LMFDB - Embedded newform 912.2.ci.h.751.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (of order $18$, degree $6$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			751.3
Character	$\chi$	$=$	912.751
Dual form			912.2.ci.h.895.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{3} +(1.72729 + 0.628683i) q^{5} +(3.53090 + 2.03857i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{3} +(1.72729 + 0.628683i) q^{5} +(3.53090 + 2.03857i) q^{7} +(0.173648 - 0.984808i) q^{9} +(4.09762 - 2.36576i) q^{11} +(2.35018 - 2.80084i) q^{13} +(-1.72729 + 0.628683i) q^{15} +(-1.27396 - 7.22499i) q^{17} +(-3.86056 + 2.02389i) q^{19} +(-4.01519 + 0.707987i) q^{21} +(1.09355 + 3.00451i) q^{23} +(-1.24192 - 1.04210i) q^{25} +(0.500000 + 0.866025i) q^{27} +(2.75189 + 0.485232i) q^{29} +(-3.49224 + 6.04874i) q^{31} +(-1.61828 + 4.44618i) q^{33} +(4.81729 + 5.74102i) q^{35} -5.49107i q^{37} +3.65624i q^{39} +(3.61386 + 4.30683i) q^{41} +(2.83629 - 7.79265i) q^{43} +(0.919073 - 1.59188i) q^{45} +(2.50233 + 0.441228i) q^{47} +(4.81151 + 8.33379i) q^{49} +(5.62004 + 4.71578i) q^{51} +(1.47763 + 4.05976i) q^{53} +(8.56510 - 1.51026i) q^{55} +(1.65643 - 4.03190i) q^{57} +(-1.29078 - 7.32037i) q^{59} +(-1.56422 + 0.569328i) q^{61} +(2.62073 - 3.12327i) q^{63} +(5.82030 - 3.36035i) q^{65} +(-1.27621 + 7.23775i) q^{67} +(-2.76897 - 1.59866i) q^{69} +(-10.8377 - 3.94458i) q^{71} +(-8.89269 + 7.46185i) q^{73} +1.62122 q^{75} +19.2911 q^{77} +(-4.80146 + 4.02890i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(9.06619 + 5.23437i) q^{83} +(2.34173 - 13.2806i) q^{85} +(-2.41997 + 1.39717i) q^{87} +(3.28025 - 3.90925i) q^{89} +(14.0080 - 5.09848i) q^{91} +(-1.21284 - 6.87837i) q^{93} +(-7.94069 + 1.06878i) q^{95} +(-18.6216 + 3.28349i) q^{97} +(-1.61828 - 4.44618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 9 q^{7}+O(q^{10}) $ 24 * q + 9 * q^7	$ 24 q + 9 q^{7} - 9 q^{11} - 9 q^{13} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 15 q^{23} + 6 q^{25} + 12 q^{27} - 6 q^{29} - 12 q^{31} - 3 q^{33} + 30 q^{41} + 9 q^{43} + 3 q^{45} + 15 q^{47} + 27 q^{49} - 3 q^{51} + 6 q^{53} - 21 q^{55} - 9 q^{57} + 36 q^{59} - 21 q^{61} + 3 q^{63} - 9 q^{65} - 45 q^{67} + 36 q^{71} - 42 q^{75} + 108 q^{77} - 36 q^{79} + 27 q^{83} - 9 q^{85} + 9 q^{87} - 27 q^{89} + 36 q^{91} - 18 q^{93} - 30 q^{95} - 51 q^{97} - 3 q^{99}+O(q^{100}) $ 24 * q + 9 * q^7 - 9 * q^11 - 9 * q^13 - 6 * q^17 + 3 * q^19 - 6 * q^21 - 15 * q^23 + 6 * q^25 + 12 * q^27 - 6 * q^29 - 12 * q^31 - 3 * q^33 + 30 * q^41 + 9 * q^43 + 3 * q^45 + 15 * q^47 + 27 * q^49 - 3 * q^51 + 6 * q^53 - 21 * q^55 - 9 * q^57 + 36 * q^59 - 21 * q^61 + 3 * q^63 - 9 * q^65 - 45 * q^67 + 36 * q^71 - 42 * q^75 + 108 * q^77 - 36 * q^79 + 27 * q^83 - 9 * q^85 + 9 * q^87 - 27 * q^89 + 36 * q^91 - 18 * q^93 - 30 * q^95 - 51 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$	$1$	$-1$

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
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$4$		0			0
$5$	1.72729	+	0.628683i	0.772469	+	0.281156i	0.698029	−	0.716070i	$-0.254061\pi$
$5$	1.72729	+	0.628683i	0.772469	+	0.281156i	0.0744402	+	0.997225i	$0.476283\pi$
$6$		0			0
$7$	3.53090	+	2.03857i	1.33456	+	0.770506i	0.985994	−	0.166780i	$-0.0533369\pi$
$7$	3.53090	+	2.03857i	1.33456	+	0.770506i	0.348562	+	0.937286i	$0.386670\pi$
$8$		0			0
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$		0			0
$11$	4.09762	−	2.36576i	1.23548	−	0.713304i	0.267312	−	0.963610i	$-0.413865\pi$
$11$	4.09762	−	2.36576i	1.23548	−	0.713304i	0.968167	+	0.250306i	$0.0805313\pi$
$12$		0			0
$13$	2.35018	−	2.80084i	0.651824	−	0.776813i	−0.334364	−	0.942444i	$-0.608522\pi$
$13$	2.35018	−	2.80084i	0.651824	−	0.776813i	0.986188	+	0.165631i	$0.0529660\pi$
$14$		0			0
$15$	−1.72729	+	0.628683i	−0.445985	+	0.162325i
$16$		0			0
$17$	−1.27396	−	7.22499i	−0.308981	−	1.75232i	−0.604149	−	0.796872i	$-0.706487\pi$
$17$	−1.27396	−	7.22499i	−0.308981	−	1.75232i	0.295168	−	0.955445i	$-0.404624\pi$
$18$		0			0
$19$	−3.86056	+	2.02389i	−0.885672	+	0.464311i
$19$	−3.86056	+	2.02389i	−0.885672	+	0.464311i
$20$		0			0
$21$	−4.01519	+	0.707987i	−0.876187	+	0.154495i
$22$		0			0
$23$	1.09355	+	3.00451i	0.228021	+	0.626483i	0.999958	−	0.00921679i	$-0.00293384\pi$
$23$	1.09355	+	3.00451i	0.228021	+	0.626483i	−0.771936	+	0.635700i	$0.780712\pi$
$24$		0			0
$25$	−1.24192	−	1.04210i	−0.248385	−	0.208420i
$26$		0			0
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$		0			0
$29$	2.75189	+	0.485232i	0.511013	+	0.0901054i	0.423208	−	0.906032i	$-0.360904\pi$
$29$	2.75189	+	0.485232i	0.511013	+	0.0901054i	0.0878046	+	0.996138i	$0.472015\pi$
$30$		0			0
$31$	−3.49224	+	6.04874i	−0.627225	+	1.08639i	0.360881	+	0.932612i	$0.382476\pi$
$31$	−3.49224	+	6.04874i	−0.627225	+	1.08639i	−0.988106	+	0.153774i	$0.950857\pi$
$32$		0			0
$33$	−1.61828	+	4.44618i	−0.281706	+	0.773980i
$34$		0			0
$35$	4.81729	+	5.74102i	0.814271	+	0.970410i
$36$		0			0
$37$		−	5.49107i		−	0.902726i	−0.892341	−	0.451363i	$-0.850938\pi$
$37$		−	5.49107i		−	0.902726i	0.892341	−	0.451363i	$-0.149062\pi$
$38$		0			0
$39$			3.65624i			0.585466i
$40$		0			0
$41$	3.61386	+	4.30683i	0.564391	+	0.672615i	0.970470	−	0.241223i	$-0.0775487\pi$
$41$	3.61386	+	4.30683i	0.564391	+	0.672615i	−0.406079	+	0.913838i	$0.633104\pi$
$42$		0			0
$43$	2.83629	−	7.79265i	0.432530	−	1.18837i	−0.511724	−	0.859150i	$-0.670993\pi$
$43$	2.83629	−	7.79265i	0.432530	−	1.18837i	0.944254	−	0.329217i	$-0.106785\pi$
$44$		0			0
$45$	0.919073	−	1.59188i	0.137007	−	0.237304i
$46$		0			0
$47$	2.50233	+	0.441228i	0.365002	+	0.0643597i	0.353141	−	0.935570i	$-0.385113\pi$
$47$	2.50233	+	0.441228i	0.365002	+	0.0643597i	0.0118606	+	0.999930i	$0.496225\pi$
$48$		0			0
$49$	4.81151	+	8.33379i	0.687359	+	1.19054i
$50$		0			0
$51$	5.62004	+	4.71578i	0.786964	+	0.660341i
$52$		0			0
$53$	1.47763	+	4.05976i	0.202968	+	0.557651i	0.998857	−	0.0477917i	$-0.0152184\pi$
$53$	1.47763	+	4.05976i	0.202968	+	0.557651i	−0.795889	+	0.605443i	$0.792996\pi$
$54$		0			0
$55$	8.56510	−	1.51026i	1.15492	−	0.203643i
$56$		0			0
$57$	1.65643	−	4.03190i	0.219399	−	0.534039i
$58$		0			0
$59$	−1.29078	−	7.32037i	−0.168045	−	0.953030i	−0.945869	−	0.324548i	$-0.894788\pi$
$59$	−1.29078	−	7.32037i	−0.168045	−	0.953030i	0.777824	−	0.628482i	$-0.216323\pi$
$60$		0			0
$61$	−1.56422	+	0.569328i	−0.200277	+	0.0728950i	−0.440211	−	0.897894i	$-0.645096\pi$
$61$	−1.56422	+	0.569328i	−0.200277	+	0.0728950i	0.239934	+	0.970789i	$0.422874\pi$
$62$		0			0
$63$	2.62073	−	3.12327i	0.330181	−	0.393495i
$64$		0			0
$65$	5.82030	−	3.36035i	0.721919	−	0.416800i
$66$		0			0
$67$	−1.27621	+	7.23775i	−0.155914	+	0.884232i	0.802032	+	0.597282i	$0.203753\pi$
$67$	−1.27621	+	7.23775i	−0.155914	+	0.884232i	−0.957946	+	0.286950i	$0.907359\pi$
$68$		0			0
$69$	−2.76897	−	1.59866i	−0.333345	−	0.192457i
$70$		0			0
