LMFDB - Embedded newform 1288.2.q.b.921.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1288,2,Mod(737,1288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1288.737");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1288 = 2^{3} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1288.q (of order $3$, 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:	$10.2847317803$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			921.9
Character	$\chi$	$=$	1288.921
Dual form			1288.2.q.b.737.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.832313 - 1.44161i) q^{3} +(-0.459953 - 0.796662i) q^{5} +(2.63299 + 0.259545i) q^{7} +(0.114512 + 0.198340i) q^{9} +O(q^{10})$	\(q+(0.832313 - 1.44161i) q^{3} +(-0.459953 - 0.796662i) q^{5} +(2.63299 + 0.259545i) q^{7} +(0.114512 + 0.198340i) q^{9} +(1.72626 - 2.98997i) q^{11} -6.19741 q^{13} -1.53130 q^{15} +(1.56444 - 2.70970i) q^{17} +(-1.51570 - 2.62526i) q^{19} +(2.56563 - 3.57972i) q^{21} +(0.500000 + 0.866025i) q^{23} +(2.07689 - 3.59727i) q^{25} +5.37511 q^{27} -1.77678 q^{29} +(3.33312 - 5.77313i) q^{31} +(-2.87358 - 4.97719i) q^{33} +(-1.00428 - 2.21698i) q^{35} +(1.96628 + 3.40569i) q^{37} +(-5.15818 + 8.93423i) q^{39} +2.20337 q^{41} -7.45869 q^{43} +(0.105340 - 0.182454i) q^{45} +(3.90949 + 6.77143i) q^{47} +(6.86527 + 1.36676i) q^{49} +(-2.60421 - 4.51063i) q^{51} +(1.26405 - 2.18940i) q^{53} -3.17600 q^{55} -5.04613 q^{57} +(-0.389087 + 0.673918i) q^{59} +(-5.64007 - 9.76888i) q^{61} +(0.250030 + 0.551948i) q^{63} +(2.85052 + 4.93724i) q^{65} +(0.0229932 - 0.0398254i) q^{67} +1.66463 q^{69} -4.20473 q^{71} +(4.34059 - 7.51812i) q^{73} +(-3.45724 - 5.98811i) q^{75} +(5.32127 - 7.42453i) q^{77} +(-1.02566 - 1.77649i) q^{79} +(4.13024 - 7.15378i) q^{81} -12.3994 q^{83} -2.87828 q^{85} +(-1.47884 + 2.56142i) q^{87} +(-6.36600 - 11.0262i) q^{89} +(-16.3177 - 1.60851i) q^{91} +(-5.54839 - 9.61010i) q^{93} +(-1.39430 + 2.41499i) q^{95} +13.0618 q^{97} +0.790708 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} - 9 q^{5} - q^{7} - 11 q^{9}+O(q^{10}) $ 22 * q + 2 * q^3 - 9 * q^5 - q^7 - 11 * q^9	$ 22 q + 2 q^{3} - 9 q^{5} - q^{7} - 11 q^{9} + 30 q^{13} - 4 q^{15} - 5 q^{17} + 3 q^{21} + 11 q^{23} - 22 q^{25} - 10 q^{27} + 10 q^{29} - 6 q^{31} - 14 q^{33} + 25 q^{35} + q^{37} - 11 q^{39} + 40 q^{41} - 14 q^{43} - 41 q^{45} + 3 q^{47} + 9 q^{49} + 13 q^{51} - 19 q^{53} - 6 q^{55} - 10 q^{57} - 7 q^{59} - 39 q^{61} + 81 q^{63} - 5 q^{65} - 7 q^{67} + 4 q^{69} - 38 q^{71} + 5 q^{73} - 16 q^{75} - 17 q^{77} - 11 q^{79} - 43 q^{81} + 66 q^{83} - 26 q^{85} + 30 q^{87} - 34 q^{89} + 8 q^{91} + 12 q^{93} - 37 q^{95} + 34 q^{97} - 98 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 - 9 * q^5 - q^7 - 11 * q^9 + 30 * q^13 - 4 * q^15 - 5 * q^17 + 3 * q^21 + 11 * q^23 - 22 * q^25 - 10 * q^27 + 10 * q^29 - 6 * q^31 - 14 * q^33 + 25 * q^35 + q^37 - 11 * q^39 + 40 * q^41 - 14 * q^43 - 41 * q^45 + 3 * q^47 + 9 * q^49 + 13 * q^51 - 19 * q^53 - 6 * q^55 - 10 * q^57 - 7 * q^59 - 39 * q^61 + 81 * q^63 - 5 * q^65 - 7 * q^67 + 4 * q^69 - 38 * q^71 + 5 * q^73 - 16 * q^75 - 17 * q^77 - 11 * q^79 - 43 * q^81 + 66 * q^83 - 26 * q^85 + 30 * q^87 - 34 * q^89 + 8 * q^91 + 12 * q^93 - 37 * q^95 + 34 * q^97 - 98 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1288\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$645$	$967$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.832313	−	1.44161i	0.480536	−	0.832313i	−0.519215	−	0.854644i	$-0.673776\pi$
$3$	0.832313	−	1.44161i	0.480536	−	0.832313i	0.999751	+	0.0223313i	$0.00710885\pi$
$4$		0			0
$5$	−0.459953	−	0.796662i	−0.205697	−	0.356278i	0.744657	−	0.667447i	$-0.232613\pi$
$5$	−0.459953	−	0.796662i	−0.205697	−	0.356278i	−0.950355	+	0.311169i	$0.899280\pi$
$6$		0			0
$7$	2.63299	+	0.259545i	0.995177	+	0.0980988i
$7$	2.63299	+	0.259545i	0.995177	+	0.0980988i
$8$		0			0
$9$	0.114512	+	0.198340i	0.0381705	+	0.0661133i
$10$		0			0
$11$	1.72626	−	2.98997i	0.520488	−	0.901511i	−0.479228	−	0.877690i	$-0.659083\pi$
$11$	1.72626	−	2.98997i	0.520488	−	0.901511i	0.999716	−	0.0238211i	$-0.00758320\pi$
$12$		0			0
$13$	−6.19741			−1.71885			−0.859426	−	0.511261i	$-0.829179\pi$
$13$	−6.19741			−1.71885			−0.859426	+	0.511261i	$0.829179\pi$
$14$		0			0
$15$	−1.53130			−0.395380
$16$		0			0
$17$	1.56444	−	2.70970i	0.379433	−	0.657198i	−0.611547	−	0.791208i	$-0.709452\pi$
$17$	1.56444	−	2.70970i	0.379433	−	0.657198i	0.990980	+	0.134011i	$0.0427856\pi$
$18$		0			0
$19$	−1.51570	−	2.62526i	−0.347725	−	0.602277i	0.638120	−	0.769937i	$-0.279712\pi$
$19$	−1.51570	−	2.62526i	−0.347725	−	0.602277i	−0.985845	+	0.167660i	$0.946379\pi$
$20$		0			0
$21$	2.56563	−	3.57972i	0.559867	−	0.781158i
$22$		0			0
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$		0			0
$25$	2.07689	−	3.59727i	0.415377	−	0.719455i
$26$		0			0
$27$	5.37511			1.03444
$28$		0			0
$29$	−1.77678			−0.329940			−0.164970	−	0.986299i	$-0.552753\pi$
$29$	−1.77678			−0.329940			−0.164970	+	0.986299i	$0.552753\pi$
$30$		0			0
$31$	3.33312	−	5.77313i	0.598646	−	1.03688i	−0.394376	−	0.918949i	$-0.629039\pi$
$31$	3.33312	−	5.77313i	0.598646	−	1.03688i	0.993021	−	0.117935i	$-0.0376275\pi$
$32$		0			0
$33$	−2.87358	−	4.97719i	−0.500226	−	0.866417i
$34$		0			0
$35$	−1.00428	−	2.21698i	−0.169755	−	0.374738i
$36$		0			0
$37$	1.96628	+	3.40569i	0.323254	+	0.559892i	0.981157	−	0.193210i	$-0.0618898\pi$
$37$	1.96628	+	3.40569i	0.323254	+	0.559892i	−0.657903	+	0.753102i	$0.728557\pi$
$38$		0			0
$39$	−5.15818	+	8.93423i	−0.825970	+	1.43062i
$40$		0			0
$41$	2.20337			0.344108			0.172054	−	0.985087i	$-0.444960\pi$
$41$	2.20337			0.344108			0.172054	+	0.985087i	$0.444960\pi$
$42$		0			0
$43$	−7.45869			−1.13744			−0.568719	−	0.822532i	$-0.692561\pi$
$43$	−7.45869			−1.13744			−0.568719	+	0.822532i	$0.692561\pi$
$44$		0			0
$45$	0.105340	−	0.182454i	0.0157031	−	0.0271986i
$46$		0			0
$47$	3.90949	+	6.77143i	0.570258	+	0.987715i	0.996539	+	0.0831245i	$0.0264899\pi$
$47$	3.90949	+	6.77143i	0.570258	+	0.987715i	−0.426282	+	0.904590i	$0.640177\pi$
$48$		0			0
$49$	6.86527	+	1.36676i	0.980753	+	0.195251i
$50$		0			0
$51$	−2.60421	−	4.51063i	−0.364663	−	0.631614i
$52$		0			0
$53$	1.26405	−	2.18940i	0.173631	−	0.300737i	−0.766056	−	0.642774i	$-0.777783\pi$
$53$	1.26405	−	2.18940i	0.173631	−	0.300737i	0.939687	+	0.342037i	$0.111117\pi$
$54$		0			0
$55$	−3.17600			−0.428252
$56$		0			0
$57$	−5.04613			−0.668376
$58$		0			0
$59$	−0.389087	+	0.673918i	−0.0506548	+	0.0877366i	−0.890241	−	0.455490i	$-0.849464\pi$
$59$	−0.389087	+	0.673918i	−0.0506548	+	0.0877366i	0.839586	+	0.543226i	$0.182797\pi$
$60$		0			0
