LMFDB - Embedded newform 1008.2.ca.e.257.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(257,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.257"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.ca (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.22
Character	$\chi$	$=$	1008.257
Dual form			1008.2.ca.e.353.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.68581 + 0.397560i) q^{3} +(-0.311798 - 0.540051i) q^{5} +(-2.62086 - 0.362103i) q^{7} +(2.68389 + 1.34042i) q^{9} +(4.50253 + 2.59954i) q^{11} +(2.74023 + 1.58207i) q^{13} +(-0.310929 - 1.03438i) q^{15} +(-0.437594 - 0.757935i) q^{17} +(1.41874 + 0.819107i) q^{19} +(-4.27430 - 1.65238i) q^{21} +(-7.14886 + 4.12740i) q^{23} +(2.30556 - 3.99335i) q^{25} +(3.99163 + 3.32670i) q^{27} +(4.96435 - 2.86617i) q^{29} +4.64486i q^{31} +(6.55693 + 6.17234i) q^{33} +(0.621624 + 1.52830i) q^{35} +(1.24291 - 2.15278i) q^{37} +(3.99054 + 3.75648i) q^{39} +(3.52382 - 6.10344i) q^{41} +(1.56398 + 2.70890i) q^{43} +(-0.112939 - 1.86738i) q^{45} +9.46768 q^{47} +(6.73776 + 1.89804i) q^{49} +(-0.436375 - 1.45170i) q^{51} +(1.15189 - 0.665044i) q^{53} -3.24212i q^{55} +(2.06607 + 1.94489i) q^{57} +6.36667 q^{59} +11.1541i q^{61} +(-6.54872 - 4.48489i) q^{63} -1.97315i q^{65} -12.0990 q^{67} +(-13.6925 + 4.11590i) q^{69} -10.5861i q^{71} +(-11.6719 + 6.73878i) q^{73} +(5.47433 - 5.81542i) q^{75} +(-10.8592 - 8.44339i) q^{77} -9.69679 q^{79} +(5.40655 + 7.19508i) q^{81} +(-0.192030 - 0.332606i) q^{83} +(-0.272882 + 0.472646i) q^{85} +(9.50841 - 2.85818i) q^{87} +(-0.0198983 + 0.0344648i) q^{89} +(-6.60888 - 5.13864i) q^{91} +(-1.84661 + 7.83033i) q^{93} -1.02159i q^{95} +(-5.94681 + 3.43339i) q^{97} +(8.59984 + 13.0122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9} - 8 q^{15} + 8 q^{21} + 12 q^{23} - 24 q^{25} + 18 q^{27} + 18 q^{29} + 10 q^{39} + 6 q^{41} + 6 q^{43} + 6 q^{45} - 36 q^{47} + 6 q^{49} + 12 q^{51} + 12 q^{53} + 4 q^{57} - 46 q^{63} + 54 q^{75}+ \cdots + 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 - 8 * q^15 + 8 * q^21 + 12 * q^23 - 24 * q^25 + 18 * q^27 + 18 * q^29 + 10 * q^39 + 6 * q^41 + 6 * q^43 + 6 * q^45 - 36 * q^47 + 6 * q^49 + 12 * q^51 + 12 * q^53 + 4 * q^57 - 46 * q^63 + 54 * q^75 - 36 * q^77 + 12 * q^79 + 24 * q^87 + 18 * q^89 - 6 * q^91 + 16 * q^93 + 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.68581	+	0.397560i	0.973301	+	0.229531i
$3$	1.68581	+	0.397560i	0.973301	+	0.229531i
$4$		0			0
$5$	−0.311798	−	0.540051i	−0.139440	−	0.241518i	0.787845	−	0.615874i	$-0.211197\pi$
$5$	−0.311798	−	0.540051i	−0.139440	−	0.241518i	−0.927285	+	0.374356i	$0.877864\pi$
$6$		0			0
$7$	−2.62086	−	0.362103i	−0.990590	−	0.136862i
$7$	−2.62086	−	0.362103i	−0.990590	−	0.136862i
$8$		0			0
$9$	2.68389	+	1.34042i	0.894631	+	0.446806i
$10$		0			0
$11$	4.50253	+	2.59954i	1.35756	+	0.783790i	0.989295	−	0.145930i	$-0.0466173\pi$
$11$	4.50253	+	2.59954i	1.35756	+	0.783790i	0.368269	+	0.929719i	$0.379951\pi$
$12$		0			0
$13$	2.74023	+	1.58207i	0.760004	+	0.438788i	0.829297	−	0.558808i	$-0.188741\pi$
$13$	2.74023	+	1.58207i	0.760004	+	0.438788i	−0.0692932	+	0.997596i	$0.522074\pi$
$14$		0			0
$15$	−0.310929	−	1.03438i	−0.0802816	−	0.267076i
$16$		0			0
$17$	−0.437594	−	0.757935i	−0.106132	−	0.183826i	0.808068	−	0.589089i	$-0.200513\pi$
$17$	−0.437594	−	0.757935i	−0.106132	−	0.183826i	−0.914200	+	0.405263i	$0.867180\pi$
$18$		0			0
$19$	1.41874	+	0.819107i	0.325480	+	0.187916i	0.653833	−	0.756639i	$-0.273160\pi$
$19$	1.41874	+	0.819107i	0.325480	+	0.187916i	−0.328352	+	0.944555i	$0.606493\pi$
$20$		0			0
$21$	−4.27430	−	1.65238i	−0.932728	−	0.360580i
$22$		0			0
$23$	−7.14886	+	4.12740i	−1.49064	+	0.860622i	−0.999943	−	0.0107077i	$-0.996592\pi$
$23$	−7.14886	+	4.12740i	−1.49064	+	0.860622i	−0.490698	+	0.871330i	$0.663258\pi$
$24$		0			0
$25$	2.30556	−	3.99335i	0.461113	−	0.798671i
$26$		0			0
$27$	3.99163	+	3.32670i	0.768189	+	0.640223i
$28$		0			0
$29$	4.96435	−	2.86617i	0.921856	−	0.532234i	0.0376295	−	0.999292i	$-0.488019\pi$
$29$	4.96435	−	2.86617i	0.921856	−	0.532234i	0.884227	+	0.467058i	$0.154686\pi$
$30$		0			0
$31$			4.64486i			0.834241i	0.908851	+	0.417120i	$0.136961\pi$
$31$			4.64486i			0.834241i	−0.908851	+	0.417120i	$0.863039\pi$
$32$		0			0
$33$	6.55693	+	6.17234i	1.14141	+	1.07447i
$34$		0			0
$35$	0.621624	+	1.52830i	0.105074	+	0.258329i
$36$		0			0
$37$	1.24291	−	2.15278i	0.204333	−	0.353916i	−0.745587	−	0.666408i	$-0.767831\pi$
$37$	1.24291	−	2.15278i	0.204333	−	0.353916i	0.949920	+	0.312493i	$0.101164\pi$
$38$		0			0
$39$	3.99054	+	3.75648i	0.638997	+	0.601518i
$40$		0			0
$41$	3.52382	−	6.10344i	0.550329	−	0.953198i	−0.447922	−	0.894073i	$-0.647836\pi$
$41$	3.52382	−	6.10344i	0.550329	−	0.953198i	0.998251	−	0.0591249i	$-0.0188310\pi$
$42$		0			0
$43$	1.56398	+	2.70890i	0.238505	+	0.413103i	0.960286	−	0.279019i	$-0.0900093\pi$
$43$	1.56398	+	2.70890i	0.238505	+	0.413103i	−0.721780	+	0.692122i	$0.756676\pi$
$44$		0			0
$45$	−0.112939	−	1.86738i	−0.0168360	−	0.278372i
$46$		0			0
$47$	9.46768			1.38100			0.690502	−	0.723331i	$-0.257390\pi$
$47$	9.46768			1.38100			0.690502	+	0.723331i	$0.257390\pi$
$48$		0			0
$49$	6.73776	+	1.89804i	0.962537	+	0.271149i
$50$		0			0
$51$	−0.436375	−	1.45170i	−0.0611047	−	0.203279i
$52$		0			0
$53$	1.15189	−	0.665044i	0.158224	−	0.0913508i	−0.418797	−	0.908080i	$-0.637548\pi$
$53$	1.15189	−	0.665044i	0.158224	−	0.0913508i	0.577021	+	0.816729i	$0.304215\pi$
$54$		0			0
$55$		−	3.24212i		−	0.437168i
$56$		0			0
$57$	2.06607	+	1.94489i	0.273658	+	0.257607i
$58$		0			0
$59$	6.36667			0.828870			0.414435	−	0.910079i	$-0.363979\pi$
$59$	6.36667			0.828870			0.414435	+	0.910079i	$0.363979\pi$
$60$		0			0
$61$			11.1541i			1.42814i	0.700075	+	0.714069i	$0.253150\pi$
$61$			11.1541i			1.42814i	−0.700075	+	0.714069i	$0.746850\pi$
$62$		0			0
$63$	−6.54872	−	4.48489i	−0.825061	−	0.565043i
$64$		0			0
$65$		−	1.97315i		−	0.244739i
$66$		0			0
$67$	−12.0990			−1.47813			−0.739065	−	0.673634i	$-0.764733\pi$
$67$	−12.0990			−1.47813			−0.739065	+	0.673634i	$0.764733\pi$
$68$		0			0
$69$	−13.6925	+	4.11590i	−1.64838	+	0.495496i
$70$		0			0
$71$		−	10.5861i		−	1.25634i	−0.778076	−	0.628171i	$-0.783804\pi$
$71$		−	10.5861i		−	1.25634i	0.778076	−	0.628171i	$-0.216196\pi$
$72$		0			0
$73$	−11.6719	+	6.73878i	−1.36609	+	0.788714i	−0.990427	−	0.138041i	$-0.955920\pi$
$73$	−11.6719	+	6.73878i	−1.36609	+	0.788714i	−0.375666	+	0.926755i	$0.622586\pi$
$74$		0			0
$75$	5.47433	−	5.81542i	0.632122	−	0.671507i
$76$		0			0
$77$	−10.8592	−	8.44339i	−1.23752	−	0.962214i
$78$		0			0
$79$	−9.69679			−1.09097			−0.545487	−	0.838119i	$-0.683655\pi$
