LMFDB - Embedded newform 1792.2.m.e.449.8

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			449.8
Root			$0.339278 + 0.0446668i$ of defining polynomial
Character	$\chi$	$=$	1792.449
Dual form			1792.2.m.e.1345.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48474 - 1.48474i) q^{3} +(1.83598 + 1.83598i) q^{5} +1.00000i q^{7} -1.40890i q^{9} +O(q^{10})$	\(q+(1.48474 - 1.48474i) q^{3} +(1.83598 + 1.83598i) q^{5} +1.00000i q^{7} -1.40890i q^{9} +(0.321444 + 0.321444i) q^{11} +(4.61789 - 4.61789i) q^{13} +5.45192 q^{15} -1.84172 q^{17} +(-3.88948 + 3.88948i) q^{19} +(1.48474 + 1.48474i) q^{21} +5.88497i q^{23} +1.74168i q^{25} +(2.36237 + 2.36237i) q^{27} +(6.14570 - 6.14570i) q^{29} +5.69821 q^{31} +0.954522 q^{33} +(-1.83598 + 1.83598i) q^{35} +(1.66877 + 1.66877i) q^{37} -13.7127i q^{39} -10.7333i q^{41} +(-0.533105 - 0.533105i) q^{43} +(2.58672 - 2.58672i) q^{45} -0.465401 q^{47} -1.00000 q^{49} +(-2.73447 + 2.73447i) q^{51} +(-0.623234 - 0.623234i) q^{53} +1.18033i q^{55} +11.5497i q^{57} +(7.32184 + 7.32184i) q^{59} +(-7.57257 + 7.57257i) q^{61} +1.40890 q^{63} +16.9567 q^{65} +(-6.16327 + 6.16327i) q^{67} +(8.73764 + 8.73764i) q^{69} -0.162532i q^{71} +3.49118i q^{73} +(2.58594 + 2.58594i) q^{75} +(-0.321444 + 0.321444i) q^{77} +8.28703 q^{79} +11.2417 q^{81} +(-2.51275 + 2.51275i) q^{83} +(-3.38136 - 3.38136i) q^{85} -18.2495i q^{87} +1.60040i q^{89} +(4.61789 + 4.61789i) q^{91} +(8.46035 - 8.46035i) q^{93} -14.2821 q^{95} -8.88621 q^{97} +(0.452882 - 0.452882i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times$.

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

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
$3$	1.48474	−	1.48474i	0.857214	−	0.857214i	−0.133795	−	0.991009i	$-0.542716\pi$
$3$	1.48474	−	1.48474i	0.857214	−	0.857214i	0.991009	+	0.133795i	$0.0427163\pi$
$4$		0			0
$5$	1.83598	+	1.83598i	0.821077	+	0.821077i	0.986263	−	0.165185i	$-0.0528222\pi$
$5$	1.83598	+	1.83598i	0.821077	+	0.821077i	−0.165185	+	0.986263i	$0.552822\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		0			0
$9$		−	1.40890i		−	0.469633i
$10$		0			0
$11$	0.321444	+	0.321444i	0.0969191	+	0.0969191i	0.753904	−	0.656985i	$-0.228168\pi$
$11$	0.321444	+	0.321444i	0.0969191	+	0.0969191i	−0.656985	+	0.753904i	$0.728168\pi$
$12$		0			0
$13$	4.61789	−	4.61789i	1.28077	−	1.28077i	0.340541	−	0.940230i	$-0.389390\pi$
$13$	4.61789	−	4.61789i	1.28077	−	1.28077i	0.940230	−	0.340541i	$-0.110610\pi$
$14$		0			0
$15$	5.45192			1.40768
$16$		0			0
$17$	−1.84172			−0.446682			−0.223341	−	0.974740i	$-0.571696\pi$
$17$	−1.84172			−0.446682			−0.223341	+	0.974740i	$0.571696\pi$
$18$		0			0
$19$	−3.88948	+	3.88948i	−0.892308	+	0.892308i	−0.994740	−	0.102432i	$-0.967338\pi$
$19$	−3.88948	+	3.88948i	−0.892308	+	0.892308i	0.102432	+	0.994740i	$0.467338\pi$
$20$		0			0
$21$	1.48474	+	1.48474i	0.323997	+	0.323997i
$22$		0			0
$23$			5.88497i			1.22710i	0.789656	+	0.613550i	$0.210259\pi$
$23$			5.88497i			1.22710i	−0.789656	+	0.613550i	$0.789741\pi$
$24$		0			0
$25$			1.74168i			0.348336i
$26$		0			0
$27$	2.36237	+	2.36237i	0.454639	+	0.454639i
$28$		0			0
$29$	6.14570	−	6.14570i	1.14123	−	1.14123i	0.153002	−	0.988226i	$-0.451106\pi$
$29$	6.14570	−	6.14570i	1.14123	−	1.14123i	0.988226	−	0.153002i	$-0.0488942\pi$
$30$		0			0
$31$	5.69821			1.02343			0.511714	−	0.859156i	$-0.329011\pi$
$31$	5.69821			1.02343			0.511714	+	0.859156i	$0.329011\pi$
$32$		0			0
$33$	0.954522			0.166161
$34$		0			0
$35$	−1.83598	+	1.83598i	−0.310338	+	0.310338i
$36$		0			0
$37$	1.66877	+	1.66877i	0.274344	+	0.274344i	0.830846	−	0.556502i	$-0.187857\pi$
$37$	1.66877	+	1.66877i	0.274344	+	0.274344i	−0.556502	+	0.830846i	$0.687857\pi$
$38$		0			0
$39$		−	13.7127i		−	2.19579i
$40$		0			0
$41$		−	10.7333i		−	1.67626i	−0.545468	−	0.838132i	$-0.683648\pi$
$41$		−	10.7333i		−	1.67626i	0.545468	−	0.838132i	$-0.316352\pi$
$42$		0			0
$43$	−0.533105	−	0.533105i	−0.0812978	−	0.0812978i	0.665289	−	0.746586i	$-0.268309\pi$
$43$	−0.533105	−	0.533105i	−0.0812978	−	0.0812978i	−0.746586	+	0.665289i	$0.768309\pi$
$44$		0			0
$45$	2.58672	−	2.58672i	0.385605	−	0.385605i
$46$		0			0
$47$	−0.465401			−0.0678856			−0.0339428	−	0.999424i	$-0.510806\pi$
$47$	−0.465401			−0.0678856			−0.0339428	+	0.999424i	$0.510806\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−2.73447	+	2.73447i	−0.382902	+	0.382902i
$52$		0			0
$53$	−0.623234	−	0.623234i	−0.0856078	−	0.0856078i	0.663006	−	0.748614i	$-0.269280\pi$
$53$	−0.623234	−	0.623234i	−0.0856078	−	0.0856078i	−0.748614	+	0.663006i	$0.769280\pi$
$54$		0			0
$55$			1.18033i			0.159156i
$56$		0			0
$57$			11.5497i			1.52980i
$58$		0			0
$59$	7.32184	+	7.32184i	0.953223	+	0.953223i	0.998954	−	0.0457310i	$-0.0145617\pi$
$59$	7.32184	+	7.32184i	0.953223	+	0.953223i	−0.0457310	+	0.998954i	$0.514562\pi$
$60$		0			0
$61$	−7.57257	+	7.57257i	−0.969569	+	0.969569i	−0.999550	−	0.0299816i	$-0.990455\pi$
$61$	−7.57257	+	7.57257i	−0.969569	+	0.969569i	0.0299816	+	0.999550i	$0.490455\pi$
$62$		0			0
$63$	1.40890			0.177504
$64$		0			0
$65$	16.9567			2.10322
$66$		0			0
$67$	−6.16327	+	6.16327i	−0.752964	+	0.752964i	−0.975031	−	0.222068i	$-0.928719\pi$
$67$	−6.16327	+	6.16327i	−0.752964	+	0.752964i	0.222068	+	0.975031i	$0.428719\pi$
$68$		0			0
$69$	8.73764	+	8.73764i	1.05189	+	1.05189i
$70$		0			0
$71$		−	0.162532i		−	0.0192890i	−0.999953	−	0.00964452i	$-0.996930\pi$
$71$		−	0.162532i		−	0.0192890i	0.999953	−	0.00964452i	$-0.00306999\pi$
$72$		0			0
$73$			3.49118i			0.408612i	0.978907	+	0.204306i	$0.0654938\pi$
$73$			3.49118i			0.408612i	−0.978907	+	0.204306i	$0.934506\pi$
$74$		0			0
$75$	2.58594	+	2.58594i	0.298599	+	0.298599i
$76$		0			0
$77$	−0.321444	+	0.321444i	−0.0366320	+	0.0366320i
$78$		0			0
$79$	8.28703			0.932363			0.466182	−	0.884689i	$-0.345629\pi$
$79$	8.28703			0.932363			0.466182	+	0.884689i	$0.345629\pi$
$80$		0			0
$81$	11.2417			1.24908
$82$		0			0
$83$	−2.51275	+	2.51275i	−0.275810	+	0.275810i	−0.831434	−	0.555624i	$-0.812479\pi$