$71$	−10.8377	−	3.94458i	−1.28619	−	0.468136i	−0.393717	−	0.919232i	$-0.628811\pi$
$71$	−10.8377	−	3.94458i	−1.28619	−	0.468136i	−0.892476	+	0.451096i	$0.851033\pi$
$72$		0			0
$73$	−8.89269	+	7.46185i	−1.04081	+	0.873344i	−0.992098	−	0.125469i	$-0.959957\pi$
$73$	−8.89269	+	7.46185i	−1.04081	+	0.873344i	−0.0487133	+	0.998813i	$0.515512\pi$
$74$		0			0
$75$	1.62122			0.187202
$76$		0			0
$77$	19.2911			2.19842
$78$		0			0
$79$	−4.80146	+	4.02890i	−0.540206	+	0.453287i	−0.871608	−	0.490203i	$-0.836923\pi$
$79$	−4.80146	+	4.02890i	−0.540206	+	0.453287i	0.331402	+	0.943490i	$0.392478\pi$
$80$		0			0
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$		0			0
$83$	9.06619	+	5.23437i	0.995144	+	0.574547i	0.906808	−	0.421544i	$-0.138512\pi$
$83$	9.06619	+	5.23437i	0.995144	+	0.574547i	0.0883361	+	0.996091i	$0.471845\pi$
$84$		0			0
$85$	2.34173	−	13.2806i	0.253996	−	1.44048i
$86$		0			0
$87$	−2.41997	+	1.39717i	−0.259448	+	0.149792i
$88$		0			0
$89$	3.28025	−	3.90925i	0.347706	−	0.414380i	−0.563640	−	0.826020i	$-0.690600\pi$
$89$	3.28025	−	3.90925i	0.347706	−	0.414380i	0.911346	+	0.411640i	$0.135044\pi$
$90$		0			0
$91$	14.0080	−	5.09848i	1.46843	−	0.534466i
$92$		0			0
$93$	−1.21284	−	6.87837i	−0.125766	−	0.713254i
$94$		0			0
$95$	−7.94069	+	1.06878i	−0.814698	+	0.109654i
$96$		0			0
$97$	−18.6216	+	3.28349i	−1.89074	+	0.333388i	−0.994019	−	0.109211i	$-0.965168\pi$
$97$	−18.6216	+	3.28349i	−1.89074	+	0.333388i	−0.896720	+	0.442599i	$0.854057\pi$
$98$		0			0
$99$	−1.61828	−	4.44618i	−0.162643	−	0.446858i
$100$		0			0
$101$	9.11743	+	7.65043i	0.907218	+	0.761246i	0.971588	−	0.236680i	$-0.0760593\pi$
$101$	9.11743	+	7.65043i	0.907218	+	0.761246i	−0.0643697	+	0.997926i	$0.520504\pi$
$102$		0			0
$103$	9.60509	+	16.6365i	0.946418	+	1.63924i	0.752888	+	0.658149i	$0.228660\pi$
$103$	9.60509	+	16.6365i	0.946418	+	1.63924i	0.193530	+	0.981094i	$0.438006\pi$
$104$		0			0
$105$	−7.38052	−	1.30138i	−0.720265	−	0.127002i
$106$		0			0
$107$	−3.71502	+	6.43460i	−0.359144	+	0.622056i	−0.987818	−	0.155613i	$-0.950265\pi$
$107$	−3.71502	+	6.43460i	−0.359144	+	0.622056i	0.628674	+	0.777669i	$0.283598\pi$
$108$		0			0
$109$	−0.142283	+	0.390920i	−0.0136283	+	0.0374433i	−0.946320	−	0.323231i	$-0.895231\pi$
$109$	−0.142283	+	0.390920i	−0.0136283	+	0.0374433i	0.932692	+	0.360674i	$0.117453\pi$
$110$		0			0
$111$	3.52959	+	4.20640i	0.335014	+	0.399254i
$112$		0			0
$113$			21.0068i			1.97615i	0.153971	+	0.988075i	$0.450794\pi$
$113$			21.0068i			1.97615i	−0.153971	+	0.988075i	$0.549206\pi$
$114$		0			0
$115$			5.87716i			0.548048i
$116$		0			0
$117$	−2.35018	−	2.80084i	−0.217275	−	0.258938i
$118$		0			0
$119$	10.2304	−	28.1078i	0.937819	−	2.57664i
$120$		0			0
$121$	5.69365	−	9.86170i	0.517605	−	0.896518i
$122$		0			0
$123$	−5.53676	−	0.976280i	−0.499233	−	0.0880282i
$124$		0			0
$125$	−6.08538	−	10.5402i	−0.544293	−	0.942744i
$126$		0			0
$127$	−11.1708	−	9.37341i	−0.991248	−	0.831756i	−0.00550011	−	0.999985i	$-0.501751\pi$
$127$	−11.1708	−	9.37341i	−0.991248	−	0.831756i	−0.985748	+	0.168229i	$0.946195\pi$
$128$		0			0
$129$	2.83629	+	7.79265i	0.249722	+	0.686104i
$130$		0			0
$131$	−6.98149	+	1.23102i	−0.609975	+	0.107555i	−0.470099	−	0.882614i	$-0.655782\pi$
$131$	−6.98149	+	1.23102i	−0.609975	+	0.107555i	−0.139877	+	0.990169i	$0.544671\pi$
$132$		0			0
$133$	−17.7571	−	0.723859i	−1.53973	−	0.0627665i
$134$		0			0
$135$	0.319191	+	1.81022i	0.0274716	+	0.155799i
$136$		0			0
$137$	−8.49957	+	3.09359i	−0.726167	+	0.264303i	−0.678542	−	0.734562i	$-0.737388\pi$
$137$	−8.49957	+	3.09359i	−0.726167	+	0.264303i	−0.0476257	+	0.998865i	$0.515165\pi$
$138$		0			0
$139$	−3.70726	+	4.41814i	−0.314446	+	0.374742i	−0.899999	−	0.435892i	$-0.856433\pi$
$139$	−3.70726	+	4.41814i	−0.314446	+	0.374742i	0.585553	+	0.810634i	$0.300877\pi$
$140$		0			0
$141$	−2.20051	+	1.27047i	−0.185316	+	0.106992i
$142$		0			0
$143$	3.00404	−	17.0367i	0.251210	−	1.42468i
$144$		0			0
$145$	4.44826	+	2.56821i	0.369408	+	0.213278i
$146$		0			0
$147$	−9.04269	−	3.29127i	−0.745828	−	0.271459i
$148$		0			0
$149$	14.9736	−	12.5643i	1.22668	−	1.02931i	0.228236	−	0.973606i	$-0.426704\pi$
$149$	14.9736	−	12.5643i	1.22668	−	1.02931i	0.998447	−	0.0557036i	$-0.0177402\pi$
$150$		0			0
$151$	−11.6558			−0.948535			−0.474268	−	0.880381i	$-0.657287\pi$
$151$	−11.6558			−0.948535			−0.474268	+	0.880381i	$0.657287\pi$
$152$		0			0
$153$	−7.33645			−0.593117
$154$		0			0
$155$	−9.83486	+	8.25243i	−0.789955	+	0.662851i
$156$		0			0
$157$	−15.0799	−	5.48865i	−1.20351	−	0.438042i	−0.339062	−	0.940764i	$-0.610110\pi$
$157$	−15.0799	−	5.48865i	−1.20351	−	0.438042i	−0.864448	+	0.502722i	$0.832332\pi$
$158$		0			0
$159$	−3.74149	−	2.16015i	−0.296720	−	0.171311i
$160$		0			0
$161$	−2.26367	+	12.8379i	−0.178402	+	1.01177i
$162$		0			0
$163$	−8.50637	+	4.91116i	−0.666271	+	0.384671i	−0.794662	−	0.607052i	$-0.792352\pi$
$163$	−8.50637	+	4.91116i	−0.666271	+	0.384671i	0.128391	+	0.991724i	$0.459019\pi$
$164$		0			0
$165$	−5.59047	+	6.66247i	−0.435218	+	0.518672i
$166$		0			0
$167$	−1.84031	+	0.669818i	−0.142408	+	0.0518321i	−0.412241	−	0.911075i	$-0.635254\pi$
$167$	−1.84031	+	0.669818i	−0.142408	+	0.0518321i	0.269833	+	0.962907i	$0.413031\pi$
$168$		0			0
$169$	−0.0639138	−	0.362473i	−0.00491645	−	0.0278826i
$170$		0			0
$171$	1.32276	+	4.15335i	0.101154	+	0.317615i
$172$		0			0
$173$	2.54788	−	0.449259i	0.193711	−	0.0341565i	−0.0759506	−	0.997112i	$-0.524199\pi$
$173$	2.54788	−	0.449259i	0.193711	−	0.0341565i	0.269662	+	0.962955i	$0.413088\pi$
$174$		0			0
$175$	−2.26073	−	6.21129i	−0.170895	−	0.469530i
$176$		0			0
$177$	5.69423	+	4.77803i	0.428005	+	0.359139i
$178$		0			0
$179$	−9.63364	−	16.6860i	−0.720052	−	1.24717i	−0.960978	−	0.276623i	$-0.910785\pi$
$179$	−9.63364	−	16.6860i	−0.720052	−	1.24717i	0.240926	−	0.970543i	$-0.422549\pi$
$180$		0			0
$181$	10.3435	+	1.82383i	0.768824	+	0.135564i	0.544284	−	0.838901i	$-0.316801\pi$
$181$	10.3435	+	1.82383i	0.768824	+	0.135564i	0.224539	+	0.974465i	$0.427912\pi$
$182$		0			0
$183$	0.832302	−	1.44159i	0.0615255	−	0.106565i
$184$		0			0
$185$	3.45214	−	9.48468i	0.253806	−	0.697327i
$186$		0			0
$187$	−22.3128	−	26.5914i	−1.63167	−	1.94455i
$188$		0			0
$189$			4.07713i			0.296568i
$190$		0			0
$191$		−	12.2829i		−	0.888761i	−0.895838	−	0.444380i	$-0.853424\pi$
$191$		−	12.2829i		−	0.888761i	0.895838	−	0.444380i	$-0.146576\pi$
$192$		0			0
$193$	7.18476	+	8.56246i	0.517170	+	0.616340i	0.959909	−	0.280311i	$-0.0904376\pi$
$193$	7.18476	+	8.56246i	0.517170	+	0.616340i	−0.442739	+	0.896651i	$0.645993\pi$
$194$		0			0
$195$	−2.29861	+	6.31539i	−0.164607	+	0.452255i
$196$		0			0
$197$	10.6625	−	18.4680i	0.759673	−	1.31579i	−0.183344	−	0.983049i	$-0.558692\pi$
$197$	10.6625	−	18.4680i	0.759673	−	1.31579i	0.943017	−	0.332744i	$-0.107974\pi$
$198$		0			0
$199$	4.31247	+	0.760404i	0.305703	+	0.0539036i	0.324395	−	0.945922i	$-0.394839\pi$
