LMFDB - Embedded newform 1148.2.k.b.729.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(337,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1148.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.k (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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			729.7
Character	$\chi$	$=$	1148.729
Dual form			1148.2.k.b.337.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.796852 + 0.796852i) q^{3} +1.53973i q^{5} +(0.707107 - 0.707107i) q^{7} +1.73005i q^{9} +O(q^{10})$	\(q+(-0.796852 + 0.796852i) q^{3} +1.53973i q^{5} +(0.707107 - 0.707107i) q^{7} +1.73005i q^{9} +(2.10815 - 2.10815i) q^{11} +(3.47617 - 3.47617i) q^{13} +(-1.22694 - 1.22694i) q^{15} +(1.03340 + 1.03340i) q^{17} +(2.78503 + 2.78503i) q^{19} +1.12692i q^{21} -4.78666 q^{23} +2.62923 q^{25} +(-3.76915 - 3.76915i) q^{27} +(1.87396 - 1.87396i) q^{29} +1.64355 q^{31} +3.35977i q^{33} +(1.08875 + 1.08875i) q^{35} +7.76973 q^{37} +5.53999i q^{39} +(-5.27426 + 3.63073i) q^{41} +7.65515i q^{43} -2.66381 q^{45} +(6.34706 + 6.34706i) q^{47} -1.00000i q^{49} -1.64693 q^{51} +(-3.97278 + 3.97278i) q^{53} +(3.24598 + 3.24598i) q^{55} -4.43852 q^{57} -4.91766 q^{59} +14.5639i q^{61} +(1.22333 + 1.22333i) q^{63} +(5.35237 + 5.35237i) q^{65} +(-11.3876 - 11.3876i) q^{67} +(3.81426 - 3.81426i) q^{69} +(6.65860 - 6.65860i) q^{71} +12.2332i q^{73} +(-2.09511 + 2.09511i) q^{75} -2.98137i q^{77} +(2.18320 - 2.18320i) q^{79} +0.816762 q^{81} +10.0315 q^{83} +(-1.59115 + 1.59115i) q^{85} +2.98653i q^{87} +(11.2796 - 11.2796i) q^{89} -4.91605i q^{91} +(-1.30967 + 1.30967i) q^{93} +(-4.28820 + 4.28820i) q^{95} +(12.3703 + 12.3703i) q^{97} +(3.64721 + 3.64721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) $ 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.796852	+	0.796852i	−0.460063	+	0.460063i	−0.898676	−	0.438613i	$-0.855470\pi$
$3$	−0.796852	+	0.796852i	−0.460063	+	0.460063i	0.438613	+	0.898676i	$0.355470\pi$
$4$		0			0
$5$			1.53973i			0.688588i	0.938862	+	0.344294i	$0.111882\pi$
$5$			1.53973i			0.688588i	−0.938862	+	0.344294i	$0.888118\pi$
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$		0			0
$9$			1.73005i			0.576684i
$10$		0			0
$11$	2.10815	−	2.10815i	0.635630	−	0.635630i	−0.313844	−	0.949475i	$-0.601617\pi$
$11$	2.10815	−	2.10815i	0.635630	−	0.635630i	0.949475	+	0.313844i	$0.101617\pi$
$12$		0			0
$13$	3.47617	−	3.47617i	0.964117	−	0.964117i	−0.0352612	−	0.999378i	$-0.511226\pi$
$13$	3.47617	−	3.47617i	0.964117	−	0.964117i	0.999378	+	0.0352612i	$0.0112263\pi$
$14$		0			0
$15$	−1.22694	−	1.22694i	−0.316794	−	0.316794i
$16$		0			0
$17$	1.03340	+	1.03340i	0.250635	+	0.250635i	0.821231	−	0.570596i	$-0.193288\pi$
$17$	1.03340	+	1.03340i	0.250635	+	0.250635i	−0.570596	+	0.821231i	$0.693288\pi$
$18$		0			0
$19$	2.78503	+	2.78503i	0.638930	+	0.638930i	0.950292	−	0.311361i	$-0.100785\pi$
$19$	2.78503	+	2.78503i	0.638930	+	0.638930i	−0.311361	+	0.950292i	$0.600785\pi$
$20$		0			0
$21$			1.12692i			0.245914i
$22$		0			0
$23$	−4.78666			−0.998087			−0.499043	−	0.866577i	$-0.666315\pi$
$23$	−4.78666			−0.998087			−0.499043	+	0.866577i	$0.666315\pi$
$24$		0			0
$25$	2.62923			0.525846
$26$		0			0
$27$	−3.76915	−	3.76915i	−0.725374	−	0.725374i
$28$		0			0
$29$	1.87396	−	1.87396i	0.347985	−	0.347985i	−0.511374	−	0.859358i	$-0.670863\pi$
$29$	1.87396	−	1.87396i	0.347985	−	0.347985i	0.859358	+	0.511374i	$0.170863\pi$
$30$		0			0
$31$	1.64355			0.295190			0.147595	−	0.989048i	$-0.452847\pi$
$31$	1.64355			0.295190			0.147595	+	0.989048i	$0.452847\pi$
$32$		0			0
$33$			3.35977i			0.584860i
$34$		0			0
$35$	1.08875	+	1.08875i	0.184033	+	0.184033i
$36$		0			0
$37$	7.76973			1.27734			0.638668	−	0.769483i	$-0.279486\pi$
$37$	7.76973			1.27734			0.638668	+	0.769483i	$0.279486\pi$
$38$		0			0
$39$			5.53999i			0.887109i
$40$		0			0
$41$	−5.27426	+	3.63073i	−0.823701	+	0.567025i
$41$	−5.27426	+	3.63073i	−0.823701	+	0.567025i
$42$		0			0
$43$			7.65515i			1.16740i	0.811970	+	0.583700i	$0.198396\pi$
$43$			7.65515i			1.16740i	−0.811970	+	0.583700i	$0.801604\pi$
$44$		0			0
$45$	−2.66381			−0.397098
$46$		0			0
$47$	6.34706	+	6.34706i	0.925813	+	0.925813i	0.997432	−	0.0716188i	$-0.0228165\pi$
$47$	6.34706	+	6.34706i	0.925813	+	0.925813i	−0.0716188	+	0.997432i	$0.522817\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−1.64693			−0.230616
$52$		0			0
$53$	−3.97278	+	3.97278i	−0.545704	+	0.545704i	−0.925195	−	0.379492i	$-0.876099\pi$
$53$	−3.97278	+	3.97278i	−0.545704	+	0.545704i	0.379492	+	0.925195i	$0.376099\pi$
$54$		0			0
$55$	3.24598	+	3.24598i	0.437688	+	0.437688i
$56$		0			0
$57$	−4.43852			−0.587896
$58$		0			0
$59$	−4.91766			−0.640225			−0.320113	−	0.947379i	$-0.603721\pi$
$59$	−4.91766			−0.640225			−0.320113	+	0.947379i	$0.603721\pi$
$60$		0			0
$61$			14.5639i			1.86472i	0.361529	+	0.932361i	$0.382255\pi$
$61$			14.5639i			1.86472i	−0.361529	+	0.932361i	$0.617745\pi$
$62$		0			0
$63$	1.22333	+	1.22333i	0.154125	+	0.154125i
$64$		0			0
$65$	5.35237	+	5.35237i	0.663879	+	0.663879i
$66$		0			0
$67$	−11.3876	−	11.3876i	−1.39122	−	1.39122i	−0.822600	−	0.568621i	$-0.807477\pi$
$67$	−11.3876	−	11.3876i	−1.39122	−	1.39122i	−0.568621	−	0.822600i	$-0.692523\pi$
$68$		0			0
$69$	3.81426	−	3.81426i	0.459183	−	0.459183i
$70$		0			0
$71$	6.65860	−	6.65860i	0.790231	−	0.790231i	−0.191301	−	0.981531i	$-0.561271\pi$
$71$	6.65860	−	6.65860i	0.790231	−	0.790231i	0.981531	+	0.191301i	$0.0612706\pi$
$72$		0			0
$73$			12.2332i			1.43178i	0.698212	+	0.715891i	$0.253979\pi$
$73$			12.2332i			1.43178i	−0.698212	+	0.715891i	$0.746021\pi$
$74$		0			0
$75$	−2.09511	+	2.09511i	−0.241922	+	0.241922i
$76$		0			0
$77$		−	2.98137i		−	0.339759i
$78$		0			0
$79$	2.18320	−	2.18320i	0.245629	−	0.245629i	−0.573545	−	0.819174i	$-0.694432\pi$
$79$	2.18320	−	2.18320i	0.245629	−	0.245629i	0.819174	+	0.573545i	$0.194432\pi$
$80$		0			0
$81$	0.816762			0.0907513
$82$		0			0
