i) q^{53} +(5.61624 + 9.72762i) q^{55} +(1.67606 - 2.90302i) q^{56} +(8.06615 + 13.9710i) q^{58} +(-7.16730 + 12.4141i) q^{59} +(5.17155 + 8.95739i) q^{61} +(-3.81426 - 6.60649i) q^{62} -6.83564 q^{64} +(-0.627606 + 1.08705i) q^{65} +0.763890 q^{67} +(7.92505 + 13.7266i) q^{68} +(-1.53488 - 2.65849i) q^{70} +(0.299796 + 0.519263i) q^{71} +(1.75541 + 3.04046i) q^{73} -5.50690 q^{74} +(-17.5291 + 3.28347i) q^{76} +(-1.90435 - 3.29843i) q^{77} -4.26958 q^{79} +(4.36362 - 7.55801i) q^{80} +(8.59890 - 14.8937i) q^{82} +(3.29968 - 5.71522i) q^{83} +7.41965 q^{85} +22.0616 q^{86} +(15.1362 - 26.2167i) q^{88} +(-2.41922 + 4.19022i) q^{89} +(0.212808 - 0.368594i) q^{91} +7.86995 q^{92} +(-14.2528 - 24.6866i) q^{94} +(-2.77170 + 7.87479i) q^{95} +2.38904 q^{97} +(-8.11782 - 14.0605i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8	$ 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} + 8 q^{13} - q^{14} + 22 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} - 8 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} - 10 q^{28} - 10 q^{29} - 10 q^{31} + 34 q^{32} - 13 q^{34} + 3 q^{35} + 2 q^{37} + 46 q^{38} + 12 q^{40} - 6 q^{41} - 14 q^{43} - 20 q^{44} + 9 q^{47} - 13 q^{49} - q^{50} - 38 q^{52} - 16 q^{53} + 15 q^{55} + 6 q^{56} - 37 q^{59} - 12 q^{61} - 54 q^{62} - 64 q^{64} - 54 q^{65} + 22 q^{67} + 2 q^{68} + 24 q^{70} - 9 q^{71} - 10 q^{73} + 12 q^{74} - 40 q^{76} - 46 q^{77} + 16 q^{79} + 24 q^{80} + 7 q^{82} - 3 q^{83} + 54 q^{85} + 34 q^{86} + 9 q^{88} - 30 q^{89} - q^{91} - 34 q^{92} - 18 q^{94} - 3 q^{95} - 18 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 + 8 * q^13 - q^14 + 22 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 - 8 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 - 10 * q^28 - 10 * q^29 - 10 * q^31 + 34 * q^32 - 13 * q^34 + 3 * q^35 + 2 * q^37 + 46 * q^38 + 12 * q^40 - 6 * q^41 - 14 * q^43 - 20 * q^44 + 9 * q^47 - 13 * q^49 - q^50 - 38 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 - 37 * q^59 - 12 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 + 22 * q^67 + 2 * q^68 + 24 * q^70 - 9 * q^71 - 10 * q^73 + 12 * q^74 - 40 * q^76 - 46 * q^77 + 16 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 + 54 * q^85 + 34 * q^86 + 9 * q^88 - 30 * q^89 - q^91 - 34 * q^92 - 18 * q^94 - 3 * q^95 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.46808			−1.74519			−0.872597	−	0.488442i	$-0.837565\pi$
$2$	−2.46808			−1.74519			−0.872597	+	0.488442i	$0.837565\pi$
$3$		0			0
$3$		0			0
$4$	4.09140			2.04570
$5$	0.957619	−	1.65865i	0.428260	−	0.741769i	−0.568458	−	0.822712i	$-0.692460\pi$
$5$	0.957619	−	1.65865i	0.428260	−	0.741769i	0.996719	+	0.0809434i	$0.0257933\pi$
$6$		0			0
$7$	−0.324708	+	0.562412i	−0.122728	+	0.212572i	−0.920843	−	0.389934i	$-0.872498\pi$
$7$	−0.324708	+	0.562412i	−0.122728	+	0.212572i	0.798114	+	0.602506i	$0.205831\pi$
$8$	−5.16173			−1.82495
$9$		0			0
$10$	−2.36348	+	4.09366i	−0.747397	+	1.29453i
$11$	−2.93240	+	5.07906i	−0.884151	+	1.53140i	−0.0374684	+	0.999298i	$0.511929\pi$
$11$	−2.93240	+	5.07906i	−0.884151	+	1.53140i	−0.846683	+	0.532097i	$0.821404\pi$
$12$		0			0
$13$	−0.655382			−0.181770			−0.0908851	−	0.995861i	$-0.528970\pi$
$13$	−0.655382			−0.181770			−0.0908851	+	0.995861i	$0.528970\pi$
$14$	0.801405	−	1.38807i	0.214185	−	0.370978i
$15$		0			0
$16$	4.55674			1.13918
$17$	1.93700	+	3.35499i	0.469792	+	0.813704i	0.999403	−	0.0345362i	$-0.0109954\pi$
$17$	1.93700	+	3.35499i	0.469792	+	0.813704i	−0.529611	+	0.848241i	$0.677662\pi$
$18$		0			0
$19$	−4.28438	+	0.802530i	−0.982905	+	0.184113i
$19$	−4.28438	+	0.802530i	−0.982905	+	0.184113i
$20$	3.91800	−	6.78618i	0.876092	−	1.51744i
$21$		0			0
$22$	7.23738	−	12.5355i	1.54302	−	2.67258i
$23$	1.92354			0.401085			0.200542	−	0.979685i	$-0.435730\pi$
$23$	1.92354			0.401085			0.200542	+	0.979685i	$0.435730\pi$
$24$		0			0
$25$	0.665931	+	1.15343i	0.133186	+	0.230685i
$26$	1.61753			0.317224
$27$		0			0
$28$	−1.32851	+	2.30105i	−0.251065	+	0.434857i
$29$	−3.26819	−	5.66068i	−0.606888	−	1.05116i	−0.991750	−	0.128187i	$-0.959084\pi$
$29$	−3.26819	−	5.66068i	−0.606888	−	1.05116i	0.384862	−	0.922974i	$-0.374249\pi$
$30$		0			0
$31$	1.54544	+	2.67678i	0.277569	+	0.480764i	0.970780	−	0.239971i	$-0.0771380\pi$
$31$	1.54544	+	2.67678i	0.277569	+	0.480764i	−0.693211	+	0.720735i	$0.743805\pi$
$32$	−0.922922			−0.163151
$33$		0			0
$34$	−4.78067	−	8.28037i	−0.819879	−	1.42007i
$35$	0.621894	+	1.07715i	0.105119	+	0.182072i
$36$		0			0
$37$	2.23125			0.366816			0.183408	−	0.983037i	$-0.441287\pi$
$37$	2.23125			0.366816			0.183408	+	0.983037i	$0.441287\pi$
$38$	10.5742	−	1.98070i	1.71536	−	0.321313i
$39$		0			0
$40$	−4.94297	+	8.56147i	−0.781552	+	1.35369i
$41$	−3.48405	+	6.03455i	−0.544117	+	0.942439i	0.454545	+	0.890724i	$0.349802\pi$
$41$	−3.48405	+	6.03455i	−0.544117	+	0.942439i	−0.998662	+	0.0517147i	$0.983531\pi$
$42$		0			0
$43$	−8.93879			−1.36315			−0.681576	−	0.731747i	$-0.738705\pi$
$43$	−8.93879			−1.36315			−0.681576	+	0.731747i	$0.738705\pi$
$44$	−11.9976	+	20.7805i	−1.80871	+	3.13277i
$45$		0			0
$46$	−4.74743			−0.699971
$47$	5.77487	+	10.0024i	0.842352	+	1.45900i	0.887901	+	0.460034i	$0.152163\pi$
$47$	5.77487	+	10.0024i	0.842352	+	1.45900i	−0.0455498	+	0.998962i	$0.514504\pi$
$48$		0			0
$49$	3.28913	+	5.69694i	0.469876	+	0.813848i
$50$	−1.64357	−	2.84674i	−0.232436	−	0.402590i
$51$		0			0
$52$	−2.68143			−0.371847
$53$	6.35124	−	11.0007i	0.872409	−	1.51106i	0.0129124	−	0.999917i	$-0.495890\pi$
$53$	6.35124	−	11.0007i	0.872409	−	1.51106i	0.859497	−	0.511141i	$-0.170777\pi$
$54$		0			0
$55$	5.61624	+	9.72762i	0.757294	+	1.31167i
$56$	1.67606	−	2.90302i	0.223972	−	0.387932i
$57$		0			0
$58$	8.06615	+	13.9710i	1.05914	+	1.83448i
$59$	−7.16730	+	12.4141i	−0.933103	+	1.61618i	−0.155121	+	0.987895i	$0.549577\pi$
$59$	−7.16730	+	12.4141i	−0.933103	+	1.61618i	−0.777982	+	0.628287i	$0.783757\pi$
$60$		0			0
$61$	5.17155	+	8.95739i	0.662150	+	1.14688i	0.980050	+	0.198752i	$0.0636890\pi$
$61$	5.17155	+	8.95739i	0.662150	+	1.14688i	−0.317900	+	0.948124i	$0.602978\pi$
$62$	−3.81426	−	6.60649i	−0.484411	−	0.839025i
$63$		0			0
$64$	−6.83564			−0.854455
$65$	−0.627606	+	1.08705i	−0.0778449	+	0.134831i
$66$		0			0
$67$	0.763890			0.0933241			0.0466620	−	0.998911i	$-0.485142\pi$
$67$	0.763890			0.0933241			0.0466620	+	0.998911i	$0.485142\pi$
$68$	7.92505	+	13.7266i	0.961054	+	1.66459i
$69$		0			0
$70$	−1.53488	−	2.65849i	−0.183453	−	0.317751i
$71$	0.299796	+	0.519263i	0.0355793	+	0.0616251i	0.883267	−	0.468871i	$-0.155339\pi$
$71$	0.299796	+	0.519263i	0.0355793	+	0.0616251i	−0.847687	+	0.530496i	$0.822006\pi$
$72$		0			0
$73$	1.75541	+	3.04046i	0.205455	+	0.355859i	0.950278	−	0.311404i	$-0.100799\pi$
$73$	1.75541	+	3.04046i	0.205455	+	0.355859i	−0.744822	+	0.667263i	$0.767466\pi$
$74$	−5.50690			−0.640165
$75$		0			0
$76$	−17.5291	+	3.28347i	−2.01073	+	0.376640i
$77$	−1.90435	−	3.29843i	−0.217021	−	0.375891i
$78$		0			0
$79$	−4.26958			−0.480365			−0.240182	−	0.970728i	$-0.577207\pi$
$79$	−4.26958			−0.480365			−0.240182	+	0.970728i	$0.577207\pi$
$80$	4.36362	−	7.55801i	0.487868	−	0.845012i