$83$	−2.51275	+	2.51275i	−0.275810	+	0.275810i	0.555624	+	0.831434i	$0.312479\pi$
$84$		0			0
$85$	−3.38136	−	3.38136i	−0.366760	−	0.366760i
$86$		0			0
$87$		−	18.2495i		−	1.95655i
$88$		0			0
$89$			1.60040i			0.169642i	0.996396	+	0.0848209i	$0.0270318\pi$
$89$			1.60040i			0.169642i	−0.996396	+	0.0848209i	$0.972968\pi$
$90$		0			0
$91$	4.61789	+	4.61789i	0.484086	+	0.484086i
$92$		0			0
$93$	8.46035	−	8.46035i	0.877297	−	0.877297i
$94$		0			0
$95$	−14.2821			−1.46531
$96$		0			0
$97$	−8.88621			−0.902258			−0.451129	−	0.892459i	$-0.648979\pi$
$97$	−8.88621			−0.902258			−0.451129	+	0.892459i	$0.648979\pi$
$98$		0			0
$99$	0.452882	−	0.452882i	0.0455164	−	0.0455164i
$100$		0			0
$101$	9.80533	+	9.80533i	0.975667	+	0.975667i	0.999711	−	0.0240439i	$-0.00765416\pi$
$101$	9.80533	+	9.80533i	0.975667	+	0.975667i	−0.0240439	+	0.999711i	$0.507654\pi$
$102$		0			0
$103$		−	14.3236i		−	1.41135i	−0.708537	−	0.705674i	$-0.750644\pi$
$103$		−	14.3236i		−	1.41135i	0.708537	−	0.705674i	$-0.249356\pi$
$104$		0			0
$105$			5.45192i			0.532052i
$106$		0			0
$107$	−10.6995	−	10.6995i	−1.03436	−	1.03436i	−0.999388	−	0.0349695i	$-0.988867\pi$
$107$	−10.6995	−	10.6995i	−1.03436	−	1.03436i	−0.0349695	−	0.999388i	$-0.511133\pi$
$108$		0			0
$109$	−7.38679	+	7.38679i	−0.707526	+	0.707526i	−0.966014	−	0.258488i	$-0.916776\pi$
$109$	−7.38679	+	7.38679i	−0.707526	+	0.707526i	0.258488	+	0.966014i	$0.416776\pi$
$110$		0			0
$111$	4.95537			0.470343
$112$		0			0
$113$	8.05995			0.758217			0.379108	−	0.925352i	$-0.376231\pi$
$113$	8.05995			0.758217			0.379108	+	0.925352i	$0.376231\pi$
$114$		0			0
$115$	−10.8047	+	10.8047i	−1.00754	+	1.00754i
$116$		0			0
$117$	−6.50613	−	6.50613i	−0.601492	−	0.601492i
$118$		0			0
$119$		−	1.84172i		−	0.168830i
$120$		0			0
$121$		−	10.7933i		−	0.981213i
$122$		0			0
$123$	−15.9362	−	15.9362i	−1.43692	−	1.43692i
$124$		0			0
$125$	5.98222	−	5.98222i	0.535066	−	0.535066i
$126$		0			0
$127$	0.367471			0.0326078			0.0163039	−	0.999867i	$-0.494810\pi$
$127$	0.367471			0.0326078			0.0163039	+	0.999867i	$0.494810\pi$
$128$		0			0
$129$	−1.58304			−0.139379
$130$		0			0
$131$	−9.30850	+	9.30850i	−0.813288	+	0.813288i	−0.985125	−	0.171838i	$-0.945030\pi$
$131$	−9.30850	+	9.30850i	−0.813288	+	0.813288i	0.171838	+	0.985125i	$0.445030\pi$
$132$		0			0
$133$	−3.88948	−	3.88948i	−0.337261	−	0.337261i
$134$		0			0
$135$			8.67456i			0.746587i
$136$		0			0
$137$		−	6.85872i		−	0.585980i	−0.956115	−	0.292990i	$-0.905350\pi$
$137$		−	6.85872i		−	0.585980i	0.956115	−	0.292990i	$-0.0946503\pi$
$138$		0			0
$139$	−16.1730	−	16.1730i	−1.37177	−	1.37177i	−0.857814	−	0.513961i	$-0.828178\pi$
$139$	−16.1730	−	16.1730i	−1.37177	−	1.37177i	−0.513961	−	0.857814i	$-0.671822\pi$
$140$		0			0
$141$	−0.690998	+	0.690998i	−0.0581925	+	0.0581925i
$142$		0			0
$143$	2.96879			0.248262
$144$		0			0
$145$	22.5668			1.87407
$146$		0			0
$147$	−1.48474	+	1.48474i	−0.122459	+	0.122459i
$148$		0			0
$149$	−15.2009	−	15.2009i	−1.24530	−	1.24530i	−0.957771	−	0.287532i	$-0.907165\pi$
$149$	−15.2009	−	15.2009i	−1.24530	−	1.24530i	−0.287532	−	0.957771i	$-0.592835\pi$
$150$		0			0
$151$		−	4.76306i		−	0.387612i	−0.981040	−	0.193806i	$-0.937917\pi$
$151$		−	4.76306i		−	0.387612i	0.981040	−	0.193806i	$-0.0620832\pi$
$152$		0			0
$153$			2.59479i			0.209776i
$154$		0			0
$155$	10.4618	+	10.4618i	0.840314	+	0.840314i
$156$		0			0
$157$	−11.7887	+	11.7887i	−0.940844	+	0.940844i	−0.998345	−	0.0575014i	$-0.981687\pi$
$157$	−11.7887	+	11.7887i	−0.940844	+	0.940844i	0.0575014	+	0.998345i	$0.481687\pi$
$158$		0			0
$159$	−1.85068			−0.146768
$160$		0			0
$161$	−5.88497			−0.463800
$162$		0			0
$163$	9.68083	−	9.68083i	0.758261	−	0.758261i	−0.217745	−	0.976006i	$-0.569870\pi$
$163$	9.68083	−	9.68083i	0.758261	−	0.758261i	0.976006	+	0.217745i	$0.0698700\pi$
$164$		0			0
$165$	1.75249	+	1.75249i	0.136431	+	0.136431i
$166$		0			0
$167$		−	13.1916i		−	1.02079i	−0.859939	−	0.510397i	$-0.829499\pi$
$167$		−	13.1916i		−	1.02079i	0.859939	−	0.510397i	$-0.170501\pi$
$168$		0			0
$169$		−	29.6497i		−	2.28075i
$170$		0			0
$171$	5.47988	+	5.47988i	0.419057	+	0.419057i
$172$		0			0
$173$	6.40858	−	6.40858i	0.487235	−	0.487235i	−0.420198	−	0.907433i	$-0.638039\pi$
$173$	6.40858	−	6.40858i	0.487235	−	0.487235i	0.907433	+	0.420198i	$0.138039\pi$
$174$		0			0
$175$	−1.74168			−0.131659
$176$		0			0
$177$	21.7420			1.63423
$178$		0			0
$179$	9.05982	−	9.05982i	0.677163	−	0.677163i	−0.282194	−	0.959357i	$-0.591062\pi$
$179$	9.05982	−	9.05982i	0.677163	−	0.677163i	0.959357	+	0.282194i	$0.0910623\pi$
$180$		0			0
$181$	13.7164	+	13.7164i	1.01953	+	1.01953i	0.999805	+	0.0197290i	$0.00628034\pi$
$181$	13.7164	+	13.7164i	1.01953	+	1.01953i	0.0197290	+	0.999805i	$0.493720\pi$
$182$		0			0
$183$			22.4866i			1.66226i
$184$		0			0
$185$			6.12766i			0.450515i
$186$		0			0
$187$	−0.592009	−	0.592009i	−0.0432920	−	0.0432920i
$188$		0			0
$189$	−2.36237	+	2.36237i	−0.171837	+	0.171837i
$190$		0			0
$191$	−19.2622			−1.39376			−0.696882	−	0.717186i	$-0.745430\pi$
$191$	−19.2622			−1.39376			−0.696882	+	0.717186i	$0.745430\pi$
$192$		0			0
$193$	−2.38323			−0.171549			−0.0857744	−	0.996315i	$-0.527336\pi$
$193$	−2.38323			−0.171549			−0.0857744	+	0.996315i	$0.527336\pi$
$194$		0			0
$195$	25.1763	−	25.1763i	1.80291	−	1.80291i
$196$		0			0
$197$	6.16266	+	6.16266i	0.439072	+	0.439072i	0.891699	−	0.452628i	$-0.149513\pi$
$197$	6.16266	+	6.16266i	0.439072	+	0.439072i	−0.452628	+	0.891699i	$0.649513\pi$
$198$		0			0
$199$			9.33136i			0.661483i	0.943721	+	0.330741i	$0.107299\pi$
$199$			9.33136i			0.661483i	−0.943721	+	0.330741i	$0.892701\pi$
$200$		0			0
$201$			18.3017i			1.29090i
$202$		0			0
$203$	6.14570	+	6.14570i	0.431344	+	0.431344i
$204$		0			0
$205$	19.7062	−	19.7062i	1.37634	−	1.37634i
$206$		0			0
$207$	8.29132			0.576286
$208$		0			0
$209$	−2.50050			−0.172963
$210$		0			0
$211$	−19.3372	+	19.3372i	−1.33123	+	1.33123i	−0.426957	+	0.904272i	$0.640414\pi$
$211$	−19.3372	+	19.3372i	−1.33123	+	1.33123i	−0.904272	+	0.426957i	$0.859586\pi$
$212$		0			0
