LMFDB - Embedded newform 1792.2.m.e.1345.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1792.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.3091920422$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1345.5
Root			$0.277956 - 0.213283i$ of defining polynomial
Character	$\chi$	$=$	1792.1345
Dual form			1792.2.m.e.449.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.328027 + 0.328027i) q^{3} +(1.40197 - 1.40197i) q^{5} -1.00000i q^{7} -2.78480i q^{9} +O(q^{10})$	\(q+(0.328027 + 0.328027i) q^{3} +(1.40197 - 1.40197i) q^{5} -1.00000i q^{7} -2.78480i q^{9} +(0.444087 - 0.444087i) q^{11} +(2.25590 + 2.25590i) q^{13} +0.919765 q^{15} +4.85578 q^{17} +(-0.114004 - 0.114004i) q^{19} +(0.328027 - 0.328027i) q^{21} +3.20529i q^{23} +1.06898i q^{25} +(1.89757 - 1.89757i) q^{27} +(-0.997091 - 0.997091i) q^{29} -5.34435 q^{31} +0.291345 q^{33} +(-1.40197 - 1.40197i) q^{35} +(2.03472 - 2.03472i) q^{37} +1.47999i q^{39} -9.57673i q^{41} +(6.86758 - 6.86758i) q^{43} +(-3.90419 - 3.90419i) q^{45} -9.70703 q^{47} -1.00000 q^{49} +(1.59282 + 1.59282i) q^{51} +(7.64426 - 7.64426i) q^{53} -1.24519i q^{55} -0.0747927i q^{57} +(1.50266 - 1.50266i) q^{59} +(-1.74157 - 1.74157i) q^{61} -2.78480 q^{63} +6.32541 q^{65} +(8.96491 + 8.96491i) q^{67} +(-1.05142 + 1.05142i) q^{69} -7.18356i q^{71} -9.04029i q^{73} +(-0.350652 + 0.350652i) q^{75} +(-0.444087 - 0.444087i) q^{77} -9.58806 q^{79} -7.10949 q^{81} +(5.30245 + 5.30245i) q^{83} +(6.80764 - 6.80764i) q^{85} -0.654145i q^{87} +2.49938i q^{89} +(2.25590 - 2.25590i) q^{91} +(-1.75309 - 1.75309i) q^{93} -0.319660 q^{95} +5.89073 q^{97} +(-1.23669 - 1.23669i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} - 4 q^{5}+O(q^{10}) $ 16 * q - 4 * q^3 - 4 * q^5	$ 16 q - 4 q^{3} - 4 q^{5} + 8 q^{11} + 12 q^{13} - 8 q^{17} - 4 q^{19} - 4 q^{21} + 56 q^{27} - 8 q^{31} + 16 q^{33} + 4 q^{35} - 8 q^{37} + 24 q^{43} - 36 q^{45} - 40 q^{47} - 16 q^{49} - 24 q^{51} - 32 q^{53} + 4 q^{59} - 20 q^{61} + 24 q^{63} + 72 q^{65} - 32 q^{67} + 56 q^{69} + 28 q^{75} - 8 q^{77} - 40 q^{81} - 36 q^{83} + 12 q^{91} + 8 q^{93} - 80 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^3 - 4 * q^5 + 8 * q^11 + 12 * q^13 - 8 * q^17 - 4 * q^19 - 4 * q^21 + 56 * q^27 - 8 * q^31 + 16 * q^33 + 4 * q^35 - 8 * q^37 + 24 * q^43 - 36 * q^45 - 40 * q^47 - 16 * q^49 - 24 * q^51 - 32 * q^53 + 4 * q^59 - 20 * q^61 + 24 * q^63 + 72 * q^65 - 32 * q^67 + 56 * q^69 + 28 * q^75 - 8 * q^77 - 40 * q^81 - 36 * q^83 + 12 * q^91 + 8 * q^93 - 80 * q^95 - 72 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.328027	+	0.328027i	0.189386	+	0.189386i	0.795431	−	0.606044i	$-0.207245\pi$
$3$	0.328027	+	0.328027i	0.189386	+	0.189386i	−0.606044	+	0.795431i	$0.707245\pi$
$4$		0			0
$5$	1.40197	−	1.40197i	0.626979	−	0.626979i	−0.320328	−	0.947307i	$-0.603793\pi$
$5$	1.40197	−	1.40197i	0.626979	−	0.626979i	0.947307	+	0.320328i	$0.103793\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$		−	2.78480i		−	0.928266i
$10$		0			0
$11$	0.444087	−	0.444087i	0.133897	−	0.133897i	−0.636982	−	0.770879i	$-0.719817\pi$
$11$	0.444087	−	0.444087i	0.133897	−	0.133897i	0.770879	+	0.636982i	$0.219817\pi$
$12$		0			0
$13$	2.25590	+	2.25590i	0.625675	+	0.625675i	0.946977	−	0.321302i	$-0.104120\pi$
$13$	2.25590	+	2.25590i	0.625675	+	0.625675i	−0.321302	+	0.946977i	$0.604120\pi$
$14$		0			0
$15$	0.919765			0.237482
$16$		0			0
$17$	4.85578			1.17770			0.588849	−	0.808243i	$-0.299581\pi$
$17$	4.85578			1.17770			0.588849	+	0.808243i	$0.299581\pi$
$18$		0			0
$19$	−0.114004	−	0.114004i	−0.0261543	−	0.0261543i	0.693909	−	0.720063i	$-0.255887\pi$
$19$	−0.114004	−	0.114004i	−0.0261543	−	0.0261543i	−0.720063	+	0.693909i	$0.755887\pi$
$20$		0			0
$21$	0.328027	−	0.328027i	0.0715813	−	0.0715813i
$22$		0			0
$23$			3.20529i			0.668350i	0.942511	+	0.334175i	$0.108458\pi$
$23$			3.20529i			0.668350i	−0.942511	+	0.334175i	$0.891542\pi$
$24$		0			0
$25$			1.06898i			0.213795i
$26$		0			0
$27$	1.89757	−	1.89757i	0.365187	−	0.365187i
$28$		0			0
$29$	−0.997091	−	0.997091i	−0.185155	−	0.185155i	0.608443	−	0.793598i	$-0.291795\pi$
$29$	−0.997091	−	0.997091i	−0.185155	−	0.185155i	−0.793598	+	0.608443i	$0.791795\pi$
$30$		0			0
$31$	−5.34435			−0.959874			−0.479937	−	0.877303i	$-0.659340\pi$
$31$	−5.34435			−0.959874			−0.479937	+	0.877303i	$0.659340\pi$
$32$		0			0
$33$	0.291345			0.0507167
$34$		0			0
$35$	−1.40197	−	1.40197i	−0.236976	−	0.236976i
$36$		0			0
$37$	2.03472	−	2.03472i	0.334507	−	0.334507i	−0.519788	−	0.854295i	$-0.673989\pi$
$37$	2.03472	−	2.03472i	0.334507	−	0.334507i	0.854295	+	0.519788i	$0.173989\pi$
$38$		0			0
$39$			1.47999i			0.236989i
$40$		0			0
$41$		−	9.57673i		−	1.49563i	−0.663905	−	0.747817i	$-0.731102\pi$
$41$		−	9.57673i		−	1.49563i	0.663905	−	0.747817i	$-0.268898\pi$
$42$		0			0
$43$	6.86758	−	6.86758i	1.04730	−	1.04730i	0.0484714	−	0.998825i	$-0.484565\pi$
$43$	6.86758	−	6.86758i	1.04730	−	1.04730i	0.998825	−	0.0484714i	$-0.0154350\pi$
$44$		0			0
$45$	−3.90419	−	3.90419i	−0.582003	−	0.582003i
$46$		0			0
$47$	−9.70703			−1.41592			−0.707958	−	0.706255i	$-0.750383\pi$
$47$	−9.70703			−1.41592			−0.707958	+	0.706255i	$0.750383\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	1.59282	+	1.59282i	0.223040	+	0.223040i
$52$		0			0
$53$	7.64426	−	7.64426i	1.05002	−	1.05002i	0.0513390	−	0.998681i	$-0.483651\pi$
$53$	7.64426	−	7.64426i	1.05002	−	1.05002i	0.998681	−	0.0513390i	$-0.0163489\pi$
$54$		0			0
$55$		−	1.24519i		−	0.167902i
$56$		0			0
$57$		−	0.0747927i		−	0.00990653i
$58$		0			0
$59$	1.50266	−	1.50266i	0.195630	−	0.195630i	−0.602494	−	0.798123i	$-0.705826\pi$
$59$	1.50266	−	1.50266i	0.195630	−	0.195630i	0.798123	+	0.602494i	$0.205826\pi$
$60$		0			0
$61$	−1.74157	−	1.74157i	−0.222985	−	0.222985i	0.586769	−	0.809754i	$-0.300399\pi$
$61$	−1.74157	−	1.74157i	−0.222985	−	0.222985i	−0.809754	+	0.586769i	$0.800399\pi$
$62$		0			0
$63$	−2.78480			−0.350851
$64$		0			0
$65$	6.32541			0.784571
$66$		0			0
$67$	8.96491	+	8.96491i	1.09524	+	1.09524i	0.994959	+	0.100279i	$0.0319735\pi$
$67$	8.96491	+	8.96491i	1.09524	+	1.09524i	0.100279	+	0.994959i	$0.468027\pi$
$68$		0			0
$69$	−1.05142	+	1.05142i	−0.126576	+	0.126576i