$79$	−9.69679			−1.09097			−0.545487	+	0.838119i	$0.683655\pi$
$80$		0			0
$81$	5.40655	+	7.19508i	0.600728	+	0.799453i
$82$		0			0
$83$	−0.192030	−	0.332606i	−0.0210781	−	0.0365083i	0.855294	−	0.518143i	$-0.173377\pi$
$83$	−0.192030	−	0.332606i	−0.0210781	−	0.0365083i	−0.876372	+	0.481635i	$0.840043\pi$
$84$		0			0
$85$	−0.272882	+	0.472646i	−0.0295982	+	0.0512656i
$86$		0			0
$87$	9.50841	−	2.85818i	1.01941	−	0.306429i
$88$		0			0
$89$	−0.0198983	+	0.0344648i	−0.00210921	+	0.00365326i	−0.867078	−	0.498172i	$-0.834005\pi$
$89$	−0.0198983	+	0.0344648i	−0.00210921	+	0.00365326i	0.864969	+	0.501826i	$0.167338\pi$
$90$		0			0
$91$	−6.60888	−	5.13864i	−0.692799	−	0.538675i
$92$		0			0
$93$	−1.84661	+	7.83033i	−0.191484	+	0.811968i
$94$		0			0
$95$		−	1.02159i		−	0.104812i
$96$		0			0
$97$	−5.94681	+	3.43339i	−0.603807	+	0.348608i	−0.770538	−	0.637394i	$-0.780012\pi$
$97$	−5.94681	+	3.43339i	−0.603807	+	0.348608i	0.166731	+	0.986002i	$0.446679\pi$
$98$		0			0
$99$	8.59984	+	13.0122i	0.864316	+	1.30777i
$100$		0			0
$101$	4.46299	−	7.73012i	0.444084	−	0.769176i	−0.553904	−	0.832581i	$-0.686863\pi$
$101$	4.46299	−	7.73012i	0.444084	−	0.769176i	0.997988	+	0.0634046i	$0.0201959\pi$
$102$		0			0
$103$	−7.68060	+	4.43439i	−0.756792	+	0.436934i	−0.828143	−	0.560517i	$-0.810602\pi$
$103$	−7.68060	+	4.43439i	−0.756792	+	0.436934i	0.0713510	+	0.997451i	$0.477269\pi$
$104$		0			0
$105$	0.440348	+	2.82355i	0.0429736	+	0.275550i
$106$		0			0
$107$	−2.64326	−	1.52609i	−0.255534	−	0.147532i	0.366762	−	0.930315i	$-0.380466\pi$
$107$	−2.64326	−	1.52609i	−0.255534	−	0.147532i	−0.622295	+	0.782782i	$0.713800\pi$
$108$		0			0
$109$	−5.55069	−	9.61408i	−0.531660	−	0.920862i	−0.999317	−	0.0369519i	$-0.988235\pi$
$109$	−5.55069	−	9.61408i	−0.531660	−	0.920862i	0.467657	−	0.883910i	$-0.345098\pi$
$110$		0			0
$111$	2.95117	−	3.13505i	0.280113	−	0.297566i
$112$		0			0
$113$	−3.13836	−	1.81193i	−0.295232	−	0.170452i	0.345067	−	0.938578i	$-0.387856\pi$
$113$	−3.13836	−	1.81193i	−0.295232	−	0.170452i	−0.640299	+	0.768126i	$0.721190\pi$
$114$		0			0
$115$	4.45801	+	2.57383i	0.415711	+	0.240011i
$116$		0			0
$117$	5.23385	+	7.91918i	0.483869	+	0.732128i
$118$		0			0
$119$	0.872420	+	2.14489i	0.0799746	+	0.196622i
$120$		0			0
$121$	8.01518	+	13.8827i	0.728653	+	1.26206i
$122$		0			0
$123$	8.36697	−	8.88830i	0.754425	−	0.801431i
$124$		0			0
$125$	−5.99347			−0.536072
$126$		0			0
$127$	10.1408			0.899852			0.449926	−	0.893066i	$-0.351450\pi$
$127$	10.1408			0.899852			0.449926	+	0.893066i	$0.351450\pi$
$128$		0			0
$129$	1.55962	+	5.18846i	0.137317	+	0.456818i
$130$		0			0
$131$	−10.8788	−	18.8426i	−0.950484	−	1.64629i	−0.744380	−	0.667756i	$-0.767255\pi$
$131$	−10.8788	−	18.8426i	−0.950484	−	1.64629i	−0.206103	−	0.978530i	$-0.566078\pi$
$132$		0			0
$133$	−3.42170	−	2.66049i	−0.296699	−	0.230694i
$134$		0			0
$135$	0.552001	−	3.19294i	0.0475087	−	0.274804i
$136$		0			0
$137$	−0.340450	−	0.196559i	−0.0290866	−	0.0167932i	0.485386	−	0.874300i	$-0.338679\pi$
$137$	−0.340450	−	0.196559i	−0.0290866	−	0.0167932i	−0.514473	+	0.857507i	$0.672012\pi$
$138$		0			0
$139$	−15.6647	−	9.04400i	−1.32866	−	0.767102i	−0.343568	−	0.939128i	$-0.611635\pi$
$139$	−15.6647	−	9.04400i	−1.32866	−	0.767102i	−0.985092	+	0.172026i	$0.944969\pi$
$140$		0			0
$141$	15.9607	+	3.76397i	1.34413	+	0.316984i
$142$		0			0
$143$	8.22532	+	14.2467i	0.687836	+	1.19137i
$144$		0			0
$145$	−3.09575	−	1.78733i	−0.257088	−	0.148430i
$146$		0			0
$147$	10.6040	+	5.87840i	0.874602	+	0.484842i
$148$		0			0
$149$	−8.87748	+	5.12542i	−0.727272	+	0.419891i	−0.817423	−	0.576038i	$-0.804598\pi$
$149$	−8.87748	+	5.12542i	−0.727272	+	0.419891i	0.0901515	+	0.995928i	$0.471265\pi$
$150$		0			0
$151$	11.9006	−	20.6124i	0.968457	−	1.67742i	0.268432	−	0.963299i	$-0.413495\pi$
$151$	11.9006	−	20.6124i	0.968457	−	1.67742i	0.700025	−	0.714118i	$-0.253172\pi$
$152$		0			0
$153$	−0.158505	−	2.62078i	−0.0128143	−	0.211877i
$154$		0			0
$155$	2.50846	−	1.44826i	0.201484	−	0.116327i
$156$		0			0
$157$		−	11.5080i		−	0.918442i	−0.888322	−	0.459221i	$-0.848129\pi$
$157$		−	11.5080i		−	0.918442i	0.888322	−	0.459221i	$-0.151871\pi$
$158$		0			0
$159$	2.20626	−	0.663190i	0.174968	−	0.0525944i
$160$		0			0
$161$	20.2307	−	8.22868i	1.59440	−	0.648511i
$162$		0			0
$163$	−10.4614	+	18.1197i	−0.819399	+	1.41924i	0.0867261	+	0.996232i	$0.472360\pi$
$163$	−10.4614	+	18.1197i	−0.819399	+	1.41924i	−0.906125	+	0.423009i	$0.860974\pi$
$164$		0			0
$165$	1.28894	−	5.46560i	0.100344	−	0.425496i
$166$		0			0
$167$	−6.69358	+	11.5936i	−0.517965	+	0.897141i	0.481817	+	0.876272i	$0.339977\pi$
$167$	−6.69358	+	11.5936i	−0.517965	+	0.897141i	−0.999782	+	0.0208697i	$0.993357\pi$
$168$		0			0
$169$	−1.49408	−	2.58782i	−0.114929	−	0.199063i
$170$		0			0
$171$	2.70979	+	4.10010i	0.207223	+	0.313542i
$172$		0			0
$173$	−5.88865			−0.447706			−0.223853	−	0.974623i	$-0.571864\pi$
$173$	−5.88865			−0.447706			−0.223853	+	0.974623i	$0.571864\pi$
$174$		0			0
$175$	−7.48856	+	9.63115i	−0.566082	+	0.728046i
$176$		0			0
$177$	10.7330	+	2.53113i	0.806740	+	0.190252i
$178$		0			0
$179$	14.4333	−	8.33310i	1.07880	−	0.622845i	0.148227	−	0.988953i	$-0.452643\pi$
$179$	14.4333	−	8.33310i	1.07880	−	0.622845i	0.930572	+	0.366109i	$0.119310\pi$
$180$		0			0
$181$		−	0.462705i		−	0.0343926i	−0.999852	−	0.0171963i	$-0.994526\pi$
$181$		−	0.462705i		−	0.0343926i	0.999852	−	0.0171963i	$-0.00547402\pi$
$182$		0			0
$183$	−4.43443	+	18.8037i	−0.327803	+	1.39001i
$184$		0			0
$185$	−1.55015			−0.113969
$186$		0			0
$187$		−	4.55017i		−	0.332741i
$188$		0			0
$189$	−9.25687	−	10.1642i	−0.673338	−	0.739335i
$190$		0			0
$191$		−	13.6385i		−	0.986850i	−0.869788	−	0.493425i	$-0.835745\pi$
$191$		−	13.6385i		−	0.986850i	0.869788	−	0.493425i	$-0.164255\pi$
$192$		0			0
$193$	−11.4787			−0.826251			−0.413126	−	0.910674i	$-0.635563\pi$
$193$	−11.4787			−0.826251			−0.413126	+	0.910674i	$0.635563\pi$
$194$		0			0
$195$	0.784447	−	3.32636i	0.0561754	−	0.238205i
$196$		0			0
$197$			4.78184i			0.340692i	0.985384	+	0.170346i	$0.0544885\pi$
$197$			4.78184i			0.340692i	−0.985384	+	0.170346i	$0.945511\pi$
$198$		0			0
$199$	−7.87833	+	4.54856i	−0.558480	+	0.322439i	−0.752535	−	0.658552i	$-0.771169\pi$
$199$	−7.87833	+	4.54856i	−0.558480	+	0.322439i	0.194055	+	0.980991i	$0.437836\pi$
$200$		0			0
$201$	−20.3966	−	4.81009i	−1.43867	−	0.339277i
$202$		0			0
$203$	−14.0487	+	5.71420i	−0.986024	+	0.401058i
$204$		0			0
$205$	−4.39489			−0.306952
$206$		0			0
$207$	−24.7192	+	1.49502i	−1.71810	+	0.103911i
$208$		0			0
$209$	4.25860	+	7.37611i	0.294573	+	0.510216i
$210$		0			0
$211$	−1.47477	+	2.55437i	−0.101527	+	0.175850i	−0.912314	−	0.409491i	$-0.865706\pi$