$83$	10.0315			1.10110			0.550551	−	0.834801i	$-0.314418\pi$
$83$	10.0315			1.10110			0.550551	+	0.834801i	$0.314418\pi$
$84$		0			0
$85$	−1.59115	+	1.59115i	−0.172585	+	0.172585i
$86$		0			0
$87$			2.98653i			0.320190i
$88$		0			0
$89$	11.2796	−	11.2796i	1.19564	−	1.19564i	0.220178	−	0.975460i	$-0.429336\pi$
$89$	11.2796	−	11.2796i	1.19564	−	1.19564i	0.975460	−	0.220178i	$-0.0706638\pi$
$90$		0			0
$91$		−	4.91605i		−	0.515342i
$92$		0			0
$93$	−1.30967	+	1.30967i	−0.135806	+	0.135806i
$94$		0			0
$95$	−4.28820	+	4.28820i	−0.439960	+	0.439960i
$96$		0			0
$97$	12.3703	+	12.3703i	1.25601	+	1.25601i	0.952981	+	0.303031i	$0.0979987\pi$
$97$	12.3703	+	12.3703i	1.25601	+	1.25601i	0.303031	+	0.952981i	$0.402001\pi$
$98$		0			0
$99$	3.64721	+	3.64721i	0.366558	+	0.366558i
$100$		0			0
$101$	2.57688	+	2.57688i	0.256409	+	0.256409i	0.823592	−	0.567183i	$-0.191967\pi$
$101$	2.57688	+	2.57688i	0.256409	+	0.256409i	−0.567183	+	0.823592i	$0.691967\pi$
$102$		0			0
$103$		−	16.2949i		−	1.60558i	−0.596259	−	0.802792i	$-0.703347\pi$
$103$		−	16.2949i		−	1.60558i	0.596259	−	0.802792i	$-0.296653\pi$
$104$		0			0
$105$	−1.73515			−0.169333
$106$		0			0
$107$	−12.2066			−1.18005			−0.590027	−	0.807383i	$-0.700883\pi$
$107$	−12.2066			−1.18005			−0.590027	+	0.807383i	$0.700883\pi$
$108$		0			0
$109$	9.78183	+	9.78183i	0.936930	+	0.936930i	0.998126	−	0.0611962i	$-0.0194915\pi$
$109$	9.78183	+	9.78183i	0.936930	+	0.936930i	−0.0611962	+	0.998126i	$0.519492\pi$
$110$		0			0
$111$	−6.19133	+	6.19133i	−0.587655	+	0.587655i
$112$		0			0
$113$	−17.7307			−1.66796			−0.833982	−	0.551791i	$-0.813945\pi$
$113$	−17.7307			−1.66796			−0.833982	+	0.551791i	$0.813945\pi$
$114$		0			0
$115$		−	7.37016i		−	0.687271i
$116$		0			0
$117$	6.01396	+	6.01396i	0.555991	+	0.555991i
$118$		0			0
$119$	1.46144			0.133970
$120$		0			0
$121$			2.11143i			0.191948i
$122$		0			0
$123$	1.30965	−	7.09596i	0.118087	−	0.639821i
$124$		0			0
$125$			11.7470i			1.05068i
$126$		0			0
$127$	−13.5312			−1.20070			−0.600349	−	0.799738i	$-0.704972\pi$
$127$	−13.5312			−1.20070			−0.600349	+	0.799738i	$0.704972\pi$
$128$		0			0
$129$	−6.10003	−	6.10003i	−0.537077	−	0.537077i
$130$		0			0
$131$			10.5159i			0.918783i	0.888234	+	0.459391i	$0.151932\pi$
$131$			10.5159i			0.918783i	−0.888234	+	0.459391i	$0.848068\pi$
$132$		0			0
$133$	3.93863			0.341523
$134$		0			0
$135$	5.80348	−	5.80348i	0.499484	−	0.499484i
$136$		0			0
$137$	−13.2794	−	13.2794i	−1.13454	−	1.13454i	−0.989413	−	0.145126i	$-0.953641\pi$
$137$	−13.2794	−	13.2794i	−1.13454	−	1.13454i	−0.145126	−	0.989413i	$-0.546359\pi$
$138$		0			0
$139$	13.0822			1.10962			0.554811	−	0.831977i	$-0.312791\pi$
$139$	13.0822			1.10962			0.554811	+	0.831977i	$0.312791\pi$
$140$		0			0
$141$	−10.1153			−0.851865
$142$		0			0
$143$		−	14.6566i		−	1.22564i
$144$		0			0
$145$	2.88538	+	2.88538i	0.239618	+	0.239618i
$146$		0			0
$147$	0.796852	+	0.796852i	0.0657233	+	0.0657233i
$148$		0			0
$149$	0.00680408	+	0.00680408i	0.000557412	+	0.000557412i	0.707385	−	0.706828i	$-0.249875\pi$
$149$	0.00680408	+	0.00680408i	0.000557412	+	0.000557412i	−0.706828	+	0.707385i	$0.749875\pi$
$150$		0			0
$151$	5.60095	−	5.60095i	0.455799	−	0.455799i	−0.441475	−	0.897274i	$-0.645544\pi$
$151$	5.60095	−	5.60095i	0.455799	−	0.455799i	0.897274	+	0.441475i	$0.145544\pi$
$152$		0			0
$153$	−1.78783	+	1.78783i	−0.144537	+	0.144537i
$154$		0			0
$155$			2.53062i			0.203265i
$156$		0			0
$157$	−3.88536	+	3.88536i	−0.310085	+	0.310085i	−0.844942	−	0.534857i	$-0.820365\pi$
$157$	−3.88536	+	3.88536i	−0.310085	+	0.310085i	0.534857	+	0.844942i	$0.320365\pi$
$158$		0			0
$159$		−	6.33144i		−	0.502116i
$160$		0			0
$161$	−3.38468	+	3.38468i	−0.266750	+	0.266750i
$162$		0			0
$163$	12.6693			0.992338			0.496169	−	0.868226i	$-0.334740\pi$
$163$	12.6693			0.992338			0.496169	+	0.868226i	$0.334740\pi$
$164$		0			0
$165$	−5.17313			−0.402728
$166$		0			0
$167$	15.0232	−	15.0232i	1.16253	−	1.16253i	0.178611	−	0.983920i	$-0.442840\pi$
$167$	15.0232	−	15.0232i	1.16253	−	1.16253i	0.983920	−	0.178611i	$-0.0571603\pi$
$168$		0			0
$169$		−	11.1676i		−	0.859043i
$170$		0			0
$171$	−4.81825	+	4.81825i	−0.368461	+	0.368461i
$172$		0			0
$173$			11.8997i			0.904715i	0.891837	+	0.452357i	$0.149417\pi$
$173$			11.8997i			0.904715i	−0.891837	+	0.452357i	$0.850583\pi$
$174$		0			0
$175$	1.85915	−	1.85915i	0.140538	−	0.140538i
$176$		0			0
$177$	3.91865	−	3.91865i	0.294544	−	0.294544i
$178$		0			0
$179$	−1.37511	−	1.37511i	−0.102781	−	0.102781i	0.653846	−	0.756627i	$-0.273154\pi$
$179$	−1.37511	−	1.37511i	−0.102781	−	0.102781i	−0.756627	+	0.653846i	$0.773154\pi$
$180$		0			0
$181$	−2.45197	−	2.45197i	−0.182254	−	0.182254i	0.610083	−	0.792337i	$-0.291136\pi$
$181$	−2.45197	−	2.45197i	−0.182254	−	0.182254i	−0.792337	+	0.610083i	$0.791136\pi$
$182$		0			0
$183$	−11.6053	−	11.6053i	−0.857889	−	0.857889i
$184$		0			0
$185$			11.9633i			0.879558i
$186$		0			0
$187$	4.35710			0.318623
$188$		0			0
$189$	−5.33039			−0.387729
$190$		0			0
$191$	2.90384	+	2.90384i	0.210114	+	0.210114i	0.804316	−	0.594202i	$-0.202532\pi$
$191$	2.90384	+	2.90384i	0.210114	+	0.210114i	−0.594202	+	0.804316i	$0.702532\pi$
$192$		0			0
$193$	15.8483	−	15.8483i	1.14079	−	1.14079i	0.152482	−	0.988306i	$-0.451273\pi$
$193$	15.8483	−	15.8483i	1.14079	−	1.14079i	0.988306	−	0.152482i	$-0.0487267\pi$
$194$		0			0
$195$	−8.53009			−0.610853
$196$		0			0
$197$		−	22.1165i		−	1.57574i	−0.615842	−	0.787869i	$-0.711184\pi$
$197$		−	22.1165i		−	1.57574i	0.615842	−	0.787869i	$-0.288816\pi$
$198$		0			0
$199$	−19.5789	−	19.5789i	−1.38791	−	1.38791i	−0.829702	−	0.558207i	$-0.811490\pi$
$199$	−19.5789	−	19.5789i	−1.38791	−	1.38791i	−0.558207	−	0.829702i	$-0.688510\pi$
$200$		0			0
$201$	18.1485			1.28010
$202$		0			0
$203$		−	2.65017i		−	0.186006i
$204$		0			0
$205$	−5.59035	−	8.12093i	−0.390447	−	0.567190i
$206$		0			0
$207$		−	8.28117i		−	0.575581i
$208$		0			0
$209$	11.7425			0.812247
$210$		0			0