$81$		0			0
$82$	8.59890	−	14.8937i	0.949590	−	1.64474i
$83$	3.29968	−	5.71522i	0.362187	−	0.627327i	−0.626133	−	0.779716i	$-0.715363\pi$
$83$	3.29968	−	5.71522i	0.362187	−	0.627327i	0.988321	+	0.152389i	$0.0486968\pi$
$84$		0			0
$85$	7.41965			0.804774
$86$	22.0616			2.37896
$87$		0			0
$88$	15.1362	−	26.2167i	1.61353	−	2.79471i
$89$	−2.41922	+	4.19022i	−0.256437	+	0.444162i	−0.965285	−	0.261200i	$-0.915882\pi$
$89$	−2.41922	+	4.19022i	−0.256437	+	0.444162i	0.708848	+	0.705361i	$0.249215\pi$
$90$		0			0
$91$	0.212808	−	0.368594i	0.0223083	−	0.0386392i
$92$	7.86995			0.820499
$93$		0			0
$94$	−14.2528	−	24.6866i	−1.47007	−	2.54623i
$95$	−2.77170	+	7.87479i	−0.284370	+	0.807936i
$96$		0			0
$97$	2.38904			0.242570			0.121285	−	0.992618i	$-0.461298\pi$
$97$	2.38904			0.242570			0.121285	+	0.992618i	$0.461298\pi$
$98$	−8.11782	−	14.0605i	−0.820024	−	1.42032i
$99$		0			0
$100$	2.72459	+	4.71912i	0.272459	+	0.471912i
$101$	−3.72207	−	6.44681i	−0.370360	−	0.641482i	0.619261	−	0.785185i	$-0.287432\pi$
$101$	−3.72207	−	6.44681i	−0.370360	−	0.641482i	−0.989621	+	0.143703i	$0.954099\pi$
$102$		0			0
$103$	−0.709718	−	1.22927i	−0.0699306	−	0.121123i	0.828940	−	0.559338i	$-0.188944\pi$
$103$	−0.709718	−	1.22927i	−0.0699306	−	0.121123i	−0.898871	+	0.438214i	$0.855611\pi$
$104$	3.38290			0.331721
$105$		0			0
$106$	−15.6753	+	27.1505i	−1.52252	+	2.63709i
$107$	−7.56837			−0.731662			−0.365831	−	0.930681i	$-0.619215\pi$
$107$	−7.56837			−0.731662			−0.365831	+	0.930681i	$0.619215\pi$
$108$		0			0
$109$	3.79611	+	6.57506i	0.363602	+	0.629776i	0.988551	−	0.150889i	$-0.0482136\pi$
$109$	3.79611	+	6.57506i	0.363602	+	0.629776i	−0.624949	+	0.780665i	$0.714880\pi$
$110$	−13.8613	−	24.0085i	−1.32162	−	2.28912i
$111$		0			0
$112$	−1.47961	+	2.56276i	−0.139810	+	0.242158i
$113$	−2.44573	−	4.23613i	−0.230075	−	0.398502i	0.727755	−	0.685837i	$-0.240564\pi$
$113$	−2.44573	−	4.23613i	−0.230075	−	0.398502i	−0.957830	+	0.287335i	$0.907231\pi$
$114$		0			0
$115$	1.84201	−	3.19046i	0.171769	−	0.297512i
$116$	−13.3715	−	23.1601i	−1.24151	−	2.15036i
$117$		0			0
$118$	17.6894	−	30.6390i	1.62845	−	2.82055i
$119$	−2.51585			−0.230627
$120$		0			0
$121$	−11.6979	−	20.2614i	−1.06345	−	1.84195i
$122$	−12.7638	−	22.1075i	−1.15558	−	2.00152i
$123$		0			0
$124$	6.32300	+	10.9518i	0.567823	+	0.983497i
$125$	12.1270			1.08467
$126$		0			0
$127$	−3.57756	+	6.19651i	−0.317457	+	0.549852i	−0.979957	−	0.199210i	$-0.936162\pi$
$127$	−3.57756	+	6.19651i	−0.317457	+	0.549852i	0.662500	+	0.749062i	$0.269496\pi$
$128$	18.7167			1.65434
$129$		0			0
$130$	1.54898	−	2.68291i	0.135854	−	0.235307i
$131$	3.41316	−	5.91177i	0.298209	−	0.516514i	−0.677517	−	0.735507i	$-0.736944\pi$
$131$	3.41316	−	5.91177i	0.298209	−	0.516514i	0.975726	+	0.218993i	$0.0702773\pi$
$132$		0			0
$133$	0.939824	−	2.67018i	0.0814930	−	0.231534i
$134$	−1.88534			−0.162869
$135$		0			0
$136$	−9.99829	−	17.3175i	−0.857346	−	1.48497i
$137$	5.14822	+	8.91698i	0.439842	+	0.761829i	0.997677	−	0.0681230i	$-0.0217010\pi$
$137$	5.14822	+	8.91698i	0.439842	+	0.761829i	−0.557835	+	0.829952i	$0.688368\pi$
$138$		0			0
$139$	2.86688			0.243165			0.121583	−	0.992581i	$-0.461203\pi$
$139$	2.86688			0.243165			0.121583	+	0.992581i	$0.461203\pi$
$140$	2.54442	+	4.40706i	0.215042	+	0.372464i
$141$		0			0
$142$	−0.739920	−	1.28158i	−0.0620927	−	0.107548i
$143$	1.92184	−	3.32872i	0.160712	−	0.278362i
$144$		0			0
$145$	−12.5187			−1.03962
$146$	−4.33249	−	7.50409i	−0.358559	−	0.621043i
$147$		0			0
$148$	9.12895			0.750395
$149$	−4.08301	+	7.07199i	−0.334493	+	0.579360i	−0.983387	−	0.181519i	$-0.941899\pi$
$149$	−4.08301	+	7.07199i	−0.334493	+	0.579360i	0.648894	+	0.760879i	$0.275232\pi$
$150$		0			0
$151$	10.2584	−	17.7681i	0.834818	−	1.44595i	−0.0593605	−	0.998237i	$-0.518906\pi$
$151$	10.2584	−	17.7681i	0.834818	−	1.44595i	0.894179	−	0.447711i	$-0.147761\pi$
$152$	22.1148	−	4.14244i	1.79375	−	0.335996i
$153$		0			0
$154$	4.70008	+	8.14077i	0.378743	+	0.656002i
$155$	5.91977			0.475487
$156$		0			0
$157$	0.730333	−	1.26497i	0.0582869	−	0.100956i	−0.835410	−	0.549628i	$-0.814770\pi$
$157$	0.730333	−	1.26497i	0.0582869	−	0.100956i	0.893696	+	0.448672i	$0.148103\pi$
$158$	10.5376			0.838330
$159$		0			0
$160$	−0.883808	+	1.53080i	−0.0698711	+	0.121020i
$161$	−0.624588	+	1.08182i	−0.0492244	+	0.0852592i
$162$		0			0
$163$	18.1874			1.42455			0.712274	−	0.701901i	$-0.247665\pi$
$163$	18.1874			1.42455			0.712274	+	0.701901i	$0.247665\pi$
$164$	−14.2546	+	24.6897i	−1.11310	+	1.92795i
$165$		0			0
$166$	−8.14387	+	14.1056i	−0.632087	+	1.09481i
$167$	8.89467			0.688290			0.344145	−	0.938916i	$-0.388169\pi$
$167$	8.89467			0.688290			0.344145	+	0.938916i	$0.388169\pi$
$168$		0			0
$169$	−12.5705			−0.966960
$170$	−18.3123			−1.40449
$171$		0			0
$172$	−36.5721			−2.78860
$173$	−9.56569			−0.727266			−0.363633	−	0.931542i	$-0.618464\pi$
$173$	−9.56569			−0.727266			−0.363633	+	0.931542i	$0.618464\pi$
$174$		0			0
$175$	−0.864933			−0.0653828
$176$	−13.3622	+	23.1440i	−1.00721	+	1.74454i
$177$		0			0
$178$	5.97082	−	10.3418i	0.447532	−	0.775148i
$179$	−0.464358			−0.0347078			−0.0173539	−	0.999849i	$-0.505524\pi$
$179$	−0.464358			−0.0347078			−0.0173539	+	0.999849i	$0.505524\pi$
$180$		0			0
$181$	4.32082	−	7.48388i	0.321164	−	0.556272i	−0.659564	−	0.751648i	$-0.729259\pi$
$181$	4.32082	−	7.48388i	0.321164	−	0.556272i	0.980728	+	0.195376i	$0.0625926\pi$
$182$	−0.525226	+	0.909718i	−0.0389324	+	0.0674328i
$183$		0			0
$184$	−9.92877			−0.731958
$185$	2.13669	−	3.70086i	0.157093	−	0.272093i
$186$		0			0
$187$	−22.7203			−1.66147
$188$	23.6273	+	40.9237i	1.72320	+	2.98467i
$189$		0			0
$190$	6.84076	−	19.4356i	0.496281	−	1.41001i
$191$	−11.1012	+	19.2279i	−0.803256	+	1.39128i	0.114206	+	0.993457i	$0.463568\pi$
$191$	−11.1012	+	19.2279i	−0.803256	+	1.39128i	−0.917462	+	0.397823i	$0.869766\pi$
$192$		0			0
$193$	2.36055	−	4.08859i	0.169916	−	0.294303i	−0.768474	−	0.639881i	$-0.778984\pi$
$193$	2.36055	−	4.08859i	0.169916	−	0.294303i	0.938390	+	0.345578i	$0.112317\pi$
$194$	−5.89634			−0.423332
$195$		0			0
$196$	13.4571	+	23.3084i	0.961224	+	1.66489i
$197$	−8.23403			−0.586650			−0.293325	−	0.956013i	$-0.594762\pi$
$197$	−8.23403			−0.586650			−0.293325	+	0.956013i	$0.594762\pi$
$198$		0			0
$199$	−1.32235	+	2.29038i	−0.0937389	+	0.162361i	−0.909082	−	0.416618i	$-0.863215\pi$
$199$	−1.32235	+	2.29038i	−0.0937389	+	0.162361i	0.815343	+	0.578979i	$0.196549\pi$
$200$	−3.43735	−	5.95367i	−0.243058	−	0.420988i
$201$		0			0
$202$	9.18635	+	15.9112i	0.646349	+	1.11951i
$203$	4.24484			0.297929
$204$		0			0
$205$	6.67279	+	11.5576i	0.466048	+	0.807218i
$206$	1.75164	+	3.03393i	0.122042	+	0.211384i
$207$		0			0
$208$	−2.98640			−0.207070
$209$	8.48742	−	24.1140i	0.587087	−	1.66800i
$210$		0			0
$211$	−8.27399	+	14.3310i	−0.569605	+	0.986585i	0.427000	+	0.904252i	$0.359571\pi$
$211$	−8.27399	+	14.3310i	−0.569605	+	0.986585i	−0.996605	+	0.0823332i	$0.973763\pi$
$212$	25.9854	−	45.0081i	1.78469	−	3.09117i
$213$		0			0
$214$	18.6793			1.27689
$215$	−8.55996	+	14.8263i	−0.583784	+	1.01114i
$216$		0			0
$217$	−2.00727			−0.136262
