LMFDB - Embedded newform 1148.2.k.b.729.18

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			729.18
Character	$\chi$	$=$	1148.729
Dual form			1148.2.k.b.337.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.38527 - 2.38527i) q^{3} -0.515487i q^{5} +(0.707107 - 0.707107i) q^{7} -8.37900i q^{9} +O(q^{10})$	\(q+(2.38527 - 2.38527i) q^{3} -0.515487i q^{5} +(0.707107 - 0.707107i) q^{7} -8.37900i q^{9} +(-3.73270 + 3.73270i) q^{11} +(0.0725409 - 0.0725409i) q^{13} +(-1.22958 - 1.22958i) q^{15} +(-4.03186 - 4.03186i) q^{17} +(-2.33728 - 2.33728i) q^{19} -3.37328i q^{21} +4.66571 q^{23} +4.73427 q^{25} +(-12.8303 - 12.8303i) q^{27} +(6.22153 - 6.22153i) q^{29} -2.93310 q^{31} +17.8070i q^{33} +(-0.364505 - 0.364505i) q^{35} -10.6326 q^{37} -0.346059i q^{39} +(5.72814 - 2.86154i) q^{41} +1.10612i q^{43} -4.31927 q^{45} +(8.99324 + 8.99324i) q^{47} -1.00000i q^{49} -19.2341 q^{51} +(3.20712 - 3.20712i) q^{53} +(1.92416 + 1.92416i) q^{55} -11.1501 q^{57} +12.6830 q^{59} +9.12150i q^{61} +(-5.92485 - 5.92485i) q^{63} +(-0.0373939 - 0.0373939i) q^{65} +(1.97135 + 1.97135i) q^{67} +(11.1290 - 11.1290i) q^{69} +(8.02127 - 8.02127i) q^{71} +11.8259i q^{73} +(11.2925 - 11.2925i) q^{75} +5.27883i q^{77} +(1.52258 - 1.52258i) q^{79} -36.0706 q^{81} +5.12597 q^{83} +(-2.07837 + 2.07837i) q^{85} -29.6800i q^{87} +(-11.3538 + 11.3538i) q^{89} -0.102588i q^{91} +(-6.99623 + 6.99623i) q^{93} +(-1.20484 + 1.20484i) q^{95} +(10.0266 + 10.0266i) q^{97} +(31.2763 + 31.2763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.38527	−	2.38527i	1.37713	−	1.37713i	0.527710	−	0.849425i	$-0.323051\pi$
$3$	2.38527	−	2.38527i	1.37713	−	1.37713i	0.849425	−	0.527710i	$-0.176949\pi$
$4$		0			0
$5$		−	0.515487i		−	0.230533i	−0.993335	−	0.115266i	$-0.963228\pi$
$5$		−	0.515487i		−	0.230533i	0.993335	−	0.115266i	$-0.0367722\pi$
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$		0			0
$9$		−	8.37900i		−	2.79300i
$10$		0			0
$11$	−3.73270	+	3.73270i	−1.12545	+	1.12545i	−0.134543	+	0.990908i	$0.542957\pi$
$11$	−3.73270	+	3.73270i	−1.12545	+	1.12545i	−0.990908	+	0.134543i	$0.957043\pi$
$12$		0			0
$13$	0.0725409	−	0.0725409i	0.0201192	−	0.0201192i	−0.696976	−	0.717095i	$-0.745471\pi$
$13$	0.0725409	−	0.0725409i	0.0201192	−	0.0201192i	0.717095	+	0.696976i	$0.245471\pi$
$14$		0			0
$15$	−1.22958	−	1.22958i	−0.317475	−	0.317475i
$16$		0			0
$17$	−4.03186	−	4.03186i	−0.977871	−	0.977871i	0.0218898	−	0.999760i	$-0.493032\pi$
$17$	−4.03186	−	4.03186i	−0.977871	−	0.977871i	−0.999760	+	0.0218898i	$0.993032\pi$
$18$		0			0
$19$	−2.33728	−	2.33728i	−0.536208	−	0.536208i	0.386205	−	0.922413i	$-0.373786\pi$
$19$	−2.33728	−	2.33728i	−0.536208	−	0.536208i	−0.922413	+	0.386205i	$0.873786\pi$
$20$		0			0
$21$		−	3.37328i		−	0.736109i
$22$		0			0
$23$	4.66571			0.972868			0.486434	−	0.873717i	$-0.338297\pi$
$23$	4.66571			0.972868			0.486434	+	0.873717i	$0.338297\pi$
$24$		0			0
$25$	4.73427			0.946855
$26$		0			0
$27$	−12.8303	−	12.8303i	−2.46920	−	2.46920i
$28$		0			0
$29$	6.22153	−	6.22153i	1.15531	−	1.15531i	0.169838	−	0.985472i	$-0.445676\pi$
$29$	6.22153	−	6.22153i	1.15531	−	1.15531i	0.985472	−	0.169838i	$-0.0543243\pi$
$30$		0			0
$31$	−2.93310			−0.526800			−0.263400	−	0.964687i	$-0.584844\pi$
$31$	−2.93310			−0.526800			−0.263400	+	0.964687i	$0.584844\pi$
$32$		0			0
$33$			17.8070i			3.09980i
$34$		0			0
$35$	−0.364505	−	0.364505i	−0.0616125	−	0.0616125i
$36$		0			0
$37$	−10.6326			−1.74799			−0.873994	−	0.485937i	$-0.838478\pi$
$37$	−10.6326			−1.74799			−0.873994	+	0.485937i	$0.838478\pi$
$38$		0			0
$39$		−	0.346059i		−	0.0554138i
$40$		0			0
$41$	5.72814	−	2.86154i	0.894585	−	0.446898i
$41$	5.72814	−	2.86154i	0.894585	−	0.446898i
$42$		0			0
$43$			1.10612i			0.168681i	0.996437	+	0.0843406i	$0.0268784\pi$
$43$			1.10612i			0.168681i	−0.996437	+	0.0843406i	$0.973122\pi$
$44$		0			0
$45$	−4.31927			−0.643878
$46$		0			0
$47$	8.99324	+	8.99324i	1.31180	+	1.31180i	0.920088	+	0.391711i	$0.128117\pi$
$47$	8.99324	+	8.99324i	1.31180	+	1.31180i	0.391711	+	0.920088i	$0.371883\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−19.2341			−2.69332
$52$		0			0
$53$	3.20712	−	3.20712i	0.440532	−	0.440532i	−0.451659	−	0.892191i	$-0.649167\pi$
$53$	3.20712	−	3.20712i	0.440532	−	0.440532i	0.892191	+	0.451659i	$0.149167\pi$
$54$		0			0
$55$	1.92416	+	1.92416i	0.259454	+	0.259454i
$56$		0			0
$57$	−11.1501			−1.47686
$58$		0			0
$59$	12.6830			1.65119			0.825593	−	0.564266i	$-0.190841\pi$
$59$	12.6830			1.65119			0.825593	+	0.564266i	$0.190841\pi$
$60$		0			0
$61$			9.12150i			1.16789i	0.811794	+	0.583944i	$0.198491\pi$
$61$			9.12150i			1.16789i	−0.811794	+	0.583944i	$0.801509\pi$
$62$		0			0
$63$	−5.92485	−	5.92485i	−0.746460	−	0.746460i
$64$		0			0
$65$	−0.0373939	−	0.0373939i	−0.00463815	−	0.00463815i
$66$		0			0
$67$	1.97135	+	1.97135i	0.240839	+	0.240839i	0.817197	−	0.576358i	$-0.195527\pi$
$67$	1.97135	+	1.97135i	0.240839	+	0.240839i	−0.576358	+	0.817197i	$0.695527\pi$
$68$		0			0
$69$	11.1290	−	11.1290i	1.33977	−	1.33977i
$70$		0			0
$71$	8.02127	−	8.02127i	0.951950	−	0.951950i	−0.0469473	−	0.998897i	$-0.514949\pi$
$71$	8.02127	−	8.02127i	0.951950	−	0.951950i	0.998897	+	0.0469473i	$0.0149493\pi$
$72$		0			0
$73$			11.8259i			1.38412i	0.721840	+	0.692060i	$0.243297\pi$
$73$			11.8259i			1.38412i	−0.721840	+	0.692060i	$0.756703\pi$
$74$		0			0
$75$	11.2925	−	11.2925i	1.30395	−	1.30395i
$76$		0			0
$77$			5.27883i			0.601579i
$78$		0			0
$79$	1.52258	−	1.52258i	0.171303	−	0.171303i	−0.616248	−	0.787552i	$-0.711348\pi$
$79$	1.52258	−	1.52258i	0.171303	−	0.171303i	0.787552	+	0.616248i	$0.211348\pi$
$80$		0			0
$81$	−36.0706			−4.00785
$82$		0			0
$83$	5.12597			0.562648			0.281324	−	0.959613i	$-0.409226\pi$
$83$	5.12597			0.562648			0.281324	+	0.959613i	$0.409226\pi$
$84$		0			0
$85$	−2.07837	+	2.07837i	−0.225431	+	0.225431i
$86$		0			0
$87$		−	29.6800i		−	3.18203i
$88$		0			0