$211$	2.45388	+	2.45388i	0.168932	+	0.168932i	0.786510	−	0.617578i	$-0.211886\pi$
$211$	2.45388	+	2.45388i	0.168932	+	0.168932i	−0.617578	+	0.786510i	$0.711886\pi$
$212$		0			0
$213$			10.6118i			0.727112i
$214$		0			0
$215$	−11.7869			−0.803857
$216$		0			0
$217$	1.16217	−	1.16217i	0.0788930	−	0.0788930i
$218$		0			0
$219$	−9.74802	−	9.74802i	−0.658710	−	0.658710i
$220$		0			0
$221$	7.18453			0.483284
$222$		0			0
$223$	−21.3444			−1.42933			−0.714664	−	0.699468i	$-0.753420\pi$
$223$	−21.3444			−1.42933			−0.714664	+	0.699468i	$0.753420\pi$
$224$		0			0
$225$			4.54871i			0.303247i
$226$		0			0
$227$	−15.4739	−	15.4739i	−1.02704	−	1.02704i	−0.999624	−	0.0274179i	$-0.991272\pi$
$227$	−15.4739	−	15.4739i	−1.02704	−	1.02704i	−0.0274179	−	0.999624i	$-0.508728\pi$
$228$		0			0
$229$	−8.90215	−	8.90215i	−0.588271	−	0.588271i	0.348892	−	0.937163i	$-0.386558\pi$
$229$	−8.90215	−	8.90215i	−0.588271	−	0.588271i	−0.937163	+	0.348892i	$0.886558\pi$
$230$		0			0
$231$	2.37571	+	2.37571i	0.156310	+	0.156310i
$232$		0			0
$233$	−11.4969	+	11.4969i	−0.753187	+	0.753187i	−0.975073	−	0.221886i	$-0.928779\pi$
$233$	−11.4969	+	11.4969i	−0.753187	+	0.753187i	0.221886	+	0.975073i	$0.428779\pi$
$234$		0			0
$235$	−9.77275	+	9.77275i	−0.637504	+	0.637504i
$236$		0			0
$237$			3.47937i			0.226010i
$238$		0			0
$239$	−12.4710	+	12.4710i	−0.806683	+	0.806683i	−0.984130	−	0.177447i	$-0.943216\pi$
$239$	−12.4710	+	12.4710i	−0.806683	+	0.806683i	0.177447	+	0.984130i	$0.443216\pi$
$240$		0			0
$241$		−	20.6633i		−	1.33104i	−0.746380	−	0.665519i	$-0.768210\pi$
$241$		−	20.6633i		−	1.33104i	0.746380	−	0.665519i	$-0.231790\pi$
$242$		0			0
$243$	10.6566	−	10.6566i	0.683623	−	0.683623i
$244$		0			0
$245$	1.53973			0.0983697
$246$		0			0
$247$	19.3625			1.23201
$248$		0			0
$249$	−7.99364	+	7.99364i	−0.506576	+	0.506576i
$250$		0			0
$251$			5.19670i			0.328013i	0.986459	+	0.164006i	$0.0524417\pi$
$251$			5.19670i			0.328013i	−0.986459	+	0.164006i	$0.947558\pi$
$252$		0			0
$253$	−10.0910	+	10.0910i	−0.634414	+	0.634414i
$254$		0			0
$255$		−	2.53582i		−	0.158800i
$256$		0			0
$257$	9.69943	−	9.69943i	0.605034	−	0.605034i	−0.336610	−	0.941644i	$-0.609280\pi$
$257$	9.69943	−	9.69943i	0.605034	−	0.605034i	0.941644	+	0.336610i	$0.109280\pi$
$258$		0			0
$259$	5.49403	−	5.49403i	0.341382	−	0.341382i
$260$		0			0
$261$	3.24204	+	3.24204i	0.200677	+	0.200677i
$262$		0			0
$263$	−12.8975	−	12.8975i	−0.795291	−	0.795291i	0.187058	−	0.982349i	$-0.440105\pi$
$263$	−12.8975	−	12.8975i	−0.795291	−	0.795291i	−0.982349	+	0.187058i	$0.940105\pi$
$264$		0			0
$265$	−6.11701	−	6.11701i	−0.375765	−	0.375765i
$266$		0			0
$267$			17.9764i			1.10014i
$268$		0			0
$269$	−21.5268			−1.31252			−0.656258	−	0.754537i	$-0.727862\pi$
$269$	−21.5268			−1.31252			−0.656258	+	0.754537i	$0.727862\pi$
$270$		0			0
$271$	10.0928			0.613094			0.306547	−	0.951856i	$-0.400826\pi$
$271$	10.0928			0.613094			0.306547	+	0.951856i	$0.400826\pi$
$272$		0			0
$273$	3.91737	+	3.91737i	0.237090	+	0.237090i
$274$		0			0
$275$	5.54281	−	5.54281i	0.334244	−	0.334244i
$276$		0			0
$277$	19.5376			1.17390			0.586951	−	0.809623i	$-0.300328\pi$
$277$	19.5376			1.17390			0.586951	+	0.809623i	$0.300328\pi$
$278$		0			0
$279$			2.84343i			0.170232i
$280$		0			0
$281$	−14.3739	−	14.3739i	−0.857473	−	0.857473i	0.133567	−	0.991040i	$-0.457357\pi$
$281$	−14.3739	−	14.3739i	−0.857473	−	0.857473i	−0.991040	+	0.133567i	$0.957357\pi$
$282$		0			0
$283$	10.7230			0.637415			0.318707	−	0.947853i	$-0.396751\pi$
$283$	10.7230			0.637415			0.318707	+	0.947853i	$0.396751\pi$
$284$		0			0
$285$		−	6.83412i		−	0.404818i
$286$		0			0
$287$	−1.16215	+	6.29678i	−0.0685994	+	0.371687i
$288$		0			0
$289$		−	14.8642i		−	0.874364i
$290$		0			0
$291$	−19.7146			−1.15569
$292$		0			0
$293$	8.30625	+	8.30625i	0.485256	+	0.485256i	0.906805	−	0.421549i	$-0.138514\pi$
$293$	8.30625	+	8.30625i	0.485256	+	0.485256i	−0.421549	+	0.906805i	$0.638514\pi$
$294$		0			0
$295$		−	7.57187i		−	0.440851i
$296$		0			0
$297$	−15.8919			−0.922140
$298$		0			0
$299$	−16.6392	+	16.6392i	−0.962272	+	0.962272i
$300$		0			0
$301$	5.41301	+	5.41301i	0.312001	+	0.312001i
$302$		0			0
$303$	−4.10678			−0.235929
$304$		0			0
$305$	−22.4245			−1.28403
$306$		0			0
$307$			0.278293i			0.0158830i	0.999968	+	0.00794151i	$0.00252789\pi$
$307$			0.278293i			0.0158830i	−0.999968	+	0.00794151i	$0.997472\pi$
$308$		0			0
$309$	12.9846	+	12.9846i	0.738670	+	0.738670i
$310$		0			0
$311$	19.3892	+	19.3892i	1.09946	+	1.09946i	0.994473	+	0.104989i	$0.0334807\pi$
$311$	19.3892	+	19.3892i	1.09946	+	1.09946i	0.104989	+	0.994473i	$0.466519\pi$
$312$		0			0
$313$	13.2824	+	13.2824i	0.750767	+	0.750767i	0.974622	−	0.223855i	$-0.0718644\pi$
$313$	13.2824	+	13.2824i	0.750767	+	0.750767i	−0.223855	+	0.974622i	$0.571864\pi$
$314$		0			0
$315$	−1.88360	+	1.88360i	−0.106129	+	0.106129i
$316$		0			0
$317$	1.98498	−	1.98498i	0.111487	−	0.111487i	−0.649162	−	0.760650i	$-0.724880\pi$
$317$	1.98498	−	1.98498i	0.111487	−	0.111487i	0.760650	+	0.649162i	$0.224880\pi$
$318$		0			0
$319$		−	7.90115i		−	0.442379i
$320$		0			0
$321$	9.72684	−	9.72684i	0.542900	−	0.542900i
$322$		0			0
$323$			5.75608i			0.320277i
$324$		0			0
$325$	9.13967	−	9.13967i	0.506977	−	0.506977i
$326$		0			0
$327$	−15.5894			−0.862093
$328$		0			0
$329$	8.97609			0.494868
$330$		0			0
$331$	−6.37823	+	6.37823i	−0.350579	+	0.350579i	−0.860325	−	0.509746i	$-0.829739\pi$
$331$	−6.37823	+	6.37823i	−0.350579	+	0.350579i	0.509746	+	0.860325i	$0.329739\pi$
$332$		0			0
$333$			13.4420i			0.736619i
$334$		0			0
$335$	17.5339	−	17.5339i	0.957978	−	0.957978i
$336$		0			0
$337$		−	29.4522i		−	1.60437i	−0.597079	−	0.802183i	$-0.703672\pi$
$337$		−	29.4522i		−	1.60437i	0.597079	−	0.802183i	$-0.296328\pi$
$338$		0			0
$339$	14.1288	−	14.1288i	0.767369	−	0.767369i
$340$		0			0
$341$	3.46485	−	3.46485i	0.187632	−	0.187632i
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$		0			0
