LMFDB - Embedded newform 735.2.g.c.734.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(734,735)] 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("735.734"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			734.21
Character	$\chi$	$=$	735.734
Dual form			735.2.g.c.734.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.903339 q^{2} +(-1.72180 - 0.188163i) q^{3} -1.18398 q^{4} +(1.94641 - 1.10068i) q^{5} +(-1.55537 - 0.169975i) q^{6} -2.87621 q^{8} +(2.92919 + 0.647957i) q^{9} +(1.75827 - 0.994285i) q^{10} +4.06437i q^{11} +(2.03858 + 0.222781i) q^{12} +2.88298 q^{13} +(-3.55843 + 1.52891i) q^{15} -0.230234 q^{16} -6.66864i q^{17} +(2.64605 + 0.585325i) q^{18} -5.70701i q^{19} +(-2.30451 + 1.30318i) q^{20} +3.67151i q^{22} +1.63185 q^{23} +(4.95226 + 0.541196i) q^{24} +(2.57701 - 4.28474i) q^{25} +2.60431 q^{26} +(-4.92156 - 1.66682i) q^{27} -5.89707i q^{29} +(-3.21447 + 1.38112i) q^{30} +1.87068i q^{31} +5.54444 q^{32} +(0.764764 - 6.99804i) q^{33} -6.02404i q^{34} +(-3.46810 - 0.767168i) q^{36} +1.59973i q^{37} -5.15537i q^{38} +(-4.96392 - 0.542470i) q^{39} +(-5.59828 + 3.16578i) q^{40} +9.12244 q^{41} -7.53359i q^{43} -4.81213i q^{44} +(6.41459 - 1.96291i) q^{45} +1.47412 q^{46} -6.91446i q^{47} +(0.396417 + 0.0433215i) q^{48} +(2.32792 - 3.87057i) q^{50} +(-1.25479 + 11.4821i) q^{51} -3.41339 q^{52} +1.51865 q^{53} +(-4.44583 - 1.50570i) q^{54} +(4.47357 + 7.91093i) q^{55} +(-1.07385 + 9.82633i) q^{57} -5.32705i q^{58} -0.991850 q^{59} +(4.21311 - 1.81019i) q^{60} +6.16485i q^{61} +1.68986i q^{62} +5.46898 q^{64} +(5.61146 - 3.17324i) q^{65} +(0.690841 - 6.32160i) q^{66} +10.0903i q^{67} +7.89553i q^{68} +(-2.80973 - 0.307054i) q^{69} -4.81213i q^{71} +(-8.42497 - 1.86366i) q^{72} -0.560619 q^{73} +1.44510i q^{74} +(-5.24333 + 6.89257i) q^{75} +6.75699i q^{76} +(-4.48410 - 0.490034i) q^{78} +3.79848 q^{79} +(-0.448130 + 0.253414i) q^{80} +(8.16030 + 3.79598i) q^{81} +8.24065 q^{82} +4.00431i q^{83} +(-7.34003 - 12.9799i) q^{85} -6.80539i q^{86} +(-1.10961 + 10.1536i) q^{87} -11.6900i q^{88} +10.4109 q^{89} +(5.79455 - 1.77317i) q^{90} -1.93208 q^{92} +(0.351993 - 3.22094i) q^{93} -6.24610i q^{94} +(-6.28159 - 11.1082i) q^{95} +(-9.54642 - 1.04326i) q^{96} -14.5370 q^{97} +(-2.63354 + 11.9053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 40 q^{9} + 16 q^{15} - 16 q^{16} + 64 q^{25} + 56 q^{30} - 16 q^{36} - 56 q^{39} - 32 q^{46} - 40 q^{51} + 8 q^{60} - 176 q^{64} + 48 q^{79} - 40 q^{81} - 64 q^{85} + 40 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 + 40 * q^9 + 16 * q^15 - 16 * q^16 + 64 * q^25 + 56 * q^30 - 16 * q^36 - 56 * q^39 - 32 * q^46 - 40 * q^51 + 8 * q^60 - 176 * q^64 + 48 * q^79 - 40 * q^81 - 64 * q^85 + 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	0.903339			0.638757			0.319378	−	0.947627i	$-0.396526\pi$
$2$	0.903339			0.638757			0.319378	+	0.947627i	$0.396526\pi$
$3$	−1.72180	−	0.188163i	−0.994082	−	0.108636i
$3$	−1.72180	−	0.188163i	−0.994082	−	0.108636i
$4$	−1.18398			−0.591990
$5$	1.94641	−	1.10068i	0.870460	−	0.492238i
$5$	1.94641	−	1.10068i	0.870460	−	0.492238i
$6$	−1.55537	−	0.169975i	−0.634976	−	0.0693919i
$7$		0			0
$7$		0			0
$8$	−2.87621			−1.01689
$9$	2.92919	+	0.647957i	0.976396	+	0.215986i
$10$	1.75827	−	0.994285i	0.556013	−	0.314421i
$11$			4.06437i			1.22545i	0.790294	+	0.612727i	$0.209928\pi$
$11$			4.06437i			1.22545i	−0.790294	+	0.612727i	$0.790072\pi$
$12$	2.03858	+	0.222781i	0.588486	+	0.0643113i
$13$	2.88298			0.799595			0.399798	−	0.916603i	$-0.369080\pi$
$13$	2.88298			0.799595			0.399798	+	0.916603i	$0.369080\pi$
$14$		0			0
$15$	−3.55843	+	1.52891i	−0.918783	+	0.394762i
$16$	−0.230234			−0.0575586
$17$		−	6.66864i		−	1.61738i	−0.588233	−	0.808691i	$-0.700176\pi$
$17$		−	6.66864i		−	1.61738i	0.588233	−	0.808691i	$-0.299824\pi$
$18$	2.64605	+	0.585325i	0.623680	+	0.137962i
$19$		−	5.70701i		−	1.30928i	−0.755941	−	0.654639i	$-0.772821\pi$
$19$		−	5.70701i		−	1.30928i	0.755941	−	0.654639i	$-0.227179\pi$
$20$	−2.30451	+	1.30318i	−0.515304	+	0.291400i
$21$		0			0
$22$			3.67151i			0.782768i
$23$	1.63185			0.340265			0.170133	−	0.985421i	$-0.445580\pi$
$23$	1.63185			0.340265			0.170133	+	0.985421i	$0.445580\pi$
$24$	4.95226	+	0.541196i	1.01088	+	0.110471i
$25$	2.57701	−	4.28474i	0.515403	−	0.856948i
$26$	2.60431			0.510747
$27$	−4.92156	−	1.66682i	−0.947154	−	0.320779i
$28$		0			0
$29$		−	5.89707i		−	1.09506i	−0.836786	−	0.547530i	$-0.815568\pi$
$29$		−	5.89707i		−	1.09506i	0.836786	−	0.547530i	$-0.184432\pi$
$30$	−3.21447	+	1.38112i	−0.586879	+	0.252157i
$31$			1.87068i			0.335985i	0.985788	+	0.167992i	$0.0537284\pi$
$31$			1.87068i			0.335985i	−0.985788	+	0.167992i	$0.946272\pi$
$32$	5.54444			0.980128
$33$	0.764764	−	6.99804i	0.133128	−	1.21820i
$34$		−	6.02404i		−	1.03311i
$35$		0			0
$36$	−3.46810	−	0.767168i	−0.578017	−	0.127861i
$37$			1.59973i			0.262994i	0.991317	+	0.131497i	$0.0419783\pi$
$37$			1.59973i			0.262994i	−0.991317	+	0.131497i	$0.958022\pi$
$38$		−	5.15537i		−	0.836311i
$39$	−4.96392	−	0.542470i	−0.794863	−	0.0868647i
$40$	−5.59828	+	3.16578i	−0.885166	+	0.500554i
$41$	9.12244			1.42469			0.712343	−	0.701832i	$-0.247634\pi$
$41$	9.12244			1.42469			0.712343	+	0.701832i	$0.247634\pi$
$42$		0			0
$43$		−	7.53359i		−	1.14886i	−0.818553	−	0.574431i	$-0.805223\pi$
$43$		−	7.53359i		−	1.14886i	0.818553	−	0.574431i	$-0.194777\pi$
$44$		−	4.81213i		−	0.725456i
$45$	6.41459	−	1.96291i	0.956231	−	0.292613i
$46$	1.47412			0.217347
$47$		−	6.91446i		−	1.00858i	−0.863535	−	0.504289i	$-0.831755\pi$
$47$		−	6.91446i		−	1.00858i	0.863535	−	0.504289i	$-0.168245\pi$
$48$	0.396417	+	0.0433215i	0.0572179	+	0.00625292i
$49$		0			0
$50$	2.32792	−	3.87057i	0.329217	−	0.547381i
$51$	−1.25479	+	11.4821i	−0.175706	+	1.60781i
$52$	−3.41339			−0.473352
$53$	1.51865			0.208603			0.104301	−	0.994546i	$-0.466739\pi$
$53$	1.51865			0.208603			0.104301	+	0.994546i	$0.466739\pi$
$54$	−4.44583	−	1.50570i	−0.605001	−	0.204900i
$55$	4.47357	+	7.91093i	0.603216	+	1.06671i
$56$		0			0
$57$	−1.07385	+	9.82633i	−0.142235	+	1.30153i
$58$		−	5.32705i		−	0.699477i
$59$	−0.991850			−0.129128			−0.0645640	−	0.997914i	$-0.520566\pi$
$59$	−0.991850			−0.129128			−0.0645640	+	0.997914i	$0.520566\pi$
$60$	4.21311	−	1.81019i	0.543910	−	0.233695i
$61$			6.16485i			0.789328i	0.918825	+	0.394664i	$0.129139\pi$
$61$			6.16485i			0.789328i	−0.918825	+	0.394664i	$0.870861\pi$
$62$			1.68986i			0.214612i
$63$		0			0
$64$	5.46898			0.683622
$65$	5.61146	−	3.17324i	0.696016	−	0.393591i
$66$	0.690841	−	6.32160i	0.0850366	−	0.778135i
$67$			10.0903i			1.23272i	0.787464	+	0.616361i	$0.211394\pi$
$67$			10.0903i			1.23272i	−0.787464	+	0.616361i	$0.788606\pi$
$68$			7.89553i			0.957474i
$69$	−2.80973	−	0.307054i	−0.338251	−	0.0369650i
$70$		0			0
$71$		−	4.81213i		−	0.571095i	−0.958365	−	0.285548i	$-0.907825\pi$
$71$		−	4.81213i		−	0.571095i	0.958365	−	0.285548i	$-0.0921755\pi$
$72$	−8.42497	−	1.86366i	−0.992892	−	0.219635i
$73$	−0.560619			−0.0656154			−0.0328077	−	0.999462i	$-0.510445\pi$
$73$	−0.560619			−0.0656154			−0.0328077	+	0.999462i	$0.510445\pi$
$74$			1.44510i			0.167989i
$75$	−5.24333	+	6.89257i	−0.605448	+	0.795885i
$76$			6.75699i			0.775079i
$77$		0			0
$78$	−4.48410	−	0.490034i	−0.507724	−	0.0554854i