$218$	−9.36909	−	16.2277i	−0.634555	−	1.09908i
$219$		0			0
$220$	22.9783	+	39.7996i	1.54920	+	2.68329i
$221$	−1.26948	−	2.19880i	−0.0853942	−	0.147907i
$222$		0			0
$223$	9.24371			0.619004			0.309502	−	0.950899i	$-0.399838\pi$
$223$	9.24371			0.619004			0.309502	+	0.950899i	$0.399838\pi$
$224$	0.299680	−	0.519062i	0.0200232	−	0.0346813i
$225$		0			0
$226$	6.03625	+	10.4551i	0.401526	+	0.695463i
$227$	−5.24132	+	9.07823i	−0.347879	+	0.602544i	−0.985872	−	0.167498i	$-0.946431\pi$
$227$	−5.24132	+	9.07823i	−0.347879	+	0.602544i	0.637994	+	0.770042i	$0.279765\pi$
$228$		0			0
$229$	−8.81057	−	15.2604i	−0.582219	−	1.00843i	−0.995216	−	0.0977001i	$-0.968851\pi$
$229$	−8.81057	−	15.2604i	−0.582219	−	1.00843i	0.412997	−	0.910732i	$-0.364482\pi$
$230$	−4.54623	+	7.87430i	−0.299770	+	0.519216i
$231$		0			0
$232$	16.8695	+	29.2189i	1.10754	+	1.91831i
$233$	3.40859	+	5.90385i	0.223304	+	0.386774i	0.955809	−	0.293987i	$-0.0949823\pi$
$233$	3.40859	+	5.90385i	0.223304	+	0.386774i	−0.732505	+	0.680762i	$0.761649\pi$
$234$		0			0
$235$	22.1205			1.44298
$236$	−29.3243	+	50.7911i	−1.90885	+	3.30622i
$237$		0			0
$238$	6.20930			0.402489
$239$	−6.77458	−	11.7339i	−0.438211	−	0.759004i	0.559340	−	0.828938i	$-0.311055\pi$
$239$	−6.77458	−	11.7339i	−0.438211	−	0.759004i	−0.997552	+	0.0699338i	$0.977721\pi$
$240$		0			0
$241$	−3.74392	−	6.48466i	−0.241167	−	0.417714i	0.719880	−	0.694099i	$-0.244197\pi$
$241$	−3.74392	−	6.48466i	−0.241167	−	0.417714i	−0.961047	+	0.276385i	$0.910864\pi$
$242$	28.8714	+	50.0067i	1.85592	+	3.21455i
$243$		0			0
$244$	21.1589	+	36.6483i	1.35456	+	2.34616i
$245$	12.5989			0.804916
$246$		0			0
$247$	2.80791	−	0.525963i	0.178663	−	0.0334662i
$248$	−7.97713	−	13.8168i	−0.506548	−	0.877368i
$249$		0			0
$250$	−29.9304			−1.89297
$251$	15.0975	−	26.1496i	0.952946	−	1.65055i	0.213945	−	0.976846i	$-0.431369\pi$
$251$	15.0975	−	26.1496i	0.952946	−	1.65055i	0.739001	−	0.673705i	$-0.235298\pi$
$252$		0			0
$253$	−5.64057	+	9.76976i	−0.354620	+	0.614219i
$254$	8.82969	−	15.2935i	0.554024	−	0.959597i
$255$		0			0
$256$	−32.5230			−2.03269
$257$	−23.2987			−1.45333			−0.726667	−	0.686990i	$-0.758932\pi$
$257$	−23.2987			−1.45333			−0.726667	+	0.686990i	$0.758932\pi$
$258$		0			0
$259$	−0.724507	+	1.25488i	−0.0450187	+	0.0779747i
$260$	−2.56779	+	4.44754i	−0.159247	+	0.275824i
$261$		0			0
$262$	−8.42394	+	14.5907i	−0.520433	+	0.901416i
$263$	15.3060			0.943806			0.471903	−	0.881651i	$-0.343567\pi$
$263$	15.3060			0.943806			0.471903	+	0.881651i	$0.343567\pi$
$264$		0			0
$265$	−12.1641	−	21.0689i	−0.747237	−	1.29425i
$266$	−2.31956	+	6.59019i	−0.142221	+	0.404071i
$267$		0			0
$268$	3.12538			0.190913
$269$	−2.30201	−	3.98719i	−0.140356	−	0.243103i	0.787275	−	0.616602i	$-0.211491\pi$
$269$	−2.30201	−	3.98719i	−0.140356	−	0.243103i	−0.927631	+	0.373499i	$0.878158\pi$
$270$		0			0
$271$	−3.67360	−	6.36286i	−0.223155	−	0.386517i	0.732609	−	0.680650i	$-0.238302\pi$
$271$	−3.67360	−	6.36286i	−0.223155	−	0.386517i	−0.955764	+	0.294133i	$0.904969\pi$
$272$	8.82642	+	15.2878i	0.535180	+	0.926960i
$273$		0			0
$274$	−12.7062	−	22.0078i	−0.767610	−	1.32954i
$275$	−7.81110			−0.471027
$276$		0			0
$277$	11.8834	−	20.5827i	0.714006	−	1.23669i	−0.249336	−	0.968417i	$-0.580212\pi$
$277$	11.8834	−	20.5827i	0.714006	−	1.23669i	0.963342	−	0.268278i	$-0.0864544\pi$
$278$	−7.07567			−0.424371
$279$		0			0
$280$	−3.21005	−	5.55997i	−0.191837	−	0.332272i
$281$	6.42046	+	11.1206i	0.383012	+	0.663397i	0.991491	−	0.130173i	$-0.0415533\pi$
$281$	6.42046	+	11.1206i	0.383012	+	0.663397i	−0.608479	+	0.793570i	$0.708220\pi$
$282$		0			0
$283$	−0.753665	+	1.30539i	−0.0448007	+	0.0775972i	−0.887556	−	0.460699i	$-0.847599\pi$
$283$	−0.753665	+	1.30539i	−0.0448007	+	0.0775972i	0.842755	+	0.538297i	$0.180932\pi$
$284$	1.22659	+	2.12451i	0.0727845	+	0.126066i
$285$		0			0
$286$	−4.74325	+	8.21554i	−0.280474	+	0.485795i
$287$	−2.26260	−	3.91894i	−0.133557	−	0.231328i
$288$		0			0
$289$	0.996032	−	1.72518i	0.0585901	−	0.101481i
$290$	30.8972			1.81435
$291$		0			0
$292$	7.18208	+	12.4397i	0.420300	+	0.727980i
$293$	−12.6882	−	21.9765i	−0.741250	−	1.28388i	−0.951926	−	0.306327i	$-0.900900\pi$
$293$	−12.6882	−	21.9765i	−0.741250	−	1.28388i	0.210677	−	0.977556i	$-0.432433\pi$
$294$		0			0
$295$	13.7271	+	23.7760i	0.799222	+	1.38429i
$296$	−11.5171			−0.669419
$297$		0			0
$298$	10.0772	−	17.4542i	0.583756	−	1.01109i
$299$	−1.26065			−0.0729053
$300$		0			0
$301$	2.90250	−	5.02728i	0.167297	−	0.289768i
$302$	−25.3185	+	43.8530i	−1.45692	+	2.52346i
$303$		0			0
$304$	−19.5228	+	3.65692i	−1.11971	+	0.209739i
$305$	19.8095			1.13429
$306$		0			0
$307$	4.18433	+	7.24746i	0.238812	+	0.413635i	0.960374	−	0.278716i	$-0.0899087\pi$
$307$	4.18433	+	7.24746i	0.238812	+	0.413635i	−0.721562	+	0.692350i	$0.756575\pi$
$308$	−7.79145	−	13.4952i	−0.443959	−	0.768960i
$309$		0			0
$310$	−14.6104			−0.829817
$311$	−3.63194	−	6.29071i	−0.205949	−	0.356713i	0.744486	−	0.667638i	$-0.232695\pi$
$311$	−3.63194	−	6.29071i	−0.205949	−	0.356713i	−0.950435	+	0.310925i	$0.899361\pi$
$312$		0			0
$313$	−7.36230	−	12.7519i	−0.416142	−	0.720778i	0.579406	−	0.815039i	$-0.303285\pi$
$313$	−7.36230	−	12.7519i	−0.416142	−	0.720778i	−0.995548	+	0.0942607i	$0.969951\pi$
$314$	−1.80252	+	3.12205i	−0.101722	+	0.176187i
$315$		0			0
$316$	−17.4685			−0.982682
$317$	−8.16770	−	14.1469i	−0.458744	−	0.794568i	0.540151	−	0.841568i	$-0.318367\pi$
$317$	−8.16770	−	14.1469i	−0.458744	−	0.794568i	−0.998895	+	0.0470004i	$0.985034\pi$
$318$		0			0
$319$	38.3346			2.14632
$320$	−6.54594	+	11.3379i	−0.365929	+	0.633808i
$321$		0			0
$322$	1.54153	−	2.67001i	0.0859062	−	0.148794i
$323$	−10.9913	−	12.8196i	−0.611575	−	0.713299i
$324$		0			0
$325$	−0.436439	−	0.755934i	−0.0242093	−	0.0419317i
$326$	−44.8879			−2.48611
$327$		0			0
$328$	17.9837	−	31.1487i	0.992985	−	1.71990i
$329$	−7.50060			−0.413521
$330$		0			0
$331$	−13.5395	+	23.4510i	−0.744195	+	1.28898i	0.206374	+	0.978473i	$0.433834\pi$
$331$	−13.5395	+	23.4510i	−0.744195	+	1.28898i	−0.950570	+	0.310511i	$0.899500\pi$
$332$	13.5003	−	23.3832i	0.740926	−	1.28332i
$333$		0			0
$334$	−21.9527			−1.20120
$335$	0.731516	−	1.26702i	0.0399670	−	0.0692249i
$336$		0			0
$337$	−8.66806	+	15.0135i	−0.472179	+	0.817838i	−0.999493	−	0.0318323i	$-0.989866\pi$
$337$	−8.66806	+	15.0135i	−0.472179	+	0.817838i	0.527314	+	0.849670i	$0.323199\pi$
$338$	31.0249			1.68753
$339$		0			0
$340$	30.3567			1.64633
$341$	−18.1274			−0.981652
$342$		0			0
$343$	−8.81795			−0.476125
$344$	46.1396			2.48768
$345$		0			0
$346$	23.6089			1.26922
$347$	0.759717	−	1.31587i	0.0407837	−	0.0706395i	−0.844913	−	0.534904i	$-0.820348\pi$
$347$	0.759717	−	1.31587i	0.0407837	−	0.0706395i	0.885697	+	0.464264i	$0.153681\pi$
$348$		0			0
$349$	−4.35421	+	7.54171i	−0.233075	+	0.403699i	−0.958712	−	0.284380i	$-0.908212\pi$
$349$	−4.35421	+	7.54171i	−0.233075	+	0.403699i	0.725636	+	0.688079i	$0.241546\pi$
$350$	2.13472			0.114106
$351$		0			0
$352$	2.70637	−	4.68758i	0.144250	−	0.249849i
$353$	4.15920	−	7.20395i	0.221372	−	0.383428i	−0.733853	−	0.679309i	$-0.762280\pi$