$345$	5.87293	+	5.87293i	0.316188	+	0.316188i
$346$		0			0
$347$	−11.1930	−	11.1930i	−0.600871	−	0.600871i	0.339673	−	0.940544i	$-0.389684\pi$
$347$	−11.1930	−	11.1930i	−0.600871	−	0.600871i	−0.940544	+	0.339673i	$0.889684\pi$
$348$		0			0
$349$			4.72869i			0.253121i	0.991959	+	0.126560i	$0.0403938\pi$
$349$			4.72869i			0.253121i	−0.991959	+	0.126560i	$0.959606\pi$
$350$		0			0
$351$	−26.2045			−1.39869
$352$		0			0
$353$	1.62589			0.0865376			0.0432688	−	0.999063i	$-0.486223\pi$
$353$	1.62589			0.0865376			0.0432688	+	0.999063i	$0.486223\pi$
$354$		0			0
$355$	10.2524	+	10.2524i	0.544143	+	0.544143i
$356$		0			0
$357$	−1.16455	+	1.16455i	−0.0616348	+	0.0616348i
$358$		0			0
$359$	20.1493			1.06344			0.531720	−	0.846920i	$-0.321546\pi$
$359$	20.1493			1.06344			0.531720	+	0.846920i	$0.321546\pi$
$360$		0			0
$361$		−	3.48718i		−	0.183536i
$362$		0			0
$363$	−1.68250	−	1.68250i	−0.0883081	−	0.0883081i
$364$		0			0
$365$	−18.8358			−0.985908
$366$		0			0
$367$		−	12.5103i		−	0.653031i	−0.945192	−	0.326515i	$-0.894126\pi$
$367$		−	12.5103i		−	0.653031i	0.945192	−	0.326515i	$-0.105874\pi$
$368$		0			0
$369$	−6.28136	−	9.12474i	−0.326994	−	0.475015i
$370$		0			0
$371$			5.61836i			0.291691i
$372$		0			0
$373$	15.4653			0.800762			0.400381	−	0.916349i	$-0.368878\pi$
$373$	15.4653			0.800762			0.400381	+	0.916349i	$0.368878\pi$
$374$		0			0
$375$	−9.36059	−	9.36059i	−0.483379	−	0.483379i
$376$		0			0
$377$		−	13.0284i		−	0.670996i
$378$		0			0
$379$	−14.2443			−0.731683			−0.365841	−	0.930677i	$-0.619219\pi$
$379$	−14.2443			−0.731683			−0.365841	+	0.930677i	$0.619219\pi$
$380$		0			0
$381$	10.7824	−	10.7824i	0.552397	−	0.552397i
$382$		0			0
$383$	9.84275	+	9.84275i	0.502941	+	0.502941i	0.912351	−	0.409409i	$-0.134265\pi$
$383$	9.84275	+	9.84275i	0.502941	+	0.502941i	−0.409409	+	0.912351i	$0.634265\pi$
$384$		0			0
$385$	4.59051			0.233954
$386$		0			0
$387$	−13.2438			−0.673221
$388$		0			0
$389$			28.6675i			1.45350i	0.686903	+	0.726749i	$0.258970\pi$
$389$			28.6675i			1.45350i	−0.686903	+	0.726749i	$0.741030\pi$
$390$		0			0
$391$	−4.94651	−	4.94651i	−0.250156	−	0.250156i
$392$		0			0
$393$	−8.37966	−	8.37966i	−0.422698	−	0.422698i
$394$		0			0
$395$	3.36153	+	3.36153i	0.169137	+	0.169137i
$396$		0			0
$397$	9.40102	−	9.40102i	0.471824	−	0.471824i	−0.430681	−	0.902504i	$-0.641727\pi$
$397$	9.40102	−	9.40102i	0.471824	−	0.471824i	0.902504	+	0.430681i	$0.141727\pi$
$398$		0			0
$399$	−3.13851	+	3.13851i	−0.157122	+	0.157122i
$400$		0			0
$401$		−	20.9770i		−	1.04754i	−0.851859	−	0.523771i	$-0.824525\pi$
$401$		−	20.9770i		−	1.04754i	0.851859	−	0.523771i	$-0.175475\pi$
$402$		0			0
$403$	5.71327	−	5.71327i	0.284598	−	0.284598i
$404$		0			0
$405$			1.25759i			0.0624903i
$406$		0			0
$407$	16.3797	−	16.3797i	0.811913	−	0.811913i
$408$		0			0
$409$	−5.84520			−0.289027			−0.144513	−	0.989503i	$-0.546162\pi$
$409$	−5.84520			−0.289027			−0.144513	+	0.989503i	$0.546162\pi$
$410$		0			0
$411$	21.1635			1.04392
$412$		0			0
$413$	−3.47731	+	3.47731i	−0.171107	+	0.171107i
$414$		0			0
$415$			15.4458i			0.758206i
$416$		0			0
$417$	−10.4246	+	10.4246i	−0.510496	+	0.510496i
$418$		0			0
$419$			9.78788i			0.478169i	0.970999	+	0.239085i	$0.0768474\pi$
$419$			9.78788i			0.478169i	−0.970999	+	0.239085i	$0.923153\pi$
$420$		0			0
$421$	−12.5522	+	12.5522i	−0.611755	+	0.611755i	−0.943403	−	0.331648i	$-0.892395\pi$
$421$	−12.5522	+	12.5522i	−0.611755	+	0.611755i	0.331648	+	0.943403i	$0.392395\pi$
$422$		0			0
$423$	−10.9807	+	10.9807i	−0.533902	+	0.533902i
$424$		0			0
$425$	2.71704	+	2.71704i	0.131796	+	0.131796i
$426$		0			0
$427$	10.2983	+	10.2983i	0.498368	+	0.498368i
$428$		0			0
$429$	11.6791	+	11.6791i	0.563873	+	0.563873i
$430$		0			0
$431$			32.8471i			1.58219i	0.611693	+	0.791095i	$0.290489\pi$
$431$			32.8471i			1.58219i	−0.611693	+	0.791095i	$0.709511\pi$
$432$		0			0
$433$	1.16476			0.0559750			0.0279875	−	0.999608i	$-0.491090\pi$
$433$	1.16476			0.0559750			0.0279875	+	0.999608i	$0.491090\pi$
$434$		0			0
$435$	−4.59845			−0.220479
$436$		0			0
$437$	−13.3310	−	13.3310i	−0.637708	−	0.637708i
$438$		0			0
$439$	−7.71968	+	7.71968i	−0.368440	+	0.368440i	−0.866908	−	0.498468i	$-0.833896\pi$
$439$	−7.71968	+	7.71968i	−0.368440	+	0.368440i	0.498468	+	0.866908i	$0.333896\pi$
$440$		0			0
$441$	1.73005			0.0823834
$442$		0			0
$443$			4.62164i			0.219581i	0.993955	+	0.109790i	$0.0350179\pi$
$443$			4.62164i			0.219581i	−0.993955	+	0.109790i	$0.964982\pi$
$444$		0			0
$445$	17.3676	+	17.3676i	0.823302	+	0.823302i
$446$		0			0
$447$	−0.0108437			−0.000512889
$448$		0			0
$449$			15.7864i			0.745006i	0.928031	+	0.372503i	$0.121500\pi$
$449$			15.7864i			0.745006i	−0.928031	+	0.372503i	$0.878500\pi$
$450$		0			0
$451$	−3.46480	+	18.7730i	−0.163151	+	0.883988i
$452$		0			0
$453$			8.92627i			0.419393i
$454$		0			0
$455$	7.56939			0.354858
$456$		0			0
$457$	7.44056	+	7.44056i	0.348055	+	0.348055i	0.859385	−	0.511330i	$-0.170847\pi$
$457$	7.44056	+	7.44056i	0.348055	+	0.348055i	−0.511330	+	0.859385i	$0.670847\pi$
$458$		0			0
$459$		−	7.79006i		−	0.363609i
$460$		0			0
$461$	−0.885724			−0.0412523			−0.0206261	−	0.999787i	$-0.506566\pi$
$461$	−0.885724			−0.0412523			−0.0206261	+	0.999787i	$0.506566\pi$
$462$		0			0
$463$	1.58178	−	1.58178i	0.0735117	−	0.0735117i	−0.669395	−	0.742907i	$-0.733447\pi$
$463$	1.58178	−	1.58178i	0.0735117	−	0.0735117i	0.742907	+	0.669395i	$0.233447\pi$
$464$		0			0
$465$	−2.01653	−	2.01653i	−0.0935145	−	0.0935145i
$466$		0			0
$467$	−5.75929			−0.266508			−0.133254	−	0.991082i	$-0.542543\pi$
$467$	−5.75929			−0.266508			−0.133254	+	0.991082i	$0.542543\pi$
$468$		0			0
$469$	−16.1045			−0.743639
$470$		0			0
$471$		−	6.19211i		−	0.285317i
$472$		0			0
$473$	16.1382	+	16.1382i	0.742035	+	0.742035i
$474$		0			0
$475$	7.32250	+	7.32250i	0.335979	+	0.335979i
$476$		0			0
$477$	−6.87312	−	6.87312i	−0.314699	−	0.314699i
$478$		0			0
$479$	−4.64839	+	4.64839i	−0.212391	+	0.212391i	−0.805282	−	0.592892i	$-0.797986\pi$