$79$	3.79848			0.427362			0.213681	−	0.976904i	$-0.431455\pi$
$79$	3.79848			0.427362			0.213681	+	0.976904i	$0.431455\pi$
$80$	−0.448130	+	0.253414i	−0.0501024	+	0.0283325i
$81$	8.16030	+	3.79598i	0.906700	+	0.421776i
$82$	8.24065			0.910028
$83$			4.00431i			0.439530i	0.975553	+	0.219765i	$0.0705291\pi$
$83$			4.00431i			0.439530i	−0.975553	+	0.219765i	$0.929471\pi$
$84$		0			0
$85$	−7.34003	−	12.9799i	−0.796138	−	1.40787i
$86$		−	6.80539i		−	0.733844i
$87$	−1.10961	+	10.1536i	−0.118963	+	1.08858i
$88$		−	11.6900i		−	1.24616i
$89$	10.4109			1.10356			0.551779	−	0.833990i	$-0.313949\pi$
$89$	10.4109			1.10356			0.551779	+	0.833990i	$0.313949\pi$
$90$	5.79455	−	1.77317i	0.610799	−	0.186908i
$91$		0			0
$92$	−1.93208			−0.201433
$93$	0.351993	−	3.22094i	0.0365000	−	0.333996i
$94$		−	6.24610i		−	0.644236i
$95$	−6.28159	−	11.1082i	−0.644477	−	1.13968i
$96$	−9.54642	−	1.04326i	−0.974328	−	0.106477i
$97$	−14.5370			−1.47601			−0.738006	−	0.674795i	$-0.764232\pi$
$97$	−14.5370			−1.47601			−0.738006	+	0.674795i	$0.764232\pi$
$98$		0			0
$99$	−2.63354	+	11.9053i	−0.264681	+	1.19653i
$100$	−3.05113	+	5.07304i	−0.305113	+	0.507304i
$101$	−13.7973			−1.37289			−0.686443	−	0.727183i	$-0.740829\pi$
$101$	−13.7973			−1.37289			−0.686443	+	0.727183i	$0.740829\pi$
$102$	−1.13350	+	10.3722i	−0.112233	+	1.02700i
$103$	−8.31359			−0.819162			−0.409581	−	0.912274i	$-0.634325\pi$
$103$	−8.31359			−0.819162			−0.409581	+	0.912274i	$0.634325\pi$
$104$	−8.29206			−0.813104
$105$		0			0
$106$	1.37186			0.133246
$107$	10.7371			1.03799			0.518996	−	0.854777i	$-0.326306\pi$
$107$	10.7371			1.03799			0.518996	+	0.854777i	$0.326306\pi$
$108$	5.82702	+	1.97348i	0.560705	+	0.189898i
$109$	0.536675			0.0514042			0.0257021	−	0.999670i	$-0.491818\pi$
$109$	0.536675			0.0514042			0.0257021	+	0.999670i	$0.491818\pi$
$110$	4.04115	+	7.14625i	0.385308	+	0.681368i
$111$	0.301010	−	2.75441i	0.0285706	−	0.261437i
$112$		0			0
$113$	12.1028			1.13854			0.569270	−	0.822151i	$-0.307226\pi$
$113$	12.1028			1.13854			0.569270	+	0.822151i	$0.307226\pi$
$114$	−0.970048	+	8.87651i	−0.0908533	+	0.831361i
$115$	3.17626	−	1.79615i	0.296187	−	0.167492i
$116$			6.98201i			0.648264i
$117$	8.44480	+	1.86805i	0.780722	+	0.172701i
$118$	−0.895977			−0.0824813
$119$		0			0
$120$	10.2348	−	4.39746i	0.934306	−	0.401431i
$121$	−5.51913			−0.501739
$122$			5.56895i			0.504189i
$123$	−15.7070	−	1.71650i	−1.41625	−	0.154772i
$124$		−	2.21485i		−	0.198899i
$125$	0.299800	−	11.1763i	0.0268150	−	0.999640i
$126$		0			0
$127$			22.2883i			1.97777i	0.148697	+	0.988883i	$0.452492\pi$
$127$			22.2883i			1.97777i	−0.148697	+	0.988883i	$0.547508\pi$
$128$	−6.14855			−0.543460
$129$	−1.41754	+	12.9713i	−0.124808	+	1.14206i
$130$	5.06905	−	2.86651i	0.444585	−	0.251409i
$131$	0.114179			0.00997586			0.00498793	−	0.999988i	$-0.498412\pi$
$131$	0.114179			0.00997586			0.00498793	+	0.999988i	$0.498412\pi$
$132$	−0.905465	+	8.28553i	−0.0788106	+	0.721163i
$133$		0			0
$134$			9.11493i			0.787410i
$135$	−11.4140	+	2.17274i	−0.982360	+	0.187000i
$136$			19.1804i			1.64471i
$137$	−12.5438			−1.07168			−0.535842	−	0.844318i	$-0.680006\pi$
$137$	−12.5438			−1.07168			−0.535842	+	0.844318i	$0.680006\pi$
$138$	−2.53813	−	0.277374i	−0.216060	−	0.0236117i
$139$			2.37640i			0.201564i	0.994909	+	0.100782i	$0.0321344\pi$
$139$			2.37640i			0.201564i	−0.994909	+	0.100782i	$0.967866\pi$
$140$		0			0
$141$	−1.30104	+	11.9053i	−0.109568	+	1.00261i
$142$		−	4.34699i		−	0.364791i
$143$			11.7175i			0.979868i
$144$	−0.674400	−	0.149182i	−0.0562000	−	0.0124318i
$145$	−6.49078	−	11.4781i	−0.539030	−	0.953206i
$146$	−0.506428			−0.0419123
$147$		0			0
$148$		−	1.89405i		−	0.155690i
$149$		−	16.4685i		−	1.34915i	−0.738207	−	0.674575i	$-0.764327\pi$
$149$		−	16.4685i		−	1.34915i	0.738207	−	0.674575i	$-0.235673\pi$
$150$	−4.73650	+	6.22632i	−0.386734	+	0.508377i
$151$	−13.1473			−1.06991			−0.534955	−	0.844881i	$-0.679671\pi$
$151$	−13.1473			−1.06991			−0.534955	+	0.844881i	$0.679671\pi$
$152$			16.4146i			1.33140i
$153$	4.32099	−	19.5337i	0.349332	−	1.57921i
$154$		0			0
$155$	2.05902	+	3.64111i	0.165385	+	0.292461i
$156$	5.87717	+	0.642273i	0.470551	+	0.0514230i
$157$	−3.18813			−0.254440			−0.127220	−	0.991874i	$-0.540605\pi$
$157$	−3.18813			−0.254440			−0.127220	+	0.991874i	$0.540605\pi$
$158$	3.43131			0.272980
$159$	−2.61481	−	0.285753i	−0.207368	−	0.0226617i
$160$	10.7918	−	6.10265i	0.853163	−	0.482457i
$161$		0			0
$162$	7.37152	+	3.42906i	0.579161	+	0.269412i
$163$			19.2794i			1.51008i	0.655679	+	0.755040i	$0.272383\pi$
$163$			19.2794i			1.51008i	−0.655679	+	0.755040i	$0.727617\pi$
$164$	−10.8008			−0.843399
$165$	−6.21405	−	14.4628i	−0.483763	−	1.12593i
$166$			3.61725i			0.280753i
$167$		−	0.883913i		−	0.0683993i	−0.999415	−	0.0341996i	$-0.989112\pi$
$167$		−	0.883913i		−	0.0683993i	0.999415	−	0.0341996i	$-0.0108882\pi$
$168$		0			0
$169$	−4.68842			−0.360648
$170$	−6.63053	−	11.7252i	−0.508538	−	0.899285i
$171$	3.69790	−	16.7169i	0.282786	−	1.27838i
$172$			8.91962i			0.680114i
$173$			12.5161i			0.951585i	0.879558	+	0.475793i	$0.157839\pi$
$173$			12.5161i			0.951585i	−0.879558	+	0.475793i	$0.842161\pi$
$174$	−1.00235	+	9.17212i	−0.0759882	+	0.695337i
$175$		0			0
$176$		−	0.935758i		−	0.0705354i
$177$	1.70777	+	0.186629i	0.128364	+	0.0140279i
$178$	9.40461			0.704906
$179$		−	12.1657i		−	0.909305i	−0.890669	−	0.454653i	$-0.849763\pi$
$179$		−	12.1657i		−	0.909305i	0.890669	−	0.454653i	$-0.150237\pi$
$180$	−7.59475	+	2.32404i	−0.566079	+	0.173224i
$181$		−	16.1773i		−	1.20245i	−0.799081	−	0.601224i	$-0.794680\pi$
$181$		−	16.1773i		−	1.20245i	0.799081	−	0.601224i	$-0.205320\pi$
$182$		0			0
$183$	1.16000	−	10.6146i	0.0857493	−	0.784657i
$184$	−4.69356			−0.346014
$185$	1.76079	+	3.11373i	0.129456	+	0.228926i
$186$	0.317969	−	2.90960i	0.0233146	−	0.213342i
$187$	27.1038			1.98203
$188$			8.18658i			0.597068i
$189$		0			0
$190$	−5.67440	−	10.0344i	−0.411664	−	0.727975i
$191$			8.27793i			0.598970i	0.954101	+	0.299485i	$0.0968148\pi$
$191$			8.27793i			0.598970i	−0.954101	+	0.299485i	$0.903185\pi$
$192$	−9.41649	−	1.02906i	−0.679576	−	0.0742659i
$193$			15.9253i			1.14633i	0.819440	+	0.573166i	$0.194285\pi$
$193$			15.9253i			1.14633i	−0.819440	+	0.573166i	$0.805715\pi$
$194$	−13.1319			−0.942812
$195$	−10.2589	+	4.40781i	−0.734655	+	0.315650i
$196$		0			0
$197$	23.8738			1.70094			0.850468	−	0.526027i	$-0.176319\pi$
$197$	23.8738			1.70094			0.850468	+	0.526027i	$0.176319\pi$
$198$	−2.37898	+	10.7545i	−0.169067	+	0.764292i
$199$		−	12.2273i		−	0.866768i	−0.901209	−	0.433384i	$-0.857319\pi$
$199$		−	12.2273i		−	0.866768i	0.901209	−	0.433384i	$-0.142681\pi$
$200$	−7.41204	+	12.3238i	−0.524110	+	0.871426i
$201$	1.89861	−	17.3734i	0.133918	−	1.22543i
$202$	−12.4637			−0.876941
$203$		0			0
$204$	1.48565	−	13.5945i	0.104016	−	0.951807i
$205$	17.7560	−	10.0409i	1.24013	−	0.701285i
$206$	−7.50998			−0.523245
$207$	4.78001	+	1.05737i	0.332234	+	0.0734925i
$208$	−0.663761			−0.0460235
$209$	23.1954			1.60446
$210$		0			0
$211$	18.8640			1.29865			0.649327	−	0.760510i	$-0.275051\pi$
$211$	18.8640			1.29865			0.649327	+	0.760510i	$0.275051\pi$
$212$	−1.79805			−0.123491
$213$	−0.905465	+	8.28553i	−0.0620414	+	0.567715i
$214$	9.69921			0.663025