$199$	4.31247	+	0.760404i	0.305703	+	0.0539036i	−0.0186926	+	0.999825i	$0.505950\pi$
$200$		0			0
$201$	−3.67470	−	6.36477i	−0.259193	−	0.448936i
$202$		0			0
$203$	8.72747	+	7.32322i	0.612549	+	0.513989i
$204$		0			0
$205$	3.53457	+	9.71114i	0.246865	+	0.678255i
$206$		0			0
$207$	3.14876	−	0.555210i	0.218854	−	0.0385898i
$208$		0			0
$209$	−11.0311	+	17.4263i	−0.763034	+	1.20540i
$210$		0			0
$211$	−2.19387	−	12.4421i	−0.151032	−	0.856546i	−0.962324	−	0.271905i	$-0.912346\pi$
$211$	−2.19387	−	12.4421i	−0.151032	−	0.856546i	0.811292	−	0.584641i	$-0.198765\pi$
$212$		0			0
$213$	10.8377	−	3.94458i	0.742584	−	0.270278i
$214$		0			0
$215$	9.79821	−	11.6771i	0.668233	−	0.796369i
$216$		0			0
$217$	−24.6615	+	14.2383i	−1.67413	+	0.966561i
$218$		0			0
$219$	2.01581	−	11.4322i	0.136216	−	0.772518i
$220$		0			0
$221$	−23.2301	−	13.4119i	−1.56262	−	0.902181i
$222$		0			0
$223$	2.88971	+	1.05177i	0.193509	+	0.0704317i	0.436957	−	0.899482i	$-0.356056\pi$
$223$	2.88971	+	1.05177i	0.193509	+	0.0704317i	−0.243448	+	0.969914i	$0.578278\pi$
$224$		0			0
$225$	−1.24192	+	1.04210i	−0.0827949	+	0.0694732i
$226$		0			0
$227$	2.58324			0.171456			0.0857279	−	0.996319i	$-0.472678\pi$
$227$	2.58324			0.171456			0.0857279	+	0.996319i	$0.472678\pi$
$228$		0			0
$229$	−2.90299			−0.191835			−0.0959174	−	0.995389i	$-0.530578\pi$
$229$	−2.90299			−0.191835			−0.0959174	+	0.995389i	$0.530578\pi$
$230$		0			0
$231$	−14.7778	+	12.4001i	−0.972308	+	0.815864i
$232$		0			0
$233$	27.1395	+	9.87799i	1.77797	+	0.647128i	0.999818	+	0.0190525i	$0.00606495\pi$
$233$	27.1395	+	9.87799i	1.77797	+	0.647128i	0.778152	+	0.628076i	$0.216157\pi$
$234$		0			0
$235$	4.04486	+	2.33530i	0.263858	+	0.152338i
$236$		0			0
$237$	1.08840	−	6.17263i	0.0706993	−	0.400956i
$238$		0			0
$239$	4.37034	−	2.52322i	0.282694	−	0.163213i	−0.351948	−	0.936019i	$-0.614481\pi$
$239$	4.37034	−	2.52322i	0.282694	−	0.163213i	0.634642	+	0.772806i	$0.281147\pi$
$240$		0			0
$241$	3.06344	−	3.65087i	0.197334	−	0.235173i	−0.658299	−	0.752756i	$-0.728724\pi$
$241$	3.06344	−	3.65087i	0.197334	−	0.235173i	0.855633	+	0.517583i	$0.173168\pi$
$242$		0			0
$243$	0.939693	−	0.342020i	0.0602813	−	0.0219406i
$244$		0			0
$245$	3.07158	+	17.4198i	0.196236	+	1.11291i
$246$		0			0
$247$	−3.40443	+	15.5693i	−0.216619	+	0.990651i
$248$		0			0
$249$	−10.3097	+	1.81788i	−0.653350	+	0.115203i
$250$		0			0
$251$	−1.92021	−	5.27574i	−0.121203	−	0.333002i	0.864223	−	0.503109i	$-0.167811\pi$
$251$	−1.92021	−	5.27574i	−0.121203	−	0.333002i	−0.985426	+	0.170107i	$0.945589\pi$
$252$		0			0
$253$	11.5889	+	9.72424i	0.728588	+	0.611358i
$254$		0			0
$255$	6.74273	+	11.6788i	0.422246	+	0.731352i
$256$		0			0
$257$	−15.1355	−	2.66880i	−0.944128	−	0.166475i	−0.319666	−	0.947530i	$-0.603571\pi$
$257$	−15.1355	−	2.66880i	−0.944128	−	0.166475i	−0.624462	+	0.781055i	$0.714682\pi$
$258$		0			0
$259$	11.1939	−	19.3884i	0.695556	−	1.20474i
$260$		0			0
$261$	0.955721	−	2.62582i	0.0591577	−	0.162534i
$262$		0			0
$263$	−2.96235	−	3.53039i	−0.182666	−	0.217693i	0.666939	−	0.745112i	$-0.267604\pi$
$263$	−2.96235	−	3.53039i	−0.182666	−	0.217693i	−0.849605	+	0.527419i	$0.823160\pi$
$264$		0			0
$265$			7.94136i			0.487834i
$266$		0			0
$267$			5.10317i			0.312309i
$268$		0			0
$269$	−8.22859	−	9.80645i	−0.501706	−	0.597910i	0.454448	−	0.890773i	$-0.349836\pi$
$269$	−8.22859	−	9.80645i	−0.501706	−	0.597910i	−0.956154	+	0.292863i	$0.905392\pi$
$270$		0			0
$271$	−4.87308	+	13.3887i	−0.296018	+	0.813304i	0.699137	+	0.714988i	$0.253568\pi$
$271$	−4.87308	+	13.3887i	−0.296018	+	0.813304i	−0.995155	+	0.0983160i	$0.968654\pi$
$272$		0			0
$273$	−7.45348	+	12.9098i	−0.451105	+	0.781337i
$274$		0			0
$275$	−7.55429	−	1.33202i	−0.455541	−	0.0803241i
$276$		0			0
$277$	8.25597	+	14.2998i	0.496053	+	0.859189i	0.999990	−	0.00455149i	$-0.00144879\pi$
$277$	8.25597	+	14.2998i	0.496053	+	0.859189i	−0.503937	+	0.863741i	$0.668115\pi$
$278$		0			0
$279$	5.35042	+	4.48954i	0.320321	+	0.268782i
$280$		0			0
$281$	−2.64737	−	7.27360i	−0.157929	−	0.433907i	0.835340	−	0.549733i	$-0.185271\pi$
$281$	−2.64737	−	7.27360i	−0.157929	−	0.433907i	−0.993269	+	0.115826i	$0.963048\pi$
$282$		0			0
$283$	−15.7281	+	2.77329i	−0.934939	+	0.164855i	−0.620307	−	0.784359i	$-0.712992\pi$
$283$	−15.7281	+	2.77329i	−0.934939	+	0.164855i	−0.314632	+	0.949214i	$0.601881\pi$
$284$		0			0
$285$	5.39593	−	5.92291i	0.319627	−	0.350843i
$286$		0			0
$287$	3.98043	+	22.5741i	0.234957	+	1.33251i
$288$		0			0
$289$	−34.6027	+	12.5944i	−2.03545	+	0.740845i
$290$		0			0
$291$	12.1544	−	14.4850i	0.712503	−	0.849128i
$292$		0			0
$293$	−9.96878	+	5.75548i	−0.582383	+	0.336239i	−0.762080	−	0.647483i	$-0.775822\pi$
$293$	−9.96878	+	5.75548i	−0.582383	+	0.336239i	0.179697	+	0.983722i	$0.442488\pi$
$294$		0			0
$295$	2.37264	−	13.4559i	0.138140	−	0.783433i
$296$		0			0
$297$	4.09762	+	2.36576i	0.237768	+	0.137275i
$298$		0			0
$299$	10.9852	+	3.99828i	0.635290	+	0.231227i
$300$		0			0
$301$	25.9005	−	21.7331i	1.49288	−	1.25268i
$302$		0			0
$303$	−11.9020			−0.683750
$304$		0			0
$305$	−3.05979			−0.175203
$306$		0			0
$307$	1.01161	−	0.848845i	0.0577358	−	0.0484461i	−0.613463	−	0.789723i	$-0.710224\pi$
$307$	1.01161	−	0.848845i	0.0577358	−	0.0484461i	0.671199	+	0.741277i	$0.265780\pi$
$308$		0			0
$309$	−18.0517	−	6.57027i	−1.02692	−	0.373770i
$310$		0			0
$311$	−12.9899	−	7.49975i	−0.736592	−	0.425272i	0.0842369	−	0.996446i	$-0.473155\pi$
$311$	−12.9899	−	7.49975i	−0.736592	−	0.425272i	−0.820829	+	0.571174i	$0.806488\pi$
$312$		0			0
$313$	5.74417	−	32.5768i	0.324680	−	1.84135i	−0.187238	−	0.982315i	$-0.559954\pi$
$313$	5.74417	−	32.5768i	0.324680	−	1.84135i	0.511917	−	0.859035i	$-0.328935\pi$
$314$		0			0
$315$	6.49032	−	3.74719i	0.365688	−	0.211130i
$316$		0			0
$317$	6.96764	−	8.30371i	0.391342	−	0.466383i	−0.534018	−	0.845473i	$-0.679319\pi$
$317$	6.96764	−	8.30371i	0.391342	−	0.466383i	0.925360	+	0.379090i	$0.123763\pi$
$318$		0			0
$319$	12.4241	−	4.52202i	0.695618	−	0.253184i
$320$		0			0
$321$	−1.29021	−	7.31716i	−0.0720126	−	0.408404i
$322$		0			0
$323$	19.5407	+	25.3141i	1.08728	+	1.40852i
$324$		0			0
$325$	−5.83750	+	1.02931i	−0.323806	+	0.0570958i
$326$		0			0
$327$	−0.142283	−	0.390920i	−0.00786828	−	0.0216179i
$328$		0			0
$329$	7.93600	+	6.65910i	0.437526	+	0.367128i
$330$		0			0
$331$	7.54595	+	13.0700i	0.414763	+	0.718391i	0.995404	−	0.0957693i	$-0.0305311\pi$
$331$	7.54595	+	13.0700i	0.414763	+	0.718391i	−0.580640	+	0.814160i	$0.697198\pi$
$332$		0			0
$333$	−5.40764	−	0.953514i	−0.296337	−	0.0522522i
$334$		0			0
$335$	−6.75464	+	11.6994i	−0.369045	+	0.639205i
$336$		0			0
$337$	9.78505	−	26.8842i	0.533026	−	1.46448i	−0.322427	−	0.946594i	$-0.604499\pi$
$337$	9.78505	−	26.8842i	0.533026	−	1.46448i	0.855452	−	0.517882i	$-0.173279\pi$
$338$		0			0
$339$	−13.5029	−	16.0921i	−0.733376	−	0.874004i