$479$	−4.64839	+	4.64839i	−0.212391	+	0.212391i	0.592892	+	0.805282i	$0.297986\pi$
$480$		0			0
$481$	27.0089	−	27.0089i	1.23150	−	1.23150i
$482$		0			0
$483$		−	5.39418i		−	0.245444i
$484$		0			0
$485$	−19.0469	+	19.0469i	−0.864875	+	0.864875i
$486$		0			0
$487$		−	22.1042i		−	1.00164i	−0.865552	−	0.500818i	$-0.833032\pi$
$487$		−	22.1042i		−	1.00164i	0.865552	−	0.500818i	$-0.166968\pi$
$488$		0			0
$489$	−10.0956	+	10.0956i	−0.456538	+	0.456538i
$490$		0			0
$491$	−28.6325			−1.29217			−0.646084	−	0.763266i	$-0.723595\pi$
$491$	−28.6325			−1.29217			−0.646084	+	0.763266i	$0.723595\pi$
$492$		0			0
$493$	3.87308			0.174435
$494$		0			0
$495$	−5.61571	+	5.61571i	−0.252407	+	0.252407i
$496$		0			0
$497$		−	9.41669i		−	0.422396i
$498$		0			0
$499$	−3.11218	+	3.11218i	−0.139320	+	0.139320i	−0.773327	−	0.634007i	$-0.781409\pi$
$499$	−3.11218	+	3.11218i	−0.139320	+	0.139320i	0.634007	+	0.773327i	$0.281409\pi$
$500$		0			0
$501$			23.9426i			1.06967i
$502$		0			0
$503$	2.93325	−	2.93325i	0.130787	−	0.130787i	−0.638683	−	0.769470i	$-0.720520\pi$
$503$	2.93325	−	2.93325i	0.130787	−	0.130787i	0.769470	+	0.638683i	$0.220520\pi$
$504$		0			0
$505$	−3.96770	+	3.96770i	−0.176560	+	0.176560i
$506$		0			0
$507$	8.89889	+	8.89889i	0.395214	+	0.395214i
$508$		0			0
$509$	13.8828	+	13.8828i	0.615344	+	0.615344i	0.944334	−	0.328989i	$-0.106708\pi$
$509$	13.8828	+	13.8828i	0.615344	+	0.615344i	−0.328989	+	0.944334i	$0.606708\pi$
$510$		0			0
$511$	8.65015	+	8.65015i	0.382660	+	0.382660i
$512$		0			0
$513$		−	20.9944i		−	0.926927i
$514$		0			0
$515$	25.0897			1.10559
$516$		0			0
$517$	26.7611			1.17695
$518$		0			0
$519$	−9.48228	−	9.48228i	−0.416226	−	0.416226i
$520$		0			0
$521$	2.27330	−	2.27330i	0.0995951	−	0.0995951i	−0.655554	−	0.755149i	$-0.727565\pi$
$521$	2.27330	−	2.27330i	0.0995951	−	0.0995951i	0.755149	+	0.655554i	$0.227565\pi$
$522$		0			0
$523$	−4.07618			−0.178239			−0.0891195	−	0.996021i	$-0.528405\pi$
$523$	−4.07618			−0.178239			−0.0891195	+	0.996021i	$0.528405\pi$
$524$		0			0
$525$			2.96293i			0.129313i
$526$		0			0
$527$	1.69844	+	1.69844i	0.0739852	+	0.0739852i
$528$		0			0
$529$	−0.0879250			−0.00382283
$530$		0			0
$531$		−	8.50781i		−	0.369208i
$532$		0			0
$533$	−5.71318	+	30.9553i	−0.247465	+	1.34082i
$534$		0			0
$535$		−	18.7948i		−	0.812572i
$536$		0			0
$537$	2.19152			0.0945712
$538$		0			0
$539$	−2.10815	−	2.10815i	−0.0908043	−	0.0908043i
$540$		0			0
$541$			12.8281i			0.551523i	0.961226	+	0.275761i	$0.0889299\pi$
$541$			12.8281i			0.551523i	−0.961226	+	0.275761i	$0.911070\pi$
$542$		0			0
$543$	3.90772			0.167696
$544$		0			0
$545$	−15.0614	+	15.0614i	−0.645159	+	0.645159i
$546$		0			0
$547$	−30.3801	−	30.3801i	−1.29896	−	1.29896i	−0.929080	−	0.369878i	$-0.879399\pi$
$547$	−30.3801	−	30.3801i	−1.29896	−	1.29896i	−0.369878	−	0.929080i	$-0.620601\pi$
$548$		0			0
$549$	−25.1964			−1.07536
$550$		0			0
$551$	10.4381			0.444676
$552$		0			0
$553$		−	3.08751i		−	0.131294i
$554$		0			0
$555$	−9.53297	−	9.53297i	−0.404652	−	0.404652i
$556$		0			0
$557$	26.7939	+	26.7939i	1.13530	+	1.13530i	0.989283	+	0.146013i	$0.0466440\pi$
$557$	26.7939	+	26.7939i	1.13530	+	1.13530i	0.146013	+	0.989283i	$0.453356\pi$
$558$		0			0
$559$	26.6106	+	26.6106i	1.12551	+	1.12551i
$560$		0			0
$561$	−3.47197	+	3.47197i	−0.146587	+	0.146587i
$562$		0			0
$563$	−14.1972	+	14.1972i	−0.598341	+	0.598341i	−0.939871	−	0.341530i	$-0.889055\pi$
$563$	−14.1972	+	14.1972i	−0.598341	+	0.598341i	0.341530	+	0.939871i	$0.389055\pi$
$564$		0			0
$565$		−	27.3005i		−	1.14854i
$566$		0			0
$567$	0.577538	−	0.577538i	0.0242543	−	0.0242543i
$568$		0			0
$569$		−	17.2476i		−	0.723059i	−0.932361	−	0.361529i	$-0.882255\pi$
$569$		−	17.2476i		−	0.723059i	0.932361	−	0.361529i	$-0.117745\pi$
$570$		0			0
$571$	−11.2139	+	11.2139i	−0.469286	+	0.469286i	−0.901683	−	0.432397i	$-0.857668\pi$
$571$	−11.2139	+	11.2139i	−0.469286	+	0.469286i	0.432397	+	0.901683i	$0.357668\pi$
$572$		0			0
$573$	−4.62786			−0.193332
$574$		0			0
$575$	−12.5852			−0.524840
$576$		0			0
$577$	1.19548	−	1.19548i	0.0497686	−	0.0497686i	−0.681785	−	0.731553i	$-0.738796\pi$
$577$	1.19548	−	1.19548i	0.0497686	−	0.0497686i	0.731553	+	0.681785i	$0.238796\pi$
$578$		0			0
$579$			25.2576i			1.04967i
$580$		0			0
$581$	7.09336	−	7.09336i	0.294282	−	0.294282i
$582$		0			0
$583$			16.7504i			0.693732i
$584$		0			0
$585$	−9.25987	+	9.25987i	−0.382849	+	0.382849i
$586$		0			0
$587$	27.6662	−	27.6662i	1.14191	−	1.14191i	0.153807	−	0.988101i	$-0.450847\pi$
$587$	27.6662	−	27.6662i	1.14191	−	1.14191i	0.988101	−	0.153807i	$-0.0491534\pi$
$588$		0			0
$589$	4.57734	+	4.57734i	0.188606	+	0.188606i
$590$		0			0
$591$	17.6236	+	17.6236i	0.724939	+	0.724939i
$592$		0			0
$593$	−31.1669	−	31.1669i	−1.27987	−	1.27987i	−0.940738	−	0.339135i	$-0.889866\pi$
$593$	−31.1669	−	31.1669i	−1.27987	−	1.27987i	−0.339135	−	0.940738i	$-0.610134\pi$
$594$		0			0
$595$			2.25023i			0.0922503i
$596$		0			0
$597$	31.2029			1.27705
$598$		0			0
$599$	−19.5895			−0.800404			−0.400202	−	0.916427i	$-0.631060\pi$
$599$	−19.5895			−0.800404			−0.400202	+	0.916427i	$0.631060\pi$
$600$		0			0
$601$	20.2511	+	20.2511i	0.826060	+	0.826060i	0.986969	−	0.160910i	$-0.0514427\pi$
$601$	20.2511	+	20.2511i	0.826060	+	0.826060i	−0.160910	+	0.986969i	$0.551443\pi$
$602$		0			0
$603$	19.7012	−	19.7012i	0.802295	−	0.802295i
$604$		0			0
$605$	−3.25103			−0.132173
$606$		0			0
$607$		−	22.1875i		−	0.900564i	−0.892886	−	0.450282i	$-0.851323\pi$
$607$		−	22.1875i		−	0.900564i	0.892886	−	0.450282i	$-0.148677\pi$
$608$		0			0
$609$	2.11180	+	2.11180i	0.0855743	+	0.0855743i
$610$		0			0
$611$	44.1269			1.78518
$612$		0			0
$613$		−	42.4171i		−	1.71321i	−0.515972	−	0.856605i	$-0.672569\pi$
$613$		−	42.4171i		−	1.71321i	0.515972	−	0.856605i	$-0.327431\pi$
$614$		0			0
$615$	10.9259	+	2.01650i	0.440573	+	0.0813133i
$616$		0			0
$617$		−	24.3536i		−	0.980439i	−0.871599	−	0.490219i	$-0.836917\pi$
