LMFDB - Embedded newform 756.2.bj.b.523.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(451,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bj (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			523.23
Character	$\chi$	$=$	756.523
Dual form			756.2.bj.b.451.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.171292 - 1.40380i) q^{2} +(-1.94132 - 0.480920i) q^{4} +(-3.50837 + 2.02556i) q^{5} +(2.35939 - 1.19719i) q^{7} +(-1.00765 + 2.64285i) q^{8} +(2.24253 + 5.27202i) q^{10} +(0.471017 + 0.271942i) q^{11} +(1.01063 + 0.583488i) q^{13} +(-1.27647 - 3.51719i) q^{14} +(3.53743 + 1.86724i) q^{16} +(5.05773 - 2.92008i) q^{17} +(1.16501 - 2.01785i) q^{19} +(7.78500 - 2.24501i) q^{20} +(0.462434 - 0.614633i) q^{22} +(-1.39849 + 0.807417i) q^{23} +(5.70579 - 9.88272i) q^{25} +(0.992214 - 1.31878i) q^{26} +(-5.15609 + 1.18945i) q^{28} +(-2.40001 - 4.15694i) q^{29} +4.49030 q^{31} +(3.22716 - 4.64601i) q^{32} +(-3.23287 - 7.60024i) q^{34} +(-5.85265 + 8.97929i) q^{35} +(-1.48498 + 2.57206i) q^{37} +(-2.63311 - 1.98108i) q^{38} +(-1.81804 - 11.3132i) q^{40} +(3.89836 + 2.25072i) q^{41} +(2.89521 - 1.67155i) q^{43} +(-0.783611 - 0.754447i) q^{44} +(0.893904 + 2.10150i) q^{46} +8.58149 q^{47} +(4.13347 - 5.64928i) q^{49} +(-12.8960 - 9.70263i) q^{50} +(-1.68134 - 1.61877i) q^{52} +(-5.84343 - 10.1211i) q^{53} -2.20334 q^{55} +(0.786554 + 7.44186i) q^{56} +(-6.24662 + 2.65709i) q^{58} +12.8781 q^{59} +2.08317i q^{61} +(0.769151 - 6.30348i) q^{62} +(-5.96929 - 5.32612i) q^{64} -4.72756 q^{65} +7.09620i q^{67} +(-11.2230 + 3.23645i) q^{68} +(11.6026 + 9.75404i) q^{70} +5.17264i q^{71} +(5.58686 - 3.22558i) q^{73} +(3.35629 + 2.52519i) q^{74} +(-3.23207 + 3.35702i) q^{76} +(1.43688 + 0.0777206i) q^{77} +4.02680i q^{79} +(-16.1928 + 0.614320i) q^{80} +(3.82732 - 5.08700i) q^{82} +(2.76985 + 4.79753i) q^{83} +(-11.8296 + 20.4895i) q^{85} +(-1.85060 - 4.35062i) q^{86} +(-1.19332 + 0.970804i) q^{88} +(7.63381 + 4.40738i) q^{89} +(3.08302 + 0.166760i) q^{91} +(3.10321 - 0.894893i) q^{92} +(1.46994 - 12.0467i) q^{94} +9.43917i q^{95} +(-13.8033 + 7.96935i) q^{97} +(-7.22244 - 6.77025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37}+ \cdots - 21 q^{98}+O(q^{100}) $ 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8 - 18 * q^10 + 18 * q^13 - 14 * q^14 + 14 * q^16 - 6 * q^17 + 24 * q^20 + 6 * q^22 + 16 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 + 18 * q^32 - 24 * q^34 + 2 * q^37 - 33 * q^38 + 6 * q^40 - 6 * q^41 + 13 * q^44 + 10 * q^46 - 28 * q^49 + 17 * q^50 - 27 * q^52 + 2 * q^53 - 58 * q^56 - 13 * q^58 - 8 * q^64 + 100 * q^65 + 18 * q^68 - 19 * q^70 + 30 * q^73 + 23 * q^74 + 2 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 + 9 * q^86 + q^88 + 102 * q^89 - 28 * q^92 + 6 * q^97 - 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.171292	−	1.40380i	0.121122	−	0.992638i
$2$	0.171292	−	1.40380i	0.121122	−	0.992638i
$3$		0			0
$3$		0			0
$4$	−1.94132	−	0.480920i	−0.970659	−	0.240460i
$5$	−3.50837	+	2.02556i	−1.56899	+	0.905858i	−0.572706	+	0.819761i	$0.694106\pi$
$5$	−3.50837	+	2.02556i	−1.56899	+	0.905858i	−0.996287	+	0.0860974i	$0.972560\pi$
$6$		0			0
$7$	2.35939	−	1.19719i	0.891767	−	0.452495i
$7$	2.35939	−	1.19719i	0.891767	−	0.452495i
$8$	−1.00765	+	2.64285i	−0.356257	+	0.934388i
$9$		0			0
$10$	2.24253	+	5.27202i	0.709150	+	1.66716i
$11$	0.471017	+	0.271942i	0.142017	+	0.0819935i	0.569325	−	0.822113i	$-0.307205\pi$
$11$	0.471017	+	0.271942i	0.142017	+	0.0819935i	−0.427308	+	0.904106i	$0.640538\pi$
$12$		0			0
$13$	1.01063	+	0.583488i	0.280298	+	0.161830i	0.633558	−	0.773695i	$-0.281594\pi$
$13$	1.01063	+	0.583488i	0.280298	+	0.161830i	−0.353260	+	0.935525i	$0.614927\pi$
$14$	−1.27647	−	3.51719i	−0.341152	−	0.940008i
$15$		0			0
$16$	3.53743	+	1.86724i	0.884358	+	0.466809i
$17$	5.05773	−	2.92008i	1.22668	−	0.708224i	0.260347	−	0.965515i	$-0.416163\pi$
$17$	5.05773	−	2.92008i	1.22668	−	0.708224i	0.966334	+	0.257291i	$0.0828298\pi$
$18$		0			0
$19$	1.16501	−	2.01785i	0.267271	−	0.462927i	−0.700885	−	0.713274i	$-0.747212\pi$
$19$	1.16501	−	2.01785i	0.267271	−	0.462927i	0.968156	+	0.250347i	$0.0805448\pi$
$20$	7.78500	−	2.24501i	1.74078	−	0.502000i
$21$		0			0
$22$	0.462434	−	0.614633i	0.0985912	−	0.131040i
$23$	−1.39849	+	0.807417i	−0.291605	+	0.168358i	−0.638665	−	0.769485i	$-0.720513\pi$
$23$	−1.39849	+	0.807417i	−0.291605	+	0.168358i	0.347061	+	0.937843i	$0.387180\pi$
$24$		0			0
$25$	5.70579	−	9.88272i	1.14116	−	1.97654i
$26$	0.992214	−	1.31878i	0.194589	−	0.258634i
$27$		0			0
$28$	−5.15609	+	1.18945i	−0.974408	+	0.224785i
$29$	−2.40001	−	4.15694i	−0.445670	−	0.771924i	0.552428	−	0.833560i	$-0.313701\pi$
$29$	−2.40001	−	4.15694i	−0.445670	−	0.771924i	−0.998099	+	0.0616368i	$0.980368\pi$
$30$		0			0
$31$	4.49030			0.806481			0.403240	−	0.915094i	$-0.367884\pi$
$31$	4.49030			0.806481			0.403240	+	0.915094i	$0.367884\pi$
$32$	3.22716	−	4.64601i	0.570487	−	0.821306i
$33$		0			0
$34$	−3.23287	−	7.60024i	−0.554433	−	1.30343i
$35$	−5.85265	+	8.97929i	−0.989279	+	1.51778i
$36$		0			0
$37$	−1.48498	+	2.57206i	−0.244129	+	0.422844i	−0.961886	−	0.273450i	$-0.911835\pi$
$37$	−1.48498	+	2.57206i	−0.244129	+	0.422844i	0.717757	+	0.696293i	$0.245169\pi$
$38$	−2.63311	−	1.98108i	−0.427146	−	0.321374i
$39$		0			0
$40$	−1.81804	−	11.3132i	−0.287458	−	1.78877i
$41$	3.89836	+	2.25072i	0.608822	+	0.351504i	0.772504	−	0.635010i	$-0.219004\pi$
$41$	3.89836	+	2.25072i	0.608822	+	0.351504i	−0.163682	+	0.986513i	$0.552337\pi$
$42$		0			0
$43$	2.89521	−	1.67155i	0.441515	−	0.254909i	−0.262725	−	0.964871i	$-0.584621\pi$
$43$	2.89521	−	1.67155i	0.441515	−	0.254909i	0.704240	+	0.709962i	$0.251288\pi$
$44$	−0.783611	−	0.754447i	−0.118134	−	0.113737i
$45$		0			0
$46$	0.893904	+	2.10150i	0.131799	+	0.309850i
$47$	8.58149			1.25174			0.625869	−	0.779928i	$-0.284744\pi$
$47$	8.58149			1.25174			0.625869	+	0.779928i	$0.284744\pi$
$48$		0			0
$49$	4.13347	−	5.64928i	0.590496	−	0.807041i
$50$	−12.8960	−	9.70263i	−1.82377	−	1.37216i
$51$		0			0
$52$	−1.68134	−	1.61877i	−0.233160	−	0.224483i
$53$	−5.84343	−	10.1211i	−0.802658	−	1.39024i	−0.917861	−	0.396902i	$-0.870085\pi$
$53$	−5.84343	−	10.1211i	−0.802658	−	1.39024i	0.115204	−	0.993342i	$-0.463248\pi$
$54$		0			0
$55$	−2.20334			−0.297098
$56$	0.786554	+	7.44186i	0.105108	+	0.994461i
$57$		0			0
$58$	−6.24662	+	2.65709i	−0.820221	+	0.348892i
$59$	12.8781			1.67658			0.838292	−	0.545222i	$-0.183555\pi$
$59$	12.8781			1.67658			0.838292	+	0.545222i	$0.183555\pi$
$60$		0			0
$61$			2.08317i			0.266722i	0.991067	+	0.133361i	$0.0425771\pi$
$61$			2.08317i			0.266722i	−0.991067	+	0.133361i	$0.957423\pi$
$62$	0.769151	−	6.30348i	0.0976823	−	0.800543i
$63$		0			0
$64$	−5.96929	−	5.32612i	−0.746161	−	0.665765i
$65$	−4.72756			−0.586381
$66$		0			0
$67$			7.09620i			0.866939i	0.901168	+	0.433470i	$0.142711\pi$
$67$			7.09620i			0.866939i	−0.901168	+	0.433470i	$0.857289\pi$
$68$	−11.2230	+	3.23645i	−1.36099	+	0.392477i
$69$		0			0
$70$	11.6026	+	9.75404i	1.38678	+	1.16583i
$71$			5.17264i			0.613879i	0.951729	+	0.306940i	$0.0993049\pi$
$71$			5.17264i			0.613879i	−0.951729	+	0.306940i	$0.900695\pi$
$72$		0			0
$73$	5.58686	−	3.22558i	0.653893	−	0.377525i	−0.136053	−	0.990702i	$-0.543442\pi$
$73$	5.58686	−	3.22558i	0.653893	−	0.377525i	0.789946	+	0.613176i	$0.210108\pi$
$74$	3.35629	+	2.52519i	0.390161	+	0.293547i
$75$		0			0
$76$	−3.23207	+	3.35702i	−0.370744	+	0.385076i
$77$	1.43688	+	0.0777206i	0.163748	+	0.00885708i
$78$		0			0