$211$	−1.47477	+	2.55437i	−0.101527	+	0.175850i	0.810787	+	0.585341i	$0.199040\pi$
$212$		0			0
$213$	4.20862	−	17.8462i	0.288370	−	1.22280i
$214$		0			0
$215$	0.975294	−	1.68926i	0.0665145	−	0.115207i
$216$		0			0
$217$	1.68192	−	12.1735i	0.114176	−	0.826391i
$218$		0			0
$219$	−22.3556	+	6.72000i	−1.51065	+	0.454095i
$220$		0			0
$221$		−	2.76923i		−	0.186278i
$222$		0			0
$223$	20.4564	−	11.8105i	1.36986	−	0.790891i	0.378954	−	0.925416i	$-0.376284\pi$
$223$	20.4564	−	11.8105i	1.36986	−	0.790891i	0.990910	+	0.134524i	$0.0429506\pi$
$224$		0			0
$225$	11.5407	−	7.62731i	0.769377	−	0.508487i
$226$		0			0
$227$	9.02534	−	15.6323i	0.599033	−	1.03755i	−0.393932	−	0.919140i	$-0.628885\pi$
$227$	9.02534	−	15.6323i	0.599033	−	1.03755i	0.992964	−	0.118415i	$-0.0377814\pi$
$228$		0			0
$229$	−10.5212	+	6.07439i	−0.695258	+	0.401407i	−0.805579	−	0.592489i	$-0.798145\pi$
$229$	−10.5212	+	6.07439i	−0.695258	+	0.401407i	0.110321	+	0.993896i	$0.464812\pi$
$230$		0			0
$231$	−14.9497	−	18.5511i	−0.983620	−	1.22057i
$232$		0			0
$233$	−3.39111	−	1.95786i	−0.222159	−	0.128264i	0.384791	−	0.923004i	$-0.374274\pi$
$233$	−3.39111	−	1.95786i	−0.222159	−	0.128264i	−0.606950	+	0.794740i	$0.707607\pi$
$234$		0			0
$235$	−2.95201	−	5.11303i	−0.192568	−	0.333537i
$236$		0			0
$237$	−16.3469	−	3.85506i	−1.06185	−	0.250413i
$238$		0			0
$239$	−10.3996	−	6.00423i	−0.672696	−	0.388381i	0.124401	−	0.992232i	$-0.460299\pi$
$239$	−10.3996	−	6.00423i	−0.672696	−	0.388381i	−0.797097	+	0.603851i	$0.793632\pi$
$240$		0			0
$241$	24.4958	+	14.1427i	1.57792	+	0.911010i	0.995150	+	0.0983690i	$0.0313626\pi$
$241$	24.4958	+	14.1427i	1.57792	+	0.911010i	0.582765	+	0.812641i	$0.301971\pi$
$242$		0			0
$243$	6.25393	+	14.2789i	0.401190	+	0.915995i
$244$		0			0
$245$	−1.07578	−	4.23054i	−0.0687294	−	0.270279i
$246$		0			0
$247$	2.59178	+	4.48909i	0.164911	+	0.285634i
$248$		0			0
$249$	−0.191495	−	0.637054i	−0.0121355	−	0.0403716i
$250$		0			0
$251$	−12.0425			−0.760117			−0.380059	−	0.924962i	$-0.624096\pi$
$251$	−12.0425			−0.760117			−0.380059	+	0.924962i	$0.624096\pi$
$252$		0			0
$253$	−42.9173			−2.69819
$254$		0			0
$255$	−0.647932	+	0.688303i	−0.0405751	+	0.0431032i
$256$		0			0
$257$	7.32521	+	12.6876i	0.456934	+	0.791433i	0.998797	−	0.0490340i	$-0.0156143\pi$
$257$	7.32521	+	12.6876i	0.456934	+	0.791433i	−0.541863	+	0.840467i	$0.682281\pi$
$258$		0			0
$259$	−4.03702	+	5.19207i	−0.250848	+	0.322620i
$260$		0			0
$261$	17.1656	−	1.03818i	1.06253	−	0.0642616i
$262$		0			0
$263$	−4.96349	−	2.86567i	−0.306062	−	0.176705i	0.339101	−	0.940750i	$-0.389877\pi$
$263$	−4.96349	−	2.86567i	−0.306062	−	0.176705i	−0.645163	+	0.764045i	$0.723210\pi$
$264$		0			0
$265$	−0.718314	−	0.414719i	−0.0441257	−	0.0254760i
$266$		0			0
$267$	−0.0472464	+	0.0501902i	−0.00289144	+	0.00307159i
$268$		0			0
$269$	−1.61724	−	2.80114i	−0.0986047	−	0.170788i	0.812503	−	0.582957i	$-0.198105\pi$
$269$	−1.61724	−	2.80114i	−0.0986047	−	0.170788i	−0.911107	+	0.412169i	$0.864771\pi$
$270$		0			0
$271$	20.6677	+	11.9325i	1.25548	+	0.724849i	0.972192	−	0.234187i	$-0.0752428\pi$
$271$	20.6677	+	11.9325i	1.25548	+	0.724849i	0.283284	+	0.959036i	$0.408576\pi$
$272$		0			0
$273$	−9.09838	−	11.2902i	−0.550659	−	0.683312i
$274$		0			0
$275$	20.7617	−	11.9868i	1.25198	−	0.722831i
$276$		0			0
$277$	3.83423	−	6.64107i	0.230376	−	0.399023i	−0.727543	−	0.686063i	$-0.759338\pi$
$277$	3.83423	−	6.64107i	0.230376	−	0.399023i	0.957919	+	0.287039i	$0.0926710\pi$
$278$		0			0
$279$	−6.22605	+	12.4663i	−0.372744	+	0.746337i
$280$		0			0
$281$	8.78880	−	5.07422i	0.524296	−	0.302702i	−0.214395	−	0.976747i	$-0.568778\pi$
$281$	8.78880	−	5.07422i	0.524296	−	0.302702i	0.738690	+	0.674045i	$0.235445\pi$
$282$		0			0
$283$			13.6685i			0.812510i	0.913760	+	0.406255i	$0.133166\pi$
$283$			13.6685i			0.812510i	−0.913760	+	0.406255i	$0.866834\pi$
$284$		0			0
$285$	0.406141	−	1.72220i	0.0240577	−	0.102014i
$286$		0			0
$287$	−11.4455	+	14.7203i	−0.675607	+	0.868909i
$288$		0			0
$289$	8.11702	−	14.0591i	0.477472	−	0.827006i
$290$		0			0
$291$	−11.3902	+	3.42382i	−0.667702	+	0.200708i
$292$		0			0
$293$	2.70903	−	4.69218i	0.158263	−	0.274120i	−0.775979	−	0.630758i	$-0.782744\pi$
$293$	2.70903	−	4.69218i	0.158263	−	0.274120i	0.934242	+	0.356639i	$0.116077\pi$
$294$		0			0
$295$	−1.98512	−	3.43833i	−0.115578	−	0.200187i
$296$		0			0
$297$	9.32455	+	25.3549i	0.541065	+	1.47124i
$298$		0			0
$299$	−26.1194			−1.51052
$300$		0			0
$301$	−3.11807	−	7.66595i	−0.179723	−	0.441858i
$302$		0			0
$303$	10.5969	−	11.2572i	0.608777	−	0.646709i
$304$		0			0
$305$	6.02379	−	3.47784i	0.344921	−	0.199140i
$306$		0			0
$307$			3.56336i			0.203372i	0.994817	+	0.101686i	$0.0324236\pi$
$307$			3.56336i			0.203372i	−0.994817	+	0.101686i	$0.967576\pi$
$308$		0			0
$309$	−14.7109	+	4.42204i	−0.836876	+	0.251561i
$310$		0			0
$311$	−11.2647			−0.638762			−0.319381	−	0.947626i	$-0.603475\pi$
$311$	−11.2647			−0.638762			−0.319381	+	0.947626i	$0.603475\pi$
$312$		0			0
$313$			11.4280i			0.645950i	0.946407	+	0.322975i	$0.104683\pi$
$313$			11.4280i			0.645950i	−0.946407	+	0.322975i	$0.895317\pi$
$314$		0			0
$315$	−0.380187	+	4.93502i	−0.0214211	+	0.278057i
$316$		0			0
$317$		−	19.4687i		−	1.09347i	−0.837305	−	0.546736i	$-0.815870\pi$
$317$		−	19.4687i		−	1.09347i	0.837305	−	0.546736i	$-0.184130\pi$
$318$		0			0
$319$	29.8028			1.66864
$320$		0			0
$321$	−3.84932	−	3.62354i	−0.214848	−	0.202247i
$322$		0			0
$323$		−	1.43375i		−	0.0797758i
$324$		0			0
$325$	12.6356	−	7.29515i	0.700895	−	0.404662i
$326$		0			0
$327$	−5.53522	−	18.4142i	−0.306098	−	1.01831i
$328$		0			0
$329$	−24.8134	−	3.42828i	−1.36801	−	0.189007i
$330$		0			0
$331$	−26.9675			−1.48227			−0.741135	−	0.671356i	$-0.765712\pi$
$331$	−26.9675			−1.48227			−0.741135	+	0.671356i	$0.765712\pi$
$332$		0			0
$333$	6.22147	−	4.11182i	0.340935	−	0.225326i
$334$		0			0
$335$	3.77245	+	6.53408i	0.206111	+	0.356995i
$336$		0			0
$337$	0.993296	−	1.72044i	0.0541083	−	0.0937183i	−0.837703	−	0.546127i	$-0.816102\pi$
$337$	0.993296	−	1.72044i	0.0541083	−	0.0937183i	0.891811	+	0.452408i	$0.149435\pi$
$338$		0			0
$339$	−4.57032	−	4.30226i	−0.248226	−	0.233666i
$340$		0			0
$341$	−12.0745	+	20.9136i	−0.653869	+	1.13254i
$342$		0			0
$343$	−16.9714	−	7.41426i	−0.916370	−	0.400332i
$344$		0			0
$345$	6.49209	+	6.11131i	0.349522	+	0.329022i
$346$		0			0
$347$		−	34.3724i		−	1.84521i	−0.385752	−	0.922603i	$-0.626058\pi$
$347$		−	34.3724i		−	1.84521i	0.385752	−	0.922603i	$-0.373942\pi$
$348$		0			0
$349$	−25.3935	+	14.6609i	−1.35928	+	0.784781i	−0.989527	−	0.144348i	$-0.953891\pi$