$89$	−11.3538	+	11.3538i	−1.20350	+	1.20350i	−0.230412	+	0.973093i	$0.574007\pi$
$89$	−11.3538	+	11.3538i	−1.20350	+	1.20350i	−0.973093	+	0.230412i	$0.925993\pi$
$90$		0			0
$91$		−	0.102588i		−	0.0107542i
$92$		0			0
$93$	−6.99623	+	6.99623i	−0.725475	+	0.725475i
$94$		0			0
$95$	−1.20484	+	1.20484i	−0.123614	+	0.123614i
$96$		0			0
$97$	10.0266	+	10.0266i	1.01805	+	1.01805i	0.999834	+	0.0182154i	$0.00579848\pi$
$97$	10.0266	+	10.0266i	1.01805	+	1.01805i	0.0182154	+	0.999834i	$0.494202\pi$
$98$		0			0
$99$	31.2763	+	31.2763i	3.14338	+	3.14338i
$100$		0			0
$101$	0.283665	+	0.283665i	0.0282257	+	0.0282257i	0.721079	−	0.692853i	$-0.243647\pi$
$101$	0.283665	+	0.283665i	0.0282257	+	0.0282257i	−0.692853	+	0.721079i	$0.743647\pi$
$102$		0			0
$103$		−	3.29717i		−	0.324880i	−0.986718	−	0.162440i	$-0.948064\pi$
$103$		−	3.29717i		−	0.324880i	0.986718	−	0.162440i	$-0.0519364\pi$
$104$		0			0
$105$	−1.73888			−0.169697
$106$		0			0
$107$	4.92775			0.476384			0.238192	−	0.971218i	$-0.423445\pi$
$107$	4.92775			0.476384			0.238192	+	0.971218i	$0.423445\pi$
$108$		0			0
$109$	−1.63794	−	1.63794i	−0.156886	−	0.156886i	0.624299	−	0.781185i	$-0.285385\pi$
$109$	−1.63794	−	1.63794i	−0.156886	−	0.156886i	−0.781185	+	0.624299i	$0.785385\pi$
$110$		0			0
$111$	−25.3616	+	25.3616i	−2.40721	+	2.40721i
$112$		0			0
$113$	−9.28969			−0.873901			−0.436950	−	0.899486i	$-0.643941\pi$
$113$	−9.28969			−0.873901			−0.436950	+	0.899486i	$0.643941\pi$
$114$		0			0
$115$		−	2.40511i		−	0.224278i
$116$		0			0
$117$	−0.607820	−	0.607820i	−0.0561930	−	0.0561930i
$118$		0			0
$119$	−5.70192			−0.522694
$120$		0			0
$121$		−	16.8661i		−	1.53328i
$122$		0			0
$123$	6.83760	−	20.4887i	0.616526	−	1.84740i
$124$		0			0
$125$		−	5.01789i		−	0.448814i
$126$		0			0
$127$	−4.19701			−0.372425			−0.186212	−	0.982510i	$-0.559621\pi$
$127$	−4.19701			−0.372425			−0.186212	+	0.982510i	$0.559621\pi$
$128$		0			0
$129$	2.63838	+	2.63838i	0.232297	+	0.232297i
$130$		0			0
$131$			16.0114i			1.39892i	0.714670	+	0.699462i	$0.246577\pi$
$131$			16.0114i			1.39892i	−0.714670	+	0.699462i	$0.753423\pi$
$132$		0			0
$133$	−3.30541			−0.286615
$134$		0			0
$135$	−6.61388	+	6.61388i	−0.569232	+	0.569232i
$136$		0			0
$137$	1.82944	+	1.82944i	0.156300	+	0.156300i	0.780925	−	0.624625i	$-0.214748\pi$
$137$	1.82944	+	1.82944i	0.156300	+	0.156300i	−0.624625	+	0.780925i	$0.714748\pi$
$138$		0			0
$139$	−6.73374			−0.571148			−0.285574	−	0.958357i	$-0.592184\pi$
$139$	−6.73374			−0.571148			−0.285574	+	0.958357i	$0.592184\pi$
$140$		0			0
$141$	42.9026			3.61305
$142$		0			0
$143$			0.541547i			0.0452864i
$144$		0			0
$145$	−3.20712	−	3.20712i	−0.266337	−	0.266337i
$146$		0			0
$147$	−2.38527	−	2.38527i	−0.196734	−	0.196734i
$148$		0			0
$149$	−7.34646	−	7.34646i	−0.601845	−	0.601845i	0.338957	−	0.940802i	$-0.389926\pi$
$149$	−7.34646	−	7.34646i	−0.601845	−	0.601845i	−0.940802	+	0.338957i	$0.889926\pi$
$150$		0			0
$151$	5.47921	−	5.47921i	0.445892	−	0.445892i	−0.448094	−	0.893986i	$-0.647897\pi$
$151$	5.47921	−	5.47921i	0.445892	−	0.445892i	0.893986	+	0.448094i	$0.147897\pi$
$152$		0			0
$153$	−33.7830	+	33.7830i	−2.73119	+	2.73119i
$154$		0			0
$155$			1.51198i			0.121445i
$156$		0			0
$157$	−6.21037	+	6.21037i	−0.495641	+	0.495641i	−0.910078	−	0.414437i	$-0.863979\pi$
$157$	−6.21037	+	6.21037i	−0.495641	+	0.495641i	0.414437	+	0.910078i	$0.363979\pi$
$158$		0			0
$159$		−	15.2997i		−	1.21334i
$160$		0			0
$161$	3.29916	−	3.29916i	0.260010	−	0.260010i
$162$		0			0
$163$	−3.81284			−0.298645			−0.149322	−	0.988789i	$-0.547709\pi$
$163$	−3.81284			−0.298645			−0.149322	+	0.988789i	$0.547709\pi$
$164$		0			0
$165$	9.17927			0.714605
$166$		0			0
$167$	9.57625	−	9.57625i	0.741033	−	0.741033i	−0.231744	−	0.972777i	$-0.574443\pi$
$167$	9.57625	−	9.57625i	0.741033	−	0.741033i	0.972777	+	0.231744i	$0.0744432\pi$
$168$		0			0
$169$			12.9895i			0.999190i
$170$		0			0
$171$	−19.5840	+	19.5840i	−1.49763	+	1.49763i
$172$		0			0
$173$		−	20.5259i		−	1.56056i	−0.625433	−	0.780278i	$-0.715078\pi$
$173$		−	20.5259i		−	1.56056i	0.625433	−	0.780278i	$-0.284922\pi$
$174$		0			0
$175$	3.34764	−	3.34764i	0.253058	−	0.253058i
$176$		0			0
$177$	30.2523	−	30.2523i	2.27391	−	2.27391i
$178$		0			0
$179$	−9.85685	−	9.85685i	−0.736735	−	0.736735i	0.235209	−	0.971945i	$-0.424422\pi$
$179$	−9.85685	−	9.85685i	−0.736735	−	0.736735i	−0.971945	+	0.235209i	$0.924422\pi$
$180$		0			0
$181$	4.50389	+	4.50389i	0.334772	+	0.334772i	0.854395	−	0.519624i	$-0.173928\pi$
$181$	4.50389	+	4.50389i	0.334772	+	0.334772i	−0.519624	+	0.854395i	$0.673928\pi$
$182$		0			0
$183$	21.7572	+	21.7572i	1.60834	+	1.60834i
$184$		0			0
$185$			5.48097i			0.402969i
$186$		0			0
$187$	30.0995			2.20109
$188$		0			0
$189$	−18.1449			−1.31984
$190$		0			0
$191$	9.82974	+	9.82974i	0.711255	+	0.711255i	0.966798	−	0.255542i	$-0.0822541\pi$
$191$	9.82974	+	9.82974i	0.711255	+	0.711255i	−0.255542	+	0.966798i	$0.582254\pi$
$192$		0			0
$193$	17.0716	−	17.0716i	1.22884	−	1.22884i	0.264442	−	0.964402i	$-0.414812\pi$
$193$	17.0716	−	17.0716i	1.22884	−	1.22884i	0.964402	−	0.264442i	$-0.0851878\pi$
$194$		0			0
$195$	−0.178389			−0.0127747
$196$		0			0
$197$		−	15.7804i		−	1.12431i	−0.827032	−	0.562155i	$-0.809973\pi$
$197$		−	15.7804i		−	1.12431i	0.827032	−	0.562155i	$-0.190027\pi$
$198$		0			0
$199$	3.06105	+	3.06105i	0.216992	+	0.216992i	0.807230	−	0.590238i	$-0.200966\pi$
$199$	3.06105	+	3.06105i	0.216992	+	0.216992i	−0.590238	+	0.807230i	$0.700966\pi$
$200$		0			0
$201$	9.40439			0.663335
$202$		0			0
$203$		−	8.79858i		−	0.617539i
$204$		0			0
$205$	−1.47509	−	2.95278i	−0.103025	−	0.206231i
$206$		0			0
$207$		−	39.0940i		−	2.71722i
$208$		0			0
$209$	17.4487			1.20695
$210$		0			0
$211$	10.2542	+	10.2542i	0.705928	+	0.705928i	0.965676	−	0.259748i	$-0.0836395\pi$
$211$	10.2542	+	10.2542i	0.705928	+	0.705928i	−0.259748	+	0.965676i	$0.583640\pi$
$212$		0			0
$213$		−	38.2658i		−	2.62193i