$215$	−8.29206	−	14.6635i	−0.565514	−	1.00004i
$216$	14.1554	+	4.79412i	0.963156	+	0.326199i
$217$		0			0
$218$	0.484799			0.0328348
$219$	0.965273	+	0.105488i	0.0652271	+	0.00712819i
$220$	−5.29661	−	9.36638i	−0.357098	−	0.631481i
$221$		−	19.2256i		−	1.29325i
$222$	0.271914	−	2.48817i	0.0182496	−	0.166995i
$223$	19.2779			1.29095			0.645473	−	0.763783i	$-0.276660\pi$
$223$	19.2779			1.29095			0.645473	+	0.763783i	$0.276660\pi$
$224$		0			0
$225$	10.3249	−	10.8810i	0.688326	−	0.725401i
$226$	10.9330			0.727250
$227$			11.5017i			0.763397i	0.924287	+	0.381698i	$0.124661\pi$
$227$			11.5017i			0.763397i	−0.924287	+	0.381698i	$0.875339\pi$
$228$	1.27141	−	11.6342i	0.0842014	−	0.770492i
$229$			17.3732i			1.14806i	0.818836	+	0.574028i	$0.194620\pi$
$229$			17.3732i			1.14806i	−0.818836	+	0.574028i	$0.805380\pi$
$230$	2.86923	−	1.62253i	0.189192	−	0.106986i
$231$		0			0
$232$			16.9612i			1.11356i
$233$	−0.462850			−0.0303223			−0.0151611	−	0.999885i	$-0.504826\pi$
$233$	−0.462850			−0.0303223			−0.0151611	+	0.999885i	$0.504826\pi$
$234$	7.62851	+	1.68748i	0.498691	+	0.110314i
$235$	−7.61060	−	13.4584i	−0.496461	−	0.877927i
$236$	1.17433			0.0764424
$237$	−6.54021	−	0.714732i	−0.424833	−	0.0464268i
$238$		0			0
$239$		−	17.3055i		−	1.11940i	−0.828696	−	0.559699i	$-0.810917\pi$
$239$		−	17.3055i		−	1.11940i	0.828696	−	0.559699i	$-0.189083\pi$
$240$	0.819273	−	0.352007i	0.0528838	−	0.0227219i
$241$			4.27939i			0.275660i	0.990456	+	0.137830i	$0.0440128\pi$
$241$			4.27939i			0.275660i	−0.990456	+	0.137830i	$0.955987\pi$
$242$	−4.98564			−0.320489
$243$	−13.3361	−	8.07138i	−0.855514	−	0.517780i
$244$		−	7.29906i		−	0.467274i
$245$		0			0
$246$	−14.1888	−	1.55058i	−0.904642	−	0.0988617i
$247$		−	16.4532i		−	1.04689i
$248$		−	5.38048i		−	0.341661i
$249$	0.753463	−	6.89462i	0.0477488	−	0.436929i
$250$	0.270821	−	10.0960i	0.0171282	−	0.638527i
$251$	−17.4145			−1.09919			−0.549597	−	0.835430i	$-0.685219\pi$
$251$	−17.4145			−1.09919			−0.549597	+	0.835430i	$0.685219\pi$
$252$		0			0
$253$			6.63247i			0.416980i
$254$			20.1339i			1.26331i
$255$	10.1957	+	23.7299i	0.638481	+	1.48602i
$256$	−16.4922			−1.03076
$257$		−	15.4161i		−	0.961630i	−0.876822	−	0.480815i	$-0.840341\pi$
$257$		−	15.4161i		−	0.961630i	0.876822	−	0.480815i	$-0.159659\pi$
$258$	−1.28052	+	11.7175i	−0.0797217	+	0.729500i
$259$		0			0
$260$	−6.64385	+	3.75704i	−0.412034	+	0.233002i
$261$	3.82105	−	17.2736i	0.236517	−	1.06921i
$262$	0.103142			0.00637215
$263$	6.21170			0.383030			0.191515	−	0.981490i	$-0.438660\pi$
$263$	6.21170			0.383030			0.191515	+	0.981490i	$0.438660\pi$
$264$	−2.19962	+	20.1278i	−0.135377	+	1.23878i
$265$	2.95591	−	1.67155i	0.181580	−	0.102682i
$266$		0			0
$267$	−17.9256	−	1.95895i	−1.09703	−	0.119886i
$268$		−	11.9467i		−	0.729759i
$269$	5.99070			0.365259			0.182630	−	0.983182i	$-0.441539\pi$
$269$	5.99070			0.365259			0.182630	+	0.983182i	$0.441539\pi$
$270$	−10.3107	+	1.96272i	−0.627489	+	0.119447i
$271$			6.24515i			0.379366i	0.981845	+	0.189683i	$0.0607460\pi$
$271$			6.24515i			0.379366i	−0.981845	+	0.189683i	$0.939254\pi$
$272$			1.53535i			0.0930942i
$273$		0			0
$274$	−11.3313			−0.684546
$275$	17.4148	+	10.4739i	1.05015	+	0.631603i
$276$	3.32666	+	0.363546i	0.200241	+	0.0218829i
$277$			8.70424i			0.522987i	0.965205	+	0.261494i	$0.0842150\pi$
$277$			8.70424i			0.522987i	−0.965205	+	0.261494i	$0.915785\pi$
$278$			2.14669i			0.128750i
$279$	−1.21212	+	5.47959i	−0.0725679	+	0.328054i
$280$		0			0
$281$		−	4.36274i		−	0.260259i	−0.991497	−	0.130130i	$-0.958461\pi$
$281$		−	4.36274i		−	0.260259i	0.991497	−	0.130130i	$-0.0415393\pi$
$282$	−1.17528	+	10.7545i	−0.0699871	+	0.640423i
$283$	−7.52075			−0.447062			−0.223531	−	0.974697i	$-0.571758\pi$
$283$	−7.52075			−0.447062			−0.223531	+	0.974697i	$0.571758\pi$
$284$			5.69747i			0.338082i
$285$	8.72549	+	20.3080i	0.516853	+	1.20294i
$286$			10.5849i			0.625897i
$287$		0			0
$288$	16.2407	+	3.59256i	0.956994	+	0.211694i
$289$	−27.4707			−1.61593
$290$	−5.86337	−	10.3686i	−0.344309	−	0.608867i
$291$	25.0298	+	2.73533i	1.46728	+	0.160348i
$292$	0.663761			0.0388437
$293$			0.105885i			0.00618587i	0.999995	+	0.00309293i	$0.000984513\pi$
$293$			0.105885i			0.00618587i	−0.999995	+	0.00309293i	$0.999015\pi$
$294$		0			0
$295$	−1.93055	+	1.09171i	−0.112401	+	0.0635617i
$296$		−	4.60116i		−	0.267437i
$297$	6.77457	−	20.0030i	0.393100	−	1.16069i
$298$		−	14.8766i		−	0.861778i
$299$	4.70461			0.272074
$300$	6.20800	−	8.16066i	0.358419	−	0.471156i
$301$		0			0
$302$	−11.8764			−0.683412
$303$	23.7563	+	2.59615i	1.36476	+	0.149145i
$304$			1.31395i			0.0753602i
$305$	6.78552	+	11.9993i	0.388538	+	0.687079i
$306$	3.90332	−	17.6455i	0.223138	−	1.00873i
$307$	−9.31270			−0.531504			−0.265752	−	0.964041i	$-0.585620\pi$
$307$	−9.31270			−0.531504			−0.265752	+	0.964041i	$0.585620\pi$
$308$		0			0
$309$	14.3143	+	1.56431i	0.814314	+	0.0889904i
$310$	1.85999	+	3.28916i	0.105641	+	0.186812i
$311$	25.3143			1.43544			0.717722	−	0.696330i	$-0.245185\pi$
$311$	25.3143			1.43544			0.717722	+	0.696330i	$0.245185\pi$
$312$	14.2773	+	1.56026i	0.808291	+	0.0883322i
$313$	−7.64982			−0.432394			−0.216197	−	0.976350i	$-0.569365\pi$
$313$	−7.64982			−0.432394			−0.216197	+	0.976350i	$0.569365\pi$
$314$	−2.87996			−0.162526
$315$		0			0
$316$	−4.49732			−0.252994
$317$	−24.7465			−1.38990			−0.694950	−	0.719058i	$-0.744574\pi$
$317$	−24.7465			−1.38990			−0.694950	+	0.719058i	$0.744574\pi$
$318$	−2.36206	−	0.258132i	−0.132458	−	0.0144753i
$319$	23.9679			1.34195
$320$	10.6449	−	6.01959i	0.595066	−	0.336505i
$321$	−18.4871	−	2.02032i	−1.03185	−	0.112763i
$322$		0			0
$323$	−38.0580			−2.11760
$324$	−9.66163	−	4.49436i	−0.536757	−	0.249687i
$325$	7.42948	−	12.3528i	0.412114	−	0.685211i
$326$			17.4158i			0.964574i
$327$	−0.924047	−	0.100982i	−0.0510999	−	0.00558434i
$328$	−26.2381			−1.44875
$329$		0			0
$330$	−5.61339	−	13.0648i	−0.309007	−	0.719194i
$331$	−16.3562			−0.899019			−0.449509	−	0.893276i	$-0.648401\pi$
$331$	−16.3562			−0.899019			−0.449509	+	0.893276i	$0.648401\pi$
$332$		−	4.74102i		−	0.260197i
$333$	−1.03656	+	4.68591i	−0.0568029	+	0.256786i
$334$		−	0.798473i		−	0.0436905i
$335$	11.1061	+	19.6398i	0.606793	+	1.07304i
$336$		0			0
$337$			3.59256i			0.195699i	0.995201	+	0.0978497i	$0.0311964\pi$
$337$			3.59256i			0.195699i	−0.995201	+	0.0978497i	$0.968804\pi$
$338$	−4.23523			−0.230366
$339$	−20.8387	−	2.27731i	−1.13180	−	0.123686i
$340$	8.69044	+	15.3679i	0.471305	+	0.833443i
$341$	−7.60315			−0.411734
$342$	3.34046	−	15.1010i	0.180631	−	0.816571i
$343$		0			0
$344$			21.6682i			1.16827i
$345$	−5.80685	+	2.49495i	−0.312630	+	0.134324i
$346$			11.3063i			0.607832i
$347$	18.9288			1.01615			0.508075	−	0.861313i	$-0.330357\pi$
$347$	18.9288			1.01615			0.508075	+	0.861313i	$0.330357\pi$
$348$	1.31376	−	12.0216i	0.0704247	−	0.644427i
$349$			24.1751i			1.29406i	0.762463	+	0.647032i	$0.223990\pi$
$349$			24.1751i			1.29406i	−0.762463	+	0.647032i	$0.776010\pi$
$350$		0			0
$351$	−14.1888	−	4.80540i	−0.757340	−	0.256493i
$352$			22.5347i			1.20110i
$353$		−	32.1044i		−	1.70875i	−0.519660	−	0.854373i	$-0.673942\pi$
$353$		−	32.1044i		−	1.70875i	0.519660	−	0.854373i	$-0.326058\pi$
$354$	1.54269	+	0.168590i	0.0819932	+	0.00896043i