$79$			4.02680i			0.453050i	0.974005	+	0.226525i	$0.0727365\pi$
$79$			4.02680i			0.453050i	−0.974005	+	0.226525i	$0.927264\pi$
$80$	−16.1928	+	0.614320i	−1.81041	+	0.0686830i
$81$		0			0
$82$	3.82732	−	5.08700i	0.422657	−	0.561765i
$83$	2.76985	+	4.79753i	0.304031	+	0.526597i	0.977045	−	0.213033i	$-0.0683340\pi$
$83$	2.76985	+	4.79753i	0.304031	+	0.526597i	−0.673014	+	0.739630i	$0.735001\pi$
$84$		0			0
$85$	−11.8296	+	20.4895i	−1.28310	+	2.22240i
$86$	−1.85060	−	4.35062i	−0.199555	−	0.469140i
$87$		0			0
$88$	−1.19332	+	0.970804i	−0.127208	+	0.103488i
$89$	7.63381	+	4.40738i	0.809183	+	0.467182i	0.846672	−	0.532115i	$-0.178603\pi$
$89$	7.63381	+	4.40738i	0.809183	+	0.467182i	−0.0374893	+	0.999297i	$0.511936\pi$
$90$		0			0
$91$	3.08302	+	0.166760i	0.323188	+	0.0174812i
$92$	3.10321	−	0.894893i	0.323532	−	0.0932991i
$93$		0			0
$94$	1.46994	−	12.0467i	0.151613	−	1.24252i
$95$			9.43917i			0.968438i
$96$		0			0
$97$	−13.8033	+	7.96935i	−1.40151	+	0.809165i	−0.994548	−	0.104278i	$-0.966747\pi$
$97$	−13.8033	+	7.96935i	−1.40151	+	0.809165i	−0.406966	+	0.913443i	$0.633413\pi$
$98$	−7.22244	−	6.77025i	−0.729577	−	0.683899i
$99$		0			0
$100$	−15.8296	+	16.4415i	−1.58296	+	1.64415i
$101$	6.41362	+	3.70290i	0.638179	+	0.368453i	0.783913	−	0.620871i	$-0.213221\pi$
$101$	6.41362	+	3.70290i	0.638179	+	0.368453i	−0.145734	+	0.989324i	$0.546554\pi$
$102$		0			0
$103$	3.23031	+	5.59507i	0.318292	+	0.551298i	0.980132	−	0.198347i	$-0.0635574\pi$
$103$	3.23031	+	5.59507i	0.318292	+	0.551298i	−0.661840	+	0.749645i	$0.730224\pi$
$104$	−2.56043	+	2.08299i	−0.251071	+	0.204254i
$105$		0			0
$106$	−15.2090	+	6.46936i	−1.47723	+	0.628359i
$107$	−9.62572	−	5.55741i	−0.930553	−	0.537255i	−0.0435667	−	0.999051i	$-0.513872\pi$
$107$	−9.62572	−	5.55741i	−0.930553	−	0.537255i	−0.886987	+	0.461795i	$0.847205\pi$
$108$		0			0
$109$	−1.67348	−	2.89856i	−0.160291	−	0.277632i	0.774682	−	0.632351i	$-0.217910\pi$
$109$	−1.67348	−	2.89856i	−0.160291	−	0.277632i	−0.934973	+	0.354719i	$0.884576\pi$
$110$	−0.377414	+	3.09305i	−0.0359850	+	0.294911i
$111$		0			0
$112$	10.5816	+	0.170566i	0.999870	+	0.0161169i
$113$	1.36060	−	2.35662i	0.127994	−	0.221692i	−0.794905	−	0.606734i	$-0.792479\pi$
$113$	1.36060	−	2.35662i	0.127994	−	0.221692i	0.922899	+	0.385041i	$0.125813\pi$
$114$		0			0
$115$	3.27095	−	5.66544i	0.305017	−	0.528305i
$116$	2.66003	+	9.22415i	0.246977	+	0.856441i
$117$		0			0
$118$	2.20591	−	18.0783i	0.203071	−	1.66424i
$119$	8.43729	−	12.9447i	0.773445	−	1.18664i
$120$		0			0
$121$	−5.35210	−	9.27010i	−0.486554	−	0.842736i
$122$	2.92436	+	0.356830i	0.264759	+	0.0323059i
$123$		0			0
$124$	−8.71709	−	2.15947i	−0.782818	−	0.193926i
$125$			25.9741i			2.32320i
$126$		0			0
$127$		−	14.2111i		−	1.26103i	−0.776178	−	0.630513i	$-0.782844\pi$
$127$		−	14.2111i		−	1.26103i	0.776178	−	0.630513i	$-0.217156\pi$
$128$	−8.49931	+	7.46738i	−0.751240	+	0.660029i
$129$		0			0
$130$	−0.809792	+	6.63655i	−0.0710235	+	0.582064i
$131$	−7.95497	−	13.7784i	−0.695029	−	1.20383i	−0.970171	−	0.242422i	$-0.922058\pi$
$131$	−7.95497	−	13.7784i	−0.695029	−	1.20383i	0.275142	−	0.961404i	$-0.411275\pi$
$132$		0			0
$133$	0.332957	−	6.15564i	0.0288711	−	0.533761i
$134$	9.96166	+	1.21552i	0.860556	+	0.105005i
$135$		0			0
$136$	2.62092	+	16.3092i	0.224742	+	1.39851i
$137$	6.27966	−	10.8767i	0.536507	−	0.929258i	−0.462581	−	0.886577i	$-0.653077\pi$
$137$	6.27966	−	10.8767i	0.536507	−	0.929258i	0.999089	−	0.0426811i	$-0.0135899\pi$
$138$		0			0
$139$	−7.10577	+	12.3076i	−0.602704	+	1.04391i	0.389706	+	0.920939i	$0.372577\pi$
$139$	−7.10577	+	12.3076i	−0.602704	+	1.04391i	−0.992410	+	0.122974i	$0.960757\pi$
$140$	15.6802	−	14.6170i	1.32522	−	1.23536i
$141$		0			0
$142$	7.26136	+	0.886031i	0.609359	+	0.0743541i
$143$	0.317349	+	0.549665i	0.0265381	+	0.0459653i
$144$		0			0
$145$	16.8403	+	9.72272i	1.39851	+	0.807428i
$146$	−3.57109	−	8.39536i	−0.295545	−	0.694805i
$147$		0			0
$148$	4.11977	−	4.27903i	0.338643	−	0.351734i
$149$	−2.11648	−	3.66585i	−0.173389	−	0.300318i	0.766214	−	0.642586i	$-0.222138\pi$
$149$	−2.11648	−	3.66585i	−0.173389	−	0.300318i	−0.939603	+	0.342267i	$0.888805\pi$
$150$		0			0
$151$	7.54013	+	4.35330i	0.613607	+	0.354266i	0.774376	−	0.632726i	$-0.218064\pi$
$151$	7.54013	+	4.35330i	0.613607	+	0.354266i	−0.160769	+	0.986992i	$0.551397\pi$
$152$	4.15896	+	5.11222i	0.337336	+	0.414656i
$153$		0			0
$154$	0.355230	−	2.00378i	0.0286253	−	0.161469i
$155$	−15.7536	+	9.09537i	−1.26536	+	0.730557i
$156$		0			0
$157$			7.63781i			0.609563i	0.952422	+	0.304782i	$0.0985835\pi$
$157$			7.63781i			0.609563i	−0.952422	+	0.304782i	$0.901417\pi$
$158$	5.65282	+	0.689758i	0.449714	+	0.0548742i
$159$		0			0
$160$	−1.91132	+	22.8368i	−0.151103	+	1.80540i
$161$	−2.33295	+	3.57927i	−0.183862	+	0.282086i
$162$		0			0
$163$	13.1093	+	7.56865i	1.02680	+	0.592822i	0.916066	−	0.401028i	$-0.131347\pi$
$163$	13.1093	+	7.56865i	1.02680	+	0.592822i	0.110732	+	0.993850i	$0.464680\pi$
$164$	−6.48555	−	6.24416i	−0.506436	−	0.487587i
$165$		0			0
$166$	7.20923	−	3.06655i	0.559545	−	0.238010i
$167$	1.88524	−	3.26533i	0.145884	−	0.252679i	−0.783818	−	0.620990i	$-0.786731\pi$
$167$	1.88524	−	3.26533i	0.145884	−	0.252679i	0.929702	+	0.368311i	$0.120064\pi$
$168$		0			0
$169$	−5.81908	−	10.0790i	−0.447622	−	0.775304i
$170$	26.7369	+	20.1161i	2.05062	+	1.54284i
$171$		0			0
$172$	−6.42440	+	1.85265i	−0.489856	+	0.141263i
$173$			6.26492i			0.476313i	0.971227	+	0.238157i	$0.0765432\pi$
$173$			6.26492i			0.476313i	−0.971227	+	0.238157i	$0.923457\pi$
$174$		0			0
$175$	1.63071	−	30.1481i	0.123270	−	2.27899i
$176$	1.15841	+	1.84147i	0.0873185	+	0.138806i
$177$		0			0
$178$	7.49470	−	9.96141i	0.561752	−	0.746639i
$179$	8.63863	−	4.98752i	0.645682	−	0.372785i	−0.141118	−	0.989993i	$-0.545070\pi$
$179$	8.63863	−	4.98752i	0.645682	−	0.372785i	0.786800	+	0.617208i	$0.211736\pi$
$180$		0			0
$181$		−	5.34622i		−	0.397382i	−0.980062	−	0.198691i	$-0.936331\pi$
$181$		−	5.34622i		−	0.397382i	0.980062	−	0.198691i	$-0.0636690\pi$
$182$	0.762194	−	4.29938i	0.0564976	−	0.318691i
$183$		0			0
$184$	−0.724698	−	4.50958i	−0.0534254	−	0.332451i
$185$		−	12.0317i		−	0.884585i
$186$		0			0
$187$	3.17637			0.232279
$188$	−16.6594	−	4.12701i	−1.21501	−	0.300993i
$189$		0			0
$190$	13.2507	+	1.61685i	0.961308	+	0.117299i
$191$			22.0104i			1.59261i	0.604893	+	0.796307i	$0.293216\pi$
$191$			22.0104i			1.59261i	−0.604893	+	0.796307i	$0.706784\pi$
$192$		0			0
$193$	−5.83438			−0.419968			−0.209984	−	0.977705i	$-0.567341\pi$
$193$	−5.83438			−0.419968			−0.209984	+	0.977705i	$0.567341\pi$
$194$	8.82299	+	20.7422i	0.633454	+	1.48920i
$195$		0			0
$196$	−10.7412	+	8.97919i	−0.767231	+	0.641371i
$197$	−14.2652			−1.01636			−0.508178	−	0.861252i	$-0.669681\pi$
$197$	−14.2652			−1.01636			−0.508178	+	0.861252i	$0.669681\pi$
$198$		0			0
$199$	−2.14848	−	3.72128i	−0.152302	−	0.263794i	0.779771	−	0.626064i	$-0.215335\pi$
$199$	−2.14848	−	3.72128i	−0.152302	−	0.263794i	−0.932073	+	0.362270i	$0.882002\pi$
$200$	20.3691	+	25.0379i	1.44031	+	1.77044i
$201$		0			0
$202$	6.29674	−	8.36917i	0.443037	−	0.588853i
$203$	−10.6392	−	6.93458i	−0.746726	−	0.486712i
$204$		0			0
$205$	−18.2359			−1.27365
$206$	8.40769	−	3.57633i	0.585791	−	0.249175i
$207$		0			0
$208$	2.48553	+	3.95113i	0.172340	+	0.273962i
$209$	1.09748	−	0.633628i	0.0759139	−	0.0438289i
$210$		0			0
$211$	0.0869189	+	0.0501826i	0.00598374	+	0.00345472i	0.502989	−	0.864293i	$-0.332234\pi$