$214$		0			0
$215$	0.570189			0.0388866
$216$		0			0
$217$	−2.07401	+	2.07401i	−0.140793	+	0.140793i
$218$		0			0
$219$	28.2080	+	28.2080i	1.90612	+	1.90612i
$220$		0			0
$221$	−0.584950			−0.0393480
$222$		0			0
$223$	2.63590			0.176513			0.0882564	−	0.996098i	$-0.471871\pi$
$223$	2.63590			0.176513			0.0882564	+	0.996098i	$0.471871\pi$
$224$		0			0
$225$		−	39.6685i		−	2.64456i
$226$		0			0
$227$	5.05013	+	5.05013i	0.335189	+	0.335189i	0.854553	−	0.519364i	$-0.173831\pi$
$227$	5.05013	+	5.05013i	0.335189	+	0.335189i	−0.519364	+	0.854553i	$0.673831\pi$
$228$		0			0
$229$	−4.14203	−	4.14203i	−0.273713	−	0.273713i	0.556880	−	0.830593i	$-0.311998\pi$
$229$	−4.14203	−	4.14203i	−0.273713	−	0.273713i	−0.830593	+	0.556880i	$0.811998\pi$
$230$		0			0
$231$	12.5914	+	12.5914i	0.828455	+	0.828455i
$232$		0			0
$233$	−14.2789	+	14.2789i	−0.935442	+	0.935442i	−0.998039	−	0.0625965i	$-0.980062\pi$
$233$	−14.2789	+	14.2789i	−0.935442	+	0.935442i	0.0625965	+	0.998039i	$0.480062\pi$
$234$		0			0
$235$	4.63590	−	4.63590i	0.302413	−	0.302413i
$236$		0			0
$237$		−	7.26350i		−	0.471815i
$238$		0			0
$239$	7.87813	−	7.87813i	0.509594	−	0.509594i	−0.404808	−	0.914402i	$-0.632662\pi$
$239$	7.87813	−	7.87813i	0.509594	−	0.509594i	0.914402	+	0.404808i	$0.132662\pi$
$240$		0			0
$241$			22.7596i			1.46607i	0.680189	+	0.733036i	$0.261897\pi$
$241$			22.7596i			1.46607i	−0.680189	+	0.733036i	$0.738103\pi$
$242$		0			0
$243$	−47.5470	+	47.5470i	−3.05014	+	3.05014i
$244$		0			0
$245$	−0.515487			−0.0329333
$246$		0			0
$247$	−0.339097			−0.0215762
$248$		0			0
$249$	12.2268	−	12.2268i	0.774842	−	0.774842i
$250$		0			0
$251$		−	3.84367i		−	0.242611i	−0.992615	−	0.121305i	$-0.961292\pi$
$251$		−	3.84367i		−	0.242611i	0.992615	−	0.121305i	$-0.0387080\pi$
$252$		0			0
$253$	−17.4157	+	17.4157i	−1.09492	+	1.09492i
$254$		0			0
$255$			9.91496i			0.620899i
$256$		0			0
$257$	−3.78522	+	3.78522i	−0.236115	+	0.236115i	−0.815239	−	0.579124i	$-0.803395\pi$
$257$	−3.78522	+	3.78522i	−0.236115	+	0.236115i	0.579124	+	0.815239i	$0.303395\pi$
$258$		0			0
$259$	−7.51838	+	7.51838i	−0.467169	+	0.467169i
$260$		0			0
$261$	−52.1302	−	52.1302i	−3.22678	−	3.22678i
$262$		0			0
$263$	−15.0562	−	15.0562i	−0.928403	−	0.928403i	0.0691998	−	0.997603i	$-0.477955\pi$
$263$	−15.0562	−	15.0562i	−0.928403	−	0.928403i	−0.997603	+	0.0691998i	$0.977955\pi$
$264$		0			0
$265$	−1.65323	−	1.65323i	−0.101557	−	0.101557i
$266$		0			0
$267$			54.1639i			3.31478i
$268$		0			0
$269$	8.47699			0.516852			0.258426	−	0.966031i	$-0.416796\pi$
$269$	8.47699			0.516852			0.258426	+	0.966031i	$0.416796\pi$
$270$		0			0
$271$	−14.3815			−0.873615			−0.436808	−	0.899555i	$-0.643891\pi$
$271$	−14.3815			−0.873615			−0.436808	+	0.899555i	$0.643891\pi$
$272$		0			0
$273$	−0.244701	−	0.244701i	−0.0148100	−	0.0148100i
$274$		0			0
$275$	−17.6716	+	17.6716i	−1.06564	+	1.06564i
$276$		0			0
$277$	−17.0460			−1.02420			−0.512099	−	0.858926i	$-0.671132\pi$
$277$	−17.0460			−1.02420			−0.512099	+	0.858926i	$0.671132\pi$
$278$		0			0
$279$			24.5764i			1.47135i
$280$		0			0
$281$	4.30611	+	4.30611i	0.256881	+	0.256881i	0.823784	−	0.566903i	$-0.191859\pi$
$281$	4.30611	+	4.30611i	0.256881	+	0.256881i	−0.566903	+	0.823784i	$0.691859\pi$
$282$		0			0
$283$	−16.5412			−0.983272			−0.491636	−	0.870801i	$-0.663601\pi$
$283$	−16.5412			−0.983272			−0.491636	+	0.870801i	$0.663601\pi$
$284$		0			0
$285$			5.74772i			0.340465i
$286$		0			0
$287$	2.02699	−	6.07382i	0.119649	−	0.358526i
$288$		0			0
$289$			15.5118i			0.912462i
$290$		0			0
$291$	47.8324			2.80398
$292$		0			0
$293$	−0.781612	−	0.781612i	−0.0456622	−	0.0456622i	0.683907	−	0.729569i	$-0.260279\pi$
$293$	−0.781612	−	0.781612i	−0.0456622	−	0.0456622i	−0.729569	+	0.683907i	$0.760279\pi$
$294$		0			0
$295$		−	6.53793i		−	0.380653i
$296$		0			0
$297$	95.7836			5.55793
$298$		0			0
$299$	0.338455	−	0.338455i	0.0195734	−	0.0195734i
$300$		0			0
$301$	0.782143	+	0.782143i	0.0450820	+	0.0450820i
$302$		0			0
$303$	1.35323			0.0777412
$304$		0			0
$305$	4.70202			0.269237
$306$		0			0
$307$			9.83325i			0.561213i	0.959823	+	0.280607i	$0.0905356\pi$
$307$			9.83325i			0.561213i	−0.959823	+	0.280607i	$0.909464\pi$
$308$		0			0
$309$	−7.86464	−	7.86464i	−0.447404	−	0.447404i
$310$		0			0
$311$	10.1168	+	10.1168i	0.573670	+	0.573670i	0.933152	−	0.359482i	$-0.117046\pi$
$311$	10.1168	+	10.1168i	0.573670	+	0.573670i	−0.359482	+	0.933152i	$0.617046\pi$
$312$		0			0
$313$	5.32121	+	5.32121i	0.300773	+	0.300773i	0.841316	−	0.540543i	$-0.181781\pi$
$313$	5.32121	+	5.32121i	0.300773	+	0.300773i	−0.540543	+	0.841316i	$0.681781\pi$
$314$		0			0
$315$	−3.05418	+	3.05418i	−0.172084	+	0.172084i
$316$		0			0
$317$	−3.29102	+	3.29102i	−0.184842	+	0.184842i	−0.793462	−	0.608620i	$-0.791723\pi$
$317$	−3.29102	+	3.29102i	−0.184842	+	0.184842i	0.608620	+	0.793462i	$0.291723\pi$
$318$		0			0
$319$			46.4462i			2.60049i
$320$		0			0
$321$	11.7540	−	11.7540i	0.656044	−	0.656044i
$322$		0			0
$323$			18.8472i			1.04868i
$324$		0			0
$325$	0.343429	−	0.343429i	0.0190500	−	0.0190500i
$326$		0			0
$327$	−7.81385			−0.432107
$328$		0			0
$329$	12.7184			0.701186
$330$		0			0
$331$	−7.94459	+	7.94459i	−0.436674	+	0.436674i	−0.890891	−	0.454217i	$-0.849919\pi$
$331$	−7.94459	+	7.94459i	−0.436674	+	0.436674i	0.454217	+	0.890891i	$0.349919\pi$
$332$		0			0
$333$			89.0905i			4.88213i
$334$		0			0
$335$	1.01621	−	1.01621i	0.0555213	−	0.0555213i
$336$		0			0
$337$		−	20.7976i		−	1.13292i	−0.824091	−	0.566458i	$-0.808313\pi$
$337$		−	20.7976i		−	1.13292i	0.824091	−	0.566458i	$-0.191687\pi$
$338$		0			0
$339$	−22.1584	+	22.1584i	−1.20348	+	1.20348i
$340$		0			0
$341$	10.9484	−	10.9484i	0.592888	−	0.592888i
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$		0			0
$345$	−5.73684	−	5.73684i	−0.308861	−	0.308861i
$346$		0			0
$347$	8.98959	+	8.98959i	0.482587	+	0.482587i	0.905957	−	0.423370i	$-0.139153\pi$