$353$	4.15920	−	7.20395i	0.221372	−	0.383428i	0.955225	+	0.295881i	$0.0956132\pi$
$354$		0			0
$355$	1.14836			0.0609488
$356$	−9.89800	+	17.1438i	−0.524593	+	0.908622i
$357$		0			0
$358$	1.14607			0.0605717
$359$	−13.7180	−	23.7604i	−0.724011	−	1.25402i	−0.959380	−	0.282118i	$-0.908963\pi$
$359$	−13.7180	−	23.7604i	−0.724011	−	1.25402i	0.235369	−	0.971906i	$-0.424370\pi$
$360$		0			0
$361$	17.7119	−	6.87669i	0.932205	−	0.361931i
$362$	−10.6641	+	18.4708i	−0.560493	+	0.970803i
$363$		0			0
$364$	0.870682	−	1.50807i	0.0456361	−	0.0790441i
$365$	6.72406			0.351953
$366$		0			0
$367$	−11.6965	−	20.2589i	−0.610553	−	1.05751i	−0.991147	−	0.132766i	$-0.957614\pi$
$367$	−11.6965	−	20.2589i	−0.610553	−	1.05751i	0.380595	−	0.924742i	$-0.375719\pi$
$368$	8.76505			0.456910
$369$		0			0
$370$	−5.27352	+	9.13400i	−0.274157	+	0.474854i
$371$	4.12460	+	7.14402i	0.214139	+	0.370899i
$372$		0			0
$373$	1.89269	+	3.27823i	0.0979996	+	0.169740i	0.910857	−	0.412723i	$-0.135422\pi$
$373$	1.89269	+	3.27823i	0.0979996	+	0.169740i	−0.812857	+	0.582463i	$0.802089\pi$
$374$	56.0753			2.89959
$375$		0			0
$376$	−29.8083	−	51.6295i	−1.53725	−	2.66259i
$377$	2.14191	+	3.70990i	0.110314	+	0.191070i
$378$		0			0
$379$	−5.16755			−0.265439			−0.132720	−	0.991154i	$-0.542371\pi$
$379$	−5.16755			−0.265439			−0.132720	+	0.991154i	$0.542371\pi$
$380$	−11.3401	+	32.2189i	−0.581735	+	1.65279i
$381$		0			0
$382$	27.3986	−	47.4558i	1.40184	−	2.42805i
$383$	−4.50054	+	7.79517i	−0.229967	+	0.398315i	−0.957798	−	0.287442i	$-0.907195\pi$
$383$	−4.50054	+	7.79517i	−0.229967	+	0.398315i	0.727831	+	0.685756i	$0.240528\pi$
$384$		0			0
$385$	−7.29457			−0.371766
$386$	−5.82602	+	10.0910i	−0.296537	+	0.513616i
$387$		0			0
$388$	9.77452			0.496226
$389$	10.3821	+	17.9823i	0.526393	+	0.911739i	0.999527	+	0.0307490i	$0.00978926\pi$
$389$	10.3821	+	17.9823i	0.526393	+	0.911739i	−0.473134	+	0.880990i	$0.656877\pi$
$390$		0			0
$391$	3.72590	+	6.45344i	0.188427	+	0.326365i
$392$	−16.9776	−	29.4060i	−0.857498	−	1.48523i
$393$		0			0
$394$	20.3222			1.02382
$395$	−4.08863	+	7.08171i	−0.205721	+	0.356320i
$396$		0			0
$397$	−2.69831	−	4.67361i	−0.135424	−	0.234562i	0.790335	−	0.612675i	$-0.209906\pi$
$397$	−2.69831	−	4.67361i	−0.135424	−	0.234562i	−0.925759	+	0.378113i	$0.876573\pi$
$398$	3.26366	−	5.65283i	0.163593	−	0.283351i
$399$		0			0
$400$	3.03447	+	5.25586i	0.151724	+	0.262793i
$401$	9.46332	−	16.3910i	0.472576	−	0.818525i	−0.526932	−	0.849908i	$-0.676658\pi$
$401$	9.46332	−	16.3910i	0.472576	−	0.818525i	0.999507	+	0.0313823i	$0.00999094\pi$
$402$		0			0
$403$	−1.01285	−	1.75431i	−0.0504538	−	0.0873885i
$404$	−15.2285	−	26.3765i	−0.757645	−	1.31228i
$405$		0			0
$406$	−10.4766			−0.519944
$407$	−6.54293	+	11.3327i	−0.324321	+	0.561740i
$408$		0			0
$409$	28.6065			1.41450			0.707250	−	0.706963i	$-0.249935\pi$
$409$	28.6065			1.41450			0.707250	+	0.706963i	$0.249935\pi$
$410$	−16.4689	−	28.5250i	−0.813343	−	1.40875i
$411$		0			0
$412$	−2.90374	−	5.02943i	−0.143057	−	0.247782i
$413$	−4.65457	−	8.06195i	−0.229036	−	0.396702i
$414$		0			0
$415$	−6.31968	−	10.9460i	−0.310221	−	0.537318i
$416$	0.604866			0.0296560
$417$		0			0
$418$	−20.9476	+	59.5152i	−1.02458	+	2.91098i
$419$	14.8913	+	25.7926i	0.727490	+	1.26005i	0.957941	+	0.286965i	$0.0926464\pi$
$419$	14.8913	+	25.7926i	0.727490	+	1.26005i	−0.230451	+	0.973084i	$0.574020\pi$
$420$		0			0
$421$	−0.632620			−0.0308320			−0.0154160	−	0.999881i	$-0.504907\pi$
$421$	−0.632620			−0.0308320			−0.0154160	+	0.999881i	$0.504907\pi$
$422$	20.4208	−	35.3699i	0.994071	−	1.72178i
$423$		0			0
$424$	−32.7834	+	56.7824i	−1.59210	+	2.75760i
$425$	−2.57982	+	4.46838i	−0.125140	+	0.216748i
$426$		0			0
$427$	−6.71699			−0.325058
$428$	−30.9652			−1.49676
$429$		0			0
$430$	21.1266	−	36.5924i	1.01882	−	1.76464i
$431$	−11.9641	+	20.7224i	−0.576289	+	0.998162i	0.419611	+	0.907704i	$0.362166\pi$
$431$	−11.9641	+	20.7224i	−0.576289	+	0.998162i	−0.995900	+	0.0904579i	$0.971167\pi$
$432$		0			0
$433$	−2.23079	+	3.86384i	−0.107205	+	0.185684i	−0.914637	−	0.404276i	$-0.867523\pi$
$433$	−2.23079	+	3.86384i	−0.107205	+	0.185684i	0.807432	+	0.589961i	$0.200857\pi$
$434$	4.95409			0.237804
$435$		0			0
$436$	15.5314	+	26.9012i	0.743819	+	1.28833i
$437$	−8.24116	+	1.54369i	−0.394228	+	0.0738449i
$438$		0			0
$439$	16.1866			0.772545			0.386273	−	0.922385i	$-0.373762\pi$
$439$	16.1866			0.772545			0.386273	+	0.922385i	$0.373762\pi$
$440$	−28.9895	−	50.2113i	−1.38202	−	2.39373i
$441$		0			0
$442$	3.13316	+	5.42680i	0.149029	+	0.258127i
$443$	−8.82461	−	15.2847i	−0.419270	−	0.726197i	0.576596	−	0.817029i	$-0.304381\pi$
$443$	−8.82461	−	15.2847i	−0.419270	−	0.726197i	−0.995866	+	0.0908323i	$0.971047\pi$
$444$		0			0
$445$	4.63339	+	8.02526i	0.219644	+	0.380434i
$446$	−22.8142			−1.08028
$447$		0			0
$448$	2.21959	−	3.84444i	0.104866	−	0.181633i
$449$	41.2241			1.94548			0.972742	−	0.231890i	$-0.0744908\pi$
$449$	41.2241			1.94548			0.972742	+	0.231890i	$0.0744908\pi$
$450$		0			0
$451$	−20.4332	−	35.3914i	−0.962164	−	1.66652i
$452$	−10.0065	−	17.3317i	−0.470665	−	0.815215i
$453$		0			0
$454$	12.9360	−	22.4058i	0.607115	−	1.05155i
$455$	−0.407578	−	0.705946i	−0.0191076	−	0.0330952i
$456$		0			0
$457$	−2.05989	+	3.56784i	−0.0963576	+	0.166896i	−0.910174	−	0.414225i	$-0.864053\pi$
$457$	−2.05989	+	3.56784i	−0.0963576	+	0.166896i	0.813817	+	0.581122i	$0.197386\pi$
$458$	21.7451	+	37.6637i	1.01608	+	1.75991i
$459$		0			0
$460$	7.53641	−	13.0535i	0.351387	−	0.608620i
$461$	14.0219			0.653065			0.326533	−	0.945186i	$-0.394120\pi$
$461$	14.0219			0.653065			0.326533	+	0.945186i	$0.394120\pi$
$462$		0			0
$463$	12.4782	+	21.6129i	0.579912	+	1.00444i	0.995489	+	0.0948795i	$0.0302466\pi$
$463$	12.4782	+	21.6129i	0.579912	+	1.00444i	−0.415576	+	0.909558i	$0.636420\pi$
$464$	−14.8923	−	25.7942i	−0.691358	−	1.19747i
$465$		0			0
$466$	−8.41266	−	14.5712i	−0.389709	−	0.674996i
$467$	23.0107			1.06481			0.532405	−	0.846490i	$-0.321288\pi$
$467$	23.0107			1.06481			0.532405	+	0.846490i	$0.321288\pi$
$468$		0			0
$469$	−0.248042	+	0.429621i	−0.0114535	+	0.0198380i
$470$	−54.5951			−2.51828
$471$		0			0
$472$	36.9957	−	64.0784i	1.70286	−	2.94945i
$473$	26.2121	−	45.4007i	1.20523	−	2.08753i
$474$		0			0
$475$	−3.77876	−	4.40729i	−0.173381	−	0.202220i
$476$	−10.2933			−0.471794
$477$		0			0
$478$	16.7202	+	28.9602i	0.764763	+	1.32461i
$479$	1.91844	+	3.32283i	0.0876557	+	0.151824i	0.906520	−	0.422163i	$-0.138729\pi$
$479$	1.91844	+	3.32283i	0.0876557	+	0.151824i	−0.818864	+	0.573987i	$0.805396\pi$
$480$		0			0
$481$	−1.46232			−0.0666762
$482$	9.24028	+	16.0046i	0.420883	+	0.728991i
$483$		0			0
$484$	−47.8609	−	82.8974i	−2.17549	−	3.76807i
$485$	2.28779	−	3.96257i	0.103883	−	0.179931i
$486$		0			0
$487$	−30.9854			−1.40408			−0.702041	−	0.712136i	$-0.747728\pi$
$487$	−30.9854			−1.40408			−0.702041	+	0.712136i	$0.747728\pi$
$488$	−26.6941	−	46.2356i	−1.20839	−	2.09299i
$489$		0			0
$490$	−31.0951			−1.40473
$491$	−13.9024	+	24.0796i	−0.627405	+	1.08670i	0.360665	+	0.932695i	$0.382550\pi$
$491$	−13.9024	+	24.0796i	−0.627405	+	1.08670i	−0.988070	+	0.154002i	$0.950784\pi$