$213$	−0.241318	−	0.241318i	−0.0165348	−	0.0165348i
$214$		0			0
$215$		−	1.95755i		−	0.133504i
$216$		0			0
$217$			5.69821i			0.386819i
$218$		0			0
$219$	5.18350	+	5.18350i	0.350268	+	0.350268i
$220$		0			0
$221$	−8.50483	+	8.50483i	−0.572097	+	0.572097i
$222$		0			0
$223$	19.2604			1.28977			0.644886	−	0.764279i	$-0.276905\pi$
$223$	19.2604			1.28977			0.644886	+	0.764279i	$0.276905\pi$
$224$		0			0
$225$	2.45385			0.163590
$226$		0			0
$227$	−0.375264	+	0.375264i	−0.0249071	+	0.0249071i	−0.719451	−	0.694544i	$-0.755606\pi$
$227$	−0.375264	+	0.375264i	−0.0249071	+	0.0249071i	0.694544	+	0.719451i	$0.255606\pi$
$228$		0			0
$229$	−9.34559	−	9.34559i	−0.617574	−	0.617574i	0.327334	−	0.944909i	$-0.393850\pi$
$229$	−9.34559	−	9.34559i	−0.617574	−	0.617574i	−0.944909	+	0.327334i	$0.893850\pi$
$230$		0			0
$231$			0.954522i			0.0628029i
$232$		0			0
$233$		−	13.8761i		−	0.909055i	−0.890733	−	0.454527i	$-0.849808\pi$
$233$		−	13.8761i		−	0.909055i	0.890733	−	0.454527i	$-0.150192\pi$
$234$		0			0
$235$	−0.854468	−	0.854468i	−0.0557394	−	0.0557394i
$236$		0			0
$237$	12.3041	−	12.3041i	0.799235	−	0.799235i
$238$		0			0
$239$	−15.2148			−0.984165			−0.492082	−	0.870549i	$-0.663764\pi$
$239$	−15.2148			−0.984165			−0.492082	+	0.870549i	$0.663764\pi$
$240$		0			0
$241$	−28.2964			−1.82273			−0.911364	−	0.411601i	$-0.864970\pi$
$241$	−28.2964			−1.82273			−0.911364	+	0.411601i	$0.864970\pi$
$242$		0			0
$243$	9.60387	−	9.60387i	0.616089	−	0.616089i
$244$		0			0
$245$	−1.83598	−	1.83598i	−0.117297	−	0.117297i
$246$		0			0
$247$			35.9223i			2.28568i
$248$		0			0
$249$			7.46154i			0.472856i
$250$		0			0
$251$	−8.92064	−	8.92064i	−0.563066	−	0.563066i	0.367111	−	0.930177i	$-0.380347\pi$
$251$	−8.92064	−	8.92064i	−0.563066	−	0.563066i	−0.930177	+	0.367111i	$0.880347\pi$
$252$		0			0
$253$	−1.89169	+	1.89169i	−0.118929	+	0.118929i
$254$		0			0
$255$	−10.0409			−0.628784
$256$		0			0
$257$	−27.4810			−1.71422			−0.857110	−	0.515133i	$-0.827742\pi$
$257$	−27.4810			−1.71422			−0.857110	+	0.515133i	$0.827742\pi$
$258$		0			0
$259$	−1.66877	+	1.66877i	−0.103692	+	0.103692i
$260$		0			0
$261$	−8.65867	−	8.65867i	−0.535958	−	0.535958i
$262$		0			0
$263$		−	14.9308i		−	0.920674i	−0.887744	−	0.460337i	$-0.847729\pi$
$263$		−	14.9308i		−	0.920674i	0.887744	−	0.460337i	$-0.152271\pi$
$264$		0			0
$265$		−	2.28850i		−	0.140581i
$266$		0			0
$267$	2.37617	+	2.37617i	0.145419	+	0.145419i
$268$		0			0
$269$	−0.00456307	+	0.00456307i	−0.000278216	+	0.000278216i	−0.707246	−	0.706968i	$-0.750063\pi$
$269$	−0.00456307	+	0.00456307i	−0.000278216	+	0.000278216i	0.706968	+	0.707246i	$0.250063\pi$
$270$		0			0
$271$	−5.74567			−0.349025			−0.174512	−	0.984655i	$-0.555835\pi$
$271$	−5.74567			−0.349025			−0.174512	+	0.984655i	$0.555835\pi$
$272$		0			0
$273$	13.7127			0.829931
$274$		0			0
$275$	−0.559854	+	0.559854i	−0.0337604	+	0.0337604i
$276$		0			0
$277$	11.2885	+	11.2885i	0.678259	+	0.678259i	0.959606	−	0.281347i	$-0.0907812\pi$
$277$	11.2885	+	11.2885i	0.678259	+	0.678259i	−0.281347	+	0.959606i	$0.590781\pi$
$278$		0			0
$279$		−	8.02819i		−	0.480635i
$280$		0			0
$281$			9.71094i			0.579306i	0.957132	+	0.289653i	$0.0935399\pi$
$281$			9.71094i			0.579306i	−0.957132	+	0.289653i	$0.906460\pi$
$282$		0			0
$283$	−12.6539	−	12.6539i	−0.752197	−	0.752197i	0.222692	−	0.974889i	$-0.428516\pi$
$283$	−12.6539	−	12.6539i	−0.752197	−	0.752197i	−0.974889	+	0.222692i	$0.928516\pi$
$284$		0			0
$285$	−21.2051	+	21.2051i	−1.25608	+	1.25608i
$286$		0			0
$287$	10.7333			0.633568
$288$		0			0
$289$	−13.6081			−0.800475
$290$		0			0
$291$	−13.1937	+	13.1937i	−0.773428	+	0.773428i
$292$		0			0
$293$	0.906335	+	0.906335i	0.0529486	+	0.0529486i	0.733085	−	0.680137i	$-0.238080\pi$
$293$	0.906335	+	0.906335i	0.0529486	+	0.0529486i	−0.680137	+	0.733085i	$0.738080\pi$
$294$		0			0
$295$			26.8856i			1.56534i
$296$		0			0
$297$			1.51874i			0.0881263i
$298$		0			0
$299$	27.1761	+	27.1761i	1.57163	+	1.57163i
$300$		0			0
$301$	0.533105	−	0.533105i	0.0307277	−	0.0307277i
$302$		0			0
$303$	29.1167			1.67271
$304$		0			0
$305$	−27.8063			−1.59218
$306$		0			0
$307$	14.7928	−	14.7928i	0.844268	−	0.844268i	−0.145143	−	0.989411i	$-0.546364\pi$
$307$	14.7928	−	14.7928i	0.844268	−	0.844268i	0.989411	+	0.145143i	$0.0463642\pi$
$308$		0			0
$309$	−21.2668	−	21.2668i	−1.20983	−	1.20983i
$310$		0			0
$311$		−	11.6043i		−	0.658022i	−0.944326	−	0.329011i	$-0.893285\pi$
$311$		−	11.6043i		−	0.658022i	0.944326	−	0.329011i	$-0.106715\pi$
$312$		0			0
$313$			18.5621i			1.04919i	0.851351	+	0.524596i	$0.175784\pi$
$313$			18.5621i			1.04919i	−0.851351	+	0.524596i	$0.824216\pi$
$314$		0			0
$315$	2.58672	+	2.58672i	0.145745	+	0.145745i
$316$		0			0
$317$	−15.8863	+	15.8863i	−0.892261	+	0.892261i	−0.994736	−	0.102474i	$-0.967324\pi$
$317$	−15.8863	+	15.8863i	−0.892261	+	0.892261i	0.102474	+	0.994736i	$0.467324\pi$
$318$		0			0
$319$	3.95100			0.221214
$320$		0			0
$321$	−31.7719			−1.77333
$322$		0			0
$323$	7.16332	−	7.16332i	0.398578	−	0.398578i
$324$		0			0
$325$	8.04288	+	8.04288i	0.446139	+	0.446139i
$326$		0			0
$327$			21.9349i			1.21300i
$328$		0			0
$329$		−	0.465401i		−	0.0256584i
$330$		0			0
$331$	5.49646	+	5.49646i	0.302113	+	0.302113i	0.841840	−	0.539727i	$-0.181473\pi$
$331$	5.49646	+	5.49646i	0.302113	+	0.302113i	−0.539727	+	0.841840i	$0.681473\pi$
$332$		0			0
$333$	2.35112	−	2.35112i	0.128841	−	0.128841i
$334$		0			0
$335$	−22.6314			−1.23648
$336$		0			0
$337$	−2.73515			−0.148993			−0.0744966	−	0.997221i	$-0.523735\pi$
$337$	−2.73515			−0.148993			−0.0744966	+	0.997221i	$0.523735\pi$
$338$		0			0
$339$	11.9669	−	11.9669i	0.649954	−	0.649954i
$340$		0			0
$341$	1.83166	+	1.83166i	0.0991897	+	0.0991897i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$			32.0843i			1.72736i
$346$		0			0
$347$	25.0209	+	25.0209i	1.34319	+	1.34319i	0.892864	+	0.450326i	$0.148692\pi$
$347$	25.0209	+	25.0209i	1.34319	+	1.34319i	0.450326	+	0.892864i	$0.351308\pi$
$348$		0			0
$349$	−8.72637	+	8.72637i	−0.467112	+	0.467112i	−0.900978	−	0.433866i	$-0.857149\pi$