$347$	8.98959	+	8.98959i	0.482587	+	0.482587i	−0.423370	+	0.905957i	$0.639153\pi$
$348$		0			0
$349$			3.68188i			0.197087i	0.995133	+	0.0985434i	$0.0314183\pi$
$349$			3.68188i			0.197087i	−0.995133	+	0.0985434i	$0.968582\pi$
$350$		0			0
$351$	−1.86145			−0.0993569
$352$		0			0
$353$	5.31309			0.282787			0.141394	−	0.989953i	$-0.454842\pi$
$353$	5.31309			0.282787			0.141394	+	0.989953i	$0.454842\pi$
$354$		0			0
$355$	−4.13487	−	4.13487i	−0.219456	−	0.219456i
$356$		0			0
$357$	−13.6006	+	13.6006i	−0.719820	+	0.719820i
$358$		0			0
$359$	12.2528			0.646678			0.323339	−	0.946283i	$-0.395195\pi$
$359$	12.2528			0.646678			0.323339	+	0.946283i	$0.395195\pi$
$360$		0			0
$361$		−	8.07427i		−	0.424962i
$362$		0			0
$363$	−40.2301	−	40.2301i	−2.11153	−	2.11153i
$364$		0			0
$365$	6.09612			0.319085
$366$		0			0
$367$		−	19.9220i		−	1.03992i	−0.854191	−	0.519960i	$-0.825947\pi$
$367$		−	19.9220i		−	1.03992i	0.854191	−	0.519960i	$-0.174053\pi$
$368$		0			0
$369$	−23.9769	−	47.9961i	−1.24818	−	2.49858i
$370$		0			0
$371$		−	4.53556i		−	0.235474i
$372$		0			0
$373$	4.62160			0.239297			0.119649	−	0.992816i	$-0.461823\pi$
$373$	4.62160			0.239297			0.119649	+	0.992816i	$0.461823\pi$
$374$		0			0
$375$	−11.9690	−	11.9690i	−0.618077	−	0.618077i
$376$		0			0
$377$		−	0.902632i		−	0.0464879i
$378$		0			0
$379$	20.8730			1.07217			0.536087	−	0.844163i	$-0.319902\pi$
$379$	20.8730			1.07217			0.536087	+	0.844163i	$0.319902\pi$
$380$		0			0
$381$	−10.0110	+	10.0110i	−0.512879	+	0.512879i
$382$		0			0
$383$	19.3933	+	19.3933i	0.990951	+	0.990951i	0.999959	−	0.00900803i	$-0.00286738\pi$
$383$	19.3933	+	19.3933i	0.990951	+	0.990951i	−0.00900803	+	0.999959i	$0.502867\pi$
$384$		0			0
$385$	2.72117			0.138684
$386$		0			0
$387$	9.26815			0.471127
$388$		0			0
$389$			26.7041i			1.35395i	0.736006	+	0.676975i	$0.236710\pi$
$389$			26.7041i			1.35395i	−0.736006	+	0.676975i	$0.763290\pi$
$390$		0			0
$391$	−18.8115	−	18.8115i	−0.951339	−	0.951339i
$392$		0			0
$393$	38.1915	+	38.1915i	1.92651	+	1.92651i
$394$		0			0
$395$	−0.784869	−	0.784869i	−0.0394911	−	0.0394911i
$396$		0			0
$397$	−17.1112	+	17.1112i	−0.858785	+	0.858785i	−0.991195	−	0.132410i	$-0.957728\pi$
$397$	−17.1112	+	17.1112i	−0.858785	+	0.858785i	0.132410	+	0.991195i	$0.457728\pi$
$398$		0			0
$399$	−7.88428	+	7.88428i	−0.394708	+	0.394708i
$400$		0			0
$401$		−	13.6710i		−	0.682699i	−0.939936	−	0.341350i	$-0.889116\pi$
$401$		−	13.6710i		−	0.682699i	0.939936	−	0.341350i	$-0.110884\pi$
$402$		0			0
$403$	−0.212770	+	0.212770i	−0.0105988	+	0.0105988i
$404$		0			0
$405$			18.5939i			0.923941i
$406$		0			0
$407$	39.6883	−	39.6883i	1.96727	−	1.96727i
$408$		0			0
$409$	−16.9515			−0.838198			−0.419099	−	0.907941i	$-0.637654\pi$
$409$	−16.9515			−0.838198			−0.419099	+	0.907941i	$0.637654\pi$
$410$		0			0
$411$	8.72743			0.430492
$412$		0			0
$413$	8.96823	−	8.96823i	0.441298	−	0.441298i
$414$		0			0
$415$		−	2.64237i		−	0.129709i
$416$		0			0
$417$	−16.0618	+	16.0618i	−0.786548	+	0.786548i
$418$		0			0
$419$		−	2.49951i		−	0.122109i	−0.998134	−	0.0610545i	$-0.980554\pi$
$419$		−	2.49951i		−	0.122109i	0.998134	−	0.0610545i	$-0.0194464\pi$
$420$		0			0
$421$	18.1546	−	18.1546i	0.884803	−	0.884803i	−0.109215	−	0.994018i	$-0.534834\pi$
$421$	18.1546	−	18.1546i	0.884803	−	0.884803i	0.994018	+	0.109215i	$0.0348339\pi$
$422$		0			0
$423$	75.3544	−	75.3544i	3.66386	−	3.66386i
$424$		0			0
$425$	−19.0879	−	19.0879i	−0.925901	−	0.925901i
$426$		0			0
$427$	6.44987	+	6.44987i	0.312131	+	0.312131i
$428$		0			0
$429$	1.29173	+	1.29173i	0.0623655	+	0.0623655i
$430$		0			0
$431$		−	1.10325i		−	0.0531418i	−0.999647	−	0.0265709i	$-0.991541\pi$
$431$		−	1.10325i		−	0.0531418i	0.999647	−	0.0265709i	$-0.00845878\pi$
$432$		0			0
$433$	13.0897			0.629052			0.314526	−	0.949249i	$-0.398154\pi$
$433$	13.0897			0.629052			0.314526	+	0.949249i	$0.398154\pi$
$434$		0			0
$435$	−15.2997			−0.733564
$436$		0			0
$437$	−10.9051	−	10.9051i	−0.521660	−	0.521660i
$438$		0			0
$439$	−12.8182	+	12.8182i	−0.611781	+	0.611781i	−0.943410	−	0.331629i	$-0.892402\pi$
$439$	−12.8182	+	12.8182i	−0.611781	+	0.611781i	0.331629	+	0.943410i	$0.392402\pi$
$440$		0			0
$441$	−8.37900			−0.399000
$442$		0			0
$443$		−	15.1642i		−	0.720475i	−0.932861	−	0.360238i	$-0.882696\pi$
$443$		−	15.1642i		−	0.720475i	0.932861	−	0.360238i	$-0.117304\pi$
$444$		0			0
$445$	5.85276	+	5.85276i	0.277448	+	0.277448i
$446$		0			0
$447$	−35.0465			−1.65764
$448$		0			0
$449$			12.2083i			0.576147i	0.957608	+	0.288074i	$0.0930148\pi$
$449$			12.2083i			0.576147i	−0.957608	+	0.288074i	$0.906985\pi$
$450$		0			0
$451$	−10.7001	+	32.0627i	−0.503850	+	1.50977i
$452$		0			0
$453$		−	26.1388i		−	1.22811i
$454$		0			0
$455$	−0.0528830			−0.00247919
$456$		0			0
$457$	−12.6069	−	12.6069i	−0.589724	−	0.589724i	0.347832	−	0.937557i	$-0.386918\pi$
$457$	−12.6069	−	12.6069i	−0.589724	−	0.589724i	−0.937557	+	0.347832i	$0.886918\pi$
$458$		0			0
$459$			103.460i			4.82912i
$460$		0			0
$461$	−22.1545			−1.03184			−0.515918	−	0.856638i	$-0.672549\pi$
$461$	−22.1545			−1.03184			−0.515918	+	0.856638i	$0.672549\pi$
$462$		0			0
$463$	15.5112	−	15.5112i	0.720867	−	0.720867i	−0.247915	−	0.968782i	$-0.579745\pi$
$463$	15.5112	−	15.5112i	0.720867	−	0.720867i	0.968782	+	0.247915i	$0.0797453\pi$
$464$		0			0
$465$	3.60647	+	3.60647i	0.167246	+	0.167246i
$466$		0			0
$467$	−4.38169			−0.202761			−0.101380	−	0.994848i	$-0.532326\pi$
$467$	−4.38169			−0.202761			−0.101380	+	0.994848i	$0.532326\pi$
$468$		0			0
$469$	2.78791			0.128734
$470$		0			0
$471$			29.6268i			1.36513i
$472$		0			0
$473$	−4.12880	−	4.12880i	−0.189842	−	0.189842i
$474$		0			0
$475$	−11.0653	−	11.0653i	−0.507711	−	0.507711i
$476$		0			0
$477$	−26.8725	−	26.8725i	−1.23041	−	1.23041i
$478$		0			0
$479$	−4.99918	+	4.99918i	−0.228418	+	0.228418i	−0.812032	−	0.583613i	$-0.801638\pi$
$479$	−4.99918	+	4.99918i	−0.228418	+	0.228418i	0.583613	+	0.812032i	$0.301638\pi$