$355$	−5.29661	−	9.36638i	−0.281115	−	0.497116i
$356$	−12.3263			−0.653295
$357$		0			0
$358$		−	10.9897i		−	0.580825i
$359$			17.0670i			0.900764i	0.892836	+	0.450382i	$0.148712\pi$
$359$			17.0670i			0.900764i	−0.892836	+	0.450382i	$0.851288\pi$
$360$	−18.4497	+	5.64573i	−0.972386	+	0.297556i
$361$	−13.5700			−0.714210
$362$		−	14.6136i		−	0.768071i
$363$	9.50284	+	1.03850i	0.498770	+	0.0545069i
$364$		0			0
$365$	−1.09119	+	0.617061i	−0.0571157	+	0.0322984i
$366$	1.04787	−	9.58861i	0.0547730	−	0.501205i
$367$	−15.6751			−0.818231			−0.409116	−	0.912483i	$-0.634163\pi$
$367$	−15.6751			−0.818231			−0.409116	+	0.912483i	$0.634163\pi$
$368$	−0.375709			−0.0195852
$369$	26.7214	+	5.91095i	1.39106	+	0.307712i
$370$	1.59059	+	2.81275i	0.0826907	+	0.146228i
$371$		0			0
$372$	−0.416753	+	3.81353i	−0.0216076	+	0.197722i
$373$		−	1.04874i		−	0.0543017i	−0.999631	−	0.0271508i	$-0.991357\pi$
$373$		−	1.04874i		−	0.0543017i	0.999631	−	0.0271508i	$-0.00864345\pi$
$374$	24.4839			1.26603
$375$	−2.61916	+	19.1870i	−0.135253	+	0.990811i
$376$			19.8875i			1.02562i
$377$		−	17.0012i		−	0.875604i
$378$		0			0
$379$	−19.7185			−1.01287			−0.506436	−	0.862278i	$-0.669037\pi$
$379$	−19.7185			−1.01287			−0.506436	+	0.862278i	$0.669037\pi$
$380$	7.43727	+	13.1519i	0.381524	+	0.674676i
$381$	4.19383	−	38.3760i	0.214856	−	1.96606i
$382$			7.47777i			0.382596i
$383$		−	2.75894i		−	0.140975i	−0.997513	−	0.0704876i	$-0.977544\pi$
$383$		−	2.75894i		−	0.140975i	0.997513	−	0.0704876i	$-0.0224555\pi$
$384$	10.5866	+	1.15693i	0.540244	+	0.0590392i
$385$		0			0
$386$			14.3860i			0.732227i
$387$	4.88145	−	22.0673i	0.248138	−	1.12174i
$388$	17.2115			0.873783
$389$			31.9024i			1.61752i	0.588141	+	0.808758i	$0.299860\pi$
$389$			31.9024i			1.61752i	−0.588141	+	0.808758i	$0.700140\pi$
$390$	−9.26726	+	3.98174i	−0.469266	+	0.201623i
$391$		−	10.8822i		−	0.550339i
$392$		0			0
$393$	−0.196593	−	0.0214842i	−0.00991682	−	0.00108374i
$394$	21.5661			1.08648
$395$	7.39339	−	4.18090i	0.372002	−	0.210364i
$396$	3.11806	−	14.0957i	0.156688	−	0.708333i
$397$	−18.8205			−0.944572			−0.472286	−	0.881445i	$-0.656571\pi$
$397$	−18.8205			−0.944572			−0.472286	+	0.881445i	$0.656571\pi$
$398$		−	11.0454i		−	0.553654i
$399$		0			0
$400$	−0.593317	+	0.986494i	−0.0296658	+	0.0493247i
$401$			3.28917i			0.164253i	0.996622	+	0.0821266i	$0.0261712\pi$
$401$			3.28917i			0.164253i	−0.996622	+	0.0821266i	$0.973829\pi$
$402$	1.71509	−	15.6941i	0.0855410	−	0.782750i
$403$			5.39314i			0.268652i
$404$	16.3358			0.812735
$405$	20.0614	−	1.59334i	0.996861	−	0.0791737i
$406$		0			0
$407$	−6.50190			−0.322287
$408$	3.60904	−	33.0248i	0.178674	−	1.63497i
$409$			4.14914i			0.205162i	0.994725	+	0.102581i	$0.0327100\pi$
$409$			4.14914i			0.205162i	−0.994725	+	0.102581i	$0.967290\pi$
$410$	16.0397	−	9.07031i	0.792143	−	0.447951i
$411$	21.5978	+	2.36027i	1.06534	+	0.116423i
$412$	9.84311			0.484935
$413$		0			0
$414$	4.31797	+	0.955165i	0.212217	+	0.0469438i
$415$	4.40746	+	7.79403i	0.216354	+	0.382594i
$416$	15.9845			0.783706
$417$	0.447150	−	4.09169i	0.0218970	−	0.200371i
$418$	20.9533			1.02486
$419$	−22.6231			−1.10521			−0.552606	−	0.833443i	$-0.686367\pi$
$419$	−22.6231			−1.10521			−0.552606	+	0.833443i	$0.686367\pi$
$420$		0			0
$421$	31.9233			1.55584			0.777922	−	0.628360i	$-0.216274\pi$
$421$	31.9233			1.55584			0.777922	+	0.628360i	$0.216274\pi$
$422$	17.0406			0.829524
$423$	4.48028	−	20.2538i	0.217839	−	0.984772i
$424$	−4.36796			−0.212127
$425$	−28.5734	−	17.1852i	−1.38601	−	0.833603i
$426$	−0.817941	+	7.48464i	−0.0396294	+	0.362632i
$427$		0			0
$428$	−12.7125			−0.614481
$429$	2.20480	−	20.1752i	0.106449	−	0.974068i
$430$	−7.49054	−	13.2461i	−0.361226	−	0.638782i
$431$		−	25.0448i		−	1.20636i	−0.797604	−	0.603182i	$-0.793899\pi$
$431$		−	25.0448i		−	1.20636i	0.797604	−	0.603182i	$-0.206101\pi$
$432$	1.13311	+	0.383758i	0.0545168	+	0.0184636i
$433$	5.10220			0.245196			0.122598	−	0.992456i	$-0.460877\pi$
$433$	5.10220			0.245196			0.122598	+	0.992456i	$0.460877\pi$
$434$		0			0
$435$	9.01607	+	20.9843i	0.432288	+	1.00612i
$436$	−0.635412			−0.0304307
$437$		−	9.31302i		−	0.445502i
$438$	0.871968	+	0.0952910i	0.0416643	+	0.00455318i
$439$		−	11.2880i		−	0.538746i	−0.963036	−	0.269373i	$-0.913184\pi$
$439$		−	11.2880i		−	0.538746i	0.963036	−	0.269373i	$-0.0868165\pi$
$440$	−12.8669	−	22.7535i	−0.613407	−	1.08473i
$441$		0			0
$442$		−	17.3672i		−	0.826073i
$443$	−21.9182			−1.04136			−0.520681	−	0.853751i	$-0.674322\pi$
$443$	−21.9182			−1.04136			−0.520681	+	0.853751i	$0.674322\pi$
$444$	−0.356389	+	3.26117i	−0.0169135	+	0.154768i
$445$	20.2640	−	11.4591i	0.960604	−	0.543214i
$446$	17.4145			0.824601
$447$	−3.09875	+	28.3554i	−0.146566	+	1.34116i
$448$		0			0
$449$		−	0.449397i		−	0.0212083i	−0.999944	−	0.0106042i	$-0.996625\pi$
$449$		−	0.449397i		−	0.0212083i	0.999944	−	0.0106042i	$-0.00337548\pi$
$450$	9.32687	−	9.82925i	0.439673	−	0.463355i
$451$			37.0770i			1.74589i
$452$	−14.3295			−0.674004
$453$	22.6370	+	2.47383i	1.06358	+	0.116231i
$454$			10.3900i			0.487625i
$455$		0			0
$456$	3.08861	−	28.2626i	0.144638	−	1.32352i
$457$			9.29288i			0.434702i	0.976093	+	0.217351i	$0.0697417\pi$
$457$			9.29288i			0.434702i	−0.976093	+	0.217351i	$0.930258\pi$
$458$			15.6939i			0.733328i
$459$	−11.1154	+	32.8201i	−0.518823	+	1.53191i
$460$	−3.76062	+	2.12660i	−0.175340	+	0.0991533i
$461$	20.8668			0.971863			0.485931	−	0.873997i	$-0.338481\pi$
$461$	20.8668			0.971863			0.485931	+	0.873997i	$0.338481\pi$
$462$		0			0
$463$		−	2.45294i		−	0.113998i	−0.998374	−	0.0569989i	$-0.981847\pi$
$463$		−	2.45294i		−	0.113998i	0.998374	−	0.0569989i	$-0.0181532\pi$
$464$			1.35771i			0.0630300i
$465$	−2.86010	−	6.65670i	−0.132634	−	0.308697i
$466$	−0.418110			−0.0193686
$467$			7.97995i			0.369268i	0.982807	+	0.184634i	$0.0591100\pi$
$467$			7.97995i			0.369268i	−0.982807	+	0.184634i	$0.940890\pi$
$468$	−9.99847	−	2.21173i	−0.462179	−	0.102237i
$469$		0			0
$470$	−6.87495	−	12.1575i	−0.317118	−	0.560782i
$471$	5.48932	+	0.599887i	0.252935	+	0.0276414i
$472$	2.85277			0.131309
$473$	30.6193			1.40788
$474$	−5.90803	−	0.645645i	−0.271365	−	0.0296555i
$475$	−24.4531	−	14.7071i	−1.12198	−	0.674806i
$476$		0			0
$477$	4.44841	+	0.984021i	0.203679	+	0.0450552i
$478$		−	15.6327i		−	0.715023i
$479$	−13.8929			−0.634784			−0.317392	−	0.948294i	$-0.602807\pi$
$479$	−13.8929			−0.634784			−0.317392	+	0.948294i	$0.602807\pi$
$480$	−19.7295	+	8.47693i	−0.900526	+	0.386917i
$481$			4.61199i			0.210289i
$482$			3.86574i			0.176080i
$483$		0			0
$484$	6.53454			0.297024
$485$	−28.2950	+	16.0006i	−1.28481	+	0.726549i
$486$	−12.0471	−	7.29119i	−0.546465	−	0.330735i
$487$		−	26.5108i		−	1.20132i	−0.799505	−	0.600659i	$-0.794905\pi$
$487$		−	26.5108i		−	1.20132i	0.799505	−	0.600659i	$-0.205095\pi$
$488$		−	17.7314i		−	0.802663i
$489$	3.62767	−	33.1953i	0.164049	−	1.50114i
$490$		0			0
$491$			2.54611i			0.114905i	0.998348	+	0.0574523i	$0.0182977\pi$
$491$			2.54611i			0.114905i	−0.998348	+	0.0574523i	$0.981702\pi$
$492$	18.5968	+	2.03231i	0.838408	+	0.0916234i
$493$	−39.3255			−1.77113
$494$		−	14.8628i		−	0.668710i
$495$	7.97798	+	26.0713i	0.358584	+	1.17182i
$496$		−	0.430695i		−	0.0193388i
$497$		0			0