$70$		0			0
$71$		−	7.18356i		−	0.852532i	−0.904598	−	0.426266i	$-0.859829\pi$
$71$		−	7.18356i		−	0.852532i	0.904598	−	0.426266i	$-0.140171\pi$
$72$		0			0
$73$		−	9.04029i		−	1.05809i	−0.848595	−	0.529043i	$-0.822551\pi$
$73$		−	9.04029i		−	1.05809i	0.848595	−	0.529043i	$-0.177449\pi$
$74$		0			0
$75$	−0.350652	+	0.350652i	−0.0404898	+	0.0404898i
$76$		0			0
$77$	−0.444087	−	0.444087i	−0.0506085	−	0.0506085i
$78$		0			0
$79$	−9.58806			−1.07874			−0.539370	−	0.842069i	$-0.681338\pi$
$79$	−9.58806			−1.07874			−0.539370	+	0.842069i	$0.681338\pi$
$80$		0			0
$81$	−7.10949			−0.789943
$82$		0			0
$83$	5.30245	+	5.30245i	0.582020	+	0.582020i	0.935458	−	0.353438i	$-0.114988\pi$
$83$	5.30245	+	5.30245i	0.582020	+	0.582020i	−0.353438	+	0.935458i	$0.614988\pi$
$84$		0			0
$85$	6.80764	−	6.80764i	0.738392	−	0.738392i
$86$		0			0
$87$		−	0.654145i		−	0.0701317i
$88$		0			0
$89$			2.49938i			0.264934i	0.991187	+	0.132467i	$0.0422898\pi$
$89$			2.49938i			0.264934i	−0.991187	+	0.132467i	$0.957710\pi$
$90$		0			0
$91$	2.25590	−	2.25590i	0.236483	−	0.236483i
$92$		0			0
$93$	−1.75309	−	1.75309i	−0.181787	−	0.181787i
$94$		0			0
$95$	−0.319660			−0.0327964
$96$		0			0
$97$	5.89073			0.598113			0.299057	−	0.954235i	$-0.403328\pi$
$97$	5.89073			0.598113			0.299057	+	0.954235i	$0.403328\pi$
$98$		0			0
$99$	−1.23669	−	1.23669i	−0.124292	−	0.124292i
$100$		0			0
$101$	−7.00499	+	7.00499i	−0.697022	+	0.697022i	−0.963767	−	0.266745i	$-0.914052\pi$
$101$	−7.00499	+	7.00499i	−0.697022	+	0.697022i	0.266745	+	0.963767i	$0.414052\pi$
$102$		0			0
$103$			8.10887i			0.798991i	0.916735	+	0.399496i	$0.130815\pi$
$103$			8.10887i			0.798991i	−0.916735	+	0.399496i	$0.869185\pi$
$104$		0			0
$105$		−	0.919765i		−	0.0897599i
$106$		0			0
$107$	−2.24367	+	2.24367i	−0.216904	+	0.216904i	−0.807192	−	0.590288i	$-0.799014\pi$
$107$	−2.24367	+	2.24367i	−0.216904	+	0.216904i	0.590288	+	0.807192i	$0.299014\pi$
$108$		0			0
$109$	0.299413	+	0.299413i	0.0286786	+	0.0286786i	0.721301	−	0.692622i	$-0.243545\pi$
$109$	0.299413	+	0.299413i	0.0286786	+	0.0286786i	−0.692622	+	0.721301i	$0.743545\pi$
$110$		0			0
$111$	1.33489			0.126702
$112$		0			0
$113$	4.67432			0.439723			0.219862	−	0.975531i	$-0.429439\pi$
$113$	4.67432			0.439723			0.219862	+	0.975531i	$0.429439\pi$
$114$		0			0
$115$	4.49372	+	4.49372i	0.419041	+	0.419041i
$116$		0			0
$117$	6.28224	−	6.28224i	0.580793	−	0.580793i
$118$		0			0
$119$		−	4.85578i		−	0.445128i
$120$		0			0
$121$			10.6056i			0.964143i
$122$		0			0
$123$	3.14142	−	3.14142i	0.283252	−	0.283252i
$124$		0			0
$125$	8.50850	+	8.50850i	0.761024	+	0.761024i
$126$		0			0
$127$	−13.7602			−1.22102			−0.610509	−	0.792009i	$-0.709035\pi$
$127$	−13.7602			−1.22102			−0.610509	+	0.792009i	$0.709035\pi$
$128$		0			0
$129$	4.50550			0.396687
$130$		0			0
$131$	6.91851	+	6.91851i	0.604473	+	0.604473i	0.941496	−	0.337023i	$-0.109420\pi$
$131$	6.91851	+	6.91851i	0.604473	+	0.604473i	−0.337023	+	0.941496i	$0.609420\pi$
$132$		0			0
$133$	−0.114004	+	0.114004i	−0.00988539	+	0.00988539i
$134$		0			0
$135$		−	5.32066i		−	0.457929i
$136$		0			0
$137$		−	7.10937i		−	0.607395i	−0.952769	−	0.303697i	$-0.901779\pi$
$137$		−	7.10937i		−	0.607395i	0.952769	−	0.303697i	$-0.0982211\pi$
$138$		0			0
$139$	10.8171	−	10.8171i	0.917496	−	0.917496i	−0.0793508	−	0.996847i	$-0.525285\pi$
$139$	10.8171	−	10.8171i	0.917496	−	0.917496i	0.996847	+	0.0793508i	$0.0252847\pi$
$140$		0			0
$141$	−3.18416	−	3.18416i	−0.268155	−	0.268155i
$142$		0			0
$143$	2.00364			0.167553
$144$		0			0
$145$	−2.79578			−0.232177
$146$		0			0
$147$	−0.328027	−	0.328027i	−0.0270552	−	0.0270552i
$148$		0			0
$149$	15.3257	−	15.3257i	1.25553	−	1.25553i	0.302325	−	0.953205i	$-0.402237\pi$
$149$	15.3257	−	15.3257i	1.25553	−	1.25553i	0.953205	−	0.302325i	$-0.0977628\pi$
$150$		0			0
$151$			21.5070i			1.75022i	0.483925	+	0.875109i	$0.339211\pi$
$151$			21.5070i			1.75022i	−0.483925	+	0.875109i	$0.660789\pi$
$152$		0			0
$153$		−	13.5224i		−	1.09322i
$154$		0			0
$155$	−7.49260	+	7.49260i	−0.601821	+	0.601821i
$156$		0			0
$157$	7.72626	+	7.72626i	0.616623	+	0.616623i	0.944664	−	0.328041i	$-0.106388\pi$
$157$	7.72626	+	7.72626i	0.616623	+	0.616623i	−0.328041	+	0.944664i	$0.606388\pi$
$158$		0			0
$159$	5.01504			0.397719
$160$		0			0
$161$	3.20529			0.252612
$162$		0			0
$163$	−16.9336	−	16.9336i	−1.32634	−	1.32634i	−0.908538	−	0.417802i	$-0.862801\pi$
$163$	−16.9336	−	16.9336i	−1.32634	−	1.32634i	−0.417802	−	0.908538i	$-0.637199\pi$
$164$		0			0
$165$	0.408456	−	0.408456i	0.0317983	−	0.0317983i
$166$		0			0
$167$			8.57678i			0.663691i	0.943334	+	0.331846i	$0.107671\pi$
$167$			8.57678i			0.663691i	−0.943334	+	0.331846i	$0.892329\pi$
$168$		0			0
$169$		−	2.82179i		−	0.217061i
$170$		0			0
$171$	−0.317478	+	0.317478i	−0.0242781	+	0.0242781i
$172$		0			0
$173$	−5.44032	−	5.44032i	−0.413620	−	0.413620i	0.469378	−	0.882997i	$-0.344478\pi$
$173$	−5.44032	−	5.44032i	−0.413620	−	0.413620i	−0.882997	+	0.469378i	$0.844478\pi$
$174$		0			0
$175$	1.06898			0.0808069
$176$		0			0
$177$	0.985825			0.0740991
$178$		0			0
$179$	8.32748	+	8.32748i	0.622425	+	0.622425i	0.946151	−	0.323726i	$-0.104936\pi$
$179$	8.32748	+	8.32748i	0.622425	+	0.622425i	−0.323726	+	0.946151i	$0.604936\pi$
$180$		0			0
$181$	−6.24148	+	6.24148i	−0.463926	+	0.463926i	−0.899940	−	0.436014i	$-0.856390\pi$
$181$	−6.24148	+	6.24148i	−0.463926	+	0.463926i	0.436014	+	0.899940i	$0.356390\pi$
$182$		0			0
$183$		−	1.14256i		−	0.0844605i
$184$		0			0
$185$		−	5.70524i		−	0.419457i
$186$		0			0
$187$	2.15639	−	2.15639i	0.157691	−	0.157691i
$188$		0			0
$189$	−1.89757	−	1.89757i	−0.138028	−	0.138028i
$190$		0			0
$191$	1.57521			0.113979			0.0569893	−	0.998375i	$-0.481850\pi$
$191$	1.57521			0.113979			0.0569893	+	0.998375i	$0.481850\pi$
$192$		0			0
$193$	0.649369			0.0467426			0.0233713	−	0.999727i	$-0.492560\pi$
$193$	0.649369			0.0467426			0.0233713	+	0.999727i	$0.492560\pi$
$194$		0			0
$195$	2.07490	+	2.07490i	0.148587	+	0.148587i
$196$		0			0
$197$	−1.16865	+	1.16865i	−0.0832632	+	0.0832632i	−0.747512	−	0.664249i	$-0.768752\pi$
$197$	−1.16865	+	1.16865i	−0.0832632	+	0.0832632i	0.664249	+	0.747512i	$0.268752\pi$