$211$	0.0869189	+	0.0501826i	0.00598374	+	0.00345472i	−0.497005	+	0.867748i	$0.665567\pi$
$212$	6.47652	+	22.4585i	0.444809	+	1.54246i
$213$		0			0
$214$	−9.45031	+	12.5607i	−0.646010	+	0.858629i
$215$	−6.77165	+	11.7288i	−0.461823	+	0.799901i
$216$		0			0
$217$	10.5944	−	5.37574i	0.719193	−	0.364929i
$218$	−4.35566	+	1.85274i	−0.295002	+	0.125483i
$219$		0			0
$220$	4.27738	+	1.05963i	0.288381	+	0.0714401i
$221$	6.81533			0.458449
$222$		0			0
$223$	−6.41092	−	11.1040i	−0.429307	−	0.743582i	0.567505	−	0.823370i	$-0.307909\pi$
$223$	−6.41092	−	11.1040i	−0.429307	−	0.743582i	−0.996812	+	0.0797885i	$0.974575\pi$
$224$	2.05199	−	14.8253i	0.137104	−	0.990557i
$225$		0			0
$226$	−3.07517	−	2.31368i	−0.204557	−	0.153904i
$227$	9.39256	−	16.2684i	0.623406	−	1.07977i	−0.365440	−	0.930835i	$-0.619082\pi$
$227$	9.39256	−	16.2684i	0.623406	−	1.07977i	0.988847	−	0.148937i	$-0.0475850\pi$
$228$		0			0
$229$	−15.6660	+	9.04474i	−1.03524	+	0.597693i	−0.918480	−	0.395467i	$-0.870583\pi$
$229$	−15.6660	+	9.04474i	−1.03524	+	0.597693i	−0.116755	+	0.993161i	$0.537249\pi$
$230$	−7.39287	−	5.56220i	−0.487472	−	0.366761i
$231$		0			0
$232$	13.4045	−	2.15413i	0.880049	−	0.141425i
$233$	5.88363	−	10.1908i	0.385450	−	0.667618i	−0.606382	−	0.795174i	$-0.707380\pi$
$233$	5.88363	−	10.1908i	0.385450	−	0.667618i	0.991831	+	0.127555i	$0.0407130\pi$
$234$		0			0
$235$	−30.1071	+	17.3823i	−1.96397	+	1.13390i
$236$	−25.0005	−	6.19332i	−1.62739	−	0.403151i
$237$		0			0
$238$	−16.7265	−	14.0616i	−1.08422	−	0.911478i
$239$	1.69786	+	0.980260i	0.109825	+	0.0634077i	0.553907	−	0.832579i	$-0.313136\pi$
$239$	1.69786	+	0.980260i	0.109825	+	0.0634077i	−0.444081	+	0.895987i	$0.646470\pi$
$240$		0			0
$241$	−5.93725	−	3.42787i	−0.382452	−	0.220809i	0.296433	−	0.955054i	$-0.404203\pi$
$241$	−5.93725	−	3.42787i	−0.382452	−	0.220809i	−0.678885	+	0.734245i	$0.737536\pi$
$242$	−13.9302	+	5.92539i	−0.895464	+	0.380898i
$243$		0			0
$244$	1.00184	−	4.04409i	0.0641361	−	0.258897i
$245$	−3.05879	+	28.1924i	−0.195419	+	1.80115i
$246$		0			0
$247$	2.35478	−	1.35953i	0.149831	−	0.0865051i
$248$	−4.52464	+	11.8672i	−0.287315	+	0.753566i
$249$		0			0
$250$	36.4625	+	4.44916i	2.30609	+	0.281389i
$251$	17.0335			1.07515			0.537574	−	0.843217i	$-0.319341\pi$
$251$	17.0335			1.07515			0.537574	+	0.843217i	$0.319341\pi$
$252$		0			0
$253$	−0.878282			−0.0552171
$254$	−19.9495	−	2.43424i	−1.25174	−	0.152738i
$255$		0			0
$256$	9.02686	+	13.2104i	0.564178	+	0.825653i
$257$	−17.9980	+	10.3911i	−1.12268	+	0.648182i	−0.942085	−	0.335375i	$-0.891137\pi$
$257$	−17.9980	+	10.3911i	−1.12268	+	0.648182i	−0.180599	+	0.983557i	$0.557804\pi$
$258$		0			0
$259$	−0.424405	+	7.84630i	−0.0263712	+	0.487545i
$260$	9.17769	+	2.27358i	0.569176	+	0.141001i
$261$		0			0
$262$	−20.7048	+	8.80707i	−1.27915	+	0.544102i
$263$	8.50377	+	4.90965i	0.524365	+	0.302742i	0.738719	−	0.674014i	$-0.235431\pi$
$263$	8.50377	+	4.90965i	0.524365	+	0.302742i	−0.214354	+	0.976756i	$0.568765\pi$
$264$		0			0
$265$	41.0019	+	23.6725i	2.51873	+	1.45419i
$266$	−8.58426	−	1.52182i	−0.526335	−	0.0933086i
$267$		0			0
$268$	3.41270	−	13.7760i	0.208464	−	0.841502i
$269$	−4.88843	+	2.82234i	−0.298053	+	0.172081i	−0.641568	−	0.767066i	$-0.721716\pi$
$269$	−4.88843	+	2.82234i	−0.298053	+	0.172081i	0.343515	+	0.939147i	$0.388382\pi$
$270$		0			0
$271$	−11.3288	+	19.6221i	−0.688177	+	1.19196i	0.284251	+	0.958750i	$0.408255\pi$
$271$	−11.3288	+	19.6221i	−0.688177	+	1.19196i	−0.972427	+	0.233207i	$0.925078\pi$
$272$	23.3439	−	0.885614i	1.41543	−	0.0536982i
$273$		0			0
$274$	−14.1931	−	10.6785i	−0.857434	−	0.645111i
$275$	5.37505	−	3.10329i	0.324128	−	0.187135i
$276$		0			0
$277$	−5.76634	+	9.98759i	−0.346466	+	0.600096i	−0.985619	−	0.168983i	$-0.945952\pi$
$277$	−5.76634	+	9.98759i	−0.346466	+	0.600096i	0.639153	+	0.769079i	$0.279285\pi$
$278$	16.0602	+	12.0833i	0.963227	+	0.724707i
$279$		0			0
$280$	−17.8335	−	24.5156i	−1.06575	−	1.46509i
$281$	−0.625840	−	1.08399i	−0.0373345	−	0.0646652i	0.846754	−	0.531984i	$-0.178553\pi$
$281$	−0.625840	−	1.08399i	−0.0373345	−	0.0646652i	−0.884089	+	0.467319i	$0.845220\pi$
$282$		0			0
$283$	0.951483			0.0565598			0.0282799	−	0.999600i	$-0.490997\pi$
$283$	0.951483			0.0565598			0.0282799	+	0.999600i	$0.490997\pi$
$284$	2.48762	−	10.0417i	0.147613	−	0.595867i
$285$		0			0
$286$	0.825980	−	0.351342i	0.0488412	−	0.0207753i
$287$	11.8923	+	0.643253i	0.701981	+	0.0379700i
$288$		0			0
$289$	8.55378	−	14.8156i	0.503164	−	0.871505i
$290$	16.5334	−	21.9750i	0.970873	−	1.29041i
$291$		0			0
$292$	−12.3971	+	3.57504i	−0.725487	+	0.209213i
$293$	−14.3254	−	8.27078i	−0.836900	−	0.483184i	0.0193095	−	0.999814i	$-0.493853\pi$
$293$	−14.3254	−	8.27078i	−0.836900	−	0.483184i	−0.856209	+	0.516629i	$0.827187\pi$
$294$		0			0
$295$	−45.1811	+	26.0853i	−2.63055	+	1.51875i
$296$	−5.30122	−	6.51630i	−0.308127	−	0.378752i
$297$		0			0
$298$	−5.50867	+	2.34319i	−0.319109	+	0.135737i
$299$	−1.88447			−0.108982
$300$		0			0
$301$	4.82977	−	7.40996i	0.278384	−	0.427103i
$302$	7.40273	−	9.83916i	0.425979	−	0.566180i
$303$		0			0
$304$	7.88894	−	4.96267i	0.452462	−	0.284628i
$305$	−4.21959	−	7.30854i	−0.241613	−	0.418486i
$306$		0			0
$307$	27.1061			1.54702			0.773512	−	0.633781i	$-0.218498\pi$
$307$	27.1061			1.54702			0.773512	+	0.633781i	$0.218498\pi$
$308$	−2.75206	−	0.841904i	−0.156813	−	0.0479719i
$309$		0			0
$310$	10.0696	+	23.6729i	0.571916	+	1.34453i
$311$	−12.4603			−0.706561			−0.353281	−	0.935517i	$-0.614934\pi$
$311$	−12.4603			−0.706561			−0.353281	+	0.935517i	$0.614934\pi$
$312$		0			0
$313$		−	19.0083i		−	1.07441i	−0.843451	−	0.537206i	$-0.819480\pi$
$313$		−	19.0083i		−	1.07441i	0.843451	−	0.537206i	$-0.180520\pi$
$314$	10.7220	+	1.30829i	0.605075	+	0.0738313i
$315$		0			0
$316$	1.93657	−	7.81729i	0.108940	−	0.439757i
$317$	20.5387			1.15357			0.576784	−	0.816897i	$-0.304308\pi$
$317$	20.5387			1.15357			0.576784	+	0.816897i	$0.304308\pi$
$318$		0			0
$319$		−	2.61065i		−	0.146168i
$320$	31.7309	+	6.59487i	1.77381	+	0.368664i
$321$		0			0
$322$	4.62497	+	3.88810i	0.257740	+	0.216675i
$323$		−	13.6077i		−	0.757151i
$324$		0			0
$325$	11.5329	−	6.65852i	0.639730	−	0.369348i
$326$	12.8704	−	17.1064i	0.712825	−	0.947435i
$327$		0			0
$328$	−9.87649	+	8.03485i	−0.545338	+	0.443650i
$329$	20.2471	−	10.2737i	1.11626	−	0.566406i
$330$		0			0
$331$		−	11.4735i		−	0.630638i	−0.948986	−	0.315319i	$-0.897888\pi$
$331$		−	11.4735i		−	0.630638i	0.948986	−	0.315319i	$-0.102112\pi$
$332$	−3.06994	−	10.6456i	−0.168485	−	0.584254i
$333$		0			0
$334$	−4.26095	−	3.20583i	−0.233149	−	0.175415i
$335$	−14.3738	−	24.8961i	−0.785324	−	1.36022i
$336$		0			0
$337$	−4.74216	+	8.21367i	−0.258322	+	0.447427i	−0.965793	−	0.259316i	$-0.916503\pi$
$337$	−4.74216	+	8.21367i	−0.258322	+	0.447427i	0.707470	+	0.706743i	$0.249836\pi$
$338$	−15.1456	+	6.44240i	−0.823813	+	0.350420i
$339$		0			0
$340$	32.8189	−	34.0875i	1.77985	−	1.84866i
$341$	2.11500	+	1.22110i	0.114534	+	0.0661262i
$342$		0			0
$343$	2.98921	−	18.2774i	0.161402	−	0.986889i
$344$	1.50030	+	9.33593i	0.0808908	+	0.503360i
$345$		0			0
$346$	8.79471	+	1.07313i	0.472807	+	0.0576919i
$347$			2.29103i			0.122989i	0.998107	+	0.0614943i	$0.0195866\pi$
$347$			2.29103i			0.122989i	−0.998107	+	0.0614943i	$0.980413\pi$
$348$		0			0
$349$	28.3807	−	16.3856i	1.51918	−	0.877100i	0.519437	−	0.854509i	$-0.326142\pi$
$349$	28.3807	−	16.3856i	1.51918	−	0.877100i	0.999745	−	0.0225916i	$-0.00719173\pi$
$350$	−42.0427	−	7.45333i	−2.24728	−	0.398397i
$351$		0			0