$498$	0.680632	−	6.22818i	0.0304999	−	0.279091i
$499$	29.6496			1.32730			0.663649	−	0.748044i	$-0.269007\pi$
$499$	29.6496			1.32730			0.663649	+	0.748044i	$0.269007\pi$
$500$	−0.354958	+	13.2325i	−0.0158742	+	0.591777i
$501$	−0.166320	+	1.52192i	−0.00743061	+	0.0679945i
$502$	−15.7312			−0.702118
$503$			31.2378i			1.39283i	0.717642	+	0.696413i	$0.245222\pi$
$503$			31.2378i			1.39283i	−0.717642	+	0.696413i	$0.754778\pi$
$504$		0			0
$505$	−26.8553	+	15.1864i	−1.19504	+	0.675787i
$506$			5.99136i			0.266349i
$507$	8.07252	+	0.882186i	0.358513	+	0.0391793i
$508$		−	26.3889i		−	1.17082i
$509$	−38.0143			−1.68496			−0.842478	−	0.538731i	$-0.818904\pi$
$509$	−38.0143			−1.68496			−0.842478	+	0.538731i	$0.818904\pi$
$510$	9.21019	+	21.4361i	0.407834	+	0.949208i
$511$		0			0
$512$	−2.60093			−0.114946
$513$	−9.51255	+	28.0874i	−0.419989	+	1.24009i
$514$		−	13.9260i		−	0.614248i
$515$	−16.1816	+	9.15058i	−0.713048	+	0.403223i
$516$	1.67834	−	15.3578i	0.0738848	−	0.676089i
$517$	28.1030			1.23597
$518$		0			0
$519$	2.35507	−	21.5503i	0.103376	−	0.945953i
$520$	−16.1397	+	9.12690i	−0.707775	+	0.400241i
$521$	39.1414			1.71481			0.857407	−	0.514639i	$-0.172074\pi$
$521$	39.1414			1.71481			0.857407	+	0.514639i	$0.172074\pi$
$522$	3.45170	−	15.6040i	0.151077	−	0.682966i
$523$	−7.97176			−0.348581			−0.174290	−	0.984694i	$-0.555763\pi$
$523$	−7.97176			−0.348581			−0.174290	+	0.984694i	$0.555763\pi$
$524$	−0.135186			−0.00590561
$525$		0			0
$526$	5.61127			0.244663
$527$	12.4749			0.543416
$528$	−0.176075	+	1.61119i	−0.00766267	+	0.0701179i
$529$	−20.3371			−0.884220
$530$	2.67019	−	1.50997i	0.115986	−	0.0655890i
$531$	−2.90532	−	0.642677i	−0.126080	−	0.0278898i
$532$		0			0
$533$	26.2998			1.13917
$534$	−16.1929	−	1.76960i	−0.700734	−	0.0765780i
$535$	20.8987	−	11.8181i	0.903531	−	0.510940i
$536$		−	29.0217i		−	1.25355i
$537$	−2.28913	+	20.9469i	−0.0987831	+	0.903923i
$538$	5.41163			0.233312
$539$		0			0
$540$	13.5139	−	2.57248i	0.581547	−	0.110702i
$541$	−8.08347			−0.347536			−0.173768	−	0.984787i	$-0.555594\pi$
$541$	−8.08347			−0.347536			−0.173768	+	0.984787i	$0.555594\pi$
$542$			5.64148i			0.242323i
$543$	−3.04396	+	27.8540i	−0.130629	+	1.19533i
$544$		−	36.9739i		−	1.58524i
$545$	1.04459	−	0.590707i	0.0447453	−	0.0253031i
$546$		0			0
$547$		−	37.0430i		−	1.58384i	−0.610623	−	0.791922i	$-0.709081\pi$
$547$		−	37.0430i		−	1.58384i	0.610623	−	0.791922i	$-0.290919\pi$
$548$	14.8515			0.634426
$549$	−3.99456	+	18.0580i	−0.170484	+	0.770697i
$550$	15.7314	+	9.46152i	0.670791	+	0.403441i
$551$	−33.6547			−1.43374
$552$	8.08137	+	0.883153i	0.343966	+	0.0375895i
$553$		0			0
$554$			7.86288i			0.334062i
$555$	−2.44584	−	5.69253i	−0.103820	−	0.241634i
$556$		−	2.81361i		−	0.119324i
$557$	8.88856			0.376620			0.188310	−	0.982110i	$-0.439699\pi$
$557$	8.88856			0.376620			0.188310	+	0.982110i	$0.439699\pi$
$558$	−1.09496	+	4.94992i	−0.0463533	+	0.209547i
$559$		−	21.7192i		−	0.918624i
$560$		0			0
$561$	−46.6674	−	5.09993i	−1.97030	−	0.215319i
$562$		−	3.94103i		−	0.166242i
$563$			39.4078i			1.66084i	0.557136	+	0.830421i	$0.311900\pi$
$563$			39.4078i			1.66084i	−0.557136	+	0.830421i	$0.688100\pi$
$564$	1.54041	−	14.0957i	0.0648630	−	0.593534i
$565$	23.5571	−	13.3213i	0.991054	−	0.560433i
$566$	−6.79378			−0.285564
$567$		0			0
$568$			13.8407i			0.580744i
$569$			17.4528i			0.731659i	0.930682	+	0.365830i	$0.119215\pi$
$569$			17.4528i			0.731659i	−0.930682	+	0.365830i	$0.880785\pi$
$570$	7.88207	+	18.3450i	0.330144	+	0.768388i
$571$	−19.3889			−0.811399			−0.405700	−	0.914006i	$-0.632972\pi$
$571$	−19.3889			−0.811399			−0.405700	+	0.914006i	$0.632972\pi$
$572$		−	13.8733i		−	0.580071i
$573$	1.55760	−	14.2529i	0.0650696	−	0.595425i
$574$		0			0
$575$	4.20531	−	6.99207i	0.175374	−	0.291590i
$576$	16.0197	+	3.54367i	0.667486	+	0.147653i
$577$	41.7306			1.73727			0.868633	−	0.495455i	$-0.164999\pi$
$577$	41.7306			1.73727			0.868633	+	0.495455i	$0.164999\pi$
$578$	−24.8154			−1.03218
$579$	2.99656	−	27.4203i	0.124533	−	1.13955i
$580$	7.68495	+	13.5899i	0.319100	+	0.564288i
$581$		0			0
$582$	22.6104	+	2.47093i	0.937232	+	0.102423i
$583$			6.17236i			0.255633i
$584$	1.61246			0.0667240
$585$	18.4931	−	5.65902i	0.764598	−	0.233972i
$586$			0.0956500i			0.00395126i
$587$			19.5477i			0.806820i	0.915019	+	0.403410i	$0.132175\pi$
$587$			19.5477i			0.806820i	−0.915019	+	0.403410i	$0.867825\pi$
$588$		0			0
$589$	10.6760			0.439897
$590$	−1.74394	+	0.986182i	−0.0717967	+	0.0406005i
$591$	−41.1059	−	4.49216i	−1.69087	−	0.184783i
$592$		−	0.368312i		−	0.0151375i
$593$		−	2.63145i		−	0.108061i	−0.998539	−	0.0540303i	$-0.982793\pi$
$593$		−	2.63145i		−	0.108061i	0.998539	−	0.0540303i	$-0.0172067\pi$
$594$	6.11973	−	18.0695i	0.251096	−	0.741401i
$595$		0			0
$596$			19.4983i			0.798683i
$597$	−2.30072	+	21.0529i	−0.0941621	+	0.861639i
$598$	4.24985			0.173789
$599$		−	31.2146i		−	1.27539i	−0.770287	−	0.637697i	$-0.779887\pi$
$599$		−	31.2146i		−	1.27539i	0.770287	−	0.637697i	$-0.220113\pi$
$600$	15.0809	−	19.8245i	0.615676	−	0.809331i
$601$			15.6798i			0.639593i	0.947486	+	0.319797i	$0.103615\pi$
$601$			15.6798i			0.639593i	−0.947486	+	0.319797i	$0.896385\pi$
$602$		0			0
$603$	−6.53806	+	29.5563i	−0.266251	+	1.20363i
$604$	15.5661			0.633376
$605$	−10.7425	+	6.07479i	−0.436744	+	0.246975i
$606$	21.4599	+	2.34520i	0.871751	+	0.0952672i
$607$	−4.81384			−0.195388			−0.0976940	−	0.995217i	$-0.531147\pi$
$607$	−4.81384			−0.195388			−0.0976940	+	0.995217i	$0.531147\pi$
$608$		−	31.6422i		−	1.28326i
$609$		0			0
$610$	6.12962	+	10.8394i	0.248181	+	0.438876i
$611$		−	19.9343i		−	0.806454i
$612$	−5.11597	+	23.1275i	−0.206801	+	0.934874i
$613$			40.0717i			1.61848i	0.587478	+	0.809240i	$0.300121\pi$
$613$			40.0717i			1.61848i	−0.587478	+	0.809240i	$0.699879\pi$
$614$	−8.41253			−0.339502
$615$	−32.4616	+	13.9474i	−1.30898	+	0.562412i
$616$		0			0
$617$	−18.4205			−0.741583			−0.370791	−	0.928716i	$-0.620913\pi$
$617$	−18.4205			−0.741583			−0.370791	+	0.928716i	$0.620913\pi$
$618$	12.9307	+	1.41310i	0.520149	+	0.0568432i
$619$		−	11.0209i		−	0.442968i	−0.975164	−	0.221484i	$-0.928910\pi$
$619$		−	11.0209i		−	0.442968i	0.975164	−	0.221484i	$-0.0710901\pi$
$620$	−2.43784	−	4.31100i	−0.0979059	−	0.173134i
$621$	−8.03126	−	2.72000i	−0.322284	−	0.109150i
$622$	22.8674			0.916899
$623$		0			0
$624$	1.14286	+	0.124895i	0.0457512	+	0.00499981i
$625$	−11.7180	−	22.0837i	−0.468720	−	0.883347i
$626$	−6.91038			−0.276194
$627$	−39.9379	−	4.36452i	−1.59497	−	0.174302i
$628$	3.77468			0.150626
$629$	10.6680			0.425362
$630$		0			0
$631$	16.0604			0.639355			0.319678	−	0.947526i	$-0.396425\pi$
$631$	16.0604			0.639355			0.319678	+	0.947526i	$0.396425\pi$
$632$	−10.9252			−0.434582
$633$	−32.4801	−	3.54951i	−1.29097	−	0.141080i
$634$	−22.3545			−0.887809
$635$	24.5322	+	43.3821i	0.973532	+	1.72157i
$636$	3.09588	+	0.338326i	0.122760	+	0.0134155i
$637$		0			0
$638$	21.6511			0.857177
$639$	3.11806	−	14.0957i	0.123348	−	0.557615i
$640$	−11.9676	+	6.76757i	−0.473060	+	0.267512i
$641$			39.7927i			1.57172i	0.618405	+	0.785859i	$0.287779\pi$
$641$			39.7927i			1.57172i	−0.618405	+	0.785859i	$0.712221\pi$
$642$	−16.7001	−	1.82503i	−0.659100	−	0.0720282i
$643$	22.4164			0.884016			0.442008	−	0.897011i	$-0.354266\pi$