$492$		0			0
$493$	12.6610	−	21.9295i	0.570223	−	0.987655i
$494$	−6.93013	+	1.29812i	−0.311801	+	0.0584051i
$495$		0			0
$496$	7.04216	+	12.1974i	0.316202	+	0.547679i
$497$	−0.389386			−0.0174663
$498$		0			0
$499$	10.8294	−	18.7571i	0.484791	−	0.839683i	−0.515056	−	0.857156i	$-0.672229\pi$
$499$	10.8294	−	18.7571i	0.484791	−	0.839683i	0.999847	+	0.0174734i	$0.00556224\pi$
$500$	49.6165			2.21892
$501$		0			0
$502$	−37.2618	+	64.5393i	−1.66307	+	2.88053i
$503$	15.3608	−	26.6057i	0.684903	−	1.18629i	−0.288564	−	0.957461i	$-0.593178\pi$
$503$	15.3608	−	26.6057i	0.684903	−	1.18629i	0.973467	−	0.228827i	$-0.0734890\pi$
$504$		0			0
$505$	−14.2573			−0.634442
$506$	13.9214	−	24.1125i	0.618880	−	1.07193i
$507$		0			0
$508$	−14.6372	+	25.3524i	−0.649421	+	1.12483i
$509$	28.0306			1.24244			0.621218	−	0.783638i	$-0.286638\pi$
$509$	28.0306			1.24244			0.621218	+	0.783638i	$0.286638\pi$
$510$		0			0
$511$	−2.27999			−0.100861
$512$	42.8358			1.89309
$513$		0			0
$514$	57.5030			2.53635
$515$	−2.71856			−0.119794
$516$		0			0
$517$	−67.7369			−2.97907
$518$	1.78814	−	3.09715i	0.0785663	−	0.136081i
$519$		0			0
$520$	3.23953	−	5.61103i	0.142063	−	0.246060i
$521$	11.7617			0.515287			0.257644	−	0.966240i	$-0.417054\pi$
$521$	11.7617			0.515287			0.257644	+	0.966240i	$0.417054\pi$
$522$		0			0
$523$	12.3785	−	21.4402i	0.541275	−	0.937516i	−0.457556	−	0.889181i	$-0.651275\pi$
$523$	12.3785	−	21.4402i	0.541275	−	0.937516i	0.998831	−	0.0483349i	$-0.0153915\pi$
$524$	13.9646	−	24.1874i	0.610047	−	1.05663i
$525$		0			0
$526$	−37.7763			−1.64712
$527$	−5.98704	+	10.3699i	−0.260800	+	0.451718i
$528$		0			0
$529$	−19.3000			−0.839131
$530$	30.0220	+	51.9996i	1.30407	+	2.25872i
$531$		0			0
$532$	3.84519	−	10.9247i	0.166710	−	0.473648i
$533$	2.28338	−	3.95493i	0.0989043	−	0.171307i
$534$		0			0
$535$	−7.24762	+	12.5532i	−0.313342	+	0.542724i
$536$	−3.94299			−0.170311
$537$		0			0
$538$	5.68152	+	9.84069i	0.244948	+	0.424262i
$539$	−38.5801			−1.66176
$540$		0			0
$541$	−18.6115	+	32.2361i	−0.800171	+	1.38594i	0.119332	+	0.992854i	$0.461925\pi$
$541$	−18.6115	+	32.2361i	−0.800171	+	1.38594i	−0.919503	+	0.393083i	$0.871409\pi$
$542$	9.06673	+	15.7040i	0.389449	+	0.674546i
$543$		0			0
$544$	−1.78770	−	3.09639i	−0.0766471	−	0.132757i
$545$	14.5409			0.622865
$546$		0			0
$547$	1.96934	+	3.41100i	0.0842030	+	0.145844i	0.905051	−	0.425302i	$-0.139832\pi$
$547$	1.96934	+	3.41100i	0.0842030	+	0.145844i	−0.820848	+	0.571146i	$0.806499\pi$
$548$	21.0634	+	36.4829i	0.899785	+	1.55847i
$549$		0			0
$550$	19.2784			0.822033
$551$	18.5451	+	21.6297i	0.790046	+	0.921456i
$552$		0			0
$553$	1.38637	−	2.40126i	0.0589544	−	0.102112i
$554$	−29.3292	+	50.7997i	−1.24608	+	2.15827i
$555$		0			0
$556$	11.7295			0.497443
$557$	−10.2612	+	17.7730i	−0.434783	+	0.753066i	−0.997278	−	0.0737345i	$-0.976508\pi$
$557$	−10.2612	+	17.7730i	−0.434783	+	0.753066i	0.562495	+	0.826801i	$0.309842\pi$
$558$		0			0
$559$	5.85832			0.247780
$560$	2.83381	+	4.90830i	0.119750	+	0.207414i
$561$		0			0
$562$	−15.8462	−	27.4464i	−0.668431	−	1.15776i
$563$	6.27581	+	10.8700i	0.264494	+	0.458117i	0.967431	−	0.253135i	$-0.0814618\pi$
$563$	6.27581	+	10.8700i	0.264494	+	0.458117i	−0.702937	+	0.711252i	$0.748128\pi$
$564$		0			0
$565$	−9.36832			−0.394128
$566$	1.86010	−	3.22179i	0.0781860	−	0.135422i
$567$		0			0
$568$	−1.54747	−	2.68029i	−0.0649303	−	0.112463i
$569$	−3.79925	+	6.58050i	−0.159273	+	0.275869i	−0.934607	−	0.355683i	$-0.884248\pi$
$569$	−3.79925	+	6.58050i	−0.159273	+	0.275869i	0.775334	+	0.631552i	$0.217582\pi$
$570$		0			0
$571$	−0.502011	−	0.869508i	−0.0210085	−	0.0363878i	0.855330	−	0.518084i	$-0.173354\pi$
$571$	−0.502011	−	0.869508i	−0.0210085	−	0.0363878i	−0.876339	+	0.481696i	$0.840021\pi$
$572$	7.86301	−	13.6191i	0.328769	−	0.569445i
$573$		0			0
$574$	5.58427	+	9.67224i	0.233083	+	0.403712i
$575$	1.28094	+	2.21866i	0.0534190	+	0.0925243i
$576$		0			0
$577$	−6.38475			−0.265801			−0.132900	−	0.991129i	$-0.542429\pi$
$577$	−6.38475			−0.265801			−0.132900	+	0.991129i	$0.542429\pi$
$578$	−2.45828	+	4.25787i	−0.102251	+	0.177104i
$579$		0			0
$580$	−51.2191			−2.12676
$581$	2.14287	+	3.71156i	0.0889012	+	0.153981i
$582$		0			0
$583$	37.2487	+	64.5167i	1.54268	+	2.67201i
$584$	−9.06095	−	15.6940i	−0.374945	−	0.649424i
$585$		0			0
$586$	31.3153	+	54.2397i	1.29362	+	2.24062i
$587$	23.7500			0.980266			0.490133	−	0.871648i	$-0.336948\pi$
$587$	23.7500			0.980266			0.490133	+	0.871648i	$0.336948\pi$
$588$		0			0
$589$	−8.76945	−	10.2281i	−0.361339	−	0.421441i
$590$	−33.8795	−	58.6810i	−1.39480	−	2.41586i
$591$		0			0
$592$	10.1672			0.417871
$593$	−4.39025	+	7.60414i	−0.180286	+	0.312264i	−0.941978	−	0.335675i	$-0.891036\pi$
$593$	−4.39025	+	7.60414i	−0.180286	+	0.312264i	0.761692	+	0.647939i	$0.224369\pi$
$594$		0			0
$595$	−2.40922	+	4.17290i	−0.0987685	+	0.171072i
$596$	−16.7052	+	28.9343i	−0.684273	+	1.18520i
$597$		0			0
$598$	3.11138			0.127234
$599$	16.8975			0.690412			0.345206	−	0.938527i	$-0.387809\pi$
$599$	16.8975			0.690412			0.345206	+	0.938527i	$0.387809\pi$
$600$		0			0
$601$	−15.1537	+	26.2469i	−0.618131	+	1.07063i	0.371696	+	0.928355i	$0.378776\pi$
$601$	−15.1537	+	26.2469i	−0.618131	+	1.07063i	−0.989827	+	0.142279i	$0.954557\pi$
$602$	−7.16359	+	12.4077i	−0.291966	+	0.505700i
$603$		0			0
$604$	41.9713	−	72.6963i	1.70779	−	2.95797i
$605$	−44.8086			−1.82173
$606$		0			0
$607$	23.8244	+	41.2651i	0.967003	+	1.67490i	0.704133	+	0.710068i	$0.251336\pi$
$607$	23.8244	+	41.2651i	0.967003	+	1.67490i	0.262870	+	0.964831i	$0.415331\pi$
$608$	3.95415	−	0.740672i	0.160362	−	0.0300382i
$609$		0			0
$610$	−48.8914			−1.97955
$611$	−3.78474	−	6.55537i	−0.153114	−	0.265202i
$612$		0			0
$613$	10.7830	+	18.6767i	0.435521	+	0.754345i	0.997338	−	0.0729168i	$-0.0232308\pi$
$613$	10.7830	+	18.6767i	0.435521	+	0.754345i	−0.561817	+	0.827262i	$0.689897\pi$
$614$	−10.3272	−	17.8873i	−0.416773	−	0.721872i
$615$		0			0
$616$	9.82973	+	17.0256i	0.396051	+	0.685981i
$617$	−2.84704			−0.114618			−0.0573088	−	0.998356i	$-0.518252\pi$
$617$	−2.84704			−0.114618			−0.0573088	+	0.998356i	$0.518252\pi$
$618$		0			0
$619$	−6.25245	+	10.8296i	−0.251307	+	0.435277i	−0.963886	−	0.266315i	$-0.914194\pi$
$619$	−6.25245	+	10.8296i	−0.251307	+	0.435277i	0.712579	+	0.701592i	$0.247527\pi$
$620$	24.2201			0.972703
$621$		0			0
$622$	8.96391	+	15.5259i	0.359420	+	0.622534i
$623$	−1.57108	−	2.72120i	−0.0629441	−	0.109022i
$624$		0			0
$625$	8.28342	−	14.3473i	0.331337	−	0.573892i
$626$	18.1707	+	31.4726i	0.726247	+	1.25790i
$627$		0			0
$628$	2.98808	−	5.17551i	0.119237	−	0.206525i
$629$	4.32195	+	7.48583i	0.172327	+	0.298480i
$630$		0			0
$631$	0.917741	−	1.58957i	0.0365347	−	0.0632799i	−0.847180	−	0.531306i	$-0.821701\pi$
$631$	0.917741	−	1.58957i	0.0365347	−	0.0632799i	0.883715	+	0.468026i	$0.155035\pi$
$632$	22.0384			0.876640
$633$		0			0
$634$	20.1585	+	34.9156i	0.800597	+	1.38667i
$635$	6.85188	+	11.8678i	0.271909	+	0.470959i
$636$		0			0
$637$	−2.15563	−	3.73367i	−0.0854094	−	0.147933i
$638$	−94.6127			−3.74575
$639$		0			0
$640$	17.9235	−	31.0444i	0.708488	−	1.22714i