$352$	2.78349	−	1.31075i	0.148361	−	0.0698631i
$353$	−18.2716	−	10.5491i	−0.972501	−	0.561474i	−0.0725034	−	0.997368i	$-0.523099\pi$
$353$	−18.2716	−	10.5491i	−0.972501	−	0.561474i	−0.899998	+	0.435894i	$0.856432\pi$
$354$		0			0
$355$	−10.4775	−	18.1475i	−0.556087	−	0.963172i
$356$	−12.7001	−	12.2274i	−0.673102	−	0.648050i
$357$		0			0
$358$	−5.52176	−	12.9812i	−0.291834	−	0.686080i
$359$	−25.9102	−	14.9593i	−1.36749	−	0.789519i	−0.376881	−	0.926262i	$-0.623003\pi$
$359$	−25.9102	−	14.9593i	−1.36749	−	0.789519i	−0.990607	+	0.136742i	$0.956337\pi$
$360$		0			0
$361$	6.78552	+	11.7529i	0.357133	+	0.618572i
$362$	−7.50504	−	0.915765i	−0.394456	−	0.0481315i
$363$		0			0
$364$	−5.90492	−	1.80642i	−0.309502	−	0.0946821i
$365$	−13.0672	+	22.6331i	−0.683969	+	1.18467i
$366$		0			0
$367$	−10.0638	+	17.4310i	−0.525325	+	0.909890i	0.474239	+	0.880396i	$0.342723\pi$
$367$	−10.0638	+	17.4310i	−0.525325	+	0.909890i	−0.999565	+	0.0294945i	$0.990610\pi$
$368$	−6.45470	+	0.244877i	−0.336474	+	0.0127651i
$369$		0			0
$370$	−16.8901	−	2.06093i	−0.878072	−	0.107142i
$371$	−25.9039	−	16.8840i	−1.34486	−	0.876574i
$372$		0			0
$373$	5.47058	+	9.47532i	0.283256	+	0.490613i	0.972185	−	0.234216i	$-0.0752522\pi$
$373$	5.47058	+	9.47532i	0.283256	+	0.490613i	−0.688929	+	0.724829i	$0.741919\pi$
$374$	0.544087	−	4.45899i	0.0281340	−	0.230569i
$375$		0			0
$376$	−8.64712	+	22.6796i	−0.445941	+	1.16961i
$377$		−	5.60150i		−	0.288492i
$378$		0			0
$379$		−	15.9358i		−	0.818566i	−0.912407	−	0.409283i	$-0.865779\pi$
$379$		−	15.9358i		−	0.818566i	0.912407	−	0.409283i	$-0.134221\pi$
$380$	4.53948	−	18.3244i	0.232870	−	0.940023i
$381$		0			0
$382$	30.8982	+	3.77020i	1.58089	+	0.192900i
$383$	−11.7448	−	20.3425i	−0.600130	−	1.03946i	−0.992801	−	0.119777i	$-0.961782\pi$
$383$	−11.7448	−	20.3425i	−0.600130	−	1.03946i	0.392671	−	0.919679i	$-0.371551\pi$
$384$		0			0
$385$	−5.19854	+	2.63781i	−0.264942	+	0.134435i
$386$	−0.999382	+	8.19031i	−0.0508672	+	0.416876i
$387$		0			0
$388$	30.6292	−	8.83275i	1.55496	−	0.448415i
$389$	−4.06677	+	7.04385i	−0.206193	+	0.357138i	−0.950512	−	0.310687i	$-0.899441\pi$
$389$	−4.06677	+	7.04385i	−0.206193	+	0.357138i	0.744319	+	0.667824i	$0.232774\pi$
$390$		0			0
$391$	−4.71545	+	8.16740i	−0.238471	+	0.413043i
$392$	10.7651	+	16.6166i	0.543720	+	0.839266i
$393$		0			0
$394$	−2.44352	+	20.0256i	−0.123103	+	1.00887i
$395$	−8.15652	−	14.1275i	−0.410399	−	0.710832i
$396$		0			0
$397$	−23.7199	−	13.6947i	−1.19047	−	0.687318i	−0.232057	−	0.972702i	$-0.574545\pi$
$397$	−23.7199	−	13.6947i	−1.19047	−	0.687318i	−0.958413	+	0.285384i	$0.907879\pi$
$398$	−5.59195	+	2.37862i	−0.280299	+	0.119229i
$399$		0			0
$400$	38.6372	−	24.3054i	1.93186	−	1.21527i
$401$	9.42465	+	16.3240i	0.470644	+	0.815180i	0.999436	−	0.0335714i	$-0.0106881\pi$
$401$	9.42465	+	16.3240i	0.470644	+	0.815180i	−0.528792	+	0.848752i	$0.677355\pi$
$402$		0			0
$403$	4.53803	+	2.62003i	0.226055	+	0.130513i
$404$	−10.6701	−	10.2730i	−0.530856	−	0.511098i
$405$		0			0
$406$	−11.5572	+	13.7475i	−0.573573	+	0.682277i
$407$	−1.39890	+	0.807655i	−0.0693409	+	0.0400340i
$408$		0			0
$409$		−	19.0825i		−	0.943567i	−0.881714	−	0.471784i	$-0.843610\pi$
$409$		−	19.0825i		−	0.943567i	0.881714	−	0.471784i	$-0.156390\pi$
$410$	−3.12366	+	25.5996i	−0.154267	+	1.26427i
$411$		0			0
$412$	−3.58029	−	12.4153i	−0.176388	−	0.611659i
$413$	30.3845	−	15.4175i	1.49512	−	0.758646i
$414$		0			0
$415$	−19.4354	−	11.2210i	−0.954045	−	0.550818i
$416$	5.97236	−	2.81239i	0.292819	−	0.137889i
$417$		0			0
$418$	−0.701499	−	1.64917i	−0.0343114	−	0.0806637i
$419$	−12.7212	+	22.0338i	−0.621473	+	1.07642i	0.367739	+	0.929929i	$0.380132\pi$
$419$	−12.7212	+	22.0338i	−0.621473	+	1.07642i	−0.989212	+	0.146493i	$0.953201\pi$
$420$		0			0
$421$	10.2492	+	17.7521i	0.499514	+	0.865183i	1.00000		0.000561434i	$-0.000178710\pi$
$421$	10.2492	+	17.7521i	0.499514	+	0.865183i	−0.500486	+	0.865745i	$0.666845\pi$
$422$	0.0853350	−	0.113421i	0.00415404	−	0.00552125i
$423$		0			0
$424$	32.6367	−	5.24478i	1.58498	−	0.254709i
$425$		−	66.6456i		−	3.23279i
$426$		0			0
$427$	2.49395	+	4.91501i	0.120691	+	0.237854i
$428$	16.0139	+	15.4179i	0.774062	+	0.745252i
$429$		0			0
$430$	15.3050	+	11.5151i	0.738075	+	0.555308i
$431$	15.2031	−	8.77752i	0.732308	−	0.422798i	−0.0869578	−	0.996212i	$-0.527715\pi$
$431$	15.2031	−	8.77752i	0.732308	−	0.422798i	0.819266	+	0.573414i	$0.194381\pi$
$432$		0			0
$433$			15.2009i			0.730507i	0.930908	+	0.365254i	$0.119018\pi$
$433$			15.2009i			0.730507i	−0.930908	+	0.365254i	$0.880982\pi$
$434$	−5.73174	−	15.7932i	−0.275132	−	0.758099i
$435$		0			0
$436$	1.85479	+	6.43184i	0.0888283	+	0.308029i
$437$			3.76259i			0.179989i
$438$		0			0
$439$	−14.5691			−0.695345			−0.347673	−	0.937616i	$-0.613028\pi$
$439$	−14.5691			−0.695345			−0.347673	+	0.937616i	$0.613028\pi$
$440$	2.22019	−	5.82309i	0.105843	−	0.277605i
$441$		0			0
$442$	1.16741	−	9.56737i	0.0555281	−	0.455074i
$443$			24.0275i			1.14158i	0.821095	+	0.570791i	$0.193363\pi$
$443$			24.0275i			1.14158i	−0.821095	+	0.570791i	$0.806637\pi$
$444$		0			0
$445$	−35.7097			−1.69280
$446$	−16.6860	+	7.09763i	−0.790105	+	0.336082i
$447$		0			0
$448$	−20.4603	−	5.42004i	−0.966658	−	0.256073i
$449$	−36.1930			−1.70806			−0.854028	−	0.520228i	$-0.825847\pi$
$449$	−36.1930			−1.70806			−0.854028	+	0.520228i	$0.825847\pi$
$450$		0			0
$451$	1.22413	+	2.12025i	0.0576420	+	0.0998389i
$452$	−3.77470	+	3.92061i	−0.177547	+	0.184410i
$453$		0			0
$454$	−21.2287	−	15.9719i	−0.996314	−	0.749600i
$455$	−11.1542	+	5.65979i	−0.522915	+	0.265335i
$456$		0			0
$457$	20.5719			0.962312			0.481156	−	0.876635i	$-0.340217\pi$
$457$	20.5719			0.962312			0.481156	+	0.876635i	$0.340217\pi$
$458$	10.0136	+	23.5412i	0.467903	+	1.10001i
$459$		0			0
$460$	−9.07457	+	9.42537i	−0.423104	+	0.439460i
$461$	−20.0785	+	11.5923i	−0.935149	+	0.539908i	−0.888436	−	0.459000i	$-0.848208\pi$
$461$	−20.0785	+	11.5923i	−0.935149	+	0.539908i	−0.0467125	+	0.998908i	$0.514874\pi$
$462$		0			0
$463$	11.0442	+	6.37637i	0.513268	+	0.296335i	0.734176	−	0.678959i	$-0.237569\pi$
$463$	11.0442	+	6.37637i	0.513268	+	0.296335i	−0.220908	+	0.975295i	$0.570902\pi$
$464$	−0.727883	−	19.1863i	−0.0337911	−	0.890700i
$465$		0			0
$466$	−13.2980	−	10.0050i	−0.616017	−	0.463475i
$467$	10.3847	−	17.9868i	0.480545	−	0.832329i	−0.519206	−	0.854649i	$-0.673772\pi$
$467$	10.3847	−	17.9868i	0.480545	−	0.832329i	0.999751	+	0.0223206i	$0.00710547\pi$
$468$		0			0
$469$	8.49550	+	16.7427i	0.392286	+	0.773108i
$470$	19.2442	+	45.2418i	0.887671	+	2.08685i
$471$		0			0
$472$	−12.9766	+	34.0348i	−0.597295	+	1.56658i
$473$	1.81826			0.0836035
$474$		0			0
$475$	−13.2946	−	23.0269i	−0.609997	−	1.05655i
$476$	−22.6048	+	21.0721i	−1.03609	+	0.965839i
$477$		0			0
$478$	1.66692	−	2.21555i	0.0762431	−	0.101337i
$479$	−9.11736	+	15.7917i	−0.416583	+	0.721543i	−0.995593	−	0.0937776i	$-0.970106\pi$
$479$	−9.11736	+	15.7917i	−0.416583	+	0.721543i	0.579010	+	0.815320i	$0.303439\pi$
$480$		0			0
$481$	−3.00153	+	1.73293i	−0.136858	+	0.0790149i
$482$	−5.82906	+	7.74756i	−0.265506	+	0.352892i
$483$		0			0
$484$	5.93195	+	20.5701i	0.269634	+	0.935007i
$485$	32.2848	−	55.9189i	1.46598	−	2.53915i
$486$		0			0
$487$	8.32199	−	4.80470i	0.377105	−	0.217722i	−0.299453	−	0.954111i	$-0.596804\pi$
$487$	8.32199	−	4.80470i	0.377105	−	0.217722i	0.676558	+	0.736389i	$0.263471\pi$
$488$	−5.50550	−	2.09910i	−0.249222	−	0.0950219i
$489$		0			0
$490$	39.0526	+	9.12307i	1.76422	+	0.412138i