$340$		0			0
$341$			33.0472i			1.78961i
$342$		0			0
$343$			10.6944i			0.577446i
$344$		0			0
$345$	−3.77777	−	4.50217i	−0.203388	−	0.242388i
$346$		0			0
$347$	1.17187	−	3.21970i	0.0629095	−	0.172842i	−0.904255	−	0.426992i	$-0.859573\pi$
$347$	1.17187	−	3.21970i	0.0629095	−	0.172842i	0.967165	+	0.254150i	$0.0817955\pi$
$348$		0			0
$349$	4.29104	−	7.43229i	0.229694	−	0.397841i	−0.728024	−	0.685552i	$-0.759561\pi$
$349$	4.29104	−	7.43229i	0.229694	−	0.397841i	0.957717	+	0.287711i	$0.0928942\pi$
$350$		0			0
$351$	3.60069	+	0.634899i	0.192191	+	0.0338884i
$352$		0			0
$353$	7.62161	+	13.2010i	0.405657	+	0.702619i	0.994398	−	0.105703i	$-0.0337093\pi$
$353$	7.62161	+	13.2010i	0.405657	+	0.702619i	−0.588740	+	0.808322i	$0.700376\pi$
$354$		0			0
$355$	−16.2399	−	13.6269i	−0.861925	−	0.723241i
$356$		0			0
$357$	10.2304	+	28.1078i	0.541450	+	1.48762i
$358$		0			0
$359$	−12.6719	+	2.23440i	−0.668798	+	0.117927i	−0.497730	−	0.867332i	$-0.665833\pi$
$359$	−12.6719	+	2.23440i	−0.668798	+	0.117927i	−0.171068	+	0.985259i	$0.554722\pi$
$360$		0			0
$361$	10.8078	−	15.6266i	0.568830	−	0.822455i
$362$		0			0
$363$	1.97739	+	11.2143i	0.103786	+	0.588599i
$364$		0			0
$365$	−20.0514	+	7.29812i	−1.04954	+	0.382001i
$366$		0			0
$367$	12.9549	−	15.4391i	0.676243	−	0.805914i	−0.313377	−	0.949629i	$-0.601460\pi$
$367$	12.9549	−	15.4391i	0.676243	−	0.805914i	0.989619	+	0.143714i	$0.0459047\pi$
$368$		0			0
$369$	4.86895	−	2.81109i	0.253467	−	0.146339i
$370$		0			0
$371$	−3.05872	+	17.3469i	−0.158801	+	0.900604i
$372$		0			0
$373$	2.75415	+	1.59011i	0.142605	+	0.0823329i	0.569605	−	0.821919i	$-0.307096\pi$
$373$	2.75415	+	1.59011i	0.142605	+	0.0823329i	−0.427000	+	0.904252i	$0.640430\pi$
$374$		0			0
$375$	11.4368	+	4.16265i	0.590593	+	0.214958i
$376$		0			0
$377$	7.82650	−	6.56722i	0.403085	−	0.338229i
$378$		0			0
$379$	10.9402			0.561962			0.280981	−	0.959713i	$-0.409340\pi$
$379$	10.9402			0.561962			0.280981	+	0.959713i	$0.409340\pi$
$380$		0			0
$381$	14.5824			0.747081
$382$		0			0
$383$	−4.15795	+	3.48894i	−0.212461	+	0.178276i	−0.742808	−	0.669505i	$-0.766506\pi$
$383$	−4.15795	+	3.48894i	−0.212461	+	0.178276i	0.530346	+	0.847781i	$0.322062\pi$
$384$		0			0
$385$	33.3213	+	12.1280i	1.69821	+	0.618098i
$386$		0			0
$387$	−7.18174	−	4.14638i	−0.365068	−	0.210772i
$388$		0			0
$389$	−1.21296	+	6.87901i	−0.0614993	+	0.348780i	0.938495	+	0.345294i	$0.112221\pi$
$389$	−1.21296	+	6.87901i	−0.0614993	+	0.348780i	−0.999994	+	0.00348603i	$0.998890\pi$
$390$		0			0
$391$	20.3144	−	11.7285i	1.02734	−	0.593137i
$392$		0			0
$393$	4.55684	−	5.43063i	0.229862	−	0.273939i
$394$		0			0
$395$	−10.8264	+	3.94050i	−0.544737	+	0.198268i
$396$		0			0
$397$	4.87620	+	27.6543i	0.244729	+	1.38793i	0.821121	+	0.570755i	$0.193349\pi$
$397$	4.87620	+	27.6543i	0.244729	+	1.38793i	−0.576391	+	0.817174i	$0.695540\pi$
$398$		0			0
$399$	14.0680	−	10.8595i	0.704281	−	0.543656i
$400$		0			0
$401$	1.59722	−	0.281633i	0.0797614	−	0.0140641i	−0.133625	−	0.991032i	$-0.542662\pi$
$401$	1.59722	−	0.281633i	0.0797614	−	0.0140641i	0.213386	+	0.976968i	$0.431551\pi$
$402$		0			0
$403$	8.73414	+	23.9969i	0.435079	+	1.19537i
$404$		0			0
$405$	−1.40810	−	1.18154i	−0.0699692	−	0.0587111i
$406$		0			0
$407$	−12.9906	−	22.5003i	−0.643918	−	1.11530i
$408$		0			0
$409$	−4.20396	−	0.741272i	−0.207872	−	0.0366535i	0.0687422	−	0.997634i	$-0.478101\pi$
$409$	−4.20396	−	0.741272i	−0.207872	−	0.0366535i	−0.276615	+	0.960981i	$0.589213\pi$
$410$		0			0
$411$	4.52253	−	7.83325i	0.223080	−	0.386386i
$412$		0			0
$413$	10.3654	−	28.4788i	0.510050	−	1.40135i
$414$		0			0
$415$	12.3692	+	14.7411i	0.607181	+	0.723610i
$416$		0			0
$417$		−	5.76748i		−	0.282435i
$418$		0			0
$419$		−	5.93004i		−	0.289702i	−0.989454	−	0.144851i	$-0.953730\pi$
$419$		−	5.93004i		−	0.289702i	0.989454	−	0.144851i	$-0.0462702\pi$
$420$		0			0
$421$	−22.7312	−	27.0900i	−1.10785	−	1.32028i	−0.942559	−	0.334040i	$-0.891588\pi$
$421$	−22.7312	−	27.0900i	−1.10785	−	1.32028i	−0.165291	−	0.986245i	$-0.552856\pi$
$422$		0			0
$423$	0.869049	−	2.38769i	0.0422546	−	0.116094i
$424$		0			0
$425$	−5.94698	+	10.3005i	−0.288471	+	0.499647i
$426$		0			0
$427$	−6.68371	−	1.17852i	−0.323447	−	0.0570325i
$428$		0			0
$429$	8.64978	+	14.9819i	0.417615	+	0.723331i
$430$		0			0
$431$	−17.2731	−	14.4938i	−0.832014	−	0.698143i	0.123738	−	0.992315i	$-0.460512\pi$
$431$	−17.2731	−	14.4938i	−0.832014	−	0.698143i	−0.955752	+	0.294172i	$0.904956\pi$
$432$		0			0
$433$	7.31214	+	20.0899i	0.351399	+	0.965460i	0.981921	+	0.189289i	$0.0606184\pi$
$433$	7.31214	+	20.0899i	0.351399	+	0.965460i	−0.630523	+	0.776171i	$0.717159\pi$
$434$		0			0
$435$	−5.05838	+	0.891928i	−0.242531	+	0.0427647i
$436$		0			0
$437$	−10.3025	−	9.38584i	−0.492835	−	0.448986i
$438$		0			0
$439$	1.47508	+	8.36560i	0.0704018	+	0.399268i	0.999562	+	0.0295913i	$0.00942058\pi$
$439$	1.47508	+	8.36560i	0.0704018	+	0.399268i	−0.929160	+	0.369677i	$0.879468\pi$
$440$		0			0
$441$	9.04269	−	3.29127i	0.430604	−	0.156727i
$442$		0			0
$443$	−18.5995	+	22.1661i	−0.883690	+	1.05314i	0.114525	+	0.993420i	$0.463465\pi$
$443$	−18.5995	+	22.1661i	−0.883690	+	1.05314i	−0.998215	+	0.0597208i	$0.980979\pi$
$444$		0			0
$445$	8.12364	−	4.69019i	0.385098	−	0.222336i
$446$		0			0
$447$	−3.39423	+	19.2497i	−0.160542	+	0.910478i
$448$		0			0
$449$	3.47097	+	2.00397i	0.163805	+	0.0945730i	0.579662	−	0.814857i	$-0.303185\pi$
$449$	3.47097	+	2.00397i	0.163805	+	0.0945730i	−0.415856	+	0.909430i	$0.636518\pi$
$450$		0			0
$451$	24.9972	+	9.09823i	1.17707	+	0.428419i
$452$		0			0
$453$	8.92886	−	7.49220i	0.419514	−	0.352014i
$454$		0			0
$455$	27.4012			1.28459
$456$		0			0
$457$	19.0274			0.890063			0.445031	−	0.895515i	$-0.353193\pi$
$457$	19.0274			0.890063			0.445031	+	0.895515i	$0.353193\pi$
$458$		0			0
$459$	5.62004	−	4.71578i	0.262321	−	0.220114i
$460$		0			0
$461$	−8.06408	−	2.93509i	−0.375582	−	0.136701i	0.147330	−	0.989087i	$-0.452932\pi$
$461$	−8.06408	−	2.93509i	−0.375582	−	0.136701i	−0.522912	+	0.852387i	$0.675154\pi$
$462$		0			0
$463$	−0.851568	−	0.491653i	−0.0395757	−	0.0228491i	0.480082	−	0.877224i	$-0.340607\pi$
$463$	−0.851568	−	0.491653i	−0.0395757	−	0.0228491i	−0.519657	+	0.854375i	$0.673940\pi$
$464$		0			0
$465$	2.22938	−	12.6435i	0.103385	−	0.586326i
$466$		0			0
$467$	−2.95759	+	1.70757i	−0.136861	+	0.0790167i	−0.566867	−	0.823809i	$-0.691845\pi$
$467$	−2.95759	+	1.70757i	−0.136861	+	0.0790167i	0.430006	+	0.902826i	$0.358511\pi$
$468$		0			0
$469$	−19.2608	+	22.9541i	−0.889382	+	1.05992i
$470$		0			0
$471$	15.0799	−	5.48865i	0.694847	−	0.252904i
$472$		0			0
$473$	−6.81350	−	38.6413i	−0.313285	−	1.77673i
$474$		0			0
$475$	6.90360	+	1.50956i	0.316759	+	0.0692636i
$476$		0			0
$477$	4.25467	−	0.750213i	0.194808	−	0.0343499i
$478$		0			0
$479$	12.8646	+	35.3452i	0.587798	+	1.61496i	0.774520	+	0.632549i	$0.217991\pi$