$198$		0			0
$199$			4.09013i			0.289942i	0.989436	+	0.144971i	$0.0463088\pi$
$199$			4.09013i			0.289942i	−0.989436	+	0.144971i	$0.953691\pi$
$200$		0			0
$201$			5.88146i			0.414846i
$202$		0			0
$203$	−0.997091	+	0.997091i	−0.0699821	+	0.0699821i
$204$		0			0
$205$	−13.4263	−	13.4263i	−0.937731	−	0.937731i
$206$		0			0
$207$	8.92609			0.620406
$208$		0			0
$209$	−0.101255			−0.00700398
$210$		0			0
$211$	−19.0421	−	19.0421i	−1.31091	−	1.31091i	−0.920745	−	0.390164i	$-0.872418\pi$
$211$	−19.0421	−	19.0421i	−1.31091	−	1.31091i	−0.390164	−	0.920745i	$-0.627582\pi$
$212$		0			0
$213$	2.35640	−	2.35640i	0.161458	−	0.161458i
$214$		0			0
$215$		−	19.2562i		−	1.31326i
$216$		0			0
$217$			5.34435i			0.362798i
$218$		0			0
$219$	2.96546	−	2.96546i	0.200387	−	0.200387i
$220$		0			0
$221$	10.9542	+	10.9542i	0.736857	+	0.736857i
$222$		0			0
$223$	26.0121			1.74190			0.870950	−	0.491372i	$-0.163504\pi$
$223$	26.0121			1.74190			0.870950	+	0.491372i	$0.163504\pi$
$224$		0			0
$225$	2.97688			0.198459
$226$		0			0
$227$	0.181612	+	0.181612i	0.0120540	+	0.0120540i	0.713108	−	0.701054i	$-0.247287\pi$
$227$	0.181612	+	0.181612i	0.0120540	+	0.0120540i	−0.701054	+	0.713108i	$0.747287\pi$
$228$		0			0
$229$	−0.679595	+	0.679595i	−0.0449089	+	0.0449089i	−0.729205	−	0.684296i	$-0.760110\pi$
$229$	−0.679595	+	0.679595i	−0.0449089	+	0.0449089i	0.684296	+	0.729205i	$0.260110\pi$
$230$		0			0
$231$		−	0.291345i		−	0.0191691i
$232$		0			0
$233$			19.6676i			1.28847i	0.764828	+	0.644235i	$0.222824\pi$
$233$			19.6676i			1.28847i	−0.764828	+	0.644235i	$0.777176\pi$
$234$		0			0
$235$	−13.6089	+	13.6089i	−0.887749	+	0.887749i
$236$		0			0
$237$	−3.14514	−	3.14514i	−0.204299	−	0.204299i
$238$		0			0
$239$	−9.44846			−0.611170			−0.305585	−	0.952165i	$-0.598852\pi$
$239$	−9.44846			−0.611170			−0.305585	+	0.952165i	$0.598852\pi$
$240$		0			0
$241$	−22.8233			−1.47018			−0.735088	−	0.677971i	$-0.762859\pi$
$241$	−22.8233			−1.47018			−0.735088	+	0.677971i	$0.762859\pi$
$242$		0			0
$243$	−8.02480	−	8.02480i	−0.514791	−	0.514791i
$244$		0			0
$245$	−1.40197	+	1.40197i	−0.0895684	+	0.0895684i
$246$		0			0
$247$		−	0.514364i		−	0.0327282i
$248$		0			0
$249$			3.47869i			0.220453i
$250$		0			0
$251$	−12.2670	+	12.2670i	−0.774287	+	0.774287i	−0.978853	−	0.204566i	$-0.934422\pi$
$251$	−12.2670	+	12.2670i	−0.774287	+	0.774287i	0.204566	+	0.978853i	$0.434422\pi$
$252$		0			0
$253$	1.42343	+	1.42343i	0.0894903	+	0.0894903i
$254$		0			0
$255$	4.46618			0.279683
$256$		0			0
$257$	7.71213			0.481070			0.240535	−	0.970641i	$-0.422677\pi$
$257$	7.71213			0.481070			0.240535	+	0.970641i	$0.422677\pi$
$258$		0			0
$259$	−2.03472	−	2.03472i	−0.126432	−	0.126432i
$260$		0			0
$261$	−2.77670	+	2.77670i	−0.171873	+	0.171873i
$262$		0			0
$263$		−	9.24972i		−	0.570362i	−0.958474	−	0.285181i	$-0.907946\pi$
$263$		−	9.24972i		−	0.570362i	0.958474	−	0.285181i	$-0.0920538\pi$
$264$		0			0
$265$		−	21.4340i		−	1.31668i
$266$		0			0
$267$	−0.819863	+	0.819863i	−0.0501748	+	0.0501748i
$268$		0			0
$269$	8.36587	+	8.36587i	0.510076	+	0.510076i	0.914550	−	0.404474i	$-0.132545\pi$
$269$	8.36587	+	8.36587i	0.510076	+	0.510076i	−0.404474	+	0.914550i	$0.632545\pi$
$270$		0			0
$271$	−1.15740			−0.0703071			−0.0351535	−	0.999382i	$-0.511192\pi$
$271$	−1.15740			−0.0703071			−0.0351535	+	0.999382i	$0.511192\pi$
$272$		0			0
$273$	1.47999			0.0895733
$274$		0			0
$275$	0.474718	+	0.474718i	0.0286266	+	0.0286266i
$276$		0			0
$277$	−16.6925	+	16.6925i	−1.00296	+	1.00296i	−0.00295975	+	0.999996i	$0.500942\pi$
$277$	−16.6925	+	16.6925i	−1.00296	+	1.00296i	−0.999996	+	0.00295975i	$0.999058\pi$
$278$		0			0
$279$			14.8829i			0.891018i
$280$		0			0
$281$			29.3656i			1.75180i	0.482490	+	0.875902i	$0.339732\pi$
$281$			29.3656i			1.75180i	−0.482490	+	0.875902i	$0.660268\pi$
$282$		0			0
$283$	13.0502	−	13.0502i	0.775752	−	0.775752i	−0.203354	−	0.979105i	$-0.565184\pi$
$283$	13.0502	−	13.0502i	0.775752	−	0.775752i	0.979105	+	0.203354i	$0.0651842\pi$
$284$		0			0
$285$	−0.104857	−	0.104857i	−0.00621118	−	0.00621118i
$286$		0			0
$287$	−9.57673			−0.565296
$288$		0			0
$289$	6.57857			0.386975
$290$		0			0
$291$	1.93232	+	1.93232i	0.113274	+	0.113274i
$292$		0			0
$293$	−19.4435	+	19.4435i	−1.13590	+	1.13590i	−0.146723	+	0.989178i	$0.546873\pi$
$293$	−19.4435	+	19.4435i	−1.13590	+	1.13590i	−0.989178	+	0.146723i	$0.953127\pi$
$294$		0			0
$295$		−	4.21336i		−	0.245311i
$296$		0			0
$297$		−	1.68537i		−	0.0977952i
$298$		0			0
$299$	−7.23084	+	7.23084i	−0.418170	+	0.418170i
$300$		0			0
$301$	−6.86758	−	6.86758i	−0.395841	−	0.395841i
$302$		0			0
$303$	−4.59564			−0.264013
$304$		0			0
$305$	−4.88324			−0.279613
$306$		0			0
$307$	19.5562	+	19.5562i	1.11613	+	1.11613i	0.992303	+	0.123830i	$0.0395178\pi$
$307$	19.5562	+	19.5562i	1.11613	+	1.11613i	0.123830	+	0.992303i	$0.460482\pi$
$308$		0			0
$309$	−2.65993	+	2.65993i	−0.151318	+	0.151318i
$310$		0			0
$311$		−	24.5927i		−	1.39453i	−0.716815	−	0.697263i	$-0.754401\pi$
$311$		−	24.5927i		−	1.39453i	0.716815	−	0.697263i	$-0.245599\pi$
$312$		0			0
$313$			18.0125i			1.01812i	0.860730	+	0.509062i	$0.170008\pi$
$313$			18.0125i			1.01812i	−0.860730	+	0.509062i	$0.829992\pi$
$314$		0			0
$315$	−3.90419	+	3.90419i	−0.219976	+	0.219976i
$316$		0			0
$317$	9.70483	+	9.70483i	0.545078	+	0.545078i	0.925013	−	0.379935i	$-0.124054\pi$
$317$	9.70483	+	9.70483i	0.545078	+	0.545078i	−0.379935	+	0.925013i	$0.624054\pi$
$318$		0			0
$319$	−0.885591			−0.0495836
$320$		0			0
$321$	−1.47197			−0.0821573
$322$		0			0
$323$	−0.553578	−	0.553578i	−0.0308019	−	0.0308019i
$324$		0			0
$325$	−2.41151	+	2.41151i	−0.133766	+	0.133766i
$326$		0			0
$327$			0.196431i			0.0108627i
$328$		0			0
$329$			9.70703i			0.535166i
$330$		0			0
$331$	1.50341	−	1.50341i	0.0826349	−	0.0826349i	−0.664581	−	0.747216i	$-0.731390\pi$
$331$	1.50341	−	1.50341i	0.0826349	−	0.0826349i	0.747216	+	0.664581i	$0.231390\pi$
$332$		0			0
$333$	−5.66630	−	5.66630i	−0.310511	−	0.310511i
$334$		0			0
$335$	25.1370			1.37338
$336$		0			0
$337$	−17.7244			−0.965512			−0.482756	−	0.875755i	$-0.660364\pi$
$337$	−17.7244			−0.965512			−0.482756	+	0.875755i	$0.660364\pi$