$491$	−1.55447	−	0.897475i	−0.0701524	−	0.0405025i	0.464514	−	0.885566i	$-0.346229\pi$
$491$	−1.55447	−	0.897475i	−0.0701524	−	0.0405025i	−0.534666	+	0.845064i	$0.679563\pi$
$492$		0			0
$493$	−24.2772	−	14.0165i	−1.09339	−	0.631269i
$494$	−1.50516	−	3.53852i	−0.0677204	−	0.159206i
$495$		0			0
$496$	15.8841	+	8.38444i	0.713218	+	0.376473i
$497$	6.19263	+	12.2043i	0.277777	+	0.547437i
$498$		0			0
$499$	−38.0844	+	21.9881i	−1.70489	+	0.984321i	−0.764254	+	0.644915i	$0.776893\pi$
$499$	−38.0844	+	21.9881i	−1.70489	+	0.984321i	−0.940640	+	0.339406i	$0.889774\pi$
$500$	12.4915	−	50.4240i	0.558635	−	2.25503i
$501$		0			0
$502$	2.91771	−	23.9117i	0.130224	−	1.06723i
$503$	18.3538			0.818355			0.409178	−	0.912455i	$-0.365816\pi$
$503$	18.3538			0.818355			0.409178	+	0.912455i	$0.365816\pi$
$504$		0			0
$505$	−30.0018			−1.33506
$506$	−0.150443	+	1.23293i	−0.00668799	+	0.0548106i
$507$		0			0
$508$	−6.83438	+	27.5882i	−0.303226	+	1.22403i
$509$	13.1711	−	7.60431i	0.583797	−	0.337055i	−0.178844	−	0.983877i	$-0.557236\pi$
$509$	13.1711	−	7.60431i	0.583797	−	0.337055i	0.762641	+	0.646822i	$0.223902\pi$
$510$		0			0
$511$	9.31998	−	14.2989i	0.412291	−	0.632548i
$512$	20.0911	−	10.4091i	0.887908	−	0.460020i
$513$		0			0
$514$	11.5042	+	27.0455i	0.507428	+	1.19293i
$515$	−22.6663	−	13.0864i	−0.998796	−	0.576655i
$516$		0			0
$517$	4.04203	+	2.33366i	0.177768	+	0.102634i
$518$	10.9419	+	1.93979i	0.480762	+	0.0852294i
$519$		0			0
$520$	4.76371	−	12.4942i	0.208903	−	0.547908i
$521$	−14.2730	+	8.24049i	−0.625309	+	0.361023i	−0.778933	−	0.627107i	$-0.784239\pi$
$521$	−14.2730	+	8.24049i	−0.625309	+	0.361023i	0.153624	+	0.988129i	$0.450906\pi$
$522$		0			0
$523$	7.92785	−	13.7314i	0.346661	−	0.600434i	−0.638993	−	0.769212i	$-0.720649\pi$
$523$	7.92785	−	13.7314i	0.346661	−	0.600434i	0.985654	+	0.168778i	$0.0539822\pi$
$524$	8.81681	+	30.5740i	0.385164	+	1.33563i
$525$		0			0
$526$	8.34880	−	11.0966i	0.364025	−	0.483836i
$527$	22.7107	−	13.1120i	0.989295	−	0.571169i
$528$		0			0
$529$	−10.1962	+	17.6603i	−0.443311	+	0.767837i
$530$	40.2547	−	53.5036i	1.74855	−	2.32405i
$531$		0			0
$532$	−3.60674	+	11.7899i	−0.156372	+	0.511158i
$533$	2.62653	+	4.54929i	0.113768	+	0.197052i
$534$		0			0
$535$	45.0275			1.94671
$536$	−18.7542	−	7.15048i	−0.810057	−	0.308853i
$537$		0			0
$538$	3.12465	+	7.34584i	0.134713	+	0.316701i
$539$	3.48321	−	1.53684i	0.150032	−	0.0661966i
$540$		0			0
$541$	16.3113	−	28.2520i	0.701278	−	1.21465i	−0.266740	−	0.963768i	$-0.585947\pi$
$541$	16.3113	−	28.2520i	0.701278	−	1.21465i	0.968018	−	0.250880i	$-0.0807201\pi$
$542$	25.6050	+	19.2645i	1.09983	+	0.827482i
$543$		0			0
$544$	2.75539	−	32.9219i	0.118136	−	1.41151i
$545$	11.7424	+	6.77949i	0.502990	+	0.290401i
$546$		0			0
$547$	30.4408	−	17.5750i	1.30155	−	0.751453i	0.320884	−	0.947119i	$-0.396020\pi$
$547$	30.4408	−	17.5750i	1.30155	−	0.751453i	0.980671	+	0.195666i	$0.0626867\pi$
$548$	−17.4216	+	18.0951i	−0.744215	+	0.772984i
$549$		0			0
$550$	−3.43570	−	8.07707i	−0.146499	−	0.344407i
$551$	−11.1841			−0.476459
$552$		0			0
$553$	4.82084	+	9.50079i	0.205003	+	0.404015i
$554$	13.0329	+	9.80559i	0.553713	+	0.416599i
$555$		0			0
$556$	19.7135	−	20.4756i	0.836039	−	0.868358i
$557$	21.0919	+	36.5322i	0.893692	+	1.54792i	0.835415	+	0.549620i	$0.185227\pi$
$557$	21.0919	+	36.5322i	0.893692	+	1.54792i	0.0582771	+	0.998300i	$0.481439\pi$
$558$		0			0
$559$	3.90131			0.165008
$560$	−37.4698	+	20.8353i	−1.58339	+	0.880453i
$561$		0			0
$562$	−1.62890	+	0.692877i	−0.0687111	+	0.0292272i
$563$	32.4344			1.36695			0.683473	−	0.729976i	$-0.260469\pi$
$563$	32.4344			1.36695			0.683473	+	0.729976i	$0.260469\pi$
$564$		0			0
$565$			11.0239i			0.463778i
$566$	0.162981	−	1.33569i	0.00685062	−	0.0561434i
$567$		0			0
$568$	−13.6705	−	5.21220i	−0.573601	−	0.218699i
$569$	−19.4904			−0.817080			−0.408540	−	0.912740i	$-0.633962\pi$
$569$	−19.4904			−0.817080			−0.408540	+	0.912740i	$0.633962\pi$
$570$		0			0
$571$		−	30.1571i		−	1.26203i	−0.775769	−	0.631017i	$-0.782638\pi$
$571$		−	30.1571i		−	1.26203i	0.775769	−	0.631017i	$-0.217362\pi$
$572$	−0.351731	−	1.21969i	−0.0147066	−	0.0509980i
$573$		0			0
$574$	2.94006	−	16.5843i	0.122716	−	0.692214i
$575$			18.4278i			0.768493i
$576$		0			0
$577$	−14.9496	+	8.63117i	−0.622361	+	0.359320i	−0.777788	−	0.628527i	$-0.783658\pi$
$577$	−14.9496	+	8.63117i	−0.622361	+	0.359320i	0.155426	+	0.987847i	$0.450325\pi$
$578$	−19.3330	−	14.5456i	−0.804145	−	0.605017i
$579$		0			0
$580$	−28.0164	−	26.9737i	−1.16332	−	1.12002i
$581$	12.2787	+	8.00321i	0.509407	+	0.332029i
$582$		0			0
$583$		−	6.35629i		−	0.263251i
$584$	2.89512	+	18.0155i	0.119801	+	0.745486i
$585$		0			0
$586$	−14.0644	+	18.6933i	−0.580994	+	0.772214i
$587$	17.3621	+	30.0720i	0.716611	+	1.24121i	0.962335	+	0.271866i	$0.0876409\pi$
$587$	17.3621	+	30.0720i	0.716611	+	1.24121i	−0.245724	+	0.969340i	$0.579026\pi$
$588$		0			0
$589$	5.23122	−	9.06074i	0.215549	−	0.373341i
$590$	28.8795	+	67.8935i	1.18895	+	2.79513i
$591$		0			0
$592$	−10.0557	+	6.32568i	−0.413285	+	0.259984i
$593$	−15.7360	−	9.08520i	−0.646201	−	0.373085i	0.140798	−	0.990038i	$-0.455033\pi$
$593$	−15.7360	−	9.08520i	−0.646201	−	0.373085i	−0.786999	+	0.616954i	$0.788367\pi$
$594$		0			0
$595$	−3.38089	+	62.5051i	−0.138603	+	2.56246i
$596$	2.34578	+	8.13445i	0.0960870	+	0.333200i
$597$		0			0
$598$	−0.322795	+	2.64542i	−0.0132001	+	0.108179i
$599$			28.3339i			1.15769i	0.815438	+	0.578845i	$0.196496\pi$
$599$			28.3339i			1.15769i	−0.815438	+	0.578845i	$0.803504\pi$
$600$		0			0
$601$	16.3852	−	9.46002i	0.668368	−	0.385882i	−0.127090	−	0.991891i	$-0.540564\pi$
$601$	16.3852	−	9.46002i	0.668368	−	0.385882i	0.795458	+	0.606009i	$0.207230\pi$
$602$	−9.57481	−	8.04931i	−0.390240	−	0.328065i
$603$		0			0
$604$	−12.5442	−	12.0773i	−0.510416	−	0.491420i
$605$	37.5543	+	21.6820i	1.52680	+	0.881498i
$606$		0			0
$607$	−3.02327	−	5.23646i	−0.122711	−	0.212542i	0.798125	−	0.602492i	$-0.205825\pi$
$607$	−3.02327	−	5.23646i	−0.122711	−	0.212542i	−0.920836	+	0.389950i	$0.872492\pi$
$608$	−5.61529	−	11.9246i	−0.227730	−	0.483605i
$609$		0			0
$610$	−10.9825	+	4.67157i	−0.444669	+	0.189146i
$611$	8.67271	+	5.00719i	0.350860	+	0.202569i
$612$		0			0
$613$	−0.0235058	−	0.0407133i	−0.000949392	−	0.00164439i	0.865550	−	0.500822i	$-0.166969\pi$
$613$	−0.0235058	−	0.0407133i	−0.000949392	−	0.00164439i	−0.866500	+	0.499178i	$0.833636\pi$
$614$	4.64305	−	38.0515i	0.187378	−	1.53564i
$615$		0			0
$616$	−1.65327	+	3.71914i	−0.0666123	+	0.149848i
$617$	10.4917	−	18.1721i	0.422379	−	0.731582i	−0.573793	−	0.819001i	$-0.694528\pi$
$617$	10.4917	−	18.1721i	0.422379	−	0.731582i	0.996172	+	0.0874187i	$0.0278618\pi$
$618$		0			0
$619$	−2.67167	+	4.62746i	−0.107383	+	0.185993i	−0.914709	−	0.404112i	$-0.867581\pi$
$619$	−2.67167	+	4.62746i	−0.107383	+	0.185993i	0.807326	+	0.590106i	$0.200914\pi$
$620$	34.9570	−	10.0808i	1.40391	−	0.404853i
$621$		0			0
$622$	−2.13436	+	17.4919i	−0.0855799	+	0.701359i
$623$	23.2876	+	1.25963i	0.933000	+	0.0504658i
$624$		0			0
$625$	−24.0832	−	41.7133i	−0.963327	−	1.66853i
$626$	−26.6838	−	3.25596i	−1.06650	−	0.130135i
$627$		0			0
$628$	3.67317	−	14.8274i	0.146576	−	0.591678i
$629$			17.3450i			0.691592i
$630$		0			0
$631$			23.1548i			0.921776i	0.887458	+	0.460888i	$0.152469\pi$
$631$			23.1548i			0.921776i	−0.887458	+	0.460888i	$0.847531\pi$
$632$	−10.6422	−	4.05759i	−0.423324	−	0.161402i
$633$		0			0
$634$	3.51811	−	28.8322i	0.139722	−	1.14507i