$349$	−8.72637	+	8.72637i	−0.467112	+	0.467112i	0.433866	+	0.900978i	$0.357149\pi$
$350$		0			0
$351$	21.8183			1.16458
$352$		0			0
$353$	−22.2643			−1.18501			−0.592504	−	0.805567i	$-0.701861\pi$
$353$	−22.2643			−1.18501			−0.592504	+	0.805567i	$0.701861\pi$
$354$		0			0
$355$	0.298407	−	0.298407i	0.0158378	−	0.0158378i
$356$		0			0
$357$	−2.73447	−	2.73447i	−0.144723	−	0.144723i
$358$		0			0
$359$			18.3142i			0.966588i	0.875458	+	0.483294i	$0.160560\pi$
$359$			18.3142i			0.966588i	−0.875458	+	0.483294i	$0.839440\pi$
$360$		0			0
$361$		−	11.2561i		−	0.592427i
$362$		0			0
$363$	−16.0253	−	16.0253i	−0.841110	−	0.841110i
$364$		0			0
$365$	−6.40976	+	6.40976i	−0.335502	+	0.335502i
$366$		0			0
$367$	−19.3398			−1.00953			−0.504764	−	0.863257i	$-0.668420\pi$
$367$	−19.3398			−1.00953			−0.504764	+	0.863257i	$0.668420\pi$
$368$		0			0
$369$	−15.1222			−0.787228
$370$		0			0
$371$	0.623234	−	0.623234i	0.0323567	−	0.0323567i
$372$		0			0
$373$	−5.63668	−	5.63668i	−0.291856	−	0.291856i	0.545957	−	0.837813i	$-0.316166\pi$
$373$	−5.63668	−	5.63668i	−0.291856	−	0.291856i	−0.837813	+	0.545957i	$0.816166\pi$
$374$		0			0
$375$		−	17.7641i		−	0.917333i
$376$		0			0
$377$		−	56.7603i		−	2.92330i
$378$		0			0
$379$	3.24191	+	3.24191i	0.166526	+	0.166526i	0.785450	−	0.618925i	$-0.212431\pi$
$379$	3.24191	+	3.24191i	0.166526	+	0.166526i	−0.618925	+	0.785450i	$0.712431\pi$
$380$		0			0
$381$	0.545598	−	0.545598i	0.0279518	−	0.0279518i
$382$		0			0
$383$	5.39804			0.275827			0.137913	−	0.990444i	$-0.455960\pi$
$383$	5.39804			0.275827			0.137913	+	0.990444i	$0.455960\pi$
$384$		0			0
$385$	−1.18033			−0.0601554
$386$		0			0
$387$	−0.751091	+	0.751091i	−0.0381801	+	0.0381801i
$388$		0			0
$389$	15.6572	+	15.6572i	0.793854	+	0.793854i	0.982118	−	0.188264i	$-0.0602862\pi$
$389$	15.6572	+	15.6572i	0.793854	+	0.793854i	−0.188264	+	0.982118i	$0.560286\pi$
$390$		0			0
$391$		−	10.8384i		−	0.548123i
$392$		0			0
$393$			27.6414i			1.39432i
$394$		0			0
$395$	15.2149	+	15.2149i	0.765542	+	0.765542i
$396$		0			0
$397$	2.24563	−	2.24563i	0.112705	−	0.112705i	−0.648505	−	0.761210i	$-0.724606\pi$
$397$	2.24563	−	2.24563i	0.112705	−	0.112705i	0.761210	+	0.648505i	$0.224606\pi$
$398$		0			0
$399$	−11.5497			−0.578209
$400$		0			0
$401$	19.3307			0.965331			0.482665	−	0.875805i	$-0.339669\pi$
$401$	19.3307			0.965331			0.482665	+	0.875805i	$0.339669\pi$
$402$		0			0
$403$	26.3137	−	26.3137i	1.31078	−	1.31078i
$404$		0			0
$405$	20.6396	+	20.6396i	1.02559	+	1.02559i
$406$		0			0
$407$			1.07283i			0.0531783i
$408$		0			0
$409$			0.497591i			0.0246043i	0.999924	+	0.0123021i	$0.00391599\pi$
$409$			0.497591i			0.0246043i	−0.999924	+	0.0123021i	$0.996084\pi$
$410$		0			0
$411$	−10.1834	−	10.1834i	−0.502311	−	0.502311i
$412$		0			0
$413$	−7.32184	+	7.32184i	−0.360284	+	0.360284i
$414$		0			0
$415$	−9.22673			−0.452922
$416$		0			0
$417$	−48.0253			−2.35181
$418$		0			0
$419$	−3.51076	+	3.51076i	−0.171512	+	0.171512i	−0.787643	−	0.616131i	$-0.788699\pi$
$419$	−3.51076	+	3.51076i	−0.171512	+	0.171512i	0.616131	+	0.787643i	$0.288699\pi$
$420$		0			0
$421$	1.35086	+	1.35086i	0.0658368	+	0.0658368i	0.739259	−	0.673422i	$-0.235176\pi$
$421$	1.35086	+	1.35086i	0.0658368	+	0.0658368i	−0.673422	+	0.739259i	$0.735176\pi$
$422$		0			0
$423$			0.655702i			0.0318813i
$424$		0			0
$425$		−	3.20768i		−	0.155595i
$426$		0			0
$427$	−7.57257	−	7.57257i	−0.366463	−	0.366463i
$428$		0			0
$429$	4.40787	−	4.40787i	0.212814	−	0.212814i
$430$		0			0
$431$	−19.6166			−0.944896			−0.472448	−	0.881358i	$-0.656630\pi$
$431$	−19.6166			−0.944896			−0.472448	+	0.881358i	$0.656630\pi$
$432$		0			0
$433$	−2.76217			−0.132741			−0.0663706	−	0.997795i	$-0.521142\pi$
$433$	−2.76217			−0.132741			−0.0663706	+	0.997795i	$0.521142\pi$
$434$		0			0
$435$	33.5058	−	33.5058i	1.60648	−	1.60648i
$436$		0			0
$437$	−22.8895	−	22.8895i	−1.09495	−	1.09495i
$438$		0			0
$439$			3.05296i			0.145710i	0.997343	+	0.0728550i	$0.0232110\pi$
$439$			3.05296i			0.145710i	−0.997343	+	0.0728550i	$0.976789\pi$
$440$		0			0
$441$			1.40890i			0.0670904i
$442$		0			0
$443$	1.37047	+	1.37047i	0.0651129	+	0.0651129i	0.738913	−	0.673800i	$-0.235339\pi$
$443$	1.37047	+	1.37047i	0.0651129	+	0.0651129i	−0.673800	+	0.738913i	$0.735339\pi$
$444$		0			0
$445$	−2.93831	+	2.93831i	−0.139289	+	0.139289i
$446$		0			0
$447$	−45.1386			−2.13498
$448$		0			0
$449$	38.6173			1.82246			0.911232	−	0.411894i	$-0.135133\pi$
$449$	38.6173			1.82246			0.911232	+	0.411894i	$0.135133\pi$
$450$		0			0
$451$	3.45017	−	3.45017i	0.162462	−	0.162462i
$452$		0			0
$453$	−7.07190	−	7.07190i	−0.332267	−	0.332267i
$454$		0			0
$455$			16.9567i			0.794944i
$456$		0			0
$457$			36.0959i			1.68849i	0.535955	+	0.844247i	$0.319952\pi$
$457$			36.0959i			1.68849i	−0.535955	+	0.844247i	$0.680048\pi$
$458$		0			0
$459$	−4.35082	−	4.35082i	−0.203079	−	0.203079i
$460$		0			0
$461$	−4.29295	+	4.29295i	−0.199943	+	0.199943i	−0.799975	−	0.600033i	$-0.795154\pi$
$461$	−4.29295	+	4.29295i	−0.199943	+	0.199943i	0.600033	+	0.799975i	$0.295154\pi$
$462$		0			0
$463$	3.38348			0.157243			0.0786217	−	0.996905i	$-0.474948\pi$
$463$	3.38348			0.157243			0.0786217	+	0.996905i	$0.474948\pi$
$464$		0			0
$465$	31.0661			1.44066
$466$		0			0
$467$	−21.7747	+	21.7747i	−1.00761	+	1.00761i	−0.00764098	+	0.999971i	$0.502432\pi$
$467$	−21.7747	+	21.7747i	−1.00761	+	1.00761i	−0.999971	+	0.00764098i	$0.997568\pi$
$468$		0			0
$469$	−6.16327	−	6.16327i	−0.284594	−	0.284594i
$470$		0			0
$471$			35.0064i			1.61301i
$472$		0			0
$473$		−	0.342727i		−	0.0157586i
$474$		0			0
$475$	−6.77424	−	6.77424i	−0.310823	−	0.310823i
$476$		0			0
$477$	−0.878073	+	0.878073i	−0.0402042	+	0.0402042i
$478$		0			0
$479$	−6.74054			−0.307983			−0.153992	−	0.988072i	$-0.549213\pi$
$479$	−6.74054			−0.307983			−0.153992	+	0.988072i	$0.549213\pi$
$480$		0			0
$481$	15.4123			0.702743
$482$		0			0
$483$	−8.73764	+	8.73764i	−0.397576	+	0.397576i
$484$		0			0
$485$	−16.3149	−	16.3149i	−0.740823	−	0.740823i