$61$	−5.64007	−	9.76888i	−0.722137	−	1.25078i	−0.960142	−	0.279513i	$-0.909827\pi$
$61$	−5.64007	−	9.76888i	−0.722137	−	1.25078i	0.238005	−	0.971264i	$-0.423506\pi$
$62$		0			0
$63$	0.250030	+	0.551948i	0.0315008	+	0.0695389i
$64$		0			0
$65$	2.85052	+	4.93724i	0.353563	+	0.612389i
$66$		0			0
$67$	0.0229932	−	0.0398254i	0.00280906	−	0.00486544i	−0.864617	−	0.502431i	$-0.832439\pi$
$67$	0.0229932	−	0.0398254i	0.00280906	−	0.00486544i	0.867427	+	0.497565i	$0.165773\pi$
$68$		0			0
$69$	1.66463			0.200397
$70$		0			0
$71$	−4.20473			−0.499009			−0.249505	−	0.968374i	$-0.580268\pi$
$71$	−4.20473			−0.499009			−0.249505	+	0.968374i	$0.580268\pi$
$72$		0			0
$73$	4.34059	−	7.51812i	0.508028	−	0.879930i	−0.491929	−	0.870635i	$-0.663708\pi$
$73$	4.34059	−	7.51812i	0.508028	−	0.879930i	0.999957	−	0.00929439i	$-0.00295854\pi$
$74$		0			0
$75$	−3.45724	−	5.98811i	−0.399207	−	0.691447i
$76$		0			0
$77$	5.32127	−	7.42453i	0.606415	−	0.846104i
$78$		0			0
$79$	−1.02566	−	1.77649i	−0.115396	−	0.199871i	0.802542	−	0.596595i	$-0.203480\pi$
$79$	−1.02566	−	1.77649i	−0.115396	−	0.199871i	−0.917938	+	0.396724i	$0.870147\pi$
$80$		0			0
$81$	4.13024	−	7.15378i	0.458915	−	0.794865i
$82$		0			0
$83$	−12.3994			−1.36101			−0.680504	−	0.732744i	$-0.738239\pi$
$83$	−12.3994			−1.36101			−0.680504	+	0.732744i	$0.738239\pi$
$84$		0			0
$85$	−2.87828			−0.312194
$86$		0			0
$87$	−1.47884	+	2.56142i	−0.158548	+	0.274613i
$88$		0			0
$89$	−6.36600	−	11.0262i	−0.674794	−	1.16878i	−0.976529	−	0.215386i	$-0.930899\pi$
$89$	−6.36600	−	11.0262i	−0.674794	−	1.16878i	0.301735	−	0.953392i	$-0.402434\pi$
$90$		0			0
$91$	−16.3177	−	1.60851i	−1.71056	−	0.168617i
$92$		0			0
$93$	−5.54839	−	9.61010i	−0.575341	−	0.996520i
$94$		0			0
$95$	−1.39430	+	2.41499i	−0.143052	+	0.247773i
$96$		0			0
$97$	13.0618			1.32622			0.663110	−	0.748522i	$-0.269236\pi$
$97$	13.0618			1.32622			0.663110	+	0.748522i	$0.269236\pi$
$98$		0			0
$99$	0.790708			0.0794692
$100$		0			0
$101$	−8.01165	+	13.8766i	−0.797189	+	1.38077i	0.124251	+	0.992251i	$0.460347\pi$
$101$	−8.01165	+	13.8766i	−0.797189	+	1.38077i	−0.921440	+	0.388521i	$0.872986\pi$
$102$		0			0
$103$	1.63272	+	2.82795i	0.160876	+	0.278646i	0.935183	−	0.354164i	$-0.115235\pi$
$103$	1.63272	+	2.82795i	0.160876	+	0.278646i	−0.774307	+	0.632810i	$0.781901\pi$
$104$		0			0
$105$	−4.03189	−	0.397441i	−0.393473	−	0.0387863i
$106$		0			0
$107$	8.39711	+	14.5442i	0.811779	+	1.40604i	0.911618	+	0.411040i	$0.134834\pi$
$107$	8.39711	+	14.5442i	0.811779	+	1.40604i	−0.0998381	+	0.995004i	$0.531832\pi$
$108$		0			0
$109$	0.428597	−	0.742352i	0.0410522	−	0.0711044i	−0.844769	−	0.535131i	$-0.820262\pi$
$109$	0.428597	−	0.742352i	0.0410522	−	0.0711044i	0.885821	+	0.464026i	$0.153596\pi$
$110$		0			0
$111$	6.54623			0.621341
$112$		0			0
$113$	5.21625			0.490704			0.245352	−	0.969434i	$-0.421096\pi$
$113$	5.21625			0.490704			0.245352	+	0.969434i	$0.421096\pi$
$114$		0			0
$115$	0.459953	−	0.796662i	0.0428908	−	0.0742891i
$116$		0			0
$117$	−0.709675	−	1.22919i	−0.0656095	−	0.113639i
$118$		0			0
$119$	4.82245	−	6.72856i	0.442074	−	0.616806i
$120$		0			0
$121$	−0.459966	−	0.796684i	−0.0418151	−	0.0724258i
$122$		0			0
$123$	1.83389	−	3.17639i	0.165356	−	0.286406i
$124$		0			0
$125$	−8.42061			−0.753162
$126$		0			0
$127$	8.65614			0.768108			0.384054	−	0.923311i	$-0.374528\pi$
$127$	8.65614			0.768108			0.384054	+	0.923311i	$0.374528\pi$
$128$		0			0
$129$	−6.20796	+	10.7525i	−0.546580	+	0.946705i
$130$		0			0
$131$	0.0722302	+	0.125106i	0.00631078	+	0.0109306i	0.869164	−	0.494525i	$-0.164658\pi$
$131$	0.0722302	+	0.125106i	0.00631078	+	0.0109306i	−0.862853	+	0.505455i	$0.831325\pi$
$132$		0			0
$133$	−3.30944	−	7.30568i	−0.286965	−	0.633483i
$134$		0			0
$135$	−2.47230	−	4.28215i	−0.212782	−	0.368549i
$136$		0			0
$137$	−3.99476	+	6.91913i	−0.341296	+	0.591141i	−0.984674	−	0.174407i	$-0.944199\pi$
$137$	−3.99476	+	6.91913i	−0.341296	+	0.591141i	0.643378	+	0.765549i	$0.277532\pi$
$138$		0			0
$139$	−0.126678			−0.0107447			−0.00537236	−	0.999986i	$-0.501710\pi$
$139$	−0.126678			−0.0107447			−0.00537236	+	0.999986i	$0.501710\pi$
$140$		0			0
$141$	13.0157			1.09612
$142$		0			0
$143$	−10.6984	+	18.5301i	−0.894641	+	1.54956i
$144$		0			0
$145$	0.817237	+	1.41550i	0.0678678	+	0.117550i
$146$		0			0
$147$	7.68438	−	8.75946i	0.633797	−	0.722468i
$148$		0			0
$149$	5.24996	+	9.09320i	0.430094	+	0.744944i	0.996881	−	0.0789200i	$-0.0251472\pi$
$149$	5.24996	+	9.09320i	0.430094	+	0.744944i	−0.566787	+	0.823864i	$0.691814\pi$
$150$		0			0
$151$	−7.73847	+	13.4034i	−0.629747	+	1.09075i	0.357855	+	0.933777i	$0.383508\pi$
$151$	−7.73847	+	13.4034i	−0.629747	+	1.09075i	−0.987602	+	0.156977i	$0.949825\pi$
$152$		0			0
$153$	0.716588			0.0579327
$154$		0			0
$155$	−6.13231			−0.492559
$156$		0			0
$157$	−0.488393	+	0.845922i	−0.0389780	+	0.0675119i	−0.884856	−	0.465864i	$-0.845744\pi$
$157$	−0.488393	+	0.845922i	−0.0389780	+	0.0675119i	0.845878	+	0.533376i	$0.179077\pi$
$158$		0			0
$159$	−2.10417	−	3.64453i	−0.166872	−	0.289030i
$160$		0			0
$161$	1.09172	+	2.41001i	0.0860398	+	0.189935i
$162$		0			0
$163$	10.2353	+	17.7280i	0.801688	+	1.38857i	0.918504	+	0.395412i	$0.129398\pi$
$163$	10.2353	+	17.7280i	0.801688	+	1.38857i	−0.116816	+	0.993154i	$0.537269\pi$
$164$		0			0
$165$	−2.64342	+	4.57854i	−0.205790	+	0.356439i
$166$		0			0
$167$	−15.5940			−1.20670			−0.603349	−	0.797477i	$-0.706167\pi$
$167$	−15.5940			−1.20670			−0.603349	+	0.797477i	$0.706167\pi$
$168$		0			0
$169$	25.4079			1.95445
$170$		0			0
$171$	0.347130	−	0.601246i	0.0265457	−	0.0459784i
$172$		0			0
$173$	−2.52258	−	4.36923i	−0.191788	−	0.332187i	0.754055	−	0.656811i	$-0.228095\pi$
$173$	−2.52258	−	4.36923i	−0.191788	−	0.332187i	−0.945843	+	0.324625i	$0.894762\pi$
$174$		0			0
$175$	6.40208	−	8.93254i	0.483951	−	0.675236i
$176$		0			0
$177$	0.647683	+	1.12182i	0.0486829	+	0.0843212i
$178$		0			0
$179$	−3.13462	+	5.42931i	−0.234292	+	0.405806i	−0.959067	−	0.283180i	$-0.908611\pi$
$179$	−3.13462	+	5.42931i	−0.234292	+	0.405806i	0.724775	+	0.688986i	$0.241944\pi$
$180$		0			0
$181$	22.6103			1.68061			0.840303	−	0.542116i	$-0.182377\pi$
$181$	22.6103			1.68061			0.840303	+	0.542116i	$0.182377\pi$
$182$		0			0
$183$	−18.7772			−1.38805
$184$		0			0
$185$	1.80879	−	3.13292i	0.132985	−	0.230337i
$186$		0			0
$187$	−5.40128	−	9.35529i	−0.394981	−	0.684127i
$188$		0			0
$189$	14.1526	+	1.39508i	1.02945	+	0.101477i
$190$		0			0
$191$	5.55423	+	9.62021i	0.401890	+	0.696094i	0.993954	−	0.109797i	$-0.0350200\pi$
$191$	5.55423	+	9.62021i	0.401890	+	0.696094i	−0.592064	+	0.805891i	$0.701687\pi$
$192$		0			0
$193$	5.93600	−	10.2814i	0.427282	−	0.740075i	−0.569348	−	0.822097i	$-0.692804\pi$