$479$	12.8646	+	35.3452i	0.587798	+	1.61496i	−0.186722	+	0.982413i	$0.559786\pi$
$480$		0			0
$481$	−15.3796	−	12.9050i	−0.701249	−	0.588418i
$482$		0			0
$483$	−6.51797	−	11.2895i	−0.296578	−	0.513688i
$484$		0			0
$485$	−34.2293	−	6.03554i	−1.55427	−	0.274060i
$486$		0			0
$487$	8.47341	−	14.6764i	0.383967	−	0.665050i	−0.607658	−	0.794198i	$-0.707891\pi$
$487$	8.47341	−	14.6764i	0.383967	−	0.665050i	0.991625	+	0.129148i	$0.0412244\pi$
$488$		0			0
$489$	3.35943	−	9.22996i	0.151919	−	0.417393i
$490$		0			0
$491$	13.2092	+	15.7421i	0.596122	+	0.710430i	0.976770	−	0.214289i	$-0.0687436\pi$
$491$	13.2092	+	15.7421i	0.596122	+	0.710430i	−0.380648	+	0.924720i	$0.624299\pi$
$492$		0			0
$493$		−	20.5005i		−	0.923298i
$494$		0			0
$495$		−	8.69723i		−	0.390912i
$496$		0			0
$497$	−30.2254	−	36.0212i	−1.35579	−	1.61577i
$498$		0			0
$499$	−6.08829	+	16.7274i	−0.272549	+	0.748823i	0.725606	+	0.688110i	$0.241559\pi$
$499$	−6.08829	+	16.7274i	−0.272549	+	0.748823i	−0.998155	+	0.0607125i	$0.980663\pi$
$500$		0			0
$501$	0.979209	−	1.69604i	0.0437478	−	0.0757735i
$502$		0			0
$503$	−15.4326	−	2.72119i	−0.688106	−	0.121332i	−0.181347	−	0.983419i	$-0.558046\pi$
$503$	−15.4326	−	2.72119i	−0.688106	−	0.121332i	−0.506760	+	0.862087i	$0.669157\pi$
$504$		0			0
$505$	10.9388	+	18.9465i	0.486769	+	0.843108i
$506$		0			0
$507$	0.281954	+	0.236588i	0.0125220	+	0.0105072i
$508$		0			0
$509$	−12.2977	−	33.7878i	−0.545088	−	1.49762i	−0.840266	−	0.542174i	$-0.817601\pi$
$509$	−12.2977	−	33.7878i	−0.545088	−	1.49762i	0.295178	−	0.955442i	$-0.404621\pi$
$510$		0			0
$511$	−46.6107	+	8.21873i	−2.06194	+	0.363575i
$512$		0			0
$513$	−3.68301	−	2.33140i	−0.162609	−	0.102934i
$514$		0			0
$515$	6.13171	+	34.7747i	0.270196	+	1.53236i
$516$		0			0
$517$	11.2974	−	4.11193i	0.496860	−	0.180842i
$518$		0			0
$519$	−1.66301	+	1.98190i	−0.0729979	+	0.0869955i
$520$		0			0
$521$	26.3261	−	15.1994i	1.15337	−	0.665897i	0.203662	−	0.979041i	$-0.434716\pi$
$521$	26.3261	−	15.1994i	1.15337	−	0.665897i	0.949706	+	0.313144i	$0.101382\pi$
$522$		0			0
$523$	−6.48850	+	36.7981i	−0.283722	+	1.60907i	0.426091	+	0.904680i	$0.359890\pi$
$523$	−6.48850	+	36.7981i	−0.283722	+	1.60907i	−0.709813	+	0.704390i	$0.751221\pi$
$524$		0			0
$525$	5.72436	+	3.30496i	0.249831	+	0.144240i
$526$		0			0
$527$	48.1510	+	17.5255i	2.09749	+	0.763425i
$528$		0			0
$529$	9.78781	−	8.21295i	0.425557	−	0.357085i
$530$		0			0
$531$	−7.43329			−0.322577
$532$		0			0
$533$	20.5560			0.890379
$534$		0			0
$535$	−10.4622	+	8.77887i	−0.452322	+	0.379544i
$536$		0			0
$537$	18.1053	+	6.58980i	0.781302	+	0.284371i
$538$		0			0
$539$	39.4315	+	22.7658i	1.69844	+	0.980592i
$540$		0			0
$541$	2.44100	−	13.8436i	0.104947	−	0.595184i	−0.886295	−	0.463122i	$-0.846729\pi$
$541$	2.44100	−	13.8436i	0.104947	−	0.595184i	0.991241	−	0.132062i	$-0.0421597\pi$
$542$		0			0
$543$	−9.09589	+	5.25151i	−0.390342	+	0.225364i
$544$		0			0
$545$	−0.491530	+	0.585782i	−0.0210548	+	0.0250921i
$546$		0			0
$547$	0.851203	−	0.309812i	0.0363948	−	0.0132466i	−0.323759	−	0.946140i	$-0.604947\pi$
$547$	0.851203	−	0.309812i	0.0363948	−	0.0132466i	0.360153	+	0.932893i	$0.382724\pi$
$548$		0			0
$549$	0.289055	+	1.63931i	0.0123366	+	0.0699642i
$550$		0			0
$551$	−11.6059	+	3.69624i	−0.494427	+	0.157465i
$552$		0			0
$553$	−25.1667	+	4.43756i	−1.07020	+	0.188704i
$554$		0			0
$555$	3.45214	+	9.48468i	0.146535	+	0.402602i
$556$		0			0
$557$	3.13462	+	2.63026i	0.132818	+	0.111448i	0.706777	−	0.707437i	$-0.250149\pi$
$557$	3.13462	+	2.63026i	0.132818	+	0.111448i	−0.573959	+	0.818884i	$0.694593\pi$
$558$		0			0
$559$	−15.1601	−	26.2581i	−0.641206	−	1.11060i
$560$		0			0
$561$	34.1852	+	6.02777i	1.44330	+	0.254493i
$562$		0			0
$563$	−9.86884	+	17.0933i	−0.415922	+	0.720398i	−0.995525	−	0.0945013i	$-0.969874\pi$
$563$	−9.86884	+	17.0933i	−0.415922	+	0.720398i	0.579603	+	0.814899i	$0.303208\pi$
$564$		0			0
$565$	−13.2066	+	36.2848i	−0.555606	+	1.52651i
$566$		0			0
$567$	−2.62073	−	3.12327i	−0.110060	−	0.131165i
$568$		0			0
$569$			18.8488i			0.790181i	0.918642	+	0.395091i	$0.129287\pi$
$569$			18.8488i			0.790181i	−0.918642	+	0.395091i	$0.870713\pi$
$570$		0			0
$571$		−	14.4967i		−	0.606668i	−0.952884	−	0.303334i	$-0.901900\pi$
$571$		−	14.4967i		−	0.606668i	0.952884	−	0.303334i	$-0.0980997\pi$
$572$		0			0
$573$	7.89531	+	9.40926i	0.329831	+	0.393078i
$574$		0			0
$575$	1.77288	−	4.87096i	0.0739343	−	0.203133i
$576$		0			0
$577$	−10.7961	+	18.6993i	−0.449446	+	0.778464i	−0.998350	−	0.0574219i	$-0.981712\pi$
$577$	−10.7961	+	18.6993i	−0.449446	+	0.778464i	0.548904	+	0.835885i	$0.315045\pi$
$578$		0			0
$579$	−11.0077	−	1.94095i	−0.457464	−	0.0806632i
$580$		0			0
$581$	21.3412	+	36.9641i	0.885383	+	1.53353i
$582$		0			0
$583$	15.6592	+	13.1396i	0.648538	+	0.544188i
$584$		0			0
$585$	−2.29861	−	6.31539i	−0.0950360	−	0.261109i
$586$		0			0
$587$	35.4468	−	6.25023i	1.46305	−	0.257974i	0.615265	−	0.788321i	$-0.289049\pi$
$587$	35.4468	−	6.25023i	1.46305	−	0.257974i	0.847781	+	0.530346i	$0.177938\pi$
$588$		0			0
$589$	1.24003	−	30.4194i	0.0510946	−	1.25341i
$590$		0			0
$591$	3.70305	+	21.0011i	0.152323	+	0.863868i
$592$		0			0
$593$	−39.8806	+	14.5154i	−1.63770	+	0.596074i	−0.986635	−	0.162947i	$-0.947900\pi$
$593$	−39.8806	+	14.5154i	−1.63770	+	0.596074i	−0.651066	+	0.759021i	$0.725678\pi$
$594$		0			0
$595$	35.3418	−	42.1187i	1.44887	−	1.72670i
$596$		0			0
$597$	−3.79232	+	2.18950i	−0.155209	+	0.0896101i
$598$		0			0
$599$	8.04771	−	45.6408i	0.328821	−	1.86483i	−0.152520	−	0.988300i	$-0.548739\pi$
$599$	8.04771	−	45.6408i	0.328821	−	1.86483i	0.481341	−	0.876534i	$-0.340150\pi$
$600$		0			0
$601$	10.7640	+	6.21462i	0.439074	+	0.253500i	0.703205	−	0.710987i	$-0.251752\pi$
$601$	10.7640	+	6.21462i	0.439074	+	0.253500i	−0.264131	+	0.964487i	$0.585085\pi$
$602$		0			0
$603$	6.90618	+	2.51364i	0.281241	+	0.102363i
$604$		0			0
$605$	16.0345	−	13.4545i	0.651895	−	0.547005i
$606$		0			0
$607$	21.7731			0.883744			0.441872	−	0.897078i	$-0.354315\pi$
$607$	21.7731			0.883744			0.441872	+	0.897078i	$0.354315\pi$
$608$		0			0
$609$	−11.3929			−0.461664
$610$		0			0
$611$	7.11674	−	5.97165i	0.287912	−	0.241587i
$612$		0			0
$613$	29.0802	+	10.5843i	1.17454	+	0.427497i	0.854270	−	0.519830i	$-0.174005\pi$
$613$	29.0802	+	10.5843i	1.17454	+	0.427497i	0.320269	+	0.947327i	$0.396227\pi$
$614$		0			0
$615$	−8.94984	−	5.16719i	−0.360892	−	0.208361i
$616$		0			0
$617$	0.287220	−	1.62891i	0.0115631	−	0.0655773i	−0.978480	−	0.206341i	$-0.933845\pi$
$617$	0.287220	−	1.62891i	0.0115631	−	0.0655773i	0.990043	+	0.140763i	$0.0449556\pi$
$618$		0			0
$619$	1.48377	−	0.856653i	0.0596376	−	0.0344318i	−0.469885	−	0.882728i	$-0.655705\pi$
$619$	1.48377	−	0.856653i	0.0596376	−	0.0344318i	0.529522	+	0.848296i	$0.322371\pi$
$620$		0			0
$621$	−2.05520	+	2.44930i	−0.0824725	+	0.0982869i