$486$		0			0
$487$			30.4472i			1.37970i	0.723954	+	0.689848i	$0.242323\pi$
$487$			30.4472i			1.37970i	−0.723954	+	0.689848i	$0.757677\pi$
$488$		0			0
$489$		−	28.7470i		−	1.29998i
$490$		0			0
$491$	−11.1585	−	11.1585i	−0.503578	−	0.503578i	0.408970	−	0.912548i	$-0.365888\pi$
$491$	−11.1585	−	11.1585i	−0.503578	−	0.503578i	−0.912548	+	0.408970i	$0.865888\pi$
$492$		0			0
$493$	−11.3186	+	11.3186i	−0.509766	+	0.509766i
$494$		0			0
$495$	1.66297			0.0747449
$496$		0			0
$497$	0.162532			0.00729057
$498$		0			0
$499$	−17.4556	+	17.4556i	−0.781420	+	0.781420i	−0.980070	−	0.198651i	$-0.936344\pi$
$499$	−17.4556	+	17.4556i	−0.781420	+	0.781420i	0.198651	+	0.980070i	$0.436344\pi$
$500$		0			0
$501$	−19.5860	−	19.5860i	−0.875039	−	0.875039i
$502$		0			0
$503$		−	26.7354i		−	1.19207i	−0.802958	−	0.596035i	$-0.796742\pi$
$503$		−	26.7354i		−	1.19207i	0.802958	−	0.596035i	$-0.203258\pi$
$504$		0			0
$505$			36.0049i			1.60220i
$506$		0			0
$507$	−44.0221	−	44.0221i	−1.95509	−	1.95509i
$508$		0			0
$509$	13.7609	−	13.7609i	0.609942	−	0.609942i	−0.332989	−	0.942931i	$-0.608057\pi$
$509$	13.7609	−	13.7609i	0.609942	−	0.609942i	0.942931	+	0.332989i	$0.108057\pi$
$510$		0			0
$511$	−3.49118			−0.154441
$512$		0			0
$513$	−18.3768			−0.811355
$514$		0			0
$515$	26.2979	−	26.2979i	1.15883	−	1.15883i
$516$		0			0
$517$	−0.149600	−	0.149600i	−0.00657942	−	0.00657942i
$518$		0			0
$519$		−	19.0301i		−	0.835330i
$520$		0			0
$521$		−	36.5859i		−	1.60286i	−0.598091	−	0.801428i	$-0.704074\pi$
$521$		−	36.5859i		−	1.60286i	0.598091	−	0.801428i	$-0.295926\pi$
$522$		0			0
$523$	4.02294	+	4.02294i	0.175911	+	0.175911i	0.789571	−	0.613660i	$-0.210303\pi$
$523$	4.02294	+	4.02294i	0.175911	+	0.175911i	−0.613660	+	0.789571i	$0.710303\pi$
$524$		0			0
$525$	−2.58594	+	2.58594i	−0.112860	+	0.112860i
$526$		0			0
$527$	−10.4945			−0.457147
$528$		0			0
$529$	−11.6328			−0.505776
$530$		0			0
$531$	10.3157	−	10.3157i	0.447664	−	0.447664i
$532$		0			0
$533$	−49.5652	−	49.5652i	−2.14691	−	2.14691i
$534$		0			0
$535$		−	39.2882i		−	1.69858i
$536$		0			0
$537$		−	26.9029i		−	1.16095i
$538$		0			0
$539$	−0.321444	−	0.321444i	−0.0138456	−	0.0138456i
$540$		0			0
$541$	−17.9463	+	17.9463i	−0.771572	+	0.771572i	−0.978381	−	0.206809i	$-0.933692\pi$
$541$	−17.9463	+	17.9463i	−0.771572	+	0.771572i	0.206809	+	0.978381i	$0.433692\pi$
$542$		0			0
$543$	40.7306			1.74792
$544$		0			0
$545$	−27.1241			−1.16187
$546$		0			0
$547$	−18.9329	+	18.9329i	−0.809512	+	0.809512i	−0.984560	−	0.175048i	$-0.943992\pi$
$547$	−18.9329	+	18.9329i	−0.809512	+	0.809512i	0.175048	+	0.984560i	$0.443992\pi$
$548$		0			0
$549$	10.6690	+	10.6690i	0.455341	+	0.455341i
$550$		0			0
$551$			47.8072i			2.03665i
$552$		0			0
$553$			8.28703i			0.352400i
$554$		0			0
$555$	9.09798	+	9.09798i	0.386188	+	0.386188i
$556$		0			0
$557$	30.3516	−	30.3516i	1.28604	−	1.28604i	0.348864	−	0.937173i	$-0.386568\pi$
$557$	30.3516	−	30.3516i	1.28604	−	1.28604i	0.937173	−	0.348864i	$-0.113432\pi$
$558$		0			0
$559$	−4.92364			−0.208248
$560$		0			0
$561$	−1.75796			−0.0742210
$562$		0			0
$563$	18.2195	−	18.2195i	0.767858	−	0.767858i	−0.209871	−	0.977729i	$-0.567304\pi$
$563$	18.2195	−	18.2195i	0.767858	−	0.767858i	0.977729	+	0.209871i	$0.0673043\pi$
$564$		0			0
$565$	14.7980	+	14.7980i	0.622555	+	0.622555i
$566$		0			0
$567$			11.2417i			0.472107i
$568$		0			0
$569$		−	40.3261i		−	1.69056i	−0.534325	−	0.845279i	$-0.679434\pi$
$569$		−	40.3261i		−	1.69056i	0.534325	−	0.845279i	$-0.320566\pi$
$570$		0			0
$571$	−18.1528	−	18.1528i	−0.759672	−	0.759672i	0.216591	−	0.976262i	$-0.430506\pi$
$571$	−18.1528	−	18.1528i	−0.759672	−	0.759672i	−0.976262	+	0.216591i	$0.930506\pi$
$572$		0			0
$573$	−28.5993	+	28.5993i	−1.19475	+	1.19475i
$574$		0			0
$575$	−10.2497			−0.427444
$576$		0			0
$577$	28.8535			1.20119			0.600594	−	0.799554i	$-0.294931\pi$
$577$	28.8535			1.20119			0.600594	+	0.799554i	$0.294931\pi$
$578$		0			0
$579$	−3.53848	+	3.53848i	−0.147054	+	0.147054i
$580$		0			0
$581$	−2.51275	−	2.51275i	−0.104246	−	0.104246i
$582$		0			0
$583$		−	0.400670i		−	0.0165941i
$584$		0			0
$585$		−	23.8903i		−	0.987743i
$586$		0			0
$587$	−22.0073	−	22.0073i	−0.908338	−	0.908338i	0.0877997	−	0.996138i	$-0.472016\pi$
$587$	−22.0073	−	22.0073i	−0.908338	−	0.908338i	−0.996138	+	0.0877997i	$0.972016\pi$
$588$		0			0
$589$	−22.1631	+	22.1631i	−0.913213	+	0.913213i
$590$		0			0
$591$	18.2999			0.752757
$592$		0			0
$593$	24.6606			1.01269			0.506344	−	0.862331i	$-0.330996\pi$
$593$	24.6606			1.01269			0.506344	+	0.862331i	$0.330996\pi$
$594$		0			0
$595$	3.38136	−	3.38136i	0.138622	−	0.138622i
$596$		0			0
$597$	13.8546	+	13.8546i	0.567033	+	0.567033i
$598$		0			0
$599$			10.8236i			0.442239i	0.975247	+	0.221120i	$0.0709711\pi$
$599$			10.8236i			0.442239i	−0.975247	+	0.221120i	$0.929029\pi$
$600$		0			0
$601$			16.6417i			0.678828i	0.940637	+	0.339414i	$0.110229\pi$
$601$			16.6417i			0.678828i	−0.940637	+	0.339414i	$0.889771\pi$
$602$		0			0
$603$	8.68342	+	8.68342i	0.353616	+	0.353616i
$604$		0			0
$605$	19.8164	−	19.8164i	0.805652	−	0.805652i
$606$		0			0
$607$	22.3716			0.908037			0.454019	−	0.890992i	$-0.349990\pi$
$607$	22.3716			0.908037			0.454019	+	0.890992i	$0.349990\pi$
$608$		0			0
$609$	18.2495			0.739508
$610$		0			0
$611$	−2.14917	+	2.14917i	−0.0869460	+	0.0869460i
$612$		0			0
$613$	32.7313	+	32.7313i	1.32201	+	1.32201i	0.912150	+	0.409857i	$0.134421\pi$
$613$	32.7313	+	32.7313i	1.32201	+	1.32201i	0.409857	+	0.912150i	$0.365579\pi$
$614$		0			0
$615$		−	58.5172i		−	2.35964i
$616$		0			0
$617$		−	3.37531i		−	0.135885i	−0.997689	−	0.0679424i	$-0.978357\pi$
$617$		−	3.37531i		−	0.135885i	0.997689	−	0.0679424i	$-0.0216434\pi$
$618$		0			0
$619$	−3.57465	−	3.57465i	−0.143677	−	0.143677i	0.631609	−	0.775287i	$-0.282395\pi$
$619$	−3.57465	−	3.57465i	−0.143677	−	0.143677i	−0.775287	+	0.631609i	$0.782395\pi$
$620$		0			0
$621$	−13.9025	+	13.9025i	−0.557887	+	0.557887i
$622$		0			0
$623$	−1.60040			−0.0641186
$624$		0			0
$625$	30.6750			1.22700