$193$	5.93600	−	10.2814i	0.427282	−	0.740075i	0.996631	+	0.0820217i	$0.0261377\pi$
$194$		0			0
$195$	9.49008			0.679599
$196$		0			0
$197$	18.9226			1.34818			0.674090	−	0.738649i	$-0.264536\pi$
$197$	18.9226			1.34818			0.674090	+	0.738649i	$0.264536\pi$
$198$		0			0
$199$	4.48457	−	7.76750i	0.317902	−	0.550623i	−0.662148	−	0.749373i	$-0.730355\pi$
$199$	4.48457	−	7.76750i	0.317902	−	0.550623i	0.980050	+	0.198750i	$0.0636882\pi$
$200$		0			0
$201$	−0.0382750	−	0.0662943i	−0.00269971	−	0.00467604i
$202$		0			0
$203$	−4.67825	−	0.461155i	−0.328349	−	0.0323668i
$204$		0			0
$205$	−1.01345	−	1.75534i	−0.0707822	−	0.122598i
$206$		0			0
$207$	−0.114512	+	0.198340i	−0.00795911	+	0.0137856i
$208$		0			0
$209$	−10.4660			−0.723946
$210$		0			0
$211$	−9.40798			−0.647672			−0.323836	−	0.946113i	$-0.604973\pi$
$211$	−9.40798			−0.647672			−0.323836	+	0.946113i	$0.604973\pi$
$212$		0			0
$213$	−3.49965	+	6.06157i	−0.239792	+	0.415332i
$214$		0			0
$215$	3.43064	+	5.94205i	0.233968	+	0.405244i
$216$		0			0
$217$	10.2745	−	14.3355i	0.697475	−	0.973157i
$218$		0			0
$219$	−7.22545	−	12.5149i	−0.488251	−	0.845675i
$220$		0			0
$221$	−9.69550	+	16.7931i	−0.652190	+	1.12963i
$222$		0			0
$223$	17.7025			1.18545			0.592724	−	0.805406i	$-0.298053\pi$
$223$	17.7025			1.18545			0.592724	+	0.805406i	$0.298053\pi$
$224$		0			0
$225$	0.951310			0.0634207
$226$		0			0
$227$	−5.36778	+	9.29726i	−0.356272	+	0.617081i	−0.987335	−	0.158651i	$-0.949286\pi$
$227$	−5.36778	+	9.29726i	−0.356272	+	0.617081i	0.631063	+	0.775732i	$0.282619\pi$
$228$		0			0
$229$	2.51891	+	4.36288i	0.166454	+	0.288307i	0.937171	−	0.348871i	$-0.113435\pi$
$229$	2.51891	+	4.36288i	0.166454	+	0.288307i	−0.770717	+	0.637178i	$0.780102\pi$
$230$		0			0
$231$	−6.27430	−	13.8507i	−0.412819	−	0.911310i
$232$		0			0
$233$	6.79295	+	11.7657i	0.445021	+	0.770799i	0.998054	−	0.0623608i	$-0.0198629\pi$
$233$	6.79295	+	11.7657i	0.445021	+	0.770799i	−0.553033	+	0.833159i	$0.686530\pi$
$234$		0			0
$235$	3.59636	−	6.22908i	0.234601	−	0.406340i
$236$		0			0
$237$	−3.41467			−0.221807
$238$		0			0
$239$	−18.5960			−1.20287			−0.601437	−	0.798920i	$-0.705405\pi$
$239$	−18.5960			−1.20287			−0.601437	+	0.798920i	$0.705405\pi$
$240$		0			0
$241$	2.55440	−	4.42435i	0.164543	−	0.284997i	−0.771950	−	0.635684i	$-0.780718\pi$
$241$	2.55440	−	4.42435i	0.164543	−	0.284997i	0.936493	+	0.350686i	$0.114052\pi$
$242$		0			0
$243$	1.18737	+	2.05658i	0.0761698	+	0.131930i
$244$		0			0
$245$	−2.06886	−	6.09795i	−0.132174	−	0.389584i
$246$		0			0
$247$	9.39339	+	16.2698i	0.597687	+	1.03522i
$248$		0			0
$249$	−10.3202	+	17.8750i	−0.654013	+	1.13278i
$250$		0			0
$251$	1.94799			0.122956			0.0614779	−	0.998108i	$-0.480419\pi$
$251$	1.94799			0.122956			0.0614779	+	0.998108i	$0.480419\pi$
$252$		0			0
$253$	3.45253			0.217058
$254$		0			0
$255$	−2.39563	+	4.14935i	−0.150020	+	0.259843i
$256$		0			0
$257$	−14.3945	−	24.9319i	−0.897902	−	1.55521i	−0.830172	−	0.557508i	$-0.811758\pi$
$257$	−14.3945	−	24.9319i	−0.897902	−	1.55521i	−0.0677301	−	0.997704i	$-0.521576\pi$
$258$		0			0
$259$	4.29326	+	9.47749i	0.266770	+	0.588903i
$260$		0			0
$261$	−0.203462	−	0.352407i	−0.0125940	−	0.0218134i
$262$		0			0
$263$	11.2950	−	19.5634i	0.696477	−	1.20633i	−0.273203	−	0.961956i	$-0.588083\pi$
$263$	11.2950	−	19.5634i	0.696477	−	1.20633i	0.969680	−	0.244377i	$-0.0785835\pi$
$264$		0			0
$265$	−2.32562			−0.142862
$266$		0			0
$267$	−21.1940			−1.29705
$268$		0			0
$269$	−4.93206	+	8.54257i	−0.300713	+	0.520850i	−0.976298	−	0.216432i	$-0.930558\pi$
$269$	−4.93206	+	8.54257i	−0.300713	+	0.520850i	0.675585	+	0.737282i	$0.263891\pi$
$270$		0			0
$271$	12.3961	+	21.4708i	0.753012	+	1.30426i	0.946357	+	0.323124i	$0.104733\pi$
$271$	12.3961	+	21.4708i	0.753012	+	1.30426i	−0.193344	+	0.981131i	$0.561933\pi$
$272$		0			0
$273$	−15.9003	+	22.1850i	−0.962328	+	1.34269i
$274$		0			0
$275$	−7.17050	−	12.4197i	−0.432398	−	0.748935i
$276$		0			0
$277$	−11.2567	+	19.4971i	−0.676347	+	1.17147i	0.299726	+	0.954025i	$0.403105\pi$
$277$	−11.2567	+	19.4971i	−0.676347	+	1.17147i	−0.976073	+	0.217443i	$0.930228\pi$
$278$		0			0
$279$	1.52672			0.0914025
$280$		0			0
$281$	1.01020			0.0602635			0.0301317	−	0.999546i	$-0.490407\pi$
$281$	1.01020			0.0602635			0.0301317	+	0.999546i	$0.490407\pi$
$282$		0			0
$283$	0.766622	−	1.32783i	0.0455709	−	0.0789312i	−0.842340	−	0.538946i	$-0.818823\pi$
$283$	0.766622	−	1.32783i	0.0455709	−	0.0789312i	0.887911	+	0.460015i	$0.152156\pi$
$284$		0			0
$285$	2.32098	+	4.02006i	0.137483	+	0.238128i
$286$		0			0
$287$	5.80145	+	0.571874i	0.342449	+	0.0337566i
$288$		0			0
$289$	3.60503	+	6.24410i	0.212061	+	0.367300i
$290$		0			0
$291$	10.8715	−	18.8299i	0.637296	−	1.10383i
$292$		0			0
$293$	25.1317			1.46821			0.734105	−	0.679036i	$-0.237602\pi$
$293$	25.1317			1.46821			0.734105	+	0.679036i	$0.237602\pi$
$294$		0			0
$295$	0.715846			0.0416782
$296$		0			0
$297$	9.27886	−	16.0715i	0.538414	−	0.932560i
$298$		0			0
$299$	−3.09870	−	5.36711i	−0.179203	−	0.310388i
$300$		0			0
$301$	−19.6386	−	1.93587i	−1.13195	−	0.111581i
$302$		0			0
$303$	13.3364	+	23.0993i	0.766156	+	1.32702i
$304$		0			0
$305$	−5.18833	+	8.98645i	−0.297083	+	0.514563i
$306$		0			0
$307$	29.2429			1.66898			0.834491	−	0.551021i	$-0.185762\pi$
$307$	29.2429			1.66898			0.834491	+	0.551021i	$0.185762\pi$
$308$		0			0
$309$	5.43572			0.309227
$310$		0			0
$311$	−13.1249	+	22.7330i	−0.744244	+	1.28907i	0.206304	+	0.978488i	$0.433857\pi$
$311$	−13.1249	+	22.7330i	−0.744244	+	1.28907i	−0.950547	+	0.310580i	$0.899477\pi$
$312$		0			0
$313$	2.66810	+	4.62128i	0.150810	+	0.261210i	0.931525	−	0.363676i	$-0.118479\pi$
$313$	2.66810	+	4.62128i	0.150810	+	0.261210i	−0.780716	+	0.624886i	$0.785145\pi$
$314$		0			0
$315$	0.324714	−	0.453059i	0.0182956	−	0.0255270i
$316$		0			0
$317$	10.2142	+	17.6915i	0.573686	+	0.993654i	0.996183	+	0.0872894i	$0.0278205\pi$
$317$	10.2142	+	17.6915i	0.573686	+	0.993654i	−0.422497	+	0.906364i	$0.638846\pi$
$318$		0			0
$319$	−3.06719	+	5.31254i	−0.171730	+	0.297445i
$320$		0			0
$321$	27.9561			1.56036
$322$		0			0
$323$	−9.48489			−0.527753
$324$		0			0
$325$	−12.8713	+	22.2938i	−0.713972	+	1.23664i
$326$		0			0
$327$	−0.713454	−	1.23574i	−0.0394541	−	0.0683365i
$328$		0			0
$329$	8.53615	+	18.8438i	0.470613	+	1.03889i
$330$		0			0
$331$	−5.73049	−	9.92550i	−0.314976	−	0.545555i	0.664456	−	0.747327i	$-0.268663\pi$
$331$	−5.73049	−	9.92550i	−0.314976	−	0.545555i	−0.979432	+	0.201772i	$0.935330\pi$
$332$		0			0
$333$	−0.450323	+	0.779982i	−0.0246776	+	0.0427428i
$334$		0			0
$335$	−0.0423031			−0.00231127
$336$		0			0