$480$		0			0
$481$	−0.771298	+	0.771298i	−0.0351682	+	0.0351682i
$482$		0			0
$483$		−	15.7387i		−	0.716137i
$484$		0			0
$485$	5.16860	−	5.16860i	0.234694	−	0.234694i
$486$		0			0
$487$			19.8721i			0.900493i	0.892904	+	0.450247i	$0.148664\pi$
$487$			19.8721i			0.900493i	−0.892904	+	0.450247i	$0.851336\pi$
$488$		0			0
$489$	−9.09464	+	9.09464i	−0.411274	+	0.411274i
$490$		0			0
$491$	−25.5055			−1.15105			−0.575524	−	0.817785i	$-0.695202\pi$
$491$	−25.5055			−1.15105			−0.575524	+	0.817785i	$0.695202\pi$
$492$		0			0
$493$	−50.1687			−2.25949
$494$		0			0
$495$	16.1225	−	16.1225i	0.724654	−	0.724654i
$496$		0			0
$497$		−	11.3438i		−	0.508839i
$498$		0			0
$499$	−1.88376	+	1.88376i	−0.0843286	+	0.0843286i	−0.748013	−	0.663684i	$-0.768992\pi$
$499$	−1.88376	+	1.88376i	−0.0843286	+	0.0843286i	0.663684	+	0.748013i	$0.268992\pi$
$500$		0			0
$501$		−	45.6839i		−	2.04100i
$502$		0			0
$503$	14.4448	−	14.4448i	0.644063	−	0.644063i	−0.307489	−	0.951552i	$-0.599489\pi$
$503$	14.4448	−	14.4448i	0.644063	−	0.644063i	0.951552	+	0.307489i	$0.0994886\pi$
$504$		0			0
$505$	0.146226	−	0.146226i	0.00650696	−	0.00650696i
$506$		0			0
$507$	30.9834	+	30.9834i	1.37602	+	1.37602i
$508$		0			0
$509$	−16.3552	−	16.3552i	−0.724933	−	0.724933i	0.244673	−	0.969606i	$-0.421319\pi$
$509$	−16.3552	−	16.3552i	−0.724933	−	0.724933i	−0.969606	+	0.244673i	$0.921319\pi$
$510$		0			0
$511$	8.36219	+	8.36219i	0.369922	+	0.369922i
$512$		0			0
$513$			59.9762i			2.64801i
$514$		0			0
$515$	−1.69965			−0.0748956
$516$		0			0
$517$	−67.1381			−2.95273
$518$		0			0
$519$	−48.9598	−	48.9598i	−2.14910	−	2.14910i
$520$		0			0
$521$	−21.7776	+	21.7776i	−0.954092	+	0.954092i	−0.998992	−	0.0448992i	$-0.985703\pi$
$521$	−21.7776	+	21.7776i	−0.954092	+	0.954092i	0.0448992	+	0.998992i	$0.485703\pi$
$522$		0			0
$523$	−8.93717			−0.390795			−0.195398	−	0.980724i	$-0.562600\pi$
$523$	−8.93717			−0.390795			−0.195398	+	0.980724i	$0.562600\pi$
$524$		0			0
$525$		−	15.9700i		−	0.696989i
$526$		0			0
$527$	11.8259	+	11.8259i	0.515143	+	0.515143i
$528$		0			0
$529$	−1.23115			−0.0535283
$530$		0			0
$531$		−	106.271i		−	4.61176i
$532$		0			0
$533$	0.207946	−	0.623103i	0.00900713	−	0.0269896i
$534$		0			0
$535$		−	2.54019i		−	0.109822i
$536$		0			0
$537$	−47.0224			−2.02917
$538$		0			0
$539$	3.73270	+	3.73270i	0.160779	+	0.160779i
$540$		0			0
$541$		−	8.68014i		−	0.373189i	−0.982437	−	0.186594i	$-0.940255\pi$
$541$		−	8.68014i		−	0.373189i	0.982437	−	0.186594i	$-0.0597450\pi$
$542$		0			0
$543$	21.4860			0.922052
$544$		0			0
$545$	−0.844338	+	0.844338i	−0.0361675	+	0.0361675i
$546$		0			0
$547$	−16.2596	−	16.2596i	−0.695210	−	0.695210i	0.268163	−	0.963373i	$-0.413583\pi$
$547$	−16.2596	−	16.2596i	−0.695210	−	0.695210i	−0.963373	+	0.268163i	$0.913583\pi$
$548$		0			0
$549$	76.4290			3.26191
$550$		0			0
$551$	−29.0829			−1.23897
$552$		0			0
$553$		−	2.15325i		−	0.0915655i
$554$		0			0
$555$	13.0736	+	13.0736i	0.554942	+	0.554942i
$556$		0			0
$557$	11.3822	+	11.3822i	0.482280	+	0.482280i	0.905859	−	0.423579i	$-0.139226\pi$
$557$	11.3822	+	11.3822i	0.482280	+	0.482280i	−0.423579	+	0.905859i	$0.639226\pi$
$558$		0			0
$559$	0.0802388	+	0.0802388i	0.00339374	+	0.00339374i
$560$		0			0
$561$	71.7953	−	71.7953i	3.03120	−	3.03120i
$562$		0			0
$563$	14.2376	−	14.2376i	0.600043	−	0.600043i	−0.340281	−	0.940324i	$-0.610522\pi$
$563$	14.2376	−	14.2376i	0.600043	−	0.600043i	0.940324	+	0.340281i	$0.110522\pi$
$564$		0			0
$565$			4.78872i			0.201463i
$566$		0			0
$567$	−25.5058	+	25.5058i	−1.07114	+	1.07114i
$568$		0			0
$569$		−	2.77716i		−	0.116425i	−0.998304	−	0.0582123i	$-0.981460\pi$
$569$		−	2.77716i		−	0.116425i	0.998304	−	0.0582123i	$-0.0185400\pi$
$570$		0			0
$571$	0.0948741	−	0.0948741i	0.00397036	−	0.00397036i	−0.705119	−	0.709089i	$-0.749106\pi$
$571$	0.0948741	−	0.0948741i	0.00397036	−	0.00397036i	0.709089	+	0.705119i	$0.249106\pi$
$572$		0			0
$573$	46.8931			1.95899
$574$		0			0
$575$	22.0887			0.921164
$576$		0			0
$577$	−18.1781	+	18.1781i	−0.756763	+	0.756763i	−0.975732	−	0.218969i	$-0.929731\pi$
$577$	−18.1781	+	18.1781i	−0.756763	+	0.756763i	0.218969	+	0.975732i	$0.429731\pi$
$578$		0			0
$579$		−	81.4408i		−	3.38457i
$580$		0			0
$581$	3.62461	−	3.62461i	0.150374	−	0.150374i
$582$		0			0
$583$			23.9424i			0.991595i
$584$		0			0
$585$	−0.313324	+	0.313324i	−0.0129543	+	0.0129543i
$586$		0			0
$587$	2.68151	−	2.68151i	0.110678	−	0.110678i	−0.649599	−	0.760277i	$-0.725063\pi$
$587$	2.68151	−	2.68151i	0.110678	−	0.110678i	0.760277	+	0.649599i	$0.225063\pi$
$588$		0			0
$589$	6.85547	+	6.85547i	0.282475	+	0.282475i
$590$		0			0
$591$	−37.6405	−	37.6405i	−1.54833	−	1.54833i
$592$		0			0
$593$	0.981314	+	0.981314i	0.0402978	+	0.0402978i	0.726969	−	0.686671i	$-0.240929\pi$
$593$	0.981314	+	0.981314i	0.0402978	+	0.0402978i	−0.686671	+	0.726969i	$0.740929\pi$
$594$		0			0
$595$			2.93927i			0.120498i
$596$		0			0
$597$	14.6028			0.597655
$598$		0			0
$599$	41.7455			1.70568			0.852838	−	0.522175i	$-0.174879\pi$
$599$	41.7455			1.70568			0.852838	+	0.522175i	$0.174879\pi$
$600$		0			0
$601$	−13.6073	−	13.6073i	−0.555052	−	0.555052i	0.372843	−	0.927895i	$-0.378383\pi$
$601$	−13.6073	−	13.6073i	−0.555052	−	0.555052i	−0.927895	+	0.372843i	$0.878383\pi$
$602$		0			0
$603$	16.5179	−	16.5179i	0.672662	−	0.672662i
$604$		0			0
$605$	−8.69425			−0.353472
$606$		0			0
$607$			6.69657i			0.271805i	0.990722	+	0.135903i	$0.0433935\pi$
$607$			6.69657i			0.271805i	−0.990722	+	0.135903i	$0.956607\pi$
$608$		0			0
$609$	−20.9870	−	20.9870i	−0.850434	−	0.850434i
$610$		0			0
$611$	1.30476			0.0527848
$612$		0			0
$613$		−	30.8965i		−	1.24790i	−0.781466	−	0.623948i	$-0.785528\pi$
$613$		−	30.8965i		−	1.24790i	0.781466	−	0.623948i	$-0.214472\pi$
$614$		0			0
$615$	−10.5617	−	3.52470i	−0.425887	−	0.142130i
$616$		0			0
$617$			4.03203i			0.162323i	0.996701	+	0.0811616i	$0.0258630\pi$