$643$	22.4164			0.884016			0.442008	+	0.897011i	$0.354266\pi$
$644$		0			0
$645$	11.5182	+	26.8078i	0.453527	+	1.05556i
$646$	−34.3793			−1.35263
$647$			25.5715i			1.00532i	0.864484	+	0.502660i	$0.167645\pi$
$647$			25.5715i			1.00532i	−0.864484	+	0.502660i	$0.832355\pi$
$648$	−23.4708	−	10.9180i	−0.922018	−	0.428901i
$649$		−	4.03125i		−	0.158240i
$650$	6.71134	−	11.1588i	0.263240	−	0.437684i
$651$		0			0
$652$		−	22.8264i		−	0.893952i
$653$	−16.9984			−0.665199			−0.332600	−	0.943068i	$-0.607926\pi$
$653$	−16.9984			−0.665199			−0.332600	+	0.943068i	$0.607926\pi$
$654$	−0.834728	−	0.0912212i	−0.0326404	−	0.00356703i
$655$	0.222239	−	0.125674i	0.00868359	−	0.00491050i
$656$	−2.10030			−0.0820029
$657$	−1.64216	−	0.363257i	−0.0640667	−	0.0141720i
$658$		0			0
$659$		−	2.82840i		−	0.110179i	−0.998481	−	0.0550894i	$-0.982456\pi$
$659$		−	2.82840i		−	0.110179i	0.998481	−	0.0550894i	$-0.0175444\pi$
$660$	7.35730	+	17.1237i	0.286383	+	0.666537i
$661$			14.5840i			0.567252i	0.958935	+	0.283626i	$0.0915374\pi$
$661$			14.5840i			0.567252i	−0.958935	+	0.283626i	$0.908463\pi$
$662$	−14.7752			−0.574254
$663$	−3.61754	+	33.1026i	−0.140493	+	1.28560i
$664$		−	11.5172i		−	0.446956i
$665$		0			0
$666$	−0.936361	+	4.23296i	−0.0362833	+	0.164024i
$667$		−	9.62317i		−	0.372611i
$668$			1.04654i			0.0404917i
$669$	−33.1927	−	3.62739i	−1.28331	−	0.140243i
$670$	10.0326	+	17.7414i	0.387593	+	0.685409i
$671$	−25.0563			−0.967286
$672$		0			0
$673$		−	13.2666i		−	0.511390i	−0.966757	−	0.255695i	$-0.917696\pi$
$673$		−	13.2666i		−	0.511390i	0.966757	−	0.255695i	$-0.0823043\pi$
$674$			3.24530i			0.125004i
$675$	−19.8248	+	16.7922i	−0.763057	+	0.646331i
$676$	5.55099			0.213500
$677$			27.3389i			1.05072i	0.850880	+	0.525360i	$0.176069\pi$
$677$			27.3389i			1.05072i	−0.850880	+	0.525360i	$0.823931\pi$
$678$	−18.8244	−	2.05718i	−0.722946	−	0.0790055i
$679$		0			0
$680$	21.1115	+	37.3329i	0.809588	+	1.43165i
$681$	2.16420	−	19.8037i	0.0829323	−	0.758879i
$682$	−6.86822			−0.262998
$683$	5.07338			0.194127			0.0970637	−	0.995278i	$-0.469055\pi$
$683$	5.07338			0.194127			0.0970637	+	0.995278i	$0.469055\pi$
$684$	−4.37824	+	19.7925i	−0.167406	+	0.756785i
$685$	−24.4153	+	13.8066i	−0.932859	+	0.527524i
$686$		0			0
$687$	3.26900	−	29.9132i	0.124720	−	1.14126i
$688$			1.73449i			0.0661268i
$689$	4.37824			0.166798
$690$	−5.24555	+	2.25379i	−0.199695	+	0.0858002i
$691$			34.2569i			1.30319i	0.758566	+	0.651596i	$0.225900\pi$
$691$			34.2569i			1.30319i	−0.758566	+	0.651596i	$0.774100\pi$
$692$		−	14.8189i		−	0.563329i
$693$		0			0
$694$	17.0991			0.649073
$695$	2.61565	+	4.62545i	0.0992173	+	0.175453i
$696$	3.19147	−	29.2038i	0.120972	−	1.10697i
$697$		−	60.8343i		−	2.30426i
$698$			21.8383i			0.826592i
$699$	0.796935	+	0.0870911i	0.0301428	+	0.00329409i
$700$		0			0
$701$			17.6912i			0.668188i	0.942540	+	0.334094i	$0.108430\pi$
$701$			17.6912i			0.668188i	−0.942540	+	0.334094i	$0.891570\pi$
$702$	−12.8172	−	4.34091i	−0.483756	−	0.163837i
$703$	9.12967			0.344332
$704$			22.2280i			0.837748i
$705$	10.5716	+	24.6046i	0.398148	+	0.926665i
$706$		−	29.0012i		−	1.09147i
$707$		0			0
$708$	−2.02196	−	0.220965i	−0.0759900	−	0.00830439i
$709$	15.6175			0.586527			0.293264	−	0.956032i	$-0.405259\pi$
$709$	15.6175			0.586527			0.293264	+	0.956032i	$0.405259\pi$
$710$	−4.78463	−	8.46101i	−0.179564	−	0.317536i
$711$	11.1265	+	2.46125i	0.417275	+	0.0923041i
$712$	−29.9441			−1.12220
$713$			3.05268i			0.114324i
$714$		0			0
$715$	12.8972	+	22.8071i	0.482328	+	0.852936i
$716$			14.4039i			0.538299i
$717$	−3.25625	+	29.7966i	−0.121607	+	1.11277i
$718$			15.4173i			0.575369i
$719$	−16.1436			−0.602054			−0.301027	−	0.953616i	$-0.597329\pi$
$719$	−16.1436			−0.602054			−0.301027	+	0.953616i	$0.597329\pi$
$720$	−1.47686	+	0.451928i	−0.0550393	+	0.0168424i
$721$		0			0
$722$	−12.2583			−0.456207
$723$	0.805223	−	7.36826i	0.0299466	−	0.274029i
$724$			19.1536i			0.711836i
$725$	−25.2674	−	15.1968i	−0.938409	−	0.564396i
$726$	8.58428	+	0.938113i	0.318592	+	0.0348166i
$727$	16.8426			0.624657			0.312329	−	0.949974i	$-0.398891\pi$
$727$	16.8426			0.624657			0.312329	+	0.949974i	$0.398891\pi$
$728$		0			0
$729$	21.4434	+	16.4067i	0.794201	+	0.607655i
$730$	−0.985717	+	0.557415i	−0.0364830	+	0.0206309i
$731$	−50.2388			−1.85815
$732$	−1.37341	+	12.5675i	−0.0507627	+	0.464509i
$733$	22.1743			0.819028			0.409514	−	0.912304i	$-0.365698\pi$
$733$	22.1743			0.819028			0.409514	+	0.912304i	$0.365698\pi$
$734$	−14.1599			−0.522651
$735$		0			0
$736$	9.04773			0.333504
$737$	−41.0106			−1.51065
$738$	24.1384	+	5.33959i	0.888548	+	0.196553i
$739$	42.4525			1.56164			0.780820	−	0.624757i	$-0.214802\pi$
$739$	42.4525			1.56164			0.780820	+	0.624757i	$0.214802\pi$
$740$	−2.08474	−	3.68659i	−0.0766364	−	0.135522i
$741$	−3.09588	+	28.3291i	−0.113730	+	1.04070i
$742$		0			0
$743$	24.5486			0.900600			0.450300	−	0.892877i	$-0.351317\pi$
$743$	24.5486			0.900600			0.450300	+	0.892877i	$0.351317\pi$
$744$	−1.01241	+	9.26411i	−0.0371166	+	0.339639i
$745$	−18.1265	−	32.0544i	−0.664103	−	1.17438i
$746$		−	0.947367i		−	0.0346856i
$747$	−2.59462	+	11.7294i	−0.0949323	+	0.429156i
$748$	−32.0904			−1.17334
$749$		0			0
$750$	−2.36599	+	17.3323i	−0.0863938	+	0.632887i
$751$	25.3766			0.926006			0.463003	−	0.886357i	$-0.346772\pi$
$751$	25.3766			0.926006			0.463003	+	0.886357i	$0.346772\pi$
$752$			1.59195i			0.0580523i
$753$	29.9843	+	3.27676i	1.09269	+	0.119412i
$754$		−	15.3578i		−	0.559298i
$755$	−25.5900	+	14.4709i	−0.931314	+	0.526651i
$756$		0			0
$757$		−	18.9214i		−	0.687709i	−0.939023	−	0.343854i	$-0.888267\pi$
$757$		−	18.9214i		−	0.687709i	0.939023	−	0.343854i	$-0.111733\pi$
$758$	−17.8125			−0.646979
$759$	1.24798	−	11.4198i	0.0452989	−	0.414512i
$760$	18.0672	+	31.9495i	0.655365	+	1.15893i
$761$	10.2582			0.371859			0.185929	−	0.982563i	$-0.440470\pi$
$761$	10.2582			0.371859			0.185929	+	0.982563i	$0.440470\pi$
$762$	3.78845	−	34.6665i	0.137241	−	1.25583i
$763$		0			0
$764$		−	9.80090i		−	0.354584i
$765$	−13.0899	−	42.7766i	−0.473267	−	1.54659i
$766$		−	2.49226i		−	0.0900489i
$767$	−2.85949			−0.103250
$768$	28.3962	+	3.10321i	1.02466	+	0.111978i
$769$			17.8947i			0.645298i	0.946519	+	0.322649i	$0.104573\pi$
$769$			17.8947i			0.645298i	−0.946519	+	0.322649i	$0.895427\pi$
$770$		0			0
$771$	−2.90074	+	26.5434i	−0.104468	+	0.955939i
$772$		−	18.8553i		−	0.678616i
$773$			10.3218i			0.371251i	0.982621	+	0.185626i	$0.0594311\pi$
$773$			10.3218i			0.371251i	−0.982621	+	0.185626i	$0.940569\pi$
$774$	4.40960	−	19.9343i	0.158500	−	0.716522i
$775$	8.01539	+	4.82078i	0.287921	+	0.173167i
$776$	41.8116			1.50095
$777$		0			0
$778$			28.8187i			1.03320i
$779$		−	52.0619i		−	1.86531i
$780$	12.1463	−	5.21875i	0.434908	−	0.186861i
$781$	19.5583			0.699851
$782$		−	9.83035i		−	0.351533i
$783$	−9.82935	+	29.0228i	−0.351272	+	1.03719i
$784$		0			0
$785$	−6.20540	+	3.50911i	−0.221480	+	0.125245i
$786$	−0.177590	−	0.0194075i	−0.00633444	−	0.000692244i
$787$	12.5268			0.446531			0.223265	−	0.974758i	$-0.428328\pi$
$787$	12.5268			0.446531			0.223265	+	0.974758i	$0.428328\pi$
$788$	−28.2661			−1.00694
$789$	−10.6953	−	1.16881i	−0.380763	−	0.0416108i
$790$	6.67873	−	3.77677i	0.237619	−	0.134371i