$338$		0			0
$339$	1.53330	+	1.53330i	0.0832776	+	0.0832776i
$340$		0			0
$341$	−2.37336	+	2.37336i	−0.128525	+	0.128525i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$			2.94812i			0.158721i
$346$		0			0
$347$	4.92098	−	4.92098i	0.264172	−	0.264172i	−0.562574	−	0.826747i	$-0.690189\pi$
$347$	4.92098	−	4.92098i	0.264172	−	0.264172i	0.826747	+	0.562574i	$0.190189\pi$
$348$		0			0
$349$	24.8975	+	24.8975i	1.33274	+	1.33274i	0.902914	+	0.429821i	$0.141423\pi$
$349$	24.8975	+	24.8975i	1.33274	+	1.33274i	0.429821	+	0.902914i	$0.358577\pi$
$350$		0			0
$351$	8.56146			0.456977
$352$		0			0
$353$	−5.71306			−0.304075			−0.152038	−	0.988375i	$-0.548584\pi$
$353$	−5.71306			−0.304075			−0.152038	+	0.988375i	$0.548584\pi$
$354$		0			0
$355$	−10.0711	−	10.0711i	−0.534519	−	0.534519i
$356$		0			0
$357$	1.59282	−	1.59282i	0.0843012	−	0.0843012i
$358$		0			0
$359$		−	25.2978i		−	1.33516i	−0.744536	−	0.667582i	$-0.767329\pi$
$359$		−	25.2978i		−	1.33516i	0.744536	−	0.667582i	$-0.232671\pi$
$360$		0			0
$361$		−	18.9740i		−	0.998632i
$362$		0			0
$363$	−3.47891	+	3.47891i	−0.182595	+	0.182595i
$364$		0			0
$365$	−12.6742	−	12.6742i	−0.663398	−	0.663398i
$366$		0			0
$367$	13.9944			0.730499			0.365250	−	0.930910i	$-0.380984\pi$
$367$	13.9944			0.730499			0.365250	+	0.930910i	$0.380984\pi$
$368$		0			0
$369$	−26.6692			−1.38835
$370$		0			0
$371$	−7.64426	−	7.64426i	−0.396870	−	0.396870i
$372$		0			0
$373$	−6.44242	+	6.44242i	−0.333576	+	0.333576i	−0.853943	−	0.520367i	$-0.825795\pi$
$373$	−6.44242	+	6.44242i	−0.333576	+	0.333576i	0.520367	+	0.853943i	$0.325795\pi$
$374$		0			0
$375$			5.58203i			0.288255i
$376$		0			0
$377$		−	4.49869i		−	0.231694i
$378$		0			0
$379$	−20.0039	+	20.0039i	−1.02753	+	1.02753i	−0.0279235	+	0.999610i	$0.508889\pi$
$379$	−20.0039	+	20.0039i	−1.02753	+	1.02753i	−0.999610	+	0.0279235i	$0.991111\pi$
$380$		0			0
$381$	−4.51371	−	4.51371i	−0.231244	−	0.231244i
$382$		0			0
$383$	−8.23256			−0.420664			−0.210332	−	0.977630i	$-0.567455\pi$
$383$	−8.23256			−0.420664			−0.210332	+	0.977630i	$0.567455\pi$
$384$		0			0
$385$	−1.24519			−0.0634609
$386$		0			0
$387$	−19.1248	−	19.1248i	−0.972169	−	0.972169i
$388$		0			0
$389$	−22.8204	+	22.8204i	−1.15704	+	1.15704i	−0.171930	+	0.985109i	$0.555000\pi$
$389$	−22.8204	+	22.8204i	−1.15704	+	1.15704i	−0.985109	+	0.171930i	$0.945000\pi$
$390$		0			0
$391$			15.5642i			0.787115i
$392$		0			0
$393$			4.53891i			0.228958i
$394$		0			0
$395$	−13.4421	+	13.4421i	−0.676348	+	0.676348i
$396$		0			0
$397$	−20.2540	−	20.2540i	−1.01652	−	1.01652i	−0.999861	−	0.0166562i	$-0.994698\pi$
$397$	−20.2540	−	20.2540i	−1.01652	−	1.01652i	−0.0166562	−	0.999861i	$-0.505302\pi$
$398$		0			0
$399$	−0.0747927			−0.00374432
$400$		0			0
$401$	−20.9844			−1.04791			−0.523956	−	0.851745i	$-0.675544\pi$
$401$	−20.9844			−1.04791			−0.523956	+	0.851745i	$0.675544\pi$
$402$		0			0
$403$	−12.0563	−	12.0563i	−0.600569	−	0.600569i
$404$		0			0
$405$	−9.96727	+	9.96727i	−0.495277	+	0.495277i
$406$		0			0
$407$		−	1.80719i		−	0.0895791i
$408$		0			0
$409$			22.9268i			1.13366i	0.823836	+	0.566828i	$0.191830\pi$
$409$			22.9268i			1.13366i	−0.823836	+	0.566828i	$0.808170\pi$
$410$		0			0
$411$	2.33206	−	2.33206i	0.115032	−	0.115032i
$412$		0			0
$413$	−1.50266	−	1.50266i	−0.0739410	−	0.0739410i
$414$		0			0
$415$	14.8677			0.729828
$416$		0			0
$417$	7.09661			0.347522
$418$		0			0
$419$	27.8867	+	27.8867i	1.36235	+	1.36235i	0.870909	+	0.491444i	$0.163531\pi$
$419$	27.8867	+	27.8867i	1.36235	+	1.36235i	0.491444	+	0.870909i	$0.336469\pi$
$420$		0			0
$421$	−3.93087	+	3.93087i	−0.191579	+	0.191579i	−0.796378	−	0.604799i	$-0.793253\pi$
$421$	−3.93087	+	3.93087i	−0.191579	+	0.191579i	0.604799	+	0.796378i	$0.293253\pi$
$422$		0			0
$423$			27.0321i			1.31435i
$424$		0			0
$425$			5.19071i			0.251786i
$426$		0			0
$427$	−1.74157	+	1.74157i	−0.0842803	+	0.0842803i
$428$		0			0
$429$	0.657247	+	0.657247i	0.0317322	+	0.0317322i
$430$		0			0
$431$	30.8494			1.48596			0.742981	−	0.669313i	$-0.233411\pi$
$431$	30.8494			1.48596			0.742981	+	0.669313i	$0.233411\pi$
$432$		0			0
$433$	−22.5480			−1.08359			−0.541794	−	0.840511i	$-0.682255\pi$
$433$	−22.5480			−1.08359			−0.541794	+	0.840511i	$0.682255\pi$
$434$		0			0
$435$	−0.917090	−	0.917090i	−0.0439711	−	0.0439711i
$436$		0			0
$437$	0.365416	−	0.365416i	0.0174802	−	0.0174802i
$438$		0			0
$439$		−	20.4983i		−	0.978329i	−0.872192	−	0.489164i	$-0.837302\pi$
$439$		−	20.4983i		−	0.978329i	0.872192	−	0.489164i	$-0.162698\pi$
$440$		0			0
$441$			2.78480i			0.132609i
$442$		0			0
$443$	−15.8801	+	15.8801i	−0.754485	+	0.754485i	−0.975313	−	0.220828i	$-0.929124\pi$
$443$	−15.8801	+	15.8801i	−0.754485	+	0.754485i	0.220828	+	0.975313i	$0.429124\pi$
$444$		0			0
$445$	3.50405	+	3.50405i	0.166108	+	0.166108i
$446$		0			0
$447$	10.0545			0.475560
$448$		0			0
$449$	28.3273			1.33685			0.668423	−	0.743781i	$-0.266969\pi$
$449$	28.3273			1.33685			0.668423	+	0.743781i	$0.266969\pi$
$450$		0			0
$451$	−4.25290	−	4.25290i	−0.200261	−	0.200261i
$452$		0			0
$453$	−7.05488	+	7.05488i	−0.331467	+	0.331467i
$454$		0			0
$455$		−	6.32541i		−	0.296540i
$456$		0			0
$457$			0.979734i			0.0458300i	0.999737	+	0.0229150i	$0.00729472\pi$
$457$			0.979734i			0.0458300i	−0.999737	+	0.0229150i	$0.992705\pi$
$458$		0			0
$459$	9.21417	−	9.21417i	0.430080	−	0.430080i
$460$		0			0
$461$	25.7845	+	25.7845i	1.20091	+	1.20091i	0.973891	+	0.227014i	$0.0728964\pi$
$461$	25.7845	+	25.7845i	1.20091	+	1.20091i	0.227014	+	0.973891i	$0.427104\pi$
$462$		0			0
$463$	−1.56380			−0.0726760			−0.0363380	−	0.999340i	$-0.511569\pi$
$463$	−1.56380			−0.0726760			−0.0363380	+	0.999340i	$0.511569\pi$
$464$		0			0
$465$	−4.91555			−0.227953
$466$		0			0
$467$	−28.6856	−	28.6856i	−1.32741	−	1.32741i	−0.907620	−	0.419792i	$-0.862103\pi$
$467$	−28.6856	−	28.6856i	−1.32741	−	1.32741i	−0.419792	−	0.907620i	$-0.637897\pi$
$468$		0			0
$469$	8.96491	−	8.96491i	0.413961	−	0.413961i
$470$		0			0
$471$			5.06884i			0.233560i
$472$		0			0
$473$		−	6.09961i		−	0.280460i
$474$		0			0
$475$	0.121867	−	0.121867i	0.00559166	−	0.00559166i
$476$		0			0