$635$	28.7853	+	49.8577i	1.14231	+	1.97854i
$636$		0			0
$637$	7.47370	−	3.29751i	0.296119	−	0.130652i
$638$	−3.66483	−	0.447183i	−0.145092	−	0.0177041i
$639$		0			0
$640$	14.6931	−	43.4142i	0.580797	−	1.71610i
$641$	−8.19831	+	14.1999i	−0.323814	+	0.560862i	−0.981272	−	0.192629i	$-0.938299\pi$
$641$	−8.19831	+	14.1999i	−0.323814	+	0.560862i	0.657458	+	0.753491i	$0.271632\pi$
$642$		0			0
$643$	4.77787	−	8.27551i	0.188421	−	0.326354i	−0.756303	−	0.654221i	$-0.772996\pi$
$643$	4.77787	−	8.27551i	0.188421	−	0.326354i	0.944724	+	0.327867i	$0.106330\pi$
$644$	6.25034	−	5.82654i	0.246298	−	0.229598i
$645$		0			0
$646$	−19.1025	−	2.33088i	−0.751577	−	0.0917074i
$647$	10.7329	+	18.5900i	0.421956	+	0.730849i	0.996131	−	0.0878838i	$-0.0280104\pi$
$647$	10.7329	+	18.5900i	0.421956	+	0.730849i	−0.574175	+	0.818733i	$0.694677\pi$
$648$		0			0
$649$	6.06579	+	3.50209i	0.238103	+	0.137469i
$650$	−7.37175	−	17.3304i	−0.289144	−	0.679756i
$651$		0			0
$652$	−21.8094	−	20.9977i	−0.854121	−	0.822332i
$653$	−1.57618	−	2.73003i	−0.0616808	−	0.106834i	0.833536	−	0.552465i	$-0.186313\pi$
$653$	−1.57618	−	2.73003i	−0.0616808	−	0.106834i	−0.895217	+	0.445631i	$0.852979\pi$
$654$		0			0
$655$	55.8180	+	32.2265i	2.18099	+	1.25920i
$656$	9.58757	+	15.2409i	0.374332	+	0.595059i
$657$		0			0
$658$	−10.9540	−	30.1827i	−0.427033	−	1.17664i
$659$	−9.56754	+	5.52382i	−0.372698	+	0.215178i	−0.674637	−	0.738150i	$-0.735700\pi$
$659$	−9.56754	+	5.52382i	−0.372698	+	0.215178i	0.301938	+	0.953327i	$0.402366\pi$
$660$		0			0
$661$		−	28.3829i		−	1.10397i	−0.833855	−	0.551983i	$-0.813871\pi$
$661$		−	28.3829i		−	1.10397i	0.833855	−	0.551983i	$-0.186129\pi$
$662$	−16.1065	−	1.96531i	−0.625995	−	0.0763840i
$663$		0			0
$664$	−15.4702	+	2.48608i	−0.600359	+	0.0964787i
$665$	11.3005	+	22.2707i	0.438214	+	0.863621i
$666$		0			0
$667$	6.71276	+	3.87562i	0.259919	+	0.150064i
$668$	−5.23021	+	5.43240i	−0.202363	+	0.210186i
$669$		0			0
$670$	−37.4113	+	15.9134i	−1.44533	+	0.614790i
$671$	−0.566500	+	0.981208i	−0.0218695	+	0.0378791i
$672$		0			0
$673$	14.8049	+	25.6429i	0.570688	+	0.988461i	0.996495	+	0.0836470i	$0.0266568\pi$
$673$	14.8049	+	25.6429i	0.570688	+	0.988461i	−0.425807	+	0.904814i	$0.640010\pi$
$674$	10.7181	+	8.06399i	0.412845	+	0.310613i
$675$		0			0
$676$	6.44953	+	22.3650i	0.248059	+	0.860191i
$677$			19.6587i			0.755545i	0.925898	+	0.377772i	$0.123310\pi$
$677$			19.6587i			0.755545i	−0.925898	+	0.377772i	$0.876690\pi$
$678$		0			0
$679$	−23.0266	+	35.3280i	−0.883681	+	1.35576i
$680$	−42.2305	−	51.9101i	−1.61947	−	1.99066i
$681$		0			0
$682$	2.07646	−	2.75988i	0.0795119	−	0.105681i
$683$	−4.93427	+	2.84880i	−0.188804	+	0.109006i	−0.591423	−	0.806362i	$-0.701434\pi$
$683$	−4.93427	+	2.84880i	−0.188804	+	0.109006i	0.402618	+	0.915368i	$0.368100\pi$
$684$		0			0
$685$			50.8793i			1.94400i
$686$	−25.1459	−	7.32704i	−0.960074	−	0.279748i
$687$		0			0
$688$	13.3628	−	0.506954i	0.509451	−	0.0193274i
$689$		−	13.6383i		−	0.519577i
$690$		0			0
$691$	17.8054			0.677347			0.338674	−	0.940904i	$-0.390022\pi$
$691$	17.8054			0.677347			0.338674	+	0.940904i	$0.390022\pi$
$692$	3.01293	−	12.1622i	0.114534	−	0.462338i
$693$		0			0
$694$	3.21614	+	0.392434i	0.122083	+	0.0148966i
$695$		−	57.5727i		−	2.18386i
$696$		0			0
$697$	26.2892			0.995774
$698$	−18.1407	−	42.6475i	−0.686637	−	1.61423i
$699$		0			0
$700$	−17.6646	+	57.7429i	−0.667658	+	2.18248i
$701$	−9.77794			−0.369308			−0.184654	−	0.982804i	$-0.559116\pi$
$701$	−9.77794			−0.369308			−0.184654	+	0.982804i	$0.559116\pi$
$702$		0			0
$703$	3.46002	+	5.99293i	0.130497	+	0.226028i
$704$	−1.36324	−	4.13199i	−0.0513791	−	0.155730i
$705$		0			0
$706$	−17.9387	+	23.8428i	−0.675131	+	0.897335i
$707$	19.5653	+	1.05829i	0.735830	+	0.0398009i
$708$		0			0
$709$	−13.0588			−0.490432			−0.245216	−	0.969468i	$-0.578859\pi$
$709$	−13.0588			−0.490432			−0.245216	+	0.969468i	$0.578859\pi$
$710$	−27.2703	+	11.5998i	−1.02343	+	0.435332i
$711$		0			0
$712$	−19.3402	+	15.7339i	−0.724806	+	0.589653i
$713$	−6.27962	+	3.62554i	−0.235174	+	0.135778i
$714$		0			0
$715$	−2.22676	−	1.28562i	−0.0832761	−	0.0480795i
$716$	−19.1689	+	5.52787i	−0.716377	+	0.206586i
$717$		0			0
$718$	−25.4380	+	33.8104i	−0.949339	+	1.26179i
$719$	−15.4289	+	26.7237i	−0.575401	+	0.996624i	0.420597	+	0.907248i	$0.361821\pi$
$719$	−15.4289	+	26.7237i	−0.575401	+	0.996624i	−0.995998	+	0.0893766i	$0.971513\pi$
$720$		0			0
$721$	14.3199	+	9.33366i	0.533302	+	0.347604i
$722$	17.6610	−	7.51235i	0.657274	−	0.279581i
$723$		0			0
$724$	−2.57111	+	10.3787i	−0.0955544	+	0.385722i
$725$	−54.7758			−2.03432
$726$		0			0
$727$	−1.75480	−	3.03940i	−0.0650819	−	0.112725i	0.831648	−	0.555303i	$-0.187398\pi$
$727$	−1.75480	−	3.03940i	−0.0650819	−	0.112725i	−0.896730	+	0.442577i	$0.854064\pi$
$728$	−3.54732	+	7.97992i	−0.131472	+	0.295755i
$729$		0			0
$730$	29.5340	+	22.2206i	1.09310	+	0.822422i
$731$	9.76213	−	16.9085i	0.361066	−	0.625384i
$732$		0			0
$733$	−2.19882	+	1.26949i	−0.0812153	+	0.0468897i	−0.540058	−	0.841628i	$-0.681598\pi$
$733$	−2.19882	+	1.26949i	−0.0812153	+	0.0468897i	0.458842	+	0.888518i	$0.348264\pi$
$734$	22.7458	+	17.1134i	0.839563	+	0.631665i
$735$		0			0
$736$	−0.761879	+	9.10306i	−0.0280832	+	0.335543i
$737$	−1.92975	+	3.34243i	−0.0710834	+	0.123120i
$738$		0			0
$739$	−7.43557	+	4.29293i	−0.273522	+	0.157918i	−0.630487	−	0.776200i	$-0.717145\pi$
$739$	−7.43557	+	4.29293i	−0.273522	+	0.157918i	0.356965	+	0.934118i	$0.383812\pi$
$740$	−5.78626	+	23.3573i	−0.212707	+	0.858630i
$741$		0			0
$742$	−28.1389	+	33.4718i	−1.03301	+	1.22879i
$743$	0.852403	+	0.492135i	0.0312716	+	0.0180547i	0.515554	−	0.856857i	$-0.327586\pi$
$743$	0.852403	+	0.492135i	0.0312716	+	0.0180547i	−0.484283	+	0.874912i	$0.660919\pi$
$744$		0			0
$745$	14.8508	+	8.57412i	0.544092	+	0.314132i
$746$	14.2385	−	6.05656i	0.521310	−	0.221746i
$747$		0			0
$748$	−6.16635	−	1.52758i	−0.225464	−	0.0558538i
$749$	−29.3641	−	1.58830i	−1.07294	−	0.0580353i
$750$		0			0
$751$	−4.18189	+	2.41442i	−0.152599	+	0.0881033i	−0.574355	−	0.818606i	$-0.694747\pi$
$751$	−4.18189	+	2.41442i	−0.152599	+	0.0881033i	0.421756	+	0.906709i	$0.361414\pi$
$752$	30.3564	+	16.0237i	1.10699	+	0.584323i
$753$		0			0
$754$	−7.86339	−	0.959492i	−0.286368	−	0.0349426i
$755$	−35.2715			−1.28366
$756$		0			0
$757$	−39.8457			−1.44822			−0.724109	−	0.689686i	$-0.757749\pi$
$757$	−39.8457			−1.44822			−0.724109	+	0.689686i	$0.757749\pi$
$758$	−22.3707	−	2.72967i	−0.812540	−	0.0991461i
$759$		0			0
$760$	−24.9463	−	9.51136i	−0.904897	−	0.345013i
$761$	−20.4850	+	11.8270i	−0.742582	+	0.428730i	−0.823007	−	0.568031i	$-0.807706\pi$
$761$	−20.4850	+	11.8270i	−0.742582	+	0.428730i	0.0804252	+	0.996761i	$0.474372\pi$
$762$		0			0
$763$	−7.41853	−	4.83536i	−0.268569	−	0.175052i
$764$	10.5852	−	42.7291i	0.382960	−	1.54588i
$765$		0			0
$766$	−30.5687	+	13.0028i	−1.10449	+	0.469811i
$767$	13.0150	+	7.51420i	0.469944	+	0.271322i
$768$		0			0
$769$	−1.86343	−	1.07585i	−0.0671971	−	0.0387963i	0.466025	−	0.884772i	$-0.345686\pi$
$769$	−1.86343	−	1.07585i	−0.0671971	−	0.0387963i	−0.533222	+	0.845975i	$0.679019\pi$
$770$	2.81250	+	7.74955i	0.101355	+	0.279275i
$771$		0			0
$772$	11.3264	+	2.80587i	0.407646	+	0.100985i
$773$	−24.9256	+	14.3908i	−0.896513	+	0.517602i	−0.876067	−	0.482189i	$-0.839842\pi$
$773$	−24.9256	+	14.3908i	−0.896513	+	0.517602i	−0.0204456	+	0.999791i	$0.506509\pi$
$774$		0			0
$775$	25.6207	−	44.3763i	0.920323	−	1.59405i
$776$	−7.15289	−	44.5104i	−0.256774	−	1.59783i