$791$		0			0
$792$	7.57462	−	34.2422i	0.269152	−	1.21674i
$793$			17.7731i			0.631143i
$794$	−17.0012			−0.603352
$795$	−5.40401	+	2.32187i	−0.191661	+	0.0823484i
$796$			14.4768i			0.513118i
$797$		−	23.4184i		−	0.829521i	−0.909931	−	0.414761i	$-0.863865\pi$
$797$		−	23.4184i		−	0.829521i	0.909931	−	0.414761i	$-0.136135\pi$
$798$		0			0
$799$	−46.1100			−1.63126
$800$	14.2881	−	23.7565i	0.505161	−	0.839919i
$801$	30.4956	+	6.74585i	1.07751	+	0.238353i
$802$			2.97123i			0.104918i
$803$		−	2.27856i		−	0.0804088i
$804$	−2.24792	+	20.5698i	−0.0792780	+	0.725440i
$805$		0			0
$806$			4.87184i			0.171603i
$807$	−10.3148	−	1.12723i	−0.363098	−	0.0396803i
$808$	39.6841			1.39608
$809$		−	10.9751i		−	0.385863i	−0.981212	−	0.192932i	$-0.938200\pi$
$809$		−	10.9751i		−	0.385863i	0.981212	−	0.192932i	$-0.0617995\pi$
$810$	18.1223	−	1.43933i	0.636752	−	0.0505727i
$811$			35.5390i			1.24794i	0.781448	+	0.623971i	$0.214482\pi$
$811$			35.5390i			1.24794i	−0.781448	+	0.623971i	$0.785518\pi$
$812$		0			0
$813$	1.17511	−	10.7529i	0.0412127	−	0.377121i
$814$	−5.87341			−0.205863
$815$	21.2204	+	37.5256i	0.743319	+	1.31446i
$816$	0.288896	−	2.64356i	0.0101134	−	0.0925432i
$817$	−42.9943			−1.50418
$818$			3.74808i			0.131048i
$819$		0			0
$820$	−21.0227	+	11.8882i	−0.734146	+	0.415154i
$821$			45.6211i			1.59219i	0.605173	+	0.796094i	$0.293104\pi$
$821$			45.6211i			1.59219i	−0.605173	+	0.796094i	$0.706896\pi$
$822$	19.5102	+	2.13212i	0.680495	+	0.0743663i
$823$			13.8784i			0.483769i	0.970305	+	0.241885i	$0.0777655\pi$
$823$			13.8784i			0.483769i	−0.970305	+	0.241885i	$0.922234\pi$
$824$	23.9116			0.833001
$825$	−28.0140	−	21.3109i	−0.975321	−	0.741949i
$826$		0			0
$827$	12.3739			0.430283			0.215141	−	0.976583i	$-0.430979\pi$
$827$	12.3739			0.430283			0.215141	+	0.976583i	$0.430979\pi$
$828$	−5.65943	−	1.25191i	−0.196679	−	0.0435068i
$829$			10.6696i			0.370569i	0.982685	+	0.185284i	$0.0593206\pi$
$829$			10.6696i			0.370569i	−0.982685	+	0.185284i	$0.940679\pi$
$830$	3.98143	+	7.04065i	0.138197	+	0.244384i
$831$	1.63781	−	14.9870i	0.0568152	−	0.519892i
$832$	15.7670			0.546621
$833$		0			0
$834$	0.403928	−	3.69618i	0.0139869	−	0.127988i
$835$	−0.972905	−	1.72046i	−0.0336687	−	0.0595389i
$836$	−27.4629			−0.949825
$837$	3.11809	−	9.20667i	0.107777	−	0.318229i
$838$	−20.4363			−0.705962
$839$	17.5497			0.605883			0.302941	−	0.953009i	$-0.402031\pi$
$839$	17.5497			0.605883			0.302941	+	0.953009i	$0.402031\pi$
$840$		0			0
$841$	−5.77548			−0.199154
$842$	28.8375			0.993807
$843$	−0.820905	+	7.51176i	−0.0282735	+	0.258719i
$844$	−22.3346			−0.768789
$845$	−9.12558	+	5.16044i	−0.313930	+	0.177525i
$846$	4.04721	−	18.2960i	0.139146	−	0.629030i
$847$		0			0
$848$	−0.349645			−0.0120069
$849$	12.9492	+	1.41513i	0.444416	+	0.0485670i
$850$	−25.8114	−	15.5240i	−0.885325	−	0.532470i
$851$			2.61053i			0.0894876i
$852$	1.07205	−	9.80990i	0.0367279	−	0.336082i
$853$	−29.6157			−1.01402			−0.507011	−	0.861940i	$-0.669250\pi$
$853$	−29.6157			−1.01402			−0.507011	+	0.861940i	$0.669250\pi$
$854$		0			0
$855$	−11.2023	−	36.6082i	−0.383112	−	1.25197i
$856$	−30.8821			−1.05553
$857$		−	44.6019i		−	1.52357i	−0.647828	−	0.761787i	$-0.724323\pi$
$857$		−	44.6019i		−	1.52357i	0.647828	−	0.761787i	$-0.275677\pi$
$858$	1.99168	−	18.2250i	0.0679949	−	0.622193i
$859$			6.43276i			0.219483i	0.993960	+	0.109741i	$0.0350023\pi$
$859$			6.43276i			0.219483i	−0.993960	+	0.109741i	$0.964998\pi$
$860$	9.81763	+	17.3612i	0.334778	+	0.592013i
$861$		0			0
$862$		−	22.6239i		−	0.770573i
$863$	53.3510			1.81609			0.908045	−	0.418872i	$-0.137575\pi$
$863$	53.3510			1.81609			0.908045	+	0.418872i	$0.137575\pi$
$864$	−27.2873	−	9.24158i	−0.928333	−	0.314405i
$865$	13.7763	+	24.3615i	0.468407	+	0.828317i
$866$	4.60902			0.156621
$867$	47.2991	+	5.16897i	1.60636	+	0.175547i
$868$		0			0
$869$			15.4384i			0.523713i
$870$	8.14457	+	18.9560i	0.276127	+	0.642667i
$871$			29.0901i			0.985679i
$872$	−1.54359			−0.0522726
$873$	−42.5817	−	9.41937i	−1.44117	−	0.318797i
$874$		−	8.41281i		−	0.284567i
$875$		0			0
$876$	−1.14286	−	0.124895i	−0.0386138	−	0.00421982i
$877$			35.4862i			1.19828i	0.800643	+	0.599142i	$0.204492\pi$
$877$			35.4862i			1.19828i	−0.800643	+	0.599142i	$0.795508\pi$
$878$		−	10.1969i		−	0.344128i
$879$	0.0199236	−	0.182313i	0.000672007	−	0.00614926i
$880$	−1.02997	−	1.82137i	−0.0347202	−	0.0613983i
$881$	25.0114			0.842655			0.421327	−	0.906909i	$-0.361564\pi$
$881$	25.0114			0.842655			0.421327	+	0.906909i	$0.361564\pi$
$882$		0			0
$883$			30.1344i			1.01410i	0.861916	+	0.507051i	$0.169264\pi$
$883$			30.1344i			1.01410i	−0.861916	+	0.507051i	$0.830736\pi$
$884$			22.7627i			0.765591i
$885$	3.52943	−	1.51645i	0.118641	−	0.0509748i
$886$	−19.7995			−0.665178
$887$			9.05903i			0.304172i	0.988367	+	0.152086i	$0.0485991\pi$
$887$			9.05903i			0.304172i	−0.988367	+	0.152086i	$0.951401\pi$
$888$	−0.865767	+	7.92227i	−0.0290532	+	0.265854i
$889$		0			0
$890$	18.3052	−	10.3515i	0.613592	−	0.346982i
$891$	−15.4283	+	33.1665i	−0.516867	+	1.11112i
$892$	−22.8247			−0.764227
$893$	−39.4609			−1.32051
$894$	−2.79922	+	25.6145i	−0.0936200	+	0.856678i
$895$	−13.3905	−	23.6794i	−0.447595	−	0.791514i
$896$		0			0
$897$	−8.10039	−	0.885232i	−0.270464	−	0.0295570i
$898$		−	0.405957i		−	0.0135470i
$899$	11.0316			0.367923
$900$	−12.2245	+	12.8829i	−0.407482	+	0.429430i
$901$		−	10.1273i		−	0.337390i
$902$			33.4931i			1.11520i
$903$		0			0
$904$	−34.8104			−1.15778
$905$	−17.8060	−	31.4876i	−0.591891	−	1.04668i
$906$	20.4489	+	2.23470i	0.679368	+	0.0742431i
$907$		−	9.48346i		−	0.314893i	−0.987528	−	0.157447i	$-0.949674\pi$
$907$		−	9.48346i		−	0.314893i	0.987528	−	0.157447i	$-0.0503262\pi$
$908$		−	13.6178i		−	0.451923i
$909$	−40.4150	−	8.94009i	−1.34048	−	0.296524i
$910$		0			0
$911$		−	56.8415i		−	1.88324i	−0.336672	−	0.941622i	$-0.609301\pi$
$911$		−	56.8415i		−	1.88324i	0.336672	−	0.941622i	$-0.390699\pi$
$912$	0.247236	−	2.26236i	0.00818682	−	0.0749142i
$913$	−16.2750			−0.538625
$914$			8.39461i			0.277669i
$915$	−9.42548	−	21.9372i	−0.311597	−	0.725222i
$916$		−	20.5695i		−	0.679637i
$917$		0			0
$918$	−10.0410	+	29.6476i	−0.331402	+	0.978518i
$919$	−57.3678			−1.89239			−0.946195	−	0.323598i	$-0.895107\pi$
$919$	−57.3678			−1.89239			−0.946195	+	0.323598i	$0.895107\pi$
$920$	−9.13558	+	5.16610i	−0.301191	+	0.170321i
$921$	16.0346	+	1.75230i	0.528358	+	0.0577404i
$922$	18.8498			0.620784
$923$		−	13.8733i		−	0.456645i
$924$		0			0
$925$	6.85442	+	4.12252i	0.225372	+	0.135548i
$926$		−	2.21584i		−	0.0728169i
$927$	−24.3521	−	5.38685i	−0.799827	−	0.176927i
$928$		−	32.6960i		−	1.07330i
$929$	10.2934			0.337714			0.168857	−	0.985641i	$-0.445992\pi$
$929$	10.2934			0.337714			0.168857	+	0.985641i	$0.445992\pi$
$930$	−2.58364	−	6.01326i	−0.0847208	−	0.197182i
$931$		0			0
$932$	0.548005			0.0179505
$933$	−43.5862	−	4.76321i	−1.42695	−	0.155941i
$934$			7.20859i			0.235872i
$935$	52.7551	−	29.8326i	1.72528	−	0.975631i
$936$	−24.2890	−	5.37290i	−0.793912	−	0.175619i
$937$	−29.0347			−0.948522			−0.474261	−	0.880384i	$-0.657285\pi$
$937$	−29.0347			−0.948522			−0.474261	+	0.880384i	$0.657285\pi$
$938$		0			0
$939$	13.1715	+	1.43941i	0.429835	+	0.0469735i
$940$	9.01079	+	15.9344i	0.293900	+	0.519724i