$477$	−21.2877	−	21.2877i	−0.974698	−	0.974698i
$478$		0			0
$479$	25.8040			1.17902			0.589508	−	0.807762i	$-0.299322\pi$
$479$	25.8040			1.17902			0.589508	+	0.807762i	$0.299322\pi$
$480$		0			0
$481$	9.18029			0.418585
$482$		0			0
$483$	1.05142	+	1.05142i	0.0478413	+	0.0478413i
$484$		0			0
$485$	8.25861	−	8.25861i	0.375004	−	0.375004i
$486$		0			0
$487$		−	2.56961i		−	0.116440i	−0.998304	−	0.0582201i	$-0.981457\pi$
$487$		−	2.56961i		−	0.116440i	0.998304	−	0.0582201i	$-0.0185425\pi$
$488$		0			0
$489$		−	11.1093i		−	0.502381i
$490$		0			0
$491$	2.11127	−	2.11127i	0.0952804	−	0.0952804i	−0.657860	−	0.753140i	$-0.728538\pi$
$491$	2.11127	−	2.11127i	0.0952804	−	0.0952804i	0.753140	+	0.657860i	$0.228538\pi$
$492$		0			0
$493$	−4.84165	−	4.84165i	−0.218057	−	0.218057i
$494$		0			0
$495$	−3.46761			−0.155857
$496$		0			0
$497$	−7.18356			−0.322227
$498$		0			0
$499$	−5.30410	−	5.30410i	−0.237444	−	0.237444i	0.578347	−	0.815791i	$-0.303698\pi$
$499$	−5.30410	−	5.30410i	−0.237444	−	0.237444i	−0.815791	+	0.578347i	$0.803698\pi$
$500$		0			0
$501$	−2.81341	+	2.81341i	−0.125694	+	0.125694i
$502$		0			0
$503$			37.3432i			1.66505i	0.553987	+	0.832525i	$0.313106\pi$
$503$			37.3432i			1.66505i	−0.553987	+	0.832525i	$0.686894\pi$
$504$		0			0
$505$			19.6415i			0.874036i
$506$		0			0
$507$	0.925621	−	0.925621i	0.0411083	−	0.0411083i
$508$		0			0
$509$	21.7303	+	21.7303i	0.963178	+	0.963178i	0.999346	−	0.0361674i	$-0.0115150\pi$
$509$	21.7303	+	21.7303i	0.963178	+	0.963178i	−0.0361674	+	0.999346i	$0.511515\pi$
$510$		0			0
$511$	−9.04029			−0.399919
$512$		0			0
$513$	−0.432660			−0.0191024
$514$		0			0
$515$	11.3684	+	11.3684i	0.500951	+	0.500951i
$516$		0			0
$517$	−4.31077	+	4.31077i	−0.189587	+	0.189587i
$518$		0			0
$519$		−	3.56914i		−	0.156668i
$520$		0			0
$521$			4.96517i			0.217528i	0.994068	+	0.108764i	$0.0346893\pi$
$521$			4.96517i			0.217528i	−0.994068	+	0.108764i	$0.965311\pi$
$522$		0			0
$523$	0.922937	−	0.922937i	0.0403572	−	0.0403572i	−0.686640	−	0.726997i	$-0.740915\pi$
$523$	0.922937	−	0.922937i	0.0403572	−	0.0403572i	0.726997	+	0.686640i	$0.240915\pi$
$524$		0			0
$525$	0.350652	+	0.350652i	0.0153037	+	0.0153037i
$526$		0			0
$527$	−25.9510			−1.13044
$528$		0			0
$529$	12.7261			0.553309
$530$		0			0
$531$	−4.18460	−	4.18460i	−0.181596	−	0.181596i
$532$		0			0
$533$	21.6042	−	21.6042i	0.935781	−	0.935781i
$534$		0			0
$535$			6.29111i			0.271989i
$536$		0			0
$537$			5.46327i			0.235757i
$538$		0			0
$539$	−0.444087	+	0.444087i	−0.0191282	+	0.0191282i
$540$		0			0
$541$	−20.1027	−	20.1027i	−0.864281	−	0.864281i	0.127551	−	0.991832i	$-0.459288\pi$
$541$	−20.1027	−	20.1027i	−0.864281	−	0.864281i	−0.991832	+	0.127551i	$0.959288\pi$
$542$		0			0
$543$	−4.09474			−0.175722
$544$		0			0
$545$	0.839535			0.0359617
$546$		0			0
$547$	−16.7415	−	16.7415i	−0.715813	−	0.715813i	0.251932	−	0.967745i	$-0.418934\pi$
$547$	−16.7415	−	16.7415i	−0.715813	−	0.715813i	−0.967745	+	0.251932i	$0.918934\pi$
$548$		0			0
$549$	−4.84991	+	4.84991i	−0.206989	+	0.206989i
$550$		0			0
$551$			0.227345i			0.00968521i
$552$		0			0
$553$			9.58806i			0.407726i
$554$		0			0
$555$	1.87147	−	1.87147i	0.0794394	−	0.0794394i
$556$		0			0
$557$	22.1766	+	22.1766i	0.939655	+	0.939655i	0.998280	−	0.0586254i	$-0.0186717\pi$
$557$	22.1766	+	22.1766i	0.939655	+	0.939655i	−0.0586254	+	0.998280i	$0.518672\pi$
$558$		0			0
$559$	30.9852			1.31053
$560$		0			0
$561$	1.41471			0.0597290
$562$		0			0
$563$	24.2669	+	24.2669i	1.02273	+	1.02273i	0.999736	+	0.0229924i	$0.00731934\pi$
$563$	24.2669	+	24.2669i	1.02273	+	1.02273i	0.0229924	+	0.999736i	$0.492681\pi$
$564$		0			0
$565$	6.55325	−	6.55325i	0.275697	−	0.275697i
$566$		0			0
$567$			7.10949i			0.298570i
$568$		0			0
$569$			42.8086i			1.79463i	0.441392	+	0.897315i	$0.354485\pi$
$569$			42.8086i			1.79463i	−0.441392	+	0.897315i	$0.645515\pi$
$570$		0			0
$571$	−6.89908	+	6.89908i	−0.288717	+	0.288717i	−0.836573	−	0.547856i	$-0.815444\pi$
$571$	−6.89908	+	6.89908i	−0.288717	+	0.288717i	0.547856	+	0.836573i	$0.315444\pi$
$572$		0			0
$573$	0.516712	+	0.516712i	0.0215860	+	0.0215860i
$574$		0			0
$575$	−3.42638			−0.142890
$576$		0			0
$577$	−2.38332			−0.0992189			−0.0496094	−	0.998769i	$-0.515798\pi$
$577$	−2.38332			−0.0992189			−0.0496094	+	0.998769i	$0.515798\pi$
$578$		0			0
$579$	0.213010	+	0.213010i	0.00885240	+	0.00885240i
$580$		0			0
$581$	5.30245	−	5.30245i	0.219983	−	0.219983i
$582$		0			0
$583$		−	6.78944i		−	0.281190i
$584$		0			0
$585$		−	17.6150i		−	0.728290i
$586$		0			0
$587$	−2.70993	+	2.70993i	−0.111851	+	0.111851i	−0.760817	−	0.648966i	$-0.775202\pi$
$587$	−2.70993	+	2.70993i	−0.111851	+	0.111851i	0.648966	+	0.760817i	$0.275202\pi$
$588$		0			0
$589$	0.609277	+	0.609277i	0.0251048	+	0.0251048i
$590$		0			0
$591$	−0.766700			−0.0315378
$592$		0			0
$593$	29.3573			1.20556			0.602780	−	0.797907i	$-0.294060\pi$
$593$	29.3573			1.20556			0.602780	+	0.797907i	$0.294060\pi$
$594$		0			0
$595$	−6.80764	−	6.80764i	−0.279086	−	0.279086i
$596$		0			0
$597$	−1.34167	+	1.34167i	−0.0549110	+	0.0549110i
$598$		0			0
$599$		−	40.3716i		−	1.64954i	−0.565468	−	0.824770i	$-0.691304\pi$
$599$		−	40.3716i		−	1.64954i	0.565468	−	0.824770i	$-0.308696\pi$
$600$		0			0
$601$		−	30.9931i		−	1.26424i	−0.774872	−	0.632118i	$-0.782186\pi$
$601$		−	30.9931i		−	1.26424i	0.774872	−	0.632118i	$-0.217814\pi$
$602$		0			0
$603$	24.9655	−	24.9655i	1.01667	−	1.01667i
$604$		0			0
$605$	14.8687	+	14.8687i	0.604497	+	0.604497i
$606$		0			0
$607$	−9.81876			−0.398531			−0.199265	−	0.979946i	$-0.563856\pi$
$607$	−9.81876			−0.398531			−0.199265	+	0.979946i	$0.563856\pi$
$608$		0			0
$609$	−0.654145			−0.0265073
$610$		0			0
$611$	−21.8981	−	21.8981i	−0.885904	−	0.885904i
$612$		0			0
$613$	−5.05548	+	5.05548i	−0.204189	+	0.204189i	−0.801792	−	0.597603i	$-0.796120\pi$
$613$	−5.05548	+	5.05548i	−0.204189	+	0.204189i	0.597603	+	0.801792i	$0.296120\pi$
$614$		0			0
$615$		−	8.80834i		−	0.355187i
$616$		0			0
$617$			34.8190i			1.40176i	0.713279	+	0.700881i	$0.247209\pi$
$617$			34.8190i			1.40176i	−0.713279	+	0.700881i	$0.752791\pi$
$618$		0			0
$619$	−34.1722	+	34.1722i	−1.37350	+	1.37350i	−0.518294	+	0.855203i	$0.673433\pi$