$641$	−3.82384			−0.151033			−0.0755163	−	0.997145i	$-0.524060\pi$
$641$	−3.82384			−0.151033			−0.0755163	+	0.997145i	$0.524060\pi$
$642$		0			0
$643$	−20.0502	+	34.7280i	−0.790705	+	1.36954i	0.134827	+	0.990869i	$0.456952\pi$
$643$	−20.0502	+	34.7280i	−0.790705	+	1.36954i	−0.925531	+	0.378671i	$0.876381\pi$
$644$	−2.55544	+	4.42615i	−0.100698	+	0.174415i
$645$		0			0
$646$	27.1275	+	31.6396i	1.06732	+	1.24484i
$647$	−5.93898			−0.233486			−0.116743	−	0.993162i	$-0.537245\pi$
$647$	−5.93898			−0.233486			−0.116743	+	0.993162i	$0.537245\pi$
$648$		0			0
$649$	−42.0348	−	72.8064i	−1.65001	−	2.85790i
$650$	1.07716	+	1.86570i	0.0422498	+	0.0731789i
$651$		0			0
$652$	74.4120			2.91420
$653$	20.0130	+	34.6636i	0.783170	+	1.35649i	0.930086	+	0.367342i	$0.119732\pi$
$653$	20.0130	+	34.6636i	0.783170	+	1.35649i	−0.146916	+	0.989149i	$0.546935\pi$
$654$		0			0
$655$	−6.53702	−	11.3225i	−0.255423	−	0.442405i
$656$	−15.8759	+	27.4979i	−0.619850	+	1.07361i
$657$		0			0
$658$	18.5120			0.721675
$659$	5.77333	+	9.99970i	0.224897	+	0.389533i	0.956289	−	0.292425i	$-0.0944621\pi$
$659$	5.77333	+	9.99970i	0.224897	+	0.389533i	−0.731392	+	0.681958i	$0.761129\pi$
$660$		0			0
$661$	20.9660			0.815482			0.407741	−	0.913098i	$-0.366317\pi$
$661$	20.9660			0.815482			0.407741	+	0.913098i	$0.366317\pi$
$662$	33.4164	−	57.8789i	1.29876	−	2.24953i
$663$		0			0
$664$	−17.0321	+	29.5004i	−0.660972	+	1.14484i
$665$	−3.52888	−	4.11585i	−0.136844	−	0.159606i
$666$		0			0
$667$	−6.28649	−	10.8885i	−0.243414	−	0.421605i
$668$	36.3916			1.40803
$669$		0			0
$670$	−1.80544	+	3.12711i	−0.0697501	+	0.120811i
$671$	−60.6602			−2.34176
$672$		0			0
$673$	16.9832	−	29.4157i	0.654654	−	1.13389i	−0.327327	−	0.944911i	$-0.606148\pi$
$673$	16.9832	−	29.4157i	0.654654	−	1.13389i	0.981981	−	0.188982i	$-0.0605188\pi$
$674$	21.3934	−	37.0545i	0.824044	−	1.42729i
$675$		0			0
$676$	−51.4308			−1.97811
$677$	−1.77679	+	3.07750i	−0.0682878	+	0.118278i	−0.898148	−	0.439694i	$-0.855087\pi$
$677$	−1.77679	+	3.07750i	−0.0682878	+	0.118278i	0.829860	+	0.557972i	$0.188420\pi$
$678$		0			0
$679$	−0.775742	+	1.34362i	−0.0297702	+	0.0515636i
$680$	−38.2982			−1.46867
$681$		0			0
$682$	44.7397			1.71317
$683$	27.1146			1.03751			0.518757	−	0.854922i	$-0.326395\pi$
$683$	27.1146			1.03751			0.518757	+	0.854922i	$0.326395\pi$
$684$		0			0
$685$	19.7201			0.753468
$686$	21.7634			0.830929
$687$		0			0
$688$	−40.7317			−1.55288
$689$	−4.16248	+	7.20963i	−0.158578	+	0.274665i
$690$		0			0
$691$	20.9193	−	36.2333i	0.795807	−	1.37838i	−0.126518	−	0.991964i	$-0.540380\pi$
$691$	20.9193	−	36.2333i	0.795807	−	1.37838i	0.922325	−	0.386415i	$-0.126287\pi$
$692$	−39.1371			−1.48777
$693$		0			0
$694$	−1.87504	+	3.24766i	−0.0711755	+	0.123280i
$695$	2.74538	−	4.75513i	0.104138	−	0.180373i
$696$		0			0
$697$	−26.9945			−1.02249
$698$	10.7465	−	18.6135i	0.406762	−	0.704532i
$699$		0			0
$700$	−3.53879			−0.133754
$701$	8.86597	+	15.3563i	0.334863	+	0.580000i	0.983459	−	0.181133i	$-0.0579766\pi$
$701$	8.86597	+	15.3563i	0.334863	+	0.580000i	−0.648595	+	0.761133i	$0.724643\pi$
$702$		0			0
$703$	−9.55955	+	1.79065i	−0.360545	+	0.0675356i
$704$	20.0448	−	34.7186i	0.755467	−	1.30851i
$705$		0			0
$706$	−10.2652	+	17.7799i	−0.386337	+	0.669155i
$707$	4.83435			0.181814
$708$		0			0
$709$	3.69299	+	6.39644i	0.138693	+	0.240224i	0.927002	−	0.375056i	$-0.122377\pi$
$709$	3.69299	+	6.39644i	0.138693	+	0.240224i	−0.788309	+	0.615279i	$0.789043\pi$
$710$	−2.83425			−0.106367
$711$		0			0
$712$	12.4874	−	21.6287i	0.467984	−	0.810572i
$713$	2.97271	+	5.14888i	0.111329	+	0.192827i
$714$		0			0
$715$	−3.68078	−	6.37530i	−0.137653	−	0.238423i
$716$	−1.89987			−0.0710016
$717$		0			0
$718$	33.8572	+	58.6424i	1.26354	+	2.18851i
$719$	4.79763	+	8.30974i	0.178921	+	0.309901i	0.941511	−	0.336981i	$-0.109406\pi$
$719$	4.79763	+	8.30974i	0.178921	+	0.309901i	−0.762590	+	0.646882i	$0.776073\pi$
$720$		0			0
$721$	0.921806			0.0343299
$722$	−43.7143	+	16.9722i	−1.62688	+	0.631640i
$723$		0			0
$724$	17.6782	−	30.6195i	0.657005	−	1.13797i
$725$	4.35278	−	7.53924i	0.161658	−	0.280000i
$726$		0			0
$727$	32.8848			1.21963			0.609815	−	0.792544i	$-0.291244\pi$
$727$	32.8848			1.21963			0.609815	+	0.792544i	$0.291244\pi$
$728$	−1.09846	+	1.90258i	−0.0407115	+	0.0705144i
$729$		0			0
$730$	−16.5955			−0.614227
$731$	−17.3145	−	29.9895i	−0.640399	−	1.10920i
$732$		0			0
$733$	−18.1159	−	31.3777i	−0.669126	−	1.15896i	−0.978149	−	0.207906i	$-0.933335\pi$
$733$	−18.1159	−	31.3777i	−0.669126	−	1.15896i	0.309022	−	0.951055i	$-0.399998\pi$
$734$	28.8679	+	50.0006i	1.06553	+	1.84556i
$735$		0			0
$736$	−1.77527			−0.0654374
$737$	−2.24003	+	3.87985i	−0.0825126	+	0.142916i
$738$		0			0
$739$	12.0565	+	20.8825i	0.443507	+	0.768177i	0.997947	−	0.0640471i	$-0.0204008\pi$
$739$	12.0565	+	20.8825i	0.443507	+	0.768177i	−0.554440	+	0.832224i	$0.687067\pi$
$740$	8.74206	−	15.1417i	0.321364	−	0.556620i
$741$		0			0
$742$	−10.1798	−	17.6320i	−0.373713	−	0.647290i
$743$	−12.1519	+	21.0478i	−0.445811	+	0.772168i	−0.998108	−	0.0614796i	$-0.980418\pi$
$743$	−12.1519	+	21.0478i	−0.445811	+	0.772168i	0.552297	+	0.833647i	$0.313751\pi$
$744$		0			0
$745$	7.81994	+	13.5445i	0.286501	+	0.496234i
$746$	−4.67129	−	8.09092i	−0.171028	−	0.296230i
$747$		0			0
$748$	−92.9577			−3.39887
$749$	2.45751	−	4.25654i	0.0897956	−	0.155531i
$750$		0			0
$751$	−21.9356			−0.800443			−0.400221	−	0.916418i	$-0.631067\pi$
$751$	−21.9356			−0.800443			−0.400221	+	0.916418i	$0.631067\pi$
$752$	26.3146	+	45.5782i	0.959594	+	1.66207i
$753$		0			0
$754$	−5.28641	−	9.15632i	−0.192520	−	0.333454i
$755$	−19.6473	−	34.0301i	−0.715039	−	1.23848i
$756$		0			0
$757$	−20.3751	−	35.2907i	−0.740545	−	1.28266i	−0.952247	−	0.305328i	$-0.901234\pi$
$757$	−20.3751	−	35.2907i	−0.740545	−	1.28266i	0.211702	−	0.977334i	$-0.432099\pi$
$758$	12.7539			0.463243
$759$		0			0
$760$	14.3067	−	40.6475i	0.518960	−	1.47444i
$761$	6.54874	+	11.3427i	0.237391	+	0.411174i	0.959965	−	0.280120i	$-0.0903743\pi$
$761$	6.54874	+	11.3427i	0.237391	+	0.411174i	−0.722574	+	0.691294i	$0.757041\pi$
$762$		0			0
$763$	−4.93052			−0.178497
$764$	−45.4195	+	78.6689i	−1.64322	+	2.84614i
$765$		0			0
$766$	11.1077	−	19.2391i	0.401337	−	0.695136i
$767$	4.69732	−	8.13599i	0.169610	−	0.293774i
$768$		0			0
$769$	40.8918			1.47459			0.737297	−	0.675568i	$-0.236102\pi$
$769$	40.8918			1.47459			0.737297	+	0.675568i	$0.236102\pi$
$770$	18.0035			0.648803
$771$		0			0
$772$	9.65795	−	16.7281i	0.347597	−	0.602056i
$773$	9.81097	−	16.9931i	0.352876	−	0.611199i	−0.633876	−	0.773435i	$-0.718537\pi$
$773$	9.81097	−	16.9931i	0.352876	−	0.611199i	0.986752	+	0.162235i	$0.0518704\pi$
$774$		0			0
$775$	−2.05831	+	3.56510i	−0.0739367	+	0.128062i
$776$	−12.3316			−0.442678
$777$		0			0
$778$	−25.6238	−	44.3817i	−0.918657	−	1.59116i
$779$	10.0841	−	28.6504i	0.361300	−	1.02651i
$780$		0			0
$781$	−3.51649			−0.125830
$782$	−9.19579	−	15.9276i	−0.328841	−	0.569569i
$783$		0			0
$784$	14.9877	+	25.9595i	0.535275	+	0.927124i
$785$	−1.39876	−	2.42273i	−0.0499239	−	0.0864708i
$786$		0			0