$617$		−	24.3536i		−	0.980439i	0.871599	−	0.490219i	$-0.163083\pi$
$618$		0			0
$619$	9.96324			0.400456			0.200228	−	0.979749i	$-0.435832\pi$
$619$	9.96324			0.400456			0.200228	+	0.979749i	$0.435832\pi$
$620$		0			0
$621$	18.0416	+	18.0416i	0.723986	+	0.723986i
$622$		0			0
$623$		−	15.9518i		−	0.639095i
$624$		0			0
$625$	−4.94098			−0.197639
$626$		0			0
$627$	−9.35706	+	9.35706i	−0.373685	+	0.373685i
$628$		0			0
$629$	8.02921	+	8.02921i	0.320145	+	0.320145i
$630$		0			0
$631$	47.3991			1.88693			0.943465	−	0.331472i	$-0.107545\pi$
$631$	47.3991			1.88693			0.943465	+	0.331472i	$0.107545\pi$
$632$		0			0
$633$	−3.91077			−0.155439
$634$		0			0
$635$		−	20.8344i		−	0.826787i
$636$		0			0
$637$	−3.47617	−	3.47617i	−0.137731	−	0.137731i
$638$		0			0
$639$	11.5197	+	11.5197i	0.455713	+	0.455713i
$640$		0			0
$641$	18.8876	+	18.8876i	0.746016	+	0.746016i	0.973728	−	0.227713i	$-0.0731247\pi$
$641$	18.8876	+	18.8876i	0.746016	+	0.746016i	−0.227713	+	0.973728i	$0.573125\pi$
$642$		0			0
$643$	−15.2009	+	15.2009i	−0.599464	+	0.599464i	−0.940170	−	0.340706i	$-0.889334\pi$
$643$	−15.2009	+	15.2009i	−0.599464	+	0.599464i	0.340706	+	0.940170i	$0.389334\pi$
$644$		0			0
$645$	9.39239	−	9.39239i	0.369825	−	0.369825i
$646$		0			0
$647$			19.2251i			0.755817i	0.925843	+	0.377908i	$0.123357\pi$
$647$			19.2251i			0.755817i	−0.925843	+	0.377908i	$0.876643\pi$
$648$		0			0
$649$	−10.3672	+	10.3672i	−0.406947	+	0.406947i
$650$		0			0
$651$			1.85215i			0.0725915i
$652$		0			0
$653$	−14.3416	+	14.3416i	−0.561231	+	0.561231i	−0.929657	−	0.368426i	$-0.879897\pi$
$653$	−14.3416	+	14.3416i	−0.561231	+	0.561231i	0.368426	+	0.929657i	$0.379897\pi$
$654$		0			0
$655$	−16.1917			−0.632663
$656$		0			0
$657$	−21.1640			−0.825686
$658$		0			0
$659$	−22.8346	+	22.8346i	−0.889509	+	0.889509i	−0.994476	−	0.104967i	$-0.966526\pi$
$659$	−22.8346	+	22.8346i	−0.889509	+	0.889509i	0.104967	+	0.994476i	$0.466526\pi$
$660$		0			0
$661$			10.9825i			0.427171i	0.976924	+	0.213586i	$0.0685143\pi$
$661$			10.9825i			0.427171i	−0.976924	+	0.213586i	$0.931486\pi$
$662$		0			0
$663$	−5.72501	+	5.72501i	−0.222341	+	0.222341i
$664$		0			0
$665$			6.06443i			0.235168i
$666$		0			0
$667$	−8.96998	+	8.96998i	−0.347319	+	0.347319i
$668$		0			0
$669$	17.0083	−	17.0083i	0.657581	−	0.657581i
$670$		0			0
$671$	30.7029	+	30.7029i	1.18527	+	1.18527i
$672$		0			0
$673$	−10.7203	−	10.7203i	−0.413239	−	0.413239i	0.469626	−	0.882865i	$-0.344389\pi$
$673$	−10.7203	−	10.7203i	−0.413239	−	0.413239i	−0.882865	+	0.469626i	$0.844389\pi$
$674$		0			0
$675$	−9.90998	−	9.90998i	−0.381435	−	0.381435i
$676$		0			0
$677$		−	0.0998855i		−	0.00383891i	−0.999998	−	0.00191946i	$-0.999389\pi$
$677$		−	0.0998855i		−	0.00383891i	0.999998	−	0.00191946i	$-0.000610982\pi$
$678$		0			0
$679$	17.4942			0.671367
$680$		0			0
$681$	24.6609			0.945008
$682$		0			0
$683$	−18.4954	−	18.4954i	−0.707705	−	0.707705i	0.258347	−	0.966052i	$-0.416822\pi$
$683$	−18.4954	−	18.4954i	−0.707705	−	0.707705i	−0.966052	+	0.258347i	$0.916822\pi$
$684$		0			0
$685$	20.4468	−	20.4468i	0.781230	−	0.781230i
$686$		0			0
$687$	14.1874			0.541283
$688$		0			0
$689$			27.6202i			1.05224i
$690$		0			0
$691$	4.26188	+	4.26188i	0.162129	+	0.162129i	0.783509	−	0.621380i	$-0.213428\pi$
$691$	4.26188	+	4.26188i	0.162129	+	0.162129i	−0.621380	+	0.783509i	$0.713428\pi$
$692$		0			0
$693$	5.15793			0.195933
$694$		0			0
$695$			20.1431i			0.764072i
$696$		0			0
$697$	−9.20238	−	1.69841i	−0.348565	−	0.0643320i
$698$		0			0
$699$		−	18.3227i		−	0.693027i
$700$		0			0
$701$	33.5159			1.26588			0.632939	−	0.774202i	$-0.281848\pi$
$701$	33.5159			1.26588			0.632939	+	0.774202i	$0.281848\pi$
$702$		0			0
$703$	21.6389	+	21.6389i	0.816128	+	0.816128i
$704$		0			0
$705$		−	15.5749i		−	0.586584i
$706$		0			0
$707$	3.64426			0.137056
$708$		0			0
$709$	−1.96607	+	1.96607i	−0.0738374	+	0.0738374i	−0.743061	−	0.669224i	$-0.766627\pi$
$709$	−1.96607	+	1.96607i	−0.0738374	+	0.0738374i	0.669224	+	0.743061i	$0.266627\pi$
$710$		0			0
$711$	3.77705	+	3.77705i	0.141650	+	0.141650i
$712$		0			0
$713$	−7.86711			−0.294626
$714$		0			0
$715$	22.5672			0.843964
$716$		0			0
$717$		−	19.8751i		−	0.742250i
$718$		0			0
$719$	−18.4776	−	18.4776i	−0.689099	−	0.689099i	0.272934	−	0.962033i	$-0.412006\pi$
$719$	−18.4776	−	18.4776i	−0.689099	−	0.689099i	−0.962033	+	0.272934i	$0.912006\pi$
$720$		0			0
$721$	−11.5222	−	11.5222i	−0.429110	−	0.429110i
$722$		0			0
$723$	16.4656	+	16.4656i	0.612362	+	0.612362i
$724$		0			0
$725$	4.92706	−	4.92706i	0.182987	−	0.182987i
$726$		0			0
$727$	−18.2309	+	18.2309i	−0.676148	+	0.676148i	−0.959126	−	0.282978i	$-0.908678\pi$
$727$	−18.2309	+	18.2309i	−0.676148	+	0.676148i	0.282978	+	0.959126i	$0.408678\pi$
$728$		0			0
$729$			19.4338i			0.719770i
$730$		0			0
$731$	−7.91080	+	7.91080i	−0.292592	+	0.292592i
$732$		0			0
$733$		−	12.7998i		−	0.472773i	−0.971659	−	0.236386i	$-0.924037\pi$
$733$		−	12.7998i		−	0.472773i	0.971659	−	0.236386i	$-0.0759631\pi$
$734$		0			0
$735$	−1.22694	+	1.22694i	−0.0452563	+	0.0452563i
$736$		0			0
$737$	−48.0136			−1.76860
$738$		0			0
$739$	33.1712			1.22022			0.610111	−	0.792316i	$-0.291125\pi$
$739$	33.1712			1.22022			0.610111	+	0.792316i	$0.291125\pi$
$740$		0			0
$741$	−15.4291	+	15.4291i	−0.566801	+	0.566801i
$742$		0			0
$743$		−	20.7424i		−	0.760965i	−0.924788	−	0.380483i	$-0.875758\pi$
$743$		−	20.7424i		−	0.760965i	0.924788	−	0.380483i	$-0.124242\pi$
$744$		0			0
$745$	−0.0104764	+	0.0104764i	−0.000383827	+	0.000383827i
$746$		0			0
$747$			17.3551i			0.634988i
$748$		0			0
$749$	−8.63136	+	8.63136i	−0.315383	+	0.315383i
$750$		0			0
$751$	−11.5095	+	11.5095i	−0.419988	+	0.419988i	−0.885199	−	0.465212i	$-0.845978\pi$
$751$	−11.5095	+	11.5095i	−0.419988	+	0.419988i	0.465212	+	0.885199i	$0.345978\pi$
$752$		0			0
$753$	−4.14100	−	4.14100i	−0.150906	−	0.150906i
$754$		0			0
$755$	8.62396	+	8.62396i	0.313858	+	0.313858i