$349$	−25.3935	+	14.6609i	−1.35928	+	0.784781i	−0.369754	+	0.929130i	$0.620558\pi$
$350$		0			0
$351$	5.67491	+	15.4310i	0.302904	+	0.823645i
$352$		0			0
$353$	0.586526	−	1.01589i	0.0312177	−	0.0540706i	−0.849994	−	0.526792i	$-0.823395\pi$
$353$	0.586526	−	1.01589i	0.0312177	−	0.0540706i	0.881212	+	0.472721i	$0.156728\pi$
$354$		0			0
$355$	−5.71704	+	3.30074i	−0.303429	+	0.175185i
$356$		0			0
$357$	0.618008	+	3.96271i	0.0327084	+	0.209729i
$358$		0			0
$359$	5.69591	+	3.28854i	0.300619	+	0.173562i	0.642721	−	0.766101i	$-0.277806\pi$
$359$	5.69591	+	3.28854i	0.300619	+	0.173562i	−0.342102	+	0.939663i	$0.611139\pi$
$360$		0			0
$361$	−8.15813	−	14.1303i	−0.429375	−	0.743699i
$362$		0			0
$363$	7.99285	+	26.5901i	0.419516	+	1.39562i
$364$		0			0
$365$	7.27856	+	4.20228i	0.380977	+	0.219957i
$366$		0			0
$367$	8.24124	+	4.75808i	0.430189	+	0.248370i	0.699427	−	0.714704i	$-0.253438\pi$
$367$	8.24124	+	4.75808i	0.430189	+	0.248370i	−0.269238	+	0.963074i	$0.586772\pi$
$368$		0			0
$369$	17.6387	−	11.6576i	0.918236	−	0.606869i
$370$		0			0
$371$	−3.25975	+	1.32588i	−0.169238	+	0.0688362i
$372$		0			0
$373$	−10.3152	−	17.8664i	−0.534098	−	0.925085i	−0.999206	−	0.0398315i	$-0.987318\pi$
$373$	−10.3152	−	17.8664i	−0.534098	−	0.925085i	0.465108	−	0.885254i	$-0.346015\pi$
$374$		0			0
$375$	−10.1038	−	2.38276i	−0.521760	−	0.123045i
$376$		0			0
$377$	18.1380			0.934153
$378$		0			0
$379$	7.98265			0.410041			0.205020	−	0.978758i	$-0.434274\pi$
$379$	7.98265			0.410041			0.205020	+	0.978758i	$0.434274\pi$
$380$		0			0
$381$	17.0955	+	4.03158i	0.875827	+	0.206544i
$382$		0			0
$383$	14.0484	+	24.3326i	0.717840	+	1.24334i	0.961854	+	0.273564i	$0.0882026\pi$
$383$	14.0484	+	24.3326i	0.717840	+	1.24334i	−0.244013	+	0.969772i	$0.578464\pi$
$384$		0			0
$385$	−1.17398	+	8.49714i	−0.0598318	+	0.433054i
$386$		0			0
$387$	0.566503	+	9.36678i	0.0287970	+	0.476140i
$388$		0			0
$389$	28.4400	+	16.4198i	1.44196	+	0.832519i	0.997981	−	0.0635162i	$-0.0202314\pi$
$389$	28.4400	+	16.4198i	1.44196	+	0.832519i	0.443984	+	0.896035i	$0.353565\pi$
$390$		0			0
$391$	6.25660	+	3.61225i	0.316410	+	0.182679i
$392$		0			0
$393$	−10.8485	−	36.0900i	−0.547233	−	1.82050i
$394$		0			0
$395$	3.02344	+	5.23676i	0.152126	+	0.263490i
$396$		0			0
$397$	9.24672	+	5.33859i	0.464079	+	0.267936i	0.713758	−	0.700392i	$-0.246992\pi$
$397$	9.24672	+	5.33859i	0.464079	+	0.267936i	−0.249679	+	0.968329i	$0.580325\pi$
$398$		0			0
$399$	−4.71062	−	5.84540i	−0.235826	−	0.292636i
$400$		0			0
$401$	−12.3658	+	7.13943i	−0.617521	+	0.356526i	−0.775903	−	0.630852i	$-0.782706\pi$
$401$	−12.3658	+	7.13943i	−0.617521	+	0.356526i	0.158382	+	0.987378i	$0.449372\pi$
$402$		0			0
$403$	−7.34851	+	12.7280i	−0.366055	+	0.634026i
$404$		0			0
$405$	2.19995	−	5.16323i	0.109317	−	0.256563i
$406$		0			0
$407$	11.1925	−	6.46198i	0.554791	−	0.320309i
$408$		0			0
$409$		−	8.13148i		−	0.402076i	−0.979583	−	0.201038i	$-0.935569\pi$
$409$		−	8.13148i		−	0.402076i	0.979583	−	0.201038i	$-0.0644314\pi$
$410$		0			0
$411$	−0.495789	−	0.466710i	−0.0244555	−	0.0230211i
$412$		0			0
$413$	−16.6861	−	2.30539i	−0.821071	−	0.113441i
$414$		0			0
$415$	−0.119750	+	0.207412i	−0.00587827	+	0.0101815i
$416$		0			0
$417$	−22.8121	−	21.4741i	−1.11711	−	1.05159i
$418$		0			0
$419$	1.53415	−	2.65723i	0.0749481	−	0.129814i	−0.826116	−	0.563501i	$-0.809454\pi$
$419$	1.53415	−	2.65723i	0.0749481	−	0.129814i	0.901064	+	0.433687i	$0.142788\pi$
$420$		0			0
$421$	4.25752	+	7.37424i	0.207499	+	0.359398i	0.950926	−	0.309418i	$-0.100134\pi$
$421$	4.25752	+	7.37424i	0.207499	+	0.359398i	−0.743427	+	0.668817i	$0.766801\pi$
$422$		0			0
$423$	25.4102	+	12.6907i	1.23549	+	0.617041i
$424$		0			0
$425$	−4.03560			−0.195756
$426$		0			0
$427$	4.03894	−	29.2333i	0.195458	−	1.41470i
$428$		0			0
$429$	8.20240	+	27.2872i	0.396016	+	1.31744i
$430$		0			0
$431$	19.8414	−	11.4554i	0.955727	−	0.551789i	0.0608716	−	0.998146i	$-0.480612\pi$
$431$	19.8414	−	11.4554i	0.955727	−	0.551789i	0.894855	+	0.446356i	$0.147279\pi$
$432$		0			0
$433$			32.7273i			1.57278i	0.617733	+	0.786388i	$0.288051\pi$
$433$			32.7273i			1.57278i	−0.617733	+	0.786388i	$0.711949\pi$
$434$		0			0
$435$	−4.50827	−	4.24384i	−0.216155	−	0.203477i
$436$		0			0
$437$	−13.5231			−0.646899
$438$		0			0
$439$		−	6.43498i		−	0.307125i	−0.988139	−	0.153562i	$-0.950925\pi$
$439$		−	6.43498i		−	0.307125i	0.988139	−	0.153562i	$-0.0490746\pi$
$440$		0			0
$441$	15.5393	+	14.1256i	0.739965	+	0.672646i
$442$		0			0
$443$		−	25.5373i		−	1.21331i	−0.794964	−	0.606656i	$-0.792510\pi$
$443$		−	25.5373i		−	1.21331i	0.794964	−	0.606656i	$-0.207490\pi$
$444$		0			0
$445$	0.0248170			0.00117644
$446$		0			0
$447$	−17.0034	+	5.11113i	−0.804233	+	0.241748i
$448$		0			0
$449$			40.1008i			1.89247i	0.323474	+	0.946237i	$0.395149\pi$
$449$			40.1008i			1.89247i	−0.323474	+	0.946237i	$0.604851\pi$
$450$		0			0
$451$	31.7322	−	18.3206i	1.49421	−	0.862684i
$452$		0			0
$453$	28.2568	−	30.0174i	1.32762	−	1.41034i
$454$		0			0
$455$	−0.714485	+	5.17135i	−0.0334956	+	0.242436i
$456$		0			0
$457$	−38.4715			−1.79962			−0.899810	−	0.436283i	$-0.856295\pi$
$457$	−38.4715			−1.79962			−0.899810	+	0.436283i	$0.856295\pi$
$458$		0			0
$459$	0.774707	−	4.48114i	0.0361602	−	0.209162i
$460$		0			0
$461$	12.0830	+	20.9283i	0.562759	+	0.974728i	0.997254	+	0.0740533i	$0.0235935\pi$
$461$	12.0830	+	20.9283i	0.562759	+	0.974728i	−0.434495	+	0.900674i	$0.643073\pi$
$462$		0			0
$463$	8.65455	−	14.9901i	0.402211	−	0.696650i	−0.591781	−	0.806098i	$-0.701575\pi$
$463$	8.65455	−	14.9901i	0.402211	−	0.696650i	0.993992	+	0.109449i	$0.0349085\pi$
$464$		0			0
$465$	4.80454	−	1.44422i	0.222805	−	0.0669742i
$466$		0			0
$467$	−5.46858	+	9.47185i	−0.253056	+	0.438305i	−0.964366	−	0.264573i	$-0.914769\pi$
$467$	−5.46858	+	9.47185i	−0.253056	+	0.438305i	0.711310	+	0.702878i	$0.248102\pi$
$468$		0			0
$469$	31.7098	+	4.38110i	1.46422	+	0.202300i
$470$		0			0
$471$	4.57514	−	19.4003i	0.210811	−	0.893920i
$472$		0			0
$473$			16.2625i			0.747751i
$474$		0			0
$475$	6.54197	−	3.77701i	0.300166	−	0.173301i
$476$		0			0
$477$	3.98298	−	0.240891i	0.182368	−	0.0110296i
$478$		0			0
$479$	−0.756744	+	1.31072i	−0.0345765	+	0.0598883i	−0.882796	−	0.469757i	$-0.844342\pi$
$479$	−0.756744	+	1.31072i	−0.0345765	+	0.0598883i	0.848219	+	0.529645i	$0.177675\pi$
$480$		0			0
$481$	6.81173	−	3.93275i	0.310588	−	0.179318i
$482$		0			0
$483$	37.3764	−	5.82907i	1.70069	−	0.265232i
$484$		0			0
$485$	3.70841	+	2.14105i	0.168390	+	0.0972201i
$486$		0			0
$487$	0.0853077	+	0.147757i	0.00386566	+	0.00669552i	0.867952	−	0.496649i	$-0.165436\pi$
$487$	0.0853077	+	0.147757i	0.00386566	+	0.00669552i	−0.864086	+	0.503344i	$0.832103\pi$