$337$	−22.6485			−1.23374			−0.616870	−	0.787065i	$-0.711600\pi$
$337$	−22.6485			−1.23374			−0.616870	+	0.787065i	$0.711600\pi$
$338$		0			0
$339$	4.34155	−	7.51979i	0.235801	−	0.408419i
$340$		0			0
$341$	−11.5077	−	19.9319i	−0.623175	−	1.07937i
$342$		0			0
$343$	17.7215	+	5.38051i	0.956869	+	0.290520i
$344$		0			0
$345$	−0.765649	−	1.32614i	−0.0412212	−	0.0713972i
$346$		0			0
$347$	1.99022	−	3.44717i	0.106841	−	0.185054i	−0.807648	−	0.589665i	$-0.799260\pi$
$347$	1.99022	−	3.44717i	0.106841	−	0.185054i	0.914489	+	0.404611i	$0.132593\pi$
$348$		0			0
$349$	−32.5779			−1.74385			−0.871927	−	0.489636i	$-0.837130\pi$
$349$	−32.5779			−1.74385			−0.871927	+	0.489636i	$0.837130\pi$
$350$		0			0
$351$	−33.3118			−1.77805
$352$		0			0
$353$	12.1208	−	20.9938i	0.645123	−	1.11739i	−0.339150	−	0.940732i	$-0.610139\pi$
$353$	12.1208	−	20.9938i	0.645123	−	1.11739i	0.984273	−	0.176654i	$-0.0565273\pi$
$354$		0			0
$355$	1.93398	+	3.34975i	0.102645	+	0.177786i
$356$		0			0
$357$	−5.68615	−	12.5524i	−0.300943	−	0.664341i
$358$		0			0
$359$	18.4603	+	31.9741i	0.974296	+	1.68753i	0.682240	+	0.731128i	$0.261006\pi$
$359$	18.4603	+	31.9741i	0.974296	+	1.68753i	0.292056	+	0.956401i	$0.405661\pi$
$360$		0			0
$361$	4.90533	−	8.49628i	0.258175	−	0.447173i
$362$		0			0
$363$	−1.53134			−0.0803746
$364$		0			0
$365$	−7.98587			−0.417999
$366$		0			0
$367$	5.93350	−	10.2771i	0.309726	−	0.536462i	−0.668576	−	0.743644i	$-0.733096\pi$
$367$	5.93350	−	10.2771i	0.309726	−	0.536462i	0.978302	+	0.207182i	$0.0664292\pi$
$368$		0			0
$369$	0.252311	+	0.437016i	0.0131348	+	0.0227501i
$370$		0			0
$371$	3.89648	−	5.43659i	0.202295	−	0.282254i
$372$		0			0
$373$	1.72419	+	2.98638i	0.0892750	+	0.154629i	0.907205	−	0.420689i	$-0.138212\pi$
$373$	1.72419	+	2.98638i	0.0892750	+	0.154629i	−0.817930	+	0.575318i	$0.804878\pi$
$374$		0			0
$375$	−7.00858	+	12.1392i	−0.361922	+	0.626866i
$376$		0			0
$377$	11.0114			0.567118
$378$		0			0
$379$	34.1466			1.75400			0.876998	−	0.480495i	$-0.159543\pi$
$379$	34.1466			1.75400			0.876998	+	0.480495i	$0.159543\pi$
$380$		0			0
$381$	7.20461	−	12.4788i	0.369104	−	0.639306i
$382$		0			0
$383$	−1.00267	−	1.73668i	−0.0512342	−	0.0887403i	0.839271	−	0.543713i	$-0.182982\pi$
$383$	−1.00267	−	1.73668i	−0.0512342	−	0.0887403i	−0.890505	+	0.454973i	$0.849649\pi$
$384$		0			0
$385$	−8.36237	−	0.824315i	−0.426186	−	0.0420110i
$386$		0			0
$387$	−0.854106	−	1.47935i	−0.0434166	−	0.0751998i
$388$		0			0
$389$	−4.72144	+	8.17777i	−0.239386	+	0.414630i	−0.960538	−	0.278147i	$-0.910280\pi$
$389$	−4.72144	+	8.17777i	−0.239386	+	0.414630i	0.721152	+	0.692777i	$0.243613\pi$
$390$		0			0
$391$	3.12889			0.158235
$392$		0			0
$393$	0.240472			0.0121302
$394$		0			0
$395$	−0.943509	+	1.63421i	−0.0474731	+	0.0822258i
$396$		0			0
$397$	−5.33171	−	9.23480i	−0.267591	−	0.463481i	0.700648	−	0.713507i	$-0.252894\pi$
$397$	−5.33171	−	9.23480i	−0.267591	−	0.463481i	−0.968239	+	0.250026i	$0.919561\pi$
$398$		0			0
$399$	−13.2864	−	1.30970i	−0.665153	−	0.0655670i
$400$		0			0
$401$	6.98676	+	12.1014i	0.348902	+	0.604317i	0.986055	−	0.166421i	$-0.0532212\pi$
$401$	6.98676	+	12.1014i	0.348902	+	0.604317i	−0.637152	+	0.770738i	$0.719888\pi$
$402$		0			0
$403$	−20.6567	+	35.7784i	−1.02898	+	1.78225i
$404$		0			0
$405$	−7.59886			−0.377591
$406$		0			0
$407$	13.5772			0.672999
$408$		0			0
$409$	−10.5360	+	18.2490i	−0.520974	+	0.902353i	0.478729	+	0.877963i	$0.341098\pi$
$409$	−10.5360	+	18.2490i	−0.520974	+	0.902353i	−0.999703	+	0.0243899i	$0.992236\pi$
$410$		0			0
$411$	6.64978	+	11.5178i	0.328010	+	0.568129i
$412$		0			0
$413$	−1.19937	+	1.67343i	−0.0590173	+	0.0823442i
$414$		0			0
$415$	5.70313	+	9.87811i	0.279956	+	0.484897i
$416$		0			0
$417$	−0.105436	+	0.182620i	−0.00516322	+	0.00894296i
$418$		0			0
$419$	28.5948			1.39695			0.698474	−	0.715636i	$-0.253863\pi$
$419$	28.5948			1.39695			0.698474	+	0.715636i	$0.253863\pi$
$420$		0			0
$421$	−9.42425			−0.459310			−0.229655	−	0.973272i	$-0.573760\pi$
$421$	−9.42425			−0.459310			−0.229655	+	0.973272i	$0.573760\pi$
$422$		0			0
$423$	−0.895364	+	1.55082i	−0.0435341	+	0.0754032i
$424$		0			0
$425$	−6.49834	−	11.2555i	−0.315216	−	0.545970i
$426$		0			0
$427$	−12.3148	−	27.1852i	−0.595954	−	1.31559i
$428$		0			0
$429$	17.8087	+	30.8457i	0.859814	+	1.48924i
$430$		0			0
$431$	−9.40826	+	16.2956i	−0.453180	+	0.784931i	−0.998582	−	0.0532443i	$-0.983044\pi$
$431$	−9.40826	+	16.2956i	−0.453180	+	0.784931i	0.545402	+	0.838175i	$0.316377\pi$
$432$		0			0
$433$	−27.1071			−1.30269			−0.651343	−	0.758784i	$-0.725794\pi$
$433$	−27.1071			−1.30269			−0.651343	+	0.758784i	$0.725794\pi$
$434$		0			0
$435$	2.72079			0.130452
$436$		0			0
$437$	1.51570	−	2.62526i	0.0725056	−	0.125583i
$438$		0			0
$439$	7.47409	+	12.9455i	0.356719	+	0.617855i	0.987411	−	0.158178i	$-0.0505621\pi$
$439$	7.47409	+	12.9455i	0.356719	+	0.617855i	−0.630692	+	0.776033i	$0.717229\pi$
$440$		0			0
$441$	0.515070	+	1.51817i	0.0245272	+	0.0722937i
$442$		0			0
$443$	−18.3072	−	31.7091i	−0.869803	−	1.50654i	−0.862197	−	0.506572i	$-0.830912\pi$
$443$	−18.3072	−	31.7091i	−0.869803	−	1.50654i	−0.00760582	−	0.999971i	$-0.502421\pi$
$444$		0			0
$445$	−5.85612	+	10.1431i	−0.277607	+	0.480829i
$446$		0			0
$447$	17.4784			0.826702
$448$		0			0
$449$	−30.4906			−1.43894			−0.719470	−	0.694523i	$-0.755615\pi$
$449$	−30.4906			−1.43894			−0.719470	+	0.694523i	$0.755615\pi$
$450$		0			0
$451$	3.80359	−	6.58802i	0.179104	−	0.310218i
$452$		0			0
$453$	12.8816	+	22.3117i	0.605232	+	1.04829i
$454$		0			0
$455$	6.22394	+	13.7395i	0.291783	+	0.644119i
$456$		0			0
$457$	−20.9283	−	36.2488i	−0.978984	−	1.69565i	−0.666108	−	0.745855i	$-0.732041\pi$
$457$	−20.9283	−	36.2488i	−0.978984	−	1.69565i	−0.312875	−	0.949794i	$-0.601292\pi$
$458$		0			0
$459$	8.40906	−	14.5649i	0.392501	−	0.679832i
$460$		0			0
$461$	18.7895			0.875115			0.437557	−	0.899190i	$-0.355844\pi$
$461$	18.7895			0.875115			0.437557	+	0.899190i	$0.355844\pi$
$462$		0			0
$463$	−24.2203			−1.12561			−0.562805	−	0.826589i	$-0.690278\pi$
$463$	−24.2203			−1.12561			−0.562805	+	0.826589i	$0.690278\pi$
$464$		0			0
$465$	−5.10400	+	8.84038i	−0.236692	+	0.409963i
$466$		0			0
$467$	7.22733	+	12.5181i	0.334441	+	0.579269i	0.983377	−	0.181574i	$-0.0581192\pi$
$467$	7.22733	+	12.5181i	0.334441	+	0.579269i	−0.648936	+	0.760843i	$0.724786\pi$
$468$		0			0
$469$	0.0708773	−	0.0988920i	0.00327281	−	0.00456641i
$470$		0			0
$471$	0.812992	+	1.40814i	0.0374607	+	0.0648838i
$472$		0			0
$473$	−12.8756	+	22.3013i	−0.592023	+	1.02541i
$474$		0			0
$475$	−12.5917			−0.577748
$476$		0			0
$477$	0.578994			0.0265103
$478$		0			0