$756$		0			0
$757$	−37.3908	−	37.3908i	−1.35899	−	1.35899i	−0.875161	−	0.483832i	$-0.839245\pi$
$757$	−37.3908	−	37.3908i	−1.35899	−	1.35899i	−0.483832	−	0.875161i	$-0.660755\pi$
$758$		0			0
$759$		−	16.0820i		−	0.583741i
$760$		0			0
$761$	−41.5281			−1.50539			−0.752696	−	0.658368i	$-0.771247\pi$
$761$	−41.5281			−1.50539			−0.752696	+	0.658368i	$0.771247\pi$
$762$		0			0
$763$	13.8336			0.500810
$764$		0			0
$765$	−2.75277	−	2.75277i	−0.0995268	−	0.0995268i
$766$		0			0
$767$	−17.0946	+	17.0946i	−0.617252	+	0.617252i
$768$		0			0
$769$	−28.8257			−1.03948			−0.519740	−	0.854324i	$-0.673971\pi$
$769$	−28.8257			−1.03948			−0.519740	+	0.854324i	$0.673971\pi$
$770$		0			0
$771$			15.4580i			0.556707i
$772$		0			0
$773$	−9.35719	−	9.35719i	−0.336555	−	0.336555i	0.518514	−	0.855069i	$-0.326485\pi$
$773$	−9.35719	−	9.35719i	−0.336555	−	0.336555i	−0.855069	+	0.518514i	$0.826485\pi$
$774$		0			0
$775$	4.32128			0.155225
$776$		0			0
$777$			8.75586i			0.314115i
$778$		0			0
$779$	−24.8007	−	4.57727i	−0.888577	−	0.163998i
$780$		0			0
$781$		−	28.0746i		−	1.00459i
$782$		0			0
$783$	−14.1264			−0.504838
$784$		0			0
$785$	−5.98240	−	5.98240i	−0.213521	−	0.213521i
$786$		0			0
$787$		−	7.83827i		−	0.279404i	−0.990194	−	0.139702i	$-0.955385\pi$
$787$		−	7.83827i		−	0.279404i	0.990194	−	0.139702i	$-0.0446145\pi$
$788$		0			0
$789$	20.5547			0.731768
$790$		0			0
$791$	−12.5375	+	12.5375i	−0.445782	+	0.445782i
$792$		0			0
$793$	50.6268	+	50.6268i	1.79781	+	1.79781i
$794$		0			0
$795$	9.74871			0.345751
$796$		0			0
$797$	−2.46476			−0.0873063			−0.0436531	−	0.999047i	$-0.513900\pi$
$797$	−2.46476			−0.0873063			−0.0436531	+	0.999047i	$0.513900\pi$
$798$		0			0
$799$			13.1180i			0.464083i
$800$		0			0
$801$	19.5143	+	19.5143i	0.689505	+	0.689505i
$802$		0			0
$803$	25.7893	+	25.7893i	0.910085	+	0.910085i
$804$		0			0
$805$	−5.21149	−	5.21149i	−0.183681	−	0.183681i
$806$		0			0
$807$	17.1537	−	17.1537i	0.603840	−	0.603840i
$808$		0			0
$809$	37.1927	−	37.1927i	1.30762	−	1.30762i	0.384499	−	0.923125i	$-0.374374\pi$
$809$	37.1927	−	37.1927i	1.30762	−	1.30762i	0.923125	−	0.384499i	$-0.125626\pi$
$810$		0			0
$811$		−	45.3121i		−	1.59112i	−0.605872	−	0.795562i	$-0.707176\pi$
$811$		−	45.3121i		−	1.59112i	0.605872	−	0.795562i	$-0.292824\pi$
$812$		0			0
$813$	−8.04247	+	8.04247i	−0.282062	+	0.282062i
$814$		0			0
$815$			19.5073i			0.683312i
$816$		0			0
$817$	−21.3198	+	21.3198i	−0.745887	+	0.745887i
$818$		0			0
$819$	8.50503			0.297190
$820$		0			0
$821$	18.1172			0.632294			0.316147	−	0.948710i	$-0.397611\pi$
$821$	18.1172			0.632294			0.316147	+	0.948710i	$0.397611\pi$
$822$		0			0
$823$	−0.0416319	+	0.0416319i	−0.00145120	+	0.00145120i	−0.707832	−	0.706381i	$-0.750327\pi$
$823$	−0.0416319	+	0.0416319i	−0.00145120	+	0.00145120i	0.706381	+	0.707832i	$0.250327\pi$
$824$		0			0
$825$			8.83360i			0.307547i
$826$		0			0
$827$	−22.5775	+	22.5775i	−0.785096	+	0.785096i	−0.980686	−	0.195590i	$-0.937338\pi$
$827$	−22.5775	+	22.5775i	−0.785096	+	0.785096i	0.195590	+	0.980686i	$0.437338\pi$
$828$		0			0
$829$			4.15708i			0.144381i	0.997391	+	0.0721907i	$0.0229990\pi$
$829$			4.15708i			0.144381i	−0.997391	+	0.0721907i	$0.977001\pi$
$830$		0			0
$831$	−15.5686	+	15.5686i	−0.540069	+	0.540069i
$832$		0			0
$833$	1.03340	−	1.03340i	0.0358051	−	0.0358051i
$834$		0			0
$835$	23.1317	+	23.1317i	0.800505	+	0.800505i
$836$		0			0
$837$	−6.19480	−	6.19480i	−0.214123	−	0.214123i
$838$		0			0
$839$	10.1033	+	10.1033i	0.348805	+	0.348805i	0.859664	−	0.510860i	$-0.170673\pi$
$839$	10.1033	+	10.1033i	0.348805	+	0.348805i	−0.510860	+	0.859664i	$0.670673\pi$
$840$		0			0
$841$			21.9766i			0.757813i
$842$		0			0
$843$	22.9077			0.788983
$844$		0			0
$845$	17.1950			0.591527
$846$		0			0
$847$	1.49300	+	1.49300i	0.0513002	+	0.0513002i
$848$		0			0
$849$	−8.54463	+	8.54463i	−0.293251	+	0.293251i
$850$		0			0
$851$	−37.1910			−1.27489
$852$		0			0
$853$		−	20.6213i		−	0.706059i	−0.935612	−	0.353030i	$-0.885151\pi$
$853$		−	20.6213i		−	0.706059i	0.935612	−	0.353030i	$-0.114849\pi$
$854$		0			0
$855$	−7.41881	−	7.41881i	−0.253718	−	0.253718i
$856$		0			0
$857$	−37.8223			−1.29199			−0.645993	−	0.763343i	$-0.723557\pi$
$857$	−37.8223			−1.29199			−0.645993	+	0.763343i	$0.723557\pi$
$858$		0			0
$859$			5.95043i			0.203026i	0.994834	+	0.101513i	$0.0323684\pi$
$859$			5.95043i			0.203026i	−0.994834	+	0.101513i	$0.967632\pi$
$860$		0			0
$861$	−4.09154	−	5.94366i	−0.139439	−	0.202560i
$862$		0			0
$863$		−	46.7731i		−	1.59218i	−0.605181	−	0.796088i	$-0.706899\pi$
$863$		−	46.7731i		−	1.59218i	0.605181	−	0.796088i	$-0.293101\pi$
$864$		0			0
$865$	−18.3223			−0.622976
$866$		0			0
$867$	11.8446	+	11.8446i	0.402262	+	0.402262i
$868$		0			0
$869$		−	9.20501i		−	0.312258i
$870$		0			0
$871$	−79.1707			−2.68260
$872$		0			0
$873$	−21.4012	+	21.4012i	−0.724322	+	0.724322i
$874$		0			0
$875$	8.30635	+	8.30635i	0.280806	+	0.280806i
$876$		0			0
$877$	−5.92942			−0.200222			−0.100111	−	0.994976i	$-0.531920\pi$
$877$	−5.92942			−0.200222			−0.100111	+	0.994976i	$0.531920\pi$
$878$		0			0
$879$	−13.2377			−0.446497
$880$		0			0
$881$		−	9.33561i		−	0.314525i	−0.987557	−	0.157262i	$-0.949733\pi$
$881$		−	9.33561i		−	0.314525i	0.987557	−	0.157262i	$-0.0502668\pi$
$882$		0			0
$883$	27.4310	+	27.4310i	0.923126	+	0.923126i	0.997249	−	0.0741233i	$-0.0236158\pi$
$883$	27.4310	+	27.4310i	0.923126	+	0.923126i	−0.0741233	+	0.997249i	$0.523616\pi$
$884$		0			0
$885$	6.03367	+	6.03367i	0.202819	+	0.202819i
$886$		0			0
$887$	−0.0340644	−	0.0340644i	−0.00114377	−	0.00114377i	0.706535	−	0.707678i	$-0.250257\pi$
$887$	−0.0340644	−	0.0340644i	−0.00114377	−	0.00114377i	−0.707678	+	0.706535i	$0.750257\pi$
$888$		0			0
$889$	−9.56800	+	9.56800i	−0.320900	+	0.320900i
$890$		0			0
$891$	1.72185	−	1.72185i	0.0576843	−	0.0576843i
$892$		0			0
$893$			35.3535i			1.18306i
$894$		0			0
$895$	2.11730	−	2.11730i	0.0707736	−	0.0707736i
$896$		0			0