$787$	−3.19894	−	5.54073i	−0.114030	−	0.197506i	0.803362	−	0.595492i	$-0.203043\pi$
$787$	−3.19894	−	5.54073i	−0.114030	−	0.197506i	−0.917392	+	0.397986i	$0.869709\pi$
$788$	−33.6887			−1.20011
$789$		0			0
$790$	10.0910	−	17.4782i	0.359023	−	0.621847i
$791$	3.17660			0.112947
$792$		0			0
$793$	−3.38934	−	5.87051i	−0.120359	−	0.208468i
$794$	6.65963	+	11.5348i	0.236342	+	0.409356i
$795$		0			0
$796$	−5.41026	+	9.37085i	−0.191762	+	0.332141i
$797$	−23.8040	−	41.2297i	−0.843179	−	1.46043i	−0.887193	−	0.461399i	$-0.847348\pi$
$797$	−23.8040	−	41.2297i	−0.843179	−	1.46043i	0.0440136	−	0.999031i	$-0.485986\pi$
$798$		0			0
$799$	−22.3719	+	38.7493i	−0.791461	+	1.37085i
$800$	−0.614602	−	1.06452i	−0.0217295	−	0.0376365i
$801$		0			0
$802$	−23.3562	+	40.4541i	−0.824736	+	1.42848i
$803$	−20.5903			−0.726614
$804$		0			0
$805$	1.19624	+	2.07194i	0.0421618	+	0.0730263i
$806$	2.49980	+	4.32977i	0.0880515	+	0.152510i
$807$		0			0
$808$	19.2123	+	33.2767i	0.675887	+	1.17067i
$809$	−4.09101			−0.143832			−0.0719160	−	0.997411i	$-0.522911\pi$
$809$	−4.09101			−0.143832			−0.0719160	+	0.997411i	$0.522911\pi$
$810$		0			0
$811$	11.1310	−	19.2794i	0.390862	−	0.676993i	−0.601702	−	0.798721i	$-0.705510\pi$
$811$	11.1310	−	19.2794i	0.390862	−	0.676993i	0.992563	+	0.121728i	$0.0388437\pi$
$812$	17.3673			0.609474
$813$		0			0
$814$	16.1484	−	27.9699i	0.566003	−	0.980345i
$815$	17.4166	−	30.1665i	0.610078	−	1.05669i
$816$		0			0
$817$	38.2972	−	7.17365i	1.33985	−	0.250974i
$818$	−70.6030			−2.46858
$819$		0			0
$820$	27.3010	+	47.2868i	0.953393	+	1.65133i
$821$	5.82455	+	10.0884i	0.203278	+	0.352088i	0.949583	−	0.313517i	$-0.101507\pi$
$821$	5.82455	+	10.0884i	0.203278	+	0.352088i	−0.746305	+	0.665605i	$0.768174\pi$
$822$		0			0
$823$	−13.5099			−0.470924			−0.235462	−	0.971884i	$-0.575660\pi$
$823$	−13.5099			−0.470924			−0.235462	+	0.971884i	$0.575660\pi$
$824$	3.66337	+	6.34515i	0.127620	+	0.221044i
$825$		0			0
$826$	11.4878	+	19.8975i	0.399712	+	0.692322i
$827$	5.09722	−	8.82865i	0.177248	−	0.307002i	−0.763689	−	0.645584i	$-0.776614\pi$
$827$	5.09722	−	8.82865i	0.177248	−	0.307002i	0.940937	+	0.338582i	$0.109947\pi$
$828$		0			0
$829$	6.76339			0.234902			0.117451	−	0.993079i	$-0.462528\pi$
$829$	6.76339			0.234902			0.117451	+	0.993079i	$0.462528\pi$
$830$	15.5974	+	27.0156i	0.541395	+	0.937724i
$831$		0			0
$832$	4.47995			0.155314
$833$	−12.7421	+	22.0700i	−0.441488	+	0.764680i
$834$		0			0
$835$	8.51771	−	14.7531i	0.294767	−	0.510552i
$836$	34.7254	−	98.6599i	1.20100	−	3.41223i
$837$		0			0
$838$	−36.7530	−	63.6580i	−1.26961	−	2.19903i
$839$	−2.23211			−0.0770609			−0.0385305	−	0.999257i	$-0.512268\pi$
$839$	−2.23211			−0.0770609			−0.0385305	+	0.999257i	$0.512268\pi$
$840$		0			0
$841$	−6.86218	+	11.8856i	−0.236627	+	0.409850i
$842$	1.56135			0.0538078
$843$		0			0
$844$	−33.8522	+	58.6337i	−1.16524	+	2.01826i
$845$	−12.0377	+	20.8500i	−0.414110	+	0.717260i
$846$		0			0
$847$	15.1937			0.522060
$848$	28.9409	−	50.1272i	0.993835	−	1.72137i
$849$		0			0
$850$	6.36719	−	11.0283i	0.218393	−	0.378268i
$851$	4.29190			0.147124
$852$		0			0
$853$	31.9771			1.09487			0.547437	−	0.836847i	$-0.315604\pi$
$853$	31.9771			1.09487			0.547437	+	0.836847i	$0.315604\pi$
$854$	16.5780			0.567289
$855$		0			0
$856$	39.0659			1.33524
$857$	31.7316			1.08393			0.541966	−	0.840401i	$-0.317680\pi$
$857$	31.7316			1.08393			0.541966	+	0.840401i	$0.317680\pi$
$858$		0			0
$859$	5.85144			0.199648			0.0998242	−	0.995005i	$-0.468172\pi$
$859$	5.85144			0.199648			0.0998242	+	0.995005i	$0.468172\pi$
$860$	−35.0222	+	60.6602i	−1.19425	+	2.06850i
$861$		0			0
$862$	29.5282	−	51.1444i	1.00574	−	1.74199i
$863$	−29.7096			−1.01133			−0.505664	−	0.862731i	$-0.668752\pi$
$863$	−29.7096			−1.01133			−0.505664	+	0.862731i	$0.668752\pi$
$864$		0			0
$865$	−9.16029	+	15.8661i	−0.311459	+	0.539463i
$866$	5.50575	−	9.53624i	0.187093	−	0.324055i
$867$		0			0
$868$	−8.21253			−0.278751
$869$	12.5201	−	21.6855i	0.424715	−	0.735629i
$870$		0			0
$871$	−0.500640			−0.0169635
$872$	−19.5945	−	33.9387i	−0.663553	−	1.14931i
$873$		0			0
$874$	20.3398	−	3.80996i	0.688005	−	0.128874i
$875$	−3.93775	+	6.82038i	−0.133120	+	0.230571i
$876$		0			0
$877$	−19.8687	+	34.4137i	−0.670920	+	1.16207i	0.306724	+	0.951799i	$0.400767\pi$
$877$	−19.8687	+	34.4137i	−0.670920	+	1.16207i	−0.977644	+	0.210269i	$0.932566\pi$
$878$	−39.9498			−1.34824
$879$		0			0
$880$	25.5918	+	44.3262i	0.862698	+	1.49424i
$881$	22.1976			0.747855			0.373927	−	0.927458i	$-0.378011\pi$
$881$	22.1976			0.747855			0.373927	+	0.927458i	$0.378011\pi$
$882$		0			0
$883$	0.944299	−	1.63557i	0.0317782	−	0.0550414i	−0.849699	−	0.527268i	$-0.823216\pi$
$883$	0.944299	−	1.63557i	0.0317782	−	0.0550414i	0.881477	+	0.472227i	$0.156550\pi$
$884$	−5.19393	−	8.99616i	−0.174691	−	0.302574i
$885$		0			0
$886$	21.7798	+	37.7237i	0.731707	+	1.26735i
$887$	−31.3497			−1.05262			−0.526309	−	0.850293i	$-0.676425\pi$
$887$	−31.3497			−1.05262			−0.526309	+	0.850293i	$0.676425\pi$
$888$		0			0
$889$	−2.32333	−	4.02412i	−0.0779219	−	0.134965i
$890$	−11.4355	−	19.8070i	−0.383320	−	0.663931i
$891$		0			0
$892$	37.8197			1.26630
$893$	−32.7690	−	38.2195i	−1.09657	−	1.27897i
$894$		0			0
$895$	−0.444678	+	0.770205i	−0.0148640	+	0.0257451i
$896$	−6.07748	+	10.5265i	−0.203034	+	0.351666i
$897$		0			0
$898$	−101.744			−3.39525
$899$	10.1016	−	17.4965i	0.336907	−	0.583540i
$900$		0			0
$901$	49.2095			1.63941
$902$	50.4308	+	87.3487i	1.67916	+	2.90839i
$903$		0			0
$904$	12.6242	+	21.8658i	0.419875	+	0.727245i
$905$	−8.27540	−	14.3334i	−0.275084	−	0.476459i
$906$		0			0
$907$	30.8751			1.02519			0.512596	−	0.858630i	$-0.328684\pi$
$907$	30.8751			1.02519			0.512596	+	0.858630i	$0.328684\pi$
$908$	−21.4443	+	37.1427i	−0.711655	+	1.23262i
$909$		0			0
$910$	1.00593	+	1.74233i	0.0333464	+	0.0577576i
$911$	18.4983	−	32.0401i	0.612877	−	1.06153i	−0.377875	−	0.925856i	$-0.623345\pi$
$911$	18.4983	−	32.0401i	0.612877	−	1.06153i	0.990753	−	0.135678i	$-0.0433214\pi$
$912$		0			0
$913$	19.3520	+	33.5186i	0.640457	+	1.10930i
$914$	5.08397	−	8.80569i	0.168163	−	0.291266i
$915$		0			0
$916$	−36.0475	−	62.4362i	−1.19104	−	2.06295i
$917$	2.21657	+	3.83920i	0.0731974	+	0.126782i
$918$		0			0
$919$	43.0561			1.42029			0.710146	−	0.704055i	$-0.248629\pi$
$919$	43.0561			1.42029			0.710146	+	0.704055i	$0.248629\pi$
$920$	−9.50798	+	16.4683i	−0.313469	+	0.542944i
$921$		0			0
$922$	−34.6071			−1.13972
$923$	−0.196481	−	0.340315i	−0.00646725	−	0.0112016i
$924$		0			0
$925$	1.48586	+	2.57359i	0.0488548	+	0.0846190i
$926$	−30.7972	−	53.3423i	−1.01206	−	1.75294i
$927$		0			0
$928$	3.01629	+	5.22436i	0.0990145	+	0.171498i
$929$	−44.2466			−1.45168			−0.725841	−	0.687862i	$-0.758549\pi$
$929$	−44.2466			−1.45168			−0.725841	+	0.687862i	$0.758549\pi$
$930$		0			0
$931$	−18.6639	−	21.7682i	−0.611683	−	0.713425i
$932$	13.9459	+	24.1550i	0.456813	+	0.791224i
$933$		0			0
$934$	−56.7922			−1.85830
$935$	−21.7574	+	37.6849i	−0.711542	+	1.23243i
$936$		0			0
$937$	1.92051	−	3.32642i	0.0627402	−	0.108669i	−0.832949	−	0.553350i	$-0.813349\pi$
$937$	1.92051	−	3.32642i	0.0627402	−	0.108669i	0.895689	+	0.444680i	$0.146683\pi$