$622$		0			0
$623$	19.5515	−	7.11618i	0.783316	−	0.285104i
$624$		0			0
$625$	−2.47719	−	14.0488i	−0.0990876	−	0.561954i
$626$		0			0
$627$	−2.75111	−	20.4399i	−0.109869	−	0.816292i
$628$		0			0
$629$	−39.6729	+	6.99540i	−1.58186	+	0.278925i
$630$		0			0
$631$	7.40808	+	20.3535i	0.294911	+	0.810261i	0.995330	+	0.0965295i	$0.0307742\pi$
$631$	7.40808	+	20.3535i	0.294911	+	0.810261i	−0.700419	+	0.713732i	$0.747004\pi$
$632$		0			0
$633$	9.67820	+	8.12097i	0.384674	+	0.322780i
$634$		0			0
$635$	−13.4023	−	23.2135i	−0.531855	−	0.921201i
$636$		0			0
$637$	34.6495	+	6.10965i	1.37286	+	0.242073i
$638$		0			0
$639$	−5.76659	+	9.98803i	−0.228123	+	0.395120i
$640$		0			0
$641$	10.9053	−	29.9620i	0.430732	−	1.18343i	−0.514632	−	0.857411i	$-0.672071\pi$
$641$	10.9053	−	29.9620i	0.430732	−	1.18343i	0.945364	−	0.326016i	$-0.105706\pi$
$642$		0			0
$643$	−29.2341	−	34.8398i	−1.15288	−	1.37395i	−0.915395	−	0.402556i	$-0.868122\pi$
$643$	−29.2341	−	34.8398i	−1.15288	−	1.37395i	−0.237484	−	0.971391i	$-0.576323\pi$
$644$		0			0
$645$			15.2433i			0.600205i
$646$		0			0
$647$			24.9697i			0.981662i	0.871255	+	0.490831i	$0.163307\pi$
$647$			24.9697i			0.981662i	−0.871255	+	0.490831i	$0.836693\pi$
$648$		0			0
$649$	−22.6074	−	26.9424i	−0.887416	−	1.05758i
$650$		0			0
$651$	9.73960	−	26.7593i	0.381725	−	1.04878i
$652$		0			0
$653$	−24.4525	+	42.3530i	−0.956900	+	1.65740i	−0.226941	+	0.973908i	$0.572872\pi$
$653$	−24.4525	+	42.3530i	−0.956900	+	1.65740i	−0.729959	+	0.683491i	$0.760461\pi$
$654$		0			0
$655$	−12.8330	−	2.26280i	−0.501427	−	0.0884150i
$656$		0			0
$657$	5.80429	+	10.0533i	0.226447	+	0.392218i
$658$		0			0
$659$	−18.6883	−	15.6813i	−0.727992	−	0.610858i	0.201591	−	0.979470i	$-0.435389\pi$
$659$	−18.6883	−	15.6813i	−0.727992	−	0.610858i	−0.929583	+	0.368612i	$0.879833\pi$
$660$		0			0
$661$	15.2533	+	41.9082i	0.593286	+	1.63004i	0.764366	+	0.644782i	$0.223052\pi$
$661$	15.2533	+	41.9082i	0.593286	+	1.63004i	−0.171080	+	0.985257i	$0.554726\pi$
$662$		0			0
$663$	26.4163	−	4.65790i	1.02592	−	0.180898i
$664$		0			0
$665$	−30.2166	−	12.4139i	−1.17175	−	0.481390i
$666$		0			0
$667$	1.55145	+	8.79870i	0.0600723	+	0.340687i
$668$		0			0
$669$	−2.88971	+	1.05177i	−0.111723	+	0.0406637i
$670$		0			0
$671$	−5.06267	+	6.03345i	−0.195442	+	0.232919i
$672$		0			0
$673$	28.4863	−	16.4466i	1.09807	−	0.633969i	0.162354	−	0.986733i	$-0.448091\pi$
$673$	28.4863	−	16.4466i	1.09807	−	0.633969i	0.935712	+	0.352764i	$0.114758\pi$
$674$		0			0
$675$	0.281521	−	1.59659i	0.0108358	−	0.0614527i
$676$		0			0
$677$	12.8691	+	7.43000i	0.494601	+	0.285558i	0.726481	−	0.687186i	$-0.241154\pi$
$677$	12.8691	+	7.43000i	0.494601	+	0.285558i	−0.231880	+	0.972744i	$0.574488\pi$
$678$		0			0
$679$	−72.4447	−	26.3677i	−2.78017	−	1.01190i
$680$		0			0
$681$	−1.97888	+	1.66048i	−0.0758308	+	0.0636296i
$682$		0			0
$683$	25.7628			0.985785			0.492892	−	0.870090i	$-0.335940\pi$
$683$	25.7628			0.985785			0.492892	+	0.870090i	$0.335940\pi$
$684$		0			0
$685$	−16.6261			−0.635252
$686$		0			0
$687$	2.22382	−	1.86600i	0.0848439	−	0.0711925i
$688$		0			0
$689$	14.8434	+	5.40257i	0.565490	+	0.205822i
$690$		0			0
$691$	17.3076	+	9.99257i	0.658414	+	0.380135i	0.791672	−	0.610946i	$-0.209211\pi$
$691$	17.3076	+	9.99257i	0.658414	+	0.380135i	−0.133258	+	0.991081i	$0.542544\pi$
$692$		0			0
$693$	3.34986	−	18.9980i	0.127251	−	0.721674i
$694$		0			0
$695$	−9.18114	+	5.30073i	−0.348260	+	0.201068i
$696$		0			0
$697$	26.5129	−	31.5969i	1.00425	−	1.19682i
$698$		0			0
$699$	−27.1395	+	9.87799i	−1.02651	+	0.373620i
$700$		0			0
$701$	1.15215	+	6.53418i	0.0435162	+	0.246793i	0.998804	−	0.0488834i	$-0.0155663\pi$
$701$	1.15215	+	6.53418i	0.0435162	+	0.246793i	−0.955288	+	0.295676i	$0.904455\pi$
$702$		0			0
$703$	11.1133	+	21.1986i	0.419146	+	0.799519i
$704$		0			0
$705$	−4.59965	+	0.811042i	−0.173233	+	0.0305456i
$706$		0			0
$707$	16.5968	+	45.5994i	0.624188	+	1.71494i
$708$		0			0
$709$	5.88514	+	4.93822i	0.221021	+	0.185459i	0.746574	−	0.665302i	$-0.231697\pi$
$709$	5.88514	+	4.93822i	0.221021	+	0.185459i	−0.525553	+	0.850761i	$0.676142\pi$
$710$		0			0
$711$	3.13393	+	5.42812i	0.117532	+	0.203571i
$712$		0			0
$713$	−21.9924	−	3.87786i	−0.823623	−	0.145227i
$714$		0			0
$715$	15.8996	−	27.5389i	0.594610	−	1.02990i
$716$		0			0
$717$	−1.72598	+	4.74210i	−0.0644580	+	0.177097i
$718$		0			0
$719$	−28.4681	−	33.9270i	−1.06168	−	1.26526i	−0.962815	−	0.270162i	$-0.912923\pi$
$719$	−28.4681	−	33.9270i	−1.06168	−	1.26526i	−0.0988669	−	0.995101i	$-0.531522\pi$
$720$		0			0
$721$			78.3225i			2.91688i
$722$		0			0
$723$			4.76587i			0.177244i
$724$		0			0
$725$	−2.91198	−	3.47036i	−0.108148	−	0.128886i
$726$		0			0
$727$	−11.9806	+	32.9163i	−0.444334	+	1.22080i	0.492281	+	0.870437i	$0.336163\pi$
$727$	−11.9806	+	32.9163i	−0.444334	+	1.22080i	−0.936615	+	0.350361i	$0.886059\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	−59.9151	−	10.5647i	−2.21604	−	0.390748i
$732$		0			0
$733$	−13.0709	−	22.6395i	−0.482785	−	0.836208i	0.517020	−	0.855973i	$-0.327041\pi$
$733$	−13.0709	−	22.6395i	−0.482785	−	0.836208i	−0.999805	+	0.0197654i	$0.993708\pi$
$734$		0			0
$735$	−13.5502	−	11.3700i	−0.499807	−	0.419388i
$736$		0			0
$737$	11.8934	+	32.6768i	0.438098	+	1.20366i
$738$		0			0
$739$	32.2650	−	5.68919i	1.18689	−	0.209280i	0.454865	−	0.890560i	$-0.349688\pi$
$739$	32.2650	−	5.68919i	1.18689	−	0.209280i	0.732023	+	0.681280i	$0.238576\pi$
$740$		0			0
$741$	−7.39981	−	14.1151i	−0.271839	−	0.518531i
$742$		0			0
$743$	−5.34142	−	30.2927i	−0.195958	−	1.11133i	−0.911048	−	0.412299i	$-0.864726\pi$
$743$	−5.34142	−	30.2927i	−0.195958	−	1.11133i	0.715091	−	0.699032i	$-0.246385\pi$
$744$		0			0
$745$	33.7627	−	12.2886i	1.23697	−	0.450221i
$746$		0			0
$747$	6.72918	−	8.01952i	0.246208	−	0.293419i
$748$		0			0
$749$	−26.2347	+	15.1466i	−0.958596	+	0.553446i
$750$		0			0
$751$	−3.84402	+	21.8005i	−0.140270	+	0.795512i	0.830773	+	0.556611i	$0.187898\pi$
$751$	−3.84402	+	21.8005i	−0.140270	+	0.795512i	−0.971044	+	0.238902i	$0.923213\pi$
$752$		0			0
$753$	4.86215	+	2.80716i	0.177187	+	0.102299i
$754$		0			0
$755$	−20.1330	−	7.32780i	−0.732714	−	0.266686i
$756$		0			0
$757$	10.2243	−	8.57920i	0.371608	−	0.311817i	−0.437789	−	0.899078i	$-0.644238\pi$
$757$	10.2243	−	8.57920i	0.371608	−	0.311817i	0.809397	+	0.587261i	$0.199794\pi$
$758$		0			0
$759$	−15.1282			−0.549120
$760$		0			0
$761$	−40.0513			−1.45186			−0.725929	−	0.687769i	$-0.758590\pi$
$761$	−40.0513			−1.45186			−0.725929	+	0.687769i	$0.758590\pi$
$762$		0			0
$763$	−1.29930	+	1.09025i	−0.0470380	+	0.0394696i
$764$		0			0
$765$	−12.6722	−	4.61230i	−0.458164	−	0.166758i
$766$		0			0
$767$	−23.5367	−	13.5889i	−0.849862	−	0.490668i
$768$		0			0
$769$	3.80417	−	21.5745i	0.137182	−	0.777998i	−0.836133	−	0.548526i	$-0.815189\pi$
$769$	3.80417	−	21.5745i	0.137182	−	0.777998i	0.973315	−	0.229472i	$-0.0736998\pi$