$479$	−8.37498	+	14.5059i	−0.382663	+	0.662791i	−0.991442	−	0.130548i	$-0.958326\pi$
$479$	−8.37498	+	14.5059i	−0.382663	+	0.662791i	0.608779	+	0.793340i	$0.291660\pi$
$480$		0			0
$481$	−12.1858	−	21.1065i	−0.555626	−	0.962372i
$482$		0			0
$483$	4.38294	+	0.432045i	0.199431	+	0.0196587i
$484$		0			0
$485$	−6.00779	−	10.4058i	−0.272800	−	0.472503i
$486$		0			0
$487$	−11.6101	+	20.1093i	−0.526105	+	0.911241i	0.473432	+	0.880830i	$0.343015\pi$
$487$	−11.6101	+	20.1093i	−0.526105	+	0.911241i	−0.999537	+	0.0304110i	$0.990318\pi$
$488$		0			0
$489$	34.0758			1.54096
$490$		0			0
$491$	−13.2143			−0.596352			−0.298176	−	0.954511i	$-0.596378\pi$
$491$	−13.2143			−0.596352			−0.298176	+	0.954511i	$0.596378\pi$
$492$		0			0
$493$	−2.77968	+	4.81454i	−0.125190	+	0.216836i
$494$		0			0
$495$	−0.363689	−	0.629927i	−0.0163466	−	0.0283131i
$496$		0			0
$497$	−11.0710	−	1.09132i	−0.496603	−	0.0489522i
$498$		0			0
$499$	−13.2088	−	22.8784i	−0.591308	−	1.02418i	−0.994056	−	0.108865i	$-0.965278\pi$
$499$	−13.2088	−	22.8784i	−0.591308	−	1.02418i	0.402748	−	0.915311i	$-0.368055\pi$
$500$		0			0
$501$	−12.9791	+	22.4804i	−0.579862	+	1.00435i
$502$		0			0
$503$	−0.709608			−0.0316399			−0.0158199	−	0.999875i	$-0.505036\pi$
$503$	−0.709608			−0.0316399			−0.0158199	+	0.999875i	$0.505036\pi$
$504$		0			0
$505$	14.7399			0.655918
$506$		0			0
$507$	21.1473	−	36.6282i	0.939184	−	1.62671i
$508$		0			0
$509$	−6.77142	−	11.7284i	−0.300138	−	0.519854i	0.676029	−	0.736875i	$-0.263699\pi$
$509$	−6.77142	−	11.7284i	−0.300138	−	0.519854i	−0.976167	+	0.217021i	$0.930366\pi$
$510$		0			0
$511$	13.3800	−	18.6686i	0.591897	−	0.825848i
$512$		0			0
$513$	−8.14704	−	14.1111i	−0.359701	−	0.623020i
$514$		0			0
$515$	1.50195	−	2.60145i	0.0661836	−	0.114633i
$516$		0			0
$517$	26.9952			1.18725
$518$		0			0
$519$	−8.39829			−0.368644
$520$		0			0
$521$	−9.42754	+	16.3290i	−0.413028	+	0.715385i	−0.995219	−	0.0976665i	$-0.968862\pi$
$521$	−9.42754	+	16.3290i	−0.413028	+	0.715385i	0.582191	+	0.813052i	$0.302195\pi$
$522$		0			0
$523$	15.3104	+	26.5183i	0.669476	+	1.15957i	0.978051	+	0.208366i	$0.0668145\pi$
$523$	15.3104	+	26.5183i	0.669476	+	1.15957i	−0.308575	+	0.951200i	$0.599852\pi$
$524$		0			0
$525$	−7.54869	−	16.6639i	−0.329452	−	0.727274i
$526$		0			0
$527$	−10.4290	−	18.0635i	−0.454292	−	0.786857i
$528$		0			0
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$		0			0
$531$	−0.178220			−0.00773407
$532$		0			0
$533$	−13.6552			−0.591471
$534$		0			0
$535$	7.72455	−	13.3793i	0.333962	−	0.578438i
$536$		0			0
$537$	5.21796	+	9.03777i	0.225172	+	0.390009i
$538$		0			0
$539$	15.9378	−	18.1676i	0.686491	−	0.782534i
$540$		0			0
$541$	0.374204	+	0.648140i	0.0160883	+	0.0278657i	0.873957	−	0.486002i	$-0.161545\pi$
$541$	0.374204	+	0.648140i	0.0160883	+	0.0278657i	−0.857869	+	0.513868i	$0.828212\pi$
$542$		0			0
$543$	18.8188	−	32.5951i	0.807592	−	1.39879i
$544$		0			0
$545$	−0.788538			−0.0337773
$546$		0			0
$547$	2.36972			0.101322			0.0506611	−	0.998716i	$-0.483867\pi$
$547$	2.36972			0.101322			0.0506611	+	0.998716i	$0.483867\pi$
$548$		0			0
$549$	1.29171	−	2.23730i	0.0551287	−	0.0954857i
$550$		0			0
$551$	2.69306	+	4.66452i	0.114728	+	0.198715i
$552$		0			0
$553$	−2.23947	−	4.94369i	−0.0952319	−	0.210227i
$554$		0			0
$555$	−3.01096	−	5.21513i	−0.127808	−	0.221370i
$556$		0			0
$557$	15.6512	−	27.1087i	0.663164	−	1.14863i	−0.316616	−	0.948554i	$-0.602547\pi$
$557$	15.6512	−	27.1087i	0.663164	−	1.14863i	0.979780	−	0.200080i	$-0.0641201\pi$
$558$		0			0
$559$	46.2245			1.95509
$560$		0			0
$561$	−17.9822			−0.759210
$562$		0			0
$563$	9.70645	−	16.8121i	0.409078	−	0.708544i	−0.585709	−	0.810522i	$-0.699184\pi$
$563$	9.70645	−	16.8121i	0.409078	−	0.708544i	0.994787	+	0.101978i	$0.0325171\pi$
$564$		0			0
$565$	−2.39923	−	4.15559i	−0.100936	−	0.174827i
$566$		0			0
$567$	12.7316	−	17.7639i	0.534677	−	0.746012i
$568$		0			0
$569$	3.28970	+	5.69792i	0.137911	+	0.238869i	0.926706	−	0.375788i	$-0.122628\pi$
$569$	3.28970	+	5.69792i	0.137911	+	0.238869i	−0.788795	+	0.614657i	$0.789294\pi$
$570$		0			0
$571$	10.0708	−	17.4432i	0.421451	−	0.729975i	−0.574630	−	0.818413i	$-0.694854\pi$
$571$	10.0708	−	17.4432i	0.421451	−	0.729975i	0.996082	+	0.0884380i	$0.0281875\pi$
$572$		0			0
$573$	18.4914			0.772490
$574$		0			0
$575$	4.15377			0.173224
$576$		0			0
$577$	0.886098	−	1.53477i	0.0368887	−	0.0638932i	−0.846992	−	0.531606i	$-0.821589\pi$
$577$	0.886098	−	1.53477i	0.0368887	−	0.0638932i	0.883880	+	0.467713i	$0.154922\pi$
$578$		0			0
$579$	−9.88121	−	17.1148i	−0.410649	−	0.711265i
$580$		0			0
$581$	−32.6474	−	3.21820i	−1.35444	−	0.133513i
$582$		0			0
$583$	−4.36417	−	7.55897i	−0.180745	−	0.313060i
$584$		0			0
$585$	−0.652834	+	1.13074i	−0.0269914	+	0.0467504i
$586$		0			0
$587$	−3.03541			−0.125285			−0.0626424	−	0.998036i	$-0.519953\pi$
$587$	−3.03541			−0.125285			−0.0626424	+	0.998036i	$0.519953\pi$
$588$		0			0
$589$	−20.2080			−0.832655
$590$		0			0
$591$	15.7495	−	27.2790i	0.647849	−	1.12211i
$592$		0			0
$593$	−10.6045	−	18.3676i	−0.435476	−	0.754266i	0.561859	−	0.827233i	$-0.310086\pi$
$593$	−10.6045	−	18.3676i	−0.435476	−	0.754266i	−0.997334	+	0.0729672i	$0.976753\pi$
$594$		0			0
$595$	−7.57849	−	0.747044i	−0.310688	−	0.0306258i
$596$		0			0
$597$	−7.46512	−	12.9300i	−0.305527	−	0.529188i
$598$		0			0
$599$	−8.44050	+	14.6194i	−0.344869	+	0.597331i	−0.985330	−	0.170660i	$-0.945410\pi$
$599$	−8.44050	+	14.6194i	−0.344869	+	0.597331i	0.640461	+	0.767991i	$0.278743\pi$
$600$		0			0
$601$	−42.3556			−1.72772			−0.863860	−	0.503732i	$-0.831960\pi$
$601$	−42.3556			−1.72772			−0.863860	+	0.503732i	$0.831960\pi$
$602$		0			0
$603$	0.0105319			0.000428894
$604$		0			0
$605$	−0.423125	+	0.732874i	−0.0172025	+	0.0297956i
$606$		0			0
$607$	−9.35619	−	16.2054i	−0.379756	−	0.657757i	0.611270	−	0.791422i	$-0.290659\pi$
$607$	−9.35619	−	16.2054i	−0.379756	−	0.657757i	−0.991027	+	0.133665i	$0.957325\pi$
$608$		0			0
$609$	−4.55857	+	6.36038i	−0.184723	+	0.257736i
$610$		0			0
$611$	−24.2287	−	41.9653i	−0.980188	−	1.69774i
$612$		0			0
$613$	20.1216	−	34.8516i	0.812703	−	1.40764i	−0.0982633	−	0.995160i	$-0.531329\pi$
$613$	20.1216	−	34.8516i	0.812703	−	1.40764i	0.910966	−	0.412482i	$-0.135338\pi$
$614$		0			0
$615$	−3.37402			−0.136053
$616$		0			0
$617$	34.9722			1.40793			0.703964	−	0.710236i	$-0.251412\pi$
$617$	34.9722			1.40793			0.703964	+	0.710236i	$0.251412\pi$
$618$		0			0
$619$	6.16882	−	10.6847i	0.247946	−	0.429454i	−0.715010	−	0.699114i	$-0.753578\pi$
$619$	6.16882	−	10.6847i	0.247946	−	0.429454i	0.962956	+	0.269660i	$0.0869112\pi$
$620$		0			0
$621$	2.68756	+	4.65498i	0.107848	+	0.186798i