$941$	−14.9717			−0.488062			−0.244031	−	0.969767i	$-0.578470\pi$
$941$	−14.9717			−0.488062			−0.244031	+	0.969767i	$0.578470\pi$
$942$	4.95872	+	0.541902i	0.161564	+	0.0176561i
$943$	14.8865			0.484771
$944$	0.228358			0.00743242
$945$		0			0
$946$	27.6596			0.899292
$947$	14.5086			0.471465			0.235733	−	0.971818i	$-0.424251\pi$
$947$	14.5086			0.471465			0.235733	+	0.971818i	$0.424251\pi$
$948$	7.74348	+	0.846228i	0.251496	+	0.0274842i
$949$	−1.61625			−0.0524658
$950$	−22.0894	−	13.2854i	−0.716675	−	0.431037i
$951$	42.6085	+	4.65637i	1.38167	+	0.150993i
$952$		0			0
$953$	−34.9591			−1.13244			−0.566218	−	0.824256i	$-0.691594\pi$
$953$	−34.9591			−1.13244			−0.566218	+	0.824256i	$0.691594\pi$
$954$	4.01842	+	0.888904i	0.130101	+	0.0287793i
$955$	9.11134	+	16.1122i	0.294836	+	0.521380i
$956$			20.4893i			0.662672i
$957$	−41.2679	−	4.50987i	−1.33400	−	0.145783i
$958$	−12.5500			−0.405473
$959$		0			0
$960$	−19.4610	+	8.36156i	−0.628101	+	0.269868i
$961$	27.5005			0.887114
$962$			4.16619i			0.134323i
$963$	31.4509	+	6.95717i	1.01349	+	0.224192i
$964$		−	5.06671i		−	0.163188i
$965$	17.5287	+	30.9972i	0.564268	+	0.997836i
$966$		0			0
$967$		−	46.6810i		−	1.50116i	−0.660779	−	0.750581i	$-0.729774\pi$
$967$		−	46.6810i		−	1.50116i	0.660779	−	0.750581i	$-0.270226\pi$
$968$	15.8742			0.510216
$969$	65.5283	+	7.16110i	2.10507	+	0.230048i
$970$	−25.5600	+	14.4540i	−0.820681	+	0.464088i
$971$	1.31338			0.0421484			0.0210742	−	0.999778i	$-0.493291\pi$
$971$	1.31338			0.0421484			0.0210742	+	0.999778i	$0.493291\pi$
$972$	15.7897	+	9.55635i	0.506456	+	0.306520i
$973$		0			0
$974$		−	23.9482i		−	0.767350i
$975$	−15.1164	+	19.8711i	−0.484113	+	0.636386i
$976$		−	1.41936i		−	0.0454326i
$977$	53.0752			1.69803			0.849013	−	0.528372i	$-0.177197\pi$
$977$	53.0752			1.69803			0.849013	+	0.528372i	$0.177197\pi$
$978$	3.27701	−	29.9866i	0.104787	−	0.958865i
$979$			42.3140i			1.35236i
$980$		0			0
$981$	1.57202	+	0.347743i	0.0501908	+	0.0111026i
$982$			2.30000i			0.0733961i
$983$		−	21.1136i		−	0.673418i	−0.941609	−	0.336709i	$-0.890686\pi$
$983$		−	21.1136i		−	0.673418i	0.941609	−	0.336709i	$-0.109314\pi$
$984$	45.1767	+	4.93703i	1.44018	+	0.157387i
$985$	46.4681	−	26.2773i	1.48060	−	0.837266i
$986$	−35.5242			−1.13132
$987$		0			0
$988$			19.4803i			0.619750i
$989$		−	12.2937i		−	0.390918i
$990$	7.20682	+	23.5512i	0.229048	+	0.748507i
$991$	−53.6348			−1.70377			−0.851883	−	0.523732i	$-0.824539\pi$
$991$	−53.6348			−1.70377			−0.851883	+	0.523732i	$0.824539\pi$
$992$			10.3719i			0.329308i
$993$	28.1621	+	3.07763i	0.893698	+	0.0976657i
$994$		0			0
$995$	−13.4583	−	23.7993i	−0.426657	−	0.754488i
$996$	−0.892084	+	8.16309i	−0.0282668	+	0.258658i
$997$	38.8870			1.23156			0.615781	−	0.787917i	$-0.288841\pi$
$997$	38.8870			1.23156			0.615781	+	0.787917i	$0.288841\pi$
$998$	26.7836			0.847820
$999$	2.66646	−	7.87316i	0.0843629	−	0.249096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.g.c.734.21	yes	32
3.2	odd	2	inner	735.2.g.c.734.10	yes	32
5.4	even	2	inner	735.2.g.c.734.12	yes	32
7.2	even	3		735.2.p.g.374.12		64
7.3	odd	6		735.2.p.g.509.10		64
7.4	even	3		735.2.p.g.509.11		64
7.5	odd	6		735.2.p.g.374.9		64
7.6	odd	2	inner	735.2.g.c.734.24	yes	32
15.14	odd	2	inner	735.2.g.c.734.23	yes	32
21.2	odd	6		735.2.p.g.374.23		64
21.5	even	6		735.2.p.g.374.22		64
21.11	odd	6		735.2.p.g.509.24		64
21.17	even	6		735.2.p.g.509.21		64
21.20	even	2	inner	735.2.g.c.734.11	yes	32
35.4	even	6		735.2.p.g.509.22		64
35.9	even	6		735.2.p.g.374.21		64
35.19	odd	6		735.2.p.g.374.24		64
35.24	odd	6		735.2.p.g.509.23		64
35.34	odd	2	inner	735.2.g.c.734.9	✓	32
105.44	odd	6		735.2.p.g.374.10		64
105.59	even	6		735.2.p.g.509.12		64
105.74	odd	6		735.2.p.g.509.9		64
105.89	even	6		735.2.p.g.374.11		64
105.104	even	2	inner	735.2.g.c.734.22	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.g.c.734.9	✓	32	35.34	odd	2	inner
735.2.g.c.734.10	yes	32	3.2	odd	2	inner
735.2.g.c.734.11	yes	32	21.20	even	2	inner
735.2.g.c.734.12	yes	32	5.4	even	2	inner
735.2.g.c.734.21	yes	32	1.1	even	1	trivial
735.2.g.c.734.22	yes	32	105.104	even	2	inner
735.2.g.c.734.23	yes	32	15.14	odd	2	inner
735.2.g.c.734.24	yes	32	7.6	odd	2	inner
735.2.p.g.374.9		64	7.5	odd	6
735.2.p.g.374.10		64	105.44	odd	6
735.2.p.g.374.11		64	105.89	even	6
735.2.p.g.374.12		64	7.2	even	3
735.2.p.g.374.21		64	35.9	even	6
735.2.p.g.374.22		64	21.5	even	6
735.2.p.g.374.23		64	21.2	odd	6
735.2.p.g.374.24		64	35.19	odd	6
735.2.p.g.509.9		64	105.74	odd	6
735.2.p.g.509.10		64	7.3	odd	6
735.2.p.g.509.11		64	7.4	even	3
735.2.p.g.509.12		64	105.59	even	6
735.2.p.g.509.21		64	21.17	even	6
735.2.p.g.509.22		64	35.4	even	6
735.2.p.g.509.23		64	35.24	odd	6
735.2.p.g.509.24		64	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.903339 q^{2} +(-1.72180 - 0.188163i) q^{3} -1.18398 q^{4} +(1.94641 - 1.10068i) q^{5} +(-1.55537 - 0.169975i) q^{6} -2.87621 q^{8} +(2.92919 + 0.647957i) q^{9} +(1.75827 - 0.994285i) q^{10} +4.06437i q^{11} +(2.03858 + 0.222781i) q^{12} +2.88298 q^{13} +(-3.55843 + 1.52891i) q^{15} -0.230234 q^{16} -6.66864i q^{17} +(2.64605 + 0.585325i) q^{18} -5.70701i q^{19} +(-2.30451 + 1.30318i) q^{20} +3.67151i q^{22} +1.63185 q^{23} +(4.95226 + 0.541196i) q^{24} +(2.57701 - 4.28474i) q^{25} +2.60431 q^{26} +(-4.92156 - 1.66682i) q^{27} -5.89707i q^{29} +(-3.21447 + 1.38112i) q^{30} +1.87068i q^{31} +5.54444 q^{32} +(0.764764 - 6.99804i) q^{33} -6.02404i q^{34} +(-3.46810 - 0.767168i) q^{36} +1.59973i q^{37} -5.15537i q^{38} +(-4.96392 - 0.542470i) q^{39} +(-5.59828 + 3.16578i) q^{40} +9.12244 q^{41} -7.53359i q^{43} -4.81213i q^{44} +(6.41459 - 1.96291i) q^{45} +1.47412 q^{46} -6.91446i q^{47} +(0.396417 + 0.0433215i) q^{48} +(2.32792 - 3.87057i) q^{50} +(-1.25479 + 11.4821i) q^{51} -3.41339 q^{52} +1.51865 q^{53} +(-4.44583 - 1.50570i) q^{54} +(4.47357 + 7.91093i) q^{55} +(-1.07385 + 9.82633i) q^{57} -5.32705i q^{58} -0.991850 q^{59} +(4.21311 - 1.81019i) q^{60} +6.16485i q^{61} +1.68986i q^{62} +5.46898 q^{64} +(5.61146 - 3.17324i) q^{65} +(0.690841 - 6.32160i) q^{66} +10.0903i q^{67} +7.89553i q^{68} +(-2.80973 - 0.307054i) q^{69} -4.81213i q^{71} +(-8.42497 - 1.86366i) q^{72} -0.560619 q^{73} +1.44510i q^{74} +(-5.24333 + 6.89257i) q^{75} +6.75699i q^{76} +(-4.48410 - 0.490034i) q^{78} +3.79848 q^{79} +(-0.448130 + 0.253414i) q^{80} +(8.16030 + 3.79598i) q^{81} +8.24065 q^{82} +4.00431i q^{83} +(-7.34003 - 12.9799i) q^{85} -6.80539i q^{86} +(-1.10961 + 10.1536i) q^{87} -11.6900i q^{88} +10.4109 q^{89} +(5.79455 - 1.77317i) q^{90} -1.93208 q^{92} +(0.351993 - 3.22094i) q^{93} -6.24610i q^{94} +(-6.28159 - 11.1082i) q^{95} +(-9.54642 - 1.04326i) q^{96} -14.5370 q^{97} +(-2.63354 + 11.9053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 40 q^{9} + 16 q^{15} - 16 q^{16} + 64 q^{25} + 56 q^{30} - 16 q^{36} - 56 q^{39} - 32 q^{46} - 40 q^{51} + 8 q^{60} - 176 q^{64} + 48 q^{79} - 40 q^{81} - 64 q^{85} + 40 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 + 40 * q^9 + 16 * q^15 - 16 * q^16 + 64 * q^25 + 56 * q^30 - 16 * q^36 - 56 * q^39 - 32 * q^46 - 40 * q^51 + 8 * q^60 - 176 * q^64 + 48 * q^79 - 40 * q^81 - 64 * q^85 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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