$770$		0			0
$771$	13.3100	−	7.68451i	0.479346	−	0.276751i
$772$		0			0
$773$	−19.4443	+	23.1728i	−0.699362	+	0.833467i	−0.992454	−	0.122617i	$-0.960871\pi$
$773$	−19.4443	+	23.1728i	−0.699362	+	0.833467i	0.293092	+	0.956084i	$0.405316\pi$
$774$		0			0
$775$	10.6405	−	3.87282i	0.382217	−	0.139116i
$776$		0			0
$777$	3.88760	+	22.0477i	0.139467	+	0.790957i
$778$		0			0
$779$	−22.6681	−	9.31273i	−0.812168	−	0.333663i
$780$		0			0
$781$	−53.7405	+	9.47590i	−1.92299	+	0.339074i
$782$		0			0
$783$	0.955721	+	2.62582i	0.0341547	+	0.0938392i
$784$		0			0
$785$	−22.5969	−	18.9610i	−0.806516	−	0.676748i
$786$		0			0
$787$	−24.0591	−	41.6715i	−0.857613	−	1.48543i	−0.874200	−	0.485566i	$-0.838613\pi$
$787$	−24.0591	−	41.6715i	−0.857613	−	1.48543i	0.0165870	−	0.999862i	$-0.494720\pi$
$788$		0			0
$789$	4.53858	+	0.800274i	0.161578	+	0.0284905i
$790$		0			0
$791$	−42.8237	+	74.1729i	−1.52264	+	2.63728i
$792$		0			0
$793$	−2.08160	+	5.71914i	−0.0739197	+	0.203093i
$794$		0			0
$795$	−5.10461	−	6.08343i	−0.181042	−	0.215757i
$796$		0			0
$797$		−	22.1131i		−	0.783286i	−0.920117	−	0.391643i	$-0.871907\pi$
$797$		−	22.1131i		−	0.783286i	0.920117	−	0.391643i	$-0.128093\pi$
$798$		0			0
$799$		−	18.6414i		−	0.659485i
$800$		0			0
$801$	−3.28025	−	3.90925i	−0.115902	−	0.138127i
$802$		0			0
$803$	−18.7859	+	51.6138i	−0.662940	+	1.82141i
$804$		0			0
$805$	−11.9810	+	20.7517i	−0.422274	+	0.731401i
$806$		0			0
$807$	12.6069	+	2.22294i	0.443785	+	0.0782513i
$808$		0			0
$809$	−10.9907	−	19.0365i	−0.386413	−	0.669287i	0.605551	−	0.795806i	$-0.292953\pi$
$809$	−10.9907	−	19.0365i	−0.386413	−	0.669287i	−0.991964	+	0.126519i	$0.959619\pi$
$810$		0			0
$811$	2.60032	+	2.18192i	0.0913094	+	0.0766177i	0.687300	−	0.726374i	$-0.258796\pi$
$811$	2.60032	+	2.18192i	0.0913094	+	0.0766177i	−0.595990	+	0.802992i	$0.703240\pi$
$812$		0			0
$813$	−4.87308	−	13.3887i	−0.170906	−	0.469561i
$814$		0			0
$815$	−17.7806	+	3.13519i	−0.622826	+	0.109821i
$816$		0			0
$817$	4.82177	+	35.8243i	0.168692	+	1.25333i
$818$		0			0
$819$	−2.58857	−	14.6805i	−0.0904519	−	0.512978i
$820$		0			0
$821$	−27.6188	+	10.0524i	−0.963903	+	0.350832i	−0.775562	−	0.631272i	$-0.782533\pi$
$821$	−27.6188	+	10.0524i	−0.963903	+	0.350832i	−0.188341	+	0.982104i	$0.560311\pi$
$822$		0			0
$823$	21.8045	−	25.9856i	0.760056	−	0.905800i	−0.237795	−	0.971315i	$-0.576425\pi$
$823$	21.8045	−	25.9856i	0.760056	−	0.905800i	0.997852	+	0.0655155i	$0.0208692\pi$
$824$		0			0
$825$	6.64313	−	3.83541i	0.231284	−	0.133532i
$826$		0			0
$827$	5.19512	−	29.4630i	0.180652	−	1.02453i	−0.750764	−	0.660571i	$-0.770314\pi$
$827$	5.19512	−	29.4630i	0.180652	−	1.02453i	0.931416	−	0.363957i	$-0.118575\pi$
$828$		0			0
$829$	−18.9566	−	10.9446i	−0.658391	−	0.380122i	0.133273	−	0.991079i	$-0.457451\pi$
$829$	−18.9566	−	10.9446i	−0.658391	−	0.380122i	−0.791664	+	0.610957i	$0.790785\pi$
$830$		0			0
$831$	−15.5161	−	5.64742i	−0.538249	−	0.195907i
$832$		0			0
$833$	54.0818	−	45.3801i	1.87382	−	1.57233i
$834$		0			0
$835$	−3.59986			−0.124578
$836$		0			0
$837$	−6.98448			−0.241419
$838$		0			0
$839$	20.4713	−	17.1775i	0.706749	−	0.593033i	−0.216936	−	0.976186i	$-0.569606\pi$
$839$	20.4713	−	17.1775i	0.706749	−	0.593033i	0.923685	+	0.383153i	$0.125162\pi$
$840$		0			0
$841$	−19.9136	−	7.24797i	−0.686677	−	0.249930i
$842$		0			0
$843$	6.70339	+	3.87020i	0.230877	+	0.133297i
$844$		0			0
$845$	0.117483	−	0.666279i	0.00404154	−	0.0229207i
$846$		0			0
$847$	40.2075	−	23.2138i	1.38155	−	0.797636i
$848$		0			0
$849$	10.2658	−	12.2343i	0.352321	−	0.419880i
$850$		0			0
$851$	16.4979	−	6.00476i	0.565542	−	0.205841i
$852$		0			0
$853$	3.44290	+	19.5256i	0.117882	+	0.668545i	0.985283	+	0.170933i	$0.0546783\pi$
$853$	3.44290	+	19.5256i	0.117882	+	0.668545i	−0.867400	+	0.497611i	$0.834211\pi$
$854$		0			0
$855$	−0.326346	+	8.00565i	−0.0111608	+	0.273787i
$856$		0			0
$857$	−2.04256	+	0.360158i	−0.0697724	+	0.0123028i	−0.208425	−	0.978038i	$-0.566834\pi$
$857$	−2.04256	+	0.360158i	−0.0697724	+	0.0123028i	0.138653	+	0.990341i	$0.455723\pi$
$858$		0			0
$859$	−2.45672	−	6.74978i	−0.0838221	−	0.230299i	0.890700	−	0.454592i	$-0.150215\pi$
$859$	−2.45672	−	6.74978i	−0.0838221	−	0.230299i	−0.974522	+	0.224293i	$0.927993\pi$
$860$		0			0
$861$	−17.5595	−	14.7342i	−0.598428	−	0.502141i
$862$		0			0
$863$	16.6697	+	28.8727i	0.567442	+	0.982839i	0.996818	+	0.0797127i	$0.0254003\pi$
$863$	16.6697	+	28.8727i	0.567442	+	0.982839i	−0.429376	+	0.903126i	$0.641266\pi$
$864$		0			0
$865$	4.68337	+	0.825804i	0.159239	+	0.0280782i
$866$		0			0
$867$	18.4117	−	31.8900i	0.625295	−	1.08304i
$868$		0			0
$869$	−10.1431	+	27.8680i	−0.344082	+	0.945357i
$870$		0			0
$871$	17.2724	+	20.5845i	0.585255	+	0.697479i
$872$		0			0
$873$			18.9089i			0.639969i
$874$		0			0
$875$		−	49.6219i		−	1.67753i
$876$		0			0
$877$	−16.9482	−	20.1981i	−0.572301	−	0.682042i	0.399800	−	0.916602i	$-0.369080\pi$
$877$	−16.9482	−	20.1981i	−0.572301	−	0.682042i	−0.972102	+	0.234560i	$0.924635\pi$
$878$		0			0
$879$	3.93698	−	10.8168i	0.132791	−	0.364840i
$880$		0			0
$881$	1.36841	−	2.37015i	0.0461028	−	0.0798525i	−0.842053	−	0.539395i	$-0.818653\pi$
$881$	1.36841	−	2.37015i	0.0461028	−	0.0798525i	0.888156	+	0.459542i	$0.151986\pi$
$882$		0			0
$883$	−18.5465	−	3.27024i	−0.624138	−	0.110052i	−0.147370	−	0.989081i	$-0.547081\pi$
$883$	−18.5465	−	3.27024i	−0.624138	−	0.110052i	−0.476768	+	0.879029i	$0.658192\pi$
$884$		0			0
$885$	6.83174	+	11.8329i	0.229647	+	0.397759i
$886$		0			0
$887$	4.18230	+	3.50936i	0.140428	+	0.117833i	0.710296	−	0.703903i	$-0.248561\pi$
$887$	4.18230	+	3.50936i	0.140428	+	0.117833i	−0.569868	+	0.821736i	$0.693006\pi$
$888$		0			0
$889$	−20.3347	−	55.8690i	−0.682003	−	1.87379i
$890$		0			0
$891$	−4.65964	+	0.821620i	−0.156104	+	0.0275253i
$892$		0			0
$893$	−10.5534	+	3.36104i	−0.353155	+	0.112473i
$894$		0			0
$895$	−6.14994	−	34.8780i	−0.205570	−	1.16584i
$896$		0			0
$897$	−10.9852	+	3.99828i	−0.366785	+	0.133499i
$898$		0			0
$899$	−12.5453	+	14.9509i	−0.418409	+	0.498641i
$900$		0			0
$901$	27.4493	−	15.8478i	0.914468	−	0.527968i
$902$		0			0
$903$	−5.87117	+	33.2970i	−0.195380	+	1.10806i
$904$		0			0
$905$	16.7196	+	9.65305i	0.555778	+	0.320878i
$906$		0			0
$907$	−28.3983	−	10.3361i	−0.942949	−	0.343206i	−0.175620	−	0.984458i	$-0.556193\pi$
$907$	−28.3983	−	10.3361i	−0.942949	−	0.343206i	−0.767330	+	0.641253i	$0.778415\pi$
$908$		0			0
$909$	9.11743	−	7.65043i	0.302406	−	0.253749i
$910$		0			0
$911$	42.6400			1.41272			0.706362	−	0.707850i	$-0.250335\pi$
$911$	42.6400			1.41272			0.706362	+	0.707850i	$0.250335\pi$
$912$		0			0
$913$	49.5331			1.63931
$914$		0			0
$915$	2.34393	−	1.96679i	0.0774880	−	0.0650202i
$916$		0			0
$917$	−27.1605	−	9.88560i	−0.896918	−	0.326451i
$918$		0			0
$919$	−23.6033	−	13.6273i	−0.778600	−	0.449525i	0.0573342	−	0.998355i	$-0.481740\pi$