$777$		0			0
$778$	9.19157	+	6.91549i	0.329534	+	0.247933i
$779$	9.08324	−	5.24421i	0.325441	−	0.187893i
$780$		0			0
$781$	−1.40666	+	2.43640i	−0.0503341	+	0.0871812i
$782$	10.6577	+	8.01857i	0.381118	+	0.286744i
$783$		0			0
$784$	25.1704	−	12.2658i	0.898944	−	0.438064i
$785$	−15.4708	−	26.7963i	−0.552178	−	0.956400i
$786$		0			0
$787$	−11.1297			−0.396731			−0.198365	−	0.980128i	$-0.563563\pi$
$787$	−11.1297			−0.396731			−0.198365	+	0.980128i	$0.563563\pi$
$788$	27.6934	+	6.86043i	0.986535	+	0.244393i
$789$		0			0
$790$	−21.2294	+	9.03021i	−0.755307	+	0.321280i
$791$	0.388857	−	7.18909i	0.0138262	−	0.255615i
$792$		0			0
$793$	−1.21550	+	2.10531i	−0.0431638	+	0.0747619i
$794$	−23.2877	+	30.9523i	−0.826450	+	1.09846i
$795$		0			0
$796$	2.38125	+	8.25743i	0.0844011	+	0.292677i
$797$	25.2083	+	14.5540i	0.892923	+	0.515529i	0.874897	−	0.484308i	$-0.160929\pi$
$797$	25.2083	+	14.5540i	0.892923	+	0.515529i	0.0180253	+	0.999838i	$0.494262\pi$
$798$		0			0
$799$	43.4029	−	25.0587i	1.53548	−	0.886512i
$800$	−27.5017	−	58.4023i	−0.972332	−	2.06483i
$801$		0			0
$802$	24.5300	−	10.4342i	0.866184	−	0.368443i
$803$	3.50867			0.123818
$804$		0			0
$805$	0.934832	−	17.2830i	0.0329485	−	0.609144i
$806$	4.45533	−	5.92170i	0.156932	−	0.208583i
$807$		0			0
$808$	−16.2489	+	13.2190i	−0.571634	+	0.465043i
$809$	−11.9462	−	20.6915i	−0.420007	−	0.727474i	0.575932	−	0.817497i	$-0.304639\pi$
$809$	−11.9462	−	20.6915i	−0.420007	−	0.727474i	−0.995940	+	0.0900232i	$0.971306\pi$
$810$		0			0
$811$	20.7873			0.729940			0.364970	−	0.931019i	$-0.381079\pi$
$811$	20.7873			0.729940			0.364970	+	0.931019i	$0.381079\pi$
$812$	17.3191	+	18.5788i	0.607781	+	0.651989i
$813$		0			0
$814$	0.894167	+	2.10212i	0.0313405	+	0.0736793i
$815$	−61.3230			−2.14805
$816$		0			0
$817$		−	7.78947i		−	0.272519i
$818$	−26.7880	−	3.26867i	−0.936621	−	0.114286i
$819$		0			0
$820$	35.4017	+	8.77000i	1.23628	+	0.306262i
$821$	5.78113			0.201763			0.100881	−	0.994898i	$-0.467834\pi$
$821$	5.78113			0.201763			0.100881	+	0.994898i	$0.467834\pi$
$822$		0			0
$823$		−	19.0746i		−	0.664899i	−0.943121	−	0.332449i	$-0.892125\pi$
$823$		−	19.0746i		−	0.664899i	0.943121	−	0.332449i	$-0.107875\pi$
$824$	−18.0419	+	2.89937i	−0.628520	+	0.101004i
$825$		0			0
$826$	−16.4385	−	45.2946i	−0.571969	−	1.57600i
$827$		−	14.6270i		−	0.508631i	−0.967121	−	0.254315i	$-0.918150\pi$
$827$		−	14.6270i		−	0.508631i	0.967121	−	0.254315i	$-0.0818501\pi$
$828$		0			0
$829$	3.92858	−	2.26817i	0.136445	−	0.0787767i	−0.430223	−	0.902722i	$-0.641565\pi$
$829$	3.92858	−	2.26817i	0.136445	−	0.0787767i	0.566669	+	0.823946i	$0.308232\pi$
$830$	−19.0812	+	25.3613i	−0.662318	+	0.880305i
$831$		0			0
$832$	−2.92502	−	8.86575i	−0.101407	−	0.307364i
$833$	4.40961	−	40.6427i	0.152784	−	1.40818i
$834$		0			0
$835$			15.2747i			0.528602i
$836$	−2.43527	+	0.702275i	−0.0842257	+	0.0242887i
$837$		0			0
$838$	28.7521	+	21.6323i	0.993223	+	0.747275i
$839$	−12.4814	−	21.6184i	−0.430906	−	0.746351i	0.566046	−	0.824374i	$-0.308473\pi$
$839$	−12.4814	−	21.6184i	−0.430906	−	0.746351i	−0.996952	+	0.0780231i	$0.975139\pi$
$840$		0			0
$841$	2.97992	−	5.16138i	0.102756	−	0.177978i
$842$	26.6760	−	11.3470i	0.919315	−	0.391044i
$843$		0			0
$844$	−0.144603	−	0.139221i	−0.00497745	−	0.00479220i
$845$	40.8311	+	23.5738i	1.40463	+	0.810964i
$846$		0			0
$847$	−23.7258	−	15.4643i	−0.815227	−	0.531361i
$848$	−1.77222	−	46.7139i	−0.0608582	−	1.60416i
$849$		0			0
$850$	−93.5572	−	11.4159i	−3.20898	−	0.391560i
$851$		−	4.79599i		−	0.164404i
$852$		0			0
$853$	−13.2403	+	7.64427i	−0.453338	+	0.261735i	−0.709239	−	0.704968i	$-0.750961\pi$
$853$	−13.2403	+	7.64427i	−0.453338	+	0.261735i	0.255901	+	0.966703i	$0.417628\pi$
$854$	7.32690	−	2.65911i	0.250721	−	0.0909928i
$855$		0			0
$856$	24.3867	−	19.8394i	0.833521	−	0.678097i
$857$	42.0171	+	24.2586i	1.43528	+	0.828658i	0.997516	−	0.0704337i	$-0.0224383\pi$
$857$	42.0171	+	24.2586i	1.43528	+	0.828658i	0.437761	+	0.899091i	$0.355772\pi$
$858$		0			0
$859$	25.8723	+	44.8121i	0.882751	+	1.52897i	0.848270	+	0.529563i	$0.177644\pi$
$859$	25.8723	+	44.8121i	0.882751	+	1.52897i	0.0344802	+	0.999405i	$0.489022\pi$
$860$	18.7866	−	19.5128i	0.640616	−	0.665381i
$861$		0			0
$862$	−9.71773	−	22.8457i	−0.330987	−	0.778127i
$863$	38.8024	+	22.4026i	1.32085	+	0.762592i	0.983864	−	0.178919i	$-0.0572599\pi$
$863$	38.8024	+	22.4026i	1.32085	+	0.762592i	0.336984	+	0.941510i	$0.390593\pi$
$864$		0			0
$865$	−12.6900	−	21.9797i	−0.431472	−	0.747332i
$866$	21.3390	+	2.60379i	0.725129	+	0.0884803i
$867$		0			0
$868$	−23.1523	+	5.34097i	−0.785842	+	0.181284i
$869$	−1.09505	+	1.89669i	−0.0371471	+	0.0643407i
$870$		0			0
$871$	−4.14055	+	7.17164i	−0.140297	+	0.243002i
$872$	9.34673	−	1.50204i	0.316520	−	0.0508653i
$873$		0			0
$874$	5.28192	+	0.644501i	0.178664	+	0.0218006i
$875$	31.0960	+	61.2831i	1.05124	+	2.07175i
$876$		0			0
$877$	18.4097	+	31.8865i	0.621651	+	1.07673i	0.989178	+	0.146718i	$0.0468710\pi$
$877$	18.4097	+	31.8865i	0.621651	+	1.07673i	−0.367527	+	0.930013i	$0.619796\pi$
$878$	−2.49557	+	20.4521i	−0.0842214	+	0.690226i
$879$		0			0
$880$	−7.79416	−	4.11415i	−0.262741	−	0.138688i
$881$			50.8325i			1.71259i	0.516486	+	0.856295i	$0.327240\pi$
$881$			50.8325i			1.71259i	−0.516486	+	0.856295i	$0.672760\pi$
$882$		0			0
$883$		−	28.5456i		−	0.960635i	−0.877095	−	0.480317i	$-0.840521\pi$
$883$		−	28.5456i		−	0.960635i	0.877095	−	0.480317i	$-0.159479\pi$
$884$	−13.2307	−	3.27763i	−0.444997	−	0.110239i
$885$		0			0
$886$	33.7299	+	4.11572i	1.13318	+	0.138270i
$887$	0.916708	+	1.58779i	0.0307800	+	0.0533126i	0.881005	−	0.473107i	$-0.156868\pi$
$887$	0.916708	+	1.58779i	0.0307800	+	0.0533126i	−0.850225	+	0.526419i	$0.823534\pi$
$888$		0			0
$889$	−17.0133	−	33.5295i	−0.570609	−	1.12454i
$890$	−6.11678	+	50.1293i	−0.205035	+	1.68034i
$891$		0			0
$892$	7.10548	+	24.6396i	0.237909	+	0.824995i
$893$	9.99749	−	17.3162i	0.334553	−	0.579463i
$894$		0			0
$895$	−20.2050	+	34.9962i	−0.675380	+	1.16979i
$896$	−11.1133	+	27.7938i	−0.371271	+	0.928525i
$897$		0			0
$898$	−6.19958	+	50.8078i	−0.206883	+	1.69548i
$899$	−10.7767	−	18.6659i	−0.359425	−	0.622542i
$900$		0			0
$901$	−59.1091	−	34.1266i	−1.96921	−	1.13692i
$902$	3.18610	−	1.35525i	0.106086	−	0.0451250i
$903$		0			0
$904$	4.85719	+	5.97049i	0.161548	+	0.198576i
$905$	10.8291	+	18.7566i	0.359972	+	0.623489i
$906$		0			0
$907$	−29.5577	−	17.0652i	−0.981448	−	0.566640i	−0.0787413	−	0.996895i	$-0.525090\pi$
$907$	−29.5577	−	17.0652i	−0.981448	−	0.566640i	−0.902707	+	0.430256i	$0.858423\pi$
$908$	−26.0577	+	27.0651i	−0.864757	+	0.898186i
$909$		0			0
$910$	6.03460	+	16.6277i	0.200045	+	0.551203i
$911$	46.1098	−	26.6215i	1.52769	−	0.882010i	0.528228	−	0.849103i	$-0.322857\pi$
$911$	46.1098	−	26.6215i	1.52769	−	0.882010i	0.999458	−	0.0329076i	$-0.0104767\pi$
$912$		0			0
$913$			3.01295i			0.0997143i
$914$	3.52380	−	28.8788i	0.116557	−	0.955227i
$915$		0			0
$916$	34.7624	−	10.0247i	1.14858	−	0.331224i
$917$	−35.2643	−	22.9851i	−1.16453	−	0.759034i
$918$		0			0
$919$	−13.4852	−	7.78568i	−0.444836	−	0.256826i	0.260811	−	0.965390i	$-0.416010\pi$
$919$	−13.4852	−	7.78568i	−0.444836	−	0.256826i	−0.705647	+	0.708564i	$0.749343\pi$
$920$	11.6769	+	14.3534i	0.384977	+	0.473217i
$921$		0			0
$922$	12.8340	+	30.1719i	0.422667	+	0.993659i
$923$	−3.01817	+	5.22762i	−0.0993442	+	0.172069i
$924$		0			0
$925$	16.9460	+	29.3513i	0.557180	+	0.965063i
$926$	10.8429	−	14.4116i	0.356321	−	0.473596i
$927$		0			0