$622$		0			0
$623$	−13.8998	−	30.6842i	−0.556884	−	1.22934i
$624$		0			0
$625$	−6.51135	−	11.2780i	−0.260454	−	0.451119i
$626$		0			0
$627$	−8.71095	+	15.0878i	−0.347882	+	0.602549i
$628$		0			0
$629$	12.3045			0.490613
$630$		0			0
$631$	42.1997			1.67994			0.839971	−	0.542632i	$-0.182572\pi$
$631$	42.1997			1.67994			0.839971	+	0.542632i	$0.182572\pi$
$632$		0			0
$633$	−7.83038	+	13.5626i	−0.311230	+	0.539065i
$634$		0			0
$635$	−3.98142	−	6.89602i	−0.157998	−	0.273660i
$636$		0			0
$637$	−42.5469	−	8.47037i	−1.68577	−	0.335608i
$638$		0			0
$639$	−0.481490	−	0.833965i	−0.0190475	−	0.0329912i
$640$		0			0
$641$	−20.0547	+	34.7358i	−0.792114	+	1.37198i	0.132541	+	0.991178i	$0.457686\pi$
$641$	−20.0547	+	34.7358i	−0.792114	+	1.37198i	−0.924655	+	0.380805i	$0.875647\pi$
$642$		0			0
$643$	44.8359			1.76816			0.884078	−	0.467339i	$-0.154787\pi$
$643$	44.8359			1.76816			0.884078	+	0.467339i	$0.154787\pi$
$644$		0			0
$645$	11.4215			0.449720
$646$		0			0
$647$	−11.4147	+	19.7709i	−0.448759	+	0.777273i	−0.998306	−	0.0581902i	$-0.981467\pi$
$647$	−11.4147	+	19.7709i	−0.448759	+	0.777273i	0.549547	+	0.835463i	$0.314800\pi$
$648$		0			0
$649$	1.34333	+	2.32672i	0.0527304	+	0.0913317i
$650$		0			0
$651$	−12.1146	−	26.7433i	−0.474809	−	1.04815i
$652$		0			0
$653$	0.511163	+	0.885361i	0.0200034	+	0.0346468i	0.875854	−	0.482577i	$-0.160299\pi$
$653$	0.511163	+	0.885361i	0.0200034	+	0.0346468i	−0.855850	+	0.517223i	$0.826966\pi$
$654$		0			0
$655$	0.0664450	−	0.115086i	0.00259622	−	0.00449679i
$656$		0			0
$657$	1.98819			0.0775667
$658$		0			0
$659$	37.6561			1.46687			0.733437	−	0.679757i	$-0.237915\pi$
$659$	37.6561			1.46687			0.733437	+	0.679757i	$0.237915\pi$
$660$		0			0
$661$	2.53155	−	4.38477i	0.0984658	−	0.170548i	−0.812584	−	0.582844i	$-0.801940\pi$
$661$	2.53155	−	4.38477i	0.0984658	−	0.170548i	0.911050	+	0.412296i	$0.135273\pi$
$662$		0			0
$663$	16.1394	+	27.9542i	0.626801	+	1.08565i
$664$		0			0
$665$	−4.29797	+	5.99677i	−0.166668	+	0.232545i
$666$		0			0
$667$	−0.888391	−	1.53874i	−0.0343987	−	0.0595802i
$668$		0			0
$669$	14.7340	−	25.5201i	0.569650	−	0.986663i
$670$		0			0
$671$	−38.9449			−1.50345
$672$		0			0
$673$	28.9235			1.11492			0.557459	−	0.830204i	$-0.311776\pi$
$673$	28.9235			1.11492			0.557459	+	0.830204i	$0.311776\pi$
$674$		0			0
$675$	11.1635	−	19.3357i	0.429683	−	0.744233i
$676$		0			0
$677$	−20.3964	−	35.3276i	−0.783897	−	1.35775i	−0.929655	−	0.368430i	$-0.879895\pi$
$677$	−20.3964	−	35.3276i	−0.783897	−	1.35775i	0.145758	−	0.989320i	$-0.453438\pi$
$678$		0			0
$679$	34.3915	+	3.39011i	1.31982	+	0.130101i
$680$		0			0
$681$	8.93534	+	15.4765i	0.342403	+	0.593059i
$682$		0			0
$683$	−20.0126	+	34.6629i	−0.765763	+	1.32634i	0.174080	+	0.984732i	$0.444305\pi$
$683$	−20.0126	+	34.6629i	−0.765763	+	1.32634i	−0.939843	+	0.341608i	$0.889028\pi$
$684$		0			0
$685$	7.34961			0.280814
$686$		0			0
$687$	8.38608			0.319949
$688$		0			0
$689$	−7.83384	+	13.5686i	−0.298446	+	0.516923i
$690$		0			0
$691$	−6.91223	−	11.9723i	−0.262954	−	0.455449i	0.704072	−	0.710129i	$-0.251363\pi$
$691$	−6.91223	−	11.9723i	−0.262954	−	0.455449i	−0.967026	+	0.254680i	$0.918030\pi$
$692$		0			0
$693$	2.08193	+	0.205225i	0.0790859	+	0.00779583i
$694$		0			0
$695$	0.0582661	+	0.100920i	0.00221016	+	0.00382811i
$696$		0			0
$697$	3.44705	−	5.97046i	0.130566	−	0.226147i
$698$		0			0
$699$	22.6154			0.855394
$700$		0			0
$701$	28.7529			1.08598			0.542992	−	0.839738i	$-0.317291\pi$
$701$	28.7529			1.08598			0.542992	+	0.839738i	$0.317291\pi$
$702$		0			0
$703$	5.96056	−	10.3240i	0.224807	−	0.389377i
$704$		0			0
$705$	−5.98659	−	10.3691i	−0.225468	−	0.390522i
$706$		0			0
$707$	−24.6962	+	34.4575i	−0.928796	+	1.29591i
$708$		0			0
$709$	−0.406750	−	0.704512i	−0.0152758	−	0.0264585i	0.858286	−	0.513171i	$-0.171529\pi$
$709$	−0.406750	−	0.704512i	−0.0152758	−	0.0264585i	−0.873562	+	0.486712i	$0.838196\pi$
$710$		0			0
$711$	0.234900	−	0.406858i	0.00880942	−	0.0152584i
$712$		0			0
$713$	6.66624			0.249652
$714$		0			0
$715$	19.6830			0.736101
$716$		0			0
$717$	−15.4777	+	26.8081i	−0.578024	+	1.00117i
$718$		0			0
$719$	−3.69468	−	6.39938i	−0.137788	−	0.238657i	0.788871	−	0.614559i	$-0.210666\pi$
$719$	−3.69468	−	6.39938i	−0.137788	−	0.238657i	−0.926659	+	0.375903i	$0.877333\pi$
$720$		0			0
$721$	3.56495	+	7.86972i	0.132766	+	0.293084i
$722$		0			0
$723$	−4.25212	−	7.36488i	−0.158138	−	0.273903i
$724$		0			0
$725$	−3.69018	+	6.39157i	−0.137050	+	0.237377i
$726$		0			0
$727$	−2.82894			−0.104920			−0.0524598	−	0.998623i	$-0.516706\pi$
$727$	−2.82894			−0.104920			−0.0524598	+	0.998623i	$0.516706\pi$
$728$		0			0
$729$	28.7345			1.06424
$730$		0			0
$731$	−11.6687	+	20.2108i	−0.431582	+	0.747522i
$732$		0			0
$733$	−15.3436	−	26.5758i	−0.566728	−	0.981601i	−0.996887	−	0.0788481i	$-0.974876\pi$
$733$	−15.3436	−	26.5758i	−0.566728	−	0.981601i	0.430159	−	0.902753i	$-0.358458\pi$
$734$		0			0
$735$	−10.5128	−	2.09292i	−0.387770	−	0.0771984i
$736$		0			0
$737$	−0.0793846	−	0.137498i	−0.00292417	−	0.00506481i
$738$		0			0
$739$	−26.1554	+	45.3025i	−0.962142	+	1.66648i	−0.245038	+	0.969514i	$0.578800\pi$
$739$	−26.1554	+	45.3025i	−0.962142	+	1.66648i	−0.717105	+	0.696966i	$0.754533\pi$
$740$		0			0
$741$	31.2729			1.14884
$742$		0			0
$743$	−31.8312			−1.16777			−0.583887	−	0.811835i	$-0.698469\pi$
$743$	−31.8312			−1.16777			−0.583887	+	0.811835i	$0.698469\pi$
$744$		0			0
$745$	4.82947	−	8.36489i	0.176938	−	0.306466i
$746$		0			0
$747$	−1.41987	−	2.45929i	−0.0519504	−	0.0899807i
$748$		0			0
$749$	18.3346	+	40.4742i	0.669933	+	1.47890i
$750$		0			0
$751$	−11.0645	−	19.1643i	−0.403749	−	0.699314i	0.590426	−	0.807092i	$-0.298960\pi$
$751$	−11.0645	−	19.1643i	−0.403749	−	0.699314i	−0.994175	+	0.107778i	$0.965626\pi$
$752$		0			0
$753$	1.62133	−	2.80823i	0.0590847	−	0.102338i
$754$		0			0
$755$	14.2373			0.518149
$756$		0			0
$757$	−21.3850			−0.777252			−0.388626	−	0.921396i	$-0.627050\pi$
$757$	−21.3850			−0.777252			−0.388626	+	0.921396i	$0.627050\pi$
$758$		0			0
$759$	2.87358	−	4.97719i	0.104304	−	0.180660i
$760$		0			0
$761$	−5.56015	−	9.63046i	−0.201555	−	0.349104i	0.747475	−	0.664290i	$-0.231266\pi$
$761$	−5.56015	−	9.63046i	−0.201555	−	0.349104i	−0.949030	+	0.315187i	$0.897933\pi$
$762$		0			0
$763$	1.32117	−	1.84337i	0.0478294	−	0.0667343i
$764$		0			0
$765$	−0.329597	−	0.570878i	−0.0119166	−	0.0206401i
$766$		0			0
$767$	2.41133	−	4.17654i	0.0870680	−	0.150806i
$768$		0			0
$769$	−15.6702			−0.565081			−0.282541	−	0.959255i	$-0.591177\pi$
$769$	−15.6702			−0.565081			−0.282541	+	0.959255i	$0.591177\pi$
$770$		0			0
$771$	−47.9228			−1.72590
$772$		0			0