$626$		0			0
$627$	−3.71259	+	3.71259i	−0.148267	+	0.148267i
$628$		0			0
$629$	−3.07340	−	3.07340i	−0.122544	−	0.122544i
$630$		0			0
$631$			31.2089i			1.24241i	0.783649	+	0.621204i	$0.213356\pi$
$631$			31.2089i			1.24241i	−0.783649	+	0.621204i	$0.786644\pi$
$632$		0			0
$633$			57.4214i			2.28230i
$634$		0			0
$635$	0.674671	+	0.674671i	0.0267735	+	0.0267735i
$636$		0			0
$637$	−4.61789	+	4.61789i	−0.182967	+	0.182967i
$638$		0			0
$639$	−0.228991			−0.00905876
$640$		0			0
$641$	25.7829			1.01836			0.509182	−	0.860659i	$-0.329948\pi$
$641$	25.7829			1.01836			0.509182	+	0.860659i	$0.329948\pi$
$642$		0			0
$643$	1.82352	−	1.82352i	0.0719127	−	0.0719127i	−0.670236	−	0.742148i	$-0.733807\pi$
$643$	1.82352	−	1.82352i	0.0719127	−	0.0719127i	0.742148	+	0.670236i	$0.233807\pi$
$644$		0			0
$645$	−2.90645	−	2.90645i	−0.114441	−	0.114441i
$646$		0			0
$647$			10.0909i			0.396713i	0.980130	+	0.198356i	$0.0635603\pi$
$647$			10.0909i			0.396713i	−0.980130	+	0.198356i	$0.936440\pi$
$648$		0			0
$649$			4.70713i			0.184771i
$650$		0			0
$651$	8.46035	+	8.46035i	0.331587	+	0.331587i
$652$		0			0
$653$	−13.8599	+	13.8599i	−0.542380	+	0.542380i	−0.924226	−	0.381846i	$-0.875288\pi$
$653$	−13.8599	+	13.8599i	−0.542380	+	0.542380i	0.381846	+	0.924226i	$0.375288\pi$
$654$		0			0
$655$	−34.1805			−1.33554
$656$		0			0
$657$	4.91872			0.191898
$658$		0			0
$659$	−13.9075	+	13.9075i	−0.541758	+	0.541758i	−0.924044	−	0.382286i	$-0.875137\pi$
$659$	−13.9075	+	13.9075i	−0.541758	+	0.541758i	0.382286	+	0.924044i	$0.375137\pi$
$660$		0			0
$661$	−1.13544	−	1.13544i	−0.0441633	−	0.0441633i	0.684680	−	0.728844i	$-0.259942\pi$
$661$	−1.13544	−	1.13544i	−0.0441633	−	0.0441633i	−0.728844	+	0.684680i	$0.759942\pi$
$662$		0			0
$663$			25.2549i			0.980820i
$664$		0			0
$665$		−	14.2821i		−	0.553834i
$666$		0			0
$667$	36.1673	+	36.1673i	1.40040	+	1.40040i
$668$		0			0
$669$	28.5967	−	28.5967i	1.10561	−	1.10561i
$670$		0			0
$671$	−4.86832			−0.187939
$672$		0			0
$673$	9.91726			0.382282			0.191141	−	0.981563i	$-0.438781\pi$
$673$	9.91726			0.382282			0.191141	+	0.981563i	$0.438781\pi$
$674$		0			0
$675$	−4.11450	+	4.11450i	−0.158367	+	0.158367i
$676$		0			0
$677$	−16.4673	−	16.4673i	−0.632890	−	0.632890i	0.315902	−	0.948792i	$-0.397693\pi$
$677$	−16.4673	−	16.4673i	−0.632890	−	0.632890i	−0.948792	+	0.315902i	$0.897693\pi$
$678$		0			0
$679$		−	8.88621i		−	0.341021i
$680$		0			0
$681$			1.11434i			0.0427015i
$682$		0			0
$683$	−5.51571	−	5.51571i	−0.211053	−	0.211053i	0.593662	−	0.804715i	$-0.297682\pi$
$683$	−5.51571	−	5.51571i	−0.211053	−	0.211053i	−0.804715	+	0.593662i	$0.797682\pi$
$684$		0			0
$685$	12.5925	−	12.5925i	0.481135	−	0.481135i
$686$		0			0
$687$	−27.7515			−1.05879
$688$		0			0
$689$	−5.75605			−0.219288
$690$		0			0
$691$	31.1271	−	31.1271i	1.18413	−	1.18413i	0.205468	−	0.978664i	$-0.434128\pi$
$691$	31.1271	−	31.1271i	1.18413	−	1.18413i	0.978664	−	0.205468i	$-0.0658717\pi$
$692$		0			0
$693$	0.452882	+	0.452882i	0.0172036	+	0.0172036i
$694$		0			0
$695$		−	59.3867i		−	2.25267i
$696$		0			0
$697$			19.7677i			0.748756i
$698$		0			0
$699$	−20.6024	−	20.6024i	−0.779255	−	0.779255i
$700$		0			0
$701$	21.7631	−	21.7631i	0.821981	−	0.821981i	−0.164411	−	0.986392i	$-0.552572\pi$
$701$	21.7631	−	21.7631i	0.821981	−	0.821981i	0.986392	+	0.164411i	$0.0525722\pi$
$702$		0			0
$703$	−12.9813			−0.489598
$704$		0			0
$705$	−2.53732			−0.0955612
$706$		0			0
$707$	−9.80533	+	9.80533i	−0.368767	+	0.368767i
$708$		0			0
$709$	−12.9756	−	12.9756i	−0.487309	−	0.487309i	0.420147	−	0.907456i	$-0.361979\pi$
$709$	−12.9756	−	12.9756i	−0.487309	−	0.487309i	−0.907456	+	0.420147i	$0.861979\pi$
$710$		0			0
$711$		−	11.6756i		−	0.437868i
$712$		0			0
$713$			33.5338i			1.25585i
$714$		0			0
$715$	5.45065	+	5.45065i	0.203843	+	0.203843i
$716$		0			0
$717$	−22.5900	+	22.5900i	−0.843640	+	0.843640i
$718$		0			0
$719$	−36.4527			−1.35946			−0.679728	−	0.733464i	$-0.737902\pi$
$719$	−36.4527			−1.35946			−0.679728	+	0.733464i	$0.737902\pi$
$720$		0			0
$721$	14.3236			0.533439
$722$		0			0
$723$	−42.0127	+	42.0127i	−1.56247	+	1.56247i
$724$		0			0
$725$	10.7039	+	10.7039i	0.397531	+	0.397531i
$726$		0			0
$727$		−	37.9281i		−	1.40668i	−0.710855	−	0.703338i	$-0.751692\pi$
$727$		−	37.9281i		−	1.40668i	0.710855	−	0.703338i	$-0.248308\pi$
$728$		0			0
$729$			5.20661i			0.192838i
$730$		0			0
$731$	0.981829	+	0.981829i	0.0363143	+	0.0363143i
$732$		0			0
$733$	12.8899	−	12.8899i	0.476099	−	0.476099i	−0.427782	−	0.903882i	$-0.640705\pi$
$733$	12.8899	−	12.8899i	0.476099	−	0.476099i	0.903882	+	0.427782i	$0.140705\pi$
$734$		0			0
$735$	−5.45192			−0.201097
$736$		0			0
$737$	−3.96230			−0.145953
$738$		0			0
$739$	−7.97047	+	7.97047i	−0.293199	+	0.293199i	−0.838342	−	0.545144i	$-0.816475\pi$
$739$	−7.97047	+	7.97047i	−0.293199	+	0.293199i	0.545144	+	0.838342i	$0.316475\pi$
$740$		0			0
$741$	53.3353	+	53.3353i	1.95932	+	1.95932i
$742$		0			0
$743$		−	41.0385i		−	1.50556i	−0.658273	−	0.752779i	$-0.728713\pi$
$743$		−	41.0385i		−	1.50556i	0.658273	−	0.752779i	$-0.271287\pi$
$744$		0			0
$745$		−	55.8171i		−	2.04498i
$746$		0			0
$747$	3.54020	+	3.54020i	0.129529	+	0.129529i
$748$		0			0
$749$	10.6995	−	10.6995i	0.390951	−	0.390951i
$750$		0			0
$751$	16.8700			0.615594			0.307797	−	0.951452i	$-0.400408\pi$
$751$	16.8700			0.615594			0.307797	+	0.951452i	$0.400408\pi$
$752$		0			0
$753$	−26.4896			−0.965336
$754$		0			0
$755$	8.74490	−	8.74490i	0.318260	−	0.318260i
$756$		0			0
$757$	21.7021	+	21.7021i	0.788778	+	0.788778i	0.981294	−	0.192516i	$-0.0616647\pi$
$757$	21.7021	+	21.7021i	0.788778	+	0.788778i	−0.192516	+	0.981294i	$0.561665\pi$
$758$		0			0
$759$			5.61733i			0.203896i
$760$		0			0
$761$		−	8.35285i		−	0.302791i	−0.988473	−	0.151395i	$-0.951623\pi$
$761$		−	8.35285i		−	0.302791i	0.988473	−	0.151395i	$-0.0483766\pi$
$762$		0			0
$763$	−7.38679	−	7.38679i	−0.267420	−	0.267420i
$764$		0			0
$765$	−4.76400	+	4.76400i	−0.172243	+	0.172243i
$766$		0			0
$767$	67.6229			2.44172
$768$		0			0