$928$	−27.0584	−	2.26465i	−0.888235	−	0.0743407i
$929$			6.16139i			0.202149i	0.994879	+	0.101074i	$0.0322280\pi$
$929$			6.16139i			0.202149i	−0.994879	+	0.101074i	$0.967772\pi$
$930$		0			0
$931$	−6.58389	−	14.9222i	−0.215778	−	0.489055i
$932$	−16.3229	+	16.9539i	−0.534676	+	0.555345i
$933$		0			0
$934$	−23.4711	−	17.6590i	−0.767996	−	0.577820i
$935$	−11.1439	+	6.43393i	−0.364444	+	0.210412i
$936$		0			0
$937$		−	20.3159i		−	0.663692i	−0.943334	−	0.331846i	$-0.892329\pi$
$937$		−	20.3159i		−	0.663692i	0.943334	−	0.331846i	$-0.107671\pi$
$938$	24.9587	−	9.05811i	0.814930	−	0.295758i
$939$		0			0
$940$	66.8069	−	19.2655i	2.17900	−	0.628373i
$941$		−	38.3234i		−	1.24931i	−0.780902	−	0.624654i	$-0.785240\pi$
$941$		−	38.3234i		−	1.24931i	0.780902	−	0.624654i	$-0.214760\pi$
$942$		0			0
$943$	−7.26908			−0.236714
$944$	45.5553	+	24.0464i	1.48270	+	0.782644i
$945$		0			0
$946$	0.311453	−	2.55247i	0.0101262	−	0.0829880i
$947$			13.2141i			0.429401i	0.976680	+	0.214700i	$0.0688775\pi$
$947$			13.2141i			0.429401i	−0.976680	+	0.214700i	$0.931123\pi$
$948$		0			0
$949$	7.52834			0.244380
$950$	−34.6024	+	14.7186i	−1.12265	+	0.477535i
$951$		0			0
$952$	25.7090	+	35.3422i	0.833235	+	1.14545i
$953$	−11.6066			−0.375976			−0.187988	−	0.982171i	$-0.560197\pi$
$953$	−11.6066			−0.375976			−0.187988	+	0.982171i	$0.560197\pi$
$954$		0			0
$955$	−44.5833	−	77.2206i	−1.44268	−	2.49880i
$956$	−2.82466	−	2.71953i	−0.0913560	−	0.0879559i
$957$		0			0
$958$	20.6067	+	15.5040i	0.665773	+	0.500910i
$959$	1.79472	−	33.1803i	0.0579545	−	1.07145i
$960$		0			0
$961$	−10.8372			−0.349589
$962$	1.91856	+	4.51039i	0.0618567	+	0.145421i
$963$		0			0
$964$	9.87756	+	9.50994i	0.318135	+	0.306294i
$965$	20.4692	−	11.8179i	0.658926	−	0.380431i
$966$		0			0
$967$	40.7431	+	23.5230i	1.31021	+	0.756449i	0.982130	−	0.188201i	$-0.0602657\pi$
$967$	40.7431	+	23.5230i	1.31021	+	0.756449i	0.328078	+	0.944651i	$0.393599\pi$
$968$	29.8925	−	4.80377i	0.960781	−	0.154399i
$969$		0			0
$970$	−72.9689	−	54.8999i	−2.34289	−	1.76273i
$971$	−17.2692	+	29.9112i	−0.554195	+	0.959895i	0.443770	+	0.896141i	$0.353641\pi$
$971$	−17.2692	+	29.9112i	−0.554195	+	0.959895i	−0.997966	+	0.0637540i	$0.979693\pi$
$972$		0			0
$973$	−2.03082	+	37.5453i	−0.0651051	+	1.20365i
$974$	−5.31936	−	12.5054i	−0.170443	−	0.400700i
$975$		0			0
$976$	−3.88977	+	7.36907i	−0.124508	+	0.235878i
$977$	27.3080			0.873659			0.436830	−	0.899544i	$-0.356101\pi$
$977$	27.3080			0.873659			0.436830	+	0.899544i	$0.356101\pi$
$978$		0			0
$979$	2.39710	+	4.15190i	0.0766117	+	0.132695i
$980$	19.4964	−	53.2594i	0.622789	−	1.70131i
$981$		0			0
$982$	−1.52615	+	2.02844i	−0.0487013	+	0.0647302i
$983$	−9.56607	+	16.5689i	−0.305110	+	0.528467i	−0.977286	−	0.211925i	$-0.932027\pi$
$983$	−9.56607	+	16.5689i	−0.305110	+	0.528467i	0.672176	+	0.740392i	$0.265360\pi$
$984$		0			0
$985$	50.0478	−	28.8951i	1.59465	−	0.920674i
$986$	−23.8348	+	31.6795i	−0.759055	+	1.00888i
$987$		0			0
$988$	−5.22521	+	1.50683i	−0.166236	+	0.0479385i
$989$	−2.69928	+	4.67528i	−0.0858320	+	0.148665i
$990$		0			0
$991$	−19.9326	+	11.5081i	−0.633179	+	0.365566i	−0.781982	−	0.623301i	$-0.785791\pi$
$991$	−19.9326	+	11.5081i	−0.633179	+	0.365566i	0.148803	+	0.988867i	$0.452458\pi$
$992$	14.4909	−	20.8620i	0.460087	−	0.662368i
$993$		0			0
$994$	18.1931	−	6.60273i	0.577051	−	0.209426i
$995$	15.0754	+	8.70376i	0.477921	+	0.275928i
$996$		0			0
$997$	52.8055	+	30.4872i	1.67237	+	0.965541i	0.966309	+	0.257385i	$0.0828609\pi$
$997$	52.8055	+	30.4872i	1.67237	+	0.965541i	0.706056	+	0.708156i	$0.250472\pi$
$998$	24.3433	+	57.2294i	0.770575	+	1.81156i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bj.b.523.23		84
3.2	odd	2		252.2.bj.b.103.20	yes	84
4.3	odd	2	inner	756.2.bj.b.523.24		84
7.3	odd	6		756.2.n.b.199.33		84
9.2	odd	6		252.2.n.b.187.38	yes	84
9.7	even	3		756.2.n.b.19.5		84
12.11	even	2		252.2.bj.b.103.19	yes	84
21.17	even	6		252.2.n.b.31.10	✓	84
28.3	even	6		756.2.n.b.199.5		84
36.7	odd	6		756.2.n.b.19.33		84
36.11	even	6		252.2.n.b.187.10	yes	84
63.38	even	6		252.2.bj.b.115.20	yes	84
63.52	odd	6	inner	756.2.bj.b.451.23		84
84.59	odd	6		252.2.n.b.31.38	yes	84
252.115	even	6	inner	756.2.bj.b.451.24		84
252.227	odd	6		252.2.bj.b.115.19	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.10	✓	84	21.17	even	6
252.2.n.b.31.38	yes	84	84.59	odd	6
252.2.n.b.187.10	yes	84	36.11	even	6
252.2.n.b.187.38	yes	84	9.2	odd	6
252.2.bj.b.103.19	yes	84	12.11	even	2
252.2.bj.b.103.20	yes	84	3.2	odd	2
252.2.bj.b.115.19	yes	84	252.227	odd	6
252.2.bj.b.115.20	yes	84	63.38	even	6
756.2.n.b.19.5		84	9.7	even	3
756.2.n.b.19.33		84	36.7	odd	6
756.2.n.b.199.5		84	28.3	even	6
756.2.n.b.199.33		84	7.3	odd	6
756.2.bj.b.451.23		84	63.52	odd	6	inner
756.2.bj.b.451.24		84	252.115	even	6	inner
756.2.bj.b.523.23		84	1.1	even	1	trivial
756.2.bj.b.523.24		84	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bj (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.171292 - 1.40380i) q^{2} +(-1.94132 - 0.480920i) q^{4} +(-3.50837 + 2.02556i) q^{5} +(2.35939 - 1.19719i) q^{7} +(-1.00765 + 2.64285i) q^{8} +(2.24253 + 5.27202i) q^{10} +(0.471017 + 0.271942i) q^{11} +(1.01063 + 0.583488i) q^{13} +(-1.27647 - 3.51719i) q^{14} +(3.53743 + 1.86724i) q^{16} +(5.05773 - 2.92008i) q^{17} +(1.16501 - 2.01785i) q^{19} +(7.78500 - 2.24501i) q^{20} +(0.462434 - 0.614633i) q^{22} +(-1.39849 + 0.807417i) q^{23} +(5.70579 - 9.88272i) q^{25} +(0.992214 - 1.31878i) q^{26} +(-5.15609 + 1.18945i) q^{28} +(-2.40001 - 4.15694i) q^{29} +4.49030 q^{31} +(3.22716 - 4.64601i) q^{32} +(-3.23287 - 7.60024i) q^{34} +(-5.85265 + 8.97929i) q^{35} +(-1.48498 + 2.57206i) q^{37} +(-2.63311 - 1.98108i) q^{38} +(-1.81804 - 11.3132i) q^{40} +(3.89836 + 2.25072i) q^{41} +(2.89521 - 1.67155i) q^{43} +(-0.783611 - 0.754447i) q^{44} +(0.893904 + 2.10150i) q^{46} +8.58149 q^{47} +(4.13347 - 5.64928i) q^{49} +(-12.8960 - 9.70263i) q^{50} +(-1.68134 - 1.61877i) q^{52} +(-5.84343 - 10.1211i) q^{53} -2.20334 q^{55} +(0.786554 + 7.44186i) q^{56} +(-6.24662 + 2.65709i) q^{58} +12.8781 q^{59} +2.08317i q^{61} +(0.769151 - 6.30348i) q^{62} +(-5.96929 - 5.32612i) q^{64} -4.72756 q^{65} +7.09620i q^{67} +(-11.2230 + 3.23645i) q^{68} +(11.6026 + 9.75404i) q^{70} +5.17264i q^{71} +(5.58686 - 3.22558i) q^{73} +(3.35629 + 2.52519i) q^{74} +(-3.23207 + 3.35702i) q^{76} +(1.43688 + 0.0777206i) q^{77} +4.02680i q^{79} +(-16.1928 + 0.614320i) q^{80} +(3.82732 - 5.08700i) q^{82} +(2.76985 + 4.79753i) q^{83} +(-11.8296 + 20.4895i) q^{85} +(-1.85060 - 4.35062i) q^{86} +(-1.19332 + 0.970804i) q^{88} +(7.63381 + 4.40738i) q^{89} +(3.08302 + 0.166760i) q^{91} +(3.10321 - 0.894893i) q^{92} +(1.46994 - 12.0467i) q^{94} +9.43917i q^{95} +(-13.8033 + 7.96935i) q^{97} +(-7.22244 - 6.77025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37}+ \cdots - 21 q^{98}+O(q^{100}) \) 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8 - 18 * q^10 + 18 * q^13 - 14 * q^14 + 14 * q^16 - 6 * q^17 + 24 * q^20 + 6 * q^22 + 16 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 + 18 * q^32 - 24 * q^34 + 2 * q^37 - 33 * q^38 + 6 * q^40 - 6 * q^41 + 13 * q^44 + 10 * q^46 - 28 * q^49 + 17 * q^50 - 27 * q^52 + 2 * q^53 - 58 * q^56 - 13 * q^58 - 8 * q^64 + 100 * q^65 + 18 * q^68 - 19 * q^70 + 30 * q^73 + 23 * q^74 + 2 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 + 9 * q^86 + q^88 + 102 * q^89 - 28 * q^92 + 6 * q^97 - 21 * q^98

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