$488$		0			0
$489$	−24.8395	+	26.3872i	−1.12328	+	1.19327i
$490$		0			0
$491$	−23.5139	−	13.5757i	−1.06117	−	0.612665i	−0.135412	−	0.990789i	$-0.543236\pi$
$491$	−23.5139	−	13.5757i	−1.06117	−	0.612665i	−0.925755	+	0.378125i	$0.876569\pi$
$492$		0			0
$493$	−4.34474	−	2.50844i	−0.195677	−	0.112974i
$494$		0			0
$495$	4.34581	−	8.70151i	0.195329	−	0.391104i
$496$		0			0
$497$	−3.83327	+	27.7447i	−0.171946	+	1.24452i
$498$		0			0
$499$	11.1327	+	19.2824i	0.498369	+	0.863200i	0.999998	−	0.00188245i	$-0.000599204\pi$
$499$	11.1327	+	19.2824i	0.498369	+	0.863200i	−0.501629	+	0.865083i	$0.667266\pi$
$500$		0			0
$501$	−15.8932	+	16.8835i	−0.710058	+	0.754300i
$502$		0			0
$503$	−32.2005			−1.43575			−0.717876	−	0.696171i	$-0.754885\pi$
$503$	−32.2005			−1.43575			−0.717876	+	0.696171i	$0.754885\pi$
$504$		0			0
$505$	−5.56621			−0.247693
$506$		0			0
$507$	−1.48992	−	4.95656i	−0.0661696	−	0.220129i
$508$		0			0
$509$	−4.60909	−	7.98317i	−0.204294	−	0.353848i	0.745613	−	0.666379i	$-0.232157\pi$
$509$	−4.60909	−	7.98317i	−0.204294	−	0.353848i	−0.949908	+	0.312531i	$0.898823\pi$
$510$		0			0
$511$	33.0305	−	13.4349i	1.46118	−	0.594326i
$512$		0			0
$513$	2.93814	+	7.98927i	0.129722	+	0.352735i
$514$		0			0
$515$	4.78959	+	2.76527i	0.211055	+	0.121853i
$516$		0			0
$517$	42.6285	+	24.6116i	1.87480	+	1.08242i
$518$		0			0
$519$	−9.92714	−	2.34109i	−0.435753	−	0.102763i
$520$		0			0
$521$	7.44581	+	12.8965i	0.326207	+	0.565007i	0.981756	−	0.190146i	$-0.0608961\pi$
$521$	7.44581	+	12.8965i	0.326207	+	0.565007i	−0.655549	+	0.755153i	$0.727563\pi$
$522$		0			0
$523$	29.3725	+	16.9582i	1.28437	+	0.741532i	0.977644	−	0.210266i	$-0.0674329\pi$
$523$	29.3725	+	16.9582i	1.28437	+	0.741532i	0.306727	+	0.951798i	$0.400766\pi$
$524$		0			0
$525$	−16.4532	+	13.2591i	−0.718077	+	0.578675i
$526$		0			0
$527$	3.52050	−	2.03256i	0.153355	−	0.0885398i
$528$		0			0
$529$	22.5708	−	39.0938i	0.981340	−	1.69973i
$530$		0			0
$531$	17.0875	+	8.53401i	0.741533	+	0.370344i
$532$		0			0
$533$	19.3122	−	11.1499i	0.836504	−	0.482956i
$534$		0			0
$535$			1.90333i			0.0822880i
$536$		0			0
$537$	27.6447	−	8.30987i	1.19296	−	0.358597i
$538$		0			0
$539$	25.4029	+	26.0610i	1.09418	+	1.12253i
$540$		0			0
$541$	−2.65164	+	4.59278i	−0.114003	+	0.197459i	−0.917381	−	0.398011i	$-0.869701\pi$
$541$	−2.65164	+	4.59278i	−0.114003	+	0.197459i	0.803378	+	0.595470i	$0.203034\pi$
$542$		0			0
$543$	0.183953	−	0.780032i	0.00789418	−	0.0334744i
$544$		0			0
$545$	−3.46139	+	5.99531i	−0.148270	+	0.256811i
$546$		0			0
$547$	4.13892	+	7.16882i	0.176967	+	0.306517i	0.940840	−	0.338850i	$-0.110038\pi$
$547$	4.13892	+	7.16882i	0.176967	+	0.306517i	−0.763873	+	0.645367i	$0.776705\pi$
$548$		0			0
$549$	−14.9512	+	29.9364i	−0.638101	+	1.27766i
$550$		0			0
$551$	9.39080			0.400061
$552$		0			0
$553$	25.4139	+	3.51124i	1.08071	+	0.149313i
$554$		0			0
$555$	−2.61325	−	0.616278i	−0.110926	−	0.0261595i
$556$		0			0
$557$	6.96801	−	4.02299i	0.295244	−	0.170459i	−0.345060	−	0.938581i	$-0.612142\pi$
$557$	6.96801	−	4.02299i	0.295244	−	0.170459i	0.640304	+	0.768121i	$0.278808\pi$
$558$		0			0
$559$			9.89735i			0.418613i
$560$		0			0
$561$	1.80896	−	7.67070i	0.0763745	−	0.323857i
$562$		0			0
$563$	29.9156			1.26079			0.630396	−	0.776274i	$-0.282892\pi$
$563$	29.9156			1.26079			0.630396	+	0.776274i	$0.282892\pi$
$564$		0			0
$565$			2.25983i			0.0950718i
$566$		0			0
$567$	−11.5644	−	20.8150i	−0.485660	−	0.874148i
$568$		0			0
$569$		−	30.8238i		−	1.29220i	−0.763252	−	0.646101i	$-0.776399\pi$
$569$		−	30.8238i		−	1.29220i	0.763252	−	0.646101i	$-0.223601\pi$
$570$		0			0
$571$	5.34693			0.223762			0.111881	−	0.993722i	$-0.464312\pi$
$571$	5.34693			0.223762			0.111881	+	0.993722i	$0.464312\pi$
$572$		0			0
$573$	5.42214	−	22.9920i	0.226513	−	0.960503i
$574$		0			0
$575$			38.0639i			1.58737i
$576$		0			0
$577$	16.3235	−	9.42437i	0.679556	−	0.392342i	−0.120132	−	0.992758i	$-0.538332\pi$
$577$	16.3235	−	9.42437i	0.679556	−	0.392342i	0.799688	+	0.600416i	$0.204998\pi$
$578$		0			0
$579$	−19.3508	−	4.56345i	−0.804192	−	0.189651i
$580$		0			0
$581$	0.382846	+	0.941248i	0.0158831	+	0.0390495i
$582$		0			0
$583$	6.91522			0.286399
$584$		0			0
$585$	2.64485	−	5.29573i	0.109351	−	0.218951i
$586$		0			0
$587$	12.3955	+	21.4697i	0.511619	+	0.886150i	0.999909	+	0.0134687i	$0.00428734\pi$
$587$	12.3955	+	21.4697i	0.511619	+	0.886150i	−0.488290	+	0.872681i	$0.662379\pi$
$588$		0			0
$589$	−3.80464	+	6.58982i	−0.156767	+	0.271529i
$590$		0			0
$591$	−1.90107	+	8.06126i	−0.0781995	+	0.331596i
$592$		0			0
$593$	−1.87451	+	3.24675i	−0.0769770	+	0.133328i	−0.901944	−	0.431852i	$-0.857860\pi$
$593$	−1.87451	+	3.24675i	−0.0769770	+	0.133328i	0.824967	+	0.565180i	$0.191193\pi$
$594$		0			0
$595$	0.886331	−	1.13992i	0.0363360	−	0.0467323i
$596$		0			0
$597$	−15.0897	+	4.53588i	−0.617579	+	0.185641i
$598$		0			0
$599$			32.0673i			1.31024i	0.755527	+	0.655118i	$0.227381\pi$
$599$			32.0673i			1.31024i	−0.755527	+	0.655118i	$0.772619\pi$
$600$		0			0
$601$	5.98069	−	3.45296i	0.243958	−	0.140849i	−0.373037	−	0.927817i	$-0.621683\pi$
$601$	5.98069	−	3.45296i	0.243958	−	0.140849i	0.616994	+	0.786968i	$0.288350\pi$
$602$		0			0
$603$	−32.4725	−	16.2178i	−1.32238	−	0.660438i
$604$		0			0
$605$	4.99824	−	8.65721i	0.203207	−	0.351966i
$606$		0			0
$607$	18.7892	−	10.8479i	0.762629	−	0.440304i	−0.0676102	−	0.997712i	$-0.521537\pi$
$607$	18.7892	−	10.8479i	0.762629	−	0.440304i	0.830239	+	0.557408i	$0.188204\pi$
$608$		0			0
$609$	−25.9551	+	4.04785i	−1.05175	+	0.164027i
$610$		0			0
$611$	25.9437	+	14.9786i	1.04957	+	0.605968i
$612$		0			0
$613$	8.96928	+	15.5352i	0.362266	+	0.627463i	0.988333	−	0.152306i	$-0.0486699\pi$
$613$	8.96928	+	15.5352i	0.362266	+	0.627463i	−0.626068	+	0.779769i	$0.715337\pi$
$614$		0			0
$615$	−7.40894	−	1.74723i	−0.298757	−	0.0704552i
$616$		0			0
$617$	32.9146	+	19.0033i	1.32509	+	0.765043i	0.984536	−	0.175181i	$-0.0560509\pi$
$617$	32.9146	+	19.0033i	1.32509	+	0.765043i	0.340557	+	0.940224i	$0.389384\pi$
$618$		0			0
$619$	−37.5659	−	21.6887i	−1.50990	−	0.871743i	−0.999933	−	0.0115498i	$-0.996323\pi$
$619$	−37.5659	−	21.6887i	−1.50990	−	0.871743i	−0.509969	−	0.860193i	$-0.670343\pi$
$620$		0			0
$621$	−42.2662	−	7.30706i	−1.69608	−	0.293222i
$622$		0			0
$623$	0.0646303	−	0.0831220i	0.00258936	−	0.00333021i
$624$		0			0
$625$	−9.65906	−	16.7300i	−0.386363	−	0.669200i
$626$		0			0
$627$	4.24673	+	14.1277i	0.169598	+	0.564208i
$628$		0			0
$629$	−2.17556			−0.0867453
$630$		0			0
$631$	−11.2735			−0.448793			−0.224396	−	0.974498i	$-0.572041\pi$
$631$	−11.2735			−0.448793			−0.224396	+	0.974498i	$0.572041\pi$