$769$	−21.8388			−0.787527			−0.393764	−	0.919212i	$-0.628827\pi$
$769$	−21.8388			−0.787527			−0.393764	+	0.919212i	$0.628827\pi$
$770$		0			0
$771$	−40.8022	+	40.8022i	−1.46945	+	1.46945i
$772$		0			0
$773$	−6.55450	−	6.55450i	−0.235749	−	0.235749i	0.579338	−	0.815087i	$-0.303311\pi$
$773$	−6.55450	−	6.55450i	−0.235749	−	0.235749i	−0.815087	+	0.579338i	$0.803311\pi$
$774$		0			0
$775$			9.92446i			0.356497i
$776$		0			0
$777$			4.95537i			0.177773i
$778$		0			0
$779$	41.7470	+	41.7470i	1.49574	+	1.49574i
$780$		0			0
$781$	0.0522451	−	0.0522451i	0.00186948	−	0.00186948i
$782$		0			0
$783$	29.0369			1.03769
$784$		0			0
$785$	−43.2879			−1.54501
$786$		0			0
$787$	−17.8764	+	17.8764i	−0.637224	+	0.637224i	−0.949870	−	0.312646i	$-0.898785\pi$
$787$	−17.8764	+	17.8764i	−0.637224	+	0.637224i	0.312646	+	0.949870i	$0.398785\pi$
$788$		0			0
$789$	−22.1684	−	22.1684i	−0.789215	−	0.789215i
$790$		0			0
$791$			8.05995i			0.286579i
$792$		0			0
$793$			69.9386i			2.48359i
$794$		0			0
$795$	−3.39782	−	3.39782i	−0.120508	−	0.120508i
$796$		0			0
$797$	−15.9981	+	15.9981i	−0.566683	+	0.566683i	−0.931198	−	0.364515i	$-0.881235\pi$
$797$	−15.9981	+	15.9981i	−0.566683	+	0.566683i	0.364515	+	0.931198i	$0.381235\pi$
$798$		0			0
$799$	0.857136			0.0303233
$800$		0			0
$801$	2.25480			0.0796694
$802$		0			0
$803$	−1.12222	+	1.12222i	−0.0396023	+	0.0396023i
$804$		0			0
$805$	−10.8047	−	10.8047i	−0.380816	−	0.380816i
$806$		0			0
$807$			0.0135499i			0.000476981i
$808$		0			0
$809$		−	13.5401i		−	0.476046i	−0.971260	−	0.238023i	$-0.923501\pi$
$809$		−	13.5401i		−	0.476046i	0.971260	−	0.238023i	$-0.0764993\pi$
$810$		0			0
$811$	−1.49897	−	1.49897i	−0.0526359	−	0.0526359i	0.680299	−	0.732935i	$-0.261850\pi$
$811$	−1.49897	−	1.49897i	−0.0526359	−	0.0526359i	−0.732935	+	0.680299i	$0.761850\pi$
$812$		0			0
$813$	−8.53082	+	8.53082i	−0.299189	+	0.299189i
$814$		0			0
$815$	35.5477			1.24518
$816$		0			0
$817$	4.14701			0.145085
$818$		0			0
$819$	6.50613	−	6.50613i	0.227343	−	0.227343i
$820$		0			0
$821$	0.576655	+	0.576655i	0.0201254	+	0.0201254i	0.717098	−	0.696972i	$-0.245470\pi$
$821$	0.576655	+	0.576655i	0.0201254	+	0.0201254i	−0.696972	+	0.717098i	$0.745470\pi$
$822$		0			0
$823$		−	14.8651i		−	0.518164i	−0.965855	−	0.259082i	$-0.916580\pi$
$823$		−	14.8651i		−	0.518164i	0.965855	−	0.259082i	$-0.0834200\pi$
$824$		0			0
$825$			1.66247i			0.0578799i
$826$		0			0
$827$	22.5725	+	22.5725i	0.784921	+	0.784921i	0.980657	−	0.195736i	$-0.0627094\pi$
$827$	22.5725	+	22.5725i	0.784921	+	0.784921i	−0.195736	+	0.980657i	$0.562709\pi$
$828$		0			0
$829$	15.4320	−	15.4320i	0.535975	−	0.535975i	−0.386369	−	0.922344i	$-0.626271\pi$
$829$	15.4320	−	15.4320i	0.535975	−	0.535975i	0.922344	+	0.386369i	$0.126271\pi$
$830$		0			0
$831$	33.5209			1.16283
$832$		0			0
$833$	1.84172			0.0638117
$834$		0			0
$835$	24.2195	−	24.2195i	0.838151	−	0.838151i
$836$		0			0
$837$	13.4613	+	13.4613i	0.465290	+	0.465290i
$838$		0			0
$839$		−	37.1968i		−	1.28418i	−0.766630	−	0.642089i	$-0.778068\pi$
$839$		−	37.1968i		−	1.28418i	0.766630	−	0.642089i	$-0.221932\pi$
$840$		0			0
$841$		−	46.5393i		−	1.60480i
$842$		0			0
$843$	14.4182	+	14.4182i	0.496589	+	0.496589i
$844$		0			0
$845$	54.4365	−	54.4365i	1.87267	−	1.87267i
$846$		0			0
$847$	10.7933			0.370864
$848$		0			0
$849$	−37.5755			−1.28959
$850$		0			0
$851$	−9.82064	+	9.82064i	−0.336647	+	0.336647i
$852$		0			0
$853$	22.4583	+	22.4583i	0.768958	+	0.768958i	0.977923	−	0.208965i	$-0.0670096\pi$
$853$	22.4583	+	22.4583i	0.768958	+	0.768958i	−0.208965	+	0.977923i	$0.567010\pi$
$854$		0			0
$855$			20.1220i			0.688156i
$856$		0			0
$857$		−	47.6664i		−	1.62825i	−0.580688	−	0.814126i	$-0.697216\pi$
$857$		−	47.6664i		−	1.62825i	0.580688	−	0.814126i	$-0.302784\pi$
$858$		0			0
$859$	22.3609	+	22.3609i	0.762945	+	0.762945i	0.976854	−	0.213909i	$-0.0686195\pi$
$859$	22.3609	+	22.3609i	0.762945	+	0.762945i	−0.213909	+	0.976854i	$0.568620\pi$
$860$		0			0
$861$	15.9362	−	15.9362i	0.543103	−	0.543103i
$862$		0			0
$863$	−6.01295			−0.204683			−0.102342	−	0.994749i	$-0.532633\pi$
$863$	−6.01295			−0.204683			−0.102342	+	0.994749i	$0.532633\pi$
$864$		0			0
$865$	23.5321			0.800115
$866$		0			0
$867$	−20.2044	+	20.2044i	−0.686179	+	0.686179i
$868$		0			0
$869$	2.66382	+	2.66382i	0.0903638	+	0.0903638i
$870$		0			0
$871$			56.9226i			1.92875i
$872$		0			0
$873$			12.5198i			0.423730i
$874$		0			0
$875$	5.98222	+	5.98222i	0.202236	+	0.202236i
$876$		0			0
$877$	−7.53722	+	7.53722i	−0.254514	+	0.254514i	−0.822818	−	0.568305i	$-0.807600\pi$
$877$	−7.53722	+	7.53722i	−0.254514	+	0.254514i	0.568305	+	0.822818i	$0.307600\pi$
$878$		0			0
$879$	2.69134			0.0907766
$880$		0			0
$881$	−18.6023			−0.626726			−0.313363	−	0.949633i	$-0.601456\pi$
$881$	−18.6023			−0.626726			−0.313363	+	0.949633i	$0.601456\pi$
$882$		0			0
$883$	−15.1111	+	15.1111i	−0.508530	+	0.508530i	−0.914075	−	0.405545i	$-0.867082\pi$
$883$	−15.1111	+	15.1111i	−0.508530	+	0.508530i	0.405545	+	0.914075i	$0.367082\pi$
$884$		0			0
$885$	39.9181	+	39.9181i	1.34183	+	1.34183i
$886$		0			0
$887$		−	56.3410i		−	1.89175i	−0.324537	−	0.945873i	$-0.605208\pi$
$887$		−	56.3410i		−	1.89175i	0.324537	−	0.945873i	$-0.394792\pi$
$888$		0			0
$889$			0.367471i			0.0123246i
$890$		0			0
$891$	3.61358	+	3.61358i	0.121060	+	0.121060i
$892$		0			0
$893$	1.81017	−	1.81017i	0.0605749	−	0.0605749i
$894$		0			0
$895$	33.2674			1.11201
$896$		0			0
$897$	80.6988			2.69446
$898$		0			0
$899$	35.0195	−	35.0195i	1.16796	−	1.16796i
$900$		0			0
$901$	1.14782	+	1.14782i	0.0382394	+	0.0382394i
$902$		0			0
$903$		−	1.58304i		−	0.0526804i
$904$		0			0
$905$			50.3663i			1.67423i
$906$		0			0
$907$	−5.23632	−	5.23632i	−0.173869	−	0.173869i	0.614808	−	0.788677i	$-0.289234\pi$
$907$	−5.23632	−	5.23632i	−0.173869	−	0.173869i	−0.788677	+	0.614808i	$0.789234\pi$
$908$		0			0
$909$	13.8147	−	13.8147i	0.458205	−	0.458205i
$910$		0			0
$911$	28.0494			0.929319			0.464660	−	0.885489i	$-0.346177\pi$
$911$	28.0494			0.929319			0.464660	+	0.885489i	$0.346177\pi$