$773$	−9.31568	+	16.1352i	−0.335062	+	0.580344i	−0.983497	−	0.180926i	$-0.942091\pi$
$773$	−9.31568	+	16.1352i	−0.335062	+	0.580344i	0.648435	+	0.761270i	$0.275424\pi$
$774$		0			0
$775$	−13.8450	−	23.9803i	−0.497328	−	0.861397i
$776$		0			0
$777$	17.2362	+	1.69904i	0.618344	+	0.0609528i
$778$		0			0
$779$	−3.33964	−	5.78442i	−0.119655	−	0.207248i
$780$		0			0
$781$	−7.25847	+	12.5720i	−0.259728	+	0.449863i
$782$		0			0
$783$	−9.55041			−0.341304
$784$		0			0
$785$	0.898552			0.0320707
$786$		0			0
$787$	16.2577	−	28.1591i	0.579523	−	1.00376i	−0.416011	−	0.909360i	$-0.636572\pi$
$787$	16.2577	−	28.1591i	0.579523	−	1.00376i	0.995534	−	0.0944039i	$-0.0300945\pi$
$788$		0			0
$789$	−18.8019	−	32.5658i	−0.669364	−	1.15937i
$790$		0			0
$791$	13.7343	+	1.35385i	0.488337	+	0.0481375i
$792$		0			0
$793$	34.9538	+	60.5417i	1.24125	+	2.14990i
$794$		0			0
$795$	−1.93564	+	3.35263i	−0.0686501	+	0.118905i
$796$		0			0
$797$	7.26112			0.257202			0.128601	−	0.991696i	$-0.458951\pi$
$797$	7.26112			0.257202			0.128601	+	0.991696i	$0.458951\pi$
$798$		0			0
$799$	24.4647			0.865499
$800$		0			0
$801$	1.45796	−	2.52526i	0.0515145	−	0.0892257i
$802$		0			0
$803$	−14.9860	−	25.9565i	−0.528844	−	0.915985i
$804$		0			0
$805$	1.41782	−	1.97822i	0.0499716	−	0.0697232i
$806$		0			0
$807$	8.21003	+	14.2202i	0.289007	+	0.500574i
$808$		0			0
$809$	4.85017	−	8.40074i	0.170523	−	0.295354i	−0.768080	−	0.640354i	$-0.778788\pi$
$809$	4.85017	−	8.40074i	0.170523	−	0.295354i	0.938603	+	0.345000i	$0.112121\pi$
$810$		0			0
$811$	−22.3029			−0.783161			−0.391580	−	0.920144i	$-0.628071\pi$
$811$	−22.3029			−0.783161			−0.391580	+	0.920144i	$0.628071\pi$
$812$		0			0
$813$	41.2699			1.44740
$814$		0			0
$815$	9.41549	−	16.3081i	0.329810	−	0.571248i
$816$		0			0
$817$	11.3051	+	19.5810i	0.395515	+	0.685053i
$818$		0			0
$819$	−1.54954	−	3.42065i	−0.0541452	−	0.119527i
$820$		0			0
$821$	−2.92122	−	5.05971i	−0.101951	−	0.176585i	0.810537	−	0.585687i	$-0.199175\pi$
$821$	−2.92122	−	5.05971i	−0.101951	−	0.176585i	−0.912489	+	0.409102i	$0.865842\pi$
$822$		0			0
$823$	−5.41055	+	9.37134i	−0.188600	+	0.326664i	−0.944784	−	0.327695i	$-0.893728\pi$
$823$	−5.41055	+	9.37134i	−0.188600	+	0.326664i	0.756184	+	0.654359i	$0.227062\pi$
$824$		0			0
$825$	−23.8724			−0.831130
$826$		0			0
$827$	−9.84654			−0.342398			−0.171199	−	0.985236i	$-0.554764\pi$
$827$	−9.84654			−0.342398			−0.171199	+	0.985236i	$0.554764\pi$
$828$		0			0
$829$	27.2881	−	47.2644i	0.947755	−	1.64156i	0.197616	−	0.980279i	$-0.436680\pi$
$829$	27.2881	−	47.2644i	0.947755	−	1.64156i	0.750139	−	0.661280i	$-0.229987\pi$
$830$		0			0
$831$	18.7381	+	32.4554i	0.650018	+	1.12586i
$832$		0			0
$833$	14.4438	−	16.4646i	0.500449	−	0.570464i
$834$		0			0
$835$	7.17250	+	12.4231i	0.248214	+	0.429920i
$836$		0			0
$837$	17.9159	−	31.0312i	0.619264	−	1.07260i
$838$		0			0
$839$	−55.1860			−1.90523			−0.952616	−	0.304174i	$-0.901620\pi$
$839$	−55.1860			−1.90523			−0.952616	+	0.304174i	$0.901620\pi$
$840$		0			0
$841$	−25.8430			−0.891139
$842$		0			0
$843$	0.840802	−	1.45631i	0.0289588	−	0.0501580i
$844$		0			0
$845$	−11.6864	−	20.2415i	−0.402025	−	0.696328i
$846$		0			0
$847$	−1.00431	−	2.21704i	−0.0345085	−	0.0761785i
$848$		0			0
$849$	−1.27614	−	2.21034i	−0.0437969	−	0.0758585i
$850$		0			0
$851$	−1.96628	+	3.40569i	−0.0674031	+	0.116746i
$852$		0			0
$853$	55.6017			1.90377			0.951883	−	0.306463i	$-0.0991456\pi$
$853$	55.6017			1.90377			0.951883	+	0.306463i	$0.0991456\pi$
$854$		0			0
$855$	−0.638653			−0.0218415
$856$		0			0
$857$	−13.0466	+	22.5974i	−0.445664	+	0.771912i	−0.998098	−	0.0616440i	$-0.980366\pi$
$857$	−13.0466	+	22.5974i	−0.445664	+	0.771912i	0.552434	+	0.833556i	$0.313699\pi$
$858$		0			0
$859$	−1.10128	−	1.90748i	−0.0375753	−	0.0650823i	0.846626	−	0.532188i	$-0.178630\pi$
$859$	−1.10128	−	1.90748i	−0.0375753	−	0.0650823i	−0.884201	+	0.467106i	$0.845297\pi$
$860$		0			0
$861$	5.65304	−	7.88744i	0.192655	−	0.268803i
$862$		0			0
$863$	−2.39243	−	4.14382i	−0.0814394	−	0.141057i	0.822429	−	0.568868i	$-0.192618\pi$
$863$	−2.39243	−	4.14382i	−0.0814394	−	0.141057i	−0.903868	+	0.427811i	$0.859285\pi$
$864$		0			0
$865$	−2.32053	+	4.01928i	−0.0789005	+	0.136660i
$866$		0			0
$867$	12.0021			0.407611
$868$		0			0
$869$	−7.08222			−0.240248
$870$		0			0
$871$	−0.142498	+	0.246814i	−0.00482837	+	0.00836297i
$872$		0			0
$873$	1.49572	+	2.59067i	0.0506225	+	0.0876808i
$874$		0			0
$875$	−22.1714	−	2.18553i	−0.749530	−	0.0738844i
$876$		0			0
$877$	−23.6029	−	40.8813i	−0.797012	−	1.38047i	−0.921554	−	0.388251i	$-0.873079\pi$
$877$	−23.6029	−	40.8813i	−0.797012	−	1.38047i	0.124542	−	0.992214i	$-0.460254\pi$
$878$		0			0
$879$	20.9174	−	36.2301i	0.705528	−	1.22201i
$880$		0			0
$881$	−34.3740			−1.15809			−0.579045	−	0.815296i	$-0.696574\pi$
$881$	−34.3740			−1.15809			−0.579045	+	0.815296i	$0.696574\pi$
$882$		0			0
$883$	−10.3267			−0.347520			−0.173760	−	0.984788i	$-0.555592\pi$
$883$	−10.3267			−0.347520			−0.173760	+	0.984788i	$0.555592\pi$
$884$		0			0
$885$	0.595808	−	1.03197i	0.0200279	−	0.0346893i
$886$		0			0
$887$	−6.31870	−	10.9443i	−0.212161	−	0.367474i	0.740229	−	0.672354i	$-0.234717\pi$
$887$	−6.31870	−	10.9443i	−0.212161	−	0.367474i	−0.952391	+	0.304880i	$0.901384\pi$
$888$		0			0
$889$	22.7915	+	2.24666i	0.764403	+	0.0753505i
$890$		0			0
$891$	−14.2598	−	24.6986i	−0.477720	−	0.827435i
$892$		0			0
$893$	11.8512	−	20.5269i	0.396585	−	0.686906i
$894$		0			0
$895$	5.76710			0.192773
$896$		0			0
$897$	−10.3164			−0.344453
$898$		0			0
$899$	−5.92223	+	10.2576i	−0.197517	+	0.342110i
$900$		0			0
$901$	−3.95508	−	6.85039i	−0.131763	−	0.228220i
$902$		0			0
$903$	−19.1362	+	26.7000i	−0.636814	+	0.888519i
$904$		0			0
$905$	−10.3997	−	18.0127i	−0.345696	−	0.598763i
$906$		0			0
$907$	−3.32530	+	5.75958i	−0.110415	+	0.191244i	−0.915938	−	0.401321i	$-0.868551\pi$
$907$	−3.32530	+	5.75958i	−0.110415	+	0.191244i	0.805523	+	0.592565i	$0.201885\pi$
$908$		0			0
$909$	−3.66971			−0.121717
$910$		0			0
$911$	−58.4181			−1.93548			−0.967739	−	0.251955i	$-0.918927\pi$
$911$	−58.4181			−1.93548			−0.967739	+	0.251955i	$0.918927\pi$
$912$		0			0
$913$	−21.4046	+	37.0738i	−0.708388	+	1.22696i
$914$		0			0
$915$	8.63663	+	14.9591i	0.285518	+	0.494532i
$916$		0			0
$917$	0.157711	+	0.348151i	0.00520806	+	0.0114970i
$918$		0			0
$919$	−23.9310	−	41.4497i	−0.789411	−	1.36730i	−0.926328	−	0.376718i	$-0.877053\pi$
$919$	−23.9310	−	41.4497i	−0.789411	−	1.36730i	0.136916	−	0.990583i	$-0.456281\pi$
$920$		0			0
$921$	24.3393	−	42.1568i	0.802006	−	1.38911i
$922$		0			0
$923$	26.0584			0.857723
$924$		0			0
$925$	16.3349			0.537089
$926$		0			0