$632$		0			0
$633$	−3.50169	+	3.71987i	−0.139179	+	0.147851i
$634$		0			0
$635$	−3.16189	−	5.47655i	−0.125476	−	0.217330i
$636$		0			0
$637$	15.4602	+	15.8607i	0.612555	+	0.628425i
$638$		0			0
$639$	14.1898	−	28.4120i	0.561341	−	1.12396i
$640$		0			0
$641$	−25.7688	−	14.8776i	−1.01781	−	0.587631i	−0.104339	−	0.994542i	$-0.533273\pi$
$641$	−25.7688	−	14.8776i	−1.01781	−	0.587631i	−0.913468	+	0.406911i	$0.866606\pi$
$642$		0			0
$643$	−37.4271	−	21.6085i	−1.47598	−	0.852158i	−0.476348	−	0.879257i	$-0.658040\pi$
$643$	−37.4271	−	21.6085i	−1.47598	−	0.852158i	−0.999633	+	0.0270991i	$0.991373\pi$
$644$		0			0
$645$	2.31574	−	2.46003i	0.0911822	−	0.0968635i
$646$		0			0
$647$	−9.42940	−	16.3322i	−0.370708	−	0.642085i	0.618967	−	0.785417i	$-0.287552\pi$
$647$	−9.42940	−	16.3322i	−0.370708	−	0.642085i	−0.989675	+	0.143332i	$0.954218\pi$
$648$		0			0
$649$	28.6661	+	16.5504i	1.12524	+	0.649660i
$650$		0			0
$651$	7.67508	−	19.8535i	0.300810	−	0.778120i
$652$		0			0
$653$	8.41584	−	4.85889i	0.329337	−	0.190143i	−0.326210	−	0.945297i	$-0.605772\pi$
$653$	8.41584	−	4.85889i	0.329337	−	0.190143i	0.655547	+	0.755155i	$0.272438\pi$
$654$		0			0
$655$	−6.78397	+	11.7502i	−0.265072	+	0.459118i
$656$		0			0
$657$	−40.3589	+	2.44091i	−1.57455	+	0.0952289i
$658$		0			0
$659$	28.5327	−	16.4734i	1.11148	−	0.641712i	0.172266	−	0.985050i	$-0.444891\pi$
$659$	28.5327	−	16.4734i	1.11148	−	0.641712i	0.939212	+	0.343338i	$0.111558\pi$
$660$		0			0
$661$			1.25812i			0.0489353i	0.999701	+	0.0244677i	$0.00778907\pi$
$661$			1.25812i			0.0489353i	−0.999701	+	0.0244677i	$0.992211\pi$
$662$		0			0
$663$	1.10093	−	4.66838i	0.0427567	−	0.181305i
$664$		0			0
$665$	−0.369920	+	2.67743i	−0.0143449	+	0.103826i
$666$		0			0
$667$	−23.6596	+	40.9797i	−0.916104	+	1.58674i
$668$		0			0
$669$	39.1810	−	11.7776i	1.51482	−	0.455349i
$670$		0			0
$671$	−28.9955	+	50.2217i	−1.11936	+	1.93879i
$672$		0			0
$673$	−12.2655	−	21.2445i	−0.472800	−	0.818914i	0.526715	−	0.850042i	$-0.323423\pi$
$673$	−12.2655	−	21.2445i	−0.472800	−	0.818914i	−0.999515	+	0.0311279i	$0.990090\pi$
$674$		0			0
$675$	22.4876	−	8.27007i	0.865549	−	0.318315i
$676$		0			0
$677$	−23.1233			−0.888699			−0.444350	−	0.895853i	$-0.646565\pi$
$677$	−23.1233			−0.888699			−0.444350	+	0.895853i	$0.646565\pi$
$678$		0			0
$679$	16.8290	−	6.84506i	0.645836	−	0.262689i
$680$		0			0
$681$	21.4298	−	22.7650i	0.821191	−	0.872357i
$682$		0			0
$683$	−12.4945	+	7.21370i	−0.478089	+	0.276025i	−0.719620	−	0.694368i	$-0.755684\pi$
$683$	−12.4945	+	7.21370i	−0.478089	+	0.276025i	0.241531	+	0.970393i	$0.422350\pi$
$684$		0			0
$685$			0.245147i			0.00936659i
$686$		0			0
$687$	−20.1516	+	6.05747i	−0.768831	+	0.231107i
$688$		0			0
$689$	4.20859			0.160335
$690$		0			0
$691$			37.4114i			1.42320i	0.702586	+	0.711599i	$0.252029\pi$
$691$			37.4114i			1.42320i	−0.702586	+	0.711599i	$0.747971\pi$
$692$		0			0
$693$	−17.8272	−	37.2170i	−0.677198	−	1.41376i
$694$		0			0
$695$			11.2796i			0.427860i
$696$		0			0
$697$	−6.16802			−0.233630
$698$		0			0
$699$	−4.93839	−	4.64874i	−0.186787	−	0.175832i
$700$		0			0
$701$			41.0429i			1.55017i	0.631859	+	0.775084i	$0.282292\pi$
$701$			41.0429i			1.55017i	−0.631859	+	0.775084i	$0.717708\pi$
$702$		0			0
$703$	3.52672	−	2.03615i	0.133013	−	0.0767950i
$704$		0			0
$705$	−2.94378	−	9.79318i	−0.110869	−	0.368832i
$706$		0			0
$707$	−14.4959	+	18.6435i	−0.545176	+	0.701160i
$708$		0			0
$709$	23.3246			0.875974			0.437987	−	0.898981i	$-0.355692\pi$
$709$	23.3246			0.875974			0.437987	+	0.898981i	$0.355692\pi$
$710$		0			0
$711$	−26.0251	−	12.9978i	−0.976019	−	0.487454i
$712$		0			0
$713$	−19.1712	−	33.2054i	−0.717966	−	1.24355i
$714$		0			0
$715$	5.12928	−	8.88418i	0.191824	−	0.332249i
$716$		0			0
$717$	−15.1447	−	14.2565i	−0.565590	−	0.532417i
$718$		0			0
$719$	−21.7489	+	37.6701i	−0.811096	+	1.40486i	0.101002	+	0.994886i	$0.467795\pi$
$719$	−21.7489	+	37.6701i	−0.811096	+	1.40486i	−0.912098	+	0.409973i	$0.865538\pi$
$720$		0			0
$721$	21.7354	−	8.84073i	0.809470	−	0.329246i
$722$		0			0
$723$	35.6727	+	33.5804i	1.32668	+	1.24887i
$724$		0			0
$725$		−	26.4325i		−	0.981679i
$726$		0			0
$727$	−11.3715	+	6.56536i	−0.421747	+	0.243496i	−0.695824	−	0.718212i	$-0.744961\pi$
$727$	−11.3715	+	6.56536i	−0.421747	+	0.243496i	0.274078	+	0.961708i	$0.411627\pi$
$728$		0			0
$729$	4.86618	+	26.5579i	0.180229	+	0.983625i
$730$		0			0
$731$	1.36878	−	2.37079i	0.0506261	−	0.0876870i
$732$		0			0
$733$	34.7965	−	20.0898i	1.28524	−	0.742032i	0.307436	−	0.951569i	$-0.400529\pi$
$733$	34.7965	−	20.0898i	1.28524	−	0.742032i	0.977801	+	0.209537i	$0.0671955\pi$
$734$		0			0
$735$	−0.131673	−	7.55956i	−0.00485683	−	0.278839i
$736$		0			0
$737$	−54.4762	−	31.4518i	−2.00666	−	1.15854i
$738$		0			0
$739$	−18.7073	−	32.4020i	−0.688158	−	1.19193i	−0.972433	−	0.233182i	$-0.925086\pi$
$739$	−18.7073	−	32.4020i	−0.688158	−	1.19193i	0.284275	−	0.958743i	$-0.408247\pi$
$740$		0			0
$741$	2.58455	+	8.59813i	0.0949460	+	0.315860i
$742$		0			0
$743$	−30.0501	−	17.3494i	−1.10243	−	0.636488i	−0.165572	−	0.986198i	$-0.552947\pi$
$743$	−30.0501	−	17.3494i	−1.10243	−	0.636488i	−0.936858	+	0.349709i	$0.886280\pi$
$744$		0			0
$745$	5.53597	+	3.19619i	0.202822	+	0.117099i
$746$		0			0
$747$	−0.0695569	−	1.15008i	−0.00254495	−	0.0420793i
$748$		0			0
$749$	6.37500	+	4.95679i	0.232938	+	0.181117i
$750$		0			0
$751$	−14.5070	−	25.1268i	−0.529367	−	0.916891i	−0.999413	−	0.0342492i	$-0.989096\pi$
$751$	−14.5070	−	25.1268i	−0.529367	−	0.916891i	0.470046	−	0.882642i	$-0.344237\pi$
$752$		0			0
$753$	−20.3014	−	4.78762i	−0.739823	−	0.174471i
$754$		0			0
$755$	−14.8423			−0.540168
$756$		0			0
$757$	−8.62406			−0.313447			−0.156723	−	0.987643i	$-0.550093\pi$
$757$	−8.62406			−0.313447			−0.156723	+	0.987643i	$0.550093\pi$
$758$		0			0
$759$	−72.3503	−	17.0622i	−2.62615	−	0.619318i
$760$		0			0
$761$	−11.4107	−	19.7638i	−0.413636	−	0.716439i	0.581648	−	0.813440i	$-0.302408\pi$
$761$	−11.4107	−	19.7638i	−0.413636	−	0.716439i	−0.995284	+	0.0970019i	$0.969075\pi$
$762$		0			0
$763$	11.0663	+	27.2070i	0.400626	+	0.984961i
$764$		0			0
$765$	−1.36593	+	0.902754i	−0.0493853	+	0.0326391i
$766$		0			0
$767$	17.4462	+	10.0725i	0.629945	+	0.363699i
$768$		0			0
$769$	−27.6397	−	15.9578i	−0.996714	−	0.575453i	−0.0894399	−	0.995992i	$-0.528508\pi$
$769$	−27.6397	−	15.9578i	−0.996714	−	0.575453i	−0.907275	+	0.420539i	$0.861841\pi$
$770$		0			0
$771$	7.30479	+	24.3011i	0.263076	+	0.875183i
$772$		0			0
$773$	17.8503	+	30.9176i	0.642030	+	1.11203i	0.984979	+	0.172675i	$0.0552410\pi$
$773$	17.8503	+	30.9176i	0.642030	+	1.11203i	−0.342949	+	0.939354i	$0.611426\pi$