$617$			4.03203i			0.162323i	−0.996701	+	0.0811616i	$0.974137\pi$
$618$		0			0
$619$	−15.0789			−0.606071			−0.303036	−	0.952979i	$-0.598000\pi$
$619$	−15.0789			−0.606071			−0.303036	+	0.952979i	$0.598000\pi$
$620$		0			0
$621$	−59.8627	−	59.8627i	−2.40221	−	2.40221i
$622$		0			0
$623$			16.0568i			0.643300i
$624$		0			0
$625$	21.0847			0.843388
$626$		0			0
$627$	41.6198	−	41.6198i	1.66214	−	1.66214i
$628$		0			0
$629$	42.8692	+	42.8692i	1.70931	+	1.70931i
$630$		0			0
$631$	−39.5990			−1.57641			−0.788206	−	0.615411i	$-0.788990\pi$
$631$	−39.5990			−1.57641			−0.788206	+	0.615411i	$0.788990\pi$
$632$		0			0
$633$	48.9180			1.94432
$634$		0			0
$635$			2.16351i			0.0858562i
$636$		0			0
$637$	−0.0725409	−	0.0725409i	−0.00287418	−	0.00287418i
$638$		0			0
$639$	−67.2102	−	67.2102i	−2.65880	−	2.65880i
$640$		0			0
$641$	3.23359	+	3.23359i	0.127719	+	0.127719i	0.768077	−	0.640358i	$-0.221214\pi$
$641$	3.23359	+	3.23359i	0.127719	+	0.127719i	−0.640358	+	0.768077i	$0.721214\pi$
$642$		0			0
$643$	4.77331	−	4.77331i	0.188241	−	0.188241i	−0.606694	−	0.794935i	$-0.707505\pi$
$643$	4.77331	−	4.77331i	0.188241	−	0.188241i	0.794935	+	0.606694i	$0.207505\pi$
$644$		0			0
$645$	1.36005	−	1.36005i	0.0535521	−	0.0535521i
$646$		0			0
$647$		−	19.4761i		−	0.765684i	−0.923814	−	0.382842i	$-0.874945\pi$
$647$		−	19.4761i		−	0.765684i	0.923814	−	0.382842i	$-0.125055\pi$
$648$		0			0
$649$	−47.3418	+	47.3418i	−1.85833	+	1.85833i
$650$		0			0
$651$			9.89416i			0.387783i
$652$		0			0
$653$	−34.6014	+	34.6014i	−1.35406	+	1.35406i	−0.472993	+	0.881066i	$0.656827\pi$
$653$	−34.6014	+	34.6014i	−1.35406	+	1.35406i	−0.881066	+	0.472993i	$0.843173\pi$
$654$		0			0
$655$	8.25368			0.322498
$656$		0			0
$657$	99.0894			3.86585
$658$		0			0
$659$	−21.6336	+	21.6336i	−0.842724	+	0.842724i	−0.989212	−	0.146489i	$-0.953203\pi$
$659$	−21.6336	+	21.6336i	−0.842724	+	0.842724i	0.146489	+	0.989212i	$0.453203\pi$
$660$		0			0
$661$		−	20.3486i		−	0.791470i	−0.918365	−	0.395735i	$-0.870490\pi$
$661$		−	20.3486i		−	0.791470i	0.918365	−	0.395735i	$-0.129510\pi$
$662$		0			0
$663$	−1.39526	+	1.39526i	−0.0541875	+	0.0541875i
$664$		0			0
$665$			1.70390i			0.0660743i
$666$		0			0
$667$	29.0279	−	29.0279i	1.12396	−	1.12396i
$668$		0			0
$669$	6.28732	−	6.28732i	0.243082	−	0.243082i
$670$		0			0
$671$	−34.0478	−	34.0478i	−1.31440	−	1.31440i
$672$		0			0
$673$	−14.2765	−	14.2765i	−0.550319	−	0.550319i	0.376214	−	0.926533i	$-0.377226\pi$
$673$	−14.2765	−	14.2765i	−0.550319	−	0.550319i	−0.926533	+	0.376214i	$0.877226\pi$
$674$		0			0
$675$	−60.7424	−	60.7424i	−2.33797	−	2.33797i
$676$		0			0
$677$		−	33.2769i		−	1.27894i	−0.768818	−	0.639468i	$-0.779155\pi$
$677$		−	33.2769i		−	1.27894i	0.768818	−	0.639468i	$-0.220845\pi$
$678$		0			0
$679$	14.1798			0.544170
$680$		0			0
$681$	24.0918			0.923200
$682$		0			0
$683$	−11.5598	−	11.5598i	−0.442323	−	0.442323i	0.450469	−	0.892792i	$-0.351257\pi$
$683$	−11.5598	−	11.5598i	−0.442323	−	0.442323i	−0.892792	+	0.450469i	$0.851257\pi$
$684$		0			0
$685$	0.943056	−	0.943056i	0.0360323	−	0.0360323i
$686$		0			0
$687$	−19.7597			−0.753880
$688$		0			0
$689$		−	0.465295i		−	0.0177263i
$690$		0			0
$691$	19.8425	+	19.8425i	0.754845	+	0.754845i	0.975379	−	0.220534i	$-0.0707801\pi$
$691$	19.8425	+	19.8425i	0.754845	+	0.754845i	−0.220534	+	0.975379i	$0.570780\pi$
$692$		0			0
$693$	44.2313			1.68021
$694$		0			0
$695$			3.47116i			0.131669i
$696$		0			0
$697$	−34.6324	−	11.5577i	−1.31180	−	0.437780i
$698$		0			0
$699$			68.1180i			2.57646i
$700$		0			0
$701$	−25.0604			−0.946518			−0.473259	−	0.880923i	$-0.656923\pi$
$701$	−25.0604			−0.946518			−0.473259	+	0.880923i	$0.656923\pi$
$702$		0			0
$703$	24.8513	+	24.8513i	0.937285	+	0.937285i
$704$		0			0
$705$		−	22.1157i		−	0.832927i
$706$		0			0
$707$	0.401163			0.0150873
$708$		0			0
$709$	−29.0627	+	29.0627i	−1.09147	+	1.09147i	−0.0961021	+	0.995371i	$0.530638\pi$
$709$	−29.0627	+	29.0627i	−1.09147	+	1.09147i	−0.995371	+	0.0961021i	$0.969362\pi$
$710$		0			0
$711$	−12.7577	−	12.7577i	−0.478450	−	0.478450i
$712$		0			0
$713$	−13.6850			−0.512507
$714$		0			0
$715$	0.279161			0.0104400
$716$		0			0
$717$		−	37.5829i		−	1.40356i
$718$		0			0
$719$	31.8265	+	31.8265i	1.18693	+	1.18693i	0.977912	+	0.209016i	$0.0670260\pi$
$719$	31.8265	+	31.8265i	1.18693	+	1.18693i	0.209016	+	0.977912i	$0.432974\pi$
$720$		0			0
$721$	−2.33145	−	2.33145i	−0.0868278	−	0.0868278i
$722$		0			0
$723$	54.2876	+	54.2876i	2.01898	+	2.01898i
$724$		0			0
$725$	29.4544	−	29.4544i	1.09391	−	1.09391i
$726$		0			0
$727$	31.1328	−	31.1328i	1.15465	−	1.15465i	0.169043	−	0.985609i	$-0.445932\pi$
$727$	31.1328	−	31.1328i	1.15465	−	1.15465i	0.985609	−	0.169043i	$-0.0540678\pi$
$728$		0			0
$729$			118.613i			4.39307i
$730$		0			0
$731$	4.45971	−	4.45971i	0.164948	−	0.164948i
$732$		0			0
$733$		−	15.1476i		−	0.559489i	−0.960075	−	0.279744i	$-0.909750\pi$
$733$		−	15.1476i		−	0.559489i	0.960075	−	0.279744i	$-0.0902497\pi$
$734$		0			0
$735$	−1.22958	+	1.22958i	−0.0453536	+	0.0453536i
$736$		0			0
$737$	−14.7169			−0.542104
$738$		0			0
$739$	−50.1459			−1.84465			−0.922323	−	0.386421i	$-0.873711\pi$
$739$	−50.1459			−1.84465			−0.922323	+	0.386421i	$0.873711\pi$
$740$		0			0
$741$	−0.808836	+	0.808836i	−0.0297133	+	0.0297133i
$742$		0			0
$743$			36.9691i			1.35627i	0.734939	+	0.678133i	$0.237211\pi$
$743$			36.9691i			1.35627i	−0.734939	+	0.678133i	$0.762789\pi$
$744$		0			0
$745$	−3.78701	+	3.78701i	−0.138745	+	0.138745i
$746$		0			0
$747$		−	42.9505i		−	1.57148i
$748$		0			0
$749$	3.48445	−	3.48445i	0.127319	−	0.127319i
$750$		0			0
$751$	5.68062	−	5.68062i	0.207289	−	0.207289i	−0.595825	−	0.803114i	$-0.703175\pi$
$751$	5.68062	−	5.68062i	0.207289	−	0.207289i	0.803114	+	0.595825i	$0.203175\pi$
$752$		0			0
$753$	−9.16819	−	9.16819i	−0.334107	−	0.334107i
$754$		0			0
$755$	−2.82446	−	2.82446i	−0.102793	−	0.102793i
$756$		0			0