$619$	−34.1722	+	34.1722i	−1.37350	+	1.37350i	−0.855203	+	0.518294i	$0.826567\pi$
$620$		0			0
$621$	6.08226	+	6.08226i	0.244073	+	0.244073i
$622$		0			0
$623$	2.49938			0.100135
$624$		0			0
$625$	18.5124			0.740497
$626$		0			0
$627$	−0.0332145	−	0.0332145i	−0.00132646	−	0.00132646i
$628$		0			0
$629$	9.88017	−	9.88017i	0.393948	−	0.393948i
$630$		0			0
$631$		−	1.37799i		−	0.0548569i	−0.999624	−	0.0274285i	$-0.991268\pi$
$631$		−	1.37799i		−	0.0548569i	0.999624	−	0.0274285i	$-0.00873184\pi$
$632$		0			0
$633$		−	12.4926i		−	0.496537i
$634$		0			0
$635$	−19.2913	+	19.2913i	−0.765553	+	0.765553i
$636$		0			0
$637$	−2.25590	−	2.25590i	−0.0893822	−	0.0893822i
$638$		0			0
$639$	−20.0048			−0.791376
$640$		0			0
$641$	−1.24423			−0.0491440			−0.0245720	−	0.999698i	$-0.507822\pi$
$641$	−1.24423			−0.0491440			−0.0245720	+	0.999698i	$0.507822\pi$
$642$		0			0
$643$	25.0773	+	25.0773i	0.988954	+	0.988954i	0.999940	−	0.0109861i	$-0.00349707\pi$
$643$	25.0773	+	25.0773i	0.988954	+	0.988954i	−0.0109861	+	0.999940i	$0.503497\pi$
$644$		0			0
$645$	6.31656	−	6.31656i	0.248714	−	0.248714i
$646$		0			0
$647$			28.0343i			1.10214i	0.834458	+	0.551071i	$0.185781\pi$
$647$			28.0343i			1.10214i	−0.834458	+	0.551071i	$0.814219\pi$
$648$		0			0
$649$		−	1.33462i		−	0.0523886i
$650$		0			0
$651$	−1.75309	+	1.75309i	−0.0687090	+	0.0687090i
$652$		0			0
$653$	−18.5604	−	18.5604i	−0.726324	−	0.726324i	0.243561	−	0.969886i	$-0.421684\pi$
$653$	−18.5604	−	18.5604i	−0.726324	−	0.726324i	−0.969886	+	0.243561i	$0.921684\pi$
$654$		0			0
$655$	19.3991			0.757984
$656$		0			0
$657$	−25.1754			−0.982185
$658$		0			0
$659$	2.92378	+	2.92378i	0.113894	+	0.113894i	0.761757	−	0.647863i	$-0.224337\pi$
$659$	2.92378	+	2.92378i	0.113894	+	0.113894i	−0.647863	+	0.761757i	$0.724337\pi$
$660$		0			0
$661$	−1.13234	+	1.13234i	−0.0440428	+	0.0440428i	−0.728785	−	0.684742i	$-0.759915\pi$
$661$	−1.13234	+	1.13234i	−0.0440428	+	0.0440428i	0.684742	+	0.728785i	$0.259915\pi$
$662$		0			0
$663$			7.18652i			0.279101i
$664$		0			0
$665$			0.319660i			0.0123959i
$666$		0			0
$667$	3.19597	−	3.19597i	0.123748	−	0.123748i
$668$		0			0
$669$	8.53267	+	8.53267i	0.329892	+	0.329892i
$670$		0			0
$671$	−1.54681			−0.0597141
$672$		0			0
$673$	−50.3603			−1.94125			−0.970623	−	0.240607i	$-0.922654\pi$
$673$	−50.3603			−1.94125			−0.970623	+	0.240607i	$0.922654\pi$
$674$		0			0
$675$	2.02845	+	2.02845i	0.0780752	+	0.0780752i
$676$		0			0
$677$	−7.37404	+	7.37404i	−0.283407	+	0.283407i	−0.834466	−	0.551059i	$-0.814224\pi$
$677$	−7.37404	+	7.37404i	−0.283407	+	0.283407i	0.551059	+	0.834466i	$0.314224\pi$
$678$		0			0
$679$		−	5.89073i		−	0.226065i
$680$		0			0
$681$			0.119147i			0.00456573i
$682$		0			0
$683$	23.3569	−	23.3569i	0.893726	−	0.893726i	−0.101146	−	0.994872i	$-0.532251\pi$
$683$	23.3569	−	23.3569i	0.893726	−	0.893726i	0.994872	+	0.101146i	$0.0322509\pi$
$684$		0			0
$685$	−9.96711	−	9.96711i	−0.380824	−	0.380824i
$686$		0			0
$687$	−0.445851			−0.0170103
$688$		0			0
$689$	34.4895			1.31394
$690$		0			0
$691$	12.1302	+	12.1302i	0.461453	+	0.461453i	0.899132	−	0.437679i	$-0.144199\pi$
$691$	12.1302	+	12.1302i	0.461453	+	0.461453i	−0.437679	+	0.899132i	$0.644199\pi$
$692$		0			0
$693$	−1.23669	+	1.23669i	−0.0469781	+	0.0469781i
$694$		0			0
$695$		−	30.3305i		−	1.15050i
$696$		0			0
$697$		−	46.5025i		−	1.76141i
$698$		0			0
$699$	−6.45151	+	6.45151i	−0.244019	+	0.244019i
$700$		0			0
$701$	4.41607	+	4.41607i	0.166793	+	0.166793i	0.785568	−	0.618775i	$-0.212371\pi$
$701$	4.41607	+	4.41607i	0.166793	+	0.166793i	−0.618775	+	0.785568i	$0.712371\pi$
$702$		0			0
$703$	−0.463933			−0.0174976
$704$		0			0
$705$	−8.92819			−0.336255
$706$		0			0
$707$	7.00499	+	7.00499i	0.263450	+	0.263450i
$708$		0			0
$709$	2.70925	−	2.70925i	0.101748	−	0.101748i	−0.654400	−	0.756148i	$-0.727079\pi$
$709$	2.70925	−	2.70925i	0.101748	−	0.101748i	0.756148	+	0.654400i	$0.227079\pi$
$710$		0			0
$711$			26.7008i			1.00136i
$712$		0			0
$713$		−	17.1302i		−	0.641531i
$714$		0			0
$715$	2.80903	−	2.80903i	0.105052	−	0.105052i
$716$		0			0
$717$	−3.09935	−	3.09935i	−0.115747	−	0.115747i
$718$		0			0
$719$	−8.99485			−0.335451			−0.167726	−	0.985834i	$-0.553642\pi$
$719$	−8.99485			−0.335451			−0.167726	+	0.985834i	$0.553642\pi$
$720$		0			0
$721$	8.10887			0.301990
$722$		0			0
$723$	−7.48664	−	7.48664i	−0.278431	−	0.278431i
$724$		0			0
$725$	1.06587	−	1.06587i	0.0395853	−	0.0395853i
$726$		0			0
$727$			33.6636i			1.24851i	0.781219	+	0.624256i	$0.214598\pi$
$727$			33.6636i			1.24851i	−0.781219	+	0.624256i	$0.785402\pi$
$728$		0			0
$729$			16.0638i			0.594954i
$730$		0			0
$731$	33.3474	−	33.3474i	1.23340	−	1.23340i
$732$		0			0
$733$	−29.0542	−	29.0542i	−1.07314	−	1.07314i	−0.997105	−	0.0760379i	$-0.975773\pi$
$733$	−29.0542	−	29.0542i	−1.07314	−	1.07314i	−0.0760379	−	0.997105i	$-0.524227\pi$
$734$		0			0
$735$	−0.919765			−0.0339261
$736$		0			0
$737$	7.96241			0.293299
$738$		0			0
$739$	5.63034	+	5.63034i	0.207115	+	0.207115i	0.803040	−	0.595925i	$-0.203214\pi$
$739$	5.63034	+	5.63034i	0.207115	+	0.207115i	−0.595925	+	0.803040i	$0.703214\pi$
$740$		0			0
$741$	0.168725	−	0.168725i	0.00619827	−	0.00619827i
$742$		0			0
$743$		−	27.7688i		−	1.01874i	−0.860548	−	0.509369i	$-0.829879\pi$
$743$		−	27.7688i		−	1.01874i	0.860548	−	0.509369i	$-0.170121\pi$
$744$		0			0
$745$		−	42.9723i		−	1.57438i
$746$		0			0
$747$	14.7663	−	14.7663i	0.540269	−	0.540269i
$748$		0			0
$749$	2.24367	+	2.24367i	0.0819820	+	0.0819820i
$750$		0			0
$751$	−45.5138			−1.66082			−0.830410	−	0.557153i	$-0.811894\pi$
$751$	−45.5138			−1.66082			−0.830410	+	0.557153i	$0.811894\pi$
$752$		0			0
$753$	−8.04781			−0.293279
$754$		0			0
$755$	30.1522	+	30.1522i	1.09735	+	1.09735i
$756$		0			0
$757$	20.7637	−	20.7637i	0.754671	−	0.754671i	−0.220676	−	0.975347i	$-0.570826\pi$
$757$	20.7637	−	20.7637i	0.754671	−	0.754671i	0.975347	+	0.220676i	$0.0708263\pi$
$758$		0			0
$759$			0.933846i			0.0338965i
$760$		0			0
$761$		−	3.64393i		−	0.132092i	−0.997817	−	0.0660461i	$-0.978962\pi$
$761$		−	3.64393i		−	0.132092i	0.997817	−	0.0660461i	$-0.0210384\pi$
$762$		0			0