$774$		0			0
$775$	18.5486	+	10.7090i	0.666284	+	0.384679i
$776$		0			0
$777$	−8.86980	+	7.14788i	−0.318202	+	0.256429i
$778$		0			0
$779$	9.99875	−	5.77278i	0.358242	−	0.206831i
$780$		0			0
$781$	27.5190	−	47.6643i	0.984708	−	1.70556i
$782$		0			0
$783$	29.3507	+	5.07420i	1.04891	+	0.181337i
$784$		0			0
$785$	−6.21492	+	3.58819i	−0.221820	+	0.128068i
$786$		0			0
$787$		−	13.8834i		−	0.494888i	−0.968902	−	0.247444i	$-0.920409\pi$
$787$		−	13.8834i		−	0.494888i	0.968902	−	0.247444i	$-0.0795907\pi$
$788$		0			0
$789$	−7.22820	−	6.80425i	−0.257331	−	0.242238i
$790$		0			0
$791$	7.56908	+	5.88522i	0.269125	+	0.209254i
$792$		0			0
$793$	−17.6466	+	30.5649i	−0.626651	+	1.08539i
$794$		0			0
$795$	−1.04606	−	0.984709i	−0.0371001	−	0.0349240i
$796$		0			0
$797$	14.2145	−	24.6203i	0.503504	−	0.872094i	−0.496488	−	0.868044i	$-0.665377\pi$
$797$	14.2145	−	24.6203i	0.503504	−	0.872094i	0.999992	−	0.00405063i	$-0.00128936\pi$
$798$		0			0
$799$	−4.14300	−	7.17589i	−0.146569	−	0.253865i
$800$		0			0
$801$	−0.0996020	+	0.0658278i	−0.00351927	+	0.00232591i
$802$		0			0
$803$	−70.0708			−2.47274
$804$		0			0
$805$	−10.7518	−	8.35990i	−0.378951	−	0.294648i
$806$		0			0
$807$	−1.61273	−	5.36512i	−0.0567708	−	0.188861i
$808$		0			0
$809$	−21.1074	+	12.1864i	−0.742096	+	0.428449i	−0.822831	−	0.568286i	$-0.807607\pi$
$809$	−21.1074	+	12.1864i	−0.742096	+	0.428449i	0.0807348	+	0.996736i	$0.474273\pi$
$810$		0			0
$811$		−	35.2739i		−	1.23863i	−0.785141	−	0.619317i	$-0.787409\pi$
$811$		−	35.2739i		−	1.23863i	0.785141	−	0.619317i	$-0.212591\pi$
$812$		0			0
$813$	30.0979	+	28.3326i	1.05558	+	0.993668i
$814$		0			0
$815$	13.0474			0.457030
$816$		0			0
$817$			5.12428i			0.179276i
$818$		0			0
$819$	−10.8496	−	22.6502i	−0.379116	−	0.791462i
$820$		0			0
$821$			19.5144i			0.681056i	0.940234	+	0.340528i	$0.110606\pi$
$821$			19.5144i			0.681056i	−0.940234	+	0.340528i	$0.889394\pi$
$822$		0			0
$823$	31.6570			1.10349			0.551747	−	0.834012i	$-0.313962\pi$
$823$	31.6570			1.10349			0.551747	+	0.834012i	$0.313962\pi$
$824$		0			0
$825$	39.7658	−	11.9534i	1.38447	−	0.416164i
$826$		0			0
$827$		−	24.4749i		−	0.851075i	−0.904941	−	0.425537i	$-0.860085\pi$
$827$		−	24.4749i		−	0.851075i	0.904941	−	0.425537i	$-0.139915\pi$
$828$		0			0
$829$	0.846010	−	0.488444i	0.0293831	−	0.0169644i	−0.485236	−	0.874383i	$-0.661266\pi$
$829$	0.846010	−	0.488444i	0.0293831	−	0.0169644i	0.514620	+	0.857419i	$0.327933\pi$
$830$		0			0
$831$	9.10399	−	9.67123i	0.315814	−	0.335491i
$832$		0			0
$833$	−1.50981	−	5.93736i	−0.0523119	−	0.205717i
$834$		0			0
$835$	8.34819			0.288901
$836$		0			0
$837$	−15.4520	+	18.5405i	−0.534100	+	0.640855i
$838$		0			0
$839$	19.6920	+	34.1075i	0.679843	+	1.17752i	0.975028	+	0.222083i	$0.0712856\pi$
$839$	19.6920	+	34.1075i	0.679843	+	1.17752i	−0.295184	+	0.955440i	$0.595381\pi$
$840$		0			0
$841$	1.92983	−	3.34257i	0.0665459	−	0.115261i
$842$		0			0
$843$	16.8335	−	5.06007i	0.579777	−	0.174278i
$844$		0			0
$845$	−0.931704	+	1.61376i	−0.0320516	+	0.0555150i
$846$		0			0
$847$	−15.9797	−	39.2869i	−0.549067	−	1.34991i
$848$		0			0
$849$	−5.43406	+	23.0425i	−0.186497	+	0.790817i
$850$		0			0
$851$			20.5199i			0.703415i
$852$		0			0
$853$	21.3507	−	12.3268i	0.731033	−	0.422062i	−0.0877672	−	0.996141i	$-0.527973\pi$
$853$	21.3507	−	12.3268i	0.731033	−	0.422062i	0.818800	+	0.574079i	$0.194640\pi$
$854$		0			0
$855$	1.36935	−	2.74182i	0.0468309	−	0.0937684i
$856$		0			0
$857$	11.4145	−	19.7705i	0.389911	−	0.675346i	−0.602526	−	0.798099i	$-0.705839\pi$
$857$	11.4145	−	19.7705i	0.389911	−	0.675346i	0.992437	+	0.122753i	$0.0391723\pi$
$858$		0			0
$859$	−41.3224	+	23.8575i	−1.40990	+	0.814007i	−0.995378	−	0.0960315i	$-0.969385\pi$
$859$	−41.3224	+	23.8575i	−1.40990	+	0.814007i	−0.414523	+	0.910039i	$0.636052\pi$
$860$		0			0
$861$	−25.1471	+	20.2652i	−0.857011	+	0.690637i
$862$		0			0
$863$	−18.0645	−	10.4296i	−0.614923	−	0.355026i	0.159967	−	0.987122i	$-0.448861\pi$
$863$	−18.0645	−	10.4296i	−0.614923	−	0.355026i	−0.774890	+	0.632096i	$0.782195\pi$
$864$		0			0
$865$	1.83607	+	3.18017i	0.0624283	+	0.108129i
$866$		0			0
$867$	19.2731	−	20.4739i	0.654548	−	0.695331i
$868$		0			0
$869$	−43.6601	−	25.2072i	−1.48107	−	0.855094i
$870$		0			0
$871$	−33.1541	−	19.1416i	−1.12339	−	0.648587i
$872$		0			0
$873$	−20.5628	+	1.24364i	−0.695944	+	0.0420907i
$874$		0			0
$875$	15.7080	+	2.17026i	0.531028	+	0.0733680i
$876$		0			0
$877$	11.7718	+	20.3894i	0.397506	+	0.688500i	0.993417	−	0.114550i	$-0.0365426\pi$
$877$	11.7718	+	20.3894i	0.397506	+	0.688500i	−0.595912	+	0.803050i	$0.703209\pi$
$878$		0			0
$879$	6.43232	−	6.83310i	0.216957	−	0.230475i
$880$		0			0
$881$	52.5975			1.77205			0.886027	−	0.463633i	$-0.153454\pi$
$881$	52.5975			1.77205			0.886027	+	0.463633i	$0.153454\pi$
$882$		0			0
$883$	33.6815			1.13347			0.566737	−	0.823899i	$-0.308206\pi$
$883$	33.6815			1.13347			0.566737	+	0.823899i	$0.308206\pi$
$884$		0			0
$885$	−1.97959	−	6.58556i	−0.0665430	−	0.221371i
$886$		0			0
$887$	−7.51139	−	13.0101i	−0.252208	−	0.436837i	0.711926	−	0.702255i	$-0.247823\pi$
$887$	−7.51139	−	13.0101i	−0.252208	−	0.436837i	−0.964133	+	0.265418i	$0.914490\pi$
$888$		0			0
$889$	−26.5776	−	3.67203i	−0.891385	−	0.123156i
$890$		0			0
$891$	5.63929	+	46.4506i	0.188923	+	1.55615i
$892$		0			0
$893$	13.4321	+	7.75505i	0.449489	+	0.259513i
$894$		0			0
$895$	−9.00059	−	5.19649i	−0.300856	−	0.173700i
$896$		0			0
$897$	−44.0323	−	10.3840i	−1.47019	−	0.346713i
$898$		0			0
$899$	13.3129	+	23.0587i	0.444011	+	0.769050i
$900$		0			0
$901$	−1.00812	−	0.582038i	−0.0335853	−	0.0193905i
$902$		0			0
$903$	−2.20879	−	14.1629i	−0.0735039	−	0.471313i
$904$		0			0
$905$	−0.249884	+	0.144271i	−0.00830643	+	0.00479572i
$906$		0			0
$907$	−5.84747	+	10.1281i	−0.194162	+	0.336299i	−0.946626	−	0.322335i	$-0.895532\pi$
$907$	−5.84747	+	10.1281i	−0.194162	+	0.336299i	0.752463	+	0.658634i	$0.228865\pi$
$908$		0			0
$909$	22.3398	−	14.7645i	0.740964	−	0.489709i
$910$		0			0
$911$	13.9026	−	8.02666i	0.460613	−	0.265935i	−0.251689	−	0.967808i	$-0.580986\pi$
$911$	13.9026	−	8.02666i	0.460613	−	0.265935i	0.712302	+	0.701873i	$0.247653\pi$
$912$		0			0
$913$		−	1.99676i		−	0.0660831i
$914$		0			0
$915$	11.5376	−	3.46814i	0.381421	−	0.114653i
$916$		0			0
$917$	21.6887	+	53.3230i	0.716225	+	1.76088i
$918$		0			0
$919$	−9.26860	+	16.0537i	−0.305743	+	0.529562i	−0.977426	−	0.211276i	$-0.932238\pi$
$919$	−9.26860	+	16.0537i	−0.305743	+	0.529562i	0.671683	+	0.740838i	$0.265572\pi$
$920$		0			0
$921$	−1.41665	+	6.00714i	−0.0466802	+	0.197942i
$922$		0			0
$923$	16.7480	−	29.0084i	0.551268	−	0.954824i
$924$		0			0