$757$	29.8059	+	29.8059i	1.08331	+	1.08331i	0.996198	+	0.0871151i	$0.0277648\pi$
$757$	29.8059	+	29.8059i	1.08331	+	1.08331i	0.0871151	+	0.996198i	$0.472235\pi$
$758$		0			0
$759$			83.0821i			3.01569i
$760$		0			0
$761$	21.9939			0.797279			0.398639	−	0.917108i	$-0.369483\pi$
$761$	21.9939			0.797279			0.398639	+	0.917108i	$0.369483\pi$
$762$		0			0
$763$	−2.31640			−0.0838593
$764$		0			0
$765$	17.4147	+	17.4147i	0.629630	+	0.629630i
$766$		0			0
$767$	0.920037	−	0.920037i	0.0332206	−	0.0332206i
$768$		0			0
$769$	−14.4592			−0.521410			−0.260705	−	0.965418i	$-0.583955\pi$
$769$	−14.4592			−0.521410			−0.260705	+	0.965418i	$0.583955\pi$
$770$		0			0
$771$			18.0575i			0.650325i
$772$		0			0
$773$	−6.62782	−	6.62782i	−0.238386	−	0.238386i	0.577795	−	0.816182i	$-0.303913\pi$
$773$	−6.62782	−	6.62782i	−0.238386	−	0.238386i	−0.816182	+	0.577795i	$0.803913\pi$
$774$		0			0
$775$	−13.8861			−0.498803
$776$		0			0
$777$			35.8667i			1.28671i
$778$		0			0
$779$	−20.0765	−	6.70003i	−0.719314	−	0.240054i
$780$		0			0
$781$			59.8820i			2.14275i
$782$		0			0
$783$	−159.649			−5.70538
$784$		0			0
$785$	3.20137	+	3.20137i	0.114262	+	0.114262i
$786$		0			0
$787$			48.0855i			1.71406i	0.515265	+	0.857031i	$0.327694\pi$
$787$			48.0855i			1.71406i	−0.515265	+	0.857031i	$0.672306\pi$
$788$		0			0
$789$	−71.8260			−2.55707
$790$		0			0
$791$	−6.56880	+	6.56880i	−0.233560	+	0.233560i
$792$		0			0
$793$	0.661682	+	0.661682i	0.0234970	+	0.0234970i
$794$		0			0
$795$	−7.88680			−0.279716
$796$		0			0
$797$	−11.0125			−0.390081			−0.195041	−	0.980795i	$-0.562484\pi$
$797$	−11.0125			−0.390081			−0.195041	+	0.980795i	$0.562484\pi$
$798$		0			0
$799$		−	72.5191i		−	2.56554i
$800$		0			0
$801$	95.1338	+	95.1338i	3.36139	+	3.36139i
$802$		0			0
$803$	−44.1426	−	44.1426i	−1.55776	−	1.55776i
$804$		0			0
$805$	−1.70067	−	1.70067i	−0.0599408	−	0.0599408i
$806$		0			0
$807$	20.2199	−	20.2199i	0.711774	−	0.711774i
$808$		0			0
$809$	6.51869	−	6.51869i	0.229185	−	0.229185i	−0.583167	−	0.812352i	$-0.698187\pi$
$809$	6.51869	−	6.51869i	0.229185	−	0.229185i	0.812352	+	0.583167i	$0.198187\pi$
$810$		0			0
$811$			26.7717i			0.940082i	0.882644	+	0.470041i	$0.155761\pi$
$811$			26.7717i			0.940082i	−0.882644	+	0.470041i	$0.844239\pi$
$812$		0			0
$813$	−34.3038	+	34.3038i	−1.20309	+	1.20309i
$814$		0			0
$815$			1.96547i			0.0688475i
$816$		0			0
$817$	2.58530	−	2.58530i	0.0904483	−	0.0904483i
$818$		0			0
$819$	−0.859588			−0.0300364
$820$		0			0
$821$	13.5241			0.471995			0.235997	−	0.971754i	$-0.424164\pi$
$821$	13.5241			0.471995			0.235997	+	0.971754i	$0.424164\pi$
$822$		0			0
$823$	36.5171	−	36.5171i	1.27291	−	1.27291i	0.328352	−	0.944556i	$-0.393507\pi$
$823$	36.5171	−	36.5171i	1.27291	−	1.27291i	0.944556	−	0.328352i	$-0.106493\pi$
$824$		0			0
$825$			84.3030i			2.93506i
$826$		0			0
$827$	25.4371	−	25.4371i	0.884534	−	0.884534i	−0.109457	−	0.993991i	$-0.534911\pi$
$827$	25.4371	−	25.4371i	0.884534	−	0.884534i	0.993991	+	0.109457i	$0.0349113\pi$
$828$		0			0
$829$			8.22557i			0.285686i	0.989745	+	0.142843i	$0.0456243\pi$
$829$			8.22557i			0.285686i	−0.989745	+	0.142843i	$0.954376\pi$
$830$		0			0
$831$	−40.6594	+	40.6594i	−1.41046	+	1.41046i
$832$		0			0
$833$	−4.03186	+	4.03186i	−0.139696	+	0.139696i
$834$		0			0
$835$	−4.93644	−	4.93644i	−0.170832	−	0.170832i
$836$		0			0
$837$	37.6327	+	37.6327i	1.30078	+	1.30078i
$838$		0			0
$839$	17.6943	+	17.6943i	0.610875	+	0.610875i	0.943174	−	0.332299i	$-0.107824\pi$
$839$	17.6943	+	17.6943i	0.610875	+	0.610875i	−0.332299	+	0.943174i	$0.607824\pi$
$840$		0			0
$841$		−	48.4149i		−	1.66948i
$842$		0			0
$843$	20.5425			0.707520
$844$		0			0
$845$	6.69591			0.230346
$846$		0			0
$847$	−11.9261	−	11.9261i	−0.409786	−	0.409786i
$848$		0			0
$849$	−39.4552	+	39.4552i	−1.35410	+	1.35410i
$850$		0			0
$851$	−49.6086			−1.70056
$852$		0			0
$853$			23.7356i			0.812690i	0.913720	+	0.406345i	$0.133197\pi$
$853$			23.7356i			0.812690i	−0.913720	+	0.406345i	$0.866803\pi$
$854$		0			0
$855$	10.0953	+	10.0953i	0.345253	+	0.345253i
$856$		0			0
$857$	−49.7509			−1.69946			−0.849729	−	0.527220i	$-0.823234\pi$
$857$	−49.7509			−1.69946			−0.849729	+	0.527220i	$0.823234\pi$
$858$		0			0
$859$			2.18034i			0.0743921i	0.999308	+	0.0371960i	$0.0118426\pi$
$859$			2.18034i			0.0743921i	−0.999308	+	0.0371960i	$0.988157\pi$
$860$		0			0
$861$	−9.65277	−	19.3226i	−0.328966	−	0.658512i
$862$		0			0
$863$			40.8783i			1.39151i	0.718277	+	0.695757i	$0.244931\pi$
$863$			40.8783i			1.39151i	−0.718277	+	0.695757i	$0.755069\pi$
$864$		0			0
$865$	−10.5808			−0.359760
$866$		0			0
$867$	36.9999	+	36.9999i	1.25658	+	1.25658i
$868$		0			0
$869$			11.3666i			0.385587i
$870$		0			0
$871$	0.286007			0.00969098
$872$		0			0
$873$	84.0131	−	84.0131i	2.84341	−	2.84341i
$874$		0			0
$875$	−3.54819	−	3.54819i	−0.119951	−	0.119951i
$876$		0			0
$877$	−1.56421			−0.0528197			−0.0264099	−	0.999651i	$-0.508407\pi$
$877$	−1.56421			−0.0528197			−0.0264099	+	0.999651i	$0.508407\pi$
$878$		0			0
$879$	−3.72871			−0.125766
$880$		0			0
$881$		−	1.40473i		−	0.0473267i	−0.999720	−	0.0236633i	$-0.992467\pi$
$881$		−	1.40473i		−	0.0473267i	0.999720	−	0.0236633i	$-0.00753297\pi$
$882$		0			0
$883$	41.1511	+	41.1511i	1.38484	+	1.38484i	0.835783	+	0.549061i	$0.185014\pi$
$883$	41.1511	+	41.1511i	1.38484	+	1.38484i	0.549061	+	0.835783i	$0.314986\pi$
$884$		0			0
$885$	−15.5947	−	15.5947i	−0.524210	−	0.524210i
$886$		0			0
$887$	−20.2592	−	20.2592i	−0.680237	−	0.680237i	0.279816	−	0.960054i	$-0.409726\pi$
$887$	−20.2592	−	20.2592i	−0.680237	−	0.680237i	−0.960054	+	0.279816i	$0.909726\pi$
$888$		0			0
$889$	−2.96774	+	2.96774i	−0.0995347	+	0.0995347i
$890$		0			0
$891$	134.641	−	134.641i	4.51063	−	4.51063i
$892$		0			0
$893$		−	42.0394i		−	1.40680i
$894$		0			0
$895$	−5.08108	+	5.08108i	−0.169842	+	0.169842i
$896$		0			0
$897$		−	1.61461i		−	0.0539103i
$898$		0			0
$899$	−18.2484	+	18.2484i	−0.608617	+	0.608617i