$919$	−23.6033	−	13.6273i	−0.778600	−	0.449525i	−0.835934	+	0.548830i	$0.815073\pi$
$920$		0			0
$921$	−0.229314	+	1.30051i	−0.00755616	+	0.0428531i
$922$		0			0
$923$	−36.5186	+	21.0840i	−1.20202	+	0.693989i
$924$		0			0
$925$	−5.72223	+	6.81949i	−0.188146	+	0.224223i
$926$		0			0
$927$	18.0517	−	6.57027i	0.592894	−	0.215796i
$928$		0			0
$929$	4.74925	+	26.9344i	0.155818	+	0.883688i	0.958034	+	0.286654i	$0.0925430\pi$
$929$	4.74925	+	26.9344i	0.155818	+	0.883688i	−0.802216	+	0.597034i	$0.796346\pi$
$930$		0			0
$931$	−35.4418	−	22.4351i	−1.16156	−	0.735280i
$932$		0			0
$933$	14.7716	−	2.60463i	0.483601	−	0.0852719i
$934$		0			0
$935$	−21.8232	−	59.9588i	−0.713695	−	1.96086i
$936$		0			0
$937$	26.5355	+	22.2660i	0.866878	+	0.727397i	0.963438	−	0.267930i	$-0.0863396\pi$
$937$	26.5355	+	22.2660i	0.866878	+	0.727397i	−0.0965602	+	0.995327i	$0.530784\pi$
$938$		0			0
$939$	16.5397	+	28.6476i	0.539752	+	0.934878i
$940$		0			0
$941$	57.8053	+	10.1926i	1.88440	+	0.332270i	0.992725	−	0.120408i	$-0.0384202\pi$
$941$	57.8053	+	10.1926i	1.88440	+	0.332270i	0.891674	+	0.452678i	$0.149531\pi$
$942$		0			0
$943$	−8.98797	+	15.5676i	−0.292689	+	0.506952i
$944$		0			0
$945$	−2.56323	+	7.04241i	−0.0833818	+	0.229089i
$946$		0			0
$947$	21.6901	+	25.8492i	0.704833	+	0.839987i	0.993064	−	0.117574i	$-0.0375117\pi$
$947$	21.6901	+	25.8492i	0.704833	+	0.839987i	−0.288231	+	0.957561i	$0.593067\pi$
$948$		0			0
$949$			42.4437i			1.37778i
$950$		0			0
$951$			10.8397i			0.351502i
$952$		0			0
$953$	−11.5997	−	13.8239i	−0.375750	−	0.447801i	0.544718	−	0.838619i	$-0.316637\pi$
$953$	−11.5997	−	13.8239i	−0.375750	−	0.447801i	−0.920468	+	0.390818i	$0.872192\pi$
$954$		0			0
$955$	7.72206	−	21.2162i	0.249880	−	0.686540i
$956$		0			0
$957$	−6.61075	+	11.4501i	−0.213695	+	0.370131i
$958$		0			0
$959$	−36.3176	−	6.40378i	−1.17276	−	0.206789i
$960$		0			0
$961$	−8.89150	−	15.4005i	−0.286822	−	0.496791i
$962$		0			0
$963$	5.69174	+	4.77593i	0.183414	+	0.153902i
$964$		0			0
$965$	7.02711	+	19.3068i	0.226211	+	0.621508i
$966$		0			0
$967$	−4.72406	+	0.832980i	−0.151916	+	0.0267868i	−0.249089	−	0.968481i	$-0.580131\pi$
$967$	−4.72406	+	0.832980i	−0.151916	+	0.0267868i	0.0971731	+	0.995268i	$0.469020\pi$
$968$		0			0
$969$	−31.2407	−	6.83119i	−1.00360	−	0.219449i
$970$		0			0
$971$	6.21703	+	35.2585i	0.199514	+	1.13150i	0.905842	+	0.423616i	$0.139239\pi$
$971$	6.21703	+	35.2585i	0.199514	+	1.13150i	−0.706328	+	0.707885i	$0.749650\pi$
$972$		0			0
$973$	−22.0967	+	8.04253i	−0.708387	+	0.257832i
$974$		0			0
$975$	3.81016	−	4.54077i	0.122023	−	0.145421i
$976$		0			0
$977$	−36.2570	+	20.9330i	−1.15996	+	0.669706i	−0.951295	−	0.308281i	$-0.900246\pi$
$977$	−36.2570	+	20.9330i	−1.15996	+	0.669706i	−0.208669	+	0.977986i	$0.566913\pi$
$978$		0			0
$979$	4.19287	−	23.7789i	0.134005	−	0.759978i
$980$		0			0
$981$	0.360274	+	0.208004i	0.0115027	+	0.00664106i
$982$		0			0
$983$	−24.6973	−	8.98907i	−0.787720	−	0.286707i	−0.0833323	−	0.996522i	$-0.526556\pi$
$983$	−24.6973	−	8.98907i	−0.787720	−	0.286707i	−0.704388	+	0.709815i	$0.748779\pi$
$984$		0			0
$985$	30.0278	−	25.1963i	0.956766	−	0.802822i
$986$		0			0
$987$	−10.3597			−0.329753
$988$		0			0
$989$	26.5147			0.843118
$990$		0			0
$991$	−18.2852	+	15.3431i	−0.580849	+	0.487390i	−0.885226	−	0.465161i	$-0.845996\pi$
$991$	−18.2852	+	15.3431i	−0.580849	+	0.487390i	0.304377	+	0.952552i	$0.401552\pi$
$992$		0			0
$993$	−14.1818	−	5.16174i	−0.450044	−	0.163803i
$994$		0			0
$995$	6.97084	+	4.02462i	0.220990	+	0.127589i
$996$		0			0
$997$	−1.69318	+	9.60248i	−0.0536235	+	0.304114i	−0.999810	−	0.0195089i	$-0.993790\pi$
$997$	−1.69318	+	9.60248i	−0.0536235	+	0.304114i	0.946186	+	0.323623i	$0.104901\pi$
$998$		0			0
$999$	4.75540	−	2.74553i	0.150454	−	0.0868648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.h.751.3	yes	24
4.3	odd	2		912.2.ci.g.751.3	✓	24
19.2	odd	18		912.2.ci.g.895.3	yes	24
76.59	even	18	inner	912.2.ci.h.895.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.g.751.3	✓	24	4.3	odd	2
912.2.ci.g.895.3	yes	24	19.2	odd	18
912.2.ci.h.751.3	yes	24	1.1	even	1	trivial
912.2.ci.h.895.3	yes	24	76.59	even	18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{3} +(1.72729 + 0.628683i) q^{5} +(3.53090 + 2.03857i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{3} +(1.72729 + 0.628683i) q^{5} +(3.53090 + 2.03857i) q^{7} +(0.173648 - 0.984808i) q^{9} +(4.09762 - 2.36576i) q^{11} +(2.35018 - 2.80084i) q^{13} +(-1.72729 + 0.628683i) q^{15} +(-1.27396 - 7.22499i) q^{17} +(-3.86056 + 2.02389i) q^{19} +(-4.01519 + 0.707987i) q^{21} +(1.09355 + 3.00451i) q^{23} +(-1.24192 - 1.04210i) q^{25} +(0.500000 + 0.866025i) q^{27} +(2.75189 + 0.485232i) q^{29} +(-3.49224 + 6.04874i) q^{31} +(-1.61828 + 4.44618i) q^{33} +(4.81729 + 5.74102i) q^{35} -5.49107i q^{37} +3.65624i q^{39} +(3.61386 + 4.30683i) q^{41} +(2.83629 - 7.79265i) q^{43} +(0.919073 - 1.59188i) q^{45} +(2.50233 + 0.441228i) q^{47} +(4.81151 + 8.33379i) q^{49} +(5.62004 + 4.71578i) q^{51} +(1.47763 + 4.05976i) q^{53} +(8.56510 - 1.51026i) q^{55} +(1.65643 - 4.03190i) q^{57} +(-1.29078 - 7.32037i) q^{59} +(-1.56422 + 0.569328i) q^{61} +(2.62073 - 3.12327i) q^{63} +(5.82030 - 3.36035i) q^{65} +(-1.27621 + 7.23775i) q^{67} +(-2.76897 - 1.59866i) q^{69} +(-10.8377 - 3.94458i) q^{71} +(-8.89269 + 7.46185i) q^{73} +1.62122 q^{75} +19.2911 q^{77} +(-4.80146 + 4.02890i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(9.06619 + 5.23437i) q^{83} +(2.34173 - 13.2806i) q^{85} +(-2.41997 + 1.39717i) q^{87} +(3.28025 - 3.90925i) q^{89} +(14.0080 - 5.09848i) q^{91} +(-1.21284 - 6.87837i) q^{93} +(-7.94069 + 1.06878i) q^{95} +(-18.6216 + 3.28349i) q^{97} +(-1.61828 - 4.44618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 9 q^{7}+O(q^{10}) \) 24 * q + 9 * q^7	\( 24 q + 9 q^{7} - 9 q^{11} - 9 q^{13} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 15 q^{23} + 6 q^{25} + 12 q^{27} - 6 q^{29} - 12 q^{31} - 3 q^{33} + 30 q^{41} + 9 q^{43} + 3 q^{45} + 15 q^{47} + 27 q^{49} - 3 q^{51} + 6 q^{53} - 21 q^{55} - 9 q^{57} + 36 q^{59} - 21 q^{61} + 3 q^{63} - 9 q^{65} - 45 q^{67} + 36 q^{71} - 42 q^{75} + 108 q^{77} - 36 q^{79} + 27 q^{83} - 9 q^{85} + 9 q^{87} - 27 q^{89} + 36 q^{91} - 18 q^{93} - 30 q^{95} - 51 q^{97} - 3 q^{99}+O(q^{100}) \) 24 * q + 9 * q^7 - 9 * q^11 - 9 * q^13 - 6 * q^17 + 3 * q^19 - 6 * q^21 - 15 * q^23 + 6 * q^25 + 12 * q^27 - 6 * q^29 - 12 * q^31 - 3 * q^33 + 30 * q^41 + 9 * q^43 + 3 * q^45 + 15 * q^47 + 27 * q^49 - 3 * q^51 + 6 * q^53 - 21 * q^55 - 9 * q^57 + 36 * q^59 - 21 * q^61 + 3 * q^63 - 9 * q^65 - 45 * q^67 + 36 * q^71 - 42 * q^75 + 108 * q^77 - 36 * q^79 + 27 * q^83 - 9 * q^85 + 9 * q^87 - 27 * q^89 + 36 * q^91 - 18 * q^93 - 30 * q^95 - 51 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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