$912$		0			0
$913$	−1.61542			−0.0534625
$914$		0			0
$915$	−41.2850	+	41.2850i	−1.36484	+	1.36484i
$916$		0			0
$917$	−9.30850	−	9.30850i	−0.307394	−	0.307394i
$918$		0			0
$919$		−	36.2282i		−	1.19506i	−0.801847	−	0.597529i	$-0.796149\pi$
$919$		−	36.2282i		−	1.19506i	0.801847	−	0.597529i	$-0.203851\pi$
$920$		0			0
$921$		−	43.9268i		−	1.44744i
$922$		0			0
$923$	−0.750555	−	0.750555i	−0.0247048	−	0.0247048i
$924$		0			0
$925$	−2.90646	+	2.90646i	−0.0955638	+	0.0955638i
$926$		0			0
$927$	−20.1805			−0.662815
$928$		0			0
$929$	16.6482			0.546210			0.273105	−	0.961984i	$-0.411949\pi$
$929$	16.6482			0.546210			0.273105	+	0.961984i	$0.411949\pi$
$930$		0			0
$931$	3.88948	−	3.88948i	0.127473	−	0.127473i
$932$		0			0
$933$	−17.2294	−	17.2294i	−0.564066	−	0.564066i
$934$		0			0
$935$		−	2.17384i		−	0.0710922i
$936$		0			0
$937$			16.4319i			0.536807i	0.963307	+	0.268403i	$0.0864960\pi$
$937$			16.4319i			0.536807i	−0.963307	+	0.268403i	$0.913504\pi$
$938$		0			0
$939$	27.5599	+	27.5599i	0.899382	+	0.899382i
$940$		0			0
$941$	11.7153	−	11.7153i	0.381907	−	0.381907i	−0.489882	−	0.871789i	$-0.662960\pi$
$941$	11.7153	−	11.7153i	0.381907	−	0.381907i	0.871789	+	0.489882i	$0.162960\pi$
$942$		0			0
$943$	63.1652			2.05694
$944$		0			0
$945$	−8.67456			−0.282183
$946$		0			0
$947$	−12.5463	+	12.5463i	−0.407699	+	0.407699i	−0.880936	−	0.473236i	$-0.843086\pi$
$947$	−12.5463	+	12.5463i	−0.407699	+	0.407699i	0.473236	+	0.880936i	$0.343086\pi$
$948$		0			0
$949$	16.1219	+	16.1219i	0.523339	+	0.523339i
$950$		0			0
$951$			47.1739i			1.52972i
$952$		0			0
$953$			21.9557i			0.711213i	0.934636	+	0.355607i	$0.115726\pi$
$953$			21.9557i			0.711213i	−0.934636	+	0.355607i	$0.884274\pi$
$954$		0			0
$955$	−35.3651	−	35.3651i	−1.14439	−	1.14439i
$956$		0			0
$957$	5.86621	−	5.86621i	0.189627	−	0.189627i
$958$		0			0
$959$	6.85872			0.221480
$960$		0			0
$961$	1.46955			0.0474047
$962$		0			0
$963$	−15.0745	+	15.0745i	−0.485768	+	0.485768i
$964$		0			0
$965$	−4.37558	−	4.37558i	−0.140855	−	0.140855i
$966$		0			0
$967$			22.2420i			0.715255i	0.933864	+	0.357628i	$0.116414\pi$
$967$			22.2420i			0.715255i	−0.933864	+	0.357628i	$0.883586\pi$
$968$		0			0
$969$		−	21.2713i		−	0.683333i
$970$		0			0
$971$	−18.7865	−	18.7865i	−0.602888	−	0.602888i	0.338190	−	0.941078i	$-0.390185\pi$
$971$	−18.7865	−	18.7865i	−0.602888	−	0.602888i	−0.941078	+	0.338190i	$0.890185\pi$
$972$		0			0
$973$	16.1730	−	16.1730i	0.518482	−	0.518482i
$974$		0			0
$975$	23.8832			0.764873
$976$		0			0
$977$	9.54985			0.305527			0.152763	−	0.988263i	$-0.451183\pi$
$977$	9.54985			0.305527			0.152763	+	0.988263i	$0.451183\pi$
$978$		0			0
$979$	−0.514439	+	0.514439i	−0.0164415	+	0.0164415i
$980$		0			0
$981$	10.4072	+	10.4072i	0.332277	+	0.332277i
$982$		0			0
$983$		−	5.65760i		−	0.180449i	−0.995921	−	0.0902247i	$-0.971241\pi$
$983$		−	5.65760i		−	0.180449i	0.995921	−	0.0902247i	$-0.0287585\pi$
$984$		0			0
$985$			22.6291i			0.721023i
$986$		0			0
$987$	−0.690998	−	0.690998i	−0.0219947	−	0.0219947i
$988$		0			0
$989$	3.13731	−	3.13731i	0.0997606	−	0.0997606i
$990$		0			0
$991$	−62.8260			−1.99573			−0.997867	−	0.0652866i	$-0.979204\pi$
$991$	−62.8260			−1.99573			−0.997867	+	0.0652866i	$0.979204\pi$
$992$		0			0
$993$	16.3216			0.517951
$994$		0			0
$995$	−17.1322	+	17.1322i	−0.543129	+	0.543129i
$996$		0			0
$997$	5.75899	+	5.75899i	0.182389	+	0.182389i	0.792396	−	0.610007i	$-0.208833\pi$
$997$	5.75899	+	5.75899i	0.182389	+	0.182389i	−0.610007	+	0.792396i	$0.708833\pi$
$998$		0			0
$999$			7.88449i			0.249454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1792.2.m.e.449.8	✓	16
4.3	odd	2		1792.2.m.g.449.1	yes	16
8.3	odd	2		1792.2.m.f.449.8	yes	16
8.5	even	2		1792.2.m.h.449.1	yes	16
16.3	odd	4		1792.2.m.g.1345.1	yes	16
16.5	even	4		1792.2.m.h.1345.1	yes	16
16.11	odd	4		1792.2.m.f.1345.8	yes	16
16.13	even	4	inner	1792.2.m.e.1345.8	yes	16
32.3	odd	8		7168.2.a.ba.1.2		8
32.13	even	8		7168.2.a.bf.1.2		8
32.19	odd	8		7168.2.a.be.1.7		8
32.29	even	8		7168.2.a.bb.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1792.2.m.e.449.8	✓	16	1.1	even	1	trivial
1792.2.m.e.1345.8	yes	16	16.13	even	4	inner
1792.2.m.f.449.8	yes	16	8.3	odd	2
1792.2.m.f.1345.8	yes	16	16.11	odd	4
1792.2.m.g.449.1	yes	16	4.3	odd	2
1792.2.m.g.1345.1	yes	16	16.3	odd	4
1792.2.m.h.449.1	yes	16	8.5	even	2
1792.2.m.h.1345.1	yes	16	16.5	even	4
7168.2.a.ba.1.2		8	32.3	odd	8
7168.2.a.bb.1.7		8	32.29	even	8
7168.2.a.be.1.7		8	32.19	odd	8
7168.2.a.bf.1.2		8	32.13	even	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)

\(f(q)\)	\(=\)	\(q+(1.48474 - 1.48474i) q^{3} +(1.83598 + 1.83598i) q^{5} +1.00000i q^{7} -1.40890i q^{9} +O(q^{10})\)	\(q+(1.48474 - 1.48474i) q^{3} +(1.83598 + 1.83598i) q^{5} +1.00000i q^{7} -1.40890i q^{9} +(0.321444 + 0.321444i) q^{11} +(4.61789 - 4.61789i) q^{13} +5.45192 q^{15} -1.84172 q^{17} +(-3.88948 + 3.88948i) q^{19} +(1.48474 + 1.48474i) q^{21} +5.88497i q^{23} +1.74168i q^{25} +(2.36237 + 2.36237i) q^{27} +(6.14570 - 6.14570i) q^{29} +5.69821 q^{31} +0.954522 q^{33} +(-1.83598 + 1.83598i) q^{35} +(1.66877 + 1.66877i) q^{37} -13.7127i q^{39} -10.7333i q^{41} +(-0.533105 - 0.533105i) q^{43} +(2.58672 - 2.58672i) q^{45} -0.465401 q^{47} -1.00000 q^{49} +(-2.73447 + 2.73447i) q^{51} +(-0.623234 - 0.623234i) q^{53} +1.18033i q^{55} +11.5497i q^{57} +(7.32184 + 7.32184i) q^{59} +(-7.57257 + 7.57257i) q^{61} +1.40890 q^{63} +16.9567 q^{65} +(-6.16327 + 6.16327i) q^{67} +(8.73764 + 8.73764i) q^{69} -0.162532i q^{71} +3.49118i q^{73} +(2.58594 + 2.58594i) q^{75} +(-0.321444 + 0.321444i) q^{77} +8.28703 q^{79} +11.2417 q^{81} +(-2.51275 + 2.51275i) q^{83} +(-3.38136 - 3.38136i) q^{85} -18.2495i q^{87} +1.60040i q^{89} +(4.61789 + 4.61789i) q^{91} +(8.46035 - 8.46035i) q^{93} -14.2821 q^{95} -8.88621 q^{97} +(0.452882 - 0.452882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} - 4 q^{5}+O(q^{10}) \) 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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