$763$	0.299413	−	0.299413i	0.0108395	−	0.0108395i
$764$		0			0
$765$	−18.9579	−	18.9579i	−0.685424	−	0.685424i
$766$		0			0
$767$	6.77971			0.244801
$768$		0			0
$769$	−6.23588			−0.224872			−0.112436	−	0.993659i	$-0.535865\pi$
$769$	−6.23588			−0.224872			−0.112436	+	0.993659i	$0.535865\pi$
$770$		0			0
$771$	2.52979	+	2.52979i	0.0911080	+	0.0911080i
$772$		0			0
$773$	−1.49286	+	1.49286i	−0.0536943	+	0.0536943i	−0.733444	−	0.679750i	$-0.762088\pi$
$773$	−1.49286	+	1.49286i	−0.0536943	+	0.0536943i	0.679750	+	0.733444i	$0.262088\pi$
$774$		0			0
$775$		−	5.71298i		−	0.205216i
$776$		0			0
$777$		−	1.33489i		−	0.0478888i
$778$		0			0
$779$	−1.09178	+	1.09178i	−0.0391172	+	0.0391172i
$780$		0			0
$781$	−3.19013	−	3.19013i	−0.114152	−	0.114152i
$782$		0			0
$783$	−3.78410			−0.135233
$784$		0			0
$785$	21.6639			0.773219
$786$		0			0
$787$	8.76929	+	8.76929i	0.312591	+	0.312591i	0.845913	−	0.533321i	$-0.179056\pi$
$787$	8.76929	+	8.76929i	0.312591	+	0.312591i	−0.533321	+	0.845913i	$0.679056\pi$
$788$		0			0
$789$	3.03416	−	3.03416i	0.108019	−	0.108019i
$790$		0			0
$791$		−	4.67432i		−	0.166200i
$792$		0			0
$793$		−	7.85761i		−	0.279032i
$794$		0			0
$795$	7.03093	−	7.03093i	0.249361	−	0.249361i
$796$		0			0
$797$	22.7473	+	22.7473i	0.805750	+	0.805750i	0.983987	−	0.178238i	$-0.0570396\pi$
$797$	22.7473	+	22.7473i	0.805750	+	0.805750i	−0.178238	+	0.983987i	$0.557040\pi$
$798$		0			0
$799$	−47.1352			−1.66752
$800$		0			0
$801$	6.96026			0.245929
$802$		0			0
$803$	−4.01468	−	4.01468i	−0.141675	−	0.141675i
$804$		0			0
$805$	4.49372	−	4.49372i	0.158383	−	0.158383i
$806$		0			0
$807$			5.48846i			0.193203i
$808$		0			0
$809$		−	2.69445i		−	0.0947319i	−0.998878	−	0.0473660i	$-0.984917\pi$
$809$		−	2.69445i		−	0.0947319i	0.998878	−	0.0473660i	$-0.0150827\pi$
$810$		0			0
$811$	30.5311	−	30.5311i	1.07209	−	1.07209i	0.0749015	−	0.997191i	$-0.476136\pi$
$811$	30.5311	−	30.5311i	1.07209	−	1.07209i	0.997191	−	0.0749015i	$-0.0238642\pi$
$812$		0			0
$813$	−0.379658	−	0.379658i	−0.0133152	−	0.0133152i
$814$		0			0
$815$	−47.4806			−1.66317
$816$		0			0
$817$	−1.56586			−0.0547826
$818$		0			0
$819$	−6.28224	−	6.28224i	−0.219519	−	0.219519i
$820$		0			0
$821$	15.4510	−	15.4510i	0.539244	−	0.539244i	−0.384063	−	0.923307i	$-0.625475\pi$
$821$	15.4510	−	15.4510i	0.539244	−	0.539244i	0.923307	+	0.384063i	$0.125475\pi$
$822$		0			0
$823$			22.4104i			0.781178i	0.920565	+	0.390589i	$0.127729\pi$
$823$			22.4104i			0.781178i	−0.920565	+	0.390589i	$0.872271\pi$
$824$		0			0
$825$			0.311441i			0.0108430i
$826$		0			0
$827$	−15.9620	+	15.9620i	−0.555052	+	0.555052i	−0.927895	−	0.372842i	$-0.878383\pi$
$827$	−15.9620	+	15.9620i	−0.555052	+	0.555052i	0.372842	+	0.927895i	$0.378383\pi$
$828$		0			0
$829$	−6.88152	−	6.88152i	−0.239005	−	0.239005i	0.577433	−	0.816438i	$-0.304054\pi$
$829$	−6.88152	−	6.88152i	−0.239005	−	0.239005i	−0.816438	+	0.577433i	$0.804054\pi$
$830$		0			0
$831$	−10.9512			−0.379892
$832$		0			0
$833$	−4.85578			−0.168243
$834$		0			0
$835$	12.0244	+	12.0244i	0.416120	+	0.416120i
$836$		0			0
$837$	−10.1413	+	10.1413i	−0.350533	+	0.350533i
$838$		0			0
$839$		−	24.1568i		−	0.833986i	−0.908910	−	0.416993i	$-0.863084\pi$
$839$		−	24.1568i		−	0.833986i	0.908910	−	0.416993i	$-0.136916\pi$
$840$		0			0
$841$		−	27.0116i		−	0.931435i
$842$		0			0
$843$	−9.63269	+	9.63269i	−0.331767	+	0.331767i
$844$		0			0
$845$	−3.95605	−	3.95605i	−0.136092	−	0.136092i
$846$		0			0
$847$	10.6056			0.364412
$848$		0			0
$849$	8.56160			0.293833
$850$		0			0
$851$	6.52189	+	6.52189i	0.223567	+	0.223567i
$852$		0			0
$853$	−21.4719	+	21.4719i	−0.735183	+	0.735183i	−0.971642	−	0.236458i	$-0.924013\pi$
$853$	−21.4719	+	21.4719i	−0.735183	+	0.735183i	0.236458	+	0.971642i	$0.424013\pi$
$854$		0			0
$855$			0.890187i			0.0304438i
$856$		0			0
$857$		−	3.52721i		−	0.120487i	−0.998184	−	0.0602436i	$-0.980812\pi$
$857$		−	3.52721i		−	0.120487i	0.998184	−	0.0602436i	$-0.0191877\pi$
$858$		0			0
$859$	38.9597	−	38.9597i	1.32929	−	1.32929i	0.423294	−	0.905992i	$-0.360874\pi$
$859$	38.9597	−	38.9597i	1.32929	−	1.32929i	0.905992	−	0.423294i	$-0.139126\pi$
$860$		0			0
$861$	−3.14142	−	3.14142i	−0.107059	−	0.107059i
$862$		0			0
$863$	−18.9798			−0.646081			−0.323040	−	0.946385i	$-0.604705\pi$
$863$	−18.9798			−0.646081			−0.323040	+	0.946385i	$0.604705\pi$
$864$		0			0
$865$	−15.2543			−0.518662
$866$		0			0
$867$	2.15795	+	2.15795i	0.0732877	+	0.0732877i
$868$		0			0
$869$	−4.25794	+	4.25794i	−0.144441	+	0.144441i
$870$		0			0
$871$			40.4480i			1.37053i
$872$		0			0
$873$		−	16.4045i		−	0.555208i
$874$		0			0
$875$	8.50850	−	8.50850i	0.287640	−	0.287640i
$876$		0			0
$877$	−6.54582	−	6.54582i	−0.221037	−	0.221037i	0.587898	−	0.808935i	$-0.299956\pi$
$877$	−6.54582	−	6.54582i	−0.221037	−	0.221037i	−0.808935	+	0.587898i	$0.799956\pi$
$878$		0			0
$879$	−12.7560			−0.430248
$880$		0			0
$881$	26.2370			0.883946			0.441973	−	0.897028i	$-0.354279\pi$
$881$	26.2370			0.883946			0.441973	+	0.897028i	$0.354279\pi$
$882$		0			0
$883$	−19.3060	−	19.3060i	−0.649700	−	0.649700i	0.303221	−	0.952920i	$-0.401938\pi$
$883$	−19.3060	−	19.3060i	−0.649700	−	0.649700i	−0.952920	+	0.303221i	$0.901938\pi$
$884$		0			0
$885$	1.38209	−	1.38209i	0.0464586	−	0.0464586i
$886$		0			0
$887$		−	3.40903i		−	0.114464i	−0.998361	−	0.0572321i	$-0.981773\pi$
$887$		−	3.40903i		−	0.114464i	0.998361	−	0.0572321i	$-0.0182275\pi$
$888$		0			0
$889$			13.7602i			0.461502i
$890$		0			0
$891$	−3.15723	+	3.15723i	−0.105771	+	0.105771i
$892$		0			0
$893$	1.10664	+	1.10664i	0.0370323	+	0.0370323i
$894$		0			0
$895$	23.3497			0.780494
$896$		0			0
$897$	−4.74381			−0.158391
$898$		0			0
$899$	5.32880	+	5.32880i	0.177726	+	0.177726i
$900$		0			0
$901$	37.1188	−	37.1188i	1.23661	−	1.23661i
$902$		0			0
$903$		−	4.50550i		−	0.149934i
$904$		0			0
$905$			17.5007i			0.581743i
$906$		0			0
$907$	17.9095	−	17.9095i	0.594675	−	0.594675i	−0.344216	−	0.938891i	$-0.611855\pi$
$907$	17.9095	−	17.9095i	0.594675	−	0.594675i	0.938891	+	0.344216i	$0.111855\pi$
$908$		0			0
$909$	19.5075	+	19.5075i	0.647022	+	0.647022i
$910$		0			0
$911$	−23.6991			−0.785186			−0.392593	−	0.919712i	$-0.628422\pi$