$900$		0			0
$901$	−25.8614			−0.861567
$902$		0			0
$903$	3.73124			0.124168
$904$		0			0
$905$	2.32170	−	2.32170i	0.0771759	−	0.0771759i
$906$		0			0
$907$			0.616177i			0.0204598i	0.999948	+	0.0102299i	$0.00325634\pi$
$907$			0.616177i			0.0204598i	−0.999948	+	0.0102299i	$0.996744\pi$
$908$		0			0
$909$	2.37683	−	2.37683i	0.0788344	−	0.0788344i
$910$		0			0
$911$		−	13.9601i		−	0.462518i	−0.972892	−	0.231259i	$-0.925716\pi$
$911$		−	13.9601i		−	0.462518i	0.972892	−	0.231259i	$-0.0742845\pi$
$912$		0			0
$913$	−19.1337	+	19.1337i	−0.633233	+	0.633233i
$914$		0			0
$915$	11.2156	−	11.2156i	0.370775	−	0.370775i
$916$		0			0
$917$	11.3218	+	11.3218i	0.373878	+	0.373878i
$918$		0			0
$919$	−2.01458	−	2.01458i	−0.0664550	−	0.0664550i	0.673098	−	0.739553i	$-0.264963\pi$
$919$	−2.01458	−	2.01458i	−0.0664550	−	0.0664550i	−0.739553	+	0.673098i	$0.764963\pi$
$920$		0			0
$921$	23.4549	+	23.4549i	0.772866	+	0.772866i
$922$		0			0
$923$		−	1.16374i		−	0.0383050i
$924$		0			0
$925$	−50.3376			−1.65509
$926$		0			0
$927$	−27.6270			−0.907390
$928$		0			0
$929$	−3.83840	−	3.83840i	−0.125934	−	0.125934i	0.641331	−	0.767264i	$-0.278383\pi$
$929$	−3.83840	−	3.83840i	−0.125934	−	0.125934i	−0.767264	+	0.641331i	$0.778383\pi$
$930$		0			0
$931$	−2.33728	+	2.33728i	−0.0766012	+	0.0766012i
$932$		0			0
$933$	48.2625			1.58004
$934$		0			0
$935$		−	15.5159i		−	0.507424i
$936$		0			0
$937$	10.2106	+	10.2106i	0.333566	+	0.333566i	0.853939	−	0.520373i	$-0.174207\pi$
$937$	10.2106	+	10.2106i	0.333566	+	0.333566i	−0.520373	+	0.853939i	$0.674207\pi$
$938$		0			0
$939$	25.3850			0.828409
$940$		0			0
$941$			1.80764i			0.0589272i	0.999566	+	0.0294636i	$0.00937992\pi$
$941$			1.80764i			0.0589272i	−0.999566	+	0.0294636i	$0.990620\pi$
$942$		0			0
$943$	26.7258	−	13.3511i	0.870313	−	0.434772i
$944$		0			0
$945$			9.35344i			0.304267i
$946$		0			0
$947$	−22.8630			−0.742946			−0.371473	−	0.928444i	$-0.621147\pi$
$947$	−22.8630			−0.742946			−0.371473	+	0.928444i	$0.621147\pi$
$948$		0			0
$949$	0.857864	+	0.857864i	0.0278474	+	0.0278474i
$950$		0			0
$951$			15.6999i			0.509105i
$952$		0			0
$953$	−2.23703			−0.0724647			−0.0362323	−	0.999343i	$-0.511536\pi$
$953$	−2.23703			−0.0724647			−0.0362323	+	0.999343i	$0.511536\pi$
$954$		0			0
$955$	5.06711	−	5.06711i	0.163968	−	0.163968i
$956$		0			0
$957$	110.787	+	110.787i	3.58122	+	3.58122i
$958$		0			0
$959$	2.58723			0.0835459
$960$		0			0
$961$	−22.3969			−0.722481
$962$		0			0
$963$		−	41.2896i		−	1.33054i
$964$		0			0
$965$	−8.80022	−	8.80022i	−0.283289	−	0.283289i
$966$		0			0
$967$	28.7103	+	28.7103i	0.923261	+	0.923261i	0.997258	−	0.0739977i	$-0.0235758\pi$
$967$	28.7103	+	28.7103i	0.923261	+	0.923261i	−0.0739977	+	0.997258i	$0.523576\pi$
$968$		0			0
$969$	44.9555	+	44.9555i	1.44418	+	1.44418i
$970$		0			0
$971$	10.5359	−	10.5359i	0.338114	−	0.338114i	−0.517543	−	0.855657i	$-0.673153\pi$
$971$	10.5359	−	10.5359i	0.338114	−	0.338114i	0.855657	+	0.517543i	$0.173153\pi$
$972$		0			0
$973$	−4.76147	+	4.76147i	−0.152646	+	0.152646i
$974$		0			0
$975$		−	1.63834i		−	0.0524688i
$976$		0			0
$977$	19.7241	−	19.7241i	0.631030	−	0.631030i	−0.317297	−	0.948326i	$-0.602775\pi$
$977$	19.7241	−	19.7241i	0.631030	−	0.631030i	0.948326	+	0.317297i	$0.102775\pi$
$978$		0			0
$979$		−	84.7609i		−	2.70897i
$980$		0			0
$981$	−13.7243	+	13.7243i	−0.438183	+	0.438183i
$982$		0			0
$983$	−43.5824			−1.39006			−0.695031	−	0.718980i	$-0.744609\pi$
$983$	−43.5824			−1.39006			−0.695031	+	0.718980i	$0.744609\pi$
$984$		0			0
$985$	−8.13461			−0.259190
$986$		0			0
$987$	30.3367	−	30.3367i	0.965628	−	0.965628i
$988$		0			0
$989$			5.16082i			0.164105i
$990$		0			0
$991$	19.1708	−	19.1708i	0.608982	−	0.608982i	−0.333698	−	0.942680i	$-0.608297\pi$
$991$	19.1708	−	19.1708i	0.608982	−	0.608982i	0.942680	+	0.333698i	$0.108297\pi$
$992$		0			0
$993$			37.8999i			1.20272i
$994$		0			0
$995$	1.57793	−	1.57793i	0.0500238	−	0.0500238i
$996$		0			0
$997$	−8.59147	+	8.59147i	−0.272095	+	0.272095i	−0.829943	−	0.557848i	$-0.811627\pi$
$997$	−8.59147	+	8.59147i	−0.272095	+	0.272095i	0.557848	+	0.829943i	$0.311627\pi$
$998$		0			0
$999$	136.420	+	136.420i	4.31613	+	4.31613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.729.18	yes	36
41.9	even	4	inner	1148.2.k.b.337.18	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.18	✓	36	41.9	even	4	inner
1148.2.k.b.729.18	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)

\(f(q)\)	\(=\)	\(q+(2.38527 - 2.38527i) q^{3} -0.515487i q^{5} +(0.707107 - 0.707107i) q^{7} -8.37900i q^{9} +O(q^{10})\)	\(q+(2.38527 - 2.38527i) q^{3} -0.515487i q^{5} +(0.707107 - 0.707107i) q^{7} -8.37900i q^{9} +(-3.73270 + 3.73270i) q^{11} +(0.0725409 - 0.0725409i) q^{13} +(-1.22958 - 1.22958i) q^{15} +(-4.03186 - 4.03186i) q^{17} +(-2.33728 - 2.33728i) q^{19} -3.37328i q^{21} +4.66571 q^{23} +4.73427 q^{25} +(-12.8303 - 12.8303i) q^{27} +(6.22153 - 6.22153i) q^{29} -2.93310 q^{31} +17.8070i q^{33} +(-0.364505 - 0.364505i) q^{35} -10.6326 q^{37} -0.346059i q^{39} +(5.72814 - 2.86154i) q^{41} +1.10612i q^{43} -4.31927 q^{45} +(8.99324 + 8.99324i) q^{47} -1.00000i q^{49} -19.2341 q^{51} +(3.20712 - 3.20712i) q^{53} +(1.92416 + 1.92416i) q^{55} -11.1501 q^{57} +12.6830 q^{59} +9.12150i q^{61} +(-5.92485 - 5.92485i) q^{63} +(-0.0373939 - 0.0373939i) q^{65} +(1.97135 + 1.97135i) q^{67} +(11.1290 - 11.1290i) q^{69} +(8.02127 - 8.02127i) q^{71} +11.8259i q^{73} +(11.2925 - 11.2925i) q^{75} +5.27883i q^{77} +(1.52258 - 1.52258i) q^{79} -36.0706 q^{81} +5.12597 q^{83} +(-2.07837 + 2.07837i) q^{85} -29.6800i q^{87} +(-11.3538 + 11.3538i) q^{89} -0.102588i q^{91} +(-6.99623 + 6.99623i) q^{93} +(-1.20484 + 1.20484i) q^{95} +(10.0266 + 10.0266i) q^{97} +(31.2763 + 31.2763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 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

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