$925$	−5.73122	−	9.92676i	−0.188441	−	0.326390i
$926$		0			0
$927$	−26.5578	+	1.60622i	−0.872274	+	0.0527551i
$928$		0			0
$929$	−53.6714			−1.76090			−0.880451	−	0.474138i	$-0.842760\pi$
$929$	−53.6714			−1.76090			−0.880451	+	0.474138i	$0.842760\pi$
$930$		0			0
$931$	8.00440	+	8.21177i	0.262334	+	0.269130i
$932$		0			0
$933$	−18.9901	−	4.47839i	−0.621707	−	0.146616i
$934$		0			0
$935$	−2.45732	+	1.41873i	−0.0803630	+	0.0463976i
$936$		0			0
$937$		−	16.7752i		−	0.548023i	−0.961726	−	0.274012i	$-0.911649\pi$
$937$		−	16.7752i		−	0.548023i	0.961726	−	0.274012i	$-0.0883506\pi$
$938$		0			0
$939$	−4.54333	+	19.2655i	−0.148266	+	0.628704i
$940$		0			0
$941$	37.0686			1.20840			0.604200	−	0.796833i	$-0.293493\pi$
$941$	37.0686			1.20840			0.604200	+	0.796833i	$0.293493\pi$
$942$		0			0
$943$			58.1769i			1.89450i
$944$		0			0
$945$	−2.60289	+	8.16835i	−0.0846720	+	0.265716i
$946$		0			0
$947$			3.16082i			0.102713i	0.998680	+	0.0513565i	$0.0163545\pi$
$947$			3.16082i			0.102713i	−0.998680	+	0.0513565i	$0.983646\pi$
$948$		0			0
$949$	−42.6450			−1.38431
$950$		0			0
$951$	7.73999	−	32.8205i	0.250986	−	1.06428i
$952$		0			0
$953$		−	38.9680i		−	1.26230i	−0.775662	−	0.631149i	$-0.782584\pi$
$953$		−	38.9680i		−	1.26230i	0.775662	−	0.631149i	$-0.217416\pi$
$954$		0			0
$955$	−7.36550	+	4.25247i	−0.238342	+	0.137607i
$956$		0			0
$957$	50.2418	+	11.8484i	1.62409	+	0.383005i
$958$		0			0
$959$	0.821096	+	0.638431i	0.0265146	+	0.0206160i
$960$		0			0
$961$	9.42531			0.304042
$962$		0			0
$963$	−5.04863	−	7.63893i	−0.162690	−	0.246161i
$964$		0			0
$965$	3.57902	+	6.19905i	0.115213	+	0.199555i
$966$		0			0
$967$	7.29560	−	12.6363i	0.234611	−	0.406357i	−0.724549	−	0.689223i	$-0.757952\pi$
$967$	7.29560	−	12.6363i	0.234611	−	0.406357i	0.959159	+	0.282866i	$0.0912852\pi$
$968$		0			0
$969$	0.570000	−	2.41702i	0.0183110	−	0.0776458i
$970$		0			0
$971$	11.3537	−	19.6652i	0.364358	−	0.631086i	−0.624315	−	0.781172i	$-0.714622\pi$
$971$	11.3537	−	19.6652i	0.364358	−	0.631086i	0.988673	+	0.150087i	$0.0479553\pi$
$972$		0			0
$973$	37.7800	+	29.3752i	1.21117	+	0.941727i
$974$		0			0
$975$	24.2014	−	7.27482i	0.775065	−	0.232981i
$976$		0			0
$977$			41.0411i			1.31302i	0.754317	+	0.656511i	$0.227968\pi$
$977$			41.0411i			1.31302i	−0.754317	+	0.656511i	$0.772032\pi$
$978$		0			0
$979$	−0.179185	+	0.103453i	−0.00572678	+	0.00330636i
$980$		0			0
$981$	−2.01056	−	33.2434i	−0.0641923	−	1.06138i
$982$		0			0
$983$	−10.4653	+	18.1263i	−0.333790	+	0.578141i	−0.983252	−	0.182253i	$-0.941661\pi$
$983$	−10.4653	+	18.1263i	−0.333790	+	0.578141i	0.649462	+	0.760394i	$0.274994\pi$
$984$		0			0
$985$	2.58243	−	1.49097i	0.0822832	−	0.0475062i
$986$		0			0
$987$	−40.4677	−	15.6442i	−1.28810	−	0.497962i
$988$		0			0
$989$	−22.3614	−	12.9104i	−0.711051	−	0.410525i
$990$		0			0
$991$	−26.9709	−	46.7149i	−0.856758	−	1.48395i	−0.875004	−	0.484116i	$-0.839141\pi$
$991$	−26.9709	−	46.7149i	−0.856758	−	1.48395i	0.0182456	−	0.999834i	$-0.494192\pi$
$992$		0			0
$993$	−45.4621	−	10.7212i	−1.44269	−	0.340227i
$994$		0			0
$995$	4.91290	+	2.83647i	0.155749	+	0.0899220i
$996$		0			0
$997$	2.78561	+	1.60827i	0.0882211	+	0.0509345i	0.543462	−	0.839434i	$-0.317113\pi$
$997$	2.78561	+	1.60827i	0.0882211	+	0.0509345i	−0.455240	+	0.890369i	$0.650447\pi$
$998$		0			0
$999$	12.1229	−	4.45833i	0.383551	−	0.141055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.ca.e.257.22		48
3.2	odd	2		3024.2.ca.e.2609.14		48
4.3	odd	2		504.2.bs.a.257.3	✓	48
7.3	odd	6		1008.2.df.e.689.14		48
9.2	odd	6		1008.2.df.e.929.14		48
9.7	even	3		3024.2.df.e.1601.14		48
12.11	even	2		1512.2.bs.a.1097.14		48
21.17	even	6		3024.2.df.e.17.14		48
28.3	even	6		504.2.cx.a.185.11	yes	48
36.7	odd	6		1512.2.cx.a.89.14		48
36.11	even	6		504.2.cx.a.425.11	yes	48
63.38	even	6	inner	1008.2.ca.e.353.22		48
63.52	odd	6		3024.2.ca.e.2033.14		48
84.59	odd	6		1512.2.cx.a.17.14		48
252.115	even	6		1512.2.bs.a.521.14		48
252.227	odd	6		504.2.bs.a.353.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.3	✓	48	4.3	odd	2
504.2.bs.a.353.3	yes	48	252.227	odd	6
504.2.cx.a.185.11	yes	48	28.3	even	6
504.2.cx.a.425.11	yes	48	36.11	even	6
1008.2.ca.e.257.22		48	1.1	even	1	trivial
1008.2.ca.e.353.22		48	63.38	even	6	inner
1008.2.df.e.689.14		48	7.3	odd	6
1008.2.df.e.929.14		48	9.2	odd	6
1512.2.bs.a.521.14		48	252.115	even	6
1512.2.bs.a.1097.14		48	12.11	even	2
1512.2.cx.a.17.14		48	84.59	odd	6
1512.2.cx.a.89.14		48	36.7	odd	6
3024.2.ca.e.2033.14		48	63.52	odd	6
3024.2.ca.e.2609.14		48	3.2	odd	2
3024.2.df.e.17.14		48	21.17	even	6
3024.2.df.e.1601.14		48	9.7	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.68581 + 0.397560i) q^{3} +(-0.311798 - 0.540051i) q^{5} +(-2.62086 - 0.362103i) q^{7} +(2.68389 + 1.34042i) q^{9} +(4.50253 + 2.59954i) q^{11} +(2.74023 + 1.58207i) q^{13} +(-0.310929 - 1.03438i) q^{15} +(-0.437594 - 0.757935i) q^{17} +(1.41874 + 0.819107i) q^{19} +(-4.27430 - 1.65238i) q^{21} +(-7.14886 + 4.12740i) q^{23} +(2.30556 - 3.99335i) q^{25} +(3.99163 + 3.32670i) q^{27} +(4.96435 - 2.86617i) q^{29} +4.64486i q^{31} +(6.55693 + 6.17234i) q^{33} +(0.621624 + 1.52830i) q^{35} +(1.24291 - 2.15278i) q^{37} +(3.99054 + 3.75648i) q^{39} +(3.52382 - 6.10344i) q^{41} +(1.56398 + 2.70890i) q^{43} +(-0.112939 - 1.86738i) q^{45} +9.46768 q^{47} +(6.73776 + 1.89804i) q^{49} +(-0.436375 - 1.45170i) q^{51} +(1.15189 - 0.665044i) q^{53} -3.24212i q^{55} +(2.06607 + 1.94489i) q^{57} +6.36667 q^{59} +11.1541i q^{61} +(-6.54872 - 4.48489i) q^{63} -1.97315i q^{65} -12.0990 q^{67} +(-13.6925 + 4.11590i) q^{69} -10.5861i q^{71} +(-11.6719 + 6.73878i) q^{73} +(5.47433 - 5.81542i) q^{75} +(-10.8592 - 8.44339i) q^{77} -9.69679 q^{79} +(5.40655 + 7.19508i) q^{81} +(-0.192030 - 0.332606i) q^{83} +(-0.272882 + 0.472646i) q^{85} +(9.50841 - 2.85818i) q^{87} +(-0.0198983 + 0.0344648i) q^{89} +(-6.60888 - 5.13864i) q^{91} +(-1.84661 + 7.83033i) q^{93} -1.02159i q^{95} +(-5.94681 + 3.43339i) q^{97} +(8.59984 + 13.0122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9} - 8 q^{15} + 8 q^{21} + 12 q^{23} - 24 q^{25} + 18 q^{27} + 18 q^{29} + 10 q^{39} + 6 q^{41} + 6 q^{43} + 6 q^{45} - 36 q^{47} + 6 q^{49} + 12 q^{51} + 12 q^{53} + 4 q^{57} - 46 q^{63} + 54 q^{75}+ \cdots + 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 - 8 * q^15 + 8 * q^21 + 12 * q^23 - 24 * q^25 + 18 * q^27 + 18 * q^29 + 10 * q^39 + 6 * q^41 + 6 * q^43 + 6 * q^45 - 36 * q^47 + 6 * q^49 + 12 * q^51 + 12 * q^53 + 4 * q^57 - 46 * q^63 + 54 * q^75 - 36 * q^77 + 12 * q^79 + 24 * q^87 + 18 * q^89 - 6 * q^91 + 16 * q^93 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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