$927$	−0.373930	+	0.647665i	−0.0122815	+	0.0212721i
$928$		0			0
$929$	21.4553	+	37.1617i	0.703927	+	1.21924i	0.967077	+	0.254482i	$0.0819050\pi$
$929$	21.4553	+	37.1617i	0.703927	+	1.21924i	−0.263151	+	0.964755i	$0.584762\pi$
$930$		0			0
$931$	−6.81756	−	20.0947i	−0.223437	−	0.658578i
$932$		0			0
$933$	21.8480	+	37.8419i	0.715272	+	1.23889i
$934$		0			0
$935$	−4.96867	+	8.60599i	−0.162493	+	0.281446i
$936$		0			0
$937$	8.70212			0.284286			0.142143	−	0.989846i	$-0.454601\pi$
$937$	8.70212			0.284286			0.142143	+	0.989846i	$0.454601\pi$
$938$		0			0
$939$	8.88276			0.289878
$940$		0			0
$941$	−21.9423	+	38.0052i	−0.715299	+	1.23893i	0.247546	+	0.968876i	$0.420376\pi$
$941$	−21.9423	+	38.0052i	−0.715299	+	1.23893i	−0.962844	+	0.270057i	$0.912957\pi$
$942$		0			0
$943$	1.10168	+	1.90817i	0.0358758	+	0.0621387i
$944$		0			0
$945$	−5.39813	−	11.9165i	−0.175601	−	0.387645i
$946$		0			0
$947$	21.4641	+	37.1770i	0.697490	+	1.20809i	0.969334	+	0.245747i	$0.0790334\pi$
$947$	21.4641	+	37.1770i	0.697490	+	1.20809i	−0.271843	+	0.962341i	$0.587633\pi$
$948$		0			0
$949$	−26.9004	+	46.5929i	−0.873224	+	1.51247i
$950$		0			0
$951$	34.0056			1.10271
$952$		0			0
$953$	5.49111			0.177874			0.0889372	−	0.996037i	$-0.471653\pi$
$953$	5.49111			0.177874			0.0889372	+	0.996037i	$0.471653\pi$
$954$		0			0
$955$	5.10937	−	8.84969i	0.165335	−	0.286369i
$956$		0			0
$957$	5.10573	+	8.84338i	0.165045	+	0.285866i
$958$		0			0
$959$	−12.3140	+	17.1812i	−0.397640	+	0.554809i
$960$		0			0
$961$	−6.71934	−	11.6382i	−0.216753	−	0.375427i
$962$		0			0
$963$	−1.92313	+	3.33096i	−0.0619721	+	0.107339i
$964$		0			0
$965$	−10.9211			−0.351563
$966$		0			0
$967$	−7.91850			−0.254642			−0.127321	−	0.991862i	$-0.540638\pi$
$967$	−7.91850			−0.254642			−0.127321	+	0.991862i	$0.540638\pi$
$968$		0			0
$969$	−7.89439	+	13.6735i	−0.253604	+	0.439256i
$970$		0			0
$971$	2.82968	+	4.90115i	0.0908087	+	0.157285i	0.907852	−	0.419291i	$-0.137721\pi$
$971$	2.82968	+	4.90115i	0.0908087	+	0.157285i	−0.817043	+	0.576577i	$0.804388\pi$
$972$		0			0
$973$	−0.333543	−	0.0328787i	−0.0106929	−	0.00105404i
$974$		0			0
$975$	21.4259	+	37.1108i	0.686178	+	1.18850i
$976$		0			0
$977$	−28.2240	+	48.8854i	−0.902966	+	1.56398i	−0.0793416	+	0.996847i	$0.525282\pi$
$977$	−28.2240	+	48.8854i	−0.902966	+	1.56398i	−0.823624	+	0.567136i	$0.808052\pi$
$978$		0			0
$979$	−43.9575			−1.40489
$980$		0			0
$981$	0.196317			0.00626793
$982$		0			0
$983$	13.3329	−	23.0932i	0.425253	−	0.736560i	−0.571191	−	0.820817i	$-0.693518\pi$
$983$	13.3329	−	23.0932i	0.425253	−	0.736560i	0.996444	+	0.0842571i	$0.0268517\pi$
$984$		0			0
$985$	−8.70352	−	15.0749i	−0.277317	−	0.480327i
$986$		0			0
$987$	34.2701	+	3.37815i	1.09083	+	0.107528i
$988$		0			0
$989$	−3.72934	−	6.45941i	−0.118586	−	0.205397i
$990$		0			0
$991$	6.85595	−	11.8749i	0.217786	−	0.377217i	−0.736344	−	0.676607i	$-0.763450\pi$
$991$	6.85595	−	11.8749i	0.217786	−	0.377217i	0.954131	+	0.299390i	$0.0967830\pi$
$992$		0			0
$993$	−19.0782			−0.605430
$994$		0			0
$995$	−8.25076			−0.261567
$996$		0			0
$997$	23.7371	−	41.1139i	0.751762	−	1.30209i	−0.195206	−	0.980762i	$-0.562537\pi$
$997$	23.7371	−	41.1139i	0.751762	−	1.30209i	0.946968	−	0.321328i	$-0.104129\pi$
$998$		0			0
$999$	10.5690	+	18.3060i	0.334387	+	0.579176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1288.2.q.b.921.9	yes	22
7.2	even	3	inner	1288.2.q.b.737.9	✓	22
7.3	odd	6		9016.2.a.bo.1.9		11
7.4	even	3		9016.2.a.bn.1.3		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.q.b.737.9	✓	22	7.2	even	3	inner
1288.2.q.b.921.9	yes	22	1.1	even	1	trivial
9016.2.a.bn.1.3		11	7.4	even	3
9016.2.a.bo.1.9		11	7.3	odd	6

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:	\( N \)	\(=\)	\( 1288 = 2^{3} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1288.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.832313 - 1.44161i) q^{3} +(-0.459953 - 0.796662i) q^{5} +(2.63299 + 0.259545i) q^{7} +(0.114512 + 0.198340i) q^{9} +O(q^{10})\)	\(q+(0.832313 - 1.44161i) q^{3} +(-0.459953 - 0.796662i) q^{5} +(2.63299 + 0.259545i) q^{7} +(0.114512 + 0.198340i) q^{9} +(1.72626 - 2.98997i) q^{11} -6.19741 q^{13} -1.53130 q^{15} +(1.56444 - 2.70970i) q^{17} +(-1.51570 - 2.62526i) q^{19} +(2.56563 - 3.57972i) q^{21} +(0.500000 + 0.866025i) q^{23} +(2.07689 - 3.59727i) q^{25} +5.37511 q^{27} -1.77678 q^{29} +(3.33312 - 5.77313i) q^{31} +(-2.87358 - 4.97719i) q^{33} +(-1.00428 - 2.21698i) q^{35} +(1.96628 + 3.40569i) q^{37} +(-5.15818 + 8.93423i) q^{39} +2.20337 q^{41} -7.45869 q^{43} +(0.105340 - 0.182454i) q^{45} +(3.90949 + 6.77143i) q^{47} +(6.86527 + 1.36676i) q^{49} +(-2.60421 - 4.51063i) q^{51} +(1.26405 - 2.18940i) q^{53} -3.17600 q^{55} -5.04613 q^{57} +(-0.389087 + 0.673918i) q^{59} +(-5.64007 - 9.76888i) q^{61} +(0.250030 + 0.551948i) q^{63} +(2.85052 + 4.93724i) q^{65} +(0.0229932 - 0.0398254i) q^{67} +1.66463 q^{69} -4.20473 q^{71} +(4.34059 - 7.51812i) q^{73} +(-3.45724 - 5.98811i) q^{75} +(5.32127 - 7.42453i) q^{77} +(-1.02566 - 1.77649i) q^{79} +(4.13024 - 7.15378i) q^{81} -12.3994 q^{83} -2.87828 q^{85} +(-1.47884 + 2.56142i) q^{87} +(-6.36600 - 11.0262i) q^{89} +(-16.3177 - 1.60851i) q^{91} +(-5.54839 - 9.61010i) q^{93} +(-1.39430 + 2.41499i) q^{95} +13.0618 q^{97} +0.790708 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} - 9 q^{5} - q^{7} - 11 q^{9}+O(q^{10}) \) 22 * q + 2 * q^3 - 9 * q^5 - q^7 - 11 * q^9	\( 22 q + 2 q^{3} - 9 q^{5} - q^{7} - 11 q^{9} + 30 q^{13} - 4 q^{15} - 5 q^{17} + 3 q^{21} + 11 q^{23} - 22 q^{25} - 10 q^{27} + 10 q^{29} - 6 q^{31} - 14 q^{33} + 25 q^{35} + q^{37} - 11 q^{39} + 40 q^{41} - 14 q^{43} - 41 q^{45} + 3 q^{47} + 9 q^{49} + 13 q^{51} - 19 q^{53} - 6 q^{55} - 10 q^{57} - 7 q^{59} - 39 q^{61} + 81 q^{63} - 5 q^{65} - 7 q^{67} + 4 q^{69} - 38 q^{71} + 5 q^{73} - 16 q^{75} - 17 q^{77} - 11 q^{79} - 43 q^{81} + 66 q^{83} - 26 q^{85} + 30 q^{87} - 34 q^{89} + 8 q^{91} + 12 q^{93} - 37 q^{95} + 34 q^{97} - 98 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 - 9 * q^5 - q^7 - 11 * q^9 + 30 * q^13 - 4 * q^15 - 5 * q^17 + 3 * q^21 + 11 * q^23 - 22 * q^25 - 10 * q^27 + 10 * q^29 - 6 * q^31 - 14 * q^33 + 25 * q^35 + q^37 - 11 * q^39 + 40 * q^41 - 14 * q^43 - 41 * q^45 + 3 * q^47 + 9 * q^49 + 13 * q^51 - 19 * q^53 - 6 * q^55 - 10 * q^57 - 7 * q^59 - 39 * q^61 + 81 * q^63 - 5 * q^65 - 7 * q^67 + 4 * q^69 - 38 * q^71 + 5 * q^73 - 16 * q^75 - 17 * q^77 - 11 * q^79 - 43 * q^81 + 66 * q^83 - 26 * q^85 + 30 * q^87 - 34 * q^89 + 8 * q^91 + 12 * q^93 - 37 * q^95 + 34 * q^97 - 98 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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