$938$	0.612186	−	1.06034i	0.0199886	−	0.0346212i
$939$		0			0
$940$	90.5038			2.95191
$941$	27.1228			0.884179			0.442090	−	0.896971i	$-0.354237\pi$
$941$	27.1228			0.884179			0.442090	+	0.896971i	$0.354237\pi$
$942$		0			0
$943$	−6.70169	+	11.6077i	−0.218237	+	0.377998i
$944$	−32.6595	+	56.5680i	−1.06298	+	1.84113i
$945$		0			0
$946$	−64.6934	+	112.052i	−2.10337	+	3.64314i
$947$	11.5550			0.375486			0.187743	−	0.982218i	$-0.439883\pi$
$947$	11.5550			0.375486			0.187743	+	0.982218i	$0.439883\pi$
$948$		0			0
$949$	−1.15046	−	1.99266i	−0.0373456	−	0.0646846i
$950$	9.32627	+	10.8775i	0.302584	+	0.352914i
$951$		0			0
$952$	12.9861			0.420882
$953$	19.4213	+	33.6388i	0.629119	+	1.08967i	0.987729	+	0.156178i	$0.0499175\pi$
$953$	19.4213	+	33.6388i	0.629119	+	1.08967i	−0.358610	+	0.933488i	$0.616749\pi$
$954$		0			0
$955$	21.2615	+	36.8260i	0.688005	+	1.19166i
$956$	−27.7175	−	48.0081i	−0.896448	−	1.55269i
$957$		0			0
$958$	−4.73485	−	8.20100i	−0.152976	−	0.264962i
$959$	−6.68668			−0.215924
$960$		0			0
$961$	10.7232	−	18.5732i	0.345911	−	0.599135i
$962$	3.60912			0.116363
$963$		0			0
$964$	−15.3179	−	26.5313i	−0.493356	−	0.854517i
$965$	−4.52102	−	7.83063i	−0.145537	−	0.252077i
$966$		0			0
$967$	22.1908	−	38.4356i	0.713608	−	1.23601i	−0.249886	−	0.968275i	$-0.580393\pi$
$967$	22.1908	−	38.4356i	0.713608	−	1.23601i	0.963494	−	0.267730i	$-0.0862736\pi$
$968$	60.3815	+	104.584i	1.94073	+	3.36145i
$969$		0			0
$970$	−5.64644	+	9.77993i	−0.181296	+	0.314015i
$971$	−4.70379	−	8.14720i	−0.150952	−	0.261456i	0.780626	−	0.624999i	$-0.214900\pi$
$971$	−4.70379	−	8.14720i	−0.150952	−	0.261456i	−0.931578	+	0.363543i	$0.881567\pi$
$972$		0			0
$973$	−0.930900	+	1.61237i	−0.0298433	+	0.0516901i
$974$	76.4743			2.45039
$975$		0			0
$976$	23.5654	+	40.8165i	0.754311	+	1.30650i
$977$	2.98306	+	5.16682i	0.0954367	+	0.165301i	0.909791	−	0.415067i	$-0.136242\pi$
$977$	2.98306	+	5.16682i	0.0954367	+	0.165301i	−0.814354	+	0.580368i	$0.802909\pi$
$978$		0			0
$979$	−14.1882	−	24.5748i	−0.453458	−	0.785413i
$980$	51.5472			1.64662
$981$		0			0
$982$	34.3121	−	59.4303i	1.09494	−	1.89650i
$983$	52.5697			1.67671			0.838356	−	0.545122i	$-0.183517\pi$
$983$	52.5697			1.67671			0.838356	+	0.545122i	$0.183517\pi$
$984$		0			0
$985$	−7.88507	+	13.6573i	−0.251239	+	0.435159i
$986$	−31.2483	+	54.1237i	−0.995149	+	1.72365i
$987$		0			0
$988$	11.4883	−	2.15193i	0.365490	−	0.0684619i
$989$	−17.1941			−0.546740
$990$		0			0
$991$	19.1553	+	33.1780i	0.608489	+	1.05393i	0.991490	+	0.130186i	$0.0415576\pi$
$991$	19.1553	+	33.1780i	0.608489	+	1.05393i	−0.383000	+	0.923748i	$0.625109\pi$
$992$	−1.42632	−	2.47046i	−0.0452857	−	0.0784371i
$993$		0			0
$994$	0.961034			0.0304821
$995$	2.53262	+	4.38662i	0.0802893	+	0.139065i
$996$		0			0
$997$	−7.66397	−	13.2744i	−0.242720	−	0.420404i	0.718768	−	0.695250i	$-0.244706\pi$
$997$	−7.66397	−	13.2744i	−0.242720	−	0.420404i	−0.961488	+	0.274846i	$0.911373\pi$
$998$	−26.7278	+	46.2939i	−0.846054	+	1.46541i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.h.c.235.1		32
3.2	odd	2		171.2.h.c.7.16	yes	32
9.4	even	3		513.2.g.c.64.16		32
9.5	odd	6		171.2.g.c.121.1	yes	32
19.11	even	3		513.2.g.c.505.16		32
57.11	odd	6		171.2.g.c.106.1	✓	32
171.49	even	3	inner	513.2.h.c.334.1		32
171.68	odd	6		171.2.h.c.49.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.1	✓	32	57.11	odd	6
171.2.g.c.121.1	yes	32	9.5	odd	6
171.2.h.c.7.16	yes	32	3.2	odd	2
171.2.h.c.49.16	yes	32	171.68	odd	6
513.2.g.c.64.16		32	9.4	even	3
513.2.g.c.505.16		32	19.11	even	3
513.2.h.c.235.1		32	1.1	even	1	trivial
513.2.h.c.334.1		32	171.49	even	3	inner

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:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.46808 q^{2} +4.09140 q^{4} +(0.957619 - 1.65865i) q^{5} +(-0.324708 + 0.562412i) q^{7} -5.16173 q^{8} +O(q^{10})\)	\(q-2.46808 q^{2} +4.09140 q^{4} +(0.957619 - 1.65865i) q^{5} +(-0.324708 + 0.562412i) q^{7} -5.16173 q^{8} +(-2.36348 + 4.09366i) q^{10} +(-2.93240 + 5.07906i) q^{11} -0.655382 q^{13} +(0.801405 - 1.38807i) q^{14} +4.55674 q^{16} +(1.93700 + 3.35499i) q^{17} +(-4.28438 + 0.802530i) q^{19} +(3.91800 - 6.78618i) q^{20} +(7.23738 - 12.5355i) q^{22} +1.92354 q^{23} +(0.665931 + 1.15343i) q^{25} +1.61753 q^{26} +(-1.32851 + 2.30105i) q^{28} +(-3.26819 - 5.66068i) q^{29} +(1.54544 + 2.67678i) q^{31} -0.922922 q^{32} +(-4.78067 - 8.28037i) q^{34} +(0.621894 + 1.07715i) q^{35} +2.23125 q^{37} +(10.5742 - 1.98070i) q^{38} +(-4.94297 + 8.56147i) q^{40} +(-3.48405 + 6.03455i) q^{41} -8.93879 q^{43} +(-11.9976 + 20.7805i) q^{44} -4.74743 q^{46} +(5.77487 + 10.0024i) q^{47} +(3.28913 + 5.69694i) q^{49} +(-1.64357 - 2.84674i) q^{50} -2.68143 q^{52} +(6.35124 - 11.0007i) q^{53} +(5.61624 + 9.72762i) q^{55} +(1.67606 - 2.90302i) q^{56} +(8.06615 + 13.9710i) q^{58} +(-7.16730 + 12.4141i) q^{59} +(5.17155 + 8.95739i) q^{61} +(-3.81426 - 6.60649i) q^{62} -6.83564 q^{64} +(-0.627606 + 1.08705i) q^{65} +0.763890 q^{67} +(7.92505 + 13.7266i) q^{68} +(-1.53488 - 2.65849i) q^{70} +(0.299796 + 0.519263i) q^{71} +(1.75541 + 3.04046i) q^{73} -5.50690 q^{74} +(-17.5291 + 3.28347i) q^{76} +(-1.90435 - 3.29843i) q^{77} -4.26958 q^{79} +(4.36362 - 7.55801i) q^{80} +(8.59890 - 14.8937i) q^{82} +(3.29968 - 5.71522i) q^{83} +7.41965 q^{85} +22.0616 q^{86} +(15.1362 - 26.2167i) q^{88} +(-2.41922 + 4.19022i) q^{89} +(0.212808 - 0.368594i) q^{91} +7.86995 q^{92} +(-14.2528 - 24.6866i) q^{94} +(-2.77170 + 7.87479i) q^{95} +2.38904 q^{97} +(-8.11782 - 14.0605i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8	\( 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} + 8 q^{13} - q^{14} + 22 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} - 8 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} - 10 q^{28} - 10 q^{29} - 10 q^{31} + 34 q^{32} - 13 q^{34} + 3 q^{35} + 2 q^{37} + 46 q^{38} + 12 q^{40} - 6 q^{41} - 14 q^{43} - 20 q^{44} + 9 q^{47} - 13 q^{49} - q^{50} - 38 q^{52} - 16 q^{53} + 15 q^{55} + 6 q^{56} - 37 q^{59} - 12 q^{61} - 54 q^{62} - 64 q^{64} - 54 q^{65} + 22 q^{67} + 2 q^{68} + 24 q^{70} - 9 q^{71} - 10 q^{73} + 12 q^{74} - 40 q^{76} - 46 q^{77} + 16 q^{79} + 24 q^{80} + 7 q^{82} - 3 q^{83} + 54 q^{85} + 34 q^{86} + 9 q^{88} - 30 q^{89} - q^{91} - 34 q^{92} - 18 q^{94} - 3 q^{95} - 18 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 + 8 * q^13 - q^14 + 22 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 - 8 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 - 10 * q^28 - 10 * q^29 - 10 * q^31 + 34 * q^32 - 13 * q^34 + 3 * q^35 + 2 * q^37 + 46 * q^38 + 12 * q^40 - 6 * q^41 - 14 * q^43 - 20 * q^44 + 9 * q^47 - 13 * q^49 - q^50 - 38 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 - 37 * q^59 - 12 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 + 22 * q^67 + 2 * q^68 + 24 * q^70 - 9 * q^71 - 10 * q^73 + 12 * q^74 - 40 * q^76 - 46 * q^77 + 16 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 + 54 * q^85 + 34 * q^86 + 9 * q^88 - 30 * q^89 - q^91 - 34 * q^92 - 18 * q^94 - 3 * q^95 - 18 * q^98

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