$911$	−23.6991			−0.785186			−0.392593	+	0.919712i	$0.628422\pi$
$912$		0			0
$913$	4.70950			0.155862
$914$		0			0
$915$	−1.60183	−	1.60183i	−0.0529549	−	0.0529549i
$916$		0			0
$917$	6.91851	−	6.91851i	0.228469	−	0.228469i
$918$		0			0
$919$		−	29.7662i		−	0.981897i	−0.871189	−	0.490949i	$-0.836650\pi$
$919$		−	29.7662i		−	0.981897i	0.871189	−	0.490949i	$-0.163350\pi$
$920$		0			0
$921$			12.8299i			0.422761i
$922$		0			0
$923$	16.2054	−	16.2054i	0.533408	−	0.533408i
$924$		0			0
$925$	2.17507	+	2.17507i	0.0715159	+	0.0715159i
$926$		0			0
$927$	22.5816			0.741676
$928$		0			0
$929$	46.6355			1.53006			0.765031	−	0.643993i	$-0.222723\pi$
$929$	46.6355			1.53006			0.765031	+	0.643993i	$0.222723\pi$
$930$		0			0
$931$	0.114004	+	0.114004i	0.00373633	+	0.00373633i
$932$		0			0
$933$	8.06707	−	8.06707i	0.264104	−	0.264104i
$934$		0			0
$935$		−	6.04638i		−	0.197738i
$936$		0			0
$937$		−	13.5471i		−	0.442564i	−0.975210	−	0.221282i	$-0.928976\pi$
$937$		−	13.5471i		−	0.442564i	0.975210	−	0.221282i	$-0.0710241\pi$
$938$		0			0
$939$	−5.90856	+	5.90856i	−0.192819	+	0.192819i
$940$		0			0
$941$	13.5931	+	13.5931i	0.443121	+	0.443121i	0.893060	−	0.449938i	$-0.148554\pi$
$941$	13.5931	+	13.5931i	0.443121	+	0.443121i	−0.449938	+	0.893060i	$0.648554\pi$
$942$		0			0
$943$	30.6962			0.999606
$944$		0			0
$945$	−5.32066			−0.173081
$946$		0			0
$947$	28.7780	+	28.7780i	0.935159	+	0.935159i	0.998022	−	0.0628630i	$-0.0200231\pi$
$947$	28.7780	+	28.7780i	0.935159	+	0.935159i	−0.0628630	+	0.998022i	$0.520023\pi$
$948$		0			0
$949$	20.3940	−	20.3940i	0.662019	−	0.662019i
$950$		0			0
$951$			6.36689i			0.206460i
$952$		0			0
$953$		−	30.3026i		−	0.981598i	−0.871273	−	0.490799i	$-0.836705\pi$
$953$		−	30.3026i		−	0.981598i	0.871273	−	0.490799i	$-0.163295\pi$
$954$		0			0
$955$	2.20840	−	2.20840i	0.0714621	−	0.0714621i
$956$		0			0
$957$	−0.290498	−	0.290498i	−0.00939045	−	0.00939045i
$958$		0			0
$959$	−7.10937			−0.229574
$960$		0			0
$961$	−2.43792			−0.0786425
$962$		0			0
$963$	6.24818	+	6.24818i	0.201345	+	0.201345i
$964$		0			0
$965$	0.910393	−	0.910393i	0.0293066	−	0.0293066i
$966$		0			0
$967$		−	18.8733i		−	0.606925i	−0.952843	−	0.303462i	$-0.901857\pi$
$967$		−	18.8733i		−	0.606925i	0.952843	−	0.303462i	$-0.0981427\pi$
$968$		0			0
$969$		−	0.363176i		−	0.0116669i
$970$		0			0
$971$	−28.5680	+	28.5680i	−0.916790	+	0.916790i	−0.996795	−	0.0800042i	$-0.974507\pi$
$971$	−28.5680	+	28.5680i	−0.916790	+	0.916790i	0.0800042	+	0.996795i	$0.474507\pi$
$972$		0			0
$973$	−10.8171	−	10.8171i	−0.346781	−	0.346781i
$974$		0			0
$975$	−1.58208			−0.0506670
$976$		0			0
$977$	16.4828			0.527331			0.263666	−	0.964614i	$-0.415068\pi$
$977$	16.4828			0.527331			0.263666	+	0.964614i	$0.415068\pi$
$978$		0			0
$979$	1.10994	+	1.10994i	0.0354739	+	0.0354739i
$980$		0			0
$981$	0.833805	−	0.833805i	0.0266213	−	0.0266213i
$982$		0			0
$983$		−	33.4039i		−	1.06542i	−0.846298	−	0.532710i	$-0.821174\pi$
$983$		−	33.4039i		−	1.06542i	0.846298	−	0.532710i	$-0.178826\pi$
$984$		0			0
$985$			3.27683i			0.104408i
$986$		0			0
$987$	−3.18416	+	3.18416i	−0.101353	+	0.101353i
$988$		0			0
$989$	22.0126	+	22.0126i	0.699960	+	0.699960i
$990$		0			0
$991$	−25.3648			−0.805740			−0.402870	−	0.915257i	$-0.631987\pi$
$991$	−25.3648			−0.805740			−0.402870	+	0.915257i	$0.631987\pi$
$992$		0			0
$993$	0.986318			0.0312998
$994$		0			0
$995$	5.73423	+	5.73423i	0.181787	+	0.181787i
$996$		0			0
$997$	11.1405	−	11.1405i	0.352824	−	0.352824i	−0.508336	−	0.861159i	$-0.669739\pi$
$997$	11.1405	−	11.1405i	0.352824	−	0.352824i	0.861159	+	0.508336i	$0.169739\pi$
$998$		0			0
$999$		−	7.72206i		−	0.244315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1792.2.m.e.1345.5	yes	16
4.3	odd	2		1792.2.m.g.1345.4	yes	16
8.3	odd	2		1792.2.m.f.1345.5	yes	16
8.5	even	2		1792.2.m.h.1345.4	yes	16
16.3	odd	4		1792.2.m.f.449.5	yes	16
16.5	even	4	inner	1792.2.m.e.449.5	✓	16
16.11	odd	4		1792.2.m.g.449.4	yes	16
16.13	even	4		1792.2.m.h.449.4	yes	16
32.5	even	8		7168.2.a.bb.1.4		8
32.11	odd	8		7168.2.a.be.1.4		8
32.21	even	8		7168.2.a.bf.1.5		8
32.27	odd	8		7168.2.a.ba.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1792.2.m.e.449.5	✓	16	16.5	even	4	inner
1792.2.m.e.1345.5	yes	16	1.1	even	1	trivial
1792.2.m.f.449.5	yes	16	16.3	odd	4
1792.2.m.f.1345.5	yes	16	8.3	odd	2
1792.2.m.g.449.4	yes	16	16.11	odd	4
1792.2.m.g.1345.4	yes	16	4.3	odd	2
1792.2.m.h.449.4	yes	16	16.13	even	4
1792.2.m.h.1345.4	yes	16	8.5	even	2
7168.2.a.ba.1.5		8	32.27	odd	8
7168.2.a.bb.1.4		8	32.5	even	8
7168.2.a.be.1.4		8	32.11	odd	8
7168.2.a.bf.1.5		8	32.21	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)

\(f(q)\)	\(=\)	\(q+(0.328027 + 0.328027i) q^{3} +(1.40197 - 1.40197i) q^{5} -1.00000i q^{7} -2.78480i q^{9} +O(q^{10})\)	\(q+(0.328027 + 0.328027i) q^{3} +(1.40197 - 1.40197i) q^{5} -1.00000i q^{7} -2.78480i q^{9} +(0.444087 - 0.444087i) q^{11} +(2.25590 + 2.25590i) q^{13} +0.919765 q^{15} +4.85578 q^{17} +(-0.114004 - 0.114004i) q^{19} +(0.328027 - 0.328027i) q^{21} +3.20529i q^{23} +1.06898i q^{25} +(1.89757 - 1.89757i) q^{27} +(-0.997091 - 0.997091i) q^{29} -5.34435 q^{31} +0.291345 q^{33} +(-1.40197 - 1.40197i) q^{35} +(2.03472 - 2.03472i) q^{37} +1.47999i q^{39} -9.57673i q^{41} +(6.86758 - 6.86758i) q^{43} +(-3.90419 - 3.90419i) q^{45} -9.70703 q^{47} -1.00000 q^{49} +(1.59282 + 1.59282i) q^{51} +(7.64426 - 7.64426i) q^{53} -1.24519i q^{55} -0.0747927i q^{57} +(1.50266 - 1.50266i) q^{59} +(-1.74157 - 1.74157i) q^{61} -2.78480 q^{63} +6.32541 q^{65} +(8.96491 + 8.96491i) q^{67} +(-1.05142 + 1.05142i) q^{69} -7.18356i q^{71} -9.04029i q^{73} +(-0.350652 + 0.350652i) q^{75} +(-0.444087 - 0.444087i) q^{77} -9.58806 q^{79} -7.10949 q^{81} +(5.30245 + 5.30245i) q^{83} +(6.80764 - 6.80764i) q^{85} -0.654145i q^{87} +2.49938i q^{89} +(2.25590 - 2.25590i) q^{91} +(-1.75309 - 1.75309i) q^{93} -0.319660 q^{95} +5.89073 q^{97} +(-1.23669 - 1.23669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} - 4 q^{5}+O(q^{10}) \) 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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Database

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