$897$		−	26.5180i		−	0.885412i
$898$		0			0
$899$	3.07994	−	3.07994i	0.102722	−	0.102722i
$900$		0			0
$901$	−8.21092			−0.273545
$902$		0			0
$903$	−8.62674			−0.287080
$904$		0			0
$905$	3.77537	−	3.77537i	0.125498	−	0.125498i
$906$		0			0
$907$		−	37.8248i		−	1.25595i	−0.778232	−	0.627977i	$-0.783883\pi$
$907$		−	37.8248i		−	1.25595i	0.778232	−	0.627977i	$-0.216117\pi$
$908$		0			0
$909$	−4.45814	+	4.45814i	−0.147867	+	0.147867i
$910$		0			0
$911$		−	30.0351i		−	0.995107i	−0.867433	−	0.497554i	$-0.834232\pi$
$911$		−	30.0351i		−	0.995107i	0.867433	−	0.497554i	$-0.165768\pi$
$912$		0			0
$913$	21.1479	−	21.1479i	0.699894	−	0.699894i
$914$		0			0
$915$	17.8690	−	17.8690i	0.590732	−	0.590732i
$916$		0			0
$917$	7.43590	+	7.43590i	0.245555	+	0.245555i
$918$		0			0
$919$	−10.7481	−	10.7481i	−0.354546	−	0.354546i	0.507252	−	0.861798i	$-0.330661\pi$
$919$	−10.7481	−	10.7481i	−0.354546	−	0.354546i	−0.861798	+	0.507252i	$0.830661\pi$
$920$		0			0
$921$	−0.221759	−	0.221759i	−0.00730719	−	0.00730719i
$922$		0			0
$923$		−	46.2929i		−	1.52375i
$924$		0			0
$925$	20.4284			0.671682
$926$		0			0
$927$	28.1910			0.925915
$928$		0			0
$929$	−19.6451	−	19.6451i	−0.644533	−	0.644533i	0.307133	−	0.951667i	$-0.400630\pi$
$929$	−19.6451	−	19.6451i	−0.644533	−	0.644533i	−0.951667	+	0.307133i	$0.900630\pi$
$930$		0			0
$931$	2.78503	−	2.78503i	0.0912758	−	0.0912758i
$932$		0			0
$933$	−30.9007			−1.01164
$934$		0			0
$935$			6.70876i			0.219400i
$936$		0			0
$937$	−32.7625	−	32.7625i	−1.07030	−	1.07030i	−0.997334	−	0.0729699i	$-0.976752\pi$
$937$	−32.7625	−	32.7625i	−1.07030	−	1.07030i	−0.0729699	−	0.997334i	$-0.523248\pi$
$938$		0			0
$939$	−21.1683			−0.690800
$940$		0			0
$941$			15.5708i			0.507594i	0.967257	+	0.253797i	$0.0816795\pi$
$941$			15.5708i			0.507594i	−0.967257	+	0.253797i	$0.918320\pi$
$942$		0			0
$943$	25.2461	−	17.3791i	0.822125	−	0.565940i
$944$		0			0
$945$		−	8.20736i		−	0.266985i
$946$		0			0
$947$	−55.7617			−1.81201			−0.906006	−	0.423264i	$-0.860884\pi$
$947$	−55.7617			−1.81201			−0.906006	+	0.423264i	$0.860884\pi$
$948$		0			0
$949$	42.5246	+	42.5246i	1.38041	+	1.38041i
$950$		0			0
$951$			3.16347i			0.102582i
$952$		0			0
$953$	−30.7532			−0.996195			−0.498098	−	0.867121i	$-0.665968\pi$
$953$	−30.7532			−0.996195			−0.498098	+	0.867121i	$0.665968\pi$
$954$		0			0
$955$	−4.47112	+	4.47112i	−0.144682	+	0.144682i
$956$		0			0
$957$	6.29605	+	6.29605i	0.203522	+	0.203522i
$958$		0			0
$959$	−18.7800			−0.606437
$960$		0			0
$961$	−28.2987			−0.912863
$962$		0			0
$963$		−	21.1180i		−	0.680519i
$964$		0			0
$965$	24.4022	+	24.4022i	0.785533	+	0.785533i
$966$		0			0
$967$	39.5399	+	39.5399i	1.27152	+	1.27152i	0.945293	+	0.326224i	$0.105776\pi$
$967$	39.5399	+	39.5399i	1.27152	+	1.27152i	0.326224	+	0.945293i	$0.394224\pi$
$968$		0			0
$969$	−4.58675	−	4.58675i	−0.147348	−	0.147348i
$970$		0			0
$971$	0.829593	−	0.829593i	0.0266229	−	0.0266229i	−0.693670	−	0.720293i	$-0.744007\pi$
$971$	0.829593	−	0.829593i	0.0266229	−	0.0266229i	0.720293	+	0.693670i	$0.244007\pi$
$972$		0			0
$973$	9.25054	−	9.25054i	0.296559	−	0.296559i
$974$		0			0
$975$			14.5659i			0.466483i
$976$		0			0
$977$	29.0700	−	29.0700i	0.930030	−	0.930030i	−0.0676772	−	0.997707i	$-0.521559\pi$
$977$	29.0700	−	29.0700i	0.930030	−	0.930030i	0.997707	+	0.0676772i	$0.0215588\pi$
$978$		0			0
$979$		−	47.5582i		−	1.51997i
$980$		0			0
$981$	−16.9231	+	16.9231i	−0.540312	+	0.540312i
$982$		0			0
$983$	34.6150			1.10405			0.552023	−	0.833829i	$-0.313856\pi$
$983$	34.6150			1.10405			0.552023	+	0.833829i	$0.313856\pi$
$984$		0			0
$985$	34.0535			1.08504
$986$		0			0
$987$	−7.15262	+	7.15262i	−0.227670	+	0.227670i
$988$		0			0
$989$		−	36.6426i		−	1.16517i
$990$		0			0
$991$	−16.6154	+	16.6154i	−0.527805	+	0.527805i	−0.919917	−	0.392112i	$-0.871744\pi$
$991$	−16.6154	+	16.6154i	−0.527805	+	0.527805i	0.392112	+	0.919917i	$0.371744\pi$
$992$		0			0
$993$		−	10.1650i		−	0.322577i
$994$		0			0
$995$	30.1462	−	30.1462i	0.955697	−	0.955697i
$996$		0			0
$997$	2.91448	−	2.91448i	0.0923024	−	0.0923024i	−0.659448	−	0.751750i	$-0.729210\pi$
$997$	2.91448	−	2.91448i	0.0923024	−	0.0923024i	0.751750	+	0.659448i	$0.229210\pi$
$998$		0			0
$999$	−29.2853	−	29.2853i	−0.926546	−	0.926546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.729.7	yes	36
41.9	even	4	inner	1148.2.k.b.337.7	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.7	✓	36	41.9	even	4	inner
1148.2.k.b.729.7	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.796852 + 0.796852i) q^{3} +1.53973i q^{5} +(0.707107 - 0.707107i) q^{7} +1.73005i q^{9} +O(q^{10})\)	\(q+(-0.796852 + 0.796852i) q^{3} +1.53973i q^{5} +(0.707107 - 0.707107i) q^{7} +1.73005i q^{9} +(2.10815 - 2.10815i) q^{11} +(3.47617 - 3.47617i) q^{13} +(-1.22694 - 1.22694i) q^{15} +(1.03340 + 1.03340i) q^{17} +(2.78503 + 2.78503i) q^{19} +1.12692i q^{21} -4.78666 q^{23} +2.62923 q^{25} +(-3.76915 - 3.76915i) q^{27} +(1.87396 - 1.87396i) q^{29} +1.64355 q^{31} +3.35977i q^{33} +(1.08875 + 1.08875i) q^{35} +7.76973 q^{37} +5.53999i q^{39} +(-5.27426 + 3.63073i) q^{41} +7.65515i q^{43} -2.66381 q^{45} +(6.34706 + 6.34706i) q^{47} -1.00000i q^{49} -1.64693 q^{51} +(-3.97278 + 3.97278i) q^{53} +(3.24598 + 3.24598i) q^{55} -4.43852 q^{57} -4.91766 q^{59} +14.5639i q^{61} +(1.22333 + 1.22333i) q^{63} +(5.35237 + 5.35237i) q^{65} +(-11.3876 - 11.3876i) q^{67} +(3.81426 - 3.81426i) q^{69} +(6.65860 - 6.65860i) q^{71} +12.2332i q^{73} +(-2.09511 + 2.09511i) q^{75} -2.98137i q^{77} +(2.18320 - 2.18320i) q^{79} +0.816762 q^{81} +10.0315 q^{83} +(-1.59115 + 1.59115i) q^{85} +2.98653i q^{87} +(11.2796 - 11.2796i) q^{89} -4.91605i q^{91} +(-1.30967 + 1.30967i) q^{93} +(-4.28820 + 4.28820i) q^{95} +(12.3703 + 12.3703i) q^{97} +(3.64721 + 3.64721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) \) 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

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